Properties

Label 983.2.a.a.1.11
Level $983$
Weight $2$
Character 983.1
Self dual yes
Analytic conductor $7.849$
Analytic rank $1$
Dimension $28$
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] = [983,2,Mod(1,983)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(983, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("983.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 983.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: \(7.84929451869\)
Analytic rank: \(1\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 983.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.930689 q^{2} -1.12871 q^{3} -1.13382 q^{4} +3.65614 q^{5} +1.05048 q^{6} -1.39504 q^{7} +2.91661 q^{8} -1.72601 q^{9} +O(q^{10})\) \(q-0.930689 q^{2} -1.12871 q^{3} -1.13382 q^{4} +3.65614 q^{5} +1.05048 q^{6} -1.39504 q^{7} +2.91661 q^{8} -1.72601 q^{9} -3.40273 q^{10} +1.37964 q^{11} +1.27976 q^{12} -4.81779 q^{13} +1.29835 q^{14} -4.12673 q^{15} -0.446823 q^{16} -2.61914 q^{17} +1.60637 q^{18} +3.96315 q^{19} -4.14539 q^{20} +1.57460 q^{21} -1.28402 q^{22} -5.45635 q^{23} -3.29202 q^{24} +8.36734 q^{25} +4.48386 q^{26} +5.33431 q^{27} +1.58172 q^{28} -0.992196 q^{29} +3.84071 q^{30} +1.16483 q^{31} -5.41737 q^{32} -1.55722 q^{33} +2.43761 q^{34} -5.10045 q^{35} +1.95698 q^{36} -0.503291 q^{37} -3.68846 q^{38} +5.43790 q^{39} +10.6635 q^{40} -2.17818 q^{41} -1.46546 q^{42} +5.94923 q^{43} -1.56426 q^{44} -6.31051 q^{45} +5.07816 q^{46} -5.66455 q^{47} +0.504335 q^{48} -5.05387 q^{49} -7.78739 q^{50} +2.95626 q^{51} +5.46249 q^{52} -7.42014 q^{53} -4.96458 q^{54} +5.04417 q^{55} -4.06878 q^{56} -4.47326 q^{57} +0.923426 q^{58} -5.25668 q^{59} +4.67896 q^{60} -3.98149 q^{61} -1.08410 q^{62} +2.40784 q^{63} +5.93553 q^{64} -17.6145 q^{65} +1.44929 q^{66} -15.3775 q^{67} +2.96963 q^{68} +6.15866 q^{69} +4.74694 q^{70} +7.91443 q^{71} -5.03409 q^{72} -3.17316 q^{73} +0.468408 q^{74} -9.44433 q^{75} -4.49349 q^{76} -1.92466 q^{77} -5.06100 q^{78} -7.26789 q^{79} -1.63365 q^{80} -0.842889 q^{81} +2.02721 q^{82} -5.01668 q^{83} -1.78531 q^{84} -9.57595 q^{85} -5.53688 q^{86} +1.11991 q^{87} +4.02388 q^{88} +0.319037 q^{89} +5.87313 q^{90} +6.72100 q^{91} +6.18650 q^{92} -1.31476 q^{93} +5.27193 q^{94} +14.4898 q^{95} +6.11466 q^{96} -9.75934 q^{97} +4.70358 q^{98} -2.38127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.930689 −0.658097 −0.329048 0.944313i \(-0.606728\pi\)
−0.329048 + 0.944313i \(0.606728\pi\)
\(3\) −1.12871 −0.651663 −0.325832 0.945428i \(-0.605644\pi\)
−0.325832 + 0.945428i \(0.605644\pi\)
\(4\) −1.13382 −0.566909
\(5\) 3.65614 1.63507 0.817537 0.575876i \(-0.195339\pi\)
0.817537 + 0.575876i \(0.195339\pi\)
\(6\) 1.05048 0.428857
\(7\) −1.39504 −0.527275 −0.263638 0.964622i \(-0.584922\pi\)
−0.263638 + 0.964622i \(0.584922\pi\)
\(8\) 2.91661 1.03118
\(9\) −1.72601 −0.575335
\(10\) −3.40273 −1.07604
\(11\) 1.37964 0.415978 0.207989 0.978131i \(-0.433308\pi\)
0.207989 + 0.978131i \(0.433308\pi\)
\(12\) 1.27976 0.369434
\(13\) −4.81779 −1.33621 −0.668107 0.744065i \(-0.732895\pi\)
−0.668107 + 0.744065i \(0.732895\pi\)
\(14\) 1.29835 0.346998
\(15\) −4.12673 −1.06552
\(16\) −0.446823 −0.111706
\(17\) −2.61914 −0.635236 −0.317618 0.948219i \(-0.602883\pi\)
−0.317618 + 0.948219i \(0.602883\pi\)
\(18\) 1.60637 0.378626
\(19\) 3.96315 0.909208 0.454604 0.890694i \(-0.349781\pi\)
0.454604 + 0.890694i \(0.349781\pi\)
\(20\) −4.14539 −0.926938
\(21\) 1.57460 0.343606
\(22\) −1.28402 −0.273754
\(23\) −5.45635 −1.13773 −0.568864 0.822432i \(-0.692617\pi\)
−0.568864 + 0.822432i \(0.692617\pi\)
\(24\) −3.29202 −0.671980
\(25\) 8.36734 1.67347
\(26\) 4.48386 0.879358
\(27\) 5.33431 1.02659
\(28\) 1.58172 0.298917
\(29\) −0.992196 −0.184246 −0.0921231 0.995748i \(-0.529365\pi\)
−0.0921231 + 0.995748i \(0.529365\pi\)
\(30\) 3.84071 0.701214
\(31\) 1.16483 0.209210 0.104605 0.994514i \(-0.466642\pi\)
0.104605 + 0.994514i \(0.466642\pi\)
\(32\) −5.41737 −0.957664
\(33\) −1.55722 −0.271078
\(34\) 2.43761 0.418046
\(35\) −5.10045 −0.862134
\(36\) 1.95698 0.326163
\(37\) −0.503291 −0.0827405 −0.0413703 0.999144i \(-0.513172\pi\)
−0.0413703 + 0.999144i \(0.513172\pi\)
\(38\) −3.68846 −0.598347
\(39\) 5.43790 0.870761
\(40\) 10.6635 1.68605
\(41\) −2.17818 −0.340174 −0.170087 0.985429i \(-0.554405\pi\)
−0.170087 + 0.985429i \(0.554405\pi\)
\(42\) −1.46546 −0.226126
\(43\) 5.94923 0.907249 0.453624 0.891193i \(-0.350131\pi\)
0.453624 + 0.891193i \(0.350131\pi\)
\(44\) −1.56426 −0.235822
\(45\) −6.31051 −0.940716
\(46\) 5.07816 0.748735
\(47\) −5.66455 −0.826259 −0.413129 0.910672i \(-0.635564\pi\)
−0.413129 + 0.910672i \(0.635564\pi\)
\(48\) 0.504335 0.0727945
\(49\) −5.05387 −0.721981
\(50\) −7.78739 −1.10130
\(51\) 2.95626 0.413960
\(52\) 5.46249 0.757511
\(53\) −7.42014 −1.01923 −0.509617 0.860401i \(-0.670213\pi\)
−0.509617 + 0.860401i \(0.670213\pi\)
\(54\) −4.96458 −0.675594
\(55\) 5.04417 0.680156
\(56\) −4.06878 −0.543714
\(57\) −4.47326 −0.592498
\(58\) 0.923426 0.121252
\(59\) −5.25668 −0.684362 −0.342181 0.939634i \(-0.611166\pi\)
−0.342181 + 0.939634i \(0.611166\pi\)
\(60\) 4.67896 0.604051
