LMFDB - Embedded newform 25.9.c.c.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,9,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	25.c (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:	$10.1844652515$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 8 x^{10} + 124 x^{9} + 1665 x^{8} - 2456 x^{7} + 4192 x^{6} + 50576 x^{5} + \cdots + 1000000 $ x^12 - 4x^11 + 8x^10 + 124x^9 + 1665x^8 - 2456x^7 + 4192x^6 + 50576x^5 + 221184x^4 + 133760x^3 + 3200x^2 - 80000*x + 1000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{6}\cdot 5^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.1
Root			$2.82685 + 2.82685i$ of defining polynomial
Character	$\chi$	$=$	25.7
Dual form			25.9.c.c.18.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-21.8383 - 21.8383i) q^{2} +(-42.5089 + 42.5089i) q^{3} +697.824i q^{4} +1856.64 q^{6} +(-432.570 - 432.570i) q^{7} +(9648.70 - 9648.70i) q^{8} +2946.99i q^{9} +O(q^{10})$	\(q+(-21.8383 - 21.8383i) q^{2} +(-42.5089 + 42.5089i) q^{3} +697.824i q^{4} +1856.64 q^{6} +(-432.570 - 432.570i) q^{7} +(9648.70 - 9648.70i) q^{8} +2946.99i q^{9} +5245.59 q^{11} +(-29663.7 - 29663.7i) q^{12} +(-20992.6 + 20992.6i) q^{13} +18893.2i q^{14} -242780. q^{16} +(141.050 + 141.050i) q^{17} +(64357.4 - 64357.4i) q^{18} -208071. i q^{19} +36776.1 q^{21} +(-114555. - 114555. i) q^{22} +(-6235.05 + 6235.05i) q^{23} +820310. i q^{24} +916887. q^{26} +(-404174. - 404174. i) q^{27} +(301858. - 301858. i) q^{28} -985631. i q^{29} +414671. q^{31} +(2.83183e6 + 2.83183e6i) q^{32} +(-222984. + 222984. i) q^{33} -6160.58i q^{34} -2.05648e6 q^{36} +(-1.70719e6 - 1.70719e6i) q^{37} +(-4.54392e6 + 4.54392e6i) q^{38} -1.78474e6i q^{39} +1.82134e6 q^{41} +(-803128. - 803128. i) q^{42} +(2.29969e6 - 2.29969e6i) q^{43} +3.66050e6i q^{44} +272326. q^{46} +(3.04461e6 + 3.04461e6i) q^{47} +(1.03203e7 - 1.03203e7i) q^{48} -5.39057e6i q^{49} -11991.7 q^{51} +(-1.46492e7 - 1.46492e7i) q^{52} +(5.37085e6 - 5.37085e6i) q^{53} +1.76530e7i q^{54} -8.34747e6 q^{56} +(8.84487e6 + 8.84487e6i) q^{57} +(-2.15245e7 + 2.15245e7i) q^{58} +7.93099e6i q^{59} -1.12343e7 q^{61} +(-9.05572e6 - 9.05572e6i) q^{62} +(1.27478e6 - 1.27478e6i) q^{63} -6.15333e7i q^{64} +9.73919e6 q^{66} +(1.52185e7 + 1.52185e7i) q^{67} +(-98427.9 + 98427.9i) q^{68} -530090. i q^{69} -3.52392e7 q^{71} +(2.84346e7 + 2.84346e7i) q^{72} +(1.13894e7 - 1.13894e7i) q^{73} +7.45642e7i q^{74} +1.45197e8 q^{76} +(-2.26908e6 - 2.26908e6i) q^{77} +(-3.89758e7 + 3.89758e7i) q^{78} -3.50241e6i q^{79} +1.50267e7 q^{81} +(-3.97749e7 - 3.97749e7i) q^{82} +(3.64180e7 - 3.64180e7i) q^{83} +2.56633e7i q^{84} -1.00443e8 q^{86} +(4.18980e7 + 4.18980e7i) q^{87} +(5.06131e7 - 5.06131e7i) q^{88} -7.49765e7i q^{89} +1.81615e7 q^{91} +(-4.35097e6 - 4.35097e6i) q^{92} +(-1.76272e7 + 1.76272e7i) q^{93} -1.32978e8i q^{94} -2.40756e8 q^{96} +(-9.73416e7 - 9.73416e7i) q^{97} +(-1.17721e8 + 1.17721e8i) q^{98} +1.54587e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6396 q^{6}+O(q^{10}) $ 12 * q - 6396 * q^6	$ 12 q - 6396 q^{6} - 118116 q^{11} - 1204068 q^{16} - 1365456 q^{21} + 5376024 q^{26} + 3223704 q^{31} + 14477592 q^{36} + 10940364 q^{41} - 51272856 q^{46} - 47621676 q^{51} - 64717200 q^{56} - 23597616 q^{61} + 264735828 q^{66} - 47870856 q^{71} + 432845700 q^{76} + 3008052 q^{81} - 105341616 q^{86} - 64237536 q^{91} - 1580181156 q^{96}+O(q^{100}) $ 12 * q - 6396 * q^6 - 118116 * q^11 - 1204068 * q^16 - 1365456 * q^21 + 5376024 * q^26 + 3223704 * q^31 + 14477592 * q^36 + 10940364 * q^41 - 51272856 * q^46 - 47621676 * q^51 - 64717200 * q^56 - 23597616 * q^61 + 264735828 * q^66 - 47870856 * q^71 + 432845700 * q^76 + 3008052 * q^81 - 105341616 * q^86 - 64237536 * q^91 - 1580181156 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−21.8383	−	21.8383i	−1.36489	−	1.36489i	−0.867557	−	0.497338i	$-0.834311\pi$
$2$	−21.8383	−	21.8383i	−1.36489	−	1.36489i	−0.497338	−	0.867557i	$-0.665689\pi$
$3$	−42.5089	+	42.5089i	−0.524801	+	0.524801i	−0.919017	−	0.394217i	$-0.871016\pi$
$3$	−42.5089	+	42.5089i	−0.524801	+	0.524801i	0.394217	+	0.919017i	$0.371016\pi$
$4$			697.824i			2.72588i
$5$		0			0
$5$		0			0
$6$	1856.64			1.43260
$7$	−432.570	−	432.570i	−0.180162	−	0.180162i	0.611264	−	0.791427i	$-0.290661\pi$
$7$	−432.570	−	432.570i	−0.180162	−	0.180162i	−0.791427	+	0.611264i	$0.790661\pi$
$8$	9648.70	−	9648.70i	2.35564	−	2.35564i
$9$			2946.99i			0.449168i
$10$		0			0
$11$	5245.59			0.358281			0.179140	−	0.983824i	$-0.442668\pi$
$11$	5245.59			0.358281			0.179140	+	0.983824i	$0.442668\pi$
$12$	−29663.7	−	29663.7i	−1.43054	−	1.43054i
$13$	−20992.6	+	20992.6i	−0.735010	+	0.735010i	−0.971608	−	0.236598i	$-0.923968\pi$
$13$	−20992.6	+	20992.6i	−0.735010	+	0.735010i	0.236598	+	0.971608i	$0.423968\pi$
$14$			18893.2i			0.491805i
$15$		0			0
$16$	−242780.			−3.70452
$17$	141.050	+	141.050i	0.00168879	+	0.00168879i	0.707951	−	0.706262i	$-0.249620\pi$
$17$	141.050	+	141.050i	0.00168879	+	0.00168879i	−0.706262	+	0.707951i	$0.749620\pi$
$18$	64357.4	−	64357.4i	0.613068	−	0.613068i
$19$		−	208071.i		−	1.59660i	−0.602257	−	0.798302i	$-0.705732\pi$
$19$		−	208071.i		−	1.59660i	0.602257	−	0.798302i	$-0.294268\pi$
$20$		0			0
$21$	36776.1			0.189099
$22$	−114555.	−	114555.i	−0.489016	−	0.489016i
$23$	−6235.05	+	6235.05i	−0.0222807	+	0.0222807i	−0.718159	−	0.695879i	$-0.755015\pi$
$23$	−6235.05	+	6235.05i	−0.0222807	+	0.0222807i	0.695879	+	0.718159i	$0.255015\pi$
$24$			820310.i			2.47248i
$25$		0			0
$26$	916887.			2.00642
$27$	−404174.	−	404174.i	−0.760525	−	0.760525i
$28$	301858.	−	301858.i	0.491100	−	0.491100i
$29$		−	985631.i		−	1.39355i	−0.717290	−	0.696775i	$-0.754618\pi$
$29$		−	985631.i		−	1.39355i	0.717290	−	0.696775i	$-0.245382\pi$
$30$		0			0
$31$	414671.			0.449011			0.224506	−	0.974473i	$-0.427923\pi$
$31$	414671.			0.449011			0.224506	+	0.974473i	$0.427923\pi$
$32$	2.83183e6	+	2.83183e6i	2.70064	+	2.70064i
$33$	−222984.	+	222984.i	−0.188026	+	0.188026i
$34$		−	6160.58i		−	0.00461005i
$35$		0			0
$36$	−2.05648e6			−1.22438
$37$	−1.70719e6	−	1.70719e6i	−0.910908	−	0.910908i	0.0854359	−	0.996344i	$-0.472772\pi$
$37$	−1.70719e6	−	1.70719e6i	−0.910908	−	0.910908i	−0.996344	+	0.0854359i	$0.972772\pi$
$38$	−4.54392e6	+	4.54392e6i	−2.17920	+	2.17920i
$39$		−	1.78474e6i		−	0.771468i
$40$		0			0
$41$	1.82134e6			0.644547			0.322274	−	0.946647i	$-0.395553\pi$
$41$	1.82134e6			0.644547			0.322274	+	0.946647i	$0.395553\pi$
$42$	−803128.	−	803128.i	−0.258100	−	0.258100i
$43$	2.29969e6	−	2.29969e6i	0.672661	−	0.672661i	−0.285668	−	0.958329i	$-0.592215\pi$
$43$	2.29969e6	−	2.29969e6i	0.672661	−	0.672661i	0.958329	+	0.285668i	$0.0922155\pi$
$44$			3.66050e6i			0.976629i
$45$		0			0
$46$	272326.			0.0608216
$47$	3.04461e6	+	3.04461e6i	0.623937	+	0.623937i	0.946536	−	0.322599i	$-0.104557\pi$
$47$	3.04461e6	+	3.04461e6i	0.623937	+	0.623937i	−0.322599	+	0.946536i	$0.604557\pi$
$48$	1.03203e7	−	1.03203e7i	1.94414	−	1.94414i
$49$		−	5.39057e6i		−	0.935083i
$50$		0			0
$51$	−11991.7			−0.00177256
$52$	−1.46492e7	−	1.46492e7i	−2.00355	−	2.00355i
$53$	5.37085e6	−	5.37085e6i	0.680675	−	0.680675i	−0.279477	−	0.960152i	$-0.590161\pi$
$53$	5.37085e6	−	5.37085e6i	0.680675	−	0.680675i	0.960152	+	0.279477i	$0.0901611\pi$
$54$			1.76530e7i			2.07607i
$55$		0			0
$56$	−8.34747e6			−0.848795
$57$	8.84487e6	+	8.84487e6i	0.837899	+	0.837899i
$58$	−2.15245e7	+	2.15245e7i	−1.90205	+	1.90205i
$59$			7.93099e6i			0.654515i	0.944935	+	0.327257i	$0.106124\pi$
$59$			7.93099e6i			0.654515i	−0.944935	+	0.327257i	$0.893876\pi$
$60$		0			0
$61$	−1.12343e7			−0.811386			−0.405693	−	0.914009i	$-0.632970\pi$
$61$	−1.12343e7			−0.811386			−0.405693	+	0.914009i	$0.632970\pi$
$62$	−9.05572e6	−	9.05572e6i	−0.612853	−	0.612853i
$63$	1.27478e6	−	1.27478e6i	0.0809232	−	0.0809232i
$64$		−	6.15333e7i		−	3.66767i
