LMFDB - Embedded newform 27.9.d.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,9,Mod(8,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, 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("27.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	27.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:	$10.9992224717$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 427 x^{12} - 1362 x^{11} + 135762 x^{10} - 371244 x^{9} + 18261508 x^{8} + \cdots + 872385888256 $ x^14 - x^13 + 427x^12 - 1362x^11 + 135762x^10 - 371244x^9 + 18261508x^8 - 29352736x^7 + 1757083840x^6 - 1434930432x^5 + 61638378240x^4 + 183604924416x^3 + 1254910111744x^2 + 1078377512960x + 872385888256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{30} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.3
Root			$-2.00397 + 3.47098i$ of defining polynomial
Character	$\chi$	$=$	27.17
Dual form			27.9.d.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.01192 + 3.47098i) q^{2} +(-103.905 + 179.968i) q^{4} +(-331.396 - 191.331i) q^{5} +(467.516 + 809.762i) q^{7} -3219.75i q^{8} +O(q^{10})$	\(q+(-6.01192 + 3.47098i) q^{2} +(-103.905 + 179.968i) q^{4} +(-331.396 - 191.331i) q^{5} +(467.516 + 809.762i) q^{7} -3219.75i q^{8} +2656.43 q^{10} +(-4890.10 + 2823.30i) q^{11} +(17663.1 - 30593.3i) q^{13} +(-5621.34 - 3245.48i) q^{14} +(-15423.9 - 26714.9i) q^{16} -152914. i q^{17} +191248. q^{19} +(68867.1 - 39760.4i) q^{20} +(19599.3 - 33947.0i) q^{22} +(-132313. - 76390.7i) q^{23} +(-122097. - 211478. i) q^{25} +245233. i q^{26} -194308. q^{28} +(-401612. + 231871. i) q^{29} +(-393956. + 682351. i) q^{31} +(899280. + 519200. i) q^{32} +(530763. + 919308. i) q^{34} -357802. i q^{35} -1.10561e6 q^{37} +(-1.14977e6 + 663818. i) q^{38} +(-616039. + 1.06701e6i) q^{40} +(3.14915e6 + 1.81816e6i) q^{41} +(-1.51318e6 - 2.62091e6i) q^{43} -1.17342e6i q^{44} +1.06060e6 q^{46} +(-4.75308e6 + 2.74419e6i) q^{47} +(2.44526e6 - 4.23531e6i) q^{49} +(1.46808e6 + 847594. i) q^{50} +(3.67054e6 + 6.35757e6i) q^{52} -1.41381e7i q^{53} +2.16075e6 q^{55} +(2.60723e6 - 1.50528e6i) q^{56} +(1.60964e6 - 2.78797e6i) q^{58} +(-7.58082e6 - 4.37679e6i) q^{59} +(-3.47102e6 - 6.01198e6i) q^{61} -5.46965e6i q^{62} +688484. q^{64} +(-1.17069e7 + 6.75900e6i) q^{65} +(7.08899e6 - 1.22785e7i) q^{67} +(2.75197e7 + 1.58885e7i) q^{68} +(1.24193e6 + 2.15108e6i) q^{70} +7.97888e6i q^{71} -4.61414e6 q^{73} +(6.64682e6 - 3.83754e6i) q^{74} +(-1.98715e7 + 3.44184e7i) q^{76} +(-4.57241e6 - 2.63988e6i) q^{77} +(-1.37621e6 - 2.38366e6i) q^{79} +1.18043e7i q^{80} -2.52433e7 q^{82} +(-3.52291e7 + 2.03395e7i) q^{83} +(-2.92573e7 + 5.06751e7i) q^{85} +(1.81943e7 + 1.05045e7i) q^{86} +(9.09033e6 + 1.57449e7i) q^{88} +2.90621e7i q^{89} +3.30311e7 q^{91} +(2.74958e7 - 1.58747e7i) q^{92} +(1.90501e7 - 3.29957e7i) q^{94} +(-6.33787e7 - 3.65917e7i) q^{95} +(-4.58061e7 - 7.93386e7i) q^{97} +3.39498e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7}+O(q^{10}) $ 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7	$ 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7} - 516 q^{10} + 28677 q^{11} + 1684 q^{13} - 120966 q^{14} - 65281 q^{16} - 269630 q^{19} - 539454 q^{20} + 61311 q^{22} + 1000452 q^{23} + 65177 q^{25} + 1075708 q^{28} - 3797682 q^{29} - 164132 q^{31} + 8461881 q^{32} + 654993 q^{34} - 1671668 q^{37} - 10967691 q^{38} + 613326 q^{40} + 10239447 q^{41} + 791815 q^{43} + 1189536 q^{46} - 31148628 q^{47} - 4826637 q^{49} + 63849453 q^{50} - 5552720 q^{52} + 8107476 q^{55} - 116638674 q^{56} + 14211822 q^{58} + 83493795 q^{59} - 5255600 q^{61} - 26813830 q^{64} - 69232992 q^{65} - 8288855 q^{67} + 77746743 q^{68} + 27813756 q^{70} - 36721682 q^{73} + 10383450 q^{74} - 42822959 q^{76} - 56158710 q^{77} - 32771822 q^{79} + 236099418 q^{82} + 198915996 q^{83} + 97486146 q^{85} - 146190669 q^{86} + 24955827 q^{88} - 201514504 q^{91} + 295365804 q^{92} - 36698244 q^{94} - 386813838 q^{95} + 127049161 q^{97}+O(q^{100}) $ 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7 - 516 * q^10 + 28677 * q^11 + 1684 * q^13 - 120966 * q^14 - 65281 * q^16 - 269630 * q^19 - 539454 * q^20 + 61311 * q^22 + 1000452 * q^23 + 65177 * q^25 + 1075708 * q^28 - 3797682 * q^29 - 164132 * q^31 + 8461881 * q^32 + 654993 * q^34 - 1671668 * q^37 - 10967691 * q^38 + 613326 * q^40 + 10239447 * q^41 + 791815 * q^43 + 1189536 * q^46 - 31148628 * q^47 - 4826637 * q^49 + 63849453 * q^50 - 5552720 * q^52 + 8107476 * q^55 - 116638674 * q^56 + 14211822 * q^58 + 83493795 * q^59 - 5255600 * q^61 - 26813830 * q^64 - 69232992 * q^65 - 8288855 * q^67 + 77746743 * q^68 + 27813756 * q^70 - 36721682 * q^73 + 10383450 * q^74 - 42822959 * q^76 - 56158710 * q^77 - 32771822 * q^79 + 236099418 * q^82 + 198915996 * q^83 + 97486146 * q^85 - 146190669 * q^86 + 24955827 * q^88 - 201514504 * q^91 + 295365804 * q^92 - 36698244 * q^94 - 386813838 * q^95 + 127049161 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

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

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 $

$2$	−6.01192	+	3.47098i	−0.375745	+	0.216937i	−0.675965	−	0.736933i	$-0.736273\pi$
$2$	−6.01192	+	3.47098i	−0.375745	+	0.216937i	0.300220	+	0.953870i	$0.402940\pi$
$3$		0			0
$3$		0			0
$4$	−103.905	+	179.968i	−0.405877	+	0.703000i
$5$	−331.396	−	191.331i	−0.530233	−	0.306130i	0.210878	−	0.977512i	$-0.432368\pi$
$5$	−331.396	−	191.331i	−0.530233	−	0.306130i	−0.741111	+	0.671382i	$0.765701\pi$
$6$		0			0
$7$	467.516	+	809.762i	0.194717	+	0.337260i	0.946808	−	0.321800i	$-0.104288\pi$
$7$	467.516	+	809.762i	0.194717	+	0.337260i	−0.752091	+	0.659060i	$0.770954\pi$
$8$		−	3219.75i		−	0.786071i
$9$		0			0
$10$	2656.43			0.265643
$11$	−4890.10	+	2823.30i	−0.334001	+	0.192835i	−0.657616	−	0.753353i	$-0.728435\pi$
$11$	−4890.10	+	2823.30i	−0.334001	+	0.192835i	0.323615	+	0.946189i	$0.395102\pi$
$12$		0			0
$13$	17663.1	−	30593.3i	0.618433	−	1.07116i	−0.371339	−	0.928497i	$-0.621101\pi$
$13$	17663.1	−	30593.3i	0.618433	−	1.07116i	0.989772	−	0.142660i	$-0.0455654\pi$
$14$	−5621.34	−	3245.48i	−0.146328	−	0.0844826i
$15$		0			0
$16$	−15423.9	−	26714.9i	−0.235350	−	0.407637i
$17$		−	152914.i		−	1.83085i	−0.402491	−	0.915424i	$-0.631856\pi$
$17$		−	152914.i		−	1.83085i	0.402491	−	0.915424i	$-0.368144\pi$
$18$		0			0
$19$	191248.			1.46751			0.733756	−	0.679413i	$-0.237766\pi$
$19$	191248.			1.46751			0.733756	+	0.679413i	$0.237766\pi$
$20$	68867.1	−	39760.4i	0.430419	−	0.248503i
$21$		0			0
$22$	19599.3	−	33947.0i	0.0836661	−	0.144914i
$23$	−132313.	−	76390.7i	−0.472814	−	0.272979i	0.244603	−	0.969623i	$-0.421342\pi$
$23$	−132313.	−	76390.7i	−0.472814	−	0.272979i	−0.717417	+	0.696644i	$0.754676\pi$
$24$		0			0
$25$	−122097.	−	211478.i	−0.312568	−	0.541384i
$26$			245233.i			0.536643i
$27$		0			0
$28$	−194308.			−0.316125
$29$	−401612.	+	231871.i	−0.567825	+	0.327834i	−0.756280	−	0.654248i	$-0.772985\pi$
$29$	−401612.	+	231871.i	−0.567825	+	0.327834i	0.188455	+	0.982082i	$0.439652\pi$
$30$		0			0
$31$	−393956.	+	682351.i	−0.426580	+	0.738858i	−0.996567	−	0.0827958i	$-0.973615\pi$
$31$	−393956.	+	682351.i	−0.426580	+	0.738858i	0.569987	+	0.821654i	$0.306948\pi$
$32$	899280.	+	519200.i	0.857621	+	0.495147i
$33$		0			0
$34$	530763.	+	919308.i	0.397178	+	0.687932i
$35$		−	357802.i		−	0.238435i
$36$		0			0
$37$	−1.10561e6			−0.589921			−0.294960	−	0.955509i	$-0.595306\pi$
$37$	−1.10561e6			−0.589921			−0.294960	+	0.955509i	$0.595306\pi$
$38$	−1.14977e6	+	663818.i	−0.551410	+	0.318357i
$39$		0			0
$40$	−616039.	+	1.06701e6i	−0.240640	+	0.416801i
$41$	3.14915e6	+	1.81816e6i	1.11444	+	0.643425i	0.939977	−	0.341238i	$-0.110846\pi$
$41$	3.14915e6	+	1.81816e6i	1.11444	+	0.643425i	0.174468	+	0.984663i	$0.444180\pi$
$42$		0			0
$43$	−1.51318e6	−	2.62091e6i	−0.442607	−	0.766617i	0.555275	−	0.831667i	$-0.312613\pi$
$43$	−1.51318e6	−	2.62091e6i	−0.442607	−	0.766617i	−0.997882	+	0.0650494i	$0.979280\pi$
$44$		−	1.17342e6i		−	0.313070i
$45$		0			0
$46$	1.06060e6			0.236876
$47$	−4.75308e6	+	2.74419e6i	−0.974055	+	0.562371i	−0.900470	−	0.434918i	$-0.856777\pi$
