Properties

Label 8007.2.a.e.1.23
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.23
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.375429 q^{2} +1.00000 q^{3} -1.85905 q^{4} +1.27795 q^{5} -0.375429 q^{6} +2.77561 q^{7} +1.44880 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.375429 q^{2} +1.00000 q^{3} -1.85905 q^{4} +1.27795 q^{5} -0.375429 q^{6} +2.77561 q^{7} +1.44880 q^{8} +1.00000 q^{9} -0.479778 q^{10} +0.396892 q^{11} -1.85905 q^{12} -5.77088 q^{13} -1.04204 q^{14} +1.27795 q^{15} +3.17419 q^{16} -1.00000 q^{17} -0.375429 q^{18} -4.30719 q^{19} -2.37577 q^{20} +2.77561 q^{21} -0.149005 q^{22} +4.90648 q^{23} +1.44880 q^{24} -3.36685 q^{25} +2.16655 q^{26} +1.00000 q^{27} -5.16001 q^{28} +7.65023 q^{29} -0.479778 q^{30} -9.12637 q^{31} -4.08928 q^{32} +0.396892 q^{33} +0.375429 q^{34} +3.54708 q^{35} -1.85905 q^{36} -4.07961 q^{37} +1.61704 q^{38} -5.77088 q^{39} +1.85149 q^{40} +6.26360 q^{41} -1.04204 q^{42} -5.27244 q^{43} -0.737843 q^{44} +1.27795 q^{45} -1.84203 q^{46} +8.22755 q^{47} +3.17419 q^{48} +0.704011 q^{49} +1.26401 q^{50} -1.00000 q^{51} +10.7284 q^{52} -6.53665 q^{53} -0.375429 q^{54} +0.507206 q^{55} +4.02130 q^{56} -4.30719 q^{57} -2.87212 q^{58} -1.83567 q^{59} -2.37577 q^{60} -10.9228 q^{61} +3.42630 q^{62} +2.77561 q^{63} -4.81314 q^{64} -7.37487 q^{65} -0.149005 q^{66} +13.8164 q^{67} +1.85905 q^{68} +4.90648 q^{69} -1.33168 q^{70} -11.6200 q^{71} +1.44880 q^{72} -15.6347 q^{73} +1.53160 q^{74} -3.36685 q^{75} +8.00729 q^{76} +1.10162 q^{77} +2.16655 q^{78} -12.8422 q^{79} +4.05644 q^{80} +1.00000 q^{81} -2.35154 q^{82} +2.21309 q^{83} -5.16001 q^{84} -1.27795 q^{85} +1.97943 q^{86} +7.65023 q^{87} +0.575017 q^{88} -9.04833 q^{89} -0.479778 q^{90} -16.0177 q^{91} -9.12140 q^{92} -9.12637 q^{93} -3.08886 q^{94} -5.50435 q^{95} -4.08928 q^{96} +19.1865 q^{97} -0.264306 q^{98} +0.396892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.375429 −0.265468 −0.132734 0.991152i \(-0.542376\pi\)
−0.132734 + 0.991152i \(0.542376\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.85905 −0.929527
\(5\) 1.27795 0.571515 0.285757 0.958302i \(-0.407755\pi\)
0.285757 + 0.958302i \(0.407755\pi\)
\(6\) −0.375429 −0.153268
\(7\) 2.77561 1.04908 0.524541 0.851385i \(-0.324237\pi\)
0.524541 + 0.851385i \(0.324237\pi\)
\(8\) 1.44880 0.512228
\(9\) 1.00000 0.333333
\(10\) −0.479778 −0.151719
\(11\) 0.396892 0.119667 0.0598337 0.998208i \(-0.480943\pi\)
0.0598337 + 0.998208i \(0.480943\pi\)
\(12\) −1.85905 −0.536662
\(13\) −5.77088 −1.60055 −0.800277 0.599630i \(-0.795314\pi\)
−0.800277 + 0.599630i \(0.795314\pi\)
\(14\) −1.04204 −0.278498
\(15\) 1.27795 0.329964
\(16\) 3.17419 0.793546
\(17\) −1.00000 −0.242536
\(18\) −0.375429 −0.0884894
\(19\) −4.30719 −0.988136 −0.494068 0.869423i \(-0.664491\pi\)
−0.494068 + 0.869423i \(0.664491\pi\)
\(20\) −2.37577 −0.531238
\(21\) 2.77561 0.605688
\(22\) −0.149005 −0.0317679
\(23\) 4.90648 1.02307 0.511535 0.859262i \(-0.329077\pi\)
0.511535 + 0.859262i \(0.329077\pi\)
\(24\) 1.44880 0.295735
\(25\) −3.36685 −0.673371
\(26\) 2.16655 0.424896
\(27\) 1.00000 0.192450
\(28\) −5.16001 −0.975150
\(29\) 7.65023 1.42061 0.710306 0.703893i \(-0.248557\pi\)
0.710306 + 0.703893i \(0.248557\pi\)
\(30\) −0.479778 −0.0875950
\(31\) −9.12637 −1.63915 −0.819573 0.572975i \(-0.805789\pi\)
−0.819573 + 0.572975i \(0.805789\pi\)
\(32\) −4.08928 −0.722889
\(33\) 0.396892 0.0690900
\(34\) 0.375429 0.0643855
\(35\) 3.54708 0.599566
\(36\) −1.85905 −0.309842
\(37\) −4.07961 −0.670684 −0.335342 0.942097i \(-0.608852\pi\)
−0.335342 + 0.942097i \(0.608852\pi\)
\(38\) 1.61704 0.262319
\(39\) −5.77088 −0.924080
\(40\) 1.85149 0.292746
\(41\) 6.26360 0.978210 0.489105 0.872225i \(-0.337323\pi\)
0.489105 + 0.872225i \(0.337323\pi\)
\(42\) −1.04204 −0.160791
\(43\) −5.27244 −0.804040 −0.402020 0.915631i \(-0.631692\pi\)
−0.402020 + 0.915631i \(0.631692\pi\)
\(44\) −0.737843 −0.111234
\(45\) 1.27795 0.190505
\(46\) −1.84203 −0.271593
\(47\) 8.22755 1.20011 0.600056 0.799958i \(-0.295145\pi\)
0.600056 + 0.799958i \(0.295145\pi\)
\(48\) 3.17419 0.458154
\(49\) 0.704011 0.100573
\(50\) 1.26401 0.178759
\(51\) −1.00000 −0.140028
\(52\) 10.7284 1.48776
\(53\) −6.53665 −0.897879 −0.448939 0.893562i \(-0.648198\pi\)
−0.448939 + 0.893562i \(0.648198\pi\)
\(54\) −0.375429 −0.0510894
\(55\) 0.507206 0.0683917
\(56\) 4.02130 0.537369
\(57\) −4.30719 −0.570501
\(58\) −2.87212 −0.377127
\(59\) −1.83567 −0.238984 −0.119492 0.992835i \(-0.538127\pi\)
−0.119492 + 0.992835i \(0.538127\pi\)
\(60\) −2.37577 −0.306710
\(61\) −10.9228 −1.39853 −0.699263 0.714865i \(-0.746488\pi\)
−0.699263 + 0.714865i \(0.746488\pi\)
\(62\) 3.42630 0.435141
\(63\) 2.77561 0.349694
\(64\) −4.81314 −0.601642
\(65\) −7.37487 −0.914740
\(66\) −0.149005 −0.0183412
\(67\) 13.8164 1.68794 0.843970 0.536390i \(-0.180212\pi\)
0.843970 + 0.536390i \(0.180212\pi\)
\(68\) 1.85905 0.225443
\(69\) 4.90648 0.590670
\(70\) −1.33168 −0.159166
\(71\) −11.6200 −1.37904 −0.689518 0.724269i \(-0.742178\pi\)
−0.689518 + 0.724269i \(0.742178\pi\)
