LMFDB - Embedded newform 45.21.g.a.28.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,21,Mod(28,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("45.28");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	45.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$114.081194296$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
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} - 2 x^{17} - 7325998 x^{16} - 141066000 x^{15} + 21914382182116 x^{14} + \cdots + 85\!\cdots\!62 $ x^18 - 2x^17 - 7325998x^16 - 141066000x^15 + 21914382182116x^14 + 1104988767829768x^13 - 34706930411331066568x^12 - 2933307788252234300400x^11 + 31623821563070032377106446x^10 + 3490410472966208019452281908x^9 - 16879153387394780948128685050308x^8 - 1993912089551257507757291738713200x^7 + 5164727809378016111602994168273128756x^6 + 534916738067236270840852573968830794888x^5 - 835493995188808646858962700222394722187688x^4 - 54915240732853615882514108100722272555520400x^3 + 55641424877135585596097905861475849305851982681x^2 + 422004689289028502357324627229300202572039493438*x + 853550979535595201047849179160229833296430030562
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{48}\cdot 3^{20}\cdot 5^{32} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			28.5
Root			$-3.77310 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	45.28
Dual form			45.21.g.a.37.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.77310 + 3.77310i) q^{2} +1.04855e6i q^{4} +(8.90462e6 - 4.00939e6i) q^{5} +(4.46902e7 - 4.46902e7i) q^{7} +(-7.91266e6 - 7.91266e6i) q^{8} +O(q^{10})$	\(q+(-3.77310 + 3.77310i) q^{2} +1.04855e6i q^{4} +(8.90462e6 - 4.00939e6i) q^{5} +(4.46902e7 - 4.46902e7i) q^{7} +(-7.91266e6 - 7.91266e6i) q^{8} +(-1.84702e7 + 4.87259e7i) q^{10} +1.60852e10 q^{11} +(-3.76718e10 - 3.76718e10i) q^{13} +3.37242e8i q^{14} -1.09942e12 q^{16} +(2.08022e12 - 2.08022e12i) q^{17} +2.99942e11i q^{19} +(4.20404e12 + 9.33691e12i) q^{20} +(-6.06910e10 + 6.06910e10i) q^{22} +(-4.11357e13 - 4.11357e13i) q^{23} +(6.32170e13 - 7.14042e13i) q^{25} +2.84279e11 q^{26} +(4.68598e13 + 4.68598e13i) q^{28} -3.65291e14i q^{29} -1.33214e15 q^{31} +(1.24453e13 - 1.24453e13i) q^{32} +1.56978e13i q^{34} +(2.18769e14 - 5.77130e14i) q^{35} +(-1.48105e15 + 1.48105e15i) q^{37} +(-1.13171e12 - 1.13171e12i) q^{38} +(-1.02184e14 - 3.87343e13i) q^{40} -2.38548e16 q^{41} +(5.02697e15 + 5.02697e15i) q^{43} +1.68661e16i q^{44} +3.10419e14 q^{46} +(1.96675e16 - 1.96675e16i) q^{47} +7.57978e16i q^{49} +(3.08912e13 + 5.07940e14i) q^{50} +(3.95006e16 - 3.95006e16i) q^{52} +(6.48453e15 + 6.48453e15i) q^{53} +(1.43232e17 - 6.44918e16i) q^{55} -7.07237e14 q^{56} +(1.37828e15 + 1.37828e15i) q^{58} -5.84951e17i q^{59} +9.66810e17 q^{61} +(5.02630e15 - 5.02630e15i) q^{62} -1.15273e18i q^{64} +(-4.86494e17 - 1.84412e17i) q^{65} +(-2.23353e18 + 2.23353e18i) q^{67} +(2.18121e18 + 2.18121e18i) q^{68} +(1.35213e15 + 3.00301e15i) q^{70} -1.33306e18 q^{71} +(-4.76853e18 - 4.76853e18i) q^{73} -1.11763e16i q^{74} -3.14504e17 q^{76} +(7.18850e17 - 7.18850e17i) q^{77} +1.15172e19i q^{79} +(-9.78993e18 + 4.40801e18i) q^{80} +(9.00068e16 - 9.00068e16i) q^{82} +(6.54386e18 + 6.54386e18i) q^{83} +(1.01831e19 - 2.68640e19i) q^{85} -3.79345e16 q^{86} +(-1.27277e17 - 1.27277e17i) q^{88} -2.48209e19i q^{89} -3.36712e18 q^{91} +(4.31328e19 - 4.31328e19i) q^{92} +1.48415e17i q^{94} +(1.20259e18 + 2.67087e18i) q^{95} +(4.02655e19 - 4.02655e19i) q^{97} +(-2.85993e17 - 2.85993e17i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 7302140 q^{5} - 585532752 q^{7} - 930113700 q^{8}+O(q^{10}) $ 18 * q + 2 * q^2 + 7302140 * q^5 - 585532752 * q^7 - 930113700 * q^8	$ 18 q + 2 q^{2} + 7302140 q^{5} - 585532752 q^{7} - 930113700 q^{8} - 17138778090 q^{10} + 6506343064 q^{11} - 369354655602 q^{13} - 6345876020232 q^{16} - 6508314764998 q^{17} - 38356516779780 q^{20} + 161054386758096 q^{22} + 81655963656152 q^{23} + 33913283845350 q^{25} - 234104101103636 q^{26} + 772213614545352 q^{28} + 17\!\cdots\!36 q^{31}+ \cdots + 27\!\cdots\!98 q^{98}+O(q^{100}) $ 18 * q + 2 * q^2 + 7302140 * q^5 - 585532752 * q^7 - 930113700 * q^8 - 17138778090 * q^10 + 6506343064 * q^11 - 369354655602 * q^13 - 6345876020232 * q^16 - 6508314764998 * q^17 - 38356516779780 * q^20 + 161054386758096 * q^22 + 81655963656152 * q^23 + 33913283845350 * q^25 - 234104101103636 * q^26 + 772213614545352 * q^28 + 1742256896900736 * q^31 + 4072699683722552 * q^32 + 4817791288113440 * q^35 + 6383289895587498 * q^37 + 14134212502378200 * q^38 + 43297629431150700 * q^40 + 30602304597564664 * q^41 - 46399469942287752 * q^43 + 17467214047538136 * q^46 + 137109249757437752 * q^47 + 40012852869983150 * q^50 - 745026624616846452 * q^52 + 184102027021671302 * q^53 + 752956242406989720 * q^55 - 685775432394721200 * q^56 - 2701246502184220800 * q^58 + 49879194030044136 * q^61 + 1190554579738283704 * q^62 - 6907070599410641170 * q^65 - 5597336519263153752 * q^67 + 25617328014464685148 * q^68 + 31706333959370270760 * q^70 - 10983277495574224736 * q^71 - 19072400700441139902 * q^73 + 75630007803532292400 * q^76 + 47766064678699704904 * q^77 - 134231700802559812960 * q^80 - 83501540658117625104 * q^82 + 119739383617210903952 * q^83 + 169044713294843560110 * q^85 - 33497378050769887736 * q^86 - 337125565675837197600 * q^88 + 86281377644254817136 * q^91 + 206921051460419061752 * q^92 - 118106834336527303800 * q^95 - 318608382222604685502 * q^97 + 27697031317753120498 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−3.77310	+	3.77310i	−0.00368467	+	0.00368467i	−0.708947	−	0.705262i	$-0.750829\pi$
$2$	−3.77310	+	3.77310i	−0.00368467	+	0.00368467i	0.705262	+	0.708947i	$0.250829\pi$
$3$		0			0
$3$		0			0
$4$			1.04855e6i			0.999973i
$5$	8.90462e6	−	4.00939e6i	0.911833	−	0.410562i
$5$	8.90462e6	−	4.00939e6i	0.911833	−	0.410562i
$6$		0			0
$7$	4.46902e7	−	4.46902e7i	0.158209	−	0.158209i	−0.623563	−	0.781773i	$-0.714316\pi$
$7$	4.46902e7	−	4.46902e7i	0.158209	−	0.158209i	0.781773	+	0.623563i	$0.214316\pi$
$8$	−7.91266e6	−	7.91266e6i	−0.00736924	−	0.00736924i
$9$		0			0
$10$	−1.84702e7	+	4.87259e7i	−0.00184702	+	0.00487259i
$11$	1.60852e10			0.620153			0.310077	−	0.950712i	$-0.399645\pi$
$11$	1.60852e10			0.620153			0.310077	+	0.950712i	$0.399645\pi$
$12$		0			0
$13$	−3.76718e10	−	3.76718e10i	−0.273264	−	0.273264i	0.557149	−	0.830413i	$-0.311895\pi$
$13$	−3.76718e10	−	3.76718e10i	−0.273264	−	0.273264i	−0.830413	+	0.557149i	$0.811895\pi$
$14$			3.37242e8i			0.00116590i
$15$		0			0
$16$	−1.09942e12			−0.999919
$17$	2.08022e12	−	2.08022e12i	1.03186	−	1.03186i	0.0323821	−	0.999476i	$-0.489691\pi$
$17$	2.08022e12	−	2.08022e12i	1.03186	−	1.03186i	0.999476	−	0.0323821i	$-0.0103094\pi$
$18$		0			0
$19$			2.99942e11i			0.0489217i	0.999701	+	0.0244609i	$0.00778691\pi$
$19$			2.99942e11i			0.0489217i	−0.999701	+	0.0244609i	$0.992213\pi$
$20$	4.20404e12	+	9.33691e12i	0.410551	+	0.911808i
$21$		0			0
$22$	−6.06910e10	+	6.06910e10i	−0.00228506	+	0.00228506i
$23$	−4.11357e13	−	4.11357e13i	−0.992981	−	0.992981i	0.00699448	−	0.999976i	$-0.497774\pi$
$23$	−4.11357e13	−	4.11357e13i	−0.992981	−	0.992981i	−0.999976	+	0.00699448i	$0.997774\pi$
$24$		0			0
$25$	6.32170e13	−	7.14042e13i	0.662878	−	0.748727i
$26$	2.84279e11			0.00201378
$27$		0			0
$28$	4.68598e13	+	4.68598e13i	0.158205	+	0.158205i
$29$		−	3.65291e14i		−	0.868279i	−0.900846	−	0.434140i	$-0.857052\pi$
$29$		−	3.65291e14i		−	0.868279i	0.900846	−	0.434140i	$-0.142948\pi$
$30$		0			0
$31$	−1.33214e15			−1.62530			−0.812649	−	0.582754i	$-0.801975\pi$
$31$	−1.33214e15			−1.62530			−0.812649	+	0.582754i	$0.801975\pi$
$32$	1.24453e13	−	1.24453e13i	0.0110536	−	0.0110536i
$33$		0			0
$34$			1.56978e13i			0.00760411i
$35$	2.18769e14	−	5.77130e14i	0.0793058	−	0.209215i
$36$		0			0
$37$	−1.48105e15	+	1.48105e15i	−0.308002	+	0.308002i	−0.844134	−	0.536132i	$-0.819885\pi$
$37$	−1.48105e15	+	1.48105e15i	−0.308002	+	0.308002i	0.536132	+	0.844134i	$0.319885\pi$
$38$	−1.13171e12	−	1.13171e12i	−0.000180260	−	0.000180260i
$39$		0			0
