Properties

Label 230.2.a.d.1.2
Level $230$
Weight $2$
Character 230.1
Self dual yes
Analytic conductor $1.837$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 230.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(1.83655924649\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.1101.1
Defining polynomial: \(x^{3} - x^{2} - 9 x + 12\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.43163\) of defining polynomial
Character \(\chi\) \(=\) 230.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.43163 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.43163 q^{6} +3.08719 q^{7} +1.00000 q^{8} -0.950444 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.43163 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.43163 q^{6} +3.08719 q^{7} +1.00000 q^{8} -0.950444 q^{9} -1.00000 q^{10} -6.46926 q^{11} +1.43163 q^{12} +3.95044 q^{13} +3.08719 q^{14} -1.43163 q^{15} +1.00000 q^{16} -3.43163 q^{17} -0.950444 q^{18} +3.08719 q^{19} -1.00000 q^{20} +4.41970 q^{21} -6.46926 q^{22} -1.00000 q^{23} +1.43163 q^{24} +1.00000 q^{25} +3.95044 q^{26} -5.65556 q^{27} +3.08719 q^{28} +0.863254 q^{29} -1.43163 q^{30} -5.95044 q^{31} +1.00000 q^{32} -9.26157 q^{33} -3.43163 q^{34} -3.08719 q^{35} -0.950444 q^{36} -7.03763 q^{37} +3.08719 q^{38} +5.65556 q^{39} -1.00000 q^{40} +5.60601 q^{41} +4.41970 q^{42} +8.00000 q^{43} -6.46926 q^{44} +0.950444 q^{45} -1.00000 q^{46} +3.90089 q^{47} +1.43163 q^{48} +2.53074 q^{49} +1.00000 q^{50} -4.91281 q^{51} +3.95044 q^{52} -6.00000 q^{53} -5.65556 q^{54} +6.46926 q^{55} +3.08719 q^{56} +4.41970 q^{57} +0.863254 q^{58} +6.86325 q^{59} -1.43163 q^{60} -13.5069 q^{61} -5.95044 q^{62} -2.93420 q^{63} +1.00000 q^{64} -3.95044 q^{65} -9.26157 q^{66} -10.0753 q^{67} -3.43163 q^{68} -1.43163 q^{69} -3.08719 q^{70} +2.56837 q^{71} -0.950444 q^{72} +5.90089 q^{73} -7.03763 q^{74} +1.43163 q^{75} +3.08719 q^{76} -19.9718 q^{77} +5.65556 q^{78} +15.8018 q^{79} -1.00000 q^{80} -5.24533 q^{81} +5.60601 q^{82} +9.03763 q^{83} +4.41970 q^{84} +3.43163 q^{85} +8.00000 q^{86} +1.23586 q^{87} -6.46926 q^{88} +16.7641 q^{89} +0.950444 q^{90} +12.1958 q^{91} -1.00000 q^{92} -8.51882 q^{93} +3.90089 q^{94} -3.08719 q^{95} +1.43163 q^{96} -14.2949 q^{97} +2.53074 q^{98} +6.14867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} + q^{3} + 3q^{4} - 3q^{5} + q^{6} + 3q^{7} + 3q^{8} + 10q^{9} + O(q^{10}) \) \( 3q + 3q^{2} + q^{3} + 3q^{4} - 3q^{5} + q^{6} + 3q^{7} + 3q^{8} + 10q^{9} - 3q^{10} + 3q^{11} + q^{12} - q^{13} + 3q^{14} - q^{15} + 3q^{16} - 7q^{17} + 10q^{18} + 3q^{19} - 3q^{20} - 22q^{21} + 3q^{22} - 3q^{23} + q^{24} + 3q^{25} - q^{26} - 14q^{27} + 3q^{28} - 4q^{29} - q^{30} - 5q^{31} + 3q^{32} - 9q^{33} - 7q^{34} - 3q^{35} + 10q^{36} - 2q^{37} + 3q^{38} + 14q^{39} - 3q^{40} + q^{41} - 22q^{42} + 24q^{43} + 3q^{44} - 10q^{45} - 3q^{46} - 14q^{47} + q^{48} + 30q^{49} + 3q^{50} - 21q^{51} - q^{52} - 18q^{53} - 14q^{54} - 3q^{55} + 3q^{56} - 22q^{57} - 4q^{58} + 14q^{59} - q^{60} + q^{61} - 5q^{62} + 8q^{63} + 3q^{64} + q^{65} - 9q^{66} + 8q^{67} - 7q^{68} - q^{69} - 3q^{70} + 11q^{71} + 10q^{72} - 8q^{73} - 2q^{74} + q^{75} + 3q^{76} - 24q^{77} + 14q^{78} - 4q^{79} - 3q^{80} + 7q^{81} + q^{82} + 8q^{83} - 22q^{84} + 7q^{85} + 24q^{86} + 36q^{87} + 3q^{88} + 18q^{89} - 10q^{90} + q^{91} - 3q^{92} - 16q^{93} - 14q^{94} - 3q^{95} + q^{96} - 33q^{97} + 30q^{98} + 57q^{99} + O(q^{100}) \)

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
\(3\) 1.43163 0.826550 0.413275 0.910606i \(-0.364385\pi\)
0.413275 + 0.910606i \(0.364385\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.43163 0.584459
\(7\) 3.08719 1.16685 0.583424 0.812168i \(-0.301713\pi\)
0.583424 + 0.812168i \(0.301713\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.950444 −0.316815
\(10\) −1.00000 −0.316228
\(11\) −6.46926 −1.95056 −0.975278 0.220983i \(-0.929074\pi\)
−0.975278 + 0.220983i \(0.929074\pi\)
\(12\) 1.43163 0.413275
\(13\) 3.95044 1.09566 0.547828 0.836591i \(-0.315455\pi\)
0.547828 + 0.836591i \(0.315455\pi\)
\(14\) 3.08719 0.825086
\(15\) −1.43163 −0.369645
\(16\) 1.00000 0.250000
\(17\) −3.43163 −0.832292 −0.416146 0.909298i \(-0.636619\pi\)
−0.416146 + 0.909298i \(0.636619\pi\)
\(18\) −0.950444 −0.224022
\(19\) 3.08719 0.708250 0.354125 0.935198i \(-0.384779\pi\)
0.354125 + 0.935198i \(0.384779\pi\)
\(20\) −1.00000 −0.223607
\(21\) 4.41970 0.964459
\(22\) −6.46926 −1.37925
\(23\) −1.00000 −0.208514
\(24\) 1.43163 0.292230
\(25\) 1.00000 0.200000
\(26\) 3.95044 0.774746
\(27\) −5.65556 −1.08841
\(28\) 3.08719 0.583424
\(29\) 0.863254 0.160302 0.0801511 0.996783i \(-0.474460\pi\)
0.0801511 + 0.996783i \(0.474460\pi\)
\(30\) −1.43163 −0.261378
\(31\) −5.95044 −1.06873 −0.534366 0.845253i \(-0.679449\pi\)
−0.534366 + 0.845253i \(0.679449\pi\)
\(32\) 1.00000 0.176777
\(33\) −9.26157 −1.61223
\(34\) −3.43163 −0.588519
\(35\) −3.08719 −0.521830
\(36\) −0.950444 −0.158407
\(37\) −7.03763 −1.15698 −0.578490 0.815690i \(-0.696358\pi\)
−0.578490 + 0.815690i \(0.696358\pi\)
\(38\) 3.08719 0.500808
\(39\) 5.65556 0.905615
\(40\) −1.00000 −0.158114
\(41\) 5.60601 0.875511 0.437756 0.899094i \(-0.355774\pi\)
0.437756 + 0.899094i \(0.355774\pi\)
\(42\) 4.41970 0.681975
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −6.46926 −0.975278
