LMFDB - Embedded newform 126.8.g.e.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,8,Mod(37,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.37"); S:= CuspForms(chi, 8); N := Newforms(S);

sage: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")

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:traces = [4,16,0,-128,-238] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$39.3605132110$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{2389})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 598x^{2} + 597x + 356409 $ x^4 - x^3 + 598x^2 + 597x + 356409
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$12.4693 + 21.5975i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.8.g.e.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-108.377 + 187.715i) q^{5} +(726.284 - 544.110i) q^{7} -512.000 q^{8} +(867.019 + 1501.72i) q^{10} +(1290.93 + 2235.95i) q^{11} -8921.97 q^{13} +(-864.567 - 7208.28i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(-5556.44 - 9624.03i) q^{17} +(4323.40 - 7488.34i) q^{19} +13872.3 q^{20} +20654.9 q^{22} +(-33028.6 + 57207.2i) q^{23} +(15571.2 + 26970.1i) q^{25} +(-35687.9 + 61813.2i) q^{26} +(-53398.7 - 22843.2i) q^{28} -128836. q^{29} +(102048. + 176752. i) q^{31} +(16384.0 + 28377.9i) q^{32} -88903.0 q^{34} +(23424.9 + 195304. i) q^{35} +(-245856. + 425834. i) q^{37} +(-34587.2 - 59906.7i) q^{38} +(55489.2 - 96110.2i) q^{40} +623293. q^{41} +422919. q^{43} +(82619.5 - 143101. i) q^{44} +(264229. + 457657. i) q^{46} +(-602714. + 1.04393e6i) q^{47} +(231433. - 790356. i) q^{49} +249139. q^{50} +(285503. + 494506. i) q^{52} +(-636483. - 1.10242e6i) q^{53} -559630. q^{55} +(-371857. + 278584. i) q^{56} +(-515342. + 892599. i) q^{58} +(840430. + 1.45567e6i) q^{59} +(-1.06128e6 + 1.83818e6i) q^{61} +1.63276e6 q^{62} +262144. q^{64} +(966940. - 1.67479e6i) q^{65} +(1.67466e6 + 2.90060e6i) q^{67} +(-355612. + 615938. i) q^{68} +(1.44680e6 + 618922. i) q^{70} -2.49257e6 q^{71} +(1.63676e6 + 2.83496e6i) q^{73} +(1.96684e6 + 3.40667e6i) q^{74} -553395. q^{76} +(2.15418e6 + 921530. i) q^{77} +(2.09920e6 - 3.63591e6i) q^{79} +(-443914. - 768881. i) q^{80} +(2.49317e6 - 4.31830e6i) q^{82} -3.35527e6 q^{83} +2.40877e6 q^{85} +(1.69168e6 - 2.93007e6i) q^{86} +(-660956. - 1.14481e6i) q^{88} +(1.19979e6 - 2.07810e6i) q^{89} +(-6.47988e6 + 4.85453e6i) q^{91} +4.22766e6 q^{92} +(4.82171e6 + 8.35145e6i) q^{94} +(937117. + 1.62313e6i) q^{95} +4.51506e6 q^{97} +(-4.55001e6 - 4.76483e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 128 q^{4} - 238 q^{5} + 168 q^{7} - 2048 q^{8} + 1904 q^{10} + 5848 q^{11} + 2632 q^{13} + 2016 q^{14} - 8192 q^{16} - 47642 q^{17} + 41048 q^{19} + 30464 q^{20} + 93568 q^{22} - 49316 q^{23}+ \cdots - 20499248 q^{98}+O(q^{100}) $ 4 * q + 16 * q^2 - 128 * q^4 - 238 * q^5 + 168 * q^7 - 2048 * q^8 + 1904 * q^10 + 5848 * q^11 + 2632 * q^13 + 2016 * q^14 - 8192 * q^16 - 47642 * q^17 + 41048 * q^19 + 30464 * q^20 + 93568 * q^22 - 49316 * q^23 + 108816 * q^25 + 10528 * q^26 + 5376 * q^28 - 345640 * q^29 + 70252 * q^31 + 65536 * q^32 - 762272 * q^34 + 36904 * q^35 + 88166 * q^37 - 328384 * q^38 + 121856 * q^40 + 2312520 * q^41 + 115088 * q^43 + 374272 * q^44 + 394528 * q^46 - 1412292 * q^47 + 465892 * q^49 + 1741056 * q^50 - 84224 * q^52 - 2361174 * q^53 - 1258040 * q^55 - 86016 * q^56 - 1382560 * q^58 + 1842512 * q^59 - 1278242 * q^61 + 1124032 * q^62 + 1048576 * q^64 + 1716372 * q^65 + 2121480 * q^67 - 3049088 * q^68 + 2595712 * q^70 - 7200320 * q^71 + 1634682 * q^73 - 705328 * q^74 - 5254144 * q^76 - 1416226 * q^77 + 9192604 * q^79 - 974848 * q^80 + 9250080 * q^82 + 56560 * q^83 + 6369676 * q^85 + 460352 * q^86 - 2994176 * q^88 + 8936550 * q^89 - 26111120 * q^91 + 6312448 * q^92 + 11298336 * q^94 + 2562604 * q^95 + 11748408 * q^97 - 20499248 * q^98

Character values

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

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

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
$5$	−108.377	+	187.715i	−0.387743	+	0.671590i	−0.992146	−	0.125089i	$-0.960078\pi$
$5$	−108.377	+	187.715i	−0.387743	+	0.671590i	0.604403	+	0.796679i	$0.293412\pi$
$6$		0			0
$7$	726.284	−	544.110i	0.800319	−	0.599575i
$7$	726.284	−	544.110i	0.800319	−	0.599575i
$8$	−512.000			−0.353553
$9$		0			0
$10$	867.019	+	1501.72i	0.274176	+	0.474886i
$11$	1290.93	+	2235.95i	0.292434	+	0.506511i	0.974385	−	0.224887i	$-0.0722015\pi$
$11$	1290.93	+	2235.95i	0.292434	+	0.506511i	−0.681951	+	0.731398i	$0.738868\pi$
$12$		0			0
$13$	−8921.97			−1.12631			−0.563156	−	0.826350i	$-0.690413\pi$
$13$	−8921.97			−1.12631			−0.563156	+	0.826350i	$0.690413\pi$
$14$	−864.567	−	7208.28i	−0.0842075	−	0.702075i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−5556.44	−	9624.03i	−0.274300	−	0.475101i	0.695659	−	0.718373i	$-0.255113\pi$
$17$	−5556.44	−	9624.03i	−0.274300	−	0.475101i	−0.969958	+	0.243272i	$0.921779\pi$
$18$		0			0
$19$	4323.40	−	7488.34i	0.144606	−	0.250466i	−0.784620	−	0.619977i	$-0.787142\pi$
$19$	4323.40	−	7488.34i	0.144606	−	0.250466i	0.929226	+	0.369512i	$0.120475\pi$
$20$	13872.3			0.387743
$21$		0			0
$22$	20654.9			0.413564
$23$	−33028.6	+	57207.2i	−0.566034	+	0.980399i	0.430919	+	0.902391i	$0.358190\pi$
$23$	−33028.6	+	57207.2i	−0.566034	+	0.980399i	−0.996953	+	0.0780088i	$0.975144\pi$
$24$		0			0
$25$	15571.2	+	26970.1i	0.199311	+	0.345217i
$26$	−35687.9	+	61813.2i	−0.398212	+	0.689723i
$27$		0			0
$28$	−53398.7	−	22843.2i	−0.459703	−	0.196655i
$29$	−128836.			−0.980941			−0.490470	−	0.871458i	$-0.663175\pi$
$29$	−128836.			−0.980941			−0.490470	+	0.871458i	$0.663175\pi$
$30$		0			0
$31$	102048.	+	176752.i	0.615229	+	1.06561i	0.990344	+	0.138630i	$0.0442698\pi$
$31$	102048.	+	176752.i	0.615229	+	1.06561i	−0.375115	+	0.926978i	$0.622397\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$		0			0
$34$	−88903.0			−0.387918
$35$	23424.9	+	195304.i	0.0923505	+	0.769967i
$36$		0			0
$37$	−245856.	+	425834.i	−0.797947	+	1.38208i	0.123004	+	0.992406i	$0.460747\pi$
$37$	−245856.	+	425834.i	−0.797947	+	1.38208i	−0.920951	+	0.389678i	$0.872586\pi$
$38$	−34587.2	−	59906.7i	−0.102252	−	0.177106i
$39$		0			0
$40$	55489.2	−	96110.2i	0.137088	−	0.237443i
$41$	623293.			1.41237			0.706185	−	0.708027i	$-0.250415\pi$
$41$	623293.			1.41237			0.706185	+	0.708027i	$0.250415\pi$
$42$		0			0
$43$	422919.			0.811181			0.405591	−	0.914055i	$-0.367066\pi$
$43$	422919.			0.811181			0.405591	+	0.914055i	$0.367066\pi$
$44$	82619.5	−	143101.i	0.146217	−	0.253255i
$45$		0			0
$46$	264229.	+	457657.i	0.400246	+	0.693247i
$47$	−602714.	+	1.04393e6i	−0.846777	+	1.46666i	0.0372922	+	0.999304i	$0.488127\pi$
$47$	−602714.	+	1.04393e6i	−0.846777	+	1.46666i	−0.884069	+	0.467356i	$0.845207\pi$
$48$		0			0
$49$	231433.	−	790356.i	0.281021	−	0.959702i
$50$	249139.			0.281868
$51$		0			0
$52$	285503.	+	494506.i	0.281578	+	0.487708i
$53$	−636483.	−	1.10242e6i	−0.587247	−	1.01714i	−0.994591	−	0.103867i	$-0.966878\pi$
$53$	−636483.	−	1.10242e6i	−0.587247	−	1.01714i	0.407344	−	0.913275i	$-0.366455\pi$
$54$		0			0
$55$	−559630.			−0.453557
$56$	−371857.	+	278584.i	−0.282955	+	0.211982i
$57$		0			0
$58$	−515342.	+	892599.i	−0.346815	+	0.600701i
$59$	840430.	+	1.45567e6i	0.532745	+	0.922741i	0.999269	+	0.0382328i	$0.0121729\pi$
$59$	840430.	+	1.45567e6i	0.532745	+	0.922741i	−0.466524	+	0.884509i	$0.654494\pi$
$60$		0			0
$61$	−1.06128e6	+	1.83818e6i	−0.598651	+	1.03689i	0.394370	+	0.918952i	$0.370963\pi$
$61$	−1.06128e6	+	1.83818e6i	−0.598651	+	1.03689i	−0.993021	+	0.117942i	$0.962370\pi$
$62$	1.63276e6			0.870065
$63$		0			0
$64$	262144.			0.125000
$65$	966940.	−	1.67479e6i	0.436720	−	0.756421i
