Properties

Label 4029.2.a.k.1.7
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73268 q^{2} +1.00000 q^{3} +1.00217 q^{4} +2.89501 q^{5} -1.73268 q^{6} +3.30216 q^{7} +1.72891 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.73268 q^{2} +1.00000 q^{3} +1.00217 q^{4} +2.89501 q^{5} -1.73268 q^{6} +3.30216 q^{7} +1.72891 q^{8} +1.00000 q^{9} -5.01613 q^{10} +3.25201 q^{11} +1.00217 q^{12} -1.42446 q^{13} -5.72157 q^{14} +2.89501 q^{15} -5.00000 q^{16} +1.00000 q^{17} -1.73268 q^{18} +2.32004 q^{19} +2.90131 q^{20} +3.30216 q^{21} -5.63469 q^{22} -8.40319 q^{23} +1.72891 q^{24} +3.38110 q^{25} +2.46812 q^{26} +1.00000 q^{27} +3.30933 q^{28} -0.650361 q^{29} -5.01613 q^{30} -0.747325 q^{31} +5.20556 q^{32} +3.25201 q^{33} -1.73268 q^{34} +9.55979 q^{35} +1.00217 q^{36} +5.76664 q^{37} -4.01988 q^{38} -1.42446 q^{39} +5.00522 q^{40} -9.70082 q^{41} -5.72157 q^{42} +10.5114 q^{43} +3.25908 q^{44} +2.89501 q^{45} +14.5600 q^{46} +6.77674 q^{47} -5.00000 q^{48} +3.90424 q^{49} -5.85836 q^{50} +1.00000 q^{51} -1.42755 q^{52} +13.2002 q^{53} -1.73268 q^{54} +9.41461 q^{55} +5.70914 q^{56} +2.32004 q^{57} +1.12687 q^{58} -7.73933 q^{59} +2.90131 q^{60} -2.72918 q^{61} +1.29487 q^{62} +3.30216 q^{63} +0.980433 q^{64} -4.12382 q^{65} -5.63469 q^{66} -2.41577 q^{67} +1.00217 q^{68} -8.40319 q^{69} -16.5640 q^{70} +13.6953 q^{71} +1.72891 q^{72} -5.37321 q^{73} -9.99174 q^{74} +3.38110 q^{75} +2.32508 q^{76} +10.7386 q^{77} +2.46812 q^{78} +1.00000 q^{79} -14.4751 q^{80} +1.00000 q^{81} +16.8084 q^{82} -4.72563 q^{83} +3.30933 q^{84} +2.89501 q^{85} -18.2128 q^{86} -0.650361 q^{87} +5.62244 q^{88} +11.4989 q^{89} -5.01613 q^{90} -4.70378 q^{91} -8.42145 q^{92} -0.747325 q^{93} -11.7419 q^{94} +6.71653 q^{95} +5.20556 q^{96} -2.34223 q^{97} -6.76479 q^{98} +3.25201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73268 −1.22519 −0.612594 0.790398i \(-0.709874\pi\)
−0.612594 + 0.790398i \(0.709874\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.00217 0.501087
\(5\) 2.89501 1.29469 0.647345 0.762197i \(-0.275879\pi\)
0.647345 + 0.762197i \(0.275879\pi\)
\(6\) −1.73268 −0.707363
\(7\) 3.30216 1.24810 0.624049 0.781385i \(-0.285487\pi\)
0.624049 + 0.781385i \(0.285487\pi\)
\(8\) 1.72891 0.611263
\(9\) 1.00000 0.333333
\(10\) −5.01613 −1.58624
\(11\) 3.25201 0.980518 0.490259 0.871577i \(-0.336902\pi\)
0.490259 + 0.871577i \(0.336902\pi\)
\(12\) 1.00217 0.289303
\(13\) −1.42446 −0.395073 −0.197536 0.980296i \(-0.563294\pi\)
−0.197536 + 0.980296i \(0.563294\pi\)
\(14\) −5.72157 −1.52916
\(15\) 2.89501 0.747489
\(16\) −5.00000 −1.25000
\(17\) 1.00000 0.242536
\(18\) −1.73268 −0.408396
\(19\) 2.32004 0.532253 0.266126 0.963938i \(-0.414256\pi\)
0.266126 + 0.963938i \(0.414256\pi\)
\(20\) 2.90131 0.648752
\(21\) 3.30216 0.720590
\(22\) −5.63469 −1.20132
\(23\) −8.40319 −1.75219 −0.876093 0.482142i \(-0.839859\pi\)
−0.876093 + 0.482142i \(0.839859\pi\)
\(24\) 1.72891 0.352913
\(25\) 3.38110 0.676220
\(26\) 2.46812 0.484039
\(27\) 1.00000 0.192450
\(28\) 3.30933 0.625405
\(29\) −0.650361 −0.120769 −0.0603845 0.998175i \(-0.519233\pi\)
−0.0603845 + 0.998175i \(0.519233\pi\)
\(30\) −5.01613 −0.915815
\(31\) −0.747325 −0.134224 −0.0671118 0.997745i \(-0.521378\pi\)
−0.0671118 + 0.997745i \(0.521378\pi\)
\(32\) 5.20556 0.920221
\(33\) 3.25201 0.566102
\(34\) −1.73268 −0.297152
\(35\) 9.55979 1.61590
\(36\) 1.00217 0.167029
\(37\) 5.76664 0.948030 0.474015 0.880517i \(-0.342804\pi\)
0.474015 + 0.880517i \(0.342804\pi\)
\(38\) −4.01988 −0.652110
\(39\) −1.42446 −0.228095
\(40\) 5.00522 0.791395
\(41\) −9.70082 −1.51501 −0.757507 0.652828i \(-0.773583\pi\)
−0.757507 + 0.652828i \(0.773583\pi\)
\(42\) −5.72157 −0.882858
\(43\) 10.5114 1.60297 0.801483 0.598017i \(-0.204044\pi\)
0.801483 + 0.598017i \(0.204044\pi\)
\(44\) 3.25908 0.491325
\(45\) 2.89501 0.431563
\(46\) 14.5600 2.14676
\(47\) 6.77674 0.988488 0.494244 0.869323i \(-0.335445\pi\)
0.494244 + 0.869323i \(0.335445\pi\)
\(48\) −5.00000 −0.721687
\(49\) 3.90424 0.557748
\(50\) −5.85836 −0.828497
\(51\) 1.00000 0.140028
\(52\) −1.42755 −0.197966
\(53\) 13.2002 1.81318 0.906591 0.422011i \(-0.138676\pi\)
0.906591 + 0.422011i \(0.138676\pi\)
\(54\) −1.73268 −0.235788
\(55\) 9.41461 1.26947
\(56\) 5.70914 0.762916
\(57\) 2.32004 0.307296
\(58\) 1.12687 0.147965
\(59\) −7.73933 −1.00757 −0.503787 0.863828i \(-0.668060\pi\)
−0.503787 + 0.863828i \(0.668060\pi\)
\(60\) 2.90131 0.374557
\(61\) −2.72918 −0.349436 −0.174718 0.984619i \(-0.555901\pi\)
−0.174718 + 0.984619i \(0.555901\pi\)
\(62\) 1.29487 0.164449
\(63\) 3.30216 0.416033
\(64\) 0.980433 0.122554
\(65\) −4.12382 −0.511497
\(66\) −5.63469 −0.693582
\(67\) −2.41577 −0.295133 −0.147567 0.989052i \(-0.547144\pi\)
−0.147567 + 0.989052i \(0.547144\pi\)
\(68\) 1.00217 0.121531
\(69\) −8.40319 −1.01162
\(70\) −16.5640 −1.97978
\(71\) 13.6953 1.62534 0.812668 0.582728i \(-0.198015\pi\)
0.812668 + 0.582728i \(0.198015\pi\)
\(72\) 1.72891 0.203754
\(73\) −5.37321 −0.628887 −0.314443 0.949276i \(-0.601818\pi\)
