LMFDB - Embedded newform 16.28.e.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,28,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$73.8968919741$
Analytic rank:	$0$
Dimension:	$106$
Relative dimension:	$53$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8488.66 + 7884.18i) q^{2} +(356479. - 356479. i) q^{3} +(9.89700e6 - 1.33852e8i) q^{4} +(8.81914e8 + 8.81914e8i) q^{5} +(-2.15483e8 + 5.83658e9i) q^{6} +2.95444e10i q^{7} +(9.71304e11 + 1.21426e12i) q^{8} +7.37144e12i q^{9} +O(q^{10})$	\(q+(-8488.66 + 7884.18i) q^{2} +(356479. - 356479. i) q^{3} +(9.89700e6 - 1.33852e8i) q^{4} +(8.81914e8 + 8.81914e8i) q^{5} +(-2.15483e8 + 5.83658e9i) q^{6} +2.95444e10i q^{7} +(9.71304e11 + 1.21426e12i) q^{8} +7.37144e12i q^{9} +(-1.44394e13 - 5.33097e11i) q^{10} +(1.02082e14 + 1.02082e14i) q^{11} +(-4.41875e13 - 5.12436e13i) q^{12} +(-3.78659e14 + 3.78659e14i) q^{13} +(-2.32934e14 - 2.50792e14i) q^{14} +6.28768e14 q^{15} +(-1.78185e16 - 2.64947e15i) q^{16} +6.37548e16 q^{17} +(-5.81178e16 - 6.25737e16i) q^{18} +(-1.58809e17 + 1.58809e17i) q^{19} +(1.26775e17 - 1.09318e17i) q^{20} +(1.05320e16 + 1.05320e16i) q^{21} +(-1.67138e18 - 6.17063e16i) q^{22} -2.63994e18i q^{23} +(7.79107e17 + 8.66075e16i) q^{24} -5.89503e18i q^{25} +(2.28891e17 - 6.19973e18i) q^{26} +(5.34613e18 + 5.34613e18i) q^{27} +(3.95459e18 + 2.92401e17i) q^{28} +(-6.45340e19 + 6.45340e19i) q^{29} +(-5.33740e18 + 4.95732e18i) q^{30} +1.55578e20 q^{31} +(1.72144e20 - 1.17994e20i) q^{32} +7.27804e19 q^{33} +(-5.41193e20 + 5.02654e20i) q^{34} +(-2.60556e19 + 2.60556e19i) q^{35} +(9.86685e20 + 7.29552e19i) q^{36} +(1.18476e21 + 1.18476e21i) q^{37} +(9.59962e19 - 2.60015e21i) q^{38} +2.69968e20i q^{39} +(-2.14263e20 + 1.92748e21i) q^{40} -8.06226e21i q^{41} +(-1.72438e20 - 6.36633e18i) q^{42} +(1.19080e22 + 1.19080e22i) q^{43} +(1.46743e22 - 1.26536e22i) q^{44} +(-6.50098e21 + 6.50098e21i) q^{45} +(2.08138e22 + 2.24096e22i) q^{46} -9.00507e21 q^{47} +(-7.29640e21 + 5.40744e21i) q^{48} +6.48395e22 q^{49} +(4.64775e22 + 5.00410e22i) q^{50} +(2.27272e22 - 2.27272e22i) q^{51} +(4.69368e22 + 5.44320e22i) q^{52} +(-4.08741e22 - 4.08741e22i) q^{53} +(-8.75314e22 - 3.23161e21i) q^{54} +1.80056e23i q^{55} +(-3.58745e22 + 2.86966e22i) q^{56} +1.13224e23i q^{57} +(3.90093e22 - 1.05661e24i) q^{58} +(-8.34138e23 - 8.34138e23i) q^{59} +(6.22292e21 - 8.41621e22i) q^{60} +(-7.17637e23 + 7.17637e23i) q^{61} +(-1.32065e24 + 1.22660e24i) q^{62} -2.17785e23 q^{63} +(-5.30988e23 + 2.35883e24i) q^{64} -6.67890e23 q^{65} +(-6.17808e23 + 5.73814e23i) q^{66} +(-9.66192e23 + 9.66192e23i) q^{67} +(6.30981e23 - 8.53373e24i) q^{68} +(-9.41085e23 - 9.41085e23i) q^{69} +(1.57500e22 - 4.26605e23i) q^{70} +1.86671e25i q^{71} +(-8.95083e24 + 7.15991e24i) q^{72} -1.51779e25i q^{73} +(-1.93978e25 - 7.16157e23i) q^{74} +(-2.10146e24 - 2.10146e24i) q^{75} +(1.96852e25 + 2.28287e25i) q^{76} +(-3.01596e24 + 3.01596e24i) q^{77} +(-2.12848e24 - 2.29167e24i) q^{78} -3.12701e25 q^{79} +(-1.33778e25 - 1.80510e25i) q^{80} -5.24001e25 q^{81} +(6.35644e25 + 6.84378e25i) q^{82} +(2.00979e25 - 2.00979e25i) q^{83} +(1.51396e24 - 1.30549e24i) q^{84} +(5.62263e25 + 5.62263e25i) q^{85} +(-1.94968e26 - 7.19812e24i) q^{86} +4.60101e25i q^{87} +(-2.48012e25 + 2.23107e26i) q^{88} +2.44018e26i q^{89} +(3.92969e24 - 1.06440e26i) q^{90} +(-1.11873e25 - 1.11873e25i) q^{91} +(-3.53363e26 - 2.61275e25i) q^{92} +(5.54602e25 - 5.54602e25i) q^{93} +(7.64410e25 - 7.09977e25i) q^{94} -2.80112e26 q^{95} +(1.93034e25 - 1.03428e26i) q^{96} -9.34666e26 q^{97} +(-5.50400e26 + 5.11206e26i) q^{98} +(-7.52493e26 + 7.52493e26i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) $ 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8	$ 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) $ 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−8488.66	+	7884.18i	−0.732714	+	0.680537i
$2$	−8488.66	+	7884.18i	−0.732714	+	0.680537i
$3$	356479.	−	356479.i	0.129091	−	0.129091i	−0.639609	−	0.768700i	$-0.720904\pi$
$3$	356479.	−	356479.i	0.129091	−	0.129091i	0.768700	+	0.639609i	$0.220904\pi$
$4$	9.89700e6	−	1.33852e8i	0.0737384	−	0.997278i
$5$	8.81914e8	+	8.81914e8i	0.323096	+	0.323096i	0.849954	−	0.526858i	$-0.176630\pi$
$5$	8.81914e8	+	8.81914e8i	0.323096	+	0.323096i	−0.526858	+	0.849954i	$0.676630\pi$
$6$	−2.15483e8	+	5.83658e9i	−0.00673553	+	0.182438i
$7$			2.95444e10i			0.115253i	0.998338	+	0.0576264i	$0.0183532\pi$
$7$			2.95444e10i			0.115253i	−0.998338	+	0.0576264i	$0.981647\pi$
$8$	9.71304e11	+	1.21426e12i	0.624655	+	0.780901i
$9$			7.37144e12i			0.966671i
$10$	−1.44394e13	−	5.33097e11i	−0.456615	−	0.0168580i
$11$	1.02082e14	+	1.02082e14i	0.891557	+	0.891557i	0.994670	−	0.103113i	$-0.0328803\pi$
$11$	1.02082e14	+	1.02082e14i	0.891557	+	0.891557i	−0.103113	+	0.994670i	$0.532880\pi$
$12$	−4.41875e13	−	5.12436e13i	−0.119221	−	0.138259i
$13$	−3.78659e14	+	3.78659e14i	−0.346747	+	0.346747i	−0.858897	−	0.512149i	$-0.828849\pi$
$13$	−3.78659e14	+	3.78659e14i	−0.346747	+	0.346747i	0.512149	+	0.858897i	$0.328849\pi$
$14$	−2.32934e14	−	2.50792e14i	−0.0784339	−	0.0844474i
$15$	6.28768e14			0.0834178
$16$	−1.78185e16	−	2.64947e15i	−0.989125	−	0.147075i
$17$	6.37548e16			1.56118			0.780589	−	0.625045i	$-0.214919\pi$
$17$	6.37548e16			1.56118			0.780589	+	0.625045i	$0.214919\pi$
$18$	−5.81178e16	−	6.25737e16i	−0.657855	−	0.708293i
$19$	−1.58809e17	+	1.58809e17i	−0.866366	+	0.866366i	−0.992068	−	0.125702i	$-0.959882\pi$
$19$	−1.58809e17	+	1.58809e17i	−0.866366	+	0.866366i	0.125702	+	0.992068i	$0.459882\pi$
$20$	1.26775e17	−	1.09318e17i	0.346041	−	0.298392i
$21$	1.05320e16	+	1.05320e16i	0.0148782	+	0.0148782i
$22$	−1.67138e18	−	6.17063e16i	−1.25999	−	0.0465183i
$23$		−	2.63994e18i		−	1.09212i	−0.837747	−	0.546058i	$-0.816128\pi$
$23$		−	2.63994e18i		−	1.09212i	0.837747	−	0.546058i	$-0.183872\pi$
$24$	7.79107e17	+	8.66075e16i	0.181445	+	0.0201699i
$25$		−	5.89503e18i		−	0.791218i
$26$	2.28891e17	−	6.19973e18i	0.0180920	−	0.490041i
$27$	5.34613e18	+	5.34613e18i	0.253880	+	0.253880i
$28$	3.95459e18	+	2.92401e17i	0.114939	+	0.00849856i
$29$	−6.45340e19	+	6.45340e19i	−1.16793	+	1.16793i	−0.185233	+	0.982695i	$0.559304\pi$
$29$	−6.45340e19	+	6.45340e19i	−1.16793	+	1.16793i	−0.982695	+	0.185233i	$0.940696\pi$
$30$	−5.33740e18	+	4.95732e18i	−0.0611213	+	0.0567689i
$31$	1.55578e20			1.14437			0.572183	−	0.820126i	$-0.306097\pi$
$31$	1.55578e20			1.14437			0.572183	+	0.820126i	$0.306097\pi$
$32$	1.72144e20	−	1.17994e20i	0.824836	−	0.565372i
$33$	7.27804e19			0.230184
$34$	−5.41193e20	+	5.02654e20i	−1.14390	+	1.06244i
$35$	−2.60556e19	+	2.60556e19i	−0.0372377	+	0.0372377i
$36$	9.86685e20	+	7.29552e19i	0.964039	+	0.0712808i
$37$	1.18476e21	+	1.18476e21i	0.799660	+	0.799660i	0.983042	−	0.183382i	$-0.0587044\pi$
$37$	1.18476e21	+	1.18476e21i	0.799660	+	0.799660i	−0.183382	+	0.983042i	$0.558704\pi$
$38$	9.59962e19	−	2.60015e21i	0.0452039	−	1.22439i
$39$			2.69968e20i			0.0895242i
$40$	−2.14263e20	+	1.92748e21i	−0.0504822	+	0.454129i
$41$		−	8.06226e21i		−	1.36105i	−0.732724	−	0.680526i	$-0.761751\pi$
$41$		−	8.06226e21i		−	1.36105i	0.732724	−	0.680526i	$-0.238249\pi$
$42$	−1.72438e20	−	6.36633e18i	−0.0210266	−	0.000776289i
$43$	1.19080e22	+	1.19080e22i	1.05685	+	1.05685i	0.998283	+	0.0585714i	$0.0186545\pi$
