Properties

Label 6025.2.a.h.1.3
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.01020\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.01020 q^{2} -0.500591 q^{3} +2.04092 q^{4} +1.00629 q^{6} +0.852319 q^{7} -0.0822476 q^{8} -2.74941 q^{9} +O(q^{10})\) \(q-2.01020 q^{2} -0.500591 q^{3} +2.04092 q^{4} +1.00629 q^{6} +0.852319 q^{7} -0.0822476 q^{8} -2.74941 q^{9} +0.719546 q^{11} -1.02166 q^{12} +1.93309 q^{13} -1.71333 q^{14} -3.91650 q^{16} -0.439843 q^{17} +5.52687 q^{18} +5.85432 q^{19} -0.426663 q^{21} -1.44643 q^{22} +7.09215 q^{23} +0.0411724 q^{24} -3.88589 q^{26} +2.87810 q^{27} +1.73951 q^{28} +10.0222 q^{29} +5.69622 q^{31} +8.03745 q^{32} -0.360198 q^{33} +0.884173 q^{34} -5.61131 q^{36} +3.17197 q^{37} -11.7684 q^{38} -0.967685 q^{39} -6.39435 q^{41} +0.857679 q^{42} -4.29669 q^{43} +1.46853 q^{44} -14.2567 q^{46} +0.642479 q^{47} +1.96056 q^{48} -6.27355 q^{49} +0.220181 q^{51} +3.94526 q^{52} -0.729714 q^{53} -5.78557 q^{54} -0.0701012 q^{56} -2.93062 q^{57} -20.1467 q^{58} +0.348904 q^{59} +1.12656 q^{61} -11.4506 q^{62} -2.34337 q^{63} -8.32390 q^{64} +0.724072 q^{66} -12.5549 q^{67} -0.897682 q^{68} -3.55026 q^{69} +0.552289 q^{71} +0.226132 q^{72} +10.9882 q^{73} -6.37630 q^{74} +11.9482 q^{76} +0.613283 q^{77} +1.94524 q^{78} +10.9569 q^{79} +6.80748 q^{81} +12.8539 q^{82} -6.62478 q^{83} -0.870783 q^{84} +8.63722 q^{86} -5.01703 q^{87} -0.0591810 q^{88} +12.5513 q^{89} +1.64760 q^{91} +14.4745 q^{92} -2.85148 q^{93} -1.29151 q^{94} -4.02347 q^{96} +5.00536 q^{97} +12.6111 q^{98} -1.97833 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 3q^{2} - q^{3} + 13q^{4} - q^{6} - 3q^{7} - 9q^{8} + 15q^{9} + O(q^{10}) \) \( 12q - 3q^{2} - q^{3} + 13q^{4} - q^{6} - 3q^{7} - 9q^{8} + 15q^{9} + 22q^{11} + 7q^{12} + 5q^{13} + 6q^{14} + 15q^{16} + 4q^{17} + q^{18} - 6q^{19} - 14q^{21} + 12q^{22} - 32q^{23} - 15q^{24} + 8q^{26} + 5q^{27} + 11q^{28} + 6q^{29} + 8q^{31} - q^{32} + 24q^{33} - 19q^{34} - 8q^{36} + 8q^{37} + 10q^{38} + 31q^{39} - q^{41} + 49q^{42} + 2q^{43} + 42q^{44} - 25q^{46} - 34q^{47} + 49q^{48} - 9q^{49} - 3q^{51} + 41q^{52} - 5q^{53} - 40q^{54} + q^{56} + 22q^{57} + 33q^{58} + 26q^{59} - 26q^{61} + 17q^{62} + 4q^{63} + 13q^{64} - 2q^{66} - 6q^{67} + 35q^{68} - 2q^{69} + 94q^{71} - 17q^{72} + 22q^{73} + 26q^{74} - 20q^{76} + 7q^{77} - 54q^{78} + 9q^{79} + 4q^{81} - 15q^{82} + 8q^{83} + 2q^{84} + 9q^{86} - 4q^{87} - 6q^{88} - 3q^{89} - 20q^{91} - 36q^{92} - 12q^{93} + 48q^{94} - 23q^{96} + 29q^{97} - 28q^{98} + 36q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.01020 −1.42143 −0.710714 0.703481i \(-0.751628\pi\)
−0.710714 + 0.703481i \(0.751628\pi\)
\(3\) −0.500591 −0.289016 −0.144508 0.989504i \(-0.546160\pi\)
−0.144508 + 0.989504i \(0.546160\pi\)
\(4\) 2.04092 1.02046
\(5\) 0 0
\(6\) 1.00629 0.410816
\(7\) 0.852319 0.322146 0.161073 0.986942i \(-0.448505\pi\)
0.161073 + 0.986942i \(0.448505\pi\)
\(8\) −0.0822476 −0.0290789
\(9\) −2.74941 −0.916470
\(10\) 0 0
\(11\) 0.719546 0.216951 0.108476 0.994099i \(-0.465403\pi\)
0.108476 + 0.994099i \(0.465403\pi\)
\(12\) −1.02166 −0.294929
\(13\) 1.93309 0.536141 0.268071 0.963399i \(-0.413614\pi\)
0.268071 + 0.963399i \(0.413614\pi\)
\(14\) −1.71333 −0.457908
\(15\) 0 0
\(16\) −3.91650 −0.979124
\(17\) −0.439843 −0.106678 −0.0533388 0.998576i \(-0.516986\pi\)
−0.0533388 + 0.998576i \(0.516986\pi\)
\(18\) 5.52687 1.30270
\(19\) 5.85432 1.34307 0.671537 0.740971i \(-0.265635\pi\)
0.671537 + 0.740971i \(0.265635\pi\)
\(20\) 0 0
\(21\) −0.426663 −0.0931055
\(22\) −1.44643 −0.308381
\(23\) 7.09215 1.47881 0.739407 0.673258i \(-0.235106\pi\)
0.739407 + 0.673258i \(0.235106\pi\)
\(24\) 0.0411724 0.00840428
\(25\) 0 0
\(26\) −3.88589 −0.762086
\(27\) 2.87810 0.553891
\(28\) 1.73951 0.328737
\(29\) 10.0222 1.86108 0.930540 0.366190i \(-0.119338\pi\)
0.930540 + 0.366190i \(0.119338\pi\)
\(30\) 0 0
\(31\) 5.69622 1.02307 0.511536 0.859262i \(-0.329077\pi\)
0.511536 + 0.859262i \(0.329077\pi\)
\(32\) 8.03745 1.42083
\(33\) −0.360198 −0.0627025
\(34\) 0.884173 0.151634
\(35\) 0 0
\(36\) −5.61131 −0.935218
\(37\) 3.17197 0.521468 0.260734 0.965411i \(-0.416035\pi\)
0.260734 + 0.965411i \(0.416035\pi\)
\(38\) −11.7684 −1.90908
\(39\) −0.967685 −0.154954
\(40\) 0 0
\(41\) −6.39435 −0.998630 −0.499315 0.866421i \(-0.666415\pi\)
−0.499315 + 0.866421i \(0.666415\pi\)
\(42\) 0.857679 0.132343
\(43\) −4.29669 −0.655239 −0.327620 0.944810i \(-0.606246\pi\)
−0.327620 + 0.944810i \(0.606246\pi\)
\(44\) 1.46853 0.221390
\(45\) 0 0
\(46\) −14.2567 −2.10203
\(47\) 0.642479 0.0937152 0.0468576 0.998902i \(-0.485079\pi\)
0.0468576 + 0.998902i \(0.485079\pi\)
\(48\) 1.96056 0.282983
\(49\) −6.27355 −0.896222
\(50\) 0 0
\(51\) 0.220181 0.0308315
\(52\) 3.94526 0.547110
\(53\) −0.729714 −0.100234 −0.0501170 0.998743i \(-0.515959\pi\)