$66$		0			0
$67$	1.67466e6	+	2.90060e6i	0.680245	+	1.17822i	0.974906	+	0.222618i	$0.0714602\pi$
$67$	1.67466e6	+	2.90060e6i	0.680245	+	1.17822i	−0.294660	+	0.955602i	$0.595207\pi$
$68$	−355612.	+	615938.i	−0.137150	+	0.237550i
$69$		0			0
$70$	1.44680e6	+	618922.i	0.504157	+	0.215672i
$71$	−2.49257e6			−0.826502			−0.413251	−	0.910617i	$-0.635607\pi$
$71$	−2.49257e6			−0.826502			−0.413251	+	0.910617i	$0.635607\pi$
$72$		0			0
$73$	1.63676e6	+	2.83496e6i	0.492443	+	0.852936i	0.999962	−	0.00870409i	$-0.00277063\pi$
$73$	1.63676e6	+	2.83496e6i	0.492443	+	0.852936i	−0.507519	+	0.861641i	$0.669437\pi$
$74$	1.96684e6	+	3.40667e6i	0.564234	+	0.977281i
$75$		0			0
$76$	−553395.			−0.144606
$77$	2.15418e6	+	921530.i	0.537731	+	0.230034i
$78$		0			0
$79$	2.09920e6	−	3.63591e6i	0.479025	−	0.829695i	−0.520686	−	0.853748i	$-0.674324\pi$
$79$	2.09920e6	−	3.63591e6i	0.479025	−	0.829695i	0.999711	+	0.0240529i	$0.00765703\pi$
$80$	−443914.	−	768881.i	−0.0969357	−	0.167898i
$81$		0			0
$82$	2.49317e6	−	4.31830e6i	0.499348	−	0.864897i
$83$	−3.35527e6			−0.644102			−0.322051	−	0.946722i	$-0.604372\pi$
$83$	−3.35527e6			−0.644102			−0.322051	+	0.946722i	$0.604372\pi$
$84$		0			0
$85$	2.40877e6			0.425431
$86$	1.69168e6	−	2.93007e6i	0.286796	−	0.496745i
$87$		0			0
$88$	−660956.	−	1.14481e6i	−0.103391	−	0.179079i
$89$	1.19979e6	−	2.07810e6i	0.180402	−	0.312466i	−0.761615	−	0.648029i	$-0.775593\pi$
$89$	1.19979e6	−	2.07810e6i	0.180402	−	0.312466i	0.942018	+	0.335564i	$0.108927\pi$
$90$		0			0
$91$	−6.47988e6	+	4.85453e6i	−0.901409	+	0.675308i
$92$	4.22766e6			0.566034
$93$		0			0
$94$	4.82171e6	+	8.35145e6i	0.598762	+	1.03709i
$95$	937117.	+	1.62313e6i	0.112140	+	0.194232i
$96$		0			0
$97$	4.51506e6			0.502299			0.251150	−	0.967948i	$-0.419191\pi$
$97$	4.51506e6			0.502299			0.251150	+	0.967948i	$0.419191\pi$
$98$	−4.55001e6	−	4.76483e6i	−0.488339	−	0.511395i
$99$		0			0
$100$	996555.	−	1.72608e6i	0.0996555	−	0.172608i
$101$	3.69997e6	+	6.40853e6i	0.357333	+	0.618919i	0.987514	−	0.157529i	$-0.0503527\pi$
$101$	3.69997e6	+	6.40853e6i	0.357333	+	0.618919i	−0.630181	+	0.776448i	$0.717019\pi$
$102$		0			0
$103$	−9.22855e6	+	1.59843e7i	−0.832153	+	1.44133i	0.0641744	+	0.997939i	$0.479559\pi$
$103$	−9.22855e6	+	1.59843e7i	−0.832153	+	1.44133i	−0.896327	+	0.443393i	$0.853775\pi$
$104$	4.56805e6			0.398212
$105$		0			0
$106$	−1.01837e7			−0.830493
$107$	−2.49697e6	+	4.32488e6i	−0.197047	+	0.341296i	−0.947570	−	0.319549i	$-0.896469\pi$
$107$	−2.49697e6	+	4.32488e6i	−0.197047	+	0.341296i	0.750523	+	0.660845i	$0.229802\pi$
$108$		0			0
$109$	−9.34351e6	−	1.61834e7i	−0.691062	−	1.19695i	−0.971490	−	0.237080i	$-0.923810\pi$
$109$	−9.34351e6	−	1.61834e7i	−0.691062	−	1.19695i	0.280428	−	0.959875i	$-0.409524\pi$
$110$	−2.23852e6	+	3.87723e6i	−0.160357	+	0.277746i
$111$		0			0
$112$	442658.	+	3.69064e6i	0.0297718	+	0.248221i
$113$	−2.49534e7			−1.62688			−0.813438	−	0.581651i	$-0.802407\pi$
$113$	−2.49534e7			−1.62688			−0.813438	+	0.581651i	$0.802407\pi$
$114$		0			0
$115$	−7.15910e6	−	1.23999e7i	−0.438951	−	0.760286i
$116$	4.12274e6	+	7.14079e6i	0.245235	+	0.424760i
$117$		0			0
$118$	1.34469e7			0.753415
$119$	−9.27208e6	−	3.96647e6i	−0.504386	−	0.215769i
$120$		0			0
$121$	6.41059e6	−	1.11035e7i	0.328965	−	0.569783i
$122$	8.49020e6	+	1.47055e7i	0.423310	+	0.733194i
$123$		0			0
$124$	6.53105e6	−	1.13121e7i	0.307614	−	0.532804i
$125$	−2.36842e7			−1.08461
$126$		0			0
$127$	−1.72080e7			−0.745449			−0.372724	−	0.927942i	$-0.621576\pi$
$127$	−1.72080e7			−0.745449			−0.372724	+	0.927942i	$0.621576\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−7.73552e6	−	1.33983e7i	−0.308807	−	0.534870i
$131$	1.34633e7	−	2.33191e7i	0.523242	−	0.906281i	−0.476392	−	0.879233i	$-0.658056\pi$
$131$	1.34633e7	−	2.33191e7i	0.523242	−	0.906281i	0.999634	−	0.0270484i	$-0.00861082\pi$
$132$		0			0
$133$	−934467.	−	7.79106e6i	−0.0344416	−	0.287155i
$134$	2.67946e7			0.962012
$135$		0			0
$136$	2.84490e6	+	4.92751e6i	0.0969796	+	0.167974i
$137$	−1.36301e7	−	2.36080e7i	−0.452873	−	0.784399i	0.545690	−	0.837987i	$-0.316268\pi$
$137$	−1.36301e7	−	2.36080e7i	−0.452873	−	0.784399i	−0.998563	+	0.0535877i	$0.982934\pi$
$138$		0			0
$139$	−1.36813e7			−0.432092			−0.216046	−	0.976383i	$-0.569316\pi$
$139$	−1.36813e7			−0.432092			−0.216046	+	0.976383i	$0.569316\pi$
$140$	1.00752e7	−	7.54805e6i	0.310318	−	0.232481i
$141$		0			0
$142$	−9.97030e6	+	1.72691e7i	−0.292213	+	0.506127i
$143$	−1.15176e7	−	1.99491e7i	−0.329372	−	0.570489i
$144$		0			0
$145$	1.39629e7	−	2.41844e7i	0.380353	−	0.658790i
$146$	2.61882e7			0.696420
$147$		0			0
$148$	3.14695e7			0.797947
$149$	1.21944e7	−	2.11214e7i	0.302002	−	0.523083i	−0.674587	−	0.738195i	$-0.735678\pi$
$149$	1.21944e7	−	2.11214e7i	0.302002	−	0.523083i	0.976589	+	0.215112i	$0.0690118\pi$
$150$		0			0
$151$	−1.69013e7	−	2.92740e7i	−0.399486	−	0.691930i	0.594177	−	0.804335i	$-0.297478\pi$
$151$	−1.69013e7	−	2.92740e7i	−0.399486	−	0.691930i	−0.993663	+	0.112405i	$0.964145\pi$
$152$	−2.21358e6	+	3.83403e6i	−0.0511261	+	0.0885530i
$153$		0			0
$154$	1.50013e7	−	1.12385e7i	0.330983	−	0.247963i
$155$	−4.42386e7			−0.954202
$156$		0			0
$157$	−3.97833e6	−	6.89067e6i	−0.0820450	−	0.142106i	0.822083	−	0.569367i	$-0.192812\pi$
$157$	−3.97833e6	−	6.89067e6i	−0.0820450	−	0.142106i	−0.904128	+	0.427261i	$0.859478\pi$
$158$	−1.67936e7	−	2.90873e7i	−0.338722	−	0.586683i
$159$		0			0
$160$	−7.10262e6			−0.137088
$161$	7.13886e6	+	5.95198e7i	0.134815	+	1.12401i
$162$		0			0
$163$	2.68214e7	−	4.64560e7i	0.485093	−	0.840205i	−0.514761	−	0.857334i	$-0.672119\pi$
$163$	2.68214e7	−	4.64560e7i	0.485093	−	0.840205i	0.999853	+	0.0171289i	$0.00545257\pi$
$164$	−1.99454e7	−	3.45464e7i	−0.353093	−	0.611574i
$165$		0			0
$166$	−1.34211e7	+	2.32460e7i	−0.227724	+	0.394430i
$167$	8.20253e7			1.36283			0.681413	−	0.731899i	$-0.261366\pi$
$167$	8.20253e7			1.36283			0.681413	+	0.731899i	$0.261366\pi$
$168$		0			0
$169$	1.68530e7			0.268581
$170$	9.63508e6	−	1.66884e7i	0.150413	−	0.260522i
$171$		0			0
$172$	−1.35334e7	−	2.34406e7i	−0.202795	−	0.351252i
$173$	−3.39592e7	+	5.88190e7i	−0.498650	+	0.863687i	−0.999999	−	0.00155811i	$-0.999504\pi$
$173$	−3.39592e7	+	5.88190e7i	−0.498650	+	0.863687i	0.501349	+	0.865245i	$0.332837\pi$
$174$		0			0
$175$	2.59838e7	+	1.11155e7i	0.366496	+	0.156782i
$176$	−1.05753e7			−0.146217
$177$		0			0
$178$	−9.59835e6	−	1.66248e7i	−0.127564	−	0.220947i
$179$	−3.04898e7	−	5.28098e7i	−0.397346	−	0.688223i	0.596052	−	0.802946i	$-0.296735\pi$
$179$	−3.04898e7	−	5.28098e7i	−0.397346	−	0.688223i	−0.993398	+	0.114723i	$0.963402\pi$
$180$		0			0
$181$	−1.53894e8			−1.92907			−0.964533	−	0.263963i	$-0.914970\pi$
$181$	−1.53894e8			−1.92907			−0.964533	+	0.263963i	$0.914970\pi$
$182$	7.71364e6	+	6.43120e7i	0.0948439	+	0.790756i
$183$		0			0
$184$	1.69106e7	−	2.92901e7i	0.200123	−	0.346624i
$185$	−5.32904e7	−	9.23016e7i	−0.618796	−	1.07179i
$186$		0			0
$187$	1.43459e7	−	2.48479e7i	0.160429	−	0.277871i
$188$	7.71474e7			0.846777
$189$		0			0
$190$	1.49939e7			0.158590
$191$	1.12603e7	−	1.95034e7i	0.116932	−	0.202532i	−0.801618	−	0.597836i	$-0.796027\pi$
$191$	1.12603e7	−	1.95034e7i	0.116932	−	0.202532i	0.918550	+	0.395304i	$0.129361\pi$
$192$		0			0
$193$	6.76381e7	+	1.17153e8i	0.677237	+	1.17301i	0.975810	+	0.218622i	$0.0701563\pi$
$193$	6.76381e7	+	1.17153e8i	0.677237	+	1.17301i	−0.298572	+	0.954387i	$0.596510\pi$
$194$	1.80602e7	−	3.12813e7i	0.177590	−	0.307594i
$195$		0			0
$196$	−5.12118e7	+	1.24641e7i	−0.485818	+	0.118240i
$197$	8.96233e7			0.835197			0.417598	−	0.908632i	$-0.362872\pi$
$197$	8.96233e7			0.835197			0.417598	+	0.908632i	$0.362872\pi$
$198$		0			0
