Properties

Label 2151.2.a.e.1.6
Level $2151$
Weight $2$
Character 2151.1
Self dual yes
Analytic conductor $17.176$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(17.1758214748\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.1767625.1
Defining polynomial: \(x^{6} - 7 x^{4} - x^{3} + 11 x^{2} + x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 717)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.65963\) of defining polynomial
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.22058 q^{2} +2.93097 q^{4} +0.0570810 q^{5} -3.64374 q^{7} +2.06730 q^{8} +O(q^{10})\) \(q+2.22058 q^{2} +2.93097 q^{4} +0.0570810 q^{5} -3.64374 q^{7} +2.06730 q^{8} +0.126753 q^{10} -3.71735 q^{11} -0.736497 q^{13} -8.09121 q^{14} -1.27135 q^{16} -1.72628 q^{17} -0.753715 q^{19} +0.167303 q^{20} -8.25467 q^{22} -1.29699 q^{23} -4.99674 q^{25} -1.63545 q^{26} -10.6797 q^{28} -2.49193 q^{29} +6.31032 q^{31} -6.95772 q^{32} -3.83334 q^{34} -0.207988 q^{35} -1.11169 q^{37} -1.67368 q^{38} +0.118003 q^{40} +0.457952 q^{41} -3.49470 q^{43} -10.8955 q^{44} -2.88007 q^{46} +6.66411 q^{47} +6.27684 q^{49} -11.0957 q^{50} -2.15865 q^{52} +0.214663 q^{53} -0.212190 q^{55} -7.53269 q^{56} -5.53352 q^{58} +7.80818 q^{59} -3.44774 q^{61} +14.0126 q^{62} -12.9075 q^{64} -0.0420400 q^{65} -11.5114 q^{67} -5.05968 q^{68} -0.461855 q^{70} +9.97235 q^{71} -2.09226 q^{73} -2.46859 q^{74} -2.20912 q^{76} +13.5451 q^{77} -14.2848 q^{79} -0.0725697 q^{80} +1.01692 q^{82} +9.92940 q^{83} -0.0985378 q^{85} -7.76025 q^{86} -7.68487 q^{88} -0.440716 q^{89} +2.68360 q^{91} -3.80144 q^{92} +14.7982 q^{94} -0.0430228 q^{95} -7.68409 q^{97} +13.9382 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{2} + 4q^{4} - 5q^{5} - 9q^{7} + 3q^{8} + O(q^{10}) \) \( 6q + 2q^{2} + 4q^{4} - 5q^{5} - 9q^{7} + 3q^{8} - 11q^{10} + 13q^{11} - q^{13} - 4q^{16} - 11q^{17} - 22q^{19} + q^{20} - 2q^{22} + 12q^{23} - q^{25} - 12q^{26} - 16q^{28} - 18q^{31} - 7q^{32} - 3q^{34} + 9q^{35} - 8q^{37} + 5q^{38} - 11q^{40} - 10q^{41} - 14q^{43} + 4q^{44} - 18q^{46} + 9q^{47} + 5q^{49} - 4q^{50} - 16q^{52} + 8q^{53} - 20q^{55} - 11q^{56} - 15q^{58} + 10q^{59} - 12q^{61} + 13q^{62} - 31q^{64} + 11q^{65} - 36q^{67} - 22q^{68} + q^{70} + 3q^{71} - 32q^{73} - 9q^{74} - 4q^{76} - 6q^{77} - q^{79} + 7q^{80} + 7q^{82} + 7q^{83} - 14q^{85} - 45q^{86} - 15q^{88} - 17q^{89} - 23q^{91} + 12q^{92} + 50q^{94} - 28q^{97} - 13q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.22058 1.57019 0.785093 0.619377i \(-0.212615\pi\)
0.785093 + 0.619377i \(0.212615\pi\)
\(3\) 0 0
\(4\) 2.93097 1.46549
\(5\) 0.0570810 0.0255274 0.0127637 0.999919i \(-0.495937\pi\)
0.0127637 + 0.999919i \(0.495937\pi\)
\(6\) 0 0
\(7\) −3.64374 −1.37720 −0.688602 0.725139i \(-0.741775\pi\)
−0.688602 + 0.725139i \(0.741775\pi\)
\(8\) 2.06730 0.730900
\(9\) 0 0
\(10\) 0.126753 0.0400828
\(11\) −3.71735 −1.12082 −0.560412 0.828214i \(-0.689357\pi\)
−0.560412 + 0.828214i \(0.689357\pi\)
\(12\) 0 0
\(13\) −0.736497 −0.204267 −0.102134 0.994771i \(-0.532567\pi\)
−0.102134 + 0.994771i \(0.532567\pi\)
\(14\) −8.09121 −2.16247
\(15\) 0 0
\(16\) −1.27135 −0.317836
\(17\) −1.72628 −0.418684 −0.209342 0.977842i \(-0.567132\pi\)
−0.209342 + 0.977842i \(0.567132\pi\)
\(18\) 0 0
\(19\) −0.753715 −0.172914 −0.0864571 0.996256i \(-0.527555\pi\)
−0.0864571 + 0.996256i \(0.527555\pi\)
\(20\) 0.167303 0.0374101
\(21\) 0 0
\(22\) −8.25467 −1.75990
\(23\) −1.29699 −0.270441 −0.135221 0.990816i \(-0.543174\pi\)
−0.135221 + 0.990816i \(0.543174\pi\)
\(24\) 0 0
\(25\) −4.99674 −0.999348
\(26\) −1.63545 −0.320738
\(27\) 0 0
\(28\) −10.6797 −2.01827
\(29\) −2.49193 −0.462739 −0.231369 0.972866i \(-0.574321\pi\)
−0.231369 + 0.972866i \(0.574321\pi\)
\(30\) 0 0
\(31\) 6.31032 1.13337 0.566684 0.823935i \(-0.308226\pi\)
0.566684 + 0.823935i \(0.308226\pi\)
\(32\) −6.95772 −1.22996
\(33\) 0 0
\(34\) −3.83334 −0.657413
\(35\) −0.207988 −0.0351565
\(36\) 0 0
\(37\) −1.11169 −0.182761 −0.0913803 0.995816i \(-0.529128\pi\)
−0.0913803 + 0.995816i \(0.529128\pi\)
\(38\) −1.67368 −0.271507
\(39\) 0 0
\(40\) 0.118003 0.0186580
\(41\) 0.457952 0.0715201 0.0357601 0.999360i \(-0.488615\pi\)
0.0357601 + 0.999360i \(0.488615\pi\)
\(42\) 0 0
\(43\) −3.49470 −0.532936 −0.266468 0.963844i \(-0.585857\pi\)
−0.266468 + 0.963844i \(0.585857\pi\)
\(44\) −10.8955 −1.64255
\(45\) 0 0
\(46\) −2.88007 −0.424643
\(47\) 6.66411 0.972061 0.486030 0.873942i \(-0.338444\pi\)
0.486030 + 0.873942i \(0.338444\pi\)
\(48\) 0 0
\(49\) 6.27684 0.896691
\(50\) −11.0957 −1.56916
\(51\) 0 0
\(52\) −2.15865 −0.299351