−0.314443 + 0.949276i \(0.601818\pi\)
\(74\) −9.99174 −1.16152
\(75\) 3.38110 0.390416
\(76\) 2.32508 0.266705
\(77\) 10.7386 1.22378
\(78\) 2.46812 0.279460
\(79\) 1.00000 0.112509
\(80\) −14.4751 −1.61836
\(81\) 1.00000 0.111111
\(82\) 16.8084 1.85618
\(83\) −4.72563 −0.518706 −0.259353 0.965783i \(-0.583509\pi\)
−0.259353 + 0.965783i \(0.583509\pi\)
\(84\) 3.30933 0.361078
\(85\) 2.89501 0.314008
\(86\) −18.2128 −1.96394
\(87\) −0.650361 −0.0697260
\(88\) 5.62244 0.599354
\(89\) 11.4989 1.21888 0.609441 0.792832i \(-0.291394\pi\)
0.609441 + 0.792832i \(0.291394\pi\)
\(90\) −5.01613 −0.528746
\(91\) −4.70378 −0.493090
\(92\) −8.42145 −0.877997
\(93\) −0.747325 −0.0774940
\(94\) −11.7419 −1.21108
\(95\) 6.71653 0.689102
\(96\) 5.20556 0.531290
\(97\) −2.34223 −0.237818 −0.118909 0.992905i \(-0.537940\pi\)
−0.118909 + 0.992905i \(0.537940\pi\)
\(98\) −6.76479 −0.683347
\(99\) 3.25201 0.326839
\(100\) 3.38845 0.338845
\(101\) 13.3969 1.33304 0.666522 0.745486i \(-0.267782\pi\)
0.666522 + 0.745486i \(0.267782\pi\)
\(102\) −1.73268 −0.171561
\(103\) −15.5382 −1.53102 −0.765511 0.643423i \(-0.777514\pi\)
−0.765511 + 0.643423i \(0.777514\pi\)
\(104\) −2.46276 −0.241493
\(105\) 9.55979 0.932940
\(106\) −22.8716 −2.22149
\(107\) 12.7561 1.23318 0.616591 0.787283i \(-0.288513\pi\)
0.616591 + 0.787283i \(0.288513\pi\)
\(108\) 1.00217 0.0964342
\(109\) 13.4313 1.28648 0.643242 0.765663i \(-0.277589\pi\)
0.643242 + 0.765663i \(0.277589\pi\)
\(110\) −16.3125 −1.55534
\(111\) 5.76664 0.547346
\(112\) −16.5108 −1.56012
\(113\) 8.28805 0.779674 0.389837 0.920884i \(-0.372531\pi\)
0.389837 + 0.920884i \(0.372531\pi\)
\(114\) −4.01988 −0.376496
\(115\) −24.3273 −2.26854
\(116\) −0.651774 −0.0605157
\(117\) −1.42446 −0.131691
\(118\) 13.4098 1.23447
\(119\) 3.30216 0.302708
\(120\) 5.00522 0.456912
\(121\) −0.424426 −0.0385842
\(122\) 4.72880 0.428125
\(123\) −9.70082 −0.874693
\(124\) −0.748950 −0.0672577
\(125\) −4.68674 −0.419194
\(126\) −5.72157 −0.509718
\(127\) −7.61952 −0.676123 −0.338061 0.941124i \(-0.609771\pi\)
−0.338061 + 0.941124i \(0.609771\pi\)
\(128\) −12.1099 −1.07037
\(129\) 10.5114 0.925473
\(130\) 7.14525 0.626680
\(131\) 4.38327 0.382968 0.191484 0.981496i \(-0.438670\pi\)
0.191484 + 0.981496i \(0.438670\pi\)
\(132\) 3.25908 0.283666
\(133\) 7.66112 0.664304
\(134\) 4.18575 0.361594
\(135\) 2.89501 0.249163
\(136\) 1.72891 0.148253
\(137\) 10.3736 0.886275 0.443137 0.896454i \(-0.353865\pi\)
0.443137 + 0.896454i \(0.353865\pi\)
\(138\) 14.5600 1.23943
\(139\) −13.2343 −1.12252 −0.561259 0.827640i \(-0.689683\pi\)
−0.561259 + 0.827640i \(0.689683\pi\)
\(140\) 9.58057 0.809706
\(141\) 6.77674 0.570704
\(142\) −23.7296 −1.99134
\(143\) −4.63235 −0.387376
\(144\) −5.00000 −0.416666
\(145\) −1.88280 −0.156358
\(146\) 9.31005 0.770505
\(147\) 3.90424 0.322016
\(148\) 5.77918 0.475046
\(149\) −3.90568 −0.319966 −0.159983 0.987120i \(-0.551144\pi\)
−0.159983 + 0.987120i \(0.551144\pi\)
\(150\) −5.85836 −0.478333
\(151\) −4.99932 −0.406839 −0.203419 0.979092i \(-0.565206\pi\)
−0.203419 + 0.979092i \(0.565206\pi\)
\(152\) 4.01114 0.325346
\(153\) 1.00000 0.0808452
\(154\) −18.6066 −1.49936
\(155\) −2.16352 −0.173778
\(156\) −1.42755 −0.114296
\(157\) −19.1845 −1.53109 −0.765543 0.643385i \(-0.777530\pi\)
−0.765543 + 0.643385i \(0.777530\pi\)
\(158\) −1.73268 −0.137844
\(159\) 13.2002 1.04684
\(160\) 15.0702 1.19140
\(161\) −27.7486 −2.18690
\(162\) −1.73268 −0.136132
\(163\) −10.4382 −0.817585 −0.408792 0.912627i \(-0.634050\pi\)
−0.408792 + 0.912627i \(0.634050\pi\)
\(164\) −9.72190 −0.759153
\(165\) 9.41461 0.732927
\(166\) 8.18800 0.635512
\(167\) 8.18465 0.633347 0.316673 0.948535i \(-0.397434\pi\)
0.316673 + 0.948535i \(0.397434\pi\)
\(168\) 5.70914 0.440470
\(169\) −10.9709 −0.843917
\(170\) −5.01613 −0.384719
\(171\) 2.32004 0.177418
\(172\) 10.5342 0.803226
\(173\) 5.56881 0.423389 0.211694 0.977336i \(-0.432102\pi\)
0.211694 + 0.977336i \(0.432102\pi\)
\(174\) 1.12687 0.0854275
\(175\) 11.1649 0.843989
\(176\) −16.2600 −1.22565
\(177\) −7.73933 −0.581723
\(178\) −19.9239 −1.49336
\(179\) −24.2661 −1.81373 −0.906867 0.421417i \(-0.861533\pi\)
−0.906867 + 0.421417i \(0.861533\pi\)
\(180\) 2.90131 0.216251
\(181\) 11.3517 0.843767 0.421884 0.906650i \(-0.361369\pi\)
0.421884 + 0.906650i \(0.361369\pi\)
\(182\) 8.15013 0.604128
\(183\) −2.72918 −0.201747
\(184\) −14.5284 −1.07105
\(185\) 16.6945 1.22740
\(186\) 1.29487 0.0949448
\(187\) 3.25201 0.237811
\(188\) 6.79147 0.495319
\(189\) 3.30216 0.240197
\(190\) −11.6376 −0.844280
\(191\) 7.93371 0.574063 0.287032 0.957921i \(-0.407332\pi\)
0.287032 + 0.957921i \(0.407332\pi\)
\(192\) 0.980433 0.0707566
\(193\) −18.0603 −1.30001 −0.650006 0.759929i \(-0.725233\pi\)
−0.650006 + 0.759929i \(0.725233\pi\)
\(194\) 4.05834 0.291371
\(195\) −4.12382 −0.295313
\(196\) 3.91273 0.279480
\(197\) 1.90395 0.135651 0.0678254 0.997697i \(-0.478394\pi\)
0.0678254 + 0.997697i \(0.478394\pi\)
\(198\) −5.63469 −0.400440
\(199\) 25.0531 1.77597 0.887984 0.459875i \(-0.152106\pi\)