\(61\) −3.98149 −0.509778 −0.254889 0.966970i \(-0.582039\pi\)
−0.254889 + 0.966970i \(0.582039\pi\)
\(62\) −1.08410 −0.137680
\(63\) 2.40784 0.303360
\(64\) 5.93553 0.741941
\(65\) −17.6145 −2.18481
\(66\) 1.44929 0.178395
\(67\) −15.3775 −1.87866 −0.939331 0.343011i \(-0.888553\pi\)
−0.939331 + 0.343011i \(0.888553\pi\)
\(68\) 2.96963 0.360121
\(69\) 6.15866 0.741415
\(70\) 4.74694 0.567367
\(71\) 7.91443 0.939270 0.469635 0.882861i \(-0.344386\pi\)
0.469635 + 0.882861i \(0.344386\pi\)
\(72\) −5.03409 −0.593273
\(73\) −3.17316 −0.371390 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(74\) 0.468408 0.0544513
\(75\) −9.44433 −1.09054
\(76\) −4.49349 −0.515438
\(77\) −1.92466 −0.219335
\(78\) −5.06100 −0.573045
\(79\) −7.26789 −0.817701 −0.408851 0.912601i \(-0.634070\pi\)
−0.408851 + 0.912601i \(0.634070\pi\)
\(80\) −1.63365 −0.182647
\(81\) −0.842889 −0.0936543
\(82\) 2.02721 0.223868
\(83\) −5.01668 −0.550652 −0.275326 0.961351i \(-0.588786\pi\)
−0.275326 + 0.961351i \(0.588786\pi\)
\(84\) −1.78531 −0.194793
\(85\) −9.57595 −1.03866
\(86\) −5.53688 −0.597058
\(87\) 1.11991 0.120066
\(88\) 4.02388 0.428947
\(89\) 0.319037 0.0338179 0.0169089 0.999857i \(-0.494617\pi\)
0.0169089 + 0.999857i \(0.494617\pi\)
\(90\) 5.87313 0.619082
\(91\) 6.72100 0.704552
\(92\) 6.18650 0.644988
\(93\) −1.31476 −0.136334
\(94\) 5.27193 0.543758
\(95\) 14.4898 1.48662
\(96\) 6.11466 0.624075
\(97\) −9.75934 −0.990911 −0.495455 0.868633i \(-0.664999\pi\)
−0.495455 + 0.868633i \(0.664999\pi\)
\(98\) 4.70358 0.475133
\(99\) −2.38127 −0.239327
\(100\) −9.48704 −0.948704
\(101\) −14.3030 −1.42320 −0.711599 0.702586i \(-0.752029\pi\)
−0.711599 + 0.702586i \(0.752029\pi\)
\(102\) −2.75136 −0.272425
\(103\) −2.31041 −0.227651 −0.113826 0.993501i \(-0.536311\pi\)
−0.113826 + 0.993501i \(0.536311\pi\)
\(104\) −14.0516 −1.37787
\(105\) 5.75695 0.561821
\(106\) 6.90584 0.670755
\(107\) −9.73060 −0.940692 −0.470346 0.882482i \(-0.655871\pi\)
−0.470346 + 0.882482i \(0.655871\pi\)
\(108\) −6.04813 −0.581982
\(109\) −11.8004 −1.13028 −0.565139 0.824996i \(-0.691177\pi\)
−0.565139 + 0.824996i \(0.691177\pi\)
\(110\) −4.69455 −0.447608
\(111\) 0.568071 0.0539190
\(112\) 0.623335 0.0588996
\(113\) 10.7265 1.00907 0.504534 0.863392i \(-0.331664\pi\)
0.504534 + 0.863392i \(0.331664\pi\)
\(114\) 4.16321 0.389921
\(115\) −19.9492 −1.86027
\(116\) 1.12497 0.104451
\(117\) 8.31553 0.768771
\(118\) 4.89234 0.450376
\(119\) 3.65381 0.334944
\(120\) −12.0361 −1.09874
\(121\) −9.09658 −0.826962
\(122\) 3.70553 0.335483
\(123\) 2.45854 0.221679
\(124\) −1.32071 −0.118603
\(125\) 12.3115 1.10117
\(126\) −2.24095 −0.199640
\(127\) 10.6710 0.946902 0.473451 0.880820i \(-0.343008\pi\)
0.473451 + 0.880820i \(0.343008\pi\)
\(128\) 5.31060 0.469395
\(129\) −6.71498 −0.591221
\(130\) 16.3936 1.43782
\(131\) 17.0389 1.48869 0.744347 0.667793i \(-0.232761\pi\)
0.744347 + 0.667793i \(0.232761\pi\)
\(132\) 1.76561 0.153676
\(133\) −5.52874 −0.479403
\(134\) 14.3117 1.23634
\(135\) 19.5030 1.67855
\(136\) −7.63902 −0.655041
\(137\) −9.19141 −0.785275 −0.392638 0.919693i \(-0.628437\pi\)
−0.392638 + 0.919693i \(0.628437\pi\)
\(138\) −5.73179 −0.487923
\(139\) −5.05347 −0.428630 −0.214315 0.976765i \(-0.568752\pi\)
−0.214315 + 0.976765i \(0.568752\pi\)
\(140\) 5.78298 0.488751
\(141\) 6.39365 0.538443
\(142\) −7.36588 −0.618131
\(143\) −6.64683 −0.555836
\(144\) 0.771218 0.0642682
\(145\) −3.62761 −0.301256
\(146\) 2.95323 0.244411
\(147\) 5.70437 0.470488
\(148\) 0.570640 0.0469063
\(149\) −0.701009 −0.0574289 −0.0287145 0.999588i \(-0.509141\pi\)
−0.0287145 + 0.999588i \(0.509141\pi\)
\(150\) 8.78974 0.717679
\(151\) 15.6362 1.27246 0.636229 0.771500i \(-0.280493\pi\)
0.636229 + 0.771500i \(0.280493\pi\)
\(152\) 11.5590 0.937555
\(153\) 4.52066 0.365473
\(154\) 1.79126 0.144344
\(155\) 4.25878 0.342074
\(156\) −6.16559 −0.493642
\(157\) 13.1604 1.05031 0.525156 0.851006i \(-0.324007\pi\)
0.525156 + 0.851006i \(0.324007\pi\)
\(158\) 6.76415 0.538127
\(159\) 8.37521 0.664197
\(160\) −19.8066 −1.56585
\(161\) 7.61182 0.599895
\(162\) 0.784468 0.0616336
\(163\) −10.2695 −0.804372 −0.402186 0.915558i \(-0.631750\pi\)
−0.402186 + 0.915558i \(0.631750\pi\)
\(164\) 2.46966 0.192848
\(165\) −5.69342 −0.443232
\(166\) 4.66897 0.362383
\(167\) 16.5575 1.28126 0.640631 0.767849i \(-0.278673\pi\)
0.640631 + 0.767849i \(0.278673\pi\)
\(168\) 4.59249 0.354318
\(169\) 10.2111 0.785467
\(170\) 8.91223 0.683537
\(171\) −6.84041 −0.523099
\(172\) −6.74534 −0.514327
\(173\) −5.59583 −0.425443 −0.212722 0.977113i \(-0.568233\pi\)
−0.212722 + 0.977113i \(0.568233\pi\)
\(174\) −1.04228 −0.0790153
\(175\) −11.6728 −0.882378
\(176\) −0.616456 −0.0464671
\(177\) 5.93329 0.445973
\(178\) −0.296925 −0.0222554
\(179\) −5.23442 −0.391239 −0.195619 0.980680i \(-0.562672\pi\)
−0.195619 + 0.980680i \(0.562672\pi\)
\(180\) 7.15497 0.533300
\(181\) 24.4388 1.81652 0.908262 0.418402i \(-0.137410\pi\)
0.908262 + 0.418402i \(0.137410\pi\)
\(182\) −6.25516 −0.463663
\(183\) 4.49396 0.332203
\(184\) −15.9140 −1.17320
\(185\) −1.84010 −0.135287
\(186\) 1.22363 0.0897212
\(187\) −3.61349 −0.264244
\(188\) 6.42256 0.468413
