Properties

Label 4015.2.a.h.1.16
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.421939 q^{2}\) \(-2.05594 q^{3}\) \(-1.82197 q^{4}\) \(+1.00000 q^{5}\) \(+0.867482 q^{6}\) \(-0.0580639 q^{7}\) \(+1.61264 q^{8}\) \(+1.22690 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.421939 q^{2}\) \(-2.05594 q^{3}\) \(-1.82197 q^{4}\) \(+1.00000 q^{5}\) \(+0.867482 q^{6}\) \(-0.0580639 q^{7}\) \(+1.61264 q^{8}\) \(+1.22690 q^{9}\) \(-0.421939 q^{10}\) \(+1.00000 q^{11}\) \(+3.74586 q^{12}\) \(+6.32922 q^{13}\) \(+0.0244994 q^{14}\) \(-2.05594 q^{15}\) \(+2.96350 q^{16}\) \(+5.86865 q^{17}\) \(-0.517676 q^{18}\) \(+0.796345 q^{19}\) \(-1.82197 q^{20}\) \(+0.119376 q^{21}\) \(-0.421939 q^{22}\) \(+8.29329 q^{23}\) \(-3.31549 q^{24}\) \(+1.00000 q^{25}\) \(-2.67054 q^{26}\) \(+3.64539 q^{27}\) \(+0.105790 q^{28}\) \(-1.17504 q^{29}\) \(+0.867482 q^{30}\) \(-0.271039 q^{31}\) \(-4.47569 q^{32}\) \(-2.05594 q^{33}\) \(-2.47621 q^{34}\) \(-0.0580639 q^{35}\) \(-2.23537 q^{36}\) \(+3.31240 q^{37}\) \(-0.336009 q^{38}\) \(-13.0125 q^{39}\) \(+1.61264 q^{40}\) \(+1.75836 q^{41}\) \(-0.0503693 q^{42}\) \(-1.18574 q^{43}\) \(-1.82197 q^{44}\) \(+1.22690 q^{45}\) \(-3.49926 q^{46}\) \(-11.5364 q^{47}\) \(-6.09279 q^{48}\) \(-6.99663 q^{49}\) \(-0.421939 q^{50}\) \(-12.0656 q^{51}\) \(-11.5316 q^{52}\) \(+3.80653 q^{53}\) \(-1.53813 q^{54}\) \(+1.00000 q^{55}\) \(-0.0936359 q^{56}\) \(-1.63724 q^{57}\) \(+0.495794 q^{58}\) \(+1.80051 q^{59}\) \(+3.74586 q^{60}\) \(+7.32347 q^{61}\) \(+0.114362 q^{62}\) \(-0.0712385 q^{63}\) \(-4.03854 q^{64}\) \(+6.32922 q^{65}\) \(+0.867482 q^{66}\) \(+11.5619 q^{67}\) \(-10.6925 q^{68}\) \(-17.0505 q^{69}\) \(+0.0244994 q^{70}\) \(-2.43721 q^{71}\) \(+1.97854 q^{72}\) \(+1.00000 q^{73}\) \(-1.39763 q^{74}\) \(-2.05594 q^{75}\) \(-1.45091 q^{76}\) \(-0.0580639 q^{77}\) \(+5.49048 q^{78}\) \(+10.1837 q^{79}\) \(+2.96350 q^{80}\) \(-11.1754 q^{81}\) \(-0.741920 q^{82}\) \(+1.69280 q^{83}\) \(-0.217499 q^{84}\) \(+5.86865 q^{85}\) \(+0.500309 q^{86}\) \(+2.41581 q^{87}\) \(+1.61264 q^{88}\) \(+10.5321 q^{89}\) \(-0.517676 q^{90}\) \(-0.367499 q^{91}\) \(-15.1101 q^{92}\) \(+0.557240 q^{93}\) \(+4.86764 q^{94}\) \(+0.796345 q^{95}\) \(+9.20176 q^{96}\) \(-17.3837 q^{97}\) \(+2.95215 q^{98}\) \(+1.22690 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.421939 −0.298356 −0.149178 0.988810i \(-0.547663\pi\)
−0.149178 + 0.988810i \(0.547663\pi\)
\(3\) −2.05594 −1.18700 −0.593499 0.804834i \(-0.702254\pi\)
−0.593499 + 0.804834i \(0.702254\pi\)
\(4\) −1.82197 −0.910984
\(5\) 1.00000 0.447214
\(6\) 0.867482 0.354148
\(7\) −0.0580639 −0.0219461 −0.0109730 0.999940i \(-0.503493\pi\)
−0.0109730 + 0.999940i \(0.503493\pi\)
\(8\) 1.61264 0.570153
\(9\) 1.22690 0.408967
\(10\) −0.421939 −0.133429
\(11\) 1.00000 0.301511
\(12\) 3.74586 1.08134
\(13\) 6.32922 1.75541 0.877704 0.479202i \(-0.159074\pi\)
0.877704 + 0.479202i \(0.159074\pi\)
\(14\) 0.0244994 0.00654774
\(15\) −2.05594 −0.530842
\(16\) 2.96350 0.740875
\(17\) 5.86865 1.42336 0.711678 0.702506i \(-0.247936\pi\)
0.711678 + 0.702506i \(0.247936\pi\)
\(18\) −0.517676 −0.122018
\(19\) 0.796345 0.182694 0.0913470 0.995819i \(-0.470883\pi\)
0.0913470 + 0.995819i \(0.470883\pi\)
\(20\) −1.82197 −0.407404
\(21\) 0.119376 0.0260500
\(22\) −0.421939 −0.0899576
\(23\) 8.29329 1.72927 0.864635 0.502400i \(-0.167549\pi\)
0.864635 + 0.502400i \(0.167549\pi\)
\(24\) −3.31549 −0.676771
\(25\) 1.00000 0.200000
\(26\) −2.67054 −0.523736
\(27\) 3.64539 0.701556
\(28\) 0.105790 0.0199925
\(29\) −1.17504 −0.218199 −0.109099 0.994031i \(-0.534797\pi\)
−0.109099 + 0.994031i \(0.534797\pi\)
\(30\) 0.867482 0.158380
\(31\) −0.271039 −0.0486800 −0.0243400 0.999704i \(-0.507748\pi\)
−0.0243400 + 0.999704i \(0.507748\pi\)
\(32\) −4.47569 −0.791197
\(33\) −2.05594 −0.357894
\(34\) −2.47621 −0.424666
\(35\) −0.0580639 −0.00981458
\(36\) −2.23537 −0.372562
\(37\) 3.31240 0.544556 0.272278 0.962219i \(-0.412223\pi\)
0.272278 + 0.962219i \(0.412223\pi\)
\(38\) −0.336009 −0.0545078
\(39\) −13.0125 −2.08367
\(40\) 1.61264 0.254980
\(41\) 1.75836 0.274610 0.137305 0.990529i \(-0.456156\pi\)
0.137305 + 0.990529i \(0.456156\pi\)
\(42\) −0.0503693 −0.00777216
\(43\) −1.18574 −0.180823 −0.0904117 0.995904i \(-0.528818\pi\)
−0.0904117 + 0.995904i \(0.528818\pi\)
\(44\) −1.82197 −0.274672
\(45\) 1.22690 0.182895
\(46\) −3.49926 −0.515938
\(47\) −11.5364 −1.68275 −0.841376 0.540450i \(-0.818254\pi\)
−0.841376 + 0.540450i \(0.818254\pi\)
\(48\) −6.09279 −0.879418
\(49\) −6.99663 −0.999518
\(50\) −0.421939 −0.0596711
\(51\) −12.0656 −1.68952
\(52\) −11.5316 −1.59915
\(53\) 3.80653 0.522867 0.261433 0.965222i \(-0.415805\pi\)
0.261433 + 0.965222i \(0.415805\pi\)
\(54\) −1.53813 −0.209313
\(55\) 1.00000 0.134840
\(56\) −0.0936359 −0.0125126
\(57\) −1.63724 −0.216858
\(58\) 0.495794 0.0651009
\(59\) 1.80051 0.234406 0.117203 0.993108i \(-0.462607\pi\)
0.117203 + 0.993108i \(0.462607\pi\)
\(60\) 3.74586 0.483589
\(61\) 7.32347 0.937674 0.468837 0.883285i \(-0.344673\pi\)
0.468837 + 0.883285i \(0.344673\pi\)
\(62\) 0.114362 0.0145240
\(63\) −0.0712385 −0.00897521
\(64\) −4.03854 −0.504817
\(65\) 6.32922 0.785043
