Properties

Label 8011.2.a.b.1.4
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.75246 q^{2}\) \(-1.71159 q^{3}\) \(+5.57605 q^{4}\) \(+1.50064 q^{5}\) \(+4.71110 q^{6}\) \(+0.944355 q^{7}\) \(-9.84296 q^{8}\) \(-0.0704466 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.75246 q^{2}\) \(-1.71159 q^{3}\) \(+5.57605 q^{4}\) \(+1.50064 q^{5}\) \(+4.71110 q^{6}\) \(+0.944355 q^{7}\) \(-9.84296 q^{8}\) \(-0.0704466 q^{9}\) \(-4.13045 q^{10}\) \(+0.611364 q^{11}\) \(-9.54394 q^{12}\) \(-3.57160 q^{13}\) \(-2.59930 q^{14}\) \(-2.56848 q^{15}\) \(+15.9403 q^{16}\) \(-5.12363 q^{17}\) \(+0.193902 q^{18}\) \(+5.61300 q^{19}\) \(+8.36763 q^{20}\) \(-1.61635 q^{21}\) \(-1.68276 q^{22}\) \(+7.81440 q^{23}\) \(+16.8471 q^{24}\) \(-2.74809 q^{25}\) \(+9.83071 q^{26}\) \(+5.25536 q^{27}\) \(+5.26578 q^{28}\) \(+7.35068 q^{29}\) \(+7.06965 q^{30}\) \(+9.10223 q^{31}\) \(-24.1891 q^{32}\) \(-1.04641 q^{33}\) \(+14.1026 q^{34}\) \(+1.41713 q^{35}\) \(-0.392814 q^{36}\) \(+1.70928 q^{37}\) \(-15.4496 q^{38}\) \(+6.11313 q^{39}\) \(-14.7707 q^{40}\) \(+9.74313 q^{41}\) \(+4.44895 q^{42}\) \(+9.00559 q^{43}\) \(+3.40900 q^{44}\) \(-0.105715 q^{45}\) \(-21.5088 q^{46}\) \(+11.4725 q^{47}\) \(-27.2833 q^{48}\) \(-6.10819 q^{49}\) \(+7.56401 q^{50}\) \(+8.76957 q^{51}\) \(-19.9155 q^{52}\) \(+5.09236 q^{53}\) \(-14.4652 q^{54}\) \(+0.917435 q^{55}\) \(-9.29525 q^{56}\) \(-9.60717 q^{57}\) \(-20.2325 q^{58}\) \(-8.13814 q^{59}\) \(-14.3220 q^{60}\) \(-13.3359 q^{61}\) \(-25.0536 q^{62}\) \(-0.0665267 q^{63}\) \(+34.6990 q^{64}\) \(-5.35968 q^{65}\) \(+2.88019 q^{66}\) \(-7.89789 q^{67}\) \(-28.5696 q^{68}\) \(-13.3751 q^{69}\) \(-3.90061 q^{70}\) \(+15.2970 q^{71}\) \(+0.693403 q^{72}\) \(-5.45219 q^{73}\) \(-4.70472 q^{74}\) \(+4.70361 q^{75}\) \(+31.2984 q^{76}\) \(+0.577344 q^{77}\) \(-16.8262 q^{78}\) \(+1.25624 q^{79}\) \(+23.9206 q^{80}\) \(-8.78370 q^{81}\) \(-26.8176 q^{82}\) \(+12.9172 q^{83}\) \(-9.01287 q^{84}\) \(-7.68870 q^{85}\) \(-24.7876 q^{86}\) \(-12.5814 q^{87}\) \(-6.01763 q^{88}\) \(+1.21934 q^{89}\) \(+0.290976 q^{90}\) \(-3.37286 q^{91}\) \(+43.5735 q^{92}\) \(-15.5793 q^{93}\) \(-31.5777 q^{94}\) \(+8.42307 q^{95}\) \(+41.4019 q^{96}\) \(-2.49661 q^{97}\) \(+16.8126 q^{98}\) \(-0.0430685 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75246 −1.94629 −0.973143 0.230203i \(-0.926061\pi\)
−0.973143 + 0.230203i \(0.926061\pi\)
\(3\) −1.71159 −0.988189 −0.494095 0.869408i \(-0.664500\pi\)
−0.494095 + 0.869408i \(0.664500\pi\)
\(4\) 5.57605 2.78803
\(5\) 1.50064 0.671105 0.335553 0.942021i \(-0.391077\pi\)
0.335553 + 0.942021i \(0.391077\pi\)
\(6\) 4.71110 1.92330
\(7\) 0.944355 0.356933 0.178466 0.983946i \(-0.442886\pi\)
0.178466 + 0.983946i \(0.442886\pi\)
\(8\) −9.84296 −3.48001
\(9\) −0.0704466 −0.0234822
\(10\) −4.13045 −1.30616
\(11\) 0.611364 0.184333 0.0921665 0.995744i \(-0.470621\pi\)
0.0921665 + 0.995744i \(0.470621\pi\)
\(12\) −9.54394 −2.75510
\(13\) −3.57160 −0.990584 −0.495292 0.868726i \(-0.664939\pi\)
−0.495292 + 0.868726i \(0.664939\pi\)
\(14\) −2.59930 −0.694693
\(15\) −2.56848 −0.663179
\(16\) 15.9403 3.98507
\(17\) −5.12363 −1.24266 −0.621331 0.783548i \(-0.713408\pi\)
−0.621331 + 0.783548i \(0.713408\pi\)
\(18\) 0.193902 0.0457031
\(19\) 5.61300 1.28771 0.643855 0.765148i \(-0.277334\pi\)
0.643855 + 0.765148i \(0.277334\pi\)
\(20\) 8.36763 1.87106
\(21\) −1.61635 −0.352717
\(22\) −1.68276 −0.358765
\(23\) 7.81440 1.62941 0.814707 0.579872i \(-0.196898\pi\)
0.814707 + 0.579872i \(0.196898\pi\)
\(24\) 16.8471 3.43891
\(25\) −2.74809 −0.549618
\(26\) 9.83071 1.92796
\(27\) 5.25536 1.01139
\(28\) 5.26578 0.995138
\(29\) 7.35068 1.36499 0.682494 0.730892i \(-0.260895\pi\)
0.682494 + 0.730892i \(0.260895\pi\)
\(30\) 7.06965 1.29074
\(31\) 9.10223 1.63481 0.817405 0.576064i \(-0.195412\pi\)
0.817405 + 0.576064i \(0.195412\pi\)
\(32\) −24.1891 −4.27607
\(33\) −1.04641 −0.182156
\(34\) 14.1026 2.41857
\(35\) 1.41713 0.239539
\(36\) −0.392814 −0.0654690
\(37\) 1.70928 0.281003 0.140502 0.990080i \(-0.455128\pi\)
0.140502 + 0.990080i \(0.455128\pi\)
\(38\) −15.4496 −2.50625
\(39\) 6.11313 0.978885
\(40\) −14.7707 −2.33545
\(41\) 9.74313 1.52162 0.760810 0.648974i \(-0.224802\pi\)
0.760810 + 0.648974i \(0.224802\pi\)
\(42\) 4.44895 0.686488
\(43\) 9.00559 1.37334 0.686670 0.726970i \(-0.259072\pi\)
0.686670 + 0.726970i \(0.259072\pi\)
\(44\) 3.40900 0.513926
\(45\) −0.105715 −0.0157590
\(46\) −21.5088 −3.17131
\(47\) 11.4725 1.67344 0.836719 0.547633i \(-0.184471\pi\)
0.836719 + 0.547633i \(0.184471\pi\)
\(48\) −27.2833 −3.93800
\(49\) −6.10819 −0.872599
\(50\) 7.56401 1.06971
\(51\) 8.76957 1.22798
\(52\) −19.9155 −2.76178
\(53\) 5.09236 0.699490 0.349745 0.936845i \(-0.386268\pi\)
0.349745 + 0.936845i \(0.386268\pi\)
\(54\) −14.4652 −1.96846
\(55\) 0.917435 0.123707
\(56\) −9.29525 −1.24213
\(57\) −9.60717 −1.27250
\(58\) −20.2325 −2.65665
\(59\) −8.13814 −1.05949 −0.529747 0.848155i \(-0.677713\pi\)
−0.529747 + 0.848155i \(0.677713\pi\)
\(60\) −14.3220 −1.84896
\(61\) −13.3359 −1.70749 −0.853744 0.520693i \(-0.825674\pi\)