\(72\) 1.44880 0.170743
\(73\) −15.6347 −1.82991 −0.914953 0.403560i \(-0.867773\pi\)
−0.914953 + 0.403560i \(0.867773\pi\)
\(74\) 1.53160 0.178045
\(75\) −3.36685 −0.388771
\(76\) 8.00729 0.918499
\(77\) 1.10162 0.125541
\(78\) 2.16655 0.245314
\(79\) −12.8422 −1.44486 −0.722431 0.691443i \(-0.756975\pi\)
−0.722431 + 0.691443i \(0.756975\pi\)
\(80\) 4.05644 0.453523
\(81\) 1.00000 0.111111
\(82\) −2.35154 −0.259684
\(83\) 2.21309 0.242919 0.121459 0.992596i \(-0.461243\pi\)
0.121459 + 0.992596i \(0.461243\pi\)
\(84\) −5.16001 −0.563003
\(85\) −1.27795 −0.138613
\(86\) 1.97943 0.213447
\(87\) 7.65023 0.820191
\(88\) 0.575017 0.0612970
\(89\) −9.04833 −0.959121 −0.479561 0.877509i \(-0.659204\pi\)
−0.479561 + 0.877509i \(0.659204\pi\)
\(90\) −0.479778 −0.0505730
\(91\) −16.0177 −1.67911
\(92\) −9.12140 −0.950972
\(93\) −9.12637 −0.946361
\(94\) −3.08886 −0.318592
\(95\) −5.50435 −0.564734
\(96\) −4.08928 −0.417360
\(97\) 19.1865 1.94809 0.974047 0.226345i \(-0.0726775\pi\)
0.974047 + 0.226345i \(0.0726775\pi\)
\(98\) −0.264306 −0.0266989
\(99\) 0.396892 0.0398891
\(100\) 6.25916 0.625916
\(101\) 10.7946 1.07410 0.537052 0.843549i \(-0.319538\pi\)
0.537052 + 0.843549i \(0.319538\pi\)
\(102\) 0.375429 0.0371730
\(103\) −4.72430 −0.465499 −0.232750 0.972537i \(-0.574772\pi\)
−0.232750 + 0.972537i \(0.574772\pi\)
\(104\) −8.36085 −0.819849
\(105\) 3.54708 0.346159
\(106\) 2.45405 0.238358
\(107\) −3.95311 −0.382162 −0.191081 0.981574i \(-0.561199\pi\)
−0.191081 + 0.981574i \(0.561199\pi\)
\(108\) −1.85905 −0.178887
\(109\) 5.67124 0.543206 0.271603 0.962409i \(-0.412446\pi\)
0.271603 + 0.962409i \(0.412446\pi\)
\(110\) −0.190420 −0.0181558
\(111\) −4.07961 −0.387219
\(112\) 8.81030 0.832495
\(113\) −6.38755 −0.600890 −0.300445 0.953799i \(-0.597135\pi\)
−0.300445 + 0.953799i \(0.597135\pi\)
\(114\) 1.61704 0.151450
\(115\) 6.27021 0.584700
\(116\) −14.2222 −1.32050
\(117\) −5.77088 −0.533518
\(118\) 0.689164 0.0634427
\(119\) −2.77561 −0.254440
\(120\) 1.85149 0.169017
\(121\) −10.8425 −0.985680
\(122\) 4.10075 0.371264
\(123\) 6.26360 0.564770
\(124\) 16.9664 1.52363
\(125\) −10.6924 −0.956356
\(126\) −1.04204 −0.0928326
\(127\) 3.56831 0.316636 0.158318 0.987388i \(-0.449393\pi\)
0.158318 + 0.987388i \(0.449393\pi\)
\(128\) 9.98555 0.882606
\(129\) −5.27244 −0.464213
\(130\) 2.76874 0.242834
\(131\) 2.75680 0.240863 0.120431 0.992722i \(-0.461572\pi\)
0.120431 + 0.992722i \(0.461572\pi\)
\(132\) −0.737843 −0.0642210
\(133\) −11.9551 −1.03664
\(134\) −5.18707 −0.448095
\(135\) 1.27795 0.109988
\(136\) −1.44880 −0.124234
\(137\) −6.05752 −0.517529 −0.258764 0.965940i \(-0.583315\pi\)
−0.258764 + 0.965940i \(0.583315\pi\)
\(138\) −1.84203 −0.156804
\(139\) −2.20550 −0.187068 −0.0935339 0.995616i \(-0.529816\pi\)
−0.0935339 + 0.995616i \(0.529816\pi\)
\(140\) −6.59421 −0.557312
\(141\) 8.22755 0.692885
\(142\) 4.36247 0.366090
\(143\) −2.29042 −0.191534
\(144\) 3.17419 0.264515
\(145\) 9.77658 0.811901
\(146\) 5.86973 0.485782
\(147\) 0.704011 0.0580658
\(148\) 7.58421 0.623418
\(149\) 2.82787 0.231668 0.115834 0.993269i \(-0.463046\pi\)
0.115834 + 0.993269i \(0.463046\pi\)
\(150\) 1.26401 0.103206
\(151\) −16.9552 −1.37979 −0.689896 0.723908i \(-0.742344\pi\)
−0.689896 + 0.723908i \(0.742344\pi\)
\(152\) −6.24025 −0.506151
\(153\) −1.00000 −0.0808452
\(154\) −0.413579 −0.0333271
\(155\) −11.6630 −0.936796
\(156\) 10.7284 0.858957
\(157\) 1.00000 0.0798087
\(158\) 4.82133 0.383565
\(159\) −6.53665 −0.518390
\(160\) −5.22588 −0.413142
\(161\) 13.6185 1.07329
\(162\) −0.375429 −0.0294965
\(163\) −4.38594 −0.343533 −0.171767 0.985138i \(-0.554948\pi\)
−0.171767 + 0.985138i \(0.554948\pi\)
\(164\) −11.6444 −0.909273
\(165\) 0.507206 0.0394859
\(166\) −0.830859 −0.0644872
\(167\) −9.85325 −0.762468 −0.381234 0.924479i \(-0.624501\pi\)
−0.381234 + 0.924479i \(0.624501\pi\)
\(168\) 4.02130 0.310250
\(169\) 20.3031 1.56177
\(170\) 0.479778 0.0367973
\(171\) −4.30719 −0.329379
\(172\) 9.80175 0.747376
\(173\) 18.6020 1.41428 0.707142 0.707072i \(-0.249984\pi\)
0.707142 + 0.707072i \(0.249984\pi\)
\(174\) −2.87212 −0.217735
\(175\) −9.34508 −0.706421
\(176\) 1.25981 0.0949616
\(177\) −1.83567 −0.137977
\(178\) 3.39700 0.254616
\(179\) −5.55686 −0.415339 −0.207670 0.978199i \(-0.566588\pi\)
−0.207670 + 0.978199i \(0.566588\pi\)
\(180\) −2.37577 −0.177079
\(181\) −11.2722 −0.837854 −0.418927 0.908020i \(-0.637594\pi\)
−0.418927 + 0.908020i \(0.637594\pi\)
\(182\) 6.01351 0.445751
\(183\) −10.9228 −0.807439
\(184\) 7.10850 0.524046
\(185\) −5.21352 −0.383306
\(186\) 3.42630 0.251229
\(187\) −0.396892 −0.0290236
\(188\) −15.2955 −1.11554
\(189\) 2.77561 0.201896
\(190\) 2.06649 0.149919
\(191\) 23.2254 1.68053 0.840267 0.542173i \(-0.182398\pi\)
0.840267 + 0.542173i \(0.182398\pi\)
\(192\) −4.81314 −0.347358
\(193\) 13.4857 0.970725 0.485362 0.874313i \(-0.338688\pi\)
0.485362 + 0.874313i \(0.338688\pi\)
\(194\) −7.20317 −0.517157
\(195\) −7.37487 −0.528126
\(196\) −1.30879 −0.0934853
\(197\) −8.81679 −0.628170 −0.314085 0.949395i \(-0.601698\pi\)
−0.314085 + 0.949395i \(0.601698\pi\)
