LMFDB - Embedded newform 126.8.g.h.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,8,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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("126.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, 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:	$39.3605132110$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 2119x^{4} - 65706x^{3} + 4519836x^{2} - 71825616x + 1150023744 $ x^6 - x^5 + 2119x^4 - 65706x^3 + 4519836x^2 - 71825616x + 1150023744
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7^{3} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$9.57894 + 16.5912i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.8.g.h.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(47.5526 + 82.3635i) q^{5} +(-906.806 + 35.2857i) q^{7} +512.000 q^{8} +(380.420 - 658.908i) q^{10} +(982.708 - 1702.10i) q^{11} -11783.0 q^{13} +(3871.69 + 6141.40i) q^{14} +(-2048.00 - 3547.24i) q^{16} +(5146.31 - 8913.67i) q^{17} +(-3935.41 - 6816.33i) q^{19} -6086.73 q^{20} -15723.3 q^{22} +(46141.4 + 79919.2i) q^{23} +(34540.0 - 59825.0i) q^{25} +(47132.1 + 81635.2i) q^{26} +(27062.1 - 51389.5i) q^{28} +4539.61 q^{29} +(-80418.5 + 139289. i) q^{31} +(-16384.0 + 28377.9i) q^{32} -82341.0 q^{34} +(-46027.2 - 73009.8i) q^{35} +(175425. + 303845. i) q^{37} +(-31483.3 + 54530.6i) q^{38} +(24346.9 + 42170.1i) q^{40} +446392. q^{41} +711226. q^{43} +(62893.3 + 108934. i) q^{44} +(369131. - 639354. i) q^{46} +(-401283. - 695043. i) q^{47} +(821053. - 63994.6i) q^{49} -552640. q^{50} +(377057. - 653082. i) q^{52} +(-31994.8 + 55416.5i) q^{53} +186921. q^{55} +(-464285. + 18066.3i) q^{56} +(-18158.5 - 31451.4i) q^{58} +(688429. - 1.19239e6i) q^{59} +(-179998. - 311766. i) q^{61} +1.28670e6 q^{62} +262144. q^{64} +(-560313. - 970491. i) q^{65} +(892775. - 1.54633e6i) q^{67} +(329364. + 570475. i) q^{68} +(-321718. + 610925. i) q^{70} +3.63355e6 q^{71} +(1.68195e6 - 2.91322e6i) q^{73} +(1.40340e6 - 2.43076e6i) q^{74} +503732. q^{76} +(-831066. + 1.57815e6i) q^{77} +(-1.40754e6 - 2.43794e6i) q^{79} +(194775. - 337361. i) q^{80} +(-1.78557e6 - 3.09269e6i) q^{82} +9.21428e6 q^{83} +978881. q^{85} +(-2.84490e6 - 4.92752e6i) q^{86} +(503146. - 871475. i) q^{88} +(2.47734e6 + 4.29088e6i) q^{89} +(1.06849e7 - 415772. i) q^{91} -5.90610e6 q^{92} +(-3.21026e6 + 5.56034e6i) q^{94} +(374278. - 648268. i) q^{95} +7.92217e6 q^{97} +(-3.72758e6 - 5.43244e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 192 q^{4} - 110 q^{5} + 635 q^{7} + 3072 q^{8} - 880 q^{10} + 548 q^{11} + 19898 q^{13} - 4568 q^{14} - 12288 q^{16} + 20972 q^{17} + 28383 q^{19} + 14080 q^{20} - 8768 q^{22} + 32732 q^{23}+ \cdots - 6110208 q^{98}+O(q^{100}) $ 6 * q - 24 * q^2 - 192 * q^4 - 110 * q^5 + 635 * q^7 + 3072 * q^8 - 880 * q^10 + 548 * q^11 + 19898 * q^13 - 4568 * q^14 - 12288 * q^16 + 20972 * q^17 + 28383 * q^19 + 14080 * q^20 - 8768 * q^22 + 32732 * q^23 + 22745 * q^25 - 79592 * q^26 - 4096 * q^28 - 234176 * q^29 - 147865 * q^31 - 98304 * q^32 - 335552 * q^34 - 876430 * q^35 - 367503 * q^37 + 227064 * q^38 - 56320 * q^40 + 2875908 * q^41 + 1498794 * q^43 + 35072 * q^44 + 261856 * q^46 - 741486 * q^47 + 1421697 * q^49 - 363920 * q^50 - 636736 * q^52 - 1032432 * q^53 - 7992560 * q^55 + 325120 * q^56 + 936704 * q^58 - 2389238 * q^59 - 1238746 * q^61 + 2365840 * q^62 + 1572864 * q^64 - 3798390 * q^65 + 2462497 * q^67 + 1342208 * q^68 + 4561840 * q^70 + 1272524 * q^71 - 4609961 * q^73 - 2940024 * q^74 - 3633024 * q^76 - 20044196 * q^77 + 6152849 * q^79 - 450560 * q^80 - 11503632 * q^82 + 24059768 * q^83 - 18273080 * q^85 - 5995176 * q^86 + 280576 * q^88 + 10646976 * q^89 + 47686115 * q^91 - 4189696 * q^92 - 5931888 * q^94 + 21560930 * q^95 + 4562944 * q^97 - 6110208 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$2$	−4.00000	−	6.92820i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	47.5526	+	82.3635i	0.170129	+	0.294672i	0.938465	−	0.345375i	$-0.112248\pi$
$5$	47.5526	+	82.3635i	0.170129	+	0.294672i	−0.768336	+	0.640047i	$0.778915\pi$
$6$		0			0
$7$	−906.806	+	35.2857i	−0.999244	+	0.0388826i
$7$	−906.806	+	35.2857i	−0.999244	+	0.0388826i
$8$	512.000			0.353553
$9$		0			0
$10$	380.420	−	658.908i	0.120300	−	0.208365i
$11$	982.708	−	1702.10i	0.222613	−	0.385577i	−0.732988	−	0.680242i	$-0.761875\pi$
$11$	982.708	−	1702.10i	0.222613	−	0.385577i	0.955601	+	0.294665i	$0.0952081\pi$
$12$		0			0
$13$	−11783.0			−1.48749			−0.743747	−	0.668461i	$-0.766953\pi$
$13$	−11783.0			−1.48749			−0.743747	+	0.668461i	$0.766953\pi$
$14$	3871.69	+	6141.40i	0.377097	+	0.598162i
$15$		0			0
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	5146.31	−	8913.67i	0.254053	−	0.440033i	−0.710585	−	0.703612i	$-0.751569\pi$
$17$	5146.31	−	8913.67i	0.254053	−	0.440033i	0.964638	+	0.263579i	$0.0849028\pi$
$18$		0			0
$19$	−3935.41	−	6816.33i	−0.131629	−	0.227989i	0.792676	−	0.609644i	$-0.208688\pi$
$19$	−3935.41	−	6816.33i	−0.131629	−	0.227989i	−0.924305	+	0.381655i	$0.875354\pi$
$20$	−6086.73			−0.170129
$21$		0			0
$22$	−15723.3			−0.314822
$23$	46141.4	+	79919.2i	0.790758	+	1.36963i	0.925498	+	0.378751i	$0.123646\pi$
$23$	46141.4	+	79919.2i	0.790758	+	1.36963i	−0.134741	+	0.990881i	$0.543020\pi$
$24$		0			0
$25$	34540.0	−	59825.0i	0.442112	−	0.765761i
$26$	47132.1	+	81635.2i	0.525908	+	0.910900i
$27$		0			0
$28$	27062.1	−	51389.5i	0.232974	−	0.442406i
$29$	4539.61			0.0345641			0.0172821	−	0.999851i	$-0.494499\pi$
$29$	4539.61			0.0345641			0.0172821	+	0.999851i	$0.494499\pi$
$30$		0			0
$31$	−80418.5	+	139289.i	−0.484831	+	0.839751i	−0.999848	−	0.0174285i	$-0.994452\pi$
$31$	−80418.5	+	139289.i	−0.484831	+	0.839751i	0.515018	+	0.857180i	$0.327785\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−82341.0			−0.359286
$35$	−46027.2	−	73009.8i	−0.181458	−	0.287835i
$36$		0			0
$37$	175425.	+	303845.i	0.569358	+	0.986157i	0.996630	+	0.0820337i	$0.0261415\pi$
$37$	175425.	+	303845.i	0.569358	+	0.986157i	−0.427272	+	0.904123i	$0.640525\pi$
$38$	−31483.3	+	54530.6i	−0.0930759	+	0.161212i
$39$		0			0
$40$	24346.9	+	42170.1i	0.0601498	+	0.104182i
$41$	446392.			1.01152			0.505758	−	0.862675i	$-0.331213\pi$
$41$	446392.			1.01152			0.505758	+	0.862675i	$0.331213\pi$
$42$		0			0
$43$	711226.			1.36417			0.682084	−	0.731273i	$-0.261074\pi$
$43$	711226.			1.36417			0.682084	+	0.731273i	$0.261074\pi$
$44$	62893.3	+	108934.i	0.111306	+	0.192788i
$45$		0			0
$46$	369131.	−	639354.i	0.559150	−	0.968476i
$47$	−401283.	−	695043.i	−0.563778	−	0.976493i	−0.997162	−	0.0752833i	$-0.976014\pi$
$47$	−401283.	−	695043.i	−0.563778	−	0.976493i	0.433384	−	0.901209i	$-0.357319\pi$
$48$		0			0
$49$	821053.	−	63994.6i	0.996976	−	0.0777065i
$50$	−552640.			−0.625241
$51$		0			0
$52$	377057.	−	653082.i	0.371873	−	0.644104i
$53$	−31994.8	+	55416.5i	−0.0295198	+	0.0511298i	−0.880408	−	0.474217i	$-0.842731\pi$
$53$	−31994.8	+	55416.5i	−0.0295198	+	0.0511298i	0.850888	+	0.525347i	$0.176064\pi$
$54$		0			0
$55$	186921.			0.151492
$56$	−464285.	+	18066.3i	−0.353286	+	0.0137471i
$57$		0			0
$58$	−18158.5	−	31451.4i	−0.0122203	−	0.0211661i
$59$	688429.	−	1.19239e6i	0.436392	−	0.755853i	−0.561016	−	0.827805i	$-0.689589\pi$
$59$	688429.	−	1.19239e6i	0.436392	−	0.755853i	0.997408	+	0.0719517i	$0.0229228\pi$
$60$		0			0
$61$	−179998.	−	311766.i	−0.101535	−	0.175863i	0.810783	−	0.585348i	$-0.199042\pi$
$61$	−179998.	−	311766.i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$62$	1.28670e6			0.685654
$63$		0			0
$64$	262144.			0.125000
$65$	−560313.	−	970491.i	−0.253066	−	0.438323i
$66$		0			0
$67$	892775.	−	1.54633e6i	0.362644	−	0.628117i	−0.625751	−	0.780023i	$-0.715208\pi$