$65$		0			0
$66$	9.73919e6			0.513272
$67$	1.52185e7	+	1.52185e7i	0.755217	+	0.755217i	0.975448	−	0.220230i	$-0.0706810\pi$
$67$	1.52185e7	+	1.52185e7i	0.755217	+	0.755217i	−0.220230	+	0.975448i	$0.570681\pi$
$68$	−98427.9	+	98427.9i	−0.00460344	+	0.00460344i
$69$		−	530090.i		−	0.0233859i
$70$		0			0
$71$	−3.52392e7			−1.38673			−0.693366	−	0.720585i	$-0.743873\pi$
$71$	−3.52392e7			−1.38673			−0.693366	+	0.720585i	$0.743873\pi$
$72$	2.84346e7	+	2.84346e7i	1.05808	+	1.05808i
$73$	1.13894e7	−	1.13894e7i	0.401060	−	0.401060i	−0.477546	−	0.878606i	$-0.658474\pi$
$73$	1.13894e7	−	1.13894e7i	0.401060	−	0.401060i	0.878606	+	0.477546i	$0.158474\pi$
$74$			7.45642e7i			2.48659i
$75$		0			0
$76$	1.45197e8			4.35215
$77$	−2.26908e6	−	2.26908e6i	−0.0645487	−	0.0645487i
$78$	−3.89758e7	+	3.89758e7i	−1.05297	+	1.05297i
$79$		−	3.50241e6i		−	0.0899204i	−0.998989	−	0.0449602i	$-0.985684\pi$
$79$		−	3.50241e6i		−	0.0899204i	0.998989	−	0.0449602i	$-0.0143161\pi$
$80$		0			0
$81$	1.50267e7			0.349079
$82$	−3.97749e7	−	3.97749e7i	−0.879739	−	0.879739i
$83$	3.64180e7	−	3.64180e7i	0.767369	−	0.767369i	−0.210274	−	0.977643i	$-0.567436\pi$
$83$	3.64180e7	−	3.64180e7i	0.767369	−	0.767369i	0.977643	+	0.210274i	$0.0674356\pi$
$84$			2.56633e7i			0.515459i
$85$		0			0
$86$	−1.00443e8			−1.83622
$87$	4.18980e7	+	4.18980e7i	0.731336	+	0.731336i
$88$	5.06131e7	−	5.06131e7i	0.843980	−	0.843980i
$89$		−	7.49765e7i		−	1.19499i	−0.801872	−	0.597496i	$-0.796162\pi$
$89$		−	7.49765e7i		−	1.19499i	0.801872	−	0.597496i	$-0.203838\pi$
$90$		0			0
$91$	1.81615e7			0.264842
$92$	−4.35097e6	−	4.35097e6i	−0.0607344	−	0.0607344i
$93$	−1.76272e7	+	1.76272e7i	−0.235641	+	0.235641i
$94$		−	1.32978e8i		−	1.70322i
$95$		0			0
$96$	−2.40756e8			−2.83460
$97$	−9.73416e7	−	9.73416e7i	−1.09954	−	1.09954i	−0.994464	−	0.105078i	$-0.966491\pi$
$97$	−9.73416e7	−	9.73416e7i	−1.09954	−	1.09954i	−0.105078	−	0.994464i	$-0.533509\pi$
$98$	−1.17721e8	+	1.17721e8i	−1.27629	+	1.27629i
$99$			1.54587e7i			0.160928i
$100$		0			0
$101$	1.00914e8			0.969760			0.484880	−	0.874581i	$-0.338863\pi$
$101$	1.00914e8			0.969760			0.484880	+	0.874581i	$0.338863\pi$
$102$	261879.	+	261879.i	0.00241936	+	0.00241936i
$103$	−6.37196e7	+	6.37196e7i	−0.566141	+	0.566141i	−0.931045	−	0.364904i	$-0.881102\pi$
$103$	−6.37196e7	+	6.37196e7i	−0.566141	+	0.566141i	0.364904	+	0.931045i	$0.381102\pi$
$104$			4.05103e8i			3.46284i
$105$		0			0
$106$	−2.34581e8			−1.85810
$107$	−6.67959e7	−	6.67959e7i	−0.509582	−	0.509582i	0.404816	−	0.914398i	$-0.367336\pi$
$107$	−6.67959e7	−	6.67959e7i	−0.509582	−	0.509582i	−0.914398	+	0.404816i	$0.867336\pi$
$108$	2.82042e8	−	2.82042e8i	2.07310	−	2.07310i
$109$		−	4.50931e7i		−	0.319451i	−0.987161	−	0.159725i	$-0.948939\pi$
$109$		−	4.50931e7i		−	0.319451i	0.987161	−	0.159725i	$-0.0510609\pi$
$110$		0			0
$111$	1.45141e8			0.956090
$112$	1.05019e8	+	1.05019e8i	0.667416	+	0.667416i
$113$	−5.54046e6	+	5.54046e6i	−0.0339807	+	0.0339807i	−0.723893	−	0.689912i	$-0.757649\pi$
$113$	−5.54046e6	+	5.54046e6i	−0.0339807	+	0.0339807i	0.689912	+	0.723893i	$0.257649\pi$
$114$		−	3.86314e8i		−	2.28729i
$115$		0			0
$116$	6.87797e8			3.79864
$117$	−6.18651e7	−	6.18651e7i	−0.330143	−	0.330143i
$118$	1.73199e8	−	1.73199e8i	0.893344	−	0.893344i
$119$		−	122028.i		−	0.000608514i
$120$		0			0
$121$	−1.86843e8			−0.871635
$122$	2.45339e8	+	2.45339e8i	1.10746	+	1.10746i
$123$	−7.74229e7	+	7.74229e7i	−0.338259	+	0.338259i
$124$			2.89368e8i			1.22395i
$125$		0			0
$126$	−5.56781e7			−0.220903
$127$	2.60537e7	+	2.60537e7i	0.100151	+	0.100151i	0.755407	−	0.655256i	$-0.227439\pi$
$127$	2.60537e7	+	2.60537e7i	0.100151	+	0.100151i	−0.655256	+	0.755407i	$0.727439\pi$
$128$	−6.18835e8	+	6.18835e8i	−2.30534	+	2.30534i
$129$			1.95515e8i			0.706025i
$130$		0			0
$131$	−1.23769e8			−0.420267			−0.210134	−	0.977673i	$-0.567390\pi$
$131$	−1.23769e8			−0.420267			−0.210134	+	0.977673i	$0.567390\pi$
$132$	−1.55604e8	−	1.55604e8i	−0.512536	−	0.512536i
$133$	−9.00053e7	+	9.00053e7i	−0.287648	+	0.287648i
$134$		−	6.64692e8i		−	2.06158i
$135$		0			0
$136$	2.72189e6			0.00795638
$137$	2.31618e7	+	2.31618e7i	0.0657492	+	0.0657492i	0.739217	−	0.673468i	$-0.235196\pi$
$137$	2.31618e7	+	2.31618e7i	0.0657492	+	0.0657492i	−0.673468	+	0.739217i	$0.735196\pi$
$138$	−1.15763e7	+	1.15763e7i	−0.0319192	+	0.0319192i
$139$			2.73190e8i			0.731822i	0.930650	+	0.365911i	$0.119243\pi$
$139$			2.73190e8i			0.731822i	−0.930650	+	0.365911i	$0.880757\pi$
$140$		0			0
$141$	−2.58846e8			−0.654885
$142$	7.69565e8	+	7.69565e8i	1.89274	+	1.89274i
$143$	−1.10119e8	+	1.10119e8i	−0.263340	+	0.263340i
$144$		−	7.15470e8i		−	1.66395i
$145$		0			0
$146$	−4.97451e8			−1.09481
$147$	2.29147e8	+	2.29147e8i	0.490732	+	0.490732i
$148$	1.19132e9	−	1.19132e9i	2.48302	−	2.48302i
$149$			6.63667e8i			1.34650i	0.739417	+	0.673248i	$0.235101\pi$
$149$			6.63667e8i			1.34650i	−0.739417	+	0.673248i	$0.764899\pi$
$150$		0			0
$151$	2.28193e8			0.438930			0.219465	−	0.975620i	$-0.429569\pi$
$151$	2.28193e8			0.438930			0.219465	+	0.975620i	$0.429569\pi$
$152$	−2.00762e9	−	2.00762e9i	−3.76102	−	3.76102i
$153$	−415673.	+	415673.i	−0.000758553	+	0.000758553i
$154$			9.91060e7i			0.176204i
$155$		0			0
$156$	1.24544e9			2.10292
$157$	5.58899e7	+	5.58899e7i	0.0919888	+	0.0919888i	0.751604	−	0.659615i	$-0.229281\pi$
$157$	5.58899e7	+	5.58899e7i	0.0919888	+	0.0919888i	−0.659615	+	0.751604i	$0.729281\pi$
$158$	−7.64867e7	+	7.64867e7i	−0.122732	+	0.122732i
$159$			4.56618e8i			0.714438i
$160$		0			0
$161$	5.39419e6			0.00802829
$162$	−3.28158e8	−	3.28158e8i	−0.476457	−	0.476457i
$163$	−4.24073e8	+	4.24073e8i	−0.600746	+	0.600746i	−0.940510	−	0.339765i	$-0.889653\pi$
$163$	−4.24073e8	+	4.24073e8i	−0.600746	+	0.600746i	0.339765	+	0.940510i	$0.389653\pi$
$164$			1.27097e9i			1.75696i
$165$		0			0
$166$	−1.59062e9			−2.09475
$167$	1.91637e8	+	1.91637e8i	0.246384	+	0.246384i	0.819485	−	0.573101i	$-0.194260\pi$
$167$	1.91637e8	+	1.91637e8i	0.246384	+	0.246384i	−0.573101	+	0.819485i	$0.694260\pi$
$168$	3.54841e8	−	3.54841e8i	0.445448	−	0.445448i
$169$		−	6.56495e7i		−	0.0804794i
$170$		0			0
$171$	6.13184e8			0.717144
$172$	1.60478e9	+	1.60478e9i	1.83359	+	1.83359i
$173$	9.65165e8	−	9.65165e8i	1.07750	−	1.07750i	0.0807670	−	0.996733i	$-0.474263\pi$
$173$	9.65165e8	−	9.65165e8i	1.07750	−	1.07750i	0.996733	−	0.0807670i	$-0.0257370\pi$
$174$		−	1.82997e9i		−	1.99639i
$175$		0			0
$176$	−1.27352e9			−1.32726
$177$	−3.37137e8	−	3.37137e8i	−0.343490	−	0.343490i
$178$	−1.63736e9	+	1.63736e9i	−1.63104	+	1.63104i
$179$		−	1.91548e9i		−	1.86580i	−0.360136	−	0.932900i	$-0.617270\pi$
$179$		−	1.91548e9i		−	1.86580i	0.360136	−	0.932900i	$-0.382730\pi$
$180$		0			0
$181$	−1.08735e9			−1.01311			−0.506554	−	0.862208i	$-0.669081\pi$
$181$	−1.08735e9			−1.01311			−0.506554	+	0.862208i	$0.669081\pi$
$182$	−3.96618e8	−	3.96618e8i	−0.361482	−	0.361482i
$183$	4.77558e8	−	4.77558e8i	0.425816	−	0.425816i
$184$			1.20320e8i			0.104971i
$185$		0			0
$186$	7.69897e8			0.643251
$187$	739889.	+	739889.i	0.000605063	+	0.000605063i
$188$	−2.12460e9	+	2.12460e9i	−1.70077	+	1.70077i
$189$			3.49667e8i			0.274036i
$190$		0			0
$191$	1.57132e9			1.18068			0.590340	−	0.807155i	$-0.298994\pi$
$191$	1.57132e9			1.18068			0.590340	+	0.807155i	$0.298994\pi$
$192$	2.61571e9	+	2.61571e9i	1.92480	+	1.92480i
$193$	−3.68737e8	+	3.68737e8i	−0.265759	+	0.265759i	−0.827389	−	0.561630i	$-0.810175\pi$
$193$	−3.68737e8	+	3.68737e8i	−0.265759	+	0.265759i	0.561630	+	0.827389i	$0.310175\pi$
$194$			4.25155e9i			3.00152i
$195$		0			0
$196$	3.76167e9			2.54892
$197$	−1.04341e9	−	1.04341e9i	−0.692770	−	0.692770i	0.270071	−	0.962841i	$-0.412953\pi$
$197$	−1.04341e9	−	1.04341e9i	−0.692770	−	0.692770i	−0.962841	+	0.270071i	$0.912953\pi$
$198$	3.37593e8	−	3.37593e8i	0.219650	−	0.219650i
