Properties

Label 6037.2.a.b.1.14
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $0$
Dimension $259$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46629 q^{2} +1.74062 q^{3} +4.08257 q^{4} -1.65001 q^{5} -4.29287 q^{6} +1.73775 q^{7} -5.13620 q^{8} +0.0297629 q^{9} +O(q^{10})\) \(q-2.46629 q^{2} +1.74062 q^{3} +4.08257 q^{4} -1.65001 q^{5} -4.29287 q^{6} +1.73775 q^{7} -5.13620 q^{8} +0.0297629 q^{9} +4.06940 q^{10} -0.125496 q^{11} +7.10620 q^{12} -4.53339 q^{13} -4.28578 q^{14} -2.87205 q^{15} +4.50221 q^{16} -4.82577 q^{17} -0.0734039 q^{18} -2.48015 q^{19} -6.73629 q^{20} +3.02476 q^{21} +0.309508 q^{22} +7.67658 q^{23} -8.94018 q^{24} -2.27746 q^{25} +11.1806 q^{26} -5.17006 q^{27} +7.09447 q^{28} +8.80551 q^{29} +7.08329 q^{30} +3.57464 q^{31} -0.831329 q^{32} -0.218440 q^{33} +11.9017 q^{34} -2.86731 q^{35} +0.121509 q^{36} +0.599906 q^{37} +6.11677 q^{38} -7.89092 q^{39} +8.47480 q^{40} -8.54751 q^{41} -7.45993 q^{42} -2.63683 q^{43} -0.512344 q^{44} -0.0491093 q^{45} -18.9326 q^{46} -5.43328 q^{47} +7.83664 q^{48} -3.98023 q^{49} +5.61686 q^{50} -8.39984 q^{51} -18.5079 q^{52} +8.47546 q^{53} +12.7508 q^{54} +0.207069 q^{55} -8.92542 q^{56} -4.31701 q^{57} -21.7169 q^{58} +9.52056 q^{59} -11.7253 q^{60} -14.8053 q^{61} -8.81608 q^{62} +0.0517205 q^{63} -6.95412 q^{64} +7.48016 q^{65} +0.538736 q^{66} +0.474532 q^{67} -19.7015 q^{68} +13.3620 q^{69} +7.07160 q^{70} +6.07265 q^{71} -0.152868 q^{72} +14.6881 q^{73} -1.47954 q^{74} -3.96419 q^{75} -10.1254 q^{76} -0.218080 q^{77} +19.4613 q^{78} +9.87498 q^{79} -7.42870 q^{80} -9.08840 q^{81} +21.0806 q^{82} -1.54007 q^{83} +12.3488 q^{84} +7.96259 q^{85} +6.50318 q^{86} +15.3271 q^{87} +0.644570 q^{88} +0.501250 q^{89} +0.121117 q^{90} -7.87790 q^{91} +31.3401 q^{92} +6.22210 q^{93} +13.4000 q^{94} +4.09229 q^{95} -1.44703 q^{96} -15.8986 q^{97} +9.81639 q^{98} -0.00373512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46629 −1.74393 −0.871964 0.489571i \(-0.837154\pi\)
−0.871964 + 0.489571i \(0.837154\pi\)
\(3\) 1.74062 1.00495 0.502474 0.864592i \(-0.332423\pi\)
0.502474 + 0.864592i \(0.332423\pi\)
\(4\) 4.08257 2.04128
\(5\) −1.65001 −0.737908 −0.368954 0.929448i \(-0.620284\pi\)
−0.368954 + 0.929448i \(0.620284\pi\)
\(6\) −4.29287 −1.75256
\(7\) 1.73775 0.656807 0.328404 0.944538i \(-0.393489\pi\)
0.328404 + 0.944538i \(0.393489\pi\)
\(8\) −5.13620 −1.81592
\(9\) 0.0297629 0.00992098
\(10\) 4.06940 1.28686
\(11\) −0.125496 −0.0378383 −0.0189192 0.999821i \(-0.506023\pi\)
−0.0189192 + 0.999821i \(0.506023\pi\)
\(12\) 7.10620 2.05138
\(13\) −4.53339 −1.25734 −0.628669 0.777673i \(-0.716400\pi\)
−0.628669 + 0.777673i \(0.716400\pi\)
\(14\) −4.28578 −1.14542
\(15\) −2.87205 −0.741560
\(16\) 4.50221 1.12555
\(17\) −4.82577 −1.17042 −0.585211 0.810881i \(-0.698988\pi\)
−0.585211 + 0.810881i \(0.698988\pi\)
\(18\) −0.0734039 −0.0173015
\(19\) −2.48015 −0.568986 −0.284493 0.958678i \(-0.591825\pi\)
−0.284493 + 0.958678i \(0.591825\pi\)
\(20\) −6.73629 −1.50628
\(21\) 3.02476 0.660057
\(22\) 0.309508 0.0659873
\(23\) 7.67658 1.60068 0.800339 0.599548i \(-0.204653\pi\)
0.800339 + 0.599548i \(0.204653\pi\)
\(24\) −8.94018 −1.82491
\(25\) −2.27746 −0.455491
\(26\) 11.1806 2.19270
\(27\) −5.17006 −0.994978
\(28\) 7.09447 1.34073
\(29\) 8.80551 1.63514 0.817571 0.575828i \(-0.195320\pi\)
0.817571 + 0.575828i \(0.195320\pi\)
\(30\) 7.08329 1.29323
\(31\) 3.57464 0.642024 0.321012 0.947075i \(-0.395977\pi\)
0.321012 + 0.947075i \(0.395977\pi\)
\(32\) −0.831329 −0.146960
\(33\) −0.218440 −0.0380256
\(34\) 11.9017 2.04113
\(35\) −2.86731 −0.484663
\(36\) 0.121509 0.0202515
\(37\) 0.599906 0.0986240 0.0493120 0.998783i \(-0.484297\pi\)
0.0493120 + 0.998783i \(0.484297\pi\)
\(38\) 6.11677 0.992271
\(39\) −7.89092 −1.26356
\(40\) 8.47480 1.33998
\(41\) −8.54751 −1.33490 −0.667448 0.744656i \(-0.732614\pi\)
−0.667448 + 0.744656i \(0.732614\pi\)
\(42\) −7.45993 −1.15109
\(43\) −2.63683 −0.402113 −0.201056 0.979580i \(-0.564437\pi\)
−0.201056 + 0.979580i \(0.564437\pi\)
\(44\) −0.512344 −0.0772387
\(45\) −0.0491093 −0.00732078
\(46\) −18.9326 −2.79146
\(47\) −5.43328 −0.792526 −0.396263 0.918137i \(-0.629693\pi\)
−0.396263 + 0.918137i \(0.629693\pi\)
\(48\) 7.83664 1.13112
\(49\) −3.98023 −0.568605
\(50\) 5.61686 0.794343
\(51\) −8.39984 −1.17621
\(52\) −18.5079 −2.56658
\(53\) 8.47546 1.16419 0.582097 0.813119i \(-0.302232\pi\)
0.582097 + 0.813119i \(0.302232\pi\)
\(54\) 12.7508 1.73517
\(55\) 0.207069 0.0279212
\(56\) −8.92542 −1.19271
\(57\) −4.31701 −0.571802
\(58\) −21.7169 −2.85157
\(59\) 9.52056 1.23947 0.619736 0.784811i \(-0.287240\pi\)
0.619736 + 0.784811i \(0.287240\pi\)
\(60\) −11.7253 −1.51373
\(61\) −14.8053 −1.89563 −0.947815 0.318821i \(-0.896713\pi\)
−0.947815 + 0.318821i \(0.896713\pi\)
\(62\) −8.81608 −1.11964
\(63\) 0.0517205 0.00651617
\(64\) −6.95412 −0.869265
\(65\) 7.48016 0.927800
\(66\) 0.538736 0.0663138
\(67\) 0.474532 0.0579733 0.0289867 0.999580i \(-0.490772\pi\)
0.0289867 + 0.999580i \(0.490772\pi\)
\(68\) −19.7015 −2.38916
\(69\) 13.3620 1.60860
\(70\) 7.07160 0.845218
