Properties

Label 8011.2.a.b.1.9
Level 8011
Weight 2
Character 8011.1
Self dual Yes
Analytic conductor 63.968
Analytic rank 0
Dimension 358
CM No

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Newspace parameters

Level: \( N \) = \( 8011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8011.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9681570592\)
Analytic rank: \(0\)
Dimension: \(358\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8011.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.67959 q^{2}\) \(-1.76320 q^{3}\) \(+5.18019 q^{4}\) \(-3.93630 q^{5}\) \(+4.72465 q^{6}\) \(-2.55729 q^{7}\) \(-8.52159 q^{8}\) \(+0.108876 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.67959 q^{2}\) \(-1.76320 q^{3}\) \(+5.18019 q^{4}\) \(-3.93630 q^{5}\) \(+4.72465 q^{6}\) \(-2.55729 q^{7}\) \(-8.52159 q^{8}\) \(+0.108876 q^{9}\) \(+10.5477 q^{10}\) \(+1.40777 q^{11}\) \(-9.13371 q^{12}\) \(-2.73241 q^{13}\) \(+6.85247 q^{14}\) \(+6.94049 q^{15}\) \(+12.4740 q^{16}\) \(-1.27752 q^{17}\) \(-0.291742 q^{18}\) \(-3.42030 q^{19}\) \(-20.3908 q^{20}\) \(+4.50901 q^{21}\) \(-3.77225 q^{22}\) \(+5.50852 q^{23}\) \(+15.0253 q^{24}\) \(+10.4945 q^{25}\) \(+7.32174 q^{26}\) \(+5.09763 q^{27}\) \(-13.2472 q^{28}\) \(+4.57184 q^{29}\) \(-18.5976 q^{30}\) \(-6.23935 q^{31}\) \(-16.3819 q^{32}\) \(-2.48218 q^{33}\) \(+3.42322 q^{34}\) \(+10.0662 q^{35}\) \(+0.563996 q^{36}\) \(-3.97944 q^{37}\) \(+9.16500 q^{38}\) \(+4.81779 q^{39}\) \(+33.5435 q^{40}\) \(+9.88896 q^{41}\) \(-12.0823 q^{42}\) \(+0.0738129 q^{43}\) \(+7.29252 q^{44}\) \(-0.428567 q^{45}\) \(-14.7606 q^{46}\) \(-3.58950 q^{47}\) \(-21.9941 q^{48}\) \(-0.460288 q^{49}\) \(-28.1208 q^{50}\) \(+2.25252 q^{51}\) \(-14.1544 q^{52}\) \(-0.0891657 q^{53}\) \(-13.6595 q^{54}\) \(-5.54141 q^{55}\) \(+21.7921 q^{56}\) \(+6.03068 q^{57}\) \(-12.2507 q^{58}\) \(-0.736911 q^{59}\) \(+35.9530 q^{60}\) \(+12.7896 q^{61}\) \(+16.7189 q^{62}\) \(-0.278426 q^{63}\) \(+18.9488 q^{64}\) \(+10.7556 q^{65}\) \(+6.65123 q^{66}\) \(-0.110608 q^{67}\) \(-6.61778 q^{68}\) \(-9.71263 q^{69}\) \(-26.9734 q^{70}\) \(-10.3081 q^{71}\) \(-0.927793 q^{72}\) \(-5.98043 q^{73}\) \(+10.6632 q^{74}\) \(-18.5038 q^{75}\) \(-17.7178 q^{76}\) \(-3.60008 q^{77}\) \(-12.9097 q^{78}\) \(-1.36862 q^{79}\) \(-49.1013 q^{80}\) \(-9.31477 q^{81}\) \(-26.4983 q^{82}\) \(-2.90034 q^{83}\) \(+23.3575 q^{84}\) \(+5.02870 q^{85}\) \(-0.197788 q^{86}\) \(-8.06108 q^{87}\) \(-11.9965 q^{88}\) \(+18.5008 q^{89}\) \(+1.14838 q^{90}\) \(+6.98756 q^{91}\) \(+28.5352 q^{92}\) \(+11.0012 q^{93}\) \(+9.61838 q^{94}\) \(+13.4633 q^{95}\) \(+28.8846 q^{96}\) \(-13.4129 q^{97}\) \(+1.23338 q^{98}\) \(+0.153272 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(358q \) \(\mathstrut +\mathstrut 33q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 391q^{4} \) \(\mathstrut +\mathstrut 76q^{5} \) \(\mathstrut +\mathstrut 32q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 99q^{8} \) \(\mathstrut +\mathstrut 451q^{9} \) \(\mathstrut +\mathstrut 21q^{10} \) \(\mathstrut +\mathstrut 70q^{11} \) \(\mathstrut +\mathstrut 20q^{12} \) \(\mathstrut +\mathstrut 53q^{13} \) \(\mathstrut +\mathstrut 69q^{14} \) \(\mathstrut +\mathstrut 28q^{15} \) \(\mathstrut +\mathstrut 449q^{16} \) \(\mathstrut +\mathstrut 88q^{17} \) \(\mathstrut +\mathstrut 86q^{18} \) \(\mathstrut +\mathstrut 44q^{19} \) \(\mathstrut +\mathstrut 136q^{20} \) \(\mathstrut +\mathstrut 125q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 104q^{23} \) \(\mathstrut +\mathstrut 84q^{24} \) \(\mathstrut +\mathstrut 444q^{25} \) \(\mathstrut +\mathstrut 100q^{26} \) \(\mathstrut +\mathstrut 32q^{27} \) \(\mathstrut +\mathstrut 46q^{28} \) \(\mathstrut +\mathstrut 373q^{29} \) \(\mathstrut +\mathstrut 99q^{30} \) \(\mathstrut +\mathstrut 30q^{31} \) \(\mathstrut +\mathstrut 221q^{32} \) \(\mathstrut +\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 26q^{34} \) \(\mathstrut +\mathstrut 164q^{35} \) \(\mathstrut +\mathstrut 599q^{36} \) \(\mathstrut +\mathstrut 81q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut +\mathstrut 143q^{39} \) \(\mathstrut +\mathstrut 42q^{40} \) \(\mathstrut +\mathstrut 182q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut +\mathstrut 40q^{43} \) \(\mathstrut +\mathstrut 184q^{44} \) \(\mathstrut +\mathstrut 198q^{45} \) \(\mathstrut +\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 5q^{48} \) \(\mathstrut +\mathstrut 479q^{49} \) \(\mathstrut +\mathstrut 184q^{50} \) \(\mathstrut +\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 64q^{52} \) \(\mathstrut +\mathstrut 221q^{53} \) \(\mathstrut +\mathstrut 67q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 174q^{56} \) \(\mathstrut +\mathstrut 84q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut +\mathstrut 127q^{59} \) \(\mathstrut +\mathstrut 29q^{60} \) \(\mathstrut +\mathstrut 174q^{61} \) \(\mathstrut +\mathstrut 86q^{62} \) \(\mathstrut +\mathstrut 48q^{63} \) \(\mathstrut +\mathstrut 549q^{64} \) \(\mathstrut +\mathstrut 202q^{65} \) \(\mathstrut +\mathstrut 32q^{66} \) \(\mathstrut +\mathstrut 29q^{67} \) \(\mathstrut +\mathstrut 172q^{68} \) \(\mathstrut +\mathstrut 249q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 185q^{71} \) \(\mathstrut +\mathstrut 218q^{72} \) \(\mathstrut +\mathstrut 57q^{73} \) \(\mathstrut +\mathstrut 272q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 84q^{76} \) \(\mathstrut +\mathstrut 384q^{77} \) \(\mathstrut +\mathstrut 12q^{78} \) \(\mathstrut +\mathstrut 93q^{79} \) \(\mathstrut +\mathstrut 215q^{80} \) \(\mathstrut +\mathstrut 702q^{81} \) \(\mathstrut +\mathstrut 48q^{82} \) \(\mathstrut +\mathstrut 121q^{83} \) \(\mathstrut +\mathstrut 179q^{84} \) \(\mathstrut +\mathstrut 177q^{85} \) \(\mathstrut +\mathstrut 209q^{86} \) \(\mathstrut +\mathstrut 91q^{87} \) \(\mathstrut +\mathstrut 36q^{88} \) \(\mathstrut +\mathstrut 186q^{89} \) \(\mathstrut +\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 272q^{92} \) \(\mathstrut +\mathstrut 220q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 170q^{95} \) \(\mathstrut +\mathstrut 162q^{96} \) \(\mathstrut +\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 196q^{98} \) \(\mathstrut +\mathstrut 152q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.67959 −1.89475 −0.947377 0.320119i \(-0.896277\pi\)