\(66\) 0.867482 0.106780
\(67\) 11.5619 1.41251 0.706257 0.707955i \(-0.250382\pi\)
0.706257 + 0.707955i \(0.250382\pi\)
\(68\) −10.6925 −1.29665
\(69\) −17.0505 −2.05264
\(70\) 0.0244994 0.00292824
\(71\) −2.43721 −0.289244 −0.144622 0.989487i \(-0.546197\pi\)
−0.144622 + 0.989487i \(0.546197\pi\)
\(72\) 1.97854 0.233173
\(73\) 1.00000 0.117041
\(74\) −1.39763 −0.162471
\(75\) −2.05594 −0.237400
\(76\) −1.45091 −0.166431
\(77\) −0.0580639 −0.00661699
\(78\) 5.49048 0.621674
\(79\) 10.1837 1.14575 0.572876 0.819642i \(-0.305828\pi\)
0.572876 + 0.819642i \(0.305828\pi\)
\(80\) 2.96350 0.331330
\(81\) −11.1754 −1.24171
\(82\) −0.741920 −0.0819314
\(83\) 1.69280 0.185809 0.0929043 0.995675i \(-0.470385\pi\)
0.0929043 + 0.995675i \(0.470385\pi\)
\(84\) −0.217499 −0.0237311
\(85\) 5.86865 0.636544
\(86\) 0.500309 0.0539497
\(87\) 2.41581 0.259002
\(88\) 1.61264 0.171908
\(89\) 10.5321 1.11640 0.558198 0.829708i \(-0.311493\pi\)
0.558198 + 0.829708i \(0.311493\pi\)
\(90\) −0.517676 −0.0545679
\(91\) −0.367499 −0.0385243
\(92\) −15.1101 −1.57534
\(93\) 0.557240 0.0577831
\(94\) 4.86764 0.502059
\(95\) 0.796345 0.0817033
\(96\) 9.20176 0.939151
\(97\) −17.3837 −1.76505 −0.882524 0.470268i \(-0.844157\pi\)
−0.882524 + 0.470268i \(0.844157\pi\)
\(98\) 2.95215 0.298212
\(99\) 1.22690 0.123308
\(100\) −1.82197 −0.182197
\(101\) 17.1524 1.70673 0.853363 0.521318i \(-0.174559\pi\)
0.853363 + 0.521318i \(0.174559\pi\)
\(102\) 5.09094 0.504078
\(103\) −7.46160 −0.735213 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(104\) 10.2067 1.00085
\(105\) 0.119376 0.0116499
\(106\) −1.60612 −0.156000
\(107\) −5.35473 −0.517661 −0.258831 0.965923i \(-0.583337\pi\)
−0.258831 + 0.965923i \(0.583337\pi\)
\(108\) −6.64179 −0.639106
\(109\) −3.32627 −0.318599 −0.159300 0.987230i \(-0.550924\pi\)
−0.159300 + 0.987230i \(0.550924\pi\)
\(110\) −0.421939 −0.0402303
\(111\) −6.81011 −0.646387
\(112\) −0.172072 −0.0162593
\(113\) −4.97691 −0.468189 −0.234094 0.972214i \(-0.575212\pi\)
−0.234094 + 0.972214i \(0.575212\pi\)
\(114\) 0.690815 0.0647007
\(115\) 8.29329 0.773353
\(116\) 2.14088 0.198776
\(117\) 7.76531 0.717903
\(118\) −0.759705 −0.0699365
\(119\) −0.340756 −0.0312371
\(120\) −3.31549 −0.302661
\(121\) 1.00000 0.0909091
\(122\) −3.09006 −0.279761
\(123\) −3.61509 −0.325961
\(124\) 0.493824 0.0443467
\(125\) 1.00000 0.0894427
\(126\) 0.0300583 0.00267781
\(127\) −9.98530 −0.886052 −0.443026 0.896509i \(-0.646095\pi\)
−0.443026 + 0.896509i \(0.646095\pi\)
\(128\) 10.6554 0.941813
\(129\) 2.43781 0.214637
\(130\) −2.67054 −0.234222
\(131\) −15.7333 −1.37463 −0.687314 0.726361i \(-0.741210\pi\)
−0.687314 + 0.726361i \(0.741210\pi\)
\(132\) 3.74586 0.326035
\(133\) −0.0462389 −0.00400942
\(134\) −4.87843 −0.421432
\(135\) 3.64539 0.313745
\(136\) 9.46399 0.811530
\(137\) −0.359744 −0.0307350 −0.0153675 0.999882i \(-0.504892\pi\)
−0.0153675 + 0.999882i \(0.504892\pi\)
\(138\) 7.19428 0.612418
\(139\) 3.22965 0.273935 0.136968 0.990576i \(-0.456264\pi\)
0.136968 + 0.990576i \(0.456264\pi\)
\(140\) 0.105790 0.00894093
\(141\) 23.7181 1.99742
\(142\) 1.02836 0.0862976
\(143\) 6.32922 0.529276
\(144\) 3.63592 0.302993
\(145\) −1.17504 −0.0975815
\(146\) −0.421939 −0.0349199
\(147\) 14.3847 1.18643
\(148\) −6.03509 −0.496082
\(149\) −3.54582 −0.290485 −0.145242 0.989396i \(-0.546396\pi\)
−0.145242 + 0.989396i \(0.546396\pi\)
\(150\) 0.867482 0.0708296
\(151\) −13.4361 −1.09342 −0.546709 0.837323i \(-0.684120\pi\)
−0.546709 + 0.837323i \(0.684120\pi\)
\(152\) 1.28421 0.104164
\(153\) 7.20024 0.582105
\(154\) 0.0244994 0.00197422
\(155\) −0.271039 −0.0217704
\(156\) 23.7084 1.89819
\(157\) 1.13284 0.0904102 0.0452051 0.998978i \(-0.485606\pi\)
0.0452051 + 0.998978i \(0.485606\pi\)
\(158\) −4.29688 −0.341841
\(159\) −7.82600 −0.620642
\(160\) −4.47569 −0.353834
\(161\) −0.481541 −0.0379507
\(162\) 4.71534 0.370472
\(163\) 3.66846 0.287336 0.143668 0.989626i \(-0.454110\pi\)
0.143668 + 0.989626i \(0.454110\pi\)
\(164\) −3.20367 −0.250165
\(165\) −2.05594 −0.160055
\(166\) −0.714256 −0.0554371
\(167\) −13.5067 −1.04518 −0.522589 0.852585i \(-0.675034\pi\)
−0.522589 + 0.852585i \(0.675034\pi\)
\(168\) 0.192510 0.0148525
\(169\) 27.0590 2.08146
\(170\) −2.47621 −0.189917
\(171\) 0.977035 0.0747158
\(172\) 2.16038 0.164727
\(173\) 8.10928 0.616537 0.308269 0.951299i \(-0.400250\pi\)
0.308269 + 0.951299i \(0.400250\pi\)
\(174\) −1.01932 −0.0772747
\(175\) −0.0580639 −0.00438922
\(176\) 2.96350 0.223382
\(177\) −3.70174 −0.278240
\(178\) −4.44389 −0.333083
\(179\) −16.7291 −1.25039 −0.625196 0.780467i \(-0.714981\pi\)
−0.625196 + 0.780467i \(0.714981\pi\)
\(180\) −2.23537 −0.166615
\(181\) 25.8052 1.91809 0.959044 0.283256i \(-0.0914145\pi\)
0.959044 + 0.283256i \(0.0914145\pi\)
\(182\) 0.155062 0.0114940
\(183\) −15.0566 −1.11302
\(184\) 13.3741 0.985949
\(185\) 3.31240 0.243533
\(186\) −0.235121 −0.0172399
\(187\) 5.86865 0.429158
\(188\) 21.0189 1.53296
\(189\) −0.211666 −0.0153964
\(190\) −0.336009 −0.0243766
\(191\) 21.0196 1.52093 0.760464 0.649380i \(-0.224972\pi\)
0.760464 + 0.649380i \(0.224972\pi\)
\(192\) 8.30300 0.599217
