LMFDB - Embedded newform 99.8.f.d.91.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(37,99)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Character	$\chi$	$=$	99.91
Dual form			99.8.f.d.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-16.2902 + 11.8355i) q^{2} +(85.7365 - 263.870i) q^{4} +(21.6619 + 15.7383i) q^{5} +(176.688 - 543.790i) q^{7} +(929.915 + 2861.99i) q^{8} +O(q^{10})$	\(q+(-16.2902 + 11.8355i) q^{2} +(85.7365 - 263.870i) q^{4} +(21.6619 + 15.7383i) q^{5} +(176.688 - 543.790i) q^{7} +(929.915 + 2861.99i) q^{8} -539.148 q^{10} +(-631.112 + 4369.08i) q^{11} +(-4422.88 + 3213.41i) q^{13} +(3557.75 + 10949.6i) q^{14} +(-20290.5 - 14741.9i) q^{16} +(6447.44 + 4684.34i) q^{17} +(-4606.28 - 14176.7i) q^{19} +(6010.08 - 4366.58i) q^{20} +(-41429.4 - 78642.6i) q^{22} -8624.88 q^{23} +(-23920.4 - 73619.4i) q^{25} +(34017.1 - 104694. i) q^{26} +(-128341. - 93245.2i) q^{28} +(43798.0 - 134796. i) q^{29} +(-131101. + 95250.4i) q^{31} +119828. q^{32} -160472. q^{34} +(12385.7 - 8998.77i) q^{35} +(77414.0 - 238256. i) q^{37} +(242825. + 176423. i) q^{38} +(-24899.1 + 76631.5i) q^{40} +(112705. + 346871. i) q^{41} +619202. q^{43} +(1.09876e6 + 541121. i) q^{44} +(140501. - 102080. i) q^{46} +(47809.2 + 147141. i) q^{47} +(401771. + 291904. i) q^{49} +(1.26099e6 + 916164. i) q^{50} +(468719. + 1.44257e6i) q^{52} +(-1.00477e6 + 730006. i) q^{53} +(-82433.1 + 84710.1i) q^{55} +1.72062e6 q^{56} +(881906. + 2.71423e6i) q^{58} +(717798. - 2.20916e6i) q^{59} +(801287. + 582169. i) q^{61} +(1.00832e6 - 3.10329e6i) q^{62} +(645170. - 468743. i) q^{64} -146382. q^{65} +595504. q^{67} +(1.78884e6 - 1.29967e6i) q^{68} +(-95261.0 + 293183. i) q^{70} +(-3.62994e6 - 2.63731e6i) q^{71} +(1.76049e6 - 5.41824e6i) q^{73} +(1.55879e6 + 4.79746e6i) q^{74} -4.13572e6 q^{76} +(2.26435e6 + 1.11516e6i) q^{77} +(1.85530e6 - 1.34795e6i) q^{79} +(-207519. - 638678. i) q^{80} +(-5.94138e6 - 4.31666e6i) q^{82} +(7.03241e6 + 5.10935e6i) q^{83} +(65940.5 + 202944. i) q^{85} +(-1.00869e7 + 7.32857e6i) q^{86} +(-1.30911e7 + 2.25664e6i) q^{88} -2.65123e6 q^{89} +(965949. + 2.97289e6i) q^{91} +(-739467. + 2.27584e6i) q^{92} +(-2.52031e6 - 1.83111e6i) q^{94} +(123336. - 379590. i) q^{95} +(8.90171e6 - 6.46747e6i) q^{97} -9.99976e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 1260 q^{4} - 3902 q^{7}+O(q^{10}) $ 56 * q - 1260 * q^4 - 3902 * q^7	$ 56 q - 1260 q^{4} - 3902 q^{7} + 20008 q^{10} - 18158 q^{13} + 54064 q^{16} - 111812 q^{19} + 16106 q^{22} - 78708 q^{25} + 69378 q^{28} - 189868 q^{31} + 1561016 q^{34} - 795786 q^{37} - 1589918 q^{40} + 355744 q^{43} + 2273926 q^{46} - 4728752 q^{49} - 438038 q^{52} + 3414760 q^{55} + 4154034 q^{58} + 1604778 q^{61} + 9561960 q^{64} - 18424972 q^{67} - 5609964 q^{70} + 17372 q^{73} + 8053960 q^{76} - 15803082 q^{79} + 7756570 q^{82} - 21218378 q^{85} + 37593088 q^{88} + 18308922 q^{91} + 68235162 q^{94} + 34988922 q^{97}+O(q^{100}) $ 56 * q - 1260 * q^4 - 3902 * q^7 + 20008 * q^10 - 18158 * q^13 + 54064 * q^16 - 111812 * q^19 + 16106 * q^22 - 78708 * q^25 + 69378 * q^28 - 189868 * q^31 + 1561016 * q^34 - 795786 * q^37 - 1589918 * q^40 + 355744 * q^43 + 2273926 * q^46 - 4728752 * q^49 - 438038 * q^52 + 3414760 * q^55 + 4154034 * q^58 + 1604778 * q^61 + 9561960 * q^64 - 18424972 * q^67 - 5609964 * q^70 + 17372 * q^73 + 8053960 * q^76 - 15803082 * q^79 + 7756570 * q^82 - 21218378 * q^85 + 37593088 * q^88 + 18308922 * q^91 + 68235162 * q^94 + 34988922 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−16.2902	+	11.8355i	−1.43986	+	1.04612i	−0.451790	+	0.892124i	$0.649214\pi$
$2$	−16.2902	+	11.8355i	−1.43986	+	1.04612i	−0.988071	+	0.153997i	$0.950786\pi$
$3$		0			0
$3$		0			0
$4$	85.7365	−	263.870i	0.669816	−	2.06148i
$5$	21.6619	+	15.7383i	0.0775001	+	0.0563071i	0.625861	−	0.779935i	$-0.284748\pi$
$5$	21.6619	+	15.7383i	0.0775001	+	0.0563071i	−0.548361	+	0.836242i	$0.684748\pi$
$6$		0			0
$7$	176.688	−	543.790i	0.194699	−	0.599222i	−0.805281	−	0.592894i	$-0.797985\pi$
$7$	176.688	−	543.790i	0.194699	−	0.599222i	0.999980	−	0.00632880i	$-0.00201453\pi$
$8$	929.915	+	2861.99i	0.642138	+	1.97630i
$9$		0			0
$10$	−539.148			−0.170493
$11$	−631.112	+	4369.08i	−0.142966	+	0.989728i
$11$	−631.112	+	4369.08i	−0.142966	+	0.989728i
$12$		0			0
$13$	−4422.88	+	3213.41i	−0.558345	+	0.405662i	−0.830853	−	0.556492i	$-0.812147\pi$
$13$	−4422.88	+	3213.41i	−0.558345	+	0.405662i	0.272508	+	0.962154i	$0.412147\pi$
$14$	3557.75	+	10949.6i	0.346519	+	1.06648i
$15$		0			0
$16$	−20290.5	−	14741.9i	−1.23844	−	0.899776i
$17$	6447.44	+	4684.34i	0.318285	+	0.231248i	0.735443	−	0.677586i	$-0.236974\pi$
$17$	6447.44	+	4684.34i	0.318285	+	0.231248i	−0.417158	+	0.908834i	$0.636974\pi$
$18$		0			0
$19$	−4606.28	−	14176.7i	−0.154068	−	0.474173i	0.843997	−	0.536348i	$-0.180196\pi$
$19$	−4606.28	−	14176.7i	−0.154068	−	0.474173i	−0.998065	+	0.0621745i	$0.980196\pi$
$20$	6010.08	−	4366.58i	0.167987	−	0.122050i
$21$		0			0
$22$	−41429.4	−	78642.6i	−0.829524	−	1.57463i
$23$	−8624.88			−0.147811			−0.0739053	−	0.997265i	$-0.523546\pi$
$23$	−8624.88			−0.147811			−0.0739053	+	0.997265i	$0.523546\pi$
$24$		0			0
$25$	−23920.4	−	73619.4i	−0.306181	−	0.942329i
$26$	34017.1	−	104694.i	0.379569	−	1.16819i
$27$		0			0
$28$	−128341.	−	93245.2i	−1.10487	−	0.802738i
$29$	43798.0	−	134796.i	0.333474	−	1.02633i	−0.633996	−	0.773337i	$-0.718586\pi$
$29$	43798.0	−	134796.i	0.333474	−	1.02633i	0.967469	−	0.252989i	$-0.0814137\pi$
$30$		0			0
$31$	−131101.	+	95250.4i	−0.790387	+	0.574250i	−0.908078	−	0.418800i	$-0.862451\pi$
$31$	−131101.	+	95250.4i	−0.790387	+	0.574250i	0.117691	+	0.993050i	$0.462451\pi$
$32$	119828.			0.646447
$33$		0			0
$34$	−160472.			−0.700200
$35$	12385.7	−	8998.77i	0.0488297	−	0.0354769i
$36$		0			0
$37$	77414.0	−	238256.i	0.251254	−	0.773281i	−0.743290	−	0.668969i	$-0.766736\pi$
$37$	77414.0	−	238256.i	0.251254	−	0.773281i	0.994545	−	0.104312i	$-0.0332641\pi$
$38$	242825.	+	176423.i	0.717880	+	0.521570i
$39$		0			0
$40$	−24899.1	+	76631.5i	−0.0615139	+	0.189320i
$41$	112705.	+	346871.i	0.255388	+	0.786003i	0.993753	+	0.111602i	$0.0355981\pi$
$41$	112705.	+	346871.i	0.255388	+	0.786003i	−0.738365	+	0.674401i	$0.764402\pi$
$42$		0			0
$43$	619202.			1.18766			0.593831	−	0.804590i	$-0.297615\pi$
$43$	619202.			1.18766			0.593831	+	0.804590i	$0.297615\pi$
$44$	1.09876e6	+	541121.i	1.94454	+	0.957657i
$45$		0			0
$46$	140501.	−	102080.i	0.212827	−	0.154628i
$47$	47809.2	+	147141.i	0.0671690	+	0.206725i	0.979008	−	0.203824i	$-0.0653371\pi$
$47$	47809.2	+	147141.i	0.0671690	+	0.206725i	−0.911839	+	0.410549i	$0.865337\pi$
$48$		0			0
$49$	401771.	+	291904.i	0.487857	+	0.354449i
$50$	1.26099e6	+	916164.i	1.42665	+	1.03652i
$51$		0			0
$52$	468719.	+	1.44257e6i	0.462276	+	1.42274i
$53$	−1.00477e6	+	730006.i	−0.927043	+	0.673536i	−0.945267	−	0.326298i	$-0.894199\pi$
$53$	−1.00477e6	+	730006.i	−0.927043	+	0.673536i	0.0182240	+	0.999834i	$0.494199\pi$
$54$		0			0
$55$	−82433.1	+	84710.1i	−0.0668086	+	0.0686540i
$56$	1.72062e6			1.30927
$57$		0			0
$58$	881906.	+	2.71423e6i	0.593505	+	1.82662i
$59$	717798.	−	2.20916e6i	0.455010	−	1.40038i	−0.416114	−	0.909312i	$-0.636608\pi$
$59$	717798.	−	2.20916e6i	0.455010	−	1.40038i	0.871124	−	0.491063i	$-0.163392\pi$
$60$		0			0
$61$	801287.	+	582169.i	0.451995	+	0.328393i	0.790383	−	0.612613i	$-0.209882\pi$
$61$	801287.	+	582169.i	0.451995	+	0.328393i	−0.338388	+	0.941007i	$0.609882\pi$
$62$	1.00832e6	−	3.10329e6i	0.537314	−	1.65368i
$63$		0			0
$64$	645170.	−	468743.i	0.307641	−	0.223514i
$65$	−146382.			−0.0661135
$66$		0			0
$67$	595504.			0.241893			0.120946	−	0.992659i	$-0.461407\pi$
$67$	595504.			0.241893			0.120946	+	0.992659i	$0.461407\pi$
$68$	1.78884e6	−	1.29967e6i	0.689905	−	0.501246i
$69$		0			0
$70$	−95261.0	+	293183.i	−0.0331949	+	0.102164i
$71$	−3.62994e6	−	2.63731e6i	−1.20364	−	0.874493i	−0.208999	−	0.977916i	$-0.567021\pi$