$199$	2.74707e7	+	4.75806e7i	0.247106	+	0.428000i	0.962722	−	0.270494i	$-0.0871870\pi$
$199$	2.74707e7	+	4.75806e7i	0.247106	+	0.428000i	−0.715616	+	0.698494i	$0.753854\pi$
$200$	−7.97244e6	−	1.38087e7i	−0.0704671	−	0.122053i
$201$		0			0
$202$	5.91995e7			0.505345
$203$	−9.35712e7	+	7.01007e7i	−0.785066	+	0.588147i
$204$		0			0
$205$	−6.75508e7	+	1.17001e8i	−0.547636	+	0.948534i
$206$	7.38284e7	+	1.27875e8i	0.588421	+	1.01918i
$207$		0			0
$208$	1.82722e7	−	3.16484e7i	0.140789	−	0.243854i
$209$	2.23248e7			0.169151
$210$		0			0
$211$	−1.24539e8			−0.912677			−0.456338	−	0.889806i	$-0.650839\pi$
$211$	−1.24539e8			−0.912677			−0.456338	+	0.889806i	$0.650839\pi$
$212$	−4.07349e7	+	7.05549e7i	−0.293624	+	0.508571i
$213$		0			0
$214$	1.99758e7	+	3.45990e7i	0.139333	+	0.241332i
$215$	−4.58349e7	+	7.93884e7i	−0.314530	+	0.544781i
$216$		0			0
$217$	1.70288e8	+	7.28467e7i	1.13129	+	0.483950i
$218$	−1.49496e8			−0.977310
$219$		0			0
$220$	1.79082e7	+	3.10179e7i	0.113389	+	0.196396i
$221$	4.95744e7	+	8.58653e7i	0.308947	+	0.535112i
$222$		0			0
$223$	2.85464e8			1.72379			0.861895	−	0.507087i	$-0.169278\pi$
$223$	2.85464e8			1.72379			0.861895	+	0.507087i	$0.169278\pi$
$224$	2.73401e7	+	1.16957e7i	0.162530	+	0.0695279i
$225$		0			0
$226$	−9.98135e7	+	1.72882e8i	−0.575188	+	0.996254i
$227$	3.37141e7	+	5.83946e7i	0.191303	+	0.331346i	0.945682	−	0.325092i	$-0.105395\pi$
$227$	3.37141e7	+	5.83946e7i	0.191303	+	0.331346i	−0.754379	+	0.656439i	$0.772062\pi$
$228$		0			0
$229$	−3.58459e7	+	6.20869e7i	−0.197249	+	0.341646i	−0.947636	−	0.319354i	$-0.896534\pi$
$229$	−3.58459e7	+	6.20869e7i	−0.197249	+	0.341646i	0.750386	+	0.660999i	$0.229867\pi$
$230$	−1.14546e8			−0.620771
$231$		0			0
$232$	6.59638e7			0.346815
$233$	1.08990e6	−	1.88777e6i	0.00564472	−	0.00977693i	−0.863189	−	0.504881i	$-0.831537\pi$
$233$	1.08990e6	−	1.88777e6i	0.00564472	−	0.00977693i	0.868834	+	0.495104i	$0.164870\pi$
$234$		0			0
$235$	−1.30641e8	−	2.26277e8i	−0.656663	−	1.13737i
$236$	5.37875e7	−	9.31627e7i	0.266373	−	0.461371i
$237$		0			0
$238$	−6.45688e7	+	4.83730e7i	−0.310458	+	0.232586i
$239$	1.87131e8			0.886654			0.443327	−	0.896360i	$-0.353798\pi$
$239$	1.87131e8			0.886654			0.443327	+	0.896360i	$0.353798\pi$
$240$		0			0
$241$	6.26650e7	+	1.08539e8i	0.288380	+	0.499489i	0.973423	−	0.229014i	$-0.0735500\pi$
$241$	6.26650e7	+	1.08539e8i	0.288380	+	0.499489i	−0.685043	+	0.728502i	$0.740217\pi$
$242$	−5.12847e7	−	8.88277e7i	−0.232613	−	0.402898i
$243$		0			0
$244$	1.35843e8			0.598651
$245$	1.23280e8	+	1.29100e8i	0.535562	+	0.560848i
$246$		0			0
$247$	−3.85732e7	+	6.68108e7i	−0.162872	+	0.282103i
$248$	−5.22484e7	−	9.04968e7i	−0.217516	−	0.376749i
$249$		0			0
$250$	−9.47369e7	+	1.64089e8i	−0.383468	+	0.664186i
$251$	−3.48978e7			−0.139296			−0.0696482	−	0.997572i	$-0.522188\pi$
$251$	−3.48978e7			−0.139296			−0.0696482	+	0.997572i	$0.522188\pi$
$252$		0			0
$253$	−1.70550e8			−0.662110
$254$	−6.88321e7	+	1.19221e8i	−0.263556	+	0.456492i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−2.96784e7	+	5.14046e7i	−0.109062	+	0.188902i	−0.915391	−	0.402567i	$-0.868118\pi$
$257$	−2.96784e7	+	5.14046e7i	−0.109062	+	0.188902i	0.806328	+	0.591468i	$0.201452\pi$
$258$		0			0
$259$	5.31396e7	+	4.43049e8i	0.190051	+	1.58454i
$260$	−1.23768e8			−0.436720
$261$		0			0
$262$	−1.07706e8	−	1.86553e8i	−0.369988	−	0.640838i
$263$	−1.06373e7	−	1.84243e7i	−0.0360567	−	0.0624521i	0.847434	−	0.530901i	$-0.178146\pi$
$263$	−1.06373e7	−	1.84243e7i	−0.0360567	−	0.0624521i	−0.883491	+	0.468449i	$0.844813\pi$
$264$		0			0
$265$	2.75921e8			0.910804
$266$	−5.77159e7	−	2.46901e7i	−0.188023	−	0.0804334i
$267$		0			0
$268$	1.07178e8	−	1.85639e8i	0.340123	−	0.589110i
$269$	5.85529e7	+	1.01417e8i	0.183407	+	0.317670i	0.943038	−	0.332684i	$-0.107954\pi$
$269$	5.85529e7	+	1.01417e8i	0.183407	+	0.317670i	−0.759632	+	0.650353i	$0.774621\pi$
$270$		0			0
$271$	1.01385e8	−	1.75603e8i	0.309442	−	0.535970i	−0.668798	−	0.743444i	$-0.733191\pi$
$271$	1.01385e8	−	1.75603e8i	0.309442	−	0.535970i	0.978240	+	0.207474i	$0.0665243\pi$
$272$	4.55183e7			0.137150
$273$		0			0
$274$	−2.18081e8			−0.640459
$275$	−4.02026e7	+	6.96329e7i	−0.116571	+	0.201906i
$276$		0			0
$277$	−5.05757e7	−	8.75996e7i	−0.142976	−	0.247641i	0.785640	−	0.618684i	$-0.212334\pi$
$277$	−5.05757e7	−	8.75996e7i	−0.142976	−	0.247641i	−0.928616	+	0.371042i	$0.879000\pi$
$278$	−5.47253e7	+	9.47869e7i	−0.152768	+	0.264601i
$279$		0			0
$280$	−1.19935e7	−	9.99954e7i	−0.0326508	−	0.272224i
$281$	−3.69631e8			−0.993793			−0.496897	−	0.867810i	$-0.665527\pi$
$281$	−3.69631e8			−0.993793			−0.496897	+	0.867810i	$0.665527\pi$
$282$		0			0
$283$	1.09831e8	+	1.90232e8i	0.288052	+	0.498921i	0.973345	−	0.229347i	$-0.0736590\pi$
$283$	1.09831e8	+	1.90232e8i	0.288052	+	0.498921i	−0.685293	+	0.728268i	$0.740326\pi$
$284$	7.97624e7	+	1.38153e8i	0.206626	+	0.357886i
$285$		0			0
$286$	−1.84282e8			−0.465803
$287$	4.52687e8	−	3.39140e8i	1.13035	−	0.846821i
$288$		0			0
$289$	1.43421e8	−	2.48413e8i	0.349519	−	0.605385i
$290$	−1.11703e8	−	1.93475e8i	−0.268950	−	0.465835i
$291$		0			0
$292$	1.04753e8	−	1.81437e8i	0.246222	−	0.426468i
$293$	7.22230e8			1.67741			0.838704	−	0.544587i	$-0.183314\pi$
$293$	7.22230e8			1.67741			0.838704	+	0.544587i	$0.183314\pi$
$294$		0			0
$295$	−3.64334e8			−0.826272
$296$	1.25878e8	−	2.18027e8i	0.282117	−	0.488641i
$297$		0			0
$298$	−9.75555e7	−	1.68971e8i	−0.213548	−	0.369875i
$299$	2.94680e8	−	5.10401e8i	0.637531	−	1.10424i
$300$		0			0
$301$	3.07159e8	−	2.30114e8i	0.649204	−	0.486364i
$302$	−2.70421e8			−0.564959
$303$		0			0
$304$	1.77086e7	+	3.06722e7i	0.0361516	+	0.0626164i
$305$	−2.30036e8	−	3.98435e8i	−0.464245	−	0.804096i
$306$		0			0
$307$	−6.39545e7			−0.126150			−0.0630750	−	0.998009i	$-0.520091\pi$
$307$	−6.39545e7			−0.126150			−0.0630750	+	0.998009i	$0.520091\pi$
$308$	−1.78575e7	−	1.48886e8i	−0.0348252	−	0.290353i
$309$		0			0
$310$	−1.76954e8	+	3.06494e8i	−0.337361	+	0.584327i
$311$	7.73216e7	+	1.33925e8i	0.145760	+	0.252464i	0.929656	−	0.368428i	$-0.120104\pi$
$311$	7.73216e7	+	1.33925e8i	0.145760	+	0.252464i	−0.783896	+	0.620892i	$0.786771\pi$
$312$		0			0
$313$	2.46992e8	−	4.27803e8i	0.455279	−	0.788567i	−0.543425	−	0.839458i	$-0.682873\pi$
$313$	2.46992e8	−	4.27803e8i	0.455279	−	0.788567i	0.998704	+	0.0508911i	$0.0162062\pi$
$314$	−6.36533e7			−0.116029
$315$		0			0
$316$	−2.68697e8			−0.479025
$317$	2.14969e8	−	3.72338e8i	0.379026	−	0.656492i	−0.611895	−	0.790939i	$-0.709592\pi$
$317$	2.14969e8	−	3.72338e8i	0.379026	−	0.656492i	0.990921	+	0.134447i	$0.0429258\pi$
$318$		0			0
$319$	−1.66318e8	−	2.88071e8i	−0.286861	−	0.496857i
$320$	−2.84105e7	+	4.92084e7i	−0.0484678	+	0.0839488i
$321$		0			0
$322$	4.40921e8	+	1.88620e8i	0.735978	+	0.314841i
$323$	−9.60907e7			−0.158662
$324$		0			0
$325$	−1.38926e8	−	2.40626e8i	−0.224487	−	0.388822i
$326$	−2.14571e8	−	3.71648e8i	−0.343012	−	0.594115i
$327$		0			0
$328$	−3.19126e8			−0.499348
$329$	1.30272e8	+	1.08613e9i	0.201681	+	1.68150i
$330$		0			0
$331$	1.64085e8	−	2.84203e8i	0.248697	−	0.430755i	−0.714468	−	0.699668i	$-0.753331\pi$
$331$	1.64085e8	−	2.84203e8i	0.248697	−	0.430755i	0.963164	+	0.268913i	$0.0866645\pi$
$332$	1.07369e8	+	1.85968e8i	0.161025	+	0.278904i
$333$		0			0
$334$	3.28101e8	−	5.68288e8i	0.481832	−	0.834557i
$335$	−7.25983e8			−1.05504
$336$		0			0
$337$	−1.14409e8			−0.162838			−0.0814189	−	0.996680i	$-0.525945\pi$
$337$	−1.14409e8			−0.162838			−0.0814189	+	0.996680i	$0.525945\pi$
$338$	6.74121e7	−	1.16761e8i	0.0949576	−	0.164471i
$339$		0			0
$340$	−7.70806e7	−	1.33508e8i	−0.106358	−	0.184217i
$341$	−2.63472e8	+	4.56348e8i	−0.359828	+	0.623240i
$342$		0			0
