Properties

Label 619.2.a.b.1.3
Level 619
Weight 2
Character 619.1
Self dual Yes
Analytic conductor 4.943
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 619 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 619.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 619.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.29572 q^{2} +2.37814 q^{3} +3.27033 q^{4} +1.23255 q^{5} -5.45954 q^{6} +1.58895 q^{7} -2.91633 q^{8} +2.65553 q^{9} +O(q^{10})\) \(q-2.29572 q^{2} +2.37814 q^{3} +3.27033 q^{4} +1.23255 q^{5} -5.45954 q^{6} +1.58895 q^{7} -2.91633 q^{8} +2.65553 q^{9} -2.82958 q^{10} +0.886722 q^{11} +7.77730 q^{12} -1.28594 q^{13} -3.64778 q^{14} +2.93116 q^{15} +0.154415 q^{16} +7.29839 q^{17} -6.09636 q^{18} -0.683286 q^{19} +4.03083 q^{20} +3.77874 q^{21} -2.03567 q^{22} +4.28827 q^{23} -6.93543 q^{24} -3.48083 q^{25} +2.95217 q^{26} -0.819191 q^{27} +5.19639 q^{28} -1.56489 q^{29} -6.72913 q^{30} +1.05127 q^{31} +5.47817 q^{32} +2.10875 q^{33} -16.7551 q^{34} +1.95845 q^{35} +8.68448 q^{36} -0.285339 q^{37} +1.56863 q^{38} -3.05815 q^{39} -3.59451 q^{40} +0.174292 q^{41} -8.67492 q^{42} -5.95067 q^{43} +2.89988 q^{44} +3.27306 q^{45} -9.84468 q^{46} -6.98344 q^{47} +0.367219 q^{48} -4.47524 q^{49} +7.99102 q^{50} +17.3566 q^{51} -4.20547 q^{52} +3.12955 q^{53} +1.88063 q^{54} +1.09293 q^{55} -4.63390 q^{56} -1.62495 q^{57} +3.59256 q^{58} +3.82207 q^{59} +9.58587 q^{60} -0.632482 q^{61} -2.41342 q^{62} +4.21950 q^{63} -12.8852 q^{64} -1.58499 q^{65} -4.84109 q^{66} -1.10009 q^{67} +23.8682 q^{68} +10.1981 q^{69} -4.49606 q^{70} +4.39889 q^{71} -7.74441 q^{72} +14.6478 q^{73} +0.655059 q^{74} -8.27789 q^{75} -2.23457 q^{76} +1.40896 q^{77} +7.02066 q^{78} +13.2226 q^{79} +0.190323 q^{80} -9.91474 q^{81} -0.400125 q^{82} +7.13246 q^{83} +12.3577 q^{84} +8.99559 q^{85} +13.6611 q^{86} -3.72153 q^{87} -2.58598 q^{88} +3.05862 q^{89} -7.51404 q^{90} -2.04330 q^{91} +14.0241 q^{92} +2.50006 q^{93} +16.0320 q^{94} -0.842181 q^{95} +13.0278 q^{96} -7.38986 q^{97} +10.2739 q^{98} +2.35472 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + O(q^{10}) \) \( 30q + 9q^{2} + q^{3} + 33q^{4} + 21q^{5} + 6q^{6} + 2q^{7} + 27q^{8} + 43q^{9} + 5q^{10} + 23q^{11} - 6q^{12} + 9q^{13} + 7q^{14} - 2q^{15} + 35q^{16} + 4q^{17} + 10q^{18} - q^{19} + 29q^{20} + 30q^{21} + 4q^{23} + 4q^{24} + 35q^{25} + q^{26} - 5q^{27} - 13q^{28} + 90q^{29} - 31q^{30} + 2q^{31} + 43q^{32} - 6q^{33} - 9q^{34} + 9q^{35} + 33q^{36} + 19q^{37} + 5q^{38} + 32q^{39} - 12q^{40} + 59q^{41} - 25q^{42} - 4q^{43} + 52q^{44} + 30q^{45} - q^{46} + 4q^{47} - 44q^{48} + 30q^{49} + 31q^{50} - 12q^{52} + 34q^{53} - 28q^{54} - 17q^{55} + 2q^{56} - 8q^{57} + 6q^{58} + 13q^{59} - 64q^{60} + 16q^{61} + 28q^{62} - 40q^{63} + 37q^{64} + 31q^{65} - 59q^{66} - 11q^{67} - 52q^{68} + 6q^{69} - 40q^{70} + 42q^{71} + 6q^{72} - 4q^{73} + 16q^{74} - 52q^{75} - 42q^{76} + 29q^{77} - 56q^{78} + 3q^{79} + 21q^{80} + 30q^{81} - 43q^{82} - 11q^{83} - 36q^{84} + 19q^{85} - 11q^{86} - 20q^{87} - 47q^{88} + 58q^{89} - 33q^{90} - 39q^{91} - 7q^{92} - 15q^{93} - 46q^{94} + 23q^{95} - 70q^{96} - 9q^{97} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29572 −1.62332 −0.811660 0.584130i \(-0.801436\pi\)
−0.811660 + 0.584130i \(0.801436\pi\)
\(3\) 2.37814 1.37302 0.686509 0.727121i \(-0.259142\pi\)
0.686509 + 0.727121i \(0.259142\pi\)
\(4\) 3.27033 1.63517
\(5\) 1.23255 0.551211 0.275606 0.961271i \(-0.411122\pi\)
0.275606 + 0.961271i \(0.411122\pi\)
\(6\) −5.45954 −2.22885
\(7\) 1.58895 0.600566 0.300283 0.953850i \(-0.402919\pi\)
0.300283 + 0.953850i \(0.402919\pi\)
\(8\) −2.91633 −1.03108
\(9\) 2.65553 0.885177
\(10\) −2.82958 −0.894792
\(11\) 0.886722 0.267357 0.133678 0.991025i \(-0.457321\pi\)
0.133678 + 0.991025i \(0.457321\pi\)
\(12\) 7.77730 2.24511
\(13\) −1.28594 −0.356657 −0.178328 0.983971i \(-0.557069\pi\)
−0.178328 + 0.983971i \(0.557069\pi\)
\(14\) −3.64778 −0.974911
\(15\) 2.93116 0.756822
\(16\) 0.154415 0.0386037
\(17\) 7.29839 1.77012 0.885059 0.465478i \(-0.154118\pi\)
0.885059 + 0.465478i \(0.154118\pi\)
\(18\) −6.09636 −1.43693
\(19\) −0.683286 −0.156757 −0.0783783 0.996924i \(-0.524974\pi\)
−0.0783783 + 0.996924i \(0.524974\pi\)
\(20\) 4.03083 0.901322
\(21\) 3.77874 0.824588
\(22\) −2.03567 −0.434006
\(23\) 4.28827 0.894167 0.447083 0.894492i \(-0.352463\pi\)
0.447083 + 0.894492i \(0.352463\pi\)
\(24\) −6.93543 −1.41569
\(25\) −3.48083 −0.696166
\(26\) 2.95217 0.578968
\(27\) −0.819191 −0.157653
\(28\) 5.19639 0.982026
\(29\) −1.56489 −0.290593 −0.145297 0.989388i \(-0.546414\pi\)
−0.145297 + 0.989388i \(0.546414\pi\)
\(30\) −6.72913 −1.22856
\(31\) 1.05127 0.188814 0.0944068 0.995534i \(-0.469905\pi\)
0.0944068 + 0.995534i \(0.469905\pi\)
\(32\) 5.47817 0.968413
\(33\) 2.10875 0.367086
\(34\) −16.7551 −2.87347
\(35\) 1.95845 0.331039
\(36\) 8.68448 1.44741
\(37\) −0.285339 −0.0469095 −0.0234547 0.999725i \(-0.507467\pi\)
−0.0234547 + 0.999725i \(0.507467\pi\)
\(38\) 1.56863 0.254466
\(39\) −3.05815 −0.489696
\(40\) −3.59451 −0.568342
\(41\) 0.174292 0.0272198 0.0136099 0.999907i \(-0.495668\pi\)
0.0136099 + 0.999907i \(0.495668\pi\)
\(42\) −8.67492 −1.33857
\(43\) −5.95067 −0.907468 −0.453734 0.891137i \(-0.649908\pi\)
