Properties

Label 4015.2.a.h.1.14
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 1.14
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.742421 q^{2}\) \(+0.782455 q^{3}\) \(-1.44881 q^{4}\) \(+1.00000 q^{5}\) \(-0.580911 q^{6}\) \(+0.262449 q^{7}\) \(+2.56047 q^{8}\) \(-2.38776 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.742421 q^{2}\) \(+0.782455 q^{3}\) \(-1.44881 q^{4}\) \(+1.00000 q^{5}\) \(-0.580911 q^{6}\) \(+0.262449 q^{7}\) \(+2.56047 q^{8}\) \(-2.38776 q^{9}\) \(-0.742421 q^{10}\) \(+1.00000 q^{11}\) \(-1.13363 q^{12}\) \(-1.63020 q^{13}\) \(-0.194848 q^{14}\) \(+0.782455 q^{15}\) \(+0.996674 q^{16}\) \(-3.94785 q^{17}\) \(+1.77273 q^{18}\) \(+3.18333 q^{19}\) \(-1.44881 q^{20}\) \(+0.205355 q^{21}\) \(-0.742421 q^{22}\) \(-4.37745 q^{23}\) \(+2.00345 q^{24}\) \(+1.00000 q^{25}\) \(+1.21030 q^{26}\) \(-4.21568 q^{27}\) \(-0.380239 q^{28}\) \(+4.80588 q^{29}\) \(-0.580911 q^{30}\) \(-0.406340 q^{31}\) \(-5.86089 q^{32}\) \(+0.782455 q^{33}\) \(+2.93097 q^{34}\) \(+0.262449 q^{35}\) \(+3.45942 q^{36}\) \(+6.86756 q^{37}\) \(-2.36337 q^{38}\) \(-1.27556 q^{39}\) \(+2.56047 q^{40}\) \(+10.8431 q^{41}\) \(-0.152460 q^{42}\) \(-9.75665 q^{43}\) \(-1.44881 q^{44}\) \(-2.38776 q^{45}\) \(+3.24991 q^{46}\) \(+7.88801 q^{47}\) \(+0.779853 q^{48}\) \(-6.93112 q^{49}\) \(-0.742421 q^{50}\) \(-3.08902 q^{51}\) \(+2.36185 q^{52}\) \(-3.45344 q^{53}\) \(+3.12981 q^{54}\) \(+1.00000 q^{55}\) \(+0.671993 q^{56}\) \(+2.49082 q^{57}\) \(-3.56799 q^{58}\) \(+5.96161 q^{59}\) \(-1.13363 q^{60}\) \(+6.28533 q^{61}\) \(+0.301675 q^{62}\) \(-0.626667 q^{63}\) \(+2.35790 q^{64}\) \(-1.63020 q^{65}\) \(-0.580911 q^{66}\) \(+15.0832 q^{67}\) \(+5.71969 q^{68}\) \(-3.42516 q^{69}\) \(-0.194848 q^{70}\) \(-0.367892 q^{71}\) \(-6.11380 q^{72}\) \(+1.00000 q^{73}\) \(-5.09862 q^{74}\) \(+0.782455 q^{75}\) \(-4.61205 q^{76}\) \(+0.262449 q^{77}\) \(+0.947003 q^{78}\) \(-9.69406 q^{79}\) \(+0.996674 q^{80}\) \(+3.86471 q^{81}\) \(-8.05015 q^{82}\) \(-7.65958 q^{83}\) \(-0.297520 q^{84}\) \(-3.94785 q^{85}\) \(+7.24354 q^{86}\) \(+3.76039 q^{87}\) \(+2.56047 q^{88}\) \(-0.317007 q^{89}\) \(+1.77273 q^{90}\) \(-0.427845 q^{91}\) \(+6.34210 q^{92}\) \(-0.317943 q^{93}\) \(-5.85622 q^{94}\) \(+3.18333 q^{95}\) \(-4.58589 q^{96}\) \(+9.10851 q^{97}\) \(+5.14581 q^{98}\) \(-2.38776 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.742421 −0.524971 −0.262486 0.964936i \(-0.584542\pi\)
−0.262486 + 0.964936i \(0.584542\pi\)
\(3\) 0.782455 0.451751 0.225875 0.974156i \(-0.427476\pi\)
0.225875 + 0.974156i \(0.427476\pi\)
\(4\) −1.44881 −0.724405
\(5\) 1.00000 0.447214
\(6\) −0.580911 −0.237156
\(7\) 0.262449 0.0991965 0.0495982 0.998769i \(-0.484206\pi\)
0.0495982 + 0.998769i \(0.484206\pi\)
\(8\) 2.56047 0.905263
\(9\) −2.38776 −0.795921
\(10\) −0.742421 −0.234774
\(11\) 1.00000 0.301511
\(12\) −1.13363 −0.327251
\(13\) −1.63020 −0.452137 −0.226068 0.974111i \(-0.572587\pi\)
−0.226068 + 0.974111i \(0.572587\pi\)
\(14\) −0.194848 −0.0520753
\(15\) 0.782455 0.202029
\(16\) 0.996674 0.249169
\(17\) −3.94785 −0.957495 −0.478747 0.877953i \(-0.658909\pi\)
−0.478747 + 0.877953i \(0.658909\pi\)
\(18\) 1.77273 0.417836
\(19\) 3.18333 0.730307 0.365153 0.930947i \(-0.381017\pi\)
0.365153 + 0.930947i \(0.381017\pi\)
\(20\) −1.44881 −0.323964
\(21\) 0.205355 0.0448121
\(22\) −0.742421 −0.158285
\(23\) −4.37745 −0.912762 −0.456381 0.889784i \(-0.650855\pi\)
−0.456381 + 0.889784i \(0.650855\pi\)
\(24\) 2.00345 0.408953
\(25\) 1.00000 0.200000
\(26\) 1.21030 0.237359
\(27\) −4.21568 −0.811309
\(28\) −0.380239 −0.0718584
\(29\) 4.80588 0.892430 0.446215 0.894926i \(-0.352772\pi\)
0.446215 + 0.894926i \(0.352772\pi\)
\(30\) −0.580911 −0.106059
\(31\) −0.406340 −0.0729808 −0.0364904 0.999334i \(-0.511618\pi\)
−0.0364904 + 0.999334i \(0.511618\pi\)
\(32\) −5.86089 −1.03607
\(33\) 0.782455 0.136208
\(34\) 2.93097 0.502657
\(35\) 0.262449 0.0443620
\(36\) 3.45942 0.576570
\(37\) 6.86756 1.12902 0.564510 0.825426i \(-0.309065\pi\)
0.564510 + 0.825426i \(0.309065\pi\)
\(38\) −2.36337 −0.383390
\(39\) −1.27556 −0.204253
\(40\) 2.56047 0.404846
\(41\) 10.8431 1.69341 0.846704 0.532064i \(-0.178584\pi\)
0.846704 + 0.532064i \(0.178584\pi\)
\(42\) −0.152460 −0.0235250
\(43\) −9.75665 −1.48787 −0.743937 0.668249i \(-0.767044\pi\)
−0.743937 + 0.668249i \(0.767044\pi\)
\(44\) −1.44881 −0.218416
\(45\) −2.38776 −0.355947
\(46\) 3.24991 0.479174
\(47\) 7.88801 1.15058 0.575292 0.817948i \(-0.304888\pi\)
0.575292 + 0.817948i \(0.304888\pi\)
\(48\) 0.779853 0.112562
\(49\) −6.93112 −0.990160
\(50\) −0.742421 −0.104994
\(51\) −3.08902 −0.432549
\(52\) 2.36185 0.327530
\(53\) −3.45344 −0.474367 −0.237184 0.971465i \(-0.576224\pi\)
−0.237184 + 0.971465i \(0.576224\pi\)
\(54\) 3.12981 0.425914
\(55\) 1.00000 0.134840
\(56\) 0.671993 0.0897989
\(57\) 2.49082 0.329917
\(58\) −3.56799 −0.468500
\(59\) 5.96161 0.776135 0.388067 0.921631i \(-0.373143\pi\)
0.388067 + 0.921631i \(0.373143\pi\)
\(60\) −1.13363 −0.146351
\(61\) 6.28533 0.804754 0.402377 0.915474i \(-0.368184\pi\)
0.402377 + 0.915474i \(0.368184\pi\)
\(62\) 0.301675 0.0383128
\(63\) −0.626667 −0.0789526