\(71\) 6.07265 0.720691 0.360345 0.932819i \(-0.382659\pi\)
0.360345 + 0.932819i \(0.382659\pi\)
\(72\) −0.152868 −0.0180157
\(73\) 14.6881 1.71911 0.859553 0.511046i \(-0.170742\pi\)
0.859553 + 0.511046i \(0.170742\pi\)
\(74\) −1.47954 −0.171993
\(75\) −3.96419 −0.457745
\(76\) −10.1254 −1.16146
\(77\) −0.218080 −0.0248525
\(78\) 19.4613 2.20355
\(79\) 9.87498 1.11102 0.555511 0.831509i \(-0.312523\pi\)
0.555511 + 0.831509i \(0.312523\pi\)
\(80\) −7.42870 −0.830554
\(81\) −9.08840 −1.00982
\(82\) 21.0806 2.32796
\(83\) −1.54007 −0.169045 −0.0845226 0.996422i \(-0.526937\pi\)
−0.0845226 + 0.996422i \(0.526937\pi\)
\(84\) 12.3488 1.34736
\(85\) 7.96259 0.863664
\(86\) 6.50318 0.701256
\(87\) 15.3271 1.64323
\(88\) 0.644570 0.0687114
\(89\) 0.501250 0.0531324 0.0265662 0.999647i \(-0.491543\pi\)
0.0265662 + 0.999647i \(0.491543\pi\)
\(90\) 0.121117 0.0127669
\(91\) −7.87790 −0.825828
\(92\) 31.3401 3.26743
\(93\) 6.22210 0.645201
\(94\) 13.4000 1.38211
\(95\) 4.09229 0.419860
\(96\) −1.44703 −0.147687
\(97\) −15.8986 −1.61426 −0.807129 0.590375i \(-0.798980\pi\)
−0.807129 + 0.590375i \(0.798980\pi\)
\(98\) 9.81639 0.991605
\(99\) −0.00373512 −0.000375393 0
\(100\) −9.29786 −0.929786
\(101\) 11.3060 1.12498 0.562492 0.826802i \(-0.309843\pi\)
0.562492 + 0.826802i \(0.309843\pi\)
\(102\) 20.7164 2.05123
\(103\) 1.94479 0.191626 0.0958130 0.995399i \(-0.469455\pi\)
0.0958130 + 0.995399i \(0.469455\pi\)
\(104\) 23.2844 2.28323
\(105\) −4.99090 −0.487062
\(106\) −20.9029 −2.03027
\(107\) −2.43108 −0.235022 −0.117511 0.993072i \(-0.537491\pi\)
−0.117511 + 0.993072i \(0.537491\pi\)
\(108\) −21.1071 −2.03103
\(109\) 0.100580 0.00963384 0.00481692 0.999988i \(-0.498467\pi\)
0.00481692 + 0.999988i \(0.498467\pi\)
\(110\) −0.510692 −0.0486926
\(111\) 1.04421 0.0991120
\(112\) 7.82370 0.739270
\(113\) 4.51665 0.424890 0.212445 0.977173i \(-0.431857\pi\)
0.212445 + 0.977173i \(0.431857\pi\)
\(114\) 10.6470 0.997181
\(115\) −12.6665 −1.18115
\(116\) 35.9491 3.33779
\(117\) −0.134927 −0.0124740
\(118\) −23.4804 −2.16155
\(119\) −8.38598 −0.768741
\(120\) 14.7514 1.34661
\(121\) −10.9843 −0.998568
\(122\) 36.5142 3.30584
\(123\) −14.8780 −1.34150
\(124\) 14.5937 1.31055
\(125\) 12.0079 1.07402
\(126\) −0.127558 −0.0113637
\(127\) 16.7858 1.48950 0.744750 0.667344i \(-0.232569\pi\)
0.744750 + 0.667344i \(0.232569\pi\)
\(128\) 18.8135 1.66289
\(129\) −4.58972 −0.404103
\(130\) −18.4482 −1.61802
\(131\) 0.432090 0.0377519 0.0188759 0.999822i \(-0.493991\pi\)
0.0188759 + 0.999822i \(0.493991\pi\)
\(132\) −0.891796 −0.0776209
\(133\) −4.30988 −0.373714
\(134\) −1.17033 −0.101101
\(135\) 8.53067 0.734203
\(136\) 24.7861 2.12539
\(137\) −7.71688 −0.659298 −0.329649 0.944104i \(-0.606930\pi\)
−0.329649 + 0.944104i \(0.606930\pi\)
\(138\) −32.9545 −2.80528
\(139\) 2.24124 0.190100 0.0950499 0.995473i \(-0.469699\pi\)
0.0950499 + 0.995473i \(0.469699\pi\)
\(140\) −11.7060 −0.989335
\(141\) −9.45729 −0.796447
\(142\) −14.9769 −1.25683
\(143\) 0.568921 0.0475755
\(144\) 0.133999 0.0111666
\(145\) −14.5292 −1.20659
\(146\) −36.2249 −2.99800
\(147\) −6.92808 −0.571418
\(148\) 2.44916 0.201319
\(149\) 6.23594 0.510868 0.255434 0.966826i \(-0.417782\pi\)
0.255434 + 0.966826i \(0.417782\pi\)
\(150\) 9.77682 0.798274
\(151\) 18.5315 1.50807 0.754036 0.656833i \(-0.228104\pi\)
0.754036 + 0.656833i \(0.228104\pi\)
\(152\) 12.7386 1.03323
\(153\) −0.143629 −0.0116117
\(154\) 0.537847 0.0433409
\(155\) −5.89820 −0.473755
\(156\) −32.2152 −2.57928
\(157\) −3.66361 −0.292388 −0.146194 0.989256i \(-0.546702\pi\)
−0.146194 + 0.989256i \(0.546702\pi\)
\(158\) −24.3545 −1.93754
\(159\) 14.7526 1.16995
\(160\) 1.37170 0.108443
\(161\) 13.3400 1.05134
\(162\) 22.4146 1.76106
\(163\) −4.48176 −0.351039 −0.175519 0.984476i \(-0.556160\pi\)
−0.175519 + 0.984476i \(0.556160\pi\)
\(164\) −34.8958 −2.72490
\(165\) 0.360429 0.0280594
\(166\) 3.79826 0.294802
\(167\) 19.5008 1.50902 0.754509 0.656290i \(-0.227875\pi\)
0.754509 + 0.656290i \(0.227875\pi\)
\(168\) −15.5358 −1.19861
\(169\) 7.55166 0.580897
\(170\) −19.6380 −1.50617
\(171\) −0.0738167 −0.00564490
\(172\) −10.7650 −0.820826
\(173\) 24.4602 1.85967 0.929836 0.367975i \(-0.119949\pi\)
0.929836 + 0.367975i \(0.119949\pi\)
\(174\) −37.8009 −2.86568
\(175\) −3.95764 −0.299170
\(176\) −0.565007 −0.0425890
\(177\) 16.5717 1.24560
\(178\) −1.23623 −0.0926591
\(179\) 2.83534 0.211924 0.105962 0.994370i \(-0.466208\pi\)
0.105962 + 0.994370i \(0.466208\pi\)
\(180\) −0.200492 −0.0149438
\(181\) −1.89165 −0.140606 −0.0703028 0.997526i \(-0.522397\pi\)
−0.0703028 + 0.997526i \(0.522397\pi\)
\(182\) 19.4291 1.44018
\(183\) −25.7705 −1.90501
\(184\) −39.4284 −2.90670
\(185\) −0.989853 −0.0727755
\(186\) −15.3455 −1.12518
\(187\) 0.605613 0.0442868
\(188\) −22.1817 −1.61777
\(189\) −8.98426 −0.653509
\(190\) −10.0927 −0.732205
\(191\) −16.7142 −1.20940 −0.604700 0.796453i \(-0.706707\pi\)
−0.604700 + 0.796453i \(0.706707\pi\)
\(192\) −12.1045 −0.873566
\(193\) 16.9962 1.22341 0.611707 0.791085i \(-0.290483\pi\)
0.611707 + 0.791085i \(0.290483\pi\)
\(194\) 39.2105 2.81515