$40$	−1.02184e14	−	3.87343e13i	−0.00974504	−	0.00369399i
$41$	−2.38548e16			−1.77721			−0.888603	−	0.458676i	$-0.848324\pi$
$41$	−2.38548e16			−1.77721			−0.888603	+	0.458676i	$0.848324\pi$
$42$		0			0
$43$	5.02697e15	+	5.02697e15i	0.232606	+	0.232606i	0.813780	−	0.581173i	$-0.197406\pi$
$43$	5.02697e15	+	5.02697e15i	0.232606	+	0.232606i	−0.581173	+	0.813780i	$0.697406\pi$
$44$			1.68661e16i			0.620136i
$45$		0			0
$46$	3.10419e14			0.00731762
$47$	1.96675e16	−	1.96675e16i	0.373913	−	0.373913i	−0.494987	−	0.868900i	$-0.664827\pi$
$47$	1.96675e16	−	1.96675e16i	0.373913	−	0.373913i	0.868900	+	0.494987i	$0.164827\pi$
$48$		0			0
$49$			7.57978e16i			0.949940i
$50$	3.08912e13	+	5.07940e14i	0.000316326	+	0.00520130i
$51$		0			0
$52$	3.95006e16	−	3.95006e16i	0.273257	−	0.273257i
$53$	6.48453e15	+	6.48453e15i	0.0370783	+	0.0370783i	0.725403	−	0.688325i	$-0.241653\pi$
$53$	6.48453e15	+	6.48453e15i	0.0370783	+	0.0370783i	−0.688325	+	0.725403i	$0.741653\pi$
$54$		0			0
$55$	1.43232e17	−	6.44918e16i	0.565476	−	0.254611i
$56$	−7.07237e14			−0.00233177
$57$		0			0
$58$	1.37828e15	+	1.37828e15i	0.00319932	+	0.00319932i
$59$		−	5.84951e17i		−	1.14446i	−0.820094	−	0.572229i	$-0.806079\pi$
$59$		−	5.84951e17i		−	1.14446i	0.820094	−	0.572229i	$-0.193921\pi$
$60$		0			0
$61$	9.66810e17			1.35532			0.677662	−	0.735374i	$-0.262993\pi$
$61$	9.66810e17			1.35532			0.677662	+	0.735374i	$0.262993\pi$
$62$	5.02630e15	−	5.02630e15i	0.00598869	−	0.00598869i
$63$		0			0
$64$		−	1.15273e18i		−	0.999837i
$65$	−4.86494e17	−	1.84412e17i	−0.361363	−	0.136979i
$66$		0			0
$67$	−2.23353e18	+	2.23353e18i	−1.22530	+	1.22530i	−0.259581	+	0.965721i	$0.583584\pi$
$67$	−2.23353e18	+	2.23353e18i	−1.22530	+	1.22530i	−0.965721	+	0.259581i	$0.916416\pi$
$68$	2.18121e18	+	2.18121e18i	1.03183	+	1.03183i
$69$		0			0
$70$	1.35213e15	+	3.00301e15i	0.000478673	+	0.00106310i
$71$	−1.33306e18			−0.409513			−0.204757	−	0.978813i	$-0.565640\pi$
$71$	−1.33306e18			−0.409513			−0.204757	+	0.978813i	$0.565640\pi$
$72$		0			0
$73$	−4.76853e18	−	4.76853e18i	−1.10957	−	1.10957i	−0.993206	−	0.116367i	$-0.962875\pi$
$73$	−4.76853e18	−	4.76853e18i	−1.10957	−	1.10957i	−0.116367	−	0.993206i	$-0.537125\pi$
$74$		−	1.11763e16i		−	0.00226977i
$75$		0			0
$76$	−3.14504e17			−0.0489204
$77$	7.18850e17	−	7.18850e17i	0.0981141	−	0.0981141i
$78$		0			0
$79$			1.15172e19i			1.21639i	0.793786	+	0.608197i	$0.208107\pi$
$79$			1.15172e19i			1.21639i	−0.793786	+	0.608197i	$0.791893\pi$
$80$	−9.78993e18	+	4.40801e18i	−0.911759	+	0.410528i
$81$		0			0
$82$	9.00068e16	−	9.00068e16i	0.00654842	−	0.00654842i
$83$	6.54386e18	+	6.54386e18i	0.421748	+	0.421748i	0.885805	−	0.464057i	$-0.153607\pi$
$83$	6.54386e18	+	6.54386e18i	0.421748	+	0.421748i	−0.464057	+	0.885805i	$0.653607\pi$
$84$		0			0
$85$	1.01831e19	−	2.68640e19i	0.517240	−	1.36452i
$86$	−3.79345e16			−0.00171415
$87$		0			0
$88$	−1.27277e17	−	1.27277e17i	−0.00457006	−	0.00457006i
$89$		−	2.48209e19i		−	0.796008i	−0.917384	−	0.398004i	$-0.869703\pi$
$89$		−	2.48209e19i		−	0.796008i	0.917384	−	0.398004i	$-0.130297\pi$
$90$		0			0
$91$	−3.36712e18			−0.0864659
$92$	4.31328e19	−	4.31328e19i	0.992954	−	0.992954i
$93$		0			0
$94$			1.48415e17i			0.00275549i
$95$	1.20259e18	+	2.67087e18i	0.0200854	+	0.0446084i
$96$		0			0
$97$	4.02655e19	−	4.02655e19i	0.546030	−	0.546030i	−0.379260	−	0.925290i	$-0.623822\pi$
$97$	4.02655e19	−	4.02655e19i	0.546030	−	0.546030i	0.925290	+	0.379260i	$0.123822\pi$
$98$	−2.85993e17	−	2.85993e17i	−0.00350021	−	0.00350021i
$99$		0			0
$100$	7.48707e19	+	6.62860e19i	0.748707	+	0.662860i
$101$	−1.10526e20			−1.00058			−0.500288	−	0.865859i	$-0.666772\pi$
$101$	−1.10526e20			−1.00058			−0.500288	+	0.865859i	$0.666772\pi$
$102$		0			0
$103$	−5.79262e19	−	5.79262e19i	−0.431025	−	0.431025i	0.457952	−	0.888977i	$-0.348583\pi$
$103$	−5.79262e19	−	5.79262e19i	−0.431025	−	0.431025i	−0.888977	+	0.457952i	$0.848583\pi$
$104$			5.96168e17i			0.00402750i
$105$		0			0
$106$	−4.89336e16			−0.000273243
$107$	−8.04515e19	+	8.04515e19i	−0.408975	+	0.408975i	−0.881381	−	0.472406i	$-0.843386\pi$
$107$	−8.04515e19	+	8.04515e19i	−0.408975	+	0.408975i	0.472406	+	0.881381i	$0.343386\pi$
$108$		0			0
$109$		−	1.45257e20i		−	0.613581i	−0.951777	−	0.306790i	$-0.900745\pi$
$109$		−	1.45257e20i		−	0.613581i	0.951777	−	0.306790i	$-0.0992551\pi$
$110$	−2.97096e17	+	7.83765e17i	−0.00114543	+	0.00302175i
$111$		0			0
$112$	−4.91334e19	+	4.91334e19i	−0.158196	+	0.158196i
$113$	−1.43712e20	−	1.43712e20i	−0.423359	−	0.423359i	0.463000	−	0.886358i	$-0.346773\pi$
$113$	−1.43712e20	−	1.43712e20i	−0.423359	−	0.423359i	−0.886358	+	0.463000i	$0.846773\pi$
$114$		0			0
$115$	−5.31227e20	−	2.01369e20i	−1.31311	−	0.497753i
$116$	3.83025e20			0.868256
$117$		0			0
$118$	2.20708e18	+	2.20708e18i	0.00421695	+	0.00421695i
$119$		−	1.85931e20i		−	0.326499i
$120$		0			0
$121$	−4.14017e20			−0.615410
$122$	−3.64787e18	+	3.64787e18i	−0.00499392	+	0.00499392i
$123$		0			0
$124$		−	1.39681e21i		−	1.62525i
$125$	2.76636e20	−	8.89289e20i	0.297035	−	0.954867i
$126$		0			0
$127$	1.28344e21	−	1.28344e21i	1.17582	−	1.17582i	0.195016	−	0.980800i	$-0.437524\pi$
$127$	1.28344e21	−	1.28344e21i	1.17582	−	1.17582i	0.980800	−	0.195016i	$-0.0624760\pi$
$128$	1.73992e19	+	1.73992e19i	0.0147377	+	0.0147377i
$129$		0			0
$130$	2.53139e18	−	1.13979e18i	0.00183623	−	0.000826779i
$131$	−9.63942e20			−0.647647			−0.323823	−	0.946118i	$-0.604968\pi$
$131$	−9.63942e20			−0.647647			−0.323823	+	0.946118i	$0.604968\pi$
$132$		0			0
$133$	1.34045e19	+	1.34045e19i	0.00773987	+	0.00773987i
$134$		−	1.68547e19i		−	0.00902967i
$135$		0			0
$136$	−3.29201e19			−0.0152080
$137$	1.38810e21	−	1.38810e21i	0.595958	−	0.595958i	−0.343276	−	0.939234i	$-0.611537\pi$
$137$	1.38810e21	−	1.38810e21i	0.595958	−	0.595958i	0.939234	+	0.343276i	$0.111537\pi$
$138$		0			0
$139$		−	2.98122e21i		−	1.10725i	−0.832766	−	0.553626i	$-0.813244\pi$
$139$		−	2.98122e21i		−	1.10725i	0.832766	−	0.553626i	$-0.186756\pi$
$140$	6.05148e20	+	2.29389e20i	0.209210	+	0.0793036i
$141$		0			0
$142$	5.02979e18	−	5.02979e18i	0.00150892	−	0.00150892i
$143$	−6.05957e20	−	6.05957e20i	−0.169466	−	0.169466i
$144$		0			0
$145$	−1.46460e21	−	3.25278e21i	−0.356482	−	0.791726i
$146$	3.59843e19			0.00817682
$147$		0			0
$148$	−1.55295e21	−	1.55295e21i	−0.307993	−	0.307993i
$149$		−	5.77191e21i		−	1.07018i	−0.844795	−	0.535090i	$-0.820278\pi$
$149$		−	5.77191e21i		−	1.07018i	0.844795	−	0.535090i	$-0.179722\pi$
$150$		0			0
$151$	−2.64955e20			−0.0429934			−0.0214967	−	0.999769i	$-0.506843\pi$
$151$	−2.64955e20			−0.0429934			−0.0214967	+	0.999769i	$0.506843\pi$
$152$	2.37334e18	−	2.37334e18i	0.000360516	−	0.000360516i
$153$		0			0
$154$			5.42459e18i			0.000723036i
$155$	−1.18622e22	+	5.34107e21i	−1.48200	+	0.667285i
$156$		0			0
$157$	6.41131e21	−	6.41131e21i	0.704612	−	0.704612i	−0.260785	−	0.965397i	$-0.583981\pi$
$157$	6.41131e21	−	6.41131e21i	0.704612	−	0.704612i	0.965397	+	0.260785i	$0.0839813\pi$
$158$	−4.34554e19	−	4.34554e19i	−0.00448201	−	0.00448201i
$159$		0			0
$160$	6.09223e19	−	1.60718e20i	0.00554086	−	0.0146172i
$161$	−3.67673e21			−0.314198
$162$		0			0
$163$	−1.36800e22	−	1.36800e22i	−1.03326	−	1.03326i	−0.999428	−	0.0338306i	$-0.989229\pi$
$163$	−1.36800e22	−	1.36800e22i	−1.03326	−	1.03326i	−0.0338306	−	0.999428i	$-0.510771\pi$
$164$		−	2.50129e22i		−	1.77716i
$165$		0			0
$166$	−4.93813e19			−0.00310801
$167$	1.38963e22	−	1.38963e22i	0.823634	−	0.823634i	−0.162993	−	0.986627i	$-0.552115\pi$
$167$	1.38963e22	−	1.38963e22i	0.823634	−	0.823634i	0.986627	+	0.162993i	$0.0521149\pi$
$168$		0			0
$169$		−	1.61666e22i		−	0.850654i
$170$	6.29385e19	+	1.39783e20i	0.00312196	+	0.00693368i
$171$		0			0
$172$	−5.27101e21	+	5.27101e21i	−0.232600	+	0.232600i
$173$	2.74845e22	+	2.74845e22i	1.14453	+	1.14453i	0.987612	+	0.156915i	$0.0501549\pi$
$173$	2.74845e22	+	2.74845e22i	1.14453	+	1.14453i	0.156915	+	0.987612i	$0.449845\pi$
$174$		0			0
$175$	−3.65888e20	−	6.01625e21i	−0.0135821	−	0.223329i
$176$	−1.76844e22			−0.620103
$177$		0			0
