Properties

Label 4730.2.a.z.1.5
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.274153\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.725847 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.725847 q^{6} -1.66243 q^{7} -1.00000 q^{8} -2.47315 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.725847 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.725847 q^{6} -1.66243 q^{7} -1.00000 q^{8} -2.47315 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.725847 q^{12} -1.34536 q^{13} +1.66243 q^{14} +0.725847 q^{15} +1.00000 q^{16} -5.15562 q^{17} +2.47315 q^{18} +1.16391 q^{19} +1.00000 q^{20} -1.20667 q^{21} -1.00000 q^{22} +7.78857 q^{23} -0.725847 q^{24} +1.00000 q^{25} +1.34536 q^{26} -3.97267 q^{27} -1.66243 q^{28} +6.41615 q^{29} -0.725847 q^{30} -8.67865 q^{31} -1.00000 q^{32} +0.725847 q^{33} +5.15562 q^{34} -1.66243 q^{35} -2.47315 q^{36} +10.9749 q^{37} -1.16391 q^{38} -0.976529 q^{39} -1.00000 q^{40} -5.51287 q^{41} +1.20667 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.47315 q^{45} -7.78857 q^{46} -2.09570 q^{47} +0.725847 q^{48} -4.23633 q^{49} -1.00000 q^{50} -3.74219 q^{51} -1.34536 q^{52} +1.29522 q^{53} +3.97267 q^{54} +1.00000 q^{55} +1.66243 q^{56} +0.844819 q^{57} -6.41615 q^{58} +10.9331 q^{59} +0.725847 q^{60} +1.69522 q^{61} +8.67865 q^{62} +4.11143 q^{63} +1.00000 q^{64} -1.34536 q^{65} -0.725847 q^{66} +0.749628 q^{67} -5.15562 q^{68} +5.65331 q^{69} +1.66243 q^{70} -5.56121 q^{71} +2.47315 q^{72} +4.89194 q^{73} -10.9749 q^{74} +0.725847 q^{75} +1.16391 q^{76} -1.66243 q^{77} +0.976529 q^{78} -0.771969 q^{79} +1.00000 q^{80} +4.53588 q^{81} +5.51287 q^{82} -4.41661 q^{83} -1.20667 q^{84} -5.15562 q^{85} -1.00000 q^{86} +4.65714 q^{87} -1.00000 q^{88} +7.92294 q^{89} +2.47315 q^{90} +2.23657 q^{91} +7.78857 q^{92} -6.29938 q^{93} +2.09570 q^{94} +1.16391 q^{95} -0.725847 q^{96} +5.76777 q^{97} +4.23633 q^{98} -2.47315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 8q^{3} + 10q^{4} + 10q^{5} - 8q^{6} + 3q^{7} - 10q^{8} + 14q^{9} - 10q^{10} + 10q^{11} + 8q^{12} + 7q^{13} - 3q^{14} + 8q^{15} + 10q^{16} + 2q^{17} - 14q^{18} - 7q^{19} + 10q^{20} - 2q^{21} - 10q^{22} + 12q^{23} - 8q^{24} + 10q^{25} - 7q^{26} + 23q^{27} + 3q^{28} - 12q^{29} - 8q^{30} + 16q^{31} - 10q^{32} + 8q^{33} - 2q^{34} + 3q^{35} + 14q^{36} + 19q^{37} + 7q^{38} + 6q^{39} - 10q^{40} + 9q^{41} + 2q^{42} + 10q^{43} + 10q^{44} + 14q^{45} - 12q^{46} + 29q^{47} + 8q^{48} + 23q^{49} - 10q^{50} - 7q^{51} + 7q^{52} + 6q^{53} - 23q^{54} + 10q^{55} - 3q^{56} + 23q^{57} + 12q^{58} + 29q^{59} + 8q^{60} - 4q^{61} - 16q^{62} + 10q^{64} + 7q^{65} - 8q^{66} + 45q^{67} + 2q^{68} + 24q^{69} - 3q^{70} - 18q^{71} - 14q^{72} + 3q^{73} - 19q^{74} + 8q^{75} - 7q^{76} + 3q^{77} - 6q^{78} - 14q^{79} + 10q^{80} + 6q^{81} - 9q^{82} + 23q^{83} - 2q^{84} + 2q^{85} - 10q^{86} + 25q^{87} - 10q^{88} + q^{89} - 14q^{90} + q^{91} + 12q^{92} + 35q^{93} - 29q^{94} - 7q^{95} - 8q^{96} + 30q^{97} - 23q^{98} + 14q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.725847 0.419068 0.209534 0.977801i \(-0.432805\pi\)
0.209534 + 0.977801i \(0.432805\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −0.725847 −0.296326
\(7\) −1.66243 −0.628339 −0.314169 0.949367i \(-0.601726\pi\)
−0.314169 + 0.949367i \(0.601726\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.47315 −0.824382
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 0.725847 0.209534
\(13\) −1.34536 −0.373137 −0.186568 0.982442i \(-0.559737\pi\)
−0.186568 + 0.982442i \(0.559737\pi\)
\(14\) 1.66243 0.444303
\(15\) 0.725847 0.187413
\(16\) 1.00000 0.250000
\(17\) −5.15562 −1.25042 −0.625211 0.780456i \(-0.714987\pi\)
−0.625211 + 0.780456i \(0.714987\pi\)
\(18\) 2.47315 0.582926
\(19\) 1.16391 0.267019 0.133509 0.991048i \(-0.457375\pi\)
0.133509 + 0.991048i \(0.457375\pi\)
\(20\) 1.00000 0.223607
\(21\) −1.20667 −0.263317
\(22\) −1.00000 −0.213201
\(23\) 7.78857 1.62403 0.812015 0.583637i \(-0.198371\pi\)
0.812015 + 0.583637i \(0.198371\pi\)
\(24\) −0.725847 −0.148163
\(25\) 1.00000 0.200000
\(26\) 1.34536 0.263848
\(27\) −3.97267 −0.764540
\(28\) −1.66243 −0.314169
\(29\) 6.41615 1.19145 0.595724 0.803189i \(-0.296865\pi\)
0.595724 + 0.803189i \(0.296865\pi\)
\(30\) −0.725847 −0.132521
\(31\) −8.67865 −1.55873 −0.779366 0.626569i \(-0.784459\pi\)
−0.779366 + 0.626569i \(0.784459\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.725847 0.126354
\(34\) 5.15562 0.884182
\(35\) −1.66243 −0.281002
\(36\) −2.47315 −0.412191
\(37\) 10.9749 1.80425 0.902127 0.431470i \(-0.142005\pi\)
0.902127 + 0.431470i \(0.142005\pi\)
\(38\) −1.16391 −0.188811
\(39\) −0.976529 −0.156370
\(40\) −1.00000 −0.158114
\(41\) −5.51287 −0.860966 −0.430483 0.902599i \(-0.641657\pi\)
−0.430483 + 0.902599i \(0.641657\pi\)
\(42\) 1.20667 0.186193
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) −2.47315 −0.368675
\(46\) −7.78857 −1.14836
\(47\) −2.09570 −0.305689 −0.152845 0.988250i \(-0.548843\pi\)
−0.152845 + 0.988250i \(0.548843\pi\)
\(48\) 0.725847 0.104767
\(49\) −4.23633 −0.605190
\(50\) −1.00000 −0.141421
\(51\) −3.74219 −0.524012
\(52\) −1.34536 −0.186568
\(53\) 1.29522 0.177912 0.0889561 0.996036i \(-0.471647\pi\)
0.0889561 + 0.996036i \(0.471647\pi\)
