Properties

Label 8034.2.a.z.1.14
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $0$
Dimension $14$
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: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + 6361 x^{6} - 14618 x^{5} - 7015 x^{4} + 15763 x^{3} + 1118 x^{2} - 6316 x + 1552\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(-4.38902\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.38902 q^{5} +1.00000 q^{6} +3.17787 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.38902 q^{5} +1.00000 q^{6} +3.17787 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.38902 q^{10} -0.317137 q^{11} -1.00000 q^{12} +1.00000 q^{13} -3.17787 q^{14} -4.38902 q^{15} +1.00000 q^{16} -0.0669713 q^{17} -1.00000 q^{18} -0.603097 q^{19} +4.38902 q^{20} -3.17787 q^{21} +0.317137 q^{22} -1.74821 q^{23} +1.00000 q^{24} +14.2635 q^{25} -1.00000 q^{26} -1.00000 q^{27} +3.17787 q^{28} -3.43665 q^{29} +4.38902 q^{30} +8.86161 q^{31} -1.00000 q^{32} +0.317137 q^{33} +0.0669713 q^{34} +13.9477 q^{35} +1.00000 q^{36} -2.15739 q^{37} +0.603097 q^{38} -1.00000 q^{39} -4.38902 q^{40} -5.16210 q^{41} +3.17787 q^{42} -7.69082 q^{43} -0.317137 q^{44} +4.38902 q^{45} +1.74821 q^{46} -9.65725 q^{47} -1.00000 q^{48} +3.09883 q^{49} -14.2635 q^{50} +0.0669713 q^{51} +1.00000 q^{52} +1.21273 q^{53} +1.00000 q^{54} -1.39192 q^{55} -3.17787 q^{56} +0.603097 q^{57} +3.43665 q^{58} +3.33339 q^{59} -4.38902 q^{60} -1.56786 q^{61} -8.86161 q^{62} +3.17787 q^{63} +1.00000 q^{64} +4.38902 q^{65} -0.317137 q^{66} +10.7087 q^{67} -0.0669713 q^{68} +1.74821 q^{69} -13.9477 q^{70} +7.48046 q^{71} -1.00000 q^{72} +1.78442 q^{73} +2.15739 q^{74} -14.2635 q^{75} -0.603097 q^{76} -1.00782 q^{77} +1.00000 q^{78} +11.2264 q^{79} +4.38902 q^{80} +1.00000 q^{81} +5.16210 q^{82} +14.1469 q^{83} -3.17787 q^{84} -0.293939 q^{85} +7.69082 q^{86} +3.43665 q^{87} +0.317137 q^{88} -5.61305 q^{89} -4.38902 q^{90} +3.17787 q^{91} -1.74821 q^{92} -8.86161 q^{93} +9.65725 q^{94} -2.64701 q^{95} +1.00000 q^{96} -14.4794 q^{97} -3.09883 q^{98} -0.317137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + 3q^{10} + 5q^{11} - 14q^{12} + 14q^{13} - 4q^{14} + 3q^{15} + 14q^{16} - 7q^{17} - 14q^{18} + 31q^{19} - 3q^{20} - 4q^{21} - 5q^{22} + 14q^{23} + 14q^{24} + 11q^{25} - 14q^{26} - 14q^{27} + 4q^{28} + 9q^{29} - 3q^{30} + 23q^{31} - 14q^{32} - 5q^{33} + 7q^{34} - 2q^{35} + 14q^{36} + 12q^{37} - 31q^{38} - 14q^{39} + 3q^{40} - 5q^{41} + 4q^{42} - 2q^{43} + 5q^{44} - 3q^{45} - 14q^{46} - 11q^{47} - 14q^{48} + 52q^{49} - 11q^{50} + 7q^{51} + 14q^{52} + 6q^{53} + 14q^{54} + 30q^{55} - 4q^{56} - 31q^{57} - 9q^{58} - 4q^{59} + 3q^{60} + 12q^{61} - 23q^{62} + 4q^{63} + 14q^{64} - 3q^{65} + 5q^{66} + 24q^{67} - 7q^{68} - 14q^{69} + 2q^{70} + 20q^{71} - 14q^{72} + 2q^{73} - 12q^{74} - 11q^{75} + 31q^{76} - 28q^{77} + 14q^{78} + 59q^{79} - 3q^{80} + 14q^{81} + 5q^{82} + q^{83} - 4q^{84} - 29q^{85} + 2q^{86} - 9q^{87} - 5q^{88} + 6q^{89} + 3q^{90} + 4q^{91} + 14q^{92} - 23q^{93} + 11q^{94} - 58q^{95} + 14q^{96} - 6q^{97} - 52q^{98} + 5q^{99} + O(q^{100}) \)

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
\(5\) 4.38902 1.96283 0.981416 0.191894i \(-0.0614630\pi\)
0.981416 + 0.191894i \(0.0614630\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.17787 1.20112 0.600560 0.799580i \(-0.294944\pi\)
0.600560 + 0.799580i \(0.294944\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −4.38902 −1.38793
\(11\) −0.317137 −0.0956205 −0.0478102 0.998856i \(-0.515224\pi\)
−0.0478102 + 0.998856i \(0.515224\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) −3.17787 −0.849320
\(15\) −4.38902 −1.13324
\(16\) 1.00000 0.250000
\(17\) −0.0669713 −0.0162429 −0.00812146 0.999967i \(-0.502585\pi\)
−0.00812146 + 0.999967i \(0.502585\pi\)
\(18\) −1.00000 −0.235702
\(19\) −0.603097 −0.138360 −0.0691800 0.997604i \(-0.522038\pi\)
−0.0691800 + 0.997604i \(0.522038\pi\)
\(20\) 4.38902 0.981416
\(21\) −3.17787 −0.693467
\(22\) 0.317137 0.0676139
\(23\) −1.74821 −0.364528 −0.182264 0.983250i \(-0.558343\pi\)
−0.182264 + 0.983250i \(0.558343\pi\)
\(24\) 1.00000 0.204124
\(25\) 14.2635 2.85271
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) 3.17787 0.600560
\(29\) −3.43665 −0.638170 −0.319085 0.947726i \(-0.603375\pi\)
−0.319085 + 0.947726i \(0.603375\pi\)
\(30\) 4.38902 0.801323
\(31\) 8.86161 1.59159 0.795796 0.605565i \(-0.207053\pi\)
0.795796 + 0.605565i \(0.207053\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.317137 0.0552065
\(34\) 0.0669713 0.0114855
\(35\) 13.9477 2.35760
\(36\) 1.00000 0.166667
\(37\) −2.15739 −0.354673 −0.177337 0.984150i \(-0.556748\pi\)
−0.177337 + 0.984150i \(0.556748\pi\)
\(38\) 0.603097 0.0978353
\(39\) −1.00000 −0.160128
\(40\) −4.38902 −0.693966
\(41\) −5.16210 −0.806185 −0.403093 0.915159i \(-0.632065\pi\)
−0.403093 + 0.915159i \(0.632065\pi\)
\(42\) 3.17787 0.490355
\(43\) −7.69082 −1.17284 −0.586420 0.810008i \(-0.699463\pi\)
−0.586420 + 0.810008i \(0.699463\pi\)
\(44\) −0.317137 −0.0478102
\(45\) 4.38902 0.654277
\(46\) 1.74821 0.257760
\(47\) −9.65725 −1.40865 −0.704327 0.709876i \(-0.748751\pi\)
−0.704327 + 0.709876i \(0.748751\pi\)
\(48\) −1.00000 −0.144338
\(49\) 3.09883 0.442690
\(50\) −14.2635 −2.01717
\(51\) 0.0669713 0.00937786
