LMFDB - Embedded newform 72.18.d.b.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,18,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, 18, names="a")

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

chi := DirichletCharacter("72.37");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 18 $
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:	$131.919902888$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 109505575668 x^{14} - 766539029536 x^{13} + \cdots + 23\!\cdots\!64 $ x^16 - 8x^15 + 109505575668x^14 - 766539029536x^13 + 4565100228876328094758x^12 - 27390601363292961184944x^11 + 92591127780943012435040881148284x^10 - 462955638653634549696621441749088x^9 + 977795346278604835725743703677218847007441x^8 - 3911181382336685511282464131494050715936008x^7 + 5486253005890750810105420612112386097148906843883912x^6 - 16458759003983117594082276228892502324980015032552768x^5 + 15550361362184906921502189748666544464631762598295918546369552x^4 - 31100722696938548840928895118996183700448942016456464597789824x^3 + 18096113985773341939458863826141502874171854160838520206186924390289152x^2 - 18096113970222980593732715905689044683436914121788987093981784054126592*x + 2314274244692410619337768589845007009310106660645582524080800163846193346084864
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{20}\cdot 7 $
Twist minimal:	no (minimal twist has level 8)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			37.5
Root			$0.500000 - 151568. i$ of defining polynomial
Character	$\chi$	$=$	72.37
Dual form			72.18.d.b.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-214.125 - 291.929i) q^{2} +(-39373.4 + 125018. i) q^{4} +1.21254e6i q^{5} +1.76580e7 q^{7} +(4.49273e7 - 1.52753e7i) q^{8} +O(q^{10})$	\(q+(-214.125 - 291.929i) q^{2} +(-39373.4 + 125018. i) q^{4} +1.21254e6i q^{5} +1.76580e7 q^{7} +(4.49273e7 - 1.52753e7i) q^{8} +(3.53976e8 - 2.59635e8i) q^{10} +7.26817e8i q^{11} +3.16645e9i q^{13} +(-3.78101e9 - 5.15488e9i) q^{14} +(-1.40793e10 - 9.84479e9i) q^{16} -4.56030e10 q^{17} +1.55789e10i q^{19} +(-1.51590e11 - 4.77419e10i) q^{20} +(2.12179e11 - 1.55629e11i) q^{22} -4.09250e11 q^{23} -7.07318e11 q^{25} +(9.24380e11 - 6.78015e11i) q^{26} +(-6.95255e11 + 2.20757e12i) q^{28} +3.11338e12i q^{29} -6.57077e12 q^{31} +(1.40750e11 + 6.21818e12i) q^{32} +(9.76472e12 + 1.33128e13i) q^{34} +2.14111e13i q^{35} -1.36898e13i q^{37} +(4.54793e12 - 3.33582e12i) q^{38} +(1.85219e13 + 5.44763e13i) q^{40} +2.81830e12 q^{41} +1.36024e13i q^{43} +(-9.08656e13 - 2.86173e13i) q^{44} +(8.76304e13 + 1.19472e14i) q^{46} -6.84132e11 q^{47} +7.91743e13 q^{49} +(1.51454e14 + 2.06487e14i) q^{50} +(-3.95865e14 - 1.24674e14i) q^{52} -2.47869e14i q^{53} -8.81297e14 q^{55} +(7.93327e14 - 2.69731e14i) q^{56} +(9.08887e14 - 6.66651e14i) q^{58} -2.03296e15i q^{59} -8.92495e14i q^{61} +(1.40696e15 + 1.91820e15i) q^{62} +(1.78513e15 - 1.37255e15i) q^{64} -3.83946e15 q^{65} +5.06693e15i q^{67} +(1.79554e15 - 5.70121e15i) q^{68} +(6.25051e15 - 4.58463e15i) q^{70} +6.85113e15 q^{71} +1.37250e15 q^{73} +(-3.99644e15 + 2.93131e15i) q^{74} +(-1.94765e15 - 6.13392e14i) q^{76} +1.28341e16i q^{77} -1.78556e16 q^{79} +(1.19372e16 - 1.70718e16i) q^{80} +(-6.03468e14 - 8.22745e14i) q^{82} +1.48017e15i q^{83} -5.52955e16i q^{85} +(3.97094e15 - 2.91261e15i) q^{86} +(1.11023e16 + 3.26540e16i) q^{88} +3.78700e16 q^{89} +5.59132e16i q^{91} +(1.61135e16 - 5.11638e16i) q^{92} +(1.46489e14 + 1.99718e14i) q^{94} -1.88900e16 q^{95} +1.28098e17 q^{97} +(-1.69532e16 - 2.31133e16i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8}+O(q^{10}) $ 16 * q - 270 * q^2 - 27436 * q^4 + 11529600 * q^7 - 24334920 * q^8	$ 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8} + 131002712 q^{10} - 16363788528 q^{14} + 26500434192 q^{16} + 7489125600 q^{17} + 209445719856 q^{20} + 223126527100 q^{22} - 746845345920 q^{23} - 1809682431664 q^{25} - 2467726531080 q^{26} + 3220542267040 q^{28} - 318979758592 q^{31} - 1455647316000 q^{32} - 4461251980292 q^{34} - 24076283913900 q^{38} + 60626292962592 q^{40} - 7482251536032 q^{41} - 193654716236040 q^{44} - 195097141003568 q^{46} + 376698804821760 q^{47} + 127691292101520 q^{49} - 474997408872102 q^{50} - 272251877663120 q^{52} + 22\!\cdots\!52 q^{55}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) $ 16 * q - 270 * q^2 - 27436 * q^4 + 11529600 * q^7 - 24334920 * q^8 + 131002712 * q^10 - 16363788528 * q^14 + 26500434192 * q^16 + 7489125600 * q^17 + 209445719856 * q^20 + 223126527100 * q^22 - 746845345920 * q^23 - 1809682431664 * q^25 - 2467726531080 * q^26 + 3220542267040 * q^28 - 318979758592 * q^31 - 1455647316000 * q^32 - 4461251980292 * q^34 - 24076283913900 * q^38 + 60626292962592 * q^40 - 7482251536032 * q^41 - 193654716236040 * q^44 - 195097141003568 * q^46 + 376698804821760 * q^47 + 127691292101520 * q^49 - 474997408872102 * q^50 - 272251877663120 * q^52 + 2209036687713152 * q^55 + 162767516076480 * q^56 - 623262610679960 * q^58 - 695695648144320 * q^62 + 1111931745501248 * q^64 - 2385987975356160 * q^65 - 5981109959771880 * q^68 - 10044559836180288 * q^70 - 9025926285576576 * q^71 + 11332002046118560 * q^73 - 11098735408189464 * q^74 + 5959440926938280 * q^76 - 45299671392008448 * q^79 - 1337342539452480 * q^80 + 15639739637081420 * q^82 + 14252032276026564 * q^86 - 66964872768837680 * q^88 + 69879174608766048 * q^89 - 57336249810701280 * q^92 - 192318922166254176 * q^94 - 93790444358203776 * q^95 + 95593398602180640 * q^97 - 339641261743253790 * 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 $

$2$	−214.125	−	291.929i	−0.591441	−	0.806348i
$2$	−214.125	−	291.929i	−0.591441	−	0.806348i
$3$		0			0
$3$		0			0
$4$	−39373.4	+	125018.i	−0.300395	+	0.953815i
$5$			1.21254e6i			1.38820i	0.719879	+	0.694100i	$0.244197\pi$
$5$			1.21254e6i			1.38820i	−0.719879	+	0.694100i	$0.755803\pi$
$6$		0			0
$7$	1.76580e7			1.15773			0.578866	−	0.815423i	$-0.303495\pi$
$7$	1.76580e7			1.15773			0.578866	+	0.815423i	$0.303495\pi$
$8$	4.49273e7	−	1.52753e7i	0.946773	−	0.321902i
$9$		0			0
$10$	3.53976e8	−	2.59635e8i	1.11937	−	0.821038i
$11$			7.26817e8i			1.02232i	0.859485	+	0.511161i	$0.170784\pi$
$11$			7.26817e8i			1.02232i	−0.859485	+	0.511161i	$0.829216\pi$
$12$		0			0
$13$			3.16645e9i			1.07660i	0.842753	+	0.538300i	$0.180933\pi$
$13$			3.16645e9i			1.07660i	−0.842753	+	0.538300i	$0.819067\pi$
$14$	−3.78101e9	−	5.15488e9i	−0.684730	−	0.933535i
$15$		0			0
$16$	−1.40793e10	−	9.84479e9i	−0.819526	−	0.573042i
$17$	−4.56030e10			−1.58554			−0.792771	−	0.609520i	$-0.791362\pi$
$17$	−4.56030e10			−1.58554			−0.792771	+	0.609520i	$0.791362\pi$
$18$		0			0
$19$			1.55789e10i			0.210441i	0.994449	+	0.105220i	$0.0335548\pi$
$19$			1.55789e10i			0.210441i	−0.994449	+	0.105220i	$0.966445\pi$
$20$	−1.51590e11	−	4.77419e10i	−1.32408	−	0.417008i
$21$		0			0
$22$	2.12179e11	−	1.55629e11i	0.824347	−	0.604643i
$23$	−4.09250e11			−1.08969			−0.544843	−	0.838538i	$-0.683411\pi$
$23$	−4.09250e11			−1.08969			−0.544843	+	0.838538i	$0.683411\pi$
$24$		0			0
$25$	−7.07318e11			−0.927096
$26$	9.24380e11	−	6.78015e11i	0.868115	−	0.636746i
$27$		0			0
$28$	−6.95255e11	+	2.20757e12i	−0.347777	+	1.10426i
$29$			3.11338e12i			1.15571i	0.816139	+	0.577855i	$0.196110\pi$
$29$			3.11338e12i			1.15571i	−0.816139	+	0.577855i	$0.803890\pi$
$30$		0			0
$31$	−6.57077e12			−1.38370			−0.691850	−	0.722041i	$-0.743204\pi$
$31$	−6.57077e12			−1.38370			−0.691850	+	0.722041i	$0.743204\pi$
$32$	1.40750e11	+	6.21818e12i	0.0226295	+	0.999744i
