Properties

Label 1150.2.a.q.1.2
Level $1150$
Weight $2$
Character 1150.1
Self dual yes
Analytic conductor $9.183$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1150.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.18279623245\)
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: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.43163\) of defining polynomial
Character \(\chi\) \(=\) 1150.1

$q$-expansion

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

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 \(-0.635615\pi\)
−0.413275 + 0.910606i \(0.635615\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.43163 0.584459
\(7\) −3.08719 −1.16685 −0.583424 0.812168i \(-0.698287\pi\)
−0.583424 + 0.812168i \(0.698287\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.950444 −0.316815
\(10\) 0 0
\(11\) −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 \(-0.684545\pi\)
−0.547828 + 0.836591i \(0.684545\pi\)
\(14\) 3.08719 0.825086
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 3.43163 0.832292 0.416146 0.909298i \(-0.363381\pi\)
0.416146 + 0.909298i \(0.363381\pi\)
\(18\) 0.950444 0.224022
\(19\) 3.08719 0.708250 0.354125 0.935198i \(-0.384779\pi\)
0.354125 + 0.935198i \(0.384779\pi\)
\(20\) 0 0
\(21\) 4.41970 0.964459
\(22\) 6.46926 1.37925
\(23\) 1.00000 0.208514
\(24\) 1.43163 0.292230
\(25\) 0 0
\(26\) 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 \(0.474460\pi\)
\(30\) 0 0
\(31\) −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
\(35\) 0 0
\(36\) −0.950444 −0.158407
\(37\) 7.03763 1.15698 0.578490 0.815690i \(-0.303642\pi\)
0.578490 + 0.815690i \(0.303642\pi\)
\(38\) −3.08719 −0.500808
\(39\) 5.65556 0.905615
\(40\) 0 0
\(41\) 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 \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −6.46926 −0.975278
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) −3.90089 −0.569003 −0.284501 0.958676i \(-0.591828\pi\)
−0.284501 + 0.958676i \(0.591828\pi\)
\(48\) −1.43163 −0.206638
\(49\) 2.53074 0.361534
\(50\) 0 0
\(51\) −4.91281 −0.687931
\(52\) −3.95044 −0.547828
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) −5.65556 −0.769625
\(55\) 0 0
\(56\) 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 \(0.352578\pi\)
\(60\) 0 0
\(61\) −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
\(65\) 0 0
\(66\) −9.26157 −1.14002
\(67\) 10.0753 1.23089 0.615445 0.788180i \(-0.288976\pi\)
0.615445 + 0.788180i \(0.288976\pi\)
\(68\) 3.43163 0.416146
\(69\) −1.43163 −0.172348
\(70\) 0 0
\(71\) 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 \(-0.612231\pi\)
−0.345323 + 0.938484i \(0.612231\pi\)
\(74\) −7.03763 −0.818108
\(75\) 0 0
\(76\) 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 \(0.151457\pi\)
\(80\) 0 0
\(81\) −5.24533 −0.582814
\(82\) −5.60601 −0.619080
\(83\) −9.03763 −0.992009 −0.496005 0.868320i \(-0.665200\pi\)
−0.496005 + 0.868320i \(0.665200\pi\)
\(84\) 4.41970 0.482229
\(85\) 0 0
\(86\) 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 0
\(91\) 12.1958 1.27846
\(92\) 1.00000 0.104257
\(93\) 8.51882 0.883360
\(94\) 3.90089 0.402346
\(95\) 0 0
\(96\) 1.43163 0.146115
\(97\) 14.2949 1.45143 0.725713 0.687998i \(-0.241510\pi\)
0.725713 + 0.687998i \(0.241510\pi\)
\(98\) −2.53074 −0.255643
\(99\) 6.14867 0.617964
\(100\) 0 0
\(101\) 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 \(-0.524028\pi\)
−0.0754141 + 0.997152i \(0.524028\pi\)
\(104\) 3.95044 0.387373
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −17.6274 −1.70410 −0.852052 0.523457i \(-0.824642\pi\)
