Properties

Label 8034.2.a.ba.1.12
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} - 4126 x^{5} - 22759 x^{4} + 2997 x^{3} + 10504 x^{2} - 506 x - 1492\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-2.56958\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56958 q^{5} +1.00000 q^{6} +3.96287 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56958 q^{5} +1.00000 q^{6} +3.96287 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56958 q^{10} -3.64940 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.96287 q^{14} -2.56958 q^{15} +1.00000 q^{16} +6.34291 q^{17} -1.00000 q^{18} +6.47887 q^{19} +2.56958 q^{20} -3.96287 q^{21} +3.64940 q^{22} +5.03341 q^{23} +1.00000 q^{24} +1.60272 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.96287 q^{28} +4.90808 q^{29} +2.56958 q^{30} +8.81196 q^{31} -1.00000 q^{32} +3.64940 q^{33} -6.34291 q^{34} +10.1829 q^{35} +1.00000 q^{36} -7.78824 q^{37} -6.47887 q^{38} +1.00000 q^{39} -2.56958 q^{40} +2.82114 q^{41} +3.96287 q^{42} +8.04229 q^{43} -3.64940 q^{44} +2.56958 q^{45} -5.03341 q^{46} -5.14489 q^{47} -1.00000 q^{48} +8.70431 q^{49} -1.60272 q^{50} -6.34291 q^{51} -1.00000 q^{52} +0.106049 q^{53} +1.00000 q^{54} -9.37741 q^{55} -3.96287 q^{56} -6.47887 q^{57} -4.90808 q^{58} -6.22700 q^{59} -2.56958 q^{60} -11.3915 q^{61} -8.81196 q^{62} +3.96287 q^{63} +1.00000 q^{64} -2.56958 q^{65} -3.64940 q^{66} -2.03830 q^{67} +6.34291 q^{68} -5.03341 q^{69} -10.1829 q^{70} +0.802323 q^{71} -1.00000 q^{72} +8.44092 q^{73} +7.78824 q^{74} -1.60272 q^{75} +6.47887 q^{76} -14.4621 q^{77} -1.00000 q^{78} +0.928481 q^{79} +2.56958 q^{80} +1.00000 q^{81} -2.82114 q^{82} -6.12343 q^{83} -3.96287 q^{84} +16.2986 q^{85} -8.04229 q^{86} -4.90808 q^{87} +3.64940 q^{88} +13.7177 q^{89} -2.56958 q^{90} -3.96287 q^{91} +5.03341 q^{92} -8.81196 q^{93} +5.14489 q^{94} +16.6480 q^{95} +1.00000 q^{96} +9.59341 q^{97} -8.70431 q^{98} -3.64940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + q^{10} - q^{11} - 14q^{12} - 14q^{13} - 5q^{14} + q^{15} + 14q^{16} - 12q^{17} - 14q^{18} + 10q^{19} - q^{20} - 5q^{21} + q^{22} - q^{23} + 14q^{24} + 19q^{25} + 14q^{26} - 14q^{27} + 5q^{28} + 6q^{29} - q^{30} + 20q^{31} - 14q^{32} + q^{33} + 12q^{34} - 16q^{35} + 14q^{36} - 3q^{37} - 10q^{38} + 14q^{39} + q^{40} + q^{41} + 5q^{42} + 6q^{43} - q^{44} - q^{45} + q^{46} - 13q^{47} - 14q^{48} + 9q^{49} - 19q^{50} + 12q^{51} - 14q^{52} - 27q^{53} + 14q^{54} + 10q^{55} - 5q^{56} - 10q^{57} - 6q^{58} - 6q^{59} + q^{60} - 4q^{61} - 20q^{62} + 5q^{63} + 14q^{64} + q^{65} - q^{66} + 13q^{67} - 12q^{68} + q^{69} + 16q^{70} + 18q^{71} - 14q^{72} + 11q^{73} + 3q^{74} - 19q^{75} + 10q^{76} - 15q^{77} - 14q^{78} + 33q^{79} - q^{80} + 14q^{81} - q^{82} - 25q^{83} - 5q^{84} + 25q^{85} - 6q^{86} - 6q^{87} + q^{88} + 3q^{89} + q^{90} - 5q^{91} - q^{92} - 20q^{93} + 13q^{94} + 30q^{95} + 14q^{96} + 11q^{97} - 9q^{98} - q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 2.56958 1.14915 0.574575 0.818452i \(-0.305168\pi\)
0.574575 + 0.818452i \(0.305168\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.96287 1.49782 0.748911 0.662670i \(-0.230577\pi\)
0.748911 + 0.662670i \(0.230577\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.56958 −0.812571
\(11\) −3.64940 −1.10034 −0.550168 0.835054i \(-0.685436\pi\)
−0.550168 + 0.835054i \(0.685436\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) −3.96287 −1.05912
\(15\) −2.56958 −0.663462
\(16\) 1.00000 0.250000
\(17\) 6.34291 1.53838 0.769190 0.639020i \(-0.220660\pi\)
0.769190 + 0.639020i \(0.220660\pi\)
\(18\) −1.00000 −0.235702
\(19\) 6.47887 1.48636 0.743178 0.669094i \(-0.233318\pi\)
0.743178 + 0.669094i \(0.233318\pi\)
\(20\) 2.56958 0.574575
\(21\) −3.96287 −0.864768
\(22\) 3.64940 0.778055
\(23\) 5.03341 1.04954 0.524769 0.851244i \(-0.324152\pi\)
0.524769 + 0.851244i \(0.324152\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.60272 0.320544
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) 3.96287 0.748911
\(29\) 4.90808 0.911408 0.455704 0.890131i \(-0.349388\pi\)
0.455704 + 0.890131i \(0.349388\pi\)
\(30\) 2.56958 0.469138
\(31\) 8.81196 1.58268 0.791338 0.611379i \(-0.209385\pi\)
0.791338 + 0.611379i \(0.209385\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.64940 0.635279
\(34\) −6.34291 −1.08780
\(35\) 10.1829 1.72122
\(36\) 1.00000 0.166667
\(37\) −7.78824 −1.28038 −0.640189 0.768217i \(-0.721144\pi\)
−0.640189 + 0.768217i \(0.721144\pi\)
\(38\) −6.47887 −1.05101
\(39\) 1.00000 0.160128
\(40\) −2.56958 −0.406286
\(41\) 2.82114 0.440588 0.220294 0.975433i \(-0.429298\pi\)
0.220294 + 0.975433i \(0.429298\pi\)
\(42\) 3.96287 0.611484
\(43\) 8.04229 1.22644 0.613219 0.789913i \(-0.289874\pi\)
0.613219 + 0.789913i \(0.289874\pi\)
\(44\) −3.64940 −0.550168
\(45\) 2.56958 0.383050
\(46\) −5.03341 −0.742136
\(47\) −5.14489 −0.750459 −0.375230 0.926932i \(-0.622436\pi\)
−0.375230 + 0.926932i \(0.622436\pi\)
\(48\) −1.00000 −0.144338
\(49\) 8.70431 1.24347
\(50\) −1.60272 −0.226659
\(51\) −6.34291 −0.888185
\(52\) −1.00000 −0.138675
\(53\) 0.106049 0.0145670 0.00728349 0.999973i \(-0.497682\pi\)
0.00728349 + 0.999973i \(0.497682\pi\)
\(54\) 1.00000 0.136083