−0.947377 + 0.320119i \(0.896277\pi\)
\(3\) −1.76320 −1.01798 −0.508992 0.860771i \(-0.669982\pi\)
−0.508992 + 0.860771i \(0.669982\pi\)
\(4\) 5.18019 2.59009
\(5\) −3.93630 −1.76037 −0.880184 0.474633i \(-0.842581\pi\)
−0.880184 + 0.474633i \(0.842581\pi\)
\(6\) 4.72465 1.92883
\(7\) −2.55729 −0.966563 −0.483282 0.875465i \(-0.660555\pi\)
−0.483282 + 0.875465i \(0.660555\pi\)
\(8\) −8.52159 −3.01284
\(9\) 0.108876 0.0362919
\(10\) 10.5477 3.33546
\(11\) 1.40777 0.424459 0.212230 0.977220i \(-0.431928\pi\)
0.212230 + 0.977220i \(0.431928\pi\)
\(12\) −9.13371 −2.63667
\(13\) −2.73241 −0.757835 −0.378917 0.925430i \(-0.623704\pi\)
−0.378917 + 0.925430i \(0.623704\pi\)
\(14\) 6.85247 1.83140
\(15\) 6.94049 1.79203
\(16\) 12.4740 3.11849
\(17\) −1.27752 −0.309844 −0.154922 0.987927i \(-0.549513\pi\)
−0.154922 + 0.987927i \(0.549513\pi\)
\(18\) −0.291742 −0.0687642
\(19\) −3.42030 −0.784672 −0.392336 0.919822i \(-0.628333\pi\)
−0.392336 + 0.919822i \(0.628333\pi\)
\(20\) −20.3908 −4.55952
\(21\) 4.50901 0.983946
\(22\) −3.77225 −0.804246
\(23\) 5.50852 1.14861 0.574303 0.818643i \(-0.305273\pi\)
0.574303 + 0.818643i \(0.305273\pi\)
\(24\) 15.0253 3.06702
\(25\) 10.4945 2.09889
\(26\) 7.32174 1.43591
\(27\) 5.09763 0.981040
\(28\) −13.2472 −2.50349
\(29\) 4.57184 0.848970 0.424485 0.905435i \(-0.360455\pi\)
0.424485 + 0.905435i \(0.360455\pi\)
\(30\) −18.5976 −3.39545
\(31\) −6.23935 −1.12062 −0.560310 0.828283i \(-0.689318\pi\)
−0.560310 + 0.828283i \(0.689318\pi\)
\(32\) −16.3819 −2.89594
\(33\) −2.48218 −0.432093
\(34\) 3.42322 0.587078
\(35\) 10.0662 1.70151
\(36\) 0.563996 0.0939993
\(37\) −3.97944 −0.654215 −0.327108 0.944987i \(-0.606074\pi\)
−0.327108 + 0.944987i \(0.606074\pi\)
\(38\) 9.16500 1.48676
\(39\) 4.81779 0.771464
\(40\) 33.5435 5.30370
\(41\) 9.88896 1.54440 0.772198 0.635382i \(-0.219157\pi\)
0.772198 + 0.635382i \(0.219157\pi\)
\(42\) −12.0823 −1.86434
\(43\) 0.0738129 0.0112564 0.00562818 0.999984i \(-0.498208\pi\)
0.00562818 + 0.999984i \(0.498208\pi\)
\(44\) 7.29252 1.09939
\(45\) −0.428567 −0.0638870
\(46\) −14.7606 −2.17633
\(47\) −3.58950 −0.523583 −0.261791 0.965125i \(-0.584313\pi\)
−0.261791 + 0.965125i \(0.584313\pi\)
\(48\) −21.9941 −3.17458
\(49\) −0.460288 −0.0657554
\(50\) −28.1208 −3.97689
\(51\) 2.25252 0.315416
\(52\) −14.1544 −1.96286
\(53\) −0.0891657 −0.0122479 −0.00612393 0.999981i \(-0.501949\pi\)
−0.00612393 + 0.999981i \(0.501949\pi\)
\(54\) −13.6595 −1.85883
\(55\) −5.54141 −0.747204
\(56\) 21.7921 2.91210
\(57\) 6.03068 0.798783
\(58\) −12.2507 −1.60859
\(59\) −0.736911 −0.0959376 −0.0479688 0.998849i \(-0.515275\pi\)
−0.0479688 + 0.998849i \(0.515275\pi\)
\(60\) 35.9530 4.64152
\(61\) 12.7896 1.63754 0.818770 0.574122i \(-0.194657\pi\)
0.818770 + 0.574122i \(0.194657\pi\)
\(62\) 16.7189 2.12330
\(63\) −0.278426 −0.0350784
\(64\) 18.9488 2.36860
\(65\) 10.7556 1.33407
\(66\) 6.65123 0.818710
\(67\) −0.110608 −0.0135129 −0.00675646 0.999977i \(-0.502151\pi\)
−0.00675646 + 0.999977i \(0.502151\pi\)
\(68\) −6.61778 −0.802524
\(69\) −9.71263 −1.16926
\(70\) −26.9734 −3.22394
\(71\) −10.3081 −1.22334 −0.611672 0.791111i \(-0.709503\pi\)
−0.611672 + 0.791111i \(0.709503\pi\)
\(72\) −0.927793 −0.109341
\(73\) −5.98043 −0.699956 −0.349978 0.936758i \(-0.613811\pi\)
−0.349978 + 0.936758i \(0.613811\pi\)
\(74\) 10.6632 1.23958
\(75\) −18.5038 −2.13664
\(76\) −17.7178 −2.03237
\(77\) −3.60008 −0.410267
\(78\) −12.9097 −1.46173
\(79\) −1.36862 −0.153982 −0.0769911 0.997032i \(-0.524531\pi\)
−0.0769911 + 0.997032i \(0.524531\pi\)
\(80\) −49.1013 −5.48969
\(81\) −9.31477 −1.03497
\(82\) −26.4983 −2.92625
\(83\) −2.90034 −0.318353 −0.159177 0.987250i \(-0.550884\pi\)
−0.159177 + 0.987250i \(0.550884\pi\)
\(84\) 23.3575 2.54851
\(85\) 5.02870 0.545439
\(86\) −0.197788 −0.0213280
\(87\) −8.06108 −0.864238
\(88\) −11.9965 −1.27883
\(89\) 18.5008 1.96108 0.980541 0.196317i \(-0.0628981\pi\)
0.980541 + 0.196317i \(0.0628981\pi\)
\(90\) 1.14838 0.121050
\(91\) 6.98756 0.732495
\(92\) 28.5352 2.97500
\(93\) 11.0012 1.14077
\(94\) 9.61838 0.992061
\(95\) 13.4633 1.38131
\(96\) 28.8846 2.94802
\(97\) −13.4129 −1.36187 −0.680936 0.732343i \(-0.738427\pi\)
−0.680936 + 0.732343i \(0.738427\pi\)
\(98\) 1.23338 0.124590
\(99\) 0.153272 0.0154044
\(100\) 54.3633 5.43633
\(101\) −0.619098 −0.0616025 −0.0308013 0.999526i \(-0.509806\pi\)
−0.0308013 + 0.999526i \(0.509806\pi\)
\(102\) −6.03583 −0.597636
\(103\) −5.13500 −0.505967 −0.252983 0.967471i \(-0.581412\pi\)
−0.252983 + 0.967471i \(0.581412\pi\)
\(104\) 23.2845 2.28323
\(105\) −17.7488 −1.73211
\(106\) 0.238927 0.0232067
\(107\) −3.57501 −0.345609 −0.172805 0.984956i \(-0.555283\pi\)
−0.172805 + 0.984956i \(0.555283\pi\)
\(108\) 26.4067 2.54099
\(109\) −2.41004 −0.230840 −0.115420 0.993317i \(-0.536821\pi\)
−0.115420 + 0.993317i \(0.536821\pi\)