0.887984 + 0.459875i \(0.152106\pi\)
\(200\) 5.84562 0.413348
\(201\) −2.41577 −0.170395
\(202\) −23.2125 −1.63323
\(203\) −2.14759 −0.150731
\(204\) 1.00217 0.0701662
\(205\) −28.0840 −1.96147
\(206\) 26.9227 1.87579
\(207\) −8.40319 −0.584062
\(208\) 7.12227 0.493841
\(209\) 7.54478 0.521884
\(210\) −16.5640 −1.14303
\(211\) −3.98468 −0.274317 −0.137158 0.990549i \(-0.543797\pi\)
−0.137158 + 0.990549i \(0.543797\pi\)
\(212\) 13.2289 0.908561
\(213\) 13.6953 0.938388
\(214\) −22.1023 −1.51088
\(215\) 30.4305 2.07534
\(216\) 1.72891 0.117638
\(217\) −2.46779 −0.167524
\(218\) −23.2721 −1.57619
\(219\) −5.37321 −0.363088
\(220\) 9.43508 0.636113
\(221\) −1.42446 −0.0958193
\(222\) −9.99174 −0.670602
\(223\) 20.0652 1.34366 0.671832 0.740703i \(-0.265508\pi\)
0.671832 + 0.740703i \(0.265508\pi\)
\(224\) 17.1896 1.14853
\(225\) 3.38110 0.225407
\(226\) −14.3605 −0.955247
\(227\) 10.9646 0.727748 0.363874 0.931448i \(-0.381454\pi\)
0.363874 + 0.931448i \(0.381454\pi\)
\(228\) 2.32508 0.153982
\(229\) 22.5916 1.49290 0.746448 0.665444i \(-0.231758\pi\)
0.746448 + 0.665444i \(0.231758\pi\)
\(230\) 42.1514 2.77938
\(231\) 10.7386 0.706551
\(232\) −1.12442 −0.0738216
\(233\) −0.530463 −0.0347518 −0.0173759 0.999849i \(-0.505531\pi\)
−0.0173759 + 0.999849i \(0.505531\pi\)
\(234\) 2.46812 0.161346
\(235\) 19.6187 1.27979
\(236\) −7.75615 −0.504882
\(237\) 1.00000 0.0649570
\(238\) −5.72157 −0.370875
\(239\) 0.0514535 0.00332825 0.00166412 0.999999i \(-0.499470\pi\)
0.00166412 + 0.999999i \(0.499470\pi\)
\(240\) −14.4751 −0.934361
\(241\) −7.69075 −0.495405 −0.247702 0.968836i \(-0.579676\pi\)
−0.247702 + 0.968836i \(0.579676\pi\)
\(242\) 0.735393 0.0472729
\(243\) 1.00000 0.0641500
\(244\) −2.73512 −0.175098
\(245\) 11.3028 0.722111
\(246\) 16.8084 1.07166
\(247\) −3.30479 −0.210279
\(248\) −1.29206 −0.0820459
\(249\) −4.72563 −0.299475
\(250\) 8.12061 0.513592
\(251\) −20.1716 −1.27322 −0.636611 0.771185i \(-0.719664\pi\)
−0.636611 + 0.771185i \(0.719664\pi\)
\(252\) 3.30933 0.208468
\(253\) −27.3273 −1.71805
\(254\) 13.2022 0.828378
\(255\) 2.89501 0.181293
\(256\) 19.0217 1.18885
\(257\) 15.7169 0.980394 0.490197 0.871612i \(-0.336925\pi\)
0.490197 + 0.871612i \(0.336925\pi\)
\(258\) −18.2128 −1.13388
\(259\) 19.0424 1.18323
\(260\) −4.13278 −0.256304
\(261\) −0.650361 −0.0402563
\(262\) −7.59480 −0.469208
\(263\) −7.62885 −0.470415 −0.235208 0.971945i \(-0.575577\pi\)
−0.235208 + 0.971945i \(0.575577\pi\)
\(264\) 5.62244 0.346037
\(265\) 38.2146 2.34751
\(266\) −13.2743 −0.813897
\(267\) 11.4989 0.703721
\(268\) −2.42102 −0.147887
\(269\) −31.3153 −1.90932 −0.954662 0.297691i \(-0.903784\pi\)
−0.954662 + 0.297691i \(0.903784\pi\)
\(270\) −5.01613 −0.305272
\(271\) −15.9376 −0.968139 −0.484069 0.875030i \(-0.660842\pi\)
−0.484069 + 0.875030i \(0.660842\pi\)
\(272\) −5.00000 −0.303169
\(273\) −4.70378 −0.284685
\(274\) −17.9741 −1.08585
\(275\) 10.9954 0.663046
\(276\) −8.42145 −0.506912
\(277\) −19.8080 −1.19015 −0.595073 0.803672i \(-0.702877\pi\)
−0.595073 + 0.803672i \(0.702877\pi\)
\(278\) 22.9308 1.37530
\(279\) −0.747325 −0.0447412
\(280\) 16.5280 0.987739
\(281\) 9.35604 0.558134 0.279067 0.960272i \(-0.409975\pi\)
0.279067 + 0.960272i \(0.409975\pi\)
\(282\) −11.7419 −0.699220
\(283\) 5.57589 0.331452 0.165726 0.986172i \(-0.447003\pi\)
0.165726 + 0.986172i \(0.447003\pi\)
\(284\) 13.7251 0.814434
\(285\) 6.71653 0.397853
\(286\) 8.02636 0.474609
\(287\) −32.0336 −1.89088
\(288\) 5.20556 0.306740
\(289\) 1.00000 0.0588235
\(290\) 3.26229 0.191568
\(291\) −2.34223 −0.137304
\(292\) −5.38489 −0.315127
\(293\) −4.63022 −0.270500 −0.135250 0.990811i \(-0.543184\pi\)
−0.135250 + 0.990811i \(0.543184\pi\)
\(294\) −6.76479 −0.394531
\(295\) −22.4055 −1.30450
\(296\) 9.97002 0.579496
\(297\) 3.25201 0.188701
\(298\) 6.76729 0.392018
\(299\) 11.9700 0.692241
\(300\) 3.38845 0.195632
\(301\) 34.7101 2.00066
\(302\) 8.66221 0.498454
\(303\) 13.3969 0.769633
\(304\) −11.6002 −0.665315
\(305\) −7.90102 −0.452411
\(306\) −1.73268 −0.0990506
\(307\) 11.0056 0.628124 0.314062 0.949402i \(-0.398310\pi\)
0.314062 + 0.949402i \(0.398310\pi\)
\(308\) 10.7620 0.613221
\(309\) −15.5382 −0.883936
\(310\) 3.74868 0.212911
\(311\) −18.3578 −1.04098 −0.520489 0.853868i \(-0.674250\pi\)
−0.520489 + 0.853868i \(0.674250\pi\)
\(312\) −2.46276 −0.139426
\(313\) 10.3244 0.583568 0.291784 0.956484i \(-0.405751\pi\)
0.291784 + 0.956484i \(0.405751\pi\)
\(314\) 33.2405 1.87587
\(315\) 9.55979 0.538633
\(316\) 1.00217 0.0563767
\(317\) −18.7935 −1.05555 −0.527775 0.849384i \(-0.676974\pi\)
−0.527775 + 0.849384i \(0.676974\pi\)
\(318\) −22.8716 −1.28258
\(319\) −2.11498 −0.118416
\(320\) 2.83837 0.158669
\(321\) 12.7561 0.711979
\(322\) 48.0795 2.67936
\(323\) 2.32004 0.129090
\(324\) 1.00217 0.0556763
\(325\) −4.81623 −0.267156
\(326\) 18.0861 1.00170
\(327\) 13.4313 0.742752
\(328\) −16.7719 −0.926071
\(329\) 22.3778 1.23373
\(330\) −16.3125 −0.897973
\(331\) −24.7950 −1.36286 −0.681428 0.731885i \(-0.738641\pi\)
−0.681428 + 0.731885i \(0.738641\pi\)