\(53\) 0.214663 0.0294862 0.0147431 0.999891i \(-0.495307\pi\)
0.0147431 + 0.999891i \(0.495307\pi\)
\(54\) 0 0
\(55\) −0.212190 −0.0286117
\(56\) −7.53269 −1.00660
\(57\) 0 0
\(58\) −5.53352 −0.726586
\(59\) 7.80818 1.01654 0.508269 0.861198i \(-0.330285\pi\)
0.508269 + 0.861198i \(0.330285\pi\)
\(60\) 0 0
\(61\) −3.44774 −0.441437 −0.220719 0.975338i \(-0.570840\pi\)
−0.220719 + 0.975338i \(0.570840\pi\)
\(62\) 14.0126 1.77960
\(63\) 0 0
\(64\) −12.9075 −1.61343
\(65\) −0.0420400 −0.00521442
\(66\) 0 0
\(67\) −11.5114 −1.40634 −0.703168 0.711024i \(-0.748232\pi\)
−0.703168 + 0.711024i \(0.748232\pi\)
\(68\) −5.05968 −0.613576
\(69\) 0 0
\(70\) −0.461855 −0.0552022
\(71\) 9.97235 1.18350 0.591750 0.806121i \(-0.298437\pi\)
0.591750 + 0.806121i \(0.298437\pi\)
\(72\) 0 0
\(73\) −2.09226 −0.244881 −0.122440 0.992476i \(-0.539072\pi\)
−0.122440 + 0.992476i \(0.539072\pi\)
\(74\) −2.46859 −0.286968
\(75\) 0 0
\(76\) −2.20912 −0.253403
\(77\) 13.5451 1.54360
\(78\) 0 0
\(79\) −14.2848 −1.60717 −0.803583 0.595193i \(-0.797076\pi\)
−0.803583 + 0.595193i \(0.797076\pi\)
\(80\) −0.0725697 −0.00811354
\(81\) 0 0
\(82\) 1.01692 0.112300
\(83\) 9.92940 1.08989 0.544947 0.838471i \(-0.316550\pi\)
0.544947 + 0.838471i \(0.316550\pi\)
\(84\) 0 0
\(85\) −0.0985378 −0.0106879
\(86\) −7.76025 −0.836810
\(87\) 0 0
\(88\) −7.68487 −0.819210
\(89\) −0.440716 −0.0467158 −0.0233579 0.999727i \(-0.507436\pi\)
−0.0233579 + 0.999727i \(0.507436\pi\)
\(90\) 0 0
\(91\) 2.68360 0.281318
\(92\) −3.80144 −0.396328
\(93\) 0 0
\(94\) 14.7982 1.52632
\(95\) −0.0430228 −0.00441405
\(96\) 0 0
\(97\) −7.68409 −0.780201 −0.390100 0.920772i \(-0.627560\pi\)
−0.390100 + 0.920772i \(0.627560\pi\)
\(98\) 13.9382 1.40797
\(99\) 0 0
\(100\) −14.6453 −1.46453
\(101\) −12.8775 −1.28135 −0.640677 0.767810i \(-0.721346\pi\)
−0.640677 + 0.767810i \(0.721346\pi\)
\(102\) 0 0
\(103\) −4.75094 −0.468124 −0.234062 0.972222i \(-0.575202\pi\)
−0.234062 + 0.972222i \(0.575202\pi\)
\(104\) −1.52256 −0.149299
\(105\) 0 0
\(106\) 0.476676 0.0462989
\(107\) 20.4655 1.97847 0.989236 0.146327i \(-0.0467452\pi\)
0.989236 + 0.146327i \(0.0467452\pi\)
\(108\) 0 0
\(109\) 11.6172 1.11272 0.556361 0.830940i \(-0.312197\pi\)
0.556361 + 0.830940i \(0.312197\pi\)
\(110\) −0.471185 −0.0449257
\(111\) 0 0
\(112\) 4.63245 0.437726
\(113\) −5.69792 −0.536015 −0.268008 0.963417i \(-0.586365\pi\)
−0.268008 + 0.963417i \(0.586365\pi\)
\(114\) 0 0
\(115\) −0.0740335 −0.00690366
\(116\) −7.30376 −0.678137
\(117\) 0 0
\(118\) 17.3387 1.59616
\(119\) 6.29011 0.576614
\(120\) 0 0
\(121\) 2.81870 0.256246
\(122\) −7.65597 −0.693139
\(123\) 0 0
\(124\) 18.4954 1.66093
\(125\) −0.570624 −0.0510382
\(126\) 0 0
\(127\) 2.93084 0.260070 0.130035 0.991509i \(-0.458491\pi\)
0.130035 + 0.991509i \(0.458491\pi\)
\(128\) −14.7466 −1.30343
\(129\) 0 0
\(130\) −0.0933531 −0.00818761
\(131\) −4.34492 −0.379617 −0.189809 0.981821i \(-0.560787\pi\)
−0.189809 + 0.981821i \(0.560787\pi\)
\(132\) 0 0
\(133\) 2.74634 0.238138
\(134\) −25.5619 −2.20821
\(135\) 0 0
\(136\) −3.56873 −0.306016
\(137\) 10.8025 0.922922 0.461461 0.887160i \(-0.347325\pi\)
0.461461 + 0.887160i \(0.347325\pi\)
\(138\) 0 0
\(139\) 1.59821 0.135558 0.0677791 0.997700i \(-0.478409\pi\)
0.0677791 + 0.997700i \(0.478409\pi\)
\(140\) −0.609608 −0.0515213
\(141\) 0 0
\(142\) 22.1444 1.85832
\(143\) 2.73782 0.228948
\(144\) 0 0
\(145\) −0.142242 −0.0118125
\(146\) −4.64603 −0.384508
\(147\) 0 0
\(148\) −3.25833 −0.267833
\(149\) −8.16766 −0.669121 −0.334560 0.942374i \(-0.608588\pi\)
−0.334560 + 0.942374i \(0.608588\pi\)
\(150\) 0 0
\(151\) −11.6281 −0.946280 −0.473140 0.880987i \(-0.656880\pi\)
−0.473140 + 0.880987i \(0.656880\pi\)
\(152\) −1.55815 −0.126383
\(153\) 0 0
\(154\) 30.0779 2.42374
\(155\) 0.360200 0.0289319
\(156\) 0 0
\(157\) 7.31612 0.583890 0.291945 0.956435i \(-0.405698\pi\)
0.291945 + 0.956435i \(0.405698\pi\)
\(158\) −31.7205 −2.52355
\(159\) 0 0
\(160\) −0.397154 −0.0313978
\(161\) 4.72590 0.372453
\(162\) 0 0
\(163\) 17.5848 1.37735 0.688675 0.725070i \(-0.258193\pi\)
0.688675 + 0.725070i \(0.258193\pi\)
\(164\) 1.34225 0.104812
\(165\) 0 0
\(166\) 22.0490 1.71134
\(167\) 3.05610 0.236488 0.118244 0.992985i \(-0.462274\pi\)
0.118244 + 0.992985i \(0.462274\pi\)
\(168\) 0 0
\(169\) −12.4576 −0.958275
\(170\) −0.218811 −0.0167820
\(171\) 0 0
\(172\) −10.2429 −0.781011
\(173\) −25.2508 −1.91978 −0.959890 0.280377i \(-0.909541\pi\)
−0.959890 + 0.280377i \(0.909541\pi\)
\(174\) 0 0
\(175\) 18.2068 1.37631
\(176\) 4.72604 0.356239
\(177\) 0 0
\(178\) −0.978645 −0.0733525