$178$	9.36518e19	+	9.36518e19i	0.00293303	+	0.00293303i
$179$		−	7.43674e21i		−	0.220218i	−0.993920	−	0.110109i	$-0.964880\pi$
$179$		−	7.43674e21i		−	0.220218i	0.993920	−	0.110109i	$-0.0351200\pi$
$180$		0			0
$181$	9.99277e21			0.264789			0.132395	−	0.991197i	$-0.457733\pi$
$181$	9.99277e21			0.264789			0.132395	+	0.991197i	$0.457733\pi$
$182$	1.27045e19	−	1.27045e19i	0.000318598	−	0.000318598i
$183$		0			0
$184$			6.50986e20i			0.0146350i
$185$	−7.25009e21	+	1.91263e22i	−0.154392	+	0.407300i
$186$		0			0
$187$	3.34607e22	−	3.34607e22i	0.639910	−	0.639910i
$188$	2.06223e22	+	2.06223e22i	0.373903	+	0.373903i
$189$		0			0
$190$	−1.46150e19	−	5.53999e18i	−0.000238375	−	9.03593e-5i
$191$	−1.85330e22			−0.286822			−0.143411	−	0.989663i	$-0.545807\pi$
$191$	−1.85330e22			−0.286822			−0.143411	+	0.989663i	$0.545807\pi$
$192$		0			0
$193$	5.77240e22	+	5.77240e22i	0.804976	+	0.804976i	0.983869	−	0.178892i	$-0.0572514\pi$
$193$	5.77240e22	+	5.77240e22i	0.804976	+	0.804976i	−0.178892	+	0.983869i	$0.557251\pi$
$194$			3.03852e20i			0.00402388i
$195$		0			0
$196$	−7.94776e22			−0.949914
$197$	−3.85613e21	+	3.85613e21i	−0.0438015	+	0.0438015i	−0.728668	−	0.684867i	$-0.759860\pi$
$197$	−3.85613e21	+	3.85613e21i	−0.0438015	+	0.0438015i	0.684867	+	0.728668i	$0.259860\pi$
$198$		0			0
$199$			5.84096e22i			0.599727i	0.953982	+	0.299863i	$0.0969411\pi$
$199$			5.84096e22i			0.599727i	−0.953982	+	0.299863i	$0.903059\pi$
$200$	−1.06521e21	+	6.47827e19i	−0.0104025	+	0.000632643i
$201$		0			0
$202$	4.17025e20	−	4.17025e20i	0.00368679	−	0.00368679i
$203$	−1.63250e22	−	1.63250e22i	−0.137370	−	0.137370i
$204$		0			0
$205$	−2.12418e23	+	9.56434e22i	−1.62052	+	0.729653i
$206$	4.37123e20			0.00317637
$207$		0			0
$208$	4.14172e22	+	4.14172e22i	0.273242	+	0.273242i
$209$			4.82463e21i			0.0303390i
$210$		0			0
$211$	1.97241e23			1.12765			0.563824	−	0.825895i	$-0.309330\pi$
$211$	1.97241e23			1.12765			0.563824	+	0.825895i	$0.309330\pi$
$212$	−6.79934e21	+	6.79934e21i	−0.0370773	+	0.0370773i
$213$		0			0
$214$		−	6.07104e20i		−	0.00301387i
$215$	6.49183e22	+	2.46081e22i	0.307597	+	0.116599i
$216$		0			0
$217$	−5.95336e22	+	5.95336e22i	−0.257137	+	0.257137i
$218$	5.48069e20	+	5.48069e20i	0.00226084	+	0.00226084i
$219$		0			0
$220$	6.76227e22	+	1.50186e23i	0.254604	+	0.565461i
$221$	−1.56731e23			−0.563939
$222$		0			0
$223$	2.39987e23	+	2.39987e23i	0.789112	+	0.789112i	0.981349	−	0.192237i	$-0.0615741\pi$
$223$	2.39987e23	+	2.39987e23i	0.789112	+	0.789112i	−0.192237	+	0.981349i	$0.561574\pi$
$224$		−	1.11236e21i		−	0.00349757i
$225$		0			0
$226$	1.08448e21			0.00311987
$227$	−3.10473e23	+	3.10473e23i	−0.854605	+	0.854605i	−0.990696	−	0.136092i	$-0.956546\pi$
$227$	−3.10473e23	+	3.10473e23i	−0.854605	+	0.854605i	0.136092	+	0.990696i	$0.456546\pi$
$228$		0			0
$229$			4.24623e23i			1.07065i	0.844645	+	0.535327i	$0.179811\pi$
$229$			4.24623e23i			1.07065i	−0.844645	+	0.535327i	$0.820189\pi$
$230$	2.76416e21	−	1.24459e21i	0.00667244	−	0.00300433i
$231$		0			0
$232$	−2.89043e21	+	2.89043e21i	−0.00639856	+	0.00639856i
$233$	4.79808e23	+	4.79808e23i	1.01744	+	1.01744i	0.999845	+	0.0175940i	$0.00560064\pi$
$233$	4.79808e23	+	4.79808e23i	1.01744	+	1.01744i	0.0175940	+	0.999845i	$0.494399\pi$
$234$		0			0
$235$	9.62768e22	−	2.53986e23i	0.187432	−	0.494460i
$236$	6.13349e23			1.14443
$237$		0			0
$238$	7.01536e20	+	7.01536e20i	0.00120304	+	0.00120304i
$239$		−	1.58870e23i		−	0.261254i	−0.991432	−	0.130627i	$-0.958301\pi$
$239$		−	1.58870e23i		−	0.261254i	0.991432	−	0.130627i	$-0.0416991\pi$
$240$		0			0
$241$	−3.90298e23			−0.590509			−0.295254	−	0.955419i	$-0.595404\pi$
$241$	−3.90298e23			−0.590509			−0.295254	+	0.955419i	$0.595404\pi$
$242$	1.56213e21	−	1.56213e21i	0.00226758	−	0.00226758i
$243$		0			0
$244$			1.01375e24i			1.35529i
$245$	3.03903e23	+	6.74951e23i	0.390009	+	0.866186i
$246$		0			0
$247$	1.12994e22	−	1.12994e22i	0.0133685	−	0.0133685i
$248$	1.05408e22	+	1.05408e22i	0.0119772	+	0.0119772i
$249$		0			0
$250$	2.31160e21	+	4.39915e21i	0.00242389	+	0.00461285i
$251$	−1.59459e24			−1.60661			−0.803307	−	0.595565i	$-0.796928\pi$
$251$	−1.59459e24			−1.60661			−0.803307	+	0.595565i	$0.796928\pi$
$252$		0			0
$253$	−6.61676e23	−	6.61676e23i	−0.615800	−	0.615800i
$254$			9.68513e21i			0.00866499i
$255$		0			0
$256$	1.20860e24			0.999728
$257$	9.80272e23	−	9.80272e23i	0.779858	−	0.779858i	−0.199948	−	0.979806i	$-0.564077\pi$
$257$	9.80272e23	−	9.80272e23i	0.779858	−	0.779858i	0.979806	+	0.199948i	$0.0640775\pi$
$258$		0			0
$259$			1.32377e23i			0.0974575i
$260$	1.93365e23	−	5.10112e23i	0.136976	−	0.361353i
$261$		0			0
$262$	3.63705e21	−	3.63705e21i	0.00238636	−	0.00238636i
$263$	−7.09161e23	−	7.09161e23i	−0.447907	−	0.447907i	0.446752	−	0.894658i	$-0.352581\pi$
$263$	−7.09161e23	−	7.09161e23i	−0.447907	−	0.447907i	−0.894658	+	0.446752i	$0.852581\pi$
$264$		0			0
$265$	8.37413e22	+	3.17432e22i	0.0490321	+	0.0185863i
$266$	−1.01153e20			−5.70378e−5
$267$		0			0
$268$	−2.34196e24	−	2.34196e24i	−1.22527	−	1.22527i
$269$		−	3.36094e23i		−	0.169409i	−0.996406	−	0.0847047i	$-0.973005\pi$
$269$		−	3.36094e23i		−	0.169409i	0.996406	−	0.0847047i	$-0.0269947\pi$
$270$		0			0
$271$	8.77461e23			0.410710			0.205355	−	0.978688i	$-0.434165\pi$
$271$	8.77461e23			0.410710			0.205355	+	0.978688i	$0.434165\pi$
$272$	−2.28704e24	+	2.28704e24i	−1.03177	+	1.03177i
$273$		0			0
$274$			1.04749e22i			0.00439182i
$275$	1.01686e24	−	1.14855e24i	0.411086	−	0.464326i
$276$		0			0
$277$	−1.37066e24	+	1.37066e24i	−0.515385	+	0.515385i	−0.916172	−	0.400786i	$-0.868737\pi$
$277$	−1.37066e24	+	1.37066e24i	−0.515385	+	0.515385i	0.400786	+	0.916172i	$0.368737\pi$
$278$	1.12485e22	+	1.12485e22i	0.00407986	+	0.00407986i
$279$		0			0
$280$	−6.29768e21	+	2.83559e21i	−0.00212618	+	0.000957334i
$281$	3.31689e24			1.08061			0.540304	−	0.841470i	$-0.318309\pi$
$281$	3.31689e24			1.08061			0.540304	+	0.841470i	$0.318309\pi$
$282$		0			0
$283$	2.37935e24	+	2.37935e24i	0.722094	+	0.722094i	0.969031	−	0.246937i	$-0.0794242\pi$
$283$	2.37935e24	+	2.37935e24i	0.722094	+	0.722094i	−0.246937	+	0.969031i	$0.579424\pi$
$284$		−	1.39778e24i		−	0.409502i
$285$		0			0
$286$	4.57268e21			0.00124885
$287$	−1.06608e24	+	1.06608e24i	−0.281171	+	0.281171i
$288$		0			0
$289$		−	4.59039e24i		−	1.12946i
$290$	1.77991e22	+	6.74700e21i	0.00423077	+	0.00160373i
$291$		0			0
$292$	5.00003e24	−	5.00003e24i	1.10954	−	1.10954i
$293$	−5.85441e24	−	5.85441e24i	−1.25547	−	1.25547i	−0.953232	−	0.302240i	$-0.902266\pi$
$293$	−5.85441e24	−	5.85441e24i	−1.25547	−	1.25547i	−0.302240	−	0.953232i	$-0.597734\pi$
$294$		0			0
$295$	−2.34530e24	−	5.20877e24i	−0.469870	−	1.04355i
$296$	2.34381e22			0.00453948
$297$		0			0
$298$	2.17780e22	+	2.17780e22i	0.00394326	+	0.00394326i
$299$			3.09931e24i			0.542692i
$300$		0			0
$301$	4.49313e23			0.0736010
$302$	9.99701e20	−	9.99701e20i	0.000158417	−	0.000158417i
$303$		0			0
$304$		−	3.29763e23i		−	0.0489177i
$305$	8.60908e24	−	3.87632e24i	1.23583	−	0.556444i
$306$		0			0
$307$	1.15304e24	−	1.15304e24i	0.155046	−	0.155046i	−0.625321	−	0.780367i	$-0.715032\pi$
$307$	1.15304e24	−	1.15304e24i	0.155046	−	0.155046i	0.780367	+	0.625321i	$0.215032\pi$
$308$	7.53749e23	+	7.53749e23i	0.0981114	+	0.0981114i
$309$		0			0
$310$	2.46049e22	−	6.49097e22i	0.00300196	−	0.00791941i
$311$	2.21080e23			0.0261183			0.0130592	−	0.999915i	$-0.495843\pi$
$311$	2.21080e23			0.0261183			0.0130592	+	0.999915i	$0.495843\pi$
$312$		0			0
$313$	−6.86614e24	−	6.86614e24i	−0.760798	−	0.760798i	0.215668	−	0.976467i	$-0.430807\pi$
$313$	−6.86614e24	−	6.86614e24i	−0.760798	−	0.760798i	−0.976467	+	0.215668i	$0.930807\pi$
$314$			4.83810e22i			0.00519253i
$315$		0			0
$316$	−1.20763e25			−1.21636
$317$	3.58531e24	−	3.58531e24i	0.349892	−	0.349892i	−0.510177	−	0.860069i	$-0.670420\pi$
$317$	3.58531e24	−	3.58531e24i	0.349892	−	0.349892i	0.860069	+	0.510177i	$0.170420\pi$
$318$		0			0
$319$		−	5.87578e24i		−	0.538466i
$320$	−4.62176e24	−	1.02647e25i	−0.410495	−	0.911684i
$321$		0			0
$322$	1.38727e22	−	1.38727e22i	0.00115772	−	0.00115772i
