Properties

Label 4015.2.a.h.1.5
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.14348 q^{2}\) \(+2.01146 q^{3}\) \(+2.59449 q^{4}\) \(+1.00000 q^{5}\) \(-4.31152 q^{6}\) \(-3.47503 q^{7}\) \(-1.27427 q^{8}\) \(+1.04598 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.14348 q^{2}\) \(+2.01146 q^{3}\) \(+2.59449 q^{4}\) \(+1.00000 q^{5}\) \(-4.31152 q^{6}\) \(-3.47503 q^{7}\) \(-1.27427 q^{8}\) \(+1.04598 q^{9}\) \(-2.14348 q^{10}\) \(+1.00000 q^{11}\) \(+5.21871 q^{12}\) \(+6.08523 q^{13}\) \(+7.44863 q^{14}\) \(+2.01146 q^{15}\) \(-2.45761 q^{16}\) \(-0.860759 q^{17}\) \(-2.24204 q^{18}\) \(+5.32833 q^{19}\) \(+2.59449 q^{20}\) \(-6.98989 q^{21}\) \(-2.14348 q^{22}\) \(+5.95868 q^{23}\) \(-2.56314 q^{24}\) \(+1.00000 q^{25}\) \(-13.0435 q^{26}\) \(-3.93043 q^{27}\) \(-9.01591 q^{28}\) \(+5.45897 q^{29}\) \(-4.31152 q^{30}\) \(-4.31699 q^{31}\) \(+7.81637 q^{32}\) \(+2.01146 q^{33}\) \(+1.84501 q^{34}\) \(-3.47503 q^{35}\) \(+2.71379 q^{36}\) \(+6.22550 q^{37}\) \(-11.4211 q^{38}\) \(+12.2402 q^{39}\) \(-1.27427 q^{40}\) \(+7.88150 q^{41}\) \(+14.9826 q^{42}\) \(+7.05333 q^{43}\) \(+2.59449 q^{44}\) \(+1.04598 q^{45}\) \(-12.7723 q^{46}\) \(-9.39039 q^{47}\) \(-4.94340 q^{48}\) \(+5.07581 q^{49}\) \(-2.14348 q^{50}\) \(-1.73138 q^{51}\) \(+15.7880 q^{52}\) \(-13.5459 q^{53}\) \(+8.42479 q^{54}\) \(+1.00000 q^{55}\) \(+4.42811 q^{56}\) \(+10.7177 q^{57}\) \(-11.7012 q^{58}\) \(-13.0360 q^{59}\) \(+5.21871 q^{60}\) \(-7.65313 q^{61}\) \(+9.25337 q^{62}\) \(-3.63482 q^{63}\) \(-11.8390 q^{64}\) \(+6.08523 q^{65}\) \(-4.31152 q^{66}\) \(-4.95049 q^{67}\) \(-2.23323 q^{68}\) \(+11.9857 q^{69}\) \(+7.44863 q^{70}\) \(+9.98830 q^{71}\) \(-1.33286 q^{72}\) \(+1.00000 q^{73}\) \(-13.3442 q^{74}\) \(+2.01146 q^{75}\) \(+13.8243 q^{76}\) \(-3.47503 q^{77}\) \(-26.2366 q^{78}\) \(-14.0370 q^{79}\) \(-2.45761 q^{80}\) \(-11.0439 q^{81}\) \(-16.8938 q^{82}\) \(-15.5205 q^{83}\) \(-18.1352 q^{84}\) \(-0.860759 q^{85}\) \(-15.1186 q^{86}\) \(+10.9805 q^{87}\) \(-1.27427 q^{88}\) \(+16.0682 q^{89}\) \(-2.24204 q^{90}\) \(-21.1463 q^{91}\) \(+15.4597 q^{92}\) \(-8.68347 q^{93}\) \(+20.1281 q^{94}\) \(+5.32833 q^{95}\) \(+15.7223 q^{96}\) \(-0.440714 q^{97}\) \(-10.8799 q^{98}\) \(+1.04598 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.14348 −1.51567 −0.757833 0.652449i \(-0.773742\pi\)
−0.757833 + 0.652449i \(0.773742\pi\)
\(3\) 2.01146 1.16132 0.580659 0.814147i \(-0.302795\pi\)
0.580659 + 0.814147i \(0.302795\pi\)
\(4\) 2.59449 1.29724
\(5\) 1.00000 0.447214
\(6\) −4.31152 −1.76017
\(7\) −3.47503 −1.31344 −0.656718 0.754136i \(-0.728056\pi\)
−0.656718 + 0.754136i \(0.728056\pi\)
\(8\) −1.27427 −0.450521
\(9\) 1.04598 0.348661
\(10\) −2.14348 −0.677826
\(11\) 1.00000 0.301511
\(12\) 5.21871 1.50651
\(13\) 6.08523 1.68774 0.843869 0.536549i \(-0.180272\pi\)
0.843869 + 0.536549i \(0.180272\pi\)
\(14\) 7.44863 1.99073
\(15\) 2.01146 0.519357
\(16\) −2.45761 −0.614403
\(17\) −0.860759 −0.208765 −0.104382 0.994537i \(-0.533287\pi\)
−0.104382 + 0.994537i \(0.533287\pi\)
\(18\) −2.24204 −0.528453
\(19\) 5.32833 1.22240 0.611201 0.791475i \(-0.290687\pi\)
0.611201 + 0.791475i \(0.290687\pi\)
\(20\) 2.59449 0.580145
\(21\) −6.98989 −1.52532
\(22\) −2.14348 −0.456990
\(23\) 5.95868 1.24247 0.621235 0.783624i \(-0.286631\pi\)
0.621235 + 0.783624i \(0.286631\pi\)
\(24\) −2.56314 −0.523199
\(25\) 1.00000 0.200000
\(26\) −13.0435 −2.55805
\(27\) −3.93043 −0.756412
\(28\) −9.01591 −1.70385
\(29\) 5.45897 1.01371 0.506853 0.862033i \(-0.330809\pi\)
0.506853 + 0.862033i \(0.330809\pi\)
\(30\) −4.31152 −0.787172
\(31\) −4.31699 −0.775355 −0.387677 0.921795i \(-0.626723\pi\)
−0.387677 + 0.921795i \(0.626723\pi\)
\(32\) 7.81637 1.38175
\(33\) 2.01146 0.350151
\(34\) 1.84501 0.316417
\(35\) −3.47503 −0.587387
\(36\) 2.71379 0.452298
\(37\) 6.22550 1.02347 0.511733 0.859145i \(-0.329004\pi\)
0.511733 + 0.859145i \(0.329004\pi\)
\(38\) −11.4211 −1.85275
\(39\) 12.2402 1.96000
\(40\) −1.27427 −0.201479
\(41\) 7.88150 1.23088 0.615442 0.788182i \(-0.288978\pi\)
0.615442 + 0.788182i \(0.288978\pi\)
\(42\) 14.9826 2.31187
\(43\) 7.05333 1.07562 0.537812 0.843065i \(-0.319251\pi\)
0.537812 + 0.843065i \(0.319251\pi\)
\(44\) 2.59449 0.391134
\(45\) 1.04598 0.155926
\(46\) −12.7723 −1.88317
\(47\) −9.39039 −1.36973 −0.684865 0.728670i \(-0.740139\pi\)
−0.684865 + 0.728670i \(0.740139\pi\)
\(48\) −4.94340 −0.713518
\(49\) 5.07581 0.725116
\(50\) −2.14348 −0.303133
\(51\) −1.73138 −0.242442
\(52\) 15.7880 2.18941
\(53\) −13.5459 −1.86068 −0.930338 0.366704i \(-0.880486\pi\)
−0.930338 + 0.366704i \(0.880486\pi\)
\(54\) 8.42479 1.14647
\(55\) 1.00000 0.134840
\(56\) 4.42811 0.591731
\(57\) 10.7177 1.41960
\(58\) −11.7012 −1.53644
\(59\) −13.0360 −1.69715 −0.848574 0.529077i \(-0.822538\pi\)
−0.848574 + 0.529077i \(0.822538\pi\)
\(60\) 5.21871 0.673733
\(61\) −7.65313 −0.979883 −0.489941 0.871755i \(-0.662982\pi\)
−0.489941 + 0.871755i \(0.662982\pi\)
\(62\) 9.25337 1.17518
\(63\) −3.63482 −0.457944
\(64\) −11.8390 −1.47987
\(65\) 6.08523 0.754780