\(179\) 2.05516 0.153610 0.0768050 0.997046i \(-0.475528\pi\)
0.0768050 + 0.997046i \(0.475528\pi\)
\(180\) 0 0
\(181\) −25.1941 −1.87266 −0.936330 0.351122i \(-0.885800\pi\)
−0.936330 + 0.351122i \(0.885800\pi\)
\(182\) 5.95915 0.441722
\(183\) 0 0
\(184\) −2.68127 −0.197666
\(185\) −0.0634564 −0.00466540
\(186\) 0 0
\(187\) 6.41719 0.469271
\(188\) 19.5323 1.42454
\(189\) 0 0
\(190\) −0.0955356 −0.00693088
\(191\) −0.594359 −0.0430063 −0.0215031 0.999769i \(-0.506845\pi\)
−0.0215031 + 0.999769i \(0.506845\pi\)
\(192\) 0 0
\(193\) 14.3926 1.03600 0.518002 0.855379i \(-0.326676\pi\)
0.518002 + 0.855379i \(0.326676\pi\)
\(194\) −17.0631 −1.22506
\(195\) 0 0
\(196\) 18.3972 1.31409
\(197\) 4.63529 0.330251 0.165125 0.986273i \(-0.447197\pi\)
0.165125 + 0.986273i \(0.447197\pi\)
\(198\) 0 0
\(199\) −12.5742 −0.891363 −0.445682 0.895192i \(-0.647039\pi\)
−0.445682 + 0.895192i \(0.647039\pi\)
\(200\) −10.3298 −0.730424
\(201\) 0 0
\(202\) −28.5954 −2.01197
\(203\) 9.07993 0.637286
\(204\) 0 0
\(205\) 0.0261404 0.00182572
\(206\) −10.5498 −0.735042
\(207\) 0 0
\(208\) 0.936342 0.0649236
\(209\) 2.80182 0.193806
\(210\) 0 0
\(211\) 8.38295 0.577106 0.288553 0.957464i \(-0.406826\pi\)
0.288553 + 0.957464i \(0.406826\pi\)
\(212\) 0.629172 0.0432117
\(213\) 0 0
\(214\) 45.4452 3.10657
\(215\) −0.199481 −0.0136045
\(216\) 0 0
\(217\) −22.9932 −1.56088
\(218\) 25.7968 1.74718
\(219\) 0 0
\(220\) −0.621924 −0.0419301
\(221\) 1.27140 0.0855236
\(222\) 0 0
\(223\) −4.69892 −0.314663 −0.157332 0.987546i \(-0.550289\pi\)
−0.157332 + 0.987546i \(0.550289\pi\)
\(224\) 25.3521 1.69391
\(225\) 0 0
\(226\) −12.6527 −0.841644
\(227\) 11.3000 0.750008 0.375004 0.927023i \(-0.377641\pi\)
0.375004 + 0.927023i \(0.377641\pi\)
\(228\) 0 0
\(229\) −6.45502 −0.426560 −0.213280 0.976991i \(-0.568415\pi\)
−0.213280 + 0.976991i \(0.568415\pi\)
\(230\) −0.164397 −0.0108400
\(231\) 0 0
\(232\) −5.15155 −0.338216
\(233\) 17.6315 1.15508 0.577540 0.816363i \(-0.304013\pi\)
0.577540 + 0.816363i \(0.304013\pi\)
\(234\) 0 0
\(235\) 0.380394 0.0248142
\(236\) 22.8856 1.48972
\(237\) 0 0
\(238\) 13.9677 0.905391
\(239\) 1.00000 0.0646846
\(240\) 0 0
\(241\) −2.36031 −0.152041 −0.0760205 0.997106i \(-0.524221\pi\)
−0.0760205 + 0.997106i \(0.524221\pi\)
\(242\) 6.25915 0.402354
\(243\) 0 0
\(244\) −10.1052 −0.646920
\(245\) 0.358288 0.0228902
\(246\) 0 0
\(247\) 0.555109 0.0353207
\(248\) 13.0453 0.828379
\(249\) 0 0
\(250\) −1.26712 −0.0801395
\(251\) 8.31979 0.525140 0.262570 0.964913i \(-0.415430\pi\)
0.262570 + 0.964913i \(0.415430\pi\)
\(252\) 0 0
\(253\) 4.82137 0.303117
\(254\) 6.50816 0.408358
\(255\) 0 0
\(256\) −6.93112 −0.433195
\(257\) −26.9279 −1.67972 −0.839858 0.542806i \(-0.817362\pi\)
−0.839858 + 0.542806i \(0.817362\pi\)
\(258\) 0 0
\(259\) 4.05071 0.251699
\(260\) −0.123218 −0.00764166
\(261\) 0 0
\(262\) −9.64824 −0.596070
\(263\) −2.32501 −0.143366 −0.0716831 0.997427i \(-0.522837\pi\)
−0.0716831 + 0.997427i \(0.522837\pi\)
\(264\) 0 0
\(265\) 0.0122532 0.000752707 0
\(266\) 6.09847 0.373921
\(267\) 0 0
\(268\) −33.7395 −2.06097
\(269\) −13.3580 −0.814452 −0.407226 0.913327i \(-0.633504\pi\)
−0.407226 + 0.913327i \(0.633504\pi\)
\(270\) 0 0
\(271\) 16.5887 1.00769 0.503847 0.863793i \(-0.331917\pi\)
0.503847 + 0.863793i \(0.331917\pi\)
\(272\) 2.19470 0.133073
\(273\) 0 0
\(274\) 23.9879 1.44916
\(275\) 18.5746 1.12009
\(276\) 0 0
\(277\) 17.5340 1.05352 0.526759 0.850015i \(-0.323407\pi\)
0.526759 + 0.850015i \(0.323407\pi\)
\(278\) 3.54895 0.212852
\(279\) 0 0
\(280\) −0.429974 −0.0256959
\(281\) −11.3858 −0.679221 −0.339610 0.940566i \(-0.610295\pi\)
−0.339610 + 0.940566i \(0.610295\pi\)
\(282\) 0 0
\(283\) −10.7683 −0.640108 −0.320054 0.947399i \(-0.603701\pi\)
−0.320054 + 0.947399i \(0.603701\pi\)
\(284\) 29.2287 1.73440
\(285\) 0 0
\(286\) 6.07954 0.359491
\(287\) −1.66866 −0.0984978
\(288\) 0 0
\(289\) −14.0200 −0.824703
\(290\) −0.315859 −0.0185479
\(291\) 0 0
\(292\) −6.13236 −0.358869
\(293\) −12.8250 −0.749246 −0.374623 0.927177i \(-0.622228\pi\)
−0.374623 + 0.927177i \(0.622228\pi\)
\(294\) 0 0
\(295\) 0.445699 0.0259496
\(296\) −2.29819 −0.133580
\(297\) 0 0
\(298\) −18.1369 −1.05064
\(299\) 0.955229 0.0552423
\(300\) 0 0
\(301\) 12.7338 0.733962
\(302\) −25.8211 −1.48584
\(303\) 0 0
\(304\) 0.958233 0.0549584
\(305\) −0.196800 −0.0112688
\(306\) 0 0
\(307\) −19.6775 −1.12305 −0.561527 0.827458i \(-0.689786\pi\)
−0.561527 + 0.827458i \(0.689786\pi\)
\(308\) 39.7002 2.26213
\(309\) 0 0
\(310\) 0.799852 0.0454285
\(311\) −25.7035 −1.45751 −0.728757 0.684772i \(-0.759902\pi\)
