LMFDB - Embedded newform 162.10.c.k.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,10,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("162.55");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not 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:	$83.4358054585$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{301})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 76x^{2} + 75x + 5625 $ x^4 - x^3 + 76x^2 + 75x + 5625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.2
Root			$-4.08734 - 7.07948i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.10.c.k.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 + 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(510.865 + 884.844i) q^{5} +(2112.96 - 3659.75i) q^{7} +4096.00 q^{8} -16347.7 q^{10} +(-25189.9 + 43630.2i) q^{11} +(-58001.5 - 100462. i) q^{13} +(33807.4 + 58556.1i) q^{14} +(-32768.0 + 56755.8i) q^{16} +182765. q^{17} +564433. q^{19} +(130781. - 226520. i) q^{20} +(-403038. - 698083. i) q^{22} +(24758.2 + 42882.5i) q^{23} +(454596. - 787384. i) q^{25} +1.85605e6 q^{26} -1.08184e6 q^{28} +(-2.96657e6 + 5.13825e6i) q^{29} +(-2.18089e6 - 3.77741e6i) q^{31} +(-524288. - 908093. i) q^{32} +(-1.46212e6 + 2.53247e6i) q^{34} +4.31775e6 q^{35} -1.15632e7 q^{37} +(-4.51546e6 + 7.82101e6i) q^{38} +(2.09250e6 + 3.62432e6i) q^{40} +(-1.32330e7 - 2.29202e7i) q^{41} +(6.71634e6 - 1.16330e7i) q^{43} +1.28972e7 q^{44} -792263. q^{46} +(-9.14532e6 + 1.58402e7i) q^{47} +(1.12476e7 + 1.94814e7i) q^{49} +(7.27354e6 + 1.25981e7i) q^{50} +(-1.48484e7 + 2.57181e7i) q^{52} +6.88018e7 q^{53} -5.14745e7 q^{55} +(8.65468e6 - 1.49904e7i) q^{56} +(-4.74651e7 - 8.22119e7i) q^{58} +(-3.60461e7 - 6.24337e7i) q^{59} +(-3.29083e7 + 5.69988e7i) q^{61} +6.97884e7 q^{62} +1.67772e7 q^{64} +(5.92618e7 - 1.02645e8i) q^{65} +(-8.06051e7 - 1.39612e8i) q^{67} +(-2.33940e7 - 4.05195e7i) q^{68} +(-3.45420e7 + 5.98285e7i) q^{70} -2.76757e8 q^{71} -4.22636e8 q^{73} +(9.25057e7 - 1.60225e8i) q^{74} +(-7.22474e7 - 1.25136e8i) q^{76} +(1.06450e8 + 1.84378e8i) q^{77} +(2.10077e8 - 3.63863e8i) q^{79} -6.69601e7 q^{80} +4.23456e8 q^{82} +(3.47123e8 - 6.01234e8i) q^{83} +(9.33684e7 + 1.61719e8i) q^{85} +(1.07461e8 + 1.86129e8i) q^{86} +(-1.03178e8 + 1.78709e8i) q^{88} +7.96299e8 q^{89} -4.90219e8 q^{91} +(6.33811e6 - 1.09779e7i) q^{92} +(-1.46325e8 - 2.53443e8i) q^{94} +(2.88349e8 + 4.99435e8i) q^{95} +(1.95814e8 - 3.39159e8i) q^{97} -3.59923e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32 q^{2} - 512 q^{4} - 1704 q^{5} - 6538 q^{7} + 16384 q^{8} + 54528 q^{10} - 14568 q^{11} - 37138 q^{13} - 104608 q^{14} - 131072 q^{16} - 175824 q^{17} + 1418300 q^{19} - 436224 q^{20} - 233088 q^{22}+ \cdots + 1696420992 q^{98}+O(q^{100}) $ 4 * q - 32 * q^2 - 512 * q^4 - 1704 * q^5 - 6538 * q^7 + 16384 * q^8 + 54528 * q^10 - 14568 * q^11 - 37138 * q^13 - 104608 * q^14 - 131072 * q^16 - 175824 * q^17 + 1418300 * q^19 - 436224 * q^20 - 233088 * q^22 - 144552 * q^23 - 4567286 * q^25 + 1188416 * q^26 + 3347456 * q^28 - 10307328 * q^29 + 2968520 * q^31 - 2097152 * q^32 + 1406592 * q^34 + 67314576 * q^35 - 58454596 * q^37 - 11346400 * q^38 - 6979584 * q^40 - 17735808 * q^41 + 30013232 * q^43 + 7458816 * q^44 + 4625664 * q^46 - 44124936 * q^47 - 53013156 * q^49 - 73076576 * q^50 - 9507328 * q^52 + 186332256 * q^53 - 298175616 * q^55 - 26779648 * q^56 - 164917248 * q^58 - 133725288 * q^59 + 3590330 * q^61 - 94992640 * q^62 + 67108864 * q^64 + 333488280 * q^65 - 132828790 * q^67 + 22505472 * q^68 - 538516608 * q^70 + 171921312 * q^71 - 880554556 * q^73 + 467636768 * q^74 - 181542400 * q^76 + 598376184 * q^77 + 376775834 * q^79 + 223346688 * q^80 + 567545856 * q^82 + 1285892400 * q^83 + 924530112 * q^85 + 480211712 * q^86 - 59670528 * q^88 - 410842512 * q^89 - 2678230604 * q^91 - 37005312 * q^92 - 705998976 * q^94 + 182237736 * q^95 + 1672271798 * q^97 + 1696420992 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	510.865	+	884.844i	0.365545	+	0.633143i	0.988863	−	0.148825i	$-0.0475492\pi$
$5$	510.865	+	884.844i	0.365545	+	0.633143i	−0.623318	+	0.781968i	$0.714216\pi$
$6$		0			0
$7$	2112.96	−	3659.75i	0.332621	−	0.576117i	−0.650404	−	0.759589i	$-0.725400\pi$
$7$	2112.96	−	3659.75i	0.332621	−	0.576117i	0.983025	+	0.183472i	$0.0587336\pi$
$8$	4096.00			0.353553
$9$		0			0
$10$	−16347.7			−0.516959
$11$	−25189.9	+	43630.2i	−0.518751	+	0.898504i	0.481011	+	0.876714i	$0.340270\pi$
$11$	−25189.9	+	43630.2i	−0.518751	+	0.898504i	−0.999763	+	0.0217893i	$0.993064\pi$
$12$		0			0
$13$	−58001.5	−	100462.i	−0.563241	−	0.975561i	−0.997211	−	0.0746342i	$-0.976221\pi$
$13$	−58001.5	−	100462.i	−0.563241	−	0.975561i	0.433970	−	0.900927i	$-0.357112\pi$
$14$	33807.4	+	58556.1i	0.235199	+	0.407376i
$15$		0			0
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	182765.			0.530730			0.265365	−	0.964148i	$-0.414508\pi$
$17$	182765.			0.530730			0.265365	+	0.964148i	$0.414508\pi$
$18$		0			0
$19$	564433.			0.993622			0.496811	−	0.867859i	$-0.334504\pi$
$19$	564433.			0.993622			0.496811	+	0.867859i	$0.334504\pi$
$20$	130781.	−	226520.i	0.182773	−	0.316571i
$21$		0			0
$22$	−403038.	−	698083.i	−0.366813	−	0.635338i
$23$	24758.2	+	42882.5i	0.0184478	+	0.0319525i	0.875102	−	0.483939i	$-0.160794\pi$
$23$	24758.2	+	42882.5i	0.0184478	+	0.0319525i	−0.856654	+	0.515891i	$0.827461\pi$
$24$		0			0
$25$	454596.	−	787384.i	0.232753	−	0.403141i
$26$	1.85605e6			0.796543
$27$		0			0
$28$	−1.08184e6			−0.332621
$29$	−2.96657e6	+	5.13825e6i	−0.778867	+	1.34904i	0.153728	+	0.988113i	$0.450872\pi$
$29$	−2.96657e6	+	5.13825e6i	−0.778867	+	1.34904i	−0.932595	+	0.360924i	$0.882461\pi$
$30$		0			0
$31$	−2.18089e6	−	3.77741e6i	−0.424137	−	0.734626i	0.572203	−	0.820112i	$-0.306089\pi$
$31$	−2.18089e6	−	3.77741e6i	−0.424137	−	0.734626i	−0.996339	+	0.0854859i	$0.972756\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−1.46212e6	+	2.53247e6i	−0.187641	+	0.325004i
$35$	4.31775e6			0.486353
$36$		0			0
$37$	−1.15632e7			−1.01431			−0.507155	−	0.861855i	$-0.669303\pi$
$37$	−1.15632e7			−1.01431			−0.507155	+	0.861855i	$0.669303\pi$
$38$	−4.51546e6	+	7.82101e6i	−0.351298	+	0.608466i
$39$		0			0
$40$	2.09250e6	+	3.62432e6i	0.129240	+	0.223850i
$41$	−1.32330e7	−	2.29202e7i	−0.731359	−	1.26675i	−0.956303	−	0.292379i	$-0.905553\pi$
$41$	−1.32330e7	−	2.29202e7i	−0.731359	−	1.26675i	0.224944	−	0.974372i	$-0.427780\pi$
$42$		0			0
$43$	6.71634e6	−	1.16330e7i	0.299588	−	0.518902i	−0.676454	−	0.736485i	$-0.736484\pi$
$43$	6.71634e6	−	1.16330e7i	0.299588	−	0.518902i	0.976042	+	0.217583i	$0.0698174\pi$
$44$	1.28972e7			0.518751
$45$		0			0
$46$	−792263.			−0.0260891
$47$	−9.14532e6	+	1.58402e7i	−0.273375	+	0.473499i	−0.969724	−	0.244204i	$-0.921473\pi$
$47$	−9.14532e6	+	1.58402e7i	−0.273375	+	0.473499i	0.696349	+	0.717703i	$0.254807\pi$
$48$		0			0
$49$	1.12476e7	+	1.94814e7i	0.278726	+	0.482768i
$50$	7.27354e6	+	1.25981e7i	0.164581	+	0.285064i
$51$		0			0
$52$	−1.48484e7	+	2.57181e7i	−0.281620	+	0.487781i
$53$	6.88018e7			1.19773			0.598864	−	0.800851i	$-0.295619\pi$
$53$	6.88018e7			1.19773			0.598864	+	0.800851i	$0.295619\pi$
$54$		0			0
$55$	−5.14745e7			−0.758508
$56$	8.65468e6	−	1.49904e7i	0.117599	−	0.203688i
$57$		0			0
$58$	−4.74651e7	−	8.22119e7i	−0.550742	−	0.953913i
$59$	−3.60461e7	−	6.24337e7i	−0.387279	−	0.670788i	0.604803	−	0.796375i	$-0.293252\pi$
$59$	−3.60461e7	−	6.24337e7i	−0.387279	−	0.670788i	−0.992083	+	0.125587i	$0.959918\pi$
$60$		0			0
$61$	−3.29083e7	+	5.69988e7i	−0.304313	+	0.527086i	−0.977108	−	0.212743i	$-0.931760\pi$
$61$	−3.29083e7	+	5.69988e7i	−0.304313	+	0.527086i	0.672795	+	0.739829i	$0.265094\pi$
$62$	6.97884e7			0.599820
$63$		0			0
$64$	1.67772e7			0.125000
