LMFDB - Embedded newform 169.12.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,12,Mod(1,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("169.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	169.a (trivial)

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:	yes
Analytic conductor:	$129.849997515$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 18433 x^{10} + 121088056 x^{8} - 340607607312 x^{6} + 380893885719552 x^{4} + \cdots + 14\!\cdots\!56 $ x^12 - 18433x^10 + 121088056x^8 - 340607607312x^6 + 380893885719552x^4 - 134825856231997440*x^2 + 1497425476589715456
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4}\cdot 13^{4} $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$3.38741$ of defining polynomial
Character	$\chi$	$=$	169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.38741 q^{2} +494.534 q^{3} -2036.53 q^{4} +9091.88 q^{5} +1675.19 q^{6} +45027.4 q^{7} -13836.0 q^{8} +67417.3 q^{9} +O(q^{10})$	\(q+3.38741 q^{2} +494.534 q^{3} -2036.53 q^{4} +9091.88 q^{5} +1675.19 q^{6} +45027.4 q^{7} -13836.0 q^{8} +67417.3 q^{9} +30797.9 q^{10} -810639. q^{11} -1.00713e6 q^{12} +152526. q^{14} +4.49625e6 q^{15} +4.12394e6 q^{16} +851428. q^{17} +228370. q^{18} -7.56605e6 q^{19} -1.85158e7 q^{20} +2.22676e7 q^{21} -2.74596e6 q^{22} -3.69275e6 q^{23} -6.84236e6 q^{24} +3.38341e7 q^{25} -5.42651e7 q^{27} -9.16995e7 q^{28} -9.33625e7 q^{29} +1.52306e7 q^{30} -2.61508e8 q^{31} +4.23055e7 q^{32} -4.00889e8 q^{33} +2.88413e6 q^{34} +4.09384e8 q^{35} -1.37297e8 q^{36} -5.38221e8 q^{37} -2.56293e7 q^{38} -1.25795e8 q^{40} -6.71292e8 q^{41} +7.54295e7 q^{42} +1.09294e9 q^{43} +1.65089e9 q^{44} +6.12950e8 q^{45} -1.25088e7 q^{46} +1.79698e9 q^{47} +2.03943e9 q^{48} +5.01432e7 q^{49} +1.14610e8 q^{50} +4.21060e8 q^{51} -5.82497e9 q^{53} -1.83818e8 q^{54} -7.37023e9 q^{55} -6.22997e8 q^{56} -3.74167e9 q^{57} -3.16257e8 q^{58} +4.74847e9 q^{59} -9.15672e9 q^{60} +6.50495e9 q^{61} -8.85834e8 q^{62} +3.03563e9 q^{63} -8.30252e9 q^{64} -1.35797e9 q^{66} +8.11940e9 q^{67} -1.73395e9 q^{68} -1.82619e9 q^{69} +1.38675e9 q^{70} -3.16640e9 q^{71} -9.32783e8 q^{72} +8.22937e9 q^{73} -1.82317e9 q^{74} +1.67321e10 q^{75} +1.54085e10 q^{76} -3.65010e10 q^{77} -3.75500e9 q^{79} +3.74943e10 q^{80} -3.87787e10 q^{81} -2.27394e9 q^{82} -6.60119e9 q^{83} -4.53486e10 q^{84} +7.74108e9 q^{85} +3.70222e9 q^{86} -4.61710e10 q^{87} +1.12160e10 q^{88} -5.68420e10 q^{89} +2.07631e9 q^{90} +7.52038e9 q^{92} -1.29325e11 q^{93} +6.08709e9 q^{94} -6.87896e10 q^{95} +2.09215e10 q^{96} +1.62006e11 q^{97} +1.69856e8 q^{98} -5.46511e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 488 q^{3} + 12290 q^{4} + 654644 q^{9}+O(q^{10}) $ 12 * q - 488 * q^3 + 12290 * q^4 + 654644 * q^9	$ 12 q - 488 q^{3} + 12290 q^{4} + 654644 q^{9} + 333446 q^{10} - 2740298 q^{12} - 5367450 q^{14} + 19025698 q^{16} - 12198768 q^{17} - 111171128 q^{22} - 5810592 q^{23} - 6102388 q^{25} - 52613336 q^{27} - 244463112 q^{29} - 426504126 q^{30} - 562027560 q^{35} + 1357546052 q^{36} - 3171817788 q^{38} + 4092185498 q^{40} + 1280452314 q^{42} - 2294519976 q^{43} - 14206061378 q^{48} + 3573617796 q^{49} - 7713246552 q^{51} - 4602062760 q^{53} - 6178744976 q^{55} - 20017912662 q^{56} - 13775649944 q^{61} - 239765256 q^{62} + 3560815378 q^{64} + 37979507040 q^{66} + 40844682210 q^{68} + 25419983328 q^{69} + 19351803414 q^{74} - 68016370832 q^{75} + 80478036048 q^{77} + 18046097296 q^{79} - 132677486692 q^{81} + 255687836096 q^{82} + 94507900752 q^{87} - 239343029120 q^{88} + 190413561204 q^{90} - 135236877012 q^{92} - 78363161402 q^{94} - 145093149648 q^{95}+O(q^{100}) $ 12 * q - 488 * q^3 + 12290 * q^4 + 654644 * q^9 + 333446 * q^10 - 2740298 * q^12 - 5367450 * q^14 + 19025698 * q^16 - 12198768 * q^17 - 111171128 * q^22 - 5810592 * q^23 - 6102388 * q^25 - 52613336 * q^27 - 244463112 * q^29 - 426504126 * q^30 - 562027560 * q^35 + 1357546052 * q^36 - 3171817788 * q^38 + 4092185498 * q^40 + 1280452314 * q^42 - 2294519976 * q^43 - 14206061378 * q^48 + 3573617796 * q^49 - 7713246552 * q^51 - 4602062760 * q^53 - 6178744976 * q^55 - 20017912662 * q^56 - 13775649944 * q^61 - 239765256 * q^62 + 3560815378 * q^64 + 37979507040 * q^66 + 40844682210 * q^68 + 25419983328 * q^69 + 19351803414 * q^74 - 68016370832 * q^75 + 80478036048 * q^77 + 18046097296 * q^79 - 132677486692 * q^81 + 255687836096 * q^82 + 94507900752 * q^87 - 239343029120 * q^88 + 190413561204 * q^90 - 135236877012 * q^92 - 78363161402 * q^94 - 145093149648 * q^95

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	3.38741	0.0748518	0.0374259	−	0.999299i	$-0.488084\pi$
$2$	3.38741	0.0748518	0.0374259	+	0.999299i	$0.488084\pi$
$3$	494.534	1.17498	0.587489	−	0.809232i	$-0.300117\pi$
$3$	494.534	1.17498	0.587489	+	0.809232i	$0.300117\pi$
$4$	−2036.53	−0.994397
$5$	9091.88	1.30112	0.650562	−	0.759453i	$-0.274533\pi$
$5$	9091.88	1.30112	0.650562	+	0.759453i	$0.274533\pi$
$6$	1675.19	0.0879492
$7$	45027.4	1.01260	0.506300	−	0.862357i	$-0.331013\pi$
$7$	45027.4	1.01260	0.506300	+	0.862357i	$0.331013\pi$
$8$	−13836.0	−0.149284
$9$	67417.3	0.380573
$10$	30797.9	0.0973915
$11$	−810639.	−1.51764	−0.758818	−	0.651303i	$-0.774223\pi$
$11$	−810639.	−1.51764	−0.758818	+	0.651303i	$0.774223\pi$
$12$	−1.00713e6	−1.16839
$13$	0	0
$13$	0	0
$14$	152526.	0.0757950
$15$	4.49625e6	1.52879
$16$	4.12394e6	0.983223
$17$	851428.	0.145438	0.0727192	−	0.997352i	$-0.476832\pi$
$17$	851428.	0.145438	0.0727192	+	0.997352i	$0.476832\pi$
$18$	228370.	0.0284866
$19$	−7.56605e6	−0.701011	−0.350505	−	0.936561i	$-0.613990\pi$
$19$	−7.56605e6	−0.701011	−0.350505	+	0.936561i	$0.613990\pi$
$20$	−1.85158e7	−1.29383
$21$	2.22676e7	1.18978
$22$	−2.74596e6	−0.113598
$23$	−3.69275e6	−0.119632	−0.0598159	−	0.998209i	$-0.519051\pi$
$23$	−3.69275e6	−0.119632	−0.0598159	+	0.998209i	$0.519051\pi$
$24$	−6.84236e6	−0.175406
$25$	3.38341e7	0.692923
$26$	0	0
$27$	−5.42651e7	−0.727813
$28$	−9.16995e7	−1.00693
$29$	−9.33625e7	−0.845247	−0.422623	−	0.906305i	$-0.638891\pi$
$29$	−9.33625e7	−0.845247	−0.422623	+	0.906305i	$0.638891\pi$
$30$	1.52306e7	0.114433
$31$	−2.61508e8	−1.64057	−0.820286	−	0.571953i	$-0.806186\pi$
$31$	−2.61508e8	−1.64057	−0.820286	+	0.571953i	$0.806186\pi$
$32$	4.23055e7	0.222880
$33$	−4.00889e8	−1.78319
$34$	2.88413e6	0.0108863
$35$	4.09384e8	1.31752
$36$	−1.37297e8	−0.378440
$37$	−5.38221e8	−1.27600	−0.638000	−	0.770036i	$-0.720238\pi$
$37$	−5.38221e8	−1.27600	−0.638000	+	0.770036i	$0.720238\pi$
