Properties

Label 8035.2.a.e.1.1
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 1.1
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.77624 q^{2}\) \(+1.54873 q^{3}\) \(+5.70752 q^{4}\) \(+1.00000 q^{5}\) \(-4.29965 q^{6}\) \(-0.285554 q^{7}\) \(-10.2930 q^{8}\) \(-0.601430 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.77624 q^{2}\) \(+1.54873 q^{3}\) \(+5.70752 q^{4}\) \(+1.00000 q^{5}\) \(-4.29965 q^{6}\) \(-0.285554 q^{7}\) \(-10.2930 q^{8}\) \(-0.601430 q^{9}\) \(-2.77624 q^{10}\) \(+5.98927 q^{11}\) \(+8.83941 q^{12}\) \(-1.66116 q^{13}\) \(+0.792766 q^{14}\) \(+1.54873 q^{15}\) \(+17.1607 q^{16}\) \(+0.925145 q^{17}\) \(+1.66971 q^{18}\) \(+4.25042 q^{19}\) \(+5.70752 q^{20}\) \(-0.442246 q^{21}\) \(-16.6277 q^{22}\) \(+3.90313 q^{23}\) \(-15.9410 q^{24}\) \(+1.00000 q^{25}\) \(+4.61179 q^{26}\) \(-5.57765 q^{27}\) \(-1.62980 q^{28}\) \(+3.04199 q^{29}\) \(-4.29965 q^{30}\) \(+6.52521 q^{31}\) \(-27.0564 q^{32}\) \(+9.27578 q^{33}\) \(-2.56843 q^{34}\) \(-0.285554 q^{35}\) \(-3.43267 q^{36}\) \(+0.670341 q^{37}\) \(-11.8002 q^{38}\) \(-2.57270 q^{39}\) \(-10.2930 q^{40}\) \(+9.69421 q^{41}\) \(+1.22778 q^{42}\) \(+2.41354 q^{43}\) \(+34.1839 q^{44}\) \(-0.601430 q^{45}\) \(-10.8360 q^{46}\) \(-1.78921 q^{47}\) \(+26.5774 q^{48}\) \(-6.91846 q^{49}\) \(-2.77624 q^{50}\) \(+1.43280 q^{51}\) \(-9.48112 q^{52}\) \(+0.986060 q^{53}\) \(+15.4849 q^{54}\) \(+5.98927 q^{55}\) \(+2.93919 q^{56}\) \(+6.58276 q^{57}\) \(-8.44529 q^{58}\) \(+0.203441 q^{59}\) \(+8.83941 q^{60}\) \(-1.06783 q^{61}\) \(-18.1156 q^{62}\) \(+0.171740 q^{63}\) \(+40.7936 q^{64}\) \(-1.66116 q^{65}\) \(-25.7518 q^{66}\) \(+4.61177 q^{67}\) \(+5.28028 q^{68}\) \(+6.04491 q^{69}\) \(+0.792766 q^{70}\) \(+4.94620 q^{71}\) \(+6.19049 q^{72}\) \(+15.6211 q^{73}\) \(-1.86103 q^{74}\) \(+1.54873 q^{75}\) \(+24.2593 q^{76}\) \(-1.71026 q^{77}\) \(+7.14242 q^{78}\) \(+8.10983 q^{79}\) \(+17.1607 q^{80}\) \(-6.83399 q^{81}\) \(-26.9135 q^{82}\) \(-9.37155 q^{83}\) \(-2.52413 q^{84}\) \(+0.925145 q^{85}\) \(-6.70058 q^{86}\) \(+4.71122 q^{87}\) \(-61.6474 q^{88}\) \(-4.22230 q^{89}\) \(+1.66971 q^{90}\) \(+0.474351 q^{91}\) \(+22.2772 q^{92}\) \(+10.1058 q^{93}\) \(+4.96729 q^{94}\) \(+4.25042 q^{95}\) \(-41.9031 q^{96}\) \(-14.1713 q^{97}\) \(+19.2073 q^{98}\) \(-3.60213 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77624 −1.96310 −0.981550 0.191208i \(-0.938760\pi\)
−0.981550 + 0.191208i \(0.938760\pi\)
\(3\) 1.54873 0.894161 0.447080 0.894494i \(-0.352464\pi\)
0.447080 + 0.894494i \(0.352464\pi\)
\(4\) 5.70752 2.85376
\(5\) 1.00000 0.447214
\(6\) −4.29965 −1.75533
\(7\) −0.285554 −0.107929 −0.0539645 0.998543i \(-0.517186\pi\)
−0.0539645 + 0.998543i \(0.517186\pi\)
\(8\) −10.2930 −3.63911
\(9\) −0.601430 −0.200477
\(10\) −2.77624 −0.877925
\(11\) 5.98927 1.80583 0.902917 0.429815i \(-0.141421\pi\)
0.902917 + 0.429815i \(0.141421\pi\)
\(12\) 8.83941 2.55172
\(13\) −1.66116 −0.460724 −0.230362 0.973105i \(-0.573991\pi\)
−0.230362 + 0.973105i \(0.573991\pi\)
\(14\) 0.792766 0.211875
\(15\) 1.54873 0.399881
\(16\) 17.1607 4.29018
\(17\) 0.925145 0.224381 0.112190 0.993687i \(-0.464213\pi\)
0.112190 + 0.993687i \(0.464213\pi\)
\(18\) 1.66971 0.393555
\(19\) 4.25042 0.975113 0.487557 0.873091i \(-0.337888\pi\)
0.487557 + 0.873091i \(0.337888\pi\)
\(20\) 5.70752 1.27624
\(21\) −0.442246 −0.0965059
\(22\) −16.6277 −3.54503
\(23\) 3.90313 0.813860 0.406930 0.913459i \(-0.366599\pi\)
0.406930 + 0.913459i \(0.366599\pi\)
\(24\) −15.9410 −3.25395
\(25\) 1.00000 0.200000
\(26\) 4.61179 0.904446
\(27\) −5.57765 −1.07342
\(28\) −1.62980 −0.308004
\(29\) 3.04199 0.564883 0.282441 0.959285i \(-0.408856\pi\)
0.282441 + 0.959285i \(0.408856\pi\)
\(30\) −4.29965 −0.785006
\(31\) 6.52521 1.17196 0.585981 0.810325i \(-0.300709\pi\)
0.585981 + 0.810325i \(0.300709\pi\)
\(32\) −27.0564 −4.78294
\(33\) 9.27578 1.61471
\(34\) −2.56843 −0.440481
\(35\) −0.285554 −0.0482674
\(36\) −3.43267 −0.572112
\(37\) 0.670341 0.110203 0.0551017 0.998481i \(-0.482452\pi\)
0.0551017 + 0.998481i \(0.482452\pi\)
\(38\) −11.8002 −1.91424
\(39\) −2.57270 −0.411961
\(40\) −10.2930 −1.62746
\(41\) 9.69421 1.51398 0.756991 0.653426i \(-0.226669\pi\)
0.756991 + 0.653426i \(0.226669\pi\)
\(42\) 1.22778 0.189451
\(43\) 2.41354 0.368062 0.184031 0.982920i \(-0.441085\pi\)
0.184031 + 0.982920i \(0.441085\pi\)
\(44\) 34.1839 5.15341
\(45\) −0.601430 −0.0896558
\(46\) −10.8360 −1.59769
\(47\) −1.78921 −0.260984 −0.130492 0.991449i \(-0.541656\pi\)
−0.130492 + 0.991449i \(0.541656\pi\)
\(48\) 26.5774 3.83611
\(49\) −6.91846 −0.988351
\(50\) −2.77624 −0.392620
\(51\) 1.43280 0.200632
\(52\) −9.48112 −1.31479
\(53\) 0.986060 0.135446 0.0677229 0.997704i \(-0.478427\pi\)
0.0677229 + 0.997704i \(0.478427\pi\)
\(54\) 15.4849 2.10723
\(55\) 5.98927 0.807594
\(56\) 2.93919 0.392766
\(57\) 6.58276 0.871908
\(58\) −8.44529 −1.10892
\(59\) 0.203441 0.0264858 0.0132429 0.999912i \(-0.495785\pi\)
0.0132429 + 0.999912i \(0.495785\pi\)
\(60\) 8.83941 1.14116
\(61\) −1.06783 −0.136721 −0.0683605 0.997661i \(-0.521777\pi\)
−0.0683605 + 0.997661i \(0.521777\pi\)
