Properties

Label 8034.2.a.ba.1.7
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: \(x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} - 4126 x^{5} - 22759 x^{4} + 2997 x^{3} + 10504 x^{2} - 506 x - 1492\)
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 1.7
Root \(0.503883\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.503883 q^{5} +1.00000 q^{6} +2.75905 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.503883 q^{5} +1.00000 q^{6} +2.75905 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.503883 q^{10} +6.03100 q^{11} -1.00000 q^{12} -1.00000 q^{13} -2.75905 q^{14} +0.503883 q^{15} +1.00000 q^{16} -6.29407 q^{17} -1.00000 q^{18} -6.31941 q^{19} -0.503883 q^{20} -2.75905 q^{21} -6.03100 q^{22} -7.22879 q^{23} +1.00000 q^{24} -4.74610 q^{25} +1.00000 q^{26} -1.00000 q^{27} +2.75905 q^{28} +9.35117 q^{29} -0.503883 q^{30} +2.92979 q^{31} -1.00000 q^{32} -6.03100 q^{33} +6.29407 q^{34} -1.39024 q^{35} +1.00000 q^{36} -2.31736 q^{37} +6.31941 q^{38} +1.00000 q^{39} +0.503883 q^{40} -3.89839 q^{41} +2.75905 q^{42} +4.29142 q^{43} +6.03100 q^{44} -0.503883 q^{45} +7.22879 q^{46} -6.99841 q^{47} -1.00000 q^{48} +0.612353 q^{49} +4.74610 q^{50} +6.29407 q^{51} -1.00000 q^{52} +3.51811 q^{53} +1.00000 q^{54} -3.03892 q^{55} -2.75905 q^{56} +6.31941 q^{57} -9.35117 q^{58} -9.24734 q^{59} +0.503883 q^{60} -0.178206 q^{61} -2.92979 q^{62} +2.75905 q^{63} +1.00000 q^{64} +0.503883 q^{65} +6.03100 q^{66} +9.08548 q^{67} -6.29407 q^{68} +7.22879 q^{69} +1.39024 q^{70} +12.4784 q^{71} -1.00000 q^{72} +4.54685 q^{73} +2.31736 q^{74} +4.74610 q^{75} -6.31941 q^{76} +16.6398 q^{77} -1.00000 q^{78} +10.0968 q^{79} -0.503883 q^{80} +1.00000 q^{81} +3.89839 q^{82} -0.865830 q^{83} -2.75905 q^{84} +3.17148 q^{85} -4.29142 q^{86} -9.35117 q^{87} -6.03100 q^{88} +0.262117 q^{89} +0.503883 q^{90} -2.75905 q^{91} -7.22879 q^{92} -2.92979 q^{93} +6.99841 q^{94} +3.18424 q^{95} +1.00000 q^{96} +18.9602 q^{97} -0.612353 q^{98} +6.03100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - q^{5} + 14q^{6} + 5q^{7} - 14q^{8} + 14q^{9} + q^{10} - q^{11} - 14q^{12} - 14q^{13} - 5q^{14} + q^{15} + 14q^{16} - 12q^{17} - 14q^{18} + 10q^{19} - q^{20} - 5q^{21} + q^{22} - q^{23} + 14q^{24} + 19q^{25} + 14q^{26} - 14q^{27} + 5q^{28} + 6q^{29} - q^{30} + 20q^{31} - 14q^{32} + q^{33} + 12q^{34} - 16q^{35} + 14q^{36} - 3q^{37} - 10q^{38} + 14q^{39} + q^{40} + q^{41} + 5q^{42} + 6q^{43} - q^{44} - q^{45} + q^{46} - 13q^{47} - 14q^{48} + 9q^{49} - 19q^{50} + 12q^{51} - 14q^{52} - 27q^{53} + 14q^{54} + 10q^{55} - 5q^{56} - 10q^{57} - 6q^{58} - 6q^{59} + q^{60} - 4q^{61} - 20q^{62} + 5q^{63} + 14q^{64} + q^{65} - q^{66} + 13q^{67} - 12q^{68} + q^{69} + 16q^{70} + 18q^{71} - 14q^{72} + 11q^{73} + 3q^{74} - 19q^{75} + 10q^{76} - 15q^{77} - 14q^{78} + 33q^{79} - q^{80} + 14q^{81} - q^{82} - 25q^{83} - 5q^{84} + 25q^{85} - 6q^{86} - 6q^{87} + q^{88} + 3q^{89} + q^{90} - 5q^{91} - q^{92} - 20q^{93} + 13q^{94} + 30q^{95} + 14q^{96} + 11q^{97} - 9q^{98} - q^{99} + O(q^{100}) \)

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
\(5\) −0.503883 −0.225344 −0.112672 0.993632i \(-0.535941\pi\)
−0.112672 + 0.993632i \(0.535941\pi\)
\(6\) 1.00000 0.408248
\(7\) 2.75905 1.04282 0.521411 0.853305i \(-0.325406\pi\)
0.521411 + 0.853305i \(0.325406\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0.503883 0.159342
\(11\) 6.03100 1.81841 0.909207 0.416344i \(-0.136689\pi\)
0.909207 + 0.416344i \(0.136689\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 −0.277350
\(14\) −2.75905 −0.737387
\(15\) 0.503883 0.130102
\(16\) 1.00000 0.250000
\(17\) −6.29407 −1.52654 −0.763269 0.646081i \(-0.776407\pi\)
−0.763269 + 0.646081i \(0.776407\pi\)
\(18\) −1.00000 −0.235702
\(19\) −6.31941 −1.44977 −0.724886 0.688869i \(-0.758107\pi\)
−0.724886 + 0.688869i \(0.758107\pi\)
\(20\) −0.503883 −0.112672
\(21\) −2.75905 −0.602074
\(22\) −6.03100 −1.28581
\(23\) −7.22879 −1.50731 −0.753653 0.657272i \(-0.771710\pi\)
−0.753653 + 0.657272i \(0.771710\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.74610 −0.949220
\(26\) 1.00000 0.196116
\(27\) −1.00000 −0.192450
\(28\) 2.75905 0.521411
\(29\) 9.35117 1.73647 0.868234 0.496155i \(-0.165255\pi\)
0.868234 + 0.496155i \(0.165255\pi\)
\(30\) −0.503883 −0.0919961
\(31\) 2.92979 0.526206 0.263103 0.964768i \(-0.415254\pi\)
0.263103 + 0.964768i \(0.415254\pi\)
\(32\) −1.00000 −0.176777
\(33\) −6.03100 −1.04986
\(34\) 6.29407 1.07942
\(35\) −1.39024 −0.234993
\(36\) 1.00000 0.166667
\(37\) −2.31736 −0.380972 −0.190486 0.981690i \(-0.561006\pi\)
−0.190486 + 0.981690i \(0.561006\pi\)
\(38\) 6.31941 1.02514
\(39\) 1.00000 0.160128
\(40\) 0.503883 0.0796710
\(41\) −3.89839 −0.608827 −0.304413 0.952540i \(-0.598460\pi\)
−0.304413 + 0.952540i \(0.598460\pi\)
\(42\) 2.75905 0.425731
\(43\) 4.29142 0.654435 0.327217 0.944949i \(-0.393889\pi\)
0.327217 + 0.944949i \(0.393889\pi\)
\(44\) 6.03100 0.909207
\(45\) −0.503883 −0.0751145
\(46\) 7.22879 1.06583
\(47\) −6.99841 −1.02082 −0.510411 0.859930i \(-0.670507\pi\)
−0.510411 + 0.859930i \(0.670507\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0.612353 0.0874790
\(50\) 4.74610 0.671200
\(51\) 6.29407 0.881347
\(52\) −1.00000 −0.138675
