Properties

Label 8017.2.a.a.1.17
Level $8017$
Weight $2$
Character 8017.1
Self dual yes
Analytic conductor $64.016$
Analytic rank $1$
Dimension $327$
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] = [8017,2,Mod(1,8017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8017, 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("8017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8017 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8017.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: \(64.0160673005\)
Analytic rank: \(1\)
Dimension: \(327\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 8017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.59947 q^{2} -1.49239 q^{3} +4.75723 q^{4} +4.02767 q^{5} +3.87942 q^{6} -3.51002 q^{7} -7.16732 q^{8} -0.772773 q^{9} +O(q^{10})\) \(q-2.59947 q^{2} -1.49239 q^{3} +4.75723 q^{4} +4.02767 q^{5} +3.87942 q^{6} -3.51002 q^{7} -7.16732 q^{8} -0.772773 q^{9} -10.4698 q^{10} +2.23298 q^{11} -7.09964 q^{12} -1.36226 q^{13} +9.12417 q^{14} -6.01085 q^{15} +9.11675 q^{16} -1.29513 q^{17} +2.00880 q^{18} -4.22580 q^{19} +19.1605 q^{20} +5.23831 q^{21} -5.80456 q^{22} -2.14241 q^{23} +10.6964 q^{24} +11.2221 q^{25} +3.54115 q^{26} +5.63045 q^{27} -16.6979 q^{28} -0.353354 q^{29} +15.6250 q^{30} -5.53930 q^{31} -9.36405 q^{32} -3.33248 q^{33} +3.36665 q^{34} -14.1372 q^{35} -3.67626 q^{36} -7.16284 q^{37} +10.9848 q^{38} +2.03302 q^{39} -28.8676 q^{40} +8.23137 q^{41} -13.6168 q^{42} -4.26310 q^{43} +10.6228 q^{44} -3.11247 q^{45} +5.56911 q^{46} +4.23999 q^{47} -13.6057 q^{48} +5.32022 q^{49} -29.1715 q^{50} +1.93284 q^{51} -6.48058 q^{52} +7.89854 q^{53} -14.6362 q^{54} +8.99370 q^{55} +25.1574 q^{56} +6.30654 q^{57} +0.918533 q^{58} -4.73553 q^{59} -28.5950 q^{60} +14.5865 q^{61} +14.3992 q^{62} +2.71245 q^{63} +6.10803 q^{64} -5.48673 q^{65} +8.66266 q^{66} -8.06693 q^{67} -6.16123 q^{68} +3.19731 q^{69} +36.7491 q^{70} +15.6313 q^{71} +5.53871 q^{72} +3.68245 q^{73} +18.6196 q^{74} -16.7477 q^{75} -20.1031 q^{76} -7.83780 q^{77} -5.28477 q^{78} -3.05013 q^{79} +36.7192 q^{80} -6.08450 q^{81} -21.3972 q^{82} +14.3652 q^{83} +24.9198 q^{84} -5.21636 q^{85} +11.0818 q^{86} +0.527343 q^{87} -16.0045 q^{88} +11.4896 q^{89} +8.09076 q^{90} +4.78156 q^{91} -10.1919 q^{92} +8.26680 q^{93} -11.0217 q^{94} -17.0201 q^{95} +13.9748 q^{96} +3.50207 q^{97} -13.8297 q^{98} -1.72559 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59947 −1.83810 −0.919050 0.394141i \(-0.871042\pi\)
−0.919050 + 0.394141i \(0.871042\pi\)
\(3\) −1.49239 −0.861632 −0.430816 0.902440i \(-0.641774\pi\)
−0.430816 + 0.902440i \(0.641774\pi\)
\(4\) 4.75723 2.37861
\(5\) 4.02767 1.80123 0.900614 0.434621i \(-0.143118\pi\)
0.900614 + 0.434621i \(0.143118\pi\)
\(6\) 3.87942 1.58377
\(7\) −3.51002 −1.32666 −0.663331 0.748326i \(-0.730858\pi\)
−0.663331 + 0.748326i \(0.730858\pi\)
\(8\) −7.16732 −2.53403
\(9\) −0.772773 −0.257591
\(10\) −10.4698 −3.31084
\(11\) 2.23298 0.673269 0.336634 0.941635i \(-0.390711\pi\)
0.336634 + 0.941635i \(0.390711\pi\)
\(12\) −7.09964 −2.04949
\(13\) −1.36226 −0.377823 −0.188911 0.981994i \(-0.560496\pi\)
−0.188911 + 0.981994i \(0.560496\pi\)
\(14\) 9.12417 2.43854
\(15\) −6.01085 −1.55199
\(16\) 9.11675 2.27919
\(17\) −1.29513 −0.314115 −0.157058 0.987589i \(-0.550201\pi\)
−0.157058 + 0.987589i \(0.550201\pi\)
\(18\) 2.00880 0.473478
\(19\) −4.22580 −0.969464 −0.484732 0.874663i \(-0.661083\pi\)
−0.484732 + 0.874663i \(0.661083\pi\)
\(20\) 19.1605 4.28442
\(21\) 5.23831 1.14309
\(22\) −5.80456 −1.23754
\(23\) −2.14241 −0.446723 −0.223361 0.974736i \(-0.571703\pi\)
−0.223361 + 0.974736i \(0.571703\pi\)
\(24\) 10.6964 2.18340
\(25\) 11.2221 2.24442
\(26\) 3.54115 0.694476
\(27\) 5.63045 1.08358
\(28\) −16.6979 −3.15561
\(29\) −0.353354 −0.0656163 −0.0328081 0.999462i \(-0.510445\pi\)
−0.0328081 + 0.999462i \(0.510445\pi\)
\(30\) 15.6250 2.85272
\(31\) −5.53930 −0.994888 −0.497444 0.867496i \(-0.665728\pi\)
−0.497444 + 0.867496i \(0.665728\pi\)
\(32\) −9.36405 −1.65535
\(33\) −3.33248 −0.580110
\(34\) 3.36665 0.577376
\(35\) −14.1372 −2.38962
\(36\) −3.67626 −0.612709
\(37\) −7.16284 −1.17756 −0.588782 0.808292i \(-0.700392\pi\)
−0.588782 + 0.808292i \(0.700392\pi\)
\(38\) 10.9848 1.78197
\(39\) 2.03302 0.325544
\(40\) −28.8676 −4.56436
\(41\) 8.23137 1.28552 0.642762 0.766066i \(-0.277788\pi\)
0.642762 + 0.766066i \(0.277788\pi\)
\(42\) −13.6168 −2.10112
\(43\) −4.26310 −0.650117 −0.325058 0.945694i \(-0.605384\pi\)
−0.325058 + 0.945694i \(0.605384\pi\)
\(44\) 10.6228 1.60145
\(45\) −3.11247 −0.463980
\(46\) 5.56911 0.821121
\(47\) 4.23999 0.618466 0.309233 0.950986i \(-0.399928\pi\)
0.309233 + 0.950986i \(0.399928\pi\)
\(48\) −13.6057 −1.96382
\(49\) 5.32022 0.760031
\(50\) −29.1715 −4.12547
\(51\) 1.93284 0.270652
\(52\) −6.48058 −0.898694
\(53\) 7.89854 1.08495 0.542474 0.840073i \(-0.317488\pi\)
0.542474 + 0.840073i \(0.317488\pi\)
\(54\) −14.6362 −1.99173
\(55\) 8.99370 1.21271
\(56\) 25.1574 3.36180
\(57\) 6.30654 0.835321
\(58\) 0.918533 0.120609
\(59\) −4.73553 −0.616514 −0.308257 0.951303i \(-0.599746\pi\)