\(62\) −18.1156 −2.30068
\(63\) 0.171740 0.0216373
\(64\) 40.7936 5.09920
\(65\) −1.66116 −0.206042
\(66\) −25.7518 −3.16983
\(67\) 4.61177 0.563418 0.281709 0.959500i \(-0.409099\pi\)
0.281709 + 0.959500i \(0.409099\pi\)
\(68\) 5.28028 0.640328
\(69\) 6.04491 0.727721
\(70\) 0.792766 0.0947536
\(71\) 4.94620 0.587007 0.293503 0.955958i \(-0.405179\pi\)
0.293503 + 0.955958i \(0.405179\pi\)
\(72\) 6.19049 0.729557
\(73\) 15.6211 1.82831 0.914153 0.405369i \(-0.132857\pi\)
0.914153 + 0.405369i \(0.132857\pi\)
\(74\) −1.86103 −0.216340
\(75\) 1.54873 0.178832
\(76\) 24.2593 2.78274
\(77\) −1.71026 −0.194902
\(78\) 7.14242 0.808720
\(79\) 8.10983 0.912428 0.456214 0.889870i \(-0.349205\pi\)
0.456214 + 0.889870i \(0.349205\pi\)
\(80\) 17.1607 1.91863
\(81\) −6.83399 −0.759333
\(82\) −26.9135 −2.97210
\(83\) −9.37155 −1.02866 −0.514330 0.857592i \(-0.671959\pi\)
−0.514330 + 0.857592i \(0.671959\pi\)
\(84\) −2.52413 −0.275405
\(85\) 0.925145 0.100346
\(86\) −6.70058 −0.722542
\(87\) 4.71122 0.505096
\(88\) −61.6474 −6.57163
\(89\) −4.22230 −0.447563 −0.223782 0.974639i \(-0.571840\pi\)
−0.223782 + 0.974639i \(0.571840\pi\)
\(90\) 1.66971 0.176003
\(91\) 0.474351 0.0497255
\(92\) 22.2772 2.32256
\(93\) 10.1058 1.04792
\(94\) 4.96729 0.512337
\(95\) 4.25042 0.436084
\(96\) −41.9031 −4.27671
\(97\) −14.1713 −1.43887 −0.719437 0.694558i \(-0.755600\pi\)
−0.719437 + 0.694558i \(0.755600\pi\)
\(98\) 19.2073 1.94023
\(99\) −3.60213 −0.362027
\(100\) 5.70752 0.570752
\(101\) −19.1738 −1.90786 −0.953932 0.300022i \(-0.903006\pi\)
−0.953932 + 0.300022i \(0.903006\pi\)
\(102\) −3.97780 −0.393861
\(103\) −14.6688 −1.44536 −0.722679 0.691184i \(-0.757090\pi\)
−0.722679 + 0.691184i \(0.757090\pi\)
\(104\) 17.0983 1.67663
\(105\) −0.442246 −0.0431588
\(106\) −2.73754 −0.265893
\(107\) 8.32461 0.804770 0.402385 0.915471i \(-0.368181\pi\)
0.402385 + 0.915471i \(0.368181\pi\)
\(108\) −31.8345 −3.06328
\(109\) −2.74202 −0.262638 −0.131319 0.991340i \(-0.541921\pi\)
−0.131319 + 0.991340i \(0.541921\pi\)
\(110\) −16.6277 −1.58539
\(111\) 1.03818 0.0985396
\(112\) −4.90030 −0.463035
\(113\) −2.07193 −0.194910 −0.0974552 0.995240i \(-0.531070\pi\)
−0.0974552 + 0.995240i \(0.531070\pi\)
\(114\) −18.2753 −1.71164
\(115\) 3.90313 0.363969
\(116\) 17.3622 1.61204
\(117\) 0.999073 0.0923643
\(118\) −0.564802 −0.0519942
\(119\) −0.264178 −0.0242172
\(120\) −15.9410 −1.45521
\(121\) 24.8714 2.26104
\(122\) 2.96454 0.268397
\(123\) 15.0137 1.35374
\(124\) 37.2427 3.34450
\(125\) 1.00000 0.0894427
\(126\) −0.476793 −0.0424761
\(127\) 6.73285 0.597444 0.298722 0.954340i \(-0.403440\pi\)
0.298722 + 0.954340i \(0.403440\pi\)
\(128\) −59.1401 −5.22730
\(129\) 3.73793 0.329106
\(130\) 4.61179 0.404481
\(131\) 8.03671 0.702171 0.351086 0.936343i \(-0.385813\pi\)
0.351086 + 0.936343i \(0.385813\pi\)
\(132\) 52.9417 4.60798
\(133\) −1.21372 −0.105243
\(134\) −12.8034 −1.10605
\(135\) −5.57765 −0.480048
\(136\) −9.52248 −0.816546
\(137\) −3.80919 −0.325441 −0.162721 0.986672i \(-0.552027\pi\)
−0.162721 + 0.986672i \(0.552027\pi\)
\(138\) −16.7821 −1.42859
\(139\) −19.8425 −1.68302 −0.841508 0.540244i \(-0.818332\pi\)
−0.841508 + 0.540244i \(0.818332\pi\)
\(140\) −1.62980 −0.137743
\(141\) −2.77101 −0.233361
\(142\) −13.7319 −1.15235
\(143\) −9.94916 −0.831990
\(144\) −10.3210 −0.860080
\(145\) 3.04199 0.252623
\(146\) −43.3678 −3.58915
\(147\) −10.7148 −0.883745
\(148\) 3.82598 0.314494
\(149\) −12.3976 −1.01565 −0.507826 0.861460i \(-0.669551\pi\)
−0.507826 + 0.861460i \(0.669551\pi\)
\(150\) −4.29965 −0.351065
\(151\) −4.22393 −0.343739 −0.171869 0.985120i \(-0.554981\pi\)
−0.171869 + 0.985120i \(0.554981\pi\)
\(152\) −43.7494 −3.54855
\(153\) −0.556410 −0.0449831
\(154\) 4.74809 0.382612
\(155\) 6.52521 0.524117
\(156\) −14.6837 −1.17564
\(157\) −10.3033 −0.822295 −0.411147 0.911569i \(-0.634872\pi\)
−0.411147 + 0.911569i \(0.634872\pi\)
\(158\) −22.5149 −1.79119
\(159\) 1.52714 0.121110
\(160\) −27.0564 −2.13899
\(161\) −1.11455 −0.0878391
\(162\) 18.9728 1.49065
\(163\) −16.8917 −1.32306 −0.661528 0.749920i \(-0.730092\pi\)
−0.661528 + 0.749920i \(0.730092\pi\)
\(164\) 55.3299 4.32054
\(165\) 9.27578 0.722118
\(166\) 26.0177 2.01936
\(167\) 10.1238 0.783404 0.391702 0.920092i \(-0.371886\pi\)
0.391702 + 0.920092i \(0.371886\pi\)
\(168\) 4.55202 0.351196
\(169\) −10.2405 −0.787734
\(170\) −2.56843 −0.196989
\(171\) −2.55633 −0.195487
\(172\) 13.7753 1.05036
\(173\) 8.72403 0.663276 0.331638 0.943407i \(-0.392399\pi\)
0.331638 + 0.943407i \(0.392399\pi\)
\(174\) −13.0795 −0.991553
\(175\) −0.285554 −0.0215858
\(176\) 102.780 7.74735
\(177\) 0.315076 0.0236825
\(178\) 11.7221 0.878611
\(179\) −4.29841 −0.321278 −0.160639 0.987013i \(-0.551356\pi\)
−0.160639 + 0.987013i \(0.551356\pi\)
\(180\) −3.43267 −0.255856
\(181\) −6.53585 −0.485806 −0.242903 0.970051i \(-0.578100\pi\)
−0.242903 + 0.970051i \(0.578100\pi\)
\(182\) −1.31691 −0.0976161
\(183\) −1.65378 −0.122251
\(184\) −40.1748 −2.96173
\(185\) 0.670341 0.0492845
\(186\) −28.0561 −2.05718
\(187\) 5.54095 0.405194
\(188\) −10.2120 −0.744785