\(53\) 3.51811 0.483249 0.241625 0.970370i \(-0.422320\pi\)
0.241625 + 0.970370i \(0.422320\pi\)
\(54\) 1.00000 0.136083
\(55\) −3.03892 −0.409768
\(56\) −2.75905 −0.368693
\(57\) 6.31941 0.837026
\(58\) −9.35117 −1.22787
\(59\) −9.24734 −1.20390 −0.601951 0.798533i \(-0.705610\pi\)
−0.601951 + 0.798533i \(0.705610\pi\)
\(60\) 0.503883 0.0650511
\(61\) −0.178206 −0.0228169 −0.0114085 0.999935i \(-0.503632\pi\)
−0.0114085 + 0.999935i \(0.503632\pi\)
\(62\) −2.92979 −0.372084
\(63\) 2.75905 0.347608
\(64\) 1.00000 0.125000
\(65\) 0.503883 0.0624990
\(66\) 6.03100 0.742365
\(67\) 9.08548 1.10997 0.554984 0.831861i \(-0.312724\pi\)
0.554984 + 0.831861i \(0.312724\pi\)
\(68\) −6.29407 −0.763269
\(69\) 7.22879 0.870244
\(70\) 1.39024 0.166165
\(71\) 12.4784 1.48091 0.740454 0.672107i \(-0.234611\pi\)
0.740454 + 0.672107i \(0.234611\pi\)
\(72\) −1.00000 −0.117851
\(73\) 4.54685 0.532168 0.266084 0.963950i \(-0.414270\pi\)
0.266084 + 0.963950i \(0.414270\pi\)
\(74\) 2.31736 0.269388
\(75\) 4.74610 0.548033
\(76\) −6.31941 −0.724886
\(77\) 16.6398 1.89628
\(78\) −1.00000 −0.113228
\(79\) 10.0968 1.13598 0.567992 0.823034i \(-0.307720\pi\)
0.567992 + 0.823034i \(0.307720\pi\)
\(80\) −0.503883 −0.0563359
\(81\) 1.00000 0.111111
\(82\) 3.89839 0.430506
\(83\) −0.865830 −0.0950372 −0.0475186 0.998870i \(-0.515131\pi\)
−0.0475186 + 0.998870i \(0.515131\pi\)
\(84\) −2.75905 −0.301037
\(85\) 3.17148 0.343995
\(86\) −4.29142 −0.462755
\(87\) −9.35117 −1.00255
\(88\) −6.03100 −0.642907
\(89\) 0.262117 0.0277843 0.0138922 0.999903i \(-0.495578\pi\)
0.0138922 + 0.999903i \(0.495578\pi\)
\(90\) 0.503883 0.0531140
\(91\) −2.75905 −0.289227
\(92\) −7.22879 −0.753653
\(93\) −2.92979 −0.303805
\(94\) 6.99841 0.721830
\(95\) 3.18424 0.326697
\(96\) 1.00000 0.102062
\(97\) 18.9602 1.92512 0.962561 0.271066i \(-0.0873761\pi\)
0.962561 + 0.271066i \(0.0873761\pi\)
\(98\) −0.612353 −0.0618570
\(99\) 6.03100 0.606138
\(100\) −4.74610 −0.474610
\(101\) 10.3574 1.03060 0.515298 0.857011i \(-0.327681\pi\)
0.515298 + 0.857011i \(0.327681\pi\)
\(102\) −6.29407 −0.623206
\(103\) 1.00000 0.0985329
\(104\) 1.00000 0.0980581
\(105\) 1.39024 0.135673
\(106\) −3.51811 −0.341709
\(107\) 2.12190 0.205132 0.102566 0.994726i \(-0.467295\pi\)
0.102566 + 0.994726i \(0.467295\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 10.6953 1.02443 0.512213 0.858859i \(-0.328826\pi\)
0.512213 + 0.858859i \(0.328826\pi\)
\(110\) 3.03892 0.289750
\(111\) 2.31736 0.219954
\(112\) 2.75905 0.260706
\(113\) −12.7474 −1.19917 −0.599585 0.800311i \(-0.704668\pi\)
−0.599585 + 0.800311i \(0.704668\pi\)
\(114\) −6.31941 −0.591867
\(115\) 3.64247 0.339662
\(116\) 9.35117 0.868234
\(117\) −1.00000 −0.0924500
\(118\) 9.24734 0.851287
\(119\) −17.3657 −1.59191
\(120\) −0.503883 −0.0459981
\(121\) 25.3729 2.30663
\(122\) 0.178206 0.0161340
\(123\) 3.89839 0.351506
\(124\) 2.92979 0.263103
\(125\) 4.91090 0.439244
\(126\) −2.75905 −0.245796
\(127\) −8.59083 −0.762313 −0.381157 0.924510i \(-0.624474\pi\)
−0.381157 + 0.924510i \(0.624474\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −4.29142 −0.377838
\(130\) −0.503883 −0.0441935
\(131\) 19.8384 1.73329 0.866645 0.498925i \(-0.166272\pi\)
0.866645 + 0.498925i \(0.166272\pi\)
\(132\) −6.03100 −0.524931
\(133\) −17.4356 −1.51185
\(134\) −9.08548 −0.784866
\(135\) 0.503883 0.0433674
\(136\) 6.29407 0.539712
\(137\) −1.81911 −0.155417 −0.0777084 0.996976i \(-0.524760\pi\)
−0.0777084 + 0.996976i \(0.524760\pi\)
\(138\) −7.22879 −0.615355
\(139\) 13.6876 1.16097 0.580485 0.814271i \(-0.302863\pi\)
0.580485 + 0.814271i \(0.302863\pi\)
\(140\) −1.39024 −0.117497
\(141\) 6.99841 0.589372
\(142\) −12.4784 −1.04716
\(143\) −6.03100 −0.504337
\(144\) 1.00000 0.0833333
\(145\) −4.71190 −0.391302
\(146\) −4.54685 −0.376300
\(147\) −0.612353 −0.0505060
\(148\) −2.31736 −0.190486
\(149\) 7.98738 0.654352 0.327176 0.944963i \(-0.393903\pi\)
0.327176 + 0.944963i \(0.393903\pi\)
\(150\) −4.74610 −0.387518
\(151\) −14.5122 −1.18098 −0.590492 0.807043i \(-0.701066\pi\)
−0.590492 + 0.807043i \(0.701066\pi\)
\(152\) 6.31941 0.512572
\(153\) −6.29407 −0.508846
\(154\) −16.6398 −1.34088
\(155\) −1.47627 −0.118577
\(156\) 1.00000 0.0800641
\(157\) 23.3549 1.86393 0.931963 0.362553i \(-0.118095\pi\)
0.931963 + 0.362553i \(0.118095\pi\)
\(158\) −10.0968 −0.803262
\(159\) −3.51811 −0.279004
\(160\) 0.503883 0.0398355
\(161\) −19.9446 −1.57185
\(162\) −1.00000 −0.0785674
\(163\) 10.9941 0.861126 0.430563 0.902561i \(-0.358315\pi\)
0.430563 + 0.902561i \(0.358315\pi\)
\(164\) −3.89839 −0.304413
\(165\) 3.03892 0.236580
\(166\) 0.865830 0.0672015
\(167\) −16.8168 −1.30132 −0.650662 0.759367i \(-0.725509\pi\)
−0.650662 + 0.759367i \(0.725509\pi\)
\(168\) 2.75905 0.212865
\(169\) 1.00000 0.0769231
\(170\) −3.17148 −0.243241
\(171\) −6.31941 −0.483257
\(172\) 4.29142 0.327217
\(173\) −3.12094 −0.237281 −0.118640 0.992937i \(-0.537854\pi\)
−0.118640 + 0.992937i \(0.537854\pi\)
\(174\) 9.35117 0.708910
\(175\) −13.0947 −0.989868
\(176\) 6.03100 0.454604
\(177\) 9.24734 0.695073
\(178\) −0.262117 −0.0196465
\(179\) −7.23510 −0.540777 −0.270388 0.962751i \(-0.587152\pi\)
−0.270388 + 0.962751i \(0.587152\pi\)
\(180\) −0.503883 −0.0375573