−0.853744 + 0.520693i \(0.825674\pi\)
\(62\) −25.0536 −3.18181
\(63\) −0.0665267 −0.00838157
\(64\) 34.6990 4.33738
\(65\) −5.35968 −0.664787
\(66\) 2.88019 0.354527
\(67\) −7.89789 −0.964881 −0.482440 0.875929i \(-0.660250\pi\)
−0.482440 + 0.875929i \(0.660250\pi\)
\(68\) −28.5696 −3.46457
\(69\) −13.3751 −1.61017
\(70\) −3.90061 −0.466212
\(71\) 15.2970 1.81541 0.907707 0.419604i \(-0.137831\pi\)
0.907707 + 0.419604i \(0.137831\pi\)
\(72\) 0.693403 0.0817184
\(73\) −5.45219 −0.638131 −0.319065 0.947733i \(-0.603369\pi\)
−0.319065 + 0.947733i \(0.603369\pi\)
\(74\) −4.70472 −0.546913
\(75\) 4.70361 0.543126
\(76\) 31.2984 3.59017
\(77\) 0.577344 0.0657945
\(78\) −16.8262 −1.90519
\(79\) 1.25624 0.141338 0.0706689 0.997500i \(-0.477487\pi\)
0.0706689 + 0.997500i \(0.477487\pi\)
\(80\) 23.9206 2.67440
\(81\) −8.78370 −0.975966
\(82\) −26.8176 −2.96151
\(83\) 12.9172 1.41785 0.708925 0.705284i \(-0.249180\pi\)
0.708925 + 0.705284i \(0.249180\pi\)
\(84\) −9.01287 −0.983385
\(85\) −7.68870 −0.833957
\(86\) −24.7876 −2.67291
\(87\) −12.5814 −1.34887
\(88\) −6.01763 −0.641481
\(89\) 1.21934 0.129250 0.0646250 0.997910i \(-0.479415\pi\)
0.0646250 + 0.997910i \(0.479415\pi\)
\(90\) 0.290976 0.0306716
\(91\) −3.37286 −0.353572
\(92\) 43.5735 4.54285
\(93\) −15.5793 −1.61550
\(94\) −31.5777 −3.25699
\(95\) 8.42307 0.864189
\(96\) 41.4019 4.22556
\(97\) −2.49661 −0.253492 −0.126746 0.991935i \(-0.540453\pi\)
−0.126746 + 0.991935i \(0.540453\pi\)
\(98\) 16.8126 1.69833
\(99\) −0.0430685 −0.00432855
\(100\) −15.3235 −1.53235
\(101\) 17.1416 1.70565 0.852827 0.522194i \(-0.174886\pi\)
0.852827 + 0.522194i \(0.174886\pi\)
\(102\) −24.1379 −2.39001
\(103\) −9.73513 −0.959231 −0.479616 0.877479i \(-0.659224\pi\)
−0.479616 + 0.877479i \(0.659224\pi\)
\(104\) 35.1551 3.44724
\(105\) −2.42556 −0.236710
\(106\) −14.0165 −1.36141
\(107\) −14.6618 −1.41741 −0.708704 0.705505i \(-0.750720\pi\)
−0.708704 + 0.705505i \(0.750720\pi\)
\(108\) 29.3042 2.81979
\(109\) 2.06717 0.197999 0.0989995 0.995087i \(-0.468436\pi\)
0.0989995 + 0.995087i \(0.468436\pi\)
\(110\) −2.52521 −0.240769
\(111\) −2.92559 −0.277684
\(112\) 15.0533 1.42240
\(113\) −19.1268 −1.79930 −0.899651 0.436610i \(-0.856179\pi\)
−0.899651 + 0.436610i \(0.856179\pi\)
\(114\) 26.4434 2.47665
\(115\) 11.7266 1.09351
\(116\) 40.9878 3.80562
\(117\) 0.251607 0.0232611
\(118\) 22.3999 2.06208
\(119\) −4.83852 −0.443547
\(120\) 25.2814 2.30787
\(121\) −10.6262 −0.966021
\(122\) 36.7066 3.32326
\(123\) −16.6763 −1.50365
\(124\) 50.7545 4.55789
\(125\) −11.6271 −1.03996
\(126\) 0.183112 0.0163129
\(127\) −8.06538 −0.715686 −0.357843 0.933782i \(-0.616488\pi\)
−0.357843 + 0.933782i \(0.616488\pi\)
\(128\) −47.1297 −4.16571
\(129\) −15.4139 −1.35712
\(130\) 14.7523 1.29386
\(131\) 8.13972 0.711171 0.355585 0.934644i \(-0.384282\pi\)
0.355585 + 0.934644i \(0.384282\pi\)
\(132\) −5.83482 −0.507856
\(133\) 5.30066 0.459626
\(134\) 21.7387 1.87793
\(135\) 7.88638 0.678752
\(136\) 50.4316 4.32448
\(137\) 10.8097 0.923536 0.461768 0.887001i \(-0.347215\pi\)
0.461768 + 0.887001i \(0.347215\pi\)
\(138\) 36.8144 3.13385
\(139\) 9.26636 0.785962 0.392981 0.919547i \(-0.371444\pi\)
0.392981 + 0.919547i \(0.371444\pi\)
\(140\) 7.90202 0.667842
\(141\) −19.6363 −1.65367
\(142\) −42.1043 −3.53331
\(143\) −2.18355 −0.182597
\(144\) −1.12294 −0.0935782
\(145\) 11.0307 0.916050
\(146\) 15.0070 1.24198
\(147\) 10.4547 0.862293
\(148\) 9.53102 0.783445
\(149\) −3.61458 −0.296118 −0.148059 0.988979i \(-0.547302\pi\)
−0.148059 + 0.988979i \(0.547302\pi\)
\(150\) −12.9465 −1.05708
\(151\) −3.25708 −0.265058 −0.132529 0.991179i \(-0.542310\pi\)
−0.132529 + 0.991179i \(0.542310\pi\)
\(152\) −55.2485 −4.48124
\(153\) 0.360942 0.0291805
\(154\) −1.58912 −0.128055
\(155\) 13.6592 1.09713
\(156\) 34.0872 2.72916
\(157\) −7.15675 −0.571170 −0.285585 0.958353i \(-0.592188\pi\)
−0.285585 + 0.958353i \(0.592188\pi\)
\(158\) −3.45775 −0.275084
\(159\) −8.71606 −0.691228
\(160\) −36.2990 −2.86969
\(161\) 7.37957 0.581591
\(162\) 24.1768 1.89951
\(163\) −7.95311 −0.622936 −0.311468 0.950257i \(-0.600821\pi\)
−0.311468 + 0.950257i \(0.600821\pi\)
\(164\) 54.3282 4.24232
\(165\) −1.57028 −0.122246
\(166\) −35.5542 −2.75954
\(167\) 6.79112 0.525513 0.262756 0.964862i \(-0.415368\pi\)
0.262756 + 0.964862i \(0.415368\pi\)
\(168\) 15.9097 1.22746
\(169\) −0.243651 −0.0187424
\(170\) 21.1629 1.62312
\(171\) −0.395417 −0.0302383
\(172\) 50.2156 3.82891
\(173\) −2.11215 −0.160584 −0.0802918 0.996771i \(-0.525585\pi\)
−0.0802918 + 0.996771i \(0.525585\pi\)
\(174\) 34.6298 2.62528
\(175\) −2.59517 −0.196177
\(176\) 9.74530 0.734580
\(177\) 13.9292 1.04698
\(178\) −3.35620 −0.251558
\(179\) −16.8490 −1.25935 −0.629675 0.776858i \(-0.716812\pi\)
−0.629675 + 0.776858i \(0.716812\pi\)
\(180\) −0.589472 −0.0439366
\(181\) −14.6311 −1.08752 −0.543760 0.839241i \(-0.683000\pi\)
−0.543760 + 0.839241i \(0.683000\pi\)
\(182\) 9.28368 0.688152
\(183\) 22.8257 1.68732
\(184\) −76.9168 −5.67038
\(185\) 2.56500 0.188583
\(186\) 42.8815 3.14423
\(187\) −3.13240 −0.229064
