Properties

Label 8034.2.a.l.1.2
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{17}) \)
Defining polynomial: \(x^{2} - x - 4\)
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 1.2
Root \(2.56155\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} +1.00000 q^{6} +3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{10} +1.56155 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.56155 q^{14} +2.00000 q^{15} +1.00000 q^{16} +7.56155 q^{17} -1.00000 q^{18} -2.00000 q^{19} -2.00000 q^{20} -3.56155 q^{21} -1.56155 q^{22} -5.12311 q^{23} +1.00000 q^{24} -1.00000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.56155 q^{28} +6.00000 q^{29} -2.00000 q^{30} -7.12311 q^{31} -1.00000 q^{32} -1.56155 q^{33} -7.56155 q^{34} -7.12311 q^{35} +1.00000 q^{36} -0.876894 q^{37} +2.00000 q^{38} +1.00000 q^{39} +2.00000 q^{40} +2.00000 q^{41} +3.56155 q^{42} -7.12311 q^{43} +1.56155 q^{44} -2.00000 q^{45} +5.12311 q^{46} +6.24621 q^{47} -1.00000 q^{48} +5.68466 q^{49} +1.00000 q^{50} -7.56155 q^{51} -1.00000 q^{52} +2.43845 q^{53} +1.00000 q^{54} -3.12311 q^{55} -3.56155 q^{56} +2.00000 q^{57} -6.00000 q^{58} -8.00000 q^{59} +2.00000 q^{60} +2.87689 q^{61} +7.12311 q^{62} +3.56155 q^{63} +1.00000 q^{64} +2.00000 q^{65} +1.56155 q^{66} -0.684658 q^{67} +7.56155 q^{68} +5.12311 q^{69} +7.12311 q^{70} -14.2462 q^{71} -1.00000 q^{72} -8.68466 q^{73} +0.876894 q^{74} +1.00000 q^{75} -2.00000 q^{76} +5.56155 q^{77} -1.00000 q^{78} -17.3693 q^{79} -2.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} -13.3693 q^{83} -3.56155 q^{84} -15.1231 q^{85} +7.12311 q^{86} -6.00000 q^{87} -1.56155 q^{88} +2.00000 q^{89} +2.00000 q^{90} -3.56155 q^{91} -5.12311 q^{92} +7.12311 q^{93} -6.24621 q^{94} +4.00000 q^{95} +1.00000 q^{96} -12.2462 q^{97} -5.68466 q^{98} +1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 2q^{3} + 2q^{4} - 4q^{5} + 2q^{6} + 3q^{7} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 2q^{3} + 2q^{4} - 4q^{5} + 2q^{6} + 3q^{7} - 2q^{8} + 2q^{9} + 4q^{10} - q^{11} - 2q^{12} - 2q^{13} - 3q^{14} + 4q^{15} + 2q^{16} + 11q^{17} - 2q^{18} - 4q^{19} - 4q^{20} - 3q^{21} + q^{22} - 2q^{23} + 2q^{24} - 2q^{25} + 2q^{26} - 2q^{27} + 3q^{28} + 12q^{29} - 4q^{30} - 6q^{31} - 2q^{32} + q^{33} - 11q^{34} - 6q^{35} + 2q^{36} - 10q^{37} + 4q^{38} + 2q^{39} + 4q^{40} + 4q^{41} + 3q^{42} - 6q^{43} - q^{44} - 4q^{45} + 2q^{46} - 4q^{47} - 2q^{48} - q^{49} + 2q^{50} - 11q^{51} - 2q^{52} + 9q^{53} + 2q^{54} + 2q^{55} - 3q^{56} + 4q^{57} - 12q^{58} - 16q^{59} + 4q^{60} + 14q^{61} + 6q^{62} + 3q^{63} + 2q^{64} + 4q^{65} - q^{66} + 11q^{67} + 11q^{68} + 2q^{69} + 6q^{70} - 12q^{71} - 2q^{72} - 5q^{73} + 10q^{74} + 2q^{75} - 4q^{76} + 7q^{77} - 2q^{78} - 10q^{79} - 4q^{80} + 2q^{81} - 4q^{82} - 2q^{83} - 3q^{84} - 22q^{85} + 6q^{86} - 12q^{87} + q^{88} + 4q^{89} + 4q^{90} - 3q^{91} - 2q^{92} + 6q^{93} + 4q^{94} + 8q^{95} + 2q^{96} - 8q^{97} + q^{98} - q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.56155 1.34614 0.673070 0.739579i \(-0.264975\pi\)
0.673070 + 0.739579i \(0.264975\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.00000 0.632456
\(11\) 1.56155 0.470826 0.235413 0.971895i \(-0.424356\pi\)
0.235413 + 0.971895i \(0.424356\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) −3.56155 −0.951865
\(15\) 2.00000 0.516398
\(16\) 1.00000 0.250000
\(17\) 7.56155 1.83395 0.916973 0.398949i \(-0.130625\pi\)
0.916973 + 0.398949i \(0.130625\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) −2.00000 −0.447214
\(21\) −3.56155 −0.777195
\(22\) −1.56155 −0.332924
\(23\) −5.12311 −1.06824 −0.534121 0.845408i \(-0.679357\pi\)
−0.534121 + 0.845408i \(0.679357\pi\)
\(24\) 1.00000 0.204124
\(25\) −1.00000 −0.200000
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) 3.56155 0.673070
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −2.00000 −0.365148
\(31\) −7.12311 −1.27935 −0.639674 0.768647i \(-0.720931\pi\)
−0.639674 + 0.768647i \(0.720931\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.56155 −0.271831
\(34\) −7.56155 −1.29680
\(35\) −7.12311 −1.20402
\(36\) 1.00000 0.166667
\(37\) −0.876894 −0.144161 −0.0720803 0.997399i \(-0.522964\pi\)
−0.0720803 + 0.997399i \(0.522964\pi\)
\(38\) 2.00000 0.324443
\(39\) 1.00000 0.160128
\(40\) 2.00000 0.316228
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 3.56155 0.549560
\(43\) −7.12311 −1.08626 −0.543132 0.839648i \(-0.682762\pi\)
−0.543132 + 0.839648i \(0.682762\pi\)
\(44\) 1.56155 0.235413
\(45\) −2.00000 −0.298142
\(46\) 5.12311 0.755361
\(47\) 6.24621 0.911104 0.455552 0.890209i \(-0.349442\pi\)
0.455552 + 0.890209i \(0.349442\pi\)
\(48\) −1.00000 −0.144338
\(49\) 5.68466 0.812094
\(50\) 1.00000 0.141421
\(51\) −7.56155 −1.05883
\(52\) −1.00000 −0.138675
\(53\) 2.43845 0.334946 0.167473 0.985877i \(-0.446439\pi\)
0.167473 + 0.985877i \(0.446439\pi\)
\(54\) 1.00000 0.136083
\(55\) −3.12311 −0.421119
\(56\) −3.56155 −0.475933
\(57\) 2.00000 0.264906
\(58\) −6.00000 −0.787839
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 2.00000 0.258199
\(61\) 2.87689 0.368349 0.184174 0.982894i \(-0.441039\pi\)