$47$	−4.75308e6	+	2.74419e6i	−0.974055	+	0.562371i	−0.0735846	+	0.997289i	$0.523444\pi$
$48$		0			0
$49$	2.44526e6	−	4.23531e6i	0.424170	−	0.734685i
$50$	1.46808e6	+	847594.i	0.234892	+	0.135615i
$51$		0			0
$52$	3.67054e6	+	6.35757e6i	0.502015	+	0.869516i
$53$		−	1.41381e7i		−	1.79179i	−0.444269	−	0.895894i	$-0.646536\pi$
$53$		−	1.41381e7i		−	1.79179i	0.444269	−	0.895894i	$-0.353464\pi$
$54$		0			0
$55$	2.16075e6			0.236131
$56$	2.60723e6	−	1.50528e6i	0.265111	−	0.153062i
$57$		0			0
$58$	1.60964e6	−	2.78797e6i	0.142238	−	0.246364i
$59$	−7.58082e6	−	4.37679e6i	−0.625617	−	0.361200i	0.153436	−	0.988159i	$-0.450966\pi$
$59$	−7.58082e6	−	4.37679e6i	−0.625617	−	0.361200i	−0.779052	+	0.626959i	$0.784299\pi$
$60$		0			0
$61$	−3.47102e6	−	6.01198e6i	−0.250690	−	0.434209i	0.713026	−	0.701138i	$-0.247324\pi$
$61$	−3.47102e6	−	6.01198e6i	−0.250690	−	0.434209i	−0.963716	+	0.266929i	$0.913991\pi$
$62$		−	5.46965e6i		−	0.370163i
$63$		0			0
$64$	688484.			0.0410368
$65$	−1.17069e7	+	6.75900e6i	−0.655827	+	0.378642i
$66$		0			0
$67$	7.08899e6	−	1.22785e7i	0.351791	−	0.609321i	−0.634772	−	0.772700i	$-0.718906\pi$
$67$	7.08899e6	−	1.22785e7i	0.351791	−	0.609321i	0.986563	+	0.163379i	$0.0522393\pi$
$68$	2.75197e7	+	1.58885e7i	1.28709	+	0.743099i
$69$		0			0
$70$	1.24193e6	+	2.15108e6i	0.0517254	+	0.0895909i
$71$			7.97888e6i			0.313985i	0.987600	+	0.156992i	$0.0501798\pi$
$71$			7.97888e6i			0.313985i	−0.987600	+	0.156992i	$0.949820\pi$
$72$		0			0
$73$	−4.61414e6			−0.162480			−0.0812399	−	0.996695i	$-0.525888\pi$
$73$	−4.61414e6			−0.162480			−0.0812399	+	0.996695i	$0.525888\pi$
$74$	6.64682e6	−	3.83754e6i	0.221660	−	0.127975i
$75$		0			0
$76$	−1.98715e7	+	3.44184e7i	−0.595630	+	1.03166i
$77$	−4.57241e6	−	2.63988e6i	−0.130071	−	0.0750968i
$78$		0			0
$79$	−1.37621e6	−	2.38366e6i	−0.0353326	−	0.0611979i	0.847818	−	0.530287i	$-0.177916\pi$
$79$	−1.37621e6	−	2.38366e6i	−0.0353326	−	0.0611979i	−0.883151	+	0.469089i	$0.844582\pi$
$80$			1.18043e7i			0.288191i
$81$		0			0
$82$	−2.52433e7			−0.558329
$83$	−3.52291e7	+	2.03395e7i	−0.742316	+	0.428577i	−0.822911	−	0.568170i	$-0.807651\pi$
$83$	−3.52291e7	+	2.03395e7i	−0.742316	+	0.428577i	0.0805945	+	0.996747i	$0.474318\pi$
$84$		0			0
$85$	−2.92573e7	+	5.06751e7i	−0.560478	+	0.970776i
$86$	1.81943e7	+	1.05045e7i	0.332614	+	0.192035i
$87$		0			0
$88$	9.09033e6	+	1.57449e7i	0.151582	+	0.262548i
$89$			2.90621e7i			0.463199i	0.972811	+	0.231599i	$0.0743958\pi$
$89$			2.90621e7i			0.463199i	−0.972811	+	0.231599i	$0.925604\pi$
$90$		0			0
$91$	3.30311e7			0.481678
$92$	2.74958e7	−	1.58747e7i	0.383808	−	0.221592i
$93$		0			0
$94$	1.90501e7	−	3.29957e7i	0.243997	−	0.422616i
$95$	−6.33787e7	−	3.65917e7i	−0.778124	−	0.449250i
$96$		0			0
$97$	−4.58061e7	−	7.93386e7i	−0.517412	−	0.896185i	−0.999795	−	0.0202242i	$-0.993562\pi$
$97$	−4.58061e7	−	7.93386e7i	−0.517412	−	0.896185i	0.482383	−	0.875960i	$-0.339771\pi$
$98$			3.39498e7i			0.368072i
$99$		0			0
$100$	5.07458e7			0.507458
$101$	1.61684e8	−	9.33484e7i	1.55375	−	0.897060i	0.555922	−	0.831235i	$-0.312365\pi$
$101$	1.61684e8	−	9.33484e7i	1.55375	−	0.897060i	0.997831	−	0.0658252i	$-0.0209680\pi$
$102$		0			0
$103$	8.19171e7	−	1.41885e8i	0.727823	−	1.26063i	−0.229979	−	0.973196i	$-0.573866\pi$
$103$	8.19171e7	−	1.41885e8i	0.727823	−	1.26063i	0.957802	−	0.287430i	$-0.0928010\pi$
$104$	−9.85028e7	−	5.68706e7i	−0.842006	−	0.486132i
$105$		0			0
$106$	4.90730e7	+	8.49969e7i	0.388704	+	0.673255i
$107$			1.15537e7i			0.0881427i	0.999028	+	0.0440714i	$0.0140329\pi$
$107$			1.15537e7i			0.0881427i	−0.999028	+	0.0440714i	$0.985967\pi$
$108$		0			0
$109$	−5.79498e7			−0.410531			−0.205265	−	0.978706i	$-0.565806\pi$
$109$	−5.79498e7			−0.410531			−0.205265	+	0.978706i	$0.565806\pi$
$110$	−1.29902e7	+	7.49992e6i	−0.0887251	+	0.0512255i
$111$		0			0
$112$	1.44218e7	−	2.49793e7i	0.0916532	−	0.158748i
$113$	−1.35905e8	−	7.84647e7i	−0.833530	−	0.481239i	0.0215297	−	0.999768i	$-0.493146\pi$
$113$	−1.35905e8	−	7.84647e7i	−0.833530	−	0.481239i	−0.855060	+	0.518529i	$0.826480\pi$
$114$		0			0
$115$	2.92319e7	+	5.06311e7i	0.167134	+	0.289485i
$116$		−	9.63696e7i		−	0.532241i
$117$		0			0
$118$	6.07671e7			0.313430
$119$	1.23824e8	−	7.14899e7i	0.617472	−	0.356498i
$120$		0			0
$121$	−9.12374e7	+	1.58028e8i	−0.425629	+	0.737211i
$122$	4.17350e7	+	2.40957e7i	0.188391	+	0.108768i
$123$		0			0
$124$	−8.18675e7	−	1.41799e8i	−0.346278	−	0.599771i
$125$			2.42922e8i			0.995007i
$126$		0			0
$127$	3.23373e7			0.124305			0.0621525	−	0.998067i	$-0.480203\pi$
$127$	3.23373e7			0.124305			0.0621525	+	0.998067i	$0.480203\pi$
$128$	−2.34355e8	+	1.35305e8i	−0.873040	+	0.504050i
$129$		0			0
$130$	4.69207e7	−	8.12691e7i	0.164283	−	0.284546i
$131$	2.30428e8	+	1.33038e8i	0.782438	+	0.451741i	0.837294	−	0.546754i	$-0.184137\pi$
$131$	2.30428e8	+	1.33038e8i	0.782438	+	0.451741i	−0.0548557	+	0.998494i	$0.517470\pi$
$132$		0			0
$133$	8.94114e7	+	1.54865e8i	0.285750	+	0.494933i
$134$			9.84231e7i			0.305266i
$135$		0			0
$136$	−4.92345e8			−1.43918
$137$	−4.61911e7	+	2.66685e7i	−0.131122	+	0.0757034i	−0.564126	−	0.825689i	$-0.690787\pi$
$137$	−4.61911e7	+	2.66685e7i	−0.131122	+	0.0757034i	0.433004	+	0.901392i	$0.357454\pi$
$138$		0			0
$139$	−2.03300e8	+	3.52126e8i	−0.544601	+	0.943277i	0.454031	+	0.890986i	$0.349986\pi$
$139$	−2.03300e8	+	3.52126e8i	−0.544601	+	0.943277i	−0.998632	+	0.0522909i	$0.983348\pi$
$140$	6.43929e7	+	3.71773e7i	0.167620	+	0.0967755i
$141$		0			0
$142$	−2.76946e7	−	4.79684e7i	−0.0681148	−	0.117978i
$143$			1.99473e8i			0.477023i
$144$		0			0
$145$	1.77456e8			0.401439
$146$	2.77398e7	−	1.60156e7i	0.0610510	−	0.0352478i
$147$		0			0
$148$	1.14878e8	−	1.98974e8i	0.239435	−	0.414714i
$149$	4.39611e7	+	2.53810e7i	0.0891915	+	0.0514948i	0.543932	−	0.839129i	$-0.316935\pi$
$149$	4.39611e7	+	2.53810e7i	0.0891915	+	0.0514948i	−0.454741	+	0.890624i	$0.650268\pi$
$150$		0			0
$151$	1.20269e8	+	2.08312e8i	0.231337	+	0.400688i	0.958202	−	0.286093i	$-0.0923566\pi$
$151$	1.20269e8	+	2.08312e8i	0.231337	+	0.400688i	−0.726865	+	0.686781i	$0.759023\pi$
$152$		−	6.15769e8i		−	1.15357i
$153$		0			0
$154$	3.66519e7			0.0651649
$155$	2.61110e8	−	1.50752e8i	0.452374	−	0.261178i
$156$		0			0
$157$	−8.71150e6	+	1.50888e7i	−0.0143382	+	0.0248345i	−0.873105	−	0.487531i	$-0.837897\pi$
$157$	−8.71150e6	+	1.50888e7i	−0.0143382	+	0.0248345i	0.858767	+	0.512366i	$0.171231\pi$
$158$	1.65473e7	+	9.55359e6i	0.0265521	+	0.0153299i
$159$		0			0
$160$	−1.98678e8	−	3.44121e8i	−0.303159	−	0.525087i
$161$		−	1.42856e8i		−	0.212615i
$162$		0			0
$163$	5.31250e8			0.752573			0.376286	−	0.926503i	$-0.377201\pi$
$163$	5.31250e8			0.752573			0.376286	+	0.926503i	$0.377201\pi$
$164$	−6.54423e8	+	3.77831e8i	−0.904655	+	0.522303i
$165$		0			0
$166$	1.41196e8	−	2.44559e8i	0.185948	−	0.322071i
$167$	4.73822e7	+	2.73561e7i	0.0609185	+	0.0351713i	0.530150	−	0.847904i	$-0.322136\pi$
$167$	4.73822e7	+	2.73561e7i	0.0609185	+	0.0351713i	−0.469231	+	0.883075i	$0.655469\pi$
$168$		0			0
$169$	−2.16102e8	−	3.74300e8i	−0.264918	−	0.458852i
$170$		−	4.06207e8i		−	0.486353i
$171$		0			0
$172$	6.28907e8			0.718576
$173$	−5.38684e8	+	3.11009e8i	−0.601381	+	0.347207i	−0.769584	−	0.638545i	$-0.779537\pi$
$173$	−5.38684e8	+	3.11009e8i	−0.601381	+	0.347207i	0.168204	+	0.985752i	$0.446203\pi$
$174$		0			0
$175$	1.14165e8	−	1.97739e8i	0.121725	−	0.210834i
$176$	1.50849e8	+	8.70925e7i	0.157214	+	0.0907675i
$177$		0			0
$178$	−1.00874e8	−	1.74719e8i	−0.100485	−	0.174045i
$179$		−	1.35171e9i		−	1.31665i	−0.752732	−	0.658327i	$-0.771264\pi$
$179$		−	1.35171e9i		−	1.31665i	0.752732	−	0.658327i	$-0.228736\pi$
$180$		0			0
$181$	−5.83247e8			−0.543423			−0.271712	−	0.962379i	$-0.587590\pi$
$181$	−5.83247e8			−0.543423			−0.271712	+	0.962379i	$0.587590\pi$
$182$	−1.98580e8	+	1.14650e8i	−0.180988	+	0.104494i
$183$		0			0
$184$	−2.45959e8	+	4.26013e8i	−0.214581	+	0.371665i
$185$	3.66393e8	+	2.11537e8i	0.312796	+	0.180593i
$186$		0			0
$187$	4.31723e8	+	7.47767e8i	0.353052	+	0.611504i
