LMFDB - Embedded newform 99.8.f.d.91.11

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			91.11
Character	$\chi$	$=$	99.91
Dual form			99.8.f.d.37.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.1078 - 7.34373i) q^{2} +(8.68266 - 26.7225i) q^{4} +(401.640 + 291.809i) q^{5} +(534.412 - 1644.75i) q^{7} +(385.706 + 1187.08i) q^{8} +O(q^{10})$	\(q+(10.1078 - 7.34373i) q^{2} +(8.68266 - 26.7225i) q^{4} +(401.640 + 291.809i) q^{5} +(534.412 - 1644.75i) q^{7} +(385.706 + 1187.08i) q^{8} +6202.66 q^{10} +(-1627.07 + 4103.63i) q^{11} +(-3297.38 + 2395.68i) q^{13} +(-6676.89 - 20549.4i) q^{14} +(15525.9 + 11280.2i) q^{16} +(18832.3 + 13682.5i) q^{17} +(-7234.20 - 22264.6i) q^{19} +(11285.2 - 8199.15i) q^{20} +(13689.9 + 53427.4i) q^{22} +24599.8 q^{23} +(52020.6 + 160103. i) q^{25} +(-15735.9 + 48430.1i) q^{26} +(-39311.7 - 28561.6i) q^{28} +(-27293.9 + 84001.9i) q^{29} +(168651. - 122532. i) q^{31} +80005.0 q^{32} +290833. q^{34} +(694594. - 504652. i) q^{35} +(110535. - 340190. i) q^{37} +(-236627. - 171919. i) q^{38} +(-191485. + 589332. i) q^{40} +(153888. + 473619. i) q^{41} -54568.2 q^{43} +(95531.9 + 79109.9i) q^{44} +(248650. - 180654. i) q^{46} +(-73467.4 - 226109. i) q^{47} +(-1.75335e6 - 1.27388e6i) q^{49} +(1.70157e6 + 1.23626e6i) q^{50} +(35388.6 + 108915. i) q^{52} +(782189. - 568294. i) q^{53} +(-1.85097e6 + 1.17339e6i) q^{55} +2.15858e6 q^{56} +(341007. + 1.04951e6i) q^{58} +(-46185.1 + 142143. i) q^{59} +(-1.35130e6 - 981777. i) q^{61} +(804842. - 2.47705e6i) q^{62} +(-1.17864e6 + 856330. i) q^{64} -2.02344e6 q^{65} +4.38780e6 q^{67} +(529144. - 384445. i) q^{68} +(3.31477e6 - 1.02018e7i) q^{70} +(-752779. - 546926. i) q^{71} +(-698821. + 2.15075e6i) q^{73} +(-1.38101e6 - 4.25031e6i) q^{74} -657777. q^{76} +(5.87992e6 + 4.86916e6i) q^{77} +(-2.83795e6 + 2.06189e6i) q^{79} +(2.94415e6 + 9.06117e6i) q^{80} +(5.03360e6 + 3.65712e6i) q^{82} +(-2.01949e6 - 1.46725e6i) q^{83} +(3.57115e6 + 1.09909e7i) q^{85} +(-551564. + 400735. i) q^{86} +(-5.49891e6 - 348674. i) q^{88} -3.39738e6 q^{89} +(2.17815e6 + 6.70364e6i) q^{91} +(213592. - 657368. i) q^{92} +(-2.40308e6 - 1.74594e6i) q^{94} +(3.59145e6 - 1.10534e7i) q^{95} +(5.76335e6 - 4.18732e6i) q^{97} -2.70775e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10.1078	−	7.34373i	0.893410	−	0.649100i	−0.0433548	−	0.999060i	$-0.513805\pi$
$2$	10.1078	−	7.34373i	0.893410	−	0.649100i	0.936765	+	0.349959i	$0.113805\pi$
$3$		0			0
$3$		0			0
$4$	8.68266	−	26.7225i	0.0678332	−	0.208769i
$5$	401.640	+	291.809i	1.43695	+	1.04401i	0.988668	+	0.150115i	$0.0479646\pi$
$5$	401.640	+	291.809i	1.43695	+	1.04401i	0.448284	+	0.893891i	$0.352035\pi$
$6$		0			0
$7$	534.412	−	1644.75i	0.588888	−	1.81241i	0.00582737	−	0.999983i	$-0.498145\pi$
$7$	534.412	−	1644.75i	0.588888	−	1.81241i	0.583061	−	0.812428i	$-0.301855\pi$
$8$	385.706	+	1187.08i	0.266343	+	0.819719i
$9$		0			0
$10$	6202.66			1.96145
$11$	−1627.07	+	4103.63i	−0.368581	+	0.929596i
$11$	−1627.07	+	4103.63i	−0.368581	+	0.929596i
$12$		0			0
$13$	−3297.38	+	2395.68i	−0.416262	+	0.302432i	−0.776132	−	0.630570i	$-0.782821\pi$
$13$	−3297.38	+	2395.68i	−0.416262	+	0.302432i	0.359870	+	0.933002i	$0.382821\pi$
$14$	−6676.89	−	20549.4i	−0.650318	−	2.00147i
$15$		0			0
$16$	15525.9	+	11280.2i	0.947623	+	0.688489i
$17$	18832.3	+	13682.5i	0.929677	+	0.675450i	0.945914	−	0.324418i	$-0.105169\pi$
$17$	18832.3	+	13682.5i	0.929677	+	0.675450i	−0.0162366	+	0.999868i	$0.505169\pi$
$18$		0			0
$19$	−7234.20	−	22264.6i	−0.241965	−	0.744692i	−0.996121	−	0.0879966i	$-0.971954\pi$
$19$	−7234.20	−	22264.6i	−0.241965	−	0.744692i	0.754156	−	0.656696i	$-0.228046\pi$
$20$	11285.2	−	8199.15i	0.315430	−	0.229173i
$21$		0			0
$22$	13689.9	+	53427.4i	0.274107	+	1.06976i
$23$	24599.8			0.421584			0.210792	−	0.977531i	$-0.432396\pi$
$23$	24599.8			0.421584			0.210792	+	0.977531i	$0.432396\pi$
$24$		0			0
$25$	52020.6	+	160103.i	0.665864	+	2.04932i
$26$	−15735.9	+	48430.1i	−0.175584	+	0.540392i
$27$		0			0
$28$	−39311.7	−	28561.6i	−0.338430	−	0.245884i
$29$	−27293.9	+	84001.9i	−0.207813	+	0.639582i	0.791773	+	0.610815i	$0.209158\pi$
$29$	−27293.9	+	84001.9i	−0.207813	+	0.639582i	−0.999586	+	0.0287670i	$0.990842\pi$
$30$		0			0
$31$	168651.	−	122532.i	1.01677	−	0.738725i	0.0511500	−	0.998691i	$-0.483711\pi$
$31$	168651.	−	122532.i	1.01677	−	0.738725i	0.965618	+	0.259966i	$0.0837113\pi$
$32$	80005.0			0.431611
$33$		0			0
$34$	290833.			1.26902
$35$	694594.	−	504652.i	2.73837	−	1.98955i
$36$		0			0
$37$	110535.	−	340190.i	0.358750	−	1.10412i	−0.595053	−	0.803686i	$-0.702869\pi$
$37$	110535.	−	340190.i	0.358750	−	1.10412i	0.953803	−	0.300433i	$-0.0971311\pi$
$38$	−236627.	−	171919.i	−0.699554	−	0.508256i
$39$		0			0
$40$	−191485.	+	589332.i	−0.473071	+	1.45596i
$41$	153888.	+	473619.i	0.348708	+	1.07321i	0.959569	+	0.281474i	$0.0908233\pi$
$41$	153888.	+	473619.i	0.348708	+	1.07321i	−0.610861	+	0.791738i	$0.709177\pi$
$42$		0			0
$43$	−54568.2			−0.104665			−0.0523324	−	0.998630i	$-0.516666\pi$
$43$	−54568.2			−0.104665			−0.0523324	+	0.998630i	$0.516666\pi$
$44$	95531.9	+	79109.9i	0.169069	+	0.140006i
$45$		0			0
$46$	248650.	−	180654.i	0.376648	−	0.273651i
$47$	−73467.4	−	226109.i	−0.103217	−	0.317670i	0.886091	−	0.463512i	$-0.153411\pi$
$47$	−73467.4	−	226109.i	−0.103217	−	0.317670i	−0.989308	+	0.145842i	$0.953411\pi$
$48$		0			0
$49$	−1.75335e6	−	1.27388e6i	−2.12903	−	1.54683i
$50$	1.70157e6	+	1.23626e6i	1.92510	+	1.39867i
$51$		0			0
$52$	35388.6	+	108915.i	0.0349021	+	0.107418i
$53$	782189.	−	568294.i	0.721683	−	0.524333i	−0.165239	−	0.986254i	$-0.552839\pi$
$53$	782189.	−	568294.i	0.721683	−	0.524333i	0.886921	+	0.461920i	$0.152839\pi$
$54$		0			0
$55$	−1.85097e6	+	1.17339e6i	−1.50014	+	0.950983i
$56$	2.15858e6			1.64252
$57$		0			0
$58$	341007.	+	1.04951e6i	0.229491	+	0.706300i
$59$	−46185.1	+	142143.i	−0.0292765	+	0.0901039i	−0.964627	−	0.263618i	$-0.915084\pi$
$59$	−46185.1	+	142143.i	−0.0292765	+	0.0901039i	0.935351	+	0.353722i	$0.115084\pi$
$60$		0			0
$61$	−1.35130e6	−	981777.i	−0.762250	−	0.553807i	0.137350	−	0.990523i	$-0.456142\pi$
$61$	−1.35130e6	−	981777.i	−0.762250	−	0.553807i	−0.899600	+	0.436716i	$0.856142\pi$
$62$	804842.	−	2.47705e6i	0.428884	−	1.31997i
$63$		0			0
$64$	−1.17864e6	+	856330.i	−0.562018	+	0.408330i
$65$	−2.02344e6			−0.913890
$66$		0			0
$67$	4.38780e6			1.78232			0.891158	−	0.453693i	$-0.149894\pi$
$67$	4.38780e6			1.78232			0.891158	+	0.453693i	$0.149894\pi$
$68$	529144.	−	384445.i	0.204076	−	0.148270i
$69$		0			0
$70$	3.31477e6	−	1.02018e7i	1.15508	−	3.55496i
$71$	−752779.	−	546926.i	−0.249611	−	0.181353i	0.455944	−	0.890009i	$-0.349302\pi$
$71$	−752779.	−	546926.i	−0.249611	−	0.181353i	−0.705554	+	0.708656i	$0.749302\pi$
$72$		0			0
$73$	−698821.	+	2.15075e6i	−0.210250	+	0.647083i	0.789207	+	0.614127i	$0.210492\pi$
$73$	−698821.	+	2.15075e6i	−0.210250	+	0.647083i	−0.999457	+	0.0329554i	$0.989508\pi$
$74$	−1.38101e6	−	4.25031e6i	−0.396173	−	1.21930i
$75$		0			0
$76$	−657777.			−0.171882
$77$	5.87992e6	+	4.86916e6i	1.46776	+	1.21545i
$78$		0			0
$79$	−2.83795e6	+	2.06189e6i	−0.647605	+	0.470513i	−0.862455	−	0.506134i	$-0.831074\pi$
$79$	−2.83795e6	+	2.06189e6i	−0.647605	+	0.470513i	0.214849	+	0.976647i	$0.431074\pi$
$80$	2.94415e6	+	9.06117e6i	0.642903	+	1.97865i
$81$		0			0
$82$	5.03360e6	+	3.65712e6i	1.00816	+	0.732472i
$83$	−2.01949e6	−	1.46725e6i	−0.387676	−	0.281663i	0.376827	−	0.926284i	$-0.377015\pi$
$83$	−2.01949e6	−	1.46725e6i	−0.387676	−	0.281663i	−0.764502	+	0.644621i	$0.777015\pi$
$84$		0			0
$85$	3.57115e6	+	1.09909e7i	0.630727	+	1.94118i
