Properties

Label 8015.2.a.l.1.18
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.34348 q^{2}\) \(-2.34976 q^{3}\) \(-0.195065 q^{4}\) \(-1.00000 q^{5}\) \(+3.15685 q^{6}\) \(-1.00000 q^{7}\) \(+2.94902 q^{8}\) \(+2.52136 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.34348 q^{2}\) \(-2.34976 q^{3}\) \(-0.195065 q^{4}\) \(-1.00000 q^{5}\) \(+3.15685 q^{6}\) \(-1.00000 q^{7}\) \(+2.94902 q^{8}\) \(+2.52136 q^{9}\) \(+1.34348 q^{10}\) \(+1.18122 q^{11}\) \(+0.458355 q^{12}\) \(-0.588443 q^{13}\) \(+1.34348 q^{14}\) \(+2.34976 q^{15}\) \(-3.57182 q^{16}\) \(+2.31546 q^{17}\) \(-3.38740 q^{18}\) \(-8.11161 q^{19}\) \(+0.195065 q^{20}\) \(+2.34976 q^{21}\) \(-1.58694 q^{22}\) \(-2.01930 q^{23}\) \(-6.92949 q^{24}\) \(+1.00000 q^{25}\) \(+0.790561 q^{26}\) \(+1.12468 q^{27}\) \(+0.195065 q^{28}\) \(+9.62218 q^{29}\) \(-3.15685 q^{30}\) \(-1.07051 q^{31}\) \(-1.09938 q^{32}\) \(-2.77558 q^{33}\) \(-3.11078 q^{34}\) \(+1.00000 q^{35}\) \(-0.491829 q^{36}\) \(+2.42896 q^{37}\) \(+10.8978 q^{38}\) \(+1.38270 q^{39}\) \(-2.94902 q^{40}\) \(+5.19778 q^{41}\) \(-3.15685 q^{42}\) \(-7.17480 q^{43}\) \(-0.230414 q^{44}\) \(-2.52136 q^{45}\) \(+2.71289 q^{46}\) \(+2.65348 q^{47}\) \(+8.39291 q^{48}\) \(+1.00000 q^{49}\) \(-1.34348 q^{50}\) \(-5.44078 q^{51}\) \(+0.114785 q^{52}\) \(+3.73499 q^{53}\) \(-1.51099 q^{54}\) \(-1.18122 q^{55}\) \(-2.94902 q^{56}\) \(+19.0603 q^{57}\) \(-12.9272 q^{58}\) \(+7.26498 q^{59}\) \(-0.458355 q^{60}\) \(-8.28356 q^{61}\) \(+1.43821 q^{62}\) \(-2.52136 q^{63}\) \(+8.62064 q^{64}\) \(+0.588443 q^{65}\) \(+3.72893 q^{66}\) \(+2.82605 q^{67}\) \(-0.451665 q^{68}\) \(+4.74487 q^{69}\) \(-1.34348 q^{70}\) \(-12.9454 q^{71}\) \(+7.43556 q^{72}\) \(+0.537958 q^{73}\) \(-3.26326 q^{74}\) \(-2.34976 q^{75}\) \(+1.58229 q^{76}\) \(-1.18122 q^{77}\) \(-1.85763 q^{78}\) \(-6.23859 q^{79}\) \(+3.57182 q^{80}\) \(-10.2068 q^{81}\) \(-6.98310 q^{82}\) \(+10.6286 q^{83}\) \(-0.458355 q^{84}\) \(-2.31546 q^{85}\) \(+9.63919 q^{86}\) \(-22.6098 q^{87}\) \(+3.48344 q^{88}\) \(+10.4769 q^{89}\) \(+3.38740 q^{90}\) \(+0.588443 q^{91}\) \(+0.393895 q^{92}\) \(+2.51544 q^{93}\) \(-3.56490 q^{94}\) \(+8.11161 q^{95}\) \(+2.58328 q^{96}\) \(+11.2081 q^{97}\) \(-1.34348 q^{98}\) \(+2.97828 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34348 −0.949983 −0.474991 0.879990i \(-0.657549\pi\)
−0.474991 + 0.879990i \(0.657549\pi\)
\(3\) −2.34976 −1.35663 −0.678317 0.734770i \(-0.737290\pi\)
−0.678317 + 0.734770i \(0.737290\pi\)
\(4\) −0.195065 −0.0975324
\(5\) −1.00000 −0.447214
\(6\) 3.15685 1.28878
\(7\) −1.00000 −0.377964
\(8\) 2.94902 1.04264
\(9\) 2.52136 0.840454
\(10\) 1.34348 0.424845
\(11\) 1.18122 0.356151 0.178076 0.984017i \(-0.443013\pi\)
0.178076 + 0.984017i \(0.443013\pi\)
\(12\) 0.458355 0.132316
\(13\) −0.588443 −0.163205 −0.0816024 0.996665i \(-0.526004\pi\)
−0.0816024 + 0.996665i \(0.526004\pi\)
\(14\) 1.34348 0.359060
\(15\) 2.34976 0.606705
\(16\) −3.57182 −0.892955
\(17\) 2.31546 0.561582 0.280791 0.959769i \(-0.409403\pi\)
0.280791 + 0.959769i \(0.409403\pi\)
\(18\) −3.38740 −0.798417
\(19\) −8.11161 −1.86093 −0.930465 0.366381i \(-0.880597\pi\)
−0.930465 + 0.366381i \(0.880597\pi\)
\(20\) 0.195065 0.0436178
\(21\) 2.34976 0.512759
\(22\) −1.58694 −0.338338
\(23\) −2.01930 −0.421054 −0.210527 0.977588i \(-0.567518\pi\)
−0.210527 + 0.977588i \(0.567518\pi\)
\(24\) −6.92949 −1.41448
\(25\) 1.00000 0.200000
\(26\) 0.790561 0.155042
\(27\) 1.12468 0.216445
\(28\) 0.195065 0.0368638
\(29\) 9.62218 1.78679 0.893397 0.449269i \(-0.148315\pi\)
0.893397 + 0.449269i \(0.148315\pi\)
\(30\) −3.15685 −0.576359
\(31\) −1.07051 −0.192269 −0.0961347 0.995368i \(-0.530648\pi\)
−0.0961347 + 0.995368i \(0.530648\pi\)
\(32\) −1.09938 −0.194345
\(33\) −2.77558 −0.483167
\(34\) −3.11078 −0.533494
\(35\) 1.00000 0.169031
\(36\) −0.491829 −0.0819715
\(37\) 2.42896 0.399319 0.199659 0.979865i \(-0.436016\pi\)
0.199659 + 0.979865i \(0.436016\pi\)
\(38\) 10.8978 1.76785
\(39\) 1.38270 0.221409
\(40\) −2.94902 −0.466281
\(41\) 5.19778 0.811756 0.405878 0.913927i \(-0.366966\pi\)
0.405878 + 0.913927i \(0.366966\pi\)
\(42\) −3.15685 −0.487113
\(43\) −7.17480 −1.09415 −0.547073 0.837085i \(-0.684258\pi\)
−0.547073 + 0.837085i \(0.684258\pi\)
\(44\) −0.230414 −0.0347363
\(45\) −2.52136 −0.375863
\(46\) 2.71289 0.399994
\(47\) 2.65348 0.387050 0.193525 0.981095i \(-0.438008\pi\)
0.193525 + 0.981095i \(0.438008\pi\)
\(48\) 8.39291 1.21141
\(49\) 1.00000 0.142857
\(50\) −1.34348 −0.189997
\(51\) −5.44078 −0.761861
\(52\) 0.114785 0.0159178
\(53\) 3.73499 0.513040 0.256520 0.966539i \(-0.417424\pi\)
0.256520 + 0.966539i \(0.417424\pi\)
\(54\) −1.51099 −0.205619
\(55\) −1.18122 −0.159276
\(56\) −2.94902 −0.394080
\(57\) 19.0603 2.52460
\(58\) −12.9272 −1.69742
\(59\) 7.26498 0.945820 0.472910 0.881111i \(-0.343204\pi\)
0.472910 + 0.881111i \(0.343204\pi\)
\(60\) −0.458355 −0.0591734
\(61\) −8.28356 −1.06060 −0.530300 0.847810i \(-0.677921\pi\)
−0.530300 + 0.847810i \(0.677921\pi\)
\(62\) 1.43821 0.182653
\(63\) −2.52136 −0.317662
\(64\) 8.62064 1.07758
\(65\) 0.588443 0.0729874