\(66\) −4.31152 −0.530711
\(67\) −4.95049 −0.604799 −0.302400 0.953181i \(-0.597788\pi\)
−0.302400 + 0.953181i \(0.597788\pi\)
\(68\) −2.23323 −0.270819
\(69\) 11.9857 1.44290
\(70\) 7.44863 0.890282
\(71\) 9.98830 1.18539 0.592696 0.805426i \(-0.298063\pi\)
0.592696 + 0.805426i \(0.298063\pi\)
\(72\) −1.33286 −0.157079
\(73\) 1.00000 0.117041
\(74\) −13.3442 −1.55123
\(75\) 2.01146 0.232264
\(76\) 13.8243 1.58575
\(77\) −3.47503 −0.396016
\(78\) −26.2366 −2.97071
\(79\) −14.0370 −1.57928 −0.789640 0.613570i \(-0.789733\pi\)
−0.789640 + 0.613570i \(0.789733\pi\)
\(80\) −2.45761 −0.274770
\(81\) −11.0439 −1.22710
\(82\) −16.8938 −1.86561
\(83\) −15.5205 −1.70360 −0.851800 0.523867i \(-0.824489\pi\)
−0.851800 + 0.523867i \(0.824489\pi\)
\(84\) −18.1352 −1.97871
\(85\) −0.860759 −0.0933624
\(86\) −15.1186 −1.63029
\(87\) 10.9805 1.17723
\(88\) −1.27427 −0.135837
\(89\) 16.0682 1.70322 0.851612 0.524172i \(-0.175625\pi\)
0.851612 + 0.524172i \(0.175625\pi\)
\(90\) −2.24204 −0.236331
\(91\) −21.1463 −2.21674
\(92\) 15.4597 1.61179
\(93\) −8.68347 −0.900434
\(94\) 20.1281 2.07605
\(95\) 5.32833 0.546675
\(96\) 15.7223 1.60465
\(97\) −0.440714 −0.0447477 −0.0223738 0.999750i \(-0.507122\pi\)
−0.0223738 + 0.999750i \(0.507122\pi\)
\(98\) −10.8799 −1.09903
\(99\) 1.04598 0.105125
\(100\) 2.59449 0.259449
\(101\) 11.1222 1.10670 0.553350 0.832949i \(-0.313349\pi\)
0.553350 + 0.832949i \(0.313349\pi\)
\(102\) 3.71118 0.367461
\(103\) 9.81539 0.967139 0.483570 0.875306i \(-0.339340\pi\)
0.483570 + 0.875306i \(0.339340\pi\)
\(104\) −7.75421 −0.760362
\(105\) −6.98989 −0.682143
\(106\) 29.0354 2.82016
\(107\) 10.8099 1.04503 0.522516 0.852629i \(-0.324993\pi\)
0.522516 + 0.852629i \(0.324993\pi\)
\(108\) −10.1975 −0.981251
\(109\) 15.0083 1.43754 0.718770 0.695248i \(-0.244706\pi\)
0.718770 + 0.695248i \(0.244706\pi\)
\(110\) −2.14348 −0.204372
\(111\) 12.5224 1.18857
\(112\) 8.54027 0.806980
\(113\) 14.5182 1.36575 0.682877 0.730534i \(-0.260729\pi\)
0.682877 + 0.730534i \(0.260729\pi\)
\(114\) −22.9732 −2.15164
\(115\) 5.95868 0.555650
\(116\) 14.1632 1.31502
\(117\) 6.36504 0.588448
\(118\) 27.9424 2.57231
\(119\) 2.99116 0.274199
\(120\) −2.56314 −0.233982
\(121\) 1.00000 0.0909091
\(122\) 16.4043 1.48517
\(123\) 15.8533 1.42945
\(124\) −11.2004 −1.00582
\(125\) 1.00000 0.0894427
\(126\) 7.79114 0.694090
\(127\) −3.43377 −0.304698 −0.152349 0.988327i \(-0.548684\pi\)
−0.152349 + 0.988327i \(0.548684\pi\)
\(128\) 9.74379 0.861238
\(129\) 14.1875 1.24914
\(130\) −13.0435 −1.14399
\(131\) −0.970461 −0.0847896 −0.0423948 0.999101i \(-0.513499\pi\)
−0.0423948 + 0.999101i \(0.513499\pi\)
\(132\) 5.21871 0.454231
\(133\) −18.5161 −1.60555
\(134\) 10.6113 0.916673
\(135\) −3.93043 −0.338278
\(136\) 1.09684 0.0940529
\(137\) −11.3261 −0.967651 −0.483825 0.875165i \(-0.660753\pi\)
−0.483825 + 0.875165i \(0.660753\pi\)
\(138\) −25.6910 −2.18696
\(139\) 17.3886 1.47488 0.737440 0.675413i \(-0.236035\pi\)
0.737440 + 0.675413i \(0.236035\pi\)
\(140\) −9.01591 −0.761983
\(141\) −18.8884 −1.59069
\(142\) −21.4097 −1.79666
\(143\) 6.08523 0.508872
\(144\) −2.57062 −0.214218
\(145\) 5.45897 0.453343
\(146\) −2.14348 −0.177395
\(147\) 10.2098 0.842090
\(148\) 16.1520 1.32768
\(149\) 7.51945 0.616017 0.308009 0.951384i \(-0.400337\pi\)
0.308009 + 0.951384i \(0.400337\pi\)
\(150\) −4.31152 −0.352034
\(151\) 13.8880 1.13019 0.565095 0.825026i \(-0.308839\pi\)
0.565095 + 0.825026i \(0.308839\pi\)
\(152\) −6.78971 −0.550719
\(153\) −0.900338 −0.0727880
\(154\) 7.44863 0.600228
\(155\) −4.31699 −0.346749
\(156\) 31.7571 2.54260
\(157\) −6.26466 −0.499974 −0.249987 0.968249i \(-0.580426\pi\)
−0.249987 + 0.968249i \(0.580426\pi\)
\(158\) 30.0879 2.39366
\(159\) −27.2471 −2.16084
\(160\) 7.81637 0.617938
\(161\) −20.7066 −1.63191
\(162\) 23.6723 1.85987
\(163\) 2.44872 0.191798 0.0958991 0.995391i \(-0.469427\pi\)
0.0958991 + 0.995391i \(0.469427\pi\)
\(164\) 20.4484 1.59676
\(165\) 2.01146 0.156592
\(166\) 33.2679 2.58209
\(167\) 2.54186 0.196695 0.0983476 0.995152i \(-0.468644\pi\)
0.0983476 + 0.995152i \(0.468644\pi\)
\(168\) 8.90698 0.687188
\(169\) 24.0300 1.84846
\(170\) 1.84501 0.141506
\(171\) 5.57334 0.426204
\(172\) 18.2998 1.39534
\(173\) 0.678878 0.0516141 0.0258071 0.999667i \(-0.491784\pi\)
0.0258071 + 0.999667i \(0.491784\pi\)
\(174\) −23.5365 −1.78429
\(175\) −3.47503 −0.262687
\(176\) −2.45761 −0.185250
\(177\) −26.2215 −1.97093
\(178\) −34.4418 −2.58152
\(179\) 14.0497 1.05012 0.525060 0.851065i \(-0.324043\pi\)
0.525060 + 0.851065i \(0.324043\pi\)
\(180\) 2.71379 0.202274
\(181\) 6.22283 0.462539 0.231270 0.972890i \(-0.425712\pi\)
0.231270 + 0.972890i \(0.425712\pi\)
\(182\) 45.3266 3.35983
\(183\) −15.3940 −1.13796
\(184\) −7.59295 −0.559760
\(185\) 6.22550 0.457708
\(186\) 18.6128 1.36476
\(187\) −0.860759 −0.0629449
\(188\) −24.3632 −1.77687
\(189\) 13.6584 0.993500
\(190\) −11.4211 −0.828577
\(191\) 25.8029 1.86703 0.933515 0.358539i \(-0.116725\pi\)
0.933515 + 0.358539i \(0.116725\pi\)
\(192\) −23.8136 −1.71860