\(193\) 12.1296 0.873110 0.436555 0.899678i \(-0.356198\pi\)
0.436555 + 0.899678i \(0.356198\pi\)
\(194\) 7.33486 0.526612
\(195\) −13.0125 −0.931845
\(196\) 12.7476 0.910545
\(197\) −18.0668 −1.28721 −0.643605 0.765358i \(-0.722562\pi\)
−0.643605 + 0.765358i \(0.722562\pi\)
\(198\) −0.517676 −0.0367897
\(199\) 11.8000 0.836482 0.418241 0.908336i \(-0.362647\pi\)
0.418241 + 0.908336i \(0.362647\pi\)
\(200\) 1.61264 0.114031
\(201\) −23.7707 −1.67665
\(202\) −7.23725 −0.509211
\(203\) 0.0682272 0.00478861
\(204\) 21.9831 1.53913
\(205\) 1.75836 0.122809
\(206\) 3.14834 0.219355
\(207\) 10.1750 0.707214
\(208\) 18.7566 1.30054
\(209\) 0.796345 0.0550843
\(210\) −0.0503693 −0.00347581
\(211\) −11.5382 −0.794322 −0.397161 0.917749i \(-0.630005\pi\)
−0.397161 + 0.917749i \(0.630005\pi\)
\(212\) −6.93537 −0.476323
\(213\) 5.01077 0.343332
\(214\) 2.25937 0.154447
\(215\) −1.18574 −0.0808667
\(216\) 5.87869 0.399994
\(217\) 0.0157376 0.00106833
\(218\) 1.40348 0.0950559
\(219\) −2.05594 −0.138928
\(220\) −1.82197 −0.122837
\(221\) 37.1439 2.49857
\(222\) 2.87345 0.192853
\(223\) 13.1748 0.882252 0.441126 0.897445i \(-0.354579\pi\)
0.441126 + 0.897445i \(0.354579\pi\)
\(224\) 0.259876 0.0173637
\(225\) 1.22690 0.0817933
\(226\) 2.09995 0.139687
\(227\) 2.72086 0.180590 0.0902949 0.995915i \(-0.471219\pi\)
0.0902949 + 0.995915i \(0.471219\pi\)
\(228\) 2.98300 0.197554
\(229\) −4.38186 −0.289562 −0.144781 0.989464i \(-0.546248\pi\)
−0.144781 + 0.989464i \(0.546248\pi\)
\(230\) −3.49926 −0.230734
\(231\) 0.119376 0.00785436
\(232\) −1.89491 −0.124407
\(233\) −16.0203 −1.04952 −0.524761 0.851250i \(-0.675845\pi\)
−0.524761 + 0.851250i \(0.675845\pi\)
\(234\) −3.27649 −0.214191
\(235\) −11.5364 −0.752550
\(236\) −3.28047 −0.213540
\(237\) −20.9370 −1.36001
\(238\) 0.143778 0.00931976
\(239\) −5.87473 −0.380004 −0.190002 0.981784i \(-0.560850\pi\)
−0.190002 + 0.981784i \(0.560850\pi\)
\(240\) −6.09279 −0.393288
\(241\) 18.3559 1.18241 0.591205 0.806521i \(-0.298652\pi\)
0.591205 + 0.806521i \(0.298652\pi\)
\(242\) −0.421939 −0.0271232
\(243\) 12.0398 0.772356
\(244\) −13.3431 −0.854206
\(245\) −6.99663 −0.446998
\(246\) 1.52535 0.0972524
\(247\) 5.04024 0.320703
\(248\) −0.437087 −0.0277550
\(249\) −3.48029 −0.220555
\(250\) −0.421939 −0.0266857
\(251\) 14.5307 0.917167 0.458584 0.888651i \(-0.348357\pi\)
0.458584 + 0.888651i \(0.348357\pi\)
\(252\) 0.129794 0.00817627
\(253\) 8.29329 0.521395
\(254\) 4.21319 0.264359
\(255\) −12.0656 −0.755577
\(256\) 3.58115 0.223822
\(257\) 10.8262 0.675318 0.337659 0.941269i \(-0.390365\pi\)
0.337659 + 0.941269i \(0.390365\pi\)
\(258\) −1.02861 −0.0640382
\(259\) −0.192331 −0.0119509
\(260\) −11.5316 −0.715161
\(261\) −1.44165 −0.0892360
\(262\) 6.63850 0.410128
\(263\) 15.7384 0.970470 0.485235 0.874384i \(-0.338734\pi\)
0.485235 + 0.874384i \(0.338734\pi\)
\(264\) −3.31549 −0.204054
\(265\) 3.80653 0.233833
\(266\) 0.0195100 0.00119623
\(267\) −21.6533 −1.32516
\(268\) −21.0655 −1.28678
\(269\) −5.28552 −0.322264 −0.161132 0.986933i \(-0.551514\pi\)
−0.161132 + 0.986933i \(0.551514\pi\)
\(270\) −1.53813 −0.0936077
\(271\) −25.1431 −1.52734 −0.763668 0.645610i \(-0.776603\pi\)
−0.763668 + 0.645610i \(0.776603\pi\)
\(272\) 17.3917 1.05453
\(273\) 0.755556 0.0457283
\(274\) 0.151790 0.00916998
\(275\) 1.00000 0.0603023
\(276\) 31.0655 1.86992
\(277\) 18.6561 1.12094 0.560468 0.828176i \(-0.310621\pi\)
0.560468 + 0.828176i \(0.310621\pi\)
\(278\) −1.36271 −0.0817302
\(279\) −0.332537 −0.0199085
\(280\) −0.0936359 −0.00559581
\(281\) 14.3401 0.855457 0.427729 0.903907i \(-0.359314\pi\)
0.427729 + 0.903907i \(0.359314\pi\)
\(282\) −10.0076 −0.595943
\(283\) −16.0739 −0.955496 −0.477748 0.878497i \(-0.658547\pi\)
−0.477748 + 0.878497i \(0.658547\pi\)
\(284\) 4.44053 0.263497
\(285\) −1.63724 −0.0969817
\(286\) −2.67054 −0.157912
\(287\) −0.102097 −0.00602660
\(288\) −5.49122 −0.323573
\(289\) 17.4410 1.02594
\(290\) 0.495794 0.0291140
\(291\) 35.7399 2.09511
\(292\) −1.82197 −0.106623
\(293\) −2.29458 −0.134051 −0.0670254 0.997751i \(-0.521351\pi\)
−0.0670254 + 0.997751i \(0.521351\pi\)
\(294\) −6.06945 −0.353977
\(295\) 1.80051 0.104830
\(296\) 5.34170 0.310480
\(297\) 3.64539 0.211527
\(298\) 1.49612 0.0866678
\(299\) 52.4900 3.03558
\(300\) 3.74586 0.216267
\(301\) 0.0688485 0.00396836
\(302\) 5.66923 0.326228
\(303\) −35.2643 −2.02588
\(304\) 2.35997 0.135354
\(305\) 7.32347 0.419341
\(306\) −3.03806 −0.173674
\(307\) −29.5989 −1.68930 −0.844650 0.535318i \(-0.820192\pi\)
−0.844650 + 0.535318i \(0.820192\pi\)
\(308\) 0.105790 0.00602797
\(309\) 15.3406 0.872697
\(310\) 0.114362 0.00649531
\(311\) 7.86269 0.445852 0.222926 0.974835i \(-0.428439\pi\)
0.222926 + 0.974835i \(0.428439\pi\)
\(312\) −20.9844 −1.18801
\(313\) 17.4585 0.986815 0.493408 0.869798i \(-0.335751\pi\)
0.493408 + 0.869798i \(0.335751\pi\)
\(314\) −0.477988 −0.0269744
\(315\) −0.0712385 −0.00401384
\(316\) −18.5543 −1.04376
\(317\) −0.269093 −0.0151138 −0.00755689 0.999971i \(-0.502405\pi\)
−0.00755689 + 0.999971i \(0.502405\pi\)
\(318\) 3.30209 0.185172
\(319\) −1.17504 −0.0657894
\(320\) −4.03854 −0.225761
\(321\) 11.0090 0.614463
\(322\) 0.203181 0.0113228