−0.0501170 + 0.998743i \(0.515959\pi\)
\(54\) −5.78557 −0.787316
\(55\) 0 0
\(56\) −0.0701012 −0.00936766
\(57\) −2.93062 −0.388170
\(58\) −20.1467 −2.64539
\(59\) 0.348904 0.0454234 0.0227117 0.999742i \(-0.492770\pi\)
0.0227117 + 0.999742i \(0.492770\pi\)
\(60\) 0 0
\(61\) 1.12656 0.144241 0.0721204 0.997396i \(-0.477023\pi\)
0.0721204 + 0.997396i \(0.477023\pi\)
\(62\) −11.4506 −1.45422
\(63\) −2.34337 −0.295237
\(64\) −8.32390 −1.04049
\(65\) 0 0
\(66\) 0.724072 0.0891270
\(67\) −12.5549 −1.53383 −0.766915 0.641749i \(-0.778209\pi\)
−0.766915 + 0.641749i \(0.778209\pi\)
\(68\) −0.897682 −0.108860
\(69\) −3.55026 −0.427401
\(70\) 0 0
\(71\) 0.552289 0.0655446 0.0327723 0.999463i \(-0.489566\pi\)
0.0327723 + 0.999463i \(0.489566\pi\)
\(72\) 0.226132 0.0266499
\(73\) 10.9882 1.28607 0.643037 0.765835i \(-0.277674\pi\)
0.643037 + 0.765835i \(0.277674\pi\)
\(74\) −6.37630 −0.741229
\(75\) 0 0
\(76\) 11.9482 1.37055
\(77\) 0.613283 0.0698901
\(78\) 1.94524 0.220255
\(79\) 10.9569 1.23275 0.616375 0.787453i \(-0.288600\pi\)
0.616375 + 0.787453i \(0.288600\pi\)
\(80\) 0 0
\(81\) 6.80748 0.756386
\(82\) 12.8539 1.41948
\(83\) −6.62478 −0.727164 −0.363582 0.931562i \(-0.618446\pi\)
−0.363582 + 0.931562i \(0.618446\pi\)
\(84\) −0.870783 −0.0950102
\(85\) 0 0
\(86\) 8.63722 0.931375
\(87\) −5.01703 −0.537882
\(88\) −0.0591810 −0.00630871
\(89\) 12.5513 1.33044 0.665219 0.746648i \(-0.268338\pi\)
0.665219 + 0.746648i \(0.268338\pi\)
\(90\) 0 0
\(91\) 1.64760 0.172716
\(92\) 14.4745 1.50907
\(93\) −2.85148 −0.295684
\(94\) −1.29151 −0.133209
\(95\) 0 0
\(96\) −4.02347 −0.410644
\(97\) 5.00536 0.508217 0.254108 0.967176i \(-0.418218\pi\)
0.254108 + 0.967176i \(0.418218\pi\)
\(98\) 12.6111 1.27391
\(99\) −1.97833 −0.198829
\(100\) 0 0
\(101\) 0.191991 0.0191038 0.00955192 0.999954i \(-0.496959\pi\)
0.00955192 + 0.999954i \(0.496959\pi\)
\(102\) −0.442609 −0.0438248
\(103\) 3.97237 0.391409 0.195705 0.980663i \(-0.437301\pi\)
0.195705 + 0.980663i \(0.437301\pi\)
\(104\) −0.158992 −0.0155904
\(105\) 0 0
\(106\) 1.46687 0.142475
\(107\) −6.70922 −0.648605 −0.324303 0.945953i \(-0.605130\pi\)
−0.324303 + 0.945953i \(0.605130\pi\)
\(108\) 5.87396 0.565222
\(109\) 4.03051 0.386053 0.193027 0.981194i \(-0.438170\pi\)
0.193027 + 0.981194i \(0.438170\pi\)
\(110\) 0 0
\(111\) −1.58786 −0.150713
\(112\) −3.33810 −0.315421
\(113\) −0.430322 −0.0404813 −0.0202407 0.999795i \(-0.506443\pi\)
−0.0202407 + 0.999795i \(0.506443\pi\)
\(114\) 5.89114 0.551756
\(115\) 0 0
\(116\) 20.4545 1.89915
\(117\) −5.31484 −0.491357
\(118\) −0.701368 −0.0645661
\(119\) −0.374886 −0.0343658
\(120\) 0 0
\(121\) −10.4823 −0.952932
\(122\) −2.26461 −0.205028
\(123\) 3.20095 0.288620
\(124\) 11.6255 1.04400
\(125\) 0 0
\(126\) 4.71065 0.419658
\(127\) 0.0290958 0.00258183 0.00129092 0.999999i \(-0.499589\pi\)
0.00129092 + 0.999999i \(0.499589\pi\)
\(128\) 0.657843 0.0581457
\(129\) 2.15088 0.189375
\(130\) 0 0
\(131\) −7.50804 −0.655980 −0.327990 0.944681i \(-0.606371\pi\)
−0.327990 + 0.944681i \(0.606371\pi\)
\(132\) −0.735134 −0.0639852
\(133\) 4.98975 0.432666
\(134\) 25.2380 2.18023
\(135\) 0 0
\(136\) 0.0361760 0.00310207
\(137\) 2.79071 0.238427 0.119213 0.992869i \(-0.461963\pi\)
0.119213 + 0.992869i \(0.461963\pi\)
\(138\) 7.13675 0.607520
\(139\) 5.56312 0.471858 0.235929 0.971770i \(-0.424187\pi\)
0.235929 + 0.971770i \(0.424187\pi\)
\(140\) 0 0
\(141\) −0.321619 −0.0270852
\(142\) −1.11021 −0.0931669
\(143\) 1.39094 0.116317
\(144\) 10.7680 0.897337
\(145\) 0 0
\(146\) −22.0886 −1.82806
\(147\) 3.14048 0.259023
\(148\) 6.47372 0.532136
\(149\) 14.8309 1.21500 0.607499 0.794321i \(-0.292173\pi\)
0.607499 + 0.794321i \(0.292173\pi\)
\(150\) 0 0
\(151\) −19.6745 −1.60109 −0.800543 0.599276i \(-0.795455\pi\)
−0.800543 + 0.599276i \(0.795455\pi\)
\(152\) −0.481504 −0.0390551
\(153\) 1.20931 0.0977667
\(154\) −1.23282 −0.0993437
\(155\) 0 0
\(156\) −1.97496 −0.158124
\(157\) −14.3437 −1.14475 −0.572377 0.819991i \(-0.693978\pi\)
−0.572377 + 0.819991i \(0.693978\pi\)
\(158\) −22.0256 −1.75227
\(159\) 0.365288 0.0289692
\(160\) 0 0
\(161\) 6.04477 0.476395
\(162\) −13.6844 −1.07515
\(163\) −4.99007 −0.390853 −0.195426 0.980718i \(-0.562609\pi\)
−0.195426 + 0.980718i \(0.562609\pi\)
\(164\) −13.0503 −1.01906
\(165\) 0 0
\(166\) 13.3172 1.03361
\(167\) −15.6290 −1.20941 −0.604703 0.796451i \(-0.706708\pi\)
−0.604703 + 0.796451i \(0.706708\pi\)
\(168\) 0.0350920 0.00270741
\(169\) −9.26318 −0.712552
\(170\) 0 0
\(171\) −16.0959 −1.23089
\(172\) −8.76918 −0.668644
\(173\) −0.833365 −0.0633596 −0.0316798 0.999498i \(-0.510086\pi\)
−0.0316798 + 0.999498i \(0.510086\pi\)
\(174\) 10.0853 0.764561
\(175\) 0 0
\(176\) −2.81810 −0.212422
\(177\) −0.174658 −0.0131281
\(178\) −25.2307 −1.89112
\(179\) 14.9985 1.12104 0.560520 0.828141i \(-0.310601\pi\)