\(55\) −9.37741 −1.26445
\(56\) −3.96287 −0.529560
\(57\) −6.47887 −0.858148
\(58\) −4.90808 −0.644463
\(59\) −6.22700 −0.810687 −0.405343 0.914164i \(-0.632848\pi\)
−0.405343 + 0.914164i \(0.632848\pi\)
\(60\) −2.56958 −0.331731
\(61\) −11.3915 −1.45853 −0.729264 0.684232i \(-0.760137\pi\)
−0.729264 + 0.684232i \(0.760137\pi\)
\(62\) −8.81196 −1.11912
\(63\) 3.96287 0.499274
\(64\) 1.00000 0.125000
\(65\) −2.56958 −0.318717
\(66\) −3.64940 −0.449210
\(67\) −2.03830 −0.249017 −0.124509 0.992219i \(-0.539735\pi\)
−0.124509 + 0.992219i \(0.539735\pi\)
\(68\) 6.34291 0.769190
\(69\) −5.03341 −0.605952
\(70\) −10.1829 −1.21709
\(71\) 0.802323 0.0952182 0.0476091 0.998866i \(-0.484840\pi\)
0.0476091 + 0.998866i \(0.484840\pi\)
\(72\) −1.00000 −0.117851
\(73\) 8.44092 0.987935 0.493967 0.869480i \(-0.335546\pi\)
0.493967 + 0.869480i \(0.335546\pi\)
\(74\) 7.78824 0.905364
\(75\) −1.60272 −0.185066
\(76\) 6.47887 0.743178
\(77\) −14.4621 −1.64811
\(78\) −1.00000 −0.113228
\(79\) 0.928481 0.104462 0.0522311 0.998635i \(-0.483367\pi\)
0.0522311 + 0.998635i \(0.483367\pi\)
\(80\) 2.56958 0.287287
\(81\) 1.00000 0.111111
\(82\) −2.82114 −0.311543
\(83\) −6.12343 −0.672134 −0.336067 0.941838i \(-0.609097\pi\)
−0.336067 + 0.941838i \(0.609097\pi\)
\(84\) −3.96287 −0.432384
\(85\) 16.2986 1.76783
\(86\) −8.04229 −0.867223
\(87\) −4.90808 −0.526202
\(88\) 3.64940 0.389027
\(89\) 13.7177 1.45408 0.727038 0.686597i \(-0.240896\pi\)
0.727038 + 0.686597i \(0.240896\pi\)
\(90\) −2.56958 −0.270857
\(91\) −3.96287 −0.415421
\(92\) 5.03341 0.524769
\(93\) −8.81196 −0.913758
\(94\) 5.14489 0.530655
\(95\) 16.6480 1.70804
\(96\) 1.00000 0.102062
\(97\) 9.59341 0.974063 0.487031 0.873384i \(-0.338080\pi\)
0.487031 + 0.873384i \(0.338080\pi\)
\(98\) −8.70431 −0.879268
\(99\) −3.64940 −0.366779
\(100\) 1.60272 0.160272
\(101\) −2.89765 −0.288327 −0.144163 0.989554i \(-0.546049\pi\)
−0.144163 + 0.989554i \(0.546049\pi\)
\(102\) 6.34291 0.628041
\(103\) 1.00000 0.0985329
\(104\) 1.00000 0.0980581
\(105\) −10.1829 −0.993748
\(106\) −0.106049 −0.0103004
\(107\) −19.1063 −1.84707 −0.923537 0.383509i \(-0.874716\pi\)
−0.923537 + 0.383509i \(0.874716\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 18.4619 1.76833 0.884163 0.467179i \(-0.154730\pi\)
0.884163 + 0.467179i \(0.154730\pi\)
\(110\) 9.37741 0.894101
\(111\) 7.78824 0.739227
\(112\) 3.96287 0.374456
\(113\) −1.45077 −0.136477 −0.0682384 0.997669i \(-0.521738\pi\)
−0.0682384 + 0.997669i \(0.521738\pi\)
\(114\) 6.47887 0.606802
\(115\) 12.9337 1.20608
\(116\) 4.90808 0.455704
\(117\) −1.00000 −0.0924500
\(118\) 6.22700 0.573242
\(119\) 25.1361 2.30422
\(120\) 2.56958 0.234569
\(121\) 2.31813 0.210739
\(122\) 11.3915 1.03133
\(123\) −2.82114 −0.254374
\(124\) 8.81196 0.791338
\(125\) −8.72957 −0.780796
\(126\) −3.96287 −0.353040
\(127\) 13.3969 1.18878 0.594390 0.804177i \(-0.297393\pi\)
0.594390 + 0.804177i \(0.297393\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.04229 −0.708085
\(130\) 2.56958 0.225367
\(131\) −19.3504 −1.69066 −0.845328 0.534248i \(-0.820595\pi\)
−0.845328 + 0.534248i \(0.820595\pi\)
\(132\) 3.64940 0.317640
\(133\) 25.6749 2.22630
\(134\) 2.03830 0.176082
\(135\) −2.56958 −0.221154
\(136\) −6.34291 −0.543900
\(137\) 3.26002 0.278522 0.139261 0.990256i \(-0.455527\pi\)
0.139261 + 0.990256i \(0.455527\pi\)
\(138\) 5.03341 0.428472
\(139\) 1.29491 0.109833 0.0549164 0.998491i \(-0.482511\pi\)
0.0549164 + 0.998491i \(0.482511\pi\)
\(140\) 10.1829 0.860611
\(141\) 5.14489 0.433278
\(142\) −0.802323 −0.0673294
\(143\) 3.64940 0.305178
\(144\) 1.00000 0.0833333
\(145\) 12.6117 1.04734
\(146\) −8.44092 −0.698575
\(147\) −8.70431 −0.717919
\(148\) −7.78824 −0.640189
\(149\) −10.5472 −0.864064 −0.432032 0.901858i \(-0.642203\pi\)
−0.432032 + 0.901858i \(0.642203\pi\)
\(150\) 1.60272 0.130862
\(151\) −6.01197 −0.489248 −0.244624 0.969618i \(-0.578664\pi\)
−0.244624 + 0.969618i \(0.578664\pi\)
\(152\) −6.47887 −0.525506
\(153\) 6.34291 0.512794
\(154\) 14.4621 1.16539
\(155\) 22.6430 1.81873
\(156\) 1.00000 0.0800641
\(157\) −10.8226 −0.863736 −0.431868 0.901937i \(-0.642145\pi\)
−0.431868 + 0.901937i \(0.642145\pi\)
\(158\) −0.928481 −0.0738660
\(159\) −0.106049 −0.00841025
\(160\) −2.56958 −0.203143
\(161\) 19.9467 1.57202
\(162\) −1.00000 −0.0785674
\(163\) −2.52012 −0.197391 −0.0986957 0.995118i \(-0.531467\pi\)
−0.0986957 + 0.995118i \(0.531467\pi\)
\(164\) 2.82114 0.220294
\(165\) 9.37741 0.730031
\(166\) 6.12343 0.475271
\(167\) −15.1049 −1.16885 −0.584427 0.811446i \(-0.698681\pi\)
−0.584427 + 0.811446i \(0.698681\pi\)
\(168\) 3.96287 0.305742
\(169\) 1.00000 0.0769231
\(170\) −16.2986 −1.25004
\(171\) 6.47887 0.495452
\(172\) 8.04229 0.613219
\(173\) 24.7945 1.88509 0.942546 0.334075i \(-0.108424\pi\)
0.942546 + 0.334075i \(0.108424\pi\)
\(174\) 4.90808 0.372081
\(175\) 6.35137 0.480118
\(176\) −3.64940 −0.275084
\(177\) 6.22700 0.468050
\(178\) −13.7177 −1.02819
\(179\) 6.86824 0.513356 0.256678 0.966497i \(-0.417372\pi\)
0.256678 + 0.966497i \(0.417372\pi\)
\(180\) 2.56958 0.191525
\(181\) −10.0027 −0.743496 −0.371748 0.928334i \(-0.621241\pi\)
−0.371748 + 0.928334i \(0.621241\pi\)