−0.308257 + 0.951303i \(0.599746\pi\)
\(60\) −28.5950 −3.69159
\(61\) 14.5865 1.86761 0.933805 0.357781i \(-0.116467\pi\)
0.933805 + 0.357781i \(0.116467\pi\)
\(62\) 14.3992 1.82870
\(63\) 2.71245 0.341736
\(64\) 6.10803 0.763504
\(65\) −5.48673 −0.680545
\(66\) 8.66266 1.06630
\(67\) −8.06693 −0.985532 −0.492766 0.870162i \(-0.664014\pi\)
−0.492766 + 0.870162i \(0.664014\pi\)
\(68\) −6.16123 −0.747159
\(69\) 3.19731 0.384910
\(70\) 36.7491 4.39236
\(71\) 15.6313 1.85509 0.927545 0.373711i \(-0.121915\pi\)
0.927545 + 0.373711i \(0.121915\pi\)
\(72\) 5.53871 0.652743
\(73\) 3.68245 0.430998 0.215499 0.976504i \(-0.430862\pi\)
0.215499 + 0.976504i \(0.430862\pi\)
\(74\) 18.6196 2.16448
\(75\) −16.7477 −1.93386
\(76\) −20.1031 −2.30598
\(77\) −7.83780 −0.893200
\(78\) −5.28477 −0.598383
\(79\) −3.05013 −0.343167 −0.171583 0.985170i \(-0.554888\pi\)
−0.171583 + 0.985170i \(0.554888\pi\)
\(80\) 36.7192 4.10533
\(81\) −6.08450 −0.676056
\(82\) −21.3972 −2.36292
\(83\) 14.3652 1.57679 0.788393 0.615171i \(-0.210913\pi\)
0.788393 + 0.615171i \(0.210913\pi\)
\(84\) 24.9198 2.71898
\(85\) −5.21636 −0.565793
\(86\) 11.0818 1.19498
\(87\) 0.527343 0.0565371
\(88\) −16.0045 −1.70608
\(89\) 11.4896 1.21789 0.608947 0.793211i \(-0.291592\pi\)
0.608947 + 0.793211i \(0.291592\pi\)
\(90\) 8.09076 0.852842
\(91\) 4.78156 0.501243
\(92\) −10.1919 −1.06258
\(93\) 8.26680 0.857227
\(94\) −11.0217 −1.13680
\(95\) −17.0201 −1.74623
\(96\) 13.9748 1.42630
\(97\) 3.50207 0.355581 0.177791 0.984068i \(-0.443105\pi\)
0.177791 + 0.984068i \(0.443105\pi\)
\(98\) −13.8297 −1.39701
\(99\) −1.72559 −0.173428
\(100\) 53.3860 5.33860
\(101\) −4.27210 −0.425090 −0.212545 0.977151i \(-0.568175\pi\)
−0.212545 + 0.977151i \(0.568175\pi\)
\(102\) −5.02435 −0.497485
\(103\) 4.43274 0.436771 0.218386 0.975863i \(-0.429921\pi\)
0.218386 + 0.975863i \(0.429921\pi\)
\(104\) 9.76375 0.957414
\(105\) 21.0982 2.05897
\(106\) −20.5320 −1.99424
\(107\) −2.47332 −0.239105 −0.119552 0.992828i \(-0.538146\pi\)
−0.119552 + 0.992828i \(0.538146\pi\)
\(108\) 26.7853 2.57742
\(109\) 14.5010 1.38895 0.694474 0.719518i \(-0.255637\pi\)
0.694474 + 0.719518i \(0.255637\pi\)
\(110\) −23.3788 −2.22908
\(111\) 10.6898 1.01463
\(112\) −31.9999 −3.02371
\(113\) 7.57853 0.712928 0.356464 0.934309i \(-0.383982\pi\)
0.356464 + 0.934309i \(0.383982\pi\)
\(114\) −16.3936 −1.53540
\(115\) −8.62890 −0.804649
\(116\) −1.68099 −0.156076
\(117\) 1.05272 0.0973238
\(118\) 12.3099 1.13321
\(119\) 4.54593 0.416725
\(120\) 43.0817 3.93280
\(121\) −6.01380 −0.546709
\(122\) −37.9171 −3.43286
\(123\) −12.2844 −1.10765
\(124\) −26.3517 −2.36645
\(125\) 25.0605 2.24148
\(126\) −7.05091 −0.628145
\(127\) −12.6084 −1.11881 −0.559405 0.828894i \(-0.688970\pi\)
−0.559405 + 0.828894i \(0.688970\pi\)
\(128\) 2.85048 0.251949
\(129\) 6.36221 0.560161
\(130\) 14.2626 1.25091
\(131\) −0.825251 −0.0721025 −0.0360512 0.999350i \(-0.511478\pi\)
−0.0360512 + 0.999350i \(0.511478\pi\)
\(132\) −15.8533 −1.37986
\(133\) 14.8326 1.28615
\(134\) 20.9697 1.81151
\(135\) 22.6776 1.95177
\(136\) 9.28262 0.795978
\(137\) −18.5960 −1.58877 −0.794383 0.607417i \(-0.792206\pi\)
−0.794383 + 0.607417i \(0.792206\pi\)
\(138\) −8.31129 −0.707504
\(139\) 7.24923 0.614871 0.307436 0.951569i \(-0.400529\pi\)
0.307436 + 0.951569i \(0.400529\pi\)
\(140\) −67.2537 −5.68398
\(141\) −6.32772 −0.532890
\(142\) −40.6330 −3.40984
\(143\) −3.04190 −0.254376
\(144\) −7.04517 −0.587098
\(145\) −1.42319 −0.118190
\(146\) −9.57241 −0.792218
\(147\) −7.93984 −0.654867
\(148\) −34.0753 −2.80097
\(149\) −12.5800 −1.03059 −0.515297 0.857012i \(-0.672318\pi\)
−0.515297 + 0.857012i \(0.672318\pi\)
\(150\) 43.5352 3.55463
\(151\) −18.4981 −1.50536 −0.752678 0.658389i \(-0.771238\pi\)
−0.752678 + 0.658389i \(0.771238\pi\)
\(152\) 30.2876 2.45665
\(153\) 1.00084 0.0809133
\(154\) 20.3741 1.64179
\(155\) −22.3105 −1.79202
\(156\) 9.67155 0.774344
\(157\) −7.46170 −0.595508 −0.297754 0.954643i \(-0.596238\pi\)
−0.297754 + 0.954643i \(0.596238\pi\)
\(158\) 7.92872 0.630775
\(159\) −11.7877 −0.934826
\(160\) −37.7153 −2.98165
\(161\) 7.51988 0.592650
\(162\) 15.8165 1.24266
\(163\) −6.22827 −0.487836 −0.243918 0.969796i \(-0.578433\pi\)
−0.243918 + 0.969796i \(0.578433\pi\)
\(164\) 39.1585 3.05776
\(165\) −13.4221 −1.04491
\(166\) −37.3419 −2.89829
\(167\) −1.51025 −0.116866 −0.0584332 0.998291i \(-0.518610\pi\)
−0.0584332 + 0.998291i \(0.518610\pi\)
\(168\) −37.5446 −2.89663
\(169\) −11.1442 −0.857250
\(170\) 13.5597 1.03998
\(171\) 3.26558 0.249725
\(172\) −20.2805 −1.54638
\(173\) −2.46849 −0.187676 −0.0938379 0.995587i \(-0.529914\pi\)
−0.0938379 + 0.995587i \(0.529914\pi\)
\(174\) −1.37081 −0.103921
\(175\) −39.3897 −2.97759
\(176\) 20.3575 1.53451
\(177\) 7.06726 0.531208
\(178\) −29.8668 −2.23861
\(179\) 19.4236 1.45179 0.725895 0.687805i \(-0.241426\pi\)
0.725895 + 0.687805i \(0.241426\pi\)
\(180\) −14.8067 −1.10363
\(181\) 9.18538 0.682744 0.341372 0.939928i \(-0.389108\pi\)
0.341372 + 0.939928i \(0.389108\pi\)
\(182\) −12.4295 −0.921335
\(183\) −21.7688 −1.60919
\(184\) 15.3553 1.13201
\(185\) −28.8495 −2.12106