\(66\) 3.72893 0.459000
\(67\) 2.82605 0.345257 0.172629 0.984987i \(-0.444774\pi\)
0.172629 + 0.984987i \(0.444774\pi\)
\(68\) −0.451665 −0.0547725
\(69\) 4.74487 0.571216
\(70\) −1.34348 −0.160576
\(71\) −12.9454 −1.53634 −0.768168 0.640249i \(-0.778831\pi\)
−0.768168 + 0.640249i \(0.778831\pi\)
\(72\) 7.43556 0.876289
\(73\) 0.537958 0.0629632 0.0314816 0.999504i \(-0.489977\pi\)
0.0314816 + 0.999504i \(0.489977\pi\)
\(74\) −3.26326 −0.379346
\(75\) −2.34976 −0.271327
\(76\) 1.58229 0.181501
\(77\) −1.18122 −0.134612
\(78\) −1.85763 −0.210335
\(79\) −6.23859 −0.701897 −0.350948 0.936395i \(-0.614141\pi\)
−0.350948 + 0.936395i \(0.614141\pi\)
\(80\) 3.57182 0.399342
\(81\) −10.2068 −1.13409
\(82\) −6.98310 −0.771155
\(83\) 10.6286 1.16665 0.583323 0.812240i \(-0.301752\pi\)
0.583323 + 0.812240i \(0.301752\pi\)
\(84\) −0.458355 −0.0500106
\(85\) −2.31546 −0.251147
\(86\) 9.63919 1.03942
\(87\) −22.6098 −2.42402
\(88\) 3.48344 0.371336
\(89\) 10.4769 1.11054 0.555272 0.831669i \(-0.312614\pi\)
0.555272 + 0.831669i \(0.312614\pi\)
\(90\) 3.38740 0.357063
\(91\) 0.588443 0.0616856
\(92\) 0.393895 0.0410664
\(93\) 2.51544 0.260839
\(94\) −3.56490 −0.367691
\(95\) 8.11161 0.832233
\(96\) 2.58328 0.263655
\(97\) 11.2081 1.13801 0.569006 0.822333i \(-0.307328\pi\)
0.569006 + 0.822333i \(0.307328\pi\)
\(98\) −1.34348 −0.135712
\(99\) 2.97828 0.299329
\(100\) −0.195065 −0.0195065
\(101\) 6.15885 0.612829 0.306414 0.951898i \(-0.400871\pi\)
0.306414 + 0.951898i \(0.400871\pi\)
\(102\) 7.30957 0.723755
\(103\) 9.84805 0.970357 0.485178 0.874415i \(-0.338755\pi\)
0.485178 + 0.874415i \(0.338755\pi\)
\(104\) −1.73533 −0.170163
\(105\) −2.34976 −0.229313
\(106\) −5.01788 −0.487379
\(107\) −3.80353 −0.367701 −0.183850 0.982954i \(-0.558856\pi\)
−0.183850 + 0.982954i \(0.558856\pi\)
\(108\) −0.219386 −0.0211104
\(109\) 4.95785 0.474875 0.237438 0.971403i \(-0.423692\pi\)
0.237438 + 0.971403i \(0.423692\pi\)
\(110\) 1.58694 0.151309
\(111\) −5.70747 −0.541729
\(112\) 3.57182 0.337505
\(113\) −2.87330 −0.270297 −0.135149 0.990825i \(-0.543151\pi\)
−0.135149 + 0.990825i \(0.543151\pi\)
\(114\) −25.6071 −2.39833
\(115\) 2.01930 0.188301
\(116\) −1.87695 −0.174270
\(117\) −1.48368 −0.137166
\(118\) −9.76035 −0.898513
\(119\) −2.31546 −0.212258
\(120\) 6.92949 0.632573
\(121\) −9.60472 −0.873156
\(122\) 11.1288 1.00755
\(123\) −12.2135 −1.10126
\(124\) 0.208819 0.0187525
\(125\) −1.00000 −0.0894427
\(126\) 3.38740 0.301773
\(127\) −19.7529 −1.75279 −0.876395 0.481593i \(-0.840058\pi\)
−0.876395 + 0.481593i \(0.840058\pi\)
\(128\) −9.38288 −0.829337
\(129\) 16.8590 1.48436
\(130\) −0.790561 −0.0693368
\(131\) −1.68532 −0.147247 −0.0736234 0.997286i \(-0.523456\pi\)
−0.0736234 + 0.997286i \(0.523456\pi\)
\(132\) 0.541418 0.0471244
\(133\) 8.11161 0.703365
\(134\) −3.79674 −0.327988
\(135\) −1.12468 −0.0967971
\(136\) 6.82835 0.585527
\(137\) −2.67251 −0.228328 −0.114164 0.993462i \(-0.536419\pi\)
−0.114164 + 0.993462i \(0.536419\pi\)
\(138\) −6.37464 −0.542645
\(139\) −10.7562 −0.912325 −0.456162 0.889897i \(-0.650776\pi\)
−0.456162 + 0.889897i \(0.650776\pi\)
\(140\) −0.195065 −0.0164860
\(141\) −6.23504 −0.525085
\(142\) 17.3919 1.45949
\(143\) −0.695081 −0.0581256
\(144\) −9.00586 −0.750488
\(145\) −9.62218 −0.799078
\(146\) −0.722735 −0.0598140
\(147\) −2.34976 −0.193805
\(148\) −0.473805 −0.0389465
\(149\) 3.31814 0.271832 0.135916 0.990720i \(-0.456602\pi\)
0.135916 + 0.990720i \(0.456602\pi\)
\(150\) 3.15685 0.257756
\(151\) −17.1574 −1.39625 −0.698126 0.715975i \(-0.745982\pi\)
−0.698126 + 0.715975i \(0.745982\pi\)
\(152\) −23.9213 −1.94027
\(153\) 5.83812 0.471984
\(154\) 1.58694 0.127880
\(155\) 1.07051 0.0859855
\(156\) −0.269716 −0.0215946
\(157\) 22.5011 1.79578 0.897891 0.440217i \(-0.145099\pi\)
0.897891 + 0.440217i \(0.145099\pi\)
\(158\) 8.38142 0.666790
\(159\) −8.77632 −0.696007
\(160\) 1.09938 0.0869137
\(161\) 2.01930 0.159143
\(162\) 13.7126 1.07737
\(163\) −18.8319 −1.47503 −0.737513 0.675333i \(-0.764000\pi\)
−0.737513 + 0.675333i \(0.764000\pi\)
\(164\) −1.01390 −0.0791725
\(165\) 2.77558 0.216079
\(166\) −14.2794 −1.10829
\(167\) 11.4516 0.886155 0.443077 0.896483i \(-0.353887\pi\)
0.443077 + 0.896483i \(0.353887\pi\)
\(168\) 6.92949 0.534622
\(169\) −12.6537 −0.973364
\(170\) 3.11078 0.238586
\(171\) −20.4523 −1.56403
\(172\) 1.39955 0.106715
\(173\) −4.05375 −0.308201 −0.154100 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(174\) 30.3758 2.30278
\(175\) −1.00000 −0.0755929
\(176\) −4.21910 −0.318027
\(177\) −17.0709 −1.28313
\(178\) −14.0754 −1.05500
\(179\) 16.2202 1.21235 0.606177 0.795330i \(-0.292702\pi\)
0.606177 + 0.795330i \(0.292702\pi\)
\(180\) 0.491829 0.0366588
\(181\) −16.2703 −1.20936 −0.604682 0.796467i \(-0.706700\pi\)
−0.604682 + 0.796467i \(0.706700\pi\)
\(182\) −0.790561 −0.0586003
\(183\) 19.4644 1.43885
\(184\) −5.95497 −0.439006
\(185\) −2.42896 −0.178581
\(186\) −3.37944 −0.247793
\(187\) 2.73507 0.200008
\(188\) −0.517601 −0.0377499
\(189\) −1.12468 −0.0818085
\(190\) −10.8978 −0.790607
\(191\) −24.7749 −1.79265 −0.896324 0.443399i \(-0.853773\pi\)
