LMFDB - Embedded newform 54.9.d.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(17,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("54.17");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.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:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 $ x^16 - 4x^15 - 150208x^14 - 1927740x^13 + 8702363206x^12 + 239206241152x^11 - 241960304158448x^10 - 9458863275320348x^9 + 3259352971808015407x^8 + 150983052056025751536x^7 - 18744835998632687401792x^6 - 866018994869774202180460x^5 + 35643731791394373752805382x^4 + 1485002234815673954960734644x^3 + 16292568366453217677347743656x^2 + 62373298381917691066182105696*x + 81301302751102601946916438161
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{36} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.1
Root			$220.333 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	54.17
Dual form			54.9.d.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-935.250 - 539.967i) q^{5} +(-2056.09 - 3561.25i) q^{7} +1448.15i q^{8} +O(q^{10})$	\(q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-935.250 - 539.967i) q^{5} +(-2056.09 - 3561.25i) q^{7} +1448.15i q^{8} +12218.1 q^{10} +(-8419.53 + 4861.02i) q^{11} +(-4116.02 + 7129.16i) q^{13} +(40291.0 + 23262.0i) q^{14} +(-8192.00 - 14189.0i) q^{16} -87809.9i q^{17} +123643. q^{19} +(-119712. + 69115.7i) q^{20} +(54996.1 - 95256.1i) q^{22} +(-92029.4 - 53133.2i) q^{23} +(387816. + 671717. i) q^{25} -93134.9i q^{26} -526359. q^{28} +(-430885. + 248772. i) q^{29} +(-577977. + 1.00109e6i) q^{31} +(160530. + 92681.9i) q^{32} +(496728. + 860358. i) q^{34} +4.44088e6i q^{35} +1.20145e6 q^{37} +(-1.21145e6 + 699428. i) q^{38} +(781955. - 1.35439e6i) q^{40} +(-1.53952e6 - 888843. i) q^{41} +(-528726. - 915780. i) q^{43} +1.24442e6i q^{44} +1.20227e6 q^{46} +(3.80689e6 - 2.19791e6i) q^{47} +(-5.57261e6 + 9.65205e6i) q^{49} +(-7.59961e6 - 4.38763e6i) q^{50} +(526851. + 912532. i) q^{52} +1.04810e6i q^{53} +1.04991e7 q^{55} +(5.15724e6 - 2.97754e6i) q^{56} +(2.81453e6 - 4.87491e6i) q^{58} +(8.70048e6 + 5.02323e6i) q^{59} +(-4.15770e6 - 7.20135e6i) q^{61} -1.30781e7i q^{62} -2.09715e6 q^{64} +(7.69902e6 - 4.44503e6i) q^{65} +(6.19183e6 - 1.07246e7i) q^{67} +(-9.73384e6 - 5.61983e6i) q^{68} +(-2.51214e7 - 4.35116e7i) q^{70} -1.69579e7i q^{71} -2.42736e7 q^{73} +(-1.17718e7 + 6.79644e6i) q^{74} +(7.91313e6 - 1.37059e7i) q^{76} +(3.46226e7 + 1.99894e7i) q^{77} +(6.39004e6 + 1.10679e7i) q^{79} +1.76936e7i q^{80} +2.01122e7 q^{82} +(2.79188e7 - 1.61189e7i) q^{83} +(-4.74144e7 + 8.21242e7i) q^{85} +(1.03609e7 + 5.98185e6i) q^{86} +(-7.03950e6 - 1.21928e7i) q^{88} +2.10088e7i q^{89} +3.38516e7 q^{91} +(-1.17798e7 + 6.80105e6i) q^{92} +(-2.48665e7 + 4.30700e7i) q^{94} +(-1.15637e8 - 6.67629e7i) q^{95} +(-4.46651e7 - 7.73622e7i) q^{97} -1.26094e8i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7}+O(q^{10}) $ 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7	$ 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29} + 542438 q^{31} + 220416 q^{34} + 3343328 q^{37} + 1314432 q^{38} - 9218592 q^{41} + 339512 q^{43} + 7417344 q^{46} + 34980606 q^{47} - 2364654 q^{49} - 27744768 q^{50} + 431360 q^{52} - 4584276 q^{55} + 12091392 q^{56} - 7852800 q^{58} - 93924216 q^{59} - 841954 q^{61} - 33554432 q^{64} + 126568134 q^{65} + 29946644 q^{67} + 5476608 q^{68} - 34359552 q^{70} - 7547764 q^{73} - 35124480 q^{74} + 23179520 q^{76} - 9309294 q^{77} + 33813002 q^{79} - 137346048 q^{82} - 114200226 q^{83} - 125696772 q^{85} + 171379584 q^{86} + 7913472 q^{88} + 268578316 q^{91} - 167825664 q^{92} - 11832576 q^{94} + 143949240 q^{95} - 89415484 q^{97}+O(q^{100}) $ 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7 - 45756 * q^11 - 3370 * q^13 + 94464 * q^14 - 131072 * q^16 + 362180 * q^19 + 112896 * q^20 - 61824 * q^22 - 1311138 * q^23 + 963394 * q^25 - 472576 * q^28 + 2851290 * q^29 + 542438 * q^31 + 220416 * q^34 + 3343328 * q^37 + 1314432 * q^38 - 9218592 * q^41 + 339512 * q^43 + 7417344 * q^46 + 34980606 * q^47 - 2364654 * q^49 - 27744768 * q^50 + 431360 * q^52 - 4584276 * q^55 + 12091392 * q^56 - 7852800 * q^58 - 93924216 * q^59 - 841954 * q^61 - 33554432 * q^64 + 126568134 * q^65 + 29946644 * q^67 + 5476608 * q^68 - 34359552 * q^70 - 7547764 * q^73 - 35124480 * q^74 + 23179520 * q^76 - 9309294 * q^77 + 33813002 * q^79 - 137346048 * q^82 - 114200226 * q^83 - 125696772 * q^85 + 171379584 * q^86 + 7913472 * q^88 + 268578316 * q^91 - 167825664 * q^92 - 11832576 * q^94 + 143949240 * q^95 - 89415484 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−9.79796	+	5.65685i	−0.612372	+	0.353553i
$2$	−9.79796	+	5.65685i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	64.0000	−	110.851i	0.250000	−	0.433013i
$5$	−935.250	−	539.967i	−1.49640	−	0.863947i	−0.496408	−	0.868089i	$-0.665348\pi$
$5$	−935.250	−	539.967i	−1.49640	−	0.863947i	−0.999991	+	0.00414227i	$0.998681\pi$
$6$		0			0
$7$	−2056.09	−	3561.25i	−0.856347	−	1.48324i	−0.875389	−	0.483419i	$-0.839395\pi$
$7$	−2056.09	−	3561.25i	−0.856347	−	1.48324i	0.0190419	−	0.999819i	$-0.493938\pi$
$8$			1448.15i			0.353553i
$9$		0			0
$10$	12218.1			1.22181
$11$	−8419.53	+	4861.02i	−0.575065	+	0.332014i	−0.759170	−	0.650893i	$-0.774395\pi$
$11$	−8419.53	+	4861.02i	−0.575065	+	0.332014i	0.184105	+	0.982907i	$0.441061\pi$
$12$		0			0
$13$	−4116.02	+	7129.16i	−0.144113	+	0.249612i	−0.929042	−	0.369975i	$-0.879366\pi$
$13$	−4116.02	+	7129.16i	−0.144113	+	0.249612i	0.784928	+	0.619586i	$0.212700\pi$
$14$	40291.0	+	23262.0i	1.04881	+	0.605529i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$		−	87809.9i		−	1.05135i	−0.850685	−	0.525676i	$-0.823813\pi$
$17$		−	87809.9i		−	1.05135i	0.850685	−	0.525676i	$-0.176187\pi$
$18$		0			0
$19$	123643.			0.948754			0.474377	−	0.880322i	$-0.342673\pi$
$19$	123643.			0.948754			0.474377	+	0.880322i	$0.342673\pi$
$20$	−119712.	+	69115.7i	−0.748200	+	0.431973i
$21$		0			0
$22$	54996.1	−	95256.1i	0.234769	−	0.406632i
$23$	−92029.4	−	53133.2i	−0.328863	−	0.189869i	0.326473	−	0.945206i	$-0.394140\pi$
$23$	−92029.4	−	53133.2i	−0.328863	−	0.189869i	−0.655336	+	0.755337i	$0.727473\pi$
$24$		0			0
$25$	387816.	+	671717.i	0.992808	+	1.71959i
$26$		−	93134.9i		−	0.203807i
$27$		0			0
$28$	−526359.			−0.856347
$29$	−430885.	+	248772.i	−0.609213	+	0.351729i	−0.772657	−	0.634823i	$-0.781073\pi$
$29$	−430885.	+	248772.i	−0.609213	+	0.351729i	0.163444	+	0.986553i	$0.447740\pi$
$30$		0			0
$31$	−577977.	+	1.00109e6i	−0.625841	+	1.08399i	0.362536	+	0.931970i	$0.381911\pi$
$31$	−577977.	+	1.00109e6i	−0.625841	+	1.08399i	−0.988378	+	0.152019i	$0.951422\pi$
$32$	160530.	+	92681.9i	0.153093	+	0.0883883i
$33$		0			0
$34$	496728.	+	860358.i	0.371709	+	0.643819i
$35$			4.44088e6i			2.95935i
$36$		0			0
$37$	1.20145e6			0.641061			0.320531	−	0.947238i	$-0.396139\pi$
$37$	1.20145e6			0.641061			0.320531	+	0.947238i	$0.396139\pi$
$38$	−1.21145e6	+	699428.i	−0.580991	+	0.335435i
$39$		0			0
$40$	781955.	−	1.35439e6i	0.305451	−	0.529057i
$41$	−1.53952e6	−	888843.i	−0.544816	−	0.314550i	0.202212	−	0.979342i	$-0.435187\pi$
$41$	−1.53952e6	−	888843.i	−0.544816	−	0.314550i	−0.747029	+	0.664792i	$0.768520\pi$
$42$		0			0
$43$	−528726.	−	915780.i	−0.154652	−	0.267866i	0.778280	−	0.627917i	$-0.216092\pi$
$43$	−528726.	−	915780.i	−0.154652	−	0.267866i	−0.932932	+	0.360052i	$0.882759\pi$
$44$			1.24442e6i			0.332014i
$45$		0			0
$46$	1.20227e6			0.268516
$47$	3.80689e6	−	2.19791e6i	0.780151	−	0.450420i	−0.0563327	−	0.998412i	$-0.517941\pi$
$47$	3.80689e6	−	2.19791e6i	0.780151	−	0.450420i	0.836484	+	0.547992i	$0.184607\pi$
$48$		0			0
$49$	−5.57261e6	+	9.65205e6i	−0.966662	+	1.67431i
$50$	−7.59961e6	−	4.38763e6i	−1.21594	−	0.702021i
$51$		0			0
$52$	526851.	+	912532.i	0.0720567	+	0.124806i
$53$			1.04810e6i			0.132831i	0.997792	+	0.0664157i	$0.0211563\pi$
$53$			1.04810e6i			0.132831i	−0.997792	+	0.0664157i	$0.978844\pi$