\(181\) −7.50319 −0.557707 −0.278854 0.960334i \(-0.589954\pi\)
−0.278854 + 0.960334i \(0.589954\pi\)
\(182\) 2.75905 0.204514
\(183\) 0.178206 0.0131733
\(184\) 7.22879 0.532913
\(185\) 1.16768 0.0858496
\(186\) 2.92979 0.214823
\(187\) −37.9596 −2.77588
\(188\) −6.99841 −0.510411
\(189\) −2.75905 −0.200691
\(190\) −3.18424 −0.231009
\(191\) −2.89259 −0.209300 −0.104650 0.994509i \(-0.533372\pi\)
−0.104650 + 0.994509i \(0.533372\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 20.2076 1.45458 0.727288 0.686333i \(-0.240781\pi\)
0.727288 + 0.686333i \(0.240781\pi\)
\(194\) −18.9602 −1.36127
\(195\) −0.503883 −0.0360838
\(196\) 0.612353 0.0437395
\(197\) −16.8072 −1.19746 −0.598732 0.800950i \(-0.704328\pi\)
−0.598732 + 0.800950i \(0.704328\pi\)
\(198\) −6.03100 −0.428604
\(199\) 1.86963 0.132535 0.0662674 0.997802i \(-0.478891\pi\)
0.0662674 + 0.997802i \(0.478891\pi\)
\(200\) 4.74610 0.335600
\(201\) −9.08548 −0.640841
\(202\) −10.3574 −0.728741
\(203\) 25.8003 1.81083
\(204\) 6.29407 0.440673
\(205\) 1.96434 0.137195
\(206\) −1.00000 −0.0696733
\(207\) −7.22879 −0.502435
\(208\) −1.00000 −0.0693375
\(209\) −38.1123 −2.63629
\(210\) −1.39024 −0.0959356
\(211\) 3.95736 0.272436 0.136218 0.990679i \(-0.456505\pi\)
0.136218 + 0.990679i \(0.456505\pi\)
\(212\) 3.51811 0.241625
\(213\) −12.4784 −0.855003
\(214\) −2.12190 −0.145050
\(215\) −2.16237 −0.147473
\(216\) 1.00000 0.0680414
\(217\) 8.08344 0.548740
\(218\) −10.6953 −0.724378
\(219\) −4.54685 −0.307248
\(220\) −3.03892 −0.204884
\(221\) 6.29407 0.423385
\(222\) −2.31736 −0.155531
\(223\) −11.4512 −0.766830 −0.383415 0.923576i \(-0.625252\pi\)
−0.383415 + 0.923576i \(0.625252\pi\)
\(224\) −2.75905 −0.184347
\(225\) −4.74610 −0.316407
\(226\) 12.7474 0.847941
\(227\) −9.36186 −0.621369 −0.310684 0.950513i \(-0.600558\pi\)
−0.310684 + 0.950513i \(0.600558\pi\)
\(228\) 6.31941 0.418513
\(229\) 13.4812 0.890861 0.445431 0.895317i \(-0.353051\pi\)
0.445431 + 0.895317i \(0.353051\pi\)
\(230\) −3.64247 −0.240177
\(231\) −16.6398 −1.09482
\(232\) −9.35117 −0.613934
\(233\) −23.5946 −1.54574 −0.772868 0.634566i \(-0.781179\pi\)
−0.772868 + 0.634566i \(0.781179\pi\)
\(234\) 1.00000 0.0653720
\(235\) 3.52638 0.230036
\(236\) −9.24734 −0.601951
\(237\) −10.0968 −0.655861
\(238\) 17.3657 1.12565
\(239\) 28.9815 1.87466 0.937329 0.348445i \(-0.113290\pi\)
0.937329 + 0.348445i \(0.113290\pi\)
\(240\) 0.503883 0.0325255
\(241\) 13.8376 0.891361 0.445681 0.895192i \(-0.352962\pi\)
0.445681 + 0.895192i \(0.352962\pi\)
\(242\) −25.3729 −1.63103
\(243\) −1.00000 −0.0641500
\(244\) −0.178206 −0.0114085
\(245\) −0.308554 −0.0197128
\(246\) −3.89839 −0.248553
\(247\) 6.31941 0.402094
\(248\) −2.92979 −0.186042
\(249\) 0.865830 0.0548698
\(250\) −4.91090 −0.310593
\(251\) −2.15987 −0.136330 −0.0681650 0.997674i \(-0.521714\pi\)
−0.0681650 + 0.997674i \(0.521714\pi\)
\(252\) 2.75905 0.173804
\(253\) −43.5968 −2.74091
\(254\) 8.59083 0.539037
\(255\) −3.17148 −0.198606
\(256\) 1.00000 0.0625000
\(257\) 16.0148 0.998978 0.499489 0.866320i \(-0.333521\pi\)
0.499489 + 0.866320i \(0.333521\pi\)
\(258\) 4.29142 0.267172
\(259\) −6.39372 −0.397286
\(260\) 0.503883 0.0312495
\(261\) 9.35117 0.578823
\(262\) −19.8384 −1.22562
\(263\) 4.66348 0.287563 0.143781 0.989609i \(-0.454074\pi\)
0.143781 + 0.989609i \(0.454074\pi\)
\(264\) 6.03100 0.371182
\(265\) −1.77272 −0.108897
\(266\) 17.4356 1.06904
\(267\) −0.262117 −0.0160413
\(268\) 9.08548 0.554984
\(269\) −4.05727 −0.247376 −0.123688 0.992321i \(-0.539472\pi\)
−0.123688 + 0.992321i \(0.539472\pi\)
\(270\) −0.503883 −0.0306654
\(271\) −15.6485 −0.950581 −0.475291 0.879829i \(-0.657657\pi\)
−0.475291 + 0.879829i \(0.657657\pi\)
\(272\) −6.29407 −0.381634
\(273\) 2.75905 0.166985
\(274\) 1.81911 0.109896
\(275\) −28.6237 −1.72608
\(276\) 7.22879 0.435122
\(277\) 19.1029 1.14778 0.573892 0.818931i \(-0.305433\pi\)
0.573892 + 0.818931i \(0.305433\pi\)
\(278\) −13.6876 −0.820930
\(279\) 2.92979 0.175402
\(280\) 1.39024 0.0830827
\(281\) −3.80257 −0.226842 −0.113421 0.993547i \(-0.536181\pi\)
−0.113421 + 0.993547i \(0.536181\pi\)
\(282\) −6.99841 −0.416749
\(283\) 4.96282 0.295009 0.147505 0.989061i \(-0.452876\pi\)
0.147505 + 0.989061i \(0.452876\pi\)
\(284\) 12.4784 0.740454
\(285\) −3.18424 −0.188618
\(286\) 6.03100 0.356620
\(287\) −10.7559 −0.634898
\(288\) −1.00000 −0.0589256
\(289\) 22.6154 1.33032
\(290\) 4.71190 0.276692
\(291\) −18.9602 −1.11147
\(292\) 4.54685 0.266084
\(293\) 4.80936 0.280966 0.140483 0.990083i \(-0.455135\pi\)
0.140483 + 0.990083i \(0.455135\pi\)
\(294\) 0.612353 0.0357132
\(295\) 4.65958 0.271291
\(296\) 2.31736 0.134694
\(297\) −6.03100 −0.349954
\(298\) −7.98738 −0.462697
\(299\) 7.22879 0.418052
\(300\) 4.74610 0.274016
\(301\) 11.8402 0.682460
\(302\) 14.5122 0.835082
\(303\) −10.3574 −0.595015
\(304\) −6.31941 −0.362443
\(305\) 0.0897949 0.00514164
\(306\) 6.29407 0.359808
\(307\) −4.41310 −0.251869 −0.125935 0.992039i \(-0.540193\pi\)
−0.125935 + 0.992039i \(0.540193\pi\)
\(308\) 16.6398 0.948142
\(309\) −1.00000 −0.0568880
\(310\) 1.47627 0.0838467
\(311\) 12.0144 0.681275 0.340638 0.940195i \(-0.389357\pi\)
0.340638 + 0.940195i \(0.389357\pi\)
\(312\) −1.00000 −0.0566139