−0.852052 + 0.523457i \(0.824642\pi\)
\(108\) 5.65556 0.544207
\(109\) −2.91281 −0.278997 −0.139498 0.990222i \(-0.544549\pi\)
−0.139498 + 0.990222i \(0.544549\pi\)
\(110\) 0 0
\(111\) −10.0753 −0.956302
\(112\) −3.08719 −0.291712
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 4.41970 0.413943
\(115\) 0 0
\(116\) 0.863254 0.0801511
\(117\) 3.75467 0.347120
\(118\) −6.86325 −0.631814
\(119\) −10.5941 −0.971158
\(120\) 0 0
\(121\) 30.8513 2.80467
\(122\) 13.5069 1.22286
\(123\) −8.02571 −0.723654
\(124\) −5.95044 −0.534366
\(125\) 0 0
\(126\) −2.93420 −0.261399
\(127\) −20.9385 −1.85799 −0.928997 0.370088i \(-0.879327\pi\)
−0.928997 + 0.370088i \(0.879327\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 11.4530 1.00838
\(130\) 0 0
\(131\) 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
\(135\) 0 0
\(136\) −3.43163 −0.294260
\(137\) −3.26157 −0.278655 −0.139327 0.990246i \(-0.544494\pi\)
−0.139327 + 0.990246i \(0.544494\pi\)
\(138\) 1.43163 0.121868
\(139\) −16.9385 −1.43671 −0.718353 0.695678i \(-0.755104\pi\)
−0.718353 + 0.695678i \(0.755104\pi\)
\(140\) 0 0
\(141\) 5.58462 0.470310
\(142\) −2.56837 −0.215533
\(143\) 25.5565 2.13714
\(144\) −0.950444 −0.0792037
\(145\) 0 0
\(146\) 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 \(0.457347\pi\)
\(150\) 0 0
\(151\) 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
\(155\) 0 0
\(156\) 5.65556 0.452807
\(157\) −7.13675 −0.569574 −0.284787 0.958591i \(-0.591923\pi\)
−0.284787 + 0.958591i \(0.591923\pi\)
\(158\) −15.8018 −1.25712
\(159\) −8.58976 −0.681212
\(160\) 0 0
\(161\) −3.08719 −0.243305
\(162\) 5.24533 0.412112
\(163\) 8.12482 0.636385 0.318193 0.948026i \(-0.396924\pi\)
0.318193 + 0.948026i \(0.396924\pi\)
\(164\) 5.60601 0.437756
\(165\) 0 0
\(166\) 9.03763 0.701456
\(167\) 7.80178 0.603719 0.301860 0.953352i \(-0.402393\pi\)
0.301860 + 0.953352i \(0.402393\pi\)
\(168\) −4.41970 −0.340988
\(169\) 2.60601 0.200462
\(170\) 0 0
\(171\) −2.93420 −0.224384
\(172\) −8.00000 −0.609994
\(173\) 19.3325 1.46982 0.734912 0.678163i \(-0.237223\pi\)
0.734912 + 0.678163i \(0.237223\pi\)
\(174\) 1.23586 0.0936902
\(175\) 0 0
\(176\) −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 0
\(181\) −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
\(185\) 0 0
\(186\) −8.51882 −0.624630
\(187\) −22.2001 −1.62343
\(188\) −3.90089 −0.284501
\(189\) −17.4598 −1.27001
\(190\) 0 0
\(191\) 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 \(-0.528080\pi\)
−0.0881008 + 0.996112i \(0.528080\pi\)
\(194\) −14.2949 −1.02631
\(195\) 0 0
\(196\) 2.53074 0.180767
\(197\) 10.7428 0.765389 0.382695 0.923875i \(-0.374996\pi\)
0.382695 + 0.923875i \(0.374996\pi\)
\(198\) −6.14867 −0.436967
\(199\) −11.3111 −0.801824 −0.400912 0.916116i \(-0.631307\pi\)
−0.400912 + 0.916116i \(0.631307\pi\)
\(200\) 0 0
\(201\) −14.4240 −1.01739
\(202\) −0.863254 −0.0607384
\(203\) −2.66503 −0.187048
\(204\) −4.91281 −0.343966
\(205\) 0 0
\(206\) 1.53074 0.106652
\(207\) −0.950444 −0.0660604
\(208\) −3.95044 −0.273914
\(209\) −19.9718 −1.38148
\(210\) 0 0
\(211\) 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
\(215\) 0 0
\(216\) −5.65556 −0.384812
\(217\) 18.3701 1.24705
\(218\) 2.91281 0.197280
\(219\) 8.44787 0.570854
\(220\) 0 0
\(221\) −13.5565 −0.911906
\(222\) 10.0753 0.676208
\(223\) 5.72651 0.383475 0.191738 0.981446i \(-0.438588\pi\)
0.191738 + 0.981446i \(0.438588\pi\)
\(224\) 3.08719 0.206272
\(225\) 0 0
\(226\) −6.00000 −0.399114
\(227\) 17.6274 1.16997 0.584986 0.811044i \(-0.301100\pi\)
0.584986 + 0.811044i \(0.301100\pi\)
\(228\) −4.41970 −0.292702
