LMFDB - Embedded newform 72.20.d.b.37.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,20,Mod(37,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("72.37");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	72.d (of order $2$, degree $1$, 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:	$164.748021521$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 9 x^{17} + 3029197094710 x^{16} - 24233576757476 x^{15} + \cdots + 11\!\cdots\!52 $ x^18 - 9x^17 + 3029197094710x^16 - 24233576757476x^15 + 3666373385397631772951150x^14 - 25664613697359334817402934x^13 + 2288558813400943515734688691172794536x^12 - 13731352880072021116343563422152991580x^11 + 797347137448451076604305820722674456768802005609x^10 - 3986735687116384648288147250006673795452858783225x^9 + 156816961995505010413790628590969656223945140307497061835402x^8 - 627267847958099627532615251355829485045232096457337309552248x^7 + 16729139446039926524800568668372570271935699643494450209774686790214560x^6 - 50187418335924342106565101598639295206702826260054714153668963065467152x^5 + 876106553890603967004320494333017909256417720590701905735688948342294947287783200x^4 - 1752213107697562236782832230977703791942517176383291832316055640309688411664317952x^3 + 18678677257259690524211679657602301764724302346110904809324415405979874812173320788961484288x^2 - 18678677256383583970371263108933435161611886146488870124597927742419621444385686885600890880*x + 113751286079151332076181426449135809801643053652804434109440434519249339410833533987328023600682237952
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{22}\cdot 5^{4}\cdot 7 $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.18
Root			$0.500000 + 695501. i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.20.d.b.37.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(696.194 + 199.004i) q^{2} +(445083. + 277090. i) q^{4} -5.56401e6i q^{5} -4.51327e6 q^{7} +(2.54722e8 + 2.81482e8i) q^{8} +O(q^{10})$	\(q+(696.194 + 199.004i) q^{2} +(445083. + 277090. i) q^{4} -5.56401e6i q^{5} -4.51327e6 q^{7} +(2.54722e8 + 2.81482e8i) q^{8} +(1.10726e9 - 3.87363e9i) q^{10} -1.78940e9i q^{11} -3.40689e10i q^{13} +(-3.14211e9 - 8.98157e8i) q^{14} +(1.21320e11 + 2.46656e11i) q^{16} +4.37021e11 q^{17} +2.55409e12i q^{19} +(1.54173e12 - 2.47645e12i) q^{20} +(3.56097e11 - 1.24577e12i) q^{22} +5.58979e12 q^{23} -1.18847e13 q^{25} +(6.77983e12 - 2.37185e13i) q^{26} +(-2.00878e12 - 1.25058e12i) q^{28} -9.17732e13i q^{29} -6.96656e13 q^{31} +(3.53767e13 + 1.95864e14i) q^{32} +(3.04251e14 + 8.69687e13i) q^{34} +2.51119e13i q^{35} -7.21521e14i q^{37} +(-5.08274e14 + 1.77814e15i) q^{38} +(1.56617e15 - 1.41728e15i) q^{40} +1.74108e15 q^{41} +3.57351e15i q^{43} +(4.95824e14 - 7.96430e14i) q^{44} +(3.89158e15 + 1.11239e15i) q^{46} +1.43582e16 q^{47} -1.13785e16 q^{49} +(-8.27408e15 - 2.36511e15i) q^{50} +(9.44015e15 - 1.51635e16i) q^{52} -1.88104e16i q^{53} -9.95622e15 q^{55} +(-1.14963e15 - 1.27040e15i) q^{56} +(1.82632e16 - 6.38919e16i) q^{58} -4.76955e16i q^{59} -1.16266e17i q^{61} +(-4.85007e16 - 1.38637e16i) q^{62} +(-1.43486e16 + 1.43399e17i) q^{64} -1.89560e17 q^{65} -1.76329e17i q^{67} +(1.94510e17 + 1.21094e17i) q^{68} +(-4.99736e15 + 1.74827e16i) q^{70} -6.82001e16 q^{71} +5.94941e17 q^{73} +(1.43585e17 - 5.02318e17i) q^{74} +(-7.07714e17 + 1.13678e18i) q^{76} +8.07603e15i q^{77} -1.48803e18 q^{79} +(1.37240e18 - 6.75026e17i) q^{80} +(1.21213e18 + 3.46481e17i) q^{82} -1.21993e18i q^{83} -2.43159e18i q^{85} +(-7.11143e17 + 2.48786e18i) q^{86} +(5.03682e17 - 4.55799e17i) q^{88} -3.29788e18 q^{89} +1.53762e17i q^{91} +(2.48792e18 + 1.54888e18i) q^{92} +(9.99609e18 + 2.85734e18i) q^{94} +1.42110e19 q^{95} +4.52106e18 q^{97} +(-7.92166e18 - 2.26437e18i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 458 q^{2} - 412108 q^{4} - 80707216 q^{7} + 173313752 q^{8}+O(q^{10}) $ 18 * q + 458 * q^2 - 412108 * q^4 - 80707216 * q^7 + 173313752 * q^8	$ 18 q + 458 q^{2} - 412108 q^{4} - 80707216 q^{7} + 173313752 q^{8} + 758800104 q^{10} + 122453668784 q^{14} - 696212072432 q^{16} - 14121426692 q^{17} - 6517087595632 q^{20} - 11074654117412 q^{22} - 2177121583952 q^{23} - 44414474211734 q^{25} - 26782030269304 q^{26} - 97002327802784 q^{28} + 428505770260416 q^{31} - 122449430282912 q^{32} - 478448330325748 q^{34} + 486194587539796 q^{38} - 16\!\cdots\!76 q^{40}+ \cdots - 88\!\cdots\!22 q^{98}+O(q^{100}) $ 18 * q + 458 * q^2 - 412108 * q^4 - 80707216 * q^7 + 173313752 * q^8 + 758800104 * q^10 + 122453668784 * q^14 - 696212072432 * q^16 - 14121426692 * q^17 - 6517087595632 * q^20 - 11074654117412 * q^22 - 2177121583952 * q^23 - 44414474211734 * q^25 - 26782030269304 * q^26 - 97002327802784 * q^28 + 428505770260416 * q^31 - 122449430282912 * q^32 - 478448330325748 * q^34 + 486194587539796 * q^38 - 1697818250610976 * q^40 - 1200260021141524 * q^41 - 7031781193616424 * q^44 - 14917443628457488 * q^46 + 1134160959992928 * q^47 + 31570092936329058 * q^49 + 34734151321861826 * q^50 - 26877456911772208 * q^52 - 51757047863478736 * q^55 - 52858270161183424 * q^56 - 20470056808312424 * q^58 - 93766686763697984 * q^62 - 253721318369185216 * q^64 + 184007586011668640 * q^65 - 201388986348307752 * q^68 - 340698473416023872 * q^70 + 1599477989199799056 * q^71 - 93004298989809068 * q^73 + 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 1813975801025264480 * q^79 - 3057120301750869696 * q^80 - 2418785089528546244 * q^82 - 1332333723895598620 * q^86 - 3097741184498130608 * q^88 - 4470509771045743540 * q^89 + 2965990502259463392 * q^92 - 3533635112749329696 * q^94 - 23809730986995679856 * q^95 + 8246429789464117220 * q^97 - 8841667592735478822 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	696.194	+	199.004i	0.961491	+	0.274838i
$2$	696.194	+	199.004i	0.961491	+	0.274838i
$3$		0			0
$3$		0			0
$4$	445083.	+	277090.i	0.848929	+	0.528508i
$5$		−	5.56401e6i		−	1.27401i	−0.770860	−	0.637005i	$-0.780173\pi$
$5$		−	5.56401e6i		−	1.27401i	0.770860	−	0.637005i	$-0.219827\pi$
$6$		0			0
$7$	−4.51327e6			−0.0422727			−0.0211363	−	0.999777i	$-0.506728\pi$
$7$	−4.51327e6			−0.0422727			−0.0211363	+	0.999777i	$0.506728\pi$
$8$	2.54722e8	+	2.81482e8i	0.670983	+	0.741473i
$9$		0			0
$10$	1.10726e9	−	3.87363e9i	0.350146	−	1.22495i
$11$		−	1.78940e9i		−	0.228811i	−0.993434	−	0.114405i	$-0.963504\pi$
$11$		−	1.78940e9i		−	0.228811i	0.993434	−	0.114405i	$-0.0364962\pi$
$12$		0			0
$13$		−	3.40689e10i		−	0.891037i	−0.895273	−	0.445519i	$-0.853019\pi$
$13$		−	3.40689e10i		−	0.891037i	0.895273	−	0.445519i	$-0.146981\pi$
$14$	−3.14211e9	−	8.98157e8i	−0.0406448	−	0.0116181i
$15$		0			0
$16$	1.21320e11	+	2.46656e11i	0.441359	+	0.897330i
$17$	4.37021e11			0.893794			0.446897	−	0.894586i	$-0.352529\pi$
$17$	4.37021e11			0.893794			0.446897	+	0.894586i	$0.352529\pi$
$18$		0			0
$19$			2.55409e12i			1.81584i	0.419144	+	0.907920i	$0.362330\pi$
$19$			2.55409e12i			1.81584i	−0.419144	+	0.907920i	$0.637670\pi$
$20$	1.54173e12	−	2.47645e12i	0.673324	−	1.08154i
$21$		0			0
$22$	3.56097e11	−	1.24577e12i	0.0628858	−	0.219999i
$23$	5.58979e12			0.647114			0.323557	−	0.946209i	$-0.395121\pi$
$23$	5.58979e12			0.647114			0.323557	+	0.946209i	$0.395121\pi$
$24$		0			0
$25$	−1.18847e13			−0.623102
$26$	6.77983e12	−	2.37185e13i	0.244891	−	0.856724i
$27$		0			0
$28$	−2.00878e12	−	1.25058e12i	−0.0358865	−	0.0223414i
$29$		−	9.17732e13i		−	1.17472i	−0.809325	−	0.587361i	$-0.800167\pi$
$29$		−	9.17732e13i		−	1.17472i	0.809325	−	0.587361i	$-0.199833\pi$
$30$		0			0
