LMFDB - Embedded newform 99.8.f.d.91.13

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			91.13
Character	$\chi$	$=$	99.91
Dual form			99.8.f.d.37.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.6343 - 10.6324i) q^{2} +(61.5594 - 189.460i) q^{4} +(142.204 + 103.317i) q^{5} +(-426.560 + 1312.82i) q^{7} +(-398.052 - 1225.08i) q^{8} +O(q^{10})$	\(q+(14.6343 - 10.6324i) q^{2} +(61.5594 - 189.460i) q^{4} +(142.204 + 103.317i) q^{5} +(-426.560 + 1312.82i) q^{7} +(-398.052 - 1225.08i) q^{8} +3179.57 q^{10} +(-827.094 + 4336.25i) q^{11} +(7183.56 - 5219.16i) q^{13} +(7716.02 + 23747.5i) q^{14} +(1778.31 + 1292.02i) q^{16} +(6428.95 + 4670.91i) q^{17} +(16896.0 + 52000.5i) q^{19} +(28328.6 - 20581.9i) q^{20} +(34001.0 + 72251.9i) q^{22} -69066.0 q^{23} +(-14594.4 - 44917.0i) q^{25} +(49633.9 - 152757. i) q^{26} +(222468. + 161632. i) q^{28} +(30430.4 - 93655.1i) q^{29} +(327.501 - 237.943i) q^{31} +204642. q^{32} +143746. q^{34} +(-196295. + 142617. i) q^{35} +(-7964.49 + 24512.2i) q^{37} +(800152. + 581344. i) q^{38} +(69967.3 - 215337. i) q^{40} +(-88746.2 - 273133. i) q^{41} +322116. q^{43} +(770633. + 423639. i) q^{44} +(-1.01073e6 + 734339. i) q^{46} +(264591. + 814328. i) q^{47} +(-875270. - 635921. i) q^{49} +(-691155. - 502153. i) q^{50} +(-546609. - 1.68229e6i) q^{52} +(1.71251e6 - 1.24421e6i) q^{53} +(-565626. + 531180. i) q^{55} +1.77810e6 q^{56} +(-550454. - 1.69412e6i) q^{58} +(-167772. + 516350. i) q^{59} +(-93244.4 - 67746.0i) q^{61} +(2262.83 - 6964.26i) q^{62} +(2.76716e6 - 2.01046e6i) q^{64} +1.56076e6 q^{65} -4.50179e6 q^{67} +(1.28071e6 - 930494. i) q^{68} +(-1.35628e6 + 4.17419e6i) q^{70} +(-252121. - 183177. i) q^{71} +(-337582. + 1.03897e6i) q^{73} +(144069. + 443400. i) q^{74} +1.08921e7 q^{76} +(-5.33989e6 - 2.93549e6i) q^{77} +(-69898.6 + 50784.3i) q^{79} +(119395. + 367461. i) q^{80} +(-4.20280e6 - 3.05351e6i) q^{82} +(5.38471e6 + 3.91222e6i) q^{83} +(431638. + 1.32844e6i) q^{85} +(4.71393e6 - 3.42487e6i) q^{86} +(5.64148e6 - 712799. i) q^{88} -3.18154e6 q^{89} +(3.78758e6 + 1.16570e7i) q^{91} +(-4.25167e6 + 1.30853e7i) q^{92} +(1.25304e7 + 9.10386e6i) q^{94} +(-2.96987e6 + 9.14033e6i) q^{95} +(-7.39815e6 + 5.37507e6i) q^{97} -1.95703e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	14.6343	−	10.6324i	1.29350	−	0.939782i	0.293630	−	0.955919i	$-0.405137\pi$
$2$	14.6343	−	10.6324i	1.29350	−	0.939782i	0.999870	+	0.0161368i	$0.00513671\pi$
$3$		0			0
$3$		0			0
$4$	61.5594	−	189.460i	0.480933	−	1.48016i
$5$	142.204	+	103.317i	0.508765	+	0.369639i	0.812355	−	0.583163i	$-0.198185\pi$
$5$	142.204	+	103.317i	0.508765	+	0.369639i	−0.303590	+	0.952803i	$0.598185\pi$
$6$		0			0
$7$	−426.560	+	1312.82i	−0.470042	+	1.44664i	0.382488	+	0.923961i	$0.375067\pi$
$7$	−426.560	+	1312.82i	−0.470042	+	1.44664i	−0.852529	+	0.522679i	$0.824933\pi$
$8$	−398.052	−	1225.08i	−0.274869	−	0.845959i
$9$		0			0
$10$	3179.57			1.00547
$11$	−827.094	+	4336.25i	−0.187362	+	0.982291i
$11$	−827.094	+	4336.25i	−0.187362	+	0.982291i
$12$		0			0
$13$	7183.56	−	5219.16i	0.906856	−	0.658869i	−0.0333621	−	0.999443i	$-0.510621\pi$
$13$	7183.56	−	5219.16i	0.906856	−	0.658869i	0.940218	+	0.340574i	$0.110621\pi$
$14$	7716.02	+	23747.5i	0.751528	+	2.31297i
$15$		0			0
$16$	1778.31	+	1292.02i	0.108539	+	0.0788585i
$17$	6428.95	+	4670.91i	0.317372	+	0.230584i	0.735053	−	0.678009i	$-0.237157\pi$
$17$	6428.95	+	4670.91i	0.317372	+	0.230584i	−0.417681	+	0.908594i	$0.637157\pi$
$18$		0			0
$19$	16896.0	+	52000.5i	0.565127	+	1.73928i	0.667575	+	0.744543i	$0.267332\pi$
$19$	16896.0	+	52000.5i	0.565127	+	1.73928i	−0.102448	+	0.994738i	$0.532668\pi$
$20$	28328.6	−	20581.9i	0.791807	−	0.575282i
$21$		0			0
$22$	34001.0	+	72251.9i	0.680788	+	1.44667i
$23$	−69066.0			−1.18363			−0.591816	−	0.806073i	$-0.701589\pi$
$23$	−69066.0			−1.18363			−0.591816	+	0.806073i	$0.701589\pi$
$24$		0			0
$25$	−14594.4	−	44917.0i	−0.186808	−	0.574937i
$26$	49633.9	−	152757.i	0.553824	−	1.70449i
$27$		0			0
$28$	222468.	+	161632.i	1.91520	+	1.39147i
$29$	30430.4	−	93655.1i	0.231694	−	0.713081i	−0.765849	−	0.643021i	$-0.777681\pi$
$29$	30430.4	−	93655.1i	0.231694	−	0.713081i	0.997543	−	0.0700599i	$-0.0223190\pi$
$30$		0			0
$31$	327.501	−	237.943i	0.00197445	−	0.00143452i	−0.586798	−	0.809734i	$-0.699612\pi$
$31$	327.501	−	237.943i	0.00197445	−	0.00143452i	0.588772	+	0.808299i	$0.299612\pi$
$32$	204642.			1.10400
$33$		0			0
$34$	143746.			0.627220
$35$	−196295.	+	142617.i	−0.773876	+	0.562254i
$36$		0			0
$37$	−7964.49	+	24512.2i	−0.0258495	+	0.0795566i	−0.963149	−	0.268968i	$-0.913317\pi$
$37$	−7964.49	+	24512.2i	−0.0258495	+	0.0795566i	0.937300	+	0.348525i	$0.113317\pi$
$38$	800152.	+	581344.i	2.36554	+	1.71866i
$39$		0			0
$40$	69967.3	−	215337.i	0.172856	−	0.531997i
$41$	−88746.2	−	273133.i	−0.201097	−	0.618914i	−0.999851	−	0.0172560i	$-0.994507\pi$
$41$	−88746.2	−	273133.i	−0.201097	−	0.618914i	0.798754	−	0.601658i	$-0.205493\pi$
$42$		0			0
$43$	322116.			0.617835			0.308918	−	0.951089i	$-0.400033\pi$
$43$	322116.			0.617835			0.308918	+	0.951089i	$0.400033\pi$
$44$	770633.	+	423639.i	1.36384	+	0.749741i
$45$		0			0
$46$	−1.01073e6	+	734339.i	−1.53103	+	1.11236i
$47$	264591.	+	814328.i	0.371735	+	1.14408i	0.945655	+	0.325171i	$0.105422\pi$
$47$	264591.	+	814328.i	0.371735	+	1.14408i	−0.573921	+	0.818911i	$0.694578\pi$
$48$		0			0
$49$	−875270.	−	635921.i	−1.06281	−	0.772177i
$50$	−691155.	−	502153.i	−0.781953	−	0.568122i
$51$		0			0
$52$	−546609.	−	1.68229e6i	−0.539095	−	1.65916i
$53$	1.71251e6	−	1.24421e6i	1.58004	−	1.14797i	0.663394	−	0.748270i	$-0.269115\pi$
$53$	1.71251e6	−	1.24421e6i	1.58004	−	1.14797i	0.916647	−	0.399697i	$-0.130885\pi$
$54$		0			0
$55$	−565626.	+	531180.i	−0.458417	+	0.430499i
$56$	1.77810e6			1.35300
$57$		0			0
$58$	−550454.	−	1.69412e6i	−0.370445	−	1.14011i
$59$	−167772.	+	516350.i	−0.106350	+	0.327312i	−0.990045	−	0.140751i	$-0.955048\pi$
$59$	−167772.	+	516350.i	−0.106350	+	0.327312i	0.883695	+	0.468063i	$0.155048\pi$
$60$		0			0
$61$	−93244.4	−	67746.0i	−0.0525979	−	0.0382146i	0.561176	−	0.827697i	$-0.310349\pi$
$61$	−93244.4	−	67746.0i	−0.0525979	−	0.0382146i	−0.613774	+	0.789482i	$0.710349\pi$
$62$	2262.83	−	6964.26i	0.00120581	−	0.00371111i
$63$		0			0
$64$	2.76716e6	−	2.01046e6i	1.31948	−	0.958661i
$65$	1.56076e6			0.704920
$66$		0			0
$67$	−4.50179e6			−1.82862			−0.914310	−	0.405015i	$-0.867266\pi$
$67$	−4.50179e6			−1.82862			−0.914310	+	0.405015i	$0.867266\pi$
$68$	1.28071e6	−	930494.i	0.493937	−	0.358866i
$69$		0			0
$70$	−1.35628e6	+	4.17419e6i	−0.472612	+	1.45455i
$71$	−252121.	−	183177.i	−0.0835998	−	0.0607388i	0.545200	−	0.838306i	$-0.316454\pi$
$71$	−252121.	−	183177.i	−0.0835998	−	0.0607388i	−0.628800	+	0.777567i	$0.716454\pi$
$72$		0			0
$73$	−337582.	+	1.03897e6i	−0.101566	+	0.312588i	−0.988909	−	0.148521i	$-0.952549\pi$
$73$	−337582.	+	1.03897e6i	−0.101566	+	0.312588i	0.887343	+	0.461110i	$0.152549\pi$
$74$	144069.	+	443400.i	0.0413296	+	0.127199i
$75$		0			0
$76$	1.08921e7			2.84620
$77$	−5.33989e6	−	2.93549e6i	−1.33295	−	0.732763i
$78$		0			0
$79$	−69898.6	+	50784.3i	−0.0159505	+	0.0115887i	−0.595732	−	0.803183i	$-0.703138\pi$
$79$	−69898.6	+	50784.3i	−0.0159505	+	0.0115887i	0.579781	+	0.814772i	$0.303138\pi$
$80$	119395.	+	367461.i	0.0260719	+	0.0802409i
$81$		0			0
$82$	−4.20280e6	−	3.05351e6i	−0.841764	−	0.611577i
$83$	5.38471e6	+	3.91222e6i	1.03369	+	0.751018i	0.969043	−	0.246890i	$-0.0794087\pi$
$83$	5.38471e6	+	3.91222e6i	1.03369	+	0.751018i	0.0646442	+	0.997908i	$0.479409\pi$
$84$		0			0
$85$	431638.	+	1.32844e6i	0.0762348	+	0.234627i