−0.453734 + 0.891137i \(0.649908\pi\)
\(44\) 2.89988 0.437173
\(45\) 3.27306 0.487920
\(46\) −9.84468 −1.45152
\(47\) −6.98344 −1.01864 −0.509320 0.860577i \(-0.670103\pi\)
−0.509320 + 0.860577i \(0.670103\pi\)
\(48\) 0.367219 0.0530036
\(49\) −4.47524 −0.639320
\(50\) 7.99102 1.13010
\(51\) 17.3566 2.43040
\(52\) −4.20547 −0.583194
\(53\) 3.12955 0.429877 0.214938 0.976628i \(-0.431045\pi\)
0.214938 + 0.976628i \(0.431045\pi\)
\(54\) 1.88063 0.255922
\(55\) 1.09293 0.147370
\(56\) −4.63390 −0.619231
\(57\) −1.62495 −0.215230
\(58\) 3.59256 0.471726
\(59\) 3.82207 0.497592 0.248796 0.968556i \(-0.419965\pi\)
0.248796 + 0.968556i \(0.419965\pi\)
\(60\) 9.58587 1.23753
\(61\) −0.632482 −0.0809811 −0.0404905 0.999180i \(-0.512892\pi\)
−0.0404905 + 0.999180i \(0.512892\pi\)
\(62\) −2.41342 −0.306505
\(63\) 4.21950 0.531607
\(64\) −12.8852 −1.61065
\(65\) −1.58499 −0.196593
\(66\) −4.84109 −0.595897
\(67\) −1.10009 −0.134397 −0.0671986 0.997740i \(-0.521406\pi\)
−0.0671986 + 0.997740i \(0.521406\pi\)
\(68\) 23.8682 2.89444
\(69\) 10.1981 1.22771
\(70\) −4.49606 −0.537381
\(71\) 4.39889 0.522052 0.261026 0.965332i \(-0.415939\pi\)
0.261026 + 0.965332i \(0.415939\pi\)
\(72\) −7.74441 −0.912688
\(73\) 14.6478 1.71439 0.857197 0.514988i \(-0.172204\pi\)
0.857197 + 0.514988i \(0.172204\pi\)
\(74\) 0.655059 0.0761490
\(75\) −8.27789 −0.955849
\(76\) −2.23457 −0.256323
\(77\) 1.40896 0.160565
\(78\) 7.02066 0.794934
\(79\) 13.2226 1.48765 0.743827 0.668372i \(-0.233009\pi\)
0.743827 + 0.668372i \(0.233009\pi\)
\(80\) 0.190323 0.0212788
\(81\) −9.91474 −1.10164
\(82\) −0.400125 −0.0441864
\(83\) 7.13246 0.782889 0.391445 0.920202i \(-0.371975\pi\)
0.391445 + 0.920202i \(0.371975\pi\)
\(84\) 12.3577 1.34834
\(85\) 8.99559 0.975709
\(86\) 13.6611 1.47311
\(87\) −3.72153 −0.398990
\(88\) −2.58598 −0.275666
\(89\) 3.05862 0.324213 0.162106 0.986773i \(-0.448171\pi\)
0.162106 + 0.986773i \(0.448171\pi\)
\(90\) −7.51404 −0.792049
\(91\) −2.04330 −0.214196
\(92\) 14.0241 1.46211
\(93\) 2.50006 0.259244
\(94\) 16.0320 1.65358
\(95\) −0.842181 −0.0864060
\(96\) 13.0278 1.32965
\(97\) −7.38986 −0.750327 −0.375163 0.926959i \(-0.622413\pi\)
−0.375163 + 0.926959i \(0.622413\pi\)
\(98\) 10.2739 1.03782
\(99\) 2.35472 0.236658
\(100\) −11.3835 −1.13835
\(101\) 3.26959 0.325336 0.162668 0.986681i \(-0.447990\pi\)
0.162668 + 0.986681i \(0.447990\pi\)
\(102\) −39.8458 −3.94532
\(103\) −6.32956 −0.623670 −0.311835 0.950136i \(-0.600944\pi\)
−0.311835 + 0.950136i \(0.600944\pi\)
\(104\) 3.75024 0.367741
\(105\) 4.65746 0.454522
\(106\) −7.18458 −0.697828
\(107\) 2.25130 0.217641 0.108821 0.994061i \(-0.465293\pi\)
0.108821 + 0.994061i \(0.465293\pi\)
\(108\) −2.67903 −0.257789
\(109\) 10.6348 1.01863 0.509316 0.860580i \(-0.329898\pi\)
0.509316 + 0.860580i \(0.329898\pi\)
\(110\) −2.50905 −0.239229
\(111\) −0.678575 −0.0644075
\(112\) 0.245357 0.0231841
\(113\) −14.5105 −1.36503 −0.682515 0.730872i \(-0.739114\pi\)
−0.682515 + 0.730872i \(0.739114\pi\)
\(114\) 3.73043 0.349386
\(115\) 5.28549 0.492875
\(116\) −5.11772 −0.475169
\(117\) −3.41487 −0.315705
\(118\) −8.77441 −0.807750
\(119\) 11.5968 1.06307
\(120\) −8.54824 −0.780344
\(121\) −10.2137 −0.928520
\(122\) 1.45200 0.131458
\(123\) 0.414489 0.0373732
\(124\) 3.43800 0.308742
\(125\) −10.4530 −0.934946
\(126\) −9.68680 −0.862969
\(127\) −7.90271 −0.701252 −0.350626 0.936516i \(-0.614031\pi\)
−0.350626 + 0.936516i \(0.614031\pi\)
\(128\) 18.6244 1.64618
\(129\) −14.1515 −1.24597
\(130\) 3.63868 0.319134
\(131\) −6.84860 −0.598365 −0.299183 0.954196i \(-0.596714\pi\)
−0.299183 + 0.954196i \(0.596714\pi\)
\(132\) 6.89630 0.600246
\(133\) −1.08571 −0.0941427
\(134\) 2.52550 0.218170
\(135\) −1.00969 −0.0869002
\(136\) −21.2845 −1.82513
\(137\) −9.63629 −0.823284 −0.411642 0.911346i \(-0.635044\pi\)
−0.411642 + 0.911346i \(0.635044\pi\)
\(138\) −23.4120 −1.99296
\(139\) −5.24014 −0.444463 −0.222232 0.974994i \(-0.571334\pi\)
−0.222232 + 0.974994i \(0.571334\pi\)
\(140\) 6.40479 0.541303
\(141\) −16.6076 −1.39861
\(142\) −10.0986 −0.847457
\(143\) −1.14028 −0.0953546
\(144\) 0.410054 0.0341711
\(145\) −1.92880 −0.160178
\(146\) −33.6272 −2.78301
\(147\) −10.6427 −0.877798
\(148\) −0.933154 −0.0767048
\(149\) 6.46539 0.529666 0.264833 0.964294i \(-0.414683\pi\)
0.264833 + 0.964294i \(0.414683\pi\)
\(150\) 19.0037 1.55165
\(151\) −10.4038 −0.846652 −0.423326 0.905977i \(-0.639137\pi\)
−0.423326 + 0.905977i \(0.639137\pi\)
\(152\) 1.99269 0.161628
\(153\) 19.3811 1.56687
\(154\) −3.23457 −0.260649
\(155\) 1.29574 0.104076
\(156\) −10.0012 −0.800735
\(157\) −10.7718 −0.859687 −0.429843 0.902903i \(-0.641431\pi\)
−0.429843 + 0.902903i \(0.641431\pi\)
\(158\) −30.3553 −2.41494
\(159\) 7.44250 0.590229
\(160\) 6.75209 0.533800
\(161\) 6.81385 0.537006
\(162\) 22.7615 1.78831
\(163\) 3.38162 0.264869 0.132435 0.991192i \(-0.457721\pi\)
0.132435 + 0.991192i \(0.457721\pi\)
\(164\) 0.569991 0.0445089
\(165\) 2.59913 0.202342
\(166\) −16.3741 −1.27088
\(167\) −17.7906 −1.37667 −0.688337 0.725391i \(-0.741659\pi\)
−0.688337 + 0.725391i \(0.741659\pi\)
\(168\) −11.0200 −0.850215
\(169\) −11.3463 −0.872796
\(170\) −20.6514 −1.58389
\(171\) −1.81449 −0.138757
\(172\) −19.4607 −1.48386