$43$	1.19080e22	+	1.19080e22i	1.05685	+	1.05685i	0.0585714	+	0.998283i	$0.481345\pi$
$44$	1.46743e22	−	1.26536e22i	0.954871	−	0.823387i
$45$	−6.50098e21	+	6.50098e21i	−0.312327	+	0.312327i
$46$	2.08138e22	+	2.24096e22i	0.743226	+	0.800208i
$47$	−9.00507e21			−0.240528			−0.120264	−	0.992742i	$-0.538374\pi$
$47$	−9.00507e21			−0.240528			−0.120264	+	0.992742i	$0.538374\pi$
$48$	−7.29640e21	+	5.40744e21i	−0.146674	+	0.108701i
$49$	6.48395e22			0.986717
$50$	4.64775e22	+	5.00410e22i	0.538453	+	0.579736i
$51$	2.27272e22	−	2.27272e22i	0.201535	−	0.201535i
$52$	4.69368e22	+	5.44320e22i	0.320235	+	0.371372i
$53$	−4.08741e22	−	4.08741e22i	−0.215638	−	0.215638i	0.591020	−	0.806657i	$-0.298726\pi$
$53$	−4.08741e22	−	4.08741e22i	−0.215638	−	0.215638i	−0.806657	+	0.591020i	$0.798726\pi$
$54$	−8.75314e22	−	3.23161e21i	−0.358796	−	0.0132466i
$55$			1.80056e23i			0.576116i
$56$	−3.58745e22	+	2.86966e22i	−0.0900010	+	0.0719933i
$57$			1.13224e23i			0.223681i
$58$	3.90093e22	−	1.05661e24i	0.0609383	−	1.65057i
$59$	−8.34138e23	−	8.34138e23i	−1.03451	−	1.03451i	−0.999383	−	0.0351293i	$-0.988816\pi$
$59$	−8.34138e23	−	8.34138e23i	−1.03451	−	1.03451i	−0.0351293	−	0.999383i	$-0.511184\pi$
$60$	6.22292e21	−	8.41621e22i	0.00615109	−	0.0831907i
$61$	−7.17637e23	+	7.17637e23i	−0.567482	+	0.567482i	−0.931422	−	0.363940i	$-0.881431\pi$
$61$	−7.17637e23	+	7.17637e23i	−0.567482	+	0.567482i	0.363940	+	0.931422i	$0.381431\pi$
$62$	−1.32065e24	+	1.22660e24i	−0.838492	+	0.778783i
$63$	−2.17785e23			−0.111412
$64$	−5.30988e23	+	2.35883e24i	−0.219611	+	0.975587i
$65$	−6.67890e23			−0.224065
$66$	−6.17808e23	+	5.73814e23i	−0.168659	+	0.156649i
$67$	−9.66192e23	+	9.66192e23i	−0.215305	+	0.215305i	−0.806516	−	0.591212i	$-0.798650\pi$
$67$	−9.66192e23	+	9.66192e23i	−0.215305	+	0.215305i	0.591212	+	0.806516i	$0.298650\pi$
$68$	6.30981e23	−	8.53373e24i	0.115119	−	1.55693i
$69$	−9.41085e23	−	9.41085e23i	−0.140983	−	0.140983i
$70$	1.57500e22	−	4.26605e23i	0.00194293	−	0.0526262i
$71$			1.86671e25i			1.90147i	0.310005	+	0.950735i	$0.399669\pi$
$71$			1.86671e25i			1.90147i	−0.310005	+	0.950735i	$0.600331\pi$
$72$	−8.95083e24	+	7.15991e24i	−0.754874	+	0.603836i
$73$		−	1.51779e25i		−	1.06256i	−0.847196	−	0.531280i	$-0.821711\pi$
$73$		−	1.51779e25i		−	1.06256i	0.847196	−	0.531280i	$-0.178289\pi$
$74$	−1.93978e25	−	7.16157e23i	−1.13012	−	0.0417234i
$75$	−2.10146e24	−	2.10146e24i	−0.102139	−	0.102139i
$76$	1.96852e25	+	2.28287e25i	0.800123	+	0.927891i
$77$	−3.01596e24	+	3.01596e24i	−0.102754	+	0.102754i
$78$	−2.12848e24	−	2.29167e24i	−0.0609245	−	0.0655956i
$79$	−3.12701e25			−0.753640			−0.376820	−	0.926287i	$-0.622982\pi$
$79$	−3.12701e25			−0.753640			−0.376820	+	0.926287i	$0.622982\pi$
$80$	−1.33778e25	−	1.80510e25i	−0.272063	−	0.367102i
$81$	−5.24001e25			−0.901123
$82$	6.35644e25	+	6.84378e25i	0.926247	+	0.997262i
$83$	2.00979e25	−	2.00979e25i	0.248655	−	0.248655i	−0.571764	−	0.820418i	$-0.693741\pi$
$83$	2.00979e25	−	2.00979e25i	0.248655	−	0.248655i	0.820418	+	0.571764i	$0.193741\pi$
$84$	1.51396e24	−	1.30549e24i	0.0159347	−	0.0137406i
$85$	5.62263e25	+	5.62263e25i	0.504410	+	0.504410i
$86$	−1.94968e26	−	7.19812e24i	−1.49360	−	0.0551429i
$87$			4.60101e25i			0.301539i
$88$	−2.48012e25	+	2.23107e26i	−0.139301	+	1.25313i
$89$			2.44018e26i			1.17668i	0.808615	+	0.588338i	$0.200218\pi$
$89$			2.44018e26i			1.17668i	−0.808615	+	0.588338i	$0.799782\pi$
$90$	3.92969e24	−	1.06440e26i	0.0162961	−	0.441397i
$91$	−1.11873e25	−	1.11873e25i	−0.0399636	−	0.0399636i
$92$	−3.53363e26	−	2.61275e25i	−1.08914	−	0.0805309i
$93$	5.54602e25	−	5.54602e25i	0.147728	−	0.147728i
$94$	7.64410e25	−	7.09977e25i	0.176238	−	0.163688i
$95$	−2.80112e26			−0.559838
$96$	1.93034e25	−	1.03428e26i	0.0334945	−	0.179464i
$97$	−9.34666e26			−1.41006			−0.705030	−	0.709177i	$-0.749067\pi$
$97$	−9.34666e26			−1.41006			−0.705030	+	0.709177i	$0.749067\pi$
$98$	−5.50400e26	+	5.11206e26i	−0.722981	+	0.671497i
$99$	−7.52493e26	+	7.52493e26i	−0.861842	+	0.861842i
$100$	−7.89064e26	−	5.83432e25i	−0.789064	−	0.0583432i
$101$	−5.02763e26	−	5.02763e26i	−0.439566	−	0.439566i	0.452300	−	0.891866i	$-0.350604\pi$
$101$	−5.02763e26	−	5.02763e26i	−0.439566	−	0.439566i	−0.891866	+	0.452300i	$0.850604\pi$
$102$	−1.37381e25	+	3.72110e26i	−0.0105154	+	0.284819i
$103$		−	7.66896e26i		−	0.514558i	−0.966337	−	0.257279i	$-0.917174\pi$
$103$		−	7.66896e26i		−	0.514558i	0.966337	−	0.257279i	$-0.0828259\pi$
$104$	−8.27583e26	−	9.19962e25i	−0.487373	−	0.0541776i
$105$			1.85766e25i			0.00961414i
$106$	6.69226e26	+	2.47075e25i	0.304750	+	0.0112512i
$107$	8.41162e26	+	8.41162e26i	0.337442	+	0.337442i	0.855404	−	0.517962i	$-0.173309\pi$
$107$	8.41162e26	+	8.41162e26i	0.337442	+	0.337442i	−0.517962	+	0.855404i	$0.673309\pi$
$108$	7.68503e26	−	6.62682e26i	0.271910	−	0.234468i
$109$	−2.58152e27	+	2.58152e27i	−0.806524	+	0.806524i	−0.984106	−	0.177582i	$-0.943172\pi$
$109$	−2.58152e27	+	2.58152e27i	−0.806524	+	0.806524i	0.177582	+	0.984106i	$0.443172\pi$
$110$	−1.41959e27	−	1.52843e27i	−0.392069	−	0.422128i
$111$	8.44681e26			0.206458
$112$	7.82771e25	−	5.26437e26i	0.0169509	−	0.114000i
$113$	6.26116e27			1.20253			0.601265	−	0.799050i	$-0.294664\pi$
$113$	6.26116e27			1.20253			0.601265	+	0.799050i	$0.294664\pi$
$114$	−8.92680e26	−	9.61121e26i	−0.152223	−	0.163894i
$115$	2.32820e27	−	2.32820e27i	0.352858	−	0.352858i
$116$	7.99934e27	+	9.27673e27i	1.07863	+	1.25087i
$117$	−2.79126e27	−	2.79126e27i	−0.335191	−	0.335191i
$118$	1.36572e28	+	5.04217e26i	1.46202	+	0.0539772i
$119$			1.88360e27i			0.179930i
$120$	6.10725e26	+	7.63486e26i	0.0521073	+	0.0651410i
$121$			7.73157e27i			0.589746i
$122$	4.33795e26	−	1.17498e28i	0.0296092	−	0.801995i
$123$	−2.87403e27	−	2.87403e27i	−0.175700	−	0.175700i
$124$	1.53975e27	−	2.08245e28i	0.0843837	−	1.14125i
$125$	1.17697e28	−	1.17697e28i	0.578735	−	0.578735i
$126$	1.84870e27	−	1.71706e27i	0.0816328	−	0.0758197i
$127$	3.42931e28			1.36099			0.680497	−	0.732751i	$-0.261764\pi$
$127$	3.42931e28			1.36099			0.680497	+	0.732751i	$0.261764\pi$
$128$	−1.40900e28	−	2.42097e28i	−0.503011	−	0.864280i
$129$	8.48992e27			0.272862
$130$	5.66949e27	−	5.26577e27i	0.164176	−	0.152485i
$131$	−2.13710e28	+	2.13710e28i	−0.558037	+	0.558037i	−0.928748	−	0.370711i	$-0.879114\pi$
$131$	−2.13710e28	+	2.13710e28i	−0.558037	+	0.558037i	0.370711	+	0.928748i	$0.379114\pi$
$132$	7.20307e26	−	9.74182e27i	0.0169734	−	0.229558i
$133$	−4.69191e27	−	4.69191e27i	−0.0998511	−	0.0998511i
$134$	5.84041e26	−	1.58193e28i	0.0112338	−	0.304280i
$135$			9.42966e27i			0.164055i
$136$	6.19253e28	+	7.74147e28i	0.975198	+	1.21912i
$137$		−	2.29643e28i		−	0.327586i	−0.986495	−	0.163793i	$-0.947627\pi$
$137$		−	2.29643e28i		−	0.327586i	0.986495	−	0.163793i	$-0.0523730\pi$
$138$	1.54082e28	+	5.68864e26i	0.199244	+	0.00735598i
$139$	2.03432e28	+	2.03432e28i	0.238626	+	0.238626i	0.816281	−	0.577655i	$-0.196032\pi$
$139$	2.03432e28	+	2.03432e28i	0.238626	+	0.238626i	−0.577655	+	0.816281i	$0.696032\pi$
$140$	3.22974e27	+	3.74548e27i	0.0343905	+	0.0398822i
$141$	−3.21012e27	+	3.21012e27i	−0.0310501	+	0.0310501i
$142$	−1.47175e29	−	1.58459e29i	−1.29402	−	1.39323i
$143$	−7.73087e28			−0.618290
$144$	1.95304e28	−	1.31348e29i	0.142173	−	0.956159i
$145$	−1.13827e29			−0.754705
$146$	1.19665e29	+	1.28840e29i	0.723111	+	0.778552i