$54$		0			0
$55$	1.04991e7			1.14737
$56$	5.15724e6	−	2.97754e6i	0.524404	−	0.302765i
$57$		0			0
$58$	2.81453e6	−	4.87491e6i	0.248710	−	0.430779i
$59$	8.70048e6	+	5.02323e6i	0.718018	+	0.414548i	0.814023	−	0.580833i	$-0.197273\pi$
$59$	8.70048e6	+	5.02323e6i	0.718018	+	0.414548i	−0.0960047	+	0.995381i	$0.530606\pi$
$60$		0			0
$61$	−4.15770e6	−	7.20135e6i	−0.300285	−	0.520109i	0.675915	−	0.736979i	$-0.263749\pi$
$61$	−4.15770e6	−	7.20135e6i	−0.300285	−	0.520109i	−0.976200	+	0.216870i	$0.930415\pi$
$62$		−	1.30781e7i		−	0.885073i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	7.69902e6	−	4.44503e6i	0.431302	−	0.249013i
$66$		0			0
$67$	6.19183e6	−	1.07246e7i	0.307270	−	0.532207i	−0.670494	−	0.741915i	$-0.733918\pi$
$67$	6.19183e6	−	1.07246e7i	0.307270	−	0.532207i	0.977764	+	0.209708i	$0.0672513\pi$
$68$	−9.73384e6	−	5.61983e6i	−0.455248	−	0.262838i
$69$		0			0
$70$	−2.51214e7	−	4.35116e7i	−1.04629	−	1.81223i
$71$		−	1.69579e7i		−	0.667328i	−0.942692	−	0.333664i	$-0.891715\pi$
$71$		−	1.69579e7i		−	0.667328i	0.942692	−	0.333664i	$-0.108285\pi$
$72$		0			0
$73$	−2.42736e7			−0.854757			−0.427378	−	0.904073i	$-0.640563\pi$
$73$	−2.42736e7			−0.854757			−0.427378	+	0.904073i	$0.640563\pi$
$74$	−1.17718e7	+	6.79644e6i	−0.392568	+	0.226649i
$75$		0			0
$76$	7.91313e6	−	1.37059e7i	0.237189	−	0.410823i
$77$	3.46226e7	+	1.99894e7i	0.984911	+	0.568639i
$78$		0			0
$79$	6.39004e6	+	1.10679e7i	0.164057	+	0.284155i	0.936320	−	0.351148i	$-0.114209\pi$
$79$	6.39004e6	+	1.10679e7i	0.164057	+	0.284155i	−0.772263	+	0.635303i	$0.780875\pi$
$80$			1.76936e7i			0.431973i
$81$		0			0
$82$	2.01122e7			0.444841
$83$	2.79188e7	−	1.61189e7i	0.588281	−	0.339644i	−0.176136	−	0.984366i	$-0.556360\pi$
$83$	2.79188e7	−	1.61189e7i	0.588281	−	0.339644i	0.764418	+	0.644722i	$0.223027\pi$
$84$		0			0
$85$	−4.74144e7	+	8.21242e7i	−0.908312	+	1.57324i
$86$	1.03609e7	+	5.98185e6i	0.189410	+	0.109356i
$87$		0			0
$88$	−7.03950e6	−	1.21928e7i	−0.117385	−	0.203316i
$89$			2.10088e7i			0.334843i	0.985885	+	0.167422i	$0.0535441\pi$
$89$			2.10088e7i			0.334843i	−0.985885	+	0.167422i	$0.946456\pi$
$90$		0			0
$91$	3.38516e7			0.493644
$92$	−1.17798e7	+	6.80105e6i	−0.164432	+	0.0949346i
$93$		0			0
$94$	−2.48665e7	+	4.30700e7i	−0.318495	+	0.551650i
$95$	−1.15637e8	−	6.67629e7i	−1.41972	−	0.819673i
$96$		0			0
$97$	−4.46651e7	−	7.73622e7i	−0.504523	−	0.873860i	−0.999986	−	0.00523116i	$-0.998335\pi$
$97$	−4.46651e7	−	7.73622e7i	−0.504523	−	0.873860i	0.495463	−	0.868629i	$-0.334998\pi$
$98$		−	1.26094e8i		−	1.36707i
$99$		0			0
$100$	9.92808e7			0.992808
$101$	3.08430e7	−	1.78072e7i	0.296395	−	0.171124i	−0.344427	−	0.938813i	$-0.611927\pi$
$101$	3.08430e7	−	1.78072e7i	0.296395	−	0.171124i	0.640822	+	0.767689i	$0.278594\pi$
$102$		0			0
$103$	−4.35300e6	+	7.53962e6i	−0.0386759	+	0.0669886i	−0.884715	−	0.466132i	$-0.845647\pi$
$103$	−4.35300e6	+	7.53962e6i	−0.0386759	+	0.0669886i	0.846040	+	0.533120i	$0.178981\pi$
$104$	−1.03241e7	−	5.96064e6i	−0.0882510	−	0.0509518i
$105$		0			0
$106$	−5.92897e6	−	1.02693e7i	−0.0469630	−	0.0813422i
$107$			2.34341e8i			1.78778i	0.448290	+	0.893888i	$0.352033\pi$
$107$			2.34341e8i			1.78778i	−0.448290	+	0.893888i	$0.647967\pi$
$108$		0			0
$109$	2.66492e8			1.88789			0.943947	−	0.330098i	$-0.107082\pi$
$109$	2.66492e8			1.88789			0.943947	+	0.330098i	$0.107082\pi$
$110$	−1.02870e8	+	5.93921e7i	−0.702617	+	0.405656i
$111$		0			0
$112$	−3.36870e7	+	5.83476e7i	−0.214087	+	0.370809i
$113$	2.47560e8	+	1.42929e8i	1.51833	+	0.876610i	0.999767	+	0.0215714i	$0.00686693\pi$
$113$	2.47560e8	+	1.42929e8i	1.51833	+	0.876610i	0.518565	+	0.855038i	$0.326466\pi$
$114$		0			0
$115$	5.73803e7	+	9.93856e7i	0.328074	+	0.568241i
$116$			6.36855e7i			0.351729i
$117$		0			0
$118$	−1.13663e8			−0.586259
$119$	−3.12713e8	+	1.80545e8i	−1.55940	+	0.900322i
$120$		0			0
$121$	−5.99205e7	+	1.03785e8i	−0.279534	+	0.484166i
$122$	8.14740e7	+	4.70390e7i	0.367773	+	0.212334i
$123$		0			0
$124$	7.39811e7	+	1.28139e8i	0.312921	+	0.541994i
$125$		−	4.15781e8i		−	1.70304i
$126$		0			0
$127$	−8.18752e7			−0.314730			−0.157365	−	0.987541i	$-0.550300\pi$
$127$	−8.18752e7			−0.314730			−0.157365	+	0.987541i	$0.550300\pi$
$128$	2.05478e7	−	1.18633e7i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−5.02898e7	+	8.71044e7i	−0.176078	+	0.304977i
$131$	−3.27800e8	−	1.89256e8i	−1.11308	−	0.642634i	−0.173451	−	0.984843i	$-0.555492\pi$
$131$	−3.27800e8	−	1.89256e8i	−1.11308	−	0.642634i	−0.939624	+	0.342208i	$0.888825\pi$
$132$		0			0
$133$	−2.54220e8	−	4.40322e8i	−0.812463	−	1.40723i
$134$			1.40105e8i			0.434545i
$135$		0			0
$136$	1.27162e8			0.371709
$137$	−8.36881e7	+	4.83174e7i	−0.237565	+	0.137158i	−0.614057	−	0.789262i	$-0.710463\pi$
$137$	−8.36881e7	+	4.83174e7i	−0.237565	+	0.137158i	0.376492	+	0.926420i	$0.377130\pi$
$138$		0			0
$139$	−2.13230e8	+	3.69325e8i	−0.571200	+	0.989348i	0.425243	+	0.905079i	$0.360189\pi$
$139$	−2.13230e8	+	3.69325e8i	−0.571200	+	0.989348i	−0.996443	+	0.0842686i	$0.973145\pi$
$140$	4.92277e8	+	2.84216e8i	1.28144	+	0.739839i
$141$		0			0
$142$	9.59286e7	+	1.66153e8i	0.235936	+	0.408653i
$143$		−	8.00322e7i		−	0.191391i
$144$		0			0
$145$	5.37313e8			1.21550
$146$	2.37832e8	−	1.37312e8i	0.523429	−	0.302202i
$147$		0			0
$148$	7.68929e7	−	1.33182e8i	0.160265	−	0.277588i
$149$	−3.73436e8	−	2.15603e8i	−0.757653	−	0.437431i	0.0707992	−	0.997491i	$-0.477445\pi$
$149$	−3.73436e8	−	2.15603e8i	−0.757653	−	0.437431i	−0.828453	+	0.560059i	$0.810778\pi$
$150$		0			0
$151$	−4.20280e8	−	7.27947e8i	−0.808409	−	1.40021i	−0.913965	−	0.405793i	$-0.866996\pi$
$151$	−4.20280e8	−	7.27947e8i	−0.808409	−	1.40021i	0.105556	−	0.994413i	$-0.466338\pi$
$152$			1.79054e8i			0.335435i
$153$		0			0
$154$	−4.52308e8			−0.804176
$155$	1.08111e9	−	6.24177e8i	1.87302	−	1.08139i
$156$		0			0
$157$	2.10919e8	−	3.65323e8i	0.347150	−	0.601282i	−0.638592	−	0.769546i	$-0.720483\pi$
$157$	2.10919e8	−	3.65323e8i	0.347150	−	0.601282i	0.985742	+	0.168264i	$0.0538160\pi$
$158$	−1.25219e8	−	7.22951e7i	−0.200928	−	0.116006i
$159$		0			0
$160$	−1.00090e8	−	1.73361e8i	−0.152726	−	0.264529i
$161$			4.36987e8i			0.650376i
$162$		0			0
$163$	−5.50818e8			−0.780293			−0.390146	−	0.920753i	$-0.627576\pi$
$163$	−5.50818e8			−0.780293			−0.390146	+	0.920753i	$0.627576\pi$
$164$	−1.97059e8	+	1.13772e8i	−0.272408	+	0.157275i
$165$		0			0
$166$	−1.82365e8	+	3.15866e8i	−0.240165	+	0.415978i
$167$	−5.25550e8	−	3.03427e8i	−0.675691	−	0.390111i	0.122538	−	0.992464i	$-0.460897\pi$
$167$	−5.25550e8	−	3.03427e8i	−0.675691	−	0.390111i	−0.798230	+	0.602353i	$0.794230\pi$
$168$		0			0
$169$	3.73982e8	+	6.47756e8i	0.458463	+	0.794081i
$170$		−	1.07287e9i		−	1.28455i
$171$		0			0
$172$	−1.35354e8			−0.154652
$173$	8.26617e8	−	4.77248e8i	0.922826	−	0.532794i	0.0382907	−	0.999267i	$-0.487809\pi$
$173$	8.26617e8	−	4.77248e8i	0.922826	−	0.532794i	0.884536	+	0.466473i	$0.154475\pi$
$174$		0			0
$175$	1.59477e9	−	2.76222e9i	1.70038	−	2.94514i
$176$	1.37946e8	+	7.96429e7i	0.143766	+	0.0830035i
$177$		0			0
$178$	−1.18844e8	−	2.05844e8i	−0.118385	−	0.205049i
$179$			9.44019e8i			0.919536i	0.888039	+	0.459768i	$0.152067\pi$
$179$			9.44019e8i			0.919536i	−0.888039	+	0.459768i	$0.847933\pi$
$180$		0			0
$181$	−8.68230e8			−0.808948			−0.404474	−	0.914550i	$-0.632545\pi$
$181$	−8.68230e8			−0.808948			−0.404474	+	0.914550i	$0.632545\pi$
$182$	−3.31677e8	+	1.91494e8i	−0.302294	+	0.174530i
$183$		0			0
$184$	7.69451e7	−	1.33273e8i	0.0671289	−	0.116271i
$185$	−1.12366e9	−	6.48744e8i	−0.959284	−	0.553843i
$186$		0			0
$187$	4.26845e8	+	7.39318e8i	0.349063	+	0.604595i
$188$		−	5.62665e8i		−	0.450420i
$189$		0			0
$190$	1.51067e9			1.15919
$191$	6.09956e7	−	3.52159e7i	0.0458316	−	0.0264609i	−0.476909	−	0.878953i	$-0.658243\pi$
$191$	6.09956e7	−	3.52159e7i	0.0458316	−	0.0264609i	0.522741	+	0.852492i	$0.324910\pi$
$192$		0			0
$193$	−1.36871e9	+	2.37068e9i	−0.986467	+	1.70861i	−0.351242	+	0.936285i	$0.614241\pi$