$71$	−3.62994e6	−	2.63731e6i	−1.20364	−	0.874493i	−0.994638	+	0.103422i	$0.967021\pi$
$72$		0			0
$73$	1.76049e6	−	5.41824e6i	0.529668	−	1.63015i	−0.225228	−	0.974306i	$-0.572313\pi$
$73$	1.76049e6	−	5.41824e6i	0.529668	−	1.63015i	0.754896	−	0.655845i	$-0.227687\pi$
$74$	1.55879e6	+	4.79746e6i	0.447174	+	1.37626i
$75$		0			0
$76$	−4.13572e6			−1.08070
$77$	2.26435e6	+	1.11516e6i	0.565232	+	0.278367i
$78$		0			0
$79$	1.85530e6	−	1.34795e6i	0.423368	−	0.307595i	−0.355623	−	0.934629i	$-0.615731\pi$
$79$	1.85530e6	−	1.34795e6i	0.423368	−	0.307595i	0.778992	+	0.627034i	$0.215731\pi$
$80$	−207519.	−	638678.i	−0.0453151	−	0.139465i
$81$		0			0
$82$	−5.94138e6	−	4.31666e6i	−1.18998	−	0.864569i
$83$	7.03241e6	+	5.10935e6i	1.34999	+	0.980826i	0.999012	+	0.0444427i	$0.0141512\pi$
$83$	7.03241e6	+	5.10935e6i	1.34999	+	0.980826i	0.350979	+	0.936383i	$0.385849\pi$
$84$		0			0
$85$	65940.5	+	202944.i	0.0116462	+	0.0358434i
$86$	−1.00869e7	+	7.32857e6i	−1.71007	+	1.24244i
$87$		0			0
$88$	−1.30911e7	+	2.25664e6i	−2.04780	+	0.352999i
$89$	−2.65123e6			−0.398642			−0.199321	−	0.979934i	$-0.563874\pi$
$89$	−2.65123e6			−0.398642			−0.199321	+	0.979934i	$0.563874\pi$
$90$		0			0
$91$	965949.	+	2.97289e6i	0.134372	+	0.413555i
$92$	−739467.	+	2.27584e6i	−0.0990059	+	0.304709i
$93$		0			0
$94$	−2.52031e6	−	1.83111e6i	−0.312973	−	0.227388i
$95$	123336.	−	379590.i	0.0147590	−	0.0454236i
$96$		0			0
$97$	8.90171e6	−	6.46747e6i	0.990312	−	0.719504i	0.0303229	−	0.999540i	$-0.490346\pi$
$97$	8.90171e6	−	6.46747e6i	0.990312	−	0.719504i	0.959989	+	0.280036i	$0.0903465\pi$
$98$	−9.99976e6			−1.07324
$99$		0			0
$100$	−2.14768e7			−2.14768
$101$	3.47150e6	−	2.52219e6i	0.335268	−	0.243587i	−0.407394	−	0.913252i	$-0.633563\pi$
$101$	3.47150e6	−	2.52219e6i	0.335268	−	0.243587i	0.742663	+	0.669666i	$0.233563\pi$
$102$		0			0
$103$	2.58198e6	−	7.94651e6i	0.232821	−	0.716549i	−0.764582	−	0.644526i	$-0.777055\pi$
$103$	2.58198e6	−	7.94651e6i	0.232821	−	0.716549i	0.997403	−	0.0720229i	$-0.0229455\pi$
$104$	−1.33096e7	−	9.67001e6i	−1.16024	−	0.842966i
$105$		0			0
$106$	7.72784e6	−	2.37839e7i	0.630214	−	1.93960i
$107$	−4.01565e6	−	1.23589e7i	−0.316893	−	0.975297i	−0.974968	−	0.222345i	$-0.928629\pi$
$107$	−4.01565e6	−	1.23589e7i	−0.316893	−	0.975297i	0.658075	−	0.752952i	$-0.271371\pi$
$108$		0			0
$109$	2.66637e7			1.97209			0.986045	−	0.166476i	$-0.0532389\pi$
$109$	2.66637e7			1.97209			0.986045	+	0.166476i	$0.0532389\pi$
$110$	340263.	−	2.35558e6i	0.0243747	−	0.168742i
$111$		0			0
$112$	−1.16016e7	+	8.42906e6i	−0.780288	+	0.566913i
$113$	−1.30897e6	−	4.02861e6i	−0.0853407	−	0.262652i	0.899275	−	0.437383i	$-0.144094\pi$
$113$	−1.30897e6	−	4.02861e6i	−0.0853407	−	0.262652i	−0.984616	+	0.174731i	$0.944094\pi$
$114$		0			0
$115$	−186832.	−	135741.i	−0.0114553	−	0.00832279i
$116$	−3.18136e7	−	2.31139e7i	−1.89239	−	1.37490i
$117$		0			0
$118$	1.44534e7	+	4.44831e7i	0.809811	+	2.49234i
$119$	3.68649e6	−	2.67839e6i	0.200539	−	0.145700i
$120$		0			0
$121$	−1.86906e7	−	5.51476e6i	−0.959122	−	0.282994i
$122$	−1.99434e7			−0.994349
$123$		0			0
$124$	1.38936e7	+	4.27600e7i	0.654392	+	2.01401i
$125$	1.28690e6	−	3.96067e6i	0.0589332	−	0.181378i
$126$		0			0
$127$	2.60899e7	+	1.89554e7i	1.13021	+	0.821145i	0.985725	−	0.168363i	$-0.0538479\pi$
$127$	2.60899e7	+	1.89554e7i	1.13021	+	0.821145i	0.144484	+	0.989507i	$0.453848\pi$
$128$	−9.70181e6	+	2.98591e7i	−0.408901	+	1.25847i
$129$		0			0
$130$	2.38458e6	−	1.73250e6i	0.0951943	−	0.0691627i
$131$	1.76143e7			0.684568			0.342284	−	0.939596i	$-0.388799\pi$
$131$	1.76143e7			0.684568			0.342284	+	0.939596i	$0.388799\pi$
$132$		0			0
$133$	−8.52301e6			−0.314132
$134$	−9.70086e6	+	7.04809e6i	−0.348292	+	0.253049i
$135$		0			0
$136$	−7.41094e6	+	2.28085e7i	−0.252631	+	0.777519i
$137$	2.89021e7	+	2.09986e7i	0.960302	+	0.697700i	0.953221	−	0.302275i	$-0.0977460\pi$
$137$	2.89021e7	+	2.09986e7i	0.960302	+	0.697700i	0.00708113	+	0.999975i	$0.497746\pi$
$138$		0			0
$139$	1.73286e7	−	5.33319e7i	0.547282	−	1.68436i	−0.168221	−	0.985749i	$-0.553802\pi$
$139$	1.73286e7	−	5.33319e7i	0.547282	−	1.68436i	0.715502	−	0.698610i	$-0.246198\pi$
$140$	−1.31259e6	−	4.03975e6i	−0.0404280	−	0.124425i
$141$		0			0
$142$	9.03463e7			2.64790
$143$	−1.12483e7	−	2.13519e7i	−0.321670	−	0.610606i
$144$		0			0
$145$	3.07022e6	−	2.23064e6i	0.0836337	−	0.0607634i
$146$	3.54488e7	+	1.09100e8i	0.942686	+	2.90129i
$147$		0			0
$148$	−5.62313e7	−	4.08544e7i	−1.42581	−	1.03591i
$149$	−4.41840e7	−	3.21015e7i	−1.09424	−	0.795013i	−0.114131	−	0.993466i	$-0.536408\pi$
$149$	−4.41840e7	−	3.21015e7i	−1.09424	−	0.795013i	−0.980110	+	0.198453i	$0.936408\pi$
$150$		0			0
$151$	2.58059e6	+	7.94225e6i	0.0609959	+	0.187726i	0.976911	−	0.213645i	$-0.0685337\pi$
$151$	2.58059e6	+	7.94225e6i	0.0609959	+	0.187726i	−0.915915	+	0.401371i	$0.868534\pi$
$152$	3.62900e7	−	2.63662e7i	0.838175	−	0.608970i
$153$		0			0
$154$	−5.00851e7	+	8.63365e6i	−1.10506	+	0.190490i
$155$	−4.33898e6			−0.0935895
$156$		0			0
$157$	1.73627e7	+	5.34370e7i	0.358071	+	1.10203i	0.954207	+	0.299146i	$0.0967018\pi$
$157$	1.73627e7	+	5.34370e7i	0.358071	+	1.10203i	−0.596136	+	0.802883i	$0.703298\pi$
$158$	−1.42694e7	+	4.39167e7i	−0.287810	+	0.885789i
$159$		0			0
$160$	2.59571e6	+	1.88589e6i	0.0500997	+	0.0363996i
$161$	−1.52391e6	+	4.69012e6i	−0.0287786	+	0.0885714i
$162$		0			0
$163$	2.18124e7	−	1.58477e7i	0.394500	−	0.286621i	−0.372797	−	0.927913i	$-0.621601\pi$
$163$	2.18124e7	−	1.58477e7i	0.394500	−	0.286621i	0.767297	+	0.641292i	$0.221601\pi$
$164$	1.01192e8			1.79139
$165$		0			0
$166$	−1.75031e8			−2.96986
$167$	7.24357e7	−	5.26276e7i	1.20350	−	0.874392i	0.208873	−	0.977943i	$-0.433021\pi$
$167$	7.24357e7	−	5.26276e7i	1.20350	−	0.874392i	0.994624	+	0.103551i	$0.0330206\pi$
$168$		0			0
$169$	−1.01545e7	+	3.12524e7i	−0.161829	+	0.498058i
$170$	−3.47613e6	−	2.52555e6i	−0.0542656	−	0.0394262i
$171$		0			0
$172$	5.30882e7	−	1.63389e8i	0.795515	−	2.44834i
$173$	−2.71236e7	−	8.34780e7i	−0.398278	−	1.22577i	−0.926379	−	0.376593i	$-0.877096\pi$
$173$	−2.71236e7	−	8.34780e7i	−0.398278	−	1.22577i	0.528101	−	0.849182i	$-0.322904\pi$
$174$		0			0
$175$	−4.42600e7			−0.624278
$176$	7.72143e7	−	7.93471e7i	1.06759	−	1.09708i
$177$		0			0
$178$	4.31891e7	−	3.13787e7i	0.573989	−	0.417028i
$179$	1.03929e7	+	3.19860e7i	0.135441	+	0.416845i	0.995658	−	0.0930827i	$-0.0296721\pi$
$179$	1.03929e7	+	3.19860e7i	0.135441	+	0.416845i	−0.860217	+	0.509928i	$0.829672\pi$
$180$		0			0
$181$	−1.03644e8	−	7.53016e7i	−1.29918	−	0.943908i	−0.299230	−	0.954181i	$-0.596730\pi$
$181$	−1.03644e8	−	7.53016e7i	−1.29918	−	0.943908i	−0.999947	+	0.0102735i	$0.996730\pi$
$182$	−5.09211e7	−	3.69963e7i	−0.626106	−	0.454893i
$183$		0			0
$184$	−8.02041e6	−	2.46843e7i	−0.0949148	−	0.292118i
$185$	5.42668e6	−	3.94272e6i	0.0630135	−	0.0457820i
$186$		0			0
$187$	−2.45353e7	+	2.52131e7i	−0.274376	+	0.281955i
$188$	4.29252e7			0.471150
$189$		0			0
$190$	2.48347e6	+	7.64333e6i	0.0262676	+	0.0808435i
$191$	9.89792e6	−	3.04627e7i	0.102784	−	0.316338i	−0.886420	−	0.462882i	$-0.846815\pi$
$191$	9.89792e6	−	3.04627e7i	0.102784	−	0.316338i	0.989204	+	0.146545i	$0.0468152\pi$
$192$		0			0
$193$	−2.76576e7	−	2.00944e7i	−0.276926	−	0.201199i	0.440649	−	0.897679i	$-0.354748\pi$
$193$	−2.76576e7	−	2.00944e7i	−0.276926	−	0.201199i	−0.717576	+	0.696481i	$0.754748\pi$
$194$	−6.84646e7	+	2.10712e8i	−0.673225	+	2.07197i
$195$		0			0
$196$	1.11471e8	−	8.09885e7i	1.05746	−	0.768293i
$197$	1.06471e8			0.992196			0.496098	−	0.868266i	$-0.334766\pi$
$197$	1.06471e8			0.992196			0.496098	+	0.868266i	$0.334766\pi$
$198$		0			0
$199$	189857.			0.00170781			0.000853907	−	1.00000i	$-0.499728\pi$
$199$	189857.			0.00170781			0.000853907		1.00000i	$0.499728\pi$
$200$	1.88454e8	−	1.36920e8i	1.66571	−	1.21021i
$201$		0			0
$202$	−2.66999e7	+	8.21740e7i	−0.227919	+	0.701463i