$323$	6.23946e23	+	6.23946e23i	0.0504803	+	0.0504803i
$324$		0			0
$325$	−5.07142e24	+	3.08427e23i	−0.385741	+	0.0234595i
$326$	1.03232e23			0.00761443
$327$		0			0
$328$	1.88755e23	+	1.88755e23i	0.0130967	+	0.0130967i
$329$		−	1.75789e24i		−	0.118313i
$330$		0			0
$331$	6.60953e24			0.418688			0.209344	−	0.977842i	$-0.432867\pi$
$331$	6.60953e24			0.418688			0.209344	+	0.977842i	$0.432867\pi$
$332$	−6.86155e24	+	6.86155e24i	−0.421737	+	0.421737i
$333$		0			0
$334$			1.04864e23i			0.00606964i
$335$	−1.09336e25	+	2.88438e25i	−0.614209	+	1.62033i
$336$		0			0
$337$	−7.50720e24	+	7.50720e24i	−0.397355	+	0.397355i	−0.877299	−	0.479944i	$-0.840657\pi$
$337$	−7.50720e24	+	7.50720e24i	−0.397355	+	0.397355i	0.479944	+	0.877299i	$0.340657\pi$
$338$	6.09984e22	+	6.09984e22i	0.00313438	+	0.00313438i
$339$		0			0
$340$	2.81681e25	+	1.06775e25i	1.36449	+	0.517226i
$341$	−2.14277e25			−1.00793
$342$		0			0
$343$	6.95336e24	+	6.95336e24i	0.308499	+	0.308499i
$344$		−	7.95534e22i		−	0.00342826i
$345$		0			0
$346$	−2.07403e23			−0.00843441
$347$	2.47822e25	−	2.47822e25i	0.979141	−	0.979141i	−0.0206460	−	0.999787i	$-0.506572\pi$
$347$	2.47822e25	−	2.47822e25i	0.979141	−	0.979141i	0.999787	+	0.0206460i	$0.00657230\pi$
$348$		0			0
$349$			1.86774e25i			0.696725i	0.937360	+	0.348363i	$0.113262\pi$
$349$			1.86774e25i			0.696725i	−0.937360	+	0.348363i	$0.886738\pi$
$350$	2.40805e22	+	2.13194e22i	0.000872940	+	0.000772849i
$351$		0			0
$352$	2.00184e23	−	2.00184e23i	0.00685493	−	0.00685493i
$353$	1.93968e25	+	1.93968e25i	0.645631	+	0.645631i	0.951934	−	0.306303i	$-0.0990922\pi$
$353$	1.93968e25	+	1.93968e25i	0.645631	+	0.645631i	−0.306303	+	0.951934i	$0.599092\pi$
$354$		0			0
$355$	−1.18704e25	+	5.34478e24i	−0.373407	+	0.168130i
$356$	2.60259e25			0.795986
$357$		0			0
$358$	2.80596e22	+	2.80596e22i	0.000811430	+	0.000811430i
$359$		−	1.14804e25i		−	0.322859i	−0.986884	−	0.161430i	$-0.948389\pi$
$359$		−	1.14804e25i		−	0.322859i	0.986884	−	0.161430i	$-0.0516105\pi$
$360$		0			0
$361$	3.75000e25			0.997607
$362$	−3.77038e22	+	3.77038e22i	−0.000975661	+	0.000975661i
$363$		0			0
$364$		−	3.53058e24i		−	0.0864635i
$365$	−6.15809e25	−	2.33430e25i	−1.46729	−	0.556197i
$366$		0			0
$367$	−3.13881e25	+	3.13881e25i	−0.708117	+	0.708117i	−0.966139	−	0.258022i	$-0.916929\pi$
$367$	−3.13881e25	+	3.13881e25i	−0.708117	+	0.708117i	0.258022	+	0.966139i	$0.416929\pi$
$368$	4.52255e25	+	4.52255e25i	0.992900	+	0.992900i
$369$		0			0
$370$	−4.48103e22	−	9.95209e22i	−0.000931881	−	0.00206965i
$371$	5.79590e23			0.0117323
$372$		0			0
$373$	3.66873e25	+	3.66873e25i	0.703765	+	0.703765i	0.965217	−	0.261452i	$-0.0842013\pi$
$373$	3.66873e25	+	3.66873e25i	0.703765	+	0.703765i	−0.261452	+	0.965217i	$0.584201\pi$
$374$			2.52501e23i			0.00471571i
$375$		0			0
$376$	−3.11244e23			−0.00551091
$377$	−1.37612e25	+	1.37612e25i	−0.237270	+	0.237270i
$378$		0			0
$379$			2.11918e25i			0.346558i	0.984873	+	0.173279i	$0.0554362\pi$
$379$			2.11918e25i			0.346558i	−0.984873	+	0.173279i	$0.944564\pi$
$380$	−2.80054e24	+	1.26097e24i	−0.0446072	+	0.0200848i
$381$		0			0
$382$	6.99269e22	−	6.99269e22i	0.00105684	−	0.00105684i
$383$	−2.94906e25	−	2.94906e25i	−0.434207	−	0.434207i	0.455850	−	0.890057i	$-0.349335\pi$
$383$	−2.94906e25	−	2.94906e25i	−0.434207	−	0.434207i	−0.890057	+	0.455850i	$0.849335\pi$
$384$		0			0
$385$	3.51893e24	−	9.28324e24i	0.0491817	−	0.129745i
$386$	−4.35597e23			−0.00593215
$387$		0			0
$388$	4.22203e25	+	4.22203e25i	0.546015	+	0.546015i
$389$			1.10150e26i			1.38831i	0.719825	+	0.694156i	$0.244222\pi$
$389$			1.10150e26i			1.38831i	−0.719825	+	0.694156i	$0.755778\pi$
$390$		0			0
$391$	−1.71143e26			−2.04923
$392$	5.99763e23	−	5.99763e23i	0.00700033	−	0.00700033i
$393$		0			0
$394$		−	2.90991e22i		−	0.000322788i
$395$	4.61768e25	+	1.02556e26i	0.499405	+	1.10915i
$396$		0			0
$397$	−2.67646e25	+	2.67646e25i	−0.275204	+	0.275204i	−0.831191	−	0.555987i	$-0.812341\pi$
$397$	−2.67646e25	+	2.67646e25i	−0.275204	+	0.275204i	0.555987	+	0.831191i	$0.312341\pi$
$398$	−2.20385e23	−	2.20385e23i	−0.00220979	−	0.00220979i
$399$		0			0
$400$	−6.95021e25	+	7.85034e25i	−0.662824	+	0.748666i
$401$	5.13198e25			0.477355			0.238677	−	0.971099i	$-0.423286\pi$
$401$	5.13198e25			0.477355			0.238677	+	0.971099i	$0.423286\pi$
$402$		0			0
$403$	5.01841e25	+	5.01841e25i	0.444135	+	0.444135i
$404$		−	1.15892e26i		−	1.00055i
$405$		0			0
$406$	1.23191e23			0.00101233
$407$	−2.38230e25	+	2.38230e25i	−0.191008	+	0.191008i
$408$		0			0
$409$		−	1.45081e26i		−	1.10759i	−0.832654	−	0.553794i	$-0.813180\pi$
$409$		−	1.45081e26i		−	1.10759i	0.832654	−	0.553794i	$-0.186820\pi$
$410$	4.40603e23	−	1.16235e24i	0.00328253	−	0.00865960i
$411$		0			0
$412$	6.07384e25	−	6.07384e25i	0.431014	−	0.431014i
$413$	−2.61416e25	−	2.61416e25i	−0.181064	−	0.181064i
$414$		0			0
$415$	8.45075e25	+	3.20337e25i	0.557717	+	0.211410i
$416$	−9.37670e23			−0.00604111
$417$		0			0
$418$	−1.82038e22	−	1.82038e22i	−0.000111789	−	0.000111789i
$419$			9.76407e25i			0.585451i	0.956196	+	0.292726i	$0.0945622\pi$
$419$			9.76407e25i			0.585451i	−0.956196	+	0.292726i	$0.905438\pi$
$420$		0			0
$421$	2.34366e26			1.33990			0.669952	−	0.742404i	$-0.266315\pi$
$421$	2.34366e26			1.33990			0.669952	+	0.742404i	$0.266315\pi$
$422$	−7.44212e23	+	7.44212e23i	−0.00415501	+	0.00415501i
$423$		0			0
$424$		−	1.02620e23i		−	0.000546478i
$425$	−1.70312e25	−	2.80042e26i	−0.0885841	−	1.45658i
$426$		0			0
$427$	4.32070e25	−	4.32070e25i	0.214425	−	0.214425i
$428$	−8.43573e25	−	8.43573e25i	−0.408964	−	0.408964i
$429$		0			0
$430$	−3.37792e23	+	1.52094e23i	−0.00156302	+	0.000703766i
$431$	1.95945e25			0.0885853			0.0442926	−	0.999019i	$-0.485897\pi$
$431$	1.95945e25			0.0885853			0.0442926	+	0.999019i	$0.485897\pi$
$432$		0			0
$433$	−2.06182e26	−	2.06182e26i	−0.889965	−	0.889965i	0.104555	−	0.994519i	$-0.466658\pi$
$433$	−2.06182e26	−	2.06182e26i	−0.889965	−	0.889965i	−0.994519	+	0.104555i	$0.966658\pi$
$434$		−	4.49253e23i		−	0.00189493i
$435$		0			0
$436$	1.52309e26			0.613564
$437$	1.23383e25	−	1.23383e25i	0.0485783	−	0.0485783i
$438$		0			0
$439$		−	7.67531e24i		−	0.0288702i	−0.999896	−	0.0144351i	$-0.995405\pi$
$439$		−	7.67531e24i		−	0.0288702i	0.999896	−	0.0144351i	$-0.00459500\pi$
$440$	−1.64365e24	−	6.23048e23i	−0.00604342	−	0.00229084i
$441$		0			0
$442$	5.91362e23	−	5.91362e23i	0.00207793	−	0.00207793i
$443$	6.26585e25	+	6.26585e25i	0.215250	+	0.215250i	0.806493	−	0.591243i	$-0.201363\pi$
$443$	6.26585e25	+	6.26585e25i	0.215250	+	0.215250i	−0.591243	+	0.806493i	$0.701363\pi$
$444$		0			0
$445$	−9.95167e25	−	2.21021e26i	−0.326810	−	0.725826i
$446$	−1.81099e24			−0.00581523
$447$		0			0
$448$	−5.15159e25	−	5.15159e25i	−0.158184	−	0.158184i
$449$		−	3.72189e26i		−	1.11763i	−0.829291	−	0.558817i	$-0.811255\pi$
$449$		−	3.72189e26i		−	1.11763i	0.829291	−	0.558817i	$-0.188745\pi$
$450$		0			0
$451$	−3.83709e26			−1.10214
$452$	1.50689e26	−	1.50689e26i	0.423347	−	0.423347i
$453$		0			0
$454$		−	2.34289e24i		−	0.00629787i
$455$	−2.99829e25	+	1.35001e25i	−0.0788424	+	0.0354996i
$456$		0			0
$457$	−1.07465e26	+	1.07465e26i	−0.270461	+	0.270461i	−0.829286	−	0.558825i	$-0.811252\pi$
$457$	−1.07465e26	+	1.07465e26i	−0.270461	+	0.270461i	0.558825	+	0.829286i	$0.311252\pi$
$458$	−1.60215e24	−	1.60215e24i	−0.00394500	−	0.00394500i
$459$		0			0
$460$	2.11145e26	−	5.57017e26i	0.497739	−	1.31308i
$461$	−1.93725e26			−0.446865			−0.223433	−	0.974719i	$-0.571726\pi$
$461$	−1.93725e26			−0.446865			−0.223433	+	0.974719i	$0.571726\pi$
$462$		0			0
$463$	−2.75418e26	−	2.75418e26i	−0.608391	−	0.608391i	0.334135	−	0.942525i	$-0.391556\pi$
$463$	−2.75418e26	−	2.75418e26i	−0.608391	−	0.608391i	−0.942525	+	0.334135i	$0.891556\pi$
$464$			4.01609e26i			0.868209i
$465$		0			0
$466$	−3.62073e24			−0.00749786
$467$	−5.17420e26	+	5.17420e26i	−1.04876	+	1.04876i	−0.0500079	+	0.998749i	$0.515925\pi$
$467$	−5.17420e26	+	5.17420e26i	−1.04876	+	1.04876i	−0.998749	+	0.0500079i	$0.984075\pi$
$468$		0			0
$469$			1.99634e26i			0.387709i