\(229\) −16.0753 −1.06228 −0.531142 0.847283i \(-0.678237\pi\)
−0.531142 + 0.847283i \(0.678237\pi\)
\(230\) 0 0
\(231\) −28.5922 −1.88123
\(232\) −0.863254 −0.0566754
\(233\) 6.44787 0.422414 0.211207 0.977441i \(-0.432261\pi\)
0.211207 + 0.977441i \(0.432261\pi\)
\(234\) −3.75467 −0.245451
\(235\) 0 0
\(236\) 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 \(0.455081\pi\)
\(240\) 0 0
\(241\) 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
\(245\) 0 0
\(246\) 8.02571 0.511701
\(247\) −12.1958 −0.775998
\(248\) 5.95044 0.377854
\(249\) 12.9385 0.819945
\(250\) 0 0
\(251\) −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
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 9.90089 0.617600 0.308800 0.951127i \(-0.400073\pi\)
0.308800 + 0.951127i \(0.400073\pi\)
\(258\) −11.4530 −0.713034
\(259\) −21.7265 −1.35002
\(260\) 0 0
\(261\) −0.820475 −0.0507861
\(262\) −10.7641 −0.665011
\(263\) 7.25725 0.447501 0.223751 0.974646i \(-0.428170\pi\)
0.223751 + 0.974646i \(0.428170\pi\)
\(264\) −9.26157 −0.570010
\(265\) 0 0
\(266\) 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 \(0.567843\pi\)
\(270\) 0 0
\(271\) −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
\(275\) 0 0
\(276\) −1.43163 −0.0861738
\(277\) 17.8018 1.06961 0.534803 0.844977i \(-0.320386\pi\)
0.534803 + 0.844977i \(0.320386\pi\)
\(278\) 16.9385 1.01590
\(279\) 5.65556 0.338590
\(280\) 0 0
\(281\) −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 \(-0.623092\pi\)
−0.377138 + 0.926157i \(0.623092\pi\)
\(284\) 2.56837 0.152405
\(285\) 0 0
\(286\) −25.5565 −1.51118
\(287\) −17.3068 −1.02159
\(288\) 0.950444 0.0560054
\(289\) −5.22394 −0.307290
\(290\) 0 0
\(291\) −20.4649 −1.19968
\(292\) −5.90089 −0.345323
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 3.62308 0.211302
\(295\) 0 0
\(296\) −7.03763 −0.409054
\(297\) −36.5873 −2.12301
\(298\) −3.26157 −0.188938
\(299\) −3.95044 −0.228460
\(300\) 0 0
\(301\) 24.6975 1.42354
\(302\) −0.294881 −0.0169685
\(303\) −1.23586 −0.0709982
\(304\) 3.08719 0.177062
\(305\) 0 0
\(306\) 3.26157 0.186451
\(307\) 22.9599 1.31039 0.655196 0.755459i \(-0.272586\pi\)
0.655196 + 0.755459i \(0.272586\pi\)
\(308\) 19.9718 1.13800
\(309\) 2.19145 0.124667
\(310\) 0 0
\(311\) 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 \(-0.640964\pi\)
−0.428516 + 0.903534i \(0.640964\pi\)
\(314\) 7.13675 0.402750
\(315\) 0 0
\(316\) 15.8018 0.888919
\(317\) −14.0257 −0.787762 −0.393881 0.919161i \(-0.628868\pi\)
−0.393881 + 0.919161i \(0.628868\pi\)
\(318\) 8.58976 0.481690
\(319\) −5.58462 −0.312678
\(320\) 0 0
\(321\) 25.2359 1.40853
\(322\) 3.08719 0.172042
\(323\) 10.5941 0.589471
\(324\) −5.24533 −0.291407
\(325\) 0 0
\(326\) −8.12482 −0.449992
\(327\) 4.17006 0.230605
\(328\) −5.60601 −0.309540
\(329\) 12.0428 0.663940
\(330\) 0 0
\(331\) −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
\(335\) 0 0
\(336\) 4.41970 0.241115
\(337\) −14.7146 −0.801555 −0.400777 0.916176i \(-0.631260\pi\)
−0.400777 + 0.916176i \(0.631260\pi\)
\(338\) −2.60601 −0.141748
\(339\) −8.58976 −0.466532
\(340\) 0 0
\(341\) 38.4950 2.08462
\(342\) 2.93420 0.158663
\(343\) 13.7975 0.744993
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −19.3325 −1.03932
\(347\) −9.43163 −0.506316 −0.253158 0.967425i \(-0.581469\pi\)
−0.253158 + 0.967425i \(0.581469\pi\)
\(348\) −1.23586 −0.0662490
\(349\) 18.3488 0.982187 0.491093 0.871107i \(-0.336597\pi\)
0.491093 + 0.871107i \(0.336597\pi\)
\(350\) 0 0
\(351\) −22.3420 −1.19253
\(352\) 6.46926 0.344813
\(353\) 33.1129 1.76242 0.881211 0.472723i \(-0.156729\pi\)