\(193\) 21.1940 1.52558 0.762788 0.646649i \(-0.223830\pi\)
0.762788 + 0.646649i \(0.223830\pi\)
\(194\) 0.944659 0.0678226
\(195\) 12.2402 0.876540
\(196\) 13.1691 0.940651
\(197\) 8.94792 0.637513 0.318757 0.947837i \(-0.396735\pi\)
0.318757 + 0.947837i \(0.396735\pi\)
\(198\) −2.24204 −0.159335
\(199\) 1.97787 0.140208 0.0701039 0.997540i \(-0.477667\pi\)
0.0701039 + 0.997540i \(0.477667\pi\)
\(200\) −1.27427 −0.0901043
\(201\) −9.95773 −0.702364
\(202\) −23.8401 −1.67739
\(203\) −18.9701 −1.33144
\(204\) −4.49205 −0.314507
\(205\) 7.88150 0.550468
\(206\) −21.0390 −1.46586
\(207\) 6.23267 0.433201
\(208\) −14.9551 −1.03695
\(209\) 5.32833 0.368568
\(210\) 14.9826 1.03390
\(211\) −20.0443 −1.37991 −0.689954 0.723853i \(-0.742369\pi\)
−0.689954 + 0.723853i \(0.742369\pi\)
\(212\) −35.1447 −2.41375
\(213\) 20.0911 1.37662
\(214\) −23.1707 −1.58392
\(215\) 7.05333 0.481033
\(216\) 5.00842 0.340780
\(217\) 15.0017 1.01838
\(218\) −32.1700 −2.17883
\(219\) 2.01146 0.135922
\(220\) 2.59449 0.174920
\(221\) −5.23791 −0.352340
\(222\) −26.8414 −1.80147
\(223\) −5.44124 −0.364372 −0.182186 0.983264i \(-0.558317\pi\)
−0.182186 + 0.983264i \(0.558317\pi\)
\(224\) −27.1621 −1.81484
\(225\) 1.04598 0.0697321
\(226\) −31.1193 −2.07003
\(227\) −21.1635 −1.40467 −0.702335 0.711846i \(-0.747859\pi\)
−0.702335 + 0.711846i \(0.747859\pi\)
\(228\) 27.8070 1.84157
\(229\) −3.73849 −0.247046 −0.123523 0.992342i \(-0.539419\pi\)
−0.123523 + 0.992342i \(0.539419\pi\)
\(230\) −12.7723 −0.842179
\(231\) −6.98989 −0.459901
\(232\) −6.95618 −0.456696
\(233\) 14.5831 0.955371 0.477686 0.878531i \(-0.341476\pi\)
0.477686 + 0.878531i \(0.341476\pi\)
\(234\) −13.6433 −0.891891
\(235\) −9.39039 −0.612562
\(236\) −33.8218 −2.20161
\(237\) −28.2348 −1.83405
\(238\) −6.41148 −0.415594
\(239\) 19.1418 1.23818 0.619090 0.785320i \(-0.287502\pi\)
0.619090 + 0.785320i \(0.287502\pi\)
\(240\) −4.94340 −0.319095
\(241\) −15.2597 −0.982964 −0.491482 0.870888i \(-0.663545\pi\)
−0.491482 + 0.870888i \(0.663545\pi\)
\(242\) −2.14348 −0.137788
\(243\) −10.4230 −0.668637
\(244\) −19.8559 −1.27115
\(245\) 5.07581 0.324282
\(246\) −33.9813 −2.16657
\(247\) 32.4241 2.06310
\(248\) 5.50100 0.349314
\(249\) −31.2190 −1.97842
\(250\) −2.14348 −0.135565
\(251\) 15.8773 1.00217 0.501083 0.865399i \(-0.332935\pi\)
0.501083 + 0.865399i \(0.332935\pi\)
\(252\) −9.43048 −0.594064
\(253\) 5.95868 0.374619
\(254\) 7.36020 0.461820
\(255\) −1.73138 −0.108423
\(256\) 2.79235 0.174522
\(257\) 22.9203 1.42973 0.714865 0.699262i \(-0.246488\pi\)
0.714865 + 0.699262i \(0.246488\pi\)
\(258\) −30.4106 −1.89328
\(259\) −21.6338 −1.34426
\(260\) 15.7880 0.979133
\(261\) 5.70998 0.353439
\(262\) 2.08016 0.128513
\(263\) −12.2937 −0.758062 −0.379031 0.925384i \(-0.623743\pi\)
−0.379031 + 0.925384i \(0.623743\pi\)
\(264\) −2.56314 −0.157750
\(265\) −13.5459 −0.832119
\(266\) 39.6888 2.43348
\(267\) 32.3206 1.97799
\(268\) −12.8440 −0.784571
\(269\) −11.6500 −0.710311 −0.355156 0.934807i \(-0.615572\pi\)
−0.355156 + 0.934807i \(0.615572\pi\)
\(270\) 8.42479 0.512716
\(271\) 20.2070 1.22749 0.613743 0.789506i \(-0.289663\pi\)
0.613743 + 0.789506i \(0.289663\pi\)
\(272\) 2.11541 0.128266
\(273\) −42.5351 −2.57434
\(274\) 24.2771 1.46663
\(275\) 1.00000 0.0603023
\(276\) 31.0966 1.87180
\(277\) −23.0018 −1.38204 −0.691022 0.722834i \(-0.742839\pi\)
−0.691022 + 0.722834i \(0.742839\pi\)
\(278\) −37.2720 −2.23542
\(279\) −4.51550 −0.270336
\(280\) 4.42811 0.264630
\(281\) 29.5901 1.76519 0.882597 0.470130i \(-0.155793\pi\)
0.882597 + 0.470130i \(0.155793\pi\)
\(282\) 40.4869 2.41096
\(283\) 0.968632 0.0575792 0.0287896 0.999585i \(-0.490835\pi\)
0.0287896 + 0.999585i \(0.490835\pi\)
\(284\) 25.9145 1.53774
\(285\) 10.7177 0.634864
\(286\) −13.0435 −0.771281
\(287\) −27.3884 −1.61669
\(288\) 8.17578 0.481762
\(289\) −16.2591 −0.956417
\(290\) −11.7012 −0.687116
\(291\) −0.886479 −0.0519663
\(292\) 2.59449 0.151831
\(293\) −10.2420 −0.598346 −0.299173 0.954199i \(-0.596711\pi\)
−0.299173 + 0.954199i \(0.596711\pi\)
\(294\) −21.8845 −1.27633
\(295\) −13.0360 −0.758988
\(296\) −7.93294 −0.461093
\(297\) −3.93043 −0.228067
\(298\) −16.1178 −0.933677
\(299\) 36.2599 2.09697
\(300\) 5.21871 0.301303
\(301\) −24.5105 −1.41276
\(302\) −29.7686 −1.71299
\(303\) 22.3719 1.28523
\(304\) −13.0950 −0.751048
\(305\) −7.65313 −0.438217
\(306\) 1.92985 0.110322
\(307\) −0.187378 −0.0106942 −0.00534711 0.999986i \(-0.501702\pi\)
−0.00534711 + 0.999986i \(0.501702\pi\)
\(308\) −9.01591 −0.513729
\(309\) 19.7433 1.12316
\(310\) 9.25337 0.525556
\(311\) 8.39962 0.476299 0.238149 0.971229i \(-0.423459\pi\)
0.238149 + 0.971229i \(0.423459\pi\)
\(312\) −15.5973 −0.883023
\(313\) 11.0663 0.625504 0.312752 0.949835i \(-0.398749\pi\)
0.312752 + 0.949835i \(0.398749\pi\)
\(314\) 13.4281 0.757793
\(315\) −3.63482 −0.204799
\(316\) −36.4187 −2.04871
\(317\) −13.5612 −0.761672 −0.380836 0.924643i \(-0.624364\pi\)
−0.380836 + 0.924643i \(0.624364\pi\)
\(318\) 58.4035 3.27511
\(319\) 5.45897 0.305644
\(320\) −11.8390 −0.661818
\(321\) 21.7437 1.21361