$203$	−6.55623e7	−	4.76338e7i	−0.550071	−	0.399650i
$204$		0			0
$205$	−3.01775e6	+	9.28768e6i	−0.0244650	+	0.0752955i
$206$	5.19901e7	+	1.60009e8i	0.414367	+	1.27529i
$207$		0			0
$208$	1.37114e8			1.05648
$209$	6.48462e7	−	1.11782e7i	0.491329	−	0.0846950i
$210$		0			0
$211$	−1.72960e8	+	1.25662e8i	−1.26752	+	0.920910i	−0.999101	−	0.0423915i	$-0.986502\pi$
$211$	−1.72960e8	+	1.25662e8i	−1.26752	+	0.920910i	−0.268422	+	0.963301i	$0.586502\pi$
$212$	1.06481e8	+	3.27716e8i	0.767534	+	2.36223i
$213$		0			0
$214$	2.11690e8	+	1.53802e8i	1.47656	+	1.07278i
$215$	1.34131e7	+	9.74520e6i	0.0920439	+	0.0668738i
$216$		0			0
$217$	2.86323e7	+	8.81210e7i	0.190216	+	0.585424i
$218$	−4.34356e8	+	3.15578e8i	−2.83954	+	2.06305i
$219$		0			0
$220$	1.52849e7	+	2.90143e7i	0.0967795	+	0.183710i
$221$	−4.35689e7			−0.271521
$222$		0			0
$223$	6.16198e6	+	1.89646e7i	0.0372095	+	0.114519i	0.967936	−	0.251197i	$-0.0808242\pi$
$223$	6.16198e6	+	1.89646e7i	0.0372095	+	0.114519i	−0.930727	+	0.365716i	$0.880824\pi$
$224$	2.11722e7	−	6.51612e7i	0.125863	−	0.387366i
$225$		0			0
$226$	6.90040e7	+	5.01343e7i	0.397644	+	0.288906i
$227$	7.14323e7	−	2.19846e8i	0.405326	−	1.24746i	−0.515297	−	0.857012i	$-0.672318\pi$
$227$	7.14323e7	−	2.19846e8i	0.405326	−	1.24746i	0.920623	−	0.390453i	$-0.127682\pi$
$228$		0			0
$229$	−1.95796e8	+	1.42254e8i	−1.07741	+	0.782781i	−0.977229	−	0.212189i	$-0.931941\pi$
$229$	−1.95796e8	+	1.42254e8i	−1.07741	+	0.782781i	−0.100177	+	0.994970i	$0.531941\pi$
$230$	4.65008e6			0.0252007
$231$		0			0
$232$	4.26514e8			2.24246
$233$	1.85512e8	−	1.34782e8i	0.960785	−	0.698051i	0.00745228	−	0.999972i	$-0.497628\pi$
$233$	1.85512e8	−	1.34782e8i	0.960785	−	0.698051i	0.953333	+	0.301921i	$0.0976278\pi$
$234$		0			0
$235$	−1.28012e6	+	3.93981e6i	−0.00643448	+	0.0198033i
$236$	−5.21388e8	−	3.78810e8i	−2.58208	−	1.87599i
$237$		0			0
$238$	−2.83534e7	+	8.72628e7i	−0.136328	+	0.419575i
$239$	9.19688e6	+	2.83051e7i	0.0435760	+	0.134113i	0.970478	−	0.241191i	$-0.0775381\pi$
$239$	9.19688e6	+	2.83051e7i	0.0435760	+	0.134113i	−0.926902	+	0.375305i	$0.877538\pi$
$240$		0			0
$241$	1.08446e8			0.499061			0.249530	−	0.968367i	$-0.419724\pi$
$241$	1.08446e8			0.499061			0.249530	+	0.968367i	$0.419724\pi$
$242$	3.69743e8	−	1.31376e8i	1.67705	−	0.595884i
$243$		0			0
$244$	2.22316e8	−	1.61522e8i	0.979731	−	0.711816i
$245$	4.10907e6	+	1.26464e7i	0.0178510	+	0.0549397i
$246$		0			0
$247$	6.59285e7	+	4.78999e7i	0.278377	+	0.202253i
$248$	−3.94518e8	−	2.86634e8i	−1.64243	−	1.19329i
$249$		0			0
$250$	2.59127e7	+	7.97511e7i	0.104887	+	0.322810i
$251$	−2.44372e8	+	1.77547e8i	−0.975424	+	0.708687i	−0.956681	−	0.291137i	$-0.905966\pi$
$251$	−2.44372e8	+	1.77547e8i	−0.975424	+	0.708687i	−0.0187428	+	0.999824i	$0.505966\pi$
$252$		0			0
$253$	5.44327e6	−	3.76828e7i	0.0211319	−	0.146292i
$254$	−6.49355e8			−2.48636
$255$		0			0
$256$	−1.63810e8	−	5.04155e8i	−0.610239	−	1.87812i
$257$	1.04502e8	−	3.21625e8i	0.384026	−	1.18191i	−0.553159	−	0.833076i	$-0.686578\pi$
$257$	1.04502e8	−	3.21625e8i	0.384026	−	1.18191i	0.937185	−	0.348834i	$-0.113422\pi$
$258$		0			0
$259$	−1.15883e8	−	8.41939e7i	−0.414448	−	0.301114i
$260$	−1.25502e7	+	3.86257e7i	−0.0442839	+	0.136292i
$261$		0			0
$262$	−2.86941e8	+	2.08475e8i	−0.985684	+	0.716141i
$263$	6.98579e6			0.0236794			0.0118397	−	0.999930i	$-0.496231\pi$
$263$	6.98579e6			0.0236794			0.0118397	+	0.999930i	$0.496231\pi$
$264$		0			0
$265$	−3.32543e7			−0.109771
$266$	1.38841e8	−	1.00874e8i	0.452307	−	0.328620i
$267$		0			0
$268$	5.10564e7	−	1.57135e8i	0.162024	−	0.498657i
$269$	−2.36328e8	−	1.71702e8i	−0.740256	−	0.537827i	0.152535	−	0.988298i	$-0.451256\pi$
$269$	−2.36328e8	−	1.71702e8i	−0.740256	−	0.537827i	−0.892791	+	0.450471i	$0.851256\pi$
$270$		0			0
$271$	−1.77688e8	+	5.46869e8i	−0.542334	+	1.66913i	0.184912	+	0.982755i	$0.440800\pi$
$271$	−1.77688e8	+	5.46869e8i	−0.542334	+	1.66913i	−0.727246	+	0.686377i	$0.759200\pi$
$272$	−6.17658e7	−	1.90096e8i	−0.186104	−	0.572771i
$273$		0			0
$274$	−7.19350e8			−2.11258
$275$	3.36746e8	−	5.80481e7i	0.976422	−	0.168315i
$276$		0			0
$277$	9.24748e7	−	6.71869e7i	0.261423	−	0.189935i	−0.449351	−	0.893355i	$-0.648345\pi$
$277$	9.24748e7	−	6.71869e7i	0.261423	−	0.189935i	0.710774	+	0.703420i	$0.248345\pi$
$278$	3.48924e8	+	1.07388e9i	0.974034	+	2.99777i
$279$		0			0
$280$	3.72721e7	+	2.70797e7i	0.101468	+	0.0737210i
$281$	−1.82185e8	−	1.32365e8i	−0.489824	−	0.355878i	0.315293	−	0.948994i	$-0.397897\pi$
$281$	−1.82185e8	−	1.32365e8i	−0.489824	−	0.355878i	−0.805116	+	0.593117i	$0.797897\pi$
$282$		0			0
$283$	−1.83002e8	−	5.63223e8i	−0.479959	−	1.47716i	−0.839151	−	0.543898i	$-0.816948\pi$
$283$	−1.83002e8	−	5.63223e8i	−0.479959	−	1.47716i	0.359193	−	0.933263i	$-0.383052\pi$
$284$	−1.00712e9	+	7.31718e8i	−2.60897	+	1.89553i
$285$		0			0
$286$	4.35948e8	+	2.14697e8i	1.10193	+	0.542682i
$287$	2.08538e8			0.520714
$288$		0			0
$289$	−1.07175e8	−	3.29851e8i	−0.261187	−	0.803851i
$290$	−2.36136e7	+	7.26752e7i	−0.0568551	+	0.174982i
$291$		0			0
$292$	−1.27877e9	−	9.29081e8i	−3.00575	−	2.18380i
$293$	−1.60392e8	+	4.93635e8i	−0.372516	+	1.14649i	0.572623	+	0.819819i	$0.305926\pi$
$293$	−1.60392e8	+	4.93635e8i	−0.372516	+	1.14649i	−0.945139	+	0.326668i	$0.894074\pi$
$294$		0			0
$295$	5.03173e7	−	3.65577e7i	0.114114	−	0.0829090i
$296$	7.53873e8			1.68957
$297$		0			0
$298$	1.09970e9			2.40723
$299$	3.81468e7	−	2.77153e7i	0.0825294	−	0.0599611i
$300$		0			0
$301$	1.09406e8	−	3.36716e8i	0.231237	−	0.711673i
$302$	−1.36039e8	−	9.88381e7i	−0.284210	−	0.206490i
$303$		0			0
$304$	−1.15528e8	+	3.55558e8i	−0.235846	+	0.725860i
$305$	8.19506e6	+	2.52218e7i	0.0165388	+	0.0509011i
$306$		0			0
$307$	−5.09445e8			−1.00488			−0.502439	−	0.864613i	$-0.667564\pi$
$307$	−5.09445e8			−1.00488			−0.502439	+	0.864613i	$0.667564\pi$
$308$	4.88394e8	−	5.01884e8i	0.952451	−	0.978760i
$309$		0			0
$310$	7.06828e7	−	5.13541e7i	0.134756	−	0.0979059i
$311$	1.35374e8	+	4.16639e8i	0.255197	+	0.785415i	0.993791	+	0.111264i	$0.0354900\pi$
$311$	1.35374e8	+	4.16639e8i	0.255197	+	0.785415i	−0.738594	+	0.674150i	$0.764510\pi$
$312$		0			0
$313$	4.94206e7	+	3.59062e7i	0.0910968	+	0.0661857i	0.632401	−	0.774641i	$-0.282069\pi$
$313$	4.94206e7	+	3.59062e7i	0.0910968	+	0.0661857i	−0.541305	+	0.840827i	$0.682069\pi$
$314$	−9.15296e8	−	6.65001e8i	−1.66843	−	1.21218i
$315$		0			0
$316$	−1.96617e8	−	6.05125e8i	−0.350523	−	1.07880i
$317$	4.90138e8	−	3.56106e8i	0.864194	−	0.627873i	−0.0648290	−	0.997896i	$-0.520650\pi$
$317$	4.90138e8	−	3.56106e8i	0.864194	−	0.627873i	0.929023	+	0.370023i	$0.120650\pi$
$318$		0			0
$319$	5.61295e8	+	2.76429e8i	0.968108	+	0.476777i
$320$	2.13529e7			0.0364276
$321$		0			0
$322$	−3.06852e7	−	9.44392e7i	−0.0512192	−	0.157636i
$323$	3.67097e7	−	1.12981e8i	0.0606139	−	0.186550i
$324$		0			0
$325$	3.42366e8	+	2.48744e8i	0.553222	+	0.401939i
$326$	−1.67763e8	+	5.16322e8i	−0.268185	+	0.825390i
$327$		0			0
$328$	−8.87933e8	+	6.45121e8i	−1.38938	+	1.00944i
$329$	8.84614e7			0.136952
$330$		0			0
$331$	1.13237e9			1.71628			0.858142	−	0.513412i	$-0.171619\pi$
$331$	1.13237e9			1.71628			0.858142	+	0.513412i	$0.171619\pi$
$332$	1.95114e9	−	1.41758e9i	2.92620	−	2.12601i
$333$		0			0
$334$	−5.57116e8	+	1.71463e9i	−0.818150	+	2.51801i
$335$	1.28998e7	+	9.37223e6i	0.0187467	+	0.0136203i
$336$		0			0
$337$	−1.21180e8	+	3.72953e8i	−0.172475	+	0.530823i	−0.999509	−	0.0313286i	$-0.990026\pi$
$337$	−1.21180e8	+	3.72953e8i	−0.172475	+	0.530823i	0.827034	+	0.562151i	$0.190026\pi$
$338$	−2.04469e8	−	6.29291e8i	−0.288017	−	0.886427i
$339$		0			0
$340$	5.92042e7			0.0816915
$341$	−3.33417e8	−	6.32905e8i	−0.455353	−	0.864366i
$342$		0			0
$343$	6.10673e8	−	4.43680e8i	0.817108	−	0.593664i
$344$	5.75805e8	+	1.77215e9i	0.762643	+	2.34717i
$345$		0			0
$346$	1.42985e9	+	1.03885e9i	1.85577	+	1.34830i
$347$	−4.81044e8	−	3.49499e8i	−0.618061	−	0.449048i	0.234183	−	0.972193i	$-0.424759\pi$