$193$	−1.36871e9	+	2.37068e9i	−0.986467	+	1.70861i	−0.635225	+	0.772327i	$0.719093\pi$
$194$	8.75254e8	+	5.05328e8i	0.617913	+	0.356752i
$195$		0			0
$196$	7.13294e8	+	1.23546e9i	0.483331	+	0.837154i
$197$			5.47276e8i			0.363364i	0.983357	+	0.181682i	$0.0581541\pi$
$197$			5.47276e8i			0.363364i	−0.983357	+	0.181682i	$0.941846\pi$
$198$		0			0
$199$	−2.66467e9			−1.69915			−0.849574	−	0.527469i	$-0.823141\pi$
$199$	−2.66467e9			−1.69915			−0.849574	+	0.527469i	$0.823141\pi$
$200$	−9.72749e8	+	5.61617e8i	−0.607968	+	0.351011i
$201$		0			0
$202$	−2.01465e8	+	3.48948e8i	−0.121003	+	0.209583i
$203$	1.77188e9	+	1.02299e9i	1.04340	+	0.602405i
$204$		0			0
$205$	9.59891e8	+	1.66258e9i	0.543509	+	0.941385i
$206$		−	9.84972e7i		−	0.0546959i
$207$		0			0
$208$	1.34874e8			0.0720567
$209$	−1.04101e9	+	6.01029e8i	−0.545595	+	0.315000i
$210$		0			0
$211$	−9.39137e8	+	1.62663e9i	−0.473804	+	0.820653i	−0.999550	−	0.0299884i	$-0.990453\pi$
$211$	−9.39137e8	+	1.62663e9i	−0.473804	+	0.820653i	0.525746	+	0.850642i	$0.323786\pi$
$212$	1.16184e8	+	6.70786e7i	0.0575176	+	0.0332078i
$213$		0			0
$214$	−1.32563e9	−	2.29606e9i	−0.632074	−	1.09478i
$215$			1.14198e9i			0.534446i
$216$		0			0
$217$	4.75349e9			2.14375
$218$	−2.61107e9	+	1.50750e9i	−1.15609	+	0.667471i
$219$		0			0
$220$	6.71945e8	−	1.16384e9i	0.286842	−	0.496826i
$221$	6.26011e8	+	3.61427e8i	0.262430	+	0.151514i
$222$		0			0
$223$	1.45052e9	+	2.51237e9i	0.586548	+	1.01593i	0.994680	+	0.103009i	$0.0328470\pi$
$223$	1.45052e9	+	2.51237e9i	0.586548	+	1.01593i	−0.408132	+	0.912923i	$0.633820\pi$
$224$		−	7.62249e8i		−	0.302765i
$225$		0			0
$226$	−3.23411e9			−1.23971
$227$	−3.60966e9	+	2.08404e9i	−1.35945	+	0.784877i	−0.989549	−	0.144195i	$-0.953941\pi$
$227$	−3.60966e9	+	2.08404e9i	−1.35945	+	0.784877i	−0.369898	+	0.929072i	$0.620607\pi$
$228$		0			0
$229$	1.80018e9	−	3.11801e9i	0.654599	−	1.13380i	−0.327396	−	0.944887i	$-0.606171\pi$
$229$	1.80018e9	−	3.11801e9i	0.654599	−	1.13380i	0.981994	−	0.188911i	$-0.0604957\pi$
$230$	−1.12442e9	−	6.49184e8i	−0.401807	−	0.231983i
$231$		0			0
$232$	−3.60260e8	−	6.23988e8i	−0.124355	−	0.215389i
$233$			2.86365e9i			0.971618i	0.874065	+	0.485809i	$0.161475\pi$
$233$			2.86365e9i			0.971618i	−0.874065	+	0.485809i	$0.838525\pi$
$234$		0			0
$235$	−4.74719e9			−1.55656
$236$	1.11366e9	−	6.42973e8i	0.359009	−	0.207274i
$237$		0			0
$238$	2.04263e9	−	3.53795e9i	0.636624	−	1.10266i
$239$	−1.21500e9	−	7.01479e8i	−0.372378	−	0.214992i	0.302119	−	0.953270i	$-0.402306\pi$
$239$	−1.21500e9	−	7.01479e8i	−0.372378	−	0.214992i	−0.674497	+	0.738278i	$0.735639\pi$
$240$		0			0
$241$	2.21808e9	+	3.84182e9i	0.657519	+	1.13886i	0.981256	+	0.192709i	$0.0617273\pi$
$241$	2.21808e9	+	3.84182e9i	0.657519	+	1.13886i	−0.323737	+	0.946147i	$0.604939\pi$
$242$		−	1.35585e9i		−	0.395320i
$243$		0			0
$244$	−1.06437e9			−0.300285
$245$	1.04236e10	−	6.01805e9i	2.89303	−	1.67029i
$246$		0			0
$247$	−5.08916e8	+	8.81468e8i	−0.136728	+	0.236820i
$248$	−1.44973e9	−	8.37001e8i	−0.383248	−	0.221268i
$249$		0			0
$250$	2.35201e9	+	4.07381e9i	0.602116	+	1.04290i
$251$		−	2.42084e9i		−	0.609916i	−0.952366	−	0.304958i	$-0.901357\pi$
$251$		−	2.42084e9i		−	0.609916i	0.952366	−	0.304958i	$-0.0986425\pi$
$252$		0			0
$253$	1.03313e9			0.252157
$254$	8.02210e8	−	4.63156e8i	0.192732	−	0.111274i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	2.08915e9	+	1.20617e9i	0.478891	+	0.276488i	0.719954	−	0.694022i	$-0.244163\pi$
$257$	2.08915e9	+	1.20617e9i	0.478891	+	0.276488i	−0.241063	+	0.970509i	$0.577496\pi$
$258$		0			0
$259$	−2.47029e9	−	4.27867e9i	−0.548971	−	0.950846i
$260$		−	1.13793e9i		−	0.249013i
$261$		0			0
$262$	4.28237e9			0.908822
$263$	−5.65030e9	+	3.26220e9i	−1.18100	+	0.681849i	−0.956245	−	0.292567i	$-0.905490\pi$
$263$	−5.65030e9	+	3.26220e9i	−1.18100	+	0.681849i	−0.224752	+	0.974416i	$0.572157\pi$
$264$		0			0
$265$	5.65941e8	−	9.80238e8i	0.114759	−	0.198769i
$266$	4.98168e9	+	2.87617e9i	0.995060	+	0.574498i
$267$		0			0
$268$	−7.92554e8	−	1.37274e9i	−0.153635	−	0.266103i
$269$		−	6.64127e9i		−	1.26836i	−0.773186	−	0.634180i	$-0.781338\pi$
$269$		−	6.64127e9i		−	1.26836i	0.773186	−	0.634180i	$-0.218662\pi$
$270$		0			0
$271$	−2.72229e9			−0.504728			−0.252364	−	0.967632i	$-0.581208\pi$
$271$	−2.72229e9			−0.504728			−0.252364	+	0.967632i	$0.581208\pi$
$272$	−1.24593e9	+	7.19339e8i	−0.227624	+	0.131419i
$273$		0			0
$274$	5.46649e8	−	9.46823e8i	0.0969853	−	0.167983i
$275$	−6.53045e9	−	3.77036e9i	−1.14186	−	0.659252i
$276$		0			0
$277$	−5.00946e9	−	8.67663e9i	−0.850886	−	1.47378i	−0.880410	−	0.474214i	$-0.842732\pi$
$277$	−5.00946e9	−	8.67663e9i	−0.850886	−	1.47378i	0.0295233	−	0.999564i	$-0.490601\pi$
$278$		−	4.82484e9i		−	0.807799i
$279$		0			0
$280$	−6.43108e9			−1.04629
$281$	6.83019e9	−	3.94341e9i	1.09549	−	0.632480i	0.160456	−	0.987043i	$-0.448704\pi$
$281$	6.83019e9	−	3.94341e9i	1.09549	−	0.632480i	0.935032	+	0.354563i	$0.115370\pi$
$282$		0			0
$283$	4.86855e8	−	8.43258e8i	0.0759021	−	0.131466i	−0.825576	−	0.564291i	$-0.809150\pi$
$283$	4.86855e8	−	8.43258e8i	0.0759021	−	0.131466i	0.901478	+	0.432824i	$0.142483\pi$
$284$	−1.87981e9	−	1.08531e9i	−0.288962	−	0.166832i
$285$		0			0
$286$	4.52730e8	+	7.84152e8i	0.0676668	+	0.117202i
$287$			7.31016e9i			1.07746i
$288$		0			0
$289$	−7.34822e8			−0.105339
$290$	−5.26458e9	+	3.03950e9i	−0.744340	+	0.429745i
$291$		0			0
$292$	−1.55351e9	+	2.69076e9i	−0.213689	+	0.370121i
$293$	4.59420e9	+	2.65246e9i	0.623361	+	0.359898i	0.778176	−	0.628046i	$-0.216145\pi$
$293$	4.59420e9	+	2.65246e9i	0.623361	+	0.359898i	−0.154815	+	0.987943i	$0.549478\pi$
$294$		0			0
$295$	−5.42475e9	−	9.39595e9i	−0.716295	−	1.24066i
$296$			1.73989e9i			0.226649i
$297$		0			0
$298$	4.87854e9			0.618621
$299$	7.57590e8	−	4.37395e8i	0.0947871	−	0.0547254i
$300$		0			0
$301$	−2.17422e9	+	3.76585e9i	−0.264872	+	0.458772i
$302$	8.23578e9	+	4.75493e9i	0.990095	+	0.571632i
$303$		0			0
$304$	−1.01288e9	−	1.75436e9i	−0.118594	−	0.205411i
$305$			8.98008e9i			1.03772i
$306$		0			0
$307$	1.34241e10			1.51124			0.755618	−	0.655013i	$-0.227337\pi$
$307$	1.34241e10			1.51124			0.755618	+	0.655013i	$0.227337\pi$
$308$	4.43169e9	−	2.55864e9i	0.492455	−	0.284319i
$309$		0			0
$310$	−7.06176e9	+	1.22313e10i	−0.764656	+	1.32442i
$311$	−1.98291e9	−	1.14483e9i	−0.211964	−	0.122377i	0.390260	−	0.920705i	$-0.372385\pi$
$311$	−1.98291e9	−	1.14483e9i	−0.211964	−	0.122377i	−0.602224	+	0.798327i	$0.705718\pi$
$312$		0			0
$313$	8.94161e9	+	1.54873e10i	0.931619	+	1.61361i	0.780555	+	0.625088i	$0.214937\pi$
$313$	8.94161e9	+	1.54873e10i	0.931619	+	1.61361i	0.151065	+	0.988524i	$0.451730\pi$
$314$			4.77256e9i			0.490945i
$315$		0			0
$316$	1.63585e9			0.164057
$317$	−5.77404e9	+	3.33364e9i	−0.571798	+	0.330128i	−0.757867	−	0.652409i	$-0.773758\pi$
$317$	−5.77404e9	+	3.33364e9i	−0.571798	+	0.330128i	0.186069	+	0.982537i	$0.440425\pi$
$318$		0			0
$319$	2.41856e9	−	4.18908e9i	0.233558	−	0.404535i
$320$	1.96136e9	+	1.13239e9i	0.187050	+	0.107993i
$321$		0			0
$322$	−2.47197e9	−	4.28158e9i	−0.229943	−	0.398272i
$323$		−	1.08570e10i		−	0.997474i
$324$		0			0
$325$	−6.38503e9			−0.572308
$326$	5.39689e9	−	3.11590e9i	0.477830	−	0.275875i
$327$		0			0
$328$	1.28718e9	−	2.22946e9i	0.111210	−	0.192622i
$329$	−1.56546e10	−	9.03820e9i	−1.33616	−	0.771433i
$330$		0			0
$331$	−7.84292e9	−	1.35843e10i	−0.653380	−	1.13169i	−0.982297	−	0.187328i	$-0.940017\pi$
$331$	−7.84292e9	−	1.35843e10i	−0.653380	−	1.13169i	0.328918	−	0.944359i	$-0.393316\pi$
$332$		−	4.12645e9i		−	0.339644i
$333$		0			0
$334$	6.86576e9			0.551700
$335$	−1.15818e10	+	6.68676e9i	−0.919597	+	0.530929i
$336$		0			0
$337$	−1.29188e9	+	2.23761e9i	−0.100162	+	0.173486i	−0.911751	−	0.410743i	$-0.865270\pi$
$337$	−1.29188e9	+	2.23761e9i	−0.100162	+	0.173486i	0.811589	+	0.584229i	$0.198603\pi$
$338$	−7.32852e9	−	4.23112e9i	−0.561500	−	0.324182i
