Properties

Label 6003.2.a.m.1.4
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 1.4
Root \(1.76484\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.76484 q^{2} +1.11465 q^{4} +2.54815 q^{5} -4.97592 q^{7} +1.56250 q^{8} +O(q^{10})\) \(q-1.76484 q^{2} +1.11465 q^{4} +2.54815 q^{5} -4.97592 q^{7} +1.56250 q^{8} -4.49707 q^{10} -0.283045 q^{11} -0.170966 q^{13} +8.78168 q^{14} -4.98686 q^{16} -5.92041 q^{17} +4.65876 q^{19} +2.84029 q^{20} +0.499527 q^{22} -1.00000 q^{23} +1.49307 q^{25} +0.301727 q^{26} -5.54640 q^{28} +1.00000 q^{29} +8.96888 q^{31} +5.67599 q^{32} +10.4486 q^{34} -12.6794 q^{35} +0.201428 q^{37} -8.22195 q^{38} +3.98148 q^{40} +6.77658 q^{41} -2.97728 q^{43} -0.315495 q^{44} +1.76484 q^{46} -7.64176 q^{47} +17.7597 q^{49} -2.63502 q^{50} -0.190567 q^{52} -2.22897 q^{53} -0.721240 q^{55} -7.77487 q^{56} -1.76484 q^{58} +15.2006 q^{59} +1.08366 q^{61} -15.8286 q^{62} -0.0434802 q^{64} -0.435647 q^{65} -4.78799 q^{67} -6.59918 q^{68} +22.3770 q^{70} -15.9000 q^{71} +5.09595 q^{73} -0.355488 q^{74} +5.19288 q^{76} +1.40841 q^{77} +15.8153 q^{79} -12.7073 q^{80} -11.9596 q^{82} +4.95563 q^{83} -15.0861 q^{85} +5.25441 q^{86} -0.442257 q^{88} +3.87577 q^{89} +0.850713 q^{91} -1.11465 q^{92} +13.4865 q^{94} +11.8712 q^{95} -16.0439 q^{97} -31.3430 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76484 −1.24793 −0.623964 0.781453i \(-0.714479\pi\)
−0.623964 + 0.781453i \(0.714479\pi\)
\(3\) 0 0
\(4\) 1.11465 0.557325
\(5\) 2.54815 1.13957 0.569784 0.821795i \(-0.307027\pi\)
0.569784 + 0.821795i \(0.307027\pi\)
\(6\) 0 0
\(7\) −4.97592 −1.88072 −0.940360 0.340182i \(-0.889511\pi\)
−0.940360 + 0.340182i \(0.889511\pi\)
\(8\) 1.56250 0.552427
\(9\) 0 0
\(10\) −4.49707 −1.42210
\(11\) −0.283045 −0.0853411 −0.0426706 0.999089i \(-0.513587\pi\)
−0.0426706 + 0.999089i \(0.513587\pi\)
\(12\) 0 0
\(13\) −0.170966 −0.0474175 −0.0237087 0.999719i \(-0.507547\pi\)
−0.0237087 + 0.999719i \(0.507547\pi\)
\(14\) 8.78168 2.34700
\(15\) 0 0
\(16\) −4.98686 −1.24671
\(17\) −5.92041 −1.43591 −0.717956 0.696089i \(-0.754922\pi\)
−0.717956 + 0.696089i \(0.754922\pi\)
\(18\) 0 0
\(19\) 4.65876 1.06879 0.534396 0.845234i \(-0.320539\pi\)
0.534396 + 0.845234i \(0.320539\pi\)
\(20\) 2.84029 0.635109
\(21\) 0 0
\(22\) 0.499527 0.106500
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 1.49307 0.298613
\(26\) 0.301727 0.0591736
\(27\) 0 0
\(28\) −5.54640 −1.04817
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 8.96888 1.61086 0.805429 0.592692i \(-0.201935\pi\)
0.805429 + 0.592692i \(0.201935\pi\)
\(32\) 5.67599 1.00338
\(33\) 0 0
\(34\) 10.4486 1.79191
\(35\) −12.6794 −2.14321
\(36\) 0 0
\(37\) 0.201428 0.0331146 0.0165573 0.999863i \(-0.494729\pi\)
0.0165573 + 0.999863i \(0.494729\pi\)
\(38\) −8.22195 −1.33378
\(39\) 0 0
\(40\) 3.98148 0.629528
\(41\) 6.77658 1.05832 0.529162 0.848521i \(-0.322507\pi\)
0.529162 + 0.848521i \(0.322507\pi\)
\(42\) 0 0
\(43\) −2.97728 −0.454031 −0.227015 0.973891i \(-0.572897\pi\)
−0.227015 + 0.973891i \(0.572897\pi\)
\(44\) −0.315495 −0.0475627
\(45\) 0 0
\(46\) 1.76484 0.260211
\(47\) −7.64176 −1.11466 −0.557332 0.830290i \(-0.688175\pi\)
−0.557332 + 0.830290i \(0.688175\pi\)
\(48\) 0 0
\(49\) 17.7597 2.53711
\(50\) −2.63502 −0.372648
\(51\) 0 0
\(52\) −0.190567 −0.0264269
\(53\) −2.22897 −0.306173 −0.153087 0.988213i \(-0.548921\pi\)
−0.153087 + 0.988213i \(0.548921\pi\)
\(54\) 0 0
\(55\) −0.721240 −0.0972520
\(56\) −7.77487 −1.03896
\(57\) 0 0
\(58\) −1.76484 −0.231734
\(59\) 15.2006 1.97895 0.989474 0.144711i \(-0.0462252\pi\)
0.989474 + 0.144711i \(0.0462252\pi\)
\(60\) 0 0
\(61\) 1.08366 0.138748 0.0693741 0.997591i \(-0.477900\pi\)
0.0693741 + 0.997591i \(0.477900\pi\)
\(62\) −15.8286 −2.01023
\(63\) 0 0
\(64\) −0.0434802 −0.00543502
\(65\) −0.435647 −0.0540354
\(66\) 0 0
\(67\) −4.78799 −0.584946 −0.292473 0.956274i \(-0.594478\pi\)