\(54\) 3.97267 0.540612
\(55\) 1.00000 0.134840
\(56\) 1.66243 0.222151
\(57\) 0.844819 0.111899
\(58\) −6.41615 −0.842481
\(59\) 10.9331 1.42337 0.711683 0.702500i \(-0.247933\pi\)
0.711683 + 0.702500i \(0.247933\pi\)
\(60\) 0.725847 0.0937065
\(61\) 1.69522 0.217050 0.108525 0.994094i \(-0.465387\pi\)
0.108525 + 0.994094i \(0.465387\pi\)
\(62\) 8.67865 1.10219
\(63\) 4.11143 0.517991
\(64\) 1.00000 0.125000
\(65\) −1.34536 −0.166872
\(66\) −0.725847 −0.0893456
\(67\) 0.749628 0.0915817 0.0457908 0.998951i \(-0.485419\pi\)
0.0457908 + 0.998951i \(0.485419\pi\)
\(68\) −5.15562 −0.625211
\(69\) 5.65331 0.680579
\(70\) 1.66243 0.198698
\(71\) −5.56121 −0.659995 −0.329997 0.943982i \(-0.607048\pi\)
−0.329997 + 0.943982i \(0.607048\pi\)
\(72\) 2.47315 0.291463
\(73\) 4.89194 0.572558 0.286279 0.958146i \(-0.407582\pi\)
0.286279 + 0.958146i \(0.407582\pi\)
\(74\) −10.9749 −1.27580
\(75\) 0.725847 0.0838136
\(76\) 1.16391 0.133509
\(77\) −1.66243 −0.189451
\(78\) 0.976529 0.110570
\(79\) −0.771969 −0.0868533 −0.0434266 0.999057i \(-0.513827\pi\)
−0.0434266 + 0.999057i \(0.513827\pi\)
\(80\) 1.00000 0.111803
\(81\) 4.53588 0.503987
\(82\) 5.51287 0.608795
\(83\) −4.41661 −0.484786 −0.242393 0.970178i \(-0.577932\pi\)
−0.242393 + 0.970178i \(0.577932\pi\)
\(84\) −1.20667 −0.131658
\(85\) −5.15562 −0.559206
\(86\) −1.00000 −0.107833
\(87\) 4.65714 0.499298
\(88\) −1.00000 −0.106600
\(89\) 7.92294 0.839830 0.419915 0.907563i \(-0.362060\pi\)
0.419915 + 0.907563i \(0.362060\pi\)
\(90\) 2.47315 0.260692
\(91\) 2.23657 0.234456
\(92\) 7.78857 0.812015
\(93\) −6.29938 −0.653215
\(94\) 2.09570 0.216155
\(95\) 1.16391 0.119414
\(96\) −0.725847 −0.0740815
\(97\) 5.76777 0.585629 0.292814 0.956169i \(-0.405408\pi\)
0.292814 + 0.956169i \(0.405408\pi\)
\(98\) 4.23633 0.427934
\(99\) −2.47315 −0.248560
\(100\) 1.00000 0.100000
\(101\) 5.94038 0.591090 0.295545 0.955329i \(-0.404499\pi\)
0.295545 + 0.955329i \(0.404499\pi\)
\(102\) 3.74219 0.370532
\(103\) 17.5535 1.72960 0.864798 0.502121i \(-0.167447\pi\)
0.864798 + 0.502121i \(0.167447\pi\)
\(104\) 1.34536 0.131924
\(105\) −1.20667 −0.117759
\(106\) −1.29522 −0.125803
\(107\) 8.34703 0.806938 0.403469 0.914993i \(-0.367804\pi\)
0.403469 + 0.914993i \(0.367804\pi\)
\(108\) −3.97267 −0.382270
\(109\) −10.2458 −0.981370 −0.490685 0.871337i \(-0.663253\pi\)
−0.490685 + 0.871337i \(0.663253\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 7.96607 0.756106
\(112\) −1.66243 −0.157085
\(113\) 2.13157 0.200522 0.100261 0.994961i \(-0.468032\pi\)
0.100261 + 0.994961i \(0.468032\pi\)
\(114\) −0.844819 −0.0791246
\(115\) 7.78857 0.726288
\(116\) 6.41615 0.595724
\(117\) 3.32728 0.307607
\(118\) −10.9331 −1.00647
\(119\) 8.57085 0.785689
\(120\) −0.725847 −0.0662605
\(121\) 1.00000 0.0909091
\(122\) −1.69522 −0.153478
\(123\) −4.00151 −0.360804
\(124\) −8.67865 −0.779366
\(125\) 1.00000 0.0894427
\(126\) −4.11143 −0.366275
\(127\) 15.5025 1.37562 0.687811 0.725890i \(-0.258572\pi\)
0.687811 + 0.725890i \(0.258572\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.725847 0.0639073
\(130\) 1.34536 0.117996
\(131\) −3.60750 −0.315189 −0.157594 0.987504i \(-0.550374\pi\)
−0.157594 + 0.987504i \(0.550374\pi\)
\(132\) 0.725847 0.0631769
\(133\) −1.93491 −0.167778
\(134\) −0.749628 −0.0647580
\(135\) −3.97267 −0.341913
\(136\) 5.15562 0.442091
\(137\) 19.4879 1.66497 0.832483 0.554050i \(-0.186918\pi\)
0.832483 + 0.554050i \(0.186918\pi\)
\(138\) −5.65331 −0.481242
\(139\) −8.10352 −0.687332 −0.343666 0.939092i \(-0.611669\pi\)
−0.343666 + 0.939092i \(0.611669\pi\)
\(140\) −1.66243 −0.140501
\(141\) −1.52116 −0.128105
\(142\) 5.56121 0.466687
\(143\) −1.34536 −0.112505
\(144\) −2.47315 −0.206095
\(145\) 6.41615 0.532832
\(146\) −4.89194 −0.404860
\(147\) −3.07493 −0.253616
\(148\) 10.9749 0.902127
\(149\) 17.2181 1.41056 0.705280 0.708928i \(-0.250821\pi\)
0.705280 + 0.708928i \(0.250821\pi\)
\(150\) −0.725847 −0.0592652
\(151\) 3.10714 0.252856 0.126428 0.991976i \(-0.459649\pi\)
0.126428 + 0.991976i \(0.459649\pi\)
\(152\) −1.16391 −0.0944053
\(153\) 12.7506 1.03082
\(154\) 1.66243 0.133962
\(155\) −8.67865 −0.697086
\(156\) −0.976529 −0.0781849
\(157\) 13.7020 1.09354 0.546770 0.837283i \(-0.315857\pi\)
0.546770 + 0.837283i \(0.315857\pi\)
\(158\) 0.771969 0.0614145
\(159\) 0.940133 0.0745574
\(160\) −1.00000 −0.0790569
\(161\) −12.9479 −1.02044
\(162\) −4.53588 −0.356373
\(163\) −8.87274 −0.694966 −0.347483 0.937686i \(-0.612964\pi\)
−0.347483 + 0.937686i \(0.612964\pi\)
\(164\) −5.51287 −0.430483
\(165\) 0.725847 0.0565071
\(166\) 4.41661 0.342795
\(167\) −2.46104 −0.190441 −0.0952205 0.995456i \(-0.530356\pi\)
−0.0952205 + 0.995456i \(0.530356\pi\)
\(168\) 1.20667 0.0930966
\(169\) −11.1900 −0.860769
\(170\) 5.15562 0.395418
\(171\) −2.87851 −0.220125
\(172\) 1.00000 0.0762493
\(173\) −12.8786 −0.979142 −0.489571 0.871963i \(-0.662847\pi\)
−0.489571 + 0.871963i \(0.662847\pi\)
\(174\) −4.65714 −0.353057
\(175\) −1.66243 −0.125668
\(176\) 1.00000 0.0753778
\(177\) 7.93575 0.596488
\(178\) −7.92294 −0.593849
\(179\) −2.89487 −0.216373 −0.108186 0.994131i \(-0.534504\pi\)
−0.108186 + 0.994131i \(0.534504\pi\)
\(180\) −2.47315 −0.184337