$65$	5.92618e7	−	1.02645e8i	0.411780	−	0.713224i
$66$		0			0
$67$	−8.06051e7	−	1.39612e8i	−0.488681	−	0.846421i	0.511234	−	0.859442i	$-0.329189\pi$
$67$	−8.06051e7	−	1.39612e8i	−0.488681	−	0.846421i	−0.999915	+	0.0130207i	$0.995855\pi$
$68$	−2.33940e7	−	4.05195e7i	−0.132683	−	0.229813i
$69$		0			0
$70$	−3.45420e7	+	5.98285e7i	−0.171952	+	0.297829i
$71$	−2.76757e8			−1.29251			−0.646257	−	0.763119i	$-0.723667\pi$
$71$	−2.76757e8			−1.29251			−0.646257	+	0.763119i	$0.723667\pi$
$72$		0			0
$73$	−4.22636e8			−1.74186			−0.870932	−	0.491404i	$-0.836484\pi$
$73$	−4.22636e8			−1.74186			−0.870932	+	0.491404i	$0.836484\pi$
$74$	9.25057e7	−	1.60225e8i	0.358613	−	0.621136i
$75$		0			0
$76$	−7.22474e7	−	1.25136e8i	−0.248405	−	0.430251i
$77$	1.06450e8	+	1.84378e8i	0.345096	+	0.597723i
$78$		0			0
$79$	2.10077e8	−	3.63863e8i	0.606814	−	1.05103i	−0.384947	−	0.922938i	$-0.625780\pi$
$79$	2.10077e8	−	3.63863e8i	0.606814	−	1.05103i	0.991762	−	0.128095i	$-0.0408862\pi$
$80$	−6.69601e7			−0.182773
$81$		0			0
$82$	4.23456e8			1.03430
$83$	3.47123e8	−	6.01234e8i	0.802845	−	1.39057i	−0.114892	−	0.993378i	$-0.536652\pi$
$83$	3.47123e8	−	6.01234e8i	0.802845	−	1.39057i	0.917737	−	0.397190i	$-0.130014\pi$
$84$		0			0
$85$	9.33684e7	+	1.61719e8i	0.194006	+	0.336028i
$86$	1.07461e8	+	1.86129e8i	0.211841	+	0.366919i
$87$		0			0
$88$	−1.03178e8	+	1.78709e8i	−0.183406	+	0.317669i
$89$	7.96299e8			1.34531			0.672653	−	0.739958i	$-0.265155\pi$
$89$	7.96299e8			1.34531			0.672653	+	0.739958i	$0.265155\pi$
$90$		0			0
$91$	−4.90219e8			−0.749383
$92$	6.33811e6	−	1.09779e7i	0.00922389	−	0.0159763i
$93$		0			0
$94$	−1.46325e8	−	2.53443e8i	−0.193305	−	0.334815i
$95$	2.88349e8	+	4.99435e8i	0.363214	+	0.629104i
$96$		0			0
$97$	1.95814e8	−	3.39159e8i	0.224579	−	0.388983i	−0.731614	−	0.681719i	$-0.761232\pi$
$97$	1.95814e8	−	3.39159e8i	0.224579	−	0.388983i	0.956193	+	0.292736i	$0.0945658\pi$
$98$	−3.59923e8			−0.394178
$99$		0			0
$100$	−2.32753e8			−0.232753
$101$	7.25589e8	−	1.25676e9i	0.693816	−	1.20172i	−0.276762	−	0.960938i	$-0.589261\pi$
$101$	7.25589e8	−	1.25676e9i	0.693816	−	1.20172i	0.970578	−	0.240786i	$-0.0774052\pi$
$102$		0			0
$103$	6.22282e8	+	1.07782e9i	0.544778	+	0.943583i	0.998621	+	0.0525012i	$0.0167193\pi$
$103$	6.22282e8	+	1.07782e9i	0.544778	+	0.943583i	−0.453843	+	0.891082i	$0.649947\pi$
$104$	−2.37574e8	−	4.11490e8i	−0.199136	−	0.344913i
$105$		0			0
$106$	−5.50414e8	+	9.53345e8i	−0.423461	+	0.733455i
$107$	2.10008e9			1.54885			0.774425	−	0.632666i	$-0.218039\pi$
$107$	2.10008e9			1.54885			0.774425	+	0.632666i	$0.218039\pi$
$108$		0			0
$109$	1.22058e9			0.828219			0.414110	−	0.910227i	$-0.364093\pi$
$109$	1.22058e9			0.828219			0.414110	+	0.910227i	$0.364093\pi$
$110$	4.11796e8	−	7.13252e8i	0.268173	−	0.464490i
$111$		0			0
$112$	1.38475e8	+	2.39846e8i	0.0831553	+	0.144029i
$113$	−2.89619e8	−	5.01635e8i	−0.167099	−	0.289424i	0.770300	−	0.637682i	$-0.220107\pi$
$113$	−2.89619e8	−	5.01635e8i	−0.167099	−	0.289424i	−0.937399	+	0.348258i	$0.886773\pi$
$114$		0			0
$115$	−2.52962e7	+	4.38143e7i	−0.0134870	+	0.0233602i
$116$	1.51888e9			0.778867
$117$		0			0
$118$	1.15348e9			0.547696
$119$	3.86176e8	−	6.68876e8i	0.176532	−	0.305763i
$120$		0			0
$121$	−9.00877e7	−	1.56037e8i	−0.0382060	−	0.0661747i
$122$	−5.26532e8	−	9.11980e8i	−0.215182	−	0.372706i
$123$		0			0
$124$	−5.58308e8	+	9.67017e8i	−0.212068	+	0.367313i
$125$	2.92452e9			1.07142
$126$		0			0
$127$	3.49732e9			1.19294			0.596470	−	0.802635i	$-0.296569\pi$
$127$	3.49732e9			1.19294			0.596470	+	0.802635i	$0.296569\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	9.48190e8	+	1.64231e9i	0.291172	+	0.504325i
$131$	−2.98414e9	−	5.16869e9i	−0.885317	−	1.53341i	−0.845350	−	0.534213i	$-0.820608\pi$
$131$	−2.98414e9	−	5.16869e9i	−0.885317	−	1.53341i	−0.0399674	−	0.999201i	$-0.512725\pi$
$132$		0			0
$133$	1.19262e9	−	2.06569e9i	0.330500	−	0.572442i
$134$	2.57936e9			0.691100
$135$		0			0
$136$	7.48607e8			0.187641
$137$	2.38898e9	−	4.13784e9i	0.579389	−	1.00353i	−0.416160	−	0.909291i	$-0.636624\pi$
$137$	2.38898e9	−	4.13784e9i	0.579389	−	1.00353i	0.995549	−	0.0942405i	$-0.0300423\pi$
$138$		0			0
$139$	−7.72545e8	−	1.33809e9i	−0.175532	−	0.304031i	0.764813	−	0.644252i	$-0.222831\pi$
$139$	−7.72545e8	−	1.33809e9i	−0.175532	−	0.304031i	−0.940345	+	0.340221i	$0.889498\pi$
$140$	−5.52672e8	−	9.57256e8i	−0.121588	−	0.210597i
$141$		0			0
$142$	2.21405e9	−	3.83485e9i	0.456973	−	0.791501i
$143$	5.84420e9			1.16873
$144$		0			0
$145$	−6.06206e9			−1.13884
$146$	3.38109e9	−	5.85622e9i	0.615842	−	1.06667i
$147$		0			0
$148$	1.48009e9	+	2.56359e9i	0.253578	+	0.439209i
$149$	−1.76830e9	−	3.06279e9i	−0.293913	−	0.509072i	0.680819	−	0.732452i	$-0.261624\pi$
$149$	−1.76830e9	−	3.06279e9i	−0.293913	−	0.509072i	−0.974731	+	0.223380i	$0.928291\pi$
$150$		0			0
$151$	−4.77068e8	+	8.26305e8i	−0.0746765	+	0.129343i	−0.900946	−	0.433932i	$-0.857126\pi$
$151$	−4.77068e8	+	8.26305e8i	−0.0746765	+	0.129343i	0.826269	+	0.563276i	$0.190459\pi$
$152$	2.31192e9			0.351298
$153$		0			0
$154$	−3.40642e9			−0.488039
$155$	2.22828e9	−	3.85949e9i	0.310082	−	0.537078i
$156$		0			0
$157$	−3.87003e9	−	6.70308e9i	−0.508353	−	0.880493i	−0.999953	−	0.00967224i	$-0.996921\pi$
$157$	−3.87003e9	−	6.70308e9i	−0.508353	−	0.880493i	0.491600	−	0.870821i	$-0.336412\pi$
$158$	3.36123e9	+	5.82182e9i	0.429083	+	0.743193i
$159$		0			0
$160$	5.35681e8	−	9.27826e8i	0.0646199	−	0.111925i
$161$	2.09253e8			0.0245445
$162$		0			0
$163$	9.86211e9			1.09427			0.547136	−	0.837044i	$-0.315718\pi$
$163$	9.86211e9			1.09427			0.547136	+	0.837044i	$0.315718\pi$
$164$	−3.38764e9	+	5.86757e9i	−0.365679	+	0.633375i
$165$		0			0
$166$	5.55396e9	+	9.61974e9i	0.567697	+	0.983280i
$167$	9.37490e9	+	1.62378e10i	0.932701	+	1.61549i	0.778683	+	0.627417i	$0.215888\pi$
$167$	9.37490e9	+	1.62378e10i	0.932701	+	1.61549i	0.154018	+	0.988068i	$0.450779\pi$
$168$		0			0
$169$	−1.42609e9	+	2.47007e9i	−0.134480	+	0.232926i
$170$	−2.98779e9			−0.274366
$171$		0			0
$172$	−3.43877e9			−0.299588
$173$	7.51420e9	−	1.30150e10i	0.637786	−	1.10468i	−0.348131	−	0.937446i	$-0.613184\pi$
$173$	7.51420e9	−	1.30150e10i	0.637786	−	1.10468i	0.985918	−	0.167232i	$-0.0534829\pi$
$174$		0			0
$175$	−1.92109e9	−	3.32742e9i	−0.154837	−	0.268186i
$176$	−1.65084e9	−	2.85935e9i	−0.129688	−	0.224626i
$177$		0			0
$178$	−6.37040e9	+	1.10338e10i	−0.475638	+	0.823829i
$179$	−4.69080e9			−0.341514			−0.170757	−	0.985313i	$-0.554621\pi$
$179$	−4.69080e9			−0.341514			−0.170757	+	0.985313i	$0.554621\pi$
$180$		0			0
$181$	−4.99664e9			−0.346038			−0.173019	−	0.984918i	$-0.555352\pi$
$181$	−4.99664e9			−0.346038			−0.173019	+	0.984918i	$0.555352\pi$
$182$	3.92175e9	−	6.79268e9i	0.264947	−	0.458902i
$183$		0			0
$184$	1.01410e8	+	1.75647e8i	0.00652228	+	0.0112969i
$185$	−5.90724e9	−	1.02316e10i	−0.370776	−	0.642203i
$186$		0			0
$187$	−4.60384e9	+	7.97408e9i	−0.275317	+	0.476863i
$188$	4.68241e9			0.273375
$189$		0			0
$190$	−9.22717e9			−0.513662
$191$	−1.59536e9	+	2.76325e9i	−0.0867380	+	0.150235i	−0.906130	−	0.422998i	$-0.860978\pi$
$191$	−1.59536e9	+	2.76325e9i	−0.0867380	+	0.150235i	0.819392	+	0.573233i	$0.194311\pi$
$192$		0			0
$193$	−1.55949e10	−	2.70112e10i	−0.809051	−	1.40132i	−0.913522	−	0.406790i	$-0.866648\pi$
$193$	−1.55949e10	−	2.70112e10i	−0.809051	−	1.40132i	0.104470	−	0.994528i	$-0.466685\pi$
$194$	3.13302e9	+	5.42655e9i	0.158802	+	0.275053i
$195$		0			0
$196$	2.87939e9	−	4.98724e9i	0.139363	−	0.241384i
$197$	−2.30042e10			−1.08820			−0.544102	−	0.839019i	$-0.683129\pi$
$197$	−2.30042e10			−1.08820			−0.544102	+	0.839019i	$0.683129\pi$
$198$		0			0
$199$	−1.04467e10			−0.472217			−0.236109	−	0.971727i	$-0.575872\pi$
$199$	−1.04467e10			−0.472217			−0.236109	+	0.971727i	$0.575872\pi$
