Properties

Label 8034.2.a.bb.1.2
Level $8034$
Weight $2$
Character 8034.1
Self dual yes
Analytic conductor $64.152$
Analytic rank $1$
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: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + 678 x^{6} - 39390 x^{5} - 3280 x^{4} + 42456 x^{3} + 10816 x^{2} - 7296 x - 2048\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(3.81560\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.81560 q^{5} -1.00000 q^{6} +4.94203 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.81560 q^{5} -1.00000 q^{6} +4.94203 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.81560 q^{10} +2.65767 q^{11} +1.00000 q^{12} -1.00000 q^{13} -4.94203 q^{14} -3.81560 q^{15} +1.00000 q^{16} -4.45654 q^{17} -1.00000 q^{18} +3.06468 q^{19} -3.81560 q^{20} +4.94203 q^{21} -2.65767 q^{22} -3.71423 q^{23} -1.00000 q^{24} +9.55882 q^{25} +1.00000 q^{26} +1.00000 q^{27} +4.94203 q^{28} +5.31017 q^{29} +3.81560 q^{30} -4.66765 q^{31} -1.00000 q^{32} +2.65767 q^{33} +4.45654 q^{34} -18.8568 q^{35} +1.00000 q^{36} -5.87682 q^{37} -3.06468 q^{38} -1.00000 q^{39} +3.81560 q^{40} -6.56132 q^{41} -4.94203 q^{42} -5.51993 q^{43} +2.65767 q^{44} -3.81560 q^{45} +3.71423 q^{46} -10.0443 q^{47} +1.00000 q^{48} +17.4236 q^{49} -9.55882 q^{50} -4.45654 q^{51} -1.00000 q^{52} -10.4448 q^{53} -1.00000 q^{54} -10.1406 q^{55} -4.94203 q^{56} +3.06468 q^{57} -5.31017 q^{58} +10.2648 q^{59} -3.81560 q^{60} -4.64313 q^{61} +4.66765 q^{62} +4.94203 q^{63} +1.00000 q^{64} +3.81560 q^{65} -2.65767 q^{66} -1.96165 q^{67} -4.45654 q^{68} -3.71423 q^{69} +18.8568 q^{70} -13.9630 q^{71} -1.00000 q^{72} -1.93219 q^{73} +5.87682 q^{74} +9.55882 q^{75} +3.06468 q^{76} +13.1343 q^{77} +1.00000 q^{78} -5.22572 q^{79} -3.81560 q^{80} +1.00000 q^{81} +6.56132 q^{82} +3.46955 q^{83} +4.94203 q^{84} +17.0044 q^{85} +5.51993 q^{86} +5.31017 q^{87} -2.65767 q^{88} +8.23562 q^{89} +3.81560 q^{90} -4.94203 q^{91} -3.71423 q^{92} -4.66765 q^{93} +10.0443 q^{94} -11.6936 q^{95} -1.00000 q^{96} +14.4149 q^{97} -17.4236 q^{98} +2.65767 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} + 14q^{3} + 14q^{4} - 6q^{5} - 14q^{6} - 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} + 14q^{3} + 14q^{4} - 6q^{5} - 14q^{6} - 4q^{7} - 14q^{8} + 14q^{9} + 6q^{10} - 8q^{11} + 14q^{12} - 14q^{13} + 4q^{14} - 6q^{15} + 14q^{16} - 4q^{17} - 14q^{18} - q^{19} - 6q^{20} - 4q^{21} + 8q^{22} - 9q^{23} - 14q^{24} + 24q^{25} + 14q^{26} + 14q^{27} - 4q^{28} - 10q^{29} + 6q^{30} - 5q^{31} - 14q^{32} - 8q^{33} + 4q^{34} - 16q^{35} + 14q^{36} - 4q^{37} + q^{38} - 14q^{39} + 6q^{40} - 24q^{41} + 4q^{42} - 8q^{44} - 6q^{45} + 9q^{46} - 32q^{47} + 14q^{48} + 24q^{49} - 24q^{50} - 4q^{51} - 14q^{52} - 5q^{53} - 14q^{54} - 8q^{55} + 4q^{56} - q^{57} + 10q^{58} - 13q^{59} - 6q^{60} + 2q^{61} + 5q^{62} - 4q^{63} + 14q^{64} + 6q^{65} + 8q^{66} - 16q^{67} - 4q^{68} - 9q^{69} + 16q^{70} - 29q^{71} - 14q^{72} + 4q^{74} + 24q^{75} - q^{76} - 9q^{77} + 14q^{78} - 21q^{79} - 6q^{80} + 14q^{81} + 24q^{82} - 40q^{83} - 4q^{84} - 7q^{85} - 10q^{87} + 8q^{88} - 48q^{89} + 6q^{90} + 4q^{91} - 9q^{92} - 5q^{93} + 32q^{94} - 26q^{95} - 14q^{96} + 18q^{97} - 24q^{98} - 8q^{99} + O(q^{100}) \)

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
\(5\) −3.81560 −1.70639 −0.853195 0.521593i \(-0.825338\pi\)
−0.853195 + 0.521593i \(0.825338\pi\)
\(6\) −1.00000 −0.408248
\(7\) 4.94203 1.86791 0.933956 0.357389i \(-0.116333\pi\)
0.933956 + 0.357389i \(0.116333\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 3.81560 1.20660
\(11\) 2.65767 0.801318 0.400659 0.916227i \(-0.368781\pi\)
0.400659 + 0.916227i \(0.368781\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 −0.277350
\(14\) −4.94203 −1.32081
\(15\) −3.81560 −0.985184
\(16\) 1.00000 0.250000
\(17\) −4.45654 −1.08087 −0.540435 0.841386i \(-0.681740\pi\)
−0.540435 + 0.841386i \(0.681740\pi\)
\(18\) −1.00000 −0.235702
\(19\) 3.06468 0.703086 0.351543 0.936172i \(-0.385657\pi\)
0.351543 + 0.936172i \(0.385657\pi\)
\(20\) −3.81560 −0.853195
\(21\) 4.94203 1.07844
\(22\) −2.65767 −0.566617
\(23\) −3.71423 −0.774470 −0.387235 0.921981i \(-0.626570\pi\)
−0.387235 + 0.921981i \(0.626570\pi\)
\(24\) −1.00000 −0.204124
\(25\) 9.55882 1.91176
\(26\) 1.00000 0.196116
\(27\) 1.00000 0.192450
\(28\) 4.94203 0.933956
\(29\) 5.31017 0.986074 0.493037 0.870008i \(-0.335887\pi\)
0.493037 + 0.870008i \(0.335887\pi\)
\(30\) 3.81560 0.696631
\(31\) −4.66765 −0.838335 −0.419167 0.907909i \(-0.637678\pi\)
−0.419167 + 0.907909i \(0.637678\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.65767 0.462641
\(34\) 4.45654 0.764291
\(35\) −18.8568 −3.18738
\(36\) 1.00000 0.166667
\(37\) −5.87682 −0.966144 −0.483072 0.875581i \(-0.660479\pi\)
−0.483072 + 0.875581i \(0.660479\pi\)
\(38\) −3.06468 −0.497157
\(39\) −1.00000 −0.160128
\(40\) 3.81560 0.603300
\(41\) −6.56132 −1.02471 −0.512353 0.858775i \(-0.671226\pi\)
−0.512353 + 0.858775i \(0.671226\pi\)
\(42\) −4.94203 −0.762572
\(43\) −5.51993 −0.841781 −0.420890 0.907111i \(-0.638282\pi\)
−0.420890 + 0.907111i \(0.638282\pi\)
\(44\) 2.65767 0.400659
\(45\) −3.81560 −0.568796
\(46\) 3.71423 0.547633
\(47\) −10.0443 −1.46511 −0.732554 0.680708i \(-0.761672\pi\)