\(195\) 13.0201 0.932391
\(196\) −16.2496 −1.16068
\(197\) 11.1822 0.796700 0.398350 0.917233i \(-0.369583\pi\)
0.398350 + 0.917233i \(0.369583\pi\)
\(198\) 0.00921186 0.000654659 0
\(199\) 4.79004 0.339557 0.169779 0.985482i \(-0.445695\pi\)
0.169779 + 0.985482i \(0.445695\pi\)
\(200\) 11.6975 0.827136
\(201\) 0.825981 0.0582602
\(202\) −27.8837 −1.96189
\(203\) 15.3018 1.07397
\(204\) −34.2929 −2.40098
\(205\) 14.1035 0.985032
\(206\) −4.79641 −0.334182
\(207\) 0.228478 0.0158803
\(208\) −20.4103 −1.41520
\(209\) 0.311248 0.0215295
\(210\) 12.3090 0.849400
\(211\) 22.4184 1.54335 0.771673 0.636020i \(-0.219420\pi\)
0.771673 + 0.636020i \(0.219420\pi\)
\(212\) 34.6016 2.37645
\(213\) 10.5702 0.724257
\(214\) 5.99574 0.409860
\(215\) 4.35081 0.296722
\(216\) 26.5545 1.80680
\(217\) 6.21182 0.421686
\(218\) −0.248060 −0.0168007
\(219\) 25.5663 1.72761
\(220\) 0.845374 0.0569951
\(221\) 21.8771 1.47162
\(222\) −2.57532 −0.172844
\(223\) 1.09376 0.0732436 0.0366218 0.999329i \(-0.488340\pi\)
0.0366218 + 0.999329i \(0.488340\pi\)
\(224\) −1.44464 −0.0965241
\(225\) −0.0677838 −0.00451892
\(226\) −11.1393 −0.740978
\(227\) −5.26043 −0.349147 −0.174573 0.984644i \(-0.555855\pi\)
−0.174573 + 0.984644i \(0.555855\pi\)
\(228\) −17.6245 −1.16721
\(229\) −13.1708 −0.870353 −0.435176 0.900345i \(-0.643314\pi\)
−0.435176 + 0.900345i \(0.643314\pi\)
\(230\) 31.2391 2.05985
\(231\) −0.379594 −0.0249754
\(232\) −45.2269 −2.96929
\(233\) 1.00202 0.0656443 0.0328221 0.999461i \(-0.489551\pi\)
0.0328221 + 0.999461i \(0.489551\pi\)
\(234\) 0.332769 0.0217538
\(235\) 8.96499 0.584811
\(236\) 38.8683 2.53011
\(237\) 17.1886 1.11652
\(238\) 20.6822 1.34063
\(239\) −16.2579 −1.05164 −0.525819 0.850597i \(-0.676241\pi\)
−0.525819 + 0.850597i \(0.676241\pi\)
\(240\) −12.9306 −0.834664
\(241\) 12.4059 0.799132 0.399566 0.916705i \(-0.369161\pi\)
0.399566 + 0.916705i \(0.369161\pi\)
\(242\) 27.0903 1.74143
\(243\) −0.309294 −0.0198412
\(244\) −60.4438 −3.86952
\(245\) 6.56744 0.419578
\(246\) 36.6933 2.33948
\(247\) 11.2435 0.715408
\(248\) −18.3601 −1.16587
\(249\) −2.68069 −0.169882
\(250\) −29.6149 −1.87301
\(251\) −6.49175 −0.409755 −0.204878 0.978788i \(-0.565680\pi\)
−0.204878 + 0.978788i \(0.565680\pi\)
\(252\) 0.211152 0.0133013
\(253\) −0.963376 −0.0605669
\(254\) −41.3986 −2.59758
\(255\) 13.8599 0.867938
\(256\) −32.4912 −2.03070
\(257\) 1.57408 0.0981883 0.0490941 0.998794i \(-0.484367\pi\)
0.0490941 + 0.998794i \(0.484367\pi\)
\(258\) 11.3196 0.704726
\(259\) 1.04249 0.0647769
\(260\) 30.5382 1.89390
\(261\) 0.262078 0.0162222
\(262\) −1.06566 −0.0658365
\(263\) 21.0899 1.30046 0.650231 0.759737i \(-0.274672\pi\)
0.650231 + 0.759737i \(0.274672\pi\)
\(264\) 1.12195 0.0690514
\(265\) −13.9846 −0.859068
\(266\) 10.6294 0.651730
\(267\) 0.872487 0.0533953
\(268\) 1.93731 0.118340
\(269\) 16.6059 1.01248 0.506240 0.862392i \(-0.331035\pi\)
0.506240 + 0.862392i \(0.331035\pi\)
\(270\) −21.0391 −1.28040
\(271\) −8.33485 −0.506306 −0.253153 0.967426i \(-0.581468\pi\)
−0.253153 + 0.967426i \(0.581468\pi\)
\(272\) −21.7266 −1.31737
\(273\) −13.7124 −0.829914
\(274\) 19.0320 1.14977
\(275\) 0.285810 0.0172350
\(276\) 54.5513 3.28360
\(277\) −7.90450 −0.474935 −0.237468 0.971395i \(-0.576317\pi\)
−0.237468 + 0.971395i \(0.576317\pi\)
\(278\) −5.52755 −0.331520
\(279\) 0.106392 0.00636951
\(280\) 14.7271 0.880111
\(281\) 20.8491 1.24375 0.621876 0.783116i \(-0.286371\pi\)
0.621876 + 0.783116i \(0.286371\pi\)
\(282\) 23.3244 1.38895
\(283\) 0.918012 0.0545701 0.0272851 0.999628i \(-0.491314\pi\)
0.0272851 + 0.999628i \(0.491314\pi\)
\(284\) 24.7920 1.47113
\(285\) 7.12312 0.421937
\(286\) −1.40312 −0.0829683
\(287\) −14.8534 −0.876770
\(288\) −0.0247428 −0.00145798
\(289\) 6.28809 0.369888
\(290\) 35.8332 2.10420
\(291\) −27.6734 −1.62225
\(292\) 59.9649 3.50918
\(293\) −7.59314 −0.443596 −0.221798 0.975093i \(-0.571193\pi\)
−0.221798 + 0.975093i \(0.571193\pi\)
\(294\) 17.0866 0.996512
\(295\) −15.7091 −0.914616
\(296\) −3.08124 −0.179093
\(297\) 0.648819 0.0376483
\(298\) −15.3796 −0.890917
\(299\) −34.8010 −2.01259
\(300\) −16.1841 −0.934387
\(301\) −4.58215 −0.264111
\(302\) −45.7040 −2.62997
\(303\) 19.6794 1.13055
\(304\) −11.1662 −0.640424
\(305\) 24.4290 1.39880
\(306\) 0.354231 0.0202500
\(307\) 8.27524 0.472293 0.236146 0.971717i \(-0.424116\pi\)
0.236146 + 0.971717i \(0.424116\pi\)
\(308\) −0.890324 −0.0507309
\(309\) 3.38514 0.192574
\(310\) 14.5467 0.826195
\(311\) −7.80741 −0.442718 −0.221359 0.975192i \(-0.571049\pi\)
−0.221359 + 0.975192i \(0.571049\pi\)
\(312\) 40.5294 2.29452
\(313\) −23.5840 −1.33305 −0.666525 0.745483i \(-0.732219\pi\)
−0.666525 + 0.745483i \(0.732219\pi\)
\(314\) 9.03550 0.509903
\(315\) −0.0853395 −0.00480834
\(316\) 40.3153 2.26791
\(317\) −18.1603 −1.01998 −0.509992 0.860179i \(-0.670351\pi\)
−0.509992 + 0.860179i \(0.670351\pi\)
\(318\) −36.3840 −2.04032
\(319\) −1.10505 −0.0618710
\(320\) 11.4744 0.641438
\(321\) −4.23159 −0.236184
\(322\) −32.9001 −1.83345
\(323\) 11.9687 0.665954
\(324\) −37.1040 −2.06133
\(325\) 10.3246 0.572706
\(326\) 11.0533 0.612186
