Properties

Label 8035.2.a.e.1.3
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.69988 q^{2} -0.494659 q^{3} +5.28933 q^{4} +1.00000 q^{5} +1.33552 q^{6} +3.45834 q^{7} -8.88080 q^{8} -2.75531 q^{9} +O(q^{10})\) \(q-2.69988 q^{2} -0.494659 q^{3} +5.28933 q^{4} +1.00000 q^{5} +1.33552 q^{6} +3.45834 q^{7} -8.88080 q^{8} -2.75531 q^{9} -2.69988 q^{10} +2.05516 q^{11} -2.61642 q^{12} -4.61042 q^{13} -9.33708 q^{14} -0.494659 q^{15} +13.3984 q^{16} +0.0376674 q^{17} +7.43900 q^{18} -6.34243 q^{19} +5.28933 q^{20} -1.71070 q^{21} -5.54869 q^{22} -5.72394 q^{23} +4.39297 q^{24} +1.00000 q^{25} +12.4476 q^{26} +2.84692 q^{27} +18.2923 q^{28} +7.38384 q^{29} +1.33552 q^{30} +0.978803 q^{31} -18.4124 q^{32} -1.01661 q^{33} -0.101697 q^{34} +3.45834 q^{35} -14.5738 q^{36} -2.58132 q^{37} +17.1238 q^{38} +2.28059 q^{39} -8.88080 q^{40} -1.56398 q^{41} +4.61868 q^{42} +2.20743 q^{43} +10.8705 q^{44} -2.75531 q^{45} +15.4539 q^{46} -11.2376 q^{47} -6.62764 q^{48} +4.96010 q^{49} -2.69988 q^{50} -0.0186325 q^{51} -24.3860 q^{52} +10.5759 q^{53} -7.68633 q^{54} +2.05516 q^{55} -30.7128 q^{56} +3.13734 q^{57} -19.9355 q^{58} -1.30853 q^{59} -2.61642 q^{60} -8.58263 q^{61} -2.64265 q^{62} -9.52880 q^{63} +22.9144 q^{64} -4.61042 q^{65} +2.74471 q^{66} -13.5641 q^{67} +0.199236 q^{68} +2.83140 q^{69} -9.33708 q^{70} +0.0361528 q^{71} +24.4694 q^{72} -6.51047 q^{73} +6.96925 q^{74} -0.494659 q^{75} -33.5472 q^{76} +7.10745 q^{77} -6.15730 q^{78} +8.52645 q^{79} +13.3984 q^{80} +6.85768 q^{81} +4.22256 q^{82} +6.10541 q^{83} -9.04846 q^{84} +0.0376674 q^{85} -5.95980 q^{86} -3.65248 q^{87} -18.2515 q^{88} +12.1970 q^{89} +7.43900 q^{90} -15.9444 q^{91} -30.2758 q^{92} -0.484174 q^{93} +30.3400 q^{94} -6.34243 q^{95} +9.10787 q^{96} -6.54569 q^{97} -13.3917 q^{98} -5.66262 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + O(q^{10}) \) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + 18q^{10} + 38q^{11} + 14q^{12} + 28q^{13} + 53q^{14} + 7q^{15} + 214q^{16} + 50q^{17} + 47q^{18} + 65q^{19} + 176q^{20} + 109q^{21} + 13q^{22} + 52q^{23} + 66q^{24} + 153q^{25} + 36q^{26} + 19q^{27} + 26q^{28} + 172q^{29} + 19q^{30} + 60q^{31} + 107q^{32} + 4q^{33} + 40q^{34} + 5q^{35} + 241q^{36} + 65q^{37} + 29q^{38} + 56q^{39} + 57q^{40} + 152q^{41} - 19q^{42} + 22q^{43} + 97q^{44} + 206q^{45} + 86q^{46} + 37q^{47} - 4q^{48} + 260q^{49} + 18q^{50} + 102q^{51} - 6q^{52} + 169q^{53} + 64q^{54} + 38q^{55} + 146q^{56} + 40q^{57} - 9q^{58} + 64q^{59} + 14q^{60} + 164q^{61} + 12q^{62} + 19q^{63} + 259q^{64} + 28q^{65} + 6q^{66} + 5q^{67} + 112q^{68} + 119q^{69} + 53q^{70} + 100q^{71} + 77q^{72} + 10q^{73} + 98q^{74} + 7q^{75} + 126q^{76} + 80q^{77} - 4q^{78} + 110q^{79} + 214q^{80} + 305q^{81} - 27q^{82} + 36q^{83} + 172q^{84} + 50q^{85} + 44q^{86} + 23q^{87} + 47q^{88} + 143q^{89} + 47q^{90} + 82q^{91} + 130q^{92} + 31q^{93} + 77q^{94} + 65q^{95} + 57q^{96} + 11q^{97} + 29q^{98} + 99q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69988 −1.90910 −0.954551 0.298049i \(-0.903664\pi\)
−0.954551 + 0.298049i \(0.903664\pi\)
\(3\) −0.494659 −0.285592 −0.142796 0.989752i \(-0.545609\pi\)
−0.142796 + 0.989752i \(0.545609\pi\)
\(4\) 5.28933 2.64467
\(5\) 1.00000 0.447214
\(6\) 1.33552 0.545223
\(7\) 3.45834 1.30713 0.653564 0.756871i \(-0.273273\pi\)
0.653564 + 0.756871i \(0.273273\pi\)
\(8\) −8.88080 −3.13984
\(9\) −2.75531 −0.918437
\(10\) −2.69988 −0.853776
\(11\) 2.05516 0.619655 0.309828 0.950793i \(-0.399729\pi\)
0.309828 + 0.950793i \(0.399729\pi\)
\(12\) −2.61642 −0.755295
\(13\) −4.61042 −1.27870 −0.639350 0.768916i \(-0.720796\pi\)
−0.639350 + 0.768916i \(0.720796\pi\)
\(14\) −9.33708 −2.49544
\(15\) −0.494659 −0.127720
\(16\) 13.3984 3.34960
\(17\) 0.0376674 0.00913569 0.00456785 0.999990i \(-0.498546\pi\)
0.00456785 + 0.999990i \(0.498546\pi\)
\(18\) 7.43900 1.75339
\(19\) −6.34243 −1.45505 −0.727526 0.686080i \(-0.759330\pi\)
−0.727526 + 0.686080i \(0.759330\pi\)
\(20\) 5.28933 1.18273
\(21\) −1.71070 −0.373305
\(22\) −5.54869 −1.18298
\(23\) −5.72394 −1.19352 −0.596762 0.802418i \(-0.703546\pi\)
−0.596762 + 0.802418i \(0.703546\pi\)
\(24\) 4.39297 0.896711
\(25\) 1.00000 0.200000
\(26\) 12.4476 2.44117
\(27\) 2.84692 0.547890
\(28\) 18.2923 3.45692
\(29\) 7.38384 1.37114 0.685572 0.728005i \(-0.259552\pi\)
0.685572 + 0.728005i \(0.259552\pi\)
\(30\) 1.33552 0.243831
\(31\) 0.978803 0.175798 0.0878991 0.996129i \(-0.471985\pi\)
0.0878991 + 0.996129i \(0.471985\pi\)
\(32\) −18.4124 −3.25488
\(33\) −1.01661 −0.176968
\(34\) −0.101697 −0.0174410
\(35\) 3.45834 0.584566
\(36\) −14.5738 −2.42896
\(37\) −2.58132 −0.424367 −0.212183 0.977230i \(-0.568057\pi\)
−0.212183 + 0.977230i \(0.568057\pi\)
\(38\) 17.1238 2.77784
\(39\) 2.28059 0.365186
\(40\) −8.88080 −1.40418
\(41\) −1.56398 −0.244253 −0.122127 0.992515i \(-0.538971\pi\)
−0.122127 + 0.992515i \(0.538971\pi\)
\(42\) 4.61868 0.712677
\(43\) 2.20743 0.336631 0.168315 0.985733i \(-0.446167\pi\)
0.168315 + 0.985733i \(0.446167\pi\)
\(44\) 10.8705 1.63878
\(45\) −2.75531 −0.410738
\(46\) 15.4539 2.27856
\(47\) −11.2376 −1.63917 −0.819583 0.572960i \(-0.805795\pi\)
−0.819583 + 0.572960i \(0.805795\pi\)
\(48\) −6.62764 −0.956617