\(182\) 3.96287 0.293747
\(183\) 11.3915 0.842081
\(184\) −5.03341 −0.371068
\(185\) −20.0125 −1.47135
\(186\) 8.81196 0.646125
\(187\) −23.1478 −1.69274
\(188\) −5.14489 −0.375230
\(189\) −3.96287 −0.288256
\(190\) −16.6480 −1.20777
\(191\) −13.2993 −0.962300 −0.481150 0.876638i \(-0.659781\pi\)
−0.481150 + 0.876638i \(0.659781\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −3.36267 −0.242050 −0.121025 0.992649i \(-0.538618\pi\)
−0.121025 + 0.992649i \(0.538618\pi\)
\(194\) −9.59341 −0.688766
\(195\) 2.56958 0.184011
\(196\) 8.70431 0.621736
\(197\) −14.3558 −1.02281 −0.511403 0.859341i \(-0.670874\pi\)
−0.511403 + 0.859341i \(0.670874\pi\)
\(198\) 3.64940 0.259352
\(199\) 15.8817 1.12582 0.562911 0.826518i \(-0.309682\pi\)
0.562911 + 0.826518i \(0.309682\pi\)
\(200\) −1.60272 −0.113329
\(201\) 2.03830 0.143770
\(202\) 2.89765 0.203878
\(203\) 19.4501 1.36513
\(204\) −6.34291 −0.444092
\(205\) 7.24914 0.506302
\(206\) −1.00000 −0.0696733
\(207\) 5.03341 0.349846
\(208\) −1.00000 −0.0693375
\(209\) −23.6440 −1.63549
\(210\) 10.1829 0.702686
\(211\) −8.19520 −0.564181 −0.282090 0.959388i \(-0.591028\pi\)
−0.282090 + 0.959388i \(0.591028\pi\)
\(212\) 0.106049 0.00728349
\(213\) −0.802323 −0.0549742
\(214\) 19.1063 1.30608
\(215\) 20.6653 1.40936
\(216\) 1.00000 0.0680414
\(217\) 34.9206 2.37057
\(218\) −18.4619 −1.25039
\(219\) −8.44092 −0.570385
\(220\) −9.37741 −0.632225
\(221\) −6.34291 −0.426670
\(222\) −7.78824 −0.522712
\(223\) 8.14729 0.545583 0.272791 0.962073i \(-0.412053\pi\)
0.272791 + 0.962073i \(0.412053\pi\)
\(224\) −3.96287 −0.264780
\(225\) 1.60272 0.106848
\(226\) 1.45077 0.0965037
\(227\) 19.9817 1.32623 0.663116 0.748517i \(-0.269234\pi\)
0.663116 + 0.748517i \(0.269234\pi\)
\(228\) −6.47887 −0.429074
\(229\) −14.5611 −0.962228 −0.481114 0.876658i \(-0.659768\pi\)
−0.481114 + 0.876658i \(0.659768\pi\)
\(230\) −12.9337 −0.852825
\(231\) 14.4621 0.951535
\(232\) −4.90808 −0.322231
\(233\) −28.6011 −1.87372 −0.936860 0.349704i \(-0.886282\pi\)
−0.936860 + 0.349704i \(0.886282\pi\)
\(234\) 1.00000 0.0653720
\(235\) −13.2202 −0.862390
\(236\) −6.22700 −0.405343
\(237\) −0.928481 −0.0603113
\(238\) −25.1361 −1.62933
\(239\) 12.0981 0.782562 0.391281 0.920271i \(-0.372032\pi\)
0.391281 + 0.920271i \(0.372032\pi\)
\(240\) −2.56958 −0.165865
\(241\) −22.0200 −1.41843 −0.709217 0.704990i \(-0.750951\pi\)
−0.709217 + 0.704990i \(0.750951\pi\)
\(242\) −2.31813 −0.149015
\(243\) −1.00000 −0.0641500
\(244\) −11.3915 −0.729264
\(245\) 22.3664 1.42894
\(246\) 2.82114 0.179869
\(247\) −6.47887 −0.412241
\(248\) −8.81196 −0.559560
\(249\) 6.12343 0.388057
\(250\) 8.72957 0.552106
\(251\) 7.00320 0.442038 0.221019 0.975270i \(-0.429062\pi\)
0.221019 + 0.975270i \(0.429062\pi\)
\(252\) 3.96287 0.249637
\(253\) −18.3689 −1.15485
\(254\) −13.3969 −0.840595
\(255\) −16.2986 −1.02066
\(256\) 1.00000 0.0625000
\(257\) 11.6004 0.723615 0.361808 0.932253i \(-0.382160\pi\)
0.361808 + 0.932253i \(0.382160\pi\)
\(258\) 8.04229 0.500691
\(259\) −30.8637 −1.91778
\(260\) −2.56958 −0.159358
\(261\) 4.90808 0.303803
\(262\) 19.3504 1.19547
\(263\) 6.22816 0.384045 0.192022 0.981391i \(-0.438495\pi\)
0.192022 + 0.981391i \(0.438495\pi\)
\(264\) −3.64940 −0.224605
\(265\) 0.272502 0.0167396
\(266\) −25.6749 −1.57423
\(267\) −13.7177 −0.839512
\(268\) −2.03830 −0.124509
\(269\) −16.5598 −1.00967 −0.504834 0.863216i \(-0.668446\pi\)
−0.504834 + 0.863216i \(0.668446\pi\)
\(270\) 2.56958 0.156379
\(271\) 15.6676 0.951736 0.475868 0.879517i \(-0.342134\pi\)
0.475868 + 0.879517i \(0.342134\pi\)
\(272\) 6.34291 0.384595
\(273\) 3.96287 0.239844
\(274\) −3.26002 −0.196945
\(275\) −5.84897 −0.352706
\(276\) −5.03341 −0.302976
\(277\) 10.8926 0.654473 0.327237 0.944942i \(-0.393883\pi\)
0.327237 + 0.944942i \(0.393883\pi\)
\(278\) −1.29491 −0.0776636
\(279\) 8.81196 0.527559
\(280\) −10.1829 −0.608544
\(281\) 4.30113 0.256584 0.128292 0.991736i \(-0.459051\pi\)
0.128292 + 0.991736i \(0.459051\pi\)
\(282\) −5.14489 −0.306374
\(283\) 26.2920 1.56290 0.781449 0.623970i \(-0.214481\pi\)
0.781449 + 0.623970i \(0.214481\pi\)
\(284\) 0.802323 0.0476091
\(285\) −16.6480 −0.986140
\(286\) −3.64940 −0.215794
\(287\) 11.1798 0.659923
\(288\) −1.00000 −0.0589256
\(289\) 23.2325 1.36662
\(290\) −12.6117 −0.740584
\(291\) −9.59341 −0.562375
\(292\) 8.44092 0.493967
\(293\) −21.5768 −1.26053 −0.630266 0.776380i \(-0.717054\pi\)
−0.630266 + 0.776380i \(0.717054\pi\)
\(294\) 8.70431 0.507646
\(295\) −16.0008 −0.931600
\(296\) 7.78824 0.452682
\(297\) 3.64940 0.211760
\(298\) 10.5472 0.610985
\(299\) −5.03341 −0.291090
\(300\) −1.60272 −0.0925331
\(301\) 31.8705 1.83699
\(302\) 6.01197 0.345950
\(303\) 2.89765 0.166465
\(304\) 6.47887 0.371589
\(305\) −29.2712 −1.67607
\(306\) −6.34291 −0.362600
\(307\) −7.06343 −0.403132 −0.201566 0.979475i \(-0.564603\pi\)
−0.201566 + 0.979475i \(0.564603\pi\)
\(308\) −14.4621 −0.824054
\(309\) −1.00000 −0.0568880
\(310\) −22.6430 −1.28604
\(311\) −11.6763 −0.662102 −0.331051 0.943613i \(-0.607403\pi\)
−0.331051 + 0.943613i \(0.607403\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −13.9503 −0.788520 −0.394260 0.918999i \(-0.628999\pi\)