\(188\) 63.9713 4.66559
\(189\) 4.96292 0.361000
\(190\) −23.1842 −1.68196
\(191\) −12.5164 −0.905652 −0.452826 0.891599i \(-0.649584\pi\)
−0.452826 + 0.891599i \(0.649584\pi\)
\(192\) −59.3907 −4.28615
\(193\) −2.50055 −0.179994 −0.0899968 0.995942i \(-0.528686\pi\)
−0.0899968 + 0.995942i \(0.528686\pi\)
\(194\) 6.87182 0.493368
\(195\) 9.17360 0.656935
\(196\) −34.0596 −2.43283
\(197\) 10.1068 0.720083 0.360042 0.932936i \(-0.382762\pi\)
0.360042 + 0.932936i \(0.382762\pi\)
\(198\) 0.118545 0.00842459
\(199\) 7.91658 0.561191 0.280596 0.959826i \(-0.409468\pi\)
0.280596 + 0.959826i \(0.409468\pi\)
\(200\) 27.0493 1.91268
\(201\) 13.5180 0.953485
\(202\) −47.1816 −3.31969
\(203\) 6.94165 0.487209
\(204\) 48.8996 3.42365
\(205\) 14.6209 1.02117
\(206\) 26.7956 1.86694
\(207\) −0.550498 −0.0382623
\(208\) −56.9323 −3.94755
\(209\) 3.43158 0.237368
\(210\) 6.67626 0.460706
\(211\) 15.9196 1.09595 0.547974 0.836496i \(-0.315399\pi\)
0.547974 + 0.836496i \(0.315399\pi\)
\(212\) 28.3953 1.95020
\(213\) −26.1822 −1.79397
\(214\) 40.3560 2.75868
\(215\) 13.5141 0.921655
\(216\) −51.7283 −3.51966
\(217\) 8.59574 0.583517
\(218\) −5.68981 −0.385363
\(219\) 9.33194 0.630594
\(220\) 5.11567 0.344898
\(221\) 18.2996 1.23096
\(222\) 8.05257 0.540453
\(223\) 14.3497 0.960924 0.480462 0.877015i \(-0.340469\pi\)
0.480462 + 0.877015i \(0.340469\pi\)
\(224\) −22.8431 −1.52627
\(225\) 0.193594 0.0129062
\(226\) 52.6459 3.50195
\(227\) 9.19679 0.610412 0.305206 0.952286i \(-0.401275\pi\)
0.305206 + 0.952286i \(0.401275\pi\)
\(228\) −53.5701 −3.54777
\(229\) 17.6167 1.16414 0.582071 0.813138i \(-0.302242\pi\)
0.582071 + 0.813138i \(0.302242\pi\)
\(230\) −32.2770 −2.12828
\(231\) −0.988179 −0.0650174
\(232\) −72.3524 −4.75017
\(233\) −22.4809 −1.47277 −0.736386 0.676562i \(-0.763469\pi\)
−0.736386 + 0.676562i \(0.763469\pi\)
\(234\) −0.692540 −0.0452728
\(235\) 17.2161 1.12305
\(236\) −45.3787 −2.95390
\(237\) −2.15017 −0.139669
\(238\) 13.3179 0.863268
\(239\) 5.10039 0.329917 0.164958 0.986301i \(-0.447251\pi\)
0.164958 + 0.986301i \(0.447251\pi\)
\(240\) −40.9423 −2.64281
\(241\) 17.4929 1.12681 0.563407 0.826179i \(-0.309490\pi\)
0.563407 + 0.826179i \(0.309490\pi\)
\(242\) 29.2483 1.88015
\(243\) −0.731950 −0.0469546
\(244\) −74.3617 −4.76052
\(245\) −9.16618 −0.585606
\(246\) 45.9008 2.92653
\(247\) −20.0474 −1.27559
\(248\) −89.5929 −5.68915
\(249\) −22.1091 −1.40110
\(250\) 32.0031 2.02405
\(251\) 4.10823 0.259309 0.129655 0.991559i \(-0.458613\pi\)
0.129655 + 0.991559i \(0.458613\pi\)
\(252\) −0.370956 −0.0233680
\(253\) 4.77744 0.300355
\(254\) 22.1997 1.39293
\(255\) 13.1599 0.824107
\(256\) 60.3246 3.77028
\(257\) −14.8678 −0.927426 −0.463713 0.885985i \(-0.653483\pi\)
−0.463713 + 0.885985i \(0.653483\pi\)
\(258\) 42.4262 2.64134
\(259\) 1.61416 0.100299
\(260\) −29.8859 −1.85344
\(261\) −0.517831 −0.0320529
\(262\) −22.4043 −1.38414
\(263\) 6.16724 0.380288 0.190144 0.981756i \(-0.439104\pi\)
0.190144 + 0.981756i \(0.439104\pi\)
\(264\) 10.2997 0.633905
\(265\) 7.64179 0.469431
\(266\) −14.5899 −0.894563
\(267\) −2.08702 −0.127724
\(268\) −44.0391 −2.69011
\(269\) −5.56928 −0.339565 −0.169782 0.985482i \(-0.554307\pi\)
−0.169782 + 0.985482i \(0.554307\pi\)
\(270\) −21.7070 −1.32104
\(271\) 28.6775 1.74203 0.871017 0.491252i \(-0.163461\pi\)
0.871017 + 0.491252i \(0.163461\pi\)
\(272\) −81.6720 −4.95209
\(273\) 5.77297 0.349396
\(274\) −29.7533 −1.79746
\(275\) −1.68008 −0.101313
\(276\) −74.5801 −4.48920
\(277\) −6.26340 −0.376331 −0.188166 0.982137i \(-0.560254\pi\)
−0.188166 + 0.982137i \(0.560254\pi\)
\(278\) −25.5053 −1.52971
\(279\) −0.641222 −0.0383889
\(280\) −13.9488 −0.833600
\(281\) 25.7411 1.53559 0.767793 0.640698i \(-0.221355\pi\)
0.767793 + 0.640698i \(0.221355\pi\)
\(282\) 54.0481 3.21852
\(283\) −1.17812 −0.0700321 −0.0350161 0.999387i \(-0.511148\pi\)
−0.0350161 + 0.999387i \(0.511148\pi\)
\(284\) 85.2966 5.06142
\(285\) −14.4169 −0.853982
\(286\) 6.01014 0.355387
\(287\) 9.20097 0.543116
\(288\) 1.70404 0.100412
\(289\) 9.25154 0.544208
\(290\) −30.3616 −1.78290
\(291\) 4.27318 0.250498
\(292\) −30.4017 −1.77913
\(293\) −28.5715 −1.66917 −0.834584 0.550881i \(-0.814292\pi\)
−0.834584 + 0.550881i \(0.814292\pi\)
\(294\) −28.7763 −1.67827
\(295\) −12.2124 −0.711033
\(296\) −16.8243 −0.977895
\(297\) 3.21293 0.186433
\(298\) 9.94899 0.576329
\(299\) −27.9099 −1.61407
\(300\) 26.2276 1.51425
\(301\) 8.50447 0.490190
\(302\) 8.96500 0.515878
\(303\) −29.3395 −1.68551
\(304\) 89.4727 5.13161
\(305\) −20.0124 −1.14590
\(306\) −0.993480 −0.0567935
\(307\) 29.7440 1.69758 0.848789 0.528732i \(-0.177333\pi\)
0.848789 + 0.528732i \(0.177333\pi\)
\(308\) 3.21930 0.183437
\(309\) 16.6626 0.947902
\(310\) −37.5963 −2.13533
\(311\) −0.164876 −0.00934926 −0.00467463 0.999989i \(-0.501488\pi\)
−0.00467463 + 0.999989i \(0.501488\pi\)
\(312\) −60.1713 −3.40653
\(313\) 15.5123 0.876807 0.438403 0.898778i \(-0.355544\pi\)
0.438403 + 0.898778i \(0.355544\pi\)
\(314\) 19.6987 1.11166
\(315\) −0.0998324 −0.00562492
\(316\) 7.00485 0.394054