\(45\) 0.950444 0.141684
\(46\) −1.00000 −0.147442
\(47\) 3.90089 0.569003 0.284501 0.958676i \(-0.408172\pi\)
0.284501 + 0.958676i \(0.408172\pi\)
\(48\) 1.43163 0.206638
\(49\) 2.53074 0.361534
\(50\) 1.00000 0.141421
\(51\) −4.91281 −0.687931
\(52\) 3.95044 0.547828
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) −5.65556 −0.769625
\(55\) 6.46926 0.872315
\(56\) 3.08719 0.412543
\(57\) 4.41970 0.585404
\(58\) 0.863254 0.113351
\(59\) 6.86325 0.893520 0.446760 0.894654i \(-0.352578\pi\)
0.446760 + 0.894654i \(0.352578\pi\)
\(60\) −1.43163 −0.184822
\(61\) −13.5069 −1.72938 −0.864690 0.502305i \(-0.832485\pi\)
−0.864690 + 0.502305i \(0.832485\pi\)
\(62\) −5.95044 −0.755707
\(63\) −2.93420 −0.369674
\(64\) 1.00000 0.125000
\(65\) −3.95044 −0.489992
\(66\) −9.26157 −1.14002
\(67\) −10.0753 −1.23089 −0.615445 0.788180i \(-0.711024\pi\)
−0.615445 + 0.788180i \(0.711024\pi\)
\(68\) −3.43163 −0.416146
\(69\) −1.43163 −0.172348
\(70\) −3.08719 −0.368990
\(71\) 2.56837 0.304810 0.152405 0.988318i \(-0.451298\pi\)
0.152405 + 0.988318i \(0.451298\pi\)
\(72\) −0.950444 −0.112011
\(73\) 5.90089 0.690647 0.345323 0.938484i \(-0.387769\pi\)
0.345323 + 0.938484i \(0.387769\pi\)
\(74\) −7.03763 −0.818108
\(75\) 1.43163 0.165310
\(76\) 3.08719 0.354125
\(77\) −19.9718 −2.27600
\(78\) 5.65556 0.640366
\(79\) 15.8018 1.77784 0.888919 0.458064i \(-0.151457\pi\)
0.888919 + 0.458064i \(0.151457\pi\)
\(80\) −1.00000 −0.111803
\(81\) −5.24533 −0.582814
\(82\) 5.60601 0.619080
\(83\) 9.03763 0.992009 0.496005 0.868320i \(-0.334800\pi\)
0.496005 + 0.868320i \(0.334800\pi\)
\(84\) 4.41970 0.482229
\(85\) 3.43163 0.372212
\(86\) 8.00000 0.862662
\(87\) 1.23586 0.132498
\(88\) −6.46926 −0.689625
\(89\) 16.7641 1.77700 0.888498 0.458881i \(-0.151750\pi\)
0.888498 + 0.458881i \(0.151750\pi\)
\(90\) 0.950444 0.100186
\(91\) 12.1958 1.27846
\(92\) −1.00000 −0.104257
\(93\) −8.51882 −0.883360
\(94\) 3.90089 0.402346
\(95\) −3.08719 −0.316739
\(96\) 1.43163 0.146115
\(97\) −14.2949 −1.45143 −0.725713 0.687998i \(-0.758490\pi\)
−0.725713 + 0.687998i \(0.758490\pi\)
\(98\) 2.53074 0.255643
\(99\) 6.14867 0.617964
\(100\) 1.00000 0.100000
\(101\) 0.863254 0.0858970 0.0429485 0.999077i \(-0.486325\pi\)
0.0429485 + 0.999077i \(0.486325\pi\)
\(102\) −4.91281 −0.486441
\(103\) 1.53074 0.150828 0.0754141 0.997152i \(-0.475972\pi\)
0.0754141 + 0.997152i \(0.475972\pi\)
\(104\) 3.95044 0.387373
\(105\) −4.41970 −0.431319
\(106\) −6.00000 −0.582772
\(107\) 17.6274 1.70410 0.852052 0.523457i \(-0.175358\pi\)
0.852052 + 0.523457i \(0.175358\pi\)
\(108\) −5.65556 −0.544207
\(109\) −2.91281 −0.278997 −0.139498 0.990222i \(-0.544549\pi\)
−0.139498 + 0.990222i \(0.544549\pi\)
\(110\) 6.46926 0.616820
\(111\) −10.0753 −0.956302
\(112\) 3.08719 0.291712
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 4.41970 0.413943
\(115\) 1.00000 0.0932505
\(116\) 0.863254 0.0801511
\(117\) −3.75467 −0.347120
\(118\) 6.86325 0.631814
\(119\) −10.5941 −0.971158
\(120\) −1.43163 −0.130689
\(121\) 30.8513 2.80467
\(122\) −13.5069 −1.22286
\(123\) 8.02571 0.723654
\(124\) −5.95044 −0.534366
\(125\) −1.00000 −0.0894427
\(126\) −2.93420 −0.261399
\(127\) 20.9385 1.85799 0.928997 0.370088i \(-0.120673\pi\)
0.928997 + 0.370088i \(0.120673\pi\)
\(128\) 1.00000 0.0883883
\(129\) 11.4530 1.00838
\(130\) −3.95044 −0.346477
\(131\) 10.7641 0.940467 0.470234 0.882542i \(-0.344170\pi\)
0.470234 + 0.882542i \(0.344170\pi\)
\(132\) −9.26157 −0.806116
\(133\) 9.53074 0.826420
\(134\) −10.0753 −0.870370
\(135\) 5.65556 0.486753
\(136\) −3.43163 −0.294260
\(137\) 3.26157 0.278655 0.139327 0.990246i \(-0.455506\pi\)
0.139327 + 0.990246i \(0.455506\pi\)
\(138\) −1.43163 −0.121868
\(139\) −16.9385 −1.43671 −0.718353 0.695678i \(-0.755104\pi\)
−0.718353 + 0.695678i \(0.755104\pi\)
\(140\) −3.08719 −0.260915
\(141\) 5.58462 0.470310
\(142\) 2.56837 0.215533
\(143\) −25.5565 −2.13714
\(144\) −0.950444 −0.0792037
\(145\) −0.863254 −0.0716894
\(146\) 5.90089 0.488361
\(147\) 3.62308 0.298826
\(148\) −7.03763 −0.578490
\(149\) 3.26157 0.267198 0.133599 0.991035i \(-0.457347\pi\)
0.133599 + 0.991035i \(0.457347\pi\)
\(150\) 1.43163 0.116892
\(151\) 0.294881 0.0239971 0.0119986 0.999928i \(-0.496181\pi\)
0.0119986 + 0.999928i \(0.496181\pi\)
\(152\) 3.08719 0.250404
\(153\) 3.26157 0.263682
\(154\) −19.9718 −1.60938
\(155\) 5.95044 0.477951
\(156\) 5.65556 0.452807
\(157\) 7.13675 0.569574 0.284787 0.958591i \(-0.408077\pi\)
0.284787 + 0.958591i \(0.408077\pi\)
\(158\) 15.8018 1.25712
\(159\) −8.58976 −0.681212
\(160\) −1.00000 −0.0790569
\(161\) −3.08719 −0.243305
\(162\) −5.24533 −0.412112
\(163\) −8.12482 −0.636385 −0.318193 0.948026i \(-0.603076\pi\)
−0.318193 + 0.948026i \(0.603076\pi\)
\(164\) 5.60601 0.437756
\(165\) 9.26157 0.721012
\(166\) 9.03763 0.701456
\(167\) −7.80178 −0.603719 −0.301860 0.953352i \(-0.597607\pi\)
−0.301860 + 0.953352i \(0.597607\pi\)
\(168\) 4.41970 0.340988
\(169\) 2.60601 0.200462
\(170\) 3.43163 0.263194
\(171\) −2.93420 −0.224384
\(172\) 8.00000 0.609994
\(173\) −19.3325 −1.46982 −0.734912 0.678163i \(-0.762777\pi\)
−0.734912 + 0.678163i \(0.762777\pi\)
\(174\) 1.23586 0.0936902
\(175\) 3.08719 0.233370
\(176\) −6.46926 −0.487639
\(177\) 9.82562 0.738539