−0.728757 + 0.684772i \(0.759902\pi\)
\(312\) 0 0
\(313\) −9.41285 −0.532046 −0.266023 0.963967i \(-0.585710\pi\)
−0.266023 + 0.963967i \(0.585710\pi\)
\(314\) 16.2460 0.916816
\(315\) 0 0
\(316\) −41.8684 −2.35528
\(317\) 1.87215 0.105151 0.0525753 0.998617i \(-0.483257\pi\)
0.0525753 + 0.998617i \(0.483257\pi\)
\(318\) 0 0
\(319\) 9.26336 0.518649
\(320\) −0.736772 −0.0411868
\(321\) 0 0
\(322\) 10.4942 0.584820
\(323\) 1.30112 0.0723964
\(324\) 0 0
\(325\) 3.68008 0.204134
\(326\) 39.0485 2.16270
\(327\) 0 0
\(328\) 0.946724 0.0522741
\(329\) −24.2823 −1.33873
\(330\) 0 0
\(331\) −16.8715 −0.927341 −0.463670 0.886008i \(-0.653468\pi\)
−0.463670 + 0.886008i \(0.653468\pi\)
\(332\) 29.1028 1.59722
\(333\) 0 0
\(334\) 6.78631 0.371330
\(335\) −0.657080 −0.0359001
\(336\) 0 0
\(337\) −19.1903 −1.04536 −0.522681 0.852528i \(-0.675068\pi\)
−0.522681 + 0.852528i \(0.675068\pi\)
\(338\) −27.6630 −1.50467
\(339\) 0 0
\(340\) −0.288812 −0.0156630
\(341\) −23.4577 −1.27031
\(342\) 0 0
\(343\) 2.63502 0.142278
\(344\) −7.22458 −0.389523
\(345\) 0 0
\(346\) −56.0713 −3.01441
\(347\) 23.8362 1.27960 0.639798 0.768543i \(-0.279018\pi\)
0.639798 + 0.768543i \(0.279018\pi\)
\(348\) 0 0
\(349\) −13.5199 −0.723703 −0.361852 0.932236i \(-0.617855\pi\)
−0.361852 + 0.932236i \(0.617855\pi\)
\(350\) 40.4297 2.16106
\(351\) 0 0
\(352\) 25.8643 1.37857
\(353\) 14.3286 0.762636 0.381318 0.924444i \(-0.375470\pi\)
0.381318 + 0.924444i \(0.375470\pi\)
\(354\) 0 0
\(355\) 0.569232 0.0302117
\(356\) −1.29173 −0.0684614
\(357\) 0 0
\(358\) 4.56365 0.241196
\(359\) 15.1952 0.801974 0.400987 0.916084i \(-0.368667\pi\)
0.400987 + 0.916084i \(0.368667\pi\)
\(360\) 0 0
\(361\) −18.4319 −0.970101
\(362\) −55.9454 −2.94042
\(363\) 0 0
\(364\) 7.86556 0.412268
\(365\) −0.119428 −0.00625117
\(366\) 0 0
\(367\) 31.2749 1.63253 0.816267 0.577675i \(-0.196040\pi\)
0.816267 + 0.577675i \(0.196040\pi\)
\(368\) 1.64892 0.0859561
\(369\) 0 0
\(370\) −0.140910 −0.00732556
\(371\) −0.782176 −0.0406086
\(372\) 0 0
\(373\) 13.6383 0.706166 0.353083 0.935592i \(-0.385133\pi\)
0.353083 + 0.935592i \(0.385133\pi\)
\(374\) 14.2499 0.736844
\(375\) 0 0
\(376\) 13.7767 0.710479
\(377\) 1.83529 0.0945225
\(378\) 0 0
\(379\) −22.3666 −1.14890 −0.574448 0.818541i \(-0.694783\pi\)
−0.574448 + 0.818541i \(0.694783\pi\)
\(380\) −0.126099 −0.00646873
\(381\) 0 0
\(382\) −1.31982 −0.0675279
\(383\) −12.1215 −0.619380 −0.309690 0.950838i \(-0.600225\pi\)
−0.309690 + 0.950838i \(0.600225\pi\)
\(384\) 0 0
\(385\) 0.773166 0.0394042
\(386\) 31.9600 1.62672
\(387\) 0 0
\(388\) −22.5218 −1.14337
\(389\) 11.4985 0.582999 0.291500 0.956571i \(-0.405846\pi\)
0.291500 + 0.956571i \(0.405846\pi\)
\(390\) 0 0
\(391\) 2.23897 0.113230
\(392\) 12.9761 0.655392
\(393\) 0 0
\(394\) 10.2930 0.518555
\(395\) −0.815391 −0.0410268
\(396\) 0 0
\(397\) −25.2172 −1.26561 −0.632807 0.774309i \(-0.718098\pi\)
−0.632807 + 0.774309i \(0.718098\pi\)
\(398\) −27.9221 −1.39961
\(399\) 0 0
\(400\) 6.35259 0.317629
\(401\) 29.3323 1.46479 0.732393 0.680883i \(-0.238404\pi\)
0.732393 + 0.680883i \(0.238404\pi\)
\(402\) 0 0
\(403\) −4.64753 −0.231510
\(404\) −37.7435 −1.87781
\(405\) 0 0
\(406\) 20.1627 1.00066
\(407\) 4.13254 0.204842
\(408\) 0 0
\(409\) 38.7995 1.91851 0.959256 0.282539i \(-0.0911767\pi\)
0.959256 + 0.282539i \(0.0911767\pi\)
\(410\) 0.0580468 0.00286673
\(411\) 0 0
\(412\) −13.9249 −0.686029
\(413\) −28.4510 −1.39998
\(414\) 0 0
\(415\) 0.566781 0.0278222
\(416\) 5.12434 0.251241
\(417\) 0 0
\(418\) 6.22167 0.304312
\(419\) 26.0609 1.27316 0.636578 0.771212i \(-0.280349\pi\)
0.636578 + 0.771212i \(0.280349\pi\)
\(420\) 0 0
\(421\) −11.7112 −0.570767 −0.285383 0.958413i \(-0.592121\pi\)
−0.285383 + 0.958413i \(0.592121\pi\)
\(422\) 18.6150 0.906164
\(423\) 0 0
\(424\) 0.443773 0.0215515
\(425\) 8.62577 0.418412
\(426\) 0 0
\(427\) 12.5626 0.607949
\(428\) 59.9838 2.89942
\(429\) 0 0
\(430\) −0.442963 −0.0213616
\(431\) −19.3962 −0.934284 −0.467142 0.884182i \(-0.654716\pi\)
−0.467142 + 0.884182i \(0.654716\pi\)
\(432\) 0 0
\(433\) −3.56849 −0.171490 −0.0857452 0.996317i \(-0.527327\pi\)
−0.0857452 + 0.996317i \(0.527327\pi\)
\(434\) −51.0582 −2.45087
\(435\) 0 0
\(436\) 34.0496 1.63068
\(437\) 0.977561 0.0467631
\(438\) 0 0
\(439\) 31.5488 1.50574 0.752872 0.658167i \(-0.228668\pi\)
0.752872 + 0.658167i \(0.228668\pi\)
\(440\) −0.438660 −0.0209123
\(441\) 0 0
\(442\) 2.82324 0.134288
\(443\) −2.17420 −0.103299 −0.0516496 0.998665i \(-0.516448\pi\)
−0.0516496 + 0.998665i \(0.516448\pi\)
\(444\) 0 0
\(445\) −0.0251565 −0.00119253