\(173\) 17.4205 1.32446 0.662228 0.749302i \(-0.269611\pi\)
0.662228 + 0.749302i \(0.269611\pi\)
\(174\) 8.54359 0.647688
\(175\) −5.53086 −0.418094
\(176\) 0.136923 0.0103210
\(177\) 9.08941 0.683202
\(178\) −7.02173 −0.526301
\(179\) −4.36884 −0.326543 −0.163271 0.986581i \(-0.552205\pi\)
−0.163271 + 0.986581i \(0.552205\pi\)
\(180\) 10.7040 0.797830
\(181\) 24.1693 1.79649 0.898244 0.439496i \(-0.144843\pi\)
0.898244 + 0.439496i \(0.144843\pi\)
\(182\) 4.69085 0.347709
\(183\) −1.50413 −0.111188
\(184\) −12.5060 −0.921957
\(185\) −0.351693 −0.0258570
\(186\) −5.73945 −0.420837
\(187\) 6.47164 0.473253
\(188\) −22.8382 −1.66565
\(189\) −1.30165 −0.0946812
\(190\) 1.93341 0.140265
\(191\) −3.26291 −0.236096 −0.118048 0.993008i \(-0.537664\pi\)
−0.118048 + 0.993008i \(0.537664\pi\)
\(192\) −30.6427 −2.21145
\(193\) −9.05710 −0.651945 −0.325972 0.945379i \(-0.605692\pi\)
−0.325972 + 0.945379i \(0.605692\pi\)
\(194\) 16.9651 1.21802
\(195\) −3.76931 −0.269926
\(196\) −14.6355 −1.04540
\(197\) −21.7562 −1.55006 −0.775031 0.631923i \(-0.782266\pi\)
−0.775031 + 0.631923i \(0.782266\pi\)
\(198\) −5.40578 −0.384172
\(199\) −1.25088 −0.0886724 −0.0443362 0.999017i \(-0.514117\pi\)
−0.0443362 + 0.999017i \(0.514117\pi\)
\(200\) 10.1513 0.717802
\(201\) −2.61616 −0.184530
\(202\) −7.50606 −0.528124
\(203\) −2.48653 −0.174520
\(204\) 56.7617 3.97412
\(205\) 0.214822 0.0150038
\(206\) 14.5309 1.01242
\(207\) 11.3877 0.791496
\(208\) −0.198569 −0.0137683
\(209\) −0.605885 −0.0419099
\(210\) −10.6922 −0.737834
\(211\) 0.992377 0.0683181 0.0341590 0.999416i \(-0.489125\pi\)
0.0341590 + 0.999416i \(0.489125\pi\)
\(212\) 10.2347 0.702920
\(213\) 10.4612 0.716786
\(214\) −5.16835 −0.353301
\(215\) −7.33446 −0.500206
\(216\) 2.38903 0.162553
\(217\) 1.67041 0.113395
\(218\) −24.4146 −1.65357
\(219\) 34.8345 2.35389
\(220\) 3.57423 0.240975
\(221\) −9.38532 −0.631325
\(222\) 1.55782 0.104554
\(223\) 3.28542 0.220008 0.110004 0.993931i \(-0.464914\pi\)
0.110004 + 0.993931i \(0.464914\pi\)
\(224\) 8.70453 0.581596
\(225\) −9.24346 −0.616231
\(226\) 33.3120 2.21588
\(227\) 18.7607 1.24519 0.622596 0.782543i \(-0.286078\pi\)
0.622596 + 0.782543i \(0.286078\pi\)
\(228\) −5.31412 −0.351936
\(229\) 7.32209 0.483858 0.241929 0.970294i \(-0.422220\pi\)
0.241929 + 0.970294i \(0.422220\pi\)
\(230\) −12.1340 −0.800093
\(231\) 3.35069 0.220459
\(232\) 4.56375 0.299625
\(233\) 2.94045 0.192635 0.0963176 0.995351i \(-0.469294\pi\)
0.0963176 + 0.995351i \(0.469294\pi\)
\(234\) 7.83958 0.512490
\(235\) −8.60741 −0.561486
\(236\) 12.4995 0.813645
\(237\) 31.4450 2.04258
\(238\) −26.6229 −1.72571
\(239\) 21.9756 1.42148 0.710740 0.703455i \(-0.248360\pi\)
0.710740 + 0.703455i \(0.248360\pi\)
\(240\) 0.452615 0.0292161
\(241\) −6.85708 −0.441703 −0.220852 0.975307i \(-0.570884\pi\)
−0.220852 + 0.975307i \(0.570884\pi\)
\(242\) 23.4479 1.50729
\(243\) −21.1210 −1.35492
\(244\) −2.06843 −0.132418
\(245\) −5.51594 −0.352400
\(246\) −0.951551 −0.0606687
\(247\) 0.878668 0.0559083
\(248\) −3.06585 −0.194682
\(249\) 16.9620 1.07492
\(250\) 23.9972 1.51772
\(251\) 4.78887 0.302271 0.151135 0.988513i \(-0.451707\pi\)
0.151135 + 0.988513i \(0.451707\pi\)
\(252\) 13.7992 0.869267
\(253\) 3.80251 0.239062
\(254\) 18.1424 1.13836
\(255\) 21.3927 1.33967
\(256\) −16.9861 −1.06163
\(257\) −22.0796 −1.37729 −0.688644 0.725099i \(-0.741794\pi\)
−0.688644 + 0.725099i \(0.741794\pi\)
\(258\) 32.4879 2.02261
\(259\) −0.453389 −0.0281722
\(260\) −5.18343 −0.321463
\(261\) −4.15562 −0.257227
\(262\) 15.7225 0.971338
\(263\) −13.2804 −0.818904 −0.409452 0.912332i \(-0.634280\pi\)
−0.409452 + 0.912332i \(0.634280\pi\)
\(264\) −6.14980 −0.378494
\(265\) 3.85731 0.236953
\(266\) 2.49248 0.152824
\(267\) 7.27381 0.445150
\(268\) −3.59766 −0.219762
\(269\) −10.6510 −0.649401 −0.324700 0.945817i \(-0.605263\pi\)
−0.324700 + 0.945817i \(0.605263\pi\)
\(270\) 2.31797 0.141067
\(271\) −26.8964 −1.63384 −0.816920 0.576752i \(-0.804320\pi\)
−0.816920 + 0.576752i \(0.804320\pi\)
\(272\) 1.12698 0.0683331
\(273\) −4.85925 −0.294095
\(274\) 22.1222 1.33645
\(275\) −3.08653 −0.186125
\(276\) 33.3512 2.00751
\(277\) −21.0454 −1.26450 −0.632248 0.774766i \(-0.717867\pi\)
−0.632248 + 0.774766i \(0.717867\pi\)
\(278\) 12.0299 0.721506
\(279\) 2.79168 0.167134
\(280\) −5.71149 −0.341327
\(281\) 6.75138 0.402753 0.201377 0.979514i \(-0.435458\pi\)
0.201377 + 0.979514i \(0.435458\pi\)
\(282\) 38.1264 2.27039
\(283\) −30.4441 −1.80971 −0.904857 0.425716i \(-0.860022\pi\)
−0.904857 + 0.425716i \(0.860022\pi\)
\(284\) 14.3858 0.853642
\(285\) −2.00282 −0.118637
\(286\) 2.61775 0.154791
\(287\) 0.276940 0.0163473
\(288\) 14.5475 0.857217
\(289\) 36.2664 2.13332
\(290\) 4.42799 0.260020
\(291\) −17.5741 −1.03021
\(292\) 47.9032 2.80332
\(293\) 11.4521 0.669040 0.334520 0.942389i \(-0.391426\pi\)
0.334520 + 0.942389i \(0.391426\pi\)
\(294\) 24.4328 1.42495
\(295\) 4.71088 0.274278
\(296\) 0.832143 0.0483673
\(297\) −0.726395 −0.0421497
\(298\) −14.8427 −0.859817
\(299\) −5.51448 −0.318911
\(300\) −27.0715 −1.56297
\(301\) −9.45530 −0.544994
\(302\) 23.8843 1.37439
\(303\) 7.77552 0.446692
\(304\) −0.105510 −0.00605139
\(305\) −0.779563 −0.0446377
\(306\) −44.4936 −2.54353
