Properties

Label 5.12.b.a.4.2
Level $5$
Weight $12$
Character 5.4
Analytic conductor $3.842$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5,12,Mod(4,5)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5.4");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 5.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.84171590280\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 142x^{2} - 2144x + 28656 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{5}\cdot 3^{2}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.2
Root \(-10.8434 - 10.0894i\) of defining polynomial
Character \(\chi\) \(=\) 5.4
Dual form 5.12.b.a.4.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-27.1071i q^{2} +524.040i q^{3} +1313.20 q^{4} +(6581.01 - 2349.13i) q^{5} +14205.2 q^{6} +66589.5i q^{7} -91112.6i q^{8} -97470.8 q^{9} +O(q^{10})\) \(q-27.1071i q^{2} +524.040i q^{3} +1313.20 q^{4} +(6581.01 - 2349.13i) q^{5} +14205.2 q^{6} +66589.5i q^{7} -91112.6i q^{8} -97470.8 q^{9} +(-63678.2 - 178392. i) q^{10} -374453. q^{11} +688170. i q^{12} -1.12751e6i q^{13} +1.80505e6 q^{14} +(1.23104e6 + 3.44871e6i) q^{15} +219635. q^{16} -5.82894e6i q^{17} +2.64216e6i q^{18} -6.03360e6 q^{19} +(8.64220e6 - 3.08488e6i) q^{20} -3.48955e7 q^{21} +1.01503e7i q^{22} -7.51593e6i q^{23} +4.77466e7 q^{24} +(3.77913e7 - 3.09193e7i) q^{25} -3.05636e7 q^{26} +4.17535e7i q^{27} +8.74454e7i q^{28} +4.87039e7 q^{29} +(9.34848e7 - 3.33699e7i) q^{30} -2.71596e8 q^{31} -1.92552e8i q^{32} -1.96228e8i q^{33} -1.58006e8 q^{34} +(1.56427e8 + 4.38226e8i) q^{35} -1.27999e8 q^{36} +542545. i q^{37} +1.63554e8i q^{38} +5.90860e8 q^{39} +(-2.14035e8 - 5.99613e8i) q^{40} +8.20963e8 q^{41} +9.45918e8i q^{42} -6.03499e8i q^{43} -4.91732e8 q^{44} +(-6.41456e8 + 2.28971e8i) q^{45} -2.03735e8 q^{46} -4.69204e8i q^{47} +1.15098e8i q^{48} -2.45683e9 q^{49} +(-8.38134e8 - 1.02441e9i) q^{50} +3.05460e9 q^{51} -1.48065e9i q^{52} +3.82491e9i q^{53} +1.13182e9 q^{54} +(-2.46428e9 + 8.79637e8i) q^{55} +6.06714e9 q^{56} -3.16185e9i q^{57} -1.32022e9i q^{58} +2.19696e9 q^{59} +(1.61660e9 + 4.52886e9i) q^{60} -7.28175e9 q^{61} +7.36220e9i q^{62} -6.49053e9i q^{63} -4.76973e9 q^{64} +(-2.64866e9 - 7.42015e9i) q^{65} -5.31918e9 q^{66} +2.11343e9i q^{67} -7.65458e9i q^{68} +3.93865e9 q^{69} +(1.18791e10 - 4.24029e9i) q^{70} -4.86982e9 q^{71} +8.88082e9i q^{72} +1.92542e10i q^{73} +1.47068e7 q^{74} +(1.62029e10 + 1.98042e10i) q^{75} -7.92334e9 q^{76} -2.49346e10i q^{77} -1.60165e10i q^{78} +4.54858e10 q^{79} +(1.44542e9 - 5.15952e8i) q^{80} -3.91472e10 q^{81} -2.22540e10i q^{82} +3.61471e10i q^{83} -4.58249e10 q^{84} +(-1.36929e10 - 3.83603e10i) q^{85} -1.63591e10 q^{86} +2.55228e10i q^{87} +3.41174e10i q^{88} -3.43834e9 q^{89} +(6.20676e9 + 1.73881e10i) q^{90} +7.50802e10 q^{91} -9.86994e9i q^{92} -1.42327e11i q^{93} -1.27188e10 q^{94} +(-3.97072e10 + 1.41737e10i) q^{95} +1.00905e11 q^{96} +1.57518e11i q^{97} +6.65976e10i q^{98} +3.64982e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 72 q^{4} - 300 q^{5} - 1752 q^{6} + 25452 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 72 q^{4} - 300 q^{5} - 1752 q^{6} + 25452 q^{9} + 91400 q^{10} - 326352 q^{11} + 1080696 q^{14} + 3433200 q^{15} - 9834976 q^{16} + 15460880 q^{19} + 35447400 q^{20} - 81019872 q^{21} + 74415840 q^{24} + 159152500 q^{25} - 325970832 q^{26} + 216242520 q^{29} + 389993400 q^{30} - 684043072 q^{31} + 265782016 q^{34} + 394292400 q^{35} - 553353336 q^{36} + 5997024 q^{39} - 275204000 q^{40} + 1012873368 q^{41} - 1553573664 q^{44} - 2766384900 q^{45} + 5241789688 q^{46} - 1900646372 q^{49} - 4621170000 q^{50} + 8691953088 q^{51} - 6403356720 q^{54} - 7772763600 q^{55} + 10366738080 q^{56} + 3200971440 q^{59} + 1922954400 q^{60} - 2310471352 q^{61} - 5401150592 q^{64} + 3229723200 q^{65} - 17010985824 q^{66} + 32956101984 q^{69} + 40783573800 q^{70} - 60335466912 q^{71} - 5525992944 q^{74} + 19332540000 q^{75} - 52987638240 q^{76} + 74637768320 q^{79} + 72046927200 q^{80} - 77727716316 q^{81} - 76499865504 q^{84} - 46117585600 q^{85} + 39045421128 q^{86} + 118272499560 q^{89} + 36519766200 q^{90} + 51565095648 q^{91} - 266098749224 q^{94} - 264706278000 q^{95} + 313591828608 q^{96} + 119560366224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 27.1071i 0.598989i −0.954098 0.299495i \(-0.903182\pi\)
0.954098 0.299495i \(-0.0968180\pi\)
\(3\) 524.040i 1.24508i 0.782588 + 0.622540i \(0.213899\pi\)
−0.782588 + 0.622540i \(0.786101\pi\)
\(4\) 1313.20 0.641212
\(5\) 6581.01 2349.13i 0.941798 0.336180i
\(6\) 14205.2 0.745790
\(7\) 66589.5i 1.49750i 0.662854 + 0.748749i \(0.269345\pi\)
−0.662854 + 0.748749i \(0.730655\pi\)
\(8\) 91112.6i 0.983068i
\(9\) −97470.8 −0.550225
\(10\) −63678.2 178392.i −0.201368 0.564127i
\(11\) −374453. −0.701031 −0.350515 0.936557i \(-0.613994\pi\)
−0.350515 + 0.936557i \(0.613994\pi\)
\(12\) 688170.i 0.798361i
\(13\) 1.12751e6i 0.842232i −0.907007 0.421116i \(-0.861639\pi\)
0.907007 0.421116i \(-0.138361\pi\)
\(14\) 1.80505e6 0.896985
\(15\) 1.23104e6 + 3.44871e6i 0.418571 + 1.17261i
\(16\) 219635. 0.0523651
\(17\) 5.82894e6i 0.995681i −0.867269 0.497841i \(-0.834126\pi\)
0.867269 0.497841i \(-0.165874\pi\)
\(18\) 2.64216e6i 0.329579i
\(19\) −6.03360e6 −0.559026 −0.279513 0.960142i \(-0.590173\pi\)
−0.279513 + 0.960142i \(0.590173\pi\)
\(20\) 8.64220e6 3.08488e6i 0.603892 0.215563i
\(21\) −3.48955e7 −1.86451
\(22\) 1.01503e7i 0.419910i
\(23\) 7.51593e6i 0.243489i −0.992561 0.121745i \(-0.961151\pi\)
0.992561 0.121745i \(-0.0388489\pi\)
\(24\) 4.77466e7 1.22400
\(25\) 3.77913e7 3.09193e7i 0.773966 0.633227i
\(26\) −3.05636e7 −0.504488
\(27\) 4.17535e7i 0.560005i
\(28\) 8.74454e7i 0.960214i
\(29\) 4.87039e7 0.440935 0.220467 0.975394i \(-0.429242\pi\)
0.220467 + 0.975394i \(0.429242\pi\)
\(30\) 9.34848e7 3.33699e7i 0.702383 0.250719i
\(31\) −2.71596e8 −1.70386 −0.851932 0.523653i \(-0.824569\pi\)
−0.851932 + 0.523653i \(0.824569\pi\)
\(32\) 1.92552e8i 1.01443i
\(33\) 1.96228e8i 0.872840i
\(34\) −1.58006e8 −0.596402
\(35\) 1.56427e8 + 4.38226e8i 0.503429 + 1.41034i
\(36\) −1.27999e8 −0.352811
\(37\) 542545.i 0.00128625i 1.00000 0.000643126i \(0.000204713\pi\)
−1.00000 0.000643126i \(0.999795\pi\)
\(38\) 1.63554e8i 0.334850i
\(39\) 5.90860e8 1.04865
\(40\) −2.14035e8 5.99613e8i −0.330488 0.925851i
\(41\) 8.20963e8 1.10666 0.553328 0.832964i \(-0.313358\pi\)
0.553328 + 0.832964i \(0.313358\pi\)
\(42\) 9.45918e8i 1.11682i
\(43\) 6.03499e8i 0.626037i −0.949747 0.313018i \(-0.898660\pi\)
