Properties

Label 23.14.a.b.1.1
Level $23$
Weight $14$
Character 23.1
Self dual yes
Analytic conductor $24.663$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [23,14,Mod(1,23)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(23, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("23.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 23.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: \(24.6631136589\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 6 x^{13} - 91997 x^{12} + 766599 x^{11} + 3278769040 x^{10} - 30986318669 x^{9} - 56829440072404 x^{8} + 496745885608086 x^{7} + \cdots - 45\!\cdots\!18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{19}\cdot 3^{4}\cdot 11 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(167.770\) of defining polynomial
Character \(\chi\) \(=\) 23.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-162.770 q^{2} -2381.17 q^{3} +18302.2 q^{4} +37078.1 q^{5} +387584. q^{6} +189022. q^{7} -1.64565e6 q^{8} +4.07566e6 q^{9} +O(q^{10})\) \(q-162.770 q^{2} -2381.17 q^{3} +18302.2 q^{4} +37078.1 q^{5} +387584. q^{6} +189022. q^{7} -1.64565e6 q^{8} +4.07566e6 q^{9} -6.03522e6 q^{10} -8.01372e6 q^{11} -4.35807e7 q^{12} +3.13553e7 q^{13} -3.07673e7 q^{14} -8.82893e7 q^{15} +1.17931e8 q^{16} +8.72430e7 q^{17} -6.63397e8 q^{18} -6.54013e7 q^{19} +6.78611e8 q^{20} -4.50095e8 q^{21} +1.30440e9 q^{22} +1.48036e8 q^{23} +3.91857e9 q^{24} +1.54082e8 q^{25} -5.10372e9 q^{26} -5.90848e9 q^{27} +3.45953e9 q^{28} -1.62740e9 q^{29} +1.43709e10 q^{30} +1.26677e9 q^{31} -5.71450e9 q^{32} +1.90820e10 q^{33} -1.42006e10 q^{34} +7.00859e9 q^{35} +7.45936e10 q^{36} +1.32290e10 q^{37} +1.06454e10 q^{38} -7.46625e10 q^{39} -6.10174e10 q^{40} +7.60558e9 q^{41} +7.32621e10 q^{42} -5.09971e9 q^{43} -1.46669e11 q^{44} +1.51118e11 q^{45} -2.40959e10 q^{46} -7.63675e10 q^{47} -2.80813e11 q^{48} -6.11595e10 q^{49} -2.50799e10 q^{50} -2.07741e11 q^{51} +5.73872e11 q^{52} +7.15348e9 q^{53} +9.61727e11 q^{54} -2.97133e11 q^{55} -3.11064e11 q^{56} +1.55732e11 q^{57} +2.64893e11 q^{58} +1.05569e11 q^{59} -1.61589e12 q^{60} +3.01020e10 q^{61} -2.06192e11 q^{62} +7.70390e11 q^{63} -3.59361e10 q^{64} +1.16260e12 q^{65} -3.10599e12 q^{66} +1.15435e12 q^{67} +1.59674e12 q^{68} -3.52499e11 q^{69} -1.14079e12 q^{70} +5.97518e11 q^{71} -6.70709e12 q^{72} +4.44729e11 q^{73} -2.15330e12 q^{74} -3.66895e11 q^{75} -1.19699e12 q^{76} -1.51477e12 q^{77} +1.21528e13 q^{78} +2.62211e12 q^{79} +4.37264e12 q^{80} +7.57120e12 q^{81} -1.23796e12 q^{82} -4.10881e12 q^{83} -8.23774e12 q^{84} +3.23480e12 q^{85} +8.30082e11 q^{86} +3.87512e12 q^{87} +1.31877e13 q^{88} +9.87837e10 q^{89} -2.45975e13 q^{90} +5.92686e12 q^{91} +2.70939e12 q^{92} -3.01639e12 q^{93} +1.24304e13 q^{94} -2.42496e12 q^{95} +1.36072e13 q^{96} +9.35623e12 q^{97} +9.95497e12 q^{98} -3.26612e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 64 q^{2} + 2056 q^{3} + 69632 q^{4} + 52182 q^{5} + 311167 q^{6} + 190602 q^{7} + 2356809 q^{8} + 12050784 q^{9} + 3585670 q^{10} + 1070730 q^{11} - 8508331 q^{12} + 23949638 q^{13} - 119280968 q^{14} - 44834930 q^{15} + 256829072 q^{16} + 69487470 q^{17} + 92449927 q^{18} + 111438548 q^{19} + 1129282316 q^{20} + 621345174 q^{21} + 2278933028 q^{22} + 2072502446 q^{23} + 8776950724 q^{24} + 5548551686 q^{25} - 925154105 q^{26} - 2006600744 q^{27} + 10886499970 q^{28} + 6082889362 q^{29} + 33591682946 q^{30} + 15979895560 q^{31} + 39045677992 q^{32} + 48341340746 q^{33} + 26300859414 q^{34} + 71251965504 q^{35} + 134660338135 q^{36} + 52356093690 q^{37} + 96969962716 q^{38} + 35694630240 q^{39} + 30337594230 q^{40} + 116782373266 q^{41} + 47161428352 q^{42} + 551363512 q^{43} - 18191926218 q^{44} + 66956385060 q^{45} + 9474296896 q^{46} - 89763073312 q^{47} + 7373438519 q^{48} + 198965141586 q^{49} - 353559739256 q^{50} - 849385907902 q^{51} + 290946305159 q^{52} - 255252512096 q^{53} - 20138610103 q^{54} - 308239853444 q^{55} - 1741462242990 q^{56} - 373036556464 q^{57} - 2063171638367 q^{58} - 844368470500 q^{59} - 3864457510716 q^{60} - 660411924036 q^{61} - 3066592203813 q^{62} - 2044550744028 q^{63} - 149179140181 q^{64} + 25563523898 q^{65} - 3128765504558 q^{66} + 343438236966 q^{67} - 687566878740 q^{68} + 304361787784 q^{69} + 2831163146300 q^{70} + 525250335580 q^{71} - 1782771811281 q^{72} + 6080256001118 q^{73} + 1193156509458 q^{74} + 3035968085076 q^{75} + 11140697506136 q^{76} - 905513956696 q^{77} + 15392222627509 q^{78} + 2029462022780 q^{79} + 6389606776510 q^{80} + 11017226960590 q^{81} + 5032544493407 q^{82} + 1645588044714 q^{83} - 8835767120594 q^{84} + 8689341605448 q^{85} - 5028664556794 q^{86} + 14107817502696 q^{87} + 35486297142892 q^{88} + 3557834996156 q^{89} - 20611184383708 q^{90} + 20574193795614 q^{91} + 10308035022848 q^{92} + 32845521705562 q^{93} - 4653170522585 q^{94} + 35338742719324 q^{95} + 44121425602615 q^{96} + 20411381883630 q^{97} - 10415391287228 q^{98} - 9767188111540 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −162.770 −1.79838 −0.899188 0.437562i \(-0.855842\pi\)
−0.899188 + 0.437562i \(0.855842\pi\)
\(3\) −2381.17 −1.88583 −0.942915 0.333033i \(-0.891928\pi\)
−0.942915 + 0.333033i \(0.891928\pi\)
\(4\) 18302.2 2.23416
\(5\) 37078.1 1.06124 0.530618 0.847611i \(-0.321960\pi\)
0.530618 + 0.847611i \(0.321960\pi\)
\(6\) 387584. 3.39143
\(7\) 189022. 0.607262 0.303631 0.952790i \(-0.401801\pi\)
0.303631 + 0.952790i \(0.401801\pi\)
\(8\) −1.64565e6 −2.21948
\(9\) 4.07566e6 2.55636
\(10\) −6.03522e6 −1.90850
\(11\) −8.01372e6 −1.36390 −0.681948 0.731400i \(-0.738867\pi\)
−0.681948 + 0.731400i \(0.738867\pi\)
\(12\) −4.35807e7 −4.21324
\(13\) 3.13553e7 1.80169 0.900844 0.434142i \(-0.142949\pi\)
0.900844 + 0.434142i \(0.142949\pi\)
\(14\) −3.07673e7 −1.09209