\(322\) 44.3840 2.47342
\(323\) −4.58641 −0.255194
\(324\) −28.6532 −1.59184
\(325\) 6.08523 0.337548
\(326\) −5.24876 −0.290702
\(327\) 30.1887 1.66944
\(328\) −10.0431 −0.554539
\(329\) 32.6319 1.79905
\(330\) −4.31152 −0.237341
\(331\) −17.4635 −0.959880 −0.479940 0.877301i \(-0.659341\pi\)
−0.479940 + 0.877301i \(0.659341\pi\)
\(332\) −40.2678 −2.20998
\(333\) 6.51176 0.356842
\(334\) −5.44842 −0.298124
\(335\) −4.95049 −0.270474
\(336\) 17.1784 0.937161
\(337\) −10.5428 −0.574303 −0.287152 0.957885i \(-0.592708\pi\)
−0.287152 + 0.957885i \(0.592708\pi\)
\(338\) −51.5077 −2.80165
\(339\) 29.2027 1.58607
\(340\) −2.23323 −0.121114
\(341\) −4.31699 −0.233778
\(342\) −11.9463 −0.645983
\(343\) 6.68661 0.361043
\(344\) −8.98783 −0.484591
\(345\) 11.9857 0.645286
\(346\) −1.45516 −0.0782298
\(347\) −4.89240 −0.262638 −0.131319 0.991340i \(-0.541921\pi\)
−0.131319 + 0.991340i \(0.541921\pi\)
\(348\) 28.4888 1.52716
\(349\) −20.6715 −1.10652 −0.553261 0.833008i \(-0.686617\pi\)
−0.553261 + 0.833008i \(0.686617\pi\)
\(350\) 7.44863 0.398146
\(351\) −23.9176 −1.27663
\(352\) 7.81637 0.416614
\(353\) 10.5329 0.560611 0.280305 0.959911i \(-0.409564\pi\)
0.280305 + 0.959911i \(0.409564\pi\)
\(354\) 56.2051 2.98727
\(355\) 9.98830 0.530124
\(356\) 41.6887 2.20950
\(357\) 6.01661 0.318433
\(358\) −30.1151 −1.59163
\(359\) −9.14214 −0.482504 −0.241252 0.970463i \(-0.577558\pi\)
−0.241252 + 0.970463i \(0.577558\pi\)
\(360\) −1.33286 −0.0702479
\(361\) 9.39110 0.494269
\(362\) −13.3385 −0.701055
\(363\) 2.01146 0.105574
\(364\) −54.8639 −2.87565
\(365\) 1.00000 0.0523424
\(366\) 32.9966 1.72476
\(367\) −1.98979 −0.103866 −0.0519331 0.998651i \(-0.516538\pi\)
−0.0519331 + 0.998651i \(0.516538\pi\)
\(368\) −14.6441 −0.763378
\(369\) 8.24391 0.429161
\(370\) −13.3442 −0.693732
\(371\) 47.0724 2.44388
\(372\) −22.5291 −1.16808
\(373\) −15.4376 −0.799328 −0.399664 0.916662i \(-0.630873\pi\)
−0.399664 + 0.916662i \(0.630873\pi\)
\(374\) 1.84501 0.0954035
\(375\) 2.01146 0.103871
\(376\) 11.9659 0.617092
\(377\) 33.2191 1.71087
\(378\) −29.2764 −1.50581
\(379\) −7.94818 −0.408271 −0.204135 0.978943i \(-0.565438\pi\)
−0.204135 + 0.978943i \(0.565438\pi\)
\(380\) 13.8243 0.709171
\(381\) −6.90690 −0.353851
\(382\) −55.3078 −2.82979
\(383\) 26.8032 1.36958 0.684789 0.728741i \(-0.259894\pi\)
0.684789 + 0.728741i \(0.259894\pi\)
\(384\) 19.5993 1.00017
\(385\) −3.47503 −0.177104
\(386\) −45.4288 −2.31226
\(387\) 7.37766 0.375028
\(388\) −1.14343 −0.0580486
\(389\) −9.55541 −0.484478 −0.242239 0.970217i \(-0.577882\pi\)
−0.242239 + 0.970217i \(0.577882\pi\)
\(390\) −26.2366 −1.32854
\(391\) −5.12898 −0.259384
\(392\) −6.46794 −0.326680
\(393\) −1.95205 −0.0984677
\(394\) −19.1797 −0.966257
\(395\) −14.0370 −0.706276
\(396\) 2.71379 0.136373
\(397\) 18.9457 0.950855 0.475428 0.879755i \(-0.342293\pi\)
0.475428 + 0.879755i \(0.342293\pi\)
\(398\) −4.23952 −0.212508
\(399\) −37.2444 −1.86455
\(400\) −2.45761 −0.122881
\(401\) 23.2141 1.15925 0.579627 0.814882i \(-0.303198\pi\)
0.579627 + 0.814882i \(0.303198\pi\)
\(402\) 21.3442 1.06455
\(403\) −26.2699 −1.30860
\(404\) 28.8564 1.43566
\(405\) −11.0439 −0.548774
\(406\) 40.6619 2.01801
\(407\) 6.22550 0.308586
\(408\) 2.20625 0.109225
\(409\) 20.7211 1.02459 0.512295 0.858809i \(-0.328795\pi\)
0.512295 + 0.858809i \(0.328795\pi\)
\(410\) −16.8938 −0.834326
\(411\) −22.7819 −1.12375
\(412\) 25.4659 1.25461
\(413\) 45.3006 2.22910
\(414\) −13.3596 −0.656587
\(415\) −15.5205 −0.761873
\(416\) 47.5644 2.33204
\(417\) 34.9765 1.71280
\(418\) −11.4211 −0.558626
\(419\) −9.83194 −0.480322 −0.240161 0.970733i \(-0.577200\pi\)
−0.240161 + 0.970733i \(0.577200\pi\)
\(420\) −18.1352 −0.884905
\(421\) 1.39939 0.0682020 0.0341010 0.999418i \(-0.489143\pi\)
0.0341010 + 0.999418i \(0.489143\pi\)
\(422\) 42.9645 2.09148
\(423\) −9.82218 −0.477571
\(424\) 17.2611 0.838274
\(425\) −0.860759 −0.0417529
\(426\) −43.0647 −2.08649
\(427\) 26.5948 1.28701
\(428\) 28.0461 1.35566
\(429\) 12.2402 0.590963
\(430\) −15.1186 −0.729086
\(431\) 24.7144 1.19045 0.595227 0.803558i \(-0.297062\pi\)
0.595227 + 0.803558i \(0.297062\pi\)
\(432\) 9.65949 0.464742
\(433\) −22.0244 −1.05843 −0.529213 0.848489i \(-0.677513\pi\)
−0.529213 + 0.848489i \(0.677513\pi\)
\(434\) −32.1557 −1.54352
\(435\) 10.9805 0.526475
\(436\) 38.9390 1.86484
\(437\) 31.7498 1.51880
\(438\) −4.31152 −0.206012
\(439\) −12.4472 −0.594071 −0.297035 0.954866i \(-0.595998\pi\)
−0.297035 + 0.954866i \(0.595998\pi\)
\(440\) −1.27427 −0.0607483
\(441\) 5.30921 0.252819
\(442\) 11.2273 0.534030
\(443\) −28.7124 −1.36416 −0.682082 0.731275i \(-0.738925\pi\)
−0.682082 + 0.731275i \(0.738925\pi\)
\(444\) 32.4891 1.54186
\(445\) 16.0682 0.761705
\(446\) 11.6632 0.552266
\(447\) 15.1251 0.715392
\(448\) 41.1407 1.94372
\(449\) −16.6133 −0.784031 −0.392016 0.919959i \(-0.628222\pi\)
−0.392016 + 0.919959i \(0.628222\pi\)
\(450\) −2.24204 −0.105691
\(451\) 7.88150 0.371125
\(452\) 37.6672 1.77171
\(453\) 27.9352 1.31251
\(454\) 45.3634 2.12901
\(455\) −21.1463 −0.991355