$33$		0			0
$34$	9.76472e12	+	1.33128e13i	0.937754	+	1.27850i
$35$			2.14111e13i			1.60716i
$36$		0			0
$37$		−	1.36898e13i		−	0.640739i	−0.947293	−	0.320369i	$-0.896193\pi$
$37$		−	1.36898e13i		−	0.640739i	0.947293	−	0.320369i	$-0.103807\pi$
$38$	4.54793e12	−	3.33582e12i	0.169689	−	0.124463i
$39$		0			0
$40$	1.85219e13	+	5.44763e13i	0.446865	+	1.31431i
$41$	2.81830e12			0.0551220			0.0275610	−	0.999620i	$-0.491226\pi$
$41$	2.81830e12			0.0551220			0.0275610	+	0.999620i	$0.491226\pi$
$42$		0			0
$43$			1.36024e13i			0.177474i	0.996055	+	0.0887369i	$0.0282830\pi$
$43$			1.36024e13i			0.177474i	−0.996055	+	0.0887369i	$0.971717\pi$
$44$	−9.08656e13	−	2.86173e13i	−0.975106	−	0.307100i
$45$		0			0
$46$	8.76304e13	+	1.19472e14i	0.644486	+	0.878667i
$47$	−6.84132e11			−0.00419091			−0.00209545	−	0.999998i	$-0.500667\pi$
$47$	−6.84132e11			−0.00419091			−0.00209545	+	0.999998i	$0.500667\pi$
$48$		0			0
$49$	7.91743e13			0.340343
$50$	1.51454e14	+	2.06487e14i	0.548323	+	0.747563i
$51$		0			0
$52$	−3.95865e14	−	1.24674e14i	−1.02688	−	0.323405i
$53$		−	2.47869e14i		−	0.546862i	−0.961892	−	0.273431i	$-0.911841\pi$
$53$		−	2.47869e14i		−	0.546862i	0.961892	−	0.273431i	$-0.0881585\pi$
$54$		0			0
$55$	−8.81297e14			−1.41919
$56$	7.93327e14	−	2.69731e14i	1.09611	−	0.372677i
$57$		0			0
$58$	9.08887e14	−	6.66651e14i	0.931905	−	0.683535i
$59$		−	2.03296e15i		−	1.80255i	−0.433245	−	0.901276i	$-0.642632\pi$
$59$		−	2.03296e15i		−	1.80255i	0.433245	−	0.901276i	$-0.357368\pi$
$60$		0			0
$61$		−	8.92495e14i		−	0.596077i	−0.954554	−	0.298038i	$-0.903668\pi$
$61$		−	8.92495e14i		−	0.596077i	0.954554	−	0.298038i	$-0.0963324\pi$
$62$	1.40696e15	+	1.91820e15i	0.818377	+	1.11574i
$63$		0			0
$64$	1.78513e15	−	1.37255e15i	0.792758	−	0.609537i
$65$	−3.83946e15			−1.49454
$66$		0			0
$67$			5.06693e15i			1.52444i	0.647321	+	0.762218i	$0.275889\pi$
$67$			5.06693e15i			1.52444i	−0.647321	+	0.762218i	$0.724111\pi$
$68$	1.79554e15	−	5.70121e15i	0.476289	−	1.51231i
$69$		0			0
$70$	6.25051e15	−	4.58463e15i	1.29593	−	0.950542i
$71$	6.85113e15			1.25912			0.629559	−	0.776953i	$-0.283236\pi$
$71$	6.85113e15			1.25912			0.629559	+	0.776953i	$0.283236\pi$
$72$		0			0
$73$	1.37250e15			0.199191			0.0995954	−	0.995028i	$-0.468245\pi$
$73$	1.37250e15			0.199191			0.0995954	+	0.995028i	$0.468245\pi$
$74$	−3.99644e15	+	2.93131e15i	−0.516659	+	0.378959i
$75$		0			0
$76$	−1.94765e15	−	6.13392e14i	−0.200722	−	0.0632154i
$77$			1.28341e16i			1.18357i
$78$		0			0
$79$	−1.78556e16			−1.32417			−0.662085	−	0.749429i	$-0.730328\pi$
$79$	−1.78556e16			−1.32417			−0.662085	+	0.749429i	$0.730328\pi$
$80$	1.19372e16	−	1.70718e16i	0.795497	−	1.13766i
$81$		0			0
$82$	−6.03468e14	−	8.22745e14i	−0.0326014	−	0.0444475i
$83$			1.48017e15i			0.0721354i	0.999349	+	0.0360677i	$0.0114832\pi$
$83$			1.48017e15i			0.0721354i	−0.999349	+	0.0360677i	$0.988517\pi$
$84$		0			0
$85$		−	5.52955e16i		−	2.20105i
$86$	3.97094e15	−	2.91261e15i	0.143106	−	0.104965i
$87$		0			0
$88$	1.11023e16	+	3.26540e16i	0.329088	+	0.967906i
$89$	3.78700e16			1.01972			0.509859	−	0.860258i	$-0.329697\pi$
$89$	3.78700e16			1.01972			0.509859	+	0.860258i	$0.329697\pi$
$90$		0			0
$91$			5.59132e16i			1.24642i
$92$	1.61135e16	−	5.11638e16i	0.327336	−	1.03936i
$93$		0			0
$94$	1.46489e14	+	1.99718e14i	0.00247868	+	0.00337933i
$95$	−1.88900e16			−0.292134
$96$		0			0
$97$	1.28098e17			1.65952			0.829760	−	0.558121i	$-0.188477\pi$
$97$	1.28098e17			1.65952			0.829760	+	0.558121i	$0.188477\pi$
$98$	−1.69532e16	−	2.31133e16i	−0.201293	−	0.274435i
$99$		0			0
$100$	2.78495e16	−	8.84278e16i	0.278495	−	0.884278i
$101$		−	6.82139e16i		−	0.626818i	−0.949618	−	0.313409i	$-0.898529\pi$
$101$		−	6.82139e16i		−	0.626818i	0.949618	−	0.313409i	$-0.101471\pi$
$102$		0			0
$103$	−3.08715e16			−0.240127			−0.120063	−	0.992766i	$-0.538310\pi$
$103$	−3.08715e16			−0.240127			−0.120063	+	0.992766i	$0.538310\pi$
$104$	4.83684e16	+	1.42260e17i	0.346560	+	1.01930i
$105$		0			0
$106$	−7.23603e16	+	5.30749e16i	−0.440961	+	0.323437i
$107$		−	2.71861e17i		−	1.52962i	−0.644253	−	0.764812i	$-0.722832\pi$
$107$		−	2.71861e17i		−	1.52962i	0.644253	−	0.764812i	$-0.277168\pi$
$108$		0			0
$109$			1.32808e17i			0.638407i	0.947686	+	0.319203i	$0.103415\pi$
$109$			1.32808e17i			0.638407i	−0.947686	+	0.319203i	$0.896585\pi$
$110$	1.88707e17	+	2.57276e17i	0.839365	+	1.14436i
$111$		0			0
$112$	−2.48613e17	−	1.73839e17i	−0.948791	−	0.663429i
$113$	3.78953e17			1.34097			0.670484	−	0.741924i	$-0.266087\pi$
$113$	3.78953e17			1.34097			0.670484	+	0.741924i	$0.266087\pi$
$114$		0			0
$115$		−	4.96232e17i		−	1.51270i
$116$	−3.89230e17	−	1.22584e17i	−1.10233	−	0.347170i
$117$		0			0
$118$	−5.93482e17	+	4.35308e17i	−1.45348	+	1.06610i
$119$	−8.05257e17			−1.83563
$120$		0			0
$121$	−2.28165e16			−0.0451413
$122$	−2.60545e17	+	1.91105e17i	−0.480646	+	0.352544i
$123$		0			0
$124$	2.58714e17	−	8.21468e17i	0.415657	−	1.31979i
$125$			6.74428e16i			0.101205i
$126$		0			0
$127$	−2.56390e17			−0.336179			−0.168089	−	0.985772i	$-0.553760\pi$
$127$	−2.56390e17			−0.336179			−0.168089	+	0.985772i	$0.553760\pi$
$128$	−7.82929e17	−	2.27234e17i	−0.960368	−	0.278734i
$129$		0			0
$130$	8.22122e17	+	1.12085e18i	0.883930	+	1.20512i
$131$			1.61862e18i			1.63057i	0.579060	+	0.815285i	$0.303420\pi$
$131$			1.61862e18i			1.63057i	−0.579060	+	0.815285i	$0.696580\pi$
$132$		0			0
$133$			2.75092e17i			0.243634i
$134$	1.47918e18	−	1.08495e18i	1.22923	−	0.901614i
$135$		0			0
$136$	−2.04882e18	+	6.96598e17i	−1.50115	+	0.510389i
$137$	3.32494e17			0.228907			0.114453	−	0.993429i	$-0.463488\pi$
$137$	3.32494e17			0.228907			0.114453	+	0.993429i	$0.463488\pi$
$138$		0			0
$139$		−	6.37994e17i		−	0.388321i	−0.980970	−	0.194161i	$-0.937802\pi$
$139$		−	6.37994e17i		−	0.388321i	0.980970	−	0.194161i	$-0.0621983\pi$
$140$	−2.67678e18	−	8.43025e17i	−1.53294	−	0.482783i
$141$		0			0
$142$	−1.46700e18	−	2.00005e18i	−0.744694	−	1.01529i
$143$	−2.30143e18			−1.10063
$144$		0			0
$145$	−3.77510e18			−1.60436
$146$	−2.93887e17	−	4.00674e17i	−0.117810	−	0.160617i
$147$		0			0
$148$	1.71147e18	+	5.39012e17i	0.611146	+	0.192475i
$149$			2.77142e18i			0.934585i	0.884103	+	0.467293i	$0.154771\pi$
$149$			2.77142e18i			0.934585i	−0.884103	+	0.467293i	$0.845229\pi$
$150$		0			0
$151$	−4.43299e18			−1.33473			−0.667364	−	0.744732i	$-0.732577\pi$
$151$	−4.43299e18			−1.33473			−0.667364	+	0.744732i	$0.732577\pi$
$152$	2.37971e17	+	6.99917e17i	0.0677414	+	0.199240i
$153$		0			0
$154$	3.74666e18	−	2.74810e18i	0.954373	−	0.700014i
$155$		−	7.96734e18i		−	1.92085i
$156$		0			0
$157$			3.50626e18i			0.758048i	0.925387	+	0.379024i	$0.123740\pi$
$157$			3.50626e18i			0.758048i	−0.925387	+	0.379024i	$0.876260\pi$
$158$	3.82332e18	+	5.21257e18i	0.783169	+	1.06774i
$159$		0			0
$160$	−7.53981e18	+	1.70665e17i	−1.38784	+	0.0314142i
$161$	−7.22653e18			−1.26157
$162$		0			0
$163$			2.12490e18i			0.333998i	0.985957	+	0.166999i	$0.0534076\pi$
$163$			2.12490e18i			0.333998i	−0.985957	+	0.166999i	$0.946592\pi$
$164$	−1.10966e17	+	3.52340e17i	−0.0165584	+	0.0525762i
$165$		0			0
$166$	4.32105e17	−	3.16941e17i	0.0581662	−	0.0426638i
$167$	−3.81083e18			−0.487450			−0.243725	−	0.969844i	$-0.578369\pi$
$167$	−3.81083e18			−0.487450			−0.243725	+	0.969844i	$0.578369\pi$
$168$		0			0
$169$	−1.37601e18			−0.159069
$170$	−1.61424e19	+	1.18401e19i	−1.77481	+	1.30179i
$171$		0			0
$172$	−1.70055e18	−	5.35573e17i	−0.169277	−	0.0533122i
$173$			8.51874e18i			0.807204i	0.914935	+	0.403602i	$0.132242\pi$