0.184174 + 0.982894i \(0.441039\pi\)
\(62\) 7.12311 0.904635
\(63\) 3.56155 0.448713
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) 1.56155 0.192214
\(67\) −0.684658 −0.0836443 −0.0418222 0.999125i \(-0.513316\pi\)
−0.0418222 + 0.999125i \(0.513316\pi\)
\(68\) 7.56155 0.916973
\(69\) 5.12311 0.616749
\(70\) 7.12311 0.851374
\(71\) −14.2462 −1.69071 −0.845357 0.534202i \(-0.820612\pi\)
−0.845357 + 0.534202i \(0.820612\pi\)
\(72\) −1.00000 −0.117851
\(73\) −8.68466 −1.01646 −0.508231 0.861221i \(-0.669700\pi\)
−0.508231 + 0.861221i \(0.669700\pi\)
\(74\) 0.876894 0.101937
\(75\) 1.00000 0.115470
\(76\) −2.00000 −0.229416
\(77\) 5.56155 0.633798
\(78\) −1.00000 −0.113228
\(79\) −17.3693 −1.95420 −0.977100 0.212779i \(-0.931749\pi\)
−0.977100 + 0.212779i \(0.931749\pi\)
\(80\) −2.00000 −0.223607
\(81\) 1.00000 0.111111
\(82\) −2.00000 −0.220863
\(83\) −13.3693 −1.46747 −0.733737 0.679434i \(-0.762225\pi\)
−0.733737 + 0.679434i \(0.762225\pi\)
\(84\) −3.56155 −0.388597
\(85\) −15.1231 −1.64033
\(86\) 7.12311 0.768104
\(87\) −6.00000 −0.643268
\(88\) −1.56155 −0.166462
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 2.00000 0.210819
\(91\) −3.56155 −0.373352
\(92\) −5.12311 −0.534121
\(93\) 7.12311 0.738632
\(94\) −6.24621 −0.644247
\(95\) 4.00000 0.410391
\(96\) 1.00000 0.102062
\(97\) −12.2462 −1.24341 −0.621707 0.783250i \(-0.713561\pi\)
−0.621707 + 0.783250i \(0.713561\pi\)
\(98\) −5.68466 −0.574237
\(99\) 1.56155 0.156942
\(100\) −1.00000 −0.100000
\(101\) 8.68466 0.864156 0.432078 0.901836i \(-0.357781\pi\)
0.432078 + 0.901836i \(0.357781\pi\)
\(102\) 7.56155 0.748705
\(103\) −1.00000 −0.0985329
\(104\) 1.00000 0.0980581
\(105\) 7.12311 0.695144
\(106\) −2.43845 −0.236843
\(107\) 4.43845 0.429081 0.214540 0.976715i \(-0.431175\pi\)
0.214540 + 0.976715i \(0.431175\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 10.2462 0.981409 0.490705 0.871326i \(-0.336739\pi\)
0.490705 + 0.871326i \(0.336739\pi\)
\(110\) 3.12311 0.297776
\(111\) 0.876894 0.0832311
\(112\) 3.56155 0.336535
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) −2.00000 −0.187317
\(115\) 10.2462 0.955464
\(116\) 6.00000 0.557086
\(117\) −1.00000 −0.0924500
\(118\) 8.00000 0.736460
\(119\) 26.9309 2.46875
\(120\) −2.00000 −0.182574
\(121\) −8.56155 −0.778323
\(122\) −2.87689 −0.260462
\(123\) −2.00000 −0.180334
\(124\) −7.12311 −0.639674
\(125\) 12.0000 1.07331
\(126\) −3.56155 −0.317288
\(127\) 0.684658 0.0607536 0.0303768 0.999539i \(-0.490329\pi\)
0.0303768 + 0.999539i \(0.490329\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.12311 0.627154
\(130\) −2.00000 −0.175412
\(131\) −3.36932 −0.294379 −0.147189 0.989108i \(-0.547023\pi\)
−0.147189 + 0.989108i \(0.547023\pi\)
\(132\) −1.56155 −0.135916
\(133\) −7.12311 −0.617652
\(134\) 0.684658 0.0591455
\(135\) 2.00000 0.172133
\(136\) −7.56155 −0.648398
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −5.12311 −0.436108
\(139\) 7.80776 0.662246 0.331123 0.943588i \(-0.392573\pi\)
0.331123 + 0.943588i \(0.392573\pi\)
\(140\) −7.12311 −0.602012
\(141\) −6.24621 −0.526026
\(142\) 14.2462 1.19552
\(143\) −1.56155 −0.130584
\(144\) 1.00000 0.0833333
\(145\) −12.0000 −0.996546
\(146\) 8.68466 0.718747
\(147\) −5.68466 −0.468863
\(148\) −0.876894 −0.0720803
\(149\) 18.6847 1.53071 0.765353 0.643610i \(-0.222564\pi\)
0.765353 + 0.643610i \(0.222564\pi\)
\(150\) −1.00000 −0.0816497
\(151\) 17.3693 1.41349 0.706747 0.707466i \(-0.250162\pi\)
0.706747 + 0.707466i \(0.250162\pi\)
\(152\) 2.00000 0.162221
\(153\) 7.56155 0.611315
\(154\) −5.56155 −0.448163
\(155\) 14.2462 1.14428
\(156\) 1.00000 0.0800641
\(157\) 13.8078 1.10198 0.550990 0.834512i \(-0.314250\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(158\) 17.3693 1.38183
\(159\) −2.43845 −0.193381
\(160\) 2.00000 0.158114
\(161\) −18.2462 −1.43800
\(162\) −1.00000 −0.0785674
\(163\) 10.4924 0.821830 0.410915 0.911674i \(-0.365209\pi\)
0.410915 + 0.911674i \(0.365209\pi\)
\(164\) 2.00000 0.156174
\(165\) 3.12311 0.243133
\(166\) 13.3693 1.03766
\(167\) −23.8078 −1.84230 −0.921150 0.389208i \(-0.872749\pi\)
−0.921150 + 0.389208i \(0.872749\pi\)
\(168\) 3.56155 0.274780
\(169\) 1.00000 0.0769231
\(170\) 15.1231 1.15989
\(171\) −2.00000 −0.152944
\(172\) −7.12311 −0.543132
\(173\) 0.192236 0.0146154 0.00730771 0.999973i \(-0.497674\pi\)
0.00730771 + 0.999973i \(0.497674\pi\)
\(174\) 6.00000 0.454859
\(175\) −3.56155 −0.269228
\(176\) 1.56155 0.117706
\(177\) 8.00000 0.601317
\(178\) −2.00000 −0.149906
\(179\) 9.80776 0.733067 0.366533 0.930405i \(-0.380545\pi\)
0.366533 + 0.930405i \(0.380545\pi\)
\(180\) −2.00000 −0.149071
\(181\) −12.9309 −0.961144 −0.480572 0.876955i \(-0.659571\pi\)
−0.480572 + 0.876955i \(0.659571\pi\)
\(182\) 3.56155 0.264000
\(183\) −2.87689 −0.212666
\(184\) 5.12311 0.377680
\(185\) 1.75379 0.128941
\(186\) −7.12311 −0.522291
\(187\) 11.8078 0.863469
\(188\) 6.24621 0.455552
\(189\) −3.56155 −0.259065
\(190\) −4.00000 −0.290191
\(191\) 8.68466 0.628400 0.314200 0.949357i \(-0.398264\pi\)