\(49\) 4.96010 0.708585
\(50\) −2.69988 −0.381820
\(51\) −0.0186325 −0.00260908
\(52\) −24.3860 −3.38174
\(53\) 10.5759 1.45271 0.726356 0.687318i \(-0.241212\pi\)
0.726356 + 0.687318i \(0.241212\pi\)
\(54\) −7.68633 −1.04598
\(55\) 2.05516 0.277118
\(56\) −30.7128 −4.10417
\(57\) 3.13734 0.415551
\(58\) −19.9355 −2.61765
\(59\) −1.30853 −0.170357 −0.0851783 0.996366i \(-0.527146\pi\)
−0.0851783 + 0.996366i \(0.527146\pi\)
\(60\) −2.61642 −0.337778
\(61\) −8.58263 −1.09889 −0.549447 0.835529i \(-0.685161\pi\)
−0.549447 + 0.835529i \(0.685161\pi\)
\(62\) −2.64265 −0.335616
\(63\) −9.52880 −1.20052
\(64\) 22.9144 2.86431
\(65\) −4.61042 −0.571852
\(66\) 2.74471 0.337851
\(67\) −13.5641 −1.65712 −0.828559 0.559902i \(-0.810839\pi\)
−0.828559 + 0.559902i \(0.810839\pi\)
\(68\) 0.199236 0.0241609
\(69\) 2.83140 0.340861
\(70\) −9.33708 −1.11600
\(71\) 0.0361528 0.00429054 0.00214527 0.999998i \(-0.499317\pi\)
0.00214527 + 0.999998i \(0.499317\pi\)
\(72\) 24.4694 2.88374
\(73\) −6.51047 −0.761993 −0.380996 0.924576i \(-0.624419\pi\)
−0.380996 + 0.924576i \(0.624419\pi\)
\(74\) 6.96925 0.810159
\(75\) −0.494659 −0.0571183
\(76\) −33.5472 −3.84813
\(77\) 7.10745 0.809969
\(78\) −6.15730 −0.697177
\(79\) 8.52645 0.959301 0.479650 0.877460i \(-0.340764\pi\)
0.479650 + 0.877460i \(0.340764\pi\)
\(80\) 13.3984 1.49799
\(81\) 6.85768 0.761965
\(82\) 4.22256 0.466304
\(83\) 6.10541 0.670155 0.335078 0.942190i \(-0.391237\pi\)
0.335078 + 0.942190i \(0.391237\pi\)
\(84\) −9.04846 −0.987268
\(85\) 0.0376674 0.00408561
\(86\) −5.95980 −0.642662
\(87\) −3.65248 −0.391587
\(88\) −18.2515 −1.94562
\(89\) 12.1970 1.29287 0.646437 0.762967i \(-0.276258\pi\)
0.646437 + 0.762967i \(0.276258\pi\)
\(90\) 7.43900 0.784140
\(91\) −15.9444 −1.67143
\(92\) −30.2758 −3.15648
\(93\) −0.484174 −0.0502065
\(94\) 30.3400 3.12933
\(95\) −6.34243 −0.650719
\(96\) 9.10787 0.929568
\(97\) −6.54569 −0.664614 −0.332307 0.943171i \(-0.607827\pi\)
−0.332307 + 0.943171i \(0.607827\pi\)
\(98\) −13.3917 −1.35276
\(99\) −5.66262 −0.569115
\(100\) 5.28933 0.528933
\(101\) 8.78624 0.874263 0.437132 0.899397i \(-0.355994\pi\)
0.437132 + 0.899397i \(0.355994\pi\)
\(102\) 0.0503056 0.00498099
\(103\) 12.3705 1.21890 0.609452 0.792823i \(-0.291389\pi\)
0.609452 + 0.792823i \(0.291389\pi\)
\(104\) 40.9442 4.01491
\(105\) −1.71070 −0.166947
\(106\) −28.5536 −2.77338
\(107\) −2.16198 −0.209006 −0.104503 0.994525i \(-0.533325\pi\)
−0.104503 + 0.994525i \(0.533325\pi\)
\(108\) 15.0583 1.44899
\(109\) −0.912287 −0.0873813 −0.0436906 0.999045i \(-0.513912\pi\)
−0.0436906 + 0.999045i \(0.513912\pi\)
\(110\) −5.54869 −0.529047
\(111\) 1.27687 0.121196
\(112\) 46.3361 4.37835
\(113\) 14.2056 1.33635 0.668177 0.744002i \(-0.267075\pi\)
0.668177 + 0.744002i \(0.267075\pi\)
\(114\) −8.47043 −0.793329
\(115\) −5.72394 −0.533760
\(116\) 39.0556 3.62622
\(117\) 12.7031 1.17441
\(118\) 3.53288 0.325228
\(119\) 0.130267 0.0119415
\(120\) 4.39297 0.401021
\(121\) −6.77630 −0.616027
\(122\) 23.1721 2.09790
\(123\) 0.773639 0.0697567
\(124\) 5.17721 0.464928
\(125\) 1.00000 0.0894427
\(126\) 25.7266 2.29191
\(127\) 4.80654 0.426512 0.213256 0.976996i \(-0.431593\pi\)
0.213256 + 0.976996i \(0.431593\pi\)
\(128\) −25.0414 −2.21336
\(129\) −1.09193 −0.0961389
\(130\) 12.4476 1.09172
\(131\) −7.86193 −0.686900 −0.343450 0.939171i \(-0.611596\pi\)
−0.343450 + 0.939171i \(0.611596\pi\)
\(132\) −5.37717 −0.468023
\(133\) −21.9343 −1.90194
\(134\) 36.6214 3.16360
\(135\) 2.84692 0.245024
\(136\) −0.334517 −0.0286846
\(137\) 8.31193 0.710136 0.355068 0.934841i \(-0.384458\pi\)
0.355068 + 0.934841i \(0.384458\pi\)
\(138\) −7.64443 −0.650737
\(139\) 22.1095 1.87530 0.937651 0.347578i \(-0.112996\pi\)
0.937651 + 0.347578i \(0.112996\pi\)
\(140\) 18.2923 1.54598
\(141\) 5.55876 0.468132
\(142\) −0.0976080 −0.00819108
\(143\) −9.47517 −0.792353
\(144\) −36.9167 −3.07640
\(145\) 7.38384 0.613194
\(146\) 17.5775 1.45472
\(147\) −2.45356 −0.202366
\(148\) −13.6535 −1.12231
\(149\) −0.359147 −0.0294225 −0.0147112 0.999892i \(-0.504683\pi\)
−0.0147112 + 0.999892i \(0.504683\pi\)
\(150\) 1.33552 0.109045
\(151\) −19.1965 −1.56219 −0.781095 0.624413i \(-0.785338\pi\)
−0.781095 + 0.624413i \(0.785338\pi\)
\(152\) 56.3258 4.56863
\(153\) −0.103786 −0.00839056
\(154\) −19.1892 −1.54631
\(155\) 0.978803 0.0786193
\(156\) 12.0628 0.965795
\(157\) 2.06065 0.164458 0.0822289 0.996613i \(-0.473796\pi\)
0.0822289 + 0.996613i \(0.473796\pi\)
\(158\) −23.0204 −1.83140
\(159\) −5.23147 −0.414883
\(160\) −18.4124 −1.45563
\(161\) −19.7953 −1.56009
\(162\) −18.5149 −1.45467
\(163\) −15.9314 −1.24784 −0.623922 0.781487i \(-0.714462\pi\)
−0.623922 + 0.781487i \(0.714462\pi\)
\(164\) −8.27243 −0.645969
\(165\) −1.01661 −0.0791427
\(166\) −16.4838 −1.27939
\(167\) −23.3184 −1.80443 −0.902217 0.431283i \(-0.858061\pi\)
−0.902217 + 0.431283i \(0.858061\pi\)
\(168\) 15.1924 1.17212
\(169\) 8.25595 0.635073
\(170\) −0.101697 −0.00779984
\(171\) 17.4754 1.33637
\(172\) 11.6759 0.890276
\(173\) 18.2523 1.38770 0.693849 0.720120i \(-0.255913\pi\)
0.693849 + 0.720120i \(0.255913\pi\)
\(174\) 9.86126 0.747580
\(175\) 3.45834 0.261426
\(176\) 27.5359 2.07560
