LMFDB - Embedded newform 81.9.d.d.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(26,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

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("81.26");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.d (of order $6$, degree $2$, not 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:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-14})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 14x^{2} + 196 $ x^4 - 14*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 3)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.1
Root			$-3.24037 + 1.87083i$ of defining polynomial
Character	$\chi$	$=$	81.53
Dual form			81.9.d.d.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.4422 + 11.2250i) q^{2} +(124.000 - 214.774i) q^{4} +(-194.422 - 112.250i) q^{5} +(875.000 + 1515.54i) q^{7} -179.600i q^{8} +O(q^{10})$	\(q+(-19.4422 + 11.2250i) q^{2} +(124.000 - 214.774i) q^{4} +(-194.422 - 112.250i) q^{5} +(875.000 + 1515.54i) q^{7} -179.600i q^{8} +5040.00 q^{10} +(-6027.09 + 3479.74i) q^{11} +(-12865.0 + 22282.8i) q^{13} +(-34023.9 - 19643.7i) q^{14} +(33760.0 + 58474.0i) q^{16} -74893.0i q^{17} +18938.0 q^{19} +(-48216.7 + 27837.9i) q^{20} +(78120.0 - 135308. i) q^{22} +(-407431. - 235231. i) q^{23} +(-170112. - 294643. i) q^{25} -577637. i q^{26} +434000. q^{28} +(-399149. + 230449. i) q^{29} +(175739. - 304389. i) q^{31} +(-1.27292e6 - 734921. i) q^{32} +(840672. + 1.45609e6i) q^{34} -392874. i q^{35} +1.33517e6 q^{37} +(-368197. + 212579. i) q^{38} +(-20160.0 + 34918.1i) q^{40} +(1.62420e6 + 937734. i) q^{41} +(1.76308e6 + 3.05374e6i) q^{43} +1.72595e6i q^{44} +1.05618e7 q^{46} +(3.53428e6 - 2.04052e6i) q^{47} +(1.35115e6 - 2.34026e6i) q^{49} +(6.61473e6 + 3.81902e6i) q^{50} +(3.19052e6 + 5.52614e6i) q^{52} +6.60177e6i q^{53} +1.56240e6 q^{55} +(272191. - 157150. i) q^{56} +(5.17356e6 - 8.96087e6i) q^{58} +(1.18774e7 + 6.85745e6i) q^{59} +(-376801. - 652638. i) q^{61} +7.89066e6i q^{62} +1.57128e7 q^{64} +(5.00248e6 - 2.88819e6i) q^{65} +(-1.13444e6 + 1.96492e6i) q^{67} +(-1.60851e7 - 9.28673e6i) q^{68} +(4.41000e6 + 7.63834e6i) q^{70} -1.70220e7i q^{71} +2.76728e7 q^{73} +(-2.59587e7 + 1.49872e7i) q^{74} +(2.34831e6 - 4.06740e6i) q^{76} +(-1.05474e7 - 6.08955e6i) q^{77} +(1.14905e7 + 1.99021e7i) q^{79} -1.51582e7i q^{80} -4.21042e7 q^{82} +(4.01794e7 - 2.31976e7i) q^{83} +(-8.40672e6 + 1.45609e7i) q^{85} +(-6.85562e7 - 3.95809e7i) q^{86} +(624960. + 1.08246e6i) q^{88} -7.26152e7i q^{89} -4.50275e7 q^{91} +(-1.01043e8 + 5.83372e7i) q^{92} +(-4.58096e7 + 7.93445e7i) q^{94} +(-3.68197e6 - 2.12579e6i) q^{95} +(-7.36355e7 - 1.27540e8i) q^{97} +6.06665e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 496 q^{4} + 3500 q^{7}+O(q^{10}) $ 4 * q + 496 * q^4 + 3500 * q^7	$ 4 q + 496 q^{4} + 3500 q^{7} + 20160 q^{10} - 51460 q^{13} + 135040 q^{16} + 75752 q^{19} + 312480 q^{22} - 680450 q^{25} + 1736000 q^{28} + 702956 q^{31} + 3362688 q^{34} + 5340680 q^{37} - 80640 q^{40} + 7052300 q^{43} + 42247296 q^{46} + 5404602 q^{49} + 12762080 q^{52} + 6249600 q^{55} + 20694240 q^{58} - 1507204 q^{61} + 62851072 q^{64} - 4537780 q^{67} + 17640000 q^{70} + 110691080 q^{73} + 9393248 q^{76} + 45961964 q^{79} - 168416640 q^{82} - 33626880 q^{85} + 2499840 q^{88} - 180110000 q^{91} - 183238272 q^{94} - 294542020 q^{97}+O(q^{100}) $ 4 * q + 496 * q^4 + 3500 * q^7 + 20160 * q^10 - 51460 * q^13 + 135040 * q^16 + 75752 * q^19 + 312480 * q^22 - 680450 * q^25 + 1736000 * q^28 + 702956 * q^31 + 3362688 * q^34 + 5340680 * q^37 - 80640 * q^40 + 7052300 * q^43 + 42247296 * q^46 + 5404602 * q^49 + 12762080 * q^52 + 6249600 * q^55 + 20694240 * q^58 - 1507204 * q^61 + 62851072 * q^64 - 4537780 * q^67 + 17640000 * q^70 + 110691080 * q^73 + 9393248 * q^76 + 45961964 * q^79 - 168416640 * q^82 - 33626880 * q^85 + 2499840 * q^88 - 180110000 * q^91 - 183238272 * q^94 - 294542020 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−19.4422	+	11.2250i	−1.21514	+	0.701561i	−0.963874	−	0.266358i	$-0.914180\pi$
$2$	−19.4422	+	11.2250i	−1.21514	+	0.701561i	−0.251265	+	0.967918i	$0.580846\pi$
$3$		0			0
$3$		0			0
$4$	124.000	−	214.774i	0.484375	−	0.838962i
$5$	−194.422	−	112.250i	−0.311076	−	0.179600i	0.336332	−	0.941743i	$-0.390814\pi$
$5$	−194.422	−	112.250i	−0.311076	−	0.179600i	−0.647408	+	0.762144i	$0.724147\pi$
$6$		0			0
$7$	875.000	+	1515.54i	0.364431	+	0.631214i	0.988685	−	0.150008i	$-0.0479300\pi$
$7$	875.000	+	1515.54i	0.364431	+	0.631214i	−0.624253	+	0.781222i	$0.714597\pi$
$8$		−	179.600i		−	0.0438475i
$9$		0			0
$10$	5040.00			0.504000
$11$	−6027.09	+	3479.74i	−0.411658	+	0.237671i	−0.691502	−	0.722375i	$-0.743051\pi$
$11$	−6027.09	+	3479.74i	−0.411658	+	0.237671i	0.279844	+	0.960046i	$0.409717\pi$
$12$		0			0
$13$	−12865.0	+	22282.8i	−0.450439	+	0.780184i	−0.998413	−	0.0563115i	$-0.982066\pi$
$13$	−12865.0	+	22282.8i	−0.450439	+	0.780184i	0.547974	+	0.836495i	$0.315399\pi$
$14$	−34023.9	−	19643.7i	−0.885670	−	0.511342i
$15$		0			0
$16$	33760.0	+	58474.0i	0.515137	+	0.892243i
$17$		−	74893.0i		−	0.896697i	−0.893859	−	0.448348i	$-0.852012\pi$
$17$		−	74893.0i		−	0.896697i	0.893859	−	0.448348i	$-0.147988\pi$
$18$		0			0
$19$	18938.0			0.145318			0.0726590	−	0.997357i	$-0.476852\pi$
$19$	18938.0			0.145318			0.0726590	+	0.997357i	$0.476852\pi$
$20$	−48216.7	+	27837.9i	−0.301354	+	0.173987i
$21$		0			0
$22$	78120.0	−	135308.i	0.333481	−	0.577607i
$23$	−407431.	−	235231.i	−1.45594	−	0.840586i	−0.457130	−	0.889400i	$-0.651123\pi$
$23$	−407431.	−	235231.i	−1.45594	−	0.840586i	−0.998808	+	0.0488134i	$0.984456\pi$
$24$		0			0
$25$	−170112.	−	294643.i	−0.435488	−	0.754287i
$26$		−	577637.i		−	1.26404i
$27$		0			0
$28$	434000.			0.706086
$29$	−399149.	+	230449.i	−0.564343	+	0.325823i	−0.754887	−	0.655855i	$-0.772308\pi$
$29$	−399149.	+	230449.i	−0.564343	+	0.325823i	0.190544	+	0.981679i	$0.438975\pi$
$30$		0			0
$31$	175739.	−	304389.i	0.190292	−	0.329596i	−0.755055	−	0.655662i	$-0.772390\pi$
$31$	175739.	−	304389.i	0.190292	−	0.329596i	0.945347	+	0.326066i	$0.105723\pi$
$32$	−1.27292e6	−	734921.i	−1.21395	−	0.700876i
$33$		0			0
$34$	840672.	+	1.45609e6i	0.629087	+	1.08961i
$35$		−	392874.i		−	0.261807i
$36$		0			0
$37$	1.33517e6			0.712409			0.356205	−	0.934408i	$-0.384071\pi$
$37$	1.33517e6			0.712409			0.356205	+	0.934408i	$0.384071\pi$
$38$	−368197.	+	212579.i	−0.176582	+	0.101949i
$39$		0			0
$40$	−20160.0	+	34918.1i	−0.00787500	+	0.0136399i
$41$	1.62420e6	+	937734.i	0.574784	+	0.331852i	0.759058	−	0.651023i	$-0.225660\pi$
$41$	1.62420e6	+	937734.i	0.574784	+	0.331852i	−0.184274	+	0.982875i	$0.558993\pi$
$42$		0			0
$43$	1.76308e6	+	3.05374e6i	0.515700	+	0.893218i	0.999834	+	0.0182245i	$0.00580135\pi$
$43$	1.76308e6	+	3.05374e6i	0.515700	+	0.893218i	−0.484134	+	0.874994i	$0.660865\pi$
$44$			1.72595e6i			0.460488i
$45$		0			0
$46$	1.05618e7			2.35889
$47$	3.53428e6	−	2.04052e6i	0.724286	−	0.418167i	−0.0920421	−	0.995755i	$-0.529339\pi$
$47$	3.53428e6	−	2.04052e6i	0.724286	−	0.418167i	0.816328	+	0.577588i	$0.196006\pi$
$48$		0			0
$49$	1.35115e6	−	2.34026e6i	0.234379	−	0.405957i
$50$	6.61473e6	+	3.81902e6i	1.05836	+	0.611043i
$51$		0			0
$52$	3.19052e6	+	5.52614e6i	0.436363	+	0.755803i
$53$			6.60177e6i			0.836675i	0.908292	+	0.418337i	$0.137387\pi$
$53$			6.60177e6i			0.836675i	−0.908292	+	0.418337i	$0.862613\pi$
$54$		0			0
$55$	1.56240e6			0.170742
$56$	272191.	−	157150.i	0.0276772	−	0.0159794i
$57$		0			0
$58$	5.17356e6	−	8.96087e6i	0.457170	−	0.791841i
$59$	1.18774e7	+	6.85745e6i	0.980201	+	0.565919i	0.902331	−	0.431044i	$-0.141855\pi$
$59$	1.18774e7	+	6.85745e6i	0.980201	+	0.565919i	0.0778701	+	0.996964i	$0.475188\pi$
$60$		0			0
$61$	−376801.	−	652638.i	−0.0272140	−	0.0471361i	0.852098	−	0.523383i	$-0.175330\pi$
$61$	−376801.	−	652638.i	−0.0272140	−	0.0471361i	−0.879312	+	0.476247i	$0.841997\pi$
