Properties

Label 8035.2.a.e.1.6
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 1.6
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.62009 q^{2}\) \(-2.60275 q^{3}\) \(+4.86488 q^{4}\) \(+1.00000 q^{5}\) \(+6.81943 q^{6}\) \(+0.626563 q^{7}\) \(-7.50624 q^{8}\) \(+3.77428 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.62009 q^{2}\) \(-2.60275 q^{3}\) \(+4.86488 q^{4}\) \(+1.00000 q^{5}\) \(+6.81943 q^{6}\) \(+0.626563 q^{7}\) \(-7.50624 q^{8}\) \(+3.77428 q^{9}\) \(-2.62009 q^{10}\) \(+6.10091 q^{11}\) \(-12.6620 q^{12}\) \(+4.02402 q^{13}\) \(-1.64165 q^{14}\) \(-2.60275 q^{15}\) \(+9.93729 q^{16}\) \(-3.04556 q^{17}\) \(-9.88896 q^{18}\) \(+5.64003 q^{19}\) \(+4.86488 q^{20}\) \(-1.63079 q^{21}\) \(-15.9849 q^{22}\) \(-1.49392 q^{23}\) \(+19.5368 q^{24}\) \(+1.00000 q^{25}\) \(-10.5433 q^{26}\) \(-2.01526 q^{27}\) \(+3.04816 q^{28}\) \(-1.31972 q^{29}\) \(+6.81943 q^{30}\) \(-7.69551 q^{31}\) \(-11.0241 q^{32}\) \(-15.8791 q^{33}\) \(+7.97965 q^{34}\) \(+0.626563 q^{35}\) \(+18.3614 q^{36}\) \(-0.882299 q^{37}\) \(-14.7774 q^{38}\) \(-10.4735 q^{39}\) \(-7.50624 q^{40}\) \(+9.53432 q^{41}\) \(+4.27281 q^{42}\) \(-1.33708 q^{43}\) \(+29.6802 q^{44}\) \(+3.77428 q^{45}\) \(+3.91421 q^{46}\) \(+2.24303 q^{47}\) \(-25.8642 q^{48}\) \(-6.60742 q^{49}\) \(-2.62009 q^{50}\) \(+7.92682 q^{51}\) \(+19.5763 q^{52}\) \(+8.07900 q^{53}\) \(+5.28016 q^{54}\) \(+6.10091 q^{55}\) \(-4.70314 q^{56}\) \(-14.6796 q^{57}\) \(+3.45778 q^{58}\) \(+5.16401 q^{59}\) \(-12.6620 q^{60}\) \(-2.24592 q^{61}\) \(+20.1629 q^{62}\) \(+2.36483 q^{63}\) \(+9.00961 q^{64}\) \(+4.02402 q^{65}\) \(+41.6047 q^{66}\) \(-10.6801 q^{67}\) \(-14.8163 q^{68}\) \(+3.88829 q^{69}\) \(-1.64165 q^{70}\) \(+6.13281 q^{71}\) \(-28.3307 q^{72}\) \(-2.65449 q^{73}\) \(+2.31170 q^{74}\) \(-2.60275 q^{75}\) \(+27.4381 q^{76}\) \(+3.82261 q^{77}\) \(+27.4415 q^{78}\) \(+5.36540 q^{79}\) \(+9.93729 q^{80}\) \(-6.07764 q^{81}\) \(-24.9808 q^{82}\) \(+1.34079 q^{83}\) \(-7.93357 q^{84}\) \(-3.04556 q^{85}\) \(+3.50328 q^{86}\) \(+3.43489 q^{87}\) \(-45.7949 q^{88}\) \(+7.31454 q^{89}\) \(-9.88896 q^{90}\) \(+2.52130 q^{91}\) \(-7.26774 q^{92}\) \(+20.0295 q^{93}\) \(-5.87695 q^{94}\) \(+5.64003 q^{95}\) \(+28.6930 q^{96}\) \(+1.91629 q^{97}\) \(+17.3120 q^{98}\) \(+23.0265 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62009 −1.85268 −0.926342 0.376683i \(-0.877065\pi\)
−0.926342 + 0.376683i \(0.877065\pi\)
\(3\) −2.60275 −1.50270 −0.751348 0.659906i \(-0.770596\pi\)
−0.751348 + 0.659906i \(0.770596\pi\)
\(4\) 4.86488 2.43244
\(5\) 1.00000 0.447214
\(6\) 6.81943 2.78402
\(7\) 0.626563 0.236819 0.118409 0.992965i \(-0.462220\pi\)
0.118409 + 0.992965i \(0.462220\pi\)
\(8\) −7.50624 −2.65386
\(9\) 3.77428 1.25809
\(10\) −2.62009 −0.828546
\(11\) 6.10091 1.83949 0.919747 0.392513i \(-0.128394\pi\)
0.919747 + 0.392513i \(0.128394\pi\)
\(12\) −12.6620 −3.65522
\(13\) 4.02402 1.11606 0.558031 0.829820i \(-0.311557\pi\)
0.558031 + 0.829820i \(0.311557\pi\)
\(14\) −1.64165 −0.438750
\(15\) −2.60275 −0.672026
\(16\) 9.93729 2.48432
\(17\) −3.04556 −0.738658 −0.369329 0.929299i \(-0.620412\pi\)
−0.369329 + 0.929299i \(0.620412\pi\)
\(18\) −9.88896 −2.33085
\(19\) 5.64003 1.29391 0.646956 0.762527i \(-0.276042\pi\)
0.646956 + 0.762527i \(0.276042\pi\)
\(20\) 4.86488 1.08782
\(21\) −1.63079 −0.355866
\(22\) −15.9849 −3.40800
\(23\) −1.49392 −0.311504 −0.155752 0.987796i \(-0.549780\pi\)
−0.155752 + 0.987796i \(0.549780\pi\)
\(24\) 19.5368 3.98794
\(25\) 1.00000 0.200000
\(26\) −10.5433 −2.06771
\(27\) −2.01526 −0.387837
\(28\) 3.04816 0.576047
\(29\) −1.31972 −0.245065 −0.122533 0.992464i \(-0.539102\pi\)
−0.122533 + 0.992464i \(0.539102\pi\)
\(30\) 6.81943 1.24505
\(31\) −7.69551 −1.38215 −0.691077 0.722781i \(-0.742864\pi\)
−0.691077 + 0.722781i \(0.742864\pi\)
\(32\) −11.0241 −1.94881
\(33\) −15.8791 −2.76420
\(34\) 7.97965 1.36850
\(35\) 0.626563 0.105909
\(36\) 18.3614 3.06024
\(37\) −0.882299 −0.145049 −0.0725245 0.997367i \(-0.523106\pi\)
−0.0725245 + 0.997367i \(0.523106\pi\)
\(38\) −14.7774 −2.39721
\(39\) −10.4735 −1.67710
\(40\) −7.50624 −1.18684
\(41\) 9.53432 1.48901 0.744505 0.667617i \(-0.232686\pi\)
0.744505 + 0.667617i \(0.232686\pi\)
\(42\) 4.27281 0.659308
\(43\) −1.33708 −0.203903 −0.101952 0.994789i \(-0.532509\pi\)
−0.101952 + 0.994789i \(0.532509\pi\)
\(44\) 29.6802 4.47446
\(45\) 3.77428 0.562637
\(46\) 3.91421 0.577118
\(47\) 2.24303 0.327180 0.163590 0.986528i \(-0.447693\pi\)
0.163590 + 0.986528i \(0.447693\pi\)
\(48\) −25.8642 −3.73318
\(49\) −6.60742 −0.943917
\(50\) −2.62009 −0.370537
\(51\) 7.92682 1.10998
\(52\) 19.5763 2.71475
\(53\) 8.07900 1.10974 0.554868 0.831939i \(-0.312769\pi\)
0.554868 + 0.831939i \(0.312769\pi\)
\(54\) 5.28016 0.718539
\(55\) 6.10091 0.822646
\(56\) −4.70314 −0.628483
\(57\) −14.6796 −1.94436
\(58\) 3.45778 0.454028
\(59\) 5.16401 0.672297 0.336149 0.941809i \(-0.390876\pi\)
0.336149 + 0.941809i \(0.390876\pi\)
\(60\) −12.6620 −1.63466
\(61\) −2.24592 −0.287560 −0.143780 0.989610i \(-0.545926\pi\)
−0.143780 + 0.989610i \(0.545926\pi\)