$173$			8.51874e18i			0.807204i	−0.914935	+	0.403602i	$0.867758\pi$
$174$		0			0
$175$	−1.24898e19			−1.07333
$176$	7.15537e18	−	1.02331e19i	0.585834	−	0.837819i
$177$		0			0
$178$	−8.10890e18	−	1.10554e19i	−0.603103	−	0.822248i
$179$		−	1.98628e19i		−	1.40860i	−0.709900	−	0.704302i	$-0.751260\pi$
$179$		−	1.98628e19i		−	1.40860i	0.709900	−	0.704302i	$-0.248740\pi$
$180$		0			0
$181$		−	2.34430e19i		−	1.51267i	−0.654182	−	0.756337i	$-0.726987\pi$
$181$		−	2.34430e19i		−	1.51267i	0.654182	−	0.756337i	$-0.273013\pi$
$182$	1.63227e19	−	1.19724e19i	1.00504	−	0.737181i
$183$		0			0
$184$	−1.83865e19	+	6.25140e18i	−1.03169	+	0.350773i
$185$	1.65994e19			0.889473
$186$		0			0
$187$		−	3.31451e19i		−	1.62093i
$188$	2.69366e16	−	8.55291e16i	0.00125893	−	0.00399735i
$189$		0			0
$190$	4.04482e18	+	5.51455e18i	0.172780	+	0.235562i
$191$	1.50710e19			0.615686			0.307843	−	0.951437i	$-0.400393\pi$
$191$	1.50710e19			0.615686			0.307843	+	0.951437i	$0.400393\pi$
$192$		0			0
$193$	9.30819e18			0.348039			0.174020	−	0.984742i	$-0.444324\pi$
$193$	9.30819e18			0.348039			0.174020	+	0.984742i	$0.444324\pi$
$194$	−2.74289e19	−	3.73955e19i	−0.981508	−	1.33815i
$195$		0			0
$196$	−3.11736e18	+	9.89824e18i	−0.102237	+	0.324625i
$197$		−	4.15016e19i		−	1.30347i	−0.758445	−	0.651737i	$-0.774041\pi$
$197$		−	4.15016e19i		−	1.30347i	0.758445	−	0.651737i	$-0.225959\pi$
$198$		0			0
$199$	1.63945e19			0.472550			0.236275	−	0.971686i	$-0.424073\pi$
$199$	1.63945e19			0.472550			0.236275	+	0.971686i	$0.424073\pi$
$200$	−3.17779e19	+	1.08045e19i	−0.877750	+	0.298435i
$201$		0			0
$202$	−1.99136e19	+	1.46063e19i	−0.505433	+	0.370726i
$203$			5.49760e19i			1.33800i
$204$		0			0
$205$			3.41731e18i			0.0765203i
$206$	6.61034e18	+	9.01228e18i	0.142021	+	0.193626i
$207$		0			0
$208$	3.11731e19	−	4.45816e19i	0.616938	−	0.882302i
$209$	−1.13230e19			−0.215138
$210$		0			0
$211$			7.37209e19i			1.29178i	0.763429	+	0.645892i	$0.223514\pi$
$211$			7.37209e19i			1.29178i	−0.763429	+	0.645892i	$0.776486\pi$
$212$	3.09882e19	+	9.75945e18i	0.521605	+	0.164275i
$213$		0			0
$214$	−7.93642e19	+	5.82121e19i	−1.23341	+	0.904683i
$215$	−1.64935e19			−0.246369
$216$		0			0
$217$	−1.16027e20			−1.60195
$218$	3.87704e19	−	2.84374e19i	0.514778	−	0.377580i
$219$		0			0
$220$	3.46996e19	−	1.10178e20i	0.426316	−	1.35364i
$221$		−	1.44400e20i		−	1.70699i
$222$		0			0
$223$	3.21618e19			0.352167			0.176083	−	0.984375i	$-0.443657\pi$
$223$	3.21618e19			0.352167			0.176083	+	0.984375i	$0.443657\pi$
$224$	2.48537e18	+	1.09801e20i	0.0261988	+	1.15744i
$225$		0			0
$226$	−8.11430e19	−	1.10627e20i	−0.793103	−	1.08129i
$227$			9.66411e19i			0.909792i	0.890545	+	0.454896i	$0.150323\pi$
$227$			9.66411e19i			0.909792i	−0.890545	+	0.454896i	$0.849677\pi$
$228$		0			0
$229$		−	3.07436e16i		−	0.000268629i	−1.00000		0.000134314i	$-0.999957\pi$
$229$		−	3.07436e16i		−	0.000268629i	1.00000		0.000134314i	$-4.27536e-5\pi$
$230$	−1.44865e20	+	1.06256e20i	−1.21976	+	0.894674i
$231$		0			0
$232$	4.75577e19	+	1.39876e20i	0.372026	+	1.09420i
$233$	−2.21535e20			−1.67077			−0.835385	−	0.549666i	$-0.814755\pi$
$233$	−2.21535e20			−1.67077			−0.835385	+	0.549666i	$0.814755\pi$
$234$		0			0
$235$		−	8.29539e17i		−	0.00581781i
$236$	2.54158e20	+	8.00447e19i	1.71930	+	0.541478i
$237$		0			0
$238$	1.72425e20	+	2.35078e20i	1.08567	+	1.48016i
$239$	4.51465e18			0.0274310			0.0137155	−	0.999906i	$-0.495634\pi$
$239$	4.51465e18			0.0274310			0.0137155	+	0.999906i	$0.495634\pi$
$240$		0			0
$241$	−1.81683e19			−0.102842			−0.0514209	−	0.998677i	$-0.516375\pi$
$241$	−1.81683e19			−0.102842			−0.0514209	+	0.998677i	$0.516375\pi$
$242$	4.88558e18	+	6.66082e18i	0.0266984	+	0.0363996i
$243$		0			0
$244$	1.11578e20	+	3.51405e19i	0.568547	+	0.179059i
$245$			9.60021e19i			0.472464i
$246$		0			0
$247$	−4.93298e19			−0.226561
$248$	−2.95207e20	+	1.00370e20i	−1.31005	+	0.445416i
$249$		0			0
$250$	1.96885e19	−	1.44412e19i	0.0816062	−	0.0598566i
$251$		−	3.26192e20i		−	1.30691i	−0.756964	−	0.653456i	$-0.773318\pi$
$251$		−	3.26192e20i		−	1.30691i	0.756964	−	0.653456i	$-0.226682\pi$
$252$		0			0
$253$		−	2.97450e20i		−	1.11401i
$254$	5.48995e19	+	7.48479e19i	0.198830	+	0.271077i
$255$		0			0
$256$	1.01308e20	+	2.77216e20i	0.343245	+	0.939246i
$257$	1.22717e20			0.402228			0.201114	−	0.979568i	$-0.435544\pi$
$257$	1.22717e20			0.402228			0.201114	+	0.979568i	$0.435544\pi$
$258$		0			0
$259$		−	2.41734e20i		−	0.741804i
$260$	1.51172e20	−	4.80003e20i	0.448951	−	1.42551i
$261$		0			0
$262$	4.72523e20	−	3.46587e20i	1.31481	−	0.964386i
$263$	−3.35733e18			−0.00904420			−0.00452210	−	0.999990i	$-0.501439\pi$
$263$	−3.35733e18			−0.00904420			−0.00452210	+	0.999990i	$0.501439\pi$
$264$		0			0
$265$	3.00552e20			0.759153
$266$	8.03073e19	−	5.89038e19i	0.196454	−	0.144095i
$267$		0			0
$268$	−6.33459e20	−	1.99502e20i	−1.45403	−	0.457933i
$269$			2.42496e20i			0.539275i	0.962962	+	0.269637i	$0.0869038\pi$
$269$			2.42496e20i			0.539275i	−0.962962	+	0.269637i	$0.913096\pi$
$270$		0			0
$271$	−2.38962e20			−0.498988			−0.249494	−	0.968376i	$-0.580264\pi$
$271$	−2.38962e20			−0.498988			−0.249494	+	0.968376i	$0.580264\pi$
$272$	6.42060e20	+	4.48952e20i	1.29939	+	0.908582i
$273$		0			0
$274$	−7.11951e19	−	9.70647e19i	−0.135385	−	0.184579i
$275$		−	5.14091e20i		−	0.947791i
$276$		0			0
$277$			5.05700e20i			0.876628i	0.898822	+	0.438314i	$0.144424\pi$
$277$			5.05700e20i			0.876628i	−0.898822	+	0.438314i	$0.855576\pi$
$278$	−1.86249e20	+	1.36610e20i	−0.313122	+	0.229669i
$279$		0			0
$280$	3.27060e20	+	9.61942e20i	0.517349	+	1.52162i
$281$	2.23986e20			0.343730			0.171865	−	0.985120i	$-0.445021\pi$
$281$	2.23986e20			0.343730			0.171865	+	0.985120i	$0.445021\pi$
$282$		0			0
$283$			5.21843e20i			0.753971i	0.926219	+	0.376986i	$0.123039\pi$
$283$			5.21843e20i			0.753971i	−0.926219	+	0.376986i	$0.876961\pi$
$284$	−2.69752e20	+	8.56518e20i	−0.378233	+	1.20097i
$285$		0			0
$286$	4.92793e20	+	6.71856e20i	0.650959	+	0.887493i
$287$	4.97656e19			0.0638165
$288$		0			0
$289$	1.25239e21			1.51394
$290$	8.08342e20	+	1.10206e21i	0.948882	+	1.29367i
$291$		0			0
$292$	−5.40401e19	+	1.71588e20i	−0.0598359	+	0.189991i
$293$		−	4.94662e20i		−	0.532027i	−0.963969	−	0.266014i	$-0.914293\pi$
$293$		−	4.94662e20i		−	0.532027i	0.963969	−	0.266014i	$-0.0857066\pi$
$294$		0			0
$295$	2.46506e21			2.50230
$296$	−2.09115e20	−	6.15044e20i	−0.206255	−	0.606634i
$297$		0			0
$298$	8.09058e20	−	5.93429e20i	0.753601	−	0.552752i
$299$		−	1.29587e21i		−	1.17316i
$300$		0			0
$301$			2.40191e20i			0.205467i
$302$	9.49212e20	+	1.29412e21i	0.789413	+	1.07626i
$303$		0			0
$304$	1.53371e20	−	2.19340e20i	0.120592	−	0.172462i
$305$	1.08219e21			0.827473
$306$		0			0
$307$		−	1.86234e21i		−	1.34705i	−0.739166	−	0.673523i	$-0.764780\pi$
$307$		−	1.86234e21i		−	1.34705i	0.739166	−	0.673523i	$-0.235220\pi$
$308$	−1.60450e21	−	5.05323e20i	−1.12891	−	0.355540i
$309$		0			0
$310$	−2.32590e21	+	1.70600e21i	−1.54888	+	1.13607i
$311$	6.47522e20			0.419557			0.209779	−	0.977749i	$-0.432726\pi$
$311$	6.47522e20			0.419557			0.209779	+	0.977749i	$0.432726\pi$
$312$		0			0
$313$	−1.62295e21			−0.995817			−0.497909	−	0.867230i	$-0.665898\pi$
$313$	−1.62295e21			−0.995817			−0.497909	+	0.867230i	$0.665898\pi$
$314$	1.02358e21	−	7.50775e20i	0.611251	−	0.448341i
$315$		0			0
$316$	7.03035e20	−	2.23228e21i	0.397774	−	1.26301i
$317$		−	2.11436e21i		−	1.16460i	−0.812976	−	0.582298i	$-0.802154\pi$
$317$		−	2.11436e21i		−	1.16460i	0.812976	−	0.582298i	$-0.197846\pi$
$318$		0			0