\(189\) 1.59272 0.115853
\(190\) −11.8002 −0.856076
\(191\) 24.6316 1.78228 0.891141 0.453726i \(-0.149906\pi\)
0.891141 + 0.453726i \(0.149906\pi\)
\(192\) 63.1783 4.55950
\(193\) −11.0658 −0.796537 −0.398268 0.917269i \(-0.630389\pi\)
−0.398268 + 0.917269i \(0.630389\pi\)
\(194\) 39.3429 2.82465
\(195\) −2.57270 −0.184235
\(196\) −39.4872 −2.82052
\(197\) 22.9506 1.63517 0.817583 0.575811i \(-0.195314\pi\)
0.817583 + 0.575811i \(0.195314\pi\)
\(198\) 10.0004 0.710696
\(199\) −8.38036 −0.594068 −0.297034 0.954867i \(-0.595997\pi\)
−0.297034 + 0.954867i \(0.595997\pi\)
\(200\) −10.2930 −0.727822
\(201\) 7.14240 0.503786
\(202\) 53.2311 3.74533
\(203\) −0.868650 −0.0609673
\(204\) 8.17774 0.572556
\(205\) 9.69421 0.677073
\(206\) 40.7241 2.83738
\(207\) −2.34746 −0.163160
\(208\) −28.5067 −1.97659
\(209\) 25.4569 1.76089
\(210\) 1.22778 0.0847250
\(211\) 19.8566 1.36698 0.683491 0.729959i \(-0.260461\pi\)
0.683491 + 0.729959i \(0.260461\pi\)
\(212\) 5.62795 0.386529
\(213\) 7.66034 0.524878
\(214\) −23.1111 −1.57984
\(215\) 2.41354 0.164602
\(216\) 57.4105 3.90629
\(217\) −1.86330 −0.126489
\(218\) 7.61251 0.515584
\(219\) 24.1928 1.63480
\(220\) 34.1839 2.30468
\(221\) −1.53682 −0.103377
\(222\) −2.88224 −0.193443
\(223\) 9.91011 0.663630 0.331815 0.943345i \(-0.392339\pi\)
0.331815 + 0.943345i \(0.392339\pi\)
\(224\) 7.72604 0.516218
\(225\) −0.601430 −0.0400953
\(226\) 5.75217 0.382629
\(227\) 24.9432 1.65554 0.827770 0.561067i \(-0.189609\pi\)
0.827770 + 0.561067i \(0.189609\pi\)
\(228\) 37.5712 2.48821
\(229\) −8.65945 −0.572232 −0.286116 0.958195i \(-0.592364\pi\)
−0.286116 + 0.958195i \(0.592364\pi\)
\(230\) −10.8360 −0.714508
\(231\) −2.64873 −0.174274
\(232\) −31.3111 −2.05567
\(233\) 7.37154 0.482925 0.241463 0.970410i \(-0.422373\pi\)
0.241463 + 0.970410i \(0.422373\pi\)
\(234\) −2.77367 −0.181320
\(235\) −1.78921 −0.116715
\(236\) 1.16114 0.0755840
\(237\) 12.5600 0.815857
\(238\) 0.733423 0.0475408
\(239\) 19.0190 1.23024 0.615118 0.788435i \(-0.289108\pi\)
0.615118 + 0.788435i \(0.289108\pi\)
\(240\) 26.5774 1.71556
\(241\) −15.6589 −1.00868 −0.504338 0.863506i \(-0.668264\pi\)
−0.504338 + 0.863506i \(0.668264\pi\)
\(242\) −69.0490 −4.43864
\(243\) 6.14892 0.394454
\(244\) −6.09463 −0.390169
\(245\) −6.91846 −0.442004
\(246\) −41.6817 −2.65753
\(247\) −7.06064 −0.449258
\(248\) −67.1637 −4.26490
\(249\) −14.5140 −0.919788
\(250\) −2.77624 −0.175585
\(251\) 26.6085 1.67952 0.839758 0.542960i \(-0.182697\pi\)
0.839758 + 0.542960i \(0.182697\pi\)
\(252\) 0.980211 0.0617475
\(253\) 23.3769 1.46970
\(254\) −18.6920 −1.17284
\(255\) 1.43280 0.0897255
\(256\) 82.6001 5.16250
\(257\) −2.12996 −0.132863 −0.0664315 0.997791i \(-0.521161\pi\)
−0.0664315 + 0.997791i \(0.521161\pi\)
\(258\) −10.3774 −0.646068
\(259\) −0.191418 −0.0118942
\(260\) −9.48112 −0.587994
\(261\) −1.82954 −0.113246
\(262\) −22.3119 −1.37843
\(263\) −0.257515 −0.0158791 −0.00793954 0.999968i \(-0.502527\pi\)
−0.00793954 + 0.999968i \(0.502527\pi\)
\(264\) −95.4753 −5.87610
\(265\) 0.986060 0.0605732
\(266\) 3.36959 0.206603
\(267\) −6.53922 −0.400193
\(268\) 26.3218 1.60786
\(269\) −11.5733 −0.705639 −0.352819 0.935691i \(-0.614777\pi\)
−0.352819 + 0.935691i \(0.614777\pi\)
\(270\) 15.4849 0.942381
\(271\) 9.51253 0.577845 0.288922 0.957352i \(-0.406703\pi\)
0.288922 + 0.957352i \(0.406703\pi\)
\(272\) 15.8762 0.962633
\(273\) 0.734642 0.0444626
\(274\) 10.5752 0.638874
\(275\) 5.98927 0.361167
\(276\) 34.5014 2.07674
\(277\) 24.3908 1.46550 0.732750 0.680498i \(-0.238236\pi\)
0.732750 + 0.680498i \(0.238236\pi\)
\(278\) 55.0875 3.30393
\(279\) −3.92445 −0.234951
\(280\) 2.93919 0.175650
\(281\) 5.23052 0.312026 0.156013 0.987755i \(-0.450136\pi\)
0.156013 + 0.987755i \(0.450136\pi\)
\(282\) 7.69300 0.458112
\(283\) −8.55517 −0.508552 −0.254276 0.967132i \(-0.581837\pi\)
−0.254276 + 0.967132i \(0.581837\pi\)
\(284\) 28.2305 1.67517
\(285\) 6.58276 0.389929
\(286\) 27.6213 1.63328
\(287\) −2.76822 −0.163403
\(288\) 16.2725 0.958867
\(289\) −16.1441 −0.949653
\(290\) −8.44529 −0.495924
\(291\) −21.9475 −1.28658
\(292\) 89.1575 5.21755
\(293\) 15.9010 0.928948 0.464474 0.885587i \(-0.346243\pi\)
0.464474 + 0.885587i \(0.346243\pi\)
\(294\) 29.7470 1.73488
\(295\) 0.203441 0.0118448
\(296\) −6.89980 −0.401043
\(297\) −33.4061 −1.93842
\(298\) 34.4188 1.99383
\(299\) −6.48374 −0.374964
\(300\) 8.83941 0.510344
\(301\) −0.689195 −0.0397246
\(302\) 11.7267 0.674793
\(303\) −29.6951 −1.70594
\(304\) 72.9403 4.18341
\(305\) −1.06783 −0.0611435
\(306\) 1.54473 0.0883062
\(307\) −10.8588 −0.619746 −0.309873 0.950778i \(-0.600287\pi\)
−0.309873 + 0.950778i \(0.600287\pi\)
\(308\) −9.76133 −0.556203
\(309\) −22.7180 −1.29238
\(310\) −18.1156 −1.02889
\(311\) 4.38222 0.248493 0.124247 0.992251i \(-0.460349\pi\)
0.124247 + 0.992251i \(0.460349\pi\)
\(312\) 26.4807 1.49917
\(313\) −17.5973 −0.994659 −0.497330 0.867562i \(-0.665686\pi\)
−0.497330 + 0.867562i \(0.665686\pi\)
\(314\) 28.6045 1.61425
\(315\) 0.171740 0.00967647
\(316\) 46.2870 2.60385
\(317\) 25.6921 1.44301 0.721507 0.692407i \(-0.243450\pi\)