$199$		−	2.74545e9i		−	1.75066i	−0.483529	−	0.875328i	$-0.660645\pi$
$199$		−	2.74545e9i		−	1.75066i	0.483529	−	0.875328i	$-0.339355\pi$
$200$		0			0
$201$	−1.29384e9			−0.792677
$202$	−2.20378e9	−	2.20378e9i	−1.32362	−	1.32362i
$203$	−4.26354e8	+	4.26354e8i	−0.251065	+	0.251065i
$204$		−	8.36812e6i		−	0.00483178i
$205$		0			0
$206$	2.78306e9			1.54544
$207$	−1.83747e7	−	1.83747e7i	−0.0100078	−	0.0100078i
$208$	5.09658e9	−	5.09658e9i	2.72286	−	2.72286i
$209$		−	1.09146e9i		−	0.572033i
$210$		0			0
$211$	1.08700e9			0.548401			0.274201	−	0.961672i	$-0.411587\pi$
$211$	1.08700e9			0.548401			0.274201	+	0.961672i	$0.411587\pi$
$212$	3.74791e9	+	3.74791e9i	1.85544	+	1.85544i
$213$	1.49798e9	−	1.49798e9i	0.727758	−	0.727758i
$214$			2.91742e9i			1.39105i
$215$		0			0
$216$	−7.79950e9			−3.58304
$217$	−1.79374e8	−	1.79374e8i	−0.0808949	−	0.0808949i
$218$	−9.84757e8	+	9.84757e8i	−0.436017	+	0.436017i
$219$			9.68301e8i			0.420953i
$220$		0			0
$221$	−5.92201e6			−0.00248256
$222$	−3.16964e9	−	3.16964e9i	−1.30496	−	1.30496i
$223$	−1.86676e9	+	1.86676e9i	−0.754866	+	0.754866i	−0.975383	−	0.220517i	$-0.929225\pi$
$223$	−1.86676e9	+	1.86676e9i	−0.754866	+	0.754866i	0.220517	+	0.975383i	$0.429225\pi$
$224$		−	2.44993e9i		−	0.973109i
$225$		0			0
$226$	2.41989e8			0.0927602
$227$	2.54901e9	+	2.54901e9i	0.959993	+	0.959993i	0.999230	−	0.0392369i	$-0.0124927\pi$
$227$	2.54901e9	+	2.54901e9i	0.959993	+	0.959993i	−0.0392369	+	0.999230i	$0.512493\pi$
$228$	−6.17216e9	+	6.17216e9i	−2.28401	+	2.28401i
$229$		−	2.69107e9i		−	0.978551i	−0.872129	−	0.489275i	$-0.837261\pi$
$229$		−	2.69107e9i		−	0.978551i	0.872129	−	0.489275i	$-0.162739\pi$
$230$		0			0
$231$	1.92912e8			0.0677504
$232$	−9.51005e9	−	9.51005e9i	−3.28270	−	3.28270i
$233$	1.95687e9	−	1.95687e9i	0.663953	−	0.663953i	−0.292356	−	0.956310i	$-0.594439\pi$
$233$	1.95687e9	−	1.95687e9i	0.663953	−	0.663953i	0.956310	+	0.292356i	$0.0944392\pi$
$234$			2.70206e9i			0.901222i
$235$		0			0
$236$	−5.53444e9			−1.78413
$237$	1.48883e8	+	1.48883e8i	0.0471903	+	0.0471903i
$238$	−2.66488e6	+	2.66488e6i	−0.000830558	+	0.000830558i
$239$			2.76542e9i			0.847559i	0.905765	+	0.423780i	$0.139297\pi$
$239$			2.76542e9i			0.847559i	−0.905765	+	0.423780i	$0.860703\pi$
$240$		0			0
$241$	−5.92970e9			−1.75778			−0.878890	−	0.477024i	$-0.841715\pi$
$241$	−5.92970e9			−1.75778			−0.878890	+	0.477024i	$0.841715\pi$
$242$	4.08033e9	+	4.08033e9i	1.18969	+	1.18969i
$243$	2.01302e9	−	2.01302e9i	0.577328	−	0.577328i
$244$		−	7.83959e9i		−	2.21174i
$245$		0			0
$246$	3.38157e9			0.923375
$247$	4.36796e9	+	4.36796e9i	1.17352	+	1.17352i
$248$	4.00104e9	−	4.00104e9i	1.05771	−	1.05771i
$249$			3.09618e9i			0.805431i
$250$		0			0
$251$	3.73671e9			0.941444			0.470722	−	0.882281i	$-0.343993\pi$
$251$	3.73671e9			0.941444			0.470722	+	0.882281i	$0.343993\pi$
$252$	8.89573e8	+	8.89573e8i	0.220587	+	0.220587i
$253$	−3.27065e7	+	3.27065e7i	−0.00798275	+	0.00798275i
$254$		−	1.13794e9i		−	0.273391i
$255$		0			0
$256$	1.12761e10			2.62542
$257$	−4.18492e9	−	4.18492e9i	−0.959300	−	0.959300i	0.0399037	−	0.999204i	$-0.487295\pi$
$257$	−4.18492e9	−	4.18492e9i	−0.959300	−	0.959300i	−0.999204	+	0.0399037i	$0.987295\pi$
$258$	4.26971e9	−	4.26971e9i	0.963650	−	0.963650i
$259$			1.47696e9i			0.328223i
$260$		0			0
$261$	2.90465e9			0.625938
$262$	2.70290e9	+	2.70290e9i	0.573621	+	0.573621i
$263$	−6.65705e8	+	6.65705e8i	−0.139142	+	0.139142i	−0.773247	−	0.634105i	$-0.781369\pi$
$263$	−6.65705e8	+	6.65705e8i	−0.139142	+	0.139142i	0.634105	+	0.773247i	$0.281369\pi$
$264$			4.30301e9i			0.885843i
$265$		0			0
$266$	3.93113e9			0.785219
$267$	3.18717e9	+	3.18717e9i	0.627133	+	0.627133i
$268$	−1.06198e10	+	1.06198e10i	−2.05863	+	2.05863i
$269$			9.65214e9i			1.84338i	0.387929	+	0.921689i	$0.373190\pi$
$269$			9.65214e9i			1.84338i	−0.387929	+	0.921689i	$0.626810\pi$
$270$		0			0
$271$	−3.33287e9			−0.617933			−0.308967	−	0.951073i	$-0.599983\pi$
$271$	−3.33287e9			−0.617933			−0.308967	+	0.951073i	$0.599983\pi$
$272$	−3.42440e7	−	3.42440e7i	−0.00625617	−	0.00625617i
$273$	−7.72027e8	+	7.72027e8i	−0.138989	+	0.138989i
$274$		−	1.01163e9i		−	0.179482i
$275$		0			0
$276$	3.69910e8			0.0637469
$277$	−5.28885e9	−	5.28885e9i	−0.898343	−	0.898343i	0.0969462	−	0.995290i	$-0.469093\pi$
$277$	−5.28885e9	−	5.28885e9i	−0.898343	−	0.898343i	−0.995290	+	0.0969462i	$0.969093\pi$
$278$	5.96601e9	−	5.96601e9i	0.998860	−	0.998860i
$279$			1.22203e9i			0.201682i
$280$		0			0
$281$	−6.62755e9			−1.06299			−0.531493	−	0.847063i	$-0.678369\pi$
$281$	−6.62755e9			−1.06299			−0.531493	+	0.847063i	$0.678369\pi$
$282$	5.65276e9	+	5.65276e9i	0.893849	+	0.893849i
$283$	−7.08176e9	+	7.08176e9i	−1.10407	+	1.10407i	−0.110153	+	0.993915i	$0.535134\pi$
$283$	−7.08176e9	+	7.08176e9i	−1.10407	+	1.10407i	−0.993915	+	0.110153i	$0.964866\pi$
$284$		−	2.45908e10i		−	3.78006i
$285$		0			0
$286$	4.80961e9			0.718863
$287$	−7.87855e8	−	7.87855e8i	−0.116123	−	0.116123i
$288$	−8.34539e9	+	8.34539e9i	−1.21304	+	1.21304i
$289$		−	6.97572e9i		−	0.999994i
$290$		0			0
$291$	8.27576e9			1.15408
$292$	7.94780e9	+	7.94780e9i	1.09324	+	1.09324i
$293$	3.70850e9	−	3.70850e9i	0.503186	−	0.503186i	−0.409241	−	0.912426i	$-0.634206\pi$
$293$	3.70850e9	−	3.70850e9i	0.503186	−	0.503186i	0.912426	+	0.409241i	$0.134206\pi$
$294$		−	1.00084e10i		−	1.33960i
$295$		0			0
$296$	−3.29443e10			−4.29154
$297$	−2.12013e9	−	2.12013e9i	−0.272481	−	0.272481i
$298$	1.44934e10	−	1.44934e10i	1.83782	−	1.83782i
$299$		−	2.61780e8i		−	0.0327531i
$300$		0			0
$301$	−1.98956e9			−0.242376
$302$	−4.98335e9	−	4.98335e9i	−0.599093	−	0.599093i
$303$	−4.28972e9	+	4.28972e9i	−0.508931	+	0.508931i
$304$			5.05154e10i			5.91466i
$305$		0			0
$306$	1.81552e7			0.00207069
$307$	2.68585e9	+	2.68585e9i	0.302363	+	0.302363i	0.841938	−	0.539575i	$-0.181415\pi$
$307$	2.68585e9	+	2.68585e9i	0.302363	+	0.302363i	−0.539575	+	0.841938i	$0.681415\pi$
$308$	1.58342e9	−	1.58342e9i	0.175952	−	0.175952i
$309$		−	5.41730e9i		−	0.594222i
$310$		0			0
$311$	1.07275e10			1.14672			0.573360	−	0.819304i	$-0.305640\pi$
$311$	1.07275e10			1.14672			0.573360	+	0.819304i	$0.305640\pi$
$312$	−1.72205e10	−	1.72205e10i	−1.81730	−	1.81730i
$313$	−7.29386e9	+	7.29386e9i	−0.759941	+	0.759941i	−0.976311	−	0.216370i	$-0.930578\pi$
$313$	−7.29386e9	+	7.29386e9i	−0.759941	+	0.759941i	0.216370	+	0.976311i	$0.430578\pi$
$314$		−	2.44108e9i		−	0.251110i
$315$		0			0
$316$	2.44406e9			0.245112
$317$	−1.19965e10	−	1.19965e10i	−1.18800	−	1.18800i	−0.977619	−	0.210383i	$-0.932529\pi$
$317$	−1.19965e10	−	1.19965e10i	−1.18800	−	1.18800i	−0.210383	−	0.977619i	$-0.567471\pi$
$318$	9.97176e9	−	9.97176e9i	0.975132	−	0.975132i
$319$		−	5.17022e9i		−	0.499282i
$320$		0			0
$321$	5.67883e9			0.534858
$322$	−1.17800e8	−	1.17800e8i	−0.0109578	−	0.0109578i
$323$	2.93484e7	−	2.93484e7i	0.00269634	−	0.00269634i
$324$			1.04860e10i			0.951547i
$325$		0			0
$326$	1.85221e10			1.63991
$327$	1.91686e9	+	1.91686e9i	0.167648	+	0.167648i
$328$	1.75735e10	−	1.75735e10i	1.51832	−	1.51832i
$329$		−	2.63401e9i		−	0.224820i
$330$		0			0
$331$	−9.74223e9			−0.811608			−0.405804	−	0.913960i	$-0.633008\pi$
$331$	−9.74223e9			−0.811608			−0.405804	+	0.913960i	$0.633008\pi$
$332$	2.54134e10	+	2.54134e10i	2.09175	+	2.09175i
$333$	5.03107e9	−	5.03107e9i	0.409151	−	0.409151i
$334$		−	8.37004e9i		−	0.672576i
$335$		0			0
$336$	−8.92849e9			−0.700520
$337$	−9.49420e7	−	9.49420e7i	−0.00736103	−	0.00736103i	0.703417	−	0.710778i	$-0.251657\pi$
$337$	−9.49420e7	−	9.49420e7i	−0.00736103	−	0.00736103i	−0.710778	+	0.703417i	$0.751657\pi$
$338$	−1.43367e9	+	1.43367e9i	−0.109846	+	0.109846i
$339$		−	4.71038e8i		−	0.0356662i
$340$		0			0
$341$	2.17520e9			0.160872
$342$	−1.33909e10	−	1.33909e10i	−0.978827	−	0.978827i
$343$	−4.82548e9	+	4.82548e9i	−0.348629	+	0.348629i