$188$		−	1.14053e9i		−	0.913013i
$189$		0			0
$190$	5.08037e8			0.389835
$191$	9.46339e8	−	5.46369e8i	0.711071	−	0.410537i	−0.100386	−	0.994949i	$-0.532008\pi$
$191$	9.46339e8	−	5.46369e8i	0.711071	−	0.410537i	0.811458	+	0.584411i	$0.198674\pi$
$192$		0			0
$193$	5.59017e8	−	9.68245e8i	0.402898	−	0.697840i	−0.591176	−	0.806543i	$-0.701336\pi$
$193$	5.59017e8	−	9.68245e8i	0.402898	−	0.697840i	0.994074	+	0.108702i	$0.0346695\pi$
$194$	5.50766e8	+	3.17985e8i	0.388830	+	0.224491i
$195$		0			0
$196$	5.08147e8	+	8.80136e8i	0.344322	+	0.596383i
$197$			2.60813e9i			1.73167i	0.500332	+	0.865834i	$0.333211\pi$
$197$			2.60813e9i			1.73167i	−0.500332	+	0.865834i	$0.666789\pi$
$198$		0			0
$199$	−1.55526e9			−0.991722			−0.495861	−	0.868402i	$-0.665147\pi$
$199$	−1.55526e9			−0.991722			−0.495861	+	0.868402i	$0.665147\pi$
$200$	−6.80907e8	+	3.93122e8i	−0.425567	+	0.245701i
$201$		0			0
$202$	−6.48022e8	+	1.12241e9i	−0.389210	+	0.674132i
$203$	−3.75520e8	−	2.16806e8i	−0.221131	−	0.127670i
$204$		0			0
$205$	−6.95744e8	−	1.20506e9i	−0.393944	−	0.682331i
$206$			1.13733e9i			0.631565i
$207$		0			0
$208$	−1.08973e9			−0.582192
$209$	−9.35221e8	+	5.39950e8i	−0.490150	+	0.282988i
$210$		0			0
$211$	−1.01997e8	+	1.76664e8i	−0.0514586	+	0.0891289i	−0.890607	−	0.454773i	$-0.849720\pi$
$211$	−1.01997e8	+	1.76664e8i	−0.0514586	+	0.0891289i	0.839149	+	0.543902i	$0.183054\pi$
$212$	2.54440e9	+	1.46901e9i	1.25963	+	0.727245i
$213$		0			0
$214$	−4.01028e7	−	6.94600e7i	−0.0191214	−	0.0331192i
$215$			1.15808e9i			0.541981i
$216$		0			0
$217$	−7.36722e8			−0.332250
$218$	3.48390e8	−	2.01143e8i	0.154255	−	0.0890591i
$219$		0			0
$220$	−2.24511e8	+	3.88865e8i	−0.0958402	+	0.166000i
$221$	−4.67815e9	−	2.70093e9i	−1.96113	−	1.13226i
$222$		0			0
$223$	9.72435e8	+	1.68431e9i	0.393225	+	0.681086i	0.992873	−	0.119178i	$-0.0380260\pi$
$223$	9.72435e8	+	1.68431e9i	0.393225	+	0.681086i	−0.599648	+	0.800264i	$0.704693\pi$
$224$			9.70937e8i			0.385655i
$225$		0			0
$226$	1.08940e9			0.417593
$227$	3.66729e9	−	2.11731e9i	1.38115	−	0.797409i	0.388856	−	0.921298i	$-0.372870\pi$
$227$	3.66729e9	−	2.11731e9i	1.38115	−	0.797409i	0.992296	+	0.123890i	$0.0395370\pi$
$228$		0			0
$229$	−2.55548e8	+	4.42621e8i	−0.0929244	+	0.160950i	−0.908740	−	0.417362i	$-0.862955\pi$
$229$	−2.55548e8	+	4.42621e8i	−0.0929244	+	0.160950i	0.815816	+	0.578311i	$0.196288\pi$
$230$	−3.51480e8	−	2.02927e8i	−0.125600	−	0.0725151i
$231$		0			0
$232$	7.46565e8	+	1.29309e9i	0.257701	+	0.446351i
$233$		−	3.64332e8i		−	0.123616i	−0.998088	−	0.0618079i	$-0.980313\pi$
$233$		−	3.64332e8i		−	0.123616i	0.998088	−	0.0618079i	$-0.0196866\pi$
$234$		0			0
$235$	2.10020e9			0.688635
$236$	1.57536e9	−	9.09537e8i	0.507847	−	0.293206i
$237$		0			0
$238$	−4.96280e8	+	8.59583e8i	−0.154675	+	0.267904i
$239$	−2.95288e9	−	1.70485e9i	−0.905012	−	0.522509i	−0.0261894	−	0.999657i	$-0.508337\pi$
$239$	−2.95288e9	−	1.70485e9i	−0.905012	−	0.522509i	−0.878823	+	0.477148i	$0.841671\pi$
$240$		0			0
$241$	−2.22976e9	−	3.86206e9i	−0.660982	−	1.14485i	−0.980358	−	0.197226i	$-0.936807\pi$
$241$	−2.22976e9	−	3.86206e9i	−0.660982	−	1.14485i	0.319376	−	0.947628i	$-0.396527\pi$
$242$		−	1.26673e9i		−	0.369338i
$243$		0			0
$244$	1.44262e9			0.406998
$245$	−1.62070e9	+	9.35709e8i	−0.449818	+	0.259703i
$246$		0			0
$247$	3.37802e9	−	5.85090e9i	0.907558	−	1.57194i
$248$	2.19700e9	+	1.26844e9i	0.580795	+	0.335322i
$249$		0			0
$250$	−8.43177e8	−	1.46043e9i	−0.215853	−	0.373869i
$251$			1.16420e8i			0.0293313i	0.999892	+	0.0146657i	$0.00466839\pi$
$251$			1.16420e8i			0.0293313i	−0.999892	+	0.0146657i	$0.995332\pi$
$252$		0			0
$253$	8.62697e8			0.210560
$254$	−1.94409e8	+	1.12242e8i	−0.0467070	+	0.0269663i
$255$		0			0
$256$	8.51156e8	−	1.47425e9i	0.198175	−	0.343250i
$257$	−1.46373e9	−	8.45087e8i	−0.335529	−	0.193717i	0.322764	−	0.946479i	$-0.395388\pi$
$257$	−1.46373e9	−	8.45087e8i	−0.335529	−	0.193717i	−0.658293	+	0.752762i	$0.728721\pi$
$258$		0			0
$259$	−5.16889e8	−	8.95278e8i	−0.114868	−	0.198957i
$260$		−	2.80916e9i		−	0.614729i
$261$		0			0
$262$	−1.84709e9			−0.391996
$263$	5.09081e9	−	2.93918e9i	1.06406	−	0.614333i	0.137504	−	0.990501i	$-0.456092\pi$
$263$	5.09081e9	−	2.93918e9i	1.06406	−	0.614333i	0.926551	+	0.376169i	$0.122759\pi$
$264$		0			0
$265$	−2.70506e9	+	4.68529e9i	−0.548520	+	0.950065i
$266$	−1.07507e9	−	6.20691e8i	−0.214738	−	0.123979i
$267$		0			0
$268$	1.47316e9	+	2.55158e9i	0.285568	+	0.494619i
$269$			5.55830e9i			1.06153i	0.847518	+	0.530766i	$0.178096\pi$
$269$			5.55830e9i			1.06153i	−0.847518	+	0.530766i	$0.821904\pi$
$270$		0			0
$271$	4.93438e9			0.914862			0.457431	−	0.889245i	$-0.348770\pi$
$271$	4.93438e9			0.914862			0.457431	+	0.889245i	$0.348770\pi$
$272$	−4.08509e9	+	2.35853e9i	−0.746322	+	0.430889i
$273$		0			0
$274$	1.85132e8	−	3.20657e8i	0.0328457	−	0.0568904i
$275$	1.19413e9	+	6.89434e8i	0.208796	+	0.120549i
$276$		0			0
$277$	1.81493e9	+	3.14355e9i	0.308277	+	0.533951i	0.977985	−	0.208673i	$-0.0669145\pi$
$277$	1.81493e9	+	3.14355e9i	0.308277	+	0.533951i	−0.669709	+	0.742624i	$0.733581\pi$
$278$		−	2.82261e9i		−	0.472576i
$279$		0			0
$280$	−1.15203e9			−0.187427
$281$	−6.06878e8	+	3.50381e8i	−0.0973366	+	0.0561973i	−0.547878	−	0.836558i	$-0.684564\pi$
$281$	−6.06878e8	+	3.50381e8i	−0.0973366	+	0.0561973i	0.450542	+	0.892755i	$0.351231\pi$
$282$		0			0
$283$	−3.91197e9	+	6.77574e9i	−0.609888	+	1.05636i	0.381370	+	0.924422i	$0.375452\pi$
$283$	−3.91197e9	+	6.77574e9i	−0.609888	+	1.05636i	−0.991258	+	0.131935i	$0.957881\pi$
$284$	−1.43594e9	−	8.29042e8i	−0.220731	−	0.127439i
$285$		0			0
$286$	−6.92367e8	−	1.19921e9i	−0.103484	−	0.179239i
$287$			3.40009e9i			0.501144i
$288$		0			0
$289$	−1.64070e10			−2.35200
$290$	−1.06685e9	+	6.15949e8i	−0.150839	+	0.0870868i
$291$		0			0
$292$	4.79430e8	−	8.30397e8i	0.0659468	−	0.114223i
$293$	7.18343e9	+	4.14736e9i	0.974679	+	0.562731i	0.900660	−	0.434526i	$-0.143084\pi$
$293$	7.18343e9	+	4.14736e9i	0.974679	+	0.562731i	0.0740196	+	0.997257i	$0.476417\pi$
$294$		0			0
$295$	1.67483e9	+	2.90090e9i	0.221148	+	0.383040i
$296$			3.55977e9i			0.463720i
$297$		0			0
$298$	−3.52388e8			−0.0446844
$299$	−4.67409e9	+	2.69859e9i	−0.584807	+	0.337638i
$300$		0			0
$301$	1.41488e9	−	2.45064e9i	0.172366	−	0.298547i
$302$	−1.44609e9	−	8.34902e8i	−0.173848	−	0.100371i
$303$		0			0
$304$	−2.94978e9	−	5.10917e9i	−0.345378	−	0.598213i
$305$			2.65646e9i			0.306976i
$306$		0			0
$307$	1.48989e10			1.67726			0.838629	−	0.544702i	$-0.183357\pi$
$307$	1.48989e10			1.67726			0.838629	+	0.544702i	$0.183357\pi$
$308$	9.50188e8	−	5.48591e8i	0.105586	−	0.0609601i
$309$		0			0
$310$	−1.04652e9	+	1.81262e9i	−0.113318	+	0.196273i
$311$	1.09865e10	+	6.34304e9i	1.17440	+	0.678041i	0.954713	−	0.297529i	$-0.0961626\pi$
$311$	1.09865e10	+	6.34304e9i	1.17440	+	0.678041i	0.219688	+	0.975570i	$0.429496\pi$
$312$		0			0
$313$	−1.59338e9	−	2.75982e9i	−0.166013	−	0.287543i	0.771002	−	0.636833i	$-0.219756\pi$
$313$	−1.59338e9	−	2.75982e9i	−0.166013	−	0.287543i	−0.937015	+	0.349290i	$0.886423\pi$
$314$		−	1.20950e8i		−	0.0124419i
$315$		0			0
$316$	5.71977e8			0.0573628
$317$	−1.29666e9	+	7.48628e8i	−0.128407	+	0.0741360i	−0.562828	−	0.826574i	$-0.690287\pi$
$317$	−1.29666e9	+	7.48628e8i	−0.128407	+	0.0741360i	0.434420	+	0.900710i	$0.356953\pi$
$318$		0			0
$319$	1.30928e9	−	2.26774e9i	0.126436	−	0.218993i
$320$	−2.28161e8	−	1.31729e8i	−0.0217591	−	0.0125626i
$321$		0			0
$322$	4.95850e8	+	8.58837e8i	0.0461239	+	0.0798890i
$323$		−	2.92445e10i		−	2.68679i
$324$		0			0
$325$	−8.62643e9			−0.773210
$326$	−3.19383e9	+	1.84396e9i	−0.282775	+	0.163260i
$327$		0			0
$328$	5.85403e9	−	1.01395e10i	0.505778	−	0.876033i
$329$	−4.44428e9	−	2.56591e9i	−0.379331	−	0.219007i
$330$		0			0
$331$	9.32077e9	+	1.61441e10i	0.776497	+	1.34493i	0.933949	+	0.357406i	$0.116339\pi$
$331$	9.32077e9	+	1.61441e10i	0.776497	+	1.34493i	−0.157452	+	0.987527i	$0.550328\pi$
$332$		−	8.45348e9i		−	0.695798i
$333$		0			0
$334$	−3.79811e8			−0.0305198
$335$	−4.69852e9	+	2.71269e9i	−0.373063	+	0.215388i