\(181\) −8.53765 −0.634599 −0.317299 0.948325i \(-0.602776\pi\)
−0.317299 + 0.948325i \(0.602776\pi\)
\(182\) −2.23657 −0.165786
\(183\) 1.23047 0.0909589
\(184\) −7.78857 −0.574181
\(185\) 10.9749 0.806887
\(186\) 6.29938 0.461893
\(187\) −5.15562 −0.377016
\(188\) −2.09570 −0.152845
\(189\) 6.60428 0.480391
\(190\) −1.16391 −0.0844387
\(191\) 9.45261 0.683967 0.341983 0.939706i \(-0.388901\pi\)
0.341983 + 0.939706i \(0.388901\pi\)
\(192\) 0.725847 0.0523835
\(193\) 15.2682 1.09903 0.549516 0.835483i \(-0.314812\pi\)
0.549516 + 0.835483i \(0.314812\pi\)
\(194\) −5.76777 −0.414102
\(195\) −0.976529 −0.0699307
\(196\) −4.23633 −0.302595
\(197\) 20.0157 1.42606 0.713031 0.701133i \(-0.247322\pi\)
0.713031 + 0.701133i \(0.247322\pi\)
\(198\) 2.47315 0.175759
\(199\) 5.22459 0.370361 0.185181 0.982705i \(-0.440713\pi\)
0.185181 + 0.982705i \(0.440713\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0.544116 0.0383790
\(202\) −5.94038 −0.417964
\(203\) −10.6664 −0.748633
\(204\) −3.74219 −0.262006
\(205\) −5.51287 −0.385036
\(206\) −17.5535 −1.22301
\(207\) −19.2623 −1.33882
\(208\) −1.34536 −0.0932842
\(209\) 1.16391 0.0805091
\(210\) 1.20667 0.0832681
\(211\) 9.53438 0.656373 0.328187 0.944613i \(-0.393562\pi\)
0.328187 + 0.944613i \(0.393562\pi\)
\(212\) 1.29522 0.0889561
\(213\) −4.03659 −0.276583
\(214\) −8.34703 −0.570591
\(215\) 1.00000 0.0681994
\(216\) 3.97267 0.270306
\(217\) 14.4276 0.979412
\(218\) 10.2458 0.693933
\(219\) 3.55080 0.239941
\(220\) 1.00000 0.0674200
\(221\) 6.93618 0.466578
\(222\) −7.96607 −0.534648
\(223\) 23.8079 1.59430 0.797148 0.603784i \(-0.206341\pi\)
0.797148 + 0.603784i \(0.206341\pi\)
\(224\) 1.66243 0.111076
\(225\) −2.47315 −0.164876
\(226\) −2.13157 −0.141790
\(227\) −13.3943 −0.889009 −0.444505 0.895777i \(-0.646620\pi\)
−0.444505 + 0.895777i \(0.646620\pi\)
\(228\) 0.844819 0.0559495
\(229\) 22.9682 1.51778 0.758889 0.651220i \(-0.225742\pi\)
0.758889 + 0.651220i \(0.225742\pi\)
\(230\) −7.78857 −0.513563
\(231\) −1.20667 −0.0793930
\(232\) −6.41615 −0.421241
\(233\) 1.93058 0.126477 0.0632384 0.997998i \(-0.479857\pi\)
0.0632384 + 0.997998i \(0.479857\pi\)
\(234\) −3.32728 −0.217511
\(235\) −2.09570 −0.136708
\(236\) 10.9331 0.711683
\(237\) −0.560332 −0.0363974
\(238\) −8.57085 −0.555566
\(239\) 11.3596 0.734792 0.367396 0.930065i \(-0.380249\pi\)
0.367396 + 0.930065i \(0.380249\pi\)
\(240\) 0.725847 0.0468533
\(241\) 6.66307 0.429206 0.214603 0.976701i \(-0.431154\pi\)
0.214603 + 0.976701i \(0.431154\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 15.2104 0.975745
\(244\) 1.69522 0.108525
\(245\) −4.23633 −0.270649
\(246\) 4.00151 0.255127
\(247\) −1.56588 −0.0996345
\(248\) 8.67865 0.551095
\(249\) −3.20578 −0.203158
\(250\) −1.00000 −0.0632456
\(251\) 11.1773 0.705506 0.352753 0.935716i \(-0.385246\pi\)
0.352753 + 0.935716i \(0.385246\pi\)
\(252\) 4.11143 0.258996
\(253\) 7.78857 0.489663
\(254\) −15.5025 −0.972711
\(255\) −3.74219 −0.234345
\(256\) 1.00000 0.0625000
\(257\) −3.34928 −0.208922 −0.104461 0.994529i \(-0.533312\pi\)
−0.104461 + 0.994529i \(0.533312\pi\)
\(258\) −0.725847 −0.0451893
\(259\) −18.2449 −1.13368
\(260\) −1.34536 −0.0834359
\(261\) −15.8681 −0.982208
\(262\) 3.60750 0.222872
\(263\) −9.84688 −0.607185 −0.303592 0.952802i \(-0.598186\pi\)
−0.303592 + 0.952802i \(0.598186\pi\)
\(264\) −0.725847 −0.0446728
\(265\) 1.29522 0.0795648
\(266\) 1.93491 0.118637
\(267\) 5.75085 0.351946
\(268\) 0.749628 0.0457908
\(269\) −9.33731 −0.569306 −0.284653 0.958631i \(-0.591878\pi\)
−0.284653 + 0.958631i \(0.591878\pi\)
\(270\) 3.97267 0.241769
\(271\) −1.10267 −0.0669822 −0.0334911 0.999439i \(-0.510663\pi\)
−0.0334911 + 0.999439i \(0.510663\pi\)
\(272\) −5.15562 −0.312605
\(273\) 1.62341 0.0982532
\(274\) −19.4879 −1.17731
\(275\) 1.00000 0.0603023
\(276\) 5.65331 0.340290
\(277\) −12.3953 −0.744759 −0.372379 0.928081i \(-0.621458\pi\)
−0.372379 + 0.928081i \(0.621458\pi\)
\(278\) 8.10352 0.486017
\(279\) 21.4636 1.28499
\(280\) 1.66243 0.0993491
\(281\) −20.6616 −1.23257 −0.616283 0.787525i \(-0.711362\pi\)
−0.616283 + 0.787525i \(0.711362\pi\)
\(282\) 1.52116 0.0905837
\(283\) −24.0191 −1.42779 −0.713894 0.700254i \(-0.753070\pi\)
−0.713894 + 0.700254i \(0.753070\pi\)
\(284\) −5.56121 −0.329997
\(285\) 0.844819 0.0500428
\(286\) 1.34536 0.0795530
\(287\) 9.16476 0.540979
\(288\) 2.47315 0.145731
\(289\) 9.58043 0.563554
\(290\) −6.41615 −0.376769
\(291\) 4.18652 0.245418
\(292\) 4.89194 0.286279
\(293\) −27.3252 −1.59635 −0.798177 0.602423i \(-0.794202\pi\)
−0.798177 + 0.602423i \(0.794202\pi\)
\(294\) 3.07493 0.179334
\(295\) 10.9331 0.636549
\(296\) −10.9749 −0.637900
\(297\) −3.97267 −0.230518
\(298\) −17.2181 −0.997417
\(299\) −10.4785 −0.605985
\(300\) 0.725847 0.0419068
\(301\) −1.66243 −0.0958208
\(302\) −3.10714 −0.178796
\(303\) 4.31181 0.247707
\(304\) 1.16391 0.0667547
\(305\) 1.69522 0.0970679
\(306\) −12.7506 −0.728903
\(307\) −33.9716 −1.93886 −0.969431 0.245363i \(-0.921093\pi\)
−0.969431 + 0.245363i \(0.921093\pi\)
\(308\) −1.66243 −0.0947257
\(309\) 12.7411 0.724818
\(310\) 8.67865 0.492914
\(311\) −22.9168 −1.29949 −0.649746 0.760152i \(-0.725125\pi\)
−0.649746 + 0.760152i \(0.725125\pi\)
\(312\) 0.976529 0.0552851