$344$		−	4.43781e10i		−	3.16909i
$345$		0			0
$346$	−4.21552e10			−2.94135
$347$	−4.89226e9	−	4.89226e9i	−0.337436	−	0.337436i	0.517965	−	0.855402i	$-0.326690\pi$
$347$	−4.89226e9	−	4.89226e9i	−0.337436	−	0.337436i	−0.855402	+	0.517965i	$0.826690\pi$
$348$	−2.92375e10	+	2.92375e10i	−1.99353	+	1.99353i
$349$			9.91896e9i			0.668597i	0.942467	+	0.334298i	$0.108499\pi$
$349$			9.91896e9i			0.668597i	−0.942467	+	0.334298i	$0.891501\pi$
$350$		0			0
$351$	1.69693e10			1.11799
$352$	1.48546e10	+	1.48546e10i	0.967590	+	0.967590i
$353$	1.85413e9	−	1.85413e9i	0.119410	−	0.119410i	−0.644877	−	0.764287i	$-0.723091\pi$
$353$	1.85413e9	−	1.85413e9i	0.119410	−	0.119410i	0.764287	+	0.644877i	$0.223091\pi$
$354$			1.47250e10i			0.937655i
$355$		0			0
$356$	5.23204e10			3.25740
$357$	5.18726e6	+	5.18726e6i	0.000319349	+	0.000319349i
$358$	−4.18308e10	+	4.18308e10i	−2.54662	+	2.54662i
$359$			1.09770e10i			0.660855i	0.943831	+	0.330427i	$0.107193\pi$
$359$			1.09770e10i			0.660855i	−0.943831	+	0.330427i	$0.892807\pi$
$360$		0			0
$361$	−2.63100e10			−1.54915
$362$	2.37459e10	+	2.37459e10i	1.38279	+	1.38279i
$363$	7.94247e9	−	7.94247e9i	0.457435	−	0.457435i
$364$			1.26736e10i			0.721927i
$365$		0			0
$366$	−2.08581e10			−1.16239
$367$	8.99634e9	+	8.99634e9i	0.495909	+	0.495909i	0.910162	−	0.414253i	$-0.135957\pi$
$367$	8.99634e9	+	8.99634e9i	0.495909	+	0.495909i	−0.414253	+	0.910162i	$0.635957\pi$
$368$	1.51374e9	−	1.51374e9i	0.0825394	−	0.0825394i
$369$			5.36747e9i			0.289510i
$370$		0			0
$371$	−4.64654e9			−0.245264
$372$	−1.23007e10	−	1.23007e10i	−0.642329	−	0.642329i
$373$	1.39677e10	−	1.39677e10i	0.721590	−	0.721590i	−0.247339	−	0.968929i	$-0.579556\pi$
$373$	1.39677e10	−	1.39677e10i	0.721590	−	0.721590i	0.968929	+	0.247339i	$0.0795562\pi$
$374$		−	3.23159e7i		−	0.00165169i
$375$		0			0
$376$	5.87531e10			2.93954
$377$	2.06910e10	+	2.06910e10i	1.02427	+	1.02427i
$378$	7.63614e9	−	7.63614e9i	0.374030	−	0.374030i
$379$		−	1.98707e10i		−	0.963064i	−0.876428	−	0.481532i	$-0.840080\pi$
$379$		−	1.98707e10i		−	0.963064i	0.876428	−	0.481532i	$-0.159920\pi$
$380$		0			0
$381$	−2.21503e9			−0.105118
$382$	−3.43151e10	−	3.43151e10i	−1.61150	−	1.61150i
$383$	1.45076e10	−	1.45076e10i	0.674217	−	0.674217i	−0.284469	−	0.958685i	$-0.591817\pi$
$383$	1.45076e10	−	1.45076e10i	0.674217	−	0.674217i	0.958685	+	0.284469i	$0.0918172\pi$
$384$		−	5.26119e10i		−	2.41969i
$385$		0			0
$386$	1.61052e10			0.725466
$387$	6.77718e9	+	6.77718e9i	0.302138	+	0.302138i
$388$	6.79273e10	−	6.79273e10i	2.99721	−	2.99721i
$389$			1.21772e10i			0.531799i	0.964001	+	0.265900i	$0.0856690\pi$
$389$			1.21772e10i			0.531799i	−0.964001	+	0.265900i	$0.914331\pi$
$390$		0			0
$391$	−1.75891e6			−7.52550e−5
$392$	−5.20120e10	−	5.20120e10i	−2.20272	−	2.20272i
$393$	5.26127e9	−	5.26127e9i	0.220557	−	0.220557i
$394$			4.55725e10i			1.89112i
$395$		0			0
$396$	−1.07875e10			−0.438671
$397$	2.54729e10	+	2.54729e10i	1.02545	+	1.02545i	0.999667	+	0.0257872i	$0.00820923\pi$
$397$	2.54729e10	+	2.54729e10i	1.02545	+	1.02545i	0.0257872	+	0.999667i	$0.491791\pi$
$398$	−5.99560e10	+	5.99560e10i	−2.38946	+	2.38946i
$399$		−	7.65205e9i		−	0.301916i
$400$		0			0
$401$	−2.52987e10			−0.978408			−0.489204	−	0.872169i	$-0.662713\pi$
$401$	−2.52987e10			−0.978408			−0.489204	+	0.872169i	$0.662713\pi$
$402$	2.82553e10	+	2.82553e10i	1.08192	+	1.08192i
$403$	−8.70503e9	+	8.70503e9i	−0.330028	+	0.330028i
$404$			7.04199e10i			2.64344i
$405$		0			0
$406$	1.86217e10			0.685355
$407$	−8.95521e9	−	8.95521e9i	−0.326361	−	0.326361i
$408$	−1.15705e8	+	1.15705e8i	−0.00417551	+	0.00417551i
$409$		−	3.46812e8i		−	0.0123937i	−0.999981	−	0.00619685i	$-0.998027\pi$
$409$		−	3.46812e8i		−	0.0123937i	0.999981	−	0.00619685i	$-0.00197253\pi$
$410$		0			0
$411$	−1.96917e9			−0.0690105
$412$	−4.44651e10	−	4.44651e10i	−1.54323	−	1.54323i
$413$	3.43071e9	−	3.43071e9i	0.117919	−	0.117919i
$414$			8.02544e8i			0.0273192i
$415$		0			0
$416$	−1.18895e11			−3.97000
$417$	−1.16130e10	−	1.16130e10i	−0.384061	−	0.384061i
$418$	−2.38356e10	+	2.38356e10i	−0.780765	+	0.780765i
$419$		−	1.32263e10i		−	0.429123i	−0.976711	−	0.214561i	$-0.931168\pi$
$419$		−	1.32263e10i		−	0.429123i	0.976711	−	0.214561i	$-0.0688322\pi$
$420$		0			0
$421$	3.73978e10			1.19047			0.595234	−	0.803552i	$-0.297059\pi$
$421$	3.73978e10			1.19047			0.595234	+	0.803552i	$0.297059\pi$
$422$	−2.37382e10	−	2.37382e10i	−0.748510	−	0.748510i
$423$	−8.97245e9	+	8.97245e9i	−0.280253	+	0.280253i
$424$		−	1.03643e11i		−	3.20685i
$425$		0			0
$426$	−6.54267e10			−1.98663
$427$	4.85963e9	+	4.85963e9i	0.146181	+	0.146181i
$428$	4.66118e10	−	4.66118e10i	1.38906	−	1.38906i
$429$		−	9.36204e9i		−	0.276402i
$430$		0			0
$431$	−3.28745e10			−0.952686			−0.476343	−	0.879259i	$-0.658038\pi$
$431$	−3.28745e10			−0.952686			−0.476343	+	0.879259i	$0.658038\pi$
$432$	9.81252e10	+	9.81252e10i	2.81738	+	2.81738i
$433$	−2.97863e10	+	2.97863e10i	−0.847355	+	0.847355i	−0.989802	−	0.142447i	$-0.954503\pi$
$433$	−2.97863e10	+	2.97863e10i	−0.847355	+	0.847355i	0.142447	+	0.989802i	$0.454503\pi$
$434$			7.83446e9i			0.220826i
$435$		0			0
$436$	3.14670e10			0.870783
$437$	1.29733e9	+	1.29733e9i	0.0355735	+	0.0355735i
$438$	2.11461e10	−	2.11461e10i	0.574557	−	0.574557i
$439$		−	1.08993e10i		−	0.293455i	−0.989177	−	0.146727i	$-0.953126\pi$
$439$		−	1.08993e10i		−	0.293455i	0.989177	−	0.146727i	$-0.0468740\pi$
$440$		0			0
$441$	1.58860e10			0.420010
$442$	1.29327e8	+	1.29327e8i	0.00338843	+	0.00338843i
$443$	3.25417e10	−	3.25417e10i	0.844940	−	0.844940i	−0.144557	−	0.989497i	$-0.546176\pi$
$443$	3.25417e10	−	3.25417e10i	0.844940	−	0.844940i	0.989497	+	0.144557i	$0.0461756\pi$
$444$			1.01283e11i			2.60618i
$445$		0			0
$446$	8.15339e10			2.06062
$447$	−2.82117e10	−	2.82117e10i	−0.706642	−	0.706642i
$448$	−2.66174e10	+	2.66174e10i	−0.660776	+	0.660776i
$449$		−	2.83197e10i		−	0.696792i	−0.937348	−	0.348396i	$-0.886727\pi$
$449$		−	2.83197e10i		−	0.696792i	0.937348	−	0.348396i	$-0.113273\pi$
$450$		0			0
$451$	9.55398e9			0.230929
$452$	−3.86627e9	−	3.86627e9i	−0.0926272	−	0.0926272i
$453$	−9.70023e9	+	9.70023e9i	−0.230351	+	0.230351i
$454$		−	1.11332e11i		−	2.62058i
$455$		0			0
$456$	1.70683e11			3.94758
$457$	−1.49030e10	−	1.49030e10i	−0.341671	−	0.341671i	0.515324	−	0.856995i	$-0.327671\pi$
$457$	−1.49030e10	−	1.49030e10i	−0.341671	−	0.341671i	−0.856995	+	0.515324i	$0.827671\pi$
$458$	−5.87685e10	+	5.87685e10i	−1.33562	+	1.33562i
$459$		−	1.14017e8i		−	0.00256874i
$460$		0			0
$461$	2.87971e10			0.637595			0.318797	−	0.947823i	$-0.396721\pi$
$461$	2.87971e10			0.637595			0.318797	+	0.947823i	$0.396721\pi$
$462$	−4.21288e9	−	4.21288e9i	−0.0924722	−	0.0924722i
$463$	1.62839e8	−	1.62839e8i	0.00354353	−	0.00354353i	−0.705333	−	0.708876i	$-0.749202\pi$
$463$	1.62839e8	−	1.62839e8i	0.00354353	−	0.00354353i	0.708876	+	0.705333i	$0.249202\pi$
$464$			2.39291e11i			5.16244i
$465$		0			0
$466$	−8.54694e10			−1.81245
$467$	−4.44920e10	−	4.44920e10i	−0.935437	−	0.935437i	0.0626014	−	0.998039i	$-0.480060\pi$
$467$	−4.44920e10	−	4.44920e10i	−0.935437	−	0.935437i	−0.998039	+	0.0626014i	$0.980060\pi$
$468$	4.31710e10	−	4.31710e10i	0.899929	−	0.899929i
$469$		−	1.31661e10i		−	0.272123i
$470$		0			0
$471$	−4.75163e9			−0.0965516
$472$	7.65237e10	+	7.65237e10i	1.54180	+	1.54180i
$473$	1.20632e10	−	1.20632e10i	0.241001	−	0.241001i
$474$		−	6.50272e9i		−	0.128820i
$475$		0			0
$476$	8.51539e7			0.00165873
$477$	1.58279e10	+	1.58279e10i	0.305738	+	0.305738i
$478$	6.03922e10	−	6.03922e10i	1.15683	−	1.15683i
$479$			2.06240e10i			0.391770i	0.980627	+	0.195885i	$0.0627580\pi$
$479$			2.06240e10i			0.391770i	−0.980627	+	0.195885i	$0.937242\pi$
$480$		0			0
$481$	7.16767e10			1.33905
$482$	1.29495e11	+	1.29495e11i	2.39918	+	2.39918i
$483$	−2.29301e8	+	2.29301e8i	−0.00421325	+	0.00421325i
