Properties

Label 6047.2.a.a.1.11
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.59272 q^{2}\) \(+3.24215 q^{3}\) \(+4.72220 q^{4}\) \(-1.12445 q^{5}\) \(-8.40598 q^{6}\) \(-0.119273 q^{7}\) \(-7.05789 q^{8}\) \(+7.51153 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.59272 q^{2}\) \(+3.24215 q^{3}\) \(+4.72220 q^{4}\) \(-1.12445 q^{5}\) \(-8.40598 q^{6}\) \(-0.119273 q^{7}\) \(-7.05789 q^{8}\) \(+7.51153 q^{9}\) \(+2.91540 q^{10}\) \(-1.92359 q^{11}\) \(+15.3101 q^{12}\) \(+3.49979 q^{13}\) \(+0.309241 q^{14}\) \(-3.64565 q^{15}\) \(+8.85475 q^{16}\) \(+0.738832 q^{17}\) \(-19.4753 q^{18}\) \(-7.27821 q^{19}\) \(-5.30990 q^{20}\) \(-0.386700 q^{21}\) \(+4.98733 q^{22}\) \(+7.57491 q^{23}\) \(-22.8827 q^{24}\) \(-3.73560 q^{25}\) \(-9.07397 q^{26}\) \(+14.6270 q^{27}\) \(-0.563229 q^{28}\) \(-3.31106 q^{29}\) \(+9.45215 q^{30}\) \(-10.0715 q^{31}\) \(-8.84210 q^{32}\) \(-6.23657 q^{33}\) \(-1.91558 q^{34}\) \(+0.134117 q^{35}\) \(+35.4709 q^{36}\) \(-10.2837 q^{37}\) \(+18.8704 q^{38}\) \(+11.3468 q^{39}\) \(+7.93628 q^{40}\) \(+1.50645 q^{41}\) \(+1.00260 q^{42}\) \(-0.406611 q^{43}\) \(-9.08357 q^{44}\) \(-8.44637 q^{45}\) \(-19.6396 q^{46}\) \(+1.47364 q^{47}\) \(+28.7084 q^{48}\) \(-6.98577 q^{49}\) \(+9.68537 q^{50}\) \(+2.39540 q^{51}\) \(+16.5267 q^{52}\) \(-8.19066 q^{53}\) \(-37.9238 q^{54}\) \(+2.16299 q^{55}\) \(+0.841814 q^{56}\) \(-23.5970 q^{57}\) \(+8.58464 q^{58}\) \(-12.0697 q^{59}\) \(-17.2155 q^{60}\) \(-3.82139 q^{61}\) \(+26.1126 q^{62}\) \(-0.895920 q^{63}\) \(+5.21559 q^{64}\) \(-3.93535 q^{65}\) \(+16.1697 q^{66}\) \(-5.32546 q^{67}\) \(+3.48891 q^{68}\) \(+24.5590 q^{69}\) \(-0.347727 q^{70}\) \(-11.2620 q^{71}\) \(-53.0156 q^{72}\) \(-4.10897 q^{73}\) \(+26.6627 q^{74}\) \(-12.1114 q^{75}\) \(-34.3691 q^{76}\) \(+0.229432 q^{77}\) \(-29.4191 q^{78}\) \(-4.08254 q^{79}\) \(-9.95677 q^{80}\) \(+24.8885 q^{81}\) \(-3.90581 q^{82}\) \(+3.38046 q^{83}\) \(-1.82607 q^{84}\) \(-0.830783 q^{85}\) \(+1.05423 q^{86}\) \(-10.7349 q^{87}\) \(+13.5765 q^{88}\) \(+2.04759 q^{89}\) \(+21.8991 q^{90}\) \(-0.417429 q^{91}\) \(+35.7702 q^{92}\) \(-32.6533 q^{93}\) \(-3.82075 q^{94}\) \(+8.18401 q^{95}\) \(-28.6674 q^{96}\) \(-1.22688 q^{97}\) \(+18.1122 q^{98}\) \(-14.4491 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59272 −1.83333 −0.916665 0.399657i \(-0.869129\pi\)
−0.916665 + 0.399657i \(0.869129\pi\)
\(3\) 3.24215 1.87186 0.935928 0.352192i \(-0.114564\pi\)
0.935928 + 0.352192i \(0.114564\pi\)
\(4\) 4.72220 2.36110
\(5\) −1.12445 −0.502871 −0.251436 0.967874i \(-0.580903\pi\)
−0.251436 + 0.967874i \(0.580903\pi\)
\(6\) −8.40598 −3.43173
\(7\) −0.119273 −0.0450808 −0.0225404 0.999746i \(-0.507175\pi\)
−0.0225404 + 0.999746i \(0.507175\pi\)
\(8\) −7.05789 −2.49534
\(9\) 7.51153 2.50384
\(10\) 2.91540 0.921929
\(11\) −1.92359 −0.579984 −0.289992 0.957029i \(-0.593653\pi\)
−0.289992 + 0.957029i \(0.593653\pi\)
\(12\) 15.3101 4.41964
\(13\) 3.49979 0.970666 0.485333 0.874329i \(-0.338698\pi\)
0.485333 + 0.874329i \(0.338698\pi\)
\(14\) 0.309241 0.0826480
\(15\) −3.64565 −0.941303
\(16\) 8.85475 2.21369
\(17\) 0.738832 0.179193 0.0895966 0.995978i \(-0.471442\pi\)
0.0895966 + 0.995978i \(0.471442\pi\)
\(18\) −19.4753 −4.59037
\(19\) −7.27821 −1.66974 −0.834868 0.550451i \(-0.814456\pi\)
−0.834868 + 0.550451i \(0.814456\pi\)
\(20\) −5.30990 −1.18733
\(21\) −0.386700 −0.0843848
\(22\) 4.98733 1.06330
\(23\) 7.57491 1.57948 0.789739 0.613443i \(-0.210216\pi\)
0.789739 + 0.613443i \(0.210216\pi\)
\(24\) −22.8827 −4.67092
\(25\) −3.73560 −0.747120
\(26\) −9.07397 −1.77955
\(27\) 14.6270 2.81498
\(28\) −0.563229 −0.106440
\(29\) −3.31106 −0.614848 −0.307424 0.951573i \(-0.599467\pi\)
−0.307424 + 0.951573i \(0.599467\pi\)
\(30\) 9.45215 1.72572
\(31\) −10.0715 −1.80890 −0.904448 0.426583i \(-0.859717\pi\)
−0.904448 + 0.426583i \(0.859717\pi\)
\(32\) −8.84210 −1.56308
\(33\) −6.23657 −1.08565
\(34\) −1.91558 −0.328520
\(35\) 0.134117 0.0226699
\(36\) 35.4709 5.91182
\(37\) −10.2837 −1.69062 −0.845312 0.534273i \(-0.820585\pi\)
−0.845312 + 0.534273i \(0.820585\pi\)
\(38\) 18.8704 3.06118
\(39\) 11.3468 1.81695
\(40\) 7.93628 1.25484
\(41\) 1.50645 0.235268 0.117634 0.993057i \(-0.462469\pi\)
0.117634 + 0.993057i \(0.462469\pi\)
\(42\) 1.00260 0.154705
\(43\) −0.406611 −0.0620075 −0.0310038 0.999519i \(-0.509870\pi\)
−0.0310038 + 0.999519i \(0.509870\pi\)
\(44\) −9.08357 −1.36940
\(45\) −8.44637 −1.25911
\(46\) −19.6396 −2.89571
\(47\) 1.47364 0.214953 0.107477 0.994208i \(-0.465723\pi\)
0.107477 + 0.994208i \(0.465723\pi\)
\(48\) 28.7084 4.14370
\(49\) −6.98577 −0.997968
\(50\) 9.68537 1.36972
\(51\) 2.39540 0.335424
\(52\) 16.5267 2.29184
\(53\) −8.19066 −1.12507 −0.562537 0.826772i \(-0.690174\pi\)
−0.562537 + 0.826772i \(0.690174\pi\)
\(54\) −37.9238 −5.16078
\(55\) 2.16299 0.291658
\(56\) 0.841814 0.112492
\(57\) −23.5970 −3.12550
\(58\) 8.58464 1.12722
\(59\) −12.0697 −1.57134 −0.785670 0.618645i \(-0.787682\pi\)
−0.785670 + 0.618645i \(0.787682\pi\)
\(60\) −17.2155 −2.22251
\(61\) −3.82139 −0.489279 −0.244640 0.969614i \(-0.578670\pi\)