\(186\) −21.4893 −1.57567
\(187\) −2.89200 −0.211484
\(188\) 20.1706 1.47109
\(189\) −19.7630 −1.43754
\(190\) 44.2432 3.20974
\(191\) 6.15737 0.445531 0.222766 0.974872i \(-0.428492\pi\)
0.222766 + 0.974872i \(0.428492\pi\)
\(192\) −9.11556 −0.657859
\(193\) −27.6051 −1.98706 −0.993529 0.113575i \(-0.963770\pi\)
−0.993529 + 0.113575i \(0.963770\pi\)
\(194\) −9.10351 −0.653594
\(195\) 8.18834 0.586379
\(196\) 25.3095 1.80782
\(197\) −24.0659 −1.71463 −0.857313 0.514796i \(-0.827868\pi\)
−0.857313 + 0.514796i \(0.827868\pi\)
\(198\) 4.48560 0.318778
\(199\) −8.12255 −0.575792 −0.287896 0.957662i \(-0.592956\pi\)
−0.287896 + 0.957662i \(0.592956\pi\)
\(200\) −80.4323 −5.68742
\(201\) 12.0390 0.849166
\(202\) 11.1052 0.781359
\(203\) 1.24028 0.0870506
\(204\) 9.19496 0.643776
\(205\) 33.1532 2.31552
\(206\) −11.5228 −0.802829
\(207\) 1.65559 0.115072
\(208\) −12.4194 −0.861129
\(209\) −9.43612 −0.652710
\(210\) −54.8440 −3.78460
\(211\) −4.04696 −0.278604 −0.139302 0.990250i \(-0.544486\pi\)
−0.139302 + 0.990250i \(0.544486\pi\)
\(212\) 37.5752 2.58067
\(213\) −23.3279 −1.59840
\(214\) 6.42932 0.439499
\(215\) −17.1703 −1.17101
\(216\) −40.3552 −2.74582
\(217\) 19.4430 1.31988
\(218\) −37.6950 −2.55303
\(219\) −5.49565 −0.371362
\(220\) 42.7851 2.88457
\(221\) 1.76431 0.118680
\(222\) −27.7877 −1.86499
\(223\) −3.95288 −0.264705 −0.132352 0.991203i \(-0.542253\pi\)
−0.132352 + 0.991203i \(0.542253\pi\)
\(224\) 32.8680 2.19608
\(225\) −8.67213 −0.578142
\(226\) −19.7001 −1.31043
\(227\) −13.8917 −0.922024 −0.461012 0.887394i \(-0.652514\pi\)
−0.461012 + 0.887394i \(0.652514\pi\)
\(228\) 30.0016 1.98691
\(229\) 25.0062 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(230\) 22.4305 1.47903
\(231\) 11.6970 0.769609
\(232\) 2.53260 0.166274
\(233\) −10.6103 −0.695106 −0.347553 0.937660i \(-0.612987\pi\)
−0.347553 + 0.937660i \(0.612987\pi\)
\(234\) −2.73650 −0.178891
\(235\) 17.0773 1.11400
\(236\) −22.5280 −1.46645
\(237\) 4.55199 0.295683
\(238\) −11.8170 −0.765982
\(239\) −12.8261 −0.829651 −0.414825 0.909901i \(-0.636157\pi\)
−0.414825 + 0.909901i \(0.636157\pi\)
\(240\) −54.7994 −3.53728
\(241\) 13.7210 0.883845 0.441922 0.897053i \(-0.354297\pi\)
0.441922 + 0.897053i \(0.354297\pi\)
\(242\) 15.6327 1.00491
\(243\) −7.81089 −0.501069
\(244\) 69.3913 4.44232
\(245\) 21.4281 1.36899
\(246\) 31.9329 2.03597
\(247\) 5.75663 0.366286
\(248\) 39.7019 2.52107
\(249\) −21.4385 −1.35861
\(250\) −65.1440 −4.12007
\(251\) −19.5255 −1.23244 −0.616218 0.787576i \(-0.711336\pi\)
−0.616218 + 0.787576i \(0.711336\pi\)
\(252\) 12.9037 0.812858
\(253\) −4.78395 −0.300764
\(254\) 32.7750 2.05649
\(255\) 7.78484 0.487505
\(256\) −19.6258 −1.22661
\(257\) 22.7552 1.41943 0.709714 0.704490i \(-0.248824\pi\)
0.709714 + 0.704490i \(0.248824\pi\)
\(258\) −16.5383 −1.02963
\(259\) 25.1417 1.56223
\(260\) −26.1016 −1.61875
\(261\) 0.273063 0.0169022
\(262\) 2.14521 0.132532
\(263\) −18.0648 −1.11392 −0.556961 0.830538i \(-0.688033\pi\)
−0.556961 + 0.830538i \(0.688033\pi\)
\(264\) 23.8849 1.47001
\(265\) 31.8127 1.95424
\(266\) −38.5569 −2.36407
\(267\) −17.1470 −1.04938
\(268\) −38.3762 −2.34420
\(269\) 25.6637 1.56474 0.782372 0.622811i \(-0.214010\pi\)
0.782372 + 0.622811i \(0.214010\pi\)
\(270\) −58.9496 −3.58756
\(271\) 11.9563 0.726293 0.363147 0.931732i \(-0.381702\pi\)
0.363147 + 0.931732i \(0.381702\pi\)
\(272\) −11.8074 −0.715928
\(273\) −7.13594 −0.431887
\(274\) 48.3398 2.92031
\(275\) 25.0587 1.51110
\(276\) 15.2103 0.915553
\(277\) −22.1823 −1.33281 −0.666404 0.745591i \(-0.732167\pi\)
−0.666404 + 0.745591i \(0.732167\pi\)
\(278\) −18.8441 −1.13020
\(279\) 4.28062 0.256274
\(280\) 101.326 6.05536
\(281\) −3.27908 −0.195614 −0.0978069 0.995205i \(-0.531183\pi\)
−0.0978069 + 0.995205i \(0.531183\pi\)
\(282\) 16.4487 0.979505
\(283\) −9.59509 −0.570369 −0.285185 0.958473i \(-0.592055\pi\)
−0.285185 + 0.958473i \(0.592055\pi\)
\(284\) 74.3615 4.41254
\(285\) 25.4006 1.50460
\(286\) 7.90731 0.467569
\(287\) −28.8922 −1.70546
\(288\) 7.23628 0.426402
\(289\) −15.3226 −0.901331
\(290\) 3.69954 0.217245
\(291\) −5.22645 −0.306380
\(292\) 17.5183 1.02518
\(293\) 19.8258 1.15823 0.579117 0.815244i \(-0.303397\pi\)
0.579117 + 0.815244i \(0.303397\pi\)
\(294\) 20.6393 1.20371
\(295\) −19.0731 −1.11048
\(296\) 51.3384 2.98398
\(297\) 12.5727 0.729541
\(298\) 32.7013 1.89433
\(299\) 2.91851 0.168782
\(300\) −79.6728 −4.59991
\(301\) 14.9636 0.862485
\(302\) 48.0853 2.76700
\(303\) 6.37565 0.366271
\(304\) −38.5255 −2.20959
\(305\) 58.7496 3.36399
\(306\) −2.60166 −0.148727
\(307\) 0.426475 0.0243402 0.0121701 0.999926i \(-0.496126\pi\)
0.0121701 + 0.999926i \(0.496126\pi\)
\(308\) −37.2862 −2.12458
\(309\) −6.61538 −0.376336
\(310\) 57.9953 3.29391
\(311\) −0.218043 −0.0123641 −0.00618204 0.999981i \(-0.501968\pi\)
−0.00618204 + 0.999981i \(0.501968\pi\)
\(312\) −14.5713 −0.824938
\(313\) −8.50023 −0.480461 −0.240231 0.970716i \(-0.577223\pi\)
−0.240231 + 0.970716i \(0.577223\pi\)
\(314\) 19.3964 1.09460
\(315\) 10.9248 0.615544
\(316\) −14.5102 −0.816261