$62$			7.89066e6i			0.534007i
$63$		0			0
$64$	1.57128e7			0.936554
$65$	5.00248e6	−	2.88819e6i	0.280241	−	0.161797i
$66$		0			0
$67$	−1.13444e6	+	1.96492e6i	−0.0562969	+	0.0975090i	−0.892800	−	0.450453i	$-0.851263\pi$
$67$	−1.13444e6	+	1.96492e6i	−0.0562969	+	0.0975090i	0.836504	+	0.547962i	$0.184596\pi$
$68$	−1.60851e7	−	9.28673e6i	−0.752295	−	0.434338i
$69$		0			0
$70$	4.41000e6	+	7.63834e6i	0.183673	+	0.318132i
$71$		−	1.70220e7i		−	0.669849i	−0.942245	−	0.334925i	$-0.891289\pi$
$71$		−	1.70220e7i		−	0.669849i	0.942245	−	0.334925i	$-0.108711\pi$
$72$		0			0
$73$	2.76728e7			0.974454			0.487227	−	0.873275i	$-0.338008\pi$
$73$	2.76728e7			0.974454			0.487227	+	0.873275i	$0.338008\pi$
$74$	−2.59587e7	+	1.49872e7i	−0.865676	+	0.499799i
$75$		0			0
$76$	2.34831e6	−	4.06740e6i	0.0703885	−	0.121916i
$77$	−1.05474e7	−	6.08955e6i	−0.300042	−	0.173230i
$78$		0			0
$79$	1.14905e7	+	1.99021e7i	0.295006	+	0.510965i	0.974986	−	0.222265i	$-0.0713452\pi$
$79$	1.14905e7	+	1.99021e7i	0.295006	+	0.510965i	−0.679981	+	0.733230i	$0.738012\pi$
$80$		−	1.51582e7i		−	0.370073i
$81$		0			0
$82$	−4.21042e7			−0.931257
$83$	4.01794e7	−	2.31976e7i	0.846625	−	0.488799i	−0.0128855	−	0.999917i	$-0.504102\pi$
$83$	4.01794e7	−	2.31976e7i	0.846625	−	0.488799i	0.859511	+	0.511118i	$0.170768\pi$
$84$		0			0
$85$	−8.40672e6	+	1.45609e7i	−0.161046	+	0.278940i
$86$	−6.85562e7	−	3.95809e7i	−1.25329	−	0.723589i
$87$		0			0
$88$	624960.	+	1.08246e6i	0.0104213	+	0.0180502i
$89$		−	7.26152e7i		−	1.15736i	−0.815555	−	0.578679i	$-0.803568\pi$
$89$		−	7.26152e7i		−	1.15736i	0.815555	−	0.578679i	$-0.196432\pi$
$90$		0			0
$91$	−4.50275e7			−0.656617
$92$	−1.01043e8	+	5.83372e7i	−1.41044	+	0.814318i
$93$		0			0
$94$	−4.58096e7	+	7.93445e7i	−0.586739	+	1.01626i
$95$	−3.68197e6	−	2.12579e6i	−0.0452049	−	0.0260991i
$96$		0			0
$97$	−7.36355e7	−	1.27540e8i	−0.831764	−	1.44066i	−0.896638	−	0.442765i	$-0.853998\pi$
$97$	−7.36355e7	−	1.27540e8i	−0.831764	−	1.44066i	0.0648734	−	0.997894i	$-0.479336\pi$
$98$			6.06665e7i			0.657726i
$99$		0			0
$100$	−8.43758e7			−0.843758
$101$	8.96724e7	−	5.17724e7i	0.861734	−	0.497522i	−0.00285856	−	0.999996i	$-0.500910\pi$
$101$	8.96724e7	−	5.17724e7i	0.861734	−	0.497522i	0.864593	+	0.502474i	$0.167577\pi$
$102$		0			0
$103$	8.30318e7	−	1.43815e8i	0.737726	−	1.27778i	−0.215790	−	0.976440i	$-0.569233\pi$
$103$	8.30318e7	−	1.43815e8i	0.737726	−	1.27778i	0.953517	−	0.301340i	$-0.0974339\pi$
$104$	4.00199e6	+	2.31055e6i	0.0342092	+	0.0197507i
$105$		0			0
$106$	−7.41046e7	−	1.28353e8i	−0.586978	−	1.01668i
$107$			2.25540e7i			0.172063i	0.996292	+	0.0860316i	$0.0274186\pi$
$107$			2.25540e7i			0.172063i	−0.996292	+	0.0860316i	$0.972581\pi$
$108$		0			0
$109$	−1.09975e8			−0.779091			−0.389546	−	0.921007i	$-0.627368\pi$
$109$	−1.09975e8			−0.779091			−0.389546	+	0.921007i	$0.627368\pi$
$110$	−3.03765e7	+	1.75379e7i	−0.207476	+	0.119786i
$111$		0			0
$112$	−5.90800e7	+	1.02330e8i	−0.375464	+	0.650323i
$113$	2.49197e8	+	1.43874e8i	1.52837	+	0.882405i	0.999430	+	0.0337466i	$0.0107439\pi$
$113$	2.49197e8	+	1.43874e8i	1.52837	+	0.882405i	0.528941	+	0.848659i	$0.322589\pi$
$114$		0			0
$115$	5.28091e7	+	9.14681e7i	0.301938	+	0.522972i
$116$			1.14303e8i			0.631283i
$117$		0			0
$118$	−3.07899e8			−1.58811
$119$	1.13504e8	−	6.55314e7i	0.566007	−	0.326785i
$120$		0			0
$121$	−8.29622e7	+	1.43695e8i	−0.387025	+	0.670347i
$122$	1.46517e7	+	8.45916e6i	0.0661376	+	0.0381846i
$123$		0			0
$124$	−4.35833e7	−	7.54884e7i	−0.184346	−	0.319296i
$125$			1.64075e8i			0.672053i
$126$		0			0
$127$	2.75994e8			1.06092			0.530462	−	0.847708i	$-0.322018\pi$
$127$	2.75994e8			1.06092			0.530462	+	0.847708i	$0.322018\pi$
$128$	2.03767e7	−	1.17645e7i	0.0759091	−	0.0438261i
$129$		0			0
$130$	−6.48396e7	+	1.12305e8i	−0.227021	+	0.393213i
$131$	2.50383e8	+	1.44559e8i	0.850198	+	0.490862i	0.860718	−	0.509082i	$-0.170015\pi$
$131$	2.50383e8	+	1.44559e8i	0.850198	+	0.490862i	−0.0105194	+	0.999945i	$0.503348\pi$
$132$		0			0
$133$	1.65708e7	+	2.87014e7i	0.0529585	+	0.0917268i
$134$		−	5.09365e7i		−	0.157983i
$135$		0			0
$136$	−1.34508e7			−0.0393180
$137$	1.79754e8	−	1.03781e8i	0.510266	−	0.294602i	−0.222677	−	0.974892i	$-0.571479\pi$
$137$	1.79754e8	−	1.03781e8i	0.510266	−	0.294602i	0.732943	+	0.680290i	$0.238146\pi$
$138$		0			0
$139$	7.13341e7	−	1.23554e8i	0.191090	−	0.330978i	−0.754522	−	0.656275i	$-0.772131\pi$
$139$	7.13341e7	−	1.23554e8i	0.191090	−	0.330978i	0.945612	+	0.325297i	$0.105464\pi$
$140$	−8.43792e7	−	4.87164e7i	−0.219646	−	0.126813i
$141$		0			0
$142$	1.91071e8	+	3.30945e8i	0.469940	+	0.813960i
$143$		−	1.79067e8i		−	0.428226i
$144$		0			0
$145$	1.03471e8			0.234071
$146$	−5.38020e8	+	3.10626e8i	−1.18410	+	0.683638i
$147$		0			0
$148$	1.65561e8	−	2.86760e8i	0.345073	−	0.597685i
$149$	−7.09479e8	−	4.09618e8i	−1.43944	−	0.831063i	−0.441632	−	0.897196i	$-0.645600\pi$
$149$	−7.09479e8	−	4.09618e8i	−1.43944	−	0.831063i	−0.997811	+	0.0661339i	$0.978934\pi$
$150$		0			0
$151$	−2.11930e8	−	3.67074e8i	−0.407648	−	0.706067i	0.586978	−	0.809603i	$-0.300318\pi$
$151$	−2.11930e8	−	3.67074e8i	−0.407648	−	0.706067i	−0.994626	+	0.103536i	$0.966984\pi$
$152$		−	3.40126e6i		−	0.00637184i
$153$		0			0
$154$	2.73420e8			0.486124
$155$	−6.83351e7	+	3.94533e7i	−0.118391	+	0.0683528i
$156$		0			0
$157$	3.79925e8	−	6.58050e8i	0.625316	−	1.08308i	−0.363163	−	0.931725i	$-0.618303\pi$
$157$	3.79925e8	−	6.58050e8i	0.625316	−	1.08308i	0.988480	−	0.151354i	$-0.0483633\pi$
$158$	−4.46801e8	−	2.57961e8i	−0.716945	−	0.413929i
$159$		0			0
$160$	1.64989e8	+	2.85770e8i	0.251754	+	0.436051i
$161$		−	8.23307e8i		−	1.22534i
$162$		0			0
$163$	6.68160e8			0.946520			0.473260	−	0.880923i	$-0.343077\pi$
$163$	6.68160e8			0.946520			0.473260	+	0.880923i	$0.343077\pi$
$164$	4.02802e8	−	2.32558e8i	0.556822	−	0.321482i
$165$		0			0
$166$	−5.20785e8	+	9.02026e8i	−0.685845	+	1.18792i
$167$	1.70006e8	+	9.81529e7i	0.218574	+	0.126194i	0.605290	−	0.796005i	$-0.293057\pi$
$167$	1.70006e8	+	9.81529e7i	0.218574	+	0.126194i	−0.386716	+	0.922199i	$0.626391\pi$
$168$		0			0
$169$	7.68489e7	+	1.33106e8i	0.0942087	+	0.163174i
$170$		−	3.77461e8i		−	0.451935i
$171$		0			0
$172$	8.74485e8			0.999168
$173$	−8.86111e8	+	5.11596e8i	−0.989245	+	0.571141i	−0.905048	−	0.425308i	$-0.860166\pi$
$173$	−8.86111e8	+	5.11596e8i	−0.989245	+	0.571141i	−0.0841963	+	0.996449i	$0.526832\pi$
$174$		0			0
$175$	2.97697e8	−	5.15626e8i	0.317411	−	0.549772i
$176$	−4.06949e8	−	2.34952e8i	−0.424121	−	0.244866i
$177$		0			0
$178$	8.15104e8	+	1.41180e9i	0.811957	+	1.40635i
$179$			1.28895e9i			1.25552i	0.778408	+	0.627759i	$0.216028\pi$
$179$			1.28895e9i			1.25552i	−0.778408	+	0.627759i	$0.783972\pi$
$180$		0			0
$181$	4.71707e8			0.439499			0.219749	−	0.975556i	$-0.429476\pi$
$181$	4.71707e8			0.439499			0.219749	+	0.975556i	$0.429476\pi$
$182$	8.75435e8	−	5.05432e8i	0.797881	−	0.460657i
$183$		0			0
$184$	−4.22473e7	+	7.31745e7i	−0.0368576	+	0.0638393i
$185$	−2.59587e8	−	1.49872e8i	−0.221613	−	0.127948i
$186$		0			0
$187$	2.60608e8	+	4.51387e8i	0.213119	+	0.369133i
$188$		−	1.01210e9i		−	0.810198i
$189$		0			0
$190$	9.54475e7			0.0732403
$191$	1.40112e8	−	8.08934e7i	0.105279	−	0.0607827i	−0.446436	−	0.894815i	$-0.647307\pi$
$191$	1.40112e8	−	8.08934e7i	0.105279	−	0.0607827i	0.551715	+	0.834033i	$0.313974\pi$
$192$		0			0
$193$	7.94199e8	−	1.37559e9i	0.572401	−	0.991427i	−0.423918	−	0.905701i	$-0.639346\pi$
$193$	7.94199e8	−	1.37559e9i	0.572401	−	0.991427i	0.996319	−	0.0857264i	$-0.0273211\pi$
$194$	2.86328e9	+	1.65311e9i	2.02142	+	1.16707i
$195$		0			0
$196$	−3.35085e8	−	5.80385e8i	−0.227055	−	0.393271i
$197$			5.37769e8i			0.357052i	0.983935	+	0.178526i	$0.0571328\pi$
$197$			5.37769e8i			0.357052i	−0.983935	+	0.178526i	$0.942867\pi$
$198$		0			0
$199$	6.47586e8			0.412938			0.206469	−	0.978453i	$-0.433803\pi$