\(178\) 16.7641 1.25653
\(179\) 2.17438 0.162521 0.0812604 0.996693i \(-0.474105\pi\)
0.0812604 + 0.996693i \(0.474105\pi\)
\(180\) 0.950444 0.0708419
\(181\) −7.26157 −0.539748 −0.269874 0.962896i \(-0.586982\pi\)
−0.269874 + 0.962896i \(0.586982\pi\)
\(182\) 12.1958 0.904011
\(183\) −19.3368 −1.42942
\(184\) −1.00000 −0.0737210
\(185\) 7.03763 0.517417
\(186\) −8.51882 −0.624630
\(187\) 22.2001 1.62343
\(188\) 3.90089 0.284501
\(189\) −17.4598 −1.27001
\(190\) −3.08719 −0.223968
\(191\) 8.58976 0.621533 0.310767 0.950486i \(-0.399414\pi\)
0.310767 + 0.950486i \(0.399414\pi\)
\(192\) 1.43163 0.103319
\(193\) 2.44787 0.176202 0.0881008 0.996112i \(-0.471920\pi\)
0.0881008 + 0.996112i \(0.471920\pi\)
\(194\) −14.2949 −1.02631
\(195\) −5.65556 −0.405003
\(196\) 2.53074 0.180767
\(197\) −10.7428 −0.765389 −0.382695 0.923875i \(-0.625004\pi\)
−0.382695 + 0.923875i \(0.625004\pi\)
\(198\) 6.14867 0.436967
\(199\) −11.3111 −0.801824 −0.400912 0.916116i \(-0.631307\pi\)
−0.400912 + 0.916116i \(0.631307\pi\)
\(200\) 1.00000 0.0707107
\(201\) −14.4240 −1.01739
\(202\) 0.863254 0.0607384
\(203\) 2.66503 0.187048
\(204\) −4.91281 −0.343966
\(205\) −5.60601 −0.391540
\(206\) 1.53074 0.106652
\(207\) 0.950444 0.0660604
\(208\) 3.95044 0.273914
\(209\) −19.9718 −1.38148
\(210\) −4.41970 −0.304989
\(211\) 23.1129 1.59116 0.795579 0.605850i \(-0.207167\pi\)
0.795579 + 0.605850i \(0.207167\pi\)
\(212\) −6.00000 −0.412082
\(213\) 3.67695 0.251941
\(214\) 17.6274 1.20498
\(215\) −8.00000 −0.545595
\(216\) −5.65556 −0.384812
\(217\) −18.3701 −1.24705
\(218\) −2.91281 −0.197280
\(219\) 8.44787 0.570854
\(220\) 6.46926 0.436157
\(221\) −13.5565 −0.911906
\(222\) −10.0753 −0.676208
\(223\) −5.72651 −0.383475 −0.191738 0.981446i \(-0.561412\pi\)
−0.191738 + 0.981446i \(0.561412\pi\)
\(224\) 3.08719 0.206272
\(225\) −0.950444 −0.0633629
\(226\) −6.00000 −0.399114
\(227\) −17.6274 −1.16997 −0.584986 0.811044i \(-0.698900\pi\)
−0.584986 + 0.811044i \(0.698900\pi\)
\(228\) 4.41970 0.292702
\(229\) −16.0753 −1.06228 −0.531142 0.847283i \(-0.678237\pi\)
−0.531142 + 0.847283i \(0.678237\pi\)
\(230\) 1.00000 0.0659380
\(231\) −28.5922 −1.88123
\(232\) 0.863254 0.0566754
\(233\) −6.44787 −0.422414 −0.211207 0.977441i \(-0.567739\pi\)
−0.211207 + 0.977441i \(0.567739\pi\)
\(234\) −3.75467 −0.245451
\(235\) −3.90089 −0.254466
\(236\) 6.86325 0.446760
\(237\) 22.6222 1.46947
\(238\) −10.5941 −0.686712
\(239\) 4.34876 0.281298 0.140649 0.990060i \(-0.455081\pi\)
0.140649 + 0.990060i \(0.455081\pi\)
\(240\) −1.43163 −0.0924111
\(241\) 0.764142 0.0492227 0.0246114 0.999697i \(-0.492165\pi\)
0.0246114 + 0.999697i \(0.492165\pi\)
\(242\) 30.8513 1.98320
\(243\) 9.45734 0.606688
\(244\) −13.5069 −0.864690
\(245\) −2.53074 −0.161683
\(246\) 8.02571 0.511701
\(247\) 12.1958 0.775998
\(248\) −5.95044 −0.377854
\(249\) 12.9385 0.819945
\(250\) −1.00000 −0.0632456
\(251\) −22.5402 −1.42273 −0.711363 0.702825i \(-0.751922\pi\)
−0.711363 + 0.702825i \(0.751922\pi\)
\(252\) −2.93420 −0.184837
\(253\) 6.46926 0.406719
\(254\) 20.9385 1.31380
\(255\) 4.91281 0.307652
\(256\) 1.00000 0.0625000
\(257\) −9.90089 −0.617600 −0.308800 0.951127i \(-0.599927\pi\)
−0.308800 + 0.951127i \(0.599927\pi\)
\(258\) 11.4530 0.713034
\(259\) −21.7265 −1.35002
\(260\) −3.95044 −0.244996
\(261\) −0.820475 −0.0507861
\(262\) 10.7641 0.665011
\(263\) −7.25725 −0.447501 −0.223751 0.974646i \(-0.571830\pi\)
−0.223751 + 0.974646i \(0.571830\pi\)
\(264\) −9.26157 −0.570010
\(265\) 6.00000 0.368577
\(266\) 9.53074 0.584367
\(267\) 24.0000 1.46878
\(268\) −10.0753 −0.615445
\(269\) −6.93852 −0.423049 −0.211525 0.977373i \(-0.567843\pi\)
−0.211525 + 0.977373i \(0.567843\pi\)
\(270\) 5.65556 0.344187
\(271\) −10.2992 −0.625632 −0.312816 0.949814i \(-0.601272\pi\)
−0.312816 + 0.949814i \(0.601272\pi\)
\(272\) −3.43163 −0.208073
\(273\) 17.4598 1.05671
\(274\) 3.26157 0.197039
\(275\) −6.46926 −0.390111
\(276\) −1.43163 −0.0861738
\(277\) −17.8018 −1.06961 −0.534803 0.844977i \(-0.679614\pi\)
−0.534803 + 0.844977i \(0.679614\pi\)
\(278\) −16.9385 −1.01590
\(279\) 5.65556 0.338590
\(280\) −3.08719 −0.184495
\(281\) −18.9385 −1.12978 −0.564889 0.825167i \(-0.691081\pi\)
−0.564889 + 0.825167i \(0.691081\pi\)
\(282\) 5.58462 0.332559
\(283\) 12.6889 0.754275 0.377138 0.926157i \(-0.376908\pi\)
0.377138 + 0.926157i \(0.376908\pi\)
\(284\) 2.56837 0.152405
\(285\) −4.41970 −0.261801
\(286\) −25.5565 −1.51118
\(287\) 17.3068 1.02159
\(288\) −0.950444 −0.0560054
\(289\) −5.22394 −0.307290
\(290\) −0.863254 −0.0506920
\(291\) −20.4649 −1.19968
\(292\) 5.90089 0.345323
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 3.62308 0.211302
\(295\) −6.86325 −0.399594
\(296\) −7.03763 −0.409054
\(297\) 36.5873 2.12301
\(298\) 3.26157 0.188938
\(299\) −3.95044 −0.228460
\(300\) 1.43163 0.0826550
\(301\) 24.6975 1.42354
\(302\) 0.294881 0.0169685
\(303\) 1.23586 0.0709982
\(304\) 3.08719 0.177062
\(305\) 13.5069 0.773402
\(306\) 3.26157 0.186451
\(307\) −22.9599 −1.31039 −0.655196 0.755459i \(-0.727414\pi\)
−0.655196 + 0.755459i \(0.727414\pi\)
\(308\) −19.9718 −1.13800
\(309\) 2.19145 0.124667
\(310\) 5.95044 0.337962
\(311\) 18.0753 1.02495 0.512477 0.858701i \(-0.328728\pi\)
0.512477 + 0.858701i \(0.328728\pi\)
\(312\) 5.65556 0.320183