$347$	−4.81044e8	−	3.49499e8i	−0.618061	−	0.449048i	−0.852244	+	0.523145i	$0.824759\pi$
$348$		0			0
$349$	4.69118e7	+	1.44380e8i	0.0590735	+	0.181810i	0.976239	−	0.216697i	$-0.0695285\pi$
$349$	4.69118e7	+	1.44380e8i	0.0590735	+	0.181810i	−0.917165	+	0.398507i	$0.869528\pi$
$350$	7.21003e8	−	5.23839e8i	0.898874	−	0.653070i
$351$		0			0
$352$	−7.56249e7	+	5.23538e8i	−0.0924198	+	0.639807i
$353$	−6.03464e8			−0.730197			−0.365099	−	0.930969i	$-0.618965\pi$
$353$	−6.03464e8			−0.730197			−0.365099	+	0.930969i	$0.618965\pi$
$354$		0			0
$355$	−3.71248e7	−	1.14258e8i	−0.0440418	−	0.135547i
$356$	−2.27307e8	+	6.99580e8i	−0.267017	+	0.821793i
$357$		0			0
$358$	−5.47873e8	−	3.98053e8i	−0.631087	−	0.458511i
$359$	−2.34700e8	+	7.22331e8i	−0.267721	+	0.823959i	0.723334	+	0.690499i	$0.242609\pi$
$359$	−2.34700e8	+	7.22331e8i	−0.267721	+	0.823959i	−0.991054	+	0.133460i	$0.957391\pi$
$360$		0			0
$361$	5.43397e8	−	3.94801e8i	0.607914	−	0.441675i
$362$	2.57961e9			2.85808
$363$		0			0
$364$	8.67271e8			0.942541
$365$	1.23410e8	−	8.96623e7i	0.132838	−	0.0965128i
$366$		0			0
$367$	1.89493e8	−	5.83200e8i	0.200107	−	0.615866i	−0.799772	−	0.600304i	$-0.795046\pi$
$367$	1.89493e8	−	5.83200e8i	0.200107	−	0.615866i	0.999879	−	0.0155618i	$-0.00495366\pi$
$368$	1.75003e8	+	1.27147e8i	0.183054	+	0.132996i
$369$		0			0
$370$	−4.17376e7	+	1.28455e8i	−0.0428372	+	0.131839i
$371$	2.19440e8	+	6.75366e8i	0.223103	+	0.686642i
$372$		0			0
$373$	1.15159e9			1.14899			0.574497	−	0.818507i	$-0.305198\pi$
$373$	1.15159e9			1.14899			0.574497	+	0.818507i	$0.305198\pi$
$374$	1.01276e8	−	7.01113e8i	0.100105	−	0.693007i
$375$		0			0
$376$	−3.76658e8	+	2.73658e8i	−0.365418	+	0.265492i
$377$	2.39443e8	+	7.36929e8i	0.230148	+	0.708322i
$378$		0			0
$379$	−9.81999e7	−	7.13464e7i	−0.0926561	−	0.0673186i	0.540493	−	0.841349i	$-0.318238\pi$
$379$	−9.81999e7	−	7.13464e7i	−0.0926561	−	0.0673186i	−0.633149	+	0.774030i	$0.718238\pi$
$380$	−8.95878e7	−	6.50894e7i	−0.0837541	−	0.0608509i
$381$		0			0
$382$	1.99302e8	+	6.13389e8i	0.182932	+	0.563008i
$383$	−7.30680e7	+	5.30870e7i	−0.0664556	+	0.0482828i	−0.620517	−	0.784193i	$-0.713077\pi$
$383$	−7.30680e7	+	5.30870e7i	−0.0664556	+	0.0482828i	0.554061	+	0.832476i	$0.313077\pi$
$384$		0			0
$385$	3.14996e7	+	5.97936e7i	0.0281314	+	0.0534001i
$386$	6.88375e8			0.609214
$387$		0			0
$388$	−9.43368e8	−	2.90339e9i	−0.819917	−	2.52345i
$389$	−6.40240e8	+	1.97046e9i	−0.551467	+	1.69724i	0.153629	+	0.988129i	$0.450904\pi$
$389$	−6.40240e8	+	1.97046e9i	−0.551467	+	1.69724i	−0.705096	+	0.709112i	$0.749096\pi$
$390$		0			0
$391$	−5.56084e7	−	4.04019e7i	−0.0470459	−	0.0341809i
$392$	−4.61812e8	+	1.42131e9i	−0.387225	+	1.19176i
$393$		0			0
$394$	−1.73442e9	+	1.26013e9i	−1.42863	+	1.03796i
$395$	6.14038e7			0.0501309
$396$		0			0
$397$	−8.25239e8			−0.661931			−0.330966	−	0.943643i	$-0.607374\pi$
$397$	−8.25239e8			−0.661931			−0.330966	+	0.943643i	$0.607374\pi$
$398$	−3.09280e6	+	2.24705e6i	−0.00245902	+	0.00178658i
$399$		0			0
$400$	−5.99935e8	+	1.84641e9i	−0.468699	+	1.44251i
$401$	−1.04601e8	−	7.59974e7i	−0.0810089	−	0.0588564i	0.546544	−	0.837431i	$-0.315943\pi$
$401$	−1.04601e8	−	7.59974e7i	−0.0810089	−	0.0588564i	−0.627553	+	0.778574i	$0.715943\pi$
$402$		0			0
$403$	2.73765e8	−	8.42562e8i	0.208358	−	0.641260i
$404$	−3.67896e8	−	1.13227e9i	−0.277582	−	0.854308i
$405$		0			0
$406$	1.63179e9			1.21011
$407$	9.92102e8	+	4.88594e8i	0.729417	+	0.359226i
$408$		0			0
$409$	−4.79755e8	+	3.48562e8i	−0.346727	+	0.251912i	−0.747495	−	0.664268i	$-0.768743\pi$
$409$	−4.79755e8	+	3.48562e8i	−0.346727	+	0.251912i	0.400768	+	0.916180i	$0.368743\pi$
$410$	−6.07647e7	−	1.87015e8i	−0.0435420	−	0.134008i
$411$		0			0
$412$	−1.87547e9	−	1.36261e9i	−1.32121	−	0.959912i
$413$	−1.07449e9	−	7.80663e8i	−0.750546	−	0.545304i
$414$		0			0
$415$	7.19231e7	+	2.21357e8i	0.0493970	+	0.152028i
$416$	−5.29984e8	+	3.85056e8i	−0.360941	+	0.262239i
$417$		0			0
$418$	−9.24056e8	+	9.49581e8i	−0.618844	+	0.635939i
$419$	−7.31177e8			−0.485594			−0.242797	−	0.970077i	$-0.578065\pi$
$419$	−7.31177e8			−0.485594			−0.242797	+	0.970077i	$0.578065\pi$
$420$		0			0
$421$	−2.10845e8	−	6.48914e8i	−0.137713	−	0.423838i	0.858289	−	0.513167i	$-0.171528\pi$
$421$	−2.10845e8	−	6.48914e8i	−0.137713	−	0.423838i	−0.996002	+	0.0893290i	$0.971528\pi$
$422$	1.33026e9	−	4.09413e9i	0.861676	−	2.65197i
$423$		0			0
$424$	−3.02362e9	−	2.19679e9i	−1.92640	−	1.39961i
$425$	1.90633e8	−	5.86709e8i	0.120458	−	0.370733i
$426$		0			0
$427$	4.58155e8	−	3.32869e8i	0.284784	−	0.206908i
$428$	−3.60543e9			−2.22282
$429$		0			0
$430$	−3.33841e8			−0.202489
$431$	1.10160e8	−	8.00356e7i	0.0662753	−	0.0481518i	−0.554154	−	0.832414i	$-0.686958\pi$
$431$	1.10160e8	−	8.00356e7i	0.0662753	−	0.0481518i	0.620430	+	0.784262i	$0.286958\pi$
$432$		0			0
$433$	−5.08960e7	+	1.56642e8i	−0.0301284	+	0.0927256i	−0.964990	−	0.262287i	$-0.915523\pi$
$433$	−5.08960e7	+	1.56642e8i	−0.0301284	+	0.0927256i	0.934862	+	0.355012i	$0.115523\pi$
$434$	−1.50938e9	−	1.09663e9i	−0.886308	−	0.643941i
$435$		0			0
$436$	2.28605e9	−	7.03573e9i	1.32094	−	4.06543i
$437$	3.97286e7	+	1.22272e8i	0.0227729	+	0.0700878i
$438$		0			0
$439$	−6.84421e7			−0.0386098			−0.0193049	−	0.999814i	$-0.506145\pi$
$439$	−6.84421e7			−0.0386098			−0.0193049	+	0.999814i	$0.506145\pi$
$440$	−3.19095e8	−	1.57149e8i	−0.178581	−	0.0879483i
$441$		0			0
$442$	7.09746e8	−	5.15660e8i	0.390953	−	0.284044i
$443$	−2.86375e8	−	8.81372e8i	−0.156503	−	0.481666i	0.841807	−	0.539778i	$-0.181492\pi$
$443$	−2.86375e8	−	8.81372e8i	−0.156503	−	0.481666i	−0.998310	+	0.0581122i	$0.981492\pi$
$444$		0			0
$445$	−5.74309e7	−	4.17260e7i	−0.0308948	−	0.0224464i
$446$	−3.24836e8	−	2.36007e8i	−0.173377	−	0.125966i
$447$		0			0
$448$	−1.40904e8	−	4.33658e8i	−0.0740373	−	0.227863i
$449$	−1.89847e9	+	1.37932e9i	−0.989787	+	0.719122i	−0.959874	−	0.280430i	$-0.909523\pi$
$449$	−1.89847e9	+	1.37932e9i	−0.989787	+	0.719122i	−0.0299124	+	0.999553i	$0.509523\pi$
$450$		0			0
$451$	−1.58664e9	+	2.73504e8i	−0.814441	+	0.140393i
$452$	−1.17525e9			−0.598614
$453$		0			0
$454$	1.43834e9	+	4.42677e9i	0.721386	+	2.22020i
$455$	−2.58639e7	+	7.96009e7i	−0.0128722	+	0.0396167i
$456$		0			0
$457$	−2.45159e8	−	1.78118e8i	−0.120155	−	0.0872974i	0.526085	−	0.850432i	$-0.323659\pi$
$457$	−2.45159e8	−	1.78118e8i	−0.120155	−	0.0872974i	−0.646240	+	0.763135i	$0.723659\pi$
$458$	1.50590e9	−	4.63468e9i	0.732432	−	2.25419i
$459$		0			0
$460$	−5.18362e7	+	3.76612e7i	−0.0248303	+	0.0180402i
$461$	−2.97735e8			−0.141539			−0.0707695	−	0.997493i	$-0.522545\pi$
$461$	−2.97735e8			−0.141539			−0.0707695	+	0.997493i	$0.522545\pi$
$462$		0			0
$463$	−1.39430e9			−0.652864			−0.326432	−	0.945221i	$-0.605846\pi$
$463$	−1.39430e9			−0.652864			−0.326432	+	0.945221i	$0.605846\pi$
$464$	−2.87584e9	+	2.08942e9i	−1.33645	+	0.970987i
$465$		0			0
$466$	−1.42681e9	+	4.39126e9i	−0.653152	+	2.01019i
$467$	7.95308e8	+	5.77825e8i	0.361349	+	0.262535i	0.753614	−	0.657317i	$-0.228309\pi$
$467$	7.95308e8	+	5.77825e8i	0.361349	+	0.262535i	−0.392266	+	0.919852i	$0.628309\pi$
$468$		0			0
$469$	1.05218e8	−	3.23829e8i	0.0470963	−	0.144948i
$470$	−2.57762e7	−	7.93310e7i	−0.0114519	−	0.0352452i
$471$		0			0
$472$	6.99007e9			3.05974
$473$	−3.90786e8	+	2.70534e9i	−0.169795	+	1.17546i
$474$		0			0
$475$	−9.33496e8	+	6.78224e8i	−0.399654	+	0.290366i
$476$	−3.90679e8	−	1.20239e9i	−0.166034	−	0.510999i
$477$		0			0
$478$	−4.84824e8	−	3.52245e8i	−0.203042	−	0.147519i
$479$	2.87464e9	+	2.08855e9i	1.19511	+	0.868300i	0.993795	−	0.111226i	$-0.0354778\pi$
$479$	2.87464e9	+	2.08855e9i	1.19511	+	0.868300i	0.201317	+	0.979526i	$0.435478\pi$
$480$		0			0
$481$	4.23220e8	+	1.30254e9i	0.173404	+	0.533682i
$482$	−1.76660e9	+	1.28351e9i	−0.718578	+	0.522078i
$483$		0			0
$484$	−3.05764e9	+	4.45906e9i	−1.22582	+	1.78766i
$485$	2.94615e8			0.117263
$486$		0			0
