Properties

Label 4031.2.a.c.1.20
Level 4031
Weight 2
Character 4031.1
Self dual Yes
Analytic conductor 32.188
Analytic rank 1
Dimension 61
CM No

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Newspace parameters

Level: \( N \) = \( 4031 = 29 \cdot 139 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1876970548\)
Analytic rank: \(1\)
Dimension: \(61\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 4031.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.13471 q^{2}\) \(+1.15618 q^{3}\) \(-0.712442 q^{4}\) \(+3.10962 q^{5}\) \(-1.31192 q^{6}\) \(-1.02298 q^{7}\) \(+3.07782 q^{8}\) \(-1.66325 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.13471 q^{2}\) \(+1.15618 q^{3}\) \(-0.712442 q^{4}\) \(+3.10962 q^{5}\) \(-1.31192 q^{6}\) \(-1.02298 q^{7}\) \(+3.07782 q^{8}\) \(-1.66325 q^{9}\) \(-3.52850 q^{10}\) \(-1.83622 q^{11}\) \(-0.823711 q^{12}\) \(+3.48520 q^{13}\) \(+1.16078 q^{14}\) \(+3.59528 q^{15}\) \(-2.06754 q^{16}\) \(-1.09492 q^{17}\) \(+1.88730 q^{18}\) \(-2.20806 q^{19}\) \(-2.21542 q^{20}\) \(-1.18275 q^{21}\) \(+2.08357 q^{22}\) \(-1.23653 q^{23}\) \(+3.55852 q^{24}\) \(+4.66973 q^{25}\) \(-3.95467 q^{26}\) \(-5.39155 q^{27}\) \(+0.728812 q^{28}\) \(-1.00000 q^{29}\) \(-4.07958 q^{30}\) \(-4.93412 q^{31}\) \(-3.80960 q^{32}\) \(-2.12300 q^{33}\) \(+1.24242 q^{34}\) \(-3.18107 q^{35}\) \(+1.18497 q^{36}\) \(-10.7505 q^{37}\) \(+2.50550 q^{38}\) \(+4.02951 q^{39}\) \(+9.57086 q^{40}\) \(-3.31015 q^{41}\) \(+1.34207 q^{42}\) \(+7.70702 q^{43}\) \(+1.30820 q^{44}\) \(-5.17207 q^{45}\) \(+1.40309 q^{46}\) \(+7.43359 q^{47}\) \(-2.39045 q^{48}\) \(-5.95352 q^{49}\) \(-5.29877 q^{50}\) \(-1.26593 q^{51}\) \(-2.48300 q^{52}\) \(-2.52651 q^{53}\) \(+6.11783 q^{54}\) \(-5.70995 q^{55}\) \(-3.14854 q^{56}\) \(-2.55292 q^{57}\) \(+1.13471 q^{58}\) \(+4.84374 q^{59}\) \(-2.56143 q^{60}\) \(-5.33508 q^{61}\) \(+5.59878 q^{62}\) \(+1.70147 q^{63}\) \(+8.45786 q^{64}\) \(+10.8376 q^{65}\) \(+2.40899 q^{66}\) \(-10.1714 q^{67}\) \(+0.780070 q^{68}\) \(-1.42965 q^{69}\) \(+3.60958 q^{70}\) \(-8.54404 q^{71}\) \(-5.11919 q^{72}\) \(+6.94608 q^{73}\) \(+12.1986 q^{74}\) \(+5.39905 q^{75}\) \(+1.57312 q^{76}\) \(+1.87841 q^{77}\) \(-4.57231 q^{78}\) \(+6.60000 q^{79}\) \(-6.42927 q^{80}\) \(-1.24386 q^{81}\) \(+3.75605 q^{82}\) \(-9.84384 q^{83}\) \(+0.842638 q^{84}\) \(-3.40480 q^{85}\) \(-8.74520 q^{86}\) \(-1.15618 q^{87}\) \(-5.65157 q^{88}\) \(-8.43394 q^{89}\) \(+5.86878 q^{90}\) \(-3.56528 q^{91}\) \(+0.880954 q^{92}\) \(-5.70473 q^{93}\) \(-8.43494 q^{94}\) \(-6.86623 q^{95}\) \(-4.40458 q^{96}\) \(-1.62517 q^{97}\) \(+6.75549 q^{98}\) \(+3.05409 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(61q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 13q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 18q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut -\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 17q^{18} \) \(\mathstrut -\mathstrut 36q^{19} \) \(\mathstrut -\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 42q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut -\mathstrut 25q^{28} \) \(\mathstrut -\mathstrut 61q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 3q^{32} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 22q^{34} \) \(\mathstrut -\mathstrut 29q^{35} \) \(\mathstrut -\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 27q^{38} \) \(\mathstrut -\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut 22q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 31q^{45} \) \(\mathstrut -\mathstrut 40q^{46} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 37q^{48} \) \(\mathstrut -\mathstrut 37q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 43q^{52} \) \(\mathstrut -\mathstrut 27q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 38q^{55} \) \(\mathstrut -\mathstrut 22q^{56} \) \(\mathstrut -\mathstrut 50q^{57} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 76q^{61} \) \(\mathstrut -\mathstrut 17q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 60q^{64} \) \(\mathstrut -\mathstrut 65q^{65} \) \(\mathstrut -\mathstrut 7q^{66} \) \(\mathstrut -\mathstrut 45q^{67} \) \(\mathstrut -\mathstrut 31q^{68} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 28q^{71} \) \(\mathstrut -\mathstrut 40q^{72} \) \(\mathstrut -\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 35q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut -\mathstrut 63q^{81} \) \(\mathstrut -\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 62q^{88} \) \(\mathstrut -\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 50q^{90} \) \(\mathstrut -\mathstrut 52q^{91} \) \(\mathstrut -\mathstrut 53q^{92} \) \(\mathstrut -\mathstrut 42q^{93} \) \(\mathstrut -\mathstrut 92q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut -\mathstrut 47q^{96} \) \(\mathstrut -\mathstrut 34q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 29q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13471 −0.802358 −0.401179 0.916000i \(-0.631400\pi\)
−0.401179 + 0.916000i \(0.631400\pi\)
\(3\) 1.15618 0.667521 0.333760 0.942658i \(-0.391682\pi\)
0.333760 + 0.942658i \(0.391682\pi\)
\(4\) −0.712442 −0.356221
\(5\) 3.10962 1.39066 0.695332 0.718689i \(-0.255257\pi\)
0.695332 + 0.718689i \(0.255257\pi\)
\(6\) −1.31192 −0.535591
\(7\) −1.02298 −0.386649 −0.193325 0.981135i \(-0.561927\pi\)
−0.193325 + 0.981135i \(0.561927\pi\)