\(313\) 15.1625 0.857033 0.428516 0.903534i \(-0.359036\pi\)
0.428516 + 0.903534i \(0.359036\pi\)
\(314\) 7.13675 0.402750
\(315\) 2.93420 0.165323
\(316\) 15.8018 0.888919
\(317\) 14.0257 0.787762 0.393881 0.919161i \(-0.371132\pi\)
0.393881 + 0.919161i \(0.371132\pi\)
\(318\) −8.58976 −0.481690
\(319\) −5.58462 −0.312678
\(320\) −1.00000 −0.0559017
\(321\) 25.2359 1.40853
\(322\) −3.08719 −0.172042
\(323\) −10.5941 −0.589471
\(324\) −5.24533 −0.291407
\(325\) 3.95044 0.219131
\(326\) −8.12482 −0.449992
\(327\) −4.17006 −0.230605
\(328\) 5.60601 0.309540
\(329\) 12.0428 0.663940
\(330\) 9.26157 0.509833
\(331\) −24.7403 −1.35985 −0.679925 0.733282i \(-0.737988\pi\)
−0.679925 + 0.733282i \(0.737988\pi\)
\(332\) 9.03763 0.496005
\(333\) 6.68888 0.366548
\(334\) −7.80178 −0.426894
\(335\) 10.0753 0.550471
\(336\) 4.41970 0.241115
\(337\) 14.7146 0.801555 0.400777 0.916176i \(-0.368740\pi\)
0.400777 + 0.916176i \(0.368740\pi\)
\(338\) 2.60601 0.141748
\(339\) −8.58976 −0.466532
\(340\) 3.43163 0.186106
\(341\) 38.4950 2.08462
\(342\) −2.93420 −0.158663
\(343\) −13.7975 −0.744993
\(344\) 8.00000 0.431331
\(345\) 1.43163 0.0770762
\(346\) −19.3325 −1.03932
\(347\) 9.43163 0.506316 0.253158 0.967425i \(-0.418531\pi\)
0.253158 + 0.967425i \(0.418531\pi\)
\(348\) 1.23586 0.0662490
\(349\) 18.3488 0.982187 0.491093 0.871107i \(-0.336597\pi\)
0.491093 + 0.871107i \(0.336597\pi\)
\(350\) 3.08719 0.165017
\(351\) −22.3420 −1.19253
\(352\) −6.46926 −0.344813
\(353\) −33.1129 −1.76242 −0.881211 0.472723i \(-0.843271\pi\)
−0.881211 + 0.472723i \(0.843271\pi\)
\(354\) 9.82562 0.522226
\(355\) −2.56837 −0.136315
\(356\) 16.7641 0.888498
\(357\) −15.1668 −0.802711
\(358\) 2.17438 0.114920
\(359\) 33.0376 1.74366 0.871830 0.489809i \(-0.162933\pi\)
0.871830 + 0.489809i \(0.162933\pi\)
\(360\) 0.950444 0.0500928
\(361\) −9.46926 −0.498382
\(362\) −7.26157 −0.381660
\(363\) 44.1676 2.31820
\(364\) 12.1958 0.639232
\(365\) −5.90089 −0.308867
\(366\) −19.3368 −1.01075
\(367\) −2.27349 −0.118675 −0.0593376 0.998238i \(-0.518899\pi\)
−0.0593376 + 0.998238i \(0.518899\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −5.32819 −0.277375
\(370\) 7.03763 0.365869
\(371\) −18.5231 −0.961673
\(372\) −8.51882 −0.441680
\(373\) 23.9762 1.24144 0.620719 0.784033i \(-0.286841\pi\)
0.620719 + 0.784033i \(0.286841\pi\)
\(374\) 22.2001 1.14794
\(375\) −1.43163 −0.0739289
\(376\) 3.90089 0.201173
\(377\) 3.41024 0.175636
\(378\) −17.4598 −0.898035
\(379\) −13.8795 −0.712942 −0.356471 0.934306i \(-0.616020\pi\)
−0.356471 + 0.934306i \(0.616020\pi\)
\(380\) −3.08719 −0.158369
\(381\) 29.9762 1.53572
\(382\) 8.58976 0.439490
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 1.43163 0.0730574
\(385\) 19.9718 1.01786
\(386\) 2.44787 0.124593
\(387\) −7.60355 −0.386510
\(388\) −14.2949 −0.725713
\(389\) −26.6436 −1.35089 −0.675443 0.737412i \(-0.736048\pi\)
−0.675443 + 0.737412i \(0.736048\pi\)
\(390\) −5.65556 −0.286381
\(391\) 3.43163 0.173545
\(392\) 2.53074 0.127822
\(393\) 15.4102 0.777344
\(394\) −10.7428 −0.541212
\(395\) −15.8018 −0.795074
\(396\) 6.14867 0.308982
\(397\) −8.66749 −0.435009 −0.217504 0.976059i \(-0.569792\pi\)
−0.217504 + 0.976059i \(0.569792\pi\)
\(398\) −11.3111 −0.566975
\(399\) 13.6445 0.683078
\(400\) 1.00000 0.0500000
\(401\) 39.9762 1.99631 0.998157 0.0606854i \(-0.0193286\pi\)
0.998157 + 0.0606854i \(0.0193286\pi\)
\(402\) −14.4240 −0.719405
\(403\) −23.5069 −1.17096
\(404\) 0.863254 0.0429485
\(405\) 5.24533 0.260642
\(406\) 2.66503 0.132263
\(407\) 45.5283 2.25675
\(408\) −4.91281 −0.243220
\(409\) 30.1248 1.48958 0.744788 0.667301i \(-0.232550\pi\)
0.744788 + 0.667301i \(0.232550\pi\)
\(410\) −5.60601 −0.276861
\(411\) 4.66935 0.230322
\(412\) 1.53074 0.0754141
\(413\) 21.1882 1.04260
\(414\) 0.950444 0.0467118
\(415\) −9.03763 −0.443640
\(416\) 3.95044 0.193686
\(417\) −24.2496 −1.18751
\(418\) −19.9718 −0.976854
\(419\) 25.8770 1.26418 0.632088 0.774897i \(-0.282198\pi\)
0.632088 + 0.774897i \(0.282198\pi\)
\(420\) −4.41970 −0.215659
\(421\) −10.7146 −0.522197 −0.261098 0.965312i \(-0.584085\pi\)
−0.261098 + 0.965312i \(0.584085\pi\)
\(422\) 23.1129 1.12512
\(423\) −3.70757 −0.180268
\(424\) −6.00000 −0.291386
\(425\) −3.43163 −0.166458
\(426\) 3.67695 0.178149
\(427\) −41.6983 −2.01792
\(428\) 17.6274 0.852052
\(429\) −36.5873 −1.76645
\(430\) −8.00000 −0.385794
\(431\) 32.2496 1.55341 0.776705 0.629864i \(-0.216889\pi\)
0.776705 + 0.629864i \(0.216889\pi\)
\(432\) −5.65556 −0.272103
\(433\) 20.6393 0.991862 0.495931 0.868362i \(-0.334827\pi\)
0.495931 + 0.868362i \(0.334827\pi\)
\(434\) −18.3701 −0.881795
\(435\) −1.23586 −0.0592549
\(436\) −2.91281 −0.139498
\(437\) −3.08719 −0.147680
\(438\) 8.44787 0.403655
\(439\) −16.2239 −0.774326 −0.387163 0.922011i \(-0.626545\pi\)
−0.387163 + 0.922011i \(0.626545\pi\)
\(440\) 6.46926 0.308410
\(441\) −2.40533 −0.114539
\(442\) −13.5565 −0.644815
\(443\) −15.6770 −0.744834 −0.372417 0.928065i \(-0.621471\pi\)
−0.372417 + 0.928065i \(0.621471\pi\)
\(444\) −10.0753 −0.478151
\(445\) −16.7641 −0.794697
\(446\) −5.72651 −0.271158
\(447\) 4.66935 0.220853
\(448\) 3.08719 0.145856
\(449\) 22.5727 1.06527 0.532636 0.846345i \(-0.321202\pi\)
0.532636 + 0.846345i \(0.321202\pi\)