\(446\) −10.4343 −0.494080
\(447\) 0 0
\(448\) 47.0315 2.22203
\(449\) −33.2412 −1.56875 −0.784375 0.620287i \(-0.787016\pi\)
−0.784375 + 0.620287i \(0.787016\pi\)
\(450\) 0 0
\(451\) −1.70237 −0.0801614
\(452\) −16.7005 −0.785523
\(453\) 0 0
\(454\) 25.0926 1.17765
\(455\) 0.153183 0.00718132
\(456\) 0 0
\(457\) −26.5058 −1.23989 −0.619944 0.784646i \(-0.712845\pi\)
−0.619944 + 0.784646i \(0.712845\pi\)
\(458\) −14.3339 −0.669779
\(459\) 0 0
\(460\) −0.216990 −0.0101172
\(461\) 36.1977 1.68590 0.842948 0.537995i \(-0.180818\pi\)
0.842948 + 0.537995i \(0.180818\pi\)
\(462\) 0 0
\(463\) 6.82777 0.317314 0.158657 0.987334i \(-0.449284\pi\)
0.158657 + 0.987334i \(0.449284\pi\)
\(464\) 3.16810 0.147075
\(465\) 0 0
\(466\) 39.1522 1.81369
\(467\) −33.8542 −1.56659 −0.783293 0.621652i \(-0.786462\pi\)
−0.783293 + 0.621652i \(0.786462\pi\)
\(468\) 0 0
\(469\) 41.9444 1.93681
\(470\) 0.844696 0.0389629
\(471\) 0 0
\(472\) 16.1418 0.742988
\(473\) 12.9910 0.597328
\(474\) 0 0
\(475\) 3.76612 0.172801
\(476\) 18.4362 0.845020
\(477\) 0 0
\(478\) 2.22058 0.101567
\(479\) −8.14302 −0.372064 −0.186032 0.982544i \(-0.559563\pi\)
−0.186032 + 0.982544i \(0.559563\pi\)
\(480\) 0 0
\(481\) 0.818755 0.0373320
\(482\) −5.24126 −0.238733
\(483\) 0 0
\(484\) 8.26154 0.375524
\(485\) −0.438616 −0.0199165
\(486\) 0 0
\(487\) −14.0940 −0.638661 −0.319330 0.947643i \(-0.603458\pi\)
−0.319330 + 0.947643i \(0.603458\pi\)
\(488\) −7.12750 −0.322647
\(489\) 0 0
\(490\) 0.795608 0.0359419
\(491\) 30.5029 1.37658 0.688289 0.725437i \(-0.258362\pi\)
0.688289 + 0.725437i \(0.258362\pi\)
\(492\) 0 0
\(493\) 4.30176 0.193742
\(494\) 1.23266 0.0554601
\(495\) 0 0
\(496\) −8.02261 −0.360226
\(497\) −36.3367 −1.62992
\(498\) 0 0
\(499\) −15.6252 −0.699479 −0.349739 0.936847i \(-0.613730\pi\)
−0.349739 + 0.936847i \(0.613730\pi\)
\(500\) −1.67248 −0.0747958
\(501\) 0 0
\(502\) 18.4747 0.824568
\(503\) −10.0657 −0.448807 −0.224404 0.974496i \(-0.572043\pi\)
−0.224404 + 0.974496i \(0.572043\pi\)
\(504\) 0 0
\(505\) −0.735058 −0.0327097
\(506\) 10.7062 0.475950
\(507\) 0 0
\(508\) 8.59020 0.381129
\(509\) 22.5797 1.00083 0.500414 0.865786i \(-0.333181\pi\)
0.500414 + 0.865786i \(0.333181\pi\)
\(510\) 0 0
\(511\) 7.62365 0.337250
\(512\) 14.1022 0.623234
\(513\) 0 0
\(514\) −59.7955 −2.63747
\(515\) −0.271188 −0.0119500
\(516\) 0 0
\(517\) −24.7728 −1.08951
\(518\) 8.99491 0.395214
\(519\) 0 0
\(520\) −0.0869092 −0.00381122
\(521\) 10.6301 0.465715 0.232857 0.972511i \(-0.425192\pi\)
0.232857 + 0.972511i \(0.425192\pi\)
\(522\) 0 0
\(523\) 12.8900 0.563642 0.281821 0.959467i \(-0.409062\pi\)
0.281821 + 0.959467i \(0.409062\pi\)
\(524\) −12.7348 −0.556324
\(525\) 0 0
\(526\) −5.16287 −0.225112
\(527\) −10.8934 −0.474523
\(528\) 0 0
\(529\) −21.3178 −0.926862
\(530\) 0.0272092 0.00118189
\(531\) 0 0
\(532\) 8.04945 0.348988
\(533\) −0.337280 −0.0146092
\(534\) 0 0
\(535\) 1.16819 0.0505053
\(536\) −23.7974 −1.02789
\(537\) 0 0
\(538\) −29.6625 −1.27884
\(539\) −23.3332 −1.00503
\(540\) 0 0
\(541\) 34.1904 1.46996 0.734980 0.678089i \(-0.237191\pi\)
0.734980 + 0.678089i \(0.237191\pi\)
\(542\) 36.8366 1.58227
\(543\) 0 0
\(544\) 12.0110 0.514966
\(545\) 0.663120 0.0284049
\(546\) 0 0
\(547\) −12.6930 −0.542714 −0.271357 0.962479i \(-0.587472\pi\)
−0.271357 + 0.962479i \(0.587472\pi\)
\(548\) 31.6619 1.35253
\(549\) 0 0
\(550\) 41.2465 1.75876
\(551\) 1.87820 0.0800141
\(552\) 0 0
\(553\) 52.0501 2.21340
\(554\) 38.9357 1.65422
\(555\) 0 0
\(556\) 4.68430 0.198659
\(557\) 32.3710 1.37160 0.685801 0.727789i \(-0.259452\pi\)
0.685801 + 0.727789i \(0.259452\pi\)
\(558\) 0 0
\(559\) 2.57383 0.108862
\(560\) 0.264425 0.0111740
\(561\) 0 0
\(562\) −25.2831 −1.06650
\(563\) −17.5807 −0.740938 −0.370469 0.928845i \(-0.620803\pi\)
−0.370469 + 0.928845i \(0.620803\pi\)
\(564\) 0 0
\(565\) −0.325243 −0.0136831
\(566\) −23.9118 −1.00509
\(567\) 0 0
\(568\) 20.6158 0.865021
\(569\) −44.7549 −1.87622 −0.938112 0.346332i \(-0.887427\pi\)
−0.938112 + 0.346332i \(0.887427\pi\)
\(570\) 0 0
\(571\) 20.9021 0.874727 0.437364 0.899285i \(-0.355912\pi\)
0.437364 + 0.899285i \(0.355912\pi\)
\(572\) 8.02447 0.335520
\(573\) 0 0
\(574\) −3.70539 −0.154660
\(575\) 6.48073 0.270265
\(576\) 0 0
\(577\) −6.77713 −0.282135 −0.141068 0.990000i \(-0.545054\pi\)
−0.141068 + 0.990000i \(0.545054\pi\)
\(578\) −31.1324 −1.29494
\(579\) 0 0
\(580\) −0.416906 −0.0173111
\(581\) −36.1802 −1.50101
\(582\) 0 0
\(583\) −0.797978 −0.0330489
\(584\) −4.32533 −0.178983
\(585\) 0 0
\(586\) −28.4790 −1.17646
\(587\) −26.4488 −1.09166 −0.545830 0.837896i \(-0.683786\pi\)