\(8\) 3.07782 1.08818
\(9\) −1.66325 −0.554416
\(10\) −3.52850 −1.11581
\(11\) −1.83622 −0.553642 −0.276821 0.960922i \(-0.589281\pi\)
−0.276821 + 0.960922i \(0.589281\pi\)
\(12\) −0.823711 −0.237785
\(13\) 3.48520 0.966620 0.483310 0.875449i \(-0.339434\pi\)
0.483310 + 0.875449i \(0.339434\pi\)
\(14\) 1.16078 0.310231
\(15\) 3.59528 0.928297
\(16\) −2.06754 −0.516885
\(17\) −1.09492 −0.265558 −0.132779 0.991146i \(-0.542390\pi\)
−0.132779 + 0.991146i \(0.542390\pi\)
\(18\) 1.88730 0.444840
\(19\) −2.20806 −0.506564 −0.253282 0.967392i \(-0.581510\pi\)
−0.253282 + 0.967392i \(0.581510\pi\)
\(20\) −2.21542 −0.495384
\(21\) −1.18275 −0.258096
\(22\) 2.08357 0.444219
\(23\) −1.23653 −0.257834 −0.128917 0.991655i \(-0.541150\pi\)
−0.128917 + 0.991655i \(0.541150\pi\)
\(24\) 3.55852 0.726380
\(25\) 4.66973 0.933946
\(26\) −3.95467 −0.775575
\(27\) −5.39155 −1.03760
\(28\) 0.728812 0.137733
\(29\) −1.00000 −0.185695
\(30\) −4.07958 −0.744827
\(31\) −4.93412 −0.886194 −0.443097 0.896474i \(-0.646120\pi\)
−0.443097 + 0.896474i \(0.646120\pi\)
\(32\) −3.80960 −0.673448
\(33\) −2.12300 −0.369568
\(34\) 1.24242 0.213073
\(35\) −3.18107 −0.537699
\(36\) 1.18497 0.197495
\(37\) −10.7505 −1.76737 −0.883684 0.468085i \(-0.844944\pi\)
−0.883684 + 0.468085i \(0.844944\pi\)
\(38\) 2.50550 0.406446
\(39\) 4.02951 0.645239
\(40\) 9.57086 1.51329
\(41\) −3.31015 −0.516959 −0.258479 0.966017i \(-0.583221\pi\)
−0.258479 + 0.966017i \(0.583221\pi\)
\(42\) 1.34207 0.207086
\(43\) 7.70702 1.17531 0.587655 0.809112i \(-0.300051\pi\)
0.587655 + 0.809112i \(0.300051\pi\)
\(44\) 1.30820 0.197219
\(45\) −5.17207 −0.771006
\(46\) 1.40309 0.206875
\(47\) 7.43359 1.08430 0.542150 0.840281i \(-0.317610\pi\)
0.542150 + 0.840281i \(0.317610\pi\)
\(48\) −2.39045 −0.345032
\(49\) −5.95352 −0.850502
\(50\) −5.29877 −0.749359
\(51\) −1.26593 −0.177266
\(52\) −2.48300 −0.344330
\(53\) −2.52651 −0.347043 −0.173521 0.984830i \(-0.555515\pi\)
−0.173521 + 0.984830i \(0.555515\pi\)
\(54\) 6.11783 0.832531
\(55\) −5.70995 −0.769930
\(56\) −3.14854 −0.420742
\(57\) −2.55292 −0.338142
\(58\) 1.13471 0.148994
\(59\) 4.84374 0.630601 0.315300 0.948992i \(-0.397895\pi\)
0.315300 + 0.948992i \(0.397895\pi\)
\(60\) −2.56143 −0.330679
\(61\) −5.33508 −0.683087 −0.341544 0.939866i \(-0.610950\pi\)
−0.341544 + 0.939866i \(0.610950\pi\)
\(62\) 5.59878 0.711045
\(63\) 1.70147 0.214364
\(64\) 8.45786 1.05723
\(65\) 10.8376 1.34424
\(66\) 2.40899 0.296526
\(67\) −10.1714 −1.24264 −0.621319 0.783557i \(-0.713403\pi\)
−0.621319 + 0.783557i \(0.713403\pi\)
\(68\) 0.780070 0.0945974
\(69\) −1.42965 −0.172109
\(70\) 3.60958 0.431427
\(71\) −8.54404 −1.01399 −0.506995 0.861949i \(-0.669244\pi\)
−0.506995 + 0.861949i \(0.669244\pi\)
\(72\) −5.11919 −0.603302
\(73\) 6.94608 0.812977 0.406488 0.913656i \(-0.366753\pi\)
0.406488 + 0.913656i \(0.366753\pi\)
\(74\) 12.1986 1.41806
\(75\) 5.39905 0.623428
\(76\) 1.57312 0.180449
\(77\) 1.87841 0.214065
\(78\) −4.57231 −0.517713
\(79\) 6.60000 0.742558 0.371279 0.928521i \(-0.378919\pi\)
0.371279 + 0.928521i \(0.378919\pi\)
\(80\) −6.42927 −0.718814
\(81\) −1.24386 −0.138207
\(82\) 3.75605 0.414786
\(83\) −9.84384 −1.08050 −0.540251 0.841504i \(-0.681671\pi\)
−0.540251 + 0.841504i \(0.681671\pi\)
\(84\) 0.842638 0.0919394
\(85\) −3.40480 −0.369302
\(86\) −8.74520 −0.943020
\(87\) −1.15618 −0.123955
\(88\) −5.65157 −0.602460
\(89\) −8.43394 −0.893995 −0.446998 0.894535i \(-0.647507\pi\)
−0.446998 + 0.894535i \(0.647507\pi\)
\(90\) 5.86878 0.618623
\(91\) −3.56528 −0.373743
\(92\) 0.880954 0.0918458
\(93\) −5.70473 −0.591553
\(94\) −8.43494 −0.869998
\(95\) −6.86623 −0.704460
\(96\) −4.40458 −0.449540
\(97\) −1.62517 −0.165011 −0.0825055 0.996591i \(-0.526292\pi\)
−0.0825055 + 0.996591i \(0.526292\pi\)
\(98\) 6.75549 0.682408
\(99\) 3.05409 0.306948
\(100\) −3.32691 −0.332691
\(101\) 4.03793 0.401789 0.200895 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(102\) 1.43646 0.142231
\(103\) 3.28005 0.323193 0.161597 0.986857i \(-0.448336\pi\)
0.161597 + 0.986857i \(0.448336\pi\)
\(104\) 10.7268 1.05185
\(105\) −3.67789 −0.358925
\(106\) 2.86684 0.278453
\(107\) −2.42399 −0.234336 −0.117168 0.993112i \(-0.537382\pi\)
−0.117168 + 0.993112i \(0.537382\pi\)
\(108\) 3.84117 0.369617
\(109\) −2.19586 −0.210326 −0.105163 0.994455i \(-0.533536\pi\)
−0.105163 + 0.994455i \(0.533536\pi\)
\(110\) 6.47912 0.617760
\(111\) −12.4295 −1.17975
\(112\) 2.11505 0.199853
\(113\) −6.09089 −0.572983 −0.286491 0.958083i \(-0.592489\pi\)
−0.286491 + 0.958083i \(0.592489\pi\)
\(114\) 2.89681 0.271311
\(115\) −3.84513 −0.358560
\(116\) 0.712442 0.0661486
\(117\) −5.79675 −0.535909
\(118\) −5.49622 −0.505968
\(119\) 1.12008 0.102678
\(120\) 11.0656 1.01015
\(121\) −7.62829 −0.693481
\(122\) 6.05375 0.548081
\(123\) −3.82713 −0.345081
\(124\) 3.51528 0.315681
\(125\) −1.02702 −0.0918593
\(126\) −1.93066 −0.171997
\(127\) −6.01420 −0.533674 −0.266837 0.963742i \(-0.585978\pi\)
−0.266837 + 0.963742i \(0.585978\pi\)
\(128\) −1.97799 −0.174831
\(129\) 8.91070 0.784544
\(130\) −12.2975 −1.07856
\(131\) −6.54336 −0.571696 −0.285848 0.958275i \(-0.592275\pi\)
−0.285848 + 0.958275i \(0.592275\pi\)
\(132\) 1.51252 0.131648
\(133\) 2.25880 0.195863
\(134\) 11.5416 0.997042
\(135\) −16.7657 −1.44296
\(136\) −3.36998 −0.288974
\(137\) −8.80948 −0.752645 −0.376322 0.926489i \(-0.622811\pi\)
−0.376322 + 0.926489i \(0.622811\pi\)
\(138\) 1.62223 0.138093