\(198\) −0.149005 −0.0105893
\(199\) 3.14598 0.223013 0.111506 0.993764i \(-0.464432\pi\)
0.111506 + 0.993764i \(0.464432\pi\)
\(200\) −4.87790 −0.344919
\(201\) 13.8164 0.974533
\(202\) −4.05260 −0.285140
\(203\) 21.2341 1.49034
\(204\) 1.85905 0.130160
\(205\) 8.00454 0.559062
\(206\) 1.77364 0.123575
\(207\) 4.90648 0.341024
\(208\) −18.3178 −1.27011
\(209\) −1.70949 −0.118248
\(210\) −1.33168 −0.0918943
\(211\) −12.5313 −0.862691 −0.431345 0.902187i \(-0.641961\pi\)
−0.431345 + 0.902187i \(0.641961\pi\)
\(212\) 12.1520 0.834602
\(213\) −11.6200 −0.796187
\(214\) 1.48411 0.101452
\(215\) −6.73789 −0.459521
\(216\) 1.44880 0.0985783
\(217\) −25.3313 −1.71960
\(218\) −2.12915 −0.144204
\(219\) −15.6347 −1.05650
\(220\) −0.942923 −0.0635719
\(221\) 5.77088 0.388191
\(222\) 1.53160 0.102794
\(223\) 1.96673 0.131702 0.0658511 0.997829i \(-0.479024\pi\)
0.0658511 + 0.997829i \(0.479024\pi\)
\(224\) −11.3502 −0.758370
\(225\) −3.36685 −0.224457
\(226\) 2.39807 0.159517
\(227\) −22.9579 −1.52377 −0.761885 0.647712i \(-0.775726\pi\)
−0.761885 + 0.647712i \(0.775726\pi\)
\(228\) 8.00729 0.530296
\(229\) −21.1476 −1.39747 −0.698737 0.715379i \(-0.746254\pi\)
−0.698737 + 0.715379i \(0.746254\pi\)
\(230\) −2.35402 −0.155219
\(231\) 1.10162 0.0724811
\(232\) 11.0836 0.727677
\(233\) −9.92716 −0.650350 −0.325175 0.945654i \(-0.605423\pi\)
−0.325175 + 0.945654i \(0.605423\pi\)
\(234\) 2.16655 0.141632
\(235\) 10.5144 0.685881
\(236\) 3.41261 0.222142
\(237\) −12.8422 −0.834191
\(238\) 1.04204 0.0675457
\(239\) 1.10968 0.0717794 0.0358897 0.999356i \(-0.488573\pi\)
0.0358897 + 0.999356i \(0.488573\pi\)
\(240\) 4.05644 0.261842
\(241\) 11.1965 0.721231 0.360615 0.932715i \(-0.382567\pi\)
0.360615 + 0.932715i \(0.382567\pi\)
\(242\) 4.07058 0.261667
\(243\) 1.00000 0.0641500
\(244\) 20.3061 1.29997
\(245\) 0.899688 0.0574789
\(246\) −2.35154 −0.149929
\(247\) 24.8563 1.58157
\(248\) −13.2223 −0.839616
\(249\) 2.21309 0.140249
\(250\) 4.01423 0.253882
\(251\) −7.07943 −0.446850 −0.223425 0.974721i \(-0.571724\pi\)
−0.223425 + 0.974721i \(0.571724\pi\)
\(252\) −5.16001 −0.325050
\(253\) 1.94734 0.122428
\(254\) −1.33965 −0.0840569
\(255\) −1.27795 −0.0800281
\(256\) 5.87741 0.367338
\(257\) 3.42515 0.213655 0.106827 0.994278i \(-0.465931\pi\)
0.106827 + 0.994278i \(0.465931\pi\)
\(258\) 1.97943 0.123234
\(259\) −11.3234 −0.703602
\(260\) 13.7103 0.850275
\(261\) 7.65023 0.473537
\(262\) −1.03498 −0.0639414
\(263\) −0.566980 −0.0349615 −0.0174807 0.999847i \(-0.505565\pi\)
−0.0174807 + 0.999847i \(0.505565\pi\)
\(264\) 0.575017 0.0353898
\(265\) −8.35349 −0.513151
\(266\) 4.48828 0.275194
\(267\) −9.04833 −0.553749
\(268\) −25.6854 −1.56899
\(269\) 22.9490 1.39923 0.699613 0.714522i \(-0.253356\pi\)
0.699613 + 0.714522i \(0.253356\pi\)
\(270\) −0.479778 −0.0291983
\(271\) 11.4834 0.697570 0.348785 0.937203i \(-0.386594\pi\)
0.348785 + 0.937203i \(0.386594\pi\)
\(272\) −3.17419 −0.192463
\(273\) −16.0177 −0.969436
\(274\) 2.27417 0.137387
\(275\) −1.33628 −0.0805805
\(276\) −9.12140 −0.549044
\(277\) 13.6403 0.819564 0.409782 0.912183i \(-0.365605\pi\)
0.409782 + 0.912183i \(0.365605\pi\)
\(278\) 0.828007 0.0496606
\(279\) −9.12637 −0.546382
\(280\) 5.13901 0.307114
\(281\) −9.28622 −0.553969 −0.276985 0.960874i \(-0.589335\pi\)
−0.276985 + 0.960874i \(0.589335\pi\)
\(282\) −3.08886 −0.183939
\(283\) 16.4139 0.975704 0.487852 0.872926i \(-0.337781\pi\)
0.487852 + 0.872926i \(0.337781\pi\)
\(284\) 21.6021 1.28185
\(285\) −5.50435 −0.326049
\(286\) 0.859888 0.0508462
\(287\) 17.3853 1.02622
\(288\) −4.08928 −0.240963
\(289\) 1.00000 0.0588235
\(290\) −3.67041 −0.215534
\(291\) 19.1865 1.12473
\(292\) 29.0658 1.70095
\(293\) 5.29694 0.309451 0.154725 0.987958i \(-0.450551\pi\)
0.154725 + 0.987958i \(0.450551\pi\)
\(294\) −0.264306 −0.0154146
\(295\) −2.34589 −0.136583
\(296\) −5.91054 −0.343543
\(297\) 0.396892 0.0230300
\(298\) −1.06166 −0.0615005
\(299\) −28.3147 −1.63748
\(300\) 6.25916 0.361373
\(301\) −14.6342 −0.843504
\(302\) 6.36546 0.366291
\(303\) 10.7946 0.620134
\(304\) −13.6718 −0.784132
\(305\) −13.9588 −0.799278
\(306\) 0.375429 0.0214618
\(307\) 13.0465 0.744601 0.372301 0.928112i \(-0.378569\pi\)
0.372301 + 0.928112i \(0.378569\pi\)
\(308\) −2.04796 −0.116694
\(309\) −4.72430 −0.268756
\(310\) 4.37863 0.248689
\(311\) −25.6124 −1.45235 −0.726174 0.687511i \(-0.758703\pi\)
−0.726174 + 0.687511i \(0.758703\pi\)
\(312\) −8.36085 −0.473340
\(313\) −10.8924 −0.615673 −0.307836 0.951439i \(-0.599605\pi\)
−0.307836 + 0.951439i \(0.599605\pi\)
\(314\) −0.375429 −0.0211867
\(315\) 3.54708 0.199855
\(316\) 23.8743 1.34304
\(317\) 7.27505 0.408607 0.204304 0.978908i \(-0.434507\pi\)
0.204304 + 0.978908i \(0.434507\pi\)
\(318\) 2.45405 0.137616
\(319\) 3.03631 0.170001
\(320\) −6.15093 −0.343847
\(321\) −3.95311 −0.220641
\(322\) −5.11276 −0.284923
\(323\) 4.30719 0.239658
\(324\) −1.85905 −0.103281
\(325\) 19.4297 1.07777
\(326\) 1.64661 0.0911972
\(327\) 5.67124 0.313620
\(328\) 9.07471 0.501067
\(329\) 22.8365 1.25902
\(330\) −0.190420 −0.0104823