$86$	4.71393e6	−	3.42487e6i	0.799169	−	0.580631i
$87$		0			0
$88$	5.64148e6	−	712799.i	0.882478	−	0.111501i
$89$	−3.18154e6			−0.478380			−0.239190	−	0.970973i	$-0.576882\pi$
$89$	−3.18154e6			−0.478380			−0.239190	+	0.970973i	$0.576882\pi$
$90$		0			0
$91$	3.78758e6	+	1.16570e7i	0.526886	+	1.62159i
$92$	−4.25167e6	+	1.30853e7i	−0.569248	+	1.75197i
$93$		0			0
$94$	1.25304e7	+	9.10386e6i	1.55603	+	1.13052i
$95$	−2.96987e6	+	9.14033e6i	−0.355390	+	1.09378i
$96$		0			0
$97$	−7.39815e6	+	5.37507e6i	−0.823042	+	0.597975i	−0.917582	−	0.397546i	$-0.869862\pi$
$97$	−7.39815e6	+	5.37507e6i	−0.823042	+	0.597975i	0.0945405	+	0.995521i	$0.469862\pi$
$98$	−1.95703e7			−2.10042
$99$		0			0
$100$	−9.40841e6			−0.940841
$101$	9.09924e6	−	6.61099e6i	0.878780	−	0.638471i	−0.0541482	−	0.998533i	$-0.517244\pi$
$101$	9.09924e6	−	6.61099e6i	0.878780	−	0.638471i	0.932929	+	0.360062i	$0.117244\pi$
$102$		0			0
$103$	−4.10474e6	+	1.26331e7i	−0.370131	+	1.13915i	0.576574	+	0.817045i	$0.304389\pi$
$103$	−4.10474e6	+	1.26331e7i	−0.370131	+	1.13915i	−0.946705	+	0.322101i	$0.895611\pi$
$104$	−9.25332e6	−	6.72293e6i	−0.806642	−	0.586060i
$105$		0			0
$106$	1.18324e7	−	3.64163e7i	0.964943	−	2.96979i
$107$	−6.61781e6	−	2.03675e7i	−0.522241	−	1.60729i	−0.769708	−	0.638397i	$-0.779598\pi$
$107$	−6.61781e6	−	2.03675e7i	−0.522241	−	1.60729i	0.247467	−	0.968896i	$-0.420402\pi$
$108$		0			0
$109$	9.37923e6			0.693704			0.346852	−	0.937920i	$-0.387251\pi$
$109$	9.37923e6			0.693704			0.346852	+	0.937920i	$0.387251\pi$
$110$	−2.62980e6	+	1.37874e7i	−0.188386	+	0.987662i
$111$		0			0
$112$	−2.45474e6	+	1.78347e6i	−0.165098	+	0.119951i
$113$	−4.62928e6	−	1.42475e7i	−0.301814	−	0.928887i	−0.980847	−	0.194780i	$-0.937601\pi$
$113$	−4.62928e6	−	1.42475e7i	−0.301814	−	0.928887i	0.679033	−	0.734107i	$-0.262399\pi$
$114$		0			0
$115$	−9.82148e6	−	7.13572e6i	−0.602191	−	0.437517i
$116$	−1.58707e7	−	1.15307e7i	−0.944044	−	0.685888i
$117$		0			0
$118$	3.03483e6	+	9.34023e6i	0.170038	+	0.523324i
$119$	−8.87437e6	+	6.44761e6i	−0.482751	+	0.350739i
$120$		0			0
$121$	−1.81190e7	−	7.17298e6i	−0.929791	−	0.368087i
$122$	−2.08487e6			−0.103949
$123$		0			0
$124$	−24920.1	−	76696.2i	−0.00117375	−	0.00361242i
$125$	6.80885e6	−	2.09555e7i	0.311809	−	0.959649i
$126$		0			0
$127$	−1.93559e7	−	1.40629e7i	−0.838497	−	0.609203i	0.0834536	−	0.996512i	$-0.473405\pi$
$127$	−1.93559e7	−	1.40629e7i	−0.838497	−	0.609203i	−0.921950	+	0.387308i	$0.873405\pi$
$128$	1.10249e7	−	3.39311e7i	0.464664	−	1.43009i
$129$		0			0
$130$	2.28406e7	−	1.65947e7i	0.911814	−	0.662472i
$131$	−1.48045e7			−0.575367			−0.287684	−	0.957725i	$-0.592885\pi$
$131$	−1.48045e7			−0.575367			−0.287684	+	0.957725i	$0.592885\pi$
$132$		0			0
$133$	−7.54742e7			−2.78175
$134$	−6.58805e7	+	4.78650e7i	−2.36532	+	1.71851i
$135$		0			0
$136$	3.16317e6	−	9.73524e6i	0.107829	−	0.331864i
$137$	2.28894e7	+	1.66301e7i	0.760523	+	0.552552i	0.899071	−	0.437803i	$-0.144243\pi$
$137$	2.28894e7	+	1.66301e7i	0.760523	+	0.552552i	−0.138548	+	0.990356i	$0.544243\pi$
$138$		0			0
$139$	1.14215e7	−	3.51516e7i	0.360719	−	1.11018i	−0.591899	−	0.806012i	$-0.701622\pi$
$139$	1.14215e7	−	3.51516e7i	0.360719	−	1.11018i	0.952618	−	0.304168i	$-0.0983784\pi$
$140$	1.49364e7	+	4.59696e7i	0.460043	+	1.41587i
$141$		0			0
$142$	−5.63723e6			−0.165218
$143$	1.66901e7	+	3.54665e7i	0.477291	+	1.01424i
$144$		0			0
$145$	1.40035e7	−	1.01742e7i	0.381460	−	0.277147i
$146$	6.10650e6	+	1.87939e7i	0.162389	+	0.499783i
$147$		0			0
$148$	4.15380e6	+	3.01791e6i	0.105325	+	0.0765228i
$149$	3.67666e7	+	2.67125e7i	0.910545	+	0.661549i	0.941153	−	0.337982i	$-0.109744\pi$
$149$	3.67666e7	+	2.67125e7i	0.910545	+	0.661549i	−0.0306079	+	0.999531i	$0.509744\pi$
$150$		0			0
$151$	2.10667e7	+	6.48368e7i	0.497941	+	1.53251i	0.812322	+	0.583209i	$0.198203\pi$
$151$	2.10667e7	+	6.48368e7i	0.497941	+	1.53251i	−0.314381	+	0.949297i	$0.601797\pi$
$152$	5.69792e7	−	4.13978e7i	1.31602	−	0.956148i
$153$		0			0
$154$	−1.09357e8	+	1.38172e7i	−2.41281	+	0.304858i
$155$	71155.7			0.00153479
$156$		0			0
$157$	2.07604e7	+	6.38938e7i	0.428140	+	1.31768i	0.899955	+	0.435982i	$0.143599\pi$
$157$	2.07604e7	+	6.38938e7i	0.428140	+	1.31768i	−0.471815	+	0.881698i	$0.656401\pi$
$158$	−482955.	+	1.48638e6i	−0.00974108	+	0.0299800i
$159$		0			0
$160$	2.91009e7	+	2.11430e7i	0.561676	+	0.408082i
$161$	2.94608e7	−	9.06709e7i	0.556357	−	1.71229i
$162$		0			0
$163$	6.82435e7	−	4.95818e7i	1.23425	−	0.896739i	0.237053	−	0.971497i	$-0.423818\pi$
$163$	6.82435e7	−	4.95818e7i	1.23425	−	0.896739i	0.997202	+	0.0747582i	$0.0238185\pi$
$164$	−5.72110e7			−1.01281
$165$		0			0
$166$	1.20398e8			2.04287
$167$	3.57029e7	−	2.59397e7i	0.593193	−	0.430980i	−0.250263	−	0.968178i	$-0.580517\pi$
$167$	3.57029e7	−	2.59397e7i	0.593193	−	0.430980i	0.843456	+	0.537198i	$0.180517\pi$
$168$		0			0
$169$	4.97354e6	−	1.53070e7i	0.0792614	−	0.243942i
$170$	2.04413e7	+	1.48515e7i	0.319108	+	0.231845i
$171$		0			0
$172$	1.98293e7	−	6.10282e7i	0.297137	−	0.914495i
$173$	−2.47798e7	−	7.62644e7i	−0.363862	−	1.11985i	−0.950691	−	0.310141i	$-0.899624\pi$
$173$	−2.47798e7	−	7.62644e7i	−0.363862	−	1.11985i	0.586829	−	0.809711i	$-0.300376\pi$
$174$		0			0
$175$	6.51931e7			0.919535
$176$	−7.07335e6	+	6.64258e6i	−0.0977982	+	0.0918423i
$177$		0			0
$178$	−4.65596e7	+	3.38275e7i	−0.618784	+	0.449573i
$179$	−4.01501e7	−	1.23569e8i	−0.523240	−	1.61037i	−0.767770	−	0.640726i	$-0.778634\pi$
$179$	−4.01501e7	−	1.23569e8i	−0.523240	−	1.61037i	0.244530	−	0.969642i	$-0.421366\pi$
$180$		0			0
$181$	1.77276e7	+	1.28799e7i	0.222216	+	0.161449i	0.693324	−	0.720626i	$-0.256146\pi$
$181$	1.77276e7	+	1.28799e7i	0.222216	+	0.161449i	−0.471108	+	0.882076i	$0.656146\pi$
$182$	1.79370e8	+	1.30320e8i	2.20547	+	1.60237i
$183$		0			0
$184$	2.74919e7	+	8.46113e7i	0.325344	+	1.00130i
$185$	−3.66512e6	+	2.66286e6i	−0.0425586	+	0.0309206i
$186$		0			0
$187$	−2.55716e7	+	2.40143e7i	−0.285964	+	0.268549i
$188$	1.70571e8			1.87220
$189$		0			0
$190$	5.37219e7	+	1.65339e8i	0.568217	+	1.74879i
$191$	7.68842e6	−	2.36625e7i	0.0798399	−	0.245722i	−0.903167	−	0.429289i	$-0.858764\pi$
$191$	7.68842e6	−	2.36625e7i	0.0798399	−	0.245722i	0.983007	+	0.183567i	$0.0587643\pi$
$192$		0			0
$193$	−9.11486e6	−	6.62233e6i	−0.0912640	−	0.0663072i	0.541218	−	0.840883i	$-0.317964\pi$
$193$	−9.11486e6	−	6.62233e6i	−0.0912640	−	0.0663072i	−0.632482	+	0.774575i	$0.717964\pi$
$194$	−5.11165e7	+	1.57320e8i	−0.502638	+	1.54696i
$195$		0			0
$196$	−1.74363e8	+	1.26682e8i	−1.65409	+	1.20176i
$197$	8.92799e7			0.831998			0.415999	−	0.909365i	$-0.363432\pi$
$197$	8.92799e7			0.831998			0.415999	+	0.909365i	$0.363432\pi$
$198$		0			0
$199$	−2.67907e7			−0.240989			−0.120495	−	0.992714i	$-0.538448\pi$
$199$	−2.67907e7			−0.240989			−0.120495	+	0.992714i	$0.538448\pi$
$200$	−4.92175e7	+	3.57586e7i	−0.435025	+	0.316064i
$201$		0			0
$202$	6.28700e7	−	1.93494e8i	0.536678	−	1.65172i
$203$	1.09972e8	+	7.98990e7i	0.922665	+	0.670355i
$204$		0			0
$205$	1.55993e7	−	4.80096e7i	0.126464	−	0.389215i
$206$	7.42505e7	+	2.28519e8i	0.591785	+	1.82133i
$207$		0			0
$208$	1.95179e7			0.150387
$209$	−2.39462e8	+	3.02559e7i	−1.81436	+	0.229244i
$210$		0			0
$211$	1.21465e8	−	8.82492e7i	0.890146	−	0.646729i	−0.0457701	−	0.998952i	$-0.514574\pi$
$211$	1.21465e8	−	8.82492e7i	0.890146	−	0.646729i	0.935916	+	0.352223i	$0.114574\pi$
$212$	−1.30308e8	−	4.01047e8i	−0.939281	−	2.89081i
$213$		0			0
$214$	−3.13403e8	−	2.27701e8i	−2.18602	−	1.58824i
$215$	4.58062e7	+	3.32802e7i	0.314333	+	0.228376i
$216$		0			0
$217$	172677.	+	531445.i	0.00114716	+	0.00353061i
