Properties

Label 4029.2.a.l.1.17
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 32
CM no
Inner twists 1

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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: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0717307 q^{2} -1.00000 q^{3} -1.99485 q^{4} -1.92367 q^{5} +0.0717307 q^{6} +3.89464 q^{7} +0.286554 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.0717307 q^{2} -1.00000 q^{3} -1.99485 q^{4} -1.92367 q^{5} +0.0717307 q^{6} +3.89464 q^{7} +0.286554 q^{8} +1.00000 q^{9} +0.137987 q^{10} +0.330322 q^{11} +1.99485 q^{12} +1.95585 q^{13} -0.279365 q^{14} +1.92367 q^{15} +3.96915 q^{16} -1.00000 q^{17} -0.0717307 q^{18} +7.45825 q^{19} +3.83745 q^{20} -3.89464 q^{21} -0.0236943 q^{22} -0.344499 q^{23} -0.286554 q^{24} -1.29948 q^{25} -0.140294 q^{26} -1.00000 q^{27} -7.76925 q^{28} -3.99093 q^{29} -0.137987 q^{30} +6.60369 q^{31} -0.857818 q^{32} -0.330322 q^{33} +0.0717307 q^{34} -7.49203 q^{35} -1.99485 q^{36} -0.669431 q^{37} -0.534985 q^{38} -1.95585 q^{39} -0.551236 q^{40} -3.05035 q^{41} +0.279365 q^{42} +4.13678 q^{43} -0.658945 q^{44} -1.92367 q^{45} +0.0247111 q^{46} +3.35605 q^{47} -3.96915 q^{48} +8.16825 q^{49} +0.0932123 q^{50} +1.00000 q^{51} -3.90163 q^{52} +10.2366 q^{53} +0.0717307 q^{54} -0.635433 q^{55} +1.11602 q^{56} -7.45825 q^{57} +0.286272 q^{58} -14.3338 q^{59} -3.83745 q^{60} +9.85944 q^{61} -0.473687 q^{62} +3.89464 q^{63} -7.87678 q^{64} -3.76241 q^{65} +0.0236943 q^{66} -7.02759 q^{67} +1.99485 q^{68} +0.344499 q^{69} +0.537408 q^{70} -12.3550 q^{71} +0.286554 q^{72} -13.8133 q^{73} +0.0480187 q^{74} +1.29948 q^{75} -14.8781 q^{76} +1.28649 q^{77} +0.140294 q^{78} +1.00000 q^{79} -7.63536 q^{80} +1.00000 q^{81} +0.218804 q^{82} -13.5470 q^{83} +7.76925 q^{84} +1.92367 q^{85} -0.296734 q^{86} +3.99093 q^{87} +0.0946551 q^{88} +14.9069 q^{89} +0.137987 q^{90} +7.61733 q^{91} +0.687225 q^{92} -6.60369 q^{93} -0.240731 q^{94} -14.3472 q^{95} +0.857818 q^{96} -8.01496 q^{97} -0.585914 q^{98} +0.330322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + O(q^{10}) \) \( 32q - q^{2} - 32q^{3} + 41q^{4} - q^{5} + q^{6} + 4q^{7} - 3q^{8} + 32q^{9} + 17q^{10} + 8q^{11} - 41q^{12} + 17q^{13} + q^{14} + q^{15} + 55q^{16} - 32q^{17} - q^{18} + 48q^{19} - 7q^{20} - 4q^{21} - 4q^{22} - 19q^{23} + 3q^{24} + 63q^{25} + 27q^{26} - 32q^{27} + 17q^{28} - 15q^{29} - 17q^{30} + 20q^{31} + 13q^{32} - 8q^{33} + q^{34} + 22q^{35} + 41q^{36} + 6q^{37} + 11q^{38} - 17q^{39} + 47q^{40} + q^{41} - q^{42} + 40q^{43} + 22q^{44} - q^{45} + 5q^{46} - 5q^{47} - 55q^{48} + 88q^{49} + 17q^{50} + 32q^{51} + 23q^{52} - 34q^{53} + q^{54} + 48q^{55} - 48q^{57} - 9q^{58} + 41q^{59} + 7q^{60} + 20q^{61} + 15q^{62} + 4q^{63} + 93q^{64} - 58q^{65} + 4q^{66} + 52q^{67} - 41q^{68} + 19q^{69} + 25q^{70} + q^{71} - 3q^{72} + 19q^{73} + 12q^{74} - 63q^{75} + 128q^{76} - 20q^{77} - 27q^{78} + 32q^{79} - 16q^{80} + 32q^{81} - 5q^{82} + 31q^{83} - 17q^{84} + q^{85} - 62q^{86} + 15q^{87} + 35q^{88} + 18q^{89} + 17q^{90} + 48q^{91} - 75q^{92} - 20q^{93} + 29q^{94} + 5q^{95} - 13q^{96} + 17q^{97} + 30q^{98} + 8q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0717307 −0.0507213 −0.0253606 0.999678i \(-0.508073\pi\)
−0.0253606 + 0.999678i \(0.508073\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.99485 −0.997427
\(5\) −1.92367 −0.860293 −0.430147 0.902759i \(-0.641538\pi\)
−0.430147 + 0.902759i \(0.641538\pi\)
\(6\) 0.0717307 0.0292839
\(7\) 3.89464 1.47204 0.736019 0.676961i \(-0.236704\pi\)
0.736019 + 0.676961i \(0.236704\pi\)
\(8\) 0.286554 0.101312
\(9\) 1.00000 0.333333
\(10\) 0.137987 0.0436352
\(11\) 0.330322 0.0995960 0.0497980 0.998759i \(-0.484142\pi\)
0.0497980 + 0.998759i \(0.484142\pi\)
\(12\) 1.99485 0.575865
\(13\) 1.95585 0.542454 0.271227 0.962515i \(-0.412571\pi\)
0.271227 + 0.962515i \(0.412571\pi\)
\(14\) −0.279365 −0.0746636
\(15\) 1.92367 0.496691
\(16\) 3.96915 0.992289
\(17\) −1.00000 −0.242536
\(18\) −0.0717307 −0.0169071
\(19\) 7.45825 1.71104 0.855520 0.517770i \(-0.173238\pi\)
0.855520 + 0.517770i \(0.173238\pi\)
\(20\) 3.83745 0.858080
\(21\) −3.89464 −0.849881
\(22\) −0.0236943 −0.00505163
\(23\) −0.344499 −0.0718330 −0.0359165 0.999355i \(-0.511435\pi\)
−0.0359165 + 0.999355i \(0.511435\pi\)
\(24\) −0.286554 −0.0584925
\(25\) −1.29948 −0.259895
\(26\) −0.140294 −0.0275140
\(27\) −1.00000 −0.192450
\(28\) −7.76925 −1.46825
\(29\) −3.99093 −0.741096 −0.370548 0.928813i \(-0.620830\pi\)
−0.370548 + 0.928813i \(0.620830\pi\)
\(30\) −0.137987 −0.0251928
\(31\) 6.60369 1.18606 0.593029 0.805181i \(-0.297932\pi\)
0.593029 + 0.805181i \(0.297932\pi\)
\(32\) −0.857818 −0.151642
\(33\) −0.330322 −0.0575018
\(34\) 0.0717307 0.0123017
\(35\) −7.49203 −1.26638
\(36\) −1.99485 −0.332476
\(37\) −0.669431 −0.110054 −0.0550269 0.998485i \(-0.517524\pi\)
−0.0550269 + 0.998485i \(0.517524\pi\)
\(38\) −0.534985 −0.0867861
\(39\) −1.95585 −0.313186
\(40\) −0.551236 −0.0871581
\(41\) −3.05035 −0.476385 −0.238192 0.971218i \(-0.576555\pi\)
−0.238192 + 0.971218i \(0.576555\pi\)
\(42\) 0.279365 0.0431070
\(43\) 4.13678 0.630854 0.315427 0.948950i \(-0.397852\pi\)
0.315427 + 0.948950i \(0.397852\pi\)
\(44\) −0.658945 −0.0993397
\(45\) −1.92367 −0.286764
\(46\) 0.0247111 0.00364346