\(110\) 14.8487 1.41577
\(111\) 7.01654 0.665981
\(112\) −31.8995 −3.01422
\(113\) −14.3872 −1.35343 −0.676716 0.736244i \(-0.736598\pi\)
−0.676716 + 0.736244i \(0.736598\pi\)
\(114\) −16.1597 −1.51350
\(115\) −21.6832 −2.02197
\(116\) 23.6830 2.19891
\(117\) −0.297493 −0.0275032
\(118\) 1.97462 0.181778
\(119\) 3.26698 0.299483
\(120\) −59.1440 −5.39908
\(121\) −9.01818 −0.819834
\(122\) −34.2708 −3.10273
\(123\) −17.4362 −1.57217
\(124\) −32.3210 −2.90251
\(125\) −21.6279 −1.93445
\(126\) 0.746067 0.0664649
\(127\) 8.49452 0.753767 0.376883 0.926261i \(-0.376996\pi\)
0.376883 + 0.926261i \(0.376996\pi\)
\(128\) −18.0112 −1.59198
\(129\) −0.130147 −0.0114588
\(130\) −28.8206 −2.52773
\(131\) 4.17126 0.364445 0.182222 0.983257i \(-0.441671\pi\)
0.182222 + 0.983257i \(0.441671\pi\)
\(132\) −12.8582 −1.11916
\(133\) 8.74670 0.758435
\(134\) 0.296384 0.0256037
\(135\) −20.0658 −1.72699
\(136\) 10.8865 0.933509
\(137\) 3.18442 0.272064 0.136032 0.990704i \(-0.456565\pi\)
0.136032 + 0.990704i \(0.456565\pi\)
\(138\) 26.0258 2.21547
\(139\) −22.1332 −1.87731 −0.938656 0.344856i \(-0.887928\pi\)
−0.938656 + 0.344856i \(0.887928\pi\)
\(140\) 52.1451 4.40706
\(141\) 6.32901 0.532999
\(142\) 27.6214 2.31794
\(143\) −3.84661 −0.321670
\(144\) 1.35811 0.113176
\(145\) −17.9961 −1.49450
\(146\) 16.0251 1.32624
\(147\) 0.811579 0.0669379
\(148\) −20.6142 −1.69448
\(149\) 0.910743 0.0746110 0.0373055 0.999304i \(-0.488123\pi\)
0.0373055 + 0.999304i \(0.488123\pi\)
\(150\) 49.5827 4.04841
\(151\) 3.94541 0.321073 0.160536 0.987030i \(-0.448678\pi\)
0.160536 + 0.987030i \(0.448678\pi\)
\(152\) 29.1464 2.36409
\(153\) −0.139091 −0.0112448
\(154\) 9.64672 0.777355
\(155\) 24.5599 1.97270
\(156\) 24.9571 1.99816
\(157\) −16.8836 −1.34746 −0.673729 0.738979i \(-0.735308\pi\)
−0.673729 + 0.738979i \(0.735308\pi\)
\(158\) 3.66735 0.291759
\(159\) 0.157217 0.0124681
\(160\) 64.4842 5.09792
\(161\) −14.0869 −1.11020
\(162\) 24.9597 1.96102
\(163\) 6.60610 0.517430 0.258715 0.965954i \(-0.416701\pi\)
0.258715 + 0.965954i \(0.416701\pi\)
\(164\) 51.2267 4.00013
\(165\) 9.77062 0.760642
\(166\) 7.77170 0.603201
\(167\) −5.52442 −0.427493 −0.213746 0.976889i \(-0.568567\pi\)
−0.213746 + 0.976889i \(0.568567\pi\)
\(168\) −38.4239 −2.96447
\(169\) −5.53392 −0.425686
\(170\) −13.4748 −1.03347
\(171\) −0.372388 −0.0284772
\(172\) 0.382365 0.0291550
\(173\) −22.9879 −1.74774 −0.873868 0.486163i \(-0.838396\pi\)
−0.873868 + 0.486163i \(0.838396\pi\)
\(174\) 21.6004 1.63752
\(175\) −26.8373 −2.02871
\(176\) 17.5605 1.32367
\(177\) 1.29932 0.0976630
\(178\) −49.5745 −3.71577
\(179\) −4.90666 −0.366741 −0.183371 0.983044i \(-0.558701\pi\)
−0.183371 + 0.983044i \(0.558701\pi\)
\(180\) −2.22006 −0.165473
\(181\) 19.4443 1.44528 0.722642 0.691223i \(-0.242928\pi\)
0.722642 + 0.691223i \(0.242928\pi\)
\(182\) −18.7238 −1.38790
\(183\) −22.5506 −1.66699
\(184\) −46.9414 −3.46057
\(185\) 15.6643 1.15166
\(186\) −29.4787 −2.16149
\(187\) −1.79845 −0.131516
\(188\) −18.5943 −1.35613
\(189\) −13.0361 −0.948237
\(190\) −36.0762 −2.61724
\(191\) 11.9773 0.866643 0.433322 0.901239i \(-0.357341\pi\)
0.433322 + 0.901239i \(0.357341\pi\)
\(192\) −33.4106 −2.41120
\(193\) −14.5795 −1.04946 −0.524728 0.851270i \(-0.675833\pi\)
−0.524728 + 0.851270i \(0.675833\pi\)
\(194\) 35.9410 2.58041
\(195\) −18.9643 −1.35806
\(196\) −2.38438 −0.170313
\(197\) −5.12730 −0.365305 −0.182653 0.983178i \(-0.558468\pi\)
−0.182653 + 0.983178i \(0.558468\pi\)
\(198\) −0.410706 −0.0291876
\(199\) 17.9179 1.27016 0.635082 0.772445i \(-0.280966\pi\)
0.635082 + 0.772445i \(0.280966\pi\)
\(200\) −89.4295 −6.32362
\(201\) 0.195024 0.0137559
\(202\) 1.65893 0.116722
\(203\) −11.6915 −0.820583
\(204\) 11.6685 0.816957
\(205\) −38.9259 −2.71870
\(206\) 13.7597 0.958683
\(207\) 0.599744 0.0416851
\(208\) −34.0840 −2.36330
\(209\) −4.81501 −0.333061
\(210\) 47.5595 3.28192
\(211\) 3.05004 0.209974 0.104987 0.994474i \(-0.466520\pi\)
0.104987 + 0.994474i \(0.466520\pi\)
\(212\) −0.461895 −0.0317231
\(213\) 18.1752 1.24535
\(214\) 9.57955 0.654845
\(215\) −0.290550 −0.0198153
\(216\) −43.4399 −2.95571
\(217\) 15.9558 1.08315
\(218\) 6.45790 0.437384
\(219\) 10.5447 0.712544
\(220\) −28.7056 −1.93533
\(221\) 3.49071 0.234810
\(222\) −18.8014 −1.26187
\(223\) −15.8701 −1.06274 −0.531370 0.847140i \(-0.678323\pi\)
−0.531370 + 0.847140i \(0.678323\pi\)
\(224\) 41.8933 2.79911
\(225\) 1.14259 0.0761727
\(226\) 38.5517 2.56442
\(227\) 3.30990 0.219686 0.109843 0.993949i \(-0.464965\pi\)
0.109843 + 0.993949i \(0.464965\pi\)
\(228\) 31.2401 2.06892
\(229\) 17.7221 1.17111 0.585554 0.810634i \(-0.300877\pi\)
0.585554 + 0.810634i \(0.300877\pi\)
\(230\) 58.1020 3.83114
\(231\) 6.34765 0.417645
\(232\) −38.9594 −2.55781
\(233\) 14.4415 0.946096 0.473048 0.881037i \(-0.343154\pi\)
0.473048 + 0.881037i \(0.343154\pi\)
\(234\) 0.797158 0.0521119
\(235\) 14.1294 0.921698
\(236\) −3.81734 −0.248487
\(237\) 2.41316 0.156751
\(238\) −8.75416 −0.567448
\(239\) −11.9333 −0.771898 −0.385949 0.922520i \(-0.626126\pi\)
−0.385949 + 0.922520i \(0.626126\pi\)
\(240\) 86.5754 5.58842
\(241\) −5.94809 −0.383150 −0.191575 0.981478i \(-0.561360\pi\)
−0.191575 + 0.981478i \(0.561360\pi\)
\(242\) 24.1650 1.55338
\(243\) 1.13092 0.0725483
\(244\) 66.2525 4.24138
\(245\) 1.81183 0.115754
\(246\) 46.7219 2.97888
\(247\) 9.34568 0.594652
\(248\) 53.1692 3.37625
\(249\) 5.11387 0.324078
\(250\) 57.9537 3.66531
\(251\) −9.09108 −0.573824 −0.286912 0.957957i \(-0.592629\pi\)
−0.286912 + 0.957957i \(0.592629\pi\)
\(252\) −1.44230 −0.0908563
\(253\) 7.75474 0.487537