\(313\) 23.0154 1.30091 0.650455 0.759545i \(-0.274578\pi\)
0.650455 + 0.759545i \(0.274578\pi\)
\(314\) −13.7020 −0.773249
\(315\) 4.11143 0.231653
\(316\) −0.771969 −0.0434266
\(317\) 2.65370 0.149047 0.0745233 0.997219i \(-0.476256\pi\)
0.0745233 + 0.997219i \(0.476256\pi\)
\(318\) −0.940133 −0.0527200
\(319\) 6.41615 0.359235
\(320\) 1.00000 0.0559017
\(321\) 6.05867 0.338162
\(322\) 12.9479 0.721561
\(323\) −6.00066 −0.333886
\(324\) 4.53588 0.251994
\(325\) −1.34536 −0.0746273
\(326\) 8.87274 0.491415
\(327\) −7.43689 −0.411261
\(328\) 5.51287 0.304398
\(329\) 3.48395 0.192077
\(330\) −0.725847 −0.0399566
\(331\) 16.8334 0.925245 0.462623 0.886555i \(-0.346909\pi\)
0.462623 + 0.886555i \(0.346909\pi\)
\(332\) −4.41661 −0.242393
\(333\) −27.1424 −1.48739
\(334\) 2.46104 0.134662
\(335\) 0.749628 0.0409566
\(336\) −1.20667 −0.0658292
\(337\) −12.0727 −0.657643 −0.328821 0.944392i \(-0.606651\pi\)
−0.328821 + 0.944392i \(0.606651\pi\)
\(338\) 11.1900 0.608656
\(339\) 1.54720 0.0840322
\(340\) −5.15562 −0.279603
\(341\) −8.67865 −0.469975
\(342\) 2.87851 0.155652
\(343\) 18.6796 1.00860
\(344\) −1.00000 −0.0539164
\(345\) 5.65331 0.304364
\(346\) 12.8786 0.692358
\(347\) 27.1039 1.45501 0.727507 0.686100i \(-0.240679\pi\)
0.727507 + 0.686100i \(0.240679\pi\)
\(348\) 4.65714 0.249649
\(349\) −2.80970 −0.150400 −0.0751999 0.997168i \(-0.523959\pi\)
−0.0751999 + 0.997168i \(0.523959\pi\)
\(350\) 1.66243 0.0888605
\(351\) 5.34468 0.285278
\(352\) −1.00000 −0.0533002
\(353\) −26.9343 −1.43357 −0.716783 0.697296i \(-0.754386\pi\)
−0.716783 + 0.697296i \(0.754386\pi\)
\(354\) −7.93575 −0.421781
\(355\) −5.56121 −0.295159
\(356\) 7.92294 0.419915
\(357\) 6.22113 0.329257
\(358\) 2.89487 0.152999
\(359\) 28.0499 1.48042 0.740209 0.672377i \(-0.234727\pi\)
0.740209 + 0.672377i \(0.234727\pi\)
\(360\) 2.47315 0.130346
\(361\) −17.6453 −0.928701
\(362\) 8.53765 0.448729
\(363\) 0.725847 0.0380971
\(364\) 2.23657 0.117228
\(365\) 4.89194 0.256056
\(366\) −1.23047 −0.0643177
\(367\) 22.3766 1.16805 0.584026 0.811735i \(-0.301477\pi\)
0.584026 + 0.811735i \(0.301477\pi\)
\(368\) 7.78857 0.406007
\(369\) 13.6341 0.709765
\(370\) −10.9749 −0.570555
\(371\) −2.15321 −0.111789
\(372\) −6.29938 −0.326607
\(373\) 33.5261 1.73591 0.867957 0.496640i \(-0.165433\pi\)
0.867957 + 0.496640i \(0.165433\pi\)
\(374\) 5.15562 0.266591
\(375\) 0.725847 0.0374826
\(376\) 2.09570 0.108078
\(377\) −8.63205 −0.444573
\(378\) −6.60428 −0.339687
\(379\) 14.3694 0.738108 0.369054 0.929408i \(-0.379682\pi\)
0.369054 + 0.929408i \(0.379682\pi\)
\(380\) 1.16391 0.0597072
\(381\) 11.2524 0.576479
\(382\) −9.45261 −0.483637
\(383\) 22.7826 1.16414 0.582069 0.813139i \(-0.302243\pi\)
0.582069 + 0.813139i \(0.302243\pi\)
\(384\) −0.725847 −0.0370407
\(385\) −1.66243 −0.0847252
\(386\) −15.2682 −0.777133
\(387\) −2.47315 −0.125717
\(388\) 5.76777 0.292814
\(389\) −39.0446 −1.97964 −0.989820 0.142327i \(-0.954541\pi\)
−0.989820 + 0.142327i \(0.954541\pi\)
\(390\) 0.976529 0.0494485
\(391\) −40.1549 −2.03072
\(392\) 4.23633 0.213967
\(393\) −2.61849 −0.132086
\(394\) −20.0157 −1.00838
\(395\) −0.771969 −0.0388420
\(396\) −2.47315 −0.124280
\(397\) −3.27182 −0.164208 −0.0821040 0.996624i \(-0.526164\pi\)
−0.0821040 + 0.996624i \(0.526164\pi\)
\(398\) −5.22459 −0.261885
\(399\) −1.40445 −0.0703105
\(400\) 1.00000 0.0500000
\(401\) 5.78768 0.289023 0.144512 0.989503i \(-0.453839\pi\)
0.144512 + 0.989503i \(0.453839\pi\)
\(402\) −0.544116 −0.0271380
\(403\) 11.6759 0.581620
\(404\) 5.94038 0.295545
\(405\) 4.53588 0.225390
\(406\) 10.6664 0.529364
\(407\) 10.9749 0.544003
\(408\) 3.74219 0.185266
\(409\) −6.24178 −0.308636 −0.154318 0.988021i \(-0.549318\pi\)
−0.154318 + 0.988021i \(0.549318\pi\)
\(410\) 5.51287 0.272261
\(411\) 14.1453 0.697735
\(412\) 17.5535 0.864798
\(413\) −18.1755 −0.894357
\(414\) 19.2623 0.946689
\(415\) −4.41661 −0.216803
\(416\) 1.34536 0.0659619
\(417\) −5.88192 −0.288039
\(418\) −1.16391 −0.0569286
\(419\) 18.2981 0.893923 0.446961 0.894553i \(-0.352506\pi\)
0.446961 + 0.894553i \(0.352506\pi\)
\(420\) −1.20667 −0.0588794
\(421\) 38.5499 1.87881 0.939403 0.342814i \(-0.111380\pi\)
0.939403 + 0.342814i \(0.111380\pi\)
\(422\) −9.53438 −0.464126
\(423\) 5.18297 0.252005
\(424\) −1.29522 −0.0629015
\(425\) −5.15562 −0.250084
\(426\) 4.03659 0.195574
\(427\) −2.81818 −0.136381
\(428\) 8.34703 0.403469
\(429\) −0.976529 −0.0471473
\(430\) −1.00000 −0.0482243
\(431\) −20.3620 −0.980801 −0.490401 0.871497i \(-0.663150\pi\)
−0.490401 + 0.871497i \(0.663150\pi\)
\(432\) −3.97267 −0.191135
\(433\) −20.1175 −0.966786 −0.483393 0.875404i \(-0.660596\pi\)
−0.483393 + 0.875404i \(0.660596\pi\)
\(434\) −14.4276 −0.692549
\(435\) 4.65714 0.223293
\(436\) −10.2458 −0.490685
\(437\) 9.06517 0.433646
\(438\) −3.55080 −0.169664
\(439\) 14.2368 0.679486 0.339743 0.940518i \(-0.389660\pi\)
0.339743 + 0.940518i \(0.389660\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 10.4771 0.498908
\(442\) −6.93618 −0.329921
\(443\) −14.6856 −0.697735 −0.348867 0.937172i \(-0.613434\pi\)
−0.348867 + 0.937172i \(0.613434\pi\)
\(444\) 7.96607 0.378053
\(445\) 7.92294 0.375583
\(446\) −23.8079 −1.12734
\(447\) 12.4977 0.591121