\(317\) −23.3794 −1.31312 −0.656560 0.754274i \(-0.727989\pi\)
−0.656560 + 0.754274i \(0.727989\pi\)
\(318\) 23.9906 1.34533
\(319\) 4.49394 0.251612
\(320\) 52.0707 2.91084
\(321\) 25.0950 1.40067
\(322\) −20.3120 −1.13194
\(323\) −28.7589 −1.60019
\(324\) −48.9784 −2.72102
\(325\) 9.81508 0.544443
\(326\) 21.8907 1.21241
\(327\) −3.53816 −0.195661
\(328\) −95.9012 −5.29526
\(329\) 10.8341 0.597305
\(330\) 4.32213 0.237925
\(331\) −0.122025 −0.00670709 −0.00335354 0.999994i \(-0.501067\pi\)
−0.00335354 + 0.999994i \(0.501067\pi\)
\(332\) 72.0272 3.95300
\(333\) −0.120413 −0.00659858
\(334\) −18.6923 −1.02280
\(335\) −11.8519 −0.647537
\(336\) −25.7651 −1.40560
\(337\) −10.9612 −0.597095 −0.298547 0.954395i \(-0.596502\pi\)
−0.298547 + 0.954395i \(0.596502\pi\)
\(338\) 0.670641 0.0364780
\(339\) 32.7374 1.77805
\(340\) −42.8726 −2.32509
\(341\) 5.56478 0.301349
\(342\) 1.08837 0.0588523
\(343\) −12.3788 −0.668392
\(344\) −88.6416 −4.77924
\(345\) −20.0711 −1.08059
\(346\) 5.81361 0.312541
\(347\) 9.45123 0.507369 0.253684 0.967287i \(-0.418358\pi\)
0.253684 + 0.967287i \(0.418358\pi\)
\(348\) −70.1545 −3.76067
\(349\) 14.5920 0.781091 0.390545 0.920584i \(-0.372286\pi\)
0.390545 + 0.920584i \(0.372286\pi\)
\(350\) 7.14311 0.381815
\(351\) −18.7701 −1.00187
\(352\) −14.7883 −0.788221
\(353\) 13.3253 0.709235 0.354618 0.935011i \(-0.384611\pi\)
0.354618 + 0.935011i \(0.384611\pi\)
\(354\) −38.3396 −2.03772
\(355\) 22.9552 1.21833
\(356\) 6.79912 0.360353
\(357\) 8.28159 0.438308
\(358\) 46.3762 2.45106
\(359\) −9.88362 −0.521638 −0.260819 0.965388i \(-0.583993\pi\)
−0.260819 + 0.965388i \(0.583993\pi\)
\(360\) 1.04055 0.0548416
\(361\) 12.5057 0.658197
\(362\) 40.2716 2.11663
\(363\) 18.1878 0.954612
\(364\) −18.8073 −0.985768
\(365\) −8.18176 −0.428253
\(366\) −62.8268 −3.28401
\(367\) −29.7747 −1.55423 −0.777113 0.629361i \(-0.783317\pi\)
−0.777113 + 0.629361i \(0.783317\pi\)
\(368\) 124.564 6.49333
\(369\) −0.686371 −0.0357310
\(370\) −7.06008 −0.367036
\(371\) 4.80900 0.249671
\(372\) −86.8712 −4.50406
\(373\) −0.847837 −0.0438993 −0.0219497 0.999759i \(-0.506987\pi\)
−0.0219497 + 0.999759i \(0.506987\pi\)
\(374\) 8.62181 0.445823
\(375\) 19.9008 1.02767
\(376\) −112.923 −5.82358
\(377\) −26.2537 −1.35214
\(378\) −13.6603 −0.702608
\(379\) −33.8622 −1.73938 −0.869691 0.493596i \(-0.835682\pi\)
−0.869691 + 0.493596i \(0.835682\pi\)
\(380\) 46.9675 2.40938
\(381\) 13.8046 0.707234
\(382\) 34.4508 1.76266
\(383\) 26.3682 1.34735 0.673676 0.739027i \(-0.264714\pi\)
0.673676 + 0.739027i \(0.264714\pi\)
\(384\) 80.6668 4.11651
\(385\) 0.866385 0.0441550
\(386\) 6.88267 0.350319
\(387\) −0.634414 −0.0322491
\(388\) −13.9212 −0.706743
\(389\) 35.9335 1.82190 0.910951 0.412515i \(-0.135350\pi\)
0.910951 + 0.412515i \(0.135350\pi\)
\(390\) −25.2500 −1.27858
\(391\) −40.0381 −2.02481
\(392\) 60.1227 3.03665
\(393\) −13.9319 −0.702771
\(394\) −27.8187 −1.40149
\(395\) 1.88516 0.0948526
\(396\) −0.240152 −0.0120681
\(397\) −3.91474 −0.196475 −0.0982376 0.995163i \(-0.531321\pi\)
−0.0982376 + 0.995163i \(0.531321\pi\)
\(398\) −21.7901 −1.09224
\(399\) −9.07258 −0.454197
\(400\) −43.8053 −2.19026
\(401\) −33.3995 −1.66789 −0.833945 0.551848i \(-0.813923\pi\)
−0.833945 + 0.551848i \(0.813923\pi\)
\(402\) −37.2077 −1.85575
\(403\) −32.5096 −1.61942
\(404\) 95.5825 4.75541
\(405\) −13.1811 −0.654976
\(406\) −19.1066 −0.948247
\(407\) 1.04499 0.0517982
\(408\) −86.3185 −4.27340
\(409\) −5.58478 −0.276150 −0.138075 0.990422i \(-0.544091\pi\)
−0.138075 + 0.990422i \(0.544091\pi\)
\(410\) −40.2435 −1.98748
\(411\) −18.5018 −0.912628
\(412\) −54.2836 −2.67436
\(413\) −7.68529 −0.378168
\(414\) 1.51523 0.0744693
\(415\) 19.3841 0.951527
\(416\) 86.3938 4.23581
\(417\) −15.8602 −0.776679
\(418\) −9.44530 −0.461985
\(419\) −19.2037 −0.938161 −0.469080 0.883155i \(-0.655415\pi\)
−0.469080 + 0.883155i \(0.655415\pi\)
\(420\) −13.5250 −0.659955
\(421\) −6.73509 −0.328248 −0.164124 0.986440i \(-0.552480\pi\)
−0.164124 + 0.986440i \(0.552480\pi\)
\(422\) −43.8180 −2.13303
\(423\) −0.808200 −0.0392960
\(424\) −50.1239 −2.43423
\(425\) 14.0802 0.682989
\(426\) 72.0655 3.49158
\(427\) −12.5938 −0.609458
\(428\) −81.7549 −3.95177
\(429\) 3.73735 0.180441
\(430\) −37.1971 −1.79380
\(431\) −5.26670 −0.253688 −0.126844 0.991923i \(-0.540485\pi\)
−0.126844 + 0.991923i \(0.540485\pi\)
\(432\) 83.7718 4.03047
\(433\) −15.2698 −0.733819 −0.366909 0.930257i \(-0.619584\pi\)
−0.366909 + 0.930257i \(0.619584\pi\)
\(434\) −23.6595 −1.13569
\(435\) −18.8801 −0.905231
\(436\) 11.5267 0.552027
\(437\) 43.8622 2.09821
\(438\) −25.6858 −1.22732
\(439\) −1.84481 −0.0880479 −0.0440240 0.999030i \(-0.514018\pi\)
−0.0440240 + 0.999030i \(0.514018\pi\)
\(440\) −9.03027 −0.430501
\(441\) 0.430302 0.0204906
\(442\) −50.3689 −2.39580
\(443\) 2.16447 0.102837 0.0514185 0.998677i \(-0.483626\pi\)
0.0514185 + 0.998677i \(0.483626\pi\)
\(444\) −16.3132 −0.774192
\(445\) 1.82979 0.0867404
\(446\) −39.4969 −1.87023
\(447\) 6.18668 0.292620
\(448\) 32.7682 1.54815
\(449\) 16.8845 0.796829 0.398415 0.917205i \(-0.369561\pi\)