0.560520 + 0.828141i \(0.310601\pi\)
\(180\) 0 0
\(181\) −14.9752 −1.11310 −0.556550 0.830814i \(-0.687875\pi\)
−0.556550 + 0.830814i \(0.687875\pi\)
\(182\) −3.31202 −0.245503
\(183\) −0.563944 −0.0416879
\(184\) −0.583312 −0.0430023
\(185\) 0 0
\(186\) 5.73204 0.420294
\(187\) −0.316487 −0.0231438
\(188\) 1.31125 0.0956324
\(189\) 2.45306 0.178434
\(190\) 0 0
\(191\) 8.51858 0.616383 0.308191 0.951324i \(-0.400276\pi\)
0.308191 + 0.951324i \(0.400276\pi\)
\(192\) 4.16687 0.300718
\(193\) 23.5303 1.69375 0.846874 0.531793i \(-0.178482\pi\)
0.846874 + 0.531793i \(0.178482\pi\)
\(194\) −10.0618 −0.722394
\(195\) 0 0
\(196\) −12.8038 −0.914556
\(197\) 26.7548 1.90620 0.953102 0.302649i \(-0.0978710\pi\)
0.953102 + 0.302649i \(0.0978710\pi\)
\(198\) 3.97684 0.282622
\(199\) −19.5915 −1.38880 −0.694401 0.719589i \(-0.744330\pi\)
−0.694401 + 0.719589i \(0.744330\pi\)
\(200\) 0 0
\(201\) 6.28488 0.443301
\(202\) −0.385941 −0.0271547
\(203\) 8.54213 0.599540
\(204\) 0.449371 0.0314623
\(205\) 0 0
\(206\) −7.98527 −0.556360
\(207\) −19.4992 −1.35529
\(208\) −7.57092 −0.524949
\(209\) 4.21246 0.291382
\(210\) 0 0
\(211\) 4.58617 0.315725 0.157862 0.987461i \(-0.449540\pi\)
0.157862 + 0.987461i \(0.449540\pi\)
\(212\) −1.48928 −0.102284
\(213\) −0.276471 −0.0189435
\(214\) 13.4869 0.921946
\(215\) 0 0
\(216\) −0.236717 −0.0161065
\(217\) 4.85500 0.329579
\(218\) −8.10215 −0.548747
\(219\) −5.50060 −0.371696
\(220\) 0 0
\(221\) −0.850254 −0.0571943
\(222\) 3.19191 0.214227
\(223\) 11.8124 0.791018 0.395509 0.918462i \(-0.370568\pi\)
0.395509 + 0.918462i \(0.370568\pi\)
\(224\) 6.85047 0.457716
\(225\) 0 0
\(226\) 0.865035 0.0575413
\(227\) 10.4668 0.694703 0.347352 0.937735i \(-0.387081\pi\)
0.347352 + 0.937735i \(0.387081\pi\)
\(228\) −5.98114 −0.396111
\(229\) −28.8373 −1.90562 −0.952811 0.303563i \(-0.901824\pi\)
−0.952811 + 0.303563i \(0.901824\pi\)
\(230\) 0 0
\(231\) −0.307004 −0.0201994
\(232\) −0.824304 −0.0541182
\(233\) −0.483058 −0.0316462 −0.0158231 0.999875i \(-0.505037\pi\)
−0.0158231 + 0.999875i \(0.505037\pi\)
\(234\) 10.6839 0.698429
\(235\) 0 0
\(236\) 0.712084 0.0463527
\(237\) −5.48494 −0.356285
\(238\) 0.753597 0.0488485
\(239\) −2.08293 −0.134734 −0.0673668 0.997728i \(-0.521460\pi\)
−0.0673668 + 0.997728i \(0.521460\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 21.0715 1.35452
\(243\) −12.0421 −0.772499
\(244\) 2.29921 0.147192
\(245\) 0 0
\(246\) −6.43456 −0.410253
\(247\) 11.3169 0.720077
\(248\) −0.468501 −0.0297498
\(249\) 3.31631 0.210162
\(250\) 0 0
\(251\) −9.67130 −0.610447 −0.305223 0.952281i \(-0.598731\pi\)
−0.305223 + 0.952281i \(0.598731\pi\)
\(252\) −4.78262 −0.301277
\(253\) 5.10313 0.320831
\(254\) −0.0584884 −0.00366989
\(255\) 0 0
\(256\) 15.3254 0.957838
\(257\) 16.0352 1.00025 0.500123 0.865954i \(-0.333288\pi\)
0.500123 + 0.865954i \(0.333288\pi\)
\(258\) −4.32371 −0.269183
\(259\) 2.70353 0.167989
\(260\) 0 0
\(261\) −27.5552 −1.70562
\(262\) 15.0927 0.932429
\(263\) −26.9402 −1.66120 −0.830602 0.556867i \(-0.812003\pi\)
−0.830602 + 0.556867i \(0.812003\pi\)
\(264\) 0.0296254 0.00182332
\(265\) 0 0
\(266\) −10.0304 −0.615004
\(267\) −6.28308 −0.384518
\(268\) −25.6236 −1.56521
\(269\) 30.7223 1.87317 0.936585 0.350441i \(-0.113968\pi\)
0.936585 + 0.350441i \(0.113968\pi\)
\(270\) 0 0
\(271\) −32.2539 −1.95928 −0.979641 0.200757i \(-0.935660\pi\)
−0.979641 + 0.200757i \(0.935660\pi\)
\(272\) 1.72264 0.104451
\(273\) −0.824776 −0.0499177
\(274\) −5.60990 −0.338906
\(275\) 0 0
\(276\) −7.24579 −0.436145
\(277\) −9.84003 −0.591230 −0.295615 0.955307i \(-0.595525\pi\)
−0.295615 + 0.955307i \(0.595525\pi\)
\(278\) −11.1830 −0.670712
\(279\) −15.6612 −0.937614
\(280\) 0 0
\(281\) 0.0623558 0.00371983 0.00185992 0.999998i \(-0.499408\pi\)
0.00185992 + 0.999998i \(0.499408\pi\)
\(282\) 0.646519 0.0384997
\(283\) 23.1136 1.37396 0.686979 0.726677i \(-0.258936\pi\)
0.686979 + 0.726677i \(0.258936\pi\)
\(284\) 1.12717 0.0668855
\(285\) 0 0
\(286\) −2.79608 −0.165336
\(287\) −5.45002 −0.321705
\(288\) −22.0982 −1.30215
\(289\) −16.8065 −0.988620
\(290\) 0 0
\(291\) −2.50564 −0.146883
\(292\) 22.4260 1.31238
\(293\) 7.59717 0.443831 0.221916 0.975066i \(-0.428769\pi\)
0.221916 + 0.975066i \(0.428769\pi\)
\(294\) −6.31301 −0.368182
\(295\) 0 0
\(296\) −0.260887 −0.0151637
\(297\) 2.07093 0.120167
\(298\) −29.8132 −1.72703
\(299\) 13.7097 0.792854
\(300\) 0 0
\(301\) −3.66215 −0.211083
\(302\) 39.5497 2.27583
\(303\) −0.0961090 −0.00552132
\(304\) −22.9284 −1.31504
\(305\) 0 0
\(306\) −2.43095 −0.138968
\(307\) 15.3566 0.876447 0.438224 0.898866i \(-0.355608\pi\)
0.438224 + 0.898866i \(0.355608\pi\)
\(308\) 1.25166 0.0713198
\(309\) −1.98853 −0.113124
\(310\) 0 0
\(311\) 25.0513 1.42053 0.710263 0.703936i \(-0.248576\pi\)
0.710263 + 0.703936i \(0.248576\pi\)