\(331\) −35.9080 −1.97368 −0.986841 0.161695i \(-0.948304\pi\)
−0.986841 + 0.161695i \(0.948304\pi\)
\(332\) −4.11426 −0.225799
\(333\) −4.07961 −0.223561
\(334\) 3.69919 0.202411
\(335\) 17.6566 0.964683
\(336\) 8.81030 0.480641
\(337\) −5.63039 −0.306707 −0.153354 0.988171i \(-0.549007\pi\)
−0.153354 + 0.988171i \(0.549007\pi\)
\(338\) −7.62235 −0.414601
\(339\) −6.38755 −0.346924
\(340\) 2.37577 0.128844
\(341\) −3.62218 −0.196152
\(342\) 1.61704 0.0874396
\(343\) −17.4752 −0.943573
\(344\) −7.63871 −0.411852
\(345\) 6.27021 0.337577
\(346\) −6.98372 −0.375447
\(347\) 23.8024 1.27778 0.638891 0.769297i \(-0.279393\pi\)
0.638891 + 0.769297i \(0.279393\pi\)
\(348\) −14.2222 −0.762389
\(349\) −10.5652 −0.565540 −0.282770 0.959188i \(-0.591253\pi\)
−0.282770 + 0.959188i \(0.591253\pi\)
\(350\) 3.50841 0.187532
\(351\) −5.77088 −0.308027
\(352\) −1.62300 −0.0865063
\(353\) 24.2089 1.28851 0.644255 0.764811i \(-0.277168\pi\)
0.644255 + 0.764811i \(0.277168\pi\)
\(354\) 0.689164 0.0366286
\(355\) −14.8497 −0.788139
\(356\) 16.8213 0.891529
\(357\) −2.77561 −0.146901
\(358\) 2.08621 0.110259
\(359\) 19.7632 1.04306 0.521532 0.853232i \(-0.325361\pi\)
0.521532 + 0.853232i \(0.325361\pi\)
\(360\) 1.85149 0.0975819
\(361\) −0.448157 −0.0235872
\(362\) 4.23190 0.222424
\(363\) −10.8425 −0.569082
\(364\) 29.7778 1.56078
\(365\) −19.9803 −1.04582
\(366\) 4.10075 0.214349
\(367\) −0.882217 −0.0460513 −0.0230257 0.999735i \(-0.507330\pi\)
−0.0230257 + 0.999735i \(0.507330\pi\)
\(368\) 15.5741 0.811854
\(369\) 6.26360 0.326070
\(370\) 1.95731 0.101755
\(371\) −18.1432 −0.941948
\(372\) 16.9664 0.879668
\(373\) 2.59509 0.134369 0.0671844 0.997741i \(-0.478598\pi\)
0.0671844 + 0.997741i \(0.478598\pi\)
\(374\) 0.149005 0.00770484
\(375\) −10.6924 −0.552152
\(376\) 11.9201 0.614731
\(377\) −44.1486 −2.27377
\(378\) −1.04204 −0.0535969
\(379\) 13.5095 0.693938 0.346969 0.937877i \(-0.387211\pi\)
0.346969 + 0.937877i \(0.387211\pi\)
\(380\) 10.2329 0.524936
\(381\) 3.56831 0.182810
\(382\) −8.71950 −0.446128
\(383\) 26.3549 1.34667 0.673335 0.739337i \(-0.264861\pi\)
0.673335 + 0.739337i \(0.264861\pi\)
\(384\) 9.98555 0.509573
\(385\) 1.40781 0.0717485
\(386\) −5.06293 −0.257697
\(387\) −5.27244 −0.268013
\(388\) −35.6687 −1.81081
\(389\) 20.2676 1.02761 0.513804 0.857908i \(-0.328236\pi\)
0.513804 + 0.857908i \(0.328236\pi\)
\(390\) 2.76874 0.140201
\(391\) −4.90648 −0.248131
\(392\) 1.01997 0.0515163
\(393\) 2.75680 0.139062
\(394\) 3.31007 0.166759
\(395\) −16.4116 −0.825759
\(396\) −0.737843 −0.0370780
\(397\) 10.2322 0.513540 0.256770 0.966472i \(-0.417342\pi\)
0.256770 + 0.966472i \(0.417342\pi\)
\(398\) −1.18109 −0.0592028
\(399\) −11.9551 −0.598502
\(400\) −10.6870 −0.534351
\(401\) −23.3330 −1.16519 −0.582596 0.812762i \(-0.697963\pi\)
−0.582596 + 0.812762i \(0.697963\pi\)
\(402\) −5.18707 −0.258708
\(403\) 52.6672 2.62354
\(404\) −20.0677 −0.998408
\(405\) 1.27795 0.0635016
\(406\) −7.97187 −0.395637
\(407\) −1.61916 −0.0802590
\(408\) −1.44880 −0.0717263
\(409\) −16.3597 −0.808934 −0.404467 0.914553i \(-0.632543\pi\)
−0.404467 + 0.914553i \(0.632543\pi\)
\(410\) −3.00514 −0.148413
\(411\) −6.05752 −0.298795
\(412\) 8.78273 0.432694
\(413\) −5.09511 −0.250714
\(414\) −1.84203 −0.0905309
\(415\) 2.82821 0.138832
\(416\) 23.5987 1.15702
\(417\) −2.20550 −0.108004
\(418\) 0.641790 0.0313910
\(419\) 3.51530 0.171733 0.0858667 0.996307i \(-0.472634\pi\)
0.0858667 + 0.996307i \(0.472634\pi\)
\(420\) −6.59421 −0.321764
\(421\) −30.9095 −1.50644 −0.753218 0.657771i \(-0.771500\pi\)
−0.753218 + 0.657771i \(0.771500\pi\)
\(422\) 4.70461 0.229017
\(423\) 8.22755 0.400037
\(424\) −9.47030 −0.459918
\(425\) 3.36685 0.163316
\(426\) 4.36247 0.211362
\(427\) −30.3175 −1.46717
\(428\) 7.34904 0.355229
\(429\) −2.29042 −0.110582
\(430\) 2.52960 0.121988
\(431\) 39.2755 1.89183 0.945917 0.324409i \(-0.105166\pi\)
0.945917 + 0.324409i \(0.105166\pi\)
\(432\) 3.17419 0.152718
\(433\) −24.3852 −1.17188 −0.585939 0.810355i \(-0.699274\pi\)
−0.585939 + 0.810355i \(0.699274\pi\)
\(434\) 9.51008 0.456499
\(435\) 9.77658 0.468751
\(436\) −10.5431 −0.504925
\(437\) −21.1331 −1.01093
\(438\) 5.86973 0.280466
\(439\) −2.21370 −0.105654 −0.0528272 0.998604i \(-0.516823\pi\)
−0.0528272 + 0.998604i \(0.516823\pi\)
\(440\) 0.734840 0.0350321
\(441\) 0.704011 0.0335243
\(442\) −2.16655 −0.103052
\(443\) −28.9195 −1.37400 −0.687002 0.726655i \(-0.741074\pi\)
−0.687002 + 0.726655i \(0.741074\pi\)
\(444\) 7.58421 0.359931
\(445\) −11.5633 −0.548152
\(446\) −0.738369 −0.0349628
\(447\) 2.82787 0.133754
\(448\) −13.3594 −0.631172
\(449\) 5.33128 0.251599 0.125799 0.992056i \(-0.459850\pi\)
0.125799 + 0.992056i \(0.459850\pi\)
\(450\) 1.26401 0.0595862
\(451\) 2.48597 0.117060
\(452\) 11.8748 0.558543
\(453\) −16.9552 −0.796623
\(454\) 8.61906 0.404513
\(455\) −20.4698 −0.959638
\(456\) −6.24025 −0.292226
\(457\) −9.39576 −0.439515 −0.219758 0.975555i \(-0.570527\pi\)
−0.219758 + 0.975555i \(0.570527\pi\)
\(458\) 7.93942 0.370985
\(459\) −1.00000 −0.0466760
\(460\) −11.6567 −0.543494