−0.545830 + 0.837896i \(0.683786\pi\)
\(588\) 0 0
\(589\) −4.75619 −0.195975
\(590\) 0.989710 0.0407457
\(591\) 0 0
\(592\) 1.41334 0.0580880
\(593\) 3.87732 0.159222 0.0796112 0.996826i \(-0.474632\pi\)
0.0796112 + 0.996826i \(0.474632\pi\)
\(594\) 0 0
\(595\) 0.359046 0.0147195
\(596\) −23.9392 −0.980587
\(597\) 0 0
\(598\) 2.12116 0.0867408
\(599\) −25.3189 −1.03450 −0.517251 0.855834i \(-0.673045\pi\)
−0.517251 + 0.855834i \(0.673045\pi\)
\(600\) 0 0
\(601\) 21.4456 0.874782 0.437391 0.899271i \(-0.355903\pi\)
0.437391 + 0.899271i \(0.355903\pi\)
\(602\) 28.2763 1.15246
\(603\) 0 0
\(604\) −34.0816 −1.38676
\(605\) 0.160894 0.00654129
\(606\) 0 0
\(607\) 44.0058 1.78614 0.893070 0.449919i \(-0.148547\pi\)
0.893070 + 0.449919i \(0.148547\pi\)
\(608\) 5.24414 0.212678
\(609\) 0 0
\(610\) −0.437011 −0.0176940
\(611\) −4.90810 −0.198560
\(612\) 0 0
\(613\) 9.11434 0.368125 0.184062 0.982915i \(-0.441075\pi\)
0.184062 + 0.982915i \(0.441075\pi\)
\(614\) −43.6955 −1.76341
\(615\) 0 0
\(616\) 28.0017 1.12822
\(617\) −2.06698 −0.0832133 −0.0416067 0.999134i \(-0.513248\pi\)
−0.0416067 + 0.999134i \(0.513248\pi\)
\(618\) 0 0
\(619\) −22.7993 −0.916383 −0.458191 0.888854i \(-0.651503\pi\)
−0.458191 + 0.888854i \(0.651503\pi\)
\(620\) 1.05574 0.0423994
\(621\) 0 0
\(622\) −57.0768 −2.28857
\(623\) 1.60585 0.0643372
\(624\) 0 0
\(625\) 24.9511 0.998045
\(626\) −20.9020 −0.835411
\(627\) 0 0
\(628\) 21.4433 0.855682
\(629\) 1.91909 0.0765190
\(630\) 0 0
\(631\) −31.4481 −1.25193 −0.625964 0.779852i \(-0.715294\pi\)
−0.625964 + 0.779852i \(0.715294\pi\)
\(632\) −29.5309 −1.17468
\(633\) 0 0
\(634\) 4.15727 0.165106
\(635\) 0.167295 0.00663891
\(636\) 0 0
\(637\) −4.62287 −0.183165
\(638\) 20.5700 0.814375
\(639\) 0 0
\(640\) −0.841753 −0.0332732
\(641\) −6.51455 −0.257309 −0.128655 0.991689i \(-0.541066\pi\)
−0.128655 + 0.991689i \(0.541066\pi\)
\(642\) 0 0
\(643\) −2.08816 −0.0823491 −0.0411746 0.999152i \(-0.513110\pi\)
−0.0411746 + 0.999152i \(0.513110\pi\)
\(644\) 13.8515 0.545824
\(645\) 0 0
\(646\) 2.88925 0.113676
\(647\) 11.2824 0.443555 0.221778 0.975097i \(-0.428814\pi\)
0.221778 + 0.975097i \(0.428814\pi\)
\(648\) 0 0
\(649\) −29.0258 −1.13936
\(650\) 8.17192 0.320529
\(651\) 0 0
\(652\) 51.5406 2.01849
\(653\) 15.7251 0.615372 0.307686 0.951488i \(-0.400445\pi\)
0.307686 + 0.951488i \(0.400445\pi\)
\(654\) 0 0
\(655\) −0.248013 −0.00969065
\(656\) −0.582216 −0.0227317
\(657\) 0 0
\(658\) −53.9207 −2.10205
\(659\) 1.91095 0.0744400 0.0372200 0.999307i \(-0.488150\pi\)
0.0372200 + 0.999307i \(0.488150\pi\)
\(660\) 0 0
\(661\) −45.7455 −1.77929 −0.889647 0.456648i \(-0.849050\pi\)
−0.889647 + 0.456648i \(0.849050\pi\)
\(662\) −37.4645 −1.45610
\(663\) 0 0
\(664\) 20.5270 0.796604
\(665\) 0.156764 0.00607905
\(666\) 0 0
\(667\) 3.23200 0.125144
\(668\) 8.95734 0.346570
\(669\) 0 0
\(670\) −1.45910 −0.0563699
\(671\) 12.8164 0.494773
\(672\) 0 0
\(673\) 36.5553 1.40910 0.704552 0.709653i \(-0.251148\pi\)
0.704552 + 0.709653i \(0.251148\pi\)
\(674\) −42.6136 −1.64141
\(675\) 0 0
\(676\) −36.5128 −1.40434
\(677\) −26.1615 −1.00547 −0.502733 0.864442i \(-0.667672\pi\)
−0.502733 + 0.864442i \(0.667672\pi\)
\(678\) 0 0
\(679\) 27.9988 1.07450
\(680\) −0.203707 −0.00781181
\(681\) 0 0
\(682\) −52.0897 −1.99462
\(683\) −32.3175 −1.23660 −0.618298 0.785944i \(-0.712177\pi\)
−0.618298 + 0.785944i \(0.712177\pi\)
\(684\) 0 0
\(685\) 0.616619 0.0235598
\(686\) 5.85126 0.223402
\(687\) 0 0
\(688\) 4.44297 0.169387
\(689\) −0.158099 −0.00602308
\(690\) 0 0
\(691\) −3.28734 −0.125056 −0.0625282 0.998043i \(-0.519916\pi\)
−0.0625282 + 0.998043i \(0.519916\pi\)
\(692\) −74.0093 −2.81341
\(693\) 0 0
\(694\) 52.9303 2.00921
\(695\) 0.0912273 0.00346045
\(696\) 0 0
\(697\) −0.790554 −0.0299444
\(698\) −30.0220 −1.13635
\(699\) 0 0
\(700\) 53.3637 2.01696
\(701\) 11.2419 0.424602 0.212301 0.977204i \(-0.431904\pi\)
0.212301 + 0.977204i \(0.431904\pi\)
\(702\) 0 0
\(703\) 0.837897 0.0316019
\(704\) 47.9816 1.80838
\(705\) 0 0
\(706\) 31.8179 1.19748
\(707\) 46.9221 1.76469
\(708\) 0 0
\(709\) 4.71294 0.176998 0.0884990 0.996076i \(-0.471793\pi\)
0.0884990 + 0.996076i \(0.471793\pi\)
\(710\) 1.26402 0.0474380
\(711\) 0 0
\(712\) −0.911091 −0.0341446
\(713\) −8.18443 −0.306509
\(714\) 0 0
\(715\) 0.156277 0.00584444
\(716\) 6.02362 0.225113
\(717\) 0 0
\(718\) 33.7422 1.25925
\(719\) −25.7339 −0.959713 −0.479856 0.877347i \(-0.659311\pi\)
−0.479856 + 0.877347i \(0.659311\pi\)
\(720\) 0 0
\(721\) 17.3112 0.644702
\(722\) −40.9295 −1.52324
\(723\) 0 0
\(724\) −73.8431 −2.74436