$470$	5.95054e23	+	1.32158e24i	0.00113130	+	0.00251255i
$471$		0			0
$472$	−4.62852e24	+	4.62852e24i	−0.00843378	+	0.00843378i
$473$	8.08597e25	+	8.08597e25i	0.144252	+	0.144252i
$474$		0			0
$475$	2.14171e25	+	1.89614e25i	0.0366290	+	0.0324291i
$476$	1.94957e26			0.326490
$477$		0			0
$478$	5.99433e23	+	5.99433e23i	0.000962636	+	0.000962636i
$479$		−	7.65347e26i		−	1.20366i	−0.798625	−	0.601829i	$-0.794439\pi$
$479$		−	7.65347e26i		−	1.20366i	0.798625	−	0.601829i	$-0.205561\pi$
$480$		0			0
$481$	1.11588e26			0.168332
$482$	1.47264e24	−	1.47264e24i	0.00217583	−	0.00217583i
$483$		0			0
$484$		−	4.34116e26i		−	0.615393i
$485$	1.97109e26	−	5.19990e26i	0.273709	−	0.722067i
$486$		0			0
$487$	1.26890e25	−	1.26890e25i	0.0169097	−	0.0169097i	−0.698601	−	0.715511i	$-0.746194\pi$
$487$	1.26890e25	−	1.26890e25i	0.0169097	−	0.0169097i	0.715511	+	0.698601i	$0.246194\pi$
$488$	−7.65004e24	−	7.65004e24i	−0.00998770	−	0.00998770i
$489$		0			0
$490$	−3.69332e24	−	1.40000e24i	−0.00462866	−	0.00175456i
$491$	5.45011e26			0.669253			0.334626	−	0.942351i	$-0.391390\pi$
$491$	5.45011e26			0.669253			0.334626	+	0.942351i	$0.391390\pi$
$492$		0			0
$493$	−7.59886e26	−	7.59886e26i	−0.895941	−	0.895941i
$494$			8.52673e22i			9.85174e-5i
$495$		0			0
$496$	1.46458e27			1.62517
$497$	−5.95750e25	+	5.95750e25i	−0.0647888	+	0.0647888i
$498$		0			0
$499$			3.36680e26i			0.351732i	0.984414	+	0.175866i	$0.0562725\pi$
$499$			3.36680e26i			0.351732i	−0.984414	+	0.175866i	$0.943727\pi$
$500$	9.32462e26	+	2.90066e26i	0.954841	+	0.297027i
$501$		0			0
$502$	6.01655e24	−	6.01655e24i	0.00591984	−	0.00591984i
$503$	−4.74966e26	−	4.74966e26i	−0.458123	−	0.458123i	0.439916	−	0.898039i	$-0.355008\pi$
$503$	−4.74966e26	−	4.74966e26i	−0.458123	−	0.458123i	−0.898039	+	0.439916i	$0.855008\pi$
$504$		0			0
$505$	−9.84190e26	+	4.43141e26i	−0.912358	+	0.410798i
$506$	4.99314e24			0.00453804
$507$		0			0
$508$	1.34575e27	+	1.34575e27i	1.17578	+	1.17578i
$509$			6.84432e26i			0.586344i	0.956060	+	0.293172i	$0.0947108\pi$
$509$			6.84432e26i			0.586344i	−0.956060	+	0.293172i	$0.905289\pi$
$510$		0			0
$511$	−4.26214e26			−0.351090
$512$	−2.28045e25	+	2.28045e25i	−0.0184214	+	0.0184214i
$513$		0			0
$514$			7.39734e24i			0.00574704i
$515$	−7.48060e26	−	2.83562e26i	−0.569986	−	0.216061i
$516$		0			0
$517$	3.16355e26	−	3.16355e26i	0.231883	−	0.231883i
$518$	−4.99472e23	−	4.99472e23i	−0.000359099	−	0.000359099i
$519$		0			0
$520$	2.39027e24	+	5.30865e24i	0.00165354	+	0.00367240i
$521$	3.25861e26			0.221134			0.110567	−	0.993869i	$-0.464733\pi$
$521$	3.25861e26			0.221134			0.110567	+	0.993869i	$0.464733\pi$
$522$		0			0
$523$	1.32995e27	+	1.32995e27i	0.868596	+	0.868596i	0.992317	−	0.123721i	$-0.0394829\pi$
$523$	1.32995e27	+	1.32995e27i	0.868596	+	0.868596i	−0.123721	+	0.992317i	$0.539483\pi$
$524$		−	1.01074e27i		−	0.647629i
$525$		0			0
$526$	5.35147e24			0.00330078
$527$	−2.77114e27	+	2.77114e27i	−1.67708	+	1.67708i
$528$		0			0
$529$			1.66814e27i			0.972023i
$530$	−4.35735e23	+	1.96194e23i	−0.000249152	+	0.000112183i
$531$		0			0
$532$	−1.40552e25	+	1.40552e25i	−0.00773966	+	0.00773966i
$533$	8.98654e26	+	8.98654e26i	0.485647	+	0.485647i
$534$		0			0
$535$	−3.93828e26	+	1.03895e27i	−0.205007	+	0.540826i
$536$	3.53463e25			0.0180591
$537$		0			0
$538$	1.26812e24	+	1.26812e24i	0.000624218	+	0.000624218i
$539$			1.21922e27i			0.589108i
$540$		0			0
$541$	−3.00958e27			−1.40130			−0.700652	−	0.713503i	$-0.747108\pi$
$541$	−3.00958e27			−1.40130			−0.700652	+	0.713503i	$0.747108\pi$
$542$	−3.31075e24	+	3.31075e24i	−0.00151333	+	0.00151333i
$543$		0			0
$544$		−	5.17777e25i		−	0.0228115i
$545$	−5.82392e26	−	1.29346e27i	−0.251913	−	0.559483i
$546$		0			0
$547$	−2.39169e27	+	2.39169e27i	−0.997311	+	0.997311i	−0.999996	−	0.00268498i	$-0.999145\pi$
$547$	−2.39169e27	+	2.39169e27i	−0.997311	+	0.997311i	0.00268498	+	0.999996i	$0.499145\pi$
$548$	1.45549e27	+	1.45549e27i	0.595942	+	0.595942i
$549$		0			0
$550$	4.96891e23	+	8.17030e24i	0.000196171	+	0.00322560i
$551$	1.09566e26			0.0424777
$552$		0			0
$553$	5.14704e26	+	5.14704e26i	0.192445	+	0.192445i
$554$		−	1.03433e25i		−	0.00379805i
$555$		0			0
$556$	3.12595e27			1.10722
$557$	1.94071e27	−	1.94071e27i	0.675162	−	0.675162i	−0.283739	−	0.958901i	$-0.591575\pi$
$557$	1.94071e27	−	1.94071e27i	0.675162	−	0.675162i	0.958901	+	0.283739i	$0.0915750\pi$
$558$		0			0
$559$		−	3.78749e26i		−	0.127126i
$560$	−2.40519e26	+	6.34509e26i	−0.0792993	+	0.209198i
$561$		0			0
$562$	−1.25150e25	+	1.25150e25i	−0.00398168	+	0.00398168i
$563$	3.04528e27	+	3.04528e27i	0.951794	+	0.951794i	0.998890	−	0.0470961i	$-0.0149967\pi$
$563$	3.04528e27	+	3.04528e27i	0.951794	+	0.951794i	−0.0470961	+	0.998890i	$0.514997\pi$
$564$		0			0
$565$	−1.85590e27	−	7.03502e26i	−0.559847	−	0.212217i
$566$	−1.79551e25			−0.00532136
$567$		0			0
$568$	1.05481e25	+	1.05481e25i	0.00301780	+	0.00301780i
$569$		−	3.26586e27i		−	0.918068i	−0.888419	−	0.459034i	$-0.848196\pi$
$569$		−	3.26586e27i		−	0.918068i	0.888419	−	0.459034i	$-0.151804\pi$
$570$		0			0
$571$	3.57523e27			0.970383			0.485191	−	0.874408i	$-0.338750\pi$
$571$	3.57523e27			0.970383			0.485191	+	0.874408i	$0.338750\pi$
$572$	6.35375e26	−	6.35375e26i	0.169461	−	0.169461i
$573$		0			0
$574$		−	8.04484e24i		−	0.00207204i
$575$	−5.53774e27	+	3.36787e26i	−1.40170	+	0.0852466i
$576$		0			0
$577$	2.63542e26	−	2.63542e26i	0.0644306	−	0.0644306i	−0.674157	−	0.738588i	$-0.735493\pi$
$577$	2.63542e26	−	2.63542e26i	0.0644306	−	0.0644306i	0.738588	+	0.674157i	$0.235493\pi$
$578$	1.73200e25	+	1.73200e25i	0.00416169	+	0.00416169i
$579$		0			0
$580$	3.41069e27	−	1.53570e27i	0.791704	−	0.356473i
$581$	5.84893e26			0.133449
$582$		0			0
$583$	1.04305e26	+	1.04305e26i	0.0229942	+	0.0229942i
$584$			7.54636e25i			0.0163534i
$585$		0			0
$586$	4.41786e25			0.00925200
$587$	−1.83539e27	+	1.83539e27i	−0.377873	+	0.377873i	−0.870334	−	0.492461i	$-0.836097\pi$
$587$	−1.83539e27	+	1.83539e27i	−0.377873	+	0.377873i	0.492461	+	0.870334i	$0.336097\pi$
$588$		0			0
$589$		−	3.99565e26i		−	0.0795124i
$590$	2.85023e25	+	1.08042e25i	0.00557647	+	0.00211383i
$591$		0			0
$592$	1.62830e27	−	1.62830e27i	0.307977	−	0.307977i
$593$	2.89387e27	+	2.89387e27i	0.538185	+	0.538185i	0.922996	−	0.384811i	$-0.125733\pi$
$593$	2.89387e27	+	2.89387e27i	0.538185	+	0.538185i	−0.384811	+	0.922996i	$0.625733\pi$
$594$		0			0
$595$	−7.45470e26	−	1.65564e27i	−0.134048	−	0.297713i
$596$	6.05212e27			1.07015
$597$		0			0
$598$	−1.16940e25	−	1.16940e25i	−0.00199964	−	0.00199964i
$599$		−	7.86676e27i		−	1.32290i	−0.749988	−	0.661451i	$-0.769941\pi$
$599$		−	7.86676e27i		−	1.32290i	0.749988	−	0.661451i	$-0.230059\pi$
$600$		0			0
$601$	−4.80387e27			−0.781351			−0.390676	−	0.920528i	$-0.627759\pi$
$601$	−4.80387e27			−0.781351			−0.390676	+	0.920528i	$0.627759\pi$
$602$	−1.69530e24	+	1.69530e24i	−0.000271195	+	0.000271195i
$603$		0			0
$604$		−	2.77817e26i		−	0.0429922i
$605$	−3.68666e27	+	1.65996e27i	−0.561151	+	0.252664i
$606$		0			0
$607$	−8.30490e27	+	8.30490e27i	−1.22306	+	1.22306i	−0.256520	+	0.966539i	$0.582576\pi$
$607$	−8.30490e27	+	8.30490e27i	−1.22306	+	1.22306i	−0.966539	+	0.256520i	$0.917424\pi$
$608$	3.73286e24	+	3.73286e24i	0.000540762	+	0.000540762i
$609$		0			0
$610$	−1.78572e25	+	4.71087e25i	−0.00250331	+	0.00660393i
$611$	−1.48182e27			−0.204354
$612$		0			0
$613$	−2.69070e26	−	2.69070e26i	−0.0359138	−	0.0359138i	0.688922	−	0.724836i	$-0.258084\pi$
$613$	−2.69070e26	−	2.69070e26i	−0.0359138	−	0.0359138i	−0.724836	+	0.688922i	$0.758084\pi$
$614$			8.70106e24i			0.00114259i
$615$		0			0
$616$	−1.13760e25			−0.00144605
$617$	−7.68618e27	+	7.68618e27i	−0.961300	+	0.961300i	−0.999279	−	0.0379785i	$-0.987908\pi$
$617$	−7.68618e27	+	7.68618e27i	−0.961300	+	0.961300i	0.0379785	+	0.999279i	$0.487908\pi$
$618$		0			0
$619$		−	1.64811e28i		−	1.99563i	−0.0660814	−	0.997814i	$-0.521050\pi$
$619$		−	1.64811e28i		−	1.99563i	0.0660814	−	0.997814i	$-0.478950\pi$
$620$	−5.60037e27	−	1.24381e28i	−0.667267	−	1.48196i
$621$		0			0
$622$	−8.34158e23	+	8.34158e23i	−9.62375e−5	+	9.62375e-5i
