Properties

Label 6003.2.a.m.1.9
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $11$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
Defining polynomial: \(x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 2001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-1.94502\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.94502 q^{2} +1.78310 q^{4} -0.890641 q^{5} -3.69089 q^{7} -0.421884 q^{8} +O(q^{10})\) \(q+1.94502 q^{2} +1.78310 q^{4} -0.890641 q^{5} -3.69089 q^{7} -0.421884 q^{8} -1.73231 q^{10} +4.50039 q^{11} -2.37833 q^{13} -7.17884 q^{14} -4.38676 q^{16} +8.08663 q^{17} +3.74291 q^{19} -1.58810 q^{20} +8.75335 q^{22} -1.00000 q^{23} -4.20676 q^{25} -4.62589 q^{26} -6.58120 q^{28} +1.00000 q^{29} +0.830492 q^{31} -7.68856 q^{32} +15.7286 q^{34} +3.28725 q^{35} -6.72421 q^{37} +7.28003 q^{38} +0.375747 q^{40} -5.54692 q^{41} -4.97595 q^{43} +8.02463 q^{44} -1.94502 q^{46} -11.9191 q^{47} +6.62264 q^{49} -8.18222 q^{50} -4.24078 q^{52} +5.72723 q^{53} -4.00823 q^{55} +1.55712 q^{56} +1.94502 q^{58} +4.08424 q^{59} -2.66889 q^{61} +1.61532 q^{62} -6.18087 q^{64} +2.11823 q^{65} -0.373417 q^{67} +14.4192 q^{68} +6.39377 q^{70} -11.6083 q^{71} -12.7226 q^{73} -13.0787 q^{74} +6.67397 q^{76} -16.6104 q^{77} -11.1606 q^{79} +3.90703 q^{80} -10.7889 q^{82} +0.182560 q^{83} -7.20228 q^{85} -9.67832 q^{86} -1.89864 q^{88} -0.217110 q^{89} +8.77813 q^{91} -1.78310 q^{92} -23.1828 q^{94} -3.33359 q^{95} +13.8496 q^{97} +12.8812 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.94502 1.37534 0.687668 0.726026i \(-0.258635\pi\)
0.687668 + 0.726026i \(0.258635\pi\)
\(3\) 0 0
\(4\) 1.78310 0.891548
\(5\) −0.890641 −0.398307 −0.199153 0.979968i \(-0.563819\pi\)
−0.199153 + 0.979968i \(0.563819\pi\)
\(6\) 0 0
\(7\) −3.69089 −1.39502 −0.697512 0.716573i \(-0.745710\pi\)
−0.697512 + 0.716573i \(0.745710\pi\)
\(8\) −0.421884 −0.149158
\(9\) 0 0
\(10\) −1.73231 −0.547805
\(11\) 4.50039 1.35692 0.678460 0.734638i \(-0.262648\pi\)
0.678460 + 0.734638i \(0.262648\pi\)
\(12\) 0 0
\(13\) −2.37833 −0.659629 −0.329815 0.944046i \(-0.606986\pi\)
−0.329815 + 0.944046i \(0.606986\pi\)
\(14\) −7.17884 −1.91863
\(15\) 0 0
\(16\) −4.38676 −1.09669
\(17\) 8.08663 1.96130 0.980648 0.195779i \(-0.0627236\pi\)
0.980648 + 0.195779i \(0.0627236\pi\)
\(18\) 0 0
\(19\) 3.74291 0.858683 0.429342 0.903142i \(-0.358746\pi\)
0.429342 + 0.903142i \(0.358746\pi\)
\(20\) −1.58810 −0.355109
\(21\) 0 0
\(22\) 8.75335 1.86622
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −4.20676 −0.841352
\(26\) −4.62589 −0.907211
\(27\) 0 0
\(28\) −6.58120 −1.24373
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 0.830492 0.149161 0.0745804 0.997215i \(-0.476238\pi\)
0.0745804 + 0.997215i \(0.476238\pi\)
\(32\) −7.68856 −1.35916
\(33\) 0 0
\(34\) 15.7286 2.69744
\(35\) 3.28725 0.555647
\(36\) 0 0
\(37\) −6.72421 −1.10545 −0.552727 0.833363i \(-0.686413\pi\)
−0.552727 + 0.833363i \(0.686413\pi\)
\(38\) 7.28003 1.18098
\(39\) 0 0
\(40\) 0.375747 0.0594108
\(41\) −5.54692 −0.866283 −0.433141 0.901326i \(-0.642595\pi\)
−0.433141 + 0.901326i \(0.642595\pi\)
\(42\) 0 0
\(43\) −4.97595 −0.758826 −0.379413 0.925227i \(-0.623874\pi\)
−0.379413 + 0.925227i \(0.623874\pi\)
\(44\) 8.02463 1.20976
\(45\) 0 0
\(46\) −1.94502 −0.286777
\(47\) −11.9191 −1.73857 −0.869286 0.494309i \(-0.835421\pi\)
−0.869286 + 0.494309i \(0.835421\pi\)
\(48\) 0 0
\(49\) 6.62264 0.946091
\(50\) −8.18222 −1.15714
\(51\) 0 0
\(52\) −4.24078 −0.588091
\(53\) 5.72723 0.786696 0.393348 0.919390i \(-0.371317\pi\)
0.393348 + 0.919390i \(0.371317\pi\)
\(54\) 0 0
\(55\) −4.00823 −0.540470
\(56\) 1.55712 0.208080
\(57\) 0 0
\(58\) 1.94502 0.255393
\(59\) 4.08424 0.531723 0.265861 0.964011i \(-0.414344\pi\)
0.265861 + 0.964011i \(0.414344\pi\)
\(60\) 0 0
\(61\) −2.66889 −0.341717 −0.170858 0.985296i \(-0.554654\pi\)
−0.170858 + 0.985296i \(0.554654\pi\)
\(62\) 1.61532 0.205146
\(63\) 0 0
\(64\) −6.18087 −0.772609
\(65\) 2.11823 0.262735
\(66\) 0 0
\(67\) −0.373417 −0.0456202 −0.0228101 0.999740i \(-0.507261\pi\)
−0.0228101 + 0.999740i \(0.507261\pi\)
\(68\) 14.4192 1.74859
\(69\) 0 0
\(70\) 6.39377 0.764201
\(71\) −11.6083 −1.37766 −0.688828 0.724925i \(-0.741875\pi\)
−0.688828 + 0.724925i \(0.741875\pi\)
\(72\) 0 0
\(73\) −12.7226 −1.48907 −0.744536 0.667582i \(-0.767329\pi\)
−0.744536 + 0.667582i \(0.767329\pi\)
\(74\) −13.0787 −1.52037
\(75\) 0 0
\(76\) 6.67397 0.765557