0.314200 + 0.949357i \(0.398264\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −25.3693 −1.82612 −0.913062 0.407821i \(-0.866289\pi\)
−0.913062 + 0.407821i \(0.866289\pi\)
\(194\) 12.2462 0.879227
\(195\) −2.00000 −0.143223
\(196\) 5.68466 0.406047
\(197\) −14.4924 −1.03254 −0.516271 0.856425i \(-0.672680\pi\)
−0.516271 + 0.856425i \(0.672680\pi\)
\(198\) −1.56155 −0.110975
\(199\) −7.31534 −0.518571 −0.259285 0.965801i \(-0.583487\pi\)
−0.259285 + 0.965801i \(0.583487\pi\)
\(200\) 1.00000 0.0707107
\(201\) 0.684658 0.0482921
\(202\) −8.68466 −0.611050
\(203\) 21.3693 1.49983
\(204\) −7.56155 −0.529415
\(205\) −4.00000 −0.279372
\(206\) 1.00000 0.0696733
\(207\) −5.12311 −0.356080
\(208\) −1.00000 −0.0693375
\(209\) −3.12311 −0.216030
\(210\) −7.12311 −0.491541
\(211\) −24.4924 −1.68613 −0.843064 0.537813i \(-0.819251\pi\)
−0.843064 + 0.537813i \(0.819251\pi\)
\(212\) 2.43845 0.167473
\(213\) 14.2462 0.976134
\(214\) −4.43845 −0.303406
\(215\) 14.2462 0.971584
\(216\) 1.00000 0.0680414
\(217\) −25.3693 −1.72218
\(218\) −10.2462 −0.693961
\(219\) 8.68466 0.586855
\(220\) −3.12311 −0.210560
\(221\) −7.56155 −0.508645
\(222\) −0.876894 −0.0588533
\(223\) 6.68466 0.447638 0.223819 0.974631i \(-0.428148\pi\)
0.223819 + 0.974631i \(0.428148\pi\)
\(224\) −3.56155 −0.237966
\(225\) −1.00000 −0.0666667
\(226\) −4.00000 −0.266076
\(227\) 15.8078 1.04920 0.524599 0.851349i \(-0.324215\pi\)
0.524599 + 0.851349i \(0.324215\pi\)
\(228\) 2.00000 0.132453
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) −10.2462 −0.675615
\(231\) −5.56155 −0.365923
\(232\) −6.00000 −0.393919
\(233\) −8.49242 −0.556357 −0.278179 0.960529i \(-0.589731\pi\)
−0.278179 + 0.960529i \(0.589731\pi\)
\(234\) 1.00000 0.0653720
\(235\) −12.4924 −0.814916
\(236\) −8.00000 −0.520756
\(237\) 17.3693 1.12826
\(238\) −26.9309 −1.74567
\(239\) 1.56155 0.101008 0.0505042 0.998724i \(-0.483917\pi\)
0.0505042 + 0.998724i \(0.483917\pi\)
\(240\) 2.00000 0.129099
\(241\) −20.6847 −1.33242 −0.666208 0.745766i \(-0.732084\pi\)
−0.666208 + 0.745766i \(0.732084\pi\)
\(242\) 8.56155 0.550357
\(243\) −1.00000 −0.0641500
\(244\) 2.87689 0.184174
\(245\) −11.3693 −0.726359
\(246\) 2.00000 0.127515
\(247\) 2.00000 0.127257
\(248\) 7.12311 0.452318
\(249\) 13.3693 0.847246
\(250\) −12.0000 −0.758947
\(251\) 22.2462 1.40417 0.702084 0.712094i \(-0.252253\pi\)
0.702084 + 0.712094i \(0.252253\pi\)
\(252\) 3.56155 0.224357
\(253\) −8.00000 −0.502956
\(254\) −0.684658 −0.0429593
\(255\) 15.1231 0.947046
\(256\) 1.00000 0.0625000
\(257\) 12.8769 0.803239 0.401619 0.915807i \(-0.368448\pi\)
0.401619 + 0.915807i \(0.368448\pi\)
\(258\) −7.12311 −0.443465
\(259\) −3.12311 −0.194060
\(260\) 2.00000 0.124035
\(261\) 6.00000 0.371391
\(262\) 3.36932 0.208157
\(263\) 12.6847 0.782170 0.391085 0.920355i \(-0.372100\pi\)
0.391085 + 0.920355i \(0.372100\pi\)
\(264\) 1.56155 0.0961069
\(265\) −4.87689 −0.299585
\(266\) 7.12311 0.436746
\(267\) −2.00000 −0.122398
\(268\) −0.684658 −0.0418222
\(269\) −28.2462 −1.72220 −0.861101 0.508434i \(-0.830225\pi\)
−0.861101 + 0.508434i \(0.830225\pi\)
\(270\) −2.00000 −0.121716
\(271\) 13.3693 0.812128 0.406064 0.913845i \(-0.366901\pi\)
0.406064 + 0.913845i \(0.366901\pi\)
\(272\) 7.56155 0.458486
\(273\) 3.56155 0.215555
\(274\) 6.00000 0.362473
\(275\) −1.56155 −0.0941652
\(276\) 5.12311 0.308375
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) −7.80776 −0.468279
\(279\) −7.12311 −0.426449
\(280\) 7.12311 0.425687
\(281\) 10.4924 0.625925 0.312963 0.949765i \(-0.398679\pi\)
0.312963 + 0.949765i \(0.398679\pi\)
\(282\) 6.24621 0.371956
\(283\) −19.6155 −1.16602 −0.583011 0.812464i \(-0.698126\pi\)
−0.583011 + 0.812464i \(0.698126\pi\)
\(284\) −14.2462 −0.845357
\(285\) −4.00000 −0.236940
\(286\) 1.56155 0.0923366
\(287\) 7.12311 0.420464
\(288\) −1.00000 −0.0589256
\(289\) 40.1771 2.36336
\(290\) 12.0000 0.704664
\(291\) 12.2462 0.717886
\(292\) −8.68466 −0.508231
\(293\) 33.6155 1.96384 0.981920 0.189296i \(-0.0606206\pi\)
0.981920 + 0.189296i \(0.0606206\pi\)
\(294\) 5.68466 0.331536
\(295\) 16.0000 0.931556
\(296\) 0.876894 0.0509685
\(297\) −1.56155 −0.0906105
\(298\) −18.6847 −1.08237
\(299\) 5.12311 0.296277
\(300\) 1.00000 0.0577350
\(301\) −25.3693 −1.46226
\(302\) −17.3693 −0.999492
\(303\) −8.68466 −0.498921
\(304\) −2.00000 −0.114708
\(305\) −5.75379 −0.329461
\(306\) −7.56155 −0.432265
\(307\) 25.5616 1.45887 0.729437 0.684048i \(-0.239782\pi\)
0.729437 + 0.684048i \(0.239782\pi\)
\(308\) 5.56155 0.316899
\(309\) 1.00000 0.0568880
\(310\) −14.2462 −0.809130
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) −1.00000 −0.0566139
\(313\) 0.246211 0.0139167 0.00695834 0.999976i \(-0.497785\pi\)
0.00695834 + 0.999976i \(0.497785\pi\)
\(314\) −13.8078 −0.779217
\(315\) −7.12311 −0.401342
\(316\) −17.3693 −0.977100
\(317\) 24.0540 1.35101 0.675503 0.737357i \(-0.263927\pi\)
0.675503 + 0.737357i \(0.263927\pi\)
\(318\) 2.43845 0.136741
\(319\) 9.36932 0.524581
\(320\) −2.00000 −0.111803
\(321\) −4.43845 −0.247730
\(322\) 18.2462 1.01682
\(323\) −15.1231 −0.841472
\(324\) 1.00000 0.0555556
\(325\) 1.00000 0.0554700
\(326\) −10.4924 −0.581122