\(450\) −0.950444 −0.0448044
\(451\) −36.2667 −1.70773
\(452\) −6.00000 −0.282216
\(453\) 0.422160 0.0198348
\(454\) −17.6274 −0.827295
\(455\) −12.1958 −0.571746
\(456\) 4.41970 0.206972
\(457\) −1.45302 −0.0679693 −0.0339846 0.999422i \(-0.510820\pi\)
−0.0339846 + 0.999422i \(0.510820\pi\)
\(458\) −16.0753 −0.751148
\(459\) 19.4078 0.905878
\(460\) 1.00000 0.0466252
\(461\) −29.7027 −1.38339 −0.691695 0.722189i \(-0.743136\pi\)
−0.691695 + 0.722189i \(0.743136\pi\)
\(462\) −28.5922 −1.33023
\(463\) 22.9624 1.06715 0.533576 0.845752i \(-0.320848\pi\)
0.533576 + 0.845752i \(0.320848\pi\)
\(464\) 0.863254 0.0400756
\(465\) 8.51882 0.395051
\(466\) −6.44787 −0.298692
\(467\) 9.48550 0.438937 0.219468 0.975620i \(-0.429568\pi\)
0.219468 + 0.975620i \(0.429568\pi\)
\(468\) −3.75467 −0.173560
\(469\) −31.1043 −1.43626
\(470\) −3.90089 −0.179935
\(471\) 10.2172 0.470782
\(472\) 6.86325 0.315907
\(473\) −51.7541 −2.37966
\(474\) 22.6222 1.03907
\(475\) 3.08719 0.141650
\(476\) −10.5941 −0.485579
\(477\) 5.70266 0.261107
\(478\) 4.34876 0.198908
\(479\) −30.5659 −1.39659 −0.698296 0.715809i \(-0.746058\pi\)
−0.698296 + 0.715809i \(0.746058\pi\)
\(480\) −1.43163 −0.0653445
\(481\) −27.8018 −1.26765
\(482\) 0.764142 0.0348057
\(483\) −4.41970 −0.201104
\(484\) 30.8513 1.40233
\(485\) 14.2949 0.649097
\(486\) 9.45734 0.428994
\(487\) −21.1367 −0.957797 −0.478899 0.877870i \(-0.658964\pi\)
−0.478899 + 0.877870i \(0.658964\pi\)
\(488\) −13.5069 −0.611428
\(489\) −11.6317 −0.526004
\(490\) −2.53074 −0.114327
\(491\) −28.0514 −1.26594 −0.632971 0.774175i \(-0.718165\pi\)
−0.632971 + 0.774175i \(0.718165\pi\)
\(492\) 8.02571 0.361827
\(493\) −2.96237 −0.133418
\(494\) 12.1958 0.548714
\(495\) −6.14867 −0.276362
\(496\) −5.95044 −0.267183
\(497\) 7.92905 0.355667
\(498\) 12.9385 0.579789
\(499\) 3.80178 0.170191 0.0850954 0.996373i \(-0.472880\pi\)
0.0850954 + 0.996373i \(0.472880\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −11.1692 −0.499005
\(502\) −22.5402 −1.00602
\(503\) 19.0872 0.851056 0.425528 0.904945i \(-0.360088\pi\)
0.425528 + 0.904945i \(0.360088\pi\)
\(504\) −2.93420 −0.130700
\(505\) −0.863254 −0.0384143
\(506\) 6.46926 0.287594
\(507\) 3.73083 0.165692
\(508\) 20.9385 0.928997
\(509\) −9.41024 −0.417101 −0.208551 0.978012i \(-0.566875\pi\)
−0.208551 + 0.978012i \(0.566875\pi\)
\(510\) 4.91281 0.217543
\(511\) 18.2172 0.805880
\(512\) 1.00000 0.0441942
\(513\) −17.4598 −0.770869
\(514\) −9.90089 −0.436709
\(515\) −1.53074 −0.0674524
\(516\) 11.4530 0.504191
\(517\) −25.2359 −1.10987
\(518\) −21.7265 −0.954608
\(519\) −27.6770 −1.21488
\(520\) −3.95044 −0.173238
\(521\) 25.8018 1.13040 0.565198 0.824955i \(-0.308800\pi\)
0.565198 + 0.824955i \(0.308800\pi\)
\(522\) −0.820475 −0.0359112
\(523\) −19.1129 −0.835749 −0.417874 0.908505i \(-0.637225\pi\)
−0.417874 + 0.908505i \(0.637225\pi\)
\(524\) 10.7641 0.470234
\(525\) 4.41970 0.192892
\(526\) −7.25725 −0.316431
\(527\) 20.4197 0.889496
\(528\) −9.26157 −0.403058
\(529\) 1.00000 0.0434783
\(530\) 6.00000 0.260623
\(531\) −6.52314 −0.283080
\(532\) 9.53074 0.413210
\(533\) 22.1462 0.959259
\(534\) 24.0000 1.03858
\(535\) −17.6274 −0.762099
\(536\) −10.0753 −0.435185
\(537\) 3.11290 0.134332
\(538\) −6.93852 −0.299141
\(539\) −16.3720 −0.705193
\(540\) 5.65556 0.243377
\(541\) 30.8394 1.32589 0.662945 0.748668i \(-0.269306\pi\)
0.662945 + 0.748668i \(0.269306\pi\)
\(542\) −10.2992 −0.442389
\(543\) −10.3959 −0.446129
\(544\) −3.43163 −0.147130
\(545\) 2.91281 0.124771
\(546\) 17.4598 0.747210
\(547\) 13.8513 0.592240 0.296120 0.955151i \(-0.404307\pi\)
0.296120 + 0.955151i \(0.404307\pi\)
\(548\) 3.26157 0.139327
\(549\) 12.8375 0.547893
\(550\) −6.46926 −0.275850
\(551\) 2.66503 0.113534
\(552\) −1.43163 −0.0609341
\(553\) 48.7831 2.07447
\(554\) −17.8018 −0.756325
\(555\) 10.0753 0.427671
\(556\) −16.9385 −0.718353
\(557\) −28.7641 −1.21878 −0.609388 0.792872i \(-0.708585\pi\)
−0.609388 + 0.792872i \(0.708585\pi\)
\(558\) 5.65556 0.239419
\(559\) 31.6036 1.33669
\(560\) −3.08719 −0.130458
\(561\) 31.7823 1.34185
\(562\) −18.9385 −0.798873
\(563\) 36.1505 1.52356 0.761782 0.647834i \(-0.224325\pi\)
0.761782 + 0.647834i \(0.224325\pi\)
\(564\) 5.58462 0.235155
\(565\) 6.00000 0.252422
\(566\) 12.6889 0.533353
\(567\) −16.1933 −0.680055
\(568\) 2.56837 0.107767
\(569\) −10.3488 −0.433843 −0.216921 0.976189i \(-0.569601\pi\)
−0.216921 + 0.976189i \(0.569601\pi\)
\(570\) −4.41970 −0.185121
\(571\) 19.6060 0.820486 0.410243 0.911976i \(-0.365444\pi\)
0.410243 + 0.911976i \(0.365444\pi\)
\(572\) −25.5565 −1.06857
\(573\) 12.2973 0.513729
\(574\) 17.3068 0.722372
\(575\) −1.00000 −0.0417029
\(576\) −0.950444 −0.0396018
\(577\) −34.1505 −1.42171 −0.710853 0.703341i \(-0.751691\pi\)
−0.710853 + 0.703341i \(0.751691\pi\)
\(578\) −5.22394 −0.217287
\(579\) 3.50444 0.145639
\(580\) −0.863254 −0.0358447
\(581\) 27.9009 1.15752
\(582\) −20.4649 −0.848299
\(583\) 38.8156 1.60758
\(584\) 5.90089 0.244180
\(585\) 3.75467 0.155237
\(586\) −6.00000 −0.247858
\(587\) −5.19062 −0.214240 −0.107120 0.994246i \(-0.534163\pi\)
−0.107120 + 0.994246i \(0.534163\pi\)
\(588\) 3.62308 0.149413
\(589\) −18.3701 −0.756929
\(590\) −6.86325 −0.282556
\(591\) −15.3796 −0.632633
\(592\) −7.03763 −0.289245
