Properties

Label 8034.2.a.z.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 $1$

Related objects

Downloads

Learn more about

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 1.7
Root \(0.664239\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.664239 q^{5} +1.00000 q^{6} +2.36162 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.664239 q^{5} +1.00000 q^{6} +2.36162 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.664239 q^{10} -3.14397 q^{11} -1.00000 q^{12} +1.00000 q^{13} -2.36162 q^{14} +0.664239 q^{15} +1.00000 q^{16} -7.53535 q^{17} -1.00000 q^{18} +5.47817 q^{19} -0.664239 q^{20} -2.36162 q^{21} +3.14397 q^{22} +1.27876 q^{23} +1.00000 q^{24} -4.55879 q^{25} -1.00000 q^{26} -1.00000 q^{27} +2.36162 q^{28} -5.06863 q^{29} -0.664239 q^{30} +6.27777 q^{31} -1.00000 q^{32} +3.14397 q^{33} +7.53535 q^{34} -1.56868 q^{35} +1.00000 q^{36} +10.8042 q^{37} -5.47817 q^{38} -1.00000 q^{39} +0.664239 q^{40} +11.1801 q^{41} +2.36162 q^{42} -6.25237 q^{43} -3.14397 q^{44} -0.664239 q^{45} -1.27876 q^{46} -8.67811 q^{47} -1.00000 q^{48} -1.42277 q^{49} +4.55879 q^{50} +7.53535 q^{51} +1.00000 q^{52} -9.70904 q^{53} +1.00000 q^{54} +2.08835 q^{55} -2.36162 q^{56} -5.47817 q^{57} +5.06863 q^{58} -10.6905 q^{59} +0.664239 q^{60} -2.60711 q^{61} -6.27777 q^{62} +2.36162 q^{63} +1.00000 q^{64} -0.664239 q^{65} -3.14397 q^{66} -6.78514 q^{67} -7.53535 q^{68} -1.27876 q^{69} +1.56868 q^{70} +1.70711 q^{71} -1.00000 q^{72} +0.395522 q^{73} -10.8042 q^{74} +4.55879 q^{75} +5.47817 q^{76} -7.42484 q^{77} +1.00000 q^{78} +2.79959 q^{79} -0.664239 q^{80} +1.00000 q^{81} -11.1801 q^{82} +11.4961 q^{83} -2.36162 q^{84} +5.00528 q^{85} +6.25237 q^{86} +5.06863 q^{87} +3.14397 q^{88} +17.4900 q^{89} +0.664239 q^{90} +2.36162 q^{91} +1.27876 q^{92} -6.27777 q^{93} +8.67811 q^{94} -3.63882 q^{95} +1.00000 q^{96} +9.21361 q^{97} +1.42277 q^{98} -3.14397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 14q^{2} - 14q^{3} + 14q^{4} - 3q^{5} + 14q^{6} + 4q^{7} - 14q^{8} + 14q^{9} + 3q^{10} + 5q^{11} - 14q^{12} + 14q^{13} - 4q^{14} + 3q^{15} + 14q^{16} - 7q^{17} - 14q^{18} + 31q^{19} - 3q^{20} - 4q^{21} - 5q^{22} + 14q^{23} + 14q^{24} + 11q^{25} - 14q^{26} - 14q^{27} + 4q^{28} + 9q^{29} - 3q^{30} + 23q^{31} - 14q^{32} - 5q^{33} + 7q^{34} - 2q^{35} + 14q^{36} + 12q^{37} - 31q^{38} - 14q^{39} + 3q^{40} - 5q^{41} + 4q^{42} - 2q^{43} + 5q^{44} - 3q^{45} - 14q^{46} - 11q^{47} - 14q^{48} + 52q^{49} - 11q^{50} + 7q^{51} + 14q^{52} + 6q^{53} + 14q^{54} + 30q^{55} - 4q^{56} - 31q^{57} - 9q^{58} - 4q^{59} + 3q^{60} + 12q^{61} - 23q^{62} + 4q^{63} + 14q^{64} - 3q^{65} + 5q^{66} + 24q^{67} - 7q^{68} - 14q^{69} + 2q^{70} + 20q^{71} - 14q^{72} + 2q^{73} - 12q^{74} - 11q^{75} + 31q^{76} - 28q^{77} + 14q^{78} + 59q^{79} - 3q^{80} + 14q^{81} + 5q^{82} + q^{83} - 4q^{84} - 29q^{85} + 2q^{86} - 9q^{87} - 5q^{88} + 6q^{89} + 3q^{90} + 4q^{91} + 14q^{92} - 23q^{93} + 11q^{94} - 58q^{95} + 14q^{96} - 6q^{97} - 52q^{98} + 5q^{99} + O(q^{100}) \)

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
\(5\) −0.664239 −0.297057 −0.148528 0.988908i \(-0.547454\pi\)
−0.148528 + 0.988908i \(0.547454\pi\)
\(6\) 1.00000 0.408248
\(7\) 2.36162 0.892607 0.446304 0.894882i \(-0.352740\pi\)
0.446304 + 0.894882i \(0.352740\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0.664239 0.210051
\(11\) −3.14397 −0.947941 −0.473971 0.880541i \(-0.657180\pi\)
−0.473971 + 0.880541i \(0.657180\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) −2.36162 −0.631169
\(15\) 0.664239 0.171506
\(16\) 1.00000 0.250000
\(17\) −7.53535 −1.82759 −0.913796 0.406174i \(-0.866863\pi\)
−0.913796 + 0.406174i \(0.866863\pi\)
\(18\) −1.00000 −0.235702
\(19\) 5.47817 1.25678 0.628389 0.777899i \(-0.283714\pi\)
0.628389 + 0.777899i \(0.283714\pi\)
\(20\) −0.664239 −0.148528
\(21\) −2.36162 −0.515347
\(22\) 3.14397 0.670296
\(23\) 1.27876 0.266641 0.133320 0.991073i \(-0.457436\pi\)
0.133320 + 0.991073i \(0.457436\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.55879 −0.911757
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) 2.36162 0.446304
\(29\) −5.06863 −0.941221 −0.470610 0.882341i \(-0.655966\pi\)
−0.470610 + 0.882341i \(0.655966\pi\)
\(30\) −0.664239 −0.121273
\(31\) 6.27777 1.12752 0.563760 0.825938i \(-0.309354\pi\)
0.563760 + 0.825938i \(0.309354\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.14397 0.547294
\(34\) 7.53535 1.29230
\(35\) −1.56868 −0.265155
\(36\) 1.00000 0.166667
\(37\) 10.8042 1.77620 0.888102 0.459647i \(-0.152024\pi\)
0.888102 + 0.459647i \(0.152024\pi\)
\(38\) −5.47817 −0.888677
\(39\) −1.00000 −0.160128
\(40\) 0.664239 0.105025
\(41\) 11.1801 1.74604 0.873022 0.487681i \(-0.162157\pi\)
0.873022 + 0.487681i \(0.162157\pi\)
\(42\) 2.36162 0.364405
\(43\) −6.25237 −0.953478 −0.476739 0.879045i \(-0.658181\pi\)
−0.476739 + 0.879045i \(0.658181\pi\)
\(44\) −3.14397 −0.473971
\(45\) −0.664239 −0.0990189
\(46\) −1.27876 −0.188543
\(47\) −8.67811 −1.26583 −0.632916 0.774220i \(-0.718142\pi\)
−0.632916 + 0.774220i \(0.718142\pi\)
\(48\) −1.00000 −0.144338
\(49\) −1.42277 −0.203252
\(50\) 4.55879 0.644710
\(51\) 7.53535 1.05516
\(52\) 1.00000 0.138675
\(53\) −9.70904 −1.33364 −0.666819 0.745219i \(-0.732345\pi\)