−0.292473 + 0.956274i \(0.594478\pi\)
\(68\) −6.59918 −0.800269
\(69\) 0 0
\(70\) 22.3770 2.67457
\(71\) −15.9000 −1.88698 −0.943489 0.331404i \(-0.892478\pi\)
−0.943489 + 0.331404i \(0.892478\pi\)
\(72\) 0 0
\(73\) 5.09595 0.596436 0.298218 0.954498i \(-0.403608\pi\)
0.298218 + 0.954498i \(0.403608\pi\)
\(74\) −0.355488 −0.0413247
\(75\) 0 0
\(76\) 5.19288 0.595664
\(77\) 1.40841 0.160503
\(78\) 0 0
\(79\) 15.8153 1.77936 0.889678 0.456588i \(-0.150929\pi\)
0.889678 + 0.456588i \(0.150929\pi\)
\(80\) −12.7073 −1.42071
\(81\) 0 0
\(82\) −11.9596 −1.32071
\(83\) 4.95563 0.543951 0.271976 0.962304i \(-0.412323\pi\)
0.271976 + 0.962304i \(0.412323\pi\)
\(84\) 0 0
\(85\) −15.0861 −1.63632
\(86\) 5.25441 0.566597
\(87\) 0 0
\(88\) −0.442257 −0.0471448
\(89\) 3.87577 0.410830 0.205415 0.978675i \(-0.434146\pi\)
0.205415 + 0.978675i \(0.434146\pi\)
\(90\) 0 0
\(91\) 0.850713 0.0891790
\(92\) −1.11465 −0.116210
\(93\) 0 0
\(94\) 13.4865 1.39102
\(95\) 11.8712 1.21796
\(96\) 0 0
\(97\) −16.0439 −1.62901 −0.814507 0.580154i \(-0.802992\pi\)
−0.814507 + 0.580154i \(0.802992\pi\)
\(98\) −31.3430 −3.16613
\(99\) 0 0
\(100\) 1.66425 0.166425
\(101\) −5.49297 −0.546571 −0.273285 0.961933i \(-0.588110\pi\)
−0.273285 + 0.961933i \(0.588110\pi\)
\(102\) 0 0
\(103\) −11.1030 −1.09401 −0.547004 0.837130i \(-0.684232\pi\)
−0.547004 + 0.837130i \(0.684232\pi\)
\(104\) −0.267135 −0.0261947
\(105\) 0 0
\(106\) 3.93378 0.382082
\(107\) −4.19747 −0.405785 −0.202892 0.979201i \(-0.565034\pi\)
−0.202892 + 0.979201i \(0.565034\pi\)
\(108\) 0 0
\(109\) −1.34044 −0.128391 −0.0641954 0.997937i \(-0.520448\pi\)
−0.0641954 + 0.997937i \(0.520448\pi\)
\(110\) 1.27287 0.121363
\(111\) 0 0
\(112\) 24.8142 2.34472
\(113\) 6.13822 0.577435 0.288718 0.957414i \(-0.406771\pi\)
0.288718 + 0.957414i \(0.406771\pi\)
\(114\) 0 0
\(115\) −2.54815 −0.237616
\(116\) 1.11465 0.103493
\(117\) 0 0
\(118\) −26.8266 −2.46958
\(119\) 29.4595 2.70055
\(120\) 0 0
\(121\) −10.9199 −0.992717
\(122\) −1.91248 −0.173148
\(123\) 0 0
\(124\) 9.99715 0.897771
\(125\) −8.93619 −0.799277
\(126\) 0 0
\(127\) 20.6626 1.83351 0.916755 0.399450i \(-0.130799\pi\)
0.916755 + 0.399450i \(0.130799\pi\)
\(128\) −11.2752 −0.996600
\(129\) 0 0
\(130\) 0.768847 0.0674323
\(131\) −14.9676 −1.30772 −0.653861 0.756614i \(-0.726852\pi\)
−0.653861 + 0.756614i \(0.726852\pi\)
\(132\) 0 0
\(133\) −23.1816 −2.01010
\(134\) 8.45002 0.729970
\(135\) 0 0
\(136\) −9.25064 −0.793236
\(137\) −7.68590 −0.656651 −0.328326 0.944565i \(-0.606484\pi\)
−0.328326 + 0.944565i \(0.606484\pi\)
\(138\) 0 0
\(139\) 18.0155 1.52806 0.764029 0.645182i \(-0.223218\pi\)
0.764029 + 0.645182i \(0.223218\pi\)
\(140\) −14.1331 −1.19446
\(141\) 0 0
\(142\) 28.0608 2.35481
\(143\) 0.0483910 0.00404666
\(144\) 0 0
\(145\) 2.54815 0.211612
\(146\) −8.99353 −0.744310
\(147\) 0 0
\(148\) 0.224522 0.0184556
\(149\) −19.5667 −1.60297 −0.801485 0.598015i \(-0.795956\pi\)
−0.801485 + 0.598015i \(0.795956\pi\)
\(150\) 0 0
\(151\) −3.32858 −0.270876 −0.135438 0.990786i \(-0.543244\pi\)
−0.135438 + 0.990786i \(0.543244\pi\)
\(152\) 7.27931 0.590430
\(153\) 0 0
\(154\) −2.48561 −0.200296
\(155\) 22.8540 1.83568
\(156\) 0 0
\(157\) −18.4270 −1.47063 −0.735317 0.677723i \(-0.762967\pi\)
−0.735317 + 0.677723i \(0.762967\pi\)
\(158\) −27.9114 −2.22051
\(159\) 0 0
\(160\) 14.4633 1.14342
\(161\) 4.97592 0.392157
\(162\) 0 0
\(163\) 2.52999 0.198164 0.0990822 0.995079i \(-0.468409\pi\)
0.0990822 + 0.995079i \(0.468409\pi\)
\(164\) 7.55350 0.589830
\(165\) 0 0
\(166\) −8.74588 −0.678812
\(167\) 1.30974 0.101350 0.0506752 0.998715i \(-0.483863\pi\)
0.0506752 + 0.998715i \(0.483863\pi\)
\(168\) 0 0
\(169\) −12.9708 −0.997752
\(170\) 26.6245 2.04201
\(171\) 0 0
\(172\) −3.31862 −0.253042
\(173\) −13.3226 −1.01290 −0.506451 0.862269i \(-0.669043\pi\)
−0.506451 + 0.862269i \(0.669043\pi\)