\(456\) −13.6573 −0.639560
\(457\) −7.42305 −0.347236 −0.173618 0.984813i \(-0.555546\pi\)
−0.173618 + 0.984813i \(0.555546\pi\)
\(458\) 8.01336 0.374440
\(459\) 3.38316 0.157912
\(460\) 15.4597 0.720813
\(461\) −9.94481 −0.463176 −0.231588 0.972814i \(-0.574392\pi\)
−0.231588 + 0.972814i \(0.574392\pi\)
\(462\) 14.9826 0.697056
\(463\) −37.2609 −1.73166 −0.865830 0.500337i \(-0.833209\pi\)
−0.865830 + 0.500337i \(0.833209\pi\)
\(464\) −13.4160 −0.622824
\(465\) −8.68347 −0.402686
\(466\) −31.2585 −1.44802
\(467\) 19.6412 0.908885 0.454442 0.890776i \(-0.349839\pi\)
0.454442 + 0.890776i \(0.349839\pi\)
\(468\) 16.5140 0.763360
\(469\) 17.2031 0.794365
\(470\) 20.1281 0.928439
\(471\) −12.6011 −0.580629
\(472\) 16.6114 0.764601
\(473\) 7.05333 0.324313
\(474\) 60.5206 2.77980
\(475\) 5.32833 0.244481
\(476\) 7.76052 0.355703
\(477\) −14.1688 −0.648744
\(478\) −41.0300 −1.87667
\(479\) −13.9792 −0.638725 −0.319362 0.947633i \(-0.603469\pi\)
−0.319362 + 0.947633i \(0.603469\pi\)
\(480\) 15.7223 0.717623
\(481\) 37.8836 1.72734
\(482\) 32.7088 1.48984
\(483\) −41.6505 −1.89516
\(484\) 2.59449 0.117931
\(485\) −0.440714 −0.0200118
\(486\) 22.3415 1.01343
\(487\) −5.54233 −0.251147 −0.125574 0.992084i \(-0.540077\pi\)
−0.125574 + 0.992084i \(0.540077\pi\)
\(488\) 9.75213 0.441458
\(489\) 4.92550 0.222739
\(490\) −10.8799 −0.491503
\(491\) 31.0809 1.40266 0.701331 0.712835i \(-0.252589\pi\)
0.701331 + 0.712835i \(0.252589\pi\)
\(492\) 41.1313 1.85434
\(493\) −4.69886 −0.211626
\(494\) −69.5003 −3.12697
\(495\) 1.04598 0.0470134
\(496\) 10.6095 0.476380
\(497\) −34.7096 −1.55694
\(498\) 66.9171 2.99863
\(499\) −5.75541 −0.257648 −0.128824 0.991667i \(-0.541120\pi\)
−0.128824 + 0.991667i \(0.541120\pi\)
\(500\) 2.59449 0.116029
\(501\) 5.11286 0.228426
\(502\) −34.0326 −1.51895
\(503\) −29.7198 −1.32514 −0.662570 0.749000i \(-0.730534\pi\)
−0.662570 + 0.749000i \(0.730534\pi\)
\(504\) 4.63173 0.206313
\(505\) 11.1222 0.494931
\(506\) −12.7723 −0.567797
\(507\) 48.3355 2.14665
\(508\) −8.90887 −0.395267
\(509\) 20.8070 0.922254 0.461127 0.887334i \(-0.347445\pi\)
0.461127 + 0.887334i \(0.347445\pi\)
\(510\) 3.71118 0.164334
\(511\) −3.47503 −0.153726
\(512\) −25.4729 −1.12575
\(513\) −20.9427 −0.924641
\(514\) −49.1292 −2.16699
\(515\) 9.81539 0.432518
\(516\) 36.8093 1.62044
\(517\) −9.39039 −0.412989
\(518\) 46.3714 2.03744
\(519\) 1.36554 0.0599405
\(520\) −7.75421 −0.340044
\(521\) 6.12846 0.268493 0.134246 0.990948i \(-0.457139\pi\)
0.134246 + 0.990948i \(0.457139\pi\)
\(522\) −12.2392 −0.535696
\(523\) −29.4407 −1.28735 −0.643676 0.765298i \(-0.722592\pi\)
−0.643676 + 0.765298i \(0.722592\pi\)
\(524\) −2.51785 −0.109993
\(525\) −6.98989 −0.305064
\(526\) 26.3512 1.14897
\(527\) 3.71589 0.161867
\(528\) −4.94340 −0.215134
\(529\) 12.5059 0.543733
\(530\) 29.0354 1.26122
\(531\) −13.6355 −0.591729
\(532\) −48.0397 −2.08279
\(533\) 47.9607 2.07741
\(534\) −69.2783 −2.99797
\(535\) 10.8099 0.467353
\(536\) 6.30825 0.272475
\(537\) 28.2604 1.21952
\(538\) 24.9714 1.07659
\(539\) 5.07581 0.218631
\(540\) −10.1975 −0.438829
\(541\) −30.1809 −1.29758 −0.648789 0.760968i \(-0.724724\pi\)
−0.648789 + 0.760968i \(0.724724\pi\)
\(542\) −43.3131 −1.86046
\(543\) 12.5170 0.537155
\(544\) −6.72801 −0.288461
\(545\) 15.0083 0.642887
\(546\) 91.1729 3.90184
\(547\) −38.5413 −1.64791 −0.823953 0.566658i \(-0.808236\pi\)
−0.823953 + 0.566658i \(0.808236\pi\)
\(548\) −29.3853 −1.25528
\(549\) −8.00503 −0.341647
\(550\) −2.14348 −0.0913981
\(551\) 29.0872 1.23916
\(552\) −15.2729 −0.650059
\(553\) 48.7788 2.07428
\(554\) 49.3037 2.09472
\(555\) 12.5224 0.531544
\(556\) 45.1144 1.91328
\(557\) 14.1873 0.601135 0.300567 0.953761i \(-0.402824\pi\)
0.300567 + 0.953761i \(0.402824\pi\)
\(558\) 9.67885 0.409739
\(559\) 42.9212 1.81537
\(560\) 8.54027 0.360892
\(561\) −1.73138 −0.0730991
\(562\) −63.4256 −2.67545
\(563\) 33.9242 1.42973 0.714867 0.699261i \(-0.246487\pi\)
0.714867 + 0.699261i \(0.246487\pi\)
\(564\) −49.0058 −2.06351
\(565\) 14.5182 0.610783
\(566\) −2.07624 −0.0872708
\(567\) 38.3777 1.61171
\(568\) −12.7278 −0.534045
\(569\) 26.4714 1.10974 0.554870 0.831937i \(-0.312768\pi\)
0.554870 + 0.831937i \(0.312768\pi\)
\(570\) −22.9732 −0.962242
\(571\) −36.2667 −1.51771 −0.758857 0.651258i \(-0.774242\pi\)
−0.758857 + 0.651258i \(0.774242\pi\)
\(572\) 15.7880 0.660131
\(573\) 51.9015 2.16822
\(574\) 58.7064 2.45036
\(575\) 5.95868 0.248494
\(576\) −12.3833 −0.515973
\(577\) −1.44734 −0.0602534 −0.0301267 0.999546i \(-0.509591\pi\)
−0.0301267 + 0.999546i \(0.509591\pi\)
\(578\) 34.8510 1.44961
\(579\) 42.6309 1.77168
\(580\) 14.1632 0.588096
\(581\) 53.9343 2.23757
\(582\) 1.90015 0.0787636
\(583\) −13.5459 −0.561015
\(584\) −1.27427 −0.0527295
\(585\) 6.36504 0.263162
\(586\) 21.9536 0.906893
\(587\) −17.9532 −0.741007 −0.370504 0.928831i \(-0.620815\pi\)
−0.370504 + 0.928831i \(0.620815\pi\)
\(588\) 26.4892 1.09240
\(589\) −23.0024 −0.947796
\(590\) 27.9424 1.15037
\(591\) 17.9984 0.740356
\(592\) −15.2999 −0.628820
\(593\) −1.56421 −0.0642345 −0.0321172 0.999484i \(-0.510225\pi\)