−0.244640 + 0.969614i \(0.578670\pi\)
\(62\) 26.1126 3.31630
\(63\) −0.895920 −0.112875
\(64\) 5.21559 0.651948
\(65\) −3.93535 −0.488120
\(66\) 16.1697 1.99035
\(67\) −5.32546 −0.650609 −0.325304 0.945609i \(-0.605467\pi\)
−0.325304 + 0.945609i \(0.605467\pi\)
\(68\) 3.48891 0.423093
\(69\) 24.5590 2.95656
\(70\) −0.347727 −0.0415613
\(71\) −11.2620 −1.33655 −0.668276 0.743913i \(-0.732967\pi\)
−0.668276 + 0.743913i \(0.732967\pi\)
\(72\) −53.0156 −6.24795
\(73\) −4.10897 −0.480918 −0.240459 0.970659i \(-0.577298\pi\)
−0.240459 + 0.970659i \(0.577298\pi\)
\(74\) 26.6627 3.09947
\(75\) −12.1114 −1.39850
\(76\) −34.3691 −3.94241
\(77\) 0.229432 0.0261462
\(78\) −29.4191 −3.33106
\(79\) −4.08254 −0.459321 −0.229661 0.973271i \(-0.573762\pi\)
−0.229661 + 0.973271i \(0.573762\pi\)
\(80\) −9.95677 −1.11320
\(81\) 24.8885 2.76539
\(82\) −3.90581 −0.431324
\(83\) 3.38046 0.371054 0.185527 0.982639i \(-0.440601\pi\)
0.185527 + 0.982639i \(0.440601\pi\)
\(84\) −1.82607 −0.199241
\(85\) −0.830783 −0.0901111
\(86\) 1.05423 0.113680
\(87\) −10.7349 −1.15091
\(88\) 13.5765 1.44726
\(89\) 2.04759 0.217044 0.108522 0.994094i \(-0.465388\pi\)
0.108522 + 0.994094i \(0.465388\pi\)
\(90\) 21.8991 2.30837
\(91\) −0.417429 −0.0437584
\(92\) 35.7702 3.72930
\(93\) −32.6533 −3.38599
\(94\) −3.82075 −0.394080
\(95\) 8.18401 0.839662
\(96\) −28.6674 −2.92585
\(97\) −1.22688 −0.124571 −0.0622853 0.998058i \(-0.519839\pi\)
−0.0622853 + 0.998058i \(0.519839\pi\)
\(98\) 18.1122 1.82960
\(99\) −14.4491 −1.45219
\(100\) −17.6402 −1.76402
\(101\) −1.22866 −0.122256 −0.0611279 0.998130i \(-0.519470\pi\)
−0.0611279 + 0.998130i \(0.519470\pi\)
\(102\) −6.21061 −0.614942
\(103\) 8.78154 0.865271 0.432635 0.901569i \(-0.357584\pi\)
0.432635 + 0.901569i \(0.357584\pi\)
\(104\) −24.7011 −2.42214
\(105\) 0.434826 0.0424347
\(106\) 21.2361 2.06263
\(107\) 4.80918 0.464921 0.232461 0.972606i \(-0.425322\pi\)
0.232461 + 0.972606i \(0.425322\pi\)
\(108\) 69.0718 6.64644
\(109\) 5.38197 0.515499 0.257750 0.966212i \(-0.417019\pi\)
0.257750 + 0.966212i \(0.417019\pi\)
\(110\) −5.60803 −0.534704
\(111\) −33.3412 −3.16460
\(112\) −1.05613 −0.0997949
\(113\) 9.48292 0.892079 0.446039 0.895013i \(-0.352834\pi\)
0.446039 + 0.895013i \(0.352834\pi\)
\(114\) 61.1805 5.73008
\(115\) −8.51765 −0.794275
\(116\) −15.6355 −1.45172
\(117\) 26.2887 2.43040
\(118\) 31.2933 2.88079
\(119\) −0.0881225 −0.00807818
\(120\) 25.7306 2.34887
\(121\) −7.29980 −0.663618
\(122\) 9.90780 0.897010
\(123\) 4.88414 0.440388
\(124\) −47.5597 −4.27098
\(125\) 9.82279 0.878577
\(126\) 2.32287 0.206938
\(127\) −4.00153 −0.355078 −0.177539 0.984114i \(-0.556814\pi\)
−0.177539 + 0.984114i \(0.556814\pi\)
\(128\) 4.16164 0.367841
\(129\) −1.31829 −0.116069
\(130\) 10.2033 0.894885
\(131\) 12.6811 1.10795 0.553974 0.832534i \(-0.313111\pi\)
0.553974 + 0.832534i \(0.313111\pi\)
\(132\) −29.4503 −2.56332
\(133\) 0.868091 0.0752730
\(134\) 13.8074 1.19278
\(135\) −16.4475 −1.41557
\(136\) −5.21460 −0.447148
\(137\) 8.03867 0.686790 0.343395 0.939191i \(-0.388423\pi\)
0.343395 + 0.939191i \(0.388423\pi\)
\(138\) −63.6746 −5.42034
\(139\) 7.81365 0.662745 0.331372 0.943500i \(-0.392488\pi\)
0.331372 + 0.943500i \(0.392488\pi\)
\(140\) 0.633326 0.0535258
\(141\) 4.77778 0.402361
\(142\) 29.1992 2.45034
\(143\) −6.73215 −0.562971
\(144\) 66.5127 5.54273
\(145\) 3.72313 0.309189
\(146\) 10.6534 0.881682
\(147\) −22.6489 −1.86805
\(148\) −48.5615 −3.99173
\(149\) 16.8025 1.37651 0.688255 0.725468i \(-0.258377\pi\)
0.688255 + 0.725468i \(0.258377\pi\)
\(150\) 31.4014 2.56391
\(151\) −0.499415 −0.0406418 −0.0203209 0.999794i \(-0.506469\pi\)
−0.0203209 + 0.999794i \(0.506469\pi\)
\(152\) 51.3688 4.16656
\(153\) 5.54976 0.448671
\(154\) −0.594852 −0.0479346
\(155\) 11.3250 0.909643
\(156\) 53.5820 4.28999
\(157\) 7.32774 0.584818 0.292409 0.956293i \(-0.405543\pi\)
0.292409 + 0.956293i \(0.405543\pi\)
\(158\) 10.5849 0.842087
\(159\) −26.5553 −2.10597
\(160\) 9.94254 0.786027
\(161\) −0.903480 −0.0712042
\(162\) −64.5289 −5.06987
\(163\) −13.9224 −1.09049 −0.545244 0.838278i \(-0.683563\pi\)
−0.545244 + 0.838278i \(0.683563\pi\)
\(164\) 7.11376 0.555491
\(165\) 7.01274 0.545941
\(166\) −8.76459 −0.680264
\(167\) 17.3960 1.34615 0.673073 0.739576i \(-0.264974\pi\)
0.673073 + 0.739576i \(0.264974\pi\)
\(168\) 2.72929 0.210569
\(169\) −0.751497 −0.0578074
\(170\) 2.15399 0.165203
\(171\) −54.6705 −4.18075
\(172\) −1.92010 −0.146406
\(173\) −5.99080 −0.455472 −0.227736 0.973723i \(-0.573132\pi\)
−0.227736 + 0.973723i \(0.573132\pi\)
\(174\) 27.8327 2.10999
\(175\) 0.445555 0.0336808
\(176\) −17.0329 −1.28390
\(177\) −39.1318 −2.94132
\(178\) −5.30884 −0.397914
\(179\) −15.9540 −1.19246 −0.596229 0.802814i \(-0.703335\pi\)
−0.596229 + 0.802814i \(0.703335\pi\)
\(180\) −39.8854 −2.97289
\(181\) 2.64305 0.196456 0.0982281 0.995164i \(-0.468683\pi\)
0.0982281 + 0.995164i \(0.468683\pi\)
\(182\) 1.08228 0.0802236
\(183\) −12.3895 −0.915860
\(184\) −53.4629 −3.94134
\(185\) 11.5635 0.850166
\(186\) 84.6610 6.20764
\(187\) −1.42121 −0.103929