\(47\) 3.35605 0.489530 0.244765 0.969582i \(-0.421289\pi\)
0.244765 + 0.969582i \(0.421289\pi\)
\(48\) −3.96915 −0.572898
\(49\) 8.16825 1.16689
\(50\) 0.0932123 0.0131822
\(51\) 1.00000 0.140028
\(52\) −3.90163 −0.541059
\(53\) 10.2366 1.40611 0.703053 0.711137i \(-0.251820\pi\)
0.703053 + 0.711137i \(0.251820\pi\)
\(54\) 0.0717307 0.00976131
\(55\) −0.635433 −0.0856818
\(56\) 1.11602 0.149135
\(57\) −7.45825 −0.987869
\(58\) 0.286272 0.0375893
\(59\) −14.3338 −1.86610 −0.933051 0.359743i \(-0.882864\pi\)
−0.933051 + 0.359743i \(0.882864\pi\)
\(60\) −3.83745 −0.495413
\(61\) 9.85944 1.26237 0.631186 0.775632i \(-0.282569\pi\)
0.631186 + 0.775632i \(0.282569\pi\)
\(62\) −0.473687 −0.0601584
\(63\) 3.89464 0.490679
\(64\) −7.87678 −0.984597
\(65\) −3.76241 −0.466670
\(66\) 0.0236943 0.00291656
\(67\) −7.02759 −0.858556 −0.429278 0.903172i \(-0.641232\pi\)
−0.429278 + 0.903172i \(0.641232\pi\)
\(68\) 1.99485 0.241912
\(69\) 0.344499 0.0414728
\(70\) 0.537408 0.0642326
\(71\) −12.3550 −1.46627 −0.733137 0.680081i \(-0.761944\pi\)
−0.733137 + 0.680081i \(0.761944\pi\)
\(72\) 0.286554 0.0337707
\(73\) −13.8133 −1.61673 −0.808364 0.588682i \(-0.799647\pi\)
−0.808364 + 0.588682i \(0.799647\pi\)
\(74\) 0.0480187 0.00558206
\(75\) 1.29948 0.150051
\(76\) −14.8781 −1.70664
\(77\) 1.28649 0.146609
\(78\) 0.140294 0.0158852
\(79\) 1.00000 0.112509
\(80\) −7.63536 −0.853660
\(81\) 1.00000 0.111111
\(82\) 0.218804 0.0241628
\(83\) −13.5470 −1.48697 −0.743486 0.668751i \(-0.766829\pi\)
−0.743486 + 0.668751i \(0.766829\pi\)
\(84\) 7.76925 0.847695
\(85\) 1.92367 0.208652
\(86\) −0.296734 −0.0319977
\(87\) 3.99093 0.427872
\(88\) 0.0946551 0.0100903
\(89\) 14.9069 1.58013 0.790064 0.613024i \(-0.210047\pi\)
0.790064 + 0.613024i \(0.210047\pi\)
\(90\) 0.137987 0.0145451
\(91\) 7.61733 0.798513
\(92\) 0.687225 0.0716482
\(93\) −6.60369 −0.684771
\(94\) −0.240731 −0.0248296
\(95\) −14.3472 −1.47200
\(96\) 0.857818 0.0875506
\(97\) −8.01496 −0.813795 −0.406898 0.913474i \(-0.633389\pi\)
−0.406898 + 0.913474i \(0.633389\pi\)
\(98\) −0.585914 −0.0591863
\(99\) 0.330322 0.0331987
\(100\) 2.59226 0.259226
\(101\) 15.2639 1.51882 0.759408 0.650615i \(-0.225489\pi\)
0.759408 + 0.650615i \(0.225489\pi\)
\(102\) −0.0717307 −0.00710240
\(103\) 4.93728 0.486484 0.243242 0.969966i \(-0.421789\pi\)
0.243242 + 0.969966i \(0.421789\pi\)
\(104\) 0.560455 0.0549571
\(105\) 7.49203 0.731147
\(106\) −0.734279 −0.0713195
\(107\) −4.27760 −0.413531 −0.206766 0.978390i \(-0.566294\pi\)
−0.206766 + 0.978390i \(0.566294\pi\)
\(108\) 1.99485 0.191955
\(109\) 16.6053 1.59050 0.795248 0.606285i \(-0.207341\pi\)
0.795248 + 0.606285i \(0.207341\pi\)
\(110\) 0.0455800 0.00434589
\(111\) 0.669431 0.0635395
\(112\) 15.4584 1.46069
\(113\) 9.39687 0.883983 0.441992 0.897019i \(-0.354272\pi\)
0.441992 + 0.897019i \(0.354272\pi\)
\(114\) 0.534985 0.0501060
\(115\) 0.662704 0.0617974
\(116\) 7.96132 0.739190
\(117\) 1.95585 0.180818
\(118\) 1.02817 0.0946511
\(119\) −3.89464 −0.357021
\(120\) 0.551236 0.0503207
\(121\) −10.8909 −0.990081
\(122\) −0.707224 −0.0640291
\(123\) 3.05035 0.275041
\(124\) −13.1734 −1.18301
\(125\) 12.1181 1.08388
\(126\) −0.279365 −0.0248879
\(127\) 10.8463 0.962452 0.481226 0.876597i \(-0.340192\pi\)
0.481226 + 0.876597i \(0.340192\pi\)
\(128\) 2.28064 0.201582
\(129\) −4.13678 −0.364224
\(130\) 0.269880 0.0236701
\(131\) 0.552478 0.0482702 0.0241351 0.999709i \(-0.492317\pi\)
0.0241351 + 0.999709i \(0.492317\pi\)
\(132\) 0.658945 0.0573538
\(133\) 29.0472 2.51871
\(134\) 0.504094 0.0435470
\(135\) 1.92367 0.165564
\(136\) −0.286554 −0.0245718
\(137\) 6.96419 0.594991 0.297495 0.954723i \(-0.403849\pi\)
0.297495 + 0.954723i \(0.403849\pi\)
\(138\) −0.0247111 −0.00210355
\(139\) −4.18547 −0.355007 −0.177503 0.984120i \(-0.556802\pi\)
−0.177503 + 0.984120i \(0.556802\pi\)
\(140\) 14.9455 1.26313
\(141\) −3.35605 −0.282630
\(142\) 0.886235 0.0743712
\(143\) 0.646060 0.0540263
\(144\) 3.96915 0.330763
\(145\) 7.67724 0.637560
\(146\) 0.990840 0.0820025
\(147\) −8.16825 −0.673706
\(148\) 1.33542 0.109771
\(149\) 6.72582 0.551000 0.275500 0.961301i \(-0.411157\pi\)
0.275500 + 0.961301i \(0.411157\pi\)
\(150\) −0.0932123 −0.00761075
\(151\) 23.2316 1.89056 0.945279 0.326263i \(-0.105790\pi\)
0.945279 + 0.326263i \(0.105790\pi\)
\(152\) 2.13719 0.173349
\(153\) −1.00000 −0.0808452
\(154\) −0.0922807 −0.00743619
\(155\) −12.7034 −1.02036
\(156\) 3.90163 0.312380
\(157\) −1.91427 −0.152776 −0.0763879 0.997078i \(-0.524339\pi\)
−0.0763879 + 0.997078i \(0.524339\pi\)
\(158\) −0.0717307 −0.00570659
\(159\) −10.2366 −0.811816
\(160\) 1.65016 0.130457
\(161\) −1.34170 −0.105741
\(162\) −0.0717307 −0.00563570
\(163\) −8.09342 −0.633926 −0.316963 0.948438i \(-0.602663\pi\)
−0.316963 + 0.948438i \(0.602663\pi\)
\(164\) 6.08501 0.475159
\(165\) 0.635433 0.0494684
\(166\) 0.971733 0.0754211
\(167\) −15.3597 −1.18857 −0.594284 0.804256i \(-0.702564\pi\)
−0.594284 + 0.804256i \(0.702564\pi\)
\(168\) −1.11602 −0.0861032
\(169\) −9.17466 −0.705743
\(170\) −0.137987 −0.0105831
\(171\) 7.45825 0.570346
\(172\) −8.25228 −0.629231
\(173\) −8.15160 −0.619755 −0.309877 0.950777i \(-0.600288\pi\)
−0.309877 + 0.950777i \(0.600288\pi\)
\(174\) −0.286272 −0.0217022
\(175\) −5.06099 −0.382575
\(176\) 1.31110 0.0988279
\(177\) 14.3338 1.07739