\(461\) −37.8496 −1.76283 −0.881415 0.472343i \(-0.843408\pi\)
−0.881415 + 0.472343i \(0.843408\pi\)
\(462\) −0.413579 −0.0192414
\(463\) −27.4378 −1.27514 −0.637570 0.770392i \(-0.720061\pi\)
−0.637570 + 0.770392i \(0.720061\pi\)
\(464\) 24.2832 1.12732
\(465\) −11.6630 −0.540859
\(466\) 3.72694 0.172647
\(467\) −37.4901 −1.73484 −0.867418 0.497579i \(-0.834222\pi\)
−0.867418 + 0.497579i \(0.834222\pi\)
\(468\) 10.7284 0.495919
\(469\) 38.3489 1.77079
\(470\) −3.94739 −0.182080
\(471\) 1.00000 0.0460776
\(472\) −2.65952 −0.122414
\(473\) −2.09259 −0.0962173
\(474\) 4.82133 0.221451
\(475\) 14.5017 0.665382
\(476\) 5.16001 0.236509
\(477\) −6.53665 −0.299293
\(478\) −0.416607 −0.0190551
\(479\) −3.85473 −0.176127 −0.0880636 0.996115i \(-0.528068\pi\)
−0.0880636 + 0.996115i \(0.528068\pi\)
\(480\) −5.22588 −0.238528
\(481\) 23.5429 1.07347
\(482\) −4.20349 −0.191464
\(483\) 13.6185 0.619662
\(484\) 20.1567 0.916216
\(485\) 24.5193 1.11336
\(486\) −0.375429 −0.0170298
\(487\) −35.1442 −1.59254 −0.796268 0.604945i \(-0.793195\pi\)
−0.796268 + 0.604945i \(0.793195\pi\)
\(488\) −15.8250 −0.716364
\(489\) −4.38594 −0.198339
\(490\) −0.337769 −0.0152588
\(491\) 8.09017 0.365104 0.182552 0.983196i \(-0.441564\pi\)
0.182552 + 0.983196i \(0.441564\pi\)
\(492\) −11.6444 −0.524969
\(493\) −7.65023 −0.344549
\(494\) −9.33175 −0.419855
\(495\) 0.507206 0.0227972
\(496\) −28.9688 −1.30074
\(497\) −32.2525 −1.44672
\(498\) −0.830859 −0.0372317
\(499\) −35.1864 −1.57516 −0.787579 0.616213i \(-0.788666\pi\)
−0.787579 + 0.616213i \(0.788666\pi\)
\(500\) 19.8777 0.888958
\(501\) −9.85325 −0.440211
\(502\) 2.65782 0.118624
\(503\) −28.8856 −1.28795 −0.643973 0.765048i \(-0.722715\pi\)
−0.643973 + 0.765048i \(0.722715\pi\)
\(504\) 4.02130 0.179123
\(505\) 13.7949 0.613866
\(506\) −0.731087 −0.0325008
\(507\) 20.3031 0.901691
\(508\) −6.63368 −0.294322
\(509\) −23.9719 −1.06254 −0.531268 0.847204i \(-0.678284\pi\)
−0.531268 + 0.847204i \(0.678284\pi\)
\(510\) 0.479778 0.0212449
\(511\) −43.3959 −1.91972
\(512\) −22.1776 −0.980123
\(513\) −4.30719 −0.190167
\(514\) −1.28590 −0.0567186
\(515\) −6.03740 −0.266040
\(516\) 9.80175 0.431498
\(517\) 3.26545 0.143614
\(518\) 4.25113 0.186784
\(519\) 18.6020 0.816537
\(520\) −10.6847 −0.468556
\(521\) 28.6313 1.25436 0.627180 0.778874i \(-0.284209\pi\)
0.627180 + 0.778874i \(0.284209\pi\)
\(522\) −2.87212 −0.125709
\(523\) 14.9032 0.651670 0.325835 0.945427i \(-0.394355\pi\)
0.325835 + 0.945427i \(0.394355\pi\)
\(524\) −5.12504 −0.223888
\(525\) −9.34508 −0.407853
\(526\) 0.212861 0.00928116
\(527\) 9.12637 0.397551
\(528\) 1.25981 0.0548261
\(529\) 1.07351 0.0466742
\(530\) 3.13614 0.136225
\(531\) −1.83567 −0.0796613
\(532\) 22.2251 0.963580
\(533\) −36.1465 −1.56568
\(534\) 3.39700 0.147003
\(535\) −5.05186 −0.218411
\(536\) 20.0172 0.864611
\(537\) −5.55686 −0.239796
\(538\) −8.61571 −0.371450
\(539\) 0.279416 0.0120353
\(540\) −2.37577 −0.102237
\(541\) −10.7320 −0.461406 −0.230703 0.973024i \(-0.574103\pi\)
−0.230703 + 0.973024i \(0.574103\pi\)
\(542\) −4.31122 −0.185183
\(543\) −11.2722 −0.483735
\(544\) 4.08928 0.175326
\(545\) 7.24754 0.310450
\(546\) 6.01351 0.257354
\(547\) −9.06967 −0.387791 −0.193896 0.981022i \(-0.562112\pi\)
−0.193896 + 0.981022i \(0.562112\pi\)
\(548\) 11.2612 0.481057
\(549\) −10.9228 −0.466175
\(550\) 0.501677 0.0213916
\(551\) −32.9510 −1.40376
\(552\) 7.10850 0.302558
\(553\) −35.6450 −1.51578
\(554\) −5.12095 −0.217568
\(555\) −5.21352 −0.221302
\(556\) 4.10014 0.173885
\(557\) −28.5064 −1.20786 −0.603928 0.797039i \(-0.706399\pi\)
−0.603928 + 0.797039i \(0.706399\pi\)
\(558\) 3.42630 0.145047
\(559\) 30.4266 1.28691
\(560\) 11.2591 0.475783
\(561\) −0.396892 −0.0167568
\(562\) 3.48631 0.147061
\(563\) −25.9561 −1.09392 −0.546960 0.837159i \(-0.684215\pi\)
−0.546960 + 0.837159i \(0.684215\pi\)
\(564\) −15.2955 −0.644055
\(565\) −8.16294 −0.343417
\(566\) −6.16224 −0.259018
\(567\) 2.77561 0.116565
\(568\) −16.8350 −0.706381
\(569\) −3.30031 −0.138356 −0.0691782 0.997604i \(-0.522038\pi\)
−0.0691782 + 0.997604i \(0.522038\pi\)
\(570\) 2.06649 0.0865558
\(571\) −23.4110 −0.979718 −0.489859 0.871802i \(-0.662952\pi\)
−0.489859 + 0.871802i \(0.662952\pi\)
\(572\) 4.25800 0.178036
\(573\) 23.2254 0.970257
\(574\) −6.52695 −0.272430
\(575\) −16.5194 −0.688906
\(576\) −4.81314 −0.200547
\(577\) 5.18200 0.215730 0.107865 0.994166i \(-0.465599\pi\)
0.107865 + 0.994166i \(0.465599\pi\)
\(578\) −0.375429 −0.0156158
\(579\) 13.4857 0.560448
\(580\) −18.1752 −0.754683
\(581\) 6.14269 0.254842
\(582\) −7.20317 −0.298581
\(583\) −2.59434 −0.107447
\(584\) −22.6516 −0.937329
\(585\) −7.37487 −0.304913
\(586\) −1.98862 −0.0821493
\(587\) −43.5318 −1.79675 −0.898375 0.439230i \(-0.855251\pi\)
−0.898375 + 0.439230i \(0.855251\pi\)
\(588\) −1.30879 −0.0539737
\(589\) 39.3090 1.61970
\(590\) 0.880714 0.0362584
\(591\) −8.81679 −0.362674
\(592\) −12.9494 −0.532219
\(593\) −17.1366 −0.703715 −0.351858 0.936054i \(-0.614450\pi\)
−0.351858 + 0.936054i \(0.614450\pi\)
\(594\) −0.149005 −0.00611373