\(327\) 0.175072 0.00968151
\(328\) 43.9017 2.42407
\(329\) −9.44168 −0.520536
\(330\) −0.888921 −0.0489335
\(331\) 23.6804 1.30160 0.650798 0.759251i \(-0.274435\pi\)
0.650798 + 0.759251i \(0.274435\pi\)
\(332\) −6.28745 −0.345069
\(333\) 0.0178550 0.000978447 0
\(334\) −48.0945 −2.63162
\(335\) −0.782984 −0.0427790
\(336\) 13.6181 0.742928
\(337\) −23.9191 −1.30296 −0.651479 0.758667i \(-0.725851\pi\)
−0.651479 + 0.758667i \(0.725851\pi\)
\(338\) −18.6246 −1.01304
\(339\) 7.86177 0.426993
\(340\) 32.5078 1.76298
\(341\) −0.448601 −0.0242931
\(342\) 0.182053 0.00984430
\(343\) −19.0809 −1.03027
\(344\) 13.5433 0.730205
\(345\) −22.0475 −1.18700
\(346\) −60.3257 −3.24313
\(347\) −19.3555 −1.03906 −0.519528 0.854454i \(-0.673892\pi\)
−0.519528 + 0.854454i \(0.673892\pi\)
\(348\) 62.5737 3.35430
\(349\) 32.2745 1.72762 0.863808 0.503821i \(-0.168073\pi\)
0.863808 + 0.503821i \(0.168073\pi\)
\(350\) 9.76068 0.521730
\(351\) 23.4379 1.25102
\(352\) 0.104328 0.00556070
\(353\) 35.5987 1.89473 0.947365 0.320156i \(-0.103735\pi\)
0.947365 + 0.320156i \(0.103735\pi\)
\(354\) −40.8705 −2.17224
\(355\) −10.0200 −0.531804
\(356\) 2.04639 0.108458
\(357\) −14.5968 −0.772545
\(358\) −6.99277 −0.369579
\(359\) −5.29711 −0.279571 −0.139785 0.990182i \(-0.544641\pi\)
−0.139785 + 0.990182i \(0.544641\pi\)
\(360\) 0.252235 0.0132940
\(361\) −12.8488 −0.676255
\(362\) 4.66536 0.245206
\(363\) −19.1194 −1.00351
\(364\) −32.1620 −1.68575
\(365\) −24.2355 −1.26854
\(366\) 63.5574 3.32220
\(367\) 29.8064 1.55588 0.777941 0.628337i \(-0.216264\pi\)
0.777941 + 0.628337i \(0.216264\pi\)
\(368\) 34.5615 1.80165
\(369\) −0.254399 −0.0132435
\(370\) 2.44126 0.126915
\(371\) 14.7282 0.764651
\(372\) 25.4021 1.31704
\(373\) 37.5011 1.94174 0.970868 0.239617i \(-0.0770217\pi\)
0.970868 + 0.239617i \(0.0770217\pi\)
\(374\) −1.49361 −0.0772330
\(375\) 20.9012 1.07933
\(376\) 27.9064 1.43916
\(377\) −39.9188 −2.05592
\(378\) 22.1577 1.13967
\(379\) −29.3343 −1.50680 −0.753401 0.657561i \(-0.771588\pi\)
−0.753401 + 0.657561i \(0.771588\pi\)
\(380\) 16.7070 0.857052
\(381\) 29.2177 1.49687
\(382\) 41.2221 2.10911
\(383\) 9.17459 0.468800 0.234400 0.972140i \(-0.424688\pi\)
0.234400 + 0.972140i \(0.424688\pi\)
\(384\) 32.7472 1.67112
\(385\) 0.359834 0.0183388
\(386\) −41.9175 −2.13354
\(387\) −0.0784798 −0.00398935
\(388\) −64.9071 −3.29516
\(389\) −3.64091 −0.184601 −0.0923007 0.995731i \(-0.529422\pi\)
−0.0923007 + 0.995731i \(0.529422\pi\)
\(390\) −32.1114 −1.62602
\(391\) −37.0454 −1.87347
\(392\) 20.4433 1.03254
\(393\) 0.752105 0.0379387
\(394\) −27.5786 −1.38939
\(395\) −16.2939 −0.819833
\(396\) −0.0152489 −0.000766284 0
\(397\) 3.62355 0.181861 0.0909304 0.995857i \(-0.471016\pi\)
0.0909304 + 0.995857i \(0.471016\pi\)
\(398\) −11.8136 −0.592163
\(399\) −7.50187 −0.375563
\(400\) −10.2536 −0.512679
\(401\) 12.1954 0.609008 0.304504 0.952511i \(-0.401509\pi\)
0.304504 + 0.952511i \(0.401509\pi\)
\(402\) −2.03710 −0.101602
\(403\) −16.2053 −0.807241
\(404\) 46.1573 2.29641
\(405\) 14.9960 0.745157
\(406\) −37.7385 −1.87293
\(407\) −0.0752855 −0.00373177
\(408\) 43.1433 2.13591
\(409\) 1.74983 0.0865236 0.0432618 0.999064i \(-0.486225\pi\)
0.0432618 + 0.999064i \(0.486225\pi\)
\(410\) −34.7833 −1.71782
\(411\) −13.4322 −0.662560
\(412\) 7.93974 0.391163
\(413\) 16.5443 0.814093
\(414\) −0.563491 −0.0276941
\(415\) 2.54114 0.124740
\(416\) 3.76874 0.184778
\(417\) 3.90116 0.191041
\(418\) −0.767627 −0.0375459
\(419\) −17.2661 −0.843506 −0.421753 0.906711i \(-0.638585\pi\)
−0.421753 + 0.906711i \(0.638585\pi\)
\(420\) −20.3757 −0.994230
\(421\) −6.04640 −0.294683 −0.147342 0.989086i \(-0.547072\pi\)
−0.147342 + 0.989086i \(0.547072\pi\)
\(422\) −55.2902 −2.69148
\(423\) −0.161711 −0.00786263
\(424\) −43.5317 −2.11408
\(425\) 10.9905 0.533117
\(426\) −26.0691 −1.26305
\(427\) −25.7280 −1.24506
\(428\) −9.92505 −0.479745
\(429\) 0.990275 0.0478109
\(430\) −10.7303 −0.517462
\(431\) 0.529026 0.0254823 0.0127411 0.999919i \(-0.495944\pi\)
0.0127411 + 0.999919i \(0.495944\pi\)
\(432\) −23.2767 −1.11990
\(433\) −7.25091 −0.348456 −0.174228 0.984705i \(-0.555743\pi\)
−0.174228 + 0.984705i \(0.555743\pi\)
\(434\) −15.3201 −0.735390
\(435\) −25.2898 −1.21256
\(436\) 0.410625 0.0196654
\(437\) −19.0391 −0.910763
\(438\) −63.0539 −3.01283
\(439\) −16.9987 −0.811303 −0.405652 0.914028i \(-0.632955\pi\)
−0.405652 + 0.914028i \(0.632955\pi\)
\(440\) −1.06355 −0.0507027
\(441\) −0.118463 −0.00564112
\(442\) −53.9553 −2.56639
\(443\) 13.5396 0.643286 0.321643 0.946861i \(-0.395765\pi\)
0.321643 + 0.946861i \(0.395765\pi\)
\(444\) 4.26305 0.202316
\(445\) −0.827070 −0.0392069
\(446\) −2.69752 −0.127731
\(447\) 10.8544 0.513396
\(448\) −12.0845 −0.570939
\(449\) 23.6345 1.11538 0.557691 0.830049i \(-0.311687\pi\)
0.557691 + 0.830049i \(0.311687\pi\)
\(450\) 0.167174 0.00788067
\(451\) 1.07267 0.0505103
\(452\) 18.4395 0.867321
\(453\) 32.2563 1.51554
\(454\) 12.9737 0.608887
\(455\) 12.9986 0.609385
\(456\) 22.1730 1.03835
\(457\) 18.5854 0.869388 0.434694 0.900578i \(-0.356857\pi\)
0.434694 + 0.900578i \(0.356857\pi\)