$86$	−551564.	+	400735.i	−0.0935085	+	0.0679379i
$87$		0			0
$88$	−5.49891e6	−	348674.i	−0.860177	−	0.0545418i
$89$	−3.39738e6			−0.510833			−0.255416	−	0.966831i	$-0.582213\pi$
$89$	−3.39738e6			−0.510833			−0.255416	+	0.966831i	$0.582213\pi$
$90$		0			0
$91$	2.17815e6	+	6.70364e6i	0.303000	+	0.932537i
$92$	213592.	−	657368.i	0.0285974	−	0.0880138i
$93$		0			0
$94$	−2.40308e6	−	1.74594e6i	−0.298415	−	0.216811i
$95$	3.59145e6	−	1.10534e7i	0.429772	−	1.32270i
$96$		0			0
$97$	5.76335e6	−	4.18732e6i	0.641171	−	0.465838i	−0.219081	−	0.975707i	$-0.570306\pi$
$97$	5.76335e6	−	4.18732e6i	0.641171	−	0.465838i	0.860252	+	0.509869i	$0.170306\pi$
$98$	−2.70775e7			−2.90614
$99$		0			0
$100$	4.73003e6			0.473003
$101$	−5.52721e6	+	4.01575e6i	−0.533803	+	0.387831i	−0.821778	−	0.569807i	$-0.807018\pi$
$101$	−5.52721e6	+	4.01575e6i	−0.533803	+	0.387831i	0.287975	+	0.957638i	$0.407018\pi$
$102$		0			0
$103$	−2.24108e6	+	6.89733e6i	−0.202082	+	0.621943i	0.797739	+	0.603003i	$0.206029\pi$
$103$	−2.24108e6	+	6.89733e6i	−0.202082	+	0.621943i	−0.999821	+	0.0189404i	$0.993971\pi$
$104$	−4.11569e6	−	2.99022e6i	−0.358778	−	0.260667i
$105$		0			0
$106$	3.73280e6	−	1.14884e7i	0.304414	−	0.936889i
$107$	−3.77622e6	−	1.16220e7i	−0.297998	−	0.917144i	−0.982198	−	0.187850i	$-0.939848\pi$
$107$	−3.77622e6	−	1.16220e7i	−0.297998	−	0.917144i	0.684200	−	0.729295i	$-0.260152\pi$
$108$		0			0
$109$	−2.30142e7			−1.70217			−0.851087	−	0.525024i	$-0.824056\pi$
$109$	−2.30142e7			−1.70217			−0.851087	+	0.525024i	$0.824056\pi$
$110$	−1.00922e7	+	2.54534e7i	−0.722954	+	1.82336i
$111$		0			0
$112$	2.68503e7	−	1.95079e7i	1.80587	−	1.31204i
$113$	−836712.	−	2.57514e6i	−0.0545508	−	0.167890i	0.920069	−	0.391756i	$-0.128132\pi$
$113$	−836712.	−	2.57514e6i	−0.0545508	−	0.167890i	−0.974620	+	0.223866i	$0.928132\pi$
$114$		0			0
$115$	9.88028e6	+	7.17844e6i	0.605796	+	0.440137i
$116$	2.00776e6	+	1.45872e6i	0.119428	+	0.0867699i
$117$		0			0
$118$	577032.	+	1.77592e6i	0.0323305	+	0.0995032i
$119$	3.25684e7	−	2.36624e7i	1.77167	−	1.28719i
$120$		0			0
$121$	−1.41924e7	−	1.33538e7i	−0.728296	−	0.685263i
$122$	−2.08686e7			−1.04048
$123$		0			0
$124$	−1.81002e6	−	5.57066e6i	−0.0852524	−	0.262380i
$125$	−1.38405e7	+	4.25967e7i	−0.633821	+	1.95070i
$126$		0			0
$127$	−6.73524e6	−	4.89344e6i	−0.291770	−	0.211983i	0.432265	−	0.901747i	$-0.357714\pi$
$127$	−6.73524e6	−	4.89344e6i	−0.291770	−	0.211983i	−0.724035	+	0.689764i	$0.757714\pi$
$128$	−8.78928e6	+	2.70506e7i	−0.370440	+	1.14010i
$129$		0			0
$130$	−2.04525e7	+	1.48596e7i	−0.816478	+	0.593206i
$131$	−4.73665e7			−1.84086			−0.920432	−	0.390902i	$-0.872163\pi$
$131$	−4.73665e7			−1.84086			−0.920432	+	0.390902i	$0.872163\pi$
$132$		0			0
$133$	−4.04857e7			−1.49218
$134$	4.43509e7	−	3.22228e7i	1.59234	−	1.15690i
$135$		0			0
$136$	−8.97846e6	+	2.76329e7i	−0.306066	+	0.941976i
$137$	−3.61872e7	−	2.62915e7i	−1.20236	−	0.873562i	−0.207841	−	0.978163i	$-0.566644\pi$
$137$	−3.61872e7	−	2.62915e7i	−1.20236	−	0.873562i	−0.994514	+	0.104600i	$0.966644\pi$
$138$		0			0
$139$	1.06259e7	−	3.27032e7i	0.335594	−	1.03285i	−0.630835	−	0.775917i	$-0.717287\pi$
$139$	1.06259e7	−	3.27032e7i	0.335594	−	1.03285i	0.966429	−	0.256935i	$-0.0827127\pi$
$140$	−7.45463e6	−	2.29430e7i	−0.229603	−	0.706646i
$141$		0			0
$142$	−1.16254e7			−0.340721
$143$	−4.46593e6	−	1.74292e7i	−0.127713	−	0.498426i
$144$		0			0
$145$	−3.54748e7	+	2.57740e7i	−0.966345	+	0.702091i
$146$	8.73100e6	+	2.68713e7i	0.232182	+	0.714584i
$147$		0			0
$148$	−8.13099e6	−	5.90751e6i	−0.206171	−	0.149792i
$149$	1.90830e7	+	1.38646e7i	0.472602	+	0.343366i	0.798455	−	0.602055i	$-0.205651\pi$
$149$	1.90830e7	+	1.38646e7i	0.472602	+	0.343366i	−0.325852	+	0.945421i	$0.605651\pi$
$150$		0			0
$151$	−1.19340e7	−	3.67292e7i	−0.282077	−	0.868144i	−0.987260	−	0.159118i	$-0.949135\pi$
$151$	−1.19340e7	−	3.67292e7i	−0.282077	−	0.868144i	0.705182	−	0.709026i	$-0.250865\pi$
$152$	2.36396e7	−	1.71752e7i	0.545993	−	0.396687i
$153$		0			0
$154$	9.51908e7	+	6.03583e6i	2.10026	+	0.133172i
$155$	1.03493e8			2.23228
$156$		0			0
$157$	3.73056e6	+	1.14815e7i	0.0769352	+	0.236782i	0.982126	−	0.188222i	$-0.0602726\pi$
$157$	3.73056e6	+	1.14815e7i	0.0769352	+	0.236782i	−0.905191	+	0.425004i	$0.860273\pi$
$158$	−1.35434e7	+	4.16823e7i	−0.273167	+	0.840722i
$159$		0			0
$160$	3.21332e7	+	2.33462e7i	0.620204	+	0.450605i
$161$	1.31464e7	−	4.04606e7i	0.248266	−	0.764084i
$162$		0			0
$163$	3.20731e7	−	2.33024e7i	0.580074	−	0.421449i	−0.258676	−	0.965964i	$-0.583286\pi$
$163$	3.20731e7	−	2.33024e7i	0.580074	−	0.421449i	0.838751	+	0.544515i	$0.183286\pi$
$164$	1.39924e7			0.247708
$165$		0			0
$166$	−3.11877e7			−0.529181
$167$	−4.16182e7	+	3.02374e7i	−0.691473	+	0.502385i	−0.877144	−	0.480227i	$-0.840554\pi$
$167$	−4.16182e7	+	3.02374e7i	−0.691473	+	0.502385i	0.185671	+	0.982612i	$0.440554\pi$
$168$		0			0
$169$	−1.42570e7	+	4.38784e7i	−0.227208	+	0.699275i
$170$	1.16810e8	+	8.48677e7i	1.82352	+	1.32486i
$171$		0			0
$172$	−473797.	+	1.45820e6i	−0.00709975	+	0.0218508i
$173$	−4.28354e6	−	1.31834e7i	−0.0628986	−	0.193582i	0.914669	−	0.404204i	$-0.132451\pi$
$173$	−4.28354e6	−	1.31834e7i	−0.0628986	−	0.193582i	−0.977568	+	0.210621i	$0.932451\pi$
$174$		0			0
$175$	2.91130e8			4.10633
$176$	−7.15515e7	+	4.53587e7i	−0.989292	+	0.627143i
$177$		0			0
$178$	−3.43399e7	+	2.49494e7i	−0.456383	+	0.331582i
$179$	−3.85177e7	−	1.18545e8i	−0.501967	−	1.54490i	−0.805810	−	0.592174i	$-0.798270\pi$
$179$	−3.85177e7	−	1.18545e8i	−0.501967	−	1.54490i	0.303843	−	0.952722i	$-0.401730\pi$
$180$		0			0
$181$	−6.35136e7	−	4.61453e7i	−0.796144	−	0.578432i	0.113636	−	0.993522i	$-0.463750\pi$
$181$	−6.35136e7	−	4.61453e7i	−0.796144	−	0.578432i	−0.909780	+	0.415090i	$0.863750\pi$
$182$	7.12460e7	+	5.17632e7i	0.876013	+	0.636461i
$183$		0			0
$184$	9.48829e6	+	2.92020e7i	0.112286	+	0.345581i
$185$	1.43666e8	−	1.04379e8i	1.66821	−	1.21203i
$186$		0			0
$187$	−8.67894e7	+	5.50184e7i	−0.970557	+	0.615266i
$188$	−6.68010e6			−0.0733213
$189$		0			0
$190$	−4.48713e7	−	1.38100e8i	−0.474603	−	1.46068i
$191$	4.54826e7	−	1.39981e8i	0.472311	−	1.45362i	−0.377238	−	0.926116i	$-0.623126\pi$
$191$	4.54826e7	−	1.39981e8i	0.472311	−	1.45362i	0.849550	−	0.527509i	$-0.176874\pi$
$192$		0			0
$193$	3.33040e7	+	2.41968e7i	0.333462	+	0.242274i	0.741898	−	0.670513i	$-0.233926\pi$
$193$	3.33040e7	+	2.41968e7i	0.333462	+	0.242274i	−0.408436	+	0.912787i	$0.633926\pi$
$194$	2.75041e7	−	8.46490e7i	0.270453	−	0.832369i
$195$		0			0
$196$	−4.92650e7	+	3.57931e7i	−0.467350	+	0.339549i
$197$	7.22881e7			0.673651			0.336826	−	0.941567i	$-0.390647\pi$
$197$	7.22881e7			0.673651			0.336826	+	0.941567i	$0.390647\pi$
$198$		0			0
$199$	1.14769e8			1.03238			0.516189	−	0.856475i	$-0.327350\pi$
$199$	1.14769e8			1.03238			0.516189	+	0.856475i	$0.327350\pi$
$200$	−1.69991e8	+	1.23505e8i	−1.50252	+	1.09164i
$201$		0			0
$202$	−2.63772e7	+	8.11807e7i	−0.225164	+	0.692984i
$203$	1.23576e8	+	8.97832e7i	1.03681	+	0.753285i
$204$		0			0
$205$	−7.63985e7	+	2.35130e8i	−0.619364	+	1.90621i
$206$	2.79998e7	+	8.61746e7i	0.223162	+	0.686822i
$207$		0			0
$208$	−7.82184e7			−0.602681
$209$	1.03136e8	+	6.53963e6i	0.781447	+	0.0495497i
$210$		0			0
$211$	−1.76979e7	+	1.28583e7i	−0.129698	+	0.0942313i	−0.650743	−	0.759298i	$-0.725542\pi$
$211$	−1.76979e7	+	1.28583e7i	−0.129698	+	0.0942313i	0.521045	+	0.853529i	$0.325542\pi$
$212$	−8.39473e6	−	2.58363e7i	−0.0605106	−	0.186232i
$213$		0			0
$214$	−1.23518e8	−	8.97411e7i	−0.861554	−	0.625955i
$215$	−2.19168e7	−	1.59235e7i	−0.150398	−	0.109271i
$216$		0			0