−0.732554 + 0.680708i \(0.761672\pi\)
\(48\) 1.00000 0.144338
\(49\) 17.4236 2.48909
\(50\) −9.55882 −1.35182
\(51\) −4.45654 −0.624041
\(52\) −1.00000 −0.138675
\(53\) −10.4448 −1.43470 −0.717348 0.696715i \(-0.754644\pi\)
−0.717348 + 0.696715i \(0.754644\pi\)
\(54\) −1.00000 −0.136083
\(55\) −10.1406 −1.36736
\(56\) −4.94203 −0.660406
\(57\) 3.06468 0.405927
\(58\) −5.31017 −0.697260
\(59\) 10.2648 1.33636 0.668179 0.744001i \(-0.267074\pi\)
0.668179 + 0.744001i \(0.267074\pi\)
\(60\) −3.81560 −0.492592
\(61\) −4.64313 −0.594492 −0.297246 0.954801i \(-0.596068\pi\)
−0.297246 + 0.954801i \(0.596068\pi\)
\(62\) 4.66765 0.592792
\(63\) 4.94203 0.622637
\(64\) 1.00000 0.125000
\(65\) 3.81560 0.473267
\(66\) −2.65767 −0.327137
\(67\) −1.96165 −0.239654 −0.119827 0.992795i \(-0.538234\pi\)
−0.119827 + 0.992795i \(0.538234\pi\)
\(68\) −4.45654 −0.540435
\(69\) −3.71423 −0.447140
\(70\) 18.8568 2.25382
\(71\) −13.9630 −1.65710 −0.828550 0.559914i \(-0.810834\pi\)
−0.828550 + 0.559914i \(0.810834\pi\)
\(72\) −1.00000 −0.117851
\(73\) −1.93219 −0.226146 −0.113073 0.993587i \(-0.536069\pi\)
−0.113073 + 0.993587i \(0.536069\pi\)
\(74\) 5.87682 0.683167
\(75\) 9.55882 1.10376
\(76\) 3.06468 0.351543
\(77\) 13.1343 1.49679
\(78\) 1.00000 0.113228
\(79\) −5.22572 −0.587940 −0.293970 0.955815i \(-0.594977\pi\)
−0.293970 + 0.955815i \(0.594977\pi\)
\(80\) −3.81560 −0.426597
\(81\) 1.00000 0.111111
\(82\) 6.56132 0.724576
\(83\) 3.46955 0.380833 0.190417 0.981703i \(-0.439016\pi\)
0.190417 + 0.981703i \(0.439016\pi\)
\(84\) 4.94203 0.539220
\(85\) 17.0044 1.84439
\(86\) 5.51993 0.595229
\(87\) 5.31017 0.569310
\(88\) −2.65767 −0.283309
\(89\) 8.23562 0.872974 0.436487 0.899710i \(-0.356222\pi\)
0.436487 + 0.899710i \(0.356222\pi\)
\(90\) 3.81560 0.402200
\(91\) −4.94203 −0.518065
\(92\) −3.71423 −0.387235
\(93\) −4.66765 −0.484013
\(94\) 10.0443 1.03599
\(95\) −11.6936 −1.19974
\(96\) −1.00000 −0.102062
\(97\) 14.4149 1.46361 0.731806 0.681512i \(-0.238677\pi\)
0.731806 + 0.681512i \(0.238677\pi\)
\(98\) −17.4236 −1.76005
\(99\) 2.65767 0.267106
\(100\) 9.55882 0.955882
\(101\) 1.10372 0.109824 0.0549121 0.998491i \(-0.482512\pi\)
0.0549121 + 0.998491i \(0.482512\pi\)
\(102\) 4.45654 0.441264
\(103\) 1.00000 0.0985329
\(104\) 1.00000 0.0980581
\(105\) −18.8568 −1.84024
\(106\) 10.4448 1.01448
\(107\) 4.79136 0.463198 0.231599 0.972811i \(-0.425604\pi\)
0.231599 + 0.972811i \(0.425604\pi\)
\(108\) 1.00000 0.0962250
\(109\) −16.7042 −1.59997 −0.799986 0.600019i \(-0.795160\pi\)
−0.799986 + 0.600019i \(0.795160\pi\)
\(110\) 10.1406 0.966870
\(111\) −5.87682 −0.557803
\(112\) 4.94203 0.466978
\(113\) −2.10850 −0.198351 −0.0991754 0.995070i \(-0.531620\pi\)
−0.0991754 + 0.995070i \(0.531620\pi\)
\(114\) −3.06468 −0.287034
\(115\) 14.1720 1.32155
\(116\) 5.31017 0.493037
\(117\) −1.00000 −0.0924500
\(118\) −10.2648 −0.944948
\(119\) −22.0244 −2.01897
\(120\) 3.81560 0.348315
\(121\) −3.93678 −0.357889
\(122\) 4.64313 0.420369
\(123\) −6.56132 −0.591614
\(124\) −4.66765 −0.419167
\(125\) −17.3947 −1.55582
\(126\) −4.94203 −0.440271
\(127\) 9.05858 0.803819 0.401910 0.915679i \(-0.368347\pi\)
0.401910 + 0.915679i \(0.368347\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.51993 −0.486002
\(130\) −3.81560 −0.334650
\(131\) −13.6776 −1.19501 −0.597507 0.801863i \(-0.703842\pi\)
−0.597507 + 0.801863i \(0.703842\pi\)
\(132\) 2.65767 0.231321
\(133\) 15.1457 1.31330
\(134\) 1.96165 0.169461
\(135\) −3.81560 −0.328395
\(136\) 4.45654 0.382145
\(137\) 14.1768 1.21121 0.605603 0.795767i \(-0.292932\pi\)
0.605603 + 0.795767i \(0.292932\pi\)
\(138\) 3.71423 0.316176
\(139\) −9.95588 −0.844446 −0.422223 0.906492i \(-0.638750\pi\)
−0.422223 + 0.906492i \(0.638750\pi\)
\(140\) −18.8568 −1.59369
\(141\) −10.0443 −0.845881
\(142\) 13.9630 1.17175
\(143\) −2.65767 −0.222246
\(144\) 1.00000 0.0833333
\(145\) −20.2615 −1.68263
\(146\) 1.93219 0.159909
\(147\) 17.4236 1.43708
\(148\) −5.87682 −0.483072
\(149\) −5.41225 −0.443389 −0.221694 0.975116i \(-0.571159\pi\)
−0.221694 + 0.975116i \(0.571159\pi\)
\(150\) −9.55882 −0.780475
\(151\) −13.5624 −1.10369 −0.551846 0.833946i \(-0.686076\pi\)
−0.551846 + 0.833946i \(0.686076\pi\)
\(152\) −3.06468 −0.248578
\(153\) −4.45654 −0.360290
\(154\) −13.1343 −1.05839
\(155\) 17.8099 1.43053
\(156\) −1.00000 −0.0800641
\(157\) 8.54028 0.681588 0.340794 0.940138i \(-0.389304\pi\)
0.340794 + 0.940138i \(0.389304\pi\)
\(158\) 5.22572 0.415736
\(159\) −10.4448 −0.828323
\(160\) 3.81560 0.301650
\(161\) −18.3558 −1.44664
\(162\) −1.00000 −0.0785674
\(163\) −0.940059 −0.0736311 −0.0368155 0.999322i \(-0.511721\pi\)
−0.0368155 + 0.999322i \(0.511721\pi\)
\(164\) −6.56132 −0.512353
\(165\) −10.1406 −0.789446
\(166\) −3.46955 −0.269290
\(167\) 18.9730 1.46818 0.734088 0.679054i \(-0.237610\pi\)
0.734088 + 0.679054i \(0.237610\pi\)
\(168\) −4.94203 −0.381286
\(169\) 1.00000 0.0769231
\(170\) −17.0044 −1.30418
\(171\) 3.06468 0.234362
\(172\) −5.51993 −0.420890
\(173\) −3.59876 −0.273609 −0.136804 0.990598i \(-0.543683\pi\)
−0.136804 + 0.990598i \(0.543683\pi\)
\(174\) −5.31017 −0.402563
\(175\) 47.2400 3.57101
\(176\) 2.65767 0.200330
\(177\) 10.2648 0.771547
