LMFDB - Embedded newform 16.28.e.a.5.2

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			5.2
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11578.9 - 382.145i) q^{2} +(-2.39173e6 + 2.39173e6i) q^{3} +(1.33926e8 + 8.84966e6i) q^{4} +(1.10058e8 + 1.10058e8i) q^{5} +(2.86077e10 - 2.67797e10i) q^{6} +2.84560e11i q^{7} +(-1.54733e12 - 1.53649e11i) q^{8} -3.81516e12i q^{9} +O(q^{10})$	\(q+(-11578.9 - 382.145i) q^{2} +(-2.39173e6 + 2.39173e6i) q^{3} +(1.33926e8 + 8.84966e6i) q^{4} +(1.10058e8 + 1.10058e8i) q^{5} +(2.86077e10 - 2.67797e10i) q^{6} +2.84560e11i q^{7} +(-1.54733e12 - 1.53649e11i) q^{8} -3.81516e12i q^{9} +(-1.23230e12 - 1.31641e12i) q^{10} +(4.44293e13 + 4.44293e13i) q^{11} +(-3.41480e14 + 2.99148e14i) q^{12} +(7.24425e14 - 7.24425e14i) q^{13} +(1.08743e14 - 3.29490e15i) q^{14} -5.26459e14 q^{15} +(1.78578e16 + 2.37039e15i) q^{16} +5.16417e16 q^{17} +(-1.45794e15 + 4.41754e16i) q^{18} +(1.93125e14 - 1.93125e14i) q^{19} +(1.37656e16 + 1.57136e16i) q^{20} +(-6.80592e17 - 6.80592e17i) q^{21} +(-4.97466e17 - 5.31423e17i) q^{22} +7.78274e17i q^{23} +(4.06829e18 - 3.33332e18i) q^{24} -7.42636e18i q^{25} +(-8.66490e18 + 8.11123e18i) q^{26} +(-9.11355e18 - 9.11355e18i) q^{27} +(-2.51826e18 + 3.81099e19i) q^{28} +(7.01270e18 - 7.01270e18i) q^{29} +(6.09583e18 + 2.01183e17i) q^{30} -2.67351e20 q^{31} +(-2.05868e20 - 3.42709e19i) q^{32} -2.12526e20 q^{33} +(-5.97955e20 - 1.97346e19i) q^{34} +(-3.13182e19 + 3.13182e19i) q^{35} +(3.37628e19 - 5.10947e20i) q^{36} +(1.02072e21 + 1.02072e21i) q^{37} +(-2.30999e18 + 2.16238e18i) q^{38} +3.46526e21i q^{39} +(-1.53386e20 - 1.87207e20i) q^{40} -2.65448e21i q^{41} +(7.62044e21 + 8.14061e21i) q^{42} +(-6.40200e21 - 6.40200e21i) q^{43} +(5.55704e21 + 6.34341e21i) q^{44} +(4.19889e20 - 4.19889e20i) q^{45} +(2.97413e20 - 9.01158e21i) q^{46} -3.84158e22 q^{47} +(-4.83803e22 + 3.70416e22i) q^{48} -1.52622e22 q^{49} +(-2.83794e21 + 8.59893e22i) q^{50} +(-1.23513e23 + 1.23513e23i) q^{51} +(1.03430e23 - 9.06082e22i) q^{52} +(-1.29330e23 - 1.29330e23i) q^{53} +(1.02042e23 + 1.09008e23i) q^{54} +9.77962e21i q^{55} +(4.37223e22 - 4.40310e23i) q^{56} +9.23807e20i q^{57} +(-8.38795e22 + 7.85198e22i) q^{58} +(-8.38558e23 - 8.38558e23i) q^{59} +(-7.05063e22 - 4.65898e21i) q^{60} +(2.51078e23 - 2.51078e23i) q^{61} +(3.09564e24 + 1.02167e23i) q^{62} +1.08564e24 q^{63} +(2.37064e24 + 4.75491e23i) q^{64} +1.59458e23 q^{65} +(2.46083e24 + 8.12157e22i) q^{66} +(1.22213e24 - 1.22213e24i) q^{67} +(6.91614e24 + 4.57011e23i) q^{68} +(-1.86142e24 - 1.86142e24i) q^{69} +(3.74599e23 - 3.50663e23i) q^{70} -5.37791e24i q^{71} +(-5.86193e23 + 5.90332e24i) q^{72} -1.12958e25i q^{73} +(-1.14287e25 - 1.22089e25i) q^{74} +(1.77618e25 + 1.77618e25i) q^{75} +(2.75735e22 - 2.41553e22i) q^{76} +(-1.26428e25 + 1.26428e25i) q^{77} +(1.32423e24 - 4.01240e25i) q^{78} -1.08583e25 q^{79} +(1.70451e24 + 2.22627e24i) q^{80} +7.26872e25 q^{81} +(-1.01439e24 + 3.07360e25i) q^{82} +(6.59344e25 - 6.59344e25i) q^{83} +(-8.51257e25 - 9.71717e25i) q^{84} +(5.68358e24 + 5.68358e24i) q^{85} +(7.16819e25 + 7.65749e25i) q^{86} +3.35450e25i q^{87} +(-6.19205e25 - 7.55735e25i) q^{88} +4.94301e25i q^{89} +(-5.02232e24 + 4.70141e24i) q^{90} +(2.06143e26 + 2.06143e26i) q^{91} +(-6.88746e24 + 1.04231e26i) q^{92} +(6.39431e26 - 6.39431e26i) q^{93} +(4.44814e26 + 1.46804e25i) q^{94} +4.25100e22 q^{95} +(5.74348e26 - 4.10414e26i) q^{96} +9.90997e26 q^{97} +(1.76720e26 + 5.83237e24i) q^{98} +(1.69505e26 - 1.69505e26i) 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 $

$2$	−11578.9	−	382.145i	−0.999456	−	0.0329855i
$2$	−11578.9	−	382.145i	−0.999456	−	0.0329855i
$3$	−2.39173e6	+	2.39173e6i	−0.866115	+	0.866115i	−0.992040	−	0.125925i	$-0.959810\pi$
$3$	−2.39173e6	+	2.39173e6i	−0.866115	+	0.866115i	0.125925	+	0.992040i	$0.459810\pi$
$4$	1.33926e8	+	8.84966e6i	0.997824	+	0.0659351i
$5$	1.10058e8	+	1.10058e8i	0.0403206	+	0.0403206i	0.726980	−	0.686659i	$-0.240923\pi$
$5$	1.10058e8	+	1.10058e8i	0.0403206	+	0.0403206i	−0.686659	+	0.726980i	$0.740923\pi$
$6$	2.86077e10	−	2.67797e10i	0.894213	−	0.837074i
$7$			2.84560e11i			1.11007i	0.831827	+	0.555035i	$0.187295\pi$
$7$			2.84560e11i			1.11007i	−0.831827	+	0.555035i	$0.812705\pi$
$8$	−1.54733e12	−	1.53649e11i	−0.995106	−	0.0988129i
$9$		−	3.81516e12i		−	0.500309i
$10$	−1.23230e12	−	1.31641e12i	−0.0389687	−	0.0416287i
$11$	4.44293e13	+	4.44293e13i	0.388033	+	0.388033i	0.873985	−	0.485952i	$-0.161527\pi$
$11$	4.44293e13	+	4.44293e13i	0.388033	+	0.388033i	−0.485952	+	0.873985i	$0.661527\pi$
$12$	−3.41480e14	+	2.99148e14i	−0.921337	+	0.807123i
$13$	7.24425e14	−	7.24425e14i	0.663374	−	0.663374i	−0.292800	−	0.956174i	$-0.594587\pi$
$13$	7.24425e14	−	7.24425e14i	0.663374	−	0.663374i	0.956174	+	0.292800i	$0.0945870\pi$
$14$	1.08743e14	−	3.29490e15i	0.0366162	−	1.10947i
$15$	−5.26459e14			−0.0698445
$16$	1.78578e16	+	2.37039e15i	0.991305	+	0.131583i
$17$	5.16417e16			1.26456			0.632280	−	0.774740i	$-0.282119\pi$
$17$	5.16417e16			1.26456			0.632280	+	0.774740i	$0.282119\pi$
$18$	−1.45794e15	+	4.41754e16i	−0.0165029	+	0.500037i
$19$	1.93125e14	−	1.93125e14i	0.00105358	−	0.00105358i	−0.706580	−	0.707633i	$-0.749763\pi$
$19$	1.93125e14	−	1.93125e14i	0.00105358	−	0.00105358i	0.707633	+	0.706580i	$0.249763\pi$
$20$	1.37656e16	+	1.57136e16i	0.0375743	+	0.0428914i
$21$	−6.80592e17	−	6.80592e17i	−0.961449	−	0.961449i
$22$	−4.97466e17	−	5.31423e17i	−0.375022	−	0.400621i
$23$			7.78274e17i			0.321964i	0.986957	+	0.160982i	$0.0514660\pi$
$23$			7.78274e17i			0.321964i	−0.986957	+	0.160982i	$0.948534\pi$
$24$	4.06829e18	−	3.33332e18i	0.947459	−	0.776293i
$25$		−	7.42636e18i		−	0.996748i
$26$	−8.66490e18	+	8.11123e18i	−0.684894	+	0.641131i
$27$	−9.11355e18	−	9.11355e18i	−0.432789	−	0.432789i
$28$	−2.51826e18	+	3.81099e19i	−0.0731926	+	1.10766i
$29$	7.01270e18	−	7.01270e18i	0.126915	−	0.126915i	−0.640796	−	0.767711i	$-0.721396\pi$
$29$	7.01270e18	−	7.01270e18i	0.126915	−	0.126915i	0.767711	+	0.640796i	$0.221396\pi$
$30$	6.09583e18	+	2.01183e17i	0.0698065	+	0.00230386i
$31$	−2.67351e20			−1.96652			−0.983261	−	0.182204i	$-0.941677\pi$
$31$	−2.67351e20			−1.96652			−0.983261	+	0.182204i	$0.941677\pi$
$32$	−2.05868e20	−	3.42709e19i	−0.986425	−	0.164210i
$33$	−2.12526e20			−0.672162
$34$	−5.97955e20	−	1.97346e19i	−1.26387	−	0.0417121i
$35$	−3.13182e19	+	3.13182e19i	−0.0447587	+	0.0447587i
$36$	3.37628e19	−	5.10947e20i	0.0329879	−	0.499221i
$37$	1.02072e21	+	1.02072e21i	0.688941	+	0.688941i	0.961998	−	0.273057i	$-0.0880348\pi$
$37$	1.02072e21	+	1.02072e21i	0.688941	+	0.688941i	−0.273057	+	0.961998i	$0.588035\pi$
$38$	−2.30999e18	+	2.16238e18i	−0.00108775	+	0.00101825i
$39$			3.46526e21i			1.14912i
$40$	−1.53386e20	−	1.87207e20i	−0.0361391	−	0.0441075i
$41$		−	2.65448e21i		−	0.448123i	−0.974575	−	0.224061i	$-0.928068\pi$
$41$		−	2.65448e21i		−	0.448123i	0.974575	−	0.224061i	$-0.0719316\pi$
$42$	7.62044e21	+	8.14061e21i	0.929212	+	0.992639i
$43$	−6.40200e21	−	6.40200e21i	−0.568188	−	0.568188i	0.363433	−	0.931620i	$-0.381605\pi$
$43$	−6.40200e21	−	6.40200e21i	−0.568188	−	0.568188i	−0.931620	+	0.363433i	$0.881605\pi$
$44$	5.55704e21	+	6.34341e21i	0.361604	+	0.412774i
$45$	4.19889e20	−	4.19889e20i	0.0201728	−	0.0201728i
$46$	2.97413e20	−	9.01158e21i	0.0106201	−	0.321788i