$38$	−2.56293e7	−0.0524719
$39$	0	0
$40$	−1.25795e8	−0.194237
$41$	−6.71292e8	−0.904899	−0.452449	−	0.891790i	$-0.649450\pi$
$41$	−6.71292e8	−0.904899	−0.452449	+	0.891790i	$0.649450\pi$
$42$	7.54295e7	0.0890574
$43$	1.09294e9	1.13375	0.566876	−	0.823803i	$-0.308152\pi$
$43$	1.09294e9	1.13375	0.566876	+	0.823803i	$0.308152\pi$
$44$	1.65089e9	1.50913
$45$	6.12950e8	0.495172
$46$	−1.25088e7	−0.00895466
$47$	1.79698e9	1.14289	0.571445	−	0.820641i	$-0.306383\pi$
$47$	1.79698e9	1.14289	0.571445	+	0.820641i	$0.306383\pi$
$48$	2.03943e9	1.15527
$49$	5.01432e7	0.0253591
$50$	1.14610e8	0.0518665
$51$	4.21060e8	0.170887
$52$	0	0
$53$	−5.82497e9	−1.91327	−0.956636	−	0.291287i	$-0.905917\pi$
$53$	−5.82497e9	−1.91327	−0.956636	+	0.291287i	$0.905917\pi$
$54$	−1.83818e8	−0.0544782
$55$	−7.37023e9	−1.97463
$56$	−6.22997e8	−0.151165
$57$	−3.74167e9	−0.823672
$58$	−3.16257e8	−0.0632683
$59$	4.74847e9	0.864704	0.432352	−	0.901705i	$-0.357684\pi$
$59$	4.74847e9	0.864704	0.432352	+	0.901705i	$0.357684\pi$
$60$	−9.15672e9	−1.52023
$61$	6.50495e9	0.986120	0.493060	−	0.869995i	$-0.335878\pi$
$61$	6.50495e9	0.986120	0.493060	+	0.869995i	$0.335878\pi$
$62$	−8.85834e8	−0.122800
$63$	3.03563e9	0.385368
$64$	−8.30252e9	−0.966540
$65$	0	0
$66$	−1.35797e9	−0.133475
$67$	8.11940e9	0.734704	0.367352	−	0.930082i	$-0.380264\pi$
$67$	8.11940e9	0.734704	0.367352	+	0.930082i	$0.380264\pi$
$68$	−1.73395e9	−0.144623
$69$	−1.82619e9	−0.140565
$70$	1.38675e9	0.0986186
$71$	−3.16640e9	−0.208279	−0.104139	−	0.994563i	$-0.533209\pi$
$71$	−3.16640e9	−0.208279	−0.104139	+	0.994563i	$0.533209\pi$
$72$	−9.32783e8	−0.0568135
$73$	8.22937e9	0.464613	0.232306	−	0.972643i	$-0.425373\pi$
$73$	8.22937e9	0.464613	0.232306	+	0.972643i	$0.425373\pi$
$74$	−1.82317e9	−0.0955110
$75$	1.67321e10	0.814169
$76$	1.54085e10	0.697083
$77$	−3.65010e10	−1.53676
$78$	0	0
$79$	−3.75500e9	−0.137297	−0.0686485	−	0.997641i	$-0.521869\pi$
$79$	−3.75500e9	−0.137297	−0.0686485	+	0.997641i	$0.521869\pi$
$80$	3.74943e10	1.27929
$81$	−3.87787e10	−1.23574
$82$	−2.27394e9	−0.0677333
$83$	−6.60119e9	−0.183947	−0.0919735	−	0.995761i	$-0.529318\pi$
$83$	−6.60119e9	−0.183947	−0.0919735	+	0.995761i	$0.529318\pi$
$84$	−4.53486e10	−1.18312
$85$	7.74108e9	0.189233
$86$	3.70222e9	0.0848634
$87$	−4.61710e10	−0.993146
$88$	1.12160e10	0.226559
$89$	−5.68420e10	−1.07901	−0.539503	−	0.841983i	$-0.681388\pi$
$89$	−5.68420e10	−1.07901	−0.539503	+	0.841983i	$0.681388\pi$
$90$	2.07631e9	0.0370645
$91$	0	0
$92$	7.52038e9	0.118962
$93$	−1.29325e11	−1.92764
$94$	6.08709e9	0.0855474
$95$	−6.87896e10	−0.912101
$96$	2.09215e10	0.261879
$97$	1.62006e11	1.91551	0.957757	−	0.287578i	$-0.0928499\pi$
$97$	1.62006e11	1.91551	0.957757	+	0.287578i	$0.0928499\pi$
$98$	1.69856e8	0.00189818
$99$	−5.46511e10	−0.577571
$100$	−6.89040e10	−0.689040
$101$	−1.31282e11	−1.24290	−0.621450	−	0.783454i	$-0.713456\pi$
$101$	−1.31282e11	−1.24290	−0.621450	+	0.783454i	$0.713456\pi$
$102$	1.42630e9	0.0127912
$103$	5.50452e10	0.467859	0.233929	−	0.972254i	$-0.424842\pi$
$103$	5.50452e10	0.467859	0.233929	+	0.972254i	$0.424842\pi$
$104$	0	0
$105$	2.02454e11	1.54805
$106$	−1.97316e10	−0.143212
$107$	1.85072e11	1.27564	0.637822	−	0.770184i	$-0.279836\pi$
$107$	1.85072e11	1.27564	0.637822	+	0.770184i	$0.279836\pi$
$108$	1.10512e11	0.723735
$109$	−2.74414e10	−0.170829	−0.0854143	−	0.996346i	$-0.527221\pi$
$109$	−2.74414e10	−0.170829	−0.0854143	+	0.996346i	$0.527221\pi$
$110$	−2.49660e10	−0.147805
$111$	−2.66169e11	−1.49927
$112$	1.85690e11	0.995612
$113$	−1.64428e11	−0.839547	−0.419773	−	0.907629i	$-0.637890\pi$
$113$	−1.64428e11	−0.839547	−0.419773	+	0.907629i	$0.637890\pi$
$114$	−1.26746e10	−0.0616533
$115$	−3.35740e10	−0.155656
$116$	1.90135e11	0.840511
$117$	0	0
$118$	1.60850e10	0.0647247
$119$	3.83376e10	0.147271
$120$	−6.22099e10	−0.228225
$121$	3.71823e11	1.30322
$122$	2.20349e10	0.0738129
$123$	−3.31977e11	−1.06324
$124$	5.32567e11	1.63138
$125$	−1.36324e11	−0.399546
$126$	1.02829e10	0.0288455
$127$	−5.48728e11	−1.47379	−0.736897	−	0.676005i	$-0.763710\pi$
$127$	−5.48728e11	−1.47379	−0.736897	+	0.676005i	$0.763710\pi$
$128$	−1.14766e11	−0.295228
$129$	5.40494e11	1.33213
$130$	0	0
$131$	3.22742e11	0.730910	0.365455	−	0.930829i	$-0.380913\pi$
$131$	3.22742e11	0.730910	0.365455	+	0.930829i	$0.380913\pi$
$132$	8.16420e11	1.77320
$133$	−3.40680e11	−0.709843
$134$	2.75037e10	0.0549940
$135$	−4.93372e11	−0.946975
$136$	−1.17803e10	−0.0217117
$137$	−1.94892e11	−0.345009	−0.172505	−	0.985009i	$-0.555186\pi$
$137$	−1.94892e11	−0.345009	−0.172505	+	0.985009i	$0.555186\pi$
$138$	−6.18606e9	−0.0105215
$139$	−6.64756e11	−1.08663	−0.543314	−	0.839530i	$-0.682831\pi$
$139$	−6.64756e11	−1.08663	−0.543314	+	0.839530i	$0.682831\pi$
$140$	−8.33721e11	−1.31014
$141$	8.88667e11	1.34287
$142$	−1.07259e10	−0.0155901
$143$	0	0
$144$	2.78025e11	0.374188
$145$	−8.48840e11	−1.09977
$146$	2.78762e10	0.0347771
$147$	2.47976e10	0.0297964
$148$	1.09610e12	1.26885
$149$	4.29539e11	0.479157	0.239578	−	0.970877i	$-0.422991\pi$
$149$	4.29539e11	0.479157	0.239578	+	0.970877i	$0.422991\pi$
$150$	5.66785e10	0.0609420
$151$	−1.20700e12	−1.25122	−0.625610	−	0.780136i	$-0.715150\pi$
$151$	−1.20700e12	−1.25122	−0.625610	+	0.780136i	$0.715150\pi$
$152$	1.04684e11	0.104650
$153$	5.74010e10	0.0553499
$154$	−1.23644e11	−0.115029
$155$	−2.37760e12	−2.13459
$156$	0	0
$157$	−9.61496e10	−0.0804450	−0.0402225	−	0.999191i	$-0.512807\pi$
$157$	−9.61496e10	−0.0804450	−0.0402225	+	0.999191i	$0.512807\pi$
$158$	−1.27197e10	−0.0102769
$159$	−2.88065e12	−2.24805
$160$	3.84636e11	0.289995
$161$	−1.66275e11	−0.121139
$162$	−1.31359e11	−0.0924972
$163$	1.50626e12	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$163$	1.50626e12	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$164$	1.36710e12	0.899829
$165$	−3.64483e12	−2.32015
$166$	−2.23609e10	−0.0137688
$167$	−1.03474e12	−0.616441	−0.308221	−	0.951315i	$-0.599734\pi$
$167$	−1.03474e12	−0.616441	−0.308221	+	0.951315i	$0.599734\pi$
$168$	−3.08094e11	−0.177616
$169$	0	0
$170$	2.62222e10	0.0141645
$171$	−5.10083e11	−0.266786
$172$	−2.22579e12	−1.12740
$173$	1.11263e11	0.0545881	0.0272941	−	0.999627i	$-0.491311\pi$
$173$	1.11263e11	0.0545881	0.0272941	+	0.999627i	$0.491311\pi$
$174$	−1.56400e11	−0.0743388
$175$	1.52346e12	0.701653
$176$	−3.34302e12	−1.49217
$177$	2.34828e12	1.01601
$178$	−1.92547e11	−0.0807656
$179$	−2.06269e12	−0.838964	−0.419482	−	0.907764i	$-0.637788\pi$