\(254\) −22.7618 −1.42820
\(255\) −8.86660 −0.555248
\(256\) 10.3650 0.647810
\(257\) 7.43202 0.463597 0.231798 0.972764i \(-0.425539\pi\)
0.231798 + 0.972764i \(0.425539\pi\)
\(258\) 0.348740 0.0217116
\(259\) 10.1766 0.632341
\(260\) 55.7160 3.45536
\(261\) 0.497762 0.0308107
\(262\) −11.1773 −0.690533
\(263\) 31.0762 1.91624 0.958121 0.286365i \(-0.0924470\pi\)
0.958121 + 0.286365i \(0.0924470\pi\)
\(264\) 21.1522 1.30183
\(265\) 0.350983 0.0215607
\(266\) −23.4375 −1.43705
\(267\) −32.6206 −1.99635
\(268\) −0.572970 −0.0349997
\(269\) −3.47735 −0.212018 −0.106009 0.994365i \(-0.533807\pi\)
−0.106009 + 0.994365i \(0.533807\pi\)
\(270\) 53.7681 3.27222
\(271\) −13.6748 −0.830683 −0.415342 0.909665i \(-0.636338\pi\)
−0.415342 + 0.909665i \(0.636338\pi\)
\(272\) −15.9357 −0.966245
\(273\) −12.3205 −0.745669
\(274\) −8.53294 −0.515494
\(275\) 14.7738 0.890894
\(276\) −50.3133 −3.02850
\(277\) −10.8085 −0.649419 −0.324709 0.945814i \(-0.605267\pi\)
−0.324709 + 0.945814i \(0.605267\pi\)
\(278\) 59.3078 3.55704
\(279\) −0.679313 −0.0406694
\(280\) −85.7804 −5.12636
\(281\) −11.1885 −0.667449 −0.333724 0.942671i \(-0.608305\pi\)
−0.333724 + 0.942671i \(0.608305\pi\)
\(282\) −16.9591 −1.00990
\(283\) −26.1812 −1.55631 −0.778156 0.628071i \(-0.783845\pi\)
−0.778156 + 0.628071i \(0.783845\pi\)
\(284\) −53.3978 −3.16858
\(285\) −23.7386 −1.40615
\(286\) 10.3073 0.609486
\(287\) −25.2889 −1.49276
\(288\) −1.78359 −0.105099
\(289\) −15.3679 −0.903997
\(290\) 48.2223 2.83171
\(291\) 23.6496 1.38636
\(292\) −30.9797 −1.81295
\(293\) −4.87985 −0.285084 −0.142542 0.989789i \(-0.545528\pi\)
−0.142542 + 0.989789i \(0.545528\pi\)
\(294\) −2.17470 −0.126831
\(295\) 2.90070 0.168885
\(296\) 33.9111 1.97104
\(297\) 7.17630 0.416411
\(298\) −2.44042 −0.141370
\(299\) −15.0516 −0.870454
\(300\) −95.8534 −5.53410
\(301\) −0.188761 −0.0108800
\(302\) −10.5721 −0.608354
\(303\) 1.09159 0.0627104
\(304\) −42.6648 −2.44699
\(305\) −50.3437 −2.88267
\(306\) 0.372705 0.0213061
\(307\) 14.8391 0.846914 0.423457 0.905916i \(-0.360817\pi\)
0.423457 + 0.905916i \(0.360817\pi\)
\(308\) −18.6491 −1.06263
\(309\) 9.05404 0.515066
\(310\) −65.8105 −3.73779
\(311\) −3.82519 −0.216907 −0.108453 0.994102i \(-0.534590\pi\)
−0.108453 + 0.994102i \(0.534590\pi\)
\(312\) −41.0553 −2.32430
\(313\) 14.6682 0.829094 0.414547 0.910028i \(-0.363940\pi\)
0.414547 + 0.910028i \(0.363940\pi\)
\(314\) 45.2411 2.55310
\(315\) 1.09597 0.0617508
\(316\) −7.08973 −0.398829
\(317\) 30.7893 1.72930 0.864649 0.502377i \(-0.167541\pi\)
0.864649 + 0.502377i \(0.167541\pi\)
\(318\) −0.421277 −0.0236240
\(319\) 6.43611 0.360353
\(320\) −74.5883 −4.16961
\(321\) 6.30346 0.351825
\(322\) 37.7470 2.10356
\(323\) 4.36950 0.243125
\(324\) −48.2523 −2.68068
\(325\) −28.6752 −1.59061
\(326\) −17.7016 −0.980402
\(327\) 4.24938 0.234991
\(328\) −84.2697 −4.65301
\(329\) 9.17938 0.506076
\(330\) −26.1812 −1.44123
\(331\) −21.9532 −1.20666 −0.603329 0.797492i \(-0.706159\pi\)
−0.603329 + 0.797492i \(0.706159\pi\)
\(332\) −15.0243 −0.824565
\(333\) −0.433263 −0.0237427
\(334\) 14.8032 0.809994
\(335\) 0.435386 0.0237877
\(336\) 56.2452 3.06843
\(337\) −27.1026 −1.47637 −0.738185 0.674598i \(-0.764317\pi\)
−0.738185 + 0.674598i \(0.764317\pi\)
\(338\) 14.8286 0.806571
\(339\) 25.3675 1.37777
\(340\) 26.0496 1.41274
\(341\) −8.78358 −0.475657
\(342\) 0.997845 0.0539573
\(343\) 19.0781 1.03012
\(344\) −0.629003 −0.0339136
\(345\) 38.2318 2.05833
\(346\) 61.5980 3.31153
\(347\) −16.9744 −0.911236 −0.455618 0.890175i \(-0.650582\pi\)
−0.455618 + 0.890175i \(0.650582\pi\)
\(348\) −41.7579 −2.23846
\(349\) −28.2467 −1.51201 −0.756005 0.654565i \(-0.772852\pi\)
−0.756005 + 0.654565i \(0.772852\pi\)
\(350\) 71.9130 3.84391
\(351\) −13.9288 −0.743466
\(352\) −23.0620 −1.22921
\(353\) −16.2422 −0.864486 −0.432243 0.901757i \(-0.642278\pi\)
−0.432243 + 0.901757i \(0.642278\pi\)
\(354\) −3.48165 −0.185047
\(355\) 40.5757 2.15353
\(356\) 95.8376 5.07938
\(357\) −5.76034 −0.304869
\(358\) 13.1478 0.694884
\(359\) −31.8933 −1.68326 −0.841631 0.540053i \(-0.818404\pi\)
−0.841631 + 0.540053i \(0.818404\pi\)
\(360\) 3.65207 0.192481
\(361\) −7.30152 −0.384291
\(362\) −52.1027 −2.73846
\(363\) 15.9009 0.834578
\(364\) 36.1969 1.89723
\(365\) 23.5408 1.23218
\(366\) 60.4263 3.15853
\(367\) −1.84572 −0.0963458 −0.0481729 0.998839i \(-0.515340\pi\)
−0.0481729 + 0.998839i \(0.515340\pi\)
\(368\) 68.7132 3.58192
\(369\) 1.07667 0.0560490
\(370\) −41.9737 −2.18211
\(371\) 0.228022 0.0118383
\(372\) 56.9884 2.95471
\(373\) 6.89626 0.357075 0.178537 0.983933i \(-0.442863\pi\)
0.178537 + 0.983933i \(0.442863\pi\)
\(374\) 4.81911 0.249190
\(375\) 38.1342 1.96924
\(376\) 30.5883 1.57747
\(377\) −12.4922 −0.643379
\(378\) 34.9314 1.79668
\(379\) −13.2930 −0.682817 −0.341408 0.939915i \(-0.610904\pi\)
−0.341408 + 0.939915i \(0.610904\pi\)
\(380\) 69.7427 3.57772
\(381\) −14.9775 −0.767323
\(382\) −32.0941 −1.64208
\(383\) −3.78187 −0.193245 −0.0966223 0.995321i \(-0.530804\pi\)
−0.0966223 + 0.995321i \(0.530804\pi\)
\(384\) 31.7574 1.62061
\(385\) 14.1710 0.722220
\(386\) 39.0671 1.98846
\(387\) 0.00803642 0.000408514 0
\(388\) −69.4813 −3.52738
\(389\) −6.19540 −0.314119 −0.157060 0.987589i \(-0.550202\pi\)
−0.157060 + 0.987589i \(0.550202\pi\)
\(390\) 50.8164 2.57319
\(391\) −7.03724 −0.355888
\(392\) 3.92238 0.198110
\(393\) −7.35477 −0.370999
\(394\) 13.7391 0.692164
\(395\) 5.38732 0.271065
\(396\) 0.793978 0.0398989
\(397\) −1.44165 −0.0723543 −0.0361771 0.999345i \(-0.511518\pi\)
−0.0361771 + 0.999345i \(0.511518\pi\)
\(398\) −48.0125 −2.40665