\(313\) 24.5115 1.38547 0.692735 0.721192i \(-0.256405\pi\)
0.692735 + 0.721192i \(0.256405\pi\)
\(314\) −23.3549 −1.31799
\(315\) −1.39024 −0.0783311
\(316\) 10.0968 0.567992
\(317\) −10.1665 −0.571008 −0.285504 0.958378i \(-0.592161\pi\)
−0.285504 + 0.958378i \(0.592161\pi\)
\(318\) 3.51811 0.197286
\(319\) 56.3969 3.15762
\(320\) −0.503883 −0.0281679
\(321\) −2.12190 −0.118433
\(322\) 19.9446 1.11147
\(323\) 39.7748 2.21313
\(324\) 1.00000 0.0555556
\(325\) 4.74610 0.263266
\(326\) −10.9941 −0.608908
\(327\) −10.6953 −0.591452
\(328\) 3.89839 0.215253
\(329\) −19.3089 −1.06454
\(330\) −3.03892 −0.167287
\(331\) 14.2271 0.781991 0.390995 0.920393i \(-0.372131\pi\)
0.390995 + 0.920393i \(0.372131\pi\)
\(332\) −0.865830 −0.0475186
\(333\) −2.31736 −0.126991
\(334\) 16.8168 0.920175
\(335\) −4.57802 −0.250124
\(336\) −2.75905 −0.150518
\(337\) 33.4153 1.82025 0.910124 0.414337i \(-0.135986\pi\)
0.910124 + 0.414337i \(0.135986\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 12.7474 0.692341
\(340\) 3.17148 0.171998
\(341\) 17.6696 0.956861
\(342\) 6.31941 0.341714
\(343\) −17.6238 −0.951598
\(344\) −4.29142 −0.231378
\(345\) −3.64247 −0.196104
\(346\) 3.12094 0.167783
\(347\) 2.61928 0.140610 0.0703051 0.997526i \(-0.477603\pi\)
0.0703051 + 0.997526i \(0.477603\pi\)
\(348\) −9.35117 −0.501275
\(349\) −11.5718 −0.619426 −0.309713 0.950830i \(-0.600233\pi\)
−0.309713 + 0.950830i \(0.600233\pi\)
\(350\) 13.0947 0.699943
\(351\) 1.00000 0.0533761
\(352\) −6.03100 −0.321453
\(353\) 34.9353 1.85942 0.929709 0.368294i \(-0.120058\pi\)
0.929709 + 0.368294i \(0.120058\pi\)
\(354\) −9.24734 −0.491491
\(355\) −6.28764 −0.333713
\(356\) 0.262117 0.0138922
\(357\) 17.3657 0.919088
\(358\) 7.23510 0.382387
\(359\) 3.37328 0.178035 0.0890175 0.996030i \(-0.471627\pi\)
0.0890175 + 0.996030i \(0.471627\pi\)
\(360\) 0.503883 0.0265570
\(361\) 20.9349 1.10184
\(362\) 7.50319 0.394359
\(363\) −25.3729 −1.33173
\(364\) −2.75905 −0.144613
\(365\) −2.29108 −0.119921
\(366\) −0.178206 −0.00931496
\(367\) 34.0021 1.77490 0.887448 0.460907i \(-0.152476\pi\)
0.887448 + 0.460907i \(0.152476\pi\)
\(368\) −7.22879 −0.376827
\(369\) −3.89839 −0.202942
\(370\) −1.16768 −0.0607048
\(371\) 9.70663 0.503943
\(372\) −2.92979 −0.151903
\(373\) −0.141490 −0.00732607 −0.00366303 0.999993i \(-0.501166\pi\)
−0.00366303 + 0.999993i \(0.501166\pi\)
\(374\) 37.9596 1.96284
\(375\) −4.91090 −0.253598
\(376\) 6.99841 0.360915
\(377\) −9.35117 −0.481610
\(378\) 2.75905 0.141910
\(379\) 30.8204 1.58314 0.791569 0.611080i \(-0.209264\pi\)
0.791569 + 0.611080i \(0.209264\pi\)
\(380\) 3.18424 0.163348
\(381\) 8.59083 0.440122
\(382\) 2.89259 0.147998
\(383\) −21.3338 −1.09011 −0.545054 0.838401i \(-0.683491\pi\)
−0.545054 + 0.838401i \(0.683491\pi\)
\(384\) 1.00000 0.0510310
\(385\) −8.38453 −0.427315
\(386\) −20.2076 −1.02854
\(387\) 4.29142 0.218145
\(388\) 18.9602 0.962561
\(389\) 22.0340 1.11717 0.558585 0.829447i \(-0.311344\pi\)
0.558585 + 0.829447i \(0.311344\pi\)
\(390\) 0.503883 0.0255151
\(391\) 45.4985 2.30096
\(392\) −0.612353 −0.0309285
\(393\) −19.8384 −1.00072
\(394\) 16.8072 0.846734
\(395\) −5.08763 −0.255987
\(396\) 6.03100 0.303069
\(397\) −29.2872 −1.46988 −0.734942 0.678130i \(-0.762790\pi\)
−0.734942 + 0.678130i \(0.762790\pi\)
\(398\) −1.86963 −0.0937162
\(399\) 17.4356 0.872870
\(400\) −4.74610 −0.237305
\(401\) −11.9102 −0.594767 −0.297383 0.954758i \(-0.596114\pi\)
−0.297383 + 0.954758i \(0.596114\pi\)
\(402\) 9.08548 0.453143
\(403\) −2.92979 −0.145943
\(404\) 10.3574 0.515298
\(405\) −0.503883 −0.0250382
\(406\) −25.8003 −1.28045
\(407\) −13.9760 −0.692765
\(408\) −6.29407 −0.311603
\(409\) −29.6075 −1.46400 −0.732000 0.681305i \(-0.761413\pi\)
−0.732000 + 0.681305i \(0.761413\pi\)
\(410\) −1.96434 −0.0970116
\(411\) 1.81911 0.0897299
\(412\) 1.00000 0.0492665
\(413\) −25.5139 −1.25546
\(414\) 7.22879 0.355276
\(415\) 0.436277 0.0214160
\(416\) 1.00000 0.0490290
\(417\) −13.6876 −0.670287
\(418\) 38.1123 1.86414
\(419\) 3.51354 0.171648 0.0858239 0.996310i \(-0.472648\pi\)
0.0858239 + 0.996310i \(0.472648\pi\)
\(420\) 1.39024 0.0678367
\(421\) −23.4775 −1.14422 −0.572112 0.820175i \(-0.693876\pi\)
−0.572112 + 0.820175i \(0.693876\pi\)
\(422\) −3.95736 −0.192641
\(423\) −6.99841 −0.340274
\(424\) −3.51811 −0.170854
\(425\) 29.8723 1.44902
\(426\) 12.4784 0.604578
\(427\) −0.491678 −0.0237940
\(428\) 2.12190 0.102566
\(429\) 6.03100 0.291179
\(430\) 2.16237 0.104279
\(431\) −3.68034 −0.177276 −0.0886379 0.996064i \(-0.528251\pi\)
−0.0886379 + 0.996064i \(0.528251\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −22.3102 −1.07216 −0.536080 0.844167i \(-0.680095\pi\)
−0.536080 + 0.844167i \(0.680095\pi\)
\(434\) −8.08344 −0.388018
\(435\) 4.71190 0.225918
\(436\) 10.6953 0.512213
\(437\) 45.6817 2.18525
\(438\) 4.54685 0.217257
\(439\) −19.5096 −0.931142 −0.465571 0.885010i \(-0.654151\pi\)
−0.465571 + 0.885010i \(0.654151\pi\)
\(440\) 3.03892 0.144875
\(441\) 0.612353 0.0291597
\(442\) −6.29407 −0.299379
\(443\) −31.9728 −1.51907 −0.759536 0.650466i \(-0.774574\pi\)
−0.759536 + 0.650466i \(0.774574\pi\)
\(444\) 2.31736 0.109977
\(445\) −0.132076 −0.00626102
\(446\) 11.4512 0.542231