$218$	1.37258e8	−	9.97239e7i	0.897306	−	0.651931i
$219$		0			0
$220$	6.58179e7	+	1.39863e8i	0.416740	+	0.885571i
$221$	7.05610e7			0.439736
$222$		0			0
$223$	−7.16258e7	−	2.20441e8i	−0.432516	−	1.33115i	−0.895611	−	0.444839i	$-0.853261\pi$
$223$	−7.16258e7	−	2.20441e8i	−0.432516	−	1.33115i	0.463095	−	0.886309i	$-0.346739\pi$
$224$	−8.72918e7	+	2.68656e8i	−0.518926	+	1.59709i
$225$		0			0
$226$	−2.19231e8	−	1.59281e8i	−1.26335	−	0.917876i
$227$	5.63622e7	−	1.73465e8i	0.319814	−	0.984286i	−0.653913	−	0.756569i	$-0.726874\pi$
$227$	5.63622e7	−	1.73465e8i	0.319814	−	0.984286i	0.973727	−	0.227717i	$-0.0731261\pi$
$228$		0			0
$229$	1.37698e8	−	1.00043e8i	0.757708	−	0.550507i	−0.140498	−	0.990081i	$-0.544870\pi$
$229$	1.37698e8	−	1.00043e8i	0.757708	−	0.550507i	0.898207	+	0.439574i	$0.144870\pi$
$230$	−2.19600e8			−1.19011
$231$		0			0
$232$	−1.26848e8			−0.666922
$233$	−1.36534e8	+	9.91976e7i	−0.707122	+	0.513754i	−0.882244	−	0.470792i	$-0.843968\pi$
$233$	−1.36534e8	+	9.91976e7i	−0.707122	+	0.513754i	0.175122	+	0.984547i	$0.443968\pi$
$234$		0			0
$235$	−4.65083e7	+	1.43138e8i	−0.233772	+	0.719477i
$236$	8.74999e7	+	6.35724e7i	0.433327	+	0.314830i
$237$		0			0
$238$	−6.13163e7	+	1.88712e8i	−0.294820	+	0.907362i
$239$	−4.45389e7	−	1.37077e8i	−0.211031	−	0.649487i	−0.999412	−	0.0342990i	$-0.989080\pi$
$239$	−4.45389e7	−	1.37077e8i	−0.211031	−	0.649487i	0.788381	−	0.615188i	$-0.210920\pi$
$240$		0			0
$241$	−1.26710e8			−0.583109			−0.291554	−	0.956554i	$-0.594172\pi$
$241$	−1.26710e8			−0.583109			−0.291554	+	0.956554i	$0.594172\pi$
$242$	−3.41425e8	+	8.76775e7i	−1.54861	+	0.397681i
$243$		0			0
$244$	−1.85753e7	+	1.34957e7i	−0.0818598	+	0.0594746i
$245$	−5.87654e7	−	1.80861e8i	−0.255294	−	0.785714i
$246$		0			0
$247$	3.92772e8	+	2.85366e8i	1.65845	+	1.20493i
$248$	−421862.	−	306501.i	−0.00175626	−	0.00127600i
$249$		0			0
$250$	−1.23165e8	−	3.79063e8i	−0.498537	−	1.53434i
$251$	3.82200e8	−	2.77685e8i	1.52557	−	1.10839i	0.566937	−	0.823761i	$-0.308128\pi$
$251$	3.82200e8	−	2.77685e8i	1.52557	−	1.10839i	0.958637	−	0.284632i	$-0.0918715\pi$
$252$		0			0
$253$	5.71241e7	−	2.99488e8i	0.221767	−	1.16267i
$254$	−4.32783e8			−1.65711
$255$		0			0
$256$	−6.41378e7	−	1.97396e8i	−0.238932	−	0.735357i
$257$	8.10709e7	−	2.49510e8i	0.297919	−	0.916902i	−0.684306	−	0.729195i	$-0.739895\pi$
$257$	8.10709e7	−	2.49510e8i	0.297919	−	0.916902i	0.982225	−	0.187707i	$-0.0601054\pi$
$258$		0			0
$259$	−2.87826e7	−	2.09118e7i	−0.102939	−	0.0747898i
$260$	9.60797e7	−	2.95703e8i	0.339020	−	1.04339i
$261$		0			0
$262$	−2.16654e8	+	1.57408e8i	−0.744238	+	0.540720i
$263$	−2.75116e8			−0.932548			−0.466274	−	0.884640i	$-0.654404\pi$
$263$	−2.75116e8			−0.932548			−0.466274	+	0.884640i	$0.654404\pi$
$264$		0			0
$265$	3.72075e8			1.22820
$266$	−1.10451e9	+	8.02473e8i	−3.59819	+	2.61424i
$267$		0			0
$268$	−2.77128e8	+	8.52911e8i	−0.879444	+	2.70665i
$269$	2.79938e8	+	2.03386e8i	0.876856	+	0.637073i	0.932418	−	0.361382i	$-0.117695\pi$
$269$	2.79938e8	+	2.03386e8i	0.876856	+	0.637073i	−0.0555621	+	0.998455i	$0.517695\pi$
$270$		0			0
$271$	−2.27123e7	+	6.99014e7i	−0.0693218	+	0.213350i	−0.979716	−	0.200392i	$-0.935779\pi$
$271$	−2.27123e7	+	6.99014e7i	−0.0693218	+	0.213350i	0.910394	+	0.413742i	$0.135779\pi$
$272$	5.39778e6	+	1.66126e7i	0.0162639	+	0.0500550i
$273$		0			0
$274$	5.11788e8			1.50302
$275$	2.06842e8	−	2.61345e7i	0.599756	−	0.0757791i
$276$		0			0
$277$	−1.06145e8	+	7.71191e7i	−0.300070	+	0.218013i	−0.727624	−	0.685976i	$-0.759375\pi$
$277$	−1.06145e8	+	7.71191e7i	−0.300070	+	0.218013i	0.427554	+	0.903990i	$0.359375\pi$
$278$	−2.06602e8	−	6.35856e8i	−0.576737	−	1.77502i
$279$		0			0
$280$	2.52853e8	+	1.83708e8i	0.688358	+	0.500121i
$281$	3.37375e7	+	2.45117e7i	0.0907070	+	0.0659025i	0.632214	−	0.774794i	$-0.282146\pi$
$281$	3.37375e7	+	2.45117e7i	0.0907070	+	0.0659025i	−0.541507	+	0.840696i	$0.682146\pi$
$282$		0			0
$283$	−8.83164e7	−	2.71810e8i	−0.231627	−	0.712874i	−0.997551	−	0.0699429i	$-0.977718\pi$
$283$	−8.83164e7	−	2.71810e8i	−0.231627	−	0.712874i	0.765924	−	0.642931i	$-0.222282\pi$
$284$	−5.02252e7	+	3.64908e7i	−0.130109	+	0.0945298i
$285$		0			0
$286$	6.21343e8	+	3.41570e8i	1.57054	+	0.863373i
$287$	3.96428e8			0.989870
$288$		0			0
$289$	−1.07288e8	−	3.30197e8i	−0.261461	−	0.804694i
$290$	9.67555e7	−	2.97783e8i	0.232961	−	0.716980i
$291$		0			0
$292$	1.76062e8	+	1.27917e8i	0.413834	+	0.300668i
$293$	−1.51488e8	+	4.66232e8i	−0.351837	+	1.08284i	0.605983	+	0.795477i	$0.292780\pi$
$293$	−1.51488e8	+	4.66232e8i	−0.351837	+	1.08284i	−0.957821	+	0.287366i	$0.907220\pi$
$294$		0			0
$295$	−7.72058e7	+	5.60933e7i	−0.175095	+	0.127214i
$296$	3.31997e7			0.0744068
$297$		0			0
$298$	8.22071e8			1.79950
$299$	−4.96140e8	+	3.60467e8i	−1.07338	+	0.779859i
$300$		0			0
$301$	−1.37402e8	+	4.22879e8i	−0.290408	+	0.893785i
$302$	9.97669e8	+	7.24849e8i	2.08431	+	1.51434i
$303$		0			0
$304$	−3.71393e7	+	1.14303e8i	−0.0758186	+	0.233346i
$305$	−6.26040e6	−	1.92675e7i	−0.0126343	−	0.0388845i
$306$		0			0
$307$	−8.70816e8			−1.71768			−0.858840	−	0.512244i	$-0.828814\pi$
$307$	−8.70816e8			−1.71768			−0.858840	+	0.512244i	$0.828814\pi$
$308$	−8.84881e8	+	8.30991e8i	−1.72567	+	1.62057i
$309$		0			0
$310$	1.04131e6	−	756558.i	0.00198525	−	0.00144237i
$311$	−3.04450e8	−	9.37000e8i	−0.573924	−	1.76636i	−0.639815	−	0.768529i	$-0.720989\pi$
$311$	−3.04450e8	−	9.37000e8i	−0.573924	−	1.76636i	0.0658908	−	0.997827i	$-0.479011\pi$
$312$		0			0
$313$	7.83013e8	+	5.68892e8i	1.44332	+	1.04864i	0.987335	+	0.158650i	$0.0507142\pi$
$313$	7.83013e8	+	5.68892e8i	1.44332	+	1.04864i	0.455989	+	0.889986i	$0.349286\pi$
$314$	9.83159e8	+	7.14307e8i	1.79213	+	1.30206i
$315$		0			0
$316$	5.31870e6	+	1.63693e7i	0.00948202	+	0.0291827i
$317$	3.81851e8	−	2.77431e8i	0.673266	−	0.489157i	−0.197851	−	0.980232i	$-0.563396\pi$
$317$	3.81851e8	−	2.77431e8i	0.673266	−	0.489157i	0.871117	+	0.491076i	$0.163396\pi$
$318$		0			0
$319$	3.80943e8	+	2.09416e8i	0.657042	+	0.361195i
$320$	6.01216e8			1.02567
$321$		0			0
$322$	−5.32915e8	−	1.64014e9i	−0.889533	−	2.73770i
$323$	−1.34266e8	+	4.13228e8i	−0.221696	+	0.682309i
$324$		0			0
$325$	−3.39269e8	−	2.46493e8i	−0.548217	−	0.398303i
$326$	4.71520e8	−	1.45119e9i	0.753769	−	2.31986i
$327$		0			0
$328$	−2.99284e8	+	2.17442e8i	−0.468300	+	0.340240i
$329$	−1.18193e9			−1.82981
$330$		0			0
$331$	−8.35352e8			−1.26611			−0.633055	−	0.774107i	$-0.718199\pi$
$331$	−8.35352e8			−1.26611			−0.633055	+	0.774107i	$0.718199\pi$
$332$	1.07269e9	−	7.79356e8i	1.60876	−	1.16883i
$333$		0			0
$334$	2.46685e8	−	7.59217e8i	0.362268	−	1.11494i
$335$	−6.40173e8	−	4.65113e8i	−0.930338	−	0.675930i
$336$		0			0
$337$	−3.74276e7	+	1.15190e8i	−0.0532706	+	0.163950i	−0.974152	−	0.225892i	$-0.927470\pi$
$337$	−3.74276e7	+	1.15190e8i	−0.0532706	+	0.163950i	0.920882	+	0.389842i	$0.127470\pi$
$338$	−8.99661e7	−	2.76887e8i	−0.126727	−	0.390027i
$339$		0			0
$340$	2.78259e8			0.383949
$341$	760909.	+	1.61693e6i	0.00103918	+	0.00220826i
$342$		0			0
$343$	2.88513e8	−	2.09617e8i	0.386043	−	0.280476i
$344$	−1.28219e8	−	3.94617e8i	−0.169824	−	0.522663i
$345$		0			0
$346$	−1.17351e9	−	8.52605e8i	−1.52307	−	1.10658i
$347$	9.51483e8	+	6.91293e8i	1.22250	+	0.888196i	0.996305	−	0.0858869i	$-0.0273724\pi$
$347$	9.51483e8	+	6.91293e8i	1.22250	+	0.888196i	0.226192	+	0.974083i	$0.427372\pi$
$348$		0			0
$349$	−6.07346e7	−	1.86922e8i	−0.0764798	−	0.235381i	0.905507	−	0.424332i	$-0.139491\pi$
$349$	−6.07346e7	−	1.86922e8i	−0.0764798	−	0.235381i	−0.981986	+	0.188951i	$0.939491\pi$
$350$	9.54053e8	−	6.93160e8i	1.18942	−	0.864163i
$351$		0			0