\(178\) −8.23562 −0.617286
\(179\) −12.3216 −0.920958 −0.460479 0.887671i \(-0.652322\pi\)
−0.460479 + 0.887671i \(0.652322\pi\)
\(180\) −3.81560 −0.284398
\(181\) −14.3167 −1.06416 −0.532078 0.846695i \(-0.678589\pi\)
−0.532078 + 0.846695i \(0.678589\pi\)
\(182\) 4.94203 0.366328
\(183\) −4.64313 −0.343230
\(184\) 3.71423 0.273816
\(185\) 22.4236 1.64862
\(186\) 4.66765 0.342249
\(187\) −11.8440 −0.866121
\(188\) −10.0443 −0.732554
\(189\) 4.94203 0.359480
\(190\) 11.6936 0.848343
\(191\) −2.81037 −0.203351 −0.101676 0.994818i \(-0.532420\pi\)
−0.101676 + 0.994818i \(0.532420\pi\)
\(192\) 1.00000 0.0721688
\(193\) −18.6496 −1.34243 −0.671214 0.741263i \(-0.734227\pi\)
−0.671214 + 0.741263i \(0.734227\pi\)
\(194\) −14.4149 −1.03493
\(195\) 3.81560 0.273241
\(196\) 17.4236 1.24455
\(197\) −2.28606 −0.162875 −0.0814375 0.996678i \(-0.525951\pi\)
−0.0814375 + 0.996678i \(0.525951\pi\)
\(198\) −2.65767 −0.188872
\(199\) 5.66189 0.401361 0.200680 0.979657i \(-0.435685\pi\)
0.200680 + 0.979657i \(0.435685\pi\)
\(200\) −9.55882 −0.675911
\(201\) −1.96165 −0.138364
\(202\) −1.10372 −0.0776575
\(203\) 26.2430 1.84190
\(204\) −4.45654 −0.312020
\(205\) 25.0354 1.74855
\(206\) −1.00000 −0.0696733
\(207\) −3.71423 −0.258157
\(208\) −1.00000 −0.0693375
\(209\) 8.14491 0.563395
\(210\) 18.8568 1.30124
\(211\) 13.0173 0.896148 0.448074 0.893996i \(-0.352110\pi\)
0.448074 + 0.893996i \(0.352110\pi\)
\(212\) −10.4448 −0.717348
\(213\) −13.9630 −0.956728
\(214\) −4.79136 −0.327530
\(215\) 21.0618 1.43641
\(216\) −1.00000 −0.0680414
\(217\) −23.0677 −1.56594
\(218\) 16.7042 1.13135
\(219\) −1.93219 −0.130565
\(220\) −10.1406 −0.683680
\(221\) 4.45654 0.299780
\(222\) 5.87682 0.394426
\(223\) 3.43833 0.230247 0.115124 0.993351i \(-0.463274\pi\)
0.115124 + 0.993351i \(0.463274\pi\)
\(224\) −4.94203 −0.330203
\(225\) 9.55882 0.637255
\(226\) 2.10850 0.140255
\(227\) −14.8404 −0.984990 −0.492495 0.870315i \(-0.663915\pi\)
−0.492495 + 0.870315i \(0.663915\pi\)
\(228\) 3.06468 0.202963
\(229\) 4.64030 0.306640 0.153320 0.988177i \(-0.451004\pi\)
0.153320 + 0.988177i \(0.451004\pi\)
\(230\) −14.1720 −0.934475
\(231\) 13.1343 0.864173
\(232\) −5.31017 −0.348630
\(233\) 18.5533 1.21547 0.607734 0.794141i \(-0.292079\pi\)
0.607734 + 0.794141i \(0.292079\pi\)
\(234\) 1.00000 0.0653720
\(235\) 38.3250 2.50005
\(236\) 10.2648 0.668179
\(237\) −5.22572 −0.339447
\(238\) 22.0244 1.42763
\(239\) 3.39069 0.219325 0.109663 0.993969i \(-0.465023\pi\)
0.109663 + 0.993969i \(0.465023\pi\)
\(240\) −3.81560 −0.246296
\(241\) −20.7142 −1.33432 −0.667158 0.744916i \(-0.732489\pi\)
−0.667158 + 0.744916i \(0.732489\pi\)
\(242\) 3.93678 0.253066
\(243\) 1.00000 0.0641500
\(244\) −4.64313 −0.297246
\(245\) −66.4817 −4.24736
\(246\) 6.56132 0.418334
\(247\) −3.06468 −0.195001
\(248\) 4.66765 0.296396
\(249\) 3.46955 0.219874
\(250\) 17.3947 1.10013
\(251\) 14.5570 0.918830 0.459415 0.888222i \(-0.348059\pi\)
0.459415 + 0.888222i \(0.348059\pi\)
\(252\) 4.94203 0.311319
\(253\) −9.87120 −0.620597
\(254\) −9.05858 −0.568386
\(255\) 17.0044 1.06486
\(256\) 1.00000 0.0625000
\(257\) 24.7082 1.54125 0.770627 0.637286i \(-0.219943\pi\)
0.770627 + 0.637286i \(0.219943\pi\)
\(258\) 5.51993 0.343656
\(259\) −29.0434 −1.80467
\(260\) 3.81560 0.236634
\(261\) 5.31017 0.328691
\(262\) 13.6776 0.845003
\(263\) −14.4358 −0.890147 −0.445074 0.895494i \(-0.646822\pi\)
−0.445074 + 0.895494i \(0.646822\pi\)
\(264\) −2.65767 −0.163568
\(265\) 39.8530 2.44815
\(266\) −15.1457 −0.928645
\(267\) 8.23562 0.504012
\(268\) −1.96165 −0.119827
\(269\) −5.54942 −0.338354 −0.169177 0.985586i \(-0.554111\pi\)
−0.169177 + 0.985586i \(0.554111\pi\)
\(270\) 3.81560 0.232210
\(271\) 18.8197 1.14321 0.571606 0.820528i \(-0.306320\pi\)
0.571606 + 0.820528i \(0.306320\pi\)
\(272\) −4.45654 −0.270218
\(273\) −4.94203 −0.299105
\(274\) −14.1768 −0.856452
\(275\) 25.4042 1.53193
\(276\) −3.71423 −0.223570
\(277\) 13.4083 0.805627 0.402814 0.915282i \(-0.368032\pi\)
0.402814 + 0.915282i \(0.368032\pi\)
\(278\) 9.95588 0.597114
\(279\) −4.66765 −0.279445
\(280\) 18.8568 1.12691
\(281\) −31.6493 −1.88804 −0.944020 0.329889i \(-0.892989\pi\)
−0.944020 + 0.329889i \(0.892989\pi\)
\(282\) 10.0443 0.598128
\(283\) 0.0113313 0.000673573 0 0.000336787 1.00000i \(-0.499893\pi\)
0.000336787 1.00000i \(0.499893\pi\)
\(284\) −13.9630 −0.828550
\(285\) −11.6936 −0.692669
\(286\) 2.65767 0.157151
\(287\) −32.4262 −1.91406
\(288\) −1.00000 −0.0589256
\(289\) 2.86078 0.168281
\(290\) 20.2615 1.18980
\(291\) 14.4149 0.845017
\(292\) −1.93219 −0.113073
\(293\) −4.41047 −0.257663 −0.128831 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(294\) −17.4236 −1.01617
\(295\) −39.1662 −2.28035
\(296\) 5.87682 0.341583
\(297\) 2.65767 0.154214
\(298\) 5.41225 0.313523
\(299\) 3.71423 0.214799
\(300\) 9.55882 0.551879
\(301\) −27.2796 −1.57237
\(302\) 13.5624 0.780428
\(303\) 1.10372 0.0634071
\(304\) 3.06468 0.175771
\(305\) 17.7163 1.01443
\(306\) 4.45654 0.254764
\(307\) 20.0406 1.14378 0.571888 0.820332i \(-0.306211\pi\)
0.571888 + 0.820332i \(0.306211\pi\)
\(308\) 13.1343 0.748396
\(309\) 1.00000 0.0568880
\(310\) −17.8099 −1.01153
\(311\) −4.04538 −0.229392 −0.114696 0.993401i \(-0.536589\pi\)