$336$		0			0
$337$	−3.21138e8	+	5.56228e8i	−0.0248985	+	0.0431254i	−0.878206	−	0.478282i	$-0.841260\pi$
$337$	−3.21138e8	+	5.56228e8i	−0.0248985	+	0.0431254i	0.853308	+	0.521408i	$0.174593\pi$
$338$	2.59838e9	+	1.50017e9i	0.199083	+	0.114941i
$339$		0			0
$340$	−6.07993e9	−	1.05308e10i	−0.454970	−	0.788032i
$341$		−	4.44902e9i		−	0.329039i
$342$		0			0
$343$	9.96307e9			0.719808
$344$	−8.43867e9	+	4.87207e9i	−0.602616	+	0.347920i
$345$		0			0
$346$	2.15902e9	−	3.73952e9i	0.150644	−	0.260923i
$347$	−8.51548e8	−	4.91642e8i	−0.0587342	−	0.0339102i	0.470345	−	0.882482i	$-0.344129\pi$
$347$	−8.51548e8	−	4.91642e8i	−0.0587342	−	0.0339102i	−0.529080	+	0.848572i	$0.677463\pi$
$348$		0			0
$349$	−1.27190e9	−	2.20299e9i	−0.0857334	−	0.148495i	0.819970	−	0.572406i	$-0.193990\pi$
$349$	−1.27190e9	−	2.20299e9i	−0.0857334	−	0.148495i	−0.905703	+	0.423912i	$0.860657\pi$
$350$			1.58506e9i			0.105626i
$351$		0			0
$352$	−5.86343e9			−0.381928
$353$	5.61563e9	−	3.24219e9i	0.361660	−	0.208804i	−0.308149	−	0.951338i	$-0.599710\pi$
$353$	5.61563e9	−	3.24219e9i	0.361660	−	0.208804i	0.669808	+	0.742534i	$0.266376\pi$
$354$		0			0
$355$	1.52661e9	−	2.64417e9i	0.0961203	−	0.166485i
$356$	−5.23025e9	−	3.01969e9i	−0.325629	−	0.188002i
$357$		0			0
$358$	4.69177e9	+	8.12638e9i	0.285630	+	0.494726i
$359$			1.35812e10i			0.817639i	0.912615	+	0.408820i	$0.134060\pi$
$359$			1.35812e10i			0.817639i	−0.912615	+	0.408820i	$0.865940\pi$
$360$		0			0
$361$	1.95921e10			1.15359
$362$	3.50643e9	−	2.02444e9i	0.204189	−	0.117888i
$363$		0			0
$364$	−3.43208e9	+	5.94453e9i	−0.195502	+	0.338620i
$365$	1.52911e9	+	8.82830e8i	0.0861522	+	0.0497400i
$366$		0			0
$367$	−1.66185e10	−	2.87842e10i	−0.916070	−	1.58668i	−0.805327	−	0.592831i	$-0.798010\pi$
$367$	−1.66185e10	−	2.87842e10i	−0.916070	−	1.58668i	−0.110744	−	0.993849i	$-0.535323\pi$
$368$			4.71296e9i			0.256982i
$369$		0			0
$370$	−2.93697e9			−0.156709
$371$	1.14485e10	−	6.60977e9i	0.604299	−	0.348892i
$372$		0			0
$373$	−6.90080e9	+	1.19525e10i	−0.356504	+	0.617482i	−0.987374	−	0.158406i	$-0.949365\pi$
$373$	−6.90080e9	+	1.19525e10i	−0.356504	+	0.617482i	0.630870	+	0.775888i	$0.282698\pi$
$374$	−5.19097e9	−	2.99701e9i	−0.265315	−	0.153180i
$375$		0			0
$376$	8.83560e9	+	1.53037e10i	0.442063	+	0.765676i
$377$			1.63822e10i			0.810972i
$378$		0			0
$379$	−2.14968e10			−1.04188			−0.520938	−	0.853594i	$-0.674418\pi$
$379$	−2.14968e10			−1.04188			−0.520938	+	0.853594i	$0.674418\pi$
$380$	1.31707e10	−	7.60408e9i	0.631645	−	0.364681i
$381$		0			0
$382$	−3.79288e9	+	6.56945e9i	−0.178121	+	0.308515i
$383$	1.44304e10	+	8.33139e9i	0.670630	+	0.387189i	0.796315	−	0.604882i	$-0.206780\pi$
$383$	1.44304e10	+	8.33139e9i	0.670630	+	0.387189i	−0.125685	+	0.992070i	$0.540113\pi$
$384$		0			0
$385$	1.01018e9	+	1.74969e9i	0.0459788	+	0.0796376i
$386$			7.76135e9i			0.349613i
$387$		0			0
$388$	1.90379e10			0.840023
$389$	−2.09033e10	+	1.20686e10i	−0.912888	+	0.527056i	−0.881359	−	0.472447i	$-0.843371\pi$
$389$	−2.09033e10	+	1.20686e10i	−0.912888	+	0.527056i	−0.0315287	+	0.999503i	$0.510038\pi$
$390$		0			0
$391$	−1.16812e10	+	2.02325e10i	−0.499783	+	0.865650i
$392$	−1.36366e10	−	7.87311e9i	−0.577514	−	0.333428i
$393$		0			0
$394$	−9.05278e9	−	1.56799e10i	−0.375662	−	0.650666i
$395$			1.05325e9i			0.0432655i
$396$		0			0
$397$	−3.25313e10			−1.30960			−0.654801	−	0.755801i	$-0.727248\pi$
$397$	−3.25313e10			−1.30960			−0.654801	+	0.755801i	$0.727248\pi$
$398$	9.35008e9	−	5.39827e9i	0.372635	−	0.215141i
$399$		0			0
$400$	−3.76642e9	+	6.52363e9i	−0.147126	+	0.254829i
$401$	−8.68342e9	−	5.01338e9i	−0.335825	−	0.193889i	0.322599	−	0.946536i	$-0.395443\pi$
$401$	−8.68342e9	−	5.01338e9i	−0.335825	−	0.193889i	−0.658424	+	0.752647i	$0.728777\pi$
$402$		0			0
$403$	1.39169e10	+	2.41048e10i	0.527622	+	0.913868i
$404$			3.87973e10i			1.45638i
$405$		0			0
$406$	3.01013e9			0.110785
$407$	5.40653e9	−	3.12146e9i	0.197034	−	0.113758i
$408$		0			0
$409$	1.86745e10	−	3.23451e10i	0.667352	−	1.15589i	−0.311289	−	0.950315i	$-0.600761\pi$
$409$	1.86745e10	−	3.23451e10i	0.667352	−	1.15589i	0.978642	−	0.205573i	$-0.0659059\pi$
$410$	8.36552e9	+	4.82983e9i	0.296045	+	0.170922i
$411$		0			0
$412$	1.70231e10	+	2.94849e10i	0.590813	+	1.02332i
$413$		−	8.18488e9i		−	0.281327i
$414$		0			0
$415$	1.55664e10			0.524801
$416$	3.17681e10	−	1.83413e10i	1.06076	−	0.612431i
$417$		0			0
$418$	3.74832e9	−	6.49227e9i	0.122781	−	0.212663i
$419$	−1.53553e10	−	8.86539e9i	−0.498198	−	0.287635i	0.229771	−	0.973245i	$-0.426202\pi$
$419$	−1.53553e10	−	8.86539e9i	−0.498198	−	0.287635i	−0.727969	+	0.685610i	$0.759536\pi$
$420$		0			0
$421$	−1.92354e10	−	3.33166e10i	−0.612311	−	1.06055i	−0.990850	−	0.134968i	$-0.956907\pi$
$421$	−1.92354e10	−	3.33166e10i	−0.612311	−	1.06055i	0.378539	−	0.925585i	$-0.376426\pi$
$422$		−	1.41612e9i		−	0.0446530i
$423$		0			0
$424$	−4.55210e10			−1.40847
$425$	−3.23380e10	+	1.86704e10i	−0.991192	+	0.572265i
$426$		0			0
$427$	3.24552e9	−	5.62140e9i	0.0976275	−	0.169096i
$428$	−2.07930e9	−	1.20048e9i	−0.0619643	−	0.0357751i
$429$		0			0
$430$	−4.01967e9	−	6.96228e9i	−0.117576	−	0.203647i
$431$		−	2.36204e10i		−	0.684508i	−0.939608	−	0.342254i	$-0.888810\pi$
$431$		−	2.36204e10i		−	0.684508i	0.939608	−	0.342254i	$-0.111190\pi$
$432$		0			0
$433$	4.85864e10			1.38218			0.691088	−	0.722770i	$-0.257132\pi$
$433$	4.85864e10			1.38218			0.691088	+	0.722770i	$0.257132\pi$
$434$	4.42912e9	−	2.55715e9i	0.124841	−	0.0720772i
$435$		0			0
$436$	6.02125e9	−	1.04291e10i	0.166625	−	0.288603i
$437$	−2.53045e10	−	1.46095e10i	−0.693860	−	0.400600i
$438$		0			0
$439$	−1.45910e9	−	2.52723e9i	−0.0392849	−	0.0680434i	0.845714	−	0.533636i	$-0.179175\pi$
$439$	−1.45910e9	−	2.52723e9i	−0.0392849	−	0.0680434i	−0.884999	+	0.465592i	$0.845841\pi$
$440$		−	6.95706e9i		−	0.185616i
$441$		0			0
$442$	3.74996e10			0.982511
$443$	6.94159e9	−	4.00773e9i	0.180237	−	0.104060i	−0.407167	−	0.913354i	$-0.633483\pi$
$443$	6.94159e9	−	4.00773e9i	0.180237	−	0.104060i	0.587404	+	0.809294i	$0.300150\pi$
$444$		0			0
$445$	5.56050e9	−	9.63107e9i	0.141799	−	0.245603i
$446$	−1.16924e10	−	6.75061e9i	−0.295505	−	0.170610i
$447$		0			0
$448$	3.21877e8	+	5.57508e8i	0.00799058	+	0.0138401i
$449$		−	5.34461e9i		−	0.131501i	−0.997836	−	0.0657507i	$-0.979056\pi$
$449$		−	5.34461e9i		−	0.131501i	0.997836	−	0.0657507i	$-0.0209442\pi$
$450$		0			0
$451$	−2.05329e10			−0.496300
$452$	2.82423e10	−	1.63057e10i	0.676622	−	0.390648i
$453$		0			0
$454$	−1.46983e10	+	2.54582e10i	−0.345974	+	0.599245i
$455$	−1.09464e10	−	6.31988e9i	−0.255402	−	0.147456i
$456$		0			0
$457$	1.77423e10	+	3.07305e10i	0.406766	+	0.704539i	0.994525	−	0.104497i	$-0.0333231\pi$
$457$	1.77423e10	+	3.07305e10i	0.406766	+	0.704539i	−0.587759	+	0.809036i	$0.699990\pi$
$458$		−	3.54801e9i		−	0.0806348i
$459$		0			0
$460$	−1.21493e10			−0.271344
$461$	4.25420e10	−	2.45616e10i	0.941920	−	0.543818i	0.0513583	−	0.998680i	$-0.483645\pi$
$461$	4.25420e10	−	2.45616e10i	0.941920	−	0.543818i	0.890562	+	0.454863i	$0.150312\pi$
$462$		0			0
$463$	3.87860e10	−	6.71794e10i	0.844017	−	1.46188i	−0.0424548	−	0.999098i	$-0.513518\pi$
$463$	3.87860e10	−	6.71794e10i	0.844017	−	1.46188i	0.886472	−	0.462782i	$-0.153149\pi$
$464$	1.23888e10	+	7.15268e9i	0.267274	+	0.154311i
$465$		0			0
$466$	1.26459e9	+	2.19034e9i	0.0268168	+	0.0464480i
$467$		−	4.39387e10i		−	0.923803i	−0.886931	−	0.461901i	$-0.847167\pi$
$467$		−	4.39387e10i		−	0.923803i	0.886931	−	0.461901i	$-0.152833\pi$
$468$		0			0
$469$	1.32569e10			0.274000
$470$	−1.26262e10	+	7.28976e9i	−0.258751	+	0.149390i
$471$		0			0
$472$	−1.40922e10	+	2.44083e10i	−0.283929	+	0.491779i
$473$	1.47993e10	+	8.54435e9i	0.295662	+	0.170700i
$474$		0			0
$475$	−2.33508e10	−	4.04447e10i	−0.458698	−	0.794488i
$476$			2.97125e10i			0.578777i
$477$		0			0
$478$	2.36700e10			0.453405
$479$	−8.49436e10	+	4.90422e10i	−1.61357	+	0.931597i	−0.625040	+	0.780592i	$0.714918\pi$
$479$	−8.49436e10	+	4.90422e10i	−1.61357	+	0.931597i	−0.988533	+	0.151005i	$0.951749\pi$
$480$		0			0