−0.896324 + 0.443399i \(0.853773\pi\)
\(192\) −20.2564 −1.46188
\(193\) −13.6464 −0.982290 −0.491145 0.871078i \(-0.663421\pi\)
−0.491145 + 0.871078i \(0.663421\pi\)
\(194\) −15.0579 −1.08109
\(195\) −1.38270 −0.0990171
\(196\) −0.195065 −0.0139332
\(197\) −5.53232 −0.394162 −0.197081 0.980387i \(-0.563146\pi\)
−0.197081 + 0.980387i \(0.563146\pi\)
\(198\) −4.00126 −0.284357
\(199\) −12.9874 −0.920649 −0.460325 0.887751i \(-0.652267\pi\)
−0.460325 + 0.887751i \(0.652267\pi\)
\(200\) 2.94902 0.208527
\(201\) −6.64054 −0.468388
\(202\) −8.27429 −0.582177
\(203\) −9.62218 −0.675344
\(204\) 1.06130 0.0743062
\(205\) −5.19778 −0.363028
\(206\) −13.2306 −0.921823
\(207\) −5.09140 −0.353877
\(208\) 2.10181 0.145735
\(209\) −9.58159 −0.662772
\(210\) 3.15685 0.217843
\(211\) −22.8288 −1.57160 −0.785799 0.618482i \(-0.787748\pi\)
−0.785799 + 0.618482i \(0.787748\pi\)
\(212\) −0.728564 −0.0500380
\(213\) 30.4185 2.08424
\(214\) 5.10996 0.349309
\(215\) 7.17480 0.489317
\(216\) 3.31671 0.225674
\(217\) 1.07051 0.0726710
\(218\) −6.66076 −0.451124
\(219\) −1.26407 −0.0854180
\(220\) 0.230414 0.0155345
\(221\) −1.36252 −0.0916529
\(222\) 7.66787 0.514634
\(223\) 5.16394 0.345803 0.172902 0.984939i \(-0.444686\pi\)
0.172902 + 0.984939i \(0.444686\pi\)
\(224\) 1.09938 0.0734555
\(225\) 2.52136 0.168091
\(226\) 3.86022 0.256778
\(227\) −5.88901 −0.390868 −0.195434 0.980717i \(-0.562611\pi\)
−0.195434 + 0.980717i \(0.562611\pi\)
\(228\) −3.71800 −0.246230
\(229\) 1.00000 0.0660819
\(230\) −2.71289 −0.178883
\(231\) 2.77558 0.182620
\(232\) 28.3760 1.86298
\(233\) 1.35253 0.0886071 0.0443036 0.999018i \(-0.485893\pi\)
0.0443036 + 0.999018i \(0.485893\pi\)
\(234\) 1.99329 0.130305
\(235\) −2.65348 −0.173094
\(236\) −1.41714 −0.0922481
\(237\) 14.6592 0.952216
\(238\) 3.11078 0.201642
\(239\) 2.06443 0.133537 0.0667684 0.997769i \(-0.478731\pi\)
0.0667684 + 0.997769i \(0.478731\pi\)
\(240\) −8.39291 −0.541760
\(241\) −16.7076 −1.07623 −0.538115 0.842871i \(-0.680863\pi\)
−0.538115 + 0.842871i \(0.680863\pi\)
\(242\) 12.9037 0.829484
\(243\) 20.6095 1.32210
\(244\) 1.61583 0.103443
\(245\) −1.00000 −0.0638877
\(246\) 16.4086 1.04617
\(247\) 4.77322 0.303713
\(248\) −3.15696 −0.200467
\(249\) −24.9747 −1.58271
\(250\) 1.34348 0.0849691
\(251\) 12.5260 0.790631 0.395316 0.918545i \(-0.370635\pi\)
0.395316 + 0.918545i \(0.370635\pi\)
\(252\) 0.491829 0.0309823
\(253\) −2.38524 −0.149959
\(254\) 26.5377 1.66512
\(255\) 5.44078 0.340715
\(256\) −4.63557 −0.289723
\(257\) −10.0770 −0.628583 −0.314292 0.949326i \(-0.601767\pi\)
−0.314292 + 0.949326i \(0.601767\pi\)
\(258\) −22.6498 −1.41011
\(259\) −2.42896 −0.150928
\(260\) −0.114785 −0.00711864
\(261\) 24.2610 1.50172
\(262\) 2.26419 0.139882
\(263\) 25.1696 1.55202 0.776011 0.630720i \(-0.217240\pi\)
0.776011 + 0.630720i \(0.217240\pi\)
\(264\) −8.18525 −0.503767
\(265\) −3.73499 −0.229438
\(266\) −10.8978 −0.668185
\(267\) −24.6181 −1.50660
\(268\) −0.551263 −0.0336738
\(269\) −13.3627 −0.814735 −0.407368 0.913264i \(-0.633553\pi\)
−0.407368 + 0.913264i \(0.633553\pi\)
\(270\) 1.51099 0.0919556
\(271\) 13.8615 0.842026 0.421013 0.907055i \(-0.361675\pi\)
0.421013 + 0.907055i \(0.361675\pi\)
\(272\) −8.27042 −0.501468
\(273\) −1.38270 −0.0836847
\(274\) 3.59046 0.216907
\(275\) 1.18122 0.0712302
\(276\) −0.925558 −0.0557120
\(277\) −4.75479 −0.285688 −0.142844 0.989745i \(-0.545625\pi\)
−0.142844 + 0.989745i \(0.545625\pi\)
\(278\) 14.4507 0.866693
\(279\) −2.69915 −0.161594
\(280\) 2.94902 0.176238
\(281\) 2.02237 0.120644 0.0603222 0.998179i \(-0.480787\pi\)
0.0603222 + 0.998179i \(0.480787\pi\)
\(282\) 8.37664 0.498822
\(283\) 18.0658 1.07390 0.536949 0.843615i \(-0.319577\pi\)
0.536949 + 0.843615i \(0.319577\pi\)
\(284\) 2.52519 0.149842
\(285\) −19.0603 −1.12904
\(286\) 0.933826 0.0552183
\(287\) −5.19778 −0.306815
\(288\) −2.77194 −0.163338
\(289\) −11.6386 −0.684625
\(290\) 12.9272 0.759111
\(291\) −26.3364 −1.54387
\(292\) −0.104937 −0.00614096
\(293\) −19.4223 −1.13466 −0.567331 0.823490i \(-0.692024\pi\)
−0.567331 + 0.823490i \(0.692024\pi\)
\(294\) 3.15685 0.184111
\(295\) −7.26498 −0.422984
\(296\) 7.16306 0.416345
\(297\) 1.32850 0.0770871
\(298\) −4.45785 −0.258236
\(299\) 1.18825 0.0687180
\(300\) 0.458355 0.0264631
\(301\) 7.17480 0.413549
\(302\) 23.0506 1.32642
\(303\) −14.4718 −0.831384
\(304\) 28.9732 1.66173
\(305\) 8.28356 0.474315
\(306\) −7.84340 −0.448377
\(307\) −9.47889 −0.540989 −0.270494 0.962722i \(-0.587187\pi\)
−0.270494 + 0.962722i \(0.587187\pi\)
\(308\) 0.230414 0.0131291
\(309\) −23.1405 −1.31642
\(310\) −1.43821 −0.0816848
\(311\) −14.6059 −0.828222 −0.414111 0.910226i \(-0.635908\pi\)
−0.414111 + 0.910226i \(0.635908\pi\)
\(312\) 4.07761 0.230849
\(313\) 30.4330 1.72017 0.860086 0.510149i \(-0.170410\pi\)
0.860086 + 0.510149i \(0.170410\pi\)
\(314\) −30.2297 −1.70596
\(315\) 2.52136 0.142063
\(316\) 1.21693 0.0684577
\(317\) −20.0525 −1.12626 −0.563132 0.826367i \(-0.690404\pi\)
−0.563132 + 0.826367i \(0.690404\pi\)
\(318\) 11.7908 0.661195
\(319\) 11.3659 0.636369
\(320\) −8.62064 −0.481908