\(139\) −1.00000 −0.0848189
\(140\) 2.26633 0.191540
\(141\) 8.59457 0.723793
\(142\) 9.69497 0.813584
\(143\) −6.39960 −0.535161
\(144\) 3.43883 0.286570
\(145\) −3.10962 −0.258240
\(146\) −7.88175 −0.652299
\(147\) −6.88334 −0.567728
\(148\) 7.65909 0.629573
\(149\) 12.2218 1.00125 0.500624 0.865665i \(-0.333104\pi\)
0.500624 + 0.865665i \(0.333104\pi\)
\(150\) −6.12633 −0.500213
\(151\) 18.2053 1.48153 0.740765 0.671765i \(-0.234463\pi\)
0.740765 + 0.671765i \(0.234463\pi\)
\(152\) −6.79603 −0.551230
\(153\) 1.82113 0.147230
\(154\) −2.13145 −0.171757
\(155\) −15.3432 −1.23240
\(156\) −2.87080 −0.229848
\(157\) 20.8300 1.66241 0.831207 0.555963i \(-0.187650\pi\)
0.831207 + 0.555963i \(0.187650\pi\)
\(158\) −7.48906 −0.595797
\(159\) −2.92110 −0.231658
\(160\) −11.8464 −0.936540
\(161\) 1.26494 0.0996911
\(162\) 1.41142 0.110891
\(163\) 10.4895 0.821603 0.410802 0.911725i \(-0.365249\pi\)
0.410802 + 0.911725i \(0.365249\pi\)
\(164\) 2.35829 0.184152
\(165\) −6.60173 −0.513944
\(166\) 11.1699 0.866950
\(167\) −12.0413 −0.931782 −0.465891 0.884842i \(-0.654266\pi\)
−0.465891 + 0.884842i \(0.654266\pi\)
\(168\) −3.64028 −0.280854
\(169\) −0.853407 −0.0656467
\(170\) 3.86344 0.296313
\(171\) 3.67255 0.280847
\(172\) −5.49081 −0.418670
\(173\) −10.1502 −0.771707 −0.385853 0.922560i \(-0.626093\pi\)
−0.385853 + 0.922560i \(0.626093\pi\)
\(174\) 1.31192 0.0994567
\(175\) −4.77703 −0.361109
\(176\) 3.79647 0.286169
\(177\) 5.60023 0.420939
\(178\) 9.57004 0.717305
\(179\) 4.37340 0.326884 0.163442 0.986553i \(-0.447740\pi\)
0.163442 + 0.986553i \(0.447740\pi\)
\(180\) 3.68480 0.274649
\(181\) −15.9108 −1.18264 −0.591321 0.806436i \(-0.701393\pi\)
−0.591321 + 0.806436i \(0.701393\pi\)
\(182\) 4.04554 0.299875
\(183\) −6.16832 −0.455975
\(184\) −3.80581 −0.280568
\(185\) −33.4299 −2.45781
\(186\) 6.47319 0.474637
\(187\) 2.01052 0.147024
\(188\) −5.29601 −0.386251
\(189\) 5.51544 0.401189
\(190\) 7.79115 0.565229
\(191\) 5.42754 0.392723 0.196362 0.980532i \(-0.437087\pi\)
0.196362 + 0.980532i \(0.437087\pi\)
\(192\) 9.77880 0.705724
\(193\) 9.78327 0.704215 0.352108 0.935960i \(-0.385465\pi\)
0.352108 + 0.935960i \(0.385465\pi\)
\(194\) 1.84409 0.132398
\(195\) 12.5303 0.897310
\(196\) 4.24154 0.302967
\(197\) 1.27664 0.0909570 0.0454785 0.998965i \(-0.485519\pi\)
0.0454785 + 0.998965i \(0.485519\pi\)
\(198\) −3.46550 −0.246282
\(199\) 11.3715 0.806105 0.403052 0.915177i \(-0.367949\pi\)
0.403052 + 0.915177i \(0.367949\pi\)
\(200\) 14.3726 1.01630
\(201\) −11.7600 −0.829487
\(202\) −4.58186 −0.322379
\(203\) 1.02298 0.0717989
\(204\) 0.901902 0.0631457
\(205\) −10.2933 −0.718916
\(206\) −3.72189 −0.259317
\(207\) 2.05665 0.142947
\(208\) −7.20579 −0.499632
\(209\) 4.05449 0.280455
\(210\) 4.17332 0.287987
\(211\) 8.33933 0.574103 0.287052 0.957915i \(-0.407325\pi\)
0.287052 + 0.957915i \(0.407325\pi\)
\(212\) 1.79999 0.123624
\(213\) −9.87845 −0.676860
\(214\) 2.75051 0.188021
\(215\) 23.9659 1.63446
\(216\) −16.5943 −1.12910
\(217\) 5.04749 0.342646
\(218\) 2.49166 0.168757
\(219\) 8.03091 0.542679
\(220\) 4.06801 0.274265
\(221\) −3.81603 −0.256694
\(222\) 14.1038 0.946586
\(223\) −3.60700 −0.241543 −0.120771 0.992680i \(-0.538537\pi\)
−0.120771 + 0.992680i \(0.538537\pi\)
\(224\) 3.89713 0.260388
\(225\) −7.76692 −0.517795
\(226\) 6.91137 0.459738
\(227\) 27.9665 1.85620 0.928101 0.372327i \(-0.121440\pi\)
0.928101 + 0.372327i \(0.121440\pi\)
\(228\) 1.81881 0.120453
\(229\) 22.9302 1.51527 0.757634 0.652679i \(-0.226355\pi\)
0.757634 + 0.652679i \(0.226355\pi\)
\(230\) 4.36309 0.287693
\(231\) 2.17178 0.142893
\(232\) −3.07782 −0.202069
\(233\) −15.2211 −0.997165 −0.498582 0.866842i \(-0.666146\pi\)
−0.498582 + 0.866842i \(0.666146\pi\)
\(234\) 6.57760 0.429991
\(235\) 23.1156 1.50790
\(236\) −3.45088 −0.224633
\(237\) 7.63078 0.495673
\(238\) −1.27096 −0.0823844
\(239\) −11.0498 −0.714751 −0.357376 0.933961i \(-0.616328\pi\)
−0.357376 + 0.933961i \(0.616328\pi\)
\(240\) −7.43339 −0.479823
\(241\) 4.97450 0.320436 0.160218 0.987082i \(-0.448780\pi\)
0.160218 + 0.987082i \(0.448780\pi\)
\(242\) 8.65586 0.556420
\(243\) 14.7365 0.945349
\(244\) 3.80094 0.243330
\(245\) −18.5132 −1.18276
\(246\) 4.34267 0.276878
\(247\) −7.69553 −0.489655
\(248\) −15.1864 −0.964335
\(249\) −11.3813 −0.721258
\(250\) 1.16536 0.0737041
\(251\) −1.91328 −0.120765 −0.0603825 0.998175i \(-0.519232\pi\)
−0.0603825 + 0.998175i \(0.519232\pi\)
\(252\) −1.21220 −0.0763612
\(253\) 2.27054 0.142747
\(254\) 6.82434 0.428197
\(255\) −3.93656 −0.246517
\(256\) −14.6713 −0.916955
\(257\) −25.8728 −1.61390 −0.806952 0.590617i \(-0.798884\pi\)
−0.806952 + 0.590617i \(0.798884\pi\)
\(258\) −10.1110 −0.629485
\(259\) 10.9975 0.683351
\(260\) −7.72119 −0.478848
\(261\) 1.66325 0.102952
\(262\) 7.42479 0.458705
\(263\) −1.31821 −0.0812845 −0.0406422 0.999174i \(-0.512940\pi\)
−0.0406422 + 0.999174i \(0.512940\pi\)
\(264\) −6.53423 −0.402154
\(265\) −7.85648 −0.482620
\(266\) −2.56307 −0.157152
\(267\) −9.75115 −0.596760
\(268\) 7.24656 0.442654
\(269\) −13.4812 −0.821965 −0.410983 0.911643i \(-0.634814\pi\)
−0.410983 + 0.911643i \(0.634814\pi\)
\(270\) 19.0241 1.15777
\(271\) −26.3532 −1.60085 −0.800423 0.599436i \(-0.795392\pi\)
−0.800423 + 0.599436i \(0.795392\pi\)
\(272\) 2.26380 0.137263
\(273\) −4.12210 −0.249481
\(274\) 9.99617 0.603891
\(275\) −8.57466 −0.517072
\(276\) 1.01854 0.0613089
\(277\) −27.9624 −1.68010 −0.840048 0.542512i \(-0.817473\pi\)