$481$	−1.95284e10	+	3.38242e10i	−0.364826	+	0.631898i
$482$	2.68103e10	+	1.54789e10i	0.496722	+	0.286782i
$483$		0			0
$484$	−1.89600e10	−	3.28396e10i	−0.345506	−	0.598434i
$485$			3.50566e10i			0.633582i
$486$		0			0
$487$	−7.42528e10			−1.32007			−0.660035	−	0.751235i	$-0.729459\pi$
$487$	−7.42528e10			−1.32007			−0.660035	+	0.751235i	$0.729459\pi$
$488$	−1.93571e10	+	1.11758e10i	−0.341319	+	0.197061i
$489$		0			0
$490$	6.49567e9	−	1.12508e10i	0.112678	−	0.195164i
$491$	7.06291e10	+	4.07777e10i	1.21523	+	0.701612i	0.963894	−	0.266288i	$-0.0857972\pi$
$491$	7.06291e10	+	4.07777e10i	1.21523	+	0.701612i	0.251335	+	0.967900i	$0.419131\pi$
$492$		0			0
$493$	3.54563e10	+	6.14121e10i	0.600213	+	1.03960i
$494$			4.69002e10i			0.787530i
$495$		0			0
$496$	2.43053e10			0.401582
$497$	−6.46099e9	+	3.73026e9i	−0.105895	+	0.0611383i
$498$		0			0
$499$	−5.69859e10	+	9.87025e10i	−0.919106	+	1.59194i	−0.118330	+	0.992974i	$0.537754\pi$
$499$	−5.69859e10	+	9.87025e10i	−0.919106	+	1.59194i	−0.800776	+	0.598964i	$0.795579\pi$
$500$	−4.37181e10	−	2.52407e10i	−0.699490	−	0.403851i
$501$		0			0
$502$	−4.04091e8	−	6.99906e8i	−0.00636303	−	0.0110211i
$503$		−	9.75128e8i		−	0.0152331i	−0.999971	−	0.00761657i	$-0.997576\pi$
$503$		−	9.75128e8i		−	0.0152331i	0.999971	−	0.00761657i	$-0.00242445\pi$
$504$		0			0
$505$	−7.14419e10			−1.09847
$506$	−5.18646e9	+	2.99441e9i	−0.0791169	+	0.0456782i
$507$		0			0
$508$	−3.35999e9	+	5.81968e9i	−0.0504526	+	0.0873864i
$509$	3.54831e10	+	2.04862e10i	0.528628	+	0.305204i	0.740458	−	0.672103i	$-0.234609\pi$
$509$	3.54831e10	+	2.04862e10i	0.528628	+	0.305204i	−0.211829	+	0.977307i	$0.567942\pi$
$510$		0			0
$511$	−2.15719e9	−	3.73635e9i	−0.0316376	−	0.0547980i
$512$		−	5.74587e10i		−	0.836134i
$513$		0			0
$514$	1.17331e10			0.168098
$515$	−5.42940e10	+	3.13466e10i	−0.771832	+	0.445617i
$516$		0			0
$517$	1.54954e10	−	2.68387e10i	0.216890	−	0.375664i
$518$	6.21499e9	+	3.58823e9i	0.0863220	+	0.0498380i
$519$		0			0
$520$	2.17623e10	+	3.76934e10i	0.297640	+	0.515527i
$521$		−	1.06574e11i		−	1.44644i	−0.690617	−	0.723221i	$-0.742661\pi$
$521$		−	1.06574e11i		−	1.44644i	0.690617	−	0.723221i	$-0.257339\pi$
$522$		0			0
$523$	6.45167e10			0.862314			0.431157	−	0.902277i	$-0.358105\pi$
$523$	6.45167e10			0.862314			0.431157	+	0.902277i	$0.358105\pi$
$524$	−4.78850e10	+	2.76464e10i	−0.635147	+	0.366702i
$525$		0			0
$526$	−2.04037e10	+	3.53403e10i	−0.266542	+	0.461665i
$527$	1.04341e11	+	6.02414e10i	1.35274	+	0.781003i
$528$		0			0
$529$	−2.74844e10	−	4.76044e10i	−0.350965	−	0.607889i
$530$		−	3.75568e10i		−	0.475976i
$531$		0			0
$532$	−3.71610e10			−0.463917
$533$	1.11247e11	−	6.42287e10i	1.37842	−	0.795830i
$534$		0			0
$535$	2.21059e9	−	3.82885e9i	0.0269832	−	0.0467362i
$536$	−3.95337e10	−	2.28248e10i	−0.478969	−	0.276533i
$537$		0			0
$538$	−1.92928e10	−	3.34161e10i	−0.230285	−	0.398866i
$539$			2.76148e10i			0.327180i
$540$		0			0
$541$	1.30431e11			1.52262			0.761308	−	0.648390i	$-0.224557\pi$
$541$	1.30431e11			1.52262			0.761308	+	0.648390i	$0.224557\pi$
$542$	−2.96651e10	+	1.71272e10i	−0.343755	+	0.198467i
$543$		0			0
$544$	7.93930e10	−	1.37513e11i	0.906540	−	1.57017i
$545$	1.92043e10	+	1.10876e10i	0.217677	+	0.125676i
$546$		0			0
$547$	1.26081e10	+	2.18378e10i	0.140831	+	0.243927i	0.927810	−	0.373053i	$-0.121689\pi$
$547$	1.26081e10	+	2.18378e10i	0.140831	+	0.243927i	−0.786979	+	0.616980i	$0.788356\pi$
$548$		−	1.10839e10i		−	0.122905i
$549$		0			0
$550$	−9.57206e9			−0.104606
$551$	−7.68073e10	+	4.43447e10i	−0.833289	+	0.481100i
$552$		0			0
$553$	1.28680e9	−	2.22880e9i	0.0137597	−	0.0238326i
$554$	−2.18224e10	−	1.25992e10i	−0.231667	−	0.133753i
$555$		0			0
$556$	−4.22476e10	−	7.31750e10i	−0.442082	−	0.765709i
$557$			2.17570e10i			0.226037i	0.993593	+	0.113018i	$0.0360519\pi$
$557$			2.17570e10i			0.226037i	−0.993593	+	0.113018i	$0.963948\pi$
$558$		0			0
$559$	−1.06910e11			−1.09489
$560$	−9.55866e9	+	5.51869e9i	−0.0971952	+	0.0561157i
$561$		0			0
$562$	2.43233e9	−	4.21293e9i	0.0243825	−	0.0422317i
$563$	−1.19979e11	−	6.92701e10i	−1.19419	−	0.689465i	−0.234935	−	0.972011i	$-0.575488\pi$
$563$	−1.19979e11	−	6.92701e10i	−1.19419	−	0.689465i	−0.959254	+	0.282546i	$0.908821\pi$
$564$		0			0
$565$	3.00255e10	+	5.20058e10i	0.294644	+	0.510338i
$566$		−	5.43136e10i		−	0.529228i
$567$		0			0
$568$	2.56900e10			0.246814
$569$	1.37998e11	−	7.96731e10i	1.31651	−	0.760086i	0.333343	−	0.942806i	$-0.391823\pi$
$569$	1.37998e11	−	7.96731e10i	1.31651	−	0.760086i	0.983165	+	0.182720i	$0.0584901\pi$
$570$		0			0
$571$	4.81604e10	−	8.34163e10i	0.453050	−	0.784705i	−0.545524	−	0.838095i	$-0.683669\pi$
$571$	4.81604e10	−	8.34163e10i	0.453050	−	0.784705i	0.998574	+	0.0533899i	$0.0170026\pi$
$572$	−3.58987e10	−	2.07261e10i	−0.335347	−	0.193613i
$573$		0			0
$574$	−1.18016e10	−	2.04410e10i	−0.108716	−	0.188302i
$575$			3.73083e10i			0.341299i
$576$		0			0
$577$	1.43893e11			1.29819			0.649093	−	0.760709i	$-0.275149\pi$
$577$	1.43893e11			1.29819			0.649093	+	0.760709i	$0.275149\pi$
$578$	9.86376e10	−	5.69484e10i	0.883754	−	0.510235i
$579$		0			0
$580$	−1.84385e10	+	3.19365e10i	−0.162935	+	0.282212i
$581$	−3.29403e10	−	1.90181e10i	−0.289084	−	0.166903i
$582$		0			0
$583$	3.99160e10	+	6.91366e10i	0.345520	+	0.598458i
$584$			1.48564e10i			0.127721i
$585$		0			0
$586$	−5.75817e10			−0.488308
$587$	−4.33157e10	+	2.50083e10i	−0.364832	+	0.210636i	−0.671198	−	0.741278i	$-0.734220\pi$
$587$	−4.33157e10	+	2.50083e10i	−0.364832	+	0.210636i	0.306366	+	0.951914i	$0.400887\pi$
$588$		0			0
$589$	−7.53431e10	+	1.30498e11i	−0.626011	+	1.08428i
$590$	−2.01380e10	−	1.16267e10i	−0.166191	−	0.0959504i
$591$		0			0
$592$	1.70527e10	+	2.95362e10i	0.138838	+	0.240474i
$593$		−	1.28923e9i		−	0.0104258i	−0.999986	−	0.00521291i	$-0.998341\pi$
$593$		−	1.28923e9i		−	0.0104258i	0.999986	−	0.00521291i	$-0.00165933\pi$
$594$		0			0
$595$	−5.47130e10			−0.436539
$596$	−9.13552e9	+	5.27439e9i	−0.0724016	+	0.0418011i
$597$		0			0
$598$	1.87335e10	−	3.24474e10i	0.146492	−	0.253732i
$599$	−1.08459e11	−	6.26186e10i	−0.842474	−	0.486403i	0.0156302	−	0.999878i	$-0.495025\pi$
$599$	−1.08459e11	−	6.26186e10i	−0.842474	−	0.486403i	−0.858105	+	0.513475i	$0.828358\pi$
$600$		0			0
$601$	6.08247e10	+	1.05351e11i	0.466211	+	0.807500i	0.999255	−	0.0385866i	$-0.0122856\pi$
$601$	6.08247e10	+	1.05351e11i	0.466211	+	0.807500i	−0.533045	+	0.846087i	$0.678952\pi$
$602$			1.96440e10i			0.149570i
$603$		0			0
$604$	−4.99859e10			−0.375578
$605$	6.04714e10	−	3.49132e10i	0.451365	−	0.260596i
$606$		0			0
$607$	1.53955e10	−	2.66659e10i	0.113407	−	0.196427i	−0.803735	−	0.594988i	$-0.797157\pi$
$607$	1.53955e10	−	2.66659e10i	0.113407	−	0.196427i	0.917142	+	0.398561i	$0.130490\pi$
$608$	1.71985e11	+	9.92957e10i	1.25857	+	0.726635i
$609$		0			0
$610$	−9.22053e9	−	1.59704e10i	−0.0665943	−	0.115345i
$611$			1.93883e11i			1.39115i
$612$		0			0
$613$	−1.12498e11			−0.796714			−0.398357	−	0.917230i	$-0.630419\pi$
$613$	−1.12498e11			−0.796714			−0.398357	+	0.917230i	$0.630419\pi$
$614$	−8.95709e10	+	5.17138e10i	−0.630222	+	0.363859i
$615$		0			0
$616$	−8.49975e9	+	1.47220e10i	−0.0590314	+	0.102245i
$617$	4.32410e10	+	2.49652e10i	0.298370	+	0.172264i	0.641710	−	0.766947i	$-0.278225\pi$
$617$	4.32410e10	+	2.49652e10i	0.298370	+	0.172264i	−0.343340	+	0.939211i	$0.611558\pi$
$618$		0			0
$619$	−7.20206e10	−	1.24743e11i	−0.490562	−	0.849678i	0.509379	−	0.860542i	$-0.329875\pi$
$619$	−7.20206e10	−	1.24743e11i	−0.490562	−	0.849678i	−0.999941	+	0.0108640i	$0.996542\pi$
$620$			6.26553e10i			0.424025i
$621$		0			0
$622$	−8.80663e10			−0.588367
$623$	−2.35334e10	+	1.35870e10i	−0.156219	+	0.0901928i
$624$		0			0
$625$	−1.21560e9	+	2.10547e9i	−0.00796653	+	0.0137984i
$626$	1.91586e10	+	1.10612e10i	0.124757	+	0.0720286i
$627$		0			0
$628$	−1.81033e9	−	3.13558e9i	−0.0116391	−	0.0201595i
$629$			1.69063e11i			1.08005i
$630$		0			0
$631$	2.70159e10			0.170412			0.0852062	−	0.996363i	$-0.472845\pi$
$631$	2.70159e10			0.170412			0.0852062	+	0.996363i	$0.472845\pi$
$632$	−7.67479e9	+	4.43104e9i	−0.0481059	+	0.0277739i