$339$		0			0
$340$	6.06905e9	+	1.05119e10i	0.454156	+	0.786621i
$341$		−	1.12382e10i		−	0.831152i
$342$		0			0
$343$	2.21253e10			1.59850
$344$	1.32619e9	−	7.65677e8i	0.0947049	−	0.0546779i
$345$		0			0
$346$	−5.39944e9	+	9.35211e9i	−0.376742	+	0.652537i
$347$	−1.45626e10	−	8.40775e9i	−1.00444	−	0.579912i	−0.0948784	−	0.995489i	$-0.530246\pi$
$347$	−1.45626e10	−	8.40775e9i	−1.00444	−	0.579912i	−0.909558	+	0.415577i	$0.863580\pi$
$348$		0			0
$349$	1.22366e10	+	2.11945e10i	0.824822	+	1.42863i	0.902055	+	0.431620i	$0.142058\pi$
$349$	1.22366e10	+	2.11945e10i	0.824822	+	1.42863i	−0.0772336	+	0.997013i	$0.524609\pi$
$350$			3.60855e10i			2.40470i
$351$		0			0
$352$	−1.80211e9			−0.117385
$353$	9.05088e9	−	5.22553e9i	0.582897	−	0.336536i	−0.179387	−	0.983779i	$-0.557411\pi$
$353$	9.05088e9	−	5.22553e9i	0.582897	−	0.336536i	0.762284	+	0.647243i	$0.224078\pi$
$354$		0			0
$355$	−9.15672e9	+	1.58599e10i	−0.576536	+	0.998590i
$356$	2.32885e9	+	1.34456e9i	0.144991	+	0.0837108i
$357$		0			0
$358$	−5.34018e9	−	9.24946e9i	−0.325105	−	0.563098i
$359$			2.37497e10i			1.42982i	0.699219	+	0.714908i	$0.253531\pi$
$359$			2.37497e10i			1.42982i	−0.699219	+	0.714908i	$0.746469\pi$
$360$		0			0
$361$	−1.69607e9			−0.0998656
$362$	8.50688e9	−	4.91145e9i	0.495377	−	0.286006i
$363$		0			0
$364$	2.16651e9	−	3.75250e9i	0.123411	−	0.213754i
$365$	2.27019e10	+	1.31069e10i	1.27906	+	0.738464i
$366$		0			0
$367$	−5.17433e9	−	8.96220e9i	−0.285226	−	0.494027i	0.687438	−	0.726243i	$-0.258735\pi$
$367$	−5.17433e9	−	8.96220e9i	−0.285226	−	0.494027i	−0.972664	+	0.232217i	$0.925402\pi$
$368$			1.74107e9i			0.0949346i
$369$		0			0
$370$	1.46794e10			0.783252
$371$	3.73256e9	−	2.15499e9i	0.197020	−	0.113750i
$372$		0			0
$373$	4.02672e9	−	6.97448e9i	0.208025	−	0.360310i	−0.743067	−	0.669217i	$-0.766630\pi$
$373$	4.02672e9	−	6.97448e9i	0.208025	−	0.360310i	0.951092	+	0.308907i	$0.0999631\pi$
$374$	−8.36443e9	−	4.82920e9i	−0.427513	−	0.246825i
$375$		0			0
$376$	3.18291e9	+	5.51296e9i	0.159248	+	0.275825i
$377$		−	4.09580e9i		−	0.202756i
$378$		0			0
$379$	−2.63218e10			−1.27573			−0.637864	−	0.770149i	$-0.720182\pi$
$379$	−2.63218e10			−1.27573			−0.637864	+	0.770149i	$0.720182\pi$
$380$	−1.48015e10	+	8.54565e9i	−0.709858	+	0.409837i
$381$		0			0
$382$	−3.98422e8	+	6.90087e8i	−0.0187107	+	0.0324079i
$383$	2.64941e10	+	1.52964e10i	1.23127	+	0.710876i	0.967295	−	0.253653i	$-0.0816321\pi$
$383$	2.64941e10	+	1.52964e10i	1.23127	+	0.710876i	0.263978	+	0.964529i	$0.414965\pi$
$384$		0			0
$385$	−2.15872e10	−	3.73901e10i	−0.982547	−	1.70182i
$386$		−	3.09704e10i		−	1.39508i
$387$		0			0
$388$	−1.14343e10			−0.504523
$389$	−3.76791e10	+	2.17540e10i	−1.64552	+	0.950039i	−0.666691	+	0.745334i	$0.732290\pi$
$389$	−3.76791e10	+	2.17540e10i	−1.64552	+	0.950039i	−0.978824	+	0.204704i	$0.934377\pi$
$390$		0			0
$391$	−4.66562e9	+	8.08109e9i	−0.199619	+	0.345751i
$392$	−1.39777e10	−	8.07001e9i	−0.591957	−	0.341767i
$393$		0			0
$394$	−3.09586e9	−	5.36219e9i	−0.128468	−	0.222514i
$395$		−	1.38016e10i		−	0.566947i
$396$		0			0
$397$	4.31419e10			1.73675			0.868375	−	0.495908i	$-0.165165\pi$
$397$	4.31419e10			1.73675			0.868375	+	0.495908i	$0.165165\pi$
$398$	2.61083e10	−	1.50737e10i	1.04051	−	0.600740i
$399$		0			0
$400$	6.35397e9	−	1.10054e10i	0.248202	−	0.429899i
$401$	1.57455e10	+	9.09069e9i	0.608948	+	0.351576i	0.772554	−	0.634950i	$-0.218979\pi$
$401$	1.57455e10	+	9.09069e9i	0.608948	+	0.351576i	−0.163606	+	0.986526i	$0.552312\pi$
$402$		0			0
$403$	−4.75794e9	−	8.24099e9i	−0.180384	−	0.312434i
$404$		−	4.55864e9i		−	0.171124i
$405$		0			0
$406$	−2.31477e10			−0.851930
$407$	−1.01157e10	+	5.84028e9i	−0.368652	+	0.212841i
$408$		0			0
$409$	3.23724e9	−	5.60707e9i	0.115686	−	0.200374i	−0.802368	−	0.596830i	$-0.796427\pi$
$409$	3.23724e9	−	5.60707e9i	0.115686	−	0.200374i	0.918054	+	0.396456i	$0.129760\pi$
$410$	−1.88099e10	−	1.08599e10i	−0.665659	−	0.384319i
$411$		0			0
$412$	5.57184e8	+	9.65071e8i	0.0193379	+	0.0334943i
$413$		−	4.13128e10i		−	1.41999i
$414$		0			0
$415$	−3.48148e10			−1.17374
$416$	−1.32149e9	+	7.62961e8i	−0.0441255	+	0.0254759i
$417$		0			0
$418$	6.79986e9	−	1.17777e10i	0.222738	−	0.385794i
$419$	3.28096e10	+	1.89427e10i	1.06450	+	0.614589i	0.926673	−	0.375868i	$-0.122655\pi$
$419$	3.28096e10	+	1.89427e10i	1.06450	+	0.614589i	0.137826	+	0.990456i	$0.455989\pi$
$420$		0			0
$421$	2.38781e10	+	4.13581e10i	0.760102	+	1.31654i	0.942798	+	0.333366i	$0.108184\pi$
$421$	2.38781e10	+	4.13581e10i	0.760102	+	1.31654i	−0.182696	+	0.983170i	$0.558482\pi$
$422$		−	2.12502e10i		−	0.670061i
$423$		0			0
$424$	−1.51782e9			−0.0469630
$425$	5.89834e10	−	3.40541e10i	1.80790	−	1.04379i
$426$		0			0
$427$	−1.70972e10	+	2.96133e10i	−0.514297	+	0.890789i
$428$	2.59770e10	+	1.49978e10i	0.774130	+	0.446944i
$429$		0			0
$430$	−6.46000e9	−	1.11890e10i	−0.188955	−	0.327280i
$431$		−	2.73395e10i		−	0.792285i	−0.918189	−	0.396143i	$-0.870349\pi$
$431$		−	2.73395e10i		−	0.792285i	0.918189	−	0.396143i	$-0.129651\pi$
$432$		0			0
$433$	−6.96958e9			−0.198269			−0.0991345	−	0.995074i	$-0.531607\pi$
$433$	−6.96958e9			−0.198269			−0.0991345	+	0.995074i	$0.531607\pi$
$434$	−4.65745e10	+	2.68898e10i	−1.31277	+	0.757930i
$435$		0			0
$436$	1.70555e10	−	2.95409e10i	0.471973	−	0.817482i
$437$	−1.13788e10	−	6.56953e9i	−0.312010	−	0.180139i
$438$		0			0
$439$	4.26214e9	+	7.38223e9i	0.114754	+	0.198760i	0.917682	−	0.397317i	$-0.130059\pi$
$439$	4.26214e9	+	7.38223e9i	0.114754	+	0.198760i	−0.802927	+	0.596077i	$0.796725\pi$
$440$			1.52044e10i			0.405656i
$441$		0			0
$442$	−8.17817e9			−0.214273
$443$	1.77214e10	−	1.02315e10i	0.460134	−	0.265658i	−0.251967	−	0.967736i	$-0.581077\pi$
$443$	1.77214e10	−	1.02315e10i	0.460134	−	0.265658i	0.712101	+	0.702077i	$0.247744\pi$
$444$		0			0
$445$	1.13441e10	−	1.96485e10i	0.289287	−	0.501060i
$446$	−2.84242e10	−	1.64107e10i	−0.718372	−	0.414752i
$447$		0			0
$448$	4.31193e9	+	7.46849e9i	0.107043	+	0.185405i
$449$			1.52992e10i			0.376430i	0.982128	+	0.188215i	$0.0602702\pi$
$449$			1.52992e10i			0.376430i	−0.982128	+	0.188215i	$0.939730\pi$
$450$		0			0
$451$	1.72827e10			0.417740
$452$	3.16877e10	−	1.82949e10i	0.759166	−	0.438305i
$453$		0			0
$454$	2.35782e10	−	4.08386e10i	0.554992	−	0.961274i
$455$	−3.16597e10	−	1.82788e10i	−0.738689	−	0.426483i
$456$		0			0
$457$	−1.20106e10	−	2.08029e10i	−0.275359	−	0.476935i	0.694867	−	0.719138i	$-0.255463\pi$
$457$	−1.20106e10	−	2.08029e10i	−0.275359	−	0.476935i	−0.970226	+	0.242203i	$0.922130\pi$
$458$			4.07335e10i			0.925742i
$459$		0			0
$460$	1.46894e10			0.328074
$461$	−4.96796e10	+	2.86825e10i	−1.09995	+	0.635058i	−0.936209	−	0.351445i	$-0.885690\pi$
$461$	−4.96796e10	+	2.86825e10i	−1.09995	+	0.635058i	−0.163744	+	0.986503i	$0.552357\pi$
$462$		0			0
$463$	3.03202e10	−	5.25162e10i	0.659795	−	1.14280i	−0.320874	−	0.947122i	$-0.603977\pi$
$463$	3.03202e10	−	5.25162e10i	0.659795	−	1.14280i	0.980669	−	0.195676i	$-0.0626900\pi$
$464$	7.05962e9	+	4.07587e9i	0.152303	+	0.0879324i
$465$		0			0
$466$	−1.61992e10	−	2.80579e10i	−0.343519	−	0.594992i
$467$			1.01091e10i			0.212543i	0.994337	+	0.106271i	$0.0338912\pi$
$467$			1.01091e10i			0.212543i	−0.994337	+	0.106271i	$0.966109\pi$
$468$		0			0
$469$	−5.09238e10			−1.05252
$470$	4.65128e10	−	2.68542e10i	0.953193	−	0.550326i
$471$		0			0
$472$	−7.27441e9	+	1.25996e10i	−0.146565	+	0.253858i
$473$	8.90324e9	+	5.14029e9i	0.177870	+	0.102693i
$474$		0			0
$475$	4.79505e10	+	8.30528e10i	0.941931	+	1.63147i
$476$			4.62195e10i			0.900322i
$477$		0			0
$478$	1.58727e10			0.304045
$479$	−1.87971e10	+	1.08525e10i	−0.357067	+	0.206153i	−0.667793	−	0.744347i	$-0.732761\pi$
$479$	−1.87971e10	+	1.08525e10i	−0.357067	+	0.206153i	0.310727	+	0.950499i	$0.399428\pi$
$480$		0			0
$481$	−4.94520e9	+	8.56534e9i	−0.0923855	+	0.160016i
$482$	−4.34652e10	−	2.50947e10i	−0.805293	−	0.464936i
$483$		0			0
$484$	7.66982e9	+	1.32845e10i	0.139767	+	0.242083i