$352$	−1.69258e8	+	8.87377e8i	−0.206847	+	1.08445i
$353$	8.45816e8			1.02345			0.511723	−	0.859151i	$-0.329008\pi$
$353$	8.45816e8			1.02345			0.511723	+	0.859151i	$0.329008\pi$
$354$		0			0
$355$	−1.69274e7	−	5.20970e7i	−0.0200812	−	0.0618036i
$356$	−1.95854e8	+	6.02777e8i	−0.230069	+	0.708078i
$357$		0			0
$358$	−1.90141e9	−	1.38145e9i	−2.19021	−	1.59128i
$359$	1.73046e8	−	5.32581e8i	0.197393	−	0.607513i	−0.802547	−	0.596588i	$-0.796523\pi$
$359$	1.73046e8	−	5.32581e8i	0.197393	−	0.607513i	0.999940	−	0.0109245i	$-0.00347745\pi$
$360$		0			0
$361$	−1.69542e9	+	1.23179e9i	−1.89671	+	1.37804i
$362$	3.96375e8			0.439163
$363$		0			0
$364$	2.44170e9			2.65361
$365$	−1.55349e8	+	1.12868e8i	−0.167218	+	0.121491i
$366$		0			0
$367$	−1.88833e8	+	5.81167e8i	−0.199410	+	0.613719i	0.800487	+	0.599350i	$0.204574\pi$
$367$	−1.88833e8	+	5.81167e8i	−0.199410	+	0.613719i	−0.999897	+	0.0143696i	$0.995426\pi$
$368$	−1.22821e8	−	8.92346e7i	−0.128471	−	0.0933396i
$369$		0			0
$370$	−2.53237e7	+	7.79382e7i	−0.0259908	+	0.0799916i
$371$	9.02934e8	+	2.77894e9i	0.918010	+	2.82534i
$372$		0			0
$373$	−3.58887e8			−0.358078			−0.179039	−	0.983842i	$-0.557299\pi$
$373$	−3.58887e8			−0.358078			−0.179039	+	0.983842i	$0.557299\pi$
$374$	−1.18892e8	+	6.23319e8i	−0.117517	+	0.616113i
$375$		0			0
$376$	8.92296e8	−	6.48291e8i	0.865668	−	0.628944i
$377$	−2.70203e8	−	8.31599e8i	−0.259714	−	0.799317i
$378$		0			0
$379$	−4.89358e8	−	3.55540e8i	−0.461732	−	0.335468i	0.332479	−	0.943111i	$-0.392115\pi$
$379$	−4.89358e8	−	3.55540e8i	−0.461732	−	0.335468i	−0.794210	+	0.607643i	$0.792115\pi$
$380$	1.54891e9	+	1.12535e9i	1.44805	+	1.05207i
$381$		0			0
$382$	−1.39076e8	−	4.28030e8i	−0.127652	−	0.392874i
$383$	−2.88644e8	+	2.09712e8i	−0.262522	+	0.190734i	−0.711258	−	0.702931i	$-0.751874\pi$
$383$	−2.88644e8	+	2.09712e8i	−0.262522	+	0.190734i	0.448736	+	0.893664i	$0.351874\pi$
$384$		0			0
$385$	−4.56068e8	−	9.69143e8i	−0.407302	−	0.865516i
$386$	−2.03801e8			−0.180364
$387$		0			0
$388$	5.62937e8	+	1.73254e9i	0.489270	+	1.50582i
$389$	−2.03003e8	+	6.24780e8i	−0.174856	+	0.538150i	−0.999627	−	0.0273163i	$-0.991304\pi$
$389$	−2.03003e8	+	6.24780e8i	−0.174856	+	0.538150i	0.824771	+	0.565467i	$0.191304\pi$
$390$		0			0
$391$	−4.44022e8	−	3.22601e8i	−0.375652	−	0.272927i
$392$	−4.30650e8	+	1.32541e9i	−0.361097	+	1.11134i
$393$		0			0
$394$	1.30655e9	−	9.49262e8i	1.07619	−	0.781897i
$395$	−1.51868e7			−0.0123987
$396$		0			0
$397$	1.89013e9			1.51609			0.758045	−	0.652202i	$-0.226155\pi$
$397$	1.89013e9			1.51609			0.758045	+	0.652202i	$0.226155\pi$
$398$	−3.92062e8	+	2.84850e8i	−0.311720	+	0.226478i
$399$		0			0
$400$	3.20802e7	−	9.87326e7i	0.0250626	−	0.0771348i
$401$	2.23476e8	+	1.62365e8i	0.173072	+	0.125744i	0.670949	−	0.741504i	$-0.265887\pi$
$401$	2.23476e8	+	1.62365e8i	0.173072	+	0.125744i	−0.497877	+	0.867247i	$0.665887\pi$
$402$		0			0
$403$	1.11076e6	−	3.41856e6i	0.000845380	−	0.00260181i
$404$	−6.92376e8	−	2.13091e9i	−0.522405	−	1.60780i
$405$		0			0
$406$	2.45887e9			1.82345
$407$	−9.97037e7	−	5.48099e7i	−0.0733045	−	0.0402976i
$408$		0			0
$409$	−5.51045e8	+	4.00358e8i	−0.398250	+	0.289345i	−0.768828	−	0.639456i	$-0.779160\pi$
$409$	−5.51045e8	+	4.00358e8i	−0.398250	+	0.289345i	0.370578	+	0.928801i	$0.379160\pi$
$410$	−2.82175e8	−	8.68445e8i	−0.202197	−	0.622298i
$411$		0			0
$412$	2.14079e9	+	1.55537e9i	1.50811	+	1.09571i
$413$	−6.06307e8	−	4.40508e8i	−0.423514	−	0.307701i
$414$		0			0
$415$	3.61528e8	+	1.11267e9i	0.248298	+	0.764183i
$416$	1.47005e9	−	1.06806e9i	1.00117	−	0.727391i
$417$		0			0
$418$	−3.18266e9	+	2.98883e9i	−2.13144	+	2.00163i
$419$	6.46609e8			0.429430			0.214715	−	0.976677i	$-0.431118\pi$
$419$	6.46609e8			0.429430			0.214715	+	0.976677i	$0.431118\pi$
$420$		0			0
$421$	7.90791e8	+	2.43381e9i	0.516505	+	1.58964i	0.780527	+	0.625122i	$0.214951\pi$
$421$	7.90791e8	+	2.43381e9i	0.516505	+	1.58964i	−0.264022	+	0.964517i	$0.585049\pi$
$422$	8.39244e8	−	2.58293e9i	0.543619	−	1.67309i
$423$		0			0
$424$	−2.20593e9	−	1.60270e9i	−1.40544	−	1.02111i
$425$	1.15976e8	−	3.56938e8i	0.0732838	−	0.225544i
$426$		0			0
$427$	1.28712e8	−	9.35149e7i	0.0800060	−	0.0581277i
$428$	−4.26623e9			−2.63021
$429$		0			0
$430$	1.02419e9			0.621213
$431$	−1.91919e9	+	1.39437e9i	−1.15464	+	0.838895i	−0.989091	−	0.147307i	$-0.952940\pi$
$431$	−1.91919e9	+	1.39437e9i	−1.15464	+	0.838895i	−0.165549	+	0.986202i	$0.552940\pi$
$432$		0			0
$433$	−1.51408e7	+	4.65986e7i	−0.00896274	+	0.0275845i	−0.955438	−	0.295192i	$-0.904616\pi$
$433$	−1.51408e7	+	4.65986e7i	−0.00896274	+	0.0275845i	0.946475	+	0.322777i	$0.104616\pi$
$434$	8.17756e6	+	5.94134e6i	0.00480186	+	0.00348876i
$435$		0			0
$436$	5.77380e8	−	1.77699e9i	0.333625	−	1.02679i
$437$	−1.16694e9	−	3.59147e9i	−0.668902	−	2.05867i
$438$		0			0
$439$	7.52328e8			0.424406			0.212203	−	0.977226i	$-0.431936\pi$
$439$	7.52328e8			0.424406			0.212203	+	0.977226i	$0.431936\pi$
$440$	8.75886e8	+	4.81500e8i	0.490189	+	0.269471i
$441$		0			0
$442$	1.03261e9	−	7.50234e8i	0.568798	−	0.413256i
$443$	9.65215e8	+	2.97063e9i	0.527486	+	1.62343i	0.759347	+	0.650686i	$0.225518\pi$
$443$	9.65215e8	+	2.97063e9i	0.527486	+	1.62343i	−0.231861	+	0.972749i	$0.574482\pi$
$444$		0			0
$445$	−4.52429e8	−	3.28709e8i	−0.243383	−	0.176828i
$446$	−3.39202e9	−	2.46445e9i	−1.81045	−	1.31537i
$447$		0			0
$448$	1.45900e9	+	4.49035e9i	0.766625	+	2.35943i
$449$	−1.02122e9	+	7.41961e8i	−0.532424	+	0.386829i	−0.821264	−	0.570549i	$-0.806731\pi$
$449$	−1.02122e9	+	7.41961e8i	−0.532424	+	0.386829i	0.288839	+	0.957378i	$0.406731\pi$
$450$		0			0
$451$	1.25777e9	−	1.58919e8i	0.645632	−	0.0815754i
$452$	−2.98431e9			−1.52005
$453$		0			0
$454$	−1.01953e9	−	3.13780e9i	−0.511336	−	1.57373i
$455$	−6.65758e8	+	2.04899e9i	−0.331342	+	1.01977i
$456$		0			0
$457$	3.10601e8	+	2.25665e8i	0.152229	+	0.110601i	0.661292	−	0.750128i	$-0.270008\pi$
$457$	3.10601e8	+	2.25665e8i	0.152229	+	0.110601i	−0.509064	+	0.860729i	$0.670008\pi$
$458$	9.51403e8	−	2.92812e9i	0.462738	−	1.42416i
$459$		0			0
$460$	−1.95654e9	+	1.42151e9i	−0.937209	+	0.680922i
$461$	3.37922e8			0.160643			0.0803217	−	0.996769i	$-0.474405\pi$
$461$	3.37922e8			0.160643			0.0803217	+	0.996769i	$0.474405\pi$
$462$		0			0
$463$	−3.20754e9			−1.50189			−0.750946	−	0.660364i	$-0.770402\pi$
$463$	−3.20754e9			−1.50189			−0.750946	+	0.660364i	$0.770402\pi$
$464$	1.75119e8	−	1.27231e8i	0.0813804	−	0.0591263i
$465$		0			0
$466$	−9.43362e8	+	2.90337e9i	−0.431845	+	1.32908i
$467$	2.42997e9	+	1.76548e9i	1.10406	+	0.802146i	0.981718	−	0.190342i	$-0.0609595\pi$
$467$	2.42997e9	+	1.76548e9i	1.10406	+	0.802146i	0.122342	+	0.992488i	$0.460960\pi$
$468$		0			0
$469$	1.92028e9	−	5.91002e9i	0.859528	−	2.64535i
$470$	8.41286e8	+	2.58921e9i	0.373767	+	1.15034i
$471$		0			0
$472$	6.99352e8			0.306125
$473$	−2.66420e8	+	1.39678e9i	−0.115759	+	0.606894i
$474$		0			0
$475$	2.08912e9	−	1.51783e9i	0.894407	−	0.649825i
$476$	6.75265e8	+	2.07825e9i	0.286979	+	0.883231i
$477$		0			0
$478$	−2.10925e9	−	1.53246e9i	−0.883345	−	0.641788i
$479$	−2.52424e9	−	1.83397e9i	−1.04944	−	0.762459i	−0.0773304	−	0.997006i	$-0.524640\pi$
$479$	−2.52424e9	−	1.83397e9i	−1.04944	−	0.762459i	−0.972105	+	0.234546i	$0.924640\pi$
$480$		0			0
$481$	7.07197e7	+	2.17653e8i	0.0289756	+	0.0891778i
$482$	−1.85430e9	+	1.34723e9i	−0.754251	+	0.547996i
$483$		0			0
$484$	−2.47439e9	+	2.99127e9i	−0.991995	+	1.19921i
$485$	−1.60738e9			−0.639770
$486$		0			0
$487$	−3.05153e8	−	9.39164e8i	−0.119720	−	0.368460i	0.873182	−	0.487394i	$-0.162052\pi$
$487$	−3.05153e8	−	9.39164e8i	−0.119720	−	0.368460i	−0.992902	+	0.118934i	$0.962052\pi$