$147$	2.31139e28	−	2.31139e28i	0.127377	−	0.127377i
$148$	1.70308e29	−	1.46857e29i	0.856449	−	0.738518i
$149$	6.75217e28	+	6.75217e28i	0.310048	+	0.310048i	0.844928	−	0.534880i	$-0.179643\pi$
$149$	6.75217e28	+	6.75217e28i	0.310048	+	0.310048i	−0.534880	+	0.844928i	$0.679643\pi$
$150$	3.44068e28	+	1.27028e27i	0.144349	+	0.00532927i
$151$			5.17489e28i			0.198478i	0.995064	+	0.0992391i	$0.0316409\pi$
$151$			5.17489e28i			0.198478i	−0.995064	+	0.0992391i	$0.968359\pi$
$152$	−3.47087e29	−	3.85830e28i	−1.21773	−	0.135365i
$153$			4.69965e29i			1.50914i
$154$	1.82308e27	−	4.93798e28i	0.00536136	−	0.145218i
$155$	1.37206e29	+	1.37206e29i	0.369740	+	0.369740i
$156$	3.61359e28	+	2.67187e27i	0.0892804	+	0.00660137i
$157$	−2.06409e29	+	2.06409e29i	−0.467825	+	0.467825i	−0.901209	−	0.433384i	$-0.857319\pi$
$157$	−2.06409e29	+	2.06409e29i	−0.467825	+	0.467825i	0.433384	+	0.901209i	$0.357319\pi$
$158$	2.65442e29	−	2.46539e29i	0.552202	−	0.512880i
$159$	−2.91416e28			−0.0556739
$160$	2.55877e29	+	4.77559e28i	0.449170	+	0.0838315i
$161$	7.79956e28			0.125870
$162$	4.44807e29	−	4.13132e29i	0.660265	−	0.613248i
$163$	−8.78961e29	+	8.78961e29i	−1.20071	+	1.20071i	−0.226754	+	0.973952i	$0.572811\pi$
$163$	−8.78961e29	+	8.78961e29i	−1.20071	+	1.20071i	−0.973952	+	0.226754i	$0.927189\pi$
$164$	−1.07915e30	−	7.97922e28i	−1.35735	−	0.100362i
$165$	6.41861e28	+	6.41861e28i	0.0743717	+	0.0743717i
$166$	−1.21487e28	+	3.29060e29i	−0.0129739	+	0.351412i
$167$			1.26472e30i			1.24544i	0.782444	+	0.622721i	$0.213973\pi$
$167$			1.26472e30i			1.24544i	−0.782444	+	0.622721i	$0.786027\pi$
$168$	−2.55877e27	+	2.30183e28i	−0.00232464	+	0.0209121i
$169$			9.05768e29i			0.759533i
$170$	−9.20584e29	−	3.39875e28i	−0.712858	−	0.0263183i
$171$	−1.17065e30	−	1.17065e30i	−0.837490	−	0.837490i
$172$	1.71177e30	−	1.47606e30i	1.13191	−	0.976047i
$173$	−1.47219e30	+	1.47219e30i	−0.900203	+	0.900203i	−0.995453	−	0.0952506i	$-0.969635\pi$
$173$	−1.47219e30	+	1.47219e30i	−0.900203	+	0.900203i	0.0952506	+	0.995453i	$0.469635\pi$
$174$	−3.62752e29	−	3.90564e29i	−0.205208	−	0.220941i
$175$	1.74165e29			0.0911902
$176$	−1.54849e30	−	2.08942e30i	−0.750735	−	1.01299i
$177$	−5.94705e29			−0.267093
$178$	−1.92388e30	−	2.07139e30i	−0.800772	−	0.862167i
$179$	−8.65337e29	+	8.65337e29i	−0.333941	+	0.333941i	−0.854081	−	0.520140i	$-0.825880\pi$
$179$	−8.65337e29	+	8.65337e29i	−0.333941	+	0.333941i	0.520140	+	0.854081i	$0.325880\pi$
$180$	8.05831e29	+	9.34512e29i	0.288447	+	0.334508i
$181$	−1.00972e30	−	1.00972e30i	−0.335383	−	0.335383i	0.519243	−	0.854627i	$-0.326214\pi$
$181$	−1.00972e30	−	1.00972e30i	−0.335383	−	0.335383i	−0.854627	+	0.519243i	$0.826214\pi$
$182$	1.83167e29	+	6.76244e27i	0.0564786	+	0.00208516i
$183$			5.11645e29i			0.146514i
$184$	3.20557e30	−	2.56419e30i	0.852834	−	0.682196i
$185$			2.08971e30i			0.516734i
$186$	−3.35244e28	+	9.08042e29i	−0.00770791	+	0.208776i
$187$	6.50823e30	+	6.50823e30i	1.39188	+	1.39188i
$188$	−8.91232e28	+	1.20535e30i	−0.0177362	+	0.239873i
$189$	−1.57948e29	+	1.57948e29i	−0.0292604	+	0.0292604i
$190$	2.37777e30	−	2.20845e30i	0.410201	−	0.380991i
$191$	−8.16692e30			−1.31253			−0.656263	−	0.754532i	$-0.727864\pi$
$191$	−8.16692e30			−1.31253			−0.656263	+	0.754532i	$0.727864\pi$
$192$	6.51586e29	+	1.03016e30i	0.0975900	+	0.154290i
$193$	6.41162e30			0.895249			0.447625	−	0.894222i	$-0.352270\pi$
$193$	6.41162e30			0.895249			0.447625	+	0.894222i	$0.352270\pi$
$194$	7.93406e30	−	7.36908e30i	1.03317	−	0.959599i
$195$	−2.38089e29	+	2.38089e29i	−0.0289249	+	0.0289249i
$196$	6.41716e29	−	8.67892e30i	0.0727589	−	0.984031i
$197$	8.31037e30	+	8.31037e30i	0.879683	+	0.879683i	0.993502	−	0.113819i	$-0.0363083\pi$
$197$	8.31037e30	+	8.31037e30i	0.879683	+	0.879683i	−0.113819	+	0.993502i	$0.536308\pi$
$198$	4.54865e29	−	1.23205e31i	0.0449678	−	1.21800i
$199$			4.48466e30i			0.414202i	0.978320	+	0.207101i	$0.0664029\pi$
$199$			4.48466e30i			0.414202i	−0.978320	+	0.207101i	$0.933597\pi$
$200$	7.15809e30	−	5.72587e30i	0.617863	−	0.494239i
$201$			6.88855e29i			0.0555880i
$202$	8.23166e30	+	3.03908e29i	0.621218	+	0.0229350i
$203$	−1.90662e30	−	1.90662e30i	−0.134607	−	0.134607i
$204$	−2.81716e30	−	3.26703e30i	−0.186125	−	0.215847i
$205$	7.11023e30	−	7.11023e30i	0.439750	−	0.439750i
$206$	6.04635e30	+	6.50992e30i	0.350176	+	0.377023i
$207$	1.94602e31			1.05572
$208$	7.75038e30	−	5.74389e30i	0.393975	−	0.291979i
$209$	−3.24231e31			−1.54483
$210$	−1.46461e29	−	1.57690e29i	−0.00654278	−	0.00704441i
$211$	8.30765e30	−	8.30765e30i	0.348069	−	0.348069i	−0.511321	−	0.859390i	$-0.670844\pi$
$211$	8.30765e30	−	8.30765e30i	0.348069	−	0.348069i	0.859390	+	0.511321i	$0.170844\pi$
$212$	−5.87563e30	+	5.06657e30i	−0.230951	+	0.199150i
$213$	6.65443e30	+	6.65443e30i	0.245463	+	0.245463i
$214$	−1.37722e31	−	5.08463e29i	−0.476889	−	0.0176065i
$215$			2.10037e31i			0.682931i
$216$	−1.29886e30	+	1.16843e31i	−0.0396676	+	0.356843i
$217$			4.59645e30i			0.131891i
$218$	1.56047e30	−	4.22668e31i	0.0420815	−	1.13982i
$219$	−5.41061e30	−	5.41061e30i	−0.137167	−	0.137167i
$220$	2.41009e31	+	1.78201e30i	0.574548	+	0.0424819i
$221$	−2.41413e31	+	2.41413e31i	−0.541334	+	0.541334i
$222$	−7.17021e30	+	6.65962e30i	−0.151275	+	0.140503i
$223$	−7.43401e31			−1.47607			−0.738036	−	0.674761i	$-0.764247\pi$
$223$	−7.43401e31			−1.47607			−0.738036	+	0.674761i	$0.764247\pi$
$224$	3.48606e30	+	5.08590e30i	0.0651608	+	0.0950647i
$225$	4.34549e31			0.764848
$226$	−5.31489e31	+	4.93642e31i	−0.881110	+	0.818366i
$227$	1.13275e31	−	1.13275e31i	0.176924	−	0.176924i	−0.613090	−	0.790013i	$-0.710074\pi$
$227$	1.13275e31	−	1.13275e31i	0.176924	−	0.176924i	0.790013	+	0.613090i	$0.210074\pi$
$228$	1.51553e31	+	1.12058e30i	0.223072	+	0.0164938i
$229$	−5.57061e31	−	5.57061e31i	−0.772900	−	0.772900i	0.205712	−	0.978613i	$-0.434049\pi$
$229$	−5.57061e31	−	5.57061e31i	−0.772900	−	0.772900i	−0.978613	+	0.205712i	$0.934049\pi$
$230$	−1.40734e30	+	3.81193e31i	−0.0184109	+	0.498677i
$231$			2.15025e30i			0.0265294i
$232$	−1.41043e32	−	1.56787e31i	−1.64159	−	0.182483i
$233$		−	3.32426e31i		−	0.365082i	−0.983198	−	0.182541i	$-0.941568\pi$
$233$		−	3.32426e31i		−	0.365082i	0.983198	−	0.182541i	$-0.0584322\pi$
$234$	4.57009e31	+	1.68725e30i	0.473708	+	0.0174891i
$235$	−7.94170e30	−	7.94170e30i	−0.0777137	−	0.0777137i
$236$	−1.19907e32	+	1.03396e32i	−1.10798	+	0.955412i
$237$	−1.11471e31	+	1.11471e31i	−0.0972884	+	0.0972884i
$238$	−1.48506e31	−	1.59892e31i	−0.122449	−	0.131837i
$239$	5.66875e31			0.441688			0.220844	−	0.975309i	$-0.429119\pi$
$239$	5.66875e31			0.441688			0.220844	+	0.975309i	$0.429119\pi$
$240$	−1.12037e31	−	1.66590e30i	−0.0825106	−	0.0122687i
$241$	6.85747e31			0.477457			0.238728	−	0.971086i	$-0.423269\pi$
$241$	6.85747e31			0.477457			0.238728	+	0.971086i	$0.423269\pi$
$242$	−6.09571e31	−	6.56307e31i	−0.401344	−	0.432115i
$243$	−5.94470e31	+	5.94470e31i	−0.370207	+	0.370207i
$244$	8.89550e31	+	1.03160e32i	0.524092	+	0.607782i
$245$	5.71829e31	+	5.71829e31i	0.318804	+	0.318804i
$246$	4.70560e31	+	1.73728e30i	0.248308	+	0.00916741i
$247$		−	1.20269e32i		−	0.600820i
$248$	1.51113e32	+	1.88911e32i	0.714834	+	0.893636i
$249$		−	1.43290e31i		−	0.0641984i
$250$	−7.11450e30	+	1.92703e32i	−0.0301963	+	0.817898i
$251$	−4.41033e31	−	4.41033e31i	−0.177368	−	0.177368i	0.612839	−	0.790208i	$-0.290027\pi$