\(321\) 8.93737 0.498835
\(322\) −2.71289 −0.151184
\(323\) −18.7821 −1.04507
\(324\) 1.99099 0.110611
\(325\) −0.588443 −0.0326410
\(326\) 25.3002 1.40125
\(327\) −11.6497 −0.644232
\(328\) 15.3284 0.846367
\(329\) −2.65348 −0.146291
\(330\) −3.72893 −0.205271
\(331\) 3.04507 0.167372 0.0836860 0.996492i \(-0.473331\pi\)
0.0836860 + 0.996492i \(0.473331\pi\)
\(332\) −2.07327 −0.113786
\(333\) 6.12429 0.335609
\(334\) −15.3850 −0.841832
\(335\) −2.82605 −0.154404
\(336\) −8.39291 −0.457871
\(337\) 27.0603 1.47407 0.737035 0.675854i \(-0.236225\pi\)
0.737035 + 0.675854i \(0.236225\pi\)
\(338\) 17.0000 0.924679
\(339\) 6.75156 0.366694
\(340\) 0.451665 0.0244950
\(341\) −1.26451 −0.0684770
\(342\) 27.4772 1.48580
\(343\) −1.00000 −0.0539949
\(344\) −21.1587 −1.14080
\(345\) −4.74487 −0.255455
\(346\) 5.44613 0.292786
\(347\) −3.17128 −0.170243 −0.0851215 0.996371i \(-0.527128\pi\)
−0.0851215 + 0.996371i \(0.527128\pi\)
\(348\) 4.41037 0.236421
\(349\) −3.71195 −0.198696 −0.0993481 0.995053i \(-0.531676\pi\)
−0.0993481 + 0.995053i \(0.531676\pi\)
\(350\) 1.34348 0.0718120
\(351\) −0.661811 −0.0353249
\(352\) −1.29861 −0.0692162
\(353\) 29.2773 1.55827 0.779136 0.626856i \(-0.215658\pi\)
0.779136 + 0.626856i \(0.215658\pi\)
\(354\) 22.9345 1.21895
\(355\) 12.9454 0.687070
\(356\) −2.04367 −0.108314
\(357\) 5.44078 0.287957
\(358\) −21.7915 −1.15172
\(359\) −13.6382 −0.719799 −0.359900 0.932991i \(-0.617189\pi\)
−0.359900 + 0.932991i \(0.617189\pi\)
\(360\) −7.43556 −0.391888
\(361\) 46.7981 2.46306
\(362\) 21.8589 1.14888
\(363\) 22.5688 1.18455
\(364\) −0.114785 −0.00601634
\(365\) −0.537958 −0.0281580
\(366\) −26.1499 −1.36688
\(367\) 31.5700 1.64794 0.823972 0.566631i \(-0.191754\pi\)
0.823972 + 0.566631i \(0.191754\pi\)
\(368\) 7.21259 0.375982
\(369\) 13.1055 0.682244
\(370\) 3.26326 0.169649
\(371\) −3.73499 −0.193911
\(372\) −0.490674 −0.0254403
\(373\) −6.90853 −0.357710 −0.178855 0.983875i \(-0.557239\pi\)
−0.178855 + 0.983875i \(0.557239\pi\)
\(374\) −3.67451 −0.190004
\(375\) 2.34976 0.121341
\(376\) 7.82518 0.403553
\(377\) −5.66210 −0.291613
\(378\) 1.51099 0.0777167
\(379\) 21.7233 1.11585 0.557925 0.829892i \(-0.311598\pi\)
0.557925 + 0.829892i \(0.311598\pi\)
\(380\) −1.58229 −0.0811697
\(381\) 46.4146 2.37789
\(382\) 33.2846 1.70299
\(383\) 16.8599 0.861501 0.430750 0.902471i \(-0.358249\pi\)
0.430750 + 0.902471i \(0.358249\pi\)
\(384\) 22.0475 1.12511
\(385\) 1.18122 0.0602005
\(386\) 18.3337 0.933158
\(387\) −18.0903 −0.919580
\(388\) −2.18631 −0.110993
\(389\) 3.02442 0.153344 0.0766720 0.997056i \(-0.475571\pi\)
0.0766720 + 0.997056i \(0.475571\pi\)
\(390\) 1.85763 0.0940646
\(391\) −4.67562 −0.236456
\(392\) 2.94902 0.148948
\(393\) 3.96008 0.199760
\(394\) 7.43256 0.374447
\(395\) 6.23859 0.313898
\(396\) −0.580958 −0.0291943
\(397\) −31.2074 −1.56625 −0.783127 0.621862i \(-0.786376\pi\)
−0.783127 + 0.621862i \(0.786376\pi\)
\(398\) 17.4482 0.874601
\(399\) −19.0603 −0.954209
\(400\) −3.57182 −0.178591
\(401\) −4.46073 −0.222758 −0.111379 0.993778i \(-0.535527\pi\)
−0.111379 + 0.993778i \(0.535527\pi\)
\(402\) 8.92142 0.444960
\(403\) 0.629935 0.0313793
\(404\) −1.20138 −0.0597707
\(405\) 10.2068 0.507181
\(406\) 12.9272 0.641566
\(407\) 2.86914 0.142218
\(408\) −16.0450 −0.794345
\(409\) −18.5904 −0.919235 −0.459618 0.888117i \(-0.652014\pi\)
−0.459618 + 0.888117i \(0.652014\pi\)
\(410\) 6.98310 0.344871
\(411\) 6.27974 0.309757
\(412\) −1.92101 −0.0946412
\(413\) −7.26498 −0.357486
\(414\) 6.84018 0.336177
\(415\) −10.6286 −0.521740
\(416\) 0.646923 0.0317180
\(417\) 25.2744 1.23769
\(418\) 12.8727 0.629622
\(419\) −3.55784 −0.173812 −0.0869060 0.996217i \(-0.527698\pi\)
−0.0869060 + 0.996217i \(0.527698\pi\)
\(420\) 0.458355 0.0223654
\(421\) 1.69987 0.0828466 0.0414233 0.999142i \(-0.486811\pi\)
0.0414233 + 0.999142i \(0.486811\pi\)
\(422\) 30.6700 1.49299
\(423\) 6.69039 0.325298
\(424\) 11.0146 0.534914
\(425\) 2.31546 0.112316
\(426\) −40.8667 −1.98000
\(427\) 8.28356 0.400869
\(428\) 0.741934 0.0358627
\(429\) 1.63327 0.0788551
\(430\) −9.63919 −0.464843
\(431\) −12.6235 −0.608053 −0.304027 0.952664i \(-0.598331\pi\)
−0.304027 + 0.952664i \(0.598331\pi\)
\(432\) −4.01716 −0.193276
\(433\) 25.7484 1.23739 0.618696 0.785631i \(-0.287661\pi\)
0.618696 + 0.785631i \(0.287661\pi\)
\(434\) −1.43821 −0.0690362
\(435\) 22.6098 1.08406
\(436\) −0.967101 −0.0463157
\(437\) 16.3798 0.783552
\(438\) 1.69825 0.0811457
\(439\) 26.7028 1.27445 0.637227 0.770676i \(-0.280081\pi\)
0.637227 + 0.770676i \(0.280081\pi\)
\(440\) −3.48344 −0.166067
\(441\) 2.52136 0.120065
\(442\) 1.83051 0.0870687
\(443\) −8.34285 −0.396381 −0.198190 0.980164i \(-0.563506\pi\)
−0.198190 + 0.980164i \(0.563506\pi\)
\(444\) 1.11333 0.0528362
\(445\) −10.4769 −0.496651
\(446\) −6.93764 −0.328507
\(447\) −7.79682 −0.368777
\(448\) −8.62064 −0.407287
\(449\) 29.4222 1.38852 0.694259 0.719725i \(-0.255732\pi\)
0.694259 + 0.719725i \(0.255732\pi\)
\(450\) −3.38740 −0.159683
\(451\) 6.13971 0.289108
\(452\) 0.560479 0.0263627
\(453\) 40.3158 1.89420
\(454\) 7.91177 0.371318