0.398415 + 0.917205i \(0.369561\pi\)
\(450\) −0.532859 −0.0251192
\(451\) 5.95659 0.280485
\(452\) −106.652 −5.01650
\(453\) 5.57480 0.261927
\(454\) −25.3138 −1.18804
\(455\) −5.06144 −0.237284
\(456\) 94.5630 4.42832
\(457\) 26.7153 1.24969 0.624843 0.780750i \(-0.285163\pi\)
0.624843 + 0.780750i \(0.285163\pi\)
\(458\) −48.4893 −2.26575
\(459\) −26.9265 −1.25682
\(460\) 65.3880 3.04873
\(461\) 4.31675 0.201051 0.100526 0.994934i \(-0.467948\pi\)
0.100526 + 0.994934i \(0.467948\pi\)
\(462\) 2.71993 0.126542
\(463\) 35.5288 1.65116 0.825581 0.564283i \(-0.190847\pi\)
0.825581 + 0.564283i \(0.190847\pi\)
\(464\) 117.172 5.43957
\(465\) −23.3789 −1.08417
\(466\) 61.8778 2.86643
\(467\) 30.2358 1.39915 0.699573 0.714561i \(-0.253374\pi\)
0.699573 + 0.714561i \(0.253374\pi\)
\(468\) 1.40298 0.0648526
\(469\) −7.45841 −0.344398
\(470\) −47.3866 −2.18578
\(471\) 12.2494 0.564424
\(472\) 80.1033 3.68705
\(473\) 5.50569 0.253152
\(474\) 5.91826 0.271835
\(475\) −15.4250 −0.707748
\(476\) −26.9799 −1.23662
\(477\) −0.358740 −0.0164256
\(478\) −14.0386 −0.642112
\(479\) −20.6712 −0.944490 −0.472245 0.881467i \(-0.656556\pi\)
−0.472245 + 0.881467i \(0.656556\pi\)
\(480\) 62.1292 2.83580
\(481\) −6.10486 −0.278358
\(482\) −48.1485 −2.19310
\(483\) −12.6308 −0.574722
\(484\) −59.2525 −2.69329
\(485\) −3.74650 −0.170120
\(486\) 2.01467 0.0913871
\(487\) 25.2315 1.14335 0.571673 0.820481i \(-0.306294\pi\)
0.571673 + 0.820481i \(0.306294\pi\)
\(488\) 131.265 5.94207
\(489\) 13.6125 0.615579
\(490\) 25.2296 1.13976
\(491\) 23.8124 1.07464 0.537319 0.843379i \(-0.319437\pi\)
0.537319 + 0.843379i \(0.319437\pi\)
\(492\) −92.9878 −4.19221
\(493\) −37.6621 −1.69622
\(494\) 55.1797 2.48265
\(495\) −0.0646302 −0.00290491
\(496\) 145.092 6.51483
\(497\) 14.4458 0.647981
\(498\) 60.8544 2.72695
\(499\) −15.5076 −0.694216 −0.347108 0.937825i \(-0.612836\pi\)
−0.347108 + 0.937825i \(0.612836\pi\)
\(500\) −64.8332 −2.89943
\(501\) −11.6236 −0.519306
\(502\) −11.3078 −0.504690
\(503\) 20.6707 0.921660 0.460830 0.887488i \(-0.347552\pi\)
0.460830 + 0.887488i \(0.347552\pi\)
\(504\) 0.654819 0.0291680
\(505\) 25.7233 1.14467
\(506\) −13.1497 −0.584577
\(507\) 0.417032 0.0185210
\(508\) −44.9730 −1.99535
\(509\) −9.35289 −0.414560 −0.207280 0.978282i \(-0.566461\pi\)
−0.207280 + 0.978282i \(0.566461\pi\)
\(510\) −36.2222 −1.60395
\(511\) −5.14881 −0.227770
\(512\) −71.7818 −3.17234
\(513\) 29.4983 1.30238
\(514\) 40.9230 1.80504
\(515\) −14.6089 −0.643745
\(516\) −85.9488 −3.78368
\(517\) 7.01388 0.308470
\(518\) −4.44293 −0.195211
\(519\) 3.61514 0.158687
\(520\) 52.7551 2.31346
\(521\) 2.79080 0.122267 0.0611336 0.998130i \(-0.480528\pi\)
0.0611336 + 0.998130i \(0.480528\pi\)
\(522\) 1.42531 0.0623841
\(523\) −1.41850 −0.0620268 −0.0310134 0.999519i \(-0.509873\pi\)
−0.0310134 + 0.999519i \(0.509873\pi\)
\(524\) 45.3875 1.98276
\(525\) 4.44188 0.193860
\(526\) −16.9751 −0.740149
\(527\) −46.6364 −2.03152
\(528\) −16.6800 −0.725904
\(529\) 38.0648 1.65499
\(530\) −21.0337 −0.913647
\(531\) 0.573304 0.0248793
\(532\) 29.5568 1.28145
\(533\) −34.7986 −1.50729
\(534\) 5.74444 0.248586
\(535\) −22.0020 −0.951231
\(536\) 77.7386 3.35780
\(537\) 28.8386 1.24448
\(538\) 15.3292 0.660890
\(539\) −3.73433 −0.160849
\(540\) 43.9749 1.89238
\(541\) −4.58534 −0.197139 −0.0985696 0.995130i \(-0.531427\pi\)
−0.0985696 + 0.995130i \(0.531427\pi\)
\(542\) −78.9338 −3.39050
\(543\) 25.0425 1.07468
\(544\) 123.936 5.31371
\(545\) 3.10207 0.132878
\(546\) −15.8899 −0.680024
\(547\) 22.1477 0.946969 0.473485 0.880802i \(-0.342996\pi\)
0.473485 + 0.880802i \(0.342996\pi\)
\(548\) 60.2755 2.57484
\(549\) 0.939470 0.0400956
\(550\) 4.62436 0.197183
\(551\) 41.2594 1.75771
\(552\) 131.650 5.60341
\(553\) 1.18634 0.0504481
\(554\) 17.2398 0.732448
\(555\) −4.39025 −0.186356
\(556\) 51.6697 2.19128
\(557\) 11.6154 0.492161 0.246081 0.969249i \(-0.420857\pi\)
0.246081 + 0.969249i \(0.420857\pi\)
\(558\) 1.76494 0.0747159
\(559\) −32.1644 −1.36041
\(560\) 22.5895 0.954581
\(561\) 5.36139 0.226358
\(562\) −70.8515 −2.98869
\(563\) 24.9084 1.04976 0.524882 0.851175i \(-0.324109\pi\)
0.524882 + 0.851175i \(0.324109\pi\)
\(564\) −109.493 −4.61048
\(565\) −28.7024 −1.20752
\(566\) 3.24274 0.136302
\(567\) −8.29493 −0.348354
\(568\) −150.567 −6.31766
\(569\) 31.5565 1.32292 0.661458 0.749982i \(-0.269938\pi\)
0.661458 + 0.749982i \(0.269938\pi\)
\(570\) 39.6819 1.66209
\(571\) 27.5027 1.15095 0.575475 0.817819i \(-0.304817\pi\)
0.575475 + 0.817819i \(0.304817\pi\)
\(572\) −12.1756 −0.509087
\(573\) 21.4229 0.894956
\(574\) −25.3253 −1.05706
\(575\) −21.4747 −0.895555
\(576\) −2.44443 −0.101851
\(577\) −41.8195 −1.74097 −0.870483 0.492198i \(-0.836194\pi\)
−0.870483 + 0.492198i \(0.836194\pi\)
\(578\) −25.4645 −1.05918
\(579\) 4.27993 0.177868
\(580\) 61.5078 2.55397
\(581\) 12.1985 0.506077
\(582\) −11.7618 −0.487541
\(583\) 3.11329 0.128939
\(584\) 53.6657 2.22070
\(585\) 0.377571 0.0156107
\(586\) 78.6421 3.24868
\(587\) 19.9585 0.823776 0.411888 0.911234i \(-0.364869\pi\)
0.411888 + 0.911234i \(0.364869\pi\)