$484$		−	1.30383e11i		−	2.37597i
$485$		0			0
$486$	−8.79218e10			−1.57598
$487$	−2.94562e10	−	2.94562e10i	−0.523674	−	0.523674i	0.395005	−	0.918679i	$-0.370743\pi$
$487$	−2.94562e10	−	2.94562e10i	−0.523674	−	0.523674i	−0.918679	+	0.395005i	$0.870743\pi$
$488$	−1.08397e11	+	1.08397e11i	−1.91133	+	1.91133i
$489$		−	3.60538e10i		−	0.630543i
$490$		0			0
$491$	−3.77103e10			−0.648834			−0.324417	−	0.945914i	$-0.605168\pi$
$491$	−3.77103e10			−0.648834			−0.324417	+	0.945914i	$0.605168\pi$
$492$	−5.40276e10	−	5.40276e10i	−0.922051	−	0.922051i
$493$	1.39023e8	−	1.39023e8i	0.00235342	−	0.00235342i
$494$		−	1.90778e11i		−	3.20346i
$495$		0			0
$496$	−1.00674e11			−1.66337
$497$	1.52434e10	+	1.52434e10i	0.249837	+	0.249837i
$498$	6.76153e10	−	6.76153e10i	1.09933	−	1.09933i
$499$			7.35362e10i			1.18604i	0.805188	+	0.593020i	$0.202064\pi$
$499$			7.35362e10i			1.18604i	−0.805188	+	0.593020i	$0.797936\pi$
$500$		0			0
$501$	−1.62925e10			−0.258605
$502$	−8.16035e10	−	8.16035e10i	−1.28497	−	1.28497i
$503$	−5.38272e10	+	5.38272e10i	−0.840872	+	0.840872i	−0.988972	−	0.148100i	$-0.952684\pi$
$503$	−5.38272e10	+	5.38272e10i	−0.840872	+	0.840872i	0.148100	+	0.988972i	$0.452684\pi$
$504$		−	2.45999e10i		−	0.381252i
$505$		0			0
$506$	1.42851e9			0.0217912
$507$	2.79069e9	+	2.79069e9i	0.0422356	+	0.0422356i
$508$	−1.81809e10	+	1.81809e10i	−0.272999	+	0.272999i
$509$			5.40508e10i			0.805251i	0.915365	+	0.402625i	$0.131902\pi$
$509$			5.40508e10i			0.805251i	−0.915365	+	0.402625i	$0.868098\pi$
$510$		0			0
$511$	−9.85342e9			−0.144512
$512$	−8.78292e10	−	8.78292e10i	−1.27808	−	1.27808i
$513$	−8.40969e10	+	8.40969e10i	−1.21426	+	1.21426i
$514$			1.82783e11i			2.61869i
$515$		0			0
$516$	−1.36435e11			−1.92454
$517$	1.59708e10	+	1.59708e10i	0.223545	+	0.223545i
$518$	3.22542e10	−	3.22542e10i	0.447989	−	0.447989i
$519$			8.20562e10i			1.13095i
$520$		0			0
$521$	1.41995e10			0.192718			0.0963591	−	0.995347i	$-0.469280\pi$
$521$	1.41995e10			0.192718			0.0963591	+	0.995347i	$0.469280\pi$
$522$	−6.34326e10	−	6.34326e10i	−0.854340	−	0.854340i
$523$	5.07076e10	−	5.07076e10i	0.677744	−	0.677744i	−0.281745	−	0.959489i	$-0.590913\pi$
$523$	5.07076e10	−	5.07076e10i	0.677744	−	0.677744i	0.959489	+	0.281745i	$0.0909132\pi$
$524$		−	8.63688e10i		−	1.14560i
$525$		0			0
$526$	2.90758e10			0.379829
$527$	5.84892e7	+	5.84892e7i	0.000758287	+	0.000758287i
$528$	5.41360e10	−	5.41360e10i	0.696547	−	0.696547i
$529$			7.82332e10i			0.999007i
$530$		0			0
$531$	−2.33726e10			−0.293987
$532$	−6.28079e10	−	6.28079e10i	−0.784093	−	0.784093i
$533$	−3.82346e10	+	3.82346e10i	−0.473749	+	0.473749i
$534$		−	1.39205e11i		−	1.71194i
$535$		0			0
$536$	2.93677e11			3.55804
$537$	8.14248e10	+	8.14248e10i	0.979173	+	0.979173i
$538$	2.10786e11	−	2.10786e11i	2.51602	−	2.51602i
$539$		−	2.82767e10i		−	0.335022i
$540$		0			0
$541$	7.09202e10			0.827906			0.413953	−	0.910298i	$-0.364148\pi$
$541$	7.09202e10			0.827906			0.413953	+	0.910298i	$0.364148\pi$
$542$	7.27843e10	+	7.27843e10i	0.843414	+	0.843414i
$543$	4.62221e10	−	4.62221e10i	0.531680	−	0.531680i
$544$			7.98858e8i			0.00912166i
$545$		0			0
$546$	3.37195e10			0.379412
$547$	4.86568e10	+	4.86568e10i	0.543494	+	0.543494i	0.924551	−	0.381058i	$-0.124440\pi$
$547$	4.86568e10	+	4.86568e10i	0.543494	+	0.543494i	−0.381058	+	0.924551i	$0.624440\pi$
$548$	−1.61629e10	+	1.61629e10i	−0.179224	+	0.179224i
$549$		−	3.31075e10i		−	0.364449i
$550$		0			0
$551$	−2.05081e11			−2.22495
$552$	−5.11468e9	−	5.11468e9i	−0.0550886	−	0.0550886i
$553$	−1.51504e9	+	1.51504e9i	−0.0162003	+	0.0162003i
$554$			2.30999e11i			2.45229i
$555$		0			0
$556$	−1.90639e11			−1.99486
$557$	−8.14997e10	−	8.14997e10i	−0.846711	−	0.846711i	0.143011	−	0.989721i	$-0.454322\pi$
$557$	−8.14997e10	−	8.14997e10i	−0.846711	−	0.846711i	−0.989721	+	0.143011i	$0.954322\pi$
$558$	2.66871e10	−	2.66871e10i	0.275274	−	0.275274i
$559$			9.65531e10i			0.988824i
$560$		0			0
$561$	−6.29037e7			−0.000635074
$562$	1.44734e11	+	1.44734e11i	1.45086	+	1.45086i
$563$	4.38653e10	−	4.38653e10i	0.436604	−	0.436604i	−0.454264	−	0.890867i	$-0.650098\pi$
$563$	4.38653e10	−	4.38653e10i	0.436604	−	0.436604i	0.890867	+	0.454264i	$0.150098\pi$
$564$		−	1.80629e11i		−	1.78513i
$565$		0			0
$566$	3.09308e11			3.01387
$567$	−6.50011e9	−	6.50011e9i	−0.0628910	−	0.0628910i
$568$	−3.40012e11	+	3.40012e11i	−3.26664	+	3.26664i
$569$		−	7.78333e10i		−	0.742534i	−0.928526	−	0.371267i	$-0.878923\pi$
$569$		−	7.78333e10i		−	0.742534i	0.928526	−	0.371267i	$-0.121077\pi$
$570$		0			0
$571$	−3.84405e10			−0.361613			−0.180807	−	0.983519i	$-0.557871\pi$
$571$	−3.84405e10			−0.361613			−0.180807	+	0.983519i	$0.557871\pi$
$572$	−7.68435e10	−	7.68435e10i	−0.717832	−	0.717832i
$573$	−6.67952e10	+	6.67952e10i	−0.619622	+	0.619622i
$574$			3.44109e10i			0.316992i
$575$		0			0
$576$	1.81338e11			1.64740
$577$	5.68122e10	+	5.68122e10i	0.512553	+	0.512553i	0.915308	−	0.402755i	$-0.131947\pi$
$577$	5.68122e10	+	5.68122e10i	0.512553	+	0.512553i	−0.402755	+	0.915308i	$0.631947\pi$
$578$	−1.52338e11	+	1.52338e11i	−1.36489	+	1.36489i
$579$		−	3.13492e10i		−	0.278941i
$580$		0			0
$581$	−3.15067e10			−0.276502
$582$	−1.80729e11	−	1.80729e11i	−1.57520	−	1.57520i
$583$	2.81733e10	−	2.81733e10i	0.243873	−	0.243873i
$584$		−	2.19786e11i		−	1.88950i
$585$		0			0
$586$	−1.61975e11			−1.37359
$587$	−3.96837e10	−	3.96837e10i	−0.334241	−	0.334241i	0.519954	−	0.854194i	$-0.325949\pi$
$587$	−3.96837e10	−	3.96837e10i	−0.334241	−	0.334241i	−0.854194	+	0.519954i	$0.825949\pi$
$588$	−1.59904e11	+	1.59904e11i	−1.33768	+	1.33768i
$589$		−	8.62811e10i		−	0.716893i
$590$		0			0
$591$	8.87081e10			0.727132
$592$	4.14470e11	+	4.14470e11i	3.37448	+	3.37448i
$593$	1.24386e11	−	1.24386e11i	1.00590	−	1.00590i	0.00591623	−	0.999982i	$-0.498117\pi$
$593$	1.24386e11	−	1.24386e11i	1.00590	−	1.00590i	0.999982	−	0.00591623i	$-0.00188321\pi$
$594$			9.26002e10i			0.743817i
$595$		0			0
$596$	−4.63123e11			−3.67038
$597$	1.16706e11	+	1.16706e11i	0.918746	+	0.918746i
$598$	−5.71684e9	+	5.71684e9i	−0.0447045	+	0.0447045i
$599$			1.13718e10i			0.0883330i	0.999024	+	0.0441665i	$0.0140632\pi$
$599$			1.13718e10i			0.0883330i	−0.999024	+	0.0441665i	$0.985937\pi$
$600$		0			0
$601$	2.29222e11			1.75695			0.878475	−	0.477789i	$-0.158562\pi$
$601$	2.29222e11			1.75695			0.878475	+	0.477789i	$0.158562\pi$
$602$	4.34485e10	+	4.34485e10i	0.330818	+	0.330818i
$603$	−4.48488e10	+	4.48488e10i	−0.339220	+	0.339220i
$604$			1.59239e11i			1.19647i
$605$		0			0
$606$	1.87361e11			1.38927
$607$	−1.86261e11	−	1.86261e11i	−1.37204	−	1.37204i	−0.857409	−	0.514636i	$-0.827927\pi$
$607$	−1.86261e11	−	1.86261e11i	−1.37204	−	1.37204i	−0.514636	−	0.857409i	$-0.672073\pi$
$608$	5.89222e11	−	5.89222e11i	4.31186	−	4.31186i
$609$		−	3.62477e10i		−	0.263518i
$610$		0			0
$611$	−1.27829e11			−0.917199
$612$	−2.90066e8	−	2.90066e8i	−0.00206772	−	0.00206772i
$613$	4.36311e10	−	4.36311e10i	0.308997	−	0.308997i	−0.535523	−	0.844520i	$-0.679886\pi$
$613$	4.36311e10	−	4.36311e10i	0.308997	−	0.308997i	0.844520	+	0.535523i	$0.179886\pi$
$614$		−	1.17309e11i		−	0.825388i
$615$		0			0
$616$	−4.37874e10			−0.304107
$617$	−1.22556e11	−	1.22556e11i	−0.845654	−	0.845654i	0.143933	−	0.989587i	$-0.454025\pi$
$617$	−1.22556e11	−	1.22556e11i	−0.845654	−	0.845654i	−0.989587	+	0.143933i	$0.954025\pi$
$618$	−1.18305e11	+	1.18305e11i	−0.811051	+	0.811051i
$619$		−	1.90511e11i		−	1.29765i	−0.760937	−	0.648826i	$-0.775260\pi$
$619$		−	1.90511e11i		−	1.29765i	0.760937	−	0.648826i	$-0.224740\pi$
$620$		0			0
$621$	5.04009e9			0.0338900
$622$	−2.34271e11	−	2.34271e11i	−1.56515	−	1.56515i
$623$	−3.24326e10	+	3.24326e10i	−0.215293	+	0.215293i
$624$			4.33300e11i			2.85792i
$625$		0			0
$626$	3.18571e11			2.07448
$627$	4.63966e10	+	4.63966e10i	0.300203	+	0.300203i