\(312\) 0.0795897 0.00450588
\(313\) 8.95197 0.505995 0.252997 0.967467i \(-0.418584\pi\)
0.252997 + 0.967467i \(0.418584\pi\)
\(314\) 28.8338 1.62718
\(315\) 0 0
\(316\) 22.3622 1.25797
\(317\) −20.7326 −1.16446 −0.582228 0.813025i \(-0.697819\pi\)
−0.582228 + 0.813025i \(0.697819\pi\)
\(318\) −0.734303 −0.0411777
\(319\) 7.21146 0.403764
\(320\) 0 0
\(321\) 3.35858 0.187457
\(322\) −12.1512 −0.677161
\(323\) −2.57498 −0.143276
\(324\) 13.8935 0.771860
\(325\) 0 0
\(326\) 10.0311 0.555569
\(327\) −2.01764 −0.111576
\(328\) 0.525920 0.0290391
\(329\) 0.547597 0.0301900
\(330\) 0 0
\(331\) 6.99950 0.384727 0.192364 0.981324i \(-0.438385\pi\)
0.192364 + 0.981324i \(0.438385\pi\)
\(332\) −13.5206 −0.742040
\(333\) −8.72103 −0.477910
\(334\) 31.4174 1.71908
\(335\) 0 0
\(336\) 1.67102 0.0911618
\(337\) −1.75653 −0.0956843 −0.0478421 0.998855i \(-0.515234\pi\)
−0.0478421 + 0.998855i \(0.515234\pi\)
\(338\) 18.6209 1.01284
\(339\) 0.215415 0.0116998
\(340\) 0 0
\(341\) 4.09870 0.221957
\(342\) 32.3561 1.74962
\(343\) −11.3133 −0.610861
\(344\) 0.353393 0.0190536
\(345\) 0 0
\(346\) 1.67523 0.0900611
\(347\) 11.0359 0.592440 0.296220 0.955120i \(-0.404274\pi\)
0.296220 + 0.955120i \(0.404274\pi\)
\(348\) −10.2393 −0.548886
\(349\) −22.8659 −1.22398 −0.611992 0.790864i \(-0.709631\pi\)
−0.611992 + 0.790864i \(0.709631\pi\)
\(350\) 0 0
\(351\) 5.56361 0.296964
\(352\) 5.78332 0.308252
\(353\) 19.2684 1.02556 0.512778 0.858522i \(-0.328617\pi\)
0.512778 + 0.858522i \(0.328617\pi\)
\(354\) 0.351098 0.0186607
\(355\) 0 0
\(356\) 25.6162 1.35766
\(357\) 0.187665 0.00993226
\(358\) −30.1500 −1.59348
\(359\) 20.1999 1.06611 0.533056 0.846080i \(-0.321043\pi\)
0.533056 + 0.846080i \(0.321043\pi\)
\(360\) 0 0
\(361\) 15.2731 0.803847
\(362\) 30.1033 1.58219
\(363\) 5.24732 0.275413
\(364\) 3.36262 0.176249
\(365\) 0 0
\(366\) 1.13364 0.0592564
\(367\) −3.91082 −0.204143 −0.102072 0.994777i \(-0.532547\pi\)
−0.102072 + 0.994777i \(0.532547\pi\)
\(368\) −27.7764 −1.44794
\(369\) 17.5807 0.915214
\(370\) 0 0
\(371\) −0.621949 −0.0322900
\(372\) −5.81962 −0.301733
\(373\) −9.05376 −0.468786 −0.234393 0.972142i \(-0.575310\pi\)
−0.234393 + 0.972142i \(0.575310\pi\)
\(374\) 0.636204 0.0328973
\(375\) 0 0
\(376\) −0.0528424 −0.00272514
\(377\) 19.3738 0.997802
\(378\) −4.93115 −0.253631
\(379\) 28.2491 1.45106 0.725530 0.688191i \(-0.241595\pi\)
0.725530 + 0.688191i \(0.241595\pi\)
\(380\) 0 0
\(381\) −0.0145651 −0.000746192 0
\(382\) −17.1241 −0.876144
\(383\) −31.6901 −1.61929 −0.809645 0.586920i \(-0.800340\pi\)
−0.809645 + 0.586920i \(0.800340\pi\)
\(384\) −0.329310 −0.0168050
\(385\) 0 0
\(386\) −47.3007 −2.40754
\(387\) 11.8134 0.600507
\(388\) 10.2155 0.518614
\(389\) 23.1689 1.17471 0.587355 0.809330i \(-0.300169\pi\)
0.587355 + 0.809330i \(0.300169\pi\)
\(390\) 0 0
\(391\) −3.11943 −0.157756
\(392\) 0.515985 0.0260612
\(393\) 3.75845 0.189589
\(394\) −53.7827 −2.70953
\(395\) 0 0
\(396\) −4.03760 −0.202897
\(397\) −30.6366 −1.53761 −0.768804 0.639484i \(-0.779148\pi\)
−0.768804 + 0.639484i \(0.779148\pi\)
\(398\) 39.3828 1.97408
\(399\) −2.49782 −0.125047
\(400\) 0 0
\(401\) −8.47109 −0.423026 −0.211513 0.977375i \(-0.567839\pi\)
−0.211513 + 0.977375i \(0.567839\pi\)
\(402\) −12.6339 −0.630121
\(403\) 11.0113 0.548511
\(404\) 0.391838 0.0194947
\(405\) 0 0
\(406\) −17.1714 −0.852203
\(407\) 2.28238 0.113133
\(408\) −0.0181094 −0.000896548 0
\(409\) 23.2857 1.15140 0.575702 0.817660i \(-0.304729\pi\)
0.575702 + 0.817660i \(0.304729\pi\)
\(410\) 0 0
\(411\) −1.39701 −0.0689092
\(412\) 8.10727 0.399416
\(413\) 0.297377 0.0146330
\(414\) 39.1974 1.92645
\(415\) 0 0
\(416\) 15.5371 0.761767
\(417\) −2.78485 −0.136375
\(418\) −8.46789 −0.414178
\(419\) −9.29059 −0.453875 −0.226937 0.973909i \(-0.572871\pi\)
−0.226937 + 0.973909i \(0.572871\pi\)
\(420\) 0 0
\(421\) 15.4991 0.755380 0.377690 0.925932i \(-0.376719\pi\)
0.377690 + 0.925932i \(0.376719\pi\)
\(422\) −9.21913 −0.448780
\(423\) −1.76644 −0.0858871
\(424\) 0.0600172 0.00291469
\(425\) 0 0
\(426\) 0.555762 0.0269268
\(427\) 0.960185 0.0464666
\(428\) −13.6930 −0.661874
\(429\) −0.696294 −0.0336174
\(430\) 0 0
\(431\) −19.5308 −0.940765 −0.470382 0.882463i \(-0.655884\pi\)
−0.470382 + 0.882463i \(0.655884\pi\)
\(432\) −11.2721 −0.542328
\(433\) 5.89329 0.283213 0.141607 0.989923i \(-0.454773\pi\)
0.141607 + 0.989923i \(0.454773\pi\)
\(434\) −9.75953 −0.468472
\(435\) 0 0
\(436\) 8.22594 0.393951
\(437\) 41.5197 1.98616
\(438\) 11.0573 0.528340
\(439\) 22.1839 1.05878 0.529390 0.848379i \(-0.322421\pi\)
0.529390 + 0.848379i \(0.322421\pi\)
\(440\) 0 0
\(441\) 17.2486 0.821360
\(442\) 1.70918 0.0812975
\(443\) 14.6268 0.694940 0.347470 0.937691i \(-0.387041\pi\)
0.347470 + 0.937691i \(0.387041\pi\)
\(444\) −3.24068 −0.153796
\(445\) 0 0