−0.840048 + 0.542512i \(0.817473\pi\)
\(278\) 1.13471 0.0680551
\(279\) 8.20667 0.491320
\(280\) −9.79077 −0.585111
\(281\) 15.8224 0.943887 0.471944 0.881629i \(-0.343553\pi\)
0.471944 + 0.881629i \(0.343553\pi\)
\(282\) −9.75231 −0.580742
\(283\) −3.79565 −0.225628 −0.112814 0.993616i \(-0.535986\pi\)
−0.112814 + 0.993616i \(0.535986\pi\)
\(284\) 6.08713 0.361205
\(285\) −7.93859 −0.470242
\(286\) 7.26166 0.429391
\(287\) 3.38621 0.199882
\(288\) 6.33631 0.373370
\(289\) −15.8011 −0.929479
\(290\) 3.52850 0.207201
\(291\) −1.87899 −0.110148
\(292\) −4.94868 −0.289599
\(293\) −13.9562 −0.815330 −0.407665 0.913132i \(-0.633657\pi\)
−0.407665 + 0.913132i \(0.633657\pi\)
\(294\) 7.81056 0.455521
\(295\) 15.0622 0.876954
\(296\) −33.0881 −1.92321
\(297\) 9.90009 0.574462
\(298\) −13.8681 −0.803360
\(299\) −4.30954 −0.249227
\(300\) −3.84651 −0.222078
\(301\) −7.88411 −0.454432
\(302\) −20.6577 −1.18872
\(303\) 4.66857 0.268203
\(304\) 4.56526 0.261836
\(305\) −16.5901 −0.949945
\(306\) −2.06645 −0.118131
\(307\) −11.9453 −0.681752 −0.340876 0.940108i \(-0.610724\pi\)
−0.340876 + 0.940108i \(0.610724\pi\)
\(308\) −1.33826 −0.0762545
\(309\) 3.79233 0.215738
\(310\) 17.4101 0.988825
\(311\) 25.1875 1.42825 0.714125 0.700018i \(-0.246825\pi\)
0.714125 + 0.700018i \(0.246825\pi\)
\(312\) 12.4021 0.702133
\(313\) −34.6271 −1.95724 −0.978620 0.205674i \(-0.934061\pi\)
−0.978620 + 0.205674i \(0.934061\pi\)
\(314\) −23.6359 −1.33385
\(315\) 5.29091 0.298109
\(316\) −4.70212 −0.264515
\(317\) −23.2512 −1.30592 −0.652959 0.757393i \(-0.726473\pi\)
−0.652959 + 0.757393i \(0.726473\pi\)
\(318\) 3.31459 0.185873
\(319\) 1.83622 0.102809
\(320\) 26.3007 1.47025
\(321\) −2.80256 −0.156424
\(322\) −1.43533 −0.0799880
\(323\) 2.41766 0.134522
\(324\) 0.886179 0.0492321
\(325\) 16.2749 0.902770
\(326\) −11.9025 −0.659220
\(327\) −2.53881 −0.140397
\(328\) −10.1881 −0.562542
\(329\) −7.60440 −0.419244
\(330\) 7.49103 0.412367
\(331\) 15.4242 0.847790 0.423895 0.905711i \(-0.360662\pi\)
0.423895 + 0.905711i \(0.360662\pi\)
\(332\) 7.01317 0.384898
\(333\) 17.8807 0.979857
\(334\) 13.6633 0.747623
\(335\) −31.6293 −1.72809
\(336\) 2.44538 0.133406
\(337\) 13.4221 0.731149 0.365575 0.930782i \(-0.380873\pi\)
0.365575 + 0.930782i \(0.380873\pi\)
\(338\) 0.968366 0.0526722
\(339\) −7.04217 −0.382478
\(340\) 2.42572 0.131553
\(341\) 9.06014 0.490634
\(342\) −4.16727 −0.225340
\(343\) 13.2512 0.715495
\(344\) 23.7209 1.27894
\(345\) −4.44566 −0.239346
\(346\) 11.5175 0.619186
\(347\) 26.5231 1.42383 0.711916 0.702264i \(-0.247828\pi\)
0.711916 + 0.702264i \(0.247828\pi\)
\(348\) 0.823711 0.0441556
\(349\) 0.159546 0.00854032 0.00427016 0.999991i \(-0.498641\pi\)
0.00427016 + 0.999991i \(0.498641\pi\)
\(350\) 5.42052 0.289739
\(351\) −18.7906 −1.00297
\(352\) 6.99527 0.372849
\(353\) 8.91712 0.474610 0.237305 0.971435i \(-0.423736\pi\)
0.237305 + 0.971435i \(0.423736\pi\)
\(354\) −6.35461 −0.337744
\(355\) −26.5687 −1.41012
\(356\) 6.00869 0.318460
\(357\) 1.29502 0.0685396
\(358\) −4.96253 −0.262278
\(359\) −17.2674 −0.911337 −0.455669 0.890149i \(-0.650600\pi\)
−0.455669 + 0.890149i \(0.650600\pi\)
\(360\) −15.9187 −0.838990
\(361\) −14.1245 −0.743393
\(362\) 18.0541 0.948903
\(363\) −8.81967 −0.462913
\(364\) 2.54005 0.133135
\(365\) 21.5996 1.13058
\(366\) 6.99923 0.365855
\(367\) −9.05603 −0.472721 −0.236360 0.971665i \(-0.575955\pi\)
−0.236360 + 0.971665i \(0.575955\pi\)
\(368\) 2.55657 0.133270
\(369\) 5.50560 0.286610
\(370\) 37.9331 1.97205
\(371\) 2.58456 0.134184
\(372\) 4.06429 0.210724
\(373\) −34.0146 −1.76121 −0.880606 0.473850i \(-0.842864\pi\)
−0.880606 + 0.473850i \(0.842864\pi\)
\(374\) −2.28135 −0.117966
\(375\) −1.18742 −0.0613180
\(376\) 22.8793 1.17991
\(377\) −3.48520 −0.179497
\(378\) −6.25840 −0.321897
\(379\) 7.26268 0.373059 0.186529 0.982449i \(-0.440276\pi\)
0.186529 + 0.982449i \(0.440276\pi\)
\(380\) 4.89179 0.250944
\(381\) −6.95349 −0.356238
\(382\) −6.15867 −0.315105
\(383\) 5.41538 0.276713 0.138356 0.990383i \(-0.455818\pi\)
0.138356 + 0.990383i \(0.455818\pi\)
\(384\) −2.28691 −0.116703
\(385\) 5.84115 0.297693
\(386\) −11.1011 −0.565033
\(387\) −12.8187 −0.651611
\(388\) 1.15784 0.0587804
\(389\) −24.2020 −1.22709 −0.613545 0.789660i \(-0.710257\pi\)
−0.613545 + 0.789660i \(0.710257\pi\)
\(390\) −14.2182 −0.719964
\(391\) 1.35390 0.0684698
\(392\) −18.3239 −0.925496
\(393\) −7.56530 −0.381619
\(394\) −1.44861 −0.0729801
\(395\) 20.5235 1.03265
\(396\) −2.17587 −0.109341
\(397\) 1.02440 0.0514133 0.0257067 0.999670i \(-0.491816\pi\)
0.0257067 + 0.999670i \(0.491816\pi\)
\(398\) −12.9033 −0.646785
\(399\) 2.61158 0.130742
\(400\) −9.65486 −0.482743
\(401\) −18.6452 −0.931096 −0.465548 0.885023i \(-0.654143\pi\)
−0.465548 + 0.885023i \(0.654143\pi\)
\(402\) 13.3442 0.665546
\(403\) −17.1964 −0.856613
\(404\) −2.87679 −0.143126
\(405\) −3.86793 −0.192199
\(406\) −1.16078 −0.0576085
\(407\) 19.7403 0.978489
\(408\) −3.89631 −0.192896
\(409\) 24.4204 1.20751 0.603756 0.797169i \(-0.293670\pi\)
0.603756 + 0.797169i \(0.293670\pi\)
\(410\) 11.6799 0.576828
\(411\) −10.1853 −0.502406
\(412\) −2.33685 −0.115128
\(413\) −4.95503 −0.243821
\(414\) −2.33369 −0.114695
\(415\) −30.6106 −1.50262
\(416\) −13.2772 −0.650968
\(417\) −1.15618 −0.0566184
\(418\) −4.60066 −0.225025
\(419\) 13.3773 0.653523 0.326761 0.945107i \(-0.394043\pi\)
0.326761 + 0.945107i \(0.394043\pi\)