\(62\) 20.1629 2.56070
\(63\) 2.36483 0.297940
\(64\) 9.00961 1.12620
\(65\) 4.02402 0.499118
\(66\) 41.6047 5.12119
\(67\) −10.6801 −1.30478 −0.652391 0.757883i \(-0.726234\pi\)
−0.652391 + 0.757883i \(0.726234\pi\)
\(68\) −14.8163 −1.79674
\(69\) 3.88829 0.468096
\(70\) −1.64165 −0.196215
\(71\) 6.13281 0.727831 0.363915 0.931432i \(-0.381440\pi\)
0.363915 + 0.931432i \(0.381440\pi\)
\(72\) −28.3307 −3.33880
\(73\) −2.65449 −0.310685 −0.155343 0.987861i \(-0.549648\pi\)
−0.155343 + 0.987861i \(0.549648\pi\)
\(74\) 2.31170 0.268730
\(75\) −2.60275 −0.300539
\(76\) 27.4381 3.14736
\(77\) 3.82261 0.435626
\(78\) 27.4415 3.10714
\(79\) 5.36540 0.603654 0.301827 0.953363i \(-0.402403\pi\)
0.301827 + 0.953363i \(0.402403\pi\)
\(80\) 9.93729 1.11102
\(81\) −6.07764 −0.675294
\(82\) −24.9808 −2.75867
\(83\) 1.34079 0.147171 0.0735854 0.997289i \(-0.476556\pi\)
0.0735854 + 0.997289i \(0.476556\pi\)
\(84\) −7.93357 −0.865624
\(85\) −3.04556 −0.330338
\(86\) 3.50328 0.377768
\(87\) 3.43489 0.368258
\(88\) −45.7949 −4.88175
\(89\) 7.31454 0.775340 0.387670 0.921798i \(-0.373280\pi\)
0.387670 + 0.921798i \(0.373280\pi\)
\(90\) −9.88896 −1.04239
\(91\) 2.52130 0.264304
\(92\) −7.26774 −0.757714
\(93\) 20.0295 2.07696
\(94\) −5.87695 −0.606161
\(95\) 5.64003 0.578655
\(96\) 28.6930 2.92846
\(97\) 1.91629 0.194570 0.0972848 0.995257i \(-0.468984\pi\)
0.0972848 + 0.995257i \(0.468984\pi\)
\(98\) 17.3120 1.74878
\(99\) 23.0265 2.31426
\(100\) 4.86488 0.486488
\(101\) 0.192878 0.0191921 0.00959606 0.999954i \(-0.496945\pi\)
0.00959606 + 0.999954i \(0.496945\pi\)
\(102\) −20.7690 −2.05644
\(103\) 8.23560 0.811478 0.405739 0.913989i \(-0.367014\pi\)
0.405739 + 0.913989i \(0.367014\pi\)
\(104\) −30.2052 −2.96187
\(105\) −1.63079 −0.159148
\(106\) −21.1677 −2.05599
\(107\) 3.98327 0.385077 0.192539 0.981289i \(-0.438328\pi\)
0.192539 + 0.981289i \(0.438328\pi\)
\(108\) −9.80399 −0.943389
\(109\) −8.39078 −0.803691 −0.401845 0.915708i \(-0.631631\pi\)
−0.401845 + 0.915708i \(0.631631\pi\)
\(110\) −15.9849 −1.52410
\(111\) 2.29640 0.217965
\(112\) 6.22634 0.588334
\(113\) 4.04417 0.380443 0.190222 0.981741i \(-0.439079\pi\)
0.190222 + 0.981741i \(0.439079\pi\)
\(114\) 38.4618 3.60228
\(115\) −1.49392 −0.139309
\(116\) −6.42026 −0.596106
\(117\) 15.1878 1.40411
\(118\) −13.5302 −1.24555
\(119\) −1.90824 −0.174928
\(120\) 19.5368 1.78346
\(121\) 26.2211 2.38374
\(122\) 5.88451 0.532759
\(123\) −24.8154 −2.23753
\(124\) −37.4377 −3.36201
\(125\) 1.00000 0.0894427
\(126\) −6.19606 −0.551989
\(127\) −3.96917 −0.352206 −0.176103 0.984372i \(-0.556349\pi\)
−0.176103 + 0.984372i \(0.556349\pi\)
\(128\) −1.55777 −0.137689
\(129\) 3.48008 0.306404
\(130\) −10.5433 −0.924708
\(131\) 3.12270 0.272832 0.136416 0.990652i \(-0.456442\pi\)
0.136416 + 0.990652i \(0.456442\pi\)
\(132\) −77.2499 −6.72374
\(133\) 3.53384 0.306423
\(134\) 27.9828 2.41735
\(135\) −2.01526 −0.173446
\(136\) 22.8607 1.96029
\(137\) 1.86729 0.159533 0.0797666 0.996814i \(-0.474583\pi\)
0.0797666 + 0.996814i \(0.474583\pi\)
\(138\) −10.1877 −0.867233
\(139\) 16.5352 1.40250 0.701248 0.712917i \(-0.252626\pi\)
0.701248 + 0.712917i \(0.252626\pi\)
\(140\) 3.04816 0.257616
\(141\) −5.83804 −0.491652
\(142\) −16.0685 −1.34844
\(143\) 24.5502 2.05299
\(144\) 37.5061 3.12551
\(145\) −1.31972 −0.109596
\(146\) 6.95502 0.575601
\(147\) 17.1974 1.41842
\(148\) −4.29228 −0.352823
\(149\) −6.30510 −0.516534 −0.258267 0.966074i \(-0.583151\pi\)
−0.258267 + 0.966074i \(0.583151\pi\)
\(150\) 6.81943 0.556804
\(151\) 8.06380 0.656223 0.328111 0.944639i \(-0.393588\pi\)
0.328111 + 0.944639i \(0.393588\pi\)
\(152\) −42.3354 −3.43386
\(153\) −11.4948 −0.929301
\(154\) −10.0156 −0.807078
\(155\) −7.69551 −0.618118
\(156\) −50.9522 −4.07944
\(157\) 1.51693 0.121064 0.0605321 0.998166i \(-0.480720\pi\)
0.0605321 + 0.998166i \(0.480720\pi\)
\(158\) −14.0578 −1.11838
\(159\) −21.0276 −1.66759
\(160\) −11.0241 −0.871533
\(161\) −0.936036 −0.0737700
\(162\) 15.9240 1.25111
\(163\) 6.94383 0.543883 0.271941 0.962314i \(-0.412334\pi\)
0.271941 + 0.962314i \(0.412334\pi\)
\(164\) 46.3833 3.62193
\(165\) −15.8791 −1.23619
\(166\) −3.51299 −0.272661
\(167\) 18.1414 1.40382 0.701910 0.712266i \(-0.252331\pi\)
0.701910 + 0.712266i \(0.252331\pi\)
\(168\) 12.2411 0.944419
\(169\) 3.19270 0.245593
\(170\) 7.97965 0.612011
\(171\) 21.2871 1.62786
\(172\) −6.50474 −0.495982
\(173\) 3.99571 0.303788 0.151894 0.988397i \(-0.451463\pi\)
0.151894 + 0.988397i \(0.451463\pi\)
\(174\) −8.99971 −0.682267
\(175\) 0.626563 0.0473637
\(176\) 60.6265 4.56989
\(177\) −13.4406 −1.01026
\(178\) −19.1648 −1.43646
\(179\) 5.19318 0.388156 0.194078 0.980986i \(-0.437828\pi\)
0.194078 + 0.980986i \(0.437828\pi\)
\(180\) 18.3614 1.36858
\(181\) −9.05641 −0.673157 −0.336579 0.941655i \(-0.609270\pi\)
−0.336579 + 0.941655i \(0.609270\pi\)
\(182\) −6.60604 −0.489672
\(183\) 5.84555 0.432116
\(184\) 11.2137 0.826687
\(185\) −0.882299 −0.0648679
\(186\) −52.4790 −3.84795
\(187\) −18.5807 −1.35876
\(188\) 10.9121 0.795845
\(189\) −1.26269 −0.0918470