$179$	−2.06269e12	−0.838964	−0.419482	+	0.907764i	$0.637788\pi$
$180$	−1.24829e12	−0.492398
$181$	−3.46724e12	−1.32663	−0.663317	−	0.748338i	$-0.730852\pi$
$181$	−3.46724e12	−1.32663	−0.663317	+	0.748338i	$0.730852\pi$
$182$	0	0
$183$	3.21692e12	1.15867
$184$	5.10927e10	0.0178592
$185$	−4.89344e12	−1.66023
$186$	−4.38075e11	−0.144287
$187$	−6.90200e11	−0.220722
$188$	−3.65959e12	−1.13649
$189$	−2.44342e12	−0.736984
$190$	−2.33018e11	−0.0682725
$191$	−4.63569e12	−1.31957	−0.659783	−	0.751456i	$-0.729352\pi$
$191$	−4.63569e12	−1.31957	−0.659783	+	0.751456i	$0.729352\pi$
$192$	−4.10588e12	−1.13566
$193$	1.13783e12	0.305852	0.152926	−	0.988238i	$-0.451130\pi$
$193$	1.13783e12	0.305852	0.152926	+	0.988238i	$0.451130\pi$
$194$	5.48779e11	0.143380
$195$	0	0
$196$	−1.02118e11	−0.0252170
$197$	−2.32298e12	−0.557803	−0.278901	−	0.960320i	$-0.589970\pi$
$197$	−2.32298e12	−0.557803	−0.278901	+	0.960320i	$0.589970\pi$
$198$	−1.85126e11	−0.0432322
$199$	−2.94354e11	−0.0668618	−0.0334309	−	0.999441i	$-0.510643\pi$
$199$	−2.94354e11	−0.0668618	−0.0334309	+	0.999441i	$0.510643\pi$
$200$	−4.68127e11	−0.103442
$201$	4.01532e12	0.863261
$202$	−4.44704e11	−0.0930333
$203$	−4.20387e12	−0.855897
$204$	−8.57500e11	−0.169929
$205$	−6.10330e12	−1.17739
$206$	1.86461e11	0.0350201
$207$	−2.48955e11	−0.0455286
$208$	0	0
$209$	6.13333e12	1.06388
$210$	6.85796e11	0.115875
$211$	8.00209e11	0.131719	0.0658597	−	0.997829i	$-0.479021\pi$
$211$	8.00209e11	0.131719	0.0658597	+	0.997829i	$0.479021\pi$
$212$	1.18627e13	1.90255
$213$	−1.56589e12	−0.244723
$214$	6.26914e11	0.0954843
$215$	9.93684e12	1.47515
$216$	7.50809e11	0.108651
$217$	−1.17750e13	−1.66124
$218$	−9.29552e10	−0.0127868
$219$	4.06971e12	0.545910
$220$	1.50097e13	1.96357
$221$	0	0
$222$	−9.01622e11	−0.112223
$223$	1.48493e13	1.80314	0.901571	−	0.432631i	$-0.142415\pi$
$223$	1.48493e13	1.80314	0.901571	+	0.432631i	$0.142415\pi$
$224$	1.90491e12	0.225689
$225$	2.28100e12	0.263707
$226$	−5.56985e11	−0.0628416
$227$	−1.57088e13	−1.72982	−0.864910	−	0.501928i	$-0.832624\pi$
$227$	−1.57088e13	−1.72982	−0.864910	+	0.501928i	$0.832624\pi$
$228$	7.62001e12	0.819057
$229$	−2.72068e12	−0.285485	−0.142742	−	0.989760i	$-0.545592\pi$
$229$	−2.72068e12	−0.285485	−0.142742	+	0.989760i	$0.545592\pi$
$230$	−1.13729e11	−0.0116511
$231$	−1.80510e13	−1.80566
$232$	1.29176e12	0.126182
$233$	8.42380e12	0.803620	0.401810	−	0.915723i	$-0.368381\pi$
$233$	8.42380e12	0.803620	0.401810	+	0.915723i	$0.368381\pi$
$234$	0	0
$235$	1.63379e13	1.48704
$236$	−9.67037e12	−0.859859
$237$	−1.85698e12	−0.161321
$238$	1.29865e11	0.0110235
$239$	2.27825e13	1.88979	0.944895	−	0.327374i	$-0.106164\pi$
$239$	2.27825e13	1.88979	0.944895	+	0.327374i	$0.106164\pi$
$240$	1.85422e13	1.50314
$241$	−6.32011e12	−0.500761	−0.250381	−	0.968147i	$-0.580556\pi$
$241$	−6.32011e12	−0.500761	−0.250381	+	0.968147i	$0.580556\pi$
$242$	1.25952e12	0.0975483
$243$	−9.56452e12	−0.724150
$244$	−1.32475e13	−0.980595
$245$	4.55896e11	0.0329953
$246$	−1.12454e12	−0.0795852
$247$	0	0
$248$	3.61821e12	0.244912
$249$	−3.26452e12	−0.216134
$250$	−4.61784e11	−0.0299067
$251$	−5.09290e12	−0.322671	−0.161335	−	0.986900i	$-0.551580\pi$
$251$	−5.09290e12	−0.322671	−0.161335	+	0.986900i	$0.551580\pi$
$252$	−6.18214e12	−0.383209
$253$	2.99349e12	0.181558
$254$	−1.85877e12	−0.110316
$255$	3.82823e12	0.222345
$256$	1.66148e13	0.944442
$257$	2.23129e13	1.24144	0.620718	−	0.784034i	$-0.286841\pi$
$257$	2.23129e13	1.24144	0.620718	+	0.784034i	$0.286841\pi$
$258$	1.83087e12	0.0997126
$259$	−2.42347e13	−1.29208
$260$	0	0
$261$	−6.29425e12	−0.321678
$262$	1.09326e12	0.0547099
$263$	1.02420e12	0.0501911	0.0250956	−	0.999685i	$-0.492011\pi$
$263$	1.02420e12	0.0501911	0.0250956	+	0.999685i	$0.492011\pi$
$264$	5.54668e12	0.266202
$265$	−5.29599e13	−2.48940
$266$	−1.15402e12	−0.0531331
$267$	−2.81103e13	−1.26781
$268$	−1.65354e13	−0.730588
$269$	−3.39292e13	−1.46871	−0.734355	−	0.678766i	$-0.762515\pi$
$269$	−3.39292e13	−1.46871	−0.734355	+	0.678766i	$0.762515\pi$
$270$	−1.67125e12	−0.0708828
$271$	−4.37089e13	−1.81651	−0.908257	−	0.418414i	$-0.862586\pi$
$271$	−4.37089e13	−1.81651	−0.908257	+	0.418414i	$0.862586\pi$
$272$	3.51123e12	0.142998
$273$	0	0
$274$	−6.60178e11	−0.0258246
$275$	−2.74272e13	−1.05160
$276$	3.71909e12	0.139777
$277$	−1.69270e13	−0.623651	−0.311826	−	0.950139i	$-0.600940\pi$
$277$	−1.69270e13	−0.623651	−0.311826	+	0.950139i	$0.600940\pi$
$278$	−2.25180e12	−0.0813361
$279$	−1.76302e13	−0.624357
$280$	−5.66422e12	−0.196685
$281$	4.31608e13	1.46962	0.734809	−	0.678274i	$-0.237272\pi$
$281$	4.31608e13	1.46962	0.734809	+	0.678274i	$0.237272\pi$
$282$	3.01028e12	0.100516
$283$	4.77458e13	1.56354	0.781772	−	0.623565i	$-0.214316\pi$
$283$	4.77458e13	1.56354	0.781772	+	0.623565i	$0.214316\pi$
$284$	6.44846e12	0.207112
$285$	−3.40188e13	−1.07170
$286$	0	0
$287$	−3.02265e13	−0.916301
$288$	2.85212e12	0.0848222
$289$	−3.35470e13	−0.978848
$290$	−2.87537e12	−0.0823198
$291$	8.01173e13	2.25069
$292$	−1.67593e13	−0.462010
$293$	1.64453e13	0.444908	0.222454	−	0.974943i	$-0.428593\pi$
$293$	1.64453e13	0.444908	0.222454	+	0.974943i	$0.428593\pi$
$294$	8.39994e10	0.00223031
$295$	4.31725e13	1.12509
$296$	7.44680e12	0.190487
$297$	4.39894e13	1.10456
$298$	1.45502e12	0.0358658
$299$	0	0
$300$	−3.40754e13	−0.809607
$301$	4.92121e13	1.14804
$302$	−4.08860e12	−0.0936561
$303$	−6.49232e13	−1.46038
$304$	−3.12019e13	−0.689250
$305$	5.91422e13	1.28306
$306$	1.94441e11	0.00414304
$307$	−5.79282e12	−0.121235	−0.0606176	−	0.998161i	$-0.519307\pi$
$307$	−5.79282e12	−0.121235	−0.0606176	+	0.998161i	$0.519307\pi$
$308$	7.43352e13	1.52815
$309$	2.72217e13	0.549724
$310$	−8.05389e12	−0.159778
$311$	−6.88588e13	−1.34208	−0.671039	−	0.741422i	$-0.734152\pi$
$311$	−6.88588e13	−1.34208	−0.671039	+	0.741422i	$0.734152\pi$
$312$	0	0
$313$	−2.94167e13	−0.553477	−0.276738	−	0.960945i	$-0.589254\pi$
$313$	−2.94167e13	−0.553477	−0.276738	+	0.960945i	$0.589254\pi$
$314$	−3.25698e11	−0.00602146
$315$	2.75996e13	0.501411
$316$	7.64715e12	0.136528
$317$	2.48320e13	0.435698	0.217849	−	0.975983i	$-0.430096\pi$
$317$	2.48320e13	0.435698	0.217849	+	0.975983i	$0.430096\pi$
$318$	−9.75793e12	−0.168271
$319$	7.56832e13	1.28278
$320$	−7.54855e13	−1.25759
$321$	9.15244e13	1.49885
$322$	−5.63241e11	−0.00906749
$323$	−6.44195e12	−0.101954
$324$	7.89739e13	1.22881
$325$	0	0
$326$	5.10231e12	0.0767486
$327$	−1.35707e13	−0.200720
$328$	9.28796e12	0.135087