$47$	−3.84158e22			−1.02610			−0.513049	−	0.858359i	$-0.671484\pi$
$47$	−3.84158e22			−1.02610			−0.513049	+	0.858359i	$0.671484\pi$
$48$	−4.83803e22	+	3.70416e22i	−0.972550	+	0.744618i
$49$	−1.52622e22			−0.232258
$50$	−2.83794e21	+	8.59893e22i	−0.0328782	+	0.996206i
$51$	−1.23513e23	+	1.23513e23i	−1.09525	+	1.09525i
$52$	1.03430e23	−	9.06082e22i	0.705670	−	0.618190i
$53$	−1.29330e23	−	1.29330e23i	−0.682300	−	0.682300i	0.278218	−	0.960518i	$-0.410256\pi$
$53$	−1.29330e23	−	1.29330e23i	−0.682300	−	0.682300i	−0.960518	+	0.278218i	$0.910256\pi$
$54$	1.02042e23	+	1.09008e23i	0.418278	+	0.446830i
$55$			9.77962e21i			0.0312914i
$56$	4.37223e22	−	4.40310e23i	0.109689	−	1.10464i
$57$			9.23807e20i			0.00182503i
$58$	−8.38795e22	+	7.85198e22i	−0.131032	+	0.122659i
$59$	−8.38558e23	−	8.38558e23i	−1.03999	−	1.03999i	−0.999166	−	0.0408275i	$-0.987001\pi$
$59$	−8.38558e23	−	8.38558e23i	−1.03999	−	1.03999i	−0.0408275	−	0.999166i	$-0.512999\pi$
$60$	−7.05063e22	−	4.65898e21i	−0.0696925	−	0.00460520i
$61$	2.51078e23	−	2.51078e23i	0.198543	−	0.198543i	−0.600832	−	0.799375i	$-0.705164\pi$
$61$	2.51078e23	−	2.51078e23i	0.198543	−	0.198543i	0.799375	+	0.600832i	$0.205164\pi$
$62$	3.09564e24	+	1.02167e23i	1.96545	+	0.0648667i
$63$	1.08564e24			0.555379
$64$	2.37064e24	+	4.75491e23i	0.980472	+	0.196659i
$65$	1.59458e23			0.0534952
$66$	2.46083e24	+	8.12157e22i	0.671796	+	0.0221716i
$67$	1.22213e24	−	1.22213e24i	0.272338	−	0.272338i	−0.557703	−	0.830041i	$-0.688317\pi$
$67$	1.22213e24	−	1.22213e24i	0.272338	−	0.272338i	0.830041	+	0.557703i	$0.188317\pi$
$68$	6.91614e24	+	4.57011e23i	1.26181	+	0.0833789i
$69$	−1.86142e24	−	1.86142e24i	−0.278857	−	0.278857i
$70$	3.74599e23	−	3.50663e23i	0.0462108	−	0.0432580i
$71$		−	5.37791e24i		−	0.547805i	−0.961757	−	0.273902i	$-0.911685\pi$
$71$		−	5.37791e24i		−	0.547805i	0.961757	−	0.273902i	$-0.0883145\pi$
$72$	−5.86193e23	+	5.90332e24i	−0.0494370	+	0.497861i
$73$		−	1.12958e25i		−	0.790786i	−0.918512	−	0.395393i	$-0.870608\pi$
$73$		−	1.12958e25i		−	0.790786i	0.918512	−	0.395393i	$-0.129392\pi$
$74$	−1.14287e25	−	1.22089e25i	−0.665841	−	0.711291i
$75$	1.77618e25	+	1.77618e25i	0.863298	+	0.863298i
$76$	2.75735e22	−	2.41553e22i	0.00112075	−	0.000981815i
$77$	−1.26428e25	+	1.26428e25i	−0.430744	+	0.430744i
$78$	1.32423e24	−	4.01240e25i	0.0379041	−	1.14849i
$79$	−1.08583e25			−0.261696			−0.130848	−	0.991402i	$-0.541770\pi$
$79$	−1.08583e25			−0.261696			−0.130848	+	0.991402i	$0.541770\pi$
$80$	1.70451e24	+	2.22627e24i	0.0346645	+	0.0452755i
$81$	7.26872e25			1.25000
$82$	−1.01439e24	+	3.07360e25i	−0.0147815	+	0.447879i
$83$	6.59344e25	−	6.59344e25i	0.815751	−	0.815751i	−0.169738	−	0.985489i	$-0.554292\pi$
$83$	6.59344e25	−	6.59344e25i	0.815751	−	0.815751i	0.985489	+	0.169738i	$0.0542923\pi$
$84$	−8.51257e25	−	9.71717e25i	−0.895963	−	1.02275i
$85$	5.68358e24	+	5.68358e24i	0.0509878	+	0.0509878i
$86$	7.16819e25	+	7.65749e25i	0.549136	+	0.586620i
$87$			3.35450e25i			0.219846i
$88$	−6.19205e25	−	7.55735e25i	−0.347791	−	0.424477i
$89$			4.94301e25i			0.238356i	0.992873	+	0.119178i	$0.0380259\pi$
$89$			4.94301e25i			0.238356i	−0.992873	+	0.119178i	$0.961974\pi$
$90$	−5.02232e24	+	4.70141e24i	−0.0208272	+	0.0194964i
$91$	2.06143e26	+	2.06143e26i	0.736392	+	0.736392i
$92$	−6.88746e24	+	1.04231e26i	−0.0212287	+	0.321263i
$93$	6.39431e26	−	6.39431e26i	1.70323	−	1.70323i
$94$	4.44814e26	+	1.46804e25i	1.02554	+	0.0338464i
$95$	4.25100e22			8.49616e−5
$96$	5.74348e26	−	4.10414e26i	0.996582	−	0.712133i
$97$	9.90997e26			1.49504			0.747522	−	0.664237i	$-0.231244\pi$
$97$	9.90997e26			1.49504			0.747522	+	0.664237i	$0.231244\pi$
$98$	1.76720e26	+	5.83237e24i	0.232131	+	0.00766113i
$99$	1.69505e26	−	1.69505e26i	0.194136	−	0.194136i
$100$	6.57207e25	−	9.94579e26i	0.0657207	−	0.994579i
$101$	−1.15508e27	−	1.15508e27i	−1.00989	−	1.00989i	−0.999951	−	0.00993858i	$-0.996836\pi$
$101$	−1.15508e27	−	1.15508e27i	−1.00989	−	1.00989i	−0.00993858	−	0.999951i	$-0.503164\pi$
$102$	1.47735e27	−	1.38295e27i	1.13079	−	1.05853i
$103$			9.05846e26i			0.607787i	0.952706	+	0.303894i	$0.0982868\pi$
$103$			9.05846e26i			0.607787i	−0.952706	+	0.303894i	$0.901713\pi$
$104$	−1.23223e27	+	1.00962e27i	−0.725677	+	0.594577i
$105$		−	1.49809e26i		−	0.0775324i
$106$	1.44808e27	+	1.54693e27i	0.659423	+	0.704435i
$107$	−2.27170e26	−	2.27170e26i	−0.0911320	−	0.0911320i	0.660071	−	0.751203i	$-0.270526\pi$
$107$	−2.27170e26	−	2.27170e26i	−0.0911320	−	0.0911320i	−0.751203	+	0.660071i	$0.770526\pi$
$108$	−1.13989e27	−	1.30119e27i	−0.403312	−	0.460384i
$109$	1.39549e27	−	1.39549e27i	0.435982	−	0.435982i	−0.454675	−	0.890657i	$-0.650245\pi$
$109$	1.39549e27	−	1.39549e27i	0.435982	−	0.435982i	0.890657	+	0.454675i	$0.150245\pi$
$110$	3.73723e24	−	1.13238e26i	0.00103216	−	0.0312744i
$111$	−4.88256e27			−1.19340
$112$	−6.74519e26	+	5.08161e27i	−0.146067	+	1.10042i
$113$	−4.22327e27			−0.811129			−0.405564	−	0.914066i	$-0.632925\pi$
$113$	−4.22327e27			−0.811129			−0.405564	+	0.914066i	$0.632925\pi$
$114$	3.53028e23	−	1.06967e25i	6.01996e−5	−	0.00182404i
$115$	−8.56554e25	+	8.56554e25i	−0.0129818	+	0.0129818i
$116$	1.00124e27	−	8.77121e26i	0.135007	−	0.118271i
$117$	−2.76380e27	−	2.76380e27i	−0.331892	−	0.331892i
$118$	9.38915e27	+	1.00301e28i	1.00512	+	1.07373i
$119$			1.46952e28i			1.40375i
$120$	8.14608e26	+	8.08896e25i	0.0695027	+	0.00690154i
$121$		−	9.16206e27i		−	0.698861i
$122$	−3.00316e27	+	2.81127e27i	−0.204984	+	0.191886i
$123$	6.34879e27	+	6.34879e27i	0.388126	+	0.388126i
$124$	−3.58051e28	−	2.36596e27i	−1.96224	−	0.129663i
$125$	1.63733e27	−	1.63733e27i	0.0805101	−	0.0805101i
$126$	−1.25706e28	−	4.14872e26i	−0.555077	−	0.0183194i
$127$	3.48607e27			0.138352			0.0691760	−	0.997604i	$-0.477963\pi$
$127$	3.48607e27			0.138352			0.0691760	+	0.997604i	$0.477963\pi$
$128$	−2.72677e28	−	6.41161e27i	−0.973452	−	0.228893i
$129$	3.06237e28			0.984231
$130$	−1.84635e27	−	6.09359e25i	−0.0534661	−	0.00176457i
$131$	−4.05378e28	+	4.05378e28i	−1.05852	+	1.05852i	−0.0603377	+	0.998178i	$0.519218\pi$
$131$	−4.05378e28	+	4.05378e28i	−1.05852	+	1.05852i	−0.998178	+	0.0603377i	$0.980782\pi$
$132$	−2.84627e28	−	1.88078e27i	−0.670699	−	0.0443191i
$133$	5.49558e25	+	5.49558e25i	0.00116954	+	0.00116954i
$134$	−1.46180e28	+	1.36840e28i	−0.281173	+	0.263207i
$135$		−	2.00604e27i		−	0.0349007i
$136$	−7.99069e28	−	7.93466e27i	−1.25837	−	0.124955i
$137$		−	4.32217e28i		−	0.616558i	−0.951296	−	0.308279i	$-0.900247\pi$
$137$		−	4.32217e28i		−	0.616558i	0.951296	−	0.308279i	$-0.0997531\pi$
$138$	2.08419e28	+	2.22646e28i	0.269507	+	0.287904i
$139$	2.00110e28	+	2.00110e28i	0.234730	+	0.234730i	0.814664	−	0.579934i	$-0.196922\pi$
$139$	2.00110e28	+	2.00110e28i	0.234730	+	0.234730i	−0.579934	+	0.814664i	$0.696922\pi$
$140$	−4.47146e27	+	3.91715e27i	−0.0476125	+	0.0417102i
$141$	9.18803e28	−	9.18803e28i	0.888719	−	0.888719i
$142$	−2.05514e27	+	6.22705e28i	−0.0180696	+	0.547507i
$143$	6.43715e28			0.514822
$144$	9.04342e27	−	6.81302e28i	0.0658323	−	0.495959i
$145$	1.54361e27			0.0102346
$146$	−4.31663e27	+	1.30793e29i	−0.0260844	+	0.790355i
$147$	3.65031e28	−	3.65031e28i	0.201162	−	0.201162i
$148$	1.27667e29	+	1.45733e29i	0.642016	+	0.732867i
$149$	1.45875e29	+	1.45875e29i	0.669833	+	0.669833i	0.957677	−	0.287844i	$-0.0929384\pi$