\(190\) −14.7774 −1.07206
\(191\) 5.36571 0.388249 0.194125 0.980977i \(-0.437813\pi\)
0.194125 + 0.980977i \(0.437813\pi\)
\(192\) −23.4497 −1.69234
\(193\) 21.3624 1.53770 0.768849 0.639431i \(-0.220830\pi\)
0.768849 + 0.639431i \(0.220830\pi\)
\(194\) −5.02085 −0.360476
\(195\) −10.4735 −0.750022
\(196\) −32.1443 −2.29602
\(197\) 20.9798 1.49475 0.747375 0.664402i \(-0.231314\pi\)
0.747375 + 0.664402i \(0.231314\pi\)
\(198\) −60.3317 −4.28758
\(199\) 5.96625 0.422936 0.211468 0.977385i \(-0.432176\pi\)
0.211468 + 0.977385i \(0.432176\pi\)
\(200\) −7.50624 −0.530772
\(201\) 27.7976 1.96069
\(202\) −0.505359 −0.0355569
\(203\) −0.826886 −0.0580360
\(204\) 38.5630 2.69995
\(205\) 9.53432 0.665906
\(206\) −21.5780 −1.50341
\(207\) −5.63848 −0.391901
\(208\) 39.9878 2.77266
\(209\) 34.4093 2.38014
\(210\) 4.27281 0.294852
\(211\) −24.5387 −1.68931 −0.844655 0.535311i \(-0.820195\pi\)
−0.844655 + 0.535311i \(0.820195\pi\)
\(212\) 39.3033 2.69936
\(213\) −15.9621 −1.09371
\(214\) −10.4365 −0.713427
\(215\) −1.33708 −0.0911883
\(216\) 15.1270 1.02926
\(217\) −4.82173 −0.327320
\(218\) 21.9846 1.48899
\(219\) 6.90897 0.466865
\(220\) 29.6802 2.00104
\(221\) −12.2554 −0.824387
\(222\) −6.01677 −0.403819
\(223\) −2.86233 −0.191676 −0.0958380 0.995397i \(-0.530553\pi\)
−0.0958380 + 0.995397i \(0.530553\pi\)
\(224\) −6.90731 −0.461514
\(225\) 3.77428 0.251619
\(226\) −10.5961 −0.704841
\(227\) −18.0424 −1.19752 −0.598759 0.800929i \(-0.704339\pi\)
−0.598759 + 0.800929i \(0.704339\pi\)
\(228\) −71.4143 −4.72953
\(229\) 28.8321 1.90528 0.952640 0.304102i \(-0.0983563\pi\)
0.952640 + 0.304102i \(0.0983563\pi\)
\(230\) 3.91421 0.258095
\(231\) −9.94927 −0.654614
\(232\) 9.90611 0.650368
\(233\) −20.5707 −1.34763 −0.673815 0.738901i \(-0.735345\pi\)
−0.673815 + 0.738901i \(0.735345\pi\)
\(234\) −39.7933 −2.60137
\(235\) 2.24303 0.146319
\(236\) 25.1223 1.63532
\(237\) −13.9648 −0.907109
\(238\) 4.99976 0.324086
\(239\) −5.97529 −0.386509 −0.193255 0.981149i \(-0.561904\pi\)
−0.193255 + 0.981149i \(0.561904\pi\)
\(240\) −25.8642 −1.66953
\(241\) 12.3264 0.794014 0.397007 0.917816i \(-0.370049\pi\)
0.397007 + 0.917816i \(0.370049\pi\)
\(242\) −68.7016 −4.41631
\(243\) 21.8643 1.40260
\(244\) −10.9261 −0.699473
\(245\) −6.60742 −0.422132
\(246\) 65.0186 4.14544
\(247\) 22.6956 1.44408
\(248\) 57.7644 3.66804
\(249\) −3.48974 −0.221153
\(250\) −2.62009 −0.165709
\(251\) −29.1954 −1.84280 −0.921398 0.388619i \(-0.872952\pi\)
−0.921398 + 0.388619i \(0.872952\pi\)
\(252\) 11.5046 0.724722
\(253\) −9.11427 −0.573009
\(254\) 10.3996 0.652527
\(255\) 7.92682 0.496397
\(256\) −13.9377 −0.871107
\(257\) 25.1420 1.56831 0.784157 0.620562i \(-0.213096\pi\)
0.784157 + 0.620562i \(0.213096\pi\)
\(258\) −9.11814 −0.567671
\(259\) −0.552816 −0.0343503
\(260\) 19.5763 1.21407
\(261\) −4.98098 −0.308315
\(262\) −8.18177 −0.505471
\(263\) −1.20312 −0.0741873 −0.0370937 0.999312i \(-0.511810\pi\)
−0.0370937 + 0.999312i \(0.511810\pi\)
\(264\) 119.192 7.33579
\(265\) 8.07900 0.496289
\(266\) −9.25898 −0.567704
\(267\) −19.0379 −1.16510
\(268\) −51.9574 −3.17380
\(269\) 19.0257 1.16002 0.580008 0.814611i \(-0.303049\pi\)
0.580008 + 0.814611i \(0.303049\pi\)
\(270\) 5.28016 0.321340
\(271\) −27.5900 −1.67597 −0.837987 0.545690i \(-0.816267\pi\)
−0.837987 + 0.545690i \(0.816267\pi\)
\(272\) −30.2646 −1.83506
\(273\) −6.56231 −0.397169
\(274\) −4.89247 −0.295565
\(275\) 6.10091 0.367899
\(276\) 18.9161 1.13861
\(277\) −19.5689 −1.17578 −0.587891 0.808940i \(-0.700041\pi\)
−0.587891 + 0.808940i \(0.700041\pi\)
\(278\) −43.3237 −2.59838
\(279\) −29.0450 −1.73888
\(280\) −4.70314 −0.281066
\(281\) −14.5771 −0.869597 −0.434799 0.900528i \(-0.643180\pi\)
−0.434799 + 0.900528i \(0.643180\pi\)
\(282\) 15.2962 0.910876
\(283\) −31.3656 −1.86449 −0.932247 0.361823i \(-0.882155\pi\)
−0.932247 + 0.361823i \(0.882155\pi\)
\(284\) 29.8354 1.77040
\(285\) −14.6796 −0.869542
\(286\) −64.3236 −3.80354
\(287\) 5.97386 0.352626
\(288\) −41.6081 −2.45178
\(289\) −7.72455 −0.454385
\(290\) 3.45778 0.203048
\(291\) −4.98761 −0.292379
\(292\) −12.9138 −0.755723
\(293\) −5.04237 −0.294578 −0.147289 0.989093i \(-0.547055\pi\)
−0.147289 + 0.989093i \(0.547055\pi\)
\(294\) −45.0588 −2.62788
\(295\) 5.16401 0.300661
\(296\) 6.62275 0.384940
\(297\) −12.2949 −0.713423
\(298\) 16.5199 0.956974
\(299\) −6.01156 −0.347657
\(300\) −12.6620 −0.731043
\(301\) −0.837767 −0.0482881
\(302\) −21.1279 −1.21577
\(303\) −0.502013 −0.0288399
\(304\) 56.0466 3.21449
\(305\) −2.24592 −0.128601
\(306\) 30.1175 1.72170
\(307\) −2.70768 −0.154535 −0.0772677 0.997010i \(-0.524620\pi\)
−0.0772677 + 0.997010i \(0.524620\pi\)
\(308\) 18.5965 1.05963
\(309\) −21.4352 −1.21940
\(310\) 20.1629 1.14518
\(311\) −16.1879 −0.917932 −0.458966 0.888454i \(-0.651780\pi\)
−0.458966 + 0.888454i \(0.651780\pi\)
\(312\) 78.6166 4.45079
\(313\) 1.97419 0.111588 0.0557938 0.998442i \(-0.482231\pi\)
0.0557938 + 0.998442i \(0.482231\pi\)
\(314\) −3.97450 −0.224294
\(315\) 2.36483 0.133243
\(316\) 26.1020 1.46835
\(317\) −8.70355 −0.488840 −0.244420 0.969669i \(-0.578598\pi\)