\(188\) 6.95884 0.507526
\(189\) −1.74461 −0.126901
\(190\) −21.2189 −1.53938
\(191\) −13.1522 −0.951663 −0.475832 0.879536i \(-0.657853\pi\)
−0.475832 + 0.879536i \(0.657853\pi\)
\(192\) 16.9097 1.22035
\(193\) 10.7481 0.773666 0.386833 0.922150i \(-0.373569\pi\)
0.386833 + 0.922150i \(0.373569\pi\)
\(194\) 3.18095 0.228379
\(195\) −12.7590 −0.913690
\(196\) −32.9882 −2.35630
\(197\) 1.10214 0.0785240 0.0392620 0.999229i \(-0.487499\pi\)
0.0392620 + 0.999229i \(0.487499\pi\)
\(198\) 37.4625 2.66234
\(199\) 10.0088 0.709508 0.354754 0.934960i \(-0.384565\pi\)
0.354754 + 0.934960i \(0.384565\pi\)
\(200\) 26.3655 1.86432
\(201\) −17.2659 −1.21785
\(202\) 3.18556 0.224135
\(203\) 0.394919 0.0277179
\(204\) 11.3116 0.791968
\(205\) −1.69394 −0.118310
\(206\) −22.7681 −1.58633
\(207\) 56.8992 3.95477
\(208\) 30.9897 2.14875
\(209\) 14.0003 0.968420
\(210\) −1.12738 −0.0777968
\(211\) −4.71785 −0.324790 −0.162395 0.986726i \(-0.551922\pi\)
−0.162395 + 0.986726i \(0.551922\pi\)
\(212\) −38.6779 −2.65641
\(213\) −36.5130 −2.50183
\(214\) −12.4689 −0.852354
\(215\) 0.457215 0.0311818
\(216\) −103.236 −7.02433
\(217\) 1.20126 0.0815466
\(218\) −13.9539 −0.945080
\(219\) −13.3219 −0.900209
\(220\) 10.2141 0.688632
\(221\) 2.58575 0.173937
\(222\) 86.4443 5.80176
\(223\) −2.74869 −0.184066 −0.0920329 0.995756i \(-0.529336\pi\)
−0.0920329 + 0.995756i \(0.529336\pi\)
\(224\) 1.05462 0.0704648
\(225\) −28.0601 −1.87067
\(226\) −24.5866 −1.63547
\(227\) 22.2245 1.47509 0.737546 0.675297i \(-0.235985\pi\)
0.737546 + 0.675297i \(0.235985\pi\)
\(228\) −111.430 −7.37962
\(229\) −13.6439 −0.901613 −0.450806 0.892622i \(-0.648864\pi\)
−0.450806 + 0.892622i \(0.648864\pi\)
\(230\) 22.0839 1.45617
\(231\) 0.743852 0.0489419
\(232\) 23.3691 1.53426
\(233\) −9.33581 −0.611609 −0.305805 0.952094i \(-0.598925\pi\)
−0.305805 + 0.952094i \(0.598925\pi\)
\(234\) −68.1594 −4.45572
\(235\) −1.65705 −0.108094
\(236\) −56.9955 −3.71009
\(237\) −13.2362 −0.859783
\(238\) 0.228477 0.0148100
\(239\) −12.8980 −0.834299 −0.417150 0.908838i \(-0.636971\pi\)
−0.417150 + 0.908838i \(0.636971\pi\)
\(240\) −32.2813 −2.08375
\(241\) −3.62854 −0.233735 −0.116867 0.993148i \(-0.537285\pi\)
−0.116867 + 0.993148i \(0.537285\pi\)
\(242\) 18.9263 1.21663
\(243\) 36.8110 2.36143
\(244\) −18.0454 −1.15524
\(245\) 7.85519 0.501849
\(246\) −12.6632 −0.807377
\(247\) −25.4722 −1.62076
\(248\) 71.0837 4.51382
\(249\) 10.9600 0.694560
\(250\) −25.4677 −1.61072
\(251\) −28.2919 −1.78577 −0.892884 0.450287i \(-0.851322\pi\)
−0.892884 + 0.450287i \(0.851322\pi\)
\(252\) −4.23071 −0.266510
\(253\) −14.5710 −0.916073
\(254\) 10.3748 0.650975
\(255\) −2.69352 −0.168675
\(256\) −21.2211 −1.32632
\(257\) 16.0068 0.998475 0.499238 0.866465i \(-0.333613\pi\)
0.499238 + 0.866465i \(0.333613\pi\)
\(258\) 3.41796 0.212793
\(259\) 1.22656 0.0762147
\(260\) −18.5835 −1.15250
\(261\) −24.8711 −1.53948
\(262\) −32.8784 −2.03124
\(263\) −6.43429 −0.396755 −0.198378 0.980126i \(-0.563567\pi\)
−0.198378 + 0.980126i \(0.563567\pi\)
\(264\) 44.0170 2.70906
\(265\) 9.21002 0.565767
\(266\) −2.25072 −0.138000
\(267\) 6.63860 0.406276
\(268\) −25.1479 −1.53615
\(269\) −17.3635 −1.05867 −0.529336 0.848412i \(-0.677559\pi\)
−0.529336 + 0.848412i \(0.677559\pi\)
\(270\) 42.6436 2.59521
\(271\) 19.9838 1.21393 0.606963 0.794730i \(-0.292387\pi\)
0.606963 + 0.794730i \(0.292387\pi\)
\(272\) 6.54217 0.396678
\(273\) −1.35337 −0.0819095
\(274\) −20.8420 −1.25911
\(275\) 7.18577 0.433318
\(276\) 115.972 6.98072
\(277\) 11.0608 0.664577 0.332289 0.943178i \(-0.392179\pi\)
0.332289 + 0.943178i \(0.392179\pi\)
\(278\) −20.2586 −1.21503
\(279\) −75.6525 −4.52919
\(280\) −0.946582 −0.0565691
\(281\) −13.8766 −0.827806 −0.413903 0.910321i \(-0.635835\pi\)
−0.413903 + 0.910321i \(0.635835\pi\)
\(282\) −12.3874 −0.737661
\(283\) 20.3260 1.20826 0.604128 0.796887i \(-0.293522\pi\)
0.604128 + 0.796887i \(0.293522\pi\)
\(284\) −53.1813 −3.15573
\(285\) 26.5338 1.57173
\(286\) 17.4546 1.03211
\(287\) −0.179678 −0.0106061
\(288\) −66.4177 −3.91370
\(289\) −16.4541 −0.967890
\(290\) −9.65304 −0.566846
\(291\) −3.97772 −0.233178
\(292\) −19.4034 −1.13550
\(293\) −20.9160 −1.22192 −0.610962 0.791660i \(-0.709217\pi\)
−0.610962 + 0.791660i \(0.709217\pi\)
\(294\) 58.7223 3.42475
\(295\) 13.5718 0.790182
\(296\) 72.5810 4.21868
\(297\) −28.1364 −1.63264
\(298\) −43.5641 −2.52360
\(299\) 26.5106 1.53315
\(300\) −57.1923 −3.30200
\(301\) 0.0484975 0.00279535
\(302\) 1.29484 0.0745099
\(303\) −3.98348 −0.228845
\(304\) −64.4467 −3.69627
\(305\) 4.29698 0.246045
\(306\) −14.3890 −0.822563
\(307\) −21.7354 −1.24050 −0.620251 0.784403i \(-0.712969\pi\)
−0.620251 + 0.784403i \(0.712969\pi\)
\(308\) 1.08342 0.0617337
\(309\) 28.4711 1.61966
\(310\) −29.3624 −1.66767
\(311\) −28.6394 −1.62399 −0.811995 0.583664i \(-0.801618\pi\)
−0.811995 + 0.583664i \(0.801618\pi\)
\(312\) −80.0847 −4.53390
\(313\) −13.8363 −0.782071 −0.391036 0.920376i \(-0.627883\pi\)
−0.391036 + 0.920376i \(0.627883\pi\)
\(314\) −18.9988 −1.07216
\(315\) 1.00742 0.0567618
\(316\) −19.2785 −1.08450