\(420\) 2.62028 0.127857
\(421\) 32.8198 1.59954 0.799769 0.600308i \(-0.204955\pi\)
0.799769 + 0.600308i \(0.204955\pi\)
\(422\) −9.46269 −0.460636
\(423\) −12.3639 −0.601154
\(424\) −7.77615 −0.377643
\(425\) −5.11300 −0.248017
\(426\) 11.2091 0.543084
\(427\) 5.45767 0.264115
\(428\) 1.72695 0.0834753
\(429\) −7.39908 −0.357231
\(430\) −27.1942 −1.31142
\(431\) 2.14292 0.103221 0.0516103 0.998667i \(-0.483565\pi\)
0.0516103 + 0.998667i \(0.483565\pi\)
\(432\) 11.1473 0.536323
\(433\) 13.9674 0.671231 0.335616 0.941999i \(-0.391056\pi\)
0.335616 + 0.941999i \(0.391056\pi\)
\(434\) −5.72742 −0.274925
\(435\) −3.59528 −0.172380
\(436\) 1.56443 0.0749225
\(437\) 2.73033 0.130609
\(438\) −9.11273 −0.435423
\(439\) 9.98146 0.476389 0.238195 0.971217i \(-0.423444\pi\)
0.238195 + 0.971217i \(0.423444\pi\)
\(440\) −17.5742 −0.837819
\(441\) 9.90218 0.471532
\(442\) 4.33007 0.205960
\(443\) −7.71677 −0.366635 −0.183317 0.983054i \(-0.558684\pi\)
−0.183317 + 0.983054i \(0.558684\pi\)
\(444\) 8.85529 0.420253
\(445\) −26.2263 −1.24325
\(446\) 4.09289 0.193804
\(447\) 14.1306 0.668354
\(448\) −8.65220 −0.408778
\(449\) 6.39685 0.301886 0.150943 0.988542i \(-0.451769\pi\)
0.150943 + 0.988542i \(0.451769\pi\)
\(450\) 8.81317 0.415457
\(451\) 6.07817 0.286210
\(452\) 4.33941 0.204109
\(453\) 21.0486 0.988952
\(454\) −31.7338 −1.48934
\(455\) −11.0867 −0.519750
\(456\) −7.85743 −0.367958
\(457\) −23.1608 −1.08342 −0.541709 0.840566i \(-0.682223\pi\)
−0.541709 + 0.840566i \(0.682223\pi\)
\(458\) −26.0190 −1.21579
\(459\) 5.90334 0.275544
\(460\) 2.73943 0.127727
\(461\) −8.80772 −0.410216 −0.205108 0.978739i \(-0.565755\pi\)
−0.205108 + 0.978739i \(0.565755\pi\)
\(462\) −2.46434 −0.114651
\(463\) −25.5369 −1.18680 −0.593401 0.804907i \(-0.702215\pi\)
−0.593401 + 0.804907i \(0.702215\pi\)
\(464\) 2.06754 0.0959832
\(465\) −17.7395 −0.822651
\(466\) 17.2714 0.800083
\(467\) −10.5970 −0.490373 −0.245186 0.969476i \(-0.578849\pi\)
−0.245186 + 0.969476i \(0.578849\pi\)
\(468\) 4.12985 0.190902
\(469\) 10.4052 0.480465
\(470\) −26.2295 −1.20987
\(471\) 24.0832 1.10970
\(472\) 14.9082 0.686204
\(473\) −14.1518 −0.650701
\(474\) −8.65870 −0.397707
\(475\) −10.3110 −0.473103
\(476\) −0.797994 −0.0365760
\(477\) 4.20221 0.192406
\(478\) 12.5383 0.573486
\(479\) −0.483332 −0.0220840 −0.0110420 0.999939i \(-0.503515\pi\)
−0.0110420 + 0.999939i \(0.503515\pi\)
\(480\) −13.6966 −0.625160
\(481\) −37.4675 −1.70837
\(482\) −5.64460 −0.257104
\(483\) 1.46250 0.0665459
\(484\) 5.43471 0.247032
\(485\) −5.05366 −0.229475
\(486\) −16.7216 −0.758509
\(487\) −13.3441 −0.604678 −0.302339 0.953200i \(-0.597768\pi\)
−0.302339 + 0.953200i \(0.597768\pi\)
\(488\) −16.4205 −0.743319
\(489\) 12.1278 0.548437
\(490\) 21.0070 0.949000
\(491\) −42.2360 −1.90609 −0.953043 0.302836i \(-0.902067\pi\)
−0.953043 + 0.302836i \(0.902067\pi\)
\(492\) 2.72661 0.122925
\(493\) 1.09492 0.0493129
\(494\) 8.73216 0.392878
\(495\) 9.49707 0.426862
\(496\) 10.2015 0.458061
\(497\) 8.74036 0.392059
\(498\) 12.9144 0.578707
\(499\) −12.1737 −0.544968 −0.272484 0.962160i \(-0.587845\pi\)
−0.272484 + 0.962160i \(0.587845\pi\)
\(500\) 0.731691 0.0327222
\(501\) −13.9219 −0.621984
\(502\) 2.17101 0.0968969
\(503\) −13.4299 −0.598808 −0.299404 0.954126i \(-0.596788\pi\)
−0.299404 + 0.954126i \(0.596788\pi\)
\(504\) 5.23681 0.233266
\(505\) 12.5564 0.558754
\(506\) −2.57639 −0.114535
\(507\) −0.986692 −0.0438205
\(508\) 4.28477 0.190106
\(509\) −17.2396 −0.764132 −0.382066 0.924135i \(-0.624787\pi\)
−0.382066 + 0.924135i \(0.624787\pi\)
\(510\) 4.46684 0.197795
\(511\) −7.10568 −0.314337
\(512\) 20.6036 0.910557
\(513\) 11.9049 0.525613
\(514\) 29.3581 1.29493
\(515\) 10.1997 0.449453
\(516\) −6.34836 −0.279471
\(517\) −13.6497 −0.600315
\(518\) −12.4789 −0.548292
\(519\) −11.7355 −0.515130
\(520\) 33.3563 1.46277
\(521\) 19.3190 0.846382 0.423191 0.906040i \(-0.360910\pi\)
0.423191 + 0.906040i \(0.360910\pi\)
\(522\) −1.88730 −0.0826048
\(523\) −1.34569 −0.0588429 −0.0294214 0.999567i \(-0.509366\pi\)
−0.0294214 + 0.999567i \(0.509366\pi\)
\(524\) 4.66176 0.203650
\(525\) −5.52310 −0.241048
\(526\) 1.49578 0.0652193
\(527\) 5.40249 0.235336
\(528\) 4.38940 0.191024
\(529\) −21.4710 −0.933522
\(530\) 8.91479 0.387234
\(531\) −8.05634 −0.349615
\(532\) −1.60926 −0.0697704
\(533\) −11.5365 −0.499702
\(534\) 11.0647 0.478816
\(535\) −7.53768 −0.325882
\(536\) −31.3059 −1.35221
\(537\) 5.05644 0.218202
\(538\) 15.2972 0.659511
\(539\) 10.9320 0.470874
\(540\) 11.9446 0.514013
\(541\) −25.3566 −1.09016 −0.545082 0.838382i \(-0.683502\pi\)
−0.545082 + 0.838382i \(0.683502\pi\)
\(542\) 29.9032 1.28445
\(543\) −18.3958 −0.789438
\(544\) 4.17122 0.178840
\(545\) −6.82830 −0.292492
\(546\) 4.67737 0.200173
\(547\) −34.5100 −1.47554 −0.737770 0.675052i \(-0.764121\pi\)
−0.737770 + 0.675052i \(0.764121\pi\)
\(548\) 6.27624 0.268108
\(549\) 8.87357 0.378715
\(550\) 9.72972 0.414877
\(551\) 2.20806 0.0940666
\(552\) −4.40020 −0.187285
\(553\) −6.75165 −0.287109
\(554\) 31.7291 1.34804
\(555\) −38.6509 −1.64064
\(556\) 0.712442 0.0302143
\(557\) 18.1572 0.769345 0.384672 0.923053i \(-0.374314\pi\)
0.384672 + 0.923053i \(0.374314\pi\)
\(558\) −9.31215 −0.394215
\(559\) 26.8605 1.13608
\(560\) 6.57699 0.277929
\(561\) 2.32453 0.0981417
\(562\) −17.9538 −0.757336
\(563\) 33.2195 1.40004 0.700018 0.714125i \(-0.253175\pi\)
0.700018 + 0.714125i \(0.253175\pi\)