−0.394260 + 0.918999i \(0.628999\pi\)
\(314\) 10.8226 0.610754
\(315\) 10.1829 0.573741
\(316\) 0.928481 0.0522311
\(317\) 10.9418 0.614554 0.307277 0.951620i \(-0.400582\pi\)
0.307277 + 0.951620i \(0.400582\pi\)
\(318\) 0.106049 0.00594695
\(319\) −17.9116 −1.00285
\(320\) 2.56958 0.143644
\(321\) 19.1063 1.06641
\(322\) −19.9467 −1.11159
\(323\) 41.0949 2.28658
\(324\) 1.00000 0.0555556
\(325\) −1.60272 −0.0889029
\(326\) 2.52012 0.139577
\(327\) −18.4619 −1.02094
\(328\) −2.82114 −0.155771
\(329\) −20.3885 −1.12405
\(330\) −9.37741 −0.516210
\(331\) 10.9179 0.600100 0.300050 0.953923i \(-0.402997\pi\)
0.300050 + 0.953923i \(0.402997\pi\)
\(332\) −6.12343 −0.336067
\(333\) −7.78824 −0.426793
\(334\) 15.1049 0.826505
\(335\) −5.23755 −0.286158
\(336\) −3.96287 −0.216192
\(337\) −18.1026 −0.986113 −0.493057 0.869997i \(-0.664120\pi\)
−0.493057 + 0.869997i \(0.664120\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 1.45077 0.0787949
\(340\) 16.2986 0.883915
\(341\) −32.1584 −1.74147
\(342\) −6.47887 −0.350337
\(343\) 6.75395 0.364679
\(344\) −8.04229 −0.433611
\(345\) −12.9337 −0.696329
\(346\) −24.7945 −1.33296
\(347\) −14.4014 −0.773106 −0.386553 0.922267i \(-0.626334\pi\)
−0.386553 + 0.922267i \(0.626334\pi\)
\(348\) −4.90808 −0.263101
\(349\) 0.791137 0.0423486 0.0211743 0.999776i \(-0.493260\pi\)
0.0211743 + 0.999776i \(0.493260\pi\)
\(350\) −6.35137 −0.339495
\(351\) 1.00000 0.0533761
\(352\) 3.64940 0.194514
\(353\) −13.7134 −0.729891 −0.364945 0.931029i \(-0.618912\pi\)
−0.364945 + 0.931029i \(0.618912\pi\)
\(354\) −6.22700 −0.330962
\(355\) 2.06163 0.109420
\(356\) 13.7177 0.727038
\(357\) −25.1361 −1.33034
\(358\) −6.86824 −0.362998
\(359\) −12.0989 −0.638555 −0.319278 0.947661i \(-0.603440\pi\)
−0.319278 + 0.947661i \(0.603440\pi\)
\(360\) −2.56958 −0.135429
\(361\) 22.9758 1.20925
\(362\) 10.0027 0.525731
\(363\) −2.31813 −0.121670
\(364\) −3.96287 −0.207711
\(365\) 21.6896 1.13528
\(366\) −11.3915 −0.595442
\(367\) 0.484231 0.0252766 0.0126383 0.999920i \(-0.495977\pi\)
0.0126383 + 0.999920i \(0.495977\pi\)
\(368\) 5.03341 0.262385
\(369\) 2.82114 0.146863
\(370\) 20.0125 1.04040
\(371\) 0.420259 0.0218188
\(372\) −8.81196 −0.456879
\(373\) −7.50161 −0.388419 −0.194209 0.980960i \(-0.562214\pi\)
−0.194209 + 0.980960i \(0.562214\pi\)
\(374\) 23.1478 1.19694
\(375\) 8.72957 0.450793
\(376\) 5.14489 0.265327
\(377\) −4.90808 −0.252779
\(378\) 3.96287 0.203828
\(379\) 6.89886 0.354371 0.177185 0.984177i \(-0.443301\pi\)
0.177185 + 0.984177i \(0.443301\pi\)
\(380\) 16.6480 0.854022
\(381\) −13.3969 −0.686343
\(382\) 13.2993 0.680449
\(383\) 26.3843 1.34818 0.674088 0.738651i \(-0.264537\pi\)
0.674088 + 0.738651i \(0.264537\pi\)
\(384\) 1.00000 0.0510310
\(385\) −37.1614 −1.89392
\(386\) 3.36267 0.171155
\(387\) 8.04229 0.408813
\(388\) 9.59341 0.487031
\(389\) −13.2394 −0.671262 −0.335631 0.941993i \(-0.608950\pi\)
−0.335631 + 0.941993i \(0.608950\pi\)
\(390\) −2.56958 −0.130116
\(391\) 31.9265 1.61459
\(392\) −8.70431 −0.439634
\(393\) 19.3504 0.976100
\(394\) 14.3558 0.723233
\(395\) 2.38580 0.120043
\(396\) −3.64940 −0.183389
\(397\) 5.70209 0.286179 0.143090 0.989710i \(-0.454296\pi\)
0.143090 + 0.989710i \(0.454296\pi\)
\(398\) −15.8817 −0.796076
\(399\) −25.6749 −1.28535
\(400\) 1.60272 0.0801360
\(401\) −28.3921 −1.41783 −0.708916 0.705293i \(-0.750816\pi\)
−0.708916 + 0.705293i \(0.750816\pi\)
\(402\) −2.03830 −0.101661
\(403\) −8.81196 −0.438955
\(404\) −2.89765 −0.144163
\(405\) 2.56958 0.127683
\(406\) −19.4501 −0.965291
\(407\) 28.4224 1.40885
\(408\) 6.34291 0.314021
\(409\) −35.0655 −1.73388 −0.866938 0.498416i \(-0.833915\pi\)
−0.866938 + 0.498416i \(0.833915\pi\)
\(410\) −7.24914 −0.358009
\(411\) −3.26002 −0.160805
\(412\) 1.00000 0.0492665
\(413\) −24.6768 −1.21427
\(414\) −5.03341 −0.247379
\(415\) −15.7346 −0.772382
\(416\) 1.00000 0.0490290
\(417\) −1.29491 −0.0634120
\(418\) 23.6440 1.15647
\(419\) −31.1781 −1.52315 −0.761575 0.648077i \(-0.775574\pi\)
−0.761575 + 0.648077i \(0.775574\pi\)
\(420\) −10.1829 −0.496874
\(421\) −32.6763 −1.59255 −0.796273 0.604937i \(-0.793198\pi\)
−0.796273 + 0.604937i \(0.793198\pi\)
\(422\) 8.19520 0.398936
\(423\) −5.14489 −0.250153
\(424\) −0.106049 −0.00515021
\(425\) 10.1659 0.493119
\(426\) 0.802323 0.0388727
\(427\) −45.1429 −2.18462
\(428\) −19.1063 −0.923537
\(429\) −3.64940 −0.176195
\(430\) −20.6653 −0.996569
\(431\) 18.5700 0.894487 0.447244 0.894412i \(-0.352406\pi\)
0.447244 + 0.894412i \(0.352406\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 26.0951 1.25405 0.627026 0.778998i \(-0.284272\pi\)
0.627026 + 0.778998i \(0.284272\pi\)
\(434\) −34.9206 −1.67624
\(435\) −12.6117 −0.604684
\(436\) 18.4619 0.884163
\(437\) 32.6108 1.55999
\(438\) 8.44092 0.403323
\(439\) 17.3656 0.828817 0.414408 0.910091i \(-0.363989\pi\)
0.414408 + 0.910091i \(0.363989\pi\)
\(440\) 9.37741 0.447051
\(441\) 8.70431 0.414491
\(442\) 6.34291 0.301701
\(443\) 1.60727 0.0763635 0.0381818 0.999271i \(-0.487843\pi\)
0.0381818 + 0.999271i \(0.487843\pi\)
\(444\) 7.78824 0.369613
\(445\) 35.2488 1.67095
\(446\) −8.14729 −0.385785
\(447\) 10.5472 0.498868
\(448\) 3.96287 0.187228