\(189\) −7.44156 −0.541294
\(190\) −13.4855 −0.978342
\(191\) 1.25181 0.0905775 0.0452887 0.998974i \(-0.485579\pi\)
0.0452887 + 0.998974i \(0.485579\pi\)
\(192\) −6.69952 −0.483496
\(193\) −1.06630 −0.0767543 −0.0383772 0.999263i \(-0.512219\pi\)
−0.0383772 + 0.999263i \(0.512219\pi\)
\(194\) 9.08291 0.652115
\(195\) 19.8817 1.42376
\(196\) 5.73016 0.409297
\(197\) −18.6784 −1.33078 −0.665389 0.746497i \(-0.731734\pi\)
−0.665389 + 0.746497i \(0.731734\pi\)
\(198\) 2.21623 0.157500
\(199\) −2.28506 −0.161983 −0.0809917 0.996715i \(-0.525809\pi\)
−0.0809917 + 0.996715i \(0.525809\pi\)
\(200\) 24.4043 1.72564
\(201\) 17.3568 1.22426
\(202\) 13.3116 0.936602
\(203\) 1.38415 0.0971484
\(204\) −3.35186 −0.234677
\(205\) −7.96372 −0.556210
\(206\) 2.15027 0.149817
\(207\) 9.41769 0.654575
\(208\) 2.15270 0.149263
\(209\) 5.46773 0.378211
\(210\) −5.35793 −0.369732
\(211\) 9.74582 0.670930 0.335465 0.942053i \(-0.391107\pi\)
0.335465 + 0.942053i \(0.391107\pi\)
\(212\) 8.41308 0.577813
\(213\) −8.93313 −0.612088
\(214\) 9.05616 0.619067
\(215\) 21.7512 1.48342
\(216\) 15.5581 1.05859
\(217\) −1.62498 −0.110311
\(218\) 10.9826 0.743832
\(219\) 3.58159 0.242021
\(220\) −5.71917 −0.385586
\(221\) 12.6185 0.848811
\(222\) −0.528698 −0.0354839
\(223\) 7.54988 0.505578 0.252789 0.967521i \(-0.418652\pi\)
0.252789 + 0.967521i \(0.418652\pi\)
\(224\) 7.55744 0.504953
\(225\) −14.4421 −0.962805
\(226\) −9.98308 −0.664065
\(227\) 16.7706 1.11310 0.556552 0.830813i \(-0.312124\pi\)
0.556552 + 0.830813i \(0.312124\pi\)
\(228\) 5.07186 0.335892
\(229\) −0.128761 −0.00850876 −0.00425438 0.999991i \(-0.501354\pi\)
−0.00425438 + 0.999991i \(0.501354\pi\)
\(230\) 18.5665 1.22424
\(231\) 2.17239 0.142933
\(232\) −2.89385 −0.189991
\(233\) −6.66070 −0.436357 −0.218179 0.975909i \(-0.570012\pi\)
−0.218179 + 0.975909i \(0.570012\pi\)
\(234\) −7.73917 −0.505925
\(235\) −20.7104 −1.35099
\(236\) 5.96012 0.387971
\(237\) 8.20337 0.532866
\(238\) −3.40056 −0.220425
\(239\) −7.99029 −0.516849 −0.258424 0.966031i \(-0.583203\pi\)
−0.258424 + 0.966031i \(0.583203\pi\)
\(240\) 1.84392 0.119024
\(241\) −25.3094 −1.63032 −0.815162 0.579234i \(-0.803352\pi\)
−0.815162 + 0.579234i \(0.803352\pi\)
\(242\) 8.46609 0.544221
\(243\) −15.0515 −0.965557
\(244\) 4.51429 0.288997
\(245\) −18.4776 −1.18049
\(246\) −2.28814 −0.145886
\(247\) −19.0936 −1.21490
\(248\) 3.39736 0.215733
\(249\) 5.66240 0.358840
\(250\) −11.4581 −0.724677
\(251\) 3.56449 0.224989 0.112494 0.993652i \(-0.464116\pi\)
0.112494 + 0.993652i \(0.464116\pi\)
\(252\) −2.73006 −0.171977
\(253\) −7.52782 −0.473270
\(254\) −9.93143 −0.623153
\(255\) 10.8085 0.676855
\(256\) −16.8136 −1.05085
\(257\) −14.9858 −0.934791 −0.467395 0.884048i \(-0.654808\pi\)
−0.467395 + 0.884048i \(0.654808\pi\)
\(258\) 6.24956 0.389080
\(259\) 0.702111 0.0436270
\(260\) 19.9716 1.23859
\(261\) 1.71254 0.106003
\(262\) −15.8579 −0.979705
\(263\) 24.0181 1.48102 0.740509 0.672047i \(-0.234585\pi\)
0.740509 + 0.672047i \(0.234585\pi\)
\(264\) −4.54181 −0.279529
\(265\) −27.1290 −1.66652
\(266\) 5.14554 0.315493
\(267\) −0.360102 −0.0220379
\(268\) 17.4353 1.06503
\(269\) −6.00483 −0.366121 −0.183060 0.983102i \(-0.558600\pi\)
−0.183060 + 0.983102i \(0.558600\pi\)
\(270\) −18.1512 −1.10465
\(271\) 18.1166 1.10051 0.550253 0.834998i \(-0.314531\pi\)
0.550253 + 0.834998i \(0.314531\pi\)
\(272\) 1.17029 0.0709594
\(273\) −7.58608 −0.459131
\(274\) 8.55435 0.516787
\(275\) 11.5440 0.696127
\(276\) −6.98279 −0.420315
\(277\) 18.1936 1.09315 0.546574 0.837411i \(-0.315932\pi\)
0.546574 + 0.837411i \(0.315932\pi\)
\(278\) 4.70321 0.282080
\(279\) −2.01051 −0.120366
\(280\) −14.8760 −0.889013
\(281\) 2.28385 0.136243 0.0681216 0.997677i \(-0.478299\pi\)
0.0681216 + 0.997677i \(0.478299\pi\)
\(282\) −5.95050 −0.354347
\(283\) −20.4761 −1.21718 −0.608590 0.793485i \(-0.708265\pi\)
−0.608590 + 0.793485i \(0.708265\pi\)
\(284\) −8.97352 −0.532480
\(285\) −16.3548 −0.968777
\(286\) 6.18613 0.365794
\(287\) 3.03864 0.179365
\(288\) 9.35041 0.550978
\(289\) −10.1401 −0.596476
\(290\) 3.37617 0.198256
\(291\) 11.0155 0.645740
\(292\) 3.59779 0.210545
\(293\) −29.8294 −1.74265 −0.871327 0.490702i \(-0.836740\pi\)
−0.871327 + 0.490702i \(0.836740\pi\)
\(294\) −5.30899 −0.309627
\(295\) −19.2192 −1.11898
\(296\) −1.46790 −0.0853202
\(297\) 7.35945 0.427038
\(298\) 0.652422 0.0377938
\(299\) 26.2875 1.52025
\(300\) 10.7081 0.618235
\(301\) −8.29941 −0.478370
\(302\) −14.5525 −0.837401
\(303\) 16.1439 0.927446
\(304\) −1.77082 −0.101564
\(305\) −14.5569 −0.833525
\(306\) −4.20733 −0.240517
\(307\) 10.3495 0.590678 0.295339 0.955393i \(-0.404567\pi\)
0.295339 + 0.955393i \(0.404567\pi\)
\(308\) 2.18221 0.124343
\(309\) 2.60779 0.148352
\(310\) −3.96360 −0.225118
\(311\) 25.1043 1.42353 0.711766 0.702416i \(-0.247895\pi\)
0.711766 + 0.702416i \(0.247895\pi\)
\(312\) 15.8602 0.897909
\(313\) 22.6769 1.28177 0.640887 0.767636i \(-0.278567\pi\)
0.640887 + 0.767636i \(0.278567\pi\)
\(314\) −12.2482 −0.691207
\(315\) 8.80341 0.496016
\(316\) 8.24046 0.463562
\(317\) 34.1075 1.91567 0.957834 0.287322i \(-0.0927649\pi\)