$31$	−6.96656e13			−0.473241			−0.236620	−	0.971602i	$-0.576040\pi$
$31$	−6.96656e13			−0.473241			−0.236620	+	0.971602i	$0.576040\pi$
$32$	3.53767e13	+	1.95864e14i	0.177743	+	0.984077i
$33$		0			0
$34$	3.04251e14	+	8.69687e13i	0.859374	+	0.245648i
$35$			2.51119e13i			0.0538558i
$36$		0			0
$37$		−	7.21521e14i		−	0.912710i	−0.889798	−	0.456355i	$-0.849155\pi$
$37$		−	7.21521e14i		−	0.912710i	0.889798	−	0.456355i	$-0.150845\pi$
$38$	−5.08274e14	+	1.77814e15i	−0.499061	+	1.74591i
$39$		0			0
$40$	1.56617e15	−	1.41728e15i	0.944644	−	0.854839i
$41$	1.74108e15			0.830561			0.415281	−	0.909693i	$-0.363683\pi$
$41$	1.74108e15			0.830561			0.415281	+	0.909693i	$0.363683\pi$
$42$		0			0
$43$			3.57351e15i			1.08429i	0.840285	+	0.542145i	$0.182388\pi$
$43$			3.57351e15i			1.08429i	−0.840285	+	0.542145i	$0.817612\pi$
$44$	4.95824e14	−	7.96430e14i	0.120928	−	0.194244i
$45$		0			0
$46$	3.89158e15	+	1.11239e15i	0.622194	+	0.177851i
$47$	1.43582e16			1.87142			0.935709	−	0.352774i	$-0.114761\pi$
$47$	1.43582e16			1.87142			0.935709	+	0.352774i	$0.114761\pi$
$48$		0			0
$49$	−1.13785e16			−0.998213
$50$	−8.27408e15	−	2.36511e15i	−0.599107	−	0.171252i
$51$		0			0
$52$	9.44015e15	−	1.51635e16i	0.470920	−	0.756427i
$53$		−	1.88104e16i		−	0.783029i	−0.920172	−	0.391515i	$-0.871951\pi$
$53$		−	1.88104e16i		−	0.783029i	0.920172	−	0.391515i	$-0.128049\pi$
$54$		0			0
$55$	−9.95622e15			−0.291507
$56$	−1.14963e15	−	1.27040e15i	−0.0283643	−	0.0313440i
$57$		0			0
$58$	1.82632e16	−	6.38919e16i	0.322858	−	1.12948i
$59$		−	4.76955e16i		−	0.716775i	−0.933573	−	0.358388i	$-0.883327\pi$
$59$		−	4.76955e16i		−	0.716775i	0.933573	−	0.358388i	$-0.116673\pi$
$60$		0			0
$61$		−	1.16266e17i		−	1.27297i	−0.771290	−	0.636484i	$-0.780388\pi$
$61$		−	1.16266e17i		−	1.27297i	0.771290	−	0.636484i	$-0.219612\pi$
$62$	−4.85007e16	−	1.38637e16i	−0.455016	−	0.130064i
$63$		0			0
$64$	−1.43486e16	+	1.43399e17i	−0.0995633	+	0.995031i
$65$	−1.89560e17			−1.13519
$66$		0			0
$67$		−	1.76329e17i		−	0.791793i	−0.918295	−	0.395897i	$-0.870434\pi$
$67$		−	1.76329e17i		−	0.791793i	0.918295	−	0.395897i	$-0.129566\pi$
$68$	1.94510e17	+	1.21094e17i	0.758767	+	0.472377i
$69$		0			0
$70$	−4.99736e15	+	1.74827e16i	−0.0148016	+	0.0517819i
$71$	−6.82001e16			−0.176535			−0.0882675	−	0.996097i	$-0.528133\pi$
$71$	−6.82001e16			−0.176535			−0.0882675	+	0.996097i	$0.528133\pi$
$72$		0			0
$73$	5.94941e17			1.18279			0.591394	−	0.806383i	$-0.298578\pi$
$73$	5.94941e17			1.18279			0.591394	+	0.806383i	$0.298578\pi$
$74$	1.43585e17	−	5.02318e17i	0.250847	−	0.877562i
$75$		0			0
$76$	−7.07714e17	+	1.13678e18i	−0.959685	+	1.54152i
$77$			8.07603e15i			0.00967244i
$78$		0			0
$79$	−1.48803e18			−1.39687			−0.698433	−	0.715676i	$-0.746119\pi$
$79$	−1.48803e18			−1.39687			−0.698433	+	0.715676i	$0.746119\pi$
$80$	1.37240e18	−	6.75026e17i	1.14321	−	0.562297i
$81$		0			0
$82$	1.21213e18	+	3.46481e17i	0.798577	+	0.228270i
$83$		−	1.21993e18i		−	0.716296i	−0.933665	−	0.358148i	$-0.883408\pi$
$83$		−	1.21993e18i		−	0.716296i	0.933665	−	0.358148i	$-0.116592\pi$
$84$		0			0
$85$		−	2.43159e18i		−	1.13870i
$86$	−7.11143e17	+	2.48786e18i	−0.298004	+	1.04253i
$87$		0			0
$88$	5.03682e17	−	4.55799e17i	0.169657	−	0.153528i
$89$	−3.29788e18			−0.997768			−0.498884	−	0.866669i	$-0.666257\pi$
$89$	−3.29788e18			−0.997768			−0.498884	+	0.866669i	$0.666257\pi$
$90$		0			0
$91$			1.53762e17i			0.0376665i
$92$	2.48792e18	+	1.54888e18i	0.549354	+	0.342005i
$93$		0			0
$94$	9.99609e18	+	2.85734e18i	1.79935	+	0.514336i
$95$	1.42110e19			2.31340
$96$		0			0
$97$	4.52106e18			0.603822			0.301911	−	0.953336i	$-0.402375\pi$
$97$	4.52106e18			0.603822			0.301911	+	0.953336i	$0.402375\pi$
$98$	−7.92166e18	−	2.26437e18i	−0.959772	−	0.274346i
$99$		0			0
$100$	−5.28969e18	−	3.29314e18i	−0.528969	−	0.329314i
$101$		−	1.01147e19i		−	0.920238i	−0.887857	−	0.460119i	$-0.847807\pi$
$101$		−	1.01147e19i		−	0.920238i	0.887857	−	0.460119i	$-0.152193\pi$
$102$		0			0
$103$	−1.82500e19			−1.37819			−0.689096	−	0.724670i	$-0.741992\pi$
$103$	−1.82500e19			−1.37819			−0.689096	+	0.724670i	$0.741992\pi$
$104$	9.58976e18	−	8.67809e18i	0.660680	−	0.597871i
$105$		0			0
$106$	3.74335e18	−	1.30957e19i	0.215206	−	0.752875i
$107$		−	2.72881e19i		−	1.43492i	−0.696600	−	0.717459i	$-0.745305\pi$
$107$		−	2.72881e19i		−	1.43492i	0.696600	−	0.717459i	$-0.254695\pi$
$108$		0			0
$109$		−	1.32939e19i		−	0.586272i	−0.956071	−	0.293136i	$-0.905301\pi$
$109$		−	1.32939e19i		−	0.586272i	0.956071	−	0.293136i	$-0.0946989\pi$
$110$	−6.93146e18	−	1.98133e18i	−0.280281	−	0.0801171i
$111$		0			0
$112$	−5.47550e17	−	1.11323e18i	−0.0186574	−	0.0379326i
$113$	−1.83425e19			−0.574399			−0.287199	−	0.957871i	$-0.592724\pi$
$113$	−1.83425e19			−0.574399			−0.287199	+	0.957871i	$0.592724\pi$
$114$		0			0
$115$		−	3.11016e19i		−	0.824430i
$116$	2.54295e19	−	4.08467e19i	0.620849	−	0.997255i
$117$		0			0
$118$	9.49158e18	−	3.32053e19i	0.196997	−	0.689173i
$119$	−1.97239e18			−0.0377831
$120$		0			0
$121$	5.79571e19			0.947646
$122$	2.31373e19	−	8.09433e19i	0.349860	−	1.22395i
$123$		0			0
$124$	−3.10070e19	−	1.93036e19i	−0.401748	−	0.250111i
$125$		−	3.99983e19i		−	0.480171i
$126$		0			0
$127$	1.55505e20			1.60550			0.802748	−	0.596319i	$-0.203370\pi$
$127$	1.55505e20			1.60550			0.802748	+	0.596319i	$0.203370\pi$
$128$	−3.85263e19	+	9.69781e19i	−0.369201	+	0.929350i
$129$		0			0
$130$	−1.31970e20	−	3.77231e19i	−1.09148	−	0.311993i
$131$			2.39001e20i			1.83790i	0.394376	+	0.918949i	$0.370961\pi$
$131$			2.39001e20i			1.83790i	−0.394376	+	0.918949i	$0.629039\pi$
$132$		0			0
$133$		−	1.15273e19i		−	0.0767604i
$134$	3.50900e19	−	1.22759e20i	0.217615	−	0.761302i
$135$		0			0
$136$	1.11319e20	+	1.23013e20i	0.599720	+	0.662723i
$137$	2.33463e20			1.17320			0.586602	−	0.809875i	$-0.300465\pi$
$137$	2.33463e20			1.17320			0.586602	+	0.809875i	$0.300465\pi$
$138$		0			0
$139$			4.01632e20i			1.75868i	0.476190	+	0.879342i	$0.342017\pi$
$139$			4.01632e20i			1.75868i	−0.476190	+	0.879342i	$0.657983\pi$
$140$	−6.95826e18	+	1.11769e19i	−0.0284632	+	0.0457198i
$141$		0			0
$142$	−4.74805e19	−	1.35721e19i	−0.169737	−	0.0485184i
$143$	−6.09627e19			−0.203879
$144$		0			0
$145$	−5.10627e20			−1.49661
$146$	4.14194e20	+	1.18395e20i	1.13724	+	0.325074i
$147$		0			0
$148$	1.99926e20	−	3.21137e20i	0.482374	−	0.774825i
$149$		−	5.08909e20i		−	1.15178i	−0.817526	−	0.575892i	$-0.804655\pi$
$149$		−	5.08909e20i		−	1.15178i	0.817526	−	0.575892i	$-0.195345\pi$
$150$		0			0
$151$	3.58863e20			0.715563			0.357782	−	0.933805i	$-0.383533\pi$
$151$	3.58863e20			0.715563			0.357782	+	0.933805i	$0.383533\pi$
$152$	−7.18930e20	+	6.50584e20i	−1.34640	+	1.21840i
$153$		0			0
$154$	−1.60716e18	+	5.62248e18i	−0.00265835	+	0.00929996i
$155$			3.87620e20i			0.602913i
$156$		0			0
$157$		−	1.45807e20i		−	0.200786i	−0.994948	−	0.100393i	$-0.967990\pi$
$157$		−	1.45807e20i		−	0.200786i	0.994948	−	0.100393i	$-0.0320099\pi$
$158$	−1.03596e21	−	2.96124e20i	−1.34307	−	0.383911i
$159$		0			0
$160$	1.08979e21	−	1.96836e20i	1.25372	−	0.226446i
$161$	−2.52282e19			−0.0273553
$162$		0			0
$163$		−	1.25859e21i		−	1.21367i	−0.794828	−	0.606835i	$-0.792439\pi$
$163$		−	1.25859e21i		−	1.21367i	0.794828	−	0.606835i	$-0.207561\pi$
$164$	7.74925e20	+	4.82436e20i	0.705087	+	0.438958i
$165$		0			0
$166$	2.42770e20	−	8.49306e20i	0.196865	−	0.688712i
$167$	−3.81697e20			−0.292356			−0.146178	−	0.989258i	$-0.546697\pi$
$167$	−3.81697e20			−0.292356			−0.146178	+	0.989258i	$0.546697\pi$
$168$		0			0
$169$	3.01232e20			0.206053