\(317\) 24.3310 1.36657 0.683283 0.730154i \(-0.260552\pi\)
0.683283 + 0.730154i \(0.260552\pi\)
\(318\) 68.8505 3.86095
\(319\) 6.36912 0.356602
\(320\) −5.86469 −0.327846
\(321\) 15.5921 0.870265
\(322\) 2.34247 0.130541
\(323\) −5.37737 −0.299205
\(324\) 117.528 6.52935
\(325\) −13.0738 −0.725204
\(326\) 36.0969 1.99922
\(327\) 17.4491 0.964940
\(328\) −10.6324 −0.587075
\(329\) −0.175766 −0.00969027
\(330\) −18.1821 −1.00089
\(331\) 25.1735 1.38366 0.691831 0.722059i \(-0.256804\pi\)
0.691831 + 0.722059i \(0.256804\pi\)
\(332\) 15.9632 0.876095
\(333\) −77.2460 −4.23306
\(334\) −45.1031 −2.46793
\(335\) 5.98824 0.327173
\(336\) −3.42413 −0.186802
\(337\) 6.87070 0.374271 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(338\) 1.94842 0.105980
\(339\) 30.7451 1.66984
\(340\) −3.92312 −0.212761
\(341\) 19.3735 1.04913
\(342\) 141.745 7.66470
\(343\) 1.66812 0.0900701
\(344\) 2.86981 0.154730
\(345\) −27.6155 −1.48677
\(346\) 15.5325 0.835031
\(347\) 31.9611 1.71576 0.857882 0.513847i \(-0.171780\pi\)
0.857882 + 0.513847i \(0.171780\pi\)
\(348\) −50.6925 −2.71740
\(349\) 13.0406 0.698047 0.349024 0.937114i \(-0.386513\pi\)
0.349024 + 0.937114i \(0.386513\pi\)
\(350\) −1.15520 −0.0617480
\(351\) 51.1915 2.73240
\(352\) 17.0086 0.906560
\(353\) 26.6921 1.42068 0.710339 0.703860i \(-0.248542\pi\)
0.710339 + 0.703860i \(0.248542\pi\)
\(354\) 101.458 5.39242
\(355\) 12.6636 0.672114
\(356\) 9.66914 0.512463
\(357\) −0.285706 −0.0151212
\(358\) 41.3643 2.18617
\(359\) 22.0160 1.16196 0.580980 0.813918i \(-0.302670\pi\)
0.580980 + 0.813918i \(0.302670\pi\)
\(360\) 59.6136 3.14191
\(361\) 33.9723 1.78802
\(362\) −6.85268 −0.360169
\(363\) −23.6670 −1.24220
\(364\) −1.97118 −0.103318
\(365\) 4.62035 0.241840
\(366\) 32.1226 1.67907
\(367\) −20.6953 −1.08029 −0.540144 0.841572i \(-0.681630\pi\)
−0.540144 + 0.841572i \(0.681630\pi\)
\(368\) 67.0740 3.49647
\(369\) 11.3158 0.589075
\(370\) −29.9809 −1.55864
\(371\) 0.976921 0.0507192
\(372\) −154.196 −7.99466
\(373\) −25.1008 −1.29967 −0.649836 0.760074i \(-0.725162\pi\)
−0.649836 + 0.760074i \(0.725162\pi\)
\(374\) 3.68480 0.190537
\(375\) 31.8469 1.64457
\(376\) −10.4008 −0.536382
\(377\) −11.5880 −0.596812
\(378\) 4.52328 0.232652
\(379\) 22.7528 1.16873 0.584366 0.811490i \(-0.301343\pi\)
0.584366 + 0.811490i \(0.301343\pi\)
\(380\) 38.6465 1.98252
\(381\) −12.9735 −0.664655
\(382\) 34.1001 1.74471
\(383\) 24.2782 1.24056 0.620278 0.784382i \(-0.287020\pi\)
0.620278 + 0.784382i \(0.287020\pi\)
\(384\) 13.4927 0.688544
\(385\) −0.257986 −0.0131482
\(386\) −27.8668 −1.41839
\(387\) −3.05427 −0.155257
\(388\) −5.79356 −0.294123
\(389\) −28.6185 −1.45101 −0.725507 0.688215i \(-0.758394\pi\)
−0.725507 + 0.688215i \(0.758394\pi\)
\(390\) 33.0805 1.67510
\(391\) 5.59659 0.283032
\(392\) 49.3049 2.49027
\(393\) 41.1139 2.07392
\(394\) −2.85753 −0.143960
\(395\) 4.59063 0.230980
\(396\) −68.2315 −3.42876
\(397\) 3.63952 0.182662 0.0913312 0.995821i \(-0.470888\pi\)
0.0913312 + 0.995821i \(0.470888\pi\)
\(398\) −25.9501 −1.30076
\(399\) 2.81448 0.140900
\(400\) −33.0778 −1.65389
\(401\) −3.60667 −0.180109 −0.0900543 0.995937i \(-0.528704\pi\)
−0.0900543 + 0.995937i \(0.528704\pi\)
\(402\) 44.7658 2.23271
\(403\) −35.2481 −1.75583
\(404\) −5.80195 −0.288658
\(405\) −27.9860 −1.39063
\(406\) −1.02391 −0.0508160
\(407\) 19.7816 0.980535
\(408\) −16.9065 −0.836997
\(409\) −19.8995 −0.983968 −0.491984 0.870604i \(-0.663728\pi\)
−0.491984 + 0.870604i \(0.663728\pi\)
\(410\) 4.39190 0.216901
\(411\) 26.0626 1.28557
\(412\) 41.4682 2.04299
\(413\) 1.43959 0.0708374
\(414\) −147.524 −7.25039
\(415\) −3.80118 −0.186592
\(416\) −30.9455 −1.51723
\(417\) 25.3330 1.24056
\(418\) −36.2988 −1.77543
\(419\) −28.4624 −1.39048 −0.695239 0.718778i \(-0.744702\pi\)
−0.695239 + 0.718778i \(0.744702\pi\)
\(420\) 2.05334 0.100193
\(421\) 33.7126 1.64305 0.821526 0.570170i \(-0.193123\pi\)
0.821526 + 0.570170i \(0.193123\pi\)
\(422\) 12.2321 0.595447
\(423\) 11.0693 0.538209
\(424\) 57.8088 2.80744
\(425\) −2.75998 −0.133879
\(426\) 94.6681 4.58668
\(427\) 0.455788 0.0220571
\(428\) 22.7099 1.09772
\(429\) −21.8266 −1.05380
\(430\) −1.18543 −0.0571666
\(431\) 12.3075 0.592829 0.296415 0.955059i \(-0.404209\pi\)
0.296415 + 0.955059i \(0.404209\pi\)
\(432\) 129.519 6.23148
\(433\) −18.1056 −0.870098 −0.435049 0.900407i \(-0.643269\pi\)
−0.435049 + 0.900407i \(0.643269\pi\)
\(434\) −3.11452 −0.149502
\(435\) 12.0710 0.578758
\(436\) 25.4147 1.21714
\(437\) −55.1318 −2.63731
\(438\) 34.5399 1.65038
\(439\) −31.7527 −1.51547 −0.757737 0.652560i \(-0.773695\pi\)
−0.757737 + 0.652560i \(0.773695\pi\)
\(440\) −15.2662 −0.727785
\(441\) −52.4738 −2.49875
\(442\) −6.70414 −0.318883
\(443\) 23.8576 1.13351 0.566755 0.823886i \(-0.308198\pi\)
0.566755 + 0.823886i \(0.308198\pi\)
\(444\) −157.444 −7.47194
\(445\) −2.30243 −0.109145
\(446\) 7.12658 0.337453
\(447\) 54.4761 2.57663
\(448\) −0.622077 −0.0293904
\(449\) −26.8846 −1.26876 −0.634382 0.773019i \(-0.718745\pi\)
−0.634382 + 0.773019i \(0.718745\pi\)
\(450\) 72.7519 3.42956