\(446\) −23.7454 −1.12438
\(447\) −7.42423 −0.351154
\(448\) −7.09462 −0.335189
\(449\) −34.2308 −1.61545 −0.807726 0.589558i \(-0.799302\pi\)
−0.807726 + 0.589558i \(0.799302\pi\)
\(450\) 0 0
\(451\) −4.60103 −0.216654
\(452\) −0.878251 −0.0413095
\(453\) 9.84886 0.462740
\(454\) −21.0403 −0.987470
\(455\) 0 0
\(456\) 0.241036 0.0112876
\(457\) 24.3534 1.13921 0.569603 0.821920i \(-0.307097\pi\)
0.569603 + 0.821920i \(0.307097\pi\)
\(458\) 57.9688 2.70871
\(459\) −1.26591 −0.0590877
\(460\) 0 0
\(461\) 10.3474 0.481924 0.240962 0.970535i \(-0.422537\pi\)
0.240962 + 0.970535i \(0.422537\pi\)
\(462\) 0.617140 0.0287119
\(463\) −30.7015 −1.42682 −0.713409 0.700748i \(-0.752850\pi\)
−0.713409 + 0.700748i \(0.752850\pi\)
\(464\) −39.2520 −1.82223
\(465\) 0 0
\(466\) 0.971044 0.0449828
\(467\) 20.5093 0.949056 0.474528 0.880240i \(-0.342619\pi\)
0.474528 + 0.880240i \(0.342619\pi\)
\(468\) −10.8471 −0.501409
\(469\) −10.7008 −0.494117
\(470\) 0 0
\(471\) 7.18033 0.330852
\(472\) −0.0286965 −0.00132086
\(473\) −3.09167 −0.142155
\(474\) 11.0258 0.506433
\(475\) 0 0
\(476\) −0.765111 −0.0350688
\(477\) 2.00628 0.0918614
\(478\) 4.18711 0.191514
\(479\) 28.0475 1.28152 0.640761 0.767740i \(-0.278619\pi\)
0.640761 + 0.767740i \(0.278619\pi\)
\(480\) 0 0
\(481\) 6.13168 0.279581
\(482\) −2.01020 −0.0915622
\(483\) −3.02596 −0.137686
\(484\) −21.3934 −0.972427
\(485\) 0 0
\(486\) 24.2070 1.09805
\(487\) −10.9035 −0.494085 −0.247043 0.969005i \(-0.579459\pi\)
−0.247043 + 0.969005i \(0.579459\pi\)
\(488\) −0.0926566 −0.00419437
\(489\) 2.49798 0.112963
\(490\) 0 0
\(491\) −27.6672 −1.24860 −0.624301 0.781184i \(-0.714616\pi\)
−0.624301 + 0.781184i \(0.714616\pi\)
\(492\) 6.53287 0.294525
\(493\) −4.40820 −0.198536
\(494\) −22.7493 −1.02354
\(495\) 0 0
\(496\) −22.3092 −1.00171
\(497\) 0.470726 0.0211149
\(498\) −6.66645 −0.298731
\(499\) −17.3522 −0.776792 −0.388396 0.921493i \(-0.626971\pi\)
−0.388396 + 0.921493i \(0.626971\pi\)
\(500\) 0 0
\(501\) 7.82371 0.349538
\(502\) 19.4413 0.867706
\(503\) 26.4875 1.18102 0.590510 0.807030i \(-0.298926\pi\)
0.590510 + 0.807030i \(0.298926\pi\)
\(504\) 0.192737 0.00858518
\(505\) 0 0
\(506\) −10.2583 −0.456038
\(507\) 4.63706 0.205939
\(508\) 0.0593820 0.00263465
\(509\) 3.50048 0.155156 0.0775780 0.996986i \(-0.475281\pi\)
0.0775780 + 0.996986i \(0.475281\pi\)
\(510\) 0 0
\(511\) 9.36547 0.414304
\(512\) −32.1229 −1.41964
\(513\) 16.8493 0.743916
\(514\) −32.2339 −1.42178
\(515\) 0 0
\(516\) 4.38977 0.193249
\(517\) 0.462293 0.0203316
\(518\) −5.43464 −0.238784
\(519\) 0.417175 0.0183119
\(520\) 0 0
\(521\) 8.93651 0.391516 0.195758 0.980652i \(-0.437283\pi\)
0.195758 + 0.980652i \(0.437283\pi\)
\(522\) 55.3915 2.42442
\(523\) −6.13438 −0.268238 −0.134119 0.990965i \(-0.542820\pi\)
−0.134119 + 0.990965i \(0.542820\pi\)
\(524\) −15.3233 −0.669400
\(525\) 0 0
\(526\) 54.1552 2.36128
\(527\) −2.50544 −0.109139
\(528\) 1.41071 0.0613935
\(529\) 27.2986 1.18689
\(530\) 0 0
\(531\) −0.959280 −0.0416292
\(532\) 10.1837 0.441517
\(533\) −12.3608 −0.535407
\(534\) 12.6303 0.546565
\(535\) 0 0
\(536\) 1.03261 0.0446021
\(537\) −7.50810 −0.323999
\(538\) −61.7580 −2.66258
\(539\) −4.51411 −0.194437
\(540\) 0 0
\(541\) 32.8484 1.41226 0.706132 0.708081i \(-0.250439\pi\)
0.706132 + 0.708081i \(0.250439\pi\)
\(542\) 64.8368 2.78498
\(543\) 7.49647 0.321704
\(544\) −3.53521 −0.151571
\(545\) 0 0
\(546\) 1.65797 0.0709544
\(547\) 27.5818 1.17931 0.589656 0.807655i \(-0.299263\pi\)
0.589656 + 0.807655i \(0.299263\pi\)
\(548\) 5.69561 0.243304
\(549\) −3.09736 −0.132192
\(550\) 0 0
\(551\) 58.6733 2.49957
\(552\) 0.292001 0.0124284
\(553\) 9.33879 0.397126
\(554\) 19.7805 0.840391
\(555\) 0 0
\(556\) 11.3539 0.481511
\(557\) −12.3393 −0.522834 −0.261417 0.965226i \(-0.584190\pi\)
−0.261417 + 0.965226i \(0.584190\pi\)
\(558\) 31.4823 1.33275
\(559\) −8.30587 −0.351301
\(560\) 0 0
\(561\) 0.158431 0.00668895
\(562\) −0.125348 −0.00528748
\(563\) 35.3473 1.48971 0.744855 0.667227i \(-0.232519\pi\)
0.744855 + 0.667227i \(0.232519\pi\)
\(564\) −0.656397 −0.0276393
\(565\) 0 0
\(566\) −46.4629 −1.95298
\(567\) 5.80214 0.243667
\(568\) −0.0454244 −0.00190597
\(569\) 19.0099 0.796938 0.398469 0.917182i \(-0.369542\pi\)
0.398469 + 0.917182i \(0.369542\pi\)
\(570\) 0 0
\(571\) 23.9059 1.00043 0.500215 0.865901i \(-0.333254\pi\)
0.500215 + 0.865901i \(0.333254\pi\)
\(572\) 2.83880 0.118696
\(573\) −4.26432 −0.178145
\(574\) 10.9557 0.457280
\(575\) 0 0
\(576\) 22.8858 0.953576
\(577\) −24.7986 −1.03238 −0.516190 0.856474i \(-0.672650\pi\)
−0.516190 + 0.856474i \(0.672650\pi\)
\(578\) 33.7845 1.40525
\(579\) −11.7791 −0.489521
\(580\) 0 0
\(581\) −5.64643 −0.234253
\(582\) 5.03683 0.208784
\(583\) −0.525063 −0.0217459
\(584\) −0.903755 −0.0373977
\(585\) 0 0
\(586\) −15.2718 −0.630874