$67$	892775.	−	1.54633e6i	0.362644	−	0.628117i	0.988395	+	0.151905i	$0.0485409\pi$
$68$	329364.	+	570475.i	0.127027	+	0.220017i
$69$		0			0
$70$	−321718.	+	610925.i	−0.112107	+	0.212885i
$71$	3.63355e6			1.20483			0.602416	−	0.798182i	$-0.294205\pi$
$71$	3.63355e6			1.20483			0.602416	+	0.798182i	$0.294205\pi$
$72$		0			0
$73$	1.68195e6	−	2.91322e6i	0.506037	−	0.876482i	−0.493938	−	0.869497i	$-0.664443\pi$
$73$	1.68195e6	−	2.91322e6i	0.506037	−	0.876482i	0.999976	−	0.00698545i	$-0.00222356\pi$
$74$	1.40340e6	−	2.43076e6i	0.402597	−	0.697318i
$75$		0			0
$76$	503732.			0.131629
$77$	−831066.	+	1.57815e6i	−0.207452	+	0.393941i
$78$		0			0
$79$	−1.40754e6	−	2.43794e6i	−0.321194	−	0.556324i	0.659541	−	0.751669i	$-0.270751\pi$
$79$	−1.40754e6	−	2.43794e6i	−0.321194	−	0.556324i	−0.980735	+	0.195345i	$0.937417\pi$
$80$	194775.	−	337361.i	0.0425323	−	0.0736681i
$81$		0			0
$82$	−1.78557e6	−	3.09269e6i	−0.357625	−	0.619425i
$83$	9.21428e6			1.76884			0.884419	−	0.466694i	$-0.154555\pi$
$83$	9.21428e6			1.76884			0.884419	+	0.466694i	$0.154555\pi$
$84$		0			0
$85$	978881.			0.172888
$86$	−2.84490e6	−	4.92752e6i	−0.482307	−	0.835379i
$87$		0			0
$88$	503146.	−	871475.i	0.0787055	−	0.136322i
$89$	2.47734e6	+	4.29088e6i	0.372495	+	0.645180i	0.989949	−	0.141427i	$-0.0451690\pi$
$89$	2.47734e6	+	4.29088e6i	0.372495	+	0.645180i	−0.617454	+	0.786607i	$0.711836\pi$
$90$		0			0
$91$	1.06849e7	−	415772.i	1.48637	−	0.0578377i
$92$	−5.90610e6			−0.790758
$93$		0			0
$94$	−3.21026e6	+	5.56034e6i	−0.398651	+	0.690485i
$95$	374278.	−	648268.i	0.0447880	−	0.0775750i
$96$		0			0
$97$	7.92217e6			0.881339			0.440670	−	0.897669i	$-0.354741\pi$
$97$	7.92217e6			0.881339			0.440670	+	0.897669i	$0.354741\pi$
$98$	−3.72758e6	−	5.43244e6i	−0.400070	−	0.583047i
$99$		0			0
$100$	2.21056e6	+	3.82880e6i	0.221056	+	0.382880i
$101$	−2.95700e6	+	5.12167e6i	−0.285579	+	0.494637i	−0.972749	−	0.231859i	$-0.925519\pi$
$101$	−2.95700e6	+	5.12167e6i	−0.285579	+	0.494637i	0.687170	+	0.726496i	$0.258853\pi$
$102$		0			0
$103$	−5.97730e6	−	1.03530e7i	−0.538982	−	0.933545i	−0.998959	−	0.0456139i	$-0.985476\pi$
$103$	−5.97730e6	−	1.03530e7i	−0.538982	−	0.933545i	0.459977	−	0.887931i	$-0.347858\pi$
$104$	−6.03291e6			−0.525908
$105$		0			0
$106$	511916.			0.0417473
$107$	4.86542e6	+	8.42715e6i	0.383952	+	0.665024i	0.991623	−	0.129164i	$-0.0412295\pi$
$107$	4.86542e6	+	8.42715e6i	0.383952	+	0.665024i	−0.607671	+	0.794189i	$0.707896\pi$
$108$		0			0
$109$	−1.01906e7	+	1.76506e7i	−0.753714	+	1.30547i	0.192297	+	0.981337i	$0.438406\pi$
$109$	−1.01906e7	+	1.76506e7i	−0.753714	+	1.30547i	−0.946011	+	0.324135i	$0.894927\pi$
$110$	−747684.	−	1.29503e6i	−0.0535604	−	0.0927694i
$111$		0			0
$112$	1.98231e6	+	3.14439e6i	0.133324	+	0.211482i
$113$	−2.06664e7			−1.34738			−0.673691	−	0.739013i	$-0.735292\pi$
$113$	−2.06664e7			−1.34738			−0.673691	+	0.739013i	$0.735292\pi$
$114$		0			0
$115$	−4.38828e6	+	7.60073e6i	−0.269062	+	0.466029i
$116$	−145268.	+	251611.i	−0.00864104	+	0.0149667i
$117$		0			0
$118$	−1.10149e7			−0.617152
$119$	−4.35218e6	+	8.26457e6i	−0.236751	+	0.449579i
$120$		0			0
$121$	7.81216e6	+	1.35311e7i	0.400887	+	0.694357i
$122$	−1.43999e6	+	2.49413e6i	−0.0717958	+	0.124354i
$123$		0			0
$124$	−5.14678e6	−	8.91449e6i	−0.242415	−	0.419876i
$125$	1.40000e7			0.641123
$126$		0			0
$127$	1.98603e6			0.0860345			0.0430173	−	0.999074i	$-0.486303\pi$
$127$	1.98603e6			0.0860345			0.0430173	+	0.999074i	$0.486303\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−4.48250e6	+	7.76393e6i	−0.178945	+	0.309941i
$131$	1.15403e7	+	1.99883e7i	0.448504	+	0.776832i	0.998289	−	0.0584743i	$-0.0186236\pi$
$131$	1.15403e7	+	1.99883e7i	0.448504	+	0.776832i	−0.549785	+	0.835306i	$0.685290\pi$
$132$		0			0
$133$	3.80917e6	+	6.04223e6i	0.140395	+	0.222698i
$134$	−1.42844e7			−0.512856
$135$		0			0
$136$	2.63491e6	−	4.56380e6i	0.0898214	−	0.155575i
$137$	2.07691e7	−	3.59731e7i	0.690073	−	1.19524i	−0.281741	−	0.959491i	$-0.590912\pi$
$137$	2.07691e7	−	3.59731e7i	0.690073	−	1.19524i	0.971814	−	0.235751i	$-0.0757549\pi$
$138$		0			0
$139$	−3.32535e7			−1.05023			−0.525117	−	0.851030i	$-0.675978\pi$
$139$	−3.32535e7			−1.05023			−0.525117	+	0.851030i	$0.675978\pi$
$140$	5.51948e6	−	214775.i	0.170001	−	0.00661507i
$141$		0			0
$142$	−1.45342e7	−	2.51740e7i	−0.425973	−	0.737806i
$143$	−1.15793e7	+	2.00559e7i	−0.331135	+	0.573543i
$144$		0			0
$145$	215870.	+	373898.i	0.00588037	+	0.0101851i
$146$	−2.69112e7			−0.715645
$147$		0			0
$148$	−2.24544e7			−0.569358
$149$	2.63327e7	+	4.56096e7i	0.652144	+	1.12955i	0.982602	+	0.185726i	$0.0594635\pi$
$149$	2.63327e7	+	4.56096e7i	0.652144	+	1.12955i	−0.330458	+	0.943821i	$0.607203\pi$
$150$		0			0
$151$	−3.24457e7	+	5.61976e7i	−0.766899	+	1.32831i	0.172338	+	0.985038i	$0.444868\pi$
$151$	−3.24457e7	+	5.61976e7i	−0.766899	+	1.32831i	−0.939237	+	0.343270i	$0.888465\pi$
$152$	−2.01493e6	−	3.48996e6i	−0.0465380	−	0.0806061i
$153$		0			0
$154$	1.42580e7	−	554809.i	0.314584	−	0.0122411i
$155$	−1.52964e7			−0.329935
$156$		0			0
$157$	−1.88920e7	+	3.27219e7i	−0.389609	+	0.674822i	−0.992397	−	0.123079i	$-0.960723\pi$
$157$	−1.88920e7	+	3.27219e7i	−0.389609	+	0.674822i	0.602788	+	0.797901i	$0.294056\pi$
$158$	−1.12604e7	+	1.95035e7i	−0.227118	+	0.393380i
$159$		0			0
$160$	−3.11640e6			−0.0601498
$161$	−4.46613e7	−	7.08432e7i	−0.843414	−	1.33785i
$162$		0			0
$163$	−4.70433e7	−	8.14813e7i	−0.850826	−	1.47367i	−0.880464	−	0.474114i	$-0.842769\pi$
$163$	−4.70433e7	−	8.14813e7i	−0.850826	−	1.47367i	0.0296372	−	0.999561i	$-0.490565\pi$
$164$	−1.42845e7	+	2.47416e7i	−0.252879	+	0.437999i
$165$		0			0
$166$	−3.68571e7	−	6.38384e7i	−0.625379	−	1.08319i
$167$	1.02438e8			1.70198			0.850989	−	0.525184i	$-0.176004\pi$
$167$	1.02438e8			1.70198			0.850989	+	0.525184i	$0.176004\pi$
$168$		0			0
$169$	7.60912e7			1.21264
$170$	−3.91552e6	−	6.78189e6i	−0.0611250	−	0.105872i
$171$		0			0
$172$	−2.27592e7	+	3.94202e7i	−0.341042	+	0.590702i
$173$	−9.69306e6	−	1.67889e7i	−0.142331	−	0.246525i	0.786043	−	0.618172i	$-0.212126\pi$
$173$	−9.69306e6	−	1.67889e7i	−0.142331	−	0.246525i	−0.928374	+	0.371647i	$0.878793\pi$
$174$		0			0
$175$	−2.92101e7	+	5.54685e7i	−0.412003	+	0.782372i
$176$	−8.05034e6			−0.111306
$177$		0			0
$178$	1.98187e7	−	3.43270e7i	0.263394	−	0.456211i
$179$	1.95660e7	−	3.38893e7i	0.254986	−	0.441649i	−0.709906	−	0.704297i	$-0.751262\pi$
$179$	1.95660e7	−	3.38893e7i	0.254986	−	0.441649i	0.964892	+	0.262648i	$0.0845958\pi$
$180$		0			0
$181$	9.90133e7			1.24113			0.620567	−	0.784154i	$-0.286903\pi$
$181$	9.90133e7			1.24113			0.620567	+	0.784154i	$0.286903\pi$
$182$	−4.56203e7	−	7.23642e7i	−0.560929	−	0.889763i
$183$		0			0
$184$	2.36244e7	+	4.09187e7i	0.279575	+	0.484238i
$185$	−1.66838e7	+	2.88972e7i	−0.193729	+	0.335548i
$186$		0			0
$187$	−1.01146e7	−	1.75191e7i	−0.113111	−	0.195914i
$188$	5.13642e7			0.563778
$189$		0			0
$190$	−5.98844e6			−0.0633397
$191$	9.46547e6	+	1.63947e7i	0.0982936	+	0.170250i	0.910978	−	0.412454i	$-0.135328\pi$
$191$	9.46547e6	+	1.63947e7i	0.0982936	+	0.170250i	−0.812685	+	0.582703i	$0.801995\pi$
$192$		0			0
$193$	−1.80881e7	+	3.13295e7i	−0.181110	+	0.313692i	−0.942259	−	0.334885i	$-0.891302\pi$
$193$	−1.80881e7	+	3.13295e7i	−0.181110	+	0.313692i	0.761149	+	0.648577i	$0.224636\pi$
$194$	−3.16887e7	−	5.48864e7i	−0.311600	−	0.539708i
$195$		0			0
$196$	−2.27267e7	+	4.75552e7i	−0.215596	+	0.451130i
$197$	−1.13940e8			−1.06181			−0.530903	−	0.847432i	$-0.678147\pi$
$197$	−1.13940e8			−1.06181			−0.530903	+	0.847432i	$0.678147\pi$
$198$		0			0
$199$	5.23862e7	−	9.07356e7i	0.471228	−	0.816191i	−0.528230	−	0.849101i	$-0.677144\pi$