\(323\) 4.67347 0.260039
\(324\) 20.3612 1.13118
\(325\) 6.32922 0.351082
\(326\) −1.54787 −0.0857283
\(327\) 6.83862 0.378177
\(328\) 2.83559 0.156570
\(329\) 0.669846 0.0369298
\(330\) 0.867482 0.0477533
\(331\) 23.9116 1.31430 0.657149 0.753760i \(-0.271762\pi\)
0.657149 + 0.753760i \(0.271762\pi\)
\(332\) −3.08422 −0.169269
\(333\) 4.06399 0.222705
\(334\) 5.69899 0.311835
\(335\) 11.5619 0.631696
\(336\) 0.353771 0.0192998
\(337\) 24.3953 1.32890 0.664448 0.747334i \(-0.268667\pi\)
0.664448 + 0.747334i \(0.268667\pi\)
\(338\) −11.4172 −0.621016
\(339\) 10.2322 0.555739
\(340\) −10.6925 −0.579881
\(341\) −0.271039 −0.0146776
\(342\) −0.412249 −0.0222919
\(343\) 0.812698 0.0438816
\(344\) −1.91216 −0.103097
\(345\) −17.0505 −0.917970
\(346\) −3.42162 −0.183947
\(347\) −6.25222 −0.335637 −0.167818 0.985818i \(-0.553672\pi\)
−0.167818 + 0.985818i \(0.553672\pi\)
\(348\) −4.40152 −0.235946
\(349\) −0.727597 −0.0389474 −0.0194737 0.999810i \(-0.506199\pi\)
−0.0194737 + 0.999810i \(0.506199\pi\)
\(350\) 0.0244994 0.00130955
\(351\) 23.0725 1.23152
\(352\) −4.47569 −0.238555
\(353\) 2.69860 0.143632 0.0718160 0.997418i \(-0.477121\pi\)
0.0718160 + 0.997418i \(0.477121\pi\)
\(354\) 1.56191 0.0830145
\(355\) −2.43721 −0.129354
\(356\) −19.1891 −1.01702
\(357\) 0.700575 0.0370784
\(358\) 7.05866 0.373062
\(359\) −8.46936 −0.446996 −0.223498 0.974704i \(-0.571748\pi\)
−0.223498 + 0.974704i \(0.571748\pi\)
\(360\) 1.97854 0.104278
\(361\) −18.3658 −0.966623
\(362\) −10.8882 −0.572273
\(363\) −2.05594 −0.107909
\(364\) 0.669571 0.0350950
\(365\) 1.00000 0.0523424
\(366\) 6.35298 0.332075
\(367\) −12.1939 −0.636515 −0.318257 0.948004i \(-0.603098\pi\)
−0.318257 + 0.948004i \(0.603098\pi\)
\(368\) 24.5772 1.28117
\(369\) 2.15733 0.112306
\(370\) −1.39763 −0.0726594
\(371\) −0.221022 −0.0114749
\(372\) −1.01527 −0.0526395
\(373\) 26.5346 1.37391 0.686955 0.726700i \(-0.258947\pi\)
0.686955 + 0.726700i \(0.258947\pi\)
\(374\) −2.47621 −0.128042
\(375\) −2.05594 −0.106168
\(376\) −18.6040 −0.959426
\(377\) −7.43706 −0.383028
\(378\) 0.0893099 0.00459361
\(379\) −11.4594 −0.588629 −0.294314 0.955709i \(-0.595091\pi\)
−0.294314 + 0.955709i \(0.595091\pi\)
\(380\) −1.45091 −0.0744304
\(381\) 20.5292 1.05174
\(382\) −8.86900 −0.453778
\(383\) −12.5491 −0.641230 −0.320615 0.947210i \(-0.603890\pi\)
−0.320615 + 0.947210i \(0.603890\pi\)
\(384\) −21.9069 −1.11793
\(385\) −0.0580639 −0.00295921
\(386\) −5.11796 −0.260497
\(387\) −1.45478 −0.0739507
\(388\) 31.6725 1.60793
\(389\) −25.3120 −1.28337 −0.641683 0.766970i \(-0.721764\pi\)
−0.641683 + 0.766970i \(0.721764\pi\)
\(390\) 5.49048 0.278021
\(391\) 48.6704 2.46137
\(392\) −11.2830 −0.569878
\(393\) 32.3468 1.63168
\(394\) 7.62310 0.384046
\(395\) 10.1837 0.512396
\(396\) −2.23537 −0.112332
\(397\) −20.5408 −1.03092 −0.515458 0.856915i \(-0.672378\pi\)
−0.515458 + 0.856915i \(0.672378\pi\)
\(398\) −4.97889 −0.249569
\(399\) 0.0950645 0.00475918
\(400\) 2.96350 0.148175
\(401\) 2.76198 0.137927 0.0689633 0.997619i \(-0.478031\pi\)
0.0689633 + 0.997619i \(0.478031\pi\)
\(402\) 10.0298 0.500239
\(403\) −1.71546 −0.0854533
\(404\) −31.2511 −1.55480
\(405\) −11.1754 −0.555311
\(406\) −0.0287877 −0.00142871
\(407\) 3.31240 0.164190
\(408\) −19.4574 −0.963286
\(409\) 12.6883 0.627397 0.313698 0.949523i \(-0.398432\pi\)
0.313698 + 0.949523i \(0.398432\pi\)
\(410\) −0.741920 −0.0366408
\(411\) 0.739614 0.0364825
\(412\) 13.5948 0.669767
\(413\) −0.104545 −0.00514430
\(414\) −4.29324 −0.211001
\(415\) 1.69280 0.0830961
\(416\) −28.3276 −1.38888
\(417\) −6.63998 −0.325161
\(418\) −0.336009 −0.0164347
\(419\) −9.15123 −0.447067 −0.223533 0.974696i \(-0.571759\pi\)
−0.223533 + 0.974696i \(0.571759\pi\)
\(420\) −0.217499 −0.0106129
\(421\) −13.8899 −0.676950 −0.338475 0.940975i \(-0.609911\pi\)
−0.338475 + 0.940975i \(0.609911\pi\)
\(422\) 4.86841 0.236991
\(423\) −14.1540 −0.688189
\(424\) 6.13854 0.298114
\(425\) 5.86865 0.284671
\(426\) −2.11424 −0.102435
\(427\) −0.425229 −0.0205783
\(428\) 9.75614 0.471581
\(429\) −13.0125 −0.628250
\(430\) 0.500309 0.0241270
\(431\) −9.50354 −0.457769 −0.228885 0.973454i \(-0.573508\pi\)
−0.228885 + 0.973454i \(0.573508\pi\)
\(432\) 10.8031 0.519766
\(433\) −34.4609 −1.65609 −0.828043 0.560664i \(-0.810546\pi\)
−0.828043 + 0.560664i \(0.810546\pi\)
\(434\) −0.00664028 −0.000318744 0
\(435\) 2.41581 0.115829
\(436\) 6.06036 0.290239
\(437\) 6.60432 0.315928
\(438\) 0.867482 0.0414499
\(439\) −24.1079 −1.15061 −0.575303 0.817940i \(-0.695116\pi\)
−0.575303 + 0.817940i \(0.695116\pi\)
\(440\) 1.61264 0.0768794
\(441\) −8.58416 −0.408770
\(442\) −15.6725 −0.745463
\(443\) 30.4108 1.44486 0.722430 0.691444i \(-0.243025\pi\)
0.722430 + 0.691444i \(0.243025\pi\)
\(444\) 12.4078 0.588848
\(445\) 10.5321 0.499268
\(446\) −5.55897 −0.263225
\(447\) 7.29000 0.344805
\(448\) 0.234493 0.0110788
\(449\) 8.93383 0.421614 0.210807 0.977528i \(-0.432391\pi\)
0.210807 + 0.977528i \(0.432391\pi\)
\(450\) −0.517676 −0.0244035
\(451\) 1.75836 0.0827979
\(452\) 9.06777 0.426512
\(453\) 27.6239 1.29789
\(454\) −1.14804 −0.0538800
\(455\) −0.367499 −0.0172286
\(456\) −2.64027 −0.123642