\(449\) −15.2697 −0.720621 −0.360311 0.932832i \(-0.617329\pi\)
−0.360311 + 0.932832i \(0.617329\pi\)
\(450\) −1.60272 −0.0755530
\(451\) −10.2955 −0.484795
\(452\) −1.45077 −0.0682384
\(453\) 6.01197 0.282467
\(454\) −19.9817 −0.937788
\(455\) −10.1829 −0.477381
\(456\) 6.47887 0.303401
\(457\) −8.07806 −0.377876 −0.188938 0.981989i \(-0.560504\pi\)
−0.188938 + 0.981989i \(0.560504\pi\)
\(458\) 14.5611 0.680398
\(459\) −6.34291 −0.296062
\(460\) 12.9337 0.603038
\(461\) 3.84513 0.179086 0.0895428 0.995983i \(-0.471459\pi\)
0.0895428 + 0.995983i \(0.471459\pi\)
\(462\) −14.4621 −0.672837
\(463\) −11.0796 −0.514913 −0.257457 0.966290i \(-0.582884\pi\)
−0.257457 + 0.966290i \(0.582884\pi\)
\(464\) 4.90808 0.227852
\(465\) −22.6430 −1.05004
\(466\) 28.6011 1.32492
\(467\) 20.7061 0.958165 0.479083 0.877770i \(-0.340969\pi\)
0.479083 + 0.877770i \(0.340969\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −8.07749 −0.372984
\(470\) 13.2202 0.609802
\(471\) 10.8226 0.498678
\(472\) 6.22700 0.286621
\(473\) −29.3496 −1.34949
\(474\) 0.928481 0.0426465
\(475\) 10.3838 0.476443
\(476\) 25.1361 1.15211
\(477\) 0.106049 0.00485566
\(478\) −12.0981 −0.553355
\(479\) 32.4908 1.48454 0.742271 0.670100i \(-0.233749\pi\)
0.742271 + 0.670100i \(0.233749\pi\)
\(480\) 2.56958 0.117285
\(481\) 7.78824 0.355113
\(482\) 22.0200 1.00298
\(483\) −19.9467 −0.907608
\(484\) 2.31813 0.105369
\(485\) 24.6510 1.11934
\(486\) 1.00000 0.0453609
\(487\) 6.93601 0.314301 0.157150 0.987575i \(-0.449769\pi\)
0.157150 + 0.987575i \(0.449769\pi\)
\(488\) 11.3915 0.515667
\(489\) 2.52012 0.113964
\(490\) −22.3664 −1.01041
\(491\) 10.0323 0.452750 0.226375 0.974040i \(-0.427313\pi\)
0.226375 + 0.974040i \(0.427313\pi\)
\(492\) −2.82114 −0.127187
\(493\) 31.1315 1.40209
\(494\) 6.47887 0.291498
\(495\) −9.37741 −0.421483
\(496\) 8.81196 0.395669
\(497\) 3.17950 0.142620
\(498\) −6.12343 −0.274398
\(499\) 41.3109 1.84933 0.924664 0.380783i \(-0.124346\pi\)
0.924664 + 0.380783i \(0.124346\pi\)
\(500\) −8.72957 −0.390398
\(501\) 15.1049 0.674838
\(502\) −7.00320 −0.312568
\(503\) 17.4388 0.777557 0.388778 0.921331i \(-0.372897\pi\)
0.388778 + 0.921331i \(0.372897\pi\)
\(504\) −3.96287 −0.176520
\(505\) −7.44572 −0.331330
\(506\) 18.3689 0.816599
\(507\) −1.00000 −0.0444116
\(508\) 13.3969 0.594390
\(509\) 24.1421 1.07008 0.535039 0.844827i \(-0.320297\pi\)
0.535039 + 0.844827i \(0.320297\pi\)
\(510\) 16.2986 0.721713
\(511\) 33.4502 1.47975
\(512\) −1.00000 −0.0441942
\(513\) −6.47887 −0.286049
\(514\) −11.6004 −0.511673
\(515\) 2.56958 0.113229
\(516\) −8.04229 −0.354042
\(517\) 18.7758 0.825757
\(518\) 30.8637 1.35607
\(519\) −24.7945 −1.08836
\(520\) 2.56958 0.112683
\(521\) 23.0329 1.00909 0.504546 0.863385i \(-0.331660\pi\)
0.504546 + 0.863385i \(0.331660\pi\)
\(522\) −4.90808 −0.214821
\(523\) 32.3049 1.41260 0.706298 0.707915i \(-0.250364\pi\)
0.706298 + 0.707915i \(0.250364\pi\)
\(524\) −19.3504 −0.845328
\(525\) −6.35137 −0.277196
\(526\) −6.22816 −0.271561
\(527\) 55.8935 2.43476
\(528\) 3.64940 0.158820
\(529\) 2.33523 0.101532
\(530\) −0.272502 −0.0118367
\(531\) −6.22700 −0.270229
\(532\) 25.6749 1.11315
\(533\) −2.82114 −0.122197
\(534\) 13.7177 0.593624
\(535\) −49.0951 −2.12256
\(536\) 2.03830 0.0880409
\(537\) −6.86824 −0.296386
\(538\) 16.5598 0.713944
\(539\) −31.7655 −1.36824
\(540\) −2.56958 −0.110577
\(541\) 26.0952 1.12192 0.560961 0.827842i \(-0.310432\pi\)
0.560961 + 0.827842i \(0.310432\pi\)
\(542\) −15.6676 −0.672979
\(543\) 10.0027 0.429258
\(544\) −6.34291 −0.271950
\(545\) 47.4391 2.03207
\(546\) −3.96287 −0.169595
\(547\) 34.1063 1.45828 0.729141 0.684364i \(-0.239920\pi\)
0.729141 + 0.684364i \(0.239920\pi\)
\(548\) 3.26002 0.139261
\(549\) −11.3915 −0.486176
\(550\) 5.84897 0.249401
\(551\) 31.7988 1.35468
\(552\) 5.03341 0.214236
\(553\) 3.67945 0.156466
\(554\) −10.8926 −0.462783
\(555\) 20.0125 0.849482
\(556\) 1.29491 0.0549164
\(557\) −24.2470 −1.02738 −0.513689 0.857977i \(-0.671721\pi\)
−0.513689 + 0.857977i \(0.671721\pi\)
\(558\) −8.81196 −0.373040
\(559\) −8.04229 −0.340153
\(560\) 10.1829 0.430305
\(561\) 23.1478 0.977301
\(562\) −4.30113 −0.181432
\(563\) −12.9740 −0.546787 −0.273393 0.961902i \(-0.588146\pi\)
−0.273393 + 0.961902i \(0.588146\pi\)
\(564\) 5.14489 0.216639
\(565\) −3.72786 −0.156832
\(566\) −26.2920 −1.10514
\(567\) 3.96287 0.166425
\(568\) −0.802323 −0.0336647
\(569\) −31.4949 −1.32033 −0.660167 0.751119i \(-0.729514\pi\)
−0.660167 + 0.751119i \(0.729514\pi\)
\(570\) 16.6480 0.697306
\(571\) −25.1199 −1.05124 −0.525618 0.850721i \(-0.676166\pi\)
−0.525618 + 0.850721i \(0.676166\pi\)
\(572\) 3.64940 0.152589
\(573\) 13.2993 0.555584
\(574\) −11.1798 −0.466636
\(575\) 8.06715 0.336423
\(576\) 1.00000 0.0416667
\(577\) 22.2285 0.925383 0.462692 0.886519i \(-0.346884\pi\)
0.462692 + 0.886519i \(0.346884\pi\)
\(578\) −23.2325 −0.966343
\(579\) 3.36267 0.139748
\(580\) 12.6117 0.523672
\(581\) −24.2663 −1.00674
\(582\) 9.59341 0.397659
\(583\) −0.387016 −0.0160286
\(584\) −8.44092 −0.349288
\(585\) −2.56958 −0.106239
\(586\) 21.5768 0.891330
\(587\) −21.1255 −0.871941 −0.435971 0.899961i \(-0.643595\pi\)
−0.435971 + 0.899961i \(0.643595\pi\)