\(448\) −1.66243 −0.0785424
\(449\) −3.04963 −0.143921 −0.0719605 0.997407i \(-0.522926\pi\)
−0.0719605 + 0.997407i \(0.522926\pi\)
\(450\) 2.47315 0.116585
\(451\) −5.51287 −0.259591
\(452\) 2.13157 0.100261
\(453\) 2.25531 0.105964
\(454\) 13.3943 0.628625
\(455\) 2.23657 0.104852
\(456\) −0.844819 −0.0395623
\(457\) 36.9106 1.72660 0.863301 0.504689i \(-0.168393\pi\)
0.863301 + 0.504689i \(0.168393\pi\)
\(458\) −22.9682 −1.07323
\(459\) 20.4816 0.955998
\(460\) 7.78857 0.363144
\(461\) −14.3831 −0.669889 −0.334945 0.942238i \(-0.608718\pi\)
−0.334945 + 0.942238i \(0.608718\pi\)
\(462\) 1.20667 0.0561393
\(463\) 24.6421 1.14522 0.572608 0.819829i \(-0.305932\pi\)
0.572608 + 0.819829i \(0.305932\pi\)
\(464\) 6.41615 0.297862
\(465\) −6.29938 −0.292127
\(466\) −1.93058 −0.0894326
\(467\) −8.12080 −0.375786 −0.187893 0.982190i \(-0.560166\pi\)
−0.187893 + 0.982190i \(0.560166\pi\)
\(468\) 3.32728 0.153804
\(469\) −1.24620 −0.0575443
\(470\) 2.09570 0.0966675
\(471\) 9.94557 0.458268
\(472\) −10.9331 −0.503236
\(473\) 1.00000 0.0459800
\(474\) 0.560332 0.0257369
\(475\) 1.16391 0.0534037
\(476\) 8.57085 0.392844
\(477\) −3.20327 −0.146668
\(478\) −11.3596 −0.519576
\(479\) 3.51328 0.160526 0.0802630 0.996774i \(-0.474424\pi\)
0.0802630 + 0.996774i \(0.474424\pi\)
\(480\) −0.725847 −0.0331303
\(481\) −14.7652 −0.673234
\(482\) −6.66307 −0.303494
\(483\) −9.39823 −0.427634
\(484\) 1.00000 0.0454545
\(485\) 5.76777 0.261901
\(486\) −15.2104 −0.689956
\(487\) 9.21794 0.417705 0.208852 0.977947i \(-0.433027\pi\)
0.208852 + 0.977947i \(0.433027\pi\)
\(488\) −1.69522 −0.0767389
\(489\) −6.44025 −0.291238
\(490\) 4.23633 0.191378
\(491\) −13.3645 −0.603132 −0.301566 0.953445i \(-0.597509\pi\)
−0.301566 + 0.953445i \(0.597509\pi\)
\(492\) −4.00151 −0.180402
\(493\) −33.0792 −1.48981
\(494\) 1.56588 0.0704522
\(495\) −2.47315 −0.111160
\(496\) −8.67865 −0.389683
\(497\) 9.24512 0.414700
\(498\) 3.20578 0.143655
\(499\) −33.2106 −1.48671 −0.743356 0.668896i \(-0.766767\pi\)
−0.743356 + 0.668896i \(0.766767\pi\)
\(500\) 1.00000 0.0447214
\(501\) −1.78634 −0.0798077
\(502\) −11.1773 −0.498868
\(503\) −3.60819 −0.160881 −0.0804407 0.996759i \(-0.525633\pi\)
−0.0804407 + 0.996759i \(0.525633\pi\)
\(504\) −4.11143 −0.183138
\(505\) 5.94038 0.264344
\(506\) −7.78857 −0.346244
\(507\) −8.12223 −0.360721
\(508\) 15.5025 0.687811
\(509\) 20.0548 0.888912 0.444456 0.895801i \(-0.353397\pi\)
0.444456 + 0.895801i \(0.353397\pi\)
\(510\) 3.74219 0.165707
\(511\) −8.13250 −0.359761
\(512\) −1.00000 −0.0441942
\(513\) −4.62382 −0.204147
\(514\) 3.34928 0.147730
\(515\) 17.5535 0.773499
\(516\) 0.725847 0.0319537
\(517\) −2.09570 −0.0921688
\(518\) 18.2449 0.801635
\(519\) −9.34790 −0.410327
\(520\) 1.34536 0.0589981
\(521\) −39.2837 −1.72105 −0.860524 0.509409i \(-0.829864\pi\)
−0.860524 + 0.509409i \(0.829864\pi\)
\(522\) 15.8681 0.694526
\(523\) 25.5670 1.11797 0.558984 0.829179i \(-0.311191\pi\)
0.558984 + 0.829179i \(0.311191\pi\)
\(524\) −3.60750 −0.157594
\(525\) −1.20667 −0.0526634
\(526\) 9.84688 0.429344
\(527\) 44.7438 1.94907
\(528\) 0.725847 0.0315885
\(529\) 37.6618 1.63747
\(530\) −1.29522 −0.0562608
\(531\) −27.0391 −1.17340
\(532\) −1.93491 −0.0838891
\(533\) 7.41682 0.321258
\(534\) −5.75085 −0.248863
\(535\) 8.34703 0.360874
\(536\) −0.749628 −0.0323790
\(537\) −2.10123 −0.0906749
\(538\) 9.33731 0.402560
\(539\) −4.23633 −0.182472
\(540\) −3.97267 −0.170956
\(541\) 3.79034 0.162959 0.0814797 0.996675i \(-0.474035\pi\)
0.0814797 + 0.996675i \(0.474035\pi\)
\(542\) 1.10267 0.0473636
\(543\) −6.19703 −0.265940
\(544\) 5.15562 0.221045
\(545\) −10.2458 −0.438882
\(546\) −1.62341 −0.0694755
\(547\) 42.9493 1.83638 0.918189 0.396143i \(-0.129651\pi\)
0.918189 + 0.396143i \(0.129651\pi\)
\(548\) 19.4879 0.832483
\(549\) −4.19252 −0.178932
\(550\) −1.00000 −0.0426401
\(551\) 7.46780 0.318139
\(552\) −5.65331 −0.240621
\(553\) 1.28334 0.0545733
\(554\) 12.3953 0.526624
\(555\) 7.96607 0.338141
\(556\) −8.10352 −0.343666
\(557\) 22.3786 0.948212 0.474106 0.880468i \(-0.342771\pi\)
0.474106 + 0.880468i \(0.342771\pi\)
\(558\) −21.4636 −0.908625
\(559\) −1.34536 −0.0569028
\(560\) −1.66243 −0.0702504
\(561\) −3.74219 −0.157996
\(562\) 20.6616 0.871556
\(563\) 39.7265 1.67427 0.837136 0.546994i \(-0.184228\pi\)
0.837136 + 0.546994i \(0.184228\pi\)
\(564\) −1.52116 −0.0640523
\(565\) 2.13157 0.0896760
\(566\) 24.0191 1.00960
\(567\) −7.54058 −0.316675
\(568\) 5.56121 0.233343
\(569\) −17.3076 −0.725573 −0.362786 0.931872i \(-0.618175\pi\)
−0.362786 + 0.931872i \(0.618175\pi\)
\(570\) −0.844819 −0.0353856
\(571\) −14.7375 −0.616747 −0.308374 0.951265i \(-0.599785\pi\)
−0.308374 + 0.951265i \(0.599785\pi\)
\(572\) −1.34536 −0.0562525
\(573\) 6.86115 0.286629
\(574\) −9.16476 −0.382530
\(575\) 7.78857 0.324806
\(576\) −2.47315 −0.103048
\(577\) 14.8862 0.619719 0.309859 0.950782i \(-0.399718\pi\)
0.309859 + 0.950782i \(0.399718\pi\)
\(578\) −9.58043 −0.398493
\(579\) 11.0824 0.460570
\(580\) 6.41615 0.266416
\(581\) 7.34229 0.304610
\(582\) −4.18652 −0.173537
\(583\) 1.29522 0.0536426
\(584\) −4.89194 −0.202430
\(585\) 3.32728 0.137566
\(586\) 27.3252 1.12879
\(587\) 41.3213 1.70551 0.852756 0.522310i \(-0.174929\pi\)