\(77\) −16.6104 −1.89294
\(78\) 0 0
\(79\) −11.1606 −1.25566 −0.627830 0.778350i \(-0.716057\pi\)
−0.627830 + 0.778350i \(0.716057\pi\)
\(80\) 3.90703 0.436819
\(81\) 0 0
\(82\) −10.7889 −1.19143
\(83\) 0.182560 0.0200385 0.0100193 0.999950i \(-0.496811\pi\)
0.0100193 + 0.999950i \(0.496811\pi\)
\(84\) 0 0
\(85\) −7.20228 −0.781197
\(86\) −9.67832 −1.04364
\(87\) 0 0
\(88\) −1.89864 −0.202396
\(89\) −0.217110 −0.0230136 −0.0115068 0.999934i \(-0.503663\pi\)
−0.0115068 + 0.999934i \(0.503663\pi\)
\(90\) 0 0
\(91\) 8.77813 0.920198
\(92\) −1.78310 −0.185901
\(93\) 0 0
\(94\) −23.1828 −2.39112
\(95\) −3.33359 −0.342019
\(96\) 0 0
\(97\) 13.8496 1.40621 0.703105 0.711086i \(-0.251797\pi\)
0.703105 + 0.711086i \(0.251797\pi\)
\(98\) 12.8812 1.30119
\(99\) 0 0
\(100\) −7.50105 −0.750105
\(101\) −2.55168 −0.253902 −0.126951 0.991909i \(-0.540519\pi\)
−0.126951 + 0.991909i \(0.540519\pi\)
\(102\) 0 0
\(103\) −12.9829 −1.27925 −0.639624 0.768688i \(-0.720910\pi\)
−0.639624 + 0.768688i \(0.720910\pi\)
\(104\) 1.00338 0.0983892
\(105\) 0 0
\(106\) 11.1396 1.08197
\(107\) 15.1805 1.46755 0.733775 0.679392i \(-0.237757\pi\)
0.733775 + 0.679392i \(0.237757\pi\)
\(108\) 0 0
\(109\) −5.87116 −0.562355 −0.281178 0.959656i \(-0.590725\pi\)
−0.281178 + 0.959656i \(0.590725\pi\)
\(110\) −7.79609 −0.743328
\(111\) 0 0
\(112\) 16.1910 1.52991
\(113\) −17.5604 −1.65195 −0.825974 0.563708i \(-0.809374\pi\)
−0.825974 + 0.563708i \(0.809374\pi\)
\(114\) 0 0
\(115\) 0.890641 0.0830527
\(116\) 1.78310 0.165556
\(117\) 0 0
\(118\) 7.94392 0.731297
\(119\) −29.8468 −2.73605
\(120\) 0 0
\(121\) 9.25354 0.841231
\(122\) −5.19105 −0.469975
\(123\) 0 0
\(124\) 1.48085 0.132984
\(125\) 8.19991 0.733423
\(126\) 0 0
\(127\) 6.07663 0.539214 0.269607 0.962970i \(-0.413106\pi\)
0.269607 + 0.962970i \(0.413106\pi\)
\(128\) 3.35522 0.296562
\(129\) 0 0
\(130\) 4.12000 0.361348
\(131\) −9.14993 −0.799433 −0.399717 0.916639i \(-0.630891\pi\)
−0.399717 + 0.916639i \(0.630891\pi\)
\(132\) 0 0
\(133\) −13.8147 −1.19788
\(134\) −0.726303 −0.0627430
\(135\) 0 0
\(136\) −3.41162 −0.292544
\(137\) −13.4962 −1.15306 −0.576529 0.817076i \(-0.695593\pi\)
−0.576529 + 0.817076i \(0.695593\pi\)
\(138\) 0 0
\(139\) 13.1825 1.11812 0.559062 0.829126i \(-0.311161\pi\)
0.559062 + 0.829126i \(0.311161\pi\)
\(140\) 5.86149 0.495386
\(141\) 0 0
\(142\) −22.5784 −1.89474
\(143\) −10.7034 −0.895064
\(144\) 0 0
\(145\) −0.890641 −0.0739637
\(146\) −24.7458 −2.04797
\(147\) 0 0
\(148\) −11.9899 −0.985564
\(149\) 6.62847 0.543025 0.271513 0.962435i \(-0.412476\pi\)
0.271513 + 0.962435i \(0.412476\pi\)
\(150\) 0 0
\(151\) 4.85570 0.395151 0.197576 0.980288i \(-0.436693\pi\)
0.197576 + 0.980288i \(0.436693\pi\)
\(152\) −1.57907 −0.128080
\(153\) 0 0
\(154\) −32.3076 −2.60342
\(155\) −0.739670 −0.0594117
\(156\) 0 0
\(157\) −11.5387 −0.920890 −0.460445 0.887688i \(-0.652310\pi\)
−0.460445 + 0.887688i \(0.652310\pi\)
\(158\) −21.7075 −1.72695
\(159\) 0 0
\(160\) 6.84775 0.541362
\(161\) 3.69089 0.290883
\(162\) 0 0
\(163\) 12.6736 0.992677 0.496338 0.868129i \(-0.334678\pi\)
0.496338 + 0.868129i \(0.334678\pi\)
\(164\) −9.89068 −0.772333
\(165\) 0 0
\(166\) 0.355082 0.0275597
\(167\) −10.0950 −0.781176 −0.390588 0.920566i \(-0.627728\pi\)
−0.390588 + 0.920566i \(0.627728\pi\)
\(168\) 0 0
\(169\) −7.34356 −0.564889
\(170\) −14.0086 −1.07441
\(171\) 0 0
\(172\) −8.87260 −0.676529
\(173\) −8.38539 −0.637529 −0.318765 0.947834i \(-0.603268\pi\)
−0.318765 + 0.947834i \(0.603268\pi\)
\(174\) 0 0
\(175\) 15.5267 1.17371
\(176\) −19.7422 −1.48812
\(177\) 0 0
\(178\) −0.422283 −0.0316515
\(179\) 0.135648 0.0101388 0.00506941 0.999987i \(-0.498386\pi\)
0.00506941 + 0.999987i \(0.498386\pi\)
\(180\) 0 0
\(181\) 13.4258 0.997929 0.498965 0.866622i \(-0.333714\pi\)
0.498965 + 0.866622i \(0.333714\pi\)
\(182\) 17.0736 1.26558
\(183\) 0 0
\(184\) 0.421884 0.0311017
\(185\) 5.98885 0.440309
\(186\) 0 0
\(187\) 36.3930 2.66132
\(188\) −21.2528 −1.55002
\(189\) 0 0
\(190\) −6.48389 −0.470391
\(191\) −14.9265 −1.08004 −0.540021 0.841651i \(-0.681584\pi\)
−0.540021 + 0.841651i \(0.681584\pi\)
\(192\) 0 0
\(193\) −20.1714 −1.45197 −0.725985 0.687710i \(-0.758616\pi\)
−0.725985 + 0.687710i \(0.758616\pi\)
\(194\) 26.9376 1.93401
\(195\) 0 0
\(196\) 11.8088 0.843485
\(197\) −3.29903 −0.235046 −0.117523 0.993070i \(-0.537495\pi\)
−0.117523 + 0.993070i \(0.537495\pi\)
\(198\) 0 0