\(64\) 2.35790 0.294738
\(65\) −1.63020 −0.202202
\(66\) −0.580911 −0.0715053
\(67\) 15.0832 1.84270 0.921351 0.388732i \(-0.127087\pi\)
0.921351 + 0.388732i \(0.127087\pi\)
\(68\) 5.71969 0.693614
\(69\) −3.42516 −0.412341
\(70\) −0.194848 −0.0232888
\(71\) −0.367892 −0.0436607 −0.0218304 0.999762i \(-0.506949\pi\)
−0.0218304 + 0.999762i \(0.506949\pi\)
\(72\) −6.11380 −0.720518
\(73\) 1.00000 0.117041
\(74\) −5.09862 −0.592703
\(75\) 0.782455 0.0903502
\(76\) −4.61205 −0.529038
\(77\) 0.262449 0.0299089
\(78\) 0.947003 0.107227
\(79\) −9.69406 −1.09067 −0.545334 0.838219i \(-0.683597\pi\)
−0.545334 + 0.838219i \(0.683597\pi\)
\(80\) 0.996674 0.111432
\(81\) 3.86471 0.429412
\(82\) −8.05015 −0.888990
\(83\) −7.65958 −0.840748 −0.420374 0.907351i \(-0.638101\pi\)
−0.420374 + 0.907351i \(0.638101\pi\)
\(84\) −0.297520 −0.0324621
\(85\) −3.94785 −0.428205
\(86\) 7.24354 0.781091
\(87\) 3.76039 0.403156
\(88\) 2.56047 0.272947
\(89\) −0.317007 −0.0336026 −0.0168013 0.999859i \(-0.505348\pi\)
−0.0168013 + 0.999859i \(0.505348\pi\)
\(90\) 1.77273 0.186862
\(91\) −0.427845 −0.0448504
\(92\) 6.34210 0.661210
\(93\) −0.317943 −0.0329691
\(94\) −5.85622 −0.604023
\(95\) 3.18333 0.326603
\(96\) −4.58589 −0.468045
\(97\) 9.10851 0.924829 0.462414 0.886664i \(-0.346983\pi\)
0.462414 + 0.886664i \(0.346983\pi\)
\(98\) 5.14581 0.519805
\(99\) −2.38776 −0.239979
\(100\) −1.44881 −0.144881
\(101\) 2.57120 0.255844 0.127922 0.991784i \(-0.459169\pi\)
0.127922 + 0.991784i \(0.459169\pi\)
\(102\) 2.29335 0.227076
\(103\) 2.19580 0.216359 0.108179 0.994131i \(-0.465498\pi\)
0.108179 + 0.994131i \(0.465498\pi\)
\(104\) −4.17408 −0.409303
\(105\) 0.205355 0.0200406
\(106\) 2.56391 0.249029
\(107\) 13.3236 1.28804 0.644021 0.765008i \(-0.277265\pi\)
0.644021 + 0.765008i \(0.277265\pi\)
\(108\) 6.10773 0.587717
\(109\) −2.88532 −0.276364 −0.138182 0.990407i \(-0.544126\pi\)
−0.138182 + 0.990407i \(0.544126\pi\)
\(110\) −0.742421 −0.0707871
\(111\) 5.37356 0.510036
\(112\) 0.261576 0.0247166
\(113\) −7.43713 −0.699626 −0.349813 0.936820i \(-0.613755\pi\)
−0.349813 + 0.936820i \(0.613755\pi\)
\(114\) −1.84923 −0.173197
\(115\) −4.37745 −0.408200
\(116\) −6.96281 −0.646481
\(117\) 3.89254 0.359865
\(118\) −4.42602 −0.407448
\(119\) −1.03611 −0.0949801
\(120\) 2.00345 0.182889
\(121\) 1.00000 0.0909091
\(122\) −4.66636 −0.422472
\(123\) 8.48424 0.764998
\(124\) 0.588709 0.0528677
\(125\) 1.00000 0.0894427
\(126\) 0.465251 0.0414478
\(127\) 4.34669 0.385706 0.192853 0.981228i \(-0.438226\pi\)
0.192853 + 0.981228i \(0.438226\pi\)
\(128\) 9.97123 0.881340
\(129\) −7.63414 −0.672149
\(130\) 1.21030 0.106150
\(131\) 0.0689576 0.00602485 0.00301243 0.999995i \(-0.499041\pi\)
0.00301243 + 0.999995i \(0.499041\pi\)
\(132\) −1.13363 −0.0986698
\(133\) 0.835463 0.0724438
\(134\) −11.1981 −0.967365
\(135\) −4.21568 −0.362828
\(136\) −10.1084 −0.866785
\(137\) 4.15943 0.355364 0.177682 0.984088i \(-0.443140\pi\)
0.177682 + 0.984088i \(0.443140\pi\)
\(138\) 2.54291 0.216467
\(139\) 4.87694 0.413656 0.206828 0.978377i \(-0.433686\pi\)
0.206828 + 0.978377i \(0.433686\pi\)
\(140\) −0.380239 −0.0321361
\(141\) 6.17201 0.519777
\(142\) 0.273131 0.0229206
\(143\) −1.63020 −0.136324
\(144\) −2.37982 −0.198318
\(145\) 4.80588 0.399107
\(146\) −0.742421 −0.0614432
\(147\) −5.42329 −0.447306
\(148\) −9.94979 −0.817868
\(149\) 6.06732 0.497055 0.248527 0.968625i \(-0.420053\pi\)
0.248527 + 0.968625i \(0.420053\pi\)
\(150\) −0.580911 −0.0474312
\(151\) 10.4720 0.852203 0.426102 0.904675i \(-0.359887\pi\)
0.426102 + 0.904675i \(0.359887\pi\)
\(152\) 8.15083 0.661119
\(153\) 9.42654 0.762090
\(154\) −0.194848 −0.0157013
\(155\) −0.406340 −0.0326380
\(156\) 1.84805 0.147962
\(157\) −5.00866 −0.399735 −0.199867 0.979823i \(-0.564051\pi\)
−0.199867 + 0.979823i \(0.564051\pi\)
\(158\) 7.19708 0.572569
\(159\) −2.70217 −0.214296
\(160\) −5.86089 −0.463344
\(161\) −1.14886 −0.0905427
\(162\) −2.86924 −0.225429
\(163\) 11.8436 0.927661 0.463830 0.885924i \(-0.346475\pi\)
0.463830 + 0.885924i \(0.346475\pi\)
\(164\) −15.7096 −1.22671
\(165\) 0.782455 0.0609141
\(166\) 5.68663 0.441368
\(167\) −12.4359 −0.962321 −0.481161 0.876632i \(-0.659785\pi\)
−0.481161 + 0.876632i \(0.659785\pi\)
\(168\) 0.525805 0.0405667
\(169\) −10.3424 −0.795572
\(170\) 2.93097 0.224795
\(171\) −7.60105 −0.581266
\(172\) 14.1355 1.07782
\(173\) 5.89071 0.447862 0.223931 0.974605i \(-0.428111\pi\)
0.223931 + 0.974605i \(0.428111\pi\)
\(174\) −2.79179 −0.211645
\(175\) 0.262449 0.0198393
\(176\) 0.996674 0.0751271
\(177\) 4.66469 0.350620
\(178\) 0.235352 0.0176404
\(179\) 11.4631 0.856792 0.428396 0.903591i \(-0.359079\pi\)
0.428396 + 0.903591i \(0.359079\pi\)
\(180\) 3.45942 0.257850
\(181\) 14.7852 1.09898 0.549489 0.835501i \(-0.314822\pi\)
0.549489 + 0.835501i \(0.314822\pi\)
\(182\) 0.317641 0.0235451
\(183\) 4.91799 0.363548
\(184\) −11.2083 −0.826290
\(185\) 6.86756 0.504913
\(186\) 0.236047 0.0173078
\(187\) −3.94785 −0.288696
\(188\) −11.4282 −0.833489
\(189\) −1.10640 −0.0804790
\(190\) −2.36337 −0.171457
\(191\) −5.07748 −0.367393 −0.183697 0.982983i \(-0.558806\pi\)
−0.183697 + 0.982983i \(0.558806\pi\)