$217$	−1.11405e8	−	3.42870e8i	−0.740111	−	2.27783i
$218$	−2.32623e8	+	1.69010e8i	−1.52074	+	1.10488i
$219$		0			0
$220$	1.52845e7	+	5.96508e7i	0.0967769	+	0.377691i
$221$	−9.48760e7			−0.591267
$222$		0			0
$223$	1.56457e7	+	4.81525e7i	0.0944774	+	0.290771i	0.987117	−	0.159999i	$-0.0511492\pi$
$223$	1.56457e7	+	4.81525e7i	0.0944774	+	0.290771i	−0.892640	+	0.450771i	$0.851149\pi$
$224$	4.27556e7	−	1.31588e8i	0.254170	−	0.782256i
$225$		0			0
$226$	−2.73684e7	−	1.98843e7i	−0.157714	−	0.114586i
$227$	−5.00554e6	+	1.54055e7i	−0.0284027	+	0.0874146i	−0.964253	−	0.264983i	$-0.914634\pi$
$227$	−5.00554e6	+	1.54055e7i	−0.0284027	+	0.0874146i	0.935850	+	0.352398i	$0.114634\pi$
$228$		0			0
$229$	2.14787e8	−	1.56052e8i	1.18191	−	0.858705i	0.189521	−	0.981877i	$-0.439307\pi$
$229$	2.14787e8	−	1.56052e8i	1.18191	−	0.858705i	0.992385	+	0.123171i	$0.0393065\pi$
$230$	1.52584e8			0.826918
$231$		0			0
$232$	−1.10244e8			−0.579627
$233$	−2.04107e8	+	1.48292e8i	−1.05709	+	0.768020i	−0.973548	−	0.228484i	$-0.926623\pi$
$233$	−2.04107e8	+	1.48292e8i	−1.05709	+	0.768020i	−0.0835416	+	0.996504i	$0.526623\pi$
$234$		0			0
$235$	3.64733e7	−	1.12253e8i	0.183331	−	0.564236i
$236$	3.39740e6	+	2.46836e6i	0.0168250	+	0.0122241i
$237$		0			0
$238$	1.55425e8	−	4.78348e8i	0.747310	−	2.29998i
$239$	9.57070e7	+	2.94556e8i	0.453473	+	1.39565i	0.872919	+	0.487866i	$0.162224\pi$
$239$	9.57070e7	+	2.94556e8i	0.453473	+	1.39565i	−0.419446	+	0.907780i	$0.637776\pi$
$240$		0			0
$241$	−1.59748e8			−0.735150			−0.367575	−	0.929994i	$-0.619812\pi$
$241$	−1.59748e8			−0.735150			−0.367575	+	0.929994i	$0.619812\pi$
$242$	−2.41521e8	−	3.07522e7i	−1.09547	−	0.139483i
$243$		0			0
$244$	−3.79684e7	+	2.75856e7i	−0.167324	+	0.121568i
$245$	−3.32485e8	−	1.02328e9i	−1.44441	−	4.44544i
$246$		0			0
$247$	7.71928e7	+	5.60838e7i	0.325940	+	0.236809i
$248$	2.10505e8	+	1.52941e8i	0.876356	+	0.636710i
$249$		0			0
$250$	1.72922e8	+	5.32199e8i	0.699939	+	2.15419i
$251$	−5.15332e7	+	3.74410e7i	−0.205697	+	0.149448i	−0.685865	−	0.727729i	$-0.740576\pi$
$251$	−5.15332e7	+	3.74410e7i	−0.205697	+	0.149448i	0.480167	+	0.877177i	$0.340576\pi$
$252$		0			0
$253$	−4.00257e7	+	1.00949e8i	−0.155388	+	0.391903i
$254$	−1.04014e8			−0.398268
$255$		0			0
$256$	5.21869e7	+	1.60615e8i	0.194411	+	0.598337i
$257$	1.15356e7	−	3.55030e7i	0.0423911	−	0.130466i	−0.927621	−	0.373522i	$-0.878150\pi$
$257$	1.15356e7	−	3.55030e7i	0.0423911	−	0.130466i	0.970012	+	0.243056i	$0.0781499\pi$
$258$		0			0
$259$	−5.00457e8	−	3.63603e8i	−1.78985	−	1.30041i
$260$	−1.75688e7	+	5.40713e7i	−0.0619921	+	0.190792i
$261$		0			0
$262$	−4.78770e8	+	3.47847e8i	−1.64465	+	1.19491i
$263$	−5.17553e8			−1.75432			−0.877162	−	0.480195i	$-0.840566\pi$
$263$	−5.17553e8			−1.75432			−0.877162	+	0.480195i	$0.840566\pi$
$264$		0			0
$265$	4.79992e8			1.58443
$266$	−4.09221e8	+	2.97316e8i	−1.33313	+	0.968575i
$267$		0			0
$268$	3.80977e7	−	1.17253e8i	0.120900	−	0.372093i
$269$	1.28272e8	+	9.31953e7i	0.401791	+	0.291918i	0.770270	−	0.637718i	$-0.220121\pi$
$269$	1.28272e8	+	9.31953e7i	0.401791	+	0.291918i	−0.368479	+	0.929636i	$0.620121\pi$
$270$		0			0
$271$	−2.84191e7	+	8.74651e7i	−0.0867398	+	0.266958i	−0.985013	−	0.172480i	$-0.944822\pi$
$271$	−2.84191e7	+	8.74651e7i	−0.0867398	+	0.266958i	0.898273	+	0.439437i	$0.144822\pi$
$272$	1.38047e8	+	4.24864e8i	0.415944	+	1.28014i
$273$		0			0
$274$	−5.58850e8			−1.64123
$275$	−7.41646e8	−	4.70260e7i	−2.15046	−	0.136356i
$276$		0			0
$277$	4.33473e8	−	3.14937e8i	1.22541	−	0.890316i	0.228877	−	0.973455i	$-0.426495\pi$
$277$	4.33473e8	−	3.14937e8i	1.22541	−	0.890316i	0.996538	+	0.0831398i	$0.0264948\pi$
$278$	−1.32759e8	−	4.08591e8i	−0.370602	−	1.14060i
$279$		0			0
$280$	8.66971e8	+	6.29892e8i	2.36022	+	1.71480i
$281$	4.63056e8	+	3.36430e8i	1.24498	+	0.904528i	0.997919	−	0.0644729i	$-0.0205366\pi$
$281$	4.63056e8	+	3.36430e8i	1.24498	+	0.904528i	0.247057	+	0.969001i	$0.420537\pi$
$282$		0			0
$283$	1.27498e8	+	3.92398e8i	0.334388	+	1.02914i	0.967023	+	0.254690i	$0.0819733\pi$
$283$	1.27498e8	+	3.92398e8i	0.334388	+	1.02914i	−0.632635	+	0.774450i	$0.718027\pi$
$284$	−2.11513e7	+	1.53673e7i	−0.0547928	+	0.0398093i
$285$		0			0
$286$	−1.73136e8	−	1.43374e8i	−0.437629	−	0.362400i
$287$	8.61224e8			2.15045
$288$		0			0
$289$	4.06440e7	+	1.25089e8i	0.0990499	+	0.304844i
$290$	−1.69295e8	+	5.21035e8i	−0.407615	+	1.25451i
$291$		0			0
$292$	5.14057e7	+	3.73484e7i	0.120829	+	0.0877875i
$293$	5.34291e7	−	1.64438e8i	0.124091	−	0.381914i	−0.869643	−	0.493681i	$-0.835651\pi$
$293$	5.34291e7	−	1.64438e8i	0.124091	−	0.381914i	0.993734	+	0.111767i	$0.0356511\pi$
$294$		0			0
$295$	−6.00284e7	+	4.36132e7i	−0.136138	+	0.0989101i
$296$	4.46467e8			1.00062
$297$		0			0
$298$	2.94705e8			0.645106
$299$	−8.11148e7	+	5.89334e7i	−0.175490	+	0.127501i
$300$		0			0
$301$	−2.91619e7	+	8.97511e7i	−0.0616358	+	0.189696i
$302$	−3.90356e8	−	2.83610e8i	−0.815523	−	0.592512i
$303$		0			0
$304$	1.38832e8	−	4.27280e8i	0.283420	−	0.872278i
$305$	−2.56246e8	−	7.88643e8i	−0.517138	−	1.59159i
$306$		0			0
$307$	3.12063e8			0.615542			0.307771	−	0.951461i	$-0.400417\pi$
$307$	3.12063e8			0.615542			0.307771	+	0.951461i	$0.400417\pi$
$308$	1.81169e8	−	1.14849e8i	0.353311	−	0.223975i
$309$		0			0
$310$	1.04608e9	−	7.60023e8i	1.99434	−	1.44897i
$311$	7.80564e6	+	2.40233e7i	0.0147145	+	0.0452867i	0.958144	−	0.286286i	$-0.0924208\pi$
$311$	7.80564e6	+	2.40233e7i	0.0147145	+	0.0452867i	−0.943430	+	0.331573i	$0.892421\pi$
$312$		0			0
$313$	−2.47804e8	−	1.80040e8i	−0.456776	−	0.331867i	0.335489	−	0.942044i	$-0.391098\pi$
$313$	−2.47804e8	−	1.80040e8i	−0.456776	−	0.331867i	−0.792265	+	0.610177i	$0.791098\pi$
$314$	1.22025e8	+	8.86560e7i	0.222430	+	0.161605i
$315$		0			0
$316$	3.04579e7	+	9.37398e7i	0.0542995	+	0.167117i
$317$	−1.59289e7	+	1.15730e7i	−0.0280853	+	0.0204052i	−0.601739	−	0.798693i	$-0.705525\pi$
$317$	−1.59289e7	+	1.15730e7i	−0.0280853	+	0.0204052i	0.573654	+	0.819098i	$0.305525\pi$
$318$		0			0
$319$	−3.00304e8	−	2.48681e8i	−0.517957	−	0.428920i
$320$	−7.23273e8			−1.23389
$321$		0			0
$322$	−1.64250e8	−	5.05510e8i	−0.274164	−	0.843790i
$323$	1.68398e8	−	5.18275e8i	0.278053	−	0.855759i
$324$		0			0
$325$	−5.55088e8	−	4.03295e8i	−0.896954	−	0.651675i
$326$	1.53061e8	−	4.71072e8i	0.244682	−	0.753053i
$327$		0			0
$328$	−5.02868e8	+	3.65355e8i	−0.786857	+	0.571685i
$329$	−4.11155e8			−0.636532
$330$		0			0
$331$	2.05081e8			0.310834			0.155417	−	0.987849i	$-0.450328\pi$
$331$	2.05081e8			0.310834			0.155417	+	0.987849i	$0.450328\pi$
$332$	−5.67430e7	+	4.12262e7i	−0.0850999	+	0.0618287i
$333$		0			0
$334$	−1.98612e8	+	6.11266e8i	−0.291671	+	0.897671i
$335$	1.76232e9	+	1.28040e9i	2.56110	+	1.86075i
$336$		0			0
$337$	−2.96817e8	+	9.13510e8i	−0.422459	+	1.30020i	0.482947	+	0.875649i	$0.339566\pi$
$337$	−2.96817e8	+	9.13510e8i	−0.422459	+	1.30020i	−0.905406	+	0.424546i	$0.860434\pi$
$338$	1.78125e8	+	5.48213e8i	0.250909	+	0.772220i
$339$		0			0
$340$	3.24710e8			0.448043
$341$	2.28418e8	+	8.91448e8i	0.311954	+	1.21746i
$342$		0			0
$343$	−1.88000e9	+	1.36590e9i	−2.51552	+	1.82764i
$344$	−2.10473e7	−	6.47769e7i	−0.0278767	−	0.0857957i
$345$		0			0
$346$	−1.40112e8	−	1.01798e8i	−0.181849	−	0.132121i
$347$	2.70563e8	+	1.96576e8i	0.347629	+	0.252567i	0.747874	−	0.663841i	$-0.231075\pi$
$347$	2.70563e8	+	1.96576e8i	0.347629	+	0.252567i	−0.400245	+	0.916408i	$0.631075\pi$
$348$		0			0
$349$	−7.62493e7	−	2.34671e8i	−0.0960167	−	0.295509i	0.891501	−	0.453019i	$-0.149653\pi$
$349$	−7.62493e7	−	2.34671e8i	−0.0960167	−	0.295509i	−0.987517	+	0.157510i	$0.949653\pi$