\(199\) −18.8208 −1.33417 −0.667087 0.744980i \(-0.732459\pi\)
−0.667087 + 0.744980i \(0.732459\pi\)
\(200\) 1.77476 0.125495
\(201\) 0 0
\(202\) −4.96307 −0.349200
\(203\) −3.69089 −0.259049
\(204\) 0 0
\(205\) 4.94031 0.345046
\(206\) −25.2521 −1.75939
\(207\) 0 0
\(208\) 10.4332 0.723409
\(209\) 16.8446 1.16516
\(210\) 0 0
\(211\) 4.25252 0.292756 0.146378 0.989229i \(-0.453238\pi\)
0.146378 + 0.989229i \(0.453238\pi\)
\(212\) 10.2122 0.701377
\(213\) 0 0
\(214\) 29.5263 2.01837
\(215\) 4.43179 0.302245
\(216\) 0 0
\(217\) −3.06525 −0.208083
\(218\) −11.4195 −0.773427
\(219\) 0 0
\(220\) −7.14706 −0.481855
\(221\) −19.2326 −1.29373
\(222\) 0 0
\(223\) −2.65381 −0.177712 −0.0888560 0.996044i \(-0.528321\pi\)
−0.0888560 + 0.996044i \(0.528321\pi\)
\(224\) 28.3776 1.89606
\(225\) 0 0
\(226\) −34.1554 −2.27198
\(227\) −23.1112 −1.53394 −0.766972 0.641681i \(-0.778237\pi\)
−0.766972 + 0.641681i \(0.778237\pi\)
\(228\) 0 0
\(229\) 17.6282 1.16490 0.582452 0.812865i \(-0.302093\pi\)
0.582452 + 0.812865i \(0.302093\pi\)
\(230\) 1.73231 0.114225
\(231\) 0 0
\(232\) −0.421884 −0.0276980
\(233\) 3.16486 0.207337 0.103668 0.994612i \(-0.466942\pi\)
0.103668 + 0.994612i \(0.466942\pi\)
\(234\) 0 0
\(235\) 10.6156 0.692485
\(236\) 7.28259 0.474056
\(237\) 0 0
\(238\) −58.0526 −3.76299
\(239\) −12.0664 −0.780509 −0.390255 0.920707i \(-0.627613\pi\)
−0.390255 + 0.920707i \(0.627613\pi\)
\(240\) 0 0
\(241\) 15.9750 1.02904 0.514519 0.857479i \(-0.327971\pi\)
0.514519 + 0.857479i \(0.327971\pi\)
\(242\) 17.9983 1.15697
\(243\) 0 0
\(244\) −4.75889 −0.304657
\(245\) −5.89839 −0.376834
\(246\) 0 0
\(247\) −8.90187 −0.566413
\(248\) −0.350371 −0.0222486
\(249\) 0 0
\(250\) 15.9490 1.00870
\(251\) −19.0291 −1.20111 −0.600555 0.799584i \(-0.705053\pi\)
−0.600555 + 0.799584i \(0.705053\pi\)
\(252\) 0 0
\(253\) −4.50039 −0.282937
\(254\) 11.8192 0.741600
\(255\) 0 0
\(256\) 18.8877 1.18048
\(257\) −3.28939 −0.205186 −0.102593 0.994723i \(-0.532714\pi\)
−0.102593 + 0.994723i \(0.532714\pi\)
\(258\) 0 0
\(259\) 24.8183 1.54213
\(260\) 3.77701 0.234240
\(261\) 0 0
\(262\) −17.7968 −1.09949
\(263\) 6.60009 0.406979 0.203489 0.979077i \(-0.434772\pi\)
0.203489 + 0.979077i \(0.434772\pi\)
\(264\) 0 0
\(265\) −5.10091 −0.313346
\(266\) −26.8698 −1.64749
\(267\) 0 0
\(268\) −0.665838 −0.0406725
\(269\) 3.23293 0.197115 0.0985575 0.995131i \(-0.468577\pi\)
0.0985575 + 0.995131i \(0.468577\pi\)
\(270\) 0 0
\(271\) −2.16831 −0.131715 −0.0658576 0.997829i \(-0.520978\pi\)
−0.0658576 + 0.997829i \(0.520978\pi\)
\(272\) −35.4741 −2.15093
\(273\) 0 0
\(274\) −26.2504 −1.58584
\(275\) −18.9321 −1.14165
\(276\) 0 0
\(277\) 9.47700 0.569418 0.284709 0.958614i \(-0.408103\pi\)
0.284709 + 0.958614i \(0.408103\pi\)
\(278\) 25.6402 1.53779
\(279\) 0 0
\(280\) −1.38684 −0.0828794
\(281\) 9.93844 0.592878 0.296439 0.955052i \(-0.404201\pi\)
0.296439 + 0.955052i \(0.404201\pi\)
\(282\) 0 0
\(283\) 30.9884 1.84207 0.921033 0.389484i \(-0.127347\pi\)
0.921033 + 0.389484i \(0.127347\pi\)
\(284\) −20.6988 −1.22825
\(285\) 0 0
\(286\) −20.8183 −1.23101
\(287\) 20.4730 1.20849
\(288\) 0 0
\(289\) 48.3936 2.84668
\(290\) −1.73231 −0.101725
\(291\) 0 0
\(292\) −22.6857 −1.32758
\(293\) −10.0605 −0.587741 −0.293871 0.955845i \(-0.594943\pi\)
−0.293871 + 0.955845i \(0.594943\pi\)
\(294\) 0 0
\(295\) −3.63759 −0.211789
\(296\) 2.83683 0.164888
\(297\) 0 0
\(298\) 12.8925 0.746842
\(299\) 2.37833 0.137542
\(300\) 0 0
\(301\) 18.3657 1.05858
\(302\) 9.44442 0.543465
\(303\) 0 0
\(304\) −16.4193 −0.941710
\(305\) 2.37703 0.136108
\(306\) 0 0
\(307\) 8.96988 0.511938 0.255969 0.966685i \(-0.417605\pi\)
0.255969 + 0.966685i \(0.417605\pi\)
\(308\) −29.6180 −1.68764
\(309\) 0 0
\(310\) −1.43867 −0.0817110
\(311\) −7.22707 −0.409810 −0.204905 0.978782i \(-0.565688\pi\)
−0.204905 + 0.978782i \(0.565688\pi\)
\(312\) 0 0
\(313\) −16.3038 −0.921543 −0.460772 0.887519i \(-0.652427\pi\)
−0.460772 + 0.887519i \(0.652427\pi\)
\(314\) −22.4430 −1.26653
\(315\) 0 0
\(316\) −19.9003 −1.11948
\(317\) 14.1617 0.795399 0.397700 0.917516i \(-0.369809\pi\)
0.397700 + 0.917516i \(0.369809\pi\)
\(318\) 0 0
\(319\) 4.50039 0.251974
\(320\) 5.50494 0.307735
\(321\) 0 0
\(322\) 7.17884 0.400061
\(323\) 30.2676 1.68413
\(324\) 0 0
\(325\) 10.0050 0.554980
\(326\) 24.6505 1.36526
\(327\) 0 0
\(328\) 2.34015 0.129213
\(329\) 43.9919 2.42535
\(330\) 0 0
\(331\) 5.91686 0.325220 0.162610 0.986690i \(-0.448009\pi\)