−0.0321172 + 0.999484i \(0.510225\pi\)
\(594\) 8.42479 0.345673
\(595\) 2.99116 0.122626
\(596\) 19.5091 0.799124
\(597\) 3.97842 0.162826
\(598\) −77.7223 −3.17830
\(599\) −8.21802 −0.335779 −0.167890 0.985806i \(-0.553695\pi\)
−0.167890 + 0.985806i \(0.553695\pi\)
\(600\) −2.56314 −0.104640
\(601\) 2.34970 0.0958463 0.0479232 0.998851i \(-0.484740\pi\)
0.0479232 + 0.998851i \(0.484740\pi\)
\(602\) 52.5377 2.14128
\(603\) −5.17813 −0.210870
\(604\) 36.0323 1.46613
\(605\) 1.00000 0.0406558
\(606\) −47.9535 −1.94798
\(607\) 12.6551 0.513654 0.256827 0.966457i \(-0.417323\pi\)
0.256827 + 0.966457i \(0.417323\pi\)
\(608\) 41.6482 1.68906
\(609\) −38.1576 −1.54622
\(610\) 16.4043 0.664190
\(611\) −57.1427 −2.31175
\(612\) −2.33592 −0.0944238
\(613\) 29.8371 1.20511 0.602555 0.798078i \(-0.294150\pi\)
0.602555 + 0.798078i \(0.294150\pi\)
\(614\) 0.401640 0.0162089
\(615\) 15.8533 0.639269
\(616\) 4.42811 0.178414
\(617\) −1.05710 −0.0425572 −0.0212786 0.999774i \(-0.506774\pi\)
−0.0212786 + 0.999774i \(0.506774\pi\)
\(618\) −42.3193 −1.70233
\(619\) −5.05379 −0.203129 −0.101565 0.994829i \(-0.532385\pi\)
−0.101565 + 0.994829i \(0.532385\pi\)
\(620\) −11.2004 −0.449818
\(621\) −23.4202 −0.939820
\(622\) −18.0044 −0.721910
\(623\) −55.8374 −2.23708
\(624\) −30.0817 −1.20423
\(625\) 1.00000 0.0400000
\(626\) −23.7203 −0.948055
\(627\) 10.7177 0.428025
\(628\) −16.2536 −0.648588
\(629\) −5.35865 −0.213663
\(630\) 7.79114 0.310406
\(631\) −18.9247 −0.753380 −0.376690 0.926339i \(-0.622938\pi\)
−0.376690 + 0.926339i \(0.622938\pi\)
\(632\) 17.8868 0.711500
\(633\) −40.3184 −1.60251
\(634\) 29.0681 1.15444
\(635\) −3.43377 −0.136265
\(636\) −70.6923 −2.80313
\(637\) 30.8875 1.22381
\(638\) −11.7012 −0.463254
\(639\) 10.4476 0.413300
\(640\) 9.74379 0.385157
\(641\) 29.9158 1.18160 0.590801 0.806817i \(-0.298812\pi\)
0.590801 + 0.806817i \(0.298812\pi\)
\(642\) −46.6071 −1.83943
\(643\) 36.0543 1.42184 0.710922 0.703271i \(-0.248278\pi\)
0.710922 + 0.703271i \(0.248278\pi\)
\(644\) −53.7229 −2.11698
\(645\) 14.1875 0.558633
\(646\) 9.83085 0.386790
\(647\) 5.97437 0.234877 0.117438 0.993080i \(-0.462532\pi\)
0.117438 + 0.993080i \(0.462532\pi\)
\(648\) 14.0728 0.552833
\(649\) −13.0360 −0.511709
\(650\) −13.0435 −0.511610
\(651\) 30.1753 1.18266
\(652\) 6.35316 0.248809
\(653\) 13.0849 0.512053 0.256027 0.966670i \(-0.417587\pi\)
0.256027 + 0.966670i \(0.417587\pi\)
\(654\) −64.7088 −2.53031
\(655\) −0.970461 −0.0379191
\(656\) −19.3697 −0.756259
\(657\) 1.04598 0.0408076
\(658\) −69.9456 −2.72676
\(659\) 46.7837 1.82244 0.911218 0.411925i \(-0.135144\pi\)
0.911218 + 0.411925i \(0.135144\pi\)
\(660\) 5.21871 0.203138
\(661\) −20.5875 −0.800759 −0.400380 0.916349i \(-0.631122\pi\)
−0.400380 + 0.916349i \(0.631122\pi\)
\(662\) 37.4325 1.45486
\(663\) −10.5359 −0.409179
\(664\) 19.7773 0.767508
\(665\) −18.5161 −0.718023
\(666\) −13.9578 −0.540853
\(667\) 32.5282 1.25950
\(668\) 6.59483 0.255161
\(669\) −10.9448 −0.423152
\(670\) 10.6113 0.409949
\(671\) −7.65313 −0.295446
\(672\) −54.6355 −2.10761
\(673\) −39.3176 −1.51558 −0.757791 0.652497i \(-0.773721\pi\)
−0.757791 + 0.652497i \(0.773721\pi\)
\(674\) 22.5983 0.870452
\(675\) −3.93043 −0.151282
\(676\) 62.3455 2.39791
\(677\) −15.1748 −0.583215 −0.291607 0.956538i \(-0.594190\pi\)
−0.291607 + 0.956538i \(0.594190\pi\)
\(678\) −62.5953 −2.40396
\(679\) 1.53149 0.0587733
\(680\) 1.09684 0.0420618
\(681\) −42.5696 −1.63127
\(682\) 9.25337 0.354330
\(683\) −33.9264 −1.29816 −0.649080 0.760721i \(-0.724846\pi\)
−0.649080 + 0.760721i \(0.724846\pi\)
\(684\) 14.4599 0.552890
\(685\) −11.3261 −0.432746
\(686\) −14.3326 −0.547221
\(687\) −7.51984 −0.286900
\(688\) −17.3344 −0.660866
\(689\) −82.4300 −3.14033
\(690\) −25.6910 −0.978038
\(691\) 36.9312 1.40493 0.702465 0.711718i \(-0.252083\pi\)
0.702465 + 0.711718i \(0.252083\pi\)
\(692\) 1.76134 0.0669561
\(693\) −3.63482 −0.138075
\(694\) 10.4867 0.398071
\(695\) 17.3886 0.659586
\(696\) −13.9921 −0.530369
\(697\) −6.78407 −0.256965
\(698\) 44.3089 1.67712
\(699\) 29.3334 1.10949
\(700\) −9.01591 −0.340769
\(701\) −29.8280 −1.12659 −0.563294 0.826257i \(-0.690466\pi\)
−0.563294 + 0.826257i \(0.690466\pi\)
\(702\) 51.2668 1.93494
\(703\) 33.1715 1.25109
\(704\) −11.8390 −0.446198
\(705\) −18.8884 −0.711379
\(706\) −22.5771 −0.849699
\(707\) −38.6499 −1.45358
\(708\) −68.0313 −2.55677
\(709\) 29.7702 1.11804 0.559021 0.829153i \(-0.311177\pi\)
0.559021 + 0.829153i \(0.311177\pi\)
\(710\) −21.4097 −0.803490
\(711\) −14.6824 −0.550633
\(712\) −20.4752 −0.767339
\(713\) −25.7236 −0.963355
\(714\) −12.8964 −0.482637
\(715\) 6.08523 0.227575
\(716\) 36.4517 1.36226
\(717\) 38.5030 1.43792
\(718\) 19.5959 0.731314
\(719\) −1.13906 −0.0424799 −0.0212399 0.999774i \(-0.506761\pi\)
−0.0212399 + 0.999774i \(0.506761\pi\)
\(720\) −2.57062 −0.0958013
\(721\) −34.1087 −1.27028
\(722\) −20.1296 −0.749146
\(723\) −30.6943 −1.14153
\(724\) 16.1450 0.600026
\(725\) 5.45897 0.202741
\(726\) −4.31152 −0.160016