\(15\) −8.82893e7 −2.00131
\(16\) 1.17931e8 1.75730
\(17\) 8.72430e7 0.876622 0.438311 0.898823i \(-0.355577\pi\)
0.438311 + 0.898823i \(0.355577\pi\)
\(18\) −6.63397e8 −4.59729
\(19\) −6.54013e7 −0.318925 −0.159462 0.987204i \(-0.550976\pi\)
−0.159462 + 0.987204i \(0.550976\pi\)
\(20\) 6.78611e8 2.37097
\(21\) −4.50095e8 −1.14519
\(22\) 1.30440e9 2.45280
\(23\) 1.48036e8 0.208514
\(24\) 3.91857e9 4.18556
\(25\) 1.54082e8 0.126224
\(26\) −5.10372e9 −3.24011
\(27\) −5.90848e9 −2.93502
\(28\) 3.45953e9 1.35672
\(29\) −1.62740e9 −0.508051 −0.254026 0.967197i \(-0.581755\pi\)
−0.254026 + 0.967197i \(0.581755\pi\)
\(30\) 1.43709e10 3.59911
\(31\) 1.26677e9 0.256357 0.128179 0.991751i \(-0.459087\pi\)
0.128179 + 0.991751i \(0.459087\pi\)
\(32\) −5.71450e9 −0.940813
\(33\) 1.90820e10 2.57208
\(34\) −1.42006e10 −1.57650
\(35\) 7.00859e9 0.644449
\(36\) 7.45936e10 5.71130
\(37\) 1.32290e10 0.847651 0.423826 0.905744i \(-0.360687\pi\)
0.423826 + 0.905744i \(0.360687\pi\)
\(38\) 1.06454e10 0.573547
\(39\) −7.46625e10 −3.39768
\(40\) −6.10174e10 −2.35539
\(41\) 7.60558e9 0.250056 0.125028 0.992153i \(-0.460098\pi\)
0.125028 + 0.992153i \(0.460098\pi\)
\(42\) 7.32621e10 2.05949
\(43\) −5.09971e9 −0.123027 −0.0615135 0.998106i \(-0.519593\pi\)
−0.0615135 + 0.998106i \(0.519593\pi\)
\(44\) −1.46669e11 −3.04716
\(45\) 1.51118e11 2.71290
\(46\) −2.40959e10 −0.374987
\(47\) −7.63675e10 −1.03341 −0.516705 0.856164i \(-0.672841\pi\)
−0.516705 + 0.856164i \(0.672841\pi\)
\(48\) −2.80813e11 −3.31398
\(49\) −6.11595e10 −0.631233
\(50\) −2.50799e10 −0.226998
\(51\) −2.07741e11 −1.65316
\(52\) 5.73872e11 4.02526
\(53\) 7.15348e9 0.0443327 0.0221664 0.999754i \(-0.492944\pi\)
0.0221664 + 0.999754i \(0.492944\pi\)
\(54\) 9.61727e11 5.27828
\(55\) −2.97133e11 −1.44742
\(56\) −3.11064e11 −1.34781
\(57\) 1.55732e11 0.601438
\(58\) 2.64893e11 0.913668
\(59\) 1.05569e11 0.325836 0.162918 0.986640i \(-0.447909\pi\)
0.162918 + 0.986640i \(0.447909\pi\)
\(60\) −1.61589e12 −4.47125
\(61\) 3.01020e10 0.0748086 0.0374043 0.999300i \(-0.488091\pi\)
0.0374043 + 0.999300i \(0.488091\pi\)
\(62\) −2.06192e11 −0.461026
\(63\) 7.70390e11 1.55238
\(64\) −3.59361e10 −0.0653674
\(65\) 1.16260e12 1.91202
\(66\) −3.10599e12 −4.62557
\(67\) 1.15435e12 1.55902 0.779512 0.626387i \(-0.215467\pi\)
0.779512 + 0.626387i \(0.215467\pi\)
\(68\) 1.59674e12 1.95851
\(69\) −3.52499e11 −0.393223
\(70\) −1.14079e12 −1.15896
\(71\) 5.97518e11 0.553569 0.276785 0.960932i \(-0.410731\pi\)
0.276785 + 0.960932i \(0.410731\pi\)
\(72\) −6.70709e12 −5.67378
\(73\) 4.44729e11 0.343951 0.171976 0.985101i \(-0.444985\pi\)
0.171976 + 0.985101i \(0.444985\pi\)
\(74\) −2.15330e12 −1.52440
\(75\) −3.66895e11 −0.238036
\(76\) −1.19699e12 −0.712528
\(77\) −1.51477e12 −0.828243
\(78\) 1.21528e13 6.11031
\(79\) 2.62211e12 1.21360 0.606798 0.794856i \(-0.292454\pi\)
0.606798 + 0.794856i \(0.292454\pi\)
\(80\) 4.37264e12 1.86492
\(81\) 7.57120e12 2.97860
\(82\) −1.23796e12 −0.449695
\(83\) −4.10881e12 −1.37946 −0.689729 0.724067i \(-0.742270\pi\)
−0.689729 + 0.724067i \(0.742270\pi\)
\(84\) −8.23774e12 −2.55854
\(85\) 3.23480e12 0.930304
\(86\) 8.30082e11 0.221249
\(87\) 3.87512e12 0.958099
\(88\) 1.31877e13 3.02714
\(89\) 9.87837e10 0.0210693 0.0105347 0.999945i \(-0.496647\pi\)
0.0105347 + 0.999945i \(0.496647\pi\)
\(90\) −2.45975e13 −4.87881
\(91\) 5.92686e12 1.09410
\(92\) 2.70939e12 0.465854
\(93\) −3.01639e12 −0.483446
\(94\) 1.24304e13 1.85846
\(95\) −2.42496e12 −0.338455
\(96\) 1.36072e13 1.77421
\(97\) 9.35623e12 1.14047 0.570236 0.821481i \(-0.306852\pi\)
0.570236 + 0.821481i \(0.306852\pi\)
\(98\) 9.95497e12 1.13519
\(99\) −3.26612e13 −3.48661
\(100\) 2.82003e12 0.282003
\(101\) −1.76126e13 −1.65095 −0.825475 0.564439i \(-0.809093\pi\)
−0.825475 + 0.564439i \(0.809093\pi\)
\(102\) 3.38140e13 2.97301
\(103\) 2.02756e13 1.67314 0.836568 0.547864i \(-0.184559\pi\)
0.836568 + 0.547864i \(0.184559\pi\)
\(104\) −5.15998e13 −3.99881
\(105\) −1.66887e13 −1.21532
\(106\) −1.16438e12 −0.0797269
\(107\) 1.68773e13 1.08720 0.543599 0.839345i \(-0.317061\pi\)
0.543599 + 0.839345i \(0.317061\pi\)
\(108\) −1.08138e14 −6.55731
\(109\) −1.34752e13 −0.769597 −0.384799 0.923001i \(-0.625729\pi\)
−0.384799 + 0.923001i \(0.625729\pi\)
\(110\) 4.83645e13 2.60300
\(111\) −3.15006e13 −1.59853
\(112\) 2.22915e13 1.06714
\(113\) −2.89653e13 −1.30879 −0.654393 0.756155i \(-0.727076\pi\)
−0.654393 + 0.756155i \(0.727076\pi\)
\(114\) −2.53485e13 −1.08161
\(115\) 5.48889e12 0.221283
\(116\) −2.97851e13 −1.13507
\(117\) 1.27794e14 4.60576
\(118\) −1.71836e13 −0.585977
\(119\) 1.64909e13 0.532339
\(120\) 1.45293e14 4.44187
\(121\) 2.96970e13 0.860215
\(122\) −4.89972e12 −0.134534
\(123\) −1.81102e13 −0.471563
\(124\) 2.31846e13 0.572742
\(125\) −3.95483e13 −0.927284
\(126\) −1.25397e14 −2.79176
\(127\) −3.35902e13 −0.710377 −0.355189 0.934795i \(-0.615583\pi\)
−0.355189 + 0.934795i \(0.615583\pi\)
\(128\) 5.26625e13 1.05837
\(129\) 1.21433e13 0.232008
\(130\) −1.89236e14 −3.43853
\(131\) 5.17174e13 0.894074 0.447037 0.894515i \(-0.352479\pi\)
0.447037 + 0.894515i \(0.352479\pi\)
\(132\) 3.49244e14 5.74643
\(133\) −1.23623e13 −0.193671
\(134\) −1.87895e14 −2.80371
\(135\) −2.19075e14 −3.11476
\(136\) −1.43571e14 −1.94565
\(137\) 1.28569e14 1.66132 0.830659 0.556781i \(-0.187964\pi\)
0.830659 + 0.556781i \(0.187964\pi\)
\(138\) 5.73764e13 0.707163
\(139\) −2.89383e13 −0.340311 −0.170156 0.985417i \(-0.554427\pi\)
−0.170156 + 0.985417i \(0.554427\pi\)
\(140\) 1.28273e14 1.43980
\(141\) 1.81844e14 1.94883
\(142\) −9.72583e13 −0.995526
\(143\) −2.51273e14 −2.45732
\(144\) 4.80645e14 4.49229
\(145\) −6.03409e13 −0.539163
\(146\) −7.23887e13 −0.618554
\(147\) 1.45631e14 1.19040
\(148\) 2.42121e14 1.89379