\(192\) 1.84495 0.133148
\(193\) 19.7757 1.42349 0.711743 0.702440i \(-0.247906\pi\)
0.711743 + 0.702440i \(0.247906\pi\)
\(194\) −6.76235 −0.485508
\(195\) −1.27556 −0.0913448
\(196\) 10.0419 0.717277
\(197\) −1.83202 −0.130526 −0.0652631 0.997868i \(-0.520789\pi\)
−0.0652631 + 0.997868i \(0.520789\pi\)
\(198\) 1.77273 0.125982
\(199\) 14.5281 1.02987 0.514935 0.857229i \(-0.327816\pi\)
0.514935 + 0.857229i \(0.327816\pi\)
\(200\) 2.56047 0.181053
\(201\) 11.8019 0.832442
\(202\) −1.90891 −0.134311
\(203\) 1.26130 0.0885259
\(204\) 4.47540 0.313341
\(205\) 10.8431 0.757315
\(206\) −1.63021 −0.113582
\(207\) 10.4523 0.726487
\(208\) −1.62478 −0.112658
\(209\) 3.18333 0.220196
\(210\) −0.152460 −0.0105207
\(211\) −5.07473 −0.349359 −0.174679 0.984625i \(-0.555889\pi\)
−0.174679 + 0.984625i \(0.555889\pi\)
\(212\) 5.00339 0.343634
\(213\) −0.287859 −0.0197238
\(214\) −9.89173 −0.676185
\(215\) −9.75665 −0.665398
\(216\) −10.7941 −0.734448
\(217\) −0.106643 −0.00723943
\(218\) 2.14212 0.145083
\(219\) 0.782455 0.0528734
\(220\) −1.44881 −0.0976788
\(221\) 6.43580 0.432919
\(222\) −3.98944 −0.267754
\(223\) 6.09231 0.407971 0.203986 0.978974i \(-0.434610\pi\)
0.203986 + 0.978974i \(0.434610\pi\)
\(224\) −1.53819 −0.102774
\(225\) −2.38776 −0.159184
\(226\) 5.52148 0.367283
\(227\) −18.1291 −1.20327 −0.601635 0.798771i \(-0.705484\pi\)
−0.601635 + 0.798771i \(0.705484\pi\)
\(228\) −3.60872 −0.238993
\(229\) −14.2432 −0.941219 −0.470610 0.882342i \(-0.655966\pi\)
−0.470610 + 0.882342i \(0.655966\pi\)
\(230\) 3.24991 0.214293
\(231\) 0.205355 0.0135113
\(232\) 12.3053 0.807884
\(233\) −16.0599 −1.05212 −0.526060 0.850447i \(-0.676331\pi\)
−0.526060 + 0.850447i \(0.676331\pi\)
\(234\) −2.88990 −0.188919
\(235\) 7.88801 0.514557
\(236\) −8.63724 −0.562236
\(237\) −7.58517 −0.492710
\(238\) 0.769230 0.0498618
\(239\) 11.4599 0.741280 0.370640 0.928777i \(-0.379138\pi\)
0.370640 + 0.928777i \(0.379138\pi\)
\(240\) 0.779853 0.0503393
\(241\) 16.0377 1.03308 0.516538 0.856264i \(-0.327221\pi\)
0.516538 + 0.856264i \(0.327221\pi\)
\(242\) −0.742421 −0.0477246
\(243\) 15.6710 1.00530
\(244\) −9.10625 −0.582968
\(245\) −6.93112 −0.442813
\(246\) −6.29888 −0.401602
\(247\) −5.18948 −0.330198
\(248\) −1.04042 −0.0660668
\(249\) −5.99328 −0.379808
\(250\) −0.742421 −0.0469548
\(251\) 9.70512 0.612582 0.306291 0.951938i \(-0.400912\pi\)
0.306291 + 0.951938i \(0.400912\pi\)
\(252\) 0.907921 0.0571937
\(253\) −4.37745 −0.275208
\(254\) −3.22707 −0.202485
\(255\) −3.08902 −0.193442
\(256\) −12.1187 −0.757416
\(257\) −24.8525 −1.55025 −0.775127 0.631805i \(-0.782314\pi\)
−0.775127 + 0.631805i \(0.782314\pi\)
\(258\) 5.66775 0.352859
\(259\) 1.80239 0.111995
\(260\) 2.36185 0.146476
\(261\) −11.4753 −0.710304
\(262\) −0.0511956 −0.00316287
\(263\) 28.4980 1.75726 0.878631 0.477502i \(-0.158458\pi\)
0.878631 + 0.477502i \(0.158458\pi\)
\(264\) 2.00345 0.123304
\(265\) −3.45344 −0.212143
\(266\) −0.620265 −0.0380309
\(267\) −0.248044 −0.0151800
\(268\) −21.8527 −1.33486
\(269\) 12.2506 0.746930 0.373465 0.927644i \(-0.378170\pi\)
0.373465 + 0.927644i \(0.378170\pi\)
\(270\) 3.12981 0.190474
\(271\) −3.50279 −0.212779 −0.106390 0.994325i \(-0.533929\pi\)
−0.106390 + 0.994325i \(0.533929\pi\)
\(272\) −3.93472 −0.238578
\(273\) −0.334770 −0.0202612
\(274\) −3.08805 −0.186556
\(275\) 1.00000 0.0603023
\(276\) 4.96241 0.298702
\(277\) 32.6492 1.96170 0.980850 0.194765i \(-0.0623944\pi\)
0.980850 + 0.194765i \(0.0623944\pi\)
\(278\) −3.62074 −0.217158
\(279\) 0.970243 0.0580869
\(280\) 0.671993 0.0401593
\(281\) 18.0971 1.07958 0.539791 0.841799i \(-0.318503\pi\)
0.539791 + 0.841799i \(0.318503\pi\)
\(282\) −4.58223 −0.272868
\(283\) 12.3586 0.734642 0.367321 0.930094i \(-0.380275\pi\)
0.367321 + 0.930094i \(0.380275\pi\)
\(284\) 0.533005 0.0316280
\(285\) 2.49082 0.147543
\(286\) 1.21030 0.0715663
\(287\) 2.84576 0.167980
\(288\) 13.9944 0.824629
\(289\) −1.41446 −0.0832038
\(290\) −3.56799 −0.209520
\(291\) 7.12700 0.417792
\(292\) −1.44881 −0.0847852
\(293\) 15.1921 0.887532 0.443766 0.896143i \(-0.353642\pi\)
0.443766 + 0.896143i \(0.353642\pi\)
\(294\) 4.02637 0.234823
\(295\) 5.96161 0.347098
\(296\) 17.5842 1.02206
\(297\) −4.21568 −0.244619
\(298\) −4.50451 −0.260939
\(299\) 7.13613 0.412693
\(300\) −1.13363 −0.0654501
\(301\) −2.56062 −0.147592
\(302\) −7.77467 −0.447382
\(303\) 2.01185 0.115578
\(304\) 3.17274 0.181969
\(305\) 6.28533 0.359897
\(306\) −6.99846 −0.400075
\(307\) 11.9756 0.683482 0.341741 0.939794i \(-0.388983\pi\)
0.341741 + 0.939794i \(0.388983\pi\)
\(308\) −0.380239 −0.0216661
\(309\) 1.71812 0.0977402
\(310\) 0.301675 0.0171340
\(311\) 23.6122 1.33892 0.669461 0.742847i \(-0.266525\pi\)
0.669461 + 0.742847i \(0.266525\pi\)
\(312\) −3.26603 −0.184903
\(313\) −22.2454 −1.25738 −0.628692 0.777654i \(-0.716409\pi\)
−0.628692 + 0.777654i \(0.716409\pi\)
\(314\) 3.71854 0.209849
\(315\) −0.626667 −0.0353087
\(316\) 14.0449 0.790085
\(317\) −13.7589 −0.772776 −0.386388 0.922336i \(-0.626277\pi\)
−0.386388 + 0.922336i \(0.626277\pi\)
\(318\) 2.00615 0.112499
\(319\) 4.80588 0.269078
\(320\) 2.35790 0.131811