−0.114696 + 0.993401i \(0.536589\pi\)
\(312\) 1.00000 0.0566139
\(313\) 8.04036 0.454468 0.227234 0.973840i \(-0.427032\pi\)
0.227234 + 0.973840i \(0.427032\pi\)
\(314\) −8.54028 −0.481956
\(315\) −18.8568 −1.06246
\(316\) −5.22572 −0.293970
\(317\) −5.58000 −0.313404 −0.156702 0.987646i \(-0.550086\pi\)
−0.156702 + 0.987646i \(0.550086\pi\)
\(318\) 10.4448 0.585713
\(319\) 14.1127 0.790159
\(320\) −3.81560 −0.213299
\(321\) 4.79136 0.267427
\(322\) 18.3558 1.02293
\(323\) −13.6579 −0.759945
\(324\) 1.00000 0.0555556
\(325\) −9.55882 −0.530228
\(326\) 0.940059 0.0520650
\(327\) −16.7042 −0.923744
\(328\) 6.56132 0.362288
\(329\) −49.6391 −2.73669
\(330\) 10.1406 0.558223
\(331\) −10.5804 −0.581552 −0.290776 0.956791i \(-0.593913\pi\)
−0.290776 + 0.956791i \(0.593913\pi\)
\(332\) 3.46955 0.190417
\(333\) −5.87682 −0.322048
\(334\) −18.9730 −1.03816
\(335\) 7.48488 0.408942
\(336\) 4.94203 0.269610
\(337\) −0.574016 −0.0312686 −0.0156343 0.999878i \(-0.504977\pi\)
−0.0156343 + 0.999878i \(0.504977\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −2.10850 −0.114518
\(340\) 17.0044 0.922193
\(341\) −12.4051 −0.671773
\(342\) −3.06468 −0.165719
\(343\) 51.5140 2.78149
\(344\) 5.51993 0.297614
\(345\) 14.1720 0.762996
\(346\) 3.59876 0.193471
\(347\) 9.56853 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(348\) 5.31017 0.284655
\(349\) −21.9927 −1.17724 −0.588622 0.808408i \(-0.700329\pi\)
−0.588622 + 0.808408i \(0.700329\pi\)
\(350\) −47.2400 −2.52508
\(351\) −1.00000 −0.0533761
\(352\) −2.65767 −0.141654
\(353\) −24.7904 −1.31946 −0.659731 0.751502i \(-0.729330\pi\)
−0.659731 + 0.751502i \(0.729330\pi\)
\(354\) −10.2648 −0.545566
\(355\) 53.2772 2.82766
\(356\) 8.23562 0.436487
\(357\) −22.0244 −1.16565
\(358\) 12.3216 0.651216
\(359\) 7.14448 0.377071 0.188536 0.982066i \(-0.439626\pi\)
0.188536 + 0.982066i \(0.439626\pi\)
\(360\) 3.81560 0.201100
\(361\) −9.60774 −0.505670
\(362\) 14.3167 0.752472
\(363\) −3.93678 −0.206627
\(364\) −4.94203 −0.259033
\(365\) 7.37247 0.385892
\(366\) 4.64313 0.242700
\(367\) 10.7740 0.562398 0.281199 0.959649i \(-0.409268\pi\)
0.281199 + 0.959649i \(0.409268\pi\)
\(368\) −3.71423 −0.193617
\(369\) −6.56132 −0.341569
\(370\) −22.4236 −1.16575
\(371\) −51.6183 −2.67989
\(372\) −4.66765 −0.242006
\(373\) 28.4760 1.47443 0.737215 0.675658i \(-0.236141\pi\)
0.737215 + 0.675658i \(0.236141\pi\)
\(374\) 11.8440 0.612440
\(375\) −17.3947 −0.898256
\(376\) 10.0443 0.517994
\(377\) −5.31017 −0.273488
\(378\) −4.94203 −0.254191
\(379\) −14.3097 −0.735038 −0.367519 0.930016i \(-0.619793\pi\)
−0.367519 + 0.930016i \(0.619793\pi\)
\(380\) −11.6936 −0.599869
\(381\) 9.05858 0.464085
\(382\) 2.81037 0.143791
\(383\) −28.4425 −1.45334 −0.726672 0.686984i \(-0.758934\pi\)
−0.726672 + 0.686984i \(0.758934\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −50.1152 −2.55411
\(386\) 18.6496 0.949240
\(387\) −5.51993 −0.280594
\(388\) 14.4149 0.731806
\(389\) 19.0716 0.966967 0.483484 0.875353i \(-0.339371\pi\)
0.483484 + 0.875353i \(0.339371\pi\)
\(390\) −3.81560 −0.193211
\(391\) 16.5526 0.837102
\(392\) −17.4236 −0.880027
\(393\) −13.6776 −0.689942
\(394\) 2.28606 0.115170
\(395\) 19.9393 1.00325
\(396\) 2.65767 0.133553
\(397\) −22.7585 −1.14221 −0.571107 0.820876i \(-0.693486\pi\)
−0.571107 + 0.820876i \(0.693486\pi\)
\(398\) −5.66189 −0.283805
\(399\) 15.1457 0.758235
\(400\) 9.55882 0.477941
\(401\) −11.5086 −0.574714 −0.287357 0.957824i \(-0.592777\pi\)
−0.287357 + 0.957824i \(0.592777\pi\)
\(402\) 1.96165 0.0978382
\(403\) 4.66765 0.232512
\(404\) 1.10372 0.0549121
\(405\) −3.81560 −0.189599
\(406\) −26.2430 −1.30242
\(407\) −15.6187 −0.774188
\(408\) 4.45654 0.220632
\(409\) −16.3617 −0.809034 −0.404517 0.914531i \(-0.632560\pi\)
−0.404517 + 0.914531i \(0.632560\pi\)
\(410\) −25.0354 −1.23641
\(411\) 14.1768 0.699290
\(412\) 1.00000 0.0492665
\(413\) 50.7287 2.49620
\(414\) 3.71423 0.182544
\(415\) −13.2384 −0.649849
\(416\) 1.00000 0.0490290
\(417\) −9.95588 −0.487541
\(418\) −8.14491 −0.398381
\(419\) −31.7684 −1.55199 −0.775994 0.630740i \(-0.782751\pi\)
−0.775994 + 0.630740i \(0.782751\pi\)
\(420\) −18.8568 −0.920118
\(421\) −8.56383 −0.417376 −0.208688 0.977982i \(-0.566919\pi\)
−0.208688 + 0.977982i \(0.566919\pi\)
\(422\) −13.0173 −0.633673
\(423\) −10.0443 −0.488370
\(424\) 10.4448 0.507242
\(425\) −42.5993 −2.06637
\(426\) 13.9630 0.676509
\(427\) −22.9465 −1.11046
\(428\) 4.79136 0.231599
\(429\) −2.65767 −0.128314
\(430\) −21.0618 −1.01569
\(431\) 25.0472 1.20648 0.603240 0.797560i \(-0.293876\pi\)
0.603240 + 0.797560i \(0.293876\pi\)
\(432\) 1.00000 0.0481125
\(433\) −26.4327 −1.27027 −0.635137 0.772399i \(-0.719056\pi\)
−0.635137 + 0.772399i \(0.719056\pi\)
\(434\) 23.0677 1.10728
\(435\) −20.2615 −0.971464
\(436\) −16.7042 −0.799986
\(437\) −11.3829 −0.544519
\(438\) 1.93219 0.0923236
\(439\) −26.3084 −1.25563 −0.627815 0.778363i \(-0.716050\pi\)
−0.627815 + 0.778363i \(0.716050\pi\)
\(440\) 10.1406 0.483435
\(441\) 17.4236 0.829697
\(442\) −4.45654 −0.211976
\(443\) 32.4551 1.54199 0.770994 0.636842i \(-0.219760\pi\)
0.770994 + 0.636842i \(0.219760\pi\)
\(444\) −5.87682 −0.278902
\(445\) −31.4239 −1.48963