\(149\) −1.55111e14 −1.16127 −0.580634 0.814165i \(-0.697195\pi\)
−0.580634 + 0.814165i \(0.697195\pi\)
\(150\) 5.97196e13 0.428079
\(151\) 1.20273e14 0.825691 0.412846 0.910801i \(-0.364535\pi\)
0.412846 + 0.910801i \(0.364535\pi\)
\(152\) 1.07627e14 0.707847
\(153\) 3.55573e14 2.24096
\(154\) 2.46560e14 1.48949
\(155\) 4.69692e13 0.272056
\(156\) −1.36649e15 −7.59095
\(157\) 1.49045e14 0.794272 0.397136 0.917760i \(-0.370004\pi\)
0.397136 + 0.917760i \(0.370004\pi\)
\(158\) −4.26801e14 −2.18250
\(159\) −1.70337e13 −0.0836040
\(160\) −2.11883e14 −0.998426
\(161\) 2.79821e13 0.126623
\(162\) −1.23237e15 −5.35665
\(163\) 1.73639e14 0.725150 0.362575 0.931955i \(-0.381898\pi\)
0.362575 + 0.931955i \(0.381898\pi\)
\(164\) 1.39199e14 0.558664
\(165\) 7.07526e14 2.72958
\(166\) 6.68793e14 2.48079
\(167\) 2.43080e14 0.867146 0.433573 0.901118i \(-0.357253\pi\)
0.433573 + 0.901118i \(0.357253\pi\)
\(168\) 7.40696e14 2.54173
\(169\) 6.80282e14 2.24608
\(170\) −5.26530e14 −1.67304
\(171\) −2.66553e14 −0.815285
\(172\) −9.33360e13 −0.274862
\(173\) −1.35247e14 −0.383556 −0.191778 0.981438i \(-0.561425\pi\)
−0.191778 + 0.981438i \(0.561425\pi\)
\(174\) −6.30755e14 −1.72302
\(175\) 2.91249e13 0.0766508
\(176\) −9.45063e14 −2.39678
\(177\) −2.51379e14 −0.614472
\(178\) −1.60791e13 −0.0378905
\(179\) 1.88153e14 0.427531 0.213765 0.976885i \(-0.431427\pi\)
0.213765 + 0.976885i \(0.431427\pi\)
\(180\) 2.76579e15 6.06105
\(181\) −2.56029e13 −0.0541226 −0.0270613 0.999634i \(-0.508615\pi\)
−0.0270613 + 0.999634i \(0.508615\pi\)
\(182\) −9.64718e14 −1.96760
\(183\) −7.16781e13 −0.141076
\(184\) −2.43615e14 −0.462794
\(185\) 4.90508e14 0.899559
\(186\) 4.90979e14 0.869418
\(187\) −6.99141e14 −1.19562
\(188\) −1.39769e15 −2.30880
\(189\) −1.11684e15 −1.78233
\(190\) 3.94711e14 0.608669
\(191\) 1.03200e15 1.53802 0.769009 0.639238i \(-0.220750\pi\)
0.769009 + 0.639238i \(0.220750\pi\)
\(192\) 8.55701e13 0.123272
\(193\) −5.29871e14 −0.737985 −0.368992 0.929432i \(-0.620297\pi\)
−0.368992 + 0.929432i \(0.620297\pi\)
\(194\) −1.52292e15 −2.05100
\(195\) −2.76834e15 −3.60574
\(196\) −1.11936e15 −1.41027
\(197\) 5.75465e14 0.701437 0.350718 0.936481i \(-0.385937\pi\)
0.350718 + 0.936481i \(0.385937\pi\)
\(198\) 5.31627e15 6.27023
\(199\) 4.03658e14 0.460754 0.230377 0.973101i \(-0.426004\pi\)
0.230377 + 0.973101i \(0.426004\pi\)
\(200\) −2.53564e14 −0.280151
\(201\) −2.74872e15 −2.94006
\(202\) 2.86681e15 2.96903
\(203\) −3.07615e14 −0.308520
\(204\) −3.80211e15 −3.69342
\(205\) 2.82000e14 0.265368
\(206\) −3.30026e15 −3.00893
\(207\) 6.03344e14 0.533037
\(208\) 3.69776e15 3.16611
\(209\) 5.24108e14 0.434981
\(210\) 2.71642e15 2.18560
\(211\) 1.42907e15 1.11485 0.557425 0.830227i \(-0.311789\pi\)
0.557425 + 0.830227i \(0.311789\pi\)
\(212\) 1.30925e14 0.0990463
\(213\) −1.42279e15 −1.04394
\(214\) −2.74713e15 −1.95519
\(215\) −1.89087e14 −0.130561
\(216\) 9.72327e15 6.51423
\(217\) 2.39447e14 0.155676
\(218\) 2.19337e15 1.38403
\(219\) −1.05898e15 −0.648634
\(220\) −5.43820e15 −3.23376
\(221\) 2.73553e15 1.57940
\(222\) 5.12737e15 2.87475
\(223\) −2.19961e15 −1.19775 −0.598873 0.800844i \(-0.704385\pi\)
−0.598873 + 0.800844i \(0.704385\pi\)
\(224\) −1.08017e15 −0.571320
\(225\) 6.27984e14 0.322672
\(226\) 4.71470e15 2.35369
\(227\) 4.52431e14 0.219474 0.109737 0.993961i \(-0.464999\pi\)
0.109737 + 0.993961i \(0.464999\pi\)
\(228\) 2.85024e15 1.34371
\(229\) 2.17418e15 0.996242 0.498121 0.867108i \(-0.334024\pi\)
0.498121 + 0.867108i \(0.334024\pi\)
\(230\) −8.93429e14 −0.397950
\(231\) 3.60693e15 1.56192
\(232\) 2.67813e15 1.12761
\(233\) 2.29330e15 0.938961 0.469480 0.882943i \(-0.344441\pi\)
0.469480 + 0.882943i \(0.344441\pi\)
\(234\) −2.08010e16 −8.28289
\(235\) −2.83156e15 −1.09669
\(236\) 1.93215e15 0.727970
\(237\) −6.24368e15 −2.28864
\(238\) −2.68423e15 −0.957346
\(239\) −1.19066e15 −0.413239 −0.206620 0.978421i \(-0.566246\pi\)
−0.206620 + 0.978421i \(0.566246\pi\)
\(240\) −1.04120e16 −3.51691
\(241\) 2.21497e15 0.728210 0.364105 0.931358i \(-0.381375\pi\)
0.364105 + 0.931358i \(0.381375\pi\)
\(242\) −4.83379e15 −1.54699
\(243\) −8.60831e15 −2.68211
\(244\) 5.50934e14 0.167134
\(245\) −2.26768e15 −0.669888
\(246\) 2.94780e15 0.848048
\(247\) −2.05068e15 −0.574603
\(248\) −2.08465e15 −0.568980
\(249\) 9.78379e15 2.60143
\(250\) 6.43729e15 1.66761
\(251\) −2.19417e15 −0.553848 −0.276924 0.960892i \(-0.589315\pi\)
−0.276924 + 0.960892i \(0.589315\pi\)
\(252\) 1.40999e16 3.46826
\(253\) −1.18632e15 −0.284392
\(254\) 5.46750e15 1.27753
\(255\) −7.70262e15 −1.75440
\(256\) −8.27752e15 −1.83798
\(257\) 4.57805e15 0.991095 0.495548 0.868581i \(-0.334967\pi\)
0.495548 + 0.868581i \(0.334967\pi\)
\(258\) −1.97657e15 −0.417238
\(259\) 2.50059e15 0.514746
\(260\) 2.12781e16 4.27175
\(261\) −6.63273e15 −1.29876
\(262\) −8.41807e15 −1.60788
\(263\) 8.12564e15 1.51407 0.757034 0.653376i \(-0.226648\pi\)
0.757034 + 0.653376i \(0.226648\pi\)
\(264\) −3.14023e16 −5.70868
\(265\) 2.65237e14 0.0470475
\(266\) 2.01222e15 0.348293
\(267\) −2.35221e14 −0.0397331
\(268\) 2.11273e16 3.48311
\(269\) −7.05029e14 −0.113453 −0.0567267 0.998390i \(-0.518066\pi\)
−0.0567267 + 0.998390i \(0.518066\pi\)
\(270\) 3.56590e16 5.60150
\(271\) −5.16985e15 −0.792825 −0.396412 0.918073i \(-0.629745\pi\)
−0.396412 + 0.918073i \(0.629745\pi\)
\(272\) 1.02886e16 1.54049
\(273\) −1.41129e16 −2.06328
\(274\) −2.09273e16 −2.98768
\(275\) −1.23477e15 −0.172156
\(276\) −6.45151e15 −0.878522
\(277\) −4.92917e15 −0.655625 −0.327812 0.944743i \(-0.606311\pi\)
−0.327812 + 0.944743i \(0.606311\pi\)
\(278\) 4.71029e15 0.612007
\(279\) 5.16290e15 0.655340
\(280\) −1.15337e16 −1.43034
\(281\) 1.52979e16 1.85371 0.926854 0.375422i \(-0.122502\pi\)
0.926854 + 0.375422i \(0.122502\pi\)
\(282\) −2.95988e16 −3.50474