$329$	8.09132e13	1.15729
$330$	−1.23465e13	−0.173667
$331$	−3.37169e13	−0.466438	−0.233219	−	0.972424i	$-0.574926\pi$
$331$	−3.37169e13	−0.466438	−0.233219	+	0.972424i	$0.574926\pi$
$332$	1.34435e13	0.182916
$333$	−3.62854e13	−0.485611
$334$	−3.50509e12	−0.0461418
$335$	7.38206e13	0.955941
$336$	9.18302e13	1.16982
$337$	8.98229e13	1.12570	0.562850	−	0.826559i	$-0.309705\pi$
$337$	8.98229e13	1.12570	0.562850	+	0.826559i	$0.309705\pi$
$338$	0	0
$339$	−8.13154e13	−0.986449
$340$	−1.57649e13	−0.188173
$341$	2.11988e14	2.48979
$342$	−1.72786e12	−0.0199694
$343$	−8.67761e13	−0.986922
$344$	−1.51218e13	−0.169251
$345$	−1.66035e13	−0.182892
$346$	3.76894e11	0.00408602
$347$	8.75394e13	0.934096	0.467048	−	0.884232i	$-0.345318\pi$
$347$	8.75394e13	0.934096	0.467048	+	0.884232i	$0.345318\pi$
$348$	9.40284e13	0.987582
$349$	−3.87065e13	−0.400169	−0.200085	−	0.979779i	$-0.564122\pi$
$349$	−3.87065e13	−0.400169	−0.200085	+	0.979779i	$0.564122\pi$
$350$	5.16059e12	0.0525201
$351$	0	0
$352$	−3.42945e13	−0.338251
$353$	3.24210e13	0.314822	0.157411	−	0.987533i	$-0.449685\pi$
$353$	3.24210e13	0.314822	0.157411	+	0.987533i	$0.449685\pi$
$354$	7.95458e12	0.0760500
$355$	−2.87885e13	−0.270996
$356$	1.15760e14	1.07296
$357$	1.89593e13	0.173040
$358$	−6.98719e12	−0.0627980
$359$	1.45534e14	1.28809	0.644043	−	0.764990i	$-0.277256\pi$
$359$	1.45534e14	1.28809	0.644043	+	0.764990i	$0.277256\pi$
$360$	−8.48075e12	−0.0739214
$361$	−5.92451e13	−0.508584
$362$	−1.17449e13	−0.0993011
$363$	1.83879e14	1.53125
$364$	0	0
$365$	7.48205e13	0.604518
$366$	1.08970e13	0.0867285
$367$	6.95668e13	0.545430	0.272715	−	0.962095i	$-0.412078\pi$
$367$	6.95668e13	0.545430	0.272715	+	0.962095i	$0.412078\pi$
$368$	−1.52287e13	−0.117625
$369$	−4.52567e13	−0.344380
$370$	−1.65761e13	−0.124272
$371$	−2.62284e14	−1.93738
$372$	2.63373e14	1.91684
$373$	1.20982e14	0.867604	0.433802	−	0.901008i	$-0.357172\pi$
$373$	1.20982e14	0.867604	0.433802	+	0.901008i	$0.357172\pi$
$374$	−2.33799e12	−0.0165215
$375$	−6.74168e13	−0.469457
$376$	−2.48629e13	−0.170615
$377$	0	0
$378$	−8.27685e12	−0.0551646
$379$	−3.22918e13	−0.212117	−0.106059	−	0.994360i	$-0.533823\pi$
$379$	−3.22918e13	−0.212117	−0.106059	+	0.994360i	$0.533823\pi$
$380$	1.40092e14	0.906991
$381$	−2.71365e14	−1.73168
$382$	−1.57030e13	−0.0987719
$383$	−6.60313e13	−0.409408	−0.204704	−	0.978824i	$-0.565623\pi$
$383$	−6.60313e13	−0.409408	−0.204704	+	0.978824i	$0.565623\pi$
$384$	−5.67556e13	−0.346886
$385$	−3.31862e14	−1.99951
$386$	3.85428e12	0.0228936
$387$	7.36828e13	0.431475
$388$	−3.29929e14	−1.90478
$389$	−1.13990e14	−0.648851	−0.324426	−	0.945911i	$-0.605171\pi$
$389$	−1.13990e14	−0.648851	−0.324426	+	0.945911i	$0.605171\pi$
$390$	0	0
$391$	−3.14411e12	−0.0173991
$392$	−6.93779e11	−0.00378572
$393$	1.59607e14	0.858803
$394$	−7.86887e12	−0.0417525
$395$	−3.41400e13	−0.178640
$396$	1.11298e14	0.574335
$397$	2.68777e14	1.36787	0.683935	−	0.729543i	$-0.260267\pi$
$397$	2.68777e14	1.36787	0.683935	+	0.729543i	$0.260267\pi$
$398$	−9.97097e11	−0.00500473
$399$	−1.68478e14	−0.834050
$400$	1.39530e14	0.681297
$401$	3.43265e14	1.65324	0.826619	−	0.562762i	$-0.190261\pi$
$401$	3.43265e14	1.65324	0.826619	+	0.562762i	$0.190261\pi$
$402$	1.36015e13	0.0646167
$403$	0	0
$404$	2.67358e14	1.23594
$405$	−3.52572e14	−1.60785
$406$	−1.42402e13	−0.0640655
$407$	4.36303e14	1.93650
$408$	−5.82577e12	−0.0255107
$409$	2.66850e14	1.15289	0.576446	−	0.817135i	$-0.304439\pi$
$409$	2.66850e14	1.15289	0.576446	+	0.817135i	$0.304439\pi$
$410$	−2.06744e13	−0.0881294
$411$	−9.63807e13	−0.405378
$412$	−1.12101e14	−0.465237
$413$	2.13811e14	0.875599
$414$	−8.43313e11	−0.00340790
$415$	−6.00172e13	−0.239338
$416$	0	0
$417$	−3.28745e14	−1.27676
$418$	2.07761e13	0.0796333
$419$	−2.13925e14	−0.809253	−0.404626	−	0.914482i	$-0.632598\pi$
$419$	−2.13925e14	−0.809253	−0.404626	+	0.914482i	$0.632598\pi$
$420$	−4.12304e14	−1.53938
$421$	1.24393e14	0.458398	0.229199	−	0.973380i	$-0.426389\pi$
$421$	1.24393e14	0.458398	0.229199	+	0.973380i	$0.426389\pi$
$422$	2.71063e12	0.00985944
$423$	1.21147e14	0.434953
$424$	8.05940e13	0.285621
$425$	2.88073e13	0.100777
$426$	−5.30432e12	−0.0183180
$427$	2.92901e14	0.998545
$428$	−3.76903e14	−1.26850
$429$	0	0
$430$	3.36601e13	0.110418
$431$	3.23913e14	1.04907	0.524535	−	0.851389i	$-0.324239\pi$
$431$	3.23913e14	1.04907	0.524535	+	0.851389i	$0.324239\pi$
$432$	−2.23786e14	−0.715603
$433$	2.35022e13	0.0742036	0.0371018	−	0.999311i	$-0.488187\pi$
$433$	2.35022e13	0.0742036	0.0371018	+	0.999311i	$0.488187\pi$
$434$	−3.98868e13	−0.124347
$435$	−4.19781e14	−1.29221
$436$	5.58851e13	0.169871
$437$	2.79395e13	0.0838632
$438$	1.37858e13	0.0408623
$439$	−4.02014e14	−1.17676	−0.588379	−	0.808586i	$-0.700233\pi$
$439$	−4.02014e14	−1.17676	−0.588379	+	0.808586i	$0.700233\pi$
$440$	1.01974e14	0.294781
$441$	3.38052e12	0.00965098
$442$	0	0
$443$	−3.08170e14	−0.858164	−0.429082	−	0.903265i	$-0.641163\pi$
$443$	−3.08170e14	−0.858164	−0.429082	+	0.903265i	$0.641163\pi$
$444$	5.42059e14	1.49087
$445$	−5.16800e14	−1.40392
$446$	5.03007e13	0.134969
$447$	2.12422e14	0.562999
$448$	−3.73841e14	−0.978719
$449$	1.99777e14	0.516643	0.258322	−	0.966059i	$-0.416831\pi$
$449$	1.99777e14	0.516643	0.258322	+	0.966059i	$0.416831\pi$
$450$	7.72669e12	0.0197390
$451$	5.44175e14	1.37331
$452$	3.34862e14	0.834843
$453$	−5.96902e14	−1.47016
$454$	−5.32121e13	−0.129480
$455$	0	0
$456$	5.17696e13	0.122961
$457$	−4.57271e13	−0.107309	−0.0536543	−	0.998560i	$-0.517087\pi$
$457$	−4.57271e13	−0.107309	−0.0536543	+	0.998560i	$0.517087\pi$
$458$	−9.21606e12	−0.0213690
$459$	−4.62028e13	−0.105852
$460$	6.83744e13	0.154784
$461$	3.40488e14	0.761635	0.380817	−	0.924650i	$-0.375643\pi$
$461$	3.40488e14	0.761635	0.380817	+	0.924650i	$0.375643\pi$
$462$	−6.11461e13	−0.135157
$463$	−3.63954e14	−0.794971	−0.397486	−	0.917608i	$-0.630117\pi$
$463$	−3.63954e14	−0.794971	−0.397486	+	0.917608i	$0.630117\pi$
$464$	−3.85021e14	−0.831066
$465$	−1.17580e15	−2.50809
$466$	2.85349e13	0.0601524
$467$	1.10274e14	0.229738	0.114869	−	0.993381i	$-0.463355\pi$
$467$	1.10274e14	0.229738	0.114869	+	0.993381i	$0.463355\pi$
$468$	0	0
$469$	3.65596e14	0.743962
$470$	5.53431e13	0.111308
$471$	−4.75493e13	−0.0945211
$472$	−6.56995e13	−0.129087
$473$	−8.85976e14	−1.72062
$474$	−6.29034e12	−0.0120752
$475$	−2.55991e14	−0.485746
$476$	−7.80755e13	−0.146446
$477$	−3.92704e14	−0.728139
$478$	7.71737e13	0.141454
$479$	1.66407e14	0.301526	0.150763	−	0.988570i	$-0.451827\pi$