$485$			9.64707e10i			1.74353i
$486$		0			0
$487$	−5.82792e9			−0.103609			−0.0518045	−	0.998657i	$-0.516497\pi$
$487$	−5.82792e9			−0.103609			−0.0518045	+	0.998657i	$0.516497\pi$
$488$	1.04287e10	−	6.02100e9i	0.183886	−	0.106167i
$489$		0			0
$490$	−6.80865e10	+	1.17929e11i	−1.18107	+	2.04568i
$491$	2.15718e10	+	1.24545e10i	0.371159	+	0.214288i	0.673964	−	0.738764i	$-0.264590\pi$
$491$	2.15718e10	+	1.24545e10i	0.371159	+	0.214288i	−0.302806	+	0.953052i	$0.597923\pi$
$492$		0			0
$493$	2.18446e10	+	3.78360e10i	0.369791	+	0.640497i
$494$		−	1.15154e10i		−	0.193363i
$495$		0			0
$496$	1.89392e10			0.312921
$497$	−6.03915e10	+	3.48670e10i	−0.989806	+	0.571465i
$498$		0			0
$499$	−8.19755e9	+	1.41986e10i	−0.132215	+	0.229004i	−0.924530	−	0.381109i	$-0.875542\pi$
$499$	−8.19755e9	+	1.41986e10i	−0.132215	+	0.229004i	0.792315	+	0.610112i	$0.208876\pi$
$500$	−4.60899e10	−	2.66100e10i	−0.737438	−	0.425760i
$501$		0			0
$502$	1.36943e10	+	2.37192e10i	0.215638	+	0.373496i
$503$		−	4.61285e10i		−	0.720606i	−0.932835	−	0.360303i	$-0.882673\pi$
$503$		−	4.61285e10i		−	0.720606i	0.932835	−	0.360303i	$-0.117327\pi$
$504$		0			0
$505$	−3.84612e10			−0.591367
$506$	−1.01225e10	+	5.84424e9i	−0.154414	+	0.0891509i
$507$		0			0
$508$	−5.24001e9	+	9.07597e9i	−0.0786824	+	0.136282i
$509$	6.69443e9	+	3.86503e9i	0.0997339	+	0.0575814i	0.549037	−	0.835798i	$-0.314994\pi$
$509$	6.69443e9	+	3.86503e9i	0.0997339	+	0.0575814i	−0.449303	+	0.893379i	$0.648328\pi$
$510$		0			0
$511$	4.99087e10	+	8.64444e10i	0.731969	+	1.26781i
$512$		−	3.03700e9i		−	0.0441942i
$513$		0			0
$514$	−2.72925e10			−0.391013
$515$	8.14229e9	−	4.70095e9i	0.115749	−	0.0668278i
$516$		0			0
$517$	−2.13681e10	+	3.70107e10i	−0.299092	+	0.518042i
$518$	4.84077e10	+	2.79482e10i	0.672349	+	0.388181i
$519$		0			0
$520$	6.43709e9	+	1.11494e10i	0.0880392	+	0.152488i
$521$			3.97902e10i			0.540039i	0.962855	+	0.270019i	$0.0870301\pi$
$521$			3.97902e10i			0.540039i	−0.962855	+	0.270019i	$0.912970\pi$
$522$		0			0
$523$	−3.49978e10			−0.467772			−0.233886	−	0.972264i	$-0.575144\pi$
$523$	−3.49978e10			−0.467772			−0.233886	+	0.972264i	$0.575144\pi$
$524$	−4.19585e10	+	2.42247e10i	−0.556538	+	0.321317i
$525$		0			0
$526$	3.69076e10	−	6.39259e10i	0.482140	−	0.835091i
$527$	8.79053e10	+	5.07521e10i	1.13965	+	0.657979i
$528$		0			0
$529$	−3.35092e10	−	5.80397e10i	−0.427899	−	0.741143i
$530$			1.28058e10i			0.162294i
$531$		0			0
$532$	−6.50804e10			−0.812463
$533$	1.26734e10	−	7.31699e9i	0.157031	−	0.0906617i
$534$		0			0
$535$	1.26536e11	−	2.19167e11i	1.54454	−	2.67523i
$536$	1.55308e10	+	8.96673e9i	0.188163	+	0.108636i
$537$		0			0
$538$	3.75687e10	+	6.50709e10i	0.448433	+	0.776708i
$539$		−	1.08354e11i		−	1.28378i
$540$		0			0
$541$	2.34001e10			0.273168			0.136584	−	0.990629i	$-0.456388\pi$
$541$	2.34001e10			0.273168			0.136584	+	0.990629i	$0.456388\pi$
$542$	2.66729e10	−	1.53996e10i	0.309081	−	0.178448i
$543$		0			0
$544$	8.13839e9	−	1.40961e10i	0.0929272	−	0.160955i
$545$	−2.49236e11	−	1.43897e11i	−2.82504	−	1.63104i
$546$		0			0
$547$	−1.16091e10	−	2.01075e10i	−0.129673	−	0.224600i	0.793877	−	0.608078i	$-0.208059\pi$
$547$	−1.16091e10	−	2.01075e10i	−0.129673	−	0.224600i	−0.923550	+	0.383478i	$0.874726\pi$
$548$			1.23692e10i			0.137158i
$549$		0			0
$550$	8.53134e10			0.932324
$551$	−5.32757e10	+	3.07588e10i	−0.577994	+	0.333705i
$552$		0			0
$553$	2.62770e10	−	4.55131e10i	0.280980	−	0.486671i
$554$	9.81649e10	+	5.66755e10i	1.04212	+	0.601667i
$555$		0			0
$556$	2.72934e10	+	4.72735e10i	0.285600	+	0.494674i
$557$		−	3.65617e10i		−	0.379844i	−0.981799	−	0.189922i	$-0.939176\pi$
$557$		−	3.65617e10i		−	0.379844i	0.981799	−	0.189922i	$-0.0608236\pi$
$558$		0			0
$559$	8.70499e9			0.0891499
$560$	6.30115e10	−	3.63797e10i	0.640719	−	0.369919i
$561$		0			0
$562$	−4.46146e10	+	7.72748e10i	−0.447231	+	0.774627i
$563$	1.15433e11	+	6.66450e10i	1.14893	+	0.663337i	0.948627	−	0.316397i	$-0.102473\pi$
$563$	1.15433e11	+	6.66450e10i	1.14893	+	0.663337i	0.200306	+	0.979733i	$0.435806\pi$
$564$		0			0
$565$	−1.54354e11	−	2.67348e11i	−1.51469	−	2.62352i
$566$			1.10163e10i			0.107342i
$567$		0			0
$568$	2.45577e10			0.235936
$569$	1.42643e11	−	8.23549e10i	1.36082	−	0.785670i	0.371087	−	0.928598i	$-0.378985\pi$
$569$	1.42643e11	−	8.23549e10i	1.36082	−	0.785670i	0.989733	+	0.142928i	$0.0456517\pi$
$570$		0			0
$571$	−6.84597e10	+	1.18576e11i	−0.644007	+	1.11545i	0.340523	+	0.940236i	$0.389396\pi$
$571$	−6.84597e10	+	1.18576e11i	−0.644007	+	1.11545i	−0.984530	+	0.175216i	$0.943937\pi$
$572$	−8.87167e9	−	5.12206e9i	−0.0828745	−	0.0478476i
$573$		0			0
$574$	−4.13525e10	−	7.16247e10i	−0.380938	−	0.659804i
$575$		−	8.24235e10i		−	0.754015i
$576$		0			0
$577$	−1.01555e11			−0.916218			−0.458109	−	0.888896i	$-0.651473\pi$
$577$	−1.01555e11			−0.916218			−0.458109	+	0.888896i	$0.651473\pi$
$578$	7.19976e9	−	4.15678e9i	0.0645070	−	0.0372431i
$579$		0			0
$580$	3.43881e10	−	5.95619e10i	0.303876	−	0.526328i
$581$	−1.14807e11	−	6.62840e10i	−1.00755	−	0.581707i
$582$		0			0
$583$	−5.09485e9	−	8.82453e9i	−0.0441018	−	0.0763866i
$584$		−	3.51519e10i		−	0.302202i
$585$		0			0
$586$	−6.00184e10			−0.508972
$587$	3.25669e10	−	1.88025e10i	0.274299	−	0.158367i	−0.356541	−	0.934280i	$-0.616044\pi$
$587$	3.25669e10	−	1.88025e10i	0.274299	−	0.158367i	0.630840	+	0.775913i	$0.282711\pi$
$588$		0			0
$589$	−7.14626e10	+	1.23777e11i	−0.593769	+	1.02844i
$590$	1.06303e11	+	6.13741e10i	0.877278	+	0.506497i
$591$		0			0
$592$	−9.84229e9	−	1.70474e10i	−0.0801326	−	0.138794i
$593$			1.30215e11i			1.05304i	0.850163	+	0.526519i	$0.176503\pi$
$593$			1.30215e11i			1.05304i	−0.850163	+	0.526519i	$0.823497\pi$
$594$		0			0
$595$	3.89953e11			3.11132
$596$	−4.77998e10	+	2.75972e10i	−0.378827	+	0.218716i
$597$		0			0
$598$	−4.94856e9	+	8.57115e9i	−0.0386967	+	0.0670246i
$599$	−1.13848e11	−	6.57304e10i	−0.884341	−	0.510575i	−0.0122537	−	0.999925i	$-0.503901\pi$
$599$	−1.13848e11	−	6.57304e10i	−0.884341	−	0.510575i	−0.872087	+	0.489350i	$0.837234\pi$
$600$		0			0
$601$	2.15092e10	+	3.72550e10i	0.164864	+	0.285553i	0.936607	−	0.350382i	$-0.113948\pi$
$601$	2.15092e10	+	3.72550e10i	0.164864	+	0.285553i	−0.771743	+	0.635935i	$0.780615\pi$
$602$		−	4.91969e10i		−	0.374586i
$603$		0			0
$604$	−1.07592e11			−0.808409
$605$	1.12081e11	−	6.47102e10i	0.836588	−	0.483004i
$606$		0			0
$607$	−1.29606e10	+	2.24485e10i	−0.0954710	+	0.165361i	−0.909805	−	0.415036i	$-0.863769\pi$
$607$	−1.29606e10	+	2.24485e10i	−0.0954710	+	0.165361i	0.814334	+	0.580396i	$0.197102\pi$
$608$	1.98483e10	+	1.14594e10i	0.145248	+	0.0838588i
$609$		0			0
$610$	−5.07990e10	−	8.79865e10i	−0.366890	−	0.635472i
$611$			3.61866e10i			0.259646i
$612$		0			0
$613$	1.28485e11			0.909933			0.454967	−	0.890508i	$-0.349651\pi$
$613$	1.28485e11			0.909933			0.454967	+	0.890508i	$0.349651\pi$
$614$	−1.31529e11	+	7.59383e10i	−0.925439	+	0.534303i
$615$		0			0
$616$	−2.89477e10	+	5.01389e10i	−0.201044	+	0.348219i
$617$	1.02289e11	+	5.90563e10i	0.705808	+	0.407498i	0.809507	−	0.587110i	$-0.199735\pi$
$617$	1.02289e11	+	5.90563e10i	0.705808	+	0.407498i	−0.103699	+	0.994609i	$0.533068\pi$
$618$		0			0
$619$	−6.40218e10	−	1.10889e11i	−0.436079	−	0.755312i	0.561304	−	0.827610i	$-0.310300\pi$
$619$	−6.40218e10	−	1.10889e11i	−0.436079	−	0.755312i	−0.997383	+	0.0722982i	$0.976967\pi$
$620$		−	1.59789e11i		−	1.08139i
$621$		0			0
$622$	2.59046e10			0.173068
$623$	7.48177e10	−	4.31960e10i	0.496652	−	0.286742i
$624$		0			0
$625$	−7.30176e10	+	1.26470e11i	−0.478528	+	0.828835i
$626$	−1.75219e11	−	1.01163e11i	−1.14100	−	0.658754i
$627$		0			0
$628$	−2.69977e10	−	4.67613e10i	−0.173575	−	0.300641i
$629$		−	1.05499e11i		−	0.673980i
$630$		0			0
$631$	−2.40613e11			−1.51775			−0.758877	−	0.651233i	$-0.774252\pi$
$631$	−2.40613e11			−1.51775			−0.758877	+	0.651233i	$0.774252\pi$
$632$	−1.60280e10	+	9.25377e9i	−0.100464	+	0.0580030i
$633$		0			0