\(174\) 0 0
\(175\) −7.42938 −0.561608
\(176\) 1.41150 0.106396
\(177\) 0 0
\(178\) −6.84009 −0.512687
\(179\) 6.31895 0.472300 0.236150 0.971717i \(-0.424114\pi\)
0.236150 + 0.971717i \(0.424114\pi\)
\(180\) 0 0
\(181\) −9.65286 −0.717491 −0.358746 0.933435i \(-0.616795\pi\)
−0.358746 + 0.933435i \(0.616795\pi\)
\(182\) −1.50137 −0.111289
\(183\) 0 0
\(184\) −1.56250 −0.115189
\(185\) 0.513270 0.0377364
\(186\) 0 0
\(187\) 1.67574 0.122542
\(188\) −8.51788 −0.621230
\(189\) 0 0
\(190\) −20.9508 −1.51993
\(191\) 1.31803 0.0953691 0.0476846 0.998862i \(-0.484816\pi\)
0.0476846 + 0.998862i \(0.484816\pi\)
\(192\) 0 0
\(193\) 21.0522 1.51537 0.757685 0.652620i \(-0.226330\pi\)
0.757685 + 0.652620i \(0.226330\pi\)
\(194\) 28.3149 2.03289
\(195\) 0 0
\(196\) 19.7959 1.41399
\(197\) −6.15267 −0.438359 −0.219180 0.975684i \(-0.570338\pi\)
−0.219180 + 0.975684i \(0.570338\pi\)
\(198\) 0 0
\(199\) 12.2203 0.866274 0.433137 0.901328i \(-0.357407\pi\)
0.433137 + 0.901328i \(0.357407\pi\)
\(200\) 2.33292 0.164962
\(201\) 0 0
\(202\) 9.69419 0.682081
\(203\) −4.97592 −0.349241
\(204\) 0 0
\(205\) 17.2677 1.20603
\(206\) 19.5949 1.36524
\(207\) 0 0
\(208\) 0.852584 0.0591160
\(209\) −1.31864 −0.0912120
\(210\) 0 0
\(211\) 4.47990 0.308409 0.154205 0.988039i \(-0.450719\pi\)
0.154205 + 0.988039i \(0.450719\pi\)
\(212\) −2.48452 −0.170638
\(213\) 0 0
\(214\) 7.40785 0.506390
\(215\) −7.58655 −0.517398
\(216\) 0 0
\(217\) −44.6284 −3.02957
\(218\) 2.36566 0.160223
\(219\) 0 0
\(220\) −0.803929 −0.0542009
\(221\) 1.01219 0.0680873
\(222\) 0 0
\(223\) 2.63867 0.176699 0.0883493 0.996090i \(-0.471841\pi\)
0.0883493 + 0.996090i \(0.471841\pi\)
\(224\) −28.2432 −1.88708
\(225\) 0 0
\(226\) −10.8330 −0.720598
\(227\) −14.3265 −0.950885 −0.475442 0.879747i \(-0.657712\pi\)
−0.475442 + 0.879747i \(0.657712\pi\)
\(228\) 0 0
\(229\) −24.0371 −1.58842 −0.794208 0.607647i \(-0.792114\pi\)
−0.794208 + 0.607647i \(0.792114\pi\)
\(230\) 4.49707 0.296528
\(231\) 0 0
\(232\) 1.56250 0.102583
\(233\) 0.647548 0.0424223 0.0212111 0.999775i \(-0.493248\pi\)
0.0212111 + 0.999775i \(0.493248\pi\)
\(234\) 0 0
\(235\) −19.4723 −1.27024
\(236\) 16.9433 1.10292
\(237\) 0 0
\(238\) −51.9912 −3.37009
\(239\) −23.0226 −1.48921 −0.744603 0.667508i \(-0.767361\pi\)
−0.744603 + 0.667508i \(0.767361\pi\)
\(240\) 0 0
\(241\) 4.27926 0.275652 0.137826 0.990456i \(-0.455989\pi\)
0.137826 + 0.990456i \(0.455989\pi\)
\(242\) 19.2718 1.23884
\(243\) 0 0
\(244\) 1.20790 0.0773278
\(245\) 45.2545 2.89120
\(246\) 0 0
\(247\) −0.796490 −0.0506795
\(248\) 14.0139 0.889881
\(249\) 0 0
\(250\) 15.7709 0.997440
\(251\) 13.5637 0.856132 0.428066 0.903747i \(-0.359195\pi\)
0.428066 + 0.903747i \(0.359195\pi\)
\(252\) 0 0
\(253\) 0.283045 0.0177949
\(254\) −36.4661 −2.28809
\(255\) 0 0
\(256\) 19.9859 1.24912
\(257\) 2.03382 0.126866 0.0634330 0.997986i \(-0.479795\pi\)
0.0634330 + 0.997986i \(0.479795\pi\)
\(258\) 0 0
\(259\) −1.00229 −0.0622793
\(260\) −0.485594 −0.0301153
\(261\) 0 0
\(262\) 26.4153 1.63194
\(263\) −11.9405 −0.736283 −0.368142 0.929770i \(-0.620006\pi\)
−0.368142 + 0.929770i \(0.620006\pi\)
\(264\) 0 0
\(265\) −5.67976 −0.348905
\(266\) 40.9117 2.50846
\(267\) 0 0
\(268\) −5.33693 −0.326005
\(269\) −15.1479 −0.923587 −0.461793 0.886988i \(-0.652794\pi\)
−0.461793 + 0.886988i \(0.652794\pi\)
\(270\) 0 0
\(271\) 20.1868 1.22626 0.613132 0.789981i \(-0.289909\pi\)
0.613132 + 0.789981i \(0.289909\pi\)
\(272\) 29.5242 1.79017
\(273\) 0 0
\(274\) 13.5644 0.819453
\(275\) −0.422604 −0.0254840
\(276\) 0 0
\(277\) −2.22660 −0.133783 −0.0668917 0.997760i \(-0.521308\pi\)
−0.0668917 + 0.997760i \(0.521308\pi\)
\(278\) −31.7945 −1.90691
\(279\) 0 0
\(280\) −19.8115 −1.18397
\(281\) −21.9565 −1.30981 −0.654907 0.755710i \(-0.727292\pi\)
−0.654907 + 0.755710i \(0.727292\pi\)
\(282\) 0 0
\(283\) 4.53617 0.269647 0.134824 0.990870i \(-0.456953\pi\)