\(458\) 32.4830 1.51783
\(459\) 24.9495 1.16454
\(460\) −51.7116 −2.41107
\(461\) −9.11275 −0.424423 −0.212212 0.977224i \(-0.568067\pi\)
−0.212212 + 0.977224i \(0.568067\pi\)
\(462\) 0.936187 0.0435554
\(463\) −40.8728 −1.89952 −0.949760 0.312979i \(-0.898673\pi\)
−0.949760 + 0.312979i \(0.898673\pi\)
\(464\) 39.6442 1.84044
\(465\) −10.2665 −0.476099
\(466\) −2.47126 −0.114479
\(467\) −11.2511 −0.520641 −0.260320 0.965522i \(-0.583828\pi\)
−0.260320 + 0.965522i \(0.583828\pi\)
\(468\) −0.550849 −0.0254630
\(469\) 0.824617 0.0380773
\(470\) −22.1102 −1.01987
\(471\) −6.37695 −0.293834
\(472\) −48.8995 −2.25078
\(473\) 0.330910 0.0152153
\(474\) −42.3920 −1.94713
\(475\) 5.64844 0.259168
\(476\) −34.2363 −1.56922
\(477\) 0.252255 0.0115499
\(478\) 40.0967 1.83398
\(479\) −2.81971 −0.128836 −0.0644179 0.997923i \(-0.520519\pi\)
−0.0644179 + 0.997923i \(0.520519\pi\)
\(480\) 2.38762 0.108979
\(481\) −2.71961 −0.124004
\(482\) −30.5964 −1.39363
\(483\) 23.2198 1.05654
\(484\) −44.8439 −2.03836
\(485\) 26.2329 1.19117
\(486\) 0.762808 0.0346017
\(487\) 17.3655 0.786908 0.393454 0.919344i \(-0.371280\pi\)
0.393454 + 0.919344i \(0.371280\pi\)
\(488\) 76.0432 3.44231
\(489\) −7.80105 −0.352776
\(490\) −16.1972 −0.731714
\(491\) −7.85222 −0.354366 −0.177183 0.984178i \(-0.556698\pi\)
−0.177183 + 0.984178i \(0.556698\pi\)
\(492\) −60.7403 −2.73839
\(493\) −42.4934 −1.91381
\(494\) −27.7297 −1.24762
\(495\) 0.00616299 0.000277006 0
\(496\) 16.0938 0.722632
\(497\) 10.5527 0.473355
\(498\) 6.61134 0.296261
\(499\) −12.3009 −0.550665 −0.275332 0.961349i \(-0.588788\pi\)
−0.275332 + 0.961349i \(0.588788\pi\)
\(500\) 49.0230 2.19238
\(501\) 33.9435 1.51648
\(502\) 16.0105 0.714584
\(503\) 9.07881 0.404804 0.202402 0.979303i \(-0.435125\pi\)
0.202402 + 0.979303i \(0.435125\pi\)
\(504\) −0.265647 −0.0118329
\(505\) −18.6550 −0.830136
\(506\) 2.37596 0.105624
\(507\) 13.1446 0.583771
\(508\) 68.5292 3.04049
\(509\) 40.1244 1.77848 0.889242 0.457437i \(-0.151232\pi\)
0.889242 + 0.457437i \(0.151232\pi\)
\(510\) −34.1824 −1.51362
\(511\) 25.5241 1.12912
\(512\) 42.5057 1.87850
\(513\) 12.8225 0.566129
\(514\) −3.88213 −0.171233
\(515\) −3.20893 −0.141402
\(516\) −18.7378 −0.824888
\(517\) 0.681853 0.0299878
\(518\) −2.57107 −0.112966
\(519\) 42.5759 1.86887
\(520\) −38.4196 −1.68481
\(521\) 10.2632 0.449637 0.224819 0.974401i \(-0.427821\pi\)
0.224819 + 0.974401i \(0.427821\pi\)
\(522\) −0.646359 −0.0282904
\(523\) 3.22833 0.141165 0.0705825 0.997506i \(-0.477514\pi\)
0.0705825 + 0.997506i \(0.477514\pi\)
\(524\) 1.76403 0.0770622
\(525\) −6.88876 −0.300650
\(526\) −52.0138 −2.26791
\(527\) −17.2504 −0.751439
\(528\) −0.983463 −0.0427997
\(529\) 35.9298 1.56217
\(530\) 34.4901 1.49815
\(531\) 0.283360 0.0122968
\(532\) −17.5954 −0.762856
\(533\) 38.7492 1.67842
\(534\) −2.15180 −0.0931176
\(535\) 4.01132 0.173424
\(536\) −2.43729 −0.105275
\(537\) 4.93526 0.212972
\(538\) −40.9549 −1.76569
\(539\) 0.499501 0.0215150
\(540\) 34.8270 1.49872
\(541\) 31.8910 1.37110 0.685551 0.728024i \(-0.259561\pi\)
0.685551 + 0.728024i \(0.259561\pi\)
\(542\) 20.5561 0.882961
\(543\) −3.29265 −0.141301
\(544\) 4.01180 0.172005
\(545\) −0.165959 −0.00710889
\(546\) 33.8188 1.44731
\(547\) −24.4679 −1.04617 −0.523086 0.852280i \(-0.675219\pi\)
−0.523086 + 0.852280i \(0.675219\pi\)
\(548\) −31.5047 −1.34581
\(549\) −0.440651 −0.0188065
\(550\) −0.704890 −0.0300566
\(551\) −21.8390 −0.930373
\(552\) −68.6300 −2.92109
\(553\) 17.1602 0.729727
\(554\) 19.4947 0.828253
\(555\) −1.72296 −0.0731356
\(556\) 9.15003 0.388048
\(557\) 27.4325 1.16235 0.581176 0.813778i \(-0.302593\pi\)
0.581176 + 0.813778i \(0.302593\pi\)
\(558\) −0.262393 −0.0111080
\(559\) 11.9538 0.505591
\(560\) −12.9092 −0.545514
\(561\) 1.05414 0.0445059
\(562\) −51.4198 −2.16901
\(563\) −7.14384 −0.301077 −0.150539 0.988604i \(-0.548101\pi\)
−0.150539 + 0.988604i \(0.548101\pi\)
\(564\) −38.6100 −1.62577
\(565\) −7.45253 −0.313530
\(566\) −2.26408 −0.0951664
\(567\) −15.7934 −0.663259
\(568\) −31.1903 −1.30872
\(569\) −13.3297 −0.558810 −0.279405 0.960173i \(-0.590137\pi\)
−0.279405 + 0.960173i \(0.590137\pi\)
\(570\) −17.5677 −0.735828
\(571\) −19.5998 −0.820225 −0.410113 0.912035i \(-0.634511\pi\)
−0.410113 + 0.912035i \(0.634511\pi\)
\(572\) 2.32266 0.0971151
\(573\) −29.0932 −1.21538
\(574\) 36.6328 1.52902
\(575\) −17.4831 −0.729094
\(576\) −0.206975 −0.00862396
\(577\) 0.515089 0.0214435 0.0107217 0.999943i \(-0.496587\pi\)
0.0107217 + 0.999943i \(0.496587\pi\)
\(578\) −15.5082 −0.645057
\(579\) 29.5840 1.22947
\(580\) −59.3164 −2.46298
\(581\) −2.67626 −0.111030
\(582\) 68.2506 2.82908
\(583\) −1.06363 −0.0440511
\(584\) −75.4408 −3.12176
\(585\) 0.222632 0.00920468
\(586\) 18.7269 0.773600
\(587\) 27.3392 1.12841 0.564204 0.825635i \(-0.309183\pi\)
0.564204 + 0.825635i \(0.309183\pi\)
\(588\) −28.2843 −1.16643
\(589\) −8.86566 −0.365303
\(590\) 38.7430 1.59502
\(591\) 19.4640 0.800643
\(592\) 2.70090 0.111006
\(593\) 31.8551 1.30813 0.654066 0.756438i \(-0.273062\pi\)
0.654066 + 0.756438i \(0.273062\pi\)