\(177\) 0.647278 0.0486524
\(178\) −32.9303 −2.46823
\(179\) 20.3194 1.51874 0.759371 0.650658i \(-0.225507\pi\)
0.759371 + 0.650658i \(0.225507\pi\)
\(180\) −14.5738 −1.08626
\(181\) −6.31209 −0.469174 −0.234587 0.972095i \(-0.575374\pi\)
−0.234587 + 0.972095i \(0.575374\pi\)
\(182\) 43.0479 3.19092
\(183\) 4.24548 0.313835
\(184\) 50.8332 3.74747
\(185\) −2.58132 −0.189782
\(186\) 1.30721 0.0958493
\(187\) 0.0774128 0.00566098
\(188\) −59.4392 −4.33505
\(189\) 9.84560 0.716162
\(190\) 17.1238 1.24229
\(191\) 17.1489 1.24085 0.620425 0.784266i \(-0.286960\pi\)
0.620425 + 0.784266i \(0.286960\pi\)
\(192\) −11.3348 −0.818022
\(193\) 19.0249 1.36944 0.684721 0.728805i \(-0.259924\pi\)
0.684721 + 0.728805i \(0.259924\pi\)
\(194\) 17.6726 1.26882
\(195\) 2.28059 0.163316
\(196\) 26.2356 1.87397
\(197\) 1.77564 0.126509 0.0632546 0.997997i \(-0.479852\pi\)
0.0632546 + 0.997997i \(0.479852\pi\)
\(198\) 15.2884 1.08650
\(199\) 26.8200 1.90122 0.950610 0.310389i \(-0.100459\pi\)
0.950610 + 0.310389i \(0.100459\pi\)
\(200\) −8.88080 −0.627967
\(201\) 6.70960 0.473259
\(202\) −23.7218 −1.66906
\(203\) 25.5358 1.79226
\(204\) −0.0985537 −0.00690014
\(205\) −1.56398 −0.109233
\(206\) −33.3989 −2.32701
\(207\) 15.7712 1.09618
\(208\) −61.7722 −4.28313
\(209\) −13.0347 −0.901631
\(210\) 4.61868 0.318719
\(211\) 25.8950 1.78268 0.891341 0.453333i \(-0.149765\pi\)
0.891341 + 0.453333i \(0.149765\pi\)
\(212\) 55.9395 3.84194
\(213\) −0.0178833 −0.00122534
\(214\) 5.83707 0.399014
\(215\) 2.20743 0.150546
\(216\) −25.2829 −1.72028
\(217\) 3.38503 0.229791
\(218\) 2.46306 0.166820
\(219\) 3.22046 0.217619
\(220\) 10.8705 0.732886
\(221\) −0.173663 −0.0116818
\(222\) −3.44740 −0.231375
\(223\) 3.32004 0.222326 0.111163 0.993802i \(-0.464542\pi\)
0.111163 + 0.993802i \(0.464542\pi\)
\(224\) −63.6763 −4.25455
\(225\) −2.75531 −0.183687
\(226\) −38.3535 −2.55123
\(227\) 9.56720 0.634997 0.317499 0.948259i \(-0.397157\pi\)
0.317499 + 0.948259i \(0.397157\pi\)
\(228\) 16.5944 1.09899
\(229\) 21.4191 1.41541 0.707706 0.706507i \(-0.249730\pi\)
0.707706 + 0.706507i \(0.249730\pi\)
\(230\) 15.4539 1.01900
\(231\) −3.51577 −0.231320
\(232\) −65.5744 −4.30517
\(233\) 5.54978 0.363578 0.181789 0.983338i \(-0.441811\pi\)
0.181789 + 0.983338i \(0.441811\pi\)
\(234\) −34.2969 −2.24206
\(235\) −11.2376 −0.733057
\(236\) −6.92127 −0.450536
\(237\) −4.21769 −0.273968
\(238\) −0.351704 −0.0227976
\(239\) 24.1435 1.56171 0.780855 0.624712i \(-0.214784\pi\)
0.780855 + 0.624712i \(0.214784\pi\)
\(240\) −6.62764 −0.427812
\(241\) 23.4184 1.50851 0.754255 0.656582i \(-0.227998\pi\)
0.754255 + 0.656582i \(0.227998\pi\)
\(242\) 18.2952 1.17606
\(243\) −11.9330 −0.765500
\(244\) −45.3964 −2.90621
\(245\) 4.96010 0.316889
\(246\) −2.08873 −0.133173
\(247\) 29.2412 1.86058
\(248\) −8.69255 −0.551977
\(249\) −3.02010 −0.191391
\(250\) −2.69988 −0.170755
\(251\) 30.4654 1.92296 0.961481 0.274872i \(-0.0886354\pi\)
0.961481 + 0.274872i \(0.0886354\pi\)
\(252\) −50.4010 −3.17496
\(253\) −11.7636 −0.739574
\(254\) −12.9771 −0.814254
\(255\) −0.0186325 −0.00116681
\(256\) 21.7797 1.36123
\(257\) −11.1355 −0.694614 −0.347307 0.937751i \(-0.612904\pi\)
−0.347307 + 0.937751i \(0.612904\pi\)
\(258\) 2.94807 0.183539
\(259\) −8.92708 −0.554702
\(260\) −24.3860 −1.51236
\(261\) −20.3448 −1.25931
\(262\) 21.2262 1.31136
\(263\) 7.04524 0.434428 0.217214 0.976124i \(-0.430303\pi\)
0.217214 + 0.976124i \(0.430303\pi\)
\(264\) 9.02827 0.555652
\(265\) 10.5759 0.649673
\(266\) 59.2198 3.63100
\(267\) −6.03334 −0.369234
\(268\) −71.7450 −4.38252
\(269\) 2.59721 0.158355 0.0791773 0.996861i \(-0.474771\pi\)
0.0791773 + 0.996861i \(0.474771\pi\)
\(270\) −7.68633 −0.467775
\(271\) −12.0230 −0.730345 −0.365173 0.930940i \(-0.618990\pi\)
−0.365173 + 0.930940i \(0.618990\pi\)
\(272\) 0.504683 0.0306009
\(273\) 7.88703 0.477345
\(274\) −22.4412 −1.35572
\(275\) 2.05516 0.123931
\(276\) 14.9762 0.901463
\(277\) −9.03660 −0.542956 −0.271478 0.962445i \(-0.587512\pi\)
−0.271478 + 0.962445i \(0.587512\pi\)
\(278\) −59.6929 −3.58014
\(279\) −2.69691 −0.161460
\(280\) −30.7128 −1.83544
\(281\) 1.34202 0.0800582 0.0400291 0.999199i \(-0.487255\pi\)
0.0400291 + 0.999199i \(0.487255\pi\)
\(282\) −15.0080 −0.893712
\(283\) 1.80348 0.107206 0.0536028 0.998562i \(-0.482930\pi\)
0.0536028 + 0.998562i \(0.482930\pi\)
\(284\) 0.191224 0.0113471
\(285\) 3.13734 0.185840
\(286\) 25.5818 1.51268
\(287\) −5.40878 −0.319270
\(288\) 50.7319 2.98941
\(289\) −16.9986 −0.999917
\(290\) −19.9355 −1.17065
\(291\) 3.23789 0.189808
\(292\) −34.4361 −2.01522
\(293\) −13.6782 −0.799089 −0.399545 0.916714i \(-0.630832\pi\)
−0.399545 + 0.916714i \(0.630832\pi\)
\(294\) 6.62430 0.386337
\(295\) −1.30853 −0.0761858
\(296\) 22.9242 1.33244
\(297\) 5.85089 0.339503
\(298\) 0.969654 0.0561705
\(299\) 26.3898 1.52616
\(300\) −2.61642 −0.151059
\(301\) 7.63405 0.440020
\(302\) 51.8282 2.98238
\(303\) −4.34619 −0.249682
\(304\) −84.9783 −4.87384
\(305\) −8.58263 −0.491440
\(306\) 0.280208 0.0160184
\(307\) −13.0469 −0.744624 −0.372312 0.928108i \(-0.621435\pi\)
−0.372312 + 0.928108i \(0.621435\pi\)
\(308\) 37.5937 2.14210
\(309\) −6.11919 −0.348109