\(451\) −2.89780 −0.136452
\(452\) 44.7802 2.10629
\(453\) −1.61918 −0.0760757
\(454\) −57.6219 −2.70433
\(455\) 0.469380 0.0220049
\(456\) 166.545 7.79920
\(457\) 10.6417 0.497799 0.248899 0.968529i \(-0.419931\pi\)
0.248899 + 0.968529i \(0.419931\pi\)
\(458\) 35.3748 1.65295
\(459\) 10.8069 0.504424
\(460\) −40.2220 −1.87536
\(461\) −14.8859 −0.693306 −0.346653 0.937994i \(-0.612682\pi\)
−0.346653 + 0.937994i \(0.612682\pi\)
\(462\) −1.92860 −0.0897266
\(463\) −20.3444 −0.945485 −0.472743 0.881201i \(-0.656736\pi\)
−0.472743 + 0.881201i \(0.656736\pi\)
\(464\) −29.3186 −1.36108
\(465\) 36.7172 1.70272
\(466\) 24.2051 1.12128
\(467\) 3.39329 0.157023 0.0785113 0.996913i \(-0.474983\pi\)
0.0785113 + 0.996913i \(0.474983\pi\)
\(468\) 124.141 5.73840
\(469\) 0.635182 0.0293300
\(470\) 4.29626 0.198172
\(471\) 23.7576 1.09469
\(472\) 85.1867 3.92103
\(473\) 0.782152 0.0359634
\(474\) 34.3177 1.57627
\(475\) 27.1885 1.24749
\(476\) −0.416132 −0.0190734
\(477\) −61.5243 −2.81701
\(478\) 33.4408 1.52955
\(479\) 29.9813 1.36988 0.684940 0.728600i \(-0.259829\pi\)
0.684940 + 0.728600i \(0.259829\pi\)
\(480\) 32.2352 1.47133
\(481\) −35.9906 −1.64103
\(482\) 9.40779 0.428513
\(483\) −2.92922 −0.133284
\(484\) −34.4711 −1.56687
\(485\) 1.37957 0.0626430
\(486\) −95.4406 −4.32928
\(487\) 7.62947 0.345724 0.172862 0.984946i \(-0.444698\pi\)
0.172862 + 0.984946i \(0.444698\pi\)
\(488\) 26.9710 1.22092
\(489\) −45.1385 −2.04123
\(490\) −20.3663 −0.920056
\(491\) −35.8022 −1.61573 −0.807865 0.589368i \(-0.799377\pi\)
−0.807865 + 0.589368i \(0.799377\pi\)
\(492\) 23.0639 1.03980
\(493\) −2.44632 −0.110177
\(494\) 66.0422 2.97138
\(495\) 16.2474 0.730265
\(496\) −89.1807 −4.00433
\(497\) 1.34325 0.0602529
\(498\) −28.4161 −1.27336
\(499\) 17.8970 0.801180 0.400590 0.916257i \(-0.368805\pi\)
0.400590 + 0.916257i \(0.368805\pi\)
\(500\) 46.3851 2.07441
\(501\) 56.4006 2.51979
\(502\) 73.3529 3.27390
\(503\) −22.0537 −0.983325 −0.491662 0.870786i \(-0.663611\pi\)
−0.491662 + 0.870786i \(0.663611\pi\)
\(504\) 6.32331 0.281663
\(505\) 1.38157 0.0614789
\(506\) 37.7786 1.67946
\(507\) −2.43646 −0.108207
\(508\) −18.8960 −0.838374
\(509\) 27.8149 1.23287 0.616436 0.787405i \(-0.288576\pi\)
0.616436 + 0.787405i \(0.288576\pi\)
\(510\) 6.98355 0.309237
\(511\) 0.490088 0.0216802
\(512\) 46.6972 2.06374
\(513\) −106.459 −4.70027
\(514\) −41.5011 −1.83053
\(515\) −9.87444 −0.435120
\(516\) −6.22523 −0.274051
\(517\) −2.83469 −0.124669
\(518\) −3.18013 −0.139727
\(519\) −19.4231 −0.852578
\(520\) 27.7753 1.21803
\(521\) −30.0241 −1.31538 −0.657690 0.753289i \(-0.728466\pi\)
−0.657690 + 0.753289i \(0.728466\pi\)
\(522\) 64.4838 2.82238
\(523\) 8.06979 0.352867 0.176434 0.984313i \(-0.443544\pi\)
0.176434 + 0.984313i \(0.443544\pi\)
\(524\) 59.8824 2.61598
\(525\) 1.44456 0.0630456
\(526\) 16.6823 0.727383
\(527\) −7.44116 −0.324142
\(528\) −55.2232 −2.40328
\(529\) 34.3793 1.49475
\(530\) −23.8790 −1.03724
\(531\) −90.6619 −3.93439
\(532\) 4.09930 0.177727
\(533\) 5.27226 0.228367
\(534\) −17.2120 −0.744838
\(535\) −5.40771 −0.233796
\(536\) 37.5866 1.62349
\(537\) −51.7252 −2.23211
\(538\) 45.0187 1.94089
\(539\) 13.4378 0.578806
\(540\) −77.6681 −3.34230
\(541\) 31.0187 1.33360 0.666799 0.745238i \(-0.267664\pi\)
0.666799 + 0.745238i \(0.267664\pi\)
\(542\) −51.8123 −2.22553
\(543\) 8.56915 0.367737
\(544\) −6.53283 −0.280093
\(545\) −6.05178 −0.259230
\(546\) 3.50890 0.150167
\(547\) −9.30593 −0.397893 −0.198946 0.980010i \(-0.563752\pi\)
−0.198946 + 0.980010i \(0.563752\pi\)
\(548\) 37.9602 1.62158
\(549\) −28.7045 −1.22508
\(550\) −18.6307 −0.794415
\(551\) 24.0986 1.02663
\(552\) −173.335 −7.37762
\(553\) 0.486935 0.0207066
\(554\) −28.6775 −1.21839
\(555\) 37.4906 1.59139
\(556\) 36.8976 1.56481
\(557\) 28.2686 1.19778 0.598889 0.800832i \(-0.295609\pi\)
0.598889 + 0.800832i \(0.295609\pi\)
\(558\) 196.146 8.30351
\(559\) −1.42305 −0.0601886
\(560\) 1.18757 0.0501840
\(561\) −4.60778 −0.194540
\(562\) 35.9780 1.51764
\(563\) −42.2320 −1.77987 −0.889933 0.456092i \(-0.849249\pi\)
−0.889933 + 0.456092i \(0.849249\pi\)
\(564\) 22.5616 0.950015
\(565\) −10.6631 −0.448601
\(566\) −52.6997 −2.21513
\(567\) −2.96852 −0.124666
\(568\) 79.4859 3.33515
\(569\) −33.7707 −1.41574 −0.707872 0.706341i \(-0.750345\pi\)
−0.707872 + 0.706341i \(0.750345\pi\)
\(570\) −68.7947 −2.88149
\(571\) 32.2616 1.35011 0.675053 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(572\) −31.7906 −1.32923
\(573\) −42.6415 −1.78138
\(574\) 0.465856 0.0194445
\(575\) −28.2969 −1.18006
\(576\) 39.1770 1.63238
\(577\) −45.7080 −1.90285 −0.951424 0.307882i \(-0.900380\pi\)
−0.951424 + 0.307882i \(0.900380\pi\)
\(578\) 42.6609 1.77446
\(579\) 34.8470 1.44819
\(580\) 17.5814 0.730027
\(581\) −0.403197 −0.0167274
\(582\) 10.3131 0.427492
\(583\) 15.7555 0.652525
\(584\) 29.0007 1.20006
\(585\) −29.5605 −1.22218
\(586\) 54.2293 2.24019
\(587\) 33.3919 1.37823 0.689115 0.724652i \(-0.258000\pi\)
0.689115 + 0.724652i \(0.258000\pi\)
\(588\) −106.953 −4.41065
\(589\) 73.3025 3.02038
\(590\) −35.1880 −1.44867
\(591\) 3.57329 0.146985