\(594\) −1.60017 −0.0656559
\(595\) 13.8370 0.567261
\(596\) 25.4586 1.04283
\(597\) 8.33765 0.341237
\(598\) 85.8291 3.50981
\(599\) 36.2383 1.48066 0.740329 0.672245i \(-0.234670\pi\)
0.740329 + 0.672245i \(0.234670\pi\)
\(600\) 20.3609 0.831229
\(601\) 15.1943 0.619789 0.309895 0.950771i \(-0.399706\pi\)
0.309895 + 0.950771i \(0.399706\pi\)
\(602\) 11.3009 0.460590
\(603\) 0.0141235 0.000575152 0
\(604\) 75.6561 3.07840
\(605\) 18.1242 0.736852
\(606\) −48.5350 −1.97160
\(607\) 26.2706 1.06629 0.533145 0.846024i \(-0.321010\pi\)
0.533145 + 0.846024i \(0.321010\pi\)
\(608\) 2.06182 0.0836180
\(609\) 26.6346 1.07929
\(610\) −60.2489 −2.43941
\(611\) 24.6312 0.996472
\(612\) −0.586376 −0.0237028
\(613\) −19.6689 −0.794418 −0.397209 0.917728i \(-0.630021\pi\)
−0.397209 + 0.917728i \(0.630021\pi\)
\(614\) −20.4091 −0.823644
\(615\) 24.5489 0.989906
\(616\) 1.12010 0.0451301
\(617\) −25.8944 −1.04247 −0.521234 0.853414i \(-0.674528\pi\)
−0.521234 + 0.853414i \(0.674528\pi\)
\(618\) −8.34873 −0.335835
\(619\) −23.6024 −0.948662 −0.474331 0.880347i \(-0.657310\pi\)
−0.474331 + 0.880347i \(0.657310\pi\)
\(620\) −24.0798 −0.967068
\(621\) −39.6884 −1.59264
\(622\) 19.2553 0.772068
\(623\) 0.871047 0.0348978
\(624\) −35.5266 −1.42220
\(625\) −8.42592 −0.337037
\(626\) 58.1650 2.32474
\(627\) 0.541765 0.0216360
\(628\) −14.9569 −0.596846
\(629\) −2.89501 −0.115432
\(630\) 0.210472 0.00838539
\(631\) −5.64748 −0.224822 −0.112411 0.993662i \(-0.535857\pi\)
−0.112411 + 0.993662i \(0.535857\pi\)
\(632\) −50.7199 −2.01753
\(633\) 39.0219 1.55098
\(634\) 44.7884 1.77878
\(635\) −27.6968 −1.09911
\(636\) 60.2283 2.38821
\(637\) 18.0440 0.714928
\(638\) 2.72537 0.107899
\(639\) 0.180740 0.00714996
\(640\) −31.0425 −1.22706
\(641\) −31.7014 −1.25213 −0.626066 0.779770i \(-0.715336\pi\)
−0.626066 + 0.779770i \(0.715336\pi\)
\(642\) 10.4363 0.411889
\(643\) 22.1341 0.872885 0.436442 0.899732i \(-0.356238\pi\)
0.436442 + 0.899732i \(0.356238\pi\)
\(644\) 54.4612 2.14607
\(645\) 7.57311 0.298191
\(646\) −29.5181 −1.16138
\(647\) −13.4886 −0.530293 −0.265146 0.964208i \(-0.585420\pi\)
−0.265146 + 0.964208i \(0.585420\pi\)
\(648\) 46.6799 1.83376
\(649\) −1.19479 −0.0468995
\(650\) −25.4634 −0.998758
\(651\) 10.8124 0.423773
\(652\) −18.2971 −0.716569
\(653\) −0.373916 −0.0146325 −0.00731623 0.999973i \(-0.502329\pi\)
−0.00731623 + 0.999973i \(0.502329\pi\)
\(654\) −0.431778 −0.0168839
\(655\) −0.712954 −0.0278574
\(656\) −38.4827 −1.50250
\(657\) 0.437160 0.0170552
\(658\) 23.2859 0.907778
\(659\) 1.69672 0.0660948 0.0330474 0.999454i \(-0.489479\pi\)
0.0330474 + 0.999454i \(0.489479\pi\)
\(660\) 1.47148 0.0572771
\(661\) 19.9670 0.776625 0.388312 0.921528i \(-0.373058\pi\)
0.388312 + 0.921528i \(0.373058\pi\)
\(662\) −58.4027 −2.26989
\(663\) 38.0798 1.47890
\(664\) 7.91013 0.306973
\(665\) 7.11136 0.275767
\(666\) −0.0440355 −0.00170634
\(667\) 67.5962 2.61733
\(668\) 79.6133 3.08033
\(669\) 1.90382 0.0736060
\(670\) 1.93106 0.0746035
\(671\) 1.85800 0.0717274
\(672\) −2.51457 −0.0970017
\(673\) 22.4269 0.864492 0.432246 0.901756i \(-0.357721\pi\)
0.432246 + 0.901756i \(0.357721\pi\)
\(674\) 58.9914 2.27226
\(675\) 11.7746 0.453204
\(676\) 30.8301 1.18577
\(677\) −30.6427 −1.17769 −0.588847 0.808245i \(-0.700418\pi\)
−0.588847 + 0.808245i \(0.700418\pi\)
\(678\) −19.3894 −0.744645
\(679\) −27.6278 −1.06026
\(680\) −40.8975 −1.56835
\(681\) −9.15641 −0.350874
\(682\) 1.10638 0.0423654
\(683\) 11.5216 0.440864 0.220432 0.975402i \(-0.429253\pi\)
0.220432 + 0.975402i \(0.429253\pi\)
\(684\) −0.301361 −0.0115228
\(685\) 12.7330 0.486502
\(686\) 47.0589 1.79672
\(687\) −22.9254 −0.874659
\(688\) −11.8716 −0.452599
\(689\) −38.4226 −1.46378
\(690\) 54.3754 2.07004
\(691\) −1.06234 −0.0404132 −0.0202066 0.999796i \(-0.506432\pi\)
−0.0202066 + 0.999796i \(0.506432\pi\)
\(692\) 99.8602 3.79611
\(693\) −0.00649069 −0.000246561 0
\(694\) 47.7361 1.81204
\(695\) −3.69808 −0.140276
\(696\) −78.7228 −2.98398
\(697\) 41.2483 1.56239
\(698\) −79.5982 −3.01284
\(699\) 1.74413 0.0659691
\(700\) −16.1573 −0.610690
\(701\) −36.9495 −1.39556 −0.697781 0.716311i \(-0.745829\pi\)
−0.697781 + 0.716311i \(0.745829\pi\)
\(702\) −57.8046 −2.18169
\(703\) −1.48786 −0.0561157
\(704\) 0.872711 0.0328915
\(705\) 15.6047 0.587705
\(706\) −87.7967 −3.30427
\(707\) 19.6469 0.738898
\(708\) 67.6550 2.54263
\(709\) 26.4047 0.991648 0.495824 0.868423i \(-0.334866\pi\)
0.495824 + 0.868423i \(0.334866\pi\)
\(710\) 24.7121 0.927427
\(711\) 0.293909 0.0110224
\(712\) −2.57452 −0.0964843
\(713\) 27.4410 1.02767
\(714\) 35.9999 1.34726
\(715\) −0.938727 −0.0351064
\(716\) 11.5755 0.432596
\(717\) −28.2989 −1.05684
\(718\) 13.0642 0.487551
\(719\) −32.3558 −1.20667 −0.603334 0.797488i \(-0.706162\pi\)
−0.603334 + 0.797488i \(0.706162\pi\)
\(720\) −0.221100 −0.00823991
\(721\) 3.37956 0.125861
\(722\) 31.6889 1.17934
\(723\) 21.5939 0.803086
\(724\) −7.72280 −0.287016
\(725\) −20.0542 −0.744793
\(726\) 47.1540 1.75005
\(727\) 32.0291 1.18789 0.593947 0.804504i \(-0.297569\pi\)
0.593947 + 0.804504i \(0.297569\pi\)
\(728\) 40.4625 1.49964