$251$	−4.41033e31	−	4.41033e31i	−0.177368	−	0.177368i	−0.790208	+	0.612839i	$0.790027\pi$
$252$	−2.15542e30	+	2.91510e31i	−0.00821531	+	0.111108i
$253$	2.69491e32	−	2.69491e32i	0.973684	−	0.973684i
$254$	−2.91102e32	+	2.70373e32i	−0.997219	+	0.926207i
$255$	4.00870e31			0.130230
$256$	3.10479e32	+	9.44193e31i	0.956738	+	0.290952i
$257$	1.38563e32			0.405089			0.202544	−	0.979273i	$-0.435079\pi$
$257$	1.38563e32			0.405089			0.202544	+	0.979273i	$0.435079\pi$
$258$	−7.20680e31	+	6.69361e31i	−0.199929	+	0.185692i
$259$	−3.50029e31	+	3.50029e31i	−0.0921632	+	0.0921632i
$260$	−6.61011e30	+	8.93986e31i	−0.0165222	+	0.223455i
$261$	−4.75709e32	−	4.75709e32i	−1.12900	−	1.12900i
$262$	1.29183e31	−	3.49905e32i	0.0291164	−	0.788647i
$263$		−	5.00087e32i		−	1.07064i	−0.844650	−	0.535319i	$-0.820191\pi$
$263$		−	5.00087e32i		−	1.07064i	0.844650	−	0.535319i	$-0.179809\pi$
$264$	7.06919e31	+	8.83741e31i	0.143786	+	0.179751i
$265$		−	7.20950e31i		−	0.139343i
$266$	7.68200e31	+	2.83615e30i	0.141115	+	0.00520988i
$267$	8.69874e31	+	8.69874e31i	0.151899	+	0.151899i
$268$	1.19765e32	+	1.38890e32i	0.198842	+	0.230595i
$269$	6.50777e32	−	6.50777e32i	1.02749	−	1.02749i	0.0278759	−	0.999611i	$-0.491126\pi$
$269$	6.50777e32	−	6.50777e32i	1.02749	−	1.02749i	0.999611	−	0.0278759i	$-0.00887432\pi$
$270$	−7.43452e31	−	8.00452e31i	−0.111646	−	0.120206i
$271$	−4.99458e32			−0.713532			−0.356766	−	0.934194i	$-0.616121\pi$
$271$	−4.99458e32			−0.713532			−0.356766	+	0.934194i	$0.616121\pi$
$272$	−1.13601e33	−	1.68917e32i	−1.54420	−	0.229611i
$273$	−7.97605e30			−0.0103179
$274$	1.81055e32	+	1.94936e32i	0.222935	+	0.240027i
$275$	6.01778e32	−	6.01778e32i	0.705416	−	0.705416i
$276$	−1.35280e32	+	1.16652e32i	−0.150995	+	0.130203i
$277$	8.22005e32	+	8.22005e32i	0.873770	+	0.873770i	0.992881	−	0.119111i	$-0.0380043\pi$
$277$	8.22005e32	+	8.22005e32i	0.873770	+	0.873770i	−0.119111	+	0.992881i	$0.538004\pi$
$278$	−3.33075e32	−	1.22970e31i	−0.337239	−	0.0124507i
$279$			1.14683e33i			1.10622i
$280$	−5.69462e31	−	6.33029e30i	−0.0523397	−	0.00581822i
$281$		−	1.13237e33i		−	0.991863i	−0.868362	−	0.495932i	$-0.834827\pi$
$281$		−	1.13237e33i		−	0.991863i	0.868362	−	0.495932i	$-0.165173\pi$
$282$	1.94044e30	−	5.25588e31i	0.00162008	−	0.0438816i
$283$	−1.13104e33	−	1.13104e33i	−0.900243	−	0.900243i	0.0952134	−	0.995457i	$-0.469647\pi$
$283$	−1.13104e33	−	1.13104e33i	−0.900243	−	0.900243i	−0.995457	+	0.0952134i	$0.969647\pi$
$284$	2.49864e33	+	1.84748e32i	1.89629	+	0.140211i
$285$	−9.98540e31	+	9.98540e31i	−0.0722703	+	0.0722703i
$286$	6.56248e32	−	6.09516e32i	0.453029	−	0.420769i
$287$	2.38195e32			0.156865
$288$	8.69785e32	+	1.26895e33i	0.546529	+	0.797345i
$289$	2.39696e33			1.43728
$290$	9.66239e32	−	8.97433e32i	0.552983	−	0.513605i
$291$	−3.33189e32	+	3.33189e32i	−0.182027	+	0.182027i
$292$	−2.03160e33	−	1.50216e32i	−1.05967	−	0.0783514i
$293$	−2.54118e31	−	2.54118e31i	−0.0126568	−	0.0126568i	0.700750	−	0.713407i	$-0.252849\pi$
$293$	−2.54118e31	−	2.54118e31i	−0.0126568	−	0.0126568i	−0.713407	+	0.700750i	$0.752849\pi$
$294$	−1.39718e31	+	3.78441e32i	−0.00664606	+	0.180015i
$295$		−	1.47128e33i		−	0.668493i
$296$	−2.87840e32	+	2.58936e33i	−0.124943	+	1.12397i
$297$			1.09149e33i			0.452697i
$298$	−1.10552e33	−	4.08153e31i	−0.438175	−	0.0161772i
$299$	9.99639e32	+	9.99639e32i	0.378688	+	0.378688i
$300$	−3.02083e32	+	2.60487e32i	−0.109393	+	0.0943298i
$301$	−3.51815e32	+	3.51815e32i	−0.121806	+	0.121806i
$302$	−4.07998e32	−	4.39279e32i	−0.135072	−	0.145428i
$303$	−3.58449e32			−0.113488
$304$	3.25050e33	−	2.40898e33i	0.984365	−	0.729523i
$305$	−1.26579e33			−0.366702
$306$	−3.70529e33	−	3.98937e33i	−1.02703	−	1.10577i
$307$	−3.53403e33	+	3.53403e33i	−0.937350	+	0.937350i	−0.998150	−	0.0608004i	$-0.980635\pi$
$307$	−3.53403e33	+	3.53403e33i	−0.937350	+	0.937350i	0.0608004	+	0.998150i	$0.480635\pi$
$308$	3.73844e32	+	4.33542e32i	0.0948978	+	0.110052i
$309$	−2.73382e32	−	2.73382e32i	−0.0664249	−	0.0664249i
$310$	−2.24646e33	−	8.29380e31i	−0.522535	−	0.0192917i
$311$			7.03219e33i			1.56612i	0.621946	+	0.783060i	$0.286342\pi$
$311$			7.03219e33i			1.56612i	−0.621946	+	0.783060i	$0.713658\pi$
$312$	−3.27811e32	+	2.62221e32i	−0.0699095	+	0.0559217i
$313$		−	1.24601e33i		−	0.254491i	−0.991871	−	0.127246i	$-0.959386\pi$
$313$		−	1.24601e33i		−	0.254491i	0.991871	−	0.127246i	$-0.0406136\pi$
$314$	1.24769e32	−	3.37950e33i	0.0244094	−	0.661154i
$315$	−1.92068e32	−	1.92068e32i	−0.0359966	−	0.0359966i
$316$	−3.09480e32	+	4.18558e33i	−0.0555722	+	0.751588i
$317$	3.22373e33	−	3.22373e33i	0.554701	−	0.554701i	−0.373093	−	0.927794i	$-0.621703\pi$
$317$	3.22373e33	−	3.22373e33i	0.554701	−	0.554701i	0.927794	+	0.373093i	$0.121703\pi$
$318$	2.47373e32	−	2.29757e32i	0.0407930	−	0.0378882i
$319$	−1.31756e34			−2.08255
$320$	−2.54857e33	+	1.61200e33i	−0.386164	+	0.244253i
$321$	5.99713e32			0.0871216
$322$	−6.62078e32	+	6.14932e32i	−0.0922263	+	0.0856589i
$323$	−1.01248e34	+	1.01248e34i	−1.35255	+	1.35255i
$324$	−5.18604e32	+	7.01387e33i	−0.0664474	+	0.898670i
$325$	2.23221e33	+	2.23221e33i	0.274353	+	0.274353i
$326$	5.31311e32	−	1.43911e34i	0.0626486	−	1.69690i
$327$			1.84051e33i			0.208230i
$328$	9.78966e33	−	7.83091e33i	1.06285	−	0.850189i
$329$		−	2.66050e32i		−	0.0277216i
$330$	−1.05091e33	−	3.87990e31i	−0.105106	−	0.00388045i
$331$	6.47437e33	+	6.47437e33i	0.621612	+	0.621612i	0.945944	−	0.324331i	$-0.105139\pi$
$331$	6.47437e33	+	6.47437e33i	0.621612	+	0.621612i	−0.324331	+	0.945944i	$0.605139\pi$
$332$	−2.49125e33	−	2.88906e33i	−0.229643	−	0.266313i
$333$	−8.73336e33	+	8.73336e33i	−0.773008	+	0.773008i
$334$	−9.97132e33	−	1.07358e34i	−0.847570	−	0.912553i
$335$	−1.70420e33			−0.139128
$336$	−1.59760e32	−	2.15568e32i	−0.0125281	−	0.0169046i
$337$	6.81440e33			0.513363			0.256681	−	0.966496i	$-0.417371\pi$
$337$	6.81440e33			0.513363			0.256681	+	0.966496i	$0.417371\pi$
$338$	−7.14124e33	−	7.68876e33i	−0.516890	−	0.556520i
$339$	2.23197e33	−	2.23197e33i	0.155236	−	0.155236i
$340$	8.08249e33	−	6.96954e33i	0.540231	−	0.465842i
$341$	1.58817e34	+	1.58817e34i	1.02027	+	1.02027i
$342$	1.91669e34	+	7.07631e32i	1.18358	+	0.0436973i
$343$			3.85708e33i			0.228975i
$344$	−2.89308e33	+	2.60257e34i	−0.165129	+	1.48547i
$345$		−	1.65991e33i		−	0.0911019i
$346$	8.89902e32	−	2.41039e34i	0.0469694	−	1.27221i
$347$	−1.95353e34	−	1.95353e34i	−0.991681	−	0.991681i	0.00828419	−	0.999966i	$-0.497363\pi$
$347$	−1.95353e34	−	1.95353e34i	−0.991681	−	0.991681i	−0.999966	+	0.00828419i	$0.997363\pi$
$348$	6.15856e33	+	4.55362e32i	0.300718	+	0.0222350i
$349$	2.97750e34	−	2.97750e34i	1.39865	−	1.39865i	0.594698	−	0.803949i	$-0.297272\pi$
$349$	2.97750e34	−	2.97750e34i	1.39865	−	1.39865i	0.803949	−	0.594698i	$-0.202728\pi$
$350$	−1.47843e33	+	1.37315e33i	−0.0668163	+	0.0620583i
$351$	−4.04872e33			−0.176065
$352$	2.96179e34	+	5.52778e33i	1.23945	+	0.231326i
$353$	1.90185e34			0.765979			0.382990	−	0.923753i	$-0.374895\pi$
$353$	1.90185e34			0.765979			0.382990	+	0.923753i	$0.374895\pi$
$354$	5.04825e33	−	4.68877e33i	0.195703	−	0.181767i
$355$	−1.64628e34	+	1.64628e34i	−0.614357	+	0.614357i
$356$	3.26624e34	+	2.41505e33i	1.17347	+	0.0867662i
$357$	6.71463e32	+	6.71463e32i	0.0232274	+	0.0232274i
$358$	5.23076e32	−	1.41680e34i	0.0174238	−	0.471942i