$633$		0			0
$634$	5.19695e9	−	9.00138e9i	0.0321656	−	0.0557124i
$635$	−1.07164e10	−	6.18714e9i	−0.0659107	−	0.0380535i
$636$		0			0
$637$	−8.63815e10	−	1.49617e11i	−0.524642	−	0.908706i
$638$			1.81780e10i			0.109714i
$639$		0			0
$640$	1.03552e11			0.617220
$641$	1.66097e11	−	9.58963e10i	0.983853	−	0.568028i	0.0804218	−	0.996761i	$-0.474373\pi$
$641$	1.66097e11	−	9.58963e10i	0.983853	−	0.568028i	0.903431	+	0.428733i	$0.141040\pi$
$642$		0			0
$643$	−7.50236e10	+	1.29945e11i	−0.438888	+	0.760177i	−0.997604	−	0.0691825i	$-0.977961\pi$
$643$	−7.50236e10	+	1.29945e11i	−0.438888	+	0.760177i	0.558716	+	0.829359i	$0.311294\pi$
$644$	2.57094e10	+	1.48433e10i	0.149468	+	0.0862955i
$645$		0			0
$646$	1.01507e11	+	1.75816e11i	0.582863	+	1.00955i
$647$		−	1.42232e10i		−	0.0811672i	−0.999176	−	0.0405836i	$-0.987078\pi$
$647$		−	1.42232e10i		−	0.0811672i	0.999176	−	0.0405836i	$-0.0129217\pi$
$648$		0			0
$649$	4.94280e10			0.278609
$650$	5.18614e10	−	2.99422e10i	0.290530	−	0.167738i
$651$		0			0
$652$	−5.51993e10	+	9.56080e10i	−0.305452	+	0.529058i
$653$	−1.64751e11	−	9.51189e10i	−0.906097	−	0.523135i	−0.0269236	−	0.999637i	$-0.508571\pi$
$653$	−1.64751e11	−	9.51189e10i	−0.906097	−	0.523135i	−0.879173	+	0.476502i	$0.841904\pi$
$654$		0			0
$655$	−5.09086e10	−	8.81762e10i	−0.276583	−	0.479056i
$656$		−	1.12173e11i		−	0.605719i
$657$		0			0
$658$	3.56249e10			0.190042
$659$	3.84135e10	−	2.21780e10i	0.203677	−	0.117593i	−0.394692	−	0.918813i	$-0.629149\pi$
$659$	3.84135e10	−	2.21780e10i	0.203677	−	0.117593i	0.598370	+	0.801220i	$0.295815\pi$
$660$		0			0
$661$	−7.71408e9	+	1.33612e10i	−0.0404090	+	0.0699905i	−0.885523	−	0.464596i	$-0.846199\pi$
$661$	−7.71408e9	+	1.33612e10i	−0.0404090	+	0.0699905i	0.845114	+	0.534587i	$0.179533\pi$
$662$	−1.12071e11	−	6.47045e10i	−0.583530	−	0.336901i
$663$		0			0
$664$	6.54881e10	+	1.13429e11i	0.336892	+	0.583514i
$665$		−	6.84288e10i		−	0.349907i
$666$		0			0
$667$	7.08510e10			0.357967
$668$	−9.84645e9	+	5.68485e9i	−0.0494509	+	0.0285505i
$669$		0			0
$670$	1.88314e10	−	3.26170e10i	0.0934511	−	0.161862i
$671$	3.39473e10	+	1.95995e10i	0.167462	+	0.0966840i
$672$		0			0
$673$	−6.47962e9	−	1.12230e10i	−0.0315856	−	0.0547079i	0.849800	−	0.527104i	$-0.176722\pi$
$673$	−6.47962e9	−	1.12230e10i	−0.0315856	−	0.0547079i	−0.881386	+	0.472397i	$0.843389\pi$
$674$		−	4.45866e9i		−	0.0216055i
$675$		0			0
$676$	8.98159e10			0.430097
$677$	−1.18359e11	+	6.83344e10i	−0.563437	+	0.325301i	−0.754524	−	0.656273i	$-0.772132\pi$
$677$	−1.18359e11	+	6.83344e10i	−0.563437	+	0.325301i	0.191087	+	0.981573i	$0.438799\pi$
$678$		0			0
$679$	4.28302e10	−	7.41841e10i	0.201498	−	0.349005i
$680$	1.63161e11	+	9.42011e10i	0.763099	+	0.440576i
$681$		0			0
$682$	1.54425e10	+	2.67472e10i	0.0713806	+	0.123635i
$683$		−	6.40947e10i		−	0.294537i	−0.989097	−	0.147268i	$-0.952952\pi$
$683$		−	6.40947e10i		−	0.294537i	0.989097	−	0.147268i	$-0.0470481\pi$
$684$		0			0
$685$	2.04101e10			0.0927005
$686$	−5.98972e10	+	3.45816e10i	−0.270464	+	0.156153i
$687$		0			0
$688$	−4.66783e10	+	8.08492e10i	−0.208335	+	0.360846i
$689$	−4.32530e11	−	2.49721e11i	−1.91929	−	1.10810i
$690$		0			0
$691$	−1.99280e11	−	3.45164e11i	−0.874082	−	1.51395i	−0.857738	−	0.514088i	$-0.828131\pi$
$691$	−1.99280e11	−	3.45164e11i	−0.874082	−	1.51395i	−0.0163441	−	0.999866i	$-0.505203\pi$
$692$		−	1.29261e11i		−	0.563694i
$693$		0			0
$694$	6.82592e9			0.0294255
$695$	1.34746e11	−	7.77954e10i	0.577531	−	0.333438i
$696$		0			0
$697$	2.78023e11	−	4.81550e11i	1.17801	−	2.04038i
$698$	1.52931e10	+	8.82947e9i	0.0644278	+	0.0371974i
$699$		0			0
$700$	2.37245e10	+	4.10920e10i	0.0988108	+	0.171145i
$701$			1.78042e11i			0.737312i	0.929566	+	0.368656i	$0.120182\pi$
$701$			1.78042e11i			0.737312i	−0.929566	+	0.368656i	$0.879818\pi$
$702$		0			0
$703$	−2.11445e11			−0.865716
$704$	−3.36676e9	+	1.94380e9i	−0.0137063	+	0.00791336i
$705$		0			0
$706$	−2.25072e10	+	3.89835e10i	−0.0905945	+	0.156914i
$707$	1.51180e11	+	8.72838e10i	0.605085	+	0.349346i
$708$		0			0
$709$	1.35665e11	+	2.34979e11i	0.536887	+	0.929916i	0.999069	+	0.0431311i	$0.0137333\pi$
$709$	1.35665e11	+	2.34979e11i	0.536887	+	0.929916i	−0.462182	+	0.886785i	$0.652933\pi$
$710$			2.11954e10i			0.0834080i
$711$		0			0
$712$	9.35727e10			0.364107
$713$	1.04251e11	−	6.01891e10i	0.403386	−	0.232895i
$714$		0			0
$715$	3.81654e10	−	6.61044e10i	0.146031	−	0.252933i
$716$	2.43265e11	+	1.40449e11i	0.925608	+	0.534400i
$717$		0			0
$718$	−4.71403e10	−	8.16494e10i	−0.177376	−	0.307224i
$719$		−	5.27584e11i		−	1.97413i	−0.160318	−	0.987065i	$-0.551252\pi$
$719$		−	5.27584e11i		−	1.97413i	0.160318	−	0.987065i	$-0.448748\pi$
$720$		0			0
$721$	1.53190e11			0.566879
$722$	−1.17786e11	+	6.80039e10i	−0.433456	+	0.250256i
$723$		0			0
$724$	6.06020e10	−	1.04966e11i	0.220563	−	0.382026i
$725$	9.80712e10	+	5.66214e10i	0.354968	+	0.204941i
$726$		0			0
$727$	1.58907e11	+	2.75236e11i	0.568861	+	0.985297i	0.996679	+	0.0814316i	$0.0259492\pi$
$727$	1.58907e11	+	2.75236e11i	0.568861	+	0.985297i	−0.427818	+	0.903865i	$0.640717\pi$
$728$		−	1.06352e11i		−	0.378633i
$729$		0			0
$730$	−1.22572e10			−0.0431617
$731$	−4.00775e11	+	2.31387e11i	−1.40356	+	0.810345i
$732$		0			0
$733$	−1.28841e11	+	2.23159e11i	−0.446312	+	0.773035i	−0.998143	−	0.0609213i	$-0.980596\pi$
$733$	−1.28841e11	+	2.23159e11i	−0.446312	+	0.773035i	0.551831	+	0.833956i	$0.313929\pi$
$734$	1.99819e11	+	1.15365e11i	0.688418	+	0.397458i
$735$		0			0
$736$	−7.93241e10	−	1.37393e11i	−0.270330	−	0.468225i
$737$			8.00575e10i			0.271351i
$738$		0			0
$739$	−4.59849e10			−0.154183			−0.0770917	−	0.997024i	$-0.524563\pi$
$739$	−4.59849e10			−0.154183			−0.0770917	+	0.997024i	$0.524563\pi$
$740$	−7.61399e10	+	4.39594e10i	−0.253913	+	0.146597i
$741$		0			0
$742$	−4.58848e10	+	7.94749e10i	−0.151375	+	0.262189i
$743$	1.15801e11	+	6.68579e10i	0.379978	+	0.219380i	0.677809	−	0.735238i	$-0.262930\pi$
$743$	1.15801e11	+	6.68579e10i	0.379978	+	0.219380i	−0.297831	+	0.954619i	$0.596263\pi$
$744$		0			0
$745$	−9.71235e9	−	1.68223e10i	−0.0315282	−	0.0546085i
$746$		−	9.58102e10i		−	0.309355i
$747$		0			0
$748$	−1.79432e11			−0.573183
$749$	−9.35575e9	+	5.40155e9i	−0.0297270	+	0.0171629i
$750$		0			0
$751$	−2.37013e11	+	4.10519e11i	−0.745097	+	1.29055i	0.205052	+	0.978751i	$0.434264\pi$
$751$	−2.37013e11	+	4.10519e11i	−0.745097	+	1.29055i	−0.950149	+	0.311795i	$0.899070\pi$
$752$	1.46622e11	+	8.46520e10i	0.458487	+	0.264707i
$753$		0			0
$754$	−5.68623e10	−	9.84883e10i	−0.175930	−	0.304719i
$755$		−	9.20448e10i		−	0.283277i
$756$		0			0
$757$	−2.39444e11			−0.729157			−0.364578	−	0.931173i	$-0.618787\pi$
$757$	−2.39444e11			−0.729157			−0.364578	+	0.931173i	$0.618787\pi$
$758$	1.29237e11	−	7.46149e10i	0.391480	−	0.226021i
$759$		0			0
$760$	−1.17816e11	+	2.04063e11i	−0.353142	+	0.611661i
$761$	−2.06197e11	−	1.19048e11i	−0.614814	−	0.354963i	0.160033	−	0.987112i	$-0.448840\pi$
$761$	−2.06197e11	−	1.19048e11i	−0.614814	−	0.354963i	−0.774847	+	0.632149i	$0.782173\pi$
$762$		0			0
$763$	−2.70925e10	−	4.69255e10i	−0.0799375	−	0.138456i
$764$			2.27081e11i			0.666511i
$765$		0			0
$766$	−1.15673e11			−0.335981
$767$	−2.67801e11	+	1.54615e11i	−0.773804	+	0.446756i
$768$		0			0
$769$	8.28677e10	−	1.43531e11i	0.236963	−	0.410431i	−0.722879	−	0.690975i	$-0.757181\pi$
$769$	8.28677e10	−	1.43531e11i	0.236963	−	0.410431i	0.959841	+	0.280544i	$0.0905148\pi$
$770$	−1.21463e10	−	7.01267e9i	−0.0345526	−	0.0199490i
$771$		0			0
$772$	1.16169e11	+	2.01210e11i	0.327054	+	0.566475i
$773$			6.52654e11i			1.82795i	0.405766	+	0.913977i	$0.367005\pi$
$773$			6.52654e11i			1.82795i	−0.405766	+	0.913977i	$0.632995\pi$
$774$		0			0
$775$	1.92403e11			0.533342
$776$	−2.55450e11	+	1.47484e11i	−0.704465	+	0.406723i
$777$		0			0
$778$	8.37795e10	−	1.45110e11i	0.228675	−	0.396077i
$779$	6.02268e11	+	3.47720e11i	1.63546	+	0.944234i
$780$		0			0
$781$	−2.25268e10	−	3.90176e10i	−0.0605474	−	0.104871i
$782$		−	1.62181e11i		−	0.433685i
$783$		0			0
$784$	−1.50861e11			−0.399313