0.721507 + 0.692407i \(0.243450\pi\)
\(318\) −4.23972 −0.237751
\(319\) 18.2193 1.02008
\(320\) 40.7936 2.28043
\(321\) 12.8926 0.719594
\(322\) 3.09427 0.172437
\(323\) 3.93226 0.218797
\(324\) −39.0051 −2.16695
\(325\) −1.66116 −0.0921447
\(326\) 46.8953 2.59729
\(327\) −4.24665 −0.234841
\(328\) −99.7821 −5.50955
\(329\) 0.510916 0.0281677
\(330\) −25.7518 −1.41759
\(331\) −20.8353 −1.14521 −0.572606 0.819831i \(-0.694068\pi\)
−0.572606 + 0.819831i \(0.694068\pi\)
\(332\) −53.4883 −2.93555
\(333\) −0.403163 −0.0220932
\(334\) −28.1061 −1.53790
\(335\) 4.61177 0.251968
\(336\) −7.58926 −0.414028
\(337\) −18.5133 −1.00848 −0.504242 0.863562i \(-0.668228\pi\)
−0.504242 + 0.863562i \(0.668228\pi\)
\(338\) 28.4302 1.54640
\(339\) −3.20886 −0.174281
\(340\) 5.28028 0.286363
\(341\) 39.0813 2.11637
\(342\) 7.09699 0.383761
\(343\) 3.97446 0.214601
\(344\) −24.8425 −1.33942
\(345\) 6.04491 0.325447
\(346\) −24.2200 −1.30208
\(347\) 34.0030 1.82538 0.912688 0.408657i \(-0.134003\pi\)
0.912688 + 0.408657i \(0.134003\pi\)
\(348\) 26.8894 1.44142
\(349\) 14.8203 0.793314 0.396657 0.917967i \(-0.370170\pi\)
0.396657 + 0.917967i \(0.370170\pi\)
\(350\) 0.792766 0.0423751
\(351\) 9.26538 0.494550
\(352\) −162.048 −8.63719
\(353\) −3.33345 −0.177422 −0.0887109 0.996057i \(-0.528275\pi\)
−0.0887109 + 0.996057i \(0.528275\pi\)
\(354\) −0.874726 −0.0464912
\(355\) 4.94620 0.262517
\(356\) −24.0989 −1.27724
\(357\) −0.409142 −0.0216541
\(358\) 11.9334 0.630701
\(359\) −21.3772 −1.12825 −0.564123 0.825691i \(-0.690785\pi\)
−0.564123 + 0.825691i \(0.690785\pi\)
\(360\) 6.19049 0.326268
\(361\) −0.933929 −0.0491542
\(362\) 18.1451 0.953685
\(363\) 38.5191 2.02173
\(364\) 2.70737 0.141905
\(365\) 15.6211 0.817644
\(366\) 4.59128 0.239990
\(367\) −22.0047 −1.14863 −0.574317 0.818633i \(-0.694732\pi\)
−0.574317 + 0.818633i \(0.694732\pi\)
\(368\) 66.9806 3.49160
\(369\) −5.83039 −0.303518
\(370\) −1.86103 −0.0967503
\(371\) −0.281573 −0.0146185
\(372\) 57.6790 2.99052
\(373\) 29.3077 1.51750 0.758748 0.651384i \(-0.225811\pi\)
0.758748 + 0.651384i \(0.225811\pi\)
\(374\) −15.3830 −0.795436
\(375\) 1.54873 0.0799762
\(376\) 18.4163 0.949749
\(377\) −5.05323 −0.260255
\(378\) −4.42177 −0.227431
\(379\) 36.3492 1.86713 0.933566 0.358406i \(-0.116680\pi\)
0.933566 + 0.358406i \(0.116680\pi\)
\(380\) 24.2593 1.24448
\(381\) 10.4274 0.534211
\(382\) −68.3833 −3.49880
\(383\) 9.47282 0.484039 0.242019 0.970271i \(-0.422190\pi\)
0.242019 + 0.970271i \(0.422190\pi\)
\(384\) −91.5922 −4.67404
\(385\) −1.71026 −0.0871628
\(386\) 30.7215 1.56368
\(387\) −1.45158 −0.0737877
\(388\) −80.8827 −4.10620
\(389\) 0.647709 0.0328402 0.0164201 0.999865i \(-0.494773\pi\)
0.0164201 + 0.999865i \(0.494773\pi\)
\(390\) 7.14242 0.361671
\(391\) 3.61097 0.182614
\(392\) 71.2114 3.59672
\(393\) 12.4467 0.627854
\(394\) −63.7165 −3.20999
\(395\) 8.10983 0.408050
\(396\) −20.5592 −1.03314
\(397\) −31.0776 −1.55974 −0.779871 0.625940i \(-0.784715\pi\)
−0.779871 + 0.625940i \(0.784715\pi\)
\(398\) 23.2659 1.16621
\(399\) −1.87973 −0.0941042
\(400\) 17.1607 0.858036
\(401\) −12.2679 −0.612627 −0.306314 0.951931i \(-0.599096\pi\)
−0.306314 + 0.951931i \(0.599096\pi\)
\(402\) −19.8290 −0.988982
\(403\) −10.8394 −0.539951
\(404\) −109.435 −5.44458
\(405\) −6.83399 −0.339584
\(406\) 2.41158 0.119685
\(407\) 4.01486 0.199009
\(408\) −14.7478 −0.730124
\(409\) −28.9145 −1.42973 −0.714865 0.699262i \(-0.753512\pi\)
−0.714865 + 0.699262i \(0.753512\pi\)
\(410\) −26.9135 −1.32916
\(411\) −5.89942 −0.290997
\(412\) −83.7223 −4.12470
\(413\) −0.0580933 −0.00285859
\(414\) 6.51712 0.320299
\(415\) −9.37155 −0.460031
\(416\) 44.9450 2.20361
\(417\) −30.7307 −1.50489
\(418\) −70.6746 −3.45681
\(419\) 1.38654 0.0677371 0.0338686 0.999426i \(-0.489217\pi\)
0.0338686 + 0.999426i \(0.489217\pi\)
\(420\) −2.52413 −0.123165
\(421\) 13.5491 0.660340 0.330170 0.943921i \(-0.392894\pi\)
0.330170 + 0.943921i \(0.392894\pi\)
\(422\) −55.1266 −2.68352
\(423\) 1.07609 0.0523211
\(424\) −10.1495 −0.492902
\(425\) 0.925145 0.0448761
\(426\) −21.2670 −1.03039
\(427\) 0.304921 0.0147562
\(428\) 47.5128 2.29662
\(429\) −15.4086 −0.743933
\(430\) −6.70058 −0.323130
\(431\) 18.5687 0.894422 0.447211 0.894428i \(-0.352417\pi\)
0.447211 + 0.894428i \(0.352417\pi\)
\(432\) −95.7165 −4.60516
\(433\) −39.0352 −1.87591 −0.937955 0.346756i \(-0.887283\pi\)
−0.937955 + 0.346756i \(0.887283\pi\)
\(434\) 5.17296 0.248310
\(435\) 4.71122 0.225886
\(436\) −15.6501 −0.749505
\(437\) 16.5900 0.793605
\(438\) −67.1651 −3.20927
\(439\) 1.26087 0.0601782 0.0300891 0.999547i \(-0.490421\pi\)
0.0300891 + 0.999547i \(0.490421\pi\)
\(440\) −61.6474 −2.93892
\(441\) 4.16097 0.198141
\(442\) 4.26657 0.202940
\(443\) −10.5450 −0.501009 −0.250504 0.968115i \(-0.580596\pi\)
−0.250504 + 0.968115i \(0.580596\pi\)
\(444\) 5.92542 0.281208
\(445\) −4.22230 −0.200156
\(446\) −27.5128 −1.30277
\(447\) −19.2006 −0.908156
\(448\) −11.6488 −0.550352
\(449\) 39.4969 1.86397 0.931986 0.362494i \(-0.118075\pi\)
0.931986 + 0.362494i \(0.118075\pi\)
\(450\) 1.66971 0.0787111
\(451\) 58.0613 2.73400