−0.244420 + 0.969669i \(0.578598\pi\)
\(318\) 55.0942 3.08953
\(319\) −8.05147 −0.450796
\(320\) 9.00961 0.503652
\(321\) −10.3674 −0.578654
\(322\) 2.45250 0.136672
\(323\) −17.1771 −0.955758
\(324\) −29.5670 −1.64261
\(325\) 4.02402 0.223212
\(326\) −18.1935 −1.00764
\(327\) 21.8391 1.20770
\(328\) −71.5669 −3.95162
\(329\) 1.40540 0.0774823
\(330\) 41.6047 2.29026
\(331\) 26.5724 1.46055 0.730277 0.683151i \(-0.239391\pi\)
0.730277 + 0.683151i \(0.239391\pi\)
\(332\) 6.52278 0.357984
\(333\) −3.33004 −0.182485
\(334\) −47.5320 −2.60084
\(335\) −10.6801 −0.583516
\(336\) −16.2056 −0.884087
\(337\) 25.7612 1.40330 0.701650 0.712522i \(-0.252447\pi\)
0.701650 + 0.712522i \(0.252447\pi\)
\(338\) −8.36518 −0.455006
\(339\) −10.5259 −0.571691
\(340\) −14.8163 −0.803526
\(341\) −46.9496 −2.54246
\(342\) −55.7741 −3.01592
\(343\) −8.52591 −0.460356
\(344\) 10.0365 0.541130
\(345\) 3.88829 0.209339
\(346\) −10.4691 −0.562824
\(347\) −23.7742 −1.27627 −0.638134 0.769926i \(-0.720293\pi\)
−0.638134 + 0.769926i \(0.720293\pi\)
\(348\) 16.7103 0.895766
\(349\) −7.33975 −0.392888 −0.196444 0.980515i \(-0.562939\pi\)
−0.196444 + 0.980515i \(0.562939\pi\)
\(350\) −1.64165 −0.0877501
\(351\) −8.10943 −0.432849
\(352\) −67.2571 −3.58482
\(353\) 26.7665 1.42464 0.712320 0.701855i \(-0.247645\pi\)
0.712320 + 0.701855i \(0.247645\pi\)
\(354\) 35.2156 1.87169
\(355\) 6.13281 0.325496
\(356\) 35.5844 1.88597
\(357\) 4.96666 0.262863
\(358\) −13.6066 −0.719131
\(359\) −32.7230 −1.72706 −0.863528 0.504301i \(-0.831750\pi\)
−0.863528 + 0.504301i \(0.831750\pi\)
\(360\) −28.3307 −1.49316
\(361\) 12.8099 0.674208
\(362\) 23.7286 1.24715
\(363\) −68.2468 −3.58203
\(364\) 12.2658 0.642904
\(365\) −2.65449 −0.138943
\(366\) −15.3159 −0.800574
\(367\) −8.97600 −0.468543 −0.234272 0.972171i \(-0.575271\pi\)
−0.234272 + 0.972171i \(0.575271\pi\)
\(368\) −14.8455 −0.773876
\(369\) 35.9852 1.87331
\(370\) 2.31170 0.120180
\(371\) 5.06200 0.262806
\(372\) 97.4409 5.05207
\(373\) −18.5307 −0.959482 −0.479741 0.877410i \(-0.659269\pi\)
−0.479741 + 0.877410i \(0.659269\pi\)
\(374\) 48.6831 2.51735
\(375\) −2.60275 −0.134405
\(376\) −16.8367 −0.868289
\(377\) −5.31056 −0.273508
\(378\) 3.30836 0.170163
\(379\) 18.2303 0.936426 0.468213 0.883616i \(-0.344898\pi\)
0.468213 + 0.883616i \(0.344898\pi\)
\(380\) 27.4381 1.40754
\(381\) 10.3307 0.529259
\(382\) −14.0586 −0.719303
\(383\) 12.5082 0.639137 0.319568 0.947563i \(-0.396462\pi\)
0.319568 + 0.947563i \(0.396462\pi\)
\(384\) 4.05448 0.206904
\(385\) 3.82261 0.194818
\(386\) −55.9714 −2.84887
\(387\) −5.04653 −0.256529
\(388\) 9.32251 0.473279
\(389\) 22.6690 1.14936 0.574681 0.818377i \(-0.305126\pi\)
0.574681 + 0.818377i \(0.305126\pi\)
\(390\) 27.4415 1.38955
\(391\) 4.54983 0.230095
\(392\) 49.5969 2.50502
\(393\) −8.12760 −0.409983
\(394\) −54.9690 −2.76930
\(395\) 5.36540 0.269962
\(396\) 112.021 5.62929
\(397\) −33.3210 −1.67233 −0.836167 0.548475i \(-0.815209\pi\)
−0.836167 + 0.548475i \(0.815209\pi\)
\(398\) −15.6321 −0.783568
\(399\) −9.19768 −0.460460
\(400\) 9.93729 0.496864
\(401\) 30.3939 1.51780 0.758898 0.651209i \(-0.225738\pi\)
0.758898 + 0.651209i \(0.225738\pi\)
\(402\) −72.8322 −3.63254
\(403\) −30.9669 −1.54257
\(404\) 0.938330 0.0466837
\(405\) −6.07764 −0.302000
\(406\) 2.16652 0.107522
\(407\) −5.38282 −0.266817
\(408\) −59.5007 −2.94572
\(409\) −31.4797 −1.55657 −0.778285 0.627911i \(-0.783910\pi\)
−0.778285 + 0.627911i \(0.783910\pi\)
\(410\) −24.9808 −1.23371
\(411\) −4.86007 −0.239730
\(412\) 40.0652 1.97387
\(413\) 3.23558 0.159213
\(414\) 14.7733 0.726069
\(415\) 1.34079 0.0658168
\(416\) −44.3612 −2.17499
\(417\) −43.0369 −2.10753
\(418\) −90.1555 −4.40965
\(419\) 15.0905 0.737220 0.368610 0.929584i \(-0.379834\pi\)
0.368610 + 0.929584i \(0.379834\pi\)
\(420\) −7.93357 −0.387119
\(421\) −0.655818 −0.0319626 −0.0159813 0.999872i \(-0.505087\pi\)
−0.0159813 + 0.999872i \(0.505087\pi\)
\(422\) 64.2935 3.12976
\(423\) 8.46584 0.411623
\(424\) −60.6429 −2.94508
\(425\) −3.04556 −0.147732
\(426\) 41.8223 2.02630
\(427\) −1.40721 −0.0680997
\(428\) 19.3781 0.936677
\(429\) −63.8978 −3.08501
\(430\) 3.50328 0.168943
\(431\) 15.9369 0.767655 0.383828 0.923405i \(-0.374606\pi\)
0.383828 + 0.923405i \(0.374606\pi\)
\(432\) −20.0262 −0.963511
\(433\) 23.7279 1.14029 0.570146 0.821544i \(-0.306887\pi\)
0.570146 + 0.821544i \(0.306887\pi\)
\(434\) 12.6334 0.606421
\(435\) 3.43489 0.164690
\(436\) −40.8201 −1.95493
\(437\) −8.42576 −0.403059
\(438\) −18.1021 −0.864954
\(439\) −13.5348 −0.645979 −0.322989 0.946403i \(-0.604688\pi\)
−0.322989 + 0.946403i \(0.604688\pi\)
\(440\) −45.7949 −2.18319
\(441\) −24.9383 −1.18754
\(442\) 32.1103 1.52733
\(443\) 37.8143 1.79661 0.898306 0.439371i \(-0.144799\pi\)
0.898306 + 0.439371i \(0.144799\pi\)
\(444\) 11.1717 0.530186
\(445\) 7.31454 0.346743
\(446\) 7.49958 0.355115
\(447\) 16.4106 0.776193
\(448\) 5.64509 0.266705
\(449\) −26.5442 −1.25270 −0.626349 0.779542i \(-0.715452\pi\)
−0.626349 + 0.779542i \(0.715452\pi\)
\(450\) −9.88896 −0.466170