$343$	−2.61954e8	−	6.99947e8i	−0.350507	−	0.936560i
$344$	−2.16535e8			−0.286796
$345$		0			0
$346$	2.71673e8	+	4.70552e8i	0.352599	+	0.610719i
$347$	−3.28339e8	−	5.68699e8i	−0.421860	−	0.730684i	0.574261	−	0.818672i	$-0.305289\pi$
$347$	−3.28339e8	−	5.68699e8i	−0.421860	−	0.730684i	−0.996121	+	0.0879887i	$0.971956\pi$
$348$		0			0
$349$	−8.85994e8			−1.11569			−0.557843	−	0.829947i	$-0.688371\pi$
$349$	−8.85994e8			−1.11569			−0.557843	+	0.829947i	$0.688371\pi$
$350$	1.80945e8	−	1.35559e8i	0.225585	−	0.169001i
$351$		0			0
$352$	−4.23012e7	+	7.32678e7i	−0.0516955	+	0.0895393i
$353$	3.43700e8	+	5.95305e8i	0.415880	+	0.720324i	0.995520	−	0.0945476i	$-0.0301405\pi$
$353$	3.43700e8	+	5.95305e8i	0.415880	+	0.720324i	−0.579641	+	0.814872i	$0.696807\pi$
$354$		0			0
$355$	2.70139e8	−	4.67894e8i	0.320470	−	0.555071i
$356$	−1.53574e8			−0.180402
$357$		0			0
$358$	−4.87836e8			−0.561932
$359$	1.61222e7	−	2.79244e7i	0.0183905	−	0.0318533i	−0.856684	−	0.515842i	$-0.827479\pi$
$359$	1.61222e7	−	2.79244e7i	0.0183905	−	0.0318533i	0.875074	+	0.483989i	$0.160812\pi$
$360$		0			0
$361$	4.09552e8	+	7.09365e8i	0.458178	+	0.793588i
$362$	−6.15577e8	+	1.06621e9i	−0.682028	+	1.18131i
$363$		0			0
$364$	4.76421e8	+	2.03806e8i	0.517770	+	0.221495i
$365$	−7.09553e8			−0.763765
$366$		0			0
$367$	3.58275e8	+	6.20551e8i	0.378343	+	0.655309i	0.990821	−	0.135178i	$-0.0431607\pi$
$367$	3.58275e8	+	6.20551e8i	0.378343	+	0.655309i	−0.612479	+	0.790487i	$0.709827\pi$
$368$	−1.35285e8	−	2.34321e8i	−0.141508	−	0.245100i
$369$		0			0
$370$	−8.52646e8			−0.875110
$371$	−1.06210e9	−	4.54353e8i	−1.07984	−	0.461940i
$372$		0			0
$373$	−6.11134e8	+	1.05852e9i	−0.609755	+	1.05613i	0.381525	+	0.924358i	$0.375399\pi$
$373$	−6.11134e8	+	1.05852e9i	−0.609755	+	1.05613i	−0.991281	+	0.131769i	$0.957934\pi$
$374$	−1.14767e8	−	1.98783e8i	−0.113441	−	0.196485i
$375$		0			0
$376$	3.08590e8	−	5.34493e8i	0.299381	−	0.518543i
$377$	1.14947e9			1.10485
$378$		0			0
$379$	−6.83298e8			−0.644723			−0.322361	−	0.946617i	$-0.604477\pi$
$379$	−6.83298e8			−0.644723			−0.322361	+	0.946617i	$0.604477\pi$
$380$	5.99755e7	−	1.03881e8i	0.0560701	−	0.0971162i
$381$		0			0
$382$	−9.00823e7	−	1.56027e8i	−0.0826833	−	0.143212i
$383$	1.01294e9	−	1.75447e9i	0.921273	−	1.59569i	0.123826	−	0.992304i	$-0.460484\pi$
$383$	1.01294e9	−	1.75447e9i	0.921273	−	1.59569i	0.797447	−	0.603388i	$-0.206183\pi$
$384$		0			0
$385$	−4.06450e8	+	3.04500e8i	−0.362990	+	0.271941i
$386$	1.08221e9			0.957758
$387$		0			0
$388$	−1.44482e8	−	2.50250e8i	−0.125575	−	0.217502i
$389$	−3.64506e8	−	6.31342e8i	−0.313965	−	0.543803i	0.665252	−	0.746619i	$-0.268324\pi$
$389$	−3.64506e8	−	6.31342e8i	−0.313965	−	0.543803i	−0.979217	+	0.202816i	$0.934991\pi$
$390$		0			0
$391$	7.34085e8			0.621052
$392$	−1.18494e8	+	4.04662e8i	−0.0993558	+	0.339306i
$393$		0			0
$394$	3.58493e8	−	6.20928e8i	0.295287	−	0.511452i
$395$	4.55011e8	+	7.88102e8i	0.371477	+	0.643417i
$396$		0			0
$397$	6.63836e8	−	1.14980e9i	0.532469	−	0.922263i	−0.466812	−	0.884356i	$-0.654598\pi$
$397$	6.63836e8	−	1.14980e9i	0.532469	−	0.922263i	0.999281	−	0.0379069i	$-0.0120690\pi$
$398$	4.39531e8			0.349461
$399$		0			0
$400$	−1.27559e8			−0.0996555
$401$	−4.28975e8	+	7.43007e8i	−0.332221	+	0.575423i	−0.982947	−	0.183889i	$-0.941131\pi$
$401$	−4.28975e8	+	7.43007e8i	−0.332221	+	0.575423i	0.650726	+	0.759312i	$0.274465\pi$
$402$		0			0
$403$	−9.10465e8	−	1.57697e9i	−0.692940	−	1.20021i
$404$	2.36798e8	−	4.10146e8i	0.178667	−	0.309460i
$405$		0			0
$406$	1.11387e8	+	9.28683e8i	0.0826025	+	0.688694i
$407$	−1.26953e9			−0.933387
$408$		0			0
$409$	1.05133e9	+	1.82096e9i	0.759814	+	1.31604i	0.942945	+	0.332948i	$0.108044\pi$
$409$	1.05133e9	+	1.82096e9i	0.759814	+	1.31604i	−0.183131	+	0.983089i	$0.558623\pi$
$410$	5.40407e8	+	9.36012e8i	0.387237	+	0.670715i
$411$		0			0
$412$	1.18125e9			0.832153
$413$	1.40243e9	+	5.99941e8i	0.979618	+	0.419067i
$414$		0			0
$415$	3.63636e8	−	6.29835e8i	0.249746	−	0.432572i
$416$	−1.46178e8	−	2.53187e8i	−0.0995529	−	0.172431i
$417$		0			0
$418$	8.92992e7	−	1.54671e8i	0.0598040	−	0.103584i
$419$	−2.47991e9			−1.64697			−0.823486	−	0.567336i	$-0.807974\pi$
$419$	−2.47991e9			−1.64697			−0.823486	+	0.567336i	$0.807974\pi$
$420$		0			0
$421$	−5.51855e7			−0.0360444			−0.0180222	−	0.999838i	$-0.505737\pi$
$421$	−5.51855e7			−0.0360444			−0.0180222	+	0.999838i	$0.505737\pi$
$422$	−4.98156e8	+	8.62832e8i	−0.322680	+	0.558898i
$423$		0			0
$424$	3.25879e8	+	5.64439e8i	0.207623	+	0.359614i
$425$	1.73041e8	−	2.99715e8i	0.109342	−	0.189386i
$426$		0			0
$427$	2.29386e8	+	1.91249e9i	0.142583	+	1.18878i
$428$	3.19612e8			0.197047
$429$		0			0
$430$	3.66679e8	+	6.35107e8i	0.222406	+	0.385219i
$431$	8.42361e8	+	1.45901e9i	0.506790	+	0.877786i	0.999969	+	0.00785824i	$0.00250138\pi$
$431$	8.42361e8	+	1.45901e9i	0.506790	+	0.877786i	−0.493179	+	0.869928i	$0.664165\pi$
$432$		0			0
$433$	−1.29692e9			−0.767724			−0.383862	−	0.923390i	$-0.625406\pi$
$433$	−1.29692e9			−0.767724			−0.383862	+	0.923390i	$0.625406\pi$
$434$	1.18585e9	−	8.88401e8i	0.696330	−	0.521669i
$435$		0			0
$436$	−5.97984e8	+	1.03574e9i	−0.345531	+	0.598477i
$437$	2.85591e8	+	4.94659e8i	0.163704	+	0.283544i
$438$		0			0
$439$	7.03191e7	−	1.21796e8i	0.0396686	−	0.0687081i	−0.845509	−	0.533960i	$-0.820703\pi$
$439$	7.03191e7	−	1.21796e8i	0.0396686	−	0.0687081i	0.885178	+	0.465252i	$0.154036\pi$
$440$	2.86531e8			0.160357
$441$		0			0
$442$	7.93190e8			0.436917
$443$	−9.24666e8	+	1.60157e9i	−0.505326	+	0.875251i	0.494655	+	0.869090i	$0.335295\pi$
$443$	−9.24666e8	+	1.60157e9i	−0.505326	+	0.875251i	−0.999981	+	0.00616141i	$0.998039\pi$
$444$		0			0
$445$	2.60061e8	+	4.50439e8i	0.139899	+	0.242313i
$446$	1.14186e9	−	1.97775e9i	0.609452	−	1.05560i
$447$		0			0
$448$	1.90391e8	−	1.42635e8i	0.100040	−	0.0749468i
$449$	2.91794e9			1.52130			0.760648	−	0.649165i	$-0.224882\pi$
$449$	2.91794e9			1.52130			0.760648	+	0.649165i	$0.224882\pi$
$450$		0			0
$451$	8.04627e8	+	1.39365e9i	0.413025	+	0.715381i
$452$	7.98508e8	+	1.38306e9i	0.406719	+	0.704458i
$453$		0			0
$454$	5.39426e8			0.270543
$455$	−2.08996e8	−	1.74249e9i	−0.104016	−	0.867224i
$456$		0			0
$457$	−1.42040e9	+	2.46021e9i	−0.696153	+	1.20577i	0.273638	+	0.961833i	$0.411773\pi$
$457$	−1.42040e9	+	2.46021e9i	−0.696153	+	1.20577i	−0.969791	+	0.243939i	$0.921560\pi$
$458$	2.86767e8	+	4.96695e8i	0.139476	+	0.241580i
$459$		0			0
$460$	−4.58183e8	+	7.93595e8i	−0.219476	+	0.380143i
$461$	−3.96057e9			−1.88280			−0.941400	−	0.337291i	$-0.890489\pi$
$461$	−3.96057e9			−1.88280			−0.941400	+	0.337291i	$0.890489\pi$
$462$		0			0
$463$	−2.19815e9			−1.02926			−0.514629	−	0.857413i	$-0.672070\pi$
$463$	−2.19815e9			−1.02926			−0.514629	+	0.857413i	$0.672070\pi$
$464$	2.63855e8	−	4.57011e8i	0.122618	−	0.212380i
$465$		0			0
$466$	−8.71922e6	−	1.51021e7i	−0.00399142	−	0.00691334i
$467$	1.56120e9	−	2.70408e9i	0.709332	−	1.22860i	−0.255773	−	0.966737i	$-0.582330\pi$
$467$	1.56120e9	−	2.70408e9i	0.709332	−	1.22860i	0.965105	−	0.261862i	$-0.0843366\pi$
$468$		0			0
$469$	2.79453e9	+	1.19546e9i	1.25084	+	0.535094i
$470$	−2.09026e9			−0.928662
$471$		0			0
$472$	−4.30300e8	−	7.45302e8i	−0.188354	−	0.326238i
$473$	5.45959e8	+	9.45629e8i	0.237217	+	0.410872i
$474$		0			0
$475$	2.69282e8			0.115287
$476$	7.68626e7	+	6.40838e8i	0.0326656	+	0.272348i
$477$		0			0
$478$	7.48526e8	−	1.29648e9i	0.313479	−	0.542962i
$479$	−6.79522e8	−	1.17697e9i	−0.282507	−	0.489317i	0.689494	−	0.724291i	$-0.257833\pi$
$479$	−6.79522e8	−	1.17697e9i	−0.282507	−	0.489317i	−0.972002	+	0.234974i	$0.924499\pi$
$480$		0			0
$481$	2.19352e9	−	3.79928e9i	0.898738	−	1.55666i
$482$	1.00264e9			0.407831
$483$		0			0
$484$	−8.20555e8			−0.328965