$628$	−3.90013e10	+	3.90013e10i	−0.250750	+	0.250750i
$629$		−	4.81597e8i		−	0.00307667i
$630$		0			0
$631$	2.40733e11			1.51851			0.759257	−	0.650791i	$-0.225563\pi$
$631$	2.40733e11			1.51851			0.759257	+	0.650791i	$0.225563\pi$
$632$	−3.37937e10	−	3.37937e10i	−0.211820	−	0.211820i
$633$	−4.62070e10	+	4.62070e10i	−0.287801	+	0.287801i
$634$			5.23966e11i			3.24300i
$635$		0			0
$636$	−3.18639e11			−1.94747
$637$	1.13162e11	+	1.13162e11i	0.687295	+	0.687295i
$638$	−1.12909e11	+	1.12909e11i	−0.681468	+	0.681468i
$639$		−	1.03850e11i		−	0.622876i
$640$		0			0
$641$	−6.64967e10			−0.393884			−0.196942	−	0.980415i	$-0.563101\pi$
$641$	−6.64967e10			−0.393884			−0.196942	+	0.980415i	$0.563101\pi$
$642$	−1.24016e11	−	1.24016e11i	−0.730026	−	0.730026i
$643$	1.86695e11	−	1.86695e11i	1.09217	−	1.09217i	0.0968698	−	0.995297i	$-0.469117\pi$
$643$	1.86695e11	−	1.86695e11i	1.09217	−	1.09217i	0.995297	−	0.0968698i	$-0.0308831\pi$
$644$			3.76420e9i			0.0218841i
$645$		0			0
$646$	−1.28184e9			−0.00736043
$647$	−4.44785e10	−	4.44785e10i	−0.253824	−	0.253824i	0.568712	−	0.822537i	$-0.307442\pi$
$647$	−4.44785e10	−	4.44785e10i	−0.253824	−	0.253824i	−0.822537	+	0.568712i	$0.807442\pi$
$648$	1.44988e11	−	1.44988e11i	0.822305	−	0.822305i
$649$			4.16027e10i			0.234500i
$650$		0			0
$651$	1.52500e10			0.0849074
$652$	−2.95929e11	−	2.95929e11i	−1.63756	−	1.63756i
$653$	−9.23897e10	+	9.23897e10i	−0.508125	+	0.508125i	−0.913951	−	0.405825i	$-0.866984\pi$
$653$	−9.23897e10	+	9.23897e10i	−0.508125	+	0.508125i	0.405825	+	0.913951i	$0.366984\pi$
$654$		−	8.37218e10i		−	0.457644i
$655$		0			0
$656$	−4.42183e11			−2.38774
$657$	3.35645e10	+	3.35645e10i	0.180143	+	0.180143i
$658$	−5.75224e10	+	5.75224e10i	−0.306855	+	0.306855i
$659$		−	2.86863e11i		−	1.52101i	−0.649330	−	0.760507i	$-0.724951\pi$
$659$		−	2.86863e11i		−	1.52101i	0.649330	−	0.760507i	$-0.275049\pi$
$660$		0			0
$661$	2.05496e10			0.107646			0.0538231	−	0.998550i	$-0.482859\pi$
$661$	2.05496e10			0.107646			0.0538231	+	0.998550i	$0.482859\pi$
$662$	2.12754e11	+	2.12754e11i	1.10776	+	1.10776i
$663$	2.51738e8	−	2.51738e8i	0.00130285	−	0.00130285i
$664$		−	7.02773e11i		−	3.61529i
$665$		0			0
$666$	−2.19740e11			−1.11690
$667$	6.14546e9	+	6.14546e9i	0.0310493	+	0.0310493i
$668$	−1.33729e11	+	1.33729e11i	−0.671612	+	0.671612i
$669$		−	1.58708e11i		−	0.792308i
$670$		0			0
$671$	−5.89307e10			−0.290704
$672$	1.04144e11	+	1.04144e11i	0.510688	+	0.510688i
$673$	2.08745e11	−	2.08745e11i	1.01755	−	1.01755i	0.0177050	−	0.999843i	$-0.494364\pi$
$673$	2.08745e11	−	2.08745e11i	1.01755	−	1.01755i	0.999843	−	0.0177050i	$-0.00563598\pi$
$674$			4.14675e9i			0.0200941i
$675$		0			0
$676$	4.58118e10			0.219377
$677$	5.40868e10	+	5.40868e10i	0.257476	+	0.257476i	0.824027	−	0.566551i	$-0.191723\pi$
$677$	5.40868e10	+	5.40868e10i	0.257476	+	0.257476i	−0.566551	+	0.824027i	$0.691723\pi$
$678$	−1.02867e10	+	1.02867e10i	−0.0486806	+	0.0486806i
$679$			8.42141e10i			0.396192i
$680$		0			0
$681$	−2.16711e11			−1.00761
$682$	−4.75026e10	−	4.75026e10i	−0.219573	−	0.219573i
$683$	−4.96219e10	+	4.96219e10i	−0.228029	+	0.228029i	−0.811869	−	0.583840i	$-0.801550\pi$
$683$	−4.96219e10	+	4.96219e10i	−0.228029	+	0.228029i	0.583840	+	0.811869i	$0.301550\pi$
$684$			4.27895e11i			1.95485i
$685$		0			0
$686$	2.10761e11			0.951684
$687$	1.14394e11	+	1.14394e11i	0.513544	+	0.513544i
$688$	−5.58318e11	+	5.58318e11i	−2.49189	+	2.49189i
$689$			2.25497e11i			1.00061i
$690$		0			0
$691$	−4.26160e10			−0.186922			−0.0934610	−	0.995623i	$-0.529793\pi$
$691$	−4.26160e10			−0.186922			−0.0934610	+	0.995623i	$0.529793\pi$
$692$	6.73516e11	+	6.73516e11i	2.93713	+	2.93713i
$693$	6.68698e9	−	6.68698e9i	0.0289933	−	0.0289933i
$694$			2.13678e11i			0.921130i
$695$		0			0
$696$	8.08523e11			3.44553
$697$	2.56899e8	+	2.56899e8i	0.00108851	+	0.00108851i
$698$	2.16613e11	−	2.16613e11i	0.912564	−	0.912564i
$699$			1.66368e11i			0.696887i
$700$		0			0
$701$	−1.99103e11			−0.824529			−0.412265	−	0.911064i	$-0.635262\pi$
$701$	−1.99103e11			−0.824529			−0.412265	+	0.911064i	$0.635262\pi$
$702$	−3.70582e11	−	3.70582e11i	−1.52593	−	1.52593i
$703$	−3.55217e11	+	3.55217e11i	−1.45436	+	1.45436i
$704$		−	3.22778e11i		−	1.31406i
$705$		0			0
$706$	−8.09821e10			−0.325964
$707$	−4.36522e10	−	4.36522e10i	−0.174714	−	0.174714i
$708$	2.35263e11	−	2.35263e11i	0.936310	−	0.936310i
$709$			1.08446e11i			0.429170i	0.976705	+	0.214585i	$0.0688400\pi$
$709$			1.08446e11i			0.429170i	−0.976705	+	0.214585i	$0.931160\pi$
$710$		0			0
$711$	1.03216e10			0.0403894
$712$	−7.23425e11	−	7.23425e11i	−2.81497	−	2.81497i
$713$	−2.58550e9	+	2.58550e9i	−0.0100043	+	0.0100043i
$714$		−	2.26562e8i		−	0.000871755i
$715$		0			0
$716$	1.33667e12			5.08594
$717$	−1.17555e11	−	1.17555e11i	−0.444800	−	0.444800i
$718$	2.39719e11	−	2.39719e11i	0.901997	−	0.901997i
$719$			3.99076e11i			1.49328i	0.665230	+	0.746639i	$0.268333\pi$
$719$			3.99076e11i			1.49328i	−0.665230	+	0.746639i	$0.731667\pi$
$720$		0			0
$721$	5.51264e10			0.203994
$722$	5.74567e11	+	5.74567e11i	2.11442	+	2.11442i
$723$	2.52065e11	−	2.52065e11i	0.922484	−	0.922484i
$724$		−	7.58781e11i		−	2.76161i
$725$		0			0
$726$	−3.46900e11			−1.24870
$727$	1.71302e11	+	1.71302e11i	0.613232	+	0.613232i	0.943787	−	0.330555i	$-0.107236\pi$
$727$	1.71302e11	+	1.71302e11i	0.613232	+	0.613232i	−0.330555	+	0.943787i	$0.607236\pi$
$728$	1.75235e11	−	1.75235e11i	0.623873	−	0.623873i
$729$			2.69732e11i			0.955043i
$730$		0			0
$731$	6.48742e8			0.00227197
$732$	3.33252e11	+	3.33252e11i	1.16072	+	1.16072i
$733$	−8.81389e10	+	8.81389e10i	−0.305318	+	0.305318i	−0.843090	−	0.537772i	$-0.819266\pi$
$733$	−8.81389e10	+	8.81389e10i	−0.305318	+	0.305318i	0.537772	+	0.843090i	$0.319266\pi$
$734$		−	3.92930e11i		−	1.35373i
$735$		0			0
$736$	−3.53132e10			−0.120345
$737$	7.98299e10	+	7.98299e10i	0.270580	+	0.270580i
$738$	1.17216e11	−	1.17216e11i	0.395151	−	0.395151i
$739$		−	2.25598e10i		−	0.0756409i	−0.999285	−	0.0378204i	$-0.987959\pi$
$739$		−	2.25598e10i		−	0.0756409i	0.999285	−	0.0378204i	$-0.0120415\pi$
$740$		0			0
$741$	−3.71354e11			−1.23173
$742$	1.01473e11	+	1.01473e11i	0.334760	+	0.334760i
$743$	1.39704e10	−	1.39704e10i	0.0458409	−	0.0458409i	−0.683815	−	0.729656i	$-0.739680\pi$
$743$	1.39704e10	−	1.39704e10i	0.0458409	−	0.0458409i	0.729656	+	0.683815i	$0.239680\pi$
$744$			3.40159e11i			1.11017i
$745$		0			0
$746$	−6.10063e11			−1.96979
$747$	1.07324e11	+	1.07324e11i	0.344678	+	0.344678i
$748$	−5.16313e8	+	5.16313e8i	−0.00164933	+	0.00164933i
$749$			5.77877e10i			0.183615i
$750$		0			0
$751$	2.26267e11			0.711314			0.355657	−	0.934616i	$-0.384257\pi$
$751$	2.26267e11			0.711314			0.355657	+	0.934616i	$0.384257\pi$
$752$	−7.39169e11	−	7.39169e11i	−2.31139	−	2.31139i
$753$	−1.58843e11	+	1.58843e11i	−0.494071	+	0.494071i
$754$		−	9.03712e11i		−	2.79605i
$755$		0			0
$756$	−2.44006e11			−0.746988
$757$	−2.14047e11	−	2.14047e11i	−0.651816	−	0.651816i	0.301614	−	0.953430i	$-0.402474\pi$
$757$	−2.14047e11	−	2.14047e11i	−0.651816	−	0.651816i	−0.953430	+	0.301614i	$0.902474\pi$
$758$	−4.33942e11	+	4.33942e11i	−1.31448	+	1.31448i
$759$		−	2.78064e9i		−	0.00837871i
$760$		0			0
$761$	3.43069e11			1.02292			0.511462	−	0.859306i	$-0.329104\pi$
$761$	3.43069e11			1.02292			0.511462	+	0.859306i	$0.329104\pi$
$762$	4.83724e10	+	4.83724e10i	0.143476	+	0.143476i
$763$	−1.95059e10	+	1.95059e10i	−0.0575530	+	0.0575530i
$764$			1.09651e12i			3.21839i
$765$		0			0
$766$	−6.33642e11			−1.84047
$767$	−1.66492e11	−	1.66492e11i	−0.481075	−	0.481075i
$768$	−4.79334e11	+	4.79334e11i	−1.37782	+	1.37782i
$769$			1.80147e11i			0.515135i	0.966260	+	0.257568i	$0.0829210\pi$
$769$			1.80147e11i			0.515135i	−0.966260	+	0.257568i	$0.917079\pi$
$770$		0			0
$771$	3.55792e11			1.00688