\(317\) 8.86492 0.497904 0.248952 0.968516i \(-0.419914\pi\)
0.248952 + 0.968516i \(0.419914\pi\)
\(318\) 30.6417 1.71830
\(319\) −0.789033 −0.0441774
\(320\) 24.6011 1.37524
\(321\) 3.69116 0.206020
\(322\) −19.5477 −1.08935
\(323\) 5.47296 0.304524
\(324\) −28.9454 −1.60808
\(325\) −15.2874 −0.847993
\(326\) 16.1902 0.896691
\(327\) −21.6412 −1.19676
\(328\) −58.9968 −3.25755
\(329\) −14.8824 −0.820495
\(330\) 34.8903 1.92065
\(331\) 18.1989 1.00030 0.500151 0.865938i \(-0.333278\pi\)
0.500151 + 0.865938i \(0.333278\pi\)
\(332\) 68.3386 3.75057
\(333\) 5.53525 0.303330
\(334\) 3.92584 0.214812
\(335\) −32.4909 −1.77517
\(336\) 47.7564 2.60532
\(337\) −25.4951 −1.38881 −0.694404 0.719586i \(-0.744332\pi\)
−0.694404 + 0.719586i \(0.744332\pi\)
\(338\) 28.9691 1.57571
\(339\) −11.3101 −0.614281
\(340\) −24.8154 −1.34580
\(341\) −12.3691 −0.669827
\(342\) −8.48877 −0.459020
\(343\) 5.89606 0.318357
\(344\) 30.5550 1.64741
\(345\) 12.8777 0.693311
\(346\) 6.41675 0.344967
\(347\) −1.89644 −0.101806 −0.0509031 0.998704i \(-0.516210\pi\)
−0.0509031 + 0.998704i \(0.516210\pi\)
\(348\) 2.50869 0.134480
\(349\) −25.8118 −1.38167 −0.690836 0.723012i \(-0.742757\pi\)
−0.690836 + 0.723012i \(0.742757\pi\)
\(350\) 102.392 5.47310
\(351\) −7.67013 −0.409401
\(352\) −20.9097 −1.11449
\(353\) −13.8009 −0.734550 −0.367275 0.930112i \(-0.619709\pi\)
−0.367275 + 0.930112i \(0.619709\pi\)
\(354\) −18.3711 −0.976413
\(355\) 62.9575 3.34144
\(356\) 54.6586 2.89690
\(357\) −6.78430 −0.359063
\(358\) −50.4911 −2.66854
\(359\) −15.7467 −0.831081 −0.415541 0.909575i \(-0.636408\pi\)
−0.415541 + 0.909575i \(0.636408\pi\)
\(360\) 22.3081 1.17574
\(361\) −1.14264 −0.0601390
\(362\) −23.8771 −1.25495
\(363\) 8.97493 0.471062
\(364\) 22.7469 1.19226
\(365\) 14.8317 0.776326
\(366\) 56.5871 2.95786
\(367\) 17.9908 0.939111 0.469556 0.882903i \(-0.344414\pi\)
0.469556 + 0.882903i \(0.344414\pi\)
\(368\) −19.5318 −1.01816
\(369\) −6.36098 −0.331139
\(370\) 74.9934 3.89872
\(371\) −27.7240 −1.43936
\(372\) 39.3270 2.03901
\(373\) −10.5044 −0.543900 −0.271950 0.962311i \(-0.587668\pi\)
−0.271950 + 0.962311i \(0.587668\pi\)
\(374\) 7.51766 0.388729
\(375\) −37.4001 −1.93133
\(376\) −30.3893 −1.56721
\(377\) 0.481361 0.0247913
\(378\) 51.3732 2.64235
\(379\) −38.5594 −1.98066 −0.990332 0.138720i \(-0.955701\pi\)
−0.990332 + 0.138720i \(0.955701\pi\)
\(380\) −80.9685 −4.15359
\(381\) 18.8166 0.964002
\(382\) −16.0059 −0.818931
\(383\) 15.4110 0.787465 0.393732 0.919225i \(-0.371184\pi\)
0.393732 + 0.919225i \(0.371184\pi\)
\(384\) −4.25402 −0.217087
\(385\) −31.5680 −1.60886
\(386\) 71.7585 3.65241
\(387\) 3.29441 0.167464
\(388\) 16.6601 0.845790
\(389\) 15.3831 0.779955 0.389977 0.920824i \(-0.372483\pi\)
0.389977 + 0.920824i \(0.372483\pi\)
\(390\) −21.2853 −1.07782
\(391\) 2.77470 0.140323
\(392\) −38.1317 −1.92594
\(393\) 1.23160 0.0621258
\(394\) 62.5585 3.15165
\(395\) −12.2849 −0.618122
\(396\) −8.20900 −0.412518
\(397\) 2.06198 0.103488 0.0517439 0.998660i \(-0.483522\pi\)
0.0517439 + 0.998660i \(0.483522\pi\)
\(398\) 21.1143 1.05836
\(399\) −22.1360 −1.10819
\(400\) 102.309 5.11545
\(401\) −35.8697 −1.79125 −0.895625 0.444810i \(-0.853271\pi\)
−0.895625 + 0.444810i \(0.853271\pi\)
\(402\) −31.2950 −1.56085
\(403\) 7.54597 0.375891
\(404\) −20.3234 −1.01113
\(405\) −24.5064 −1.21773
\(406\) −3.22407 −0.160008
\(407\) −15.9945 −0.792817
\(408\) −13.8533 −0.685840
\(409\) −8.67264 −0.428835 −0.214417 0.976742i \(-0.568785\pi\)
−0.214417 + 0.976742i \(0.568785\pi\)
\(410\) −86.1807 −4.25616
\(411\) 27.7525 1.36893
\(412\) 21.0876 1.03891
\(413\) 16.6218 0.817905
\(414\) −4.30366 −0.211513
\(415\) 57.8583 2.84015
\(416\) 12.7563 0.625427
\(417\) −10.8187 −0.529793
\(418\) 24.5289 1.19975
\(419\) −25.2913 −1.23556 −0.617779 0.786351i \(-0.711968\pi\)
−0.617779 + 0.786351i \(0.711968\pi\)
\(420\) 100.369 4.89750
\(421\) −2.61582 −0.127487 −0.0637437 0.997966i \(-0.520304\pi\)
−0.0637437 + 0.997966i \(0.520304\pi\)
\(422\) 10.5199 0.512102
\(423\) −3.27655 −0.159311
\(424\) −56.6114 −2.74929
\(425\) −14.5341 −0.705007
\(426\) 60.6402 2.93803
\(427\) −51.1989 −2.47769
\(428\) −11.7661 −0.568738
\(429\) 4.53970 0.219179
\(430\) 44.6337 2.15243
\(431\) −14.0539 −0.676951 −0.338475 0.940975i \(-0.609911\pi\)
−0.338475 + 0.940975i \(0.609911\pi\)
\(432\) 51.3314 2.46968
\(433\) 33.6468 1.61696 0.808482 0.588521i \(-0.200290\pi\)
0.808482 + 0.588521i \(0.200290\pi\)
\(434\) −50.5415 −2.42607
\(435\) 2.12396 0.101836
\(436\) 68.9847 3.30377
\(437\) 9.05337 0.433082
\(438\) 14.2858 0.682600
\(439\) 20.0222 0.955609 0.477804 0.878466i \(-0.341433\pi\)
0.477804 + 0.878466i \(0.341433\pi\)
\(440\) −64.4607 −3.07304
\(441\) −4.11132 −0.195777
\(442\) −4.58625 −0.218146
\(443\) 5.44302 0.258606 0.129303 0.991605i \(-0.458726\pi\)
0.129303 + 0.991605i \(0.458726\pi\)
\(444\) 50.8536 2.41340
\(445\) 46.2763 2.19370
\(446\) 10.2754 0.486554
\(447\) 18.7743 0.887992
\(448\) −21.4393 −1.01291
\(449\) −11.7769 −0.555784 −0.277892 0.960612i \(-0.589636\pi\)
−0.277892 + 0.960612i \(0.589636\pi\)
\(450\) 22.5429 1.06268
\(451\) 18.3805 0.865503