\(725\) 12.4515 0.462437
\(726\) 0 0
\(727\) −10.9895 −0.407576 −0.203788 0.979015i \(-0.565325\pi\)
−0.203788 + 0.979015i \(0.565325\pi\)
\(728\) 5.54780 0.205615
\(729\) 0 0
\(730\) −0.265200 −0.00981550
\(731\) 6.03283 0.223132
\(732\) 0 0
\(733\) −27.7612 −1.02538 −0.512692 0.858572i \(-0.671352\pi\)
−0.512692 + 0.858572i \(0.671352\pi\)
\(734\) 69.4483 2.56338
\(735\) 0 0
\(736\) 9.02410 0.332633
\(737\) 42.7918 1.57625
\(738\) 0 0
\(739\) −25.7282 −0.946426 −0.473213 0.880948i \(-0.656906\pi\)
−0.473213 + 0.880948i \(0.656906\pi\)
\(740\) −0.185989 −0.00683709
\(741\) 0 0
\(742\) −1.73688 −0.0637630
\(743\) 38.6081 1.41639 0.708197 0.706015i \(-0.249509\pi\)
0.708197 + 0.706015i \(0.249509\pi\)
\(744\) 0 0
\(745\) −0.466218 −0.0170809
\(746\) 30.2850 1.10881
\(747\) 0 0
\(748\) 18.8086 0.687711
\(749\) −74.5709 −2.72476
\(750\) 0 0
\(751\) −31.2572 −1.14059 −0.570296 0.821439i \(-0.693171\pi\)
−0.570296 + 0.821439i \(0.693171\pi\)
\(752\) −8.47239 −0.308956
\(753\) 0 0
\(754\) 4.07542 0.148418
\(755\) −0.663743 −0.0241561
\(756\) 0 0
\(757\) −22.2245 −0.807764 −0.403882 0.914811i \(-0.632339\pi\)
−0.403882 + 0.914811i \(0.632339\pi\)
\(758\) −49.6668 −1.80398
\(759\) 0 0
\(760\) −0.0889410 −0.00322623
\(761\) −29.5640 −1.07170 −0.535848 0.844314i \(-0.680008\pi\)
−0.535848 + 0.844314i \(0.680008\pi\)
\(762\) 0 0
\(763\) −42.3299 −1.53245
\(764\) −1.74205 −0.0630251
\(765\) 0 0
\(766\) −26.9168 −0.972543
\(767\) −5.75070 −0.207646
\(768\) 0 0
\(769\) 31.5926 1.13926 0.569628 0.821902i \(-0.307087\pi\)
0.569628 + 0.821902i \(0.307087\pi\)
\(770\) 1.71688 0.0618719
\(771\) 0 0
\(772\) 42.1844 1.51825
\(773\) −46.1914 −1.66139 −0.830694 0.556729i \(-0.812056\pi\)
−0.830694 + 0.556729i \(0.812056\pi\)
\(774\) 0 0
\(775\) −31.5311 −1.13263
\(776\) −15.8853 −0.570249
\(777\) 0 0
\(778\) 25.5334 0.915418
\(779\) −0.345166 −0.0123668
\(780\) 0 0
\(781\) −37.0707 −1.32650
\(782\) 4.97181 0.177791
\(783\) 0 0
\(784\) −7.98003 −0.285001
\(785\) 0.417611 0.0149052
\(786\) 0 0
\(787\) 12.5553 0.447549 0.223775 0.974641i \(-0.428162\pi\)
0.223775 + 0.974641i \(0.428162\pi\)
\(788\) 13.5859 0.483978
\(789\) 0 0
\(790\) −1.81064 −0.0644197
\(791\) 20.7617 0.738203
\(792\) 0 0
\(793\) 2.53925 0.0901713
\(794\) −55.9968 −1.98725
\(795\) 0 0
\(796\) −36.8547 −1.30628
\(797\) −44.8797 −1.58972 −0.794860 0.606793i \(-0.792456\pi\)
−0.794860 + 0.606793i \(0.792456\pi\)
\(798\) 0 0
\(799\) −11.5041 −0.406987
\(800\) 34.7659 1.22916
\(801\) 0 0
\(802\) 65.1347 2.29999
\(803\) 7.77767 0.274468
\(804\) 0 0
\(805\) 0.269759 0.00950775
\(806\) −10.3202 −0.363514
\(807\) 0 0
\(808\) −26.6215 −0.936542
\(809\) −41.3567 −1.45402 −0.727011 0.686625i \(-0.759091\pi\)
−0.727011 + 0.686625i \(0.759091\pi\)
\(810\) 0 0
\(811\) −48.3830 −1.69896 −0.849479 0.527623i \(-0.823083\pi\)
−0.849479 + 0.527623i \(0.823083\pi\)
\(812\) 26.6130 0.933934
\(813\) 0 0
\(814\) 9.17663 0.321641
\(815\) 1.00376 0.0351602
\(816\) 0 0
\(817\) 2.63401 0.0921522
\(818\) 86.1574 3.01242
\(819\) 0 0
\(820\) 0.0766167 0.00267557
\(821\) 36.0285 1.25740 0.628702 0.777647i \(-0.283587\pi\)
0.628702 + 0.777647i \(0.283587\pi\)
\(822\) 0 0
\(823\) 37.4334 1.30484 0.652422 0.757856i \(-0.273753\pi\)
0.652422 + 0.757856i \(0.273753\pi\)
\(824\) −9.82161 −0.342152
\(825\) 0 0
\(826\) −63.1777 −2.19823
\(827\) −32.3428 −1.12467 −0.562335 0.826909i \(-0.690097\pi\)
−0.562335 + 0.826909i \(0.690097\pi\)
\(828\) 0 0
\(829\) 16.6445 0.578087 0.289043 0.957316i \(-0.406663\pi\)
0.289043 + 0.957316i \(0.406663\pi\)
\(830\) 1.25858 0.0436860
\(831\) 0 0
\(832\) 9.50631 0.329572
\(833\) −10.8356 −0.375431
\(834\) 0 0
\(835\) 0.174445 0.00603693
\(836\) 8.21207 0.284020
\(837\) 0 0
\(838\) 57.8702 1.99909
\(839\) 37.2541 1.28615 0.643077 0.765802i \(-0.277658\pi\)
0.643077 + 0.765802i \(0.277658\pi\)
\(840\) 0 0
\(841\) −22.7903 −0.785873
\(842\) −26.0055 −0.896210
\(843\) 0 0
\(844\) 24.5702 0.845741
\(845\) −0.711091 −0.0244623
\(846\) 0 0
\(847\) −10.2706 −0.352903
\(848\) −0.272911 −0.00937181
\(849\) 0 0
\(850\) 19.1542 0.656984
\(851\) 1.44185 0.0494260
\(852\) 0 0
\(853\) −45.4165 −1.55503 −0.777515 0.628864i \(-0.783520\pi\)
−0.777515 + 0.628864i \(0.783520\pi\)
\(854\) 27.8964 0.954594
\(855\) 0 0
\(856\) 42.3082 1.44607
\(857\) 46.3601 1.58363 0.791815 0.610761i \(-0.209137\pi\)
0.791815 + 0.610761i \(0.209137\pi\)
\(858\) 0 0
\(859\) −36.7731 −1.25468 −0.627341 0.778745i \(-0.715857\pi\)
−0.627341 + 0.778745i \(0.715857\pi\)
\(860\) −0.584673 −0.0199372
\(861\) 0 0
\(862\) −43.0709 −1.46700