\(593\) −2.09911 −0.0862002 −0.0431001 0.999071i \(-0.513723\pi\)
−0.0431001 + 0.999071i \(0.513723\pi\)
\(594\) 36.5873 1.50120
\(595\) 10.5941 0.434315
\(596\) 3.26157 0.133599
\(597\) −16.1933 −0.662748
\(598\) −3.95044 −0.161546
\(599\) 11.1581 0.455909 0.227955 0.973672i \(-0.426796\pi\)
0.227955 + 0.973672i \(0.426796\pi\)
\(600\) 1.43163 0.0584459
\(601\) 9.57784 0.390688 0.195344 0.980735i \(-0.437418\pi\)
0.195344 + 0.980735i \(0.437418\pi\)
\(602\) 24.6975 1.00660
\(603\) 9.57597 0.389964
\(604\) 0.294881 0.0119986
\(605\) −30.8513 −1.25428
\(606\) 1.23586 0.0502033
\(607\) −24.6975 −1.00244 −0.501221 0.865320i \(-0.667115\pi\)
−0.501221 + 0.865320i \(0.667115\pi\)
\(608\) 3.08719 0.125202
\(609\) 3.81533 0.154605
\(610\) 13.5069 0.546878
\(611\) 15.4102 0.623431
\(612\) 3.26157 0.131841
\(613\) −26.3488 −1.06422 −0.532108 0.846676i \(-0.678600\pi\)
−0.532108 + 0.846676i \(0.678600\pi\)
\(614\) −22.9599 −0.926587
\(615\) −8.02571 −0.323628
\(616\) −19.9718 −0.804688
\(617\) 5.94612 0.239382 0.119691 0.992811i \(-0.461810\pi\)
0.119691 + 0.992811i \(0.461810\pi\)
\(618\) 2.19145 0.0881530
\(619\) 39.6856 1.59510 0.797549 0.603254i \(-0.206129\pi\)
0.797549 + 0.603254i \(0.206129\pi\)
\(620\) 5.95044 0.238976
\(621\) 5.65556 0.226950
\(622\) 18.0753 0.724752
\(623\) 51.7541 2.07348
\(624\) 5.65556 0.226404
\(625\) 1.00000 0.0400000
\(626\) 15.1625 0.606014
\(627\) −28.5922 −1.14186
\(628\) 7.13675 0.284787
\(629\) 24.1505 0.962945
\(630\) 2.93420 0.116901
\(631\) −23.0138 −0.916164 −0.458082 0.888910i \(-0.651463\pi\)
−0.458082 + 0.888910i \(0.651463\pi\)
\(632\) 15.8018 0.628561
\(633\) 33.0891 1.31517
\(634\) 14.0257 0.557032
\(635\) −20.9385 −0.830920
\(636\) −8.58976 −0.340606
\(637\) 9.99754 0.396117
\(638\) −5.58462 −0.221097
\(639\) −2.44109 −0.0965682
\(640\) −1.00000 −0.0395285
\(641\) 25.4617 1.00568 0.502838 0.864381i \(-0.332289\pi\)
0.502838 + 0.864381i \(0.332289\pi\)
\(642\) 25.2359 0.995980
\(643\) −16.4479 −0.648641 −0.324320 0.945947i \(-0.605136\pi\)
−0.324320 + 0.945947i \(0.605136\pi\)
\(644\) −3.08719 −0.121652
\(645\) −11.4530 −0.450962
\(646\) −10.5941 −0.416819
\(647\) −34.9147 −1.37264 −0.686319 0.727301i \(-0.740774\pi\)
−0.686319 + 0.727301i \(0.740774\pi\)
\(648\) −5.24533 −0.206056
\(649\) −44.4002 −1.74286
\(650\) 3.95044 0.154949
\(651\) −26.2992 −1.03075
\(652\) −8.12482 −0.318193
\(653\) −34.2754 −1.34130 −0.670649 0.741775i \(-0.733984\pi\)
−0.670649 + 0.741775i \(0.733984\pi\)
\(654\) −4.17006 −0.163062
\(655\) −10.7641 −0.420590
\(656\) 5.60601 0.218878
\(657\) −5.60846 −0.218807
\(658\) 12.0428 0.469476
\(659\) 35.2548 1.37333 0.686666 0.726973i \(-0.259074\pi\)
0.686666 + 0.726973i \(0.259074\pi\)
\(660\) 9.26157 0.360506
\(661\) 28.5684 1.11118 0.555590 0.831456i \(-0.312492\pi\)
0.555590 + 0.831456i \(0.312492\pi\)
\(662\) −24.7403 −0.961559
\(663\) −19.4078 −0.753736
\(664\) 9.03763 0.350728
\(665\) −9.53074 −0.369586
\(666\) 6.68888 0.259189
\(667\) −0.863254 −0.0334253
\(668\) −7.80178 −0.301860
\(669\) −8.19822 −0.316962
\(670\) 10.0753 0.389242
\(671\) 87.3796 3.37325
\(672\) 4.41970 0.170494
\(673\) −23.8770 −0.920392 −0.460196 0.887817i \(-0.652221\pi\)
−0.460196 + 0.887817i \(0.652221\pi\)
\(674\) 14.7146 0.566785
\(675\) −5.65556 −0.217683
\(676\) 2.60601 0.100231
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) −8.58976 −0.329888
\(679\) −44.1310 −1.69359
\(680\) 3.43163 0.131597
\(681\) −25.2359 −0.967040
\(682\) 38.4950 1.47405
\(683\) 34.6480 1.32577 0.662884 0.748722i \(-0.269332\pi\)
0.662884 + 0.748722i \(0.269332\pi\)
\(684\) −2.93420 −0.112192
\(685\) −3.26157 −0.124618
\(686\) −13.7975 −0.526789
\(687\) −23.0138 −0.878031
\(688\) 8.00000 0.304997
\(689\) −23.7027 −0.903000
\(690\) 1.43163 0.0545011
\(691\) −18.1744 −0.691386 −0.345693 0.938348i \(-0.612356\pi\)
−0.345693 + 0.938348i \(0.612356\pi\)
\(692\) −19.3325 −0.734912
\(693\) 18.9821 0.721071
\(694\) 9.43163 0.358020
\(695\) 16.9385 0.642515
\(696\) 1.23586 0.0468451
\(697\) −19.2377 −0.728681
\(698\) 18.3488 0.694511
\(699\) −9.23095 −0.349146
\(700\) 3.08719 0.116685
\(701\) −40.6907 −1.53687 −0.768434 0.639929i \(-0.778964\pi\)
−0.768434 + 0.639929i \(0.778964\pi\)
\(702\) −22.3420 −0.843244
\(703\) −21.7265 −0.819431
\(704\) −6.46926 −0.243819
\(705\) −5.58462 −0.210329
\(706\) −33.1129 −1.24622
\(707\) 2.66503 0.100229
\(708\) 9.82562 0.369269
\(709\) −26.4454 −0.993178 −0.496589 0.867986i \(-0.665414\pi\)
−0.496589 + 0.867986i \(0.665414\pi\)
\(710\) −2.56837 −0.0963893
\(711\) −15.0187 −0.563245
\(712\) 16.7641 0.628263
\(713\) 5.95044 0.222846
\(714\) −15.1668 −0.567602
\(715\) 25.5565 0.955757
\(716\) 2.17438 0.0812604
\(717\) 6.22580 0.232507
\(718\) 33.0376 1.23295
\(719\) −2.24778 −0.0838281 −0.0419140 0.999121i \(-0.513346\pi\)
−0.0419140 + 0.999121i \(0.513346\pi\)
\(720\) 0.950444 0.0354209
\(721\) 4.72568 0.175994
\(722\) −9.46926 −0.352409
\(723\) 1.09397 0.0406850
\(724\) −7.26157 −0.269874
\(725\) 0.863254 0.0320605
\(726\) 44.1676 1.63921
\(727\) 21.4830 0.796762 0.398381 0.917220i \(-0.369572\pi\)
0.398381 + 0.917220i \(0.369572\pi\)
\(728\) 12.1958 0.452005
\(729\) 29.2754 1.08427
\(730\) −5.90089 −0.218402
\(731\) −27.4530 −1.01539
\(732\) −19.3368 −0.714710