\(587\) 45.8195 1.89117 0.945586 0.325373i \(-0.105490\pi\)
0.945586 + 0.325373i \(0.105490\pi\)
\(588\) 6.40946 0.264322
\(589\) 33.3475 1.37406
\(590\) 0 0
\(591\) −13.3932 −0.550924
\(592\) −12.4230 −0.510582
\(593\) −12.9205 −0.530581 −0.265290 0.964169i \(-0.585468\pi\)
−0.265290 + 0.964169i \(0.585468\pi\)
\(594\) −4.16298 −0.170809
\(595\) 0 0
\(596\) 30.2687 1.23985
\(597\) 9.80730 0.401386
\(598\) −27.5593 −1.12698
\(599\) 26.4741 1.08170 0.540851 0.841118i \(-0.318102\pi\)
0.540851 + 0.841118i \(0.318102\pi\)
\(600\) 0 0
\(601\) 12.3729 0.504702 0.252351 0.967636i \(-0.418796\pi\)
0.252351 + 0.967636i \(0.418796\pi\)
\(602\) 7.36166 0.300039
\(603\) 34.5186 1.40571
\(604\) −40.1539 −1.63384
\(605\) 0 0
\(606\) 0.193199 0.00784816
\(607\) 6.58880 0.267431 0.133716 0.991020i \(-0.457309\pi\)
0.133716 + 0.991020i \(0.457309\pi\)
\(608\) 47.0538 1.90828
\(609\) −4.27611 −0.173277
\(610\) 0 0
\(611\) 1.24197 0.0502446
\(612\) 2.46809 0.0997668
\(613\) 32.6185 1.31745 0.658724 0.752384i \(-0.271096\pi\)
0.658724 + 0.752384i \(0.271096\pi\)
\(614\) −30.8699 −1.24581
\(615\) 0 0
\(616\) −0.0504410 −0.00203233
\(617\) −44.7802 −1.80278 −0.901391 0.433006i \(-0.857453\pi\)
−0.901391 + 0.433006i \(0.857453\pi\)
\(618\) 3.99735 0.160797
\(619\) 36.4386 1.46459 0.732296 0.680986i \(-0.238449\pi\)
0.732296 + 0.680986i \(0.238449\pi\)
\(620\) 0 0
\(621\) 20.4119 0.819102
\(622\) −50.3581 −2.01918
\(623\) 10.6977 0.428596
\(624\) 3.78993 0.151719
\(625\) 0 0
\(626\) −17.9953 −0.719235
\(627\) −2.10872 −0.0842140
\(628\) −29.2743 −1.16817
\(629\) −1.39517 −0.0556290
\(630\) 0 0
\(631\) 19.4629 0.774804 0.387402 0.921911i \(-0.373373\pi\)
0.387402 + 0.921911i \(0.373373\pi\)
\(632\) −0.901181 −0.0358470
\(633\) −2.29579 −0.0912496
\(634\) 41.6767 1.65519
\(635\) 0 0
\(636\) 0.745522 0.0295619
\(637\) −12.1273 −0.480502
\(638\) −14.4965 −0.573921
\(639\) −1.51847 −0.0600696
\(640\) 0 0
\(641\) 27.8560 1.10025 0.550123 0.835084i \(-0.314581\pi\)
0.550123 + 0.835084i \(0.314581\pi\)
\(642\) −6.75142 −0.266457
\(643\) 5.63664 0.222288 0.111144 0.993804i \(-0.464549\pi\)
0.111144 + 0.993804i \(0.464549\pi\)
\(644\) 12.3369 0.486140
\(645\) 0 0
\(646\) 5.17624 0.203656
\(647\) 17.7323 0.697127 0.348563 0.937285i \(-0.386670\pi\)
0.348563 + 0.937285i \(0.386670\pi\)
\(648\) −0.559899 −0.0219949
\(649\) 0.251053 0.00985468
\(650\) 0 0
\(651\) −2.43037 −0.0952536
\(652\) −10.1843 −0.398849
\(653\) −14.1435 −0.553477 −0.276739 0.960945i \(-0.589254\pi\)
−0.276739 + 0.960945i \(0.589254\pi\)
\(654\) 4.05586 0.158597
\(655\) 0 0
\(656\) 25.0434 0.977782
\(657\) −30.2111 −1.17865
\(658\) −1.10078 −0.0429129
\(659\) 20.0695 0.781798 0.390899 0.920434i \(-0.372164\pi\)
0.390899 + 0.920434i \(0.372164\pi\)
\(660\) 0 0
\(661\) −6.85193 −0.266509 −0.133255 0.991082i \(-0.542543\pi\)
−0.133255 + 0.991082i \(0.542543\pi\)
\(662\) −14.0704 −0.546862
\(663\) 0.425629 0.0165301
\(664\) 0.544873 0.0211452
\(665\) 0 0
\(666\) 17.5310 0.679314
\(667\) 71.0791 2.75219
\(668\) −31.8974 −1.23415
\(669\) −5.91319 −0.228617
\(670\) 0 0
\(671\) 0.810610 0.0312932
\(672\) −3.42928 −0.132287
\(673\) −17.5575 −0.676791 −0.338396 0.941004i \(-0.609884\pi\)
−0.338396 + 0.941004i \(0.609884\pi\)
\(674\) 3.53098 0.136008
\(675\) 0 0
\(676\) −18.9054 −0.727129
\(677\) −22.0052 −0.845728 −0.422864 0.906193i \(-0.638975\pi\)
−0.422864 + 0.906193i \(0.638975\pi\)
\(678\) −0.433028 −0.0166304
\(679\) 4.26616 0.163720
\(680\) 0 0
\(681\) −5.23956 −0.200780
\(682\) −8.23921 −0.315496
\(683\) −32.7325 −1.25248 −0.626238 0.779632i \(-0.715406\pi\)
−0.626238 + 0.779632i \(0.715406\pi\)
\(684\) −32.8504 −1.25607
\(685\) 0 0
\(686\) 22.7420 0.868294
\(687\) 14.4357 0.550756
\(688\) 16.8280 0.641560
\(689\) −1.41060 −0.0537396
\(690\) 0 0
\(691\) −42.8793 −1.63121 −0.815604 0.578611i \(-0.803595\pi\)
−0.815604 + 0.578611i \(0.803595\pi\)
\(692\) −1.70083 −0.0646558
\(693\) −1.68617 −0.0640521
\(694\) −22.1844 −0.842110
\(695\) 0 0
\(696\) 0.412639 0.0156410
\(697\) 2.81251 0.106531
\(698\) 45.9651 1.73980
\(699\) 0.241814 0.00914626
\(700\) 0 0
\(701\) −9.59945 −0.362566 −0.181283 0.983431i \(-0.558025\pi\)
−0.181283 + 0.983431i \(0.558025\pi\)
\(702\) −11.1840 −0.422113
\(703\) 18.5697 0.700370
\(704\) −5.98944 −0.225735
\(705\) 0 0
\(706\) −38.7335 −1.45775
\(707\) 0.163638 0.00615423
\(708\) −0.356462 −0.0133967
\(709\) −20.6550 −0.775717 −0.387858 0.921719i \(-0.626785\pi\)
−0.387858 + 0.921719i \(0.626785\pi\)
\(710\) 0 0
\(711\) −30.1251 −1.12978
\(712\) −1.03232 −0.0386877
\(713\) 40.3984 1.51293
\(714\) −0.377244 −0.0141180
\(715\) 0 0
\(716\) 30.6106 1.14397
\(717\) 1.04270 0.0389402
\(718\) −40.6060 −1.51540
\(719\) −36.5196 −1.36195 −0.680975 0.732307i \(-0.738444\pi\)
−0.680975 + 0.732307i \(0.738444\pi\)
\(720\) 0 0
\(721\) 3.38572 0.126091