$149$	1.45875e29	+	1.45875e29i	0.669833	+	0.669833i	−0.287844	+	0.957677i	$0.592938\pi$
$150$	−1.98876e29	−	2.12451e29i	−0.834352	−	0.891305i
$151$		−	1.93196e29i		−	0.740983i	−0.928836	−	0.370492i	$-0.879189\pi$
$151$		−	1.93196e29i		−	0.740983i	0.928836	−	0.370492i	$-0.120811\pi$
$152$	−3.28503e26	+	2.69156e26i	−0.00115253	+	0.000944312i
$153$		−	1.97021e29i		−	0.632671i
$154$	1.51222e29	−	1.41559e29i	0.444718	−	0.416301i
$155$	−2.94241e28	−	2.94241e28i	−0.0792913	−	0.0792913i
$156$	−3.06664e28	+	4.64087e29i	−0.0757670	+	1.14661i
$157$	−2.72256e29	+	2.72256e29i	−0.617066	+	0.617066i	−0.944778	−	0.327712i	$-0.893722\pi$
$157$	−2.72256e29	+	2.72256e29i	−0.617066	+	0.617066i	0.327712	+	0.944778i	$0.393722\pi$
$158$	1.25728e29	+	4.14946e27i	0.261554	+	0.00863219i
$159$	6.18646e29			1.18190
$160$	−1.88857e28	−	2.64292e28i	−0.0331522	−	0.0463943i
$161$	−2.21466e29			−0.357402
$162$	−8.41640e29	−	2.77770e28i	−1.24932	−	0.0412319i
$163$	4.33582e29	−	4.33582e29i	0.592296	−	0.592296i	−0.345955	−	0.938251i	$-0.612445\pi$
$163$	4.33582e29	−	4.33582e29i	0.592296	−	0.592296i	0.938251	+	0.345955i	$0.112445\pi$
$164$	2.34912e28	−	3.55503e29i	0.0295470	−	0.447147i
$165$	−2.33902e28	−	2.33902e28i	−0.0271020	−	0.0271020i
$166$	−7.88646e29	+	7.38253e29i	−0.842215	+	0.788399i
$167$		−	1.91169e30i		−	1.88254i	−0.337652	−	0.941271i	$-0.609633\pi$
$167$		−	1.91169e30i		−	1.88254i	0.337652	−	0.941271i	$-0.390367\pi$
$168$	9.48531e29	+	1.15767e30i	0.861740	+	1.05175i
$169$			1.42950e29i			0.119871i
$170$	−6.36379e28	−	6.79818e28i	−0.0492782	−	0.0526420i
$171$	−7.36803e26	−	7.36803e26i	−0.000527113	−	0.000527113i
$172$	−8.00737e29	−	9.14048e29i	−0.529488	−	0.604415i
$173$	1.69024e30	−	1.69024e30i	1.03353	−	1.03353i	0.0341166	−	0.999418i	$-0.489138\pi$
$173$	1.69024e30	−	1.69024e30i	1.03353	−	1.03353i	0.999418	−	0.0341166i	$-0.0108618\pi$
$174$	1.28190e28	−	3.88415e29i	0.00725172	−	0.219726i
$175$	2.11325e30			1.10646
$176$	6.88094e29	+	8.98724e29i	0.333600	+	0.435718i
$177$	4.01121e30			1.80151
$178$	1.88894e28	−	5.72347e29i	0.00786229	−	0.238226i
$179$	2.82837e30	−	2.82837e30i	1.09149	−	1.09149i	0.0961234	−	0.995369i	$-0.469356\pi$
$179$	2.82837e30	−	2.82837e30i	1.09149	−	1.09149i	0.995369	−	0.0961234i	$-0.0306444\pi$
$180$	5.99498e28	−	5.25180e28i	0.0214590	−	0.0187988i
$181$	3.65382e30	+	3.65382e30i	1.21363	+	1.21363i	0.969823	+	0.243808i	$0.0783967\pi$
$181$	3.65382e30	+	3.65382e30i	1.21363	+	1.21363i	0.243808	+	0.969823i	$0.421603\pi$
$182$	−2.30814e30	−	2.46569e30i	−0.711701	−	0.760281i
$183$			1.20102e30i			0.343923i
$184$	1.19581e29	−	1.20425e30i	0.0318142	−	0.320388i
$185$			2.24676e29i			0.0555570i
$186$	−7.64829e30	+	7.15958e30i	−1.75849	+	1.64612i
$187$	2.29440e30	+	2.29440e30i	0.490691	+	0.490691i
$188$	−5.14487e30	−	3.39967e29i	−1.02387	−	0.0676559i
$189$	2.59335e30	−	2.59335e30i	0.480427	−	0.480427i
$190$	−4.92221e26	−	1.62450e25i	−8.49153e−5	−	2.80250e-6i
$191$	−3.24440e29			−0.0521416			−0.0260708	−	0.999660i	$-0.508300\pi$
$191$	−3.24440e29			−0.0521416			−0.0260708	+	0.999660i	$0.508300\pi$
$192$	−6.80717e30	+	4.53268e30i	−1.01953	+	0.678872i
$193$	−1.09683e31			−1.53149			−0.765745	−	0.643144i	$-0.777630\pi$
$193$	−1.09683e31			−1.53149			−0.765745	+	0.643144i	$0.777630\pi$
$194$	−1.14747e31	−	3.78704e29i	−1.49423	−	0.0493147i
$195$	−3.81380e29	+	3.81380e29i	−0.0463330	+	0.0463330i
$196$	−2.04400e30	−	1.35065e29i	−0.231752	−	0.0153139i
$197$	−6.26017e30	−	6.26017e30i	−0.662662	−	0.662662i	0.293345	−	0.956007i	$-0.405232\pi$
$197$	−6.26017e30	−	6.26017e30i	−0.662662	−	0.662662i	−0.956007	+	0.293345i	$0.905232\pi$
$198$	−2.02746e30	+	1.89791e30i	−0.200435	+	0.187627i
$199$		−	1.24189e31i		−	1.14701i	−0.819202	−	0.573505i	$-0.805583\pi$
$199$		−	1.24189e31i		−	1.14701i	0.819202	−	0.573505i	$-0.194417\pi$
$200$	−1.14105e30	+	1.14911e31i	−0.0984916	+	0.991870i
$201$			5.84603e30i			0.471753i
$202$	1.29332e31	+	1.38160e31i	0.976028	+	1.04265i
$203$	1.99554e30	+	1.99554e30i	0.140885	+	0.140885i
$204$	−1.76346e31	+	1.54485e31i	−1.16509	+	1.02066i
$205$	2.92147e29	−	2.92147e29i	0.0180686	−	0.0180686i
$206$	3.46164e29	−	1.04887e31i	0.0200482	−	0.607457i
$207$	2.96924e30			0.161081
$208$	1.46538e31	−	1.12194e31i	0.744894	−	0.570317i
$209$	1.71609e28			0.000817644
$210$	−5.72488e28	+	1.73463e30i	−0.00255744	+	0.0774902i
$211$	−2.83699e31	+	2.83699e31i	−1.18863	+	1.18863i	−0.211178	+	0.977448i	$0.567730\pi$
$211$	−2.83699e31	+	2.83699e31i	−1.18863	+	1.18863i	−0.977448	+	0.211178i	$0.932270\pi$
$212$	−1.61761e31	−	1.84651e31i	−0.635828	−	0.725803i
$213$	1.28625e31	+	1.28625e31i	0.474462	+	0.474462i
$214$	2.54358e30	+	2.71720e30i	0.0880764	+	0.0940884i
$215$		−	1.40918e30i		−	0.0458193i
$216$	1.27014e31	+	1.55020e31i	0.387906	+	0.473437i
$217$		−	7.60774e31i		−	2.18298i
$218$	−1.66916e31	+	1.56250e31i	−0.450126	+	0.421364i
$219$	2.70165e31	+	2.70165e31i	0.684911	+	0.684911i
$220$	−8.65462e28	+	1.30974e30i	−0.00206320	+	0.0312234i
$221$	3.74105e31	−	3.74105e31i	0.838876	−	0.838876i
$222$	5.65348e31	+	1.86584e30i	1.19275	+	0.0393650i
$223$	1.61294e31			0.320260			0.160130	−	0.987096i	$-0.448809\pi$
$223$	1.61294e31			0.320260			0.160130	+	0.987096i	$0.448809\pi$
$224$	9.75213e30	−	5.85819e31i	0.182285	−	1.09500i
$225$	−2.83327e31			−0.498682
$226$	4.89010e31	+	1.61390e30i	0.810687	+	0.0267555i
$227$	−4.87355e31	+	4.87355e31i	−0.761196	+	0.761196i	−0.976539	−	0.215342i	$-0.930913\pi$
$227$	−4.87355e31	+	4.87355e31i	−0.761196	+	0.761196i	0.215342	+	0.976539i	$0.430913\pi$
$228$	−8.17538e27	+	1.23722e29i	−0.000120334	+	0.00182106i
$229$	9.30556e31	+	9.30556e31i	1.29111	+	1.29111i	0.934101	+	0.357010i	$0.116204\pi$
$229$	9.30556e31	+	9.30556e31i	1.29111	+	1.29111i	0.357010	+	0.934101i	$0.383796\pi$
$230$	1.02453e30	−	9.59065e29i	0.0134029	−	0.0125465i
$231$		−	6.04765e31i		−	0.746148i
$232$	−1.19285e31	+	9.77351e30i	−0.138835	+	0.113753i
$233$		−	1.08529e32i		−	1.19190i	−0.803022	−	0.595949i	$-0.796776\pi$
$233$		−	1.08529e32i		−	1.19190i	0.803022	−	0.595949i	$-0.203224\pi$
$234$	3.09456e31	+	3.30580e31i	0.320764	+	0.342659i
$235$	−4.22797e30	−	4.22797e30i	−0.0413729	−	0.0413729i
$236$	−1.04883e32	−	1.19725e32i	−0.969159	−	1.10630i
$237$	2.59702e31	−	2.59702e31i	0.226659	−	0.226659i
$238$	5.61568e30	−	1.70154e32i	0.0463034	−	1.40299i
$239$	1.46153e32			1.13877			0.569387	−	0.822070i	$-0.307181\pi$
$239$	1.46153e32			1.13877			0.569387	+	0.822070i	$0.307181\pi$
$240$	−9.40138e30	−	1.24791e30i	−0.0692372	−	0.00919036i
$241$	−1.84029e32			−1.28131			−0.640657	−	0.767827i	$-0.721338\pi$
$241$	−1.84029e32			−1.28131			−0.640657	+	0.767827i	$0.721338\pi$
$242$	−3.50123e30	+	1.06087e32i	−0.0230523	+	0.698481i
$243$	−1.04352e32	+	1.04352e32i	−0.649854	+	0.649854i
$244$	3.58477e31	−	3.14038e31i	0.211202	−	0.185020i
$245$	−1.67973e30	−	1.67973e30i	−0.00936477	−	0.00936477i
$246$	−7.10861e31	−	7.59384e31i	−0.375112	−	0.400717i
$247$		−	2.79810e29i		−	0.00139783i
$248$	4.13681e32	+	4.10781e31i	1.95690	+	0.194318i
$249$			3.15394e32i			1.41307i
$250$	−1.95842e31	+	1.83328e31i	−0.0831220	+	0.0778106i
$251$	1.15829e32	+	1.15829e32i	0.465824	+	0.465824i	0.900559	−	0.434734i	$-0.143158\pi$
$251$	1.15829e32	+	1.15829e32i	0.465824	+	0.465824i	−0.434734	+	0.900559i	$0.643158\pi$