$170$	4.83895e20	−	1.69286e21i	0.312958	−	1.09485i
$171$		0			0
$172$	−9.90186e20	+	1.59051e21i	−0.573055	+	0.920484i
$173$		−	7.20483e20i		−	0.394626i	−0.980341	−	0.197313i	$-0.936778\pi$
$173$		−	7.20483e20i		−	0.394626i	0.980341	−	0.197313i	$-0.0632216\pi$
$174$		0			0
$175$	5.36390e19			0.0263402
$176$	4.41366e20	−	2.17090e20i	0.205319	−	0.100988i
$177$		0			0
$178$	−2.29596e21	−	6.56290e20i	−0.959345	−	0.274224i
$179$			1.54740e21i			0.613055i	0.951862	+	0.306528i	$0.0991672\pi$
$179$			1.54740e21i			0.613055i	−0.951862	+	0.306528i	$0.900833\pi$
$180$		0			0
$181$		−	3.95197e21i		−	1.40886i	−0.709774	−	0.704429i	$-0.751203\pi$
$181$		−	3.95197e21i		−	1.40886i	0.709774	−	0.704429i	$-0.248797\pi$
$182$	−3.05992e19	+	1.07048e20i	−0.0103522	+	0.0362160i
$183$		0			0
$184$	1.42384e21	+	1.57342e21i	0.434203	+	0.479817i
$185$	−4.01455e21			−1.16280
$186$		0			0
$187$		−	7.82003e20i		−	0.204509i
$188$	6.39060e21	+	3.97852e21i	1.58870	+	0.989058i
$189$		0			0
$190$	9.89361e21	+	2.82804e21i	2.22431	+	0.635809i
$191$	4.73400e21			1.01254			0.506269	−	0.862375i	$-0.331024\pi$
$191$	4.73400e21			1.01254			0.506269	+	0.862375i	$0.331024\pi$
$192$		0			0
$193$	7.86311e21			1.52335			0.761676	−	0.647959i	$-0.224377\pi$
$193$	7.86311e21			1.52335			0.761676	+	0.647959i	$0.224377\pi$
$194$	3.14753e21	+	8.99708e20i	0.580569	+	0.165953i
$195$		0			0
$196$	−5.06439e21	−	3.15288e21i	−0.847412	−	0.527563i
$197$		−	5.32685e21i		−	0.849261i	−0.905367	−	0.424630i	$-0.860404\pi$
$197$		−	5.32685e21i		−	0.849261i	0.905367	−	0.424630i	$-0.139596\pi$
$198$		0			0
$199$	−1.72615e21			−0.250019			−0.125010	−	0.992156i	$-0.539896\pi$
$199$	−1.72615e21			−0.250019			−0.125010	+	0.992156i	$0.539896\pi$
$200$	−3.02730e21	−	3.34533e21i	−0.418091	−	0.462013i
$201$		0			0
$202$	2.01286e21	−	7.04179e21i	0.252916	−	0.884800i
$203$			4.14197e20i			0.0496586i
$204$		0			0
$205$		−	9.68738e21i		−	1.05814i
$206$	−1.27055e22	−	3.63182e21i	−1.32512	−	0.378779i
$207$		0			0
$208$	8.40330e21	−	4.13323e21i	0.799555	−	0.393268i
$209$	4.57029e21			0.415483
$210$		0			0
$211$			1.43551e22i			1.19213i	0.802936	+	0.596065i	$0.203270\pi$
$211$			1.43551e22i			1.19213i	−0.802936	+	0.596065i	$0.796730\pi$
$212$	5.21219e21	−	8.37221e21i	0.413837	−	0.664736i
$213$		0			0
$214$	5.43043e21	−	1.89978e22i	0.394370	−	1.37966i
$215$	1.98831e22			1.38140
$216$		0			0
$217$	3.14419e20			0.0200052
$218$	2.64553e21	−	9.25510e21i	0.161130	−	0.563695i
$219$		0			0
$220$	−4.43135e21	−	2.75877e21i	−0.247469	−	0.154064i
$221$		−	1.48888e22i		−	0.796403i
$222$		0			0
$223$	1.36844e22			0.671938			0.335969	−	0.941873i	$-0.390936\pi$
$223$	1.36844e22			0.671938			0.335969	+	0.941873i	$0.390936\pi$
$224$	−1.59664e20	−	8.83985e20i	−0.00751367	−	0.0415996i
$225$		0			0
$226$	−1.27699e22	−	3.65023e21i	−0.552279	−	0.157866i
$227$		−	2.28444e22i		−	0.947400i	−0.880686	−	0.473700i	$-0.842918\pi$
$227$		−	2.28444e22i		−	0.947400i	0.880686	−	0.473700i	$-0.157082\pi$
$228$		0			0
$229$			1.15938e22i			0.442371i	0.975232	+	0.221186i	$0.0709927\pi$
$229$			1.15938e22i			0.442371i	−0.975232	+	0.221186i	$0.929007\pi$
$230$	6.18934e21	−	2.16528e22i	0.226584	−	0.792682i
$231$		0			0
$232$	2.58325e22	−	2.33767e22i	0.871024	−	0.788218i
$233$	1.44196e22			0.466736			0.233368	−	0.972388i	$-0.425025\pi$
$233$	1.44196e22			0.466736			0.233368	+	0.972388i	$0.425025\pi$
$234$		0			0
$235$		−	7.98892e22i		−	2.38421i
$236$	1.32160e22	−	2.12285e22i	0.378821	−	0.608491i
$237$		0			0
$238$	−1.37317e21	−	3.92513e20i	−0.0363281	−	0.0103842i
$239$	−5.79540e22			−1.47334			−0.736671	−	0.676252i	$-0.763603\pi$
$239$	−5.79540e22			−1.47334			−0.736671	+	0.676252i	$0.763603\pi$
$240$		0			0
$241$	2.53834e22			0.596195			0.298097	−	0.954535i	$-0.403648\pi$
$241$	2.53834e22			0.596195			0.298097	+	0.954535i	$0.403648\pi$
$242$	4.03494e22	+	1.15337e22i	0.911153	+	0.260449i
$243$		0			0
$244$	3.22160e22	−	5.17478e22i	0.672774	−	1.08066i
$245$			6.33102e22i			1.27173i
$246$		0			0
$247$	8.70151e22			1.61798
$248$	−1.77454e22	−	1.96096e22i	−0.317536	−	0.350895i
$249$		0			0
$250$	7.95981e21	−	2.78466e22i	0.131969	−	0.461680i
$251$		−	2.45272e22i		−	0.391514i	−0.980652	−	0.195757i	$-0.937284\pi$
$251$		−	2.45272e22i		−	0.391514i	0.980652	−	0.195757i	$-0.0627164\pi$
$252$		0			0
$253$		−	1.00023e22i		−	0.148067i
$254$	1.08262e23	+	3.09461e22i	1.54367	+	0.441251i
$255$		0			0
$256$	−4.61208e22	+	5.98487e22i	−0.610404	+	0.792090i
$257$	7.84682e22			1.00076			0.500379	−	0.865807i	$-0.333194\pi$
$257$	7.84682e22			1.00076			0.500379	+	0.865807i	$0.333194\pi$
$258$		0			0
$259$			3.25642e21i			0.0385827i
$260$	−8.43698e22	−	5.25251e22i	−0.963696	−	0.599957i
$261$		0			0
$262$	−4.75620e22	+	1.66391e23i	−0.505124	+	1.76712i
$263$	−6.14964e22			−0.629898			−0.314949	−	0.949109i	$-0.601987\pi$
$263$	−6.14964e22			−0.629898			−0.314949	+	0.949109i	$0.601987\pi$
$264$		0			0
$265$	−1.04661e23			−0.997588
$266$	2.29398e21	−	8.02524e21i	0.0210967	−	0.0738044i
$267$		0			0
$268$	4.88589e22	−	7.84808e22i	0.418469	−	0.672176i
$269$		−	3.37452e21i		−	0.0278975i	−0.999903	−	0.0139487i	$-0.995560\pi$
$269$		−	3.37452e21i		−	0.0278975i	0.999903	−	0.0139487i	$-0.00444016\pi$
$270$		0			0
$271$	−1.70540e23			−1.31407			−0.657035	−	0.753860i	$-0.728189\pi$
$271$	−1.70540e23			−1.31407			−0.657035	+	0.753860i	$0.728189\pi$
$272$	5.30193e22	+	1.07794e23i	0.394484	+	0.802028i
$273$		0			0
$274$	1.62536e23	+	4.64601e22i	1.12802	+	0.322441i
$275$			2.12665e22i			0.142572i
$276$		0			0
$277$			9.88428e22i			0.618568i	0.950970	+	0.309284i	$0.100089\pi$
$277$			9.88428e22i			0.618568i	−0.950970	+	0.309284i	$0.899911\pi$
$278$	−7.99263e22	+	2.79614e23i	−0.483353	+	1.69096i
$279$		0			0
$280$	−7.06853e21	+	6.39655e21i	−0.0399326	+	0.0361364i
$281$	−1.54967e23			−0.846309			−0.423154	−	0.906058i	$-0.639077\pi$
$281$	−1.54967e23			−0.846309			−0.423154	+	0.906058i	$0.639077\pi$
$282$		0			0
$283$			9.10357e22i			0.464773i	0.972624	+	0.232386i	$0.0746534\pi$
$283$			9.10357e22i			0.464773i	−0.972624	+	0.232386i	$0.925347\pi$
$284$	−3.03547e22	−	1.88976e22i	−0.149866	−	0.0933001i
$285$		0			0
$286$	−4.24419e22	−	1.21318e22i	−0.196028	−	0.0560336i
$287$	−7.85796e21			−0.0351101
$288$		0			0
$289$	−4.80854e22			−0.201133
$290$	−3.55495e23	−	1.01617e23i	−1.43897	−	0.411324i
$291$		0			0
$292$	2.64798e23	+	1.64852e23i	1.00410	+	0.625112i
$293$			3.76601e23i			1.38242i	0.722655	+	0.691209i	$0.242922\pi$
$293$			3.76601e23i			1.38242i	−0.722655	+	0.691209i	$0.757078\pi$
$294$		0			0
$295$	−2.65378e23			−0.913179
$296$	2.03095e23	−	1.83787e23i	0.676749	−	0.612413i
$297$		0			0
$298$	1.01275e23	−	3.54299e23i	0.316553	−	1.10743i
$299$		−	1.90438e23i		−	0.576603i
$300$		0			0
$301$		−	1.61282e22i		−	0.0458358i
$302$	2.49838e23	+	7.14151e22i	0.688008	+	0.196664i
$303$		0			0
$304$	−6.29983e23	+	3.09862e23i	−1.62941	+	0.801438i
$305$	−6.46903e23			−1.62178
$306$		0			0
$307$			4.06724e22i			0.0958265i	0.998852	+	0.0479132i	$0.0152571\pi$
$307$			4.06724e22i			0.0958265i	−0.998852	+	0.0479132i	$0.984743\pi$
$308$	−2.23779e21	+	3.59450e21i	−0.00511196	+	0.00821121i
$309$		0			0
$310$	−7.71378e22	+	2.69859e23i	−0.165703	+	0.579696i
$311$	2.11001e23			0.439604			0.219802	−	0.975544i	$-0.429459\pi$
$311$	2.11001e23			0.439604			0.219802	+	0.975544i	$0.429459\pi$
$312$		0			0
$313$	4.32064e23			0.846988			0.423494	−	0.905899i	$-0.360803\pi$
$313$	4.32064e23			0.846988			0.423494	+	0.905899i	$0.360803\pi$
$314$	2.90162e22	−	1.01510e23i	0.0551834	−	0.193053i
$315$		0			0
$316$	−6.62297e23	−	4.12319e23i	−1.18584	−	0.738254i