$487$	1.35959e9	+	4.18439e9i	0.533404	+	1.64165i	0.747072	+	0.664744i	$0.231459\pi$
$487$	1.35959e9	+	4.18439e9i	0.533404	+	1.64165i	−0.213667	+	0.976907i	$0.568541\pi$
$488$	−9.21030e8	+	2.83464e9i	−0.358760	+	1.10415i
$489$		0			0
$490$	−2.16614e8	−	1.57379e8i	−0.0831765	−	0.0604313i
$491$	−2.95732e8	+	9.10169e8i	−0.112749	+	0.347006i	−0.991471	−	0.130328i	$-0.958397\pi$
$491$	−2.95732e8	+	9.10169e8i	−0.112749	+	0.347006i	0.878722	+	0.477334i	$0.158397\pi$
$492$		0			0
$493$	9.13818e8	−	6.63928e8i	0.343475	−	0.249549i
$494$	−1.64091e9			−0.612406
$495$		0			0
$496$	4.06428e9			1.49554
$497$	−2.07551e9	+	1.50795e9i	−0.758363	+	0.550983i
$498$		0			0
$499$	−4.56500e8	+	1.40496e9i	−0.164471	+	0.506189i	−0.998997	−	0.0447796i	$-0.985741\pi$
$499$	−4.56500e8	+	1.40496e9i	−0.164471	+	0.506189i	0.834526	+	0.550968i	$0.185741\pi$
$500$	−9.34767e8	−	6.79148e8i	−0.334432	−	0.242979i
$501$		0			0
$502$	1.87951e9	−	5.78453e9i	0.663104	−	2.04082i
$503$	1.25729e9	+	3.86954e9i	0.440502	+	1.35572i	0.887342	+	0.461111i	$0.152549\pi$
$503$	1.25729e9	+	3.86954e9i	0.440502	+	1.35572i	−0.446841	+	0.894613i	$0.647451\pi$
$504$		0			0
$505$	1.14895e8			0.0396990
$506$	3.57323e8	+	6.78283e8i	0.122612	+	0.232747i
$507$		0			0
$508$	7.23860e9	−	5.25915e9i	2.44981	−	1.77989i
$509$	−9.86117e8	−	3.03496e9i	−0.331449	−	1.02009i	−0.968445	−	0.249227i	$-0.919823\pi$
$509$	−9.86117e8	−	3.03496e9i	−0.331449	−	1.02009i	0.636996	−	0.770867i	$-0.280177\pi$
$510$		0			0
$511$	−2.63532e9	−	1.91467e9i	−0.873697	−	0.634778i
$512$	5.38427e9	+	3.91190e9i	1.77289	+	1.28808i
$513$		0			0
$514$	2.10424e9	+	6.47617e9i	0.683476	+	2.10352i
$515$	1.80995e8	−	1.31501e8i	0.0583905	−	0.0424232i
$516$		0			0
$517$	−6.73046e8	+	1.16019e8i	−0.214204	+	0.0369244i
$518$	2.88423e9			0.911751
$519$		0			0
$520$	−1.36123e8	−	4.18942e8i	−0.0424540	−	0.130660i
$521$	1.68294e9	−	5.17957e9i	0.521360	−	1.60458i	−0.250044	−	0.968235i	$-0.580445\pi$
$521$	1.68294e9	−	5.17957e9i	0.521360	−	1.60458i	0.771404	−	0.636346i	$-0.219555\pi$
$522$		0			0
$523$	6.86973e6	+	4.99115e6i	0.00209983	+	0.00152562i	0.588835	−	0.808254i	$-0.299587\pi$
$523$	6.86973e6	+	4.99115e6i	0.00209983	+	0.00152562i	−0.586735	+	0.809779i	$0.699587\pi$
$524$	1.51019e9	−	4.64789e9i	0.458535	−	1.41123i
$525$		0			0
$526$	−1.13800e8	+	8.26804e7i	−0.0340950	+	0.0247715i
$527$	−1.29145e9			−0.384363
$528$		0			0
$529$	−3.33044e9			−0.978152
$530$	5.41718e8	−	3.93581e8i	0.158055	−	0.114834i
$531$		0			0
$532$	−7.30733e8	+	2.24897e9i	−0.210411	+	0.647578i
$533$	−1.61312e9	−	1.17200e9i	−0.461446	−	0.335260i
$534$		0			0
$535$	1.07522e8	−	3.30918e8i	0.0303569	−	0.0934290i
$536$	5.53768e8	+	1.70432e9i	0.155329	+	0.478052i
$537$		0			0
$538$	5.88200e9			1.62850
$539$	−1.52892e9	+	1.57115e9i	−0.420555	+	0.432172i
$540$		0			0
$541$	−3.74752e9	+	2.72273e9i	−1.01754	+	0.739289i	−0.965778	−	0.259370i	$-0.916485\pi$
$541$	−3.74752e9	+	2.72273e9i	−1.01754	+	0.739289i	−0.0517664	+	0.998659i	$0.516485\pi$
$542$	−3.57789e9	−	1.10116e10i	−0.965228	−	2.97067i
$543$		0			0
$544$	7.72584e8	+	5.61315e8i	0.205755	+	0.149489i
$545$	5.77586e8	+	4.19641e8i	0.152837	+	0.111043i
$546$		0			0
$547$	6.54333e8	+	2.01383e9i	0.170940	+	0.526098i	0.999425	−	0.0339128i	$-0.0107969\pi$
$547$	6.54333e8	+	2.01383e9i	0.170940	+	0.526098i	−0.828485	+	0.560011i	$0.810797\pi$
$548$	8.01887e9	−	5.82605e9i	2.08152	−	1.51231i
$549$		0			0
$550$	−4.79862e9	+	4.93117e9i	−1.22984	+	1.26381i
$551$	−2.11271e9			−0.538034
$552$		0			0
$553$	−4.05194e8	−	1.24706e9i	−0.101888	−	0.313580i
$554$	−7.11240e8	+	2.18897e9i	−0.177718	+	0.546961i
$555$		0			0
$556$	−1.25870e10	−	9.14497e9i	−3.10570	−	2.25642i
$557$	−8.78265e8	+	2.70302e9i	−0.215344	+	0.662760i	0.783785	+	0.621032i	$0.213286\pi$
$557$	−8.78265e8	+	2.70302e9i	−0.215344	+	0.662760i	−0.999129	+	0.0417283i	$0.986714\pi$
$558$		0			0
$559$	−2.73865e9	+	1.98975e9i	−0.663125	+	0.481789i
$560$	−3.83973e8			−0.0923937
$561$		0			0
$562$	4.53443e9			1.07757
$563$	2.66811e9	−	1.93850e9i	0.630122	−	0.457811i	−0.226320	−	0.974053i	$-0.572670\pi$
$563$	2.66811e9	−	1.93850e9i	0.630122	−	0.457811i	0.856443	+	0.516242i	$0.172670\pi$
$564$		0			0
$565$	3.50486e7	−	1.07868e8i	0.00817525	−	0.0251608i
$566$	9.64717e9	+	7.00908e9i	2.23636	+	1.62481i
$567$		0			0
$568$	4.17240e9	−	1.28413e10i	0.955358	−	2.94029i
$569$	−1.90934e9	−	5.87635e9i	−0.434501	−	1.33726i	−0.893597	−	0.448871i	$-0.851826\pi$
$569$	−1.90934e9	−	5.87635e9i	−0.434501	−	1.33726i	0.459096	−	0.888387i	$-0.348174\pi$
$570$		0			0
$571$	−1.55894e8			−0.0350432			−0.0175216	−	0.999846i	$-0.505578\pi$
$571$	−1.55894e8			−0.0350432			−0.0175216	+	0.999846i	$0.505578\pi$
$572$	−6.59851e9	+	1.13745e9i	−1.47421	+	0.254124i
$573$		0			0
$574$	−3.39713e9	+	2.46816e9i	−0.749757	+	0.544730i
$575$	2.06311e8	+	6.34959e8i	0.0452568	+	0.139286i
$576$		0			0
$577$	4.57208e8	+	3.32181e8i	0.0990829	+	0.0719880i	0.636224	−	0.771505i	$-0.280496\pi$
$577$	4.57208e8	+	3.32181e8i	0.0990829	+	0.0719880i	−0.537141	+	0.843493i	$0.680496\pi$
$578$	5.64986e9	+	4.10486e9i	1.21700	+	0.884201i
$579$		0			0
$580$	−3.25370e8	−	1.00139e9i	−0.0692435	−	0.213110i
$581$	4.02095e9	−	2.92139e9i	0.850575	−	0.617979i
$582$		0			0
$583$	−2.55533e9	−	4.85062e9i	−0.534082	−	1.01381i
$584$	1.71440e10			3.56178
$585$		0			0
$586$	−3.22961e9	−	9.93971e9i	−0.662992	−	2.04048i
$587$	−2.29147e9	+	7.05242e9i	−0.467607	+	1.43914i	0.388068	+	0.921631i	$0.373143\pi$
$587$	−2.29147e9	+	7.05242e9i	−0.467607	+	1.43914i	−0.855675	+	0.517514i	$0.826857\pi$
$588$		0			0
$589$	1.95422e9	+	1.41983e9i	0.394068	+	0.286307i
$590$	−3.86999e8	+	1.19106e9i	−0.0775762	+	0.238755i
$591$		0			0
$592$	−5.08312e9	+	3.69310e9i	−1.00694	+	0.731586i
$593$	−2.79810e9			−0.551025			−0.275512	−	0.961298i	$-0.588847\pi$
$593$	−2.79810e9			−0.551025			−0.275512	+	0.961298i	$0.588847\pi$
$594$		0			0
$595$	1.22010e8			0.0237457
$596$	−1.22588e10	+	8.90654e9i	−2.37184	+	1.72325i
$597$		0			0
$598$	−2.93394e8	+	9.02973e8i	−0.0561043	+	0.172671i
$599$	7.44854e9	+	5.41168e9i	1.41605	+	1.02882i	0.992408	+	0.122986i	$0.0392470\pi$
$599$	7.44854e9	+	5.41168e9i	1.41605	+	1.02882i	0.423638	+	0.905832i	$0.360753\pi$
$600$		0			0
$601$	4.35067e8	−	1.33900e9i	0.0817515	−	0.251605i	−0.901824	−	0.432104i	$-0.857771\pi$
$601$	4.35067e8	−	1.33900e9i	0.0817515	−	0.251605i	0.983575	+	0.180499i	$0.0577713\pi$
$602$	2.20296e9	+	6.78003e9i	0.411547	+	1.26661i
$603$		0			0
$604$	2.31697e9			0.427850
$605$	−3.18081e8	−	4.13619e8i	−0.0583974	−	0.0759375i
$606$		0			0
$607$	3.92455e9	−	2.85135e9i	0.712244	−	0.517476i	−0.171653	−	0.985158i	$-0.554911\pi$
$607$	3.92455e9	−	2.85135e9i	0.712244	−	0.517476i	0.883897	+	0.467682i	$0.154911\pi$
$608$	−5.51962e8	−	1.69876e9i	−0.0995970	−	0.306528i
$609$		0			0
$610$	−4.32012e8	−	3.13875e8i	−0.0770622	−	0.0559890i
$611$	−6.84279e8	−	4.97158e8i	−0.121364	−	0.0881760i
$612$		0			0
$613$	−1.72822e9	−	5.31891e9i	−0.303031	−	0.932633i	−0.980405	−	0.196994i	$-0.936882\pi$
$613$	−1.72822e9	−	5.31891e9i	−0.303031	−	0.932633i	0.677374	−	0.735639i	$-0.263118\pi$
$614$	8.29896e9	−	6.02954e9i	1.44689	−	1.05122i
$615$		0			0
$616$	−1.08591e9	+	7.51754e9i	−0.187180	+	1.29582i
$617$	−7.09718e9			−1.21643			−0.608216	−	0.793772i	$-0.708114\pi$
$617$	−7.09718e9			−1.21643			−0.608216	+	0.793772i	$0.708114\pi$
$618$		0			0
$619$	2.33630e8	+	7.19038e8i	0.0395923	+	0.121853i	0.968899	−	0.247456i	$-0.0795946\pi$
$619$	2.33630e8	+	7.19038e8i	0.0395923	+	0.121853i	−0.929307	+	0.369309i	$0.879595\pi$
$620$	−3.72009e8	+	1.14493e9i	−0.0626877	+	0.192933i
$621$		0			0
$622$	−7.13641e9	−	5.18491e9i	−1.18909	−	0.863922i
$623$	−4.68441e8	+	1.44171e9i	−0.0776153	+	0.238875i
$624$		0			0
$625$	−4.80232e9	+	3.48909e9i	−0.786813	+	0.571653i
$626$	−1.23004e9			−0.200405
$627$		0			0
$628$	1.55890e10			2.51166
$629$	1.61519e9	−	1.17351e9i	0.258790	−	0.188022i
$630$		0			0