\(457\) −18.0465 −0.844178 −0.422089 0.906554i \(-0.638703\pi\)
−0.422089 + 0.906554i \(0.638703\pi\)
\(458\) 1.84888 0.0863924
\(459\) 21.3935 0.998564
\(460\) −15.1101 −0.704513
\(461\) −21.9323 −1.02149 −0.510744 0.859733i \(-0.670630\pi\)
−0.510744 + 0.859733i \(0.670630\pi\)
\(462\) −0.0503693 −0.00234339
\(463\) 11.7722 0.547100 0.273550 0.961858i \(-0.411802\pi\)
0.273550 + 0.961858i \(0.411802\pi\)
\(464\) −3.48222 −0.161658
\(465\) 0.557240 0.0258414
\(466\) 6.75957 0.313131
\(467\) −7.31958 −0.338710 −0.169355 0.985555i \(-0.554168\pi\)
−0.169355 + 0.985555i \(0.554168\pi\)
\(468\) −14.1482 −0.653998
\(469\) −0.671330 −0.0309992
\(470\) 4.86764 0.224527
\(471\) −2.32905 −0.107317
\(472\) 2.90357 0.133647
\(473\) −1.18574 −0.0545203
\(474\) 8.83414 0.405765
\(475\) 0.796345 0.0365388
\(476\) 0.620847 0.0284565
\(477\) 4.67023 0.213835
\(478\) 2.47877 0.113376
\(479\) 32.6962 1.49393 0.746964 0.664864i \(-0.231511\pi\)
0.746964 + 0.664864i \(0.231511\pi\)
\(480\) 9.20176 0.420001
\(481\) 20.9649 0.955918
\(482\) −7.74508 −0.352779
\(483\) 0.990020 0.0450475
\(484\) −1.82197 −0.0828167
\(485\) −17.3837 −0.789353
\(486\) −5.08007 −0.230437
\(487\) 30.1482 1.36615 0.683074 0.730350i \(-0.260643\pi\)
0.683074 + 0.730350i \(0.260643\pi\)
\(488\) 11.8101 0.534618
\(489\) −7.54214 −0.341068
\(490\) 2.95215 0.133364
\(491\) 39.3210 1.77453 0.887267 0.461256i \(-0.152601\pi\)
0.887267 + 0.461256i \(0.152601\pi\)
\(492\) 6.58657 0.296946
\(493\) −6.89587 −0.310575
\(494\) −2.12667 −0.0956835
\(495\) 1.22690 0.0551450
\(496\) −0.803224 −0.0360658
\(497\) 0.141514 0.00634777
\(498\) 1.46847 0.0658037
\(499\) −7.48890 −0.335249 −0.167625 0.985851i \(-0.553610\pi\)
−0.167625 + 0.985851i \(0.553610\pi\)
\(500\) −1.82197 −0.0814809
\(501\) 27.7690 1.24063
\(502\) −6.13105 −0.273642
\(503\) −9.35534 −0.417134 −0.208567 0.978008i \(-0.566880\pi\)
−0.208567 + 0.978008i \(0.566880\pi\)
\(504\) −0.114882 −0.00511724
\(505\) 17.1524 0.763271
\(506\) −3.49926 −0.155561
\(507\) −55.6317 −2.47069
\(508\) 18.1929 0.807179
\(509\) 13.4172 0.594707 0.297353 0.954768i \(-0.403896\pi\)
0.297353 + 0.954768i \(0.403896\pi\)
\(510\) 5.09094 0.225431
\(511\) −0.0580639 −0.00256859
\(512\) −22.8218 −1.00859
\(513\) 2.90299 0.128170
\(514\) −4.56798 −0.201485
\(515\) −7.46160 −0.328797
\(516\) −4.44161 −0.195531
\(517\) −11.5364 −0.507369
\(518\) 0.0811519 0.00356561
\(519\) −16.6722 −0.731829
\(520\) 10.2067 0.447594
\(521\) −5.77327 −0.252932 −0.126466 0.991971i \(-0.540363\pi\)
−0.126466 + 0.991971i \(0.540363\pi\)
\(522\) 0.608289 0.0266241
\(523\) −10.3779 −0.453793 −0.226896 0.973919i \(-0.572858\pi\)
−0.226896 + 0.973919i \(0.572858\pi\)
\(524\) 28.6656 1.25226
\(525\) 0.119376 0.00520999
\(526\) −6.64063 −0.289545
\(527\) −1.59063 −0.0692889
\(528\) −6.09279 −0.265155
\(529\) 45.7787 1.99038
\(530\) −1.60612 −0.0697654
\(531\) 2.20904 0.0958644
\(532\) 0.0842457 0.00365252
\(533\) 11.1290 0.482052
\(534\) 9.13637 0.395370
\(535\) −5.35473 −0.231505
\(536\) 18.6452 0.805349
\(537\) 34.3941 1.48421
\(538\) 2.23017 0.0961493
\(539\) −6.99663 −0.301366
\(540\) −6.64179 −0.285817
\(541\) −3.11922 −0.134106 −0.0670529 0.997749i \(-0.521360\pi\)
−0.0670529 + 0.997749i \(0.521360\pi\)
\(542\) 10.6089 0.455689
\(543\) −53.0541 −2.27677
\(544\) −26.2662 −1.12616
\(545\) −3.32627 −0.142482
\(546\) −0.318798 −0.0136433
\(547\) −33.8721 −1.44827 −0.724134 0.689659i \(-0.757760\pi\)
−0.724134 + 0.689659i \(0.757760\pi\)
\(548\) 0.655443 0.0279991
\(549\) 8.98516 0.383477
\(550\) −0.421939 −0.0179915
\(551\) −0.935735 −0.0398636
\(552\) −27.4963 −1.17032
\(553\) −0.591303 −0.0251447
\(554\) −7.87173 −0.334438
\(555\) −6.81011 −0.289073
\(556\) −5.88432 −0.249551
\(557\) 7.61945 0.322847 0.161423 0.986885i \(-0.448392\pi\)
0.161423 + 0.986885i \(0.448392\pi\)
\(558\) 0.140310 0.00593981
\(559\) −7.50479 −0.317419
\(560\) −0.172072 −0.00727138
\(561\) −12.0656 −0.509410
\(562\) −6.05063 −0.255231
\(563\) −12.1437 −0.511797 −0.255899 0.966704i \(-0.582371\pi\)
−0.255899 + 0.966704i \(0.582371\pi\)
\(564\) −43.2136 −1.81962
\(565\) −4.97691 −0.209380
\(566\) 6.78221 0.285078
\(567\) 0.648888 0.0272507
\(568\) −3.93034 −0.164913
\(569\) −42.0698 −1.76366 −0.881830 0.471568i \(-0.843688\pi\)
−0.881830 + 0.471568i \(0.843688\pi\)
\(570\) 0.690815 0.0289350
\(571\) 1.39958 0.0585708 0.0292854 0.999571i \(-0.490677\pi\)
0.0292854 + 0.999571i \(0.490677\pi\)
\(572\) −11.5316 −0.482162
\(573\) −43.2152 −1.80534
\(574\) 0.0430787 0.00179807
\(575\) 8.29329 0.345854
\(576\) −4.95488 −0.206453
\(577\) 28.8807 1.20232 0.601159 0.799129i \(-0.294706\pi\)
0.601159 + 0.799129i \(0.294706\pi\)
\(578\) −7.35903 −0.306095
\(579\) −24.9378 −1.03638
\(580\) 2.14088 0.0888952
\(581\) −0.0982903 −0.00407777
\(582\) −15.0800 −0.625088
\(583\) 3.80653 0.157650
\(584\) 1.61264 0.0667314
\(585\) 7.76531 0.321056
\(586\) 0.968172 0.0399948
\(587\) −33.1395 −1.36781 −0.683907 0.729569i \(-0.739721\pi\)
−0.683907 + 0.729569i \(0.739721\pi\)
\(588\) −26.2084 −1.08082
\(589\) −0.215840 −0.00889355
\(590\) −0.759705 −0.0312765
\(591\) 37.1444 1.52792
\(592\) 9.81631 0.403448