$199$	6.47586e8			0.412938			0.206469	+	0.978453i	$0.433803\pi$
$200$	−5.29178e7	+	3.05521e7i	−0.0330737	+	0.0190951i
$201$		0			0
$202$	−1.16229e9	+	2.01314e9i	−0.698084	+	1.20912i
$203$	−6.98510e8	−	4.03285e8i	−0.411328	−	0.237481i
$204$		0			0
$205$	−2.10521e8	−	3.64633e8i	−0.119201	−	0.206462i
$206$			3.72812e9i			2.07024i
$207$		0			0
$208$	−1.73729e9			−0.928152
$209$	−1.14141e8	+	6.58993e7i	−0.0598214	+	0.0345379i
$210$		0			0
$211$	−2.90552e7	+	5.03250e7i	−0.0146586	+	0.0253895i	−0.873262	−	0.487252i	$-0.837999\pi$
$211$	−2.90552e7	+	5.03250e7i	−0.0146586	+	0.0253895i	0.858603	+	0.512641i	$0.171333\pi$
$212$	1.41789e9	+	8.18619e8i	0.701938	+	0.405264i
$213$		0			0
$214$	−2.53168e8	−	4.38499e8i	−0.120713	−	0.209081i
$215$		−	7.91619e8i		−	0.370478i
$216$		0			0
$217$	6.15086e8			0.277394
$218$	2.13816e9	−	1.23447e9i	0.946704	−	0.546580i
$219$		0			0
$220$	1.93738e8	−	3.35563e8i	0.0827034	−	0.143246i
$221$	1.66883e9	+	9.63499e8i	0.699588	+	0.403908i
$222$		0			0
$223$	−2.20100e9	−	3.81224e9i	−0.890021	−	1.54156i	−0.839848	−	0.542821i	$-0.817356\pi$
$223$	−2.20100e9	−	3.81224e9i	−0.890021	−	1.54156i	−0.0501724	−	0.998741i	$-0.515977\pi$
$224$		−	2.57222e9i		−	1.02168i
$225$		0			0
$226$	−6.45992e9			−2.47624
$227$	−3.06220e9	+	1.76796e9i	−1.15327	+	0.665839i	−0.949681	−	0.313218i	$-0.898593\pi$
$227$	−3.06220e9	+	1.76796e9i	−1.15327	+	0.665839i	−0.203586	+	0.979057i	$0.565260\pi$
$228$		0			0
$229$	9.32847e8	−	1.61574e9i	0.339210	−	0.587529i	−0.645074	−	0.764120i	$-0.723174\pi$
$229$	9.32847e8	−	1.61574e9i	0.339210	−	0.587529i	0.984284	+	0.176591i	$0.0565070\pi$
$230$	−2.05345e9	−	1.18556e9i	−0.733793	−	0.423656i
$231$		0			0
$232$	4.13885e7	+	7.16870e7i	0.0142866	+	0.0247450i
$233$			2.72132e9i			0.923328i	0.887055	+	0.461664i	$0.152747\pi$
$233$			2.72132e9i			0.923328i	−0.887055	+	0.461664i	$0.847253\pi$
$234$		0			0
$235$	−9.16191e8			−0.300410
$236$	2.94561e9	−	1.70065e9i	0.949570	−	0.548234i
$237$		0			0
$238$	−1.47118e9	+	2.54815e9i	−0.458518	+	0.794177i
$239$	−1.96987e9	−	1.13730e9i	−0.603734	−	0.348566i	0.166775	−	0.985995i	$-0.446665\pi$
$239$	−1.96987e9	−	1.13730e9i	−0.603734	−	0.348566i	−0.770509	+	0.637429i	$0.779998\pi$
$240$		0			0
$241$	8.73336e8	+	1.51266e9i	0.258889	+	0.448408i	0.965945	−	0.258749i	$-0.0833104\pi$
$241$	8.73336e8	+	1.51266e9i	0.258889	+	0.448408i	−0.707056	+	0.707158i	$0.749977\pi$
$242$		−	3.72500e9i		−	1.08609i
$243$		0			0
$244$	−1.86893e8			−0.0527272
$245$	−5.25387e8	+	3.03333e8i	−0.145819	+	0.0841889i
$246$		0			0
$247$	−2.43637e8	+	4.21992e8i	−0.0654570	+	0.113375i
$248$	−5.46681e7	−	3.15626e7i	−0.0144520	−	0.00834385i
$249$		0			0
$250$	−1.84174e9	−	3.18999e9i	−0.471486	−	0.816638i
$251$		−	1.37549e9i		−	0.346547i	−0.984874	−	0.173274i	$-0.944566\pi$
$251$		−	1.37549e9i		−	0.346547i	0.984874	−	0.173274i	$-0.0554345\pi$
$252$		0			0
$253$	3.27417e9			0.799132
$254$	−5.36594e9	+	3.09802e9i	−1.28917	+	0.744303i
$255$		0			0
$256$	−2.27535e9	+	3.94102e9i	−0.529770	+	0.917589i
$257$	−6.87340e9	−	3.96836e9i	−1.57558	−	0.909659i	−0.995466	−	0.0951209i	$-0.969676\pi$
$257$	−6.87340e9	−	3.96836e9i	−1.57558	−	0.909659i	−0.580110	−	0.814538i	$-0.696990\pi$
$258$		0			0
$259$	1.16827e9	+	2.02351e9i	0.259624	+	0.449683i
$260$		−	1.43254e9i		−	0.313483i
$261$		0			0
$262$	−6.49068e9			−1.37748
$263$	−2.79340e8	+	1.61277e8i	−0.0583863	+	0.0337093i	−0.528909	−	0.848679i	$-0.677399\pi$
$263$	−2.79340e8	+	1.61277e8i	−0.0583863	+	0.0337093i	0.470523	+	0.882388i	$0.344065\pi$
$264$		0			0
$265$	7.41046e8	−	1.28353e9i	0.150266	−	0.260269i
$266$	−6.44344e8	−	3.72012e8i	−0.128704	−	0.0743072i
$267$		0			0
$268$	2.81342e8	+	4.87299e8i	0.0545376	+	0.0944619i
$269$		−	3.47314e9i		−	0.663304i	−0.943402	−	0.331652i	$-0.892394\pi$
$269$		−	3.47314e9i		−	0.663304i	0.943402	−	0.331652i	$-0.107606\pi$
$270$		0			0
$271$	−1.44216e9			−0.267385			−0.133693	−	0.991023i	$-0.542683\pi$
$271$	−1.44216e9			−0.267385			−0.133693	+	0.991023i	$0.542683\pi$
$272$	4.37930e9	−	2.52839e9i	0.800071	−	0.461921i
$273$		0			0
$274$	−2.32988e9	+	4.03547e9i	−0.413363	+	0.715966i
$275$	2.05057e9	+	1.18390e9i	0.358544	+	0.207006i
$276$		0			0
$277$	−1.69023e9	−	2.92757e9i	−0.287096	−	0.497265i	0.686019	−	0.727583i	$-0.259357\pi$
$277$	−1.69023e9	−	2.92757e9i	−0.287096	−	0.497265i	−0.973115	+	0.230318i	$0.926023\pi$
$278$			3.20289e9i			0.536245i
$279$		0			0
$280$	−7.05600e7			−0.0114796
$281$	−3.48369e9	+	2.01131e9i	−0.558745	+	0.322592i	−0.752642	−	0.658430i	$-0.771221\pi$
$281$	−3.48369e9	+	2.01131e9i	−0.558745	+	0.322592i	0.193896	+	0.981022i	$0.437887\pi$
$282$		0			0
$283$	5.21264e9	−	9.02856e9i	0.812666	−	1.40758i	−0.0983264	−	0.995154i	$-0.531349\pi$
$283$	5.21264e9	−	9.02856e9i	0.812666	−	1.40758i	0.910992	−	0.412424i	$-0.135318\pi$
$284$	−3.65589e9	−	2.11073e9i	−0.561978	−	0.324458i
$285$		0			0
$286$	2.01003e9	+	3.48147e9i	0.300426	+	0.520354i
$287$			3.28207e9i			0.483749i
$288$		0			0
$289$	1.36679e9			0.195935
$290$	−2.01171e9	+	1.16146e9i	−0.284429	+	0.164215i
$291$		0			0
$292$	3.43142e9	−	5.94340e9i	0.472001	−	0.817530i
$293$	9.00032e9	+	5.19634e9i	1.22120	+	0.705061i	0.965174	−	0.261608i	$-0.0842528\pi$
$293$	9.00032e9	+	5.19634e9i	1.22120	+	0.705061i	0.256028	+	0.966669i	$0.417586\pi$
$294$		0			0
$295$	−1.53949e9	−	2.66648e9i	−0.203278	−	0.352087i
$296$		−	2.39796e8i		−	0.0312374i
$297$		0			0
$298$	1.83918e10			2.33216
$299$	1.04832e10	−	6.05248e9i	1.31162	−	0.757266i
$300$		0			0
$301$	−3.08538e9	+	5.34404e9i	−0.375874	+	0.651034i
$302$	8.24079e9	+	4.75782e9i	0.990698	+	0.571980i
$303$		0			0
$304$	6.39347e8	+	1.10738e9i	0.0748587	+	0.129659i
$305$			1.69183e8i			0.0195505i
$306$		0			0
$307$	−2.99309e9			−0.336951			−0.168476	−	0.985706i	$-0.553884\pi$
$307$	−2.99309e9			−0.336951			−0.168476	+	0.985706i	$0.553884\pi$
$308$	−2.61576e9	+	1.51021e9i	−0.290666	+	0.167816i
$309$		0			0
$310$	8.85725e8	−	1.53412e9i	0.0959074	−	0.166116i
$311$	5.58441e9	+	3.22416e9i	0.596947	+	0.344647i	0.767840	−	0.640642i	$-0.221332\pi$
$311$	5.58441e9	+	3.22416e9i	0.596947	+	0.344647i	−0.170893	+	0.985290i	$0.554665\pi$
$312$		0			0
$313$	−1.63869e7	−	2.83829e7i	−0.00170733	−	0.00295719i	0.865170	−	0.501478i	$-0.167210\pi$
$313$	−1.63869e7	−	2.83829e7i	−0.00170733	−	0.00295719i	−0.866878	+	0.498521i	$0.833877\pi$
$314$			1.70586e10i			1.75479i
$315$		0			0
$316$	5.69928e9			0.571573
$317$	1.02015e10	−	5.88983e9i	1.01024	−	0.583264i	0.0989806	−	0.995089i	$-0.468442\pi$
$317$	1.02015e10	−	5.88983e9i	1.01024	−	0.583264i	0.911263	+	0.411825i	$0.135108\pi$
$318$		0			0
$319$	1.60380e9	−	2.77787e9i	0.154878	−	0.268256i
$320$	−3.05491e9	−	1.76375e9i	−0.291339	−	0.168205i
$321$		0			0
$322$	9.24160e9	+	1.60069e10i	0.859654	+	1.48896i
$323$		−	1.41832e9i		−	0.130306i
$324$		0			0
$325$	8.75399e9			0.784644
$326$	−1.29905e10	+	7.50008e9i	−1.15015	+	0.664042i
$327$		0			0
$328$	1.68417e8	−	2.91706e8i	0.0145509	−	0.0252029i
$329$	6.18500e9	+	3.57091e9i	0.527905	+	0.304786i
$330$		0			0
$331$	6.00499e9	+	1.04009e10i	0.500265	+	0.866484i	1.00000		0.000305936i	$9.73825e-5\pi$
$331$	6.00499e9	+	1.04009e10i	0.500265	+	0.866484i	−0.499735	+	0.866178i	$0.666569\pi$
$332$		−	1.15060e10i		−	0.947049i
$333$		0			0
$334$	−4.40705e9			−0.354130
$335$	4.41123e8	−	2.54682e8i	0.0350252	−	0.0202218i
$336$		0			0
$337$	−7.96069e9	+	1.37883e10i	−0.617207	+	1.06903i	0.372786	+	0.927917i	$0.378403\pi$
$337$	−7.96069e9	+	1.37883e10i	−0.617207	+	1.06903i	−0.989993	+	0.141117i	$0.954931\pi$
$338$	−2.98823e9	−	1.72525e9i	−0.228953	−	0.132186i
$339$		0			0
$340$	2.08487e9	+	3.61109e9i	0.156014	+	0.270224i
$341$			2.44611e9i			0.180908i
$342$		0			0
$343$	1.48174e10			1.07052
$344$	5.48450e8	−	3.16647e8i	0.0391654	−	0.0226122i
$345$		0			0
$346$	1.14853e10	−	1.98931e10i	0.801380	−	1.38803i
$347$	−4.28503e9	−	2.47396e9i	−0.295553	−	0.170638i	0.344890	−	0.938643i	$-0.387916\pi$