$252$	1.45395e32	+	9.60756e30i	0.554170	+	0.0366189i
$253$	−3.45782e31	+	3.45782e31i	−0.124932	+	0.124932i
$254$	−4.03650e31	−	1.33218e30i	−0.138277	−	0.00456361i
$255$	−2.71872e31			−0.0883226
$256$	3.13281e32	+	8.46598e31i	0.965372	+	0.260878i
$257$	−5.21998e32			−1.52606			−0.763030	−	0.646363i	$-0.776289\pi$
$257$	−5.21998e32			−1.52606			−0.763030	+	0.646363i	$0.776289\pi$
$258$	−3.54590e32	−	1.17027e31i	−0.983696	−	0.0324653i
$259$	−2.90455e32	+	2.90455e32i	−0.764773	+	0.764773i
$260$	2.13555e31	+	1.41115e30i	0.0533788	+	0.00352721i
$261$	−2.67546e31	−	2.67546e31i	−0.0634967	−	0.0634967i
$262$	4.84875e32	−	4.53893e32i	1.09286	−	1.02302i
$263$		−	6.40615e32i		−	1.37150i	−0.727839	−	0.685748i	$-0.759475\pi$
$263$		−	6.40615e32i		−	1.37150i	0.727839	−	0.685748i	$-0.240525\pi$
$264$	3.28849e32	+	3.26543e31i	0.668873	+	0.0664183i
$265$		−	2.84677e31i		−	0.0550215i
$266$	−6.15328e29	−	6.57330e29i	−0.00113033	−	0.00120748i
$267$	−1.18223e32	−	1.18223e32i	−0.206444	−	0.206444i
$268$	1.74491e32	−	1.52860e32i	0.289702	−	0.253789i
$269$	−5.05095e32	+	5.05095e32i	−0.797475	+	0.797475i	−0.982697	−	0.185222i	$-0.940700\pi$
$269$	−5.05095e32	+	5.05095e32i	−0.797475	+	0.797475i	0.185222	+	0.982697i	$0.440700\pi$
$270$	−7.66597e29	+	2.32278e31i	−0.00115122	+	0.0348817i
$271$	−1.16718e33			−1.66745			−0.833727	−	0.552178i	$-0.813797\pi$
$271$	−1.16718e33			−1.66745			−0.833727	+	0.552178i	$0.813797\pi$
$272$	9.22204e32	+	1.22411e32i	1.25357	+	0.166395i
$273$	−9.86075e32			−1.27560
$274$	−1.65169e31	+	5.00461e32i	−0.0203375	+	0.616223i
$275$	3.29948e32	−	3.29948e32i	0.386771	−	0.386771i
$276$	−2.32819e32	−	2.65765e32i	−0.259864	−	0.296637i
$277$	−1.71970e32	−	1.71970e32i	−0.182799	−	0.182799i	0.609775	−	0.792574i	$-0.291260\pi$
$277$	−1.71970e32	−	1.71970e32i	−0.182799	−	0.182799i	−0.792574	+	0.609775i	$0.791260\pi$
$278$	−2.24059e32	−	2.39353e32i	−0.226859	−	0.242345i
$279$			1.01999e33i			0.983869i
$280$	5.32717e31	−	4.36477e31i	0.0489624	−	0.0401169i
$281$		−	2.82172e32i		−	0.247160i	−0.992335	−	0.123580i	$-0.960562\pi$
$281$		−	2.82172e32i		−	0.247160i	0.992335	−	0.123580i	$-0.0394376\pi$
$282$	−1.09899e33	+	1.02876e33i	−0.917550	+	0.858921i
$283$	9.60054e32	+	9.60054e32i	0.764150	+	0.764150i	0.977070	−	0.212919i	$-0.0682972\pi$
$283$	9.60054e32	+	9.60054e32i	0.764150	+	0.764150i	−0.212919	+	0.977070i	$0.568297\pi$
$284$	4.75927e31	−	7.20240e32i	0.0361195	−	0.546613i
$285$	−1.01673e29	+	1.01673e29i	−7.35865e−5	+	7.35865e-5i
$286$	−7.45353e32	−	2.45992e31i	−0.514541	−	0.0169816i
$287$	7.55359e32			0.497448
$288$	−1.30749e32	+	7.85419e32i	−0.0821559	+	0.493518i
$289$	9.99149e32			0.599114
$290$	−1.78734e31	−	5.89882e29i	−0.0102290	−	0.000337592i
$291$	−2.37020e33	+	2.37020e33i	−1.29488	+	1.29488i
$292$	9.99640e31	−	1.51280e33i	0.0521405	−	0.789065i
$293$	−2.88235e31	−	2.88235e31i	−0.0143560	−	0.0143560i	0.699892	−	0.714248i	$-0.253231\pi$
$293$	−2.88235e31	−	2.88235e31i	−0.0143560	−	0.0143560i	−0.714248	+	0.699892i	$0.753231\pi$
$294$	−4.36616e32	+	4.08717e32i	−0.207688	+	0.194417i
$295$		−	1.84580e32i		−	0.0838663i
$296$	−1.42256e33	−	1.73622e33i	−0.617493	−	0.753645i
$297$		−	8.09818e32i		−	0.335873i
$298$	−1.63333e33	−	1.74482e33i	−0.647374	−	0.691564i
$299$	5.63801e32	+	5.63801e32i	0.213582	+	0.213582i
$300$	2.22158e33	+	2.53595e33i	0.804498	+	0.918342i
$301$	1.82176e33	−	1.82176e33i	0.630729	−	0.630729i
$302$	−7.38287e31	+	2.23700e33i	−0.0244417	+	0.740580i
$303$	5.52528e33			1.74936
$304$	3.90657e30	−	2.99100e30i	0.00118305	−	0.000905782i
$305$	5.52663e31			0.0160108
$306$	−7.52905e31	+	2.28129e33i	−0.0208690	+	0.632327i
$307$	3.25456e33	−	3.25456e33i	0.863225	−	0.863225i	−0.128486	−	0.991711i	$-0.541012\pi$
$307$	3.25456e33	−	3.25456e33i	0.863225	−	0.863225i	0.991711	+	0.128486i	$0.0410117\pi$
$308$	−1.80508e33	+	1.58131e33i	−0.458208	+	0.401406i
$309$	−2.16654e33	−	2.16654e33i	−0.526414	−	0.526414i
$310$	3.29456e32	+	3.51944e32i	0.0766327	+	0.0818636i
$311$			6.39215e33i			1.42358i	0.702393	+	0.711790i	$0.252115\pi$
$311$			6.39215e33i			1.42358i	−0.702393	+	0.711790i	$0.747885\pi$
$312$	5.32432e32	−	5.36192e33i	0.113547	−	1.14349i
$313$		−	8.21270e33i		−	1.67740i	−0.544592	−	0.838701i	$-0.683315\pi$
$313$		−	8.21270e33i		−	1.67740i	0.544592	−	0.838701i	$-0.316685\pi$
$314$	3.25647e33	−	3.04839e33i	0.637084	−	0.596376i
$315$	1.19484e32	+	1.19484e32i	0.0223932	+	0.0223932i
$316$	−1.45421e33	−	9.60926e31i	−0.261127	−	0.0172550i
$317$	4.77051e33	−	4.77051e33i	0.820852	−	0.820852i	−0.165378	−	0.986230i	$-0.552884\pi$
$317$	4.77051e33	−	4.77051e33i	0.820852	−	0.820852i	0.986230	+	0.165378i	$0.0528844\pi$
$318$	−7.16326e33	−	2.36412e32i	−1.18126	−	0.0389856i
$319$	6.23140e32			0.0984943
$320$	2.08576e32	+	3.13239e32i	0.0316038	+	0.0474626i
$321$	1.08666e33			0.157862
$322$	2.56434e33	+	8.46320e31i	0.357208	+	0.0117891i
$323$	9.97331e30	−	9.97331e30i	0.00133231	−	0.00133231i
$324$	9.73468e33	+	6.43256e32i	1.24728	+	0.0824188i
$325$	−5.37984e33	−	5.37984e33i	−0.661217	−	0.661217i
$326$	−5.18611e33	+	4.85473e33i	−0.611511	+	0.572436i
$327$			6.67527e33i			0.755221i
$328$	−4.07856e32	+	4.10736e33i	−0.0442803	+	0.445930i
$329$		−	1.09316e34i		−	1.13904i
$330$	2.61895e32	+	2.79772e32i	0.0261933	+	0.0279812i
$331$	1.18627e34	+	1.18627e34i	1.13895	+	1.13895i	0.988639	+	0.150310i	$0.0480271\pi$
$331$	1.18627e34	+	1.18627e34i	1.13895	+	1.13895i	0.150310	+	0.988639i	$0.451973\pi$
$332$	9.41380e33	−	8.24681e33i	0.867762	−	0.760189i
$333$	3.89419e33	−	3.89419e33i	0.344683	−	0.344683i
$334$	−7.30541e32	+	2.21353e34i	−0.0620966	+	1.88152i
$335$	2.69011e32			0.0219617
$336$	−1.05406e34	−	1.37671e34i	−0.826579	−	1.07960i
$337$	1.91300e34			1.44116			0.720579	−	0.693373i	$-0.243876\pi$
$337$	1.91300e34			1.44116			0.720579	+	0.693373i	$0.243876\pi$
$338$	5.46276e31	−	1.65521e33i	0.00395400	−	0.119806i
$339$	1.01009e34	−	1.01009e34i	0.702531	−	0.702531i
$340$	7.10880e32	+	8.11475e32i	0.0475150	+	0.0542388i
$341$	−1.18782e34	−	1.18782e34i	−0.763075	−	0.763075i
$342$	8.24983e30	+	8.81296e30i	0.000509439	+	0.000544214i
$343$			1.43561e34i			0.852249i
$344$	8.92238e33	+	1.08897e34i	0.509263	+	0.621551i
$345$		−	4.09729e32i		−	0.0224874i
$346$	−2.02170e34	+	1.89252e34i	−1.06706	+	0.998880i
$347$	−8.30261e33	−	8.30261e33i	−0.421470	−	0.421470i	0.464240	−	0.885710i	$-0.346328\pi$
$347$	−8.30261e33	−	8.30261e33i	−0.421470	−	0.421470i	−0.885710	+	0.464240i	$0.846328\pi$
$348$	−2.96862e32	+	4.49254e33i	−0.0144955	+	0.219367i
$349$	−1.59528e34	+	1.59528e34i	−0.749367	+	0.749367i	−0.974360	−	0.224993i	$-0.927764\pi$
$349$	−1.59528e34	+	1.59528e34i	−0.749367	+	0.749367i	0.224993	+	0.974360i	$0.427764\pi$
$350$	−2.44691e34	−	8.07566e32i	−1.10586	−	0.0364972i
$351$	−1.32042e34			−0.574202
$352$	−7.62395e33	−	1.06692e34i	−0.319047	−	0.446485i
$353$	−7.09580e33			−0.285787			−0.142894	−	0.989738i	$-0.545641\pi$
$353$	−7.09580e33			−0.285787			−0.142894	+	0.989738i	$0.545641\pi$
$354$	−4.64455e34	−	1.53286e33i	−1.80053	−	0.0594236i
$355$	5.91883e32	−	5.91883e32i	0.0220878	−	0.0220878i
$356$	−4.37439e32	+	6.61995e33i	−0.0157160	+	0.237837i
$357$	−3.51469e34	−	3.51469e34i	−1.21581	−	1.21581i
$358$	−3.38304e34	+	3.16687e34i	−1.12690	+	1.05490i
$359$			4.84852e34i			1.55537i	0.628652	+	0.777686i	$0.283607\pi$