\(729\) 26.7268 0.989883
\(730\) 59.7716 2.21225
\(731\) 12.7247 0.470642
\(732\) −105.210 −3.88866
\(733\) 43.2615 1.59790 0.798949 0.601398i \(-0.205390\pi\)
0.798949 + 0.601398i \(0.205390\pi\)
\(734\) −73.5111 −2.71335
\(735\) 11.4314 0.421654
\(736\) −6.38176 −0.235235
\(737\) −0.0595516 −0.00219361
\(738\) 0.627421 0.0230957
\(739\) 2.59385 0.0954164 0.0477082 0.998861i \(-0.484808\pi\)
0.0477082 + 0.998861i \(0.484808\pi\)
\(740\) −4.04114 −0.148555
\(741\) 19.5707 0.718948
\(742\) −36.3240 −1.33350
\(743\) −1.66035 −0.0609124 −0.0304562 0.999536i \(-0.509696\pi\)
−0.0304562 + 0.999536i \(0.509696\pi\)
\(744\) −31.9579 −1.17163
\(745\) −10.2894 −0.376974
\(746\) −92.4885 −3.38625
\(747\) −0.0458372 −0.00167709
\(748\) 2.47245 0.0904019
\(749\) −4.22461 −0.154364
\(750\) −51.5483 −1.88228
\(751\) 31.1455 1.13652 0.568258 0.822850i \(-0.307617\pi\)
0.568258 + 0.822850i \(0.307617\pi\)
\(752\) −24.4618 −0.892029
\(753\) −11.2997 −0.411783
\(754\) 98.4513 3.58538
\(755\) −30.5772 −1.11282
\(756\) −36.6788 −1.33400
\(757\) −19.7791 −0.718884 −0.359442 0.933167i \(-0.617033\pi\)
−0.359442 + 0.933167i \(0.617033\pi\)
\(758\) 72.3468 2.62775
\(759\) −1.67687 −0.0608666
\(760\) −21.0188 −0.762432
\(761\) 38.3531 1.39030 0.695149 0.718866i \(-0.255338\pi\)
0.695149 + 0.718866i \(0.255338\pi\)
\(762\) −72.0593 −2.61043
\(763\) 0.174783 0.00632758
\(764\) −68.2370 −2.46873
\(765\) 0.236990 0.00856840
\(766\) −22.6272 −0.817552
\(767\) −43.1604 −1.55843
\(768\) −56.5549 −2.04075
\(769\) 7.24954 0.261425 0.130713 0.991420i \(-0.458273\pi\)
0.130713 + 0.991420i \(0.458273\pi\)
\(770\) −0.887454 −0.0319816
\(771\) 2.73987 0.0986741
\(772\) 69.3881 2.49733
\(773\) 0.878836 0.0316095 0.0158048 0.999875i \(-0.494969\pi\)
0.0158048 + 0.999875i \(0.494969\pi\)
\(774\) 0.193554 0.00695714
\(775\) −8.14108 −0.292436
\(776\) 81.6584 2.93137
\(777\) 1.81457 0.0650974
\(778\) 8.97952 0.321931
\(779\) 21.1991 0.759538
\(780\) 53.1555 1.90327
\(781\) −0.762090 −0.0272697
\(782\) 91.3646 3.26719
\(783\) −45.5250 −1.62693
\(784\) −17.9198 −0.639994
\(785\) 6.04500 0.215755
\(786\) −1.85491 −0.0661623
\(787\) −35.5312 −1.26655 −0.633276 0.773926i \(-0.718290\pi\)
−0.633276 + 0.773926i \(0.718290\pi\)
\(788\) 45.6521 1.62629
\(789\) 36.7096 1.30690
\(790\) 40.1853 1.42973
\(791\) 7.84879 0.279071
\(792\) 0.0191843 0.000681685 0
\(793\) 67.1184 2.38345
\(794\) −8.93672 −0.317152
\(795\) −24.3419 −0.863319
\(796\) 19.5557 0.693132
\(797\) 34.5344 1.22327 0.611636 0.791139i \(-0.290512\pi\)
0.611636 + 0.791139i \(0.290512\pi\)
\(798\) 18.5018 0.654955
\(799\) 26.2198 0.927590
\(800\) 1.89331 0.0669388
\(801\) 0.0149187 0.000527126 0
\(802\) −30.0773 −1.06207
\(803\) −1.84328 −0.0650481
\(804\) 3.37212 0.118925
\(805\) −22.0111 −0.775790
\(806\) 39.9668 1.40777
\(807\) 28.9046 1.01749
\(808\) −58.0697 −2.04288
\(809\) 0.249494 0.00877175 0.00438588 0.999990i \(-0.498604\pi\)
0.00438588 + 0.999990i \(0.498604\pi\)
\(810\) −36.9844 −1.29950
\(811\) −42.6669 −1.49824 −0.749119 0.662435i \(-0.769523\pi\)
−0.749119 + 0.662435i \(0.769523\pi\)
\(812\) 62.4704 2.19228
\(813\) −14.5078 −0.508811
\(814\) 0.185676 0.00650793
\(815\) 7.39497 0.259034
\(816\) −37.8178 −1.32389
\(817\) 6.53975 0.228797
\(818\) −4.31559 −0.150891
\(819\) −0.234469 −0.00819302
\(820\) 57.5785 2.01073
\(821\) −35.5510 −1.24074 −0.620369 0.784310i \(-0.713017\pi\)
−0.620369 + 0.784310i \(0.713017\pi\)
\(822\) 33.1276 1.15546
\(823\) 1.88372 0.0656624 0.0328312 0.999461i \(-0.489548\pi\)
0.0328312 + 0.999461i \(0.489548\pi\)
\(824\) −9.98884 −0.347978
\(825\) 0.497488 0.0173203
\(826\) −40.8031 −1.41972
\(827\) −54.9009 −1.90909 −0.954546 0.298064i \(-0.903659\pi\)
−0.954546 + 0.298064i \(0.903659\pi\)
\(828\) 0.932775 0.0324162
\(829\) 31.1984 1.08356 0.541782 0.840519i \(-0.317750\pi\)
0.541782 + 0.840519i \(0.317750\pi\)
\(830\) −6.26719 −0.217537
\(831\) −13.7587 −0.477285
\(832\) 31.5258 1.09296
\(833\) 19.2077 0.665507
\(834\) −9.62137 −0.333161
\(835\) −32.1766 −1.11352
\(836\) 1.27069 0.0439478
\(837\) −18.4811 −0.638800
\(838\) 42.5832 1.47101
\(839\) −30.7617 −1.06201 −0.531006 0.847368i \(-0.678186\pi\)
−0.531006 + 0.847368i \(0.678186\pi\)
\(840\) 25.6342 0.884466
\(841\) 48.5370 1.67369
\(842\) 14.9121 0.513907
\(843\) 36.2903 1.24991
\(844\) 91.5245 3.15040
\(845\) −12.4603 −0.428649
\(846\) 0.398824 0.0137119
\(847\) −19.0879 −0.655867
\(848\) 38.1583 1.31036
\(849\) 1.59791 0.0548402
\(850\) −27.1057 −0.929717
\(851\) 4.60523 0.157865
\(852\) 43.1535 1.47841
\(853\) −13.7046 −0.469235 −0.234618 0.972088i \(-0.575384\pi\)
−0.234618 + 0.972088i \(0.575384\pi\)
\(854\) 63.4525 2.17130
\(855\) 0.121799 0.00416542
\(856\) 12.4865 0.426781
\(857\) 19.8086 0.676648 0.338324 0.941030i \(-0.390140\pi\)
0.338324 + 0.941030i \(0.390140\pi\)
\(858\) −2.44230 −0.0833788
\(859\) −1.40390 −0.0479003 −0.0239502 0.999713i \(-0.507624\pi\)
−0.0239502 + 0.999713i \(0.507624\pi\)
\(860\) 17.7624 0.605694
\(861\) −25.8542 −0.881108
\(862\) −1.30473 −0.0444392
\(863\) 47.7147 1.62423 0.812114 0.583498i \(-0.198317\pi\)