$623$	−1.10925e27	−	1.10925e27i	−0.125936	−	0.125936i
$624$		0			0
$625$	−1.10217e27	−	9.02792e27i	−0.121185	−	0.992630i
$626$	5.18133e25			0.00560658
$627$		0			0
$628$	6.72256e27	+	6.72256e27i	0.704593	+	0.704593i
$629$			6.16183e27i			0.635628i
$630$		0			0
$631$	4.08536e27			0.408260			0.204130	−	0.978944i	$-0.434563\pi$
$631$	4.08536e27			0.408260			0.204130	+	0.978944i	$0.434563\pi$
$632$	9.11313e25	−	9.11313e25i	0.00896390	−	0.00896390i
$633$		0			0
$634$			2.70555e25i			0.00257847i
$635$	6.28274e27	−	1.65744e28i	0.589403	−	1.55489i
$636$		0			0
$637$	2.85544e27	−	2.85544e27i	0.259584	−	0.259584i
$638$	2.21699e25	+	2.21699e25i	0.00198407	+	0.00198407i
$639$		0			0
$640$	2.24693e26	+	8.51729e25i	0.0194890	+	0.00738757i
$641$	2.99650e27			0.255878			0.127939	−	0.991782i	$-0.459164\pi$
$641$	2.99650e27			0.255878			0.127939	+	0.991782i	$0.459164\pi$
$642$		0			0
$643$	−1.09767e28	−	1.09767e28i	−0.908577	−	0.908577i	0.0875802	−	0.996157i	$-0.472087\pi$
$643$	−1.09767e28	−	1.09767e28i	−0.908577	−	0.908577i	−0.996157	+	0.0875802i	$0.972087\pi$
$644$		−	3.85523e27i		−	0.314189i
$645$		0			0
$646$	−4.70842e24			−0.000372006
$647$	−2.13474e27	+	2.13474e27i	−0.166074	+	0.166074i	−0.785251	−	0.619177i	$-0.787466\pi$
$647$	−2.13474e27	+	2.13474e27i	−0.166074	+	0.166074i	0.619177	+	0.785251i	$0.287466\pi$
$648$		0			0
$649$		−	9.40905e27i		−	0.709739i
$650$	1.79713e25	−	2.02987e25i	0.00133489	−	0.00150777i
$651$		0			0
$652$	1.43441e28	−	1.43441e28i	1.03323	−	1.03323i
$653$	−1.51870e28	−	1.51870e28i	−1.07731	−	1.07731i	−0.996750	−	0.0805577i	$-0.974330\pi$
$653$	−1.51870e28	−	1.51870e28i	−1.07731	−	1.07731i	−0.0805577	−	0.996750i	$-0.525670\pi$
$654$		0			0
$655$	−8.58354e27	+	3.86482e27i	−0.590545	+	0.265899i
$656$	2.62265e28			1.77706
$657$		0			0
$658$	6.63270e24	+	6.63270e24i	0.000435945	+	0.000435945i
$659$			7.70752e27i			0.498954i	0.968381	+	0.249477i	$0.0802587\pi$
$659$			7.70752e27i			0.498954i	−0.968381	+	0.249477i	$0.919741\pi$
$660$		0			0
$661$	−1.06771e28			−0.670561			−0.335280	−	0.942118i	$-0.608831\pi$
$661$	−1.06771e28			−0.670561			−0.335280	+	0.942118i	$0.608831\pi$
$662$	−2.49384e25	+	2.49384e25i	−0.00154273	+	0.00154273i
$663$		0			0
$664$		−	1.03559e26i		−	0.00621593i
$665$	1.73106e26	+	6.56180e25i	0.0102352	+	0.00387977i
$666$		0			0
$667$	−1.50265e28	+	1.50265e28i	−0.862185	+	0.862185i
$668$	1.45709e28	+	1.45709e28i	0.823612	+	0.823612i
$669$		0			0
$670$	−6.75769e25	−	1.50084e26i	−0.00370724	−	0.00823355i
$671$	1.55513e28			0.840508
$672$		0			0
$673$	1.34303e28	+	1.34303e28i	0.704590	+	0.704590i	0.965392	−	0.260802i	$-0.0839871\pi$
$673$	1.34303e28	+	1.34303e28i	0.704590	+	0.704590i	−0.260802	+	0.965392i	$0.583987\pi$
$674$		−	5.66509e25i		−	0.00292825i
$675$		0			0
$676$	1.69515e28			0.850630
$677$	−1.97993e28	+	1.97993e28i	−0.978955	+	0.978955i	−0.999783	−	0.0208277i	$-0.993370\pi$
$677$	−1.97993e28	+	1.97993e28i	−0.978955	+	0.978955i	0.0208277	+	0.999783i	$0.493370\pi$
$678$		0			0
$679$		−	3.59895e27i		−	0.172774i
$680$	−2.93141e26	+	1.31990e26i	−0.0138672	+	0.00624383i
$681$		0			0
$682$	8.08490e25	−	8.08490e25i	0.00371390	−	0.00371390i
$683$	−6.17987e27	−	6.17987e27i	−0.279752	−	0.279752i	0.553258	−	0.833010i	$-0.313384\pi$
$683$	−6.17987e27	−	6.17987e27i	−0.279752	−	0.279752i	−0.833010	+	0.553258i	$0.813384\pi$
$684$		0			0
$685$	6.79507e27	−	1.79260e28i	0.298736	−	0.788091i
$686$	−5.24715e25			−0.00227343
$687$		0			0
$688$	−5.52676e27	−	5.52676e27i	−0.232587	−	0.232587i
$689$		−	4.88567e26i		−	0.0202643i
$690$		0			0
$691$	2.87344e28			1.15777			0.578884	−	0.815410i	$-0.303489\pi$
$691$	2.87344e28			1.15777			0.578884	+	0.815410i	$0.303489\pi$
$692$	−2.88188e28	+	2.88188e28i	−1.14450	+	1.14450i
$693$		0			0
$694$			1.87012e26i			0.00721562i
$695$	−1.19529e28	−	2.65466e28i	−0.454595	−	1.00963i
$696$		0			0
$697$	−4.96233e28	+	4.96233e28i	−1.83382	+	1.83382i
$698$	−7.04716e25	−	7.04716e25i	−0.00256720	−	0.00256720i
$699$		0			0
$700$	6.30833e27	−	3.83651e26i	0.223323	−	0.0135818i
$701$	−1.27524e27			−0.0445053			−0.0222527	−	0.999752i	$-0.507084\pi$
$701$	−1.27524e27			−0.0445053			−0.0222527	+	0.999752i	$0.507084\pi$
$702$		0			0
$703$	−4.44230e26	−	4.44230e26i	−0.0150680	−	0.0150680i
$704$		−	1.85419e28i		−	0.620052i
$705$		0			0
$706$	−1.46373e26			−0.00475787
$707$	−4.93942e27	+	4.93942e27i	−0.158300	+	0.158300i
$708$		0			0
$709$			3.99111e28i			1.24346i	0.783232	+	0.621729i	$0.213570\pi$
$709$			3.99111e28i			1.24346i	−0.783232	+	0.621729i	$0.786430\pi$
$710$	2.46220e25	−	6.49548e25i	0.000756378	−	0.00199539i
$711$		0			0
$712$	−1.96399e26	+	1.96399e26i	−0.00586598	+	0.00586598i
$713$	5.47986e28	+	5.47986e28i	1.61389	+	1.61389i
$714$		0			0
$715$	−7.82534e27	−	2.96630e27i	−0.224100	−	0.0849482i
$716$	7.79778e27			0.220212
$717$		0			0
$718$	4.33168e25	+	4.33168e25i	0.00118963	+	0.00118963i
$719$		−	3.78806e28i		−	1.02595i	−0.858402	−	0.512977i	$-0.828543\pi$
$719$		−	3.78806e28i		−	1.02595i	0.858402	−	0.512977i	$-0.171457\pi$
$720$		0			0
$721$	−5.17747e27			−0.136384
$722$	−1.41491e26	+	1.41491e26i	−0.00367585	+	0.00367585i
$723$		0			0
$724$			1.04779e28i			0.264782i
$725$	−2.60833e28	−	2.30926e28i	−0.650104	−	0.575563i
$726$		0			0
$727$	−6.81066e26	+	6.81066e26i	−0.0165137	+	0.0165137i	−0.715315	−	0.698802i	$-0.753717\pi$
$727$	−6.81066e26	+	6.81066e26i	−0.0165137	+	0.0165137i	0.698802	+	0.715315i	$0.253717\pi$
$728$	2.66429e25	+	2.66429e25i	0.000637188	+	0.000637188i
$729$		0			0
$730$	3.20427e26	−	1.44275e26i	0.00745590	−	0.00335709i
$731$	2.09144e28			0.480033
$732$		0			0
$733$	3.19735e28	+	3.19735e28i	0.714087	+	0.714087i	0.967388	−	0.253301i	$-0.0815163\pi$
$733$	3.19735e28	+	3.19735e28i	0.714087	+	0.714087i	−0.253301	+	0.967388i	$0.581516\pi$
$734$		−	2.36861e26i		−	0.00521835i
$735$		0			0
$736$	−1.02389e27			−0.0219521
$737$	−3.59267e28	+	3.59267e28i	−0.759875	+	0.759875i
$738$		0			0
$739$			5.44973e28i			1.12184i	0.827871	+	0.560919i	$0.189552\pi$
$739$			5.44973e28i			1.12184i	−0.827871	+	0.560919i	$0.810448\pi$
$740$	−2.00549e28	−	7.60206e27i	−0.407289	−	0.154388i
$741$		0			0
$742$	−2.18685e24	+	2.18685e24i	−4.32295e−5	+	4.32295e-5i
$743$	3.02473e28	+	3.02473e28i	0.589928	+	0.589928i	0.937612	−	0.347684i	$-0.113032\pi$
$743$	3.02473e28	+	3.02473e28i	0.589928	+	0.589928i	−0.347684	+	0.937612i	$0.613032\pi$
$744$		0			0
$745$	−2.31419e28	−	5.13967e28i	−0.439375	−	0.975825i
$746$	−2.76850e26			−0.00518628
$747$		0			0
$748$	3.50851e28	+	3.50851e28i	0.639893	+	0.639893i
$749$			7.19079e27i			0.129407i
$750$		0			0
$751$	7.71306e28			1.35153			0.675767	−	0.737115i	$-0.263812\pi$
$751$	7.71306e28			1.35153			0.675767	+	0.737115i	$0.263812\pi$
$752$	−2.16229e28	+	2.16229e28i	−0.373882	+	0.373882i
$753$		0			0
$754$		−	1.03845e26i		−	0.00174852i
$755$	−2.35932e27	+	1.06231e27i	−0.0392028	+	0.0176514i
$756$		0			0
$757$	7.96584e27	−	7.96584e27i	0.128906	−	0.128906i	−0.639710	−	0.768616i	$-0.720946\pi$
$757$	7.96584e27	−	7.96584e27i	0.128906	−	0.128906i	0.768616	+	0.639710i	$0.220946\pi$
$758$	−7.99588e25	−	7.99588e25i	−0.00127695	−	0.00127695i
$759$		0			0
$760$	1.16180e25	−	3.06494e25i	0.000180716	−	0.000476744i
$761$	4.63585e28			0.711677			0.355839	−	0.934547i	$-0.384195\pi$
$761$	4.63585e28			0.711677			0.355839	+	0.934547i	$0.384195\pi$
$762$		0			0
$763$	−6.49156e27	−	6.49156e27i	−0.0970742	−	0.0970742i
$764$		−	1.94327e28i		−	0.286814i
$765$		0			0
$766$	2.22542e26			0.00319982
$767$	−2.20362e28	+	2.20362e28i	−0.312739	+	0.312739i
$768$		0			0
$769$		−	5.21119e28i		−	0.720565i	−0.932843	−	0.360283i	$-0.882680\pi$
$769$		−	5.21119e28i		−	0.720565i	0.932843	−	0.360283i	$-0.117320\pi$
$770$	2.17493e25	+	4.83039e25i	0.000296851	+	0.000659288i
$771$		0			0
$772$	−6.05263e28	+	6.05263e28i	−0.804955	+	0.804955i
$773$	8.28103e28	+	8.28103e28i	1.08715	+	1.08715i	0.995821	+	0.0913294i	$0.0291116\pi$
$773$	8.28103e28	+	8.28103e28i	1.08715	+	1.08715i	0.0913294	+	0.995821i	$0.470888\pi$
$774$		0			0
$775$	−8.42139e28	+	9.51204e28i	−1.07737	+	1.21690i