0.881211 + 0.472723i \(0.156729\pi\)
\(354\) 9.82562 0.522226
\(355\) 0 0
\(356\) 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 0
\(361\) −9.46926 −0.498382
\(362\) 7.26157 0.381660
\(363\) −44.1676 −2.31820
\(364\) 12.1958 0.639232
\(365\) 0 0
\(366\) −19.3368 −1.01075
\(367\) 2.27349 0.118675 0.0593376 0.998238i \(-0.481101\pi\)
0.0593376 + 0.998238i \(0.481101\pi\)
\(368\) 1.00000 0.0521286
\(369\) −5.32819 −0.277375
\(370\) 0 0
\(371\) −18.5231 −0.961673
\(372\) 8.51882 0.441680
\(373\) −23.9762 −1.24144 −0.620719 0.784033i \(-0.713159\pi\)
−0.620719 + 0.784033i \(0.713159\pi\)
\(374\) 22.2001 1.14794
\(375\) 0 0
\(376\) 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 \(0.616020\pi\)
\(380\) 0 0
\(381\) 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
\(385\) 0 0
\(386\) 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 \(0.736048\pi\)
\(390\) 0 0
\(391\) 3.43163 0.173545
\(392\) −2.53074 −0.127822
\(393\) −15.4102 −0.777344
\(394\) −10.7428 −0.541212
\(395\) 0 0
\(396\) 6.14867 0.308982
\(397\) 8.66749 0.435009 0.217504 0.976059i \(-0.430208\pi\)
0.217504 + 0.976059i \(0.430208\pi\)
\(398\) 11.3111 0.566975
\(399\) 13.6445 0.683078
\(400\) 0 0
\(401\) 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
\(405\) 0 0
\(406\) 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 \(0.232550\pi\)
\(410\) 0 0
\(411\) 4.66935 0.230322
\(412\) −1.53074 −0.0754141
\(413\) −21.1882 −1.04260
\(414\) 0.950444 0.0467118
\(415\) 0 0
\(416\) 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 \(0.282198\pi\)
\(420\) 0 0
\(421\) −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
\(425\) 0 0
\(426\) 3.67695 0.178149
\(427\) 41.6983 2.01792
\(428\) −17.6274 −0.852052
\(429\) −36.5873 −1.76645
\(430\) 0 0
\(431\) 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 \(-0.665173\pi\)
−0.495931 + 0.868362i \(0.665173\pi\)
\(434\) −18.3701 −0.881795
\(435\) 0 0
\(436\) −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 \(0.626545\pi\)
\(440\) 0 0
\(441\) −2.40533 −0.114539
\(442\) 13.5565 0.644815
\(443\) 15.6770 0.744834 0.372417 0.928065i \(-0.378529\pi\)
0.372417 + 0.928065i \(0.378529\pi\)
\(444\) −10.0753 −0.478151
\(445\) 0 0
\(446\) −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 0
\(451\) −36.2667 −1.70773
\(452\) 6.00000 0.282216
\(453\) −0.422160 −0.0198348
\(454\) −17.6274 −0.827295
\(455\) 0 0
\(456\) 4.41970 0.206972
\(457\) 1.45302 0.0679693 0.0339846 0.999422i \(-0.489180\pi\)
0.0339846 + 0.999422i \(0.489180\pi\)
\(458\) 16.0753 0.751148
\(459\) 19.4078 0.905878
\(460\) 0 0
\(461\) −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 \(-0.679152\pi\)
−0.533576 + 0.845752i \(0.679152\pi\)
\(464\) 0.863254 0.0400756
\(465\) 0 0
\(466\) −6.44787 −0.298692
\(467\) −9.48550 −0.438937 −0.219468 0.975620i \(-0.570432\pi\)
−0.219468 + 0.975620i \(0.570432\pi\)
\(468\) 3.75467 0.173560
\(469\) −31.1043 −1.43626
\(470\) 0 0
\(471\) 10.2172 0.470782
\(472\) −6.86325 −0.315907
\(473\) 51.7541 2.37966
\(474\) 22.6222 1.03907
\(475\) 0 0
\(476\) −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 \(0.746058\pi\)
\(480\) 0 0
\(481\) −27.8018 −1.26765
\(482\) −0.764142 −0.0348057
\(483\) 4.41970 0.201104
\(484\) 30.8513 1.40233
\(485\) 0 0
\(486\) 9.45734 0.428994
\(487\) 21.1367 0.957797 0.478899 0.877870i \(-0.341036\pi\)
0.478899 + 0.877870i \(0.341036\pi\)
\(488\) 13.5069 0.611428
\(489\) −11.6317 −0.526004
\(490\) 0 0
\(491\) −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
\(495\) 0 0
\(496\) −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 \(0.472880\pi\)