\(332\) −4.73591 −0.259917
\(333\) 5.76664 0.316010
\(334\) −14.1814 −0.775969
\(335\) −6.99369 −0.382106
\(336\) −16.5108 −0.900736
\(337\) −6.81474 −0.371223 −0.185611 0.982623i \(-0.559427\pi\)
−0.185611 + 0.982623i \(0.559427\pi\)
\(338\) 19.0091 1.03396
\(339\) 8.28805 0.450145
\(340\) 2.90131 0.157345
\(341\) −2.43031 −0.131609
\(342\) −4.01988 −0.217370
\(343\) −10.2227 −0.551973
\(344\) 18.1732 0.979834
\(345\) −24.3273 −1.30974
\(346\) −9.64895 −0.518731
\(347\) 25.4044 1.36378 0.681889 0.731455i \(-0.261159\pi\)
0.681889 + 0.731455i \(0.261159\pi\)
\(348\) −0.651774 −0.0349388
\(349\) −31.5518 −1.68893 −0.844464 0.535613i \(-0.820081\pi\)
−0.844464 + 0.535613i \(0.820081\pi\)
\(350\) −19.3452 −1.03405
\(351\) −1.42446 −0.0760318
\(352\) 16.9285 0.902294
\(353\) −9.54881 −0.508232 −0.254116 0.967174i \(-0.581785\pi\)
−0.254116 + 0.967174i \(0.581785\pi\)
\(354\) 13.4098 0.712721
\(355\) 39.6481 2.10430
\(356\) 11.5239 0.610765
\(357\) 3.30216 0.174769
\(358\) 42.0454 2.22217
\(359\) 35.3269 1.86448 0.932242 0.361835i \(-0.117850\pi\)
0.932242 + 0.361835i \(0.117850\pi\)
\(360\) 5.00522 0.263798
\(361\) −13.6174 −0.716707
\(362\) −19.6689 −1.03377
\(363\) −0.424426 −0.0222766
\(364\) −4.71400 −0.247081
\(365\) −15.5555 −0.814213
\(366\) 4.72880 0.247178
\(367\) −6.91799 −0.361116 −0.180558 0.983564i \(-0.557790\pi\)
−0.180558 + 0.983564i \(0.557790\pi\)
\(368\) 42.0159 2.19023
\(369\) −9.70082 −0.505004
\(370\) −28.9262 −1.50380
\(371\) 43.5890 2.26303
\(372\) −0.748950 −0.0388312
\(373\) −4.97404 −0.257546 −0.128773 0.991674i \(-0.541104\pi\)
−0.128773 + 0.991674i \(0.541104\pi\)
\(374\) −5.63469 −0.291363
\(375\) −4.68674 −0.242022
\(376\) 11.7164 0.604226
\(377\) 0.926410 0.0477125
\(378\) −5.72157 −0.294286
\(379\) −17.1110 −0.878934 −0.439467 0.898259i \(-0.644833\pi\)
−0.439467 + 0.898259i \(0.644833\pi\)
\(380\) 6.73113 0.345300
\(381\) −7.61952 −0.390360
\(382\) −13.7466 −0.703336
\(383\) 18.6188 0.951377 0.475688 0.879614i \(-0.342199\pi\)
0.475688 + 0.879614i \(0.342199\pi\)
\(384\) −12.1099 −0.617980
\(385\) 31.0885 1.58442
\(386\) 31.2927 1.59276
\(387\) 10.5114 0.534322
\(388\) −2.34732 −0.119167
\(389\) −18.4109 −0.933470 −0.466735 0.884397i \(-0.654570\pi\)
−0.466735 + 0.884397i \(0.654570\pi\)
\(390\) 7.14525 0.361814
\(391\) −8.40319 −0.424967
\(392\) 6.75008 0.340931
\(393\) 4.38327 0.221107
\(394\) −3.29893 −0.166198
\(395\) 2.89501 0.145664
\(396\) 3.25908 0.163775
\(397\) 5.48451 0.275260 0.137630 0.990484i \(-0.456052\pi\)
0.137630 + 0.990484i \(0.456052\pi\)
\(398\) −43.4090 −2.17590
\(399\) 7.66112 0.383536
\(400\) −16.9055 −0.845274
\(401\) 21.9988 1.09857 0.549283 0.835636i \(-0.314901\pi\)
0.549283 + 0.835636i \(0.314901\pi\)
\(402\) 4.18575 0.208766
\(403\) 1.06453 0.0530281
\(404\) 13.4260 0.667970
\(405\) 2.89501 0.143854
\(406\) 3.72109 0.184674
\(407\) 18.7532 0.929561
\(408\) 1.72891 0.0855939
\(409\) 20.8864 1.03277 0.516384 0.856357i \(-0.327278\pi\)
0.516384 + 0.856357i \(0.327278\pi\)
\(410\) 48.6605 2.40317
\(411\) 10.3736 0.511691
\(412\) −15.5719 −0.767175
\(413\) −25.5565 −1.25755
\(414\) 14.5600 0.715586
\(415\) −13.6808 −0.671563
\(416\) −7.41509 −0.363555
\(417\) −13.2343 −0.648086
\(418\) −13.0727 −0.639406
\(419\) −3.09533 −0.151217 −0.0756083 0.997138i \(-0.524090\pi\)
−0.0756083 + 0.997138i \(0.524090\pi\)
\(420\) 9.58057 0.467484
\(421\) 7.34024 0.357742 0.178871 0.983873i \(-0.442756\pi\)
0.178871 + 0.983873i \(0.442756\pi\)
\(422\) 6.90417 0.336090
\(423\) 6.77674 0.329496
\(424\) 22.8219 1.10833
\(425\) 3.38110 0.164007
\(426\) −23.7296 −1.14970
\(427\) −9.01219 −0.436130
\(428\) 12.7839 0.617932
\(429\) −4.63235 −0.223652
\(430\) −52.7263 −2.54269
\(431\) −24.5569 −1.18286 −0.591432 0.806355i \(-0.701437\pi\)
−0.591432 + 0.806355i \(0.701437\pi\)
\(432\) −5.00000 −0.240562
\(433\) 28.8618 1.38701 0.693505 0.720451i \(-0.256065\pi\)
0.693505 + 0.720451i \(0.256065\pi\)
\(434\) 4.27588 0.205249
\(435\) −1.88280 −0.0902735
\(436\) 13.4605 0.644640
\(437\) −19.4957 −0.932606
\(438\) 9.31005 0.444851
\(439\) −10.2511 −0.489259 −0.244630 0.969617i \(-0.578666\pi\)
−0.244630 + 0.969617i \(0.578666\pi\)
\(440\) 16.2770 0.775977
\(441\) 3.90424 0.185916
\(442\) 2.46812 0.117397
\(443\) 14.3162 0.680184 0.340092 0.940392i \(-0.389542\pi\)
0.340092 + 0.940392i \(0.389542\pi\)
\(444\) 5.77918 0.274268
\(445\) 33.2895 1.57807
\(446\) −34.7665 −1.64624
\(447\) −3.90568 −0.184732
\(448\) 3.23754 0.152959
\(449\) 34.8130 1.64293 0.821463 0.570262i \(-0.193158\pi\)
0.821463 + 0.570262i \(0.193158\pi\)
\(450\) −5.85836 −0.276166
\(451\) −31.5472 −1.48550
\(452\) 8.30606 0.390684
\(453\) −4.99932 −0.234889
\(454\) −18.9982 −0.891628
\(455\) −13.6175 −0.638398
\(456\) 4.01114 0.187839
\(457\) 14.8635 0.695286 0.347643 0.937627i \(-0.386982\pi\)
0.347643 + 0.937627i \(0.386982\pi\)
\(458\) −39.1440 −1.82908
\(459\) 1.00000 0.0466760
\(460\) −24.3802 −1.13673
\(461\) 0.316575 0.0147444 0.00737219 0.999973i \(-0.497653\pi\)
0.00737219 + 0.999973i \(0.497653\pi\)