\(283\) 1.54101e16 1.78317 0.891586 0.452852i \(-0.149593\pi\)
0.891586 + 0.452852i \(0.149593\pi\)
\(284\) 1.09359e16 1.23676
\(285\) 5.77424e15 0.638268
\(286\) 4.08998e16 4.41918
\(287\) 1.43762e15 0.151849
\(288\) −2.32903e16 −2.40505
\(289\) −2.29324e15 −0.231533
\(290\) 9.82172e15 0.969618
\(291\) −2.22788e16 −2.15074
\(292\) 8.13953e15 0.768441
\(293\) −7.92823e15 −0.732044 −0.366022 0.930606i \(-0.619280\pi\)
−0.366022 + 0.930606i \(0.619280\pi\)
\(294\) −2.37045e16 −2.14078
\(295\) 3.91431e15 0.345790
\(296\) −2.17703e16 −1.88135
\(297\) 4.73489e16 4.00307
\(298\) 2.52475e16 2.08840
\(299\) 4.64172e15 0.375678
\(300\) −6.71499e15 −0.531811
\(301\) −9.63959e14 −0.0747096
\(302\) −1.95769e16 −1.48490
\(303\) 4.19386e16 3.11341
\(304\) −7.71282e15 −0.560448
\(305\) 1.11613e15 0.0793897
\(306\) −5.78767e16 −4.03009
\(307\) −1.91914e16 −1.30830 −0.654151 0.756364i \(-0.726974\pi\)
−0.654151 + 0.756364i \(0.726974\pi\)
\(308\) −2.77237e16 −1.85042
\(309\) −4.82796e16 −3.15525
\(310\) −7.64521e15 −0.489258
\(311\) −1.45504e16 −0.911869 −0.455934 0.890013i \(-0.650695\pi\)
−0.455934 + 0.890013i \(0.650695\pi\)
\(312\) 1.22868e17 7.54108
\(313\) −1.66747e16 −1.00235 −0.501177 0.865345i \(-0.667099\pi\)
−0.501177 + 0.865345i \(0.667099\pi\)
\(314\) −2.42601e16 −1.42840
\(315\) 2.85646e16 1.64744
\(316\) 4.79903e16 2.71136
\(317\) −1.42181e16 −0.786966 −0.393483 0.919332i \(-0.628730\pi\)
−0.393483 + 0.919332i \(0.628730\pi\)
\(318\) 2.77258e15 0.150351
\(319\) 1.30415e16 0.692930
\(320\) −1.33244e15 −0.0693703
\(321\) −4.01878e16 −2.05027
\(322\) −4.55466e15 −0.227716
\(323\) −5.70581e15 −0.279577
\(324\) 1.38570e17 6.65466
\(325\) 4.83128e15 0.227416
\(326\) −2.82633e16 −1.30409
\(327\) 3.20868e16 1.45133
\(328\) −1.25161e16 −0.554994
\(329\) −1.44352e16 −0.627550
\(330\) −1.15164e17 −4.90882
\(331\) 2.48098e16 1.03691 0.518455 0.855105i \(-0.326508\pi\)
0.518455 + 0.855105i \(0.326508\pi\)
\(332\) −7.52004e16 −3.08193
\(333\) 5.39170e16 2.16690
\(334\) −3.95662e16 −1.55945
\(335\) 4.28013e16 1.65449
\(336\) −5.30800e16 −2.01245
\(337\) −1.84939e16 −0.687755 −0.343877 0.939015i \(-0.611740\pi\)
−0.343877 + 0.939015i \(0.611740\pi\)
\(338\) −1.10730e17 −4.03930
\(339\) 6.89714e16 2.46815
\(340\) 5.92041e16 2.07845
\(341\) −1.01515e16 −0.349645
\(342\) 4.33870e16 1.46619
\(343\) −2.98747e16 −0.990586
\(344\) 8.39231e15 0.273056
\(345\) −1.30700e16 −0.417303
\(346\) 2.20142e16 0.689777
\(347\) 2.57363e16 0.791416 0.395708 0.918376i \(-0.370499\pi\)
0.395708 + 0.918376i \(0.370499\pi\)
\(348\) 7.09233e16 2.14054
\(349\) 6.00461e16 1.77877 0.889384 0.457161i \(-0.151134\pi\)
0.889384 + 0.457161i \(0.151134\pi\)
\(350\) −4.74067e15 −0.137847
\(351\) −1.85263e17 −5.28800
\(352\) 4.57944e16 1.28317
\(353\) 2.06395e16 0.567759 0.283880 0.958860i \(-0.408378\pi\)
0.283880 + 0.958860i \(0.408378\pi\)
\(354\) 4.09170e16 1.10505
\(355\) 2.21548e16 0.587468
\(356\) 1.80796e15 0.0470722
\(357\) −3.92676e16 −1.00390
\(358\) −3.06258e16 −0.768861
\(359\) 2.66939e16 0.658109 0.329054 0.944311i \(-0.393270\pi\)
0.329054 + 0.944311i \(0.393270\pi\)
\(360\) −2.48686e17 −6.02123
\(361\) −3.77756e16 −0.898287
\(362\) 4.16740e15 0.0973329
\(363\) −7.07136e16 −1.62222
\(364\) 1.08475e17 2.44438
\(365\) 1.64897e16 0.365014
\(366\) 1.16671e16 0.253708
\(367\) 2.30658e16 0.492763 0.246382 0.969173i \(-0.420758\pi\)
0.246382 + 0.969173i \(0.420758\pi\)
\(368\) 1.74580e16 0.366423
\(369\) 3.09977e16 0.639232
\(370\) −7.98401e16 −1.61775
\(371\) 1.35217e15 0.0269216
\(372\) −5.52066e16 −1.08009
\(373\) 3.39408e16 0.652552 0.326276 0.945275i \(-0.394206\pi\)
0.326276 + 0.945275i \(0.394206\pi\)
\(374\) 1.13799e17 2.15018
\(375\) 9.41713e16 1.74870
\(376\) 1.25674e17 2.29363
\(377\) −5.10277e16 −0.915350
\(378\) 1.81788e17 3.20530
\(379\) −7.43215e16 −1.28813 −0.644065 0.764971i \(-0.722753\pi\)
−0.644065 + 0.764971i \(0.722753\pi\)
\(380\) −4.43821e16 −0.756161
\(381\) 7.99842e16 1.33965
\(382\) −1.67979e17 −2.76594
\(383\) −3.24509e16 −0.525333 −0.262666 0.964887i \(-0.584602\pi\)
−0.262666 + 0.964887i \(0.584602\pi\)
\(384\) −1.25399e17 −1.99590
\(385\) −5.61648e16 −0.878961
\(386\) 8.62473e16 1.32717
\(387\) −2.07847e16 −0.314501
\(388\) 1.71240e17 2.54799
\(389\) 4.26831e16 0.624573 0.312287 0.949988i \(-0.398905\pi\)
0.312287 + 0.949988i \(0.398905\pi\)
\(390\) 4.50604e17 6.48448
\(391\) 1.29151e16 0.182788
\(392\) 1.00647e17 1.40101
\(393\) −1.23148e17 −1.68607
\(394\) −9.36687e16 −1.26145
\(395\) 9.72226e16 1.28791
\(396\) −5.97772e17 −7.78963
\(397\) −5.73276e16 −0.734895 −0.367448 0.930044i \(-0.619768\pi\)
−0.367448 + 0.930044i \(0.619768\pi\)
\(398\) −6.57036e16 −0.828609
\(399\) 2.94368e16 0.365230
\(400\) 1.81709e16 0.221813
\(401\) −2.84487e16 −0.341684 −0.170842 0.985298i \(-0.554649\pi\)
−0.170842 + 0.985298i \(0.554649\pi\)
\(402\) 4.47410e17 5.28733
\(403\) 3.97199e16 0.461876
\(404\) −3.22349e17 −3.68848
\(405\) 2.80726e17 3.16100
\(406\) 5.00707e16 0.554835
\(407\) −1.06014e17 −1.15611
\(408\) 3.41867e17 3.66916
\(409\) −5.23729e15 −0.0553229 −0.0276615 0.999617i \(-0.508806\pi\)
−0.0276615 + 0.999617i \(0.508806\pi\)
\(410\) −4.59013e16 −0.477232
\(411\) −3.06145e17 −3.13297
\(412\) 3.71088e17 3.73805
\(413\) 1.99550e16 0.197868
\(414\) −9.82065e16 −0.958601
\(415\) −1.52347e17 −1.46393
\(416\) −1.79180e17 −1.69505
\(417\) 6.89070e16 0.641769
\(418\) −8.53093e16 −0.782259
\(419\) −1.67230e16 −0.150982 −0.0754908 0.997147i \(-0.524052\pi\)
−0.0754908 + 0.997147i \(0.524052\pi\)
\(420\) −3.05439e17 −2.71522
\(421\) 7.74959e16 0.678337 0.339168 0.940726i \(-0.389854\pi\)
0.339168 + 0.940726i \(0.389854\pi\)
\(422\) −2.32610e17 −2.00492
\(423\) −3.11248e17 −2.64176
\(424\) −1.17721e16 −0.0983956
\(425\) 1.34425e16 0.110650