$631$	4.66697e8	−	1.43634e9i	0.0739489	−	0.227591i	−0.907250	−	0.420593i	$-0.861822\pi$
$631$	4.66697e8	−	1.43634e9i	0.0739489	−	0.227591i	0.981198	+	0.193001i	$0.0618222\pi$
$632$	5.58309e9	+	4.05635e9i	0.879761	+	0.639183i
$633$		0			0
$634$	−3.76974e9	+	1.16021e10i	−0.587488	+	1.80810i
$635$	2.66831e8	+	8.21221e8i	0.0413550	+	0.127278i
$636$		0			0
$637$	−2.71499e9			−0.416179
$638$	−1.24153e10	+	2.14014e9i	−1.89271	+	0.326264i
$639$		0			0
$640$	−6.80092e8	+	4.94116e8i	−0.102550	+	0.0745073i
$641$	−3.45691e9	−	1.06393e10i	−0.518424	−	1.59555i	−0.776964	−	0.629545i	$-0.783241\pi$
$641$	−3.45691e9	−	1.06393e10i	−0.518424	−	1.59555i	0.258540	−	0.966001i	$-0.416759\pi$
$642$		0			0
$643$	7.63009e9	+	5.54359e9i	1.13186	+	0.822342i	0.985964	−	0.166958i	$-0.0533945\pi$
$643$	7.63009e9	+	5.54359e9i	1.13186	+	0.822342i	0.145893	+	0.989300i	$0.453395\pi$
$644$	1.10693e9	+	8.04229e8i	0.163312	+	0.118653i
$645$		0			0
$646$	7.39178e8	+	2.27496e9i	0.107879	+	0.332016i
$647$	9.44183e9	−	6.85989e9i	1.37054	−	0.995755i	0.372844	−	0.927894i	$-0.378383\pi$
$647$	9.44183e9	−	6.85989e9i	1.37054	−	0.995755i	0.997695	−	0.0678610i	$-0.0216174\pi$
$648$		0			0
$649$	9.19897e9	+	4.53035e9i	1.32094	+	0.650541i
$650$	−8.52121e9			−1.21704
$651$		0			0
$652$	−2.31160e9	−	7.11436e9i	−0.326622	−	1.00524i
$653$	2.18385e9	−	6.72121e9i	0.306921	−	0.944607i	−0.672032	−	0.740522i	$-0.734578\pi$
$653$	2.18385e9	−	6.72121e9i	0.306921	−	0.944607i	0.978953	−	0.204085i	$-0.0654218\pi$
$654$		0			0
$655$	3.81561e8	+	2.77220e8i	0.0530541	+	0.0385461i
$656$	2.82670e9	−	8.69968e9i	0.390945	−	1.20321i
$657$		0			0
$658$	−1.44105e9	+	1.04698e9i	−0.197192	+	0.143268i
$659$	9.71656e9			1.32255			0.661277	−	0.750141i	$-0.270015\pi$
$659$	9.71656e9			1.32255			0.661277	+	0.750141i	$0.270015\pi$
$660$		0			0
$661$	5.84525e9			0.787223			0.393611	−	0.919277i	$-0.371226\pi$
$661$	5.84525e9			0.787223			0.393611	+	0.919277i	$0.371226\pi$
$662$	−1.84465e10	+	1.34021e10i	−2.47121	+	1.79544i
$663$		0			0
$664$	−8.08332e9	+	2.48779e10i	−1.07152	+	3.29781i
$665$	−1.84625e8	−	1.34138e8i	−0.0243453	−	0.0176879i
$666$		0			0
$667$	−3.77753e8	+	1.16260e9i	−0.0492909	+	0.151702i
$668$	−7.67645e9	−	2.36257e10i	−0.996421	−	3.06667i
$669$		0			0
$670$	−3.21065e8			−0.0412411
$671$	−3.04924e9	+	3.13347e9i	−0.389640	+	0.400403i
$672$		0			0
$673$	9.66421e9	−	7.02146e9i	1.22212	−	0.887922i	0.225845	−	0.974163i	$-0.427486\pi$
$673$	9.66421e9	−	7.02146e9i	1.22212	−	0.887922i	0.996274	+	0.0862415i	$0.0274857\pi$
$674$	−2.44005e9	−	7.50969e9i	−0.306965	−	0.944741i
$675$		0			0
$676$	7.37594e9	+	5.35894e9i	0.918341	+	0.667214i
$677$	−3.08435e9	−	2.24091e9i	−0.382035	−	0.277565i	0.380149	−	0.924925i	$-0.375873\pi$
$677$	−3.08435e9	−	2.24091e9i	−0.382035	−	0.277565i	−0.762184	+	0.647361i	$0.775873\pi$
$678$		0			0
$679$	−1.94412e9	−	5.98338e9i	−0.238330	−	0.733504i
$680$	−5.19503e8	+	3.77441e8i	−0.0633588	+	0.0460329i
$681$		0			0
$682$	1.29222e10	+	6.36396e9i	1.55988	+	0.768214i
$683$	2.15644e9			0.258980			0.129490	−	0.991581i	$-0.458666\pi$
$683$	2.15644e9			0.258980			0.129490	+	0.991581i	$0.458666\pi$
$684$		0			0
$685$	2.95593e8	+	9.09742e8i	0.0351380	+	0.108144i
$686$	−4.69680e9	+	1.44553e10i	−0.555479	+	1.70959i
$687$		0			0
$688$	−1.25639e10	−	9.12823e9i	−1.47084	−	1.06863i
$689$	2.09815e9	−	6.45745e9i	0.244382	−	0.752132i
$690$		0			0
$691$	1.17564e10	−	8.54154e9i	1.35551	−	0.984834i	0.356791	−	0.934184i	$-0.383871\pi$
$691$	1.17564e10	−	8.54154e9i	1.35551	−	0.984834i	0.998716	−	0.0506495i	$-0.0161291\pi$
$692$	−2.43528e10			−2.79368
$693$		0			0
$694$	1.19728e10			1.35968
$695$	1.21472e9	−	8.82549e8i	0.137256	−	0.0997222i
$696$		0			0
$697$	−8.98201e8	+	2.76438e9i	−0.100475	+	0.309231i
$698$	−2.47301e9	−	1.79674e9i	−0.275253	−	0.199983i
$699$		0			0
$700$	−3.79469e9	+	1.16789e10i	−0.418151	+	1.28694i
$701$	3.51558e9	+	1.08198e10i	0.385464	+	1.18634i	0.936143	+	0.351619i	$0.114369\pi$
$701$	3.51558e9	+	1.08198e10i	0.385464	+	1.18634i	−0.550680	+	0.834717i	$0.685631\pi$
$702$		0			0
$703$	−3.73427e9			−0.405380
$704$	1.64080e9	+	3.11463e9i	0.177236	+	0.336435i
$705$		0			0
$706$	9.83054e9	−	7.14230e9i	1.05138	−	0.763874i
$707$	−7.58171e8	−	2.33341e9i	−0.0806862	−	0.248326i
$708$		0			0
$709$	8.55659e8	+	6.21673e8i	0.0901652	+	0.0655088i	0.631955	−	0.775005i	$-0.282253\pi$
$709$	8.55659e8	+	6.21673e8i	0.0901652	+	0.0655088i	−0.541789	+	0.840514i	$0.682253\pi$
$710$	1.95708e9	+	1.42190e9i	0.205212	+	0.149095i
$711$		0			0
$712$	−2.46542e9	−	7.58779e9i	−0.255983	−	0.787835i
$713$	1.13073e9	−	8.21524e8i	0.116828	−	0.0848803i
$714$		0			0
$715$	9.23833e7	−	6.39554e8i	0.00945197	−	0.0654343i
$716$	9.33119e9			0.950039
$717$		0			0
$718$	−4.72586e9	−	1.45447e10i	−0.476480	−	1.46646i
$719$	3.48871e9	−	1.07371e10i	0.350037	−	1.07730i	−0.608795	−	0.793327i	$-0.708347\pi$
$719$	3.48871e9	−	1.07371e10i	0.350037	−	1.07730i	0.958832	−	0.283974i	$-0.0916531\pi$
$720$		0			0
$721$	−3.86503e9	−	2.80811e9i	−0.384042	−	0.279023i
$722$	−4.17936e9	+	1.28628e10i	−0.413266	+	1.27190i
$723$		0			0
$724$	−2.87559e10	+	2.08924e10i	−2.81606	+	2.04599i
$725$	−1.09713e10			−1.06924
$726$		0			0
$727$	1.29980e10			1.25460			0.627300	−	0.778778i	$-0.284160\pi$
$727$	1.29980e10			1.25460			0.627300	+	0.778778i	$0.284160\pi$
$728$	−7.61011e9	+	5.52907e9i	−0.731023	+	0.531119i
$729$		0			0
$730$	−9.49165e8	+	2.92123e9i	−0.0903050	+	0.277930i
$731$	3.99227e9	+	2.90055e9i	0.378015	+	0.274644i
$732$		0			0
$733$	−8.91160e8	+	2.74271e9i	−0.0835780	+	0.257226i	−0.984109	−	0.177565i	$-0.943178\pi$
$733$	−8.91160e8	+	2.74271e9i	−0.0835780	+	0.257226i	0.900531	+	0.434792i	$0.143178\pi$
$734$	3.81559e9	+	1.17432e10i	0.356144	+	1.09610i
$735$		0			0
$736$	−1.03350e9			−0.0955518
$737$	−3.75830e8	+	2.60181e9i	−0.0345824	+	0.239408i
$738$		0			0
$739$	−1.13192e10	+	8.22389e9i	−1.03172	+	0.749587i	−0.968652	−	0.248423i	$-0.920088\pi$
$739$	−1.13192e10	+	8.22389e9i	−1.03172	+	0.749587i	−0.0630658	+	0.998009i	$0.520088\pi$
$740$	−5.75099e8	−	1.76997e9i	−0.0521713	−	0.160567i
$741$		0			0
$742$	−1.15680e10	−	8.40465e9i	−1.03955	−	0.755276i
$743$	3.01234e9	+	2.18859e9i	0.269428	+	0.195751i	0.714293	−	0.699847i	$-0.246748\pi$
$743$	3.01234e9	+	2.18859e9i	0.269428	+	0.195751i	−0.444865	+	0.895598i	$0.646748\pi$
$744$		0			0
$745$	−4.51886e8	−	1.39076e9i	−0.0400389	−	0.123227i
$746$	−1.87596e10	+	1.36297e10i	−1.65439	+	1.20199i
$747$		0			0
$748$	4.54939e9	+	8.63581e9i	0.397464	+	0.754479i
$749$	−7.43017e9			−0.646119
$750$		0			0
$751$	−3.80430e9	−	1.17084e10i	−0.327745	−	1.00869i	−0.970186	−	0.242360i	$-0.922079\pi$
$751$	−3.80430e9	−	1.17084e10i	−0.327745	−	1.00869i	0.642442	−	0.766334i	$-0.277921\pi$
$752$	1.19908e9	−	3.69038e9i	0.102822	−	0.316452i
$753$		0			0
$754$	−1.26225e10	−	9.17077e9i	−1.07237	−	0.779123i
$755$	−6.90970e7	+	2.12659e8i	−0.00584312	+	0.0179833i
$756$		0			0
$757$	−2.12815e9	+	1.54619e9i	−0.178306	+	0.129547i	−0.673359	−	0.739316i	$-0.735149\pi$
$757$	−2.12815e9	+	1.54619e9i	−0.178306	+	0.129547i	0.495052	+	0.868863i	$0.335149\pi$
$758$	2.44411e9			0.203835
$759$		0			0
$760$	1.20107e9			0.0992480
$761$	1.24422e10	−	9.03978e9i	1.02341	−	0.743552i	0.0564326	−	0.998406i	$-0.482027\pi$
$761$	1.24422e10	−	9.03978e9i	1.02341	−	0.743552i	0.966980	+	0.254854i	$0.0820274\pi$
$762$		0			0
$763$	4.71115e9	−	1.44994e10i	0.383964	−	1.18172i
$764$	−7.18956e9	−	5.22352e9i	−0.583278	−	0.423776i
$765$		0			0
$766$	5.61979e8	−	1.72959e9i	0.0451772	−	0.139041i
$767$	3.92419e9	+	1.20774e10i	0.314026	+	0.966473i
$768$		0			0
$769$	−2.04701e9			−0.162322			−0.0811610	−	0.996701i	$-0.525863\pi$
$769$	−2.04701e9			−0.162322			−0.0811610	+	0.996701i	$0.525863\pi$
$770$	−1.22082e9	−	6.01234e8i	−0.0963683	−	0.0474598i
$771$		0			0
$772$	−7.67358e9	+	5.57518e9i	−0.600257	+	0.436112i
$773$	−6.70424e9	−	2.06335e10i	−0.522061	−	1.60674i	−0.770055	−	0.637977i	$-0.779772\pi$