\(588\) 58.2962 2.40410
\(589\) 51.0908 2.10516
\(590\) 33.6141 1.38387
\(591\) −17.2988 −0.711578
\(592\) 27.2463 1.11982
\(593\) 26.2358 1.07738 0.538688 0.842505i \(-0.318920\pi\)
0.538688 + 0.842505i \(0.318920\pi\)
\(594\) −8.84348 −0.362853
\(595\) −7.26087 −0.297667
\(596\) −20.1551 −0.825584
\(597\) −13.5500 −0.554563
\(598\) 76.8211 3.14145
\(599\) −24.7231 −1.01016 −0.505080 0.863073i \(-0.668537\pi\)
−0.505080 + 0.863073i \(0.668537\pi\)
\(600\) −46.2974 −1.89008
\(601\) 13.8333 0.564273 0.282137 0.959374i \(-0.408957\pi\)
0.282137 + 0.959374i \(0.408957\pi\)
\(602\) −23.4083 −0.954049
\(603\) 0.556380 0.0226575
\(604\) −18.1617 −0.738988
\(605\) −15.9461 −0.648302
\(606\) 80.7558 3.28048
\(607\) −30.9280 −1.25533 −0.627664 0.778484i \(-0.715989\pi\)
−0.627664 + 0.778484i \(0.715989\pi\)
\(608\) −135.773 −5.50633
\(609\) −11.8813 −0.481454
\(610\) 55.0833 2.23026
\(611\) −40.9753 −1.65768
\(612\) 2.01263 0.0813559
\(613\) 35.3420 1.42745 0.713726 0.700425i \(-0.247006\pi\)
0.713726 + 0.700425i \(0.247006\pi\)
\(614\) −81.8691 −3.30397
\(615\) −25.0250 −1.00911
\(616\) −5.68278 −0.228966
\(617\) 34.0593 1.37118 0.685588 0.727990i \(-0.259545\pi\)
0.685588 + 0.727990i \(0.259545\pi\)
\(618\) −45.8632 −1.84489
\(619\) −16.7521 −0.673323 −0.336662 0.941626i \(-0.609298\pi\)
−0.336662 + 0.941626i \(0.609298\pi\)
\(620\) 76.1642 3.05883
\(621\) 41.0675 1.64798
\(622\) 0.453815 0.0181963
\(623\) 1.15149 0.0461336
\(624\) 97.4450 3.90092
\(625\) −3.70757 −0.148303
\(626\) −42.6970 −1.70652
\(627\) −5.87348 −0.234564
\(628\) −39.9064 −1.59244
\(629\) −8.75770 −0.349192
\(630\) 0.274785 0.0109477
\(631\) −23.0795 −0.918781 −0.459390 0.888235i \(-0.651932\pi\)
−0.459390 + 0.888235i \(0.651932\pi\)
\(632\) −12.3651 −0.491857
\(633\) −27.2478 −1.08300
\(634\) 64.3510 2.55571
\(635\) −12.1032 −0.480301
\(636\) −48.6012 −1.92716
\(637\) 21.8160 0.864383
\(638\) −12.3694 −0.489709
\(639\) −1.07762 −0.0426299
\(640\) −70.7245 −2.79563
\(641\) 32.0696 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(642\) −69.0732 −2.72610
\(643\) 36.4086 1.43582 0.717908 0.696138i \(-0.245100\pi\)
0.717908 + 0.696138i \(0.245100\pi\)
\(644\) 41.1489 1.62149
\(645\) −23.1307 −0.910770
\(646\) 79.1578 3.11442
\(647\) 31.9188 1.25486 0.627428 0.778675i \(-0.284108\pi\)
0.627428 + 0.778675i \(0.284108\pi\)
\(648\) 86.4575 3.39637
\(649\) −4.97536 −0.195300
\(650\) −27.0156 −1.05964
\(651\) −14.7124 −0.576625
\(652\) −44.3470 −1.73676
\(653\) −24.6483 −0.964564 −0.482282 0.876016i \(-0.660192\pi\)
−0.482282 + 0.876016i \(0.660192\pi\)
\(654\) 9.73865 0.380811
\(655\) 12.2148 0.477271
\(656\) 155.308 6.06376
\(657\) 0.384089 0.0149847
\(658\) −29.8205 −1.16253
\(659\) 47.1202 1.83554 0.917772 0.397109i \(-0.129986\pi\)
0.917772 + 0.397109i \(0.129986\pi\)
\(660\) −8.75594 −0.340825
\(661\) 19.8936 0.773772 0.386886 0.922128i \(-0.373551\pi\)
0.386886 + 0.922128i \(0.373551\pi\)
\(662\) 0.335869 0.0130539
\(663\) −31.3214 −1.21642
\(664\) −127.144 −4.93413
\(665\) 7.95437 0.308457
\(666\) 0.331432 0.0128427
\(667\) 57.4412 2.22413
\(668\) 37.8677 1.46514
\(669\) −24.5608 −0.949575
\(670\) 32.6218 1.26029
\(671\) −8.15309 −0.314746
\(672\) 39.0981 1.50824
\(673\) 34.6907 1.33723 0.668615 0.743609i \(-0.266888\pi\)
0.668615 + 0.743609i \(0.266888\pi\)
\(674\) 30.1703 1.16212
\(675\) −14.4422 −0.555880
\(676\) −1.35861 −0.0522543
\(677\) −23.9765 −0.921490 −0.460745 0.887532i \(-0.652418\pi\)
−0.460745 + 0.887532i \(0.652418\pi\)
\(678\) −90.1084 −3.46059
\(679\) −2.35768 −0.0904796
\(680\) 75.6796 2.90218
\(681\) −15.7412 −0.603203
\(682\) −15.3168 −0.586512
\(683\) 8.22951 0.314893 0.157447 0.987527i \(-0.449674\pi\)
0.157447 + 0.987527i \(0.449674\pi\)
\(684\) −2.20487 −0.0843051
\(685\) 16.2214 0.619790
\(686\) 34.0722 1.30088
\(687\) −30.1526 −1.15039
\(688\) 143.552 5.47285
\(689\) −18.1879 −0.692904
\(690\) 55.2451 2.10314
\(691\) −20.9088 −0.795409 −0.397704 0.917514i \(-0.630193\pi\)
−0.397704 + 0.917514i \(0.630193\pi\)
\(692\) −11.7774 −0.447711
\(693\) −0.0406720 −0.00154500
\(694\) −26.0142 −0.987484
\(695\) 13.9054 0.527463
\(696\) 123.838 4.69407
\(697\) −49.9201 −1.89086
\(698\) −40.1639 −1.52023
\(699\) 38.4782 1.45538
\(700\) −14.4708 −0.546945
\(701\) −23.9326 −0.903922 −0.451961 0.892038i \(-0.649275\pi\)
−0.451961 + 0.892038i \(0.649275\pi\)
\(702\) 51.6639 1.94993
\(703\) 9.59417 0.361851
\(704\) 21.2137 0.799523
\(705\) −29.4669 −1.10979
\(706\) −36.6774 −1.38037
\(707\) 16.1878 0.608803
\(708\) 77.6699 2.91901
\(709\) −31.9484 −1.19985 −0.599923 0.800058i \(-0.704802\pi\)
−0.599923 + 0.800058i \(0.704802\pi\)
\(710\) −63.1833 −2.37123
\(711\) −0.0884978 −0.00331893
\(712\) −12.0019 −0.449792
\(713\) 71.1285 2.66378
\(714\) −22.7948 −0.853072
\(715\) −3.27671 −0.122542
\(716\) −93.9507 −3.51110
\(717\) −8.72979 −0.326020
\(718\) 27.2043 1.01526
\(719\) 14.8505 0.553830 0.276915 0.960894i \(-0.410688\pi\)
0.276915 + 0.960894i \(0.410688\pi\)
\(720\) −1.68512 −0.0628008
\(721\) −9.19342 −0.342381
\(722\) −34.4216 −1.28104
\(723\) −29.9407 −1.11351