$785$	5.77391e9	−	3.33357e9i	0.0152052	−	0.00877871i
$786$		0			0
$787$	−3.84551e9	+	6.66061e9i	−0.0100243	+	0.0173626i	−0.870994	−	0.491294i	$-0.836524\pi$
$787$	−3.84551e9	+	6.66061e9i	−0.0100243	+	0.0173626i	0.860970	+	0.508656i	$0.169858\pi$
$788$	−4.69380e11	−	2.70997e11i	−1.21736	−	0.702844i
$789$		0			0
$790$	−3.65581e9	−	6.33204e9i	−0.00938587	−	0.0162568i
$791$		−	1.46734e11i		−	0.374822i
$792$		0			0
$793$	−2.45235e11			−0.620141
$794$	1.95576e11	−	1.12916e11i	0.492077	−	0.284101i
$795$		0			0
$796$	1.61598e11	−	2.79896e11i	0.402517	−	0.697180i
$797$	3.40517e11	+	1.96598e11i	0.843928	+	0.487242i	0.858598	−	0.512650i	$-0.171336\pi$
$797$	3.40517e11	+	1.96598e11i	0.843928	+	0.487242i	−0.0146694	+	0.999892i	$0.504670\pi$
$798$		0			0
$799$	4.19626e11	+	7.26813e11i	1.02961	+	1.78335i
$800$		−	2.53571e11i		−	0.619070i
$801$		0			0
$802$	6.96054e10			0.168246
$803$	2.25636e10	−	1.30271e10i	0.0542684	−	0.0313319i
$804$		0			0
$805$	−2.73328e10	+	4.73417e10i	−0.0650879	+	0.112736i
$806$	−1.67335e11	−	9.66108e10i	−0.396503	−	0.228921i
$807$		0			0
$808$	−3.00558e11	−	5.20582e11i	−0.705153	−	1.22136i
$809$		−	2.82726e10i		−	0.0660043i	−0.999455	−	0.0330021i	$-0.989493\pi$
$809$		−	2.82726e10i		−	0.0660043i	0.999455	−	0.0330021i	$-0.0105068\pi$
$810$		0			0
$811$	3.13486e11			0.724661			0.362330	−	0.932050i	$-0.381981\pi$
$811$	3.13486e11			0.724661			0.362330	+	0.932050i	$0.381981\pi$
$812$	7.80364e10	−	4.50543e10i	0.179504	−	0.103636i
$813$		0			0
$814$	−2.16691e10	+	3.75320e10i	−0.0493564	+	0.0854877i
$815$	−1.76054e11	−	1.01645e11i	−0.399039	−	0.230385i
$816$		0			0
$817$	−2.89393e11	−	5.01243e11i	−0.649531	−	1.12502i
$818$			2.59275e11i			0.579092i
$819$		0			0
$820$	2.89164e11			0.639571
$821$	4.79842e11	−	2.77037e11i	1.05615	−	0.609769i	0.131786	−	0.991278i	$-0.457929\pi$
$821$	4.79842e11	−	2.77037e11i	1.05615	−	0.609769i	0.924365	+	0.381509i	$0.124596\pi$
$822$		0			0
$823$	1.04720e11	−	1.81381e11i	0.228261	−	0.395359i	−0.729032	−	0.684480i	$-0.760029\pi$
$823$	1.04720e11	−	1.81381e11i	0.228261	−	0.395359i	0.957293	+	0.289120i	$0.0933628\pi$
$824$	−4.56833e11	−	2.63752e11i	−0.990942	−	0.572121i
$825$		0			0
$826$	2.84096e10	+	4.92069e10i	0.0610302	+	0.105707i
$827$		−	3.89638e11i		−	0.832990i	−0.909138	−	0.416495i	$-0.863258\pi$
$827$		−	3.89638e11i		−	0.832990i	0.909138	−	0.416495i	$-0.136742\pi$
$828$		0			0
$829$	2.80930e11			0.594813			0.297406	−	0.954751i	$-0.403878\pi$
$829$	2.80930e11			0.594813			0.297406	+	0.954751i	$0.403878\pi$
$830$	−9.35837e10	+	5.40306e10i	−0.197191	+	0.113849i
$831$		0			0
$832$	1.21607e10	−	2.10630e10i	0.0253785	−	0.0439569i
$833$	−6.47639e11	−	3.73915e11i	−1.34510	−	0.776591i
$834$		0			0
$835$	−1.04682e10	−	1.81314e10i	−0.0215340	−	0.0372980i
$836$		−	2.24413e11i		−	0.459434i
$837$		0			0
$838$	1.23087e11			0.249594
$839$	7.79523e11	−	4.50058e11i	1.57319	−	0.908281i	0.577414	−	0.816451i	$-0.304062\pi$
$839$	7.79523e11	−	4.50058e11i	1.57319	−	0.908281i	0.995775	−	0.0918295i	$-0.0292715\pi$
$840$		0			0
$841$	−1.42595e11	+	2.46982e11i	−0.285050	+	0.493721i
$842$	2.31283e11	+	1.33531e11i	0.460145	+	0.265665i
$843$		0			0
$844$	−2.11959e10	−	3.67124e10i	−0.0417717	−	0.0723508i
$845$			1.65388e11i			0.324398i
$846$		0			0
$847$	−1.70620e11			−0.331509
$848$	−3.77697e11	+	2.18064e11i	−0.730399	+	0.421696i
$849$		0			0
$850$	1.29609e11	−	2.24490e11i	0.248290	−	0.430052i
$851$	1.46286e11	+	8.44581e10i	0.278922	+	0.161036i
$852$		0			0
$853$	7.98028e10	+	1.38222e11i	0.150738	+	0.261085i	0.931499	−	0.363744i	$-0.118502\pi$
$853$	7.98028e10	+	1.38222e11i	0.150738	+	0.261085i	−0.780761	+	0.624830i	$0.785168\pi$
$854$			4.50605e10i			0.0847159i
$855$		0			0
$856$	3.72000e10			0.0692865
$857$	1.34558e11	−	7.76871e10i	0.249452	−	0.144021i	−0.370062	−	0.929007i	$-0.620663\pi$
$857$	1.34558e11	−	7.76871e10i	0.249452	−	0.144021i	0.619513	+	0.784986i	$0.287330\pi$
$858$		0			0
$859$	2.08291e11	−	3.60771e11i	0.382559	−	0.662612i	−0.608868	−	0.793271i	$-0.708376\pi$
$859$	2.08291e11	−	3.60771e11i	0.382559	−	0.662612i	0.991427	+	0.130660i	$0.0417095\pi$
$860$	−2.08417e11	−	1.20330e11i	−0.381013	−	0.219978i
$861$		0			0
$862$	8.19861e10	+	1.42004e11i	0.148495	+	0.257200i
$863$			3.88147e11i			0.699766i	0.936793	+	0.349883i	$0.113779\pi$
$863$			3.88147e11i			0.699766i	−0.936793	+	0.349883i	$0.886221\pi$
$864$		0			0
$865$	2.38023e11			0.425163
$866$	−2.92098e11	+	1.68643e11i	−0.519346	+	0.299845i
$867$		0			0
$868$	7.65488e10	−	1.32586e11i	0.134853	−	0.233572i
$869$	1.34596e10	+	7.77091e9i	0.0236022	+	0.0136268i
$870$		0			0
$871$	−2.50427e11	−	4.33752e11i	−0.435119	−	0.753648i
$872$			1.86584e11i			0.322707i
$873$		0			0
$874$	2.02838e11			0.347619
$875$	−1.96709e11	+	1.13570e11i	−0.335576	+	0.193745i
$876$		0			0
$877$	−2.87925e11	+	4.98700e11i	−0.486722	+	0.843026i	−0.999883	−	0.0152653i	$-0.995141\pi$
$877$	−2.87925e11	+	4.98700e11i	−0.486722	+	0.843026i	0.513162	+	0.858292i	$0.328474\pi$
$878$	1.75439e10	+	1.01290e10i	0.0295222	+	0.0170447i
$879$		0			0
$880$	−3.33271e10	−	5.77242e10i	−0.0555733	−	0.0962558i
$881$			3.11023e11i			0.516284i	0.966107	+	0.258142i	$0.0831102\pi$
$881$			3.11023e11i			0.516284i	−0.966107	+	0.258142i	$0.916890\pi$
$882$		0			0
$883$	3.94761e11			0.649368			0.324684	−	0.945822i	$-0.394742\pi$
$883$	3.94761e11			0.649368			0.324684	+	0.945822i	$0.394742\pi$
$884$	9.72163e11	−	5.61278e11i	1.59195	−	0.919114i
$885$		0			0
$886$	−2.78215e10	+	4.81883e10i	−0.0451488	+	0.0782000i
$887$	9.38596e10	+	5.41899e10i	0.151630	+	0.0875435i	0.573895	−	0.818929i	$-0.305432\pi$
$887$	9.38596e10	+	5.41899e10i	0.151630	+	0.0875435i	−0.422265	+	0.906472i	$0.638765\pi$
$888$		0			0
$889$	1.51182e10	+	2.61855e10i	0.0242043	+	0.0419231i
$890$			7.72016e10i			0.123046i
$891$		0			0
$892$	−4.04162e11			−0.638404
$893$	−9.09014e11	+	5.24820e11i	−1.42944	+	0.825286i
$894$		0			0
$895$	−2.58625e11	+	4.47951e11i	−0.403068	+	0.698134i
$896$	−2.19129e11	−	1.26514e11i	−0.339992	−	0.196294i
$897$		0			0
$898$	1.85511e10	+	3.21314e10i	0.0285275	+	0.0494110i
$899$		−	3.65387e11i		−	0.559389i
$900$		0			0
$901$	−2.16191e12			−3.28049
$902$	1.23442e11	−	7.12695e10i	0.186482	−	0.107666i
$903$		0			0
$904$	−2.52637e11	+	4.37579e11i	−0.378288	+	0.655214i
$905$	1.93286e11	+	1.11593e11i	0.288141	+	0.166358i
$906$		0			0
$907$	4.57478e11	+	7.92375e11i	0.675991	+	1.17085i	0.976178	+	0.216970i	$0.0696175\pi$
$907$	4.57478e11	+	7.92375e11i	0.675991	+	1.17085i	−0.300187	+	0.953880i	$0.597049\pi$
$908$			8.79992e11i			1.29460i
$909$		0			0
$910$	8.77448e10			0.127955
$911$	7.18063e10	−	4.14574e10i	0.104253	−	0.0601905i	−0.446967	−	0.894550i	$-0.647496\pi$
$911$	7.18063e10	−	4.14574e10i	0.104253	−	0.0601905i	0.551220	+	0.834360i	$0.314163\pi$
$912$		0			0
$913$	1.14849e11	−	1.98925e11i	0.165289	−	0.286290i
$914$	−2.13330e11	−	1.23166e11i	−0.305681	−	0.176485i
$915$		0			0
$916$	−5.31051e10	−	9.19807e10i	−0.0754318	−	0.130652i
$917$			2.48789e11i			0.351847i
$918$		0			0
$919$	1.16192e12			1.62898			0.814488	−	0.580180i	$-0.197018\pi$
$919$	1.16192e12			1.62898			0.814488	+	0.580180i	$0.197018\pi$
$920$	1.63019e11	−	9.41193e10i	0.227556	−	0.131379i
$921$		0			0
$922$	−1.70506e11	+	2.95325e11i	−0.235948	+	0.408674i
$923$	2.44100e11	+	1.40931e11i	0.336327	+	0.194179i
$924$		0			0
$925$	1.34991e11	+	2.33812e11i	0.184391	+	0.319374i
$926$			5.38503e11i			0.732393i
$927$		0			0
$928$	−4.81548e11			−0.649304
$929$	4.03658e11	−	2.33052e11i	0.541939	−	0.312889i	−0.203925	−	0.978986i	$-0.565370\pi$
$929$	4.03658e11	−	2.33052e11i	0.541939	−	0.312889i	0.745864	+	0.666098i	$0.232037\pi$
$930$		0			0
$931$	4.67650e11	−	8.09993e11i	0.622475	−	1.07816i
$932$	6.55682e10	+	3.78558e10i	0.0869019	+	0.0501728i
$933$		0			0
$934$	1.52510e11	+	2.64156e11i	0.200407	+	0.347114i
$935$		−	3.30409e11i		−	0.432320i
$936$		0			0
$937$	1.53650e11			0.199331			0.0996653	−	0.995021i	$-0.468223\pi$
$937$	1.53650e11			0.199331			0.0996653	+	0.995021i	$0.468223\pi$
$938$	−7.96993e10	+	4.60144e10i	−0.102954	+	0.0594405i
$939$		0			0