$773$	−6.70424e9	−	2.06335e10i	−0.522061	−	1.60674i	0.247995	−	0.968761i	$-0.420228\pi$
$774$		0			0
$775$	1.01483e10	+	7.37315e9i	0.783134	+	0.568980i
$776$	2.67876e10	+	1.94624e10i	2.05787	+	1.49513i
$777$		0			0
$778$	−1.28917e10	−	3.96767e10i	−0.981482	−	3.02069i
$779$	4.39833e9	−	3.19557e9i	0.333354	−	0.242196i
$780$		0			0
$781$	1.38135e10	−	1.41951e10i	1.03759	−	1.06625i
$782$	1.38405e9			0.103497
$783$		0			0
$784$	−3.84893e9	−	1.18458e10i	−0.285255	−	0.877925i
$785$	−4.64898e8	+	1.43081e9i	−0.0343016	+	0.105569i
$786$		0			0
$787$	−5.58210e9	−	4.05564e9i	−0.408213	−	0.296584i	0.364665	−	0.931139i	$-0.381183\pi$
$787$	−5.58210e9	−	4.05564e9i	−0.408213	−	0.296584i	−0.772878	+	0.634555i	$0.781183\pi$
$788$	9.12840e9	−	2.80943e10i	0.664589	−	2.04539i
$789$		0			0
$790$	−1.00028e9	+	7.26745e8i	−0.0721815	+	0.0524430i
$791$	−2.42200e9			−0.174003
$792$		0			0
$793$	−5.41474e9			−0.385586
$794$	1.34433e10	−	9.76712e9i	0.953090	−	0.692460i
$795$		0			0
$796$	1.62777e7	−	5.00975e7i	0.00114392	−	0.00352063i
$797$	−2.18216e10	−	1.58543e10i	−1.52680	−	1.10929i	−0.957984	−	0.286820i	$-0.907402\pi$
$797$	−2.18216e10	−	1.58543e10i	−1.52680	−	1.10929i	−0.568816	−	0.822465i	$-0.692598\pi$
$798$		0			0
$799$	−3.81014e8	+	1.17264e9i	−0.0264258	+	0.0813301i
$800$	−2.86633e9	−	8.82167e9i	−0.197930	−	0.609166i
$801$		0			0
$802$	2.60344e9			0.178212
$803$	2.25616e10	+	1.11112e10i	1.53768	+	0.757283i
$804$		0			0
$805$	−1.06826e8	+	7.76133e7i	−0.00721755	+	0.00524386i
$806$	5.51247e9	+	1.69656e10i	0.370829	+	1.14129i
$807$		0			0
$808$	1.04467e10	+	7.58996e9i	0.696689	+	0.506174i
$809$	−1.28962e10	−	9.36962e9i	−0.856330	−	0.622160i	0.0705542	−	0.997508i	$-0.477523\pi$
$809$	−1.28962e10	−	9.36962e9i	−0.856330	−	0.622160i	−0.926884	+	0.375348i	$0.877523\pi$
$810$		0			0
$811$	7.22305e9	+	2.22303e10i	0.475497	+	1.46343i	0.845287	+	0.534313i	$0.179430\pi$
$811$	7.22305e9	+	2.22303e10i	0.475497	+	1.46343i	−0.369790	+	0.929115i	$0.620570\pi$
$812$	−1.81902e10	+	1.32160e10i	−1.19232	+	0.866269i
$813$		0			0
$814$	−2.19443e10	+	3.78274e9i	−1.42605	+	0.245822i
$815$	7.21915e8			0.0467126
$816$		0			0
$817$	−2.85222e9	−	8.77823e9i	−0.182981	−	0.563157i
$818$	3.68988e9	−	1.13563e10i	0.235709	−	0.725437i
$819$		0			0
$820$	2.19201e9	+	1.59259e9i	0.138833	+	0.100868i
$821$	1.43851e9	−	4.42727e9i	0.0907216	−	0.279213i	−0.895393	−	0.445276i	$-0.853106\pi$
$821$	1.43851e9	−	4.42727e9i	0.0907216	−	0.279213i	0.986115	+	0.166063i	$0.0531056\pi$
$822$		0			0
$823$	−1.55366e10	+	1.12880e10i	−0.971533	+	0.705860i	−0.955800	−	0.294016i	$-0.905008\pi$
$823$	−1.55366e10	+	1.12880e10i	−0.971533	+	0.705860i	−0.0157326	+	0.999876i	$0.505008\pi$
$824$	2.51438e10			1.56562
$825$		0			0
$826$	2.67432e10			1.65114
$827$	8.31494e9	−	6.04116e9i	0.511199	−	0.371408i	−0.302079	−	0.953283i	$-0.597681\pi$
$827$	8.31494e9	−	6.04116e9i	0.511199	−	0.371408i	0.813278	+	0.581875i	$0.197681\pi$
$828$		0			0
$829$	−3.68636e9	+	1.13454e10i	−0.224728	+	0.691641i	0.773592	+	0.633685i	$0.218458\pi$
$829$	−3.68636e9	+	1.13454e10i	−0.224728	+	0.691641i	−0.998319	+	0.0579559i	$0.981542\pi$
$830$	−3.79151e9	−	2.75469e9i	−0.230165	−	0.167224i
$831$		0			0
$832$	−1.34724e9	+	4.14638e9i	−0.0810987	+	0.249596i
$833$	1.22302e9	+	3.76407e9i	0.0733122	+	0.225632i
$834$		0			0
$835$	2.39737e9			0.142506
$836$	2.61011e9	−	1.80693e10i	0.154503	−	1.06960i
$837$		0			0
$838$	1.19110e10	−	8.65385e9i	0.699188	−	0.507990i
$839$	5.90519e8	+	1.81743e9i	0.0345197	+	0.106241i	0.966832	−	0.255414i	$-0.0822118\pi$
$839$	5.90519e8	+	1.81743e9i	0.0345197	+	0.106241i	−0.932312	+	0.361655i	$0.882212\pi$
$840$		0			0
$841$	−2.29636e9	−	1.66841e9i	−0.133123	−	0.0967199i
$842$	1.11149e10	+	8.07546e9i	0.641673	+	0.466203i
$843$		0			0
$844$	1.83296e10	+	5.64126e10i	1.04943	+	3.22982i
$845$	−7.11827e8	+	5.17172e8i	−0.0405860	+	0.0294874i
$846$		0			0
$847$	−6.30127e9	+	9.18935e9i	−0.356317	+	0.519628i
$848$	3.11490e10			1.75411
$849$		0			0
$850$	3.83855e9	+	1.18138e10i	0.214388	+	0.659818i
$851$	−6.67687e8	+	2.05493e9i	−0.0371381	+	0.114299i
$852$		0			0
$853$	1.37119e10	+	9.96228e9i	0.756443	+	0.549588i	0.897817	−	0.440368i	$-0.145152\pi$
$853$	1.37119e10	+	9.96228e9i	0.756443	+	0.549588i	−0.141374	+	0.989956i	$0.545152\pi$
$854$	−3.52375e9	+	1.08450e10i	−0.193599	+	0.595836i
$855$		0			0
$856$	3.16368e10	−	2.29855e10i	1.72399	−	1.25255i
$857$	1.39034e10			0.754548			0.377274	−	0.926102i	$-0.376862\pi$
$857$	1.39034e10			0.754548			0.377274	+	0.926102i	$0.376862\pi$
$858$		0			0
$859$	−2.54744e10			−1.37128			−0.685642	−	0.727939i	$-0.740478\pi$
$859$	−2.54744e10			−1.37128			−0.685642	+	0.727939i	$0.740478\pi$
$860$	3.72145e9	−	2.70380e9i	0.199512	−	0.144954i
$861$		0			0
$862$	−8.47257e8	+	2.60759e9i	−0.0450547	+	0.138664i
$863$	1.10657e10	+	8.03968e9i	0.586057	+	0.425796i	0.840903	−	0.541186i	$-0.182025\pi$
$863$	1.10657e10	+	8.03968e9i	0.586057	+	0.425796i	−0.254845	+	0.966982i	$0.582025\pi$
$864$		0			0
$865$	7.26252e8	−	2.23518e9i	0.0381532	−	0.117424i
$866$	−1.02483e9	−	3.15410e9i	−0.0536215	−	0.165030i
$867$		0			0
$868$	2.57073e10			1.33425
$869$	4.71841e9	+	8.95665e9i	0.243908	+	0.462995i
$870$		0			0
$871$	−2.63384e9	+	1.91360e9i	−0.135060	+	0.0981266i
$872$	2.47949e10	+	7.63110e10i	1.26635	+	3.89744i
$873$		0			0
$874$	−2.09434e9	−	1.52163e9i	−0.106110	−	0.0770936i
$875$	−1.92639e9	−	1.39961e9i	−0.0972113	−	0.0706281i
$876$		0			0
$877$	−2.46200e9	−	7.57726e9i	−0.123251	−	0.379327i	0.870328	−	0.492473i	$-0.163907\pi$
$877$	−2.46200e9	−	7.57726e9i	−0.123251	−	0.379327i	−0.993578	+	0.113146i	$0.963907\pi$
$878$	1.11493e9	−	8.10046e8i	0.0555927	−	0.0403905i
$879$		0			0
$880$	2.92140e9	−	5.03590e8i	0.144511	−	0.0249108i
$881$	−3.67639e10			−1.81136			−0.905682	−	0.423958i	$-0.860641\pi$
$881$	−3.67639e10			−1.81136			−0.905682	+	0.423958i	$0.860641\pi$
$882$		0			0
$883$	5.47937e9	+	1.68638e10i	0.267836	+	0.824313i	0.991027	+	0.133665i	$0.0426746\pi$
$883$	5.47937e9	+	1.68638e10i	0.267836	+	0.824313i	−0.723191	+	0.690648i	$0.757325\pi$
$884$	−3.73545e9	+	1.14965e10i	−0.181869	+	0.559736i
$885$		0			0
$886$	1.50966e10	+	1.09683e10i	0.729223	+	0.529812i
$887$	−9.60349e9	+	2.95565e10i	−0.462058	+	1.42207i	0.400587	+	0.916259i	$0.368806\pi$
$887$	−9.60349e9	+	2.95565e10i	−0.462058	+	1.42207i	−0.862645	+	0.505810i	$0.831194\pi$
$888$		0			0
$889$	1.49175e10	−	1.08382e10i	0.712099	−	0.517370i
$890$	1.42941e9			0.0679659
$891$		0			0
$892$	5.53250e9			0.261002
$893$	1.86576e9	−	1.35555e9i	0.0876748	−	0.0636995i
$894$		0			0
$895$	−2.78276e8	+	8.56446e8i	−0.0129746	+	0.0399318i
$896$	1.45229e10	+	1.05515e10i	0.674489	+	0.490045i
$897$		0			0
$898$	1.46015e10	−	4.49387e10i	0.672867	−	2.07087i
$899$	7.09746e9	+	2.18437e10i	0.325795	+	1.00269i
$900$		0			0
$901$	−9.89778e9			−0.450818
$902$	2.26095e10	−	2.32341e10i	1.02581	−	1.05415i
$903$		0			0
$904$	1.03126e10	−	7.49253e9i	0.464278	−	0.337317i
$905$	−1.06000e9	−	3.26236e9i	−0.0475377	−	0.146306i
$906$		0			0
$907$	−1.59369e10	−	1.15788e10i	−0.709214	−	0.515274i	0.173706	−	0.984798i	$-0.444426\pi$
$907$	−1.59369e10	−	1.15788e10i	−0.709214	−	0.515274i	−0.882920	+	0.469524i	$0.844426\pi$
$908$	−5.18864e10	−	3.76976e10i	−2.30013	−	1.67114i
$909$		0			0
$910$	−5.20789e8	−	1.60282e9i	−0.0229096	−	0.0705085i
$911$	1.04964e10	−	7.62609e9i	0.459967	−	0.334185i	−0.333551	−	0.942732i	$-0.608247\pi$
$911$	1.04964e10	−	7.62609e9i	0.459967	−	0.334185i	0.793518	+	0.608546i	$0.208247\pi$
$912$		0			0
$913$	−2.67614e10	+	2.75006e10i	−1.16375	+	1.19590i
$914$	6.10180e9			0.264330
$915$		0			0
$916$	2.07497e10	+	6.38609e10i	0.892025	+	2.74537i
$917$	3.11224e9	−	9.57850e9i	0.133285	−	0.410209i
$918$		0			0
$919$	−1.05395e10	−	7.65737e9i	−0.447934	−	0.325443i	0.340845	−	0.940119i	$-0.389287\pi$
$919$	−1.05395e10	−	7.65737e9i	−0.447934	−	0.325443i	−0.788780	+	0.614676i	$0.789287\pi$
$920$	2.14751e8	−	6.60937e8i	0.00909241	−	0.0279835i
$921$		0			0