0.957834 + 0.287322i \(0.0927649\pi\)
\(318\) −7.79472 −0.437106
\(319\) −1.36888 −0.0766424
\(320\) 21.7011 1.21313
\(321\) 10.9831 0.613015
\(322\) −7.08424 −0.394789
\(323\) −10.3801 −0.577561
\(324\) 0.955682 0.0530935
\(325\) −40.3121 −2.23611
\(326\) 9.55775 0.529355
\(327\) 13.3193 0.736561
\(328\) −6.35290 −0.350780
\(329\) 7.90226 0.435666
\(330\) 5.29881 0.291690
\(331\) 25.4658 1.39973 0.699864 0.714277i \(-0.253244\pi\)
0.699864 + 0.714277i \(0.253244\pi\)
\(332\) 5.68800 0.312170
\(333\) 0.868683 0.0476035
\(334\) −15.4099 −0.843194
\(335\) −56.2223 −3.07175
\(336\) −0.703567 −0.0383827
\(337\) −19.8215 −1.07975 −0.539873 0.841747i \(-0.681528\pi\)
−0.539873 + 0.841747i \(0.681528\pi\)
\(338\) −9.50333 −0.516913
\(339\) −12.1072 −0.657573
\(340\) 10.8574 0.588824
\(341\) 1.60705 0.0870268
\(342\) 6.36630 0.344250
\(343\) 16.8156 0.907958
\(344\) 17.3516 0.935535
\(345\) 22.5169 1.21227
\(346\) 5.20798 0.279983
\(347\) −11.2446 −0.603643 −0.301822 0.953364i \(-0.597595\pi\)
−0.301822 + 0.953364i \(0.597595\pi\)
\(348\) −1.26977 −0.0680667
\(349\) −32.7339 −1.75221 −0.876104 0.482122i \(-0.839866\pi\)
−0.876104 + 0.482122i \(0.839866\pi\)
\(350\) 10.8637 0.580690
\(351\) −25.6996 −1.37174
\(352\) −7.47404 −0.398368
\(353\) 2.29608 0.122208 0.0611041 0.998131i \(-0.480538\pi\)
0.0611041 + 0.998131i \(0.480538\pi\)
\(354\) −5.52205 −0.293494
\(355\) 28.9362 1.53578
\(356\) −0.361730 −0.0191717
\(357\) −4.12410 −0.218271
\(358\) 4.87162 0.257473
\(359\) 17.1885 0.907175 0.453587 0.891212i \(-0.350144\pi\)
0.453587 + 0.891212i \(0.350144\pi\)
\(360\) −18.4053 −0.970045
\(361\) −3.29347 −0.173340
\(362\) −22.7450 −1.19545
\(363\) 10.2674 0.538901
\(364\) −7.62039 −0.399417
\(365\) −11.6015 −0.607251
\(366\) −4.18248 −0.218622
\(367\) 18.4902 0.965183 0.482591 0.875846i \(-0.339696\pi\)
0.482591 + 0.875846i \(0.339696\pi\)
\(368\) 2.43802 0.127091
\(369\) 3.75955 0.195714
\(370\) 1.71256 0.0890319
\(371\) 10.3514 0.537417
\(372\) 1.49070 0.0772891
\(373\) 9.72193 0.503382 0.251691 0.967808i \(-0.419013\pi\)
0.251691 + 0.967808i \(0.419013\pi\)
\(374\) 3.36303 0.173898
\(375\) −13.8961 −0.717592
\(376\) −16.5213 −0.852020
\(377\) 4.78019 0.246192
\(378\) 6.92578 0.356224
\(379\) 17.3861 0.893064 0.446532 0.894768i \(-0.352659\pi\)
0.446532 + 0.894768i \(0.352659\pi\)
\(380\) −16.4288 −0.842780
\(381\) −12.0446 −0.617061
\(382\) −1.16504 −0.0596087
\(383\) −24.4993 −1.25185 −0.625927 0.779882i \(-0.715279\pi\)
−0.625927 + 0.779882i \(0.715279\pi\)
\(384\) −5.99415 −0.305888
\(385\) −7.03681 −0.358629
\(386\) 0.992399 0.0505118
\(387\) −10.2684 −0.521972
\(388\) 11.0653 0.561756
\(389\) −7.29617 −0.369930 −0.184965 0.982745i \(-0.559217\pi\)
−0.184965 + 0.982745i \(0.559217\pi\)
\(390\) −18.5037 −0.936971
\(391\) 14.2910 0.722725
\(392\) −14.7402 −0.744491
\(393\) −19.2320 −0.970127
\(394\) 17.3837 0.875781
\(395\) −26.5724 −1.33700
\(396\) 2.69993 0.135677
\(397\) −5.32902 −0.267456 −0.133728 0.991018i \(-0.542695\pi\)
−0.133728 + 0.991018i \(0.542695\pi\)
\(398\) 2.12668 0.106601
\(399\) 6.24037 0.312409
\(400\) −3.73872 −0.186936
\(401\) 18.5132 0.924503 0.462252 0.886749i \(-0.347042\pi\)
0.462252 + 0.886749i \(0.347042\pi\)
\(402\) −16.1538 −0.805678
\(403\) −5.61191 −0.279549
\(404\) 16.2169 0.806823
\(405\) −3.08172 −0.153132
\(406\) −1.28822 −0.0639331
\(407\) −0.694363 −0.0344183
\(408\) 8.62227 0.426866
\(409\) −21.9890 −1.08728 −0.543642 0.839317i \(-0.682955\pi\)
−0.543642 + 0.839317i \(0.682955\pi\)
\(410\) 7.41175 0.366040
\(411\) 10.3745 0.511735
\(412\) 2.61958 0.129058
\(413\) 7.33328 0.360847
\(414\) −8.76494 −0.430773
\(415\) −18.3417 −0.900358
\(416\) 26.0997 1.27964
\(417\) 5.70393 0.279322
\(418\) −5.08876 −0.248899
\(419\) 3.13878 0.153340 0.0766698 0.997057i \(-0.475571\pi\)
0.0766698 + 0.997057i \(0.475571\pi\)
\(420\) −6.52733 −0.318501
\(421\) 25.6436 1.24979 0.624897 0.780707i \(-0.285141\pi\)
0.624897 + 0.780707i \(0.285141\pi\)
\(422\) −9.07033 −0.441537
\(423\) 9.77704 0.475376
\(424\) −21.6417 −1.05101
\(425\) −21.9153 −1.06305
\(426\) 8.31396 0.402813
\(427\) 5.55434 0.268793
\(428\) 11.0327 0.533287
\(429\) 7.50237 0.362218
\(430\) −20.2436 −0.976233
\(431\) 11.0459 0.532064 0.266032 0.963964i \(-0.414287\pi\)
0.266032 + 0.963964i \(0.414287\pi\)
\(432\) −2.38349 −0.114676
\(433\) 16.5427 0.794992 0.397496 0.917604i \(-0.369879\pi\)
0.397496 + 0.917604i \(0.369879\pi\)
\(434\) 1.51236 0.0725954
\(435\) 4.09453 0.196318
\(436\) 13.3796 0.640765
\(437\) −21.6243 −1.03443
\(438\) −3.33335 −0.159274
\(439\) −4.20024 −0.200467 −0.100233 0.994964i \(-0.531959\pi\)
−0.100233 + 0.994964i \(0.531959\pi\)
\(440\) 14.7119 0.701361
\(441\) 8.72300 0.415381
\(442\) −11.7439 −0.558599
\(443\) 3.63885 0.172887 0.0864436 0.996257i \(-0.472450\pi\)
0.0864436 + 0.996257i \(0.472450\pi\)
\(444\) −0.644089 −0.0305671
\(445\) 1.16644 0.0552948
\(446\) −7.02660 −0.332719
\(447\) 0.791239 0.0374243
\(448\) −8.28030 −0.391207
\(449\) 27.1676 1.28212 0.641060 0.767491i \(-0.278495\pi\)
0.641060 + 0.767491i \(0.278495\pi\)
\(450\) 13.4411 0.633619
\(451\) −3.00511 −0.141505
\(452\) −12.1619 −0.572050