\(52\) 1.00000 0.138675
\(53\) 1.21273 0.166581 0.0832907 0.996525i \(-0.473457\pi\)
0.0832907 + 0.996525i \(0.473457\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.39192 −0.187687
\(56\) −3.17787 −0.424660
\(57\) 0.603097 0.0798822
\(58\) 3.43665 0.451254
\(59\) 3.33339 0.433970 0.216985 0.976175i \(-0.430378\pi\)
0.216985 + 0.976175i \(0.430378\pi\)
\(60\) −4.38902 −0.566621
\(61\) −1.56786 −0.200744 −0.100372 0.994950i \(-0.532003\pi\)
−0.100372 + 0.994950i \(0.532003\pi\)
\(62\) −8.86161 −1.12543
\(63\) 3.17787 0.400373
\(64\) 1.00000 0.125000
\(65\) 4.38902 0.544391
\(66\) −0.317137 −0.0390369
\(67\) 10.7087 1.30827 0.654136 0.756377i \(-0.273033\pi\)
0.654136 + 0.756377i \(0.273033\pi\)
\(68\) −0.0669713 −0.00812146
\(69\) 1.74821 0.210460
\(70\) −13.9477 −1.66707
\(71\) 7.48046 0.887767 0.443883 0.896085i \(-0.353600\pi\)
0.443883 + 0.896085i \(0.353600\pi\)
\(72\) −1.00000 −0.117851
\(73\) 1.78442 0.208851 0.104425 0.994533i \(-0.466700\pi\)
0.104425 + 0.994533i \(0.466700\pi\)
\(74\) 2.15739 0.250792
\(75\) −14.2635 −1.64701
\(76\) −0.603097 −0.0691800
\(77\) −1.00782 −0.114852
\(78\) 1.00000 0.113228
\(79\) 11.2264 1.26307 0.631534 0.775349i \(-0.282426\pi\)
0.631534 + 0.775349i \(0.282426\pi\)
\(80\) 4.38902 0.490708
\(81\) 1.00000 0.111111
\(82\) 5.16210 0.570059
\(83\) 14.1469 1.55282 0.776412 0.630225i \(-0.217037\pi\)
0.776412 + 0.630225i \(0.217037\pi\)
\(84\) −3.17787 −0.346734
\(85\) −0.293939 −0.0318821
\(86\) 7.69082 0.829322
\(87\) 3.43665 0.368447
\(88\) 0.317137 0.0338069
\(89\) −5.61305 −0.594982 −0.297491 0.954725i \(-0.596150\pi\)
−0.297491 + 0.954725i \(0.596150\pi\)
\(90\) −4.38902 −0.462644
\(91\) 3.17787 0.333131
\(92\) −1.74821 −0.182264
\(93\) −8.86161 −0.918906
\(94\) 9.65725 0.996069
\(95\) −2.64701 −0.271577
\(96\) 1.00000 0.102062
\(97\) −14.4794 −1.47016 −0.735079 0.677982i \(-0.762855\pi\)
−0.735079 + 0.677982i \(0.762855\pi\)
\(98\) −3.09883 −0.313029
\(99\) −0.317137 −0.0318735
\(100\) 14.2635 1.42635
\(101\) −1.49945 −0.149200 −0.0746002 0.997214i \(-0.523768\pi\)
−0.0746002 + 0.997214i \(0.523768\pi\)
\(102\) −0.0669713 −0.00663115
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −13.9477 −1.36116
\(106\) −1.21273 −0.117791
\(107\) 17.6611 1.70736 0.853681 0.520797i \(-0.174365\pi\)
0.853681 + 0.520797i \(0.174365\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 11.2269 1.07534 0.537669 0.843156i \(-0.319305\pi\)
0.537669 + 0.843156i \(0.319305\pi\)
\(110\) 1.39192 0.132715
\(111\) 2.15739 0.204771
\(112\) 3.17787 0.300280
\(113\) 7.46423 0.702175 0.351088 0.936343i \(-0.385812\pi\)
0.351088 + 0.936343i \(0.385812\pi\)
\(114\) −0.603097 −0.0564852
\(115\) −7.67296 −0.715507
\(116\) −3.43665 −0.319085
\(117\) 1.00000 0.0924500
\(118\) −3.33339 −0.306863
\(119\) −0.212826 −0.0195097
\(120\) 4.38902 0.400661
\(121\) −10.8994 −0.990857
\(122\) 1.56786 0.141947
\(123\) 5.16210 0.465451
\(124\) 8.86161 0.795796
\(125\) 40.6579 3.63655
\(126\) −3.17787 −0.283107
\(127\) 11.4443 1.01552 0.507758 0.861499i \(-0.330474\pi\)
0.507758 + 0.861499i \(0.330474\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 7.69082 0.677139
\(130\) −4.38902 −0.384943
\(131\) 15.2916 1.33604 0.668018 0.744145i \(-0.267143\pi\)
0.668018 + 0.744145i \(0.267143\pi\)
\(132\) 0.317137 0.0276032
\(133\) −1.91656 −0.166187
\(134\) −10.7087 −0.925087
\(135\) −4.38902 −0.377747
\(136\) 0.0669713 0.00574274
\(137\) 12.0394 1.02860 0.514298 0.857611i \(-0.328052\pi\)
0.514298 + 0.857611i \(0.328052\pi\)
\(138\) −1.74821 −0.148818
\(139\) 12.8288 1.08813 0.544063 0.839044i \(-0.316885\pi\)
0.544063 + 0.839044i \(0.316885\pi\)
\(140\) 13.9477 1.17880
\(141\) 9.65725 0.813287
\(142\) −7.48046 −0.627746
\(143\) −0.317137 −0.0265203
\(144\) 1.00000 0.0833333
\(145\) −15.0835 −1.25262
\(146\) −1.78442 −0.147680
\(147\) −3.09883 −0.255587
\(148\) −2.15739 −0.177337
\(149\) −5.78864 −0.474224 −0.237112 0.971482i \(-0.576201\pi\)
−0.237112 + 0.971482i \(0.576201\pi\)
\(150\) 14.2635 1.16461
\(151\) 13.8353 1.12590 0.562949 0.826492i \(-0.309667\pi\)
0.562949 + 0.826492i \(0.309667\pi\)
\(152\) 0.603097 0.0489176
\(153\) −0.0669713 −0.00541431
\(154\) 1.00782 0.0812124
\(155\) 38.8938 3.12403
\(156\) −1.00000 −0.0800641
\(157\) −2.66183 −0.212437 −0.106219 0.994343i \(-0.533874\pi\)
−0.106219 + 0.994343i \(0.533874\pi\)
\(158\) −11.2264 −0.893123
\(159\) −1.21273 −0.0961758
\(160\) −4.38902 −0.346983
\(161\) −5.55559 −0.437842
\(162\) −1.00000 −0.0785674
\(163\) 13.8385 1.08391 0.541956 0.840407i \(-0.317684\pi\)
0.541956 + 0.840407i \(0.317684\pi\)
\(164\) −5.16210 −0.403093
\(165\) 1.39192 0.108361
\(166\) −14.1469 −1.09801
\(167\) −14.7810 −1.14379 −0.571894 0.820327i \(-0.693791\pi\)
−0.571894 + 0.820327i \(0.693791\pi\)
\(168\) 3.17787 0.245178
\(169\) 1.00000 0.0769231
\(170\) 0.293939 0.0225441
\(171\) −0.603097 −0.0461200
\(172\) −7.69082 −0.586420
\(173\) −11.2344 −0.854139 −0.427069 0.904219i \(-0.640454\pi\)
−0.427069 + 0.904219i \(0.640454\pi\)
\(174\) −3.43665 −0.260532
\(175\) 45.3276 3.42644
\(176\) −0.317137 −0.0239051
\(177\) −3.33339 −0.250553
\(178\) 5.61305 0.420716
\(179\) 0.0728347 0.00544392 0.00272196 0.999996i \(-0.499134\pi\)
0.00272196 + 0.999996i \(0.499134\pi\)