$485$	−4.89330e8	+	8.47545e8i	−0.194763	+	0.337339i
$486$		0			0
$487$	−1.19733e9	−	2.07383e9i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$487$	−1.19733e9	−	2.07383e9i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$488$	5.43373e8	−	9.41149e8i	0.211655	−	0.366597i
$489$		0			0
$490$	1.38755e9	−	3.37706e8i	0.532798	−	0.129674i
$491$	1.95738e9			0.746261			0.373130	−	0.927779i	$-0.378284\pi$
$491$	1.95738e9			0.746261			0.373130	+	0.927779i	$0.378284\pi$
$492$		0			0
$493$	7.15867e8	+	1.23992e9i	0.269072	+	0.466046i
$494$	3.08586e8	+	5.34486e8i	0.115168	+	0.199477i
$495$		0			0
$496$	−8.35974e8			−0.307614
$497$	−1.81032e9	+	1.35623e9i	−0.661465	+	0.495550i
$498$		0			0
$499$	−1.47577e8	+	2.55611e8i	−0.0531699	+	0.0920931i	−0.891385	−	0.453246i	$-0.850266\pi$
$499$	−1.47577e8	+	2.55611e8i	−0.0531699	+	0.0920931i	0.838215	+	0.545339i	$0.183599\pi$
$500$	7.57895e8	+	1.31271e9i	0.271153	+	0.469650i
$501$		0			0
$502$	−1.39591e8	+	2.41779e8i	−0.0492487	+	0.0853013i
$503$	−2.51431e9			−0.880909			−0.440454	−	0.897775i	$-0.645183\pi$
$503$	−2.51431e9			−0.880909			−0.440454	+	0.897775i	$0.645183\pi$
$504$		0			0
$505$	−1.60397e9			−0.554213
$506$	−6.82201e8	+	1.18161e9i	−0.234091	+	0.405458i
$507$		0			0
$508$	5.50657e8	+	9.53765e8i	0.186362	+	0.322789i
$509$	−1.11783e9	+	1.93615e9i	−0.375721	+	0.650767i	−0.990435	−	0.137983i	$-0.955938\pi$
$509$	−1.11783e9	+	1.93615e9i	−0.375721	+	0.650767i	0.614714	+	0.788750i	$0.289271\pi$
$510$		0			0
$511$	2.73128e9	+	1.16840e9i	0.905511	+	0.387365i
$512$	−1.34218e8			−0.0441942
$513$		0			0
$514$	2.37427e8	+	4.11236e8i	0.0771188	+	0.133574i
$515$	−2.00033e9	−	3.46468e9i	−0.645323	−	1.11773i
$516$		0			0
$517$	−3.11225e9			−0.990506
$518$	3.28209e9	+	1.40403e9i	1.03752	+	0.443837i
$519$		0			0
$520$	−4.95073e8	+	8.57492e8i	−0.154404	+	0.267435i
$521$	1.59740e9	+	2.76677e9i	0.494858	+	0.857120i	0.999982	−	0.00592705i	$-0.00188665\pi$
$521$	1.59740e9	+	2.76677e9i	0.494858	+	0.857120i	−0.505124	+	0.863047i	$0.668553\pi$
$522$		0			0
$523$	4.70741e8	−	8.15348e8i	0.143889	−	0.249222i	−0.785069	−	0.619408i	$-0.787373\pi$
$523$	4.70741e8	−	8.15348e8i	0.143889	−	0.249222i	0.928958	+	0.370186i	$0.120706\pi$
$524$	−1.72330e9			−0.523242
$525$		0			0
$526$	−1.70197e8			−0.0509919
$527$	1.13404e9	−	1.96422e9i	0.337514	−	0.584592i
$528$		0			0
$529$	−4.79361e8	−	8.30278e8i	−0.140789	−	0.243853i
$530$	1.10369e9	−	1.91164e9i	0.322018	−	0.557751i
$531$		0			0
$532$	−4.01921e8	+	3.01107e8i	−0.115731	+	0.0867023i
$533$	−5.56100e9			−1.59077
$534$		0			0
$535$	−5.41230e8	−	9.37438e8i	−0.152807	−	0.264670i
$536$	−8.57428e8	−	1.48511e9i	−0.240503	−	0.416564i
$537$		0			0
$538$	9.36846e8			0.259376
$539$	2.06596e9	−	5.02820e8i	0.568279	−	0.138309i
$540$		0			0
$541$	−1.93667e9	+	3.35441e9i	−0.525854	+	0.910806i	0.473692	+	0.880691i	$0.342921\pi$
$541$	−1.93667e9	+	3.35441e9i	−0.525854	+	0.910806i	−0.999546	+	0.0301159i	$0.990412\pi$
$542$	−8.11077e8	−	1.40483e9i	−0.218809	−	0.378988i
$543$		0			0
$544$	1.82073e8	−	3.15360e8i	0.0484898	−	0.0839868i
$545$	4.05050e9			1.07182
$546$		0			0
$547$	−1.92865e9			−0.503845			−0.251922	−	0.967747i	$-0.581063\pi$
$547$	−1.92865e9			−0.503845			−0.251922	+	0.967747i	$0.581063\pi$
$548$	−8.72326e8	+	1.51091e9i	−0.226437	+	0.392200i
$549$		0			0
$550$	3.21621e8	+	5.57063e8i	0.0824279	+	0.142769i
$551$	−5.57007e8	+	9.64765e8i	−0.141850	+	0.245692i
$552$		0			0
$553$	−4.53724e8	−	3.78290e9i	−0.114092	−	0.951232i
$554$	−8.09210e8			−0.202198
$555$		0			0
$556$	4.37802e8	+	7.58295e8i	0.108023	+	0.187101i
$557$	1.65798e9	+	2.87170e9i	0.406524	+	0.704120i	0.994498	−	0.104760i	$-0.0334075\pi$
$557$	1.65798e9	+	2.87170e9i	0.406524	+	0.704120i	−0.587974	+	0.808880i	$0.700074\pi$
$558$		0			0
$559$	−3.77327e9			−0.913644
$560$	−7.40763e8	−	3.16888e8i	−0.178247	−	0.0762514i
$561$		0			0
$562$	−1.47852e9	+	2.56088e9i	−0.351359	+	0.608572i
$563$	−9.36100e8	−	1.62137e9i	−0.221077	−	0.382916i	0.734059	−	0.679086i	$-0.237624\pi$
$563$	−9.36100e8	−	1.62137e9i	−0.221077	−	0.382916i	−0.955135	+	0.296170i	$0.904290\pi$
$564$		0			0
$565$	2.70438e9	−	4.68413e9i	0.630810	−	1.09259i
$566$	1.75729e9			0.407367
$567$		0			0
$568$	1.27620e9			0.292213
$569$	−3.17886e8	+	5.50595e8i	−0.0723400	+	0.125297i	−0.899926	−	0.436042i	$-0.856380\pi$
$569$	−3.17886e8	+	5.50595e8i	−0.0723400	+	0.125297i	0.827586	+	0.561338i	$0.189713\pi$
$570$		0			0
$571$	−2.85689e9	−	4.94828e9i	−0.642196	−	1.11232i	−0.984942	−	0.172887i	$-0.944690\pi$
$571$	−2.85689e9	−	4.94828e9i	−0.642196	−	1.11232i	0.342746	−	0.939428i	$-0.388643\pi$
$572$	−7.37128e8	+	1.27674e9i	−0.164686	+	0.285245i
$573$		0			0
$574$	−5.38878e8	−	4.49287e9i	−0.118932	−	0.991590i
$575$	−2.05718e9			−0.451267
$576$		0			0
$577$	3.17926e9	+	5.50664e9i	0.688986	+	1.19336i	0.972166	+	0.234292i	$0.0752773\pi$
$577$	3.17926e9	+	5.50664e9i	0.688986	+	1.19336i	−0.283180	+	0.959067i	$0.591389\pi$
$578$	−1.14737e9	−	1.98730e9i	−0.247148	−	0.428072i
$579$		0			0
$580$	−1.78725e9			−0.380353
$581$	−2.43688e9	+	1.82564e9i	−0.515487	+	0.386187i
$582$		0			0
$583$	1.64331e9	−	2.84629e9i	0.343462	−	0.594894i
$584$	−8.38023e8	−	1.45150e9i	−0.174105	−	0.301559i
$585$		0			0
$586$	2.88892e9	−	5.00376e9i	0.593054	−	1.02720i
$587$	−7.71077e8			−0.157349			−0.0786745	−	0.996900i	$-0.525069\pi$
$587$	−7.71077e8			−0.157349			−0.0786745	+	0.996900i	$0.525069\pi$
$588$		0			0
$589$	1.76477e9			0.355864
$590$	−1.45734e9	+	2.52418e9i	−0.292131	+	0.505986i
$591$		0			0
$592$	−1.00702e9	−	1.74422e9i	−0.199487	−	0.345521i
$593$	3.20093e9	−	5.54417e9i	0.630354	−	1.09181i	−0.357125	−	0.934057i	$-0.616243\pi$
$593$	3.20093e9	−	5.54417e9i	0.630354	−	1.09181i	0.987479	−	0.157749i	$-0.0504238\pi$
$594$		0			0
$595$	1.74945e9	−	1.31063e9i	0.340480	−	0.255078i
$596$	−1.56089e9			−0.302002
$597$		0			0
$598$	−2.35744e9	−	4.08321e9i	−0.450803	−	0.780813i
$599$	−6.60575e8	−	1.14415e9i	−0.125582	−	0.217515i	0.796378	−	0.604799i	$-0.206747\pi$
$599$	−6.60575e8	−	1.14415e9i	−0.125582	−	0.217515i	−0.921960	+	0.387284i	$0.873413\pi$
$600$		0			0
$601$	−2.93204e9			−0.550947			−0.275474	−	0.961309i	$-0.588835\pi$
$601$	−2.93204e9			−0.550947			−0.275474	+	0.961309i	$0.588835\pi$
$602$	−3.65642e8	−	3.04852e9i	−0.0683075	−	0.569510i
$603$		0			0
$604$	−1.08169e9	+	1.87353e9i	−0.199743	+	0.345965i
$605$	1.38953e9	+	2.40673e9i	0.255107	+	0.441859i
$606$		0			0
$607$	2.76216e9	−	4.78420e9i	0.501289	−	0.868258i	−0.498710	−	0.866769i	$-0.666193\pi$
$607$	2.76216e9	−	4.78420e9i	0.501289	−	0.868258i	0.999999	−	0.00148902i	$-0.000473971\pi$
$608$	2.83338e8			0.0511261
$609$		0			0
$610$	−3.68058e9			−0.656542
$611$	5.37740e9	−	9.31393e9i	0.953736	−	1.65192i
$612$		0			0
$613$	3.14956e9	+	5.45520e9i	0.552253	+	0.956530i	0.998112	+	0.0614270i	$0.0195651\pi$
$613$	3.14956e9	+	5.45520e9i	0.552253	+	0.956530i	−0.445858	+	0.895103i	$0.647102\pi$
$614$	−2.55818e8	+	4.43090e8i	−0.0446007	+	0.0772507i
$615$		0			0
$616$	−1.10294e9	−	4.71824e8i	−0.190117	−	0.0813293i
$617$	4.76835e9			0.817278			0.408639	−	0.912696i	$-0.366004\pi$
$617$	4.76835e9			0.817278			0.408639	+	0.912696i	$0.366004\pi$
$618$		0			0
$619$	−3.93891e8	−	6.82239e8i	−0.0667511	−	0.115616i	0.830718	−	0.556693i	$-0.187930\pi$
$619$	−3.93891e8	−	6.82239e8i	−0.0667511	−	0.115616i	−0.897469	+	0.441077i	$0.854597\pi$
$620$	1.41564e9	+	2.45195e9i	0.238551	+	0.413182i
$621$		0			0
$622$	1.23715e9			0.206136
$623$	−2.59326e8	−	2.16211e9i	−0.0429672	−	0.358237i
$624$		0			0
$625$	1.35034e9	−	2.33885e9i	0.221239	−	0.383197i
$626$	−1.97594e9	−	3.42242e9i	−0.321931	−	0.557601i
$627$		0			0
$628$	−2.54613e8	+	4.41003e8i	−0.0410225	+	0.0710531i
$629$	5.46432e9			0.875506