\(455\) −0.588443 −0.0275866
\(456\) 56.2093 2.63224
\(457\) 28.1428 1.31646 0.658232 0.752816i \(-0.271305\pi\)
0.658232 + 0.752816i \(0.271305\pi\)
\(458\) −1.34348 −0.0627766
\(459\) 2.60416 0.121552
\(460\) −0.393895 −0.0183655
\(461\) −32.8624 −1.53055 −0.765276 0.643702i \(-0.777398\pi\)
−0.765276 + 0.643702i \(0.777398\pi\)
\(462\) −3.72893 −0.173486
\(463\) −9.16872 −0.426107 −0.213053 0.977041i \(-0.568341\pi\)
−0.213053 + 0.977041i \(0.568341\pi\)
\(464\) −34.3687 −1.59553
\(465\) −2.51544 −0.116651
\(466\) −1.81709 −0.0841753
\(467\) 20.3466 0.941530 0.470765 0.882259i \(-0.343978\pi\)
0.470765 + 0.882259i \(0.343978\pi\)
\(468\) 0.289413 0.0133781
\(469\) −2.82605 −0.130495
\(470\) 3.56490 0.164436
\(471\) −52.8721 −2.43622
\(472\) 21.4246 0.986147
\(473\) −8.47502 −0.389682
\(474\) −19.6943 −0.904589
\(475\) −8.11161 −0.372186
\(476\) 0.451665 0.0207021
\(477\) 9.41726 0.431187
\(478\) −2.77351 −0.126858
\(479\) −32.6342 −1.49109 −0.745547 0.666453i \(-0.767812\pi\)
−0.745547 + 0.666453i \(0.767812\pi\)
\(480\) −2.58328 −0.117910
\(481\) −1.42931 −0.0651707
\(482\) 22.4463 1.02240
\(483\) −4.74487 −0.215899
\(484\) 1.87354 0.0851610
\(485\) −11.2081 −0.508935
\(486\) −27.6884 −1.25597
\(487\) 21.5038 0.974428 0.487214 0.873283i \(-0.338013\pi\)
0.487214 + 0.873283i \(0.338013\pi\)
\(488\) −24.4284 −1.10582
\(489\) 44.2503 2.00107
\(490\) 1.34348 0.0606922
\(491\) 40.5459 1.82981 0.914906 0.403667i \(-0.132265\pi\)
0.914906 + 0.403667i \(0.132265\pi\)
\(492\) 2.38243 0.107408
\(493\) 22.2798 1.00343
\(494\) −6.41272 −0.288522
\(495\) −2.97828 −0.133864
\(496\) 3.82367 0.171688
\(497\) 12.9454 0.580680
\(498\) 33.5530 1.50355
\(499\) 34.7688 1.55646 0.778232 0.627976i \(-0.216117\pi\)
0.778232 + 0.627976i \(0.216117\pi\)
\(500\) 0.195065 0.00872356
\(501\) −26.9086 −1.20219
\(502\) −16.8284 −0.751086
\(503\) 23.0853 1.02932 0.514661 0.857394i \(-0.327918\pi\)
0.514661 + 0.857394i \(0.327918\pi\)
\(504\) −7.43556 −0.331206
\(505\) −6.15885 −0.274065
\(506\) 3.20452 0.142458
\(507\) 29.7332 1.32050
\(508\) 3.85310 0.170954
\(509\) 21.8248 0.967369 0.483684 0.875242i \(-0.339298\pi\)
0.483684 + 0.875242i \(0.339298\pi\)
\(510\) −7.30957 −0.323673
\(511\) −0.537958 −0.0237979
\(512\) 24.9936 1.10457
\(513\) −9.12297 −0.402789
\(514\) 13.5382 0.597143
\(515\) −9.84805 −0.433957
\(516\) −3.28861 −0.144773
\(517\) 3.13434 0.137848
\(518\) 3.26326 0.143379
\(519\) 9.52533 0.418116
\(520\) 1.73533 0.0760994
\(521\) 6.09504 0.267029 0.133514 0.991047i \(-0.457374\pi\)
0.133514 + 0.991047i \(0.457374\pi\)
\(522\) −32.5941 −1.42661
\(523\) −35.0802 −1.53395 −0.766976 0.641676i \(-0.778239\pi\)
−0.766976 + 0.641676i \(0.778239\pi\)
\(524\) 0.328746 0.0143613
\(525\) 2.34976 0.102552
\(526\) −33.8148 −1.47439
\(527\) −2.47873 −0.107975
\(528\) 9.91387 0.431446
\(529\) −18.9224 −0.822714
\(530\) 5.01788 0.217963
\(531\) 18.3177 0.794918
\(532\) −1.58229 −0.0686009
\(533\) −3.05860 −0.132482
\(534\) 33.0739 1.43125
\(535\) 3.80353 0.164441
\(536\) 8.33409 0.359978
\(537\) −38.1135 −1.64472
\(538\) 17.9524 0.773985
\(539\) 1.18122 0.0508787
\(540\) 0.219386 0.00944086
\(541\) 6.81669 0.293072 0.146536 0.989205i \(-0.453188\pi\)
0.146536 + 0.989205i \(0.453188\pi\)
\(542\) −18.6226 −0.799911
\(543\) 38.2314 1.64067
\(544\) −2.54558 −0.109141
\(545\) −4.95785 −0.212371
\(546\) 1.85763 0.0794991
\(547\) −39.6774 −1.69648 −0.848242 0.529609i \(-0.822339\pi\)
−0.848242 + 0.529609i \(0.822339\pi\)
\(548\) 0.521312 0.0222693
\(549\) −20.8859 −0.891387
\(550\) −1.58694 −0.0676675
\(551\) −78.0513 −3.32510
\(552\) 13.9927 0.595571
\(553\) 6.23859 0.265292
\(554\) 6.38796 0.271398
\(555\) 5.70747 0.242269
\(556\) 2.09815 0.0889812
\(557\) 1.03626 0.0439079 0.0219540 0.999759i \(-0.493011\pi\)
0.0219540 + 0.999759i \(0.493011\pi\)
\(558\) 3.62625 0.153511
\(559\) 4.22196 0.178570
\(560\) −3.57182 −0.150937
\(561\) −6.42676 −0.271338
\(562\) −2.71701 −0.114610
\(563\) −33.0047 −1.39098 −0.695491 0.718535i \(-0.744813\pi\)
−0.695491 + 0.718535i \(0.744813\pi\)
\(564\) 1.21624 0.0512128
\(565\) 2.87330 0.120881
\(566\) −24.2710 −1.02018
\(567\) 10.2068 0.428646
\(568\) −38.1763 −1.60184
\(569\) −39.3399 −1.64921 −0.824607 0.565707i \(-0.808604\pi\)
−0.824607 + 0.565707i \(0.808604\pi\)
\(570\) 25.6071 1.07256
\(571\) −39.7548 −1.66369 −0.831843 0.555011i \(-0.812714\pi\)
−0.831843 + 0.555011i \(0.812714\pi\)
\(572\) 0.135586 0.00566913
\(573\) 58.2150 2.43197
\(574\) 6.98310 0.291469
\(575\) −2.01930 −0.0842108
\(576\) 21.7358 0.905656
\(577\) 45.2193 1.88251 0.941253 0.337703i \(-0.109650\pi\)
0.941253 + 0.337703i \(0.109650\pi\)
\(578\) 15.6363 0.650382
\(579\) 32.0657 1.33261
\(580\) 1.87695 0.0779360
\(581\) −10.6286 −0.440951
\(582\) 35.3824 1.46665
\(583\) 4.41184 0.182720
\(584\) 1.58645 0.0656478
\(585\) 1.48368 0.0613426
\(586\) 26.0934 1.07791
\(587\) −17.2896 −0.713617 −0.356808 0.934178i \(-0.616135\pi\)
−0.356808 + 0.934178i \(0.616135\pi\)
\(588\) 0.458355 0.0189022
\(589\) 8.68356 0.357800
\(590\) 9.76035 0.401827
\(591\) 12.9996 0.534733
\(592\) −8.67581 −0.356574