\(327\) −10.2462 −0.566617
\(328\) −2.00000 −0.110432
\(329\) 22.2462 1.22647
\(330\) −3.12311 −0.171921
\(331\) −6.93087 −0.380955 −0.190478 0.981692i \(-0.561004\pi\)
−0.190478 + 0.981692i \(0.561004\pi\)
\(332\) −13.3693 −0.733737
\(333\) −0.876894 −0.0480535
\(334\) 23.8078 1.30270
\(335\) 1.36932 0.0748138
\(336\) −3.56155 −0.194299
\(337\) 0.930870 0.0507077 0.0253539 0.999679i \(-0.491929\pi\)
0.0253539 + 0.999679i \(0.491929\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −4.00000 −0.217250
\(340\) −15.1231 −0.820166
\(341\) −11.1231 −0.602350
\(342\) 2.00000 0.108148
\(343\) −4.68466 −0.252948
\(344\) 7.12311 0.384052
\(345\) −10.2462 −0.551637
\(346\) −0.192236 −0.0103347
\(347\) −25.1231 −1.34868 −0.674339 0.738421i \(-0.735572\pi\)
−0.674339 + 0.738421i \(0.735572\pi\)
\(348\) −6.00000 −0.321634
\(349\) 18.2462 0.976697 0.488349 0.872649i \(-0.337599\pi\)
0.488349 + 0.872649i \(0.337599\pi\)
\(350\) 3.56155 0.190373
\(351\) 1.00000 0.0533761
\(352\) −1.56155 −0.0832310
\(353\) −26.6847 −1.42028 −0.710141 0.704060i \(-0.751369\pi\)
−0.710141 + 0.704060i \(0.751369\pi\)
\(354\) −8.00000 −0.425195
\(355\) 28.4924 1.51222
\(356\) 2.00000 0.106000
\(357\) −26.9309 −1.42533
\(358\) −9.80776 −0.518356
\(359\) −18.0540 −0.952852 −0.476426 0.879214i \(-0.658068\pi\)
−0.476426 + 0.879214i \(0.658068\pi\)
\(360\) 2.00000 0.105409
\(361\) −15.0000 −0.789474
\(362\) 12.9309 0.679631
\(363\) 8.56155 0.449365
\(364\) −3.56155 −0.186676
\(365\) 17.3693 0.909152
\(366\) 2.87689 0.150378
\(367\) −30.2462 −1.57884 −0.789420 0.613854i \(-0.789618\pi\)
−0.789420 + 0.613854i \(0.789618\pi\)
\(368\) −5.12311 −0.267060
\(369\) 2.00000 0.104116
\(370\) −1.75379 −0.0911751
\(371\) 8.68466 0.450885
\(372\) 7.12311 0.369316
\(373\) −4.63068 −0.239768 −0.119884 0.992788i \(-0.538252\pi\)
−0.119884 + 0.992788i \(0.538252\pi\)
\(374\) −11.8078 −0.610565
\(375\) −12.0000 −0.619677
\(376\) −6.24621 −0.322124
\(377\) −6.00000 −0.309016
\(378\) 3.56155 0.183187
\(379\) 7.80776 0.401058 0.200529 0.979688i \(-0.435734\pi\)
0.200529 + 0.979688i \(0.435734\pi\)
\(380\) 4.00000 0.205196
\(381\) −0.684658 −0.0350761
\(382\) −8.68466 −0.444346
\(383\) −28.4924 −1.45589 −0.727947 0.685633i \(-0.759526\pi\)
−0.727947 + 0.685633i \(0.759526\pi\)
\(384\) 1.00000 0.0510310
\(385\) −11.1231 −0.566886
\(386\) 25.3693 1.29126
\(387\) −7.12311 −0.362088
\(388\) −12.2462 −0.621707
\(389\) −1.56155 −0.0791739 −0.0395869 0.999216i \(-0.512604\pi\)
−0.0395869 + 0.999216i \(0.512604\pi\)
\(390\) 2.00000 0.101274
\(391\) −38.7386 −1.95910
\(392\) −5.68466 −0.287119
\(393\) 3.36932 0.169960
\(394\) 14.4924 0.730118
\(395\) 34.7386 1.74789
\(396\) 1.56155 0.0784710
\(397\) −23.6155 −1.18523 −0.592615 0.805486i \(-0.701904\pi\)
−0.592615 + 0.805486i \(0.701904\pi\)
\(398\) 7.31534 0.366685
\(399\) 7.12311 0.356601
\(400\) −1.00000 −0.0500000
\(401\) −19.3693 −0.967258 −0.483629 0.875273i \(-0.660682\pi\)
−0.483629 + 0.875273i \(0.660682\pi\)
\(402\) −0.684658 −0.0341477
\(403\) 7.12311 0.354827
\(404\) 8.68466 0.432078
\(405\) −2.00000 −0.0993808
\(406\) −21.3693 −1.06054
\(407\) −1.36932 −0.0678745
\(408\) 7.56155 0.374353
\(409\) −3.36932 −0.166602 −0.0833010 0.996524i \(-0.526546\pi\)
−0.0833010 + 0.996524i \(0.526546\pi\)
\(410\) 4.00000 0.197546
\(411\) 6.00000 0.295958
\(412\) −1.00000 −0.0492665
\(413\) −28.4924 −1.40202
\(414\) 5.12311 0.251787
\(415\) 26.7386 1.31255
\(416\) 1.00000 0.0490290
\(417\) −7.80776 −0.382348
\(418\) 3.12311 0.152756
\(419\) 8.93087 0.436302 0.218151 0.975915i \(-0.429998\pi\)
0.218151 + 0.975915i \(0.429998\pi\)
\(420\) 7.12311 0.347572
\(421\) −20.0540 −0.977371 −0.488685 0.872460i \(-0.662523\pi\)
−0.488685 + 0.872460i \(0.662523\pi\)
\(422\) 24.4924 1.19227
\(423\) 6.24621 0.303701
\(424\) −2.43845 −0.118421
\(425\) −7.56155 −0.366789
\(426\) −14.2462 −0.690231
\(427\) 10.2462 0.495849
\(428\) 4.43845 0.214540
\(429\) 1.56155 0.0753925
\(430\) −14.2462 −0.687013
\(431\) −32.0000 −1.54139 −0.770693 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 10.4924 0.504234 0.252117 0.967697i \(-0.418873\pi\)
0.252117 + 0.967697i \(0.418873\pi\)
\(434\) 25.3693 1.21777
\(435\) 12.0000 0.575356
\(436\) 10.2462 0.490705
\(437\) 10.2462 0.490143
\(438\) −8.68466 −0.414969
\(439\) 26.0540 1.24349 0.621744 0.783220i \(-0.286424\pi\)
0.621744 + 0.783220i \(0.286424\pi\)
\(440\) 3.12311 0.148888
\(441\) 5.68466 0.270698
\(442\) 7.56155 0.359666
\(443\) 20.4924 0.973624 0.486812 0.873507i \(-0.338160\pi\)
0.486812 + 0.873507i \(0.338160\pi\)
\(444\) 0.876894 0.0416156
\(445\) −4.00000 −0.189618
\(446\) −6.68466 −0.316528
\(447\) −18.6847 −0.883754
\(448\) 3.56155 0.168268
\(449\) −38.6847 −1.82564 −0.912821 0.408360i \(-0.866101\pi\)
−0.912821 + 0.408360i \(0.866101\pi\)
\(450\) 1.00000 0.0471405
\(451\) 3.12311 0.147061
\(452\) 4.00000 0.188144
\(453\) −17.3693 −0.816082
\(454\) −15.8078 −0.741895
\(455\) 7.12311 0.333936
\(456\) −2.00000 −0.0936586
\(457\) 33.3693 1.56095 0.780475 0.625186i \(-0.214977\pi\)
0.780475 + 0.625186i \(0.214977\pi\)
\(458\) 6.00000 0.280362