\(462\) −18.6066 −0.865658
\(463\) −5.22500 −0.242826 −0.121413 0.992602i \(-0.538743\pi\)
−0.121413 + 0.992602i \(0.538743\pi\)
\(464\) 3.25180 0.150961
\(465\) −2.16352 −0.100331
\(466\) 0.919122 0.0425775
\(467\) −16.2752 −0.753126 −0.376563 0.926391i \(-0.622894\pi\)
−0.376563 + 0.926391i \(0.622894\pi\)
\(468\) −1.42755 −0.0659886
\(469\) −7.97726 −0.368355
\(470\) −33.9930 −1.56798
\(471\) −19.1845 −0.883973
\(472\) −13.3806 −0.615893
\(473\) 34.1830 1.57174
\(474\) −1.73268 −0.0795845
\(475\) 7.84427 0.359920
\(476\) 3.30933 0.151683
\(477\) 13.2002 0.604394
\(478\) −0.0891523 −0.00407773
\(479\) 30.6770 1.40167 0.700833 0.713325i \(-0.252812\pi\)
0.700833 + 0.713325i \(0.252812\pi\)
\(480\) 15.0702 0.687856
\(481\) −8.21433 −0.374541
\(482\) 13.3256 0.606964
\(483\) −27.7486 −1.26261
\(484\) −0.425348 −0.0193340
\(485\) −6.78079 −0.307900
\(486\) −1.73268 −0.0785959
\(487\) −4.28298 −0.194080 −0.0970401 0.995280i \(-0.530938\pi\)
−0.0970401 + 0.995280i \(0.530938\pi\)
\(488\) −4.71852 −0.213597
\(489\) −10.4382 −0.472033
\(490\) −19.5842 −0.884722
\(491\) −5.59334 −0.252424 −0.126212 0.992003i \(-0.540282\pi\)
−0.126212 + 0.992003i \(0.540282\pi\)
\(492\) −9.72190 −0.438297
\(493\) −0.650361 −0.0292908
\(494\) 5.72614 0.257631
\(495\) 9.41461 0.423155
\(496\) 3.73662 0.167779
\(497\) 45.2241 2.02858
\(498\) 8.18800 0.366913
\(499\) −6.05647 −0.271125 −0.135562 0.990769i \(-0.543284\pi\)
−0.135562 + 0.990769i \(0.543284\pi\)
\(500\) −4.69692 −0.210053
\(501\) 8.18465 0.365663
\(502\) 34.9510 1.55994
\(503\) 22.6653 1.01059 0.505297 0.862945i \(-0.331383\pi\)
0.505297 + 0.862945i \(0.331383\pi\)
\(504\) 5.70914 0.254305
\(505\) 38.7843 1.72588
\(506\) 47.3493 2.10493
\(507\) −10.9709 −0.487236
\(508\) −7.63608 −0.338796
\(509\) −24.1078 −1.06856 −0.534280 0.845308i \(-0.679417\pi\)
−0.534280 + 0.845308i \(0.679417\pi\)
\(510\) −5.01613 −0.222118
\(511\) −17.7432 −0.784912
\(512\) −8.73867 −0.386198
\(513\) 2.32004 0.102432
\(514\) −27.2323 −1.20117
\(515\) −44.9832 −1.98220
\(516\) 10.5342 0.463742
\(517\) 22.0380 0.969231
\(518\) −32.9943 −1.44969
\(519\) 5.56881 0.244443
\(520\) −7.12972 −0.312659
\(521\) 26.6737 1.16860 0.584298 0.811539i \(-0.301370\pi\)
0.584298 + 0.811539i \(0.301370\pi\)
\(522\) 1.12687 0.0493216
\(523\) −41.1586 −1.79974 −0.899870 0.436158i \(-0.856339\pi\)
−0.899870 + 0.436158i \(0.856339\pi\)
\(524\) 4.39280 0.191900
\(525\) 11.1649 0.487277
\(526\) 13.2183 0.576347
\(527\) −0.747325 −0.0325540
\(528\) −16.2600 −0.707627
\(529\) 47.6136 2.07015
\(530\) −66.2137 −2.87614
\(531\) −7.73933 −0.335858
\(532\) 7.67778 0.332874
\(533\) 13.8184 0.598541
\(534\) −19.9239 −0.862191
\(535\) 36.9292 1.59659
\(536\) −4.17666 −0.180404
\(537\) −24.2661 −1.04716
\(538\) 54.2593 2.33928
\(539\) 12.6966 0.546882
\(540\) 2.90131 0.124852
\(541\) −12.9681 −0.557544 −0.278772 0.960357i \(-0.589927\pi\)
−0.278772 + 0.960357i \(0.589927\pi\)
\(542\) 27.6147 1.18615
\(543\) 11.3517 0.487149
\(544\) 5.20556 0.223186
\(545\) 38.8837 1.66560
\(546\) 8.15013 0.348793
\(547\) −11.8639 −0.507262 −0.253631 0.967301i \(-0.581625\pi\)
−0.253631 + 0.967301i \(0.581625\pi\)
\(548\) 10.3961 0.444100
\(549\) −2.72918 −0.116479
\(550\) −19.0514 −0.812356
\(551\) −1.50886 −0.0642796
\(552\) −14.5284 −0.618369
\(553\) 3.30216 0.140422
\(554\) 34.3208 1.45815
\(555\) 16.6945 0.708642
\(556\) −13.2631 −0.562479
\(557\) −15.3175 −0.649024 −0.324512 0.945882i \(-0.605200\pi\)
−0.324512 + 0.945882i \(0.605200\pi\)
\(558\) 1.29487 0.0548164
\(559\) −14.9730 −0.633289
\(560\) −47.7989 −2.01987
\(561\) 3.25201 0.137300
\(562\) −16.2110 −0.683820
\(563\) 8.49218 0.357903 0.178951 0.983858i \(-0.442730\pi\)
0.178951 + 0.983858i \(0.442730\pi\)
\(564\) 6.79147 0.285972
\(565\) 23.9940 1.00944
\(566\) −9.66123 −0.406092
\(567\) 3.30216 0.138678
\(568\) 23.6780 0.993507
\(569\) −35.3929 −1.48375 −0.741873 0.670540i \(-0.766062\pi\)
−0.741873 + 0.670540i \(0.766062\pi\)
\(570\) −11.6376 −0.487445
\(571\) 20.4482 0.855731 0.427866 0.903842i \(-0.359266\pi\)
0.427866 + 0.903842i \(0.359266\pi\)
\(572\) −4.64241 −0.194109
\(573\) 7.93371 0.331435
\(574\) 55.5040 2.31669
\(575\) −28.4120 −1.18486
\(576\) 0.980433 0.0408514
\(577\) 13.4627 0.560459 0.280229 0.959933i \(-0.409589\pi\)
0.280229 + 0.959933i \(0.409589\pi\)
\(578\) −1.73268 −0.0720699
\(579\) −18.0603 −0.750562
\(580\) −1.88690 −0.0783491
\(581\) −15.6048 −0.647396
\(582\) 4.05834 0.168223
\(583\) 42.9271 1.77786
\(584\) −9.28981 −0.384415
\(585\) −4.12382 −0.170499
\(586\) 8.02268 0.331414
\(587\) −14.9574 −0.617359 −0.308679 0.951166i \(-0.599887\pi\)
−0.308679 + 0.951166i \(0.599887\pi\)
\(588\) 3.91273 0.161358
\(589\) −1.73382 −0.0714409
\(590\) 38.8214 1.59825
\(591\) 1.90395 0.0783181
\(592\) −28.8332 −1.18504
\(593\) 22.7972 0.936167 0.468084 0.883684i \(-0.344945\pi\)
0.468084 + 0.883684i \(0.344945\pi\)
\(594\) −5.63469 −0.231194
\(595\) 9.55979 0.391913
\(596\) −3.91417 −0.160331
\(597\) 25.0531 1.02536
\(598\) −20.7401 −0.848126