\(727\) −50.2602 −1.86405 −0.932024 0.362397i \(-0.881958\pi\)
−0.932024 + 0.362397i \(0.881958\pi\)
\(728\) 26.9461 0.998688
\(729\) 12.1661 0.450595
\(730\) −2.14348 −0.0793336
\(731\) −6.07122 −0.224552
\(732\) −39.9395 −1.47621
\(733\) 24.4876 0.904468 0.452234 0.891899i \(-0.350627\pi\)
0.452234 + 0.891899i \(0.350627\pi\)
\(734\) 4.26507 0.157427
\(735\) 10.2098 0.376594
\(736\) 46.5752 1.71679
\(737\) −4.95049 −0.182354
\(738\) −17.6706 −0.650464
\(739\) 15.5961 0.573713 0.286856 0.957974i \(-0.407390\pi\)
0.286856 + 0.957974i \(0.407390\pi\)
\(740\) 16.1520 0.593758
\(741\) 65.2199 2.39591
\(742\) −100.899 −3.70410
\(743\) 9.05995 0.332377 0.166189 0.986094i \(-0.446854\pi\)
0.166189 + 0.986094i \(0.446854\pi\)
\(744\) 11.0651 0.405665
\(745\) 7.51945 0.275491
\(746\) 33.0901 1.21151
\(747\) −16.2342 −0.593978
\(748\) −2.23323 −0.0816549
\(749\) −37.5647 −1.37258
\(750\) −4.31152 −0.157434
\(751\) 18.1498 0.662295 0.331147 0.943579i \(-0.392564\pi\)
0.331147 + 0.943579i \(0.392564\pi\)
\(752\) 23.0779 0.841566
\(753\) 31.9366 1.16383
\(754\) −71.2043 −2.59311
\(755\) 13.8880 0.505437
\(756\) 35.4364 1.28881
\(757\) −13.4169 −0.487647 −0.243823 0.969820i \(-0.578402\pi\)
−0.243823 + 0.969820i \(0.578402\pi\)
\(758\) 17.0367 0.618802
\(759\) 11.9857 0.435052
\(760\) −6.78971 −0.246289
\(761\) 40.9690 1.48513 0.742563 0.669776i \(-0.233610\pi\)
0.742563 + 0.669776i \(0.233610\pi\)
\(762\) 14.8048 0.536320
\(763\) −52.1544 −1.88812
\(764\) 66.9452 2.42199
\(765\) −0.900338 −0.0325518
\(766\) −57.4519 −2.07582
\(767\) −79.3273 −2.86434
\(768\) 5.61671 0.202675
\(769\) 45.1176 1.62698 0.813492 0.581576i \(-0.197564\pi\)
0.813492 + 0.581576i \(0.197564\pi\)
\(770\) 7.44863 0.268430
\(771\) 46.1034 1.66037
\(772\) 54.9875 1.97904
\(773\) −19.8257 −0.713081 −0.356541 0.934280i \(-0.616044\pi\)
−0.356541 + 0.934280i \(0.616044\pi\)
\(774\) −15.8138 −0.568416
\(775\) −4.31699 −0.155071
\(776\) 0.561587 0.0201598
\(777\) −43.5155 −1.56111
\(778\) 20.4818 0.734308
\(779\) 41.9952 1.50464
\(780\) 31.7571 1.13709
\(781\) 9.98830 0.357409
\(782\) 10.9939 0.393139
\(783\) −21.4561 −0.766779
\(784\) −12.4744 −0.445513
\(785\) −6.26466 −0.223595
\(786\) 4.18416 0.149244
\(787\) −20.0822 −0.715853 −0.357926 0.933750i \(-0.616516\pi\)
−0.357926 + 0.933750i \(0.616516\pi\)
\(788\) 23.2153 0.827010
\(789\) −24.7283 −0.880352
\(790\) 30.0879 1.07048
\(791\) −50.4510 −1.79383
\(792\) −1.33286 −0.0473611
\(793\) −46.5710 −1.65379
\(794\) −40.6096 −1.44118
\(795\) −27.2471 −0.966356
\(796\) 5.13157 0.181884
\(797\) −50.2117 −1.77859 −0.889294 0.457336i \(-0.848804\pi\)
−0.889294 + 0.457336i \(0.848804\pi\)
\(798\) 79.8325 2.82604
\(799\) 8.08286 0.285951
\(800\) 7.81637 0.276350
\(801\) 16.8070 0.593848
\(802\) −49.7588 −1.75704
\(803\) 1.00000 0.0352892
\(804\) −25.8352 −0.911137
\(805\) −20.7066 −0.729811
\(806\) 56.3089 1.98339
\(807\) −23.4335 −0.824898
\(808\) −14.1726 −0.498592
\(809\) −10.4267 −0.366585 −0.183292 0.983058i \(-0.558675\pi\)
−0.183292 + 0.983058i \(0.558675\pi\)
\(810\) 23.6723 0.831758
\(811\) 51.4982 1.80835 0.904174 0.427165i \(-0.140488\pi\)
0.904174 + 0.427165i \(0.140488\pi\)
\(812\) −49.2176 −1.72720
\(813\) 40.6456 1.42550
\(814\) −13.3442 −0.467714
\(815\) 2.44872 0.0857748
\(816\) 4.25507 0.148957
\(817\) 37.5825 1.31484
\(818\) −44.4151 −1.55294
\(819\) −22.1187 −0.772889
\(820\) 20.4484 0.714091
\(821\) 16.4254 0.573249 0.286625 0.958043i \(-0.407467\pi\)
0.286625 + 0.958043i \(0.407467\pi\)
\(822\) 48.8325 1.70323
\(823\) −32.1197 −1.11962 −0.559811 0.828620i \(-0.689126\pi\)
−0.559811 + 0.828620i \(0.689126\pi\)
\(824\) −12.5074 −0.435717
\(825\) 2.01146 0.0700301
\(826\) −97.1007 −3.37856
\(827\) −11.3431 −0.394438 −0.197219 0.980359i \(-0.563191\pi\)
−0.197219 + 0.980359i \(0.563191\pi\)
\(828\) 16.1706 0.561967
\(829\) 6.84713 0.237811 0.118905 0.992906i \(-0.462062\pi\)
0.118905 + 0.992906i \(0.462062\pi\)
\(830\) 33.2679 1.15474
\(831\) −46.2672 −1.60499
\(832\) −72.0428 −2.49763
\(833\) −4.36905 −0.151379
\(834\) −74.9712 −2.59604
\(835\) 2.54186 0.0879648
\(836\) 13.8243 0.478123
\(837\) 16.9677 0.586488
\(838\) 21.0745 0.728007
\(839\) −2.66868 −0.0921330 −0.0460665 0.998938i \(-0.514669\pi\)
−0.0460665 + 0.998938i \(0.514669\pi\)
\(840\) 8.90698 0.307320
\(841\) 0.800348 0.0275982
\(842\) −2.99955 −0.103371
\(843\) 59.5193 2.04995
\(844\) −52.0047 −1.79008
\(845\) 24.0300 0.826658
\(846\) 21.0536 0.723838
\(847\) −3.47503 −0.119403
\(848\) 33.2906 1.14321
\(849\) 1.94837 0.0668678
\(850\) 1.84501 0.0632835
\(851\) 37.0957 1.27163
\(852\) 52.1260 1.78581
\(853\) 47.6656 1.63204 0.816019 0.578025i \(-0.196176\pi\)
0.816019 + 0.578025i \(0.196176\pi\)
\(854\) −57.0053 −1.95068
\(855\) 5.57334 0.190604
\(856\) −13.7747 −0.470809
\(857\) −22.7766 −0.778033 −0.389016 0.921231i \(-0.627185\pi\)
−0.389016 + 0.921231i \(0.627185\pi\)
\(858\) −26.2366 −0.895702
\(859\) −42.2964 −1.44313 −0.721567 0.692344i \(-0.756578\pi\)
−0.721567 + 0.692344i \(0.756578\pi\)
\(860\) 18.2998 0.624017
\(861\) −55.0908 −1.87749