\(593\) 20.1371 0.826933 0.413466 0.910519i \(-0.364318\pi\)
0.413466 + 0.910519i \(0.364318\pi\)
\(594\) −1.78481 −0.0732315
\(595\) 2.31546 0.0949247
\(596\) −0.647252 −0.0265125
\(597\) 30.5172 1.24898
\(598\) −1.59638 −0.0652809
\(599\) 25.3359 1.03520 0.517598 0.855624i \(-0.326826\pi\)
0.517598 + 0.855624i \(0.326826\pi\)
\(600\) −6.92949 −0.282895
\(601\) −21.9537 −0.895509 −0.447755 0.894156i \(-0.647776\pi\)
−0.447755 + 0.894156i \(0.647776\pi\)
\(602\) −9.63919 −0.392864
\(603\) 7.12550 0.290173
\(604\) 3.34681 0.136180
\(605\) 9.60472 0.390487
\(606\) 19.4426 0.789801
\(607\) 2.43986 0.0990310 0.0495155 0.998773i \(-0.484232\pi\)
0.0495155 + 0.998773i \(0.484232\pi\)
\(608\) 8.91775 0.361662
\(609\) 22.6098 0.916195
\(610\) −11.1288 −0.450591
\(611\) −1.56142 −0.0631684
\(612\) −1.13881 −0.0460338
\(613\) 13.1917 0.532809 0.266405 0.963861i \(-0.414164\pi\)
0.266405 + 0.963861i \(0.414164\pi\)
\(614\) 12.7347 0.513930
\(615\) 12.2135 0.492496
\(616\) −3.48344 −0.140352
\(617\) −19.3368 −0.778470 −0.389235 0.921138i \(-0.627261\pi\)
−0.389235 + 0.921138i \(0.627261\pi\)
\(618\) 31.0888 1.25058
\(619\) −30.6643 −1.23250 −0.616252 0.787549i \(-0.711350\pi\)
−0.616252 + 0.787549i \(0.711350\pi\)
\(620\) −0.208819 −0.00838637
\(621\) −2.27107 −0.0911350
\(622\) 19.6227 0.786797
\(623\) −10.4769 −0.419746
\(624\) −4.93875 −0.197708
\(625\) 1.00000 0.0400000
\(626\) −40.8860 −1.63413
\(627\) 22.5144 0.899139
\(628\) −4.38917 −0.175147
\(629\) 5.62417 0.224250
\(630\) −3.38740 −0.134957
\(631\) 19.5300 0.777478 0.388739 0.921348i \(-0.372911\pi\)
0.388739 + 0.921348i \(0.372911\pi\)
\(632\) −18.3978 −0.731823
\(633\) 53.6421 2.13208
\(634\) 26.9402 1.06993
\(635\) 19.7529 0.783871
\(636\) 1.71195 0.0678832
\(637\) −0.588443 −0.0233150
\(638\) −15.2699 −0.604539
\(639\) −32.6400 −1.29122
\(640\) 9.38288 0.370891
\(641\) 46.7753 1.84751 0.923757 0.382978i \(-0.125102\pi\)
0.923757 + 0.382978i \(0.125102\pi\)
\(642\) −12.0072 −0.473885
\(643\) 11.3562 0.447843 0.223922 0.974607i \(-0.428114\pi\)
0.223922 + 0.974607i \(0.428114\pi\)
\(644\) −0.393895 −0.0155216
\(645\) −16.8590 −0.663824
\(646\) 25.2334 0.992794
\(647\) 24.9919 0.982533 0.491267 0.871009i \(-0.336534\pi\)
0.491267 + 0.871009i \(0.336534\pi\)
\(648\) −30.1001 −1.18245
\(649\) 8.58154 0.336855
\(650\) 0.790561 0.0310083
\(651\) −2.51544 −0.0985879
\(652\) 3.67343 0.143863
\(653\) 4.83804 0.189327 0.0946636 0.995509i \(-0.469822\pi\)
0.0946636 + 0.995509i \(0.469822\pi\)
\(654\) 15.6512 0.612009
\(655\) 1.68532 0.0658507
\(656\) −18.5655 −0.724862
\(657\) 1.35639 0.0529177
\(658\) 3.56490 0.138974
\(659\) 4.31741 0.168182 0.0840912 0.996458i \(-0.473201\pi\)
0.0840912 + 0.996458i \(0.473201\pi\)
\(660\) −0.541418 −0.0210747
\(661\) −38.7835 −1.50850 −0.754251 0.656587i \(-0.772000\pi\)
−0.754251 + 0.656587i \(0.772000\pi\)
\(662\) −4.09098 −0.159000
\(663\) 3.20159 0.124339
\(664\) 31.3441 1.21639
\(665\) −8.11161 −0.314555
\(666\) −8.22786 −0.318823
\(667\) −19.4301 −0.752336
\(668\) −2.23381 −0.0864288
\(669\) −12.1340 −0.469128
\(670\) 3.79674 0.146681
\(671\) −9.78470 −0.377734
\(672\) −2.58328 −0.0996522
\(673\) 11.4099 0.439820 0.219910 0.975520i \(-0.429424\pi\)
0.219910 + 0.975520i \(0.429424\pi\)
\(674\) −36.3550 −1.40034
\(675\) 1.12468 0.0432890
\(676\) 2.46830 0.0949345
\(677\) −11.4807 −0.441239 −0.220619 0.975360i \(-0.570808\pi\)
−0.220619 + 0.975360i \(0.570808\pi\)
\(678\) −9.07057 −0.348353
\(679\) −11.2081 −0.430128
\(680\) −6.82835 −0.261855
\(681\) 13.8378 0.530264
\(682\) 1.69884 0.0650520
\(683\) 9.22267 0.352896 0.176448 0.984310i \(-0.443539\pi\)
0.176448 + 0.984310i \(0.443539\pi\)
\(684\) 3.98952 0.152543
\(685\) 2.67251 0.102111
\(686\) 1.34348 0.0512943
\(687\) −2.34976 −0.0896489
\(688\) 25.6271 0.977024
\(689\) −2.19783 −0.0837306
\(690\) 6.37464 0.242678
\(691\) 24.7109 0.940049 0.470024 0.882653i \(-0.344245\pi\)
0.470024 + 0.882653i \(0.344245\pi\)
\(692\) 0.790744 0.0300596
\(693\) −2.97828 −0.113136
\(694\) 4.26054 0.161728
\(695\) 10.7562 0.408004
\(696\) −66.6768 −2.52738
\(697\) 12.0353 0.455868
\(698\) 4.98693 0.188758
\(699\) −3.17812 −0.120207
\(700\) 0.195065 0.00737276
\(701\) 47.2226 1.78357 0.891786 0.452457i \(-0.149453\pi\)
0.891786 + 0.452457i \(0.149453\pi\)
\(702\) 0.889129 0.0335580
\(703\) −19.7028 −0.743104
\(704\) 10.1829 0.383781
\(705\) 6.23504 0.234825
\(706\) −39.3334 −1.48033
\(707\) −6.15885 −0.231628
\(708\) 3.32994 0.125147
\(709\) 7.22005 0.271155 0.135577 0.990767i \(-0.456711\pi\)
0.135577 + 0.990767i \(0.456711\pi\)
\(710\) −17.3919 −0.652705
\(711\) −15.7298 −0.589912
\(712\) 30.8965 1.15790
\(713\) 2.16169 0.0809558
\(714\) −7.30957 −0.273554
\(715\) 0.695081 0.0259945
\(716\) −3.16399 −0.118244
\(717\) −4.85091 −0.181160
\(718\) 18.3227 0.683797
\(719\) 43.8422 1.63504 0.817518 0.575902i \(-0.195349\pi\)
0.817518 + 0.575902i \(0.195349\pi\)
\(720\) 9.00586 0.335628
\(721\) −9.84805 −0.366760
\(722\) −62.8723 −2.33987
\(723\) 39.2588 1.46005
\(724\) 3.17377 0.117952
\(725\) 9.62218 0.357359
\(726\) −30.3207 −1.12531