\(447\) −7.98738 −0.377790
\(448\) 2.75905 0.130353
\(449\) 25.0632 1.18281 0.591403 0.806376i \(-0.298574\pi\)
0.591403 + 0.806376i \(0.298574\pi\)
\(450\) 4.74610 0.223733
\(451\) −23.5112 −1.10710
\(452\) −12.7474 −0.599585
\(453\) 14.5122 0.681842
\(454\) 9.36186 0.439374
\(455\) 1.39024 0.0651754
\(456\) −6.31941 −0.295933
\(457\) 41.1417 1.92453 0.962264 0.272116i \(-0.0877235\pi\)
0.962264 + 0.272116i \(0.0877235\pi\)
\(458\) −13.4812 −0.629934
\(459\) 6.29407 0.293782
\(460\) 3.64247 0.169831
\(461\) −21.6234 −1.00710 −0.503551 0.863965i \(-0.667974\pi\)
−0.503551 + 0.863965i \(0.667974\pi\)
\(462\) 16.6398 0.774155
\(463\) −37.9222 −1.76239 −0.881196 0.472750i \(-0.843261\pi\)
−0.881196 + 0.472750i \(0.843261\pi\)
\(464\) 9.35117 0.434117
\(465\) 1.47627 0.0684606
\(466\) 23.5946 1.09300
\(467\) 28.5116 1.31936 0.659680 0.751546i \(-0.270692\pi\)
0.659680 + 0.751546i \(0.270692\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 25.0673 1.15750
\(470\) −3.52638 −0.162660
\(471\) −23.3549 −1.07614
\(472\) 9.24734 0.425643
\(473\) 25.8815 1.19003
\(474\) 10.0968 0.463764
\(475\) 29.9926 1.37615
\(476\) −17.3657 −0.795954
\(477\) 3.51811 0.161083
\(478\) −28.9815 −1.32558
\(479\) −6.33889 −0.289632 −0.144816 0.989459i \(-0.546259\pi\)
−0.144816 + 0.989459i \(0.546259\pi\)
\(480\) −0.503883 −0.0229990
\(481\) 2.31736 0.105663
\(482\) −13.8376 −0.630288
\(483\) 19.9446 0.907510
\(484\) 25.3729 1.15332
\(485\) −9.55376 −0.433814
\(486\) 1.00000 0.0453609
\(487\) 7.00106 0.317248 0.158624 0.987339i \(-0.449294\pi\)
0.158624 + 0.987339i \(0.449294\pi\)
\(488\) 0.178206 0.00806699
\(489\) −10.9941 −0.497171
\(490\) 0.308554 0.0139391
\(491\) −12.4695 −0.562739 −0.281369 0.959600i \(-0.590789\pi\)
−0.281369 + 0.959600i \(0.590789\pi\)
\(492\) 3.89839 0.175753
\(493\) −58.8569 −2.65078
\(494\) −6.31941 −0.284324
\(495\) −3.03892 −0.136589
\(496\) 2.92979 0.131552
\(497\) 34.4284 1.54432
\(498\) −0.865830 −0.0387988
\(499\) 27.5059 1.23133 0.615666 0.788007i \(-0.288887\pi\)
0.615666 + 0.788007i \(0.288887\pi\)
\(500\) 4.91090 0.219622
\(501\) 16.8168 0.751320
\(502\) 2.15987 0.0963998
\(503\) 15.9920 0.713048 0.356524 0.934286i \(-0.383962\pi\)
0.356524 + 0.934286i \(0.383962\pi\)
\(504\) −2.75905 −0.122898
\(505\) −5.21890 −0.232238
\(506\) 43.5968 1.93811
\(507\) −1.00000 −0.0444116
\(508\) −8.59083 −0.381157
\(509\) −22.1900 −0.983554 −0.491777 0.870721i \(-0.663653\pi\)
−0.491777 + 0.870721i \(0.663653\pi\)
\(510\) 3.17148 0.140435
\(511\) 12.5450 0.554957
\(512\) −1.00000 −0.0441942
\(513\) 6.31941 0.279009
\(514\) −16.0148 −0.706384
\(515\) −0.503883 −0.0222038
\(516\) −4.29142 −0.188919
\(517\) −42.2074 −1.85628
\(518\) 6.39372 0.280924
\(519\) 3.12094 0.136994
\(520\) −0.503883 −0.0220967
\(521\) 19.7796 0.866559 0.433279 0.901260i \(-0.357356\pi\)
0.433279 + 0.901260i \(0.357356\pi\)
\(522\) −9.35117 −0.409289
\(523\) 26.0735 1.14011 0.570057 0.821605i \(-0.306921\pi\)
0.570057 + 0.821605i \(0.306921\pi\)
\(524\) 19.8384 0.866645
\(525\) 13.0947 0.571501
\(526\) −4.66348 −0.203337
\(527\) −18.4403 −0.803274
\(528\) −6.03100 −0.262466
\(529\) 29.2554 1.27197
\(530\) 1.77272 0.0770019
\(531\) −9.24734 −0.401301
\(532\) −17.4356 −0.755927
\(533\) 3.89839 0.168858
\(534\) 0.262117 0.0113429
\(535\) −1.06919 −0.0462252
\(536\) −9.08548 −0.392433
\(537\) 7.23510 0.312218
\(538\) 4.05727 0.174921
\(539\) 3.69310 0.159073
\(540\) 0.503883 0.0216837
\(541\) −13.4090 −0.576499 −0.288249 0.957555i \(-0.593073\pi\)
−0.288249 + 0.957555i \(0.593073\pi\)
\(542\) 15.6485 0.672163
\(543\) 7.50319 0.321993
\(544\) 6.29407 0.269856
\(545\) −5.38919 −0.230848
\(546\) −2.75905 −0.118076
\(547\) 12.3792 0.529298 0.264649 0.964345i \(-0.414744\pi\)
0.264649 + 0.964345i \(0.414744\pi\)
\(548\) −1.81911 −0.0777084
\(549\) −0.178206 −0.00760563
\(550\) 28.6237 1.22052
\(551\) −59.0938 −2.51748
\(552\) −7.22879 −0.307678
\(553\) 27.8577 1.18463
\(554\) −19.1029 −0.811606
\(555\) −1.16768 −0.0495653
\(556\) 13.6876 0.580485
\(557\) 9.07673 0.384593 0.192297 0.981337i \(-0.438406\pi\)
0.192297 + 0.981337i \(0.438406\pi\)
\(558\) −2.92979 −0.124028
\(559\) −4.29142 −0.181508
\(560\) −1.39024 −0.0587483
\(561\) 37.9596 1.60265
\(562\) 3.80257 0.160402
\(563\) −11.8934 −0.501247 −0.250623 0.968085i \(-0.580636\pi\)
−0.250623 + 0.968085i \(0.580636\pi\)
\(564\) 6.99841 0.294686
\(565\) 6.42318 0.270225
\(566\) −4.96282 −0.208603
\(567\) 2.75905 0.115869
\(568\) −12.4784 −0.523580
\(569\) −15.3651 −0.644137 −0.322068 0.946716i \(-0.604378\pi\)
−0.322068 + 0.946716i \(0.604378\pi\)
\(570\) 3.18424 0.133373
\(571\) 11.4601 0.479592 0.239796 0.970823i \(-0.422919\pi\)
0.239796 + 0.970823i \(0.422919\pi\)
\(572\) −6.03100 −0.252169
\(573\) 2.89259 0.120840
\(574\) 10.7559 0.448941
\(575\) 34.3086 1.43077
\(576\) 1.00000 0.0416667
\(577\) 4.06515 0.169234 0.0846172 0.996414i \(-0.473033\pi\)
0.0846172 + 0.996414i \(0.473033\pi\)
\(578\) −22.6154 −0.940676
\(579\) −20.2076 −0.839800
\(580\) −4.71190 −0.195651
\(581\) −2.38887 −0.0991070
\(582\) 18.9602 0.785928
\(583\) 21.2177 0.878748
\(584\) −4.54685 −0.188150
\(585\) 0.503883 0.0208330
\(586\) −4.80936 −0.198673
\(587\) 23.9173 0.987173 0.493586 0.869697i \(-0.335686\pi\)