\(307\) −12.0514 −0.687808 −0.343904 0.939005i \(-0.611749\pi\)
−0.343904 + 0.939005i \(0.611749\pi\)
\(308\) 4.60775 0.262551
\(309\) −15.0525 −0.856310
\(310\) −2.97465 −0.168949
\(311\) −26.8292 −1.52135 −0.760673 0.649136i \(-0.775131\pi\)
−0.760673 + 0.649136i \(0.775131\pi\)
\(312\) 8.91858 0.504915
\(313\) 1.71581 0.0969835 0.0484917 0.998824i \(-0.484559\pi\)
0.0484917 + 0.998824i \(0.484559\pi\)
\(314\) 24.7292 1.39555
\(315\) 5.20073 0.293028
\(316\) 43.2422 2.43256
\(317\) 0.888576 0.0499074 0.0249537 0.999689i \(-0.492056\pi\)
0.0249537 + 0.999689i \(0.492056\pi\)
\(318\) −17.0859 −0.958130
\(319\) −1.38763 −0.0776921
\(320\) −15.8816 −0.887806
\(321\) 5.35390 0.298825
\(322\) −15.6427 −0.871733
\(323\) −4.98689 −0.277478
\(324\) −32.4245 −1.80136
\(325\) 4.47616 0.248293
\(326\) −7.76326 −0.429967
\(327\) 25.2911 1.39860
\(328\) −0.508292 −0.0280657
\(329\) −11.0963 −0.611760
\(330\) −5.96687 −0.328465
\(331\) −31.2292 −1.71651 −0.858256 0.513222i \(-0.828452\pi\)
−0.858256 + 0.513222i \(0.828452\pi\)
\(332\) 23.3255 1.28015
\(333\) −0.757727 −0.0415232
\(334\) 40.8421 2.23478
\(335\) −1.35591 −0.0740812
\(336\) 0.583493 0.0318321
\(337\) −14.8366 −0.808202 −0.404101 0.914714i \(-0.632416\pi\)
−0.404101 + 0.914714i \(0.632416\pi\)
\(338\) 26.0480 1.41683
\(339\) −34.5079 −1.87421
\(340\) 29.4186 1.59545
\(341\) 0.932184 0.0504806
\(342\) 4.16556 0.225248
\(343\) −18.2336 −0.984520
\(344\) 17.3541 0.935671
\(345\) 12.5696 0.676726
\(346\) −39.9926 −2.15002
\(347\) 14.5384 0.780461 0.390231 0.920717i \(-0.372395\pi\)
0.390231 + 0.920717i \(0.372395\pi\)
\(348\) −12.1706 −0.652415
\(349\) −2.48605 −0.133075 −0.0665375 0.997784i \(-0.521195\pi\)
−0.0665375 + 0.997784i \(0.521195\pi\)
\(350\) 12.6973 0.678700
\(351\) 1.05343 0.0562281
\(352\) 4.85761 0.258912
\(353\) −11.3461 −0.603893 −0.301947 0.953325i \(-0.597636\pi\)
−0.301947 + 0.953325i \(0.597636\pi\)
\(354\) −20.8667 −1.10906
\(355\) 5.42183 0.287761
\(356\) 10.0027 0.530142
\(357\) 27.5787 1.45962
\(358\) 10.0296 0.530083
\(359\) 8.73284 0.460902 0.230451 0.973084i \(-0.425980\pi\)
0.230451 + 0.973084i \(0.425980\pi\)
\(360\) −9.54534 −0.503084
\(361\) −18.5331 −0.975427
\(362\) −55.4859 −2.91628
\(363\) −24.2896 −1.27487
\(364\) −6.68227 −0.350246
\(365\) 18.0541 0.944993
\(366\) 3.45306 0.180494
\(367\) 11.4963 0.600104 0.300052 0.953923i \(-0.402996\pi\)
0.300052 + 0.953923i \(0.402996\pi\)
\(368\) 0.662173 0.0345182
\(369\) 0.462837 0.0240943
\(370\) 0.807390 0.0419742
\(371\) 4.97269 0.258169
\(372\) 8.17604 0.423908
\(373\) 9.94088 0.514719 0.257360 0.966316i \(-0.417147\pi\)
0.257360 + 0.966316i \(0.417147\pi\)
\(374\) −14.8571 −0.768241
\(375\) −24.8587 −1.28370
\(376\) 20.3660 1.05030
\(377\) 2.01237 0.103642
\(378\) 2.98823 0.153698
\(379\) 25.8225 1.32641 0.663207 0.748436i \(-0.269195\pi\)
0.663207 + 0.748436i \(0.269195\pi\)
\(380\) −2.75421 −0.141288
\(381\) −18.7937 −0.962832
\(382\) 7.49072 0.383259
\(383\) 5.98909 0.306028 0.153014 0.988224i \(-0.451102\pi\)
0.153014 + 0.988224i \(0.451102\pi\)
\(384\) 44.2914 2.26024
\(385\) 1.73660 0.0885054
\(386\) 20.7926 1.05831
\(387\) −15.8022 −0.803270
\(388\) −24.1673 −1.22691
\(389\) 8.96719 0.454655 0.227327 0.973818i \(-0.427001\pi\)
0.227327 + 0.973818i \(0.427001\pi\)
\(390\) 8.65328 0.438176
\(391\) 31.2975 1.58278
\(392\) 13.0513 0.659190
\(393\) −16.2869 −0.821566
\(394\) 49.9461 2.51625
\(395\) 16.2974 0.820011
\(396\) 7.70072 0.386976
\(397\) 35.7120 1.79233 0.896167 0.443717i \(-0.146340\pi\)
0.896167 + 0.443717i \(0.146340\pi\)
\(398\) 2.87167 0.143944
\(399\) −2.58196 −0.129260
\(400\) −0.537492 −0.0268746
\(401\) 29.9885 1.49755 0.748776 0.662823i \(-0.230642\pi\)
0.748776 + 0.662823i \(0.230642\pi\)
\(402\) 6.00597 0.299551
\(403\) −1.35187 −0.0673417
\(404\) 10.6926 0.531979
\(405\) −12.2204 −0.607235
\(406\) 5.70839 0.283303
\(407\) −0.253017 −0.0125416
\(408\) −50.6175 −2.50594
\(409\) 26.2183 1.29641 0.648206 0.761465i \(-0.275520\pi\)
0.648206 + 0.761465i \(0.275520\pi\)
\(410\) −0.493172 −0.0243560
\(411\) −22.9164 −1.13038
\(412\) −20.6998 −1.01980
\(413\) 6.07308 0.298837
\(414\) −26.1429 −1.28485
\(415\) 8.79108 0.431537
\(416\) −7.04462 −0.345391
\(417\) −12.4618 −0.610256
\(418\) 1.39094 0.0680332
\(419\) −12.5753 −0.614344 −0.307172 0.951654i \(-0.599383\pi\)
−0.307172 + 0.951654i \(0.599383\pi\)
\(420\) 15.2315 0.743219
\(421\) 27.1337 1.32242 0.661208 0.750202i \(-0.270044\pi\)
0.661208 + 0.750202i \(0.270044\pi\)
\(422\) −2.27822 −0.110902
\(423\) −18.5448 −0.901677
\(424\) −9.12681 −0.443237
\(425\) −25.4045 −1.23230
\(426\) −24.0159 −1.16357
\(427\) −1.00498 −0.0486345
\(428\) 7.36250 0.355880
\(429\) −2.71173 −0.130924
\(430\) 16.8379 0.811995
\(431\) −4.65747 −0.224342 −0.112171 0.993689i \(-0.535780\pi\)
−0.112171 + 0.993689i \(0.535780\pi\)
\(432\) −0.126495 −0.00608600
\(433\) −1.07692 −0.0517535 −0.0258767 0.999665i \(-0.508238\pi\)
−0.0258767 + 0.999665i \(0.508238\pi\)
\(434\) −3.83480 −0.184076
\(435\) −4.58695 −0.219928
\(436\) 34.7794 1.66563
\(437\) −2.93012 −0.140167
\(438\) −79.9702 −3.82112
\(439\) 5.07319 0.242130 0.121065 0.992645i \(-0.461369\pi\)
0.121065 + 0.992645i \(0.461369\pi\)