0.852756 + 0.522310i \(0.174929\pi\)
\(588\) −3.07493 −0.126808
\(589\) −10.1011 −0.416210
\(590\) −10.9331 −0.450108
\(591\) 14.5284 0.597617
\(592\) 10.9749 0.451064
\(593\) −16.5084 −0.677918 −0.338959 0.940801i \(-0.610075\pi\)
−0.338959 + 0.940801i \(0.610075\pi\)
\(594\) 3.97267 0.163001
\(595\) 8.57085 0.351371
\(596\) 17.2181 0.705280
\(597\) 3.79225 0.155207
\(598\) 10.4785 0.428496
\(599\) 37.2132 1.52049 0.760245 0.649637i \(-0.225079\pi\)
0.760245 + 0.649637i \(0.225079\pi\)
\(600\) −0.725847 −0.0296326
\(601\) −7.05214 −0.287663 −0.143831 0.989602i \(-0.545942\pi\)
−0.143831 + 0.989602i \(0.545942\pi\)
\(602\) 1.66243 0.0677555
\(603\) −1.85394 −0.0754983
\(604\) 3.10714 0.126428
\(605\) 1.00000 0.0406558
\(606\) −4.31181 −0.175155
\(607\) −24.1400 −0.979814 −0.489907 0.871775i \(-0.662969\pi\)
−0.489907 + 0.871775i \(0.662969\pi\)
\(608\) −1.16391 −0.0472027
\(609\) −7.74217 −0.313728
\(610\) −1.69522 −0.0686374
\(611\) 2.81948 0.114064
\(612\) 12.7506 0.515412
\(613\) 5.92142 0.239164 0.119582 0.992824i \(-0.461845\pi\)
0.119582 + 0.992824i \(0.461845\pi\)
\(614\) 33.9716 1.37098
\(615\) −4.00151 −0.161356
\(616\) 1.66243 0.0669812
\(617\) 28.2835 1.13865 0.569325 0.822112i \(-0.307204\pi\)
0.569325 + 0.822112i \(0.307204\pi\)
\(618\) −12.7411 −0.512524
\(619\) 10.2965 0.413852 0.206926 0.978357i \(-0.433654\pi\)
0.206926 + 0.978357i \(0.433654\pi\)
\(620\) −8.67865 −0.348543
\(621\) −30.9414 −1.24164
\(622\) 22.9168 0.918879
\(623\) −13.1713 −0.527698
\(624\) −0.976529 −0.0390924
\(625\) 1.00000 0.0400000
\(626\) −23.0154 −0.919882
\(627\) 0.844819 0.0337388
\(628\) 13.7020 0.546770
\(629\) −56.5822 −2.25608
\(630\) −4.11143 −0.163803
\(631\) 11.9813 0.476970 0.238485 0.971146i \(-0.423349\pi\)
0.238485 + 0.971146i \(0.423349\pi\)
\(632\) 0.771969 0.0307073
\(633\) 6.92050 0.275065
\(634\) −2.65370 −0.105392
\(635\) 15.5025 0.615197
\(636\) 0.940133 0.0372787
\(637\) 5.69941 0.225819
\(638\) −6.41615 −0.254018
\(639\) 13.7537 0.544088
\(640\) −1.00000 −0.0395285
\(641\) −31.9150 −1.26057 −0.630284 0.776365i \(-0.717062\pi\)
−0.630284 + 0.776365i \(0.717062\pi\)
\(642\) −6.05867 −0.239117
\(643\) −27.5708 −1.08729 −0.543643 0.839317i \(-0.682955\pi\)
−0.543643 + 0.839317i \(0.682955\pi\)
\(644\) −12.9479 −0.510220
\(645\) 0.725847 0.0285802
\(646\) 6.00066 0.236093
\(647\) 16.4761 0.647743 0.323871 0.946101i \(-0.395015\pi\)
0.323871 + 0.946101i \(0.395015\pi\)
\(648\) −4.53588 −0.178186
\(649\) 10.9331 0.429161
\(650\) 1.34536 0.0527695
\(651\) 10.4723 0.410440
\(652\) −8.87274 −0.347483
\(653\) −17.3434 −0.678698 −0.339349 0.940661i \(-0.610207\pi\)
−0.339349 + 0.940661i \(0.610207\pi\)
\(654\) 7.43689 0.290805
\(655\) −3.60750 −0.140957
\(656\) −5.51287 −0.215242
\(657\) −12.0985 −0.472007
\(658\) −3.48395 −0.135819
\(659\) 31.9820 1.24584 0.622920 0.782286i \(-0.285946\pi\)
0.622920 + 0.782286i \(0.285946\pi\)
\(660\) 0.725847 0.0282536
\(661\) 26.6028 1.03473 0.517365 0.855765i \(-0.326913\pi\)
0.517365 + 0.855765i \(0.326913\pi\)
\(662\) −16.8334 −0.654247
\(663\) 5.03461 0.195528
\(664\) 4.41661 0.171398
\(665\) −1.93491 −0.0750327
\(666\) 27.1424 1.05175
\(667\) 49.9726 1.93495
\(668\) −2.46104 −0.0952205
\(669\) 17.2809 0.668119
\(670\) −0.749628 −0.0289607
\(671\) 1.69522 0.0654432
\(672\) 1.20667 0.0465483
\(673\) 9.46755 0.364947 0.182474 0.983211i \(-0.441590\pi\)
0.182474 + 0.983211i \(0.441590\pi\)
\(674\) 12.0727 0.465024
\(675\) −3.97267 −0.152908
\(676\) −11.1900 −0.430384
\(677\) −3.30003 −0.126831 −0.0634153 0.997987i \(-0.520199\pi\)
−0.0634153 + 0.997987i \(0.520199\pi\)
\(678\) −1.54720 −0.0594197
\(679\) −9.58851 −0.367973
\(680\) 5.15562 0.197709
\(681\) −9.72220 −0.372556
\(682\) 8.67865 0.332323
\(683\) 27.8674 1.06632 0.533158 0.846016i \(-0.321005\pi\)
0.533158 + 0.846016i \(0.321005\pi\)
\(684\) −2.87851 −0.110063
\(685\) 19.4879 0.744596
\(686\) −18.6796 −0.713190
\(687\) 16.6714 0.636053
\(688\) 1.00000 0.0381246
\(689\) −1.74254 −0.0663856
\(690\) −5.65331 −0.215218
\(691\) −16.2061 −0.616508 −0.308254 0.951304i \(-0.599745\pi\)
−0.308254 + 0.951304i \(0.599745\pi\)
\(692\) −12.8786 −0.489571
\(693\) 4.11143 0.156180
\(694\) −27.1039 −1.02885
\(695\) −8.10352 −0.307384
\(696\) −4.65714 −0.176529
\(697\) 28.4223 1.07657
\(698\) 2.80970 0.106349
\(699\) 1.40131 0.0530024
\(700\) −1.66243 −0.0628339
\(701\) −9.47972 −0.358044 −0.179022 0.983845i \(-0.557293\pi\)
−0.179022 + 0.983845i \(0.557293\pi\)
\(702\) −5.34468 −0.201722
\(703\) 12.7737 0.481770
\(704\) 1.00000 0.0376889
\(705\) −1.52116 −0.0572902
\(706\) 26.9343 1.01368
\(707\) −9.87546 −0.371405
\(708\) 7.93575 0.298244
\(709\) −17.4239 −0.654370 −0.327185 0.944960i \(-0.606100\pi\)
−0.327185 + 0.944960i \(0.606100\pi\)
\(710\) 5.56121 0.208709
\(711\) 1.90919 0.0716002
\(712\) −7.92294 −0.296925
\(713\) −67.5943 −2.53143
\(714\) −6.22113 −0.232820
\(715\) −1.34536 −0.0503137
\(716\) −2.89487 −0.108186
\(717\) 8.24534 0.307928
\(718\) −28.0499 −1.04681
\(719\) −30.4682 −1.13627 −0.568136 0.822935i \(-0.692335\pi\)
−0.568136 + 0.822935i \(0.692335\pi\)
\(720\) −2.47315 −0.0921687
\(721\) −29.1814 −1.08677
\(722\) 17.6453 0.656691
\(723\) 4.83637 0.179867
\(724\) −8.53765 −0.317299