0.949747 0.313018i \(-0.101340\pi\)
\(44\) −4.91732e8 −0.449509
\(45\) −6.41456e8 + 2.28971e8i −0.518201 + 0.184975i
\(46\) −2.03735e8 −0.145847
\(47\) 4.69204e8i 0.298417i −0.988806 0.149208i \(-0.952327\pi\)
0.988806 0.149208i \(-0.0476725\pi\)
\(48\) 1.15098e8i 0.0651988i
\(49\) −2.45683e9 −1.24250
\(50\) −8.38134e8 1.02441e9i −0.379296 0.463597i
\(51\) 3.05460e9 1.23970
\(52\) 1.48065e9i 0.540049i
\(53\) 3.82491e9i 1.25633i 0.778079 + 0.628166i \(0.216194\pi\)
−0.778079 + 0.628166i \(0.783806\pi\)
\(54\) 1.13182e9 0.335437
\(55\) −2.46428e9 + 8.79637e8i −0.660229 + 0.235672i
\(56\) 6.06714e9 1.47214
\(57\) 3.16185e9i 0.696032i
\(58\) 1.32022e9i 0.264115i
\(59\) 2.19696e9 0.400069 0.200035 0.979789i \(-0.435895\pi\)
0.200035 + 0.979789i \(0.435895\pi\)
\(60\) 1.61660e9 + 4.52886e9i 0.268393 + 0.751894i
\(61\) −7.28175e9 −1.10388 −0.551940 0.833884i \(-0.686112\pi\)
−0.551940 + 0.833884i \(0.686112\pi\)
\(62\) 7.36220e9i 1.02060i
\(63\) 6.49053e9i 0.823962i
\(64\) −4.76973e9 −0.555270
\(65\) −2.64866e9 7.42015e9i −0.283141 0.793212i
\(66\) −5.31918e9 −0.522821
\(67\) 2.11343e9i 0.191239i 0.995418 + 0.0956197i \(0.0304833\pi\)
−0.995418 + 0.0956197i \(0.969517\pi\)
\(68\) 7.65458e9i 0.638443i
\(69\) 3.93865e9 0.303164
\(70\) 1.18791e10 4.24029e9i 0.844778 0.301548i
\(71\) −4.86982e9 −0.320326 −0.160163 0.987091i \(-0.551202\pi\)
−0.160163 + 0.987091i \(0.551202\pi\)
\(72\) 8.88082e9i 0.540909i
\(73\) 1.92542e10i 1.08705i 0.839393 + 0.543524i \(0.182910\pi\)
−0.839393 + 0.543524i \(0.817090\pi\)
\(74\) 1.47068e7 0.000770451
\(75\) 1.62029e10 + 1.98042e10i 0.788418 + 0.963650i
\(76\) −7.92334e9 −0.358454
\(77\) 2.49346e10i 1.04979i
\(78\) 1.60165e10i 0.628128i
\(79\) 4.54858e10 1.66313 0.831566 0.555426i \(-0.187445\pi\)
0.831566 + 0.555426i \(0.187445\pi\)
\(80\) 1.44542e9 5.15952e8i 0.0493174 0.0176041i
\(81\) −3.91472e10 −1.24748
\(82\) 2.22540e10i 0.662874i
\(83\) 3.61471e10i 1.00726i 0.863918 + 0.503632i \(0.168003\pi\)
−0.863918 + 0.503632i \(0.831997\pi\)
\(84\) −4.58249e10 −1.19554
\(85\) −1.36929e10 3.83603e10i −0.334728 0.937730i
\(86\) −1.63591e10 −0.374989
\(87\) 2.55228e10i 0.548999i
\(88\) 3.41174e10i 0.689161i
\(89\) −3.43834e9 −0.0652685 −0.0326342 0.999467i \(-0.510390\pi\)
−0.0326342 + 0.999467i \(0.510390\pi\)
\(90\) 6.20676e9 + 1.73881e10i 0.110798 + 0.310397i
\(91\) 7.50802e10 1.26124
\(92\) 9.86994e9i 0.156128i
\(93\) 1.42327e11i 2.12145i
\(94\) −1.27188e10 −0.178748
\(95\) −3.97072e10 + 1.41737e10i −0.526489 + 0.187933i
\(96\) 1.00905e11 1.26305
\(97\) 1.57518e11i 1.86246i 0.364436 + 0.931228i \(0.381262\pi\)
−0.364436 + 0.931228i \(0.618738\pi\)
\(98\) 6.65976e10i 0.744244i
\(99\) 3.64982e10 0.385725
\(100\) 4.96277e10 4.06033e10i 0.496277 0.406033i
\(101\) −3.14292e10 −0.297554 −0.148777 0.988871i \(-0.547534\pi\)
−0.148777 + 0.988871i \(0.547534\pi\)
\(102\) 8.28014e10i 0.742569i
\(103\) 3.42578e10i 0.291176i −0.989345 0.145588i \(-0.953493\pi\)
0.989345 0.145588i \(-0.0465074\pi\)
\(104\) −1.02730e11 −0.827971
\(105\) −2.29648e11 + 8.19741e10i −1.75599 + 0.626809i
\(106\) 1.03683e11 0.752529
\(107\) 2.10883e11i 1.45355i −0.686874 0.726776i \(-0.741018\pi\)
0.686874 0.726776i \(-0.258982\pi\)
\(108\) 5.48308e10i 0.359082i
\(109\) −1.44958e10 −0.0902394 −0.0451197 0.998982i \(-0.514367\pi\)
−0.0451197 + 0.998982i \(0.514367\pi\)
\(110\) 2.38444e10 + 6.67995e10i 0.141165 + 0.395470i
\(111\) −2.84315e8 −0.00160149
\(112\) 1.46254e10i 0.0784167i
\(113\) 2.14619e9i 0.0109581i 0.999985 + 0.00547906i \(0.00174405\pi\)
−0.999985 + 0.00547906i \(0.998256\pi\)
\(114\) −8.57087e10 −0.416916
\(115\) −1.76559e10 4.94624e10i −0.0818562 0.229318i
\(116\) 6.39580e10 0.282733
\(117\) 1.09899e11i 0.463417i
\(118\) 5.95532e10i 0.239637i
\(119\) 3.88146e11 1.49103
\(120\) 3.14221e11 1.12163e11i 1.15276 0.411484i
\(121\) −1.45097e11 −0.508556
\(122\) 1.97388e11i 0.661212i
\(123\) 4.30217e11i 1.37787i
\(124\) −3.56661e11 −1.09254
\(125\) 1.76072e11 2.92257e11i 0.516042 0.856563i
\(126\) −1.75940e11 −0.493544
\(127\) 2.28294e8i 0.000613160i −1.00000 0.000306580i \(-0.999902\pi\)
1.00000 0.000306580i \(-9.75875e-5\pi\)
\(128\) 2.65053e11i 0.681834i
\(129\) 3.16257e11 0.779466
\(130\) −2.01139e11 + 7.17977e10i −0.475125 + 0.169599i
\(131\) −5.23011e11 −1.18446 −0.592228 0.805771i \(-0.701751\pi\)
−0.592228 + 0.805771i \(0.701751\pi\)
\(132\) 2.57687e11i 0.559675i
\(133\) 4.01774e11i 0.837140i
\(134\) 5.72892e10 0.114550
\(135\) 9.80843e10 + 2.74780e11i 0.188263 + 0.527412i
\(136\) −5.31090e11 −0.978822
\(137\) 2.04327e11i 0.361712i 0.983510 + 0.180856i \(0.0578868\pi\)
−0.983510 + 0.180856i \(0.942113\pi\)
\(138\) 1.06766e11i 0.181592i
\(139\) 1.10282e11 0.180270 0.0901348 0.995930i \(-0.471270\pi\)
0.0901348 + 0.995930i \(0.471270\pi\)
\(140\) 2.05421e11 + 5.75480e11i 0.322805 + 0.904327i
\(141\) 2.45881e11 0.371553
\(142\) 1.32007e11i 0.191872i
\(143\) 4.22199e11i 0.590430i
\(144\) −2.14080e10 −0.0288126
\(145\) 3.20521e11 1.14412e11i 0.415272 0.148233i
\(146\) 5.21926e11 0.651130
\(147\) 1.28748e12i 1.54701i
\(148\) 7.12471e8i 0.000824761i
\(149\) 5.11067e11 0.570102 0.285051 0.958512i \(-0.407989\pi\)
0.285051 + 0.958512i \(0.407989\pi\)
\(150\) 5.36834e11 4.39215e11i 0.577216 0.472254i
\(151\) −3.26638e10 −0.0338605 −0.0169303 0.999857i \(-0.505389\pi\)
−0.0169303 + 0.999857i \(0.505389\pi\)
\(152\) 5.49737e11i 0.549560i
\(153\) 5.68151e11i 0.547849i
\(154\) −6.75906e11 −0.628814
\(155\) −1.78738e12 + 6.38015e11i −1.60469 + 0.572804i
\(156\) 7.75919e11 0.672405
\(157\) 1.29615e12i 1.08444i 0.840236 + 0.542221i \(0.182416\pi\)
−0.840236 + 0.542221i \(0.817584\pi\)
\(158\) 1.23299e12i 0.996198i
\(159\) −2.00441e12 −1.56423
\(160\) −4.52330e11 1.26719e12i −0.341032 0.955392i
\(161\) 5.00482e11 0.364625
\(162\) 1.06117e12i 0.747225i
\(163\) 9.53484e11i 0.649055i −0.945876 0.324527i \(-0.894795\pi\)
0.945876 0.324527i \(-0.105205\pi\)
\(164\) 1.07809e12 0.709601
\(165\) −4.60965e11 1.29138e12i −0.293431 0.822038i
\(166\) 9.79844e11 0.603340
\(167\) 2.16450e12i 1.28949i −0.764398 0.644745i \(-0.776964\pi\)
0.764398 0.644745i \(-0.223036\pi\)
\(168\) 3.17942e12i 1.83294i
\(169\) 5.20883e11 0.290645
\(170\) −1.03984e12 + 3.71176e11i −0.561690 + 0.200498i
\(171\) 5.88100e11 0.307590
\(172\) 7.92516e11i 0.401422i
\(173\) 3.76047e11i 0.184497i 0.995736 + 0.0922483i \(0.0294054\pi\)
−0.995736 + 0.0922483i \(0.970595\pi\)
\(174\) 6.91850e11 0.328845