0.134824 + 0.990870i \(0.456953\pi\)
\(284\) −17.7229 −1.05166
\(285\) 0 0
\(286\) −0.0854023 −0.00504994
\(287\) −33.7197 −1.99041
\(288\) 0 0
\(289\) 18.0513 1.06184
\(290\) −4.49707 −0.264077
\(291\) 0 0
\(292\) 5.68020 0.332409
\(293\) 11.0848 0.647581 0.323790 0.946129i \(-0.395043\pi\)
0.323790 + 0.946129i \(0.395043\pi\)
\(294\) 0 0
\(295\) 38.7334 2.25514
\(296\) 0.314732 0.0182934
\(297\) 0 0
\(298\) 34.5321 2.00039
\(299\) 0.170966 0.00988723
\(300\) 0 0
\(301\) 14.8147 0.853904
\(302\) 5.87440 0.338034
\(303\) 0 0
\(304\) −23.2326 −1.33248
\(305\) 2.76132 0.158113
\(306\) 0 0
\(307\) −11.6843 −0.666856 −0.333428 0.942776i \(-0.608205\pi\)
−0.333428 + 0.942776i \(0.608205\pi\)
\(308\) 1.56988 0.0894521
\(309\) 0 0
\(310\) −40.3337 −2.29080
\(311\) −18.4799 −1.04790 −0.523949 0.851750i \(-0.675542\pi\)
−0.523949 + 0.851750i \(0.675542\pi\)
\(312\) 0 0
\(313\) 1.66419 0.0940656 0.0470328 0.998893i \(-0.485023\pi\)
0.0470328 + 0.998893i \(0.485023\pi\)
\(314\) 32.5206 1.83525
\(315\) 0 0
\(316\) 17.6285 0.991679
\(317\) −6.66769 −0.374495 −0.187247 0.982313i \(-0.559957\pi\)
−0.187247 + 0.982313i \(0.559957\pi\)
\(318\) 0 0
\(319\) −0.283045 −0.0158475
\(320\) −0.110794 −0.00619357
\(321\) 0 0
\(322\) −8.78168 −0.489384
\(323\) −27.5818 −1.53469
\(324\) 0 0
\(325\) −0.255264 −0.0141595
\(326\) −4.46503 −0.247295
\(327\) 0 0
\(328\) 10.5884 0.584646
\(329\) 38.0247 2.09637
\(330\) 0 0
\(331\) 19.8701 1.09216 0.546080 0.837733i \(-0.316119\pi\)
0.546080 + 0.837733i \(0.316119\pi\)
\(332\) 5.52379 0.303157
\(333\) 0 0
\(334\) −2.31147 −0.126478
\(335\) −12.2005 −0.666585
\(336\) 0 0
\(337\) −12.8728 −0.701228 −0.350614 0.936520i \(-0.614027\pi\)
−0.350614 + 0.936520i \(0.614027\pi\)
\(338\) 22.8913 1.24512
\(339\) 0 0
\(340\) −16.8157 −0.911960
\(341\) −2.53859 −0.137472
\(342\) 0 0
\(343\) −53.5396 −2.89087
\(344\) −4.65199 −0.250819
\(345\) 0 0
\(346\) 23.5123 1.26403
\(347\) −9.77259 −0.524620 −0.262310 0.964984i \(-0.584484\pi\)
−0.262310 + 0.964984i \(0.584484\pi\)
\(348\) 0 0
\(349\) 13.1699 0.704971 0.352486 0.935817i \(-0.385337\pi\)
0.352486 + 0.935817i \(0.385337\pi\)
\(350\) 13.1116 0.700846
\(351\) 0 0
\(352\) −1.60656 −0.0856298
\(353\) 14.5533 0.774593 0.387297 0.921955i \(-0.373409\pi\)
0.387297 + 0.921955i \(0.373409\pi\)
\(354\) 0 0
\(355\) −40.5155 −2.15034
\(356\) 4.32012 0.228966
\(357\) 0 0
\(358\) −11.1519 −0.589397
\(359\) 11.6926 0.617113 0.308556 0.951206i \(-0.400154\pi\)
0.308556 + 0.951206i \(0.400154\pi\)
\(360\) 0 0
\(361\) 2.70404 0.142318
\(362\) 17.0357 0.895378
\(363\) 0 0
\(364\) 0.948247 0.0497016
\(365\) 12.9853 0.679679
\(366\) 0 0
\(367\) −0.437440 −0.0228342 −0.0114171 0.999935i \(-0.503634\pi\)
−0.0114171 + 0.999935i \(0.503634\pi\)
\(368\) 4.98686 0.259958
\(369\) 0 0
\(370\) −0.905838 −0.0470923
\(371\) 11.0912 0.575826
\(372\) 0 0
\(373\) 14.7884 0.765714 0.382857 0.923808i \(-0.374940\pi\)
0.382857 + 0.923808i \(0.374940\pi\)
\(374\) −2.95741 −0.152924
\(375\) 0 0
\(376\) −11.9402 −0.615771
\(377\) −0.170966 −0.00880521
\(378\) 0 0
\(379\) −14.0767 −0.723073 −0.361537 0.932358i \(-0.617748\pi\)
−0.361537 + 0.932358i \(0.617748\pi\)
\(380\) 13.2322 0.678800
\(381\) 0 0
\(382\) −2.32610 −0.119014
\(383\) 14.7132 0.751809 0.375905 0.926658i \(-0.377332\pi\)
0.375905 + 0.926658i \(0.377332\pi\)
\(384\) 0 0
\(385\) 3.58883 0.182904
\(386\) −37.1537 −1.89107
\(387\) 0 0
\(388\) −17.8833 −0.907889
\(389\) −11.4361 −0.579835 −0.289917 0.957052i \(-0.593628\pi\)
−0.289917 + 0.957052i \(0.593628\pi\)
\(390\) 0 0
\(391\) 5.92041 0.299408
\(392\) 27.7496 1.40157
\(393\) 0 0
\(394\) 10.8585 0.547041
\(395\) 40.2997 2.02770
\(396\) 0 0
\(397\) 31.0202 1.55686 0.778430 0.627732i \(-0.216016\pi\)
0.778430 + 0.627732i \(0.216016\pi\)
\(398\) −21.5668 −1.08105
\(399\) 0 0
\(400\) −7.44571 −0.372285