$319$	−2.26286e21			−1.18151
$320$	1.66428e21	+	2.16455e21i	0.846158	+	1.10051i
$321$		0			0
$322$	1.54738e21	+	2.10964e21i	0.746142	+	1.01726i
$323$		−	7.10443e20i		−	0.333663i
$324$		0			0
$325$		−	2.23969e21i		−	0.998113i
$326$	6.20320e20	−	4.54993e20i	0.269318	−	0.197540i
$327$		0			0
$328$	1.26619e20	−	4.30504e19i	0.0521880	−	0.0177439i
$329$	−1.20804e19			−0.00485195
$330$		0			0
$331$		−	4.36509e21i		−	1.66516i	−0.553908	−	0.832578i	$-0.686864\pi$
$331$		−	4.36509e21i		−	1.66516i	0.553908	−	0.832578i	$-0.313136\pi$
$332$	−1.85049e20	−	5.82793e19i	−0.0688038	−	0.0216691i
$333$		0			0
$334$	8.15993e20	+	1.11249e21i	0.288298	+	0.393054i
$335$	−6.14386e21			−2.11622
$336$		0			0
$337$	−2.59518e21			−0.849792			−0.424896	−	0.905242i	$-0.639689\pi$
$337$	−2.59518e21			−0.849792			−0.424896	+	0.905242i	$0.639689\pi$
$338$	2.94638e20	+	4.01698e20i	0.0940799	+	0.128265i
$339$		0			0
$340$	6.91296e21	+	2.17717e21i	2.09939	+	0.661183i
$341$		−	4.77575e21i		−	1.41459i
$342$		0			0
$343$	−2.70973e21			−0.763706
$344$	2.07781e20	+	6.11120e20i	0.0571292	+	0.168027i
$345$		0			0
$346$	2.48687e21	−	1.82407e21i	0.650888	−	0.477414i
$347$		−	7.40818e20i		−	0.189195i	−0.995516	−	0.0945977i	$-0.969844\pi$
$347$		−	7.40818e20i		−	0.189195i	0.995516	−	0.0945977i	$-0.0301565\pi$
$348$		0			0
$349$		−	1.81507e20i		−	0.0441446i	−0.999756	−	0.0220723i	$-0.992974\pi$
$349$		−	1.81507e20i		−	0.0441446i	0.999756	−	0.0220723i	$-0.00702640\pi$
$350$	2.67438e21	+	3.64615e21i	0.634811	+	0.865477i
$351$		0			0
$352$	−4.51948e21	+	1.02300e20i	−1.02206	+	0.0231346i
$353$	−3.26526e21			−0.720830			−0.360415	−	0.932792i	$-0.617365\pi$
$353$	−3.26526e21			−0.720830			−0.360415	+	0.932792i	$0.617365\pi$
$354$		0			0
$355$			8.30728e21i			1.74791i
$356$	−1.49107e21	+	4.73445e21i	−0.306318	+	0.972623i
$357$		0			0
$358$	−5.79852e21	+	4.25311e21i	−1.13583	+	0.833107i
$359$	−2.19419e21			−0.419732			−0.209866	−	0.977730i	$-0.567303\pi$
$359$	−2.19419e21			−0.419732			−0.209866	+	0.977730i	$0.567303\pi$
$360$		0			0
$361$	5.23769e21			0.955715
$362$	−6.84370e21	+	5.01972e21i	−1.21974	+	0.894658i
$363$		0			0
$364$	−6.99018e21	−	2.20149e21i	−1.18885	−	0.374417i
$365$			1.66422e21i			0.276516i
$366$		0			0
$367$	−1.08265e22			−1.71723			−0.858615	−	0.512621i	$-0.828675\pi$
$367$	−1.08265e22			−1.71723			−0.858615	+	0.512621i	$0.828675\pi$
$368$	5.76197e21	+	4.02898e21i	0.893026	+	0.624437i
$369$		0			0
$370$	−3.55434e21	−	4.84585e21i	−0.526071	−	0.717225i
$371$		−	4.37687e21i		−	0.633120i
$372$		0			0
$373$			5.20618e20i			0.0719439i	0.999353	+	0.0359719i	$0.0114527\pi$
$373$			5.20618e20i			0.0719439i	−0.999353	+	0.0359719i	$0.988547\pi$
$374$	−9.67601e21	+	7.09717e21i	−1.30704	+	0.958686i
$375$		0			0
$376$	−3.07362e19	+	1.04503e19i	−0.00396784	+	0.00134906i
$377$	−9.85837e21			−1.24424
$378$		0			0
$379$		−	2.99720e21i		−	0.361645i	−0.983516	−	0.180823i	$-0.942124\pi$
$379$		−	2.99720e21i		−	0.361645i	0.983516	−	0.180823i	$-0.0578760\pi$
$380$	7.43764e20	−	2.36160e21i	0.0877556	−	0.278642i
$381$		0			0
$382$	−3.22708e21	−	4.39968e21i	−0.364142	−	0.496458i
$383$	1.22679e22			1.35388			0.676939	−	0.736039i	$-0.263306\pi$
$383$	1.22679e22			1.35388			0.676939	+	0.736039i	$0.263306\pi$
$384$		0			0
$385$	−1.55619e22			−1.64304
$386$	−1.99311e21	−	2.71733e21i	−0.205845	−	0.280641i
$387$		0			0
$388$	−5.04365e21	+	1.60146e22i	−0.498511	+	1.58287i
$389$			1.60002e21i			0.154722i	0.997003	+	0.0773612i	$0.0246495\pi$
$389$			1.60002e21i			0.154722i	−0.997003	+	0.0773612i	$0.975351\pi$
$390$		0			0
$391$	1.86630e22			1.72774
$392$	3.55709e21	−	1.20941e21i	0.322228	−	0.109557i
$393$		0			0
$394$	−1.21155e22	+	8.88652e21i	−1.05105	+	0.770928i
$395$		−	2.16506e22i		−	1.83821i
$396$		0			0
$397$		−	2.44521e22i		−	1.98883i	−0.105546	−	0.994414i	$-0.533659\pi$
$397$		−	2.44521e22i		−	1.98883i	0.105546	−	0.994414i	$-0.466341\pi$
$398$	−3.51047e21	−	4.78604e21i	−0.279485	−	0.381040i
$399$		0			0
$400$	9.95858e21	+	6.96340e21i	0.759779	+	0.531266i
$401$	−2.46119e22			−1.83830			−0.919152	−	0.393903i	$-0.871125\pi$
$401$	−2.46119e22			−1.83830			−0.919152	+	0.393903i	$0.871125\pi$
$402$		0			0
$403$		−	2.08061e22i		−	1.48969i
$404$	8.52799e21	+	2.68581e21i	0.597868	+	0.188293i
$405$		0			0
$406$	1.60491e22	−	1.17717e22i	1.07890	−	0.791350i
$407$	9.94995e21			0.655041
$408$		0			0
$409$	−5.67464e21			−0.358336			−0.179168	−	0.983819i	$-0.557341\pi$
$409$	−5.67464e21			−0.358336			−0.179168	+	0.983819i	$0.557341\pi$
$410$	9.97613e20	−	7.31730e20i	0.0617020	−	0.0452573i
$411$		0			0
$412$	1.21551e21	−	3.85950e21i	0.0721329	−	0.229037i
$413$		−	3.58981e22i		−	2.08687i
$414$		0			0
$415$	−1.79477e21			−0.100138
$416$	−1.96896e22	+	4.45679e20i	−1.07632	+	0.0243629i
$417$		0			0
$418$	2.42453e21	+	3.30551e21i	0.127242	+	0.173476i
$419$			2.70146e22i			1.38925i	0.719374	+	0.694623i	$0.244429\pi$
$419$			2.70146e22i			1.38925i	−0.719374	+	0.694623i	$0.755571\pi$
$420$		0			0
$421$			1.26169e22i			0.623094i	0.950231	+	0.311547i	$0.100847\pi$
$421$			1.26169e22i			0.623094i	−0.950231	+	0.311547i	$0.899153\pi$
$422$	2.15213e22	−	1.57855e22i	1.04163	−	0.764014i
$423$		0			0
$424$	−3.78627e21	−	1.11361e22i	−0.176036	−	0.517754i
$425$	3.22558e22			1.46995
$426$		0			0
$427$		−	1.57597e22i		−	0.690097i
$428$	3.39876e22	+	1.07041e22i	1.45898	+	0.459492i
$429$		0			0
$430$	3.53166e21	+	4.81493e21i	0.145713	+	0.198659i
$431$	−4.26128e21			−0.172378			−0.0861892	−	0.996279i	$-0.527469\pi$
$431$	−4.26128e21			−0.172378			−0.0861892	+	0.996279i	$0.527469\pi$
$432$		0			0
$433$	−1.62172e21			−0.0630707			−0.0315353	−	0.999503i	$-0.510040\pi$
$433$	−1.62172e21			−0.0630707			−0.0315353	+	0.999503i	$0.510040\pi$
$434$	2.48442e22	+	3.38716e22i	0.947462	+	1.29173i
$435$		0			0
$436$	−1.66034e22	−	5.22908e21i	−0.608922	−	0.191774i
$437$		−	6.37565e21i		−	0.229315i
$438$		0			0
$439$	1.56475e22			0.541375			0.270687	−	0.962667i	$-0.412749\pi$
$439$	1.56475e22			0.541375			0.270687	+	0.962667i	$0.412749\pi$
$440$	−3.95943e22	+	1.34620e22i	−1.34365	+	0.456839i
$441$		0			0
$442$	−4.21545e22	+	3.09195e22i	−1.37643	+	1.00959i
$443$		−	3.08815e22i		−	0.989161i	−0.869132	−	0.494581i	$-0.835322\pi$
$443$		−	3.08815e22i		−	0.989161i	0.869132	−	0.494581i	$-0.164678\pi$
$444$		0			0
$445$			4.59190e22i			1.41557i
$446$	−6.88662e21	−	9.38896e21i	−0.208286	−	0.283969i
$447$		0			0
$448$	3.15218e22	−	2.42366e22i	0.917801	−	0.705680i
$449$	1.44678e22			0.413340			0.206670	−	0.978411i	$-0.433737\pi$
$449$	1.44678e22			0.413340			0.206670	+	0.978411i	$0.433737\pi$
$450$		0			0
$451$			2.04839e21i			0.0563524i
$452$	−1.49206e22	+	4.73761e22i	−0.402820	+	1.27903i
$453$		0			0
$454$	2.82124e22	−	2.06932e22i	0.733609	−	0.538088i
$455$	−6.77971e22			−1.73027
$456$		0			0
$457$	−1.09366e22			−0.268903			−0.134452	−	0.990920i	$-0.542927\pi$
$457$	−1.09366e22			−0.268903			−0.134452	+	0.990920i	$0.542927\pi$
$458$	−8.97495e18	+	6.58295e18i	−0.000216608	+	0.000158878i
$459$		0			0
$460$	6.20382e22	+	1.95383e22i	1.44284	+	0.454408i
$461$			3.78938e22i			0.865187i	0.901589	+	0.432594i	$0.142402\pi$
$461$			3.78938e22i			0.865187i	−0.901589	+	0.432594i	$0.857598\pi$
$462$		0			0
$463$	5.34510e21			0.117630			0.0588149	−	0.998269i	$-0.481268\pi$
$463$	5.34510e21			0.117630			0.0588149	+	0.998269i	$0.481268\pi$
$464$	3.06506e22	−	4.38343e22i	0.662271	−	0.947135i
$465$		0			0
$466$	4.74360e22	+	6.46725e22i	0.988162	+	1.34722i
$467$			2.81699e21i			0.0576224i	0.999585	+	0.0288112i	$0.00917216\pi$