0.162610 + 0.986690i \(0.448009\pi\)
\(332\) 0.325522 0.0178653
\(333\) 0 0
\(334\) −19.6350 −1.07438
\(335\) 0.332580 0.0181708
\(336\) 0 0
\(337\) −27.4448 −1.49501 −0.747506 0.664256i \(-0.768749\pi\)
−0.747506 + 0.664256i \(0.768749\pi\)
\(338\) −14.2834 −0.776912
\(339\) 0 0
\(340\) −12.8424 −0.696474
\(341\) 3.73754 0.202399
\(342\) 0 0
\(343\) 1.39280 0.0752039
\(344\) 2.09927 0.113185
\(345\) 0 0
\(346\) −16.3097 −0.876817
\(347\) 20.7086 1.11170 0.555849 0.831283i \(-0.312393\pi\)
0.555849 + 0.831283i \(0.312393\pi\)
\(348\) 0 0
\(349\) −5.21746 −0.279284 −0.139642 0.990202i \(-0.544595\pi\)
−0.139642 + 0.990202i \(0.544595\pi\)
\(350\) 30.1997 1.61424
\(351\) 0 0
\(352\) −34.6016 −1.84427
\(353\) 30.2413 1.60958 0.804791 0.593559i \(-0.202277\pi\)
0.804791 + 0.593559i \(0.202277\pi\)
\(354\) 0 0
\(355\) 10.3389 0.548730
\(356\) −0.387128 −0.0205177
\(357\) 0 0
\(358\) 0.263838 0.0139443
\(359\) 3.46133 0.182682 0.0913411 0.995820i \(-0.470885\pi\)
0.0913411 + 0.995820i \(0.470885\pi\)
\(360\) 0 0
\(361\) −4.99060 −0.262663
\(362\) 26.1134 1.37249
\(363\) 0 0
\(364\) 15.6522 0.820401
\(365\) 11.3313 0.593107
\(366\) 0 0
\(367\) 2.14876 0.112164 0.0560821 0.998426i \(-0.482139\pi\)
0.0560821 + 0.998426i \(0.482139\pi\)
\(368\) 4.38676 0.228676
\(369\) 0 0
\(370\) 11.6484 0.605573
\(371\) −21.1386 −1.09746
\(372\) 0 0
\(373\) −35.8019 −1.85375 −0.926877 0.375365i \(-0.877517\pi\)
−0.926877 + 0.375365i \(0.877517\pi\)
\(374\) 70.7851 3.66021
\(375\) 0 0
\(376\) 5.02845 0.259323
\(377\) −2.37833 −0.122490
\(378\) 0 0
\(379\) 21.1506 1.08643 0.543216 0.839593i \(-0.317206\pi\)
0.543216 + 0.839593i \(0.317206\pi\)
\(380\) −5.94411 −0.304926
\(381\) 0 0
\(382\) −29.0323 −1.48542
\(383\) 12.5981 0.643732 0.321866 0.946785i \(-0.395690\pi\)
0.321866 + 0.946785i \(0.395690\pi\)
\(384\) 0 0
\(385\) 14.7939 0.753969
\(386\) −39.2338 −1.99695
\(387\) 0 0
\(388\) 24.6951 1.25370
\(389\) 27.2193 1.38008 0.690038 0.723773i \(-0.257594\pi\)
0.690038 + 0.723773i \(0.257594\pi\)
\(390\) 0 0
\(391\) −8.08663 −0.408958
\(392\) −2.79398 −0.141117
\(393\) 0 0
\(394\) −6.41668 −0.323268
\(395\) 9.94005 0.500138
\(396\) 0 0
\(397\) 1.53013 0.0767952 0.0383976 0.999263i \(-0.487775\pi\)
0.0383976 + 0.999263i \(0.487775\pi\)
\(398\) −36.6069 −1.83494
\(399\) 0 0
\(400\) 18.4541 0.922703
\(401\) 24.0237 1.19969 0.599843 0.800118i \(-0.295230\pi\)
0.599843 + 0.800118i \(0.295230\pi\)
\(402\) 0 0
\(403\) −1.97518 −0.0983908
\(404\) −4.54989 −0.226366
\(405\) 0 0
\(406\) −7.17884 −0.356280
\(407\) −30.2616 −1.50001
\(408\) 0 0
\(409\) 3.44189 0.170190 0.0850951 0.996373i \(-0.472881\pi\)
0.0850951 + 0.996373i \(0.472881\pi\)
\(410\) 9.60899 0.474554
\(411\) 0 0
\(412\) −23.1498 −1.14051
\(413\) −15.0745 −0.741766
\(414\) 0 0
\(415\) −0.162595 −0.00798149
\(416\) 18.2859 0.896541
\(417\) 0 0
\(418\) 32.7630 1.60249
\(419\) 4.54765 0.222167 0.111084 0.993811i \(-0.464568\pi\)
0.111084 + 0.993811i \(0.464568\pi\)
\(420\) 0 0
\(421\) −7.22743 −0.352243 −0.176122 0.984368i \(-0.556355\pi\)
−0.176122 + 0.984368i \(0.556355\pi\)
\(422\) 8.27123 0.402637
\(423\) 0 0
\(424\) −2.41623 −0.117342
\(425\) −34.0185 −1.65014
\(426\) 0 0
\(427\) 9.85059 0.476703
\(428\) 27.0682 1.30839
\(429\) 0 0
\(430\) 8.61991 0.415689
\(431\) 30.8300 1.48503 0.742515 0.669830i \(-0.233633\pi\)
0.742515 + 0.669830i \(0.233633\pi\)
\(432\) 0 0
\(433\) 6.41433 0.308253 0.154126 0.988051i \(-0.450744\pi\)
0.154126 + 0.988051i \(0.450744\pi\)
\(434\) −5.96197 −0.286184
\(435\) 0 0
\(436\) −10.4688 −0.501367
\(437\) −3.74291 −0.179048
\(438\) 0 0
\(439\) −5.00105 −0.238687 −0.119344 0.992853i \(-0.538079\pi\)
−0.119344 + 0.992853i \(0.538079\pi\)
\(440\) 1.69101 0.0806156
\(441\) 0 0
\(442\) −37.4078 −1.77931
\(443\) −32.0940 −1.52483 −0.762416 0.647087i \(-0.775987\pi\)
−0.762416 + 0.647087i \(0.775987\pi\)
\(444\) 0 0
\(445\) 0.193367 0.00916648
\(446\) −5.16170 −0.244414
\(447\) 0 0
\(448\) 22.8129 1.07781
\(449\) −4.71662 −0.222591 −0.111296 0.993787i \(-0.535500\pi\)
−0.111296 + 0.993787i \(0.535500\pi\)
\(450\) 0 0
\(451\) −24.9633 −1.17548
\(452\) −31.3119 −1.47279
\(453\) 0 0
\(454\) −44.9517 −2.10969
\(455\) −7.81816 −0.366521
\(456\) 0 0
\(457\) −15.3936 −0.720083 −0.360042 0.932936i \(-0.617237\pi\)
−0.360042 + 0.932936i \(0.617237\pi\)
\(458\) 34.2871 1.60213
\(459\) 0 0
\(460\) 1.58810 0.0740454
\(461\) −5.23341 −0.243744 −0.121872 0.992546i \(-0.538890\pi\)