\(310\) −2.64265 −0.150092
\(311\) 3.04693 0.172776 0.0863878 0.996262i \(-0.472468\pi\)
0.0863878 + 0.996262i \(0.472468\pi\)
\(312\) −20.2534 −1.14662
\(313\) −9.70956 −0.548817 −0.274409 0.961613i \(-0.588482\pi\)
−0.274409 + 0.961613i \(0.588482\pi\)
\(314\) −5.56350 −0.313966
\(315\) −9.52880 −0.536887
\(316\) 45.0992 2.53703
\(317\) −22.9909 −1.29130 −0.645649 0.763634i \(-0.723413\pi\)
−0.645649 + 0.763634i \(0.723413\pi\)
\(318\) 14.1243 0.792053
\(319\) 15.1750 0.849637
\(320\) 22.9144 1.28096
\(321\) 1.06944 0.0596904
\(322\) 53.4449 2.97837
\(323\) −0.238903 −0.0132929
\(324\) 36.2726 2.01514
\(325\) −4.61042 −0.255740
\(326\) 43.0128 2.38226
\(327\) 0.451271 0.0249554
\(328\) 13.8894 0.766915
\(329\) −38.8633 −2.14260
\(330\) 2.74471 0.151091
\(331\) −8.73695 −0.480226 −0.240113 0.970745i \(-0.577185\pi\)
−0.240113 + 0.970745i \(0.577185\pi\)
\(332\) 32.2935 1.77234
\(333\) 7.11235 0.389754
\(334\) 62.9569 3.44485
\(335\) −13.5641 −0.741085
\(336\) −22.9206 −1.25042
\(337\) 17.7358 0.966128 0.483064 0.875585i \(-0.339524\pi\)
0.483064 + 0.875585i \(0.339524\pi\)
\(338\) −22.2900 −1.21242
\(339\) −7.02695 −0.381651
\(340\) 0.199236 0.0108051
\(341\) 2.01160 0.108934
\(342\) −47.1813 −2.55127
\(343\) −7.05467 −0.380916
\(344\) −19.6038 −1.05696
\(345\) 2.83140 0.152438
\(346\) −49.2790 −2.64926
\(347\) −23.7116 −1.27291 −0.636453 0.771316i \(-0.719599\pi\)
−0.636453 + 0.771316i \(0.719599\pi\)
\(348\) −19.3192 −1.03562
\(349\) −14.4329 −0.772574 −0.386287 0.922379i \(-0.626243\pi\)
−0.386287 + 0.922379i \(0.626243\pi\)
\(350\) −9.33708 −0.499088
\(351\) −13.1255 −0.700586
\(352\) −37.8405 −2.01691
\(353\) 4.71838 0.251134 0.125567 0.992085i \(-0.459925\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(354\) −1.74757 −0.0928823
\(355\) 0.0361528 0.00191879
\(356\) 64.5138 3.41922
\(357\) −0.0644376 −0.00341040
\(358\) −54.8598 −2.89943
\(359\) 36.7926 1.94184 0.970919 0.239407i \(-0.0769530\pi\)
0.970919 + 0.239407i \(0.0769530\pi\)
\(360\) 24.4694 1.28965
\(361\) 21.2264 1.11718
\(362\) 17.0419 0.895700
\(363\) 3.35196 0.175932
\(364\) −84.3352 −4.42036
\(365\) −6.51047 −0.340774
\(366\) −11.4623 −0.599142
\(367\) 5.52458 0.288381 0.144190 0.989550i \(-0.453942\pi\)
0.144190 + 0.989550i \(0.453942\pi\)
\(368\) −76.6916 −3.99783
\(369\) 4.30926 0.224331
\(370\) 6.96925 0.362314
\(371\) 36.5751 1.89888
\(372\) −2.56096 −0.132779
\(373\) 22.2820 1.15372 0.576860 0.816843i \(-0.304278\pi\)
0.576860 + 0.816843i \(0.304278\pi\)
\(374\) −0.209005 −0.0108074
\(375\) −0.494659 −0.0255441
\(376\) 99.7985 5.14671
\(377\) −34.0426 −1.75328
\(378\) −26.5819 −1.36723
\(379\) −17.5074 −0.899296 −0.449648 0.893206i \(-0.648451\pi\)
−0.449648 + 0.893206i \(0.648451\pi\)
\(380\) −33.5472 −1.72094
\(381\) −2.37760 −0.121808
\(382\) −46.2999 −2.36891
\(383\) 24.4038 1.24698 0.623488 0.781833i \(-0.285715\pi\)
0.623488 + 0.781833i \(0.285715\pi\)
\(384\) 12.3869 0.632118
\(385\) 7.10745 0.362229
\(386\) −51.3649 −2.61440
\(387\) −6.08217 −0.309174
\(388\) −34.6224 −1.75768
\(389\) 8.79603 0.445977 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(390\) −6.15730 −0.311787
\(391\) −0.215606 −0.0109037
\(392\) −44.0496 −2.22484
\(393\) 3.88898 0.196173
\(394\) −4.79401 −0.241519
\(395\) 8.52645 0.429012
\(396\) −29.9515 −1.50512
\(397\) −23.4910 −1.17898 −0.589491 0.807775i \(-0.700671\pi\)
−0.589491 + 0.807775i \(0.700671\pi\)
\(398\) −72.4107 −3.62962
\(399\) 10.8500 0.543178
\(400\) 13.3984 0.669919
\(401\) −31.6820 −1.58212 −0.791061 0.611737i \(-0.790471\pi\)
−0.791061 + 0.611737i \(0.790471\pi\)
\(402\) −18.1151 −0.903499
\(403\) −4.51269 −0.224793
\(404\) 46.4734 2.31214
\(405\) 6.85768 0.340761
\(406\) −68.9435 −3.42161
\(407\) −5.30504 −0.262961
\(408\) 0.165472 0.00819208
\(409\) 11.6817 0.577622 0.288811 0.957386i \(-0.406740\pi\)
0.288811 + 0.957386i \(0.406740\pi\)
\(410\) 4.22256 0.208538
\(411\) −4.11157 −0.202809
\(412\) 65.4318 3.22360
\(413\) −4.52535 −0.222678
\(414\) −42.5804 −2.09271
\(415\) 6.10541 0.299703
\(416\) 84.8889 4.16202
\(417\) −10.9367 −0.535571
\(418\) 35.1922 1.72131
\(419\) −12.2576 −0.598822 −0.299411 0.954124i \(-0.596790\pi\)
−0.299411 + 0.954124i \(0.596790\pi\)
\(420\) −9.04846 −0.441519
\(421\) 10.7425 0.523557 0.261779 0.965128i \(-0.415691\pi\)
0.261779 + 0.965128i \(0.415691\pi\)
\(422\) −69.9132 −3.40332
\(423\) 30.9630 1.50547
\(424\) −93.9225 −4.56128
\(425\) 0.0376674 0.00182714
\(426\) 0.0482827 0.00233930
\(427\) −29.6816 −1.43640
\(428\) −11.4354 −0.552751
\(429\) 4.68698 0.226289
\(430\) −5.95980 −0.287407
\(431\) −24.7757 −1.19340 −0.596702 0.802463i \(-0.703523\pi\)
−0.596702 + 0.802463i \(0.703523\pi\)
\(432\) 38.1441 1.83521
\(433\) −27.4946 −1.32130 −0.660652 0.750692i \(-0.729720\pi\)
−0.660652 + 0.750692i \(0.729720\pi\)
\(434\) −9.13916 −0.438694
\(435\) −3.65248 −0.175123
\(436\) −4.82539 −0.231094
\(437\) 36.3037 1.73664
\(438\) −8.69486 −0.415456
\(439\) 13.5808 0.648174 0.324087 0.946027i \(-0.394943\pi\)
0.324087 + 0.946027i \(0.394943\pi\)
\(440\) −18.2515 −0.870106
\(441\) −13.6666 −0.650791
\(442\) 0.468867 0.0223018
\(443\) 4.57912 0.217561 0.108780 0.994066i \(-0.465305\pi\)