\(863\) −4.40567 −0.149971 −0.0749854 0.997185i \(-0.523891\pi\)
−0.0749854 + 0.997185i \(0.523891\pi\)
\(864\) 0 0
\(865\) −1.44134 −0.0490070
\(866\) −7.92411 −0.269272
\(867\) 0 0
\(868\) −67.3924 −2.28745
\(869\) 53.1016 1.80135
\(870\) 0 0
\(871\) 8.47807 0.287269
\(872\) 24.0161 0.813289
\(873\) 0 0
\(874\) 2.17075 0.0734268
\(875\) 2.07921 0.0702900
\(876\) 0 0
\(877\) 14.8414 0.501158 0.250579 0.968096i \(-0.419379\pi\)
0.250579 + 0.968096i \(0.419379\pi\)
\(878\) 70.0567 2.36430
\(879\) 0 0
\(880\) 0.269767 0.00909385
\(881\) −17.1858 −0.579003 −0.289502 0.957178i \(-0.593490\pi\)
−0.289502 + 0.957178i \(0.593490\pi\)
\(882\) 0 0
\(883\) −13.2297 −0.445216 −0.222608 0.974908i \(-0.571457\pi\)
−0.222608 + 0.974908i \(0.571457\pi\)
\(884\) 3.72644 0.125334
\(885\) 0 0
\(886\) −4.82797 −0.162199
\(887\) 24.0644 0.808002 0.404001 0.914759i \(-0.367619\pi\)
0.404001 + 0.914759i \(0.367619\pi\)
\(888\) 0 0
\(889\) −10.6792 −0.358169
\(890\) −0.0558620 −0.00187250
\(891\) 0 0
\(892\) −13.7724 −0.461135
\(893\) −5.02284 −0.168083
\(894\) 0 0
\(895\) 0.117311 0.00392127
\(896\) 53.7329 1.79509
\(897\) 0 0
\(898\) −73.8147 −2.46323
\(899\) −15.7249 −0.524453
\(900\) 0 0
\(901\) −0.370569 −0.0123454
\(902\) −3.78025 −0.125868
\(903\) 0 0
\(904\) −11.7793 −0.391774
\(905\) −1.43810 −0.0478041
\(906\) 0 0
\(907\) −19.6429 −0.652233 −0.326117 0.945330i \(-0.605740\pi\)
−0.326117 + 0.945330i \(0.605740\pi\)
\(908\) 33.1200 1.09913
\(909\) 0 0
\(910\) 0.340154 0.0112760
\(911\) −4.93178 −0.163397 −0.0816986 0.996657i \(-0.526034\pi\)
−0.0816986 + 0.996657i \(0.526034\pi\)
\(912\) 0 0
\(913\) −36.9111 −1.22158
\(914\) −58.8582 −1.94686
\(915\) 0 0
\(916\) −18.9195 −0.625118
\(917\) 15.8318 0.522811
\(918\) 0 0
\(919\) 6.26183 0.206559 0.103279 0.994652i \(-0.467066\pi\)
0.103279 + 0.994652i \(0.467066\pi\)
\(920\) −0.153049 −0.00504589
\(921\) 0 0
\(922\) 80.3799 2.64717
\(923\) −7.34460 −0.241751
\(924\) 0 0
\(925\) 5.55482 0.182641
\(926\) 15.1616 0.498242
\(927\) 0 0
\(928\) 17.3381 0.569152
\(929\) −19.8755 −0.652094 −0.326047 0.945353i \(-0.605717\pi\)
−0.326047 + 0.945353i \(0.605717\pi\)
\(930\) 0 0
\(931\) −4.73095 −0.155051
\(932\) 51.6775 1.69275
\(933\) 0 0
\(934\) −75.1760 −2.45983
\(935\) 0.366300 0.0119793
\(936\) 0 0
\(937\) −16.1857 −0.528764 −0.264382 0.964418i \(-0.585168\pi\)
−0.264382 + 0.964418i \(0.585168\pi\)
\(938\) 93.1408 3.04116
\(939\) 0 0
\(940\) 1.11493 0.0363649
\(941\) 26.8508 0.875310 0.437655 0.899143i \(-0.355809\pi\)
0.437655 + 0.899143i \(0.355809\pi\)
\(942\) 0 0
\(943\) −0.593960 −0.0193420
\(944\) −9.92690 −0.323093
\(945\) 0 0
\(946\) 28.8476 0.937916
\(947\) −18.3250 −0.595481 −0.297741 0.954647i \(-0.596233\pi\)
−0.297741 + 0.954647i \(0.596233\pi\)
\(948\) 0 0
\(949\) 1.54094 0.0500211
\(950\) 8.36297 0.271331
\(951\) 0 0
\(952\) 13.0035 0.421447
\(953\) 24.6170 0.797423 0.398711 0.917076i \(-0.369458\pi\)
0.398711 + 0.917076i \(0.369458\pi\)
\(954\) 0 0
\(955\) −0.0339266 −0.00109784
\(956\) 2.93097 0.0947944
\(957\) 0 0
\(958\) −18.0822 −0.584210
\(959\) −39.3616 −1.27105
\(960\) 0 0
\(961\) 8.82019 0.284522
\(962\) 1.81811 0.0586183
\(963\) 0 0
\(964\) −6.91800 −0.222814
\(965\) 0.821547 0.0264465
\(966\) 0 0
\(967\) −57.4790 −1.84840 −0.924200 0.381908i \(-0.875267\pi\)
−0.924200 + 0.381908i \(0.875267\pi\)
\(968\) 5.82710 0.187290
\(969\) 0 0
\(970\) −0.973981 −0.0312726
\(971\) 10.4481 0.335295 0.167648 0.985847i \(-0.446383\pi\)
0.167648 + 0.985847i \(0.446383\pi\)
\(972\) 0 0
\(973\) −5.82345 −0.186691
\(974\) −31.2969 −1.00282
\(975\) 0 0
\(976\) 4.38326 0.140305
\(977\) 5.55962 0.177868 0.0889340 0.996038i \(-0.471654\pi\)
0.0889340 + 0.996038i \(0.471654\pi\)
\(978\) 0 0
\(979\) 1.63830 0.0523602
\(980\) 1.05013 0.0335453
\(981\) 0 0
\(982\) 67.7342 2.16148
\(983\) 20.8116 0.663787 0.331894 0.943317i \(-0.392312\pi\)
0.331894 + 0.943317i \(0.392312\pi\)
\(984\) 0 0
\(985\) 0.264587 0.00843044
\(986\) 9.55240 0.304210
\(987\) 0 0
\(988\) 1.62701 0.0517620
\(989\) 4.53259 0.144128
\(990\) 0 0
\(991\) 56.1881 1.78487 0.892437 0.451173i \(-0.148994\pi\)
0.892437 + 0.451173i \(0.148994\pi\)
\(992\) −43.9055 −1.39400
\(993\) 0 0
\(994\) −80.6884 −2.55928
\(995\) −0.717750 −0.0227542
\(996\) 0 0
\(997\) 43.1483 1.36652 0.683261 0.730175i \(-0.260561\pi\)
0.683261 + 0.730175i \(0.260561\pi\)
\(998\) −34.6969 −1.09831
\(999\) 0 0
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 2151.2.a.e.1.6 6
3.2 odd 2 717.2.a.d.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
717.2.a.d.1.1 6 3.2 odd 2
2151.2.a.e.1.6 6 1.1 even 1 trivial