−0.121872 + 0.992546i \(0.538890\pi\)
\(462\) 0 0
\(463\) 25.7280 1.19568 0.597841 0.801615i \(-0.296026\pi\)
0.597841 + 0.801615i \(0.296026\pi\)
\(464\) −4.38676 −0.203650
\(465\) 0 0
\(466\) 6.15571 0.285158
\(467\) −14.6282 −0.676914 −0.338457 0.940982i \(-0.609905\pi\)
−0.338457 + 0.940982i \(0.609905\pi\)
\(468\) 0 0
\(469\) 1.37824 0.0636412
\(470\) 20.6475 0.952399
\(471\) 0 0
\(472\) −1.72307 −0.0793109
\(473\) −22.3937 −1.02967
\(474\) 0 0
\(475\) −15.7455 −0.722455
\(476\) −53.2197 −2.43932
\(477\) 0 0
\(478\) −23.4693 −1.07346
\(479\) −26.9689 −1.23224 −0.616121 0.787652i \(-0.711297\pi\)
−0.616121 + 0.787652i \(0.711297\pi\)
\(480\) 0 0
\(481\) 15.9924 0.729189
\(482\) 31.0716 1.41527
\(483\) 0 0
\(484\) 16.4999 0.749997
\(485\) −12.3350 −0.560102
\(486\) 0 0
\(487\) −9.49480 −0.430251 −0.215125 0.976586i \(-0.569016\pi\)
−0.215125 + 0.976586i \(0.569016\pi\)
\(488\) 1.12596 0.0509700
\(489\) 0 0
\(490\) −11.4725 −0.518274
\(491\) −40.7189 −1.83762 −0.918810 0.394701i \(-0.870848\pi\)
−0.918810 + 0.394701i \(0.870848\pi\)
\(492\) 0 0
\(493\) 8.08663 0.364204
\(494\) −17.3143 −0.779007
\(495\) 0 0
\(496\) −3.64317 −0.163583
\(497\) 42.8451 1.92186
\(498\) 0 0
\(499\) 7.73103 0.346088 0.173044 0.984914i \(-0.444640\pi\)
0.173044 + 0.984914i \(0.444640\pi\)
\(500\) 14.6212 0.653881
\(501\) 0 0
\(502\) −37.0120 −1.65193
\(503\) 17.0295 0.759309 0.379655 0.925128i \(-0.376043\pi\)
0.379655 + 0.925128i \(0.376043\pi\)
\(504\) 0 0
\(505\) 2.27263 0.101131
\(506\) −8.75335 −0.389134
\(507\) 0 0
\(508\) 10.8352 0.480735
\(509\) 43.3883 1.92315 0.961576 0.274538i \(-0.0885250\pi\)
0.961576 + 0.274538i \(0.0885250\pi\)
\(510\) 0 0
\(511\) 46.9578 2.07729
\(512\) 30.0265 1.32700
\(513\) 0 0
\(514\) −6.39792 −0.282200
\(515\) 11.5631 0.509533
\(516\) 0 0
\(517\) −53.6404 −2.35910
\(518\) 48.2720 2.12095
\(519\) 0 0
\(520\) −0.893648 −0.0391891
\(521\) 29.4799 1.29154 0.645769 0.763533i \(-0.276537\pi\)
0.645769 + 0.763533i \(0.276537\pi\)
\(522\) 0 0
\(523\) −29.3504 −1.28340 −0.641702 0.766954i \(-0.721771\pi\)
−0.641702 + 0.766954i \(0.721771\pi\)
\(524\) −16.3152 −0.712733
\(525\) 0 0
\(526\) 12.8373 0.559732
\(527\) 6.71588 0.292548
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −9.92136 −0.430956
\(531\) 0 0
\(532\) −24.6329 −1.06797
\(533\) 13.1924 0.571425
\(534\) 0 0
\(535\) −13.5203 −0.584535
\(536\) 0.157539 0.00680463
\(537\) 0 0
\(538\) 6.28810 0.271099
\(539\) 29.8045 1.28377
\(540\) 0 0
\(541\) −13.9790 −0.601005 −0.300503 0.953781i \(-0.597154\pi\)
−0.300503 + 0.953781i \(0.597154\pi\)
\(542\) −4.21739 −0.181153
\(543\) 0 0
\(544\) −62.1746 −2.66571
\(545\) 5.22910 0.223990
\(546\) 0 0
\(547\) −15.1676 −0.648522 −0.324261 0.945968i \(-0.605116\pi\)
−0.324261 + 0.945968i \(0.605116\pi\)
\(548\) −24.0650 −1.02801
\(549\) 0 0
\(550\) −36.8232 −1.57015
\(551\) 3.74291 0.159453
\(552\) 0 0
\(553\) 41.1923 1.75168
\(554\) 18.4329 0.783141
\(555\) 0 0
\(556\) 23.5056 0.996860
\(557\) −16.5036 −0.699282 −0.349641 0.936884i \(-0.613696\pi\)
−0.349641 + 0.936884i \(0.613696\pi\)
\(558\) 0 0
\(559\) 11.8344 0.500544
\(560\) −14.4204 −0.609373
\(561\) 0 0
\(562\) 19.3304 0.815406
\(563\) 37.6335 1.58606 0.793032 0.609181i \(-0.208502\pi\)
0.793032 + 0.609181i \(0.208502\pi\)
\(564\) 0 0
\(565\) 15.6400 0.657982
\(566\) 60.2729 2.53346
\(567\) 0 0
\(568\) 4.89737 0.205489
\(569\) −27.3924 −1.14835 −0.574174 0.818733i \(-0.694677\pi\)
−0.574174 + 0.818733i \(0.694677\pi\)
\(570\) 0 0
\(571\) 37.6260 1.57460 0.787300 0.616570i \(-0.211478\pi\)
0.787300 + 0.616570i \(0.211478\pi\)
\(572\) −19.0852 −0.797992
\(573\) 0 0
\(574\) 39.8204 1.66207
\(575\) 4.20676 0.175434
\(576\) 0 0
\(577\) 2.57125 0.107043 0.0535213 0.998567i \(-0.482956\pi\)
0.0535213 + 0.998567i \(0.482956\pi\)
\(578\) 94.1264 3.91514
\(579\) 0 0
\(580\) −1.58810 −0.0659421
\(581\) −0.673808 −0.0279543
\(582\) 0 0
\(583\) 25.7748 1.06748
\(584\) 5.36747 0.222108
\(585\) 0 0
\(586\) −19.5679 −0.808341
\(587\) 31.4684 1.29884 0.649421 0.760429i \(-0.275011\pi\)
0.649421 + 0.760429i \(0.275011\pi\)
\(588\) 0 0
\(589\) 3.10846 0.128082
\(590\) −7.07518 −0.291281
\(591\) 0 0
\(592\) 29.4975 1.21234
\(593\) −17.9331 −0.736426 −0.368213 0.929742i \(-0.620030\pi\)
−0.368213 + 0.929742i \(0.620030\pi\)
\(594\) 0 0
\(595\) 26.5828 1.08979
\(596\) 11.8192 0.484133
\(597\) 0 0
\(598\) 4.62589 0.189167
\(599\) −36.3152 −1.48380 −0.741900 0.670510i \(-0.766075\pi\)