\(401\) 37.4659 1.87096 0.935480 0.353379i \(-0.114968\pi\)
0.935480 + 0.353379i \(0.114968\pi\)
\(402\) 0 0
\(403\) −1.53337 −0.0763828
\(404\) −6.12273 −0.304617
\(405\) 0 0
\(406\) 8.78168 0.435827
\(407\) −0.0570132 −0.00282604
\(408\) 0 0
\(409\) −30.1554 −1.49109 −0.745544 0.666456i \(-0.767810\pi\)
−0.745544 + 0.666456i \(0.767810\pi\)
\(410\) −30.4747 −1.50504
\(411\) 0 0
\(412\) −12.3759 −0.609718
\(413\) −75.6369 −3.72185
\(414\) 0 0
\(415\) 12.6277 0.619869
\(416\) −0.970402 −0.0475779
\(417\) 0 0
\(418\) 2.32718 0.113826
\(419\) −21.3187 −1.04149 −0.520745 0.853713i \(-0.674346\pi\)
−0.520745 + 0.853713i \(0.674346\pi\)
\(420\) 0 0
\(421\) −39.1557 −1.90833 −0.954165 0.299280i \(-0.903254\pi\)
−0.954165 + 0.299280i \(0.903254\pi\)
\(422\) −7.90629 −0.384872
\(423\) 0 0
\(424\) −3.48277 −0.169138
\(425\) −8.83957 −0.428782
\(426\) 0 0
\(427\) −5.39219 −0.260946
\(428\) −4.67871 −0.226154
\(429\) 0 0
\(430\) 13.3890 0.645676
\(431\) −17.4143 −0.838818 −0.419409 0.907797i \(-0.637763\pi\)
−0.419409 + 0.907797i \(0.637763\pi\)
\(432\) 0 0
\(433\) −12.3095 −0.591555 −0.295778 0.955257i \(-0.595579\pi\)
−0.295778 + 0.955257i \(0.595579\pi\)
\(434\) 78.7618 3.78069
\(435\) 0 0
\(436\) −1.49412 −0.0715554
\(437\) −4.65876 −0.222859
\(438\) 0 0
\(439\) −14.3065 −0.682814 −0.341407 0.939916i \(-0.610903\pi\)
−0.341407 + 0.939916i \(0.610903\pi\)
\(440\) −1.12694 −0.0537246
\(441\) 0 0
\(442\) −1.78635 −0.0849680
\(443\) 13.9006 0.660439 0.330220 0.943904i \(-0.392877\pi\)
0.330220 + 0.943904i \(0.392877\pi\)
\(444\) 0 0
\(445\) 9.87603 0.468169
\(446\) −4.65683 −0.220507
\(447\) 0 0
\(448\) 0.216354 0.0102217
\(449\) −29.6600 −1.39974 −0.699872 0.714268i \(-0.746760\pi\)
−0.699872 + 0.714268i \(0.746760\pi\)
\(450\) 0 0
\(451\) −1.91807 −0.0903185
\(452\) 6.84196 0.321819
\(453\) 0 0
\(454\) 25.2840 1.18664
\(455\) 2.16774 0.101625
\(456\) 0 0
\(457\) 38.3682 1.79479 0.897394 0.441230i \(-0.145458\pi\)
0.897394 + 0.441230i \(0.145458\pi\)
\(458\) 42.4215 1.98223
\(459\) 0 0
\(460\) −2.84029 −0.132429
\(461\) 28.6130 1.33264 0.666321 0.745665i \(-0.267868\pi\)
0.666321 + 0.745665i \(0.267868\pi\)
\(462\) 0 0
\(463\) 6.51659 0.302852 0.151426 0.988469i \(-0.451614\pi\)
0.151426 + 0.988469i \(0.451614\pi\)
\(464\) −4.98686 −0.231509
\(465\) 0 0
\(466\) −1.14282 −0.0529400
\(467\) 16.6592 0.770895 0.385448 0.922730i \(-0.374047\pi\)
0.385448 + 0.922730i \(0.374047\pi\)
\(468\) 0 0
\(469\) 23.8246 1.10012
\(470\) 34.3655 1.58516
\(471\) 0 0
\(472\) 23.7509 1.09322
\(473\) 0.842702 0.0387475
\(474\) 0 0
\(475\) 6.95584 0.319156
\(476\) 32.8370 1.50508
\(477\) 0 0
\(478\) 40.6310 1.85842
\(479\) 9.73200 0.444666 0.222333 0.974971i \(-0.428633\pi\)
0.222333 + 0.974971i \(0.428633\pi\)
\(480\) 0 0
\(481\) −0.0344375 −0.00157021
\(482\) −7.55220 −0.343993
\(483\) 0 0
\(484\) −12.1718 −0.553266
\(485\) −40.8823 −1.85637
\(486\) 0 0
\(487\) −10.4945 −0.475551 −0.237775 0.971320i \(-0.576418\pi\)
−0.237775 + 0.971320i \(0.576418\pi\)
\(488\) 1.69321 0.0766482
\(489\) 0 0
\(490\) −79.8668 −3.60801
\(491\) −31.9404 −1.44145 −0.720726 0.693220i \(-0.756191\pi\)
−0.720726 + 0.693220i \(0.756191\pi\)
\(492\) 0 0
\(493\) −5.92041 −0.266642
\(494\) 1.40568 0.0632443
\(495\) 0 0
\(496\) −44.7265 −2.00828
\(497\) 79.1169 3.54888
\(498\) 0 0
\(499\) 2.06782 0.0925684 0.0462842 0.998928i \(-0.485262\pi\)
0.0462842 + 0.998928i \(0.485262\pi\)
\(500\) −9.96072 −0.445457
\(501\) 0 0
\(502\) −23.9377 −1.06839
\(503\) 39.4576 1.75933 0.879663 0.475598i \(-0.157768\pi\)
0.879663 + 0.475598i \(0.157768\pi\)
\(504\) 0 0
\(505\) −13.9969 −0.622854
\(506\) −0.499527 −0.0222067
\(507\) 0 0
\(508\) 23.0316 1.02186
\(509\) −26.0870 −1.15629 −0.578143 0.815935i \(-0.696223\pi\)
−0.578143 + 0.815935i \(0.696223\pi\)
\(510\) 0 0
\(511\) −25.3570 −1.12173
\(512\) −12.7214 −0.562212
\(513\) 0 0
\(514\) −3.58936 −0.158320