\(426\) 2.31589e17 1.87739
\(427\) 5.68995e15 0.0454284
\(428\) 3.08892e17 2.42897
\(429\) 5.98324e17 4.63408
\(430\) 3.07779e16 0.234797
\(431\) −9.90993e16 −0.744678 −0.372339 0.928097i \(-0.621444\pi\)
−0.372339 + 0.928097i \(0.621444\pi\)
\(432\) −6.96792e17 −5.15773
\(433\) 7.08003e16 0.516254 0.258127 0.966111i \(-0.416895\pi\)
0.258127 + 0.966111i \(0.416895\pi\)
\(434\) −3.89749e16 −0.279964
\(435\) 1.43682e17 1.01677
\(436\) −2.46626e17 −1.71940
\(437\) −9.68175e15 −0.0665004
\(438\) 1.72370e17 1.16649
\(439\) 1.98677e17 1.32474 0.662368 0.749179i \(-0.269552\pi\)
0.662368 + 0.749179i \(0.269552\pi\)
\(440\) 4.88976e17 3.21252
\(441\) −2.49265e17 −1.61366
\(442\) −4.45264e17 −2.84036
\(443\) 1.81878e16 0.114329 0.0571646 0.998365i \(-0.481794\pi\)
0.0571646 + 0.998365i \(0.481794\pi\)
\(444\) −5.76531e17 −3.57136
\(445\) 3.66271e15 0.0223595
\(446\) 3.58032e17 2.15400
\(447\) 3.69346e17 2.18995
\(448\) −6.79273e15 −0.0396951
\(449\) 3.99244e16 0.229952 0.114976 0.993368i \(-0.463321\pi\)
0.114976 + 0.993368i \(0.463321\pi\)
\(450\) −1.02217e17 −0.580287
\(451\) −6.09489e16 −0.341050
\(452\) −5.30130e17 −2.92403
\(453\) −2.86390e17 −1.55711
\(454\) −7.36424e16 −0.394698
\(455\) 2.19757e17 1.16110
\(456\) −2.56279e17 −1.33488
\(457\) −8.13503e16 −0.417738 −0.208869 0.977944i \(-0.566978\pi\)
−0.208869 + 0.977944i \(0.566978\pi\)
\(458\) −3.53892e17 −1.79162
\(459\) −5.15474e17 −2.57291
\(460\) 1.00459e17 0.494382
\(461\) 4.00641e17 1.94401 0.972006 0.234955i \(-0.0754943\pi\)
0.972006 + 0.234955i \(0.0754943\pi\)
\(462\) −5.87102e17 −2.80893
\(463\) 1.77015e17 0.835090 0.417545 0.908656i \(-0.362891\pi\)
0.417545 + 0.908656i \(0.362891\pi\)
\(464\) −1.91920e17 −0.892801
\(465\) −1.11842e17 −0.513051
\(466\) −3.73282e17 −1.68860
\(467\) −3.59491e17 −1.60372 −0.801861 0.597511i \(-0.796156\pi\)
−0.801861 + 0.597511i \(0.796156\pi\)
\(468\) 2.33891e18 10.2900
\(469\) 2.18199e17 0.946736
\(470\) 4.60894e17 1.97226
\(471\) −3.54901e17 −1.49786
\(472\) −1.73730e17 −0.723188
\(473\) 4.08676e16 0.167796
\(474\) 1.01629e18 4.11583
\(475\) −1.00771e16 −0.0402558
\(476\) 3.01820e17 1.18933
\(477\) 2.91551e16 0.113330
\(478\) 1.93804e17 0.743159
\(479\) 7.55857e16 0.285929 0.142965 0.989728i \(-0.454336\pi\)
0.142965 + 0.989728i \(0.454336\pi\)
\(480\) 5.04529e17 1.88286
\(481\) 4.14801e17 1.52720
\(482\) −3.60532e17 −1.30960
\(483\) −6.66302e16 −0.238789
\(484\) 5.43520e17 1.92186
\(485\) 3.46911e17 1.21031
\(486\) 1.40118e18 4.82345
\(487\) 4.43593e17 1.50677 0.753384 0.657581i \(-0.228420\pi\)
0.753384 + 0.657581i \(0.228420\pi\)
\(488\) −4.95372e16 −0.166036
\(489\) −4.13464e17 −1.36751
\(490\) 3.69111e17 1.20471
\(491\) −6.02305e17 −1.93993 −0.969966 0.243240i \(-0.921790\pi\)
−0.969966 + 0.243240i \(0.921790\pi\)
\(492\) −3.31457e17 −1.05355
\(493\) −1.41979e17 −0.445369
\(494\) 3.33790e17 1.03335
\(495\) −1.21101e18 −3.70012
\(496\) 1.49391e17 0.450497
\(497\) 1.12944e17 0.336161
\(498\) −1.59251e18 −4.67834
\(499\) −6.24220e17 −1.81002 −0.905011 0.425387i \(-0.860138\pi\)
−0.905011 + 0.425387i \(0.860138\pi\)
\(500\) −7.23822e17 −2.07170
\(501\) −5.78815e17 −1.63529
\(502\) 3.57146e17 0.996027
\(503\) 1.59160e17 0.438168 0.219084 0.975706i \(-0.429693\pi\)
0.219084 + 0.975706i \(0.429693\pi\)
\(504\) −1.26779e18 −3.44547
\(505\) −6.53040e17 −1.75205
\(506\) 1.93097e17 0.511444
\(507\) −1.61987e18 −4.23573
\(508\) −6.14776e17 −1.58709
\(509\) 4.29007e17 1.09345 0.546725 0.837312i \(-0.315874\pi\)
0.546725 + 0.837312i \(0.315874\pi\)
\(510\) 1.25376e18 3.15506
\(511\) 8.40637e16 0.208868
\(512\) 9.15923e17 2.24701
\(513\) 3.86423e17 0.936052
\(514\) −7.45172e17 −1.78236
\(515\) 7.51779e17 1.77559
\(516\) 2.22249e17 0.518343
\(517\) 6.11987e17 1.40946
\(518\) −4.07021e17 −0.925708
\(519\) 3.22047e17 0.723321
\(520\) −1.91322e18 −4.24369
\(521\) 8.00451e17 1.75343 0.876717 0.481006i \(-0.159728\pi\)
0.876717 + 0.481006i \(0.159728\pi\)
\(522\) 1.07961e18 2.33566
\(523\) −2.10512e17 −0.449797 −0.224898 0.974382i \(-0.572205\pi\)
−0.224898 + 0.974382i \(0.572205\pi\)
\(524\) 9.46544e17 1.99750
\(525\) −6.93513e16 −0.144550
\(526\) −1.32261e18 −2.72286
\(527\) 1.10516e17 0.224728
\(528\) 2.25036e18 4.51992
\(529\) 2.19146e16 0.0434783
\(530\) −4.31728e16 −0.0846091
\(531\) 4.30264e17 0.832954
\(532\) −2.26258e17 −0.432691
\(533\) 2.38475e17 0.450523
\(534\) 3.82870e16 0.0714551
\(535\) 6.25779e17 1.15378
\(536\) −1.89966e18 −3.46022
\(537\) −4.48026e17 −0.806250
\(538\) 1.14758e17 0.204032
\(539\) 4.90115e17 0.860937
\(540\) −4.00956e18 −6.95886
\(541\) 8.80059e17 1.50914 0.754570 0.656220i \(-0.227845\pi\)
0.754570 + 0.656220i \(0.227845\pi\)
\(542\) 8.41498e17 1.42580
\(543\) 6.09650e16 0.102066
\(544\) −4.98550e17 −0.824738
\(545\) −4.99635e17 −0.816725
\(546\) 2.29716e18 3.71056
\(547\) −8.28017e17 −1.32167 −0.660833 0.750533i \(-0.729797\pi\)
−0.660833 + 0.750533i \(0.729797\pi\)
\(548\) 2.35310e18 3.71165
\(549\) 1.22686e17 0.191237
\(550\) 2.00983e17 0.309601
\(551\) 1.06434e17 0.162030
\(552\) 5.80088e17 0.872750
\(553\) 4.95637e17 0.736970
\(554\) 8.02323e17 1.17906
\(555\) −1.16798e18 −1.69642
\(556\) −5.29634e17 −0.760309
\(557\) −3.64214e17 −0.516771 −0.258386 0.966042i \(-0.583190\pi\)
−0.258386 + 0.966042i \(0.583190\pi\)
\(558\) −8.40368e17 −1.17855
\(559\) −1.59903e17 −0.221656
\(560\) 8.26528e17 1.13249
\(561\) 1.66477e18 2.25474
\(562\) −2.49005e18 −3.33366
\(563\) 9.72416e17 1.28691 0.643454 0.765485i \(-0.277501\pi\)
0.643454 + 0.765485i \(0.277501\pi\)
\(564\) 3.32815e18 4.35400
\(565\) −1.07398e18 −1.38893
\(566\) −2.50831e18 −3.20681
\(567\) 1.43113e18 1.80879
\(568\) −9.83303e17 −1.22864
\(569\) 5.07825e16 0.0627313 0.0313656 0.999508i \(-0.490014\pi\)
0.0313656 + 0.999508i \(0.490014\pi\)