0.108780 + 0.994066i \(0.465305\pi\)
\(444\) 6.75381 0.320522
\(445\) 12.1970 0.578191
\(446\) −8.96369 −0.424443
\(447\) 0.177656 0.00840282
\(448\) 79.2459 3.74402
\(449\) 19.4625 0.918492 0.459246 0.888309i \(-0.348120\pi\)
0.459246 + 0.888309i \(0.348120\pi\)
\(450\) 7.43900 0.350678
\(451\) −3.21424 −0.151353
\(452\) 75.1383 3.53421
\(453\) 9.49573 0.446148
\(454\) −25.8303 −1.21227
\(455\) −15.9444 −0.747484
\(456\) −27.8621 −1.30476
\(457\) −8.80778 −0.412011 −0.206005 0.978551i \(-0.566046\pi\)
−0.206005 + 0.978551i \(0.566046\pi\)
\(458\) −57.8288 −2.70216
\(459\) 0.107236 0.00500535
\(460\) −30.2758 −1.41162
\(461\) −20.5626 −0.957698 −0.478849 0.877897i \(-0.658946\pi\)
−0.478849 + 0.877897i \(0.658946\pi\)
\(462\) 9.49214 0.441614
\(463\) 6.53896 0.303891 0.151946 0.988389i \(-0.451446\pi\)
0.151946 + 0.988389i \(0.451446\pi\)
\(464\) 98.9315 4.59278
\(465\) −0.484174 −0.0224530
\(466\) −14.9837 −0.694107
\(467\) 11.8221 0.547060 0.273530 0.961864i \(-0.411809\pi\)
0.273530 + 0.961864i \(0.411809\pi\)
\(468\) 67.1912 3.10591
\(469\) −46.9092 −2.16607
\(470\) 30.3400 1.39948
\(471\) −1.01932 −0.0469678
\(472\) 11.6208 0.534892
\(473\) 4.53664 0.208595
\(474\) 11.3872 0.523033
\(475\) −6.34243 −0.291011
\(476\) 0.689024 0.0315814
\(477\) −29.1399 −1.33423
\(478\) −65.1844 −2.98146
\(479\) 20.3005 0.927555 0.463777 0.885952i \(-0.346494\pi\)
0.463777 + 0.885952i \(0.346494\pi\)
\(480\) 9.10787 0.415715
\(481\) 11.9010 0.542637
\(482\) −63.2267 −2.87990
\(483\) 9.79194 0.445549
\(484\) −35.8421 −1.62919
\(485\) −6.54569 −0.297225
\(486\) 32.2176 1.46142
\(487\) 9.14739 0.414508 0.207254 0.978287i \(-0.433547\pi\)
0.207254 + 0.978287i \(0.433547\pi\)
\(488\) 76.2206 3.45035
\(489\) 7.88062 0.356374
\(490\) −13.3917 −0.604973
\(491\) −12.3373 −0.556774 −0.278387 0.960469i \(-0.589800\pi\)
−0.278387 + 0.960469i \(0.589800\pi\)
\(492\) 4.09204 0.184483
\(493\) 0.278130 0.0125264
\(494\) −78.9477 −3.55203
\(495\) −5.66262 −0.254516
\(496\) 13.1144 0.588853
\(497\) 0.125028 0.00560829
\(498\) 8.15389 0.365384
\(499\) −11.2217 −0.502353 −0.251176 0.967941i \(-0.580817\pi\)
−0.251176 + 0.967941i \(0.580817\pi\)
\(500\) 5.28933 0.236546
\(501\) 11.5347 0.515331
\(502\) −82.2529 −3.67113
\(503\) −24.6211 −1.09780 −0.548901 0.835887i \(-0.684954\pi\)
−0.548901 + 0.835887i \(0.684954\pi\)
\(504\) 84.6233 3.76942
\(505\) 8.78624 0.390982
\(506\) 31.7604 1.41192
\(507\) −4.08388 −0.181372
\(508\) 25.4234 1.12798
\(509\) 29.2776 1.29771 0.648854 0.760913i \(-0.275248\pi\)
0.648854 + 0.760913i \(0.275248\pi\)
\(510\) 0.0503056 0.00222757
\(511\) −22.5154 −0.996023
\(512\) −8.71979 −0.385364
\(513\) −18.0564 −0.797208
\(514\) 30.0645 1.32609
\(515\) 12.3705 0.545110
\(516\) −5.77557 −0.254255
\(517\) −23.0950 −1.01572
\(518\) 24.1020 1.05898
\(519\) −9.02868 −0.396315
\(520\) 40.9442 1.79552
\(521\) 12.5853 0.551370 0.275685 0.961248i \(-0.411095\pi\)
0.275685 + 0.961248i \(0.411095\pi\)
\(522\) 54.9284 2.40415
\(523\) −9.66475 −0.422610 −0.211305 0.977420i \(-0.567771\pi\)
−0.211305 + 0.977420i \(0.567771\pi\)
\(524\) −41.5844 −1.81662
\(525\) −1.71070 −0.0746610
\(526\) −19.0213 −0.829367
\(527\) 0.0368690 0.00160604
\(528\) −13.6209 −0.592773
\(529\) 9.76352 0.424501
\(530\) −28.5536 −1.24029
\(531\) 3.60542 0.156462
\(532\) −116.018 −5.03000
\(533\) 7.21062 0.312327
\(534\) 16.2893 0.704906
\(535\) −2.16198 −0.0934703
\(536\) 120.460 5.20308
\(537\) −10.0512 −0.433740
\(538\) −7.01214 −0.302315
\(539\) 10.1938 0.439079
\(540\) 15.0583 0.648006
\(541\) 14.9162 0.641297 0.320648 0.947198i \(-0.396099\pi\)
0.320648 + 0.947198i \(0.396099\pi\)
\(542\) 32.4606 1.39430
\(543\) 3.12233 0.133992
\(544\) −0.693548 −0.0297356
\(545\) −0.912287 −0.0390781
\(546\) −21.2940 −0.911300
\(547\) 7.80378 0.333666 0.166833 0.985985i \(-0.446646\pi\)
0.166833 + 0.985985i \(0.446646\pi\)
\(548\) 43.9646 1.87807
\(549\) 23.6478 1.00926
\(550\) −5.54869 −0.236597
\(551\) −46.8315 −1.99509
\(552\) −25.1451 −1.07025
\(553\) 29.4873 1.25393
\(554\) 24.3977 1.03656
\(555\) 1.27687 0.0542003
\(556\) 116.944 4.95955
\(557\) −27.1701 −1.15124 −0.575618 0.817719i \(-0.695238\pi\)
−0.575618 + 0.817719i \(0.695238\pi\)
\(558\) 7.28132 0.308243
\(559\) −10.1772 −0.430450
\(560\) 46.3361 1.95806
\(561\) −0.0382929 −0.00161673
\(562\) −3.62329 −0.152839
\(563\) 34.7229 1.46340 0.731698 0.681629i \(-0.238728\pi\)
0.731698 + 0.681629i \(0.238728\pi\)
\(564\) 29.4021 1.23805
\(565\) 14.2056 0.597636
\(566\) −4.86917 −0.204666
\(567\) 23.7162 0.995986
\(568\) −0.321065 −0.0134716
\(569\) −5.59082 −0.234379 −0.117190 0.993110i \(-0.537389\pi\)
−0.117190 + 0.993110i \(0.537389\pi\)
\(570\) −8.47043 −0.354787
\(571\) 28.0726 1.17480 0.587401 0.809296i \(-0.300151\pi\)
0.587401 + 0.809296i \(0.300151\pi\)
\(572\) −50.1173 −2.09551
\(573\) −8.48285 −0.354376
\(574\) 14.6030 0.609520
\(575\) −5.72394 −0.238705
\(576\) −63.1364 −2.63068
\(577\) −14.1695 −0.589884 −0.294942 0.955515i \(-0.595300\pi\)
−0.294942 + 0.955515i \(0.595300\pi\)
\(578\) 45.8941 1.90894
\(579\) −9.41084 −0.391101
\(580\) 39.0556 1.62170
\(581\) 21.1146 0.875979
\(582\) −8.74190 −0.362363
\(583\) 21.7352 0.900181
\(584\) 57.8182 2.39253