\(595\) −3.54708 −0.145416
\(596\) −5.25716 −0.215342
\(597\) 3.14598 0.128757
\(598\) 10.6301 0.434699
\(599\) 31.7486 1.29721 0.648606 0.761125i \(-0.275352\pi\)
0.648606 + 0.761125i \(0.275352\pi\)
\(600\) −4.87790 −0.199139
\(601\) −2.57769 −0.105146 −0.0525731 0.998617i \(-0.516742\pi\)
−0.0525731 + 0.998617i \(0.516742\pi\)
\(602\) 5.49411 0.223923
\(603\) 13.8164 0.562647
\(604\) 31.5206 1.28255
\(605\) −13.8561 −0.563330
\(606\) −4.05260 −0.164626
\(607\) −20.8986 −0.848249 −0.424124 0.905604i \(-0.639418\pi\)
−0.424124 + 0.905604i \(0.639418\pi\)
\(608\) 17.6133 0.714313
\(609\) 21.2341 0.860447
\(610\) 5.24053 0.212183
\(611\) −47.4802 −1.92084
\(612\) 1.85905 0.0751478
\(613\) 15.4420 0.623695 0.311847 0.950132i \(-0.399052\pi\)
0.311847 + 0.950132i \(0.399052\pi\)
\(614\) −4.89802 −0.197668
\(615\) 8.00454 0.322774
\(616\) 1.59602 0.0643056
\(617\) 5.41493 0.217997 0.108998 0.994042i \(-0.465236\pi\)
0.108998 + 0.994042i \(0.465236\pi\)
\(618\) 1.77364 0.0713462
\(619\) 0.143099 0.00575163 0.00287581 0.999996i \(-0.499085\pi\)
0.00287581 + 0.999996i \(0.499085\pi\)
\(620\) 21.6822 0.870776
\(621\) 4.90648 0.196890
\(622\) 9.61565 0.385552
\(623\) −25.1146 −1.00620
\(624\) −18.3178 −0.733301
\(625\) 3.16999 0.126799
\(626\) 4.08931 0.163442
\(627\) −1.70949 −0.0682703
\(628\) −1.85905 −0.0741843
\(629\) 4.07961 0.162665
\(630\) −1.33168 −0.0530552
\(631\) 18.4817 0.735745 0.367872 0.929876i \(-0.380086\pi\)
0.367872 + 0.929876i \(0.380086\pi\)
\(632\) −18.6058 −0.740098
\(633\) −12.5313 −0.498075
\(634\) −2.73126 −0.108472
\(635\) 4.56011 0.180962
\(636\) 12.1520 0.481858
\(637\) −4.06276 −0.160973
\(638\) −1.13992 −0.0451298
\(639\) −11.6200 −0.459679
\(640\) 12.7610 0.504422
\(641\) 33.5412 1.32480 0.662399 0.749151i \(-0.269538\pi\)
0.662399 + 0.749151i \(0.269538\pi\)
\(642\) 1.48411 0.0585732
\(643\) 43.9063 1.73149 0.865747 0.500482i \(-0.166844\pi\)
0.865747 + 0.500482i \(0.166844\pi\)
\(644\) −25.3174 −0.997647
\(645\) −6.73789 −0.265304
\(646\) −1.61704 −0.0636216
\(647\) −23.8228 −0.936571 −0.468286 0.883577i \(-0.655128\pi\)
−0.468286 + 0.883577i \(0.655128\pi\)
\(648\) 1.44880 0.0569142
\(649\) −0.728563 −0.0285986
\(650\) −7.29447 −0.286113
\(651\) −25.3313 −0.992810
\(652\) 8.15370 0.319323
\(653\) 29.7782 1.16531 0.582655 0.812719i \(-0.302014\pi\)
0.582655 + 0.812719i \(0.302014\pi\)
\(654\) −2.12915 −0.0832562
\(655\) 3.52304 0.137657
\(656\) 19.8818 0.776255
\(657\) −15.6347 −0.609969
\(658\) −8.57347 −0.334229
\(659\) 20.2268 0.787924 0.393962 0.919127i \(-0.371104\pi\)
0.393962 + 0.919127i \(0.371104\pi\)
\(660\) −0.942923 −0.0367032
\(661\) 39.1822 1.52401 0.762006 0.647570i \(-0.224215\pi\)
0.762006 + 0.647570i \(0.224215\pi\)
\(662\) 13.4809 0.523950
\(663\) 5.77088 0.224122
\(664\) 3.20633 0.124430
\(665\) −15.2779 −0.592453
\(666\) 1.53160 0.0593484
\(667\) 37.5357 1.45339
\(668\) 18.3177 0.708734
\(669\) 1.96673 0.0760383
\(670\) −6.62879 −0.256093
\(671\) −4.33518 −0.167358
\(672\) −11.3502 −0.437845
\(673\) 48.0477 1.85210 0.926052 0.377396i \(-0.123180\pi\)
0.926052 + 0.377396i \(0.123180\pi\)
\(674\) 2.11381 0.0814210
\(675\) −3.36685 −0.129590
\(676\) −37.7445 −1.45171
\(677\) −36.9221 −1.41903 −0.709516 0.704689i \(-0.751086\pi\)
−0.709516 + 0.704689i \(0.751086\pi\)
\(678\) 2.39807 0.0920973
\(679\) 53.2543 2.04371
\(680\) −1.85149 −0.0710013
\(681\) −22.9579 −0.879749
\(682\) 1.35987 0.0520722
\(683\) −19.1950 −0.734476 −0.367238 0.930127i \(-0.619697\pi\)
−0.367238 + 0.930127i \(0.619697\pi\)
\(684\) 8.00729 0.306166
\(685\) −7.74118 −0.295775
\(686\) 6.56070 0.250489
\(687\) −21.1476 −0.806832
\(688\) −16.7357 −0.638043
\(689\) 37.7223 1.43710
\(690\) −2.35402 −0.0896159
\(691\) 46.4410 1.76670 0.883350 0.468715i \(-0.155283\pi\)
0.883350 + 0.468715i \(0.155283\pi\)
\(692\) −34.5821 −1.31461
\(693\) 1.10162 0.0418470
\(694\) −8.93612 −0.339211
\(695\) −2.81851 −0.106912
\(696\) 11.0836 0.420125
\(697\) −6.26360 −0.237251
\(698\) 3.96646 0.150133
\(699\) −9.92716 −0.375480
\(700\) 17.3730 0.656637
\(701\) −37.1331 −1.40250 −0.701249 0.712916i \(-0.747374\pi\)
−0.701249 + 0.712916i \(0.747374\pi\)
\(702\) 2.16655 0.0817713
\(703\) 17.5716 0.662727
\(704\) −1.91030 −0.0719970
\(705\) 10.5144 0.395994
\(706\) −9.08872 −0.342058
\(707\) 29.9616 1.12682
\(708\) 3.41261 0.128254
\(709\) 16.6067 0.623679 0.311839 0.950135i \(-0.399055\pi\)
0.311839 + 0.950135i \(0.399055\pi\)
\(710\) 5.57500 0.209226
\(711\) −12.8422 −0.481620
\(712\) −13.1092 −0.491289
\(713\) −44.7783 −1.67696
\(714\) 1.04204 0.0389975
\(715\) −2.92703 −0.109465
\(716\) 10.3305 0.386069
\(717\) 1.10968 0.0414419
\(718\) −7.41969 −0.276900
\(719\) 15.8066 0.589487 0.294743 0.955576i \(-0.404766\pi\)
0.294743 + 0.955576i \(0.404766\pi\)
\(720\) 4.05644 0.151174
\(721\) −13.1128 −0.488347
\(722\) 0.168251 0.00626165
\(723\) 11.1965 0.416403
\(724\) 20.9556 0.778807
\(725\) −25.7572 −0.956599
\(726\) 4.07058 0.151073
\(727\) −38.9526 −1.44467 −0.722336 0.691542i \(-0.756932\pi\)
−0.722336 + 0.691542i \(0.756932\pi\)