$199$	5.23862e7	−	9.07356e7i	0.471228	−	0.816191i	0.999458	+	0.0329100i	$0.0104775\pi$
$200$	1.76845e7	−	3.06304e7i	0.156310	−	0.270737i
$201$		0			0
$202$	4.73120e7			0.403870
$203$	−4.11655e6	+	160183.i	−0.0345380	+	0.00134395i
$204$		0			0
$205$	2.12271e7	+	3.67664e7i	0.172088	+	0.298066i
$206$	−4.78184e7	+	8.28239e7i	−0.381118	+	0.660116i
$207$		0			0
$208$	2.41316e7	+	4.17972e7i	0.185937	+	0.322052i
$209$	−1.54694e7			−0.117209
$210$		0			0
$211$	1.99022e8			1.45852			0.729261	−	0.684236i	$-0.239864\pi$
$211$	1.99022e8			1.45852			0.729261	+	0.684236i	$0.239864\pi$
$212$	−2.04766e6	−	3.54666e6i	−0.0147599	−	0.0255649i
$213$		0			0
$214$	3.89233e7	−	6.74172e7i	0.271495	−	0.470243i
$215$	3.38206e7	+	5.85790e7i	0.232085	+	0.401983i
$216$		0			0
$217$	6.80091e7	−	1.29146e8i	0.451812	−	0.857968i
$218$	1.63050e8			1.06591
$219$		0			0
$220$	−5.98148e6	+	1.03602e7i	−0.0378729	+	0.0655978i
$221$	−6.06391e7	+	1.05030e8i	−0.377903	+	0.654546i
$222$		0			0
$223$	−7.56972e7			−0.457101			−0.228551	−	0.973532i	$-0.573399\pi$
$223$	−7.56972e7			−0.457101			−0.228551	+	0.973532i	$0.573399\pi$
$224$	1.38558e7	−	2.63114e7i	0.0823688	−	0.156414i
$225$		0			0
$226$	8.26657e7	+	1.43181e8i	0.476372	+	0.825100i
$227$	5.04095e7	−	8.73118e7i	0.286037	−	0.495430i	−0.686823	−	0.726824i	$-0.740995\pi$
$227$	5.04095e7	−	8.73118e7i	0.286037	−	0.495430i	0.972860	+	0.231394i	$0.0743287\pi$
$228$		0			0
$229$	−1.49807e8	−	2.59474e8i	−0.824344	−	1.42781i	−0.902419	−	0.430859i	$-0.858211\pi$
$229$	−1.49807e8	−	2.59474e8i	−0.824344	−	1.42781i	0.0780748	−	0.996948i	$-0.475123\pi$
$230$	7.02125e7			0.380511
$231$		0			0
$232$	2.32428e6			0.0122203
$233$	8.00429e7	+	1.38638e8i	0.414550	+	0.718022i	0.995381	−	0.0960024i	$-0.0306056\pi$
$233$	8.00429e7	+	1.38638e8i	0.414550	+	0.718022i	−0.580831	+	0.814024i	$0.697272\pi$
$234$		0			0
$235$	3.81641e7	−	6.61021e7i	0.191830	−	0.332260i
$236$	4.40594e7	+	7.63132e7i	0.218196	+	0.377927i
$237$		0			0
$238$	7.46673e7	−	2.90546e6i	0.359014	−	0.0139700i
$239$	1.62871e8			0.771703			0.385851	−	0.922561i	$-0.373908\pi$
$239$	1.62871e8			0.771703			0.385851	+	0.922561i	$0.373908\pi$
$240$		0			0
$241$	−1.07114e8	+	1.85526e8i	−0.492929	+	0.853779i	−0.999967	−	0.00814543i	$-0.997407\pi$
$241$	−1.07114e8	+	1.85526e8i	−0.492929	+	0.853779i	0.507038	+	0.861924i	$0.330741\pi$
$242$	6.24972e7	−	1.08248e8i	0.283470	−	0.490984i
$243$		0			0
$244$	2.30398e7			0.101535
$245$	4.43140e7	+	6.45816e7i	0.192513	+	0.280561i
$246$		0			0
$247$	4.63710e7	+	8.03170e7i	0.195798	+	0.339131i
$248$	−4.11743e7	+	7.13159e7i	−0.171413	+	0.296897i
$249$		0			0
$250$	−5.59998e7	−	9.69945e7i	−0.226671	−	0.392606i
$251$	3.42740e8			1.36807			0.684033	−	0.729451i	$-0.260224\pi$
$251$	3.42740e8			1.36807			0.684033	+	0.729451i	$0.260224\pi$
$252$		0			0
$253$	1.81374e8			0.704131
$254$	−7.94412e6	−	1.37596e7i	−0.0304178	−	0.0526852i
$255$		0			0
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−2.40807e8	−	4.17090e8i	−0.884919	−	1.53272i	−0.845807	−	0.533489i	$-0.820881\pi$
$257$	−2.40807e8	−	4.17090e8i	−0.884919	−	1.53272i	−0.0391117	−	0.999235i	$-0.512453\pi$
$258$		0			0
$259$	−1.69798e8	−	2.69339e8i	−0.607272	−	0.963273i
$260$	7.17201e7			0.253066
$261$		0			0
$262$	9.23222e7	−	1.59907e8i	0.317140	−	0.549303i
$263$	−1.55787e8	+	2.69832e8i	−0.528065	+	0.914635i	0.471400	+	0.881920i	$0.343749\pi$
$263$	−1.55787e8	+	2.69832e8i	−0.528065	+	0.914635i	−0.999465	+	0.0327154i	$0.989585\pi$
$264$		0			0
$265$	−6.08573e6			−0.0200887
$266$	2.66251e7	−	5.05596e7i	0.0867372	−	0.164709i
$267$		0			0
$268$	5.71376e7	+	9.89652e7i	0.181322	+	0.314059i
$269$	1.27652e8	−	2.21099e8i	0.399847	−	0.692555i	−0.593860	−	0.804568i	$-0.702397\pi$
$269$	1.27652e8	−	2.21099e8i	0.399847	−	0.692555i	0.993707	+	0.112014i	$0.0357300\pi$
$270$		0			0
$271$	−4.71187e7	−	8.16120e7i	−0.143814	−	0.249093i	0.785116	−	0.619349i	$-0.212603\pi$
$271$	−4.71187e7	−	8.16120e7i	−0.143814	−	0.249093i	−0.928930	+	0.370256i	$0.879270\pi$
$272$	−4.21586e7			−0.127027
$273$		0			0
$274$	−3.32305e8			−0.975910
$275$	−6.78855e7	−	1.17581e8i	−0.196840	−	0.340936i
$276$		0			0
$277$	6.18031e7	−	1.07046e8i	0.174715	−	0.302616i	−0.765347	−	0.643617i	$-0.777433\pi$
$277$	6.18031e7	−	1.07046e8i	0.174715	−	0.302616i	0.940063	+	0.341002i	$0.110766\pi$
$278$	1.33014e8	+	2.30387e8i	0.371314	+	0.643134i
$279$		0			0
$280$	−2.35659e7	−	3.73810e7i	−0.0641552	−	0.101765i
$281$	−4.28566e8			−1.15225			−0.576123	−	0.817363i	$-0.695435\pi$
$281$	−4.28566e8			−1.15225			−0.576123	+	0.817363i	$0.695435\pi$
$282$		0			0
$283$	−1.51802e8	+	2.62928e8i	−0.398130	+	0.689581i	−0.993495	−	0.113874i	$-0.963674\pi$
$283$	−1.51802e8	+	2.62928e8i	−0.398130	+	0.689581i	0.595366	+	0.803455i	$0.297007\pi$
$284$	−1.16274e8	+	2.01392e8i	−0.301208	+	0.521708i
$285$		0			0
$286$	1.85268e8			0.468296
$287$	−4.04791e8	+	1.57513e7i	−1.01075	+	0.0393304i
$288$		0			0
$289$	1.52200e8	+	2.63619e8i	0.370914	+	0.642442i
$290$	1.72696e6	−	2.99119e6i	0.00415805	−	0.00720195i
$291$		0			0
$292$	1.07645e8	+	1.86446e8i	0.253019	+	0.438241i
$293$	−4.09102e8			−0.950156			−0.475078	−	0.879944i	$-0.657580\pi$
$293$	−4.09102e8			−0.950156			−0.475078	+	0.879944i	$0.657580\pi$
$294$		0			0
$295$	1.30946e8			0.296972
$296$	8.98176e7	+	1.55569e8i	0.201298	+	0.348659i
$297$		0			0
$298$	2.10662e8	−	3.64877e8i	0.461135	−	0.798710i
$299$	−5.43685e8	−	9.41691e8i	−1.17625	−	2.03732i
$300$		0			0
$301$	−6.44944e8	+	2.50961e7i	−1.36314	+	0.0530425i
$302$	5.19132e8			1.08456
$303$		0			0
$304$	−1.61194e7	+	2.79197e7i	−0.0329073	+	0.0569971i
$305$	1.71188e7	−	2.96506e7i	0.0345480	−	0.0598389i
$306$		0			0
$307$	4.05634e8			0.800111			0.400056	−	0.916491i	$-0.368991\pi$
$307$	4.05634e8			0.800111			0.400056	+	0.916491i	$0.368991\pi$
$308$	−6.08759e7	−	9.65632e7i	−0.118718	−	0.188315i
$309$		0			0
$310$	6.11857e7	+	1.05977e8i	0.116650	+	0.202043i
$311$	3.27246e8	−	5.66807e8i	0.616898	−	1.06850i	−0.373150	−	0.927771i	$-0.621722\pi$
$311$	3.27246e8	−	5.66807e8i	0.616898	−	1.06850i	0.990048	−	0.140728i	$-0.0449443\pi$
$312$		0			0
$313$	1.15882e8	+	2.00714e8i	0.213605	+	0.369975i	0.952840	−	0.303472i	$-0.0981460\pi$
$313$	1.15882e8	+	2.00714e8i	0.213605	+	0.369975i	−0.739235	+	0.673448i	$0.764813\pi$
$314$	3.02272e8			0.550990
$315$		0			0
$316$	1.80166e8			0.321194
$317$	−8.76270e7	−	1.51774e8i	−0.154501	−	0.267603i	0.778376	−	0.627798i	$-0.216044\pi$
$317$	−8.76270e7	−	1.51774e8i	−0.154501	−	0.267603i	−0.932877	+	0.360195i	$0.882710\pi$
$318$		0			0
$319$	4.46111e6	−	7.72687e6i	0.00769442	−	0.0133271i
$320$	1.24656e7	+	2.15911e7i	0.0212662	+	0.0368341i
$321$		0			0
$322$	−3.12170e8	+	5.92795e8i	−0.521070	+	0.989485i
$323$	−8.10114e7			−0.133763
$324$		0			0
$325$	−4.06986e8	+	7.04920e8i	−0.657639	+	1.13906i
$326$	−3.76346e8	+	6.51851e8i	−0.601625	+	1.04205i
$327$		0			0
$328$	2.28553e8			0.357625
$329$	3.88411e8	+	6.16110e8i	0.601321	+	0.953833i
$330$		0			0
$331$	−6.22285e7	−	1.07783e8i	−0.0943172	−	0.163362i	0.815006	−	0.579452i	$-0.196733\pi$
$331$	−6.22285e7	−	1.07783e8i	−0.0943172	−	0.163362i	−0.909323	+	0.416090i	$0.863400\pi$
$332$	−2.94857e8	+	5.10707e8i	−0.442209	+	0.765929i
$333$		0			0
$334$	−4.09752e8	−	7.09712e8i	−0.601740	−	1.04224i
$335$	1.69815e8			0.246785
$336$		0			0
$337$	−7.96655e8			−1.13388			−0.566938	−	0.823760i	$-0.691872\pi$
$337$	−7.96655e8			−1.13388			−0.566938	+	0.823760i	$0.691872\pi$
$338$	−3.04365e8	−	5.27175e8i	−0.428732	−	0.742586i
$339$		0			0
$340$	−3.13242e7	+	5.42551e7i	−0.0432219	+	0.0748625i
$341$	1.58056e8	+	2.73761e8i	0.215859	+	0.373879i
$342$		0			0
$343$	−7.42278e8	+	8.70022e7i	−0.993201	+	0.116413i
$344$	3.64148e8			0.482307