$350$	2.94268e9	−	2.13798e9i	3.66864	−	2.66542i
$351$		0			0
$352$	−1.30174e8	+	3.28311e8i	−0.159084	+	0.401223i
$353$	8.88626e8			1.07524			0.537622	−	0.843186i	$-0.319323\pi$
$353$	8.88626e8			1.07524			0.537622	+	0.843186i	$0.319323\pi$
$354$		0			0
$355$	−1.42749e8	−	4.39335e8i	−0.169345	−	0.521191i
$356$	−2.94983e7	+	9.07863e7i	−0.0346514	+	0.106646i
$357$		0			0
$358$	−1.25990e9	−	9.15367e8i	−1.45126	−	1.05440i
$359$	−9.36274e7	+	2.88155e8i	−0.106800	+	0.328697i	−0.990149	−	0.140019i	$-0.955284\pi$
$359$	−9.36274e7	+	2.88155e8i	−0.106800	+	0.328697i	0.883348	+	0.468717i	$0.155284\pi$
$360$		0			0
$361$	2.79779e8	−	2.03272e8i	0.312997	−	0.227406i
$362$	−9.80860e8			−1.08674
$363$		0			0
$364$	1.98050e8			0.215238
$365$	−9.08282e8	+	6.59906e8i	−0.977678	+	0.710325i
$366$		0			0
$367$	1.11498e8	−	3.43156e8i	0.117743	−	0.362377i	−0.874766	−	0.484546i	$-0.838985\pi$
$367$	1.11498e8	−	3.43156e8i	0.117743	−	0.362377i	0.992509	+	0.122169i	$0.0389850\pi$
$368$	3.81933e8	+	2.77491e8i	0.399503	+	0.290256i
$369$		0			0
$370$	6.85608e8	−	2.11008e9i	0.703671	−	2.16568i
$371$	−5.16690e8	−	1.59021e9i	−0.525317	−	1.61676i
$372$		0			0
$373$	1.19548e9			1.19279			0.596394	−	0.802692i	$-0.296600\pi$
$373$	1.19548e9			1.19279			0.596394	+	0.802692i	$0.296600\pi$
$374$	−4.73207e8	+	1.19347e9i	−0.467736	+	1.17967i
$375$		0			0
$376$	2.40073e8	−	1.74423e8i	0.232909	−	0.169218i
$377$	−1.11244e8	−	3.42373e8i	−0.106926	−	0.329083i
$378$		0			0
$379$	−1.29833e9	−	9.43294e8i	−1.22504	−	0.890041i	−0.228528	−	0.973537i	$-0.573391\pi$
$379$	−1.29833e9	−	9.43294e8i	−1.22504	−	0.890041i	−0.996508	+	0.0834964i	$0.973391\pi$
$380$	−2.64190e8	−	1.91945e8i	−0.246986	−	0.179446i
$381$		0			0
$382$	−5.68255e8	−	1.74891e9i	−0.521581	−	1.60526i
$383$	5.68418e8	−	4.12980e8i	0.516978	−	0.375607i	−0.298486	−	0.954414i	$-0.596482\pi$
$383$	5.68418e8	−	4.12980e8i	0.516978	−	0.375607i	0.815464	+	0.578807i	$0.196482\pi$
$384$		0			0
$385$	9.40750e8	+	3.67146e9i	0.840160	+	3.27889i
$386$	5.14324e8			0.455178
$387$		0			0
$388$	−6.18543e7	−	1.90368e8i	−0.0537599	−	0.165456i
$389$	−3.53420e8	+	1.08771e9i	−0.304416	+	0.936896i	0.675478	+	0.737380i	$0.263937\pi$
$389$	−3.53420e8	+	1.08771e9i	−0.304416	+	0.936896i	−0.979894	+	0.199516i	$0.936063\pi$
$390$		0			0
$391$	4.63271e8	+	3.36586e8i	0.391937	+	0.284759i
$392$	8.35923e8	−	2.57271e9i	0.700915	−	2.15719i
$393$		0			0
$394$	7.30672e8	−	5.30864e8i	0.601847	−	0.437267i
$395$	−1.74152e9			−1.42180
$396$		0			0
$397$	1.60825e9			1.28999			0.644996	−	0.764186i	$-0.276859\pi$
$397$	1.60825e9			1.28999			0.644996	+	0.764186i	$0.276859\pi$
$398$	1.16006e9	−	8.42833e8i	0.922337	−	0.670117i
$399$		0			0
$400$	−9.98329e8	+	3.07254e9i	−0.779945	+	2.40042i
$401$	−5.19457e8	−	3.77408e8i	−0.402295	−	0.292284i	0.368180	−	0.929754i	$-0.379981\pi$
$401$	−5.19457e8	−	3.77408e8i	−0.402295	−	0.292284i	−0.770475	+	0.637470i	$0.779981\pi$
$402$		0			0
$403$	−2.62557e8	+	8.08067e8i	−0.199828	+	0.615006i
$404$	5.93199e7	+	1.82568e8i	0.0447575	+	0.137749i
$405$		0			0
$406$	1.90842e9			1.41525
$407$	1.21617e9	+	1.00711e9i	0.894156	+	0.740450i
$408$		0			0
$409$	7.46189e8	−	5.42138e8i	0.539284	−	0.391813i	−0.284535	−	0.958666i	$-0.591839\pi$
$409$	7.46189e8	−	5.42138e8i	0.539284	−	0.391813i	0.823819	+	0.566853i	$0.191839\pi$
$410$	9.54515e8	+	2.93770e9i	0.683974	+	2.10505i
$411$		0			0
$412$	1.64855e8	+	1.19774e8i	0.116135	+	0.0843769i
$413$	2.09108e8	+	1.51926e8i	0.146065	+	0.106122i
$414$		0			0
$415$	−3.82954e8	−	1.17861e9i	−0.263014	−	0.809473i
$416$	−2.63807e8	+	1.91667e8i	−0.179663	+	0.130533i
$417$		0			0
$418$	1.09050e9	−	6.91304e8i	0.730315	−	0.462969i
$419$	−1.28867e9			−0.855838			−0.427919	−	0.903817i	$-0.640753\pi$
$419$	−1.28867e9			−0.855838			−0.427919	+	0.903817i	$0.640753\pi$
$420$		0			0
$421$	−6.86261e8	−	2.11209e9i	−0.448231	−	1.37951i	−0.878901	−	0.477003i	$-0.841723\pi$
$421$	−6.86261e8	−	2.11209e9i	−0.448231	−	1.37951i	0.430671	−	0.902509i	$-0.358277\pi$
$422$	−8.44589e7	+	2.59938e8i	−0.0547081	+	0.168374i
$423$		0			0
$424$	9.76306e8	+	7.09328e8i	0.622021	+	0.451925i
$425$	−1.21094e9	+	3.72688e9i	−0.765174	+	2.35496i
$426$		0			0
$427$	−2.33693e9	+	1.69788e9i	−1.45261	+	1.05538i
$428$	−3.43356e8			−0.211686
$429$		0			0
$430$	−3.38468e8			−0.205295
$431$	1.81810e9	−	1.32092e9i	1.09382	−	0.794708i	0.113781	−	0.993506i	$-0.463704\pi$
$431$	1.81810e9	−	1.32092e9i	1.09382	−	0.794708i	0.980040	+	0.198798i	$0.0637038\pi$
$432$		0			0
$433$	−6.35853e8	+	1.95695e9i	−0.376399	+	1.15844i	0.566130	+	0.824316i	$0.308440\pi$
$433$	−6.35853e8	+	1.95695e9i	−0.376399	+	1.15844i	−0.942530	+	0.334122i	$0.891560\pi$
$434$	−3.64401e9	−	2.64753e9i	−2.13976	−	1.55463i
$435$		0			0
$436$	−1.99825e8	+	6.14997e8i	−0.115464	+	0.355362i
$437$	−1.77960e8	−	5.47705e8i	−0.102009	−	0.313951i
$438$		0			0
$439$	3.23360e9			1.82415			0.912074	−	0.410026i	$-0.134480\pi$
$439$	3.23360e9			1.82415			0.912074	+	0.410026i	$0.134480\pi$
$440$	−2.10684e9	−	1.74467e9i	−1.17909	−	0.976404i
$441$		0			0
$442$	−9.58986e8	+	6.96744e8i	−0.528244	+	0.383792i
$443$	−6.03980e8	−	1.85886e9i	−0.330073	−	1.01586i	−0.969099	−	0.246674i	$-0.920662\pi$
$443$	−6.03980e8	−	1.85886e9i	−0.330073	−	1.01586i	0.639026	−	0.769185i	$-0.279338\pi$
$444$		0			0
$445$	−1.36452e9	−	9.91384e8i	−0.734042	−	0.533313i
$446$	5.11762e8	+	3.71817e8i	0.273147	+	0.198453i
$447$		0			0
$448$	7.78572e8	+	2.39620e9i	0.409096	+	1.25907i
$449$	−1.80656e9	+	1.31255e9i	−0.941870	+	0.684309i	−0.948870	−	0.315667i	$-0.897772\pi$
$449$	−1.80656e9	+	1.31255e9i	−0.941870	+	0.684309i	0.00699997	+	0.999975i	$0.497772\pi$
$450$		0			0
$451$	−2.19394e9	−	1.39113e8i	−1.12618	−	0.0714085i
$452$	−7.60788e7			−0.0387507
$453$		0			0
$454$	6.25387e7	+	1.92474e8i	0.0313656	+	0.0965334i
$455$	−1.08135e9	+	3.32805e9i	−0.538179	+	1.65634i
$456$		0			0
$457$	−7.58783e8	−	5.51288e8i	−0.371887	−	0.270192i	0.386106	−	0.922454i	$-0.373820\pi$
$457$	−7.58783e8	−	5.51288e8i	−0.371887	−	0.270192i	−0.757993	+	0.652263i	$0.773820\pi$
$458$	1.02501e9	−	3.15467e9i	0.498541	−	1.53435i
$459$		0			0
$460$	2.77613e8	−	2.01697e8i	0.132980	−	0.0966158i
$461$	−2.98736e9			−1.42015			−0.710076	−	0.704125i	$-0.751339\pi$
$461$	−2.98736e9			−1.42015			−0.710076	+	0.704125i	$0.751339\pi$
$462$		0			0
$463$	1.39263e7			0.00652082			0.00326041	−	0.999995i	$-0.498962\pi$
$463$	1.39263e7			0.00652082			0.00326041	+	0.999995i	$0.498962\pi$
$464$	−1.37132e9	+	9.96322e8i	−0.637273	+	0.463006i
$465$		0			0
$466$	−9.74048e8	+	2.99781e9i	−0.445892	+	1.37231i
$467$	4.34897e7	+	3.15971e7i	0.0197596	+	0.0143562i	0.597621	−	0.801779i	$-0.296113\pi$
$467$	4.34897e7	+	3.15971e7i	0.0197596	+	0.0143562i	−0.577862	+	0.816135i	$0.696113\pi$
$468$		0			0
$469$	2.34489e9	−	7.21683e9i	1.04959	−	3.23029i
$470$	−4.55693e8	−	1.40248e9i	−0.202456	−	0.623095i
$471$		0			0
$472$	−1.86549e8			−0.0816575
$473$	8.87866e7	−	2.23928e8i	0.0385774	−	0.0972959i
$474$		0			0
$475$	3.18830e9	−	2.31644e9i	1.36500	−	0.991728i
$476$	−3.49536e8	−	1.07576e9i	−0.148548	−	0.457185i
$477$		0			0
$478$	3.13053e9	+	2.27446e9i	1.31105	+	0.952535i
$479$	1.56531e9	+	1.13727e9i	0.650769	+	0.472811i	0.863533	−	0.504292i	$-0.168247\pi$
$479$	1.56531e9	+	1.13727e9i	0.650769	+	0.472811i	−0.212764	+	0.977104i	$0.568247\pi$
$480$		0			0
$481$	4.50515e8	+	1.38654e9i	0.184587	+	0.568100i
$482$	−1.61470e9	+	1.17315e9i	−0.656790	+	0.477186i
$483$		0			0
$484$	−4.80075e8	+	2.63310e8i	−0.192464	+	0.105562i
$485$	3.53669e9			1.40767
$486$		0			0
$487$	−1.17478e8	−	3.61559e8i	−0.0460897	−	0.141850i	0.925363	−	0.379081i	$-0.123760\pi$