−0.666819 + 0.745219i \(0.732345\pi\)
\(54\) 1.00000 0.136083
\(55\) 2.08835 0.281592
\(56\) −2.36162 −0.315584
\(57\) −5.47817 −0.725602
\(58\) 5.06863 0.665543
\(59\) −10.6905 −1.39179 −0.695893 0.718145i \(-0.744991\pi\)
−0.695893 + 0.718145i \(0.744991\pi\)
\(60\) 0.664239 0.0857529
\(61\) −2.60711 −0.333807 −0.166903 0.985973i \(-0.553377\pi\)
−0.166903 + 0.985973i \(0.553377\pi\)
\(62\) −6.27777 −0.797277
\(63\) 2.36162 0.297536
\(64\) 1.00000 0.125000
\(65\) −0.664239 −0.0823887
\(66\) −3.14397 −0.386995
\(67\) −6.78514 −0.828937 −0.414469 0.910064i \(-0.636033\pi\)
−0.414469 + 0.910064i \(0.636033\pi\)
\(68\) −7.53535 −0.913796
\(69\) −1.27876 −0.153945
\(70\) 1.56868 0.187493
\(71\) 1.70711 0.202596 0.101298 0.994856i \(-0.467700\pi\)
0.101298 + 0.994856i \(0.467700\pi\)
\(72\) −1.00000 −0.117851
\(73\) 0.395522 0.0462923 0.0231462 0.999732i \(-0.492632\pi\)
0.0231462 + 0.999732i \(0.492632\pi\)
\(74\) −10.8042 −1.25597
\(75\) 4.55879 0.526403
\(76\) 5.47817 0.628389
\(77\) −7.42484 −0.846139
\(78\) 1.00000 0.113228
\(79\) 2.79959 0.314979 0.157489 0.987521i \(-0.449660\pi\)
0.157489 + 0.987521i \(0.449660\pi\)
\(80\) −0.664239 −0.0742642
\(81\) 1.00000 0.111111
\(82\) −11.1801 −1.23464
\(83\) 11.4961 1.26186 0.630929 0.775841i \(-0.282674\pi\)
0.630929 + 0.775841i \(0.282674\pi\)
\(84\) −2.36162 −0.257674
\(85\) 5.00528 0.542899
\(86\) 6.25237 0.674211
\(87\) 5.06863 0.543414
\(88\) 3.14397 0.335148
\(89\) 17.4900 1.85393 0.926967 0.375142i \(-0.122406\pi\)
0.926967 + 0.375142i \(0.122406\pi\)
\(90\) 0.664239 0.0700170
\(91\) 2.36162 0.247565
\(92\) 1.27876 0.133320
\(93\) −6.27777 −0.650974
\(94\) 8.67811 0.895079
\(95\) −3.63882 −0.373335
\(96\) 1.00000 0.102062
\(97\) 9.21361 0.935501 0.467750 0.883861i \(-0.345065\pi\)
0.467750 + 0.883861i \(0.345065\pi\)
\(98\) 1.42277 0.143721
\(99\) −3.14397 −0.315980
\(100\) −4.55879 −0.455879
\(101\) 14.3771 1.43057 0.715285 0.698832i \(-0.246297\pi\)
0.715285 + 0.698832i \(0.246297\pi\)
\(102\) −7.53535 −0.746111
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) 1.56868 0.153087
\(106\) 9.70904 0.943025
\(107\) 12.2751 1.18668 0.593341 0.804952i \(-0.297809\pi\)
0.593341 + 0.804952i \(0.297809\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 19.6836 1.88534 0.942672 0.333721i \(-0.108304\pi\)
0.942672 + 0.333721i \(0.108304\pi\)
\(110\) −2.08835 −0.199116
\(111\) −10.8042 −1.02549
\(112\) 2.36162 0.223152
\(113\) −12.4526 −1.17144 −0.585721 0.810513i \(-0.699188\pi\)
−0.585721 + 0.810513i \(0.699188\pi\)
\(114\) 5.47817 0.513078
\(115\) −0.849405 −0.0792074
\(116\) −5.06863 −0.470610
\(117\) 1.00000 0.0924500
\(118\) 10.6905 0.984142
\(119\) −17.7956 −1.63132
\(120\) −0.664239 −0.0606365
\(121\) −1.11548 −0.101407
\(122\) 2.60711 0.236037
\(123\) −11.1801 −1.00808
\(124\) 6.27777 0.563760
\(125\) 6.34932 0.567901
\(126\) −2.36162 −0.210390
\(127\) −12.7497 −1.13135 −0.565676 0.824627i \(-0.691385\pi\)
−0.565676 + 0.824627i \(0.691385\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.25237 0.550491
\(130\) 0.664239 0.0582576
\(131\) −6.54233 −0.571606 −0.285803 0.958288i \(-0.592260\pi\)
−0.285803 + 0.958288i \(0.592260\pi\)
\(132\) 3.14397 0.273647
\(133\) 12.9373 1.12181
\(134\) 6.78514 0.586147
\(135\) 0.664239 0.0571686
\(136\) 7.53535 0.646151
\(137\) 18.3434 1.56718 0.783592 0.621276i \(-0.213386\pi\)
0.783592 + 0.621276i \(0.213386\pi\)
\(138\) 1.27876 0.108856
\(139\) 4.49746 0.381470 0.190735 0.981642i \(-0.438913\pi\)
0.190735 + 0.981642i \(0.438913\pi\)
\(140\) −1.56868 −0.132578
\(141\) 8.67811 0.730829
\(142\) −1.70711 −0.143257
\(143\) −3.14397 −0.262912
\(144\) 1.00000 0.0833333
\(145\) 3.36678 0.279596
\(146\) −0.395522 −0.0327336
\(147\) 1.42277 0.117348
\(148\) 10.8042 0.888102
\(149\) 10.5024 0.860392 0.430196 0.902736i \(-0.358444\pi\)
0.430196 + 0.902736i \(0.358444\pi\)
\(150\) −4.55879 −0.372223
\(151\) −0.330883 −0.0269269 −0.0134635 0.999909i \(-0.504286\pi\)
−0.0134635 + 0.999909i \(0.504286\pi\)
\(152\) −5.47817 −0.444338
\(153\) −7.53535 −0.609197
\(154\) 7.42484 0.598311
\(155\) −4.16994 −0.334938
\(156\) −1.00000 −0.0800641
\(157\) 6.48802 0.517800 0.258900 0.965904i \(-0.416640\pi\)
0.258900 + 0.965904i \(0.416640\pi\)
\(158\) −2.79959 −0.222724
\(159\) 9.70904 0.769977
\(160\) 0.664239 0.0525127
\(161\) 3.01995 0.238005
\(162\) −1.00000 −0.0785674
\(163\) −10.2456 −0.802499 −0.401249 0.915969i \(-0.631424\pi\)
−0.401249 + 0.915969i \(0.631424\pi\)
\(164\) 11.1801 0.873022
\(165\) −2.08835 −0.162577
\(166\) −11.4961 −0.892268
\(167\) 1.93544 0.149769 0.0748846 0.997192i \(-0.476141\pi\)
0.0748846 + 0.997192i \(0.476141\pi\)
\(168\) 2.36162 0.182203
\(169\) 1.00000 0.0769231
\(170\) −5.00528 −0.383887
\(171\) 5.47817 0.418926
\(172\) −6.25237 −0.476739
\(173\) −2.22848 −0.169428 −0.0847142 0.996405i \(-0.526998\pi\)
−0.0847142 + 0.996405i \(0.526998\pi\)
\(174\) −5.06863 −0.384252
\(175\) −10.7661 −0.813841
\(176\) −3.14397 −0.236985
\(177\) 10.6905 0.803548
\(178\) −17.4900 −1.31093
\(179\) −5.40080 −0.403675 −0.201838 0.979419i \(-0.564691\pi\)
−0.201838 + 0.979419i \(0.564691\pi\)
\(180\) −0.664239 −0.0495095
\(181\) −14.4182 −1.07170 −0.535848 0.844314i \(-0.680008\pi\)