$345$		0			0
$346$	−7.75445e7	+	1.34311e8i	−0.100643	+	0.174319i
$347$	−3.40840e8	+	5.90353e8i	−0.437923	+	0.758505i	−0.997529	−	0.0702539i	$-0.977619\pi$
$347$	−3.40840e8	+	5.90353e8i	−0.437923	+	0.758505i	0.559606	+	0.828759i	$0.310952\pi$
$348$		0			0
$349$	−9.65104e8			−1.21530			−0.607652	−	0.794203i	$-0.707888\pi$
$349$	−9.65104e8			−1.21530			−0.607652	+	0.794203i	$0.707888\pi$
$350$	5.01138e8	−	1.95003e7i	0.624768	−	0.0243110i
$351$		0			0
$352$	3.22014e7	+	5.57744e7i	0.0393527	+	0.0681610i
$353$	−7.71034e8	+	1.33547e9i	−0.932958	+	1.61593i	−0.154722	+	0.987958i	$0.549448\pi$
$353$	−7.71034e8	+	1.33547e9i	−0.932958	+	1.61593i	−0.778236	+	0.627972i	$0.783885\pi$
$354$		0			0
$355$	1.72785e8	+	2.99272e8i	0.204977	+	0.355031i
$356$	−3.17099e8			−0.372495
$357$		0			0
$358$	−3.13056e8			−0.360605
$359$	6.75450e8	+	1.16991e9i	0.770482	+	1.33451i	0.937299	+	0.348526i	$0.113318\pi$
$359$	6.75450e8	+	1.16991e9i	0.770482	+	1.33451i	−0.166817	+	0.985988i	$0.553349\pi$
$360$		0			0
$361$	4.15961e8	−	7.20466e8i	0.465347	−	0.806005i
$362$	−3.96053e8	−	6.85984e8i	−0.438807	−	0.760036i
$363$		0			0
$364$	−3.18873e8	+	6.05523e8i	−0.346548	+	0.658076i
$365$	3.19924e8			0.344367
$366$		0			0
$367$	−3.69324e8	+	6.39688e8i	−0.390010	+	0.675518i	−0.992450	−	0.122646i	$-0.960862\pi$
$367$	−3.69324e8	+	6.39688e8i	−0.390010	+	0.675518i	0.602440	+	0.798164i	$0.294195\pi$
$368$	1.88995e8	−	3.27349e8i	0.197689	−	0.342408i
$369$		0			0
$370$	2.66941e8			0.273974
$371$	2.70576e7	−	5.13810e7i	0.0275094	−	0.0522389i
$372$		0			0
$373$	−3.69601e8	−	6.40168e8i	−0.368767	−	0.638724i	0.620606	−	0.784123i	$-0.286887\pi$
$373$	−3.69601e8	−	6.40168e8i	−0.368767	−	0.638724i	−0.989373	+	0.145399i	$0.953553\pi$
$374$	−8.09171e7	+	1.40153e8i	−0.0799815	+	0.138532i
$375$		0			0
$376$	−2.05457e8	−	3.55862e8i	−0.199326	−	0.345242i
$377$	−5.34904e7			−0.0514139
$378$		0			0
$379$	1.38862e9			1.31023			0.655115	−	0.755529i	$-0.272620\pi$
$379$	1.38862e9			1.31023			0.655115	+	0.755529i	$0.272620\pi$
$380$	2.39538e7	+	4.14891e7i	0.0223940	+	0.0387875i
$381$		0			0
$382$	7.57237e7	−	1.31157e8i	0.0695041	−	0.120385i
$383$	−7.44411e8	−	1.28936e9i	−0.677044	−	1.17267i	−0.975867	−	0.218366i	$-0.929927\pi$
$383$	−7.44411e8	−	1.28936e9i	−0.677044	−	1.17267i	0.298823	−	0.954309i	$-0.403406\pi$
$384$		0			0
$385$	−1.69501e8	+	6.59564e6i	−0.151377	+	0.00589040i
$386$	2.89410e8			0.256128
$387$		0			0
$388$	−2.53509e8	+	4.39091e8i	−0.220335	+	0.381631i
$389$	3.52737e8	−	6.10959e8i	0.303828	−	0.526245i	−0.673172	−	0.739486i	$-0.735069\pi$
$389$	3.52737e8	−	6.10959e8i	0.303828	−	0.526245i	0.977000	+	0.213241i	$0.0684019\pi$
$390$		0			0
$391$	9.49832e8			0.803578
$392$	4.20379e8	−	3.27652e7i	0.352484	−	0.0274734i
$393$		0			0
$394$	4.55761e8	+	7.89401e8i	0.375405	+	0.650221i
$395$	1.33865e8	−	2.31860e8i	0.109289	−	0.189294i
$396$		0			0
$397$	−7.71562e8	−	1.33638e9i	−0.618877	−	1.07193i	−0.989691	−	0.143219i	$-0.954255\pi$
$397$	−7.71562e8	−	1.33638e9i	−0.618877	−	1.07193i	0.370814	−	0.928707i	$-0.379079\pi$
$398$	−8.38180e8			−0.666417
$399$		0			0
$400$	−2.82952e8			−0.221056
$401$	9.60469e8	+	1.66358e9i	0.743838	+	1.28836i	0.950736	+	0.310002i	$0.100330\pi$
$401$	9.60469e8	+	1.66358e9i	0.743838	+	1.28836i	−0.206898	+	0.978363i	$0.566337\pi$
$402$		0			0
$403$	9.47573e8	−	1.64124e9i	0.721182	−	1.24912i
$404$	−1.89248e8	−	3.27787e8i	−0.142789	−	0.247319i
$405$		0			0
$406$	1.75760e7	+	2.78796e7i	0.0130340	+	0.0206750i
$407$	6.89566e8			0.506985
$408$		0			0
$409$	−7.74628e8	+	1.34170e9i	−0.559837	+	0.969666i	0.437672	+	0.899134i	$0.355803\pi$
$409$	−7.74628e8	+	1.34170e9i	−0.559837	+	0.969666i	−0.997510	+	0.0705317i	$0.977530\pi$
$410$	1.69817e8	−	2.94131e8i	0.121685	−	0.210764i
$411$		0			0
$412$	7.65094e8			0.538982
$413$	−5.82197e8	+	1.10556e9i	−0.406672	+	0.772250i
$414$		0			0
$415$	4.38163e8	+	7.58920e8i	0.300931	+	0.521228i
$416$	1.93053e8	−	3.34378e8i	0.131477	−	0.227725i
$417$		0			0
$418$	6.18777e7	+	1.07175e8i	0.0414398	+	0.0717758i
$419$	−5.42846e6			−0.00360519			−0.00180259	−	0.999998i	$-0.500574\pi$
$419$	−5.42846e6			−0.00360519			−0.00180259	+	0.999998i	$0.500574\pi$
$420$		0			0
$421$	2.83478e9			1.85154			0.925769	−	0.378091i	$-0.123419\pi$
$421$	2.83478e9			1.85154			0.925769	+	0.378091i	$0.123419\pi$
$422$	−7.96089e8	−	1.37887e9i	−0.515665	−	0.893159i
$423$		0			0
$424$	−1.63813e7	+	2.83733e7i	−0.0104368	+	0.0180771i
$425$	−3.55507e8	−	6.15757e8i	−0.224640	−	0.389088i
$426$		0			0
$427$	1.74224e8	+	2.76360e8i	0.108296	+	0.171782i
$428$	−6.22773e8			−0.383952
$429$		0			0
$430$	2.70565e8	−	4.68632e8i	0.164109	−	0.284245i
$431$	1.22536e9	−	2.12239e9i	0.737216	−	1.27690i	−0.216529	−	0.976276i	$-0.569473\pi$
$431$	1.22536e9	−	2.12239e9i	0.737216	−	1.27690i	0.953744	−	0.300619i	$-0.0971932\pi$
$432$		0			0
$433$	1.55968e9			0.923269			0.461635	−	0.887070i	$-0.347263\pi$
$433$	1.55968e9			0.923269			0.461635	+	0.887070i	$0.347263\pi$
$434$	−1.16678e9	+	4.54020e7i	−0.685135	+	0.0266600i
$435$		0			0
$436$	−6.52198e8	−	1.12964e9i	−0.376857	−	0.652736i
$437$	3.63171e8	−	6.29030e8i	0.208174	−	0.360567i
$438$		0			0
$439$	−2.60662e8	−	4.51480e8i	−0.147046	−	0.254690i	0.783089	−	0.621910i	$-0.213643\pi$
$439$	−2.60662e8	−	4.51480e8i	−0.147046	−	0.254690i	−0.930134	+	0.367220i	$0.880310\pi$
$440$	9.57036e7			0.0535604
$441$		0			0
$442$	9.70226e8			0.534435
$443$	−1.15868e9	−	2.00689e9i	−0.633215	−	1.09676i	−0.986890	−	0.161392i	$-0.948402\pi$
$443$	−1.15868e9	−	2.00689e9i	−0.633215	−	1.09676i	0.353676	−	0.935368i	$-0.384932\pi$
$444$		0			0
$445$	−2.35608e8	+	4.08084e8i	−0.126745	+	0.219528i
$446$	3.02789e8	+	5.24445e8i	0.161610	+	0.279916i
$447$		0			0
$448$	−2.37714e8	+	9.24994e6i	−0.124905	+	0.00486033i
$449$	2.77082e9			1.44459			0.722297	−	0.691583i	$-0.243086\pi$
$449$	2.77082e9			1.44459			0.722297	+	0.691583i	$0.243086\pi$
$450$		0			0
$451$	4.38673e8	−	7.59804e8i	0.225176	−	0.390017i
$452$	6.61326e8	−	1.14545e9i	0.336846	−	0.583434i
$453$		0			0
$454$	−8.06552e8			−0.404517
$455$	5.42340e8	+	8.60276e8i	0.269918	+	0.428152i
$456$		0			0
$457$	1.25384e8	+	2.17171e8i	0.0614517	+	0.106437i	0.895115	−	0.445836i	$-0.147094\pi$
$457$	1.25384e8	+	2.17171e8i	0.0614517	+	0.106437i	−0.833663	+	0.552274i	$0.813760\pi$
$458$	−1.19846e9	+	2.07579e9i	−0.582900	+	1.00961i
$459$		0			0
$460$	−2.80850e8	−	4.86447e8i	−0.134531	−	0.233014i
$461$	−2.63549e9			−1.25287			−0.626437	−	0.779472i	$-0.715487\pi$
$461$	−2.63549e9			−1.25287			−0.626437	+	0.779472i	$0.715487\pi$
$462$		0			0
$463$	3.89548e9			1.82401			0.912006	−	0.410178i	$-0.134533\pi$
$463$	3.89548e9			1.82401			0.912006	+	0.410178i	$0.134533\pi$
$464$	−9.29713e6	−	1.61031e7i	−0.00432052	−	0.00748336i
$465$		0			0
$466$	6.40343e8	−	1.10911e9i	0.293131	−	0.507718i
$467$	1.45172e9	+	2.51446e9i	0.659591	+	1.14244i	0.980722	+	0.195410i	$0.0626037\pi$
$467$	1.45172e9	+	2.51446e9i	0.659591	+	1.14244i	−0.321131	+	0.947035i	$0.604063\pi$
$468$		0			0
$469$	−7.55011e8	+	1.43373e9i	−0.337947	+	0.641743i
$470$	−6.10625e8			−0.271289
$471$		0			0
$472$	3.52475e8	−	6.10505e8i	0.154288	−	0.267234i
$473$	6.98927e8	−	1.21058e9i	0.303681	−	0.525992i
$474$		0			0
$475$	−5.43716e8			−0.232780
$476$	−3.18799e8	−	5.05689e8i	−0.135485	−	0.214911i
$477$		0			0
$478$	−6.51482e8	−	1.12840e9i	−0.272838	−	0.472570i
$479$	1.19799e9	−	2.07498e9i	0.498056	−	0.862658i	−0.501942	−	0.864902i	$-0.667381\pi$
$479$	1.19799e9	−	2.07498e9i	0.498056	−	0.862658i	0.999997	+	0.00224334i	$0.000714078\pi$
$480$		0			0
$481$	−2.06704e9	−	3.58021e9i	−0.846916	−	1.46690i
$482$	1.71382e9			0.697107
$483$		0			0
$484$	−9.99956e8			−0.400887