\(570\) −9.39876e17 −1.14785
\(571\) −1.89682e17 −0.229030 −0.114515 0.993422i \(-0.536531\pi\)
−0.114515 + 0.993422i \(0.536531\pi\)
\(572\) −4.59885e18 −5.49004
\(573\) −2.45736e18 −2.90044
\(574\) −2.34003e17 −0.273082
\(575\) 2.28096e16 0.0263194
\(576\) −1.46463e17 −0.167102
\(577\) −8.27893e17 −0.933966 −0.466983 0.884266i \(-0.654659\pi\)
−0.466983 + 0.884266i \(0.654659\pi\)
\(578\) 3.73271e17 0.416384
\(579\) 1.26171e18 1.39171
\(580\) −1.10437e18 −1.20457
\(581\) −7.76657e17 −0.837693
\(582\) 3.62633e18 3.86783
\(583\) −5.73260e16 −0.0604652
\(584\) −7.31866e17 −0.763393
\(585\) 4.73834e18 4.88780
\(586\) 1.29048e18 1.31649
\(587\) 7.80410e17 0.787364 0.393682 0.919247i \(-0.371201\pi\)
0.393682 + 0.919247i \(0.371201\pi\)
\(588\) 2.66538e18 2.65954
\(589\) −8.28482e16 −0.0817586
\(590\) −6.37134e17 −0.621860
\(591\) −1.37028e18 −1.32279
\(592\) 1.56011e18 1.48958
\(593\) 1.70361e18 1.60885 0.804425 0.594054i \(-0.202474\pi\)
0.804425 + 0.594054i \(0.202474\pi\)
\(594\) −7.70701e18 −7.19903
\(595\) 6.11450e17 0.564938
\(596\) −2.83888e18 −2.59446
\(597\) −9.61180e17 −0.868903
\(598\) −7.55534e17 −0.675611
\(599\) 6.34568e17 0.561311 0.280655 0.959809i \(-0.409448\pi\)
0.280655 + 0.959809i \(0.409448\pi\)
\(600\) 6.03778e17 0.528317
\(601\) −1.58119e18 −1.36867 −0.684336 0.729167i \(-0.739908\pi\)
−0.684336 + 0.729167i \(0.739908\pi\)
\(602\) 1.56904e17 0.134356
\(603\) 4.70475e18 3.98542
\(604\) 2.20126e18 1.84472
\(605\) 1.10111e18 0.912892
\(606\) −6.82636e18 −5.59909
\(607\) 1.14804e18 0.931602 0.465801 0.884889i \(-0.345766\pi\)
0.465801 + 0.884889i \(0.345766\pi\)
\(608\) 3.73736e17 0.300049
\(609\) 7.32485e17 0.581817
\(610\) −1.81672e17 −0.142773
\(611\) −2.39453e18 −1.86188
\(612\) 6.50777e18 5.00666
\(613\) 2.01236e17 0.153184 0.0765919 0.997063i \(-0.475596\pi\)
0.0765919 + 0.997063i \(0.475596\pi\)
\(614\) 3.12380e18 2.35282
\(615\) −6.71491e17 −0.500440
\(616\) 2.49278e18 1.83827
\(617\) 1.46232e18 1.06706 0.533530 0.845781i \(-0.320865\pi\)
0.533530 + 0.845781i \(0.320865\pi\)
\(618\) 7.85849e18 5.67433
\(619\) −1.45866e17 −0.104223 −0.0521116 0.998641i \(-0.516595\pi\)
−0.0521116 + 0.998641i \(0.516595\pi\)
\(620\) 8.59642e17 0.607815
\(621\) −8.74668e17 −0.611995
\(622\) 2.36837e18 1.63988
\(623\) 1.86723e16 0.0127946
\(624\) −8.80499e18 −5.97075
\(625\) −1.65446e18 −1.11029
\(626\) 2.71415e18 1.80261
\(627\) −1.24799e18 −0.820300
\(628\) 2.72785e18 1.77453
\(629\) 1.15414e18 0.743070
\(630\) −4.64947e18 −2.96272
\(631\) −1.33503e18 −0.841977 −0.420988 0.907066i \(-0.638317\pi\)
−0.420988 + 0.907066i \(0.638317\pi\)
\(632\) −4.31506e18 −2.69355
\(633\) −3.40286e18 −2.10242
\(634\) 2.31428e18 1.41526
\(635\) −1.24546e18 −0.753878
\(636\) −3.11754e17 −0.186784
\(637\) −1.91768e18 −1.13729
\(638\) −2.12278e18 −1.24615
\(639\) 2.43528e18 1.41512
\(640\) 1.95263e18 1.12318
\(641\) 1.08968e18 0.620469 0.310235 0.950660i \(-0.399592\pi\)
0.310235 + 0.950660i \(0.399592\pi\)
\(642\) 6.54139e18 3.68716
\(643\) −6.30973e17 −0.352079 −0.176039 0.984383i \(-0.556329\pi\)
−0.176039 + 0.984383i \(0.556329\pi\)
\(644\) 5.12135e17 0.282895
\(645\) 4.50250e17 0.246215
\(646\) 9.28737e17 0.502784
\(647\) 5.64504e17 0.302545 0.151272 0.988492i \(-0.451663\pi\)
0.151272 + 0.988492i \(0.451663\pi\)
\(648\) −1.24595e19 −6.61095
\(649\) −8.46003e17 −0.444407
\(650\) −7.86389e17 −0.408979
\(651\) −5.70165e17 −0.293578
\(652\) 3.17798e18 1.62010
\(653\) −2.48932e18 −1.25645 −0.628224 0.778033i \(-0.716218\pi\)
−0.628224 + 0.778033i \(0.716218\pi\)
\(654\) −5.22278e18 −2.61004
\(655\) 1.91758e18 0.948824
\(656\) 8.96931e17 0.439424
\(657\) 1.81256e18 0.879262
\(658\) 2.34962e18 1.12857
\(659\) −2.89893e18 −1.37874 −0.689370 0.724410i \(-0.742112\pi\)
−0.689370 + 0.724410i \(0.742112\pi\)
\(660\) 1.29493e19 6.09832
\(661\) −3.27467e18 −1.52707 −0.763534 0.645768i \(-0.776537\pi\)
−0.763534 + 0.645768i \(0.776537\pi\)
\(662\) −4.03830e18 −1.86475
\(663\) −6.51378e18 −2.97848
\(664\) 6.76165e18 3.06168
\(665\) −4.58371e17 −0.205531
\(666\) −8.77610e18 −3.89690
\(667\) −2.40914e17 −0.105936
\(668\) 4.44890e18 1.93734
\(669\) 5.23766e18 2.25875
\(670\) −6.96678e18 −2.97540
\(671\) −2.41229e17 −0.102031
\(672\) 2.57207e18 1.07741
\(673\) −3.53625e18 −1.46705 −0.733525 0.679663i \(-0.762126\pi\)
−0.733525 + 0.679663i \(0.762126\pi\)
\(674\) 3.01026e18 1.23684
\(675\) −9.10388e17 −0.370469
\(676\) 1.24507e19 5.01810
\(677\) 2.85848e18 1.14106 0.570531 0.821276i \(-0.306737\pi\)
0.570531 + 0.821276i \(0.306737\pi\)
\(678\) −1.12265e19 −4.43866
\(679\) 1.76854e18 0.692565
\(680\) −5.32334e18 −2.06479
\(681\) −1.07732e18 −0.413892
\(682\) 1.65236e18 0.628793
\(683\) −2.67594e18 −1.00865 −0.504326 0.863513i \(-0.668259\pi\)
−0.504326 + 0.863513i \(0.668259\pi\)
\(684\) −4.87852e18 −1.82148
\(685\) 4.76710e18 1.76305
\(686\) 4.86272e18 1.78145
\(687\) −5.17710e18 −1.87874
\(688\) −6.01412e17 −0.216196
\(689\) 2.24300e17 0.0798737
\(690\) 2.12741e18 0.750467
\(691\) 1.96852e18 0.687913 0.343956 0.938986i \(-0.388233\pi\)
0.343956 + 0.938986i \(0.388233\pi\)
\(692\) −2.47532e18 −0.856924
\(693\) −6.17369e18 −2.11728
\(694\) −4.18911e18 −1.42326
\(695\) −1.07298e18 −0.361151
\(696\) −6.37708e18 −2.12648
\(697\) 6.63533e17 0.219205
\(698\) −9.77372e18 −3.19889
\(699\) −5.46074e18 −1.77072
\(700\) 5.33050e17 0.171250
\(701\) 3.82780e18 1.21838 0.609189 0.793025i \(-0.291495\pi\)
0.609189 + 0.793025i \(0.291495\pi\)
\(702\) 3.01553e19 9.50981
\(703\) −8.65197e17 −0.270337
\(704\) 2.87982e17 0.0891544
\(705\) 6.74243e18 2.06817
\(706\) −3.35951e18 −1.02104
\(707\) −3.32917e18 −1.00256
\(708\) −4.60079e18 −1.37283
\(709\) −1.30255e18 −0.385117 −0.192558 0.981286i \(-0.561679\pi\)
−0.192558 + 0.981286i \(0.561679\pi\)
\(710\) −3.60615e18 −1.05649