$200$	1.86203e9	−	3.22513e9i	0.0822907	−	0.142532i
$201$		0			0
$202$	1.16094e10	+	2.01081e10i	0.490602	+	0.849748i
$203$	1.25365e10	+	2.17138e10i	0.518136	+	0.897437i
$204$		0			0
$205$	1.35205e10	−	2.34183e10i	0.534690	−	0.926109i
$206$	−1.99130e10			−0.770432
$207$		0			0
$208$	7.60237e9			0.281620
$209$	−1.42180e10	+	2.46263e10i	−0.515443	+	0.892773i
$210$		0			0
$211$	−2.41061e10	−	4.17530e10i	−0.837253	−	1.45016i	−0.892183	−	0.451674i	$-0.850827\pi$
$211$	−2.41061e10	−	4.17530e10i	−0.837253	−	1.45016i	0.0549307	−	0.998490i	$-0.482506\pi$
$212$	−8.80662e9	−	1.52535e10i	−0.299432	−	0.518631i
$213$		0			0
$214$	−1.68007e10	+	2.90996e10i	−0.547601	+	0.948473i
$215$	1.37246e10			0.438052
$216$		0			0
$217$	−1.84325e10			−0.564308
$218$	−9.76460e9	+	1.69128e10i	−0.292820	+	0.507179i
$219$		0			0
$220$	6.58874e9	+	1.14120e10i	0.189627	+	0.328444i
$221$	−1.06007e10	−	1.83609e10i	−0.298929	−	0.517760i
$222$		0			0
$223$	2.39949e10	−	4.15604e10i	0.649751	−	1.12540i	−0.333432	−	0.942774i	$-0.608207\pi$
$223$	2.39949e10	−	4.15604e10i	0.649751	−	1.12540i	0.983182	−	0.182627i	$-0.0584601\pi$
$224$	−4.43120e9			−0.117599
$225$		0			0
$226$	9.26782e9			0.236314
$227$	−2.81836e10	+	4.88154e10i	−0.704498	+	1.22023i	0.262374	+	0.964966i	$0.415495\pi$
$227$	−2.81836e10	+	4.88154e10i	−0.704498	+	1.22023i	−0.966872	+	0.255261i	$0.917839\pi$
$228$		0			0
$229$	2.88693e10	+	5.00030e10i	0.693707	+	1.20154i	0.970615	+	0.240639i	$0.0773571\pi$
$229$	2.88693e10	+	5.00030e10i	0.693707	+	1.20154i	−0.276907	+	0.960897i	$0.589310\pi$
$230$	−4.04740e8	−	7.01029e8i	−0.00953675	−	0.0165181i
$231$		0			0
$232$	−1.21511e10	+	2.10463e10i	−0.275371	+	0.476957i
$233$	2.54451e10			0.565592			0.282796	−	0.959180i	$-0.408738\pi$
$233$	2.54451e10			0.565592			0.282796	+	0.959180i	$0.408738\pi$
$234$		0			0
$235$	−1.86881e10			−0.399724
$236$	−9.22780e9	+	1.59830e10i	−0.193640	+	0.335394i
$237$		0			0
$238$	6.17881e9	+	1.07020e10i	0.124827	+	0.216207i
$239$	−1.86944e10	−	3.23797e10i	−0.370614	−	0.641922i	0.619046	−	0.785354i	$-0.287519\pi$
$239$	−1.86944e10	−	3.23797e10i	−0.370614	−	0.641922i	−0.989660	+	0.143433i	$0.954186\pi$
$240$		0			0
$241$	2.80968e10	−	4.86650e10i	0.536512	−	0.929266i	−0.462576	−	0.886579i	$-0.653075\pi$
$241$	2.80968e10	−	4.86650e10i	0.536512	−	0.929266i	0.999089	−	0.0426868i	$-0.0135918\pi$
$242$	2.88281e9			0.0540314
$243$		0			0
$244$	1.68490e10			0.304313
$245$	−1.14920e10	+	1.99048e10i	−0.203774	+	0.352947i
$246$		0			0
$247$	−3.27379e10	−	5.67038e10i	−0.559648	−	0.969339i
$248$	−8.93292e9	−	1.54723e10i	−0.149955	−	0.259730i
$249$		0			0
$250$	−2.33961e10	+	4.05233e10i	−0.378803	+	0.656107i
$251$	−7.14751e10			−1.13664			−0.568320	−	0.822807i	$-0.692407\pi$
$251$	−7.14751e10			−1.13664			−0.568320	+	0.822807i	$0.692407\pi$
$252$		0			0
$253$	−2.49463e9			−0.0382793
$254$	−2.79786e10	+	4.84603e10i	−0.421768	+	0.730524i
$255$		0			0
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	1.01810e10	+	1.76340e10i	0.145576	+	0.252146i	0.929588	−	0.368601i	$-0.120163\pi$
$257$	1.01810e10	+	1.76340e10i	0.145576	+	0.252146i	−0.784011	+	0.620746i	$0.786830\pi$
$258$		0			0
$259$	−2.44326e10	+	4.23185e10i	−0.337381	+	0.584362i
$260$	−3.03421e10			−0.411780
$261$		0			0
$262$	9.54926e10			1.25203
$263$	−4.31385e10	+	7.47180e10i	−0.555986	+	0.962996i	0.441840	+	0.897094i	$0.354326\pi$
$263$	−4.31385e10	+	7.47180e10i	−0.555986	+	0.962996i	−0.997826	+	0.0659019i	$0.979008\pi$
$264$		0			0
$265$	3.51484e10	+	6.08788e10i	0.437824	+	0.758333i
$266$	1.90820e10	+	3.30510e10i	0.233699	+	0.404778i
$267$		0			0
$268$	−2.06349e10	+	3.57407e10i	−0.244341	+	0.423210i
$269$	−9.80326e10			−1.14152			−0.570762	−	0.821115i	$-0.693352\pi$
$269$	−9.80326e10			−1.14152			−0.570762	+	0.821115i	$0.693352\pi$
$270$		0			0
$271$	9.35838e10			1.05400			0.526998	−	0.849867i	$-0.323318\pi$
$271$	9.35838e10			1.05400			0.526998	+	0.849867i	$0.323318\pi$
$272$	−5.98885e9	+	1.03730e10i	−0.0663413	+	0.114906i
$273$		0			0
$274$	3.82237e10	+	6.62054e10i	0.409690	+	0.709604i
$275$	2.29025e10	+	3.96682e10i	0.241482	+	0.418260i
$276$		0			0
$277$	5.04765e10	−	8.74279e10i	0.515146	−	0.892259i	−0.484699	−	0.874681i	$-0.661071\pi$
$277$	5.04765e10	−	8.74279e10i	0.515146	−	0.892259i	0.999845	−	0.0175783i	$-0.00559564\pi$
$278$	2.47214e10			0.248240
$279$		0			0
$280$	1.76855e10			0.171952
$281$	−5.11334e10	+	8.85657e10i	−0.489245	+	0.847398i	−0.999923	−	0.0123744i	$-0.996061\pi$
$281$	−5.11334e10	+	8.85657e10i	−0.489245	+	0.847398i	0.510678	+	0.859772i	$0.329394\pi$
$282$		0			0
$283$	−1.09960e10	−	1.90457e10i	−0.101905	−	0.176505i	0.810564	−	0.585650i	$-0.199161\pi$
$283$	−1.09960e10	−	1.90457e10i	−0.101905	−	0.176505i	−0.912470	+	0.409144i	$0.865827\pi$
$284$	3.54249e10	+	6.13577e10i	0.323129	+	0.559675i
$285$		0			0
$286$	−4.67536e10	+	8.09797e10i	−0.413208	+	0.715696i
$287$	−1.11843e11			−0.973062
$288$		0			0
$289$	−8.51847e10			−0.718326
$290$	4.84965e10	−	8.39984e10i	0.402642	−	0.697397i
$291$		0			0
$292$	5.40975e10	+	9.36995e10i	0.435466	+	0.754249i
$293$	4.07586e10	+	7.05960e10i	0.323084	+	0.559598i	0.981123	−	0.193386i	$-0.0619470\pi$
$293$	4.07586e10	+	7.05960e10i	0.323084	+	0.559598i	−0.658039	+	0.752984i	$0.728614\pi$
$294$		0			0
$295$	3.68294e10	−	6.37904e10i	0.283136	−	0.490406i
$296$	−4.73629e10			−0.358613
$297$		0			0
$298$	5.65857e10			0.415656
$299$	2.87203e9	−	4.97450e9i	0.0207811	−	0.0359939i
$300$		0			0
$301$	−2.83827e10	−	4.91603e10i	−0.199299	−	0.345196i
$302$	−7.63308e9	−	1.32209e10i	−0.0528042	−	0.0914596i
$303$		0			0
$304$	−1.84953e10	+	3.20349e10i	−0.124203	+	0.215125i
$305$	−6.72467e10			−0.444961
$306$		0			0
$307$	−2.76415e10			−0.177598			−0.0887991	−	0.996050i	$-0.528303\pi$
$307$	−2.76415e10			−0.177598			−0.0887991	+	0.996050i	$0.528303\pi$
$308$	2.72513e10	−	4.72007e10i	0.172548	−	0.298862i
$309$		0			0
$310$	3.56525e10	+	6.17519e10i	0.219261	+	0.379772i
$311$	1.33228e9	+	2.30757e9i	0.00807557	+	0.0139873i	0.870035	−	0.492990i	$-0.164096\pi$
$311$	1.33228e9	+	2.30757e9i	0.00807557	+	0.0139873i	−0.861959	+	0.506977i	$0.830763\pi$
$312$		0			0
$313$	1.22662e11	−	2.12456e11i	0.722370	−	1.25118i	−0.237678	−	0.971344i	$-0.576386\pi$
$313$	1.22662e11	−	2.12456e11i	0.722370	−	1.25118i	0.960048	−	0.279837i	$-0.0902803\pi$
$314$	1.23841e11			0.718920
$315$		0			0
$316$	−1.07559e11			−0.606814
$317$	1.61358e11	−	2.79481e11i	0.897480	−	1.55448i	0.0667752	−	0.997768i	$-0.478729\pi$
$317$	1.61358e11	−	2.79481e11i	0.897480	−	1.55448i	0.830705	−	0.556713i	$-0.187938\pi$
$318$		0			0
$319$	−1.49455e11	−	2.58864e11i	−0.808077	−	1.39963i
$320$	8.57089e9	+	1.48452e10i	0.0456932	+	0.0791429i
$321$		0			0
$322$	−1.67402e9	+	2.89949e9i	−0.00867779	+	0.0150304i
$323$	1.03159e11			0.527345
$324$		0			0
$325$	−1.05469e11			−0.524385
$326$	−7.88969e10	+	1.36653e11i	−0.386884	+	0.670102i
$327$		0			0
$328$	−5.42023e10	−	9.38812e10i	−0.258574	−	0.447864i
$329$	3.86474e10	+	6.69393e10i	0.181861	+	0.314992i
$330$		0			0
$331$	−1.31822e11	+	2.28322e11i	−0.603617	+	1.04550i	0.388651	+	0.921385i	$0.372941\pi$
$331$	−1.31822e11	+	2.28322e11i	−0.603617	+	1.04550i	−0.992268	+	0.124111i	$0.960392\pi$
$332$	−1.77727e11			−0.802845
$333$		0			0
$334$	−2.99997e11			−1.31904
$335$	8.23566e10	−	1.42646e11i	0.357270	−	0.618810i
$336$		0			0
$337$	−3.08775e8	−	5.34815e8i	−0.00130409	−	0.00225875i	0.865373	−	0.501129i	$-0.167082\pi$
$337$	−3.08775e8	−	5.34815e8i	−0.00130409	−	0.00225875i	−0.866677	+	0.498870i	$0.833748\pi$
$338$	−2.28175e10	−	3.95211e10i	−0.0950917	−	0.164704i
$339$		0			0
$340$	2.39023e10	−	4.14000e10i	0.0970029	−	0.168014i
$341$	2.19745e11			0.880086
$342$		0			0
$343$	2.65594e11			1.03608