\(175\) 2.05890e12 + 2.51650e12i 0.948256 + 1.15901i
\(176\) −8.22430e10 −0.0367096
\(177\) 1.15129e12i 0.498119i
\(178\) 9.32035e10i 0.0390951i
\(179\) −9.97885e11 −0.405872 −0.202936 0.979192i \(-0.565048\pi\)
−0.202936 + 0.979192i \(0.565048\pi\)
\(180\) −8.42362e11 + 3.00686e11i −0.332277 + 0.118608i
\(181\) 3.32751e12 1.27317 0.636587 0.771205i \(-0.280346\pi\)
0.636587 + 0.771205i \(0.280346\pi\)
\(182\) 2.03521e12i 0.755469i
\(183\) 3.81593e12i 1.37442i
\(184\) −6.84796e11 −0.239366
\(185\) 1.27451e9 + 3.57049e9i 0.000432412 + 0.00121139i
\(186\) −3.85809e12 −1.27072
\(187\) 2.18266e12i 0.698003i
\(188\) 6.16160e11i 0.191348i
\(189\) −2.78034e12 −0.838607
\(190\) 3.84209e11 + 1.07635e12i 0.112570 + 0.315361i
\(191\) −4.02856e12 −1.14674 −0.573372 0.819295i \(-0.694365\pi\)
−0.573372 + 0.819295i \(0.694365\pi\)
\(192\) 2.49953e12i 0.691356i
\(193\) 1.01858e12i 0.273798i 0.990585 + 0.136899i \(0.0437135\pi\)
−0.990585 + 0.136899i \(0.956286\pi\)
\(194\) 4.26987e12 1.11559
\(195\) 3.88846e12 1.38801e12i 0.987613 0.352534i
\(196\) −3.22631e12 −0.796706
\(197\) 4.56750e12i 1.09677i 0.836227 + 0.548384i \(0.184757\pi\)
−0.836227 + 0.548384i \(0.815243\pi\)
\(198\) 9.89362e11i 0.231045i
\(199\) 2.19872e12 0.499435 0.249717 0.968319i \(-0.419662\pi\)
0.249717 + 0.968319i \(0.419662\pi\)
\(200\) −2.81714e12 3.44327e12i −0.622505 0.760862i
\(201\) −1.10752e12 −0.238108
\(202\) 8.51955e11i 0.178231i
\(203\) 3.24316e12i 0.660299i
\(204\) 4.01130e12 0.794913
\(205\) 5.40277e12 1.92855e12i 1.04225 0.372035i
\(206\) −9.28632e11 −0.174411
\(207\) 7.32584e11i 0.133974i
\(208\) 2.47641e11i 0.0441036i
\(209\) 2.25930e12 0.391894
\(210\) 2.22208e12 + 6.22510e12i 0.375452 + 1.05182i
\(211\) 8.39469e11 0.138182 0.0690910 0.997610i \(-0.477990\pi\)
0.0690910 + 0.997610i \(0.477990\pi\)
\(212\) 5.02289e12i 0.805575i
\(213\) 2.55198e12i 0.398831i
\(214\) −5.71644e12 −0.870662
\(215\) −1.41770e12 3.97163e12i −0.210461 0.589600i
\(216\) 3.80427e12 0.550524
\(217\) 1.80855e13i 2.55153i
\(218\) 3.92940e11i 0.0540524i
\(219\) −1.00900e13 −1.35346
\(220\) −3.23609e12 + 1.15514e12i −0.423347 + 0.151116i
\(221\) −6.57218e12 −0.838595
\(222\) 7.70697e9i 0.000959274i
\(223\) 1.61958e13i 1.96665i 0.181867 + 0.983323i \(0.441786\pi\)
−0.181867 + 0.983323i \(0.558214\pi\)
\(224\) 1.28220e13 1.51911
\(225\) −3.68355e12 + 3.01373e12i −0.425856 + 0.348418i
\(226\) 5.81770e10 0.00656379
\(227\) 6.08481e11i 0.0670046i 0.999439 + 0.0335023i \(0.0106661\pi\)
−0.999439 + 0.0335023i \(0.989334\pi\)
\(228\) 4.15215e12i 0.446304i
\(229\) −1.59740e13 −1.67617 −0.838083 0.545542i \(-0.816324\pi\)
−0.838083 + 0.545542i \(0.816324\pi\)
\(230\) −1.34079e12 + 4.78601e11i −0.137359 + 0.0490309i
\(231\) 1.30667e13 1.30708
\(232\) 4.43754e12i 0.433469i
\(233\) 1.09497e13i 1.04459i −0.852764 0.522296i \(-0.825076\pi\)
0.852764 0.522296i \(-0.174924\pi\)
\(234\) 2.97905e12 0.277582
\(235\) −1.10222e12 3.08784e12i −0.100322 0.281048i
\(236\) 2.88505e12 0.256529
\(237\) 2.38364e13i 2.07073i
\(238\) 1.05215e13i 0.893111i
\(239\) 2.11532e13 1.75464 0.877321 0.479905i \(-0.159329\pi\)
0.877321 + 0.479905i \(0.159329\pi\)
\(240\) 2.70379e11 + 7.57459e11i 0.0219185 + 0.0614041i
\(241\) 1.41468e13 1.12089 0.560447 0.828190i \(-0.310629\pi\)
0.560447 + 0.828190i \(0.310629\pi\)
\(242\) 3.93317e12i 0.304619i
\(243\) 1.31182e13i 0.993204i
\(244\) −9.56242e12 −0.707821
\(245\) −1.61684e13 + 5.77141e12i −1.17018 + 0.417704i
\(246\) 1.16620e13 0.825332
\(247\) 6.80294e12i 0.470829i
\(248\) 2.47459e13i 1.67501i
\(249\) −1.89425e13 −1.25413
\(250\) −7.92225e12 4.77280e12i −0.513072 0.309103i
\(251\) −1.64508e12 −0.104227 −0.0521136 0.998641i \(-0.516596\pi\)
−0.0521136 + 0.998641i \(0.516596\pi\)
\(252\) 8.52338e12i 0.528334i
\(253\) 2.81436e12i 0.170693i
\(254\) −6.18840e9 −0.000367276
\(255\) 2.01023e13 7.17564e12i 1.16755 0.416763i
\(256\) −1.69533e13 −0.963681
\(257\) 3.16010e13i 1.75820i −0.476635 0.879101i \(-0.658144\pi\)
0.476635 0.879101i \(-0.341856\pi\)
\(258\) 8.57284e12i 0.466892i
\(259\) −3.61278e10 −0.00192616
\(260\) −3.47823e12 9.74416e12i −0.181554 0.508617i
\(261\) −4.74720e12 −0.242614
\(262\) 1.41773e13i 0.709476i
\(263\) 1.50443e12i 0.0737250i −0.999320 0.0368625i \(-0.988264\pi\)
0.999320 0.0368625i \(-0.0117364\pi\)
\(264\) −1.78789e13 −0.858061
\(265\) 8.98521e12 + 2.51718e13i 0.422353 + 1.18321i
\(266\) −1.08910e13 −0.501438
\(267\) 1.80183e12i 0.0812645i
\(268\) 2.77537e12i 0.122625i
\(269\) 3.90666e13 1.69110 0.845548 0.533900i \(-0.179274\pi\)
0.845548 + 0.533900i \(0.179274\pi\)
\(270\) 7.44851e12 2.65879e12i 0.315914 0.112767i
\(271\) −4.54729e12 −0.188982 −0.0944912 0.995526i \(-0.530122\pi\)
−0.0944912 + 0.995526i \(0.530122\pi\)
\(272\) 1.28024e12i 0.0521390i
\(273\) 3.93450e13i 1.57035i
\(274\) 5.53873e12 0.216662
\(275\) −1.41511e13 + 1.15778e13i −0.542574 + 0.443911i
\(276\) 5.17224e12 0.194392
\(277\) 2.22049e13i 0.818105i −0.912511 0.409053i \(-0.865859\pi\)
0.912511 0.409053i \(-0.134141\pi\)
\(278\) 2.98943e12i 0.107980i
\(279\) 2.64727e13 0.937509
\(280\) 3.99279e13 1.42525e13i 1.38646 0.494905i
\(281\) −2.26709e13 −0.771941 −0.385970 0.922511i \(-0.626133\pi\)
−0.385970 + 0.922511i \(0.626133\pi\)
\(282\) 6.66515e12i 0.222556i
\(283\) 2.94259e13i 0.963617i −0.876276 0.481809i \(-0.839980\pi\)
0.876276 0.481809i \(-0.160020\pi\)
\(284\) −6.39505e12 −0.205397
\(285\) −7.42758e12 2.08082e13i −0.233992 0.655521i
\(286\) 1.14446e13 0.353661
\(287\) 5.46675e13i 1.65721i
\(288\) 1.87682e13i 0.558168i
\(289\) 2.95383e11 0.00861880
\(290\) −3.10137e12 8.68840e12i −0.0887902 0.248743i
\(291\) −8.25458e13 −2.31891
\(292\) 2.52846e13i 0.697029i
\(293\) 4.02146e13i 1.08796i −0.839099 0.543979i \(-0.816917\pi\)
0.839099 0.543979i \(-0.183083\pi\)
\(294\) −3.48998e13 −0.926644
\(295\) 1.44582e13 5.16093e12i 0.376785 0.134495i
\(296\) 4.94327e10 0.00126447
\(297\) 1.56347e13i 0.392581i
\(298\) 1.38536e13i 0.341485i
\(299\) −8.47428e12 −0.205074
\(300\) 2.12777e13 + 2.60069e13i 0.505543 + 0.617904i
\(301\) 4.01866e13 0.937489
\(302\) 8.85423e11i 0.0202821i
\(303\) 1.64701e13i 0.370478i
\(304\) −1.32519e12 −0.0292735
\(305\) −4.79213e13 + 1.71058e13i −1.03963 + 0.371102i
\(306\) 1.54010e13 0.328156
\(307\) 1.17567e13i 0.246050i 0.992404 + 0.123025i \(0.0392595\pi\)
−0.992404 + 0.123025i \(0.960740\pi\)
\(308\) 3.27442e13i 0.673139i
\(309\) 1.79525e13 0.362537
\(310\) 1.72948e13 + 4.84508e13i 0.343104 + 0.961195i
\(311\) 9.66888e12 0.188449 0.0942245 0.995551i \(-0.469963\pi\)