\(178\) −1.06928 −0.0801461
\(179\) 12.8997 0.964167 0.482084 0.876125i \(-0.339880\pi\)
0.482084 + 0.876125i \(0.339880\pi\)
\(180\) 3.83745 0.286027
\(181\) 15.4930 1.15158 0.575792 0.817596i \(-0.304694\pi\)
0.575792 + 0.817596i \(0.304694\pi\)
\(182\) −0.546396 −0.0405016
\(183\) −9.85944 −0.728831
\(184\) −0.0987174 −0.00727754
\(185\) 1.28777 0.0946785
\(186\) 0.473687 0.0347325
\(187\) −0.330322 −0.0241556
\(188\) −6.69482 −0.488270
\(189\) −3.89464 −0.283294
\(190\) 1.02914 0.0746615
\(191\) 14.9801 1.08392 0.541960 0.840404i \(-0.317682\pi\)
0.541960 + 0.840404i \(0.317682\pi\)
\(192\) 7.87678 0.568457
\(193\) 7.67006 0.552103 0.276051 0.961143i \(-0.410974\pi\)
0.276051 + 0.961143i \(0.410974\pi\)
\(194\) 0.574918 0.0412767
\(195\) 3.76241 0.269432
\(196\) −16.2945 −1.16389
\(197\) 17.8042 1.26850 0.634249 0.773129i \(-0.281309\pi\)
0.634249 + 0.773129i \(0.281309\pi\)
\(198\) −0.0236943 −0.00168388
\(199\) 5.74954 0.407574 0.203787 0.979015i \(-0.434675\pi\)
0.203787 + 0.979015i \(0.434675\pi\)
\(200\) −0.372369 −0.0263305
\(201\) 7.02759 0.495688
\(202\) −1.09489 −0.0770363
\(203\) −15.5432 −1.09092
\(204\) −1.99485 −0.139668
\(205\) 5.86788 0.409831
\(206\) −0.354154 −0.0246751
\(207\) −0.344499 −0.0239443
\(208\) 7.76306 0.538271
\(209\) 2.46363 0.170413
\(210\) −0.537408 −0.0370847
\(211\) −7.55785 −0.520304 −0.260152 0.965568i \(-0.583773\pi\)
−0.260152 + 0.965568i \(0.583773\pi\)
\(212\) −20.4205 −1.40249
\(213\) 12.3550 0.846553
\(214\) 0.306835 0.0209748
\(215\) −7.95783 −0.542719
\(216\) −0.286554 −0.0194975
\(217\) 25.7190 1.74592
\(218\) −1.19111 −0.0806719
\(219\) 13.8133 0.933419
\(220\) 1.26760 0.0854613
\(221\) −1.95585 −0.131564
\(222\) −0.0480187 −0.00322281
\(223\) 25.3149 1.69521 0.847606 0.530626i \(-0.178043\pi\)
0.847606 + 0.530626i \(0.178043\pi\)
\(224\) −3.34089 −0.223223
\(225\) −1.29948 −0.0866317
\(226\) −0.674044 −0.0448367
\(227\) 13.9165 0.923668 0.461834 0.886966i \(-0.347192\pi\)
0.461834 + 0.886966i \(0.347192\pi\)
\(228\) 14.8781 0.985327
\(229\) −17.0794 −1.12864 −0.564319 0.825557i \(-0.690861\pi\)
−0.564319 + 0.825557i \(0.690861\pi\)
\(230\) −0.0475362 −0.00313444
\(231\) −1.28649 −0.0846447
\(232\) −1.14361 −0.0750820
\(233\) 13.5356 0.886749 0.443375 0.896336i \(-0.353781\pi\)
0.443375 + 0.896336i \(0.353781\pi\)
\(234\) −0.140294 −0.00917132
\(235\) −6.45594 −0.421139
\(236\) 28.5939 1.86130
\(237\) −1.00000 −0.0649570
\(238\) 0.279365 0.0181086
\(239\) 3.09713 0.200336 0.100168 0.994971i \(-0.468062\pi\)
0.100168 + 0.994971i \(0.468062\pi\)
\(240\) 7.63536 0.492861
\(241\) −12.6937 −0.817671 −0.408836 0.912608i \(-0.634065\pi\)
−0.408836 + 0.912608i \(0.634065\pi\)
\(242\) 0.781211 0.0502181
\(243\) −1.00000 −0.0641500
\(244\) −19.6681 −1.25912
\(245\) −15.7131 −1.00387
\(246\) −0.218804 −0.0139504
\(247\) 14.5872 0.928161
\(248\) 1.89231 0.120162
\(249\) 13.5470 0.858504
\(250\) −0.869243 −0.0549757
\(251\) 22.2222 1.40265 0.701327 0.712840i \(-0.252591\pi\)
0.701327 + 0.712840i \(0.252591\pi\)
\(252\) −7.76925 −0.489417
\(253\) −0.113796 −0.00715427
\(254\) −0.778011 −0.0488168
\(255\) −1.92367 −0.120465
\(256\) 15.5900 0.974373
\(257\) 5.17485 0.322798 0.161399 0.986889i \(-0.448399\pi\)
0.161399 + 0.986889i \(0.448399\pi\)
\(258\) 0.296734 0.0184739
\(259\) −2.60719 −0.162003
\(260\) 7.50547 0.465469
\(261\) −3.99093 −0.247032
\(262\) −0.0396296 −0.00244833
\(263\) 9.97141 0.614864 0.307432 0.951570i \(-0.400530\pi\)
0.307432 + 0.951570i \(0.400530\pi\)
\(264\) −0.0946551 −0.00582562
\(265\) −19.6919 −1.20966
\(266\) −2.08358 −0.127752
\(267\) −14.9069 −0.912288
\(268\) 14.0190 0.856347
\(269\) −3.62992 −0.221320 −0.110660 0.993858i \(-0.535296\pi\)
−0.110660 + 0.993858i \(0.535296\pi\)
\(270\) −0.137987 −0.00839759
\(271\) −25.8916 −1.57280 −0.786401 0.617717i \(-0.788058\pi\)
−0.786401 + 0.617717i \(0.788058\pi\)
\(272\) −3.96915 −0.240665
\(273\) −7.61733 −0.461022
\(274\) −0.499546 −0.0301787
\(275\) −0.429246 −0.0258845
\(276\) −0.687225 −0.0413661
\(277\) 18.4623 1.10929 0.554645 0.832087i \(-0.312854\pi\)
0.554645 + 0.832087i \(0.312854\pi\)
\(278\) 0.300227 0.0180064
\(279\) 6.60369 0.395353
\(280\) −2.14687 −0.128300
\(281\) 8.04062 0.479663 0.239832 0.970814i \(-0.422908\pi\)
0.239832 + 0.970814i \(0.422908\pi\)
\(282\) 0.240731 0.0143354
\(283\) 7.20662 0.428389 0.214195 0.976791i \(-0.431287\pi\)
0.214195 + 0.976791i \(0.431287\pi\)
\(284\) 24.6465 1.46250
\(285\) 14.3472 0.849857
\(286\) −0.0463423 −0.00274028
\(287\) −11.8800 −0.701256
\(288\) −0.857818 −0.0505474
\(289\) 1.00000 0.0588235
\(290\) −0.550694 −0.0323379
\(291\) 8.01496 0.469845
\(292\) 27.5556 1.61257
\(293\) −21.4899 −1.25545 −0.627727 0.778434i \(-0.716015\pi\)
−0.627727 + 0.778434i \(0.716015\pi\)
\(294\) 0.585914 0.0341712
\(295\) 27.5736 1.60540
\(296\) −0.191828 −0.0111498
\(297\) −0.330322 −0.0191673
\(298\) −0.482448 −0.0279474
\(299\) −0.673787 −0.0389661
\(300\) −2.59226 −0.149664
\(301\) 16.1113 0.928640
\(302\) −1.66642 −0.0958915
\(303\) −15.2639 −0.876889
\(304\) 29.6029 1.69784
\(305\) −18.9663 −1.08601
\(306\) 0.0717307 0.00410057
\(307\) −9.65818 −0.551221 −0.275611 0.961269i \(-0.588880\pi\)
−0.275611 + 0.961269i \(0.588880\pi\)
\(308\) −2.56636 −0.146232
\(309\) −4.93728 −0.280872
\(310\) 0.911221 0.0517539