$359$			3.40343e34i			1.09180i	0.837852	+	0.545898i	$0.183811\pi$
$359$			3.40343e34i			1.09180i	−0.837852	+	0.545898i	$0.816189\pi$
$360$	−1.42083e34	−	1.57943e33i	−0.438994	−	0.0487997i
$361$		−	1.68399e34i		−	0.501178i
$362$	1.65320e34	+	6.10354e32i	0.473981	+	0.0174991i
$363$	2.75614e33	+	2.75614e33i	0.0761312	+	0.0761312i
$364$	−1.60816e33	+	1.38672e33i	−0.0428017	+	0.0369080i
$365$	1.33856e34	−	1.33856e34i	0.343309	−	0.343309i
$366$	−4.03391e33	−	4.34318e33i	−0.0997083	−	0.107353i
$367$	−2.44287e33			−0.0581981			−0.0290990	−	0.999577i	$-0.509264\pi$
$367$	−2.44287e33			−0.0581981			−0.0290990	+	0.999577i	$0.509264\pi$
$368$	−6.99446e33	+	4.70398e34i	−0.160623	+	1.08024i
$369$	5.94305e34			1.31569
$370$	−1.64756e34	−	1.77388e34i	−0.351657	−	0.378618i
$371$	1.20760e33	−	1.20760e33i	0.0248529	−	0.0248529i
$372$	−6.87459e33	−	7.97237e33i	−0.136432	−	0.158219i
$373$	−1.93289e34	−	1.93289e34i	−0.369946	−	0.369946i	0.497512	−	0.867457i	$-0.334247\pi$
$373$	−1.93289e34	−	1.93289e34i	−0.369946	−	0.369946i	−0.867457	+	0.497512i	$0.834247\pi$
$374$	−1.06558e35	−	3.93407e33i	−1.96707	−	0.0726233i
$375$		−	8.39130e33i		−	0.149419i
$376$	−8.74667e33	−	1.09345e34i	−0.150247	−	0.187829i
$377$		−	4.88728e34i		−	0.809952i
$378$	9.54760e31	−	2.58606e33i	0.00152670	−	0.0413523i
$379$	−1.19170e34	−	1.19170e34i	−0.183881	−	0.183881i	0.609163	−	0.793045i	$-0.291505\pi$
$379$	−1.19170e34	−	1.19170e34i	−0.183881	−	0.183881i	−0.793045	+	0.609163i	$0.791505\pi$
$380$	−2.77227e33	+	3.74936e34i	−0.0412816	+	0.558314i
$381$	1.22248e34	−	1.22248e34i	0.175693	−	0.175693i
$382$	6.93262e34	−	6.43895e34i	0.961706	−	0.893223i
$383$	−1.05829e35			−1.41717			−0.708587	−	0.705624i	$-0.750667\pi$
$383$	−1.05829e35			−1.41717			−0.708587	+	0.705624i	$0.750667\pi$
$384$	−1.36530e34	−	3.60744e33i	−0.176505	−	0.0466367i
$385$	−5.31964e33			−0.0663991
$386$	−5.44260e34	+	5.05504e34i	−0.655961	+	0.609250i
$387$	−8.77793e34	+	8.77793e34i	−1.02163	+	1.02163i
$388$	−9.25039e33	+	1.25107e35i	−0.103976	+	1.40622i
$389$	2.89363e34	+	2.89363e34i	0.314140	+	0.314140i	0.846511	−	0.532371i	$-0.178699\pi$
$389$	2.89363e34	+	2.89363e34i	0.314140	+	0.314140i	−0.532371	+	0.846511i	$0.678699\pi$
$390$	1.43919e32	−	3.89819e33i	0.00150920	−	0.0408781i
$391$		−	1.68309e35i		−	1.70499i
$392$	6.29789e34	+	7.87318e34i	0.616358	+	0.770528i
$393$			1.52367e34i			0.144076i
$394$	−1.36064e35	−	5.02342e33i	−1.24321	−	0.0458987i
$395$	−2.75776e34	−	2.75776e34i	−0.243498	−	0.243498i
$396$	9.32756e34	+	1.08170e35i	0.795945	+	0.923046i
$397$	1.22893e35	−	1.22893e35i	1.01357	−	1.01357i	0.0136677	−	0.999907i	$-0.495649\pi$
$397$	1.22893e35	−	1.22893e35i	1.01357	−	1.01357i	0.999907	−	0.0136677i	$-0.00435068\pi$
$398$	−3.53579e34	−	3.80687e34i	−0.281880	−	0.303492i
$399$	−3.34514e33			−0.0257798
$400$	−1.56187e34	+	1.05041e35i	−0.116369	+	0.782614i
$401$	8.71880e34			0.628070			0.314035	−	0.949411i	$-0.398319\pi$
$401$	8.71880e34			0.628070			0.314035	+	0.949411i	$0.398319\pi$
$402$	−5.43106e33	−	5.84746e33i	−0.0378297	−	0.0407301i
$403$	−5.89109e34	+	5.89109e34i	−0.396806	+	0.396806i
$404$	−7.22718e34	+	6.23201e34i	−0.470783	+	0.405957i
$405$	−4.62124e34	−	4.62124e34i	−0.291149	−	0.291149i
$406$	3.12168e34	+	1.15251e33i	0.190233	+	0.00702332i
$407$			2.41885e35i			1.42588i
$408$	4.96718e34	+	5.52164e33i	0.283268	+	0.0314888i
$409$		−	6.30364e34i		−	0.347797i	−0.984764	−	0.173899i	$-0.944363\pi$
$409$		−	6.30364e34i		−	0.347797i	0.984764	−	0.173899i	$-0.0556365\pi$
$410$	−4.29797e33	+	1.16415e35i	−0.0229446	+	0.621478i
$411$	−8.18630e33	−	8.18630e33i	−0.0422886	−	0.0422886i
$412$	−1.02651e35	−	7.58997e33i	−0.513157	−	0.0379427i
$413$	2.46441e34	−	2.46441e34i	0.119230	−	0.119230i
$414$	−1.65191e35	+	1.53428e35i	−0.773538	+	0.718455i
$415$	3.54493e34			0.160679
$416$	−2.05045e34	+	1.09863e35i	−0.0899682	+	0.482051i
$417$	1.45038e34			0.0616092
$418$	2.75229e35	−	2.55630e35i	1.13192	−	1.05131i
$419$	1.91869e35	−	1.91869e35i	0.764040	−	0.764040i	−0.213010	−	0.977050i	$-0.568327\pi$
$419$	1.91869e35	−	1.91869e35i	0.764040	−	0.764040i	0.977050	+	0.213010i	$0.0683268\pi$
$420$	2.48652e33	+	1.83852e32i	0.00958796	+	0.000708931i
$421$	−1.19957e35	−	1.19957e35i	−0.447936	−	0.447936i	0.446732	−	0.894668i	$-0.352588\pi$
$421$	−1.19957e35	−	1.19957e35i	−0.447936	−	0.447936i	−0.894668	+	0.446732i	$0.852588\pi$
$422$	−5.02178e33	+	1.36020e35i	−0.0181610	+	0.491908i
$423$		−	6.63804e34i		−	0.232512i
$424$	9.93048e33	−	8.93329e34i	0.0336923	−	0.303091i
$425$		−	3.75837e35i		−	1.23523i
$426$	−1.08952e35	−	4.02245e33i	−0.346901	−	0.0128074i
$427$	−2.12022e34	−	2.12022e34i	−0.0654040	−	0.0654040i
$428$	1.20916e35	−	1.04266e35i	0.361405	−	0.311640i
$429$	−2.75589e34	+	2.75589e34i	−0.0798159	+	0.0798159i
$430$	−1.65597e35	−	1.78293e35i	−0.464760	−	0.500393i
$431$	−3.01119e35			−0.819020			−0.409510	−	0.912306i	$-0.634300\pi$
$431$	−3.01119e35			−0.819020			−0.409510	+	0.912306i	$0.634300\pi$
$432$	−8.10956e34	−	1.09424e35i	−0.213780	−	0.288459i
$433$	3.25073e35			0.830603			0.415302	−	0.909684i	$-0.363676\pi$
$433$	3.25073e35			0.830603			0.415302	+	0.909684i	$0.363676\pi$
$434$	−3.62393e34	−	3.90177e34i	−0.0897570	−	0.0966386i
$435$	−4.05769e34	+	4.05769e34i	−0.0974259	+	0.0974259i
$436$	3.19993e35	+	3.71091e35i	0.744856	+	0.863800i
$437$	4.19247e35	+	4.19247e35i	0.946172	+	0.946172i
$438$	8.85870e34	+	3.27059e33i	0.193852	+	0.00715690i
$439$			7.87181e34i			0.167033i	0.996506	+	0.0835167i	$0.0266152\pi$
$439$			7.87181e34i			0.167033i	−0.996506	+	0.0835167i	$0.973385\pi$
$440$	−2.18634e35	+	1.74889e35i	−0.449890	+	0.359874i
$441$			4.77961e35i			0.953830i
$442$	1.45929e34	−	3.95262e35i	0.0282449	−	0.765041i
$443$	1.32821e34	+	1.32821e34i	0.0249353	+	0.0249353i	0.719465	−	0.694529i	$-0.244387\pi$
$443$	1.32821e34	+	1.32821e34i	0.0249353	+	0.0249353i	−0.694529	+	0.719465i	$0.744387\pi$
$444$	8.35981e33	−	1.13063e35i	0.0152239	−	0.205896i
$445$	−2.15203e35	+	2.15203e35i	−0.380179	+	0.380179i
$446$	6.31048e35	−	5.86111e35i	1.08154	−	1.00452i
$447$	4.81401e34			0.0800490
$448$	−6.96901e34	−	1.56877e34i	−0.112439	−	0.0253109i
$449$	−5.83016e35			−0.912756			−0.456378	−	0.889786i	$-0.650853\pi$
$449$	−5.83016e35			−0.912756			−0.456378	+	0.889786i	$0.650853\pi$
$450$	−3.68874e35	+	3.42607e35i	−0.560414	+	0.520507i
$451$	8.23014e35	−	8.23014e35i	1.21346	−	1.21346i
$452$	6.19667e34	−	8.38071e35i	0.0886726	−	1.19926i
$453$	1.84474e34	+	1.84474e34i	0.0256218	+	0.0256218i
$454$	−6.84723e33	+	1.85464e35i	−0.00923126	+	0.250038i
$455$		−	1.97324e34i		−	0.0258242i
$456$	−1.37483e35	+	1.09975e35i	−0.174672	+	0.139723i
$457$		−	8.01742e35i		−	0.988931i	−0.869197	−	0.494466i	$-0.835364\pi$
$457$		−	8.01742e35i		−	0.988931i	0.869197	−	0.494466i	$-0.164636\pi$
$458$	9.12067e35	+	3.36730e34i	1.09230	+	0.0403272i
$459$	3.40841e35	+	3.40841e35i	0.396352	+	0.396352i
$460$	−2.88593e35	−	3.34678e35i	−0.325878	−	0.377917i
$461$	−8.34772e34	+	8.34772e34i	−0.0915388	+	0.0915388i	−0.751393	−	0.659855i	$-0.770618\pi$
$461$	−8.34772e34	+	8.34772e34i	−0.0915388	+	0.0915388i	0.659855	+	0.751393i	$0.270618\pi$
$462$	−1.69530e34	−	1.82528e34i	−0.0180543	−	0.0194385i
$463$	−4.31806e35			−0.446627			−0.223314	−	0.974747i	$-0.571687\pi$
$463$	−4.31806e35			−0.446627			−0.223314	+	0.974747i	$0.571687\pi$