\(453\) −17.6488 −0.829215
\(454\) −15.6082 −0.732529
\(455\) 24.5729 1.15200
\(456\) −13.0468 −0.610970
\(457\) 22.0173 1.02993 0.514963 0.857212i \(-0.327806\pi\)
0.514963 + 0.857212i \(0.327806\pi\)
\(458\) 0.119836 0.00559958
\(459\) −13.9713 −0.652125
\(460\) 22.6187 1.05460
\(461\) −15.3966 −0.717093 −0.358546 0.933512i \(-0.616727\pi\)
−0.358546 + 0.933512i \(0.616727\pi\)
\(462\) −2.02182 −0.0940634
\(463\) −37.8087 −1.75712 −0.878561 0.477631i \(-0.841496\pi\)
−0.878561 + 0.477631i \(0.841496\pi\)
\(464\) 0.443336 0.0205813
\(465\) −4.80695 −0.222917
\(466\) 6.19904 0.287165
\(467\) 15.9218 0.736773 0.368386 0.929673i \(-0.379910\pi\)
0.368386 + 0.929673i \(0.379910\pi\)
\(468\) −9.42829 −0.435823
\(469\) 21.4522 0.990572
\(470\) 19.2749 0.889085
\(471\) −14.8543 −0.684450
\(472\) −15.3317 −0.705699
\(473\) 8.20782 0.377396
\(474\) −7.63478 −0.350677
\(475\) 33.1610 1.52153
\(476\) −4.14275 −0.189883
\(477\) 12.8072 0.586401
\(478\) 7.43648 0.340137
\(479\) −10.5176 −0.480562 −0.240281 0.970703i \(-0.577240\pi\)
−0.240281 + 0.970703i \(0.577240\pi\)
\(480\) 22.3560 1.02041
\(481\) 2.42475 0.110559
\(482\) 23.5552 1.07291
\(483\) −8.59156 −0.390930
\(484\) 10.3139 0.468812
\(485\) −35.6815 −1.62021
\(486\) 14.0083 0.635430
\(487\) −26.2427 −1.18917 −0.594586 0.804032i \(-0.702684\pi\)
−0.594586 + 0.804032i \(0.702684\pi\)
\(488\) −11.6125 −0.525671
\(489\) 11.5914 0.524180
\(490\) 17.1969 0.776878
\(491\) −18.5837 −0.838671 −0.419336 0.907831i \(-0.637737\pi\)
−0.419336 + 0.907831i \(0.637737\pi\)
\(492\) −2.78754 −0.125672
\(493\) 2.59870 0.117040
\(494\) 17.7702 0.799519
\(495\) −8.70626 −0.391317
\(496\) −0.520473 −0.0233699
\(497\) −11.0409 −0.495254
\(498\) −5.26993 −0.236151
\(499\) 35.6758 1.59707 0.798533 0.601951i \(-0.205610\pi\)
0.798533 + 0.601951i \(0.205610\pi\)
\(500\) −13.9590 −0.624263
\(501\) −18.6887 −0.834951
\(502\) −3.31743 −0.148064
\(503\) 7.96197 0.355007 0.177503 0.984120i \(-0.443198\pi\)
0.177503 + 0.984120i \(0.443198\pi\)
\(504\) 7.02274 0.312818
\(505\) −52.2936 −2.32703
\(506\) 7.00606 0.311457
\(507\) −11.5254 −0.511860
\(508\) −12.0990 −0.536807
\(509\) 12.1070 0.536633 0.268317 0.963331i \(-0.413533\pi\)
0.268317 + 0.963331i \(0.413533\pi\)
\(510\) −10.0594 −0.445436
\(511\) 4.42668 0.195825
\(512\) 5.02702 0.222165
\(513\) 21.1406 0.933382
\(514\) 13.9472 0.615183
\(515\) −8.44717 −0.372227
\(516\) 7.61356 0.335168
\(517\) −7.81506 −0.343706
\(518\) −0.653447 −0.0287108
\(519\) 6.31609 0.277246
\(520\) −51.3746 −2.25293
\(521\) 8.29086 0.363229 0.181615 0.983370i \(-0.441868\pi\)
0.181615 + 0.983370i \(0.441868\pi\)
\(522\) −1.59384 −0.0697604
\(523\) −42.8812 −1.87507 −0.937533 0.347896i \(-0.886896\pi\)
−0.937533 + 0.347896i \(0.886896\pi\)
\(524\) −19.3190 −0.843954
\(525\) 13.1752 0.575013
\(526\) −22.3534 −0.974653
\(527\) −3.05086 −0.132898
\(528\) 0.695803 0.0302809
\(529\) 6.77174 0.294423
\(530\) 25.2487 1.09673
\(531\) 9.07306 0.393737
\(532\) 6.26859 0.271778
\(533\) 10.4940 0.454546
\(534\) 0.335143 0.0145031
\(535\) −35.5764 −1.53810
\(536\) −44.8502 −1.93723
\(537\) 5.90816 0.254956
\(538\) 5.58863 0.240943
\(539\) −6.97254 −0.300328
\(540\) −22.1128 −0.951583
\(541\) 34.2565 1.47280 0.736401 0.676546i \(-0.236524\pi\)
0.736401 + 0.676546i \(0.236524\pi\)
\(542\) −16.8610 −0.724240
\(543\) −27.5844 −1.18376
\(544\) 14.1889 0.608343
\(545\) −43.1441 −1.84809
\(546\) 7.06029 0.302152
\(547\) −40.2915 −1.72274 −0.861371 0.507977i \(-0.830394\pi\)
−0.861371 + 0.507977i \(0.830394\pi\)
\(548\) 10.4214 0.445179
\(549\) 6.87208 0.293293
\(550\) −10.7438 −0.458119
\(551\) −3.93222 −0.167518
\(552\) 17.9624 0.764530
\(553\) 10.1390 0.431154
\(554\) −16.9326 −0.719397
\(555\) 2.07695 0.0881615
\(556\) 5.72972 0.242994
\(557\) −41.8987 −1.77531 −0.887653 0.460513i \(-0.847665\pi\)
−0.887653 + 0.460513i \(0.847665\pi\)
\(558\) 1.87116 0.0792123
\(559\) −28.6621 −1.21228
\(560\) 2.27900 0.0963053
\(561\) 4.07859 0.172198
\(562\) −2.12556 −0.0896612
\(563\) −14.9368 −0.629509 −0.314754 0.949173i \(-0.601922\pi\)
−0.314754 + 0.949173i \(0.601922\pi\)
\(564\) −7.24923 −0.305248
\(565\) 39.2177 1.64990
\(566\) 19.0569 0.801022
\(567\) 1.17586 0.0493816
\(568\) 23.0833 0.968554
\(569\) −9.80169 −0.410908 −0.205454 0.978667i \(-0.565867\pi\)
−0.205454 + 0.978667i \(0.565867\pi\)
\(570\) 15.2213 0.637549
\(571\) −34.8837 −1.45984 −0.729920 0.683533i \(-0.760443\pi\)
−0.729920 + 0.683533i \(0.760443\pi\)
\(572\) 7.53629 0.315108
\(573\) −1.41293 −0.0590260
\(574\) −2.82803 −0.118040
\(575\) −45.6551 −1.90395
\(576\) −10.2448 −0.426865
\(577\) −30.6694 −1.27678 −0.638391 0.769712i \(-0.720400\pi\)
−0.638391 + 0.769712i \(0.720400\pi\)
\(578\) 9.43727 0.392539
\(579\) 1.20355 0.0500180
\(580\) 4.11304 0.170785
\(581\) 6.99847 0.290345
\(582\) −10.2520 −0.424959
\(583\) −10.2371 −0.423979
\(584\) −9.25488 −0.382969
\(585\) 30.4027 1.25700
\(586\) 27.7619 1.14684
\(587\) 8.44245 0.348457 0.174229 0.984705i \(-0.444257\pi\)
0.174229 + 0.984705i \(0.444257\pi\)
\(588\) −6.46771 −0.266724
\(589\) 4.61640 0.190215
\(590\) 17.8871 0.736399
\(591\) 21.0825 0.867219