\(585\) 12.7031 0.525210
\(586\) 36.9295 1.52554
\(587\) 10.0003 0.412757 0.206379 0.978472i \(-0.433832\pi\)
0.206379 + 0.978472i \(0.433832\pi\)
\(588\) −12.9777 −0.535191
\(589\) −6.20799 −0.255796
\(590\) 3.53288 0.145446
\(591\) −0.878337 −0.0361300
\(592\) −34.5855 −1.42146
\(593\) −4.59197 −0.188570 −0.0942848 0.995545i \(-0.530056\pi\)
−0.0942848 + 0.995545i \(0.530056\pi\)
\(594\) −15.7967 −0.648145
\(595\) 0.130267 0.00534041
\(596\) −1.89965 −0.0778127
\(597\) −13.2668 −0.542972
\(598\) −71.2491 −2.91359
\(599\) 4.41617 0.180440 0.0902200 0.995922i \(-0.471243\pi\)
0.0902200 + 0.995922i \(0.471243\pi\)
\(600\) 4.39297 0.179342
\(601\) 41.5314 1.69410 0.847051 0.531512i \(-0.178376\pi\)
0.847051 + 0.531512i \(0.178376\pi\)
\(602\) −20.6110 −0.840042
\(603\) 37.3733 1.52196
\(604\) −101.537 −4.13147
\(605\) −6.77630 −0.275496
\(606\) 11.7342 0.476669
\(607\) −15.6479 −0.635128 −0.317564 0.948237i \(-0.602865\pi\)
−0.317564 + 0.948237i \(0.602865\pi\)
\(608\) 116.779 4.73603
\(609\) −12.6315 −0.511855
\(610\) 23.1721 0.938209
\(611\) 51.8098 2.09600
\(612\) −0.548956 −0.0221902
\(613\) 3.21572 0.129882 0.0649409 0.997889i \(-0.479314\pi\)
0.0649409 + 0.997889i \(0.479314\pi\)
\(614\) 35.2249 1.42156
\(615\) 0.773639 0.0311961
\(616\) −63.1198 −2.54317
\(617\) 10.4263 0.419746 0.209873 0.977729i \(-0.432695\pi\)
0.209873 + 0.977729i \(0.432695\pi\)
\(618\) 16.5211 0.664575
\(619\) −30.7181 −1.23466 −0.617331 0.786703i \(-0.711786\pi\)
−0.617331 + 0.786703i \(0.711786\pi\)
\(620\) 5.17721 0.207922
\(621\) −16.2956 −0.653920
\(622\) −8.22634 −0.329846
\(623\) 42.1812 1.68995
\(624\) 30.5562 1.22323
\(625\) 1.00000 0.0400000
\(626\) 26.2146 1.04775
\(627\) 6.44775 0.257498
\(628\) 10.8995 0.434936
\(629\) −0.0972317 −0.00387688
\(630\) 25.7266 1.02497
\(631\) −44.9682 −1.79016 −0.895078 0.445910i \(-0.852880\pi\)
−0.895078 + 0.445910i \(0.852880\pi\)
\(632\) −75.7217 −3.01205
\(633\) −12.8092 −0.509119
\(634\) 62.0727 2.46522
\(635\) 4.80654 0.190742
\(636\) −27.6710 −1.09723
\(637\) −22.8681 −0.906068
\(638\) −40.9706 −1.62204
\(639\) −0.0996121 −0.00394059
\(640\) −25.0414 −0.989847
\(641\) −4.38997 −0.173394 −0.0866968 0.996235i \(-0.527631\pi\)
−0.0866968 + 0.996235i \(0.527631\pi\)
\(642\) −2.88736 −0.113955
\(643\) 49.6659 1.95863 0.979316 0.202335i \(-0.0648529\pi\)
0.979316 + 0.202335i \(0.0648529\pi\)
\(644\) −104.704 −4.12592
\(645\) −1.09193 −0.0429946
\(646\) 0.645008 0.0253775
\(647\) −25.4735 −1.00147 −0.500734 0.865601i \(-0.666936\pi\)
−0.500734 + 0.865601i \(0.666936\pi\)
\(648\) −60.9017 −2.39244
\(649\) −2.68925 −0.105562
\(650\) 12.4476 0.488233
\(651\) −1.67444 −0.0656263
\(652\) −84.2665 −3.30013
\(653\) 11.8937 0.465437 0.232718 0.972544i \(-0.425238\pi\)
0.232718 + 0.972544i \(0.425238\pi\)
\(654\) −1.21838 −0.0476423
\(655\) −7.86193 −0.307191
\(656\) −20.9549 −0.818150
\(657\) 17.9384 0.699843
\(658\) 104.926 4.09044
\(659\) −18.3202 −0.713653 −0.356827 0.934171i \(-0.616141\pi\)
−0.356827 + 0.934171i \(0.616141\pi\)
\(660\) −5.37717 −0.209306
\(661\) 34.7971 1.35345 0.676726 0.736235i \(-0.263398\pi\)
0.676726 + 0.736235i \(0.263398\pi\)
\(662\) 23.5887 0.916800
\(663\) 0.0859038 0.00333623
\(664\) −54.2209 −2.10418
\(665\) −21.9343 −0.850574
\(666\) −19.2025 −0.744080
\(667\) −42.2647 −1.63649
\(668\) −123.339 −4.77213
\(669\) −1.64229 −0.0634945
\(670\) 36.6214 1.41481
\(671\) −17.6387 −0.680935
\(672\) 31.4981 1.21506
\(673\) 42.3762 1.63348 0.816742 0.577003i \(-0.195778\pi\)
0.816742 + 0.577003i \(0.195778\pi\)
\(674\) −47.8844 −1.84444
\(675\) 2.84692 0.109578
\(676\) 43.6685 1.67956
\(677\) −4.07445 −0.156594 −0.0782970 0.996930i \(-0.524948\pi\)
−0.0782970 + 0.996930i \(0.524948\pi\)
\(678\) 18.9719 0.728611
\(679\) −22.6372 −0.868736
\(680\) −0.334517 −0.0128281
\(681\) −4.73250 −0.181350
\(682\) −5.43107 −0.207967
\(683\) −3.39848 −0.130039 −0.0650196 0.997884i \(-0.520711\pi\)
−0.0650196 + 0.997884i \(0.520711\pi\)
\(684\) 92.4331 3.53427
\(685\) 8.31193 0.317582
\(686\) 19.0467 0.727208
\(687\) −10.5951 −0.404230
\(688\) 29.5761 1.12758
\(689\) −48.7593 −1.85758
\(690\) −7.64443 −0.291019
\(691\) −42.3141 −1.60970 −0.804852 0.593476i \(-0.797755\pi\)
−0.804852 + 0.593476i \(0.797755\pi\)
\(692\) 96.5426 3.67000
\(693\) −19.5833 −0.743906
\(694\) 64.0184 2.43011
\(695\) 22.1095 0.838661
\(696\) 32.4370 1.22952
\(697\) −0.0589112 −0.00223142
\(698\) 38.9670 1.47492
\(699\) −2.74525 −0.103835
\(700\) 18.2923 0.691384
\(701\) −2.31169 −0.0873113 −0.0436557 0.999047i \(-0.513900\pi\)
−0.0436557 + 0.999047i \(0.513900\pi\)
\(702\) 35.4372 1.33749
\(703\) 16.3718 0.617476
\(704\) 47.0929 1.77488
\(705\) 5.55876 0.209355
\(706\) −12.7390 −0.479440
\(707\) 30.3858 1.14277
\(708\) 3.42367 0.128669
\(709\) 14.2956 0.536882 0.268441 0.963296i \(-0.413492\pi\)
0.268441 + 0.963296i \(0.413492\pi\)
\(710\) −0.0976080 −0.00366316
\(711\) −23.4930 −0.881058
\(712\) −108.319 −4.05941
\(713\) −5.60261 −0.209819
\(714\) 0.173974 0.00651080
\(715\) −9.47517 −0.354351
\(716\) 107.476 4.01657
\(717\) −11.9428 −0.446012
\(718\) −99.3355 −3.70717
\(719\) 21.2871 0.793876 0.396938 0.917845i \(-0.370073\pi\)
0.396938 + 0.917845i \(0.370073\pi\)