$479$	1.66407e14	0.301526	0.150763	+	0.988570i	$0.451827\pi$
$480$	1.90216e14	0.340738
$481$	0	0
$482$	−2.14088e13	−0.0374829
$483$	−8.22287e13	−0.142336
$484$	−7.57228e14	−1.29592
$485$	1.47293e15	2.49232
$486$	−3.23989e13	−0.0542040
$487$	4.21283e13	0.0696891	0.0348446	−	0.999393i	$-0.488906\pi$
$487$	4.21283e13	0.0696891	0.0348446	+	0.999393i	$0.488906\pi$
$488$	−9.00021e13	−0.147212
$489$	7.44897e14	1.20475
$490$	1.54431e12	0.00246976
$491$	−3.56448e13	−0.0563700	−0.0281850	−	0.999603i	$-0.508973\pi$
$491$	−3.56448e13	−0.0563700	−0.0281850	+	0.999603i	$0.508973\pi$
$492$	6.76079e14	1.05728
$493$	−7.94914e13	−0.122931
$494$	0	0
$495$	−4.96881e14	−0.751491
$496$	−1.07844e15	−1.61305
$497$	−1.42575e14	−0.210903
$498$	−1.10582e13	−0.0161780
$499$	2.70054e14	0.390748	0.195374	−	0.980729i	$-0.437408\pi$
$499$	2.70054e14	0.390748	0.195374	+	0.980729i	$0.437408\pi$
$500$	2.77627e14	0.397307
$501$	−5.11716e14	−0.724305
$502$	−1.72517e13	−0.0241525
$503$	−4.93264e14	−0.683054	−0.341527	−	0.939872i	$-0.610944\pi$
$503$	−4.93264e14	−0.683054	−0.341527	+	0.939872i	$0.610944\pi$
$504$	−4.20008e13	−0.0575294
$505$	−1.19360e15	−1.61717
$506$	1.01402e13	0.0135899
$507$	0	0
$508$	1.11750e15	1.46554
$509$	−7.49682e14	−0.972589	−0.486294	−	0.873795i	$-0.661652\pi$
$509$	−7.49682e14	−0.972589	−0.486294	+	0.873795i	$0.661652\pi$
$510$	1.29678e13	0.0166429
$511$	3.70548e14	0.470467
$512$	2.91321e14	0.365921
$513$	4.10573e14	0.510205
$514$	7.55830e13	0.0929238
$515$	5.00464e14	0.608742
$516$	−1.10073e15	−1.32467
$517$	−1.45670e15	−1.73449
$518$	−8.20928e13	−0.0967145
$519$	5.50235e13	0.0641398
$520$	0	0
$521$	1.28499e15	1.46654	0.733270	−	0.679938i	$-0.237993\pi$
$521$	1.28499e15	1.46654	0.733270	+	0.679938i	$0.237993\pi$
$522$	−2.13212e13	−0.0240782
$523$	1.71007e14	0.191097	0.0955486	−	0.995425i	$-0.469539\pi$
$523$	1.71007e14	0.191097	0.0955486	+	0.995425i	$0.469539\pi$
$524$	−6.57273e14	−0.726815
$525$	7.53405e14	0.824427
$526$	3.46937e12	0.00375690
$527$	−2.22655e14	−0.238602
$528$	−1.65324e15	−1.75327
$529$	−9.39173e14	−0.985688
$530$	−1.79397e14	−0.186336
$531$	3.20129e14	0.329083
$532$	6.93803e14	0.705866
$533$	0	0
$534$	−9.52211e13	−0.0948978
$535$	1.68265e15	1.65977
$536$	−1.12340e14	−0.109680
$537$	−1.02007e15	−0.985764
$538$	−1.14932e14	−0.109936
$539$	−4.06480e13	−0.0384859
$540$	1.00476e15	0.941669
$541$	1.59371e15	1.47851	0.739256	−	0.673424i	$-0.235177\pi$
$541$	1.59371e15	1.47851	0.739256	+	0.673424i	$0.235177\pi$
$542$	−1.48060e14	−0.135969
$543$	−1.71467e15	−1.55877
$544$	3.60201e13	0.0324153
$545$	−2.49494e14	−0.222269
$546$	0	0
$547$	1.12365e15	0.981073	0.490537	−	0.871421i	$-0.336801\pi$
$547$	1.12365e15	0.981073	0.490537	+	0.871421i	$0.336801\pi$
$548$	3.96902e14	0.343076
$549$	4.38546e14	0.375290
$550$	−9.29072e13	−0.0787145
$551$	7.06386e14	0.592527
$552$	2.52671e13	0.0209841
$553$	−1.69078e14	−0.139027
$554$	−5.73387e13	−0.0466814
$555$	−2.41997e15	−1.95074
$556$	1.35379e15	1.08054
$557$	−5.45822e14	−0.431368	−0.215684	−	0.976463i	$-0.569198\pi$
$557$	−5.45822e14	−0.431368	−0.215684	+	0.976463i	$0.569198\pi$
$558$	−5.97205e13	−0.0467343
$559$	0	0
$560$	1.68827e15	1.29541
$561$	−3.41328e14	−0.259344
$562$	1.46203e14	0.110004
$563$	1.07491e15	0.800897	0.400448	−	0.916319i	$-0.368854\pi$
$563$	1.07491e15	0.800897	0.400448	+	0.916319i	$0.368854\pi$
$564$	−1.80979e15	−1.33535
$565$	−1.49496e15	−1.09235
$566$	1.61735e14	0.117034
$567$	−1.74611e15	−1.25131
$568$	4.38102e13	0.0310928
$569$	3.71485e14	0.261110	0.130555	−	0.991441i	$-0.458324\pi$
$569$	3.71485e14	0.261110	0.130555	+	0.991441i	$0.458324\pi$
$570$	−1.15236e14	−0.0802186
$571$	−5.89713e14	−0.406576	−0.203288	−	0.979119i	$-0.565163\pi$
$571$	−5.89713e14	−0.406576	−0.203288	+	0.979119i	$0.565163\pi$
$572$	0	0
$573$	−2.29251e15	−1.55046
$574$	−1.02390e14	−0.0685868
$575$	−1.24941e14	−0.0828956
$576$	−5.59733e14	−0.367839
$577$	−4.47961e14	−0.291590	−0.145795	−	0.989315i	$-0.546574\pi$
$577$	−4.47961e14	−0.291590	−0.145795	+	0.989315i	$0.546574\pi$
$578$	−1.13637e14	−0.0732686
$579$	5.62695e14	0.359369
$580$	1.72869e15	1.09361
$581$	−2.97235e14	−0.186265
$582$	2.71390e14	0.168468
$583$	4.72195e15	2.90365
$584$	−1.13861e14	−0.0693594
$585$	0	0
$586$	5.57070e13	0.0333022
$587$	2.90281e14	0.171913	0.0859567	−	0.996299i	$-0.472605\pi$
$587$	2.90281e14	0.171913	0.0859567	+	0.996299i	$0.472605\pi$
$588$	−5.05009e13	−0.0296294
$589$	1.97858e15	1.15006
$590$	1.46243e14	0.0842148
$591$	−1.14879e15	−0.655406
$592$	−2.21959e15	−1.25459
$593$	−1.53135e15	−0.857581	−0.428790	−	0.903404i	$-0.641060\pi$
$593$	−1.53135e15	−0.857581	−0.428790	+	0.903404i	$0.641060\pi$
$594$	1.49010e14	0.0826780
$595$	3.48561e14	0.191618
$596$	−8.74767e14	−0.476472
$597$	−1.45568e14	−0.0785611
$598$	0	0
$599$	−2.34047e14	−0.124009	−0.0620047	−	0.998076i	$-0.519749\pi$
$599$	−2.34047e14	−0.124009	−0.0620047	+	0.998076i	$0.519749\pi$
$600$	−2.31505e14	−0.121543
$601$	−2.19750e15	−1.14319	−0.571597	−	0.820535i	$-0.693676\pi$
$601$	−2.19750e15	−1.14319	−0.571597	+	0.820535i	$0.693676\pi$
$602$	1.66701e14	0.0859327
$603$	5.47388e14	0.279608
$604$	2.45808e15	1.24421
$605$	3.38057e15	1.69565
$606$	−2.19921e14	−0.109312
$607$	3.02645e15	1.49072	0.745360	−	0.666662i	$-0.232277\pi$
$607$	3.02645e15	1.49072	0.745360	+	0.666662i	$0.232277\pi$
$608$	−3.20086e14	−0.156241
$609$	−2.07896e15	−1.00566
$610$	2.00339e14	0.0960397
$611$	0	0
$612$	−1.16899e14	−0.0550397
$613$	1.31524e15	0.613724	0.306862	−	0.951754i	$-0.400721\pi$
$613$	1.31524e15	0.613724	0.306862	+	0.951754i	$0.400721\pi$
$614$	−1.96226e13	−0.00907468
$615$	−3.01829e15	−1.38340
$616$	5.05026e14	0.229414
$617$	7.90565e14	0.355934	0.177967	−	0.984036i	$-0.443048\pi$
$617$	7.90565e14	0.355934	0.177967	+	0.984036i	$0.443048\pi$
$618$	9.22111e13	0.0411478
$619$	−5.75601e13	−0.0254579	−0.0127290	−	0.999919i	$-0.504052\pi$
$619$	−5.75601e13	−0.0254579	−0.0127290	+	0.999919i	$0.504052\pi$
$620$	4.84204e15	2.12263
$621$	2.00387e14	0.0870696
$622$	−2.33253e14	−0.100457
$623$	−2.55945e15	−1.09260
$624$	0	0
$625$	−2.89150e15	−1.21278
$626$	−9.96462e13	−0.0414288
$627$	3.03315e15	1.25003
$628$	1.95811e14	0.0799943
$629$	−4.58256e14	−0.185579
$630$	9.34910e13	0.0375316
$631$	−3.34887e15	−1.33271	−0.666356	−	0.745633i	$-0.732147\pi$
$631$	−3.34887e15	−1.33271	−0.666356	+	0.745633i	$0.732147\pi$
$632$	5.19540e13	0.0204963
$633$	3.95731e14	0.154767
$634$	8.41160e13	0.0326128