\(452\) −11.8256 −0.556228
\(453\) −6.54174 −0.307358
\(454\) −69.2485 −3.24999
\(455\) 0.474351 0.0222379
\(456\) −67.7561 −3.17297
\(457\) 17.4277 0.815232 0.407616 0.913153i \(-0.366360\pi\)
0.407616 + 0.913153i \(0.366360\pi\)
\(458\) 24.0407 1.12335
\(459\) −5.16013 −0.240854
\(460\) 22.2772 1.03868
\(461\) −14.5109 −0.675838 −0.337919 0.941175i \(-0.609723\pi\)
−0.337919 + 0.941175i \(0.609723\pi\)
\(462\) 7.35352 0.342117
\(463\) 36.2033 1.68251 0.841255 0.540638i \(-0.181817\pi\)
0.841255 + 0.540638i \(0.181817\pi\)
\(464\) 52.2027 2.42345
\(465\) 10.1058 0.468645
\(466\) −20.4652 −0.948030
\(467\) −15.9154 −0.736475 −0.368238 0.929732i \(-0.620039\pi\)
−0.368238 + 0.929732i \(0.620039\pi\)
\(468\) 5.70222 0.263585
\(469\) −1.31691 −0.0608092
\(470\) 4.96729 0.229124
\(471\) −15.9571 −0.735264
\(472\) −2.09401 −0.0963847
\(473\) 14.4554 0.664658
\(474\) −34.8695 −1.60161
\(475\) 4.25042 0.195023
\(476\) −1.50780 −0.0691100
\(477\) −0.593046 −0.0271537
\(478\) −52.8013 −2.41508
\(479\) −6.84437 −0.312727 −0.156364 0.987700i \(-0.549977\pi\)
−0.156364 + 0.987700i \(0.549977\pi\)
\(480\) −41.9031 −1.91260
\(481\) −1.11355 −0.0507733
\(482\) 43.4728 1.98013
\(483\) −1.72614 −0.0785423
\(484\) 141.954 6.45245
\(485\) −14.1713 −0.643484
\(486\) −17.0709 −0.774352
\(487\) 10.1919 0.461840 0.230920 0.972973i \(-0.425826\pi\)
0.230920 + 0.972973i \(0.425826\pi\)
\(488\) 10.9911 0.497543
\(489\) −26.1606 −1.18303
\(490\) 19.2073 0.867698
\(491\) −5.36581 −0.242155 −0.121078 0.992643i \(-0.538635\pi\)
−0.121078 + 0.992643i \(0.538635\pi\)
\(492\) 85.6911 3.86325
\(493\) 2.81428 0.126749
\(494\) 19.6020 0.881938
\(495\) −3.60213 −0.161904
\(496\) 111.977 5.02793
\(497\) −1.41241 −0.0633551
\(498\) 40.2944 1.80564
\(499\) −6.64210 −0.297341 −0.148671 0.988887i \(-0.547499\pi\)
−0.148671 + 0.988887i \(0.547499\pi\)
\(500\) 5.70752 0.255248
\(501\) 15.6791 0.700489
\(502\) −73.8718 −3.29706
\(503\) −14.8976 −0.664253 −0.332126 0.943235i \(-0.607766\pi\)
−0.332126 + 0.943235i \(0.607766\pi\)
\(504\) −1.76772 −0.0787404
\(505\) −19.1738 −0.853223
\(506\) −64.9000 −2.88516
\(507\) −15.8598 −0.704361
\(508\) 38.4279 1.70496
\(509\) −10.3839 −0.460260 −0.230130 0.973160i \(-0.573915\pi\)
−0.230130 + 0.973160i \(0.573915\pi\)
\(510\) −3.97780 −0.176140
\(511\) −4.46065 −0.197327
\(512\) −111.038 −4.90721
\(513\) −23.7074 −1.04671
\(514\) 5.91328 0.260823
\(515\) −14.6688 −0.646384
\(516\) 21.3343 0.939190
\(517\) −10.7161 −0.471293
\(518\) 0.531423 0.0233494
\(519\) 13.5112 0.593075
\(520\) 17.0983 0.749810
\(521\) 29.3053 1.28389 0.641945 0.766751i \(-0.278128\pi\)
0.641945 + 0.766751i \(0.278128\pi\)
\(522\) 5.07925 0.222313
\(523\) −2.15564 −0.0942595 −0.0471297 0.998889i \(-0.515007\pi\)
−0.0471297 + 0.998889i \(0.515007\pi\)
\(524\) 45.8697 2.00383
\(525\) −0.442246 −0.0193012
\(526\) 0.714925 0.0311722
\(527\) 6.03677 0.262966
\(528\) 159.179 6.92738
\(529\) −7.76554 −0.337632
\(530\) −2.73754 −0.118911
\(531\) −0.122356 −0.00530978
\(532\) −6.92734 −0.300338
\(533\) −16.1037 −0.697527
\(534\) 18.1544 0.785619
\(535\) 8.32461 0.359904
\(536\) −47.4688 −2.05034
\(537\) −6.65709 −0.287275
\(538\) 32.1304 1.38524
\(539\) −41.4365 −1.78480
\(540\) −31.8345 −1.36994
\(541\) −30.3456 −1.30466 −0.652330 0.757935i \(-0.726208\pi\)
−0.652330 + 0.757935i \(0.726208\pi\)
\(542\) −26.4091 −1.13437
\(543\) −10.1223 −0.434388
\(544\) −25.0311 −1.07320
\(545\) −2.74202 −0.117455
\(546\) −2.03954 −0.0872844
\(547\) −1.54945 −0.0662497 −0.0331249 0.999451i \(-0.510546\pi\)
−0.0331249 + 0.999451i \(0.510546\pi\)
\(548\) −21.7410 −0.928731
\(549\) 0.642222 0.0274094
\(550\) −16.6277 −0.709006
\(551\) 12.9297 0.550825
\(552\) −62.2200 −2.64826
\(553\) −2.31579 −0.0984775
\(554\) −67.7147 −2.87692
\(555\) 1.03818 0.0440682
\(556\) −113.251 −4.80292
\(557\) 0.441314 0.0186991 0.00934954 0.999956i \(-0.497024\pi\)
0.00934954 + 0.999956i \(0.497024\pi\)
\(558\) 10.8952 0.461232
\(559\) −4.00929 −0.169575
\(560\) −4.90030 −0.207076
\(561\) 8.58144 0.362309
\(562\) −14.5212 −0.612539
\(563\) −17.7172 −0.746690 −0.373345 0.927693i \(-0.621789\pi\)
−0.373345 + 0.927693i \(0.621789\pi\)
\(564\) −15.8156 −0.665957
\(565\) −2.07193 −0.0871666
\(566\) 23.7512 0.998339
\(567\) 1.95147 0.0819541
\(568\) −50.9111 −2.13618
\(569\) −3.16538 −0.132700 −0.0663498 0.997796i \(-0.521135\pi\)
−0.0663498 + 0.997796i \(0.521135\pi\)
\(570\) −18.2753 −0.765470
\(571\) 19.8078 0.828930 0.414465 0.910065i \(-0.363969\pi\)
0.414465 + 0.910065i \(0.363969\pi\)
\(572\) −56.7850 −2.37430
\(573\) 38.1478 1.59365
\(574\) 7.68524 0.320776
\(575\) 3.90313 0.162772
\(576\) −24.5345 −1.02227
\(577\) −11.9990 −0.499524 −0.249762 0.968307i \(-0.580352\pi\)
−0.249762 + 0.968307i \(0.580352\pi\)
\(578\) 44.8199 1.86426
\(579\) −17.1380 −0.712232
\(580\) 17.3622 0.720926
\(581\) 2.67608 0.111022
\(582\) 60.9315 2.52569
\(583\) 5.90578 0.244592
\(584\) −160.787 −6.65341
\(585\) 0.999073 0.0413066
\(586\) −44.1451 −1.82362
\(587\) −6.58103 −0.271628 −0.135814 0.990734i \(-0.543365\pi\)
−0.135814 + 0.990734i \(0.543365\pi\)
\(588\) −61.1551 −2.52199