\(599\) 0.906214 0.0370269 0.0185134 0.999829i \(-0.494107\pi\)
0.0185134 + 0.999829i \(0.494107\pi\)
\(600\) 5.84562 0.238647
\(601\) 7.70721 0.314384 0.157192 0.987568i \(-0.449756\pi\)
0.157192 + 0.987568i \(0.449756\pi\)
\(602\) −60.1415 −2.45119
\(603\) −2.41577 −0.0983778
\(604\) −5.01019 −0.203862
\(605\) −1.22872 −0.0499545
\(606\) −23.2125 −0.942945
\(607\) −30.5002 −1.23796 −0.618982 0.785405i \(-0.712455\pi\)
−0.618982 + 0.785405i \(0.712455\pi\)
\(608\) 12.0771 0.489790
\(609\) −2.14759 −0.0870249
\(610\) 13.6899 0.554289
\(611\) −9.65316 −0.390525
\(612\) 1.00217 0.0405105
\(613\) −9.01178 −0.363982 −0.181991 0.983300i \(-0.558254\pi\)
−0.181991 + 0.983300i \(0.558254\pi\)
\(614\) −19.0692 −0.769571
\(615\) −28.0840 −1.13246
\(616\) 18.5662 0.748053
\(617\) −14.8958 −0.599682 −0.299841 0.953989i \(-0.596934\pi\)
−0.299841 + 0.953989i \(0.596934\pi\)
\(618\) 26.9227 1.08299
\(619\) 16.7953 0.675060 0.337530 0.941315i \(-0.390409\pi\)
0.337530 + 0.941315i \(0.390409\pi\)
\(620\) −2.16822 −0.0870778
\(621\) −8.40319 −0.337208
\(622\) 31.8082 1.27539
\(623\) 37.9712 1.52128
\(624\) 7.12227 0.285119
\(625\) −30.4737 −1.21895
\(626\) −17.8888 −0.714980
\(627\) 7.54478 0.301310
\(628\) −19.2262 −0.767207
\(629\) 5.76664 0.229931
\(630\) −16.5640 −0.659927
\(631\) 37.6810 1.50006 0.750029 0.661405i \(-0.230040\pi\)
0.750029 + 0.661405i \(0.230040\pi\)
\(632\) 1.72891 0.0687724
\(633\) −3.98468 −0.158377
\(634\) 32.5631 1.29325
\(635\) −22.0586 −0.875369
\(636\) 13.2289 0.524558
\(637\) −5.56141 −0.220351
\(638\) 3.66458 0.145082
\(639\) 13.6953 0.541778
\(640\) −35.0583 −1.38580
\(641\) −46.6921 −1.84423 −0.922113 0.386920i \(-0.873539\pi\)
−0.922113 + 0.386920i \(0.873539\pi\)
\(642\) −22.1023 −0.872308
\(643\) 2.03218 0.0801413 0.0400707 0.999197i \(-0.487242\pi\)
0.0400707 + 0.999197i \(0.487242\pi\)
\(644\) −27.8090 −1.09583
\(645\) 30.4305 1.19820
\(646\) −4.01988 −0.158160
\(647\) −7.22391 −0.284001 −0.142001 0.989867i \(-0.545353\pi\)
−0.142001 + 0.989867i \(0.545353\pi\)
\(648\) 1.72891 0.0679181
\(649\) −25.1684 −0.987945
\(650\) 8.34497 0.327317
\(651\) −2.46779 −0.0967201
\(652\) −10.4609 −0.409681
\(653\) −17.3032 −0.677128 −0.338564 0.940943i \(-0.609941\pi\)
−0.338564 + 0.940943i \(0.609941\pi\)
\(654\) −23.2721 −0.910011
\(655\) 12.6896 0.495825
\(656\) 48.5040 1.89376
\(657\) −5.37321 −0.209629
\(658\) −38.7736 −1.51155
\(659\) 25.5753 0.996272 0.498136 0.867099i \(-0.334018\pi\)
0.498136 + 0.867099i \(0.334018\pi\)
\(660\) 9.43508 0.367260
\(661\) 31.0826 1.20897 0.604486 0.796616i \(-0.293379\pi\)
0.604486 + 0.796616i \(0.293379\pi\)
\(662\) 42.9618 1.66976
\(663\) −1.42446 −0.0553213
\(664\) −8.17021 −0.317065
\(665\) 22.1791 0.860067
\(666\) −9.99174 −0.387172
\(667\) 5.46510 0.211610
\(668\) 8.20244 0.317362
\(669\) 20.0652 0.775765
\(670\) 12.1178 0.468152
\(671\) −8.87533 −0.342628
\(672\) 17.1896 0.663102
\(673\) −29.0271 −1.11891 −0.559457 0.828860i \(-0.688990\pi\)
−0.559457 + 0.828860i \(0.688990\pi\)
\(674\) 11.8078 0.454818
\(675\) 3.38110 0.130139
\(676\) −10.9948 −0.422876
\(677\) 10.2887 0.395427 0.197714 0.980260i \(-0.436648\pi\)
0.197714 + 0.980260i \(0.436648\pi\)
\(678\) −14.3605 −0.551512
\(679\) −7.73442 −0.296820
\(680\) 5.00522 0.191942
\(681\) 10.9646 0.420165
\(682\) 4.21095 0.161245
\(683\) −14.2011 −0.543390 −0.271695 0.962383i \(-0.587584\pi\)
−0.271695 + 0.962383i \(0.587584\pi\)
\(684\) 2.32508 0.0889016
\(685\) 30.0316 1.14745
\(686\) 17.7126 0.676271
\(687\) 22.5916 0.861923
\(688\) −52.5567 −2.00371
\(689\) −18.8030 −0.716339
\(690\) 42.1514 1.60468
\(691\) 24.1178 0.917484 0.458742 0.888569i \(-0.348300\pi\)
0.458742 + 0.888569i \(0.348300\pi\)
\(692\) 5.58091 0.212154
\(693\) 10.7386 0.407928
\(694\) −44.0176 −1.67089
\(695\) −38.3135 −1.45331
\(696\) −1.12442 −0.0426209
\(697\) −9.70082 −0.367445
\(698\) 54.6691 2.06925
\(699\) −0.530463 −0.0200640
\(700\) 11.1892 0.422912
\(701\) −7.23044 −0.273090 −0.136545 0.990634i \(-0.543600\pi\)
−0.136545 + 0.990634i \(0.543600\pi\)
\(702\) 2.46812 0.0931533
\(703\) 13.3788 0.504592
\(704\) 3.18838 0.120167
\(705\) 19.6187 0.738884
\(706\) 16.5450 0.622680
\(707\) 44.2387 1.66377
\(708\) −7.75615 −0.291494
\(709\) −42.4767 −1.59525 −0.797624 0.603155i \(-0.793910\pi\)
−0.797624 + 0.603155i \(0.793910\pi\)
\(710\) −68.6974 −2.57817
\(711\) 1.00000 0.0375029
\(712\) 19.8806 0.745057
\(713\) 6.27991 0.235185
\(714\) −5.72157 −0.214125
\(715\) −13.4107 −0.501532
\(716\) −24.3189 −0.908838
\(717\) 0.0514535 0.00192157
\(718\) −61.2102 −2.28434
\(719\) 34.6722 1.29306 0.646528 0.762891i \(-0.276221\pi\)
0.646528 + 0.762891i \(0.276221\pi\)
\(720\) −14.4751 −0.539453
\(721\) −51.3095 −1.91086
\(722\) 23.5946 0.878101
\(723\) −7.69075 −0.286022
\(724\) 11.3764 0.422801
\(725\) −2.19893 −0.0816664
\(726\) 0.735393 0.0272930
\(727\) −21.3405 −0.791476 −0.395738 0.918364i \(-0.629511\pi\)
−0.395738 + 0.918364i \(0.629511\pi\)
\(728\) −8.13241 −0.301407
\(729\) 1.00000 0.0370370
\(730\) 26.9527 0.997564
\(731\) 10.5114 0.388777