\(515\) −28.2920 −1.24670
\(516\) 0 0
\(517\) 2.16296 0.0951267
\(518\) 1.76888 0.0777202
\(519\) 0 0
\(520\) −0.680699 −0.0298506
\(521\) −35.0010 −1.53342 −0.766711 0.641992i \(-0.778108\pi\)
−0.766711 + 0.641992i \(0.778108\pi\)
\(522\) 0 0
\(523\) −14.5683 −0.637026 −0.318513 0.947919i \(-0.603183\pi\)
−0.318513 + 0.947919i \(0.603183\pi\)
\(524\) −16.6836 −0.728826
\(525\) 0 0
\(526\) 21.0730 0.918828
\(527\) −53.0995 −2.31305
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 10.0238 0.435408
\(531\) 0 0
\(532\) −25.8393 −1.12028
\(533\) −1.15857 −0.0501830
\(534\) 0 0
\(535\) −10.6958 −0.462419
\(536\) −7.48123 −0.323140
\(537\) 0 0
\(538\) 26.7337 1.15257
\(539\) −5.02680 −0.216519
\(540\) 0 0
\(541\) −25.5258 −1.09744 −0.548719 0.836007i \(-0.684884\pi\)
−0.548719 + 0.836007i \(0.684884\pi\)
\(542\) −35.6265 −1.53029
\(543\) 0 0
\(544\) −33.6042 −1.44077
\(545\) −3.41564 −0.146310
\(546\) 0 0
\(547\) 8.84906 0.378358 0.189179 0.981943i \(-0.439417\pi\)
0.189179 + 0.981943i \(0.439417\pi\)
\(548\) −8.56709 −0.365968
\(549\) 0 0
\(550\) 0.745828 0.0318022
\(551\) 4.65876 0.198470
\(552\) 0 0
\(553\) −78.6955 −3.34647
\(554\) 3.92959 0.166952
\(555\) 0 0
\(556\) 20.0810 0.851625
\(557\) −26.6759 −1.13029 −0.565147 0.824990i \(-0.691181\pi\)
−0.565147 + 0.824990i \(0.691181\pi\)
\(558\) 0 0
\(559\) 0.509014 0.0215290
\(560\) 63.2302 2.67197
\(561\) 0 0
\(562\) 38.7496 1.63455
\(563\) 16.5834 0.698906 0.349453 0.936954i \(-0.386367\pi\)
0.349453 + 0.936954i \(0.386367\pi\)
\(564\) 0 0
\(565\) 15.6411 0.658026
\(566\) −8.00560 −0.336501
\(567\) 0 0
\(568\) −24.8437 −1.04242
\(569\) −24.5455 −1.02900 −0.514500 0.857491i \(-0.672022\pi\)
−0.514500 + 0.857491i \(0.672022\pi\)
\(570\) 0 0
\(571\) −26.4099 −1.10522 −0.552611 0.833439i \(-0.686368\pi\)
−0.552611 + 0.833439i \(0.686368\pi\)
\(572\) 0.0539390 0.00225530
\(573\) 0 0
\(574\) 59.5097 2.48389
\(575\) −1.49307 −0.0622652
\(576\) 0 0
\(577\) −20.0446 −0.834469 −0.417234 0.908799i \(-0.637001\pi\)
−0.417234 + 0.908799i \(0.637001\pi\)
\(578\) −31.8576 −1.32510
\(579\) 0 0
\(580\) 2.84029 0.117937
\(581\) −24.6588 −1.02302
\(582\) 0 0
\(583\) 0.630899 0.0261292
\(584\) 7.96243 0.329488
\(585\) 0 0
\(586\) −19.5629 −0.808134
\(587\) −2.29610 −0.0947702 −0.0473851 0.998877i \(-0.515089\pi\)
−0.0473851 + 0.998877i \(0.515089\pi\)
\(588\) 0 0
\(589\) 41.7838 1.72167
\(590\) −68.3581 −2.81426
\(591\) 0 0
\(592\) −1.00449 −0.0412845
\(593\) 12.5883 0.516940 0.258470 0.966019i \(-0.416782\pi\)
0.258470 + 0.966019i \(0.416782\pi\)
\(594\) 0 0
\(595\) 75.0672 3.07745
\(596\) −21.8101 −0.893375
\(597\) 0 0
\(598\) −0.301727 −0.0123386
\(599\) −26.0338 −1.06371 −0.531857 0.846834i \(-0.678506\pi\)
−0.531857 + 0.846834i \(0.678506\pi\)
\(600\) 0 0
\(601\) 14.9942 0.611628 0.305814 0.952091i \(-0.401071\pi\)
0.305814 + 0.952091i \(0.401071\pi\)
\(602\) −26.1455 −1.06561
\(603\) 0 0
\(604\) −3.71020 −0.150966
\(605\) −27.8255 −1.13127
\(606\) 0 0
\(607\) −6.38075 −0.258987 −0.129493 0.991580i \(-0.541335\pi\)
−0.129493 + 0.991580i \(0.541335\pi\)
\(608\) 26.4431 1.07241
\(609\) 0 0
\(610\) −4.87328 −0.197313
\(611\) 1.30648 0.0528546
\(612\) 0 0
\(613\) −21.4514 −0.866413 −0.433206 0.901295i \(-0.642618\pi\)
−0.433206 + 0.901295i \(0.642618\pi\)
\(614\) 20.6208 0.832188
\(615\) 0 0
\(616\) 2.20063 0.0886661
\(617\) −27.6955 −1.11498 −0.557489 0.830184i \(-0.688235\pi\)
−0.557489 + 0.830184i \(0.688235\pi\)
\(618\) 0 0
\(619\) 11.3783 0.457332 0.228666 0.973505i \(-0.426564\pi\)
0.228666 + 0.973505i \(0.426564\pi\)
\(620\) 25.4742 1.02307
\(621\) 0 0
\(622\) 32.6140 1.30770
\(623\) −19.2855 −0.772657
\(624\) 0 0
\(625\) −30.2361 −1.20944
\(626\) −2.93702 −0.117387
\(627\) 0 0
\(628\) −20.5396 −0.819621
\(629\) −1.19254 −0.0475497
\(630\) 0 0
\(631\) −45.9809 −1.83047 −0.915235 0.402921i \(-0.867995\pi\)