\(446\) −3.43833 −0.162809
\(447\) −5.41225 −0.255991
\(448\) 4.94203 0.233489
\(449\) −26.6480 −1.25760 −0.628798 0.777569i \(-0.716453\pi\)
−0.628798 + 0.777569i \(0.716453\pi\)
\(450\) −9.55882 −0.450607
\(451\) −17.4378 −0.821115
\(452\) −2.10850 −0.0991754
\(453\) −13.5624 −0.637217
\(454\) 14.8404 0.696493
\(455\) 18.8568 0.884021
\(456\) −3.06468 −0.143517
\(457\) 32.2187 1.50713 0.753565 0.657374i \(-0.228333\pi\)
0.753565 + 0.657374i \(0.228333\pi\)
\(458\) −4.64030 −0.216827
\(459\) −4.45654 −0.208014
\(460\) 14.1720 0.660774
\(461\) −25.5852 −1.19162 −0.595811 0.803125i \(-0.703169\pi\)
−0.595811 + 0.803125i \(0.703169\pi\)
\(462\) −13.1343 −0.611062
\(463\) −26.6474 −1.23841 −0.619204 0.785230i \(-0.712545\pi\)
−0.619204 + 0.785230i \(0.712545\pi\)
\(464\) 5.31017 0.246518
\(465\) 17.8099 0.825914
\(466\) −18.5533 −0.859466
\(467\) 38.6873 1.79023 0.895117 0.445830i \(-0.147092\pi\)
0.895117 + 0.445830i \(0.147092\pi\)
\(468\) −1.00000 −0.0462250
\(469\) −9.69453 −0.447652
\(470\) −38.3250 −1.76780
\(471\) 8.54028 0.393515
\(472\) −10.2648 −0.472474
\(473\) −14.6702 −0.674534
\(474\) 5.22572 0.240025
\(475\) 29.2947 1.34413
\(476\) −22.0244 −1.00949
\(477\) −10.4448 −0.478232
\(478\) −3.39069 −0.155086
\(479\) −29.5370 −1.34958 −0.674790 0.738009i \(-0.735766\pi\)
−0.674790 + 0.738009i \(0.735766\pi\)
\(480\) 3.81560 0.174158
\(481\) 5.87682 0.267960
\(482\) 20.7142 0.943504
\(483\) −18.3558 −0.835219
\(484\) −3.93678 −0.178945
\(485\) −55.0016 −2.49749
\(486\) −1.00000 −0.0453609
\(487\) 3.40617 0.154348 0.0771741 0.997018i \(-0.475410\pi\)
0.0771741 + 0.997018i \(0.475410\pi\)
\(488\) 4.64313 0.210185
\(489\) −0.940059 −0.0425109
\(490\) 66.4817 3.00334
\(491\) 30.1435 1.36036 0.680179 0.733047i \(-0.261902\pi\)
0.680179 + 0.733047i \(0.261902\pi\)
\(492\) −6.56132 −0.295807
\(493\) −23.6650 −1.06582
\(494\) 3.06468 0.137886
\(495\) −10.1406 −0.455787
\(496\) −4.66765 −0.209584
\(497\) −69.0055 −3.09532
\(498\) −3.46955 −0.155474
\(499\) −0.262235 −0.0117392 −0.00586962 0.999983i \(-0.501868\pi\)
−0.00586962 + 0.999983i \(0.501868\pi\)
\(500\) −17.3947 −0.777912
\(501\) 18.9730 0.847652
\(502\) −14.5570 −0.649711
\(503\) −41.8959 −1.86805 −0.934023 0.357212i \(-0.883727\pi\)
−0.934023 + 0.357212i \(0.883727\pi\)
\(504\) −4.94203 −0.220135
\(505\) −4.21136 −0.187403
\(506\) 9.87120 0.438828
\(507\) 1.00000 0.0444116
\(508\) 9.05858 0.401910
\(509\) 12.8289 0.568631 0.284316 0.958731i \(-0.408234\pi\)
0.284316 + 0.958731i \(0.408234\pi\)
\(510\) −17.0044 −0.752967
\(511\) −9.54893 −0.422420
\(512\) −1.00000 −0.0441942
\(513\) 3.06468 0.135309
\(514\) −24.7082 −1.08983
\(515\) −3.81560 −0.168136
\(516\) −5.51993 −0.243001
\(517\) −26.6944 −1.17402
\(518\) 29.0434 1.27609
\(519\) −3.59876 −0.157968
\(520\) −3.81560 −0.167325
\(521\) −10.6316 −0.465780 −0.232890 0.972503i \(-0.574818\pi\)
−0.232890 + 0.972503i \(0.574818\pi\)
\(522\) −5.31017 −0.232420
\(523\) 34.8435 1.52360 0.761800 0.647813i \(-0.224316\pi\)
0.761800 + 0.647813i \(0.224316\pi\)
\(524\) −13.6776 −0.597507
\(525\) 47.2400 2.06172
\(526\) 14.4358 0.629429
\(527\) 20.8016 0.906132
\(528\) 2.65767 0.115660
\(529\) −9.20451 −0.400196
\(530\) −39.8530 −1.73110
\(531\) 10.2648 0.445453
\(532\) 15.1457 0.656651
\(533\) 6.56132 0.284202
\(534\) −8.23562 −0.356390
\(535\) −18.2819 −0.790396
\(536\) 1.96165 0.0847304
\(537\) −12.3216 −0.531715
\(538\) 5.54942 0.239252
\(539\) 46.3063 1.99455
\(540\) −3.81560 −0.164197
\(541\) −32.8110 −1.41066 −0.705329 0.708881i \(-0.749200\pi\)
−0.705329 + 0.708881i \(0.749200\pi\)
\(542\) −18.8197 −0.808373
\(543\) −14.3167 −0.614390
\(544\) 4.45654 0.191073
\(545\) 63.7366 2.73017
\(546\) 4.94203 0.211499
\(547\) −23.5696 −1.00776 −0.503881 0.863773i \(-0.668095\pi\)
−0.503881 + 0.863773i \(0.668095\pi\)
\(548\) 14.1768 0.605603
\(549\) −4.64313 −0.198164
\(550\) −25.4042 −1.08324
\(551\) 16.2740 0.693295
\(552\) 3.71423 0.158088
\(553\) −25.8257 −1.09822
\(554\) −13.4083 −0.569664
\(555\) 22.4236 0.951830
\(556\) −9.95588 −0.422223
\(557\) 14.7282 0.624055 0.312027 0.950073i \(-0.398992\pi\)
0.312027 + 0.950073i \(0.398992\pi\)
\(558\) 4.66765 0.197597
\(559\) 5.51993 0.233468
\(560\) −18.8568 −0.796846
\(561\) −11.8440 −0.500055
\(562\) 31.6493 1.33505
\(563\) 22.8162 0.961586 0.480793 0.876834i \(-0.340349\pi\)
0.480793 + 0.876834i \(0.340349\pi\)
\(564\) −10.0443 −0.422941
\(565\) 8.04519 0.338464
\(566\) −0.0113313 −0.000476288 0
\(567\) 4.94203 0.207546
\(568\) 13.9630 0.585874
\(569\) −35.6251 −1.49348 −0.746741 0.665115i \(-0.768383\pi\)
−0.746741 + 0.665115i \(0.768383\pi\)
\(570\) 11.6936 0.489791
\(571\) −14.2946 −0.598210 −0.299105 0.954220i \(-0.596688\pi\)
−0.299105 + 0.954220i \(0.596688\pi\)
\(572\) −2.65767 −0.111123
\(573\) −2.81037 −0.117405
\(574\) 32.4262 1.35344
\(575\) −35.5036 −1.48060
\(576\) 1.00000 0.0416667
\(577\) −40.3880 −1.68137 −0.840686 0.541522i \(-0.817848\pi\)
−0.840686 + 0.541522i \(0.817848\pi\)
\(578\) −2.86078 −0.118993
\(579\) −18.6496 −0.775051
\(580\) −20.2615 −0.841313
\(581\) 17.1466 0.711362
\(582\) −14.4149 −0.597517
\(583\) −27.7587 −1.14965
\(584\) 1.93219 0.0799546
\(585\) 3.81560 0.157756
\(586\) 4.41047 0.182195