$488$	−4.58781e7	+	1.41198e8i	−0.0178705	+	0.0549996i
$489$		0			0
$490$	−2.78298e9	−	2.02196e9i	−1.06862	−	0.776400i
$491$	−1.25938e9	+	3.87598e9i	−0.480145	+	1.47773i	0.358747	+	0.933435i	$0.383204\pi$
$491$	−1.25938e9	+	3.87598e9i	−0.480145	+	1.47773i	−0.838892	+	0.544298i	$0.816796\pi$
$492$		0			0
$493$	6.33090e8	−	4.59967e8i	0.237958	−	0.172887i
$494$	8.78207e9			3.27757
$495$		0			0
$496$	889826.			0.000327431
$497$	3.48022e8	−	2.52853e8i	0.127163	−	0.0923891i
$498$		0			0
$499$	−1.01148e8	+	3.11300e8i	−0.0364421	+	0.112157i	−0.967623	−	0.252401i	$-0.918780\pi$
$499$	−1.01148e8	+	3.11300e8i	−0.0364421	+	0.112157i	0.931181	+	0.364558i	$0.118780\pi$
$500$	−3.55108e9	−	2.58001e9i	−1.27047	−	0.923054i
$501$		0			0
$502$	2.64076e9	−	8.12743e9i	0.931679	−	2.86741i
$503$	−8.32734e8	−	2.56289e9i	−0.291755	−	0.897930i	−0.984292	−	0.176547i	$-0.943507\pi$
$503$	−8.32734e8	−	2.56289e9i	−0.291755	−	0.897930i	0.692537	−	0.721382i	$-0.256493\pi$
$504$		0			0
$505$	1.97698e9			0.683097
$506$	−2.34831e9	−	4.99015e9i	−0.805803	−	1.71233i
$507$		0			0
$508$	−3.85591e9	+	2.80148e9i	−1.30498	+	0.948123i
$509$	1.49672e8	+	4.60643e8i	0.0503070	+	0.154829i	0.973054	−	0.230577i	$-0.0740614\pi$
$509$	1.49672e8	+	4.60643e8i	0.0503070	+	0.154829i	−0.922747	+	0.385406i	$0.874061\pi$
$510$		0			0
$511$	−1.21998e9	−	8.86365e8i	−0.404463	−	0.293859i
$512$	6.57124e8	+	4.77428e8i	0.216373	+	0.157204i
$513$		0			0
$514$	−1.46649e9	−	4.51339e9i	−0.476330	−	1.46599i
$515$	−1.88893e9	+	1.37239e9i	−0.609383	+	0.442743i
$516$		0			0
$517$	−3.74998e9	+	4.73808e8i	−1.19347	+	0.150795i
$518$	−6.43557e8			−0.203438
$519$		0			0
$520$	−6.21265e8	−	1.91206e9i	−0.193761	−	0.596334i
$521$	1.77189e8	−	5.45332e8i	0.0548915	−	0.168939i	−0.919852	−	0.392265i	$-0.871692\pi$
$521$	1.77189e8	−	5.45332e8i	0.0548915	−	0.168939i	0.974744	+	0.223326i	$0.0716916\pi$
$522$		0			0
$523$	1.58262e9	+	1.14984e9i	0.483749	+	0.351464i	0.802775	−	0.596282i	$-0.203356\pi$
$523$	1.58262e9	+	1.14984e9i	0.483749	+	0.351464i	−0.319027	+	0.947746i	$0.603356\pi$
$524$	−9.11359e8	+	2.80487e9i	−0.276713	+	0.851636i
$525$		0			0
$526$	−4.02613e9	+	2.92515e9i	−1.20625	+	0.876392i
$527$	3.21690e6			0.000957416
$528$		0			0
$529$	1.36529e9			0.400987
$530$	5.44505e9	−	3.95606e9i	1.58868	−	1.15424i
$531$		0			0
$532$	−4.64615e9	+	1.42994e10i	−1.33783	+	4.11743i
$533$	−2.06304e9	−	1.49889e9i	−0.590150	−	0.428769i
$534$		0			0
$535$	1.16324e9	−	3.58008e9i	0.328421	−	1.01078i
$536$	1.79195e9	+	5.51505e9i	0.502630	+	1.54694i
$537$		0			0
$538$	6.25917e9			1.73292
$539$	3.48145e9	−	3.26943e9i	0.957633	−	0.899313i
$540$		0			0
$541$	4.41144e8	−	3.20510e8i	0.119782	−	0.0870265i	−0.526282	−	0.850310i	$-0.676414\pi$
$541$	4.41144e8	−	3.20510e8i	0.119782	−	0.0870265i	0.646063	+	0.763284i	$0.276414\pi$
$542$	4.10843e8	+	1.26444e9i	0.110835	+	0.341116i
$543$		0			0
$544$	1.31563e9	+	9.55861e8i	0.350379	+	0.254565i
$545$	1.33377e9	+	9.69037e8i	0.352932	+	0.256420i
$546$		0			0
$547$	1.63217e9	+	5.02330e9i	0.426393	+	1.31230i	0.901654	+	0.432458i	$0.142353\pi$
$547$	1.63217e9	+	5.02330e9i	0.426393	+	1.31230i	−0.475261	+	0.879845i	$0.657647\pi$
$548$	4.55981e9	−	3.31289e9i	1.18363	−	0.859955i
$549$		0			0
$550$	2.74911e9	−	2.58169e9i	0.704569	−	0.661661i
$551$	5.38426e9			1.37118
$552$		0			0
$553$	−3.68545e7	−	1.13427e8i	−0.00926729	−	0.0285218i
$554$	−7.33397e8	+	2.25717e9i	−0.183255	+	0.564000i
$555$		0			0
$556$	−5.95674e9	−	4.32783e9i	−1.46976	−	1.06784i
$557$	−1.50249e9	+	4.62417e9i	−0.368398	+	1.13381i	0.579428	+	0.815023i	$0.303276\pi$
$557$	−1.50249e9	+	4.62417e9i	−0.368398	+	1.13381i	−0.947826	+	0.318788i	$0.896724\pi$
$558$		0			0
$559$	2.31394e9	−	1.68118e9i	0.560287	−	0.407072i
$560$	−5.33337e8			−0.128335
$561$		0			0
$562$	7.54343e8			0.179263
$563$	5.39962e9	−	3.92305e9i	1.27522	−	0.926498i	0.275818	−	0.961210i	$-0.411051\pi$
$563$	5.39962e9	−	3.92305e9i	1.27522	−	0.926498i	0.999397	+	0.0347116i	$0.0110513\pi$
$564$		0			0
$565$	8.13707e8	−	2.50433e9i	0.189801	−	0.584147i
$566$	−4.18244e9	−	3.03872e9i	−0.969555	−	0.704423i
$567$		0			0
$568$	−1.24049e8	+	3.81783e8i	−0.0284036	+	0.0874172i
$569$	−7.53527e8	−	2.31912e9i	−0.171477	−	0.527752i	0.827978	−	0.560761i	$-0.189491\pi$
$569$	−7.53527e8	−	2.31912e9i	−0.171477	−	0.527752i	−0.999455	+	0.0330084i	$0.989491\pi$
$570$		0			0
$571$	7.02799e9			1.57981			0.789904	−	0.613230i	$-0.210130\pi$
$571$	7.02799e9			1.57981			0.789904	+	0.613230i	$0.210130\pi$
$572$	7.74693e9	−	9.78823e8i	1.73079	−	0.218684i
$573$		0			0
$574$	5.80144e9	−	4.21500e9i	1.28040	−	0.930263i
$575$	1.00798e9	+	3.10224e9i	0.221113	+	0.680515i
$576$		0			0
$577$	7.37733e8	+	5.35994e8i	0.159876	+	0.116157i	0.664847	−	0.746980i	$-0.268497\pi$
$577$	7.37733e8	+	5.35994e8i	0.159876	+	0.116157i	−0.504971	+	0.863136i	$0.668497\pi$
$578$	−5.08087e9	−	3.69147e9i	−1.09444	−	0.795155i
$579$		0			0
$580$	−1.06555e9	−	3.27943e9i	−0.226765	−	0.697912i
$581$	−7.43293e9	+	5.40034e9i	−1.57233	+	1.14236i
$582$		0			0
$583$	3.97881e9	+	8.45497e9i	0.831599	+	1.76715i
$584$	1.40720e9			0.292354
$585$		0			0
$586$	2.74026e9	+	8.43366e9i	0.562536	+	1.73131i
$587$	1.83390e9	−	5.64416e9i	0.374233	−	1.15177i	−0.569762	−	0.821810i	$-0.692965\pi$
$587$	1.83390e9	−	5.64416e9i	0.374233	−	1.15177i	0.943995	−	0.329961i	$-0.107035\pi$
$588$		0			0
$589$	1.79066e7	+	1.30099e7i	0.00361086	+	0.00262344i
$590$	−5.33443e8	+	1.64177e9i	−0.106932	+	0.329102i
$591$		0			0
$592$	−4.58335e7	+	3.33000e7i	−0.00907941	+	0.00659657i
$593$	4.25088e9			0.837119			0.418560	−	0.908189i	$-0.362535\pi$
$593$	4.25088e9			0.837119			0.418560	+	0.908189i	$0.362535\pi$
$594$		0			0
$595$	−1.92812e9			−0.375254
$596$	7.32429e9	−	5.32141e9i	1.41711	−	1.02959i
$597$		0			0
$598$	−3.42801e9	+	1.05503e10i	−0.655524	+	2.01749i
$599$	2.79010e9	+	2.02713e9i	0.530427	+	0.385378i	0.820518	−	0.571621i	$-0.193685\pi$
$599$	2.79010e9	+	2.02713e9i	0.530427	+	0.385378i	−0.290090	+	0.956999i	$0.593685\pi$
$600$		0			0
$601$	−2.55371e9	+	7.85951e9i	−0.479856	+	1.47685i	0.359439	+	0.933169i	$0.382968\pi$
$601$	−2.55371e9	+	7.85951e9i	−0.479856	+	1.47685i	−0.839295	+	0.543677i	$0.817032\pi$
$602$	2.48545e9	+	7.64944e9i	0.464320	+	1.42903i
$603$		0			0
$604$	1.35809e10			2.50783
$605$	−1.83550e9	−	2.89203e9i	−0.336986	−	0.530957i
$606$		0			0
$607$	−2.30461e9	+	1.67440e9i	−0.418251	+	0.303877i	−0.776934	−	0.629582i	$-0.783226\pi$
$607$	−2.30461e9	+	1.67440e9i	−0.418251	+	0.303877i	0.358683	+	0.933460i	$0.383226\pi$
$608$	3.45762e9	+	1.06415e10i	0.623899	+	1.92017i
$609$		0			0
$610$	−2.96477e8	−	2.15403e8i	−0.0528855	−	0.0384236i
$611$	6.15082e9	+	4.46883e9i	1.09091	+	0.792592i
$612$		0			0
$613$	−1.38822e9	−	4.27249e9i	−0.243414	−	0.749152i	−0.995893	−	0.0905356i	$-0.971142\pi$
$613$	−1.38822e9	−	4.27249e9i	−0.243414	−	0.749152i	0.752479	−	0.658616i	$-0.228858\pi$
$614$	−1.27438e10	+	9.25889e9i	−2.22182	+	1.61425i
$615$		0			0
$616$	−1.47065e9	+	7.71027e9i	−0.253500	+	1.32904i
$617$	−7.29433e9			−1.25022			−0.625111	−	0.780536i	$-0.714946\pi$
$617$	−7.29433e9			−1.25022			−0.625111	+	0.780536i	$0.714946\pi$
$618$		0			0
$619$	−3.10846e9	−	9.56686e9i	−0.526779	−	1.62126i	−0.760771	−	0.649020i	$-0.775179\pi$
$619$	−3.10846e9	−	9.56686e9i	−0.526779	−	1.62126i	0.233992	−	0.972238i	$-0.424821\pi$
$620$	4.38031e6	−	1.34812e7i	0.000738131	−	0.00227173i
$621$		0			0
$622$	−1.44180e10	−	1.04753e10i	−2.40236	−	1.74542i
$623$	1.35712e9	−	4.17678e9i	0.224858	−	0.692043i
$624$		0			0
$625$	1.48258e8	−	1.07716e8i	0.0242907	−	0.0176482i
$626$	1.75075e10			2.85243
$627$		0			0