\(564\) −6.12313 −0.257830
\(565\) −18.9404 −0.796827
\(566\) 4.30695 0.181034
\(567\) 1.27244 0.0534375
\(568\) −26.2971 −1.10340
\(569\) 31.0751 1.30274 0.651368 0.758762i \(-0.274196\pi\)
0.651368 + 0.758762i \(0.274196\pi\)
\(570\) 9.00797 0.377302
\(571\) 19.2105 0.803934 0.401967 0.915654i \(-0.368327\pi\)
0.401967 + 0.915654i \(0.368327\pi\)
\(572\) 4.55934 0.190636
\(573\) 6.27522 0.262151
\(574\) −3.84235 −0.160377
\(575\) −5.77424 −0.240803
\(576\) −14.0675 −0.586146
\(577\) −46.2815 −1.92673 −0.963363 0.268201i \(-0.913571\pi\)
−0.963363 + 0.268201i \(0.913571\pi\)
\(578\) 17.9296 0.745775
\(579\) 11.3112 0.470078
\(580\) 2.21542 0.0919905
\(581\) 10.0700 0.417775
\(582\) 2.13210 0.0883784
\(583\) 4.63923 0.192137
\(584\) 21.3788 0.884661
\(585\) −18.0257 −0.745270
\(586\) 15.8362 0.654187
\(587\) 14.4568 0.596695 0.298347 0.954457i \(-0.403565\pi\)
0.298347 + 0.954457i \(0.403565\pi\)
\(588\) 4.90398 0.202237
\(589\) 10.8948 0.448914
\(590\) −17.0911 −0.703631
\(591\) 1.47603 0.0607157
\(592\) 22.2271 0.913526
\(593\) 33.9034 1.39225 0.696124 0.717922i \(-0.254907\pi\)
0.696124 + 0.717922i \(0.254907\pi\)
\(594\) −11.2337 −0.460924
\(595\) 3.48303 0.142790
\(596\) −8.70732 −0.356666
\(597\) 13.1475 0.538091
\(598\) 4.89006 0.199969
\(599\) 18.1098 0.739948 0.369974 0.929042i \(-0.379367\pi\)
0.369974 + 0.929042i \(0.379367\pi\)
\(600\) 16.6173 0.678399
\(601\) 25.0280 1.02091 0.510457 0.859903i \(-0.329476\pi\)
0.510457 + 0.859903i \(0.329476\pi\)
\(602\) 8.94615 0.364618
\(603\) 16.9176 0.688939
\(604\) −12.9703 −0.527752
\(605\) −23.7211 −0.964398
\(606\) −5.29746 −0.215195
\(607\) 7.62872 0.309640 0.154820 0.987943i \(-0.450520\pi\)
0.154820 + 0.987943i \(0.450520\pi\)
\(608\) 8.41182 0.341145
\(609\) 1.18275 0.0479273
\(610\) 18.8249 0.762196
\(611\) 25.9075 1.04811
\(612\) −1.29745 −0.0524463
\(613\) 46.5036 1.87826 0.939131 0.343558i \(-0.111632\pi\)
0.939131 + 0.343558i \(0.111632\pi\)
\(614\) 13.5544 0.547010
\(615\) −11.9009 −0.479891
\(616\) 5.78143 0.232940
\(617\) 6.20042 0.249619 0.124810 0.992181i \(-0.460168\pi\)
0.124810 + 0.992181i \(0.460168\pi\)
\(618\) −4.30318 −0.173099
\(619\) 5.86974 0.235925 0.117962 0.993018i \(-0.462364\pi\)
0.117962 + 0.993018i \(0.462364\pi\)
\(620\) 10.9312 0.439006
\(621\) 6.66680 0.267529
\(622\) −28.5804 −1.14597
\(623\) 8.62773 0.345663
\(624\) −8.33119 −0.333514
\(625\) −26.5423 −1.06169
\(626\) 39.2916 1.57041
\(627\) 4.68772 0.187210
\(628\) −14.8402 −0.592187
\(629\) 11.7710 0.469339
\(630\) −6.00363 −0.239190
\(631\) 20.3125 0.808627 0.404314 0.914620i \(-0.367510\pi\)
0.404314 + 0.914620i \(0.367510\pi\)
\(632\) 20.3136 0.808033
\(633\) 9.64177 0.383226
\(634\) 26.3833 1.04781
\(635\) −18.7019 −0.742160
\(636\) 2.08111 0.0825215
\(637\) −20.7492 −0.822112
\(638\) −2.08357 −0.0824894
\(639\) 14.2109 0.562173
\(640\) −6.15078 −0.243131
\(641\) 40.2965 1.59162 0.795808 0.605549i \(-0.207047\pi\)
0.795808 + 0.605549i \(0.207047\pi\)
\(642\) 3.18009 0.125508
\(643\) 13.1288 0.517750 0.258875 0.965911i \(-0.416648\pi\)
0.258875 + 0.965911i \(0.416648\pi\)
\(644\) −0.901196 −0.0355121
\(645\) 27.7089 1.09104
\(646\) −2.74333 −0.107935
\(647\) 20.7344 0.815155 0.407577 0.913171i \(-0.366374\pi\)
0.407577 + 0.913171i \(0.366374\pi\)
\(648\) −3.82838 −0.150393
\(649\) −8.89418 −0.349127
\(650\) −18.4672 −0.724345
\(651\) 5.83581 0.228723
\(652\) −7.47318 −0.292672
\(653\) −19.0052 −0.743730 −0.371865 0.928287i \(-0.621281\pi\)
−0.371865 + 0.928287i \(0.621281\pi\)
\(654\) 2.88081 0.112649
\(655\) −20.3473 −0.795036
\(656\) 6.84388 0.267208
\(657\) −11.5530 −0.450727
\(658\) 8.62876 0.336384
\(659\) 27.7789 1.08211 0.541055 0.840987i \(-0.318025\pi\)
0.541055 + 0.840987i \(0.318025\pi\)
\(660\) 4.70335 0.183078
\(661\) 16.2944 0.633777 0.316889 0.948463i \(-0.397362\pi\)
0.316889 + 0.948463i \(0.397362\pi\)
\(662\) −17.5019 −0.680232
\(663\) −4.41201 −0.171348
\(664\) −30.2976 −1.17578
\(665\) 7.02400 0.272379
\(666\) −20.2893 −0.786196
\(667\) 1.23653 0.0478785
\(668\) 8.57871 0.331920
\(669\) −4.17034 −0.161235
\(670\) 35.8899 1.38655
\(671\) 9.79640 0.378186
\(672\) 4.50579 0.173814
\(673\) −34.6053 −1.33394 −0.666968 0.745087i \(-0.732408\pi\)
−0.666968 + 0.745087i \(0.732408\pi\)
\(674\) −15.2302 −0.586644
\(675\) −25.1771 −0.969067
\(676\) 0.608003 0.0233847
\(677\) 26.9314 1.03506 0.517529 0.855666i \(-0.326852\pi\)
0.517529 + 0.855666i \(0.326852\pi\)
\(678\) 7.99079 0.306884
\(679\) 1.66251 0.0638014
\(680\) −10.4794 −0.401865
\(681\) 32.3343 1.23905
\(682\) −10.2806 −0.393665
\(683\) 17.8228 0.681972 0.340986 0.940068i \(-0.389239\pi\)
0.340986 + 0.940068i \(0.389239\pi\)
\(684\) −2.61648 −0.100044
\(685\) −27.3941 −1.04668
\(686\) −15.0362 −0.574083
\(687\) 26.5114 1.01147
\(688\) −15.9346 −0.607500
\(689\) −8.80538 −0.335458
\(690\) 5.04451 0.192041
\(691\) 8.42965 0.320679 0.160339 0.987062i \(-0.448741\pi\)
0.160339 + 0.987062i \(0.448741\pi\)
\(692\) 7.23145 0.274898
\(693\) −3.12427 −0.118681
\(694\) −30.0959 −1.14242
\(695\) −3.10962 −0.117955
\(696\) −3.55852 −0.134885
\(697\) 3.62436 0.137283
\(698\) −0.181038 −0.00685240
\(699\) −17.5983 −0.665628
\(700\) 3.40336 0.128635
\(701\) −20.5531 −0.776281 −0.388141 0.921600i \(-0.626882\pi\)
−0.388141 + 0.921600i \(0.626882\pi\)
\(702\) 21.3218 0.804741
\(703\) 23.7377 0.895285
\(704\) −15.5305 −0.585328
\(705\) 26.7258 1.00655
\(706\) −10.1183 −0.380808
\(707\) −4.13071 −0.155351