$359$			4.84852e34i			1.55537i	−0.628652	+	0.777686i	$0.716393\pi$
$360$	−7.14224e32	+	5.85193e32i	−0.0220674	+	0.0180807i
$361$			3.36005e34i			0.999998i
$362$	−4.09111e34	−	4.37037e34i	−1.17294	−	1.25300i
$363$	2.19132e34	+	2.19132e34i	0.605294	+	0.605294i
$364$	2.57835e34	+	2.94321e34i	0.686235	+	0.783343i
$365$	1.24320e33	−	1.24320e33i	0.0318850	−	0.0318850i
$366$	4.58964e32	−	1.39065e34i	0.0113445	−	0.343736i
$367$	5.71242e34			1.36091			0.680453	−	0.732791i	$-0.261783\pi$
$367$	5.71242e34			1.36091			0.680453	+	0.732791i	$0.261783\pi$
$368$	−1.84481e33	+	1.38982e34i	−0.0423650	+	0.319164i
$369$	−1.01272e34			−0.224200
$370$	8.58588e31	−	2.60151e33i	0.00183257	−	0.0555268i
$371$	3.68022e34	−	3.68022e34i	0.757402	−	0.757402i
$372$	9.12950e34	−	7.99775e34i	1.81183	−	1.58722i
$373$	−1.49771e34	−	1.49771e34i	−0.286654	−	0.286654i	0.549102	−	0.835756i	$-0.314970\pi$
$373$	−1.49771e34	−	1.49771e34i	−0.286654	−	0.286654i	−0.835756	+	0.549102i	$0.814970\pi$
$374$	−2.56900e34	−	2.74435e34i	−0.474239	−	0.506610i
$375$			7.83209e33i			0.139462i
$376$	5.94421e34	+	5.90254e33i	1.02108	+	0.101392i
$377$		−	1.01604e34i		−	0.168384i
$378$	−3.10193e34	+	2.90372e34i	−0.496013	+	0.464319i
$379$	2.38128e34	+	2.38128e34i	0.367436	+	0.367436i	0.866541	−	0.499105i	$-0.166338\pi$
$379$	2.38128e34	+	2.38128e34i	0.367436	+	0.367436i	−0.499105	+	0.866541i	$0.666338\pi$
$380$	5.69318e30	+	3.76199e29i	8.47767e−5	+	5.60195e-6i
$381$	−8.33774e33	+	8.33774e33i	−0.119829	+	0.119829i
$382$	3.75667e33	+	1.23983e32i	0.0521132	+	0.00171992i
$383$	−6.39308e34			−0.856104			−0.428052	−	0.903754i	$-0.640800\pi$
$383$	−6.39308e34			−0.856104			−0.428052	+	0.903754i	$0.640800\pi$
$384$	8.05519e34	−	4.98822e34i	1.04137	−	0.644873i
$385$	−2.78289e33			−0.0347357
$386$	1.27001e35	+	4.19146e33i	1.53066	+	0.0505169i
$387$	−2.44246e34	+	2.44246e34i	−0.284269	+	0.284269i
$388$	1.32720e35	+	8.76998e33i	1.49179	+	0.0985758i
$389$	−4.18739e34	−	4.18739e34i	−0.454594	−	0.454594i	0.442282	−	0.896876i	$-0.354169\pi$
$389$	−4.18739e34	−	4.18739e34i	−0.454594	−	0.454594i	−0.896876	+	0.442282i	$0.854169\pi$
$390$	4.56171e33	−	4.27023e33i	0.0478361	−	0.0447795i
$391$			4.01914e34i			0.407142i
$392$	2.36157e34	+	2.34501e33i	0.231121	+	0.0229500i
$393$		−	1.93911e35i		−	1.83359i
$394$	7.00938e34	+	7.48784e34i	0.640443	+	0.684160i
$395$	−1.19505e33	−	1.19505e33i	−0.0105518	−	0.0105518i
$396$	2.42011e34	−	2.12010e34i	0.206514	−	0.180914i
$397$	−4.03916e34	+	4.03916e34i	−0.333135	+	0.333135i	−0.853776	−	0.520641i	$-0.825693\pi$
$397$	−4.03916e34	+	4.03916e34i	−0.333135	+	0.333135i	0.520641	+	0.853776i	$0.325693\pi$
$398$	−4.74582e33	+	1.43798e35i	−0.0378347	+	1.14639i
$399$	−2.62879e32			−0.00202592
$400$	1.76034e34	−	1.32618e35i	0.131155	−	0.988082i
$401$	−2.37609e35			−1.71165			−0.855824	−	0.517266i	$-0.826950\pi$
$401$	−2.37609e35			−1.71165			−0.855824	+	0.517266i	$0.826950\pi$
$402$	2.23403e33	−	6.76908e34i	0.0155610	−	0.471496i
$403$	−1.93676e35	+	1.93676e35i	−1.30454	+	1.30454i
$404$	−1.44473e35	−	1.64917e35i	−0.941104	−	1.07428i
$405$	7.99981e33	+	7.99981e33i	0.0504007	+	0.0504007i
$406$	−2.23436e34	−	2.38688e34i	−0.136161	−	0.145455i
$407$			9.06995e34i			0.534663i
$408$	2.10093e35	−	1.72138e35i	1.19812	−	0.981669i
$409$		−	1.75134e33i		−	0.00966284i	−0.999988	−	0.00483142i	$-0.998462\pi$
$409$		−	1.75134e33i		−	0.00966284i	0.999988	−	0.00483142i	$-0.00153790\pi$
$410$	−3.49439e33	+	3.27110e33i	−0.0186547	+	0.0174627i
$411$	1.03375e35	+	1.03375e35i	0.534010	+	0.534010i
$412$	−8.01642e33	+	1.21316e35i	−0.0400745	+	0.606465i
$413$	2.38620e35	−	2.38620e35i	1.15447	−	1.15447i
$414$	−3.43806e34	−	1.13468e33i	−0.160994	−	0.00531335i
$415$	1.45132e34			0.0657831
$416$	−1.73963e35	+	1.24309e35i	−0.763301	+	0.545436i
$417$	−9.57217e34			−0.406606
$418$	−1.98704e32	−	6.55793e30i	−0.000817199	−	2.69704e-5i
$419$	−2.08304e35	+	2.08304e35i	−0.829484	+	0.829484i	−0.987445	−	0.157961i	$-0.949508\pi$
$419$	−2.08304e35	+	2.08304e35i	−0.829484	+	0.829484i	0.157961	+	0.987445i	$0.449508\pi$
$420$	1.32576e33	−	2.00633e34i	0.00511210	−	0.0773637i
$421$	9.64197e34	+	9.64197e34i	0.360046	+	0.360046i	0.863830	−	0.503784i	$-0.168059\pi$
$421$	9.64197e34	+	9.64197e34i	0.360046	+	0.360046i	−0.503784	+	0.863830i	$0.668059\pi$
$422$	3.39335e35	−	3.17652e35i	1.22719	−	1.14877i
$423$			1.46562e35i			0.513367i
$424$	1.80246e35	+	2.19988e35i	0.611541	+	0.746381i
$425$		−	3.83509e35i		−	1.26045i
$426$	−1.44019e35	−	1.53850e35i	−0.458553	−	0.489854i
$427$	7.14468e34	+	7.14468e34i	0.220397	+	0.220397i
$428$	−2.84136e34	−	3.24343e34i	−0.0849249	−	0.0969425i
$429$	−1.53959e35	+	1.53959e35i	−0.445895	+	0.445895i
$430$	−5.38512e32	+	1.63169e34i	−0.00151137	+	0.0457944i
$431$	5.40179e35			1.46925			0.734623	−	0.678476i	$-0.237359\pi$
$431$	5.40179e35			1.46925			0.734623	+	0.678476i	$0.237359\pi$
$432$	−1.41145e35	−	1.84350e35i	−0.372079	−	0.485974i
$433$	1.71619e35			0.438510			0.219255	−	0.975668i	$-0.429637\pi$
$433$	1.71619e35			0.438510			0.219255	+	0.975668i	$0.429637\pi$
$434$	−2.90726e34	+	8.80896e35i	−0.0720066	+	2.18179i
$435$	−3.69190e33	+	3.69190e33i	−0.00886431	+	0.00886431i
$436$	1.99241e35	−	1.74542e35i	0.463780	−	0.406287i
$437$	1.50304e32	+	1.50304e32i	0.000339213	+	0.000339213i
$438$	−3.02498e35	−	3.23147e35i	−0.661946	−	0.707130i
$439$		−	6.02057e35i		−	1.27752i	−0.769407	−	0.638758i	$-0.779448\pi$
$439$		−	6.02057e35i		−	1.27752i	0.769407	−	0.638758i	$-0.220552\pi$
$440$	1.50262e33	−	1.51323e34i	0.00309200	−	0.0311383i
$441$			5.82277e34i			0.116201i
$442$	−4.47470e35	+	4.18877e35i	−0.866090	+	0.810749i
$443$	3.66645e35	+	3.66645e35i	0.688327	+	0.688327i	0.961862	−	0.273535i	$-0.0881929\pi$
$443$	3.66645e35	+	3.66645e35i	0.688327	+	0.688327i	−0.273535	+	0.961862i	$0.588193\pi$
$444$	−6.53900e35	−	4.32090e34i	−1.19081	−	0.0786871i
$445$	−5.44018e33	+	5.44018e33i	−0.00961065	+	0.00961065i
$446$	−1.86761e35	−	6.16377e33i	−0.320086	−	0.0105639i
$447$	−6.97788e35			−1.16031
$448$	−1.35306e35	+	6.74589e35i	−0.218305	+	1.08839i
$449$	−8.33632e35			−1.30511			−0.652557	−	0.757739i	$-0.726304\pi$
$449$	−8.33632e35			−1.30511			−0.652557	+	0.757739i	$0.726304\pi$
$450$	3.28063e35	+	1.08272e34i	0.498411	+	0.0164493i
$451$	1.17937e35	−	1.17937e35i	0.173886	−	0.173886i
$452$	−5.65604e35	−	3.73745e34i	−0.809364	−	0.0534818i
$453$	4.62072e35	+	4.62072e35i	0.641776	+	0.641776i
$454$	5.82930e35	−	5.45682e35i	0.785891	−	0.735674i
$455$			4.53753e34i			0.0593835i
$456$	1.41942e32	−	1.42944e33i	0.000180337	−	0.00181610i
$457$			6.54695e35i			0.807552i	0.914858	+	0.403776i	$0.132303\pi$
$457$			6.54695e35i			0.807552i	−0.914858	+	0.403776i	$0.867697\pi$
$458$	−1.04192e36	−	1.11304e36i	−1.24782	−	1.33300i
$459$	−4.70639e35	−	4.70639e35i	−0.547289	−	0.547289i
$460$	−1.22295e34	+	1.07134e34i	−0.0138095	+	0.0120976i
$461$	5.10724e35	−	5.10724e35i	0.560047	−	0.560047i	−0.369274	−	0.929321i	$-0.620394\pi$
$461$	5.10724e35	−	5.10724e35i	0.560047	−	0.560047i	0.929321	+	0.369274i	$0.120394\pi$
$462$	−2.31108e34	+	7.00253e35i	−0.0246120	+	0.745742i
$463$	−8.05556e35			−0.833206			−0.416603	−	0.909089i	$-0.636779\pi$
$463$	−8.05556e35			−0.833206			−0.416603	+	0.909089i	$0.636779\pi$
$464$	1.41854e35	−	1.08608e35i	0.142511	−	0.109112i
$465$	1.40749e35			0.137351