$344$	2.75101e10	−	4.76490e10i	0.105920	−	0.183460i
$345$		0			0
$346$	1.20227e11	+	2.08239e11i	0.450983	+	0.781125i
$347$	−1.34265e11	−	2.32553e11i	−0.497141	−	0.861073i	0.502854	−	0.864371i	$-0.332283\pi$
$347$	−1.34265e11	−	2.32553e11i	−0.497141	−	0.861073i	−0.999995	+	0.00329862i	$0.998950\pi$
$348$		0			0
$349$	3.66403e10	−	6.34628e10i	0.132204	−	0.228984i	−0.792322	−	0.610103i	$-0.791128\pi$
$349$	3.66403e10	−	6.34628e10i	0.132204	−	0.228984i	0.924526	+	0.381119i	$0.124461\pi$
$350$	6.14748e10			0.218973
$351$		0			0
$352$	5.28270e10			0.183406
$353$	−8.78842e10	+	1.52220e11i	−0.301248	+	0.521778i	−0.976419	−	0.215884i	$-0.930737\pi$
$353$	−8.78842e10	+	1.52220e11i	−0.301248	+	0.521778i	0.675171	+	0.737662i	$0.264070\pi$
$354$		0			0
$355$	−1.41385e11	−	2.44887e11i	−0.472473	−	0.818347i
$356$	−1.01926e11	−	1.76542e11i	−0.336327	−	0.582535i
$357$		0			0
$358$	3.75264e10	−	6.49977e10i	0.120743	−	0.209134i
$359$	2.63152e11			0.836146			0.418073	−	0.908413i	$-0.362706\pi$
$359$	2.63152e11			0.836146			0.418073	+	0.908413i	$0.362706\pi$
$360$		0			0
$361$	−4.10336e9			−0.0127162
$362$	3.99731e10	−	6.92354e10i	0.122343	−	0.211904i
$363$		0			0
$364$	6.27481e10	+	1.08683e11i	0.187346	+	0.324493i
$365$	−2.15910e11	−	3.73967e11i	−0.636730	−	1.10285i
$366$		0			0
$367$	−1.83601e11	+	3.18006e11i	−0.528296	+	0.915036i	0.471159	+	0.882048i	$0.343836\pi$
$367$	−1.83601e11	+	3.18006e11i	−0.528296	+	0.915036i	−0.999456	+	0.0329881i	$0.989498\pi$
$368$	−3.24511e9			−0.00922389
$369$		0			0
$370$	1.89032e11			0.524357
$371$	1.45375e11	−	2.51797e11i	0.398390	−	0.690031i
$372$		0			0
$373$	−1.18671e11	−	2.05543e11i	−0.317434	−	0.549812i	0.662518	−	0.749046i	$-0.269488\pi$
$373$	−1.18671e11	−	2.05543e11i	−0.317434	−	0.549812i	−0.979952	+	0.199234i	$0.936154\pi$
$374$	−7.36614e10	−	1.27585e11i	−0.194678	−	0.337193i
$375$		0			0
$376$	−3.74593e10	+	6.48813e10i	−0.0966527	+	0.167407i
$377$	6.88261e11			1.75476
$378$		0			0
$379$	−3.00656e11			−0.748504			−0.374252	−	0.927327i	$-0.622100\pi$
$379$	−3.00656e11			−0.748504			−0.374252	+	0.927327i	$0.622100\pi$
$380$	7.38173e10	−	1.27855e11i	0.181607	−	0.314552i
$381$		0			0
$382$	−2.55258e10	−	4.42120e10i	−0.0613330	−	0.106232i
$383$	1.10343e11	+	1.91120e11i	0.262030	+	0.453849i	0.966781	−	0.255605i	$-0.0822747\pi$
$383$	1.10343e11	+	1.91120e11i	0.262030	+	0.453849i	−0.704751	+	0.709455i	$0.748941\pi$
$384$		0			0
$385$	−1.08764e11	+	1.88384e11i	−0.252296	+	0.436990i
$386$	4.99038e11			1.14417
$387$		0			0
$388$	−1.00257e11			−0.224579
$389$	−4.05914e10	+	7.03064e10i	−0.0898795	+	0.155676i	−0.907460	−	0.420138i	$-0.861982\pi$
$389$	−4.05914e10	+	7.03064e10i	−0.0898795	+	0.155676i	0.817581	+	0.575814i	$0.195315\pi$
$390$		0			0
$391$	4.52494e9	+	7.83743e9i	0.00979079	+	0.0169582i
$392$	4.60702e10	+	7.97959e10i	0.0985446	+	0.170684i
$393$		0			0
$394$	1.84034e11	−	3.18756e11i	0.384738	−	0.666386i
$395$	4.29283e11			0.887272
$396$		0			0
$397$	−3.51282e11			−0.709739			−0.354870	−	0.934916i	$-0.615475\pi$
$397$	−3.51282e11			−0.709739			−0.354870	+	0.934916i	$0.615475\pi$
$398$	8.35739e10	−	1.44754e11i	0.166954	−	0.289173i
$399$		0			0
$400$	2.97924e10	+	5.16020e10i	0.0581883	+	0.100785i
$401$	1.86045e11	+	3.22239e11i	0.359309	+	0.622342i	0.987846	−	0.155438i	$-0.0496790\pi$
$401$	1.86045e11	+	3.22239e11i	0.359309	+	0.622342i	−0.628536	+	0.777780i	$0.716346\pi$
$402$		0			0
$403$	−2.52990e11	+	4.38191e11i	−0.477782	+	0.827543i
$404$	−3.71501e11			−0.693816
$405$		0			0
$406$	−4.01167e11			−0.732754
$407$	2.91276e11	−	5.04505e11i	0.526175	−	0.911362i
$408$		0			0
$409$	4.06034e11	+	7.03272e11i	0.717476	+	1.24271i	0.961997	+	0.273061i	$0.0880362\pi$
$409$	4.06034e11	+	7.03272e11i	0.717476	+	1.24271i	−0.244520	+	0.969644i	$0.578630\pi$
$410$	2.16329e11	+	3.74692e11i	0.378083	+	0.654858i
$411$		0			0
$412$	1.59304e11	−	2.75923e11i	0.272389	−	0.471791i
$413$	−3.04656e11			−0.515270
$414$		0			0
$415$	7.09331e11			1.17390
$416$	−6.08190e10	+	1.05342e11i	−0.0995678	+	0.172457i
$417$		0			0
$418$	−2.27488e11	−	3.94021e11i	−0.364473	−	0.631286i
$419$	−6.49581e10	−	1.12511e11i	−0.102960	−	0.178333i	0.809943	−	0.586509i	$-0.199498\pi$
$419$	−6.49581e10	−	1.12511e11i	−0.102960	−	0.178333i	−0.912903	+	0.408176i	$0.866165\pi$
$420$		0			0
$421$	6.09043e11	−	1.05489e12i	0.944884	−	1.63659i	0.188899	−	0.981996i	$-0.439508\pi$
$421$	6.09043e11	−	1.05489e12i	0.944884	−	1.63659i	0.755984	−	0.654590i	$-0.227159\pi$
$422$	7.71396e11			1.18405
$423$		0			0
$424$	2.81812e11			0.423461
$425$	8.30845e10	−	1.43907e11i	0.123529	−	0.213959i
$426$		0			0
$427$	1.39068e11	+	2.40872e11i	0.202442	+	0.350640i
$428$	−2.68811e11	−	4.65593e11i	−0.387212	−	0.670672i
$429$		0			0
$430$	−1.09797e11	+	1.90173e11i	−0.154875	+	0.268251i
$431$	−1.33990e11			−0.187036			−0.0935179	−	0.995618i	$-0.529811\pi$
$431$	−1.33990e11			−0.187036			−0.0935179	+	0.995618i	$0.529811\pi$
$432$		0			0
$433$	−4.46482e10			−0.0610392			−0.0305196	−	0.999534i	$-0.509716\pi$
$433$	−4.46482e10			−0.0610392			−0.0305196	+	0.999534i	$0.509716\pi$
$434$	1.47460e11	−	2.55409e11i	0.199513	−	0.345566i
$435$		0			0
$436$	−1.56234e11	−	2.70605e11i	−0.207055	−	0.358630i
$437$	1.39744e10	+	2.42043e10i	0.0183301	+	0.0317487i
$438$		0			0
$439$	1.14481e11	−	1.98286e11i	0.147110	−	0.254801i	−0.783048	−	0.621961i	$-0.786336\pi$
$439$	1.14481e11	−	1.98286e11i	0.147110	−	0.254801i	0.930158	+	0.367159i	$0.119670\pi$
$440$	−2.10840e11			−0.268173
$441$		0			0
$442$	3.39221e11			0.422749
$443$	4.19646e11	−	7.26849e11i	0.517686	−	0.896659i	−0.482103	−	0.876115i	$-0.660127\pi$
$443$	4.19646e11	−	7.26849e11i	0.517686	−	0.896659i	0.999789	−	0.0205442i	$-0.00653987\pi$
$444$		0			0
$445$	4.06801e11	+	7.04601e11i	0.491770	+	0.851771i
$446$	3.83918e11	+	6.64966e11i	0.459443	+	0.795779i
$447$		0			0
$448$	3.54496e10	−	6.14005e10i	0.0415777	−	0.0720146i
$449$	−1.21847e12			−1.41484			−0.707420	−	0.706793i	$-0.750141\pi$
$449$	−1.21847e12			−1.41484			−0.707420	+	0.706793i	$0.750141\pi$
$450$		0			0
$451$	1.33335e12			1.51757
$452$	−7.41425e10	+	1.28419e11i	−0.0835496	+	0.144712i
$453$		0			0
$454$	−4.50938e11	−	7.81047e11i	−0.498156	−	0.862831i
$455$	−2.50436e11	−	4.33768e11i	−0.273934	−	0.474467i
$456$		0			0
$457$	−4.95467e11	+	8.58174e11i	−0.531364	+	0.920349i	0.467966	+	0.883746i	$0.344987\pi$
$457$	−4.95467e11	+	8.58174e11i	−0.531364	+	0.920349i	−0.999330	+	0.0366026i	$0.988346\pi$
$458$	−9.23817e11			−0.981050
$459$		0			0
$460$	1.29517e10			0.0134870
$461$	4.15501e11	−	7.19669e11i	0.428468	−	0.742128i	−0.568270	−	0.822842i	$-0.692387\pi$
$461$	4.15501e11	−	7.19669e11i	0.428468	−	0.742128i	0.996737	+	0.0807148i	$0.0257203\pi$
$462$		0			0
$463$	−1.50482e9	−	2.60643e9i	−0.00152185	−	0.00263592i	0.865263	−	0.501317i	$-0.167151\pi$
$463$	−1.50482e9	−	2.60643e9i	−0.00152185	−	0.00263592i	−0.866785	+	0.498681i	$0.833818\pi$
$464$	−1.94417e11	−	3.36740e11i	−0.194717	−	0.337259i
$465$		0			0
$466$	−2.03561e11	+	3.52578e11i	−0.199967	+	0.346353i
$467$	−3.46119e10			−0.0336743			−0.0168372	−	0.999858i	$-0.505360\pi$
$467$	−3.46119e10			−0.0336743			−0.0168372	+	0.999858i	$0.505360\pi$
$468$		0			0
$469$	−6.81261e11			−0.650183
$470$	1.49505e11	−	2.58950e11i	0.141324	−	0.244780i
$471$		0			0
$472$	−1.47645e11	−	2.55728e11i	−0.136924	−	0.237159i
$473$	3.38368e11	+	5.86070e11i	0.310824	+	0.538362i
$474$		0			0
$475$	2.56589e11	−	4.44425e11i	0.231269	−	0.400569i
$476$	−1.97722e11			−0.176532
$477$		0			0
$478$	5.98221e11			0.524127
$479$	−8.31890e11	+	1.44088e12i	−0.722031	+	1.25059i	0.238153	+	0.971228i	$0.423458\pi$
$479$	−8.31890e11	+	1.44088e12i	−0.722031	+	1.25059i	−0.960184	+	0.279367i	$0.909875\pi$
$480$		0			0
$481$	6.70684e11	+	1.16166e12i	0.571301	+	0.989522i