$485$	3.76719e8	+	6.52497e8i	0.149942	+	0.259706i
$486$		0			0
$487$	6.75499e8	−	1.17000e9i	0.265017	−	0.459022i	−0.702551	−	0.711633i	$-0.747956\pi$
$487$	6.75499e8	−	1.17000e9i	0.265017	−	0.459022i	0.967568	+	0.252611i	$0.0812892\pi$
$488$	−9.21591e7	−	1.59624e8i	−0.0358979	−	0.0621770i
$489$		0			0
$490$	2.70179e8	−	5.65343e8i	0.103744	−	0.217083i
$491$	2.89904e9			1.10527			0.552636	−	0.833423i	$-0.313622\pi$
$491$	2.89904e9			1.10527			0.552636	+	0.833423i	$0.313622\pi$
$492$		0			0
$493$	2.33623e7	−	4.04646e7i	0.00878113	−	0.0152094i
$494$	3.70968e8	−	6.42536e8i	0.138450	−	0.239802i
$495$		0			0
$496$	6.58788e8			0.242415
$497$	−3.29493e9	+	1.28212e8i	−1.20392	+	0.0468471i
$498$		0			0
$499$	5.44922e8	+	9.43833e8i	0.196328	+	0.340051i	0.947335	−	0.320244i	$-0.103765\pi$
$499$	5.44922e8	+	9.43833e8i	0.196328	+	0.340051i	−0.751007	+	0.660294i	$0.770432\pi$
$500$	−4.47998e8	+	7.75956e8i	−0.160281	+	0.277614i
$501$		0			0
$502$	−1.37096e9	−	2.37457e9i	−0.483684	−	0.837766i
$503$	4.47095e9			1.56643			0.783216	−	0.621750i	$-0.213578\pi$
$503$	4.47095e9			1.56643			0.783216	+	0.621750i	$0.213578\pi$
$504$		0			0
$505$	−5.62451e8			−0.194341
$506$	−7.25496e8	−	1.25660e9i	−0.248948	−	0.431190i
$507$		0			0
$508$	−6.35529e7	+	1.10077e8i	−0.0215086	+	0.0372540i
$509$	1.58472e9	+	2.74482e9i	0.532649	+	0.922575i	0.999273	+	0.0381191i	$0.0121366\pi$
$509$	1.58472e9	+	2.74482e9i	0.532649	+	0.922575i	−0.466624	+	0.884456i	$0.654530\pi$
$510$		0			0
$511$	−1.42241e9	+	2.70108e9i	−0.471575	+	0.895496i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	−1.92646e9	+	3.33672e9i	−0.625732	+	1.08380i
$515$	5.68472e8	−	9.84622e8i	0.183393	−	0.317646i
$516$		0			0
$517$	−1.57738e9			−0.502017
$518$	−1.18684e9	+	2.25375e9i	−0.375179	+	0.712445i
$519$		0			0
$520$	−2.86880e8	−	4.96891e8i	−0.0894724	−	0.154971i
$521$	−7.53997e8	+	1.30596e9i	−0.233581	+	0.404574i	−0.958859	−	0.283881i	$-0.908378\pi$
$521$	−7.53997e8	+	1.30596e9i	−0.233581	+	0.404574i	0.725278	+	0.688456i	$0.241711\pi$
$522$		0			0
$523$	−1.15180e9	−	1.99497e9i	−0.352062	−	0.609790i	0.634548	−	0.772883i	$-0.281186\pi$
$523$	−1.15180e9	−	1.99497e9i	−0.352062	−	0.609790i	−0.986611	+	0.163093i	$0.947853\pi$
$524$	−1.47715e9			−0.448504
$525$		0			0
$526$	2.49260e9			0.746796
$527$	8.27717e8	+	1.43365e9i	0.246346	+	0.426683i
$528$		0			0
$529$	−2.55564e9	+	4.42651e9i	−0.750595	+	1.30007i
$530$	2.43429e7	+	4.21632e7i	0.00710243	+	0.0123018i
$531$		0			0
$532$	−4.56788e8	+	1.77746e7i	−0.131530	+	0.00511809i
$533$	−5.25985e9			−1.50462
$534$		0			0
$535$	−4.62726e8	+	8.01465e8i	−0.130643	+	0.226280i
$536$	4.57101e8	−	7.91722e8i	0.128214	−	0.222073i
$537$		0			0
$538$	−2.04243e9			−0.565469
$539$	6.97930e8	−	1.46040e9i	0.191978	−	0.401709i
$540$		0			0
$541$	3.21839e9	+	5.57442e9i	0.873873	+	1.51359i	0.857958	+	0.513720i	$0.171733\pi$
$541$	3.21839e9	+	5.57442e9i	0.873873	+	1.51359i	0.0159155	+	0.999873i	$0.494934\pi$
$542$	−3.76950e8	+	6.52896e8i	−0.101692	+	0.176135i
$543$		0			0
$544$	1.68634e8	+	2.92083e8i	0.0449107	+	0.0777876i
$545$	−1.93836e9			−0.512915
$546$		0			0
$547$	4.02910e9			1.05257			0.526287	−	0.850307i	$-0.323584\pi$
$547$	4.02910e9			1.05257			0.526287	+	0.850307i	$0.323584\pi$
$548$	1.32922e9	+	2.30228e9i	0.345036	+	0.597621i
$549$		0			0
$550$	−5.43084e8	+	9.40649e8i	−0.139187	+	0.241078i
$551$	−1.78652e7	−	3.09435e7i	−0.00454965	−	0.00788023i
$552$		0			0
$553$	1.36239e9	+	2.16107e9i	0.342582	+	0.543414i
$554$	−9.88849e8			−0.247085
$555$		0			0
$556$	1.06411e9	−	1.84310e9i	0.262558	−	0.454764i
$557$	−2.36357e9	+	4.09383e9i	−0.579530	+	1.00378i	0.416003	+	0.909363i	$0.363430\pi$
$557$	−2.36357e9	+	4.09383e9i	−0.579530	+	1.00378i	−0.995533	+	0.0944121i	$0.969903\pi$
$558$		0			0
$559$	−8.38040e9			−2.02919
$560$	−1.64719e8	+	3.12794e8i	−0.0396357	+	0.0752662i
$561$		0			0
$562$	1.71426e9	+	2.96919e9i	0.407381	+	0.705604i
$563$	−2.52081e9	+	4.36617e9i	−0.595333	+	1.03115i	0.398166	+	0.917313i	$0.369647\pi$
$563$	−2.52081e9	+	4.36617e9i	−0.595333	+	1.03115i	−0.993500	+	0.113834i	$0.963687\pi$
$564$		0			0
$565$	−9.82741e8	−	1.70216e9i	−0.229229	−	0.397036i
$566$	2.42883e9			0.563040
$567$		0			0
$568$	1.86038e9			0.425973
$569$	−2.28115e9	−	3.95106e9i	−0.519111	−	0.899127i	−0.999753	−	0.0222104i	$-0.992930\pi$
$569$	−2.28115e9	−	3.95106e9i	−0.519111	−	0.899127i	0.480642	−	0.876917i	$-0.340404\pi$
$570$		0			0
$571$	3.10593e9	−	5.37963e9i	0.698177	−	1.20928i	−0.270921	−	0.962602i	$-0.587328\pi$
$571$	3.10593e9	−	5.37963e9i	0.698177	−	1.20928i	0.969098	−	0.246676i	$-0.0793385\pi$
$572$	−7.41073e8	−	1.28358e9i	−0.165568	−	0.286771i
$573$		0			0
$574$	1.72829e9	+	2.74147e9i	0.381439	+	0.605051i
$575$	6.37490e9			1.39841
$576$		0			0
$577$	4.81150e8	−	8.33376e8i	0.104271	−	0.180603i	−0.809169	−	0.587576i	$-0.800082\pi$
$577$	4.81150e8	−	8.33376e8i	0.104271	−	0.180603i	0.913440	+	0.406973i	$0.133416\pi$
$578$	1.21760e9	−	2.10895e9i	0.262276	−	0.454275i
$579$		0			0
$580$	−2.76314e7			−0.00588037
$581$	−8.35557e9	+	3.25132e8i	−1.76750	+	0.0687771i
$582$		0			0
$583$	6.28830e7	+	1.08917e8i	0.0131430	+	0.0227643i
$584$	8.61157e8	−	1.49157e9i	0.178911	−	0.309883i
$585$		0			0
$586$	1.63641e9	+	2.83434e9i	0.335931	+	0.581849i
$587$	−7.88681e9			−1.60942			−0.804708	−	0.593671i	$-0.797678\pi$
$587$	−7.88681e9			−1.60942			−0.804708	+	0.593671i	$0.797678\pi$
$588$		0			0
$589$	1.26592e9			0.255272
$590$	−5.23785e8	−	9.07222e8i	−0.104996	−	0.181858i
$591$		0			0
$592$	7.18541e8	−	1.24455e9i	0.142340	−	0.246539i
$593$	1.19425e8	+	2.06850e8i	0.0235182	+	0.0407347i	0.877545	−	0.479494i	$-0.159180\pi$
$593$	1.19425e8	+	2.06850e8i	0.0235182	+	0.0407347i	−0.854027	+	0.520229i	$0.825847\pi$
$594$		0			0
$595$	−8.87656e8	+	3.45405e7i	−0.172757	+	0.00672232i
$596$	−3.37059e9			−0.652144
$597$		0			0
$598$	−4.34948e9	+	7.53352e9i	−0.831732	+	1.44060i
$599$	4.74012e9	−	8.21013e9i	0.901147	−	1.56083i	0.0751399	−	0.997173i	$-0.476060\pi$
$599$	4.74012e9	−	8.21013e9i	0.901147	−	1.56083i	0.826007	−	0.563660i	$-0.190607\pi$
$600$		0			0
$601$	1.13408e8			0.0213100			0.0106550	−	0.999943i	$-0.496608\pi$
$601$	1.13408e8			0.0213100			0.0106550	+	0.999943i	$0.496608\pi$
$602$	2.75365e9	+	4.36792e9i	0.514424	+	0.815994i
$603$		0			0
$604$	−2.07653e9	−	3.59665e9i	−0.383450	−	0.664154i
$605$	−7.42976e8	+	1.28687e9i	−0.136405	+	0.236261i
$606$		0			0
$607$	−3.26388e9	−	5.65320e9i	−0.592343	−	1.02597i	−0.993916	−	0.110141i	$-0.964870\pi$
$607$	−3.26388e9	−	5.65320e9i	−0.592343	−	1.02597i	0.401573	−	0.915827i	$-0.368464\pi$
$608$	2.57911e8			0.0465380
$609$		0			0
$610$	−2.73900e8			−0.0488582
$611$	4.72833e9	+	8.18971e9i	0.838617	+	1.45253i
$612$		0			0
$613$	−2.64156e9	+	4.57531e9i	−0.463179	+	0.802249i	−0.999117	−	0.0420080i	$-0.986625\pi$
$613$	−2.64156e9	+	4.57531e9i	−0.463179	+	0.802249i	0.535939	+	0.844257i	$0.319958\pi$
$614$	−1.62254e9	−	2.81032e9i	−0.282882	−	0.489966i
$615$		0			0
$616$	−4.25506e8	+	8.08013e8i	−0.0733454	+	0.139279i
$617$	−3.54184e9			−0.607058			−0.303529	−	0.952822i	$-0.598165\pi$
$617$	−3.54184e9			−0.607058			−0.303529	+	0.952822i	$0.598165\pi$
$618$		0			0
$619$	−1.02848e9	+	1.78138e9i	−0.174292	+	0.301883i	−0.939916	−	0.341405i	$-0.889097\pi$
$619$	−1.02848e9	+	1.78138e9i	−0.174292	+	0.301883i	0.765624	+	0.643289i	$0.222430\pi$
$620$	4.89485e8	−	8.47814e8i	0.0824838	−	0.142866i
$621$		0			0
$622$	−5.23594e9			−0.872426
$623$	−2.39787e9	−	3.80358e9i	−0.397300	−	0.630209i
$624$		0			0
$625$	−2.03270e9	−	3.52075e9i	−0.333038	−	0.576839i
$626$	9.27058e8	−	1.60571e9i	0.151042	−	0.261612i
$627$		0			0
$628$	−1.20909e9	−	2.09420e9i	−0.194804	−	0.337411i
$629$	3.61117e9			0.578589
$630$		0			0