\(587\) 1.24044 0.0511984 0.0255992 0.999672i \(-0.491851\pi\)
0.0255992 + 0.999672i \(0.491851\pi\)
\(588\) 17.4236 0.718539
\(589\) −14.3049 −0.589421
\(590\) 39.1662 1.61245
\(591\) −2.28606 −0.0940359
\(592\) −5.87682 −0.241536
\(593\) 36.9172 1.51601 0.758005 0.652249i \(-0.226174\pi\)
0.758005 + 0.652249i \(0.226174\pi\)
\(594\) −2.65767 −0.109046
\(595\) 84.0362 3.44515
\(596\) −5.41225 −0.221694
\(597\) 5.66189 0.231726
\(598\) −3.71423 −0.151886
\(599\) 30.8445 1.26027 0.630136 0.776485i \(-0.282999\pi\)
0.630136 + 0.776485i \(0.282999\pi\)
\(600\) −9.55882 −0.390237
\(601\) −8.74978 −0.356911 −0.178455 0.983948i \(-0.557110\pi\)
−0.178455 + 0.983948i \(0.557110\pi\)
\(602\) 27.2796 1.11183
\(603\) −1.96165 −0.0798846
\(604\) −13.5624 −0.551846
\(605\) 15.0212 0.610698
\(606\) −1.10372 −0.0448356
\(607\) −30.0722 −1.22059 −0.610297 0.792173i \(-0.708950\pi\)
−0.610297 + 0.792173i \(0.708950\pi\)
\(608\) −3.06468 −0.124289
\(609\) 26.2430 1.06342
\(610\) −17.7163 −0.717313
\(611\) 10.0443 0.406348
\(612\) −4.45654 −0.180145
\(613\) 26.8435 1.08420 0.542100 0.840314i \(-0.317629\pi\)
0.542100 + 0.840314i \(0.317629\pi\)
\(614\) −20.0406 −0.808771
\(615\) 25.0354 1.00952
\(616\) −13.1343 −0.529196
\(617\) −37.9223 −1.52669 −0.763346 0.645989i \(-0.776445\pi\)
−0.763346 + 0.645989i \(0.776445\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 16.3961 0.659017 0.329508 0.944153i \(-0.393117\pi\)
0.329508 + 0.944153i \(0.393117\pi\)
\(620\) 17.8099 0.715263
\(621\) −3.71423 −0.149047
\(622\) 4.04538 0.162205
\(623\) 40.7007 1.63064
\(624\) −1.00000 −0.0400320
\(625\) 18.5770 0.743079
\(626\) −8.04036 −0.321358
\(627\) 8.14491 0.325276
\(628\) 8.54028 0.340794
\(629\) 26.1903 1.04428
\(630\) 18.8568 0.751274
\(631\) −5.27790 −0.210110 −0.105055 0.994466i \(-0.533502\pi\)
−0.105055 + 0.994466i \(0.533502\pi\)
\(632\) 5.22572 0.207868
\(633\) 13.0173 0.517391
\(634\) 5.58000 0.221610
\(635\) −34.5640 −1.37163
\(636\) −10.4448 −0.414161
\(637\) −17.4236 −0.690350
\(638\) −14.1127 −0.558727
\(639\) −13.9630 −0.552367
\(640\) 3.81560 0.150825
\(641\) −1.36628 −0.0539647 −0.0269824 0.999636i \(-0.508590\pi\)
−0.0269824 + 0.999636i \(0.508590\pi\)
\(642\) −4.79136 −0.189100
\(643\) −4.41093 −0.173950 −0.0869751 0.996210i \(-0.527720\pi\)
−0.0869751 + 0.996210i \(0.527720\pi\)
\(644\) −18.3558 −0.723321
\(645\) 21.0618 0.829309
\(646\) 13.6579 0.537362
\(647\) −0.0113644 −0.000446779 0 −0.000223389 1.00000i \(-0.500071\pi\)
−0.000223389 1.00000i \(0.500071\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 27.2804 1.07085
\(650\) 9.55882 0.374928
\(651\) −23.0677 −0.904093
\(652\) −0.940059 −0.0368155
\(653\) 40.4851 1.58430 0.792152 0.610323i \(-0.208960\pi\)
0.792152 + 0.610323i \(0.208960\pi\)
\(654\) 16.7042 0.653186
\(655\) 52.1882 2.03916
\(656\) −6.56132 −0.256176
\(657\) −1.93219 −0.0753819
\(658\) 49.6391 1.93513
\(659\) 11.5193 0.448727 0.224363 0.974506i \(-0.427970\pi\)
0.224363 + 0.974506i \(0.427970\pi\)
\(660\) −10.1406 −0.394723
\(661\) −3.18690 −0.123956 −0.0619780 0.998078i \(-0.519741\pi\)
−0.0619780 + 0.998078i \(0.519741\pi\)
\(662\) 10.5804 0.411219
\(663\) 4.45654 0.173078
\(664\) −3.46955 −0.134645
\(665\) −57.7901 −2.24100
\(666\) 5.87682 0.227722
\(667\) −19.7232 −0.763685
\(668\) 18.9730 0.734088
\(669\) 3.43833 0.132933
\(670\) −7.48488 −0.289166
\(671\) −12.3399 −0.476377
\(672\) −4.94203 −0.190643
\(673\) 11.8399 0.456393 0.228197 0.973615i \(-0.426717\pi\)
0.228197 + 0.973615i \(0.426717\pi\)
\(674\) 0.574016 0.0221103
\(675\) 9.55882 0.367919
\(676\) 1.00000 0.0384615
\(677\) −14.0643 −0.540534 −0.270267 0.962785i \(-0.587112\pi\)
−0.270267 + 0.962785i \(0.587112\pi\)
\(678\) 2.10850 0.0809764
\(679\) 71.2389 2.73390
\(680\) −17.0044 −0.652089
\(681\) −14.8404 −0.568684
\(682\) 12.4051 0.475015
\(683\) −39.0515 −1.49426 −0.747132 0.664675i \(-0.768570\pi\)
−0.747132 + 0.664675i \(0.768570\pi\)
\(684\) 3.06468 0.117181
\(685\) −54.0930 −2.06679
\(686\) −51.5140 −1.96681
\(687\) 4.64030 0.177039
\(688\) −5.51993 −0.210445
\(689\) 10.4448 0.397913
\(690\) −14.1720 −0.539519
\(691\) 36.2791 1.38012 0.690062 0.723751i \(-0.257583\pi\)
0.690062 + 0.723751i \(0.257583\pi\)
\(692\) −3.59876 −0.136804
\(693\) 13.1343 0.498930
\(694\) −9.56853 −0.363216
\(695\) 37.9877 1.44095
\(696\) −5.31017 −0.201281
\(697\) 29.2408 1.10757
\(698\) 21.9927 0.832438
\(699\) 18.5533 0.701751
\(700\) 47.2400 1.78550
\(701\) −32.6043 −1.23145 −0.615723 0.787963i \(-0.711136\pi\)
−0.615723 + 0.787963i \(0.711136\pi\)
\(702\) 1.00000 0.0377426
\(703\) −18.0106 −0.679282
\(704\) 2.65767 0.100165
\(705\) 38.3250 1.44340
\(706\) 24.7904 0.933000
\(707\) 5.45462 0.205142
\(708\) 10.2648 0.385773
\(709\) 22.1362 0.831342 0.415671 0.909515i \(-0.363547\pi\)
0.415671 + 0.909515i \(0.363547\pi\)
\(710\) −53.2772 −1.99946
\(711\) −5.22572 −0.195980
\(712\) −8.23562 −0.308643
\(713\) 17.3367 0.649265
\(714\) 22.0244 0.824241
\(715\) 10.1406 0.379238
\(716\) −12.3216 −0.460479
\(717\) 3.39069 0.126628
\(718\) −7.14448 −0.266630
\(719\) 52.8553 1.97117 0.985585 0.169183i \(-0.0541129\pi\)
0.985585 + 0.169183i \(0.0541129\pi\)
\(720\) −3.81560 −0.142199
\(721\) 4.94203 0.184051