\(451\) 58.1680 2.73902
\(452\) 19.6744 0.925405
\(453\) −20.9880 −0.986103
\(454\) 47.2728 2.21862
\(455\) 2.52130 0.118200
\(456\) 110.188 5.16004
\(457\) 37.8726 1.77161 0.885804 0.464060i \(-0.153608\pi\)
0.885804 + 0.464060i \(0.153608\pi\)
\(458\) −75.5427 −3.52988
\(459\) 6.13760 0.286478
\(460\) −7.26774 −0.338860
\(461\) −15.8036 −0.736049 −0.368024 0.929816i \(-0.619966\pi\)
−0.368024 + 0.929816i \(0.619966\pi\)
\(462\) 26.0680 1.21279
\(463\) −12.7170 −0.591008 −0.295504 0.955342i \(-0.595488\pi\)
−0.295504 + 0.955342i \(0.595488\pi\)
\(464\) −13.1144 −0.608821
\(465\) 20.0295 0.928844
\(466\) 53.8970 2.49673
\(467\) −30.2718 −1.40081 −0.700407 0.713744i \(-0.746998\pi\)
−0.700407 + 0.713744i \(0.746998\pi\)
\(468\) 73.8867 3.41541
\(469\) −6.69176 −0.308997
\(470\) −5.87695 −0.271083
\(471\) −3.94818 −0.181923
\(472\) −38.7624 −1.78418
\(473\) −8.15742 −0.375078
\(474\) 36.5889 1.68059
\(475\) 5.64003 0.258782
\(476\) −9.28335 −0.425502
\(477\) 30.4924 1.39615
\(478\) 15.6558 0.716079
\(479\) 27.4045 1.25214 0.626072 0.779766i \(-0.284662\pi\)
0.626072 + 0.779766i \(0.284662\pi\)
\(480\) 28.6930 1.30965
\(481\) −3.55038 −0.161884
\(482\) −32.2963 −1.47106
\(483\) 2.43626 0.110854
\(484\) 127.562 5.79829
\(485\) 1.91629 0.0870142
\(486\) −57.2865 −2.59857
\(487\) −13.9645 −0.632792 −0.316396 0.948627i \(-0.602473\pi\)
−0.316396 + 0.948627i \(0.602473\pi\)
\(488\) 16.8584 0.763144
\(489\) −18.0730 −0.817290
\(490\) 17.3120 0.782078
\(491\) −6.99845 −0.315836 −0.157918 0.987452i \(-0.550478\pi\)
−0.157918 + 0.987452i \(0.550478\pi\)
\(492\) −120.724 −5.44265
\(493\) 4.01928 0.181019
\(494\) −59.4645 −2.67543
\(495\) 23.0265 1.03497
\(496\) −76.4725 −3.43372
\(497\) 3.84259 0.172364
\(498\) 9.14343 0.409727
\(499\) −31.3138 −1.40180 −0.700900 0.713259i \(-0.747218\pi\)
−0.700900 + 0.713259i \(0.747218\pi\)
\(500\) 4.86488 0.217564
\(501\) −47.2173 −2.10951
\(502\) 76.4946 3.41412
\(503\) 1.68753 0.0752434 0.0376217 0.999292i \(-0.488022\pi\)
0.0376217 + 0.999292i \(0.488022\pi\)
\(504\) −17.7510 −0.790691
\(505\) 0.192878 0.00858298
\(506\) 23.8802 1.06161
\(507\) −8.30980 −0.369051
\(508\) −19.3095 −0.856721
\(509\) 44.6396 1.97862 0.989309 0.145838i \(-0.0465877\pi\)
0.989309 + 0.145838i \(0.0465877\pi\)
\(510\) −20.7690 −0.919667
\(511\) −1.66321 −0.0735761
\(512\) 39.6336 1.75158
\(513\) −11.3661 −0.501826
\(514\) −65.8743 −2.90559
\(515\) 8.23560 0.362904
\(516\) 16.9302 0.745310
\(517\) 13.6845 0.601845
\(518\) 1.44843 0.0636403
\(519\) −10.3998 −0.456501
\(520\) −30.2052 −1.32459
\(521\) 0.358264 0.0156958 0.00784791 0.999969i \(-0.497502\pi\)
0.00784791 + 0.999969i \(0.497502\pi\)
\(522\) 13.0506 0.571210
\(523\) −10.6545 −0.465890 −0.232945 0.972490i \(-0.574836\pi\)
−0.232945 + 0.972490i \(0.574836\pi\)
\(524\) 15.1916 0.663647
\(525\) −1.63079 −0.0711733
\(526\) 3.15227 0.137446
\(527\) 23.4372 1.02094
\(528\) −157.795 −6.86716
\(529\) −20.7682 −0.902965
\(530\) −21.1677 −0.919467
\(531\) 19.4904 0.845813
\(532\) 17.1917 0.745354
\(533\) 38.3662 1.66183
\(534\) 49.8810 2.15856
\(535\) 3.98327 0.172212
\(536\) 80.1674 3.46270
\(537\) −13.5165 −0.583281
\(538\) −49.8490 −2.14914
\(539\) −40.3113 −1.73633
\(540\) −9.80399 −0.421896
\(541\) 12.0066 0.516204 0.258102 0.966118i \(-0.416903\pi\)
0.258102 + 0.966118i \(0.416903\pi\)
\(542\) 72.2883 3.10505
\(543\) 23.5715 1.01155
\(544\) 33.5746 1.43950
\(545\) −8.39078 −0.359421
\(546\) 17.1938 0.735828
\(547\) 6.88138 0.294227 0.147113 0.989120i \(-0.453002\pi\)
0.147113 + 0.989120i \(0.453002\pi\)
\(548\) 9.08413 0.388055
\(549\) −8.47673 −0.361778
\(550\) −15.9849 −0.681600
\(551\) −7.44324 −0.317093
\(552\) −29.1865 −1.24226
\(553\) 3.36176 0.142957
\(554\) 51.2723 2.17835
\(555\) 2.29640 0.0974767
\(556\) 80.4417 3.41149
\(557\) 30.4904 1.29192 0.645961 0.763371i \(-0.276457\pi\)
0.645961 + 0.763371i \(0.276457\pi\)
\(558\) 76.1006 3.22160
\(559\) −5.38044 −0.227568
\(560\) 6.22634 0.263111
\(561\) 48.3608 2.04180
\(562\) 38.1933 1.61109
\(563\) −35.7166 −1.50527 −0.752637 0.658435i \(-0.771219\pi\)
−0.752637 + 0.658435i \(0.771219\pi\)
\(564\) −28.4014 −1.19591
\(565\) 4.04417 0.170139
\(566\) 82.1808 3.45432
\(567\) −3.80803 −0.159922
\(568\) −46.0344 −1.93156
\(569\) 10.0744 0.422341 0.211171 0.977449i \(-0.432272\pi\)
0.211171 + 0.977449i \(0.432272\pi\)
\(570\) 38.4618 1.61099
\(571\) 14.5338 0.608221 0.304111 0.952637i \(-0.401641\pi\)
0.304111 + 0.952637i \(0.401641\pi\)
\(572\) 119.434 4.99377
\(573\) −13.9656 −0.583420
\(574\) −15.6520 −0.653304
\(575\) −1.49392 −0.0623008
\(576\) 34.0048 1.41687
\(577\) 34.7707 1.44752 0.723761 0.690051i \(-0.242412\pi\)
0.723761 + 0.690051i \(0.242412\pi\)
\(578\) 20.2390 0.841832
\(579\) −55.6008 −2.31069
\(580\) −6.42026 −0.266587
\(581\) 0.840090 0.0348528
\(582\) 13.0680 0.541686
\(583\) 49.2892 2.04135
\(584\) 19.9253 0.824514
\(585\) 15.1878 0.627937
\(586\) 13.2115 0.545760
\(587\) −39.2003 −1.61797 −0.808985 0.587830i \(-0.799983\pi\)
−0.808985 + 0.587830i \(0.799983\pi\)
\(588\) 83.6634 3.45022
\(589\) −43.4029 −1.78839