$467$			2.81699e21i			0.0576224i	−0.999585	+	0.0288112i	$0.990828\pi$
$468$		0			0
$469$			8.94718e22i			1.76489i
$470$	−2.42167e20	+	1.77625e20i	−0.00469118	+	0.00344089i
$471$		0			0
$472$	−3.10541e22	−	9.13357e22i	−0.580246	−	1.70661i
$473$	−9.88647e21			−0.181435
$474$		0			0
$475$		−	1.10192e22i		−	0.195099i
$476$	3.17057e22	−	1.00672e23i	0.551415	−	1.75085i
$477$		0			0
$478$	−9.66697e20	−	1.31796e21i	−0.0162238	−	0.0221190i
$479$	9.05318e22			1.49262			0.746310	−	0.665598i	$-0.231823\pi$
$479$	9.05318e22			1.49262			0.746310	+	0.665598i	$0.231823\pi$
$480$		0			0
$481$	4.33480e22			0.689820
$482$	3.89028e21	+	5.30386e21i	0.0608249	+	0.0829263i
$483$		0			0
$484$	8.98364e20	−	2.85249e21i	0.0135602	−	0.0430565i
$485$			1.55324e23i			2.30374i
$486$		0			0
$487$	−3.07462e22			−0.440347			−0.220173	−	0.975461i	$-0.570662\pi$
$487$	−3.07462e22			−0.440347			−0.220173	+	0.975461i	$0.570662\pi$
$488$	−1.36331e22	−	4.00974e22i	−0.191879	−	0.564350i
$489$		0			0
$490$	2.80258e22	−	2.05564e22i	0.380971	−	0.279435i
$491$			1.94168e22i			0.259409i	0.991553	+	0.129704i	$0.0414028\pi$
$491$			1.94168e22i			0.259409i	−0.991553	+	0.129704i	$0.958597\pi$
$492$		0			0
$493$		−	1.41979e23i		−	1.83243i
$494$	1.05627e22	+	1.44008e22i	0.133997	+	0.182687i
$495$		0			0
$496$	9.25122e22	+	6.46879e22i	1.13398	+	0.792919i
$497$	1.20977e23			1.45772
$498$		0			0
$499$			7.79434e22i			0.907664i	0.891087	+	0.453832i	$0.149943\pi$
$499$			7.79434e22i			0.907664i	−0.891087	+	0.453832i	$0.850057\pi$
$500$	−8.43159e21	−	2.65545e21i	−0.0965305	−	0.0304014i
$501$		0			0
$502$	−9.52249e22	+	6.98457e22i	−1.05383	+	0.772962i
$503$	−1.18157e23			−1.28568			−0.642838	−	0.766002i	$-0.722243\pi$
$503$	−1.18157e23			−1.28568			−0.642838	+	0.766002i	$0.722243\pi$
$504$		0			0
$505$	8.27122e22			0.870148
$506$	−8.68343e22	+	6.36913e22i	−0.898280	+	0.658871i
$507$		0			0
$508$	1.00950e22	−	3.20535e22i	0.100986	−	0.320652i
$509$		−	2.87932e21i		−	0.0283262i	−0.999900	−	0.0141631i	$-0.995492\pi$
$509$		−	2.87932e21i		−	0.0283262i	0.999900	−	0.0141631i	$-0.00450841\pi$
$510$		0			0
$511$	2.42357e22			0.230610
$512$	5.92351e22	−	8.89336e22i	0.554350	−	0.832284i
$513$		0			0
$514$	−2.62767e22	−	3.58246e22i	−0.237894	−	0.324336i
$515$		−	3.74329e22i		−	0.333344i
$516$		0			0
$517$		−	4.97239e20i		−	0.00428446i
$518$	−7.05691e22	+	5.17611e22i	−0.598152	+	0.438733i
$519$		0			0
$520$	−1.72497e23	+	5.86488e22i	−1.41499	+	0.481095i
$521$	−1.28391e23			−1.03613			−0.518066	−	0.855340i	$-0.673348\pi$
$521$	−1.28391e23			−1.03613			−0.518066	+	0.855340i	$0.673348\pi$
$522$		0			0
$523$		−	1.89027e22i		−	0.147659i	−0.997271	−	0.0738293i	$-0.976478\pi$
$523$		−	1.89027e22i		−	0.147659i	0.997271	−	0.0738293i	$-0.0235220\pi$
$524$	−2.02358e23	−	6.37306e22i	−1.55526	−	0.489815i
$525$		0			0
$526$	7.18887e20	+	9.80103e20i	0.00534911	+	0.00729277i
$527$	2.99647e23			2.19391
$528$		0			0
$529$	2.64353e22			0.187418
$530$	−6.43555e22	−	8.77399e22i	−0.448995	−	0.612142i
$531$		0			0
$532$	−3.43915e22	−	1.08313e22i	−0.232382	−	0.0731865i
$533$			8.92403e21i			0.0593444i
$534$		0			0
$535$	3.29643e23			2.12342
$536$	7.73987e22	+	2.27644e23i	0.490719	+	1.44329i
$537$		0			0
$538$	7.07916e22	−	5.19243e22i	0.434843	−	0.318949i
$539$			5.75452e22i			0.347940i
$540$		0			0
$541$			3.25660e23i			1.90804i	0.299744	+	0.954020i	$0.403099\pi$
$541$			3.25660e23i			1.90804i	−0.299744	+	0.954020i	$0.596901\pi$
$542$	5.11676e22	+	6.97600e22i	0.295122	+	0.402358i
$543$		0			0
$544$	−6.41863e21	−	2.83568e23i	−0.0358799	−	1.58514i
$545$	−1.61035e23			−0.886236
$546$		0			0
$547$		−	4.90295e22i		−	0.261556i	−0.991412	−	0.130778i	$-0.958252\pi$
$547$		−	4.90295e22i		−	0.261556i	0.991412	−	0.130778i	$-0.0417476\pi$
$548$	−1.30914e22	+	4.15679e22i	−0.0687625	+	0.218335i
$549$		0			0
$550$	−1.50078e23	+	1.10080e23i	−0.764249	+	0.560562i
$551$	−4.85029e22			−0.243209
$552$		0			0
$553$	−3.15294e23			−1.53303
$554$	1.47629e23	−	1.08283e23i	0.706867	−	0.518473i
$555$		0			0
$556$	7.97611e22	+	2.51200e22i	0.370387	+	0.116650i
$557$			2.60011e23i			1.18911i	0.804054	+	0.594556i	$0.202672\pi$
$557$			2.60011e23i			1.18911i	−0.804054	+	0.594556i	$0.797328\pi$
$558$		0			0
$559$	−4.30714e22			−0.191068
$560$	2.10787e23	−	3.01454e23i	0.920972	−	1.31711i
$561$		0			0
$562$	−4.79610e22	−	6.53882e22i	−0.203296	−	0.277166i
$563$			1.80701e23i			0.754467i	0.926118	+	0.377233i	$0.123125\pi$
$563$			1.80701e23i			0.754467i	−0.926118	+	0.377233i	$0.876875\pi$
$564$		0			0
$565$			4.59496e23i			1.86153i
$566$	1.52341e23	−	1.11739e23i	0.607963	−	0.445930i
$567$		0			0
$568$	3.07803e23	−	1.04653e23i	1.19210	−	0.405313i
$569$	3.54026e23			1.35077			0.675384	−	0.737467i	$-0.263978\pi$
$569$	3.54026e23			1.35077			0.675384	+	0.737467i	$0.263978\pi$
$570$		0			0
$571$		−	1.77850e23i		−	0.658637i	−0.944219	−	0.329318i	$-0.893181\pi$
$571$		−	1.77850e23i		−	0.658637i	0.944219	−	0.329318i	$-0.106819\pi$
$572$	9.06152e22	−	2.87722e23i	0.330624	−	1.04980i
$573$		0			0
$574$	−1.06560e22	−	1.45280e22i	−0.0377437	−	0.0514583i
$575$	2.89470e23			1.01024
$576$		0			0
$577$	−3.55869e23			−1.20586			−0.602928	−	0.797796i	$-0.705999\pi$
$577$	−3.55869e23			−1.20586			−0.602928	+	0.797796i	$0.705999\pi$
$578$	−2.68168e23	−	3.65610e23i	−0.895407	−	1.22076i
$579$		0			0
$580$	1.48639e23	−	4.71958e23i	0.481941	−	1.53026i
$581$			2.61369e22i			0.0835134i
$582$		0			0
$583$	1.80156e23			0.559069
$584$	6.16629e22	−	2.09654e22i	0.188588	−	0.0641200i
$585$		0			0
$586$	−1.44406e23	+	1.05919e23i	−0.428999	+	0.314663i
$587$			2.22604e23i			0.651791i	0.945406	+	0.325896i	$0.105666\pi$
$587$			2.22604e23i			0.651791i	−0.945406	+	0.325896i	$0.894334\pi$
$588$		0			0
$589$		−	1.02365e23i		−	0.291187i
$590$	−5.27829e23	−	7.19622e23i	−1.47996	−	2.01773i
$591$		0			0
$592$	−1.34773e23	+	1.92743e23i	−0.367170	+	0.525102i
$593$	−6.01922e23			−1.61650			−0.808250	−	0.588840i	$-0.799585\pi$
$593$	−6.01922e23			−1.61650			−0.808250	+	0.588840i	$0.799585\pi$
$594$		0			0
$595$		−	9.76408e23i		−	2.54822i
$596$	−3.46478e23	−	1.09120e23i	−0.891421	−	0.280745i
$597$		0			0
$598$	−3.78302e23	+	2.77478e23i	−0.945974	+	0.693854i
$599$	−2.83674e23			−0.699346			−0.349673	−	0.936872i	$-0.613707\pi$
$599$	−2.83674e23			−0.699346			−0.349673	+	0.936872i	$0.613707\pi$
$600$		0			0
$601$	−4.18303e23			−1.00244			−0.501220	−	0.865320i	$-0.667115\pi$
$601$	−4.18303e23			−1.00244			−0.501220	+	0.865320i	$0.667115\pi$
$602$	7.01189e22	−	5.14309e22i	0.165678	−	0.121522i
$603$		0			0
$604$	1.74542e23	−	5.54205e23i	0.400946	−	1.27308i
$605$		−	2.76660e22i		−	0.0626651i
$606$		0			0
$607$	−2.31638e23			−0.510159			−0.255080	−	0.966920i	$-0.582102\pi$
$607$	−2.31638e23			−0.510159			−0.255080	+	0.966920i	$0.582102\pi$
$608$	−9.68723e22	+	2.19273e21i	−0.210387	+	0.00476216i
$609$		0			0
$610$	−2.31723e23	−	3.15922e23i	−0.489402	−	0.667232i
$611$		−	2.16627e21i		−	0.00451193i
$612$		0			0
$613$			2.79613e23i			0.566425i	0.959057	+	0.283213i	$0.0914002\pi$
$613$			2.79613e23i			0.566425i	−0.959057	+	0.283213i	$0.908600\pi$
$614$	−5.43671e23	+	3.98772e23i	−1.08619	+	0.796699i
$615$		0			0
$616$	1.96045e23	+	5.76604e23i	0.380995	+	1.12058i
$617$	1.73444e23			0.332457			0.166229	−	0.986087i	$-0.446841\pi$
$617$	1.73444e23			0.332457			0.166229	+	0.986087i	$0.446841\pi$
$618$		0			0
$619$			6.77105e23i			1.26266i	0.775515	+	0.631329i	$0.217490\pi$
$619$			6.77105e23i			1.26266i	−0.775515	+	0.631329i	$0.782510\pi$
$620$	9.96064e23	+	3.13701e23i	1.83214	+	0.577014i
$621$		0			0