−0.535848 + 0.844314i \(0.680008\pi\)
\(182\) −2.36162 −0.175055
\(183\) 2.60711 0.192723
\(184\) −1.27876 −0.0942717
\(185\) −7.17659 −0.527633
\(186\) 6.27777 0.460308
\(187\) 23.6909 1.73245
\(188\) −8.67811 −0.632916
\(189\) −2.36162 −0.171782
\(190\) 3.63882 0.263988
\(191\) 10.8810 0.787324 0.393662 0.919255i \(-0.371208\pi\)
0.393662 + 0.919255i \(0.371208\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −27.6749 −1.99209 −0.996043 0.0888700i \(-0.971674\pi\)
−0.996043 + 0.0888700i \(0.971674\pi\)
\(194\) −9.21361 −0.661499
\(195\) 0.664239 0.0475672
\(196\) −1.42277 −0.101626
\(197\) −22.7122 −1.61817 −0.809087 0.587689i \(-0.800038\pi\)
−0.809087 + 0.587689i \(0.800038\pi\)
\(198\) 3.14397 0.223432
\(199\) −10.5958 −0.751118 −0.375559 0.926799i \(-0.622549\pi\)
−0.375559 + 0.926799i \(0.622549\pi\)
\(200\) 4.55879 0.322355
\(201\) 6.78514 0.478587
\(202\) −14.3771 −1.01157
\(203\) −11.9702 −0.840140
\(204\) 7.53535 0.527580
\(205\) −7.42629 −0.518674
\(206\) 1.00000 0.0696733
\(207\) 1.27876 0.0888802
\(208\) 1.00000 0.0693375
\(209\) −17.2232 −1.19135
\(210\) −1.56868 −0.108249
\(211\) −23.9450 −1.64844 −0.824220 0.566269i \(-0.808386\pi\)
−0.824220 + 0.566269i \(0.808386\pi\)
\(212\) −9.70904 −0.666819
\(213\) −1.70711 −0.116969
\(214\) −12.2751 −0.839110
\(215\) 4.15307 0.283237
\(216\) 1.00000 0.0680414
\(217\) 14.8257 1.00643
\(218\) −19.6836 −1.33314
\(219\) −0.395522 −0.0267269
\(220\) 2.08835 0.140796
\(221\) −7.53535 −0.506883
\(222\) 10.8042 0.725132
\(223\) 9.14462 0.612369 0.306185 0.951972i \(-0.400948\pi\)
0.306185 + 0.951972i \(0.400948\pi\)
\(224\) −2.36162 −0.157792
\(225\) −4.55879 −0.303919
\(226\) 12.4526 0.828334
\(227\) −0.990850 −0.0657650 −0.0328825 0.999459i \(-0.510469\pi\)
−0.0328825 + 0.999459i \(0.510469\pi\)
\(228\) −5.47817 −0.362801
\(229\) −0.230645 −0.0152414 −0.00762072 0.999971i \(-0.502426\pi\)
−0.00762072 + 0.999971i \(0.502426\pi\)
\(230\) 0.849405 0.0560081
\(231\) 7.42484 0.488519
\(232\) 5.06863 0.332772
\(233\) 29.6243 1.94075 0.970377 0.241598i \(-0.0776714\pi\)
0.970377 + 0.241598i \(0.0776714\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 5.76434 0.376024
\(236\) −10.6905 −0.695893
\(237\) −2.79959 −0.181853
\(238\) 17.7956 1.15352
\(239\) −12.1630 −0.786760 −0.393380 0.919376i \(-0.628694\pi\)
−0.393380 + 0.919376i \(0.628694\pi\)
\(240\) 0.664239 0.0428765
\(241\) −9.36359 −0.603162 −0.301581 0.953441i \(-0.597514\pi\)
−0.301581 + 0.953441i \(0.597514\pi\)
\(242\) 1.11548 0.0717057
\(243\) −1.00000 −0.0641500
\(244\) −2.60711 −0.166903
\(245\) 0.945057 0.0603775
\(246\) 11.1801 0.712820
\(247\) 5.47817 0.348568
\(248\) −6.27777 −0.398639
\(249\) −11.4961 −0.728534
\(250\) −6.34932 −0.401566
\(251\) 24.7530 1.56239 0.781196 0.624286i \(-0.214610\pi\)
0.781196 + 0.624286i \(0.214610\pi\)
\(252\) 2.36162 0.148768
\(253\) −4.02039 −0.252760
\(254\) 12.7497 0.799987
\(255\) −5.00528 −0.313443
\(256\) 1.00000 0.0625000
\(257\) −9.92601 −0.619167 −0.309584 0.950872i \(-0.600190\pi\)
−0.309584 + 0.950872i \(0.600190\pi\)
\(258\) −6.25237 −0.389256
\(259\) 25.5154 1.58545
\(260\) −0.664239 −0.0411944
\(261\) −5.06863 −0.313740
\(262\) 6.54233 0.404186
\(263\) 23.0280 1.41997 0.709983 0.704219i \(-0.248703\pi\)
0.709983 + 0.704219i \(0.248703\pi\)
\(264\) −3.14397 −0.193498
\(265\) 6.44912 0.396166
\(266\) −12.9373 −0.793239
\(267\) −17.4900 −1.07037
\(268\) −6.78514 −0.414469
\(269\) 11.0757 0.675296 0.337648 0.941273i \(-0.390369\pi\)
0.337648 + 0.941273i \(0.390369\pi\)
\(270\) −0.664239 −0.0404243
\(271\) 13.7124 0.832970 0.416485 0.909143i \(-0.363262\pi\)
0.416485 + 0.909143i \(0.363262\pi\)
\(272\) −7.53535 −0.456898
\(273\) −2.36162 −0.142932
\(274\) −18.3434 −1.10817
\(275\) 14.3327 0.864292
\(276\) −1.27876 −0.0769725
\(277\) 25.1561 1.51148 0.755742 0.654869i \(-0.227276\pi\)
0.755742 + 0.654869i \(0.227276\pi\)
\(278\) −4.49746 −0.269740
\(279\) 6.27777 0.375840
\(280\) 1.56868 0.0937465
\(281\) −19.4460 −1.16005 −0.580026 0.814598i \(-0.696957\pi\)
−0.580026 + 0.814598i \(0.696957\pi\)
\(282\) −8.67811 −0.516774
\(283\) −16.6056 −0.987100 −0.493550 0.869717i \(-0.664301\pi\)
−0.493550 + 0.869717i \(0.664301\pi\)
\(284\) 1.70711 0.101298
\(285\) 3.63882 0.215545
\(286\) 3.14397 0.185907
\(287\) 26.4032 1.55853
\(288\) −1.00000 −0.0589256
\(289\) 39.7815 2.34009
\(290\) −3.36678 −0.197704
\(291\) −9.21361 −0.540112
\(292\) 0.395522 0.0231462
\(293\) 22.3887 1.30796 0.653982 0.756511i \(-0.273097\pi\)
0.653982 + 0.756511i \(0.273097\pi\)
\(294\) −1.42277 −0.0829774
\(295\) 7.10106 0.413440
\(296\) −10.8042 −0.627983
\(297\) 3.14397 0.182431
\(298\) −10.5024 −0.608389
\(299\) 1.27876 0.0739528
\(300\) 4.55879 0.263202
\(301\) −14.7657 −0.851081
\(302\) 0.330883 0.0190402
\(303\) −14.3771 −0.825940
\(304\) 5.47817 0.314195
\(305\) 1.73175 0.0991596
\(306\) 7.53535 0.430767
\(307\) 8.75392 0.499612 0.249806 0.968296i \(-0.419633\pi\)
0.249806 + 0.968296i \(0.419633\pi\)
\(308\) −7.42484 −0.423070
\(309\) 1.00000 0.0568880
\(310\) 4.16994 0.236837
\(311\) 3.32236 0.188394 0.0941968 0.995554i \(-0.469972\pi\)
0.0941968 + 0.995554i \(0.469972\pi\)
\(312\) 1.00000 0.0566139