\(725\) 6.41615 0.238290
\(726\) −0.725847 −0.0269387
\(727\) −19.1274 −0.709395 −0.354697 0.934981i \(-0.615416\pi\)
−0.354697 + 0.934981i \(0.615416\pi\)
\(728\) −2.23657 −0.0828928
\(729\) −2.56725 −0.0950832
\(730\) −4.89194 −0.181059
\(731\) −5.15562 −0.190688
\(732\) 1.23047 0.0454795
\(733\) −21.3728 −0.789423 −0.394711 0.918805i \(-0.629155\pi\)
−0.394711 + 0.918805i \(0.629155\pi\)
\(734\) −22.3766 −0.825937
\(735\) −3.07493 −0.113421
\(736\) −7.78857 −0.287091
\(737\) 0.749628 0.0276129
\(738\) −13.6341 −0.501880
\(739\) 1.61737 0.0594958 0.0297479 0.999557i \(-0.490530\pi\)
0.0297479 + 0.999557i \(0.490530\pi\)
\(740\) 10.9749 0.403444
\(741\) −1.13659 −0.0417536
\(742\) 2.15321 0.0790469
\(743\) −25.8471 −0.948239 −0.474119 0.880461i \(-0.657233\pi\)
−0.474119 + 0.880461i \(0.657233\pi\)
\(744\) 6.29938 0.230946
\(745\) 17.2181 0.630822
\(746\) −33.5261 −1.22748
\(747\) 10.9229 0.399648
\(748\) −5.15562 −0.188508
\(749\) −13.8763 −0.507030
\(750\) −0.725847 −0.0265042
\(751\) 36.5242 1.33279 0.666393 0.745601i \(-0.267837\pi\)
0.666393 + 0.745601i \(0.267837\pi\)
\(752\) −2.09570 −0.0764223
\(753\) 8.11303 0.295655
\(754\) 8.63205 0.314361
\(755\) 3.10714 0.113081
\(756\) 6.60428 0.240195
\(757\) −5.42796 −0.197283 −0.0986413 0.995123i \(-0.531450\pi\)
−0.0986413 + 0.995123i \(0.531450\pi\)
\(758\) −14.3694 −0.521921
\(759\) 5.65331 0.205202
\(760\) −1.16391 −0.0422193
\(761\) −25.1423 −0.911407 −0.455703 0.890132i \(-0.650612\pi\)
−0.455703 + 0.890132i \(0.650612\pi\)
\(762\) −11.2524 −0.407632
\(763\) 17.0329 0.616633
\(764\) 9.45261 0.341983
\(765\) 12.7506 0.460999
\(766\) −22.7826 −0.823170
\(767\) −14.7090 −0.531110
\(768\) 0.725847 0.0261918
\(769\) −37.5144 −1.35280 −0.676401 0.736534i \(-0.736461\pi\)
−0.676401 + 0.736534i \(0.736461\pi\)
\(770\) 1.66243 0.0599098
\(771\) −2.43107 −0.0875527
\(772\) 15.2682 0.549516
\(773\) −39.6749 −1.42701 −0.713503 0.700652i \(-0.752892\pi\)
−0.713503 + 0.700652i \(0.752892\pi\)
\(774\) 2.47315 0.0888954
\(775\) −8.67865 −0.311746
\(776\) −5.76777 −0.207051
\(777\) −13.2430 −0.475091
\(778\) 39.0446 1.39982
\(779\) −6.41647 −0.229894
\(780\) −0.976529 −0.0349653
\(781\) −5.56121 −0.198996
\(782\) 40.1549 1.43594
\(783\) −25.4892 −0.910910
\(784\) −4.23633 −0.151298
\(785\) 13.7020 0.489046
\(786\) 2.61849 0.0933986
\(787\) 4.79221 0.170824 0.0854119 0.996346i \(-0.472779\pi\)
0.0854119 + 0.996346i \(0.472779\pi\)
\(788\) 20.0157 0.713031
\(789\) −7.14733 −0.254452
\(790\) 0.771969 0.0274654
\(791\) −3.54359 −0.125995
\(792\) 2.47315 0.0878794
\(793\) −2.28068 −0.0809895
\(794\) 3.27182 0.116113
\(795\) 0.940133 0.0333431
\(796\) 5.22459 0.185181
\(797\) −40.7575 −1.44370 −0.721852 0.692047i \(-0.756709\pi\)
−0.721852 + 0.692047i \(0.756709\pi\)
\(798\) 1.40445 0.0497170
\(799\) 10.8046 0.382241
\(800\) −1.00000 −0.0353553
\(801\) −19.5946 −0.692340
\(802\) −5.78768 −0.204370
\(803\) 4.89194 0.172633
\(804\) 0.544116 0.0191895
\(805\) −12.9479 −0.456355
\(806\) −11.6759 −0.411267
\(807\) −6.77746 −0.238578
\(808\) −5.94038 −0.208982
\(809\) 29.1429 1.02461 0.512306 0.858803i \(-0.328791\pi\)
0.512306 + 0.858803i \(0.328791\pi\)
\(810\) −4.53588 −0.159375
\(811\) −16.3237 −0.573202 −0.286601 0.958050i \(-0.592525\pi\)
−0.286601 + 0.958050i \(0.592525\pi\)
\(812\) −10.6664 −0.374317
\(813\) −0.800368 −0.0280701
\(814\) −10.9749 −0.384668
\(815\) −8.87274 −0.310798
\(816\) −3.74219 −0.131003
\(817\) 1.16391 0.0407200
\(818\) 6.24178 0.218239
\(819\) −5.53136 −0.193282
\(820\) −5.51287 −0.192518
\(821\) −40.6484 −1.41864 −0.709320 0.704887i \(-0.750998\pi\)
−0.709320 + 0.704887i \(0.750998\pi\)
\(822\) −14.1453 −0.493373
\(823\) −23.5895 −0.822280 −0.411140 0.911572i \(-0.634869\pi\)
−0.411140 + 0.911572i \(0.634869\pi\)
\(824\) −17.5535 −0.611504
\(825\) 0.725847 0.0252708
\(826\) 18.1755 0.632406
\(827\) 0.558107 0.0194073 0.00970363 0.999953i \(-0.496911\pi\)
0.00970363 + 0.999953i \(0.496911\pi\)
\(828\) −19.2623 −0.669410
\(829\) 29.0461 1.00881 0.504407 0.863466i \(-0.331711\pi\)
0.504407 + 0.863466i \(0.331711\pi\)
\(830\) 4.41661 0.153303
\(831\) −8.99707 −0.312105
\(832\) −1.34536 −0.0466421
\(833\) 21.8409 0.756743
\(834\) 5.88192 0.203674
\(835\) −2.46104 −0.0851678
\(836\) 1.16391 0.0402546
\(837\) 34.4774 1.19171
\(838\) −18.2981 −0.632099
\(839\) −32.5345 −1.12322 −0.561608 0.827403i \(-0.689817\pi\)
−0.561608 + 0.827403i \(0.689817\pi\)
\(840\) 1.20667 0.0416341
\(841\) 12.1669 0.419549
\(842\) −38.5499 −1.32852
\(843\) −14.9972 −0.516529
\(844\) 9.53438 0.328187
\(845\) −11.1900 −0.384948
\(846\) −5.18297 −0.178194
\(847\) −1.66243 −0.0571217
\(848\) 1.29522 0.0444781
\(849\) −17.4342 −0.598340
\(850\) 5.15562 0.176836
\(851\) 85.4784 2.93016
\(852\) −4.03659 −0.138291
\(853\) 31.1007 1.06487 0.532434 0.846471i \(-0.321277\pi\)
0.532434 + 0.846471i \(0.321277\pi\)
\(854\) 2.81818 0.0964361
\(855\) −2.87851 −0.0984430
\(856\) −8.34703 −0.285296
\(857\) −26.9867 −0.921848 −0.460924 0.887440i \(-0.652482\pi\)
−0.460924 + 0.887440i \(0.652482\pi\)
\(858\) 0.976529 0.0333381
\(859\) −1.97488 −0.0673822 −0.0336911 0.999432i \(-0.510726\pi\)
−0.0336911 + 0.999432i \(0.510726\pi\)
\(860\) 1.00000 0.0340997
\(861\) 6.65222 0.226707