\(589\) 27.7349 1.14280
\(590\) −0.564802 −0.0232525
\(591\) 35.5444 1.46210
\(592\) 11.5035 0.472793
\(593\) −30.9072 −1.26921 −0.634603 0.772838i \(-0.718836\pi\)
−0.634603 + 0.772838i \(0.718836\pi\)
\(594\) 92.7433 3.80530
\(595\) −0.264178 −0.0108303
\(596\) −70.7596 −2.89843
\(597\) −12.9789 −0.531192
\(598\) 18.0004 0.736092
\(599\) 35.8813 1.46607 0.733035 0.680191i \(-0.238103\pi\)
0.733035 + 0.680191i \(0.238103\pi\)
\(600\) −15.9410 −0.650790
\(601\) 32.8710 1.34084 0.670419 0.741983i \(-0.266115\pi\)
0.670419 + 0.741983i \(0.266115\pi\)
\(602\) 1.91337 0.0779833
\(603\) −2.77366 −0.112952
\(604\) −24.1082 −0.980947
\(605\) 24.8714 1.01117
\(606\) 82.4407 3.34892
\(607\) 39.8301 1.61665 0.808326 0.588735i \(-0.200374\pi\)
0.808326 + 0.588735i \(0.200374\pi\)
\(608\) −115.001 −4.66390
\(609\) −1.34531 −0.0545145
\(610\) 2.96454 0.120031
\(611\) 2.97218 0.120241
\(612\) −3.17572 −0.128371
\(613\) 38.7089 1.56344 0.781719 0.623631i \(-0.214343\pi\)
0.781719 + 0.623631i \(0.214343\pi\)
\(614\) 30.1467 1.21662
\(615\) 15.0137 0.605412
\(616\) 17.6036 0.709270
\(617\) −1.97709 −0.0795948 −0.0397974 0.999208i \(-0.512671\pi\)
−0.0397974 + 0.999208i \(0.512671\pi\)
\(618\) 63.0707 2.53708
\(619\) 28.1183 1.13017 0.565085 0.825033i \(-0.308843\pi\)
0.565085 + 0.825033i \(0.308843\pi\)
\(620\) 37.2427 1.49570
\(621\) −21.7703 −0.873613
\(622\) −12.1661 −0.487817
\(623\) 1.20569 0.0483051
\(624\) −44.1493 −1.76739
\(625\) 1.00000 0.0400000
\(626\) 48.8544 1.95261
\(627\) 39.4260 1.57452
\(628\) −58.8064 −2.34663
\(629\) 0.620163 0.0247275
\(630\) −0.476793 −0.0189959
\(631\) −45.6834 −1.81863 −0.909315 0.416109i \(-0.863393\pi\)
−0.909315 + 0.416109i \(0.863393\pi\)
\(632\) −83.4742 −3.32043
\(633\) 30.7525 1.22230
\(634\) −71.3276 −2.83278
\(635\) 6.73285 0.267185
\(636\) 8.71619 0.345619
\(637\) 11.4927 0.455357
\(638\) −50.5812 −2.00253
\(639\) −2.97479 −0.117681
\(640\) −59.1401 −2.33772
\(641\) 13.6467 0.539014 0.269507 0.962998i \(-0.413139\pi\)
0.269507 + 0.962998i \(0.413139\pi\)
\(642\) −35.7929 −1.41263
\(643\) −12.5653 −0.495527 −0.247764 0.968820i \(-0.579696\pi\)
−0.247764 + 0.968820i \(0.579696\pi\)
\(644\) −6.36133 −0.250672
\(645\) 3.73793 0.147181
\(646\) −10.9169 −0.429519
\(647\) −2.83106 −0.111300 −0.0556502 0.998450i \(-0.517723\pi\)
−0.0556502 + 0.998450i \(0.517723\pi\)
\(648\) 70.3420 2.76330
\(649\) 1.21846 0.0478289
\(650\) 4.61179 0.180889
\(651\) −2.88575 −0.113101
\(652\) −96.4094 −3.77568
\(653\) −5.24539 −0.205268 −0.102634 0.994719i \(-0.532727\pi\)
−0.102634 + 0.994719i \(0.532727\pi\)
\(654\) 11.7897 0.461015
\(655\) 8.03671 0.314020
\(656\) 166.360 6.49525
\(657\) −9.39497 −0.366533
\(658\) −1.41843 −0.0552961
\(659\) 32.8830 1.28094 0.640470 0.767983i \(-0.278739\pi\)
0.640470 + 0.767983i \(0.278739\pi\)
\(660\) 52.9417 2.06075
\(661\) −13.1534 −0.511610 −0.255805 0.966728i \(-0.582340\pi\)
−0.255805 + 0.966728i \(0.582340\pi\)
\(662\) 57.8438 2.24816
\(663\) −2.38012 −0.0924361
\(664\) 96.4610 3.74341
\(665\) −1.21372 −0.0470661
\(666\) 1.11928 0.0433712
\(667\) 11.8733 0.459735
\(668\) 57.7818 2.23565
\(669\) 15.3481 0.593392
\(670\) −12.8034 −0.494638
\(671\) −6.39550 −0.246895
\(672\) 11.9656 0.461582
\(673\) −18.3678 −0.708026 −0.354013 0.935241i \(-0.615183\pi\)
−0.354013 + 0.935241i \(0.615183\pi\)
\(674\) 51.3974 1.97976
\(675\) −5.57765 −0.214684
\(676\) −58.4480 −2.24800
\(677\) −32.0777 −1.23285 −0.616423 0.787415i \(-0.711419\pi\)
−0.616423 + 0.787415i \(0.711419\pi\)
\(678\) 8.90857 0.342132
\(679\) 4.04665 0.155296
\(680\) −9.52248 −0.365171
\(681\) 38.6304 1.48032
\(682\) −108.499 −4.15464
\(683\) 37.8885 1.44976 0.724881 0.688874i \(-0.241895\pi\)
0.724881 + 0.688874i \(0.241895\pi\)
\(684\) −14.5903 −0.557874
\(685\) −3.80919 −0.145542
\(686\) −11.0341 −0.421283
\(687\) −13.4112 −0.511668
\(688\) 41.4181 1.57905
\(689\) −1.63801 −0.0624030
\(690\) −16.7821 −0.638885
\(691\) 44.8339 1.70556 0.852781 0.522269i \(-0.174914\pi\)
0.852781 + 0.522269i \(0.174914\pi\)
\(692\) 49.7926 1.89283
\(693\) 1.02860 0.0390733
\(694\) −94.4005 −3.58339
\(695\) −19.8425 −0.752668
\(696\) −48.4924 −1.83810
\(697\) 8.96855 0.339708
\(698\) −41.1448 −1.55735
\(699\) 11.4165 0.431813
\(700\) −1.62980 −0.0616007
\(701\) −18.6258 −0.703489 −0.351744 0.936096i \(-0.614411\pi\)
−0.351744 + 0.936096i \(0.614411\pi\)
\(702\) −25.7229 −0.970850
\(703\) 2.84923 0.107461
\(704\) 244.324 9.20831
\(705\) −2.77101 −0.104362
\(706\) 9.25447 0.348297
\(707\) 5.47515 0.205914
\(708\) 1.79830 0.0675843
\(709\) −12.6545 −0.475248 −0.237624 0.971357i \(-0.576369\pi\)
−0.237624 + 0.971357i \(0.576369\pi\)
\(710\) −13.7319 −0.515348
\(711\) −4.87749 −0.182920
\(712\) 43.4600 1.62873
\(713\) 25.4688 0.953813
\(714\) 1.13588 0.0425091
\(715\) −9.94916 −0.372077
\(716\) −24.5333 −0.916851
\(717\) 29.4553 1.10003
\(718\) 59.3483 2.21486
\(719\) −1.92185 −0.0716729 −0.0358365 0.999358i \(-0.511410\pi\)
−0.0358365 + 0.999358i \(0.511410\pi\)
\(720\) −10.3210 −0.384640
\(721\) 4.18872 0.155996
\(722\) 2.59281 0.0964945
\(723\) −24.2514 −0.901919
\(724\) −37.3035 −1.38637