$635$	−4.98897e15	−1.91759
$636$	5.86652e15	2.23546
$637$	0	0
$638$	2.56370e14	0.0960182
$639$	−2.13470e14	−0.0792652
$640$	−1.04344e15	−0.384128
$641$	5.29783e14	0.193365	0.0966827	−	0.995315i	$-0.469177\pi$
$641$	5.29783e14	0.193365	0.0966827	+	0.995315i	$0.469177\pi$
$642$	3.10030e14	0.112192
$643$	−1.01506e15	−0.364194	−0.182097	−	0.983281i	$-0.558288\pi$
$643$	−1.01506e15	−0.364194	−0.182097	+	0.983281i	$0.558288\pi$
$644$	3.38623e14	0.120460
$645$	4.91411e15	1.73327
$646$	−2.18215e13	−0.00763143
$647$	−1.92293e14	−0.0666793	−0.0333396	−	0.999444i	$-0.510614\pi$
$647$	−1.92293e14	−0.0666793	−0.0333396	+	0.999444i	$0.510614\pi$
$648$	5.36541e14	0.184476
$649$	−3.84929e15	−1.31231
$650$	0	0
$651$	−5.82316e15	−1.95192
$652$	−3.06753e15	−1.01959
$653$	−2.34263e15	−0.772114	−0.386057	−	0.922475i	$-0.626163\pi$
$653$	−2.34263e15	−0.772114	−0.386057	+	0.922475i	$0.626163\pi$
$654$	−4.59695e13	−0.0150242
$655$	2.93433e15	0.951004
$656$	−2.76836e15	−0.889717
$657$	5.54802e14	0.176819
$658$	2.74086e14	0.0866253
$659$	5.91488e15	1.85386	0.926928	−	0.375239i	$-0.122440\pi$
$659$	5.91488e15	1.85386	0.926928	+	0.375239i	$0.122440\pi$
$660$	7.42279e15	2.30715
$661$	4.81720e15	1.48486	0.742432	−	0.669922i	$-0.233672\pi$
$661$	4.81720e15	1.48486	0.742432	+	0.669922i	$0.233672\pi$
$662$	−1.14213e14	−0.0349138
$663$	0	0
$664$	9.13337e13	0.0274604
$665$	−3.09742e15	−0.923594
$666$	−1.22913e14	−0.0363489
$667$	3.44764e14	0.101118
$668$	2.10728e15	0.612988
$669$	7.34350e15	2.11865
$670$	2.50060e14	0.0715540
$671$	−5.27316e15	−1.49657
$672$	9.42042e14	0.265179
$673$	1.84391e15	0.514821	0.257410	−	0.966302i	$-0.417131\pi$
$673$	1.84391e15	0.514821	0.257410	+	0.966302i	$0.417131\pi$
$674$	3.04267e14	0.0842607
$675$	−1.83601e15	−0.504318
$676$	0	0
$677$	−2.85026e15	−0.770276	−0.385138	−	0.922859i	$-0.625846\pi$
$677$	−2.85026e15	−0.770276	−0.385138	+	0.922859i	$0.625846\pi$
$678$	−2.75448e14	−0.0738375
$679$	7.29470e15	1.93965
$680$	−1.07105e14	−0.0282495
$681$	−7.76854e15	−2.03250
$682$	7.18091e14	0.186365
$683$	−4.69918e15	−1.20978	−0.604892	−	0.796308i	$-0.706784\pi$
$683$	−4.69918e15	−1.20978	−0.604892	+	0.796308i	$0.706784\pi$
$684$	1.03880e15	0.265291
$685$	−1.77193e15	−0.448899
$686$	−2.93946e14	−0.0738729
$687$	−1.34547e15	−0.335438
$688$	4.50720e15	1.11473
$689$	0	0
$690$	−5.62429e13	−0.0136898
$691$	−2.34559e15	−0.566399	−0.283199	−	0.959061i	$-0.591396\pi$
$691$	−2.34559e15	−0.566399	−0.283199	+	0.959061i	$0.591396\pi$
$692$	−2.26590e14	−0.0542823
$693$	−2.46080e15	−0.584848
$694$	2.96532e14	0.0699188
$695$	−6.04388e15	−1.41384
$696$	6.38819e14	0.148261
$697$	−5.71556e14	−0.131607
$698$	−1.31115e14	−0.0299534
$699$	4.16586e15	0.944236
$700$	−3.10257e15	−0.697722
$701$	−2.09935e15	−0.468421	−0.234210	−	0.972186i	$-0.575250\pi$
$701$	−2.09935e15	−0.468421	−0.234210	+	0.972186i	$0.575250\pi$
$702$	0	0
$703$	4.07221e15	0.894490
$704$	6.73034e15	1.46686
$705$	8.07965e15	1.74724
$706$	1.09823e14	0.0235650
$707$	−5.91127e15	−1.25856
$708$	−4.78233e15	−1.01031
$709$	6.10587e15	1.27995	0.639975	−	0.768396i	$-0.278945\pi$
$709$	6.10587e15	1.27995	0.639975	+	0.768396i	$0.278945\pi$
$710$	−9.75185e13	−0.0202846
$711$	−2.53152e14	−0.0522515
$712$	7.86463e14	0.161079
$713$	9.65683e14	0.196265
$714$	6.42228e13	0.0129524
$715$	0	0
$716$	4.20073e15	0.834263
$717$	1.12667e16	2.22046
$718$	4.92983e14	0.0964156
$719$	−5.91981e15	−1.14894	−0.574472	−	0.818524i	$-0.694793\pi$
$719$	−5.91981e15	−1.14894	−0.574472	+	0.818524i	$0.694793\pi$
$720$	2.52777e15	0.486865
$721$	2.47854e15	0.473754
$722$	−2.00687e14	−0.0380685
$723$	−3.12551e15	−0.588384
$724$	7.06112e15	1.31920
$725$	−3.15884e15	−0.585690
$726$	6.22875e14	0.114617
$727$	−2.61053e15	−0.476748	−0.238374	−	0.971173i	$-0.576614\pi$
$727$	−2.61053e15	−0.476748	−0.238374	+	0.971173i	$0.576614\pi$
$728$	0	0
$729$	2.13955e15	0.384876
$730$	2.53447e14	0.0452493
$731$	9.30556e14	0.164891
$732$	−6.55134e15	−1.15218
$733$	9.10402e15	1.58914	0.794568	−	0.607175i	$-0.207697\pi$
$733$	9.10402e15	1.58914	0.794568	+	0.607175i	$0.207697\pi$
$734$	2.35651e14	0.0408264
$735$	2.25456e14	0.0387688
$736$	−1.56224e14	−0.0266636
$737$	−6.58190e15	−1.11501
$738$	−1.53303e14	−0.0257775
$739$	2.00804e15	0.335141	0.167570	−	0.985860i	$-0.446408\pi$
$739$	2.00804e15	0.335141	0.167570	+	0.985860i	$0.446408\pi$
$740$	9.96561e15	1.65093
$741$	0	0
$742$	−8.88461e14	−0.145016
$743$	−8.48953e15	−1.37545	−0.687725	−	0.725971i	$-0.741391\pi$
$743$	−8.48953e15	−1.37545	−0.687725	+	0.725971i	$0.741391\pi$
$744$	1.78933e15	0.287766
$745$	3.90531e15	0.623442
$746$	4.09815e14	0.0649417
$747$	−4.45035e14	−0.0700052
$748$	1.40561e15	0.219486
$749$	8.33331e15	1.29172
$750$	−2.28368e14	−0.0351397
$751$	5.75001e15	0.878312	0.439156	−	0.898411i	$-0.355278\pi$
$751$	5.75001e15	0.878312	0.439156	+	0.898411i	$0.355278\pi$
$752$	7.41062e15	1.12372
$753$	−2.51861e15	−0.379131
$754$	0	0
$755$	−1.09739e16	−1.62799
$756$	4.97608e15	0.732855
$757$	4.57782e15	0.669317	0.334658	−	0.942339i	$-0.391379\pi$
$757$	4.57782e15	0.669317	0.334658	+	0.942339i	$0.391379\pi$
$758$	−1.09385e14	−0.0158774
$759$	1.48038e15	0.213326
$760$	9.51770e14	0.136162
$761$	3.71156e15	0.527158	0.263579	−	0.964638i	$-0.415097\pi$
$761$	3.71156e15	0.527158	0.263579	+	0.964638i	$0.415097\pi$
$762$	−9.19224e14	−0.129619
$763$	−1.23562e15	−0.172981
$764$	9.44070e15	1.31217
$765$	5.21883e14	0.0720170
$766$	−2.23675e14	−0.0306450
$767$	0	0
$768$	8.21659e15	1.10970
$769$	−2.37640e15	−0.318658	−0.159329	−	0.987226i	$-0.550933\pi$
$769$	−2.37640e15	−0.318658	−0.159329	+	0.987226i	$0.550933\pi$
$770$	−1.12415e15	−0.149667
$771$	1.10345e16	1.45866
$772$	−2.31721e15	−0.304138
$773$	4.48843e15	0.584934	0.292467	−	0.956276i	$-0.405524\pi$
$773$	4.48843e15	0.584934	0.292467	+	0.956276i	$0.405524\pi$
$774$	2.49594e14	0.0322967
$775$	−8.84788e15	−1.13679
$776$	−2.24150e15	−0.285956
$777$	−1.19849e16	−1.51816
$778$	−3.86132e14	−0.0485677
$779$	5.07903e15	0.634344
$780$	0	0
$781$	2.56681e15	0.316091
$782$	−1.06504e13	−0.00130235
$783$	5.06633e15	0.615182
$784$	2.06788e14	0.0249337
$785$	−8.74180e14	−0.104669
$786$	5.40655e14	0.0642830
$787$	−1.79432e15	−0.211856	−0.105928	−	0.994374i	$-0.533781\pi$
$787$	−1.79432e15	−0.211856	−0.105928	+	0.994374i	$0.533781\pi$
$788$	4.73080e15	0.554677
$789$	5.06501e14	0.0589735
$790$	−1.15646e14	−0.0133716
$791$	−7.40378e15	−0.850125
$792$	7.56150e14	0.0862223
$793$	0	0
$794$	9.10458e14	0.102388