$487$	−1.17478e8	−	3.61559e8i	−0.0460897	−	0.141850i	−0.971453	+	0.237232i	$0.923760\pi$
$488$	6.44244e8	−	1.98278e9i	0.250946	−	0.772334i
$489$		0			0
$490$	−1.08754e10	−	7.90145e9i	−4.17599	−	3.03403i
$491$	−6.51853e8	+	2.00620e9i	−0.248522	+	0.764872i	0.746515	+	0.665368i	$0.231725\pi$
$491$	−6.51853e8	+	2.00620e9i	−0.248522	+	0.764872i	−0.995037	+	0.0995035i	$0.968275\pi$
$492$		0			0
$493$	−1.66336e9	+	1.20850e9i	−0.625204	+	0.454238i
$494$	1.19211e9			0.444911
$495$		0			0
$496$	4.00063e9			1.47212
$497$	−1.30185e9	+	9.45850e8i	−0.475679	+	0.345601i
$498$		0			0
$499$	2.03318e8	−	6.25750e8i	0.0732529	−	0.225449i	−0.907726	−	0.419563i	$-0.862183\pi$
$499$	2.03318e8	−	6.25750e8i	0.0732529	−	0.225449i	0.980979	+	0.194114i	$0.0621832\pi$
$500$	1.01812e9	+	7.39705e8i	0.364252	+	0.264645i
$501$		0			0
$502$	−2.45929e8	+	7.56891e8i	−0.0867654	+	0.267036i
$503$	8.02981e8	+	2.47132e9i	0.281331	+	0.865847i	0.987475	+	0.157778i	$0.0504332\pi$
$503$	8.02981e8	+	2.47132e9i	0.281331	+	0.865847i	−0.706144	+	0.708068i	$0.749567\pi$
$504$		0			0
$505$	−3.39178e9			−1.17195
$506$	3.36768e8	+	1.31430e9i	0.115559	+	0.450992i
$507$		0			0
$508$	−1.89245e8	+	1.37494e8i	−0.0640472	+	0.0465330i
$509$	7.75675e8	+	2.38728e9i	0.260716	+	0.802401i	0.992649	+	0.121025i	$0.0386181\pi$
$509$	7.75675e8	+	2.38728e9i	0.260716	+	0.802401i	−0.731934	+	0.681376i	$0.761382\pi$
$510$		0			0
$511$	3.16399e9	+	2.29877e9i	1.04897	+	0.762119i
$512$	−1.23836e9	−	8.99718e8i	−0.407756	−	0.296252i
$513$		0			0
$514$	−1.44125e8	−	4.43571e8i	−0.0468132	−	0.144076i
$515$	−2.91281e9	+	2.11628e9i	−0.939695	+	0.682728i
$516$		0			0
$517$	1.04741e9	+	6.64137e7i	0.333349	+	0.0211369i
$518$	−7.72872e9			−2.44317
$519$		0			0
$520$	−7.80453e8	−	2.40199e9i	−0.243408	−	0.749133i
$521$	1.88604e9	−	5.80463e9i	0.584276	−	1.79822i	−0.0178805	−	0.999840i	$-0.505692\pi$
$521$	1.88604e9	−	5.80463e9i	0.584276	−	1.79822i	0.602157	−	0.798378i	$-0.294308\pi$
$522$		0			0
$523$	−4.45285e8	−	3.23518e8i	−0.136107	−	0.0988878i	0.517648	−	0.855594i	$-0.326808\pi$
$523$	−4.45285e8	−	3.23518e8i	−0.136107	−	0.0988878i	−0.653756	+	0.756706i	$0.726808\pi$
$524$	−4.11267e8	+	1.26575e9i	−0.124872	+	0.384316i
$525$		0			0
$526$	−5.23131e9	+	3.80077e9i	−1.56733	+	1.13873i
$527$	4.85261e9			1.44424
$528$		0			0
$529$	−2.79967e9			−0.822267
$530$	4.85165e9	−	3.52493e9i	1.41555	−	1.02846i
$531$		0			0
$532$	−3.51524e8	+	1.08188e9i	−0.101219	+	0.311521i
$533$	−1.64207e9	−	1.19303e9i	−0.469727	−	0.341277i
$534$		0			0
$535$	1.87472e9	−	5.76980e9i	0.529296	−	1.62900i
$536$	1.69240e9	+	5.20867e9i	0.474707	+	1.46100i
$537$		0			0
$538$	1.98095e9			0.548448
$539$	8.08037e9	−	5.12239e9i	2.22265	−	1.40900i
$540$		0			0
$541$	8.27726e7	−	6.01378e7i	0.0224748	−	0.0163289i	−0.576491	−	0.817103i	$-0.695578\pi$
$541$	8.27726e7	−	6.01378e7i	0.0224748	−	0.0163289i	0.598966	+	0.800774i	$0.295578\pi$
$542$	3.55066e8	+	1.09278e9i	0.0957881	+	0.294806i
$543$		0			0
$544$	1.50668e9	+	1.09467e9i	0.401259	+	0.291531i
$545$	−9.24345e9	−	6.71576e9i	−2.44594	−	1.77708i
$546$		0			0
$547$	1.84717e9	+	5.68500e9i	0.482559	+	1.48516i	0.835485	+	0.549513i	$0.185187\pi$
$547$	1.84717e9	+	5.68500e9i	0.482559	+	1.48516i	−0.352926	+	0.935651i	$0.614813\pi$
$548$	−1.01678e9	+	7.38731e8i	−0.263933	+	0.191758i
$549$		0			0
$550$	−7.84174e9	+	4.97112e9i	−2.00975	+	1.27404i
$551$	2.06772e9			0.526575
$552$		0			0
$553$	1.87466e9	+	5.76963e9i	0.471396	+	1.45081i
$554$	2.06864e9	−	6.36662e9i	0.516893	−	1.59083i
$555$		0			0
$556$	−7.81649e8	−	5.67901e8i	−0.192863	−	0.140123i
$557$	6.55509e7	−	2.01745e8i	0.0160726	−	0.0494663i	−0.942699	−	0.333646i	$-0.891721\pi$
$557$	6.55509e7	−	2.01745e8i	0.0160726	−	0.0494663i	0.958771	+	0.284179i	$0.0917211\pi$
$558$		0			0
$559$	1.79932e8	−	1.30728e8i	0.0435679	−	0.0316540i
$560$	1.64767e10			3.96473
$561$		0			0
$562$	7.15111e9			1.69940
$563$	−4.20158e9	+	3.05263e9i	−0.992279	+	0.720933i	−0.960419	−	0.278560i	$-0.910143\pi$
$563$	−4.20158e9	+	3.05263e9i	−0.992279	+	0.720933i	−0.0318599	+	0.999492i	$0.510143\pi$
$564$		0			0
$565$	4.15390e8	−	1.27844e9i	0.0968916	−	0.298202i
$566$	4.17039e9	+	3.02996e9i	0.966760	+	0.702393i
$567$		0			0
$568$	3.58894e8	−	1.10456e9i	0.0821764	−	0.252913i
$569$	−2.25642e8	−	6.94454e8i	−0.0513484	−	0.158034i	0.922094	−	0.386966i	$-0.126477\pi$
$569$	−2.25642e8	−	6.94454e8i	−0.0513484	−	0.158034i	−0.973443	+	0.228932i	$0.926477\pi$
$570$		0			0
$571$	−6.19858e8			−0.139337			−0.0696684	−	0.997570i	$-0.522194\pi$
$571$	−6.19858e8			−0.139337			−0.0696684	+	0.997570i	$0.522194\pi$
$572$	−5.04527e8	−	3.19909e7i	−0.112719	−	0.00714727i
$573$		0			0
$574$	8.70507e9	−	6.32460e9i	1.92123	−	1.39586i
$575$	1.27970e9	+	3.93851e9i	0.280718	+	0.863961i
$576$		0			0
$577$	−1.34608e9	−	9.77983e8i	−0.291712	−	0.211942i	0.432297	−	0.901731i	$-0.357703\pi$
$577$	−1.34608e9	−	9.77983e8i	−0.291712	−	0.211942i	−0.724010	+	0.689790i	$0.757703\pi$
$578$	1.32944e9	+	9.65897e8i	0.286367	+	0.208058i
$579$		0			0
$580$	3.80728e8	+	1.17176e9i	0.0810247	+	0.249368i
$581$	−3.49250e9	+	2.53745e9i	−0.738787	+	0.536760i
$582$		0			0
$583$	1.05939e9	+	4.13447e9i	0.221419	+	0.864133i
$584$	−2.82265e9			−0.586425
$585$		0			0
$586$	−6.67538e8	−	2.05447e9i	−0.137036	−	0.421753i
$587$	−2.10609e9	+	6.48189e9i	−0.429778	+	1.32272i	0.468566	+	0.883428i	$0.344771\pi$
$587$	−2.10609e9	+	6.48189e9i	−0.429778	+	1.32272i	−0.898344	+	0.439292i	$0.855229\pi$
$588$		0			0
$589$	−3.94817e9	−	2.86851e9i	−0.796145	−	0.578434i
$590$	−2.86470e8	+	8.81665e8i	−0.0574246	+	0.176735i
$591$		0			0
$592$	5.55356e9	−	4.03490e9i	1.10013	−	0.799294i
$593$	4.52946e9			0.891981			0.445990	−	0.895038i	$-0.352852\pi$
$593$	4.52946e9			0.891981			0.445990	+	0.895038i	$0.352852\pi$
$594$		0			0
$595$	1.99857e10			3.88964
$596$	5.36189e8	−	3.89564e8i	0.103742	−	0.0753732i
$597$		0			0
$598$	−3.87100e8	+	1.19137e9i	−0.0740234	+	0.227821i
$599$	4.91721e9	+	3.57256e9i	0.934813	+	0.679182i	0.947167	−	0.320742i	$-0.103932\pi$
$599$	4.91721e9	+	3.57256e9i	0.934813	+	0.679182i	−0.0123534	+	0.999924i	$0.503932\pi$
$600$		0			0
$601$	−5.62971e6	+	1.73265e7i	−0.00105785	+	0.00325574i	−0.951584	−	0.307389i	$-0.900545\pi$
$601$	−5.62971e6	+	1.73265e7i	−0.00105785	+	0.00325574i	0.950526	+	0.310644i	$0.100545\pi$
$602$	3.64346e8	+	1.12134e9i	0.0680654	+	0.209484i
$603$		0			0
$604$	−1.08511e9			−0.200376
$605$	−1.80349e9	−	9.50491e9i	−0.331107	−	1.74504i
$606$		0			0
$607$	1.05594e9	−	7.67187e8i	0.191637	−	0.139232i	−0.487830	−	0.872939i	$-0.662211\pi$
$607$	1.05594e9	−	7.67187e8i	0.191637	−	0.139232i	0.679467	+	0.733706i	$0.262211\pi$
$608$	−5.78772e8	−	1.78128e9i	−0.104435	−	0.321417i
$609$		0			0
$610$	−8.38166e9	−	6.08963e9i	−1.49512	−	1.08627i
$611$	7.83937e8	+	5.69563e8i	0.139039	+	0.101018i
$612$		0			0
$613$	4.95513e8	+	1.52503e9i	0.0868846	+	0.267403i	0.985054	−	0.172246i	$-0.0551025\pi$
$613$	4.95513e8	+	1.52503e9i	0.0868846	+	0.267403i	−0.898169	+	0.439650i	$0.855103\pi$
$614$	3.15426e9	−	2.29170e9i	0.549931	−	0.399548i
$615$		0			0
$616$	−3.51217e9	+	8.85801e9i	−0.605400	+	1.52687i
$617$	7.98397e9			1.36842			0.684212	−	0.729283i	$-0.260146\pi$
$617$	7.98397e9			1.36842			0.684212	+	0.729283i	$0.260146\pi$
$618$		0			0
$619$	−1.25309e9	−	3.85662e9i	−0.212357	−	0.653567i	−0.999331	−	0.0365807i	$-0.988353\pi$
$619$	−1.25309e9	−	3.85662e9i	−0.212357	−	0.653567i	0.786974	−	0.616986i	$-0.211647\pi$
$620$	8.98592e8	−	2.76558e9i	0.151423	−	0.466032i
$621$		0			0
$622$	2.55318e8	+	1.85500e8i	0.0425418	+	0.0309084i
$623$	−1.81560e9	+	5.58784e9i	−0.300823	+	0.925839i
$624$		0			0
$625$	−7.34901e9	+	5.33937e9i	−1.20406	+	0.874802i