\(311\) 27.6205 1.56622 0.783108 0.621885i \(-0.213633\pi\)
0.783108 + 0.621885i \(0.213633\pi\)
\(312\) −0.560455 −0.0317295
\(313\) −1.18468 −0.0669623 −0.0334811 0.999439i \(-0.510659\pi\)
−0.0334811 + 0.999439i \(0.510659\pi\)
\(314\) 0.137312 0.00774898
\(315\) −7.49203 −0.422128
\(316\) −1.99485 −0.112219
\(317\) 4.56237 0.256248 0.128124 0.991758i \(-0.459104\pi\)
0.128124 + 0.991758i \(0.459104\pi\)
\(318\) 0.734279 0.0411763
\(319\) −1.31829 −0.0738102
\(320\) 15.1524 0.847043
\(321\) 4.27760 0.238753
\(322\) 0.0962411 0.00536331
\(323\) −7.45825 −0.414988
\(324\) −1.99485 −0.110825
\(325\) −2.54157 −0.140981
\(326\) 0.580547 0.0321535
\(327\) −16.6053 −0.918273
\(328\) −0.874089 −0.0482635
\(329\) 13.0706 0.720606
\(330\) −0.0455800 −0.00250910
\(331\) −14.5436 −0.799390 −0.399695 0.916648i \(-0.630884\pi\)
−0.399695 + 0.916648i \(0.630884\pi\)
\(332\) 27.0242 1.48315
\(333\) −0.669431 −0.0366846
\(334\) 1.10176 0.0602856
\(335\) 13.5188 0.738610
\(336\) −15.4584 −0.843327
\(337\) −15.5897 −0.849225 −0.424613 0.905375i \(-0.639590\pi\)
−0.424613 + 0.905375i \(0.639590\pi\)
\(338\) 0.658105 0.0357962
\(339\) −9.39687 −0.510368
\(340\) −3.83745 −0.208115
\(341\) 2.18135 0.118127
\(342\) −0.534985 −0.0289287
\(343\) 4.54992 0.245673
\(344\) 1.18541 0.0639131
\(345\) −0.662704 −0.0356788
\(346\) 0.584720 0.0314347
\(347\) 0.992376 0.0532735 0.0266368 0.999645i \(-0.491520\pi\)
0.0266368 + 0.999645i \(0.491520\pi\)
\(348\) −7.96132 −0.426771
\(349\) 0.260426 0.0139403 0.00697015 0.999976i \(-0.497781\pi\)
0.00697015 + 0.999976i \(0.497781\pi\)
\(350\) 0.363029 0.0194047
\(351\) −1.95585 −0.104395
\(352\) −0.283356 −0.0151029
\(353\) −20.0726 −1.06835 −0.534177 0.845373i \(-0.679378\pi\)
−0.534177 + 0.845373i \(0.679378\pi\)
\(354\) −1.02817 −0.0546468
\(355\) 23.7671 1.26143
\(356\) −29.7371 −1.57606
\(357\) 3.89464 0.206126
\(358\) −0.925303 −0.0489038
\(359\) −26.0056 −1.37252 −0.686261 0.727355i \(-0.740749\pi\)
−0.686261 + 0.727355i \(0.740749\pi\)
\(360\) −0.551236 −0.0290527
\(361\) 36.6254 1.92766
\(362\) −1.11132 −0.0584098
\(363\) 10.8909 0.571623
\(364\) −15.1955 −0.796459
\(365\) 26.5724 1.39086
\(366\) 0.707224 0.0369672
\(367\) −4.22155 −0.220363 −0.110182 0.993911i \(-0.535143\pi\)
−0.110182 + 0.993911i \(0.535143\pi\)
\(368\) −1.36737 −0.0712791
\(369\) −3.05035 −0.158795
\(370\) −0.0923724 −0.00480221
\(371\) 39.8679 2.06984
\(372\) 13.1734 0.683009
\(373\) 24.6489 1.27627 0.638137 0.769923i \(-0.279705\pi\)
0.638137 + 0.769923i \(0.279705\pi\)
\(374\) 0.0236943 0.00122520
\(375\) −12.1181 −0.625778
\(376\) 0.961687 0.0495952
\(377\) −7.80564 −0.402011
\(378\) 0.279365 0.0143690
\(379\) −15.3554 −0.788756 −0.394378 0.918948i \(-0.629040\pi\)
−0.394378 + 0.918948i \(0.629040\pi\)
\(380\) 28.6207 1.46821
\(381\) −10.8463 −0.555672
\(382\) −1.07453 −0.0549778
\(383\) 11.2504 0.574871 0.287435 0.957800i \(-0.407197\pi\)
0.287435 + 0.957800i \(0.407197\pi\)
\(384\) −2.28064 −0.116384
\(385\) −2.47478 −0.126127
\(386\) −0.550178 −0.0280033
\(387\) 4.13678 0.210285
\(388\) 15.9887 0.811702
\(389\) −0.427537 −0.0216770 −0.0108385 0.999941i \(-0.503450\pi\)
−0.0108385 + 0.999941i \(0.503450\pi\)
\(390\) −0.269880 −0.0136659
\(391\) 0.344499 0.0174221
\(392\) 2.34064 0.118220
\(393\) −0.552478 −0.0278688
\(394\) −1.27711 −0.0643398
\(395\) −1.92367 −0.0967906
\(396\) −0.658945 −0.0331132
\(397\) 22.6863 1.13859 0.569296 0.822132i \(-0.307216\pi\)
0.569296 + 0.822132i \(0.307216\pi\)
\(398\) −0.412419 −0.0206727
\(399\) −29.0472 −1.45418
\(400\) −5.15782 −0.257891
\(401\) 0.432949 0.0216204 0.0108102 0.999942i \(-0.496559\pi\)
0.0108102 + 0.999942i \(0.496559\pi\)
\(402\) −0.504094 −0.0251419
\(403\) 12.9158 0.643382
\(404\) −30.4493 −1.51491
\(405\) −1.92367 −0.0955882
\(406\) 1.11493 0.0553329
\(407\) −0.221128 −0.0109609
\(408\) 0.286554 0.0141865
\(409\) −23.7771 −1.17570 −0.587851 0.808969i \(-0.700026\pi\)
−0.587851 + 0.808969i \(0.700026\pi\)
\(410\) −0.420907 −0.0207871
\(411\) −6.96419 −0.343518
\(412\) −9.84915 −0.485233
\(413\) −55.8251 −2.74697
\(414\) 0.0247111 0.00121449
\(415\) 26.0600 1.27923
\(416\) −1.67776 −0.0822589
\(417\) 4.18547 0.204963
\(418\) −0.176718 −0.00864354
\(419\) −5.21594 −0.254815 −0.127408 0.991850i \(-0.540666\pi\)
−0.127408 + 0.991850i \(0.540666\pi\)
\(420\) −14.9455 −0.729266
\(421\) 8.88717 0.433134 0.216567 0.976268i \(-0.430514\pi\)
0.216567 + 0.976268i \(0.430514\pi\)
\(422\) 0.542130 0.0263905
\(423\) 3.35605 0.163177
\(424\) 2.93334 0.142455
\(425\) 1.29948 0.0630338
\(426\) −0.886235 −0.0429382
\(427\) 38.3990 1.85826
\(428\) 8.53320 0.412468
\(429\) −0.646060 −0.0311921
\(430\) 0.570820 0.0275274
\(431\) −28.0996 −1.35351 −0.676754 0.736209i \(-0.736614\pi\)
−0.676754 + 0.736209i \(0.736614\pi\)
\(432\) −3.96915 −0.190966
\(433\) 35.3210 1.69742 0.848710 0.528858i \(-0.177380\pi\)
0.848710 + 0.528858i \(0.177380\pi\)
\(434\) −1.84484 −0.0885553
\(435\) −7.67724 −0.368096
\(436\) −33.1251 −1.58640
\(437\) −2.56936 −0.122909
\(438\) −0.990840 −0.0473442
\(439\) −8.16860 −0.389866 −0.194933 0.980817i \(-0.562449\pi\)
−0.194933 + 0.980817i \(0.562449\pi\)
\(440\) −0.182086 −0.00868059
\(441\) 8.16825 0.388964
\(442\) 0.140294 0.00667312
\(443\) 2.22455 0.105692 0.0528458 0.998603i \(-0.483171\pi\)