\(592\) −91.0593 −3.74251
\(593\) −34.6999 −1.42496 −0.712478 0.701695i \(-0.752427\pi\)
−0.712478 + 0.701695i \(0.752427\pi\)
\(594\) 72.9499 2.99317
\(595\) 0.0990897 0.00406228
\(596\) 79.3445 3.25008
\(597\) 32.4502 1.32810
\(598\) −68.7345 −2.81076
\(599\) −40.3188 −1.64738 −0.823691 0.567039i \(-0.808089\pi\)
−0.823691 + 0.567039i \(0.808089\pi\)
\(600\) 85.4808 3.48974
\(601\) 33.1497 1.35220 0.676102 0.736808i \(-0.263668\pi\)
0.676102 + 0.736808i \(0.263668\pi\)
\(602\) −0.125741 −0.00512480
\(603\) −40.0024 −1.62902
\(604\) −2.35834 −0.0959594
\(605\) 8.20829 0.333715
\(606\) 10.3281 0.419549
\(607\) −2.18882 −0.0888416 −0.0444208 0.999013i \(-0.514144\pi\)
−0.0444208 + 0.999013i \(0.514144\pi\)
\(608\) 64.3546 2.60992
\(609\) 1.28039 0.0518838
\(610\) −11.1409 −0.451081
\(611\) 5.15744 0.208648
\(612\) 26.2071 1.05936
\(613\) −29.4892 −1.19106 −0.595529 0.803334i \(-0.703058\pi\)
−0.595529 + 0.803334i \(0.703058\pi\)
\(614\) 56.3537 2.27425
\(615\) −5.49199 −0.221459
\(616\) −1.61931 −0.0652437
\(617\) −10.6977 −0.430674 −0.215337 0.976540i \(-0.569085\pi\)
−0.215337 + 0.976540i \(0.569085\pi\)
\(618\) −73.8175 −2.96937
\(619\) 21.0858 0.847511 0.423756 0.905777i \(-0.360712\pi\)
0.423756 + 0.905777i \(0.360712\pi\)
\(620\) 53.4787 2.14776
\(621\) 110.799 4.44620
\(622\) 74.2539 2.97731
\(623\) −0.244222 −0.00978454
\(624\) 100.473 4.02215
\(625\) 7.63273 0.305309
\(626\) 35.8735 1.43379
\(627\) 45.3910 1.81274
\(628\) 34.6030 1.38081
\(629\) −7.59790 −0.302948
\(630\) −2.61196 −0.104063
\(631\) 27.1868 1.08229 0.541145 0.840929i \(-0.317991\pi\)
0.541145 + 0.840929i \(0.317991\pi\)
\(632\) 28.8141 1.14616
\(633\) −15.2960 −0.607960
\(634\) −63.0835 −2.50537
\(635\) 4.49954 0.178559
\(636\) −125.399 −4.97241
\(637\) −24.4487 −0.968693
\(638\) −16.5133 −0.653769
\(639\) −84.5947 −3.34652
\(640\) −4.67958 −0.184977
\(641\) 27.0558 1.06864 0.534319 0.845283i \(-0.320568\pi\)
0.534319 + 0.845283i \(0.320568\pi\)
\(642\) −40.4259 −1.59548
\(643\) 0.185986 0.00733459 0.00366729 0.999993i \(-0.498833\pi\)
0.00366729 + 0.999993i \(0.498833\pi\)
\(644\) −4.26641 −0.168120
\(645\) 1.48236 0.0583679
\(646\) 13.9420 0.548542
\(647\) 28.1939 1.10842 0.554208 0.832378i \(-0.313021\pi\)
0.554208 + 0.832378i \(0.313021\pi\)
\(648\) −175.660 −6.90059
\(649\) 23.2172 0.911353
\(650\) 33.8967 1.32954
\(651\) 3.89465 0.152643
\(652\) −65.7444 −2.57475
\(653\) 31.0888 1.21660 0.608299 0.793708i \(-0.291852\pi\)
0.608299 + 0.793708i \(0.291852\pi\)
\(654\) −45.2407 −1.76905
\(655\) −14.2593 −0.557156
\(656\) 13.3393 0.520810
\(657\) −30.8646 −1.20414
\(658\) 0.455711 0.0177655
\(659\) −5.22569 −0.203564 −0.101782 0.994807i \(-0.532454\pi\)
−0.101782 + 0.994807i \(0.532454\pi\)
\(660\) 33.1155 1.28902
\(661\) −26.5381 −1.03221 −0.516106 0.856525i \(-0.672619\pi\)
−0.516106 + 0.856525i \(0.672619\pi\)
\(662\) −65.2679 −2.53671
\(663\) 8.38340 0.325584
\(664\) −23.8590 −0.925907
\(665\) −0.976129 −0.0378527
\(666\) 200.277 7.76059
\(667\) −25.0810 −0.971139
\(668\) 82.1476 3.17838
\(669\) −8.91165 −0.344544
\(670\) −15.5258 −0.599815
\(671\) 7.35080 0.283774
\(672\) 3.41924 0.131900
\(673\) −30.4768 −1.17480 −0.587398 0.809299i \(-0.699847\pi\)
−0.587398 + 0.809299i \(0.699847\pi\)
\(674\) −17.8138 −0.686162
\(675\) −54.6408 −2.10313
\(676\) −3.54871 −0.136489
\(677\) 21.2258 0.815773 0.407887 0.913033i \(-0.366266\pi\)
0.407887 + 0.913033i \(0.366266\pi\)
\(678\) −79.7133 −3.06137
\(679\) 0.146333 0.00561575
\(680\) 5.86358 0.224858
\(681\) 72.0551 2.76116
\(682\) −50.2300 −1.92340
\(683\) −20.7787 −0.795077 −0.397538 0.917586i \(-0.630135\pi\)
−0.397538 + 0.917586i \(0.630135\pi\)
\(684\) −258.165 −9.87117
\(685\) −9.03912 −0.345367
\(686\) −4.32497 −0.165128
\(687\) −44.2355 −1.68769
\(688\) −3.60044 −0.137265
\(689\) −28.6655 −1.09207
\(690\) 71.5992 2.72574
\(691\) −41.6051 −1.58273 −0.791366 0.611343i \(-0.790629\pi\)
−0.791366 + 0.611343i \(0.790629\pi\)
\(692\) −28.2897 −1.07541
\(693\) 1.72338 0.0654659
\(694\) −82.8663 −3.14556
\(695\) −8.78609 −0.333275
\(696\) 75.7661 2.87191
\(697\) 1.11301 0.0421584
\(698\) −33.8106 −1.27975
\(699\) −30.2681 −1.14484
\(700\) 2.10400 0.0795237
\(701\) 17.6004 0.664758 0.332379 0.943146i \(-0.392149\pi\)
0.332379 + 0.943146i \(0.392149\pi\)
\(702\) −132.725 −5.00939
\(703\) 74.8466 2.82289
\(704\) −10.0327 −0.378120
\(705\) −5.37239 −0.202336
\(706\) −69.2051 −2.60457
\(707\) 0.146545 0.00551139
\(708\) −184.788 −6.94475
\(709\) 16.2408 0.609935 0.304968 0.952363i \(-0.401354\pi\)
0.304968 + 0.952363i \(0.401354\pi\)
\(710\) −32.8332 −1.23221
\(711\) −30.6661 −1.15007
\(712\) −14.4517 −0.541600
\(713\) −76.2908 −2.85711
\(714\) 0.740756 0.0277221
\(715\) 7.57000 0.283102
\(716\) −75.3379 −2.81551
\(717\) −41.8171 −1.56169
\(718\) −57.0813 −2.13026
\(719\) 52.2709 1.94938 0.974688 0.223568i \(-0.0717706\pi\)
0.974688 + 0.223568i \(0.0717706\pi\)
\(720\) −74.7905 −2.78728
\(721\) −1.04740 −0.0390071
\(722\) −88.0806 −3.27802
\(723\) −11.7643 −0.437518
\(724\) 12.4810 0.463852
\(725\) 12.3688 0.459365