\(708\) −3.98984 −0.149947
\(709\) −23.5312 −0.883733 −0.441866 0.897081i \(-0.645683\pi\)
−0.441866 + 0.897081i \(0.645683\pi\)
\(710\) 30.1477 1.13142
\(711\) −10.9774 −0.411686
\(712\) −25.9582 −0.972824
\(713\) 6.10117 0.228491
\(714\) −1.46946 −0.0549933
\(715\) −19.9003 −0.744229
\(716\) −3.11580 −0.116443
\(717\) −12.7755 −0.477111
\(718\) 19.5934 0.731219
\(719\) 23.8108 0.887993 0.443996 0.896029i \(-0.353560\pi\)
0.443996 + 0.896029i \(0.353560\pi\)
\(720\) 10.6935 0.398522
\(721\) −3.35542 −0.124962
\(722\) 16.0271 0.596467
\(723\) 5.75142 0.213898
\(724\) 11.3355 0.421282
\(725\) −4.66973 −0.173429
\(726\) 10.0077 0.371422
\(727\) −33.7258 −1.25082 −0.625411 0.780296i \(-0.715069\pi\)
−0.625411 + 0.780296i \(0.715069\pi\)
\(728\) −10.9733 −0.406697
\(729\) 20.7697 0.769247
\(730\) −24.5093 −0.907128
\(731\) −8.43861 −0.312113
\(732\) 4.39457 0.162428
\(733\) −34.7441 −1.28330 −0.641650 0.766997i \(-0.721750\pi\)
−0.641650 + 0.766997i \(0.721750\pi\)
\(734\) 10.2759 0.379291
\(735\) −21.4046 −0.789519
\(736\) 4.71067 0.173637
\(737\) 18.6770 0.687977
\(738\) −6.24724 −0.229964
\(739\) −48.4882 −1.78367 −0.891833 0.452365i \(-0.850580\pi\)
−0.891833 + 0.452365i \(0.850580\pi\)
\(740\) 23.8169 0.875525
\(741\) −8.89741 −0.326855
\(742\) −2.93272 −0.107663
\(743\) −35.6302 −1.30715 −0.653573 0.756863i \(-0.726731\pi\)
−0.653573 + 0.756863i \(0.726731\pi\)
\(744\) −17.5582 −0.643713
\(745\) 38.0051 1.39240
\(746\) 38.5966 1.41312
\(747\) 16.3728 0.599048
\(748\) −1.43238 −0.0523731
\(749\) 2.47968 0.0906057
\(750\) 1.34737 0.0491990
\(751\) −19.1689 −0.699483 −0.349742 0.936846i \(-0.613731\pi\)
−0.349742 + 0.936846i \(0.613731\pi\)
\(752\) −15.3693 −0.560459
\(753\) −2.21209 −0.0806132
\(754\) 3.95467 0.144021
\(755\) 56.6117 2.06031
\(756\) −3.92943 −0.142912
\(757\) 20.8207 0.756740 0.378370 0.925654i \(-0.376485\pi\)
0.378370 + 0.925654i \(0.376485\pi\)
\(758\) −8.24101 −0.299327
\(759\) 2.62515 0.0952869
\(760\) −21.1330 −0.766576
\(761\) 27.8987 1.01133 0.505664 0.862730i \(-0.331247\pi\)
0.505664 + 0.862730i \(0.331247\pi\)
\(762\) 7.89017 0.285831
\(763\) 2.24632 0.0813222
\(764\) −3.86681 −0.139896
\(765\) 5.66302 0.204747
\(766\) −6.14486 −0.222023
\(767\) 16.8814 0.609551
\(768\) −16.9626 −0.612086
\(769\) −5.28632 −0.190630 −0.0953148 0.995447i \(-0.530386\pi\)
−0.0953148 + 0.995447i \(0.530386\pi\)
\(770\) −6.62799 −0.238856
\(771\) −29.9137 −1.07731
\(772\) −6.97001 −0.250856
\(773\) −45.2651 −1.62807 −0.814037 0.580813i \(-0.802735\pi\)
−0.814037 + 0.580813i \(0.802735\pi\)
\(774\) 14.5454 0.522825
\(775\) −23.0410 −0.827657
\(776\) −5.00199 −0.179561
\(777\) 12.7151 0.456151
\(778\) 27.4621 0.984565
\(779\) 7.30902 0.261873
\(780\) −8.92708 −0.319641
\(781\) 15.6888 0.561388
\(782\) −1.53628 −0.0549373
\(783\) 5.39155 0.192678
\(784\) 12.3091 0.439612
\(785\) 64.7733 2.31186
\(786\) 8.58439 0.306195
\(787\) −9.12880 −0.325407 −0.162703 0.986675i \(-0.552021\pi\)
−0.162703 + 0.986675i \(0.552021\pi\)
\(788\) −0.909534 −0.0324008
\(789\) −1.52409 −0.0542591
\(790\) −23.2881 −0.828554
\(791\) 6.23084 0.221543
\(792\) 9.39997 0.334013
\(793\) −18.5938 −0.660286
\(794\) −1.16240 −0.0412519
\(795\) −9.08350 −0.322159
\(796\) −8.10154 −0.287151
\(797\) −3.03946 −0.107663 −0.0538316 0.998550i \(-0.517143\pi\)
−0.0538316 + 0.998550i \(0.517143\pi\)
\(798\) −2.96337 −0.104902
\(799\) −8.13922 −0.287945
\(800\) −17.7898 −0.628964
\(801\) 14.0277 0.495645
\(802\) 21.1568 0.747073
\(803\) −12.7545 −0.450098
\(804\) 8.37833 0.295481
\(805\) 3.93348 0.138637
\(806\) 19.5128 0.687310
\(807\) −15.5867 −0.548679
\(808\) 12.4280 0.437217
\(809\) 13.4793 0.473909 0.236954 0.971521i \(-0.423851\pi\)
0.236954 + 0.971521i \(0.423851\pi\)
\(810\) 4.38897 0.154213
\(811\) −8.73276 −0.306649 −0.153324 0.988176i \(-0.548998\pi\)
−0.153324 + 0.988176i \(0.548998\pi\)
\(812\) −0.728812 −0.0255763
\(813\) −30.4691 −1.06860
\(814\) −22.3994 −0.785099
\(815\) 32.6184 1.14257
\(816\) 2.61736 0.0916260
\(817\) −17.0176 −0.595370
\(818\) −27.7100 −0.968857
\(819\) 5.92994 0.207209
\(820\) 7.33339 0.256093
\(821\) −32.7753 −1.14387 −0.571933 0.820300i \(-0.693806\pi\)
−0.571933 + 0.820300i \(0.693806\pi\)
\(822\) 11.5574 0.403109
\(823\) 44.4981 1.55111 0.775553 0.631282i \(-0.217471\pi\)
0.775553 + 0.631282i \(0.217471\pi\)
\(824\) 10.0954 0.351691
\(825\) −9.91385 −0.345156
\(826\) 5.62251 0.195632
\(827\) 3.49530 0.121543 0.0607717 0.998152i \(-0.480644\pi\)
0.0607717 + 0.998152i \(0.480644\pi\)
\(828\) −1.46524 −0.0509208
\(829\) 32.0909 1.11456 0.557281 0.830324i \(-0.311845\pi\)
0.557281 + 0.830324i \(0.311845\pi\)
\(830\) 34.7340 1.20564
\(831\) −32.3295 −1.12150
\(832\) 29.4773 1.02194
\(833\) 6.51865 0.225858
\(834\) 1.31192 0.0454282
\(835\) −37.4438 −1.29579
\(836\) −2.88859 −0.0999040
\(837\) 26.6026 0.919519
\(838\) −15.1793 −0.524359
\(839\) −25.2239 −0.870827 −0.435414 0.900231i \(-0.643398\pi\)
−0.435414 + 0.900231i \(0.643398\pi\)
\(840\) −11.3199 −0.390573
\(841\) 1.00000 0.0344828
\(842\) −37.2408 −1.28340
\(843\) 18.2936 0.630064
\(844\) −5.94129 −0.204508
\(845\) −2.65377 −0.0912925
\(846\) 14.0294 0.482341
\(847\) 7.80356 0.268134
\(848\) 5.22366 0.179381
\(849\) −4.38845 −0.150611
\(850\) 5.80175 0.198998
\(851\) 13.2932 0.455687
\(852\) 7.03782 0.241112
\(853\) 0.785023 0.0268787 0.0134393 0.999910i \(-0.495722\pi\)
0.0134393 + 0.999910i \(0.495722\pi\)