$626$	−3.82692e9			−0.623504
$627$		0			0
$628$	3.39204e8			0.0546516
$629$	6.73626e9	−	4.89418e9i	1.07930	−	0.784157i
$630$		0			0
$631$	−2.93591e9	+	9.03581e9i	−0.465201	+	1.43174i	0.393529	+	0.919312i	$0.371254\pi$
$631$	−2.93591e9	+	9.03581e9i	−0.465201	+	1.43174i	−0.858730	+	0.512429i	$0.828746\pi$
$632$	−3.54225e9	−	2.57359e9i	−0.558174	−	0.405537i
$633$		0			0
$634$	−7.60168e7	+	2.33956e8i	−0.0118467	+	0.0364604i
$635$	−1.27720e9	−	3.93080e9i	−0.197947	−	0.609219i
$636$		0			0
$637$	8.83326e9			1.35404
$638$	−4.86166e9	−	3.08266e8i	−0.741160	−	0.0469952i
$639$		0			0
$640$	−1.14237e10	+	8.29983e9i	−1.72258	+	1.25152i
$641$	4.79840e8	+	1.47680e9i	0.0719604	+	0.221471i	0.980568	−	0.196179i	$-0.0628535\pi$
$641$	4.79840e8	+	1.47680e9i	0.0719604	+	0.221471i	−0.908608	+	0.417651i	$0.862854\pi$
$642$		0			0
$643$	4.08103e8	+	2.96504e8i	0.0605384	+	0.0439837i	0.617643	−	0.786459i	$-0.288088\pi$
$643$	4.08103e8	+	2.96504e8i	0.0605384	+	0.0439837i	−0.557104	+	0.830442i	$0.688088\pi$
$644$	−9.67060e8	−	7.02610e8i	−0.142677	−	0.103661i
$645$		0			0
$646$	−2.10395e9	−	6.47528e9i	−0.307058	−	0.945028i
$647$	−5.56390e9	+	4.04241e9i	−0.807634	+	0.586780i	−0.913144	−	0.407638i	$-0.866353\pi$
$647$	−5.56390e9	+	4.04241e9i	−0.807634	+	0.586780i	0.105510	+	0.994418i	$0.466353\pi$
$648$		0			0
$649$	−5.08156e8	−	4.20804e8i	−0.0729694	−	0.0604259i
$650$	−8.57240e9			−1.22435
$651$		0			0
$652$	−3.44219e8	−	1.05940e9i	−0.0486372	−	0.149690i
$653$	1.92774e9	−	5.93298e9i	0.270928	−	0.833829i	−0.719341	−	0.694657i	$-0.755556\pi$
$653$	1.92774e9	−	5.93298e9i	0.270928	−	0.833829i	0.990268	−	0.139172i	$-0.0444440\pi$
$654$		0			0
$655$	−1.90243e10	−	1.38220e10i	−2.64523	−	1.92188i
$656$	−2.95327e9	+	9.08923e9i	−0.408451	+	1.25708i
$657$		0			0
$658$	−4.15587e9	+	3.01942e9i	−0.568684	+	0.413173i
$659$	2.32233e9			0.316101			0.158050	−	0.987431i	$-0.449479\pi$
$659$	2.32233e9			0.316101			0.158050	+	0.987431i	$0.449479\pi$
$660$		0			0
$661$	−1.01562e10			−1.36781			−0.683904	−	0.729572i	$-0.739719\pi$
$661$	−1.01562e10			−1.36781			−0.683904	+	0.729572i	$0.739719\pi$
$662$	2.07292e9	−	1.50606e9i	0.277702	−	0.201762i
$663$		0			0
$664$	9.62810e8	−	2.96323e9i	0.127630	−	0.392804i
$665$	−1.62607e10	−	1.18141e10i	−2.14419	−	1.55785i
$666$		0			0
$667$	−6.71424e8	+	2.06643e9i	−0.0876106	+	0.269638i
$668$	4.46661e8	+	1.37468e9i	0.0579776	+	0.178437i
$669$		0			0
$670$	2.72160e10			3.49593
$671$	6.22752e9	−	3.94782e9i	0.795768	−	0.504461i
$672$		0			0
$673$	−5.82120e9	+	4.22935e9i	−0.736139	+	0.534836i	−0.891500	−	0.453021i	$-0.850346\pi$
$673$	−5.82120e9	+	4.22935e9i	−0.736139	+	0.534836i	0.155361	+	0.987858i	$0.450346\pi$
$674$	3.70841e9	+	1.14133e10i	0.466528	+	1.43583i
$675$		0			0
$676$	1.04875e9	+	7.61963e8i	0.130575	+	0.0948681i
$677$	−8.61321e9	−	6.25787e9i	−1.06685	−	0.775115i	−0.0915096	−	0.995804i	$-0.529169\pi$
$677$	−8.61321e9	−	6.25787e9i	−1.06685	−	0.775115i	−0.975344	+	0.220690i	$0.929169\pi$
$678$		0			0
$679$	−3.80709e9	−	1.17170e10i	−0.466712	−	1.43639i
$680$	−1.16696e10	+	8.47848e9i	−1.42323	+	1.03404i
$681$		0			0
$682$	8.85536e9	+	7.33312e9i	1.06896	+	0.885204i
$683$	3.39278e9			0.407458			0.203729	−	0.979027i	$-0.434694\pi$
$683$	3.39278e9			0.407458			0.203729	+	0.979027i	$0.434694\pi$
$684$		0			0
$685$	−6.86213e9	−	2.11195e10i	−0.815722	−	2.51053i
$686$	−8.97182e9	+	2.76124e10i	−1.06108	+	3.26566i
$687$		0			0
$688$	−8.47219e8	−	6.15541e8i	−0.0991828	−	0.0720605i
$689$	−1.21772e9	+	3.74776e9i	−0.141834	+	0.436520i
$690$		0			0
$691$	−4.81253e8	+	3.49651e8i	−0.0554882	+	0.0403145i	−0.615184	−	0.788384i	$-0.710918\pi$
$691$	−4.81253e8	+	3.49651e8i	−0.0554882	+	0.0403145i	0.559695	+	0.828698i	$0.310918\pi$
$692$	−3.89485e8			−0.0446806
$693$		0			0
$694$	4.17839e9			0.474516
$695$	1.38109e10	−	1.00342e10i	1.56054	−	1.13380i
$696$		0			0
$697$	−3.58221e9	+	1.10249e10i	−0.400715	+	1.23327i
$698$	−2.49407e9	−	1.81205e9i	−0.277597	−	0.201686i
$699$		0			0
$700$	2.52778e9	−	7.77971e9i	0.278546	−	0.857275i
$701$	−2.13674e9	−	6.57622e9i	−0.234282	−	0.721047i	−0.997216	−	0.0745697i	$-0.976242\pi$
$701$	−2.13674e9	−	6.57622e9i	−0.234282	−	0.721047i	0.762934	−	0.646477i	$-0.223758\pi$
$702$		0			0
$703$	−8.37382e9			−0.909034
$704$	−1.59633e9	−	6.23001e9i	−0.172433	−	0.672952i
$705$		0			0
$706$	8.98204e9	−	6.52583e9i	0.960635	−	0.697942i
$707$	3.65110e9	+	1.12369e10i	0.388558	+	1.19586i
$708$		0			0
$709$	9.51952e9	+	6.91634e9i	1.00312	+	0.728810i	0.962755	−	0.270375i	$-0.0871477\pi$
$709$	9.51952e9	+	6.91634e9i	1.00312	+	0.728810i	0.0403657	+	0.999185i	$0.487148\pi$
$710$	−4.66923e9	−	3.39240e9i	−0.489600	−	0.355715i
$711$		0			0
$712$	−1.31039e9	−	4.03296e9i	−0.136057	−	0.418740i
$713$	4.14877e9	−	3.01426e9i	0.428653	−	0.311435i
$714$		0			0
$715$	3.29229e9	−	8.30346e9i	0.336842	−	0.849548i
$716$	−3.50226e9			−0.356577
$717$		0			0
$718$	1.16977e9	+	3.60019e9i	0.117941	+	0.362986i
$719$	3.54829e9	−	1.09205e10i	0.356015	−	1.09570i	−0.599404	−	0.800447i	$-0.704596\pi$
$719$	3.54829e9	−	1.09205e10i	0.356015	−	1.09570i	0.955419	−	0.295255i	$-0.0954045\pi$
$720$		0			0
$721$	1.01467e10	+	7.37203e9i	1.00821	+	0.732510i
$722$	1.33518e9	−	4.10925e9i	0.132026	−	0.406333i
$723$		0			0
$724$	−1.78458e9	+	1.29658e9i	−0.174764	+	0.126973i
$725$	−1.48688e10			−1.44908
$726$		0			0
$727$	−1.14616e10			−1.10630			−0.553152	−	0.833080i	$-0.686575\pi$
$727$	−1.14616e10			−1.10630			−0.553152	+	0.833080i	$0.686575\pi$
$728$	−7.11764e9	+	5.17127e9i	−0.683717	+	0.496749i
$729$		0			0
$730$	−4.33455e9	+	1.33404e10i	−0.412395	+	1.26922i
$731$	−1.02765e9	−	7.46628e8i	−0.0973044	−	0.0706958i
$732$		0			0
$733$	2.50970e9	−	7.72405e9i	0.235373	−	0.724405i	−0.761698	−	0.647932i	$-0.775634\pi$
$733$	2.50970e9	−	7.72405e9i	0.235373	−	0.724405i	0.997072	−	0.0764729i	$-0.0243659\pi$
$734$	−1.39305e9	−	4.28736e9i	−0.130026	−	0.400178i
$735$		0			0
$736$	1.96811e9			0.181960
$737$	−7.13927e9	+	1.80059e10i	−0.656928	+	1.65683i
$738$		0			0
$739$	7.85425e9	−	5.70645e9i	0.715895	−	0.520128i	−0.169175	−	0.985586i	$-0.554110\pi$
$739$	7.85425e9	−	5.70645e9i	0.715895	−	0.520128i	0.885070	+	0.465458i	$0.154110\pi$
$740$	−1.54187e9	−	4.74539e9i	−0.139874	−	0.430488i
$741$		0			0
$742$	−1.69007e10	−	1.22791e10i	−1.51876	−	1.10345i
$743$	5.82208e8	+	4.22999e8i	0.0520735	+	0.0378336i	0.613518	−	0.789681i	$-0.289754\pi$
$743$	5.82208e8	+	4.22999e8i	0.0520735	+	0.0378336i	−0.561444	+	0.827515i	$0.689754\pi$
$744$		0			0
$745$	3.61870e9	+	1.11372e10i	0.320631	+	0.986800i
$746$	1.20837e10	−	8.77932e9i	1.06565	−	0.774239i
$747$		0			0
$748$	7.16666e8	+	2.79693e9i	0.0626125	+	0.244358i
$749$	−2.11333e10			−1.83773
$750$		0			0
$751$	6.06644e9	+	1.86706e10i	0.522630	+	1.60849i	0.768955	+	0.639302i	$0.220777\pi$
$751$	6.06644e9	+	1.86706e10i	0.522630	+	1.60849i	−0.246325	+	0.969187i	$0.579223\pi$
$752$	1.40991e9	−	4.33927e9i	0.120901	−	0.372096i
$753$		0			0
$754$	−3.63873e9	−	2.64369e9i	−0.309136	−	0.224601i
$755$	5.92471e9	−	1.82344e10i	0.501017	−	1.54197i
$756$		0			0
$757$	−4.79470e9	+	3.48355e9i	−0.401722	+	0.291868i	−0.770242	−	0.637752i	$-0.779865\pi$
$757$	−4.79470e9	+	3.48355e9i	−0.401722	+	0.291868i	0.368520	+	0.929620i	$0.379865\pi$
$758$	−2.00506e10			−1.67219
$759$		0			0
$760$	1.45065e10			1.19871
$761$	−1.08500e10	+	7.88297e9i	−0.892447	+	0.648401i	−0.936515	−	0.350628i	$-0.885968\pi$
$761$	−1.08500e10	+	7.88297e9i	−0.892447	+	0.648401i	0.0440678	+	0.999029i	$0.485968\pi$
$762$		0			0
$763$	−1.22991e10	+	3.78527e10i	−1.00239	+	3.08504i
$764$	−3.34573e9	−	2.43081e9i	−0.271434	−	0.197208i