$940$	−2.18220e11	+	3.77968e11i	−0.279501	+	0.484110i
$941$	−1.35458e11	−	7.82067e10i	−0.172761	−	0.0997437i	0.411126	−	0.911579i	$-0.365136\pi$
$941$	−1.35458e11	−	7.82067e10i	−0.172761	−	0.0997437i	−0.583887	+	0.811835i	$0.698469\pi$
$942$		0			0
$943$	−2.77782e11	−	4.81132e11i	−0.351283	−	0.608440i
$944$			2.70028e11i			0.340033i
$945$		0			0
$946$	−1.18629e11			−0.148125
$947$	−2.57065e11	+	1.48417e11i	−0.319627	+	0.184537i	−0.651226	−	0.758883i	$-0.725745\pi$
$947$	−2.57065e11	+	1.48417e11i	−0.319627	+	0.184537i	0.331599	+	0.943420i	$0.392412\pi$
$948$		0			0
$949$	−8.14998e10	+	1.41162e11i	−0.100483	+	0.174041i
$950$	2.80766e11	+	1.62100e11i	0.344707	+	0.199017i
$951$		0			0
$952$	−2.30179e11	−	3.98682e11i	−0.280233	−	0.485377i
$953$		−	4.43879e11i		−	0.538138i	−0.963121	−	0.269069i	$-0.913284\pi$
$953$		−	4.43879e11i		−	0.538138i	0.963121	−	0.269069i	$-0.0867159\pi$
$954$		0			0
$955$	−4.18150e11			−0.502712
$956$	6.13636e11	−	3.54283e11i	0.734648	−	0.424149i
$957$		0			0
$958$	3.40450e11	−	5.89676e11i	0.404195	−	0.700086i
$959$	−4.31902e10	−	2.49359e10i	−0.0510635	−	0.0294815i
$960$		0			0
$961$	1.16044e11	+	2.00993e11i	0.136059	+	0.235661i
$962$		−	2.71131e11i		−	0.316577i
$963$		0			0
$964$	9.26728e11			1.07311
$965$	−3.70512e11	+	2.13915e11i	−0.427260	+	0.246679i
$966$		0			0
$967$	3.44613e11	−	5.96888e11i	0.394118	−	0.682632i	−0.598870	−	0.800846i	$-0.704383\pi$
$967$	3.44613e11	−	5.96888e11i	0.394118	−	0.682632i	0.992988	+	0.118214i	$0.0377168\pi$
$968$	5.08809e11	+	2.93761e11i	0.579500	+	0.334575i
$969$		0			0
$970$	−1.21681e11	−	2.10758e11i	−0.137447	−	0.238065i
$971$		−	4.89136e11i		−	0.550241i	−0.961410	−	0.275121i	$-0.911282\pi$
$971$		−	4.89136e11i		−	0.550241i	0.961410	−	0.275121i	$-0.0887178\pi$
$972$		0			0
$973$	−3.80185e11			−0.424173
$974$	4.46402e11	−	2.57730e11i	0.496010	−	0.286371i
$975$		0			0
$976$	−1.07073e11	+	1.85456e11i	−0.118000	+	0.204382i
$977$	−6.26502e11	−	3.61711e11i	−0.687614	−	0.396994i	0.115104	−	0.993353i	$-0.463280\pi$
$977$	−6.26502e11	−	3.61711e11i	−0.687614	−	0.396994i	−0.802717	+	0.596360i	$0.796613\pi$
$978$		0			0
$979$	−8.20512e10	−	1.42117e11i	−0.0893211	−	0.154709i
$980$		−	3.88898e11i		−	0.421630i
$981$		0			0
$982$	−5.66156e11			−0.608821
$983$	−1.39027e12	+	8.02670e11i	−1.48896	+	0.859653i	−0.999921	−	0.0126073i	$-0.995987\pi$
$983$	−1.39027e12	+	8.02670e11i	−1.48896	+	0.859653i	−0.489042	+	0.872260i	$0.662654\pi$
$984$		0			0
$985$	4.99018e11	−	8.64324e11i	0.530116	−	0.918188i
$986$	−4.26321e11	−	2.46137e11i	−0.451055	−	0.260416i
$987$		0			0
$988$	7.01983e11	+	1.21587e12i	0.736714	+	1.27603i
$989$			4.62373e11i			0.483289i
$990$		0			0
$991$	8.39412e11			0.870323			0.435162	−	0.900352i	$-0.356691\pi$
$991$	8.39412e11			0.870323			0.435162	+	0.900352i	$0.356691\pi$
$992$	−7.08553e11	+	4.09083e11i	−0.731688	+	0.422440i
$993$		0			0
$994$	2.58953e10	−	4.48520e10i	0.0265262	−	0.0459448i
$995$	5.15406e11	+	2.97570e11i	0.525844	+	0.303596i
$996$		0			0
$997$	−7.28767e11	−	1.26226e12i	−0.737578	−	1.27752i	−0.953583	−	0.301130i	$-0.902636\pi$
$997$	−7.28767e11	−	1.26226e12i	−0.737578	−	1.27752i	0.216005	−	0.976392i	$-0.430697\pi$
$998$		−	7.91189e11i		−	0.797550i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.9.d.a.17.3		14
3.2	odd	2		9.9.d.a.5.5	yes	14
4.3	odd	2		432.9.q.a.17.3		14
9.2	odd	6	inner	27.9.d.a.8.3		14
9.4	even	3		81.9.b.a.80.6		14
9.5	odd	6		81.9.b.a.80.9		14
9.7	even	3		9.9.d.a.2.5	✓	14
12.11	even	2		144.9.q.a.113.4		14
36.7	odd	6		144.9.q.a.65.4		14
36.11	even	6		432.9.q.a.305.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.5	✓	14	9.7	even	3
9.9.d.a.5.5	yes	14	3.2	odd	2
27.9.d.a.8.3		14	9.2	odd	6	inner
27.9.d.a.17.3		14	1.1	even	1	trivial
81.9.b.a.80.6		14	9.4	even	3
81.9.b.a.80.9		14	9.5	odd	6
144.9.q.a.65.4		14	36.7	odd	6
144.9.q.a.113.4		14	12.11	even	2
432.9.q.a.17.3		14	4.3	odd	2
432.9.q.a.305.3		14	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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-6.01192 + 3.47098i) q^{2} +(-103.905 + 179.968i) q^{4} +(-331.396 - 191.331i) q^{5} +(467.516 + 809.762i) q^{7} -3219.75i q^{8} +O(q^{10})\)	\(q+(-6.01192 + 3.47098i) q^{2} +(-103.905 + 179.968i) q^{4} +(-331.396 - 191.331i) q^{5} +(467.516 + 809.762i) q^{7} -3219.75i q^{8} +2656.43 q^{10} +(-4890.10 + 2823.30i) q^{11} +(17663.1 - 30593.3i) q^{13} +(-5621.34 - 3245.48i) q^{14} +(-15423.9 - 26714.9i) q^{16} -152914. i q^{17} +191248. q^{19} +(68867.1 - 39760.4i) q^{20} +(19599.3 - 33947.0i) q^{22} +(-132313. - 76390.7i) q^{23} +(-122097. - 211478. i) q^{25} +245233. i q^{26} -194308. q^{28} +(-401612. + 231871. i) q^{29} +(-393956. + 682351. i) q^{31} +(899280. + 519200. i) q^{32} +(530763. + 919308. i) q^{34} -357802. i q^{35} -1.10561e6 q^{37} +(-1.14977e6 + 663818. i) q^{38} +(-616039. + 1.06701e6i) q^{40} +(3.14915e6 + 1.81816e6i) q^{41} +(-1.51318e6 - 2.62091e6i) q^{43} -1.17342e6i q^{44} +1.06060e6 q^{46} +(-4.75308e6 + 2.74419e6i) q^{47} +(2.44526e6 - 4.23531e6i) q^{49} +(1.46808e6 + 847594. i) q^{50} +(3.67054e6 + 6.35757e6i) q^{52} -1.41381e7i q^{53} +2.16075e6 q^{55} +(2.60723e6 - 1.50528e6i) q^{56} +(1.60964e6 - 2.78797e6i) q^{58} +(-7.58082e6 - 4.37679e6i) q^{59} +(-3.47102e6 - 6.01198e6i) q^{61} -5.46965e6i q^{62} +688484. q^{64} +(-1.17069e7 + 6.75900e6i) q^{65} +(7.08899e6 - 1.22785e7i) q^{67} +(2.75197e7 + 1.58885e7i) q^{68} +(1.24193e6 + 2.15108e6i) q^{70} +7.97888e6i q^{71} -4.61414e6 q^{73} +(6.64682e6 - 3.83754e6i) q^{74} +(-1.98715e7 + 3.44184e7i) q^{76} +(-4.57241e6 - 2.63988e6i) q^{77} +(-1.37621e6 - 2.38366e6i) q^{79} +1.18043e7i q^{80} -2.52433e7 q^{82} +(-3.52291e7 + 2.03395e7i) q^{83} +(-2.92573e7 + 5.06751e7i) q^{85} +(1.81943e7 + 1.05045e7i) q^{86} +(9.09033e6 + 1.57449e7i) q^{88} +2.90621e7i q^{89} +3.30311e7 q^{91} +(2.74958e7 - 1.58747e7i) q^{92} +(1.90501e7 - 3.29957e7i) q^{94} +(-6.33787e7 - 3.65917e7i) q^{95} +(-4.58061e7 - 7.93386e7i) q^{97} +3.39498e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7}+O(q^{10}) \) 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7	\( 14 q + 3 q^{2} + 767 q^{4} - 438 q^{5} + 922 q^{7} - 516 q^{10} + 28677 q^{11} + 1684 q^{13} - 120966 q^{14} - 65281 q^{16} - 269630 q^{19} - 539454 q^{20} + 61311 q^{22} + 1000452 q^{23} + 65177 q^{25} + 1075708 q^{28} - 3797682 q^{29} - 164132 q^{31} + 8461881 q^{32} + 654993 q^{34} - 1671668 q^{37} - 10967691 q^{38} + 613326 q^{40} + 10239447 q^{41} + 791815 q^{43} + 1189536 q^{46} - 31148628 q^{47} - 4826637 q^{49} + 63849453 q^{50} - 5552720 q^{52} + 8107476 q^{55} - 116638674 q^{56} + 14211822 q^{58} + 83493795 q^{59} - 5255600 q^{61} - 26813830 q^{64} - 69232992 q^{65} - 8288855 q^{67} + 77746743 q^{68} + 27813756 q^{70} - 36721682 q^{73} + 10383450 q^{74} - 42822959 q^{76} - 56158710 q^{77} - 32771822 q^{79} + 236099418 q^{82} + 198915996 q^{83} + 97486146 q^{85} - 146190669 q^{86} + 24955827 q^{88} - 201514504 q^{91} + 295365804 q^{92} - 36698244 q^{94} - 386813838 q^{95} + 127049161 q^{97}+O(q^{100}) \) 14 * q + 3 * q^2 + 767 * q^4 - 438 * q^5 + 922 * q^7 - 516 * q^10 + 28677 * q^11 + 1684 * q^13 - 120966 * q^14 - 65281 * q^16 - 269630 * q^19 - 539454 * q^20 + 61311 * q^22 + 1000452 * q^23 + 65177 * q^25 + 1075708 * q^28 - 3797682 * q^29 - 164132 * q^31 + 8461881 * q^32 + 654993 * q^34 - 1671668 * q^37 - 10967691 * q^38 + 613326 * q^40 + 10239447 * q^41 + 791815 * q^43 + 1189536 * q^46 - 31148628 * q^47 - 4826637 * q^49 + 63849453 * q^50 - 5552720 * q^52 + 8107476 * q^55 - 116638674 * q^56 + 14211822 * q^58 + 83493795 * q^59 - 5255600 * q^61 - 26813830 * q^64 - 69232992 * q^65 - 8288855 * q^67 + 77746743 * q^68 + 27813756 * q^70 - 36721682 * q^73 + 10383450 * q^74 - 42822959 * q^76 - 56158710 * q^77 - 32771822 * q^79 + 236099418 * q^82 + 198915996 * q^83 + 97486146 * q^85 - 146190669 * q^86 + 24955827 * q^88 - 201514504 * q^91 + 295365804 * q^92 - 36698244 * q^94 - 386813838 * q^95 + 127049161 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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