$634$	3.77159e10	−	6.53258e10i	0.233436	−	0.404322i
$635$	7.65738e10	+	4.42099e10i	0.470961	+	0.271910i
$636$		0			0
$637$	−4.58740e10	−	7.94561e10i	−0.278618	−	0.482580i
$638$			5.47259e10i			0.330301i
$639$		0			0
$640$	−2.56231e10			−0.152726
$641$	−1.87111e11	+	1.08029e11i	−1.10833	+	0.639893i	−0.938396	−	0.345563i	$-0.887688\pi$
$641$	−1.87111e11	+	1.08029e11i	−1.10833	+	0.639893i	−0.169932	+	0.985456i	$0.554355\pi$
$642$		0			0
$643$	−1.85669e10	+	3.21588e10i	−0.108616	+	0.188129i	−0.915210	−	0.402977i	$-0.867975\pi$
$643$	−1.85669e10	+	3.21588e10i	−0.108616	+	0.188129i	0.806594	+	0.591106i	$0.201309\pi$
$644$	4.84405e10	+	2.79671e10i	0.281621	+	0.162594i
$645$		0			0
$646$	6.14167e10	+	1.06377e11i	0.352660	+	0.610825i
$647$			5.88598e10i			0.335894i	0.985796	+	0.167947i	$0.0537137\pi$
$647$			5.88598e10i			0.335894i	−0.985796	+	0.167947i	$0.946286\pi$
$648$		0			0
$649$	−9.76719e10			−0.550543
$650$	6.25603e10	−	3.61192e10i	0.350465	−	0.202341i
$651$		0			0
$652$	−3.52523e10	+	6.10588e10i	−0.195073	+	0.337877i
$653$	1.48938e11	+	8.59893e10i	0.819129	+	0.472925i	0.850116	−	0.526595i	$-0.176532\pi$
$653$	1.48938e11	+	8.59893e10i	0.819129	+	0.472925i	−0.0309867	+	0.999520i	$0.509865\pi$
$654$		0			0
$655$	2.04384e11	+	3.54003e11i	1.11040	+	1.92328i
$656$			2.91256e10i			0.157275i
$657$		0			0
$658$	2.04511e11			1.09097
$659$	−2.34850e11	+	1.35591e11i	−1.24523	+	0.718934i	−0.970154	−	0.242489i	$-0.922036\pi$
$659$	−2.34850e11	+	1.35591e11i	−1.24523	+	0.718934i	−0.275075	+	0.961423i	$0.588703\pi$
$660$		0			0
$661$	1.21597e11	−	2.10613e11i	0.636968	−	1.10326i	−0.349126	−	0.937076i	$-0.613522\pi$
$661$	1.21597e11	−	2.10613e11i	0.636968	−	1.10326i	0.986095	−	0.166185i	$-0.0531451\pi$
$662$	1.53689e11	+	8.87325e10i	0.800223	+	0.462009i
$663$		0			0
$664$	2.33427e10	+	4.04308e10i	0.120082	+	0.207989i
$665$			5.49082e11i			2.80770i
$666$		0			0
$667$	5.28721e10			0.267130
$668$	−6.72704e10	+	3.88386e10i	−0.337846	+	0.195055i
$669$		0			0
$670$	7.56521e10	−	1.31033e11i	0.375424	−	0.650253i
$671$	7.00118e10	+	4.04213e10i	0.345367	+	0.199398i
$672$		0			0
$673$	1.44609e10	+	2.50471e10i	0.0704914	+	0.122095i	0.899117	−	0.437709i	$-0.144210\pi$
$673$	1.44609e10	+	2.50471e10i	0.0704914	+	0.122095i	−0.828625	+	0.559804i	$0.810877\pi$
$674$		−	2.92320e10i		−	0.141651i
$675$		0			0
$676$	9.57394e10			0.458463
$677$	−1.58076e11	+	9.12654e10i	−0.752509	+	0.434462i	−0.826600	−	0.562790i	$-0.809728\pi$
$677$	−1.58076e11	+	9.12654e10i	−0.752509	+	0.434462i	0.0740905	+	0.997252i	$0.476395\pi$
$678$		0			0
$679$	−1.83671e11	+	3.18127e11i	−0.864095	+	1.49666i
$680$	−1.18929e11	−	6.86634e10i	−0.556225	−	0.321137i
$681$		0			0
$682$	6.35730e10	+	1.10112e11i	0.293857	+	0.508974i
$683$		−	3.71514e11i		−	1.70723i	−0.520903	−	0.853616i	$-0.674405\pi$
$683$		−	3.71514e11i		−	1.70723i	0.520903	−	0.853616i	$-0.325595\pi$
$684$		0			0
$685$	1.04359e11			0.473989
$686$	−2.16783e11	+	1.25159e11i	−0.978876	+	0.565155i
$687$		0			0
$688$	−8.66264e9	+	1.50041e10i	−0.0386631	+	0.0669665i
$689$	−7.47209e9	−	4.31401e9i	−0.0331562	−	0.0191428i
$690$		0			0
$691$	−9.88238e10	−	1.71168e11i	−0.433460	−	0.750775i	0.563708	−	0.825974i	$-0.309374\pi$
$691$	−9.88238e10	−	1.71168e11i	−0.433460	−	0.750775i	−0.997169	+	0.0751987i	$0.976041\pi$
$692$		−	1.22175e11i		−	0.532794i
$693$		0			0
$694$	1.90246e11			0.820119
$695$	3.98846e11	−	2.30274e11i	1.70949	−	0.986973i
$696$		0			0
$697$	−7.80492e10	+	1.35185e11i	−0.330702	+	0.572793i
$698$	−2.39788e11	−	1.38442e11i	−1.01020	−	0.583237i
$699$		0			0
$700$	−2.04130e11	−	3.53564e11i	−0.850189	−	1.47257i
$701$		−	6.70096e10i		−	0.277501i	−0.990327	−	0.138751i	$-0.955691\pi$
$701$		−	6.70096e10i		−	0.277501i	0.990327	−	0.138751i	$-0.0443087\pi$
$702$		0			0
$703$	1.48551e11			0.608209
$704$	1.76570e10	−	1.01943e10i	0.0718831	−	0.0415017i
$705$		0			0
$706$	−5.91201e10	+	1.02399e11i	−0.237967	+	0.412170i
$707$	−1.26832e11	−	7.32264e10i	−0.507634	−	0.293083i
$708$		0			0
$709$	5.70291e10	+	9.87774e10i	0.225690	+	0.390906i	0.956526	−	0.291647i	$-0.0942031\pi$
$709$	5.70291e10	+	9.87774e10i	0.225690	+	0.390906i	−0.730836	+	0.682553i	$0.760870\pi$
$710$		−	2.07193e11i		−	0.815345i
$711$		0			0
$712$	−3.04240e10			−0.118385
$713$	1.06382e11	−	6.14196e10i	0.411632	−	0.237656i
$714$		0			0
$715$	−4.32147e10	+	7.48501e10i	−0.165351	+	0.286397i
$716$	1.04646e11	+	6.04172e10i	0.398171	+	0.229884i
$717$		0			0
$718$	−1.34348e11	−	2.32698e11i	−0.505516	−	0.875580i
$719$			2.31072e11i			0.864633i	0.901722	+	0.432317i	$0.142304\pi$
$719$			2.31072e11i			0.864633i	−0.901722	+	0.432317i	$0.857696\pi$
$720$		0			0
$721$	3.58007e10			0.132480
$722$	1.66181e10	−	9.59444e9i	0.0611549	−	0.0353078i
$723$		0			0
$724$	−5.55667e10	+	9.62444e10i	−0.202237	+	0.350285i
$725$	−3.34208e11	−	1.92955e11i	−1.20966	−	0.698400i
$726$		0			0
$727$	1.70637e11	+	2.95551e11i	0.610850	+	1.05802i	0.991097	+	0.133138i	$0.0425055\pi$
$727$	1.70637e11	+	2.95551e11i	0.610850	+	1.05802i	−0.380248	+	0.924885i	$0.624161\pi$
$728$			4.90224e10i			0.174530i
$729$		0			0
$730$	−2.96576e11			−1.04435
$731$	−8.04145e10	+	4.64274e10i	−0.281621	+	0.162594i
$732$		0			0
$733$	2.07203e11	−	3.58887e11i	0.717763	−	1.24320i	−0.244122	−	0.969745i	$-0.578500\pi$
$733$	2.07203e11	−	3.58887e11i	0.717763	−	1.24320i	0.961884	−	0.273457i	$-0.0881670\pi$
$734$	1.01396e11	+	5.85408e10i	0.349330	+	0.201685i
$735$		0			0
$736$	−9.84897e9	−	1.70589e10i	−0.0335645	−	0.0581353i
$737$			1.20394e11i			0.408071i
$738$		0			0
$739$	2.71838e11			0.911449			0.455725	−	0.890121i	$-0.349380\pi$
$739$	2.71838e11			0.911449			0.455725	+	0.890121i	$0.349380\pi$
$740$	−1.43828e11	+	8.30392e10i	−0.479642	+	0.276921i
$741$		0			0
$742$	−2.43810e10	+	4.22291e10i	−0.0804332	+	0.139314i
$743$	2.96676e11	+	1.71286e11i	0.973479	+	0.562039i	0.900295	−	0.435280i	$-0.143351\pi$
$743$	2.96676e11	+	1.71286e11i	0.973479	+	0.562039i	0.0731842	+	0.997318i	$0.476684\pi$
$744$		0			0
$745$	2.32837e11	+	4.03286e11i	0.755835	+	1.30914i
$746$			9.11142e10i			0.294192i
$747$		0			0
$748$	1.09272e11			0.349063
$749$	8.34547e11	−	4.81826e11i	2.65170	−	1.53096i
$750$		0			0
$751$	−5.25839e10	+	9.10780e10i	−0.165308	+	0.286321i	−0.936765	−	0.349960i	$-0.886195\pi$
$751$	−5.25839e10	+	9.10780e10i	−0.165308	+	0.286321i	0.771457	+	0.636282i	$0.219528\pi$
$752$	−6.23721e10	−	3.60105e10i	−0.195038	−	0.112605i
$753$		0			0
$754$	2.31693e10	+	4.01304e10i	0.0716849	+	0.124162i
$755$			9.07750e11i			2.79369i
$756$		0			0
$757$	−4.23531e11			−1.28974			−0.644869	−	0.764293i	$-0.723088\pi$
$757$	−4.23531e11			−1.28974			−0.644869	+	0.764293i	$0.723088\pi$
$758$	2.57900e11	−	1.48898e11i	0.781221	−	0.451038i
$759$		0			0
$760$	9.66830e10	−	1.67460e11i	0.289798	−	0.501945i
$761$	−4.62418e11	−	2.66977e11i	−1.37878	−	0.796041i	−0.386770	−	0.922176i	$-0.626409\pi$
$761$	−4.62418e11	−	2.66977e11i	−1.37878	−	0.796041i	−0.992013	+	0.126135i	$0.959743\pi$
$762$		0			0
$763$	−5.47931e11	−	9.49044e11i	−1.61669	−	2.80019i
$764$		−	9.01526e9i		−	0.0264609i
$765$		0			0
$766$	−3.46118e11			−1.00533
$767$	−7.16228e10	+	4.13514e10i	−0.206952	+	0.119484i
$768$		0			0
$769$	−5.66789e10	+	9.81707e10i	−0.162075	+	0.280722i	−0.935613	−	0.353028i	$-0.885152\pi$
$769$	−5.66789e10	+	9.81707e10i	−0.162075	+	0.280722i	0.773538	+	0.633750i	$0.218485\pi$
$770$	4.23021e11	+	2.44231e11i	1.20337	+	0.694766i
$771$		0			0
$772$	1.75195e11	+	3.03447e11i	0.493234	+	0.854306i
$773$		−	2.83942e11i		−	0.795265i	−0.917545	−	0.397632i	$-0.869832\pi$
$773$		−	2.83942e11i		−	0.795265i	0.917545	−	0.397632i	$-0.130168\pi$
$774$		0			0
$775$	−8.96595e11			−2.48536
$776$	1.12032e11	−	6.46820e10i	0.308956	−	0.178376i
$777$		0			0
$778$	2.46119e11	−	4.26290e11i	0.671779	−	1.16355i
$779$	−1.90350e11	−	1.09899e11i	−0.516897	−	0.298430i
$780$		0			0
$781$	8.24328e10	+	1.42778e11i	0.221562	+	0.383757i
$782$		−	1.05571e11i		−	0.282304i
$783$		0			0
$784$	1.82603e11			0.483331