\(180\) 4.38902 0.327139
\(181\) 16.0467 1.19274 0.596370 0.802709i \(-0.296609\pi\)
0.596370 + 0.802709i \(0.296609\pi\)
\(182\) −3.17787 −0.235559
\(183\) 1.56786 0.115899
\(184\) 1.74821 0.128880
\(185\) −9.46885 −0.696163
\(186\) 8.86161 0.649765
\(187\) 0.0212391 0.00155316
\(188\) −9.65725 −0.704327
\(189\) −3.17787 −0.231156
\(190\) 2.64701 0.192034
\(191\) 15.8199 1.14469 0.572344 0.820013i \(-0.306034\pi\)
0.572344 + 0.820013i \(0.306034\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 13.8895 0.999791 0.499896 0.866086i \(-0.333372\pi\)
0.499896 + 0.866086i \(0.333372\pi\)
\(194\) 14.4794 1.03956
\(195\) −4.38902 −0.314305
\(196\) 3.09883 0.221345
\(197\) −4.52312 −0.322259 −0.161129 0.986933i \(-0.551514\pi\)
−0.161129 + 0.986933i \(0.551514\pi\)
\(198\) 0.317137 0.0225380
\(199\) 12.3308 0.874105 0.437053 0.899436i \(-0.356022\pi\)
0.437053 + 0.899436i \(0.356022\pi\)
\(200\) −14.2635 −1.00858
\(201\) −10.7087 −0.755331
\(202\) 1.49945 0.105501
\(203\) −10.9212 −0.766518
\(204\) 0.0669713 0.00468893
\(205\) −22.6566 −1.58241
\(206\) 1.00000 0.0696733
\(207\) −1.74821 −0.121509
\(208\) 1.00000 0.0693375
\(209\) 0.191264 0.0132300
\(210\) 13.9477 0.962485
\(211\) −22.7432 −1.56571 −0.782853 0.622207i \(-0.786236\pi\)
−0.782853 + 0.622207i \(0.786236\pi\)
\(212\) 1.21273 0.0832907
\(213\) −7.48046 −0.512552
\(214\) −17.6611 −1.20729
\(215\) −33.7552 −2.30209
\(216\) 1.00000 0.0680414
\(217\) 28.1610 1.91169
\(218\) −11.2269 −0.760379
\(219\) −1.78442 −0.120580
\(220\) −1.39192 −0.0938434
\(221\) −0.0669713 −0.00450498
\(222\) −2.15739 −0.144795
\(223\) −3.36894 −0.225601 −0.112800 0.993618i \(-0.535982\pi\)
−0.112800 + 0.993618i \(0.535982\pi\)
\(224\) −3.17787 −0.212330
\(225\) 14.2635 0.950902
\(226\) −7.46423 −0.496513
\(227\) −15.7592 −1.04598 −0.522988 0.852340i \(-0.675183\pi\)
−0.522988 + 0.852340i \(0.675183\pi\)
\(228\) 0.603097 0.0399411
\(229\) −15.2657 −1.00879 −0.504393 0.863474i \(-0.668284\pi\)
−0.504393 + 0.863474i \(0.668284\pi\)
\(230\) 7.67296 0.505940
\(231\) 1.00782 0.0663096
\(232\) 3.43665 0.225627
\(233\) −9.72180 −0.636896 −0.318448 0.947940i \(-0.603162\pi\)
−0.318448 + 0.947940i \(0.603162\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −42.3859 −2.76495
\(236\) 3.33339 0.216985
\(237\) −11.2264 −0.729232
\(238\) 0.212826 0.0137954
\(239\) 19.8048 1.28106 0.640532 0.767931i \(-0.278714\pi\)
0.640532 + 0.767931i \(0.278714\pi\)
\(240\) −4.38902 −0.283310
\(241\) −3.02712 −0.194994 −0.0974971 0.995236i \(-0.531084\pi\)
−0.0974971 + 0.995236i \(0.531084\pi\)
\(242\) 10.8994 0.700642
\(243\) −1.00000 −0.0641500
\(244\) −1.56786 −0.100372
\(245\) 13.6008 0.868925
\(246\) −5.16210 −0.329124
\(247\) −0.603097 −0.0383741
\(248\) −8.86161 −0.562713
\(249\) −14.1469 −0.896524
\(250\) −40.6579 −2.57143
\(251\) −28.3596 −1.79004 −0.895020 0.446025i \(-0.852839\pi\)
−0.895020 + 0.446025i \(0.852839\pi\)
\(252\) 3.17787 0.200187
\(253\) 0.554424 0.0348563
\(254\) −11.4443 −0.718079
\(255\) 0.293939 0.0184071
\(256\) 1.00000 0.0625000
\(257\) −14.9816 −0.934525 −0.467263 0.884119i \(-0.654760\pi\)
−0.467263 + 0.884119i \(0.654760\pi\)
\(258\) −7.69082 −0.478810
\(259\) −6.85590 −0.426005
\(260\) 4.38902 0.272196
\(261\) −3.43665 −0.212723
\(262\) −15.2916 −0.944720
\(263\) 6.77691 0.417882 0.208941 0.977928i \(-0.432998\pi\)
0.208941 + 0.977928i \(0.432998\pi\)
\(264\) −0.317137 −0.0195184
\(265\) 5.32270 0.326971
\(266\) 1.91656 0.117512
\(267\) 5.61305 0.343513
\(268\) 10.7087 0.654136
\(269\) −12.0887 −0.737064 −0.368532 0.929615i \(-0.620139\pi\)
−0.368532 + 0.929615i \(0.620139\pi\)
\(270\) 4.38902 0.267108
\(271\) 5.54164 0.336630 0.168315 0.985733i \(-0.446167\pi\)
0.168315 + 0.985733i \(0.446167\pi\)
\(272\) −0.0669713 −0.00406073
\(273\) −3.17787 −0.192333
\(274\) −12.0394 −0.727328
\(275\) −4.52350 −0.272777
\(276\) 1.74821 0.105230
\(277\) −7.68176 −0.461552 −0.230776 0.973007i \(-0.574126\pi\)
−0.230776 + 0.973007i \(0.574126\pi\)
\(278\) −12.8288 −0.769422
\(279\) 8.86161 0.530531
\(280\) −13.9477 −0.833536
\(281\) 8.11844 0.484306 0.242153 0.970238i \(-0.422146\pi\)
0.242153 + 0.970238i \(0.422146\pi\)
\(282\) −9.65725 −0.575081
\(283\) −17.9023 −1.06418 −0.532091 0.846687i \(-0.678594\pi\)
−0.532091 + 0.846687i \(0.678594\pi\)
\(284\) 7.48046 0.443883
\(285\) 2.64701 0.156795
\(286\) 0.317137 0.0187527
\(287\) −16.4045 −0.968325
\(288\) −1.00000 −0.0589256
\(289\) −16.9955 −0.999736
\(290\) 15.0835 0.885736
\(291\) 14.4794 0.848796
\(292\) 1.78442 0.104425
\(293\) 13.4611 0.786407 0.393204 0.919451i \(-0.371367\pi\)
0.393204 + 0.919451i \(0.371367\pi\)
\(294\) 3.09883 0.180727
\(295\) 14.6303 0.851810
\(296\) 2.15739 0.125396
\(297\) 0.317137 0.0184022
\(298\) 5.78864 0.335327
\(299\) −1.74821 −0.101102
\(300\) −14.2635 −0.823506
\(301\) −24.4404 −1.40872
\(302\) −13.8353 −0.796130
\(303\) 1.49945 0.0861409
\(304\) −0.603097 −0.0345900
\(305\) −6.88137 −0.394026
\(306\) 0.0669713 0.00382849
\(307\) 16.7095 0.953660 0.476830 0.878996i \(-0.341786\pi\)
0.476830 + 0.878996i \(0.341786\pi\)
\(308\) −1.00782 −0.0574258
\(309\) 1.00000 0.0568880
\(310\) −38.8938 −2.20902
\(311\) −5.70647 −0.323584 −0.161792 0.986825i \(-0.551727\pi\)