$347$	−4.28503e9	−	2.47396e9i	−0.295553	−	0.170638i	−0.640444	+	0.768005i	$0.721249\pi$
$348$		0			0
$349$	3.64784e9	+	6.31824e9i	0.245886	+	0.425887i	0.962380	−	0.271706i	$-0.0875878\pi$
$349$	3.64784e9	+	6.31824e9i	0.245886	+	0.425887i	−0.716494	+	0.697593i	$0.754254\pi$
$350$			1.33666e10i			0.890733i
$351$		0			0
$352$	1.02293e10			0.666311
$353$	6.00913e9	−	3.46938e9i	0.387002	−	0.223436i	−0.293858	−	0.955849i	$-0.594939\pi$
$353$	6.00913e9	−	3.46938e9i	0.387002	−	0.223436i	0.680860	+	0.732413i	$0.261606\pi$
$354$		0			0
$355$	−1.91071e9	+	3.30945e9i	−0.120305	+	0.208374i
$356$	−1.55959e10	−	9.00429e9i	−0.970980	−	0.560595i
$357$		0			0
$358$	−1.44684e10	−	2.50600e10i	−0.880822	−	1.52563i
$359$		−	1.60096e10i		−	0.963838i	−0.876216	−	0.481919i	$-0.839940\pi$
$359$		−	1.60096e10i		−	0.963838i	0.876216	−	0.481919i	$-0.160060\pi$
$360$		0			0
$361$	−1.66249e10			−0.978883
$362$	−9.17102e9	+	5.29489e9i	−0.534052	+	0.308335i
$363$		0			0
$364$	−5.58341e9	+	9.67075e9i	−0.318049	+	0.550877i
$365$	−5.38020e9	−	3.10626e9i	−0.303129	−	0.175011i
$366$		0			0
$367$	−6.81822e9	−	1.18095e10i	−0.375843	−	0.650980i	0.614610	−	0.788831i	$-0.289314\pi$
$367$	−6.81822e9	−	1.18095e10i	−0.375843	−	0.650980i	−0.990453	+	0.137852i	$0.955980\pi$
$368$		−	3.17655e10i		−	1.73207i
$369$		0			0
$370$	6.72926e9			0.359054
$371$	−1.00053e10	+	5.77654e9i	−0.528121	+	0.304911i
$372$		0			0
$373$	1.22031e10	−	2.11364e10i	0.630427	−	1.09193i	−0.357037	−	0.934090i	$-0.616213\pi$
$373$	1.22031e10	−	2.11364e10i	0.630427	−	1.09193i	0.987464	−	0.157842i	$-0.0504536\pi$
$374$	−1.01336e10	−	5.85064e9i	−0.517938	−	0.299032i
$375$		0			0
$376$	−3.66477e8	−	6.34756e8i	−0.0183356	−	0.0317582i
$377$		−	1.18589e10i		−	0.587055i
$378$		0			0
$379$	−1.98392e10			−0.961542			−0.480771	−	0.876846i	$-0.659643\pi$
$379$	−1.98392e10			−0.961542			−0.480771	+	0.876846i	$0.659643\pi$
$380$	−9.13128e8	+	5.27195e8i	−0.0437923	+	0.0252835i
$381$		0			0
$382$	−1.81605e9	+	3.14550e9i	−0.0852855	+	0.147719i
$383$	−1.30885e10	−	7.55663e9i	−0.608266	−	0.351183i	0.164020	−	0.986457i	$-0.447554\pi$
$383$	−1.30885e10	−	7.55663e9i	−0.608266	−	0.351183i	−0.772287	+	0.635274i	$0.780887\pi$
$384$		0			0
$385$	1.36710e9	+	2.36789e9i	0.0622239	+	0.107775i
$386$			3.56594e10i			1.60630i
$387$		0			0
$388$	−3.65232e10			−1.61154
$389$	1.55877e10	−	8.99957e9i	0.680744	−	0.393028i	−0.119391	−	0.992847i	$-0.538094\pi$
$389$	1.55877e10	−	8.99957e9i	0.680744	−	0.393028i	0.800135	+	0.599819i	$0.204761\pi$
$390$		0			0
$391$	−1.76171e10	+	3.05138e10i	−0.753751	+	1.30554i
$392$	−4.20310e8	−	2.42666e8i	−0.0178002	−	0.0102770i
$393$		0			0
$394$	−6.03645e9	−	1.04554e10i	−0.250494	−	0.433867i
$395$		−	5.15922e9i		−	0.211931i
$396$		0			0
$397$	−2.35673e10			−0.948739			−0.474370	−	0.880326i	$-0.657324\pi$
$397$	−2.35673e10			−0.948739			−0.474370	+	0.880326i	$0.657324\pi$
$398$	−1.25905e10	+	7.26914e9i	−0.501778	+	0.289701i
$399$		0			0
$400$	1.14860e10	−	1.98943e10i	0.448672	−	0.777122i
$401$	1.19245e10	+	6.88461e9i	0.461172	+	0.266257i	0.712537	−	0.701635i	$-0.247546\pi$
$401$	1.19245e10	+	6.88461e9i	0.461172	+	0.266257i	−0.251365	+	0.967892i	$0.580880\pi$
$402$		0			0
$403$	4.52176e9	+	7.83193e9i	0.171430	+	0.296926i
$404$		−	2.56791e10i		−	0.963950i
$405$		0			0
$406$	1.81075e10			0.666428
$407$	−8.04719e9	+	4.64605e9i	−0.293269	+	0.169319i
$408$		0			0
$409$	−1.79240e10	+	3.10452e10i	−0.640533	+	1.10944i	0.344781	+	0.938683i	$0.387953\pi$
$409$	−1.79240e10	+	3.10452e10i	−0.640533	+	1.10944i	−0.985314	+	0.170752i	$0.945380\pi$
$410$	8.18598e9	+	4.72618e9i	0.289691	+	0.167253i
$411$		0			0
$412$	−2.05919e10	−	3.56662e10i	−0.714672	−	1.23785i
$413$			2.40011e10i			0.824955i
$414$		0			0
$415$	−1.04157e10			−0.351153
$416$	3.27523e10	−	1.89095e10i	1.09362	−	0.631404i
$417$		0			0
$418$	1.47944e9	−	2.56246e9i	0.0484609	−	0.0839367i
$419$	1.93987e10	+	1.11998e10i	0.629384	+	0.363375i	0.780513	−	0.625139i	$-0.214958\pi$
$419$	1.93987e10	+	1.11998e10i	0.629384	+	0.363375i	−0.151130	+	0.988514i	$0.548291\pi$
$420$		0			0
$421$	7.47674e9	+	1.29501e10i	0.238004	+	0.412235i	0.960141	−	0.279515i	$-0.0901736\pi$
$421$	7.47674e9	+	1.29501e10i	0.238004	+	0.412235i	−0.722138	+	0.691750i	$0.756840\pi$
$422$		−	1.30457e9i		−	0.0411357i
$423$		0			0
$424$	1.18567e9			0.0366861
$425$	−2.20667e10	+	1.27402e10i	−0.676367	+	0.390501i
$426$		0			0
$427$	6.59402e8	−	1.14212e9i	0.0198353	−	0.0343557i
$428$	4.84401e9	+	2.79669e9i	0.144355	+	0.0833431i
$429$		0			0
$430$	8.88590e9	+	1.53908e10i	0.259913	+	0.450182i
$431$			6.40436e10i			1.85595i	0.372640	+	0.927976i	$0.378453\pi$
$431$			6.40436e10i			1.85595i	−0.372640	+	0.927976i	$0.621547\pi$
$432$		0			0
$433$	−5.22954e9			−0.148769			−0.0743843	−	0.997230i	$-0.523699\pi$
$433$	−5.22954e9			−0.148769			−0.0743843	+	0.997230i	$0.523699\pi$
$434$	−1.19586e10	+	6.90433e9i	−0.337072	+	0.194609i
$435$		0			0
$436$	−1.36369e10	+	2.36198e10i	−0.377372	+	0.653628i
$437$	−7.71593e9	−	4.45480e9i	−0.211574	−	0.122152i
$438$		0			0
$439$	−2.17401e10	−	3.76549e10i	−0.585332	−	1.01383i	−0.994834	−	0.101516i	$-0.967631\pi$
$439$	−2.17401e10	−	3.76549e10i	−0.585332	−	1.01383i	0.409501	−	0.912309i	$-0.365703\pi$
$440$		−	2.80606e8i		−	0.00748664i
$441$		0			0
$442$	−4.32610e10			−1.13346
$443$	3.27996e10	−	1.89368e10i	0.851634	−	0.491691i	−0.00956760	−	0.999954i	$-0.503046\pi$
$443$	3.27996e10	−	1.89368e10i	0.851634	−	0.491691i	0.861202	+	0.508263i	$0.169712\pi$
$444$		0			0
$445$	−8.15104e9	+	1.41180e10i	−0.207861	+	0.360026i
$446$	8.55846e10	+	4.94123e10i	2.16300	+	1.24881i
$447$		0			0
$448$	1.37487e10	+	2.38134e10i	0.341310	+	0.591166i
$449$		−	2.95505e10i		−	0.727076i	−0.931579	−	0.363538i	$-0.881569\pi$
$449$		−	2.95505e10i		−	0.727076i	0.931579	−	0.363538i	$-0.118431\pi$
$450$		0			0
$451$	−1.30523e10			−0.315486
$452$	6.18008e10	−	3.56807e10i	1.48061	−	0.854830i
$453$		0			0
$454$	3.96906e10	−	6.87462e10i	0.934253	−	1.61817i
$455$	8.75435e9	+	5.05432e9i	0.204258	+	0.117928i
$456$		0			0
$457$	1.01091e10	+	1.75094e10i	0.231764	+	0.401427i	0.958327	−	0.285672i	$-0.0922169\pi$
$457$	1.01091e10	+	1.75094e10i	0.231764	+	0.401427i	−0.726563	+	0.687100i	$0.758884\pi$
$458$			4.18847e10i			0.951905i
$459$		0			0
$460$	2.61933e10			0.585005
$461$	−6.07799e10	+	3.50913e10i	−1.34573	+	0.776955i	−0.987641	−	0.156734i	$-0.949903\pi$
$461$	−6.07799e10	+	3.50913e10i	−1.34573	+	0.776955i	−0.358085	+	0.933689i	$0.616570\pi$
$462$		0			0
$463$	−2.08004e9	+	3.60274e9i	−0.0452635	+	0.0783987i	−0.887770	−	0.460288i	$-0.847746\pi$
$463$	−2.08004e9	+	3.60274e9i	−0.0452635	+	0.0783987i	0.842506	+	0.538687i	$0.181079\pi$
$464$	−2.69505e10	−	1.55599e10i	−0.581427	−	0.335687i
$465$		0			0
$466$	−3.05467e10	−	5.29085e10i	−0.647770	−	1.12197i
$467$		−	2.88138e10i		−	0.605806i	−0.953021	−	0.302903i	$-0.902044\pi$
$467$		−	2.88138e10i		−	0.605806i	0.953021	−	0.302903i	$-0.0979558\pi$
$468$		0			0
$469$	−3.97056e9			−0.0820654
$470$	1.78128e10	−	1.02842e10i	0.365040	−	0.210756i
$471$		0			0
$472$	1.23159e9	−	2.13318e9i	0.0248142	−	0.0429794i
$473$	−2.12524e10	−	1.22701e10i	−0.424584	−	0.245134i
$474$		0			0
$475$	−3.22159e9	−	5.57996e9i	−0.0632843	−	0.109612i
$476$		−	3.25036e10i		−	0.633145i
$477$		0			0
$478$	5.10649e10			0.978161
$479$	−3.87242e10	+	2.23574e10i	−0.735598	+	0.424698i	−0.820467	−	0.571694i	$-0.806286\pi$
$479$	−3.87242e10	+	2.23574e10i	−0.735598	+	0.424698i	0.0848686	+	0.996392i	$0.472953\pi$
$480$		0			0
$481$	−1.71770e10	+	2.97514e10i	−0.320897	+	0.555810i
$482$	−3.39592e10	−	1.96063e10i	−0.629172	−	0.363252i
$483$		0			0
$484$	2.05746e10	+	3.56363e10i	0.374930	+	0.649399i
$485$			3.30623e10i			0.597538i
$486$		0			0
$487$	5.72836e10			1.01839			0.509195	−	0.860651i	$-0.329943\pi$
$487$	5.72836e10			1.01839			0.509195	+	0.860651i	$0.329943\pi$
$488$	−1.17214e8	+	6.76733e7i	−0.00206680	+	0.00119327i
$489$		0			0