\(452\) 36.0528 1.69578
\(453\) 27.6064 1.29706
\(454\) 36.1110 1.69477
\(455\) 19.2585 0.902853
\(456\) −45.2009 −2.11673
\(457\) −6.35760 −0.297396 −0.148698 0.988883i \(-0.547508\pi\)
−0.148698 + 0.988883i \(0.547508\pi\)
\(458\) −65.0027 −3.03738
\(459\) −7.29217 −0.340369
\(460\) −41.0496 −1.91395
\(461\) 11.7091 0.545349 0.272674 0.962106i \(-0.412092\pi\)
0.272674 + 0.962106i \(0.412092\pi\)
\(462\) −30.4061 −1.41462
\(463\) 16.8431 0.782767 0.391384 0.920228i \(-0.371997\pi\)
0.391384 + 0.920228i \(0.371997\pi\)
\(464\) −3.22144 −0.149552
\(465\) 33.2959 1.54406
\(466\) 27.5812 1.27767
\(467\) −33.0153 −1.52777 −0.763883 0.645355i \(-0.776709\pi\)
−0.763883 + 0.645355i \(0.776709\pi\)
\(468\) 5.00801 0.231496
\(469\) 28.3151 1.30747
\(470\) −44.3918 −2.04764
\(471\) 11.1358 0.513109
\(472\) 33.9410 1.56226
\(473\) −9.51942 −0.437703
\(474\) −11.8327 −0.543496
\(475\) −47.4223 −2.17588
\(476\) 21.6260 0.991227
\(477\) −6.10378 −0.279473
\(478\) 33.3410 1.52498
\(479\) 20.0977 0.918287 0.459143 0.888362i \(-0.348156\pi\)
0.459143 + 0.888362i \(0.348156\pi\)
\(480\) 56.2859 2.56909
\(481\) 9.75766 0.444911
\(482\) −35.6672 −1.62460
\(483\) −11.2226 −0.510646
\(484\) −28.6090 −1.30041
\(485\) 14.1052 0.640482
\(486\) 20.3042 0.921015
\(487\) −8.41434 −0.381290 −0.190645 0.981659i \(-0.561058\pi\)
−0.190645 + 0.981659i \(0.561058\pi\)
\(488\) −104.546 −4.73258
\(489\) 9.29501 0.420335
\(490\) −55.7015 −2.51634
\(491\) −27.8242 −1.25569 −0.627845 0.778338i \(-0.716063\pi\)
−0.627845 + 0.778338i \(0.716063\pi\)
\(492\) −58.4397 −2.63467
\(493\) 0.457640 0.0206111
\(494\) −14.9642 −0.673270
\(495\) −6.95009 −0.312383
\(496\) −50.5004 −2.26754
\(497\) −54.8660 −2.46108
\(498\) 55.7286 2.49726
\(499\) 0.537870 0.0240784 0.0120392 0.999928i \(-0.496168\pi\)
0.0120392 + 0.999928i \(0.496168\pi\)
\(500\) 119.219 5.33162
\(501\) 2.25388 0.100696
\(502\) 50.7558 2.26534
\(503\) −13.1843 −0.587861 −0.293930 0.955827i \(-0.594963\pi\)
−0.293930 + 0.955827i \(0.594963\pi\)
\(504\) −19.4410 −0.865969
\(505\) −17.2066 −0.765684
\(506\) 12.4357 0.552835
\(507\) 16.6316 0.738634
\(508\) −59.9808 −2.66122
\(509\) 29.4147 1.30378 0.651891 0.758313i \(-0.273976\pi\)
0.651891 + 0.758313i \(0.273976\pi\)
\(510\) −20.2364 −0.896084
\(511\) −12.9255 −0.571789
\(512\) 45.3156 2.00269
\(513\) −23.7931 −1.05049
\(514\) −59.1513 −2.60905
\(515\) 17.8536 0.786724
\(516\) 30.2665 1.33241
\(517\) 9.46781 0.416394
\(518\) −65.3550 −2.87153
\(519\) 3.68395 0.161707
\(520\) 39.3251 1.72452
\(521\) 25.9814 1.13827 0.569134 0.822245i \(-0.307279\pi\)
0.569134 + 0.822245i \(0.307279\pi\)
\(522\) −0.709817 −0.0310679
\(523\) −16.8680 −0.737584 −0.368792 0.929512i \(-0.620229\pi\)
−0.368792 + 0.929512i \(0.620229\pi\)
\(524\) −3.92590 −0.171504
\(525\) 58.7849 2.56558
\(526\) 46.9588 2.04750
\(527\) 7.17412 0.312510
\(528\) −30.3813 −1.32218
\(529\) −18.4101 −0.800439
\(530\) −82.6960 −3.59209
\(531\) 3.65949 0.158808
\(532\) 70.5621 3.05926
\(533\) −11.2133 −0.485700
\(534\) 44.5729 1.92886
\(535\) −9.96171 −0.430682
\(536\) 57.8182 2.49737
\(537\) −28.9876 −1.25091
\(538\) −66.7120 −2.87616
\(539\) 11.8799 0.511705
\(540\) 107.882 4.64251
\(541\) −4.42766 −0.190360 −0.0951799 0.995460i \(-0.530343\pi\)
−0.0951799 + 0.995460i \(0.530343\pi\)
\(542\) −31.0800 −1.33500
\(543\) −13.7082 −0.588274
\(544\) 12.1277 0.519970
\(545\) 58.4053 2.50181
\(546\) 18.5496 0.793852
\(547\) 3.77903 0.161579 0.0807897 0.996731i \(-0.474256\pi\)
0.0807897 + 0.996731i \(0.474256\pi\)
\(548\) −88.4655 −3.77906
\(549\) −11.2721 −0.481080
\(550\) −65.1393 −2.77755
\(551\) 1.49320 0.0636126
\(552\) −22.9161 −0.975374
\(553\) 10.7060 0.455266
\(554\) 57.6623 2.44983
\(555\) 43.0548 1.82757
\(556\) 34.4862 1.46254
\(557\) 21.4370 0.908314 0.454157 0.890922i \(-0.349940\pi\)
0.454157 + 0.890922i \(0.349940\pi\)
\(558\) −11.1273 −0.471058
\(559\) 5.80745 0.245629
\(560\) −128.885 −5.44639
\(561\) 4.31599 0.182221
\(562\) 8.52387 0.359558
\(563\) −41.0285 −1.72914 −0.864572 0.502509i \(-0.832410\pi\)
−0.864572 + 0.502509i \(0.832410\pi\)
\(564\) −30.1024 −1.26754
\(565\) 30.5238 1.28415
\(566\) 24.9421 1.04840
\(567\) 21.3567 0.896898
\(568\) −112.034 −4.70085
\(569\) 39.8989 1.67265 0.836325 0.548234i \(-0.184700\pi\)
0.836325 + 0.548234i \(0.184700\pi\)
\(570\) −66.0281 −2.76561
\(571\) 41.6885 1.74461 0.872304 0.488964i \(-0.162625\pi\)
0.872304 + 0.488964i \(0.162625\pi\)
\(572\) −14.4710 −0.605063
\(573\) −9.18919 −0.383884
\(574\) 75.1044 3.13480
\(575\) −24.0423 −1.00263
\(576\) −4.72012 −0.196672
\(577\) −10.2985 −0.428732 −0.214366 0.976753i \(-0.568769\pi\)
−0.214366 + 0.976753i \(0.568769\pi\)
\(578\) 39.8307 1.65674
\(579\) 41.1976 1.71211
\(580\) −6.77045 −0.281128
\(581\) −50.4221 −2.09186
\(582\) 13.5860 0.563157
\(583\) 17.6373 0.730462
\(584\) −26.3933 −1.09216
\(585\) 4.23999 0.175302
\(586\) −51.5364 −2.12895
\(587\) −24.4774 −1.01029 −0.505146 0.863034i \(-0.668561\pi\)
−0.505146 + 0.863034i \(0.668561\pi\)
\(588\) −37.7716 −1.55768
\(589\) 23.4080 0.964508
\(590\) 49.5800 2.04118
\(591\) 35.9157 1.47738
\(592\) −65.3018 −2.68389