−0.915235 + 0.402921i \(0.867995\pi\)
\(632\) 24.7114 0.982965
\(633\) 0 0
\(634\) 11.7674 0.467342
\(635\) 52.6514 2.08941
\(636\) 0 0
\(637\) −3.03632 −0.120303
\(638\) 0.499527 0.0197765
\(639\) 0 0
\(640\) −28.7310 −1.13569
\(641\) −8.77087 −0.346428 −0.173214 0.984884i \(-0.555415\pi\)
−0.173214 + 0.984884i \(0.555415\pi\)
\(642\) 0 0
\(643\) −42.4849 −1.67544 −0.837721 0.546098i \(-0.816113\pi\)
−0.837721 + 0.546098i \(0.816113\pi\)
\(644\) 5.54640 0.218559
\(645\) 0 0
\(646\) 48.6773 1.91518
\(647\) 7.83180 0.307900 0.153950 0.988079i \(-0.450801\pi\)
0.153950 + 0.988079i \(0.450801\pi\)
\(648\) 0 0
\(649\) −4.30244 −0.168886
\(650\) 0.450499 0.0176700
\(651\) 0 0
\(652\) 2.82006 0.110442
\(653\) 19.9384 0.780248 0.390124 0.920762i \(-0.372432\pi\)
0.390124 + 0.920762i \(0.372432\pi\)
\(654\) 0 0
\(655\) −38.1396 −1.49024
\(656\) −33.7938 −1.31943
\(657\) 0 0
\(658\) −67.1075 −2.61612
\(659\) −13.1611 −0.512684 −0.256342 0.966586i \(-0.582517\pi\)
−0.256342 + 0.966586i \(0.582517\pi\)
\(660\) 0 0
\(661\) −9.99619 −0.388807 −0.194403 0.980922i \(-0.562277\pi\)
−0.194403 + 0.980922i \(0.562277\pi\)
\(662\) −35.0675 −1.36294
\(663\) 0 0
\(664\) 7.74317 0.300493
\(665\) −59.0702 −2.29064
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 1.45990 0.0564851
\(669\) 0 0
\(670\) 21.5319 0.831850
\(671\) −0.306723 −0.0118409
\(672\) 0 0
\(673\) −44.4817 −1.71464 −0.857322 0.514781i \(-0.827873\pi\)
−0.857322 + 0.514781i \(0.827873\pi\)
\(674\) 22.7185 0.875082
\(675\) 0 0
\(676\) −14.4579 −0.556071
\(677\) −23.2960 −0.895339 −0.447670 0.894199i \(-0.647746\pi\)
−0.447670 + 0.894199i \(0.647746\pi\)
\(678\) 0 0
\(679\) 79.8332 3.06372
\(680\) −23.5720 −0.903946
\(681\) 0 0
\(682\) 4.48020 0.171556
\(683\) −46.6962 −1.78678 −0.893391 0.449280i \(-0.851680\pi\)
−0.893391 + 0.449280i \(0.851680\pi\)
\(684\) 0 0
\(685\) −19.5848 −0.748298
\(686\) 94.4886 3.60759
\(687\) 0 0
\(688\) 14.8473 0.566046
\(689\) 0.381079 0.0145180
\(690\) 0 0
\(691\) −47.2859 −1.79884 −0.899421 0.437084i \(-0.856011\pi\)
−0.899421 + 0.437084i \(0.856011\pi\)
\(692\) −14.8501 −0.564515
\(693\) 0 0
\(694\) 17.2470 0.654688
\(695\) 45.9063 1.74133
\(696\) 0 0
\(697\) −40.1201 −1.51966
\(698\) −23.2428 −0.879753
\(699\) 0 0
\(700\) −8.28115 −0.312998
\(701\) −46.4140 −1.75303 −0.876517 0.481371i \(-0.840139\pi\)
−0.876517 + 0.481371i \(0.840139\pi\)
\(702\) 0 0
\(703\) 0.938407 0.0353927
\(704\) 0.0123068 0.000463831 0
\(705\) 0 0
\(706\) −25.6842 −0.966637
\(707\) 27.3326 1.02795
\(708\) 0 0
\(709\) 11.3444 0.426047 0.213024 0.977047i \(-0.431669\pi\)
0.213024 + 0.977047i \(0.431669\pi\)
\(710\) 71.5032 2.68347
\(711\) 0 0
\(712\) 6.05588 0.226954
\(713\) −8.96888 −0.335887
\(714\) 0 0
\(715\) 0.123308 0.00461144
\(716\) 7.04341 0.263225
\(717\) 0 0
\(718\) −20.6356 −0.770112
\(719\) −37.1842 −1.38674 −0.693369 0.720582i \(-0.743874\pi\)
−0.693369 + 0.720582i \(0.743874\pi\)
\(720\) 0 0
\(721\) 55.2475 2.05752
\(722\) −4.77218 −0.177602
\(723\) 0 0
\(724\) −10.7596 −0.399876
\(725\) 1.49307 0.0554511
\(726\) 0 0
\(727\) 16.0657 0.595843 0.297922 0.954590i \(-0.403707\pi\)
0.297922 + 0.954590i \(0.403707\pi\)
\(728\) 1.32924 0.0492649
\(729\) 0 0
\(730\) −22.9169 −0.848191
\(731\) 17.6267 0.651948
\(732\) 0 0
\(733\) 35.3061 1.30406 0.652031 0.758193i \(-0.273917\pi\)
0.652031 + 0.758193i \(0.273917\pi\)
\(734\) 0.772009 0.0284954
\(735\) 0 0
\(736\) −5.67599 −0.209220
\(737\) 1.35521 0.0499199
\(738\) 0 0
\(739\) −3.60959 −0.132781 −0.0663905 0.997794i \(-0.521148\pi\)
−0.0663905 + 0.997794i \(0.521148\pi\)
\(740\) 0.572116 0.0210314
\(741\) 0 0
\(742\) −19.5741 −0.718589
\(743\) −31.2299 −1.14572 −0.572858 0.819655i \(-0.694165\pi\)
−0.572858 + 0.819655i \(0.694165\pi\)
\(744\) 0 0
\(745\) −49.8590 −1.82669
\(746\) −26.0991 −0.955556
\(747\) 0 0
\(748\) 1.86786 0.0682958
\(749\) 20.8863 0.763167
\(750\) 0 0