0.0528458 + 0.998603i \(0.483171\pi\)
\(444\) −1.33542 −0.0633761
\(445\) −28.6760 −1.35937
\(446\) −1.81586 −0.0859833
\(447\) −6.72582 −0.318120
\(448\) −30.6772 −1.44936
\(449\) −27.8572 −1.31466 −0.657331 0.753602i \(-0.728315\pi\)
−0.657331 + 0.753602i \(0.728315\pi\)
\(450\) 0.0932123 0.00439407
\(451\) −1.00760 −0.0474460
\(452\) −18.7454 −0.881709
\(453\) −23.2316 −1.09151
\(454\) −0.998238 −0.0468496
\(455\) −14.6533 −0.686955
\(456\) −2.13719 −0.100083
\(457\) 1.14253 0.0534455 0.0267228 0.999643i \(-0.491493\pi\)
0.0267228 + 0.999643i \(0.491493\pi\)
\(458\) 1.22512 0.0572460
\(459\) 1.00000 0.0466760
\(460\) −1.32200 −0.0616385
\(461\) 15.9503 0.742879 0.371439 0.928457i \(-0.378864\pi\)
0.371439 + 0.928457i \(0.378864\pi\)
\(462\) 0.0922807 0.00429329
\(463\) −7.73487 −0.359470 −0.179735 0.983715i \(-0.557524\pi\)
−0.179735 + 0.983715i \(0.557524\pi\)
\(464\) −15.8406 −0.735381
\(465\) 12.7034 0.589104
\(466\) −0.970921 −0.0449770
\(467\) −30.8369 −1.42696 −0.713480 0.700675i \(-0.752882\pi\)
−0.713480 + 0.700675i \(0.752882\pi\)
\(468\) −3.90163 −0.180353
\(469\) −27.3699 −1.26383
\(470\) 0.463089 0.0213607
\(471\) 1.91427 0.0882051
\(472\) −4.10740 −0.189059
\(473\) 1.36647 0.0628305
\(474\) 0.0717307 0.00329470
\(475\) −9.69181 −0.444691
\(476\) 7.76925 0.356103
\(477\) 10.2366 0.468702
\(478\) −0.222159 −0.0101613
\(479\) 36.0430 1.64685 0.823424 0.567426i \(-0.192061\pi\)
0.823424 + 0.567426i \(0.192061\pi\)
\(480\) −1.65016 −0.0753192
\(481\) −1.30930 −0.0596991
\(482\) 0.910526 0.0414733
\(483\) 1.34170 0.0610495
\(484\) 21.7257 0.987534
\(485\) 15.4182 0.700103
\(486\) 0.0717307 0.00325377
\(487\) −32.4321 −1.46964 −0.734820 0.678262i \(-0.762733\pi\)
−0.734820 + 0.678262i \(0.762733\pi\)
\(488\) 2.82526 0.127893
\(489\) 8.09342 0.365997
\(490\) 1.12711 0.0509176
\(491\) 36.7844 1.66006 0.830028 0.557722i \(-0.188325\pi\)
0.830028 + 0.557722i \(0.188325\pi\)
\(492\) −6.08501 −0.274333
\(493\) 3.99093 0.179742
\(494\) −1.04635 −0.0470775
\(495\) −0.635433 −0.0285606
\(496\) 26.2111 1.17691
\(497\) −48.1185 −2.15841
\(498\) −0.971733 −0.0435444
\(499\) 32.0547 1.43497 0.717484 0.696575i \(-0.245294\pi\)
0.717484 + 0.696575i \(0.245294\pi\)
\(500\) −24.1739 −1.08109
\(501\) 15.3597 0.686220
\(502\) −1.59402 −0.0711444
\(503\) 21.6955 0.967353 0.483676 0.875247i \(-0.339301\pi\)
0.483676 + 0.875247i \(0.339301\pi\)
\(504\) 1.11602 0.0497117
\(505\) −29.3628 −1.30663
\(506\) 0.00816264 0.000362874 0
\(507\) 9.17466 0.407461
\(508\) −21.6368 −0.959976
\(509\) −38.5911 −1.71052 −0.855261 0.518197i \(-0.826603\pi\)
−0.855261 + 0.518197i \(0.826603\pi\)
\(510\) 0.137987 0.00611015
\(511\) −53.7980 −2.37988
\(512\) −5.67956 −0.251004
\(513\) −7.45825 −0.329290
\(514\) −0.371196 −0.0163727
\(515\) −9.49771 −0.418519
\(516\) 8.25228 0.363287
\(517\) 1.10858 0.0487552
\(518\) 0.187016 0.00821700
\(519\) 8.15160 0.357816
\(520\) −1.07813 −0.0472793
\(521\) −3.73243 −0.163521 −0.0817604 0.996652i \(-0.526054\pi\)
−0.0817604 + 0.996652i \(0.526054\pi\)
\(522\) 0.286272 0.0125298
\(523\) 31.7896 1.39006 0.695031 0.718979i \(-0.255390\pi\)
0.695031 + 0.718979i \(0.255390\pi\)
\(524\) −1.10211 −0.0481460
\(525\) 5.06099 0.220880
\(526\) −0.715256 −0.0311867
\(527\) −6.60369 −0.287661
\(528\) −1.31110 −0.0570583
\(529\) −22.8813 −0.994840
\(530\) 1.41251 0.0613557
\(531\) −14.3338 −0.622034
\(532\) −57.9450 −2.51223
\(533\) −5.96602 −0.258417
\(534\) 1.06928 0.0462724
\(535\) 8.22872 0.355758
\(536\) −2.01378 −0.0869821
\(537\) −12.8997 −0.556662
\(538\) 0.260377 0.0112256
\(539\) 2.69816 0.116218
\(540\) −3.83745 −0.165138
\(541\) 2.37942 0.102299 0.0511496 0.998691i \(-0.483711\pi\)
0.0511496 + 0.998691i \(0.483711\pi\)
\(542\) 1.85722 0.0797745
\(543\) −15.4930 −0.664867
\(544\) 0.857818 0.0367786
\(545\) −31.9431 −1.36829
\(546\) 0.546396 0.0233836
\(547\) 39.6860 1.69685 0.848426 0.529315i \(-0.177551\pi\)
0.848426 + 0.529315i \(0.177551\pi\)
\(548\) −13.8925 −0.593460
\(549\) 9.85944 0.420790
\(550\) 0.0307901 0.00131289
\(551\) −29.7653 −1.26804
\(552\) 0.0987174 0.00420169
\(553\) 3.89464 0.165617
\(554\) −1.32431 −0.0562646
\(555\) −1.28777 −0.0546627
\(556\) 8.34940 0.354094
\(557\) 8.96781 0.379978 0.189989 0.981786i \(-0.439155\pi\)
0.189989 + 0.981786i \(0.439155\pi\)
\(558\) −0.473687 −0.0200528
\(559\) 8.09092 0.342209
\(560\) −29.7370 −1.25662
\(561\) 0.330322 0.0139462
\(562\) −0.576759 −0.0243291
\(563\) 29.1037 1.22657 0.613286 0.789861i \(-0.289847\pi\)
0.613286 + 0.789861i \(0.289847\pi\)
\(564\) 6.69482 0.281903
\(565\) −18.0765 −0.760485
\(566\) −0.516936 −0.0217284
\(567\) 3.89464 0.163560
\(568\) −3.54038 −0.148551
\(569\) 26.7071 1.11962 0.559809 0.828621i \(-0.310874\pi\)
0.559809 + 0.828621i \(0.310874\pi\)
\(570\) −1.02914 −0.0431058
\(571\) 13.1837 0.551720 0.275860 0.961198i \(-0.411037\pi\)
0.275860 + 0.961198i \(0.411037\pi\)
\(572\) −1.28880 −0.0538873
\(573\) −14.9801 −0.625801
\(574\) 0.852163 0.0355686
\(575\) 0.447668 0.0186690
\(576\) −7.87678 −0.328199
\(577\) −27.2076 −1.13267 −0.566334 0.824176i \(-0.691639\pi\)
−0.566334 + 0.824176i \(0.691639\pi\)
\(578\) −0.0717307 −0.00298360
\(579\) −7.67006 −0.318757
\(580\) −15.3150 −0.635920
\(581\) −52.7606 −2.18888
\(582\) −0.574918 −0.0238311
\(583\) 3.38138 0.140042