\(727\) 31.0870 1.15295 0.576476 0.817114i \(-0.304428\pi\)
0.576476 + 0.817114i \(0.304428\pi\)
\(728\) 1.73533 0.0643157
\(729\) −17.8069 −0.659515
\(730\) 0.722735 0.0267496
\(731\) −16.6130 −0.614454
\(732\) −3.79681 −0.140334
\(733\) −13.6443 −0.503965 −0.251982 0.967732i \(-0.581082\pi\)
−0.251982 + 0.967732i \(0.581082\pi\)
\(734\) −42.4137 −1.56552
\(735\) 2.34976 0.0866721
\(736\) 2.21998 0.0818297
\(737\) 3.33819 0.122964
\(738\) −17.6069 −0.648120
\(739\) −44.5250 −1.63788 −0.818940 0.573879i \(-0.805438\pi\)
−0.818940 + 0.573879i \(0.805438\pi\)
\(740\) 0.473805 0.0174174
\(741\) −11.2159 −0.412027
\(742\) 5.01788 0.184212
\(743\) 38.0854 1.39722 0.698609 0.715503i \(-0.253803\pi\)
0.698609 + 0.715503i \(0.253803\pi\)
\(744\) 7.41810 0.271961
\(745\) −3.31814 −0.121567
\(746\) 9.28147 0.339819
\(747\) 26.7987 0.980512
\(748\) −0.533516 −0.0195073
\(749\) 3.80353 0.138978
\(750\) −3.15685 −0.115272
\(751\) −42.4382 −1.54859 −0.774297 0.632823i \(-0.781896\pi\)
−0.774297 + 0.632823i \(0.781896\pi\)
\(752\) −9.47776 −0.345618
\(753\) −29.4330 −1.07260
\(754\) 7.60692 0.277028
\(755\) 17.1574 0.624423
\(756\) 0.219386 0.00797898
\(757\) 44.3242 1.61099 0.805496 0.592602i \(-0.201899\pi\)
0.805496 + 0.592602i \(0.201899\pi\)
\(758\) −29.1848 −1.06004
\(759\) 5.60474 0.203439
\(760\) 23.9213 0.867717
\(761\) −17.8626 −0.647518 −0.323759 0.946140i \(-0.604947\pi\)
−0.323759 + 0.946140i \(0.604947\pi\)
\(762\) −62.3571 −2.25896
\(763\) −4.95785 −0.179486
\(764\) 4.83271 0.174841
\(765\) −5.83812 −0.211078
\(766\) −22.6509 −0.818411
\(767\) −4.27503 −0.154362
\(768\) 10.8925 0.393048
\(769\) −1.26385 −0.0455757 −0.0227878 0.999740i \(-0.507254\pi\)
−0.0227878 + 0.999740i \(0.507254\pi\)
\(770\) −1.58694 −0.0571895
\(771\) 23.6784 0.852757
\(772\) 2.66193 0.0958051
\(773\) −33.9385 −1.22068 −0.610341 0.792139i \(-0.708967\pi\)
−0.610341 + 0.792139i \(0.708967\pi\)
\(774\) 24.3039 0.873586
\(775\) −1.07051 −0.0384539
\(776\) 33.0530 1.18653
\(777\) 5.70747 0.204754
\(778\) −4.06324 −0.145674
\(779\) −42.1623 −1.51062
\(780\) 0.269716 0.00965738
\(781\) −15.2914 −0.547168
\(782\) 6.28160 0.224630
\(783\) 10.8219 0.386743
\(784\) −3.57182 −0.127565
\(785\) −22.5011 −0.803098
\(786\) −5.32029 −0.189768
\(787\) 33.3308 1.18812 0.594058 0.804422i \(-0.297525\pi\)
0.594058 + 0.804422i \(0.297525\pi\)
\(788\) 1.07916 0.0384435
\(789\) −59.1424 −2.10552
\(790\) −8.38142 −0.298197
\(791\) 2.87330 0.102163
\(792\) 8.78303 0.312091
\(793\) 4.87440 0.173095
\(794\) 41.9265 1.48791
\(795\) 8.77632 0.311264
\(796\) 2.53338 0.0897932
\(797\) −41.2385 −1.46074 −0.730371 0.683051i \(-0.760653\pi\)
−0.730371 + 0.683051i \(0.760653\pi\)
\(798\) 25.6071 0.906482
\(799\) 6.14404 0.217360
\(800\) −1.09938 −0.0388690
\(801\) 26.4160 0.933362
\(802\) 5.99289 0.211616
\(803\) 0.635447 0.0224244
\(804\) 1.29534 0.0456830
\(805\) −2.01930 −0.0711711
\(806\) −0.846304 −0.0298098
\(807\) 31.3990 1.10530
\(808\) 18.1626 0.638958
\(809\) 55.1572 1.93922 0.969612 0.244647i \(-0.0786721\pi\)
0.969612 + 0.244647i \(0.0786721\pi\)
\(810\) −13.7126 −0.481813
\(811\) −2.84299 −0.0998307 −0.0499154 0.998753i \(-0.515895\pi\)
−0.0499154 + 0.998753i \(0.515895\pi\)
\(812\) 1.87695 0.0658680
\(813\) −32.5712 −1.14232
\(814\) −3.85462 −0.135105
\(815\) 18.8319 0.659652
\(816\) 19.4335 0.680308
\(817\) 58.1992 2.03613
\(818\) 24.9758 0.873258
\(819\) 1.48368 0.0518439
\(820\) 1.01390 0.0354070
\(821\) −45.9213 −1.60267 −0.801333 0.598219i \(-0.795875\pi\)
−0.801333 + 0.598219i \(0.795875\pi\)
\(822\) −8.43670 −0.294264
\(823\) 42.5417 1.48291 0.741456 0.671002i \(-0.234136\pi\)
0.741456 + 0.671002i \(0.234136\pi\)
\(824\) 29.0421 1.01173
\(825\) −2.77558 −0.0966333
\(826\) 9.76035 0.339606
\(827\) 52.1980 1.81510 0.907552 0.419940i \(-0.137949\pi\)
0.907552 + 0.419940i \(0.137949\pi\)
\(828\) 0.993152 0.0345144
\(829\) 9.43933 0.327841 0.163921 0.986474i \(-0.447586\pi\)
0.163921 + 0.986474i \(0.447586\pi\)
\(830\) 14.2794 0.495644
\(831\) 11.1726 0.387574
\(832\) −5.07275 −0.175866
\(833\) 2.31546 0.0802261
\(834\) −33.9556 −1.17578
\(835\) −11.4516 −0.396300
\(836\) 1.86903 0.0646418
\(837\) −1.20398 −0.0416158
\(838\) 4.77989 0.165118
\(839\) 9.69987 0.334877 0.167438 0.985883i \(-0.446450\pi\)
0.167438 + 0.985883i \(0.446450\pi\)
\(840\) −6.92949 −0.239090
\(841\) 63.5863 2.19263
\(842\) −2.28374 −0.0787028
\(843\) −4.75208 −0.163670
\(844\) 4.45309 0.153282
\(845\) 12.6537 0.435302
\(846\) −8.98840 −0.309027
\(847\) 9.60472 0.330022
\(848\) −13.3407 −0.458122
\(849\) −42.4502 −1.45689
\(850\) −3.11078 −0.106699
\(851\) −4.90481 −0.168135
\(852\) −5.93359 −0.203281
\(853\) −30.7939 −1.05436 −0.527182 0.849752i \(-0.676751\pi\)
−0.527182 + 0.849752i \(0.676751\pi\)
\(854\) −11.1288 −0.380819
\(855\) 20.4523 0.699454
\(856\) −11.2167 −0.383378
\(857\) 38.3000 1.30830 0.654151 0.756364i \(-0.273026\pi\)
0.654151 + 0.756364i \(0.273026\pi\)
\(858\) −2.19427 −0.0749110
\(859\) 47.2572 1.61240 0.806198 0.591646i \(-0.201522\pi\)
0.806198 + 0.591646i \(0.201522\pi\)
\(860\) −1.39955 −0.0477243
\(861\) 12.2135 0.416235