$785$	−3.94524e11	+	2.27779e11i	−1.03895	+	0.599839i
$786$		0			0
$787$	3.25568e11	−	5.63900e11i	0.848678	−	1.46995i	−0.0337110	−	0.999432i	$-0.510733\pi$
$787$	3.25568e11	−	5.63900e11i	0.848678	−	1.46995i	0.882389	−	0.470521i	$-0.155934\pi$
$788$	6.06662e10	+	3.50257e10i	0.157341	+	0.0908409i
$789$		0			0
$790$	7.80739e10	+	1.35228e11i	0.200446	+	0.347183i
$791$		−	1.17550e12i		−	3.00273i
$792$		0			0
$793$	6.84528e10			0.173100
$794$	−4.22703e11	+	2.44047e11i	−1.06354	+	0.614034i
$795$		0			0
$796$	−1.70539e11	+	2.95382e11i	−0.424787	+	0.735753i
$797$	−4.16469e11	−	2.40448e11i	−1.03216	−	0.595921i	−0.114561	−	0.993416i	$-0.536546\pi$
$797$	−4.16469e11	−	2.40448e11i	−1.03216	−	0.595921i	−0.917604	+	0.397496i	$0.869879\pi$
$798$		0			0
$799$	−1.92998e11	−	3.34283e11i	−0.473550	−	0.820213i
$800$			1.43774e11i			0.351011i
$801$		0			0
$802$	−2.05699e11			−0.497204
$803$	2.04372e11	−	1.17994e11i	0.491541	−	0.283791i
$804$		0			0
$805$	2.35958e11	−	4.08692e11i	0.561890	−	0.973223i
$806$	9.32361e10	+	5.38299e10i	0.220925	+	0.127551i
$807$		0			0
$808$	2.57876e10	+	4.46654e10i	0.0605013	+	0.104791i
$809$			1.97505e11i			0.461089i	0.973062	+	0.230545i	$0.0740508\pi$
$809$			1.97505e11i			0.461089i	−0.973062	+	0.230545i	$0.925949\pi$
$810$		0			0
$811$	−1.30697e11			−0.302121			−0.151061	−	0.988524i	$-0.548269\pi$
$811$	−1.30697e11			−0.302121			−0.151061	+	0.988524i	$0.548269\pi$
$812$	2.26800e11	−	1.30943e11i	0.521698	−	0.301203i
$813$		0			0
$814$	6.60752e10	−	1.14446e11i	0.150501	−	0.260676i
$815$	5.15152e11	+	2.97423e11i	1.16763	+	0.674131i
$816$		0			0
$817$	−6.53730e10	−	1.13229e11i	−0.146727	−	0.254139i
$818$			7.32504e10i			0.163605i
$819$		0			0
$820$	2.45732e11			0.543509
$821$	−2.25465e10	+	1.30172e10i	−0.0496256	+	0.0286514i	−0.524608	−	0.851344i	$-0.675788\pi$
$821$	−2.25465e10	+	1.30172e10i	−0.0496256	+	0.0286514i	0.474982	+	0.879996i	$0.342455\pi$
$822$		0			0
$823$	1.02310e11	−	1.77206e11i	0.223007	−	0.386260i	−0.732712	−	0.680539i	$-0.761746\pi$
$823$	1.02310e11	−	1.77206e11i	0.223007	−	0.386260i	0.955720	+	0.294278i	$0.0950792\pi$
$824$	−1.09185e10	−	6.30382e9i	−0.0236840	−	0.0136740i
$825$		0			0
$826$	2.33701e11	+	4.04781e11i	0.502042	+	0.869562i
$827$		−	2.31574e11i		−	0.495072i	−0.968879	−	0.247536i	$-0.920379\pi$
$827$		−	2.31574e11i		−	0.495072i	0.968879	−	0.247536i	$-0.0796208\pi$
$828$		0			0
$829$	7.98205e11			1.69004			0.845019	−	0.534736i	$-0.179589\pi$
$829$	7.98205e11			1.69004			0.845019	+	0.534736i	$0.179589\pi$
$830$	3.41114e11	−	1.96942e11i	0.718765	−	0.414979i
$831$		0			0
$832$	8.63192e9	−	1.49509e10i	0.0180142	−	0.0312015i
$833$	8.47545e11	+	4.89331e11i	1.76029	+	1.01630i
$834$		0			0
$835$	3.27681e11	+	5.67559e11i	0.674070	+	1.16752i
$836$			1.53863e11i			0.315000i
$837$		0			0
$838$	−4.28623e11			−0.869160
$839$	−5.56790e11	+	3.21463e11i	−1.12368	+	0.648758i	−0.942338	−	0.334662i	$-0.891378\pi$
$839$	−5.56790e11	+	3.21463e11i	−1.12368	+	0.648758i	−0.181343	+	0.983420i	$0.558045\pi$
$840$		0			0
$841$	−1.26349e11	+	2.18842e11i	−0.252573	+	0.437469i
$842$	−4.67914e11	−	2.70150e11i	−0.930931	−	0.537473i
$843$		0			0
$844$	1.20210e11	+	2.08209e11i	0.236902	+	0.410327i
$845$		−	8.07752e11i		−	1.58435i
$846$		0			0
$847$	4.92808e11			0.957511
$848$	1.48715e10	−	8.58606e9i	0.0287588	−	0.0166039i
$849$		0			0
$850$	−3.85278e11	+	6.67321e11i	−0.738071	+	1.27838i
$851$	−1.10569e11	−	6.38370e10i	−0.210821	−	0.121718i
$852$		0			0
$853$	9.75384e10	+	1.68942e11i	0.184238	+	0.319110i	0.943320	−	0.331886i	$-0.107685\pi$
$853$	9.75384e10	+	1.68942e11i	0.184238	+	0.319110i	−0.759081	+	0.650996i	$0.774352\pi$
$854$		−	3.86866e11i		−	0.727326i
$855$		0			0
$856$	−3.39362e11			−0.632074
$857$	3.84904e10	−	2.22224e10i	0.0713557	−	0.0411972i	−0.463898	−	0.885889i	$-0.653549\pi$
$857$	3.84904e10	−	2.22224e10i	0.0713557	−	0.0411972i	0.535253	+	0.844692i	$0.320216\pi$
$858$		0			0
$859$	−1.25294e11	+	2.17015e11i	−0.230122	+	0.398582i	−0.957844	−	0.287290i	$-0.907246\pi$
$859$	−1.25294e11	+	2.17015e11i	−0.230122	+	0.398582i	0.727722	+	0.685872i	$0.240579\pi$
$860$	1.26590e11	+	7.30866e10i	0.231422	+	0.133611i
$861$		0			0
$862$	1.54656e11	+	2.67871e11i	0.280115	+	0.485174i
$863$			3.91558e11i			0.705915i	0.935639	+	0.352958i	$0.114824\pi$
$863$			3.91558e11i			0.705915i	−0.935639	+	0.352958i	$0.885176\pi$
$864$		0			0
$865$	−1.03079e12			−1.84122
$866$	6.82876e10	−	3.94259e10i	0.121415	−	0.0700987i
$867$		0			0
$868$	3.04224e11	−	5.26931e11i	0.535937	−	0.928271i
$869$	−1.07602e11	−	6.21242e10i	−0.188687	−	0.108939i
$870$		0			0
$871$	5.09714e10	+	8.82851e10i	0.0885633	+	0.153396i
$872$			3.85921e11i			0.667471i
$873$		0			0
$874$	1.48651e11			0.254755
$875$	−1.48070e12	+	8.54884e11i	−2.52601	+	1.45839i
$876$		0			0
$877$	3.99055e10	−	6.91184e10i	0.0674582	−	0.116841i	−0.830324	−	0.557282i	$-0.811844\pi$
$877$	3.99055e10	−	6.91184e10i	0.0674582	−	0.116841i	0.897782	+	0.440441i	$0.145178\pi$
$878$	−8.35204e10	−	4.82206e10i	−0.140545	−	0.0811436i
$879$		0			0
$880$	−8.60090e10	−	1.48972e11i	−0.143421	−	0.248413i
$881$			5.84453e11i			0.970166i	0.874468	+	0.485083i	$0.161211\pi$
$881$			5.84453e11i			0.970166i	−0.874468	+	0.485083i	$0.838789\pi$
$882$		0			0
$883$	7.52384e10			0.123765			0.0618823	−	0.998083i	$-0.480290\pi$
$883$	7.52384e10			0.123765			0.0618823	+	0.998083i	$0.480290\pi$
$884$	8.01294e10	−	4.62627e10i	0.131215	−	0.0757569i
$885$		0			0
$886$	−1.15756e11	+	2.00495e11i	−0.187849	+	0.325364i
$887$	−6.05896e11	−	3.49814e11i	−0.978822	−	0.565123i	−0.0769076	−	0.997038i	$-0.524505\pi$
$887$	−6.05896e11	−	3.49814e11i	−0.978822	−	0.565123i	−0.901914	+	0.431915i	$0.857838\pi$
$888$		0			0
$889$	1.68343e11	+	2.91578e11i	0.269518	+	0.466819i
$890$			2.56687e11i			0.409113i
$891$		0			0
$892$	3.71333e11			0.586548
$893$	4.70694e11	−	2.71755e11i	0.740172	−	0.427338i
$894$		0			0
$895$	5.09739e11	−	8.82894e11i	0.794430	−	1.37599i
$896$	−8.44963e10	−	4.87840e10i	−0.131101	−	0.0756911i
$897$		0			0
$898$	−8.65455e10	−	1.49901e11i	−0.133088	−	0.230515i
$899$		−	5.75137e11i		−	0.880507i
$900$		0			0
$901$	9.20338e10			0.139652
$902$	−1.69335e11	+	9.77658e10i	−0.255812	+	0.147693i
$903$		0			0
$904$	−2.06983e11	+	3.58505e11i	−0.309928	+	0.536812i
$905$	8.12012e11	+	4.68815e11i	1.21051	+	0.698888i
$906$		0			0
$907$	−5.79947e10	−	1.00450e11i	−0.0856958	−	0.148429i	0.819992	−	0.572375i	$-0.193978\pi$
$907$	−5.79947e10	−	1.00450e11i	−0.0856958	−	0.148429i	−0.905687	+	0.423946i	$0.860645\pi$
$908$			5.33513e11i			0.784877i
$909$		0			0
$910$	4.13601e11			0.603137
$911$	−9.81176e11	+	5.66482e11i	−1.42454	+	0.822456i	−0.996682	−	0.0813913i	$-0.974064\pi$
$911$	−9.81176e11	+	5.66482e11i	−1.42454	+	0.822456i	−0.427854	+	0.903848i	$0.640730\pi$
$912$		0			0
$913$	−1.56709e11	+	2.71428e11i	−0.225533	+	0.390635i
$914$	2.35358e11	+	1.35884e11i	0.337244	+	0.194708i
$915$		0			0
$916$	−2.30424e11	−	3.99105e11i	−0.327299	−	0.566899i
$917$			1.55651e12i			2.20127i
$918$		0			0
$919$	−3.06256e11			−0.429361			−0.214680	−	0.976684i	$-0.568871\pi$
$919$	−3.06256e11			−0.429361			−0.214680	+	0.976684i	$0.568871\pi$
$920$	−1.43926e11	+	8.30956e10i	−0.200903	+	0.115992i
$921$		0			0
$922$	3.24506e11	−	5.62060e11i	0.449054	−	0.777784i
$923$	1.20896e11	+	6.97992e10i	0.166573	+	0.0961709i
$924$		0			0
$925$	4.65942e11	+	8.07035e11i	0.636451	+	1.10237i
$926$			6.86069e11i			0.933090i
$927$		0			0
$928$	−9.22265e10			−0.124355
$929$	8.75115e11	−	5.05248e11i	1.17490	−	0.678331i	0.220074	−	0.975483i	$-0.429370\pi$
$929$	8.75115e11	−	5.05248e11i	1.17490	−	0.678331i	0.954830	+	0.297152i	$0.0960369\pi$
$930$		0			0
$931$	−6.89012e11	+	1.19340e12i	−0.917124	+	1.58851i
$932$	3.17439e11	+	1.83273e11i	0.420723	+	0.242905i
$933$		0			0
$934$	−5.71858e10	−	9.90488e10i	−0.0751452	−	0.130155i
$935$		−	9.21929e11i		−	1.20629i
$936$		0			0
$937$	−3.80033e11			−0.493018			−0.246509	−	0.969141i	$-0.579283\pi$