$317$		−	2.37604e22i		−	0.0412849i	−0.999787	−	0.0206424i	$-0.993429\pi$
$317$		−	2.37604e22i		−	0.0412849i	0.999787	−	0.0206424i	$-0.00657116\pi$
$318$		0			0
$319$	−1.64219e23			−0.268789
$320$	7.97874e23	+	7.98357e22i	1.26768	+	0.126845i
$321$		0			0
$322$	−1.75637e22	−	5.02051e21i	−0.0263018	−	0.00751825i
$323$			1.11619e24i			1.62299i
$324$		0			0
$325$			4.04900e23i			0.555208i
$326$	2.50463e23	−	8.76220e23i	0.333562	−	1.16693i
$327$		0			0
$328$	4.43491e23	+	4.90082e23i	0.557293	+	0.615839i
$329$	−6.48025e22			−0.0791098
$330$		0			0
$331$			1.23591e24i			1.42437i	0.701994	+	0.712183i	$0.252293\pi$
$331$			1.23591e24i			1.42437i	−0.701994	+	0.712183i	$0.747707\pi$
$332$	3.38030e23	−	5.42970e23i	0.378568	−	0.608084i
$333$		0			0
$334$	−2.65735e23	−	7.59591e22i	−0.281098	−	0.0803504i
$335$	−9.81094e23			−1.00875
$336$		0			0
$337$	−6.39486e23			−0.621366			−0.310683	−	0.950514i	$-0.600558\pi$
$337$	−6.39486e23			−0.621366			−0.310683	+	0.950514i	$0.600558\pi$
$338$	2.09716e23	+	5.99463e22i	0.198118	+	0.0566310i
$339$		0			0
$340$	6.73769e23	−	1.08226e24i	0.601813	−	0.966677i
$341$			1.24659e23i			0.108282i
$342$		0			0
$343$	1.02801e23			0.0844698
$344$	−1.00588e24	+	9.10253e23i	−0.803971	+	0.727540i
$345$		0			0
$346$	1.43379e23	−	5.01596e23i	0.108458	−	0.379429i
$347$			6.84162e23i			0.503534i	0.967788	+	0.251767i	$0.0810117\pi$
$347$			6.84162e23i			0.503534i	−0.967788	+	0.251767i	$0.918988\pi$
$348$		0			0
$349$			3.64379e23i			0.253928i	0.991907	+	0.126964i	$0.0405233\pi$
$349$			3.64379e23i			0.253928i	−0.991907	+	0.126964i	$0.959477\pi$
$350$	3.73431e22	+	1.06744e22i	0.0253259	+	0.00723928i
$351$		0			0
$352$	3.50478e23	−	6.33029e22i	0.225167	−	0.0406694i
$353$	5.48650e23			0.343112			0.171556	−	0.985174i	$-0.445121\pi$
$353$	5.48650e23			0.343112			0.171556	+	0.985174i	$0.445121\pi$
$354$		0			0
$355$			3.79466e23i			0.224907i
$356$	−1.46783e24	−	9.13810e23i	−0.847034	−	0.527328i
$357$		0			0
$358$	−3.07939e23	+	1.07729e24i	−0.168491	+	0.589447i
$359$	−1.28269e24			−0.683479			−0.341739	−	0.939795i	$-0.611016\pi$
$359$	−1.28269e24			−0.683479			−0.341739	+	0.939795i	$0.611016\pi$
$360$		0			0
$361$	−4.54497e24			−2.29727
$362$	7.86457e23	−	2.75134e24i	0.387207	−	1.35460i
$363$		0			0
$364$	−4.26059e22	+	6.84369e22i	−0.0199071	+	0.0319762i
$365$		−	3.31026e24i		−	1.50688i
$366$		0			0
$367$	−1.23278e24			−0.532793			−0.266396	−	0.963864i	$-0.585833\pi$
$367$	−1.23278e24			−0.532793			−0.266396	+	0.963864i	$0.585833\pi$
$368$	6.78153e23	+	1.37876e24i	0.285610	+	0.580675i
$369$		0			0
$370$	−2.79491e24	−	7.98911e23i	−1.11802	−	0.319582i
$371$			8.48965e22i			0.0331008i
$372$		0			0
$373$			1.86125e24i			0.689559i	0.938684	+	0.344780i	$0.112046\pi$
$373$			1.86125e24i			0.689559i	−0.938684	+	0.344780i	$0.887954\pi$
$374$	1.55622e23	−	5.44426e23i	0.0562069	−	0.196634i
$375$		0			0
$376$	3.65735e24	+	4.04157e24i	1.25569	+	1.38760i
$377$	−3.12661e24			−1.04672
$378$		0			0
$379$		−	1.18195e24i		−	0.376292i	−0.982141	−	0.188146i	$-0.939752\pi$
$379$		−	1.18195e24i		−	0.376292i	0.982141	−	0.188146i	$-0.0602479\pi$
$380$	6.32508e24	+	3.93773e24i	1.96391	+	1.22265i
$381$		0			0
$382$	3.29578e24	+	9.42084e23i	0.973546	+	0.278284i
$383$	−3.42588e24			−0.987150			−0.493575	−	0.869703i	$-0.664310\pi$
$383$	−3.42588e24			−0.987150			−0.493575	+	0.869703i	$0.664310\pi$
$384$		0			0
$385$	4.49351e22			0.0123228
$386$	5.47425e24	+	1.56479e24i	1.46469	+	0.418674i
$387$		0			0
$388$	2.01225e24	+	1.25274e24i	0.512602	+	0.319125i
$389$			6.91661e24i			1.71938i	0.510815	+	0.859691i	$0.329344\pi$
$389$			6.91661e24i			1.71938i	−0.510815	+	0.859691i	$0.670656\pi$
$390$		0			0
$391$	2.44285e24			0.578387
$392$	−2.89836e24	−	3.20285e24i	−0.669784	−	0.740148i
$393$		0			0
$394$	1.06006e24	−	3.70852e24i	0.233409	−	0.816556i
$395$			8.27942e24i			1.77962i
$396$		0			0
$397$		−	6.65245e24i		−	1.36293i	−0.731853	−	0.681463i	$-0.761344\pi$
$397$		−	6.65245e24i		−	1.36293i	0.731853	−	0.681463i	$-0.238656\pi$
$398$	−1.20173e24	−	3.43510e23i	−0.240391	−	0.0687147i
$399$		0			0
$400$	−1.44186e24	−	2.93145e24i	−0.275012	−	0.559129i
$401$	−6.41010e24			−1.19397			−0.596984	−	0.802253i	$-0.703635\pi$
$401$	−6.41010e24			−1.19397			−0.596984	+	0.802253i	$0.703635\pi$
$402$		0			0
$403$			2.37343e24i			0.421675i
$404$	2.80269e24	−	4.50188e24i	0.486353	−	0.781216i
$405$		0			0
$406$	−8.24268e22	+	2.88361e23i	−0.0136481	+	0.0477463i
$407$	−1.29109e24			−0.208838
$408$		0			0
$409$	5.52154e24			0.852490			0.426245	−	0.904608i	$-0.359836\pi$
$409$	5.52154e24			0.852490			0.426245	+	0.904608i	$0.359836\pi$
$410$	1.92782e24	−	6.74429e24i	0.290818	−	1.01740i
$411$		0			0
$412$	−8.12277e24	−	5.05690e24i	−1.16999	−	0.728385i
$413$			2.15263e23i			0.0303000i
$414$		0			0
$415$	−6.78770e24			−0.912569
$416$	6.67285e24	−	1.20524e24i	0.876849	−	0.158376i
$417$		0			0
$418$	3.18180e24	+	9.09504e23i	0.399483	+	0.114190i
$419$		−	3.31446e24i		−	0.406799i	−0.979096	−	0.203400i	$-0.934801\pi$
$419$		−	3.31446e24i		−	0.406799i	0.979096	−	0.203400i	$-0.0651990\pi$
$420$		0			0
$421$			3.93632e24i			0.461754i	0.972983	+	0.230877i	$0.0741595\pi$
$421$			3.93632e24i			0.461754i	−0.972983	+	0.230877i	$0.925841\pi$
$422$	−2.85672e24	+	9.99395e24i	−0.327642	+	1.14622i
$423$		0			0
$424$	5.29479e24	−	4.79143e24i	0.580595	−	0.525399i
$425$	−5.19388e24			−0.556925
$426$		0			0
$427$			5.24738e23i			0.0538118i
$428$	7.56126e24	−	1.21455e25i	0.758365	−	1.21814i
$429$		0			0
$430$	1.38425e25	+	3.95681e24i	1.32820	+	0.379660i
$431$	−1.03414e24			−0.0970610			−0.0485305	−	0.998822i	$-0.515454\pi$
$431$	−1.03414e24			−0.0970610			−0.0485305	+	0.998822i	$0.515454\pi$
$432$		0			0
$433$	−2.24817e24			−0.201927			−0.100963	−	0.994890i	$-0.532193\pi$
$433$	−2.24817e24			−0.201927			−0.100963	+	0.994890i	$0.532193\pi$
$434$	2.18897e23	+	6.25706e22i	0.0192348	+	0.00549817i
$435$		0			0
$436$	3.68360e24	−	5.91687e24i	0.309849	−	0.497703i
$437$			1.42768e25i			1.17506i
$438$		0			0
$439$	−1.13798e25			−0.896856			−0.448428	−	0.893819i	$-0.648016\pi$
$439$	−1.13798e25			−0.896856			−0.448428	+	0.893819i	$0.648016\pi$
$440$	−2.53607e24	−	2.80249e24i	−0.195596	−	0.216145i
$441$		0			0
$442$	2.96293e24	−	1.03655e25i	0.218882	−	0.765734i
$443$		−	2.12719e25i		−	1.53805i	−0.639216	−	0.769027i	$-0.720741\pi$
$443$		−	2.12719e25i		−	1.53805i	0.639216	−	0.769027i	$-0.279259\pi$
$444$		0			0
$445$			1.83494e25i			1.27117i
$446$	9.52698e24	+	2.72324e24i	0.646062	+	0.184674i
$447$		0			0
$448$	6.47590e22	−	6.47199e23i	0.00420881	−	0.0420626i
$449$	−5.43638e24			−0.345915			−0.172958	−	0.984929i	$-0.555332\pi$
$449$	−5.43638e24			−0.345915			−0.172958	+	0.984929i	$0.555332\pi$
$450$		0			0
$451$		−	3.11548e24i		−	0.190041i
$452$	−8.16394e24	−	5.08253e24i	−0.487624	−	0.303574i
$453$		0			0
$454$	4.54611e24	−	1.59041e25i	0.260381	−	0.910916i
$455$	8.55533e23			0.0479876
$456$		0			0
$457$	1.03816e25			0.558549			0.279274	−	0.960211i	$-0.409906\pi$
$457$	1.03816e25			0.558549			0.279274	+	0.960211i	$0.409906\pi$
$458$	−2.30720e24	+	8.07150e24i	−0.121580	+	0.425336i
$459$		0			0
$460$	8.61796e24	−	1.38428e25i	0.435718	−	0.699882i
$461$			2.01328e25i			0.997117i	0.866856	+	0.498559i	$0.166137\pi$
$461$			2.01328e25i			0.997117i	−0.866856	+	0.498559i	$0.833863\pi$
$462$		0			0
$463$	1.68246e25			0.799699			0.399849	−	0.916581i	$-0.369062\pi$
$463$	1.68246e25			0.799699			0.399849	+	0.916581i	$0.369062\pi$
$464$	2.26364e25	−	1.11339e25i	1.05411	−	0.518475i
$465$		0			0