$482$	4.49548e11	+	7.78640e11i	0.379371	+	0.657090i
$483$		0			0
$484$	−2.30625e10	+	3.99454e10i	−0.0191030	+	0.0330874i
$485$	4.00137e11			0.328376
$486$		0			0
$487$	−1.18819e12			−0.957203			−0.478601	−	0.878032i	$-0.658856\pi$
$487$	−1.18819e12			−0.957203			−0.478601	+	0.878032i	$0.658856\pi$
$488$	−1.34792e11	+	2.33467e11i	−0.107591	+	0.186353i
$489$		0			0
$490$	−1.83872e11	−	3.18476e11i	−0.144090	−	0.249571i
$491$	3.38983e10	+	5.87136e10i	0.0263215	+	0.0455902i	0.878886	−	0.477032i	$-0.158287\pi$
$491$	3.38983e10	+	5.87136e10i	0.0263215	+	0.0455902i	−0.852565	+	0.522622i	$0.824954\pi$
$492$		0			0
$493$	−5.42186e11	+	9.39093e11i	−0.413368	+	0.715975i
$494$	1.04761e12			0.791462
$495$		0			0
$496$	2.85853e11			0.212068
$497$	−5.84776e11	+	1.01286e12i	−0.429918	+	0.744640i
$498$		0			0
$499$	1.05094e12	+	1.82029e12i	0.758800	+	1.31428i	0.943463	+	0.331478i	$0.107547\pi$
$499$	1.05094e12	+	1.82029e12i	0.758800	+	1.31428i	−0.184663	+	0.982802i	$0.559119\pi$
$500$	−3.74338e11	−	6.48373e11i	−0.267854	−	0.463938i
$501$		0			0
$502$	5.71801e11	−	9.90388e11i	0.401863	−	0.696047i
$503$	−1.66977e12			−1.16306			−0.581528	−	0.813527i	$-0.697545\pi$
$503$	−1.66977e12			−1.16306			−0.581528	+	0.813527i	$0.697545\pi$
$504$		0			0
$505$	1.48271e12			1.01448
$506$	1.99570e10	−	3.45666e10i	0.0135338	−	0.0234412i
$507$		0			0
$508$	−4.47657e11	−	7.75365e11i	−0.298235	−	0.516558i
$509$	−1.38057e10	−	2.39121e10i	−0.00911648	−	0.0157902i	0.861431	−	0.507874i	$-0.169569\pi$
$509$	−1.38057e10	−	2.39121e10i	−0.00911648	−	0.0157902i	−0.870548	+	0.492084i	$0.836235\pi$
$510$		0			0
$511$	−8.93014e11	+	1.54675e12i	−0.579381	+	1.00352i
$512$	6.87195e10			0.0441942
$513$		0			0
$514$	−3.25792e11			−0.205876
$515$	−6.35804e11	+	1.10124e12i	−0.398282	+	0.689844i
$516$		0			0
$517$	−4.60740e11	−	7.98024e11i	−0.283627	−	0.491257i
$518$	−3.90922e11	−	6.77096e11i	−0.238565	−	0.413206i
$519$		0			0
$520$	2.42737e11	−	4.20432e11i	0.145586	−	0.252163i
$521$	1.30088e12			0.773511			0.386756	−	0.922182i	$-0.373596\pi$
$521$	1.30088e12			0.773511			0.386756	+	0.922182i	$0.373596\pi$
$522$		0			0
$523$	−1.91657e12			−1.12013			−0.560063	−	0.828450i	$-0.689223\pi$
$523$	−1.91657e12			−1.12013			−0.560063	+	0.828450i	$0.689223\pi$
$524$	−7.63941e11	+	1.32318e12i	−0.442659	+	0.766707i
$525$		0			0
$526$	−6.90215e11	−	1.19549e12i	−0.393141	−	0.680941i
$527$	−3.98591e11	−	6.90380e11i	−0.225102	−	0.389888i
$528$		0			0
$529$	8.99350e11	−	1.55772e12i	0.499319	−	0.864846i
$530$	−1.12475e12			−0.619176
$531$		0			0
$532$	−6.10623e11			−0.330500
$533$	−1.53507e12	+	2.65881e12i	−0.823862	+	1.42697i
$534$		0			0
$535$	1.07286e12	+	1.85825e12i	0.566175	+	0.980643i
$536$	−3.30158e11	−	5.71851e11i	−0.172775	−	0.299255i
$537$		0			0
$538$	7.84261e11	−	1.35838e12i	0.403590	−	0.699038i
$539$	−1.13330e12			−0.578358
$540$		0			0
$541$	7.15583e10			0.0359147			0.0179573	−	0.999839i	$-0.494284\pi$
$541$	7.15583e10			0.0359147			0.0179573	+	0.999839i	$0.494284\pi$
$542$	−7.48671e11	+	1.29674e12i	−0.372644	+	0.645438i
$543$		0			0
$544$	−9.58217e10	−	1.65968e11i	−0.0469104	−	0.0812511i
$545$	6.23549e11	+	1.08002e12i	0.302752	+	0.524381i
$546$		0			0
$547$	−7.44479e11	+	1.28948e12i	−0.355557	+	0.615843i	−0.987213	−	0.159406i	$-0.949042\pi$
$547$	−7.44479e11	+	1.28948e12i	−0.355557	+	0.615843i	0.631656	+	0.775249i	$0.282376\pi$
$548$	−1.22316e12			−0.579389
$549$		0			0
$550$	−7.32879e11			−0.341508
$551$	−1.67443e12	+	2.90019e12i	−0.773899	+	1.34043i
$552$		0			0
$553$	−8.87767e11	−	1.53766e12i	−0.403679	−	0.699192i
$554$	8.07624e11	+	1.39885e12i	0.364263	+	0.630922i
$555$		0			0
$556$	−1.97771e11	+	3.42550e11i	−0.0877661	+	0.152015i
$557$	2.89221e11			0.127315			0.0636577	−	0.997972i	$-0.479723\pi$
$557$	2.89221e11			0.127315			0.0636577	+	0.997972i	$0.479723\pi$
$558$		0			0
$559$	−1.55823e12			−0.674961
$560$	−1.41484e11	+	2.45057e11i	−0.0607941	+	0.105298i
$561$		0			0
$562$	−8.18135e11	−	1.41705e12i	−0.345949	−	0.599201i
$563$	6.06414e11	+	1.05034e12i	0.254379	+	0.440598i	0.964727	−	0.263253i	$-0.0847955\pi$
$563$	6.06414e11	+	1.05034e12i	0.254379	+	0.440598i	−0.710347	+	0.703851i	$0.751462\pi$
$564$		0			0
$565$	2.95913e11	−	5.12536e11i	0.122165	−	0.211595i
$566$	3.51873e11			0.144116
$567$		0			0
$568$	−1.13360e12			−0.456973
$569$	7.48882e11	−	1.29710e12i	0.299508	−	0.518763i	−0.676516	−	0.736428i	$-0.736511\pi$
$569$	7.48882e11	−	1.29710e12i	0.299508	−	0.518763i	0.976023	+	0.217666i	$0.0698442\pi$
$570$		0			0
$571$	−1.78403e12	−	3.09003e12i	−0.702327	−	1.21647i	−0.967647	−	0.252306i	$-0.918811\pi$
$571$	−1.78403e12	−	3.09003e12i	−0.702327	−	1.21647i	0.265320	−	0.964160i	$-0.414522\pi$
$572$	−7.48058e11	−	1.29567e12i	−0.292182	−	0.506074i
$573$		0			0
$574$	8.94745e11	−	1.54974e12i	0.344029	−	0.595877i
$575$	4.50200e10			0.0171751
$576$		0			0
$577$	1.09711e12			0.412060			0.206030	−	0.978546i	$-0.433946\pi$
$577$	1.09711e12			0.412060			0.206030	+	0.978546i	$0.433946\pi$
$578$	6.81478e11	−	1.18035e12i	0.253966	−	0.439883i
$579$		0			0
$580$	7.75944e11	+	1.34397e12i	0.284711	+	0.493134i
$581$	−1.46691e12	−	2.54077e12i	−0.534086	−	0.925065i
$582$		0			0
$583$	−1.73311e12	+	3.00183e12i	−0.621323	+	1.07616i
$584$	−1.73112e12			−0.615842
$585$		0			0
$586$	−1.30428e12			−0.456910
$587$	6.48821e11	−	1.12379e12i	0.225556	−	0.390674i	−0.730930	−	0.682452i	$-0.760914\pi$
$587$	6.48821e11	−	1.12379e12i	0.225556	−	0.390674i	0.956486	+	0.291778i	$0.0942469\pi$
$588$		0			0
$589$	−1.23097e12	−	2.13209e12i	−0.421431	−	0.729941i
$590$	5.89270e11	+	1.02065e12i	0.200208	+	0.346770i
$591$		0			0
$592$	3.78903e11	−	6.56280e11i	0.126789	−	0.219605i
$593$	−4.72631e12			−1.56955			−0.784777	−	0.619778i	$-0.787223\pi$
$593$	−4.72631e12			−1.56955			−0.784777	+	0.619778i	$0.787223\pi$
$594$		0			0
$595$	7.89135e11			0.258122
$596$	−4.52686e11	+	7.84075e11i	−0.146956	+	0.254536i
$597$		0			0
$598$	4.59524e10	+	7.95920e10i	0.0146944	+	0.0254515i
$599$	1.57135e12	+	2.72166e12i	0.498715	+	0.863799i	0.999999	−	0.00148367i	$-0.000472268\pi$
$599$	1.57135e12	+	2.72166e12i	0.498715	+	0.863799i	−0.501284	+	0.865283i	$0.667139\pi$
$600$		0			0
$601$	−1.74874e12	+	3.02891e12i	−0.546752	+	0.947002i	0.451743	+	0.892148i	$0.350802\pi$
$601$	−1.74874e12	+	3.02891e12i	−0.546752	+	0.947002i	−0.998494	+	0.0548534i	$0.982531\pi$
$602$	9.08247e11			0.281851
$603$		0			0
$604$	2.44259e11			0.0746765
$605$	9.20453e10	−	1.59427e11i	0.0279320	−	0.0483797i
$606$		0			0
$607$	1.57652e12	+	2.73060e12i	0.471356	+	0.816413i	0.999463	−	0.0327652i	$-0.0104314\pi$
$607$	1.57652e12	+	2.73060e12i	0.471356	+	0.816413i	−0.528107	+	0.849178i	$0.677098\pi$
$608$	−2.95925e11	−	5.12558e11i	−0.0878246	−	0.152117i
$609$		0			0
$610$	5.37974e11	−	9.31798e11i	0.157317	−	0.272482i
$611$	2.12177e12			0.615904
$612$		0			0
$613$	6.51322e12			1.86304			0.931522	−	0.363684i	$-0.118481\pi$
$613$	6.51322e12			1.86304			0.931522	+	0.363684i	$0.118481\pi$
$614$	2.21132e11	−	3.83012e11i	0.0627905	−	0.108756i
$615$		0			0
$616$	4.36021e11	+	7.55211e11i	0.122010	+	0.211327i
$617$	−1.41102e12	−	2.44395e12i	−0.391966	−	0.678905i	0.600743	−	0.799443i	$-0.294872\pi$
$617$	−1.41102e12	−	2.44395e12i	−0.391966	−	0.678905i	−0.992709	+	0.120537i	$0.961538\pi$
$618$		0			0
$619$	4.22132e11	−	7.31154e11i	0.115569	−	0.200171i	−0.802438	−	0.596735i	$-0.796464\pi$
$619$	4.22132e11	−	7.31154e11i	0.115569	−	0.200171i	0.918007	+	0.396564i	$0.129798\pi$
$620$	−1.14088e12			−0.310082
$621$		0			0
$622$	−4.26329e10			−0.0114206
$623$	1.68255e12	−	2.91426e12i	0.447478	−	0.775054i
$624$		0			0
$625$	6.06149e11	+	1.04988e12i	0.158898	+	0.275220i
$626$	1.96259e12	+	3.39930e12i	0.510792	+	0.884718i
$627$		0			0