\(313\) 13.9039 0.785894 0.392947 0.919561i \(-0.371456\pi\)
0.392947 + 0.919561i \(0.371456\pi\)
\(314\) −6.48802 −0.366140
\(315\) −1.56868 −0.0883850
\(316\) 2.79959 0.157489
\(317\) −12.9648 −0.728177 −0.364089 0.931364i \(-0.618619\pi\)
−0.364089 + 0.931364i \(0.618619\pi\)
\(318\) −9.70904 −0.544456
\(319\) 15.9356 0.892222
\(320\) −0.664239 −0.0371321
\(321\) −12.2751 −0.685131
\(322\) −3.01995 −0.168295
\(323\) −41.2800 −2.29688
\(324\) 1.00000 0.0555556
\(325\) −4.55879 −0.252876
\(326\) 10.2456 0.567452
\(327\) −19.6836 −1.08850
\(328\) −11.1801 −0.617320
\(329\) −20.4944 −1.12989
\(330\) 2.08835 0.114960
\(331\) 28.9193 1.58955 0.794773 0.606906i \(-0.207590\pi\)
0.794773 + 0.606906i \(0.207590\pi\)
\(332\) 11.4961 0.630929
\(333\) 10.8042 0.592068
\(334\) −1.93544 −0.105903
\(335\) 4.50696 0.246242
\(336\) −2.36162 −0.128837
\(337\) −24.6699 −1.34386 −0.671929 0.740616i \(-0.734534\pi\)
−0.671929 + 0.740616i \(0.734534\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 12.4526 0.676332
\(340\) 5.00528 0.271449
\(341\) −19.7371 −1.06882
\(342\) −5.47817 −0.296226
\(343\) −19.8913 −1.07403
\(344\) 6.25237 0.337105
\(345\) 0.849405 0.0457304
\(346\) 2.22848 0.119804
\(347\) −3.17151 −0.170255 −0.0851277 0.996370i \(-0.527130\pi\)
−0.0851277 + 0.996370i \(0.527130\pi\)
\(348\) 5.06863 0.271707
\(349\) −31.3835 −1.67992 −0.839961 0.542646i \(-0.817422\pi\)
−0.839961 + 0.542646i \(0.817422\pi\)
\(350\) 10.7661 0.575473
\(351\) −1.00000 −0.0533761
\(352\) 3.14397 0.167574
\(353\) 17.0417 0.907037 0.453519 0.891247i \(-0.350169\pi\)
0.453519 + 0.891247i \(0.350169\pi\)
\(354\) −10.6905 −0.568194
\(355\) −1.13393 −0.0601826
\(356\) 17.4900 0.926967
\(357\) 17.7956 0.941844
\(358\) 5.40080 0.285441
\(359\) 25.2917 1.33484 0.667422 0.744680i \(-0.267398\pi\)
0.667422 + 0.744680i \(0.267398\pi\)
\(360\) 0.664239 0.0350085
\(361\) 11.0104 0.579493
\(362\) 14.4182 0.757804
\(363\) 1.11548 0.0585475
\(364\) 2.36162 0.123782
\(365\) −0.262721 −0.0137515
\(366\) −2.60711 −0.136276
\(367\) 13.0779 0.682662 0.341331 0.939943i \(-0.389122\pi\)
0.341331 + 0.939943i \(0.389122\pi\)
\(368\) 1.27876 0.0666601
\(369\) 11.1801 0.582015
\(370\) 7.17659 0.373093
\(371\) −22.9290 −1.19042
\(372\) −6.27777 −0.325487
\(373\) −25.9846 −1.34543 −0.672717 0.739900i \(-0.734873\pi\)
−0.672717 + 0.739900i \(0.734873\pi\)
\(374\) −23.6909 −1.22503
\(375\) −6.34932 −0.327878
\(376\) 8.67811 0.447539
\(377\) −5.06863 −0.261048
\(378\) 2.36162 0.121468
\(379\) −14.4762 −0.743590 −0.371795 0.928315i \(-0.621258\pi\)
−0.371795 + 0.928315i \(0.621258\pi\)
\(380\) −3.63882 −0.186667
\(381\) 12.7497 0.653187
\(382\) −10.8810 −0.556722
\(383\) 29.6314 1.51409 0.757046 0.653362i \(-0.226642\pi\)
0.757046 + 0.653362i \(0.226642\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.93187 0.251351
\(386\) 27.6749 1.40862
\(387\) −6.25237 −0.317826
\(388\) 9.21361 0.467750
\(389\) −31.9402 −1.61943 −0.809716 0.586822i \(-0.800379\pi\)
−0.809716 + 0.586822i \(0.800379\pi\)
\(390\) −0.664239 −0.0336351
\(391\) −9.63593 −0.487310
\(392\) 1.42277 0.0718605
\(393\) 6.54233 0.330017
\(394\) 22.7122 1.14422
\(395\) −1.85960 −0.0935666
\(396\) −3.14397 −0.157990
\(397\) −1.91074 −0.0958973 −0.0479486 0.998850i \(-0.515268\pi\)
−0.0479486 + 0.998850i \(0.515268\pi\)
\(398\) 10.5958 0.531120
\(399\) −12.9373 −0.647677
\(400\) −4.55879 −0.227939
\(401\) 24.2814 1.21255 0.606277 0.795254i \(-0.292662\pi\)
0.606277 + 0.795254i \(0.292662\pi\)
\(402\) −6.78514 −0.338412
\(403\) 6.27777 0.312718
\(404\) 14.3771 0.715285
\(405\) −0.664239 −0.0330063
\(406\) 11.9702 0.594069
\(407\) −33.9681 −1.68374
\(408\) −7.53535 −0.373056
\(409\) 8.85686 0.437944 0.218972 0.975731i \(-0.429730\pi\)
0.218972 + 0.975731i \(0.429730\pi\)
\(410\) 7.42629 0.366758
\(411\) −18.3434 −0.904814
\(412\) −1.00000 −0.0492665
\(413\) −25.2469 −1.24232
\(414\) −1.27876 −0.0628478
\(415\) −7.63614 −0.374844
\(416\) −1.00000 −0.0490290
\(417\) −4.49746 −0.220242
\(418\) 17.2232 0.842414
\(419\) 24.4543 1.19467 0.597334 0.801992i \(-0.296227\pi\)
0.597334 + 0.801992i \(0.296227\pi\)
\(420\) 1.56868 0.0765437
\(421\) 28.6102 1.39437 0.697187 0.716889i \(-0.254435\pi\)
0.697187 + 0.716889i \(0.254435\pi\)
\(422\) 23.9450 1.16562
\(423\) −8.67811 −0.421944
\(424\) 9.70904 0.471512
\(425\) 34.3521 1.66632
\(426\) 1.70711 0.0827095
\(427\) −6.15701 −0.297958
\(428\) 12.2751 0.593341
\(429\) 3.14397 0.151792
\(430\) −4.15307 −0.200279
\(431\) −0.310658 −0.0149639 −0.00748193 0.999972i \(-0.502382\pi\)
−0.00748193 + 0.999972i \(0.502382\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −7.72676 −0.371324 −0.185662 0.982614i \(-0.559443\pi\)
−0.185662 + 0.982614i \(0.559443\pi\)
\(434\) −14.8257 −0.711656
\(435\) −3.36678 −0.161425
\(436\) 19.6836 0.942672
\(437\) 7.00528 0.335108
\(438\) 0.395522 0.0188988
\(439\) 22.7682 1.08667 0.543333 0.839517i \(-0.317162\pi\)
0.543333 + 0.839517i \(0.317162\pi\)
\(440\) −2.08835 −0.0995580
\(441\) −1.42277 −0.0677508
\(442\) 7.53535 0.358420
\(443\) 16.7094 0.793888 0.396944 0.917843i \(-0.370071\pi\)
0.396944 + 0.917843i \(0.370071\pi\)
\(444\) −10.8042 −0.512746
\(445\) −11.6175 −0.550724
\(446\) −9.14462 −0.433010