\(593\) −20.3765 −0.836763 −0.418382 0.908271i \(-0.637403\pi\)
−0.418382 + 0.908271i \(0.637403\pi\)
\(594\) −1.53813 −0.0631103
\(595\) −0.340756 −0.0139696
\(596\) 6.46036 0.264627
\(597\) −24.2602 −0.992903
\(598\) −22.1476 −0.905682
\(599\) −36.4738 −1.49028 −0.745140 0.666908i \(-0.767618\pi\)
−0.745140 + 0.666908i \(0.767618\pi\)
\(600\) −3.31549 −0.135354
\(601\) 1.23151 0.0502345 0.0251172 0.999685i \(-0.492004\pi\)
0.0251172 + 0.999685i \(0.492004\pi\)
\(602\) −0.0290499 −0.00118398
\(603\) 14.1853 0.577671
\(604\) 24.4802 0.996086
\(605\) 1.00000 0.0406558
\(606\) 14.8794 0.604433
\(607\) −45.9718 −1.86594 −0.932968 0.359958i \(-0.882791\pi\)
−0.932968 + 0.359958i \(0.882791\pi\)
\(608\) −3.56419 −0.144547
\(609\) −0.140271 −0.00568407
\(610\) −3.09006 −0.125113
\(611\) −73.0162 −2.95392
\(612\) −13.1186 −0.530288
\(613\) 12.5456 0.506710 0.253355 0.967373i \(-0.418466\pi\)
0.253355 + 0.967373i \(0.418466\pi\)
\(614\) 12.4889 0.504013
\(615\) −3.61509 −0.145774
\(616\) −0.0936359 −0.00377270
\(617\) 12.3123 0.495674 0.247837 0.968802i \(-0.420280\pi\)
0.247837 + 0.968802i \(0.420280\pi\)
\(618\) −6.47280 −0.260374
\(619\) 26.5602 1.06754 0.533772 0.845629i \(-0.320774\pi\)
0.533772 + 0.845629i \(0.320774\pi\)
\(620\) 0.493824 0.0198324
\(621\) 30.2323 1.21318
\(622\) −3.31757 −0.133023
\(623\) −0.611532 −0.0245005
\(624\) −38.5626 −1.54374
\(625\) 1.00000 0.0400000
\(626\) −7.36644 −0.294422
\(627\) −1.63724 −0.0653851
\(628\) −2.06399 −0.0823623
\(629\) 19.4393 0.775097
\(630\) 0.0300583 0.00119755
\(631\) −23.2148 −0.924166 −0.462083 0.886837i \(-0.652898\pi\)
−0.462083 + 0.886837i \(0.652898\pi\)
\(632\) 16.4225 0.653254
\(633\) 23.7219 0.942860
\(634\) 0.113541 0.00450928
\(635\) −9.98530 −0.396255
\(636\) 14.2587 0.565395
\(637\) −44.2832 −1.75456
\(638\) 0.495794 0.0196287
\(639\) −2.99022 −0.118291
\(640\) 10.6554 0.421191
\(641\) −2.79433 −0.110369 −0.0551847 0.998476i \(-0.517575\pi\)
−0.0551847 + 0.998476i \(0.517575\pi\)
\(642\) −4.64513 −0.183329
\(643\) −47.9516 −1.89103 −0.945513 0.325586i \(-0.894439\pi\)
−0.945513 + 0.325586i \(0.894439\pi\)
\(644\) 0.877351 0.0345725
\(645\) 2.43781 0.0959887
\(646\) −1.97192 −0.0775840
\(647\) 42.0348 1.65256 0.826279 0.563261i \(-0.190453\pi\)
0.826279 + 0.563261i \(0.190453\pi\)
\(648\) −18.0219 −0.707966
\(649\) 1.80051 0.0706762
\(650\) −2.67054 −0.104747
\(651\) −0.0323555 −0.00126811
\(652\) −6.68382 −0.261758
\(653\) 32.3619 1.26642 0.633209 0.773981i \(-0.281738\pi\)
0.633209 + 0.773981i \(0.281738\pi\)
\(654\) −2.88548 −0.112831
\(655\) −15.7333 −0.614752
\(656\) 5.21090 0.203452
\(657\) 1.22690 0.0478659
\(658\) −0.282634 −0.0110182
\(659\) −13.5290 −0.527014 −0.263507 0.964657i \(-0.584879\pi\)
−0.263507 + 0.964657i \(0.584879\pi\)
\(660\) 3.74586 0.145807
\(661\) 10.6160 0.412915 0.206457 0.978456i \(-0.433807\pi\)
0.206457 + 0.978456i \(0.433807\pi\)
\(662\) −10.0892 −0.392129
\(663\) −76.3658 −2.96580
\(664\) 2.72987 0.105939
\(665\) −0.0462389 −0.00179307
\(666\) −1.71475 −0.0664453
\(667\) −9.74492 −0.377325
\(668\) 24.6087 0.952141
\(669\) −27.0867 −1.04723
\(670\) −4.87843 −0.188470
\(671\) 7.32347 0.282719
\(672\) −0.534290 −0.0206107
\(673\) −27.0125 −1.04125 −0.520627 0.853784i \(-0.674302\pi\)
−0.520627 + 0.853784i \(0.674302\pi\)
\(674\) −10.2933 −0.396484
\(675\) 3.64539 0.140311
\(676\) −49.3006 −1.89618
\(677\) 1.25101 0.0480803 0.0240402 0.999711i \(-0.492347\pi\)
0.0240402 + 0.999711i \(0.492347\pi\)
\(678\) −4.31738 −0.165808
\(679\) 1.00936 0.0387359
\(680\) 9.46399 0.362927
\(681\) −5.59393 −0.214360
\(682\) 0.114362 0.00437914
\(683\) 27.9142 1.06811 0.534053 0.845451i \(-0.320668\pi\)
0.534053 + 0.845451i \(0.320668\pi\)
\(684\) −1.78013 −0.0680649
\(685\) −0.359744 −0.0137451
\(686\) −0.342909 −0.0130923
\(687\) 9.00886 0.343709
\(688\) −3.51394 −0.133968
\(689\) 24.0923 0.917845
\(690\) 7.19428 0.273882
\(691\) 10.0972 0.384115 0.192057 0.981384i \(-0.438484\pi\)
0.192057 + 0.981384i \(0.438484\pi\)
\(692\) −14.7748 −0.561655
\(693\) −0.0712385 −0.00270613
\(694\) 2.63805 0.100139
\(695\) 3.22965 0.122508
\(696\) 3.89582 0.147671
\(697\) 10.3192 0.390867
\(698\) 0.307001 0.0116202
\(699\) 32.9367 1.24578
\(700\) 0.105790 0.00399850
\(701\) 24.0837 0.909630 0.454815 0.890586i \(-0.349705\pi\)
0.454815 + 0.890586i \(0.349705\pi\)
\(702\) −9.73517 −0.367430
\(703\) 2.63782 0.0994871
\(704\) −4.03854 −0.152208
\(705\) 23.7181 0.893275
\(706\) −1.13864 −0.0428535
\(707\) −0.995933 −0.0374559
\(708\) 6.74446 0.253472
\(709\) 18.6612 0.700834 0.350417 0.936594i \(-0.386040\pi\)
0.350417 + 0.936594i \(0.386040\pi\)
\(710\) 1.02836 0.0385935
\(711\) 12.4943 0.468574
\(712\) 16.9844 0.636517
\(713\) −2.24780 −0.0841809
\(714\) −0.295600 −0.0110625
\(715\) 6.32922 0.236699
\(716\) 30.4799 1.13909
\(717\) 12.0781 0.451065
\(718\) 3.57355 0.133364
\(719\) −41.7871 −1.55839 −0.779197 0.626779i \(-0.784373\pi\)
−0.779197 + 0.626779i \(0.784373\pi\)
\(720\) 3.63592 0.135503
\(721\) 0.433249 0.0161350
\(722\) 7.74926 0.288397
\(723\) −37.7388 −1.40352
\(724\) −47.0163 −1.74735
\(725\) −1.17504 −0.0436398
\(726\) 0.867482 0.0321953