$622$	−1.38650e23	−	1.89031e23i	−0.248143	−	0.338309i
$623$	6.68708e23			1.18056
$624$		0			0
$625$	−6.21418e23			−1.06759
$626$	3.47514e23	+	4.73788e23i	0.588967	+	0.802975i
$627$		0			0
$628$	−4.38347e23	−	1.38053e23i	−0.723037	−	0.227714i
$629$			6.24294e23i			1.01592i
$630$		0			0
$631$	1.02867e24			1.62940			0.814698	−	0.579885i	$-0.196903\pi$
$631$	1.02867e24			1.62940			0.814698	+	0.579885i	$0.196903\pi$
$632$	−8.02204e23	+	2.72749e23i	−1.25369	+	0.426253i
$633$		0			0
$634$	−6.17243e23	+	4.52736e23i	−0.939070	+	0.688790i
$635$		−	3.10884e23i		−	0.466683i
$636$		0			0
$637$			2.50702e23i			0.366414i
$638$	4.84534e23	+	6.60595e23i	0.698792	+	0.952707i
$639$		0			0
$640$	2.75531e23	−	9.49335e23i	0.386938	−	1.33318i
$641$	−7.31083e23			−1.01315			−0.506575	−	0.862196i	$-0.669089\pi$
$641$	−7.31083e23			−1.01315			−0.506575	+	0.862196i	$0.669089\pi$
$642$		0			0
$643$			5.31860e23i			0.717801i	0.933376	+	0.358901i	$0.116848\pi$
$643$			5.31860e23i			0.717801i	−0.933376	+	0.358901i	$0.883152\pi$
$644$	2.84533e23	−	9.03449e23i	0.378968	−	1.20330i
$645$		0			0
$646$	−2.07399e23	+	1.52123e23i	−0.269048	+	0.197342i
$647$	−7.87216e23			−1.00788			−0.503939	−	0.863740i	$-0.668116\pi$
$647$	−7.87216e23			−1.00788			−0.503939	+	0.863740i	$0.668116\pi$
$648$		0			0
$649$	1.47759e24			1.84279
$650$	−6.53831e23	+	4.79573e23i	−0.804826	+	0.590325i
$651$		0			0
$652$	−2.65651e23	−	8.36644e22i	−0.318572	−	0.100331i
$653$		−	2.77252e22i		−	0.0328180i	−0.999865	−	0.0164090i	$-0.994777\pi$
$653$		−	2.77252e22i		−	0.0328180i	0.999865	−	0.0164090i	$-0.00522338\pi$
$654$		0			0
$655$	−1.96265e24			−2.26356
$656$	−3.96799e22	−	2.77456e22i	−0.0451739	−	0.0315872i
$657$		0			0
$658$	2.58671e21	+	3.52662e21i	0.00286964	+	0.00391236i
$659$		−	1.48992e24i		−	1.63169i	−0.578273	−	0.815843i	$-0.696273\pi$
$659$		−	1.48992e24i		−	1.63169i	0.578273	−	0.815843i	$-0.303727\pi$
$660$		0			0
$661$		−	2.01553e22i		−	0.0215118i	−0.999942	−	0.0107559i	$-0.996576\pi$
$661$		−	2.01553e22i		−	0.0215118i	0.999942	−	0.0107559i	$-0.00342377\pi$
$662$	−1.27430e24	+	9.34672e23i	−1.34270	+	0.984842i
$663$		0			0
$664$	2.26100e22	+	6.65002e22i	0.0232205	+	0.0682958i
$665$	−3.33560e23			−0.338213
$666$		0			0
$667$		−	1.27415e24i		−	1.25936i
$668$	1.50045e23	−	4.76424e23i	0.146427	−	0.464937i
$669$		0			0
$670$	1.31555e24	+	1.79357e24i	1.25162	+	1.70641i
$671$	6.48681e23			0.609382
$672$		0			0
$673$	−7.70622e23			−0.705851			−0.352926	−	0.935651i	$-0.614813\pi$
$673$	−7.70622e23			−0.705851			−0.352926	+	0.935651i	$0.614813\pi$
$674$	5.55691e23	+	7.57608e23i	0.502602	+	0.685228i
$675$		0			0
$676$	5.41782e22	−	1.72027e23i	0.0477835	−	0.151722i
$677$			8.03721e23i			0.700006i	0.936749	+	0.350003i	$0.113819\pi$
$677$			8.03721e23i			0.700006i	−0.936749	+	0.350003i	$0.886181\pi$
$678$		0			0
$679$	2.26195e24			1.92128
$680$	−8.44655e23	−	2.48428e24i	−0.708522	−	2.08389i
$681$		0			0
$682$	−1.39418e24	+	1.02261e24i	−1.14065	+	0.836645i
$683$			3.12264e23i			0.252317i	0.992010	+	0.126158i	$0.0402647\pi$
$683$			3.12264e23i			0.252317i	−0.992010	+	0.126158i	$0.959735\pi$
$684$		0			0
$685$			4.03163e23i			0.317768i
$686$	5.80220e23	+	7.91049e23i	0.451687	+	0.615813i
$687$		0			0
$688$	1.33913e23	−	1.91513e23i	0.101700	−	0.145444i
$689$	7.84867e23			0.588752
$690$		0			0
$691$		−	1.46577e24i		−	1.07276i	−0.843977	−	0.536379i	$-0.819792\pi$
$691$		−	1.46577e24i		−	1.07276i	0.843977	−	0.536379i	$-0.180208\pi$
$692$	−1.06500e24	−	3.35411e23i	−0.769923	−	0.242480i
$693$		0			0
$694$	−2.16266e23	+	1.58627e23i	−0.152557	+	0.111898i
$695$	7.73595e23			0.539067
$696$		0			0
$697$	−1.28523e23			−0.0873982
$698$	−5.29872e22	+	3.88651e22i	−0.0355959	+	0.0261089i
$699$		0			0
$700$	4.91767e23	−	1.56146e24i	0.322423	−	1.02376i
$701$			2.04249e24i			1.32299i	0.749950	+	0.661495i	$0.230078\pi$
$701$			2.04249e24i			1.32299i	−0.749950	+	0.661495i	$0.769922\pi$
$702$		0			0
$703$	2.13271e23			0.134838
$704$	9.97597e23	+	1.29746e24i	0.623143	+	0.810453i
$705$		0			0
$706$	6.99172e23	+	9.53225e23i	0.426328	+	0.581240i
$707$		−	1.20452e24i		−	0.725687i
$708$		0			0
$709$			2.96920e24i			1.74641i	0.487352	+	0.873206i	$0.337963\pi$
$709$			2.96920e24i			1.74641i	−0.487352	+	0.873206i	$0.662037\pi$
$710$	2.42514e24	−	1.77879e24i	1.40942	−	1.03378i
$711$		0			0
$712$	1.70140e24	−	5.78475e23i	0.965442	−	0.328250i
$713$	2.68909e24			1.50780
$714$		0			0
$715$		−	2.79058e24i		−	1.52790i
$716$	2.48321e24	+	7.82064e23i	1.34355	+	0.423138i
$717$		0			0
$718$	4.69831e23	+	6.40549e23i	0.248247	+	0.338450i
$719$	−4.13376e23			−0.215849			−0.107924	−	0.994159i	$-0.534420\pi$
$719$	−4.13376e23			−0.215849			−0.107924	+	0.994159i	$0.534420\pi$
$720$		0			0
$721$	−5.45128e23			−0.278003
$722$	−1.12152e24	−	1.52903e24i	−0.565249	−	0.770639i
$723$		0			0
$724$	2.93081e24	+	9.23030e23i	1.44281	+	0.454400i
$725$		−	2.20215e24i		−	1.07146i
$726$		0			0
$727$	2.92465e24			1.39005			0.695027	−	0.718983i	$-0.255392\pi$
$727$	2.92465e24			1.39005			0.695027	+	0.718983i	$0.255392\pi$
$728$	8.54090e23	+	2.51203e24i	0.401224	+	1.18007i
$729$		0			0
$730$	4.85834e23	−	3.56350e23i	0.222969	−	0.163543i
$731$		−	6.20311e23i		−	0.281392i
$732$		0			0
$733$			3.06846e24i			1.35999i	0.733216	+	0.679996i	$0.238018\pi$
$733$			3.06846e24i			1.35999i	−0.733216	+	0.679996i	$0.761982\pi$
$734$	2.31823e24	+	3.16059e24i	1.01564	+	1.38469i
$735$		0			0
$736$	−5.76020e22	−	2.54479e24i	−0.0246590	−	1.08941i
$737$	−3.68273e24			−1.55846
$738$		0			0
$739$		−	3.06955e24i		−	1.26939i	−0.772761	−	0.634697i	$-0.781125\pi$
$739$		−	3.06955e24i		−	1.26939i	0.772761	−	0.634697i	$-0.218875\pi$
$740$	−6.53574e23	+	2.07523e24i	−0.267193	+	0.848393i
$741$		0			0
$742$	−1.27774e24	+	9.37196e23i	−0.510515	+	0.374453i
$743$	−4.34334e24			−1.71561			−0.857805	−	0.513975i	$-0.828172\pi$
$743$	−4.34334e24			−1.71561			−0.857805	+	0.513975i	$0.828172\pi$
$744$		0			0
$745$	−3.36046e24			−1.29739
$746$	1.51984e23	−	1.11477e23i	0.0580118	−	0.0425506i
$747$		0			0
$748$	4.14374e24	+	1.30503e24i	1.54607	+	0.486920i
$749$		−	4.80052e24i		−	1.77090i
$750$		0			0
$751$	7.59956e23			0.274062			0.137031	−	0.990567i	$-0.456244\pi$
$751$	7.59956e23			0.274062			0.137031	+	0.990567i	$0.456244\pi$
$752$	9.63213e21	+	6.73514e21i	0.00343456	+	0.00240157i
$753$		0			0
$754$	2.11092e24	+	2.87795e24i	0.735894	+	1.00329i
$755$		−	5.37519e24i		−	1.85287i
$756$		0			0
$757$		−	2.36037e24i		−	0.795544i	−0.917484	−	0.397772i	$-0.869783\pi$
$757$		−	2.36037e24i		−	0.795544i	0.917484	−	0.397772i	$-0.130217\pi$
$758$	−8.74971e23	+	6.41774e23i	−0.291612	+	0.213892i
$759$		0			0
$760$	−8.48679e23	+	2.88550e23i	−0.276584	+	0.0940386i
$761$	3.99857e23			0.128865			0.0644326	−	0.997922i	$-0.479476\pi$
$761$	3.99857e23			0.128865			0.0644326	+	0.997922i	$0.479476\pi$
$762$		0			0
$763$			2.34511e24i			0.739104i
$764$	−5.93398e23	+	1.88416e24i	−0.184949	+	0.587251i
$765$		0			0
$766$	−2.62685e24	−	3.58135e24i	−0.800739	−	1.09170i
$767$	6.43729e24			1.94063
$768$		0			0
$769$	−3.40521e24			−1.00408			−0.502042	−	0.864843i	$-0.667418\pi$
$769$	−3.40521e24			−1.00408			−0.502042	+	0.864843i	$0.667418\pi$
$770$	3.33219e24	+	4.54298e24i	0.971759	+	1.32486i
$771$		0			0
$772$	−3.66495e23	+	1.16370e24i	−0.104549	+	0.331965i
$773$		−	9.20037e23i		−	0.259585i	−0.991541	−	0.129793i	$-0.958569\pi$
$773$		−	9.20037e23i		−	0.259585i	0.991541	−	0.129793i	$-0.0414311\pi$
$774$		0			0
$775$	4.64763e24			1.28282
$776$	5.75510e24	−	1.95673e24i	1.57119	−	0.534203i
$777$		0			0