$628$	1.33833e10			2.15628
$629$	−1.65697e8	+	1.20386e8i	−0.0265484	+	0.0192886i
$630$		0			0
$631$	5.90655e8	−	1.81785e9i	0.0935903	−	0.288041i	−0.893293	−	0.449474i	$-0.851611\pi$
$631$	5.90655e8	−	1.81785e9i	0.0935903	−	0.288041i	0.986884	+	0.161433i	$0.0516114\pi$
$632$	9.00381e7	+	6.54165e7i	0.0141879	+	0.0103081i
$633$		0			0
$634$	2.63835e9	−	8.12001e9i	0.411169	−	1.26545i
$635$	−1.29955e9	−	3.99961e9i	−0.201412	−	0.619883i
$636$		0			0
$637$	−9.60654e9			−1.47258
$638$	7.80143e9	−	9.85708e8i	1.18933	−	0.150271i
$639$		0			0
$640$	5.07345e9	−	3.68608e9i	0.765022	−	0.555821i
$641$	2.07873e9	+	6.39768e9i	0.311742	+	0.959444i	0.977075	+	0.212897i	$0.0682899\pi$
$641$	2.07873e9	+	6.39768e9i	0.311742	+	0.959444i	−0.665332	+	0.746547i	$0.731710\pi$
$642$		0			0
$643$	−1.96467e9	−	1.42742e9i	−0.291441	−	0.211745i	0.432451	−	0.901657i	$-0.357649\pi$
$643$	−1.96467e9	−	1.42742e9i	−0.291441	−	0.211745i	−0.723892	+	0.689913i	$0.757649\pi$
$644$	−1.53650e10	−	1.11633e10i	−2.26689	−	1.64699i
$645$		0			0
$646$	2.42873e9	+	7.47487e9i	0.354459	+	1.09091i
$647$	−3.37054e9	+	2.44884e9i	−0.489255	+	0.355464i	−0.804898	−	0.593414i	$-0.797780\pi$
$647$	−3.37054e9	+	2.44884e9i	−0.489255	+	0.355464i	0.315643	+	0.948878i	$0.397780\pi$
$648$		0			0
$649$	−2.10026e9	−	1.15457e9i	−0.301590	−	0.165792i
$650$	−7.58578e9			−1.08344
$651$		0			0
$652$	−5.19276e9	−	1.59817e10i	−0.733722	−	2.25817i
$653$	2.07125e9	−	6.37467e9i	0.291097	−	0.895904i	−0.693408	−	0.720545i	$-0.743892\pi$
$653$	2.07125e9	−	6.37467e9i	0.291097	−	0.895904i	0.984505	−	0.175358i	$-0.0561084\pi$
$654$		0			0
$655$	−2.10527e9	−	1.52957e9i	−0.292727	−	0.212679i
$656$	1.95074e8	−	6.00377e8i	0.0269797	−	0.0830349i
$657$		0			0
$658$	−1.72966e10	+	1.25667e10i	−2.36685	+	1.71962i
$659$	−4.65151e8			−0.0633133			−0.0316567	−	0.999499i	$-0.510078\pi$
$659$	−4.65151e8			−0.0633133			−0.0316567	+	0.999499i	$0.510078\pi$
$660$		0			0
$661$	1.10868e10			1.49315			0.746573	−	0.665304i	$-0.231698\pi$
$661$	1.10868e10			1.49315			0.746573	+	0.665304i	$0.231698\pi$
$662$	−1.22248e10	+	8.88182e9i	−1.63771	+	1.18987i
$663$		0			0
$664$	2.64939e9	−	8.15397e9i	0.351202	−	1.08089i
$665$	−1.07327e10	−	7.79779e9i	−1.41526	−	1.02824i
$666$		0			0
$667$	−2.10171e9	+	6.46839e9i	−0.274241	+	0.844026i
$668$	−2.71669e9	−	8.36112e9i	−0.352633	−	1.08529i
$669$		0			0
$670$	−1.43138e10			−1.83862
$671$	3.70886e8	−	3.48299e8i	0.0473927	−	0.0445065i
$672$		0			0
$673$	−8.53975e9	+	6.20449e9i	−1.07992	+	0.784610i	−0.977669	−	0.210149i	$-0.932605\pi$
$673$	−8.53975e9	+	6.20449e9i	−1.07992	+	0.784610i	−0.102253	+	0.994758i	$0.532605\pi$
$674$	6.77027e8	+	2.08367e9i	0.0851719	+	0.262132i
$675$		0			0
$676$	−2.59390e9	−	1.88458e9i	−0.322953	−	0.234639i
$677$	−8.34558e9	−	6.06342e9i	−1.03370	−	0.751030i	−0.0646572	−	0.997908i	$-0.520595\pi$
$677$	−8.34558e9	−	6.06342e9i	−1.03370	−	0.751030i	−0.969047	+	0.246878i	$0.920595\pi$
$678$		0			0
$679$	−3.90072e9	−	1.20052e10i	−0.478190	−	1.47172i
$680$	1.45564e9	−	1.05758e9i	0.177530	−	0.128983i
$681$		0			0
$682$	2.83272e7	+	1.55723e7i	0.00341947	+	0.00187978i
$683$	4.71279e9			0.565986			0.282993	−	0.959122i	$-0.408673\pi$
$683$	4.71279e9			0.565986			0.282993	+	0.959122i	$0.408673\pi$
$684$		0			0
$685$	1.53679e9	+	4.72974e9i	0.182682	+	0.562239i
$686$	1.99344e9	−	6.13518e9i	0.235759	−	0.725592i
$687$		0			0
$688$	5.72822e8	+	4.16180e8i	0.0670595	+	0.0487216i
$689$	5.80819e9	−	1.78758e10i	0.676509	−	2.08208i
$690$		0			0
$691$	−7.33884e9	+	5.33198e9i	−0.846164	+	0.614774i	−0.924086	−	0.382186i	$-0.875171\pi$
$691$	−7.33884e9	+	5.33198e9i	−0.846164	+	0.614774i	0.0779220	+	0.996959i	$0.475171\pi$
$692$	−1.59745e10			−1.83255
$693$		0			0
$694$	2.12744e10			2.41601
$695$	5.25595e9	−	3.81867e9i	0.593888	−	0.431485i
$696$		0			0
$697$	7.05233e8	−	2.17048e9i	0.0788892	−	0.242796i
$698$	−2.87624e9	−	2.08971e9i	−0.320133	−	0.232590i
$699$		0			0
$700$	4.01325e9	−	1.23515e10i	0.442235	−	1.36106i
$701$	−2.60419e9	−	8.01489e9i	−0.285536	−	0.878788i	−0.986238	−	0.165334i	$-0.947130\pi$
$701$	−2.60419e9	−	8.01489e9i	−0.285536	−	0.878788i	0.700702	−	0.713454i	$-0.252870\pi$
$702$		0			0
$703$	−1.40921e9			−0.152979
$704$	6.42915e9	+	1.36619e10i	0.694463	+	1.47573i
$705$		0			0
$706$	1.23779e10	−	8.99308e9i	1.32383	−	0.961816i
$707$	4.79763e9	+	1.47656e10i	0.510575	+	1.57139i
$708$		0			0
$709$	−7.85642e8	−	5.70802e8i	−0.0827871	−	0.0601484i	0.545622	−	0.838032i	$-0.316294\pi$
$709$	−7.85642e8	−	5.70802e8i	−0.0827871	−	0.0601484i	−0.628409	+	0.777883i	$0.716294\pi$
$710$	−8.01637e8	−	5.82424e8i	−0.0840570	−	0.0610710i
$711$		0			0
$712$	1.26642e9	+	3.89764e9i	0.131492	+	0.404689i
$713$	−2.26192e7	+	1.64338e7i	−0.00233703	+	0.00169795i
$714$		0			0
$715$	−1.29090e9	+	6.76786e9i	−0.132075	+	0.692437i
$716$	−2.58831e10			−2.63524
$717$		0			0
$718$	−3.13023e9	−	9.63384e9i	−0.315602	−	0.971324i
$719$	−4.43918e9	+	1.36624e10i	−0.445402	+	1.37081i	0.436641	+	0.899636i	$0.356168\pi$
$719$	−4.43918e9	+	1.36624e10i	−0.445402	+	1.37081i	−0.882042	+	0.471170i	$0.843832\pi$
$720$		0			0
$721$	−1.48340e10	−	1.07775e10i	−1.47396	−	1.07089i
$722$	−1.17143e10	+	3.60528e10i	−1.15834	+	3.56500i
$723$		0			0
$724$	3.53153e9	−	2.56580e9i	0.345842	−	0.251269i
$725$	−4.65082e9			−0.453259
$726$		0			0
$727$	3.30169e9			0.318688			0.159344	−	0.987223i	$-0.449062\pi$
$727$	3.30169e9			0.318688			0.159344	+	0.987223i	$0.449062\pi$
$728$	1.27731e10	−	9.28017e9i	1.22697	−	0.891448i
$729$		0			0
$730$	−1.07336e9	+	3.30348e9i	−0.102121	+	0.314298i
$731$	2.07087e9	+	1.50457e9i	0.196084	+	0.142463i
$732$		0			0
$733$	−5.85628e9	+	1.80238e10i	−0.549235	+	1.69037i	0.161467	+	0.986878i	$0.448377\pi$
$733$	−5.85628e9	+	1.80238e10i	−0.549235	+	1.69037i	−0.710702	+	0.703493i	$0.751623\pi$
$734$	3.41579e9	+	1.05127e10i	0.318827	+	0.981247i
$735$		0			0
$736$	−1.41338e10			−1.30673
$737$	3.72341e9	−	1.95209e10i	0.342613	−	1.79624i
$738$		0			0
$739$	1.97509e9	−	1.43499e9i	0.180024	−	0.130795i	−0.494124	−	0.869392i	$-0.664511\pi$
$739$	1.97509e9	−	1.43499e9i	0.180024	−	0.130795i	0.674148	+	0.738596i	$0.264511\pi$
$740$	2.78885e8	+	8.58320e8i	0.0252996	+	0.0778642i
$741$		0			0
$742$	4.27607e10	+	3.10675e10i	3.84265	+	2.79185i
$743$	−3.02904e8	−	2.20073e8i	−0.0270922	−	0.0196836i	0.574157	−	0.818745i	$-0.305330\pi$
$743$	−3.02904e8	−	2.20073e8i	−0.0270922	−	0.0196836i	−0.601249	+	0.799062i	$0.705330\pi$
$744$		0			0
$745$	2.46850e9	+	7.59725e9i	0.218719	+	0.673146i
$746$	−5.25206e9	+	3.81584e9i	−0.463173	+	0.336515i
$747$		0			0
$748$	2.97558e9	+	6.32311e9i	0.259966	+	0.552427i
$749$	2.95617e10			2.57065
$750$		0			0
$751$	−1.85696e9	−	5.71512e9i	−0.159979	−	0.492363i	0.838653	−	0.544667i	$-0.183344\pi$
$751$	−1.85696e9	−	5.71512e9i	−0.159979	−	0.492363i	−0.998631	+	0.0523031i	$0.983344\pi$
$752$	−5.81602e8	+	1.78999e9i	−0.0498727	+	0.153492i
$753$		0			0
$754$	−1.27961e10	−	9.29693e9i	−1.08712	−	0.789842i
$755$	−3.70299e9	+	1.13966e10i	−0.313139	+	0.963744i
$756$		0			0
$757$	8.14660e9	−	5.91885e9i	0.682560	−	0.495909i	−0.191646	−	0.981464i	$-0.561382\pi$
$757$	8.14660e9	−	5.91885e9i	0.682560	−	0.495909i	0.874206	+	0.485555i	$0.161382\pi$
$758$	−1.09417e10			−0.912516
$759$		0			0
$760$	1.23798e10			1.02298
$761$	−4.73927e9	+	3.44328e9i	−0.389821	+	0.283221i	−0.765382	−	0.643576i	$-0.777450\pi$
$761$	−4.73927e9	+	3.44328e9i	−0.389821	+	0.283221i	0.375561	+	0.926798i	$0.377450\pi$
$762$		0			0
$763$	−4.00080e9	+	1.23132e10i	−0.326070	+	1.00354i
$764$	−4.00982e9	−	2.91330e9i	−0.325310	−	0.236352i
$765$		0			0
$766$	−1.99435e9	+	6.13797e9i	−0.160324	+	0.493428i