$466$	1.00388e25	+	2.86955e24i	0.448763	+	0.128277i
$467$			2.96900e25i			1.30047i	0.759734	+	0.650234i	$0.225329\pi$
$467$			2.96900e25i			1.30047i	−0.759734	+	0.650234i	$0.774671\pi$
$468$		0			0
$469$			7.95818e23i			0.0334712i
$470$	1.58983e25	−	5.56184e25i	0.655269	−	2.29239i
$471$		0			0
$472$	1.34254e25	−	1.21491e25i	0.531469	−	0.480944i
$473$	6.39444e24			0.248097
$474$		0			0
$475$		−	3.03547e25i		−	1.13145i
$476$	−8.77878e23	−	5.46530e23i	−0.0320751	−	0.0199686i
$477$		0			0
$478$	−4.03472e25	−	1.15331e25i	−1.41660	−	0.404930i
$479$	−3.48219e25			−1.19857			−0.599287	−	0.800534i	$-0.704549\pi$
$479$	−3.48219e25			−1.19857			−0.599287	+	0.800534i	$0.704549\pi$
$480$		0			0
$481$	−2.45814e25			−0.813258
$482$	1.76718e25	+	5.05139e24i	0.573236	+	0.163857i
$483$		0			0
$484$	2.57957e25	+	1.60594e25i	0.804484	+	0.500838i
$485$		−	2.51552e25i		−	0.769276i
$486$		0			0
$487$	3.81856e25			1.12299			0.561494	−	0.827481i	$-0.310227\pi$
$487$	3.81856e25			1.12299			0.561494	+	0.827481i	$0.310227\pi$
$488$	3.27266e25	−	2.96154e25i	0.943871	−	0.854140i
$489$		0			0
$490$	−1.25990e25	+	4.40762e25i	−0.349520	+	1.22276i
$491$		−	4.66960e25i		−	1.27059i	−0.772270	−	0.635294i	$-0.780879\pi$
$491$		−	4.66960e25i		−	1.27059i	0.772270	−	0.635294i	$-0.219121\pi$
$492$		0			0
$493$		−	4.01068e25i		−	1.04996i
$494$	6.05793e25	+	1.73163e25i	1.55567	+	0.444682i
$495$		0			0
$496$	−8.45182e24	−	1.71834e25i	−0.208869	−	0.424653i
$497$	3.07805e23			0.00746261
$498$		0			0
$499$			1.20220e25i			0.280558i	0.990112	+	0.140279i	$0.0447999\pi$
$499$			1.20220e25i			0.280558i	−0.990112	+	0.140279i	$0.955200\pi$
$500$	1.10831e25	−	1.78026e25i	0.253774	−	0.407631i
$501$		0			0
$502$	4.88100e24	−	1.70757e25i	0.107603	−	0.376437i
$503$	−3.04737e25			−0.659218			−0.329609	−	0.944118i	$-0.606917\pi$
$503$	−3.04737e25			−0.659218			−0.329609	+	0.944118i	$0.606917\pi$
$504$		0			0
$505$	−5.62783e25			−1.17239
$506$	1.99050e24	−	6.96357e24i	0.0406943	−	0.142365i
$507$		0			0
$508$	6.92127e25	+	4.30889e25i	1.36295	+	0.848517i
$509$		−	1.44729e25i		−	0.279728i	−0.990171	−	0.139864i	$-0.955333\pi$
$509$		−	1.44729e25i		−	0.279728i	0.990171	−	0.139864i	$-0.0446665\pi$
$510$		0			0
$511$	−2.68513e24			−0.0499996
$512$	−4.40191e25	+	3.24880e25i	−0.804594	+	0.593826i
$513$		0			0
$514$	5.46290e25	+	1.56155e25i	0.962219	+	0.275046i
$515$			1.01543e26i			1.75583i
$516$		0			0
$517$		−	2.56925e25i		−	0.428200i
$518$	−6.48039e23	+	2.26710e24i	−0.0106040	+	0.0370969i
$519$		0			0
$520$	−4.82850e25	−	5.33575e25i	−0.761694	−	0.841713i
$521$	−4.00543e25			−0.620426			−0.310213	−	0.950667i	$-0.600400\pi$
$521$	−4.00543e25			−0.620426			−0.310213	+	0.950667i	$0.600400\pi$
$522$		0			0
$523$			2.12968e25i			0.318088i	0.987271	+	0.159044i	$0.0508412\pi$
$523$			2.12968e25i			0.318088i	−0.987271	+	0.159044i	$0.949159\pi$
$524$	−6.62247e25	+	1.06375e26i	−0.971343	+	1.56024i
$525$		0			0
$526$	−4.28134e25	−	1.22380e25i	−0.605641	−	0.173120i
$527$	−3.04453e25			−0.422979
$528$		0			0
$529$	−4.33697e25			−0.581243
$530$	−7.28646e25	−	2.08280e25i	−0.959171	−	0.274175i
$531$		0			0
$532$	3.19410e24	−	5.13061e24i	0.0405685	−	0.0651641i
$533$		−	5.93166e25i		−	0.740061i
$534$		0			0
$535$	−1.51831e26			−1.82810
$536$	4.96332e25	−	4.49148e25i	0.587093	−	0.531280i
$537$		0			0
$538$	6.71541e23	−	2.34932e24i	0.00766727	−	0.0268232i
$539$			2.03607e25i			0.228402i
$540$		0			0
$541$			1.51095e26i			1.63635i	0.574971	+	0.818174i	$0.305013\pi$
$541$			1.51095e26i			1.63635i	−0.574971	+	0.818174i	$0.694987\pi$
$542$	−1.18729e26	−	3.39381e25i	−1.26347	−	0.361156i
$543$		0			0
$544$	1.54603e25	+	8.55965e25i	0.158865	+	0.879562i
$545$	−7.39672e25			−0.746917
$546$		0			0
$547$			1.21086e26i			1.18090i	0.807075	+	0.590449i	$0.201049\pi$
$547$			1.21086e26i			1.18090i	−0.807075	+	0.590449i	$0.798951\pi$
$548$	1.03911e26	+	6.46904e25i	0.995967	+	0.620047i
$549$		0			0
$550$	−4.23211e24	+	1.48056e25i	−0.0391843	+	0.137082i
$551$	2.34397e26			2.13311
$552$		0			0
$553$	6.71589e24			0.0590493
$554$	−1.96701e25	+	6.88137e25i	−0.170006	+	0.594747i
$555$		0			0
$556$	−1.11288e26	+	1.78760e26i	−0.929478	+	1.49300i
$557$			2.13063e26i			1.74938i	0.484683	+	0.874690i	$0.338935\pi$
$557$			2.13063e26i			1.74938i	−0.484683	+	0.874690i	$0.661065\pi$
$558$		0			0
$559$	1.21746e26			0.966142
$560$	−6.19400e24	+	3.04657e24i	−0.0483265	+	0.0237698i
$561$		0			0
$562$	−1.07887e26	−	3.08390e25i	−0.813718	−	0.232597i
$563$		−	2.61624e25i		−	0.194020i	−0.995283	−	0.0970102i	$-0.969072\pi$
$563$		−	2.61624e25i		−	0.194020i	0.995283	−	0.0970102i	$-0.0309279\pi$
$564$		0			0
$565$			1.02058e26i			0.731790i
$566$	−1.81164e25	+	6.33785e25i	−0.127737	+	0.446875i
$567$		0			0
$568$	−1.73721e25	−	1.91971e25i	−0.118452	−	0.130896i
$569$	−1.22661e26			−0.822508			−0.411254	−	0.911521i	$-0.634909\pi$
$569$	−1.22661e26			−0.822508			−0.411254	+	0.911521i	$0.634909\pi$
$570$		0			0
$571$			2.63692e25i			0.171023i	0.996337	+	0.0855113i	$0.0272524\pi$
$571$			2.63692e25i			0.171023i	−0.996337	+	0.0855113i	$0.972748\pi$
$572$	−2.71335e25	−	1.68922e25i	−0.173079	−	0.107751i
$573$		0			0
$574$	−5.47066e24	−	1.56376e24i	−0.0337580	−	0.00964957i
$575$	−6.64332e25			−0.403218
$576$		0			0
$577$	1.48000e26			0.869141			0.434571	−	0.900638i	$-0.356900\pi$
$577$	1.48000e26			0.869141			0.434571	+	0.900638i	$0.356900\pi$
$578$	−3.34767e25	−	9.56917e24i	−0.193388	−	0.0552790i
$579$		0			0
$580$	−2.27272e26	−	1.41490e26i	−1.27051	−	0.790968i
$581$			5.50587e24i			0.0302798i
$582$		0			0
$583$	−3.36593e25			−0.179165
$584$	1.51545e26	+	1.67465e26i	0.793630	+	0.877005i
$585$		0			0
$586$	−7.49451e25	+	2.62187e26i	−0.379941	+	1.32918i
$587$			3.16221e26i			1.57735i	0.614809	+	0.788676i	$0.289233\pi$
$587$			3.16221e26i			1.57735i	−0.614809	+	0.788676i	$0.710767\pi$
$588$		0			0
$589$		−	1.77932e26i		−	0.859329i
$590$	−1.84755e26	−	5.28112e25i	−0.878013	−	0.250976i
$591$		0			0
$592$	1.77968e26	−	8.75349e25i	0.819002	−	0.402833i
$593$	−4.11232e25			−0.186238			−0.0931188	−	0.995655i	$-0.529684\pi$
$593$	−4.11232e25			−0.186238			−0.0931188	+	0.995655i	$0.529684\pi$
$594$		0			0
$595$			1.09744e25i			0.0481360i
$596$	1.41014e26	−	2.26507e26i	0.608726	−	0.977782i
$597$		0			0
$598$	3.78978e25	−	1.32582e26i	0.158472	−	0.554398i
$599$	1.03552e26			0.426191			0.213096	−	0.977031i	$-0.431645\pi$
$599$	1.03552e26			0.426191			0.213096	+	0.977031i	$0.431645\pi$
$600$		0			0
$601$	−1.98522e26			−0.791592			−0.395796	−	0.918338i	$-0.629531\pi$
$601$	−1.98522e26			−0.791592			−0.395796	+	0.918338i	$0.629531\pi$
$602$	3.20958e24	−	1.12284e25i	0.0125974	−	0.0440707i
$603$		0			0
$604$	1.59724e26	+	9.94375e25i	0.607462	+	0.378181i
$605$		−	3.22474e26i		−	1.20731i
$606$		0			0
$607$	4.20554e26			1.52591			0.762956	−	0.646450i	$-0.223747\pi$
$607$	4.20554e26			1.52591			0.762956	+	0.646450i	$0.223747\pi$
$608$	−5.00254e26	+	9.03553e25i	−1.78693	+	0.322753i
$609$		0			0
$610$	−4.50370e26	−	1.28736e26i	−1.55932	−	0.445725i
$611$		−	4.89168e26i		−	1.66750i
$612$		0			0
$613$		−	2.47119e26i		−	0.816641i	−0.912839	−	0.408320i	$-0.866115\pi$
$613$		−	2.47119e26i		−	0.816641i	0.912839	−	0.408320i	$-0.133885\pi$
$614$	−8.09396e24	+	2.83159e25i	−0.0263367	+	0.0921363i
$615$		0			0
$616$	−2.27325e24	+	2.05714e24i	−0.00717185	+	0.00649004i
$617$	4.47234e26			1.38939			0.694697	−	0.719303i	$-0.255538\pi$
$617$	4.47234e26			1.38939			0.694697	+	0.719303i	$0.255538\pi$
$618$		0			0
$619$		−	9.70369e25i		−	0.292331i	−0.989260	−	0.146166i	$-0.953307\pi$
$619$		−	9.70369e25i		−	0.292331i	0.989260	−	0.146166i	$-0.0466933\pi$