\(720\) −36.9167 −1.37581
\(721\) 42.7814 1.59326
\(722\) −57.3086 −2.13281
\(723\) −11.5841 −0.430818
\(724\) −33.3867 −1.24081
\(725\) 7.38384 0.274229
\(726\) −9.04988 −0.335872
\(727\) −4.22454 −0.156679 −0.0783397 0.996927i \(-0.524962\pi\)
−0.0783397 + 0.996927i \(0.524962\pi\)
\(728\) 141.599 5.24800
\(729\) −14.6703 −0.543344
\(730\) 17.5775 0.650571
\(731\) 0.0831484 0.00307535
\(732\) 22.4558 0.829989
\(733\) −35.7796 −1.32155 −0.660775 0.750584i \(-0.729772\pi\)
−0.660775 + 0.750584i \(0.729772\pi\)
\(734\) −14.9157 −0.550548
\(735\) −2.45356 −0.0905009
\(736\) 105.392 3.88478
\(737\) −27.8764 −1.02684
\(738\) −11.6345 −0.428271
\(739\) −5.33288 −0.196173 −0.0980866 0.995178i \(-0.531272\pi\)
−0.0980866 + 0.995178i \(0.531272\pi\)
\(740\) −13.6535 −0.501912
\(741\) −14.4644 −0.531365
\(742\) −98.7481 −3.62516
\(743\) 48.4887 1.77888 0.889439 0.457054i \(-0.151095\pi\)
0.889439 + 0.457054i \(0.151095\pi\)
\(744\) 4.29985 0.157640
\(745\) −0.359147 −0.0131581
\(746\) −60.1587 −2.20257
\(747\) −16.8223 −0.615496
\(748\) 0.409462 0.0149714
\(749\) −7.47684 −0.273198
\(750\) 1.33552 0.0487663
\(751\) 1.63587 0.0596939 0.0298469 0.999554i \(-0.490498\pi\)
0.0298469 + 0.999554i \(0.490498\pi\)
\(752\) −150.565 −5.49055
\(753\) −15.0700 −0.549182
\(754\) 91.9108 3.34719
\(755\) −19.1965 −0.698632
\(756\) 52.0767 1.89401
\(757\) 51.0030 1.85374 0.926869 0.375386i \(-0.122490\pi\)
0.926869 + 0.375386i \(0.122490\pi\)
\(758\) 47.2679 1.71685
\(759\) 5.81899 0.211216
\(760\) 56.3258 2.04315
\(761\) −22.1501 −0.802942 −0.401471 0.915872i \(-0.631501\pi\)
−0.401471 + 0.915872i \(0.631501\pi\)
\(762\) 6.41923 0.232544
\(763\) −3.15500 −0.114219
\(764\) 90.7062 3.28163
\(765\) −0.103786 −0.00375237
\(766\) −65.8873 −2.38060
\(767\) 6.03288 0.217835
\(768\) −10.7735 −0.388756
\(769\) 4.45711 0.160727 0.0803637 0.996766i \(-0.474392\pi\)
0.0803637 + 0.996766i \(0.474392\pi\)
\(770\) −19.1892 −0.691532
\(771\) 5.50828 0.198376
\(772\) 100.629 3.62172
\(773\) 36.9116 1.32762 0.663809 0.747902i \(-0.268939\pi\)
0.663809 + 0.747902i \(0.268939\pi\)
\(774\) 16.4211 0.590245
\(775\) 0.978803 0.0351596
\(776\) 58.1310 2.08678
\(777\) 4.41586 0.158418
\(778\) −23.7482 −0.851414
\(779\) 9.91945 0.355401
\(780\) 12.0628 0.431917
\(781\) 0.0742999 0.00265866
\(782\) 0.582110 0.0208162
\(783\) 21.0212 0.751236
\(784\) 66.4573 2.37348
\(785\) 2.06065 0.0735477
\(786\) −10.4998 −0.374514
\(787\) 27.7929 0.990709 0.495355 0.868691i \(-0.335038\pi\)
0.495355 + 0.868691i \(0.335038\pi\)
\(788\) 9.39196 0.334575
\(789\) −3.48499 −0.124069
\(790\) −23.0204 −0.819028
\(791\) 49.1279 1.74679
\(792\) 50.2886 1.78693
\(793\) 39.5695 1.40515
\(794\) 63.4229 2.25079
\(795\) −5.23147 −0.185541
\(796\) 141.860 5.02809
\(797\) −8.65304 −0.306506 −0.153253 0.988187i \(-0.548975\pi\)
−0.153253 + 0.988187i \(0.548975\pi\)
\(798\) −29.2936 −1.03698
\(799\) −0.423290 −0.0149749
\(800\) −18.4124 −0.650977
\(801\) −33.6064 −1.18742
\(802\) 85.5374 3.02043
\(803\) −13.3801 −0.472173
\(804\) 35.4893 1.25161
\(805\) −19.7953 −0.697694
\(806\) 12.1837 0.429153
\(807\) −1.28473 −0.0452247
\(808\) −78.0288 −2.74504
\(809\) 27.0759 0.951938 0.475969 0.879462i \(-0.342097\pi\)
0.475969 + 0.879462i \(0.342097\pi\)
\(810\) −18.5149 −0.650547
\(811\) −28.1103 −0.987085 −0.493543 0.869722i \(-0.664298\pi\)
−0.493543 + 0.869722i \(0.664298\pi\)
\(812\) 135.067 4.73994
\(813\) 5.94729 0.208580
\(814\) 14.3230 0.502019
\(815\) −15.9314 −0.558053
\(816\) −0.249646 −0.00873936
\(817\) −14.0005 −0.489815
\(818\) −31.5391 −1.10274
\(819\) 43.9317 1.53510
\(820\) −8.27243 −0.288886
\(821\) −23.2022 −0.809761 −0.404881 0.914370i \(-0.632687\pi\)
−0.404881 + 0.914370i \(0.632687\pi\)
\(822\) 11.1007 0.387183
\(823\) −30.7176 −1.07075 −0.535374 0.844615i \(-0.679829\pi\)
−0.535374 + 0.844615i \(0.679829\pi\)
\(824\) −109.860 −3.82716
\(825\) −1.01661 −0.0353937
\(826\) 12.2179 0.425115
\(827\) 53.9267 1.87521 0.937607 0.347696i \(-0.113036\pi\)
0.937607 + 0.347696i \(0.113036\pi\)
\(828\) 83.4194 2.89902
\(829\) −26.1499 −0.908225 −0.454113 0.890944i \(-0.650044\pi\)
−0.454113 + 0.890944i \(0.650044\pi\)
\(830\) −16.4838 −0.572163
\(831\) 4.47004 0.155064
\(832\) −105.645 −3.66259
\(833\) 0.186834 0.00647342
\(834\) 29.5276 1.02246
\(835\) −23.3184 −0.806967
\(836\) −68.9451 −2.38451
\(837\) 2.78657 0.0963180
\(838\) 33.0940 1.14321
\(839\) −23.1411 −0.798921 −0.399461 0.916750i \(-0.630803\pi\)
−0.399461 + 0.916750i \(0.630803\pi\)
\(840\) 15.1924 0.524186
\(841\) 25.5211 0.880037
\(842\) −29.0034 −0.999524
\(843\) −0.663843 −0.0228640
\(844\) 136.967 4.71460
\(845\) 8.25595 0.284013
\(846\) −83.5962 −2.87410
\(847\) −23.4347 −0.805227
\(848\) 141.700 4.86600
\(849\) −0.892107 −0.0306170
\(850\) −0.101697 −0.00348819
\(851\) 14.7753 0.506492
\(852\) −0.0945907 −0.00324062
\(853\) 32.2512 1.10426 0.552130 0.833758i \(-0.313815\pi\)
0.552130 + 0.833758i \(0.313815\pi\)
\(854\) 80.1368 2.74222
\(855\) 17.4754 0.597645
\(856\) 19.2001 0.656245
\(857\) 54.1109 1.84839 0.924197 0.381915i \(-0.124735\pi\)
0.924197 + 0.381915i \(0.124735\pi\)
\(858\) −12.6543 −0.432009
\(859\) 14.6440 0.499646 0.249823 0.968292i \(-0.419628\pi\)