\(724\) −81.5838 −3.03204
\(725\) −20.2003 −0.750221
\(726\) −50.0612 −1.85795
\(727\) −26.3571 −0.977529 −0.488764 0.872416i \(-0.662552\pi\)
−0.488764 + 0.872416i \(0.662552\pi\)
\(728\) 33.1989 1.23043
\(729\) 27.6039 1.02237
\(730\) 22.5200 0.833502
\(731\) −46.1413 −1.70660
\(732\) 127.277 4.70430
\(733\) 13.5951 0.502147 0.251073 0.967968i \(-0.419216\pi\)
0.251073 + 0.967968i \(0.419216\pi\)
\(734\) 81.9537 3.02497
\(735\) 15.6888 0.578689
\(736\) −189.023 −6.96749
\(737\) −4.82848 −0.177859
\(738\) 1.88921 0.0695428
\(739\) 3.04740 0.112100 0.0560502 0.998428i \(-0.482149\pi\)
0.0560502 + 0.998428i \(0.482149\pi\)
\(740\) 14.3026 0.525774
\(741\) 34.3130 1.26052
\(742\) −13.2366 −0.485931
\(743\) −24.5291 −0.899886 −0.449943 0.893057i \(-0.648556\pi\)
−0.449943 + 0.893057i \(0.648556\pi\)
\(744\) 153.347 5.62196
\(745\) −5.42417 −0.198726
\(746\) 2.33364 0.0854407
\(747\) −0.909976 −0.0332943
\(748\) −17.4664 −0.638636
\(749\) −13.8459 −0.505920
\(750\) −54.7763 −2.00015
\(751\) −3.25735 −0.118862 −0.0594311 0.998232i \(-0.518929\pi\)
−0.0594311 + 0.998232i \(0.518929\pi\)
\(752\) 182.875 6.66876
\(753\) −7.03162 −0.256247
\(754\) 72.2624 2.63164
\(755\) −4.88770 −0.177882
\(756\) 27.6735 1.00648
\(757\) 20.2033 0.734300 0.367150 0.930162i \(-0.380334\pi\)
0.367150 + 0.930162i \(0.380334\pi\)
\(758\) 93.2044 3.38533
\(759\) −8.17704 −0.296808
\(760\) −82.9079 −3.00739
\(761\) −15.4696 −0.560771 −0.280386 0.959887i \(-0.590462\pi\)
−0.280386 + 0.959887i \(0.590462\pi\)
\(762\) −37.9968 −1.37648
\(763\) 1.95214 0.0706723
\(764\) −69.7919 −2.52498
\(765\) 0.541643 0.0195832
\(766\) −72.5775 −2.62233
\(767\) 29.0662 1.04952
\(768\) −103.251 −3.72575
\(769\) −33.9822 −1.22543 −0.612714 0.790305i \(-0.709922\pi\)
−0.612714 + 0.790305i \(0.709922\pi\)
\(770\) −2.38469 −0.0859383
\(771\) 25.4476 0.916472
\(772\) −13.9432 −0.501827
\(773\) −8.36360 −0.300818 −0.150409 0.988624i \(-0.548059\pi\)
−0.150409 + 0.988624i \(0.548059\pi\)
\(774\) 1.74620 0.0627659
\(775\) −25.0137 −0.898520
\(776\) 24.5740 0.882155
\(777\) −2.76279 −0.0991147
\(778\) −98.9057 −3.54594
\(779\) 54.6881 1.95941
\(780\) 51.1525 1.83155
\(781\) 9.35200 0.334641
\(782\) 110.203 3.94086
\(783\) 38.6305 1.38054
\(784\) −97.3662 −3.47737
\(785\) −10.7397 −0.383316
\(786\) 38.3470 1.36779
\(787\) −34.5988 −1.23332 −0.616658 0.787232i \(-0.711514\pi\)
−0.616658 + 0.787232i \(0.711514\pi\)
\(788\) 56.3563 2.00761
\(789\) −10.5558 −0.375797
\(790\) −5.18883 −0.184610
\(791\) −18.0625 −0.642230
\(792\) 0.423922 0.0150634
\(793\) 47.6306 1.69141
\(794\) 10.7752 0.382397
\(795\) −13.0796 −0.463887
\(796\) 44.1433 1.56462
\(797\) −26.2878 −0.931163 −0.465581 0.885005i \(-0.654155\pi\)
−0.465581 + 0.885005i \(0.654155\pi\)
\(798\) 24.9719 0.883997
\(799\) −58.7808 −2.07952
\(800\) 66.4737 2.35020
\(801\) −0.0858986 −0.00303508
\(802\) 91.9308 3.24619
\(803\) −3.33327 −0.117629
\(804\) 75.3770 2.65834
\(805\) 11.0741 0.390309
\(806\) 89.4814 3.15185
\(807\) 9.53234 0.335554
\(808\) −168.724 −5.93569
\(809\) 43.0017 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(810\) 36.2806 1.27477
\(811\) 7.09563 0.249161 0.124581 0.992209i \(-0.460241\pi\)
0.124581 + 0.992209i \(0.460241\pi\)
\(812\) 38.7070 1.35835
\(813\) −49.0843 −1.72146
\(814\) −2.87630 −0.100814
\(815\) −11.9347 −0.418056
\(816\) 139.789 4.89360
\(817\) 50.5483 1.76846
\(818\) 15.3719 0.537466
\(819\) 0.237607 0.00830265
\(820\) 81.5269 2.84704
\(821\) 17.1138 0.597277 0.298639 0.954366i \(-0.403467\pi\)
0.298639 + 0.954366i \(0.403467\pi\)
\(822\) 50.9256 1.77623
\(823\) −28.2620 −0.985151 −0.492576 0.870270i \(-0.663944\pi\)
−0.492576 + 0.870270i \(0.663944\pi\)
\(824\) 95.8225 3.33813
\(825\) 2.87562 0.100116
\(826\) 21.1535 0.736024
\(827\) 31.2483 1.08661 0.543306 0.839535i \(-0.317173\pi\)
0.543306 + 0.839535i \(0.317173\pi\)
\(828\) −3.06961 −0.106676
\(829\) −52.4772 −1.82261 −0.911304 0.411734i \(-0.864923\pi\)
−0.911304 + 0.411734i \(0.864923\pi\)
\(830\) −53.3540 −1.85194
\(831\) 10.7204 0.371887
\(832\) −123.931 −4.29654
\(833\) 31.2961 1.08435
\(834\) 43.6547 1.51164
\(835\) 10.1910 0.352674
\(836\) 19.1347 0.661787
\(837\) 47.8355 1.65344
\(838\) 52.8574 1.82593
\(839\) 2.93793 0.101429 0.0507144 0.998713i \(-0.483850\pi\)
0.0507144 + 0.998713i \(0.483850\pi\)
\(840\) 23.8747 0.823754
\(841\) 25.0325 0.863190
\(842\) 18.5381 0.638864
\(843\) −44.0583 −1.51745
\(844\) 88.7683 3.05553
\(845\) −0.365632 −0.0125781
\(846\) 2.22454 0.0764813
\(847\) −10.0349 −0.344805
\(848\) 81.1736 2.78751
\(849\) 2.01647 0.0692050
\(850\) −38.7552 −1.32929
\(851\) 13.3570 0.457871
\(852\) −145.993 −5.00164
\(853\) −18.3308 −0.627633 −0.313817 0.949484i \(-0.601608\pi\)
−0.313817 + 0.949484i \(0.601608\pi\)
\(854\) 34.6641 1.18618
\(855\) −0.593377 −0.0202931
\(856\) 144.315 4.93260
\(857\) −40.2916 −1.37633 −0.688167 0.725553i \(-0.741584\pi\)
−0.688167 + 0.725553i \(0.741584\pi\)
\(858\) −10.2869 −0.351189
\(859\) 26.6612 0.909668 0.454834 0.890576i \(-0.349699\pi\)
0.454834 + 0.890576i \(0.349699\pi\)
\(860\) 75.3555 2.56960