$630$		0			0
$631$	−9.52407e9			−1.50911			−0.754553	−	0.656239i	$-0.772146\pi$
$631$	−9.52407e9			−1.50911			−0.754553	+	0.656239i	$0.772146\pi$
$632$	−1.07479e9	+	1.86159e9i	−0.169361	+	0.293342i
$633$		0			0
$634$	−1.71975e9	−	2.97870e9i	−0.268012	−	0.464210i
$635$	1.86496e9	−	3.23021e9i	0.289042	−	0.500636i
$636$		0			0
$637$	−2.06484e9	+	7.05153e9i	−0.316517	+	1.08092i
$638$	−2.66108e9			−0.405682
$639$		0			0
$640$	2.27284e8	+	3.93667e8i	0.0342719	+	0.0593607i
$641$	−1.32160e9	−	2.28909e9i	−0.198198	−	0.343288i	0.749746	−	0.661725i	$-0.230175\pi$
$641$	−1.32160e9	−	2.28909e9i	−0.198198	−	0.343288i	−0.947944	+	0.318437i	$0.896842\pi$
$642$		0			0
$643$	7.78643e9			1.15505			0.577524	−	0.816374i	$-0.304019\pi$
$643$	7.78643e9			1.15505			0.577524	+	0.816374i	$0.304019\pi$
$644$	3.07048e9	−	2.30031e9i	0.453008	−	0.339380i
$645$		0			0
$646$	−3.84363e8	+	6.65736e8i	−0.0560955	+	0.0971602i
$647$	4.77250e9	+	8.26622e9i	0.692757	+	1.19989i	0.970931	+	0.239360i	$0.0769377\pi$
$647$	4.77250e9	+	8.26622e9i	0.692757	+	1.19989i	−0.278173	+	0.960531i	$0.589729\pi$
$648$		0			0
$649$	−2.16987e9	+	3.75833e9i	−0.311586	+	0.539682i
$650$	−2.22281e9			−0.317472
$651$		0			0
$652$	−3.43314e9			−0.485093
$653$	−5.15813e8	+	8.93414e8i	−0.0724930	+	0.125562i	−0.899993	−	0.435904i	$-0.856429\pi$
$653$	−5.15813e8	+	8.93414e8i	−0.0724930	+	0.125562i	0.827500	+	0.561465i	$0.189762\pi$
$654$		0			0
$655$	2.91824e9	+	5.05453e9i	0.405766	+	0.702808i
$656$	−1.27650e9	+	2.21097e9i	−0.176546	+	0.305787i
$657$		0			0
$658$	8.04604e9	+	3.44198e9i	1.10101	+	0.470997i
$659$	−9.97213e9			−1.35734			−0.678671	−	0.734443i	$-0.737444\pi$
$659$	−9.97213e9			−1.35734			−0.678671	+	0.734443i	$0.737444\pi$
$660$		0			0
$661$	−4.39852e9	−	7.61845e9i	−0.592381	−	1.02603i	−0.993911	−	0.110188i	$-0.964855\pi$
$661$	−4.39852e9	−	7.61845e9i	−0.592381	−	1.02603i	0.401530	−	0.915846i	$-0.368479\pi$
$662$	−1.31268e9	−	2.27362e9i	−0.175855	−	0.304590i
$663$		0			0
$664$	1.71790e9			0.227724
$665$	1.56378e9	+	6.68961e8i	0.206205	+	0.0882115i
$666$		0			0
$667$	4.25526e9	−	7.37032e9i	0.555246	−	0.961714i
$668$	−2.62481e9	−	4.54630e9i	−0.340706	−	0.590121i
$669$		0			0
$670$	−2.90393e9	+	5.02975e9i	−0.373013	+	0.646078i
$671$	−5.48012e9			−0.700264
$672$		0			0
$673$	7.42386e9			0.938808			0.469404	−	0.882983i	$-0.344469\pi$
$673$	7.42386e9			0.938808			0.469404	+	0.882983i	$0.344469\pi$
$674$	−4.57636e8	+	7.92648e8i	−0.0575719	+	0.0997174i
$675$		0			0
$676$	−5.39297e8	−	9.34090e8i	−0.0671451	−	0.116299i
$677$	−5.72981e8	+	9.92432e8i	−0.0709708	+	0.122925i	−0.899327	−	0.437277i	$-0.855943\pi$
$677$	−5.72981e8	+	9.92432e8i	−0.0709708	+	0.122925i	0.828356	+	0.560202i	$0.189276\pi$
$678$		0			0
$679$	3.27921e9	−	2.45669e9i	0.402000	−	0.301166i
$680$	−1.23329e9			−0.150413
$681$		0			0
$682$	2.10778e9	+	3.65078e9i	0.254437	+	0.440697i
$683$	5.29365e9	+	9.16887e9i	0.635745	+	1.10114i	0.986357	+	0.164621i	$0.0526402\pi$
$683$	5.29365e9	+	9.16887e9i	0.635745	+	1.10114i	−0.350612	+	0.936521i	$0.614026\pi$
$684$		0			0
$685$	5.90877e9			0.702393
$686$	−5.89719e9	−	9.84915e8i	−0.697446	−	0.116484i
$687$		0			0
$688$	−8.66139e8	+	1.50020e9i	−0.101398	+	0.175626i
$689$	5.67868e9	+	9.83576e9i	0.661424	+	1.14562i
$690$		0			0
$691$	−3.78065e9	+	6.54827e9i	−0.435906	+	0.755011i	−0.997369	−	0.0724904i	$-0.976905\pi$
$691$	−3.78065e9	+	6.54827e9i	−0.435906	+	0.755011i	0.561463	+	0.827502i	$0.310239\pi$
$692$	4.34678e9			0.498650
$693$		0			0
$694$	−5.25342e9			−0.596601
$695$	1.48275e9	−	2.56819e9i	0.167540	−	0.290189i
$696$		0			0
$697$	−3.46329e9	−	5.99859e9i	−0.387413	−	0.671018i
$698$	−3.54398e9	+	6.13835e9i	−0.394454	+	0.683215i
$699$		0			0
$700$	−2.15397e8	−	1.79586e9i	−0.0237354	−	0.197893i
$701$	1.31100e10			1.43744			0.718719	−	0.695301i	$-0.244729\pi$
$701$	1.31100e10			1.43744			0.718719	+	0.695301i	$0.244729\pi$
$702$		0			0
$703$	2.12586e9	+	3.68210e9i	0.230776	+	0.399716i
$704$	3.38409e8	+	5.86142e8i	0.0365543	+	0.0633138i
$705$		0			0
$706$	5.49919e9			0.588142
$707$	6.17417e9	+	2.64122e9i	0.657069	+	0.281085i
$708$		0			0
$709$	−1.55398e8	+	2.69157e8i	−0.0163750	+	0.0283624i	−0.874097	−	0.485752i	$-0.838546\pi$
$709$	−1.55398e8	+	2.69157e8i	−0.0163750	+	0.0283624i	0.857722	+	0.514114i	$0.171879\pi$
$710$	−2.16111e9	−	3.74315e9i	−0.226607	−	0.392494i
$711$		0			0
$712$	−6.14295e8	+	1.06399e9i	−0.0637818	+	0.110473i
$713$	−1.34819e10			−1.39296
$714$		0			0
$715$	4.99300e9			0.510847
$716$	−1.95135e9	+	3.37983e9i	−0.198673	+	0.344112i
$717$		0			0
$718$	−1.28977e8	−	2.23395e8i	−0.0130040	−	0.0225237i
$719$	2.09243e9	−	3.62420e9i	0.209943	−	0.363631i	−0.741754	−	0.670673i	$-0.766006\pi$
$719$	2.09243e9	−	3.62420e9i	0.209943	−	0.363631i	0.951696	+	0.307041i	$0.0993389\pi$
$720$		0			0
$721$	1.99468e9	+	1.66305e10i	0.198198	+	1.65246i
$722$	6.55284e9			0.647962
$723$		0			0
$724$	4.92461e9	+	8.52968e9i	0.482266	+	0.835310i
$725$	−2.00612e9	−	3.47471e9i	−0.195512	−	0.338637i
$726$		0			0
$727$	−9.54370e9			−0.921184			−0.460592	−	0.887612i	$-0.652363\pi$
$727$	−9.54370e9			−0.921184			−0.460592	+	0.887612i	$0.652363\pi$
$728$	3.31770e9	−	2.48552e9i	0.318696	−	0.238758i
$729$		0			0
$730$	−2.83821e9	+	4.91593e9i	−0.270032	+	0.467709i
$731$	−2.34993e9	−	4.07019e9i	−0.222507	−	0.385393i
$732$		0			0
$733$	−5.03140e9	+	8.71464e9i	−0.471873	+	0.817307i	−0.999482	−	0.0321796i	$-0.989755\pi$
$733$	−5.03140e9	+	8.71464e9i	−0.471873	+	0.817307i	0.527609	+	0.849487i	$0.323088\pi$
$734$	5.73240e9			0.535057
$735$		0			0
$736$	−2.16456e9			−0.200123
$737$	−4.32374e9	+	7.48894e9i	−0.397854	+	0.689103i
$738$		0			0
$739$	3.54880e9	+	6.14670e9i	0.323464	+	0.560256i	0.981200	−	0.192992i	$-0.0618193\pi$
$739$	3.54880e9	+	6.14670e9i	0.323464	+	0.560256i	−0.657736	+	0.753248i	$0.728486\pi$
$740$	−3.41058e9	+	5.90730e9i	−0.309398	+	0.535893i
$741$		0			0
$742$	−7.39627e9	+	5.54106e9i	−0.664659	+	0.497943i
$743$	−3.16400e8			−0.0282993			−0.0141497	−	0.999900i	$-0.504504\pi$
$743$	−3.16400e8			−0.0282993			−0.0141497	+	0.999900i	$0.504504\pi$
$744$		0			0
$745$	2.64320e9	+	4.57816e9i	0.234198	+	0.405643i
$746$	4.88907e9	+	8.46812e9i	0.431162	+	0.746794i
$747$		0			0
$748$	−1.83628e9			−0.160429
$749$	5.39699e8	+	4.49971e9i	0.0469316	+	0.391290i
$750$		0			0
$751$	−3.22967e9	+	5.59396e9i	−0.278240	+	0.481925i	−0.970947	−	0.239293i	$-0.923084\pi$
$751$	−3.22967e9	+	5.59396e9i	−0.278240	+	0.481925i	0.692708	+	0.721218i	$0.256418\pi$
$752$	−2.46872e9	−	4.27594e9i	−0.211694	−	0.366665i
$753$		0			0
$754$	4.59787e9	−	7.96374e9i	0.390622	−	0.676577i
$755$	7.32689e9			0.619591
$756$		0			0
$757$	1.07167e10			0.897892			0.448946	−	0.893559i	$-0.351800\pi$
$757$	1.07167e10			0.897892			0.448946	+	0.893559i	$0.351800\pi$
$758$	−2.73319e9	+	4.73403e9i	−0.227944	+	0.394810i
$759$		0			0
$760$	−4.79804e8	−	8.31045e8i	−0.0396475	−	0.0686715i
$761$	−4.51415e9	+	7.81874e9i	−0.371304	+	0.643117i	−0.989766	−	0.142697i	$-0.954423\pi$
$761$	−4.51415e9	+	7.81874e9i	−0.371304	+	0.643117i	0.618462	+	0.785814i	$0.287756\pi$
$762$		0			0
$763$	−1.55916e10	−	6.66987e9i	−1.27073	−	0.543602i
$764$	−1.44132e9			−0.116932
$765$		0			0
$766$	−8.10353e9	−	1.40357e10i	−0.651439	−	1.12832i
$767$	−7.49829e9	−	1.29874e10i	−0.600038	−	1.03930i
$768$		0			0
$769$	8.30919e9			0.658895			0.329448	−	0.944174i	$-0.393137\pi$
$769$	8.30919e9			0.658895			0.329448	+	0.944174i	$0.393137\pi$
$770$	4.83838e8	+	4.03397e9i	0.0381929	+	0.318431i
$771$		0			0
$772$	4.32884e9	−	7.49777e9i	0.338619	−	0.586505i
$773$	5.63091e9	+	9.75302e9i	0.438480	+	0.759470i	0.997573	−	0.0696352i	$-0.0221835\pi$
$773$	5.63091e9	+	9.75302e9i	0.438480	+	0.759470i	−0.559092	+	0.829106i	$0.688850\pi$