\(590\) −13.5302 −0.557029
\(591\) −54.6051 −2.24615
\(592\) −8.76766 −0.360348
\(593\) 5.61098 0.230415 0.115208 0.993341i \(-0.463247\pi\)
0.115208 + 0.993341i \(0.463247\pi\)
\(594\) 32.2138 1.32175
\(595\) −1.90824 −0.0782302
\(596\) −30.6735 −1.25644
\(597\) −15.5286 −0.635545
\(598\) 15.7508 0.644099
\(599\) −19.4745 −0.795705 −0.397853 0.917449i \(-0.630244\pi\)
−0.397853 + 0.917449i \(0.630244\pi\)
\(600\) 19.5368 0.797588
\(601\) −34.4715 −1.40612 −0.703061 0.711129i \(-0.748184\pi\)
−0.703061 + 0.711129i \(0.748184\pi\)
\(602\) 2.19503 0.0894626
\(603\) −40.3097 −1.64154
\(604\) 39.2294 1.59622
\(605\) 26.2211 1.06604
\(606\) 1.31532 0.0534313
\(607\) 21.8789 0.888038 0.444019 0.896017i \(-0.353552\pi\)
0.444019 + 0.896017i \(0.353552\pi\)
\(608\) −62.1763 −2.52158
\(609\) 2.15217 0.0872105
\(610\) 5.88451 0.238257
\(611\) 9.02600 0.365153
\(612\) −55.9209 −2.26047
\(613\) 30.5389 1.23346 0.616728 0.787177i \(-0.288458\pi\)
0.616728 + 0.787177i \(0.288458\pi\)
\(614\) 7.09437 0.286305
\(615\) −24.8154 −1.00065
\(616\) −28.6934 −1.15609
\(617\) −0.480408 −0.0193405 −0.00967024 0.999953i \(-0.503078\pi\)
−0.00967024 + 0.999953i \(0.503078\pi\)
\(618\) 56.1621 2.25917
\(619\) 23.0096 0.924835 0.462417 0.886662i \(-0.346982\pi\)
0.462417 + 0.886662i \(0.346982\pi\)
\(620\) −37.4377 −1.50354
\(621\) 3.01064 0.120813
\(622\) 42.4138 1.70064
\(623\) 4.58303 0.183615
\(624\) −104.078 −4.16646
\(625\) 1.00000 0.0400000
\(626\) −5.17255 −0.206737
\(627\) −89.5587 −3.57663
\(628\) 7.37968 0.294481
\(629\) 2.68710 0.107142
\(630\) −6.19606 −0.246857
\(631\) 7.04647 0.280516 0.140258 0.990115i \(-0.455207\pi\)
0.140258 + 0.990115i \(0.455207\pi\)
\(632\) −40.2740 −1.60201
\(633\) 63.8679 2.53852
\(634\) 22.8041 0.905667
\(635\) −3.96917 −0.157512
\(636\) −102.297 −4.05632
\(637\) −26.5884 −1.05347
\(638\) 21.0956 0.835182
\(639\) 23.1470 0.915679
\(640\) −1.55777 −0.0615763
\(641\) −10.3928 −0.410490 −0.205245 0.978711i \(-0.565799\pi\)
−0.205245 + 0.978711i \(0.565799\pi\)
\(642\) 27.1636 1.07206
\(643\) 12.3653 0.487642 0.243821 0.969820i \(-0.421599\pi\)
0.243821 + 0.969820i \(0.421599\pi\)
\(644\) −4.55370 −0.179441
\(645\) 3.48008 0.137028
\(646\) 45.0055 1.77072
\(647\) 36.1866 1.42264 0.711321 0.702868i \(-0.248097\pi\)
0.711321 + 0.702868i \(0.248097\pi\)
\(648\) 45.6203 1.79213
\(649\) 31.5052 1.23669
\(650\) −10.5433 −0.413542
\(651\) 12.5497 0.491862
\(652\) 33.7809 1.32296
\(653\) −33.8840 −1.32599 −0.662993 0.748626i \(-0.730714\pi\)
−0.662993 + 0.748626i \(0.730714\pi\)
\(654\) −57.2203 −2.23749
\(655\) 3.12270 0.122014
\(656\) 94.7453 3.69918
\(657\) −10.0188 −0.390871
\(658\) −3.68228 −0.143550
\(659\) 5.04584 0.196558 0.0982790 0.995159i \(-0.468666\pi\)
0.0982790 + 0.995159i \(0.468666\pi\)
\(660\) −77.2499 −3.00695
\(661\) −4.91246 −0.191073 −0.0955363 0.995426i \(-0.530457\pi\)
−0.0955363 + 0.995426i \(0.530457\pi\)
\(662\) −69.6222 −2.70594
\(663\) 31.8977 1.23880
\(664\) −10.0643 −0.390571
\(665\) 3.53384 0.137036
\(666\) 8.72502 0.338088
\(667\) 1.97155 0.0763388
\(668\) 88.2555 3.41471
\(669\) 7.44993 0.288031
\(670\) 27.9828 1.08107
\(671\) −13.7021 −0.528965
\(672\) 17.9780 0.693515
\(673\) 28.6388 1.10394 0.551972 0.833863i \(-0.313876\pi\)
0.551972 + 0.833863i \(0.313876\pi\)
\(674\) −67.4966 −2.59987
\(675\) −2.01526 −0.0775673
\(676\) 15.5321 0.597389
\(677\) 7.64880 0.293967 0.146984 0.989139i \(-0.453044\pi\)
0.146984 + 0.989139i \(0.453044\pi\)
\(678\) 27.5789 1.05916
\(679\) 1.20068 0.0460777
\(680\) 22.8607 0.876669
\(681\) 46.9599 1.79951
\(682\) 123.012 4.71038
\(683\) −13.1156 −0.501854 −0.250927 0.968006i \(-0.580735\pi\)
−0.250927 + 0.968006i \(0.580735\pi\)
\(684\) 103.559 3.95968
\(685\) 1.86729 0.0713454
\(686\) 22.3387 0.852894
\(687\) −75.0426 −2.86305
\(688\) −13.2870 −0.506561
\(689\) 32.5100 1.23853
\(690\) −10.1877 −0.387839
\(691\) −21.0883 −0.802237 −0.401119 0.916026i \(-0.631378\pi\)
−0.401119 + 0.916026i \(0.631378\pi\)
\(692\) 19.4387 0.738947
\(693\) 14.4276 0.548059
\(694\) 62.2906 2.36452
\(695\) 16.5352 0.627215
\(696\) −25.7831 −0.977305
\(697\) −29.0374 −1.09987
\(698\) 19.2308 0.727897
\(699\) 53.5402 2.02508
\(700\) 3.04816 0.115209
\(701\) 1.04672 0.0395339 0.0197669 0.999805i \(-0.493708\pi\)
0.0197669 + 0.999805i \(0.493708\pi\)
\(702\) 21.2475 0.801933
\(703\) −4.97619 −0.187681
\(704\) 54.9668 2.07164
\(705\) −5.83804 −0.219873
\(706\) −70.1308 −2.63941
\(707\) 0.120851 0.00454505
\(708\) −65.3870 −2.45739
\(709\) −25.4130 −0.954404 −0.477202 0.878794i \(-0.658349\pi\)
−0.477202 + 0.878794i \(0.658349\pi\)
\(710\) −16.0685 −0.603041
\(711\) 20.2505 0.759454
\(712\) −54.9047 −2.05764
\(713\) 11.4965 0.430547
\(714\) −13.0131 −0.487003
\(715\) 24.5502 0.918124
\(716\) 25.2642 0.944167
\(717\) 15.5521 0.580806
\(718\) 85.7374 3.19969
\(719\) 4.14597 0.154619 0.0773093 0.997007i \(-0.475367\pi\)
0.0773093 + 0.997007i \(0.475367\pi\)
\(720\) 37.5061 1.39777
\(721\) 5.16013 0.192173
\(722\) −33.5632 −1.24909
\(723\) −32.0825 −1.19316
\(724\) −44.0583 −1.63741
\(725\) −1.31972 −0.0490130