\(459\) −7.56155 −0.352943
\(460\) 10.2462 0.477732
\(461\) −8.24621 −0.384064 −0.192032 0.981389i \(-0.561508\pi\)
−0.192032 + 0.981389i \(0.561508\pi\)
\(462\) 5.56155 0.258747
\(463\) 4.87689 0.226649 0.113324 0.993558i \(-0.463850\pi\)
0.113324 + 0.993558i \(0.463850\pi\)
\(464\) 6.00000 0.278543
\(465\) −14.2462 −0.660652
\(466\) 8.49242 0.393404
\(467\) 7.17708 0.332116 0.166058 0.986116i \(-0.446896\pi\)
0.166058 + 0.986116i \(0.446896\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −2.43845 −0.112597
\(470\) 12.4924 0.576232
\(471\) −13.8078 −0.636228
\(472\) 8.00000 0.368230
\(473\) −11.1231 −0.511441
\(474\) −17.3693 −0.797799
\(475\) 2.00000 0.0917663
\(476\) 26.9309 1.23437
\(477\) 2.43845 0.111649
\(478\) −1.56155 −0.0714238
\(479\) 3.12311 0.142698 0.0713492 0.997451i \(-0.477270\pi\)
0.0713492 + 0.997451i \(0.477270\pi\)
\(480\) −2.00000 −0.0912871
\(481\) 0.876894 0.0399829
\(482\) 20.6847 0.942160
\(483\) 18.2462 0.830231
\(484\) −8.56155 −0.389161
\(485\) 24.4924 1.11214
\(486\) 1.00000 0.0453609
\(487\) −35.6155 −1.61389 −0.806947 0.590624i \(-0.798882\pi\)
−0.806947 + 0.590624i \(0.798882\pi\)
\(488\) −2.87689 −0.130231
\(489\) −10.4924 −0.474484
\(490\) 11.3693 0.513613
\(491\) 19.5616 0.882801 0.441400 0.897310i \(-0.354482\pi\)
0.441400 + 0.897310i \(0.354482\pi\)
\(492\) −2.00000 −0.0901670
\(493\) 45.3693 2.04333
\(494\) −2.00000 −0.0899843
\(495\) −3.12311 −0.140373
\(496\) −7.12311 −0.319837
\(497\) −50.7386 −2.27594
\(498\) −13.3693 −0.599093
\(499\) −26.7386 −1.19699 −0.598493 0.801128i \(-0.704233\pi\)
−0.598493 + 0.801128i \(0.704233\pi\)
\(500\) 12.0000 0.536656
\(501\) 23.8078 1.06365
\(502\) −22.2462 −0.992897
\(503\) −35.3693 −1.57704 −0.788520 0.615009i \(-0.789152\pi\)
−0.788520 + 0.615009i \(0.789152\pi\)
\(504\) −3.56155 −0.158644
\(505\) −17.3693 −0.772924
\(506\) 8.00000 0.355643
\(507\) −1.00000 −0.0444116
\(508\) 0.684658 0.0303768
\(509\) −20.9309 −0.927744 −0.463872 0.885902i \(-0.653540\pi\)
−0.463872 + 0.885902i \(0.653540\pi\)
\(510\) −15.1231 −0.669662
\(511\) −30.9309 −1.36830
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 0.0883022
\(514\) −12.8769 −0.567975
\(515\) 2.00000 0.0881305
\(516\) 7.12311 0.313577
\(517\) 9.75379 0.428971
\(518\) 3.12311 0.137221
\(519\) −0.192236 −0.00843822
\(520\) −2.00000 −0.0877058
\(521\) 15.1231 0.662555 0.331278 0.943533i \(-0.392520\pi\)
0.331278 + 0.943533i \(0.392520\pi\)
\(522\) −6.00000 −0.262613
\(523\) −22.4384 −0.981165 −0.490582 0.871395i \(-0.663216\pi\)
−0.490582 + 0.871395i \(0.663216\pi\)
\(524\) −3.36932 −0.147189
\(525\) 3.56155 0.155439
\(526\) −12.6847 −0.553077
\(527\) −53.8617 −2.34625
\(528\) −1.56155 −0.0679579
\(529\) 3.24621 0.141140
\(530\) 4.87689 0.211839
\(531\) −8.00000 −0.347170
\(532\) −7.12311 −0.308826
\(533\) −2.00000 −0.0866296
\(534\) 2.00000 0.0865485
\(535\) −8.87689 −0.383782
\(536\) 0.684658 0.0295727
\(537\) −9.80776 −0.423236
\(538\) 28.2462 1.21778
\(539\) 8.87689 0.382355
\(540\) 2.00000 0.0860663
\(541\) −12.4384 −0.534771 −0.267385 0.963590i \(-0.586160\pi\)
−0.267385 + 0.963590i \(0.586160\pi\)
\(542\) −13.3693 −0.574261
\(543\) 12.9309 0.554917
\(544\) −7.56155 −0.324199
\(545\) −20.4924 −0.877799
\(546\) −3.56155 −0.152420
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −6.00000 −0.256307
\(549\) 2.87689 0.122783
\(550\) 1.56155 0.0665848
\(551\) −12.0000 −0.511217
\(552\) −5.12311 −0.218054
\(553\) −61.8617 −2.63063
\(554\) −6.00000 −0.254916
\(555\) −1.75379 −0.0744442
\(556\) 7.80776 0.331123
\(557\) 13.1231 0.556044 0.278022 0.960575i \(-0.410321\pi\)
0.278022 + 0.960575i \(0.410321\pi\)
\(558\) 7.12311 0.301545
\(559\) 7.12311 0.301275
\(560\) −7.12311 −0.301006
\(561\) −11.8078 −0.498524
\(562\) −10.4924 −0.442596
\(563\) −7.61553 −0.320956 −0.160478 0.987039i \(-0.551304\pi\)
−0.160478 + 0.987039i \(0.551304\pi\)
\(564\) −6.24621 −0.263013
\(565\) −8.00000 −0.336563
\(566\) 19.6155 0.824502
\(567\) 3.56155 0.149571
\(568\) 14.2462 0.597758
\(569\) 25.3693 1.06354 0.531769 0.846890i \(-0.321528\pi\)
0.531769 + 0.846890i \(0.321528\pi\)
\(570\) 4.00000 0.167542
\(571\) −9.75379 −0.408183 −0.204092 0.978952i \(-0.565424\pi\)
−0.204092 + 0.978952i \(0.565424\pi\)
\(572\) −1.56155 −0.0652918
\(573\) −8.68466 −0.362807
\(574\) −7.12311 −0.297313
\(575\) 5.12311 0.213648
\(576\) 1.00000 0.0416667
\(577\) −0.192236 −0.00800289 −0.00400144 0.999992i \(-0.501274\pi\)
−0.00400144 + 0.999992i \(0.501274\pi\)
\(578\) −40.1771 −1.67115
\(579\) 25.3693 1.05431
\(580\) −12.0000 −0.498273
\(581\) −47.6155 −1.97542
\(582\) −12.2462 −0.507622
\(583\) 3.80776 0.157701
\(584\) 8.68466 0.359374
\(585\) 2.00000 0.0826898
\(586\) −33.6155 −1.38864
\(587\) −3.50758 −0.144773 −0.0723866 0.997377i \(-0.523062\pi\)
−0.0723866 + 0.997377i \(0.523062\pi\)
\(588\) −5.68466 −0.234431
\(589\) 14.2462 0.587005
\(590\) −16.0000 −0.658710
\(591\) 14.4924 0.596139
\(592\) −0.876894 −0.0360401
\(593\) 1.31534 0.0540146 0.0270073 0.999635i \(-0.491402\pi\)
0.0270073 + 0.999635i \(0.491402\pi\)
\(594\) 1.56155 0.0640713
\(595\) −53.8617 −2.20812