$464$	1.32088e36	−	9.78918e35i	1.32700	−	0.983453i
$465$	9.78224e34			0.0954604
$466$	2.62091e35	+	2.82185e35i	0.248452	+	0.267500i
$467$	−1.47714e36	+	1.47714e36i	−1.36033	+	1.36033i	−0.486841	+	0.873491i	$0.661851\pi$
$467$	−1.47714e36	+	1.47714e36i	−1.36033	+	1.36033i	−0.873491	+	0.486841i	$0.838149\pi$
$468$	−4.01242e35	+	3.45992e35i	−0.358994	+	0.309562i
$469$	−2.85456e34	−	2.85456e34i	−0.0248145	−	0.0248145i
$470$	1.30028e35	+	4.80057e33i	0.109829	+	0.00405482i
$471$			1.47161e35i			0.120784i
$472$	2.02656e35	−	1.82306e36i	0.161638	−	1.45406i
$473$			2.43119e36i			1.88449i
$474$	6.73819e33	−	1.82511e35i	0.00507616	−	0.137493i
$475$	9.36184e35	+	9.36184e35i	0.685484	+	0.685484i
$476$	2.52124e35	+	1.86420e34i	0.179440	+	0.0132678i
$477$	3.01301e35	−	3.01301e35i	0.208451	−	0.208451i
$478$	−4.81201e35	+	4.46935e35i	−0.323631	+	0.300585i
$479$	1.49942e36			0.980379			0.490190	−	0.871616i	$-0.336928\pi$
$479$	1.49942e36			0.980379			0.490190	+	0.871616i	$0.336928\pi$
$480$	1.08239e35	−	7.41908e34i	0.0688059	−	0.0471621i
$481$	−8.97237e35			−0.554560
$482$	−5.82108e35	+	5.40656e35i	−0.349839	+	0.324927i
$483$	2.78038e34	−	2.78038e34i	0.0162487	−	0.0162487i
$484$	1.03489e36	+	7.65194e34i	0.588141	+	0.0434870i
$485$	−8.24295e35	−	8.24295e35i	−0.455585	−	0.455585i
$486$	3.59343e34	−	9.73316e35i	0.0193161	−	0.523196i
$487$			1.09266e36i			0.571272i	0.958338	+	0.285636i	$0.0922049\pi$
$487$			1.09266e36i			0.571272i	−0.958338	+	0.285636i	$0.907795\pi$
$488$	−1.56844e36	−	1.74352e35i	−0.797628	−	0.0886664i
$489$			6.26662e35i			0.310002i
$490$	−9.36246e35	−	3.45657e34i	−0.450550	−	0.0166341i
$491$	−1.01305e35	−	1.01305e35i	−0.0474274	−	0.0474274i	0.682995	−	0.730423i	$-0.260677\pi$
$491$	−1.01305e35	−	1.01305e35i	−0.0474274	−	0.0474274i	−0.730423	+	0.682995i	$0.760677\pi$
$492$	−4.13140e35	+	3.56251e35i	−0.188178	+	0.162266i
$493$	−4.11435e36	+	4.11435e36i	−1.82334	+	1.82334i
$494$	9.48222e35	+	1.02092e36i	0.408880	+	0.440229i
$495$	−1.32727e36			−0.556915
$496$	−2.77216e36	−	4.12199e35i	−1.13192	−	0.168308i
$497$	−5.51509e35			−0.219150
$498$	1.12972e35	+	1.21634e35i	0.0436894	+	0.0470391i
$499$	1.50384e36	−	1.50384e36i	0.566036	−	0.566036i	−0.364980	−	0.931015i	$-0.618924\pi$
$499$	1.50384e36	−	1.50384e36i	0.566036	−	0.566036i	0.931015	+	0.364980i	$0.118924\pi$
$500$	−1.45892e36	−	1.69189e36i	−0.534485	−	0.619835i
$501$	4.50848e35	+	4.50848e35i	0.160776	+	0.160776i
$502$	7.22096e35	+	2.66594e34i	0.250666	+	0.00925444i
$503$		−	4.62394e36i		−	1.56259i	−0.624162	−	0.781295i	$-0.714560\pi$
$503$		−	4.62394e36i		−	1.56259i	0.624162	−	0.781295i	$-0.285440\pi$
$504$	−2.11535e35	−	2.64447e35i	−0.0695939	−	0.0870014i
$505$		−	8.86787e35i		−	0.284044i
$506$	−1.62901e35	+	4.41234e36i	−0.0508033	+	1.37606i
$507$	3.22887e35	+	3.22887e35i	0.0980491	+	0.0980491i
$508$	3.39399e35	−	4.59021e36i	0.100358	−	1.35729i
$509$	−2.32148e36	+	2.32148e36i	−0.668460	+	0.668460i	−0.957359	−	0.288900i	$-0.906711\pi$
$509$	−2.32148e36	+	2.32148e36i	−0.668460	+	0.668460i	0.288900	+	0.957359i	$0.406711\pi$
$510$	−3.40285e35	+	3.16053e35i	−0.0954212	+	0.0886263i
$511$	4.48422e35			0.122463
$512$	−3.37997e36	+	1.64638e36i	−0.899018	+	0.437911i
$513$	−1.69803e36			−0.439906
$514$	−1.17622e36	+	1.09246e36i	−0.296814	+	0.275678i
$515$	6.76337e35	−	6.76337e35i	0.166251	−	0.166251i
$516$	8.40247e34	−	1.13640e36i	0.0201204	−	0.272119i
$517$	−9.19258e35	−	9.19258e35i	−0.214445	−	0.214445i
$518$	2.11584e34	−	5.73097e35i	0.00480875	−	0.130250i
$519$			1.04961e36i			0.232417i
$520$	−6.48724e35	−	8.10990e35i	−0.139964	−	0.174973i
$521$		−	4.34881e36i		−	0.914241i	−0.889405	−	0.457121i	$-0.848881\pi$
$521$		−	4.34881e36i		−	0.914241i	0.889405	−	0.457121i	$-0.151119\pi$
$522$	7.78871e36	+	2.87555e35i	1.59556	+	0.0589073i
$523$	−1.67243e36	−	1.67243e36i	−0.333868	−	0.333868i	0.520185	−	0.854053i	$-0.325863\pi$
$523$	−1.67243e36	−	1.67243e36i	−0.333868	−	0.333868i	−0.854053	+	0.520185i	$0.825863\pi$
$524$	2.64905e36	+	3.07207e36i	0.515369	+	0.597667i
$525$	6.20863e34	−	6.20863e34i	0.0117719	−	0.0117719i
$526$	3.94278e36	+	4.24507e36i	0.728610	+	0.784472i
$527$	9.91883e36			1.78656
$528$	−1.29684e36	−	1.92830e35i	−0.227681	−	0.0338545i
$529$	−1.12609e36			−0.192718
$530$	5.68410e35	+	6.11990e35i	0.0948282	+	0.102099i
$531$	6.14880e36	−	6.14880e36i	1.00003	−	1.00003i
$532$	−6.74460e35	+	5.81588e35i	−0.106942	+	0.0922164i
$533$	3.05285e36	+	3.05285e36i	0.471941	+	0.471941i
$534$	−1.42423e36	−	5.25818e34i	−0.214671	−	0.00792554i
$535$			1.48367e36i			0.218052i
$536$	−2.11167e36	−	2.34739e35i	−0.302623	−	0.0336404i
$537$			6.16949e35i			0.0862177i
$538$	−3.93379e35	+	1.06551e37i	−0.0536106	+	1.45210i
$539$	6.61896e36	+	6.61896e36i	0.879714	+	0.879714i
$540$	1.26218e36	+	9.33254e34i	0.163609	+	0.0120972i
$541$	6.91363e36	−	6.91363e36i	0.874063	−	0.874063i	−0.118849	−	0.992912i	$-0.537920\pi$
$541$	6.91363e36	−	6.91363e36i	0.874063	−	0.874063i	0.992912	+	0.118849i	$0.0379205\pi$
$542$	4.23973e36	−	3.93782e36i	0.522814	−	0.485585i
$543$	−7.19891e35			−0.0865902
$544$	1.09750e37	−	7.52267e36i	1.28772	−	0.882647i
$545$	−4.55335e36			−0.521169
$546$	6.77060e34	−	6.28846e34i	0.00756008	−	0.00702173i
$547$	1.08557e37	−	1.08557e37i	1.18257	−	1.18257i	0.203498	−	0.979075i	$-0.434769\pi$
$547$	1.08557e37	−	1.08557e37i	1.18257	−	1.18257i	0.979075	−	0.203498i	$-0.0652311\pi$
$548$	−3.07383e36	−	2.27278e35i	−0.326695	−	0.0241557i
$549$	−5.29002e36	−	5.29002e36i	−0.548568	−	0.548568i
$550$	−3.63761e35	+	9.85282e36i	−0.0368061	+	0.996929i
$551$		−	2.04972e37i		−	2.02370i
$552$	2.28639e35	−	2.05680e36i	0.0220279	−	0.198159i
$553$		−	9.23857e35i		−	0.0868592i
$554$	−1.34586e37	−	4.96882e35i	−1.23486	−	0.0455902i
$555$	7.44937e35	+	7.44937e35i	0.0667059	+	0.0667059i
$556$	2.92431e36	−	2.52164e36i	0.255573	−	0.220381i
$557$	−1.11021e37	+	1.11021e37i	−0.947020	+	0.947020i	−0.998665	−	0.0516455i	$-0.983553\pi$
$557$	−1.11021e37	+	1.11021e37i	−0.947020	+	0.947020i	0.0516455	+	0.998665i	$0.483553\pi$
$558$	−9.04184e36	−	9.73508e36i	−0.752827	−	0.810546i
$559$	−9.01816e36			−0.732923
$560$	5.33306e35	−	3.95239e35i	0.0423095	−	0.0313560i
$561$	4.64010e36			0.359359
$562$	8.92779e36	+	9.61228e36i	0.675000	+	0.726752i
$563$	−6.62528e36	+	6.62528e36i	−0.489036	+	0.489036i	−0.908002	−	0.418966i	$-0.862393\pi$
$563$	−6.62528e36	+	6.62528e36i	−0.489036	+	0.489036i	0.418966	+	0.908002i	$0.362393\pi$
$564$	3.97912e35	+	4.61453e35i	0.0286760	+	0.0332552i
$565$	5.52181e36	+	5.52181e36i	0.388532	+	0.388532i
$566$	1.85183e37	+	6.83685e35i	1.27227	+	0.0469715i
$567$		−	1.54813e36i		−	0.103857i
$568$	−2.26667e37	+	1.81314e37i	−1.48486	+	1.18776i
$569$		−	3.03635e37i		−	1.94239i	−0.238285	−	0.971195i	$-0.576585\pi$
$569$		−	3.03635e37i		−	1.94239i	0.238285	−	0.971195i	$-0.423415\pi$
$570$	6.03594e34	−	1.63489e36i	0.00377081	−	0.102136i
$571$	9.55744e36	+	9.55744e36i	0.583115	+	0.583115i	0.935758	−	0.352643i	$-0.114717\pi$
$571$	9.55744e36	+	9.55744e36i	0.583115	+	0.583115i	−0.352643	+	0.935758i	$0.614717\pi$
$572$	−7.65125e35	+	1.03480e37i	−0.0455917	+	0.616607i
$573$	−2.91134e36	+	2.91134e36i	−0.169436	+	0.169436i
$574$	−2.02196e36	+	1.87797e36i	−0.114937	+	0.106753i
$575$	−1.55626e37			−0.864102
$576$	−1.73879e37	−	3.91415e36i	−0.943072	−	0.212292i