\(711\) 1.06868e19 3.10238
\(712\) −1.62563e17 −0.0467629
\(713\) 1.87527e17 0.0534541
\(714\) 6.39161e18 1.80539
\(715\) −9.31672e18 −2.60780
\(716\) 3.44362e18 0.955171
\(717\) 2.83517e18 0.779299
\(718\) −4.34497e18 −1.18353
\(719\) 1.60657e18 0.433674 0.216837 0.976208i \(-0.430426\pi\)
0.216837 + 0.976208i \(0.430426\pi\)
\(720\) 1.78214e19 4.76739
\(721\) 3.83254e18 1.01603
\(722\) 6.14876e18 1.61546
\(723\) −5.27422e18 −1.37328
\(724\) −4.68590e17 −0.120918
\(725\) −2.50752e17 −0.0641281
\(726\) 1.15101e19 2.91736
\(727\) 1.70155e18 0.427435 0.213718 0.976895i \(-0.431443\pi\)
0.213718 + 0.976895i \(0.431443\pi\)
\(728\) −9.75351e18 −2.42833
\(729\) 8.42691e18 2.07941
\(730\) −2.68404e18 −0.656432
\(731\) −4.44914e17 −0.107848
\(732\) −1.31187e18 −0.315187
\(733\) 5.61258e16 0.0133656 0.00668278 0.999978i \(-0.497873\pi\)
0.00668278 + 0.999978i \(0.497873\pi\)
\(734\) −3.75443e18 −0.886174
\(735\) 5.39973e18 1.26329
\(736\) −8.45951e17 −0.196173
\(737\) −9.25067e18 −2.12635
\(738\) −5.04551e18 −1.14958
\(739\) 1.36630e18 0.308572 0.154286 0.988026i \(-0.450692\pi\)
0.154286 + 0.988026i \(0.450692\pi\)
\(740\) 8.97738e18 2.00976
\(741\) 4.88302e18 1.08360
\(742\) −2.20093e17 −0.0484151
\(743\) 6.30358e18 1.37455 0.687274 0.726399i \(-0.258807\pi\)
0.687274 + 0.726399i \(0.258807\pi\)
\(744\) 4.96390e18 1.07300
\(745\) −5.75123e18 −1.23238
\(746\) −5.52456e18 −1.17353
\(747\) −1.67461e19 −3.52639
\(748\) −1.27958e19 −2.67121
\(749\) 3.19019e18 0.660214
\(750\) −1.53283e19 −3.14482
\(751\) 6.46039e18 1.31401 0.657006 0.753886i \(-0.271823\pi\)
0.657006 + 0.753886i \(0.271823\pi\)
\(752\) −9.00607e18 −1.81601
\(753\) 5.22469e18 1.04446
\(754\) 8.30580e18 1.64614
\(755\) 4.45949e18 0.876254
\(756\) −2.04406e19 −3.98200
\(757\) −2.01550e18 −0.389278 −0.194639 0.980875i \(-0.562354\pi\)
−0.194639 + 0.980875i \(0.562354\pi\)
\(758\) 1.20974e19 2.31654
\(759\) 2.82483e18 0.536315
\(760\) 3.99062e18 0.751194
\(761\) 5.12180e17 0.0955923 0.0477961 0.998857i \(-0.484780\pi\)
0.0477961 + 0.998857i \(0.484780\pi\)
\(762\) −1.30191e19 −2.40920
\(763\) −2.54712e18 −0.467347
\(764\) 1.88878e19 3.43618
\(765\) 1.31840e19 2.37819
\(766\) 5.28204e18 0.944746
\(767\) 3.31016e18 0.587056
\(768\) 1.97102e19 3.46611
\(769\) −3.57203e18 −0.622865 −0.311432 0.950268i \(-0.600809\pi\)
−0.311432 + 0.950268i \(0.600809\pi\)
\(770\) 9.14198e18 1.58070
\(771\) −1.09011e19 −1.86904
\(772\) −9.69781e18 −1.64877
\(773\) −3.36335e18 −0.567030 −0.283515 0.958968i \(-0.591501\pi\)
−0.283515 + 0.958968i \(0.591501\pi\)
\(774\) 3.38313e18 0.565591
\(775\) 1.95185e17 0.0323583
\(776\) −1.53970e19 −2.53125
\(777\) −5.95432e18 −0.970724
\(778\) −6.94754e18 −1.12322
\(779\) −4.97415e17 −0.0797490
\(780\) −5.06668e19 −8.05580
\(781\) −4.78834e18 −0.755011
\(782\) −2.10220e18 −0.328722
\(783\) 9.61547e18 1.49114
\(784\) −7.21259e18 −1.10927
\(785\) 5.52630e18 0.842911
\(786\) 2.00449e19 3.03219
\(787\) 1.14381e19 1.71601 0.858005 0.513641i \(-0.171704\pi\)
0.858005 + 0.513641i \(0.171704\pi\)
\(788\) 1.05323e19 1.56712
\(789\) −1.93485e19 −2.85527
\(790\) −1.58250e19 −2.31615
\(791\) −5.47510e18 −0.794776
\(792\) 5.37487e19 7.73846
\(793\) 9.43859e17 0.134782
\(794\) 9.33124e18 1.32162
\(795\) −6.31576e17 −0.0887236
\(796\) 7.38784e18 1.02940
\(797\) −6.36200e18 −0.879255 −0.439627 0.898180i \(-0.644889\pi\)
−0.439627 + 0.898180i \(0.644889\pi\)
\(798\) −4.79144e18 −0.656822
\(799\) −6.66253e18 −0.905910
\(800\) −8.80499e17 −0.118753
\(801\) 4.02609e17 0.0538607
\(802\) 4.63061e18 0.614476
\(803\) −3.56393e18 −0.469114
\(804\) −5.03076e19 −6.56855
\(805\) 1.03752e18 0.134377
\(806\) −6.46522e18 −0.830626
\(807\) 1.67880e18 0.213954
\(808\) 2.89840e19 3.66425
\(809\) 5.78945e18 0.726060 0.363030 0.931778i \(-0.381742\pi\)
0.363030 + 0.931778i \(0.381742\pi\)
\(810\) −4.56939e19 −5.68467
\(811\) −4.83603e18 −0.596833 −0.298417 0.954436i \(-0.596459\pi\)
−0.298417 + 0.954436i \(0.596459\pi\)
\(812\) −5.63004e18 −0.689283
\(813\) 1.23103e19 1.49513
\(814\) 1.72559e19 2.07912
\(815\) 6.43820e18 0.769556
\(816\) −2.44990e19 −2.90511
\(817\) 3.33528e17 0.0392364
\(818\) 8.52476e17 0.0994915
\(819\) 2.41559e19 2.79690
\(820\) 5.16123e18 0.592875
\(821\) −9.30560e18 −1.06051 −0.530254 0.847839i \(-0.677903\pi\)
−0.530254 + 0.847839i \(0.677903\pi\)
\(822\) 4.98314e19 5.63425
\(823\) −6.35671e18 −0.713072 −0.356536 0.934282i \(-0.616042\pi\)
−0.356536 + 0.934282i \(0.616042\pi\)
\(824\) −3.33664e19 −3.71349
\(825\) 2.94019e18 0.324657
\(826\) −3.24808e18 −0.355841
\(827\) 3.51042e18 0.381569 0.190785 0.981632i \(-0.438897\pi\)
0.190785 + 0.981632i \(0.438897\pi\)
\(828\) 1.10425e19 1.19089
\(829\) 1.30969e19 1.40140 0.700701 0.713455i \(-0.252871\pi\)
0.700701 + 0.713455i \(0.252871\pi\)
\(830\) 2.47976e19 2.63270
\(831\) 1.17372e19 1.23640
\(832\) −1.12679e18 −0.117772
\(833\) −5.33574e18 −0.553353
\(834\) −1.12160e19 −1.15414
\(835\) 9.01294e18 0.920247
\(836\) 9.59234e18 0.971815
\(837\) −7.48467e18 −0.752414
\(838\) 2.72202e18 0.271522
\(839\) −1.05635e19 −1.04558 −0.522789 0.852462i \(-0.675108\pi\)
−0.522789 + 0.852462i \(0.675108\pi\)
\(840\) 2.74636e19 2.69738
\(841\) −7.61219e18 −0.741884
\(842\) −1.26140e19 −1.21990
\(843\) −3.64270e19 −3.49578
\(844\) 2.61551e19 2.49075
\(845\) 2.52236e19 2.38362
\(846\) 5.06619e19 4.75088
\(847\) 5.61339e18 0.522376
\(848\) 8.43615e17 0.0779060
\(849\) −3.66941e19 −3.36276
\(850\) −2.18805e18 −0.198991
\(851\) 1.95837e18 0.176748
\(852\) −2.60403e19 −2.33232
\(853\) 6.70695e18 0.596151 0.298076 0.954542i \(-0.403655\pi\)
0.298076 + 0.954542i \(0.403655\pi\)
\(854\) −9.26157e17 −0.0816974
\(855\) −9.88329e18 −0.865211
\(856\) −2.77741e19 −2.41302
\(857\) 8.12179e18 0.700288 0.350144 0.936696i \(-0.386133\pi\)