$767$	1.48971e9	+	4.58486e9i	0.119212	+	0.366896i
$768$		0			0
$769$	8.07351e9			0.640206			0.320103	−	0.947383i	$-0.396282\pi$
$769$	8.07351e9			0.640206			0.320103	+	0.947383i	$0.396282\pi$
$770$	−1.69786e10	−	9.33360e9i	−1.34024	−	0.736769i
$771$		0			0
$772$	−1.81578e9	+	1.31924e9i	−0.142037	+	0.103196i
$773$	−5.66215e9	−	1.74263e10i	−0.440913	−	1.35699i	−0.886904	−	0.461954i	$-0.847148\pi$
$773$	−5.66215e9	−	1.74263e10i	−0.440913	−	1.35699i	0.445991	−	0.895038i	$-0.352852\pi$
$774$		0			0
$775$	−1.54674e7	−	1.12377e7i	−0.00119361	−	0.000867206i
$776$	9.52973e9	+	6.92376e9i	0.732090	+	0.531895i
$777$		0			0
$778$	3.67212e9	+	1.13016e10i	0.279569	+	0.860423i
$779$	1.27036e10	−	9.22969e9i	0.962820	−	0.699530i
$780$		0			0
$781$	1.00283e9	−	9.41757e8i	0.0753266	−	0.0707392i
$782$	−9.92797e9			−0.742398
$783$		0			0
$784$	−7.34881e8	−	2.26173e9i	−0.0544642	−	0.167623i
$785$	−3.64913e9	+	1.12309e10i	−0.269244	+	0.828647i
$786$		0			0
$787$	6.45322e9	+	4.68854e9i	0.471916	+	0.342867i	0.798187	−	0.602409i	$-0.205792\pi$
$787$	6.45322e9	+	4.68854e9i	0.471916	+	0.342867i	−0.326272	+	0.945276i	$0.605792\pi$
$788$	5.49602e9	−	1.69150e10i	0.400135	−	1.23149i
$789$		0			0
$790$	−2.22248e8	+	1.61472e8i	−0.0160377	+	0.0116521i
$791$	2.06789e10			1.48563
$792$		0			0
$793$	−1.02340e9			−0.0728771
$794$	2.76607e10	−	2.00967e10i	1.96106	−	1.42479i
$795$		0			0
$796$	−1.64922e9	+	5.07578e9i	−0.115900	+	0.356703i
$797$	−1.06135e10	−	7.71115e9i	−0.742599	−	0.539529i	0.150925	−	0.988545i	$-0.451775\pi$
$797$	−1.06135e10	−	7.71115e9i	−0.742599	−	0.539529i	−0.893524	+	0.449016i	$0.851775\pi$
$798$		0			0
$799$	−2.10261e9	+	6.47116e9i	−0.145829	+	0.448816i
$800$	−2.98662e9	−	9.19188e9i	−0.206236	−	0.634730i
$801$		0			0
$802$	4.99674e9			0.342040
$803$	−4.22602e9	−	2.32317e9i	−0.288023	−	0.158335i
$804$		0			0
$805$	1.35573e10	−	9.84997e9i	0.915985	−	0.665502i
$806$	−2.00925e7	−	6.18383e7i	−0.00135164	−	0.00415992i
$807$		0			0
$808$	−1.17210e10	−	8.51577e9i	−0.781670	−	0.567916i
$809$	−1.56855e10	−	1.13962e10i	−1.04154	−	0.756727i	−0.0709583	−	0.997479i	$-0.522606\pi$
$809$	−1.56855e10	−	1.13962e10i	−1.04154	−	0.756727i	−0.970586	+	0.240753i	$0.922606\pi$
$810$		0			0
$811$	−1.51642e9	−	4.66708e9i	−0.0998270	−	0.307236i	0.888655	−	0.458577i	$-0.151641\pi$
$811$	−1.51642e9	−	4.66708e9i	−0.0998270	−	0.307236i	−0.988482	+	0.151341i	$0.951641\pi$
$812$	2.19075e10	−	1.59167e10i	1.43597	−	1.04330i
$813$		0			0
$814$	−2.04185e9	+	2.57988e8i	−0.132690	+	0.0167654i
$815$	1.48272e10			0.959416
$816$		0			0
$817$	5.44246e9	+	1.67502e10i	0.349155	+	1.07459i
$818$	−3.80737e9	+	1.17179e10i	−0.243214	+	0.748536i
$819$		0			0
$820$	−8.13565e9	−	5.91089e9i	−0.515280	−	0.374373i
$821$	2.83976e9	−	8.73987e9i	0.179094	−	0.551193i	−0.820703	−	0.571355i	$-0.806418\pi$
$821$	2.83976e9	−	8.73987e9i	0.179094	−	0.551193i	0.999797	+	0.0201614i	$0.00641802\pi$
$822$		0			0
$823$	−1.32266e10	+	9.60965e9i	−0.827080	+	0.600908i	−0.918732	−	0.394883i	$-0.870785\pi$
$823$	−1.32266e10	+	9.60965e9i	−0.827080	+	0.600908i	0.0916520	+	0.995791i	$0.470785\pi$
$824$	1.71104e10			1.06541
$825$		0			0
$826$	−1.35565e10			−0.836986
$827$	−1.86890e10	+	1.35784e10i	−1.14899	+	0.834791i	−0.988346	−	0.152221i	$-0.951357\pi$
$827$	−1.86890e10	+	1.35784e10i	−1.14899	+	0.834791i	−0.160645	+	0.987012i	$0.551357\pi$
$828$		0			0
$829$	3.31307e9	−	1.01966e10i	0.201971	−	0.621603i	−0.797853	−	0.602852i	$-0.794031\pi$
$829$	3.31307e9	−	1.01966e10i	0.201971	−	0.621603i	0.999824	−	0.0187513i	$-0.00596907\pi$
$830$	1.71211e10	+	1.24392e10i	1.03934	+	0.755125i
$831$		0			0
$832$	9.38514e9	−	2.88845e10i	0.564949	−	1.73873i
$833$	−2.65674e9	−	8.17661e9i	−0.159255	−	0.490135i
$834$		0			0
$835$	7.75712e9			0.461103
$836$	−9.00883e9	+	4.72311e10i	−0.533269	+	2.79580i
$837$		0			0
$838$	9.46266e9	−	6.87502e9i	0.555468	−	0.403571i
$839$	2.91853e9	+	8.98231e9i	0.170607	+	0.525075i	0.999406	−	0.0344723i	$-0.0109750\pi$
$839$	2.91853e9	+	8.98231e9i	0.170607	+	0.525075i	−0.828798	+	0.559547i	$0.810975\pi$
$840$		0			0
$841$	6.11017e9	+	4.43930e9i	0.354215	+	0.257352i
$842$	3.74499e10	+	2.72090e10i	2.16201	+	1.57080i
$843$		0			0
$844$	−9.24244e9	−	2.84453e10i	−0.529161	−	1.62859i
$845$	2.28873e9	−	1.66286e9i	0.130496	−	0.0948108i
$846$		0			0
$847$	1.71456e10	−	2.07272e10i	0.969531	−	1.17206i
$848$	4.65293e9			0.262024
$849$		0			0
$850$	−2.09789e9	−	6.45664e9i	−0.117170	−	0.360612i
$851$	5.50076e8	−	1.69296e9i	0.0305963	−	0.0941658i
$852$		0			0
$853$	−1.63704e10	−	1.18938e10i	−0.903103	−	0.656143i	0.0361584	−	0.999346i	$-0.488488\pi$
$853$	−1.63704e10	−	1.18938e10i	−0.903103	−	0.656143i	−0.939261	+	0.343204i	$0.888488\pi$
$854$	8.89321e8	−	2.73705e9i	0.0488603	−	0.150376i
$855$		0			0
$856$	−2.23176e10	+	1.62147e10i	−1.21616	+	0.883589i
$857$	−2.72057e10			−1.47648			−0.738238	−	0.674540i	$-0.764342\pi$
$857$	−2.72057e10			−1.47648			−0.738238	+	0.674540i	$0.764342\pi$
$858$		0			0
$859$	5.30465e9			0.285549			0.142775	−	0.989755i	$-0.454398\pi$
$859$	5.30465e9			0.285549			0.142775	+	0.989755i	$0.454398\pi$
$860$	9.12508e9	−	6.62976e9i	0.489206	−	0.355429i
$861$		0			0
$862$	−1.32604e10	+	4.08112e10i	−0.705147	+	2.17022i
$863$	1.40892e10	+	1.02364e10i	0.746188	+	0.542137i	0.894643	−	0.446782i	$-0.147430\pi$
$863$	1.40892e10	+	1.02364e10i	0.746188	+	0.542137i	−0.148455	+	0.988919i	$0.547430\pi$
$864$		0			0
$865$	4.35565e9	−	1.34053e10i	0.228821	−	0.704239i
$866$	2.73881e8	+	8.42919e8i	0.0143301	+	0.0441035i
$867$		0			0
$868$	1.11318e8			0.00577758
$869$	−1.62401e8	−	3.45102e8i	−0.00839497	−	0.0178393i
$870$		0			0
$871$	−3.23389e10	+	2.34956e10i	−1.65829	+	1.20482i
$872$	−3.73342e9	−	1.14903e10i	−0.190678	−	0.586845i
$873$		0			0
$874$	−5.52633e10	−	4.01511e10i	−2.79993	−	2.03427i
$875$	2.46063e10	+	1.78775e10i	1.24170	+	0.902150i
$876$		0			0
$877$	−7.68059e9	−	2.36384e10i	−0.384500	−	1.18337i	−0.936843	−	0.349751i	$-0.886266\pi$
$877$	−7.68059e9	−	2.36384e10i	−0.384500	−	1.18337i	0.552343	−	0.833617i	$-0.313734\pi$
$878$	1.10098e10	−	7.99907e9i	0.548969	−	0.398849i
$879$		0			0
$880$	−1.69215e9	+	2.13803e8i	−0.0837048	+	0.0105761i
$881$	9.02439e9			0.444634			0.222317	−	0.974974i	$-0.428638\pi$
$881$	9.02439e9			0.444634			0.222317	+	0.974974i	$0.428638\pi$
$882$		0			0
$883$	3.88678e9	+	1.19623e10i	0.189989	+	0.584725i	0.999999	−	0.00169147i	$-0.000538413\pi$
$883$	3.88678e9	+	1.19623e10i	0.189989	+	0.584725i	−0.810010	+	0.586416i	$0.800538\pi$
$884$	4.34370e9	−	1.33685e10i	0.211483	−	0.650879i
$885$		0			0
$886$	4.57102e10	+	3.32104e10i	2.20798	+	1.60419i
$887$	9.03164e9	−	2.77965e10i	0.434544	−	1.33739i	−0.459009	−	0.888432i	$-0.651795\pi$
$887$	9.03164e9	−	2.77965e10i	0.434544	−	1.33739i	0.893553	−	0.448958i	$-0.148205\pi$
$888$		0			0
$889$	2.67185e10	−	1.94121e10i	1.27543	−	0.926652i
$890$	−1.01159e10			−0.480995
$891$		0			0
$892$	−4.61742e10			−2.17832
$893$	−3.78749e10	+	2.75177e10i	−1.77980	+	1.29310i
$894$		0			0
$895$	7.05734e9	−	2.17203e10i	0.329049	−	1.01271i
$896$	3.98425e10	+	2.89473e10i	1.85041	+	1.34440i
$897$		0			0
$898$	−7.05600e9	+	2.17161e10i	−0.325156	+	1.00073i
$899$	−1.23186e7	−	3.79129e7i	−0.000565462	−	0.00174031i
$900$		0			0
$901$	1.68213e10			0.766165
$902$	1.67169e10	−	1.56989e10i	0.758461	−	0.712271i
$903$		0			0
$904$	−1.56116e10	+	1.13425e10i	−0.702841	+	0.510644i
$905$	1.19023e9	+	3.66314e9i	0.0533776	+	0.164280i
$906$		0			0
$907$	−3.01282e10	−	2.18894e10i	−1.34075	−	0.974112i	−0.999416	−	0.0341698i	$-0.989121\pi$
$907$	−3.01282e10	−	2.18894e10i	−1.34075	−	0.974112i	−0.341334	−	0.939942i	$-0.610879\pi$