\(725\) 3.04199 0.112977
\(726\) −106.938 −3.96886
\(727\) 30.5601 1.13341 0.566706 0.823920i \(-0.308218\pi\)
0.566706 + 0.823920i \(0.308218\pi\)
\(728\) −4.88248 −0.180957
\(729\) 30.0250 1.11204
\(730\) −43.3678 −1.60512
\(731\) 2.23288 0.0825859
\(732\) −9.43895 −0.348874
\(733\) −2.21924 −0.0819696 −0.0409848 0.999160i \(-0.513050\pi\)
−0.0409848 + 0.999160i \(0.513050\pi\)
\(734\) 61.0903 2.25488
\(735\) −10.7148 −0.395223
\(736\) −105.605 −3.89264
\(737\) 27.6212 1.01744
\(738\) 16.1866 0.595835
\(739\) 3.72729 0.137110 0.0685552 0.997647i \(-0.478161\pi\)
0.0685552 + 0.997647i \(0.478161\pi\)
\(740\) 3.82598 0.140646
\(741\) −10.9350 −0.401709
\(742\) 0.781714 0.0286976
\(743\) 44.4285 1.62992 0.814962 0.579514i \(-0.196758\pi\)
0.814962 + 0.579514i \(0.196758\pi\)
\(744\) −104.019 −3.81351
\(745\) −12.3976 −0.454213
\(746\) −81.3653 −2.97900
\(747\) 5.63633 0.206222
\(748\) 31.6251 1.15633
\(749\) −2.37712 −0.0868581
\(750\) −4.29965 −0.157001
\(751\) 26.2193 0.956757 0.478378 0.878154i \(-0.341225\pi\)
0.478378 + 0.878154i \(0.341225\pi\)
\(752\) −30.7042 −1.11967
\(753\) 41.2095 1.50176
\(754\) 14.0290 0.510906
\(755\) −4.22393 −0.153725
\(756\) 9.09046 0.330617
\(757\) 2.50635 0.0910949 0.0455474 0.998962i \(-0.485497\pi\)
0.0455474 + 0.998962i \(0.485497\pi\)
\(758\) −100.914 −3.66536
\(759\) 36.2046 1.31414
\(760\) −43.7494 −1.58696
\(761\) −43.1566 −1.56443 −0.782213 0.623012i \(-0.785909\pi\)
−0.782213 + 0.623012i \(0.785909\pi\)
\(762\) −28.9489 −1.04871
\(763\) 0.782994 0.0283463
\(764\) 140.585 5.08620
\(765\) −0.556410 −0.0201170
\(766\) −26.2988 −0.950216
\(767\) −0.337949 −0.0122026
\(768\) 127.925 4.61611
\(769\) 10.2971 0.371321 0.185661 0.982614i \(-0.440558\pi\)
0.185661 + 0.982614i \(0.440558\pi\)
\(770\) 4.74809 0.171109
\(771\) −3.29873 −0.118801
\(772\) −63.1585 −2.27312
\(773\) −40.3745 −1.45217 −0.726086 0.687604i \(-0.758662\pi\)
−0.726086 + 0.687604i \(0.758662\pi\)
\(774\) 4.02993 0.144853
\(775\) 6.52521 0.234392
\(776\) 145.864 5.23622
\(777\) −0.296456 −0.0106353
\(778\) −1.79820 −0.0644685
\(779\) 41.2045 1.47630
\(780\) −14.6837 −0.525761
\(781\) 29.6242 1.06004
\(782\) −10.0249 −0.358490
\(783\) −16.9671 −0.606356
\(784\) −118.726 −4.24020
\(785\) −10.3033 −0.367741
\(786\) −34.5551 −1.23254
\(787\) −30.9322 −1.10261 −0.551307 0.834303i \(-0.685871\pi\)
−0.551307 + 0.834303i \(0.685871\pi\)
\(788\) 130.991 4.66637
\(789\) −0.398822 −0.0141984
\(790\) −22.5149 −0.801043
\(791\) 0.591646 0.0210365
\(792\) 37.0766 1.31746
\(793\) 1.77383 0.0629906
\(794\) 86.2790 3.06193
\(795\) 1.52714 0.0541621
\(796\) −47.8310 −1.69533
\(797\) −51.6555 −1.82973 −0.914866 0.403758i \(-0.867704\pi\)
−0.914866 + 0.403758i \(0.867704\pi\)
\(798\) 5.21859 0.184736
\(799\) −1.65528 −0.0585597
\(800\) −27.0564 −0.956587
\(801\) 2.53942 0.0897259
\(802\) 34.0585 1.20265
\(803\) 93.5588 3.30162
\(804\) 40.7654 1.43768
\(805\) −1.11455 −0.0392829
\(806\) 30.0929 1.05998
\(807\) −17.9240 −0.630955
\(808\) 197.355 6.94293
\(809\) 35.2649 1.23985 0.619923 0.784662i \(-0.287164\pi\)
0.619923 + 0.784662i \(0.287164\pi\)
\(810\) 18.9728 0.666637
\(811\) 0.700052 0.0245821 0.0122911 0.999924i \(-0.496088\pi\)
0.0122911 + 0.999924i \(0.496088\pi\)
\(812\) −4.95783 −0.173986
\(813\) 14.7324 0.516686
\(814\) −11.1462 −0.390675
\(815\) −16.8917 −0.591689
\(816\) 24.5879 0.860749
\(817\) 10.2586 0.358902
\(818\) 80.2736 2.80670
\(819\) −0.285289 −0.00996879
\(820\) 55.3299 1.93220
\(821\) −44.8393 −1.56490 −0.782451 0.622712i \(-0.786031\pi\)
−0.782451 + 0.622712i \(0.786031\pi\)
\(822\) 16.3782 0.571256
\(823\) 13.9672 0.486867 0.243434 0.969918i \(-0.421726\pi\)
0.243434 + 0.969918i \(0.421726\pi\)
\(824\) 150.985 5.25982
\(825\) 9.27578 0.322941
\(826\) 0.161281 0.00561169
\(827\) −17.3792 −0.604335 −0.302168 0.953255i \(-0.597710\pi\)
−0.302168 + 0.953255i \(0.597710\pi\)
\(828\) −13.3982 −0.465619
\(829\) −26.9205 −0.934987 −0.467494 0.883996i \(-0.654843\pi\)
−0.467494 + 0.883996i \(0.654843\pi\)
\(830\) 26.0177 0.903087
\(831\) 37.7748 1.31039
\(832\) −67.7648 −2.34932
\(833\) −6.40058 −0.221767
\(834\) 85.3158 2.95424
\(835\) 10.1238 0.350349
\(836\) 145.296 5.02516
\(837\) −36.3953 −1.25801
\(838\) −3.84938 −0.132975
\(839\) 15.9222 0.549695 0.274847 0.961488i \(-0.411373\pi\)
0.274847 + 0.961488i \(0.411373\pi\)
\(840\) 4.55202 0.157060
\(841\) −19.7463 −0.680908
\(842\) −37.6154 −1.29631
\(843\) 8.10067 0.279002
\(844\) 113.332 3.90104
\(845\) −10.2405 −0.352285
\(846\) −2.98748 −0.102712
\(847\) −7.10212 −0.244032
\(848\) 16.9215 0.581086
\(849\) −13.2497 −0.454727
\(850\) −2.56843 −0.0880963
\(851\) 2.61643 0.0896901
\(852\) 43.7216 1.49788
\(853\) 4.35922 0.149257 0.0746285 0.997211i \(-0.476223\pi\)
0.0746285 + 0.997211i \(0.476223\pi\)
\(854\) −0.846535 −0.0289678
\(855\) −2.55633 −0.0874246
\(856\) −85.6849 −2.92865
\(857\) −9.40077 −0.321124 −0.160562 0.987026i \(-0.551331\pi\)
−0.160562 + 0.987026i \(0.551331\pi\)
\(858\) 42.7779 1.46041
\(859\) −7.95490 −0.271418 −0.135709 0.990749i \(-0.543331\pi\)
−0.135709 + 0.990749i \(0.543331\pi\)