0.812114 + 0.583498i \(0.198317\pi\)
\(864\) 4.29802 0.146222
\(865\) −40.3596 −1.37227
\(866\) 17.8828 0.607683
\(867\) 10.9452 0.371718
\(868\) 25.3602 0.860780
\(869\) −1.23927 −0.0420392
\(870\) 62.3720 2.11461
\(871\) −2.15124 −0.0728920
\(872\) −0.516600 −0.0174943
\(873\) −0.473189 −0.0160150
\(874\) 46.9558 1.58831
\(875\) 20.8667 0.705423
\(876\) 104.376 3.52655
\(877\) 28.2516 0.953990 0.476995 0.878906i \(-0.341726\pi\)
0.476995 + 0.878906i \(0.341726\pi\)
\(878\) 41.9236 1.41485
\(879\) −13.2168 −0.445791
\(880\) 0.932269 0.0314268
\(881\) −25.0078 −0.842534 −0.421267 0.906937i \(-0.638415\pi\)
−0.421267 + 0.906937i \(0.638415\pi\)
\(882\) 0.292165 0.00983770
\(883\) 43.7692 1.47295 0.736475 0.676465i \(-0.236489\pi\)
0.736475 + 0.676465i \(0.236489\pi\)
\(884\) 89.3148 3.00398
\(885\) −27.3435 −0.919142
\(886\) −33.3925 −1.12184
\(887\) 10.6167 0.356475 0.178237 0.983988i \(-0.442961\pi\)
0.178237 + 0.983988i \(0.442961\pi\)
\(888\) −5.36327 −0.179980
\(889\) 29.1695 0.978314
\(890\) 2.03979 0.0683739
\(891\) 1.14055 0.0382100
\(892\) 4.46534 0.149511
\(893\) 13.4754 0.450936
\(894\) −26.7701 −0.895326
\(895\) −4.67836 −0.156380
\(896\) 32.6931 1.09220
\(897\) −60.5753 −2.02255
\(898\) −58.2895 −1.94515
\(899\) 31.4765 1.04980
\(900\) −0.276732 −0.00922439
\(901\) −40.9006 −1.36260
\(902\) −2.64552 −0.0880862
\(903\) −7.97578 −0.265417
\(904\) −23.1984 −0.771567
\(905\) 3.12125 0.103754
\(906\) −79.5534 −2.64298
\(907\) 33.8126 1.12273 0.561365 0.827569i \(-0.310277\pi\)
0.561365 + 0.827569i \(0.310277\pi\)
\(908\) −21.4760 −0.712707
\(909\) 0.336499 0.0111610
\(910\) −32.0583 −1.06272
\(911\) 29.9735 0.993065 0.496532 0.868018i \(-0.334606\pi\)
0.496532 + 0.868018i \(0.334606\pi\)
\(912\) −19.4361 −0.643593
\(913\) 0.193272 0.00639638
\(914\) −45.8369 −1.51615
\(915\) 42.5217 1.40572
\(916\) −53.7708 −1.77664
\(917\) 0.750863 0.0247957
\(918\) −61.5327 −2.03088
\(919\) −15.7052 −0.518068 −0.259034 0.965868i \(-0.583404\pi\)
−0.259034 + 0.965868i \(0.583404\pi\)
\(920\) 65.0575 2.14488
\(921\) 14.4041 0.474630
\(922\) 22.4746 0.740163
\(923\) −27.5297 −0.906151
\(924\) −1.54972 −0.0509819
\(925\) −1.36626 −0.0449223
\(926\) 100.804 3.31263
\(927\) 0.0578827 0.00190112
\(928\) −7.32027 −0.240300
\(929\) 7.38567 0.242316 0.121158 0.992633i \(-0.461339\pi\)
0.121158 + 0.992633i \(0.461339\pi\)
\(930\) 25.3202 0.830283
\(931\) 9.87159 0.323528
\(932\) 4.09080 0.133999
\(933\) −13.5897 −0.444908
\(934\) 27.7485 0.907960
\(935\) −0.999269 −0.0326796
\(936\) 0.693013 0.0226518
\(937\) −31.8439 −1.04030 −0.520148 0.854076i \(-0.674123\pi\)
−0.520148 + 0.854076i \(0.674123\pi\)
\(938\) −2.03374 −0.0664040
\(939\) −41.0509 −1.33965
\(940\) 36.6002 1.19377
\(941\) 28.0486 0.914360 0.457180 0.889374i \(-0.348860\pi\)
0.457180 + 0.889374i \(0.348860\pi\)
\(942\) 15.7274 0.512426
\(943\) −65.6156 −2.13674
\(944\) 42.8635 1.39509
\(945\) 14.8241 0.482230
\(946\) −0.816119 −0.0265343
\(947\) 59.9734 1.94887 0.974437 0.224662i \(-0.0721279\pi\)
0.974437 + 0.224662i \(0.0721279\pi\)
\(948\) 70.1736 2.27913
\(949\) −66.5867 −2.16150
\(950\) −13.9307 −0.451971
\(951\) −31.6102 −1.02503
\(952\) 43.0721 1.39597
\(953\) −31.6692 −1.02587 −0.512933 0.858429i \(-0.671441\pi\)
−0.512933 + 0.858429i \(0.671441\pi\)
\(954\) −0.622132 −0.0201423
\(955\) 27.5787 0.892426
\(956\) −66.3740 −2.14669
\(957\) −1.92348 −0.0621772
\(958\) 6.95421 0.224680
\(959\) −13.4100 −0.433032
\(960\) 19.9726 0.644612
\(961\) −18.2219 −0.587805
\(962\) 6.70734 0.216253
\(963\) −0.0723562 −0.00233164
\(964\) 50.6477 1.63125
\(965\) −28.0440 −0.902767
\(966\) −57.2667 −1.84253
\(967\) −23.3765 −0.751738 −0.375869 0.926673i \(-0.622656\pi\)
−0.375869 + 0.926673i \(0.622656\pi\)
\(968\) 56.4173 1.81332
\(969\) 20.8329 0.669249
\(970\) −64.6978 −2.07732
\(971\) 49.5848 1.59125 0.795625 0.605789i \(-0.207143\pi\)
0.795625 + 0.605789i \(0.207143\pi\)
\(972\) −1.26271 −0.0405016
\(973\) 3.89472 0.124859
\(974\) −42.8284 −1.37231
\(975\) 17.9712 0.575540
\(976\) −66.6567 −2.13363
\(977\) 7.93951 0.254007 0.127004 0.991902i \(-0.459464\pi\)
0.127004 + 0.991902i \(0.459464\pi\)
\(978\) 19.2396 0.615215
\(979\) −0.0629047 −0.00201044
\(980\) 26.8120 0.856477
\(981\) 0.00299357 9.55772e−5 0
\(982\) 19.3658 0.617988
\(983\) 8.21675 0.262074 0.131037 0.991377i \(-0.458169\pi\)
0.131037 + 0.991377i \(0.458169\pi\)
\(984\) 76.4163 2.43606
\(985\) −18.4508 −0.587892
\(986\) 104.801 3.33754
\(987\) −16.4344 −0.523112
\(988\) 45.9024 1.46035
\(989\) −20.2418 −0.643653
\(990\) −0.0151997 −0.000483078 0
\(991\) −1.00672 −0.0319795 −0.0159897 0.999872i \(-0.505090\pi\)
−0.0159897 + 0.999872i \(0.505090\pi\)
\(992\) −2.97170 −0.0943516
\(993\) 41.2187 1.30804
\(994\) −26.0261 −0.825496
\(995\) −7.90364 −0.250562
\(996\) −10.9441 −0.346776
\(997\) 42.0400 1.33142 0.665710 0.746211i \(-0.268129\pi\)
0.665710 + 0.746211i \(0.268129\pi\)
\(998\) 30.3376 0.960319
\(999\) −3.10155 −0.0981287
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 6037.2.a.b.1.14 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.14 259 1.1 even 1 trivial