\(500\) 0 0
\(501\) −11.1692 −0.499005
\(502\) 22.5402 1.00602
\(503\) −19.0872 −0.851056 −0.425528 0.904945i \(-0.639912\pi\)
−0.425528 + 0.904945i \(0.639912\pi\)
\(504\) −2.93420 −0.130700
\(505\) 0 0
\(506\) 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 \(0.566875\pi\)
\(510\) 0 0
\(511\) 18.2172 0.805880
\(512\) −1.00000 −0.0441942
\(513\) 17.4598 0.770869
\(514\) −9.90089 −0.436709
\(515\) 0 0
\(516\) 11.4530 0.504191
\(517\) 25.2359 1.10987
\(518\) 21.7265 0.954608
\(519\) −27.6770 −1.21488
\(520\) 0 0
\(521\) 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 \(-0.362775\pi\)
0.417874 + 0.908505i \(0.362775\pi\)
\(524\) 10.7641 0.470234
\(525\) 0 0
\(526\) −7.25725 −0.316431
\(527\) −20.4197 −0.889496
\(528\) 9.26157 0.403058
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −6.52314 −0.283080
\(532\) −9.53074 −0.413210
\(533\) −22.1462 −0.959259
\(534\) 24.0000 1.03858
\(535\) 0 0
\(536\) −10.0753 −0.435185
\(537\) −3.11290 −0.134332
\(538\) 6.93852 0.299141
\(539\) −16.3720 −0.705193
\(540\) 0 0
\(541\) 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
\(545\) 0 0
\(546\) 17.4598 0.747210
\(547\) −13.8513 −0.592240 −0.296120 0.955151i \(-0.595693\pi\)
−0.296120 + 0.955151i \(0.595693\pi\)
\(548\) −3.26157 −0.139327
\(549\) 12.8375 0.547893
\(550\) 0 0
\(551\) 2.66503 0.113534
\(552\) 1.43163 0.0609341
\(553\) −48.7831 −2.07447
\(554\) −17.8018 −0.756325
\(555\) 0 0
\(556\) −16.9385 −0.718353
\(557\) 28.7641 1.21878 0.609388 0.792872i \(-0.291415\pi\)
0.609388 + 0.792872i \(0.291415\pi\)
\(558\) −5.65556 −0.239419
\(559\) 31.6036 1.33669
\(560\) 0 0
\(561\) 31.7823 1.34185
\(562\) 18.9385 0.798873
\(563\) −36.1505 −1.52356 −0.761782 0.647834i \(-0.775675\pi\)
−0.761782 + 0.647834i \(0.775675\pi\)
\(564\) 5.58462 0.235155
\(565\) 0 0
\(566\) 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 \(0.569601\pi\)
\(570\) 0 0
\(571\) 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
\(575\) 0 0
\(576\) −0.950444 −0.0396018
\(577\) 34.1505 1.42171 0.710853 0.703341i \(-0.248309\pi\)
0.710853 + 0.703341i \(0.248309\pi\)
\(578\) 5.22394 0.217287
\(579\) 3.50444 0.145639
\(580\) 0 0
\(581\) 27.9009 1.15752
\(582\) 20.4649 0.848299
\(583\) −38.8156 −1.60758
\(584\) 5.90089 0.244180
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) 5.19062 0.214240 0.107120 0.994246i \(-0.465837\pi\)
0.107120 + 0.994246i \(0.465837\pi\)
\(588\) −3.62308 −0.149413
\(589\) −18.3701 −0.756929
\(590\) 0 0
\(591\) −15.3796 −0.632633
\(592\) 7.03763 0.289245
\(593\) 2.09911 0.0862002 0.0431001 0.999071i \(-0.486277\pi\)
0.0431001 + 0.999071i \(0.486277\pi\)
\(594\) 36.5873 1.50120
\(595\) 0 0
\(596\) 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 \(0.426796\pi\)
\(600\) 0 0
\(601\) 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
\(605\) 0 0
\(606\) 1.23586 0.0502033
\(607\) 24.6975 1.00244 0.501221 0.865320i \(-0.332885\pi\)
0.501221 + 0.865320i \(0.332885\pi\)
\(608\) −3.08719 −0.125202
\(609\) 3.81533 0.154605
\(610\) 0 0
\(611\) 15.4102 0.623431
\(612\) −3.26157 −0.131841
\(613\) 26.3488 1.06422 0.532108 0.846676i \(-0.321400\pi\)
0.532108 + 0.846676i \(0.321400\pi\)
\(614\) −22.9599 −0.926587
\(615\) 0 0
\(616\) −19.9718 −0.804688
\(617\) −5.94612 −0.239382 −0.119691 0.992811i \(-0.538190\pi\)
−0.119691 + 0.992811i \(0.538190\pi\)
\(618\) −2.19145 −0.0881530
\(619\) 39.6856 1.59510 0.797549 0.603254i \(-0.206129\pi\)
0.797549 + 0.603254i \(0.206129\pi\)
\(620\) 0 0
\(621\) 5.65556 0.226950
\(622\) −18.0753 −0.724752
\(623\) −51.7541 −2.07348