−0.161792 + 0.986825i \(0.551727\pi\)
\(312\) 1.00000 0.0566139
\(313\) −9.73053 −0.550002 −0.275001 0.961444i \(-0.588678\pi\)
−0.275001 + 0.961444i \(0.588678\pi\)
\(314\) 2.66183 0.150216
\(315\) 13.9477 0.785865
\(316\) 11.2264 0.631534
\(317\) 23.1815 1.30200 0.651002 0.759076i \(-0.274349\pi\)
0.651002 + 0.759076i \(0.274349\pi\)
\(318\) 1.21273 0.0680065
\(319\) 1.08989 0.0610221
\(320\) 4.38902 0.245354
\(321\) −17.6611 −0.985745
\(322\) 5.55559 0.309601
\(323\) 0.0403902 0.00224737
\(324\) 1.00000 0.0555556
\(325\) 14.2635 0.791199
\(326\) −13.8385 −0.766442
\(327\) −11.2269 −0.620847
\(328\) 5.16210 0.285030
\(329\) −30.6894 −1.69196
\(330\) −1.39192 −0.0766228
\(331\) 12.7331 0.699877 0.349938 0.936773i \(-0.386203\pi\)
0.349938 + 0.936773i \(0.386203\pi\)
\(332\) 14.1469 0.776412
\(333\) −2.15739 −0.118224
\(334\) 14.7810 0.808781
\(335\) 47.0006 2.56792
\(336\) −3.17787 −0.173367
\(337\) 27.4814 1.49701 0.748504 0.663130i \(-0.230772\pi\)
0.748504 + 0.663130i \(0.230772\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −7.46423 −0.405401
\(340\) −0.293939 −0.0159411
\(341\) −2.81034 −0.152189
\(342\) 0.603097 0.0326118
\(343\) −12.3974 −0.669397
\(344\) 7.69082 0.414661
\(345\) 7.67296 0.413098
\(346\) 11.2344 0.603967
\(347\) 3.55121 0.190639 0.0953194 0.995447i \(-0.469613\pi\)
0.0953194 + 0.995447i \(0.469613\pi\)
\(348\) 3.43665 0.184224
\(349\) 2.95104 0.157966 0.0789829 0.996876i \(-0.474833\pi\)
0.0789829 + 0.996876i \(0.474833\pi\)
\(350\) −45.3276 −2.42286
\(351\) −1.00000 −0.0533761
\(352\) 0.317137 0.0169035
\(353\) −1.76397 −0.0938864 −0.0469432 0.998898i \(-0.514948\pi\)
−0.0469432 + 0.998898i \(0.514948\pi\)
\(354\) 3.33339 0.177168
\(355\) 32.8319 1.74254
\(356\) −5.61305 −0.297491
\(357\) 0.212826 0.0112639
\(358\) −0.0728347 −0.00384943
\(359\) −32.2239 −1.70071 −0.850356 0.526208i \(-0.823613\pi\)
−0.850356 + 0.526208i \(0.823613\pi\)
\(360\) −4.38902 −0.231322
\(361\) −18.6363 −0.980857
\(362\) −16.0467 −0.843395
\(363\) 10.8994 0.572071
\(364\) 3.17787 0.166565
\(365\) 7.83187 0.409939
\(366\) −1.56786 −0.0819533
\(367\) 12.6441 0.660014 0.330007 0.943978i \(-0.392949\pi\)
0.330007 + 0.943978i \(0.392949\pi\)
\(368\) −1.74821 −0.0911320
\(369\) −5.16210 −0.268728
\(370\) 9.46885 0.492262
\(371\) 3.85389 0.200084
\(372\) −8.86161 −0.459453
\(373\) 25.9329 1.34276 0.671378 0.741115i \(-0.265703\pi\)
0.671378 + 0.741115i \(0.265703\pi\)
\(374\) −0.0212391 −0.00109825
\(375\) −40.6579 −2.09956
\(376\) 9.65725 0.498034
\(377\) −3.43665 −0.176996
\(378\) 3.17787 0.163452
\(379\) −12.5057 −0.642373 −0.321187 0.947016i \(-0.604082\pi\)
−0.321187 + 0.947016i \(0.604082\pi\)
\(380\) −2.64701 −0.135789
\(381\) −11.4443 −0.586309
\(382\) −15.8199 −0.809417
\(383\) −15.7274 −0.803634 −0.401817 0.915720i \(-0.631621\pi\)
−0.401817 + 0.915720i \(0.631621\pi\)
\(384\) 1.00000 0.0510310
\(385\) −4.42334 −0.225434
\(386\) −13.8895 −0.706959
\(387\) −7.69082 −0.390946
\(388\) −14.4794 −0.735079
\(389\) −24.0985 −1.22184 −0.610921 0.791692i \(-0.709201\pi\)
−0.610921 + 0.791692i \(0.709201\pi\)
\(390\) 4.38902 0.222247
\(391\) 0.117080 0.00592100
\(392\) −3.09883 −0.156514
\(393\) −15.2916 −0.771361
\(394\) 4.52312 0.227872
\(395\) 49.2729 2.47919
\(396\) −0.317137 −0.0159367
\(397\) −13.8368 −0.694447 −0.347224 0.937782i \(-0.612876\pi\)
−0.347224 + 0.937782i \(0.612876\pi\)
\(398\) −12.3308 −0.618086
\(399\) 1.91656 0.0959481
\(400\) 14.2635 0.713177
\(401\) 6.88741 0.343941 0.171970 0.985102i \(-0.444987\pi\)
0.171970 + 0.985102i \(0.444987\pi\)
\(402\) 10.7087 0.534099
\(403\) 8.86161 0.441428
\(404\) −1.49945 −0.0746002
\(405\) 4.38902 0.218092
\(406\) 10.9212 0.542010
\(407\) 0.684189 0.0339140
\(408\) −0.0669713 −0.00331557
\(409\) 25.9075 1.28104 0.640522 0.767940i \(-0.278718\pi\)
0.640522 + 0.767940i \(0.278718\pi\)
\(410\) 22.6566 1.11893
\(411\) −12.0394 −0.593861
\(412\) −1.00000 −0.0492665
\(413\) 10.5931 0.521250
\(414\) 1.74821 0.0859201
\(415\) 62.0911 3.04793
\(416\) −1.00000 −0.0490290
\(417\) −12.8288 −0.628230
\(418\) −0.191264 −0.00935505
\(419\) −4.11772 −0.201164 −0.100582 0.994929i \(-0.532070\pi\)
−0.100582 + 0.994929i \(0.532070\pi\)
\(420\) −13.9477 −0.680579
\(421\) −27.3877 −1.33479 −0.667397 0.744702i \(-0.732591\pi\)
−0.667397 + 0.744702i \(0.732591\pi\)
\(422\) 22.7432 1.10712
\(423\) −9.65725 −0.469551
\(424\) −1.21273 −0.0588954
\(425\) −0.955247 −0.0463363
\(426\) 7.48046 0.362429
\(427\) −4.98244 −0.241117
\(428\) 17.6611 0.853681
\(429\) 0.317137 0.0153115
\(430\) 33.7552 1.62782
\(431\) −11.4537 −0.551704 −0.275852 0.961200i \(-0.588960\pi\)
−0.275852 + 0.961200i \(0.588960\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −0.352422 −0.0169363 −0.00846816 0.999964i \(-0.502696\pi\)
−0.00846816 + 0.999964i \(0.502696\pi\)
\(434\) −28.1610 −1.35177
\(435\) 15.0835 0.723200
\(436\) 11.2269 0.537669
\(437\) 1.05434 0.0504361
\(438\) 1.78442 0.0852630
\(439\) 13.8515 0.661094 0.330547 0.943790i \(-0.392767\pi\)
0.330547 + 0.943790i \(0.392767\pi\)
\(440\) 1.39192 0.0663573
\(441\) 3.09883 0.147563
\(442\) 0.0669713 0.00318550
\(443\) −33.3882 −1.58632 −0.793160 0.609014i \(-0.791566\pi\)
−0.793160 + 0.609014i \(0.791566\pi\)
\(444\) 2.15739 0.102385
\(445\) −24.6358 −1.16785