\(593\) −24.5084 −1.00644 −0.503219 0.864159i \(-0.667851\pi\)
−0.503219 + 0.864159i \(0.667851\pi\)
\(594\) −32.6823 −1.34097
\(595\) 18.3095 0.750616
\(596\) −59.8459 −2.45138
\(597\) 12.1220 0.496121
\(598\) −7.58658 −0.310238
\(599\) −47.1516 −1.92656 −0.963282 0.268492i \(-0.913475\pi\)
−0.963282 + 0.268492i \(0.913475\pi\)
\(600\) 120.036 4.90046
\(601\) 13.5494 0.552690 0.276345 0.961059i \(-0.410877\pi\)
0.276345 + 0.961059i \(0.410877\pi\)
\(602\) −38.8972 −1.58533
\(603\) 6.23390 0.253864
\(604\) −87.9998 −3.58066
\(605\) −24.2216 −0.984747
\(606\) −16.5733 −0.673243
\(607\) 0.385009 0.0156270 0.00781351 0.999969i \(-0.497513\pi\)
0.00781351 + 0.999969i \(0.497513\pi\)
\(608\) 39.5706 1.60480
\(609\) −1.85098 −0.0750055
\(610\) −152.718 −6.18335
\(611\) −5.77597 −0.233671
\(612\) 4.76123 0.192461
\(613\) −18.5161 −0.747859 −0.373930 0.927457i \(-0.621990\pi\)
−0.373930 + 0.927457i \(0.621990\pi\)
\(614\) −1.10861 −0.0447398
\(615\) −49.4775 −1.99513
\(616\) 56.1760 2.26339
\(617\) 27.4384 1.10463 0.552313 0.833637i \(-0.313745\pi\)
0.552313 + 0.833637i \(0.313745\pi\)
\(618\) 17.1965 0.691743
\(619\) 47.6959 1.91706 0.958531 0.284989i \(-0.0919900\pi\)
0.958531 + 0.284989i \(0.0919900\pi\)
\(620\) −106.136 −4.26252
\(621\) −12.0627 −0.484060
\(622\) 0.566795 0.0227264
\(623\) −40.3287 −1.61573
\(624\) 18.5346 0.741976
\(625\) 44.8250 1.79300
\(626\) 22.0961 0.883136
\(627\) 14.0824 0.562396
\(628\) −35.4970 −1.41648
\(629\) 9.27682 0.369891
\(630\) −28.3987 −1.13143
\(631\) −27.1429 −1.08054 −0.540270 0.841492i \(-0.681678\pi\)
−0.540270 + 0.841492i \(0.681678\pi\)
\(632\) 21.8613 0.869595
\(633\) 6.03964 0.240054
\(634\) −23.0441 −0.915197
\(635\) −50.7822 −2.01523
\(636\) −56.0768 −2.22359
\(637\) −7.24752 −0.287157
\(638\) 2.05107 0.0812025
\(639\) −12.0794 −0.477855
\(640\) 11.4808 0.453817
\(641\) 21.9832 0.868286 0.434143 0.900844i \(-0.357051\pi\)
0.434143 + 0.900844i \(0.357051\pi\)
\(642\) −9.59504 −0.378686
\(643\) 42.0389 1.65785 0.828925 0.559359i \(-0.188953\pi\)
0.828925 + 0.559359i \(0.188953\pi\)
\(644\) 35.7738 1.40968
\(645\) 25.6248 1.00898
\(646\) −14.2268 −0.559745
\(647\) −25.3347 −0.996009 −0.498005 0.867174i \(-0.665934\pi\)
−0.498005 + 0.867174i \(0.665934\pi\)
\(648\) 43.6096 1.71315
\(649\) −10.5743 −0.415079
\(650\) 39.7391 1.55870
\(651\) −29.0166 −1.13725
\(652\) −29.6293 −1.16037
\(653\) −40.1446 −1.57098 −0.785490 0.618875i \(-0.787589\pi\)
−0.785490 + 0.618875i \(0.787589\pi\)
\(654\) 56.2556 2.19977
\(655\) −3.32383 −0.129873
\(656\) 75.0433 2.92995
\(657\) −2.84570 −0.111021
\(658\) 38.6864 1.50815
\(659\) −24.3984 −0.950426 −0.475213 0.879871i \(-0.657629\pi\)
−0.475213 + 0.879871i \(0.657629\pi\)
\(660\) −63.8520 −2.48543
\(661\) −26.1812 −1.01833 −0.509165 0.860669i \(-0.670046\pi\)
−0.509165 + 0.860669i \(0.670046\pi\)
\(662\) −47.3074 −1.83866
\(663\) −2.63303 −0.102258
\(664\) −102.960 −3.99562
\(665\) 59.7408 2.31665
\(666\) −14.3887 −0.557551
\(667\) 0.757029 0.0293123
\(668\) −7.18459 −0.277980
\(669\) 5.89924 0.228078
\(670\) 84.4590 3.26294
\(671\) 32.5714 1.25740
\(672\) −49.0518 −1.89221
\(673\) 33.6298 1.29634 0.648168 0.761498i \(-0.275536\pi\)
0.648168 + 0.761498i \(0.275536\pi\)
\(674\) 66.2737 2.55277
\(675\) 63.1854 2.43201
\(676\) −53.0157 −2.03907
\(677\) −25.9059 −0.995646 −0.497823 0.867279i \(-0.665867\pi\)
−0.497823 + 0.867279i \(0.665867\pi\)
\(678\) 29.4003 1.12911
\(679\) −12.2923 −0.471736
\(680\) 37.3873 1.43374
\(681\) 20.7318 0.794445
\(682\) 32.1532 1.23121
\(683\) 3.72372 0.142484 0.0712422 0.997459i \(-0.477304\pi\)
0.0712422 + 0.997459i \(0.477304\pi\)
\(684\) 15.5351 0.594000
\(685\) −74.8986 −2.86173
\(686\) −15.3266 −0.585173
\(687\) −37.3189 −1.42381
\(688\) −38.8656 −1.48174
\(689\) −10.7599 −0.409918
\(690\) −33.4751 −1.27438
\(691\) −21.2141 −0.807022 −0.403511 0.914975i \(-0.632210\pi\)
−0.403511 + 0.914975i \(0.632210\pi\)
\(692\) −11.7432 −0.446408
\(693\) 6.05684 0.230080
\(694\) 4.92973 0.187130
\(695\) 29.1975 1.10752
\(696\) −3.77963 −0.143267
\(697\) −10.6607 −0.403803
\(698\) 67.0968 2.53965
\(699\) 15.8347 0.598925
\(700\) −187.386 −7.08252
\(701\) −26.2422 −0.991153 −0.495576 0.868564i \(-0.665043\pi\)
−0.495576 + 0.868564i \(0.665043\pi\)
\(702\) 19.9383 0.752521
\(703\) 30.2687 1.14161
\(704\) 13.6391 0.514043
\(705\) −25.4859 −0.959856
\(706\) 35.8751 1.35018
\(707\) 14.9952 0.563951
\(708\) 33.6205 1.26354
\(709\) 25.2961 0.950015 0.475007 0.879982i \(-0.342445\pi\)
0.475007 + 0.879982i \(0.342445\pi\)
\(710\) −163.656 −6.14190
\(711\) 2.35706 0.0883967
\(712\) −82.3496 −3.08618
\(713\) 11.8674 0.444439
\(714\) 17.6356 0.659995
\(715\) −12.2518 −0.458190
\(716\) 92.4026 3.45325
\(717\) 19.1415 0.714853
\(718\) 40.9331 1.52761
\(719\) 32.4592 1.21052 0.605262 0.796027i \(-0.293069\pi\)
0.605262 + 0.796027i \(0.293069\pi\)
\(720\) −28.3756 −1.05750
\(721\) −15.5590 −0.579447
\(722\) 2.97026 0.110542
\(723\) −20.4770 −0.761548
\(724\) 43.6969 1.62398
\(725\) −3.96538 −0.147270
\(726\) −23.3300 −0.865859
\(727\) −3.20301 −0.118793 −0.0593966 0.998234i \(-0.518918\pi\)