$577$	−4.98560e36			−0.264146			−0.132073	−	0.991240i	$-0.542163\pi$
$577$	−4.98560e36			−0.264146			−0.132073	+	0.991240i	$0.542163\pi$
$578$	−2.03470e37	+	1.88981e37i	−1.05311	+	0.978119i
$579$	2.28561e36	−	2.28561e36i	0.115569	−	0.115569i
$580$	−1.12655e36	+	1.52360e37i	−0.0556507	+	0.752650i
$581$	5.93782e35	+	5.93782e35i	0.0286582	+	0.0286582i
$582$	2.01405e35	−	5.45525e36i	0.00949750	−	0.257249i
$583$		−	8.34505e36i		−	0.384506i
$584$	1.84299e37	−	1.47424e37i	0.829753	−	0.663734i
$585$		−	4.92331e36i		−	0.216597i
$586$	4.16064e35	+	1.53608e34i	0.0178872	+	0.000660385i
$587$	3.19986e35	+	3.19986e35i	0.0134436	+	0.0134436i	0.713797	−	0.700353i	$-0.246974\pi$
$587$	3.19986e35	+	3.19986e35i	0.0134436	+	0.0134436i	−0.700353	+	0.713797i	$0.746974\pi$
$588$	−2.86509e36	−	3.32261e36i	−0.117637	−	0.136422i
$589$	−2.47071e37	+	2.47071e37i	−0.991439	+	0.991439i
$590$	1.15998e37	+	1.24892e37i	0.454934	+	0.489814i
$591$	5.92494e36			0.227119
$592$	−1.79716e37	−	2.42495e37i	−0.673354	−	0.908575i
$593$	3.32855e37			1.21904			0.609519	−	0.792772i	$-0.291363\pi$
$593$	3.32855e37			1.21904			0.609519	+	0.792772i	$0.291363\pi$
$594$	−8.60551e36	−	9.26529e36i	−0.308077	−	0.331697i
$595$	−1.66117e36	+	1.66117e36i	−0.0581347	+	0.0581347i
$596$	9.70620e36	−	8.36967e36i	0.332066	−	0.286341i
$597$	1.59869e36	+	1.59869e36i	0.0534699	+	0.0534699i
$598$	−1.63669e37	−	6.04258e35i	−0.535182	−	0.0197586i
$599$			4.44590e37i			1.42134i	0.703526	+	0.710669i	$0.251608\pi$
$599$			4.44590e37i			1.42134i	−0.703526	+	0.710669i	$0.748392\pi$
$600$	5.10554e35	−	4.59286e36i	0.0159588	−	0.143563i
$601$			3.24472e37i			0.991681i	0.868414	+	0.495841i	$0.165140\pi$
$601$			3.24472e37i			0.991681i	−0.868414	+	0.495841i	$0.834860\pi$
$602$	2.12664e35	−	5.76022e36i	0.00635538	−	0.172142i
$603$	−7.12223e36	−	7.12223e36i	−0.208129	−	0.208129i
$604$	6.92672e36	+	5.12159e35i	0.197938	+	0.0146355i
$605$	−6.81858e36	+	6.81858e36i	−0.190545	+	0.190545i
$606$	3.04275e36	−	2.82608e36i	0.0831545	−	0.0772331i
$607$	−6.27243e37			−1.67644			−0.838221	−	0.545331i	$-0.816404\pi$
$607$	−6.27243e37			−1.67644			−0.838221	+	0.545331i	$0.816404\pi$
$608$	−8.59955e36	+	4.60765e37i	−0.224790	+	1.20443i
$609$	−1.35934e36			−0.0347532
$610$	1.07449e37	−	9.97972e36i	0.268688	−	0.249554i
$611$	3.40985e36	−	3.40985e36i	0.0834025	−	0.0834025i
$612$	6.29059e37	+	4.65124e36i	1.50504	+	0.111282i
$613$	3.99698e36	+	3.99698e36i	0.0935438	+	0.0935438i	0.752330	−	0.658786i	$-0.228930\pi$
$613$	3.99698e36	+	3.99698e36i	0.0935438	+	0.0935438i	−0.658786	+	0.752330i	$0.728930\pi$
$614$	2.13624e36	−	5.78620e37i	0.0489076	−	1.32471i
$615$		−	5.06929e36i		−	0.113536i
$616$	−6.59156e36	−	7.32735e35i	−0.144427	−	0.0160549i
$617$		−	3.72533e37i		−	0.798573i	−0.916826	−	0.399287i	$-0.869258\pi$
$617$		−	3.72533e37i		−	0.798573i	0.916826	−	0.399287i	$-0.130742\pi$
$618$	4.47605e36	+	1.65253e35i	0.0938751	+	0.00346582i
$619$	4.20160e37	+	4.20160e37i	0.862165	+	0.862165i	0.991589	−	0.129424i	$-0.0413129\pi$
$619$	4.20160e37	+	4.20160e37i	0.862165	+	0.862165i	−0.129424	+	0.991589i	$0.541313\pi$
$620$	1.97233e37	−	1.70075e37i	0.395997	−	0.341469i
$621$	1.41135e37	−	1.41135e37i	0.277267	−	0.277267i
$622$	−5.54431e37	−	5.96939e37i	−1.06580	−	1.14752i
$623$	−7.20937e36			−0.135615
$624$	7.15273e35	−	4.81043e36i	0.0131668	−	0.0885506i
$625$	−2.31617e37			−0.417244
$626$	9.82377e36	+	1.05770e37i	0.173191	+	0.186469i
$627$	−1.15582e37	+	1.15582e37i	−0.199424	+	0.199424i
$628$	2.55855e37	+	2.96711e37i	0.432055	+	0.501048i
$629$	7.55338e37	+	7.55338e37i	1.24841	+	1.24841i
$630$	3.14469e36	+	1.16100e35i	0.0508723	+	0.00187818i
$631$			1.89598e37i			0.300218i	0.988669	+	0.150109i	$0.0479625\pi$
$631$			1.89598e37i			0.300218i	−0.988669	+	0.150109i	$0.952038\pi$
$632$	−3.03728e37	−	3.79700e37i	−0.470765	−	0.588518i
$633$		−	5.92301e36i		−	0.0898653i
$634$	−1.94867e36	+	5.27816e37i	−0.0289423	+	0.783931i
$635$	3.02436e37	+	3.02436e37i	0.439731	+	0.439731i
$636$	−2.88414e35	+	3.90067e36i	−0.00410530	+	0.0555223i
$637$	−2.45521e37	+	2.45521e37i	−0.342141	+	0.342141i
$638$	1.11843e38	−	1.03879e38i	1.52591	−	1.41725i
$639$	−1.37604e38			−1.83810
$640$	8.92465e36	−	3.37771e37i	0.116724	−	0.441766i
$641$	8.37795e37			1.07289			0.536444	−	0.843936i	$-0.319767\pi$
$641$	8.37795e37			1.07289			0.536444	+	0.843936i	$0.319767\pi$
$642$	−5.09076e36	+	4.72825e36i	−0.0638352	+	0.0592895i
$643$	−4.54090e37	+	4.54090e37i	−0.557563	+	0.557563i	−0.928613	−	0.371050i	$-0.878998\pi$
$643$	−4.54090e37	+	4.54090e37i	−0.557563	+	0.557563i	0.371050	+	0.928613i	$0.378998\pi$
$644$	7.71922e35	−	1.04399e37i	0.00928142	−	0.125527i
$645$	7.48738e36	+	7.48738e36i	0.0881604	+	0.0881604i
$646$	6.12022e36	−	1.65772e38i	0.0705713	−	1.91149i
$647$		−	5.09272e37i		−	0.575099i	−0.957766	−	0.287549i	$-0.907159\pi$
$647$		−	5.09272e37i		−	0.575099i	0.957766	−	0.287549i	$-0.0928405\pi$
$648$	−5.08964e37	−	6.36272e37i	−0.562892	−	0.703688i
$649$		−	1.70301e38i		−	1.84465i
$650$	−3.65476e37	−	1.34932e36i	−0.387729	−	0.0143148i
$651$	1.63854e36	+	1.63854e36i	0.0170260	+	0.0170260i
$652$	1.08952e38	+	1.26350e38i	1.10890	+	1.28598i
$653$	2.57981e36	−	2.57981e36i	0.0257193	−	0.0257193i	−0.694130	−	0.719849i	$-0.744211\pi$
$653$	2.57981e36	−	2.57981e36i	0.0257193	−	0.0257193i	0.719849	+	0.694130i	$0.244211\pi$
$654$	−1.45109e37	−	1.56235e37i	−0.141709	−	0.152573i
$655$	−3.76949e37			−0.360599
$656$	−2.13608e37	+	1.43657e38i	−0.200177	+	1.34625i
$657$	1.11883e38			1.02715
$658$	2.09758e36	+	2.25840e36i	0.0188656	+	0.0203120i
$659$	−2.05247e37	+	2.05247e37i	−0.180852	+	0.180852i	−0.791727	−	0.610875i	$-0.790818\pi$
$659$	−2.05247e37	+	2.05247e37i	−0.180852	+	0.180852i	0.610875	+	0.791727i	$0.290818\pi$
$660$	9.22670e36	−	7.95620e36i	0.0796532	−	0.0686851i
$661$	−9.95176e37	−	9.95176e37i	−0.841744	−	0.841744i	0.147342	−	0.989086i	$-0.452928\pi$
$661$	−9.95176e37	−	9.95176e37i	−0.841744	−	0.841744i	−0.989086	+	0.147342i	$0.952928\pi$
$662$	−1.06004e38	−	3.91361e36i	−0.878494	−	0.0324335i
$663$			1.72118e37i			0.139763i
$664$	4.39253e37	+	4.88285e36i	0.349498	+	0.0388512i
$665$		−	8.27573e36i		−	0.0645230i
$666$	5.27911e36	−	1.42990e38i	0.0403328	−	1.09245i
$667$	1.70366e38	+	1.70366e38i	1.27551	+	1.27551i
$668$	1.69286e38	+	1.25170e37i	1.24205	+	0.0918369i
$669$	−2.65007e37	+	2.65007e37i	−0.190548	+	0.190548i
$670$	1.44664e37	−	1.34362e37i	0.101941	−	0.0946819i
$671$	−1.46516e38			−1.01188
$672$	3.05572e36	+	5.70309e35i	0.0206837	+	0.00386033i
$673$	1.72543e38			1.14471			0.572353	−	0.820008i	$-0.306031\pi$
$673$	1.72543e38			1.14471			0.572353	+	0.820008i	$0.306031\pi$
$674$	−5.78452e37	+	5.37260e37i	−0.376148	+	0.349362i
$675$	3.15156e37	−	3.15156e37i	0.200875	−	0.200875i
$676$	1.21239e38	+	8.96439e36i	0.757465	+	0.0560067i
$677$	1.49218e38	+	1.49218e38i	0.913850	+	0.913850i	0.996573	−	0.0827227i	$-0.0263616\pi$
$677$	1.49218e38	+	1.49218e38i	0.913850	+	0.913850i	−0.0827227	+	0.996573i	$0.526362\pi$
$678$	−1.34918e36	+	3.65438e37i	−0.00809967	+	0.219388i
$679$		−	2.76141e37i		−	0.162514i
$680$	−1.36603e37	+	1.22886e38i	−0.0788117	+	0.708976i
$681$		−	8.07606e36i		−	0.0456787i
$682$	−2.60029e38	−	9.60013e36i	−1.44189	−	0.0532339i
$683$	−4.42913e37	−	4.42913e37i	−0.240790	−	0.240790i	0.576387	−	0.817177i	$-0.304462\pi$
$683$	−4.42913e37	−	4.42913e37i	−0.240790	−	0.240790i	−0.817177	+	0.576387i	$0.804462\pi$