\(862\) −52.9748 −1.80433
\(863\) −41.6476 −1.41770 −0.708850 0.705359i \(-0.750786\pi\)
−0.708850 + 0.705359i \(0.750786\pi\)
\(864\) −30.7217 −1.04517
\(865\) 0.678878 0.0230825
\(866\) 47.2088 1.60422
\(867\) −32.7046 −1.11071
\(868\) 38.9216 1.32109
\(869\) −14.0370 −0.476171
\(870\) −23.5365 −0.797961
\(871\) −30.1249 −1.02074
\(872\) −19.1246 −0.647642
\(873\) −0.460979 −0.0156018
\(874\) −68.0549 −2.30199
\(875\) −3.47503 −0.117477
\(876\) 5.21871 0.176324
\(877\) −30.5965 −1.03317 −0.516586 0.856236i \(-0.672797\pi\)
−0.516586 + 0.856236i \(0.672797\pi\)
\(878\) 26.6802 0.900413
\(879\) −20.6015 −0.694871
\(880\) −2.45761 −0.0828461
\(881\) 12.0095 0.404609 0.202304 0.979323i \(-0.435157\pi\)
0.202304 + 0.979323i \(0.435157\pi\)
\(882\) −11.3802 −0.383190
\(883\) −41.1405 −1.38449 −0.692245 0.721663i \(-0.743378\pi\)
−0.692245 + 0.721663i \(0.743378\pi\)
\(884\) −13.5897 −0.457071
\(885\) −26.2215 −0.881426
\(886\) 61.5442 2.06762
\(887\) 29.9927 1.00705 0.503527 0.863979i \(-0.332035\pi\)
0.503527 + 0.863979i \(0.332035\pi\)
\(888\) −15.9568 −0.535476
\(889\) 11.9324 0.400201
\(890\) −34.4418 −1.15449
\(891\) −11.0439 −0.369983
\(892\) −14.1172 −0.472679
\(893\) −50.0351 −1.67436
\(894\) −32.4203 −1.08430
\(895\) 14.0497 0.469628
\(896\) −33.8599 −1.13118
\(897\) 72.9355 2.43525
\(898\) 35.6103 1.18833
\(899\) −23.5663 −0.785981
\(900\) 2.71379 0.0904595
\(901\) 11.6598 0.388443
\(902\) −16.8938 −0.562502
\(903\) −49.3020 −1.64067
\(904\) −18.5000 −0.615301
\(905\) 6.22283 0.206854
\(906\) −59.8785 −1.98933
\(907\) −33.8969 −1.12553 −0.562764 0.826618i \(-0.690262\pi\)
−0.562764 + 0.826618i \(0.690262\pi\)
\(908\) −54.9084 −1.82220
\(909\) 11.6336 0.385863
\(910\) 45.3266 1.50256
\(911\) −37.1666 −1.23138 −0.615691 0.787987i \(-0.711123\pi\)
−0.615691 + 0.787987i \(0.711123\pi\)
\(912\) −26.3401 −0.872206
\(913\) −15.5205 −0.513655
\(914\) 15.9111 0.526293
\(915\) −15.3940 −0.508909
\(916\) −9.69946 −0.320479
\(917\) 3.37238 0.111366
\(918\) −7.25171 −0.239342
\(919\) −13.0921 −0.431867 −0.215934 0.976408i \(-0.569279\pi\)
−0.215934 + 0.976408i \(0.569279\pi\)
\(920\) −7.59295 −0.250332
\(921\) −0.376903 −0.0124194
\(922\) 21.3165 0.702020
\(923\) 60.7811 2.00063
\(924\) −18.1352 −0.596603
\(925\) 6.22550 0.204693
\(926\) 79.8678 2.62462
\(927\) 10.2667 0.337203
\(928\) 42.6693 1.40069
\(929\) −58.1511 −1.90787 −0.953937 0.300006i \(-0.903011\pi\)
−0.953937 + 0.300006i \(0.903011\pi\)
\(930\) 18.6128 0.610338
\(931\) 27.0456 0.886383
\(932\) 37.8357 1.23935
\(933\) 16.8955 0.553135
\(934\) −42.1003 −1.37757
\(935\) −0.860759 −0.0281498
\(936\) −8.11076 −0.265109
\(937\) 14.2872 0.466743 0.233372 0.972388i \(-0.425024\pi\)
0.233372 + 0.972388i \(0.425024\pi\)
\(938\) −36.8744 −1.20399
\(939\) 22.2594 0.726409
\(940\) −24.3632 −0.794641
\(941\) −29.1327 −0.949700 −0.474850 0.880067i \(-0.657498\pi\)
−0.474850 + 0.880067i \(0.657498\pi\)
\(942\) 27.0102 0.880040
\(943\) 46.9633 1.52934
\(944\) 32.0375 1.04273
\(945\) 13.6584 0.444307
\(946\) −15.1186 −0.491550
\(947\) 41.1640 1.33765 0.668825 0.743420i \(-0.266798\pi\)
0.668825 + 0.743420i \(0.266798\pi\)
\(948\) −73.2548 −2.37921
\(949\) 6.08523 0.197535
\(950\) −11.4211 −0.370551
\(951\) −27.2778 −0.884544
\(952\) −3.81154 −0.123533
\(953\) 39.3961 1.27617 0.638083 0.769968i \(-0.279728\pi\)
0.638083 + 0.769968i \(0.279728\pi\)
\(954\) 30.3705 0.983280
\(955\) 25.8029 0.834961
\(956\) 49.6632 1.60622
\(957\) 10.9805 0.354950
\(958\) 29.9640 0.968094
\(959\) 39.3584 1.27095
\(960\) −23.8136 −0.768582
\(961\) −12.3636 −0.398825
\(962\) −81.2025 −2.61807
\(963\) 11.3070 0.364362
\(964\) −39.5911 −1.27514
\(965\) 21.1940 0.682258
\(966\) 89.2768 2.87243
\(967\) −55.2335 −1.77619 −0.888095 0.459659i \(-0.847972\pi\)
−0.888095 + 0.459659i \(0.847972\pi\)
\(968\) −1.27427 −0.0409565
\(969\) −9.22539 −0.296362
\(970\) 0.944659 0.0303312
\(971\) 16.2648 0.521963 0.260982 0.965344i \(-0.415954\pi\)
0.260982 + 0.965344i \(0.415954\pi\)
\(972\) −27.0424 −0.867385
\(973\) −60.4257 −1.93716
\(974\) 11.8799 0.380655
\(975\) 12.2402 0.392000
\(976\) 18.8084 0.602043
\(977\) 7.13298 0.228204 0.114102 0.993469i \(-0.463601\pi\)
0.114102 + 0.993469i \(0.463601\pi\)
\(978\) −10.5577 −0.337598
\(979\) 16.0682 0.513542
\(980\) 13.1691 0.420672
\(981\) 15.6985 0.501213
\(982\) −66.6212 −2.12597
\(983\) −9.56032 −0.304927 −0.152463 0.988309i \(-0.548721\pi\)
−0.152463 + 0.988309i \(0.548721\pi\)
\(984\) −20.2014 −0.643997
\(985\) 8.94792 0.285105
\(986\) 10.0719 0.320754
\(987\) 65.6378 2.08927
\(988\) 84.1239 2.67634
\(989\) 42.0286 1.33643
\(990\) −2.24204 −0.0712566
\(991\) 31.1509 0.989540 0.494770 0.869024i \(-0.335252\pi\)
0.494770 + 0.869024i \(0.335252\pi\)
\(992\) −33.7432 −1.07135
\(993\) −35.1271 −1.11473
\(994\) 74.3992 2.35980
\(995\) 1.97787 0.0627028
\(996\) −80.9972 −2.56649
\(997\) 13.1014 0.414927 0.207463 0.978243i \(-0.433479\pi\)
0.207463 + 0.978243i \(0.433479\pi\)
\(998\) 12.3366 0.390508
\(999\) −24.4689 −0.774162
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 \(a_p\))