0.0942245 + 0.995551i \(0.469963\pi\)
\(312\) 5.38348e13i 1.03089i
\(313\) 7.95938e13i 1.49756i 0.662817 + 0.748782i \(0.269361\pi\)
−0.662817 + 0.748782i \(0.730639\pi\)
\(314\) 3.51349e13 0.649569
\(315\) −1.52471e13 4.27142e13i −0.276999 0.776005i
\(316\) 5.97321e13 1.06642
\(317\) 3.01135e13i 0.528366i −0.964473 0.264183i \(-0.914898\pi\)
0.964473 0.264183i \(-0.0851023\pi\)
\(318\) 5.43338e13i 0.936959i
\(319\) −1.82373e13 −0.309109
\(320\) −3.13897e13 + 1.12047e13i −0.522952 + 0.186671i
\(321\) 1.10511e14 1.80979
\(322\) 1.35666e13i 0.218406i
\(323\) 3.51695e13i 0.556611i
\(324\) −5.14082e13 −0.799898
\(325\) −3.48618e13 4.26101e13i −0.533324 0.651859i
\(326\) −2.58462e13 −0.388777
\(327\) 7.59637e12i 0.112355i
\(328\) 7.48001e13i 1.08792i
\(329\) 3.12440e13 0.446879
\(330\) −3.50056e13 + 1.24954e13i −0.492392 + 0.175762i
\(331\) −9.09460e13 −1.25814 −0.629071 0.777348i \(-0.716564\pi\)
−0.629071 + 0.777348i \(0.716564\pi\)
\(332\) 4.74684e13i 0.645870i
\(333\) 5.28823e10i 0.000707729i
\(334\) −5.86735e13 −0.772390
\(335\) 4.96473e12 + 1.39085e13i 0.0642908 + 0.180109i
\(336\) −7.66429e12 −0.0976351
\(337\) 6.71550e13i 0.841616i 0.907150 + 0.420808i \(0.138253\pi\)
−0.907150 + 0.420808i \(0.861747\pi\)
\(338\) 1.41197e13i 0.174093i
\(339\) −1.12469e12 −0.0136437
\(340\) −1.79816e13 5.03749e13i −0.214632 0.601284i
\(341\) 1.01700e14 1.19446
\(342\) 1.59417e13i 0.184243i
\(343\) 3.19298e13i 0.363144i
\(344\) −5.49863e13 −0.615437
\(345\) 2.59203e13 9.25239e12i 0.285519 0.101918i
\(346\) 1.01936e13 0.110511
\(347\) 1.00178e14i 1.06895i −0.845183 0.534476i \(-0.820509\pi\)
0.845183 0.534476i \(-0.179491\pi\)
\(348\) 3.35166e13i 0.352025i
\(349\) −3.57336e12 −0.0369434 −0.0184717 0.999829i \(-0.505880\pi\)
−0.0184717 + 0.999829i \(0.505880\pi\)
\(350\) 6.82152e13 5.58109e13i 0.694236 0.567995i
\(351\) 4.70775e13 0.471655
\(352\) 7.21017e13i 0.711149i
\(353\) 4.27043e13i 0.414677i 0.978269 + 0.207339i \(0.0664802\pi\)
−0.978269 + 0.207339i \(0.933520\pi\)
\(354\) 3.12083e13 0.298368
\(355\) −3.20483e13 + 1.14398e13i −0.301682 + 0.107687i
\(356\) −4.51523e12 −0.0418509
\(357\) 2.03404e14i 1.85645i
\(358\) 2.70498e13i 0.243113i
\(359\) 1.34889e14 1.19387 0.596934 0.802290i \(-0.296385\pi\)
0.596934 + 0.802290i \(0.296385\pi\)
\(360\) 2.08622e13 + 5.84448e13i 0.181843 + 0.509427i
\(361\) −8.00859e13 −0.687490
\(362\) 9.01994e13i 0.762617i
\(363\) 7.60366e13i 0.633193i
\(364\) 9.85956e13 0.808723
\(365\) 4.52305e13 + 1.26712e14i 0.365444 + 1.02378i
\(366\) −1.03439e14 −0.823262
\(367\) 1.04526e14i 0.819519i −0.912193 0.409760i \(-0.865613\pi\)
0.912193 0.409760i \(-0.134387\pi\)
\(368\) 1.65076e12i 0.0127503i
\(369\) −8.00199e13 −0.608910
\(370\) 9.67859e10 3.45483e10i 0.000725609 0.000259010i
\(371\) −2.54699e14 −1.88135
\(372\) 1.86905e14i 1.36030i
\(373\) 2.42814e14i 1.74131i −0.491896 0.870654i \(-0.663696\pi\)
0.491896 0.870654i \(-0.336304\pi\)
\(374\) 5.91657e13 0.418096
\(375\) 1.53154e14 + 9.22686e13i 1.06649 + 0.642513i
\(376\) −4.27504e13 −0.293364
\(377\) 5.49141e13i 0.371369i
\(378\) 7.53672e13i 0.502316i
\(379\) −1.40487e14 −0.922827 −0.461413 0.887185i \(-0.652657\pi\)
−0.461413 + 0.887185i \(0.652657\pi\)
\(380\) −5.21436e13 + 1.86129e13i −0.337591 + 0.120505i
\(381\) 1.19635e11 0.000763434
\(382\) 1.09203e14i 0.686886i
\(383\) 2.17176e14i 1.34654i 0.739398 + 0.673269i \(0.235110\pi\)
−0.739398 + 0.673269i \(0.764890\pi\)
\(384\) 1.38899e14 0.848938
\(385\) −5.85745e13 1.64095e14i −0.352919 0.988692i
\(386\) 2.76108e13 0.164002
\(387\) 5.88235e13i 0.344461i
\(388\) 2.06853e14i 1.19423i
\(389\) −2.28055e14 −1.29812 −0.649062 0.760735i \(-0.724839\pi\)
−0.649062 + 0.760735i \(0.724839\pi\)
\(390\) −3.76249e13 1.05405e14i −0.211164 0.591569i
\(391\) −4.38099e13 −0.242438
\(392\) 2.23848e14i 1.22146i
\(393\) 2.74079e14i 1.47474i
\(394\) 1.23812e14 0.656951
\(395\) 2.99343e14 1.06852e14i 1.56633 0.559112i
\(396\) 4.79295e13 0.247332
\(397\) 7.68462e13i 0.391088i −0.980695 0.195544i \(-0.937353\pi\)
0.980695 0.195544i \(-0.0626473\pi\)
\(398\) 5.96011e13i 0.299156i
\(399\) 2.10546e14 1.04231
\(400\) 8.30031e12 6.79097e12i 0.0405289 0.0331590i
\(401\) 2.93708e14 1.41456 0.707282 0.706932i \(-0.249921\pi\)
0.707282 + 0.706932i \(0.249921\pi\)
\(402\) 3.00218e13i 0.142624i
\(403\) 3.06228e14i 1.43505i
\(404\) −4.12728e13 −0.190795
\(405\) −2.57628e14 + 9.19617e13i −1.17487 + 0.419377i
\(406\) 8.79129e13 0.395512
\(407\) 2.03157e11i 0.000901702i
\(408\) 2.78312e14i 1.21871i
\(409\) −1.31901e14 −0.569861 −0.284930 0.958548i \(-0.591970\pi\)
−0.284930 + 0.958548i \(0.591970\pi\)
\(410\) −5.22774e13 1.46454e14i −0.222845 0.624294i
\(411\) −1.07076e14 −0.450361
\(412\) 4.49875e13i 0.186705i
\(413\) 1.46294e14i 0.599103i
\(414\) 1.98583e13 0.0802489
\(415\) 8.49141e13 + 2.37884e14i 0.338622 + 0.948639i
\(416\) −2.17105e14 −0.854389
\(417\) 5.77921e13i 0.224450i
\(418\) 6.12431e13i 0.234740i
\(419\) −3.47913e14 −1.31612 −0.658058 0.752967i \(-0.728622\pi\)
−0.658058 + 0.752967i \(0.728622\pi\)
\(420\) −3.01574e14 + 1.07649e14i −1.12596 + 0.401918i
\(421\) 3.60019e14 1.32670 0.663351 0.748308i \(-0.269134\pi\)
0.663351 + 0.748308i \(0.269134\pi\)
\(422\) 2.27556e13i 0.0827695i
\(423\) 4.57337e13i 0.164197i
\(424\) 3.48498e14 1.23506
\(425\) −1.80227e14 2.20283e14i −0.630492 0.770624i
\(426\) −6.91768e13 −0.238896
\(427\) 4.84888e14i 1.65306i
\(428\) 2.76932e14i 0.932035i
\(429\) −2.21249e14 −0.735133
\(430\) −1.07660e14 + 3.84297e13i −0.353164 + 0.126064i
\(431\) 4.03045e14 1.30535 0.652677 0.757636i \(-0.273646\pi\)
0.652677 + 0.757636i \(0.273646\pi\)
\(432\) 9.17055e12i 0.0293248i
\(433\) 3.79440e14i 1.19801i 0.800746 + 0.599004i \(0.204437\pi\)
−0.800746 + 0.599004i \(0.795563\pi\)
\(434\) −4.90245e14 −1.52834
\(435\) 5.99563e13 + 1.67966e14i 0.184563 + 0.517047i
\(436\) −1.90359e13 −0.0578626
\(437\) 4.53481e13i 0.136117i
\(438\) 2.73510e14i 0.810710i
\(439\) 5.70014e14 1.66852 0.834259 0.551373i \(-0.185896\pi\)
0.834259 + 0.551373i \(0.185896\pi\)
\(440\) 8.01460e13 + 2.24527e14i 0.231682 + 0.649050i
\(441\) 2.39469e14 0.683655
\(442\) 1.78153e14i 0.502309i
\(443\) 6.54692e14i 1.82312i −0.411162 0.911562i \(-0.634877\pi\)
0.411162 0.911562i \(-0.365123\pi\)
\(444\) −3.73363e11 −0.00102689
\(445\) −2.26277e13 + 8.07709e12i −0.0614697 + 0.0219419i
\(446\) 4.39023e14 1.17800
\(447\) 2.67819e14i 0.709824i
\(448\) 3.17614e14i 0.831515i