$490$	6.80980e9	−	1.17949e10i	0.118127	−	0.204602i
$491$	−6.28095e10	−	3.62631e10i	−1.08069	−	0.623934i	−0.149604	−	0.988746i	$-0.547800\pi$
$491$	−6.28095e10	−	3.62631e10i	−1.08069	−	0.623934i	−0.931081	+	0.364812i	$0.881133\pi$
$492$		0			0
$493$	1.72590e10	+	2.98935e10i	0.292165	+	0.506044i
$494$		−	1.09393e10i		−	0.183688i
$495$		0			0
$496$	2.37318e10			0.392106
$497$	2.57976e10	−	1.48942e10i	0.422818	−	0.244114i
$498$		0			0
$499$	1.32184e10	−	2.28949e10i	0.213195	−	0.369264i	−0.739518	−	0.673137i	$-0.764946\pi$
$499$	1.32184e10	−	2.28949e10i	0.213195	−	0.369264i	0.952713	+	0.303873i	$0.0982798\pi$
$500$	3.52392e10	+	2.03454e10i	0.563827	+	0.325526i
$501$		0			0
$502$	1.54398e10	+	2.67426e10i	0.243124	+	0.421103i
$503$		−	7.52828e10i		−	1.17604i	−0.808845	−	0.588022i	$-0.799907\pi$
$503$		−	7.52828e10i		−	1.17604i	0.808845	−	0.588022i	$-0.200093\pi$
$504$		0			0
$505$	−2.32457e10			−0.357419
$506$	−6.36571e10	+	3.67524e10i	−0.971056	+	0.560640i
$507$		0			0
$508$	3.42232e10	−	5.92764e10i	0.513886	−	0.890076i
$509$	−5.58746e10	−	3.22592e10i	−0.832421	−	0.480599i	0.0222598	−	0.999752i	$-0.492914\pi$
$509$	−5.58746e10	−	3.22592e10i	−0.832421	−	0.480599i	−0.854681	+	0.519154i	$0.826247\pi$
$510$		0			0
$511$	2.42137e10	+	4.19393e10i	0.355122	+	0.615089i
$512$		−	9.61394e10i		−	1.39901i
$513$		0			0
$514$	1.78179e11			2.55272
$515$	−3.22864e10	+	1.86406e10i	−0.458977	+	0.264991i
$516$		0			0
$517$	−1.42010e10	+	2.45968e10i	−0.198772	+	0.344284i
$518$	−4.54277e10	−	2.62277e10i	−0.630959	−	0.364285i
$519$		0			0
$520$	−5.18717e8	−	8.98444e8i	−0.00709442	−	0.0122879i
$521$			7.65146e10i			1.03847i	0.854632	+	0.519235i	$0.173783\pi$
$521$			7.65146e10i			1.03847i	−0.854632	+	0.519235i	$0.826217\pi$
$522$		0			0
$523$	−8.46771e10			−1.13177			−0.565886	−	0.824483i	$-0.691466\pi$
$523$	−8.46771e10			−1.13177			−0.565886	+	0.824483i	$0.691466\pi$
$524$	6.20951e10	−	3.58506e10i	0.823630	−	0.475523i
$525$		0			0
$526$	3.62067e9	−	6.27118e9i	0.0472983	−	0.0819231i
$527$	−2.27966e10	−	1.31616e10i	−0.295548	−	0.170635i
$528$		0			0
$529$	7.15113e10	+	1.23861e11i	0.913171	+	1.58166i
$530$			3.32729e10i			0.421684i
$531$		0			0
$532$	8.21909e9			0.102607
$533$	−4.17907e10	+	2.41279e10i	−0.517811	+	0.298958i
$534$		0			0
$535$	2.53168e9	−	4.38499e9i	0.0309025	−	0.0535247i
$536$	3.52898e8	+	2.03746e8i	0.00427553	+	0.00246848i
$537$		0			0
$538$	3.89859e10	+	6.75255e10i	0.465348	+	0.806007i
$539$			1.88066e10i			0.222821i
$540$		0			0
$541$	1.43470e11			1.67483			0.837415	−	0.546568i	$-0.184066\pi$
$541$	1.43470e11			1.67483			0.837415	+	0.546568i	$0.184066\pi$
$542$	2.80389e10	−	1.61883e10i	0.324910	−	0.187587i
$543$		0			0
$544$	−5.50405e10	+	9.53329e10i	−0.628473	+	1.08855i
$545$	2.13816e10	+	1.23447e10i	0.242356	+	0.139924i
$546$		0			0
$547$	−8.20857e10	−	1.42177e11i	−0.916892	−	1.58810i	−0.804107	−	0.594485i	$-0.797356\pi$
$547$	−8.20857e10	−	1.42177e11i	−0.916892	−	1.58810i	−0.112786	−	0.993619i	$-0.535977\pi$
$548$		−	5.14755e10i		−	0.570792i
$549$		0			0
$550$	−5.31568e10			−0.580908
$551$	−7.55908e9	+	4.36424e9i	−0.0820092	+	0.0473480i
$552$		0			0
$553$	−2.01084e10	+	3.48287e10i	−0.215019	+	0.372423i
$554$	6.57237e10	+	3.79456e10i	0.697723	+	0.402831i
$555$		0			0
$556$	−1.76909e10	−	3.06415e10i	−0.185119	−	0.320635i
$557$		−	1.54420e11i		−	1.60429i	−0.597130	−	0.802145i	$-0.703692\pi$
$557$		−	1.54420e11i		−	1.60429i	0.597130	−	0.802145i	$-0.296308\pi$
$558$		0			0
$559$	−9.07278e10			−0.929166
$560$	2.29729e10	−	1.32634e10i	0.233595	−	0.134866i
$561$		0			0
$562$	4.51538e10	−	7.82086e10i	0.452636	−	0.783988i
$563$	1.33907e11	+	7.73112e10i	1.33281	+	0.769500i	0.985730	−	0.168334i	$-0.0538386\pi$
$563$	1.33907e11	+	7.73112e10i	1.33281	+	0.769500i	0.347084	+	0.937834i	$0.387172\pi$
$564$		0			0
$565$	−3.22996e10	−	5.59446e10i	−0.316959	−	0.548990i
$566$			2.34047e11i			2.28054i
$567$		0			0
$568$	−3.05714e9			−0.0293712
$569$	9.99216e10	−	5.76898e10i	0.953258	−	0.550364i	0.0591666	−	0.998248i	$-0.481156\pi$
$569$	9.99216e10	−	5.76898e10i	0.953258	−	0.550364i	0.894092	+	0.447884i	$0.147822\pi$
$570$		0			0
$571$	8.17051e10	−	1.41517e11i	0.768608	−	1.33127i	−0.169710	−	0.985494i	$-0.554283\pi$
$571$	8.17051e10	−	1.41517e11i	0.768608	−	1.33127i	0.938318	−	0.345774i	$-0.112384\pi$
$572$	−3.84591e10	−	2.22044e10i	−0.359265	−	0.207422i
$573$		0			0
$574$	−3.68411e10	−	6.38107e10i	−0.339379	−	0.587822i
$575$			1.60063e11i			1.46426i
$576$		0			0
$577$	7.42282e10			0.669678			0.334839	−	0.942275i	$-0.391318\pi$
$577$	7.42282e10			0.669678			0.334839	+	0.942275i	$0.391318\pi$
$578$	−2.65735e10	+	1.53422e10i	−0.238088	+	0.137460i
$579$		0			0
$580$	1.28304e10	−	2.22230e10i	0.113378	−	0.196377i
$581$	7.03140e10	+	4.05958e10i	0.617074	+	0.356268i
$582$		0			0
$583$	−2.29724e10	−	3.97894e10i	−0.198853	−	0.344424i
$584$		−	4.97002e9i		−	0.0427274i
$585$		0			0
$586$	−2.33315e11			−1.97857
$587$	5.82728e10	−	3.36438e10i	0.490810	−	0.283369i	−0.234100	−	0.972212i	$-0.575214\pi$
$587$	5.82728e10	−	3.36438e10i	0.490810	−	0.283369i	0.724911	+	0.688843i	$0.241881\pi$
$588$		0			0
$589$	3.32815e9	−	5.76452e9i	0.0276529	−	0.0478963i
$590$	5.98623e10	+	3.45615e10i	0.494021	+	0.285223i
$591$		0			0
$592$	4.50753e10	+	7.80728e10i	0.366988	+	0.635642i
$593$			2.36444e10i			0.191210i	0.995419	+	0.0956048i	$0.0304785\pi$
$593$			2.36444e10i			0.191210i	−0.995419	+	0.0956048i	$0.969521\pi$
$594$		0			0
$595$	−2.94235e10			−0.234761
$596$	−1.75951e11	+	1.01585e11i	−1.39446	+	0.805092i
$597$		0			0
$598$	−1.35878e11	+	2.35347e11i	−1.06254	+	1.84037i
$599$	2.62726e10	+	1.51685e10i	0.204078	+	0.117825i	0.598556	−	0.801081i	$-0.295741\pi$
$599$	2.62726e10	+	1.51685e10i	0.204078	+	0.117825i	−0.394478	+	0.918905i	$0.629075\pi$
$600$		0			0
$601$	−1.68956e10	−	2.92640e10i	−0.129501	−	0.224303i	0.793982	−	0.607941i	$-0.208004\pi$
$601$	−1.68956e10	−	2.92640e10i	−0.129501	−	0.224303i	−0.923484	+	0.383638i	$0.874671\pi$
$602$		−	1.38533e11i		−	1.05480i
$603$		0			0
$604$	−1.05117e11			−0.789818
$605$	3.22594e10	−	1.86250e10i	0.240788	−	0.139019i
$606$		0			0
$607$	1.91183e10	−	3.31139e10i	0.140830	−	0.243925i	−0.786979	−	0.616979i	$-0.788356\pi$
$607$	1.91183e10	−	3.31139e10i	0.140830	−	0.243925i	0.927809	+	0.373055i	$0.121690\pi$
$608$	−2.41066e10	−	1.39179e10i	−0.176409	−	0.101850i
$609$		0			0
$610$	−1.89908e9	−	3.28930e9i	−0.0137159	−	0.0237566i
$611$			1.05005e11i			0.753435i
$612$		0			0
$613$	1.08066e11			0.765330			0.382665	−	0.923887i	$-0.375006\pi$
$613$	1.08066e11			0.765330			0.382665	+	0.923887i	$0.375006\pi$
$614$	5.81924e10	−	3.35974e10i	0.409442	−	0.236392i
$615$		0			0
$616$	−1.09368e9	+	1.89431e9i	−0.00759569	+	0.0131561i
$617$	−4.09230e9	−	2.36269e9i	−0.0282375	−	0.0163029i	0.485815	−	0.874062i	$-0.338523\pi$
$617$	−4.09230e9	−	2.36269e9i	−0.0282375	−	0.0163029i	−0.514052	+	0.857759i	$0.671856\pi$
$618$		0			0
$619$	−1.14923e10	−	1.99052e10i	−0.0782786	−	0.135583i	0.824229	−	0.566257i	$-0.191609\pi$
$619$	−1.14923e10	−	1.99052e10i	−0.0782786	−	0.135583i	−0.902507	+	0.430674i	$0.858276\pi$
$620$			1.95688e10i			0.132434i
$621$		0			0
$622$	−1.44764e11			−0.967165
$623$	1.10052e11	−	6.35383e10i	0.730540	−	0.421778i
$624$		0			0
$625$	−4.80328e10	+	8.31952e10i	−0.314788	+	0.545228i
$626$	6.37194e8	+	3.67884e8i	0.00414930	+	0.00239560i
$627$		0			0
$628$	−9.42215e10	−	1.63196e11i	−0.605775	−	1.04923i
$629$		−	9.99949e10i		−	0.638815i
$630$		0			0
$631$	−1.01892e11			−0.642722			−0.321361	−	0.946957i	$-0.604140\pi$
$631$	−1.01892e11			−0.642722			−0.321361	+	0.946957i	$0.604140\pi$
$632$	3.57441e9	−	2.06369e9i	0.0224045	−	0.0129353i
$633$		0			0
$634$	−1.32226e11	+	2.29023e11i	−0.818391	+	1.41749i
$635$	−5.36594e10	−	3.09802e10i	−0.330028	−	0.190542i
$636$		0			0
$637$	3.47651e10	+	6.02149e10i	0.211147	+	0.365718i
$638$			7.20106e10i			0.434624i
$639$		0			0