\(722\) −30.7020 −1.14261
\(723\) −0.500591 −0.0186172
\(724\) −30.5632 −1.13587
\(725\) 0 0
\(726\) −10.5482 −0.391479
\(727\) −53.4718 −1.98316 −0.991579 0.129503i \(-0.958662\pi\)
−0.991579 + 0.129503i \(0.958662\pi\)
\(728\) −0.135512 −0.00502239
\(729\) −14.3943 −0.533122
\(730\) 0 0
\(731\) 1.88987 0.0698993
\(732\) −1.15096 −0.0425408
\(733\) 47.4390 1.75220 0.876100 0.482129i \(-0.160136\pi\)
0.876100 + 0.482129i \(0.160136\pi\)
\(734\) 7.86154 0.290175
\(735\) 0 0
\(736\) 57.0027 2.10115
\(737\) −9.03386 −0.332766
\(738\) −35.3407 −1.30091
\(739\) 24.6810 0.907904 0.453952 0.891026i \(-0.350014\pi\)
0.453952 + 0.891026i \(0.350014\pi\)
\(740\) 0 0
\(741\) −5.66514 −0.208114
\(742\) 1.25024 0.0458979
\(743\) 41.1925 1.51121 0.755603 0.655030i \(-0.227344\pi\)
0.755603 + 0.655030i \(0.227344\pi\)
\(744\) 0.234527 0.00859818
\(745\) 0 0
\(746\) 18.1999 0.666345
\(747\) 18.2142 0.666424
\(748\) −0.645924 −0.0236173
\(749\) −5.71840 −0.208946
\(750\) 0 0
\(751\) −16.0787 −0.586719 −0.293360 0.956002i \(-0.594773\pi\)
−0.293360 + 0.956002i \(0.594773\pi\)
\(752\) −2.51627 −0.0917588
\(753\) 4.84136 0.176429
\(754\) −38.9453 −1.41830
\(755\) 0 0
\(756\) 5.00649 0.182084
\(757\) 38.0614 1.38336 0.691682 0.722202i \(-0.256870\pi\)
0.691682 + 0.722202i \(0.256870\pi\)
\(758\) −56.7865 −2.06258
\(759\) −2.55458 −0.0927253
\(760\) 0 0
\(761\) 29.7253 1.07754 0.538770 0.842453i \(-0.318889\pi\)
0.538770 + 0.842453i \(0.318889\pi\)
\(762\) 0.0292788 0.00106066
\(763\) 3.43528 0.124366
\(764\) 17.3857 0.628992
\(765\) 0 0
\(766\) 63.7036 2.30170
\(767\) 0.674461 0.0243534
\(768\) −7.67176 −0.276831
\(769\) −50.1093 −1.80699 −0.903494 0.428602i \(-0.859006\pi\)
−0.903494 + 0.428602i \(0.859006\pi\)
\(770\) 0 0
\(771\) −8.02705 −0.289087
\(772\) 48.0234 1.72840
\(773\) −1.44897 −0.0521159 −0.0260579 0.999660i \(-0.508295\pi\)
−0.0260579 + 0.999660i \(0.508295\pi\)
\(774\) −23.7473 −0.853577
\(775\) 0 0
\(776\) −0.411679 −0.0147784
\(777\) −1.35336 −0.0485515
\(778\) −46.5742 −1.66976
\(779\) −37.4346 −1.34123
\(780\) 0 0
\(781\) 0.397397 0.0142200
\(782\) 6.27069 0.224239
\(783\) 28.8450 1.03084
\(784\) 24.5703 0.877512
\(785\) 0 0
\(786\) −7.55525 −0.269487
\(787\) −10.5396 −0.375695 −0.187848 0.982198i \(-0.560151\pi\)
−0.187848 + 0.982198i \(0.560151\pi\)
\(788\) 54.6044 1.94520
\(789\) 13.4860 0.480115
\(790\) 0 0
\(791\) −0.366772 −0.0130409
\(792\) 0.162713 0.00578174
\(793\) 2.17773 0.0773335
\(794\) 61.5858 2.18560
\(795\) 0 0
\(796\) −39.9845 −1.41721
\(797\) −31.2275 −1.10614 −0.553068 0.833136i \(-0.686543\pi\)
−0.553068 + 0.833136i \(0.686543\pi\)
\(798\) 5.02113 0.177746
\(799\) −0.282590 −0.00999731
\(800\) 0 0
\(801\) −34.5087 −1.21931
\(802\) 17.0286 0.601301
\(803\) 7.90654 0.279016
\(804\) 12.8269 0.452370
\(805\) 0 0
\(806\) −22.1349 −0.779669
\(807\) −15.3793 −0.541376
\(808\) −0.0157908 −0.000555519 0
\(809\) −38.9547 −1.36957 −0.684787 0.728743i \(-0.740105\pi\)
−0.684787 + 0.728743i \(0.740105\pi\)
\(810\) 0 0
\(811\) 3.89413 0.136741 0.0683707 0.997660i \(-0.478220\pi\)
0.0683707 + 0.997660i \(0.478220\pi\)
\(812\) 17.4338 0.611805
\(813\) 16.1460 0.566264
\(814\) −4.58804 −0.160811
\(815\) 0 0
\(816\) −0.862339 −0.0301879
\(817\) −25.1542 −0.880035
\(818\) −46.8090 −1.63664
\(819\) −4.52994 −0.158289
\(820\) 0 0
\(821\) −14.5536 −0.507923 −0.253962 0.967214i \(-0.581734\pi\)
−0.253962 + 0.967214i \(0.581734\pi\)
\(822\) 2.80826 0.0979495
\(823\) −37.0978 −1.29315 −0.646575 0.762851i \(-0.723799\pi\)
−0.646575 + 0.762851i \(0.723799\pi\)
\(824\) −0.326718 −0.0113818
\(825\) 0 0
\(826\) −0.597789 −0.0207997
\(827\) 46.8558 1.62934 0.814668 0.579928i \(-0.196919\pi\)
0.814668 + 0.579928i \(0.196919\pi\)
\(828\) −39.7962 −1.38301
\(829\) 43.4487 1.50904 0.754518 0.656280i \(-0.227871\pi\)
0.754518 + 0.656280i \(0.227871\pi\)
\(830\) 0 0
\(831\) 4.92583 0.170875
\(832\) −16.0908 −0.557849
\(833\) 2.75938 0.0956068
\(834\) 5.59811 0.193847
\(835\) 0 0
\(836\) 8.59727 0.297343
\(837\) 16.3943 0.566670
\(838\) 18.6760 0.645150
\(839\) 45.0114 1.55397 0.776983 0.629521i \(-0.216749\pi\)
0.776983 + 0.629521i \(0.216749\pi\)
\(840\) 0 0
\(841\) 71.4450 2.46362
\(842\) −31.1563 −1.07372
\(843\) −0.0312147 −0.00107509
\(844\) 9.35998 0.322184
\(845\) 0 0
\(846\) 3.55090 0.122082
\(847\) −8.93422 −0.306983
\(848\) 2.85792 0.0981415
\(849\) −11.5704 −0.397096
\(850\) 0 0
\(851\) 22.4961 0.771155
\(852\) −0.564253 −0.0193310
\(853\) −5.62487 −0.192592 −0.0962959 0.995353i \(-0.530700\pi\)
−0.0962959 + 0.995353i \(0.530700\pi\)
\(854\) −1.93017 −0.0660490
\(855\) 0 0
\(856\) 0.551818 0.0188607
\(857\) 1.42125 0.0485491 0.0242746 0.999705i \(-0.492272\pi\)
0.0242746 + 0.999705i \(0.492272\pi\)
\(858\) 1.39969 0.0477847
\(859\) −2.58506 −0.0882010 −0.0441005 0.999027i \(-0.514042\pi\)