\(722\) 9.60774 0.357563
\(723\) −20.7142 −0.770368
\(724\) −14.3167 −0.532078
\(725\) 50.7590 1.88514
\(726\) 3.93678 0.146108
\(727\) 10.6192 0.393843 0.196922 0.980419i \(-0.436906\pi\)
0.196922 + 0.980419i \(0.436906\pi\)
\(728\) 4.94203 0.183164
\(729\) 1.00000 0.0370370
\(730\) −7.37247 −0.272867
\(731\) 24.5998 0.909856
\(732\) −4.64313 −0.171615
\(733\) −7.45444 −0.275336 −0.137668 0.990478i \(-0.543961\pi\)
−0.137668 + 0.990478i \(0.543961\pi\)
\(734\) −10.7740 −0.397676
\(735\) −66.4817 −2.45221
\(736\) 3.71423 0.136908
\(737\) −5.21342 −0.192039
\(738\) 6.56132 0.241525
\(739\) 7.53788 0.277286 0.138643 0.990342i \(-0.455726\pi\)
0.138643 + 0.990342i \(0.455726\pi\)
\(740\) 22.4236 0.824309
\(741\) −3.06468 −0.112584
\(742\) 51.6183 1.89497
\(743\) −10.8326 −0.397409 −0.198704 0.980059i \(-0.563673\pi\)
−0.198704 + 0.980059i \(0.563673\pi\)
\(744\) 4.66765 0.171124
\(745\) 20.6510 0.756594
\(746\) −28.4760 −1.04258
\(747\) 3.46955 0.126944
\(748\) −11.8440 −0.433061
\(749\) 23.6790 0.865212
\(750\) 17.3947 0.635163
\(751\) 33.7846 1.23282 0.616408 0.787427i \(-0.288587\pi\)
0.616408 + 0.787427i \(0.288587\pi\)
\(752\) −10.0443 −0.366277
\(753\) 14.5570 0.530487
\(754\) 5.31017 0.193385
\(755\) 51.7487 1.88333
\(756\) 4.94203 0.179740
\(757\) −37.6181 −1.36725 −0.683626 0.729833i \(-0.739598\pi\)
−0.683626 + 0.729833i \(0.739598\pi\)
\(758\) 14.3097 0.519751
\(759\) −9.87120 −0.358302
\(760\) 11.6936 0.424171
\(761\) −19.3563 −0.701665 −0.350832 0.936438i \(-0.614101\pi\)
−0.350832 + 0.936438i \(0.614101\pi\)
\(762\) −9.05858 −0.328158
\(763\) −82.5526 −2.98861
\(764\) −2.81037 −0.101676
\(765\) 17.0044 0.614795
\(766\) 28.4425 1.02767
\(767\) −10.2648 −0.370639
\(768\) 1.00000 0.0360844
\(769\) 18.5088 0.667445 0.333722 0.942671i \(-0.391695\pi\)
0.333722 + 0.942671i \(0.391695\pi\)
\(770\) 50.1152 1.80603
\(771\) 24.7082 0.889844
\(772\) −18.6496 −0.671214
\(773\) −43.5265 −1.56554 −0.782769 0.622312i \(-0.786193\pi\)
−0.782769 + 0.622312i \(0.786193\pi\)
\(774\) 5.51993 0.198410
\(775\) −44.6172 −1.60270
\(776\) −14.4149 −0.517465
\(777\) −29.0434 −1.04193
\(778\) −19.0716 −0.683749
\(779\) −20.1083 −0.720456
\(780\) 3.81560 0.136620
\(781\) −37.1090 −1.32787
\(782\) −16.5526 −0.591920
\(783\) 5.31017 0.189770
\(784\) 17.4236 0.622273
\(785\) −32.5863 −1.16306
\(786\) 13.6776 0.487863
\(787\) −15.5787 −0.555321 −0.277661 0.960679i \(-0.589559\pi\)
−0.277661 + 0.960679i \(0.589559\pi\)
\(788\) −2.28606 −0.0814375
\(789\) −14.4358 −0.513927
\(790\) −19.9393 −0.709408
\(791\) −10.4203 −0.370502
\(792\) −2.65767 −0.0944362
\(793\) 4.64313 0.164882
\(794\) 22.7585 0.807667
\(795\) 39.8530 1.41344
\(796\) 5.66189 0.200680
\(797\) 50.3766 1.78443 0.892215 0.451611i \(-0.149151\pi\)
0.892215 + 0.451611i \(0.149151\pi\)
\(798\) −15.1457 −0.536153
\(799\) 44.7628 1.58359
\(800\) −9.55882 −0.337955
\(801\) 8.23562 0.290991
\(802\) 11.5086 0.406384
\(803\) −5.13512 −0.181215
\(804\) −1.96165 −0.0691821
\(805\) 70.0385 2.46853
\(806\) −4.66765 −0.164411
\(807\) −5.54942 −0.195349
\(808\) −1.10372 −0.0388288
\(809\) 9.00214 0.316499 0.158249 0.987399i \(-0.449415\pi\)
0.158249 + 0.987399i \(0.449415\pi\)
\(810\) 3.81560 0.134067
\(811\) −42.0442 −1.47637 −0.738186 0.674597i \(-0.764317\pi\)
−0.738186 + 0.674597i \(0.764317\pi\)
\(812\) 26.2430 0.920949
\(813\) 18.8197 0.660034
\(814\) 15.6187 0.547434
\(815\) 3.58689 0.125643
\(816\) −4.45654 −0.156010
\(817\) −16.9168 −0.591844
\(818\) 16.3617 0.572073
\(819\) −4.94203 −0.172688
\(820\) 25.0354 0.874273
\(821\) 1.80159 0.0628760 0.0314380 0.999506i \(-0.489991\pi\)
0.0314380 + 0.999506i \(0.489991\pi\)
\(822\) −14.1768 −0.494473
\(823\) −19.9754 −0.696299 −0.348150 0.937439i \(-0.613190\pi\)
−0.348150 + 0.937439i \(0.613190\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 25.4042 0.884461
\(826\) −50.7287 −1.76508
\(827\) −26.8586 −0.933965 −0.466982 0.884267i \(-0.654659\pi\)
−0.466982 + 0.884267i \(0.654659\pi\)
\(828\) −3.71423 −0.129078
\(829\) −11.1674 −0.387861 −0.193930 0.981015i \(-0.562124\pi\)
−0.193930 + 0.981015i \(0.562124\pi\)
\(830\) 13.2384 0.459513
\(831\) 13.4083 0.465129
\(832\) −1.00000 −0.0346688
\(833\) −77.6492 −2.69039
\(834\) 9.95588 0.344744
\(835\) −72.3935 −2.50528
\(836\) 8.14491 0.281698
\(837\) −4.66765 −0.161338
\(838\) 31.7684 1.09742
\(839\) −7.51830 −0.259560 −0.129780 0.991543i \(-0.541427\pi\)
−0.129780 + 0.991543i \(0.541427\pi\)
\(840\) 18.8568 0.650622
\(841\) −0.802092 −0.0276584
\(842\) 8.56383 0.295129
\(843\) −31.6493 −1.09006
\(844\) 13.0173 0.448074
\(845\) −3.81560 −0.131261
\(846\) 10.0443 0.345329
\(847\) −19.4557 −0.668505
\(848\) −10.4448 −0.358674
\(849\) 0.0113313 0.000388888 0
\(850\) 42.5993 1.46114
\(851\) 21.8279 0.748249
\(852\) −13.9630 −0.478364
\(853\) −42.4262 −1.45264 −0.726322 0.687354i \(-0.758772\pi\)
−0.726322 + 0.687354i \(0.758772\pi\)
\(854\) 22.9465 0.785212
\(855\) −11.6936 −0.399913
\(856\) −4.79136 −0.163765
\(857\) 25.5464 0.872647 0.436324 0.899790i \(-0.356280\pi\)
0.436324 + 0.899790i \(0.356280\pi\)
\(858\) 2.65767 0.0907314
\(859\) 55.0691 1.87894 0.939468 0.342638i \(-0.111320\pi\)
0.939468 + 0.342638i \(0.111320\pi\)