\(447\) −10.5024 −0.496748
\(448\) 2.36162 0.111576
\(449\) 28.7189 1.35533 0.677664 0.735372i \(-0.262992\pi\)
0.677664 + 0.735372i \(0.262992\pi\)
\(450\) 4.55879 0.214903
\(451\) −35.1500 −1.65515
\(452\) −12.4526 −0.585721
\(453\) 0.330883 0.0155463
\(454\) 0.990850 0.0465029
\(455\) −1.56868 −0.0735408
\(456\) 5.47817 0.256539
\(457\) 1.32877 0.0621571 0.0310786 0.999517i \(-0.490106\pi\)
0.0310786 + 0.999517i \(0.490106\pi\)
\(458\) 0.230645 0.0107773
\(459\) 7.53535 0.351720
\(460\) −0.849405 −0.0396037
\(461\) 7.92563 0.369133 0.184567 0.982820i \(-0.440912\pi\)
0.184567 + 0.982820i \(0.440912\pi\)
\(462\) −7.42484 −0.345435
\(463\) 13.7247 0.637840 0.318920 0.947782i \(-0.396680\pi\)
0.318920 + 0.947782i \(0.396680\pi\)
\(464\) −5.06863 −0.235305
\(465\) 4.16994 0.193376
\(466\) −29.6243 −1.37232
\(467\) 23.7417 1.09863 0.549317 0.835614i \(-0.314888\pi\)
0.549317 + 0.835614i \(0.314888\pi\)
\(468\) 1.00000 0.0462250
\(469\) −16.0239 −0.739915
\(470\) −5.76434 −0.265889
\(471\) −6.48802 −0.298952
\(472\) 10.6905 0.492071
\(473\) 19.6572 0.903841
\(474\) 2.79959 0.128589
\(475\) −24.9738 −1.14588
\(476\) −17.7956 −0.815661
\(477\) −9.70904 −0.444546
\(478\) 12.1630 0.556323
\(479\) −37.4668 −1.71190 −0.855951 0.517057i \(-0.827028\pi\)
−0.855951 + 0.517057i \(0.827028\pi\)
\(480\) −0.664239 −0.0303182
\(481\) 10.8042 0.492630
\(482\) 9.36359 0.426500
\(483\) −3.01995 −0.137412
\(484\) −1.11548 −0.0507036
\(485\) −6.12004 −0.277897
\(486\) 1.00000 0.0453609
\(487\) 38.2613 1.73379 0.866893 0.498494i \(-0.166113\pi\)
0.866893 + 0.498494i \(0.166113\pi\)
\(488\) 2.60711 0.118019
\(489\) 10.2456 0.463323
\(490\) −0.945057 −0.0426933
\(491\) 33.2072 1.49862 0.749311 0.662218i \(-0.230385\pi\)
0.749311 + 0.662218i \(0.230385\pi\)
\(492\) −11.1801 −0.504040
\(493\) 38.1939 1.72017
\(494\) −5.47817 −0.246475
\(495\) 2.08835 0.0938642
\(496\) 6.27777 0.281880
\(497\) 4.03153 0.180839
\(498\) 11.4961 0.515151
\(499\) 17.9832 0.805039 0.402520 0.915411i \(-0.368135\pi\)
0.402520 + 0.915411i \(0.368135\pi\)
\(500\) 6.34932 0.283950
\(501\) −1.93544 −0.0864693
\(502\) −24.7530 −1.10478
\(503\) 10.8923 0.485663 0.242832 0.970068i \(-0.421924\pi\)
0.242832 + 0.970068i \(0.421924\pi\)
\(504\) −2.36162 −0.105195
\(505\) −9.54981 −0.424961
\(506\) 4.02039 0.178728
\(507\) −1.00000 −0.0444116
\(508\) −12.7497 −0.565676
\(509\) −44.1708 −1.95784 −0.978918 0.204256i \(-0.934523\pi\)
−0.978918 + 0.204256i \(0.934523\pi\)
\(510\) 5.00528 0.221637
\(511\) 0.934071 0.0413209
\(512\) −1.00000 −0.0441942
\(513\) −5.47817 −0.241867
\(514\) 9.92601 0.437817
\(515\) 0.664239 0.0292699
\(516\) 6.25237 0.275245
\(517\) 27.2837 1.19993
\(518\) −25.5154 −1.12108
\(519\) 2.22848 0.0978195
\(520\) 0.664239 0.0291288
\(521\) 15.4635 0.677470 0.338735 0.940882i \(-0.390001\pi\)
0.338735 + 0.940882i \(0.390001\pi\)
\(522\) 5.06863 0.221848
\(523\) 24.4856 1.07068 0.535341 0.844636i \(-0.320183\pi\)
0.535341 + 0.844636i \(0.320183\pi\)
\(524\) −6.54233 −0.285803
\(525\) 10.7661 0.469871
\(526\) −23.0280 −1.00407
\(527\) −47.3052 −2.06065
\(528\) 3.14397 0.136824
\(529\) −21.3648 −0.928903
\(530\) −6.44912 −0.280132
\(531\) −10.6905 −0.463929
\(532\) 12.9373 0.560905
\(533\) 11.1801 0.484266
\(534\) 17.4900 0.756866
\(535\) −8.15362 −0.352512
\(536\) 6.78514 0.293074
\(537\) 5.40080 0.233062
\(538\) −11.0757 −0.477506
\(539\) 4.47313 0.192671
\(540\) 0.664239 0.0285843
\(541\) 12.8639 0.553063 0.276531 0.961005i \(-0.410815\pi\)
0.276531 + 0.961005i \(0.410815\pi\)
\(542\) −13.7124 −0.588999
\(543\) 14.4182 0.618744
\(544\) 7.53535 0.323076
\(545\) −13.0746 −0.560054
\(546\) 2.36162 0.101068
\(547\) 31.9973 1.36810 0.684052 0.729433i \(-0.260216\pi\)
0.684052 + 0.729433i \(0.260216\pi\)
\(548\) 18.3434 0.783592
\(549\) −2.60711 −0.111269
\(550\) −14.3327 −0.611147
\(551\) −27.7668 −1.18291
\(552\) 1.27876 0.0544278
\(553\) 6.61156 0.281152
\(554\) −25.1561 −1.06878
\(555\) 7.17659 0.304629
\(556\) 4.49746 0.190735
\(557\) −33.3350 −1.41245 −0.706225 0.707987i \(-0.749603\pi\)
−0.706225 + 0.707987i \(0.749603\pi\)
\(558\) −6.27777 −0.265759
\(559\) −6.25237 −0.264447
\(560\) −1.56868 −0.0662888
\(561\) −23.6909 −1.00023
\(562\) 19.4460 0.820280
\(563\) 13.5663 0.571753 0.285877 0.958266i \(-0.407715\pi\)
0.285877 + 0.958266i \(0.407715\pi\)
\(564\) 8.67811 0.365414
\(565\) 8.27150 0.347985
\(566\) 16.6056 0.697985
\(567\) 2.36162 0.0991786
\(568\) −1.70711 −0.0716286
\(569\) 8.42617 0.353244 0.176622 0.984279i \(-0.443483\pi\)
0.176622 + 0.984279i \(0.443483\pi\)
\(570\) −3.63882 −0.152413
\(571\) 2.49998 0.104621 0.0523105 0.998631i \(-0.483341\pi\)
0.0523105 + 0.998631i \(0.483341\pi\)
\(572\) −3.14397 −0.131456
\(573\) −10.8810 −0.454561
\(574\) −26.4032 −1.10205
\(575\) −5.82961 −0.243111
\(576\) 1.00000 0.0416667
\(577\) −8.45831 −0.352124 −0.176062 0.984379i \(-0.556336\pi\)
−0.176062 + 0.984379i \(0.556336\pi\)
\(578\) −39.7815 −1.65469
\(579\) 27.6749 1.15013
\(580\) 3.36678 0.139798
\(581\) 27.1493 1.12634
\(582\) 9.21361 0.381917
\(583\) 30.5249 1.26421
\(584\) −0.395522 −0.0163668
\(585\) −0.664239 −0.0274629
\(586\) −22.3887 −0.924870
\(587\) 12.8004 0.528327 0.264164 0.964478i \(-0.414904\pi\)