\(440\) −3.18733 −0.151950
\(441\) −11.8842 −0.565912
\(442\) 21.5461 1.02484
\(443\) −35.8484 −1.70321 −0.851603 0.524187i \(-0.824369\pi\)
−0.851603 + 0.524187i \(0.824369\pi\)
\(444\) −2.21917 −0.105317
\(445\) 3.76989 0.178710
\(446\) −7.54240 −0.357143
\(447\) 15.3756 0.727240
\(448\) −20.4739 −0.967300
\(449\) 27.4850 1.29710 0.648548 0.761174i \(-0.275377\pi\)
0.648548 + 0.761174i \(0.275377\pi\)
\(450\) 21.2204 1.00034
\(451\) 0.154548 0.00727739
\(452\) −47.4541 −2.23205
\(453\) −24.7417 −1.16247
\(454\) −43.0694 −2.02135
\(455\) −2.51846 −0.118067
\(456\) 4.73889 0.221919
\(457\) −14.6879 −0.687072 −0.343536 0.939139i \(-0.611625\pi\)
−0.343536 + 0.939139i \(0.611625\pi\)
\(458\) −16.8095 −0.785456
\(459\) −5.97877 −0.279065
\(460\) 17.2853 0.805932
\(461\) −6.30188 −0.293508 −0.146754 0.989173i \(-0.546883\pi\)
−0.146754 + 0.989173i \(0.546883\pi\)
\(462\) −7.69225 −0.357876
\(463\) 29.8205 1.38587 0.692937 0.720998i \(-0.256316\pi\)
0.692937 + 0.720998i \(0.256316\pi\)
\(464\) −0.241643 −0.0112180
\(465\) 3.08144 0.142898
\(466\) −6.75045 −0.312709
\(467\) −37.0003 −1.71217 −0.856085 0.516835i \(-0.827110\pi\)
−0.856085 + 0.516835i \(0.827110\pi\)
\(468\) −11.1678 −0.516230
\(469\) −1.74798 −0.0807144
\(470\) 19.7602 0.911470
\(471\) −25.6169 −1.18037
\(472\) −11.1464 −0.513056
\(473\) −5.27659 −0.242618
\(474\) −72.1891 −3.31575
\(475\) 2.37840 0.109129
\(476\) 37.9253 1.73830
\(477\) 8.31062 0.380517
\(478\) −50.4497 −2.30752
\(479\) −4.15963 −0.190058 −0.0950292 0.995474i \(-0.530294\pi\)
−0.0950292 + 0.995474i \(0.530294\pi\)
\(480\) 16.0574 0.732916
\(481\) 0.366930 0.0167306
\(482\) 15.7419 0.717026
\(483\) 16.2043 0.737319
\(484\) −33.4023 −1.51829
\(485\) −9.10834 −0.413588
\(486\) 48.4880 2.19946
\(487\) −10.7350 −0.486448 −0.243224 0.969970i \(-0.578205\pi\)
−0.243224 + 0.969970i \(0.578205\pi\)
\(488\) 1.84453 0.0834979
\(489\) 8.04196 0.363670
\(490\) 12.6631 0.572059
\(491\) 25.8440 1.16632 0.583161 0.812357i \(-0.301816\pi\)
0.583161 + 0.812357i \(0.301816\pi\)
\(492\) 1.35552 0.0611114
\(493\) −11.4212 −0.514385
\(494\) −2.01718 −0.0907571
\(495\) 2.90230 0.130449
\(496\) 0.162332 0.00728891
\(497\) 6.98960 0.313527
\(498\) −38.9399 −1.74494
\(499\) −34.0984 −1.52645 −0.763226 0.646132i \(-0.776386\pi\)
−0.763226 + 0.646132i \(0.776386\pi\)
\(500\) −34.1848 −1.52879
\(501\) −42.3084 −1.89020
\(502\) −10.9939 −0.490682
\(503\) −6.79558 −0.303000 −0.151500 0.988457i \(-0.548410\pi\)
−0.151500 + 0.988457i \(0.548410\pi\)
\(504\) −12.3055 −0.548129
\(505\) 4.02991 0.179329
\(506\) −8.72949 −0.388073
\(507\) −26.9832 −1.19836
\(508\) −25.8445 −1.14666
\(509\) 24.6142 1.09101 0.545503 0.838109i \(-0.316338\pi\)
0.545503 + 0.838109i \(0.316338\pi\)
\(510\) −49.1118 −2.17471
\(511\) 23.2746 1.02961
\(512\) 1.74656 0.0771878
\(513\) 0.559742 0.0247132
\(514\) 50.6886 2.23578
\(515\) −7.80146 −0.343774
\(516\) −46.2801 −2.03737
\(517\) −6.19237 −0.272340
\(518\) 1.04085 0.0457325
\(519\) 41.4283 1.81850
\(520\) 4.62234 0.202703
\(521\) 43.9291 1.92457 0.962284 0.272047i \(-0.0877006\pi\)
0.962284 + 0.272047i \(0.0877006\pi\)
\(522\) 9.54015 0.417561
\(523\) 33.5193 1.46570 0.732849 0.680392i \(-0.238190\pi\)
0.732849 + 0.680392i \(0.238190\pi\)
\(524\) −22.3972 −0.978427
\(525\) −13.1531 −0.574050
\(526\) 30.4881 1.32934
\(527\) 7.67257 0.334223
\(528\) 0.325622 0.0141709
\(529\) −4.61071 −0.200466
\(530\) −8.85531 −0.384650
\(531\) 10.1496 0.440457
\(532\) −3.55062 −0.153939
\(533\) −0.224129 −0.00970812
\(534\) −16.6986 −0.722621
\(535\) 2.77483 0.119966
\(536\) 3.20822 0.138574
\(537\) −10.3897 −0.448349
\(538\) 24.4516 1.05419
\(539\) −3.96830 −0.170927
\(540\) −3.30202 −0.142096
\(541\) 0.414672 0.0178281 0.00891407 0.999960i \(-0.497163\pi\)
0.00891407 + 0.999960i \(0.497163\pi\)
\(542\) 61.7466 2.65224
\(543\) 57.4778 2.46661
\(544\) 39.9818 1.71421
\(545\) 13.1079 0.561481
\(546\) 11.1555 0.477410
\(547\) −36.8701 −1.57645 −0.788226 0.615386i \(-0.789000\pi\)
−0.788226 + 0.615386i \(0.789000\pi\)
\(548\) −31.5139 −1.34621
\(549\) −1.67958 −0.0716826
\(550\) 7.08581 0.302140
\(551\) 1.06927 0.0455524
\(552\) −29.7410 −1.26586
\(553\) 21.0100 0.893434
\(554\) 48.3143 2.05268
\(555\) −0.836375 −0.0355021
\(556\) −17.1370 −0.726771
\(557\) −0.0876469 −0.00371372 −0.00185686 0.999998i \(-0.500591\pi\)
−0.00185686 + 0.999998i \(0.500591\pi\)
\(558\) −6.40892 −0.271311
\(559\) 7.65223 0.323655
\(560\) 0.302414 0.0127793
\(561\) 15.3904 0.649785
\(562\) −15.4993 −0.653798
\(563\) 20.8536 0.878875 0.439437 0.898273i \(-0.355178\pi\)
0.439437 + 0.898273i \(0.355178\pi\)
\(564\) −54.3123 −2.28696
\(565\) −17.8848 −0.752419
\(566\) 69.8911 2.93774
\(567\) −15.7540 −0.661606
\(568\) −12.8286 −0.538276
\(569\) −22.3044 −0.935049 −0.467525 0.883980i \(-0.654854\pi\)
−0.467525 + 0.883980i \(0.654854\pi\)
\(570\) 4.59792 0.192586
\(571\) −15.7505 −0.659136 −0.329568 0.944132i \(-0.606903\pi\)
−0.329568 + 0.944132i \(0.606903\pi\)
\(572\) −3.72908 −0.155921
\(573\) −7.75964 −0.324164
\(574\) −0.635777 −0.0265368
\(575\) −14.9268 −0.622489
\(576\) −34.2170 −1.42571
\(577\) −4.92947 −0.205216 −0.102608 0.994722i \(-0.532719\pi\)
−0.102608 + 0.994722i \(0.532719\pi\)
\(578\) −83.2576 −3.46306