\(321\) 10.4251 0.581874
\(322\) 0.852937 0.0475323
\(323\) −12.5673 −0.699265
\(324\) −5.59923 −0.311068
\(325\) −1.63020 −0.0904274
\(326\) −8.79293 −0.486995
\(327\) −2.25764 −0.124848
\(328\) 27.7634 1.53298
\(329\) 2.07020 0.114134
\(330\) −0.580911 −0.0319781
\(331\) 23.3190 1.28173 0.640865 0.767653i \(-0.278576\pi\)
0.640865 + 0.767653i \(0.278576\pi\)
\(332\) 11.0973 0.609042
\(333\) −16.3981 −0.898611
\(334\) 9.23270 0.505191
\(335\) 15.0832 0.824081
\(336\) 0.204672 0.0111658
\(337\) 15.9904 0.871051 0.435526 0.900176i \(-0.356563\pi\)
0.435526 + 0.900176i \(0.356563\pi\)
\(338\) 7.67845 0.417652
\(339\) −5.81922 −0.316057
\(340\) 5.71969 0.310194
\(341\) −0.406340 −0.0220045
\(342\) 5.64318 0.305148
\(343\) −3.65621 −0.197417
\(344\) −24.9816 −1.34692
\(345\) −3.42516 −0.184404
\(346\) −4.37339 −0.235115
\(347\) 11.2907 0.606114 0.303057 0.952972i \(-0.401993\pi\)
0.303057 + 0.952972i \(0.401993\pi\)
\(348\) −5.44809 −0.292048
\(349\) 9.58688 0.513174 0.256587 0.966521i \(-0.417402\pi\)
0.256587 + 0.966521i \(0.417402\pi\)
\(350\) −0.194848 −0.0104151
\(351\) 6.87242 0.366823
\(352\) −5.86089 −0.312387
\(353\) −7.39528 −0.393611 −0.196806 0.980443i \(-0.563057\pi\)
−0.196806 + 0.980443i \(0.563057\pi\)
\(354\) −3.46316 −0.184065
\(355\) −0.367892 −0.0195257
\(356\) 0.459283 0.0243419
\(357\) −0.810710 −0.0429073
\(358\) −8.51045 −0.449791
\(359\) 11.3521 0.599141 0.299570 0.954074i \(-0.403157\pi\)
0.299570 + 0.954074i \(0.403157\pi\)
\(360\) −6.11380 −0.322225
\(361\) −8.86639 −0.466652
\(362\) −10.9769 −0.576932
\(363\) 0.782455 0.0410683
\(364\) 0.619867 0.0324898
\(365\) 1.00000 0.0523424
\(366\) −3.65122 −0.190852
\(367\) −5.33937 −0.278713 −0.139356 0.990242i \(-0.544503\pi\)
−0.139356 + 0.990242i \(0.544503\pi\)
\(368\) −4.36289 −0.227432
\(369\) −25.8908 −1.34782
\(370\) −5.09862 −0.265065
\(371\) −0.906354 −0.0470555
\(372\) 0.460639 0.0238830
\(373\) −7.74645 −0.401096 −0.200548 0.979684i \(-0.564272\pi\)
−0.200548 + 0.979684i \(0.564272\pi\)
\(374\) 2.93097 0.151557
\(375\) 0.782455 0.0404058
\(376\) 20.1970 1.04158
\(377\) −7.83456 −0.403500
\(378\) 0.821417 0.0422491
\(379\) 18.3349 0.941800 0.470900 0.882187i \(-0.343929\pi\)
0.470900 + 0.882187i \(0.343929\pi\)
\(380\) −4.61205 −0.236593
\(381\) 3.40109 0.174243
\(382\) 3.76963 0.192871
\(383\) −20.7955 −1.06260 −0.531300 0.847184i \(-0.678296\pi\)
−0.531300 + 0.847184i \(0.678296\pi\)
\(384\) 7.80204 0.398146
\(385\) 0.262449 0.0133756
\(386\) −14.6819 −0.747289
\(387\) 23.2966 1.18423
\(388\) −13.1965 −0.669951
\(389\) 18.1668 0.921095 0.460548 0.887635i \(-0.347653\pi\)
0.460548 + 0.887635i \(0.347653\pi\)
\(390\) 0.947003 0.0479534
\(391\) 17.2815 0.873965
\(392\) −17.7469 −0.896355
\(393\) 0.0539562 0.00272173
\(394\) 1.36013 0.0685225
\(395\) −9.69406 −0.487761
\(396\) 3.45942 0.173842
\(397\) 21.6082 1.08449 0.542243 0.840221i \(-0.317575\pi\)
0.542243 + 0.840221i \(0.317575\pi\)
\(398\) −10.7860 −0.540652
\(399\) 0.653712 0.0327266
\(400\) 0.996674 0.0498337
\(401\) 3.30414 0.165001 0.0825003 0.996591i \(-0.473709\pi\)
0.0825003 + 0.996591i \(0.473709\pi\)
\(402\) −8.76198 −0.437008
\(403\) 0.662416 0.0329973
\(404\) −3.72518 −0.185335
\(405\) 3.86471 0.192039
\(406\) −0.936416 −0.0464735
\(407\) 6.86756 0.340412
\(408\) −7.90934 −0.391571
\(409\) −22.9983 −1.13719 −0.568596 0.822617i \(-0.692513\pi\)
−0.568596 + 0.822617i \(0.692513\pi\)
\(410\) −8.05015 −0.397568
\(411\) 3.25456 0.160536
\(412\) −3.18130 −0.156731
\(413\) 1.56462 0.0769898
\(414\) −7.76003 −0.381384
\(415\) −7.65958 −0.375994
\(416\) 9.55444 0.468445
\(417\) 3.81598 0.186870
\(418\) −2.36337 −0.115596
\(419\) 16.3517 0.798834 0.399417 0.916769i \(-0.369213\pi\)
0.399417 + 0.916769i \(0.369213\pi\)
\(420\) −0.297520 −0.0145175
\(421\) −22.5554 −1.09928 −0.549642 0.835400i \(-0.685236\pi\)
−0.549642 + 0.835400i \(0.685236\pi\)
\(422\) 3.76759 0.183403
\(423\) −18.8347 −0.915774
\(424\) −8.84244 −0.429427
\(425\) −3.94785 −0.191499
\(426\) 0.213712 0.0103544
\(427\) 1.64958 0.0798287
\(428\) −19.3034 −0.933064
\(429\) −1.27556 −0.0615846
\(430\) 7.24354 0.349315
\(431\) −13.9230 −0.670649 −0.335324 0.942103i \(-0.608846\pi\)
−0.335324 + 0.942103i \(0.608846\pi\)
\(432\) −4.20166 −0.202153
\(433\) −13.3480 −0.641464 −0.320732 0.947170i \(-0.603929\pi\)
−0.320732 + 0.947170i \(0.603929\pi\)
\(434\) 0.0791744 0.00380049
\(435\) 3.76039 0.180297
\(436\) 4.18028 0.200199
\(437\) −13.9349 −0.666596
\(438\) −0.580911 −0.0277570
\(439\) 6.22477 0.297092 0.148546 0.988905i \(-0.452541\pi\)
0.148546 + 0.988905i \(0.452541\pi\)
\(440\) 2.56047 0.122066
\(441\) 16.5499 0.788089
\(442\) −4.77807 −0.227270
\(443\) −6.34420 −0.301422 −0.150711 0.988578i \(-0.548156\pi\)
−0.150711 + 0.988578i \(0.548156\pi\)
\(444\) −7.78527 −0.369473
\(445\) −0.317007 −0.0150276
\(446\) −4.52306 −0.214173
\(447\) 4.74741 0.224545
\(448\) 0.618830 0.0292369
\(449\) 29.2233 1.37913 0.689567 0.724222i \(-0.257801\pi\)
0.689567 + 0.724222i \(0.257801\pi\)
\(450\) 1.77273 0.0835671
\(451\) 10.8431 0.510582
\(452\) 10.7750 0.506813
\(453\) 8.19391 0.384983
\(454\) 13.4594 0.631682
\(455\) −0.427845 −0.0200577