$778$	4.67092e23	−	3.42603e23i	0.124760	−	0.0915092i
$779$			4.39060e22i			0.0115999i
$780$		0			0
$781$			4.97952e24i			1.28722i
$782$	−3.99621e24	−	5.44828e24i	−1.02186	−	1.39316i
$783$		0			0
$784$	−1.11472e24	−	7.79454e23i	−0.278920	−	0.195031i
$785$	−4.25148e24			−1.05232
$786$		0			0
$787$		−	7.43784e24i		−	1.80161i	−0.434220	−	0.900807i	$-0.642976\pi$
$787$		−	7.43784e24i		−	1.80161i	0.434220	−	0.900807i	$-0.357024\pi$
$788$	5.18847e24	+	1.63406e24i	1.24327	+	0.391557i
$789$		0			0
$790$	−6.32046e24	+	4.63593e24i	−1.48224	+	1.08719i
$791$	6.69154e24			1.55248
$792$		0			0
$793$	2.82605e24			0.641737
$794$	−7.13829e24	+	5.23580e24i	−1.60369	+	1.17628i
$795$		0			0
$796$	−6.45508e23	+	2.04962e24i	−0.141952	+	0.450725i
$797$			6.58511e24i			1.43274i	0.697721	+	0.716369i	$0.254197\pi$
$797$			6.58511e24i			1.43274i	−0.697721	+	0.716369i	$0.745803\pi$
$798$		0			0
$799$	3.11985e22			0.00664486
$800$	−9.95552e22	−	4.39824e24i	−0.0209797	−	0.926859i
$801$		0			0
$802$	5.27000e24	+	7.18492e24i	1.08725	+	1.48231i
$803$			9.97560e23i			0.203637i
$804$		0			0
$805$		−	8.76247e24i		−	1.75130i
$806$	−6.07389e24	+	4.45509e24i	−1.20121	+	0.881066i
$807$		0			0
$808$	−1.04199e24	−	3.06467e24i	−0.201774	−	0.593454i
$809$	−6.49816e24			−1.24517			−0.622584	−	0.782553i	$-0.713917\pi$
$809$	−6.49816e24			−1.24517			−0.622584	+	0.782553i	$0.713917\pi$
$810$		0			0
$811$			5.42750e24i			1.01841i	0.860645	+	0.509205i	$0.170060\pi$
$811$			5.42750e24i			1.01841i	−0.860645	+	0.509205i	$0.829940\pi$
$812$	−6.87302e24	−	2.16459e24i	−1.27621	−	0.401929i
$813$		0			0
$814$	−2.13053e24	−	2.90468e24i	−0.387418	−	0.528191i
$815$	−2.57653e24			−0.463655
$816$		0			0
$817$	−2.11910e23			−0.0373477
$818$	1.21508e24	+	1.65659e24i	0.211934	+	0.288943i
$819$		0			0
$820$	−4.27227e23	−	1.34551e23i	−0.0729862	−	0.0229863i
$821$			1.44666e24i			0.244595i	0.992493	+	0.122298i	$0.0390263\pi$
$821$			1.44666e24i			0.244595i	−0.992493	+	0.122298i	$0.960974\pi$
$822$		0			0
$823$	−5.56998e24			−0.922476			−0.461238	−	0.887276i	$-0.652595\pi$
$823$	−5.56998e24			−0.922476			−0.461238	+	0.887276i	$0.652595\pi$
$824$	−1.38697e24	+	4.71570e23i	−0.227346	+	0.0772974i
$825$		0			0
$826$	−1.04797e25	+	7.68666e24i	−1.68275	+	1.23426i
$827$		−	5.21332e24i		−	0.828548i	−0.910152	−	0.414274i	$-0.864036\pi$
$827$		−	5.21332e24i		−	0.828548i	0.910152	−	0.414274i	$-0.135964\pi$
$828$		0			0
$829$		−	3.83347e24i		−	0.596869i	−0.954430	−	0.298434i	$-0.903536\pi$
$829$		−	3.83347e24i		−	0.596869i	0.954430	−	0.298434i	$-0.0964644\pi$
$830$	3.84304e23	+	5.23946e23i	0.0592259	+	0.0807463i
$831$		0			0
$832$	4.34613e24	+	5.65254e24i	0.656228	+	0.853484i
$833$	−3.61058e24			−0.539628
$834$		0			0
$835$		−	4.62079e24i		−	0.676677i
$836$	4.45824e23	−	1.41558e24i	0.0646265	−	0.205202i
$837$		0			0
$838$	7.88634e24	−	5.78448e24i	1.12022	−	0.821657i
$839$	−4.72339e24			−0.664167			−0.332083	−	0.943250i	$-0.607752\pi$
$839$	−4.72339e24			−0.664167			−0.332083	+	0.943250i	$0.607752\pi$
$840$		0			0
$841$	−2.43599e24			−0.335667
$842$	3.68323e24	−	2.70158e24i	0.502430	−	0.368523i
$843$		0			0
$844$	−9.21648e24	−	2.90264e24i	−1.23212	−	0.388045i
$845$		−	1.66847e24i		−	0.220819i
$846$		0			0
$847$	−4.02894e23			−0.0522616
$848$	−2.44022e24	+	3.48984e24i	−0.313375	+	0.448168i
$849$		0			0
$850$	−6.90677e24	−	9.41642e24i	−0.869389	−	1.18529i
$851$			5.60253e24i			0.698205i
$852$		0			0
$853$			7.83079e24i			0.956619i	0.878191	+	0.478309i	$0.158750\pi$
$853$			7.83079e24i			0.956619i	−0.878191	+	0.478309i	$0.841250\pi$
$854$	−4.60071e24	+	3.37453e24i	−0.556459	+	0.408152i
$855$		0			0
$856$	−4.15275e24	−	1.22140e25i	−0.492390	−	1.44821i
$857$	4.64085e24			0.544830			0.272415	−	0.962180i	$-0.412178\pi$
$857$	4.64085e24			0.544830			0.272415	+	0.962180i	$0.412178\pi$
$858$		0			0
$859$			6.90901e24i			0.795195i	0.917560	+	0.397598i	$0.130156\pi$
$859$			6.90901e24i			0.795195i	−0.917560	+	0.397598i	$0.869844\pi$
$860$	6.49404e23	−	2.06199e24i	0.0740080	−	0.234990i
$861$		0			0
$862$	9.12444e23	+	1.24399e24i	0.101952	+	0.138997i
$863$	−4.17194e24			−0.461579			−0.230790	−	0.973004i	$-0.574131\pi$
$863$	−4.17194e24			−0.461579			−0.230790	+	0.973004i	$0.574131\pi$
$864$		0			0
$865$	−1.03293e25			−1.12056
$866$	3.47249e23	+	4.73426e23i	0.0373026	+	0.0508569i
$867$		0			0
$868$	4.56836e24	−	1.45055e25i	0.481219	−	1.52797i
$869$		−	1.29778e25i		−	1.35373i
$870$		0			0
$871$	−1.60442e25			−1.64121
$872$	2.02867e24	+	5.96669e24i	0.205505	+	0.604426i
$873$		0			0
$874$	−1.86124e24	+	1.36518e24i	−0.184908	+	0.135626i
$875$			1.19090e24i			0.117168i
$876$		0			0
$877$			2.21294e24i			0.213537i	0.994284	+	0.106768i	$0.0340504\pi$
$877$			2.21294e24i			0.213537i	−0.994284	+	0.106768i	$0.965950\pi$
$878$	−3.35052e24	−	4.56798e24i	−0.320191	−	0.436536i
$879$		0			0
$880$	1.24081e25	+	8.67618e24i	1.16306	+	0.813254i
$881$	1.30646e24			0.121283			0.0606415	−	0.998160i	$-0.480685\pi$
$881$	1.30646e24			0.121283			0.0606415	+	0.998160i	$0.480685\pi$
$882$		0			0
$883$		−	2.46757e24i		−	0.224700i	−0.993669	−	0.112350i	$-0.964162\pi$
$883$		−	2.46757e24i		−	0.224700i	0.993669	−	0.112350i	$-0.0358378\pi$
$884$	1.80526e25	+	5.68551e24i	1.62816	+	0.512773i
$885$		0			0
$886$	−9.01522e24	+	6.61249e24i	−0.797608	+	0.585031i
$887$	−2.19751e24			−0.192567			−0.0962833	−	0.995354i	$-0.530695\pi$
$887$	−2.19751e24			−0.192567			−0.0962833	+	0.995354i	$0.530695\pi$
$888$		0			0
$889$	−4.52734e24			−0.389205
$890$	1.34051e25	−	9.83238e24i	1.14144	−	0.837227i
$891$		0			0
$892$	−1.26632e24	+	4.02081e24i	−0.105789	+	0.335902i
$893$		−	1.06580e22i		−	0.000881939i
$894$		0			0
$895$	2.40844e25			1.95542
$896$	−1.38250e25	−	4.01251e24i	−1.11185	−	0.322699i
$897$		0			0
$898$	−3.09790e24	−	4.22356e24i	−0.244466	−	0.333296i
$899$		−	2.04573e25i		−	1.59916i
$900$		0			0
$901$			1.13036e25i			0.867073i
$902$	5.97986e23	−	4.38611e23i	0.0454397	−	0.0333291i
$903$		0			0
$904$	1.70253e25	−	5.78861e24i	1.26959	−	0.431660i
$905$	2.84256e25			2.09989
$906$		0			0
$907$		−	2.67764e25i		−	1.94129i	−0.240512	−	0.970646i	$-0.577315\pi$
$907$		−	2.67764e25i		−	1.94129i	0.240512	−	0.970646i	$-0.422685\pi$
$908$	−1.20819e25	−	3.80508e24i	−0.867773	−	0.273297i
$909$		0			0
$910$	1.45170e25	+	1.97920e25i	1.02335	+	1.39520i
$911$	−2.35546e25			−1.64501			−0.822506	−	0.568757i	$-0.807424\pi$
$911$	−2.35546e25			−1.64501			−0.822506	+	0.568757i	$0.807424\pi$
$912$		0			0
$913$	−1.07581e24			−0.0737456
$914$	2.34180e24	+	3.19272e24i	0.159040	+	0.216830i
$915$		0			0
$916$	3.84351e21	+	1.21048e21i	0.000256222	+	8.06948e-5i
$917$			2.85816e25i			1.88776i
$918$		0			0
$919$	−5.71735e24			−0.370692			−0.185346	−	0.982673i	$-0.559341\pi$
$919$	−5.71735e24			−0.370692			−0.185346	+	0.982673i	$0.559341\pi$
$920$	−7.58009e24	−	2.22944e25i	−0.486942	−	1.43219i
$921$		0			0
$922$	1.10623e25	−	8.11399e24i	0.697642	−	0.511707i
$923$			2.16938e25i			1.35557i
$924$		0			0
$925$			9.68302e24i			0.594027i
$926$	−1.14452e24	−	1.56039e24i	−0.0695711	−	0.0948505i
$927$		0			0
$928$	−1.93596e25	+	4.38209e23i	−1.15541	+	0.0261531i
$929$	−2.14170e25			−1.26656			−0.633278	−	0.773925i	$-0.718291\pi$
$929$	−2.14170e25			−1.26656			−0.633278	+	0.773925i	$0.718291\pi$
$930$		0			0
$931$			1.23345e24i			0.0716222i
$932$	8.72257e24	−	2.76959e25i	0.501891	−	1.59360i
$933$		0			0
$934$	8.22361e23	−	6.03186e23i	0.0464637	−	0.0340803i
$935$	4.01898e25			2.25018
$936$		0			0
$937$	1.03504e25			0.569076			0.284538	−	0.958665i	$-0.408160\pi$
$937$	1.03504e25			0.569076			0.284538	+	0.958665i	$0.408160\pi$