$466$	−4.14736e34	+	1.25664e36i	−0.0393153	+	1.19125i
$467$	6.63377e35	−	6.63377e35i	0.610917	−	0.610917i	−0.332268	−	0.943185i	$-0.607814\pi$
$467$	6.63377e35	−	6.63377e35i	0.610917	−	0.610917i	0.943185	+	0.332268i	$0.107814\pi$
$468$	−3.45684e35	−	3.94602e35i	−0.309286	−	0.353053i
$469$	3.47771e35	+	3.47771e35i	0.302315	+	0.302315i
$470$	4.73397e34	+	5.05711e34i	0.0399857	+	0.0427151i
$471$		−	1.30232e36i		−	1.06890i
$472$	1.16869e36	+	1.42637e36i	0.932139	+	1.13767i
$473$		−	5.68874e35i		−	0.440951i
$474$	−3.10632e35	+	2.90783e35i	−0.234012	+	0.219059i
$475$	−1.43422e33	−	1.43422e33i	−0.00105015	−	0.00105015i
$476$	−1.30047e35	+	1.96806e36i	−0.0925565	+	1.40070i
$477$	−4.93415e35	+	4.93415e35i	−0.341361	+	0.341361i
$478$	−1.69230e36	−	5.58518e34i	−1.13815	−	0.0375630i
$479$	1.58203e36			1.03439			0.517197	−	0.855866i	$-0.326975\pi$
$479$	1.58203e36			1.03439			0.517197	+	0.855866i	$0.326975\pi$
$480$	1.08381e35	+	1.80422e34i	0.0688964	+	0.0114692i
$481$	1.47887e36			0.914050
$482$	2.13086e36	+	7.03256e34i	1.28062	+	0.0422648i
$483$	5.29687e35	−	5.29687e35i	0.309551	−	0.309551i
$484$	8.10811e34	−	1.22704e36i	0.0460794	−	0.697340i
$485$	1.09067e35	+	1.09067e35i	0.0602810	+	0.0602810i
$486$	1.24816e36	−	1.16841e36i	0.670936	−	0.628064i
$487$		−	1.57697e36i		−	0.824483i	−0.911075	−	0.412242i	$-0.864746\pi$
$487$		−	1.57697e36i		−	0.824483i	0.911075	−	0.412242i	$-0.135254\pi$
$488$	−4.27079e35	+	3.49924e35i	−0.217190	+	0.177953i
$489$			2.07402e36i			1.02599i
$490$	1.88076e34	+	2.00914e34i	0.00905077	+	0.00966857i
$491$	−1.18562e36	−	1.18562e36i	−0.555065	−	0.555065i	0.372833	−	0.927898i	$-0.378386\pi$
$491$	−1.18562e36	−	1.18562e36i	−0.555065	−	0.555065i	−0.927898	+	0.372833i	$0.878386\pi$
$492$	7.94082e35	+	9.06451e35i	0.361690	+	0.412872i
$493$	3.62148e35	−	3.62148e35i	0.160492	−	0.160492i
$494$	−1.06928e32	+	3.23990e33i	−4.61080e−5	+	0.00139707i
$495$	3.73108e34			0.0156554
$496$	−4.77429e36	−	6.33726e35i	−1.94942	−	0.258761i
$497$	1.53034e36			0.608102
$498$	1.20526e35	−	3.65193e36i	0.0466107	−	1.41230i
$499$	3.28956e36	−	3.28956e36i	1.23817	−	1.23817i	0.277425	−	0.960747i	$-0.410519\pi$
$499$	3.28956e36	−	3.28956e36i	1.23817	−	1.23817i	0.960747	−	0.277425i	$-0.0894810\pi$
$500$	2.33770e35	−	2.04790e35i	0.0856433	−	0.0750265i
$501$	4.57224e36	+	4.57224e36i	1.63050	+	1.63050i
$502$	−1.29691e36	−	1.38544e36i	−0.450206	−	0.480936i
$503$		−	1.78436e36i		−	0.602997i	−0.953467	−	0.301498i	$-0.902513\pi$
$503$		−	1.78436e36i		−	0.602997i	0.953467	−	0.301498i	$-0.0974868\pi$
$504$	−1.67985e36	−	1.66807e35i	−0.552661	−	0.0548786i
$505$		−	2.54252e35i		−	0.0814387i
$506$	4.13593e35	−	3.87165e35i	0.128985	−	0.120744i
$507$	−3.41898e35	−	3.41898e35i	−0.103822	−	0.103822i
$508$	4.66874e35	+	3.08505e34i	0.138051	+	0.00912225i
$509$	−3.77562e35	+	3.77562e35i	−0.108717	+	0.108717i	−0.759373	−	0.650656i	$-0.774494\pi$
$509$	−3.77562e35	+	3.77562e35i	−0.108717	+	0.108717i	0.650656	+	0.759373i	$0.274494\pi$
$510$	3.14799e35	+	1.03894e34i	0.0882746	+	0.00291337i
$511$	3.21434e36			0.877828
$512$	−3.59511e36	−	1.09999e36i	−0.956241	−	0.292579i
$513$	−3.52011e33			−0.000911953
$514$	6.04418e36	+	1.99479e35i	1.52523	+	0.0503378i
$515$	−9.96957e34	+	9.96957e34i	−0.0245064	+	0.0245064i
$516$	4.10130e36	+	2.71010e35i	0.982089	+	0.0648954i
$517$	−1.70679e36	−	1.70679e36i	−0.398160	−	0.398160i
$518$	3.47416e36	−	3.25217e36i	0.789583	−	0.739131i
$519$			8.08518e36i			1.79032i
$520$	−2.46734e35	−	2.45004e34i	−0.0532334	−	0.00528602i
$521$		−	5.85271e36i		−	1.23041i	−0.788369	−	0.615203i	$-0.789074\pi$
$521$		−	5.85271e36i		−	1.23041i	0.788369	−	0.615203i	$-0.210926\pi$
$522$	2.99565e35	+	3.20013e35i	0.0613677	+	0.0655566i
$523$	−3.62392e36	−	3.62392e36i	−0.723446	−	0.723446i	0.245859	−	0.969306i	$-0.420930\pi$
$523$	−3.62392e36	−	3.62392e36i	−0.723446	−	0.723446i	−0.969306	+	0.245859i	$0.920930\pi$
$524$	−5.78779e36	+	5.07030e36i	−1.12601	+	0.986419i
$525$	−5.05432e36	+	5.05432e36i	−0.958323	+	0.958323i
$526$	−2.44808e35	+	7.41764e36i	−0.0452395	+	1.37075i
$527$	−1.38064e37			−2.48679
$528$	−3.79524e36	−	5.03770e35i	−0.666318	−	0.0884452i
$529$	5.23750e36			0.896339
$530$	−1.08788e34	+	3.29625e35i	−0.00181491	+	0.0549916i
$531$	−3.19923e36	+	3.19923e36i	−0.520318	+	0.520318i
$532$	6.87365e33	+	7.84633e33i	0.00108988	+	0.00124411i
$533$	−1.92297e36	−	1.92297e36i	−0.297273	−	0.297273i
$534$	1.32372e36	+	1.41408e36i	0.199522	+	0.213141i
$535$		−	5.00039e34i		−	0.00734899i
$536$	−2.07883e36	+	1.70327e36i	−0.297916	+	0.244095i
$537$			1.35294e37i			1.89072i
$538$	6.04147e36	−	5.65544e36i	0.823346	−	0.770736i
$539$	−6.78089e35	−	6.78089e35i	−0.0901236	−	0.0901236i
$540$	1.77528e34	−	2.68660e35i	0.00230118	−	0.0348247i
$541$	−2.15850e36	+	2.15850e36i	−0.272891	+	0.272891i	−0.830263	−	0.557372i	$-0.811810\pi$
$541$	−2.15850e36	+	2.15850e36i	−0.272891	+	0.272891i	0.557372	+	0.830263i	$0.311810\pi$
$542$	1.35147e37	+	4.46033e35i	1.66655	+	0.0550017i
$543$	−1.74779e37			−2.10229
$544$	−1.06314e37	−	1.76980e36i	−1.24739	−	0.207654i
$545$	3.07170e35			0.0351581
$546$	1.14177e37	+	3.76823e35i	1.27491	+	0.0420763i
$547$	−1.59028e36	+	1.59028e36i	−0.173239	+	0.173239i	−0.788401	−	0.615162i	$-0.789091\pi$
$547$	−1.59028e36	+	1.59028e36i	−0.173239	+	0.173239i	0.615162	+	0.788401i	$0.289091\pi$
$548$	3.82497e35	−	5.78850e36i	0.0406528	−	0.615217i
$549$	−9.57901e35	−	9.57901e35i	−0.0993331	−	0.0993331i
$550$	−3.94653e36	+	3.69436e36i	−0.399319	+	0.373803i
$551$		−	2.70866e33i		−	0.000267429i
$552$	2.59424e36	+	3.16625e36i	0.249938	+	0.305047i
$553$		−	3.08985e36i		−	0.290502i
$554$	1.92551e36	+	2.05694e36i	0.176670	+	0.188730i
$555$	−5.37365e35	−	5.37365e35i	−0.0481187	−	0.0481187i
$556$	2.50289e36	+	2.85707e36i	0.218742	+	0.249696i
$557$	−5.39157e36	+	5.39157e36i	−0.459907	+	0.459907i	−0.898625	−	0.438718i	$-0.855433\pi$
$557$	−5.39157e36	+	5.39157e36i	−0.459907	+	0.459907i	0.438718	+	0.898625i	$0.355433\pi$
$558$	3.89782e35	−	1.18103e37i	0.0324534	−	0.983334i
$559$	−9.27554e36			−0.753841
$560$	−6.33509e35	+	4.85036e35i	−0.0502591	+	0.0384801i
$561$	−1.09752e37			−0.849990
$562$	−1.07831e35	+	3.26725e36i	−0.00815270	+	0.247026i
$563$	1.55967e37	−	1.55967e37i	1.15125	−	1.15125i	0.164951	−	0.986302i	$-0.447254\pi$
$563$	1.55967e37	−	1.55967e37i	1.15125	−	1.15125i	0.986302	−	0.164951i	$-0.0527465\pi$
$564$	1.31182e37	−	1.14920e37i	0.945383	−	0.828187i
$565$	−4.64805e35	−	4.64805e35i	−0.0327052	−	0.0327052i
$566$	−1.07495e37	−	1.14833e37i	−0.738529	−	0.788940i
$567$			2.06839e37i			1.38759i
$568$	−8.26308e35	+	8.32143e36i	−0.0541302	+	0.545124i
$569$			4.35800e36i			0.278786i	0.990237	+	0.139393i	$0.0445152\pi$
$569$			4.35800e36i			0.278786i	−0.990237	+	0.139393i	$0.955485\pi$
$570$	1.21611e33	−	1.13841e33i	7.59737e−5	−	7.11191e-5i
$571$	−9.35262e36	−	9.35262e36i	−0.570618	−	0.570618i	0.361683	−	0.932301i	$-0.382202\pi$
$571$	−9.35262e36	−	9.35262e36i	−0.570618	−	0.570618i	−0.932301	+	0.361683i	$0.882202\pi$
$572$	8.62099e36	+	5.69665e35i	0.513701	+	0.0339448i
$573$	7.75974e35	−	7.75974e35i	0.0451606	−	0.0451606i
$574$	−8.74625e36	−	2.88656e35i	−0.497177	−	0.0164086i
$575$	5.77974e36			0.320917
$576$	1.81407e36	−	9.04435e36i	0.0983901	−	0.490539i
$577$	−5.52716e35			−0.0292839			−0.0146419	−	0.999893i	$-0.504661\pi$