\(446\) 3.36894 0.159524
\(447\) 5.78864 0.273793
\(448\) 3.17787 0.150140
\(449\) 7.89519 0.372597 0.186299 0.982493i \(-0.440351\pi\)
0.186299 + 0.982493i \(0.440351\pi\)
\(450\) −14.2635 −0.672389
\(451\) 1.63710 0.0770878
\(452\) 7.46423 0.351088
\(453\) −13.8353 −0.650037
\(454\) 15.7592 0.739617
\(455\) 13.9477 0.653880
\(456\) −0.603097 −0.0282426
\(457\) 17.9603 0.840147 0.420073 0.907490i \(-0.362004\pi\)
0.420073 + 0.907490i \(0.362004\pi\)
\(458\) 15.2657 0.713319
\(459\) 0.0669713 0.00312595
\(460\) −7.67296 −0.357753
\(461\) 38.6363 1.79947 0.899736 0.436435i \(-0.143759\pi\)
0.899736 + 0.436435i \(0.143759\pi\)
\(462\) −1.00782 −0.0468880
\(463\) 10.1677 0.472532 0.236266 0.971688i \(-0.424076\pi\)
0.236266 + 0.971688i \(0.424076\pi\)
\(464\) −3.43665 −0.159542
\(465\) −38.8938 −1.80366
\(466\) 9.72180 0.450354
\(467\) −27.6914 −1.28141 −0.640704 0.767788i \(-0.721357\pi\)
−0.640704 + 0.767788i \(0.721357\pi\)
\(468\) 1.00000 0.0462250
\(469\) 34.0307 1.57139
\(470\) 42.3859 1.95512
\(471\) 2.66183 0.122651
\(472\) −3.33339 −0.153432
\(473\) 2.43904 0.112147
\(474\) 11.2264 0.515645
\(475\) −8.60230 −0.394700
\(476\) −0.212826 −0.00975485
\(477\) 1.21273 0.0555271
\(478\) −19.8048 −0.905849
\(479\) 29.5369 1.34958 0.674788 0.738012i \(-0.264235\pi\)
0.674788 + 0.738012i \(0.264235\pi\)
\(480\) 4.38902 0.200331
\(481\) −2.15739 −0.0983686
\(482\) 3.02712 0.137882
\(483\) 5.55559 0.252788
\(484\) −10.8994 −0.495428
\(485\) −63.5503 −2.88567
\(486\) 1.00000 0.0453609
\(487\) 28.9844 1.31341 0.656704 0.754149i \(-0.271950\pi\)
0.656704 + 0.754149i \(0.271950\pi\)
\(488\) 1.56786 0.0709736
\(489\) −13.8385 −0.625797
\(490\) −13.6008 −0.614423
\(491\) 12.1292 0.547383 0.273691 0.961818i \(-0.411755\pi\)
0.273691 + 0.961818i \(0.411755\pi\)
\(492\) 5.16210 0.232726
\(493\) 0.230157 0.0103657
\(494\) 0.603097 0.0271346
\(495\) −1.39192 −0.0625623
\(496\) 8.86161 0.397898
\(497\) 23.7719 1.06631
\(498\) 14.1469 0.633938
\(499\) −32.1520 −1.43932 −0.719662 0.694325i \(-0.755703\pi\)
−0.719662 + 0.694325i \(0.755703\pi\)
\(500\) 40.6579 1.81828
\(501\) 14.7810 0.660367
\(502\) 28.3596 1.26575
\(503\) −33.3572 −1.48733 −0.743663 0.668555i \(-0.766913\pi\)
−0.743663 + 0.668555i \(0.766913\pi\)
\(504\) −3.17787 −0.141553
\(505\) −6.58110 −0.292855
\(506\) −0.554424 −0.0246471
\(507\) −1.00000 −0.0444116
\(508\) 11.4443 0.507758
\(509\) −36.3137 −1.60958 −0.804789 0.593561i \(-0.797722\pi\)
−0.804789 + 0.593561i \(0.797722\pi\)
\(510\) −0.293939 −0.0130158
\(511\) 5.67065 0.250855
\(512\) −1.00000 −0.0441942
\(513\) 0.603097 0.0266274
\(514\) 14.9816 0.660809
\(515\) −4.38902 −0.193404
\(516\) 7.69082 0.338569
\(517\) 3.06267 0.134696
\(518\) 6.85590 0.301231
\(519\) 11.2344 0.493137
\(520\) −4.38902 −0.192471
\(521\) −9.95854 −0.436292 −0.218146 0.975916i \(-0.570001\pi\)
−0.218146 + 0.975916i \(0.570001\pi\)
\(522\) 3.43665 0.150418
\(523\) −32.8462 −1.43626 −0.718132 0.695907i \(-0.755002\pi\)
−0.718132 + 0.695907i \(0.755002\pi\)
\(524\) 15.2916 0.668018
\(525\) −45.3276 −1.97826
\(526\) −6.77691 −0.295488
\(527\) −0.593473 −0.0258521
\(528\) 0.317137 0.0138016
\(529\) −19.9437 −0.867119
\(530\) −5.32270 −0.231203
\(531\) 3.33339 0.144657
\(532\) −1.91656 −0.0830935
\(533\) −5.16210 −0.223596
\(534\) −5.61305 −0.242900
\(535\) 77.5149 3.35126
\(536\) −10.7087 −0.462544
\(537\) −0.0728347 −0.00314305
\(538\) 12.0887 0.521183
\(539\) −0.982754 −0.0423302
\(540\) −4.38902 −0.188874
\(541\) 24.0208 1.03274 0.516368 0.856367i \(-0.327284\pi\)
0.516368 + 0.856367i \(0.327284\pi\)
\(542\) −5.54164 −0.238034
\(543\) −16.0467 −0.688629
\(544\) 0.0669713 0.00287137
\(545\) 49.2750 2.11071
\(546\) 3.17787 0.136000
\(547\) −13.9019 −0.594404 −0.297202 0.954815i \(-0.596053\pi\)
−0.297202 + 0.954815i \(0.596053\pi\)
\(548\) 12.0394 0.514298
\(549\) −1.56786 −0.0669146
\(550\) 4.52350 0.192883
\(551\) 2.07263 0.0882971
\(552\) −1.74821 −0.0744090
\(553\) 35.6759 1.51710
\(554\) 7.68176 0.326367
\(555\) 9.46885 0.401930
\(556\) 12.8288 0.544063
\(557\) −27.0255 −1.14511 −0.572553 0.819868i \(-0.694047\pi\)
−0.572553 + 0.819868i \(0.694047\pi\)
\(558\) −8.86161 −0.375142
\(559\) −7.69082 −0.325287
\(560\) 13.9477 0.589399
\(561\) −0.0212391 −0.000896715 0
\(562\) −8.11844 −0.342456
\(563\) −42.4281 −1.78813 −0.894065 0.447938i \(-0.852159\pi\)
−0.894065 + 0.447938i \(0.852159\pi\)
\(564\) 9.65725 0.406643
\(565\) 32.7607 1.37825
\(566\) 17.9023 0.752490
\(567\) 3.17787 0.133458
\(568\) −7.48046 −0.313873
\(569\) 9.34527 0.391774 0.195887 0.980626i \(-0.437241\pi\)
0.195887 + 0.980626i \(0.437241\pi\)
\(570\) −2.64701 −0.110871
\(571\) −38.3495 −1.60488 −0.802439 0.596734i \(-0.796465\pi\)
−0.802439 + 0.596734i \(0.796465\pi\)
\(572\) −0.317137 −0.0132602
\(573\) −15.8199 −0.660886
\(574\) 16.4045 0.684709
\(575\) −24.9357 −1.03989
\(576\) 1.00000 0.0416667
\(577\) −16.6561 −0.693401 −0.346701 0.937976i \(-0.612698\pi\)
−0.346701 + 0.937976i \(0.612698\pi\)
\(578\) 16.9955 0.706920
\(579\) −13.8895 −0.577230
\(580\) −15.0835 −0.626310
\(581\) 44.9570 1.86513
\(582\) −14.4794 −0.600189
\(583\) −0.384602 −0.0159286
\(584\) −1.78442 −0.0738399
\(585\) 4.38902 0.181464
\(586\) −13.4611 −0.556074