0.249823 + 0.968292i \(0.419628\pi\)
\(860\) 11.6759 0.398144
\(861\) 2.67550 0.0911810
\(862\) 66.8914 2.27833
\(863\) 26.6152 0.905991 0.452996 0.891513i \(-0.350355\pi\)
0.452996 + 0.891513i \(0.350355\pi\)
\(864\) −52.4186 −1.78332
\(865\) 18.2523 0.620598
\(866\) 74.2319 2.52250
\(867\) 8.40851 0.285568
\(868\) 17.9046 0.607720
\(869\) 17.5233 0.594436
\(870\) 9.86126 0.334328
\(871\) 62.5361 2.11896
\(872\) 8.10184 0.274363
\(873\) 18.0354 0.610407
\(874\) −98.0155 −3.31542
\(875\) 3.45834 0.116913
\(876\) 17.0341 0.575529
\(877\) −52.3344 −1.76721 −0.883604 0.468236i \(-0.844890\pi\)
−0.883604 + 0.468236i \(0.844890\pi\)
\(878\) −36.6664 −1.23743
\(879\) 6.76605 0.228213
\(880\) 27.5359 0.928235
\(881\) 16.6091 0.559575 0.279788 0.960062i \(-0.409736\pi\)
0.279788 + 0.960062i \(0.409736\pi\)
\(882\) 36.8982 1.24243
\(883\) −1.52258 −0.0512389 −0.0256194 0.999672i \(-0.508156\pi\)
−0.0256194 + 0.999672i \(0.508156\pi\)
\(884\) −0.918559 −0.0308945
\(885\) 0.647278 0.0217580
\(886\) −12.3631 −0.415345
\(887\) −10.8814 −0.365363 −0.182681 0.983172i \(-0.558478\pi\)
−0.182681 + 0.983172i \(0.558478\pi\)
\(888\) −11.3397 −0.380534
\(889\) 16.6226 0.557506
\(890\) −32.9303 −1.10383
\(891\) 14.0937 0.472156
\(892\) 17.5608 0.587979
\(893\) 71.2734 2.38507
\(894\) −0.479648 −0.0160418
\(895\) 20.3194 0.679202
\(896\) −86.6015 −2.89315
\(897\) −13.0539 −0.435858
\(898\) −52.5463 −1.75349
\(899\) 7.22732 0.241045
\(900\) −14.5738 −0.485792
\(901\) 0.398367 0.0132715
\(902\) 8.67806 0.288948
\(903\) −3.77626 −0.125666
\(904\) −126.157 −4.19593
\(905\) −6.31209 −0.209821
\(906\) −25.6373 −0.851742
\(907\) 48.6254 1.61458 0.807290 0.590154i \(-0.200933\pi\)
0.807290 + 0.590154i \(0.200933\pi\)
\(908\) 50.6041 1.67936
\(909\) −24.2088 −0.802956
\(910\) 43.0479 1.42702
\(911\) 28.3575 0.939524 0.469762 0.882793i \(-0.344340\pi\)
0.469762 + 0.882793i \(0.344340\pi\)
\(912\) 42.0353 1.39193
\(913\) 12.5476 0.415265
\(914\) 23.7799 0.786570
\(915\) 4.24548 0.140351
\(916\) 113.293 3.74329
\(917\) −27.1892 −0.897867
\(918\) −0.289524 −0.00955572
\(919\) −20.9148 −0.689917 −0.344959 0.938618i \(-0.612107\pi\)
−0.344959 + 0.938618i \(0.612107\pi\)
\(920\) 50.8332 1.67592
\(921\) 6.45375 0.212658
\(922\) 55.5166 1.82834
\(923\) −0.166679 −0.00548632
\(924\) −18.5961 −0.611766
\(925\) −2.58132 −0.0848733
\(926\) −17.6544 −0.580159
\(927\) −34.0847 −1.11949
\(928\) −135.954 −4.46292
\(929\) −30.0134 −0.984708 −0.492354 0.870395i \(-0.663863\pi\)
−0.492354 + 0.870395i \(0.663863\pi\)
\(930\) 1.30721 0.0428651
\(931\) −31.4591 −1.03103
\(932\) 29.3546 0.961543
\(933\) −1.50719 −0.0493433
\(934\) −31.9181 −1.04439
\(935\) 0.0774128 0.00253167
\(936\) −112.814 −3.68744
\(937\) −37.2078 −1.21552 −0.607762 0.794119i \(-0.707933\pi\)
−0.607762 + 0.794119i \(0.707933\pi\)
\(938\) 126.649 4.13524
\(939\) 4.80293 0.156738
\(940\) −59.4392 −1.93869
\(941\) 5.92644 0.193196 0.0965982 0.995323i \(-0.469204\pi\)
0.0965982 + 0.995323i \(0.469204\pi\)
\(942\) 2.75204 0.0896662
\(943\) 8.95215 0.291522
\(944\) −17.5322 −0.570626
\(945\) 9.84560 0.320278
\(946\) −12.2484 −0.398229
\(947\) 47.5559 1.54536 0.772679 0.634797i \(-0.218916\pi\)
0.772679 + 0.634797i \(0.218916\pi\)
\(948\) −22.3088 −0.724555
\(949\) 30.0160 0.974360
\(950\) 17.1238 0.555569
\(951\) 11.3727 0.368784
\(952\) −1.15687 −0.0374944
\(953\) 45.6961 1.48024 0.740121 0.672473i \(-0.234768\pi\)
0.740121 + 0.672473i \(0.234768\pi\)
\(954\) 78.6742 2.54717
\(955\) 17.1489 0.554925
\(956\) 127.703 4.13021
\(957\) −7.50646 −0.242649
\(958\) −54.8089 −1.77080
\(959\) 28.7454 0.928239
\(960\) −11.3348 −0.365830
\(961\) −30.0419 −0.969095
\(962\) −32.1311 −1.03595
\(963\) 5.95692 0.191959
\(964\) 123.868 3.98951
\(965\) 19.0249 0.612433
\(966\) −26.4370 −0.850598
\(967\) 26.0762 0.838553 0.419277 0.907859i \(-0.362284\pi\)
0.419277 + 0.907859i \(0.362284\pi\)
\(968\) 60.1789 1.93422
\(969\) 0.118176 0.00379635
\(970\) 17.6726 0.567432
\(971\) −8.82536 −0.283219 −0.141610 0.989923i \(-0.545228\pi\)
−0.141610 + 0.989923i \(0.545228\pi\)
\(972\) −63.1175 −2.02449
\(973\) 76.4621 2.45126
\(974\) −24.6968 −0.791337
\(975\) 2.28059 0.0730372
\(976\) −114.993 −3.68085
\(977\) 47.2630 1.51208 0.756039 0.654526i \(-0.227132\pi\)
0.756039 + 0.654526i \(0.227132\pi\)
\(978\) −21.2767 −0.680354
\(979\) 25.0668 0.801137
\(980\) 26.2356 0.838066
\(981\) 2.51364 0.0802542
\(982\) 33.3091 1.06294
\(983\) −28.2186 −0.900033 −0.450016 0.893020i \(-0.648582\pi\)
−0.450016 + 0.893020i \(0.648582\pi\)
\(984\) −6.87053 −0.219025
\(985\) 1.77564 0.0565766
\(986\) −0.750917 −0.0239141
\(987\) 19.2241 0.611909
\(988\) 154.667 4.92060
\(989\) −12.6352 −0.401777
\(990\) 15.2884 0.485896
\(991\) 19.9285 0.633050 0.316525 0.948584i \(-0.397484\pi\)
0.316525 + 0.948584i \(0.397484\pi\)
\(992\) −18.0221 −0.572203
\(993\) 4.32181 0.137149
\(994\) −0.337561 −0.0107068
\(995\) 26.8200 0.850251
\(996\) −15.9743 −0.506165
\(997\) 55.6230 1.76160 0.880799 0.473491i \(-0.157006\pi\)
0.880799 + 0.473491i \(0.157006\pi\)
\(998\) 30.2972 0.959043
\(999\) −7.34881 −0.232506
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 \(a_p\))