$577$	−5.52716e35			−0.0292839			−0.0146419	+	0.999893i	$0.504661\pi$
$578$	−1.15691e37	−	3.81819e35i	−0.598788	−	0.0197621i
$579$	2.62331e37	−	2.62331e37i	1.32645	−	1.32645i
$580$	2.06729e35	+	1.36604e34i	0.0102123	+	0.000674817i
$581$	1.87623e37	+	1.87623e37i	0.905541	+	0.905541i
$582$	2.83501e37	−	2.65386e37i	1.33689	−	1.25146i
$583$		−	1.14921e37i		−	0.529510i
$584$	−1.73558e36	+	1.74784e37i	−0.0781398	+	0.786916i
$585$		−	6.08356e35i		−	0.0267642i
$586$	3.22730e35	+	3.44760e35i	0.0138746	+	0.0148217i
$587$	2.02113e37	+	2.02113e37i	0.849140	+	0.849140i	0.990026	−	0.140886i	$-0.0449950\pi$
$587$	2.02113e37	+	2.02113e37i	0.849140	+	0.849140i	−0.140886	+	0.990026i	$0.544995\pi$
$588$	5.21174e36	−	4.56566e36i	0.213988	−	0.187460i
$589$	−5.16322e34	+	5.16322e34i	−0.00207188	+	0.00207188i
$590$	−7.05363e34	+	2.13724e36i	−0.00276637	+	0.0838207i
$591$	2.99453e37			1.14788
$592$	1.58082e37	+	2.06472e37i	0.592297	+	0.773603i
$593$	4.73145e35			0.0173283			0.00866415	−	0.999962i	$-0.497242\pi$
$593$	4.73145e35			0.0173283			0.00866415	+	0.999962i	$0.497242\pi$
$594$	−3.09468e35	+	9.37683e36i	−0.0110789	+	0.335690i
$595$	−1.61732e36	+	1.61732e36i	−0.0566001	+	0.0566001i
$596$	1.82455e37	+	2.08274e37i	0.624210	+	0.712541i
$597$	2.97027e37	+	2.97027e37i	0.993442	+	0.993442i
$598$	−6.31276e36	−	6.74367e36i	−0.206421	−	0.220511i
$599$		−	3.90154e37i		−	1.24731i	−0.781701	−	0.623654i	$-0.785647\pi$
$599$		−	3.90154e37i		−	1.24731i	0.781701	−	0.623654i	$-0.214353\pi$
$600$	−2.47544e37	−	3.02126e37i	−0.773769	−	0.944379i
$601$		−	2.89762e37i		−	0.885597i	−0.896621	−	0.442799i	$-0.853986\pi$
$601$		−	2.89762e37i		−	0.885597i	0.896621	−	0.442799i	$-0.146014\pi$
$602$	−2.17902e37	+	2.03978e37i	−0.651190	+	0.609580i
$603$	−4.66263e36	−	4.66263e36i	−0.136253	−	0.136253i
$604$	1.70971e36	−	2.58738e37i	0.0488568	−	0.739371i
$605$	1.00836e36	−	1.00836e36i	0.0281785	−	0.0281785i
$606$	−6.39769e37	−	2.11146e36i	−1.74841	−	0.0577035i
$607$	−2.11146e37			−0.564334			−0.282167	−	0.959365i	$-0.591053\pi$
$607$	−2.11146e37			−0.564334			−0.282167	+	0.959365i	$0.591053\pi$
$608$	−4.63769e34	+	3.31398e34i	−0.00121228	+	0.000866265i
$609$	−9.54558e36			−0.244044
$610$	−6.39925e35	−	2.11197e34i	−0.0160021	−	0.000528123i
$611$	−2.78294e37	+	2.78294e37i	−0.680687	+	0.680687i
$612$	1.74357e36	−	2.63862e37i	0.0417152	−	0.631295i
$613$	−1.24980e36	−	1.24980e36i	−0.0292498	−	0.0292498i	0.692331	−	0.721580i	$-0.256584\pi$
$613$	−1.24980e36	−	1.24980e36i	−0.0292498	−	0.0292498i	−0.721580	+	0.692331i	$0.756584\pi$
$614$	−3.89280e37	+	3.64406e37i	−0.891230	+	0.834282i
$615$			1.39747e36i			0.0312989i
$616$	2.15052e37	−	1.76201e37i	0.471199	−	0.386073i
$617$		−	8.27994e37i		−	1.77491i	−0.460890	−	0.887457i	$-0.652470\pi$
$617$		−	8.27994e37i		−	1.77491i	0.460890	−	0.887457i	$-0.347530\pi$
$618$	2.42583e37	+	2.59141e37i	0.508763	+	0.543491i
$619$	4.28402e37	+	4.28402e37i	0.879078	+	0.879078i	0.993439	−	0.114361i	$-0.0364821\pi$
$619$	4.28402e37	+	4.28402e37i	0.879078	+	0.879078i	−0.114361	+	0.993439i	$0.536482\pi$
$620$	−3.68025e36	−	4.20104e36i	−0.0738907	−	0.0843469i
$621$	7.09284e36	−	7.09284e36i	0.139342	−	0.139342i
$622$	2.44273e36	−	7.40143e37i	0.0469574	−	1.42280i
$623$	−1.40658e37			−0.264592
$624$	−8.21402e36	+	6.18818e37i	−0.151204	+	1.13912i
$625$	−5.49703e37			−0.990256
$626$	−3.13844e36	+	9.50943e37i	−0.0553299	+	1.67649i
$627$	−4.10442e34	+	4.10442e34i	−0.000708173	+	0.000708173i
$628$	−3.88714e37	+	3.40526e37i	−0.656409	+	0.575037i
$629$	5.27115e37	+	5.27115e37i	0.871207	+	0.871207i
$630$	−1.33783e36	−	1.42915e36i	−0.0216424	−	0.0231197i
$631$			3.85612e37i			0.610596i	0.952257	+	0.305298i	$0.0987561\pi$
$631$			3.85612e37i			0.610596i	−0.952257	+	0.305298i	$0.901244\pi$
$632$	1.68015e37	+	1.66837e36i	0.260416	+	0.0258590i
$633$		−	1.35706e38i		−	2.05897i
$634$	−5.70605e37	+	5.34144e37i	−0.847482	+	0.793329i
$635$	3.83670e35	+	3.83670e35i	0.00557844	+	0.00557844i
$636$	8.28525e37	+	5.47480e36i	1.17933	+	0.0779287i
$637$	−1.10563e37	+	1.10563e37i	−0.154074	+	0.154074i
$638$	−7.21529e36	−	2.38130e35i	−0.0984407	−	0.00324888i
$639$	−2.05176e37			−0.274072
$640$	−2.29539e36	−	3.70668e36i	−0.0300211	−	0.0484793i
$641$	−1.05690e38			−1.35347			−0.676736	−	0.736226i	$-0.736606\pi$
$641$	−1.05690e38			−1.35347			−0.676736	+	0.736226i	$0.736606\pi$
$642$	−1.25824e37	−	4.15262e35i	−0.157776	−	0.00520714i
$643$	6.35597e37	−	6.35597e37i	0.780430	−	0.780430i	−0.199473	−	0.979903i	$-0.563923\pi$
$643$	6.35597e37	−	6.35597e37i	0.780430	−	0.780430i	0.979903	+	0.199473i	$0.0639232\pi$
$644$	−2.96600e37	−	1.95990e36i	−0.356625	−	0.0235654i
$645$	3.37039e36	+	3.37039e36i	0.0396848	+	0.0396848i
$646$	−1.19292e35	+	1.11669e35i	−0.00137553	+	0.00128764i
$647$		−	6.52349e36i		−	0.0736668i	−0.999321	−	0.0368334i	$-0.988273\pi$
$647$		−	6.52349e36i		−	0.0736668i	0.999321	−	0.0368334i	$-0.0117271\pi$
$648$	−1.12471e38	−	1.11683e37i	−1.24388	−	0.123516i
$649$		−	7.45131e37i		−	0.807104i
$650$	6.02369e37	+	6.43487e37i	0.639046	+	0.682667i
$651$	1.81957e38	+	1.81957e38i	1.89071	+	1.89071i
$652$	6.19048e37	−	5.42307e37i	0.630060	−	0.551954i
$653$	1.02394e38	−	1.02394e38i	1.02081	−	1.02081i	0.0210340	−	0.999779i	$-0.493304\pi$
$653$	1.02394e38	−	1.02394e38i	1.02081	−	1.02081i	0.999779	−	0.0210340i	$-0.00669582\pi$
$654$	2.55092e36	−	7.72925e37i	0.0249113	−	0.754810i
$655$	−8.92302e36			−0.0853600
$656$	6.29215e36	−	4.74030e37i	0.0589654	−	0.444226i
$657$	−4.30953e37			−0.395637
$658$	−4.17746e36	+	1.26576e38i	−0.0375719	+	1.13842i
$659$	−1.46646e35	+	1.46646e35i	−0.00129217	+	0.00129217i	−0.707753	−	0.706460i	$-0.750291\pi$
$659$	−1.46646e35	+	1.46646e35i	−0.00129217	+	0.00129217i	0.706460	+	0.707753i	$0.250291\pi$
$660$	−2.92555e36	−	3.33955e36i	−0.0252560	−	0.0288300i
$661$	1.66122e37	+	1.66122e37i	0.140510	+	0.140510i	0.773863	−	0.633353i	$-0.218322\pi$
$661$	1.66122e37	+	1.66122e37i	0.140510	+	0.140510i	−0.633353	+	0.773863i	$0.718322\pi$
$662$	−1.32824e38	−	1.41890e38i	−1.10076	−	1.17590i
$663$			1.78952e38i			1.45313i
$664$	−1.12153e38	+	9.18918e37i	−0.892365	+	0.731152i
$665$			1.20967e34i			9.43134e-5i
$666$	−4.65788e37	+	4.36025e37i	−0.355865	+	0.333126i
$667$	5.45781e36	+	5.45781e36i	0.0408620	+	0.0408620i
$668$	1.69178e37	−	2.56024e38i	0.124126	−	1.87845i
$669$	−3.85772e37	+	3.85772e37i	−0.277382	+	0.277382i
$670$	−3.11487e36	−	1.02801e35i	−0.0219497	−	0.000724417i
$671$	2.23104e37			0.154083
$672$	1.16788e38	+	1.63437e38i	0.790518	+	1.10628i
$673$	9.02708e37			0.598885			0.299443	−	0.954114i	$-0.403199\pi$
$673$	9.02708e37			0.598885			0.299443	+	0.954114i	$0.403199\pi$
$674$	−2.21505e38	−	7.31043e36i	−1.44037	−	0.0475373i
$675$	−6.76804e37	+	6.76804e37i	−0.431382	+	0.431382i
$676$	−1.26506e36	+	1.91447e37i	−0.00790370	+	0.119610i
$677$	−6.16184e37	−	6.16184e37i	−0.377367	−	0.377367i	0.492785	−	0.870151i	$-0.335979\pi$
$677$	−6.16184e37	−	6.16184e37i	−0.377367	−	0.377367i	−0.870151	+	0.492785i	$0.835979\pi$
$678$	−1.20818e38	+	1.13098e38i	−0.725322	+	0.678975i
$679$			2.81998e38i			1.65960i
$680$	−7.92113e36	−	9.66768e36i	−0.0457001	−	0.0557766i
$681$		−	2.33125e38i		−	1.31857i
$682$	1.32998e38	+	1.42076e38i	0.737489	+	0.787830i
$683$	−1.05374e38	−	1.05374e38i	−0.572866	−	0.572866i	0.360062	−	0.932928i	$-0.382755\pi$