0.264164 + 0.964478i \(0.414904\pi\)
\(588\) 1.42277 0.0586739
\(589\) 34.3907 1.41704
\(590\) −7.10106 −0.292346
\(591\) 22.7122 0.934253
\(592\) 10.8042 0.444051
\(593\) 45.6065 1.87284 0.936418 0.350887i \(-0.114120\pi\)
0.936418 + 0.350887i \(0.114120\pi\)
\(594\) −3.14397 −0.128998
\(595\) 11.8205 0.484595
\(596\) 10.5024 0.430196
\(597\) 10.5958 0.433658
\(598\) −1.27876 −0.0522925
\(599\) 20.6359 0.843162 0.421581 0.906791i \(-0.361475\pi\)
0.421581 + 0.906791i \(0.361475\pi\)
\(600\) −4.55879 −0.186112
\(601\) 42.0920 1.71697 0.858483 0.512842i \(-0.171407\pi\)
0.858483 + 0.512842i \(0.171407\pi\)
\(602\) 14.7657 0.601805
\(603\) −6.78514 −0.276312
\(604\) −0.330883 −0.0134635
\(605\) 0.740945 0.0301237
\(606\) 14.3771 0.584028
\(607\) 5.21766 0.211778 0.105889 0.994378i \(-0.466231\pi\)
0.105889 + 0.994378i \(0.466231\pi\)
\(608\) −5.47817 −0.222169
\(609\) 11.9702 0.485055
\(610\) −1.73175 −0.0701164
\(611\) −8.67811 −0.351079
\(612\) −7.53535 −0.304599
\(613\) 7.11873 0.287523 0.143761 0.989612i \(-0.454080\pi\)
0.143761 + 0.989612i \(0.454080\pi\)
\(614\) −8.75392 −0.353279
\(615\) 7.42629 0.299457
\(616\) 7.42484 0.299155
\(617\) 20.5398 0.826900 0.413450 0.910527i \(-0.364324\pi\)
0.413450 + 0.910527i \(0.364324\pi\)
\(618\) −1.00000 −0.0402259
\(619\) 14.3158 0.575400 0.287700 0.957721i \(-0.407109\pi\)
0.287700 + 0.957721i \(0.407109\pi\)
\(620\) −4.16994 −0.167469
\(621\) −1.27876 −0.0513150
\(622\) −3.32236 −0.133214
\(623\) 41.3046 1.65484
\(624\) −1.00000 −0.0400320
\(625\) 18.5765 0.743058
\(626\) −13.9039 −0.555711
\(627\) 17.2232 0.687828
\(628\) 6.48802 0.258900
\(629\) −81.4136 −3.24617
\(630\) 1.56868 0.0624977
\(631\) −3.55289 −0.141438 −0.0707191 0.997496i \(-0.522529\pi\)
−0.0707191 + 0.997496i \(0.522529\pi\)
\(632\) −2.79959 −0.111362
\(633\) 23.9450 0.951728
\(634\) 12.9648 0.514899
\(635\) 8.46885 0.336076
\(636\) 9.70904 0.384988
\(637\) −1.42277 −0.0563720
\(638\) −15.9356 −0.630896
\(639\) 1.70711 0.0675321
\(640\) 0.664239 0.0262564
\(641\) −3.75222 −0.148204 −0.0741018 0.997251i \(-0.523609\pi\)
−0.0741018 + 0.997251i \(0.523609\pi\)
\(642\) 12.2751 0.484461
\(643\) −8.72343 −0.344018 −0.172009 0.985095i \(-0.555026\pi\)
−0.172009 + 0.985095i \(0.555026\pi\)
\(644\) 3.01995 0.119003
\(645\) −4.15307 −0.163527
\(646\) 41.2800 1.62414
\(647\) 45.6646 1.79526 0.897630 0.440749i \(-0.145287\pi\)
0.897630 + 0.440749i \(0.145287\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 33.6106 1.31933
\(650\) 4.55879 0.178810
\(651\) −14.8257 −0.581064
\(652\) −10.2456 −0.401249
\(653\) −41.8437 −1.63747 −0.818734 0.574173i \(-0.805324\pi\)
−0.818734 + 0.574173i \(0.805324\pi\)
\(654\) 19.6836 0.769689
\(655\) 4.34567 0.169799
\(656\) 11.1801 0.436511
\(657\) 0.395522 0.0154308
\(658\) 20.4944 0.798954
\(659\) 27.0576 1.05402 0.527008 0.849860i \(-0.323314\pi\)
0.527008 + 0.849860i \(0.323314\pi\)
\(660\) −2.08835 −0.0812887
\(661\) −22.9241 −0.891643 −0.445822 0.895122i \(-0.647088\pi\)
−0.445822 + 0.895122i \(0.647088\pi\)
\(662\) −28.9193 −1.12398
\(663\) 7.53535 0.292649
\(664\) −11.4961 −0.446134
\(665\) −8.59349 −0.333241
\(666\) −10.8042 −0.418655
\(667\) −6.48157 −0.250968
\(668\) 1.93544 0.0748846
\(669\) −9.14462 −0.353552
\(670\) −4.50696 −0.174119
\(671\) 8.19668 0.316429
\(672\) 2.36162 0.0911013
\(673\) −20.6263 −0.795084 −0.397542 0.917584i \(-0.630137\pi\)
−0.397542 + 0.917584i \(0.630137\pi\)
\(674\) 24.6699 0.950251
\(675\) 4.55879 0.175468
\(676\) 1.00000 0.0384615
\(677\) −32.8317 −1.26183 −0.630913 0.775854i \(-0.717320\pi\)
−0.630913 + 0.775854i \(0.717320\pi\)
\(678\) −12.4526 −0.478239
\(679\) 21.7590 0.835035
\(680\) −5.00528 −0.191944
\(681\) 0.990850 0.0379694
\(682\) 19.7371 0.755772
\(683\) 9.15816 0.350427 0.175214 0.984530i \(-0.443938\pi\)
0.175214 + 0.984530i \(0.443938\pi\)
\(684\) 5.47817 0.209463
\(685\) −12.1844 −0.465543
\(686\) 19.8913 0.759455
\(687\) 0.230645 0.00879965
\(688\) −6.25237 −0.238370
\(689\) −9.70904 −0.369885
\(690\) −0.849405 −0.0323363
\(691\) −38.4791 −1.46381 −0.731907 0.681404i \(-0.761370\pi\)
−0.731907 + 0.681404i \(0.761370\pi\)
\(692\) −2.22848 −0.0847142
\(693\) −7.42484 −0.282046
\(694\) 3.17151 0.120389
\(695\) −2.98739 −0.113318
\(696\) −5.06863 −0.192126
\(697\) −84.2463 −3.19106
\(698\) 31.3835 1.18788
\(699\) −29.6243 −1.12049
\(700\) −10.7661 −0.406921
\(701\) 13.1508 0.496699 0.248350 0.968670i \(-0.420112\pi\)
0.248350 + 0.968670i \(0.420112\pi\)
\(702\) 1.00000 0.0377426
\(703\) 59.1874 2.23229
\(704\) −3.14397 −0.118493
\(705\) −5.76434 −0.217098
\(706\) −17.0417 −0.641372
\(707\) 33.9531 1.27694
\(708\) 10.6905 0.401774
\(709\) 25.9875 0.975981 0.487991 0.872849i \(-0.337730\pi\)
0.487991 + 0.872849i \(0.337730\pi\)
\(710\) 1.13393 0.0425555
\(711\) 2.79959 0.104993
\(712\) −17.4900 −0.655465
\(713\) 8.02778 0.300643
\(714\) −17.7956 −0.665984
\(715\) 2.08835 0.0780997
\(716\) −5.40080 −0.201838
\(717\) 12.1630 0.454236
\(718\) −25.2917 −0.943877
\(719\) 19.2146 0.716585 0.358293 0.933609i \(-0.383359\pi\)
0.358293 + 0.933609i \(0.383359\pi\)
\(720\) −0.664239 −0.0247547
\(721\) −2.36162 −0.0879512
\(722\) −11.0104 −0.409763
\(723\) 9.36359 0.348236
\(724\) −14.4182 −0.535848