\(860\) 21.0618 0.718203
\(861\) −32.4262 −1.10508
\(862\) −25.0472 −0.853110
\(863\) 49.7915 1.69492 0.847460 0.530859i \(-0.178130\pi\)
0.847460 + 0.530859i \(0.178130\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 13.7315 0.466883
\(866\) 26.4327 0.898220
\(867\) 2.86078 0.0971573
\(868\) −23.0677 −0.782968
\(869\) −13.8883 −0.471127
\(870\) 20.2615 0.686929
\(871\) 1.96165 0.0664680
\(872\) 16.7042 0.565675
\(873\) 14.4149 0.487871
\(874\) 11.3829 0.385033
\(875\) −85.9649 −2.90614
\(876\) −1.93219 −0.0652826
\(877\) 40.4708 1.36660 0.683301 0.730137i \(-0.260544\pi\)
0.683301 + 0.730137i \(0.260544\pi\)
\(878\) 26.3084 0.887864
\(879\) −4.41047 −0.148762
\(880\) −10.1406 −0.341840
\(881\) −43.7069 −1.47252 −0.736262 0.676697i \(-0.763411\pi\)
−0.736262 + 0.676697i \(0.763411\pi\)
\(882\) −17.4236 −0.586685
\(883\) −33.3296 −1.12163 −0.560815 0.827941i \(-0.689512\pi\)
−0.560815 + 0.827941i \(0.689512\pi\)
\(884\) 4.45654 0.149890
\(885\) −39.1662 −1.31656
\(886\) −32.4551 −1.09035
\(887\) −12.7487 −0.428061 −0.214031 0.976827i \(-0.568659\pi\)
−0.214031 + 0.976827i \(0.568659\pi\)
\(888\) 5.87682 0.197213
\(889\) 44.7678 1.50146
\(890\) 31.4239 1.05333
\(891\) 2.65767 0.0890353
\(892\) 3.43833 0.115124
\(893\) −30.7825 −1.03010
\(894\) 5.41225 0.181013
\(895\) 47.0142 1.57151
\(896\) −4.94203 −0.165102
\(897\) 3.71423 0.124014
\(898\) 26.6480 0.889254
\(899\) −24.7860 −0.826660
\(900\) 9.55882 0.318627
\(901\) 46.5475 1.55072
\(902\) 17.4378 0.580616
\(903\) −27.2796 −0.907809
\(904\) 2.10850 0.0701276
\(905\) 54.6270 1.81586
\(906\) 13.5624 0.450580
\(907\) −26.3431 −0.874710 −0.437355 0.899289i \(-0.644085\pi\)
−0.437355 + 0.899289i \(0.644085\pi\)
\(908\) −14.8404 −0.492495
\(909\) 1.10372 0.0366081
\(910\) −18.8568 −0.625097
\(911\) −33.1966 −1.09985 −0.549926 0.835213i \(-0.685344\pi\)
−0.549926 + 0.835213i \(0.685344\pi\)
\(912\) 3.06468 0.101482
\(913\) 9.22094 0.305168
\(914\) −32.2187 −1.06570
\(915\) 17.7163 0.585684
\(916\) 4.64030 0.153320
\(917\) −67.5949 −2.23218
\(918\) 4.45654 0.147088
\(919\) −12.7869 −0.421801 −0.210900 0.977508i \(-0.567640\pi\)
−0.210900 + 0.977508i \(0.567640\pi\)
\(920\) −14.1720 −0.467238
\(921\) 20.0406 0.660359
\(922\) 25.5852 0.842604
\(923\) 13.9630 0.459597
\(924\) 13.1343 0.432086
\(925\) −56.1755 −1.84704
\(926\) 26.6474 0.875687
\(927\) 1.00000 0.0328443
\(928\) −5.31017 −0.174315
\(929\) −43.9133 −1.44075 −0.720375 0.693585i \(-0.756030\pi\)
−0.720375 + 0.693585i \(0.756030\pi\)
\(930\) −17.8099 −0.584010
\(931\) 53.3979 1.75005
\(932\) 18.5533 0.607734
\(933\) −4.04538 −0.132440
\(934\) −38.6873 −1.26589
\(935\) 45.1921 1.47794
\(936\) 1.00000 0.0326860
\(937\) −39.0533 −1.27582 −0.637908 0.770112i \(-0.720200\pi\)
−0.637908 + 0.770112i \(0.720200\pi\)
\(938\) 9.69453 0.316538
\(939\) 8.04036 0.262387
\(940\) 38.3250 1.25002
\(941\) 41.1817 1.34249 0.671243 0.741237i \(-0.265761\pi\)
0.671243 + 0.741237i \(0.265761\pi\)
\(942\) −8.54028 −0.278257
\(943\) 24.3702 0.793604
\(944\) 10.2648 0.334089
\(945\) −18.8568 −0.613412
\(946\) 14.6702 0.476968
\(947\) −47.1613 −1.53254 −0.766268 0.642521i \(-0.777888\pi\)
−0.766268 + 0.642521i \(0.777888\pi\)
\(948\) −5.22572 −0.169724
\(949\) 1.93219 0.0627215
\(950\) −29.2947 −0.950447
\(951\) −5.58000 −0.180944
\(952\) 22.0244 0.713814
\(953\) −24.2561 −0.785732 −0.392866 0.919596i \(-0.628516\pi\)
−0.392866 + 0.919596i \(0.628516\pi\)
\(954\) 10.4448 0.338161
\(955\) 10.7233 0.346996
\(956\) 3.39069 0.109663
\(957\) 14.1127 0.456198
\(958\) 29.5370 0.954298
\(959\) 70.0621 2.26242
\(960\) −3.81560 −0.123148
\(961\) −9.21303 −0.297195
\(962\) −5.87682 −0.189476
\(963\) 4.79136 0.154399
\(964\) −20.7142 −0.667158
\(965\) 71.1595 2.29071
\(966\) 18.3558 0.590589
\(967\) −53.9653 −1.73541 −0.867704 0.497082i \(-0.834405\pi\)
−0.867704 + 0.497082i \(0.834405\pi\)
\(968\) 3.93678 0.126533
\(969\) −13.6579 −0.438754
\(970\) 55.0016 1.76599
\(971\) 11.2320 0.360453 0.180226 0.983625i \(-0.442317\pi\)
0.180226 + 0.983625i \(0.442317\pi\)
\(972\) 1.00000 0.0320750
\(973\) −49.2022 −1.57735
\(974\) −3.40617 −0.109141
\(975\) −9.55882 −0.306127
\(976\) −4.64313 −0.148623
\(977\) −51.8538 −1.65895 −0.829475 0.558544i \(-0.811360\pi\)
−0.829475 + 0.558544i \(0.811360\pi\)
\(978\) 0.940059 0.0300598
\(979\) 21.8876 0.699530
\(980\) −66.4817 −2.12368
\(981\) −16.7042 −0.533324
\(982\) −30.1435 −0.961918
\(983\) 30.3957 0.969474 0.484737 0.874660i \(-0.338915\pi\)
0.484737 + 0.874660i \(0.338915\pi\)
\(984\) 6.56132 0.209167
\(985\) 8.72269 0.277928
\(986\) 23.6650 0.753647
\(987\) −49.6391 −1.58003
\(988\) −3.06468 −0.0975005
\(989\) 20.5023 0.651934
\(990\) 10.1406 0.322290
\(991\) −58.4368 −1.85631 −0.928153 0.372198i \(-0.878604\pi\)
−0.928153 + 0.372198i \(0.878604\pi\)
\(992\) 4.66765 0.148198
\(993\) −10.5804 −0.335759
\(994\) 69.0055 2.18872
\(995\) −21.6035 −0.684878
\(996\) 3.46955 0.109937
\(997\) 24.6228 0.779811 0.389906 0.920855i \(-0.372508\pi\)
0.389906 + 0.920855i \(0.372508\pi\)
\(998\) 0.262235 0.00830090
\(999\) −5.87682 −0.185934
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.bb.1.2 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.bb.1.2 14 1.1 even 1 trivial