$908$	−2.93951e10	−	2.13568e10i	−1.30309	−	0.946752i
$909$		0			0
$910$	1.20429e10	+	3.70642e10i	0.529767	+	1.63046i
$911$	−7.82497e9	+	5.68517e9i	−0.342901	+	0.249132i	−0.745885	−	0.666075i	$-0.767973\pi$
$911$	−7.82497e9	+	5.68517e9i	−0.342901	+	0.249132i	0.402984	+	0.915207i	$0.367973\pi$
$912$		0			0
$913$	−2.14181e10	+	2.01137e10i	−0.931392	+	0.874670i
$914$	6.94479e9			0.300848
$915$		0			0
$916$	−1.04776e10	−	3.22468e10i	−0.450432	−	1.38629i
$917$	6.31502e9	−	1.94356e10i	0.270447	−	0.832350i
$918$		0			0
$919$	1.65869e10	+	1.20511e10i	0.704955	+	0.512180i	0.881542	−	0.472105i	$-0.156506\pi$
$919$	1.65869e10	+	1.20511e10i	0.704955	+	0.512180i	−0.176587	+	0.984285i	$0.556506\pi$
$920$	−4.83236e9	+	1.48725e10i	−0.204598	+	0.629689i
$921$		0			0
$922$	4.94524e9	−	3.59293e9i	0.207792	−	0.150970i
$923$	−2.76716e9			−0.115832
$924$		0			0
$925$	1.21725e9			0.0505689
$926$	−4.69400e10	+	3.41039e10i	−1.94270	+	1.41145i
$927$		0			0
$928$	6.22732e9	−	1.91657e10i	0.255790	−	0.787240i
$929$	−4.22367e9	−	3.06867e9i	−0.172836	−	0.125573i	0.498004	−	0.867175i	$-0.334066\pi$
$929$	−4.22367e9	−	3.06867e9i	−0.172836	−	0.125573i	−0.670840	+	0.741602i	$0.734066\pi$
$930$		0			0
$931$	1.82797e10	−	5.62590e10i	0.742411	−	2.28490i
$932$	1.03891e10	+	3.19743e10i	0.420360	+	1.29374i
$933$		0			0
$934$	5.43323e10			2.18194
$935$	−6.11748e9	+	7.72942e8i	−0.244755	+	0.0309247i
$936$		0			0
$937$	1.99949e10	−	1.45272e10i	0.794020	−	0.576889i	−0.115134	−	0.993350i	$-0.536730\pi$
$937$	1.99949e10	−	1.45272e10i	0.794020	−	0.576889i	0.909154	+	0.416461i	$0.136730\pi$
$938$	−3.47359e10	−	1.06906e11i	−1.37426	−	4.22953i
$939$		0			0
$940$	2.42559e10	+	1.76230e10i	0.952512	+	0.692040i
$941$	1.38146e10	+	1.00369e10i	0.540474	+	0.392677i	0.824261	−	0.566210i	$-0.191591\pi$
$941$	1.38146e10	+	1.00369e10i	0.540474	+	0.392677i	−0.283787	+	0.958887i	$0.591591\pi$
$942$		0			0
$943$	6.12935e9	+	1.88642e10i	0.238025	+	0.732567i
$944$	−9.65484e8	+	7.01466e8i	−0.0373545	+	0.0271397i
$945$		0			0
$946$	1.09522e10	+	2.32735e10i	0.420614	+	0.893805i
$947$	−6.22527e8			−0.0238195			−0.0119098	−	0.999929i	$-0.503791\pi$
$947$	−6.22527e8			−0.0238195			−0.0119098	+	0.999929i	$0.503791\pi$
$948$		0			0
$949$	2.99751e9	+	9.22540e9i	0.113849	+	0.350391i
$950$	1.44345e10	−	4.44248e10i	0.546221	−	1.68110i
$951$		0			0
$952$	1.14313e10	+	8.30532e9i	0.429404	+	0.311980i
$953$	7.47165e9	−	2.29954e10i	0.279635	−	0.860627i	−0.708321	−	0.705890i	$-0.750547\pi$
$953$	7.47165e9	−	2.29954e10i	0.279635	−	0.860627i	0.987956	−	0.154737i	$-0.0494529\pi$
$954$		0			0
$955$	3.53807e9	−	2.57056e9i	0.131448	−	0.0955028i
$956$	−2.87124e10			−1.06284
$957$		0			0
$958$	−5.64399e10			−2.07399
$959$	−3.15960e10	+	2.29558e10i	−1.15682	+	0.840480i
$960$		0			0
$961$	−8.50181e9	+	2.61659e10i	−0.309015	+	0.951051i
$962$	3.34911e9	+	2.43327e9i	0.121288	+	0.0881206i
$963$		0			0
$964$	−7.80017e9	+	2.40065e10i	−0.280436	+	0.863094i
$965$	−6.11969e8	−	1.88345e9i	−0.0219222	−	0.0674695i
$966$		0			0
$967$	1.84531e10			0.656261			0.328131	−	0.944632i	$-0.393581\pi$
$967$	1.84531e10			0.656261			0.328131	+	0.944632i	$0.393581\pi$
$968$	−1.57516e9	+	2.50524e10i	−0.0558162	+	0.887741i
$969$		0			0
$970$	−2.35229e10	+	1.70904e10i	−0.827542	+	0.601245i
$971$	8.61419e9	+	2.65118e10i	0.301959	+	0.929333i	0.980795	+	0.195043i	$0.0624847\pi$
$971$	8.61419e9	+	2.65118e10i	0.301959	+	0.929333i	−0.678836	+	0.734290i	$0.737515\pi$
$972$		0			0
$973$	4.12756e10	+	2.99885e10i	1.43648	+	1.04366i
$974$	−1.44513e10	−	1.04995e10i	−0.501130	−	0.364092i
$975$		0			0
$976$	−7.82884e7	−	2.40947e8i	−0.00269540	−	0.00829558i
$977$	8.17776e9	−	5.94149e9i	0.280546	−	0.203828i	−0.438610	−	0.898678i	$-0.644529\pi$
$977$	8.17776e9	−	5.94149e9i	0.280546	−	0.203828i	0.719155	+	0.694849i	$0.244529\pi$
$978$		0			0
$979$	2.63144e9	−	1.37960e10i	0.0896300	−	0.469908i
$980$	−3.78836e10			−1.28576
$981$		0			0
$982$	2.27809e10	+	7.01124e10i	0.767681	+	2.36268i
$983$	−9.43328e9	+	2.90327e10i	−0.316757	+	0.974876i	0.658269	+	0.752783i	$0.271289\pi$
$983$	−9.43328e9	+	2.90327e10i	−0.316757	+	0.974876i	−0.975025	+	0.222093i	$0.928711\pi$
$984$		0			0
$985$	1.26960e10	+	9.22417e9i	0.423291	+	0.307539i
$986$	4.37425e9	−	1.34626e10i	0.145323	−	0.447258i
$987$		0			0
$988$	7.82444e10	−	5.68479e10i	2.58109	−	1.87527i
$989$	−2.22473e10			−0.731290
$990$		0			0
$991$	−1.35620e9			−0.0442655			−0.0221328	−	0.999755i	$-0.507046\pi$
$991$	−1.35620e9			−0.0442655			−0.0221328	+	0.999755i	$0.507046\pi$
$992$	6.70203e7	−	4.86931e7i	0.00217980	−	0.00158371i
$993$		0			0
$994$	2.40461e9	−	7.40064e9i	0.0776592	−	0.239010i
$995$	−3.80975e9	−	2.76794e9i	−0.122607	−	0.0890792i
$996$		0			0
$997$	1.95679e9	−	6.02239e9i	0.0625334	−	0.192458i	−0.914909	−	0.403660i	$-0.867738\pi$
$997$	1.95679e9	−	6.02239e9i	0.0625334	−	0.192458i	0.977442	+	0.211202i	$0.0677378\pi$
$998$	1.82965e9	+	5.63110e9i	0.0582656	+	0.179323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.f.d.91.13	yes	56
3.2	odd	2	inner	99.8.f.d.91.2	yes	56
11.4	even	5	inner	99.8.f.d.37.13	yes	56
33.26	odd	10	inner	99.8.f.d.37.2	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.8.f.d.37.2	✓	56	33.26	odd	10	inner
99.8.f.d.37.13	yes	56	11.4	even	5	inner
99.8.f.d.91.2	yes	56	3.2	odd	2	inner
99.8.f.d.91.13	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)

\(f(q)\)	\(=\)	\(q+(14.6343 - 10.6324i) q^{2} +(61.5594 - 189.460i) q^{4} +(142.204 + 103.317i) q^{5} +(-426.560 + 1312.82i) q^{7} +(-398.052 - 1225.08i) q^{8} +O(q^{10})\)	\(q+(14.6343 - 10.6324i) q^{2} +(61.5594 - 189.460i) q^{4} +(142.204 + 103.317i) q^{5} +(-426.560 + 1312.82i) q^{7} +(-398.052 - 1225.08i) q^{8} +3179.57 q^{10} +(-827.094 + 4336.25i) q^{11} +(7183.56 - 5219.16i) q^{13} +(7716.02 + 23747.5i) q^{14} +(1778.31 + 1292.02i) q^{16} +(6428.95 + 4670.91i) q^{17} +(16896.0 + 52000.5i) q^{19} +(28328.6 - 20581.9i) q^{20} +(34001.0 + 72251.9i) q^{22} -69066.0 q^{23} +(-14594.4 - 44917.0i) q^{25} +(49633.9 - 152757. i) q^{26} +(222468. + 161632. i) q^{28} +(30430.4 - 93655.1i) q^{29} +(327.501 - 237.943i) q^{31} +204642. q^{32} +143746. q^{34} +(-196295. + 142617. i) q^{35} +(-7964.49 + 24512.2i) q^{37} +(800152. + 581344. i) q^{38} +(69967.3 - 215337. i) q^{40} +(-88746.2 - 273133. i) q^{41} +322116. q^{43} +(770633. + 423639. i) q^{44} +(-1.01073e6 + 734339. i) q^{46} +(264591. + 814328. i) q^{47} +(-875270. - 635921. i) q^{49} +(-691155. - 502153. i) q^{50} +(-546609. - 1.68229e6i) q^{52} +(1.71251e6 - 1.24421e6i) q^{53} +(-565626. + 531180. i) q^{55} +1.77810e6 q^{56} +(-550454. - 1.69412e6i) q^{58} +(-167772. + 516350. i) q^{59} +(-93244.4 - 67746.0i) q^{61} +(2262.83 - 6964.26i) q^{62} +(2.76716e6 - 2.01046e6i) q^{64} +1.56076e6 q^{65} -4.50179e6 q^{67} +(1.28071e6 - 930494. i) q^{68} +(-1.35628e6 + 4.17419e6i) q^{70} +(-252121. - 183177. i) q^{71} +(-337582. + 1.03897e6i) q^{73} +(144069. + 443400. i) q^{74} +1.08921e7 q^{76} +(-5.33989e6 - 2.93549e6i) q^{77} +(-69898.6 + 50784.3i) q^{79} +(119395. + 367461. i) q^{80} +(-4.20280e6 - 3.05351e6i) q^{82} +(5.38471e6 + 3.91222e6i) q^{83} +(431638. + 1.32844e6i) q^{85} +(4.71393e6 - 3.42487e6i) q^{86} +(5.64148e6 - 712799. i) q^{88} -3.18154e6 q^{89} +(3.78758e6 + 1.16570e7i) q^{91} +(-4.25167e6 + 1.30853e7i) q^{92} +(1.25304e7 + 9.10386e6i) q^{94} +(-2.96987e6 + 9.14033e6i) q^{95} +(-7.39815e6 + 5.37507e6i) q^{97} -1.95703e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 1260 q^{4} - 3902 q^{7}+O(q^{10}) \) 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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