\(727\) −4.24284 −0.157358 −0.0786791 0.996900i \(-0.525070\pi\)
−0.0786791 + 0.996900i \(0.525070\pi\)
\(728\) −0.592642 −0.0219648
\(729\) 8.77304 0.324927
\(730\) −0.421939 −0.0156167
\(731\) −6.95868 −0.257376
\(732\) 27.4327 1.01394
\(733\) −1.98876 −0.0734566 −0.0367283 0.999325i \(-0.511694\pi\)
−0.0367283 + 0.999325i \(0.511694\pi\)
\(734\) 5.14507 0.189908
\(735\) 14.3847 0.530586
\(736\) −37.1182 −1.36819
\(737\) 11.5619 0.425889
\(738\) −0.910261 −0.0335072
\(739\) 36.6734 1.34905 0.674526 0.738251i \(-0.264348\pi\)
0.674526 + 0.738251i \(0.264348\pi\)
\(740\) −6.03509 −0.221854
\(741\) −10.3624 −0.380674
\(742\) 0.0932576 0.00342359
\(743\) 20.5285 0.753116 0.376558 0.926393i \(-0.377108\pi\)
0.376558 + 0.926393i \(0.377108\pi\)
\(744\) 0.898625 0.0329452
\(745\) −3.54582 −0.129909
\(746\) −11.1960 −0.409914
\(747\) 2.07689 0.0759895
\(748\) −10.6925 −0.390956
\(749\) 0.310916 0.0113606
\(750\) 0.867482 0.0316760
\(751\) 28.2983 1.03262 0.516310 0.856402i \(-0.327305\pi\)
0.516310 + 0.856402i \(0.327305\pi\)
\(752\) −34.1880 −1.24671
\(753\) −29.8742 −1.08868
\(754\) 3.13798 0.114279
\(755\) −13.4361 −0.488991
\(756\) 0.385648 0.0140259
\(757\) −20.7624 −0.754622 −0.377311 0.926087i \(-0.623151\pi\)
−0.377311 + 0.926087i \(0.623151\pi\)
\(758\) 4.83515 0.175621
\(759\) −17.0505 −0.618895
\(760\) 1.28421 0.0465834
\(761\) −7.83255 −0.283930 −0.141965 0.989872i \(-0.545342\pi\)
−0.141965 + 0.989872i \(0.545342\pi\)
\(762\) −8.66207 −0.313794
\(763\) 0.193136 0.00699200
\(764\) −38.2971 −1.38554
\(765\) 7.20024 0.260325
\(766\) 5.29496 0.191315
\(767\) 11.3958 0.411479
\(768\) −7.36264 −0.265676
\(769\) 5.47033 0.197265 0.0986326 0.995124i \(-0.468553\pi\)
0.0986326 + 0.995124i \(0.468553\pi\)
\(770\) 0.0244994 0.000882897 0
\(771\) −22.2580 −0.801602
\(772\) −22.0998 −0.795389
\(773\) 1.72694 0.0621139 0.0310569 0.999518i \(-0.490113\pi\)
0.0310569 + 0.999518i \(0.490113\pi\)
\(774\) 0.613829 0.0220636
\(775\) −0.271039 −0.00973600
\(776\) −28.0336 −1.00635
\(777\) 0.395421 0.0141857
\(778\) 10.6801 0.382900
\(779\) 1.40026 0.0501696
\(780\) 23.7084 0.848896
\(781\) −2.43721 −0.0872104
\(782\) −20.5359 −0.734363
\(783\) −4.28347 −0.153079
\(784\) −20.7345 −0.740519
\(785\) 1.13284 0.0404327
\(786\) −13.6484 −0.486822
\(787\) −44.3928 −1.58243 −0.791216 0.611537i \(-0.790551\pi\)
−0.791216 + 0.611537i \(0.790551\pi\)
\(788\) 32.9172 1.17263
\(789\) −32.3572 −1.15195
\(790\) −4.29688 −0.152876
\(791\) 0.288979 0.0102749
\(792\) 1.97854 0.0703045
\(793\) 46.3518 1.64600
\(794\) 8.66698 0.307579
\(795\) −7.82600 −0.277560
\(796\) −21.4993 −0.762021
\(797\) 31.4065 1.11247 0.556237 0.831024i \(-0.312245\pi\)
0.556237 + 0.831024i \(0.312245\pi\)
\(798\) −0.0401114 −0.00141993
\(799\) −67.7028 −2.39515
\(800\) −4.47569 −0.158239
\(801\) 12.9218 0.456569
\(802\) −1.16539 −0.0411512
\(803\) 1.00000 0.0352892
\(804\) 43.3094 1.52740
\(805\) −0.481541 −0.0169721
\(806\) 0.723820 0.0254955
\(807\) 10.8667 0.382527
\(808\) 27.6605 0.973095
\(809\) 0.367867 0.0129335 0.00646675 0.999979i \(-0.497942\pi\)
0.00646675 + 0.999979i \(0.497942\pi\)
\(810\) 4.71534 0.165680
\(811\) −13.9338 −0.489283 −0.244642 0.969614i \(-0.578670\pi\)
−0.244642 + 0.969614i \(0.578670\pi\)
\(812\) −0.124308 −0.00436235
\(813\) 51.6928 1.81295
\(814\) −1.39763 −0.0489870
\(815\) 3.66846 0.128501
\(816\) −35.7564 −1.25173
\(817\) −0.944257 −0.0330354
\(818\) −5.35369 −0.187187
\(819\) −0.450884 −0.0157552
\(820\) −3.20367 −0.111877
\(821\) −6.97646 −0.243480 −0.121740 0.992562i \(-0.538847\pi\)
−0.121740 + 0.992562i \(0.538847\pi\)
\(822\) −0.312072 −0.0108848
\(823\) 25.5197 0.889561 0.444781 0.895640i \(-0.353282\pi\)
0.444781 + 0.895640i \(0.353282\pi\)
\(824\) −12.0328 −0.419184
\(825\) −2.05594 −0.0715787
\(826\) 0.0441114 0.00153483
\(827\) −13.1983 −0.458951 −0.229476 0.973314i \(-0.573701\pi\)
−0.229476 + 0.973314i \(0.573701\pi\)
\(828\) −18.5386 −0.644260
\(829\) −18.0657 −0.627448 −0.313724 0.949514i \(-0.601577\pi\)
−0.313724 + 0.949514i \(0.601577\pi\)
\(830\) −0.714256 −0.0247922
\(831\) −38.3558 −1.33055
\(832\) −25.5608 −0.886161
\(833\) −41.0607 −1.42267
\(834\) 2.80166 0.0970137
\(835\) −13.5067 −0.467418
\(836\) −1.45091 −0.0501809
\(837\) −0.988043 −0.0341517
\(838\) 3.86126 0.133385
\(839\) 0.449001 0.0155012 0.00775062 0.999970i \(-0.497533\pi\)
0.00775062 + 0.999970i \(0.497533\pi\)
\(840\) 0.192510 0.00664223
\(841\) −27.6193 −0.952389
\(842\) 5.86067 0.201972
\(843\) −29.4824 −1.01543
\(844\) 21.0222 0.723615
\(845\) 27.0590 0.930857
\(846\) 5.97210 0.205325
\(847\) −0.0580639 −0.00199510
\(848\) 11.2806 0.387379
\(849\) 33.0471 1.13417
\(850\) −2.47621 −0.0849333
\(851\) 27.4707 0.941685
\(852\) −9.12946 −0.312770
\(853\) −15.9855 −0.547335 −0.273667 0.961824i \(-0.588237\pi\)
−0.273667 + 0.961824i \(0.588237\pi\)
\(854\) 0.179421 0.00613965
\(855\) 0.977035 0.0334139
\(856\) −8.63523 −0.295146
\(857\) 9.41864 0.321735 0.160867 0.986976i \(-0.448571\pi\)
0.160867 + 0.986976i \(0.448571\pi\)
\(858\) 5.49048 0.187442
\(859\) −30.8026 −1.05097 −0.525485 0.850803i \(-0.676116\pi\)
−0.525485 + 0.850803i \(0.676116\pi\)
\(860\) 2.16038 0.0736682
\(861\) 0.209906 0.00715357