\(588\) −8.70431 −0.358960
\(589\) 57.0916 2.35242
\(590\) 16.0008 0.658741
\(591\) 14.3558 0.590517
\(592\) −7.78824 −0.320095
\(593\) −39.2122 −1.61025 −0.805126 0.593103i \(-0.797903\pi\)
−0.805126 + 0.593103i \(0.797903\pi\)
\(594\) −3.64940 −0.149737
\(595\) 64.5891 2.64789
\(596\) −10.5472 −0.432032
\(597\) −15.8817 −0.649993
\(598\) 5.03341 0.205831
\(599\) 44.3292 1.81124 0.905621 0.424089i \(-0.139406\pi\)
0.905621 + 0.424089i \(0.139406\pi\)
\(600\) 1.60272 0.0654308
\(601\) 11.3666 0.463653 0.231827 0.972757i \(-0.425530\pi\)
0.231827 + 0.972757i \(0.425530\pi\)
\(602\) −31.8705 −1.29895
\(603\) −2.03830 −0.0830058
\(604\) −6.01197 −0.244624
\(605\) 5.95660 0.242170
\(606\) −2.89765 −0.117709
\(607\) 46.4716 1.88622 0.943112 0.332477i \(-0.107884\pi\)
0.943112 + 0.332477i \(0.107884\pi\)
\(608\) −6.47887 −0.262753
\(609\) −19.4501 −0.788157
\(610\) 29.2712 1.18516
\(611\) 5.14489 0.208140
\(612\) 6.34291 0.256397
\(613\) −19.0608 −0.769857 −0.384929 0.922946i \(-0.625774\pi\)
−0.384929 + 0.922946i \(0.625774\pi\)
\(614\) 7.06343 0.285057
\(615\) −7.24914 −0.292313
\(616\) 14.4621 0.582694
\(617\) −41.9363 −1.68829 −0.844147 0.536112i \(-0.819892\pi\)
−0.844147 + 0.536112i \(0.819892\pi\)
\(618\) 1.00000 0.0402259
\(619\) −9.12921 −0.366934 −0.183467 0.983026i \(-0.558732\pi\)
−0.183467 + 0.983026i \(0.558732\pi\)
\(620\) 22.6430 0.909365
\(621\) −5.03341 −0.201984
\(622\) 11.6763 0.468177
\(623\) 54.3615 2.17795
\(624\) 1.00000 0.0400320
\(625\) −30.4449 −1.21780
\(626\) 13.9503 0.557568
\(627\) 23.6440 0.944251
\(628\) −10.8226 −0.431868
\(629\) −49.4001 −1.96971
\(630\) −10.1829 −0.405696
\(631\) −7.70347 −0.306670 −0.153335 0.988174i \(-0.549001\pi\)
−0.153335 + 0.988174i \(0.549001\pi\)
\(632\) −0.928481 −0.0369330
\(633\) 8.19520 0.325730
\(634\) −10.9418 −0.434555
\(635\) 34.4243 1.36609
\(636\) −0.106049 −0.00420513
\(637\) −8.70431 −0.344877
\(638\) 17.9116 0.709125
\(639\) 0.802323 0.0317394
\(640\) −2.56958 −0.101571
\(641\) −3.59372 −0.141944 −0.0709718 0.997478i \(-0.522610\pi\)
−0.0709718 + 0.997478i \(0.522610\pi\)
\(642\) −19.1063 −0.754065
\(643\) −23.6294 −0.931854 −0.465927 0.884823i \(-0.654279\pi\)
−0.465927 + 0.884823i \(0.654279\pi\)
\(644\) 19.9467 0.786011
\(645\) −20.6653 −0.813695
\(646\) −41.0949 −1.61686
\(647\) −35.4676 −1.39437 −0.697187 0.716889i \(-0.745565\pi\)
−0.697187 + 0.716889i \(0.745565\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 22.7248 0.892028
\(650\) 1.60272 0.0628639
\(651\) −34.9206 −1.36865
\(652\) −2.52012 −0.0986957
\(653\) 32.0405 1.25384 0.626921 0.779083i \(-0.284315\pi\)
0.626921 + 0.779083i \(0.284315\pi\)
\(654\) 18.4619 0.721916
\(655\) −49.7224 −1.94282
\(656\) 2.82114 0.110147
\(657\) 8.44092 0.329312
\(658\) 20.3885 0.794827
\(659\) 9.55962 0.372390 0.186195 0.982513i \(-0.440384\pi\)
0.186195 + 0.982513i \(0.440384\pi\)
\(660\) 9.37741 0.365015
\(661\) 43.2638 1.68277 0.841383 0.540439i \(-0.181742\pi\)
0.841383 + 0.540439i \(0.181742\pi\)
\(662\) −10.9179 −0.424335
\(663\) 6.34291 0.246338
\(664\) 6.12343 0.237635
\(665\) 65.9736 2.55835
\(666\) 7.78824 0.301788
\(667\) 24.7044 0.956558
\(668\) −15.1049 −0.584427
\(669\) −8.14729 −0.314992
\(670\) 5.23755 0.202344
\(671\) 41.5720 1.60487
\(672\) 3.96287 0.152871
\(673\) 14.7913 0.570164 0.285082 0.958503i \(-0.407979\pi\)
0.285082 + 0.958503i \(0.407979\pi\)
\(674\) 18.1026 0.697287
\(675\) −1.60272 −0.0616887
\(676\) 1.00000 0.0384615
\(677\) −21.5254 −0.827288 −0.413644 0.910439i \(-0.635744\pi\)
−0.413644 + 0.910439i \(0.635744\pi\)
\(678\) −1.45077 −0.0557164
\(679\) 38.0174 1.45897
\(680\) −16.2986 −0.625022
\(681\) −19.9817 −0.765700
\(682\) 32.1584 1.23141
\(683\) 40.6402 1.55505 0.777527 0.628849i \(-0.216474\pi\)
0.777527 + 0.628849i \(0.216474\pi\)
\(684\) 6.47887 0.247726
\(685\) 8.37687 0.320064
\(686\) −6.75395 −0.257867
\(687\) 14.5611 0.555542
\(688\) 8.04229 0.306610
\(689\) −0.106049 −0.00404016
\(690\) 12.9337 0.492379
\(691\) 30.5525 1.16227 0.581135 0.813807i \(-0.302609\pi\)
0.581135 + 0.813807i \(0.302609\pi\)
\(692\) 24.7945 0.942546
\(693\) −14.4621 −0.549369
\(694\) 14.4014 0.546669
\(695\) 3.32737 0.126214
\(696\) 4.90808 0.186040
\(697\) 17.8942 0.677793
\(698\) −0.791137 −0.0299450
\(699\) 28.6011 1.08179
\(700\) 6.35137 0.240059
\(701\) −6.29600 −0.237797 −0.118898 0.992906i \(-0.537936\pi\)
−0.118898 + 0.992906i \(0.537936\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −50.4590 −1.90310
\(704\) −3.64940 −0.137542
\(705\) 13.2202 0.497901
\(706\) 13.7134 0.516111
\(707\) −11.4830 −0.431862
\(708\) 6.22700 0.234025
\(709\) 16.7586 0.629382 0.314691 0.949194i \(-0.398099\pi\)
0.314691 + 0.949194i \(0.398099\pi\)
\(710\) −2.06163 −0.0773715
\(711\) 0.928481 0.0348208
\(712\) −13.7177 −0.514094
\(713\) 44.3542 1.66108
\(714\) 25.1361 0.940694
\(715\) 9.37741 0.350695
\(716\) 6.86824 0.256678
\(717\) −12.0981 −0.451812
\(718\) 12.0989 0.451527
\(719\) −18.3058 −0.682690 −0.341345 0.939938i \(-0.610882\pi\)
−0.341345 + 0.939938i \(0.610882\pi\)
\(720\) 2.56958 0.0957624
\(721\) 3.96287 0.147585
\(722\) −22.9758 −0.855071
\(723\) 22.0200 0.818933
\(724\) −10.0027 −0.371748
\(725\) 7.86628 0.292146