$937$	−3.80033e11			−0.493018			−0.246509	+	0.969141i	$0.579283\pi$
$938$	4.98950e11	−	2.88069e11i	0.644533	−	0.372121i
$939$		0			0
$940$	−3.03820e11	+	5.26232e11i	−0.389139	+	0.674009i
$941$	−4.20722e11	−	2.42904e11i	−0.536583	−	0.309796i	0.207110	−	0.978318i	$-0.433594\pi$
$941$	−4.20722e11	−	2.42904e11i	−0.536583	−	0.309796i	−0.743693	+	0.668521i	$0.766928\pi$
$942$		0			0
$943$	9.44541e10	+	1.63599e11i	0.119447	+	0.206888i
$944$		−	1.64601e11i		−	0.207274i
$945$		0			0
$946$	−1.16311e11			−0.145231
$947$	−4.64773e9	+	2.68337e9i	−0.00577885	+	0.00333642i	−0.502887	−	0.864352i	$-0.667729\pi$
$947$	−4.64773e9	+	2.68337e9i	−0.00577885	+	0.00333642i	0.497108	+	0.867689i	$0.334395\pi$
$948$		0			0
$949$	9.99106e10	−	1.73050e11i	0.123182	−	0.213357i
$950$	−9.39635e11	−	5.42498e11i	−1.15363	−	0.666046i
$951$		0			0
$952$	−2.61457e11	−	4.52857e11i	−0.318312	−	0.551332i
$953$		−	2.87948e11i		−	0.349094i	−0.984649	−	0.174547i	$-0.944154\pi$
$953$		−	2.87948e11i		−	0.349094i	0.984649	−	0.174547i	$-0.0558462\pi$
$954$		0			0
$955$	−7.60616e10			−0.0914433
$956$	−1.55520e11	+	8.97893e10i	−0.186189	+	0.107496i
$957$		0			0
$958$	1.22782e11	−	2.12665e11i	0.145772	−	0.252484i
$959$	3.44141e11	+	1.98690e11i	0.406876	+	0.234910i
$960$		0			0
$961$	−2.41670e11	−	4.18585e11i	−0.283354	−	0.490784i
$962$		−	1.11897e11i		−	0.130653i
$963$		0			0
$964$	5.67827e11			0.657519
$965$	2.56017e12	−	1.47812e12i	2.95230	−	1.70451i
$966$		0			0
$967$	−4.51417e11	+	7.81877e11i	−0.516264	+	0.894195i	0.483558	+	0.875312i	$0.339344\pi$
$967$	−4.51417e11	+	7.81877e11i	−0.516264	+	0.894195i	−0.999822	+	0.0188827i	$0.993989\pi$
$968$	−1.50297e11	−	8.67741e10i	−0.171179	−	0.0988300i
$969$		0			0
$970$	−5.45721e11	−	9.45216e11i	−0.616429	−	1.06769i
$971$		−	8.08040e11i		−	0.908983i	−0.890751	−	0.454492i	$-0.849821\pi$
$971$		−	8.08040e11i		−	0.908983i	0.890751	−	0.454492i	$-0.150179\pi$
$972$		0			0
$973$	1.75368e12			1.95658
$974$	5.71017e10	−	3.29677e10i	0.0634473	−	0.0366313i
$975$		0			0
$976$	−6.81198e10	+	1.17987e11i	−0.0750713	+	0.130027i
$977$	−1.39658e12	−	8.06317e11i	−1.53281	−	0.884968i	−0.999231	−	0.0392176i	$-0.987513\pi$
$977$	−1.39658e12	−	8.06317e11i	−1.53281	−	0.884968i	−0.533579	−	0.845750i	$-0.679153\pi$
$978$		0			0
$979$	−1.02124e11	−	1.76884e11i	−0.111173	−	0.192557i
$980$		−	1.54062e12i		−	1.67029i
$981$		0			0
$982$	−2.81812e11			−0.303050
$983$	−1.24469e12	+	7.18625e11i	−1.33306	+	0.769641i	−0.985767	−	0.168117i	$-0.946231\pi$
$983$	−1.24469e12	+	7.18625e11i	−1.33306	+	0.769641i	−0.347290	+	0.937758i	$0.612898\pi$
$984$		0			0
$985$	2.95511e11	−	5.11840e11i	0.313927	−	0.543737i
$986$	−4.28065e11	−	2.47143e11i	−0.452900	−	0.261482i
$987$		0			0
$988$	6.51412e10	+	1.12828e11i	0.0683641	+	0.118410i
$989$			1.12372e11i			0.117455i
$990$		0			0
$991$	−1.11953e12			−1.16075			−0.580377	−	0.814348i	$-0.697095\pi$
$991$	−1.11953e12			−1.16075			−0.580377	+	0.814348i	$0.697095\pi$
$992$	−1.85565e11	+	1.07136e11i	−0.191624	+	0.110634i
$993$		0			0
$994$	3.94476e11	−	6.83252e11i	0.404087	−	0.699899i
$995$	2.49213e12	+	1.43883e12i	2.54261	+	1.46797i
$996$		0			0
$997$	−4.45668e11	−	7.71920e11i	−0.451057	−	0.781253i	0.547395	−	0.836874i	$-0.315619\pi$
$997$	−4.45668e11	−	7.71920e11i	−0.451057	−	0.781253i	−0.998452	+	0.0556212i	$0.982286\pi$
$998$		−	1.85489e11i		−	0.186981i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.9.d.a.17.1		16
3.2	odd	2		18.9.d.a.5.6	✓	16
4.3	odd	2		432.9.q.c.17.1		16
9.2	odd	6	inner	54.9.d.a.35.1		16
9.4	even	3		162.9.b.c.161.8		16
9.5	odd	6		162.9.b.c.161.9		16
9.7	even	3		18.9.d.a.11.6	yes	16
12.11	even	2		144.9.q.b.113.5		16
36.7	odd	6		144.9.q.b.65.5		16
36.11	even	6		432.9.q.c.305.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.6	✓	16	3.2	odd	2
18.9.d.a.11.6	yes	16	9.7	even	3
54.9.d.a.17.1		16	1.1	even	1	trivial
54.9.d.a.35.1		16	9.2	odd	6	inner
144.9.q.b.65.5		16	36.7	odd	6
144.9.q.b.113.5		16	12.11	even	2
162.9.b.c.161.8		16	9.4	even	3
162.9.b.c.161.9		16	9.5	odd	6
432.9.q.c.17.1		16	4.3	odd	2
432.9.q.c.305.1		16	36.11	even	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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-935.250 - 539.967i) q^{5} +(-2056.09 - 3561.25i) q^{7} +1448.15i q^{8} +O(q^{10})\)	\(q+(-9.79796 + 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(-935.250 - 539.967i) q^{5} +(-2056.09 - 3561.25i) q^{7} +1448.15i q^{8} +12218.1 q^{10} +(-8419.53 + 4861.02i) q^{11} +(-4116.02 + 7129.16i) q^{13} +(40291.0 + 23262.0i) q^{14} +(-8192.00 - 14189.0i) q^{16} -87809.9i q^{17} +123643. q^{19} +(-119712. + 69115.7i) q^{20} +(54996.1 - 95256.1i) q^{22} +(-92029.4 - 53133.2i) q^{23} +(387816. + 671717. i) q^{25} -93134.9i q^{26} -526359. q^{28} +(-430885. + 248772. i) q^{29} +(-577977. + 1.00109e6i) q^{31} +(160530. + 92681.9i) q^{32} +(496728. + 860358. i) q^{34} +4.44088e6i q^{35} +1.20145e6 q^{37} +(-1.21145e6 + 699428. i) q^{38} +(781955. - 1.35439e6i) q^{40} +(-1.53952e6 - 888843. i) q^{41} +(-528726. - 915780. i) q^{43} +1.24442e6i q^{44} +1.20227e6 q^{46} +(3.80689e6 - 2.19791e6i) q^{47} +(-5.57261e6 + 9.65205e6i) q^{49} +(-7.59961e6 - 4.38763e6i) q^{50} +(526851. + 912532. i) q^{52} +1.04810e6i q^{53} +1.04991e7 q^{55} +(5.15724e6 - 2.97754e6i) q^{56} +(2.81453e6 - 4.87491e6i) q^{58} +(8.70048e6 + 5.02323e6i) q^{59} +(-4.15770e6 - 7.20135e6i) q^{61} -1.30781e7i q^{62} -2.09715e6 q^{64} +(7.69902e6 - 4.44503e6i) q^{65} +(6.19183e6 - 1.07246e7i) q^{67} +(-9.73384e6 - 5.61983e6i) q^{68} +(-2.51214e7 - 4.35116e7i) q^{70} -1.69579e7i q^{71} -2.42736e7 q^{73} +(-1.17718e7 + 6.79644e6i) q^{74} +(7.91313e6 - 1.37059e7i) q^{76} +(3.46226e7 + 1.99894e7i) q^{77} +(6.39004e6 + 1.10679e7i) q^{79} +1.76936e7i q^{80} +2.01122e7 q^{82} +(2.79188e7 - 1.61189e7i) q^{83} +(-4.74144e7 + 8.21242e7i) q^{85} +(1.03609e7 + 5.98185e6i) q^{86} +(-7.03950e6 - 1.21928e7i) q^{88} +2.10088e7i q^{89} +3.38516e7 q^{91} +(-1.17798e7 + 6.80105e6i) q^{92} +(-2.48665e7 + 4.30700e7i) q^{94} +(-1.15637e8 - 6.67629e7i) q^{95} +(-4.46651e7 - 7.73622e7i) q^{97} -1.26094e8i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7}+O(q^{10}) \) 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7	\( 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29} + 542438 q^{31} + 220416 q^{34} + 3343328 q^{37} + 1314432 q^{38} - 9218592 q^{41} + 339512 q^{43} + 7417344 q^{46} + 34980606 q^{47} - 2364654 q^{49} - 27744768 q^{50} + 431360 q^{52} - 4584276 q^{55} + 12091392 q^{56} - 7852800 q^{58} - 93924216 q^{59} - 841954 q^{61} - 33554432 q^{64} + 126568134 q^{65} + 29946644 q^{67} + 5476608 q^{68} - 34359552 q^{70} - 7547764 q^{73} - 35124480 q^{74} + 23179520 q^{76} - 9309294 q^{77} + 33813002 q^{79} - 137346048 q^{82} - 114200226 q^{83} - 125696772 q^{85} + 171379584 q^{86} + 7913472 q^{88} + 268578316 q^{91} - 167825664 q^{92} - 11832576 q^{94} + 143949240 q^{95} - 89415484 q^{97}+O(q^{100}) \) 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7 - 45756 * q^11 - 3370 * q^13 + 94464 * q^14 - 131072 * q^16 + 362180 * q^19 + 112896 * q^20 - 61824 * q^22 - 1311138 * q^23 + 963394 * q^25 - 472576 * q^28 + 2851290 * q^29 + 542438 * q^31 + 220416 * q^34 + 3343328 * q^37 + 1314432 * q^38 - 9218592 * q^41 + 339512 * q^43 + 7417344 * q^46 + 34980606 * q^47 - 2364654 * q^49 - 27744768 * q^50 + 431360 * q^52 - 4584276 * q^55 + 12091392 * q^56 - 7852800 * q^58 - 93924216 * q^59 - 841954 * q^61 - 33554432 * q^64 + 126568134 * q^65 + 29946644 * q^67 + 5476608 * q^68 - 34359552 * q^70 - 7547764 * q^73 - 35124480 * q^74 + 23179520 * q^76 - 9309294 * q^77 + 33813002 * q^79 - 137346048 * q^82 - 114200226 * q^83 - 125696772 * q^85 + 171379584 * q^86 + 7913472 * q^88 + 268578316 * q^91 - 167825664 * q^92 - 11832576 * q^94 + 143949240 * q^95 - 89415484 * q^97

Introduction

L-functions

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Database

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