$774$		0			0
$775$	−3.17800e9	+	5.50446e9i	−0.245244	+	0.424775i
$776$	−2.31171e9			−0.177590
$777$		0			0
$778$	−5.83209e9			−0.444013
$779$	2.69474e9	−	4.66743e9i	0.204238	−	0.353750i
$780$		0			0
$781$	−3.21774e9	−	5.57328e9i	−0.241697	−	0.418632i
$782$	2.93634e9	−	5.08589e9i	0.219575	−	0.380315i
$783$		0			0
$784$	2.32961e9	+	2.43960e9i	0.172654	+	0.180805i
$785$	1.72465e9			0.127249
$786$		0			0
$787$	1.11102e10	+	1.92434e10i	0.812475	+	1.40725i	0.911127	+	0.412127i	$0.135214\pi$
$787$	1.11102e10	+	1.92434e10i	0.812475	+	1.40725i	−0.0986511	+	0.995122i	$0.531453\pi$
$788$	−2.86794e9	−	4.96743e9i	−0.208799	−	0.361651i
$789$		0			0
$790$	7.28017e9			0.525348
$791$	−1.81232e10	+	1.35774e10i	−1.30202	+	0.975434i
$792$		0			0
$793$	9.46866e9	−	1.64002e10i	0.674268	−	1.16787i
$794$	−5.31069e9	−	9.19839e9i	−0.376512	−	0.652139i
$795$		0			0
$796$	1.75812e9	−	3.04516e9i	0.123553	−	0.214000i
$797$	6.49195e9			0.454225			0.227113	−	0.973868i	$-0.427071\pi$
$797$	6.49195e9			0.454225			0.227113	+	0.973868i	$0.427071\pi$
$798$		0			0
$799$	1.33958e10			0.929082
$800$	−5.10236e8	+	8.83755e8i	−0.0352336	+	0.0610263i
$801$		0			0
$802$	3.43180e9	+	5.94405e9i	0.234916	+	0.406886i
$803$	−4.22589e9	+	7.31946e9i	−0.288014	+	0.498855i
$804$		0			0
$805$	−1.19465e10	−	5.11053e9i	−0.807149	−	0.345287i
$806$	−1.45674e10			−0.979966
$807$		0			0
$808$	−1.89438e9	−	3.28117e9i	−0.126336	−	0.218821i
$809$	−5.80562e9	−	1.00556e10i	−0.385504	−	0.667712i	0.606335	−	0.795209i	$-0.292639\pi$
$809$	−5.80562e9	−	1.00556e10i	−0.385504	−	0.667712i	−0.991839	+	0.127497i	$0.959306\pi$
$810$		0			0
$811$	−1.72427e10			−1.13510			−0.567548	−	0.823340i	$-0.692108\pi$
$811$	−1.72427e10			−1.13510			−0.567548	+	0.823340i	$0.692108\pi$
$812$	6.87965e9	+	2.94302e9i	0.450942	+	0.192907i
$813$		0			0
$814$	−5.07811e9	+	8.79555e9i	−0.330002	+	0.571581i
$815$	5.81366e9	+	1.00696e10i	0.376182	+	0.651567i
$816$		0			0
$817$	1.82845e9	−	3.16696e9i	0.117302	−	0.203173i
$818$	1.68213e10			1.07454
$819$		0			0
$820$	8.64651e9			0.547636
$821$	7.15770e9	−	1.23975e10i	0.451412	−	0.781868i	−0.547062	−	0.837092i	$-0.684254\pi$
$821$	7.15770e9	−	1.23975e10i	0.451412	−	0.781868i	0.998474	+	0.0552240i	$0.0175873\pi$
$822$		0			0
$823$	2.33905e9	+	4.05135e9i	0.146265	+	0.253338i	0.929844	−	0.367954i	$-0.119941\pi$
$823$	2.33905e9	+	4.05135e9i	0.146265	+	0.253338i	−0.783579	+	0.621292i	$0.786608\pi$
$824$	4.72502e9	−	8.18397e9i	0.294211	−	0.509588i
$825$		0			0
$826$	9.76625e9	−	7.31657e9i	0.602972	−	0.451729i
$827$	1.01540e10			0.624264			0.312132	−	0.950039i	$-0.398957\pi$
$827$	1.01540e10			0.624264			0.312132	+	0.950039i	$0.398957\pi$
$828$		0			0
$829$	−5.51455e9	−	9.55148e9i	−0.336178	−	0.582278i	0.647532	−	0.762038i	$-0.275801\pi$
$829$	−5.51455e9	−	9.55148e9i	−0.336178	−	0.582278i	−0.983710	+	0.179760i	$0.942468\pi$
$830$	−2.90909e9	−	5.03868e9i	−0.176597	−	0.305875i
$831$		0			0
$832$	−2.33884e9			−0.140789
$833$	−8.89235e9	+	2.16425e9i	−0.533039	+	0.129733i
$834$		0			0
$835$	−8.88969e9	+	1.53974e10i	−0.528426	+	0.915260i
$836$	−7.14393e8	−	1.23737e9i	−0.0422878	−	0.0732447i
$837$		0			0
$838$	−9.91963e9	+	1.71813e10i	−0.582293	+	1.00856i
$839$	1.71068e10			1.00001			0.500003	−	0.866023i	$-0.333332\pi$
$839$	1.71068e10			1.00001			0.500003	+	0.866023i	$0.333332\pi$
$840$		0			0
$841$	−6.51269e8			−0.0377550
$842$	−2.20742e8	+	3.82337e8i	−0.0127436	+	0.0220726i
$843$		0			0
$844$	3.98525e9	+	6.90266e9i	0.228169	+	0.395201i
$845$	−1.82649e9	+	3.16357e9i	−0.104140	+	0.180376i
$846$		0			0
$847$	−1.38560e9	−	1.15523e10i	−0.0783510	−	0.653247i
$848$	5.21407e9			0.293624
$849$		0			0
$850$	−1.38432e9	−	2.39772e9i	−0.0773164	−	0.133916i
$851$	−1.62405e10	−	2.81294e10i	−0.903330	−	1.56461i
$852$		0			0
$853$	−2.88309e9			−0.159051			−0.0795256	−	0.996833i	$-0.525341\pi$
$853$	−2.88309e9			−0.159051			−0.0795256	+	0.996833i	$0.525341\pi$
$854$	1.41677e10	+	6.06073e9i	0.778388	+	0.332983i
$855$		0			0
$856$	1.27845e9	−	2.21434e9i	0.0696667	−	0.120666i
$857$	−1.20159e10	−	2.08122e10i	−0.652116	−	1.12950i	−0.982608	−	0.185690i	$-0.940548\pi$
$857$	−1.20159e10	−	2.08122e10i	−0.652116	−	1.12950i	0.330492	−	0.943809i	$-0.392785\pi$
$858$		0			0
$859$	1.70872e10	−	2.95958e10i	0.919801	−	1.59314i	0.120084	−	0.992764i	$-0.461683\pi$
$859$	1.70872e10	−	2.95958e10i	0.919801	−	1.59314i	0.799716	−	0.600378i	$-0.204983\pi$
$860$	5.86687e9			0.314530
$861$		0			0
$862$	1.34778e10			0.716709
$863$	1.48357e10	−	2.56962e10i	0.785724	−	1.36091i	−0.142841	−	0.989746i	$-0.545624\pi$
$863$	1.48357e10	−	2.56962e10i	0.785724	−	1.36091i	0.928566	−	0.371168i	$-0.121043\pi$
$864$		0			0
$865$	−7.36082e9	−	1.27493e10i	−0.386696	−	0.669777i
$866$	−5.18768e9	+	8.98532e9i	−0.271432	+	0.470133i
$867$		0			0
$868$	−1.41163e9	−	1.17694e10i	−0.0732660	−	0.610851i
$869$	1.08397e10			0.560333
$870$		0			0
$871$	−1.49413e10	−	2.58791e10i	−0.766169	−	1.32704i
$872$	4.78388e9	+	8.28592e9i	0.244327	+	0.423187i
$873$		0			0
$874$	4.56946e9			0.231513
$875$	−1.72015e10	+	1.28868e10i	−0.868035	+	0.650305i
$876$		0			0
$877$	3.70786e9	−	6.42220e9i	0.185620	−	0.321503i	−0.758165	−	0.652062i	$-0.773904\pi$
$877$	3.70786e9	−	6.42220e9i	0.185620	−	0.321503i	0.943785	+	0.330559i	$0.107237\pi$
$878$	−5.62552e8	−	9.74369e8i	−0.0280500	−	0.0485840i
$879$		0			0
$880$	1.14612e9	−	1.98514e9i	0.0566946	−	0.0981979i
$881$	−3.89699e10			−1.92005			−0.960027	−	0.279907i	$-0.909696\pi$
$881$	−3.89699e10			−1.92005			−0.960027	+	0.279907i	$0.909696\pi$
$882$		0			0
$883$	−6.37811e9			−0.311767			−0.155883	−	0.987775i	$-0.549822\pi$
$883$	−6.37811e9			−0.311767			−0.155883	+	0.987775i	$0.549822\pi$
$884$	3.17276e9	−	5.49538e9i	0.154474	−	0.267556i
$885$		0			0
$886$	7.39733e9	+	1.28126e10i	0.357320	+	0.618896i
$887$	−1.84996e10	+	3.20422e10i	−0.890079	+	1.54166i	−0.0503004	+	0.998734i	$0.516018\pi$
$887$	−1.84996e10	+	3.20422e10i	−0.890079	+	1.54166i	−0.839779	+	0.542928i	$0.817315\pi$
$888$		0			0
$889$	−1.24979e10	+	9.36305e9i	−0.596597	+	0.446952i
$890$	4.16098e9			0.197847
$891$		0			0
$892$	−9.13484e9	−	1.58220e10i	−0.430947	−	0.746423i
$893$	5.21155e9	+	9.02666e9i	0.244899	+	0.424177i
$894$		0			0
$895$	1.32176e10			0.616272
$896$	−2.26641e8	−	1.88961e9i	−0.0105259	−	0.0877594i
$897$		0			0
$898$	1.16717e10	−	2.02161e10i	0.537859	−	0.931599i
$899$	−1.31474e10	−	2.27719e10i	−0.603503	−	1.04530i
$900$		0			0
$901$	−7.07315e9	+	1.22511e10i	−0.322163	+	0.558003i
$902$	1.28740e10			0.584106
$903$		0			0
$904$	1.27761e10			0.575188
$905$	1.66786e10	−	2.88883e10i	0.747981	−	1.29554i
$906$		0			0
$907$	3.20212e9	+	5.54623e9i	0.142499	+	0.246816i	0.928437	−	0.371490i	$-0.121153\pi$
$907$	3.20212e9	+	5.54623e9i	0.142499	+	0.246816i	−0.785938	+	0.618305i	$0.787820\pi$
$908$	2.15770e9	−	3.73725e9i	0.0956514	−	0.165673i
$909$		0			0
$910$	−1.29083e10	−	5.52200e9i	−0.567839	−	0.242914i
$911$	2.59678e9			0.113794			0.0568971	−	0.998380i	$-0.481879\pi$
$911$	2.59678e9			0.113794			0.0568971	+	0.998380i	$0.481879\pi$
$912$		0			0
$913$	−4.33142e9	−	7.50224e9i	−0.188357	−	0.326244i
$914$	1.13632e10	+	1.96817e10i	0.492254	+	0.852609i
$915$		0			0
$916$	4.58827e9			0.197249
$917$	−2.90998e9	−	2.42618e10i	−0.124623	−	1.03904i
$918$		0			0
$919$	1.87721e10	−	3.25142e10i	0.797825	−	1.38187i	−0.123205	−	0.992381i	$-0.539317\pi$
$919$	1.87721e10	−	3.25142e10i	0.797825	−	1.38187i	0.921030	−	0.389492i	$-0.127349\pi$
$920$	3.66546e9	+	6.34876e9i	0.155193	+	0.268802i
$921$		0			0
$922$	−1.58423e10	+	2.74396e10i	−0.665671	+	1.15298i
$923$	2.22387e10			0.930900
$924$		0			0
$925$	−1.53130e10			−0.636159
$926$	−8.79260e9	+	1.52292e10i	−0.363897	+	0.630289i
$927$		0			0