\(456\) 6.37766 0.298661
\(457\) −9.50883 −0.444804 −0.222402 0.974955i \(-0.571390\pi\)
−0.222402 + 0.974955i \(0.571390\pi\)
\(458\) 10.5745 0.494113
\(459\) 16.6429 0.776824
\(460\) 6.34210 0.295702
\(461\) 12.4996 0.582163 0.291081 0.956698i \(-0.405985\pi\)
0.291081 + 0.956698i \(0.405985\pi\)
\(462\) −0.152460 −0.00709307
\(463\) 1.84423 0.0857085 0.0428543 0.999081i \(-0.486355\pi\)
0.0428543 + 0.999081i \(0.486355\pi\)
\(464\) 4.78990 0.222365
\(465\) −0.317943 −0.0147442
\(466\) 11.9232 0.552333
\(467\) 4.85468 0.224648 0.112324 0.993672i \(-0.464171\pi\)
0.112324 + 0.993672i \(0.464171\pi\)
\(468\) −5.63955 −0.260688
\(469\) 3.95856 0.182789
\(470\) −5.85622 −0.270127
\(471\) −3.91905 −0.180580
\(472\) 15.2645 0.702606
\(473\) −9.75665 −0.448611
\(474\) 5.63139 0.258658
\(475\) 3.18333 0.146061
\(476\) 1.50113 0.0688041
\(477\) 8.24601 0.377559
\(478\) −8.50808 −0.389150
\(479\) −21.3478 −0.975407 −0.487703 0.873009i \(-0.662165\pi\)
−0.487703 + 0.873009i \(0.662165\pi\)
\(480\) −4.58589 −0.209316
\(481\) −11.1955 −0.510471
\(482\) −11.9067 −0.542335
\(483\) −0.898931 −0.0409028
\(484\) −1.44881 −0.0658550
\(485\) 9.10851 0.413596
\(486\) −11.6345 −0.527751
\(487\) −24.5936 −1.11444 −0.557220 0.830365i \(-0.688132\pi\)
−0.557220 + 0.830365i \(0.688132\pi\)
\(488\) 16.0934 0.728514
\(489\) 9.26707 0.419072
\(490\) 5.14581 0.232464
\(491\) −15.1991 −0.685927 −0.342963 0.939349i \(-0.611431\pi\)
−0.342963 + 0.939349i \(0.611431\pi\)
\(492\) −12.2921 −0.554169
\(493\) −18.9729 −0.854497
\(494\) 3.85278 0.173345
\(495\) −2.38776 −0.107322
\(496\) −0.404988 −0.0181845
\(497\) −0.0965528 −0.00433099
\(498\) 4.44954 0.199388
\(499\) −21.0788 −0.943617 −0.471809 0.881701i \(-0.656399\pi\)
−0.471809 + 0.881701i \(0.656399\pi\)
\(500\) −1.44881 −0.0647928
\(501\) −9.73056 −0.434729
\(502\) −7.20529 −0.321588
\(503\) 2.49171 0.111100 0.0555499 0.998456i \(-0.482309\pi\)
0.0555499 + 0.998456i \(0.482309\pi\)
\(504\) −1.60456 −0.0714728
\(505\) 2.57120 0.114417
\(506\) 3.24991 0.144476
\(507\) −8.09250 −0.359400
\(508\) −6.29753 −0.279408
\(509\) 7.72200 0.342271 0.171136 0.985247i \(-0.445256\pi\)
0.171136 + 0.985247i \(0.445256\pi\)
\(510\) 2.29335 0.101551
\(511\) 0.262449 0.0116101
\(512\) −10.9453 −0.483719
\(513\) −13.4199 −0.592504
\(514\) 18.4510 0.813839
\(515\) 2.19580 0.0967585
\(516\) 11.0604 0.486908
\(517\) 7.88801 0.346914
\(518\) −1.33813 −0.0587940
\(519\) 4.60922 0.202322
\(520\) −4.17408 −0.183046
\(521\) −5.25200 −0.230094 −0.115047 0.993360i \(-0.536702\pi\)
−0.115047 + 0.993360i \(0.536702\pi\)
\(522\) 8.51951 0.372889
\(523\) −8.35019 −0.365128 −0.182564 0.983194i \(-0.558440\pi\)
−0.182564 + 0.983194i \(0.558440\pi\)
\(524\) −0.0999065 −0.00436443
\(525\) 0.205355 0.00896242
\(526\) −21.1575 −0.922511
\(527\) 1.60417 0.0698787
\(528\) 0.779853 0.0339387
\(529\) −3.83791 −0.166866
\(530\) 2.56391 0.111369
\(531\) −14.2349 −0.617742
\(532\) −1.21043 −0.0524787
\(533\) −17.6764 −0.765652
\(534\) 0.184153 0.00796907
\(535\) 13.3236 0.576030
\(536\) 38.6200 1.66813
\(537\) 8.96936 0.387057
\(538\) −9.09508 −0.392117
\(539\) −6.93112 −0.298544
\(540\) 6.10773 0.262835
\(541\) 18.9737 0.815744 0.407872 0.913039i \(-0.366271\pi\)
0.407872 + 0.913039i \(0.366271\pi\)
\(542\) 2.60054 0.111703
\(543\) 11.5688 0.496464
\(544\) 23.1379 0.992031
\(545\) −2.88532 −0.123594
\(546\) 0.248540 0.0106365
\(547\) −20.6868 −0.884502 −0.442251 0.896891i \(-0.645820\pi\)
−0.442251 + 0.896891i \(0.645820\pi\)
\(548\) −6.02622 −0.257427
\(549\) −15.0079 −0.640521
\(550\) −0.742421 −0.0316569
\(551\) 15.2987 0.651747
\(552\) −8.77002 −0.373277
\(553\) −2.54420 −0.108190
\(554\) −24.2395 −1.02984
\(555\) 5.37356 0.228095
\(556\) −7.06576 −0.299655
\(557\) −18.7538 −0.794624 −0.397312 0.917684i \(-0.630057\pi\)
−0.397312 + 0.917684i \(0.630057\pi\)
\(558\) −0.720329 −0.0304940
\(559\) 15.9053 0.672723
\(560\) 0.261576 0.0110536
\(561\) −3.08902 −0.130418
\(562\) −13.4357 −0.566749
\(563\) 40.2870 1.69789 0.848947 0.528478i \(-0.177237\pi\)
0.848947 + 0.528478i \(0.177237\pi\)
\(564\) −8.94208 −0.376529
\(565\) −7.43713 −0.312882
\(566\) −9.17528 −0.385666
\(567\) 1.01429 0.0425961
\(568\) −0.941976 −0.0395244
\(569\) −12.6667 −0.531015 −0.265507 0.964109i \(-0.585539\pi\)
−0.265507 + 0.964109i \(0.585539\pi\)
\(570\) −1.84923 −0.0774559
\(571\) −20.6223 −0.863016 −0.431508 0.902109i \(-0.642018\pi\)
−0.431508 + 0.902109i \(0.642018\pi\)
\(572\) 2.36185 0.0987541
\(573\) −3.97290 −0.165970
\(574\) −2.11275 −0.0881847
\(575\) −4.37745 −0.182552
\(576\) −5.63011 −0.234588
\(577\) −26.8082 −1.11604 −0.558020 0.829828i \(-0.688439\pi\)
−0.558020 + 0.829828i \(0.688439\pi\)
\(578\) 1.05013 0.0436796
\(579\) 15.4736 0.643061
\(580\) −6.96281 −0.289115
\(581\) −2.01025 −0.0833992
\(582\) −5.29124 −0.219329
\(583\) −3.45344 −0.143027
\(584\) 2.56047 0.105953
\(585\) 3.89254 0.160937
\(586\) −11.2789 −0.465929
\(587\) 12.7941 0.528068 0.264034 0.964513i \(-0.414947\pi\)
0.264034 + 0.964513i \(0.414947\pi\)
\(588\) 7.85732 0.324031
\(589\) −1.29351 −0.0532983
\(590\) −4.42602 −0.182216
\(591\) −1.43348 −0.0589653
\(592\) 6.84472 0.281316