0.493586 + 0.869697i \(0.335686\pi\)
\(588\) −0.612353 −0.0252530
\(589\) −18.5146 −0.762879
\(590\) −4.65958 −0.191832
\(591\) 16.8072 0.691356
\(592\) −2.31736 −0.0952430
\(593\) −25.2899 −1.03853 −0.519266 0.854613i \(-0.673795\pi\)
−0.519266 + 0.854613i \(0.673795\pi\)
\(594\) 6.03100 0.247455
\(595\) 8.75027 0.358726
\(596\) 7.98738 0.327176
\(597\) −1.86963 −0.0765190
\(598\) −7.22879 −0.295607
\(599\) 25.4212 1.03868 0.519342 0.854566i \(-0.326177\pi\)
0.519342 + 0.854566i \(0.326177\pi\)
\(600\) −4.74610 −0.193759
\(601\) −18.3380 −0.748025 −0.374012 0.927424i \(-0.622018\pi\)
−0.374012 + 0.927424i \(0.622018\pi\)
\(602\) −11.8402 −0.482572
\(603\) 9.08548 0.369989
\(604\) −14.5122 −0.590492
\(605\) −12.7850 −0.519784
\(606\) 10.3574 0.420739
\(607\) −6.87350 −0.278987 −0.139493 0.990223i \(-0.544547\pi\)
−0.139493 + 0.990223i \(0.544547\pi\)
\(608\) 6.31941 0.256286
\(609\) −25.8003 −1.04548
\(610\) −0.0897949 −0.00363569
\(611\) 6.99841 0.283125
\(612\) −6.29407 −0.254423
\(613\) 10.2451 0.413794 0.206897 0.978363i \(-0.433664\pi\)
0.206897 + 0.978363i \(0.433664\pi\)
\(614\) 4.41310 0.178098
\(615\) −1.96434 −0.0792097
\(616\) −16.6398 −0.670438
\(617\) −27.7863 −1.11863 −0.559317 0.828954i \(-0.688937\pi\)
−0.559317 + 0.828954i \(0.688937\pi\)
\(618\) 1.00000 0.0402259
\(619\) −38.1871 −1.53487 −0.767435 0.641127i \(-0.778467\pi\)
−0.767435 + 0.641127i \(0.778467\pi\)
\(620\) −1.47627 −0.0592886
\(621\) 7.22879 0.290081
\(622\) −12.0144 −0.481734
\(623\) 0.723194 0.0289741
\(624\) 1.00000 0.0400320
\(625\) 21.2560 0.850239
\(626\) −24.5115 −0.979676
\(627\) 38.1123 1.52206
\(628\) 23.3549 0.931963
\(629\) 14.5856 0.581568
\(630\) 1.39024 0.0553885
\(631\) 3.13563 0.124828 0.0624138 0.998050i \(-0.480120\pi\)
0.0624138 + 0.998050i \(0.480120\pi\)
\(632\) −10.0968 −0.401631
\(633\) −3.95736 −0.157291
\(634\) 10.1665 0.403764
\(635\) 4.32878 0.171782
\(636\) −3.51811 −0.139502
\(637\) −0.612353 −0.0242623
\(638\) −56.3969 −2.23277
\(639\) 12.4784 0.493636
\(640\) 0.503883 0.0199177
\(641\) 11.2172 0.443053 0.221526 0.975154i \(-0.428896\pi\)
0.221526 + 0.975154i \(0.428896\pi\)
\(642\) 2.12190 0.0837448
\(643\) −2.65135 −0.104559 −0.0522794 0.998632i \(-0.516649\pi\)
−0.0522794 + 0.998632i \(0.516649\pi\)
\(644\) −19.9446 −0.785927
\(645\) 2.16237 0.0851434
\(646\) −39.7748 −1.56492
\(647\) 29.2799 1.15111 0.575557 0.817762i \(-0.304785\pi\)
0.575557 + 0.817762i \(0.304785\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −55.7707 −2.18919
\(650\) −4.74610 −0.186157
\(651\) −8.08344 −0.316815
\(652\) 10.9941 0.430563
\(653\) −10.6861 −0.418180 −0.209090 0.977896i \(-0.567050\pi\)
−0.209090 + 0.977896i \(0.567050\pi\)
\(654\) 10.6953 0.418220
\(655\) −9.99625 −0.390586
\(656\) −3.89839 −0.152207
\(657\) 4.54685 0.177389
\(658\) 19.3089 0.752741
\(659\) −31.4957 −1.22690 −0.613449 0.789734i \(-0.710218\pi\)
−0.613449 + 0.789734i \(0.710218\pi\)
\(660\) 3.03892 0.118290
\(661\) 35.2958 1.37285 0.686424 0.727201i \(-0.259179\pi\)
0.686424 + 0.727201i \(0.259179\pi\)
\(662\) −14.2271 −0.552951
\(663\) −6.29407 −0.244442
\(664\) 0.865830 0.0336007
\(665\) 8.78549 0.340687
\(666\) 2.31736 0.0897959
\(667\) −67.5976 −2.61739
\(668\) −16.8168 −0.650662
\(669\) 11.4512 0.442730
\(670\) 4.57802 0.176865
\(671\) −1.07476 −0.0414906
\(672\) 2.75905 0.106433
\(673\) −30.2560 −1.16628 −0.583141 0.812371i \(-0.698176\pi\)
−0.583141 + 0.812371i \(0.698176\pi\)
\(674\) −33.4153 −1.28711
\(675\) 4.74610 0.182678
\(676\) 1.00000 0.0384615
\(677\) 8.31515 0.319577 0.159789 0.987151i \(-0.448919\pi\)
0.159789 + 0.987151i \(0.448919\pi\)
\(678\) −12.7474 −0.489559
\(679\) 52.3123 2.00756
\(680\) −3.17148 −0.121621
\(681\) 9.36186 0.358747
\(682\) −17.6696 −0.676603
\(683\) −3.33370 −0.127561 −0.0637803 0.997964i \(-0.520316\pi\)
−0.0637803 + 0.997964i \(0.520316\pi\)
\(684\) −6.31941 −0.241629
\(685\) 0.916618 0.0350222
\(686\) 17.6238 0.672881
\(687\) −13.4812 −0.514339
\(688\) 4.29142 0.163609
\(689\) −3.51811 −0.134029
\(690\) 3.64247 0.138666
\(691\) 37.5626 1.42895 0.714474 0.699662i \(-0.246666\pi\)
0.714474 + 0.699662i \(0.246666\pi\)
\(692\) −3.12094 −0.118640
\(693\) 16.6398 0.632095
\(694\) −2.61928 −0.0994264
\(695\) −6.89698 −0.261617
\(696\) 9.35117 0.354455
\(697\) 24.5368 0.929397
\(698\) 11.5718 0.438001
\(699\) 23.5946 0.892432
\(700\) −13.0947 −0.494934
\(701\) 25.7722 0.973404 0.486702 0.873568i \(-0.338200\pi\)
0.486702 + 0.873568i \(0.338200\pi\)
\(702\) −1.00000 −0.0377426
\(703\) 14.6444 0.552322
\(704\) 6.03100 0.227302
\(705\) −3.52638 −0.132811
\(706\) −34.9353 −1.31481
\(707\) 28.5765 1.07473
\(708\) 9.24734 0.347536
\(709\) 15.6569 0.588007 0.294004 0.955804i \(-0.405012\pi\)
0.294004 + 0.955804i \(0.405012\pi\)
\(710\) 6.28764 0.235971
\(711\) 10.0968 0.378661
\(712\) −0.262117 −0.00982325
\(713\) −21.1788 −0.793154
\(714\) −17.3657 −0.649894
\(715\) 3.03892 0.113649
\(716\) −7.23510 −0.270388
\(717\) −28.9815 −1.08233
\(718\) −3.37328 −0.125890
\(719\) 5.85120 0.218213 0.109106 0.994030i \(-0.465201\pi\)
0.109106 + 0.994030i \(0.465201\pi\)
\(720\) −0.503883 −0.0187786
\(721\) 2.75905 0.102752
\(722\) −20.9349 −0.779117
\(723\) −13.8376 −0.514628