$628$	−9.90727e11	+	1.71599e12i	−0.254177	+	0.440247i
$629$	−2.11336e12			−0.538325
$630$		0			0
$631$	−5.28923e12			−1.32819			−0.664095	−	0.747648i	$-0.731183\pi$
$631$	−5.28923e12			−1.32819			−0.664095	+	0.747648i	$0.731183\pi$
$632$	8.60474e11	−	1.49038e12i	0.214541	−	0.371596i
$633$		0			0
$634$	2.58173e12	+	4.47169e12i	0.634614	+	1.09918i
$635$	1.78666e12	+	3.09458e12i	0.436074	+	0.755302i
$636$		0			0
$637$	1.30476e12	−	2.25990e12i	0.313980	−	0.543829i
$638$	4.78256e12			1.14279
$639$		0			0
$640$	−2.74269e11			−0.0646199
$641$	1.96187e12	−	3.39807e12i	0.458997	−	0.795006i	−0.539911	−	0.841722i	$-0.681542\pi$
$641$	1.96187e12	−	3.39807e12i	0.458997	−	0.795006i	0.998908	+	0.0467156i	$0.0148755\pi$
$642$		0			0
$643$	6.09246e11	+	1.05524e12i	0.140554	+	0.243447i	0.927705	−	0.373313i	$-0.121778\pi$
$643$	6.09246e11	+	1.05524e12i	0.140554	+	0.243447i	−0.787151	+	0.616760i	$0.788445\pi$
$644$	−2.67843e10	−	4.63918e10i	−0.00613613	−	0.0106281i
$645$		0			0
$646$	−8.25270e11	+	1.42941e12i	−0.186445	+	0.322931i
$647$	−3.90059e12			−0.875107			−0.437554	−	0.899192i	$-0.644155\pi$
$647$	−3.90059e12			−0.875107			−0.437554	+	0.899192i	$0.644155\pi$
$648$		0			0
$649$	3.63199e12			0.803607
$650$	8.43753e11	−	1.46142e12i	0.185398	−	0.321119i
$651$		0			0
$652$	−1.26235e12	−	2.18645e12i	−0.273568	−	0.473834i
$653$	1.59642e12	+	2.76508e12i	0.343587	+	0.595111i	0.985096	−	0.172005i	$-0.0550245\pi$
$653$	1.59642e12	+	2.76508e12i	0.343587	+	0.595111i	−0.641509	+	0.767116i	$0.721691\pi$
$654$		0			0
$655$	3.04899e12	−	5.28100e12i	0.647247	−	1.12106i
$656$	1.73447e12			0.365679
$657$		0			0
$658$	−1.23672e12			−0.257190
$659$	5.42899e10	−	9.40328e10i	0.0112133	−	0.0194220i	−0.860364	−	0.509680i	$-0.829764\pi$
$659$	5.42899e10	−	9.40328e10i	0.0112133	−	0.0194220i	0.871578	+	0.490258i	$0.163097\pi$
$660$		0			0
$661$	1.04451e12	+	1.80914e12i	0.212816	+	0.368608i	0.952595	−	0.304242i	$-0.0984032\pi$
$661$	1.04451e12	+	1.80914e12i	0.212816	+	0.368608i	−0.739779	+	0.672850i	$0.765070\pi$
$662$	−2.10915e12	−	3.65316e12i	−0.426822	−	0.739277i
$663$		0			0
$664$	1.42181e12	−	2.46265e12i	0.283848	−	0.491640i
$665$	2.43708e12			0.483250
$666$		0			0
$667$	−2.93788e11			−0.0574735
$668$	2.39997e12	−	4.15688e12i	0.466351	−	0.807743i
$669$		0			0
$670$	1.31771e12	+	2.28233e12i	0.252628	+	0.437565i
$671$	−1.65791e12	−	2.87159e12i	−0.315726	−	0.546853i
$672$		0			0
$673$	−2.54285e12	+	4.40434e12i	−0.477807	+	0.827585i	−0.999676	−	0.0254399i	$-0.991901\pi$
$673$	−2.54285e12	+	4.40434e12i	−0.477807	+	0.827585i	0.521870	+	0.853025i	$0.325235\pi$
$674$	9.88081e9			0.00184426
$675$		0			0
$676$	7.30160e11			0.134480
$677$	8.71741e11	−	1.50990e12i	0.159492	−	0.276248i	−0.775194	−	0.631724i	$-0.782348\pi$
$677$	8.71741e11	−	1.50990e12i	0.159492	−	0.276248i	0.934686	+	0.355476i	$0.115681\pi$
$678$		0			0
$679$	−8.27493e11	−	1.43326e12i	−0.149400	−	0.258768i
$680$	3.82437e11	+	6.62400e11i	0.0685914	+	0.118804i
$681$		0			0
$682$	−1.75796e12	+	3.04488e12i	−0.311157	+	0.538940i
$683$	9.07541e12			1.59578			0.797890	−	0.602803i	$-0.205950\pi$
$683$	9.07541e12			1.59578			0.797890	+	0.602803i	$0.205950\pi$
$684$		0			0
$685$	4.88179e12			0.847172
$686$	−2.12475e12	+	3.68018e12i	−0.366311	+	0.634469i
$687$		0			0
$688$	4.40162e11	+	7.62383e11i	0.0748971	+	0.129725i
$689$	−3.99060e12	−	6.91193e12i	−0.674609	−	1.16846i
$690$		0			0
$691$	1.75389e12	−	3.03782e12i	0.292651	−	0.506887i	−0.681784	−	0.731553i	$-0.738796\pi$
$691$	1.75389e12	−	3.03782e12i	0.292651	−	0.506887i	0.974436	+	0.224666i	$0.0721291\pi$
$692$	−3.84727e12			−0.637786
$693$		0			0
$694$	4.29647e12			0.703063
$695$	7.89332e11	−	1.36716e12i	0.128330	−	0.222274i
$696$		0			0
$697$	−2.41853e12	−	4.18902e12i	−0.388154	−	0.672303i
$698$	5.86244e11	+	1.01540e12i	0.0934822	+	0.161916i
$699$		0			0
$700$	−4.91799e11	+	8.51820e11i	−0.0774187	+	0.134093i
$701$	7.26347e12			1.13609			0.568045	−	0.822997i	$-0.307700\pi$
$701$	7.26347e12			1.13609			0.568045	+	0.822997i	$0.307700\pi$
$702$		0			0
$703$	−6.52666e12			−1.00784
$704$	−4.22616e11	+	7.31993e11i	−0.0648439	+	0.112313i
$705$		0			0
$706$	−1.40615e12	−	2.43552e12i	−0.213015	−	0.368953i
$707$	−3.06628e12	−	5.31095e12i	−0.461556	−	0.799438i
$708$		0			0
$709$	4.41297e12	−	7.64348e12i	0.655877	−	1.13601i	−0.325796	−	0.945440i	$-0.605632\pi$
$709$	4.41297e12	−	7.64348e12i	0.655877	−	1.13601i	0.981673	−	0.190572i	$-0.0610344\pi$
$710$	4.52433e12			0.668177
$711$		0			0
$712$	3.26164e12			0.475638
$713$	1.07990e11	−	1.87044e11i	0.0156488	−	0.0271045i
$714$		0			0
$715$	2.98560e12	+	5.17121e12i	0.427223	+	0.739971i
$716$	6.00423e11	+	1.03996e12i	0.0853785	+	0.147880i
$717$		0			0
$718$	−2.10522e12	+	3.64635e12i	−0.295622	+	0.512033i
$719$	9.15261e12			1.27722			0.638609	−	0.769532i	$-0.279510\pi$
$719$	9.15261e12			1.27722			0.638609	+	0.769532i	$0.279510\pi$
$720$		0			0
$721$	5.25942e12			0.724819
$722$	3.28269e10	−	5.68578e10i	0.00449586	−	0.00778705i
$723$		0			0
$724$	6.39569e11	+	1.10777e12i	0.0865096	+	0.149839i
$725$	2.69718e12	+	4.67166e12i	0.362568	+	0.627986i
$726$		0			0
$727$	−2.23846e12	+	3.87713e12i	−0.297197	+	0.514760i	−0.975494	−	0.220028i	$-0.929385\pi$
$727$	−2.23846e12	+	3.87713e12i	−0.297197	+	0.514760i	0.678297	+	0.734788i	$0.262719\pi$
$728$	−2.00794e12			−0.264947
$729$		0			0
$730$	6.90912e12			0.900472
$731$	1.22751e12	−	2.12612e12i	0.159000	−	0.275397i
$732$		0			0
$733$	−3.93655e12	−	6.81830e12i	−0.503672	−	0.872385i	−0.999991	−	0.00424498i	$-0.998649\pi$
$733$	−3.93655e12	−	6.81830e12i	−0.503672	−	0.872385i	0.496319	−	0.868140i	$-0.334685\pi$
$734$	−2.93762e12	−	5.08810e12i	−0.373562	−	0.647028i
$735$		0			0
$736$	2.59609e10	−	4.49656e10i	0.00326114	−	0.00564846i
$737$	8.12173e12			1.01402
$738$		0			0
$739$	−1.32902e13			−1.63919			−0.819597	−	0.572941i	$-0.805803\pi$
$739$	−1.32902e13			−1.63919			−0.819597	+	0.572941i	$0.805803\pi$
$740$	−1.51225e12	+	2.61930e12i	−0.185388	+	0.321102i
$741$		0			0
$742$	2.32601e12	+	4.02876e12i	0.281704	+	0.487926i
$743$	3.92044e12	+	6.79041e12i	0.471939	+	0.817422i	0.999485	−	0.0321047i	$-0.0102210\pi$
$743$	3.92044e12	+	6.79041e12i	0.471939	+	0.817422i	−0.527546	+	0.849527i	$0.676888\pi$
$744$		0			0
$745$	1.80673e12	−	3.12935e12i	0.214877	−	0.372178i
$746$	3.79746e12			0.448919
$747$		0			0
$748$	2.35717e12			0.275317
$749$	4.43739e12	−	7.68578e12i	0.515180	−	0.892319i
$750$		0			0
$751$	−2.36410e12	−	4.09473e12i	−0.271197	−	0.469727i	0.697971	−	0.716126i	$-0.254086\pi$
$751$	−2.36410e12	−	4.09473e12i	−0.271197	−	0.469727i	−0.969169	+	0.246398i	$0.920753\pi$
$752$	−5.99348e11	−	1.03810e12i	−0.0683437	−	0.118375i
$753$		0			0
$754$	−5.50609e12	+	9.53683e12i	−0.620401	+	1.07457i
$755$	−9.74869e11			−0.109190
$756$		0			0
$757$	−7.45548e12			−0.825171			−0.412586	−	0.910919i	$-0.635374\pi$
$757$	−7.45548e12			−0.825171			−0.412586	+	0.910919i	$0.635374\pi$
$758$	2.40525e12	−	4.16602e12i	0.264636	−	0.458363i
$759$		0			0
$760$	1.18108e12	+	2.04569e12i	0.128415	+	0.222422i
$761$	7.26577e10	+	1.25847e11i	0.00785328	+	0.0136023i	0.869925	−	0.493183i	$-0.164167\pi$
$761$	7.26577e10	+	1.25847e11i	0.00785328	+	0.0136023i	−0.862072	+	0.506786i	$0.830834\pi$
$762$		0			0
$763$	2.57903e12	−	4.46701e12i	0.275483	−	0.477151i
$764$	8.16826e11			0.0867380
$765$		0			0
$766$	−3.53098e12			−0.370566
$767$	−4.18146e12	+	7.24249e12i	−0.436263	+	0.755630i
$768$		0			0
$769$	−5.43002e12	−	9.40507e12i	−0.559929	−	0.969825i	−0.997502	−	0.0706422i	$-0.977495\pi$
$769$	−5.43002e12	−	9.40507e12i	−0.559929	−	0.969825i	0.437573	−	0.899183i	$-0.355838\pi$
$770$	−1.74022e12	−	3.01415e12i	−0.178400	−	0.308998i
$771$		0			0
$772$	−3.99231e12	+	6.91488e12i	−0.404526	+	0.700659i