\(449\) −2.16742e14 −0.560515 −0.280258 0.959925i \(-0.590420\pi\)
−0.280258 + 0.959925i \(0.590420\pi\)
\(450\) 8.16935e13 + 9.98505e13i 0.208698 + 0.255083i
\(451\) −3.07412e14 −0.775799
\(452\) 2.81838e12i 0.00702648i
\(453\) 1.71171e13i 0.0421591i
\(454\) 1.64942e13 0.0401350
\(455\) 4.94104e14 1.76373e14i 1.18783 0.424004i
\(456\) −2.88084e14 −0.684247
\(457\) 4.04825e14i 0.950011i 0.879983 + 0.475006i \(0.157554\pi\)
−0.879983 + 0.475006i \(0.842446\pi\)
\(458\) 4.33008e14i 1.00401i
\(459\) 2.43379e14 0.557587
\(460\) −2.31858e13 6.49542e13i −0.0524872 0.147041i
\(461\) −4.78062e14 −1.06937 −0.534686 0.845051i \(-0.679570\pi\)
−0.534686 + 0.845051i \(0.679570\pi\)
\(462\) 3.54202e14i 0.782924i
\(463\) 7.90859e13i 0.172744i 0.996263 + 0.0863721i \(0.0275274\pi\)
−0.996263 + 0.0863721i \(0.972473\pi\)
\(464\) 1.06971e13 0.0230896
\(465\) −3.34345e14 9.36658e14i −0.713188 1.99797i
\(466\) −2.96816e14 −0.625699
\(467\) 3.83987e14i 0.799970i 0.916522 + 0.399985i \(0.130985\pi\)
−0.916522 + 0.399985i \(0.869015\pi\)
\(468\) 1.44320e14i 0.297149i
\(469\) −1.40732e14 −0.286381
\(470\) −8.37024e13 + 2.98780e13i −0.168345 + 0.0600916i
\(471\) −6.79233e14 −1.35022
\(472\) 2.00170e14i 0.393295i
\(473\) 2.25982e14i 0.438871i
\(474\) 6.46136e14 1.24035
\(475\) −2.28018e14 + 1.86555e14i −0.432667 + 0.353990i
\(476\) 5.09714e14 0.956067
\(477\) 3.72817e14i 0.691266i
\(478\) 5.73404e14i 1.05101i
\(479\) −4.33999e14 −0.786400 −0.393200 0.919453i \(-0.628632\pi\)
−0.393200 + 0.919453i \(0.628632\pi\)
\(480\) 6.64058e14 2.37039e14i 1.18954 0.424613i
\(481\) 6.11724e11 0.00108332
\(482\) 3.83480e14i 0.671404i
\(483\) 2.62272e14i 0.453987i
\(484\) −1.90542e14 −0.326092
\(485\) 3.70030e14 + 1.03663e15i 0.626120 + 1.75406i
\(486\) −3.55596e14 −0.594918
\(487\) 3.35969e14i 0.555763i −0.960615 0.277881i \(-0.910368\pi\)
0.960615 0.277881i \(-0.0896322\pi\)
\(488\) 6.63460e14i 1.08519i
\(489\) 4.99663e14 0.808126
\(490\) 1.56446e14 + 4.38280e14i 0.250200 + 0.700928i
\(491\) −6.44062e14 −1.01854 −0.509272 0.860606i \(-0.670085\pi\)
−0.509272 + 0.860606i \(0.670085\pi\)
\(492\) 5.64962e14i 0.883510i
\(493\) 2.83892e14i 0.439031i
\(494\) 1.84408e14 0.282022
\(495\) 2.40195e14 8.57389e13i 0.363275 0.129673i
\(496\) −5.96522e13 −0.0892231
\(497\) 3.24278e14i 0.479687i
\(498\) 5.13477e14i 0.751207i
\(499\) 6.77869e14 0.980828 0.490414 0.871490i \(-0.336846\pi\)
0.490414 + 0.871490i \(0.336846\pi\)
\(500\) 2.31218e14 3.83792e14i 0.330892 0.549239i
\(501\) 1.13429e15 1.60552
\(502\) 4.45934e13i 0.0624310i
\(503\) 9.66327e14i 1.33814i −0.743202 0.669068i \(-0.766694\pi\)
0.743202 0.669068i \(-0.233306\pi\)
\(504\) −5.91369e14 −0.810010
\(505\) −2.06836e14 + 7.38311e13i −0.280235 + 0.100032i
\(506\) 7.62893e13 0.102243
\(507\) 2.72963e14i 0.361877i
\(508\) 2.99796e11i 0.000393166i
\(509\) −1.19572e13 −0.0155125 −0.00775626 0.999970i \(-0.502469\pi\)
−0.00775626 + 0.999970i \(0.502469\pi\)
\(510\) −1.94511e14 5.44917e14i −0.249637 0.699350i
\(511\) −1.28212e15 −1.62785
\(512\) 8.32750e13i 0.104600i
\(513\) 2.51924e14i 0.313057i
\(514\) −8.56614e14 −1.05314
\(515\) −8.04760e13 2.25451e14i −0.0978874 0.274229i
\(516\) 4.15310e14 0.499803
\(517\) 1.75695e14i 0.209199i
\(518\) 9.79321e11i 0.00115375i
\(519\) −1.97064e14 −0.229713
\(520\) −6.76070e14 + 2.41327e14i −0.779782 + 0.278347i
\(521\) 1.26458e15 1.44324 0.721618 0.692292i \(-0.243399\pi\)
0.721618 + 0.692292i \(0.243399\pi\)
\(522\) 1.28683e14i 0.145323i
\(523\) 7.08792e13i 0.0792062i −0.999215 0.0396031i \(-0.987391\pi\)
0.999215 0.0396031i \(-0.0126094\pi\)
\(524\) −6.86820e14 −0.759487
\(525\) −1.31875e15 + 1.07894e15i −1.44306 + 1.18066i
\(526\) −4.07807e13 −0.0441605
\(527\) 1.58312e15i 1.69650i
\(528\) 4.30986e13i 0.0457064i
\(529\) 8.96321e14 0.940713
\(530\) 6.82336e14 2.43563e14i 0.708730 0.252985i
\(531\) −2.14139e14 −0.220128
\(532\) 5.27611e14i 0.536784i
\(533\) 9.25643e14i 0.932060i
\(534\) −4.88424e13 −0.0486765
\(535\) −4.95391e14 1.38782e15i −0.488655 1.36895i
\(536\) 1.92560e14 0.188001
\(537\) 5.22932e14i 0.505343i
\(538\) 1.05898e15i 1.01295i
\(539\) 9.19966e14 0.871031
\(540\) 1.28805e14 + 3.60842e14i 0.120716 + 0.338183i
\(541\) 1.90242e15 1.76491 0.882453 0.470400i \(-0.155890\pi\)
0.882453 + 0.470400i \(0.155890\pi\)
\(542\) 1.23264e14i 0.113198i
\(543\) 1.74375e15i 1.58520i
\(544\) −1.12238e15 −1.01005
\(545\) −9.53970e13 + 3.40525e13i −0.0849873 + 0.0303367i
\(546\) 1.06653e15 0.940620
\(547\) 1.94867e13i 0.0170141i 0.999964 + 0.00850704i \(0.00270791\pi\)
−0.999964 + 0.00850704i \(0.997292\pi\)
\(548\) 2.68323e14i 0.231934i
\(549\) 7.09758e14 0.607383
\(550\) 3.13841e14 + 3.83595e14i 0.265898 + 0.324996i
\(551\) −2.93860e14 −0.246494
\(552\) 3.58861e14i 0.298031i
\(553\) 3.02888e15i 2.49054i
\(554\) −6.01910e14 −0.490036
\(555\) −1.87108e12 + 6.67893e11i −0.00150828 + 0.000538388i
\(556\) 1.44822e14 0.115591
\(557\) 1.67247e15i 1.32177i −0.750489 0.660883i \(-0.770182\pi\)
0.750489 0.660883i \(-0.229818\pi\)
\(558\) 7.17600e14i 0.561558i
\(559\) −6.80450e14 −0.527268
\(560\) 3.43569e13 + 9.62499e13i 0.0263621 + 0.0738527i
\(561\) −1.14380e15 −0.869070
\(562\) 6.14544e14i 0.462384i
\(563\) 7.96866e13i 0.0593730i −0.999559 0.0296865i \(-0.990549\pi\)
0.999559 0.0296865i \(-0.00945090\pi\)
\(564\) 3.22892e14 0.238244
\(565\) 5.04166e12 + 1.41241e13i 0.00368390 + 0.0103203i
\(566\) −7.97653e14 −0.577196
\(567\) 2.60679e15i 1.86810i
\(568\) 4.43702e14i 0.314902i
\(569\) −2.11263e15 −1.48493 −0.742467 0.669883i \(-0.766344\pi\)
−0.742467 + 0.669883i \(0.766344\pi\)
\(570\) −5.64050e14 + 2.01341e14i −0.392650 + 0.140159i
\(571\) 1.05231e15 0.725513 0.362756 0.931884i \(-0.381836\pi\)
0.362756 + 0.931884i \(0.381836\pi\)
\(572\) 5.54432e14i 0.378591i
\(573\) 2.11113e15i 1.42779i
\(574\) 1.48188e15 0.992653
\(575\) −2.32387e14 2.84037e14i −0.154184 0.188452i
\(576\) 4.64910e14 0.305524
\(577\) 1.13168e15i 0.736642i 0.929699 + 0.368321i \(0.120067\pi\)
−0.929699 + 0.368321i \(0.879933\pi\)
\(578\) 8.00698e12i 0.00516257i
\(579\) −5.33776e14 −0.340900
\(580\) 4.20909e14 1.50246e14i 0.266277 0.0950491i
\(581\) −2.40701e15 −1.50838
\(582\) 2.23758e15i 1.38900i
\(583\) 1.43225e15i 0.880727i
\(584\) 1.75430e15 1.06864
\(585\) 2.58167e14 + 7.23248e14i 0.155792 + 0.436446i
\(586\) −1.09010e15 −0.651675
\(587\) 8.84276e14i 0.523695i 0.965109 + 0.261847i \(0.0843317\pi\)
−0.965109 + 0.261847i \(0.915668\pi\)
\(588\) 1.69072e15i 0.991964i
\(589\) 1.63870e15 0.952503