\(728\) −23.2065 −0.860088
\(729\) 1.00000 0.0370370
\(730\) 7.50119 0.277632
\(731\) 5.27244 0.195008
\(732\) 20.3061 0.750536
\(733\) 35.7281 1.31965 0.659824 0.751420i \(-0.270631\pi\)
0.659824 + 0.751420i \(0.270631\pi\)
\(734\) 0.331210 0.0122252
\(735\) 0.899688 0.0331855
\(736\) −20.0640 −0.739567
\(737\) 5.48361 0.201991
\(738\) −2.35154 −0.0865613
\(739\) −3.55977 −0.130948 −0.0654741 0.997854i \(-0.520856\pi\)
−0.0654741 + 0.997854i \(0.520856\pi\)
\(740\) 9.69221 0.356293
\(741\) 24.8563 0.913117
\(742\) 6.81148 0.250057
\(743\) −8.80981 −0.323200 −0.161600 0.986856i \(-0.551666\pi\)
−0.161600 + 0.986856i \(0.551666\pi\)
\(744\) −13.2223 −0.484753
\(745\) 3.61386 0.132402
\(746\) −0.974272 −0.0356706
\(747\) 2.21309 0.0809729
\(748\) 0.737843 0.0269782
\(749\) −10.9723 −0.400919
\(750\) 4.01423 0.146579
\(751\) −47.8799 −1.74716 −0.873581 0.486678i \(-0.838208\pi\)
−0.873581 + 0.486678i \(0.838208\pi\)
\(752\) 26.1158 0.952344
\(753\) −7.07943 −0.257989
\(754\) 16.5746 0.603613
\(755\) −21.6678 −0.788572
\(756\) −5.16001 −0.187668
\(757\) −12.4592 −0.452838 −0.226419 0.974030i \(-0.572702\pi\)
−0.226419 + 0.974030i \(0.572702\pi\)
\(758\) −5.07187 −0.184218
\(759\) 1.94734 0.0706840
\(760\) −7.97470 −0.289273
\(761\) 31.0759 1.12650 0.563251 0.826286i \(-0.309550\pi\)
0.563251 + 0.826286i \(0.309550\pi\)
\(762\) −1.33965 −0.0485302
\(763\) 15.7412 0.569868
\(764\) −43.1773 −1.56210
\(765\) −1.27795 −0.0462042
\(766\) −9.89437 −0.357498
\(767\) 10.5934 0.382507
\(768\) 5.87741 0.212083
\(769\) −9.86603 −0.355778 −0.177889 0.984051i \(-0.556927\pi\)
−0.177889 + 0.984051i \(0.556927\pi\)
\(770\) −0.528531 −0.0190469
\(771\) 3.42515 0.123354
\(772\) −25.0707 −0.902314
\(773\) −32.2160 −1.15873 −0.579364 0.815069i \(-0.696699\pi\)
−0.579364 + 0.815069i \(0.696699\pi\)
\(774\) 1.97943 0.0711490
\(775\) 30.7272 1.10375
\(776\) 27.7974 0.997869
\(777\) −11.3234 −0.406225
\(778\) −7.60903 −0.272797
\(779\) −26.9785 −0.966605
\(780\) 13.7103 0.490907
\(781\) −4.61187 −0.165026
\(782\) 1.84203 0.0658709
\(783\) 7.65023 0.273397
\(784\) 2.23466 0.0798093
\(785\) 1.27795 0.0456118
\(786\) −1.03498 −0.0369166
\(787\) 8.32247 0.296664 0.148332 0.988938i \(-0.452610\pi\)
0.148332 + 0.988938i \(0.452610\pi\)
\(788\) 16.3909 0.583901
\(789\) −0.566980 −0.0201850
\(790\) 6.16140 0.219213
\(791\) −17.7293 −0.630383
\(792\) 0.575017 0.0204323
\(793\) 63.0344 2.23842
\(794\) −3.84147 −0.136329
\(795\) −8.35349 −0.296268
\(796\) −5.84855 −0.207296
\(797\) 45.0712 1.59650 0.798251 0.602324i \(-0.205759\pi\)
0.798251 + 0.602324i \(0.205759\pi\)
\(798\) 4.48828 0.158883
\(799\) −8.22755 −0.291070
\(800\) 13.7680 0.486773
\(801\) −9.04833 −0.319707
\(802\) 8.75986 0.309322
\(803\) −6.20530 −0.218980
\(804\) −25.6854 −0.905855
\(805\) 17.4037 0.613398
\(806\) −19.7728 −0.696467
\(807\) 22.9490 0.807843
\(808\) 15.6392 0.550186
\(809\) −10.2441 −0.360162 −0.180081 0.983652i \(-0.557636\pi\)
−0.180081 + 0.983652i \(0.557636\pi\)
\(810\) −0.479778 −0.0168577
\(811\) −19.3672 −0.680075 −0.340038 0.940412i \(-0.610440\pi\)
−0.340038 + 0.940412i \(0.610440\pi\)
\(812\) −39.4752 −1.38531
\(813\) 11.4834 0.402742
\(814\) 0.607881 0.0213062
\(815\) −5.60499 −0.196334
\(816\) −3.17419 −0.111119
\(817\) 22.7094 0.794501
\(818\) 6.14190 0.214746
\(819\) −16.0177 −0.559704
\(820\) −14.8809 −0.519663
\(821\) 20.7051 0.722614 0.361307 0.932447i \(-0.382331\pi\)
0.361307 + 0.932447i \(0.382331\pi\)
\(822\) 2.27417 0.0793206
\(823\) −32.8577 −1.14535 −0.572674 0.819783i \(-0.694094\pi\)
−0.572674 + 0.819783i \(0.694094\pi\)
\(824\) −6.84457 −0.238442
\(825\) −1.33628 −0.0465232
\(826\) 1.91285 0.0665566
\(827\) 35.9954 1.25168 0.625842 0.779950i \(-0.284756\pi\)
0.625842 + 0.779950i \(0.284756\pi\)
\(828\) −9.12140 −0.316991
\(829\) −11.1846 −0.388457 −0.194228 0.980956i \(-0.562220\pi\)
−0.194228 + 0.980956i \(0.562220\pi\)
\(830\) −1.06179 −0.0368554
\(831\) 13.6403 0.473176
\(832\) 27.7760 0.962961
\(833\) −0.704011 −0.0243925
\(834\) 0.828007 0.0286715
\(835\) −12.5919 −0.435761
\(836\) 3.17803 0.109914
\(837\) −9.12637 −0.315454
\(838\) −1.31974 −0.0455898
\(839\) −14.2790 −0.492967 −0.246483 0.969147i \(-0.579275\pi\)
−0.246483 + 0.969147i \(0.579275\pi\)
\(840\) 5.13901 0.177313
\(841\) 29.5260 1.01814
\(842\) 11.6043 0.399911
\(843\) −9.28622 −0.319834
\(844\) 23.2964 0.801894
\(845\) 25.9462 0.892577
\(846\) −3.08886 −0.106197
\(847\) −30.0945 −1.03406
\(848\) −20.7486 −0.712508
\(849\) 16.4139 0.563323
\(850\) −1.26401 −0.0433553
\(851\) −20.0165 −0.686157
\(852\) 21.6021 0.740077
\(853\) −3.72272 −0.127463 −0.0637317 0.997967i \(-0.520300\pi\)
−0.0637317 + 0.997967i \(0.520300\pi\)
\(854\) 11.3821 0.389486
\(855\) −5.50435 −0.188245
\(856\) −5.72727 −0.195754
\(857\) −27.9758 −0.955635 −0.477818 0.878459i \(-0.658572\pi\)
−0.477818 + 0.878459i \(0.658572\pi\)
\(858\) 0.859888 0.0293561
\(859\) 25.6566 0.875391 0.437696 0.899123i \(-0.355795\pi\)
0.437696 + 0.899123i \(0.355795\pi\)
\(860\) 12.5261 0.427137
\(861\) 17.3853 0.592490
\(862\) −14.7451 −0.502222