\(579\) −21.5390 −0.895131
\(580\) −6.30782 −0.261918
\(581\) 11.3331 0.470177
\(582\) 40.3452 1.67236
\(583\) 2.77504 0.114931
\(584\) −42.7178 −1.76768
\(585\) −4.20898 −0.174020
\(586\) −26.2909 −1.08607
\(587\) −4.32731 −0.178607 −0.0893036 0.996004i \(-0.528464\pi\)
−0.0893036 + 0.996004i \(0.528464\pi\)
\(588\) −34.8053 −1.43535
\(589\) −0.718318 −0.0295978
\(590\) −10.8149 −0.445241
\(591\) −51.7391 −2.12826
\(592\) −0.0440606 −0.00181088
\(593\) −42.4209 −1.74202 −0.871009 0.491267i \(-0.836534\pi\)
−0.871009 + 0.491267i \(0.836534\pi\)
\(594\) 1.66760 0.0684224
\(595\) 14.2935 0.585978
\(596\) 21.1440 0.866092
\(597\) −2.97476 −0.121749
\(598\) 12.6597 0.517694
\(599\) −12.1937 −0.498222 −0.249111 0.968475i \(-0.580138\pi\)
−0.249111 + 0.968475i \(0.580138\pi\)
\(600\) 24.1411 0.985555
\(601\) 35.7522 1.45836 0.729182 0.684320i \(-0.239901\pi\)
0.729182 + 0.684320i \(0.239901\pi\)
\(602\) 21.7067 0.884700
\(603\) −2.92132 −0.118965
\(604\) −34.0240 −1.38442
\(605\) −12.5889 −0.511811
\(606\) −17.8504 −0.725124
\(607\) 38.1033 1.54656 0.773282 0.634062i \(-0.218614\pi\)
0.773282 + 0.634062i \(0.218614\pi\)
\(608\) −3.74316 −0.151805
\(609\) −5.91332 −0.239620
\(610\) 1.78966 0.0724612
\(611\) 8.98032 0.363305
\(612\) 63.3827 2.56209
\(613\) 46.0775 1.86105 0.930527 0.366224i \(-0.119349\pi\)
0.930527 + 0.366224i \(0.119349\pi\)
\(614\) 27.6666 1.11653
\(615\) 0.510877 0.0206005
\(616\) −4.10898 −0.165556
\(617\) −17.4268 −0.701575 −0.350788 0.936455i \(-0.614086\pi\)
−0.350788 + 0.936455i \(0.614086\pi\)
\(618\) 34.5564 1.39006
\(619\) 1.00000 0.0401934
\(620\) 4.23749 0.170182
\(621\) −3.51291 −0.140968
\(622\) 61.5924 2.46963
\(623\) 4.85999 0.194711
\(624\) −0.472224 −0.0189041
\(625\) 4.52035 0.180814
\(626\) −3.93903 −0.157435
\(627\) −1.44088 −0.0575431
\(628\) −35.2275 −1.40573
\(629\) −2.08252 −0.0830353
\(630\) −11.9394 −0.475678
\(631\) −2.18545 −0.0870015 −0.0435008 0.999053i \(-0.513851\pi\)
−0.0435008 + 0.999053i \(0.513851\pi\)
\(632\) −38.5614 −1.53389
\(633\) 2.36001 0.0938019
\(634\) −2.03992 −0.0810156
\(635\) −9.74045 −0.386538
\(636\) 24.3395 0.965122
\(637\) 5.75492 0.228018
\(638\) 3.18560 0.126119
\(639\) 11.6814 0.462108
\(640\) 22.9555 0.907394
\(641\) 26.7023 1.05468 0.527339 0.849655i \(-0.323190\pi\)
0.527339 + 0.849655i \(0.323190\pi\)
\(642\) −12.2910 −0.485089
\(643\) −24.5173 −0.966867 −0.483434 0.875381i \(-0.660611\pi\)
−0.483434 + 0.875381i \(0.660611\pi\)
\(644\) 22.2835 0.878095
\(645\) −17.4424 −0.686792
\(646\) 11.4485 0.450435
\(647\) −5.35518 −0.210534 −0.105267 0.994444i \(-0.533570\pi\)
−0.105267 + 0.994444i \(0.533570\pi\)
\(648\) 28.9147 1.13588
\(649\) 3.38912 0.133034
\(650\) −10.2760 −0.403058
\(651\) 3.97247 0.155693
\(652\) 11.0590 0.433105
\(653\) 31.0856 1.21648 0.608238 0.793755i \(-0.291877\pi\)
0.608238 + 0.793755i \(0.291877\pi\)
\(654\) −58.0613 −2.27037
\(655\) −8.44121 −0.329826
\(656\) 0.0269132 0.00105078
\(657\) 38.8977 1.51754
\(658\) 25.4741 0.993083
\(659\) 27.8723 1.08575 0.542875 0.839814i \(-0.317336\pi\)
0.542875 + 0.839814i \(0.317336\pi\)
\(660\) 8.50001 0.330862
\(661\) 39.9814 1.55510 0.777549 0.628822i \(-0.216463\pi\)
0.777549 + 0.628822i \(0.216463\pi\)
\(662\) 71.6935 2.78645
\(663\) −22.3196 −0.866820
\(664\) −20.8006 −0.807221
\(665\) −1.33818 −0.0518925
\(666\) 1.73953 0.0674054
\(667\) −6.71069 −0.259839
\(668\) −58.1810 −2.25109
\(669\) 7.81317 0.302075
\(670\) 3.11279 0.120257
\(671\) −0.560836 −0.0216508
\(672\) 20.7006 0.798541
\(673\) 3.95407 0.152418 0.0762092 0.997092i \(-0.475718\pi\)
0.0762092 + 0.997092i \(0.475718\pi\)
\(674\) 34.0607 1.31197
\(675\) 2.85147 0.109753
\(676\) −37.1063 −1.42717
\(677\) −15.9051 −0.611281 −0.305641 0.952147i \(-0.598871\pi\)
−0.305641 + 0.952147i \(0.598871\pi\)
\(678\) 79.2204 3.04244
\(679\) −11.7421 −0.450621
\(680\) −26.2341 −1.00603
\(681\) 44.6156 1.70967
\(682\) −2.14003 −0.0819462
\(683\) −45.2333 −1.73080 −0.865401 0.501079i \(-0.832937\pi\)
−0.865401 + 0.501079i \(0.832937\pi\)
\(684\) −5.93398 −0.226892
\(685\) −11.8772 −0.453803
\(686\) 41.8592 1.59819
\(687\) 17.4129 0.664345
\(688\) −0.918871 −0.0350316
\(689\) −4.02443 −0.153319
\(690\) −28.8563 −1.09854
\(691\) 11.3211 0.430676 0.215338 0.976540i \(-0.430915\pi\)
0.215338 + 0.976540i \(0.430915\pi\)
\(692\) 56.9709 2.16571
\(693\) 3.74153 0.142129
\(694\) −33.3761 −1.26694
\(695\) −6.45871 −0.244993
\(696\) 10.8532 0.411390
\(697\) 1.27205 0.0481822
\(698\) 5.70727 0.216023
\(699\) 6.99279 0.264492
\(700\) −18.0878 −0.683653
\(701\) 26.9662 1.01850 0.509251 0.860618i \(-0.329923\pi\)
0.509251 + 0.860618i \(0.329923\pi\)
\(702\) −2.41839 −0.0912763
\(703\) 0.194968 0.00735337
\(704\) −11.4256 −0.430617
\(705\) −20.4696 −0.770930
\(706\) 26.0475 0.980311
\(707\) 5.19521 0.195386
\(708\) 29.7254 1.11715
\(709\) 32.3145 1.21360 0.606799 0.794855i \(-0.292453\pi\)
0.606799 + 0.794855i \(0.292453\pi\)
\(710\) −12.4470 −0.467128
\(711\) 35.1129 1.31684
\(712\) −8.91994 −0.334289
\(713\) 4.50813 0.168831
\(714\) −63.3129 −2.36943
\(715\) −1.40544 −0.0525605
\(716\) −14.2876 −0.533952
\(717\) 52.2609 1.95172
\(718\) −20.0482 −0.748191
\(719\) −7.42994 −0.277090 −0.138545 0.990356i \(-0.544243\pi\)