\(862\) 16.9594 0.577640
\(863\) −42.3782 −1.44257 −0.721286 0.692637i \(-0.756449\pi\)
−0.721286 + 0.692637i \(0.756449\pi\)
\(864\) −1.23645 −0.0420650
\(865\) 4.05375 0.137832
\(866\) −34.5925 −1.17550
\(867\) 27.3480 0.928785
\(868\) −0.208819 −0.00708778
\(869\) −7.36915 −0.249981
\(870\) −30.3758 −1.02984
\(871\) −1.66297 −0.0563476
\(872\) 14.6208 0.495123
\(873\) 28.2597 0.956448
\(874\) −22.0059 −0.744361
\(875\) 1.00000 0.0338062
\(876\) 0.246576 0.00833103
\(877\) 18.9651 0.640406 0.320203 0.947349i \(-0.396249\pi\)
0.320203 + 0.947349i \(0.396249\pi\)
\(878\) −35.8746 −1.21071
\(879\) 45.6376 1.53932
\(880\) 4.21910 0.142226
\(881\) 9.04517 0.304739 0.152370 0.988324i \(-0.451310\pi\)
0.152370 + 0.988324i \(0.451310\pi\)
\(882\) −3.38740 −0.114060
\(883\) −54.5193 −1.83472 −0.917360 0.398059i \(-0.869684\pi\)
−0.917360 + 0.398059i \(0.869684\pi\)
\(884\) 0.265779 0.00893913
\(885\) 17.0709 0.573834
\(886\) 11.2084 0.376555
\(887\) −1.38125 −0.0463777 −0.0231888 0.999731i \(-0.507382\pi\)
−0.0231888 + 0.999731i \(0.507382\pi\)
\(888\) −16.8315 −0.564827
\(889\) 19.7529 0.662492
\(890\) 14.0754 0.471810
\(891\) −12.0565 −0.403908
\(892\) −1.00730 −0.0337270
\(893\) −21.5240 −0.720273
\(894\) 10.4749 0.350332
\(895\) −16.2202 −0.542181
\(896\) 9.38288 0.313460
\(897\) −2.79209 −0.0932251
\(898\) −39.5281 −1.31907
\(899\) −10.3006 −0.343546
\(900\) −0.491829 −0.0163943
\(901\) 8.64823 0.288114
\(902\) −8.24858 −0.274648
\(903\) −16.8590 −0.561034
\(904\) −8.47342 −0.281822
\(905\) 16.2703 0.540844
\(906\) −54.1634 −1.79946
\(907\) 12.0485 0.400065 0.200033 0.979789i \(-0.435895\pi\)
0.200033 + 0.979789i \(0.435895\pi\)
\(908\) 1.14874 0.0381223
\(909\) 15.5287 0.515055
\(910\) 0.790561 0.0262068
\(911\) 35.4322 1.17392 0.586961 0.809615i \(-0.300324\pi\)
0.586961 + 0.809615i \(0.300324\pi\)
\(912\) −68.0800 −2.25435
\(913\) 12.5548 0.415502
\(914\) −37.8092 −1.25062
\(915\) −19.4644 −0.643472
\(916\) −0.195065 −0.00644512
\(917\) 1.68532 0.0556540
\(918\) −3.49863 −0.115472
\(919\) 43.6474 1.43980 0.719898 0.694080i \(-0.244189\pi\)
0.719898 + 0.694080i \(0.244189\pi\)
\(920\) 5.95497 0.196330
\(921\) 22.2731 0.733924
\(922\) 44.1499 1.45400
\(923\) 7.61763 0.250737
\(924\) −0.541418 −0.0178113
\(925\) 2.42896 0.0798638
\(926\) 12.3180 0.404794
\(927\) 24.8305 0.815541
\(928\) −10.5784 −0.347254
\(929\) 30.4460 0.998901 0.499451 0.866342i \(-0.333535\pi\)
0.499451 + 0.866342i \(0.333535\pi\)
\(930\) 3.37944 0.110816
\(931\) −8.11161 −0.265847
\(932\) −0.263831 −0.00864207
\(933\) 34.3202 1.12359
\(934\) −27.3353 −0.894437
\(935\) −2.73507 −0.0894464
\(936\) −4.37540 −0.143015
\(937\) −18.3231 −0.598590 −0.299295 0.954161i \(-0.596751\pi\)
−0.299295 + 0.954161i \(0.596751\pi\)
\(938\) 3.79674 0.123968
\(939\) −71.5101 −2.33364
\(940\) 0.517601 0.0168823
\(941\) −15.7355 −0.512963 −0.256481 0.966549i \(-0.582563\pi\)
−0.256481 + 0.966549i \(0.582563\pi\)
\(942\) 71.0326 2.31437
\(943\) −10.4959 −0.341793
\(944\) −25.9492 −0.844575
\(945\) 1.12468 0.0365859
\(946\) 11.3860 0.370191
\(947\) −37.8295 −1.22929 −0.614647 0.788802i \(-0.710702\pi\)
−0.614647 + 0.788802i \(0.710702\pi\)
\(948\) −2.85949 −0.0928719
\(949\) −0.316558 −0.0102759
\(950\) 10.8978 0.353570
\(951\) 47.1186 1.52793
\(952\) −6.82835 −0.221308
\(953\) −43.7274 −1.41647 −0.708235 0.705977i \(-0.750508\pi\)
−0.708235 + 0.705977i \(0.750508\pi\)
\(954\) −12.6519 −0.409620
\(955\) 24.7749 0.801697
\(956\) −0.402697 −0.0130242
\(957\) −26.7071 −0.863319
\(958\) 43.8433 1.41651
\(959\) 2.67251 0.0862997
\(960\) 20.2564 0.653773
\(961\) −29.8540 −0.963032
\(962\) 1.92024 0.0619111
\(963\) −9.59007 −0.309036
\(964\) 3.25906 0.104967
\(965\) 13.6464 0.439293
\(966\) 6.37464 0.205101
\(967\) −11.1226 −0.357678 −0.178839 0.983878i \(-0.557234\pi\)
−0.178839 + 0.983878i \(0.557234\pi\)
\(968\) −28.3245 −0.910385
\(969\) 44.1335 1.41777
\(970\) 15.0579 0.483479
\(971\) 28.8786 0.926759 0.463380 0.886160i \(-0.346637\pi\)
0.463380 + 0.886160i \(0.346637\pi\)
\(972\) −4.02019 −0.128948
\(973\) 10.7562 0.344826
\(974\) −28.8898 −0.925690
\(975\) 1.38270 0.0442818
\(976\) 29.5874 0.947069
\(977\) 23.7443 0.759649 0.379824 0.925059i \(-0.375984\pi\)
0.379824 + 0.925059i \(0.375984\pi\)
\(978\) −59.4494 −1.90098
\(979\) 12.3755 0.395522
\(980\) 0.195065 0.00623112
\(981\) 12.5005 0.399111
\(982\) −54.4726 −1.73829
\(983\) 24.8690 0.793197 0.396599 0.917992i \(-0.370190\pi\)
0.396599 + 0.917992i \(0.370190\pi\)
\(984\) −36.0179 −1.14821
\(985\) 5.53232 0.176274
\(986\) −29.9324 −0.953243
\(987\) 6.23504 0.198463
\(988\) −0.931087 −0.0296218
\(989\) 14.4881 0.460695
\(990\) 4.00126 0.127168
\(991\) −41.2045 −1.30890 −0.654452 0.756103i \(-0.727101\pi\)
−0.654452 + 0.756103i \(0.727101\pi\)
\(992\) 1.17690 0.0373666
\(993\) −7.15517 −0.227062
\(994\) −17.3919 −0.551636
\(995\) 12.9874 0.411727
\(996\) 4.87169 0.154366
\(997\) 12.4015 0.392760 0.196380 0.980528i \(-0.437081\pi\)
0.196380 + 0.980528i \(0.437081\pi\)
\(998\) −46.7111 −1.47861
\(999\) 2.73181 0.0864306
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 \(a_p\))