\(624\) 5.65556 0.226404
\(625\) 0 0
\(626\) 15.1625 0.606014
\(627\) 28.5922 1.14186
\(628\) −7.13675 −0.284787
\(629\) 24.1505 0.962945
\(630\) 0 0
\(631\) −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
\(635\) 0 0
\(636\) −8.58976 −0.340606
\(637\) −9.99754 −0.396117
\(638\) 5.58462 0.221097
\(639\) −2.44109 −0.0965682
\(640\) 0 0
\(641\) 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 \(-0.394864\pi\)
0.324320 + 0.945947i \(0.394864\pi\)
\(644\) −3.08719 −0.121652
\(645\) 0 0
\(646\) −10.5941 −0.416819
\(647\) 34.9147 1.37264 0.686319 0.727301i \(-0.259226\pi\)
0.686319 + 0.727301i \(0.259226\pi\)
\(648\) 5.24533 0.206056
\(649\) −44.4002 −1.74286
\(650\) 0 0
\(651\) −26.2992 −1.03075
\(652\) 8.12482 0.318193
\(653\) 34.2754 1.34130 0.670649 0.741775i \(-0.266016\pi\)
0.670649 + 0.741775i \(0.266016\pi\)
\(654\) −4.17006 −0.163062
\(655\) 0 0
\(656\) 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 \(0.259074\pi\)
\(660\) 0 0
\(661\) 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
\(665\) 0 0
\(666\) 6.68888 0.259189
\(667\) 0.863254 0.0334253
\(668\) 7.80178 0.301860
\(669\) −8.19822 −0.316962
\(670\) 0 0
\(671\) 87.3796 3.37325
\(672\) −4.41970 −0.170494
\(673\) 23.8770 0.920392 0.460196 0.887817i \(-0.347779\pi\)
0.460196 + 0.887817i \(0.347779\pi\)
\(674\) 14.7146 0.566785
\(675\) 0 0
\(676\) 2.60601 0.100231
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 8.58976 0.329888
\(679\) −44.1310 −1.69359
\(680\) 0 0
\(681\) −25.2359 −0.967040
\(682\) −38.4950 −1.47405
\(683\) −34.6480 −1.32577 −0.662884 0.748722i \(-0.730668\pi\)
−0.662884 + 0.748722i \(0.730668\pi\)
\(684\) −2.93420 −0.112192
\(685\) 0 0
\(686\) −13.7975 −0.526789
\(687\) 23.0138 0.878031
\(688\) −8.00000 −0.304997
\(689\) −23.7027 −0.903000
\(690\) 0 0
\(691\) −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
\(695\) 0 0
\(696\) 1.23586 0.0468451
\(697\) 19.2377 0.728681
\(698\) −18.3488 −0.694511
\(699\) −9.23095 −0.349146
\(700\) 0 0
\(701\) −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
\(705\) 0 0
\(706\) −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 \(0.665414\pi\)
\(710\) 0 0
\(711\) −15.0187 −0.563245
\(712\) −16.7641 −0.628263
\(713\) −5.95044 −0.222846
\(714\) −15.1668 −0.567602
\(715\) 0 0
\(716\) 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 0
\(721\) 4.72568 0.175994
\(722\) 9.46926 0.352409
\(723\) −1.09397 −0.0406850
\(724\) −7.26157 −0.269874
\(725\) 0 0
\(726\) 44.1676 1.63921
\(727\) −21.4830 −0.796762 −0.398381 0.917220i \(-0.630428\pi\)
−0.398381 + 0.917220i \(0.630428\pi\)
\(728\) −12.1958 −0.452005
\(729\) 29.2754 1.08427
\(730\) 0 0
\(731\) −27.4530 −1.01539
\(732\) 19.3368 0.714710
\(733\) −11.3778 −0.420247 −0.210123 0.977675i \(-0.567387\pi\)
−0.210123 + 0.977675i \(0.567387\pi\)
\(734\) −2.27349 −0.0839161
\(735\) 0 0
\(736\) −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 \(0.368183\pi\)
\(740\) 0 0
\(741\) 17.4598 0.641402
\(742\) 18.5231 0.680006
\(743\) −5.36068 −0.196664 −0.0983322 0.995154i \(-0.531351\pi\)
−0.0983322 + 0.995154i \(0.531351\pi\)
\(744\) −8.51882 −0.312315
\(745\) 0 0
\(746\) 23.9762 0.877829
\(747\) 8.58976 0.314283
\(748\) −22.2001 −0.811716
\(749\) 54.4191 1.98843
\(750\) 0 0
\(751\) 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 0
\(756\) −17.4598 −0.635007
\(757\) −41.9437 −1.52447 −0.762234 0.647301i \(-0.775898\pi\)
−0.762234 + 0.647301i \(0.775898\pi\)
\(758\) 13.8795 0.504126
\(759\) 9.26157 0.336174
\(760\) 0 0
\(761\) −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
\(765\) 0 0