\(862\) 20.3620 0.693531
\(863\) 25.4791 0.867320 0.433660 0.901077i \(-0.357222\pi\)
0.433660 + 0.901077i \(0.357222\pi\)
\(864\) 3.97267 0.135153
\(865\) −12.8786 −0.437886
\(866\) 20.1175 0.683621
\(867\) 6.95393 0.236168
\(868\) 14.4276 0.489706
\(869\) −0.771969 −0.0261872
\(870\) −4.65714 −0.157892
\(871\) −1.00852 −0.0341725
\(872\) 10.2458 0.346967
\(873\) −14.2645 −0.482782
\(874\) −9.06517 −0.306634
\(875\) −1.66243 −0.0562003
\(876\) 3.55080 0.119970
\(877\) −34.5634 −1.16712 −0.583562 0.812068i \(-0.698342\pi\)
−0.583562 + 0.812068i \(0.698342\pi\)
\(878\) −14.2368 −0.480469
\(879\) −19.8339 −0.668981
\(880\) 1.00000 0.0337100
\(881\) 46.2609 1.55857 0.779285 0.626670i \(-0.215583\pi\)
0.779285 + 0.626670i \(0.215583\pi\)
\(882\) −10.4771 −0.352781
\(883\) −22.4064 −0.754036 −0.377018 0.926206i \(-0.623051\pi\)
−0.377018 + 0.926206i \(0.623051\pi\)
\(884\) 6.93618 0.233289
\(885\) 7.93575 0.266757
\(886\) 14.6856 0.493373
\(887\) −22.3812 −0.751488 −0.375744 0.926723i \(-0.622613\pi\)
−0.375744 + 0.926723i \(0.622613\pi\)
\(888\) −7.96607 −0.267324
\(889\) −25.7717 −0.864356
\(890\) −7.92294 −0.265578
\(891\) 4.53588 0.151958
\(892\) 23.8079 0.797148
\(893\) −2.43920 −0.0816247
\(894\) −12.4977 −0.417986
\(895\) −2.89487 −0.0967648
\(896\) 1.66243 0.0555378
\(897\) −7.60576 −0.253949
\(898\) 3.04963 0.101767
\(899\) −55.6835 −1.85715
\(900\) −2.47315 −0.0824382
\(901\) −6.67767 −0.222465
\(902\) 5.51287 0.183559
\(903\) −1.20667 −0.0401554
\(904\) −2.13157 −0.0708951
\(905\) −8.53765 −0.283801
\(906\) −2.25531 −0.0749277
\(907\) 42.3764 1.40709 0.703543 0.710653i \(-0.251600\pi\)
0.703543 + 0.710653i \(0.251600\pi\)
\(908\) −13.3943 −0.444505
\(909\) −14.6914 −0.487284
\(910\) −2.23657 −0.0741416
\(911\) 13.6647 0.452733 0.226366 0.974042i \(-0.427315\pi\)
0.226366 + 0.974042i \(0.427315\pi\)
\(912\) 0.844819 0.0279748
\(913\) −4.41661 −0.146168
\(914\) −36.9106 −1.22089
\(915\) 1.23047 0.0406781
\(916\) 22.9682 0.758889
\(917\) 5.99721 0.198045
\(918\) −20.4816 −0.675993
\(919\) −6.36128 −0.209839 −0.104920 0.994481i \(-0.533459\pi\)
−0.104920 + 0.994481i \(0.533459\pi\)
\(920\) −7.78857 −0.256782
\(921\) −24.6582 −0.812516
\(922\) 14.3831 0.473683
\(923\) 7.48185 0.246268
\(924\) −1.20667 −0.0396965
\(925\) 10.9749 0.360851
\(926\) −24.6421 −0.809790
\(927\) −43.4123 −1.42585
\(928\) −6.41615 −0.210620
\(929\) −46.5834 −1.52835 −0.764176 0.645007i \(-0.776854\pi\)
−0.764176 + 0.645007i \(0.776854\pi\)
\(930\) 6.29938 0.206565
\(931\) −4.93070 −0.161597
\(932\) 1.93058 0.0632384
\(933\) −16.6341 −0.544575
\(934\) 8.12080 0.265721
\(935\) −5.15562 −0.168607
\(936\) −3.32728 −0.108756
\(937\) 22.6834 0.741034 0.370517 0.928826i \(-0.379181\pi\)
0.370517 + 0.928826i \(0.379181\pi\)
\(938\) 1.24620 0.0406900
\(939\) 16.7057 0.545170
\(940\) −2.09570 −0.0683542
\(941\) −40.0804 −1.30658 −0.653291 0.757107i \(-0.726612\pi\)
−0.653291 + 0.757107i \(0.726612\pi\)
\(942\) −9.94557 −0.324044
\(943\) −42.9374 −1.39823
\(944\) 10.9331 0.355842
\(945\) 6.60428 0.214837
\(946\) −1.00000 −0.0325128
\(947\) −55.3428 −1.79840 −0.899199 0.437540i \(-0.855850\pi\)
−0.899199 + 0.437540i \(0.855850\pi\)
\(948\) −0.560332 −0.0181987
\(949\) −6.58144 −0.213642
\(950\) −1.16391 −0.0377621
\(951\) 1.92618 0.0624607
\(952\) −8.57085 −0.277783
\(953\) 55.5477 1.79937 0.899684 0.436542i \(-0.143797\pi\)
0.899684 + 0.436542i \(0.143797\pi\)
\(954\) 3.20327 0.103710
\(955\) 9.45261 0.305879
\(956\) 11.3596 0.367396
\(957\) 4.65714 0.150544
\(958\) −3.51328 −0.113509
\(959\) −32.3973 −1.04616
\(960\) 0.725847 0.0234266
\(961\) 44.3190 1.42964
\(962\) 14.7652 0.476048
\(963\) −20.6434 −0.665225
\(964\) 6.66307 0.214603
\(965\) 15.2682 0.491502
\(966\) 9.39823 0.302383
\(967\) 18.0659 0.580960 0.290480 0.956881i \(-0.406185\pi\)
0.290480 + 0.956881i \(0.406185\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −4.35557 −0.139921
\(970\) −5.76777 −0.185192
\(971\) 16.2962 0.522971 0.261485 0.965207i \(-0.415788\pi\)
0.261485 + 0.965207i \(0.415788\pi\)
\(972\) 15.2104 0.487873
\(973\) 13.4715 0.431877
\(974\) −9.21794 −0.295362
\(975\) −0.976529 −0.0312739
\(976\) 1.69522 0.0542626
\(977\) 26.3379 0.842624 0.421312 0.906916i \(-0.361570\pi\)
0.421312 + 0.906916i \(0.361570\pi\)
\(978\) 6.44025 0.205937
\(979\) 7.92294 0.253218
\(980\) −4.23633 −0.135325
\(981\) 25.3394 0.809024
\(982\) 13.3645 0.426479
\(983\) 11.0128 0.351255 0.175628 0.984457i \(-0.443805\pi\)
0.175628 + 0.984457i \(0.443805\pi\)
\(984\) 4.00151 0.127563
\(985\) 20.0157 0.637754
\(986\) 33.0792 1.05346
\(987\) 2.52882 0.0804932
\(988\) −1.56588 −0.0498172
\(989\) 7.78857 0.247662
\(990\) 2.47315 0.0786017
\(991\) −18.6838 −0.593512 −0.296756 0.954953i \(-0.595905\pi\)
−0.296756 + 0.954953i \(0.595905\pi\)
\(992\) 8.67865 0.275547
\(993\) 12.2185 0.387741
\(994\) −9.24512 −0.293237
\(995\) 5.22459 0.165631
\(996\) −3.20578 −0.101579
\(997\) −51.8224 −1.64123 −0.820617 0.571479i \(-0.806370\pi\)
−0.820617 + 0.571479i \(0.806370\pi\)
\(998\) 33.2106 1.05126
\(999\) −43.5995 −1.37943
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 4730.2.a.z.1.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.z.1.5 10 1.1 even 1 trivial