$640$	−5.28224e9			−0.0314846
$641$	−1.02021e11	+	5.89017e10i	−0.604305	+	0.348896i	−0.770733	−	0.637158i	$-0.780110\pi$
$641$	−1.02021e11	+	5.89017e10i	−0.604305	+	0.348896i	0.166428	+	0.986054i	$0.446777\pi$
$642$		0			0
$643$	1.31340e10	−	2.27488e10i	0.0768339	−	0.133080i	−0.825048	−	0.565062i	$-0.808852\pi$
$643$	1.31340e10	−	2.27488e10i	0.0768339	−	0.133080i	0.901882	+	0.431982i	$0.142186\pi$
$644$	−1.76825e11	−	1.02090e11i	−1.02802	−	0.593526i
$645$		0			0
$646$	1.59206e10	+	2.75754e10i	0.0914178	+	0.158340i
$647$		−	3.10527e11i		−	1.77208i	−0.463612	−	0.886038i	$-0.653447\pi$
$647$		−	3.10527e11i		−	1.77208i	0.463612	−	0.886038i	$-0.346553\pi$
$648$		0			0
$649$	−9.54486e10			−0.538010
$650$	−1.70197e11	+	9.82633e10i	−0.953451	+	0.550475i
$651$		0			0
$652$	8.28518e10	−	1.43504e11i	0.458471	−	0.794095i
$653$	3.01676e10	+	1.74172e10i	0.165916	+	0.0957914i	0.580659	−	0.814147i	$-0.302795\pi$
$653$	3.01676e10	+	1.74172e10i	0.165916	+	0.0957914i	−0.414743	+	0.909939i	$0.636128\pi$
$654$		0			0
$655$	−3.24534e10	−	5.62109e10i	−0.176317	−	0.305390i
$656$			1.26632e11i			0.683796i
$657$		0			0
$658$	−1.60333e11			−0.855304
$659$	−3.26595e10	+	1.88560e10i	−0.173168	+	0.0999787i	−0.584079	−	0.811697i	$-0.698544\pi$
$659$	−3.26595e10	+	1.88560e10i	−0.173168	+	0.0999787i	0.410911	+	0.911676i	$0.365211\pi$
$660$		0			0
$661$	6.98094e10	−	1.20913e11i	0.365686	−	0.633387i	−0.623200	−	0.782062i	$-0.714168\pi$
$661$	6.98094e10	−	1.20913e11i	0.365686	−	0.633387i	0.988886	+	0.148676i	$0.0475011\pi$
$662$	−2.33501e11	−	1.34812e11i	−1.21578	−	0.701932i
$663$		0			0
$664$	−4.16628e9	−	7.21620e9i	−0.0214327	−	0.0371224i
$665$		−	7.44025e9i		−	0.0380453i
$666$		0			0
$667$	2.16834e11			1.09553
$668$	4.21614e10	−	2.43419e10i	0.211743	−	0.122250i
$669$		0			0
$670$	−5.71760e9	+	9.90318e9i	−0.0283736	+	0.0491446i
$671$	4.54203e9	+	2.62234e9i	0.0224058	+	0.0129360i
$672$		0			0
$673$	6.48916e10	+	1.12396e11i	0.316321	+	0.547884i	0.979717	−	0.200384i	$-0.0642190\pi$
$673$	6.48916e10	+	1.12396e11i	0.316321	+	0.547884i	−0.663396	+	0.748268i	$0.730886\pi$
$674$		−	3.57434e11i		−	1.73203i
$675$		0			0
$676$	3.81171e10			0.182529
$677$	2.95009e11	−	1.70324e11i	1.40437	−	0.810813i	0.409532	−	0.912296i	$-0.365692\pi$
$677$	2.95009e11	−	1.70324e11i	1.40437	−	0.810813i	0.994837	+	0.101483i	$0.0323588\pi$
$678$		0			0
$679$	1.28862e11	−	2.23196e11i	0.606242	−	1.05004i
$680$	2.61513e9	+	1.50984e9i	0.0122309	+	0.00706149i
$681$		0			0
$682$	−2.74575e10	−	4.75577e10i	−0.126918	−	0.219828i
$683$		−	1.02876e11i		−	0.472750i	−0.971662	−	0.236375i	$-0.924041\pi$
$683$		−	1.02876e11i		−	0.472750i	0.971662	−	0.236375i	$-0.0759593\pi$
$684$		0			0
$685$	−4.65976e10			−0.211642
$686$	−2.88084e11	+	1.66325e11i	−1.30084	+	0.751038i
$687$		0			0
$688$	−1.19043e11	+	2.06188e11i	−0.531312	+	0.920259i
$689$	−1.47106e11	−	8.49317e10i	−0.652760	−	0.376871i
$690$		0			0
$691$	−1.79130e11	−	3.10262e11i	−0.785698	−	1.36087i	−0.928581	−	0.371129i	$-0.878971\pi$
$691$	−1.79130e11	−	3.10262e11i	−0.785698	−	1.36087i	0.142884	−	0.989740i	$-0.454363\pi$
$692$			2.53752e11i			1.10659i
$693$		0			0
$694$	1.11081e11			0.478851
$695$	−2.77379e10	+	1.60145e10i	−0.118887	+	0.0686394i
$696$		0			0
$697$	7.02297e10	−	1.21641e11i	0.297571	−	0.515407i
$698$	−1.41844e11	−	8.18937e10i	−0.597571	−	0.345008i
$699$		0			0
$700$	−7.38288e10	−	1.27875e11i	−0.307492	−	0.532592i
$701$			2.49323e11i			1.03250i	0.856438	+	0.516250i	$0.172673\pi$
$701$			2.49323e11i			1.03250i	−0.856438	+	0.516250i	$0.827327\pi$
$702$		0			0
$703$	2.52854e10			0.103526
$704$	−9.47022e10	+	5.46764e10i	−0.385540	+	0.222592i
$705$		0			0
$706$	−7.78873e10	+	1.34905e11i	−0.313507	+	0.543011i
$707$	1.56927e11	+	9.06017e10i	0.628086	+	0.362626i
$708$		0			0
$709$	1.94437e11	+	3.36775e11i	0.769474	+	1.33277i	0.937848	+	0.347045i	$0.112815\pi$
$709$	1.94437e11	+	3.36775e11i	0.769474	+	1.33277i	−0.168374	+	0.985723i	$0.553852\pi$
$710$		−	8.57909e10i		−	0.337604i
$711$		0			0
$712$	−1.30417e10			−0.0507473
$713$	−1.43203e11	+	8.26784e10i	−0.554108	+	0.319914i
$714$		0			0
$715$	−2.01003e10	+	3.48147e10i	−0.0769091	+	0.133211i
$716$	2.76833e11	+	1.59829e11i	1.05333	+	0.608142i
$717$		0			0
$718$	1.79708e11	+	3.11263e11i	0.676191	+	1.17120i
$719$		−	3.35735e10i		−	0.125626i	−0.998025	−	0.0628132i	$-0.979993\pi$
$719$		−	3.35735e10i		−	0.125626i	0.998025	−	0.0628132i	$-0.0200072\pi$
$720$		0			0
$721$	2.90611e11			1.07540
$722$	3.23225e11	−	1.86614e11i	1.18948	−	0.686746i
$723$		0			0
$724$	5.84916e10	−	1.01310e11i	0.212882	−	0.368723i
$725$	1.35800e11	+	7.84044e10i	0.491529	+	0.283784i
$726$		0			0
$727$	−1.26557e11	−	2.19202e11i	−0.453051	−	0.784707i	0.545523	−	0.838096i	$-0.316331\pi$
$727$	−1.26557e11	−	2.19202e11i	−0.453051	−	0.784707i	−0.998574	+	0.0533888i	$0.982998\pi$
$728$			8.08692e9i			0.0287911i
$729$		0			0
$730$	1.39471e11			0.491125
$731$	2.28703e11	−	1.32042e11i	0.800946	−	0.462426i
$732$		0			0
$733$	−1.03801e11	+	1.79789e11i	−0.359572	+	0.622797i	−0.987889	−	0.155160i	$-0.950411\pi$
$733$	−1.03801e11	+	1.79789e11i	−0.359572	+	0.622797i	0.628317	+	0.777957i	$0.283744\pi$
$734$	2.65123e11	+	1.53069e11i	0.913403	+	0.527354i
$735$		0			0
$736$	3.45752e11	+	5.98860e11i	1.17829	+	2.04086i
$737$		−	1.57903e10i		−	0.0535205i
$738$		0			0
$739$	4.15014e11			1.39151			0.695753	−	0.718281i	$-0.255071\pi$
$739$	4.15014e11			1.39151			0.695753	+	0.718281i	$0.255071\pi$
$740$	−6.43775e10	+	3.71684e10i	−0.214688	+	0.123950i
$741$		0			0
$742$	1.29683e11	−	2.24618e11i	0.427827	−	0.741017i
$743$	−2.86386e11	−	1.65345e11i	−0.939715	−	0.542545i	−0.0498441	−	0.998757i	$-0.515872\pi$
$743$	−2.86386e11	−	1.65345e11i	−0.939715	−	0.542545i	−0.889871	+	0.456212i	$0.849206\pi$
$744$		0			0
$745$	9.19590e10	+	1.59278e11i	0.298517	+	0.517046i
$746$			5.47918e11i			1.76913i
$747$		0			0
$748$	1.29262e11			0.412918
$749$	−3.41816e10	+	1.97347e10i	−0.108609	+	0.0627053i
$750$		0			0
$751$	2.38989e11	−	4.13941e11i	0.751308	−	1.30130i	−0.195881	−	0.980628i	$-0.562757\pi$
$751$	2.38989e11	−	4.13941e11i	0.751308	−	1.30130i	0.947189	−	0.320676i	$-0.103910\pi$
$752$	2.38635e11	+	1.37776e11i	0.746213	+	0.430826i
$753$		0			0
$754$	1.33116e11	+	2.30563e11i	0.411855	+	0.713353i
$755$			9.51565e10i			0.292854i
$756$		0			0
$757$	−8.95066e10			−0.272566			−0.136283	−	0.990670i	$-0.543516\pi$
$757$	−8.95066e10			−0.272566			−0.136283	+	0.990670i	$0.543516\pi$
$758$	3.85719e11	−	2.22695e11i	1.16841	−	0.674580i
$759$		0			0
$760$	−3.81790e8	+	6.61280e8i	−0.00114438	+	0.00198212i
$761$	4.94910e11	+	2.85737e11i	1.47567	+	0.851976i	0.999623	−	0.0274462i	$-0.00873751\pi$
$761$	4.94910e11	+	2.85737e11i	1.47567	+	0.851976i	0.476042	+	0.879422i	$0.342071\pi$
$762$		0			0
$763$	−9.62282e10	−	1.66672e11i	−0.283925	−	0.491773i
$764$		−	4.01231e10i		−	0.117766i
$765$		0			0
$766$	3.39292e11			0.985504
$767$	−3.05607e11	+	1.76442e11i	−0.883042	+	0.509825i
$768$		0			0
$769$	−1.28097e11	+	2.21871e11i	−0.366298	+	0.634447i	−0.988984	−	0.148026i	$-0.952708\pi$
$769$	−1.28097e11	+	2.21871e11i	−0.366298	+	0.634447i	0.622686	+	0.782472i	$0.286042\pi$
$770$	−5.31589e10	−	3.06913e10i	−0.151221	−	0.0873077i
$771$		0			0
$772$	−1.96961e11	−	3.41147e11i	−0.554513	−	0.960445i
$773$			1.00523e11i			0.281543i	0.990042	+	0.140772i	$0.0449584\pi$
$773$			1.00523e11i			0.281543i	−0.990042	+	0.140772i	$0.955042\pi$
$774$		0			0
$775$	−1.19582e11			−0.331480
$776$	−2.29062e10	+	1.32249e10i	−0.0631693	+	0.0364708i
$777$		0			0
$778$	−2.02040e11	+	3.49943e11i	−0.551466	+	0.955167i
$779$	3.07592e10	+	1.77588e10i	0.0835266	+	0.0482241i
$780$		0			0
$781$	5.92321e10	+	1.02593e11i	0.159204	+	0.275749i
$782$		−	7.91007e11i		−	2.11521i
$783$		0			0
$784$	1.82459e11			0.482950
$785$	−1.47732e11	+	8.52930e10i	−0.389041	+	0.224613i
$786$		0			0
$787$	1.07894e11	−	1.86878e11i	0.281254	−	0.487146i	−0.690440	−	0.723390i	$-0.742583\pi$