\(587\) 38.3225 1.58174 0.790869 0.611986i \(-0.209629\pi\)
0.790869 + 0.611986i \(0.209629\pi\)
\(588\) −3.09883 −0.127794
\(589\) −5.34441 −0.220213
\(590\) −14.6303 −0.602321
\(591\) 4.52312 0.186056
\(592\) −2.15739 −0.0886683
\(593\) −24.4873 −1.00557 −0.502786 0.864411i \(-0.667692\pi\)
−0.502786 + 0.864411i \(0.667692\pi\)
\(594\) −0.317137 −0.0130123
\(595\) −0.934097 −0.0382943
\(596\) −5.78864 −0.237112
\(597\) −12.3308 −0.504665
\(598\) 1.74821 0.0714898
\(599\) 35.9217 1.46772 0.733861 0.679300i \(-0.237716\pi\)
0.733861 + 0.679300i \(0.237716\pi\)
\(600\) 14.2635 0.582306
\(601\) 8.37411 0.341587 0.170794 0.985307i \(-0.445367\pi\)
0.170794 + 0.985307i \(0.445367\pi\)
\(602\) 24.4404 0.996116
\(603\) 10.7087 0.436090
\(604\) 13.8353 0.562949
\(605\) −47.8378 −1.94488
\(606\) −1.49945 −0.0609108
\(607\) −26.1849 −1.06281 −0.531407 0.847117i \(-0.678337\pi\)
−0.531407 + 0.847117i \(0.678337\pi\)
\(608\) 0.603097 0.0244588
\(609\) 10.9212 0.442550
\(610\) 6.88137 0.278618
\(611\) −9.65725 −0.390690
\(612\) −0.0669713 −0.00270715
\(613\) −3.17994 −0.128436 −0.0642182 0.997936i \(-0.520455\pi\)
−0.0642182 + 0.997936i \(0.520455\pi\)
\(614\) −16.7095 −0.674339
\(615\) 22.6566 0.913602
\(616\) 1.00782 0.0406062
\(617\) −42.0831 −1.69420 −0.847102 0.531431i \(-0.821655\pi\)
−0.847102 + 0.531431i \(0.821655\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 42.0366 1.68959 0.844796 0.535088i \(-0.179721\pi\)
0.844796 + 0.535088i \(0.179721\pi\)
\(620\) 38.8938 1.56201
\(621\) 1.74821 0.0701534
\(622\) 5.70647 0.228809
\(623\) −17.8375 −0.714645
\(624\) −1.00000 −0.0400320
\(625\) 107.131 4.28523
\(626\) 9.73053 0.388910
\(627\) −0.191264 −0.00763837
\(628\) −2.66183 −0.106219
\(629\) 0.144483 0.00576093
\(630\) −13.9477 −0.555691
\(631\) 45.4876 1.81083 0.905416 0.424526i \(-0.139559\pi\)
0.905416 + 0.424526i \(0.139559\pi\)
\(632\) −11.2264 −0.446562
\(633\) 22.7432 0.903961
\(634\) −23.1815 −0.920656
\(635\) 50.2293 1.99329
\(636\) −1.21273 −0.0480879
\(637\) 3.09883 0.122780
\(638\) −1.08989 −0.0431491
\(639\) 7.48046 0.295922
\(640\) −4.38902 −0.173491
\(641\) 1.95185 0.0770934 0.0385467 0.999257i \(-0.487727\pi\)
0.0385467 + 0.999257i \(0.487727\pi\)
\(642\) 17.6611 0.697027
\(643\) 14.3020 0.564015 0.282008 0.959412i \(-0.409000\pi\)
0.282008 + 0.959412i \(0.409000\pi\)
\(644\) −5.55559 −0.218921
\(645\) 33.7552 1.32911
\(646\) −0.0403902 −0.00158913
\(647\) −6.47633 −0.254611 −0.127305 0.991864i \(-0.540633\pi\)
−0.127305 + 0.991864i \(0.540633\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −1.05714 −0.0414964
\(650\) −14.2635 −0.559462
\(651\) −28.1610 −1.10372
\(652\) 13.8385 0.541956
\(653\) −29.5779 −1.15747 −0.578737 0.815514i \(-0.696454\pi\)
−0.578737 + 0.815514i \(0.696454\pi\)
\(654\) 11.2269 0.439005
\(655\) 67.1153 2.62241
\(656\) −5.16210 −0.201546
\(657\) 1.78442 0.0696170
\(658\) 30.6894 1.19640
\(659\) −19.8732 −0.774152 −0.387076 0.922048i \(-0.626515\pi\)
−0.387076 + 0.922048i \(0.626515\pi\)
\(660\) 1.39192 0.0541805
\(661\) 8.23911 0.320464 0.160232 0.987079i \(-0.448776\pi\)
0.160232 + 0.987079i \(0.448776\pi\)
\(662\) −12.7331 −0.494888
\(663\) 0.0669713 0.00260095
\(664\) −14.1469 −0.549007
\(665\) −8.41183 −0.326197
\(666\) 2.15739 0.0835972
\(667\) 6.00800 0.232631
\(668\) −14.7810 −0.571894
\(669\) 3.36894 0.130251
\(670\) −47.0006 −1.81579
\(671\) 0.497226 0.0191952
\(672\) 3.17787 0.122589
\(673\) 38.7797 1.49485 0.747424 0.664348i \(-0.231291\pi\)
0.747424 + 0.664348i \(0.231291\pi\)
\(674\) −27.4814 −1.05854
\(675\) −14.2635 −0.549004
\(676\) 1.00000 0.0384615
\(677\) 8.72540 0.335345 0.167672 0.985843i \(-0.446375\pi\)
0.167672 + 0.985843i \(0.446375\pi\)
\(678\) 7.46423 0.286662
\(679\) −46.0135 −1.76584
\(680\) 0.293939 0.0112720
\(681\) 15.7592 0.603894
\(682\) 2.81034 0.107614
\(683\) 13.2062 0.505320 0.252660 0.967555i \(-0.418695\pi\)
0.252660 + 0.967555i \(0.418695\pi\)
\(684\) −0.603097 −0.0230600
\(685\) 52.8413 2.01896
\(686\) 12.3974 0.473335
\(687\) 15.2657 0.582423
\(688\) −7.69082 −0.293210
\(689\) 1.21273 0.0462013
\(690\) −7.67296 −0.292104
\(691\) 45.8194 1.74305 0.871526 0.490349i \(-0.163131\pi\)
0.871526 + 0.490349i \(0.163131\pi\)
\(692\) −11.2344 −0.427069
\(693\) −1.00782 −0.0382839
\(694\) −3.55121 −0.134802
\(695\) 56.3060 2.13581
\(696\) −3.43665 −0.130266
\(697\) 0.345713 0.0130948
\(698\) −2.95104 −0.111699
\(699\) 9.72180 0.367712
\(700\) 45.3276 1.71322
\(701\) 0.867844 0.0327780 0.0163890 0.999866i \(-0.494783\pi\)
0.0163890 + 0.999866i \(0.494783\pi\)
\(702\) 1.00000 0.0377426
\(703\) 1.30112 0.0490725
\(704\) −0.317137 −0.0119526
\(705\) 42.3859 1.59634
\(706\) 1.76397 0.0663877
\(707\) −4.76503 −0.179208
\(708\) −3.33339 −0.125276
\(709\) −36.4419 −1.36860 −0.684301 0.729199i \(-0.739893\pi\)
−0.684301 + 0.729199i \(0.739893\pi\)
\(710\) −32.8319 −1.23216
\(711\) 11.2264 0.421022
\(712\) 5.61305 0.210358
\(713\) −15.4920 −0.580180
\(714\) −0.212826 −0.00796480
\(715\) −1.39192 −0.0520550
\(716\) 0.0728347 0.00272196
\(717\) −19.8048 −0.739623
\(718\) 32.2239 1.20259
\(719\) 2.34595 0.0874891 0.0437446 0.999043i \(-0.486071\pi\)
0.0437446 + 0.999043i \(0.486071\pi\)
\(720\) 4.38902 0.163569
\(721\) −3.17787 −0.118350
\(722\) 18.6363 0.693570