\(733\) 11.3778 0.420247 0.210123 0.977675i \(-0.432613\pi\)
0.210123 + 0.977675i \(0.432613\pi\)
\(734\) −2.27349 −0.0839161
\(735\) −3.62308 −0.133639
\(736\) −1.00000 −0.0368605
\(737\) 65.1795 2.40092
\(738\) −5.32819 −0.196134
\(739\) 21.8770 0.804760 0.402380 0.915473i \(-0.368183\pi\)
0.402380 + 0.915473i \(0.368183\pi\)
\(740\) 7.03763 0.258709
\(741\) 17.4598 0.641402
\(742\) −18.5231 −0.680006
\(743\) 5.36068 0.196664 0.0983322 0.995154i \(-0.468649\pi\)
0.0983322 + 0.995154i \(0.468649\pi\)
\(744\) −8.51882 −0.312315
\(745\) −3.26157 −0.119495
\(746\) 23.9762 0.877829
\(747\) −8.58976 −0.314283
\(748\) 22.2001 0.811716
\(749\) 54.4191 1.98843
\(750\) −1.43163 −0.0522756
\(751\) 24.3915 0.890060 0.445030 0.895516i \(-0.353193\pi\)
0.445030 + 0.895516i \(0.353193\pi\)
\(752\) 3.90089 0.142251
\(753\) −32.2692 −1.17595
\(754\) 3.41024 0.124194
\(755\) −0.294881 −0.0107318
\(756\) −17.4598 −0.635007
\(757\) 41.9437 1.52447 0.762234 0.647301i \(-0.224102\pi\)
0.762234 + 0.647301i \(0.224102\pi\)
\(758\) −13.8795 −0.504126
\(759\) 9.26157 0.336174
\(760\) −3.08719 −0.111984
\(761\) −18.3745 −0.666074 −0.333037 0.942914i \(-0.608073\pi\)
−0.333037 + 0.942914i \(0.608073\pi\)
\(762\) 29.9762 1.08592
\(763\) −8.99240 −0.325547
\(764\) 8.58976 0.310767
\(765\) −3.26157 −0.117922
\(766\) 0 0
\(767\) 27.1129 0.978990
\(768\) 1.43163 0.0516594
\(769\) 42.4993 1.53256 0.766282 0.642505i \(-0.222105\pi\)
0.766282 + 0.642505i \(0.222105\pi\)
\(770\) 19.9718 0.719735
\(771\) −14.1744 −0.510478
\(772\) 2.44787 0.0881008
\(773\) −15.0376 −0.540866 −0.270433 0.962739i \(-0.587167\pi\)
−0.270433 + 0.962739i \(0.587167\pi\)
\(774\) −7.60355 −0.273304
\(775\) −5.95044 −0.213746
\(776\) −14.2949 −0.513156
\(777\) −31.1043 −1.11586
\(778\) −26.6436 −0.955221
\(779\) 17.3068 0.620081
\(780\) −5.65556 −0.202502
\(781\) −16.6155 −0.594548
\(782\) 3.43163 0.122715
\(783\) −4.88219 −0.174475
\(784\) 2.53074 0.0903836
\(785\) −7.13675 −0.254721
\(786\) 15.4102 0.549665
\(787\) −8.39154 −0.299126 −0.149563 0.988752i \(-0.547787\pi\)
−0.149563 + 0.988752i \(0.547787\pi\)
\(788\) −10.7428 −0.382695
\(789\) −10.3897 −0.369882
\(790\) −15.8018 −0.562202
\(791\) −18.5231 −0.658607
\(792\) 6.14867 0.218483
\(793\) −53.3582 −1.89481
\(794\) −8.66749 −0.307598
\(795\) 8.58976 0.304647
\(796\) −11.3111 −0.400912
\(797\) −22.0514 −0.781101 −0.390551 0.920581i \(-0.627715\pi\)
−0.390551 + 0.920581i \(0.627715\pi\)
\(798\) 13.6445 0.483009
\(799\) −13.3864 −0.473576
\(800\) 1.00000 0.0353553
\(801\) −15.9334 −0.562978
\(802\) 39.9762 1.41161
\(803\) −38.1744 −1.34714
\(804\) −14.4240 −0.508696
\(805\) 3.08719 0.108809
\(806\) −23.5069 −0.827995
\(807\) −9.93337 −0.349671
\(808\) 0.863254 0.0303692
\(809\) 2.04524 0.0719066 0.0359533 0.999353i \(-0.488553\pi\)
0.0359533 + 0.999353i \(0.488553\pi\)
\(810\) 5.24533 0.184302
\(811\) 4.24965 0.149225 0.0746126 0.997213i \(-0.476228\pi\)
0.0746126 + 0.997213i \(0.476228\pi\)
\(812\) 2.66503 0.0935242
\(813\) −14.7446 −0.517116
\(814\) 45.5283 1.59577
\(815\) 8.12482 0.284600
\(816\) −4.91281 −0.171983
\(817\) 24.6975 0.864057
\(818\) 30.1248 1.05329
\(819\) −11.5914 −0.405036
\(820\) −5.60601 −0.195770
\(821\) −29.2548 −1.02100 −0.510500 0.859878i \(-0.670540\pi\)
−0.510500 + 0.859878i \(0.670540\pi\)
\(822\) 4.66935 0.162862
\(823\) 13.5846 0.473530 0.236765 0.971567i \(-0.423913\pi\)
0.236765 + 0.971567i \(0.423913\pi\)
\(824\) 1.53074 0.0533258
\(825\) −9.26157 −0.322446
\(826\) 21.1882 0.737231
\(827\) 24.7880 0.861963 0.430981 0.902361i \(-0.358167\pi\)
0.430981 + 0.902361i \(0.358167\pi\)
\(828\) 0.950444 0.0330302
\(829\) 26.1505 0.908246 0.454123 0.890939i \(-0.349953\pi\)
0.454123 + 0.890939i \(0.349953\pi\)
\(830\) −9.03763 −0.313701
\(831\) −25.4855 −0.884082
\(832\) 3.95044 0.136957
\(833\) −8.68455 −0.300902
\(834\) −24.2496 −0.839697
\(835\) 7.80178 0.269992
\(836\) −19.9718 −0.690740
\(837\) 33.6531 1.16322
\(838\) 25.8770 0.893908
\(839\) 6.37260 0.220007 0.110003 0.993931i \(-0.464914\pi\)
0.110003 + 0.993931i \(0.464914\pi\)
\(840\) −4.41970 −0.152494
\(841\) −28.2548 −0.974303
\(842\) −10.7146 −0.369249
\(843\) −27.1129 −0.933818
\(844\) 23.1129 0.795579
\(845\) −2.60601 −0.0896493
\(846\) −3.70757 −0.127469
\(847\) 95.2439 3.27262
\(848\) −6.00000 −0.206041
\(849\) 18.1657 0.623447
\(850\) −3.43163 −0.117704
\(851\) 7.03763 0.241247
\(852\) 3.67695 0.125970
\(853\) −33.6293 −1.15144 −0.575722 0.817646i \(-0.695279\pi\)
−0.575722 + 0.817646i \(0.695279\pi\)
\(854\) −41.6983 −1.42689
\(855\) 2.93420 0.100348
\(856\) 17.6274 0.602492
\(857\) 11.1795 0.381885 0.190943 0.981601i \(-0.438846\pi\)
0.190943 + 0.981601i \(0.438846\pi\)
\(858\) −36.5873 −1.24907
\(859\) 47.9009 1.63436 0.817179 0.576385i \(-0.195537\pi\)
0.817179 + 0.576385i \(0.195537\pi\)
\(860\) −8.00000 −0.272798
\(861\) 24.7769 0.844394
\(862\) 32.2496 1.09843
\(863\) −30.1180 −1.02523 −0.512615 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(864\) −5.65556 −0.192406
\(865\) 19.3325 0.657325
\(866\) 20.6393 0.701353
\(867\) −7.47873 −0.253991
\(868\) −18.3701 −0.623523
\(869\) −102.226 −3.46777
\(870\) −1.23586 −0.0418995
\(871\) −39.8018 −1.34863
\(872\) −2.91281 −0.0986402
\(873\) 13.5865 0.459833
\(874\) −3.08719 −0.104426
\(875\) −3.08719 −0.104366