0.350144 + 0.936696i \(0.386133\pi\)
\(858\) −9.73894e19 −8.33383
\(859\) 1.31202e19 1.11426 0.557129 0.830426i \(-0.311903\pi\)
0.557129 + 0.830426i \(0.311903\pi\)
\(860\) −3.46072e18 −0.291693
\(861\) −3.42323e18 −0.286362
\(862\) 1.61304e19 1.33921
\(863\) 2.07543e19 1.71016 0.855082 0.518493i \(-0.173507\pi\)
0.855082 + 0.518493i \(0.173507\pi\)
\(864\) 3.37640e19 2.76131
\(865\) −5.01470e18 −0.407043
\(866\) −1.15242e19 −0.928420
\(867\) 5.46059e18 0.436632
\(868\) 4.38241e18 0.347804
\(869\) −2.10128e19 −1.65522
\(870\) −2.33872e19 −1.82853
\(871\) 3.61952e19 2.80888
\(872\) 2.21754e19 1.70811
\(873\) 3.81328e19 2.91545
\(874\) 1.57590e18 0.119593
\(875\) −7.47551e18 −0.563104
\(876\) −1.93816e19 −1.44915
\(877\) 3.78205e17 0.0280692 0.0140346 0.999902i \(-0.495533\pi\)
0.0140346 + 0.999902i \(0.495533\pi\)
\(878\) −3.23388e19 −2.38237
\(879\) 1.88785e19 1.38051
\(880\) −3.50411e19 −2.54355
\(881\) −3.37859e18 −0.243440 −0.121720 0.992564i \(-0.538841\pi\)
−0.121720 + 0.992564i \(0.538841\pi\)
\(882\) 4.05730e19 2.90196
\(883\) −2.54109e18 −0.180416 −0.0902082 0.995923i \(-0.528753\pi\)
−0.0902082 + 0.995923i \(0.528753\pi\)
\(884\) 5.00663e19 3.52863
\(885\) −9.32064e18 −0.652101
\(886\) −2.96044e18 −0.205607
\(887\) 3.03810e18 0.209459 0.104729 0.994501i \(-0.466602\pi\)
0.104729 + 0.994501i \(0.466602\pi\)
\(888\) 5.18389e19 3.54790
\(889\) −6.34931e18 −0.431385
\(890\) −5.96181e17 −0.0402108
\(891\) −6.06735e19 −4.06250
\(892\) −4.02578e19 −2.67595
\(893\) 4.99454e18 0.329580
\(894\) −6.01187e19 −3.93836
\(895\) 6.97637e18 0.453711
\(896\) 9.95440e18 0.642707
\(897\) −1.10527e19 −0.708465
\(898\) −6.49852e18 −0.413541
\(899\) −2.06154e18 −0.130243
\(900\) 1.14935e19 0.720901
\(901\) 6.24091e17 0.0388630
\(902\) 9.92069e18 0.613337
\(903\) 2.29535e18 0.140890
\(904\) 4.76667e19 2.90483
\(905\) −9.49308e17 −0.0574369
\(906\) 4.66159e19 2.80028
\(907\) −1.76653e19 −1.05360 −0.526798 0.849991i \(-0.676607\pi\)
−0.526798 + 0.849991i \(0.676607\pi\)
\(908\) 8.28049e18 0.490341
\(909\) −7.17828e19 −4.22042
\(910\) −3.57699e19 −2.08809
\(911\) −2.96918e19 −1.72094 −0.860471 0.509499i \(-0.829831\pi\)
−0.860471 + 0.509499i \(0.829831\pi\)
\(912\) 1.83656e19 1.05691
\(913\) 3.29269e19 1.88144
\(914\) 1.32414e19 0.751250
\(915\) −2.65769e18 −0.149715
\(916\) 3.97923e19 2.22576
\(917\) 9.77575e18 0.542937
\(918\) 8.39039e19 4.62706
\(919\) −2.40974e19 −1.31953 −0.659766 0.751471i \(-0.729344\pi\)
−0.659766 + 0.751471i \(0.729344\pi\)
\(920\) −9.03276e18 −0.491134
\(921\) 4.56981e19 2.46723
\(922\) −6.52125e19 −3.49607
\(923\) 1.87354e19 0.997359
\(924\) 6.60149e19 3.48959
\(925\) 2.03835e18 0.106994
\(926\) −2.88128e19 −1.50181
\(927\) 8.26363e19 4.27713
\(928\) 9.29978e18 0.477981
\(929\) −1.44715e19 −0.738605 −0.369302 0.929309i \(-0.620403\pi\)
−0.369302 + 0.929309i \(0.620403\pi\)
\(930\) 1.82046e19 0.922658
\(931\) 3.99992e18 0.201316
\(932\) 4.19725e19 2.09779
\(933\) 3.46470e19 1.71963
\(934\) 5.85146e19 2.88409
\(935\) −2.59228e19 −1.26884
\(936\) −2.10303e20 −10.2224
\(937\) −1.83486e19 −0.885718 −0.442859 0.896591i \(-0.646036\pi\)
−0.442859 + 0.896591i \(0.646036\pi\)
\(938\) −3.55163e19 −1.70259
\(939\) 3.97054e19 1.89027
\(940\) −5.18238e19 −2.45018
\(941\) −4.09261e19 −1.92162 −0.960810 0.277209i \(-0.910590\pi\)
−0.960810 + 0.277209i \(0.910590\pi\)
\(942\) 5.77675e19 2.69372
\(943\) 1.12590e18 0.0521403
\(944\) 1.24499e19 0.572594
\(945\) −4.14101e19 −1.89147
\(946\) −6.65204e18 −0.301761
\(947\) 1.28440e19 0.578664 0.289332 0.957229i \(-0.406567\pi\)
0.289332 + 0.957229i \(0.406567\pi\)
\(948\) −1.14273e20 −5.11317
\(949\) 1.39446e19 0.619693
\(950\) 1.64026e18 0.0723951
\(951\) 3.38557e19 1.48408
\(952\) −2.71381e19 −1.18152
\(953\) 2.24332e18 0.0970033 0.0485017 0.998823i \(-0.484555\pi\)
0.0485017 + 0.998823i \(0.484555\pi\)
\(954\) −4.74560e18 −0.203810
\(955\) 3.82645e19 1.63220
\(956\) −2.17917e19 −0.923241
\(957\) −3.10541e19 −1.30675
\(958\) −1.23031e19 −0.514208
\(959\) 2.43024e19 1.00886
\(960\) 3.17278e18 0.130821
\(961\) −2.28129e19 −0.934281
\(962\) −6.75174e19 −2.74649
\(963\) 6.87862e19 2.77927
\(964\) 4.05389e19 1.62694
\(965\) −1.96466e19 −0.783177
\(966\) 1.08454e19 0.429433
\(967\) −3.11794e19 −1.22630 −0.613148 0.789968i \(-0.710097\pi\)
−0.613148 + 0.789968i \(0.710097\pi\)
\(968\) −4.88707e19 −1.90923
\(969\) 1.35865e19 0.527234
\(970\) −5.64669e19 −2.17659
\(971\) −1.54433e19 −0.591310 −0.295655 0.955295i \(-0.595538\pi\)
−0.295655 + 0.955295i \(0.595538\pi\)
\(972\) −1.57551e20 −5.99226
\(973\) −5.46998e18 −0.206658
\(974\) −7.22038e19 −2.70974
\(975\) −1.15041e19 −0.428867
\(976\) 3.54995e18 0.131461
\(977\) 2.59027e19 0.952863 0.476431 0.879212i \(-0.341930\pi\)
0.476431 + 0.879212i \(0.341930\pi\)
\(978\) 6.72998e19 2.45930
\(979\) −7.91625e17 −0.0287364
\(980\) −4.15036e19 −1.49664
\(981\) −5.49204e19 −1.96736
\(982\) 9.80374e19 3.48873
\(983\) 2.25386e19 0.796762 0.398381 0.917220i \(-0.369572\pi\)
0.398381 + 0.917220i \(0.369572\pi\)
\(984\) 2.98029e19 1.04662
\(985\) 2.13371e19 0.744390
\(986\) 2.31100e19 0.800941
\(987\) 3.43726e19 1.18345
\(988\) −3.75320e19 −1.28375
\(989\) −7.54940e17 −0.0256529
\(990\) 1.97117e20 6.65420
\(991\) 1.01248e17 0.00339553 0.00169776 0.999999i \(-0.499460\pi\)
0.00169776 + 0.999999i \(0.499460\pi\)
\(992\) −7.23893e18 −0.241184
\(993\) −5.90763e19 −1.95543
\(994\) −1.83840e19 −0.604545
\(995\) 1.49669e19 0.488969
\(996\) 1.79065e20 5.81199
\(997\) 3.91495e18 0.126243 0.0631216 0.998006i \(-0.479894\pi\)
0.0631216 + 0.998006i \(0.479894\pi\)
\(998\) 1.01605e20 3.25510
\(999\) −7.81636e19 −2.48788
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 23.14.a.b.1.1 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.14.a.b.1.1 14 1.1 even 1 trivial