−0.138545 + 0.990356i \(0.544243\pi\)
\(720\) 0.505410 0.0188355
\(721\) −10.0573 −0.374555
\(722\) 42.5469 1.58343
\(723\) −16.3071 −0.606466
\(724\) 79.0416 2.93756
\(725\) 5.44713 0.202301
\(726\) 55.7622 2.06953
\(727\) −36.0936 −1.33864 −0.669318 0.742976i \(-0.733414\pi\)
−0.669318 + 0.742976i \(0.733414\pi\)
\(728\) 5.95894 0.220853
\(729\) −20.4845 −0.758685
\(730\) −41.4471 −1.53403
\(731\) −43.4303 −1.60633
\(732\) −4.91900 −0.181812
\(733\) 30.9713 1.14395 0.571975 0.820271i \(-0.306177\pi\)
0.571975 + 0.820271i \(0.306177\pi\)
\(734\) −26.3924 −0.974160
\(735\) −13.1177 −0.483852
\(736\) 23.4919 0.865923
\(737\) −0.975473 −0.0359320
\(738\) −1.06254 −0.0391128
\(739\) 19.8451 0.730013 0.365007 0.931005i \(-0.381067\pi\)
0.365007 + 0.931005i \(0.381067\pi\)
\(740\) −1.15015 −0.0422805
\(741\) 2.08959 0.0767631
\(742\) −11.4159 −0.419092
\(743\) −38.6318 −1.41726 −0.708631 0.705579i \(-0.750687\pi\)
−0.708631 + 0.705579i \(0.750687\pi\)
\(744\) −7.29101 −0.267301
\(745\) 7.96889 0.291957
\(746\) −22.8215 −0.835554
\(747\) 18.9405 0.692996
\(748\) 21.1644 0.773848
\(749\) 3.57720 0.130708
\(750\) 57.0686 2.08385
\(751\) −12.4844 −0.455562 −0.227781 0.973712i \(-0.573147\pi\)
−0.227781 + 0.973712i \(0.573147\pi\)
\(752\) −1.07835 −0.0393233
\(753\) 11.3886 0.415023
\(754\) −4.61983 −0.168244
\(755\) −12.8232 −0.466684
\(756\) −4.25684 −0.154820
\(757\) −3.77413 −0.137173 −0.0685865 0.997645i \(-0.521849\pi\)
−0.0685865 + 0.997645i \(0.521849\pi\)
\(758\) −59.2813 −2.15319
\(759\) 9.04288 0.328236
\(760\) 2.45608 0.0890914
\(761\) 24.0444 0.871608 0.435804 0.900041i \(-0.356464\pi\)
0.435804 + 0.900041i \(0.356464\pi\)
\(762\) 43.1451 1.56298
\(763\) 16.8982 0.611756
\(764\) −10.6708 −0.386056
\(765\) 23.8881 0.863676
\(766\) −13.7493 −0.496781
\(767\) −4.91497 −0.177469
\(768\) −40.3953 −1.45764
\(769\) 48.4431 1.74690 0.873451 0.486913i \(-0.161877\pi\)
0.873451 + 0.486913i \(0.161877\pi\)
\(770\) −3.98675 −0.143673
\(771\) −52.5083 −1.89104
\(772\) −29.6197 −1.06604
\(773\) 27.3322 0.983070 0.491535 0.870858i \(-0.336436\pi\)
0.491535 + 0.870858i \(0.336436\pi\)
\(774\) 36.2774 1.30396
\(775\) −3.65929 −0.131446
\(776\) 21.5513 0.773646
\(777\) −1.07822 −0.0386810
\(778\) −20.5862 −0.738050
\(779\) −0.119091 −0.00426688
\(780\) −12.3269 −0.441374
\(781\) 3.90059 0.139574
\(782\) −71.8503 −2.56936
\(783\) 1.28195 0.0458130
\(784\) −0.691044 −0.0246801
\(785\) −13.2768 −0.473869
\(786\) 37.3902 1.33366
\(787\) 48.7456 1.73759 0.868797 0.495168i \(-0.164894\pi\)
0.868797 + 0.495168i \(0.164894\pi\)
\(788\) −71.1499 −2.53461
\(789\) −31.5826 −1.12437
\(790\) −37.4143 −1.33114
\(791\) −23.0564 −0.819790
\(792\) −6.86714 −0.244013
\(793\) 0.813337 0.0288825
\(794\) −81.9848 −2.90953
\(795\) 9.17322 0.325341
\(796\) −4.09079 −0.144994
\(797\) 1.26368 0.0447620 0.0223810 0.999750i \(-0.492875\pi\)
0.0223810 + 0.999750i \(0.492875\pi\)
\(798\) 5.92745 0.209830
\(799\) −50.9679 −1.80311
\(800\) −19.0686 −0.674176
\(801\) 8.12226 0.286986
\(802\) −68.8452 −2.43101
\(803\) 12.9885 0.458355
\(804\) −8.55572 −0.301737
\(805\) 8.39837 0.296004
\(806\) 3.10353 0.109317
\(807\) −25.3294 −0.891639
\(808\) −9.53520 −0.335447
\(809\) 51.9851 1.82770 0.913850 0.406053i \(-0.133095\pi\)
0.913850 + 0.406053i \(0.133095\pi\)
\(810\) 28.0546 0.985737
\(811\) −34.5911 −1.21466 −0.607329 0.794450i \(-0.707759\pi\)
−0.607329 + 0.794450i \(0.707759\pi\)
\(812\) −8.13180 −0.285370
\(813\) −63.9633 −2.24329
\(814\) 0.580855 0.0203590
\(815\) 4.16800 0.145999
\(816\) 2.68011 0.0938226
\(817\) 4.06601 0.142252
\(818\) −60.1899 −2.10449
\(819\) −5.42605 −0.189601
\(820\) 0.702540 0.0245338
\(821\) −15.5898 −0.544089 −0.272044 0.962285i \(-0.587700\pi\)
−0.272044 + 0.962285i \(0.587700\pi\)
\(822\) 52.6097 1.83497
\(823\) 42.7901 1.49157 0.745784 0.666188i \(-0.232075\pi\)
0.745784 + 0.666188i \(0.232075\pi\)
\(824\) 18.4591 0.643053
\(825\) −7.34019 −0.255553
\(826\) −13.9421 −0.485107
\(827\) 47.0912 1.63752 0.818761 0.574135i \(-0.194662\pi\)
0.818761 + 0.574135i \(0.194662\pi\)
\(828\) 37.2414 1.29423
\(829\) −17.7774 −0.617436 −0.308718 0.951154i \(-0.599900\pi\)
−0.308718 + 0.951154i \(0.599900\pi\)
\(830\) −20.1819 −0.700523
\(831\) −50.0488 −1.73617
\(832\) 16.5696 0.574448
\(833\) −32.6621 −1.13167
\(834\) 28.6087 0.990640
\(835\) −21.9277 −0.758838
\(836\) −1.98145 −0.0685298
\(837\) −0.861190 −0.0297671
\(838\) 28.8694 0.997277
\(839\) 33.1147 1.14325 0.571624 0.820516i \(-0.306314\pi\)
0.571624 + 0.820516i \(0.306314\pi\)
\(840\) −13.5827 −0.468648
\(841\) −26.5511 −0.915556
\(842\) −62.2914 −2.14670
\(843\) 16.0557 0.552988
\(844\) 3.24541 0.111711
\(845\) −13.9849 −0.481095
\(846\) 42.5736 1.46371
\(847\) −16.2291 −0.557638
\(848\) 0.483249 0.0165948
\(849\) −72.4002 −2.48477
\(850\) 58.3215 2.00041
\(851\) −1.22361 −0.0419449
\(852\) 34.2115 1.17207
\(853\) 37.2476 1.27533 0.637666 0.770313i \(-0.279900\pi\)
0.637666 + 0.770313i \(0.279900\pi\)
\(854\) 2.30716 0.0789493
\(855\) −2.23644 −0.0764846
\(856\) −6.56553 −0.224405
\(857\) −48.8641 −1.66916 −0.834582 0.550883i \(-0.814291\pi\)
−0.834582 + 0.550883i \(0.814291\pi\)
\(858\) 6.22538 0.212531
\(859\) −51.1884 −1.74652 −0.873262 0.487250i \(-0.838000\pi\)