\(725\) 23.1068 0.858165
\(726\) −1.11548 −0.0413993
\(727\) 45.1083 1.67297 0.836487 0.547986i \(-0.184605\pi\)
0.836487 + 0.547986i \(0.184605\pi\)
\(728\) −2.36162 −0.0875273
\(729\) 1.00000 0.0370370
\(730\) 0.262721 0.00972375
\(731\) 47.1138 1.74257
\(732\) 2.60711 0.0963617
\(733\) 39.0830 1.44356 0.721782 0.692120i \(-0.243323\pi\)
0.721782 + 0.692120i \(0.243323\pi\)
\(734\) −13.0779 −0.482715
\(735\) −0.945057 −0.0348590
\(736\) −1.27876 −0.0471358
\(737\) 21.3323 0.785784
\(738\) −11.1801 −0.411547
\(739\) 38.5615 1.41851 0.709254 0.704954i \(-0.249032\pi\)
0.709254 + 0.704954i \(0.249032\pi\)
\(740\) −7.17659 −0.263817
\(741\) −5.47817 −0.201246
\(742\) 22.9290 0.841751
\(743\) −11.8727 −0.435568 −0.217784 0.975997i \(-0.569883\pi\)
−0.217784 + 0.975997i \(0.569883\pi\)
\(744\) 6.27777 0.230154
\(745\) −6.97612 −0.255585
\(746\) 25.9846 0.951365
\(747\) 11.4961 0.420619
\(748\) 23.6909 0.866225
\(749\) 28.9891 1.05924
\(750\) 6.34932 0.231844
\(751\) 12.6541 0.461755 0.230878 0.972983i \(-0.425840\pi\)
0.230878 + 0.972983i \(0.425840\pi\)
\(752\) −8.67811 −0.316458
\(753\) −24.7530 −0.902048
\(754\) 5.06863 0.184589
\(755\) 0.219786 0.00799882
\(756\) −2.36162 −0.0858912
\(757\) −38.6113 −1.40335 −0.701675 0.712497i \(-0.747564\pi\)
−0.701675 + 0.712497i \(0.747564\pi\)
\(758\) 14.4762 0.525798
\(759\) 4.02039 0.145931
\(760\) 3.63882 0.131994
\(761\) −27.9940 −1.01478 −0.507392 0.861716i \(-0.669390\pi\)
−0.507392 + 0.861716i \(0.669390\pi\)
\(762\) −12.7497 −0.461873
\(763\) 46.4851 1.68287
\(764\) 10.8810 0.393662
\(765\) 5.00528 0.180966
\(766\) −29.6314 −1.07062
\(767\) −10.6905 −0.386012
\(768\) −1.00000 −0.0360844
\(769\) 0.756287 0.0272724 0.0136362 0.999907i \(-0.495659\pi\)
0.0136362 + 0.999907i \(0.495659\pi\)
\(770\) −4.93187 −0.177732
\(771\) 9.92601 0.357476
\(772\) −27.6749 −0.996043
\(773\) −47.1362 −1.69537 −0.847686 0.530498i \(-0.822005\pi\)
−0.847686 + 0.530498i \(0.822005\pi\)
\(774\) 6.25237 0.224737
\(775\) −28.6190 −1.02802
\(776\) −9.21361 −0.330749
\(777\) −25.5154 −0.915361
\(778\) 31.9402 1.14511
\(779\) 61.2467 2.19439
\(780\) 0.664239 0.0237836
\(781\) −5.36708 −0.192049
\(782\) 9.63593 0.344580
\(783\) 5.06863 0.181138
\(784\) −1.42277 −0.0508131
\(785\) −4.30960 −0.153816
\(786\) −6.54233 −0.233357
\(787\) −32.8581 −1.17127 −0.585633 0.810577i \(-0.699154\pi\)
−0.585633 + 0.810577i \(0.699154\pi\)
\(788\) −22.7122 −0.809087
\(789\) −23.0280 −0.819818
\(790\) 1.85960 0.0661615
\(791\) −29.4083 −1.04564
\(792\) 3.14397 0.111716
\(793\) −2.60711 −0.0925814
\(794\) 1.91074 0.0678096
\(795\) −6.44912 −0.228727
\(796\) −10.5958 −0.375559
\(797\) 30.1082 1.06649 0.533243 0.845962i \(-0.320973\pi\)
0.533243 + 0.845962i \(0.320973\pi\)
\(798\) 12.9373 0.457977
\(799\) 65.3926 2.31342
\(800\) 4.55879 0.161177
\(801\) 17.4900 0.617978
\(802\) −24.2814 −0.857405
\(803\) −1.24351 −0.0438824
\(804\) 6.78514 0.239294
\(805\) −2.00597 −0.0707011
\(806\) −6.27777 −0.221125
\(807\) −11.0757 −0.389882
\(808\) −14.3771 −0.505783
\(809\) −42.1891 −1.48329 −0.741645 0.670792i \(-0.765954\pi\)
−0.741645 + 0.670792i \(0.765954\pi\)
\(810\) 0.664239 0.0233390
\(811\) 49.6828 1.74460 0.872300 0.488971i \(-0.162628\pi\)
0.872300 + 0.488971i \(0.162628\pi\)
\(812\) −11.9702 −0.420070
\(813\) −13.7124 −0.480915
\(814\) 33.9681 1.19058
\(815\) 6.80554 0.238388
\(816\) 7.53535 0.263790
\(817\) −34.2516 −1.19831
\(818\) −8.85686 −0.309673
\(819\) 2.36162 0.0825216
\(820\) −7.42629 −0.259337
\(821\) 7.94747 0.277369 0.138684 0.990337i \(-0.455713\pi\)
0.138684 + 0.990337i \(0.455713\pi\)
\(822\) 18.3434 0.639800
\(823\) −4.62944 −0.161372 −0.0806860 0.996740i \(-0.525711\pi\)
−0.0806860 + 0.996740i \(0.525711\pi\)
\(824\) 1.00000 0.0348367
\(825\) −14.3327 −0.498999
\(826\) 25.2469 0.878452
\(827\) 5.49732 0.191161 0.0955804 0.995422i \(-0.469529\pi\)
0.0955804 + 0.995422i \(0.469529\pi\)
\(828\) 1.27876 0.0444401
\(829\) −19.6703 −0.683179 −0.341589 0.939849i \(-0.610965\pi\)
−0.341589 + 0.939849i \(0.610965\pi\)
\(830\) 7.63614 0.265054
\(831\) −25.1561 −0.872656
\(832\) 1.00000 0.0346688
\(833\) 10.7210 0.371462
\(834\) 4.49746 0.155734
\(835\) −1.28560 −0.0444900
\(836\) −17.2232 −0.595676
\(837\) −6.27777 −0.216991
\(838\) −24.4543 −0.844758
\(839\) 8.90073 0.307287 0.153644 0.988126i \(-0.450899\pi\)
0.153644 + 0.988126i \(0.450899\pi\)
\(840\) −1.56868 −0.0541246
\(841\) −3.30901 −0.114104
\(842\) −28.6102 −0.985972
\(843\) 19.4460 0.669756
\(844\) −23.9450 −0.824220
\(845\) −0.664239 −0.0228505
\(846\) 8.67811 0.298360
\(847\) −2.63433 −0.0905168
\(848\) −9.70904 −0.333410
\(849\) 16.6056 0.569903
\(850\) −34.3521 −1.17827
\(851\) 13.8160 0.473608
\(852\) −1.70711 −0.0584845
\(853\) 36.4129 1.24675 0.623376 0.781922i \(-0.285760\pi\)
0.623376 + 0.781922i \(0.285760\pi\)
\(854\) 6.15701 0.210688
\(855\) −3.63882 −0.124445
\(856\) −12.2751 −0.419555
\(857\) −24.7991 −0.847121 −0.423561 0.905868i \(-0.639220\pi\)
−0.423561 + 0.905868i \(0.639220\pi\)
\(858\) −3.14397 −0.107333
\(859\) 36.7409 1.25358 0.626792 0.779187i \(-0.284368\pi\)
0.626792 + 0.779187i \(0.284368\pi\)
\(860\) 4.15307 0.141619
\(861\) −26.4032 −0.899819
\(862\) 0.310658 0.0105810