−0.0441005 + 0.999027i \(0.514042\pi\)
\(860\) 0 0
\(861\) 2.72823 0.0929779
\(862\) 39.2608 1.33723
\(863\) 46.3980 1.57941 0.789703 0.613490i \(-0.210235\pi\)
0.789703 + 0.613490i \(0.210235\pi\)
\(864\) 23.1326 0.786986
\(865\) 0 0
\(866\) −11.8467 −0.402567
\(867\) 8.41320 0.285727
\(868\) 9.90864 0.336321
\(869\) 7.88402 0.267447
\(870\) 0 0
\(871\) −24.2698 −0.822349
\(872\) −0.331500 −0.0112260
\(873\) −13.7618 −0.465765
\(874\) −83.4630 −2.82318
\(875\) 0 0
\(876\) −11.2263 −0.379300
\(877\) 9.47791 0.320046 0.160023 0.987113i \(-0.448843\pi\)
0.160023 + 0.987113i \(0.448843\pi\)
\(878\) −44.5941 −1.50498
\(879\) −3.80307 −0.128274
\(880\) 0 0
\(881\) 50.5681 1.70368 0.851841 0.523800i \(-0.175486\pi\)
0.851841 + 0.523800i \(0.175486\pi\)
\(882\) −34.6731 −1.16750
\(883\) 18.3321 0.616925 0.308462 0.951237i \(-0.400186\pi\)
0.308462 + 0.951237i \(0.400186\pi\)
\(884\) −1.73530 −0.0583643
\(885\) 0 0
\(886\) −29.4028 −0.987807
\(887\) −22.4382 −0.753401 −0.376701 0.926335i \(-0.622941\pi\)
−0.376701 + 0.926335i \(0.622941\pi\)
\(888\) 0.130597 0.00438256
\(889\) 0.0247989 0.000831728 0
\(890\) 0 0
\(891\) 4.89829 0.164099
\(892\) 24.1082 0.807201
\(893\) 3.76128 0.125866
\(894\) 14.9242 0.499140
\(895\) 0 0
\(896\) 0.560692 0.0187314
\(897\) −6.86296 −0.229148
\(898\) 68.8109 2.29625
\(899\) 57.0888 1.90402
\(900\) 0 0
\(901\) 0.320960 0.0106927
\(902\) 9.24900 0.307958
\(903\) 1.83324 0.0610064
\(904\) 0.0353930 0.00117715
\(905\) 0 0
\(906\) −19.7982 −0.657751
\(907\) 44.1063 1.46452 0.732262 0.681023i \(-0.238465\pi\)
0.732262 + 0.681023i \(0.238465\pi\)
\(908\) 21.3618 0.708915
\(909\) −0.527862 −0.0175081
\(910\) 0 0
\(911\) 36.5594 1.21127 0.605633 0.795744i \(-0.292920\pi\)
0.605633 + 0.795744i \(0.292920\pi\)
\(912\) 11.4778 0.380067
\(913\) −4.76684 −0.157759
\(914\) −48.9554 −1.61930
\(915\) 0 0
\(916\) −58.8545 −1.94461
\(917\) −6.39924 −0.211322
\(918\) 2.54474 0.0839889
\(919\) −47.3887 −1.56321 −0.781605 0.623774i \(-0.785599\pi\)
−0.781605 + 0.623774i \(0.785599\pi\)
\(920\) 0 0
\(921\) −7.68737 −0.253307
\(922\) −20.8003 −0.685021
\(923\) 1.06762 0.0351412
\(924\) −0.626568 −0.0206126
\(925\) 0 0
\(926\) 61.7162 2.02812
\(927\) −10.9217 −0.358715
\(928\) 80.5531 2.64428
\(929\) 23.8472 0.782400 0.391200 0.920306i \(-0.372060\pi\)
0.391200 + 0.920306i \(0.372060\pi\)
\(930\) 0 0
\(931\) −36.7274 −1.20369
\(932\) −0.985880 −0.0322936
\(933\) −12.5404 −0.410555
\(934\) −41.2278 −1.34901
\(935\) 0 0
\(936\) 0.437133 0.0142881
\(937\) −31.9624 −1.04417 −0.522083 0.852895i \(-0.674845\pi\)
−0.522083 + 0.852895i \(0.674845\pi\)
\(938\) 21.5108 0.702352
\(939\) −4.48127 −0.146241
\(940\) 0 0
\(941\) 23.8740 0.778271 0.389136 0.921180i \(-0.372774\pi\)
0.389136 + 0.921180i \(0.372774\pi\)
\(942\) −14.4339 −0.470283
\(943\) −45.3497 −1.47679
\(944\) −1.36648 −0.0444752
\(945\) 0 0
\(946\) 6.21488 0.202063
\(947\) −44.4722 −1.44515 −0.722575 0.691292i \(-0.757042\pi\)
−0.722575 + 0.691292i \(0.757042\pi\)
\(948\) −11.1943 −0.363574
\(949\) 21.2412 0.689518
\(950\) 0 0
\(951\) 10.3785 0.336547
\(952\) 0.0308335 0.000999319 0
\(953\) 54.1645 1.75456 0.877280 0.479980i \(-0.159356\pi\)
0.877280 + 0.479980i \(0.159356\pi\)
\(954\) −4.03303 −0.130574
\(955\) 0 0
\(956\) −4.25109 −0.137490
\(957\) −3.60999 −0.116694
\(958\) −56.3811 −1.82159
\(959\) 2.37858 0.0768083
\(960\) 0 0
\(961\) 1.44694 0.0466756
\(962\) −12.3259 −0.397404
\(963\) 18.4464 0.594427
\(964\) 2.04092 0.0657334
\(965\) 0 0
\(966\) 6.08278 0.195710
\(967\) 35.3826 1.13783 0.568914 0.822397i \(-0.307364\pi\)
0.568914 + 0.822397i \(0.307364\pi\)
\(968\) 0.862140 0.0277102
\(969\) 1.28901 0.0414090
\(970\) 0 0
\(971\) −8.91001 −0.285936 −0.142968 0.989727i \(-0.545665\pi\)
−0.142968 + 0.989727i \(0.545665\pi\)
\(972\) −24.5768 −0.788302
\(973\) 4.74155 0.152007
\(974\) 21.9183 0.702307
\(975\) 0 0
\(976\) −4.41215 −0.141230
\(977\) −21.0250 −0.672650 −0.336325 0.941746i \(-0.609184\pi\)
−0.336325 + 0.941746i \(0.609184\pi\)
\(978\) −5.02146 −0.160568
\(979\) 9.03126 0.288640
\(980\) 0 0
\(981\) −11.0815 −0.353806
\(982\) 55.6166 1.77480
\(983\) 33.5818 1.07109 0.535546 0.844506i \(-0.320106\pi\)
0.535546 + 0.844506i \(0.320106\pi\)
\(984\) −0.263271 −0.00839276
\(985\) 0 0
\(986\) 8.86138 0.282204
\(987\) −0.274122 −0.00872540
\(988\) 23.0968 0.734808
\(989\) −30.4728 −0.968978
\(990\) 0 0
\(991\) −32.0529 −1.01819 −0.509097 0.860709i \(-0.670021\pi\)
−0.509097 + 0.860709i \(0.670021\pi\)
\(992\) 45.7831 1.45361
\(993\) −3.50389 −0.111192
\(994\) −0.946255 −0.0300134
\(995\) 0 0
\(996\) 6.76830 0.214462
\(997\) −37.4198 −1.18510 −0.592548 0.805535i \(-0.701878\pi\)
−0.592548 + 0.805535i \(0.701878\pi\)
\(998\) 34.8815 1.10415
\(999\) 9.12924 0.288836
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 \(a_p\))