\(593\) 22.1445 0.909367 0.454684 0.890653i \(-0.349752\pi\)
0.454684 + 0.890653i \(0.349752\pi\)
\(594\) 3.12981 0.128418
\(595\) −1.03611 −0.0424764
\(596\) −8.79040 −0.360069
\(597\) 11.3676 0.465244
\(598\) −5.29802 −0.216652
\(599\) 7.17355 0.293103 0.146552 0.989203i \(-0.453183\pi\)
0.146552 + 0.989203i \(0.453183\pi\)
\(600\) 2.00345 0.0817907
\(601\) 37.7082 1.53815 0.769075 0.639158i \(-0.220717\pi\)
0.769075 + 0.639158i \(0.220717\pi\)
\(602\) 1.90106 0.0774815
\(603\) −36.0150 −1.46665
\(604\) −15.1720 −0.617341
\(605\) 1.00000 0.0406558
\(606\) −1.49364 −0.0606750
\(607\) −6.75720 −0.274266 −0.137133 0.990553i \(-0.543789\pi\)
−0.137133 + 0.990553i \(0.543789\pi\)
\(608\) −18.6572 −0.756648
\(609\) 0.986911 0.0399916
\(610\) −4.66636 −0.188935
\(611\) −12.8590 −0.520221
\(612\) −13.6573 −0.552062
\(613\) 31.3503 1.26623 0.633114 0.774059i \(-0.281777\pi\)
0.633114 + 0.774059i \(0.281777\pi\)
\(614\) −8.89092 −0.358808
\(615\) 8.48424 0.342118
\(616\) 0.671993 0.0270754
\(617\) −4.15148 −0.167132 −0.0835662 0.996502i \(-0.526631\pi\)
−0.0835662 + 0.996502i \(0.526631\pi\)
\(618\) −1.27557 −0.0513108
\(619\) −6.53303 −0.262585 −0.131292 0.991344i \(-0.541913\pi\)
−0.131292 + 0.991344i \(0.541913\pi\)
\(620\) 0.588709 0.0236431
\(621\) 18.4540 0.740532
\(622\) −17.5302 −0.702895
\(623\) −0.0831981 −0.00333326
\(624\) −1.27132 −0.0508935
\(625\) 1.00000 0.0400000
\(626\) 16.5155 0.660090
\(627\) 2.49082 0.0994736
\(628\) 7.25660 0.289570
\(629\) −27.1121 −1.08103
\(630\) 0.465251 0.0185360
\(631\) 35.0672 1.39600 0.698002 0.716095i \(-0.254072\pi\)
0.698002 + 0.716095i \(0.254072\pi\)
\(632\) −24.8214 −0.987341
\(633\) −3.97075 −0.157823
\(634\) 10.2149 0.405685
\(635\) 4.34669 0.172493
\(636\) 3.91493 0.155237
\(637\) 11.2991 0.447688
\(638\) −3.56799 −0.141258
\(639\) 0.878438 0.0347505
\(640\) 9.97123 0.394147
\(641\) 11.4969 0.454099 0.227049 0.973883i \(-0.427092\pi\)
0.227049 + 0.973883i \(0.427092\pi\)
\(642\) −7.73984 −0.305467
\(643\) −47.7381 −1.88261 −0.941304 0.337561i \(-0.890398\pi\)
−0.941304 + 0.337561i \(0.890398\pi\)
\(644\) 1.66448 0.0655897
\(645\) −7.63414 −0.300594
\(646\) 9.33025 0.367094
\(647\) 10.8148 0.425174 0.212587 0.977142i \(-0.431811\pi\)
0.212587 + 0.977142i \(0.431811\pi\)
\(648\) 9.89546 0.388731
\(649\) 5.96161 0.234013
\(650\) 1.21030 0.0474717
\(651\) −0.0834438 −0.00327042
\(652\) −17.1591 −0.672003
\(653\) 32.3593 1.26632 0.633158 0.774022i \(-0.281758\pi\)
0.633158 + 0.774022i \(0.281758\pi\)
\(654\) 1.67612 0.0655413
\(655\) 0.0689576 0.00269440
\(656\) 10.8070 0.421944
\(657\) −2.38776 −0.0931555
\(658\) −1.53696 −0.0599170
\(659\) 2.31484 0.0901734 0.0450867 0.998983i \(-0.485644\pi\)
0.0450867 + 0.998983i \(0.485644\pi\)
\(660\) −1.13363 −0.0441265
\(661\) −27.3510 −1.06383 −0.531915 0.846798i \(-0.678527\pi\)
−0.531915 + 0.846798i \(0.678527\pi\)
\(662\) −17.3126 −0.672871
\(663\) 5.03572 0.195571
\(664\) −19.6121 −0.761098
\(665\) 0.835463 0.0323979
\(666\) 12.1743 0.471745
\(667\) −21.0375 −0.814576
\(668\) 18.0173 0.697111
\(669\) 4.76696 0.184301
\(670\) −11.1981 −0.432619
\(671\) 6.28533 0.242642
\(672\) −1.20356 −0.0464284
\(673\) 3.27968 0.126423 0.0632113 0.998000i \(-0.479866\pi\)
0.0632113 + 0.998000i \(0.479866\pi\)
\(674\) −11.8716 −0.457277
\(675\) −4.21568 −0.162262
\(676\) 14.9842 0.576317
\(677\) −7.22766 −0.277781 −0.138891 0.990308i \(-0.544354\pi\)
−0.138891 + 0.990308i \(0.544354\pi\)
\(678\) 4.32031 0.165921
\(679\) 2.39052 0.0917397
\(680\) −10.1084 −0.387638
\(681\) −14.1852 −0.543579
\(682\) 0.301675 0.0115517
\(683\) −15.8438 −0.606245 −0.303122 0.952952i \(-0.598029\pi\)
−0.303122 + 0.952952i \(0.598029\pi\)
\(684\) 11.0125 0.421073
\(685\) 4.15943 0.158923
\(686\) 2.71445 0.103638
\(687\) −11.1447 −0.425196
\(688\) −9.72420 −0.370732
\(689\) 5.62981 0.214479
\(690\) 2.54291 0.0968070
\(691\) −18.6355 −0.708928 −0.354464 0.935070i \(-0.615337\pi\)
−0.354464 + 0.935070i \(0.615337\pi\)
\(692\) −8.53452 −0.324434
\(693\) −0.626667 −0.0238051
\(694\) −8.38242 −0.318192
\(695\) 4.87694 0.184993
\(696\) 9.62836 0.364962
\(697\) −42.8070 −1.62143
\(698\) −7.11750 −0.269401
\(699\) −12.5662 −0.475296
\(700\) −0.380239 −0.0143717
\(701\) 28.0362 1.05891 0.529456 0.848337i \(-0.322396\pi\)
0.529456 + 0.848337i \(0.322396\pi\)
\(702\) −5.10223 −0.192571
\(703\) 21.8617 0.824531
\(704\) 2.35790 0.0888668
\(705\) 6.17201 0.232451
\(706\) 5.49041 0.206634
\(707\) 0.674810 0.0253788
\(708\) −6.75825 −0.253991
\(709\) 11.7009 0.439436 0.219718 0.975563i \(-0.429486\pi\)
0.219718 + 0.975563i \(0.429486\pi\)
\(710\) 0.273131 0.0102504
\(711\) 23.1471 0.868085
\(712\) −0.811686 −0.0304192
\(713\) 1.77873 0.0666141
\(714\) 0.601888 0.0225251
\(715\) −1.63020 −0.0609661
\(716\) −16.6079 −0.620665
\(717\) 8.96687 0.334874
\(718\) −8.42804 −0.314532
\(719\) 1.97747 0.0737473 0.0368736 0.999320i \(-0.488260\pi\)
0.0368736 + 0.999320i \(0.488260\pi\)
\(720\) −2.37982 −0.0886907
\(721\) 0.576286 0.0214620
\(722\) 6.58260 0.244979
\(723\) 12.5487 0.466693
\(724\) −21.4210 −0.796105
\(725\) 4.80588 0.178486
\(726\) −0.580911 −0.0215596