\(590\) −1.39898e14 3.91921e14i −0.0805612 0.225690i
\(591\) −2.39355e15 −1.36556
\(592\) 1.19162e11i 6.73548e-5i
\(593\) 2.89873e15i 1.62333i 0.584123 + 0.811665i \(0.301438\pi\)
−0.584123 + 0.811665i \(0.698562\pi\)
\(594\) −4.23812e14 −0.235152
\(595\) 2.55439e15 9.11804e14i 1.40425 0.501254i
\(596\) 6.71134e14 0.365557
\(597\) 1.15222e15i 0.621836i
\(598\) 2.29714e14i 0.122837i
\(599\) 2.28284e15 1.20956 0.604781 0.796392i \(-0.293261\pi\)
0.604781 + 0.796392i \(0.293261\pi\)
\(600\) 1.80441e15 1.47629e15i 0.947334 0.775069i
\(601\) 1.28437e15 0.668159 0.334080 0.942545i \(-0.391575\pi\)
0.334080 + 0.942545i \(0.391575\pi\)
\(602\) 1.08935e15i 0.561545i
\(603\) 2.05998e14i 0.105225i
\(604\) −4.28942e13 −0.0217118
\(605\) −9.54885e14 + 3.40851e14i −0.478957 + 0.170966i
\(606\) −4.46458e14 −0.221912
\(607\) 5.70541e14i 0.281027i 0.990079 + 0.140514i \(0.0448754\pi\)
−0.990079 + 0.140514i \(0.955125\pi\)
\(608\) 1.16178e15i 0.567095i
\(609\) −1.69955e15 −0.822126
\(610\) 4.63689e14 + 1.29901e15i 0.222286 + 0.622728i
\(611\) −5.29032e14 −0.251336
\(612\) 7.46098e14i 0.351288i
\(613\) 3.14628e15i 1.46813i −0.679080 0.734065i \(-0.737621\pi\)
0.679080 0.734065i \(-0.262379\pi\)
\(614\) 3.18690e14 0.147381
\(615\) 1.01064e15 + 2.83127e15i 0.463214 + 1.29768i
\(616\) −2.27186e15 −1.03202
\(617\) 3.60874e15i 1.62475i −0.583135 0.812375i \(-0.698174\pi\)
0.583135 0.812375i \(-0.301826\pi\)
\(618\) 4.86640e14i 0.217156i
\(619\) −2.19239e15 −0.969660 −0.484830 0.874608i \(-0.661118\pi\)
−0.484830 + 0.874608i \(0.661118\pi\)
\(620\) −2.34719e15 + 8.37843e14i −1.02895 + 0.367289i
\(621\) 3.13817e14 0.136355
\(622\) 2.62096e14i 0.112879i
\(623\) 2.28957e14i 0.0977394i
\(624\) 1.29774e14 0.0549125
\(625\) 4.72182e14 2.33696e15i 0.198048 0.980192i
\(626\) 2.15756e15 0.897024
\(627\) 1.18396e15i 0.487940i
\(628\) 1.70210e15i 0.695357i
\(629\) 3.16246e12 0.00128070
\(630\) −1.15786e15 + 4.13305e14i −0.464819 + 0.165920i
\(631\) 3.99257e14 0.158888 0.0794441 0.996839i \(-0.474685\pi\)
0.0794441 + 0.996839i \(0.474685\pi\)
\(632\) 4.14433e15i 1.63497i
\(633\) 4.39915e14i 0.172048i
\(634\) −8.16291e14 −0.316486
\(635\) −5.36292e11 1.50241e12i −0.000206132 0.000577473i
\(636\) −2.63219e15 −1.00301
\(637\) 2.77010e15i 1.04647i
\(638\) 4.94361e14i 0.185153i
\(639\) 4.74665e14 0.176251
\(640\) −6.22644e14 1.74432e15i −0.229219 0.642149i
\(641\) −1.23875e15 −0.452132 −0.226066 0.974112i \(-0.572586\pi\)
−0.226066 + 0.974112i \(0.572586\pi\)
\(642\) 2.99564e15i 1.08404i
\(643\) 2.78159e15i 0.998005i 0.866601 + 0.499003i \(0.166300\pi\)
−0.866601 + 0.499003i \(0.833700\pi\)
\(644\) 6.57234e14 0.233802
\(645\) 2.08129e15 7.42929e14i 0.734099 0.262041i
\(646\) 9.53345e14 0.333404
\(647\) 3.99567e15i 1.38553i 0.721163 + 0.692766i \(0.243608\pi\)
−0.721163 + 0.692766i \(0.756392\pi\)
\(648\) 3.56680e15i 1.22636i
\(649\) −8.22656e14 −0.280461
\(650\) −1.15504e15 + 9.45003e14i −0.390456 + 0.319455i
\(651\) 9.47750e15 3.17686
\(652\) 1.25212e15i 0.416182i
\(653\) 1.37144e15i 0.452016i −0.974125 0.226008i \(-0.927432\pi\)
0.974125 0.226008i \(-0.0725675\pi\)
\(654\) −2.05916e14 −0.0672996
\(655\) −3.44194e15 + 1.22862e15i −1.11552 + 0.398190i
\(656\) 1.80312e14 0.0579502
\(657\) 1.87672e15i 0.598122i
\(658\) 8.46936e14i 0.267675i
\(659\) 4.53043e15 1.41994 0.709969 0.704233i \(-0.248709\pi\)
0.709969 + 0.704233i \(0.248709\pi\)
\(660\) −6.05340e14 1.69584e15i −0.188152 0.527101i
\(661\) −8.53788e13 −0.0263174 −0.0131587 0.999913i \(-0.504189\pi\)
−0.0131587 + 0.999913i \(0.504189\pi\)
\(662\) 2.46529e15i 0.753613i
\(663\) 3.44409e15i 1.04412i
\(664\) 3.29345e15 0.990209
\(665\) −9.43819e14 2.64408e15i −0.281430 0.788417i
\(666\) −1.43349e12 −0.000423922
\(667\) 3.66055e14i 0.107363i
\(668\) 2.84243e15i 0.826836i
\(669\) −8.48726e15 −2.44863
\(670\) 3.77021e14 1.34580e14i 0.107883 0.0385095i
\(671\) 2.72667e15 0.773854
\(672\) 6.71922e15i 1.89142i
\(673\) 2.76196e13i 0.00771143i 0.999993 + 0.00385571i \(0.00122732\pi\)
−0.999993 + 0.00385571i \(0.998773\pi\)
\(674\) 1.82038e15 0.504119
\(675\) 1.29099e15 + 1.57792e15i 0.354611 + 0.433425i
\(676\) 6.84025e14 0.186365
\(677\) 5.40053e15i 1.45948i 0.683724 + 0.729741i \(0.260359\pi\)
−0.683724 + 0.729741i \(0.739641\pi\)
\(678\) 3.04871e13i 0.00817245i
\(679\) −1.04891e16 −2.78903
\(680\) −3.49511e15 + 1.24760e15i −0.921853 + 0.329060i
\(681\) −3.18868e14 −0.0834261
\(682\) 2.75680e15i 0.715469i
\(683\) 1.45094e15i 0.373539i −0.982404 0.186769i \(-0.940198\pi\)
0.982404 0.186769i \(-0.0598017\pi\)
\(684\) 7.72294e14 0.197231
\(685\) 4.79991e14 + 1.34468e15i 0.121600 + 0.340660i
\(686\) −8.65527e14 −0.217519
\(687\) 8.37099e15i 2.08696i
\(688\) 1.32550e14i 0.0327825i
\(689\) 4.31263e15 1.05812
\(690\) −2.50806e14 7.02625e14i −0.0610475 0.171023i
\(691\) −3.79473e15 −0.916330 −0.458165 0.888867i \(-0.651493\pi\)
−0.458165 + 0.888867i \(0.651493\pi\)
\(692\) 4.93826e14i 0.118302i
\(693\) 2.43039e15i 0.577622i
\(694\) −2.71553e15 −0.640291
\(695\) 7.25766e14 2.59066e14i 0.169778 0.0606030i
\(696\) 2.32545e15 0.539704
\(697\) 4.78534e15i 1.10188i
\(698\) 9.68636e13i 0.0221287i
\(699\) 5.73810e15 1.30060
\(700\) 2.70375e15 + 3.30468e15i 0.608033 + 0.743173i
\(701\) −3.00014e15 −0.669410 −0.334705 0.942323i \(-0.608637\pi\)
−0.334705 + 0.942323i \(0.608637\pi\)
\(702\) 1.27614e15i 0.282516i
\(703\) 3.27350e12i 0.000719048i
\(704\) 1.78604e15 0.389261
\(705\) 1.61815e15 5.77607e14i 0.349928 0.124909i
\(706\) 1.15759e15 0.248387
\(707\) 2.09285e15i 0.445586i
\(708\) 1.51188e15i 0.319400i
\(709\) 3.33135e14 0.0698338 0.0349169 0.999390i \(-0.488883\pi\)
0.0349169 + 0.999390i \(0.488883\pi\)
\(710\) 3.10101e14 + 8.68739e14i 0.0645033 + 0.180704i
\(711\) −4.43354e15 −0.915098
\(712\) 3.13276e14i 0.0641634i
\(713\) 2.04130e15i 0.414872i
\(714\) 5.51370e15 1.11200
\(715\) 9.91799e14 + 2.77850e15i 0.198491 + 0.556066i
\(716\) −1.31043e15 −0.260250
\(717\) 1.10851e16i 2.18467i
\(718\) 3.65645e15i 0.715114i
\(719\) −1.88706e15 −0.366249 −0.183124 0.983090i \(-0.558621\pi\)
−0.183124 + 0.983090i \(0.558621\pi\)
\(720\) −1.40887e14 + 5.02902e13i −0.0271357 + 0.00968623i
\(721\) 2.28121e15 0.436035
\(722\) 2.17090e15i 0.411799i
\(723\) 7.41349e15i 1.39560i
\(724\) 4.36970e15 0.816374
\(725\) 1.84058e15 1.50589e15i 0.341269 0.279212i
\(726\) −2.06114e15 −0.379276
\(727\) 3.20690e15i 0.585660i −0.956164 0.292830i \(-0.905403\pi\)
0.956164 0.292830i \(-0.0945970\pi\)
\(728\) 6.84076e15i 1.23989i
\(729\) −6.03607e13 −0.0108581