\(592\) 0.224882 0.00924259
\(593\) 48.0421 1.97285 0.986426 0.164208i \(-0.0525068\pi\)
0.986426 + 0.164208i \(0.0525068\pi\)
\(594\) −6.84936 −0.281032
\(595\) 13.3588 0.547658
\(596\) 0.794816 0.0325569
\(597\) 2.57918 0.105559
\(598\) −24.4655 −1.00047
\(599\) 18.1382 0.741105 0.370553 0.928811i \(-0.379168\pi\)
0.370553 + 0.928811i \(0.379168\pi\)
\(600\) −27.5454 −1.12454
\(601\) 28.5285 1.16370 0.581850 0.813296i \(-0.302329\pi\)
0.581850 + 0.813296i \(0.302329\pi\)
\(602\) 7.72417 0.314814
\(603\) 26.5417 1.08086
\(604\) −17.7286 −0.721368
\(605\) −33.2584 −1.35214
\(606\) −15.0250 −0.610349
\(607\) −19.6002 −0.795549 −0.397774 0.917483i \(-0.630217\pi\)
−0.397774 + 0.917483i \(0.630217\pi\)
\(608\) −21.4698 −0.870716
\(609\) −1.56231 −0.0633081
\(610\) 13.5479 0.548540
\(611\) 27.2906 1.10406
\(612\) −5.12560 −0.207190
\(613\) −41.6567 −1.68250 −0.841249 0.540648i \(-0.818179\pi\)
−0.841249 + 0.540648i \(0.818179\pi\)
\(614\) −9.63218 −0.388723
\(615\) 8.98876 0.362462
\(616\) −5.61347 −0.226173
\(617\) 21.0187 0.846182 0.423091 0.906087i \(-0.360945\pi\)
0.423091 + 0.906087i \(0.360945\pi\)
\(618\) −2.42704 −0.0976300
\(619\) −15.8469 −0.636941 −0.318471 0.947933i \(-0.603169\pi\)
−0.318471 + 0.947933i \(0.603169\pi\)
\(620\) −4.82868 −0.193925
\(621\) −29.1058 −1.16798
\(622\) −23.3643 −0.936822
\(623\) −0.445069 −0.0178313
\(624\) −2.42978 −0.0972690
\(625\) 3.17569 0.127028
\(626\) −21.1051 −0.843531
\(627\) −6.17150 −0.246466
\(628\) −14.9215 −0.595431
\(629\) 1.31819 0.0525597
\(630\) −8.19324 −0.326426
\(631\) 9.45459 0.376381 0.188191 0.982133i \(-0.439738\pi\)
0.188191 + 0.982133i \(0.439738\pi\)
\(632\) −21.1976 −0.843195
\(633\) −11.0002 −0.437220
\(634\) −31.7435 −1.26069
\(635\) 39.0148 1.54826
\(636\) −9.49596 −0.376539
\(637\) 24.3485 0.964721
\(638\) 1.27400 0.0504381
\(639\) −13.6603 −0.540395
\(640\) 19.4163 0.767496
\(641\) 33.9176 1.33966 0.669832 0.742513i \(-0.266366\pi\)
0.669832 + 0.742513i \(0.266366\pi\)
\(642\) −10.2218 −0.403423
\(643\) −29.7215 −1.17210 −0.586051 0.810274i \(-0.699318\pi\)
−0.586051 + 0.810274i \(0.699318\pi\)
\(644\) −8.63041 −0.340086
\(645\) −24.5509 −0.966690
\(646\) 9.66060 0.380091
\(647\) −12.6090 −0.495711 −0.247856 0.968797i \(-0.579726\pi\)
−0.247856 + 0.968797i \(0.579726\pi\)
\(648\) −2.45838 −0.0965742
\(649\) −7.25235 −0.284680
\(650\) 37.5180 1.47158
\(651\) 1.83414 0.0718857
\(652\) 11.6438 0.456006
\(653\) −17.2643 −0.675606 −0.337803 0.941217i \(-0.609684\pi\)
−0.337803 + 0.941217i \(0.609684\pi\)
\(654\) −12.3962 −0.484728
\(655\) 62.2965 2.43413
\(656\) 0.973259 0.0379994
\(657\) 5.47689 0.213674
\(658\) −7.35455 −0.286710
\(659\) 42.1769 1.64298 0.821488 0.570225i \(-0.193144\pi\)
0.821488 + 0.570225i \(0.193144\pi\)
\(660\) 6.45530 0.251272
\(661\) 5.32523 0.207127 0.103564 0.994623i \(-0.466975\pi\)
0.103564 + 0.994623i \(0.466975\pi\)
\(662\) −23.7007 −0.921156
\(663\) −14.2426 −0.553139
\(664\) −14.6317 −0.567820
\(665\) −20.2138 −0.783859
\(666\) −0.808474 −0.0313277
\(667\) 5.41377 0.209622
\(668\) −18.7732 −0.726358
\(669\) −8.52166 −0.329466
\(670\) 52.3255 2.02151
\(671\) −5.49304 −0.212057
\(672\) −8.53018 −0.329059
\(673\) 2.73271 0.105338 0.0526692 0.998612i \(-0.483227\pi\)
0.0526692 + 0.998612i \(0.483227\pi\)
\(674\) 18.4477 0.710577
\(675\) 44.6340 1.71796
\(676\) −11.5775 −0.445288
\(677\) −1.03727 −0.0398656 −0.0199328 0.999801i \(-0.506345\pi\)
−0.0199328 + 0.999801i \(0.506345\pi\)
\(678\) 11.2680 0.432747
\(679\) 13.6147 0.522483
\(680\) −27.9293 −1.07104
\(681\) −18.9292 −0.725368
\(682\) −1.49567 −0.0572720
\(683\) 34.4325 1.31752 0.658761 0.752352i \(-0.271081\pi\)
0.658761 + 0.752352i \(0.271081\pi\)
\(684\) 7.75578 0.296550
\(685\) −33.6051 −1.28398
\(686\) −15.6501 −0.597524
\(687\) 0.145334 0.00554484
\(688\) −2.65825 −0.101345
\(689\) 35.7486 1.36191
\(690\) −20.9562 −0.797790
\(691\) −42.1965 −1.60523 −0.802615 0.596498i \(-0.796558\pi\)
−0.802615 + 0.596498i \(0.796558\pi\)
\(692\) 6.34465 0.241188
\(693\) 3.32197 0.126191
\(694\) 10.4653 0.397255
\(695\) −18.4762 −0.700842
\(696\) 3.26633 0.123810
\(697\) 5.70496 0.216091
\(698\) 30.4651 1.15312
\(699\) 7.51803 0.284358
\(700\) 13.2348 0.500228
\(701\) 43.7951 1.65412 0.827059 0.562115i \(-0.190012\pi\)
0.827059 + 0.562115i \(0.190012\pi\)
\(702\) 23.9183 0.902738
\(703\) −1.99462 −0.0752284
\(704\) 8.18892 0.308632
\(705\) 23.3761 0.880394
\(706\) −2.13694 −0.0804248
\(707\) 19.9532 0.750417
\(708\) −6.72727 −0.252826
\(709\) 0.0332206 0.00124763 0.000623813 1.00000i \(-0.499801\pi\)
0.000623813 1.00000i \(0.499801\pi\)
\(710\) −26.9307 −1.01069
\(711\) 12.5444 0.470452
\(712\) 0.930508 0.0348722
\(713\) −6.35573 −0.238024
\(714\) 3.83826 0.143643
\(715\) −24.3017 −0.908833
\(716\) 5.93488 0.221797
\(717\) 9.01875 0.336811
\(718\) −15.9972 −0.597009
\(719\) −28.2468 −1.05343 −0.526713 0.850043i \(-0.676576\pi\)
−0.526713 + 0.850043i \(0.676576\pi\)
\(720\) 2.81968 0.105083
\(721\) 3.22311 0.120035
\(722\) 3.06519 0.114075
\(723\) 28.5671 1.06242
\(724\) −27.7092 −1.02980
\(725\) −8.30204 −0.308330
\(726\) −9.55579 −0.354649