\(854\) −6.19285 −0.211915
\(855\) 11.4202 0.390564
\(856\) −7.46061 −0.254998
\(857\) 18.6587 0.637368 0.318684 0.947861i \(-0.396759\pi\)
0.318684 + 0.947861i \(0.396759\pi\)
\(858\) 8.39579 0.286627
\(859\) 44.1153 1.50519 0.752597 0.658481i \(-0.228801\pi\)
0.752597 + 0.658481i \(0.228801\pi\)
\(860\) −17.0743 −0.582229
\(861\) 3.91507 0.133425
\(862\) −2.43158 −0.0828199
\(863\) 45.7919 1.55878 0.779388 0.626542i \(-0.215530\pi\)
0.779388 + 0.626542i \(0.215530\pi\)
\(864\) 20.5396 0.698773
\(865\) −31.5633 −1.07318
\(866\) −15.8489 −0.538568
\(867\) −18.2690 −0.620446
\(868\) −3.59605 −0.122058
\(869\) −12.1191 −0.411111
\(870\) 4.07958 0.138311
\(871\) −35.4495 −1.20116
\(872\) −6.75849 −0.228871
\(873\) 2.70306 0.0914848
\(874\) −3.09812 −0.104795
\(875\) 1.05062 0.0355173
\(876\) −5.72156 −0.193314
\(877\) 35.4618 1.19746 0.598730 0.800951i \(-0.295672\pi\)
0.598730 + 0.800951i \(0.295672\pi\)
\(878\) −11.3260 −0.382235
\(879\) −16.1359 −0.544250
\(880\) 11.8056 0.397966
\(881\) 20.6969 0.697297 0.348649 0.937253i \(-0.386641\pi\)
0.348649 + 0.937253i \(0.386641\pi\)
\(882\) −11.2361 −0.378338
\(883\) 26.0174 0.875555 0.437778 0.899083i \(-0.355766\pi\)
0.437778 + 0.899083i \(0.355766\pi\)
\(884\) 2.71870 0.0914397
\(885\) 17.4146 0.585385
\(886\) 8.75627 0.294173
\(887\) −20.1889 −0.677877 −0.338939 0.940809i \(-0.610068\pi\)
−0.338939 + 0.940809i \(0.610068\pi\)
\(888\) −38.2558 −1.28378
\(889\) 6.15239 0.206344
\(890\) 29.7592 0.997530
\(891\) 2.28400 0.0765170
\(892\) 2.56978 0.0860426
\(893\) −16.4138 −0.549268
\(894\) −16.0341 −0.536259
\(895\) 13.5996 0.454585
\(896\) 2.02343 0.0675982
\(897\) −4.98260 −0.166364
\(898\) −7.25854 −0.242221
\(899\) 4.93412 0.164562
\(900\) 5.53348 0.184449
\(901\) 2.76634 0.0921600
\(902\) −6.89694 −0.229643
\(903\) −9.11545 −0.303343
\(904\) −18.7467 −0.623506
\(905\) −49.4766 −1.64466
\(906\) −23.8840 −0.793494
\(907\) 8.27034 0.274612 0.137306 0.990529i \(-0.456156\pi\)
0.137306 + 0.990529i \(0.456156\pi\)
\(908\) −19.9245 −0.661219
\(909\) −6.71608 −0.222758
\(910\) 12.5801 0.417026
\(911\) −20.6807 −0.685182 −0.342591 0.939485i \(-0.611304\pi\)
−0.342591 + 0.939485i \(0.611304\pi\)
\(912\) 5.27826 0.174781
\(913\) 18.0755 0.598211
\(914\) 26.2808 0.869290
\(915\) −19.1811 −0.634108
\(916\) −16.3364 −0.539771
\(917\) 6.69371 0.221046
\(918\) −6.69856 −0.221085
\(919\) 17.0450 0.562264 0.281132 0.959669i \(-0.409290\pi\)
0.281132 + 0.959669i \(0.409290\pi\)
\(920\) −11.8346 −0.390176
\(921\) −13.8109 −0.455084
\(922\) 9.99417 0.329141
\(923\) −29.7777 −0.980143
\(924\) −1.54727 −0.0509015
\(925\) −50.2018 −1.65062
\(926\) 28.9769 0.952241
\(927\) −5.45554 −0.179183
\(928\) 3.80960 0.125056
\(929\) 22.3370 0.732852 0.366426 0.930447i \(-0.380581\pi\)
0.366426 + 0.930447i \(0.380581\pi\)
\(930\) 20.1292 0.660061
\(931\) 13.1457 0.430834
\(932\) 10.8441 0.355211
\(933\) 29.1213 0.953387
\(934\) 12.0245 0.393455
\(935\) 6.25197 0.204461
\(936\) −17.8414 −0.583163
\(937\) 15.3988 0.503058 0.251529 0.967850i \(-0.419067\pi\)
0.251529 + 0.967850i \(0.419067\pi\)
\(938\) −11.8068 −0.385505
\(939\) −40.0352 −1.30650
\(940\) −16.4686 −0.537145
\(941\) −24.1663 −0.787797 −0.393899 0.919154i \(-0.628874\pi\)
−0.393899 + 0.919154i \(0.628874\pi\)
\(942\) −27.3274 −0.890374
\(943\) 4.09309 0.133289
\(944\) −10.0146 −0.325948
\(945\) 17.1509 0.557919
\(946\) 16.0581 0.522095
\(947\) −21.4752 −0.697851 −0.348925 0.937150i \(-0.613453\pi\)
−0.348925 + 0.937150i \(0.613453\pi\)
\(948\) −5.43649 −0.176569
\(949\) 24.2084 0.785839
\(950\) 11.7000 0.379598
\(951\) −26.8826 −0.871728
\(952\) 3.44742 0.111731
\(953\) 42.8180 1.38701 0.693506 0.720451i \(-0.256065\pi\)
0.693506 + 0.720451i \(0.256065\pi\)
\(954\) −4.76827 −0.154379
\(955\) 16.8776 0.546146
\(956\) 7.87233 0.254609
\(957\) 2.12300 0.0686270
\(958\) 0.548440 0.0177193
\(959\) 9.01190 0.291009
\(960\) 30.4083 0.981425
\(961\) −6.65446 −0.214660
\(962\) 42.5146 1.37073
\(963\) 4.03169 0.129919
\(964\) −3.54405 −0.114146
\(965\) 30.4222 0.979326
\(966\) −1.65950 −0.0533936
\(967\) −8.68920 −0.279426 −0.139713 0.990192i \(-0.544618\pi\)
−0.139713 + 0.990192i \(0.544618\pi\)
\(968\) −23.4785 −0.754628
\(969\) 2.79525 0.0897964
\(970\) 5.73442 0.184121
\(971\) 21.4172 0.687312 0.343656 0.939096i \(-0.388335\pi\)
0.343656 + 0.939096i \(0.388335\pi\)
\(972\) −10.4989 −0.336753
\(973\) 1.02298 0.0327951
\(974\) 15.1416 0.485169
\(975\) 18.8167 0.602618
\(976\) 11.0305 0.353078
\(977\) 54.5753 1.74602 0.873009 0.487704i \(-0.162166\pi\)
0.873009 + 0.487704i \(0.162166\pi\)
\(978\) −13.7615 −0.440043
\(979\) 15.4866 0.494953
\(980\) 13.1896 0.421325
\(981\) 3.65227 0.116608
\(982\) 47.9255 1.52936
\(983\) −54.5397 −1.73955 −0.869773 0.493452i \(-0.835735\pi\)
−0.869773 + 0.493452i \(0.835735\pi\)
\(984\) −11.7792 −0.375508
\(985\) 3.96987 0.126491
\(986\) −1.24242 −0.0395666
\(987\) −8.79205 −0.279854
\(988\) 5.48262 0.174425
\(989\) −9.52993 −0.303034
\(990\) −10.7764 −0.342496
\(991\) −8.84470 −0.280961 −0.140481 0.990083i \(-0.544865\pi\)
−0.140481 + 0.990083i \(0.544865\pi\)
\(992\) 18.7970 0.596806
\(993\) 17.8331 0.565918
\(994\) −9.91774 −0.314572
\(995\) 35.3610 1.12102
\(996\) 8.10849 0.256927
\(997\) −14.4225 −0.456765 −0.228382 0.973571i \(-0.573344\pi\)
−0.228382 + 0.973571i \(0.573344\pi\)
\(998\) 13.8135 0.437260
\(999\) 57.9618 1.83383
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 \(a_p\))