$620$	−1.07406e26	+	1.72523e26i	−0.318644	+	0.511830i
$621$		0			0
$622$	1.46898e26	+	4.19901e25i	0.422675	+	0.120820i
$623$	1.48842e25			0.0421783
$624$		0			0
$625$	−4.49234e26			−1.23485
$626$	3.00800e26	+	8.59824e25i	0.814371	+	0.232784i
$627$		0			0
$628$	4.04018e25	−	6.48963e25i	0.106117	−	0.170453i
$629$		−	3.15320e26i		−	0.815774i
$630$		0			0
$631$	−1.42435e26			−0.357551			−0.178776	−	0.983890i	$-0.557214\pi$
$631$	−1.42435e26			−0.357551			−0.178776	+	0.983890i	$0.557214\pi$
$632$	−3.79034e26	−	4.18853e26i	−0.937273	−	1.03574i
$633$		0			0
$634$	4.72841e24	−	1.65419e25i	0.0113466	−	0.0396950i
$635$		−	8.65232e26i		−	2.04542i
$636$		0			0
$637$			3.87654e26i			0.889445i
$638$	−1.14328e26	−	3.26801e25i	−0.258438	−	0.0738733i
$639$		0			0
$640$	5.39587e26	+	2.14361e26i	1.18400	+	0.470366i
$641$	7.22851e26			1.56278			0.781389	−	0.624044i	$-0.214512\pi$
$641$	7.22851e26			1.56278			0.781389	+	0.624044i	$0.214512\pi$
$642$		0			0
$643$		−	9.33528e26i		−	1.95940i	−0.200470	−	0.979700i	$-0.564247\pi$
$643$		−	9.33528e26i		−	1.95940i	0.200470	−	0.979700i	$-0.435753\pi$
$644$	−1.12287e25	−	6.99049e24i	−0.0232227	−	0.0144575i
$645$		0			0
$646$	−2.22126e26	+	7.77085e26i	−0.446058	+	1.56049i
$647$	5.11281e26			1.01174			0.505870	−	0.862610i	$-0.331172\pi$
$647$	5.11281e26			1.01174			0.505870	+	0.862610i	$0.331172\pi$
$648$		0			0
$649$	−8.53461e25			−0.164006
$650$	−8.05765e25	+	2.81888e26i	−0.152592	+	0.533827i
$651$		0			0
$652$	3.48742e26	−	5.60175e26i	0.641434	−	1.03032i
$653$			3.98338e26i			0.722065i	0.932553	+	0.361033i	$0.117576\pi$
$653$			3.98338e26i			0.722065i	−0.932553	+	0.361033i	$0.882424\pi$
$654$		0			0
$655$	1.32980e27			2.34150
$656$	2.11228e26	+	4.29448e26i	0.366576	+	0.745288i
$657$		0			0
$658$	−4.51151e25	−	1.28959e25i	−0.0760634	−	0.0217424i
$659$			4.20018e26i			0.698001i	0.937123	+	0.349000i	$0.113479\pi$
$659$			4.20018e26i			0.698001i	−0.937123	+	0.349000i	$0.886521\pi$
$660$		0			0
$661$			4.64134e26i			0.749427i	0.927141	+	0.374713i	$0.122259\pi$
$661$			4.64134e26i			0.749427i	−0.927141	+	0.374713i	$0.877741\pi$
$662$	−2.45951e26	+	8.60434e26i	−0.391469	+	1.36951i
$663$		0			0
$664$	3.43387e26	−	3.10743e26i	0.531114	−	0.480623i
$665$	−6.41381e25			−0.0977936
$666$		0			0
$667$		−	5.12993e26i		−	0.760179i
$668$	−1.69887e26	−	1.05764e26i	−0.248189	−	0.154512i
$669$		0			0
$670$	−6.83031e26	−	1.95241e26i	−0.969907	−	0.277243i
$671$	−2.08045e26			−0.291269
$672$		0			0
$673$	2.53795e26			0.345414			0.172707	−	0.984973i	$-0.444749\pi$
$673$	2.53795e26			0.345414			0.172707	+	0.984973i	$0.444749\pi$
$674$	−4.45206e26	−	1.27260e26i	−0.597437	−	0.170775i
$675$		0			0
$676$	1.34073e26	+	8.34685e25i	0.174924	+	0.108900i
$677$			6.54796e26i			0.842391i	0.906970	+	0.421195i	$0.138389\pi$
$677$			6.54796e26i			0.842391i	−0.906970	+	0.421195i	$0.861611\pi$
$678$		0			0
$679$	−2.04048e25			−0.0255252
$680$	6.84447e26	−	6.19379e26i	0.844317	−	0.764050i
$681$		0			0
$682$	−2.48077e25	+	8.67870e25i	−0.0297601	+	0.104113i
$683$		−	1.26437e27i		−	1.49582i	−0.663802	−	0.747909i	$-0.731058\pi$
$683$		−	1.26437e27i		−	1.49582i	0.663802	−	0.747909i	$-0.268942\pi$
$684$		0			0
$685$		−	1.29899e27i		−	1.49467i
$686$	7.15691e25	+	2.04577e25i	0.0812170	+	0.0232155i
$687$		0			0
$688$	−8.81430e26	+	4.33539e26i	−0.972966	+	0.478561i
$689$	−6.40850e26			−0.697708
$690$		0			0
$691$		−	8.15641e25i		−	0.0863889i	−0.999067	−	0.0431944i	$-0.986247\pi$
$691$		−	8.15641e25i		−	0.0863889i	0.999067	−	0.0431944i	$-0.0137535\pi$
$692$	1.99639e26	−	3.20675e26i	0.208563	−	0.335009i
$693$		0			0
$694$	−1.36151e26	+	4.76310e26i	−0.138390	+	0.484144i
$695$	2.23469e27			2.24058
$696$		0			0
$697$	7.60887e26			0.742350
$698$	−7.25127e25	+	2.53678e26i	−0.0697891	+	0.244150i
$699$		0			0
$700$	2.38738e25	+	1.48628e25i	0.0223610	+	0.0139210i
$701$		−	1.50490e27i		−	1.39055i	−0.718744	−	0.695275i	$-0.755283\pi$
$701$		−	1.50490e27i		−	1.39055i	0.718744	−	0.695275i	$-0.244717\pi$
$702$		0			0
$703$	1.84283e27			1.65733
$704$	2.56598e26	+	2.56753e25i	0.227674	+	0.0227811i
$705$		0			0
$706$	3.81966e26	+	1.09183e26i	0.329899	+	0.0943000i
$707$			4.56504e25i			0.0389009i
$708$		0			0
$709$			1.48850e25i			0.0123484i	0.999981	+	0.00617420i	$0.00196532\pi$
$709$			1.48850e25i			0.0123484i	−0.999981	+	0.00617420i	$0.998035\pi$
$710$	−7.55152e25	+	2.64182e26i	−0.0618130	+	0.216246i
$711$		0			0
$712$	−8.40042e26	−	9.28292e26i	−0.669486	−	0.739818i
$713$	−3.89416e26			−0.306241
$714$		0			0
$715$			3.39197e26i			0.259744i
$716$	−4.28770e26	+	6.88723e26i	−0.324004	+	0.520440i
$717$		0			0
$718$	−8.93002e26	−	2.55260e26i	−0.657158	−	0.187846i
$719$	−5.98917e25			−0.0434953			−0.0217476	−	0.999763i	$-0.506923\pi$
$719$	−5.98917e25			−0.0434953			−0.0217476	+	0.999763i	$0.506923\pi$
$720$		0			0
$721$	8.23672e25			0.0582599
$722$	−3.16418e27	−	9.04466e26i	−2.20881	−	0.631377i
$723$		0			0
$724$	1.09505e27	−	1.75896e27i	0.744593	−	1.19602i
$725$			1.09070e27i			0.731972i
$726$		0			0
$727$	−1.58883e27			−1.03872			−0.519362	−	0.854554i	$-0.673831\pi$
$727$	−1.58883e27			−1.03872			−0.519362	+	0.854554i	$0.673831\pi$
$728$	−4.32812e25	+	3.91666e25i	−0.0279287	+	0.0252736i
$729$		0			0
$730$	6.58754e26	−	2.30458e27i	0.414148	−	1.44885i
$731$			1.56170e27i			0.969131i
$732$		0			0
$733$			7.88881e26i			0.477006i	0.971142	+	0.238503i	$0.0766566\pi$
$733$			7.88881e26i			0.477006i	−0.971142	+	0.238503i	$0.923343\pi$
$734$	−8.58254e26	−	2.45328e26i	−0.512275	−	0.146432i
$735$		0			0
$736$	1.97748e26	+	1.09484e27i	0.115020	+	0.636810i
$737$	−3.15522e26			−0.181171
$738$		0			0
$739$			7.06002e26i			0.395079i	0.980295	+	0.197539i	$0.0632950\pi$
$739$			7.06002e26i			0.395079i	−0.980295	+	0.197539i	$0.936705\pi$
$740$	−1.78681e27	−	1.11239e27i	−0.987135	−	0.614549i
$741$		0			0
$742$	−1.68947e25	+	5.91044e25i	−0.00909733	+	0.0318261i
$743$	3.24185e27			1.72345			0.861726	−	0.507373i	$-0.169384\pi$
$743$	3.24185e27			1.72345			0.861726	+	0.507373i	$0.169384\pi$
$744$		0			0
$745$	−2.83158e27			−1.46738
$746$	−3.70396e26	+	1.29579e27i	−0.189517	+	0.663005i
$747$		0			0
$748$	2.16685e26	−	3.48056e26i	0.108085	−	0.173614i
$749$			1.23158e26i			0.0606579i
$750$		0			0
$751$	3.47111e27			1.66682			0.833411	−	0.552654i	$-0.186385\pi$
$751$	3.47111e27			1.66682			0.833411	+	0.552654i	$0.186385\pi$
$752$	1.74194e27	+	3.54154e27i	0.825968	+	1.67928i
$753$		0			0
$754$	−2.17673e27	−	6.22207e26i	−1.00641	−	0.287678i
$755$		−	1.99672e27i		−	0.911635i
$756$		0			0
$757$			8.85845e26i			0.394409i	0.980362	+	0.197205i	$0.0631863\pi$
$757$			8.85845e26i			0.394409i	−0.980362	+	0.197205i	$0.936814\pi$
$758$	2.35212e26	−	8.22864e26i	0.103419	−	0.361802i
$759$		0			0
$760$	3.61986e27	+	4.00014e27i	1.55225	+	1.71532i
$761$	−3.97430e26			−0.168309			−0.0841543	−	0.996453i	$-0.526819\pi$
$761$	−3.97430e26			−0.168309			−0.0841543	+	0.996453i	$0.526819\pi$
$762$		0			0
$763$			5.99988e25i			0.0247833i
$764$	2.10702e27	+	1.31175e27i	0.859573	+	0.535134i
$765$		0			0
$766$	−2.38507e27	−	6.81762e26i	−0.949136	−	0.271306i
$767$	−1.62493e27			−0.638674
$768$		0			0
$769$	−2.90265e27			−1.11300			−0.556499	−	0.830848i	$-0.687856\pi$
$769$	−2.90265e27			−1.11300			−0.556499	+	0.830848i	$0.687856\pi$
$770$	3.12835e25	+	8.94225e24i	0.0118482	+	0.00338677i
$771$		0			0
$772$	3.49974e27	+	2.17879e27i	1.29322	+	0.805103i
$773$		−	3.03505e27i		−	1.10780i	−0.832584	−	0.553899i	$-0.813139\pi$
$773$		−	3.03505e27i		−	1.10780i	0.832584	−	0.553899i	$-0.186861\pi$
$774$		0			0