\(862\) 4.00991 0.136578
\(863\) 36.6797 1.24859 0.624295 0.781189i \(-0.285386\pi\)
0.624295 + 0.781189i \(0.285386\pi\)
\(864\) −16.3156 −0.555069
\(865\) 8.10928 0.275724
\(866\) 14.5404 0.494103
\(867\) −35.8577 −1.21779
\(868\) −0.0286733 −0.000973236 0
\(869\) 10.1837 0.345457
\(870\) −1.01932 −0.0345583
\(871\) 73.1780 2.47954
\(872\) −5.36407 −0.181650
\(873\) −21.3281 −0.721845
\(874\) −2.78662 −0.0942588
\(875\) −0.0580639 −0.00196292
\(876\) 3.74586 0.126561
\(877\) 7.05155 0.238114 0.119057 0.992887i \(-0.462013\pi\)
0.119057 + 0.992887i \(0.462013\pi\)
\(878\) 10.1720 0.343290
\(879\) 4.71753 0.159118
\(880\) 2.96350 0.0998996
\(881\) −10.9248 −0.368067 −0.184034 0.982920i \(-0.558916\pi\)
−0.184034 + 0.982920i \(0.558916\pi\)
\(882\) 3.62199 0.121959
\(883\) 43.6605 1.46929 0.734646 0.678451i \(-0.237348\pi\)
0.734646 + 0.678451i \(0.237348\pi\)
\(884\) −67.6750 −2.27616
\(885\) −3.70174 −0.124433
\(886\) −12.8315 −0.431082
\(887\) −25.6433 −0.861018 −0.430509 0.902586i \(-0.641666\pi\)
−0.430509 + 0.902586i \(0.641666\pi\)
\(888\) −10.9822 −0.368540
\(889\) 0.579785 0.0194454
\(890\) −4.44389 −0.148959
\(891\) −11.1754 −0.374391
\(892\) −24.0041 −0.803718
\(893\) −9.18693 −0.307429
\(894\) −3.07593 −0.102875
\(895\) −16.7291 −0.559193
\(896\) −0.618693 −0.0206691
\(897\) −107.917 −3.60323
\(898\) −3.76953 −0.125791
\(899\) 0.318480 0.0106219
\(900\) −2.23537 −0.0745124
\(901\) 22.3392 0.744225
\(902\) −0.741920 −0.0247032
\(903\) −0.141549 −0.00471044
\(904\) −8.02595 −0.266939
\(905\) 25.8052 0.857795
\(906\) −11.6556 −0.387232
\(907\) 29.5453 0.981034 0.490517 0.871432i \(-0.336808\pi\)
0.490517 + 0.871432i \(0.336808\pi\)
\(908\) −4.95732 −0.164514
\(909\) 21.0442 0.697994
\(910\) 0.155062 0.00514025
\(911\) 26.3096 0.871677 0.435838 0.900025i \(-0.356452\pi\)
0.435838 + 0.900025i \(0.356452\pi\)
\(912\) −4.85196 −0.160665
\(913\) 1.69280 0.0560234
\(914\) 7.61450 0.251865
\(915\) −15.0566 −0.497757
\(916\) 7.98362 0.263786
\(917\) 0.913538 0.0301677
\(918\) −9.02675 −0.297927
\(919\) 53.2713 1.75726 0.878629 0.477505i \(-0.158459\pi\)
0.878629 + 0.477505i \(0.158459\pi\)
\(920\) 13.3741 0.440930
\(921\) 60.8537 2.00520
\(922\) 9.25408 0.304767
\(923\) −15.4257 −0.507742
\(924\) −0.217499 −0.00715520
\(925\) 3.31240 0.108911
\(926\) −4.96714 −0.163230
\(927\) −9.15463 −0.300678
\(928\) 5.25910 0.172638
\(929\) 38.9317 1.27731 0.638654 0.769494i \(-0.279492\pi\)
0.638654 + 0.769494i \(0.279492\pi\)
\(930\) −0.235121 −0.00770993
\(931\) −5.57173 −0.182606
\(932\) 29.1884 0.956098
\(933\) −16.1652 −0.529226
\(934\) 3.08842 0.101056
\(935\) 5.86865 0.191925
\(936\) 12.5226 0.409315
\(937\) 46.6511 1.52403 0.762013 0.647562i \(-0.224211\pi\)
0.762013 + 0.647562i \(0.224211\pi\)
\(938\) 0.283260 0.00924878
\(939\) −35.8938 −1.17135
\(940\) 21.0189 0.685560
\(941\) 50.3438 1.64116 0.820581 0.571530i \(-0.193650\pi\)
0.820581 + 0.571530i \(0.193650\pi\)
\(942\) 0.982716 0.0320186
\(943\) 14.5826 0.474875
\(944\) 5.33581 0.173666
\(945\) −0.211666 −0.00688548
\(946\) 0.500309 0.0162664
\(947\) 25.3314 0.823162 0.411581 0.911373i \(-0.364977\pi\)
0.411581 + 0.911373i \(0.364977\pi\)
\(948\) 38.1466 1.23894
\(949\) 6.32922 0.205455
\(950\) −0.336009 −0.0109016
\(951\) 0.553240 0.0179400
\(952\) −0.549516 −0.0178099
\(953\) 39.2750 1.27224 0.636120 0.771590i \(-0.280538\pi\)
0.636120 + 0.771590i \(0.280538\pi\)
\(954\) −1.97055 −0.0637989
\(955\) 21.0196 0.680180
\(956\) 10.7036 0.346178
\(957\) 2.41581 0.0780920
\(958\) −13.7958 −0.445722
\(959\) 0.0208881 0.000674514 0
\(960\) 8.30300 0.267978
\(961\) −30.9265 −0.997630
\(962\) −8.84591 −0.285204
\(963\) −6.56972 −0.211706
\(964\) −33.4439 −1.07716
\(965\) 12.1296 0.390467
\(966\) −0.417728 −0.0134402
\(967\) 35.6000 1.14482 0.572409 0.819968i \(-0.306009\pi\)
0.572409 + 0.819968i \(0.306009\pi\)
\(968\) 1.61264 0.0518321
\(969\) −9.60838 −0.308666
\(970\) 7.33486 0.235508
\(971\) 5.02580 0.161286 0.0806428 0.996743i \(-0.474303\pi\)
0.0806428 + 0.996743i \(0.474303\pi\)
\(972\) −21.9362 −0.703604
\(973\) −0.187526 −0.00601181
\(974\) −12.7207 −0.407598
\(975\) −13.0125 −0.416734
\(976\) 21.7031 0.694700
\(977\) −18.9735 −0.607015 −0.303507 0.952829i \(-0.598158\pi\)
−0.303507 + 0.952829i \(0.598158\pi\)
\(978\) 3.18232 0.101759
\(979\) 10.5321 0.336606
\(980\) 12.7476 0.407208
\(981\) −4.08100 −0.130296
\(982\) −16.5911 −0.529442
\(983\) −31.2871 −0.997904 −0.498952 0.866630i \(-0.666282\pi\)
−0.498952 + 0.866630i \(0.666282\pi\)
\(984\) −5.82982 −0.185848
\(985\) −18.0668 −0.575657
\(986\) 2.90964 0.0926617
\(987\) −1.37716 −0.0438356
\(988\) −9.18316 −0.292155
\(989\) −9.83367 −0.312693
\(990\) −0.517676 −0.0164528
\(991\) −20.8298 −0.661680 −0.330840 0.943687i \(-0.607332\pi\)
−0.330840 + 0.943687i \(0.607332\pi\)
\(992\) 1.21308 0.0385155
\(993\) −49.1608 −1.56007
\(994\) −0.0597103 −0.00189389
\(995\) 11.8000 0.374086
\(996\) 6.34098 0.200922
\(997\) −34.4365 −1.09061 −0.545307 0.838236i \(-0.683587\pi\)
−0.545307 + 0.838236i \(0.683587\pi\)
\(998\) 3.15986 0.100023
\(999\) 12.0750 0.382036
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 \(a_p\))