$683$	−1.05374e38	−	1.05374e38i	−0.572866	−	0.572866i	−0.932928	+	0.360062i	$0.882755\pi$
$684$	−9.21564e34	−	1.05197e35i	−0.000491211	−	0.000560722i
$685$	4.75690e36	−	4.75690e36i	0.0248600	−	0.0248600i
$686$	5.48611e36	−	1.66228e38i	0.0281118	−	0.851785i
$687$	−4.45128e38			−2.23650
$688$	−9.91502e37	−	1.29501e38i	−0.488483	−	0.638011i
$689$	−1.87380e38			−0.905240
$690$	−1.56576e35	+	4.74423e36i	−0.000741758	+	0.0224752i
$691$	2.18408e38	−	2.18408e38i	1.01465	−	1.01465i	0.0147576	−	0.999891i	$-0.495302\pi$
$691$	2.18408e38	−	2.18408e38i	1.01465	−	1.01465i	0.999891	−	0.0147576i	$-0.00469766\pi$
$692$	2.41324e38	−	2.11408e38i	1.09943	−	0.963139i
$693$	4.82344e37	+	4.82344e37i	0.215505	+	0.215505i
$694$	9.29625e37	+	9.93081e37i	0.407338	+	0.435143i
$695$			4.40474e36i			0.0189289i
$696$	5.15414e36	−	5.19053e37i	0.0217236	−	0.218770i
$697$		−	1.37082e38i		−	0.566678i
$698$	1.90813e38	−	1.78620e38i	0.773677	−	0.724241i
$699$	2.59571e38	+	2.59571e38i	1.03232	+	1.03232i
$700$	2.83018e38	+	1.87015e37i	1.10405	+	0.0729546i
$701$	−1.36670e38	+	1.36670e38i	−0.522973	+	0.522973i	−0.918468	−	0.395495i	$-0.870573\pi$
$701$	−1.36670e38	+	1.36670e38i	−0.522973	+	0.522973i	0.395495	+	0.918468i	$0.370573\pi$
$702$	1.52890e38	+	5.04590e36i	0.573890	+	0.0189403i
$703$	3.94252e35			0.00145170
$704$	8.42000e37	+	1.26452e38i	0.304145	+	0.456765i
$705$	2.02244e37			0.0716674
$706$	8.21618e37	+	2.71162e36i	0.285632	+	0.00942683i
$707$	3.28690e38	−	3.28690e38i	1.12105	−	1.12105i
$708$	5.37204e38	+	3.54978e37i	1.79759	+	0.118783i
$709$	2.67586e38	+	2.67586e38i	0.878495	+	0.878495i	0.993379	−	0.114884i	$-0.0366498\pi$
$709$	2.67586e38	+	2.67586e38i	0.878495	+	0.878495i	−0.114884	+	0.993379i	$0.536650\pi$
$710$	−7.07955e36	+	6.62718e36i	−0.0228044	+	0.0213472i
$711$			4.14263e37i			0.130929i
$712$	7.59486e36	−	7.64848e37i	0.0235526	−	0.237189i
$713$		−	2.08072e38i		−	0.633148i
$714$	3.93532e38	+	4.20395e38i	1.17504	+	1.25525i
$715$	7.08460e36	+	7.08460e36i	0.0207579	+	0.0207579i
$716$	4.03822e38	−	3.53762e38i	1.16109	−	1.01715i
$717$	−3.49560e38	+	3.49560e38i	−0.986309	+	0.986309i
$718$	1.85284e37	−	5.61407e38i	0.0513047	−	1.55453i
$719$	−6.37115e38			−1.73132			−0.865661	−	0.500631i	$-0.833101\pi$
$719$	−6.37115e38			−1.73132			−0.865661	+	0.500631i	$0.833101\pi$
$720$	8.49358e36	−	6.50298e36i	0.0226518	−	0.0173430i
$721$	−2.57768e38			−0.674687
$722$	1.28403e37	−	3.89058e38i	0.0329854	−	0.999454i
$723$	4.40147e38	−	4.40147e38i	1.10977	−	1.10977i
$724$	4.57006e38	+	5.21676e38i	1.13097	+	1.29101i
$725$	−5.20788e37	−	5.20788e37i	−0.126502	−	0.126502i
$726$	−2.45357e38	−	2.62105e38i	−0.584998	−	0.624930i
$727$			2.68698e38i			0.628854i	0.949282	+	0.314427i	$0.101812\pi$
$727$			2.68698e38i			0.628854i	−0.949282	+	0.314427i	$0.898188\pi$
$728$	−2.87298e38	−	3.50645e38i	−0.660023	−	0.805553i
$729$			5.51197e37i			0.124304i
$730$	−1.48700e37	+	1.39198e37i	−0.0329193	+	0.0308159i
$731$	−3.30610e38	−	3.30610e38i	−0.718508	−	0.718508i
$732$	−1.06286e37	+	1.60848e38i	−0.0226766	+	0.343174i
$733$	−5.13505e38	+	5.13505e38i	−1.07558	+	1.07558i	−0.0786760	+	0.996900i	$0.525069\pi$
$733$	−5.13505e38	+	5.13505e38i	−1.07558	+	1.07558i	−0.996900	+	0.0786760i	$0.974931\pi$
$734$	−6.61437e38	−	2.18297e37i	−1.36017	−	0.0448902i
$735$	8.03492e36			0.0162219
$736$	2.66721e37	−	1.60222e38i	0.0528697	−	0.317593i
$737$	1.08597e38			0.211353
$738$	1.17263e38	+	3.87007e36i	0.224078	+	0.00739534i
$739$	−1.83876e38	+	1.83876e38i	−0.345005	+	0.345005i	−0.858245	−	0.513240i	$-0.828445\pi$
$739$	−1.83876e38	+	1.83876e38i	−0.345005	+	0.345005i	0.513240	+	0.858245i	$0.328445\pi$
$740$	−1.98831e36	+	3.00899e37i	−0.00366316	+	0.0554361i
$741$	6.69229e35	+	6.69229e35i	0.00121068	+	0.00121068i
$742$

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)

\(f(q)\)	\(=\)	\(q+(-11578.9 - 382.145i) q^{2} +(-2.39173e6 + 2.39173e6i) q^{3} +(1.33926e8 + 8.84966e6i) q^{4} +(1.10058e8 + 1.10058e8i) q^{5} +(2.86077e10 - 2.67797e10i) q^{6} +2.84560e11i q^{7} +(-1.54733e12 - 1.53649e11i) q^{8} -3.81516e12i q^{9} +O(q^{10})\)	\(q+(-11578.9 - 382.145i) q^{2} +(-2.39173e6 + 2.39173e6i) q^{3} +(1.33926e8 + 8.84966e6i) q^{4} +(1.10058e8 + 1.10058e8i) q^{5} +(2.86077e10 - 2.67797e10i) q^{6} +2.84560e11i q^{7} +(-1.54733e12 - 1.53649e11i) q^{8} -3.81516e12i q^{9} +(-1.23230e12 - 1.31641e12i) q^{10} +(4.44293e13 + 4.44293e13i) q^{11} +(-3.41480e14 + 2.99148e14i) q^{12} +(7.24425e14 - 7.24425e14i) q^{13} +(1.08743e14 - 3.29490e15i) q^{14} -5.26459e14 q^{15} +(1.78578e16 + 2.37039e15i) q^{16} +5.16417e16 q^{17} +(-1.45794e15 + 4.41754e16i) q^{18} +(1.93125e14 - 1.93125e14i) q^{19} +(1.37656e16 + 1.57136e16i) q^{20} +(-6.80592e17 - 6.80592e17i) q^{21} +(-4.97466e17 - 5.31423e17i) q^{22} +7.78274e17i q^{23} +(4.06829e18 - 3.33332e18i) q^{24} -7.42636e18i q^{25} +(-8.66490e18 + 8.11123e18i) q^{26} +(-9.11355e18 - 9.11355e18i) q^{27} +(-2.51826e18 + 3.81099e19i) q^{28} +(7.01270e18 - 7.01270e18i) q^{29} +(6.09583e18 + 2.01183e17i) q^{30} -2.67351e20 q^{31} +(-2.05868e20 - 3.42709e19i) q^{32} -2.12526e20 q^{33} +(-5.97955e20 - 1.97346e19i) q^{34} +(-3.13182e19 + 3.13182e19i) q^{35} +(3.37628e19 - 5.10947e20i) q^{36} +(1.02072e21 + 1.02072e21i) q^{37} +(-2.30999e18 + 2.16238e18i) q^{38} +3.46526e21i q^{39} +(-1.53386e20 - 1.87207e20i) q^{40} -2.65448e21i q^{41} +(7.62044e21 + 8.14061e21i) q^{42} +(-6.40200e21 - 6.40200e21i) q^{43} +(5.55704e21 + 6.34341e21i) q^{44} +(4.19889e20 - 4.19889e20i) q^{45} +(2.97413e20 - 9.01158e21i) q^{46} -3.84158e22 q^{47} +(-4.83803e22 + 3.70416e22i) q^{48} -1.52622e22 q^{49} +(-2.83794e21 + 8.59893e22i) q^{50} +(-1.23513e23 + 1.23513e23i) q^{51} +(1.03430e23 - 9.06082e22i) q^{52} +(-1.29330e23 - 1.29330e23i) q^{53} +(1.02042e23 + 1.09008e23i) q^{54} +9.77962e21i q^{55} +(4.37223e22 - 4.40310e23i) q^{56} +9.23807e20i q^{57} +(-8.38795e22 + 7.85198e22i) q^{58} +(-8.38558e23 - 8.38558e23i) q^{59} +(-7.05063e22 - 4.65898e21i) q^{60} +(2.51078e23 - 2.51078e23i) q^{61} +(3.09564e24 + 1.02167e23i) q^{62} +1.08564e24 q^{63} +(2.37064e24 + 4.75491e23i) q^{64} +1.59458e23 q^{65} +(2.46083e24 + 8.12157e22i) q^{66} +(1.22213e24 - 1.22213e24i) q^{67} +(6.91614e24 + 4.57011e23i) q^{68} +(-1.86142e24 - 1.86142e24i) q^{69} +(3.74599e23 - 3.50663e23i) q^{70} -5.37791e24i q^{71} +(-5.86193e23 + 5.90332e24i) q^{72} -1.12958e25i q^{73} +(-1.14287e25 - 1.22089e25i) q^{74} +(1.77618e25 + 1.77618e25i) q^{75} +(2.75735e22 - 2.41553e22i) q^{76} +(-1.26428e25 + 1.26428e25i) q^{77} +(1.32423e24 - 4.01240e25i) q^{78} -1.08583e25 q^{79} +(1.70451e24 + 2.22627e24i) q^{80} +7.26872e25 q^{81} +(-1.01439e24 + 3.07360e25i) q^{82} +(6.59344e25 - 6.59344e25i) q^{83} +(-8.51257e25 - 9.71717e25i) q^{84} +(5.68358e24 + 5.68358e24i) q^{85} +(7.16819e25 + 7.65749e25i) q^{86} +3.35450e25i q^{87} +(-6.19205e25 - 7.55735e25i) q^{88} +4.94301e25i q^{89} +(-5.02232e24 + 4.70141e24i) q^{90} +(2.06143e26 + 2.06143e26i) q^{91} +(-6.88746e24 + 1.04231e26i) q^{92} +(6.39431e26 - 6.39431e26i) q^{93} +(4.44814e26 + 1.46804e25i) q^{94} +4.25100e22 q^{95} +(5.74348e26 - 4.10414e26i) q^{96} +9.90997e26 q^{97} +(1.76720e26 + 5.83237e24i) q^{98} +(1.69505e26 - 1.69505e26i) 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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