\(596\) 18.6847 0.765353
\(597\) 7.31534 0.299397
\(598\) −5.12311 −0.209499
\(599\) −18.9309 −0.773494 −0.386747 0.922186i \(-0.626401\pi\)
−0.386747 + 0.922186i \(0.626401\pi\)
\(600\) −1.00000 −0.0408248
\(601\) 20.2462 0.825860 0.412930 0.910763i \(-0.364505\pi\)
0.412930 + 0.910763i \(0.364505\pi\)
\(602\) 25.3693 1.03398
\(603\) −0.684658 −0.0278814
\(604\) 17.3693 0.706747
\(605\) 17.1231 0.696153
\(606\) 8.68466 0.352790
\(607\) −23.1231 −0.938538 −0.469269 0.883055i \(-0.655483\pi\)
−0.469269 + 0.883055i \(0.655483\pi\)
\(608\) 2.00000 0.0811107
\(609\) −21.3693 −0.865928
\(610\) 5.75379 0.232964
\(611\) −6.24621 −0.252695
\(612\) 7.56155 0.305658
\(613\) 42.7926 1.72838 0.864189 0.503168i \(-0.167832\pi\)
0.864189 + 0.503168i \(0.167832\pi\)
\(614\) −25.5616 −1.03158
\(615\) 4.00000 0.161296
\(616\) −5.56155 −0.224081
\(617\) 4.24621 0.170946 0.0854730 0.996340i \(-0.472760\pi\)
0.0854730 + 0.996340i \(0.472760\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 26.4924 1.06482 0.532410 0.846487i \(-0.321286\pi\)
0.532410 + 0.846487i \(0.321286\pi\)
\(620\) 14.2462 0.572142
\(621\) 5.12311 0.205583
\(622\) 18.0000 0.721734
\(623\) 7.12311 0.285381
\(624\) 1.00000 0.0400320
\(625\) −19.0000 −0.760000
\(626\) −0.246211 −0.00984058
\(627\) 3.12311 0.124725
\(628\) 13.8078 0.550990
\(629\) −6.63068 −0.264383
\(630\) 7.12311 0.283791
\(631\) 0.0539753 0.00214872 0.00107436 0.999999i \(-0.499658\pi\)
0.00107436 + 0.999999i \(0.499658\pi\)
\(632\) 17.3693 0.690914
\(633\) 24.4924 0.973486
\(634\) −24.0540 −0.955305
\(635\) −1.36932 −0.0543397
\(636\) −2.43845 −0.0966907
\(637\) −5.68466 −0.225234
\(638\) −9.36932 −0.370935
\(639\) −14.2462 −0.563571
\(640\) 2.00000 0.0790569
\(641\) −18.1922 −0.718550 −0.359275 0.933232i \(-0.616976\pi\)
−0.359275 + 0.933232i \(0.616976\pi\)
\(642\) 4.43845 0.175172
\(643\) 24.7386 0.975596 0.487798 0.872956i \(-0.337800\pi\)
0.487798 + 0.872956i \(0.337800\pi\)
\(644\) −18.2462 −0.719001
\(645\) −14.2462 −0.560944
\(646\) 15.1231 0.595011
\(647\) 8.24621 0.324192 0.162096 0.986775i \(-0.448175\pi\)
0.162096 + 0.986775i \(0.448175\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −12.4924 −0.490370
\(650\) −1.00000 −0.0392232
\(651\) 25.3693 0.994302
\(652\) 10.4924 0.410915
\(653\) 27.1231 1.06141 0.530705 0.847557i \(-0.321927\pi\)
0.530705 + 0.847557i \(0.321927\pi\)
\(654\) 10.2462 0.400659
\(655\) 6.73863 0.263300
\(656\) 2.00000 0.0780869
\(657\) −8.68466 −0.338821
\(658\) −22.2462 −0.867248
\(659\) −48.5464 −1.89110 −0.945550 0.325478i \(-0.894475\pi\)
−0.945550 + 0.325478i \(0.894475\pi\)
\(660\) 3.12311 0.121567
\(661\) −1.75379 −0.0682145 −0.0341072 0.999418i \(-0.510859\pi\)
−0.0341072 + 0.999418i \(0.510859\pi\)
\(662\) 6.93087 0.269376
\(663\) 7.56155 0.293666
\(664\) 13.3693 0.518830
\(665\) 14.2462 0.552444
\(666\) 0.876894 0.0339790
\(667\) −30.7386 −1.19020
\(668\) −23.8078 −0.921150
\(669\) −6.68466 −0.258444
\(670\) −1.36932 −0.0529013
\(671\) 4.49242 0.173428
\(672\) 3.56155 0.137390
\(673\) 10.6847 0.411863 0.205932 0.978566i \(-0.433978\pi\)
0.205932 + 0.978566i \(0.433978\pi\)
\(674\) −0.930870 −0.0358558
\(675\) 1.00000 0.0384900
\(676\) 1.00000 0.0384615
\(677\) −7.75379 −0.298002 −0.149001 0.988837i \(-0.547606\pi\)
−0.149001 + 0.988837i \(0.547606\pi\)
\(678\) 4.00000 0.153619
\(679\) −43.6155 −1.67381
\(680\) 15.1231 0.579945
\(681\) −15.8078 −0.605755
\(682\) 11.1231 0.425926
\(683\) 9.56155 0.365863 0.182931 0.983126i \(-0.441441\pi\)
0.182931 + 0.983126i \(0.441441\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 12.0000 0.458496
\(686\) 4.68466 0.178861
\(687\) 6.00000 0.228914
\(688\) −7.12311 −0.271566
\(689\) −2.43845 −0.0928974
\(690\) 10.2462 0.390067
\(691\) −38.2462 −1.45495 −0.727477 0.686132i \(-0.759307\pi\)
−0.727477 + 0.686132i \(0.759307\pi\)
\(692\) 0.192236 0.00730771
\(693\) 5.56155 0.211266
\(694\) 25.1231 0.953660
\(695\) −15.6155 −0.592331
\(696\) 6.00000 0.227429
\(697\) 15.1231 0.572828
\(698\) −18.2462 −0.690629
\(699\) 8.49242 0.321213
\(700\) −3.56155 −0.134614
\(701\) 7.36932 0.278335 0.139168 0.990269i \(-0.455557\pi\)
0.139168 + 0.990269i \(0.455557\pi\)
\(702\) −1.00000 −0.0377426
\(703\) 1.75379 0.0661454
\(704\) 1.56155 0.0588532
\(705\) 12.4924 0.470492
\(706\) 26.6847 1.00429
\(707\) 30.9309 1.16328
\(708\) 8.00000 0.300658
\(709\) −40.7386 −1.52997 −0.764986 0.644047i \(-0.777254\pi\)
−0.764986 + 0.644047i \(0.777254\pi\)
\(710\) −28.4924 −1.06930
\(711\) −17.3693 −0.651400
\(712\) −2.00000 −0.0749532
\(713\) 36.4924 1.36665
\(714\) 26.9309 1.00786
\(715\) 3.12311 0.116798
\(716\) 9.80776 0.366533
\(717\) −1.56155 −0.0583173
\(718\) 18.0540 0.673768
\(719\) 31.8078 1.18623 0.593115 0.805118i \(-0.297898\pi\)
0.593115 + 0.805118i \(0.297898\pi\)
\(720\) −2.00000 −0.0745356
\(721\) −3.56155 −0.132639
\(722\) 15.0000 0.558242
\(723\) 20.6847 0.769271
\(724\) −12.9309 −0.480572
\(725\) −6.00000 −0.222834
\(726\) −8.56155 −0.317749
\(727\) 6.93087 0.257052 0.128526 0.991706i \(-0.458975\pi\)
0.128526 + 0.991706i \(0.458975\pi\)
\(728\) 3.56155 0.132000
\(729\) 1.00000 0.0370370