\(723\) 3.02712 0.112580
\(724\) 16.0467 0.596370
\(725\) −49.0188 −1.82051
\(726\) −10.8994 −0.404516
\(727\) −22.8839 −0.848717 −0.424358 0.905494i \(-0.639500\pi\)
−0.424358 + 0.905494i \(0.639500\pi\)
\(728\) −3.17787 −0.117780
\(729\) 1.00000 0.0370370
\(730\) −7.83187 −0.289871
\(731\) 0.515064 0.0190503
\(732\) 1.56786 0.0579497
\(733\) 16.5668 0.611908 0.305954 0.952046i \(-0.401025\pi\)
0.305954 + 0.952046i \(0.401025\pi\)
\(734\) −12.6441 −0.466701
\(735\) −13.6008 −0.501674
\(736\) 1.74821 0.0644400
\(737\) −3.39611 −0.125097
\(738\) 5.16210 0.190020
\(739\) −24.5264 −0.902218 −0.451109 0.892469i \(-0.648971\pi\)
−0.451109 + 0.892469i \(0.648971\pi\)
\(740\) −9.46885 −0.348082
\(741\) 0.603097 0.0221553
\(742\) −3.85389 −0.141481
\(743\) 35.4256 1.29964 0.649819 0.760089i \(-0.274845\pi\)
0.649819 + 0.760089i \(0.274845\pi\)
\(744\) 8.86161 0.324882
\(745\) −25.4065 −0.930822
\(746\) −25.9329 −0.949472
\(747\) 14.1469 0.517608
\(748\) 0.0212391 0.000776578 0
\(749\) 56.1245 2.05075
\(750\) 40.6579 1.48462
\(751\) −31.2108 −1.13890 −0.569448 0.822027i \(-0.692843\pi\)
−0.569448 + 0.822027i \(0.692843\pi\)
\(752\) −9.65725 −0.352164
\(753\) 28.3596 1.03348
\(754\) 3.43665 0.125155
\(755\) 60.7233 2.20995
\(756\) −3.17787 −0.115578
\(757\) 20.9244 0.760510 0.380255 0.924882i \(-0.375836\pi\)
0.380255 + 0.924882i \(0.375836\pi\)
\(758\) 12.5057 0.454227
\(759\) −0.554424 −0.0201243
\(760\) 2.64701 0.0960171
\(761\) 22.9920 0.833458 0.416729 0.909031i \(-0.363176\pi\)
0.416729 + 0.909031i \(0.363176\pi\)
\(762\) 11.4443 0.414583
\(763\) 35.6774 1.29161
\(764\) 15.8199 0.572344
\(765\) −0.293939 −0.0106274
\(766\) 15.7274 0.568255
\(767\) 3.33339 0.120362
\(768\) −1.00000 −0.0360844
\(769\) −11.9987 −0.432684 −0.216342 0.976318i \(-0.569413\pi\)
−0.216342 + 0.976318i \(0.569413\pi\)
\(770\) 4.42334 0.159406
\(771\) 14.9816 0.539548
\(772\) 13.8895 0.499896
\(773\) −31.8019 −1.14383 −0.571917 0.820311i \(-0.693800\pi\)
−0.571917 + 0.820311i \(0.693800\pi\)
\(774\) 7.69082 0.276441
\(775\) 126.398 4.54034
\(776\) 14.4794 0.519779
\(777\) 6.85590 0.245954
\(778\) 24.0985 0.863973
\(779\) 3.11325 0.111544
\(780\) −4.38902 −0.157152
\(781\) −2.37233 −0.0848887
\(782\) −0.117080 −0.00418678
\(783\) 3.43665 0.122816
\(784\) 3.09883 0.110672
\(785\) −11.6828 −0.416979
\(786\) 15.2916 0.545434
\(787\) 19.1991 0.684373 0.342187 0.939632i \(-0.388832\pi\)
0.342187 + 0.939632i \(0.388832\pi\)
\(788\) −4.52312 −0.161129
\(789\) −6.77691 −0.241265
\(790\) −49.2729 −1.75305
\(791\) 23.7203 0.843397
\(792\) 0.317137 0.0112690
\(793\) −1.56786 −0.0556763
\(794\) 13.8368 0.491048
\(795\) −5.32270 −0.188777
\(796\) 12.3308 0.437053
\(797\) −34.5685 −1.22448 −0.612239 0.790673i \(-0.709731\pi\)
−0.612239 + 0.790673i \(0.709731\pi\)
\(798\) −1.91656 −0.0678455
\(799\) 0.646758 0.0228807
\(800\) −14.2635 −0.504292
\(801\) −5.61305 −0.198327
\(802\) −6.88741 −0.243203
\(803\) −0.565907 −0.0199704
\(804\) −10.7087 −0.377665
\(805\) −24.3836 −0.859410
\(806\) −8.86161 −0.312137
\(807\) 12.0887 0.425544
\(808\) 1.49945 0.0527503
\(809\) −9.49050 −0.333668 −0.166834 0.985985i \(-0.553354\pi\)
−0.166834 + 0.985985i \(0.553354\pi\)
\(810\) −4.38902 −0.154215
\(811\) −45.2590 −1.58926 −0.794630 0.607094i \(-0.792335\pi\)
−0.794630 + 0.607094i \(0.792335\pi\)
\(812\) −10.9212 −0.383259
\(813\) −5.54164 −0.194354
\(814\) −0.684189 −0.0239808
\(815\) 60.7374 2.12754
\(816\) 0.0669713 0.00234446
\(817\) 4.63831 0.162274
\(818\) −25.9075 −0.905835
\(819\) 3.17787 0.111044
\(820\) −22.6566 −0.791203
\(821\) 6.50891 0.227162 0.113581 0.993529i \(-0.463768\pi\)
0.113581 + 0.993529i \(0.463768\pi\)
\(822\) 12.0394 0.419923
\(823\) −16.1757 −0.563850 −0.281925 0.959436i \(-0.590973\pi\)
−0.281925 + 0.959436i \(0.590973\pi\)
\(824\) 1.00000 0.0348367
\(825\) 4.52350 0.157488
\(826\) −10.5931 −0.368580
\(827\) 32.9949 1.14735 0.573673 0.819085i \(-0.305518\pi\)
0.573673 + 0.819085i \(0.305518\pi\)
\(828\) −1.74821 −0.0607547
\(829\) 8.53777 0.296529 0.148265 0.988948i \(-0.452631\pi\)
0.148265 + 0.988948i \(0.452631\pi\)
\(830\) −62.0911 −2.15521
\(831\) 7.68176 0.266477
\(832\) 1.00000 0.0346688
\(833\) −0.207533 −0.00719058
\(834\) 12.8288 0.444226
\(835\) −64.8742 −2.24506
\(836\) 0.191264 0.00661502
\(837\) −8.86161 −0.306302
\(838\) 4.11772 0.142244
\(839\) −46.7210 −1.61299 −0.806494 0.591242i \(-0.798638\pi\)
−0.806494 + 0.591242i \(0.798638\pi\)
\(840\) 13.9477 0.481242
\(841\) −17.1894 −0.592739
\(842\) 27.3877 0.943841
\(843\) −8.11844 −0.279614
\(844\) −22.7432 −0.782853
\(845\) 4.38902 0.150987
\(846\) 9.65725 0.332023
\(847\) −34.6369 −1.19014
\(848\) 1.21273 0.0416453
\(849\) 17.9023 0.614406
\(850\) 0.955247 0.0327647
\(851\) 3.77158 0.129288
\(852\) −7.48046 −0.256276
\(853\) −38.2934 −1.31114 −0.655571 0.755134i \(-0.727572\pi\)
−0.655571 + 0.755134i \(0.727572\pi\)
\(854\) 4.98244 0.170496
\(855\) −2.64701 −0.0905257
\(856\) −17.6611 −0.603643
\(857\) 15.5298 0.530487 0.265243 0.964181i \(-0.414548\pi\)
0.265243 + 0.964181i \(0.414548\pi\)
\(858\) −0.317137 −0.0108269
\(859\) 54.9452 1.87471 0.937353 0.348380i \(-0.113268\pi\)
0.937353 + 0.348380i \(0.113268\pi\)
\(860\) −33.7552 −1.15104
\(861\) 16.4045 0.559063