$787$	1.07894e11	−	1.86878e11i	0.281254	−	0.487146i	0.971694	+	0.236244i	$0.0759164\pi$
$788$	1.15499e11	+	6.66834e10i	0.299553	+	0.172947i
$789$		0			0
$790$	5.79121e10	+	1.00307e11i	0.148683	+	0.257526i
$791$			5.03559e11i			1.28631i
$792$		0			0
$793$	1.93902e10			0.0490331
$794$	4.58200e11	−	2.64542e11i	1.15285	−	0.665598i
$795$		0			0
$796$	8.03007e10	−	1.39085e11i	0.200017	−	0.346440i
$797$	−5.80035e11	−	3.34883e11i	−1.43754	−	0.829966i	−0.439864	−	0.898064i	$-0.644973\pi$
$797$	−5.80035e11	−	3.34883e11i	−1.43754	−	0.829966i	−0.997679	+	0.0680988i	$0.978307\pi$
$798$		0			0
$799$	−1.52821e11	−	2.64693e11i	−0.374969	−	0.649465i
$800$			5.00077e11i			1.22089i
$801$		0			0
$802$	−3.09118e11			−0.747183
$803$	−1.66786e11	+	9.62941e10i	−0.401142	+	0.231599i
$804$		0			0
$805$	−9.24160e10	+	1.60069e11i	−0.220071	+	0.381175i
$806$	−1.75826e11	−	1.01513e11i	−0.416623	−	0.240538i
$807$		0			0
$808$	−9.29830e9	−	1.61051e10i	−0.0218151	−	0.0377849i
$809$		−	9.93417e10i		−	0.231920i	−0.993254	−	0.115960i	$-0.963006\pi$
$809$		−	9.93417e10i		−	0.231920i	0.993254	−	0.115960i	$-0.0369944\pi$
$810$		0			0
$811$	−2.71549e11			−0.627718			−0.313859	−	0.949470i	$-0.601622\pi$
$811$	−2.71549e11			−0.627718			−0.313859	+	0.949470i	$0.601622\pi$
$812$	−1.73231e11	+	1.00015e11i	−0.398474	+	0.230059i
$813$		0			0
$814$	1.04303e11	−	1.80659e11i	0.237575	−	0.411492i
$815$	−1.29905e11	−	7.50008e10i	−0.294439	−	0.169995i
$816$		0			0
$817$	3.33891e10	+	5.78316e10i	0.0749405	+	0.129801i
$818$		−	8.04785e11i		−	1.79749i
$819$		0			0
$820$	−1.04418e11			−0.230952
$821$	−4.87769e11	+	2.81614e11i	−1.07360	+	0.619842i	−0.929162	−	0.369672i	$-0.879470\pi$
$821$	−4.87769e11	+	2.81614e11i	−1.07360	+	0.619842i	−0.144436	+	0.989514i	$0.546137\pi$
$822$		0			0
$823$	2.21136e11	−	3.83018e11i	0.482014	−	0.834873i	−0.517773	−	0.855518i	$-0.673239\pi$
$823$	2.21136e11	−	3.83018e11i	0.482014	−	0.834873i	0.999787	+	0.0206454i	$0.00657211\pi$
$824$	−2.58291e10	−	1.49125e10i	−0.0560275	−	0.0323475i
$825$		0			0
$826$	−2.69411e11	−	4.66634e11i	−0.578756	−	1.00244i
$827$		−	4.54543e11i		−	0.971745i	−0.874030	−	0.485873i	$-0.838502\pi$
$827$		−	4.54543e11i		−	0.971745i	0.874030	−	0.485873i	$-0.161498\pi$
$828$		0			0
$829$	−1.32535e11			−0.280615			−0.140308	−	0.990108i	$-0.544809\pi$
$829$	−1.32535e11			−0.280615			−0.140308	+	0.990108i	$0.544809\pi$
$830$	2.02504e11	−	1.16916e11i	0.426699	−	0.246355i
$831$		0			0
$832$	−2.02145e11	+	3.50125e11i	−0.421861	+	0.730684i
$833$	−1.75269e11	−	1.01192e11i	−0.364020	−	0.210167i
$834$		0			0
$835$	−2.20353e10	−	3.81662e10i	−0.0453286	−	0.0785115i
$836$			3.26861e10i			0.0669172i
$837$		0			0
$838$	−5.02871e11			−1.01972
$839$	−4.21932e10	+	2.43603e10i	−0.0851520	+	0.0491625i	−0.541971	−	0.840397i	$-0.682322\pi$
$839$	−4.21932e10	+	2.43603e10i	−0.0851520	+	0.0491625i	0.456819	+	0.889559i	$0.348989\pi$
$840$		0			0
$841$	−1.43910e11	+	2.49259e11i	−0.287678	+	0.498273i
$842$	−2.90729e11	−	1.67852e11i	−0.578416	−	0.333948i
$843$		0			0
$844$	7.20568e9	+	1.24806e10i	0.0142006	+	0.0245961i
$845$		−	3.45051e10i		−	0.0676793i
$846$		0			0
$847$	−2.90368e11			−0.564176
$848$	−3.86032e11	+	2.22876e11i	−0.746517	+	0.431002i
$849$		0			0
$850$	2.86018e11	−	4.95397e11i	0.547920	−	0.949025i
$851$	−5.43990e11	−	3.14073e11i	−1.03722	−	0.598842i
$852$		0			0
$853$	3.62250e11	+	6.27436e11i	0.684247	+	1.18515i	0.973673	+	0.227950i	$0.0732022\pi$
$853$	3.62250e11	+	6.27436e11i	0.684247	+	1.18515i	−0.289426	+	0.957200i	$0.593464\pi$
$854$			2.96071e10i			0.0556626i
$855$		0			0
$856$	4.05068e9			0.00754455
$857$	3.60840e11	−	2.08331e11i	0.668946	−	0.386216i	−0.126731	−	0.991937i	$-0.540448\pi$
$857$	3.60840e11	−	2.08331e11i	0.668946	−	0.386216i	0.795677	+	0.605721i	$0.207115\pi$
$858$		0			0
$859$	−3.77222e11	+	6.53367e11i	−0.692826	+	1.20001i	0.278083	+	0.960557i	$0.410301\pi$
$859$	−3.77222e11	+	6.53367e11i	−0.692826	+	1.20001i	−0.970908	+	0.239452i	$0.923032\pi$
$860$	−1.70019e11	−	9.81607e10i	−0.310817	−	0.179450i
$861$		0			0
$862$	−7.18888e11	−	1.24515e12i	−1.30206	−	2.25524i
$863$			2.06295e10i			0.0371916i	0.999827	+	0.0185958i	$0.00591957\pi$
$863$			2.06295e10i			0.0371916i	−0.999827	+	0.0185958i	$0.994080\pi$
$864$		0			0
$865$	2.29706e11			0.410306
$866$	1.01674e11	−	5.87014e10i	0.180775	−	0.104370i
$867$		0			0
$868$	7.62707e10	−	1.32105e11i	0.134363	−	0.232723i
$869$	−1.38508e11	−	7.99679e10i	−0.242883	−	0.140229i
$870$		0			0
$871$	−2.91893e10	−	5.05573e10i	−0.0507167	−	0.0878438i
$872$			1.97515e10i			0.0341612i
$873$		0			0
$874$	2.00020e11			0.342789
$875$	−2.48664e11	+	1.43566e11i	−0.424209	+	0.244917i
$876$		0			0
$877$	−2.99079e11	+	5.18020e11i	−0.505577	+	0.875685i	0.494402	+	0.869233i	$0.335387\pi$
$877$	−2.99079e11	+	5.18020e11i	−0.505577	+	0.875685i	−0.999979	+	0.00645170i	$0.997946\pi$
$878$	8.45350e11	+	4.88063e11i	1.42252	+	0.821293i
$879$		0			0
$880$	5.27466e10	+	9.13598e10i	0.0879557	+	0.152344i
$881$		−	1.62306e11i		−	0.269420i	−0.990885	−	0.134710i	$-0.956990\pi$
$881$		−	1.62306e11i		−	0.269420i	0.990885	−	0.134710i	$-0.0430103\pi$
$882$		0			0
$883$	−6.06459e11			−0.997605			−0.498803	−	0.866716i	$-0.666227\pi$
$883$	−6.06459e11			−0.997605			−0.498803	+	0.866716i	$0.666227\pi$
$884$	4.13869e11	−	2.38948e11i	0.677726	−	0.391285i
$885$		0			0
$886$	−4.25131e11	+	7.36348e11i	−0.689903	+	1.19495i
$887$	4.03485e11	+	2.32952e11i	0.651828	+	0.376333i	0.789156	−	0.614193i	$-0.210518\pi$
$887$	4.03485e11	+	2.32952e11i	0.651828	+	0.376333i	−0.137328	+	0.990526i	$0.543852\pi$
$888$		0			0
$889$	2.41495e11	+	4.18281e11i	0.386634	+	0.669670i
$890$		−	3.65981e11i		−	0.583308i
$891$		0			0
$892$	−1.09170e12			−1.72442
$893$	6.69323e10	−	3.86434e10i	0.105252	−	0.0607672i
$894$		0			0
$895$	1.44684e11	−	2.50600e11i	0.225490	−	0.390561i
$896$	3.56592e10	+	2.05879e10i	0.0553273	+	0.0319432i
$897$		0			0
$898$	3.31704e11	+	5.74528e11i	0.510088	+	0.883498i
$899$			1.61995e11i			0.248007i
$900$		0			0
$901$	4.94426e11			0.750243
$902$	2.53766e11	−	1.46512e11i	0.383360	−	0.221333i
$903$		0			0
$904$	2.58397e10	−	4.47556e10i	0.0386913	−	0.0670153i
$905$	−9.17102e10	−	5.29489e10i	−0.136717	−	0.0789338i
$906$		0			0
$907$	−3.73555e11	−	6.47017e11i	−0.551983	−	0.956063i	−0.998131	−	0.0611039i	$-0.980538\pi$
$907$	−3.73555e11	−	6.47017e11i	−0.551983	−	0.956063i	0.446148	−	0.894959i	$-0.352795\pi$
$908$			8.76909e11i			1.29006i
$909$		0			0
$910$	−2.26939e11			−0.330935
$911$	−7.80333e11	+	4.50526e11i	−1.13294	+	0.654103i	−0.944672	−	0.328015i	$-0.893620\pi$
$911$	−7.80333e11	+	4.50526e11i	−1.13294	+	0.654103i	−0.188267	+	0.982118i	$0.560287\pi$
$912$		0			0
$913$	−1.61443e11	+	2.79628e11i	−0.232347	+	0.402437i
$914$	−3.93086e11	−	2.26948e11i	−0.563252	−	0.325193i
$915$		0			0
$916$	−2.31346e11	−	4.00703e11i	−0.328610	−	0.569169i
$917$			5.05956e11i			0.715543i
$918$		0			0
$919$	−1.14699e12			−1.60804			−0.804021	−	0.594601i	$-0.797310\pi$
$919$	−1.14699e12			−1.60804			−0.804021	+	0.594601i	$0.797310\pi$
$920$	1.64276e10	−	9.48449e9i	0.0229310	−	0.0132392i
$921$		0			0
$922$	7.87798e11	−	1.36451e12i	1.09016	−	1.88822i
$923$	3.79298e11	+	2.18988e11i	0.522606	+	0.301727i
$924$		0			0
$925$	−2.27129e11	−	3.93399e11i	−0.310246	−	0.537361i
$926$		−	9.33937e10i		−	0.127020i
$927$		0			0
$928$	6.77447e11			0.913447
$929$	3.77634e11	−	2.18027e11i	0.507000	−	0.292716i	−0.224600	−	0.974451i	$-0.572107\pi$
$929$	3.77634e11	−	2.18027e11i	0.507000	−	0.292716i	0.731599	+	0.681735i	$0.238774\pi$
$930$		0			0
$931$	2.55881e10	−	4.43199e10i	0.0340596	−	0.0589929i
$932$	5.84469e11	+	3.37444e11i	0.774637	+	0.447237i
$933$		0			0
$934$	3.23434e11	+	5.60205e11i	0.425010	+	0.736138i
$935$		−	1.17013e11i		−	0.153104i
$936$		0			0
$937$	1.98881e11			0.258009			0.129004	−	0.991644i	$-0.458822\pi$
$937$	1.98881e11			0.258009			0.129004	+	0.991644i	$0.458822\pi$