$922$	4.85015e9	−	3.52384e9i	0.203797	−	0.148067i
$923$	2.45295e10			1.02679
$924$		0			0
$925$	−1.93920e10			−0.805615
$926$	2.27134e10	−	1.65022e10i	0.940034	−	0.682974i
$927$		0			0
$928$	5.24822e9	−	1.61524e10i	0.215573	−	0.663466i
$929$	−7.44680e9	−	5.41042e9i	−0.304730	−	0.221399i	0.424902	−	0.905239i	$-0.360309\pi$
$929$	−7.44680e9	−	5.41042e9i	−0.304730	−	0.221399i	−0.729632	+	0.683840i	$0.760309\pi$
$930$		0			0
$931$	2.28756e9	−	7.04038e9i	0.0929070	−	0.285938i
$932$	−1.96598e10	−	6.05068e10i	−0.795471	−	2.44821i
$933$		0			0
$934$	−1.97946e10			−0.794936
$935$	−9.28294e8	+	1.60019e8i	−0.0371403	+	0.00640222i
$936$		0			0
$937$	−1.52893e10	+	1.11083e10i	−0.607155	+	0.441124i	−0.848411	−	0.529337i	$-0.822441\pi$
$937$	−1.52893e10	+	1.11083e10i	−0.607155	+	0.441124i	0.241256	+	0.970461i	$0.422441\pi$
$938$	2.11865e9	+	6.52055e9i	0.0838205	+	0.257973i
$939$		0			0
$940$	9.29842e8	+	6.75570e8i	0.0365142	+	0.0265291i
$941$	−3.39421e10	−	2.46604e10i	−1.32793	−	0.964797i	−0.999797	−	0.0201646i	$-0.993581\pi$
$941$	−3.39421e10	−	2.46604e10i	−1.32793	−	0.964797i	−0.328132	−	0.944632i	$-0.606419\pi$
$942$		0			0
$943$	−9.72068e8	−	2.99172e9i	−0.0377490	−	0.116180i
$944$	−4.71317e10	+	3.42432e10i	−1.82352	+	1.32487i
$945$		0			0
$946$	−2.56531e10	−	4.86957e10i	−0.985193	−	1.87013i
$947$	−3.25004e10			−1.24355			−0.621775	−	0.783196i	$-0.713588\pi$
$947$	−3.25004e10			−1.24355			−0.621775	+	0.783196i	$0.713588\pi$
$948$		0			0
$949$	9.62456e9	+	2.96214e10i	0.365552	+	1.12505i
$950$	7.17968e9	−	2.20968e10i	0.271689	−	0.836174i
$951$		0			0
$952$	1.10936e10	+	8.05999e9i	0.416720	+	0.302765i
$953$	−1.08725e10	+	3.34622e10i	−0.406916	+	1.25236i	0.512368	+	0.858766i	$0.328768\pi$
$953$	−1.08725e10	+	3.34622e10i	−0.406916	+	1.25236i	−0.919284	+	0.393594i	$0.871232\pi$
$954$		0			0
$955$	6.93839e8	−	5.04104e8i	0.0257779	−	0.0187287i
$956$	8.25736e9			0.305660
$957$		0			0
$958$	−7.15473e10			−2.62914
$959$	1.65255e10	−	1.20065e10i	0.605048	−	0.439593i
$960$		0			0
$961$	−3.87043e8	+	1.19120e9i	−0.0140678	+	0.0432964i
$962$	−2.23105e10	−	1.62096e10i	−0.807974	−	0.587027i
$963$		0			0
$964$	9.29776e9	−	2.86156e10i	0.334279	−	1.02880i
$965$	−2.82865e8	−	8.70569e8i	−0.0101329	−	0.0311858i
$966$		0			0
$967$	7.67029e9			0.272784			0.136392	−	0.990655i	$-0.456449\pi$
$967$	7.67029e9			0.272784			0.136392	+	0.990655i	$0.456449\pi$
$968$	−1.59748e9	−	5.86204e10i	−0.0566073	−	2.07723i
$969$		0			0
$970$	−4.79934e9	+	3.48692e9i	−0.168842	+	0.122671i
$971$	9.03966e9	+	2.78212e10i	0.316873	+	0.975234i	0.974977	+	0.222307i	$0.0713587\pi$
$971$	9.03966e9	+	2.78212e10i	0.316873	+	0.975234i	−0.658104	+	0.752927i	$0.728641\pi$
$972$		0			0
$973$	−2.59396e10	−	1.88462e10i	−0.902751	−	0.655887i
$974$	−7.16723e10	−	5.20730e10i	−2.48539	−	1.80574i
$975$		0			0
$976$	−7.67624e9	−	2.36250e10i	−0.264286	−	0.813388i
$977$	3.32131e10	−	2.41307e10i	1.13940	−	0.827826i	0.152368	−	0.988324i	$-0.451310\pi$
$977$	3.32131e10	−	2.41307e10i	1.13940	−	0.827826i	0.987036	+	0.160498i	$0.0513100\pi$
$978$		0			0
$979$	1.67323e9	−	1.15835e10i	0.0569922	−	0.394547i
$980$	3.68930e9			0.125214
$981$		0			0
$982$	−5.95479e9	−	1.83270e10i	−0.200667	−	0.617590i
$983$	−2.48996e9	+	7.66330e9i	−0.0836093	+	0.257323i	−0.984118	−	0.177515i	$-0.943194\pi$
$983$	−2.48996e9	+	7.66330e9i	−0.0836093	+	0.257323i	0.900509	+	0.434838i	$0.143194\pi$
$984$		0			0
$985$	2.30636e9	+	1.67567e9i	0.0768953	+	0.0558677i
$986$	−7.02834e9	+	2.16310e10i	−0.233498	+	0.718633i
$987$		0			0
$988$	1.82918e10	−	1.32898e10i	0.603402	−	0.438397i
$989$	−5.34054e9			−0.175549
$990$		0			0
$991$	−1.28001e10			−0.417787			−0.208894	−	0.977938i	$-0.566986\pi$
$991$	−1.28001e10			−0.417787			−0.208894	+	0.977938i	$0.566986\pi$
$992$	−1.57096e10	+	1.14137e10i	−0.510944	+	0.371222i
$993$		0			0
$994$	1.59631e10	−	4.91294e10i	0.515543	−	1.58668i
$995$	4.11267e6	+	2.98803e6i	0.000132356	+	9.61621e-5i
$996$		0			0
$997$	1.41404e10	−	4.35196e10i	0.451885	−	1.39076i	−0.422868	−	0.906191i	$-0.638977\pi$
$997$	1.41404e10	−	4.35196e10i	0.451885	−	1.39076i	0.874753	−	0.484568i	$-0.161023\pi$
$998$	−9.19197e9	−	2.82900e10i	−0.292719	−	0.900898i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.d.91.1	yes	56
3.2	odd	2	inner	99.8.f.d.91.14	yes	56
11.4	even	5	inner	99.8.f.d.37.1	✓	56
33.26	odd	10	inner	99.8.f.d.37.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.8.f.d.37.1	✓	56	11.4	even	5	inner
99.8.f.d.37.14	yes	56	33.26	odd	10	inner
99.8.f.d.91.1	yes	56	1.1	even	1	trivial
99.8.f.d.91.14	yes	56	3.2	odd	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-16.2902 + 11.8355i) q^{2} +(85.7365 - 263.870i) q^{4} +(21.6619 + 15.7383i) q^{5} +(176.688 - 543.790i) q^{7} +(929.915 + 2861.99i) q^{8} +O(q^{10})\)	\(q+(-16.2902 + 11.8355i) q^{2} +(85.7365 - 263.870i) q^{4} +(21.6619 + 15.7383i) q^{5} +(176.688 - 543.790i) q^{7} +(929.915 + 2861.99i) q^{8} -539.148 q^{10} +(-631.112 + 4369.08i) q^{11} +(-4422.88 + 3213.41i) q^{13} +(3557.75 + 10949.6i) q^{14} +(-20290.5 - 14741.9i) q^{16} +(6447.44 + 4684.34i) q^{17} +(-4606.28 - 14176.7i) q^{19} +(6010.08 - 4366.58i) q^{20} +(-41429.4 - 78642.6i) q^{22} -8624.88 q^{23} +(-23920.4 - 73619.4i) q^{25} +(34017.1 - 104694. i) q^{26} +(-128341. - 93245.2i) q^{28} +(43798.0 - 134796. i) q^{29} +(-131101. + 95250.4i) q^{31} +119828. q^{32} -160472. q^{34} +(12385.7 - 8998.77i) q^{35} +(77414.0 - 238256. i) q^{37} +(242825. + 176423. i) q^{38} +(-24899.1 + 76631.5i) q^{40} +(112705. + 346871. i) q^{41} +619202. q^{43} +(1.09876e6 + 541121. i) q^{44} +(140501. - 102080. i) q^{46} +(47809.2 + 147141. i) q^{47} +(401771. + 291904. i) q^{49} +(1.26099e6 + 916164. i) q^{50} +(468719. + 1.44257e6i) q^{52} +(-1.00477e6 + 730006. i) q^{53} +(-82433.1 + 84710.1i) q^{55} +1.72062e6 q^{56} +(881906. + 2.71423e6i) q^{58} +(717798. - 2.20916e6i) q^{59} +(801287. + 582169. i) q^{61} +(1.00832e6 - 3.10329e6i) q^{62} +(645170. - 468743. i) q^{64} -146382. q^{65} +595504. q^{67} +(1.78884e6 - 1.29967e6i) q^{68} +(-95261.0 + 293183. i) q^{70} +(-3.62994e6 - 2.63731e6i) q^{71} +(1.76049e6 - 5.41824e6i) q^{73} +(1.55879e6 + 4.79746e6i) q^{74} -4.13572e6 q^{76} +(2.26435e6 + 1.11516e6i) q^{77} +(1.85530e6 - 1.34795e6i) q^{79} +(-207519. - 638678. i) q^{80} +(-5.94138e6 - 4.31666e6i) q^{82} +(7.03241e6 + 5.10935e6i) q^{83} +(65940.5 + 202944. i) q^{85} +(-1.00869e7 + 7.32857e6i) q^{86} +(-1.30911e7 + 2.25664e6i) q^{88} -2.65123e6 q^{89} +(965949. + 2.97289e6i) q^{91} +(-739467. + 2.27584e6i) q^{92} +(-2.52031e6 - 1.83111e6i) q^{94} +(123336. - 379590. i) q^{95} +(8.90171e6 - 6.46747e6i) q^{97} -9.99976e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 1260 q^{4} - 3902 q^{7}+O(q^{10}) \) 56 * q - 1260 * q^4 - 3902 * q^7	\( 56 q - 1260 q^{4} - 3902 q^{7} + 20008 q^{10} - 18158 q^{13} + 54064 q^{16} - 111812 q^{19} + 16106 q^{22} - 78708 q^{25} + 69378 q^{28} - 189868 q^{31} + 1561016 q^{34} - 795786 q^{37} - 1589918 q^{40} + 355744 q^{43} + 2273926 q^{46} - 4728752 q^{49} - 438038 q^{52} + 3414760 q^{55} + 4154034 q^{58} + 1604778 q^{61} + 9561960 q^{64} - 18424972 q^{67} - 5609964 q^{70} + 17372 q^{73} + 8053960 q^{76} - 15803082 q^{79} + 7756570 q^{82} - 21218378 q^{85} + 37593088 q^{88} + 18308922 q^{91} + 68235162 q^{94} + 34988922 q^{97}+O(q^{100}) \) 56 * q - 1260 * q^4 - 3902 * q^7 + 20008 * q^10 - 18158 * q^13 + 54064 * q^16 - 111812 * q^19 + 16106 * q^22 - 78708 * q^25 + 69378 * q^28 - 189868 * q^31 + 1561016 * q^34 - 795786 * q^37 - 1589918 * q^40 + 355744 * q^43 + 2273926 * q^46 - 4728752 * q^49 - 438038 * q^52 + 3414760 * q^55 + 4154034 * q^58 + 1604778 * q^61 + 9561960 * q^64 - 18424972 * q^67 - 5609964 * q^70 + 17372 * q^73 + 8053960 * q^76 - 15803082 * q^79 + 7756570 * q^82 - 21218378 * q^85 + 37593088 * q^88 + 18308922 * q^91 + 68235162 * q^94 + 34988922 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more