\(726\) 2.31813 0.0860337
\(727\) 1.01083 0.0374895 0.0187448 0.999824i \(-0.494033\pi\)
0.0187448 + 0.999824i \(0.494033\pi\)
\(728\) 3.96287 0.146874
\(729\) 1.00000 0.0370370
\(730\) −21.6896 −0.802768
\(731\) 51.0115 1.88673
\(732\) 11.3915 0.421041
\(733\) −12.0537 −0.445212 −0.222606 0.974909i \(-0.571456\pi\)
−0.222606 + 0.974909i \(0.571456\pi\)
\(734\) −0.484231 −0.0178733
\(735\) −22.3664 −0.824996
\(736\) −5.03341 −0.185534
\(737\) 7.43856 0.274003
\(738\) −2.82114 −0.103848
\(739\) −34.9428 −1.28539 −0.642696 0.766121i \(-0.722184\pi\)
−0.642696 + 0.766121i \(0.722184\pi\)
\(740\) −20.0125 −0.735673
\(741\) 6.47887 0.238007
\(742\) −0.420259 −0.0154282
\(743\) 0.0325569 0.00119440 0.000597198 1.00000i \(-0.499810\pi\)
0.000597198 1.00000i \(0.499810\pi\)
\(744\) 8.81196 0.323062
\(745\) −27.1019 −0.992938
\(746\) 7.50161 0.274653
\(747\) −6.12343 −0.224045
\(748\) −23.1478 −0.846368
\(749\) −75.7157 −2.76659
\(750\) −8.72957 −0.318759
\(751\) 9.62378 0.351177 0.175588 0.984464i \(-0.443817\pi\)
0.175588 + 0.984464i \(0.443817\pi\)
\(752\) −5.14489 −0.187615
\(753\) −7.00320 −0.255211
\(754\) 4.90808 0.178742
\(755\) −15.4482 −0.562218
\(756\) −3.96287 −0.144128
\(757\) −29.3975 −1.06847 −0.534235 0.845336i \(-0.679400\pi\)
−0.534235 + 0.845336i \(0.679400\pi\)
\(758\) −6.89886 −0.250578
\(759\) 18.3689 0.666750
\(760\) −16.6480 −0.603885
\(761\) −26.4579 −0.959098 −0.479549 0.877515i \(-0.659200\pi\)
−0.479549 + 0.877515i \(0.659200\pi\)
\(762\) 13.3969 0.485318
\(763\) 73.1619 2.64864
\(764\) −13.2993 −0.481150
\(765\) 16.2986 0.589276
\(766\) −26.3843 −0.953305
\(767\) 6.22700 0.224844
\(768\) −1.00000 −0.0360844
\(769\) 14.4811 0.522203 0.261102 0.965311i \(-0.415914\pi\)
0.261102 + 0.965311i \(0.415914\pi\)
\(770\) 37.1614 1.33921
\(771\) −11.6004 −0.417779
\(772\) −3.36267 −0.121025
\(773\) 11.6143 0.417736 0.208868 0.977944i \(-0.433022\pi\)
0.208868 + 0.977944i \(0.433022\pi\)
\(774\) −8.04229 −0.289074
\(775\) 14.1231 0.507317
\(776\) −9.59341 −0.344383
\(777\) 30.8637 1.10723
\(778\) 13.2394 0.474654
\(779\) 18.2778 0.654871
\(780\) 2.56958 0.0920056
\(781\) −2.92800 −0.104772
\(782\) −31.9265 −1.14169
\(783\) −4.90808 −0.175401
\(784\) 8.70431 0.310868
\(785\) −27.8095 −0.992562
\(786\) −19.3504 −0.690207
\(787\) 20.1342 0.717707 0.358854 0.933394i \(-0.383168\pi\)
0.358854 + 0.933394i \(0.383168\pi\)
\(788\) −14.3558 −0.511403
\(789\) −6.22816 −0.221728
\(790\) −2.38580 −0.0848831
\(791\) −5.74920 −0.204418
\(792\) 3.64940 0.129676
\(793\) 11.3915 0.404523
\(794\) −5.70209 −0.202359
\(795\) −0.272502 −0.00966464
\(796\) 15.8817 0.562911
\(797\) 32.2599 1.14271 0.571353 0.820704i \(-0.306419\pi\)
0.571353 + 0.820704i \(0.306419\pi\)
\(798\) 25.6749 0.908882
\(799\) −32.6336 −1.15449
\(800\) −1.60272 −0.0566647
\(801\) 13.7177 0.484692
\(802\) 28.3921 1.00256
\(803\) −30.8043 −1.08706
\(804\) 2.03830 0.0718851
\(805\) 51.2547 1.80649
\(806\) 8.81196 0.310388
\(807\) 16.5598 0.582932
\(808\) 2.89765 0.101939
\(809\) 12.8362 0.451296 0.225648 0.974209i \(-0.427550\pi\)
0.225648 + 0.974209i \(0.427550\pi\)
\(810\) −2.56958 −0.0902857
\(811\) 27.6128 0.969618 0.484809 0.874620i \(-0.338889\pi\)
0.484809 + 0.874620i \(0.338889\pi\)
\(812\) 19.4501 0.682564
\(813\) −15.6676 −0.549485
\(814\) −28.4224 −0.996205
\(815\) −6.47565 −0.226832
\(816\) −6.34291 −0.222046
\(817\) 52.1050 1.82292
\(818\) 35.0655 1.22604
\(819\) −3.96287 −0.138474
\(820\) 7.24914 0.253151
\(821\) 39.8917 1.39223 0.696115 0.717930i \(-0.254910\pi\)
0.696115 + 0.717930i \(0.254910\pi\)
\(822\) 3.26002 0.113706
\(823\) −56.1930 −1.95876 −0.979382 0.202018i \(-0.935250\pi\)
−0.979382 + 0.202018i \(0.935250\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 5.84897 0.203635
\(826\) 24.6768 0.858615
\(827\) −39.6806 −1.37983 −0.689915 0.723890i \(-0.742352\pi\)
−0.689915 + 0.723890i \(0.742352\pi\)
\(828\) 5.03341 0.174923
\(829\) −21.0786 −0.732091 −0.366045 0.930597i \(-0.619288\pi\)
−0.366045 + 0.930597i \(0.619288\pi\)
\(830\) 15.7346 0.546157
\(831\) −10.8926 −0.377860
\(832\) −1.00000 −0.0346688
\(833\) 55.2106 1.91293
\(834\) 1.29491 0.0448391
\(835\) −38.8132 −1.34319
\(836\) −23.6440 −0.817745
\(837\) −8.81196 −0.304586
\(838\) 31.1781 1.07703
\(839\) 40.5913 1.40137 0.700684 0.713472i \(-0.252878\pi\)
0.700684 + 0.713472i \(0.252878\pi\)
\(840\) 10.1829 0.351343
\(841\) −4.91074 −0.169336
\(842\) 32.6763 1.12610
\(843\) −4.30113 −0.148139
\(844\) −8.19520 −0.282090
\(845\) 2.56958 0.0883961
\(846\) 5.14489 0.176885
\(847\) 9.18643 0.315649
\(848\) 0.106049 0.00364175
\(849\) −26.2920 −0.902339
\(850\) −10.1659 −0.348688
\(851\) −39.2014 −1.34381
\(852\) −0.802323 −0.0274871
\(853\) 36.4092 1.24663 0.623314 0.781971i \(-0.285786\pi\)
0.623314 + 0.781971i \(0.285786\pi\)
\(854\) 45.1429 1.54476
\(855\) 16.6480 0.569348
\(856\) 19.1063 0.653039
\(857\) −7.13672 −0.243786 −0.121893 0.992543i \(-0.538896\pi\)
−0.121893 + 0.992543i \(0.538896\pi\)
\(858\) 3.64940 0.124588
\(859\) 17.6543 0.602356 0.301178 0.953568i \(-0.402620\pi\)
0.301178 + 0.953568i \(0.402620\pi\)
\(860\) 20.6653 0.704680
\(861\) −11.1798 −0.381007
\(862\) −18.5700 −0.632498