\(399\) −15.4222 −0.772075
\(400\) 130.908 6.54538
\(401\) 15.7940 0.788716 0.394358 0.918957i \(-0.370967\pi\)
0.394358 + 0.918957i \(0.370967\pi\)
\(402\) −0.522584 −0.0260641
\(403\) 17.0485 0.849245
\(404\) −3.20704 −0.159556
\(405\) 36.6657 1.82194
\(406\) 31.3284 1.55480
\(407\) −5.60214 −0.277688
\(408\) −19.1951 −0.950297
\(409\) −0.0784059 −0.00387692 −0.00193846 0.999998i \(-0.500617\pi\)
−0.00193846 + 0.999998i \(0.500617\pi\)
\(410\) 104.305 5.15128
\(411\) −5.61478 −0.276957
\(412\) −26.6003 −1.31050
\(413\) 1.88449 0.0927298
\(414\) −1.60707 −0.0789830
\(415\) 11.4166 0.560418
\(416\) 44.7622 2.19465
\(417\) 39.0252 1.91107
\(418\) 12.9022 0.631069
\(419\) −10.3094 −0.503648 −0.251824 0.967773i \(-0.581030\pi\)
−0.251824 + 0.967773i \(0.581030\pi\)
\(420\) −91.9422 −4.48632
\(421\) 10.5306 0.513228 0.256614 0.966514i \(-0.417393\pi\)
0.256614 + 0.966514i \(0.417393\pi\)
\(422\) −8.17285 −0.397848
\(423\) −0.390809 −0.0190018
\(424\) 0.759834 0.0369008
\(425\) −13.4069 −0.650328
\(426\) −48.7021 −2.35962
\(427\) −32.7066 −1.58279
\(428\) −18.5192 −0.895161
\(429\) 6.78235 0.327455
\(430\) 0.778553 0.0375452
\(431\) −8.94280 −0.430759 −0.215380 0.976530i \(-0.569099\pi\)
−0.215380 + 0.976530i \(0.569099\pi\)
\(432\) 63.5877 3.05937
\(433\) −26.0613 −1.25243 −0.626213 0.779652i \(-0.715396\pi\)
−0.626213 + 0.779652i \(0.715396\pi\)
\(434\) −42.7550 −2.05230
\(435\) 31.7308 1.52138
\(436\) −12.4844 −0.597896
\(437\) −18.8408 −0.901279
\(438\) −28.2554 −1.35010
\(439\) 19.8924 0.949410 0.474705 0.880145i \(-0.342555\pi\)
0.474705 + 0.880145i \(0.342555\pi\)
\(440\) 47.2217 2.25120
\(441\) −0.0501141 −0.00238638
\(442\) −9.35365 −0.444908
\(443\) 14.2506 0.677066 0.338533 0.940954i \(-0.390069\pi\)
0.338533 + 0.940954i \(0.390069\pi\)
\(444\) 36.3470 1.72495
\(445\) −72.8247 −3.45222
\(446\) 42.5253 2.01363
\(447\) −1.60582 −0.0759528
\(448\) −48.4576 −2.28941
\(449\) −2.89085 −0.136428 −0.0682139 0.997671i \(-0.521730\pi\)
−0.0682139 + 0.997671i \(0.521730\pi\)
\(450\) −3.06167 −0.144329
\(451\) 13.9214 0.655533
\(452\) −74.5283 −3.50552
\(453\) −6.95655 −0.326847
\(454\) −8.86917 −0.416251
\(455\) −27.5051 −1.28946
\(456\) −51.3910 −2.40660
\(457\) −39.7598 −1.85989 −0.929943 0.367703i \(-0.880144\pi\)
−0.929943 + 0.367703i \(0.880144\pi\)
\(458\) −47.4878 −2.21896
\(459\) −6.51232 −0.303969
\(460\) −112.323 −5.23709
\(461\) 15.5939 0.726281 0.363140 0.931734i \(-0.381705\pi\)
0.363140 + 0.931734i \(0.381705\pi\)
\(462\) −17.0091 −0.791335
\(463\) 17.3940 0.808366 0.404183 0.914678i \(-0.367556\pi\)
0.404183 + 0.914678i \(0.367556\pi\)
\(464\) 57.0291 2.64751
\(465\) −43.3041 −2.00818
\(466\) −38.6973 −1.79262
\(467\) 29.8479 1.38120 0.690598 0.723239i \(-0.257347\pi\)
0.690598 + 0.723239i \(0.257347\pi\)
\(468\) −1.54107 −0.0712360
\(469\) 0.282856 0.0130611
\(470\) −37.8608 −1.74639
\(471\) 29.7692 1.37169
\(472\) 6.27965 0.289045
\(473\) 0.103912 0.00477787
\(474\) −6.46627 −0.297006
\(475\) −35.8942 −1.64694
\(476\) 16.9236 0.775690
\(477\) −0.00970797 −0.000444497 0
\(478\) 31.9762 1.46256
\(479\) −17.3541 −0.792928 −0.396464 0.918050i \(-0.629763\pi\)
−0.396464 + 0.918050i \(0.629763\pi\)
\(480\) −113.698 −5.18960
\(481\) 10.8735 0.495787
\(482\) 15.9384 0.725975
\(483\) 24.8380 1.13017
\(484\) −46.7159 −2.12345
\(485\) 52.7972 2.39740
\(486\) −3.03039 −0.137461
\(487\) −24.5512 −1.11252 −0.556260 0.831008i \(-0.687764\pi\)
−0.556260 + 0.831008i \(0.687764\pi\)
\(488\) −108.988 −4.93364
\(489\) −11.6479 −0.526735
\(490\) −4.85496 −0.219325
\(491\) 28.7218 1.29620 0.648098 0.761557i \(-0.275565\pi\)
0.648098 + 0.761557i \(0.275565\pi\)
\(492\) −90.3229 −4.07207
\(493\) −5.84061 −0.263048
\(494\) −25.0426 −1.12672
\(495\) −0.603324 −0.0271174
\(496\) −77.8295 −3.49465
\(497\) 26.3607 1.18244
\(498\) −13.7031 −0.614049
\(499\) 2.55228 0.114256 0.0571279 0.998367i \(-0.481806\pi\)
0.0571279 + 0.998367i \(0.481806\pi\)
\(500\) −112.036 −5.01042
\(501\) 9.74067 0.435181
\(502\) 24.3604 1.08726
\(503\) −25.6503 −1.14369 −0.571845 0.820362i \(-0.693772\pi\)
−0.571845 + 0.820362i \(0.693772\pi\)
\(504\) 2.37263 0.105685
\(505\) 2.43696 0.108443
\(506\) −20.7795 −0.923762
\(507\) 9.75741 0.433342
\(508\) 44.0032 1.95233
\(509\) −34.4210 −1.52568 −0.762841 0.646586i \(-0.776196\pi\)
−0.762841 + 0.646586i \(0.776196\pi\)
\(510\) 23.7588 1.05206
\(511\) 15.2937 0.676552
\(512\) 8.24862 0.364541
\(513\) −17.4354 −0.769794
\(514\) −19.9147 −0.878402
\(515\) 20.2129 0.890687
\(516\) −0.674186 −0.0296794
\(517\) −5.05320 −0.222239
\(518\) −27.2690 −1.19813
\(519\) 40.5322 1.77917
\(520\) −91.6548 −4.01933
\(521\) 4.67049 0.204618 0.102309 0.994753i \(-0.467377\pi\)
0.102309 + 0.994753i \(0.467377\pi\)
\(522\) −1.33380 −0.0583787
\(523\) −12.3436 −0.539747 −0.269874 0.962896i \(-0.586982\pi\)
−0.269874 + 0.962896i \(0.586982\pi\)
\(524\) 21.6079 0.943946
\(525\) 47.3196 2.06520
\(526\) −83.2714 −3.63081
\(527\) 7.97088 0.347217
\(528\) −30.9627 −1.34748
\(529\) 7.34383 0.319297
\(530\) −0.940490 −0.0408523
\(531\) −0.0802316 −0.00348175
\(532\) 45.3095 1.96442
\(533\) −27.0207 −1.17040
\(534\) 87.4098 3.78259
\(535\) 14.0723 0.608399
\(536\) 0.942556 0.0407122
\(537\) 8.65143 0.373337
\(538\) 9.31786 0.401721
\(539\) −0.647980 −0.0279105
\(540\) −103.945 −4.47307
\(541\) −20.7266 −0.891105 −0.445552 0.895256i \(-0.646993\pi\)
−0.445552 + 0.895256i \(0.646993\pi\)
\(542\) 36.6428 1.57394
\(543\) −34.2842 −1.47128
\(544\) 20.9282 0.897289
\(545\) 9.48663 0.406362
\(546\) 33.0138 1.41286
\(547\) 25.1093 1.07360 0.536798 0.843711i \(-0.319634\pi\)
0.536798 + 0.843711i \(0.319634\pi\)