\(724\) −7.50319 −0.278854
\(725\) −44.3816 −1.64829
\(726\) 25.3729 0.941678
\(727\) −10.2008 −0.378326 −0.189163 0.981946i \(-0.560577\pi\)
−0.189163 + 0.981946i \(0.560577\pi\)
\(728\) 2.75905 0.102257
\(729\) 1.00000 0.0370370
\(730\) 2.29108 0.0847967
\(731\) −27.0105 −0.999019
\(732\) 0.178206 0.00658667
\(733\) −27.2842 −1.00777 −0.503883 0.863772i \(-0.668096\pi\)
−0.503883 + 0.863772i \(0.668096\pi\)
\(734\) −34.0021 −1.25504
\(735\) 0.308554 0.0113812
\(736\) 7.22879 0.266457
\(737\) 54.7945 2.01838
\(738\) 3.89839 0.143502
\(739\) −5.82201 −0.214166 −0.107083 0.994250i \(-0.534151\pi\)
−0.107083 + 0.994250i \(0.534151\pi\)
\(740\) 1.16768 0.0429248
\(741\) −6.31941 −0.232149
\(742\) −9.70663 −0.356342
\(743\) 11.3652 0.416949 0.208474 0.978028i \(-0.433150\pi\)
0.208474 + 0.978028i \(0.433150\pi\)
\(744\) 2.92979 0.107411
\(745\) −4.02471 −0.147454
\(746\) 0.141490 0.00518031
\(747\) −0.865830 −0.0316791
\(748\) −37.9596 −1.38794
\(749\) 5.85443 0.213916
\(750\) 4.91090 0.179321
\(751\) 28.3200 1.03341 0.516706 0.856163i \(-0.327158\pi\)
0.516706 + 0.856163i \(0.327158\pi\)
\(752\) −6.99841 −0.255206
\(753\) 2.15987 0.0787101
\(754\) 9.35117 0.340549
\(755\) 7.31245 0.266127
\(756\) −2.75905 −0.100346
\(757\) 25.4858 0.926296 0.463148 0.886281i \(-0.346720\pi\)
0.463148 + 0.886281i \(0.346720\pi\)
\(758\) −30.8204 −1.11945
\(759\) 43.5968 1.58246
\(760\) −3.18424 −0.115505
\(761\) 29.3339 1.06335 0.531676 0.846948i \(-0.321562\pi\)
0.531676 + 0.846948i \(0.321562\pi\)
\(762\) −8.59083 −0.311213
\(763\) 29.5089 1.06829
\(764\) −2.89259 −0.104650
\(765\) 3.17148 0.114665
\(766\) 21.3338 0.770823
\(767\) 9.24734 0.333902
\(768\) −1.00000 −0.0360844
\(769\) −25.1097 −0.905479 −0.452740 0.891643i \(-0.649553\pi\)
−0.452740 + 0.891643i \(0.649553\pi\)
\(770\) 8.38453 0.302157
\(771\) −16.0148 −0.576760
\(772\) 20.2076 0.727288
\(773\) 31.2150 1.12273 0.561363 0.827570i \(-0.310277\pi\)
0.561363 + 0.827570i \(0.310277\pi\)
\(774\) −4.29142 −0.154252
\(775\) −13.9051 −0.499486
\(776\) −18.9602 −0.680633
\(777\) 6.39372 0.229373
\(778\) −22.0340 −0.789959
\(779\) 24.6355 0.882660
\(780\) −0.503883 −0.0180419
\(781\) 75.2569 2.69290
\(782\) −45.4985 −1.62702
\(783\) −9.35117 −0.334183
\(784\) 0.612353 0.0218697
\(785\) −11.7682 −0.420024
\(786\) 19.8384 0.707613
\(787\) 26.8139 0.955814 0.477907 0.878410i \(-0.341396\pi\)
0.477907 + 0.878410i \(0.341396\pi\)
\(788\) −16.8072 −0.598732
\(789\) −4.66348 −0.166024
\(790\) 5.08763 0.181010
\(791\) −35.1706 −1.25052
\(792\) −6.03100 −0.214302
\(793\) 0.178206 0.00632827
\(794\) 29.2872 1.03936
\(795\) 1.77272 0.0628718
\(796\) 1.86963 0.0662674
\(797\) 9.27410 0.328505 0.164253 0.986418i \(-0.447479\pi\)
0.164253 + 0.986418i \(0.447479\pi\)
\(798\) −17.4356 −0.617212
\(799\) 44.0485 1.55832
\(800\) 4.74610 0.167800
\(801\) 0.262117 0.00926145
\(802\) 11.9102 0.420563
\(803\) 27.4220 0.967703
\(804\) −9.08548 −0.320420
\(805\) 10.0497 0.354207
\(806\) 2.92979 0.103198
\(807\) 4.05727 0.142823
\(808\) −10.3574 −0.364371
\(809\) −0.168548 −0.00592582 −0.00296291 0.999996i \(-0.500943\pi\)
−0.00296291 + 0.999996i \(0.500943\pi\)
\(810\) 0.503883 0.0177047
\(811\) 30.9742 1.08765 0.543826 0.839198i \(-0.316975\pi\)
0.543826 + 0.839198i \(0.316975\pi\)
\(812\) 25.8003 0.905414
\(813\) 15.6485 0.548818
\(814\) 13.9760 0.489859
\(815\) −5.53975 −0.194049
\(816\) 6.29407 0.220337
\(817\) −27.1192 −0.948781
\(818\) 29.6075 1.03520
\(819\) −2.75905 −0.0964090
\(820\) 1.96434 0.0685976
\(821\) 38.8853 1.35711 0.678553 0.734551i \(-0.262607\pi\)
0.678553 + 0.734551i \(0.262607\pi\)
\(822\) −1.81911 −0.0634487
\(823\) −12.3747 −0.431356 −0.215678 0.976465i \(-0.569196\pi\)
−0.215678 + 0.976465i \(0.569196\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 28.6237 0.996550
\(826\) 25.5139 0.887741
\(827\) 3.84890 0.133839 0.0669196 0.997758i \(-0.478683\pi\)
0.0669196 + 0.997758i \(0.478683\pi\)
\(828\) −7.22879 −0.251218
\(829\) −5.45892 −0.189596 −0.0947981 0.995497i \(-0.530221\pi\)
−0.0947981 + 0.995497i \(0.530221\pi\)
\(830\) −0.436277 −0.0151434
\(831\) −19.1029 −0.662674
\(832\) −1.00000 −0.0346688
\(833\) −3.85420 −0.133540
\(834\) 13.6876 0.473964
\(835\) 8.47372 0.293245
\(836\) −38.1123 −1.31814
\(837\) −2.92979 −0.101268
\(838\) −3.51354 −0.121373
\(839\) 26.3422 0.909432 0.454716 0.890636i \(-0.349741\pi\)
0.454716 + 0.890636i \(0.349741\pi\)
\(840\) −1.39024 −0.0479678
\(841\) 58.4443 2.01532
\(842\) 23.4775 0.809089
\(843\) 3.80257 0.130968
\(844\) 3.95736 0.136218
\(845\) −0.503883 −0.0173341
\(846\) 6.99841 0.240610
\(847\) 70.0052 2.40541
\(848\) 3.51811 0.120812
\(849\) −4.96282 −0.170324
\(850\) −29.8723 −1.02461
\(851\) 16.7517 0.574241
\(852\) −12.4784 −0.427501
\(853\) 25.8598 0.885423 0.442712 0.896664i \(-0.354017\pi\)
0.442712 + 0.896664i \(0.354017\pi\)
\(854\) 0.491678 0.0168249
\(855\) 3.18424 0.108899
\(856\) −2.12190 −0.0725251
\(857\) −21.8546 −0.746539 −0.373269 0.927723i \(-0.621763\pi\)
−0.373269 + 0.927723i \(0.621763\pi\)
\(858\) −6.03100 −0.205895
\(859\) 4.92636 0.168085 0.0840427 0.996462i \(-0.473217\pi\)
0.0840427 + 0.996462i \(0.473217\pi\)
\(860\) −2.16237 −0.0737363
\(861\) 10.7559 0.366559
\(862\) 3.68034 0.125353