$776$	−6.37215e26			−0.00804765
$777$		0			0
$778$	−4.15606e26	−	4.15606e26i	−0.00511547	−	0.00511547i
$779$		−	7.15508e27i		−	0.0869440i
$780$		0			0
$781$	−2.14426e28			−0.253961
$782$	6.45739e26	−	6.45739e26i	0.00755074	−	0.00755074i
$783$		0			0
$784$		−	8.33338e28i		−	0.949862i
$785$	3.13848e28	−	8.27957e28i	0.353202	−	0.931775i
$786$		0			0
$787$	8.66634e28	−	8.66634e28i	0.950798	−	0.950798i	−0.0480469	−	0.998845i	$-0.515300\pi$
$787$	8.66634e28	−	8.66634e28i	0.950798	−	0.950798i	0.998845	+	0.0480469i	$0.0152997\pi$
$788$	−4.04333e27	−	4.04333e27i	−0.0438003	−	0.0438003i
$789$		0			0
$790$	−5.61183e26	−	2.12724e26i	−0.00592699	−	0.00224670i
$791$	−1.28450e28			−0.133959
$792$		0			0
$793$	−3.64215e28	−	3.64215e28i	−0.370361	−	0.370361i
$794$		−	2.01971e26i		−	0.00202808i
$795$		0			0
$796$	−6.12452e28			−0.599710
$797$	−5.24123e28	+	5.24123e28i	−0.506815	+	0.506815i	−0.913547	−	0.406732i	$-0.866668\pi$
$797$	−5.24123e28	+	5.24123e28i	−0.506815	+	0.506815i	0.406732	+	0.913547i	$0.366668\pi$
$798$		0			0
$799$		−	8.18254e28i		−	0.771650i
$800$	−1.01892e26	−	1.67540e27i	−0.000948943	−	0.0156033i
$801$		0			0
$802$	−1.93635e26	+	1.93635e26i	−0.00175889	+	0.00175889i
$803$	−7.67027e28	−	7.67027e28i	−0.688106	−	0.688106i
$804$		0			0
$805$	−3.27399e28	+	1.47415e28i	−0.286496	+	0.128998i
$806$	−3.78699e26			−0.00327299
$807$		0			0
$808$	8.74553e26	+	8.74553e26i	0.00737348	+	0.00737348i
$809$		−	2.16772e29i		−	1.80517i	−0.430509	−	0.902586i	$-0.641666\pi$
$809$		−	2.16772e29i		−	1.80517i	0.430509	−	0.902586i	$-0.358334\pi$
$810$		0			0
$811$	6.24252e28			0.507167			0.253584	−	0.967313i	$-0.418391\pi$
$811$	6.24252e28			0.507167			0.253584	+	0.967313i	$0.418391\pi$
$812$	1.71175e28	−	1.71175e28i	0.137366	−	0.137366i
$813$		0			0
$814$		−	1.79773e26i		−	0.00140761i
$815$	−1.76663e29	−	6.69665e28i	−1.36638	−	0.517942i
$816$		0			0
$817$	−1.50780e27	+	1.50780e27i	−0.0113795	+	0.0113795i
$818$	5.47406e26	+	5.47406e26i	0.00408109	+	0.00408109i
$819$		0			0
$820$	−1.00287e29	−	2.22731e29i	−0.729633	−	1.62047i
$821$	1.45291e29			1.04425			0.522127	−	0.852868i	$-0.325139\pi$
$821$	1.45291e29			1.04425			0.522127	+	0.852868i	$0.325139\pi$
$822$		0			0
$823$	1.58958e29	+	1.58958e29i	1.11502	+	1.11502i	0.992461	+	0.122560i	$0.0391103\pi$
$823$	1.58958e29	+	1.58958e29i	1.11502	+	1.11502i	0.122560	+	0.992461i	$0.460890\pi$
$824$			9.16701e26i			0.00635266i
$825$		0			0
$826$	1.97270e26			0.00133432
$827$	−1.28860e29	+	1.28860e29i	−0.861122	+	0.861122i	−0.991468	−	0.130347i	$-0.958391\pi$
$827$	−1.28860e29	+	1.28860e29i	−0.861122	+	0.861122i	0.130347	+	0.991468i	$0.458391\pi$
$828$		0			0
$829$		−	1.27029e29i		−	0.828624i	−0.910135	−	0.414312i	$-0.864022\pi$
$829$		−	1.27029e29i		−	0.828624i	0.910135	−	0.414312i	$-0.135978\pi$
$830$	−4.39722e26	+	1.97989e26i	−0.00283398	+	0.00127603i
$831$		0			0
$832$	−4.34255e28	+	4.34255e28i	−0.273220	+	0.273220i
$833$	1.57676e29	+	1.57676e29i	0.980202	+	0.980202i
$834$		0			0
$835$	6.80255e28	−	1.79457e29i	0.412864	−	1.08917i
$836$	−5.05885e27			−0.0303381
$837$		0			0
$838$	−3.68408e26	−	3.68408e26i	−0.00215719	−	0.00215719i
$839$		−	1.51592e29i		−	0.877114i	−0.898703	−	0.438557i	$-0.855490\pi$
$839$		−	1.51592e29i		−	0.877114i	0.898703	−	0.438557i	$-0.144510\pi$
$840$		0			0
$841$	4.35568e28			0.246091
$842$	−8.84287e26	+	8.84287e26i	−0.00493710	+	0.00493710i
$843$		0			0
$844$			2.06817e29i			1.12762i
$845$	−6.48184e28	−	1.43958e29i	−0.349246	−	0.775654i
$846$		0			0
$847$	−1.85025e28	+	1.85025e28i	−0.0973636	+	0.0973636i
$848$	−7.12923e27	−	7.12923e27i	−0.0370753	−	0.0370753i
$849$		0			0
$850$	1.12089e27	+	9.92365e26i	0.00569341	+	0.00504060i
$851$	1.21848e29			0.611680
$852$		0			0
$853$	−2.18327e29	−	2.18327e29i	−1.07058	−	1.07058i	−0.997313	−	0.0732623i	$-0.976659\pi$
$853$	−2.18327e29	−	2.18327e29i	−1.07058	−	1.07058i	−0.0732623	−	0.997313i	$-0.523341\pi$
$854$			3.26049e26i			0.00158017i
$855$		0			0
$856$	1.27317e27			0.00602767
$857$	4.94404e28	−	4.94404e28i	0.231352	−	0.231352i	−0.581905	−	0.813257i	$-0.697692\pi$
$857$	4.94404e28	−	4.94404e28i	0.231352	−	0.231352i	0.813257	+	0.581905i	$0.197692\pi$
$858$		0			0
$859$		−	2.18722e29i		−	0.999910i	−0.866052	−	0.499955i	$-0.833350\pi$
$859$		−	2.18722e29i		−	0.999910i	0.866052	−	0.499955i	$-0.166650\pi$
$860$	−2.58028e28	+	6.80699e28i	−0.116596	+	0.307589i
$861$		0			0
$862$	−7.39321e25	+	7.39321e25i	−0.000326408	+	0.000326408i
$863$	3.26266e28	+	3.26266e28i	0.142385	+	0.142385i	0.774706	−	0.632321i	$-0.217898\pi$
$863$	3.26266e28	+	3.26266e28i	0.142385	+	0.142385i	−0.632321	+	0.774706i	$0.717898\pi$
$864$		0			0
$865$	3.54935e29	+	1.34543e29i	1.51352	+	0.573718i
$866$	1.55589e27			0.00655845
$867$		0			0
$868$	−6.24239e28	−	6.24239e28i	−0.257130	−	0.257130i
$869$			1.85255e29i			0.754351i
$870$		0			0
$871$	1.68282e29			0.669662
$872$	−1.14937e27	+	1.14937e27i	−0.00452162	+	0.00452162i
$873$		0			0
$874$			9.31077e25i			0.000357990i
$875$	−2.73796e28	−	5.21054e28i	−0.104075	−	0.198063i
$876$		0			0
$877$	−6.53451e28	+	6.53451e28i	−0.242782	+	0.242782i	−0.818000	−	0.575218i	$-0.804917\pi$
$877$	−6.53451e28	+	6.53451e28i	−0.242782	+	0.242782i	0.575218	+	0.818000i	$0.304917\pi$
$878$	2.89597e25	+	2.89597e25i	0.000106377	+	0.000106377i
$879$		0			0
$880$	−1.57473e29	+	7.09037e28i	−0.565430	+	0.254590i
$881$	−1.64158e29			−0.582779			−0.291390	−	0.956604i	$-0.594118\pi$
$881$	−1.64158e29			−0.582779			−0.291390	+	0.956604i	$0.594118\pi$
$882$		0			0
$883$	−3.18805e28	−	3.18805e28i	−0.110642	−	0.110642i	0.649619	−	0.760260i	$-0.274929\pi$
$883$	−3.18805e28	−	3.18805e28i	−0.110642	−	0.110642i	−0.760260	+	0.649619i	$0.774929\pi$
$884$		−	1.64340e29i		−	0.563924i
$885$		0			0
$886$	−4.72834e26			−0.00158625
$887$	3.31815e28	−	3.31815e28i	0.110068	−	0.110068i	−0.649928	−	0.759996i	$-0.725201\pi$
$887$	3.31815e28	−	3.31815e28i	0.110068	−	0.110068i	0.759996	+	0.649928i	$0.225201\pi$
$888$		0			0
$889$		−	1.14715e29i		−	0.372050i
$890$	1.20942e27	+	4.58447e26i	0.00387862	+	0.00147024i
$891$		0			0
$892$	−2.51637e29	+	2.51637e29i	−0.789091	+	0.789091i
$893$	5.89911e27	+	5.89911e27i	0.0182925	+	0.0182925i
$894$		0			0
$895$	−2.98168e28	−	6.62214e28i	−0.0904130	−	0.200802i
$896$	1.55515e27			0.00466328
$897$		0			0
$898$	1.40431e27	+	1.40431e27i	0.00411811	+	0.00411811i
$899$			4.86619e29i			1.41121i
$900$		0			0
$901$	2.69785e28			0.0765190
$902$	1.44777e27	−	1.44777e27i	0.00406102	−	0.00406102i
$903$		0			0
$904$			2.27429e27i			0.00623966i
$905$	8.89818e28	−	4.00649e28i	0.241443	−	0.108712i
$906$		0			0
$907$	−5.55720e28	+	5.55720e28i	−0.147497	+	0.147497i	−0.776999	−	0.629502i	$-0.783259\pi$
$907$	−5.55720e28	+	5.55720e28i	−0.147497	+	0.147497i	0.629502	+	0.776999i	$0.283259\pi$
$908$	−3.25546e29	−	3.25546e29i	−0.854581	−	0.854581i
$909$		0			0
$910$	6.21913e25	−	1.64066e26i	0.000159704	−	0.000421312i
$911$	6.81980e29			1.73216			0.866080	−	0.499906i	$-0.166632\pi$
$911$	6.81980e29			1.73216			0.866080	+	0.499906i	$0.166632\pi$
$912$		0			0
$913$	1.05259e29	+	1.05259e29i	0.261548	+	0.261548i
$914$		−	8.10953e26i		−	0.00199312i
$915$		0			0
$916$	−4.45238e29			−1.07062
$917$	−4.30788e28	+	4.30788e28i	−0.102464	+	0.102464i
$918$		0			0
$919$			6.49458e29i			1.51146i	0.654885	+	0.755728i	$0.272717\pi$
$919$			6.49458e29i			1.51146i	−0.654885	+	0.755728i	$0.727283\pi$
$920$	2.61006e27	+	5.79678e27i	0.00600858	+	0.0133447i
$921$		0			0
$922$	7.30944e26	−	7.30944e26i	0.00164655	−	0.00164655i
$923$	5.02189e28	+	5.02189e28i	0.111905	+	0.111905i
$924$		0			0
$925$	1.21257e28	+	1.99381e29i	0.0264417	+	0.434777i
$926$	2.07836e27			0.00448344
$927$		0			0
$928$	−4.54615e27	−	4.54615e27i	−0.00959762	−	0.00959762i
$929$			2.76287e29i			0.577037i	0.957474	+	0.288518i	$0.0931627\pi$
$929$			2.76287e29i			0.577037i	−0.957474	+	0.288518i	$0.906837\pi$
$930$		0			0
$931$	−2.27350e28			−0.0464727
$932$	−5.03102e29	+	5.03102e29i	−1.01741	+	1.01741i
$933$		0			0
$934$		−	3.90456e27i		−	0.00772865i
$935$	1.63798e29	−	4.32112e29i	0.320768	−	0.846213i
$936$		0			0