\(548\) 16.4959 0.704671
\(549\) 1.39247 0.0594293
\(550\) −39.5877 −1.68803
\(551\) −15.6371 −0.666163
\(552\) 82.7671 3.52280
\(553\) 3.49996 0.148834
\(554\) 28.9623 1.23049
\(555\) −27.6192 −1.17237
\(556\) −114.654 −4.86241
\(557\) 9.08336 0.384874 0.192437 0.981309i \(-0.438361\pi\)
0.192437 + 0.981309i \(0.438361\pi\)
\(558\) 1.82028 0.0770585
\(559\) −0.201687 −0.00853046
\(560\) 125.566 5.30614
\(561\) 3.17103 0.133881
\(562\) 29.9805 1.26465
\(563\) −26.3365 −1.10995 −0.554976 0.831866i \(-0.687273\pi\)
−0.554976 + 0.831866i \(0.687273\pi\)
\(564\) 32.7855 1.38052
\(565\) 56.6323 2.38254
\(566\) 70.1549 2.94883
\(567\) 23.8205 1.00037
\(568\) 87.8413 3.68574
\(569\) −11.2263 −0.470632 −0.235316 0.971919i \(-0.575613\pi\)
−0.235316 + 0.971919i \(0.575613\pi\)
\(570\) 63.6096 2.66431
\(571\) 20.4743 0.856823 0.428412 0.903584i \(-0.359073\pi\)
0.428412 + 0.903584i \(0.359073\pi\)
\(572\) −19.9262 −0.833156
\(573\) −21.1183 −0.882229
\(574\) 67.7638 2.82841
\(575\) 57.8090 2.41080
\(576\) 2.06306 0.0859610
\(577\) −25.8342 −1.07549 −0.537746 0.843107i \(-0.680724\pi\)
−0.537746 + 0.843107i \(0.680724\pi\)
\(578\) 41.1798 1.71285
\(579\) 25.7066 1.06833
\(580\) −93.2234 −3.87089
\(581\) 7.41699 0.307708
\(582\) −63.3712 −2.62682
\(583\) −0.125525 −0.00519871
\(584\) 50.9628 2.10885
\(585\) 1.17102 0.0484158
\(586\) 13.0760 0.540164
\(587\) −28.0740 −1.15874 −0.579368 0.815066i \(-0.696701\pi\)
−0.579368 + 0.815066i \(0.696701\pi\)
\(588\) 4.20413 0.173376
\(589\) 21.3405 0.879319
\(590\) −7.77269 −0.319996
\(591\) 9.04046 0.371875
\(592\) −49.6394 −2.04017
\(593\) −26.2442 −1.07772 −0.538859 0.842396i \(-0.681145\pi\)
−0.538859 + 0.842396i \(0.681145\pi\)
\(594\) −19.2295 −0.788997
\(595\) −12.8598 −0.527201
\(596\) 4.71782 0.193250
\(597\) −31.5928 −1.29301
\(598\) 40.3320 1.64930
\(599\) 22.7241 0.928482 0.464241 0.885709i \(-0.346327\pi\)
0.464241 + 0.885709i \(0.346327\pi\)
\(600\) 157.682 6.43735
\(601\) 4.57880 0.186773 0.0933866 0.995630i \(-0.470231\pi\)
0.0933866 + 0.995630i \(0.470231\pi\)
\(602\) 0.505801 0.0206149
\(603\) −0.0120425 −0.000490409 0
\(604\) 20.4380 0.831609
\(605\) 35.4983 1.44321
\(606\) −2.92502 −0.118821
\(607\) 26.3845 1.07091 0.535457 0.844562i \(-0.320139\pi\)
0.535457 + 0.844562i \(0.320139\pi\)
\(608\) 56.0311 2.27236
\(609\) 20.6145 0.835341
\(610\) 134.900 5.46195
\(611\) 9.80800 0.396789
\(612\) −0.720515 −0.0291251
\(613\) −5.30786 −0.214383 −0.107191 0.994238i \(-0.534186\pi\)
−0.107191 + 0.994238i \(0.534186\pi\)
\(614\) −39.7627 −1.60469
\(615\) 68.6342 2.76760
\(616\) 30.6784 1.23607
\(617\) 46.1306 1.85715 0.928575 0.371145i \(-0.121035\pi\)
0.928575 + 0.371145i \(0.121035\pi\)
\(618\) −24.2611 −0.975924
\(619\) −32.5442 −1.30806 −0.654030 0.756468i \(-0.726923\pi\)
−0.654030 + 0.756468i \(0.726923\pi\)
\(620\) 127.225 5.10949
\(621\) 28.0804 1.12683
\(622\) 10.2499 0.410985
\(623\) −47.3118 −1.89551
\(624\) 60.0970 2.40581
\(625\) 32.6614 1.30646
\(626\) −39.3046 −1.57093
\(627\) 8.48982 0.339051
\(628\) −87.4602 −3.49004
\(629\) 5.08380 0.202704
\(630\) −2.93674 −0.117003
\(631\) 47.0883 1.87455 0.937277 0.348585i \(-0.113338\pi\)
0.937277 + 0.348585i \(0.113338\pi\)
\(632\) 11.6629 0.463924
\(633\) −5.37783 −0.213750
\(634\) −82.5025 −3.27659
\(635\) −33.4370 −1.32691
\(636\) 0.814414 0.0322936
\(637\) 1.25770 0.0498317
\(638\) −17.2461 −0.682781
\(639\) −1.12230 −0.0443974
\(640\) 70.8976 2.80247
\(641\) −20.9382 −0.827008 −0.413504 0.910502i \(-0.635695\pi\)
−0.413504 + 0.910502i \(0.635695\pi\)
\(642\) −16.8907 −0.666622
\(643\) −1.46300 −0.0576951 −0.0288475 0.999584i \(-0.509184\pi\)
−0.0288475 + 0.999584i \(0.509184\pi\)
\(644\) −72.9726 −2.87553
\(645\) 0.512297 0.0201717
\(646\) −11.7085 −0.460663
\(647\) −45.5453 −1.79057 −0.895285 0.445495i \(-0.853028\pi\)
−0.895285 + 0.445495i \(0.853028\pi\)
\(648\) 79.3767 3.11821
\(649\) −1.03740 −0.0407216
\(650\) 76.8377 3.01382
\(651\) −28.1333 −1.10263
\(652\) 34.2208 1.34019
\(653\) −1.62927 −0.0637583 −0.0318792 0.999492i \(-0.510149\pi\)
−0.0318792 + 0.999492i \(0.510149\pi\)
\(654\) −11.3866 −0.445250
\(655\) −16.4193 −0.641557
\(656\) 123.355 4.81619
\(657\) −0.651122 −0.0254027
\(658\) −24.5970 −0.958889
\(659\) 9.01689 0.351248 0.175624 0.984457i \(-0.443806\pi\)
0.175624 + 0.984457i \(0.443806\pi\)
\(660\) 50.6137 1.97013
\(661\) −40.8048 −1.58712 −0.793561 0.608491i \(-0.791775\pi\)
−0.793561 + 0.608491i \(0.791775\pi\)
\(662\) 58.8256 2.28632
\(663\) −6.15482 −0.239033
\(664\) 24.7155 0.959146
\(665\) −34.4296 −1.33512
\(666\) 1.16097 0.0449866
\(667\) 25.1841 0.975133
\(668\) −28.6176 −1.10725
\(669\) 27.9822 1.08185
\(670\) −1.16666 −0.0450718
\(671\) 18.0048 0.695069
\(672\) −73.8662 −2.84945
\(673\) −25.9461 −1.00015 −0.500075 0.865982i \(-0.666694\pi\)
−0.500075 + 0.865982i \(0.666694\pi\)
\(674\) 72.6237 2.79736
\(675\) 53.4969 2.05910
\(676\) −28.6668 −1.10257
\(677\) −25.9626 −0.997825 −0.498912 0.866652i \(-0.666267\pi\)
−0.498912 + 0.866652i \(0.666267\pi\)
\(678\) −67.9744 −2.61054
\(679\) 34.3006 1.31634
\(680\) −42.8525 −1.64332
\(681\) −5.83602 −0.223637
\(682\) 23.5364 0.901254
\(683\) 6.35212 0.243057 0.121529 0.992588i \(-0.461220\pi\)
0.121529 + 0.992588i \(0.461220\pi\)
\(684\) −1.92904 −0.0737586
\(685\) −12.5348 −0.478932
\(686\) −51.1214 −1.95182
\(687\) −31.2476 −1.19217
\(688\) 0.920740 0.0351029
\(689\) 0.243637 0.00928185
\(690\) −102.446 −3.90004
\(691\) 32.8473 1.24957 0.624785 0.780797i \(-0.285187\pi\)
0.624785 + 0.780797i \(0.285187\pi\)
\(692\) −119.082 −4.52680
\(693\) −0.391960 −0.0148893