\(730\) 3.43480e15 1.22607e15i 0.613233 0.218897i
\(731\) −3.51776e15 −0.623333
\(732\) 5.01109e15i 0.881294i
\(733\) 4.94602e15i 0.863344i −0.902031 0.431672i \(-0.857924\pi\)
0.902031 0.431672i \(-0.142076\pi\)
\(734\) −2.83339e15 −0.490883
\(735\) −3.02445e15 8.47290e15i −0.520075 1.45697i
\(736\) −1.44721e15 −0.247004
\(737\) 7.91381e14i 0.134065i
\(738\) 2.16911e15i 0.364730i
\(739\) −2.24992e15 −0.375511 −0.187756 0.982216i \(-0.560121\pi\)
−0.187756 + 0.982216i \(0.560121\pi\)
\(740\) 1.67369e12 + 4.68878e12i 0.000277268 + 0.000776758i
\(741\) −3.56501e15 −0.586220
\(742\) 6.90416e15i 1.12691i
\(743\) 6.59378e15i 1.06831i 0.845387 + 0.534154i \(0.179370\pi\)
−0.845387 + 0.534154i \(0.820630\pi\)
\(744\) −1.29678e16 −2.08553
\(745\) 3.36333e15 1.20056e15i 0.536921 0.191657i
\(746\) −6.58200e15 −1.04302
\(747\) 3.52328e15i 0.554222i
\(748\) 2.86628e15i 0.447568i
\(749\) 1.40426e16 2.17669
\(750\) 2.50114e15 4.15157e15i 0.384858 0.638816i
\(751\) 4.76790e15 0.728295 0.364147 0.931341i \(-0.381360\pi\)
0.364147 + 0.931341i \(0.381360\pi\)
\(752\) 1.03054e14i 0.0156266i
\(753\) 8.62087e14i 0.129771i
\(754\) −1.48856e15 −0.222446
\(755\) −2.14961e14 + 7.67315e13i −0.0318898 + 0.0113832i
\(756\) −3.65115e15 −0.537725
\(757\) 3.60332e15i 0.526836i 0.964682 + 0.263418i \(0.0848499\pi\)
−0.964682 + 0.263418i \(0.915150\pi\)
\(758\) 3.80820e15i 0.552763i
\(759\) −1.47484e15 −0.212527
\(760\) 1.29140e15 + 3.61783e15i 0.184751 + 0.517575i
\(761\) −1.00138e16 −1.42227 −0.711136 0.703054i \(-0.751819\pi\)
−0.711136 + 0.703054i \(0.751819\pi\)
\(762\) 3.24297e12i 0.000457289i
\(763\) 9.65267e14i 0.135133i
\(764\) −5.29031e15 −0.735306
\(765\) 1.33466e15 + 3.73901e15i 0.184176 + 0.515963i
\(766\) 5.88702e15 0.806561
\(767\) 2.47709e15i 0.336951i
\(768\) 8.88418e15i 1.19986i
\(769\) 1.14898e16 1.54070 0.770351 0.637620i \(-0.220081\pi\)
0.770351 + 0.637620i \(0.220081\pi\)
\(770\) −4.44814e15 + 1.58779e15i −0.592216 + 0.211395i
\(771\) 1.65602e16 2.18910
\(772\) 1.33760e15i 0.175562i
\(773\) 1.24078e16i 1.61699i −0.588501 0.808497i \(-0.700282\pi\)
0.588501 0.808497i \(-0.299718\pi\)
\(774\) 1.59454e15 0.206329
\(775\) −1.02640e16 + 8.39757e15i −1.31873 + 1.07893i
\(776\) 1.43519e16 1.83092
\(777\) 1.89324e13i 0.00239822i
\(778\) 6.18192e15i 0.777562i
\(779\) −4.95336e15 −0.618649
\(780\) 5.10633e15 1.82273e15i 0.633269 0.226049i
\(781\) 1.82352e15 0.224558
\(782\) 1.18756e15i 0.145217i
\(783\) 2.03356e15i 0.246926i
\(784\) −5.39607e14 −0.0650637
\(785\) 3.04482e15 + 8.52996e15i 0.364568 + 1.02133i
\(786\) −7.42949e15 −0.883355
\(787\) 3.57890e15i 0.422560i −0.977426 0.211280i \(-0.932237\pi\)
0.977426 0.211280i \(-0.0677631\pi\)
\(788\) 5.99805e15i 0.703260i
\(789\) 7.88380e14 0.0917935
\(790\) −2.89645e15 8.11433e15i −0.334902 0.938217i
\(791\) −1.42913e14 −0.0164098
\(792\) 3.32545e15i 0.379194i
\(793\) 8.21024e15i 0.929723i
\(794\) −2.08308e15 −0.234258
\(795\) −1.31910e16 + 4.70861e15i −1.47319 + 0.525864i
\(796\) 2.88737e15 0.320244
\(797\) 1.25596e16i 1.38343i −0.722172 0.691714i \(-0.756856\pi\)
0.722172 0.691714i \(-0.243144\pi\)
\(798\) 5.70729e15i 0.624330i
\(799\) −2.73496e15 −0.297128
\(800\) −5.95358e15 7.27681e15i −0.642367 0.785138i
\(801\) 3.35137e14 0.0359124
\(802\) 7.96160e15i 0.847308i
\(803\) 7.20977e15i 0.762055i
\(804\) −1.45440e15 −0.152678
\(805\) 3.29368e15 1.17570e15i 0.343403 0.122579i
\(806\) 8.30095e15 0.859578
\(807\) 2.04725e16i 2.10555i
\(808\) 2.86359e15i 0.292515i
\(809\) −8.95686e15 −0.908738 −0.454369 0.890813i \(-0.650135\pi\)
−0.454369 + 0.890813i \(0.650135\pi\)
\(810\) 2.49282e15 + 6.98356e15i 0.251202 + 0.703735i
\(811\) −8.33940e15 −0.834680 −0.417340 0.908750i \(-0.637038\pi\)
−0.417340 + 0.908750i \(0.637038\pi\)
\(812\) 4.25893e15i 0.423392i
\(813\) 2.38296e15i 0.235298i
\(814\) −5.50702e12 −0.000540110
\(815\) −2.23985e15 6.27489e15i −0.218199 0.611278i
\(816\) 6.70897e14 0.0649173
\(817\) 3.64127e15i 0.349971i
\(818\) 3.57545e15i 0.341340i
\(819\) −7.31813e15 −0.693967
\(820\) 7.09493e15 2.53257e15i 0.668300 0.238553i
\(821\) 3.07549e15 0.287757 0.143879 0.989595i \(-0.454042\pi\)
0.143879 + 0.989595i \(0.454042\pi\)
\(822\) 2.90251e15i 0.269761i
\(823\) 1.67606e16i 1.54736i −0.633579 0.773678i \(-0.718415\pi\)
0.633579 0.773678i \(-0.281585\pi\)
\(824\) −3.12132e15 −0.286246
\(825\) −6.06723e15 7.41572e15i −0.552705 0.675548i
\(826\) 3.96562e15 0.358856
\(827\) 1.18413e16i 1.06443i 0.846608 + 0.532217i \(0.178641\pi\)
−0.846608 + 0.532217i \(0.821359\pi\)
\(828\) 9.62031e14i 0.0859057i
\(829\) 3.10234e15 0.275195 0.137597 0.990488i \(-0.456062\pi\)
0.137597 + 0.990488i \(0.456062\pi\)
\(830\) 6.44836e15 2.30178e15i 0.568225 0.202831i
\(831\) 1.16362e16 1.01861
\(832\) 5.37792e15i 0.467666i
\(833\) 1.43207e16i 1.23713i
\(834\) 1.56658e15 0.134443
\(835\) −5.08470e15 1.42446e16i −0.433500 1.21444i
\(836\) 2.96691e15 0.251287
\(837\) 1.13401e16i 0.954173i
\(838\) 9.43094e15i 0.788339i
\(839\) 2.08909e16 1.73487 0.867436 0.497549i \(-0.165767\pi\)
0.867436 + 0.497549i \(0.165767\pi\)
\(840\) 7.46887e15 + 2.09238e16i 0.616196 + 1.72626i
\(841\) −9.82844e15 −0.805576
\(842\) 9.75908e15i 0.794680i
\(843\) 1.18805e16i 0.961129i
\(844\) 1.10239e15 0.0886039
\(845\) 3.42794e15 1.22362e15i 0.273729 0.0977091i
\(846\) 1.23971e15 0.0983519
\(847\) 9.66193e15i 0.761562i
\(848\) 8.40086e14i 0.0657880i
\(849\) 1.54204e16 1.19978
\(850\) −5.97125e15 + 4.88543e15i −0.461595 + 0.377658i
\(851\) 4.07773e12 0.000313189
\(852\) 3.35126e15i 0.255735i
\(853\) 2.42451e16i 1.83825i 0.393968 + 0.919124i \(0.371102\pi\)
−0.393968 + 0.919124i \(0.628898\pi\)
\(854\) −1.31439e16 −0.990164
\(855\) 3.87029e15 1.38152e15i 0.289688 0.103406i
\(856\) −1.92141e16 −1.42894
\(857\) 9.53835e15i 0.704821i 0.935846 + 0.352410i \(0.114638\pi\)
−0.935846 + 0.352410i \(0.885362\pi\)
\(858\) 5.99743e15i 0.440337i
\(859\) −4.70173e15 −0.343001 −0.171500 0.985184i \(-0.554861\pi\)
−0.171500 + 0.985184i \(0.554861\pi\)
\(860\) −1.86172e15 5.21556e15i −0.134950 0.378059i
\(861\) −2.86479e16 −2.06336
\(862\) 1.09254e16i 0.781893i
\(863\) 1.12556e16i 0.800401i 0.916428 + 0.400201i \(0.131060\pi\)
−0.916428 + 0.400201i \(0.868940\pi\)
\(864\) 8.03974e15 0.568089
\(865\) 8.83383e14 + 2.47477e15i 0.0620241 + 0.173759i
\(866\) 1.02855e16 0.717593
\(867\) 1.54792e14i 0.0107311i
\(868\) 2.37499e16i 1.63607i
\(869\) −1.70323e16 −1.16591
\(870\) 4.55307e15 1.62524e15i 0.309705 0.110551i