$928$	−2.11084e9	−	3.65609e9i	−0.0867037	−	0.150175i
$929$	1.26185e10	−	2.18559e10i	0.516361	−	0.894363i	−0.483459	−	0.875367i	$-0.660620\pi$
$929$	1.26185e10	−	2.18559e10i	0.516361	−	0.894363i	0.999820	−	0.0189960i	$-0.00604698\pi$
$930$		0			0
$931$	−4.91788e9	−	5.15007e9i	−0.199735	−	0.209165i
$932$	−1.39508e8			−0.00564472
$933$		0			0
$934$	−1.24896e10	−	2.16326e10i	−0.501573	−	0.868751i
$935$	3.10955e9	+	5.38590e9i	0.124410	+	0.215485i
$936$		0			0
$937$	−6.75432e9			−0.268221			−0.134111	−	0.990966i	$-0.542818\pi$
$937$	−6.75432e9			−0.268221			−0.134111	+	0.990966i	$0.542818\pi$
$938$	1.94605e10	−	1.45792e10i	0.769917	−	0.576798i
$939$		0			0
$940$	−8.36104e9	+	1.44817e10i	−0.328332	+	0.568687i
$941$	−4.73345e9	−	8.19857e9i	−0.185188	−	0.320756i	0.758452	−	0.651729i	$-0.225956\pi$
$941$	−4.73345e9	−	8.19857e9i	−0.185188	−	0.320756i	−0.943640	+	0.330974i	$0.892623\pi$
$942$		0			0
$943$	−2.05865e10	+	3.56568e10i	−0.799449	+	1.38469i
$944$	−6.88480e9			−0.266373
$945$		0			0
$946$	8.73534e9			0.335476
$947$	−2.51579e10	+	4.35748e10i	−0.962608	+	1.66729i	−0.246701	+	0.969092i	$0.579346\pi$
$947$	−2.51579e10	+	4.35748e10i	−0.962608	+	1.66729i	−0.715908	+	0.698195i	$0.753987\pi$
$948$		0			0
$949$	−1.46032e10	−	2.52934e10i	−0.554645	−	0.960673i
$950$	1.07713e9	−	1.86564e9i	0.0407600	−	0.0705983i
$951$		0			0
$952$	4.74730e9	+	2.03083e9i	0.178327	+	0.0762859i
$953$	2.56329e9			0.0959342			0.0479671	−	0.998849i	$-0.484726\pi$
$953$	2.56329e9			0.0959342			0.0479671	+	0.998849i	$0.484726\pi$
$954$		0			0
$955$	2.44072e9	+	4.22745e9i	0.0906790	+	0.157061i
$956$	−5.98820e9	−	1.03719e10i	−0.221663	−	0.383932i
$957$		0			0
$958$	−1.08724e10			−0.399525
$959$	−2.27446e10	−	9.72984e9i	−0.832749	−	0.356238i
$960$		0			0
$961$	−7.07111e9	+	1.22475e10i	−0.257013	+	0.445160i
$962$	−1.75481e10	−	3.03942e10i	−0.635504	−	1.10072i
$963$		0			0
$964$	4.01056e9	−	6.94649e9i	0.144190	−	0.249744i
$965$	−2.93218e10			−1.05038
$966$		0			0
$967$	1.17322e10			0.417241			0.208621	−	0.977997i	$-0.433103\pi$
$967$	1.17322e10			0.417241			0.208621	+	0.977997i	$0.433103\pi$
$968$	−3.28222e9	+	5.68498e9i	−0.116307	+	0.201449i
$969$		0			0
$970$	3.91464e9	+	6.78036e9i	0.137718	+	0.238535i
$971$	−8.01185e9	+	1.38769e10i	−0.280844	+	0.486437i	−0.971593	−	0.236658i	$-0.923948\pi$
$971$	−8.01185e9	+	1.38769e10i	−0.280844	+	0.486437i	0.690749	+	0.723095i	$0.257281\pi$
$972$		0			0
$973$	−9.93651e9	+	7.44413e9i	−0.345811	+	0.259071i
$974$	−1.91573e10			−0.664319
$975$		0			0
$976$	−4.34698e9	−	7.52919e9i	−0.149663	−	0.259223i
$977$	2.08302e10	+	3.60790e10i	0.714601	+	1.23772i	0.963113	+	0.269096i	$0.0867249\pi$
$977$	2.08302e10	+	3.60790e10i	0.714601	+	1.23772i	−0.248513	+	0.968629i	$0.579942\pi$
$978$		0			0
$979$	6.19540e9			0.211023
$980$	3.21050e9	−	1.09641e10i	0.108964	−	0.372117i
$981$		0			0
$982$	7.82953e9	−	1.35611e10i	0.263843	−	0.456989i
$983$	2.36038e10	+	4.08830e10i	0.792584	+	1.37280i	0.924362	+	0.381516i	$0.124598\pi$
$983$	2.36038e10	+	4.08830e10i	0.792584	+	1.37280i	−0.131778	+	0.991279i	$0.542069\pi$
$984$		0			0
$985$	−9.71314e9	+	1.68236e10i	−0.323842	+	0.560910i
$986$	1.14539e10			0.380525
$987$		0			0
$988$	4.93737e9			0.162872
$989$	−1.39684e10	+	2.41940e10i	−0.459156	+	0.795282i
$990$		0			0
$991$	3.20329e9	+	5.54826e9i	0.104553	+	0.181092i	0.913556	−	0.406714i	$-0.133325\pi$
$991$	3.20329e9	+	5.54826e9i	0.104553	+	0.181092i	−0.809002	+	0.587806i	$0.799992\pi$
$992$	−3.34390e9	+	5.79180e9i	−0.108758	+	0.188375i
$993$		0			0
$994$	2.15500e9	+	1.79672e10i	0.0695977	+	0.580266i
$995$	−1.19088e10			−0.383254
$996$		0			0
$997$	6.01597e9	+	1.04200e10i	0.192253	+	0.332991i	0.945996	−	0.324177i	$-0.105087\pi$
$997$	6.01597e9	+	1.04200e10i	0.192253	+	0.332991i	−0.753744	+	0.657168i	$0.771754\pi$
$998$	1.18061e9	+	2.04488e9i	0.0375968	+	0.0651196i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.e.37.1		4
3.2	odd	2		14.8.c.a.9.1	✓	4
7.4	even	3	inner	126.8.g.e.109.1		4
12.11	even	2		112.8.i.a.65.2		4
21.2	odd	6		98.8.a.h.1.2		2
21.5	even	6		98.8.a.k.1.1		2
21.11	odd	6		14.8.c.a.11.1	yes	4
21.17	even	6		98.8.c.h.67.2		4
21.20	even	2		98.8.c.h.79.2		4
84.11	even	6		112.8.i.a.81.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.c.a.9.1	✓	4	3.2	odd	2
14.8.c.a.11.1	yes	4	21.11	odd	6
98.8.a.h.1.2		2	21.2	odd	6
98.8.a.k.1.1		2	21.5	even	6
98.8.c.h.67.2		4	21.17	even	6
98.8.c.h.79.2		4	21.20	even	2
112.8.i.a.65.2		4	12.11	even	2
112.8.i.a.81.2		4	84.11	even	6
126.8.g.e.37.1		4	1.1	even	1	trivial
126.8.g.e.109.1		4	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-108.377 + 187.715i) q^{5} +(726.284 - 544.110i) q^{7} -512.000 q^{8} +(867.019 + 1501.72i) q^{10} +(1290.93 + 2235.95i) q^{11} -8921.97 q^{13} +(-864.567 - 7208.28i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(-5556.44 - 9624.03i) q^{17} +(4323.40 - 7488.34i) q^{19} +13872.3 q^{20} +20654.9 q^{22} +(-33028.6 + 57207.2i) q^{23} +(15571.2 + 26970.1i) q^{25} +(-35687.9 + 61813.2i) q^{26} +(-53398.7 - 22843.2i) q^{28} -128836. q^{29} +(102048. + 176752. i) q^{31} +(16384.0 + 28377.9i) q^{32} -88903.0 q^{34} +(23424.9 + 195304. i) q^{35} +(-245856. + 425834. i) q^{37} +(-34587.2 - 59906.7i) q^{38} +(55489.2 - 96110.2i) q^{40} +623293. q^{41} +422919. q^{43} +(82619.5 - 143101. i) q^{44} +(264229. + 457657. i) q^{46} +(-602714. + 1.04393e6i) q^{47} +(231433. - 790356. i) q^{49} +249139. q^{50} +(285503. + 494506. i) q^{52} +(-636483. - 1.10242e6i) q^{53} -559630. q^{55} +(-371857. + 278584. i) q^{56} +(-515342. + 892599. i) q^{58} +(840430. + 1.45567e6i) q^{59} +(-1.06128e6 + 1.83818e6i) q^{61} +1.63276e6 q^{62} +262144. q^{64} +(966940. - 1.67479e6i) q^{65} +(1.67466e6 + 2.90060e6i) q^{67} +(-355612. + 615938. i) q^{68} +(1.44680e6 + 618922. i) q^{70} -2.49257e6 q^{71} +(1.63676e6 + 2.83496e6i) q^{73} +(1.96684e6 + 3.40667e6i) q^{74} -553395. q^{76} +(2.15418e6 + 921530. i) q^{77} +(2.09920e6 - 3.63591e6i) q^{79} +(-443914. - 768881. i) q^{80} +(2.49317e6 - 4.31830e6i) q^{82} -3.35527e6 q^{83} +2.40877e6 q^{85} +(1.69168e6 - 2.93007e6i) q^{86} +(-660956. - 1.14481e6i) q^{88} +(1.19979e6 - 2.07810e6i) q^{89} +(-6.47988e6 + 4.85453e6i) q^{91} +4.22766e6 q^{92} +(4.82171e6 + 8.35145e6i) q^{94} +(937117. + 1.62313e6i) q^{95} +4.51506e6 q^{97} +(-4.55001e6 - 4.76483e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 128 q^{4} - 238 q^{5} + 168 q^{7} - 2048 q^{8} + 1904 q^{10} + 5848 q^{11} + 2632 q^{13} + 2016 q^{14} - 8192 q^{16} - 47642 q^{17} + 41048 q^{19} + 30464 q^{20} + 93568 q^{22} - 49316 q^{23}+ \cdots - 20499248 q^{98}+O(q^{100}) \) 4 * q + 16 * q^2 - 128 * q^4 - 238 * q^5 + 168 * q^7 - 2048 * q^8 + 1904 * q^10 + 5848 * q^11 + 2632 * q^13 + 2016 * q^14 - 8192 * q^16 - 47642 * q^17 + 41048 * q^19 + 30464 * q^20 + 93568 * q^22 - 49316 * q^23 + 108816 * q^25 + 10528 * q^26 + 5376 * q^28 - 345640 * q^29 + 70252 * q^31 + 65536 * q^32 - 762272 * q^34 + 36904 * q^35 + 88166 * q^37 - 328384 * q^38 + 121856 * q^40 + 2312520 * q^41 + 115088 * q^43 + 374272 * q^44 + 394528 * q^46 - 1412292 * q^47 + 465892 * q^49 + 1741056 * q^50 - 84224 * q^52 - 2361174 * q^53 - 1258040 * q^55 - 86016 * q^56 - 1382560 * q^58 + 1842512 * q^59 - 1278242 * q^61 + 1124032 * q^62 + 1048576 * q^64 + 1716372 * q^65 + 2121480 * q^67 - 3049088 * q^68 + 2595712 * q^70 - 7200320 * q^71 + 1634682 * q^73 - 705328 * q^74 - 5254144 * q^76 - 1416226 * q^77 + 9192604 * q^79 - 974848 * q^80 + 9250080 * q^82 + 56560 * q^83 + 6369676 * q^85 + 460352 * q^86 - 2994176 * q^88 + 8936550 * q^89 - 26111120 * q^91 + 6312448 * q^92 + 11298336 * q^94 + 2562604 * q^95 + 11748408 * q^97 - 20499248 * q^98

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