$772$	−2.57314e11	−	2.57314e11i	−0.724426	−	0.724426i
$773$	5.19451e10	−	5.19451e10i	0.145488	−	0.145488i	−0.630611	−	0.776099i	$-0.717196\pi$
$773$	5.19451e10	−	5.19451e10i	0.145488	−	0.145488i	0.776099	+	0.630611i	$0.217196\pi$
$774$		−	2.96004e11i		−	0.824773i
$775$		0			0
$776$	−1.87844e12			−5.18025
$777$	−6.27837e10	−	6.27837e10i	−0.172251	−	0.172251i
$778$	2.65929e11	−	2.65929e11i	0.725850	−	0.725850i
$779$		−	3.78968e11i		−	1.02909i
$780$		0			0
$781$	−1.84850e11			−0.496840
$782$	3.84115e7	+	3.84115e7i	0.000102715	+	0.000102715i
$783$	−3.98366e11	+	3.98366e11i	−1.05983	+	1.05983i
$784$			1.30872e12i			3.46404i
$785$		0			0
$786$	−2.29794e11			−0.602073
$787$	4.40214e11	+	4.40214e11i	1.14753	+	1.14753i	0.987037	+	0.160495i	$0.0513092\pi$
$787$	4.40214e11	+	4.40214e11i	1.14753	+	1.14753i	0.160495	+	0.987037i	$0.448691\pi$
$788$	7.28115e11	−	7.28115e11i	1.88840	−	1.88840i
$789$		−	5.65967e10i		−	0.146044i
$790$		0			0
$791$	4.79327e9			0.0122441
$792$	1.49157e11	+	1.49157e11i	0.379089	+	0.379089i
$793$	2.35838e11	−	2.35838e11i	0.596377	−	0.596377i
$794$		−	1.11257e12i		−	2.79928i
$795$		0			0
$796$	1.91584e12			4.77207
$797$	−2.88205e11	−	2.88205e11i	−0.714280	−	0.714280i	0.253148	−	0.967428i	$-0.418534\pi$
$797$	−2.88205e11	−	2.88205e11i	−0.714280	−	0.714280i	−0.967428	+	0.253148i	$0.918534\pi$
$798$	−1.67108e11	+	1.67108e11i	−0.412083	+	0.412083i
$799$			8.58883e8i			0.00210740i
$800$		0			0
$801$	2.20955e11			0.536753
$802$	5.52480e11	+	5.52480e11i	1.33542	+	1.33542i
$803$	5.97441e10	−	5.97441e10i	0.143692	−	0.143692i
$804$		−	9.02873e11i		−	2.16074i
$805$		0			0
$806$	3.80207e11			0.900906
$807$	−4.10301e11	−	4.10301e11i	−0.967406	−	0.967406i
$808$	9.73685e11	−	9.73685e11i	2.28440	−	2.28440i
$809$		−	1.96949e11i		−	0.459789i	−0.973216	−	0.229895i	$-0.926162\pi$
$809$		−	1.96949e11i		−	0.459789i	0.973216	−	0.229895i	$-0.0738382\pi$
$810$		0			0
$811$	2.03833e11			0.471185			0.235592	−	0.971852i	$-0.424297\pi$
$811$	2.03833e11			0.471185			0.235592	+	0.971852i	$0.424297\pi$
$812$	−2.97520e11	−	2.97520e11i	−0.684372	−	0.684372i
$813$	1.41677e11	−	1.41677e11i	0.324292	−	0.324292i
$814$			3.91133e11i			0.890897i
$815$		0			0
$816$	2.91135e9			0.00656649
$817$	−4.78500e11	−	4.78500e11i	−1.07397	−	1.07397i
$818$	−7.57379e9	+	7.57379e9i	−0.0169161	+	0.0169161i
$819$			5.35220e10i			0.118959i
$820$		0			0
$821$	−1.71589e11			−0.377673			−0.188837	−	0.982009i	$-0.560472\pi$
$821$	−1.71589e11			−0.377673			−0.188837	+	0.982009i	$0.560472\pi$
$822$	4.30033e10	+	4.30033e10i	0.0941921	+	0.0941921i
$823$	−6.29660e11	+	6.29660e11i	−1.37248	+	1.37248i	−0.515735	+	0.856748i	$0.672481\pi$
$823$	−6.29660e11	+	6.29660e11i	−1.37248	+	1.37248i	−0.856748	+	0.515735i	$0.827519\pi$
$824$			1.22962e12i			2.66725i
$825$		0			0
$826$	−1.49842e11			−0.321894
$827$	2.59931e11	+	2.59931e11i	0.555694	+	0.555694i	0.928078	−	0.372385i	$-0.121460\pi$
$827$	2.59931e11	+	2.59931e11i	0.555694	+	0.555694i	−0.372385	+	0.928078i	$0.621460\pi$
$828$	1.28223e10	−	1.28223e10i	0.0272800	−	0.0272800i
$829$		−	2.71752e11i		−	0.575381i	−0.957723	−	0.287690i	$-0.907113\pi$
$829$		−	2.71752e11i		−	0.575381i	0.957723	−	0.287690i	$-0.0928874\pi$
$830$		0			0
$831$	4.49646e11			0.942903
$832$	1.29174e12	+	1.29174e12i	2.69577	+	2.69577i
$833$	7.60338e8	−	7.60338e8i	0.00157916	−	0.00157916i
$834$			5.07216e11i			1.04840i
$835$		0			0
$836$	7.61645e11			1.55929
$837$	−1.67599e11	−	1.67599e11i	−0.341484	−	0.341484i
$838$	−2.88840e11	+	2.88840e11i	−0.585707	+	0.585707i
$839$			6.11730e11i			1.23456i	0.786743	+	0.617280i	$0.211765\pi$
$839$			6.11730e11i			1.23456i	−0.786743	+	0.617280i	$0.788235\pi$
$840$		0			0
$841$	−4.71222e11			−0.941980
$842$	−8.16705e11	−	8.16705e11i	−1.62486	−	1.62486i
$843$	2.81730e11	−	2.81730e11i	0.557856	−	0.557856i
$844$			7.58533e11i			1.49487i
$845$		0			0
$846$	3.91886e11			0.765031
$847$	8.08225e10	+	8.08225e10i	0.157036	+	0.157036i
$848$	−1.30393e12	+	1.30393e12i	−2.52158	+	2.52158i
$849$		−	6.02075e11i		−	1.15883i
$850$		0			0
$851$	2.12888e10			0.0405913
$852$	1.04533e12	+	1.04533e12i	1.98378	+	1.98378i
$853$	−2.75670e11	+	2.75670e11i	−0.520707	+	0.520707i	−0.917785	−	0.397078i	$-0.870024\pi$
$853$	−2.75670e11	+	2.75670e11i	−0.520707	+	0.520707i	0.397078	+	0.917785i	$0.370024\pi$
$854$		−	2.12252e11i		−	0.399044i
$855$		0			0
$856$	−1.28899e12			−2.40078
$857$	−5.11458e11	−	5.11458e11i	−0.948172	−	0.948172i	0.0505498	−	0.998722i	$-0.483903\pi$
$857$	−5.11458e11	−	5.11458e11i	−0.948172	−	0.948172i	−0.998722	+	0.0505498i	$0.983903\pi$
$858$	−2.04451e11	+	2.04451e11i	−0.377260	+	0.377260i
$859$		−	7.65165e11i		−	1.40534i	−0.711514	−	0.702672i	$-0.751990\pi$
$859$		−	7.65165e11i		−	1.40534i	0.711514	−	0.702672i	$-0.248010\pi$
$860$		0			0
$861$	6.69816e10			0.121883
$862$	7.17924e11	+	7.17924e11i	1.30032	+	1.30032i
$863$	1.42889e10	−	1.42889e10i	0.0257606	−	0.0257606i	−0.694109	−	0.719870i	$-0.744202\pi$
$863$	1.42889e10	−	1.42889e10i	0.0257606	−	0.0257606i	0.719870	+	0.694109i	$0.244202\pi$
$864$		−	2.28911e12i		−	4.10781i
$865$		0			0
$866$	1.30097e12			2.31310
$867$	2.96530e11	+	2.96530e11i	0.524798	+	0.524798i
$868$	1.25172e11	−	1.25172e11i	0.220509	−	0.220509i
$869$		−	1.83722e10i		−	0.0322168i
$870$		0			0
$871$	−6.38951e11			−1.11018
$872$	−4.35089e11	−	4.35089e11i	−0.752510	−	0.752510i
$873$	2.86865e11	−	2.86865e11i	0.493879	−	0.493879i
$874$		−	5.66632e10i		−	0.0971081i
$875$		0			0
$876$	−6.75704e11			−1.14747
$877$	3.24520e11	+	3.24520e11i	0.548583	+	0.548583i	0.926031	−	0.377448i	$-0.123198\pi$
$877$	3.24520e11	+	3.24520e11i	0.548583	+	0.548583i	−0.377448	+	0.926031i	$0.623198\pi$
$878$	−2.38023e11	+	2.38023e11i	−0.400535	+	0.400535i
$879$			3.15289e11i			0.528144i
$880$		0			0
$881$	−3.35430e11			−0.556798			−0.278399	−	0.960465i	$-0.589804\pi$
$881$	−3.35430e11			−0.556798			−0.278399	+	0.960465i	$0.589804\pi$
$882$	−3.46923e11	−	3.46923e11i	−0.573269	−	0.573269i
$883$	−3.09069e10	+	3.09069e10i	−0.0508409	+	0.0508409i	−0.732070	−	0.681229i	$-0.761446\pi$
$883$	−3.09069e10	+	3.09069e10i	−0.0508409	+	0.0508409i	0.681229	+	0.732070i	$0.261446\pi$
$884$		−	4.13252e9i		−	0.00676715i
$885$		0			0
$886$	−1.42131e12			−2.30651
$887$	8.32066e11	+	8.32066e11i	1.34420	+	1.34420i	0.891833	+	0.452364i	$0.149419\pi$
$887$	8.32066e11	+	8.32066e11i	1.34420	+	1.34420i	0.452364	+	0.891833i	$0.350581\pi$
$888$	1.40042e12	−	1.40042e12i	2.25220	−	2.25220i
$889$		−	2.25401e10i		−	0.0360868i
$890$		0			0
$891$	7.88240e10			0.125068
$892$	−1.30267e12	−	1.30267e12i	−2.05767	−	2.05767i
$893$	6.33496e11	−	6.33496e11i	0.996180	−	0.996180i
$894$			1.23219e12i			1.92898i
$895$		0			0
$896$	5.35378e11			0.830670
$897$	1.11280e10	+	1.11280e10i	0.0171888	+	0.0171888i
$898$	−6.18454e11	+	6.18454e11i	−0.951047	+	0.951047i
$899$		−	4.08713e11i		−	0.625719i
$900$		0			0
$901$	1.51511e9			0.00229904
$902$	−2.08643e11	−	2.08643e11i	−0.315194	−	0.315194i
$903$	8.45737e10	−	8.45737e10i	0.127199	−	0.127199i
$904$			1.06917e11i			0.160093i
$905$		0			0
$906$	4.23673e11			0.628809
$907$	3.88349e11	+	3.88349e11i	0.573842	+	0.573842i	0.933200	−	0.359358i	$-0.117004\pi$
$907$	3.88349e11	+	3.88349e11i	0.573842	+	0.573842i	−0.359358	+	0.933200i	$0.617004\pi$
$908$	−1.77876e12	+	1.77876e12i	−2.61682	+	2.61682i
$909$			2.97392e11i			0.435585i
$910$		0			0
$911$	8.45018e11			1.22685			0.613427	−	0.789752i	$-0.289791\pi$
$911$	8.45018e11			1.22685			0.613427	+	0.789752i	$0.289791\pi$
$912$	−2.14735e12	−	2.14735e12i	−3.10402	−	3.10402i
$913$	1.91034e11	−	1.91034e11i	0.274934	−	0.274934i
$914$			6.50911e11i			0.932689i
$915$		0			0
$916$	1.87790e12			2.66741
$917$	5.35386e10	+	5.35386e10i	0.0757164	+	0.0757164i
$918$	−2.48994e9	+	2.48994e9i	−0.00350606	+	0.00350606i
$919$			6.42569e11i			0.900861i	0.892812	+	0.450430i	$0.148729\pi$