\(584\) −3.95826 −0.163794
\(585\) −3.76241 −0.155557
\(586\) 1.54149 0.0636782
\(587\) −18.9662 −0.782818 −0.391409 0.920217i \(-0.628012\pi\)
−0.391409 + 0.920217i \(0.628012\pi\)
\(588\) 16.2945 0.671973
\(589\) 49.2520 2.02939
\(590\) −1.97787 −0.0814277
\(591\) −17.8042 −0.732368
\(592\) −2.65707 −0.109205
\(593\) −43.4843 −1.78569 −0.892843 0.450368i \(-0.851293\pi\)
−0.892843 + 0.450368i \(0.851293\pi\)
\(594\) 0.0236943 0.000972187 0
\(595\) 7.49203 0.307143
\(596\) −13.4170 −0.549583
\(597\) −5.74954 −0.235313
\(598\) 0.0483312 0.00197641
\(599\) −22.5081 −0.919655 −0.459828 0.888008i \(-0.652089\pi\)
−0.459828 + 0.888008i \(0.652089\pi\)
\(600\) 0.372369 0.0152019
\(601\) 45.2772 1.84690 0.923448 0.383723i \(-0.125358\pi\)
0.923448 + 0.383723i \(0.125358\pi\)
\(602\) −1.15567 −0.0471018
\(603\) −7.02759 −0.286185
\(604\) −46.3436 −1.88569
\(605\) 20.9505 0.851760
\(606\) 1.09489 0.0444769
\(607\) 6.49095 0.263460 0.131730 0.991286i \(-0.457947\pi\)
0.131730 + 0.991286i \(0.457947\pi\)
\(608\) −6.39782 −0.259466
\(609\) 15.5432 0.629844
\(610\) 1.36047 0.0550838
\(611\) 6.56391 0.265547
\(612\) 1.99485 0.0806372
\(613\) 29.4811 1.19073 0.595365 0.803456i \(-0.297008\pi\)
0.595365 + 0.803456i \(0.297008\pi\)
\(614\) 0.692788 0.0279586
\(615\) −5.86788 −0.236616
\(616\) 0.368648 0.0148532
\(617\) −15.9041 −0.640277 −0.320138 0.947371i \(-0.603729\pi\)
−0.320138 + 0.947371i \(0.603729\pi\)
\(618\) 0.354154 0.0142462
\(619\) 36.5940 1.47084 0.735418 0.677614i \(-0.236986\pi\)
0.735418 + 0.677614i \(0.236986\pi\)
\(620\) 25.3414 1.01773
\(621\) 0.344499 0.0138243
\(622\) −1.98124 −0.0794405
\(623\) 58.0571 2.32601
\(624\) −7.76306 −0.310771
\(625\) −16.8140 −0.672559
\(626\) 0.0849781 0.00339641
\(627\) −2.46363 −0.0983878
\(628\) 3.81870 0.152383
\(629\) 0.669431 0.0266919
\(630\) 0.537408 0.0214109
\(631\) −8.02315 −0.319396 −0.159698 0.987166i \(-0.551052\pi\)
−0.159698 + 0.987166i \(0.551052\pi\)
\(632\) 0.286554 0.0113985
\(633\) 7.55785 0.300398
\(634\) −0.327262 −0.0129972
\(635\) −20.8647 −0.827991
\(636\) 20.4205 0.809727
\(637\) 15.9758 0.632986
\(638\) 0.0945620 0.00374375
\(639\) −12.3550 −0.488758
\(640\) −4.38721 −0.173420
\(641\) 46.0760 1.81989 0.909947 0.414726i \(-0.136122\pi\)
0.909947 + 0.414726i \(0.136122\pi\)
\(642\) −0.306835 −0.0121098
\(643\) −13.2817 −0.523779 −0.261889 0.965098i \(-0.584346\pi\)
−0.261889 + 0.965098i \(0.584346\pi\)
\(644\) 2.67650 0.105469
\(645\) 7.95783 0.313339
\(646\) 0.534985 0.0210487
\(647\) 35.2452 1.38563 0.692816 0.721115i \(-0.256370\pi\)
0.692816 + 0.721115i \(0.256370\pi\)
\(648\) 0.286554 0.0112569
\(649\) −4.73478 −0.185856
\(650\) 0.182309 0.00715074
\(651\) −25.7190 −1.00801
\(652\) 16.1452 0.632295
\(653\) 18.8204 0.736498 0.368249 0.929727i \(-0.379957\pi\)
0.368249 + 0.929727i \(0.379957\pi\)
\(654\) 1.19111 0.0465759
\(655\) −1.06279 −0.0415266
\(656\) −12.1073 −0.472711
\(657\) −13.8133 −0.538910
\(658\) −0.937563 −0.0365500
\(659\) 17.6101 0.685994 0.342997 0.939337i \(-0.388558\pi\)
0.342997 + 0.939337i \(0.388558\pi\)
\(660\) −1.26760 −0.0493411
\(661\) 21.9406 0.853389 0.426694 0.904396i \(-0.359678\pi\)
0.426694 + 0.904396i \(0.359678\pi\)
\(662\) 1.04322 0.0405461
\(663\) 1.95585 0.0759588
\(664\) −3.88193 −0.150648
\(665\) −55.8774 −2.16683
\(666\) 0.0480187 0.00186069
\(667\) 1.37487 0.0532351
\(668\) 30.6403 1.18551
\(669\) −25.3149 −0.978731
\(670\) −0.969712 −0.0374632
\(671\) 3.25679 0.125727
\(672\) 3.34089 0.128878
\(673\) −38.5660 −1.48661 −0.743305 0.668953i \(-0.766743\pi\)
−0.743305 + 0.668953i \(0.766743\pi\)
\(674\) 1.11826 0.0430738
\(675\) 1.29948 0.0500168
\(676\) 18.3021 0.703928
\(677\) 5.13280 0.197270 0.0986348 0.995124i \(-0.468552\pi\)
0.0986348 + 0.995124i \(0.468552\pi\)
\(678\) 0.674044 0.0258865
\(679\) −31.2154 −1.19794
\(680\) 0.551236 0.0211389
\(681\) −13.9165 −0.533280
\(682\) −0.156470 −0.00599153
\(683\) −29.9446 −1.14580 −0.572898 0.819627i \(-0.694181\pi\)
−0.572898 + 0.819627i \(0.694181\pi\)
\(684\) −14.8781 −0.568879
\(685\) −13.3968 −0.511867
\(686\) −0.326369 −0.0124608
\(687\) 17.0794 0.651620
\(688\) 16.4195 0.625989
\(689\) 20.0212 0.762748
\(690\) 0.0475362 0.00180967
\(691\) −15.8527 −0.603065 −0.301533 0.953456i \(-0.597498\pi\)
−0.301533 + 0.953456i \(0.597498\pi\)
\(692\) 16.2613 0.618161
\(693\) 1.28649 0.0488696
\(694\) −0.0711838 −0.00270210
\(695\) 8.05148 0.305410
\(696\) 1.14361 0.0433486
\(697\) 3.05035 0.115540
\(698\) −0.0186805 −0.000707069 0
\(699\) −13.5356 −0.511965
\(700\) 10.0959 0.381591
\(701\) 23.3229 0.880894 0.440447 0.897779i \(-0.354820\pi\)
0.440447 + 0.897779i \(0.354820\pi\)
\(702\) 0.140294 0.00529506
\(703\) −4.99278 −0.188306
\(704\) −2.60188 −0.0980619
\(705\) 6.45594 0.243145
\(706\) 1.43982 0.0541883
\(707\) 59.4475 2.23575
\(708\) −28.5939 −1.07462
\(709\) −37.8546 −1.42166 −0.710830 0.703364i \(-0.751680\pi\)
−0.710830 + 0.703364i \(0.751680\pi\)
\(710\) −1.70483 −0.0639811
\(711\) 1.00000 0.0375029
\(712\) 4.27163 0.160086
\(713\) −2.27496 −0.0851981
\(714\) −0.279365 −0.0104550
\(715\) −1.24281 −0.0464784
\(716\) −25.7330 −0.961687
\(717\) −3.09713 −0.115664
\(718\) 1.86540 0.0696161
\(719\) −45.6181 −1.70127 −0.850634 0.525758i \(-0.823782\pi\)
−0.850634 + 0.525758i \(0.823782\pi\)
\(720\) −7.63536 −0.284553