\(727\) 19.0989 0.708339 0.354169 0.935181i \(-0.384764\pi\)
0.354169 + 0.935181i \(0.384764\pi\)
\(728\) 19.6025 0.726518
\(729\) 19.5175 0.722872
\(730\) 10.7974 0.399630
\(731\) −15.5819 −0.576317
\(732\) −5.09534 −0.188329
\(733\) 27.2179 1.00532 0.502659 0.864485i \(-0.332355\pi\)
0.502659 + 0.864485i \(0.332355\pi\)
\(734\) −17.2087 −0.635183
\(735\) 20.8560 0.769284
\(736\) 29.5590 1.08956
\(737\) −21.2155 −0.781483
\(738\) −3.49897 −0.128799
\(739\) 23.4362 0.862115 0.431057 0.902325i \(-0.358141\pi\)
0.431057 + 0.902325i \(0.358141\pi\)
\(740\) 2.08634 0.0766953
\(741\) 21.5512 0.791703
\(742\) −9.63392 −0.353672
\(743\) −11.7677 −0.431716 −0.215858 0.976425i \(-0.569255\pi\)
−0.215858 + 0.976425i \(0.569255\pi\)
\(744\) −3.83465 −0.140585
\(745\) −2.56299 −0.0939005
\(746\) −9.04809 −0.331274
\(747\) 8.65882 0.316810
\(748\) 4.09703 0.149802
\(749\) 13.5746 0.496004
\(750\) 12.9330 0.472245
\(751\) −10.1956 −0.372043 −0.186021 0.982546i \(-0.559559\pi\)
−0.186021 + 0.982546i \(0.559559\pi\)
\(752\) 2.53105 0.0922978
\(753\) −4.02329 −0.146617
\(754\) −4.44887 −0.162018
\(755\) 57.1682 2.08056
\(756\) 8.43738 0.306864
\(757\) −1.24101 −0.0451052 −0.0225526 0.999746i \(-0.507179\pi\)
−0.0225526 + 0.999746i \(0.507179\pi\)
\(758\) −16.1811 −0.587723
\(759\) 8.49675 0.308413
\(760\) 42.2611 1.53297
\(761\) 27.0312 0.979881 0.489941 0.871756i \(-0.337018\pi\)
0.489941 + 0.871756i \(0.337018\pi\)
\(762\) 11.2097 0.406086
\(763\) 16.4621 0.595967
\(764\) −1.41932 −0.0513492
\(765\) 16.5281 0.597576
\(766\) 22.8012 0.823841
\(767\) 25.3256 0.914454
\(768\) 18.9777 0.684799
\(769\) 35.8201 1.29171 0.645854 0.763461i \(-0.276502\pi\)
0.645854 + 0.763461i \(0.276502\pi\)
\(770\) 6.54908 0.236013
\(771\) 16.9147 0.609169
\(772\) 1.20900 0.0435127
\(773\) 52.9323 1.90384 0.951921 0.306343i \(-0.0991054\pi\)
0.951921 + 0.306343i \(0.0991054\pi\)
\(774\) 9.55669 0.343508
\(775\) 9.74654 0.350106
\(776\) −28.4642 −1.02180
\(777\) −0.792482 −0.0284301
\(778\) 6.79047 0.243450
\(779\) −8.63244 −0.309289
\(780\) −22.5422 −0.807142
\(781\) 10.9191 0.390716
\(782\) −13.3004 −0.475623
\(783\) −5.29268 −0.189145
\(784\) 2.25818 0.0806494
\(785\) 48.1162 1.71734
\(786\) 17.8990 0.638437
\(787\) −17.1660 −0.611903 −0.305951 0.952047i \(-0.598974\pi\)
−0.305951 + 0.952047i \(0.598974\pi\)
\(788\) 21.1779 0.754430
\(789\) −27.1095 −0.965124
\(790\) 24.7306 0.879877
\(791\) −14.9640 −0.532057
\(792\) −6.94525 −0.246789
\(793\) 19.1820 0.681172
\(794\) 4.95966 0.176012
\(795\) 30.6209 1.08601
\(796\) 2.59084 0.0918299
\(797\) −14.6775 −0.519902 −0.259951 0.965622i \(-0.583706\pi\)
−0.259951 + 0.965622i \(0.583706\pi\)
\(798\) −5.80784 −0.205595
\(799\) 14.8363 0.524869
\(800\) −45.3290 −1.60262
\(801\) −0.550660 −0.0194566
\(802\) −17.2300 −0.608412
\(803\) −4.37783 −0.154490
\(804\) −19.6795 −0.694041
\(805\) 27.8299 0.980873
\(806\) 5.22294 0.183970
\(807\) 6.77773 0.238587
\(808\) −41.7162 −1.46757
\(809\) 51.6201 1.81486 0.907432 0.420199i \(-0.138040\pi\)
0.907432 + 0.420199i \(0.138040\pi\)
\(810\) 2.86812 0.100776
\(811\) −20.0135 −0.702769 −0.351385 0.936231i \(-0.614289\pi\)
−0.351385 + 0.936231i \(0.614289\pi\)
\(812\) −1.56938 −0.0550743
\(813\) −20.4485 −0.717160
\(814\) 0.646236 0.0226506
\(815\) −37.5468 −1.31521
\(816\) −1.32093 −0.0462416
\(817\) 23.5777 0.824878
\(818\) 20.4649 0.715538
\(819\) −11.6005 −0.405354
\(820\) 9.02940 0.315320
\(821\) 46.1263 1.60982 0.804909 0.593398i \(-0.202214\pi\)
0.804909 + 0.593398i \(0.202214\pi\)
\(822\) −9.65541 −0.336771
\(823\) −47.5554 −1.65768 −0.828839 0.559487i \(-0.810998\pi\)
−0.828839 + 0.559487i \(0.810998\pi\)
\(824\) −6.73856 −0.234749
\(825\) −13.0298 −0.453640
\(826\) −6.82500 −0.237472
\(827\) −55.6918 −1.93660 −0.968298 0.249799i \(-0.919635\pi\)
−0.968298 + 0.249799i \(0.919635\pi\)
\(828\) −10.6779 −0.371084
\(829\) 23.8072 0.826859 0.413430 0.910536i \(-0.364331\pi\)
0.413430 + 0.910536i \(0.364331\pi\)
\(830\) 17.0704 0.592522
\(831\) −20.5354 −0.712364
\(832\) −28.5961 −0.991392
\(833\) 13.2368 0.458628
\(834\) −5.30858 −0.183821
\(835\) 60.5367 2.09496
\(836\) −6.19941 −0.214411
\(837\) 6.21357 0.214772
\(838\) −2.92123 −0.100912
\(839\) 33.9473 1.17199 0.585996 0.810314i \(-0.300703\pi\)
0.585996 + 0.810314i \(0.300703\pi\)
\(840\) 16.7908 0.579337
\(841\) −28.0155 −0.966053
\(842\) −23.8662 −0.822485
\(843\) −2.57782 −0.0887847
\(844\) −11.0500 −0.380356
\(845\) 37.3331 1.28430
\(846\) −9.09938 −0.312843
\(847\) 12.6901 0.436036
\(848\) 3.31549 0.113854
\(849\) 23.1117 0.793191
\(850\) 20.3963 0.699587
\(851\) 2.74613 0.0941362
\(852\) 10.1285 0.346998
\(853\) 4.94436 0.169292 0.0846458 0.996411i \(-0.473024\pi\)
0.0846458 + 0.996411i \(0.473024\pi\)
\(854\) −5.16936 −0.176892
\(855\) −25.0095 −0.855307
\(856\) −28.3804 −0.970021
\(857\) −41.4317 −1.41528 −0.707641 0.706573i \(-0.750240\pi\)
−0.707641 + 0.706573i \(0.750240\pi\)
\(858\) −6.98237 −0.238374
\(859\) 19.7989 0.675528 0.337764 0.941231i \(-0.390329\pi\)
0.337764 + 0.941231i \(0.390329\pi\)
\(860\) −24.6619 −0.840964
\(861\) −3.42976 −0.116886
\(862\) −10.2803 −0.350150
\(863\) 7.69678 0.262001 0.131001 0.991382i \(-0.458181\pi\)