\(726\) 178.813 6.63637
\(727\) −31.6888 −1.17527 −0.587637 0.809125i \(-0.699942\pi\)
−0.587637 + 0.809125i \(0.699942\pi\)
\(728\) −18.9255 −0.701426
\(729\) −38.6743 −1.43238
\(730\) 6.95502 0.257417
\(731\) 4.07217 0.150615
\(732\) 28.4379 1.05110
\(733\) −16.8920 −0.623921 −0.311961 0.950095i \(-0.600986\pi\)
−0.311961 + 0.950095i \(0.600986\pi\)
\(734\) 23.5179 0.868063
\(735\) 17.1974 0.634337
\(736\) 16.4691 0.607061
\(737\) −65.1583 −2.40014
\(738\) −94.2845 −3.47066
\(739\) 21.7263 0.799216 0.399608 0.916686i \(-0.369146\pi\)
0.399608 + 0.916686i \(0.369146\pi\)
\(740\) −4.29228 −0.157787
\(741\) −59.0708 −2.17002
\(742\) −13.2629 −0.486897
\(743\) −10.1453 −0.372194 −0.186097 0.982531i \(-0.559584\pi\)
−0.186097 + 0.982531i \(0.559584\pi\)
\(744\) −150.346 −5.51195
\(745\) −6.30510 −0.231001
\(746\) 48.5521 1.77762
\(747\) 5.06052 0.185155
\(748\) −90.3929 −3.30509
\(749\) 2.49577 0.0911936
\(750\) 6.81943 0.249010
\(751\) −24.5494 −0.895821 −0.447910 0.894078i \(-0.647832\pi\)
−0.447910 + 0.894078i \(0.647832\pi\)
\(752\) 22.2897 0.812820
\(753\) 75.9882 2.76916
\(754\) 13.9142 0.506724
\(755\) 8.06380 0.293472
\(756\) −6.14282 −0.223412
\(757\) 2.88109 0.104715 0.0523576 0.998628i \(-0.483326\pi\)
0.0523576 + 0.998628i \(0.483326\pi\)
\(758\) −47.7650 −1.73490
\(759\) 23.7221 0.861059
\(760\) −42.3354 −1.53567
\(761\) −2.74630 −0.0995532 −0.0497766 0.998760i \(-0.515851\pi\)
−0.0497766 + 0.998760i \(0.515851\pi\)
\(762\) −27.0674 −0.980550
\(763\) −5.25735 −0.190329
\(764\) 26.1035 0.944392
\(765\) −11.4948 −0.415596
\(766\) −32.7725 −1.18412
\(767\) 20.7801 0.750325
\(768\) 36.2763 1.30901
\(769\) 11.1330 0.401465 0.200733 0.979646i \(-0.435668\pi\)
0.200733 + 0.979646i \(0.435668\pi\)
\(770\) −10.0156 −0.360936
\(771\) −65.4382 −2.35670
\(772\) 103.925 3.74036
\(773\) −4.90884 −0.176559 −0.0882793 0.996096i \(-0.528137\pi\)
−0.0882793 + 0.996096i \(0.528137\pi\)
\(774\) 13.2224 0.475268
\(775\) −7.69551 −0.276431
\(776\) −14.3841 −0.516360
\(777\) 1.43884 0.0516181
\(778\) −59.3948 −2.12941
\(779\) 53.7738 1.92665
\(780\) −50.9522 −1.82438
\(781\) 37.4157 1.33884
\(782\) −11.9210 −0.426293
\(783\) 2.65957 0.0950453
\(784\) −65.6598 −2.34499
\(785\) 1.51693 0.0541416
\(786\) 21.2951 0.759570
\(787\) −12.5494 −0.447337 −0.223669 0.974665i \(-0.571803\pi\)
−0.223669 + 0.974665i \(0.571803\pi\)
\(788\) 102.064 3.63589
\(789\) 3.13140 0.111481
\(790\) −14.0578 −0.500155
\(791\) 2.53393 0.0900961
\(792\) −172.843 −6.14170
\(793\) −9.03761 −0.320935
\(794\) 87.3041 3.09831
\(795\) −21.0276 −0.745771
\(796\) 29.0251 1.02877
\(797\) 10.4149 0.368914 0.184457 0.982841i \(-0.440947\pi\)
0.184457 + 0.982841i \(0.440947\pi\)
\(798\) 24.0988 0.853087
\(799\) −6.83130 −0.241674
\(800\) −11.0241 −0.389761
\(801\) 27.6071 0.975451
\(802\) −79.6347 −2.81200
\(803\) −16.1948 −0.571503
\(804\) 135.232 4.76926
\(805\) −0.936036 −0.0329909
\(806\) 81.1360 2.85789
\(807\) −49.5190 −1.74315
\(808\) −1.44779 −0.0509332
\(809\) 51.0084 1.79336 0.896680 0.442680i \(-0.145972\pi\)
0.896680 + 0.442680i \(0.145972\pi\)
\(810\) 15.9240 0.559511
\(811\) 9.86857 0.346532 0.173266 0.984875i \(-0.444568\pi\)
0.173266 + 0.984875i \(0.444568\pi\)
\(812\) −4.02270 −0.141169
\(813\) 71.8098 2.51848
\(814\) 14.1035 0.494327
\(815\) 6.94383 0.243232
\(816\) 78.7711 2.75754
\(817\) −7.54119 −0.263833
\(818\) 82.4796 2.88383
\(819\) 9.51610 0.332520
\(820\) 46.3833 1.61977
\(821\) 12.5308 0.437327 0.218664 0.975800i \(-0.429830\pi\)
0.218664 + 0.975800i \(0.429830\pi\)
\(822\) 12.7338 0.444144
\(823\) 25.6924 0.895580 0.447790 0.894139i \(-0.352211\pi\)
0.447790 + 0.894139i \(0.352211\pi\)
\(824\) −61.8184 −2.15355
\(825\) −15.8791 −0.552840
\(826\) −8.47752 −0.294971
\(827\) 21.0995 0.733701 0.366851 0.930280i \(-0.380436\pi\)
0.366851 + 0.930280i \(0.380436\pi\)
\(828\) −27.4305 −0.953276
\(829\) 34.3049 1.19146 0.595729 0.803185i \(-0.296863\pi\)
0.595729 + 0.803185i \(0.296863\pi\)
\(830\) −3.51299 −0.121938
\(831\) 50.9329 1.76684
\(832\) 36.2548 1.25691
\(833\) 20.1233 0.697231
\(834\) 112.761 3.90458
\(835\) 18.1414 0.627807
\(836\) 167.397 5.78955
\(837\) 15.5084 0.536050
\(838\) −39.5385 −1.36584
\(839\) −0.996633 −0.0344076 −0.0172038 0.999852i \(-0.505476\pi\)
−0.0172038 + 0.999852i \(0.505476\pi\)
\(840\) 12.2411 0.422357
\(841\) −27.2583 −0.939943
\(842\) 1.71830 0.0592167
\(843\) 37.9405 1.30674
\(844\) −119.378 −4.10915
\(845\) 3.19270 0.109832
\(846\) −22.1813 −0.762608
\(847\) 16.4292 0.564513
\(848\) 80.2833 2.75694
\(849\) 81.6368 2.80177
\(850\) 7.97965 0.273700
\(851\) 1.31808 0.0451833
\(852\) −77.6539 −2.66038
\(853\) 57.0630 1.95380 0.976900 0.213696i \(-0.0685502\pi\)
0.976900 + 0.213696i \(0.0685502\pi\)
\(854\) 3.68702 0.126167
\(855\) 21.2871 0.728002
\(856\) −29.8994 −1.02194
\(857\) −35.4405 −1.21062 −0.605312 0.795988i \(-0.706952\pi\)
−0.605312 + 0.795988i \(0.706952\pi\)
\(858\) 167.418 5.71556
\(859\) −0.230402 −0.00786120 −0.00393060 0.999992i \(-0.501251\pi\)
−0.00393060 + 0.999992i \(0.501251\pi\)
\(860\) −6.50474 −0.221810