\(871\) 2.38292e15 0.161068
\(872\) 1.32075e15i 0.0887115i
\(873\) 1.53534e16i 1.02477i
\(874\) 1.22926e15 0.0815324
\(875\) 1.94612e16 + 1.17245e16i 1.28270 + 0.772771i
\(876\) −1.32501e16 −0.867857
\(877\) 9.19338e15i 0.598381i −0.954193 0.299190i \(-0.903283\pi\)
0.954193 0.299190i \(-0.0967165\pi\)
\(878\) 1.54515e16i 0.999424i
\(879\) 2.10741e16 1.35460
\(880\) −5.41242e14 + 1.93199e14i −0.0345730 + 0.0123410i
\(881\) −1.98624e16 −1.26085 −0.630425 0.776250i \(-0.717120\pi\)
−0.630425 + 0.776250i \(0.717120\pi\)
\(882\) 6.49133e15i 0.409502i
\(883\) 5.79702e15i 0.363430i −0.983351 0.181715i \(-0.941835\pi\)
0.983351 0.181715i \(-0.0581648\pi\)
\(884\) −8.63061e15 −0.537717
\(885\) 2.70453e15 + 7.57667e15i 0.167457 + 0.469127i
\(886\) −1.77468e16 −1.09203
\(887\) 8.29351e15i 0.507176i 0.967312 + 0.253588i \(0.0816107\pi\)
−0.967312 + 0.253588i \(0.918389\pi\)
\(888\) 2.59047e13i 0.00157437i
\(889\) 1.52020e13 0.000918206
\(890\) 2.18947e14 + 6.13374e14i 0.0131430 + 0.0368197i
\(891\) 1.46588e16 0.874520
\(892\) 2.12684e16i 1.26104i
\(893\) 2.83099e15i 0.166823i
\(894\) 7.25982e15 0.425176
\(895\) −6.56710e15 + 2.34416e15i −0.382249 + 0.136446i
\(896\) 1.76498e16 1.02104
\(897\) 4.44086e15i 0.255334i
\(898\) 5.87525e15i 0.335742i
\(899\) −1.32278e16 −0.751293
\(900\) −4.83725e15 + 3.95763e15i −0.273064 + 0.223410i
\(901\) 2.22952e16 1.25091
\(902\) 8.33305e15i 0.464695i
\(903\) 2.10594e16i 1.16725i
\(904\) 1.95545e14 0.0107726
\(905\) 2.18984e16 7.81675e15i 1.19907 0.428015i
\(906\) −4.63997e14 −0.0252528
\(907\) 2.89763e16i 1.56748i 0.621088 + 0.783741i \(0.286691\pi\)
−0.621088 + 0.783741i \(0.713309\pi\)
\(908\) 7.99059e14i 0.0429642i
\(909\) 3.06342e15 0.163722
\(910\) −4.78097e15 1.33938e16i −0.253974 0.711499i
\(911\) 1.91910e16 1.01332 0.506659 0.862147i \(-0.330880\pi\)
0.506659 + 0.862147i \(0.330880\pi\)
\(912\) 6.94454e14i 0.0364478i
\(913\) 1.35354e16i 0.706123i
\(914\) 1.09737e16 0.569046
\(915\) −8.96411e15 2.51127e16i −0.462052 1.29443i
\(916\) −2.09770e16 −1.07478
\(917\) 3.48270e16i 1.77372i
\(918\) 6.59730e15i 0.333988i
\(919\) 5.30946e15 0.267187 0.133593 0.991036i \(-0.457348\pi\)
0.133593 + 0.991036i \(0.457348\pi\)
\(920\) −4.50665e15 + 1.60867e15i −0.225435 + 0.0804702i
\(921\) −6.16096e15 −0.306352
\(922\) 1.29589e16i 0.640542i
\(923\) 5.49076e15i 0.269788i
\(924\) 1.71593e16 0.838113
\(925\) 1.67751e13 + 2.05035e13i 0.000814489 + 0.000995516i
\(926\) 2.14379e15 0.103472
\(927\) 3.33914e15i 0.160212i
\(928\) 9.37804e15i 0.447299i
\(929\) −3.41655e16 −1.61995 −0.809974 0.586466i \(-0.800519\pi\)
−0.809974 + 0.586466i \(0.800519\pi\)
\(930\) −2.53901e16 + 9.06314e15i −1.19676 + 0.427192i
\(931\) 1.48235e16 0.694590
\(932\) 1.43792e16i 0.669805i
\(933\) 5.06688e15i 0.234634i
\(934\) 1.04088e16 0.479174
\(935\) 5.12735e15 + 1.43641e16i 0.234655 + 0.657378i
\(936\) 1.00132e16 0.455571
\(937\) 1.15303e16i 0.521524i 0.965403 + 0.260762i \(0.0839738\pi\)
−0.965403 + 0.260762i \(0.916026\pi\)
\(938\) 3.81485e15i 0.171539i
\(939\) −4.17103e16 −1.86459
\(940\) −1.44744e15 4.05495e15i −0.0643275 0.180212i
\(941\) −3.10666e16 −1.37262 −0.686310 0.727309i \(-0.740771\pi\)
−0.686310 + 0.727309i \(0.740771\pi\)
\(942\) 1.84121e16i 0.808766i
\(943\) 6.17030e15i 0.269459i
\(944\) 4.82529e14 0.0209497
\(945\) −1.82975e16 + 6.53138e15i −0.789798 + 0.281923i
\(946\) 6.12572e15 0.262879
\(947\) 3.79319e16i 1.61838i −0.587550 0.809188i \(-0.699908\pi\)
0.587550 0.809188i \(-0.300092\pi\)
\(948\) 3.13020e16i 1.32778i
\(949\) 2.17093e16 0.915547
\(950\) 5.05696e15 + 6.18091e15i 0.212036 + 0.259163i
\(951\) 1.57807e16 0.657858
\(952\) 3.53650e16i 1.46578i
\(953\) 1.52578e16i 0.628756i −0.949298 0.314378i \(-0.898204\pi\)
0.949298 0.314378i \(-0.101796\pi\)
\(954\) −1.01060e16 −0.414061
\(955\) −2.65120e16 + 9.46360e15i −1.08000 + 0.385512i
\(956\) 2.77785e16 1.12510
\(957\) 9.55707e15i 0.384865i
\(958\) 1.17645e16i 0.471045i
\(959\) −1.36060e16 −0.541663
\(960\) −5.87171e15 1.64494e16i −0.232420 0.651117i
\(961\) 4.83561e16 1.90315
\(962\) 1.65821e13i 0.000648898i
\(963\) 2.05549e16i 0.799782i
\(964\) 1.85776e16 0.718731
\(965\) 2.39277e15 + 6.70328e15i 0.0920452 + 0.257862i
\(966\) 7.10946e15 0.271933
\(967\) 8.70387e15i 0.331029i 0.986207 + 0.165515i \(0.0529285\pi\)
−0.986207 + 0.165515i \(0.947071\pi\)
\(968\) 1.32202e16i 0.499945i
\(969\) −1.84302e16 −0.693026
\(970\) 2.81001e16 1.00305e16i 1.05066 0.375039i
\(971\) −6.67861e15 −0.248302 −0.124151 0.992263i \(-0.539621\pi\)
−0.124151 + 0.992263i \(0.539621\pi\)
\(972\) 1.72268e16i 0.636855i
\(973\) 7.34361e15i 0.269953i
\(974\) −9.10715e15 −0.332896
\(975\) 2.23294e16 1.82690e16i 0.811617 0.664031i
\(976\) −1.59933e15 −0.0578048
\(977\) 3.64352e16i 1.30949i 0.755851 + 0.654744i \(0.227223\pi\)
−0.755851 + 0.654744i \(0.772777\pi\)
\(978\) 1.35445e16i 0.484058i
\(979\) 1.28749e15 0.0457552
\(980\) −2.12324e16 + 7.57903e15i −0.750336 + 0.267837i
\(981\) 1.41292e15 0.0496520
\(982\) 1.74587e16i 0.610097i
\(983\) 3.91117e16i 1.35913i −0.733613 0.679567i \(-0.762168\pi\)
0.733613 0.679567i \(-0.237832\pi\)
\(984\) 3.91982e16 1.35454
\(985\) 1.07296e16 + 3.00588e16i 0.368711 + 1.03293i
\(986\) −7.69550e15 −0.262975
\(987\) 1.63731e16i 0.556400i
\(988\) 8.93364e15i 0.301901i
\(989\) −4.53585e15 −0.152433
\(990\) −2.32414e15 6.51100e15i −0.0776727 0.217598i
\(991\) −3.51778e15 −0.116913 −0.0584566 0.998290i \(-0.518618\pi\)
−0.0584566 + 0.998290i \(0.518618\pi\)
\(992\) 5.22965e16i 1.72846i
\(993\) 4.76593e16i 1.56649i
\(994\) −8.79026e15 −0.287327
\(995\) 1.44698e16 5.16508e15i 0.470366 0.167900i
\(996\) −2.48753e16 −0.804160
\(997\) 2.71445e15i 0.0872687i 0.999048 + 0.0436343i \(0.0138937\pi\)
−0.999048 + 0.0436343i \(0.986106\pi\)
\(998\) 1.83751e16i 0.587505i
\(999\) −2.26532e13 −0.000720308
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 5.12.b.a.4.2 4
3.2 odd 2 45.12.b.b.19.3 4
4.3 odd 2 80.12.c.a.49.1 4
5.2 odd 4 25.12.a.e.1.3 4
5.3 odd 4 25.12.a.e.1.2 4
5.4 even 2 inner 5.12.b.a.4.3 yes 4
15.2 even 4 225.12.a.r.1.2 4
15.8 even 4 225.12.a.r.1.3 4
15.14 odd 2 45.12.b.b.19.2 4
20.19 odd 2 80.12.c.a.49.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.12.b.a.4.2 4 1.1 even 1 trivial
5.12.b.a.4.3 yes 4 5.4 even 2 inner
25.12.a.e.1.2 4 5.3 odd 4
25.12.a.e.1.3 4 5.2 odd 4
45.12.b.b.19.2 4 15.14 odd 2
45.12.b.b.19.3 4 3.2 odd 2
80.12.c.a.49.1 4 4.3 odd 2
80.12.c.a.49.4 4 20.19 odd 2
225.12.a.r.1.2 4 15.2 even 4
225.12.a.r.1.3 4 15.8 even 4