\(732\) −2.73512 −0.101093
\(733\) −33.9813 −1.25513 −0.627564 0.778565i \(-0.715948\pi\)
−0.627564 + 0.778565i \(0.715948\pi\)
\(734\) 11.9867 0.442435
\(735\) 11.3028 0.416911
\(736\) −43.7433 −1.61240
\(737\) −7.85611 −0.289384
\(738\) 16.8084 0.618726
\(739\) 29.7665 1.09498 0.547489 0.836813i \(-0.315584\pi\)
0.547489 + 0.836813i \(0.315584\pi\)
\(740\) 16.7308 0.615036
\(741\) −3.30479 −0.121404
\(742\) −75.5257 −2.77264
\(743\) −30.0331 −1.10181 −0.550904 0.834568i \(-0.685717\pi\)
−0.550904 + 0.834568i \(0.685717\pi\)
\(744\) −1.29206 −0.0473692
\(745\) −11.3070 −0.414256
\(746\) 8.61841 0.315543
\(747\) −4.72563 −0.172902
\(748\) 3.25908 0.119164
\(749\) 42.1228 1.53913
\(750\) 8.12061 0.296523
\(751\) −39.7193 −1.44938 −0.724689 0.689076i \(-0.758017\pi\)
−0.724689 + 0.689076i \(0.758017\pi\)
\(752\) −33.8836 −1.23561
\(753\) −20.1716 −0.735095
\(754\) −1.60517 −0.0584569
\(755\) −14.4731 −0.526730
\(756\) 3.30933 0.120359
\(757\) 4.61255 0.167646 0.0838230 0.996481i \(-0.473287\pi\)
0.0838230 + 0.996481i \(0.473287\pi\)
\(758\) 29.6479 1.07686
\(759\) −27.3273 −0.991917
\(760\) 11.6123 0.421222
\(761\) 22.4080 0.812288 0.406144 0.913809i \(-0.366873\pi\)
0.406144 + 0.913809i \(0.366873\pi\)
\(762\) 13.2022 0.478264
\(763\) 44.3522 1.60566
\(764\) 7.95096 0.287655
\(765\) 2.89501 0.104669
\(766\) −32.2604 −1.16562
\(767\) 11.0243 0.398065
\(768\) 19.0217 0.686386
\(769\) −32.3445 −1.16637 −0.583185 0.812339i \(-0.698194\pi\)
−0.583185 + 0.812339i \(0.698194\pi\)
\(770\) −53.8664 −1.94121
\(771\) 15.7169 0.566030
\(772\) −18.0996 −0.651418
\(773\) −7.69642 −0.276821 −0.138410 0.990375i \(-0.544199\pi\)
−0.138410 + 0.990375i \(0.544199\pi\)
\(774\) −18.2128 −0.654646
\(775\) −2.52678 −0.0907647
\(776\) −4.04951 −0.145369
\(777\) 19.0424 0.683141
\(778\) 31.9002 1.14368
\(779\) −22.5062 −0.806370
\(780\) −4.13278 −0.147977
\(781\) 44.5373 1.59367
\(782\) 14.5600 0.520665
\(783\) −0.650361 −0.0232420
\(784\) −19.5212 −0.697185
\(785\) −55.5392 −1.98228
\(786\) −7.59480 −0.270897
\(787\) 5.50440 0.196211 0.0981053 0.995176i \(-0.468722\pi\)
0.0981053 + 0.995176i \(0.468722\pi\)
\(788\) 1.90809 0.0679729
\(789\) −7.62885 −0.271594
\(790\) −5.01613 −0.178466
\(791\) 27.3684 0.973109
\(792\) 5.62244 0.199785
\(793\) 3.88760 0.138053
\(794\) −9.50289 −0.337245
\(795\) 38.2146 1.35533
\(796\) 25.1076 0.889914
\(797\) 32.4486 1.14939 0.574694 0.818368i \(-0.305121\pi\)
0.574694 + 0.818368i \(0.305121\pi\)
\(798\) −13.2743 −0.469904
\(799\) 6.77674 0.239744
\(800\) 17.6005 0.622272
\(801\) 11.4989 0.406294
\(802\) −38.1168 −1.34595
\(803\) −17.4737 −0.616635
\(804\) −2.42102 −0.0853829
\(805\) −80.3327 −2.83135
\(806\) −1.84449 −0.0649694
\(807\) −31.3153 −1.10235
\(808\) 23.1621 0.814840
\(809\) −44.6435 −1.56958 −0.784791 0.619761i \(-0.787229\pi\)
−0.784791 + 0.619761i \(0.787229\pi\)
\(810\) −5.01613 −0.176249
\(811\) −38.5940 −1.35522 −0.677610 0.735421i \(-0.736984\pi\)
−0.677610 + 0.735421i \(0.736984\pi\)
\(812\) −2.15226 −0.0755296
\(813\) −15.9376 −0.558955
\(814\) −32.4932 −1.13889
\(815\) −30.2188 −1.05852
\(816\) −5.00000 −0.175035
\(817\) 24.3867 0.853184
\(818\) −36.1895 −1.26534
\(819\) −4.70378 −0.164363
\(820\) −28.1450 −0.982867
\(821\) 11.6148 0.405358 0.202679 0.979245i \(-0.435035\pi\)
0.202679 + 0.979245i \(0.435035\pi\)
\(822\) −17.9741 −0.626918
\(823\) 45.7841 1.59593 0.797967 0.602702i \(-0.205909\pi\)
0.797967 + 0.602702i \(0.205909\pi\)
\(824\) −26.8641 −0.935856
\(825\) 10.9954 0.382810
\(826\) 44.2811 1.54074
\(827\) 18.8140 0.654226 0.327113 0.944985i \(-0.393924\pi\)
0.327113 + 0.944985i \(0.393924\pi\)
\(828\) −8.42145 −0.292666
\(829\) 18.8467 0.654573 0.327287 0.944925i \(-0.393866\pi\)
0.327287 + 0.944925i \(0.393866\pi\)
\(830\) 23.7044 0.822791
\(831\) −19.8080 −0.687131
\(832\) −1.39658 −0.0484178
\(833\) 3.90424 0.135274
\(834\) 22.9308 0.794028
\(835\) 23.6947 0.819987
\(836\) 7.56118 0.261509
\(837\) −0.747325 −0.0258313
\(838\) 5.36321 0.185269
\(839\) 12.2399 0.422567 0.211284 0.977425i \(-0.432236\pi\)
0.211284 + 0.977425i \(0.432236\pi\)
\(840\) 16.5280 0.570271
\(841\) −28.5770 −0.985415
\(842\) −12.7183 −0.438301
\(843\) 9.35604 0.322239
\(844\) −3.99334 −0.137456
\(845\) −31.7610 −1.09261
\(846\) −11.7419 −0.403695
\(847\) −1.40152 −0.0481568
\(848\) −66.0008 −2.26648
\(849\) 5.57589 0.191364
\(850\) −5.85836 −0.200940
\(851\) −48.4582 −1.66113
\(852\) 13.7251 0.470214
\(853\) −19.3697 −0.663205 −0.331603 0.943419i \(-0.607589\pi\)
−0.331603 + 0.943419i \(0.607589\pi\)
\(854\) 15.6152 0.534342
\(855\) 6.71653 0.229701
\(856\) 22.0543 0.753799
\(857\) −6.39647 −0.218499 −0.109250 0.994014i \(-0.534845\pi\)
−0.109250 + 0.994014i \(0.534845\pi\)
\(858\) 8.02636 0.274016
\(859\) −15.0393 −0.513134 −0.256567 0.966526i \(-0.582591\pi\)
−0.256567 + 0.966526i \(0.582591\pi\)
\(860\) 30.4967 1.03993
\(861\) −32.0336 −1.09170
\(862\) 42.5492 1.44923
\(863\) −34.9273 −1.18894 −0.594469 0.804118i \(-0.702638\pi\)
−0.594469 + 0.804118i \(0.702638\pi\)