$775$	8.27957e26			0.294877
$776$	1.15161e27	+	1.27260e27i	0.405154	+	0.447717i
$777$		0			0
$778$	−1.37643e27	+	4.81530e27i	−0.472551	+	1.65317i
$779$			4.44688e27i			1.50817i
$780$		0			0
$781$			1.22037e26i			0.0403931i
$782$	1.70070e27	+	4.86137e26i	0.556113	+	0.158962i
$783$		0			0
$784$	−1.38044e27	−	2.80659e27i	−0.440571	−	0.895727i
$785$	−8.11273e26			−0.255803
$786$		0			0
$787$		−	1.60790e27i		−	0.494879i	−0.968903	−	0.247440i	$-0.920411\pi$
$787$		−	1.60790e27i		−	0.494879i	0.968903	−	0.247440i	$-0.0795892\pi$
$788$	1.47602e27	−	2.37089e27i	0.448841	−	0.720962i
$789$		0			0
$790$	−1.64764e27	+	5.76408e27i	−0.489107	+	1.71109i
$791$	8.27847e25			0.0242814
$792$		0			0
$793$	−3.96104e27			−1.13426
$794$	1.32386e27	−	4.63140e27i	0.374583	−	1.31044i
$795$		0			0
$796$	−7.68279e26	−	4.78299e26i	−0.212249	−	0.132137i
$797$		−	2.46654e27i		−	0.673341i	−0.941623	−	0.336670i	$-0.890699\pi$
$797$		−	2.46654e27i		−	0.673341i	0.941623	−	0.336670i	$-0.109301\pi$
$798$		0			0
$799$	6.27483e27			1.67266
$800$	−4.20442e26	−	2.32779e27i	−0.110752	−	0.613181i
$801$		0			0
$802$	−4.46267e27	−	1.27563e27i	−1.14799	−	0.328148i
$803$		−	1.06459e27i		−	0.270634i
$804$		0			0
$805$			1.40370e26i			0.0348509i
$806$	−4.72321e26	+	1.65236e27i	−0.115892	+	0.405437i
$807$		0			0
$808$	2.84710e27	−	2.57644e27i	0.682331	−	0.617464i
$809$	−3.85670e27			−0.913492			−0.456746	−	0.889597i	$-0.650985\pi$
$809$	−3.85670e27			−0.913492			−0.456746	+	0.889597i	$0.650985\pi$
$810$		0			0
$811$		−	3.23598e27i		−	0.748700i	−0.927288	−	0.374350i	$-0.877866\pi$
$811$		−	3.23598e27i		−	0.748700i	0.927288	−	0.374350i	$-0.122134\pi$
$812$	−1.14770e26	+	1.84352e26i	−0.0262450	+	0.0421566i
$813$		0			0
$814$	−8.98847e26	−	2.56931e26i	−0.200795	−	0.0573964i
$815$	−7.00279e27			−1.54623
$816$		0			0
$817$	−9.12709e27			−1.96890
$818$	3.84406e27	+	1.09881e27i	0.819661	+	0.234296i
$819$		0			0
$820$	2.68428e27	−	4.31169e27i	0.559237	−	0.898289i
$821$			8.58529e27i			1.76805i	0.467439	+	0.884026i	$0.345177\pi$
$821$			8.58529e27i			1.76805i	−0.467439	+	0.884026i	$0.654823\pi$
$822$		0			0
$823$	3.42172e25			0.00688566			0.00344283	−	0.999994i	$-0.498904\pi$
$823$	3.42172e25			0.00688566			0.00344283	+	0.999994i	$0.498904\pi$
$824$	−4.64868e27	−	5.13704e27i	−0.924743	−	1.02189i
$825$		0			0
$826$	−4.28380e25	+	1.49864e26i	−0.00832759	+	0.0291332i
$827$		−	7.32223e25i		−	0.0140715i	−0.999975	−	0.00703576i	$-0.997760\pi$
$827$		−	7.32223e25i		−	0.0140715i	0.999975	−	0.00703576i	$-0.00223957\pi$
$828$		0			0
$829$		−	3.74412e26i		−	0.0703205i	−0.999382	−	0.0351602i	$-0.988806\pi$
$829$		−	3.74412e26i		−	0.0703205i	0.999382	−	0.0351602i	$-0.0111942\pi$
$830$	−4.72555e27	−	1.35078e27i	−0.877426	−	0.250808i
$831$		0			0
$832$	4.88545e27	+	4.88840e26i	0.886610	+	0.0887146i
$833$	−4.97265e27			−0.892196
$834$		0			0
$835$			2.12377e27i			0.372465i
$836$	2.03416e27	+	1.26638e27i	0.352716	+	0.219586i
$837$		0			0
$838$	6.59590e26	−	2.30751e27i	0.111804	−	0.391134i
$839$	8.83835e27			1.48126			0.740632	−	0.671911i	$-0.234526\pi$
$839$	8.83835e27			1.48126			0.740632	+	0.671911i	$0.234526\pi$
$840$		0			0
$841$	−2.31906e27			−0.379971
$842$	−7.83342e26	+	2.74044e27i	−0.126907	+	0.443972i
$843$		0			0
$844$	−3.97766e27	+	6.38922e27i	−0.630050	+	1.01203i
$845$		−	1.67606e27i		−	0.262513i
$846$		0			0
$847$	−2.61576e26			−0.0400595
$848$	4.63971e27	−	2.28208e27i	0.702636	−	0.345597i
$849$		0			0
$850$	−3.61594e27	−	1.03360e27i	−0.535478	−	0.153064i
$851$		−	4.03315e27i		−	0.590627i
$852$		0			0
$853$			1.18640e28i			1.69908i	0.527525	+	0.849540i	$0.323120\pi$
$853$			1.18640e28i			1.69908i	−0.527525	+	0.849540i	$0.676880\pi$
$854$	−1.04425e26	+	3.65319e26i	−0.0147895	+	0.0517395i
$855$		0			0
$856$	7.68110e27	−	6.95088e27i	1.06395	−	0.962806i
$857$	2.48012e27			0.339746			0.169873	−	0.985466i	$-0.445664\pi$
$857$	2.48012e27			0.339746			0.169873	+	0.985466i	$0.445664\pi$
$858$		0			0
$859$			8.04241e27i			1.07758i	0.842439	+	0.538792i	$0.181119\pi$
$859$			8.04241e27i			1.07758i	−0.842439	+	0.538792i	$0.818881\pi$
$860$	8.84962e27	+	5.50941e27i	1.17271	+	0.730078i
$861$		0			0
$862$	−7.19961e26	−	2.05797e26i	−0.0933233	−	0.0266760i
$863$	−4.84578e27			−0.621242			−0.310621	−	0.950534i	$-0.600537\pi$
$863$	−4.84578e27			−0.621242			−0.310621	+	0.950534i	$0.600537\pi$
$864$		0			0
$865$	−4.00878e27			−0.502758
$866$	−1.56516e27	−	4.47394e26i	−0.194151	−	0.0554971i
$867$		0			0
$868$	1.39943e26	+	8.71225e25i	0.0169829	+	0.0105729i
$869$			2.66268e27i			0.319618i
$870$		0			0
$871$	−6.00731e27			−0.705517
$872$	3.74198e27	−	3.38624e27i	0.434705	−	0.393379i
$873$		0			0
$874$	−2.84114e27	+	9.93945e27i	−0.322950	+	1.12981i
$875$			1.80523e26i			0.0202981i
$876$		0			0
$877$			1.11292e28i			1.22452i	0.790655	+	0.612261i	$0.209740\pi$
$877$			1.11292e28i			1.22452i	−0.790655	+	0.612261i	$0.790260\pi$
$878$	−7.92256e27	−	2.26463e27i	−0.862319	−	0.246490i
$879$		0			0
$880$	−1.20789e27	−	2.45577e27i	−0.128659	−	0.261578i
$881$	−1.49766e28			−1.57813			−0.789065	−	0.614310i	$-0.789435\pi$
$881$	−1.49766e28			−1.57813			−0.789065	+	0.614310i	$0.789435\pi$
$882$		0			0
$883$		−	1.18632e28i		−	1.22342i	−0.791082	−	0.611711i	$-0.790482\pi$
$883$		−	1.18632e28i		−	1.22342i	0.791082	−	0.611711i	$-0.209518\pi$
$884$	4.12554e27	−	6.62675e27i	0.420905	−	0.676090i
$885$		0			0
$886$	4.23320e27	−	1.48094e28i	0.422715	−	1.47883i
$887$	1.21862e28			1.20391			0.601953	−	0.798532i	$-0.294389\pi$
$887$	1.21862e28			1.20391			0.601953	+	0.798532i	$0.294389\pi$
$888$		0			0
$889$	−7.01836e26			−0.0678686
$890$	−3.65161e27	+	1.27748e28i	−0.349365	+	1.22222i
$891$		0			0
$892$	6.09069e27	+	3.79181e27i	0.570427	+	0.355124i
$893$			3.66722e28i			3.39819i
$894$		0			0
$895$	8.60976e27			0.781039
$896$	1.73880e26	−	4.37688e26i	0.0156071	−	0.0392861i
$897$		0			0
$898$	−3.78477e27	−	1.08186e27i	−0.332594	−	0.0950705i
$899$			6.39343e27i			0.555926i
$900$		0			0
$901$		−	8.22055e27i		−	0.699867i
$902$	6.19992e26	−	2.16898e27i	0.0522305	−	0.182723i
$903$		0			0
$904$	−4.67224e27	−	5.16308e27i	−0.385412	−	0.425901i
$905$	−2.19888e28			−1.79490
$906$		0			0
$907$			2.10303e28i			1.68103i	0.541789	+	0.840515i	$0.317747\pi$
$907$			2.10303e28i			1.68103i	−0.541789	+	0.840515i	$0.682253\pi$
$908$	6.32995e27	−	1.01676e28i	0.500708	−	0.804275i
$909$		0			0
$910$	5.95617e26	+	1.70254e26i	0.0461396	+	0.0131888i
$911$	−9.47120e27			−0.726074			−0.363037	−	0.931775i	$-0.618260\pi$
$911$	−9.47120e27			−0.726074			−0.363037	+	0.931775i	$0.618260\pi$
$912$		0			0
$913$	−2.18294e27			−0.163896
$914$	7.22761e27	+	2.06598e27i	0.537039	+	0.153510i
$915$		0			0
$916$	−3.21252e27	+	5.16018e27i	−0.233797	+	0.375542i
$917$		−	1.07867e27i		−	0.0776929i
$918$		0			0
$919$	1.97843e28			1.39580			0.697901	−	0.716194i	$-0.254117\pi$
$919$	1.97843e28			1.39580			0.697901	+	0.716194i	$0.254117\pi$
$920$	8.75454e27	−	7.92227e27i	0.611292	−	0.553179i
$921$		0			0
$922$	−4.00651e27	+	1.40164e28i	−0.274045	+	0.958719i
$923$			2.32350e27i			0.157299i
$924$		0			0
$925$			8.57509e27i			0.568712i
$926$	1.17132e28	+	3.34817e27i	0.768903	+	0.219787i
$927$		0			0
$928$	1.79750e28	−	3.24663e27i	1.15602	−	0.208798i
$929$	−2.35154e27			−0.149693			−0.0748467	−	0.997195i	$-0.523847\pi$
$929$	−2.35154e27			−0.149693			−0.0748467	+	0.997195i	$0.523847\pi$
$930$		0			0
$931$		−	2.90618e28i		−	1.81259i
$932$	6.41791e27	+	3.99553e27i	0.396226	+	0.246674i
$933$		0			0
$934$	−5.90842e27	+	2.06700e28i	−0.357418	+	1.25039i
$935$	−4.35108e27			−0.260547
$936$		0			0