$773$	−2.92938e12			−0.295099			−0.147550	−	0.989055i	$-0.547139\pi$
$773$	−2.92938e12			−0.295099			−0.147550	+	0.989055i	$0.547139\pi$
$774$		0			0
$775$	−3.96570e12			−0.394877
$776$	8.02052e11	−	1.38920e12i	0.0794008	−	0.137526i
$777$		0			0
$778$	−6.49462e11	−	1.12490e12i	−0.0635544	−	0.110079i
$779$	−7.46913e12	−	1.29369e13i	−0.726694	−	1.25867i
$780$		0			0
$781$	6.97147e12	−	1.20749e13i	0.670494	−	1.16133i
$782$	−1.44798e11			−0.0138463
$783$		0			0
$784$	−1.47425e12			−0.139363
$785$	3.95412e12	−	6.84874e12i	0.371652	−	0.643720i
$786$		0			0
$787$	4.04102e12	+	6.99925e12i	0.375496	+	0.650377i	0.990401	−	0.138223i	$-0.0441392\pi$
$787$	4.04102e12	+	6.99925e12i	0.375496	+	0.650377i	−0.614906	+	0.788601i	$0.710806\pi$
$788$	2.94454e12	+	5.10010e12i	0.272051	+	0.471206i
$789$		0			0
$790$	−3.43427e12	+	5.94832e12i	−0.313698	+	0.543341i
$791$	−2.44782e12			−0.222323
$792$		0			0
$793$	7.63491e12			0.685606
$794$	2.81026e12	−	4.86751e12i	0.250931	−	0.434625i
$795$		0			0
$796$	1.33718e12	+	2.31607e12i	0.118054	+	0.204476i
$797$	2.23779e12	+	3.87597e12i	0.196452	+	0.340265i	0.947376	−	0.320124i	$-0.103725\pi$
$797$	2.23779e12	+	3.87597e12i	0.196452	+	0.340265i	−0.750923	+	0.660389i	$0.770391\pi$
$798$		0			0
$799$	−1.67145e12	+	2.89503e12i	−0.145088	+	0.251300i
$800$	−9.53358e11			−0.0822907
$801$		0			0
$802$	−5.95344e12			−0.508140
$803$	1.06462e13	−	1.84397e13i	0.903594	−	1.56507i
$804$		0			0
$805$	1.06900e11	+	1.85156e11i	0.00897213	+	0.0155402i
$806$	−4.04783e12	−	7.01105e12i	−0.337843	−	0.585161i
$807$		0			0
$808$	2.97201e12	−	5.14767e12i	0.245301	−	0.424874i
$809$	−8.92004e12			−0.732147			−0.366074	−	0.930586i	$-0.619298\pi$
$809$	−8.92004e12			−0.732147			−0.366074	+	0.930586i	$0.619298\pi$
$810$		0			0
$811$	−3.57780e12			−0.290417			−0.145208	−	0.989401i	$-0.546385\pi$
$811$	−3.57780e12			−0.290417			−0.145208	+	0.989401i	$0.546385\pi$
$812$	3.20934e12	−	5.55874e12i	0.259068	−	0.448719i
$813$		0			0
$814$	4.66042e12	+	8.07208e12i	0.372062	+	0.644430i
$815$	5.03821e12	+	8.72643e12i	0.400006	+	0.692831i
$816$		0			0
$817$	3.79092e12	−	6.56607e12i	0.297677	−	0.515592i
$818$	−1.29931e13			−1.01466
$819$		0			0
$820$	−6.92252e12			−0.534690
$821$	−1.12798e13	+	1.95372e13i	−0.866480	+	1.50079i	−0.000910006		1.00000i	$0.500290\pi$
$821$	−1.12798e13	+	1.95372e13i	−0.866480	+	1.50079i	−0.865570	+	0.500788i	$0.833044\pi$
$822$		0			0
$823$	2.30210e12	+	3.98735e12i	0.174914	+	0.302960i	0.940132	−	0.340812i	$-0.110702\pi$
$823$	2.30210e12	+	3.98735e12i	0.174914	+	0.302960i	−0.765217	+	0.643772i	$0.777369\pi$
$824$	2.54887e12	+	4.41476e12i	0.192608	+	0.333607i
$825$		0			0
$826$	2.43725e12	−	4.22144e12i	0.182175	−	0.315537i
$827$	−1.99344e13			−1.48193			−0.740964	−	0.671544i	$-0.765631\pi$
$827$	−1.99344e13			−1.48193			−0.740964	+	0.671544i	$0.765631\pi$
$828$		0			0
$829$	−7.17277e12			−0.527462			−0.263731	−	0.964596i	$-0.584953\pi$
$829$	−7.17277e12			−0.527462			−0.263731	+	0.964596i	$0.584953\pi$
$830$	−5.67465e12	+	9.82878e12i	−0.415038	+	0.718866i
$831$		0			0
$832$	−9.73103e11	−	1.68546e12i	−0.0704051	−	0.121945i
$833$	2.05567e12	+	3.56053e12i	0.147928	+	0.256219i
$834$		0			0
$835$	−9.57861e12	+	1.65906e13i	−0.681889	+	1.18107i
$836$	7.27962e12			0.515443
$837$		0			0
$838$	2.07866e12			0.145608
$839$	−5.75903e12	+	9.97493e12i	−0.401255	+	0.694994i	−0.993878	−	0.110486i	$-0.964759\pi$
$839$	−5.75903e12	+	9.97493e12i	−0.401255	+	0.694994i	0.592623	+	0.805480i	$0.298093\pi$
$840$		0			0
$841$	−1.03475e13	−	1.79224e13i	−0.713268	−	1.23542i
$842$	9.74468e12	+	1.68783e13i	0.668134	+	1.15724i
$843$		0			0
$844$	−6.17117e12	+	1.06888e13i	−0.418626	+	0.725082i
$845$	−2.91416e12			−0.196634
$846$		0			0
$847$	−7.61407e11			−0.0508325
$848$	−2.25450e12	+	3.90490e12i	−0.149716	+	0.259316i
$849$		0			0
$850$	1.32935e12	+	2.30250e12i	0.0873483	+	0.151292i
$851$	−2.86285e11	−	4.95860e11i	−0.0187118	−	0.0324098i
$852$		0			0
$853$	9.19812e12	−	1.59316e13i	0.594878	−	1.03036i	−0.398686	−	0.917088i	$-0.630533\pi$
$853$	9.19812e12	−	1.59316e13i	0.594878	−	1.03036i	0.993564	−	0.113272i	$-0.0361332\pi$
$854$	−4.45016e12			−0.286296
$855$		0			0
$856$	8.60194e12			0.547601
$857$	−5.35024e12	+	9.26689e12i	−0.338813	+	0.586841i	−0.984210	−	0.177007i	$-0.943359\pi$
$857$	−5.35024e12	+	9.26689e12i	−0.338813	+	0.586841i	0.645397	+	0.763847i	$0.276692\pi$
$858$		0			0
$859$	−1.04183e13	−	1.80451e13i	−0.652873	−	1.13081i	−0.982423	−	0.186671i	$-0.940230\pi$
$859$	−1.04183e13	−	1.80451e13i	−0.652873	−	1.13081i	0.329550	−	0.944138i	$-0.393103\pi$
$860$	−1.75675e12	−	3.04277e12i	−0.109513	−	0.189682i
$861$		0			0
$862$	1.07192e12	−	1.85662e12i	0.0661271	−	0.114536i
$863$	−3.16653e13			−1.94328			−0.971641	−	0.236463i	$-0.924012\pi$
$863$	−3.16653e13			−1.94328			−0.971641	+	0.236463i	$0.924012\pi$
$864$		0			0
$865$	1.53550e13			0.932559
$866$	3.57186e11	−	6.18664e11i	0.0215806	−	0.0373787i
$867$		0			0
$868$	2.35936e12	+	4.08654e12i	0.141077	+	0.244352i
$869$	1.05836e13	+	1.83314e13i	0.629572	+	1.09045i
$870$		0			0
$871$	−9.35043e12	+	1.61954e13i	−0.550490	+	0.953477i
$872$	4.99948e12			0.292820
$873$		0			0
$874$	−4.47179e11			−0.0259227
$875$	6.17939e12	−	1.07030e13i	0.356376	−	0.617262i
$876$		0			0
$877$	−1.00962e13	−	1.74872e13i	−0.576316	−	0.998209i	−0.995897	−	0.0904913i	$-0.971156\pi$
$877$	−1.00962e13	−	1.74872e13i	−0.576316	−	0.998209i	0.419581	−	0.907718i	$-0.362177\pi$
$878$	1.83169e12	+	3.17258e12i	0.104022	+	0.180172i
$879$		0			0
$880$	1.68672e12	−	2.92148e12i	0.0948135	−	0.164222i
$881$	1.79064e13			1.00142			0.500709	−	0.865616i	$-0.333073\pi$
$881$	1.79064e13			1.00142			0.500709	+	0.865616i	$0.333073\pi$
$882$		0			0
$883$	−8.66103e12			−0.479453			−0.239727	−	0.970840i	$-0.577058\pi$
$883$	−8.66103e12			−0.479453			−0.239727	+	0.970840i	$0.577058\pi$
$884$	−2.71377e12	+	4.70039e12i	−0.149464	+	0.258880i
$885$		0			0
$886$	6.71434e12	+	1.16296e13i	0.366059	+	0.634034i
$887$	−1.26421e13	−	2.18967e13i	−0.685745	−	1.18774i	−0.973202	−	0.229951i	$-0.926143\pi$
$887$	−1.26421e13	−	2.18967e13i	−0.685745	−	1.18774i	0.287458	−	0.957793i	$-0.407190\pi$
$888$		0			0
$889$	7.38970e12	−	1.27993e13i	0.396797	−	0.687273i
$890$	−1.30176e13			−0.695469
$891$		0			0
$892$	−1.22854e13			−0.649751
$893$	−5.16192e12	+	8.94071e12i	−0.271631	+	0.470479i
$894$		0			0
$895$	−2.39637e12	−	4.15063e12i	−0.124839	−	0.216227i
$896$	5.67193e11	+	9.82408e11i	0.0293998	+	0.0509220i
$897$		0			0
$898$	9.74778e12	−	1.68837e13i	0.500221	−	0.866409i
$899$	2.58790e13			1.32138
$900$		0			0
$901$	1.25746e13			0.635670
$902$	−1.06668e13	+	1.84754e13i	−0.536543	+	0.929320i
$903$		0			0
$904$	−1.18628e12	−	2.05470e12i	−0.0590785	−	0.102327i
$905$	−2.55261e12	−	4.42124e12i	−0.126493	−	0.219092i
$906$		0			0
$907$	−9.66450e12	+	1.67394e13i	−0.474184	+	0.821311i	−0.999563	−	0.0295576i	$-0.990590\pi$
$907$	−9.66450e12	+	1.67394e13i	−0.474184	+	0.821311i	0.525379	+	0.850868i	$0.323923\pi$
$908$	1.44300e13			0.704498
$909$		0			0
$910$	8.01395e12			0.387400
$911$	−1.39808e13	+	2.42154e13i	−0.672509	+	1.16482i	0.304682	+	0.952454i	$0.401450\pi$
$911$	−1.39808e13	+	2.42154e13i	−0.672509	+	1.16482i	−0.977190	+	0.212365i	$0.931883\pi$
$912$		0			0
$913$	1.74880e13	+	3.02900e13i	0.832953	+	1.44272i
$914$	−7.92747e12	−	1.37308e13i	−0.375731	−	0.650785i
$915$		0			0
$916$	7.39053e12	−	1.28008e13i	0.346854	−	0.600768i
$917$	−2.52215e13			−1.17790
$918$		0			0
$919$	2.44191e13			1.12930			0.564650	−	0.825331i	$-0.309011\pi$
$919$	2.44191e13			1.12930			0.564650	+	0.825331i	$0.309011\pi$
$920$	−1.03613e11	+	1.79464e11i	−0.00476837	+	0.00825907i
$921$		0			0
$922$	6.64802e12	+	1.15147e13i	0.302972	+	0.524763i
$923$	1.60523e13	+	2.78034e13i	0.727997	+	1.26093i