$631$	−8.96586e9			−1.42066			−0.710328	−	0.703870i	$-0.751454\pi$
$631$	−8.96586e9			−1.42066			−0.710328	+	0.703870i	$0.751454\pi$
$632$	−7.20663e8	−	1.24822e9i	−0.113559	−	0.196690i
$633$		0			0
$634$	−7.01016e8	+	1.21420e9i	−0.109248	+	0.189224i
$635$	9.44408e7	+	1.63576e8i	0.0146370	+	0.0253520i
$636$		0			0
$637$	−9.67449e9	+	7.54050e8i	−1.48300	+	0.115588i
$638$	−7.13778e7			−0.0108816
$639$		0			0
$640$	9.97250e7	−	1.72729e8i	0.0150374	−	0.0260456i
$641$	7.49838e7	−	1.29876e8i	0.0112451	−	0.0194771i	−0.860348	−	0.509707i	$-0.829754\pi$
$641$	7.49838e7	−	1.29876e8i	0.0112451	−	0.0194771i	0.871593	+	0.490230i	$0.163087\pi$
$642$		0			0
$643$	8.16574e9			1.21132			0.605658	−	0.795725i	$-0.292910\pi$
$643$	8.16574e9			1.21132			0.605658	+	0.795725i	$0.292910\pi$
$644$	5.35569e9	−	2.08401e8i	0.790160	−	0.0307467i
$645$		0			0
$646$	3.24045e8	+	5.61263e8i	0.0472925	+	0.0819130i
$647$	3.46080e9	−	5.99428e9i	0.502356	−	0.870106i	−0.497640	−	0.867384i	$-0.665800\pi$
$647$	3.46080e9	−	5.99428e9i	0.502356	−	0.870106i	0.999996	−	0.00272280i	$-0.000866696\pi$
$648$		0			0
$649$	−1.35305e9	−	2.34355e9i	−0.194293	−	0.336525i
$650$	6.51177e9			0.930042
$651$		0			0
$652$	6.02154e9			0.850826
$653$	−1.24757e7	−	2.16085e7i	−0.00175335	−	0.00303688i	0.865147	−	0.501518i	$-0.167225\pi$
$653$	−1.24757e7	−	2.16085e7i	−0.00175335	−	0.00303688i	−0.866901	+	0.498481i	$0.833891\pi$
$654$		0			0
$655$	−1.09754e9	+	1.90099e9i	−0.152607	+	0.264324i
$656$	−9.14211e8	−	1.58346e9i	−0.126440	−	0.219000i
$657$		0			0
$658$	2.71489e9	−	5.15543e9i	0.371502	−	0.705463i
$659$	1.65846e9			0.225739			0.112870	−	0.993610i	$-0.463996\pi$
$659$	1.65846e9			0.225739			0.112870	+	0.993610i	$0.463996\pi$
$660$		0			0
$661$	6.15465e9	−	1.06602e10i	0.828893	−	1.43568i	−0.0700151	−	0.997546i	$-0.522305\pi$
$661$	6.15465e9	−	1.06602e10i	0.828893	−	1.43568i	0.898908	−	0.438138i	$-0.144362\pi$
$662$	−4.97828e8	+	8.62263e8i	−0.0666924	+	0.115515i
$663$		0			0
$664$	4.71771e9			0.625379
$665$	−3.16523e8	+	6.01060e8i	−0.0417378	+	0.0792578i
$666$		0			0
$667$	2.09464e8	+	3.62802e8i	0.0273319	+	0.0473402i
$668$	−3.27802e9	+	5.67769e9i	−0.425494	+	0.736978i
$669$		0			0
$670$	−6.79260e8	−	1.17651e9i	−0.0872517	−	0.151124i
$671$	−7.07543e8			−0.0904116
$672$		0			0
$673$	4.85194e9			0.613569			0.306784	−	0.951779i	$-0.400747\pi$
$673$	4.85194e9			0.613569			0.306784	+	0.951779i	$0.400747\pi$
$674$	3.18662e9	+	5.51939e9i	0.400886	+	0.694355i
$675$		0			0
$676$	−2.43492e9	+	4.21740e9i	−0.303159	+	0.525087i
$677$	−4.40705e9	−	7.63323e9i	−0.545868	−	0.945471i	−0.998552	−	0.0537999i	$-0.982867\pi$
$677$	−4.40705e9	−	7.63323e9i	−0.545868	−	0.945471i	0.452684	−	0.891671i	$-0.350467\pi$
$678$		0			0
$679$	−7.18387e9	+	2.79539e8i	−0.880673	+	0.0342688i
$680$	5.01187e8			0.0611250
$681$		0			0
$682$	1.26445e9	−	2.19008e9i	0.152635	−	0.264372i
$683$	−5.23834e9	+	9.07307e9i	−0.629102	+	1.08964i	0.358630	+	0.933480i	$0.383244\pi$
$683$	−5.23834e9	+	9.07307e9i	−0.629102	+	1.08964i	−0.987732	+	0.156157i	$0.950089\pi$
$684$		0			0
$685$	3.95049e9			0.469606
$686$	3.57188e9	+	4.79464e9i	0.422438	+	0.567051i
$687$		0			0
$688$	−1.45659e9	−	2.52289e9i	−0.170521	−	0.295351i
$689$	3.76995e8	−	6.52975e8i	0.0439105	−	0.0760552i
$690$		0			0
$691$	2.45431e9	+	4.25099e9i	0.282980	+	0.490136i	0.972117	−	0.234495i	$-0.0753435\pi$
$691$	2.45431e9	+	4.25099e9i	0.282980	+	0.490136i	−0.689137	+	0.724631i	$0.742010\pi$
$692$	1.24071e9			0.142331
$693$		0			0
$694$	5.45344e9			0.619317
$695$	−1.58129e9	−	2.73887e9i	−0.178675	−	0.309475i
$696$		0			0
$697$	2.29727e9	−	3.97899e9i	0.256979	−	0.445101i
$698$	3.86041e9	+	6.68643e9i	0.429675	+	0.744219i
$699$		0			0
$700$	−2.13965e9	−	3.39398e9i	−0.235776	−	0.373996i
$701$	9.55909e9			1.04810			0.524051	−	0.851687i	$-0.324420\pi$
$701$	9.55909e9			1.04810			0.524051	+	0.851687i	$0.324420\pi$
$702$		0			0
$703$	1.38074e9	−	2.39151e9i	0.149888	−	0.259614i
$704$	2.57611e8	−	4.46195e8i	0.0278266	−	0.0481971i
$705$		0			0
$706$	1.23365e10			1.31940
$707$	2.50070e9	−	4.74870e9i	0.266130	−	0.505367i
$708$		0			0
$709$	3.46644e9	+	6.00404e9i	0.365276	+	0.632677i	0.988820	−	0.149111i	$-0.0476412\pi$
$709$	3.46644e9	+	6.00404e9i	0.365276	+	0.632677i	−0.623544	+	0.781788i	$0.714308\pi$
$710$	1.38228e9	−	2.39417e9i	0.144941	−	0.251045i
$711$		0			0
$712$	1.26840e9	+	2.19693e9i	0.131697	+	0.228106i
$713$	−1.48425e10			−1.53353
$714$		0			0
$715$	−2.20250e9			−0.225343
$716$	1.25222e9	+	2.16892e9i	0.127493	+	0.220824i
$717$		0			0
$718$	5.40360e9	−	9.35930e9i	0.544813	−	0.943644i
$719$	−5.22335e9	−	9.04711e9i	−0.524081	−	0.907734i	−0.999607	−	0.0280327i	$-0.991076\pi$
$719$	−5.22335e9	−	9.04711e9i	−0.524081	−	0.907734i	0.475526	−	0.879701i	$-0.342258\pi$
$720$		0			0
$721$	5.78556e9	+	9.17724e9i	0.574873	+	0.911882i
$722$	−6.65538e9			−0.658101
$723$		0			0
$724$	−3.16843e9	+	5.48787e9i	−0.310283	+	0.537427i
$725$	1.56798e8	−	2.71583e8i	0.0152812	−	0.0264679i
$726$		0			0
$727$	1.31125e10			1.26566			0.632828	−	0.774293i	$-0.281894\pi$
$727$	1.31125e10			1.26566			0.632828	+	0.774293i	$0.281894\pi$
$728$	5.47068e9	−	2.12875e8i	0.525511	−	0.0204487i
$729$		0			0
$730$	−1.27970e9	−	2.21650e9i	−0.121752	−	0.210881i
$731$	3.66019e9	−	6.33964e9i	0.346572	−	0.600280i
$732$		0			0
$733$	5.15193e9	+	8.92341e9i	0.483177	+	0.836887i	0.999813	−	0.0193179i	$-0.00614945\pi$
$733$	5.15193e9	+	8.92341e9i	0.483177	+	0.836887i	−0.516636	+	0.856205i	$0.672816\pi$
$734$	5.90918e9			0.551558
$735$		0			0
$736$	−3.02392e9			−0.279575
$737$	−1.75467e9	−	3.03918e9i	−0.161458	−	0.279654i
$738$		0			0
$739$	3.46618e9	−	6.00360e9i	0.315933	−	0.547213i	−0.663702	−	0.747997i	$-0.731016\pi$
$739$	3.46618e9	−	6.00360e9i	0.315933	−	0.547213i	0.979635	+	0.200784i	$0.0643491\pi$
$740$	−1.06776e9	−	1.84942e9i	−0.0968644	−	0.167774i
$741$		0			0
$742$	−4.64209e8	+	1.80633e7i	−0.0417157	+	0.00162324i
$743$	1.63033e10			1.45820			0.729098	−	0.684409i	$-0.239940\pi$
$743$	1.63033e10			1.45820			0.729098	+	0.684409i	$0.239940\pi$
$744$		0			0
$745$	−2.50437e9	+	4.33770e9i	−0.221897	+	0.384338i
$746$	−2.95681e9	+	5.12134e9i	−0.260758	+	0.451646i
$747$		0			0
$748$	1.29467e9			0.113111
$749$	−4.70935e9	−	7.47011e9i	−0.409519	−	0.649592i
$750$		0			0
$751$	2.17154e7	+	3.76122e7i	0.00187080	+	0.00324033i	0.866959	−	0.498379i	$-0.166071\pi$
$751$	2.17154e7	+	3.76122e7i	0.00187080	+	0.00324033i	−0.865088	+	0.501619i	$0.832738\pi$
$752$	−1.64366e9	+	2.84689e9i	−0.140945	+	0.244123i
$753$		0			0
$754$	2.13961e8	+	3.70592e8i	0.0181776	+	0.0314845i
$755$	−6.17151e9			−0.521888
$756$		0			0
$757$	−1.40955e10			−1.18098			−0.590491	−	0.807044i	$-0.701066\pi$
$757$	−1.40955e10			−1.18098			−0.590491	+	0.807044i	$0.701066\pi$
$758$	−5.55450e9	−	9.62067e9i	−0.463236	−	0.802348i
$759$		0			0
$760$	1.91630e8	−	3.31913e8i	0.0158349	−	0.0274269i
$761$	5.41737e9	+	9.38316e9i	0.445597	+	0.771797i	0.998094	−	0.0617185i	$-0.0196581\pi$
$761$	5.41737e9	+	9.38316e9i	0.445597	+	0.771797i	−0.552497	+	0.833515i	$0.686325\pi$
$762$		0			0
$763$	8.61808e9	−	1.63653e10i	0.702384	−	1.33379i
$764$	−1.21158e9			−0.0982936
$765$		0			0
$766$	−5.95529e9	+	1.03149e10i	−0.478743	+	0.829206i
$767$	−8.11177e9	+	1.40500e10i	−0.649130	+	1.12433i
$768$		0			0
$769$	−3.10964e9			−0.246585			−0.123293	−	0.992370i	$-0.539345\pi$
$769$	−3.10964e9			−0.246585			−0.123293	+	0.992370i	$0.539345\pi$
$770$	7.23701e8	+	1.14796e9i	0.0571270	+	0.0906166i
$771$		0			0
$772$	−1.15764e9	−	2.00509e9i	−0.0905551	−	0.156846i
$773$	−2.16694e9	+	3.75326e9i	−0.168741	+	0.292267i	−0.937977	−	0.346697i	$-0.887303\pi$
$773$	−2.16694e9	+	3.75326e9i	−0.168741	+	0.292267i	0.769237	+	0.638964i	$0.220637\pi$