−0.0593966 + 0.998234i \(0.518918\pi\)
\(728\) −34.2709 −1.27016
\(729\) 29.9104 1.10779
\(730\) −38.5545 −1.42697
\(731\) 5.52127 0.204212
\(732\) −103.559 −3.82765
\(733\) 23.0781 0.852408 0.426204 0.904627i \(-0.359851\pi\)
0.426204 + 0.904627i \(0.359851\pi\)
\(734\) −46.7664 −1.72618
\(735\) −31.9790 −1.17956
\(736\) 20.0616 0.739480
\(737\) −18.0133 −0.663528
\(738\) 16.5352 0.608667
\(739\) −44.9883 −1.65492 −0.827460 0.561525i \(-0.810215\pi\)
−0.827460 + 0.561525i \(0.810215\pi\)
\(740\) −137.244 −5.04518
\(741\) −8.59114 −0.315603
\(742\) 72.0677 2.64569
\(743\) 20.2450 0.742718 0.371359 0.928489i \(-0.378892\pi\)
0.371359 + 0.928489i \(0.378892\pi\)
\(744\) −59.2507 −2.17224
\(745\) −50.6680 −1.85633
\(746\) 27.3060 0.999742
\(747\) −11.1010 −0.406166
\(748\) −13.7579 −0.503039
\(749\) 8.68140 0.317211
\(750\) 97.2202 3.54998
\(751\) −23.0639 −0.841615 −0.420808 0.907150i \(-0.638253\pi\)
−0.420808 + 0.907150i \(0.638253\pi\)
\(752\) 38.6549 1.40960
\(753\) 29.1396 1.06191
\(754\) −1.25128 −0.0455690
\(755\) −74.5043 −2.71149
\(756\) −94.0169 −3.41936
\(757\) 39.0657 1.41987 0.709933 0.704269i \(-0.248725\pi\)
0.709933 + 0.704269i \(0.248725\pi\)
\(758\) 100.234 3.64066
\(759\) 7.13952 0.259148
\(760\) 121.988 4.42499
\(761\) 7.94331 0.287945 0.143972 0.989582i \(-0.454012\pi\)
0.143972 + 0.989582i \(0.454012\pi\)
\(762\) −48.9131 −1.77193
\(763\) −50.8989 −1.84266
\(764\) 29.2920 1.05975
\(765\) 4.03106 0.145743
\(766\) −40.0603 −1.44744
\(767\) 6.45102 0.232933
\(768\) 29.2893 1.05689
\(769\) −4.36395 −0.157368 −0.0786840 0.996900i \(-0.525072\pi\)
−0.0786840 + 0.996900i \(0.525072\pi\)
\(770\) 82.0600 2.95724
\(771\) −33.9596 −1.22302
\(772\) −131.324 −4.72644
\(773\) −0.811750 −0.0291966 −0.0145983 0.999893i \(-0.504647\pi\)
−0.0145983 + 0.999893i \(0.504647\pi\)
\(774\) −8.56370 −0.307816
\(775\) −62.1626 −2.23295
\(776\) −25.1004 −0.901053
\(777\) −37.5212 −1.34607
\(778\) −39.9879 −1.43363
\(779\) −34.7841 −1.24627
\(780\) 38.9538 1.39477
\(781\) 34.9043 1.24897
\(782\) −7.21273 −0.257927
\(783\) −1.98954 −0.0711005
\(784\) 48.5031 1.73225
\(785\) −30.0532 −1.07265
\(786\) −3.20149 −0.114193
\(787\) 13.4356 0.478926 0.239463 0.970906i \(-0.423029\pi\)
0.239463 + 0.970906i \(0.423029\pi\)
\(788\) −114.487 −4.07843
\(789\) 26.9597 0.959791
\(790\) 31.9342 1.13617
\(791\) −26.6008 −0.945815
\(792\) 12.3678 0.439471
\(793\) −19.8706 −0.705626
\(794\) −5.36005 −0.190221
\(795\) −47.4769 −1.68383
\(796\) −38.6408 −1.36959
\(797\) −0.792719 −0.0280796 −0.0140398 0.999901i \(-0.504469\pi\)
−0.0140398 + 0.999901i \(0.504469\pi\)
\(798\) 57.5419 2.03696
\(799\) −5.49134 −0.194270
\(800\) −105.084 −3.71529
\(801\) −8.87885 −0.313719
\(802\) 93.2422 3.29250
\(803\) 8.22284 0.290178
\(804\) 57.2722 2.01984
\(805\) 30.2876 1.06750
\(806\) −19.6155 −0.690926
\(807\) −38.3003 −1.34823
\(808\) 30.6195 1.07719
\(809\) −26.9593 −0.947838 −0.473919 0.880569i \(-0.657161\pi\)
−0.473919 + 0.880569i \(0.657161\pi\)
\(810\) 63.7034 2.23831
\(811\) −44.1083 −1.54885 −0.774425 0.632666i \(-0.781961\pi\)
−0.774425 + 0.632666i \(0.781961\pi\)
\(812\) 5.90029 0.207060
\(813\) −17.8435 −0.625797
\(814\) 41.5771 1.45728
\(815\) −25.0854 −0.878703
\(816\) 17.6212 0.616866
\(817\) 18.0150 0.630265
\(818\) 22.5442 0.788241
\(819\) −3.69506 −0.129116
\(820\) 157.717 5.50773
\(821\) −26.7055 −0.932028 −0.466014 0.884777i \(-0.654310\pi\)
−0.466014 + 0.884777i \(0.654310\pi\)
\(822\) −72.1418 −2.51623
\(823\) −4.04766 −0.141092 −0.0705462 0.997509i \(-0.522474\pi\)
−0.0705462 + 0.997509i \(0.522474\pi\)
\(824\) −31.7709 −1.10679
\(825\) −37.3974 −1.30201
\(826\) −43.2078 −1.50339
\(827\) 6.87816 0.239177 0.119589 0.992824i \(-0.461842\pi\)
0.119589 + 0.992824i \(0.461842\pi\)
\(828\) 7.87603 0.273711
\(829\) −0.319932 −0.0111117 −0.00555586 0.999985i \(-0.501768\pi\)
−0.00555586 + 0.999985i \(0.501768\pi\)
\(830\) −150.401 −5.22048
\(831\) 33.1047 1.14839
\(832\) −8.32072 −0.288469
\(833\) −6.89038 −0.238738
\(834\) 28.1228 0.973812
\(835\) −6.08277 −0.210503
\(836\) −44.8898 −1.55254
\(837\) −31.1887 −1.07804
\(838\) 65.7438 2.27108
\(839\) −10.5949 −0.365778 −0.182889 0.983134i \(-0.558545\pi\)
−0.182889 + 0.983134i \(0.558545\pi\)
\(840\) −151.217 −5.21749
\(841\) −28.8751 −0.995695
\(842\) 6.79974 0.234335
\(843\) 4.89367 0.168547
\(844\) −19.2523 −0.662691
\(845\) −44.8853 −1.54410
\(846\) 8.51728 0.292830
\(847\) 21.1085 0.725298
\(848\) 72.0090 2.47280
\(849\) 14.3196 0.491448
\(850\) 37.7809 1.29587
\(851\) 15.3457 0.526045
\(852\) −110.976 −3.80199
\(853\) −12.0349 −0.412066 −0.206033 0.978545i \(-0.566055\pi\)
−0.206033 + 0.978545i \(0.566055\pi\)
\(854\) 133.090 4.55424
\(855\) 13.1527 0.449812
\(856\) 17.7271 0.605899
\(857\) −19.6152 −0.670044 −0.335022 0.942210i \(-0.608744\pi\)
−0.335022 + 0.942210i \(0.608744\pi\)
\(858\) −11.8008 −0.402872
\(859\) 35.0648 1.19640 0.598198 0.801348i \(-0.295884\pi\)
0.598198 + 0.801348i \(0.295884\pi\)
\(860\) −81.6832 −2.78537
\(861\) 43.1185 1.46947
\(862\) 36.5326 1.24430
\(863\) −21.1499 −0.719950 −0.359975 0.932962i \(-0.617215\pi\)