\(863\) −10.8869 −0.370595 −0.185298 0.982682i \(-0.559325\pi\)
−0.185298 + 0.982682i \(0.559325\pi\)
\(864\) 1.00000 0.0340207
\(865\) 63.7114 2.16625
\(866\) −26.0951 −0.886749
\(867\) −23.2325 −0.789016
\(868\) 34.9206 1.18528
\(869\) −3.38840 −0.114944
\(870\) 12.6117 0.427576
\(871\) 2.03830 0.0690650
\(872\) −18.4619 −0.625197
\(873\) 9.59341 0.324688
\(874\) −32.6108 −1.10308
\(875\) −34.5941 −1.16949
\(876\) −8.44092 −0.285192
\(877\) −25.2601 −0.852973 −0.426486 0.904494i \(-0.640249\pi\)
−0.426486 + 0.904494i \(0.640249\pi\)
\(878\) −17.3656 −0.586062
\(879\) 21.5768 0.727768
\(880\) −9.37741 −0.316113
\(881\) −52.3880 −1.76500 −0.882498 0.470316i \(-0.844140\pi\)
−0.882498 + 0.470316i \(0.844140\pi\)
\(882\) −8.70431 −0.293089
\(883\) 40.0791 1.34877 0.674384 0.738381i \(-0.264409\pi\)
0.674384 + 0.738381i \(0.264409\pi\)
\(884\) −6.34291 −0.213335
\(885\) 16.0008 0.537860
\(886\) −1.60727 −0.0539972
\(887\) −48.6269 −1.63273 −0.816367 0.577534i \(-0.804015\pi\)
−0.816367 + 0.577534i \(0.804015\pi\)
\(888\) −7.78824 −0.261356
\(889\) 53.0900 1.78058
\(890\) −35.2488 −1.18154
\(891\) −3.64940 −0.122260
\(892\) 8.14729 0.272791
\(893\) −33.3331 −1.11545
\(894\) −10.5472 −0.352753
\(895\) 17.6485 0.589923
\(896\) −3.96287 −0.132390
\(897\) 5.03341 0.168061
\(898\) 15.2697 0.509556
\(899\) 43.2498 1.44246
\(900\) 1.60272 0.0534240
\(901\) 0.672661 0.0224096
\(902\) 10.2955 0.342802
\(903\) −31.8705 −1.06059
\(904\) 1.45077 0.0482518
\(905\) −25.7027 −0.854388
\(906\) −6.01197 −0.199734
\(907\) 8.81552 0.292715 0.146357 0.989232i \(-0.453245\pi\)
0.146357 + 0.989232i \(0.453245\pi\)
\(908\) 19.9817 0.663116
\(909\) −2.89765 −0.0961089
\(910\) 10.1829 0.337559
\(911\) 21.1300 0.700068 0.350034 0.936737i \(-0.386170\pi\)
0.350034 + 0.936737i \(0.386170\pi\)
\(912\) −6.47887 −0.214537
\(913\) 22.3469 0.739573
\(914\) 8.07806 0.267198
\(915\) 29.2712 0.967677
\(916\) −14.5611 −0.481114
\(917\) −76.6832 −2.53230
\(918\) 6.34291 0.209347
\(919\) −34.7196 −1.14529 −0.572647 0.819802i \(-0.694083\pi\)
−0.572647 + 0.819802i \(0.694083\pi\)
\(920\) −12.9337 −0.426413
\(921\) 7.06343 0.232748
\(922\) −3.84513 −0.126633
\(923\) −0.802323 −0.0264088
\(924\) 14.4621 0.475768
\(925\) −12.4824 −0.410418
\(926\) 11.0796 0.364099
\(927\) 1.00000 0.0328443
\(928\) −4.90808 −0.161116
\(929\) 26.7065 0.876211 0.438105 0.898924i \(-0.355650\pi\)
0.438105 + 0.898924i \(0.355650\pi\)
\(930\) 22.6430 0.742494
\(931\) 56.3941 1.84824
\(932\) −28.6011 −0.936860
\(933\) 11.6763 0.382265
\(934\) −20.7061 −0.677525
\(935\) −59.4800 −1.94521
\(936\) 1.00000 0.0326860
\(937\) −23.9416 −0.782137 −0.391068 0.920362i \(-0.627894\pi\)
−0.391068 + 0.920362i \(0.627894\pi\)
\(938\) 8.07749 0.263739
\(939\) 13.9503 0.455252
\(940\) −13.2202 −0.431195
\(941\) 36.4880 1.18947 0.594737 0.803920i \(-0.297256\pi\)
0.594737 + 0.803920i \(0.297256\pi\)
\(942\) −10.8226 −0.352619
\(943\) 14.2000 0.462415
\(944\) −6.22700 −0.202672
\(945\) −10.1829 −0.331249
\(946\) 29.3496 0.954236
\(947\) −54.2638 −1.76334 −0.881668 0.471870i \(-0.843579\pi\)
−0.881668 + 0.471870i \(0.843579\pi\)
\(948\) −0.928481 −0.0301557
\(949\) −8.44092 −0.274004
\(950\) −10.3838 −0.336896
\(951\) −10.9418 −0.354813
\(952\) −25.1361 −0.814665
\(953\) 5.38962 0.174587 0.0872935 0.996183i \(-0.472178\pi\)
0.0872935 + 0.996183i \(0.472178\pi\)
\(954\) −0.106049 −0.00343347
\(955\) −34.1734 −1.10583
\(956\) 12.0981 0.391281
\(957\) 17.9116 0.578998
\(958\) −32.4908 −1.04973
\(959\) 12.9190 0.417177
\(960\) −2.56958 −0.0829327
\(961\) 46.6507 1.50486
\(962\) −7.78824 −0.251103
\(963\) −19.1063 −0.615691
\(964\) −22.0200 −0.709217
\(965\) −8.64063 −0.278152
\(966\) 19.9467 0.641776
\(967\) −27.1920 −0.874435 −0.437217 0.899356i \(-0.644036\pi\)
−0.437217 + 0.899356i \(0.644036\pi\)
\(968\) −2.31813 −0.0745074
\(969\) −41.0949 −1.32016
\(970\) −24.6510 −0.791495
\(971\) 9.12949 0.292979 0.146490 0.989212i \(-0.453202\pi\)
0.146490 + 0.989212i \(0.453202\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 5.13156 0.164510
\(974\) −6.93601 −0.222244
\(975\) 1.60272 0.0513281
\(976\) −11.3915 −0.364632
\(977\) 25.1744 0.805401 0.402701 0.915332i \(-0.368072\pi\)
0.402701 + 0.915332i \(0.368072\pi\)
\(978\) −2.52012 −0.0805847
\(979\) −50.0615 −1.59997
\(980\) 22.3664 0.714468
\(981\) 18.4619 0.589442
\(982\) −10.0323 −0.320142
\(983\) −24.9510 −0.795812 −0.397906 0.917426i \(-0.630263\pi\)
−0.397906 + 0.917426i \(0.630263\pi\)
\(984\) 2.82114 0.0899347
\(985\) −36.8882 −1.17536
\(986\) −31.1315 −0.991429
\(987\) 20.3885 0.648973
\(988\) −6.47887 −0.206120
\(989\) 40.4802 1.28719
\(990\) 9.37741 0.298034
\(991\) 9.90044 0.314498 0.157249 0.987559i \(-0.449738\pi\)
0.157249 + 0.987559i \(0.449738\pi\)
\(992\) −8.81196 −0.279780
\(993\) −10.9179 −0.346468
\(994\) −3.17950 −0.100848
\(995\) 40.8091 1.29374
\(996\) 6.12343 0.194028
\(997\) −44.8987 −1.42196 −0.710978 0.703215i \(-0.751747\pi\)
−0.710978 + 0.703215i \(0.751747\pi\)
\(998\) −41.3109 −1.30767
\(999\) 7.78824 0.246409
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 8034.2.a.ba.1.12 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.ba.1.12 14 1.1 even 1 trivial