\(726\) 61.3620 2.27736
\(727\) 20.4661 0.759046 0.379523 0.925182i \(-0.376088\pi\)
0.379523 + 0.925182i \(0.376088\pi\)
\(728\) 2.94617 0.109192
\(729\) 44.6813 1.65486
\(730\) −11.9793 −0.443373
\(731\) −0.300417 −0.0111113
\(732\) −58.5058 −2.16244
\(733\) 12.4794 0.460936 0.230468 0.973080i \(-0.425974\pi\)
0.230468 + 0.973080i \(0.425974\pi\)
\(734\) 53.6572 1.98053
\(735\) 25.4677 0.939390
\(736\) −66.9781 −2.46885
\(737\) 10.2440 0.377343
\(738\) −29.3386 −1.07997
\(739\) −36.1426 −1.32953 −0.664763 0.747054i \(-0.731468\pi\)
−0.664763 + 0.747054i \(0.731468\pi\)
\(740\) 54.6052 2.00733
\(741\) −82.5846 −3.03382
\(742\) −2.53288 −0.0929851
\(743\) −5.54972 −0.203600 −0.101800 0.994805i \(-0.532460\pi\)
−0.101800 + 0.994805i \(0.532460\pi\)
\(744\) 230.464 8.44921
\(745\) −18.8936 −0.692208
\(746\) 65.0794 2.38273
\(747\) 25.3924 0.929061
\(748\) −6.71124 −0.245387
\(749\) −0.573604 −0.0209590
\(750\) −82.5702 −3.01504
\(751\) −9.10768 −0.332344 −0.166172 0.986097i \(-0.553141\pi\)
−0.166172 + 0.986097i \(0.553141\pi\)
\(752\) 13.0488 0.475839
\(753\) −91.7265 −3.34270
\(754\) 30.0444 1.09415
\(755\) 0.561570 0.0204376
\(756\) −8.23838 −0.299627
\(757\) −39.6710 −1.44187 −0.720934 0.693003i \(-0.756287\pi\)
−0.720934 + 0.693003i \(0.756287\pi\)
\(758\) −58.9916 −2.14267
\(759\) −47.2414 −1.71476
\(760\) −57.7619 −2.09524
\(761\) 1.41801 0.0514028 0.0257014 0.999670i \(-0.491818\pi\)
0.0257014 + 0.999670i \(0.491818\pi\)
\(762\) 33.6368 1.21853
\(763\) −0.641922 −0.0232391
\(764\) −62.1075 −2.24697
\(765\) −6.24045 −0.225624
\(766\) −62.9465 −2.27435
\(767\) −42.2414 −1.52525
\(768\) −68.8021 −2.48268
\(769\) −35.8399 −1.29242 −0.646210 0.763160i \(-0.723647\pi\)
−0.646210 + 0.763160i \(0.723647\pi\)
\(770\) 0.668884 0.0241049
\(771\) 51.8963 1.86900
\(772\) 50.7547 1.82670
\(773\) −5.41977 −0.194935 −0.0974677 0.995239i \(-0.531074\pi\)
−0.0974677 + 0.995239i \(0.531074\pi\)
\(774\) 7.91886 0.284638
\(775\) 37.6232 1.35146
\(776\) 8.65918 0.310846
\(777\) 3.97669 0.142663
\(778\) 74.1996 2.66019
\(779\) −10.9643 −0.392836
\(780\) −60.2505 −2.15731
\(781\) 21.6634 0.775179
\(782\) −14.5104 −0.518890
\(783\) −48.4310 −1.73078
\(784\) −61.8573 −2.20919
\(785\) −8.23971 −0.294088
\(786\) −106.597 −3.80218
\(787\) 32.7892 1.16881 0.584404 0.811463i \(-0.301328\pi\)
0.584404 + 0.811463i \(0.301328\pi\)
\(788\) 5.20450 0.185403
\(789\) −20.8609 −0.742669
\(790\) −11.9022 −0.423462
\(791\) −1.13105 −0.0402156
\(792\) 101.980 3.62371
\(793\) −13.3741 −0.474927
\(794\) −9.43626 −0.334880
\(795\) 29.8603 1.05903
\(796\) 47.2637 1.67522
\(797\) −1.49075 −0.0528052 −0.0264026 0.999651i \(-0.508405\pi\)
−0.0264026 + 0.999651i \(0.508405\pi\)
\(798\) −7.29716 −0.258317
\(799\) 1.08878 0.0385181
\(800\) 33.0306 1.16781
\(801\) 15.3806 0.543445
\(802\) 9.35109 0.330199
\(803\) 7.90397 0.278925
\(804\) −81.5332 −2.87545
\(805\) 1.01592 0.0358066
\(806\) 91.3886 3.21902
\(807\) −56.2951 −1.98168
\(808\) 8.67172 0.305070
\(809\) −26.6165 −0.935788 −0.467894 0.883785i \(-0.654987\pi\)
−0.467894 + 0.883785i \(0.654987\pi\)
\(810\) 72.5598 2.54949
\(811\) 29.9915 1.05315 0.526573 0.850130i \(-0.323477\pi\)
0.526573 + 0.850130i \(0.323477\pi\)
\(812\) 1.86488 0.0654446
\(813\) 64.7903 2.27230
\(814\) −51.2880 −1.79764
\(815\) 15.6551 0.548375
\(816\) 21.2107 0.742523
\(817\) 2.95940 0.103536
\(818\) 51.5939 1.80394
\(819\) −3.13553 −0.109564
\(820\) −7.99910 −0.279341
\(821\) 53.3974 1.86358 0.931790 0.362997i \(-0.118246\pi\)
0.931790 + 0.362997i \(0.118246\pi\)
\(822\) −67.5730 −2.35688
\(823\) 8.09162 0.282056 0.141028 0.990006i \(-0.454959\pi\)
0.141028 + 0.990006i \(0.454959\pi\)
\(824\) −61.9792 −2.15915
\(825\) 23.2973 0.811109
\(826\) −3.73244 −0.129868
\(827\) 8.74577 0.304120 0.152060 0.988371i \(-0.451409\pi\)
0.152060 + 0.988371i \(0.451409\pi\)
\(828\) 268.689 9.33759
\(829\) 18.6336 0.647170 0.323585 0.946199i \(-0.395112\pi\)
0.323585 + 0.946199i \(0.395112\pi\)
\(830\) 9.85539 0.342086
\(831\) 35.8607 1.24399
\(832\) 18.2534 0.632824
\(833\) −5.16131 −0.178829
\(834\) −65.6814 −2.27436
\(835\) −19.5611 −0.676939
\(836\) 66.1121 2.28654
\(837\) −147.316 −5.09200
\(838\) 73.7950 2.54921
\(839\) −33.9259 −1.17125 −0.585627 0.810581i \(-0.699152\pi\)
−0.585627 + 0.810581i \(0.699152\pi\)
\(840\) −3.06896 −0.105889
\(841\) −18.0369 −0.621962
\(842\) −87.4074 −3.01226
\(843\) −44.9899 −1.54953
\(844\) −22.2786 −0.766861
\(845\) 0.845024 0.0290697
\(846\) −28.6997 −0.986715
\(847\) 0.870667 0.0299165
\(848\) −72.5262 −2.49056
\(849\) 65.8999 2.26168
\(850\) 7.15586 0.245444
\(851\) −77.8978 −2.67030
\(852\) −172.422 −5.90707
\(853\) −38.5876 −1.32121 −0.660607 0.750732i \(-0.729701\pi\)
−0.660607 + 0.750732i \(0.729701\pi\)
\(854\) −1.18173 −0.0404380
\(855\) 61.4745 2.10238
\(856\) −33.9427 −1.16014
\(857\) −32.0381 −1.09440 −0.547201 0.837001i \(-0.684307\pi\)
−0.547201 + 0.837001i \(0.684307\pi\)
\(858\) 56.5904 1.93196
\(859\) 25.3434 0.864705 0.432352 0.901705i \(-0.357684\pi\)
0.432352 + 0.901705i \(0.357684\pi\)
\(860\) 2.15906 0.0736233
\(861\) −0.582544 −0.0198531