$938$	2.61194e25	−	1.91581e25i	1.42311	−	1.04383i
$939$		0			0
$940$	1.03708e23	+	3.26617e22i	0.00554912	+	0.00174764i
$941$			1.49549e25i			0.792997i	0.918035	+	0.396498i	$0.129775\pi$
$941$			1.49549e25i			0.792997i	−0.918035	+	0.396498i	$0.870225\pi$
$942$		0			0
$943$	−1.15339e24			−0.0600657
$944$	−2.00141e25	+	2.86228e25i	−1.03294	+	1.47724i
$945$		0			0
$946$	2.11694e24	+	2.88615e24i	0.107308	+	0.146300i
$947$			2.05139e25i			1.03056i	0.857021	+	0.515281i	$0.172312\pi$
$947$			2.05139e25i			1.03056i	−0.857021	+	0.515281i	$0.827688\pi$
$948$		0			0
$949$			4.34597e24i			0.214449i
$950$	−3.21683e24	+	2.35949e24i	−0.157318	+	0.115390i
$951$		0			0
$952$	−3.61781e25	+	1.23005e25i	−1.73793	+	0.590894i
$953$	1.91249e25			0.910563			0.455281	−	0.890348i	$-0.349539\pi$
$953$	1.91249e25			0.910563			0.455281	+	0.890348i	$0.349539\pi$
$954$		0			0
$955$			1.82743e25i			0.854695i
$956$	−1.77757e23	+	5.64414e23i	−0.00824014	+	0.0261641i
$957$		0			0
$958$	−1.93851e25	−	2.64289e25i	−0.882797	−	1.20357i
$959$	5.87117e24			0.265013
$960$		0			0
$961$	2.06250e25			0.914627
$962$	−9.28186e24	−	1.26545e25i	−0.407988	−	0.556235i
$963$		0			0
$964$	7.15348e23	−	2.27137e24i	0.0308932	−	0.0980921i
$965$			1.12866e25i			0.483148i
$966$		0			0
$967$	−8.63419e24			−0.363159			−0.181579	−	0.983376i	$-0.558121\pi$
$967$	−8.63419e24			−0.363159			−0.181579	+	0.983376i	$0.558121\pi$
$968$	−1.02509e24	+	3.48529e23i	−0.0427386	+	0.0145311i
$969$		0			0
$970$	4.53436e25	−	3.32587e25i	1.85762	−	1.36253i
$971$		−	7.31893e24i		−	0.297224i	−0.988896	−	0.148612i	$-0.952519\pi$
$971$		−	7.31893e24i		−	0.297224i	0.988896	−	0.148612i	$-0.0474806\pi$
$972$		0			0
$973$		−	1.12657e25i		−	0.449572i
$974$	6.58351e24	+	8.97571e24i	0.260439	+	0.355073i
$975$		0			0
$976$	−8.78643e24	+	1.25657e25i	−0.341577	+	0.488500i
$977$	1.91796e25			0.739154			0.369577	−	0.929200i	$-0.379503\pi$
$977$	1.91796e25			0.739154			0.369577	+	0.929200i	$0.379503\pi$
$978$		0			0
$979$			2.75246e25i			1.04248i
$980$	−1.20020e25	−	3.77993e24i	−0.450644	−	0.141926i
$981$		0			0
$982$	5.66832e24	−	4.15761e24i	0.209174	−	0.153425i
$983$	−9.21150e24			−0.336996			−0.168498	−	0.985702i	$-0.553892\pi$
$983$	−9.21150e24			−0.336996			−0.168498	+	0.985702i	$0.553892\pi$
$984$		0			0
$985$	5.03225e25			1.80948
$986$	−4.14480e25	+	3.04013e25i	−1.47757	+	1.08377i
$987$		0			0
$988$	1.94228e24	−	6.16713e24i	0.0680577	−	0.216097i
$989$		−	5.56678e24i		−	0.193391i
$990$		0			0
$991$	5.52241e25			1.88583			0.942915	−	0.333034i	$-0.108073\pi$
$991$	5.52241e25			1.88583			0.942915	+	0.333034i	$0.108073\pi$
$992$	−9.24837e23	−	4.08583e25i	−0.0313124	−	1.38335i
$993$		0			0
$994$	−2.59042e25	−	3.53168e25i	−0.862156	−	1.17543i
$995$			1.98790e25i			0.655993i
$996$		0			0
$997$		−	3.29322e25i		−	1.06835i	−0.845375	−	0.534174i	$-0.820623\pi$
$997$		−	3.29322e25i		−	1.06835i	0.845375	−	0.534174i	$-0.179377\pi$
$998$	2.27540e25	−	1.66896e25i	0.731893	−	0.536830i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.18.d.b.37.5		16
3.2	odd	2		8.18.b.a.5.12	yes	16
8.5	even	2	inner	72.18.d.b.37.6		16
12.11	even	2		32.18.b.a.17.9		16
24.5	odd	2		8.18.b.a.5.11	✓	16
24.11	even	2		32.18.b.a.17.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.18.b.a.5.11	✓	16	24.5	odd	2
8.18.b.a.5.12	yes	16	3.2	odd	2
32.18.b.a.17.8		16	24.11	even	2
32.18.b.a.17.9		16	12.11	even	2
72.18.d.b.37.5		16	1.1	even	1	trivial
72.18.d.b.37.6		16	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	72.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-214.125 - 291.929i) q^{2} +(-39373.4 + 125018. i) q^{4} +1.21254e6i q^{5} +1.76580e7 q^{7} +(4.49273e7 - 1.52753e7i) q^{8} +O(q^{10})\)	\(q+(-214.125 - 291.929i) q^{2} +(-39373.4 + 125018. i) q^{4} +1.21254e6i q^{5} +1.76580e7 q^{7} +(4.49273e7 - 1.52753e7i) q^{8} +(3.53976e8 - 2.59635e8i) q^{10} +7.26817e8i q^{11} +3.16645e9i q^{13} +(-3.78101e9 - 5.15488e9i) q^{14} +(-1.40793e10 - 9.84479e9i) q^{16} -4.56030e10 q^{17} +1.55789e10i q^{19} +(-1.51590e11 - 4.77419e10i) q^{20} +(2.12179e11 - 1.55629e11i) q^{22} -4.09250e11 q^{23} -7.07318e11 q^{25} +(9.24380e11 - 6.78015e11i) q^{26} +(-6.95255e11 + 2.20757e12i) q^{28} +3.11338e12i q^{29} -6.57077e12 q^{31} +(1.40750e11 + 6.21818e12i) q^{32} +(9.76472e12 + 1.33128e13i) q^{34} +2.14111e13i q^{35} -1.36898e13i q^{37} +(4.54793e12 - 3.33582e12i) q^{38} +(1.85219e13 + 5.44763e13i) q^{40} +2.81830e12 q^{41} +1.36024e13i q^{43} +(-9.08656e13 - 2.86173e13i) q^{44} +(8.76304e13 + 1.19472e14i) q^{46} -6.84132e11 q^{47} +7.91743e13 q^{49} +(1.51454e14 + 2.06487e14i) q^{50} +(-3.95865e14 - 1.24674e14i) q^{52} -2.47869e14i q^{53} -8.81297e14 q^{55} +(7.93327e14 - 2.69731e14i) q^{56} +(9.08887e14 - 6.66651e14i) q^{58} -2.03296e15i q^{59} -8.92495e14i q^{61} +(1.40696e15 + 1.91820e15i) q^{62} +(1.78513e15 - 1.37255e15i) q^{64} -3.83946e15 q^{65} +5.06693e15i q^{67} +(1.79554e15 - 5.70121e15i) q^{68} +(6.25051e15 - 4.58463e15i) q^{70} +6.85113e15 q^{71} +1.37250e15 q^{73} +(-3.99644e15 + 2.93131e15i) q^{74} +(-1.94765e15 - 6.13392e14i) q^{76} +1.28341e16i q^{77} -1.78556e16 q^{79} +(1.19372e16 - 1.70718e16i) q^{80} +(-6.03468e14 - 8.22745e14i) q^{82} +1.48017e15i q^{83} -5.52955e16i q^{85} +(3.97094e15 - 2.91261e15i) q^{86} +(1.11023e16 + 3.26540e16i) q^{88} +3.78700e16 q^{89} +5.59132e16i q^{91} +(1.61135e16 - 5.11638e16i) q^{92} +(1.46489e14 + 1.99718e14i) q^{94} -1.88900e16 q^{95} +1.28098e17 q^{97} +(-1.69532e16 - 2.31133e16i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8}+O(q^{10}) \) 16 * q - 270 * q^2 - 27436 * q^4 + 11529600 * q^7 - 24334920 * q^8	\( 16 q - 270 q^{2} - 27436 q^{4} + 11529600 q^{7} - 24334920 q^{8} + 131002712 q^{10} - 16363788528 q^{14} + 26500434192 q^{16} + 7489125600 q^{17} + 209445719856 q^{20} + 223126527100 q^{22} - 746845345920 q^{23} - 1809682431664 q^{25} - 2467726531080 q^{26} + 3220542267040 q^{28} - 318979758592 q^{31} - 1455647316000 q^{32} - 4461251980292 q^{34} - 24076283913900 q^{38} + 60626292962592 q^{40} - 7482251536032 q^{41} - 193654716236040 q^{44} - 195097141003568 q^{46} + 376698804821760 q^{47} + 127691292101520 q^{49} - 474997408872102 q^{50} - 272251877663120 q^{52} + 22\!\cdots\!52 q^{55}+ \cdots - 33\!\cdots\!90 q^{98}+O(q^{100}) \) 16 * q - 270 * q^2 - 27436 * q^4 + 11529600 * q^7 - 24334920 * q^8 + 131002712 * q^10 - 16363788528 * q^14 + 26500434192 * q^16 + 7489125600 * q^17 + 209445719856 * q^20 + 223126527100 * q^22 - 746845345920 * q^23 - 1809682431664 * q^25 - 2467726531080 * q^26 + 3220542267040 * q^28 - 318979758592 * q^31 - 1455647316000 * q^32 - 4461251980292 * q^34 - 24076283913900 * q^38 + 60626292962592 * q^40 - 7482251536032 * q^41 - 193654716236040 * q^44 - 195097141003568 * q^46 + 376698804821760 * q^47 + 127691292101520 * q^49 - 474997408872102 * q^50 - 272251877663120 * q^52 + 2209036687713152 * q^55 + 162767516076480 * q^56 - 623262610679960 * q^58 - 695695648144320 * q^62 + 1111931745501248 * q^64 - 2385987975356160 * q^65 - 5981109959771880 * q^68 - 10044559836180288 * q^70 - 9025926285576576 * q^71 + 11332002046118560 * q^73 - 11098735408189464 * q^74 + 5959440926938280 * q^76 - 45299671392008448 * q^79 - 1337342539452480 * q^80 + 15639739637081420 * q^82 + 14252032276026564 * q^86 - 66964872768837680 * q^88 + 69879174608766048 * q^89 - 57336249810701280 * q^92 - 192318922166254176 * q^94 - 93790444358203776 * q^95 + 95593398602180640 * q^97 - 339641261743253790 * q^98

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