\(766\) 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 \(0.222105\pi\)
\(770\) 0 0
\(771\) −14.1744 −0.510478
\(772\) −2.44787 −0.0881008
\(773\) 15.0376 0.540866 0.270433 0.962739i \(-0.412833\pi\)
0.270433 + 0.962739i \(0.412833\pi\)
\(774\) −7.60355 −0.273304
\(775\) 0 0
\(776\) −14.2949 −0.513156
\(777\) 31.1043 1.11586
\(778\) 26.6436 0.955221
\(779\) 17.3068 0.620081
\(780\) 0 0
\(781\) −16.6155 −0.594548
\(782\) −3.43163 −0.122715
\(783\) 4.88219 0.174475
\(784\) 2.53074 0.0903836
\(785\) 0 0
\(786\) 15.4102 0.549665
\(787\) 8.39154 0.299126 0.149563 0.988752i \(-0.452213\pi\)
0.149563 + 0.988752i \(0.452213\pi\)
\(788\) 10.7428 0.382695
\(789\) −10.3897 −0.369882
\(790\) 0 0
\(791\) −18.5231 −0.658607
\(792\) −6.14867 −0.218483
\(793\) 53.3582 1.89481
\(794\) −8.66749 −0.307598
\(795\) 0 0
\(796\) −11.3111 −0.400912
\(797\) 22.0514 0.781101 0.390551 0.920581i \(-0.372285\pi\)
0.390551 + 0.920581i \(0.372285\pi\)
\(798\) −13.6445 −0.483009
\(799\) −13.3864 −0.473576
\(800\) 0 0
\(801\) −15.9334 −0.562978
\(802\) −39.9762 −1.41161
\(803\) 38.1744 1.34714
\(804\) −14.4240 −0.508696
\(805\) 0 0
\(806\) −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 \(0.488553\pi\)
\(810\) 0 0
\(811\) 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
\(815\) 0 0
\(816\) −4.91281 −0.171983
\(817\) −24.6975 −0.864057
\(818\) −30.1248 −1.05329
\(819\) −11.5914 −0.405036
\(820\) 0 0
\(821\) −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 \(-0.576087\pi\)
−0.236765 + 0.971567i \(0.576087\pi\)
\(824\) 1.53074 0.0533258
\(825\) 0 0
\(826\) 21.1882 0.737231
\(827\) −24.7880 −0.861963 −0.430981 0.902361i \(-0.641833\pi\)
−0.430981 + 0.902361i \(0.641833\pi\)
\(828\) −0.950444 −0.0330302
\(829\) 26.1505 0.908246 0.454123 0.890939i \(-0.349953\pi\)
0.454123 + 0.890939i \(0.349953\pi\)
\(830\) 0 0
\(831\) −25.4855 −0.884082
\(832\) −3.95044 −0.136957
\(833\) 8.68455 0.300902
\(834\) −24.2496 −0.839697
\(835\) 0 0
\(836\) −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 \(0.464914\pi\)
\(840\) 0 0
\(841\) −28.2548 −0.974303
\(842\) 10.7146 0.369249
\(843\) 27.1129 0.933818
\(844\) 23.1129 0.795579
\(845\) 0 0
\(846\) −3.70757 −0.127469
\(847\) −95.2439 −3.27262
\(848\) 6.00000 0.206041
\(849\) 18.1657 0.623447
\(850\) 0 0
\(851\) 7.03763 0.241247
\(852\) −3.67695 −0.125970
\(853\) 33.6293 1.15144 0.575722 0.817646i \(-0.304721\pi\)
0.575722 + 0.817646i \(0.304721\pi\)
\(854\) −41.6983 −1.42689
\(855\) 0 0
\(856\) 17.6274 0.602492
\(857\) −11.1795 −0.381885 −0.190943 0.981601i \(-0.561154\pi\)
−0.190943 + 0.981601i \(0.561154\pi\)
\(858\) 36.5873 1.24907
\(859\) 47.9009 1.63436 0.817179 0.576385i \(-0.195537\pi\)
0.817179 + 0.576385i \(0.195537\pi\)
\(860\) 0 0
\(861\) 24.7769 0.844394
\(862\) −32.2496 −1.09843
\(863\) 30.1180 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(864\) −5.65556 −0.192406
\(865\) 0 0
\(866\) 20.6393 0.701353
\(867\) 7.47873 0.253991
\(868\) 18.3701 0.623523
\(869\) −102.226 −3.46777
\(870\) 0 0
\(871\) −39.8018 −1.34863
\(872\) 2.91281 0.0986402
\(873\) −13.5865 −0.459833
\(874\) −3.08719 −0.104426
\(875\) 0 0
\(876\) 8.44787 0.285427
\(877\) 22.3940 0.756191 0.378096 0.925767i \(-0.376579\pi\)
0.378096 + 0.925767i \(0.376579\pi\)
\(878\) 16.2239 0.547531
\(879\) −8.58976 −0.289726
\(880\) 0 0
\(881\) 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 \(-0.809545\pi\)
−0.826276 + 0.563265i \(0.809545\pi\)
\(884\) −13.5565 −0.455953
\(885\) 0 0
\(886\) −15.6770 −0.526678
\(887\) 43.0566 1.44570 0.722849 0.691006i \(-0.242832\pi\)
0.722849 + 0.691006i \(0.242832\pi\)