\(727\) −20.3130 −0.753369 −0.376684 0.926342i \(-0.622936\pi\)
−0.376684 + 0.926342i \(0.622936\pi\)
\(728\) −1.09548 −0.0406014
\(729\) 0.667751 0.0247315
\(730\) −0.742421 −0.0274782
\(731\) 38.5178 1.42463
\(732\) −7.12523 −0.263356
\(733\) −31.2218 −1.15320 −0.576601 0.817026i \(-0.695621\pi\)
−0.576601 + 0.817026i \(0.695621\pi\)
\(734\) 3.96406 0.146316
\(735\) −5.42329 −0.200041
\(736\) 25.6558 0.945685
\(737\) 15.0832 0.555596
\(738\) 19.2218 0.707566
\(739\) −10.5084 −0.386557 −0.193278 0.981144i \(-0.561912\pi\)
−0.193278 + 0.981144i \(0.561912\pi\)
\(740\) −9.94979 −0.365762
\(741\) −4.06053 −0.149167
\(742\) 0.672896 0.0247028
\(743\) −30.7966 −1.12982 −0.564910 0.825153i \(-0.691089\pi\)
−0.564910 + 0.825153i \(0.691089\pi\)
\(744\) −0.814083 −0.0298457
\(745\) 6.06732 0.222290
\(746\) 5.75113 0.210564
\(747\) 18.2893 0.669169
\(748\) 5.71969 0.209133
\(749\) 3.49677 0.127769
\(750\) −0.580911 −0.0212119
\(751\) −32.9457 −1.20220 −0.601102 0.799172i \(-0.705272\pi\)
−0.601102 + 0.799172i \(0.705272\pi\)
\(752\) 7.86177 0.286689
\(753\) 7.59383 0.276734
\(754\) 5.81654 0.211826
\(755\) 10.4720 0.381117
\(756\) 1.60297 0.0582994
\(757\) 8.72273 0.317033 0.158517 0.987356i \(-0.449329\pi\)
0.158517 + 0.987356i \(0.449329\pi\)
\(758\) −13.6122 −0.494418
\(759\) −3.42516 −0.124325
\(760\) 8.15083 0.295662
\(761\) 1.00156 0.0363065 0.0181533 0.999835i \(-0.494221\pi\)
0.0181533 + 0.999835i \(0.494221\pi\)
\(762\) −2.52504 −0.0914725
\(763\) −0.757250 −0.0274143
\(764\) 7.35631 0.266142
\(765\) 9.42654 0.340817
\(766\) 15.4390 0.557834
\(767\) −9.71862 −0.350919
\(768\) −9.48231 −0.342163
\(769\) −5.68964 −0.205174 −0.102587 0.994724i \(-0.532712\pi\)
−0.102587 + 0.994724i \(0.532712\pi\)
\(770\) −0.194848 −0.00702183
\(771\) −19.4460 −0.700329
\(772\) −28.6512 −1.03118
\(773\) 38.9512 1.40098 0.700489 0.713663i \(-0.252965\pi\)
0.700489 + 0.713663i \(0.252965\pi\)
\(774\) −17.2959 −0.621687
\(775\) −0.406340 −0.0145962
\(776\) 23.3221 0.837213
\(777\) 1.41029 0.0505937
\(778\) −13.4874 −0.483548
\(779\) 34.5172 1.23671
\(780\) 1.84805 0.0661707
\(781\) −0.367892 −0.0131642
\(782\) −12.8302 −0.458806
\(783\) −20.2601 −0.724036
\(784\) −6.90807 −0.246717
\(785\) −5.00866 −0.178767
\(786\) −0.0400582 −0.00142883
\(787\) 1.56057 0.0556283 0.0278142 0.999613i \(-0.491145\pi\)
0.0278142 + 0.999613i \(0.491145\pi\)
\(788\) 2.65425 0.0945539
\(789\) 22.2984 0.793844
\(790\) 7.19708 0.256060
\(791\) −1.95187 −0.0694004
\(792\) −6.11380 −0.217244
\(793\) −10.2464 −0.363859
\(794\) −16.0424 −0.569324
\(795\) −2.70217 −0.0958360
\(796\) −21.0485 −0.746043
\(797\) 7.67988 0.272035 0.136018 0.990706i \(-0.456570\pi\)
0.136018 + 0.990706i \(0.456570\pi\)
\(798\) −0.485330 −0.0171805
\(799\) −31.1407 −1.10168
\(800\) −5.86089 −0.207214
\(801\) 0.756937 0.0267451
\(802\) −2.45306 −0.0866206
\(803\) 1.00000 0.0352892
\(804\) −17.0987 −0.603026
\(805\) −1.14886 −0.0404919
\(806\) −0.491792 −0.0173226
\(807\) 9.58552 0.337426
\(808\) 6.58348 0.231606
\(809\) −2.30974 −0.0812060 −0.0406030 0.999175i \(-0.512928\pi\)
−0.0406030 + 0.999175i \(0.512928\pi\)
\(810\) −2.86924 −0.100815
\(811\) 26.1957 0.919856 0.459928 0.887956i \(-0.347875\pi\)
0.459928 + 0.887956i \(0.347875\pi\)
\(812\) −1.82738 −0.0641286
\(813\) −2.74077 −0.0961232
\(814\) −5.09862 −0.178707
\(815\) 11.8436 0.414863
\(816\) −3.07874 −0.107778
\(817\) −31.0587 −1.08660
\(818\) 17.0744 0.596993
\(819\) 1.02159 0.0356974
\(820\) −15.7096 −0.548603
\(821\) 23.4241 0.817505 0.408753 0.912645i \(-0.365964\pi\)
0.408753 + 0.912645i \(0.365964\pi\)
\(822\) −2.41626 −0.0842767
\(823\) −27.4849 −0.958063 −0.479032 0.877798i \(-0.659012\pi\)
−0.479032 + 0.877798i \(0.659012\pi\)
\(824\) 5.62228 0.195861
\(825\) 0.782455 0.0272416
\(826\) −1.16161 −0.0404174
\(827\) 43.5697 1.51507 0.757534 0.652795i \(-0.226404\pi\)
0.757534 + 0.652795i \(0.226404\pi\)
\(828\) −15.1434 −0.526271
\(829\) −51.9306 −1.80362 −0.901811 0.432130i \(-0.857762\pi\)
−0.901811 + 0.432130i \(0.857762\pi\)
\(830\) 5.68663 0.197386
\(831\) 25.5465 0.886200
\(832\) −3.84386 −0.133262
\(833\) 27.3630 0.948073
\(834\) −2.83307 −0.0981011
\(835\) −12.4359 −0.430363
\(836\) −4.61205 −0.159511
\(837\) 1.71300 0.0592099
\(838\) −12.1399 −0.419364
\(839\) −10.9087 −0.376609 −0.188305 0.982111i \(-0.560299\pi\)
−0.188305 + 0.982111i \(0.560299\pi\)
\(840\) 0.525805 0.0181420
\(841\) −5.90350 −0.203569
\(842\) 16.7456 0.577093
\(843\) 14.1602 0.487702
\(844\) 7.35232 0.253077
\(845\) −10.3424 −0.355791
\(846\) 13.9833 0.480755
\(847\) 0.262449 0.00901786
\(848\) −3.44196 −0.118197
\(849\) 9.67005 0.331875
\(850\) 2.93097 0.100531
\(851\) −30.0624 −1.03053
\(852\) 0.417053 0.0142880
\(853\) −8.21416 −0.281247 −0.140624 0.990063i \(-0.544911\pi\)
−0.140624 + 0.990063i \(0.544911\pi\)
\(854\) −1.22468 −0.0419078
\(855\) −7.60105 −0.259950
\(856\) 34.1147 1.16602
\(857\) 10.7298 0.366524 0.183262 0.983064i \(-0.441334\pi\)
0.183262 + 0.983064i \(0.441334\pi\)
\(858\) 0.947003 0.0323302
\(859\) 17.3576 0.592233 0.296116 0.955152i \(-0.404308\pi\)
0.296116 + 0.955152i \(0.404308\pi\)
\(860\) 14.1355 0.482018
\(861\) 2.22668 0.0758851
\(862\) 10.3367 0.352071