\(730\) −17.3693 −0.642867
\(731\) −53.8617 −1.99215
\(732\) −2.87689 −0.106333
\(733\) −28.1080 −1.03819 −0.519095 0.854716i \(-0.673731\pi\)
−0.519095 + 0.854716i \(0.673731\pi\)
\(734\) 30.2462 1.11641
\(735\) 11.3693 0.419364
\(736\) 5.12311 0.188840
\(737\) −1.06913 −0.0393819
\(738\) −2.00000 −0.0736210
\(739\) −0.630683 −0.0232001 −0.0116000 0.999933i \(-0.503692\pi\)
−0.0116000 + 0.999933i \(0.503692\pi\)
\(740\) 1.75379 0.0644706
\(741\) −2.00000 −0.0734718
\(742\) −8.68466 −0.318824
\(743\) −42.7386 −1.56793 −0.783964 0.620806i \(-0.786805\pi\)
−0.783964 + 0.620806i \(0.786805\pi\)
\(744\) −7.12311 −0.261146
\(745\) −37.3693 −1.36911
\(746\) 4.63068 0.169541
\(747\) −13.3693 −0.489158
\(748\) 11.8078 0.431735
\(749\) 15.8078 0.577603
\(750\) 12.0000 0.438178
\(751\) 30.7386 1.12167 0.560834 0.827928i \(-0.310480\pi\)
0.560834 + 0.827928i \(0.310480\pi\)
\(752\) 6.24621 0.227776
\(753\) −22.2462 −0.810697
\(754\) 6.00000 0.218507
\(755\) −34.7386 −1.26427
\(756\) −3.56155 −0.129532
\(757\) −34.4924 −1.25365 −0.626824 0.779161i \(-0.715646\pi\)
−0.626824 + 0.779161i \(0.715646\pi\)
\(758\) −7.80776 −0.283591
\(759\) 8.00000 0.290382
\(760\) −4.00000 −0.145095
\(761\) −3.75379 −0.136075 −0.0680374 0.997683i \(-0.521674\pi\)
−0.0680374 + 0.997683i \(0.521674\pi\)
\(762\) 0.684658 0.0248026
\(763\) 36.4924 1.32111
\(764\) 8.68466 0.314200
\(765\) −15.1231 −0.546777
\(766\) 28.4924 1.02947
\(767\) 8.00000 0.288863
\(768\) −1.00000 −0.0360844
\(769\) −22.9309 −0.826908 −0.413454 0.910525i \(-0.635678\pi\)
−0.413454 + 0.910525i \(0.635678\pi\)
\(770\) 11.1231 0.400849
\(771\) −12.8769 −0.463750
\(772\) −25.3693 −0.913062
\(773\) −7.94602 −0.285799 −0.142899 0.989737i \(-0.545643\pi\)
−0.142899 + 0.989737i \(0.545643\pi\)
\(774\) 7.12311 0.256035
\(775\) 7.12311 0.255870
\(776\) 12.2462 0.439613
\(777\) 3.12311 0.112041
\(778\) 1.56155 0.0559844
\(779\) −4.00000 −0.143315
\(780\) −2.00000 −0.0716115
\(781\) −22.2462 −0.796032
\(782\) 38.7386 1.38529
\(783\) −6.00000 −0.214423
\(784\) 5.68466 0.203024
\(785\) −27.6155 −0.985640
\(786\) −3.36932 −0.120180
\(787\) −11.8617 −0.422825 −0.211413 0.977397i \(-0.567806\pi\)
−0.211413 + 0.977397i \(0.567806\pi\)
\(788\) −14.4924 −0.516271
\(789\) −12.6847 −0.451586
\(790\) −34.7386 −1.23595
\(791\) 14.2462 0.506537
\(792\) −1.56155 −0.0554874
\(793\) −2.87689 −0.102162
\(794\) 23.6155 0.838084
\(795\) 4.87689 0.172966
\(796\) −7.31534 −0.259285
\(797\) −16.7386 −0.592913 −0.296456 0.955046i \(-0.595805\pi\)
−0.296456 + 0.955046i \(0.595805\pi\)
\(798\) −7.12311 −0.252155
\(799\) 47.2311 1.67091
\(800\) 1.00000 0.0353553
\(801\) 2.00000 0.0706665
\(802\) 19.3693 0.683954
\(803\) −13.5616 −0.478577
\(804\) 0.684658 0.0241460
\(805\) 36.4924 1.28619
\(806\) −7.12311 −0.250901
\(807\) 28.2462 0.994314
\(808\) −8.68466 −0.305525
\(809\) 1.36932 0.0481426 0.0240713 0.999710i \(-0.492337\pi\)
0.0240713 + 0.999710i \(0.492337\pi\)
\(810\) 2.00000 0.0702728
\(811\) 43.2311 1.51805 0.759024 0.651063i \(-0.225677\pi\)
0.759024 + 0.651063i \(0.225677\pi\)
\(812\) 21.3693 0.749916
\(813\) −13.3693 −0.468882
\(814\) 1.36932 0.0479945
\(815\) −20.9848 −0.735067
\(816\) −7.56155 −0.264707
\(817\) 14.2462 0.498412
\(818\) 3.36932 0.117805
\(819\) −3.56155 −0.124451
\(820\) −4.00000 −0.139686
\(821\) −43.1771 −1.50689 −0.753445 0.657511i \(-0.771609\pi\)
−0.753445 + 0.657511i \(0.771609\pi\)
\(822\) −6.00000 −0.209274
\(823\) 8.00000 0.278862 0.139431 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) 1.00000 0.0348367
\(825\) 1.56155 0.0543663
\(826\) 28.4924 0.991378
\(827\) 18.2462 0.634483 0.317241 0.948345i \(-0.397243\pi\)
0.317241 + 0.948345i \(0.397243\pi\)
\(828\) −5.12311 −0.178040
\(829\) −33.2311 −1.15416 −0.577081 0.816687i \(-0.695808\pi\)
−0.577081 + 0.816687i \(0.695808\pi\)
\(830\) −26.7386 −0.928112
\(831\) −6.00000 −0.208138
\(832\) −1.00000 −0.0346688
\(833\) 42.9848 1.48934
\(834\) 7.80776 0.270361
\(835\) 47.6155 1.64780
\(836\) −3.12311 −0.108015
\(837\) 7.12311 0.246211
\(838\) −8.93087 −0.308512
\(839\) −29.7538 −1.02721 −0.513607 0.858025i \(-0.671691\pi\)
−0.513607 + 0.858025i \(0.671691\pi\)
\(840\) −7.12311 −0.245770
\(841\) 7.00000 0.241379
\(842\) 20.0540 0.691106
\(843\) −10.4924 −0.361378
\(844\) −24.4924 −0.843064
\(845\) −2.00000 −0.0688021
\(846\) −6.24621 −0.214749
\(847\) −30.4924 −1.04773
\(848\) 2.43845 0.0837366
\(849\) 19.6155 0.673203
\(850\) 7.56155 0.259359
\(851\) 4.49242 0.153998
\(852\) 14.2462 0.488067
\(853\) −30.3002 −1.03746 −0.518729 0.854939i \(-0.673595\pi\)
−0.518729 + 0.854939i \(0.673595\pi\)
\(854\) −10.2462 −0.350618
\(855\) 4.00000 0.136797
\(856\) −4.43845 −0.151703
\(857\) 7.06913 0.241477 0.120738 0.992684i \(-0.461474\pi\)
0.120738 + 0.992684i \(0.461474\pi\)
\(858\) −1.56155 −0.0533105
\(859\) −35.6155 −1.21519 −0.607593 0.794248i \(-0.707865\pi\)
−0.607593 + 0.794248i \(0.707865\pi\)
\(860\) 14.2462 0.485792
\(861\) −7.12311 −0.242755
\(862\) 32.0000 1.08992
\(863\) −46.2462 −1.57424 −0.787120 0.616800i \(-0.788429\pi\)
−0.787120 + 0.616800i \(0.788429\pi\)