\(721\) 19.2289 0.716123
\(722\) −2.62717 −0.0977731
\(723\) 12.6937 0.472083
\(724\) −30.9062 −1.14862
\(725\) 5.18611 0.192607
\(726\) −0.781211 −0.0289935
\(727\) 45.5646 1.68990 0.844949 0.534846i \(-0.179631\pi\)
0.844949 + 0.534846i \(0.179631\pi\)
\(728\) 2.18277 0.0808990
\(729\) 1.00000 0.0370370
\(730\) −1.90605 −0.0705462
\(731\) −4.13678 −0.153004
\(732\) 19.6681 0.726955
\(733\) −17.0282 −0.628950 −0.314475 0.949266i \(-0.601828\pi\)
−0.314475 + 0.949266i \(0.601828\pi\)
\(734\) 0.302815 0.0111771
\(735\) 15.7131 0.579585
\(736\) 0.295517 0.0108929
\(737\) −2.32137 −0.0855087
\(738\) 0.218804 0.00805428
\(739\) −23.3844 −0.860210 −0.430105 0.902779i \(-0.641523\pi\)
−0.430105 + 0.902779i \(0.641523\pi\)
\(740\) −2.56891 −0.0944349
\(741\) −14.5872 −0.535874
\(742\) −2.85975 −0.104985
\(743\) −18.6895 −0.685652 −0.342826 0.939399i \(-0.611384\pi\)
−0.342826 + 0.939399i \(0.611384\pi\)
\(744\) −1.89231 −0.0693755
\(745\) −12.9383 −0.474022
\(746\) −1.76809 −0.0647342
\(747\) −13.5470 −0.495658
\(748\) 0.658945 0.0240934
\(749\) −16.6597 −0.608734
\(750\) 0.869243 0.0317403
\(751\) −17.5804 −0.641518 −0.320759 0.947161i \(-0.603938\pi\)
−0.320759 + 0.947161i \(0.603938\pi\)
\(752\) 13.3207 0.485755
\(753\) −22.2222 −0.809823
\(754\) 0.559904 0.0203905
\(755\) −44.6900 −1.62643
\(756\) 7.76925 0.282565
\(757\) −47.6274 −1.73105 −0.865523 0.500869i \(-0.833014\pi\)
−0.865523 + 0.500869i \(0.833014\pi\)
\(758\) 1.10146 0.0400067
\(759\) 0.113796 0.00413052
\(760\) −4.11125 −0.149131
\(761\) 32.6918 1.18508 0.592538 0.805542i \(-0.298126\pi\)
0.592538 + 0.805542i \(0.298126\pi\)
\(762\) 0.778011 0.0281844
\(763\) 64.6716 2.34127
\(764\) −29.8831 −1.08113
\(765\) 1.92367 0.0695506
\(766\) −0.807002 −0.0291582
\(767\) −28.0347 −1.01228
\(768\) −15.5900 −0.562554
\(769\) 13.7155 0.494593 0.247297 0.968940i \(-0.420458\pi\)
0.247297 + 0.968940i \(0.420458\pi\)
\(770\) 0.177518 0.00639731
\(771\) −5.17485 −0.186368
\(772\) −15.3006 −0.550682
\(773\) −33.0422 −1.18845 −0.594223 0.804300i \(-0.702540\pi\)
−0.594223 + 0.804300i \(0.702540\pi\)
\(774\) −0.296734 −0.0106659
\(775\) −8.58134 −0.308251
\(776\) −2.29672 −0.0824473
\(777\) 2.60719 0.0935326
\(778\) 0.0306675 0.00109948
\(779\) −22.7503 −0.815113
\(780\) −7.50547 −0.268739
\(781\) −4.08115 −0.146035
\(782\) −0.0247111 −0.000883669 0
\(783\) 3.99093 0.142624
\(784\) 32.4211 1.15789
\(785\) 3.68244 0.131432
\(786\) 0.0396296 0.00141354
\(787\) 12.9936 0.463171 0.231585 0.972815i \(-0.425609\pi\)
0.231585 + 0.972815i \(0.425609\pi\)
\(788\) −35.5168 −1.26523
\(789\) −9.97141 −0.354992
\(790\) 0.137987 0.00490934
\(791\) 36.5975 1.30126
\(792\) 0.0946551 0.00336342
\(793\) 19.2835 0.684779
\(794\) −1.62730 −0.0577508
\(795\) 19.6919 0.698400
\(796\) −11.4695 −0.406526
\(797\) 12.7179 0.450490 0.225245 0.974302i \(-0.427682\pi\)
0.225245 + 0.974302i \(0.427682\pi\)
\(798\) 2.08358 0.0737578
\(799\) −3.35605 −0.118728
\(800\) 1.11471 0.0394111
\(801\) 14.9069 0.526709
\(802\) −0.0310557 −0.00109662
\(803\) −4.56285 −0.161020
\(804\) −14.0190 −0.494412
\(805\) 2.58100 0.0909681
\(806\) −0.926460 −0.0326332
\(807\) 3.62992 0.127779
\(808\) 4.37393 0.153874
\(809\) −12.0999 −0.425410 −0.212705 0.977116i \(-0.568227\pi\)
−0.212705 + 0.977116i \(0.568227\pi\)
\(810\) 0.137987 0.00484835
\(811\) 36.3321 1.27579 0.637897 0.770122i \(-0.279805\pi\)
0.637897 + 0.770122i \(0.279805\pi\)
\(812\) 31.0065 1.08811
\(813\) 25.8916 0.908057
\(814\) 0.0158617 0.000555951 0
\(815\) 15.5691 0.545362
\(816\) 3.96915 0.138948
\(817\) 30.8532 1.07942
\(818\) 1.70555 0.0596331
\(819\) 7.61733 0.266171
\(820\) −11.7056 −0.408776
\(821\) 10.7638 0.375660 0.187830 0.982202i \(-0.439855\pi\)
0.187830 + 0.982202i \(0.439855\pi\)
\(822\) 0.499546 0.0174237
\(823\) 21.5152 0.749974 0.374987 0.927030i \(-0.377647\pi\)
0.374987 + 0.927030i \(0.377647\pi\)
\(824\) 1.41479 0.0492867
\(825\) 0.429246 0.0149444
\(826\) 4.00437 0.139330
\(827\) 43.9232 1.52736 0.763679 0.645596i \(-0.223391\pi\)
0.763679 + 0.645596i \(0.223391\pi\)
\(828\) 0.687225 0.0238827
\(829\) −16.9067 −0.587193 −0.293596 0.955930i \(-0.594852\pi\)
−0.293596 + 0.955930i \(0.594852\pi\)
\(830\) −1.86930 −0.0648843
\(831\) −18.4623 −0.640449
\(832\) −15.4058 −0.534099
\(833\) −8.16825 −0.283013
\(834\) −0.300227 −0.0103960
\(835\) 29.5470 1.02252
\(836\) −4.91458 −0.169974
\(837\) −6.60369 −0.228257
\(838\) 0.374143 0.0129245
\(839\) 36.2251 1.25063 0.625315 0.780372i \(-0.284970\pi\)
0.625315 + 0.780372i \(0.284970\pi\)
\(840\) 2.14687 0.0740740
\(841\) −13.0725 −0.450776
\(842\) −0.637483 −0.0219691
\(843\) −8.04062 −0.276934
\(844\) 15.0768 0.518966
\(845\) 17.6491 0.607146
\(846\) −0.240731 −0.00827652
\(847\) −42.4161 −1.45744
\(848\) 40.6307 1.39526
\(849\) −7.20662 −0.247331
\(850\) −0.0932123 −0.00319715
\(851\) 0.230618 0.00790549
\(852\) −24.6465 −0.844375
\(853\) 32.7287 1.12061 0.560305 0.828286i \(-0.310684\pi\)
0.560305 + 0.828286i \(0.310684\pi\)
\(854\) −2.75439 −0.0942532
\(855\) −14.3472 −0.490665
\(856\) −1.22576 −0.0418957
\(857\) 8.73749 0.298467 0.149234 0.988802i \(-0.452319\pi\)
0.149234 + 0.988802i \(0.452319\pi\)
\(858\) 0.0463423 0.00158210
\(859\) 39.8009 1.35799 0.678995 0.734143i \(-0.262416\pi\)
0.678995 + 0.734143i \(0.262416\pi\)