$684$	−1.68280e38	+	1.45108e38i	−0.896966	+	0.773455i
$685$	2.02526e37	−	2.02526e37i	0.105842	−	0.105842i
$686$	−3.04099e37	−	3.27414e37i	−0.155826	−	0.167773i
$687$	−3.97161e37			−0.199549
$688$	−1.80633e38	−	2.43733e38i	−0.889924	−	1.20080i
$689$	3.09547e37			0.149544
$690$	1.30871e37	+	1.40904e37i	0.0619982	+	0.0667516i
$691$	7.98139e37	−	7.98139e37i	0.370787	−	0.370787i	−0.496977	−	0.867764i	$-0.665557\pi$
$691$	7.98139e37	−	7.98139e37i	0.370787	−	0.370787i	0.867764	+	0.496977i	$0.165557\pi$
$692$	1.82485e38	+	2.11626e38i	0.831373	+	0.964132i
$693$	−2.22320e37	−	2.22320e37i	−0.0993298	−	0.0993298i
$694$	3.19848e38	+	1.18086e37i	1.40149	+	0.0517424i
$695$			3.58818e37i			0.154198i
$696$	−5.58681e37	+	4.46898e37i	−0.235472	+	0.188358i
$697$		−	5.14008e38i		−	2.12485i
$698$	−1.79983e37	+	4.87501e38i	−0.0729764	+	1.97664i
$699$	−1.18503e37	−	1.18503e37i	−0.0471289	−	0.0471289i
$700$	1.72371e36	−	2.33124e37i	0.00672422	−	0.0909419i
$701$	−3.10378e38	+	3.10378e38i	−1.18768	+	1.18768i	−0.209968	+	0.977708i	$0.567336\pi$
$701$	−3.10378e38	+	3.10378e38i	−1.18768	+	1.18768i	−0.977708	+	0.209968i	$0.932664\pi$
$702$	3.43682e37	−	3.19209e37i	0.129005	−	0.119818i
$703$	−3.76299e38			−1.38560
$704$	−2.94999e38	+	1.86590e38i	−1.06559	+	0.673995i
$705$	−5.66210e36			−0.0200643
$706$	−1.61441e38	+	1.49945e38i	−0.561243	+	0.521277i
$707$	1.48538e37	−	1.48538e37i	0.0506613	−	0.0506613i
$708$	−5.88580e36	+	7.96027e37i	−0.0196950	+	0.266366i
$709$	1.05736e38	+	1.05736e38i	0.347137	+	0.347137i	0.859042	−	0.511905i	$-0.171060\pi$
$709$	1.05736e38	+	1.05736e38i	0.347137	+	0.347137i	−0.511905	+	0.859042i	$0.671060\pi$
$710$	9.95137e36	−	2.69543e38i	0.0320550	−	0.868240i
$711$		−	2.30506e38i		−	0.728522i
$712$	−2.96301e38	+	2.37016e38i	−0.918867	+	0.735017i
$713$		−	4.10717e38i		−	1.24978i
$714$	−1.09938e37	−	4.05884e35i	−0.0328262	−	0.00121192i
$715$	−6.81797e37	−	6.81797e37i	−0.199767	−	0.199767i
$716$	1.07263e38	+	1.24392e38i	0.308407	+	0.357656i
$717$	2.02079e37	−	2.02079e37i	0.0570181	−	0.0570181i
$718$	−2.68333e38	−	2.88906e38i	−0.743008	−	0.799974i
$719$	−6.17701e38			−1.67857			−0.839283	−	0.543695i	$-0.817025\pi$
$719$	−6.17701e38			−1.67857			−0.839283	+	0.543695i	$0.817025\pi$
$720$	1.33062e38	−	9.86135e37i	0.354866	−	0.262995i
$721$	2.26575e37			0.0593042
$722$	1.32769e38	+	1.42948e38i	0.341071	+	0.367220i
$723$	2.44455e37	−	2.44455e37i	0.0616355	−	0.0616355i
$724$	−1.45147e38	+	1.25161e38i	−0.359201	+	0.309740i
$725$	3.80430e38	+	3.80430e38i	0.924086	+	0.924086i
$726$	−4.51259e37	−	1.66602e36i	−0.107592	−	0.00397225i
$727$		−	5.77867e38i		−	1.35243i	−0.736706	−	0.676213i	$-0.763620\pi$
$727$		−	5.77867e38i		−	1.35243i	0.736706	−	0.676213i	$-0.236380\pi$
$728$	2.71797e36	−	2.44504e37i	0.00624413	−	0.0561711i
$729$		−	3.57199e38i		−	0.805542i
$730$	−8.09129e36	+	2.19161e38i	−0.0179126	+	0.485181i
$731$	7.59193e38	+	7.59193e38i	1.64994	+	1.64994i
$732$	6.84849e37	+	5.06375e36i	0.146115	+	0.0108037i
$733$	−1.38272e38	+	1.38272e38i	−0.289622	+	0.289622i	−0.836931	−	0.547309i	$-0.815652\pi$
$733$	−1.38272e38	+	1.38272e38i	−0.289622	+	0.289622i	0.547309	+	0.836931i	$0.315652\pi$
$734$	2.07367e37	−	1.92600e37i	0.0426425	−	0.0396059i
$735$	4.07690e37			0.0823097
$736$	−3.11497e38	−	4.54451e38i	−0.617452	−	0.900817i
$737$	−1.97262e38			−0.383913
$738$	−5.04486e38	+	4.68561e38i	−0.964024	+	0.895376i
$739$	7.40148e38	−	7.40148e38i	1.38873	−	1.38873i	0.560744	−	0.827989i	$-0.310515\pi$
$739$	7.40148e38	−	7.40148e38i	1.38873	−	1.38873i	0.827989	−	0.560744i	$-0.189485\pi$
$740$	2.79712e38	+	2.06818e37i	0.515327	+	0.0381031i
$741$	−4.28733e37	−	4.28733e37i	−0.0775606	−	0.0775606i
$742$	−7.29967e35	+	1.97719e37i

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8488.66 + 7884.18i) q^{2} +(356479. - 356479. i) q^{3} +(9.89700e6 - 1.33852e8i) q^{4} +(8.81914e8 + 8.81914e8i) q^{5} +(-2.15483e8 + 5.83658e9i) q^{6} +2.95444e10i q^{7} +(9.71304e11 + 1.21426e12i) q^{8} +7.37144e12i q^{9} +O(q^{10})\)	\(q+(-8488.66 + 7884.18i) q^{2} +(356479. - 356479. i) q^{3} +(9.89700e6 - 1.33852e8i) q^{4} +(8.81914e8 + 8.81914e8i) q^{5} +(-2.15483e8 + 5.83658e9i) q^{6} +2.95444e10i q^{7} +(9.71304e11 + 1.21426e12i) q^{8} +7.37144e12i q^{9} +(-1.44394e13 - 5.33097e11i) q^{10} +(1.02082e14 + 1.02082e14i) q^{11} +(-4.41875e13 - 5.12436e13i) q^{12} +(-3.78659e14 + 3.78659e14i) q^{13} +(-2.32934e14 - 2.50792e14i) q^{14} +6.28768e14 q^{15} +(-1.78185e16 - 2.64947e15i) q^{16} +6.37548e16 q^{17} +(-5.81178e16 - 6.25737e16i) q^{18} +(-1.58809e17 + 1.58809e17i) q^{19} +(1.26775e17 - 1.09318e17i) q^{20} +(1.05320e16 + 1.05320e16i) q^{21} +(-1.67138e18 - 6.17063e16i) q^{22} -2.63994e18i q^{23} +(7.79107e17 + 8.66075e16i) q^{24} -5.89503e18i q^{25} +(2.28891e17 - 6.19973e18i) q^{26} +(5.34613e18 + 5.34613e18i) q^{27} +(3.95459e18 + 2.92401e17i) q^{28} +(-6.45340e19 + 6.45340e19i) q^{29} +(-5.33740e18 + 4.95732e18i) q^{30} +1.55578e20 q^{31} +(1.72144e20 - 1.17994e20i) q^{32} +7.27804e19 q^{33} +(-5.41193e20 + 5.02654e20i) q^{34} +(-2.60556e19 + 2.60556e19i) q^{35} +(9.86685e20 + 7.29552e19i) q^{36} +(1.18476e21 + 1.18476e21i) q^{37} +(9.59962e19 - 2.60015e21i) q^{38} +2.69968e20i q^{39} +(-2.14263e20 + 1.92748e21i) q^{40} -8.06226e21i q^{41} +(-1.72438e20 - 6.36633e18i) q^{42} +(1.19080e22 + 1.19080e22i) q^{43} +(1.46743e22 - 1.26536e22i) q^{44} +(-6.50098e21 + 6.50098e21i) q^{45} +(2.08138e22 + 2.24096e22i) q^{46} -9.00507e21 q^{47} +(-7.29640e21 + 5.40744e21i) q^{48} +6.48395e22 q^{49} +(4.64775e22 + 5.00410e22i) q^{50} +(2.27272e22 - 2.27272e22i) q^{51} +(4.69368e22 + 5.44320e22i) q^{52} +(-4.08741e22 - 4.08741e22i) q^{53} +(-8.75314e22 - 3.23161e21i) q^{54} +1.80056e23i q^{55} +(-3.58745e22 + 2.86966e22i) q^{56} +1.13224e23i q^{57} +(3.90093e22 - 1.05661e24i) q^{58} +(-8.34138e23 - 8.34138e23i) q^{59} +(6.22292e21 - 8.41621e22i) q^{60} +(-7.17637e23 + 7.17637e23i) q^{61} +(-1.32065e24 + 1.22660e24i) q^{62} -2.17785e23 q^{63} +(-5.30988e23 + 2.35883e24i) q^{64} -6.67890e23 q^{65} +(-6.17808e23 + 5.73814e23i) q^{66} +(-9.66192e23 + 9.66192e23i) q^{67} +(6.30981e23 - 8.53373e24i) q^{68} +(-9.41085e23 - 9.41085e23i) q^{69} +(1.57500e22 - 4.26605e23i) q^{70} +1.86671e25i q^{71} +(-8.95083e24 + 7.15991e24i) q^{72} -1.51779e25i q^{73} +(-1.93978e25 - 7.16157e23i) q^{74} +(-2.10146e24 - 2.10146e24i) q^{75} +(1.96852e25 + 2.28287e25i) q^{76} +(-3.01596e24 + 3.01596e24i) q^{77} +(-2.12848e24 - 2.29167e24i) q^{78} -3.12701e25 q^{79} +(-1.33778e25 - 1.80510e25i) q^{80} -5.24001e25 q^{81} +(6.35644e25 + 6.84378e25i) q^{82} +(2.00979e25 - 2.00979e25i) q^{83} +(1.51396e24 - 1.30549e24i) q^{84} +(5.62263e25 + 5.62263e25i) q^{85} +(-1.94968e26 - 7.19812e24i) q^{86} +4.60101e25i q^{87} +(-2.48012e25 + 2.23107e26i) q^{88} +2.44018e26i q^{89} +(3.92969e24 - 1.06440e26i) q^{90} +(-1.11873e25 - 1.11873e25i) q^{91} +(-3.53363e26 - 2.61275e25i) q^{92} +(5.54602e25 - 5.54602e25i) q^{93} +(7.64410e25 - 7.09977e25i) q^{94} -2.80112e26 q^{95} +(1.93034e25 - 1.03428e26i) q^{96} -9.34666e26 q^{97} +(-5.50400e26 + 5.11206e26i) q^{98} +(-7.52493e26 + 7.52493e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) \) 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

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