\(864\) 1.00000 0.0340207
\(865\) −0.384472 −0.0130724
\(866\) −10.4924 −0.356547
\(867\) −40.1771 −1.36449
\(868\) −25.3693 −0.861091
\(869\) −27.1231 −0.920088
\(870\) −12.0000 −0.406838
\(871\) 0.684658 0.0231988
\(872\) −10.2462 −0.346980
\(873\) −12.2462 −0.414471
\(874\) −10.2462 −0.346583
\(875\) 42.7386 1.44483
\(876\) 8.68466 0.293427
\(877\) 28.9848 0.978749 0.489374 0.872074i \(-0.337225\pi\)
0.489374 + 0.872074i \(0.337225\pi\)
\(878\) −26.0540 −0.879279
\(879\) −33.6155 −1.13382
\(880\) −3.12311 −0.105280
\(881\) −46.7386 −1.57466 −0.787332 0.616529i \(-0.788538\pi\)
−0.787332 + 0.616529i \(0.788538\pi\)
\(882\) −5.68466 −0.191412
\(883\) 55.9157 1.88171 0.940857 0.338804i \(-0.110023\pi\)
0.940857 + 0.338804i \(0.110023\pi\)
\(884\) −7.56155 −0.254323
\(885\) −16.0000 −0.537834
\(886\) −20.4924 −0.688456
\(887\) 22.8769 0.768131 0.384065 0.923306i \(-0.374524\pi\)
0.384065 + 0.923306i \(0.374524\pi\)
\(888\) −0.876894 −0.0294266
\(889\) 2.43845 0.0817829
\(890\) 4.00000 0.134080
\(891\) 1.56155 0.0523140
\(892\) 6.68466 0.223819
\(893\) −12.4924 −0.418043
\(894\) 18.6847 0.624908
\(895\) −19.6155 −0.655675
\(896\) −3.56155 −0.118983
\(897\) −5.12311 −0.171056
\(898\) 38.6847 1.29092
\(899\) −42.7386 −1.42541
\(900\) −1.00000 −0.0333333
\(901\) 18.4384 0.614274
\(902\) −3.12311 −0.103988
\(903\) 25.3693 0.844238
\(904\) −4.00000 −0.133038
\(905\) 25.8617 0.859673
\(906\) 17.3693 0.577057
\(907\) 14.5464 0.483005 0.241503 0.970400i \(-0.422360\pi\)
0.241503 + 0.970400i \(0.422360\pi\)
\(908\) 15.8078 0.524599
\(909\) 8.68466 0.288052
\(910\) −7.12311 −0.236129
\(911\) −38.7386 −1.28347 −0.641734 0.766927i \(-0.721785\pi\)
−0.641734 + 0.766927i \(0.721785\pi\)
\(912\) 2.00000 0.0662266
\(913\) −20.8769 −0.690924
\(914\) −33.3693 −1.10376
\(915\) 5.75379 0.190214
\(916\) −6.00000 −0.198246
\(917\) −12.0000 −0.396275
\(918\) 7.56155 0.249568
\(919\) −12.1922 −0.402185 −0.201092 0.979572i \(-0.564449\pi\)
−0.201092 + 0.979572i \(0.564449\pi\)
\(920\) −10.2462 −0.337808
\(921\) −25.5616 −0.842282
\(922\) 8.24621 0.271575
\(923\) 14.2462 0.468920
\(924\) −5.56155 −0.182962
\(925\) 0.876894 0.0288321
\(926\) −4.87689 −0.160265
\(927\) −1.00000 −0.0328443
\(928\) −6.00000 −0.196960
\(929\) 41.6155 1.36536 0.682681 0.730717i \(-0.260814\pi\)
0.682681 + 0.730717i \(0.260814\pi\)
\(930\) 14.2462 0.467152
\(931\) −11.3693 −0.372614
\(932\) −8.49242 −0.278179
\(933\) 18.0000 0.589294
\(934\) −7.17708 −0.234841
\(935\) −23.6155 −0.772310
\(936\) 1.00000 0.0326860
\(937\) −0.738634 −0.0241301 −0.0120651 0.999927i \(-0.503841\pi\)
−0.0120651 + 0.999927i \(0.503841\pi\)
\(938\) 2.43845 0.0796181
\(939\) −0.246211 −0.00803480
\(940\) −12.4924 −0.407458
\(941\) −23.5616 −0.768085 −0.384042 0.923315i \(-0.625468\pi\)
−0.384042 + 0.923315i \(0.625468\pi\)
\(942\) 13.8078 0.449881
\(943\) −10.2462 −0.333663
\(944\) −8.00000 −0.260378
\(945\) 7.12311 0.231715
\(946\) 11.1231 0.361643
\(947\) −12.0000 −0.389948 −0.194974 0.980808i \(-0.562462\pi\)
−0.194974 + 0.980808i \(0.562462\pi\)
\(948\) 17.3693 0.564129
\(949\) 8.68466 0.281916
\(950\) −2.00000 −0.0648886
\(951\) −24.0540 −0.780004
\(952\) −26.9309 −0.872835
\(953\) 33.8078 1.09514 0.547570 0.836760i \(-0.315553\pi\)
0.547570 + 0.836760i \(0.315553\pi\)
\(954\) −2.43845 −0.0789476
\(955\) −17.3693 −0.562058
\(956\) 1.56155 0.0505042
\(957\) −9.36932 −0.302867
\(958\) −3.12311 −0.100903
\(959\) −21.3693 −0.690051
\(960\) 2.00000 0.0645497
\(961\) 19.7386 0.636730
\(962\) −0.876894 −0.0282722
\(963\) 4.43845 0.143027
\(964\) −20.6847 −0.666208
\(965\) 50.7386 1.63333
\(966\) −18.2462 −0.587062
\(967\) 8.87689 0.285462 0.142731 0.989762i \(-0.454412\pi\)
0.142731 + 0.989762i \(0.454412\pi\)
\(968\) 8.56155 0.275179
\(969\) 15.1231 0.485824
\(970\) −24.4924 −0.786404
\(971\) −27.6155 −0.886224 −0.443112 0.896466i \(-0.646126\pi\)
−0.443112 + 0.896466i \(0.646126\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 27.8078 0.891476
\(974\) 35.6155 1.14120
\(975\) −1.00000 −0.0320256
\(976\) 2.87689 0.0920871
\(977\) −6.87689 −0.220011 −0.110006 0.993931i \(-0.535087\pi\)
−0.110006 + 0.993931i \(0.535087\pi\)
\(978\) 10.4924 0.335511
\(979\) 3.12311 0.0998149
\(980\) −11.3693 −0.363180
\(981\) 10.2462 0.327136
\(982\) −19.5616 −0.624234
\(983\) 0.192236 0.00613137 0.00306569 0.999995i \(-0.499024\pi\)
0.00306569 + 0.999995i \(0.499024\pi\)
\(984\) 2.00000 0.0637577
\(985\) 28.9848 0.923534
\(986\) −45.3693 −1.44485
\(987\) −22.2462 −0.708105
\(988\) 2.00000 0.0636285
\(989\) 36.4924 1.16039
\(990\) 3.12311 0.0992588
\(991\) 1.86174 0.0591401 0.0295701 0.999563i \(-0.490586\pi\)
0.0295701 + 0.999563i \(0.490586\pi\)
\(992\) 7.12311 0.226159
\(993\) 6.93087 0.219945
\(994\) 50.7386 1.60933
\(995\) 14.6307 0.463824
\(996\) 13.3693 0.423623
\(997\) 17.5076 0.554471 0.277235 0.960802i \(-0.410582\pi\)
0.277235 + 0.960802i \(0.410582\pi\)
\(998\) 26.7386 0.846397
\(999\) 0.876894 0.0277437
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 8034.2.a.l.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.l.1.2 2 1.1 even 1 trivial