−0.873262 + 0.487250i \(0.838000\pi\)
\(860\) −23.9861 −0.817921
\(861\) 0.658602 0.0224451
\(862\) 10.6922 0.364179
\(863\) −5.69769 −0.193951 −0.0969757 0.995287i \(-0.530917\pi\)
−0.0969757 + 0.995287i \(0.530917\pi\)
\(864\) −4.48767 −0.152673
\(865\) 21.4716 0.730055
\(866\) 2.47231 0.0840124
\(867\) 86.2466 2.92909
\(868\) 5.46281 0.185420
\(869\) 11.7247 0.397734
\(870\) 10.5304 0.357013
\(871\) 1.41465 0.0479337
\(872\) −31.0147 −1.05029
\(873\) −19.6240 −0.664173
\(874\) 6.72673 0.227535
\(875\) −16.6093 −0.561497
\(876\) 113.920 3.84901
\(877\) −19.4427 −0.656533 −0.328266 0.944585i \(-0.606464\pi\)
−0.328266 + 0.944585i \(0.606464\pi\)
\(878\) −11.6466 −0.393054
\(879\) 27.2347 0.918603
\(880\) 0.168764 0.00568903
\(881\) 5.37476 0.181080 0.0905401 0.995893i \(-0.471141\pi\)
0.0905401 + 0.995893i \(0.471141\pi\)
\(882\) 27.2827 0.918656
\(883\) −9.77223 −0.328862 −0.164431 0.986389i \(-0.552579\pi\)
−0.164431 + 0.986389i \(0.552579\pi\)
\(884\) −30.6931 −1.03232
\(885\) 11.2031 0.376588
\(886\) 82.2978 2.76485
\(887\) 36.0013 1.20881 0.604403 0.796679i \(-0.293412\pi\)
0.604403 + 0.796679i \(0.293412\pi\)
\(888\) 1.97895 0.0664092
\(889\) −12.5570 −0.421148
\(890\) −8.65460 −0.290103
\(891\) −8.79162 −0.294530
\(892\) 10.7444 0.359749
\(893\) 4.77169 0.159679
\(894\) −35.2980 −1.18054
\(895\) −5.38480 −0.179994
\(896\) 29.5933 0.988641
\(897\) −13.1142 −0.437870
\(898\) −63.0978 −2.10560
\(899\) −1.64512 −0.0548680
\(900\) −30.2292 −1.00764
\(901\) 22.8407 0.760933
\(902\) −0.354799 −0.0118135
\(903\) −22.4860 −0.748287
\(904\) 42.3173 1.40745
\(905\) 29.7897 0.990244
\(906\) 56.8001 1.88706
\(907\) −47.8956 −1.59035 −0.795174 0.606381i \(-0.792621\pi\)
−0.795174 + 0.606381i \(0.792621\pi\)
\(908\) 61.3538 2.03610
\(909\) 8.68250 0.287980
\(910\) 5.78168 0.191661
\(911\) −33.6374 −1.11446 −0.557229 0.830359i \(-0.688135\pi\)
−0.557229 + 0.830359i \(0.688135\pi\)
\(912\) −0.250916 −0.00830866
\(913\) 6.32451 0.209311
\(914\) 33.7194 1.11534
\(915\) −1.85391 −0.0612883
\(916\) 23.9457 0.791188
\(917\) −10.8821 −0.359358
\(918\) 13.7256 0.453012
\(919\) 2.11560 0.0697872 0.0348936 0.999391i \(-0.488891\pi\)
0.0348936 + 0.999391i \(0.488891\pi\)
\(920\) −15.4142 −0.508193
\(921\) −28.6598 −0.944373
\(922\) 14.4674 0.476457
\(923\) −5.65672 −0.186193
\(924\) 10.9579 0.360487
\(925\) 0.993218 0.0326568
\(926\) −68.4595 −2.24972
\(927\) −16.8083 −0.552058
\(928\) −8.57275 −0.281414
\(929\) 11.7523 0.385580 0.192790 0.981240i \(-0.438246\pi\)
0.192790 + 0.981240i \(0.438246\pi\)
\(930\) −7.07413 −0.231970
\(931\) 3.05787 0.100218
\(932\) 9.61625 0.314991
\(933\) −63.8035 −2.08883
\(934\) 84.9424 2.77940
\(935\) 7.97659 0.260862
\(936\) 9.95889 0.325516
\(937\) 17.1081 0.558898 0.279449 0.960160i \(-0.409848\pi\)
0.279449 + 0.960160i \(0.409848\pi\)
\(938\) 4.01288 0.131025
\(939\) 4.08044 0.133160
\(940\) −28.1491 −0.918122
\(941\) 24.0508 0.784034 0.392017 0.919958i \(-0.371777\pi\)
0.392017 + 0.919958i \(0.371777\pi\)
\(942\) 58.8093 1.91611
\(943\) 0.747410 0.0243390
\(944\) 0.590185 0.0192089
\(945\) −1.60434 −0.0521893
\(946\) 12.1136 0.393846
\(947\) −5.70842 −0.185499 −0.0927494 0.995689i \(-0.529566\pi\)
−0.0927494 + 0.995689i \(0.529566\pi\)
\(948\) 102.836 3.33995
\(949\) −18.8363 −0.611451
\(950\) −5.46015 −0.177151
\(951\) 2.11315 0.0685237
\(952\) −33.8200 −1.09611
\(953\) 56.3967 1.82687 0.913435 0.406985i \(-0.133420\pi\)
0.913435 + 0.406985i \(0.133420\pi\)
\(954\) −19.0789 −0.617701
\(955\) −4.02168 −0.130139
\(956\) 71.8674 2.32436
\(957\) −3.29996 −0.106673
\(958\) 9.54936 0.308526
\(959\) −15.3116 −0.494436
\(960\) −37.7685 −1.21897
\(961\) −29.8948 −0.964349
\(962\) −0.842370 −0.0271591
\(963\) 5.97840 0.192651
\(964\) −22.4249 −0.722258
\(965\) −11.1633 −0.359359
\(966\) −37.2004 −1.19690
\(967\) −20.5830 −0.661906 −0.330953 0.943647i \(-0.607370\pi\)
−0.330953 + 0.943647i \(0.607370\pi\)
\(968\) 29.7866 0.957378
\(969\) −11.8595 −0.380982
\(970\) 20.9102 0.671386
\(971\) −9.40675 −0.301877 −0.150938 0.988543i \(-0.548230\pi\)
−0.150938 + 0.988543i \(0.548230\pi\)
\(972\) −69.0729 −2.21551
\(973\) −8.32631 −0.266929
\(974\) 24.6445 0.789661
\(975\) 10.6449 0.340910
\(976\) −0.0976646 −0.00312617
\(977\) 30.9387 0.989816 0.494908 0.868945i \(-0.335202\pi\)
0.494908 + 0.868945i \(0.335202\pi\)
\(978\) −18.4621 −0.590353
\(979\) 2.71214 0.0866805
\(980\) −18.0390 −0.576234
\(981\) 28.2411 0.901670
\(982\) −59.3305 −1.89331
\(983\) 18.0662 0.576222 0.288111 0.957597i \(-0.406973\pi\)
0.288111 + 0.957597i \(0.406973\pi\)
\(984\) −1.20879 −0.0385347
\(985\) −26.8155 −0.854412
\(986\) 26.2199 0.835011
\(987\) −26.3886 −0.839958
\(988\) 2.87354 0.0914194
\(989\) −25.5181 −0.811428
\(990\) −6.66287 −0.211760
\(991\) −36.4417 −1.15761 −0.578804 0.815467i \(-0.696480\pi\)
−0.578804 + 0.815467i \(0.696480\pi\)
\(992\) 5.75903 0.182850
\(993\) −74.2673 −2.35680
\(994\) −16.0462 −0.508954
\(995\) −1.54176 −0.0488772
\(996\) 55.4713 1.75767
\(997\) 12.7205 0.402861 0.201431 0.979503i \(-0.435441\pi\)
0.201431 + 0.979503i \(0.435441\pi\)
\(998\) 78.2803 2.47792
\(999\) 0.233747 0.00739543
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 \(a_p\))