−0.359975 + 0.932962i \(0.617215\pi\)
\(864\) −52.7238 −1.79370
\(865\) −9.94225 −0.338047
\(866\) −87.4638 −2.97214
\(867\) 22.8673 0.776616
\(868\) 92.4949 3.13948
\(869\) −6.81089 −0.231044
\(870\) −5.52116 −0.187185
\(871\) 10.9893 0.372357
\(872\) −103.934 −3.51963
\(873\) −2.70630 −0.0915945
\(874\) −23.5339 −0.796048
\(875\) −87.9629 −2.97369
\(876\) −26.1441 −0.883326
\(877\) −2.93266 −0.0990288 −0.0495144 0.998773i \(-0.515767\pi\)
−0.0495144 + 0.998773i \(0.515767\pi\)
\(878\) −52.0471 −1.75651
\(879\) −29.5878 −0.997971
\(880\) 81.9933 2.76399
\(881\) 40.0242 1.34845 0.674225 0.738526i \(-0.264478\pi\)
0.674225 + 0.738526i \(0.264478\pi\)
\(882\) 10.6872 0.359858
\(883\) 22.6408 0.761922 0.380961 0.924591i \(-0.375593\pi\)
0.380961 + 0.924591i \(0.375593\pi\)
\(884\) 8.39320 0.282294
\(885\) 28.4646 0.956826
\(886\) −14.1490 −0.475344
\(887\) −4.89817 −0.164464 −0.0822322 0.996613i \(-0.526205\pi\)
−0.0822322 + 0.996613i \(0.526205\pi\)
\(888\) −76.6169 −2.57109
\(889\) 44.2555 1.48428
\(890\) −120.294 −4.03225
\(891\) −13.5866 −0.455167
\(892\) −18.8048 −0.629630
\(893\) −17.9173 −0.599581
\(894\) −48.8030 −1.63222
\(895\) 78.2319 2.61500
\(896\) −10.0052 −0.334251
\(897\) −4.35556 −0.145428
\(898\) 30.6135 1.02159
\(899\) 1.95734 0.0652808
\(900\) −41.2553 −1.37518
\(901\) −10.2296 −0.340799
\(902\) −47.7795 −1.59088
\(903\) −22.3315 −0.743144
\(904\) −54.3177 −1.80658
\(905\) 36.9956 1.22978
\(906\) −71.7619 −2.38413
\(907\) −22.6748 −0.752905 −0.376452 0.926436i \(-0.622856\pi\)
−0.376452 + 0.926436i \(0.622856\pi\)
\(908\) −66.0859 −2.19314
\(909\) 3.30137 0.109499
\(910\) −50.0618 −1.65953
\(911\) −23.5333 −0.779692 −0.389846 0.920880i \(-0.627472\pi\)
−0.389846 + 0.920880i \(0.627472\pi\)
\(912\) 57.4951 1.90385
\(913\) 32.0772 1.06160
\(914\) 16.5264 0.546644
\(915\) −87.6773 −2.89852
\(916\) 118.960 3.93055
\(917\) 2.89664 0.0956556
\(918\) 18.9557 0.625633
\(919\) −16.3232 −0.538453 −0.269227 0.963077i \(-0.586768\pi\)
−0.269227 + 0.963077i \(0.586768\pi\)
\(920\) 61.8460 2.03900
\(921\) −0.636467 −0.0209723
\(922\) −30.4375 −1.00241
\(923\) −21.2939 −0.700896
\(924\) 55.6455 1.83060
\(925\) −80.3821 −2.64295
\(926\) −43.7832 −1.43881
\(927\) −3.42550 −0.112508
\(928\) 3.30883 0.108618
\(929\) −52.5136 −1.72292 −0.861458 0.507829i \(-0.830448\pi\)
−0.861458 + 0.507829i \(0.830448\pi\)
\(930\) −86.5516 −2.83814
\(931\) −22.4822 −0.736823
\(932\) −50.4757 −1.65339
\(933\) 0.325405 0.0106533
\(934\) 85.8221 2.80819
\(935\) −11.6480 −0.380931
\(936\) −7.54516 −0.246621
\(937\) −28.6251 −0.935142 −0.467571 0.883956i \(-0.654871\pi\)
−0.467571 + 0.883956i \(0.654871\pi\)
\(938\) −73.6040 −2.40326
\(939\) 12.6857 0.413981
\(940\) 81.2404 2.64977
\(941\) 4.68441 0.152707 0.0763536 0.997081i \(-0.475672\pi\)
0.0763536 + 0.997081i \(0.475672\pi\)
\(942\) −28.9470 −0.943145
\(943\) −17.6349 −0.574273
\(944\) −43.1726 −1.40515
\(945\) −79.5986 −2.58934
\(946\) 24.7454 0.804542
\(947\) 30.7789 1.00018 0.500090 0.865973i \(-0.333300\pi\)
0.500090 + 0.865973i \(0.333300\pi\)
\(948\) 21.6548 0.703316
\(949\) −5.01646 −0.162841
\(950\) 123.273 3.99949
\(951\) −13.2299 −0.429009
\(952\) −32.5821 −1.05599
\(953\) −3.12000 −0.101067 −0.0505334 0.998722i \(-0.516092\pi\)
−0.0505334 + 0.998722i \(0.516092\pi\)
\(954\) 15.8666 0.513699
\(955\) 24.7998 0.802503
\(956\) −61.0166 −1.97342
\(957\) 1.17755 0.0380646
\(958\) −52.2433 −1.68790
\(959\) 65.2724 2.10776
\(960\) −36.7144 −1.18495
\(961\) −0.316139 −0.0101980
\(962\) −25.3647 −0.817791
\(963\) 1.91132 0.0615913
\(964\) 65.2737 2.10232
\(965\) −111.184 −3.57914
\(966\) 29.1728 0.938618
\(967\) 36.7361 1.18135 0.590676 0.806909i \(-0.298861\pi\)
0.590676 + 0.806909i \(0.298861\pi\)
\(968\) 43.1028 1.38538
\(969\) −8.16779 −0.262387
\(970\) −36.6659 −1.17727
\(971\) −14.8858 −0.477709 −0.238855 0.971055i \(-0.576772\pi\)
−0.238855 + 0.971055i \(0.576772\pi\)
\(972\) −37.1582 −1.19185
\(973\) −25.4449 −0.815726
\(974\) 21.8728 0.700850
\(975\) 22.8148 0.730658
\(976\) 132.981 4.25663
\(977\) −26.2048 −0.838367 −0.419184 0.907902i \(-0.637684\pi\)
−0.419184 + 0.907902i \(0.637684\pi\)
\(978\) −24.1621 −0.772618
\(979\) 25.6560 0.819970
\(980\) 101.938 3.25630
\(981\) −11.2060 −0.357780
\(982\) 72.3282 2.30808
\(983\) 17.9934 0.573900 0.286950 0.957946i \(-0.407359\pi\)
0.286950 + 0.957946i \(0.407359\pi\)
\(984\) 88.0463 2.80681
\(985\) −96.9295 −3.08843
\(986\) −1.18962 −0.0378852
\(987\) 22.2104 0.706964
\(988\) 27.3856 0.871252
\(989\) 9.13329 0.290422
\(990\) 18.0665 0.574192
\(991\) 15.8588 0.503772 0.251886 0.967757i \(-0.418949\pi\)
0.251886 + 0.967757i \(0.418949\pi\)
\(992\) 51.8703 1.64688
\(993\) −27.1599 −0.861892
\(994\) 142.622 4.52371
\(995\) −32.7149 −1.03713
\(996\) −101.988 −3.23161
\(997\) 9.67200 0.306315 0.153158 0.988202i \(-0.451056\pi\)
0.153158 + 0.988202i \(0.451056\pi\)
\(998\) −1.39817 −0.0442585
\(999\) −40.3300 −1.27599
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 8017.2.a.a.1.17 327
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8017.2.a.a.1.17 327 1.1 even 1 trivial