$795$	−2.61905e16	−2.92499
$796$	5.99459e14	0.0664872
$797$	−1.29926e15	−0.143111	−0.0715556	−	0.997437i	$-0.522796\pi$
$797$	−1.29926e15	−0.143111	−0.0715556	+	0.997437i	$0.522796\pi$
$798$	−5.70704e14	−0.0624302
$799$	1.53000e15	0.166220
$800$	1.43137e15	0.154439
$801$	−3.83213e15	−0.410641
$802$	1.16278e15	0.123748
$803$	−6.67105e15	−0.705113
$804$	−8.17731e15	−0.858425
$805$	−1.51175e15	−0.157617
$806$	0	0
$807$	−1.67791e16	−1.72570
$808$	1.81641e15	0.185545
$809$	−1.71565e16	−1.74065	−0.870326	−	0.492476i	$-0.836092\pi$
$809$	−1.71565e16	−1.74065	−0.870326	+	0.492476i	$0.836092\pi$
$810$	−1.19430e15	−0.120350
$811$	−8.99602e15	−0.900401	−0.450200	−	0.892928i	$-0.648647\pi$
$811$	−8.99602e15	−0.900401	−0.450200	+	0.892928i	$0.648647\pi$
$812$	8.56130e15	0.851102
$813$	−2.16155e16	−2.13436
$814$	1.47793e15	0.144951
$815$	1.36947e16	1.33409
$816$	1.73643e15	0.168020
$817$	−8.26921e15	−0.794772
$818$	9.03929e14	0.0862961
$819$	0	0
$820$	1.24295e16	1.17079
$821$	1.60428e16	1.50104	0.750520	−	0.660848i	$-0.229803\pi$
$821$	1.60428e16	1.50104	0.750520	+	0.660848i	$0.229803\pi$
$822$	−3.26481e14	−0.0303433
$823$	5.49308e15	0.507128	0.253564	−	0.967319i	$-0.418397\pi$
$823$	5.49308e15	0.507128	0.253564	+	0.967319i	$0.418397\pi$
$824$	−7.61603e14	−0.0698440
$825$	−1.35637e16	−1.23561
$826$	7.24266e14	0.0655402
$827$	8.14813e15	0.732450	0.366225	−	0.930526i	$-0.380650\pi$
$827$	8.14813e15	0.732450	0.366225	+	0.930526i	$0.380650\pi$
$828$	5.07004e14	0.0452735
$829$	−1.98376e16	−1.75971	−0.879853	−	0.475246i	$-0.842359\pi$
$829$	−1.98376e16	−1.75971	−0.879853	+	0.475246i	$0.842359\pi$
$830$	−2.03303e14	−0.0179149
$831$	−8.37100e15	−0.732776
$832$	0	0
$833$	4.26934e13	0.00368819
$834$	−1.11359e15	−0.0955681
$835$	−9.40775e15	−0.802066
$836$	−1.24907e16	−1.05792
$837$	1.41907e16	1.19403
$838$	−7.24651e14	−0.0605741
$839$	−2.34908e15	−0.195077	−0.0975387	−	0.995232i	$-0.531097\pi$
$839$	−2.34908e15	−0.195077	−0.0975387	+	0.995232i	$0.531097\pi$
$840$	−2.80115e15	−0.231100
$841$	−3.48395e15	−0.285558
$842$	4.21368e14	0.0343119
$843$	2.13445e16	1.72677
$844$	−1.62965e15	−0.130981
$845$	0	0
$846$	4.10375e14	0.0325570
$847$	1.67423e16	1.31964
$848$	−2.40218e16	−1.88117
$849$	2.36120e16	1.83713
$850$	9.75821e13	0.00754338
$851$	1.98751e15	0.152650
$852$	3.18898e15	0.243352
$853$	1.56183e16	1.18417	0.592086	−	0.805875i	$-0.298305\pi$
$853$	1.56183e16	1.18417	0.592086	+	0.805875i	$0.298305\pi$
$854$	9.92175e14	0.0747429
$855$	−4.63761e15	−0.347121
$856$	−2.56064e15	−0.190434
$857$	−1.24481e16	−0.919834	−0.459917	−	0.887962i	$-0.652121\pi$
$857$	−1.24481e16	−0.919834	−0.459917	+	0.887962i	$0.652121\pi$
$858$	0	0
$859$	−1.17701e16	−0.858651	−0.429326	−	0.903150i	$-0.641249\pi$
$859$	−1.17701e16	−0.858651	−0.429326	+	0.903150i	$0.641249\pi$
$860$	−2.02366e16	−1.46689
$861$	−1.49481e16	−1.07663
$862$	1.09723e15	0.0785247
$863$	4.09282e15	0.291047	0.145524	−	0.989355i	$-0.453513\pi$
$863$	4.09282e15	0.291047	0.145524	+	0.989355i	$0.453513\pi$
$864$	−2.29571e15	−0.162215
$865$	1.01159e15	0.0710259
$866$	7.96115e13	0.00555428
$867$	−1.65901e16	−1.15012
$868$	2.39801e16	1.65194
$869$	3.04395e15	0.208367
$870$	−1.42197e15	−0.0967240
$871$	0	0
$872$	3.79678e14	0.0255020
$873$	1.09220e16	0.728993
$874$	9.46426e13	0.00627731
$875$	−6.13831e15	−0.404580
$876$	−8.28807e15	−0.542851
$877$	−1.66555e16	−1.08408	−0.542038	−	0.840354i	$-0.682347\pi$
$877$	−1.66555e16	−1.08408	−0.542038	+	0.840354i	$0.682347\pi$
$878$	−1.36179e15	−0.0880824
$879$	8.13278e15	0.522757
$880$	−3.03943e16	−1.94150
$881$	−2.33295e16	−1.48094	−0.740472	−	0.672087i	$-0.765398\pi$
$881$	−2.33295e16	−1.48094	−0.740472	+	0.672087i	$0.765398\pi$
$882$	1.14512e13	0.000722394 0
$883$	−5.66211e14	−0.0354972	−0.0177486	−	0.999842i	$-0.505650\pi$
$883$	−5.66211e14	−0.0354972	−0.0177486	+	0.999842i	$0.505650\pi$
$884$	0	0
$885$	2.13503e16	1.32195
$886$	−1.04390e15	−0.0642352
$887$	8.53270e15	0.521803	0.260901	−	0.965365i	$-0.415980\pi$
$887$	8.53270e15	0.521803	0.260901	+	0.965365i	$0.415980\pi$
$888$	3.68270e15	0.223818
$889$	−2.47078e16	−1.49236
$890$	−1.75061e15	−0.105086
$891$	3.14355e16	1.87540
$892$	−3.02410e16	−1.79304
$893$	−1.35960e16	−0.801177
$894$	7.19559e14	0.0421415
$895$	−1.87538e16	−1.09160
$896$	−5.16760e15	−0.298948
$897$	0	0
$898$	6.76726e14	0.0386717
$899$	2.44150e16	1.38669
$900$	−4.64532e15	−0.262230
$901$	−4.95954e15	−0.278263
$902$	1.84334e15	0.102795
$903$	2.43371e16	1.34892
$904$	2.27502e15	0.125331
$905$	−3.15237e16	−1.72612
$906$	−2.02195e15	−0.110044
$907$	−9.92538e15	−0.536917	−0.268458	−	0.963291i	$-0.586514\pi$
$907$	−9.92538e15	−0.536917	−0.268458	+	0.963291i	$0.586514\pi$
$908$	3.19914e16	1.72013
$909$	−8.85065e15	−0.473014
$910$	0	0
$911$	1.06854e16	0.564208	0.282104	−	0.959384i	$-0.408968\pi$
$911$	1.06854e16	0.564208	0.282104	+	0.959384i	$0.408968\pi$
$912$	−1.54304e16	−0.809853
$913$	5.35118e15	0.279165
$914$	−1.54896e14	−0.00803225
$915$	2.92478e16	1.50757
$916$	5.54074e15	0.283885
$917$	1.45323e16	0.740119
$918$	−1.56508e14	−0.00792321
$919$	−6.16827e15	−0.310405	−0.155202	−	0.987883i	$-0.549603\pi$
$919$	−6.16827e15	−0.310405	−0.155202	+	0.987883i	$0.549603\pi$
$920$	4.64529e14	0.0232370
$921$	−2.86475e15	−0.142449
$922$	1.15337e15	0.0570098
$923$	0	0
$924$	3.67613e16	1.79554
$925$	−1.82102e16	−0.884170
$926$	−1.23286e15	−0.0595051
$927$	3.71100e15	0.178054
$928$	−3.94975e15	−0.188389
$929$	1.71984e16	0.815460	0.407730	−	0.913103i	$-0.366320\pi$
$929$	1.71984e16	0.815460	0.407730	+	0.913103i	$0.366320\pi$
$930$	−3.98293e15	−0.187735
$931$	−3.79386e14	−0.0177770
$932$	−1.71553e16	−0.799117
$933$	−3.40531e16	−1.57691
$934$	3.73544e14	0.0171963
$935$	−6.27522e15	−0.287187
$936$	0	0
$937$	−1.38540e16	−0.626626	−0.313313	−	0.949650i	$-0.601439\pi$
$937$	−1.38540e16	−0.626626	−0.313313	+	0.949650i	$0.601439\pi$
$938$	1.23842e15	0.0556869
$939$	−1.45476e16	−0.650323
$940$	−3.32725e16	−1.47871
$941$	3.01742e16	1.33319	0.666597	−	0.745419i	$-0.267750\pi$
$941$	3.01742e16	1.33319	0.666597	+	0.745419i	$0.267750\pi$
$942$	−1.61069e14	−0.00707508
$943$	2.47891e15	0.108255
$944$	1.95824e16	0.850196
$945$	−2.22153e16	−0.958907
$946$	−3.00116e15	−0.128792
$947$	1.47817e16	0.630665	0.315333	−	0.948981i	$-0.397884\pi$
$947$	1.47817e16	0.630665	0.315333	+	0.948981i	$0.397884\pi$
$948$	3.78178e15	0.160417
$949$	0	0
$950$	−8.67145e14	−0.0363590
$951$	1.22803e16	0.511935
$952$	−5.30437e14	−0.0219852