$774$		0			0
$775$	5.55531e9	+	9.62208e9i	0.428699	+	0.742528i
$776$	4.05615e9			0.311600
$777$		0			0
$778$	−5.64380e9			−0.429678
$779$	−1.75674e9	−	3.04275e9i	−0.133145	−	0.230614i
$780$		0			0
$781$	3.57072e9	−	6.18466e9i	0.268211	−	0.464555i
$782$	−3.79933e9	−	6.58063e9i	−0.284108	−	0.492089i
$783$		0			0
$784$	−1.90852e9	−	2.78141e9i	−0.141446	−	0.206138i
$785$	−3.59345e9			−0.265135
$786$		0			0
$787$	6.84958e9	−	1.18638e10i	0.500902	−	0.867587i	−0.499098	−	0.866546i	$-0.666335\pi$
$787$	6.84958e9	−	1.18638e10i	0.500902	−	0.867587i	0.999999	−	0.00104158i	$-0.000331546\pi$
$788$	3.64609e9	−	6.31521e9i	0.265452	−	0.459776i
$789$		0			0
$790$	−2.14183e9			−0.154558
$791$	1.87404e10	−	7.29229e8i	1.34636	−	0.0523898i
$792$		0			0
$793$	2.12092e9	+	3.67355e9i	0.151032	+	0.261595i
$794$	−6.17250e9	+	1.06911e10i	−0.437612	+	0.757966i
$795$		0			0
$796$	3.35272e9	+	5.80708e9i	0.235614	+	0.408096i
$797$	1.25491e10			0.878025			0.439012	−	0.898481i	$-0.355328\pi$
$797$	1.25491e10			0.878025			0.439012	+	0.898481i	$0.355328\pi$
$798$		0			0
$799$	−8.26051e9			−0.572919
$800$	1.13181e9	+	1.96035e9i	0.0781551	+	0.135369i
$801$		0			0
$802$	7.68375e9	−	1.33087e10i	0.525973	−	0.911011i
$803$	−3.30573e9	−	5.72569e9i	−0.225301	−	0.390232i
$804$		0			0
$805$	3.71113e9	−	7.04723e9i	0.250738	−	0.476138i
$806$	−1.51612e10			−1.01991
$807$		0			0
$808$	−1.51398e9	+	2.62229e9i	−0.100967	+	0.174881i
$809$	−7.35066e9	+	1.27317e10i	−0.488097	+	0.845409i	−0.999906	−	0.0136899i	$-0.995642\pi$
$809$	−7.35066e9	+	1.27317e10i	−0.488097	+	0.845409i	0.511809	+	0.859099i	$0.328976\pi$
$810$		0			0
$811$	−1.13444e9			−0.0746810			−0.0373405	−	0.999303i	$-0.511889\pi$
$811$	−1.13444e9			−0.0746810			−0.0373405	+	0.999303i	$0.511889\pi$
$812$	1.22851e8	−	2.33288e8i	0.00805256	−	0.0152914i
$813$		0			0
$814$	−2.75826e9	−	4.77745e9i	−0.179246	−	0.310464i
$815$	4.47406e9	−	7.74929e9i	0.289501	−	0.501430i
$816$		0			0
$817$	−2.79897e9	−	4.84795e9i	−0.179565	−	0.311015i
$818$	1.23940e10			0.791729
$819$		0			0
$820$	−2.71707e9			−0.172088
$821$	1.38267e10	+	2.39485e10i	0.872002	+	1.51035i	0.859922	+	0.510425i	$0.170512\pi$
$821$	1.38267e10	+	2.39485e10i	0.872002	+	1.51035i	0.0120795	+	0.999927i	$0.496155\pi$
$822$		0			0
$823$	−2.51993e9	+	4.36465e9i	−0.157576	+	0.272929i	−0.933994	−	0.357289i	$-0.883701\pi$
$823$	−2.51993e9	+	4.36465e9i	−0.157576	+	0.272929i	0.776418	+	0.630218i	$0.217035\pi$
$824$	−3.06038e9	−	5.30073e9i	−0.190559	−	0.330058i
$825$		0			0
$826$	9.98834e9	−	3.88667e8i	0.616685	−	0.0239965i
$827$	1.34824e9			0.0828891			0.0414446	−	0.999141i	$-0.486804\pi$
$827$	1.34824e9			0.0828891			0.0414446	+	0.999141i	$0.486804\pi$
$828$		0			0
$829$	1.01197e9	−	1.75279e9i	0.0616920	−	0.106854i	−0.833530	−	0.552474i	$-0.813684\pi$
$829$	1.01197e9	−	1.75279e9i	0.0616920	−	0.106854i	0.895222	+	0.445621i	$0.147017\pi$
$830$	3.50530e9	−	6.07136e9i	0.212790	−	0.368564i
$831$		0			0
$832$	−3.08885e9			−0.185937
$833$	3.65497e9	−	7.64793e9i	0.219092	−	0.458444i
$834$		0			0
$835$	4.87119e9	+	8.43715e9i	0.289556	+	0.501526i
$836$	4.95022e8	−	8.57403e8i	0.0293023	−	0.0507532i
$837$		0			0
$838$	2.17139e7	+	3.76095e7i	0.00127463	+	0.00220772i
$839$	9.19653e9			0.537598			0.268799	−	0.963196i	$-0.413373\pi$
$839$	9.19653e9			0.537598			0.268799	+	0.963196i	$0.413373\pi$
$840$		0			0
$841$	−1.72293e10			−0.998805
$842$	−1.13391e10	−	1.96399e10i	−0.654617	−	1.13383i
$843$		0			0
$844$	−6.36871e9	+	1.10309e10i	−0.364630	+	0.631559i
$845$	3.61833e9	+	6.26713e9i	0.206305	+	0.357331i
$846$		0			0
$847$	−7.56157e9	−	1.19944e10i	−0.427582	−	0.678244i
$848$	2.62101e8			0.0147599
$849$		0			0
$850$	−2.84406e9	+	4.92605e9i	−0.158844	+	0.275127i
$851$	−1.61887e10	+	2.80397e10i	−0.900448	+	1.55962i
$852$		0			0
$853$	−2.80320e10			−1.54644			−0.773220	−	0.634138i	$-0.781355\pi$
$853$	−2.80320e10			−1.54644			−0.773220	+	0.634138i	$0.781355\pi$
$854$	1.21778e9	−	2.31250e9i	0.0669063	−	0.127052i
$855$		0			0
$856$	2.49109e9	+	4.31470e9i	0.135747	+	0.235122i
$857$	1.00958e10	−	1.74864e10i	0.547906	−	0.949000i	−0.450512	−	0.892770i	$-0.648759\pi$
$857$	1.00958e10	−	1.74864e10i	0.547906	−	0.949000i	0.998418	−	0.0562301i	$-0.0179080\pi$
$858$		0			0
$859$	5.94937e9	+	1.03046e10i	0.320254	+	0.554697i	0.980540	−	0.196317i	$-0.0628983\pi$
$859$	5.94937e9	+	1.03046e10i	0.320254	+	0.554697i	−0.660286	+	0.751014i	$0.729565\pi$
$860$	−4.32904e9			−0.232085
$861$		0			0
$862$	−1.96058e10			−1.04258
$863$	−3.49693e9	−	6.05687e9i	−0.185204	−	0.320782i	0.758441	−	0.651741i	$-0.225961\pi$
$863$	−3.49693e9	−	6.05687e9i	−0.185204	−	0.320782i	−0.943645	+	0.330959i	$0.892628\pi$
$864$		0			0
$865$	9.21860e8	−	1.59671e9i	0.0484293	−	0.0838821i
$866$	−6.23873e9	−	1.08058e10i	−0.326425	−	0.565385i
$867$		0			0
$868$	4.98169e9	+	7.90211e9i	0.258558	+	0.410132i
$869$	−5.53282e9			−0.286007
$870$		0			0
$871$	−1.05196e10	+	1.82205e10i	−0.539430	+	0.934320i
$872$	−5.21758e9	+	9.03712e9i	−0.266478	+	0.461554i
$873$		0			0
$874$	−5.81073e9			−0.294402
$875$	−1.26952e10	+	4.93998e8i	−0.640638	+	0.0249286i
$876$		0			0
$877$	−7.11756e9	−	1.23280e10i	−0.356314	−	0.617154i	0.631028	−	0.775760i	$-0.282633\pi$
$877$	−7.11756e9	−	1.23280e10i	−0.356314	−	0.617154i	−0.987342	+	0.158606i	$0.949300\pi$
$878$	−2.08530e9	+	3.61184e9i	−0.103977	+	0.180093i
$879$		0			0
$880$	−3.82814e8	−	6.63054e8i	−0.0189365	−	0.0327989i
$881$	2.34184e10			1.15383			0.576914	−	0.816805i	$-0.304257\pi$
$881$	2.34184e10			1.15383			0.576914	+	0.816805i	$0.304257\pi$
$882$		0			0
$883$	1.15637e10			0.565241			0.282621	−	0.959232i	$-0.408796\pi$
$883$	1.15637e10			0.565241			0.282621	+	0.959232i	$0.408796\pi$
$884$	−3.88090e9	−	6.72192e9i	−0.188951	−	0.327273i
$885$		0			0
$886$	−9.26945e9	+	1.60552e10i	−0.447750	+	0.775526i
$887$	−3.72367e9	−	6.44958e9i	−0.179159	−	0.310312i	0.762434	−	0.647066i	$-0.224004\pi$
$887$	−3.72367e9	−	6.44958e9i	−0.179159	−	0.310312i	−0.941593	+	0.336754i	$0.890671\pi$
$888$		0			0
$889$	−1.80094e9	+	7.00785e7i	−0.0859694	+	0.00334525i
$890$	3.76972e9			0.179244
$891$		0			0
$892$	2.42231e9	−	4.19556e9i	0.114275	−	0.197931i
$893$	−3.15843e9	+	5.47056e9i	−0.148419	+	0.257070i
$894$		0			0
$895$	3.72165e9			0.173522
$896$	1.01494e9	+	1.60993e9i	0.0471371	+	0.0747703i
$897$		0			0
$898$	−1.10833e10	−	1.91968e10i	−0.510741	−	0.884630i
$899$	−3.65069e8	+	6.32318e8i	−0.0167578	+	0.0290253i
$900$		0			0
$901$	3.29310e8	+	5.70381e8i	0.0149992	+	0.0259794i
$902$	−7.01877e9			−0.318448
$903$		0			0
$904$	−1.05812e10			−0.476372
$905$	4.70834e9	+	8.15508e9i	0.211153	+	0.365728i
$906$		0			0
$907$	−9.50494e9	+	1.64630e10i	−0.422984	+	0.732630i	−0.996230	−	0.0867537i	$-0.972351\pi$
$907$	−9.50494e9	+	1.64630e10i	−0.422984	+	0.732630i	0.573246	+	0.819383i	$0.305684\pi$
$908$	3.22621e9	+	5.58796e9i	0.143018	+	0.247715i
$909$		0			0
$910$	3.79081e9	−	7.19855e9i	0.166758	−	0.316665i
$911$	−8.43646e9			−0.369697			−0.184849	−	0.982767i	$-0.559179\pi$
$911$	−8.43646e9			−0.369697			−0.184849	+	0.982767i	$0.559179\pi$
$912$		0			0
$913$	9.05494e9	−	1.56836e10i	0.393766	−	0.682022i
$914$	1.00307e9	−	1.73737e9i	0.0434529	−	0.0752626i
$915$		0			0
$916$	1.91753e10			0.824344
$917$	−1.11701e10	−	1.77183e10i	−0.478370	−	0.758806i
$918$		0			0
$919$	8.63092e9	+	1.49492e10i	0.366820	+	0.635351i	0.989066	−	0.147471i	$-0.0471132\pi$
$919$	8.63092e9	+	1.49492e10i	0.366820	+	0.635351i	−0.622247	+	0.782821i	$0.713780\pi$
$920$	−2.24680e9	+	3.89157e9i	−0.0951278	+	0.164766i
$921$		0			0
$922$	1.05419e10	+	1.82592e10i	0.442958	+	0.767225i
$923$	−4.28142e10			−1.79218
$924$		0			0
$925$	2.42367e10			1.00688