\(876\) 8.44787 0.285427
\(877\) −22.3940 −0.756191 −0.378096 0.925767i \(-0.623421\pi\)
−0.378096 + 0.925767i \(0.623421\pi\)
\(878\) −16.2239 −0.547531
\(879\) −8.58976 −0.289726
\(880\) 6.46926 0.218079
\(881\) 21.1129 0.711312 0.355656 0.934617i \(-0.384258\pi\)
0.355656 + 0.934617i \(0.384258\pi\)
\(882\) −2.40533 −0.0809915
\(883\) 49.1061 1.65255 0.826276 0.563265i \(-0.190455\pi\)
0.826276 + 0.563265i \(0.190455\pi\)
\(884\) −13.5565 −0.455953
\(885\) −9.82562 −0.330285
\(886\) −15.6770 −0.526678
\(887\) −43.0566 −1.44570 −0.722849 0.691006i \(-0.757168\pi\)
−0.722849 + 0.691006i \(0.757168\pi\)
\(888\) −10.0753 −0.338104
\(889\) 64.6412 2.16800
\(890\) −16.7641 −0.561935
\(891\) 33.9334 1.13681
\(892\) −5.72651 −0.191738
\(893\) 12.0428 0.402996
\(894\) 4.66935 0.156166
\(895\) −2.17438 −0.0726815
\(896\) 3.08719 0.103136
\(897\) −5.65556 −0.188834
\(898\) 22.5727 0.753261
\(899\) −5.13675 −0.171320
\(900\) −0.950444 −0.0316815
\(901\) 20.5898 0.685944
\(902\) −36.2667 −1.20755
\(903\) 35.3576 1.17663
\(904\) −6.00000 −0.199557
\(905\) 7.26157 0.241383
\(906\) 0.422160 0.0140253
\(907\) −37.9762 −1.26098 −0.630489 0.776198i \(-0.717146\pi\)
−0.630489 + 0.776198i \(0.717146\pi\)
\(908\) −17.6274 −0.584986
\(909\) −0.820475 −0.0272134
\(910\) −12.1958 −0.404286
\(911\) −15.7504 −0.521833 −0.260916 0.965361i \(-0.584025\pi\)
−0.260916 + 0.965361i \(0.584025\pi\)
\(912\) 4.41970 0.146351
\(913\) −58.4668 −1.93497
\(914\) −1.45302 −0.0480615
\(915\) 19.3368 0.639256
\(916\) −16.0753 −0.531142
\(917\) 33.2309 1.09738
\(918\) 19.4078 0.640552
\(919\) 30.4240 1.00360 0.501798 0.864985i \(-0.332672\pi\)
0.501798 + 0.864985i \(0.332672\pi\)
\(920\) 1.00000 0.0329690
\(921\) −32.8700 −1.08310
\(922\) −29.7027 −0.978205
\(923\) 10.1462 0.333967
\(924\) −28.5922 −0.940615
\(925\) −7.03763 −0.231396
\(926\) 22.9624 0.754590
\(927\) −1.45488 −0.0477846
\(928\) 0.863254 0.0283377
\(929\) −37.8018 −1.24024 −0.620118 0.784509i \(-0.712915\pi\)
−0.620118 + 0.784509i \(0.712915\pi\)
\(930\) 8.51882 0.279343
\(931\) 7.81287 0.256057
\(932\) −6.44787 −0.211207
\(933\) 25.8770 0.847176
\(934\) 9.48550 0.310375
\(935\) −22.2001 −0.726021
\(936\) −3.75467 −0.122725
\(937\) −32.6907 −1.06796 −0.533980 0.845497i \(-0.679304\pi\)
−0.533980 + 0.845497i \(0.679304\pi\)
\(938\) −31.1043 −1.01559
\(939\) 21.7070 0.708381
\(940\) −3.90089 −0.127233
\(941\) −46.4882 −1.51547 −0.757736 0.652561i \(-0.773694\pi\)
−0.757736 + 0.652561i \(0.773694\pi\)
\(942\) 10.2172 0.332893
\(943\) −5.60601 −0.182557
\(944\) 6.86325 0.223380
\(945\) 17.4598 0.567967
\(946\) −51.7541 −1.68267
\(947\) −37.2052 −1.20901 −0.604504 0.796602i \(-0.706629\pi\)
−0.604504 + 0.796602i \(0.706629\pi\)
\(948\) 22.6222 0.734737
\(949\) 23.3111 0.756711
\(950\) 3.08719 0.100162
\(951\) 20.0796 0.651125
\(952\) −10.5941 −0.343356
\(953\) 49.1104 1.59084 0.795422 0.606056i \(-0.207249\pi\)
0.795422 + 0.606056i \(0.207249\pi\)
\(954\) 5.70266 0.184631
\(955\) −8.58976 −0.277958
\(956\) 4.34876 0.140649
\(957\) −7.99509 −0.258445
\(958\) −30.5659 −0.987540
\(959\) 10.0691 0.325148
\(960\) −1.43163 −0.0462056
\(961\) 4.40778 0.142187
\(962\) −27.8018 −0.896365
\(963\) −16.7538 −0.539885
\(964\) 0.764142 0.0246114
\(965\) −2.44787 −0.0787997
\(966\) −4.41970 −0.142202
\(967\) 1.96751 0.0632709 0.0316355 0.999499i \(-0.489928\pi\)
0.0316355 + 0.999499i \(0.489928\pi\)
\(968\) 30.8513 0.991599
\(969\) −15.1668 −0.487227
\(970\) 14.2949 0.458981
\(971\) 26.1205 0.838247 0.419123 0.907929i \(-0.362337\pi\)
0.419123 + 0.907929i \(0.362337\pi\)
\(972\) 9.45734 0.303344
\(973\) −52.2924 −1.67642
\(974\) −21.1367 −0.677265
\(975\) 5.65556 0.181123
\(976\) −13.5069 −0.432345
\(977\) −0.639319 −0.0204536 −0.0102268 0.999948i \(-0.503255\pi\)
−0.0102268 + 0.999948i \(0.503255\pi\)
\(978\) −11.6317 −0.371941
\(979\) −108.452 −3.46613
\(980\) −2.53074 −0.0808415
\(981\) 2.76846 0.0883902
\(982\) −28.0514 −0.895157
\(983\) −6.46926 −0.206337 −0.103169 0.994664i \(-0.532898\pi\)
−0.103169 + 0.994664i \(0.532898\pi\)
\(984\) 8.02571 0.255850
\(985\) 10.7428 0.342293
\(986\) −2.96237 −0.0943410
\(987\) 17.2408 0.548780
\(988\) 12.1958 0.387999
\(989\) −8.00000 −0.254385
\(990\) −6.14867 −0.195418
\(991\) 37.2334 1.18276 0.591379 0.806394i \(-0.298584\pi\)
0.591379 + 0.806394i \(0.298584\pi\)
\(992\) −5.95044 −0.188927
\(993\) −35.4189 −1.12398
\(994\) 7.92905 0.251494
\(995\) 11.3111 0.358587
\(996\) 12.9385 0.409973
\(997\) 9.65124 0.305658 0.152829 0.988253i \(-0.451162\pi\)
0.152829 + 0.988253i \(0.451162\pi\)
\(998\) 3.80178 0.120343
\(999\) 39.8018 1.25927
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 230.2.a.d.1.2 3
3.2 odd 2 2070.2.a.z.1.2 3
4.3 odd 2 1840.2.a.r.1.2 3
5.2 odd 4 1150.2.b.j.599.5 6
5.3 odd 4 1150.2.b.j.599.2 6
5.4 even 2 1150.2.a.q.1.2 3
8.3 odd 2 7360.2.a.ce.1.2 3
8.5 even 2 7360.2.a.bz.1.2 3
20.19 odd 2 9200.2.a.cf.1.2 3
23.22 odd 2 5290.2.a.r.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.d.1.2 3 1.1 even 1 trivial
1150.2.a.q.1.2 3 5.4 even 2
1150.2.b.j.599.2 6 5.3 odd 4
1150.2.b.j.599.5 6 5.2 odd 4
1840.2.a.r.1.2 3 4.3 odd 2
2070.2.a.z.1.2 3 3.2 odd 2
5290.2.a.r.1.2 3 23.22 odd 2
7360.2.a.bz.1.2 3 8.5 even 2
7360.2.a.ce.1.2 3 8.3 odd 2
9200.2.a.cf.1.2 3 20.19 odd 2