$924$		0			0
$925$	−5.25660e12	+	9.10469e12i	−0.236084	+	0.408910i
$926$	4.81543e10			0.00215222
$927$		0			0
$928$	6.22134e12			0.275371
$929$	−2.23938e13	+	3.87872e13i	−0.986410	+	1.70851i	−0.350915	+	0.936407i	$0.614129\pi$
$929$	−2.23938e13	+	3.87872e13i	−0.986410	+	1.70851i	−0.635495	+	0.772105i	$0.719204\pi$
$930$		0			0
$931$	6.34852e12	+	1.09960e13i	0.276948	+	0.479688i
$932$	−3.25698e12	−	5.64125e12i	−0.141398	−	0.244908i
$933$		0			0
$934$	2.76895e11	−	4.79596e11i	0.0119057	−	0.0206212i
$935$	−9.40776e12			−0.402563
$936$		0			0
$937$	1.82556e13			0.773693			0.386846	−	0.922144i	$-0.373564\pi$
$937$	1.82556e13			0.773693			0.386846	+	0.922144i	$0.373564\pi$
$938$	5.45009e12	−	9.43983e12i	0.229875	−	0.398154i
$939$		0			0
$940$	2.39208e12	+	4.14320e12i	0.0999309	+	0.173085i
$941$	−1.49048e13	−	2.58159e13i	−0.619688	−	1.07333i	−0.989543	−	0.144242i	$-0.953926\pi$
$941$	−1.49048e13	−	2.58159e13i	−0.619688	−	1.07333i	0.369854	−	0.929090i	$-0.379408\pi$
$942$		0			0
$943$	6.55251e11	−	1.13493e12i	0.0269839	−	0.0467375i
$944$	4.72464e12			0.193640
$945$		0			0
$946$	−1.08278e13			−0.439571
$947$	−1.99044e13	+	3.44755e13i	−0.804219	+	1.39295i	0.112598	+	0.993641i	$0.464083\pi$
$947$	−1.99044e13	+	3.44755e13i	−0.804219	+	1.39295i	−0.916817	+	0.399308i	$0.869250\pi$
$948$		0			0
$949$	2.45135e13	+	4.24587e13i	0.981088	+	1.69929i
$950$	4.10543e12	+	7.11081e12i	0.163532	+	0.283245i
$951$		0			0
$952$	1.58178e12	−	2.73972e12i	0.0624135	−	0.108103i
$953$	−2.35374e13			−0.924358			−0.462179	−	0.886787i	$-0.652932\pi$
$953$	−2.35374e13			−0.924358			−0.462179	+	0.886787i	$0.652932\pi$
$954$		0			0
$955$	−3.26006e12			−0.126827
$956$	−4.78577e12	+	8.28920e12i	−0.185307	+	0.320961i
$957$		0			0
$958$	−1.33102e13	−	2.30540e13i	−0.510553	−	0.884304i
$959$	−1.00957e13	−	1.74862e13i	−0.385435	−	0.667592i
$960$		0			0
$961$	3.70726e12	−	6.42116e12i	0.140216	−	0.242861i
$962$	−2.14619e13			−0.807941
$963$		0			0
$964$	−1.43855e13			−0.536512
$965$	1.59338e13	−	2.75982e13i	0.591490	−	1.02449i
$966$		0			0
$967$	5.57666e12	+	9.65906e12i	0.205095	+	0.355235i	0.950163	−	0.311754i	$-0.100916\pi$
$967$	5.57666e12	+	9.65906e12i	0.205095	+	0.355235i	−0.745068	+	0.666988i	$0.767583\pi$
$968$	−3.68999e11	−	6.39126e11i	−0.0135079	−	0.0233963i
$969$		0			0
$970$	−3.20110e12	+	5.54446e12i	−0.116098	+	0.201088i
$971$	2.52461e13			0.911397			0.455699	−	0.890134i	$-0.349389\pi$
$971$	2.52461e13			0.911397			0.455699	+	0.890134i	$0.349389\pi$
$972$		0			0
$973$	−6.52942e12			−0.233543
$974$	9.50549e12	−	1.64640e13i	0.338422	−	0.586165i
$975$		0			0
$976$	−2.15668e12	−	3.73547e12i	−0.0760783	−	0.131771i
$977$	2.21080e12	+	3.82922e12i	0.0776290	+	0.134457i	0.902227	−	0.431262i	$-0.141932\pi$
$977$	2.21080e12	+	3.82922e12i	0.0776290	+	0.134457i	−0.824597	+	0.565720i	$0.808598\pi$
$978$		0			0
$979$	−2.00587e13	+	3.47427e13i	−0.697880	+	1.20876i
$980$	5.88391e12			0.203774
$981$		0			0
$982$	−1.08475e12			−0.0372243
$983$	5.01789e12	−	8.69124e12i	0.171408	−	0.296887i	−0.767505	−	0.641044i	$-0.778502\pi$
$983$	5.01789e12	−	8.69124e12i	0.171408	−	0.296887i	0.938912	+	0.344157i	$0.111835\pi$
$984$		0			0
$985$	−1.17521e13	−	2.03552e13i	−0.397788	−	0.688988i
$986$	−8.67497e12	−	1.50255e13i	−0.292295	−	0.506270i
$987$		0			0
$988$	−8.38091e12	+	1.45162e13i	−0.279824	+	0.484669i
$989$	6.65139e11			0.0221070
$990$		0			0
$991$	−2.59687e13			−0.855300			−0.427650	−	0.903944i	$-0.640658\pi$
$991$	−2.59687e13			−0.855300			−0.427650	+	0.903944i	$0.640658\pi$
$992$	−2.28683e12	+	3.96090e12i	−0.0749775	+	0.129865i
$993$		0			0
$994$	−9.35641e12	−	1.62058e13i	−0.303998	−	0.526540i
$995$	−5.33687e12	−	9.24373e12i	−0.172617	−	0.298981i
$996$		0			0
$997$	2.48168e13	−	4.29839e13i	0.795457	−	1.37777i	−0.127091	−	0.991891i	$-0.540564\pi$
$997$	2.48168e13	−	4.29839e13i	0.795457	−	1.37777i	0.922548	−	0.385881i	$-0.126103\pi$
$998$	−3.36302e13			−1.07311
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.10.c.k.55.2		4
3.2	odd	2		162.10.c.p.55.1		4
9.2	odd	6		54.10.a.e.1.2	✓	2
9.4	even	3	inner	162.10.c.k.109.2		4
9.5	odd	6		162.10.c.p.109.1		4
9.7	even	3		54.10.a.h.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.10.a.e.1.2	✓	2	9.2	odd	6
54.10.a.h.1.1	yes	2	9.7	even	3
162.10.c.k.55.2		4	1.1	even	1	trivial
162.10.c.k.109.2		4	9.4	even	3	inner
162.10.c.p.55.1		4	3.2	odd	2
162.10.c.p.109.1		4	9.5	odd	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(510.865 + 884.844i) q^{5} +(2112.96 - 3659.75i) q^{7} +4096.00 q^{8} -16347.7 q^{10} +(-25189.9 + 43630.2i) q^{11} +(-58001.5 - 100462. i) q^{13} +(33807.4 + 58556.1i) q^{14} +(-32768.0 + 56755.8i) q^{16} +182765. q^{17} +564433. q^{19} +(130781. - 226520. i) q^{20} +(-403038. - 698083. i) q^{22} +(24758.2 + 42882.5i) q^{23} +(454596. - 787384. i) q^{25} +1.85605e6 q^{26} -1.08184e6 q^{28} +(-2.96657e6 + 5.13825e6i) q^{29} +(-2.18089e6 - 3.77741e6i) q^{31} +(-524288. - 908093. i) q^{32} +(-1.46212e6 + 2.53247e6i) q^{34} +4.31775e6 q^{35} -1.15632e7 q^{37} +(-4.51546e6 + 7.82101e6i) q^{38} +(2.09250e6 + 3.62432e6i) q^{40} +(-1.32330e7 - 2.29202e7i) q^{41} +(6.71634e6 - 1.16330e7i) q^{43} +1.28972e7 q^{44} -792263. q^{46} +(-9.14532e6 + 1.58402e7i) q^{47} +(1.12476e7 + 1.94814e7i) q^{49} +(7.27354e6 + 1.25981e7i) q^{50} +(-1.48484e7 + 2.57181e7i) q^{52} +6.88018e7 q^{53} -5.14745e7 q^{55} +(8.65468e6 - 1.49904e7i) q^{56} +(-4.74651e7 - 8.22119e7i) q^{58} +(-3.60461e7 - 6.24337e7i) q^{59} +(-3.29083e7 + 5.69988e7i) q^{61} +6.97884e7 q^{62} +1.67772e7 q^{64} +(5.92618e7 - 1.02645e8i) q^{65} +(-8.06051e7 - 1.39612e8i) q^{67} +(-2.33940e7 - 4.05195e7i) q^{68} +(-3.45420e7 + 5.98285e7i) q^{70} -2.76757e8 q^{71} -4.22636e8 q^{73} +(9.25057e7 - 1.60225e8i) q^{74} +(-7.22474e7 - 1.25136e8i) q^{76} +(1.06450e8 + 1.84378e8i) q^{77} +(2.10077e8 - 3.63863e8i) q^{79} -6.69601e7 q^{80} +4.23456e8 q^{82} +(3.47123e8 - 6.01234e8i) q^{83} +(9.33684e7 + 1.61719e8i) q^{85} +(1.07461e8 + 1.86129e8i) q^{86} +(-1.03178e8 + 1.78709e8i) q^{88} +7.96299e8 q^{89} -4.90219e8 q^{91} +(6.33811e6 - 1.09779e7i) q^{92} +(-1.46325e8 - 2.53443e8i) q^{94} +(2.88349e8 + 4.99435e8i) q^{95} +(1.95814e8 - 3.39159e8i) q^{97} -3.59923e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32 q^{2} - 512 q^{4} - 1704 q^{5} - 6538 q^{7} + 16384 q^{8} + 54528 q^{10} - 14568 q^{11} - 37138 q^{13} - 104608 q^{14} - 131072 q^{16} - 175824 q^{17} + 1418300 q^{19} - 436224 q^{20} - 233088 q^{22}+ \cdots + 1696420992 q^{98}+O(q^{100}) \) 4 * q - 32 * q^2 - 512 * q^4 - 1704 * q^5 - 6538 * q^7 + 16384 * q^8 + 54528 * q^10 - 14568 * q^11 - 37138 * q^13 - 104608 * q^14 - 131072 * q^16 - 175824 * q^17 + 1418300 * q^19 - 436224 * q^20 - 233088 * q^22 - 144552 * q^23 - 4567286 * q^25 + 1188416 * q^26 + 3347456 * q^28 - 10307328 * q^29 + 2968520 * q^31 - 2097152 * q^32 + 1406592 * q^34 + 67314576 * q^35 - 58454596 * q^37 - 11346400 * q^38 - 6979584 * q^40 - 17735808 * q^41 + 30013232 * q^43 + 7458816 * q^44 + 4625664 * q^46 - 44124936 * q^47 - 53013156 * q^49 - 73076576 * q^50 - 9507328 * q^52 + 186332256 * q^53 - 298175616 * q^55 - 26779648 * q^56 - 164917248 * q^58 - 133725288 * q^59 + 3590330 * q^61 - 94992640 * q^62 + 67108864 * q^64 + 333488280 * q^65 - 132828790 * q^67 + 22505472 * q^68 - 538516608 * q^70 + 171921312 * q^71 - 880554556 * q^73 + 467636768 * q^74 - 181542400 * q^76 + 598376184 * q^77 + 376775834 * q^79 + 223346688 * q^80 + 567545856 * q^82 + 1285892400 * q^83 + 924530112 * q^85 + 480211712 * q^86 - 59670528 * q^88 - 410842512 * q^89 - 2678230604 * q^91 - 37005312 * q^92 - 705998976 * q^94 + 182237736 * q^95 + 1672271798 * q^97 + 1696420992 * q^98

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