\(863\) 43.5578 1.48272 0.741362 0.671105i \(-0.234180\pi\)
0.741362 + 0.671105i \(0.234180\pi\)
\(864\) −4.08928 −0.139120
\(865\) 23.7723 0.808284
\(866\) 9.15491 0.311097
\(867\) 1.00000 0.0339618
\(868\) 47.0922 1.59841
\(869\) −5.09697 −0.172903
\(870\) −3.67041 −0.124438
\(871\) −79.7327 −2.70164
\(872\) 8.21649 0.278246
\(873\) 19.1865 0.649365
\(874\) 7.93397 0.268371
\(875\) −29.6779 −1.00330
\(876\) 29.0658 0.982042
\(877\) −47.1069 −1.59069 −0.795343 0.606160i \(-0.792709\pi\)
−0.795343 + 0.606160i \(0.792709\pi\)
\(878\) 0.831088 0.0280479
\(879\) 5.29694 0.178661
\(880\) 1.60997 0.0542720
\(881\) −38.8398 −1.30855 −0.654273 0.756258i \(-0.727025\pi\)
−0.654273 + 0.756258i \(0.727025\pi\)
\(882\) −0.264306 −0.00889964
\(883\) −16.2736 −0.547650 −0.273825 0.961779i \(-0.588289\pi\)
−0.273825 + 0.961779i \(0.588289\pi\)
\(884\) −10.7284 −0.360834
\(885\) −2.34589 −0.0788562
\(886\) 10.8572 0.364755
\(887\) 35.2686 1.18420 0.592102 0.805863i \(-0.298298\pi\)
0.592102 + 0.805863i \(0.298298\pi\)
\(888\) −5.91054 −0.198345
\(889\) 9.90424 0.332177
\(890\) 4.34119 0.145517
\(891\) 0.396892 0.0132964
\(892\) −3.65626 −0.122421
\(893\) −35.4376 −1.18587
\(894\) −1.06166 −0.0355073
\(895\) −7.10137 −0.237373
\(896\) 27.7160 0.925926
\(897\) −28.3147 −0.945400
\(898\) −2.00152 −0.0667914
\(899\) −69.8189 −2.32859
\(900\) 6.25916 0.208639
\(901\) 6.53665 0.217768
\(902\) −0.933306 −0.0310757
\(903\) −14.6342 −0.486997
\(904\) −9.25427 −0.307793
\(905\) −14.4052 −0.478846
\(906\) 6.36546 0.211478
\(907\) 4.28502 0.142282 0.0711408 0.997466i \(-0.477336\pi\)
0.0711408 + 0.997466i \(0.477336\pi\)
\(908\) 42.6800 1.41639
\(909\) 10.7946 0.358034
\(910\) 7.68494 0.254753
\(911\) −36.4247 −1.20681 −0.603403 0.797437i \(-0.706189\pi\)
−0.603403 + 0.797437i \(0.706189\pi\)
\(912\) −13.6718 −0.452719
\(913\) 0.878359 0.0290694
\(914\) 3.52744 0.116677
\(915\) −13.9588 −0.461463
\(916\) 39.3145 1.29899
\(917\) 7.65181 0.252685
\(918\) 0.375429 0.0123910
\(919\) −41.6903 −1.37523 −0.687617 0.726073i \(-0.741343\pi\)
−0.687617 + 0.726073i \(0.741343\pi\)
\(920\) 9.08428 0.299500
\(921\) 13.0465 0.429896
\(922\) 14.2098 0.467975
\(923\) 67.0574 2.20722
\(924\) −2.04796 −0.0673731
\(925\) 13.7355 0.451619
\(926\) 10.3009 0.338509
\(927\) −4.72430 −0.155166
\(928\) −31.2839 −1.02695
\(929\) 50.1124 1.64414 0.822068 0.569389i \(-0.192820\pi\)
0.822068 + 0.569389i \(0.192820\pi\)
\(930\) 4.37863 0.143581
\(931\) −3.03231 −0.0993798
\(932\) 18.4551 0.604517
\(933\) −25.6124 −0.838514
\(934\) 14.0749 0.460544
\(935\) −0.507206 −0.0165874
\(936\) −8.36085 −0.273283
\(937\) 33.3016 1.08791 0.543957 0.839113i \(-0.316925\pi\)
0.543957 + 0.839113i \(0.316925\pi\)
\(938\) −14.3973 −0.470088
\(939\) −10.8924 −0.355459
\(940\) −19.5468 −0.637545
\(941\) 4.22967 0.137883 0.0689416 0.997621i \(-0.478038\pi\)
0.0689416 + 0.997621i \(0.478038\pi\)
\(942\) −0.375429 −0.0122321
\(943\) 30.7322 1.00078
\(944\) −5.82676 −0.189645
\(945\) 3.54708 0.115386
\(946\) 0.785618 0.0255426
\(947\) 26.1621 0.850155 0.425077 0.905157i \(-0.360247\pi\)
0.425077 + 0.905157i \(0.360247\pi\)
\(948\) 23.8743 0.775403
\(949\) 90.2262 2.92886
\(950\) −5.44434 −0.176638
\(951\) 7.27505 0.235910
\(952\) −4.02130 −0.130331
\(953\) 4.56816 0.147977 0.0739885 0.997259i \(-0.476427\pi\)
0.0739885 + 0.997259i \(0.476427\pi\)
\(954\) 2.45405 0.0794527
\(955\) 29.6809 0.960450
\(956\) −2.06296 −0.0667209
\(957\) 3.03631 0.0981501
\(958\) 1.44718 0.0467562
\(959\) −16.8133 −0.542930
\(960\) −6.15093 −0.198520
\(961\) 52.2907 1.68680
\(962\) −8.83870 −0.284971
\(963\) −3.95311 −0.127387
\(964\) −20.8149 −0.670403
\(965\) 17.2340 0.554783
\(966\) −5.11276 −0.164500
\(967\) 0.119589 0.00384573 0.00192286 0.999998i \(-0.499388\pi\)
0.00192286 + 0.999998i \(0.499388\pi\)
\(968\) −15.7086 −0.504893
\(969\) 4.30719 0.138367
\(970\) −9.20525 −0.295563
\(971\) 44.5530 1.42977 0.714887 0.699240i \(-0.246478\pi\)
0.714887 + 0.699240i \(0.246478\pi\)
\(972\) −1.85905 −0.0596292
\(973\) −6.12160 −0.196250
\(974\) 13.1941 0.422767
\(975\) 19.4297 0.622249
\(976\) −34.6711 −1.10979
\(977\) 24.3821 0.780052 0.390026 0.920804i \(-0.372466\pi\)
0.390026 + 0.920804i \(0.372466\pi\)
\(978\) 1.64661 0.0526527
\(979\) −3.59121 −0.114776
\(980\) −1.67257 −0.0534282
\(981\) 5.67124 0.181069
\(982\) −3.03728 −0.0969236
\(983\) −25.2532 −0.805453 −0.402726 0.915320i \(-0.631937\pi\)
−0.402726 + 0.915320i \(0.631937\pi\)
\(984\) 9.07471 0.289291
\(985\) −11.2674 −0.359008
\(986\) 2.87212 0.0914668
\(987\) 22.8365 0.726893
\(988\) −46.2091 −1.47011
\(989\) −25.8691 −0.822590
\(990\) −0.190420 −0.00605194
\(991\) −15.7671 −0.500858 −0.250429 0.968135i \(-0.580572\pi\)
−0.250429 + 0.968135i \(0.580572\pi\)
\(992\) 37.3203 1.18492
\(993\) −35.9080 −1.13951
\(994\) 12.1085 0.384059
\(995\) 4.02040 0.127455
\(996\) −4.11426 −0.130365
\(997\) 4.50451 0.142659 0.0713297 0.997453i \(-0.477276\pi\)
0.0713297 + 0.997453i \(0.477276\pi\)
\(998\) 13.2100 0.418155
\(999\) −4.07961 −0.129073
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 \(a_p\))