0.131001 + 0.991382i \(0.458181\pi\)
\(864\) −28.8979 −0.983127
\(865\) −20.4591 −0.695632
\(866\) −15.3961 −0.523182
\(867\) 11.4453 0.388701
\(868\) 1.84244 0.0625364
\(869\) −10.0271 −0.340146
\(870\) −3.81073 −0.129196
\(871\) 74.0856 2.51029
\(872\) −34.4173 −1.16552
\(873\) 16.8447 0.570106
\(874\) 20.1255 0.680756
\(875\) −17.1750 −0.580620
\(876\) −4.06087 −0.137204
\(877\) −0.324494 −0.0109574 −0.00547868 0.999985i \(-0.501744\pi\)
−0.00547868 + 0.999985i \(0.501744\pi\)
\(878\) 3.90912 0.131926
\(879\) 33.6689 1.13562
\(880\) −2.25385 −0.0759772
\(881\) −10.8507 −0.365571 −0.182785 0.983153i \(-0.558511\pi\)
−0.182785 + 0.983153i \(0.558511\pi\)
\(882\) −8.11840 −0.273361
\(883\) −20.5832 −0.692679 −0.346340 0.938109i \(-0.612576\pi\)
−0.346340 + 0.938109i \(0.612576\pi\)
\(884\) −14.3070 −0.481198
\(885\) 21.6929 0.729200
\(886\) −3.38664 −0.113776
\(887\) −20.0521 −0.673284 −0.336642 0.941633i \(-0.609291\pi\)
−0.336642 + 0.941633i \(0.609291\pi\)
\(888\) 1.65684 0.0556000
\(889\) −14.8865 −0.499278
\(890\) −1.08560 −0.0363893
\(891\) −1.16289 −0.0389582
\(892\) −8.56019 −0.286616
\(893\) −22.4494 −0.751241
\(894\) −0.736397 −0.0246288
\(895\) −19.1378 −0.639705
\(896\) −7.40849 −0.247500
\(897\) −29.6711 −0.990689
\(898\) −25.2846 −0.843759
\(899\) −1.15574 −0.0385461
\(900\) 16.3747 0.545823
\(901\) 19.4344 0.647454
\(902\) 2.79682 0.0931241
\(903\) 9.36765 0.311736
\(904\) 31.2852 1.04053
\(905\) 89.3517 2.97015
\(906\) 16.4256 0.545703
\(907\) 32.5307 1.08016 0.540082 0.841612i \(-0.318393\pi\)
0.540082 + 0.841612i \(0.318393\pi\)
\(908\) −19.0148 −0.631028
\(909\) 24.6870 0.818816
\(910\) −22.8697 −0.758124
\(911\) −2.26910 −0.0751786 −0.0375893 0.999293i \(-0.511968\pi\)
−0.0375893 + 0.999293i \(0.511968\pi\)
\(912\) 1.99875 0.0661853
\(913\) −6.92124 −0.229059
\(914\) −20.4913 −0.677791
\(915\) 16.4306 0.543177
\(916\) 0.145991 0.00482369
\(917\) −23.7699 −0.784951
\(918\) 13.0030 0.429161
\(919\) 8.15596 0.269040 0.134520 0.990911i \(-0.457051\pi\)
0.134520 + 0.990911i \(0.457051\pi\)
\(920\) −58.1839 −1.91827
\(921\) −11.6816 −0.384923
\(922\) 14.3295 0.471916
\(923\) −38.1300 −1.25507
\(924\) −2.46309 −0.0810297
\(925\) −4.21121 −0.138464
\(926\) 35.1882 1.15636
\(927\) 3.98778 0.130976
\(928\) 5.37509 0.176446
\(929\) −41.7468 −1.36967 −0.684834 0.728699i \(-0.740125\pi\)
−0.684834 + 0.728699i \(0.740125\pi\)
\(930\) 4.47377 0.146701
\(931\) −20.0292 −0.656431
\(932\) 7.55202 0.247375
\(933\) −28.3355 −0.927664
\(934\) −14.8182 −0.484868
\(935\) −13.2114 −0.432059
\(936\) 24.2531 0.792739
\(937\) −11.5755 −0.378156 −0.189078 0.981962i \(-0.560550\pi\)
−0.189078 + 0.981962i \(0.560550\pi\)
\(938\) −19.9654 −0.651892
\(939\) −25.5957 −0.835284
\(940\) 23.4818 0.765891
\(941\) −13.7623 −0.448639 −0.224320 0.974516i \(-0.572016\pi\)
−0.224320 + 0.974516i \(0.572016\pi\)
\(942\) 13.8247 0.450434
\(943\) 11.8849 0.387026
\(944\) 2.34881 0.0764471
\(945\) −27.2074 −0.885056
\(946\) −7.63893 −0.248363
\(947\) 45.1759 1.46802 0.734010 0.679139i \(-0.237647\pi\)
0.734010 + 0.679139i \(0.237647\pi\)
\(948\) −9.30112 −0.302086
\(949\) 15.2876 0.496257
\(950\) −30.8626 −1.00131
\(951\) −38.4976 −1.24837
\(952\) 10.6567 0.345387
\(953\) −25.3947 −0.822616 −0.411308 0.911497i \(-0.634928\pi\)
−0.411308 + 0.911497i \(0.634928\pi\)
\(954\) −11.9195 −0.385909
\(955\) 4.57677 0.148101
\(956\) 9.05953 0.293006
\(957\) 1.54507 0.0499451
\(958\) 9.78863 0.316256
\(959\) 12.8224 0.414056
\(960\) −24.4943 −0.790552
\(961\) −29.6432 −0.956231
\(962\) −2.25669 −0.0727585
\(963\) 16.7951 0.541213
\(964\) 28.6963 0.924244
\(965\) −3.89856 −0.125499
\(966\) 7.99607 0.257269
\(967\) −15.3953 −0.495078 −0.247539 0.968878i \(-0.579622\pi\)
−0.247539 + 0.968878i \(0.579622\pi\)
\(968\) −26.5312 −0.852745
\(969\) 11.7161 0.376376
\(970\) 33.2084 1.06626
\(971\) −37.9457 −1.21773 −0.608867 0.793272i \(-0.708376\pi\)
−0.608867 + 0.793272i \(0.708376\pi\)
\(972\) 17.0657 0.547383
\(973\) 7.04979 0.226006
\(974\) 24.4238 0.782590
\(975\) 45.5008 1.45719
\(976\) 1.77902 0.0569451
\(977\) −29.0856 −0.930532 −0.465266 0.885171i \(-0.654041\pi\)
−0.465266 + 0.885171i \(0.654041\pi\)
\(978\) −10.7880 −0.344961
\(979\) 0.440158 0.0140675
\(980\) 20.9503 0.669232
\(981\) 20.3676 0.650289
\(982\) 17.2957 0.551927
\(983\) −1.00000 −0.0318950
\(984\) 7.17060 0.228590
\(985\) −68.2907 −2.17592
\(986\) −2.41859 −0.0770235
\(987\) −8.91939 −0.283907
\(988\) 21.6487 0.688735
\(989\) −32.4611 −1.03220
\(990\) 8.10282 0.257525
\(991\) 29.2932 0.930529 0.465264 0.885172i \(-0.345959\pi\)
0.465264 + 0.885172i \(0.345959\pi\)
\(992\) −6.31032 −0.200353
\(993\) −28.7436 −0.912151
\(994\) 10.2757 0.325925
\(995\) −8.35449 −0.264855
\(996\) −6.42013 −0.203429
\(997\) 38.5516 1.22094 0.610471 0.792038i \(-0.290980\pi\)
0.610471 + 0.792038i \(0.290980\pi\)
\(998\) −33.2030 −1.05102
\(999\) −2.68471 −0.0849404
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 983.2.a.a.1.11 28
3.2 odd 2 8847.2.a.b.1.18 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.2.a.a.1.11 28 1.1 even 1 trivial
8847.2.a.b.1.18 28 3.2 odd 2