\(863\) −38.5056 −1.31075 −0.655374 0.755305i \(-0.727489\pi\)
−0.655374 + 0.755305i \(0.727489\pi\)
\(864\) 1.00000 0.0340207
\(865\) 1.57259 0.0534697
\(866\) 22.3102 0.758131
\(867\) −22.6154 −0.768058
\(868\) 8.08344 0.274370
\(869\) 60.8941 2.06569
\(870\) −4.71190 −0.159748
\(871\) −9.08548 −0.307850
\(872\) −10.6953 −0.362189
\(873\) 18.9602 0.641707
\(874\) −45.6817 −1.54521
\(875\) 13.5494 0.458054
\(876\) −4.54685 −0.153624
\(877\) −0.00168568 −5.69213e−5 0 −2.84607e−5 1.00000i \(-0.500009\pi\)
−2.84607e−5 1.00000i \(0.500009\pi\)
\(878\) 19.5096 0.658417
\(879\) −4.80936 −0.162216
\(880\) −3.03892 −0.102442
\(881\) 1.68023 0.0566084 0.0283042 0.999599i \(-0.490989\pi\)
0.0283042 + 0.999599i \(0.490989\pi\)
\(882\) −0.612353 −0.0206190
\(883\) −14.5958 −0.491188 −0.245594 0.969373i \(-0.578983\pi\)
−0.245594 + 0.969373i \(0.578983\pi\)
\(884\) 6.29407 0.211693
\(885\) −4.65958 −0.156630
\(886\) 31.9728 1.07415
\(887\) −44.9844 −1.51043 −0.755214 0.655478i \(-0.772467\pi\)
−0.755214 + 0.655478i \(0.772467\pi\)
\(888\) −2.31736 −0.0777656
\(889\) −23.7025 −0.794957
\(890\) 0.132076 0.00442721
\(891\) 6.03100 0.202046
\(892\) −11.4512 −0.383415
\(893\) 44.2258 1.47996
\(894\) 7.98738 0.267138
\(895\) 3.64565 0.121861
\(896\) −2.75905 −0.0921734
\(897\) −7.22879 −0.241362
\(898\) −25.0632 −0.836370
\(899\) 27.3970 0.913740
\(900\) −4.74610 −0.158203
\(901\) −22.1432 −0.737698
\(902\) 23.5112 0.782838
\(903\) −11.8402 −0.394018
\(904\) 12.7474 0.423971
\(905\) 3.78073 0.125676
\(906\) −14.5122 −0.482135
\(907\) 7.34618 0.243926 0.121963 0.992535i \(-0.461081\pi\)
0.121963 + 0.992535i \(0.461081\pi\)
\(908\) −9.36186 −0.310684
\(909\) 10.3574 0.343532
\(910\) −1.39024 −0.0460860
\(911\) 34.0544 1.12827 0.564136 0.825682i \(-0.309209\pi\)
0.564136 + 0.825682i \(0.309209\pi\)
\(912\) 6.31941 0.209256
\(913\) −5.22182 −0.172817
\(914\) −41.1417 −1.36085
\(915\) −0.0897949 −0.00296853
\(916\) 13.4812 0.445431
\(917\) 54.7352 1.80751
\(918\) −6.29407 −0.207735
\(919\) −23.4227 −0.772642 −0.386321 0.922364i \(-0.626254\pi\)
−0.386321 + 0.922364i \(0.626254\pi\)
\(920\) −3.64247 −0.120089
\(921\) 4.41310 0.145417
\(922\) 21.6234 0.712129
\(923\) −12.4784 −0.410730
\(924\) −16.6398 −0.547410
\(925\) 10.9984 0.361626
\(926\) 37.9222 1.24620
\(927\) 1.00000 0.0328443
\(928\) −9.35117 −0.306967
\(929\) −54.3395 −1.78282 −0.891411 0.453195i \(-0.850284\pi\)
−0.891411 + 0.453195i \(0.850284\pi\)
\(930\) −1.47627 −0.0484089
\(931\) −3.86971 −0.126825
\(932\) −23.5946 −0.772868
\(933\) −12.0144 −0.393335
\(934\) −28.5116 −0.932929
\(935\) 19.1272 0.625526
\(936\) 1.00000 0.0326860
\(937\) −35.0824 −1.14609 −0.573045 0.819524i \(-0.694238\pi\)
−0.573045 + 0.819524i \(0.694238\pi\)
\(938\) −25.0673 −0.818476
\(939\) −24.5115 −0.799902
\(940\) 3.52638 0.115018
\(941\) −10.1397 −0.330543 −0.165272 0.986248i \(-0.552850\pi\)
−0.165272 + 0.986248i \(0.552850\pi\)
\(942\) 23.3549 0.760945
\(943\) 28.1807 0.917689
\(944\) −9.24734 −0.300975
\(945\) 1.39024 0.0452245
\(946\) −25.8815 −0.841481
\(947\) 45.2354 1.46995 0.734976 0.678093i \(-0.237193\pi\)
0.734976 + 0.678093i \(0.237193\pi\)
\(948\) −10.0968 −0.327930
\(949\) −4.54685 −0.147597
\(950\) −29.9926 −0.973087
\(951\) 10.1665 0.329672
\(952\) 17.3657 0.562824
\(953\) −26.9631 −0.873419 −0.436710 0.899603i \(-0.643856\pi\)
−0.436710 + 0.899603i \(0.643856\pi\)
\(954\) −3.51811 −0.113903
\(955\) 1.45753 0.0471645
\(956\) 28.9815 0.937329
\(957\) −56.3969 −1.82305
\(958\) 6.33889 0.204800
\(959\) −5.01901 −0.162072
\(960\) 0.503883 0.0162628
\(961\) −22.4163 −0.723107
\(962\) −2.31736 −0.0747147
\(963\) 2.12190 0.0683774
\(964\) 13.8376 0.445681
\(965\) −10.1823 −0.327779
\(966\) −19.9446 −0.641706
\(967\) 40.6646 1.30769 0.653843 0.756630i \(-0.273156\pi\)
0.653843 + 0.756630i \(0.273156\pi\)
\(968\) −25.3729 −0.815517
\(969\) −39.7748 −1.27775
\(970\) 9.55376 0.306753
\(971\) −11.7350 −0.376595 −0.188297 0.982112i \(-0.560297\pi\)
−0.188297 + 0.982112i \(0.560297\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 37.7649 1.21069
\(974\) −7.00106 −0.224328
\(975\) −4.74610 −0.151997
\(976\) −0.178206 −0.00570423
\(977\) 47.2456 1.51152 0.755761 0.654848i \(-0.227267\pi\)
0.755761 + 0.654848i \(0.227267\pi\)
\(978\) 10.9941 0.351553
\(979\) 1.58083 0.0505234
\(980\) −0.308554 −0.00985641
\(981\) 10.6953 0.341475
\(982\) 12.4695 0.397917
\(983\) 3.11285 0.0992843 0.0496422 0.998767i \(-0.484192\pi\)
0.0496422 + 0.998767i \(0.484192\pi\)
\(984\) −3.89839 −0.124276
\(985\) 8.46887 0.269841
\(986\) 58.8569 1.87439
\(987\) 19.3089 0.614611
\(988\) 6.31941 0.201047
\(989\) −31.0217 −0.986434
\(990\) 3.03892 0.0965832
\(991\) 4.85277 0.154153 0.0770767 0.997025i \(-0.475441\pi\)
0.0770767 + 0.997025i \(0.475441\pi\)
\(992\) −2.92979 −0.0930210
\(993\) −14.2271 −0.451482
\(994\) −34.4284 −1.09200
\(995\) −0.942077 −0.0298658
\(996\) 0.865830 0.0274349
\(997\) −55.7601 −1.76594 −0.882970 0.469430i \(-0.844460\pi\)
−0.882970 + 0.469430i \(0.844460\pi\)
\(998\) −27.5059 −0.870684
\(999\) 2.31736 0.0733181
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.ba.1.7 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.ba.1.7 14 1.1 even 1 trivial