\(861\) −15.5484 −0.529889
\(862\) −41.7562 −1.42222
\(863\) 48.4731 1.65004 0.825021 0.565102i \(-0.191163\pi\)
0.825021 + 0.565102i \(0.191163\pi\)
\(864\) 22.2164 0.755819
\(865\) 3.99571 0.135858
\(866\) −62.1693 −2.11260
\(867\) 20.1050 0.682802
\(868\) −23.4571 −0.796186
\(869\) 32.7338 1.11042
\(870\) −8.99971 −0.305119
\(871\) −42.9769 −1.45622
\(872\) 62.9832 2.13288
\(873\) 7.23261 0.244787
\(874\) 22.0762 0.746740
\(875\) 0.626563 0.0211817
\(876\) 33.6113 1.13562
\(877\) 22.3829 0.755818 0.377909 0.925843i \(-0.376643\pi\)
0.377909 + 0.925843i \(0.376643\pi\)
\(878\) 35.4623 1.19680
\(879\) 13.1240 0.442661
\(880\) 60.6265 2.04372
\(881\) −23.8491 −0.803496 −0.401748 0.915750i \(-0.631597\pi\)
−0.401748 + 0.915750i \(0.631597\pi\)
\(882\) 65.3405 2.20013
\(883\) 14.8684 0.500363 0.250181 0.968199i \(-0.419510\pi\)
0.250181 + 0.968199i \(0.419510\pi\)
\(884\) −59.6210 −2.00527
\(885\) −13.4406 −0.451801
\(886\) −99.0769 −3.32855
\(887\) 16.3149 0.547802 0.273901 0.961758i \(-0.411686\pi\)
0.273901 + 0.961758i \(0.411686\pi\)
\(888\) −17.2373 −0.578447
\(889\) −2.48693 −0.0834091
\(890\) −19.1648 −0.642405
\(891\) −37.0791 −1.24220
\(892\) −13.9249 −0.466240
\(893\) 12.6508 0.423342
\(894\) −42.9972 −1.43804
\(895\) 5.19318 0.173589
\(896\) −0.976042 −0.0326073
\(897\) 15.6466 0.522423
\(898\) 69.5483 2.32086
\(899\) 10.1559 0.338718
\(900\) 18.3614 0.612047
\(901\) −24.6051 −0.819715
\(902\) −152.405 −5.07455
\(903\) 2.18049 0.0725623
\(904\) −30.3565 −1.00964
\(905\) −9.05641 −0.301045
\(906\) 54.9905 1.82694
\(907\) 23.8246 0.791083 0.395542 0.918448i \(-0.370557\pi\)
0.395542 + 0.918448i \(0.370557\pi\)
\(908\) −87.7743 −2.91289
\(909\) 0.727978 0.0241455
\(910\) −6.60604 −0.218988
\(911\) 45.6863 1.51365 0.756827 0.653615i \(-0.226748\pi\)
0.756827 + 0.653615i \(0.226748\pi\)
\(912\) −145.875 −4.83040
\(913\) 8.18004 0.270720
\(914\) −99.2298 −3.28223
\(915\) 5.84555 0.193248
\(916\) 140.265 4.63448
\(917\) 1.95657 0.0646117
\(918\) −16.0811 −0.530754
\(919\) −47.1923 −1.55673 −0.778366 0.627811i \(-0.783951\pi\)
−0.778366 + 0.627811i \(0.783951\pi\)
\(920\) 11.2137 0.369706
\(921\) 7.04740 0.232220
\(922\) 41.4070 1.36367
\(923\) 24.6785 0.812303
\(924\) −48.4020 −1.59231
\(925\) −0.882299 −0.0290098
\(926\) 33.3196 1.09495
\(927\) 31.0835 1.02092
\(928\) 14.5487 0.477585
\(929\) 16.3712 0.537120 0.268560 0.963263i \(-0.413452\pi\)
0.268560 + 0.963263i \(0.413452\pi\)
\(930\) −52.4790 −1.72085
\(931\) −37.2660 −1.22135
\(932\) −100.074 −3.27803
\(933\) 42.1330 1.37937
\(934\) 79.3150 2.59526
\(935\) −18.5807 −0.607654
\(936\) −114.003 −3.72631
\(937\) −36.4723 −1.19150 −0.595749 0.803170i \(-0.703145\pi\)
−0.595749 + 0.803170i \(0.703145\pi\)
\(938\) 17.5330 0.572473
\(939\) −5.13830 −0.167682
\(940\) 10.9121 0.355913
\(941\) 37.5503 1.22411 0.612053 0.790817i \(-0.290344\pi\)
0.612053 + 0.790817i \(0.290344\pi\)
\(942\) 10.3446 0.337045
\(943\) −14.2435 −0.463832
\(944\) 51.3163 1.67020
\(945\) −1.26269 −0.0410752
\(946\) 21.3732 0.694902
\(947\) 0.875581 0.0284526 0.0142263 0.999899i \(-0.495471\pi\)
0.0142263 + 0.999899i \(0.495471\pi\)
\(948\) −67.9369 −2.20649
\(949\) −10.6817 −0.346744
\(950\) −14.7774 −0.479442
\(951\) 22.6531 0.734578
\(952\) 14.3237 0.464234
\(953\) 10.0550 0.325713 0.162857 0.986650i \(-0.447929\pi\)
0.162857 + 0.986650i \(0.447929\pi\)
\(954\) −79.8929 −2.58663
\(955\) 5.36571 0.173630
\(956\) −29.0690 −0.940160
\(957\) 20.9559 0.677409
\(958\) −71.8023 −2.31983
\(959\) 1.16997 0.0377804
\(960\) −23.4497 −0.756836
\(961\) 28.2209 0.910351
\(962\) 9.30233 0.299919
\(963\) 15.0340 0.484464
\(964\) 59.9665 1.93139
\(965\) 21.3624 0.687679
\(966\) −6.38323 −0.205377
\(967\) 43.4751 1.39806 0.699032 0.715091i \(-0.253615\pi\)
0.699032 + 0.715091i \(0.253615\pi\)
\(968\) −196.822 −6.32609
\(969\) 44.7075 1.43621
\(970\) −5.02085 −0.161210
\(971\) −14.8491 −0.476531 −0.238266 0.971200i \(-0.576579\pi\)
−0.238266 + 0.971200i \(0.576579\pi\)
\(972\) 106.367 3.41173
\(973\) 10.3603 0.332137
\(974\) 36.5883 1.17236
\(975\) −10.4735 −0.335420
\(976\) −22.3183 −0.714392
\(977\) −58.5320 −1.87260 −0.936302 0.351196i \(-0.885775\pi\)
−0.936302 + 0.351196i \(0.885775\pi\)
\(978\) 47.3530 1.51418
\(979\) 44.6254 1.42623
\(980\) −32.1443 −1.02681
\(981\) −31.6692 −1.01112
\(982\) 18.3366 0.585144
\(983\) 4.66524 0.148798 0.0743991 0.997229i \(-0.476296\pi\)
0.0743991 + 0.997229i \(0.476296\pi\)
\(984\) 186.270 5.93808
\(985\) 20.9798 0.668473
\(986\) −10.5309 −0.335372
\(987\) −3.65790 −0.116432
\(988\) 110.411 3.51265
\(989\) 1.99749 0.0635166
\(990\) −60.3317 −1.91747
\(991\) −0.589351 −0.0187214 −0.00936068 0.999956i \(-0.502980\pi\)
−0.00936068 + 0.999956i \(0.502980\pi\)
\(992\) 84.8362 2.69355
\(993\) −69.1613 −2.19477
\(994\) −10.0679 −0.319336
\(995\) 5.96625 0.189143
\(996\) −16.9771 −0.537941
\(997\) 38.7294 1.22657 0.613287 0.789860i \(-0.289847\pi\)
0.613287 + 0.789860i \(0.289847\pi\)
\(998\) 82.0451 2.59709
\(999\) 1.77806 0.0562553
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 \(a_p\))