$765$		0			0
$766$	2.71263e9	−	8.34862e9i	0.218067	−	0.671141i
$767$	−1.88240e8	−	5.79344e8i	−0.0150636	−	0.0463610i
$768$		0			0
$769$	3.95227e9			0.313404			0.156702	−	0.987646i	$-0.449914\pi$
$769$	3.95227e9			0.313404			0.156702	+	0.987646i	$0.449914\pi$
$770$	3.64712e10	+	3.02017e10i	2.87894	+	2.38404i
$771$		0			0
$772$	9.35764e8	−	6.79873e8i	0.0731991	−	0.0531823i
$773$	6.58453e8	+	2.02651e9i	0.0512739	+	0.157805i	0.973415	−	0.229049i	$-0.0735617\pi$
$773$	6.58453e8	+	2.02651e9i	0.0512739	+	0.157805i	−0.922141	+	0.386854i	$0.873562\pi$
$774$		0			0
$775$	2.83910e10	+	2.06273e10i	2.19091	+	1.59179i
$776$	7.19364e9	+	5.22649e9i	0.552628	+	0.401508i
$777$		0			0
$778$	4.41560e9	+	1.35898e10i	0.336171	+	1.03463i
$779$	9.43167e9	−	6.85251e9i	0.714838	−	0.519360i
$780$		0			0
$781$	3.46921e9	−	2.19924e9i	0.260587	−	0.165194i
$782$	7.15444e9			0.534998
$783$		0			0
$784$	−1.28526e10	−	3.95562e10i	−0.952543	−	2.93163i
$785$	−1.85205e9	+	5.70003e9i	−0.136650	+	0.420565i
$786$		0			0
$787$	−7.89734e9	−	5.73775e9i	−0.577523	−	0.419595i	0.260307	−	0.965526i	$-0.416176\pi$
$787$	−7.89734e9	−	5.73775e9i	−0.577523	−	0.419595i	−0.837830	+	0.545931i	$0.816176\pi$
$788$	6.27653e8	−	1.93172e9i	0.0456959	−	0.140638i
$789$		0			0
$790$	−1.76029e10	+	1.27892e10i	−1.27025	+	0.922889i
$791$	−4.68260e9			−0.336411
$792$		0			0
$793$	6.80777e9			0.484785
$794$	1.62559e10	−	1.18106e10i	1.15249	−	0.837335i
$795$		0			0
$796$	9.96500e8	−	3.06691e9i	0.0700296	−	0.215529i
$797$	1.66585e10	+	1.21031e10i	1.16555	+	0.846825i	0.990470	−	0.137729i	$-0.0439802\pi$
$797$	1.66585e10	+	1.21031e10i	1.16555	+	0.846825i	0.175084	+	0.984553i	$0.443980\pi$
$798$		0			0
$799$	1.71017e9	−	5.26338e9i	0.118612	−	0.365049i
$800$	4.16191e9	+	1.28090e10i	0.287394	+	0.884508i
$801$		0			0
$802$	−8.02214e9			−0.549136
$803$	−7.68885e9	−	6.36713e9i	−0.524031	−	0.433950i
$804$		0			0
$805$	1.70869e10	−	1.24143e10i	1.15446	−	0.838761i
$806$	3.28036e9	+	1.00959e10i	0.220673	+	0.679161i
$807$		0			0
$808$	−6.89890e9	−	5.01234e9i	−0.460087	−	0.334273i
$809$	9.78628e9	+	7.11015e9i	0.649827	+	0.472127i	0.863212	−	0.504841i	$-0.168449\pi$
$809$	9.78628e9	+	7.11015e9i	0.649827	+	0.472127i	−0.213385	+	0.976968i	$0.568449\pi$
$810$		0			0
$811$	−5.15622e9	−	1.58692e10i	−0.339437	−	1.04468i	−0.964495	−	0.264101i	$-0.914925\pi$
$811$	−5.15622e9	−	1.58692e10i	−0.339437	−	1.04468i	0.625058	−	0.780578i	$-0.285075\pi$
$812$	3.47220e9	−	2.52270e9i	0.227593	−	0.165356i
$813$		0			0
$814$	1.96887e10	+	1.24841e9i	1.27947	+	0.0811285i
$815$	1.96817e10			1.27353
$816$		0			0
$817$	3.94758e8	+	1.21494e9i	0.0253252	+	0.0779430i
$818$	3.56100e9	−	1.09596e10i	0.227476	−	0.700099i
$819$		0			0
$820$	5.61992e9	+	4.08311e9i	0.355944	+	0.258608i
$821$	8.92060e9	−	2.74548e10i	0.562592	−	1.73148i	−0.112409	−	0.993662i	$-0.535857\pi$
$821$	8.92060e9	−	2.74548e10i	0.562592	−	1.73148i	0.675001	−	0.737817i	$-0.264143\pi$
$822$		0			0
$823$	2.09598e10	−	1.52282e10i	1.31065	−	0.952245i	0.310655	−	0.950523i	$-0.399452\pi$
$823$	2.09598e10	−	1.52282e10i	1.31065	−	0.952245i	0.999999	−	0.00172256i	$-0.000548307\pi$
$824$	−9.05208e9			−0.563642
$825$		0			0
$826$	3.22932e9			0.199380
$827$	8.04081e8	−	5.84199e8i	0.0494346	−	0.0359163i	−0.562794	−	0.826597i	$-0.690273\pi$
$827$	8.04081e8	−	5.84199e8i	0.0494346	−	0.0359163i	0.612228	+	0.790681i	$0.290273\pi$
$828$		0			0
$829$	4.87562e9	−	1.50056e10i	0.297227	−	0.914772i	−0.685237	−	0.728320i	$-0.740301\pi$
$829$	4.87562e9	−	1.50056e10i	0.297227	−	0.914772i	0.982464	−	0.186452i	$-0.0596988\pi$
$830$	−1.25262e10	−	9.10083e9i	−0.760408	−	0.552469i
$831$		0			0
$832$	1.83491e9	−	5.64728e9i	0.110455	−	0.339945i
$833$	−1.55897e10	−	4.79802e10i	−0.934503	−	2.87611i
$834$		0			0
$835$	−2.55391e10			−1.51811
$836$	1.07025e9	−	2.69927e9i	0.0633525	−	0.159781i
$837$		0			0
$838$	−1.30256e10	+	9.46363e9i	−0.764614	+	0.555525i
$839$	9.36148e9	+	2.88117e10i	0.547240	+	1.68423i	0.715604	+	0.698506i	$0.246151\pi$
$839$	9.36148e9	+	2.88117e10i	0.547240	+	1.68423i	−0.168365	+	0.985725i	$0.553849\pi$
$840$		0			0
$841$	7.64408e9	+	5.55375e9i	0.443138	+	0.321959i
$842$	−2.24472e10	−	1.63089e10i	−1.29590	−	0.941524i
$843$		0			0
$844$	1.89940e8	+	5.84577e8i	0.0108747	+	0.0334690i
$845$	−1.85303e10	+	1.34630e10i	−1.05653	+	0.767617i
$846$		0			0
$847$	−2.95483e10	+	1.62066e10i	−1.67086	+	0.916429i
$848$	1.85546e10			1.04488
$849$		0			0
$850$	1.51293e10	+	4.65633e10i	0.844993	+	2.60062i
$851$	2.71913e9	−	8.36862e9i	0.151243	−	0.465479i
$852$		0			0
$853$	−1.01881e10	−	7.40206e9i	−0.562044	−	0.408349i	0.270163	−	0.962815i	$-0.412923\pi$
$853$	−1.01881e10	−	7.40206e9i	−0.562044	−	0.408349i	−0.832206	+	0.554466i	$0.812923\pi$
$854$	−1.11524e10	+	3.43236e10i	−0.612725	+	1.88577i
$855$		0			0
$856$	1.23397e10	−	8.96535e9i	0.672431	−	0.488550i
$857$	2.81147e10			1.52581			0.762905	−	0.646511i	$-0.223772\pi$
$857$	2.81147e10			1.52581			0.762905	+	0.646511i	$0.223772\pi$
$858$		0			0
$859$	−2.07263e10			−1.11570			−0.557848	−	0.829943i	$-0.688373\pi$
$859$	−2.07263e10			−1.11570			−0.557848	+	0.829943i	$0.688373\pi$
$860$	−6.15811e8	+	4.47413e8i	−0.0330144	+	0.0239863i
$861$		0			0
$862$	8.67640e9	−	2.67032e10i	0.461386	−	1.42000i
$863$	5.01906e8	+	3.64656e8i	0.0265818	+	0.0193128i	0.600997	−	0.799251i	$-0.294770\pi$
$863$	5.01906e8	+	3.64656e8i	0.0265818	+	0.0193128i	−0.574415	+	0.818564i	$0.694770\pi$
$864$		0			0
$865$	2.12658e9	−	6.54495e9i	0.111719	−	0.343835i
$866$	7.94428e9	+	2.44500e10i	0.415664	+	1.27928i
$867$		0			0
$868$	−1.01296e10			−0.525745
$869$	−3.84369e9	−	1.50008e10i	−0.198692	−	0.775433i
$870$		0			0
$871$	−1.44682e10	+	1.05118e10i	−0.741911	+	0.539030i
$872$	−8.87673e9	−	2.73198e10i	−0.453362	−	1.39531i
$873$		0			0
$874$	−5.82098e9	−	4.22919e9i	−0.294921	−	0.214273i
$875$	6.26644e10	+	4.55284e10i	3.16222	+	2.29749i
$876$		0			0
$877$	−1.51709e9	−	4.66912e9i	−0.0759474	−	0.233742i	0.905875	−	0.423546i	$-0.139215\pi$
$877$	−1.51709e9	−	4.66912e9i	−0.0759474	−	0.233742i	−0.981822	+	0.189804i	$0.939215\pi$
$878$	3.26845e10	−	2.37467e10i	1.62971	−	1.18406i
$879$		0			0
$880$	−4.19741e10	−	2.66148e9i	−2.07631	−	0.131654i
$881$	9.03576e9			0.445194			0.222597	−	0.974911i	$-0.428547\pi$
$881$	9.03576e9			0.445194			0.222597	+	0.974911i	$0.428547\pi$
$882$		0			0
$883$	−1.18650e9	−	3.65168e9i	−0.0579971	−	0.178497i	0.917861	−	0.396902i	$-0.129915\pi$
$883$	−1.18650e9	−	3.65168e9i	−0.0579971	−	0.178497i	−0.975858	+	0.218405i	$0.929915\pi$
$884$	−8.23776e8	+	2.53532e9i	−0.0401076	+	0.123438i
$885$		0			0
$886$	−1.97559e10	−	1.43535e10i	−0.954285	−	0.693329i
$887$	8.03961e9	−	2.47434e10i	0.386814	−	1.19049i	−0.548342	−	0.836254i	$-0.684741\pi$
$887$	8.03961e9	−	2.47434e10i	0.386814	−	1.19049i	0.935156	−	0.354237i	$-0.115259\pi$
$888$		0			0
$889$	−1.16479e10	+	8.46268e9i	−0.556020	+	0.403972i
$890$	−2.10728e10			−1.00197
$891$		0			0
$892$	1.42260e9			0.0671128
$893$	−4.50276e9	+	3.27144e9i	−0.211592	+	0.153730i
$894$		0			0
$895$	1.91223e10	−	5.88524e10i	0.891579	−	2.74400i
$896$	3.97944e10	+	2.89123e10i	1.84818	+	1.34278i
$897$		0			0
$898$	−8.62137e9	+	2.65338e10i	−0.397291	+	1.22274i
$899$	5.68978e9	+	1.75113e10i	0.261178	+	0.803823i
$900$		0			0
$901$	2.25061e10			1.02509
$902$	−2.31975e10	+	1.47056e10i	−1.05249	+	0.667207i
$903$		0			0
$904$	2.73417e9	−	1.98649e9i	0.123094	−	0.0894328i
$905$	−1.20440e10	−	3.70676e10i	−0.540133	−	1.66236i
$906$		0			0
$907$	−1.03246e10	−	7.50124e9i	−0.459459	−	0.333816i	0.333860	−	0.942623i	$-0.391649\pi$
$907$	−1.03246e10	−	7.50124e9i	−0.459459	−	0.333816i	−0.793319	+	0.608806i	$0.791649\pi$