$953$	2.28957e16	0.943501	0.471750	−	0.881732i	$-0.343622\pi$
$953$	2.28957e16	0.943501	0.471750	+	0.881732i	$0.343622\pi$
$954$	−1.33025e15	−0.0545025
$955$	−4.21471e16	−1.71692
$956$	−4.63972e16	−1.87920
$957$	3.74280e16	1.50723
$958$	5.63687e14	0.0225698
$959$	−8.77548e15	−0.349356
$960$	−3.73302e16	−1.47764
$961$	4.29779e16	1.69148
$962$	0	0
$963$	1.24770e16	0.485475
$964$	1.28711e16	0.497956
$965$	1.03450e16	0.397951
$966$	−2.78542e14	−0.0106541
$967$	−3.65782e16	−1.39116	−0.695580	−	0.718448i	$-0.744853\pi$
$967$	−3.65782e16	−1.39116	−0.695580	+	0.718448i	$0.744853\pi$
$968$	−5.14453e15	−0.194550
$969$	−3.18577e15	−0.119793
$970$	4.98943e15	0.186555
$971$	2.24568e16	0.834915	0.417458	−	0.908696i	$-0.362921\pi$
$971$	2.24568e16	0.834915	0.417458	+	0.908696i	$0.362921\pi$
$972$	1.94784e16	0.720093
$973$	−2.99323e16	−1.10032
$974$	1.42706e14	0.00521636
$975$	0	0
$976$	2.68260e16	0.969575
$977$	−2.77848e16	−0.998590	−0.499295	−	0.866432i	$-0.666408\pi$
$977$	−2.77848e16	−0.998590	−0.499295	+	0.866432i	$0.666408\pi$
$978$	2.52327e15	0.0901779
$979$	4.60783e16	1.63754
$980$	−9.28444e14	−0.0328105
$981$	−1.85003e15	−0.0650127
$982$	−1.20744e14	−0.00421940
$983$	6.91991e15	0.240467	0.120234	−	0.992746i	$-0.461636\pi$
$983$	6.91991e15	0.240467	0.120234	+	0.992746i	$0.461636\pi$
$984$	4.59322e15	0.158724
$985$	−2.11202e16	−0.725770
$986$	−2.69270e14	−0.00920163
$987$	4.00144e16	1.35979
$988$	0	0
$989$	−4.03594e15	−0.135633
$990$	−1.68314e15	−0.0562505
$991$	4.49174e16	1.49283	0.746414	−	0.665482i	$-0.231774\pi$
$991$	4.49174e16	1.49283	0.746414	+	0.665482i	$0.231774\pi$
$992$	−1.10632e16	−0.365651
$993$	−1.66742e16	−0.548054
$994$	−4.82959e14	−0.0157865
$995$	−2.67623e15	−0.0869954
$996$	6.64827e15	0.214923
$997$	−4.98182e16	−1.60164	−0.800819	−	0.598907i	$-0.795602\pi$
$997$	−4.98182e16	−1.60164	−0.800819	+	0.598907i	$0.795602\pi$
$998$	9.14782e14	0.0292482
$999$	2.92066e16	0.928690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.12.a.e.1.7		12
13.5	odd	4		13.12.b.a.12.6	✓	12
13.8	odd	4		13.12.b.a.12.7	yes	12
13.12	even	2	inner	169.12.a.e.1.6		12
39.5	even	4		117.12.b.b.64.7		12
39.8	even	4		117.12.b.b.64.6		12
52.31	even	4		208.12.f.b.129.3		12
52.47	even	4		208.12.f.b.129.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.12.b.a.12.6	✓	12	13.5	odd	4
13.12.b.a.12.7	yes	12	13.8	odd	4
117.12.b.b.64.6		12	39.8	even	4
117.12.b.b.64.7		12	39.5	even	4
169.12.a.e.1.6		12	13.12	even	2	inner
169.12.a.e.1.7		12	1.1	even	1	trivial
208.12.f.b.129.3		12	52.31	even	4
208.12.f.b.129.4		12	52.47	even	4

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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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q+3.38741 q^{2} +494.534 q^{3} -2036.53 q^{4} +9091.88 q^{5} +1675.19 q^{6} +45027.4 q^{7} -13836.0 q^{8} +67417.3 q^{9} +O(q^{10})\)	\(q+3.38741 q^{2} +494.534 q^{3} -2036.53 q^{4} +9091.88 q^{5} +1675.19 q^{6} +45027.4 q^{7} -13836.0 q^{8} +67417.3 q^{9} +30797.9 q^{10} -810639. q^{11} -1.00713e6 q^{12} +152526. q^{14} +4.49625e6 q^{15} +4.12394e6 q^{16} +851428. q^{17} +228370. q^{18} -7.56605e6 q^{19} -1.85158e7 q^{20} +2.22676e7 q^{21} -2.74596e6 q^{22} -3.69275e6 q^{23} -6.84236e6 q^{24} +3.38341e7 q^{25} -5.42651e7 q^{27} -9.16995e7 q^{28} -9.33625e7 q^{29} +1.52306e7 q^{30} -2.61508e8 q^{31} +4.23055e7 q^{32} -4.00889e8 q^{33} +2.88413e6 q^{34} +4.09384e8 q^{35} -1.37297e8 q^{36} -5.38221e8 q^{37} -2.56293e7 q^{38} -1.25795e8 q^{40} -6.71292e8 q^{41} +7.54295e7 q^{42} +1.09294e9 q^{43} +1.65089e9 q^{44} +6.12950e8 q^{45} -1.25088e7 q^{46} +1.79698e9 q^{47} +2.03943e9 q^{48} +5.01432e7 q^{49} +1.14610e8 q^{50} +4.21060e8 q^{51} -5.82497e9 q^{53} -1.83818e8 q^{54} -7.37023e9 q^{55} -6.22997e8 q^{56} -3.74167e9 q^{57} -3.16257e8 q^{58} +4.74847e9 q^{59} -9.15672e9 q^{60} +6.50495e9 q^{61} -8.85834e8 q^{62} +3.03563e9 q^{63} -8.30252e9 q^{64} -1.35797e9 q^{66} +8.11940e9 q^{67} -1.73395e9 q^{68} -1.82619e9 q^{69} +1.38675e9 q^{70} -3.16640e9 q^{71} -9.32783e8 q^{72} +8.22937e9 q^{73} -1.82317e9 q^{74} +1.67321e10 q^{75} +1.54085e10 q^{76} -3.65010e10 q^{77} -3.75500e9 q^{79} +3.74943e10 q^{80} -3.87787e10 q^{81} -2.27394e9 q^{82} -6.60119e9 q^{83} -4.53486e10 q^{84} +7.74108e9 q^{85} +3.70222e9 q^{86} -4.61710e10 q^{87} +1.12160e10 q^{88} -5.68420e10 q^{89} +2.07631e9 q^{90} +7.52038e9 q^{92} -1.29325e11 q^{93} +6.08709e9 q^{94} -6.87896e10 q^{95} +2.09215e10 q^{96} +1.62006e11 q^{97} +1.69856e8 q^{98} -5.46511e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 488 q^{3} + 12290 q^{4} + 654644 q^{9}+O(q^{10}) \) 12 * q - 488 * q^3 + 12290 * q^4 + 654644 * q^9	\( 12 q - 488 q^{3} + 12290 q^{4} + 654644 q^{9} + 333446 q^{10} - 2740298 q^{12} - 5367450 q^{14} + 19025698 q^{16} - 12198768 q^{17} - 111171128 q^{22} - 5810592 q^{23} - 6102388 q^{25} - 52613336 q^{27} - 244463112 q^{29} - 426504126 q^{30} - 562027560 q^{35} + 1357546052 q^{36} - 3171817788 q^{38} + 4092185498 q^{40} + 1280452314 q^{42} - 2294519976 q^{43} - 14206061378 q^{48} + 3573617796 q^{49} - 7713246552 q^{51} - 4602062760 q^{53} - 6178744976 q^{55} - 20017912662 q^{56} - 13775649944 q^{61} - 239765256 q^{62} + 3560815378 q^{64} + 37979507040 q^{66} + 40844682210 q^{68} + 25419983328 q^{69} + 19351803414 q^{74} - 68016370832 q^{75} + 80478036048 q^{77} + 18046097296 q^{79} - 132677486692 q^{81} + 255687836096 q^{82} + 94507900752 q^{87} - 239343029120 q^{88} + 190413561204 q^{90} - 135236877012 q^{92} - 78363161402 q^{94} - 145093149648 q^{95}+O(q^{100}) \) 12 * q - 488 * q^3 + 12290 * q^4 + 654644 * q^9 + 333446 * q^10 - 2740298 * q^12 - 5367450 * q^14 + 19025698 * q^16 - 12198768 * q^17 - 111171128 * q^22 - 5810592 * q^23 - 6102388 * q^25 - 52613336 * q^27 - 244463112 * q^29 - 426504126 * q^30 - 562027560 * q^35 + 1357546052 * q^36 - 3171817788 * q^38 + 4092185498 * q^40 + 1280452314 * q^42 - 2294519976 * q^43 - 14206061378 * q^48 + 3573617796 * q^49 - 7713246552 * q^51 - 4602062760 * q^53 - 6178744976 * q^55 - 20017912662 * q^56 - 13775649944 * q^61 - 239765256 * q^62 + 3560815378 * q^64 + 37979507040 * q^66 + 40844682210 * q^68 + 25419983328 * q^69 + 19351803414 * q^74 - 68016370832 * q^75 + 80478036048 * q^77 + 18046097296 * q^79 - 132677486692 * q^81 + 255687836096 * q^82 + 94507900752 * q^87 - 239343029120 * q^88 + 190413561204 * q^90 - 135236877012 * q^92 - 78363161402 * q^94 - 145093149648 * q^95

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