\(860\) 13.7753 0.469735
\(861\) −4.28722 −0.146108
\(862\) −51.5512 −1.75584
\(863\) −10.3495 −0.352302 −0.176151 0.984363i \(-0.556365\pi\)
−0.176151 + 0.984363i \(0.556365\pi\)
\(864\) 150.911 5.13409
\(865\) 8.72403 0.296626
\(866\) 108.371 3.68260
\(867\) −25.0029 −0.849143
\(868\) −10.6348 −0.360969
\(869\) 48.5720 1.64769
\(870\) −13.0795 −0.443436
\(871\) −7.66091 −0.259580
\(872\) 28.2235 0.955769
\(873\) 8.52302 0.288460
\(874\) −46.0577 −1.55793
\(875\) −0.285554 −0.00965347
\(876\) 138.081 4.66532
\(877\) −7.22609 −0.244008 −0.122004 0.992530i \(-0.538932\pi\)
−0.122004 + 0.992530i \(0.538932\pi\)
\(878\) −3.50049 −0.118136
\(879\) 24.6264 0.830629
\(880\) 102.780 3.46472
\(881\) 9.10623 0.306797 0.153398 0.988164i \(-0.450978\pi\)
0.153398 + 0.988164i \(0.450978\pi\)
\(882\) −11.5518 −0.388971
\(883\) 48.6147 1.63602 0.818008 0.575207i \(-0.195079\pi\)
0.818008 + 0.575207i \(0.195079\pi\)
\(884\) −8.77141 −0.295014
\(885\) 0.315076 0.0105912
\(886\) 29.2755 0.983530
\(887\) −56.2648 −1.88919 −0.944593 0.328244i \(-0.893543\pi\)
−0.944593 + 0.328244i \(0.893543\pi\)
\(888\) −10.6859 −0.358597
\(889\) −1.92259 −0.0644816
\(890\) 11.7221 0.392927
\(891\) −40.9307 −1.37123
\(892\) 56.5621 1.89384
\(893\) −7.60491 −0.254489
\(894\) 53.3054 1.78280
\(895\) −4.29841 −0.143680
\(896\) 16.8877 0.564177
\(897\) −10.0416 −0.335278
\(898\) −109.653 −3.65916
\(899\) 19.8496 0.662021
\(900\) −3.43267 −0.114422
\(901\) 0.912248 0.0303914
\(902\) −161.192 −5.36711
\(903\) −1.06738 −0.0355201
\(904\) 21.3263 0.709301
\(905\) −6.53585 −0.217259
\(906\) 18.1614 0.603374
\(907\) 38.0406 1.26312 0.631560 0.775327i \(-0.282415\pi\)
0.631560 + 0.775327i \(0.282415\pi\)
\(908\) 142.364 4.72451
\(909\) 11.5317 0.382482
\(910\) −1.31691 −0.0436552
\(911\) 21.4882 0.711937 0.355969 0.934498i \(-0.384151\pi\)
0.355969 + 0.934498i \(0.384151\pi\)
\(912\) 112.965 3.74064
\(913\) −56.1288 −1.85759
\(914\) −48.3834 −1.60038
\(915\) −1.65378 −0.0546721
\(916\) −49.4239 −1.63301
\(917\) −2.29491 −0.0757847
\(918\) 14.3258 0.472821
\(919\) 34.3064 1.13166 0.565831 0.824521i \(-0.308555\pi\)
0.565831 + 0.824521i \(0.308555\pi\)
\(920\) −40.1748 −1.32452
\(921\) −16.8174 −0.554153
\(922\) 40.2857 1.32674
\(923\) −8.21645 −0.270448
\(924\) −15.1177 −0.497335
\(925\) 0.670341 0.0220407
\(926\) −100.509 −3.30293
\(927\) 8.82224 0.289760
\(928\) −82.3051 −2.70180
\(929\) −36.7886 −1.20699 −0.603497 0.797365i \(-0.706227\pi\)
−0.603497 + 0.797365i \(0.706227\pi\)
\(930\) −28.0561 −0.919997
\(931\) −29.4064 −0.963754
\(932\) 42.0732 1.37815
\(933\) 6.78689 0.222193
\(934\) 44.1849 1.44577
\(935\) 5.54095 0.181208
\(936\) −10.2834 −0.336124
\(937\) 57.2491 1.87025 0.935124 0.354321i \(-0.115288\pi\)
0.935124 + 0.354321i \(0.115288\pi\)
\(938\) 3.65605 0.119374
\(939\) −27.2535 −0.889385
\(940\) −10.2120 −0.333078
\(941\) 19.4172 0.632983 0.316491 0.948595i \(-0.397495\pi\)
0.316491 + 0.948595i \(0.397495\pi\)
\(942\) 44.3007 1.44340
\(943\) 37.8378 1.23217
\(944\) 3.49120 0.113629
\(945\) 1.59272 0.0518111
\(946\) −40.1316 −1.30479
\(947\) −34.1457 −1.10959 −0.554793 0.831988i \(-0.687203\pi\)
−0.554793 + 0.831988i \(0.687203\pi\)
\(948\) 71.6862 2.32826
\(949\) −25.9491 −0.842344
\(950\) −11.8002 −0.382849
\(951\) 39.7902 1.29029
\(952\) 2.71918 0.0881291
\(953\) −20.7739 −0.672933 −0.336467 0.941695i \(-0.609232\pi\)
−0.336467 + 0.941695i \(0.609232\pi\)
\(954\) 1.64644 0.0533054
\(955\) 24.6316 0.797061
\(956\) 108.551 3.51080
\(957\) 28.2168 0.912119
\(958\) 19.0016 0.613915
\(959\) 1.08773 0.0351246
\(960\) 63.1783 2.03907
\(961\) 11.5784 0.373496
\(962\) 3.09147 0.0996731
\(963\) −5.00667 −0.161338
\(964\) −89.3733 −2.87852
\(965\) −11.0658 −0.356222
\(966\) 4.79219 0.154186
\(967\) −55.1610 −1.77386 −0.886929 0.461906i \(-0.847166\pi\)
−0.886929 + 0.461906i \(0.847166\pi\)
\(968\) −256.000 −8.22817
\(969\) 6.09001 0.195639
\(970\) 39.3429 1.26322
\(971\) −3.33609 −0.107060 −0.0535301 0.998566i \(-0.517047\pi\)
−0.0535301 + 0.998566i \(0.517047\pi\)
\(972\) 35.0951 1.12568
\(973\) 5.66609 0.181646
\(974\) −28.2952 −0.906637
\(975\) −2.57270 −0.0823922
\(976\) −18.3247 −0.586558
\(977\) 21.0890 0.674697 0.337348 0.941380i \(-0.390470\pi\)
0.337348 + 0.941380i \(0.390470\pi\)
\(978\) 72.6283 2.32240
\(979\) −25.2885 −0.808225
\(980\) −39.4872 −1.26137
\(981\) 1.64913 0.0526528
\(982\) 14.8968 0.475375
\(983\) 43.9875 1.40298 0.701491 0.712678i \(-0.252518\pi\)
0.701491 + 0.712678i \(0.252518\pi\)
\(984\) −154.536 −4.92642
\(985\) 22.9506 0.731268
\(986\) −7.81312 −0.248820
\(987\) 0.791273 0.0251865
\(988\) −40.2987 −1.28207
\(989\) 9.42038 0.299551
\(990\) 10.0004 0.317833
\(991\) 45.5447 1.44678 0.723388 0.690442i \(-0.242584\pi\)
0.723388 + 0.690442i \(0.242584\pi\)
\(992\) −176.549 −5.60542
\(993\) −32.2683 −1.02400
\(994\) 3.92118 0.124372
\(995\) −8.38036 −0.265675
\(996\) −82.8390 −2.62485
\(997\) 53.0497 1.68010 0.840051 0.542508i \(-0.182525\pi\)
0.840051 + 0.542508i \(0.182525\pi\)
\(998\) 18.4401 0.583710
\(999\) −3.73893 −0.118294
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 \(a_p\))