$926$	−1.55819e10	−	2.69887e10i	−0.644885	−	1.11697i
$927$		0			0
$928$	−7.43770e7	+	1.28825e8i	−0.00305507	+	0.00529153i
$929$	1.51806e10	+	2.62936e10i	0.621205	+	1.07596i	0.989262	+	0.146156i	$0.0466900\pi$
$929$	1.51806e10	+	2.62936e10i	0.621205	+	1.07596i	−0.368056	+	0.929804i	$0.619977\pi$
$930$		0			0
$931$	−3.66739e9	−	5.34472e9i	−0.148947	−	0.217071i
$932$	−1.02455e10			−0.414550
$933$		0			0
$934$	1.16138e10	−	2.01157e10i	0.466401	−	0.807830i
$935$	9.61954e8	−	1.66615e9i	0.0384870	−	0.0666614i
$936$		0			0
$937$	−7.46897e9			−0.296601			−0.148300	−	0.988942i	$-0.547380\pi$
$937$	−7.46897e9			−0.296601			−0.148300	+	0.988942i	$0.547380\pi$
$938$	1.29532e10	−	5.04035e8i	0.512468	−	0.0199412i
$939$		0			0
$940$	2.44250e9	+	4.23054e9i	0.0959152	+	0.166130i
$941$	8.47872e9	−	1.46856e10i	0.331716	−	0.574549i	−0.651132	−	0.758964i	$-0.725706\pi$
$941$	8.47872e9	−	1.46856e10i	0.331716	−	0.574549i	0.982848	+	0.184415i	$0.0590390\pi$
$942$		0			0
$943$	2.05971e10	+	3.56753e10i	0.799864	+	1.38541i
$944$	−5.63961e9			−0.218196
$945$		0			0
$946$	−1.11828e10			−0.429470
$947$	−3.93228e9	−	6.81090e9i	−0.150459	−	0.260603i	0.780937	−	0.624610i	$-0.214742\pi$
$947$	−3.93228e9	−	6.81090e9i	−0.150459	−	0.260603i	−0.931396	+	0.364007i	$0.881409\pi$
$948$		0			0
$949$	−1.98184e10	+	3.43265e10i	−0.752727	+	1.30376i
$950$	2.17487e9	+	3.76698e9i	0.0823000	+	0.142548i
$951$		0			0
$952$	−2.22832e9	+	4.23146e9i	−0.0837043	+	0.158950i
$953$	−2.00508e10			−0.750425			−0.375212	−	0.926939i	$-0.622430\pi$
$953$	−2.00508e10			−0.750425			−0.375212	+	0.926939i	$0.622430\pi$
$954$		0			0
$955$	−9.00215e8	+	1.55922e9i	−0.0334452	+	0.0579288i
$956$	−5.21186e9	+	9.02721e9i	−0.192926	+	0.334157i
$957$		0			0
$958$	−1.91678e10			−0.704357
$959$	−1.75642e10	+	3.33535e10i	−0.643077	+	1.22117i
$960$		0			0
$961$	8.22039e8	+	1.42381e9i	0.0298786	+	0.0517513i
$962$	−1.65363e10	+	2.86417e10i	−0.598860	+	1.03726i
$963$		0			0
$964$	−6.85526e9	−	1.18737e10i	−0.246465	−	0.426889i
$965$	−3.44055e9			−0.123249
$966$		0			0
$967$	−3.35149e10			−1.19192			−0.595958	−	0.803016i	$-0.703228\pi$
$967$	−3.35149e10			−1.19192			−0.595958	+	0.803016i	$0.703228\pi$
$968$	3.99982e9	+	6.92790e9i	0.141735	+	0.245492i
$969$		0			0
$970$	3.01376e9	−	5.21998e9i	0.106025	−	0.183640i
$971$	1.98936e10	+	3.44567e10i	0.697342	+	1.20783i	0.969385	+	0.245547i	$0.0789674\pi$
$971$	1.98936e10	+	3.44567e10i	0.697342	+	1.20783i	−0.272043	+	0.962285i	$0.587699\pi$
$972$		0			0
$973$	3.01545e10	−	1.17337e9i	1.04944	−	0.0408358i
$974$	−1.08080e10			−0.374790
$975$		0			0
$976$	−7.37273e8	+	1.27699e9i	−0.0253836	+	0.0439658i
$977$	2.72987e10	−	4.72827e10i	0.936507	−	1.62208i	0.164583	−	0.986363i	$-0.447372\pi$
$977$	2.72987e10	−	4.72827e10i	0.936507	−	1.62208i	0.771924	−	0.635715i	$-0.219294\pi$
$978$		0			0
$979$	9.73800e9			0.331689
$980$	−4.99753e9	+	3.89518e8i	−0.169615	+	0.0132201i
$981$		0			0
$982$	−1.15962e10	−	2.00851e10i	−0.390772	−	0.676838i
$983$	1.73751e10	−	3.00945e10i	0.583431	−	1.01053i	−0.411638	−	0.911347i	$-0.635043\pi$
$983$	1.73751e10	−	3.00945e10i	0.583431	−	1.01053i	0.995069	−	0.0991843i	$-0.0316233\pi$
$984$		0			0
$985$	−5.41815e9	−	9.38451e9i	−0.180644	−	0.312885i
$986$	−3.73796e8			−0.0124184
$987$		0			0
$988$	−5.93549e9			−0.195798
$989$	3.28170e10	+	5.68407e10i	1.07873	+	1.86841i
$990$		0			0
$991$	−8.18462e9	+	1.41762e10i	−0.267141	+	0.462702i	−0.968122	−	0.250478i	$-0.919412\pi$
$991$	−8.18462e9	+	1.41762e10i	−0.267141	+	0.462702i	0.700981	+	0.713180i	$0.252746\pi$
$992$	−2.63515e9	−	4.56422e9i	−0.0857067	−	0.148448i
$993$		0			0
$994$	1.40680e10	+	2.23151e10i	0.454338	+	0.720686i
$995$	9.96440e9			0.320679
$996$		0			0
$997$	1.62152e10	−	2.80855e10i	0.518189	−	0.897530i	−0.481587	−	0.876398i	$-0.659940\pi$
$997$	1.62152e10	−	2.80855e10i	0.518189	−	0.897530i	0.999777	−	0.0211323i	$-0.00672712\pi$
$998$	4.35938e9	−	7.55067e9i	0.138825	−	0.240452i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.h.109.2		6
3.2	odd	2		42.8.e.e.25.2	✓	6
7.2	even	3	inner	126.8.g.h.37.2		6
21.2	odd	6		42.8.e.e.37.2	yes	6
21.5	even	6		294.8.e.ba.79.2		6
21.11	odd	6		294.8.a.v.1.2		3
21.17	even	6		294.8.a.w.1.2		3
21.20	even	2		294.8.e.ba.67.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.e.25.2	✓	6	3.2	odd	2
42.8.e.e.37.2	yes	6	21.2	odd	6
126.8.g.h.37.2		6	7.2	even	3	inner
126.8.g.h.109.2		6	1.1	even	1	trivial
294.8.a.v.1.2		3	21.11	odd	6
294.8.a.w.1.2		3	21.17	even	6
294.8.e.ba.67.2		6	21.20	even	2
294.8.e.ba.79.2		6	21.5	even	6

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(47.5526 + 82.3635i) q^{5} +(-906.806 + 35.2857i) q^{7} +512.000 q^{8} +(380.420 - 658.908i) q^{10} +(982.708 - 1702.10i) q^{11} -11783.0 q^{13} +(3871.69 + 6141.40i) q^{14} +(-2048.00 - 3547.24i) q^{16} +(5146.31 - 8913.67i) q^{17} +(-3935.41 - 6816.33i) q^{19} -6086.73 q^{20} -15723.3 q^{22} +(46141.4 + 79919.2i) q^{23} +(34540.0 - 59825.0i) q^{25} +(47132.1 + 81635.2i) q^{26} +(27062.1 - 51389.5i) q^{28} +4539.61 q^{29} +(-80418.5 + 139289. i) q^{31} +(-16384.0 + 28377.9i) q^{32} -82341.0 q^{34} +(-46027.2 - 73009.8i) q^{35} +(175425. + 303845. i) q^{37} +(-31483.3 + 54530.6i) q^{38} +(24346.9 + 42170.1i) q^{40} +446392. q^{41} +711226. q^{43} +(62893.3 + 108934. i) q^{44} +(369131. - 639354. i) q^{46} +(-401283. - 695043. i) q^{47} +(821053. - 63994.6i) q^{49} -552640. q^{50} +(377057. - 653082. i) q^{52} +(-31994.8 + 55416.5i) q^{53} +186921. q^{55} +(-464285. + 18066.3i) q^{56} +(-18158.5 - 31451.4i) q^{58} +(688429. - 1.19239e6i) q^{59} +(-179998. - 311766. i) q^{61} +1.28670e6 q^{62} +262144. q^{64} +(-560313. - 970491. i) q^{65} +(892775. - 1.54633e6i) q^{67} +(329364. + 570475. i) q^{68} +(-321718. + 610925. i) q^{70} +3.63355e6 q^{71} +(1.68195e6 - 2.91322e6i) q^{73} +(1.40340e6 - 2.43076e6i) q^{74} +503732. q^{76} +(-831066. + 1.57815e6i) q^{77} +(-1.40754e6 - 2.43794e6i) q^{79} +(194775. - 337361. i) q^{80} +(-1.78557e6 - 3.09269e6i) q^{82} +9.21428e6 q^{83} +978881. q^{85} +(-2.84490e6 - 4.92752e6i) q^{86} +(503146. - 871475. i) q^{88} +(2.47734e6 + 4.29088e6i) q^{89} +(1.06849e7 - 415772. i) q^{91} -5.90610e6 q^{92} +(-3.21026e6 + 5.56034e6i) q^{94} +(374278. - 648268. i) q^{95} +7.92217e6 q^{97} +(-3.72758e6 - 5.43244e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 192 q^{4} - 110 q^{5} + 635 q^{7} + 3072 q^{8} - 880 q^{10} + 548 q^{11} + 19898 q^{13} - 4568 q^{14} - 12288 q^{16} + 20972 q^{17} + 28383 q^{19} + 14080 q^{20} - 8768 q^{22} + 32732 q^{23}+ \cdots - 6110208 q^{98}+O(q^{100}) \) 6 * q - 24 * q^2 - 192 * q^4 - 110 * q^5 + 635 * q^7 + 3072 * q^8 - 880 * q^10 + 548 * q^11 + 19898 * q^13 - 4568 * q^14 - 12288 * q^16 + 20972 * q^17 + 28383 * q^19 + 14080 * q^20 - 8768 * q^22 + 32732 * q^23 + 22745 * q^25 - 79592 * q^26 - 4096 * q^28 - 234176 * q^29 - 147865 * q^31 - 98304 * q^32 - 335552 * q^34 - 876430 * q^35 - 367503 * q^37 + 227064 * q^38 - 56320 * q^40 + 2875908 * q^41 + 1498794 * q^43 + 35072 * q^44 + 261856 * q^46 - 741486 * q^47 + 1421697 * q^49 - 363920 * q^50 - 636736 * q^52 - 1032432 * q^53 - 7992560 * q^55 + 325120 * q^56 + 936704 * q^58 - 2389238 * q^59 - 1238746 * q^61 + 2365840 * q^62 + 1572864 * q^64 - 3798390 * q^65 + 2462497 * q^67 + 1342208 * q^68 + 4561840 * q^70 + 1272524 * q^71 - 4609961 * q^73 - 2940024 * q^74 - 3633024 * q^76 - 20044196 * q^77 + 6152849 * q^79 - 450560 * q^80 - 11503632 * q^82 + 24059768 * q^83 - 18273080 * q^85 - 5995176 * q^86 + 280576 * q^88 + 10646976 * q^89 + 47686115 * q^91 - 4189696 * q^92 - 5931888 * q^94 + 21560930 * q^95 + 4562944 * q^97 - 6110208 * q^98

Introduction

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