\(694\) 45.4845 1.72657
\(695\) 87.1228 3.30476
\(696\) 68.6932 2.60381
\(697\) −12.6333 −0.478521
\(698\) 75.6895 2.86489
\(699\) −25.4633 −0.963110
\(700\) −139.022 −5.25456
\(701\) 39.1416 1.47836 0.739179 0.673509i \(-0.235214\pi\)
0.739179 + 0.673509i \(0.235214\pi\)
\(702\) 37.3235 1.40869
\(703\) 13.6109 0.513344
\(704\) 26.6756 1.00538
\(705\) −24.9129 −0.938274
\(706\) 43.5225 1.63799
\(707\) 1.58321 0.0595428
\(708\) 6.73073 0.252956
\(709\) 32.2835 1.21243 0.606217 0.795299i \(-0.292686\pi\)
0.606217 + 0.795299i \(0.292686\pi\)
\(710\) −108.726 −4.08042
\(711\) −0.149010 −0.00558830
\(712\) −157.656 −5.90842
\(713\) −34.3696 −1.28715
\(714\) 15.4353 0.577653
\(715\) 15.1414 0.566257
\(716\) −25.4174 −0.949894
\(717\) 21.0407 0.785780
\(718\) 85.4608 3.18937
\(719\) −4.01496 −0.149733 −0.0748664 0.997194i \(-0.523853\pi\)
−0.0748664 + 0.997194i \(0.523853\pi\)
\(720\) −5.34593 −0.199231
\(721\) 13.1317 0.489049
\(722\) 19.5651 0.728136
\(723\) 10.4877 0.390041
\(724\) 100.725 3.74342
\(725\) 47.9790 1.78190
\(726\) −42.6077 −1.58132
\(727\) 3.12013 0.115719 0.0578597 0.998325i \(-0.481572\pi\)
0.0578597 + 0.998325i \(0.481572\pi\)
\(728\) −59.5451 −2.20689
\(729\) 25.9503 0.961122
\(730\) −63.0795 −2.33468
\(731\) −0.0942973 −0.00348771
\(732\) −116.816 −4.31766
\(733\) 50.5369 1.86662 0.933311 0.359068i \(-0.116905\pi\)
0.933311 + 0.359068i \(0.116905\pi\)
\(734\) 4.94577 0.182552
\(735\) −3.19462 −0.117835
\(736\) −90.2402 −3.32630
\(737\) −0.155711 −0.00573568
\(738\) −2.88502 −0.106199
\(739\) −0.672270 −0.0247299 −0.0123649 0.999924i \(-0.503936\pi\)
−0.0123649 + 0.999924i \(0.503936\pi\)
\(740\) 81.1438 2.98291
\(741\) −16.4783 −0.605346
\(742\) −0.611005 −0.0224307
\(743\) −35.7447 −1.31135 −0.655673 0.755045i \(-0.727615\pi\)
−0.655673 + 0.755045i \(0.727615\pi\)
\(744\) −93.7479 −3.43697
\(745\) −3.58496 −0.131343
\(746\) −18.4791 −0.676569
\(747\) −0.315776 −0.0115536
\(748\) −9.31633 −0.340639
\(749\) 9.14233 0.334053
\(750\) −102.184 −3.73123
\(751\) 12.4924 0.455855 0.227928 0.973678i \(-0.426805\pi\)
0.227928 + 0.973678i \(0.426805\pi\)
\(752\) −44.7754 −1.63279
\(753\) 16.0294 0.584144
\(754\) 33.4738 1.21905
\(755\) −15.5303 −0.565206
\(756\) −67.5295 −2.45602
\(757\) 33.7346 1.22610 0.613052 0.790042i \(-0.289941\pi\)
0.613052 + 0.790042i \(0.289941\pi\)
\(758\) 35.6198 1.29377
\(759\) −13.6732 −0.496305
\(760\) −114.729 −4.16166
\(761\) 9.11708 0.330494 0.165247 0.986252i \(-0.447158\pi\)
0.165247 + 0.986252i \(0.447158\pi\)
\(762\) 40.1336 1.45389
\(763\) 6.16315 0.223121
\(764\) 62.0444 2.24469
\(765\) 0.547502 0.0197950
\(766\) 10.1339 0.366151
\(767\) 2.01354 0.0727049
\(768\) −18.2755 −0.659460
\(769\) 14.6084 0.526792 0.263396 0.964688i \(-0.415157\pi\)
0.263396 + 0.964688i \(0.415157\pi\)
\(770\) −37.9724 −1.36843
\(771\) −13.1041 −0.471934
\(772\) −75.5246 −2.71819
\(773\) −22.8709 −0.822608 −0.411304 0.911498i \(-0.634927\pi\)
−0.411304 + 0.911498i \(0.634927\pi\)
\(774\) −0.0215343 −0.000774034 0
\(775\) −65.4786 −2.35206
\(776\) 114.299 4.10310
\(777\) −17.9433 −0.643713
\(778\) 16.6011 0.595179
\(779\) −33.8232 −1.21184
\(780\) −98.2385 −3.51750
\(781\) −14.5114 −0.519260
\(782\) 18.8569 0.674321
\(783\) 23.3056 0.832873
\(784\) −5.74162 −0.205058
\(785\) 66.4589 2.37202
\(786\) 19.7077 0.702952
\(787\) −41.3364 −1.47348 −0.736742 0.676174i \(-0.763637\pi\)
−0.736742 + 0.676174i \(0.763637\pi\)
\(788\) −26.5604 −0.946175
\(789\) −54.7936 −1.95070
\(790\) −14.4358 −0.513602
\(791\) 36.7922 1.30818
\(792\) −1.30612 −0.0464110
\(793\) −34.9464 −1.24098
\(794\) 3.86302 0.137094
\(795\) −0.618853 −0.0219485
\(796\) 92.8179 3.28984
\(797\) 8.82065 0.312444 0.156222 0.987722i \(-0.450069\pi\)
0.156222 + 0.987722i \(0.450069\pi\)
\(798\) 41.3251 1.46289
\(799\) 4.58565 0.162229
\(800\) −171.919 −6.07827
\(801\) 2.01429 0.0711713
\(802\) −42.3215 −1.49442
\(803\) −8.41908 −0.297103
\(804\) 1.01026 0.0356292
\(805\) 55.4502 1.95436
\(806\) −45.6829 −1.60911
\(807\) 6.13126 0.215831
\(808\) 5.27570 0.185598
\(809\) 22.8529 0.803464 0.401732 0.915757i \(-0.368408\pi\)
0.401732 + 0.915757i \(0.368408\pi\)
\(810\) −98.2491 −3.45212
\(811\) 7.26827 0.255223 0.127612 0.991824i \(-0.459269\pi\)
0.127612 + 0.991824i \(0.459269\pi\)
\(812\) −60.5642 −2.12539
\(813\) 24.1114 0.845623
\(814\) 15.0114 0.526150
\(815\) −26.0036 −0.910866
\(816\) 28.0979 0.983623
\(817\) −0.252463 −0.00883255
\(818\) 0.210095 0.00734582
\(819\) 0.760775 0.0265836
\(820\) −201.644 −7.04170
\(821\) 55.1608 1.92512 0.962562 0.271062i \(-0.0873750\pi\)
0.962562 + 0.271062i \(0.0873750\pi\)
\(822\) 15.0453 0.524765
\(823\) −7.46788 −0.260314 −0.130157 0.991493i \(-0.541548\pi\)
−0.130157 + 0.991493i \(0.541548\pi\)
\(824\) 43.7584 1.52440
\(825\) −26.0492 −0.906916
\(826\) −5.04966 −0.175700
\(827\) −44.0972 −1.53341 −0.766706 0.641999i \(-0.778105\pi\)
−0.766706 + 0.641999i \(0.778105\pi\)
\(828\) 3.10679 0.107968
\(829\) 32.3580 1.12384 0.561920 0.827192i \(-0.310063\pi\)
0.561920 + 0.827192i \(0.310063\pi\)
\(830\) −30.5918 −1.06186
\(831\) 19.0575 0.661098
\(832\) −51.7760 −1.79501
\(833\) 0.588026 0.0203739
\(834\) −104.571 −3.62101
\(835\) 21.7458 0.752544
\(836\) −24.9426 −0.862659
\(837\) −31.8059 −1.09937
\(838\) 27.6250 0.954290
\(839\) 37.1210 1.28156 0.640780 0.767725i \(-0.278611\pi\)
0.640780 + 0.767725i \(0.278611\pi\)
\(840\) 151.248 5.21856
\(841\) −8.09825 −0.279250
\(842\) −28.2175 −0.972441
\(843\) 19.7275 0.679452
\(844\) 15.7998 0.543851
\(845\) 21.7832 0.749364
\(846\) 1.04721 0.0360037
\(847\) 23.0621 0.792422
\(848\) −1.11225 −0.0381948