\(863\) −15.9874 −0.544217 −0.272109 0.962267i \(-0.587721\pi\)
−0.272109 + 0.962267i \(0.587721\pi\)
\(864\) 1.00000 0.0340207
\(865\) 1.48025 0.0503299
\(866\) 7.72676 0.262566
\(867\) −39.7815 −1.35105
\(868\) 14.8257 0.503216
\(869\) −8.80182 −0.298581
\(870\) 3.36678 0.114145
\(871\) −6.78514 −0.229906
\(872\) −19.6836 −0.666570
\(873\) 9.21361 0.311834
\(874\) −7.00528 −0.236957
\(875\) 14.9947 0.506912
\(876\) −0.395522 −0.0133634
\(877\) 6.44711 0.217703 0.108852 0.994058i \(-0.465283\pi\)
0.108852 + 0.994058i \(0.465283\pi\)
\(878\) −22.7682 −0.768389
\(879\) −22.3887 −0.755153
\(880\) 2.08835 0.0703981
\(881\) −0.521288 −0.0175627 −0.00878133 0.999961i \(-0.502795\pi\)
−0.00878133 + 0.999961i \(0.502795\pi\)
\(882\) 1.42277 0.0479070
\(883\) −5.73123 −0.192871 −0.0964355 0.995339i \(-0.530744\pi\)
−0.0964355 + 0.995339i \(0.530744\pi\)
\(884\) −7.53535 −0.253441
\(885\) −7.10106 −0.238700
\(886\) −16.7094 −0.561363
\(887\) −21.9178 −0.735927 −0.367963 0.929840i \(-0.619945\pi\)
−0.367963 + 0.929840i \(0.619945\pi\)
\(888\) 10.8042 0.362566
\(889\) −30.1099 −1.00985
\(890\) 11.6175 0.389421
\(891\) −3.14397 −0.105327
\(892\) 9.14462 0.306185
\(893\) −47.5402 −1.59087
\(894\) 10.5024 0.351254
\(895\) 3.58743 0.119914
\(896\) −2.36162 −0.0788961
\(897\) −1.27876 −0.0426967
\(898\) −28.7189 −0.958362
\(899\) −31.8197 −1.06125
\(900\) −4.55879 −0.151960
\(901\) 73.1610 2.43735
\(902\) 35.1500 1.17037
\(903\) 14.7657 0.491372
\(904\) 12.4526 0.414167
\(905\) 9.57714 0.318355
\(906\) −0.330883 −0.0109929
\(907\) 28.4556 0.944851 0.472426 0.881370i \(-0.343378\pi\)
0.472426 + 0.881370i \(0.343378\pi\)
\(908\) −0.990850 −0.0328825
\(909\) 14.3771 0.476857
\(910\) 1.56868 0.0520012
\(911\) 18.7391 0.620853 0.310427 0.950597i \(-0.399528\pi\)
0.310427 + 0.950597i \(0.399528\pi\)
\(912\) −5.47817 −0.181400
\(913\) −36.1433 −1.19617
\(914\) −1.32877 −0.0439517
\(915\) −1.73175 −0.0572498
\(916\) −0.230645 −0.00762072
\(917\) −15.4505 −0.510220
\(918\) −7.53535 −0.248704
\(919\) −47.2334 −1.55809 −0.779044 0.626970i \(-0.784295\pi\)
−0.779044 + 0.626970i \(0.784295\pi\)
\(920\) 0.849405 0.0280040
\(921\) −8.75392 −0.288451
\(922\) −7.92563 −0.261017
\(923\) 1.70711 0.0561901
\(924\) 7.42484 0.244259
\(925\) −49.2541 −1.61947
\(926\) −13.7247 −0.451021
\(927\) −1.00000 −0.0328443
\(928\) 5.06863 0.166386
\(929\) −10.0189 −0.328709 −0.164354 0.986401i \(-0.552554\pi\)
−0.164354 + 0.986401i \(0.552554\pi\)
\(930\) −4.16994 −0.136738
\(931\) −7.79416 −0.255443
\(932\) 29.6243 0.970377
\(933\) −3.32236 −0.108769
\(934\) −23.7417 −0.776851
\(935\) −15.7364 −0.514636
\(936\) −1.00000 −0.0326860
\(937\) −43.2306 −1.41228 −0.706140 0.708072i \(-0.749565\pi\)
−0.706140 + 0.708072i \(0.749565\pi\)
\(938\) 16.0239 0.523199
\(939\) −13.9039 −0.453736
\(940\) 5.76434 0.188012
\(941\) 6.82721 0.222561 0.111280 0.993789i \(-0.464505\pi\)
0.111280 + 0.993789i \(0.464505\pi\)
\(942\) 6.48802 0.211391
\(943\) 14.2967 0.465566
\(944\) −10.6905 −0.347947
\(945\) 1.56868 0.0510291
\(946\) −19.6572 −0.639112
\(947\) −26.7614 −0.869630 −0.434815 0.900520i \(-0.643186\pi\)
−0.434815 + 0.900520i \(0.643186\pi\)
\(948\) −2.79959 −0.0909265
\(949\) 0.395522 0.0128392
\(950\) 24.9738 0.810258
\(951\) 12.9648 0.420413
\(952\) 17.7956 0.576759
\(953\) 38.6543 1.25213 0.626067 0.779769i \(-0.284663\pi\)
0.626067 + 0.779769i \(0.284663\pi\)
\(954\) 9.70904 0.314342
\(955\) −7.22761 −0.233880
\(956\) −12.1630 −0.393380
\(957\) −15.9356 −0.515125
\(958\) 37.4668 1.21050
\(959\) 43.3201 1.39888
\(960\) 0.664239 0.0214382
\(961\) 8.41038 0.271302
\(962\) −10.8042 −0.348342
\(963\) 12.2751 0.395560
\(964\) −9.36359 −0.301581
\(965\) 18.3828 0.591763
\(966\) 3.01995 0.0971653
\(967\) −4.22906 −0.135997 −0.0679986 0.997685i \(-0.521661\pi\)
−0.0679986 + 0.997685i \(0.521661\pi\)
\(968\) 1.11548 0.0358529
\(969\) 41.2800 1.32610
\(970\) 6.12004 0.196503
\(971\) −17.2273 −0.552851 −0.276426 0.961035i \(-0.589150\pi\)
−0.276426 + 0.961035i \(0.589150\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 10.6213 0.340503
\(974\) −38.2613 −1.22597
\(975\) 4.55879 0.145998
\(976\) −2.60711 −0.0834517
\(977\) 25.4933 0.815604 0.407802 0.913070i \(-0.366295\pi\)
0.407802 + 0.913070i \(0.366295\pi\)
\(978\) −10.2456 −0.327619
\(979\) −54.9879 −1.75742
\(980\) 0.945057 0.0301887
\(981\) 19.6836 0.628448
\(982\) −33.2072 −1.05969
\(983\) 13.7769 0.439414 0.219707 0.975566i \(-0.429490\pi\)
0.219707 + 0.975566i \(0.429490\pi\)
\(984\) 11.1801 0.356410
\(985\) 15.0863 0.480690
\(986\) −38.1939 −1.21634
\(987\) 20.4944 0.652343
\(988\) 5.47817 0.174284
\(989\) −7.99531 −0.254236
\(990\) −2.08835 −0.0663720
\(991\) 14.8256 0.470952 0.235476 0.971880i \(-0.424335\pi\)
0.235476 + 0.971880i \(0.424335\pi\)
\(992\) −6.27777 −0.199319
\(993\) −28.9193 −0.917725
\(994\) −4.03153 −0.127872
\(995\) 7.03816 0.223125
\(996\) −11.4961 −0.364267
\(997\) −18.5990 −0.589036 −0.294518 0.955646i \(-0.595159\pi\)
−0.294518 + 0.955646i \(0.595159\pi\)
\(998\) −17.9832 −0.569249
\(999\) −10.8042 −0.341830
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.1.7 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.z.1.7 14 1.1 even 1 trivial