$937$	−2.37072e28			−1.39109			−0.695544	−	0.718483i	$-0.744837\pi$
$937$	−2.37072e28			−1.39109			−0.695544	+	0.718483i	$0.744837\pi$
$938$	−1.58371e26	+	5.54043e26i	−0.00919915	+	0.0321823i
$939$		0			0
$940$	2.21365e28	−	3.55573e28i	1.26007	−	2.02402i
$941$		−	1.63014e28i		−	0.918592i	−0.888283	−	0.459296i	$-0.848102\pi$
$941$		−	1.63014e28i		−	0.918592i	0.888283	−	0.459296i	$-0.151898\pi$
$942$		0			0
$943$	9.73226e27			0.537468
$944$	1.17644e28	−	5.78641e27i	0.643184	−	0.316356i
$945$		0			0
$946$	4.45177e27	+	1.27252e27i	0.238543	+	0.0681864i
$947$		−	1.67186e28i		−	0.886899i	−0.896299	−	0.443449i	$-0.853755\pi$
$947$		−	1.67186e28i		−	0.886899i	0.896299	−	0.443449i	$-0.146245\pi$
$948$		0			0
$949$		−	2.02690e28i		−	1.05391i
$950$	6.04070e27	−	2.11328e28i	0.310966	−	1.08788i
$951$		0			0
$952$	−5.02412e26	−	5.55192e26i	−0.0253518	−	0.0280151i
$953$	4.74178e27			0.236896			0.118448	−	0.992960i	$-0.462208\pi$
$953$	4.74178e27			0.236896			0.118448	+	0.992960i	$0.462208\pi$
$954$		0			0
$955$		−	2.63400e28i		−	1.28998i
$956$	−2.57943e28	−	1.60585e28i	−1.25076	−	0.778672i
$957$		0			0
$958$	−2.42428e28	−	6.92968e27i	−1.15242	−	0.329413i
$959$	−1.05368e27			−0.0495945
$960$		0			0
$961$	−1.68174e28			−0.776043
$962$	−1.71134e28	−	4.89179e27i	−0.781940	−	0.223514i
$963$		0			0
$964$	1.12977e28	+	7.03350e27i	0.506127	+	0.315093i
$965$		−	4.37504e28i		−	1.94077i
$966$		0			0
$967$	3.60277e27			0.156706			0.0783529	−	0.996926i	$-0.475034\pi$
$967$	3.60277e27			0.156706			0.0783529	+	0.996926i	$0.475034\pi$
$968$	1.47630e28	+	1.63139e28i	0.635854	+	0.702653i
$969$		0			0
$970$	5.00599e27	−	1.75129e28i	0.211426	−	0.739651i
$971$		−	4.48458e27i		−	0.187559i	−0.995593	−	0.0937797i	$-0.970105\pi$
$971$		−	4.48458e27i		−	0.187559i	0.995593	−	0.0937797i	$-0.0298949\pi$
$972$		0			0
$973$		−	1.81267e27i		−	0.0743443i
$974$	2.65846e28	+	7.59908e27i	1.07974	+	0.308639i
$975$		0			0
$976$	2.86776e28	−	1.41053e28i	1.14227	−	0.561837i
$977$	3.13619e28			1.23710			0.618550	−	0.785746i	$-0.287721\pi$
$977$	3.13619e28			1.23710			0.618550	+	0.785746i	$0.287721\pi$
$978$		0			0
$979$			5.90121e27i			0.228300i
$980$	−1.75426e28	+	2.81783e28i	−0.672121	+	1.07961i
$981$		0			0
$982$	9.29267e27	−	3.25094e28i	0.349206	−	1.22166i
$983$	−5.43983e27			−0.202454			−0.101227	−	0.994863i	$-0.532277\pi$
$983$	−5.43983e27			−0.202454			−0.101227	+	0.994863i	$0.532277\pi$
$984$		0			0
$985$	−2.96386e28			−1.08197
$986$	7.98140e27	−	2.79221e28i	0.288568	−	1.00953i
$987$		0			0
$988$	3.87289e28	+	2.41110e28i	1.37355	+	0.855115i
$989$			1.99752e28i			0.701659i
$990$		0			0
$991$	4.64392e28			1.60024			0.800120	−	0.599841i	$-0.204769\pi$
$991$	4.64392e28			1.60024			0.800120	+	0.599841i	$0.204769\pi$
$992$	−2.46454e27	−	1.36450e28i	−0.0841151	−	0.465705i
$993$		0			0
$994$	2.14292e26	+	6.12544e25i	0.00717523	+	0.00205101i
$995$			9.60430e27i			0.318527i
$996$		0			0
$997$			8.60787e27i			0.280086i	0.990145	+	0.140043i	$0.0447241\pi$
$997$			8.60787e27i			0.280086i	−0.990145	+	0.140043i	$0.955276\pi$
$998$	−2.39243e27	+	8.36965e27i	−0.0771078	+	0.269754i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.20.d.b.37.18		18
3.2	odd	2		8.20.b.a.5.1	✓	18
8.5	even	2	inner	72.20.d.b.37.17		18
12.11	even	2		32.20.b.a.17.10		18
24.5	odd	2		8.20.b.a.5.2	yes	18
24.11	even	2		32.20.b.a.17.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.20.b.a.5.1	✓	18	3.2	odd	2
8.20.b.a.5.2	yes	18	24.5	odd	2
32.20.b.a.17.9		18	24.11	even	2
32.20.b.a.17.10		18	12.11	even	2
72.20.d.b.37.17		18	8.5	even	2	inner
72.20.d.b.37.18		18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(696.194 + 199.004i) q^{2} +(445083. + 277090. i) q^{4} -5.56401e6i q^{5} -4.51327e6 q^{7} +(2.54722e8 + 2.81482e8i) q^{8} +O(q^{10})\)	\(q+(696.194 + 199.004i) q^{2} +(445083. + 277090. i) q^{4} -5.56401e6i q^{5} -4.51327e6 q^{7} +(2.54722e8 + 2.81482e8i) q^{8} +(1.10726e9 - 3.87363e9i) q^{10} -1.78940e9i q^{11} -3.40689e10i q^{13} +(-3.14211e9 - 8.98157e8i) q^{14} +(1.21320e11 + 2.46656e11i) q^{16} +4.37021e11 q^{17} +2.55409e12i q^{19} +(1.54173e12 - 2.47645e12i) q^{20} +(3.56097e11 - 1.24577e12i) q^{22} +5.58979e12 q^{23} -1.18847e13 q^{25} +(6.77983e12 - 2.37185e13i) q^{26} +(-2.00878e12 - 1.25058e12i) q^{28} -9.17732e13i q^{29} -6.96656e13 q^{31} +(3.53767e13 + 1.95864e14i) q^{32} +(3.04251e14 + 8.69687e13i) q^{34} +2.51119e13i q^{35} -7.21521e14i q^{37} +(-5.08274e14 + 1.77814e15i) q^{38} +(1.56617e15 - 1.41728e15i) q^{40} +1.74108e15 q^{41} +3.57351e15i q^{43} +(4.95824e14 - 7.96430e14i) q^{44} +(3.89158e15 + 1.11239e15i) q^{46} +1.43582e16 q^{47} -1.13785e16 q^{49} +(-8.27408e15 - 2.36511e15i) q^{50} +(9.44015e15 - 1.51635e16i) q^{52} -1.88104e16i q^{53} -9.95622e15 q^{55} +(-1.14963e15 - 1.27040e15i) q^{56} +(1.82632e16 - 6.38919e16i) q^{58} -4.76955e16i q^{59} -1.16266e17i q^{61} +(-4.85007e16 - 1.38637e16i) q^{62} +(-1.43486e16 + 1.43399e17i) q^{64} -1.89560e17 q^{65} -1.76329e17i q^{67} +(1.94510e17 + 1.21094e17i) q^{68} +(-4.99736e15 + 1.74827e16i) q^{70} -6.82001e16 q^{71} +5.94941e17 q^{73} +(1.43585e17 - 5.02318e17i) q^{74} +(-7.07714e17 + 1.13678e18i) q^{76} +8.07603e15i q^{77} -1.48803e18 q^{79} +(1.37240e18 - 6.75026e17i) q^{80} +(1.21213e18 + 3.46481e17i) q^{82} -1.21993e18i q^{83} -2.43159e18i q^{85} +(-7.11143e17 + 2.48786e18i) q^{86} +(5.03682e17 - 4.55799e17i) q^{88} -3.29788e18 q^{89} +1.53762e17i q^{91} +(2.48792e18 + 1.54888e18i) q^{92} +(9.99609e18 + 2.85734e18i) q^{94} +1.42110e19 q^{95} +4.52106e18 q^{97} +(-7.92166e18 - 2.26437e18i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 458 q^{2} - 412108 q^{4} - 80707216 q^{7} + 173313752 q^{8}+O(q^{10}) \) 18 * q + 458 * q^2 - 412108 * q^4 - 80707216 * q^7 + 173313752 * q^8	\( 18 q + 458 q^{2} - 412108 q^{4} - 80707216 q^{7} + 173313752 q^{8} + 758800104 q^{10} + 122453668784 q^{14} - 696212072432 q^{16} - 14121426692 q^{17} - 6517087595632 q^{20} - 11074654117412 q^{22} - 2177121583952 q^{23} - 44414474211734 q^{25} - 26782030269304 q^{26} - 97002327802784 q^{28} + 428505770260416 q^{31} - 122449430282912 q^{32} - 478448330325748 q^{34} + 486194587539796 q^{38} - 16\!\cdots\!76 q^{40}+ \cdots - 88\!\cdots\!22 q^{98}+O(q^{100}) \) 18 * q + 458 * q^2 - 412108 * q^4 - 80707216 * q^7 + 173313752 * q^8 + 758800104 * q^10 + 122453668784 * q^14 - 696212072432 * q^16 - 14121426692 * q^17 - 6517087595632 * q^20 - 11074654117412 * q^22 - 2177121583952 * q^23 - 44414474211734 * q^25 - 26782030269304 * q^26 - 97002327802784 * q^28 + 428505770260416 * q^31 - 122449430282912 * q^32 - 478448330325748 * q^34 + 486194587539796 * q^38 - 1697818250610976 * q^40 - 1200260021141524 * q^41 - 7031781193616424 * q^44 - 14917443628457488 * q^46 + 1134160959992928 * q^47 + 31570092936329058 * q^49 + 34734151321861826 * q^50 - 26877456911772208 * q^52 - 51757047863478736 * q^55 - 52858270161183424 * q^56 - 20470056808312424 * q^58 - 93766686763697984 * q^62 - 253721318369185216 * q^64 + 184007586011668640 * q^65 - 201388986348307752 * q^68 - 340698473416023872 * q^70 + 1599477989199799056 * q^71 - 93004298989809068 * q^73 + 93558253821761240 * q^74 - 1090379619519933176 * q^76 + 1813975801025264480 * q^79 - 3057120301750869696 * q^80 - 2418785089528546244 * q^82 - 1332333723895598620 * q^86 - 3097741184498130608 * q^88 - 4470509771045743540 * q^89 + 2965990502259463392 * q^92 - 3533635112749329696 * q^94 - 23809730986995679856 * q^95 + 8246429789464117220 * q^97 - 8841667592735478822 * q^98

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