\(862\) 11.4537 0.390114
\(863\) −22.9931 −0.782695 −0.391348 0.920243i \(-0.627991\pi\)
−0.391348 + 0.920243i \(0.627991\pi\)
\(864\) 1.00000 0.0340207
\(865\) −49.3082 −1.67653
\(866\) 0.352422 0.0119758
\(867\) 16.9955 0.577198
\(868\) 28.1610 0.955846
\(869\) −3.56030 −0.120775
\(870\) −15.0835 −0.511380
\(871\) 10.7087 0.362849
\(872\) −11.2269 −0.380189
\(873\) −14.4794 −0.490053
\(874\) −1.05434 −0.0356637
\(875\) 129.205 4.36794
\(876\) −1.78442 −0.0602900
\(877\) 30.5964 1.03317 0.516583 0.856237i \(-0.327204\pi\)
0.516583 + 0.856237i \(0.327204\pi\)
\(878\) −13.8515 −0.467464
\(879\) −13.4611 −0.454032
\(880\) −1.39192 −0.0469217
\(881\) −37.3051 −1.25684 −0.628421 0.777874i \(-0.716298\pi\)
−0.628421 + 0.777874i \(0.716298\pi\)
\(882\) −3.09883 −0.104343
\(883\) 4.76054 0.160205 0.0801024 0.996787i \(-0.474475\pi\)
0.0801024 + 0.996787i \(0.474475\pi\)
\(884\) −0.0669713 −0.00225249
\(885\) −14.6303 −0.491793
\(886\) 33.3882 1.12170
\(887\) 8.76624 0.294342 0.147171 0.989111i \(-0.452983\pi\)
0.147171 + 0.989111i \(0.452983\pi\)
\(888\) −2.15739 −0.0723973
\(889\) 36.3684 1.21976
\(890\) 24.6358 0.825794
\(891\) −0.317137 −0.0106245
\(892\) −3.36894 −0.112800
\(893\) 5.82426 0.194901
\(894\) −5.78864 −0.193601
\(895\) 0.319673 0.0106855
\(896\) −3.17787 −0.106165
\(897\) 1.74821 0.0583712
\(898\) −7.89519 −0.263466
\(899\) −30.4542 −1.01571
\(900\) 14.2635 0.475451
\(901\) −0.0812181 −0.00270577
\(902\) −1.63710 −0.0545093
\(903\) 24.4404 0.813325
\(904\) −7.46423 −0.248257
\(905\) 70.4293 2.34115
\(906\) 13.8353 0.459646
\(907\) −30.0811 −0.998827 −0.499413 0.866364i \(-0.666451\pi\)
−0.499413 + 0.866364i \(0.666451\pi\)
\(908\) −15.7592 −0.522988
\(909\) −1.49945 −0.0497335
\(910\) −13.9477 −0.462363
\(911\) −12.8048 −0.424241 −0.212121 0.977244i \(-0.568037\pi\)
−0.212121 + 0.977244i \(0.568037\pi\)
\(912\) 0.603097 0.0199705
\(913\) −4.48651 −0.148482
\(914\) −17.9603 −0.594073
\(915\) 6.88137 0.227491
\(916\) −15.2657 −0.504393
\(917\) 48.5947 1.60474
\(918\) −0.0669713 −0.00221038
\(919\) −24.7901 −0.817750 −0.408875 0.912591i \(-0.634079\pi\)
−0.408875 + 0.912591i \(0.634079\pi\)
\(920\) 7.67296 0.252970
\(921\) −16.7095 −0.550596
\(922\) −38.6363 −1.27242
\(923\) 7.48046 0.246222
\(924\) 1.00782 0.0331548
\(925\) −30.7720 −1.01178
\(926\) −10.1677 −0.334131
\(927\) −1.00000 −0.0328443
\(928\) 3.43665 0.112814
\(929\) −46.8194 −1.53609 −0.768047 0.640394i \(-0.778771\pi\)
−0.768047 + 0.640394i \(0.778771\pi\)
\(930\) 38.8938 1.27538
\(931\) −1.86889 −0.0612505
\(932\) −9.72180 −0.318448
\(933\) 5.70647 0.186821
\(934\) 27.6914 0.906092
\(935\) 0.0932189 0.00304858
\(936\) −1.00000 −0.0326860
\(937\) 5.43242 0.177469 0.0887346 0.996055i \(-0.471718\pi\)
0.0887346 + 0.996055i \(0.471718\pi\)
\(938\) −34.0307 −1.11114
\(939\) 9.73053 0.317544
\(940\) −42.3859 −1.38248
\(941\) 30.8656 1.00619 0.503094 0.864232i \(-0.332195\pi\)
0.503094 + 0.864232i \(0.332195\pi\)
\(942\) −2.66183 −0.0867272
\(943\) 9.02447 0.293877
\(944\) 3.33339 0.108493
\(945\) −13.9477 −0.453720
\(946\) −2.43904 −0.0793002
\(947\) −48.5229 −1.57678 −0.788391 0.615174i \(-0.789086\pi\)
−0.788391 + 0.615174i \(0.789086\pi\)
\(948\) −11.2264 −0.364616
\(949\) 1.78442 0.0579248
\(950\) 8.60230 0.279095
\(951\) −23.1815 −0.751713
\(952\) 0.212826 0.00689772
\(953\) 11.0417 0.357676 0.178838 0.983879i \(-0.442766\pi\)
0.178838 + 0.983879i \(0.442766\pi\)
\(954\) −1.21273 −0.0392636
\(955\) 69.4340 2.24683
\(956\) 19.8048 0.640532
\(957\) −1.08989 −0.0352311
\(958\) −29.5369 −0.954294
\(959\) 38.2596 1.23547
\(960\) −4.38902 −0.141655
\(961\) 47.5281 1.53316
\(962\) 2.15739 0.0695571
\(963\) 17.6611 0.569120
\(964\) −3.02712 −0.0974971
\(965\) 60.9615 1.96242
\(966\) −5.55559 −0.178748
\(967\) −36.0131 −1.15810 −0.579051 0.815291i \(-0.696577\pi\)
−0.579051 + 0.815291i \(0.696577\pi\)
\(968\) 10.8994 0.350321
\(969\) −0.0403902 −0.00129752
\(970\) 63.5503 2.04048
\(971\) −33.1873 −1.06503 −0.532516 0.846420i \(-0.678753\pi\)
−0.532516 + 0.846420i \(0.678753\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 40.7683 1.30697
\(974\) −28.9844 −0.928719
\(975\) −14.2635 −0.456799
\(976\) −1.56786 −0.0501859
\(977\) 2.33302 0.0746399 0.0373199 0.999303i \(-0.488118\pi\)
0.0373199 + 0.999303i \(0.488118\pi\)
\(978\) 13.8385 0.442505
\(979\) 1.78011 0.0568925
\(980\) 13.6008 0.434463
\(981\) 11.2269 0.358446
\(982\) −12.1292 −0.387058
\(983\) 8.08186 0.257771 0.128886 0.991659i \(-0.458860\pi\)
0.128886 + 0.991659i \(0.458860\pi\)
\(984\) −5.16210 −0.164562
\(985\) −19.8521 −0.632540
\(986\) −0.230157 −0.00732969
\(987\) 30.6894 0.976855
\(988\) −0.603097 −0.0191871
\(989\) 13.4452 0.427533
\(990\) 1.39192 0.0442382
\(991\) 22.9225 0.728157 0.364078 0.931368i \(-0.381384\pi\)
0.364078 + 0.931368i \(0.381384\pi\)
\(992\) −8.86161 −0.281356
\(993\) −12.7331 −0.404074
\(994\) −23.7719 −0.753998
\(995\) 54.1200 1.71572
\(996\) −14.1469 −0.448262
\(997\) 20.9069 0.662128 0.331064 0.943608i \(-0.392592\pi\)
0.331064 + 0.943608i \(0.392592\pi\)
\(998\) 32.1520 1.01776
\(999\) 2.15739 0.0682569
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.z.1.14 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.z.1.14 14 1.1 even 1 trivial