$908$	3.68211e8	+	2.67521e8i	0.0163228	+	0.0118592i
$909$		0			0
$910$	1.35103e10	+	4.15804e10i	0.594319	+	1.82913i
$911$	1.20303e10	−	8.74051e9i	0.527183	−	0.383021i	−0.292120	−	0.956382i	$-0.594361\pi$
$911$	1.20303e10	−	8.74051e9i	0.527183	−	0.383021i	0.819303	+	0.573361i	$0.194361\pi$
$912$		0			0
$913$	9.30691e9	−	5.89993e9i	0.404723	−	0.256566i
$914$	−1.17181e10			−0.507629
$915$		0			0
$916$	−2.30517e9	−	7.09457e9i	−0.0990987	−	0.304994i
$917$	−2.53132e10	+	7.79061e10i	−1.08406	+	3.33640i
$918$		0			0
$919$	−1.24558e10	−	9.04964e9i	−0.529378	−	0.384616i	0.290747	−	0.956800i	$-0.406096\pi$
$919$	−1.24558e10	−	9.04964e9i	−0.529378	−	0.384616i	−0.820125	+	0.572184i	$0.806096\pi$
$920$	−4.71051e9	+	1.44975e10i	−0.199439	+	0.613810i
$921$		0			0
$922$	−3.01956e10	+	2.19384e10i	−1.26878	+	0.921821i
$923$	3.79246e9			0.158750
$924$		0			0
$925$	6.02156e10			2.50157
$926$	1.40764e8	−	1.02271e8i	0.00582577	−	0.00423267i
$927$		0			0
$928$	−2.18365e9	+	6.72058e9i	−0.0896942	+	0.276050i
$929$	−3.48468e10	−	2.53177e10i	−1.42596	−	1.03602i	−0.990751	−	0.135694i	$-0.956674\pi$
$929$	−3.48468e10	−	2.53177e10i	−1.42596	−	1.03602i	−0.435212	−	0.900328i	$-0.643326\pi$
$930$		0			0
$931$	−1.56784e10	+	4.82531e10i	−0.636762	+	1.95975i
$932$	2.19055e9	+	6.74181e9i	0.0886332	+	0.272785i
$933$		0			0
$934$	6.71626e8			0.0269720
$935$	−5.09130e10	−	3.22828e9i	−2.03699	−	0.129161i
$936$		0			0
$937$	−1.46733e10	+	1.06608e10i	−0.582694	+	0.423352i	−0.839694	−	0.543060i	$-0.817266\pi$
$937$	−1.46733e10	+	1.06608e10i	−0.582694	+	0.423352i	0.257001	+	0.966411i	$0.417266\pi$
$938$	−2.92968e10	−	9.01664e10i	−1.15907	−	3.56726i
$939$		0			0
$940$	−2.68300e9	−	1.94931e9i	−0.105359	−	0.0765479i
$941$	−9.79368e9	−	7.11553e9i	−0.383162	−	0.278383i	0.379486	−	0.925198i	$-0.376101\pi$
$941$	−9.79368e9	−	7.11553e9i	−0.383162	−	0.278383i	−0.762648	+	0.646814i	$0.776101\pi$
$942$		0			0
$943$	3.78562e9	+	1.16509e10i	0.147010	+	0.452449i
$944$	−2.32047e9	+	1.68592e9i	−0.0897787	+	0.0652280i
$945$		0			0
$946$	−7.47032e8	−	2.91544e9i	−0.0286893	−	0.111966i
$947$	2.38057e10			0.910870			0.455435	−	0.890269i	$-0.349484\pi$
$947$	2.38057e10			0.910870			0.455435	+	0.890269i	$0.349484\pi$
$948$		0			0
$949$	−2.84824e9	−	8.76598e9i	−0.108180	−	0.332942i
$950$	1.52154e10	−	4.68281e10i	0.575771	−	1.77204i
$951$		0			0
$952$	4.06510e10	+	2.95347e10i	1.52701	+	1.10944i
$953$	3.53096e9	−	1.08672e10i	0.132150	−	0.406716i	−0.862986	−	0.505228i	$-0.831408\pi$
$953$	3.53096e9	−	1.08672e10i	0.132150	−	0.406716i	0.995136	+	0.0985122i	$0.0314084\pi$
$954$		0			0
$955$	5.91153e10	−	4.29498e10i	2.19628	−	1.59569i
$956$	8.70225e9			0.322129
$957$		0			0
$958$	2.41736e10			0.888305
$959$	−6.25819e10	+	4.54684e10i	−2.29131	+	1.66473i
$960$		0			0
$961$	4.92710e9	−	1.51640e10i	0.179085	−	0.551167i
$962$	1.47361e10	+	1.07064e10i	0.533666	+	0.387731i
$963$		0			0
$964$	−1.38704e9	+	4.26886e9i	−0.0498676	+	0.153477i
$965$	6.31540e9	+	1.94368e10i	0.226233	+	0.696272i
$966$		0			0
$967$	5.14161e10			1.82855			0.914274	−	0.405097i	$-0.132762\pi$
$967$	5.14161e10			1.82855			0.914274	+	0.405097i	$0.132762\pi$
$968$	1.03780e10	−	2.19982e10i	0.367747	−	0.779513i
$969$		0			0
$970$	3.57481e10	−	2.59725e10i	1.25763	−	0.913719i
$971$	3.07748e9	+	9.47151e9i	0.107877	+	0.332011i	0.990395	−	0.138268i	$-0.0441535\pi$
$971$	3.07748e9	+	9.47151e9i	0.107877	+	0.332011i	−0.882518	+	0.470278i	$0.844153\pi$
$972$		0			0
$973$	−4.81100e10	−	3.49539e10i	−1.67433	−	1.21647i
$974$	−3.84263e9	−	2.79184e9i	−0.133252	−	0.0968130i
$975$		0			0
$976$	−9.90546e9	−	3.04859e10i	−0.341036	−	1.04960i
$977$	−9.07942e9	+	6.59659e9i	−0.311478	+	0.226302i	−0.732530	−	0.680734i	$-0.761661\pi$
$977$	−9.07942e9	+	6.59659e9i	−0.311478	+	0.226302i	0.421053	+	0.907036i	$0.361661\pi$
$978$		0			0
$979$	5.52779e9	−	1.39416e10i	0.188283	−	0.474868i
$980$	−3.02315e10			−1.02605
$981$		0			0
$982$	8.14419e9	+	2.50652e10i	0.274447	+	0.844660i
$983$	5.93855e9	−	1.82770e10i	0.199408	−	0.613715i	−0.800489	−	0.599348i	$-0.795427\pi$
$983$	5.93855e9	−	1.82770e10i	0.199408	−	0.613715i	0.999897	−	0.0143673i	$-0.00457343\pi$
$984$		0			0
$985$	2.90338e10	+	2.10943e10i	0.968004	+	0.703296i
$986$	−7.93797e9	+	2.44305e10i	−0.263718	+	0.811641i
$987$		0			0
$988$	2.16894e9	−	1.57582e9i	0.0715480	−	0.0519827i
$989$	−1.34237e9			−0.0441250
$990$		0			0
$991$	−4.82078e10			−1.57347			−0.786737	−	0.617288i	$-0.788231\pi$
$991$	−4.82078e10			−1.57347			−0.786737	+	0.617288i	$0.788231\pi$
$992$	1.34929e10	−	9.80316e9i	0.438848	−	0.318842i
$993$		0			0
$994$	−6.21275e9	+	1.91209e10i	−0.200647	+	0.617527i
$995$	4.60959e10	+	3.34906e10i	1.48348	+	1.07781i
$996$		0			0
$997$	1.38693e10	−	4.26853e10i	0.443222	−	1.36410i	−0.441200	−	0.897409i	$-0.645447\pi$
$997$	1.38693e10	−	4.26853e10i	0.443222	−	1.36410i	0.884422	−	0.466688i	$-0.154553\pi$
$998$	−2.54024e9	−	7.81806e9i	−0.0808943	−	0.248967i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.d.91.11	yes	56
3.2	odd	2	inner	99.8.f.d.91.4	yes	56
11.4	even	5	inner	99.8.f.d.37.11	yes	56
33.26	odd	10	inner	99.8.f.d.37.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.8.f.d.37.4	✓	56	33.26	odd	10	inner
99.8.f.d.37.11	yes	56	11.4	even	5	inner
99.8.f.d.91.4	yes	56	3.2	odd	2	inner
99.8.f.d.91.11	yes	56	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(10.1078 - 7.34373i) q^{2} +(8.68266 - 26.7225i) q^{4} +(401.640 + 291.809i) q^{5} +(534.412 - 1644.75i) q^{7} +(385.706 + 1187.08i) q^{8} +O(q^{10})\)	\(q+(10.1078 - 7.34373i) q^{2} +(8.68266 - 26.7225i) q^{4} +(401.640 + 291.809i) q^{5} +(534.412 - 1644.75i) q^{7} +(385.706 + 1187.08i) q^{8} +6202.66 q^{10} +(-1627.07 + 4103.63i) q^{11} +(-3297.38 + 2395.68i) q^{13} +(-6676.89 - 20549.4i) q^{14} +(15525.9 + 11280.2i) q^{16} +(18832.3 + 13682.5i) q^{17} +(-7234.20 - 22264.6i) q^{19} +(11285.2 - 8199.15i) q^{20} +(13689.9 + 53427.4i) q^{22} +24599.8 q^{23} +(52020.6 + 160103. i) q^{25} +(-15735.9 + 48430.1i) q^{26} +(-39311.7 - 28561.6i) q^{28} +(-27293.9 + 84001.9i) q^{29} +(168651. - 122532. i) q^{31} +80005.0 q^{32} +290833. q^{34} +(694594. - 504652. i) q^{35} +(110535. - 340190. i) q^{37} +(-236627. - 171919. i) q^{38} +(-191485. + 589332. i) q^{40} +(153888. + 473619. i) q^{41} -54568.2 q^{43} +(95531.9 + 79109.9i) q^{44} +(248650. - 180654. i) q^{46} +(-73467.4 - 226109. i) q^{47} +(-1.75335e6 - 1.27388e6i) q^{49} +(1.70157e6 + 1.23626e6i) q^{50} +(35388.6 + 108915. i) q^{52} +(782189. - 568294. i) q^{53} +(-1.85097e6 + 1.17339e6i) q^{55} +2.15858e6 q^{56} +(341007. + 1.04951e6i) q^{58} +(-46185.1 + 142143. i) q^{59} +(-1.35130e6 - 981777. i) q^{61} +(804842. - 2.47705e6i) q^{62} +(-1.17864e6 + 856330. i) q^{64} -2.02344e6 q^{65} +4.38780e6 q^{67} +(529144. - 384445. i) q^{68} +(3.31477e6 - 1.02018e7i) q^{70} +(-752779. - 546926. i) q^{71} +(-698821. + 2.15075e6i) q^{73} +(-1.38101e6 - 4.25031e6i) q^{74} -657777. q^{76} +(5.87992e6 + 4.86916e6i) q^{77} +(-2.83795e6 + 2.06189e6i) q^{79} +(2.94415e6 + 9.06117e6i) q^{80} +(5.03360e6 + 3.65712e6i) q^{82} +(-2.01949e6 - 1.46725e6i) q^{83} +(3.57115e6 + 1.09909e7i) q^{85} +(-551564. + 400735. i) q^{86} +(-5.49891e6 - 348674. i) q^{88} -3.39738e6 q^{89} +(2.17815e6 + 6.70364e6i) q^{91} +(213592. - 657368. i) q^{92} +(-2.40308e6 - 1.74594e6i) q^{94} +(3.59145e6 - 1.10534e7i) q^{95} +(5.76335e6 - 4.18732e6i) q^{97} -2.70775e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 1260 q^{4} - 3902 q^{7}+O(q^{10}) \) 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

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