\(862\) −31.9098 −1.08685
\(863\) −26.7100 −0.909218 −0.454609 0.890691i \(-0.650221\pi\)
−0.454609 + 0.890691i \(0.650221\pi\)
\(864\) −129.334 −4.40003
\(865\) 6.73638 0.229044
\(866\) 46.9426 1.59518
\(867\) −53.3467 −1.81175
\(868\) 5.67257 0.192540
\(869\) 7.85313 0.266399
\(870\) −31.2966 −1.06105
\(871\) −18.6380 −0.631524
\(872\) −37.9854 −1.28635
\(873\) −9.21573 −0.311905
\(874\) 142.941 4.83506
\(875\) −1.17159 −0.0396070
\(876\) −62.9086 −2.12548
\(877\) −3.65822 −0.123529 −0.0617647 0.998091i \(-0.519673\pi\)
−0.0617647 + 0.998091i \(0.519673\pi\)
\(878\) 82.3259 2.77836
\(879\) −67.8127 −2.28727
\(880\) 19.1527 0.645639
\(881\) 34.1044 1.14901 0.574503 0.818502i \(-0.305195\pi\)
0.574503 + 0.818502i \(0.305195\pi\)
\(882\) 136.050 4.58104
\(883\) −0.738932 −0.0248670 −0.0124335 0.999923i \(-0.503958\pi\)
−0.0124335 + 0.999923i \(0.503958\pi\)
\(884\) 12.2104 0.410682
\(885\) 44.0019 1.47911
\(886\) −61.8562 −2.07810
\(887\) −40.0494 −1.34473 −0.672364 0.740221i \(-0.734721\pi\)
−0.672364 + 0.740221i \(0.734721\pi\)
\(888\) 235.318 7.89677
\(889\) 0.477273 0.0160072
\(890\) 5.96954 0.200100
\(891\) −47.8752 −1.60388
\(892\) −12.9798 −0.434597
\(893\) −10.7255 −0.358915
\(894\) −141.241 −4.72381
\(895\) 17.9396 0.599653
\(896\) −0.496370 −0.0165826
\(897\) 85.9512 2.86983
\(898\) 69.7043 2.32606
\(899\) 33.3474 1.11220
\(900\) −132.505 −4.41684
\(901\) −6.05152 −0.201605
\(902\) 7.51317 0.250161
\(903\) 0.157236 0.00523249
\(904\) −66.9295 −2.22604
\(905\) −2.97199 −0.0987922
\(906\) 4.19808 0.139472
\(907\) −29.3966 −0.976097 −0.488048 0.872817i \(-0.662291\pi\)
−0.488048 + 0.872817i \(0.662291\pi\)
\(908\) 104.948 3.48284
\(909\) −9.22908 −0.306109
\(910\) −1.21697 −0.0403422
\(911\) 25.0465 0.829827 0.414913 0.909861i \(-0.363812\pi\)
0.414913 + 0.909861i \(0.363812\pi\)
\(912\) −208.946 −6.91889
\(913\) −6.50263 −0.215206
\(914\) −27.5910 −0.912629
\(915\) 13.9315 0.460560
\(916\) −64.4291 −2.12880
\(917\) −1.51250 −0.0499473
\(918\) −28.0194 −0.924776
\(919\) 48.9471 1.61462 0.807308 0.590130i \(-0.200924\pi\)
0.807308 + 0.590130i \(0.200924\pi\)
\(920\) 60.1167 1.98199
\(921\) −70.4693 −2.32204
\(922\) 38.5950 1.27106
\(923\) −39.4145 −1.29735
\(924\) 3.51262 0.115557
\(925\) 38.4157 1.26310
\(926\) 52.7474 1.73339
\(927\) 65.9628 2.16650
\(928\) 29.2767 0.961055
\(929\) −48.0397 −1.57613 −0.788066 0.615590i \(-0.788918\pi\)
−0.788066 + 0.615590i \(0.788918\pi\)
\(930\) −95.1974 −3.12165
\(931\) 50.8439 1.66634
\(932\) −44.0855 −1.44407
\(933\) −92.8531 −3.03988
\(934\) −8.79784 −0.287874
\(935\) 1.59809 0.0522630
\(936\) −185.543 −6.06467
\(937\) 49.1965 1.60718 0.803589 0.595184i \(-0.202921\pi\)
0.803589 + 0.595184i \(0.202921\pi\)
\(938\) −1.64685 −0.0537715
\(939\) −44.8592 −1.46392
\(940\) −7.82490 −0.255220
\(941\) −22.4504 −0.731862 −0.365931 0.930642i \(-0.619249\pi\)
−0.365931 + 0.930642i \(0.619249\pi\)
\(942\) −61.5969 −2.00694
\(943\) 11.4112 0.371601
\(944\) −106.874 −3.47846
\(945\) 1.96173 0.0638151
\(946\) −2.02790 −0.0659328
\(947\) −25.4133 −0.825820 −0.412910 0.910772i \(-0.635488\pi\)
−0.412910 + 0.910772i \(0.635488\pi\)
\(948\) −62.5039 −2.03003
\(949\) −14.3805 −0.466811
\(950\) −70.4921 −2.28707
\(951\) 78.8848 2.55801
\(952\) 0.621959 0.0201578
\(953\) −33.3017 −1.07875 −0.539374 0.842066i \(-0.681339\pi\)
−0.539374 + 0.842066i \(0.681339\pi\)
\(954\) 159.515 5.16450
\(955\) 14.7891 0.478564
\(956\) −60.9067 −1.96986
\(957\) 20.6496 0.667508
\(958\) −77.7330 −2.51144
\(959\) −0.958794 −0.0309611
\(960\) −19.0142 −0.613681
\(961\) 70.4354 2.27211
\(962\) 93.3136 3.00855
\(963\) 36.1243 1.16409
\(964\) −17.1347 −0.551871
\(965\) −12.0858 −0.389055
\(966\) 7.59464 0.244354
\(967\) 51.7462 1.66405 0.832023 0.554742i \(-0.187183\pi\)
0.832023 + 0.554742i \(0.187183\pi\)
\(968\) 51.5212 1.65595
\(969\) −17.4342 −0.560069
\(970\) −3.57684 −0.114845
\(971\) −39.6891 −1.27368 −0.636842 0.770994i \(-0.719760\pi\)
−0.636842 + 0.770994i \(0.719760\pi\)
\(972\) 173.829 5.57556
\(973\) −0.931955 −0.0298771
\(974\) −19.7811 −0.633827
\(975\) −42.3872 −1.35748
\(976\) −33.8375 −1.08311
\(977\) 13.4665 0.430833 0.215416 0.976522i \(-0.430889\pi\)
0.215416 + 0.976522i \(0.430889\pi\)
\(978\) 117.032 3.74226
\(979\) −3.93873 −0.125882
\(980\) 37.0937 1.18492
\(981\) 40.4268 1.29073
\(982\) 92.8250 2.96217
\(983\) 16.6239 0.530219 0.265110 0.964218i \(-0.414592\pi\)
0.265110 + 0.964218i \(0.414592\pi\)
\(984\) −34.4717 −1.09892
\(985\) −1.23930 −0.0394875
\(986\) 6.34261 0.201990
\(987\) −0.569858 −0.0181388
\(988\) −120.285 −3.82676
\(989\) −3.08004 −0.0979396
\(990\) −42.1249 −1.33882
\(991\) 20.1224 0.639208 0.319604 0.947551i \(-0.396450\pi\)
0.319604 + 0.947551i \(0.396450\pi\)
\(992\) 89.0533 2.82745
\(993\) 81.6163 2.59002
\(994\) −3.48266 −0.110463
\(995\) −11.2545 −0.356791
\(996\) 51.7551 1.63992
\(997\) −3.27490 −0.103717 −0.0518585 0.998654i \(-0.516514\pi\)
−0.0518585 + 0.998654i \(0.516514\pi\)
\(998\) −46.4019 −1.46883
\(999\) −150.420 −4.75907
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 \(a_p\))