\(864\) 5.20556 0.177097
\(865\) 16.1218 0.548157
\(866\) −50.0083 −1.69935
\(867\) 1.00000 0.0339618
\(868\) −2.47315 −0.0839442
\(869\) 3.25201 0.110317
\(870\) 3.26229 0.110602
\(871\) 3.44116 0.116599
\(872\) 23.2215 0.786380
\(873\) −2.34223 −0.0792726
\(874\) 33.7798 1.14262
\(875\) −15.4763 −0.523196
\(876\) −5.38489 −0.181939
\(877\) 48.8667 1.65011 0.825056 0.565050i \(-0.191143\pi\)
0.825056 + 0.565050i \(0.191143\pi\)
\(878\) 17.7619 0.599435
\(879\) −4.63022 −0.156174
\(880\) −47.0730 −1.58683
\(881\) −21.5267 −0.725254 −0.362627 0.931934i \(-0.618120\pi\)
−0.362627 + 0.931934i \(0.618120\pi\)
\(882\) −6.76479 −0.227782
\(883\) −48.4105 −1.62914 −0.814572 0.580062i \(-0.803028\pi\)
−0.814572 + 0.580062i \(0.803028\pi\)
\(884\) −1.42755 −0.0480138
\(885\) −22.4055 −0.753151
\(886\) −24.8054 −0.833354
\(887\) 52.3777 1.75867 0.879335 0.476204i \(-0.157988\pi\)
0.879335 + 0.476204i \(0.157988\pi\)
\(888\) 9.97002 0.334572
\(889\) −25.1608 −0.843868
\(890\) −57.6799 −1.93344
\(891\) 3.25201 0.108946
\(892\) 20.1088 0.673293
\(893\) 15.7223 0.526126
\(894\) 6.76729 0.226332
\(895\) −70.2507 −2.34822
\(896\) −39.9888 −1.33593
\(897\) 11.9700 0.399666
\(898\) −60.3197 −2.01289
\(899\) 0.486031 0.0162100
\(900\) 3.38845 0.112948
\(901\) 13.2002 0.439761
\(902\) 54.6611 1.82001
\(903\) 34.7101 1.15508
\(904\) 14.3293 0.476586
\(905\) 32.8634 1.09242
\(906\) 8.66221 0.287783
\(907\) 6.98423 0.231908 0.115954 0.993255i \(-0.463008\pi\)
0.115954 + 0.993255i \(0.463008\pi\)
\(908\) 10.9885 0.364665
\(909\) 13.3969 0.444348
\(910\) 23.5947 0.782158
\(911\) −54.4137 −1.80281 −0.901403 0.432981i \(-0.857462\pi\)
−0.901403 + 0.432981i \(0.857462\pi\)
\(912\) −11.6002 −0.384120
\(913\) −15.3678 −0.508600
\(914\) −25.7537 −0.851857
\(915\) −7.90102 −0.261200
\(916\) 22.6407 0.748070
\(917\) 14.4742 0.477982
\(918\) −1.73268 −0.0571869
\(919\) −11.7468 −0.387491 −0.193746 0.981052i \(-0.562064\pi\)
−0.193746 + 0.981052i \(0.562064\pi\)
\(920\) −42.0598 −1.38667
\(921\) 11.0056 0.362648
\(922\) −0.548523 −0.0180647
\(923\) −19.5084 −0.642126
\(924\) 10.7620 0.354044
\(925\) 19.4976 0.641077
\(926\) 9.05324 0.297508
\(927\) −15.5382 −0.510341
\(928\) −3.38549 −0.111134
\(929\) −0.356652 −0.0117014 −0.00585069 0.999983i \(-0.501862\pi\)
−0.00585069 + 0.999983i \(0.501862\pi\)
\(930\) 3.74868 0.122924
\(931\) 9.05798 0.296863
\(932\) −0.531616 −0.0174137
\(933\) −18.3578 −0.601009
\(934\) 28.1997 0.922721
\(935\) 9.41461 0.307891
\(936\) −2.46276 −0.0804978
\(937\) 5.46143 0.178417 0.0892085 0.996013i \(-0.471566\pi\)
0.0892085 + 0.996013i \(0.471566\pi\)
\(938\) 13.8220 0.451305
\(939\) 10.3244 0.336923
\(940\) 19.6614 0.641284
\(941\) 32.0106 1.04352 0.521758 0.853094i \(-0.325276\pi\)
0.521758 + 0.853094i \(0.325276\pi\)
\(942\) 33.2405 1.08303
\(943\) 81.5178 2.65458
\(944\) 38.6966 1.25947
\(945\) 9.55979 0.310980
\(946\) −59.2282 −1.92568
\(947\) −3.22143 −0.104683 −0.0523413 0.998629i \(-0.516668\pi\)
−0.0523413 + 0.998629i \(0.516668\pi\)
\(948\) 1.00217 0.0325491
\(949\) 7.65390 0.248456
\(950\) −13.5916 −0.440970
\(951\) −18.7935 −0.609422
\(952\) 5.70914 0.185034
\(953\) −18.1062 −0.586519 −0.293259 0.956033i \(-0.594740\pi\)
−0.293259 + 0.956033i \(0.594740\pi\)
\(954\) −22.8716 −0.740496
\(955\) 22.9682 0.743233
\(956\) 0.0515653 0.00166774
\(957\) −2.11498 −0.0683676
\(958\) −53.1533 −1.71730
\(959\) 34.2552 1.10616
\(960\) 2.83837 0.0916078
\(961\) −30.4415 −0.981984
\(962\) 14.2328 0.458883
\(963\) 12.7561 0.411061
\(964\) −7.70747 −0.248241
\(965\) −52.2849 −1.68311
\(966\) 48.0795 1.54693
\(967\) −12.0886 −0.388742 −0.194371 0.980928i \(-0.562267\pi\)
−0.194371 + 0.980928i \(0.562267\pi\)
\(968\) −0.733795 −0.0235851
\(969\) 2.32004 0.0745303
\(970\) 11.7489 0.377236
\(971\) −59.8453 −1.92053 −0.960264 0.279095i \(-0.909966\pi\)
−0.960264 + 0.279095i \(0.909966\pi\)
\(972\) 1.00217 0.0321447
\(973\) −43.7017 −1.40101
\(974\) 7.42102 0.237785
\(975\) −4.81623 −0.154243
\(976\) 13.6459 0.436795
\(977\) −20.9069 −0.668873 −0.334436 0.942418i \(-0.608546\pi\)
−0.334436 + 0.942418i \(0.608546\pi\)
\(978\) 18.0861 0.578329
\(979\) 37.3946 1.19514
\(980\) 11.3274 0.361840
\(981\) 13.4313 0.428828
\(982\) 9.69145 0.309267
\(983\) 23.4501 0.747943 0.373971 0.927440i \(-0.377996\pi\)
0.373971 + 0.927440i \(0.377996\pi\)
\(984\) −16.7719 −0.534667
\(985\) 5.51196 0.175626
\(986\) 1.12687 0.0358867
\(987\) 22.3778 0.712295
\(988\) −3.31197 −0.105368
\(989\) −88.3289 −2.80870
\(990\) −16.3125 −0.518445
\(991\) −61.3153 −1.94775 −0.973873 0.227094i \(-0.927078\pi\)
−0.973873 + 0.227094i \(0.927078\pi\)
\(992\) −3.89025 −0.123515
\(993\) −24.7950 −0.786846
\(994\) −78.3588 −2.48539
\(995\) 72.5291 2.29933
\(996\) −4.73591 −0.150063
\(997\) −62.0644 −1.96560 −0.982799 0.184679i \(-0.940875\pi\)
−0.982799 + 0.184679i \(0.940875\pi\)
\(998\) 10.4939 0.332179
\(999\) 5.76664 0.182449
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4029.2.a.k.1.7 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.7 31 1.1 even 1 trivial