$919$			6.42569e11i			0.900861i	−0.892812	+	0.450430i	$0.851271\pi$
$920$		0			0
$921$	−2.28345e11			−0.317361
$922$	−6.28880e11	−	6.28880e11i	−0.870250	−	0.870250i
$923$	7.39763e11	−	7.39763e11i	1.01926	−	1.01926i
$924$			1.34619e11i			0.184679i
$925$		0			0
$926$	−7.11228e9			−0.00967308
$927$	−1.87781e11	−	1.87781e11i	−0.254292	−	0.254292i
$928$	2.79114e12	−	2.79114e12i	3.76348	−	3.76348i
$929$			6.54171e11i			0.878271i	0.898421	+	0.439135i	$0.144715\pi$
$929$			6.54171e11i			0.878271i	−0.898421	+	0.439135i	$0.855285\pi$
$930$		0			0
$931$	−1.12162e12			−1.49296
$932$	1.36555e12	+	1.36555e12i	1.80985	+	1.80985i
$933$	−4.56014e11	+	4.56014e11i	−0.601799	+	0.601799i
$934$			1.94326e12i			2.55355i
$935$		0			0
$936$	−1.19384e12			−1.55540
$937$	5.01561e11	+	5.01561e11i	0.650677	+	0.650677i	0.953156	−	0.302479i	$-0.0978142\pi$
$937$	5.01561e11	+	5.01561e11i	0.650677	+	0.650677i	−0.302479	+	0.953156i	$0.597814\pi$
$938$	−2.87526e11	+	2.87526e11i	−0.371420	+	0.371420i
$939$		−	6.20107e11i		−	0.797635i
$940$		0			0
$941$	−2.08765e11			−0.266256			−0.133128	−	0.991099i	$-0.542502\pi$
$941$	−2.08765e11			−0.266256			−0.133128	+	0.991099i	$0.542502\pi$
$942$	1.03768e11	+	1.03768e11i	0.131783	+	0.131783i
$943$	−1.13561e10	+	1.13561e10i	−0.0143610	+	0.0143610i
$944$		−	1.92548e12i		−	2.42466i
$945$		0			0
$946$	−5.26882e11			−0.657883
$947$	5.88181e11	+	5.88181e11i	0.731326	+	0.731326i	0.970883	−	0.239556i	$-0.0770019\pi$
$947$	5.88181e11	+	5.88181e11i	0.731326	+	0.731326i	−0.239556	+	0.970883i	$0.577002\pi$
$948$	−1.03894e11	+	1.03894e11i	−0.128635	+	0.128635i
$949$			4.78187e11i			0.589566i
$950$		0			0
$951$	1.01991e12			1.24693
$952$	−1.17741e9	−	1.17741e9i	−0.00143344	−	0.00143344i
$953$	7.87397e10	−	7.87397e10i	0.0954601	−	0.0954601i	−0.657764	−	0.753224i	$-0.728498\pi$
$953$	7.87397e10	−	7.87397e10i	0.0954601	−	0.0954601i	0.753224	+	0.657764i	$0.228498\pi$
$954$		−	6.91308e11i		−	0.834600i
$955$		0			0
$956$	−1.92978e12			−2.31034
$957$	2.19780e11	+	2.19780e11i	0.262024	+	0.262024i
$958$	4.50394e11	−	4.50394e11i	0.534725	−	0.534725i
$959$		−	2.00382e10i		−	0.0236911i
$960$		0			0
$961$	−6.80939e11			−0.798389
$962$	−1.56530e12	−	1.56530e12i	−1.82767	−	1.82767i
$963$	1.96847e11	−	1.96847e11i	0.228888	−	0.228888i
$964$		−	4.13789e12i		−	4.79149i
$965$		0			0
$966$	1.00151e10			0.0115013
$967$	−9.67178e11	−	9.67178e11i	−1.10612	−	1.10612i	−0.993656	−	0.112460i	$-0.964127\pi$
$967$	−9.67178e11	−	9.67178e11i	−1.10612	−	1.10612i	−0.112460	−	0.993656i	$-0.535873\pi$
$968$	−1.80279e12	+	1.80279e12i	−2.05326	+	2.05326i
$969$			2.49513e9i			0.00283008i
$970$		0			0
$971$	5.86949e11			0.660272			0.330136	−	0.943933i	$-0.392905\pi$
$971$	5.86949e11			0.660272			0.330136	+	0.943933i	$0.392905\pi$
$972$	1.40473e12	+	1.40473e12i	1.57372	+	1.57372i
$973$	1.18174e11	−	1.18174e11i	0.131847	−	0.131847i
$974$			1.28655e12i			1.42952i
$975$		0			0
$976$	2.72747e12			3.00580
$977$	2.05615e11	+	2.05615e11i	0.225671	+	0.225671i	0.810881	−	0.585210i	$-0.198988\pi$
$977$	2.05615e11	+	2.05615e11i	0.225671	+	0.225671i	−0.585210	+	0.810881i	$0.698988\pi$
$978$	−7.87353e11	+	7.87353e11i	−0.860626	+	0.860626i
$979$		−	3.93296e11i		−	0.428143i
$980$		0			0
$981$	1.32889e11			0.143487
$982$	8.23528e11	+	8.23528e11i	0.885590	+	0.885590i
$983$	−1.03277e12	+	1.03277e12i	−1.10609	+	1.10609i	−0.112426	+	0.993660i	$0.535862\pi$
$983$	−1.03277e12	+	1.03277e12i	−1.10609	+	1.10609i	−0.993660	+	0.112426i	$0.964138\pi$
$984$			1.49406e12i			1.59363i
$985$		0			0
$986$	−6.07206e9			−0.00642433
$987$	1.11969e11	+	1.11969e11i	0.117986	+	0.117986i
$988$	−3.04807e12	+	3.04807e12i	−3.19887	+	3.19887i
$989$			2.86774e10i			0.0299747i
$990$		0			0
$991$	−4.91539e11			−0.509640			−0.254820	−	0.966988i	$-0.582016\pi$
$991$	−4.91539e11			−0.509640			−0.254820	+	0.966988i	$0.582016\pi$
$992$	1.17428e12	+	1.17428e12i	1.21262	+	1.21262i
$993$	4.14131e11	−	4.14131e11i	0.425932	−	0.425932i
$994$		−	6.65781e11i		−	0.682002i
$995$		0			0
$996$	−2.16059e12			−2.19551
$997$	−5.35595e11	−	5.35595e11i	−0.542070	−	0.542070i	0.382065	−	0.924135i	$-0.375213\pi$
$997$	−5.35595e11	−	5.35595e11i	−0.542070	−	0.542070i	−0.924135	+	0.382065i	$0.875213\pi$
$998$	1.60591e12	−	1.60591e12i	1.61882	−	1.61882i
$999$			1.38000e12i			1.38554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.c.c.7.1	✓	12
5.2	odd	4	inner	25.9.c.c.18.6	yes	12
5.3	odd	4	inner	25.9.c.c.18.1	yes	12
5.4	even	2	inner	25.9.c.c.7.6	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.9.c.c.7.1	✓	12	1.1	even	1	trivial
25.9.c.c.7.6	yes	12	5.4	even	2	inner
25.9.c.c.18.1	yes	12	5.3	odd	4	inner
25.9.c.c.18.6	yes	12	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-21.8383 - 21.8383i) q^{2} +(-42.5089 + 42.5089i) q^{3} +697.824i q^{4} +1856.64 q^{6} +(-432.570 - 432.570i) q^{7} +(9648.70 - 9648.70i) q^{8} +2946.99i q^{9} +O(q^{10})\)	\(q+(-21.8383 - 21.8383i) q^{2} +(-42.5089 + 42.5089i) q^{3} +697.824i q^{4} +1856.64 q^{6} +(-432.570 - 432.570i) q^{7} +(9648.70 - 9648.70i) q^{8} +2946.99i q^{9} +5245.59 q^{11} +(-29663.7 - 29663.7i) q^{12} +(-20992.6 + 20992.6i) q^{13} +18893.2i q^{14} -242780. q^{16} +(141.050 + 141.050i) q^{17} +(64357.4 - 64357.4i) q^{18} -208071. i q^{19} +36776.1 q^{21} +(-114555. - 114555. i) q^{22} +(-6235.05 + 6235.05i) q^{23} +820310. i q^{24} +916887. q^{26} +(-404174. - 404174. i) q^{27} +(301858. - 301858. i) q^{28} -985631. i q^{29} +414671. q^{31} +(2.83183e6 + 2.83183e6i) q^{32} +(-222984. + 222984. i) q^{33} -6160.58i q^{34} -2.05648e6 q^{36} +(-1.70719e6 - 1.70719e6i) q^{37} +(-4.54392e6 + 4.54392e6i) q^{38} -1.78474e6i q^{39} +1.82134e6 q^{41} +(-803128. - 803128. i) q^{42} +(2.29969e6 - 2.29969e6i) q^{43} +3.66050e6i q^{44} +272326. q^{46} +(3.04461e6 + 3.04461e6i) q^{47} +(1.03203e7 - 1.03203e7i) q^{48} -5.39057e6i q^{49} -11991.7 q^{51} +(-1.46492e7 - 1.46492e7i) q^{52} +(5.37085e6 - 5.37085e6i) q^{53} +1.76530e7i q^{54} -8.34747e6 q^{56} +(8.84487e6 + 8.84487e6i) q^{57} +(-2.15245e7 + 2.15245e7i) q^{58} +7.93099e6i q^{59} -1.12343e7 q^{61} +(-9.05572e6 - 9.05572e6i) q^{62} +(1.27478e6 - 1.27478e6i) q^{63} -6.15333e7i q^{64} +9.73919e6 q^{66} +(1.52185e7 + 1.52185e7i) q^{67} +(-98427.9 + 98427.9i) q^{68} -530090. i q^{69} -3.52392e7 q^{71} +(2.84346e7 + 2.84346e7i) q^{72} +(1.13894e7 - 1.13894e7i) q^{73} +7.45642e7i q^{74} +1.45197e8 q^{76} +(-2.26908e6 - 2.26908e6i) q^{77} +(-3.89758e7 + 3.89758e7i) q^{78} -3.50241e6i q^{79} +1.50267e7 q^{81} +(-3.97749e7 - 3.97749e7i) q^{82} +(3.64180e7 - 3.64180e7i) q^{83} +2.56633e7i q^{84} -1.00443e8 q^{86} +(4.18980e7 + 4.18980e7i) q^{87} +(5.06131e7 - 5.06131e7i) q^{88} -7.49765e7i q^{89} +1.81615e7 q^{91} +(-4.35097e6 - 4.35097e6i) q^{92} +(-1.76272e7 + 1.76272e7i) q^{93} -1.32978e8i q^{94} -2.40756e8 q^{96} +(-9.73416e7 - 9.73416e7i) q^{97} +(-1.17721e8 + 1.17721e8i) q^{98} +1.54587e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6396 q^{6}+O(q^{10}) \) 12 * q - 6396 * q^6	\( 12 q - 6396 q^{6} - 118116 q^{11} - 1204068 q^{16} - 1365456 q^{21} + 5376024 q^{26} + 3223704 q^{31} + 14477592 q^{36} + 10940364 q^{41} - 51272856 q^{46} - 47621676 q^{51} - 64717200 q^{56} - 23597616 q^{61} + 264735828 q^{66} - 47870856 q^{71} + 432845700 q^{76} + 3008052 q^{81} - 105341616 q^{86} - 64237536 q^{91} - 1580181156 q^{96}+O(q^{100}) \) 12 * q - 6396 * q^6 - 118116 * q^11 - 1204068 * q^16 - 1365456 * q^21 + 5376024 * q^26 + 3223704 * q^31 + 14477592 * q^36 + 10940364 * q^41 - 51272856 * q^46 - 47621676 * q^51 - 64717200 * q^56 - 23597616 * q^61 + 264735828 * q^66 - 47870856 * q^71 + 432845700 * q^76 + 3008052 * q^81 - 105341616 * q^86 - 64237536 * q^91 - 1580181156 * q^96

Introduction

L-functions

Modular forms

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Database

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