\(860\) 15.8747 0.541323
\(861\) 11.8800 0.404870
\(862\) 2.01560 0.0686516
\(863\) −56.2817 −1.91585 −0.957925 0.287018i \(-0.907336\pi\)
−0.957925 + 0.287018i \(0.907336\pi\)
\(864\) 0.857818 0.0291835
\(865\) 15.6810 0.533171
\(866\) −2.53360 −0.0860953
\(867\) −1.00000 −0.0339618
\(868\) −51.3057 −1.74143
\(869\) 0.330322 0.0112054
\(870\) 0.550694 0.0186703
\(871\) −13.7449 −0.465728
\(872\) 4.75830 0.161136
\(873\) −8.01496 −0.271265
\(874\) 0.184302 0.00623410
\(875\) 47.1958 1.59551
\(876\) −27.5556 −0.931017
\(877\) 51.2504 1.73060 0.865302 0.501251i \(-0.167127\pi\)
0.865302 + 0.501251i \(0.167127\pi\)
\(878\) 0.585939 0.0197745
\(879\) 21.4899 0.724837
\(880\) −2.52213 −0.0850210
\(881\) −30.5057 −1.02776 −0.513881 0.857862i \(-0.671793\pi\)
−0.513881 + 0.857862i \(0.671793\pi\)
\(882\) −0.585914 −0.0197288
\(883\) 41.2152 1.38700 0.693501 0.720456i \(-0.256067\pi\)
0.693501 + 0.720456i \(0.256067\pi\)
\(884\) 3.90163 0.131226
\(885\) −27.5736 −0.926876
\(886\) −0.159569 −0.00536081
\(887\) −4.35717 −0.146299 −0.0731497 0.997321i \(-0.523305\pi\)
−0.0731497 + 0.997321i \(0.523305\pi\)
\(888\) 0.191828 0.00643732
\(889\) 42.2424 1.41676
\(890\) 2.05695 0.0689492
\(891\) 0.330322 0.0110662
\(892\) −50.4996 −1.69085
\(893\) 25.0302 0.837604
\(894\) 0.482448 0.0161355
\(895\) −24.8148 −0.829467
\(896\) 8.88229 0.296736
\(897\) 0.673787 0.0224971
\(898\) 1.99821 0.0666813
\(899\) −26.3548 −0.878983
\(900\) 2.59226 0.0864088
\(901\) −10.2366 −0.341031
\(902\) 0.0722758 0.00240652
\(903\) −16.1113 −0.536151
\(904\) 2.69271 0.0895581
\(905\) −29.8034 −0.990700
\(906\) 1.66642 0.0553630
\(907\) −22.6739 −0.752874 −0.376437 0.926442i \(-0.622851\pi\)
−0.376437 + 0.926442i \(0.622851\pi\)
\(908\) −27.7613 −0.921292
\(909\) 15.2639 0.506272
\(910\) 1.05109 0.0348432
\(911\) −44.4725 −1.47344 −0.736720 0.676198i \(-0.763626\pi\)
−0.736720 + 0.676198i \(0.763626\pi\)
\(912\) −29.6029 −0.980251
\(913\) −4.47487 −0.148096
\(914\) −0.0819548 −0.00271082
\(915\) 18.9663 0.627008
\(916\) 34.0709 1.12574
\(917\) 2.15170 0.0710556
\(918\) −0.0717307 −0.00236747
\(919\) 29.4689 0.972088 0.486044 0.873934i \(-0.338439\pi\)
0.486044 + 0.873934i \(0.338439\pi\)
\(920\) 0.189900 0.00626082
\(921\) 9.65818 0.318248
\(922\) −1.14412 −0.0376797
\(923\) −24.1646 −0.795386
\(924\) 2.56636 0.0844270
\(925\) 0.869909 0.0286024
\(926\) 0.554827 0.0182328
\(927\) 4.93728 0.162161
\(928\) 3.42349 0.112381
\(929\) 17.6254 0.578269 0.289135 0.957288i \(-0.406632\pi\)
0.289135 + 0.957288i \(0.406632\pi\)
\(930\) −0.911221 −0.0298801
\(931\) 60.9208 1.99660
\(932\) −27.0016 −0.884468
\(933\) −27.6205 −0.904255
\(934\) 2.21195 0.0723772
\(935\) 0.635433 0.0207809
\(936\) 0.560455 0.0183190
\(937\) 52.1125 1.70244 0.851221 0.524808i \(-0.175863\pi\)
0.851221 + 0.524808i \(0.175863\pi\)
\(938\) 1.96326 0.0641029
\(939\) 1.18468 0.0386607
\(940\) 12.8787 0.420056
\(941\) −51.3286 −1.67327 −0.836633 0.547764i \(-0.815479\pi\)
−0.836633 + 0.547764i \(0.815479\pi\)
\(942\) −0.137312 −0.00447387
\(943\) 1.05084 0.0342201
\(944\) −56.8931 −1.85171
\(945\) 7.49203 0.243716
\(946\) −0.0980180 −0.00318684
\(947\) 2.43683 0.0791863 0.0395932 0.999216i \(-0.487394\pi\)
0.0395932 + 0.999216i \(0.487394\pi\)
\(948\) 1.99485 0.0647899
\(949\) −27.0168 −0.877001
\(950\) 0.695200 0.0225553
\(951\) −4.56237 −0.147945
\(952\) −1.11602 −0.0361706
\(953\) 31.1967 1.01056 0.505280 0.862955i \(-0.331389\pi\)
0.505280 + 0.862955i \(0.331389\pi\)
\(954\) −0.734279 −0.0237732
\(955\) −28.8168 −0.932489
\(956\) −6.17832 −0.199821
\(957\) 1.31829 0.0426143
\(958\) −2.58539 −0.0835302
\(959\) 27.1230 0.875848
\(960\) −15.1524 −0.489040
\(961\) 12.6088 0.406734
\(962\) 0.0939173 0.00302801
\(963\) −4.27760 −0.137844
\(964\) 25.3220 0.815568
\(965\) −14.7547 −0.474970
\(966\) −0.0962411 −0.00309651
\(967\) 24.4261 0.785490 0.392745 0.919647i \(-0.371525\pi\)
0.392745 + 0.919647i \(0.371525\pi\)
\(968\) −3.12082 −0.100307
\(969\) 7.45825 0.239593
\(970\) −1.10596 −0.0355101
\(971\) 24.6118 0.789830 0.394915 0.918718i \(-0.370774\pi\)
0.394915 + 0.918718i \(0.370774\pi\)
\(972\) 1.99485 0.0639850
\(973\) −16.3009 −0.522583
\(974\) 2.32638 0.0745420
\(975\) 2.54157 0.0813955
\(976\) 39.1336 1.25264
\(977\) 11.7712 0.376595 0.188297 0.982112i \(-0.439703\pi\)
0.188297 + 0.982112i \(0.439703\pi\)
\(978\) −0.580547 −0.0185638
\(979\) 4.92408 0.157374
\(980\) 31.3453 1.00129
\(981\) 16.6053 0.530165
\(982\) −2.63857 −0.0842001
\(983\) −31.2321 −0.996150 −0.498075 0.867134i \(-0.665960\pi\)
−0.498075 + 0.867134i \(0.665960\pi\)
\(984\) 0.874089 0.0278649
\(985\) −34.2495 −1.09128
\(986\) −0.286272 −0.00911675
\(987\) −13.0706 −0.416042
\(988\) −29.0993 −0.925773
\(989\) −1.42512 −0.0453161
\(990\) 0.0455800 0.00144863
\(991\) 28.0232 0.890187 0.445093 0.895484i \(-0.353171\pi\)
0.445093 + 0.895484i \(0.353171\pi\)
\(992\) −5.66476 −0.179856
\(993\) 14.5436 0.461528
\(994\) 3.45157 0.109477
\(995\) −11.0603 −0.350634
\(996\) −27.0242 −0.856295
\(997\) 42.3951 1.34267 0.671334 0.741155i \(-0.265722\pi\)
0.671334 + 0.741155i \(0.265722\pi\)
\(998\) −2.29931 −0.0727833
\(999\) 0.669431 0.0211798
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.l.1.17 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.l.1.17 32 1.1 even 1 trivial