$938$	7.71965e10	−	4.45694e10i	0.0997209	−	0.0575739i
$939$		0			0
$940$	−1.13608e11	+	1.96774e11i	−0.145511	+	0.252033i
$941$	1.10911e12	+	6.40346e11i	1.41455	+	0.816689i	0.995812	−	0.0914205i	$-0.0291407\pi$
$941$	1.10911e12	+	6.40346e11i	1.41455	+	0.816689i	0.418734	+	0.908109i	$0.362474\pi$
$942$		0			0
$943$	−4.41167e11	−	7.64124e11i	−0.557900	−	0.966312i
$944$			9.26030e11i			1.16610i
$945$		0			0
$946$	5.50926e11			0.687905
$947$	1.17484e12	−	6.78292e11i	1.46076	−	0.843367i	0.461709	−	0.887031i	$-0.347236\pi$
$947$	1.17484e12	−	6.78292e11i	1.46076	−	0.843367i	0.999046	+	0.0436640i	$0.0139031\pi$
$948$		0			0
$949$	−3.56010e11	+	6.16628e11i	−0.438932	+	0.760253i
$950$	1.25270e11	+	7.23245e10i	0.153798	+	0.0887955i
$951$		0			0
$952$	−1.17694e10	−	2.03852e10i	−0.0143287	−	0.0248180i
$953$			5.01575e11i			0.608085i	0.952658	+	0.304042i	$0.0983365\pi$
$953$			5.01575e11i			0.608085i	−0.952658	+	0.304042i	$0.901664\pi$
$954$		0			0
$955$	−3.63211e10			−0.0436662
$956$	−4.88528e11	+	2.82052e11i	−0.584868	+	0.337673i
$957$		0			0
$958$	5.01923e11	−	8.69356e11i	0.595902	−	1.03213i
$959$	3.14570e11	+	1.81617e11i	0.371914	+	0.214725i
$960$		0			0
$961$	3.64677e11	+	6.31639e11i	0.427578	+	0.740586i
$962$		−	7.71244e11i		−	0.900516i
$963$		0			0
$964$	4.33175e11			0.501597
$965$	−3.08820e11	+	1.78297e11i	−0.356120	+	0.205606i
$966$		0			0
$967$	−5.54942e10	+	9.61188e10i	−0.0634661	+	0.109926i	−0.896013	−	0.444029i	$-0.853549\pi$
$967$	−5.54942e10	+	9.61188e10i	−0.0634661	+	0.109926i	0.832546	+	0.553955i	$0.186882\pi$
$968$	2.58075e10	+	1.49000e10i	0.0293931	+	0.0169701i
$969$		0			0
$970$	−3.71123e11	−	6.42804e11i	−0.419209	−	0.726092i
$971$			2.95380e11i			0.332280i	0.986102	+	0.166140i	$0.0531304\pi$
$971$			2.95380e11i			0.332280i	−0.986102	+	0.166140i	$0.946870\pi$
$972$		0			0
$973$	2.49669e11			0.278557
$974$	−1.11372e12	+	6.43006e11i	−1.23749	+	0.714462i
$975$		0			0
$976$	2.54416e10	−	4.40661e10i	0.0280379	−	0.0485630i
$977$	−5.27488e11	−	3.04545e11i	−0.578941	−	0.334252i	0.181771	−	0.983341i	$-0.441817\pi$
$977$	−5.27488e11	−	3.04545e11i	−0.578941	−	0.334252i	−0.760712	+	0.649089i	$0.775150\pi$
$978$		0			0
$979$	2.52682e11	+	4.37659e11i	0.275070	+	0.476436i
$980$			1.50453e11i			0.163116i
$981$		0			0
$982$	1.62821e12			1.75091
$983$	1.59359e12	−	9.20061e11i	1.70672	−	0.985378i	0.768170	−	0.640246i	$-0.221168\pi$
$983$	1.59359e12	−	9.20061e11i	1.70672	−	0.985378i	0.938554	−	0.345132i	$-0.112166\pi$
$984$		0			0
$985$	6.03645e10	−	1.04554e11i	0.0641263	−	0.111070i
$986$	−6.71106e11	−	3.87464e11i	−0.710042	−	0.409943i
$987$		0			0
$988$	6.04221e10	+	1.04654e11i	0.0634115	+	0.109832i
$989$		−	1.65892e12i		−	1.73396i
$990$		0			0
$991$	−5.72336e11			−0.593412			−0.296706	−	0.954969i	$-0.595888\pi$
$991$	−5.72336e11			−0.593412			−0.296706	+	0.954969i	$0.595888\pi$
$992$	−4.47404e11	+	2.58309e11i	−0.462012	+	0.266743i
$993$		0			0
$994$	−3.34375e11	+	5.79155e11i	−0.342522	+	0.593265i
$995$	−1.25905e11	−	7.26914e10i	−0.128455	−	0.0741636i
$996$		0			0
$997$	7.23071e11	+	1.25240e12i	0.731813	+	1.26754i	0.956107	+	0.293016i	$0.0946591\pi$
$997$	7.23071e11	+	1.25240e12i	0.731813	+	1.26754i	−0.224294	+	0.974522i	$0.572008\pi$
$998$			5.93504e11i			0.598276i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.d.d.53.1		4
3.2	odd	2	inner	81.9.d.d.53.2		4
9.2	odd	6	inner	81.9.d.d.26.1		4
9.4	even	3		3.9.b.a.2.1	✓	2
9.5	odd	6		3.9.b.a.2.2	yes	2
9.7	even	3	inner	81.9.d.d.26.2		4
36.23	even	6		48.9.e.b.17.2		2
36.31	odd	6		48.9.e.b.17.1		2
45.4	even	6		75.9.c.c.26.2		2
45.13	odd	12		75.9.d.b.74.2		4
45.14	odd	6		75.9.c.c.26.1		2
45.22	odd	12		75.9.d.b.74.3		4
45.23	even	12		75.9.d.b.74.4		4
45.32	even	12		75.9.d.b.74.1		4
72.5	odd	6		192.9.e.e.65.2		2
72.13	even	6		192.9.e.e.65.1		2
72.59	even	6		192.9.e.f.65.1		2
72.67	odd	6		192.9.e.f.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.9.b.a.2.1	✓	2	9.4	even	3
3.9.b.a.2.2	yes	2	9.5	odd	6
48.9.e.b.17.1		2	36.31	odd	6
48.9.e.b.17.2		2	36.23	even	6
75.9.c.c.26.1		2	45.14	odd	6
75.9.c.c.26.2		2	45.4	even	6
75.9.d.b.74.1		4	45.32	even	12
75.9.d.b.74.2		4	45.13	odd	12
75.9.d.b.74.3		4	45.22	odd	12
75.9.d.b.74.4		4	45.23	even	12
81.9.d.d.26.1		4	9.2	odd	6	inner
81.9.d.d.26.2		4	9.7	even	3	inner
81.9.d.d.53.1		4	1.1	even	1	trivial
81.9.d.d.53.2		4	3.2	odd	2	inner
192.9.e.e.65.1		2	72.13	even	6
192.9.e.e.65.2		2	72.5	odd	6
192.9.e.f.65.1		2	72.59	even	6
192.9.e.f.65.2		2	72.67	odd	6

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-19.4422 + 11.2250i) q^{2} +(124.000 - 214.774i) q^{4} +(-194.422 - 112.250i) q^{5} +(875.000 + 1515.54i) q^{7} -179.600i q^{8} +O(q^{10})\)	\(q+(-19.4422 + 11.2250i) q^{2} +(124.000 - 214.774i) q^{4} +(-194.422 - 112.250i) q^{5} +(875.000 + 1515.54i) q^{7} -179.600i q^{8} +5040.00 q^{10} +(-6027.09 + 3479.74i) q^{11} +(-12865.0 + 22282.8i) q^{13} +(-34023.9 - 19643.7i) q^{14} +(33760.0 + 58474.0i) q^{16} -74893.0i q^{17} +18938.0 q^{19} +(-48216.7 + 27837.9i) q^{20} +(78120.0 - 135308. i) q^{22} +(-407431. - 235231. i) q^{23} +(-170112. - 294643. i) q^{25} -577637. i q^{26} +434000. q^{28} +(-399149. + 230449. i) q^{29} +(175739. - 304389. i) q^{31} +(-1.27292e6 - 734921. i) q^{32} +(840672. + 1.45609e6i) q^{34} -392874. i q^{35} +1.33517e6 q^{37} +(-368197. + 212579. i) q^{38} +(-20160.0 + 34918.1i) q^{40} +(1.62420e6 + 937734. i) q^{41} +(1.76308e6 + 3.05374e6i) q^{43} +1.72595e6i q^{44} +1.05618e7 q^{46} +(3.53428e6 - 2.04052e6i) q^{47} +(1.35115e6 - 2.34026e6i) q^{49} +(6.61473e6 + 3.81902e6i) q^{50} +(3.19052e6 + 5.52614e6i) q^{52} +6.60177e6i q^{53} +1.56240e6 q^{55} +(272191. - 157150. i) q^{56} +(5.17356e6 - 8.96087e6i) q^{58} +(1.18774e7 + 6.85745e6i) q^{59} +(-376801. - 652638. i) q^{61} +7.89066e6i q^{62} +1.57128e7 q^{64} +(5.00248e6 - 2.88819e6i) q^{65} +(-1.13444e6 + 1.96492e6i) q^{67} +(-1.60851e7 - 9.28673e6i) q^{68} +(4.41000e6 + 7.63834e6i) q^{70} -1.70220e7i q^{71} +2.76728e7 q^{73} +(-2.59587e7 + 1.49872e7i) q^{74} +(2.34831e6 - 4.06740e6i) q^{76} +(-1.05474e7 - 6.08955e6i) q^{77} +(1.14905e7 + 1.99021e7i) q^{79} -1.51582e7i q^{80} -4.21042e7 q^{82} +(4.01794e7 - 2.31976e7i) q^{83} +(-8.40672e6 + 1.45609e7i) q^{85} +(-6.85562e7 - 3.95809e7i) q^{86} +(624960. + 1.08246e6i) q^{88} -7.26152e7i q^{89} -4.50275e7 q^{91} +(-1.01043e8 + 5.83372e7i) q^{92} +(-4.58096e7 + 7.93445e7i) q^{94} +(-3.68197e6 - 2.12579e6i) q^{95} +(-7.36355e7 - 1.27540e8i) q^{97} +6.06665e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 496 q^{4} + 3500 q^{7}+O(q^{10}) \) 4 * q + 496 * q^4 + 3500 * q^7	\( 4 q + 496 q^{4} + 3500 q^{7} + 20160 q^{10} - 51460 q^{13} + 135040 q^{16} + 75752 q^{19} + 312480 q^{22} - 680450 q^{25} + 1736000 q^{28} + 702956 q^{31} + 3362688 q^{34} + 5340680 q^{37} - 80640 q^{40} + 7052300 q^{43} + 42247296 q^{46} + 5404602 q^{49} + 12762080 q^{52} + 6249600 q^{55} + 20694240 q^{58} - 1507204 q^{61} + 62851072 q^{64} - 4537780 q^{67} + 17640000 q^{70} + 110691080 q^{73} + 9393248 q^{76} + 45961964 q^{79} - 168416640 q^{82} - 33626880 q^{85} + 2499840 q^{88} - 180110000 q^{91} - 183238272 q^{94} - 294542020 q^{97}+O(q^{100}) \) 4 * q + 496 * q^4 + 3500 * q^7 + 20160 * q^10 - 51460 * q^13 + 135040 * q^16 + 75752 * q^19 + 312480 * q^22 - 680450 * q^25 + 1736000 * q^28 + 702956 * q^31 + 3362688 * q^34 + 5340680 * q^37 - 80640 * q^40 + 7052300 * q^43 + 42247296 * q^46 + 5404602 * q^49 + 12762080 * q^52 + 6249600 * q^55 + 20694240 * q^58 - 1507204 * q^61 + 62851072 * q^64 - 4537780 * q^67 + 17640000 * q^70 + 110691080 * q^73 + 9393248 * q^76 + 45961964 * q^79 - 168416640 * q^82 - 33626880 * q^85 + 2499840 * q^88 - 180110000 * q^91 - 183238272 * q^94 - 294542020 * q^97

Introduction

L-functions

Modular forms

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Database

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