\(849\) 46.1627 1.58430
\(850\) 35.9249 1.23221
\(851\) −21.9208 −0.751436
\(852\) 94.1510 3.22556
\(853\) 23.5796 0.807352 0.403676 0.914902i \(-0.367732\pi\)
0.403676 + 0.914902i \(0.367732\pi\)
\(854\) 87.6403 2.99899
\(855\) 1.46583 0.0501303
\(856\) 30.4648 1.04127
\(857\) 6.10651 0.208595 0.104297 0.994546i \(-0.466741\pi\)
0.104297 + 0.994546i \(0.466741\pi\)
\(858\) −18.1739 −0.620447
\(859\) 34.5877 1.18012 0.590059 0.807360i \(-0.299105\pi\)
0.590059 + 0.807360i \(0.299105\pi\)
\(860\) −1.50510 −0.0513236
\(861\) 44.5894 1.51960
\(862\) 23.9630 0.816183
\(863\) 23.1648 0.788541 0.394270 0.918995i \(-0.370997\pi\)
0.394270 + 0.918995i \(0.370997\pi\)
\(864\) −83.5090 −2.84103
\(865\) 90.4872 3.07666
\(866\) 69.8335 2.37304
\(867\) 27.0968 0.920255
\(868\) 82.6540 2.80546
\(869\) −1.92671 −0.0653592
\(870\) −85.0255 −2.88263
\(871\) 0.302227 0.0102406
\(872\) 20.5373 0.695482
\(873\) −1.46034 −0.0494249
\(874\) 50.4856 1.70770
\(875\) 55.3086 1.86977
\(876\) 54.6235 1.84556
\(877\) 49.6852 1.67775 0.838875 0.544324i \(-0.183214\pi\)
0.838875 + 0.544324i \(0.183214\pi\)
\(878\) −53.3033 −1.79890
\(879\) 8.60415 0.290211
\(880\) −69.1234 −2.33015
\(881\) −25.9924 −0.875705 −0.437853 0.899047i \(-0.644261\pi\)
−0.437853 + 0.899047i \(0.644261\pi\)
\(882\) 0.134285 0.00452161
\(883\) 52.3121 1.76044 0.880221 0.474564i \(-0.157394\pi\)
0.880221 + 0.474564i \(0.157394\pi\)
\(884\) 18.0825 0.608181
\(885\) −5.11452 −0.171923
\(886\) −38.1857 −1.28287
\(887\) 27.1327 0.911027 0.455514 0.890229i \(-0.349456\pi\)
0.455514 + 0.890229i \(0.349456\pi\)
\(888\) −59.7921 −2.00649
\(889\) −21.7229 −0.728563
\(890\) 195.140 6.54111
\(891\) −13.1131 −0.439305
\(892\) −82.2101 −2.75260
\(893\) 12.2772 0.410840
\(894\) 4.30294 0.143912
\(895\) 19.3141 0.645599
\(896\) 46.0598 1.53875
\(897\) 26.5389 0.886109
\(898\) 7.74629 0.258497
\(899\) −28.5253 −0.951373
\(900\) 5.91883 0.197294
\(901\) 0.113911 0.00379492
\(902\) −37.3036 −1.24207
\(903\) 0.332823 0.0110757
\(904\) 122.602 4.07767
\(905\) −76.5386 −2.54423
\(906\) 18.6407 0.619295
\(907\) 37.8100 1.25546 0.627730 0.778431i \(-0.283984\pi\)
0.627730 + 0.778431i \(0.283984\pi\)
\(908\) 17.1459 0.569007
\(909\) −0.0674046 −0.00223567
\(910\) 73.7024 2.44321
\(911\) −15.3308 −0.507932 −0.253966 0.967213i \(-0.581735\pi\)
−0.253966 + 0.967213i \(0.581735\pi\)
\(912\) 75.2266 2.49100
\(913\) −4.08301 −0.135128
\(914\) 106.540 3.52403
\(915\) 88.7660 2.93451
\(916\) 91.8037 3.03328
\(917\) −10.6671 −0.352259
\(918\) 17.4503 0.575946
\(919\) −31.3384 −1.03376 −0.516879 0.856059i \(-0.672906\pi\)
−0.516879 + 0.856059i \(0.672906\pi\)
\(920\) 184.775 6.09187
\(921\) −26.1644 −0.862145
\(922\) −41.7852 −1.37612
\(923\) 28.1659 0.927093
\(924\) 32.8820 1.08174
\(925\) −41.7620 −1.37313
\(926\) −46.6087 −1.53166
\(927\) −0.559076 −0.0183625
\(928\) −74.8956 −2.45857
\(929\) 40.4213 1.32618 0.663090 0.748540i \(-0.269245\pi\)
0.663090 + 0.748540i \(0.269245\pi\)
\(930\) 116.037 3.80501
\(931\) 1.57432 0.0515964
\(932\) 74.8098 2.45048
\(933\) 6.74458 0.220808
\(934\) −79.9800 −2.61703
\(935\) 7.07926 0.231516
\(936\) 2.53511 0.0828628
\(937\) −46.1999 −1.50928 −0.754642 0.656136i \(-0.772190\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(938\) −0.757938 −0.0247476
\(939\) −25.8629 −0.844005
\(940\) 73.1927 2.38728
\(941\) 30.4574 0.992883 0.496441 0.868070i \(-0.334640\pi\)
0.496441 + 0.868070i \(0.334640\pi\)
\(942\) −79.7691 −2.59902
\(943\) 54.4736 1.77390
\(944\) −9.19221 −0.299181
\(945\) 51.3140 1.66925
\(946\) −0.278441 −0.00905288
\(947\) −50.7411 −1.64886 −0.824431 0.565962i \(-0.808505\pi\)
−0.824431 + 0.565962i \(0.808505\pi\)
\(948\) 12.5006 0.406001
\(949\) 16.3410 0.530451
\(950\) 96.1818 3.12055
\(951\) −54.2876 −1.76040
\(952\) −27.8399 −0.902295
\(953\) 57.9225 1.87629 0.938147 0.346238i \(-0.112541\pi\)
0.938147 + 0.346238i \(0.112541\pi\)
\(954\) 0.0260133 0.000842213 0
\(955\) −47.1461 −1.52561
\(956\) −61.8165 −1.99929
\(957\) −11.3482 −0.366834
\(958\) 46.5017 1.50240
\(959\) −8.14348 −0.262967
\(960\) 131.514 4.24460
\(961\) 7.92946 0.255789
\(962\) −29.1364 −0.939395
\(963\) −0.389231 −0.0125428
\(964\) −30.8122 −0.992395
\(965\) 57.3893 1.84743
\(966\) −66.5555 −2.14139
\(967\) 34.0320 1.09440 0.547198 0.837003i \(-0.315695\pi\)
0.547198 + 0.837003i \(0.315695\pi\)
\(968\) 76.8492 2.47003
\(969\) −7.70430 −0.247498
\(970\) −141.475 −4.54248
\(971\) −29.1470 −0.935372 −0.467686 0.883895i \(-0.654912\pi\)
−0.467686 + 0.883895i \(0.654912\pi\)
\(972\) 5.85836 0.187907
\(973\) 56.6009 1.81454
\(974\) 65.7870 2.10795
\(975\) 50.5601 1.61922
\(976\) 159.537 5.10666
\(977\) −23.4948 −0.751666 −0.375833 0.926687i \(-0.622643\pi\)
−0.375833 + 0.926687i \(0.622643\pi\)
\(978\) 31.2115 0.998034
\(979\) 26.0449 0.832399
\(980\) 9.38562 0.299813
\(981\) −0.262394 −0.00837760
\(982\) −76.9625 −2.45597
\(983\) 8.10480 0.258503 0.129251 0.991612i \(-0.458743\pi\)
0.129251 + 0.991612i \(0.458743\pi\)
\(984\) 148.584 4.73670
\(985\) 20.1826 0.643071
\(986\) 15.6504 0.498411
\(987\) −16.1851 −0.515177
\(988\) 48.4124 1.54020
\(989\) 0.406600 0.0129291
\(990\) 1.61666 0.0513808
\(991\) −21.9803 −0.698229 −0.349114 0.937080i \(-0.613518\pi\)
−0.349114 + 0.937080i \(0.613518\pi\)
\(992\) 102.212 3.24525
\(993\) 38.7079 1.22836
\(994\) −70.6358 −2.24043
\(995\) −70.5301 −2.23595
\(996\) 26.4908 0.839394
\(997\) 12.2064 0.386579 0.193290 0.981142i \(-0.438084\pi\)
0.193290 + 0.981142i \(0.438084\pi\)
\(998\) −6.83906 −0.216487
\(999\) −20.2857 −0.641811
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 \(a_p\))