\(861\) −15.7483 −0.536702
\(862\) 14.4964 0.493749
\(863\) 32.7476 1.11474 0.557371 0.830263i \(-0.311810\pi\)
0.557371 + 0.830263i \(0.311810\pi\)
\(864\) −127.122 −4.32479
\(865\) −3.16957 −0.107768
\(866\) 42.0295 1.42822
\(867\) −15.8349 −0.537781
\(868\) 47.9303 1.62686
\(869\) 0.768018 0.0260532
\(870\) 51.9667 1.76184
\(871\) 28.2081 0.955796
\(872\) −20.3471 −0.689039
\(873\) 0.175878 0.00595256
\(874\) −120.729 −4.08372
\(875\) −10.9801 −0.371195
\(876\) 52.0354 1.75811
\(877\) 20.9037 0.705869 0.352934 0.935648i \(-0.385184\pi\)
0.352934 + 0.935648i \(0.385184\pi\)
\(878\) 5.07777 0.171366
\(879\) 48.9029 1.64945
\(880\) 14.6242 0.492980
\(881\) −35.4510 −1.19437 −0.597187 0.802102i \(-0.703715\pi\)
−0.597187 + 0.802102i \(0.703715\pi\)
\(882\) −1.18439 −0.0398805
\(883\) 41.6814 1.40269 0.701346 0.712821i \(-0.252583\pi\)
0.701346 + 0.712821i \(0.252583\pi\)
\(884\) 102.039 3.43195
\(885\) 20.9026 0.702635
\(886\) −5.95762 −0.200150
\(887\) −1.92146 −0.0645164 −0.0322582 0.999480i \(-0.510270\pi\)
−0.0322582 + 0.999480i \(0.510270\pi\)
\(888\) 28.7964 0.966345
\(889\) −7.61658 −0.255452
\(890\) −5.03643 −0.168822
\(891\) −5.37003 −0.179903
\(892\) 80.0145 2.67908
\(893\) 64.3952 2.15490
\(894\) −17.0286 −0.569522
\(895\) −25.2842 −0.845157
\(896\) −44.5071 −1.48688
\(897\) 47.7705 1.59501
\(898\) −46.4740 −1.55086
\(899\) 66.9076 2.23149
\(900\) 1.07949 0.0359829
\(901\) −26.0914 −0.869229
\(902\) −16.3953 −0.545904
\(903\) −14.5562 −0.484400
\(904\) 188.265 6.26159
\(905\) −21.9560 −0.729841
\(906\) −15.3444 −0.509785
\(907\) −54.8672 −1.82184 −0.910918 0.412587i \(-0.864625\pi\)
−0.910918 + 0.412587i \(0.864625\pi\)
\(908\) 51.2818 1.70185
\(909\) −1.20757 −0.0400525
\(910\) 13.9314 0.461822
\(911\) −36.1490 −1.19767 −0.598835 0.800873i \(-0.704369\pi\)
−0.598835 + 0.800873i \(0.704369\pi\)
\(912\) −153.141 −5.07100
\(913\) 7.89713 0.261357
\(914\) −73.5328 −2.43225
\(915\) 34.2530 1.13237
\(916\) 98.2316 3.24566
\(917\) 7.68679 0.253840
\(918\) 74.1142 2.44613
\(919\) −28.7768 −0.949260 −0.474630 0.880185i \(-0.657418\pi\)
−0.474630 + 0.880185i \(0.657418\pi\)
\(920\) −115.424 −3.80542
\(921\) −50.9096 −1.67753
\(922\) −11.8817 −0.391303
\(923\) −54.6346 −1.79832
\(924\) −5.51014 −0.181270
\(925\) −4.69724 −0.154444
\(926\) −97.7917 −3.21363
\(927\) 0.685807 0.0225249
\(928\) −177.806 −5.83678
\(929\) 19.3341 0.634332 0.317166 0.948370i \(-0.397269\pi\)
0.317166 + 0.948370i \(0.397269\pi\)
\(930\) 64.3496 2.11011
\(931\) −34.2853 −1.12365
\(932\) −125.355 −4.10613
\(933\) 0.282201 0.00923884
\(934\) −83.2229 −2.72314
\(935\) −4.70059 −0.153726
\(936\) −2.47656 −0.0809489
\(937\) 16.6280 0.543215 0.271607 0.962408i \(-0.412445\pi\)
0.271607 + 0.962408i \(0.412445\pi\)
\(938\) 20.5290 0.670296
\(939\) −26.5507 −0.866451
\(940\) 95.9978 3.13110
\(941\) −24.0769 −0.784884 −0.392442 0.919777i \(-0.628370\pi\)
−0.392442 + 0.919777i \(0.628370\pi\)
\(942\) −33.7161 −1.09853
\(943\) 76.1367 2.47935
\(944\) −129.724 −4.22216
\(945\) 7.44755 0.242269
\(946\) −15.1542 −0.492706
\(947\) 41.0617 1.33433 0.667164 0.744911i \(-0.267508\pi\)
0.667164 + 0.744911i \(0.267508\pi\)
\(948\) −11.9895 −0.389400
\(949\) 19.4731 0.632122
\(950\) 42.4568 1.37748
\(951\) 40.0161 1.29761
\(952\) 47.6254 1.54355
\(953\) −36.1456 −1.17087 −0.585436 0.810719i \(-0.699076\pi\)
−0.585436 + 0.810719i \(0.699076\pi\)
\(954\) 0.987418 0.0319688
\(955\) −18.7825 −0.607788
\(956\) 28.4400 0.919816
\(957\) −7.69180 −0.248641
\(958\) 56.8966 1.83825
\(959\) 10.2082 0.329640
\(960\) −89.1238 −2.87646
\(961\) 51.8507 1.67260
\(962\) 16.8034 0.541763
\(963\) 1.03287 0.0332839
\(964\) 97.5412 3.14159
\(965\) −3.75242 −0.120795
\(966\) 34.7659 1.11857
\(967\) 53.5904 1.72335 0.861675 0.507461i \(-0.169416\pi\)
0.861675 + 0.507461i \(0.169416\pi\)
\(968\) 104.594 3.36176
\(969\) 49.2236 1.58129
\(970\) 10.3121 0.331102
\(971\) −24.7388 −0.793905 −0.396953 0.917839i \(-0.629932\pi\)
−0.396953 + 0.917839i \(0.629932\pi\)
\(972\) −4.08139 −0.130911
\(973\) 8.75073 0.280536
\(974\) −69.4487 −2.22528
\(975\) −16.7994 −0.538012
\(976\) −212.578 −6.80445
\(977\) 17.7151 0.566756 0.283378 0.959008i \(-0.408545\pi\)
0.283378 + 0.959008i \(0.408545\pi\)
\(978\) −37.4679 −1.19809
\(979\) 0.745462 0.0238251
\(980\) −51.1111 −1.63268
\(981\) −0.145625 −0.00464946
\(982\) −65.5428 −2.09155
\(983\) 9.64708 0.307694 0.153847 0.988095i \(-0.450834\pi\)
0.153847 + 0.988095i \(0.450834\pi\)
\(984\) 164.144 5.23272
\(985\) 15.1667 0.483252
\(986\) 103.664 3.30132
\(987\) −18.5436 −0.590250
\(988\) −111.785 −3.55637
\(989\) 70.3733 2.23774
\(990\) 0.177892 0.00565379
\(991\) 23.6945 0.752682 0.376341 0.926481i \(-0.377182\pi\)
0.376341 + 0.926481i \(0.377182\pi\)
\(992\) −220.175 −6.99056
\(993\) 0.208857 0.00662787
\(994\) −39.7614 −1.26116
\(995\) 11.8799 0.376618
\(996\) −123.281 −3.90632
\(997\) 37.4332 1.18552 0.592761 0.805379i \(-0.298038\pi\)
0.592761 + 0.805379i \(0.298038\pi\)
\(998\) 42.6841 1.35114
\(999\) 8.98286 0.284205
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 \(a_p\))