−0.741900 + 0.670510i \(0.766075\pi\)
\(600\) 0 0
\(601\) −20.3773 −0.831208 −0.415604 0.909546i \(-0.636430\pi\)
−0.415604 + 0.909546i \(0.636430\pi\)
\(602\) 35.7216 1.45590
\(603\) 0 0
\(604\) 8.65817 0.352296
\(605\) −8.24158 −0.335068
\(606\) 0 0
\(607\) 33.7527 1.36998 0.684991 0.728552i \(-0.259806\pi\)
0.684991 + 0.728552i \(0.259806\pi\)
\(608\) −28.7776 −1.16709
\(609\) 0 0
\(610\) 4.62336 0.187194
\(611\) 28.3474 1.14681
\(612\) 0 0
\(613\) 8.15566 0.329404 0.164702 0.986343i \(-0.447334\pi\)
0.164702 + 0.986343i \(0.447334\pi\)
\(614\) 17.4466 0.704087
\(615\) 0 0
\(616\) 7.00767 0.282347
\(617\) −39.4382 −1.58772 −0.793861 0.608099i \(-0.791932\pi\)
−0.793861 + 0.608099i \(0.791932\pi\)
\(618\) 0 0
\(619\) −22.8899 −0.920024 −0.460012 0.887913i \(-0.652155\pi\)
−0.460012 + 0.887913i \(0.652155\pi\)
\(620\) −1.31890 −0.0529684
\(621\) 0 0
\(622\) −14.0568 −0.563626
\(623\) 0.801329 0.0321046
\(624\) 0 0
\(625\) 13.7306 0.549225
\(626\) −31.7111 −1.26743
\(627\) 0 0
\(628\) −20.5746 −0.821017
\(629\) −54.3762 −2.16812
\(630\) 0 0
\(631\) 10.4183 0.414747 0.207374 0.978262i \(-0.433508\pi\)
0.207374 + 0.978262i \(0.433508\pi\)
\(632\) 4.70846 0.187292
\(633\) 0 0
\(634\) 27.5447 1.09394
\(635\) −5.41210 −0.214773
\(636\) 0 0
\(637\) −15.7508 −0.624069
\(638\) 8.75335 0.346548
\(639\) 0 0
\(640\) −2.98830 −0.118123
\(641\) −34.5328 −1.36396 −0.681982 0.731369i \(-0.738882\pi\)
−0.681982 + 0.731369i \(0.738882\pi\)
\(642\) 0 0
\(643\) 1.08338 0.0427243 0.0213621 0.999772i \(-0.493200\pi\)
0.0213621 + 0.999772i \(0.493200\pi\)
\(644\) 6.58120 0.259336
\(645\) 0 0
\(646\) 58.8710 2.31625
\(647\) 37.1584 1.46085 0.730424 0.682994i \(-0.239322\pi\)
0.730424 + 0.682994i \(0.239322\pi\)
\(648\) 0 0
\(649\) 18.3807 0.721505
\(650\) 19.4600 0.763284
\(651\) 0 0
\(652\) 22.5983 0.885019
\(653\) 23.3144 0.912362 0.456181 0.889887i \(-0.349217\pi\)
0.456181 + 0.889887i \(0.349217\pi\)
\(654\) 0 0
\(655\) 8.14930 0.318419
\(656\) 24.3330 0.950044
\(657\) 0 0
\(658\) 85.5650 3.33567
\(659\) 48.4850 1.88871 0.944355 0.328929i \(-0.106688\pi\)
0.944355 + 0.328929i \(0.106688\pi\)
\(660\) 0 0
\(661\) −2.79308 −0.108638 −0.0543191 0.998524i \(-0.517299\pi\)
−0.0543191 + 0.998524i \(0.517299\pi\)
\(662\) 11.5084 0.447287
\(663\) 0 0
\(664\) −0.0770190 −0.00298892
\(665\) 12.3039 0.477125
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) −18.0004 −0.696456
\(669\) 0 0
\(670\) 0.646875 0.0249910
\(671\) −12.0111 −0.463682
\(672\) 0 0
\(673\) 13.8118 0.532406 0.266203 0.963917i \(-0.414231\pi\)
0.266203 + 0.963917i \(0.414231\pi\)
\(674\) −53.3805 −2.05614
\(675\) 0 0
\(676\) −13.0943 −0.503626
\(677\) −28.5318 −1.09657 −0.548284 0.836292i \(-0.684719\pi\)
−0.548284 + 0.836292i \(0.684719\pi\)
\(678\) 0 0
\(679\) −51.1171 −1.96170
\(680\) 3.03852 0.116522
\(681\) 0 0
\(682\) 7.26958 0.278367
\(683\) 6.40227 0.244976 0.122488 0.992470i \(-0.460913\pi\)
0.122488 + 0.992470i \(0.460913\pi\)
\(684\) 0 0
\(685\) 12.0203 0.459271
\(686\) 2.70901 0.103431
\(687\) 0 0
\(688\) 21.8283 0.832197
\(689\) −13.6212 −0.518928
\(690\) 0 0
\(691\) −13.6105 −0.517767 −0.258883 0.965909i \(-0.583355\pi\)
−0.258883 + 0.965909i \(0.583355\pi\)
\(692\) −14.9519 −0.568388
\(693\) 0 0
\(694\) 40.2787 1.52896
\(695\) −11.7409 −0.445356
\(696\) 0 0
\(697\) −44.8559 −1.69904
\(698\) −10.1481 −0.384110
\(699\) 0 0
\(700\) 27.6855 1.04641
\(701\) 34.8262 1.31537 0.657683 0.753295i \(-0.271537\pi\)
0.657683 + 0.753295i \(0.271537\pi\)
\(702\) 0 0
\(703\) −25.1681 −0.949234
\(704\) −27.8164 −1.04837
\(705\) 0 0
\(706\) 58.8199 2.21371
\(707\) 9.41797 0.354199
\(708\) 0 0
\(709\) 20.7395 0.778887 0.389444 0.921050i \(-0.372667\pi\)
0.389444 + 0.921050i \(0.372667\pi\)
\(710\) 20.1093 0.754687
\(711\) 0 0
\(712\) 0.0915952 0.00343268
\(713\) −0.830492 −0.0311022
\(714\) 0 0
\(715\) 9.53289 0.356510
\(716\) 0.241874 0.00903924
\(717\) 0 0
\(718\) 6.73235 0.251249
\(719\) −34.7376 −1.29549 −0.647747 0.761856i \(-0.724289\pi\)
−0.647747 + 0.761856i \(0.724289\pi\)
\(720\) 0 0
\(721\) 47.9186 1.78458
\(722\) −9.70680 −0.361250
\(723\) 0 0
\(724\) 23.9394 0.889702
\(725\) −4.20676 −0.156235
\(726\) 0 0
\(727\) −48.7362 −1.80753 −0.903763 0.428033i \(-0.859207\pi\)
−0.903763 + 0.428033i \(0.859207\pi\)
\(728\) −3.70335 −0.137255
\(729\) 0 0
\(730\) 22.0396 0.815722
\(731\) −40.2387 −1.48828
\(732\) 0 0