\(863\) −2.48905 −0.0847282 −0.0423641 0.999102i \(-0.513489\pi\)
−0.0423641 + 0.999102i \(0.513489\pi\)
\(864\) 24.7077 0.840572
\(865\) 5.89071 0.200290
\(866\) 9.90984 0.336750
\(867\) −1.10676 −0.0375874
\(868\) 0.154506 0.00524428
\(869\) −9.69406 −0.328849
\(870\) −2.79179 −0.0946506
\(871\) −24.5886 −0.833153
\(872\) −7.38778 −0.250182
\(873\) −21.7490 −0.736091
\(874\) 10.3456 0.349944
\(875\) 0.262449 0.00887240
\(876\) −1.13363 −0.0383018
\(877\) −39.3816 −1.32982 −0.664911 0.746923i \(-0.731530\pi\)
−0.664911 + 0.746923i \(0.731530\pi\)
\(878\) −4.62140 −0.155965
\(879\) 11.8871 0.400943
\(880\) 0.996674 0.0335979
\(881\) 40.7335 1.37235 0.686173 0.727438i \(-0.259289\pi\)
0.686173 + 0.727438i \(0.259289\pi\)
\(882\) −12.2870 −0.413724
\(883\) −9.37698 −0.315561 −0.157780 0.987474i \(-0.550434\pi\)
−0.157780 + 0.987474i \(0.550434\pi\)
\(884\) −9.32425 −0.313609
\(885\) 4.66469 0.156802
\(886\) 4.71007 0.158238
\(887\) −40.2547 −1.35162 −0.675810 0.737076i \(-0.736206\pi\)
−0.675810 + 0.737076i \(0.736206\pi\)
\(888\) 13.7588 0.461716
\(889\) 1.14078 0.0382607
\(890\) 0.235352 0.00788903
\(891\) 3.86471 0.129473
\(892\) −8.82661 −0.295537
\(893\) 25.1101 0.840279
\(894\) −3.52458 −0.117880
\(895\) 11.4631 0.383169
\(896\) 2.61694 0.0874258
\(897\) 5.58371 0.186435
\(898\) −21.6960 −0.724006
\(899\) −1.95282 −0.0651302
\(900\) 3.45942 0.115314
\(901\) 13.6337 0.454204
\(902\) −8.05015 −0.268041
\(903\) −2.00357 −0.0666748
\(904\) −19.0425 −0.633345
\(905\) 14.7852 0.491478
\(906\) −6.08333 −0.202105
\(907\) −3.40449 −0.113044 −0.0565222 0.998401i \(-0.518001\pi\)
−0.0565222 + 0.998401i \(0.518001\pi\)
\(908\) 26.2656 0.871656
\(909\) −6.13942 −0.203632
\(910\) 0.317641 0.0105297
\(911\) −44.2734 −1.46684 −0.733422 0.679774i \(-0.762078\pi\)
−0.733422 + 0.679774i \(0.762078\pi\)
\(912\) 2.48253 0.0822048
\(913\) −7.65958 −0.253495
\(914\) 7.05956 0.233509
\(915\) 4.91799 0.162584
\(916\) 20.6357 0.681824
\(917\) 0.0180979 0.000597644 0
\(918\) −12.3560 −0.407810
\(919\) −40.5443 −1.33743 −0.668716 0.743518i \(-0.733156\pi\)
−0.668716 + 0.743518i \(0.733156\pi\)
\(920\) −11.2083 −0.369528
\(921\) 9.37036 0.308764
\(922\) −9.27994 −0.305619
\(923\) 0.599738 0.0197406
\(924\) −0.297520 −0.00978769
\(925\) 6.86756 0.225804
\(926\) −1.36919 −0.0449945
\(927\) −5.24305 −0.172204
\(928\) −28.1668 −0.924619
\(929\) 3.21196 0.105381 0.0526904 0.998611i \(-0.483220\pi\)
0.0526904 + 0.998611i \(0.483220\pi\)
\(930\) 0.236047 0.00774030
\(931\) −22.0641 −0.723120
\(932\) 23.2678 0.762161
\(933\) 18.4755 0.604859
\(934\) −3.60422 −0.117934
\(935\) −3.94785 −0.129109
\(936\) 9.96673 0.325773
\(937\) 4.41039 0.144081 0.0720406 0.997402i \(-0.477049\pi\)
0.0720406 + 0.997402i \(0.477049\pi\)
\(938\) −2.93892 −0.0959592
\(939\) −17.4060 −0.568024
\(940\) −11.4282 −0.372748
\(941\) −35.1747 −1.14666 −0.573331 0.819324i \(-0.694349\pi\)
−0.573331 + 0.819324i \(0.694349\pi\)
\(942\) 2.90959 0.0947995
\(943\) −47.4652 −1.54568
\(944\) 5.94178 0.193388
\(945\) −1.10640 −0.0359913
\(946\) 7.24354 0.235508
\(947\) −33.4352 −1.08650 −0.543249 0.839572i \(-0.682806\pi\)
−0.543249 + 0.839572i \(0.682806\pi\)
\(948\) 10.9895 0.356922
\(949\) −1.63020 −0.0529186
\(950\) −2.36337 −0.0766780
\(951\) −10.7657 −0.349102
\(952\) −2.65293 −0.0859819
\(953\) −44.4917 −1.44123 −0.720613 0.693337i \(-0.756140\pi\)
−0.720613 + 0.693337i \(0.756140\pi\)
\(954\) −6.12201 −0.198207
\(955\) −5.07748 −0.164303
\(956\) −16.6032 −0.536987
\(957\) 3.76039 0.121556
\(958\) 15.8491 0.512060
\(959\) 1.09164 0.0352508
\(960\) 1.84495 0.0595456
\(961\) −30.8349 −0.994674
\(962\) 8.31179 0.267983
\(963\) −31.8136 −1.02518
\(964\) −23.2355 −0.748366
\(965\) 19.7757 0.636602
\(966\) 0.667385 0.0214728
\(967\) −21.9377 −0.705469 −0.352735 0.935723i \(-0.614748\pi\)
−0.352735 + 0.935723i \(0.614748\pi\)
\(968\) 2.56047 0.0822966
\(969\) −9.83337 −0.315893
\(970\) −6.76235 −0.217126
\(971\) −10.5663 −0.339089 −0.169544 0.985523i \(-0.554230\pi\)
−0.169544 + 0.985523i \(0.554230\pi\)
\(972\) −22.7043 −0.728242
\(973\) 1.27995 0.0410332
\(974\) 18.2588 0.585049
\(975\) −1.27556 −0.0408506
\(976\) 6.26442 0.200519
\(977\) 14.8859 0.476242 0.238121 0.971235i \(-0.423469\pi\)
0.238121 + 0.971235i \(0.423469\pi\)
\(978\) −6.88007 −0.220000
\(979\) −0.317007 −0.0101316
\(980\) 10.0419 0.320776
\(981\) 6.88946 0.219964
\(982\) 11.2842 0.360092
\(983\) −36.1008 −1.15144 −0.575719 0.817648i \(-0.695278\pi\)
−0.575719 + 0.817648i \(0.695278\pi\)
\(984\) 21.7236 0.692525
\(985\) −1.83202 −0.0583731
\(986\) 14.0859 0.448586
\(987\) 1.61984 0.0515601
\(988\) 7.51857 0.239198
\(989\) 42.7093 1.35808
\(990\) 1.77273 0.0563409
\(991\) −60.5793 −1.92436 −0.962182 0.272406i \(-0.912181\pi\)
−0.962182 + 0.272406i \(0.912181\pi\)
\(992\) 2.38151 0.0756131
\(993\) 18.2461 0.579023
\(994\) 0.0716829 0.00227364
\(995\) 14.5281 0.460572
\(996\) 8.68312 0.275135
\(997\) −0.797706 −0.0252636 −0.0126318 0.999920i \(-0.504021\pi\)
−0.0126318 + 0.999920i \(0.504021\pi\)
\(998\) 15.6494 0.495372
\(999\) −28.9515 −0.915984
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 \(a_p\))