$937$	2.92472e29	−	2.92472e29i	0.560646	−	0.560646i	−0.368845	−	0.929491i	$-0.620247\pi$
$937$	2.92472e29	−	2.92472e29i	0.560646	−	0.560646i	0.929491	+	0.368845i	$0.120247\pi$
$938$	−7.53238e26	−	7.53238e26i	−0.00142858	−	0.00142858i
$939$		0			0
$940$	2.66317e29	+	1.00951e29i	0.494447	+	0.187427i
$941$	−4.28555e29			−0.787246			−0.393623	−	0.919272i	$-0.628778\pi$
$941$	−4.28555e29			−0.787246			−0.393623	+	0.919272i	$0.628778\pi$
$942$		0			0
$943$	9.81287e29	+	9.81287e29i	1.76473	+	1.76473i
$944$			6.43108e29i			1.14436i
$945$		0			0
$946$	−6.10183e26			−0.00106304
$947$	−1.53144e29	+	1.53144e29i	−0.263998	+	0.263998i	−0.826676	−	0.562678i	$-0.809771\pi$
$947$	−1.53144e29	+	1.53144e29i	−0.263998	+	0.263998i	0.562678	+	0.826676i	$0.309771\pi$
$948$		0			0
$949$			3.59278e29i			0.606413i
$950$	−1.52353e26	+	9.26558e24i	−0.000254457	+	1.54752e-5i
$951$		0			0
$952$	−1.47121e27	+	1.47121e27i	−0.00240605	+	0.00240605i
$953$	−1.42012e29	−	1.42012e29i	−0.229825	−	0.229825i	0.582795	−	0.812620i	$-0.301959\pi$
$953$	−1.42012e29	−	1.42012e29i	−0.229825	−	0.229825i	−0.812620	+	0.582795i	$0.801959\pi$
$954$		0			0
$955$	−1.65029e29	+	7.43061e28i	−0.261534	+	0.117758i
$956$	1.66583e29			0.261247
$957$		0			0
$958$	2.88773e27	+	2.88773e27i	0.00443509	+	0.00443509i
$959$		−	1.24069e29i		−	0.188572i
$960$		0			0
$961$	1.10281e30			1.64159
$962$	−4.21032e26	+	4.21032e26i	−0.000620246	+	0.000620246i
$963$		0			0
$964$		−	4.09246e29i		−	0.590492i
$965$	7.45448e29	+	2.82572e29i	1.06450	+	0.403511i
$966$		0			0
$967$	−5.27619e29	+	5.27619e29i	−0.737999	+	0.737999i	−0.972191	−	0.234191i	$-0.924756\pi$
$967$	−5.27619e29	+	5.27619e29i	−0.737999	+	0.737999i	0.234191	+	0.972191i	$0.424756\pi$
$968$	3.27598e27	+	3.27598e27i	0.00453510	+	0.00453510i
$969$		0			0
$970$	1.21826e27	+	2.70569e27i	0.00165205	+	0.00366910i
$971$	−1.97947e29			−0.265679			−0.132840	−	0.991138i	$-0.542410\pi$
$971$	−1.97947e29			−0.265679			−0.132840	+	0.991138i	$0.542410\pi$
$972$		0			0
$973$	−1.33231e29	−	1.33231e29i	−0.175177	−	0.175177i
$974$			9.57535e25i			0.000124614i
$975$		0			0
$976$	−1.06293e30			−1.35521
$977$	9.76815e29	−	9.76815e29i	1.23273	−	1.23273i	0.269813	−	0.962913i	$-0.413038\pi$
$977$	9.76815e29	−	9.76815e29i	1.23273	−	1.23273i	0.962913	−	0.269813i	$-0.0869620\pi$
$978$		0			0
$979$		−	3.99249e29i		−	0.493647i
$980$	−7.07718e29	+	3.18657e29i	−0.866163	+	0.389998i
$981$		0			0
$982$	−2.05638e27	+	2.05638e27i	−0.00246598	+	0.00246598i
$983$	1.45347e29	+	1.45347e29i	0.172532	+	0.172532i	0.788091	−	0.615559i	$-0.211070\pi$
$983$	1.45347e29	+	1.45347e29i	0.172532	+	0.172532i	−0.615559	+	0.788091i	$0.711070\pi$
$984$		0			0
$985$	−1.88766e28	+	4.97981e28i	−0.0219564	+	0.0579229i
$986$	5.73426e27			0.00660249
$987$		0			0
$988$	1.18479e28	+	1.18479e28i	0.0133682	+	0.0133682i
$989$		−	4.13576e29i		−	0.461947i
$990$		0			0
$991$	−3.82280e29			−0.418452			−0.209226	−	0.977867i	$-0.567094\pi$
$991$	−3.82280e29			−0.418452			−0.209226	+	0.977867i	$0.567094\pi$
$992$	−1.65788e28	+	1.65788e28i	−0.0179654	+	0.0179654i
$993$		0			0
$994$		−	4.49565e26i		−	0.000477451i
$995$	2.34187e29	+	5.20115e29i	0.246225	+	0.546850i
$996$		0			0
$997$	2.89012e29	−	2.89012e29i	0.297827	−	0.297827i	−0.542335	−	0.840162i	$-0.682460\pi$
$997$	2.89012e29	−	2.89012e29i	0.297827	−	0.297827i	0.840162	+	0.542335i	$0.182460\pi$
$998$	−1.27033e27	−	1.27033e27i	−0.00129602	−	0.00129602i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.21.g.a.28.5		18
3.2	odd	2		5.21.c.a.3.5	yes	18
5.2	odd	4	inner	45.21.g.a.37.5		18
15.2	even	4		5.21.c.a.2.5	✓	18
15.8	even	4		25.21.c.b.7.5		18
15.14	odd	2		25.21.c.b.18.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.21.c.a.2.5	✓	18	15.2	even	4
5.21.c.a.3.5	yes	18	3.2	odd	2
25.21.c.b.7.5		18	15.8	even	4
25.21.c.b.18.5		18	15.14	odd	2
45.21.g.a.28.5		18	1.1	even	1	trivial
45.21.g.a.37.5		18	5.2	odd	4	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.77310 + 3.77310i) q^{2} +1.04855e6i q^{4} +(8.90462e6 - 4.00939e6i) q^{5} +(4.46902e7 - 4.46902e7i) q^{7} +(-7.91266e6 - 7.91266e6i) q^{8} +O(q^{10})\)	\(q+(-3.77310 + 3.77310i) q^{2} +1.04855e6i q^{4} +(8.90462e6 - 4.00939e6i) q^{5} +(4.46902e7 - 4.46902e7i) q^{7} +(-7.91266e6 - 7.91266e6i) q^{8} +(-1.84702e7 + 4.87259e7i) q^{10} +1.60852e10 q^{11} +(-3.76718e10 - 3.76718e10i) q^{13} +3.37242e8i q^{14} -1.09942e12 q^{16} +(2.08022e12 - 2.08022e12i) q^{17} +2.99942e11i q^{19} +(4.20404e12 + 9.33691e12i) q^{20} +(-6.06910e10 + 6.06910e10i) q^{22} +(-4.11357e13 - 4.11357e13i) q^{23} +(6.32170e13 - 7.14042e13i) q^{25} +2.84279e11 q^{26} +(4.68598e13 + 4.68598e13i) q^{28} -3.65291e14i q^{29} -1.33214e15 q^{31} +(1.24453e13 - 1.24453e13i) q^{32} +1.56978e13i q^{34} +(2.18769e14 - 5.77130e14i) q^{35} +(-1.48105e15 + 1.48105e15i) q^{37} +(-1.13171e12 - 1.13171e12i) q^{38} +(-1.02184e14 - 3.87343e13i) q^{40} -2.38548e16 q^{41} +(5.02697e15 + 5.02697e15i) q^{43} +1.68661e16i q^{44} +3.10419e14 q^{46} +(1.96675e16 - 1.96675e16i) q^{47} +7.57978e16i q^{49} +(3.08912e13 + 5.07940e14i) q^{50} +(3.95006e16 - 3.95006e16i) q^{52} +(6.48453e15 + 6.48453e15i) q^{53} +(1.43232e17 - 6.44918e16i) q^{55} -7.07237e14 q^{56} +(1.37828e15 + 1.37828e15i) q^{58} -5.84951e17i q^{59} +9.66810e17 q^{61} +(5.02630e15 - 5.02630e15i) q^{62} -1.15273e18i q^{64} +(-4.86494e17 - 1.84412e17i) q^{65} +(-2.23353e18 + 2.23353e18i) q^{67} +(2.18121e18 + 2.18121e18i) q^{68} +(1.35213e15 + 3.00301e15i) q^{70} -1.33306e18 q^{71} +(-4.76853e18 - 4.76853e18i) q^{73} -1.11763e16i q^{74} -3.14504e17 q^{76} +(7.18850e17 - 7.18850e17i) q^{77} +1.15172e19i q^{79} +(-9.78993e18 + 4.40801e18i) q^{80} +(9.00068e16 - 9.00068e16i) q^{82} +(6.54386e18 + 6.54386e18i) q^{83} +(1.01831e19 - 2.68640e19i) q^{85} -3.79345e16 q^{86} +(-1.27277e17 - 1.27277e17i) q^{88} -2.48209e19i q^{89} -3.36712e18 q^{91} +(4.31328e19 - 4.31328e19i) q^{92} +1.48415e17i q^{94} +(1.20259e18 + 2.67087e18i) q^{95} +(4.02655e19 - 4.02655e19i) q^{97} +(-2.85993e17 - 2.85993e17i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 7302140 q^{5} - 585532752 q^{7} - 930113700 q^{8}+O(q^{10}) \) 18 * q + 2 * q^2 + 7302140 * q^5 - 585532752 * q^7 - 930113700 * q^8	\( 18 q + 2 q^{2} + 7302140 q^{5} - 585532752 q^{7} - 930113700 q^{8} - 17138778090 q^{10} + 6506343064 q^{11} - 369354655602 q^{13} - 6345876020232 q^{16} - 6508314764998 q^{17} - 38356516779780 q^{20} + 161054386758096 q^{22} + 81655963656152 q^{23} + 33913283845350 q^{25} - 234104101103636 q^{26} + 772213614545352 q^{28} + 17\!\cdots\!36 q^{31}+ \cdots + 27\!\cdots\!98 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 7302140 * q^5 - 585532752 * q^7 - 930113700 * q^8 - 17138778090 * q^10 + 6506343064 * q^11 - 369354655602 * q^13 - 6345876020232 * q^16 - 6508314764998 * q^17 - 38356516779780 * q^20 + 161054386758096 * q^22 + 81655963656152 * q^23 + 33913283845350 * q^25 - 234104101103636 * q^26 + 772213614545352 * q^28 + 1742256896900736 * q^31 + 4072699683722552 * q^32 + 4817791288113440 * q^35 + 6383289895587498 * q^37 + 14134212502378200 * q^38 + 43297629431150700 * q^40 + 30602304597564664 * q^41 - 46399469942287752 * q^43 + 17467214047538136 * q^46 + 137109249757437752 * q^47 + 40012852869983150 * q^50 - 745026624616846452 * q^52 + 184102027021671302 * q^53 + 752956242406989720 * q^55 - 685775432394721200 * q^56 - 2701246502184220800 * q^58 + 49879194030044136 * q^61 + 1190554579738283704 * q^62 - 6907070599410641170 * q^65 - 5597336519263153752 * q^67 + 25617328014464685148 * q^68 + 31706333959370270760 * q^70 - 10983277495574224736 * q^71 - 19072400700441139902 * q^73 + 75630007803532292400 * q^76 + 47766064678699704904 * q^77 - 134231700802559812960 * q^80 - 83501540658117625104 * q^82 + 119739383617210903952 * q^83 + 169044713294843560110 * q^85 - 33497378050769887736 * q^86 - 337125565675837197600 * q^88 + 86281377644254817136 * q^91 + 206921051460419061752 * q^92 - 118106834336527303800 * q^95 - 318608382222604685502 * q^97 + 27697031317753120498 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more