\(733\) 34.5425 1.27586 0.637929 0.770095i \(-0.279791\pi\)
0.637929 + 0.770095i \(0.279791\pi\)
\(734\) 4.17937 0.154264
\(735\) 0 0
\(736\) 7.68856 0.283404
\(737\) −1.68052 −0.0619029
\(738\) 0 0
\(739\) 0.863005 0.0317462 0.0158731 0.999874i \(-0.494947\pi\)
0.0158731 + 0.999874i \(0.494947\pi\)
\(740\) 10.6787 0.392557
\(741\) 0 0
\(742\) −41.1149 −1.50938
\(743\) −18.8605 −0.691924 −0.345962 0.938249i \(-0.612447\pi\)
−0.345962 + 0.938249i \(0.612447\pi\)
\(744\) 0 0
\(745\) −5.90358 −0.216290
\(746\) −69.6354 −2.54953
\(747\) 0 0
\(748\) 64.8922 2.37269
\(749\) −56.0293 −2.04727
\(750\) 0 0
\(751\) 35.9838 1.31307 0.656534 0.754297i \(-0.272022\pi\)
0.656534 + 0.754297i \(0.272022\pi\)
\(752\) 52.2860 1.90668
\(753\) 0 0
\(754\) −4.62589 −0.168465
\(755\) −4.32468 −0.157391
\(756\) 0 0
\(757\) −29.0366 −1.05535 −0.527676 0.849446i \(-0.676936\pi\)
−0.527676 + 0.849446i \(0.676936\pi\)
\(758\) 41.1383 1.49421
\(759\) 0 0
\(760\) 1.40639 0.0510150
\(761\) 23.6765 0.858274 0.429137 0.903239i \(-0.358818\pi\)
0.429137 + 0.903239i \(0.358818\pi\)
\(762\) 0 0
\(763\) 21.6698 0.784499
\(764\) −26.6153 −0.962909
\(765\) 0 0
\(766\) 24.5035 0.885347
\(767\) −9.71366 −0.350740
\(768\) 0 0
\(769\) −25.5332 −0.920752 −0.460376 0.887724i \(-0.652285\pi\)
−0.460376 + 0.887724i \(0.652285\pi\)
\(770\) 28.7745 1.03696
\(771\) 0 0
\(772\) −35.9676 −1.29450
\(773\) −11.8275 −0.425407 −0.212703 0.977117i \(-0.568227\pi\)
−0.212703 + 0.977117i \(0.568227\pi\)
\(774\) 0 0
\(775\) −3.49368 −0.125497
\(776\) −5.84290 −0.209748
\(777\) 0 0
\(778\) 52.9421 1.89807
\(779\) −20.7616 −0.743863
\(780\) 0 0
\(781\) −52.2421 −1.86937
\(782\) −15.7286 −0.562455
\(783\) 0 0
\(784\) −29.0519 −1.03757
\(785\) 10.2768 0.366796
\(786\) 0 0
\(787\) −25.5112 −0.909374 −0.454687 0.890651i \(-0.650249\pi\)
−0.454687 + 0.890651i \(0.650249\pi\)
\(788\) −5.88249 −0.209555
\(789\) 0 0
\(790\) 19.3336 0.687857
\(791\) 64.8136 2.30451
\(792\) 0 0
\(793\) 6.34750 0.225406
\(794\) 2.97614 0.105619
\(795\) 0 0
\(796\) −33.5594 −1.18948
\(797\) −47.4936 −1.68231 −0.841154 0.540795i \(-0.818124\pi\)
−0.841154 + 0.540795i \(0.818124\pi\)
\(798\) 0 0
\(799\) −96.3850 −3.40985
\(800\) 32.3439 1.14353
\(801\) 0 0
\(802\) 46.7265 1.64997
\(803\) −57.2569 −2.02055
\(804\) 0 0
\(805\) −3.28725 −0.115860
\(806\) −3.84176 −0.135320
\(807\) 0 0
\(808\) 1.07651 0.0378716
\(809\) −11.2763 −0.396453 −0.198226 0.980156i \(-0.563518\pi\)
−0.198226 + 0.980156i \(0.563518\pi\)
\(810\) 0 0
\(811\) −42.6721 −1.49842 −0.749210 0.662333i \(-0.769567\pi\)
−0.749210 + 0.662333i \(0.769567\pi\)
\(812\) −6.58120 −0.230955
\(813\) 0 0
\(814\) −58.8593 −2.06302
\(815\) −11.2877 −0.395390
\(816\) 0 0
\(817\) −18.6246 −0.651591
\(818\) 6.69453 0.234069
\(819\) 0 0
\(820\) 8.80904 0.307625
\(821\) −14.8975 −0.519925 −0.259963 0.965619i \(-0.583710\pi\)
−0.259963 + 0.965619i \(0.583710\pi\)
\(822\) 0 0
\(823\) 49.7000 1.73243 0.866216 0.499669i \(-0.166545\pi\)
0.866216 + 0.499669i \(0.166545\pi\)
\(824\) 5.47729 0.190810
\(825\) 0 0
\(826\) −29.3201 −1.02018
\(827\) −3.92447 −0.136467 −0.0682336 0.997669i \(-0.521736\pi\)
−0.0682336 + 0.997669i \(0.521736\pi\)
\(828\) 0 0
\(829\) 40.1066 1.39296 0.696480 0.717576i \(-0.254749\pi\)
0.696480 + 0.717576i \(0.254749\pi\)
\(830\) −0.316251 −0.0109772
\(831\) 0 0
\(832\) 14.7001 0.509635
\(833\) 53.5548 1.85557
\(834\) 0 0
\(835\) 8.99104 0.311148
\(836\) 30.0355 1.03880
\(837\) 0 0
\(838\) 8.84526 0.305554
\(839\) −10.9698 −0.378719 −0.189360 0.981908i \(-0.560641\pi\)
−0.189360 + 0.981908i \(0.560641\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −14.0575 −0.484453
\(843\) 0 0
\(844\) 7.58265 0.261006
\(845\) 6.54048 0.224999
\(846\) 0 0
\(847\) −34.1538 −1.17354
\(848\) −25.1240 −0.862762
\(849\) 0 0
\(850\) −66.1666 −2.26950
\(851\) 6.72421 0.230503
\(852\) 0 0
\(853\) −46.2251 −1.58272 −0.791359 0.611351i \(-0.790626\pi\)
−0.791359 + 0.611351i \(0.790626\pi\)
\(854\) 19.1596 0.655627
\(855\) 0 0
\(856\) −6.40439 −0.218897
\(857\) 19.2667 0.658137 0.329069 0.944306i \(-0.393265\pi\)
0.329069 + 0.944306i \(0.393265\pi\)
\(858\) 0 0
\(859\) −1.44604 −0.0493382 −0.0246691 0.999696i \(-0.507853\pi\)
−0.0246691 + 0.999696i \(0.507853\pi\)
\(860\) 7.90230 0.269466
\(861\) 0 0
\(862\) 59.9649 2.04241
\(863\) −5.63105 −0.191683 −0.0958416 0.995397i \(-0.530554\pi\)
−0.0958416 + 0.995397i \(0.530554\pi\)
\(864\) 0 0
\(865\) 7.46837 0.253932