\(888\) 10.0753 0.338104
\(889\) 64.6412 2.16800
\(890\) 0 0
\(891\) 33.9334 1.13681
\(892\) 5.72651 0.191738
\(893\) −12.0428 −0.402996
\(894\) 4.66935 0.156166
\(895\) 0 0
\(896\) 3.08719 0.103136
\(897\) 5.65556 0.188834
\(898\) −22.5727 −0.753261
\(899\) −5.13675 −0.171320
\(900\) 0 0
\(901\) 20.5898 0.685944
\(902\) 36.2667 1.20755
\(903\) −35.3576 −1.17663
\(904\) −6.00000 −0.199557
\(905\) 0 0
\(906\) 0.422160 0.0140253
\(907\) 37.9762 1.26098 0.630489 0.776198i \(-0.282854\pi\)
0.630489 + 0.776198i \(0.282854\pi\)
\(908\) 17.6274 0.584986
\(909\) −0.820475 −0.0272134
\(910\) 0 0
\(911\) −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
\(915\) 0 0
\(916\) −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 \(0.332672\pi\)
\(920\) 0 0
\(921\) −32.8700 −1.08310
\(922\) 29.7027 0.978205
\(923\) −10.1462 −0.333967
\(924\) −28.5922 −0.940615
\(925\) 0 0
\(926\) 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 \(0.712915\pi\)
\(930\) 0 0
\(931\) 7.81287 0.256057
\(932\) 6.44787 0.211207
\(933\) −25.8770 −0.847176
\(934\) 9.48550 0.310375
\(935\) 0 0
\(936\) −3.75467 −0.122725
\(937\) 32.6907 1.06796 0.533980 0.845497i \(-0.320696\pi\)
0.533980 + 0.845497i \(0.320696\pi\)
\(938\) 31.1043 1.01559
\(939\) 21.7070 0.708381
\(940\) 0 0
\(941\) −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
\(945\) 0 0
\(946\) −51.7541 −1.68267
\(947\) 37.2052 1.20901 0.604504 0.796602i \(-0.293371\pi\)
0.604504 + 0.796602i \(0.293371\pi\)
\(948\) −22.6222 −0.734737
\(949\) 23.3111 0.756711
\(950\) 0 0
\(951\) 20.0796 0.651125
\(952\) 10.5941 0.343356
\(953\) −49.1104 −1.59084 −0.795422 0.606056i \(-0.792751\pi\)
−0.795422 + 0.606056i \(0.792751\pi\)
\(954\) 5.70266 0.184631
\(955\) 0 0
\(956\) 4.34876 0.140649
\(957\) 7.99509 0.258445
\(958\) 30.5659 0.987540
\(959\) 10.0691 0.325148
\(960\) 0 0
\(961\) 4.40778 0.142187
\(962\) 27.8018 0.896365
\(963\) 16.7538 0.539885
\(964\) 0.764142 0.0246114
\(965\) 0 0
\(966\) −4.41970 −0.142202
\(967\) −1.96751 −0.0632709 −0.0316355 0.999499i \(-0.510072\pi\)
−0.0316355 + 0.999499i \(0.510072\pi\)
\(968\) −30.8513 −0.991599
\(969\) −15.1668 −0.487227
\(970\) 0 0
\(971\) 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
\(975\) 0 0
\(976\) −13.5069 −0.432345
\(977\) 0.639319 0.0204536 0.0102268 0.999948i \(-0.496745\pi\)
0.0102268 + 0.999948i \(0.496745\pi\)
\(978\) 11.6317 0.371941
\(979\) −108.452 −3.46613
\(980\) 0 0
\(981\) 2.76846 0.0883902
\(982\) 28.0514 0.895157
\(983\) 6.46926 0.206337 0.103169 0.994664i \(-0.467102\pi\)
0.103169 + 0.994664i \(0.467102\pi\)
\(984\) 8.02571 0.255850
\(985\) 0 0
\(986\) −2.96237 −0.0943410
\(987\) −17.2408 −0.548780
\(988\) −12.1958 −0.387999
\(989\) −8.00000 −0.254385
\(990\) 0 0
\(991\) 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
\(995\) 0 0
\(996\) 12.9385 0.409973
\(997\) −9.65124 −0.305658 −0.152829 0.988253i \(-0.548838\pi\)
−0.152829 + 0.988253i \(0.548838\pi\)
\(998\) −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 1150.2.a.q.1.2 3
4.3 odd 2 9200.2.a.cf.1.2 3
5.2 odd 4 1150.2.b.j.599.2 6
5.3 odd 4 1150.2.b.j.599.5 6
5.4 even 2 230.2.a.d.1.2 3
15.14 odd 2 2070.2.a.z.1.2 3
20.19 odd 2 1840.2.a.r.1.2 3
40.19 odd 2 7360.2.a.ce.1.2 3
40.29 even 2 7360.2.a.bz.1.2 3
115.114 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 5.4 even 2
1150.2.a.q.1.2 3 1.1 even 1 trivial
1150.2.b.j.599.2 6 5.2 odd 4
1150.2.b.j.599.5 6 5.3 odd 4
1840.2.a.r.1.2 3 20.19 odd 2
2070.2.a.z.1.2 3 15.14 odd 2
5290.2.a.r.1.2 3 115.114 odd 2
7360.2.a.bz.1.2 3 40.29 even 2
7360.2.a.ce.1.2 3 40.19 odd 2
9200.2.a.cf.1.2 3 4.3 odd 2