\(866\) 12.4760 0.423951
\(867\) 0 0
\(868\) −5.46563 −0.185516
\(869\) −50.2269 −1.70383
\(870\) 0 0
\(871\) 0.888108 0.0300924
\(872\) 2.47695 0.0838800
\(873\) 0 0
\(874\) −7.28003 −0.246251
\(875\) −30.2649 −1.02314
\(876\) 0 0
\(877\) 4.44244 0.150011 0.0750053 0.997183i \(-0.476103\pi\)
0.0750053 + 0.997183i \(0.476103\pi\)
\(878\) −9.72714 −0.328275
\(879\) 0 0
\(880\) 17.5832 0.592728
\(881\) −35.8832 −1.20894 −0.604468 0.796630i \(-0.706614\pi\)
−0.604468 + 0.796630i \(0.706614\pi\)
\(882\) 0 0
\(883\) −9.76965 −0.328775 −0.164387 0.986396i \(-0.552565\pi\)
−0.164387 + 0.986396i \(0.552565\pi\)
\(884\) −34.2936 −1.15342
\(885\) 0 0
\(886\) −62.4234 −2.09716
\(887\) 11.7923 0.395948 0.197974 0.980207i \(-0.436564\pi\)
0.197974 + 0.980207i \(0.436564\pi\)
\(888\) 0 0
\(889\) −22.4282 −0.752216
\(890\) 0.376102 0.0126070
\(891\) 0 0
\(892\) −4.73199 −0.158439
\(893\) −44.6120 −1.49288
\(894\) 0 0
\(895\) −0.120814 −0.00403836
\(896\) −12.3837 −0.413712
\(897\) 0 0
\(898\) −9.17392 −0.306138
\(899\) 0.830492 0.0276985
\(900\) 0 0
\(901\) 46.3140 1.54294
\(902\) −48.5541 −1.61667
\(903\) 0 0
\(904\) 7.40847 0.246402
\(905\) −11.9575 −0.397482
\(906\) 0 0
\(907\) 19.0093 0.631194 0.315597 0.948893i \(-0.397795\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(908\) −41.2094 −1.36758
\(909\) 0 0
\(910\) −15.2065 −0.504089
\(911\) 45.1868 1.49711 0.748553 0.663075i \(-0.230749\pi\)
0.748553 + 0.663075i \(0.230749\pi\)
\(912\) 0 0
\(913\) 0.821591 0.0271907
\(914\) −29.9409 −0.990356
\(915\) 0 0
\(916\) 31.4327 1.03857
\(917\) 33.7713 1.11523
\(918\) 0 0
\(919\) 10.6947 0.352785 0.176392 0.984320i \(-0.443557\pi\)
0.176392 + 0.984320i \(0.443557\pi\)
\(920\) −0.375747 −0.0123880
\(921\) 0 0
\(922\) −10.1791 −0.335230
\(923\) 27.6084 0.908742
\(924\) 0 0
\(925\) 28.2871 0.930075
\(926\) 50.0414 1.64446
\(927\) 0 0
\(928\) −7.68856 −0.252389
\(929\) −43.2595 −1.41930 −0.709649 0.704556i \(-0.751146\pi\)
−0.709649 + 0.704556i \(0.751146\pi\)
\(930\) 0 0
\(931\) 24.7880 0.812393
\(932\) 5.64325 0.184851
\(933\) 0 0
\(934\) −28.4522 −0.930984
\(935\) −32.4131 −1.06002
\(936\) 0 0
\(937\) −15.7181 −0.513487 −0.256744 0.966480i \(-0.582650\pi\)
−0.256744 + 0.966480i \(0.582650\pi\)
\(938\) 2.68070 0.0875280
\(939\) 0 0
\(940\) 18.9286 0.617383
\(941\) −27.5774 −0.898997 −0.449499 0.893281i \(-0.648397\pi\)
−0.449499 + 0.893281i \(0.648397\pi\)
\(942\) 0 0
\(943\) 5.54692 0.180632
\(944\) −17.9166 −0.583135
\(945\) 0 0
\(946\) −43.5562 −1.41614
\(947\) 11.1517 0.362383 0.181191 0.983448i \(-0.442005\pi\)
0.181191 + 0.983448i \(0.442005\pi\)
\(948\) 0 0
\(949\) 30.2586 0.982236
\(950\) −30.6254 −0.993618
\(951\) 0 0
\(952\) 12.5919 0.408106
\(953\) 8.64031 0.279887 0.139944 0.990159i \(-0.455308\pi\)
0.139944 + 0.990159i \(0.455308\pi\)
\(954\) 0 0
\(955\) 13.2941 0.430188
\(956\) −21.5155 −0.695861
\(957\) 0 0
\(958\) −52.4550 −1.69475
\(959\) 49.8130 1.60854
\(960\) 0 0
\(961\) −30.3103 −0.977751
\(962\) 31.1054 1.00288
\(963\) 0 0
\(964\) 28.4849 0.917436
\(965\) 17.9655 0.578330
\(966\) 0 0
\(967\) −38.8650 −1.24981 −0.624907 0.780699i \(-0.714863\pi\)
−0.624907 + 0.780699i \(0.714863\pi\)
\(968\) −3.90392 −0.125477
\(969\) 0 0
\(970\) −23.9918 −0.770329
\(971\) 18.1124 0.581254 0.290627 0.956836i \(-0.406136\pi\)
0.290627 + 0.956836i \(0.406136\pi\)
\(972\) 0 0
\(973\) −48.6550 −1.55981
\(974\) −18.4676 −0.591739
\(975\) 0 0
\(976\) 11.7078 0.374758
\(977\) −39.3962 −1.26040 −0.630198 0.776435i \(-0.717026\pi\)
−0.630198 + 0.776435i \(0.717026\pi\)
\(978\) 0 0
\(979\) −0.977081 −0.0312276
\(980\) −10.5174 −0.335966
\(981\) 0 0
\(982\) −79.1990 −2.52734
\(983\) −11.8203 −0.377010 −0.188505 0.982072i \(-0.560364\pi\)
−0.188505 + 0.982072i \(0.560364\pi\)
\(984\) 0 0
\(985\) 2.93825 0.0936205
\(986\) 15.7286 0.500902
\(987\) 0 0
\(988\) −15.8729 −0.504984
\(989\) 4.97595 0.158226
\(990\) 0 0
\(991\) 48.6281 1.54472 0.772361 0.635183i \(-0.219076\pi\)
0.772361 + 0.635183i \(0.219076\pi\)
\(992\) −6.38529 −0.202733
\(993\) 0 0
\(994\) 83.3344 2.64321
\(995\) 16.7626 0.531410
\(996\) 0 0
\(997\) −14.8680 −0.470874 −0.235437 0.971890i \(-0.575652\pi\)
−0.235437 + 0.971890i \(0.575652\pi\)
\(998\) 15.0370 0.475988
\(999\) 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 6003.2.a.m.1.9 11
3.2 odd 2 2001.2.a.l.1.3 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.3 11 3.2 odd 2
6003.2.a.m.1.9 11 1.1 even 1 trivial