\(751\) 20.0119 0.730246 0.365123 0.930959i \(-0.381027\pi\)
0.365123 + 0.930959i \(0.381027\pi\)
\(752\) 38.1083 1.38967
\(753\) 0 0
\(754\) 0.301727 0.0109883
\(755\) −8.48172 −0.308681
\(756\) 0 0
\(757\) 31.3437 1.13921 0.569604 0.821920i \(-0.307097\pi\)
0.569604 + 0.821920i \(0.307097\pi\)
\(758\) 24.8431 0.902343
\(759\) 0 0
\(760\) 18.5488 0.672835
\(761\) −14.4059 −0.522215 −0.261107 0.965310i \(-0.584088\pi\)
−0.261107 + 0.965310i \(0.584088\pi\)
\(762\) 0 0
\(763\) 6.66992 0.241467
\(764\) 1.46914 0.0531516
\(765\) 0 0
\(766\) −25.9664 −0.938204
\(767\) −2.59879 −0.0938367
\(768\) 0 0
\(769\) −19.9701 −0.720140 −0.360070 0.932925i \(-0.617247\pi\)
−0.360070 + 0.932925i \(0.617247\pi\)
\(770\) −6.33370 −0.228251
\(771\) 0 0
\(772\) 23.4658 0.844553
\(773\) 9.65289 0.347190 0.173595 0.984817i \(-0.444462\pi\)
0.173595 + 0.984817i \(0.444462\pi\)
\(774\) 0 0
\(775\) 13.3911 0.481024
\(776\) −25.0686 −0.899911
\(777\) 0 0
\(778\) 20.1829 0.723592
\(779\) 31.5704 1.13113
\(780\) 0 0
\(781\) 4.50040 0.161037
\(782\) −10.4486 −0.373640
\(783\) 0 0
\(784\) −88.5653 −3.16305
\(785\) −46.9547 −1.67589
\(786\) 0 0
\(787\) 37.1608 1.32464 0.662320 0.749221i \(-0.269572\pi\)
0.662320 + 0.749221i \(0.269572\pi\)
\(788\) −6.85807 −0.244309
\(789\) 0 0
\(790\) −71.1223 −2.53042
\(791\) −30.5433 −1.08599
\(792\) 0 0
\(793\) −0.185269 −0.00657909
\(794\) −54.7456 −1.94285
\(795\) 0 0
\(796\) 13.6213 0.482796
\(797\) 18.0087 0.637900 0.318950 0.947772i \(-0.396670\pi\)
0.318950 + 0.947772i \(0.396670\pi\)
\(798\) 0 0
\(799\) 45.2424 1.60056
\(800\) 8.47463 0.299623
\(801\) 0 0
\(802\) −66.1213 −2.33482
\(803\) −1.44238 −0.0509006
\(804\) 0 0
\(805\) 12.6794 0.446889
\(806\) 2.70616 0.0953203
\(807\) 0 0
\(808\) −8.58276 −0.301941
\(809\) −4.86545 −0.171060 −0.0855301 0.996336i \(-0.527258\pi\)
−0.0855301 + 0.996336i \(0.527258\pi\)
\(810\) 0 0
\(811\) 13.8980 0.488025 0.244012 0.969772i \(-0.421536\pi\)
0.244012 + 0.969772i \(0.421536\pi\)
\(812\) −5.54640 −0.194641
\(813\) 0 0
\(814\) 0.100619 0.00352670
\(815\) 6.44680 0.225822
\(816\) 0 0
\(817\) −13.8704 −0.485264
\(818\) 53.2193 1.86077
\(819\) 0 0
\(820\) 19.2475 0.672150
\(821\) 45.1277 1.57497 0.787483 0.616336i \(-0.211384\pi\)
0.787483 + 0.616336i \(0.211384\pi\)
\(822\) 0 0
\(823\) −20.1767 −0.703315 −0.351658 0.936129i \(-0.614382\pi\)
−0.351658 + 0.936129i \(0.614382\pi\)
\(824\) −17.3484 −0.604360
\(825\) 0 0
\(826\) 133.487 4.64460
\(827\) −54.0105 −1.87813 −0.939064 0.343742i \(-0.888305\pi\)
−0.939064 + 0.343742i \(0.888305\pi\)
\(828\) 0 0
\(829\) −15.7634 −0.547485 −0.273742 0.961803i \(-0.588262\pi\)
−0.273742 + 0.961803i \(0.588262\pi\)
\(830\) −22.2858 −0.773552
\(831\) 0 0
\(832\) 0.00743364 0.000257715 0
\(833\) −105.145 −3.64306
\(834\) 0 0
\(835\) 3.33740 0.115496
\(836\) −1.46982 −0.0508347
\(837\) 0 0
\(838\) 37.6241 1.29970
\(839\) −19.8149 −0.684086 −0.342043 0.939684i \(-0.611119\pi\)
−0.342043 + 0.939684i \(0.611119\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 69.1034 2.38146
\(843\) 0 0
\(844\) 4.99352 0.171884
\(845\) −33.0515 −1.13700
\(846\) 0 0
\(847\) 54.3364 1.86702
\(848\) 11.1156 0.381710
\(849\) 0 0
\(850\) 15.6004 0.535089
\(851\) −0.201428 −0.00690488
\(852\) 0 0
\(853\) −28.3860 −0.971918 −0.485959 0.873982i \(-0.661529\pi\)
−0.485959 + 0.873982i \(0.661529\pi\)
\(854\) 9.51634 0.325642
\(855\) 0 0
\(856\) −6.55855 −0.224167
\(857\) 46.0087 1.57163 0.785814 0.618462i \(-0.212244\pi\)
0.785814 + 0.618462i \(0.212244\pi\)
\(858\) 0 0
\(859\) 46.3189 1.58038 0.790191 0.612861i \(-0.209982\pi\)
0.790191 + 0.612861i \(0.209982\pi\)
\(860\) −8.45634 −0.288359
\(861\) 0 0
\(862\) 30.7334 1.04678
\(863\) −17.1707 −0.584497 −0.292249 0.956342i \(-0.594403\pi\)
−0.292249 + 0.956342i \(0.594403\pi\)
\(864\) 0 0
\(865\) −33.9481 −1.15427
\(866\) 21.7242 0.738219
\(867\) 0 0
\(868\) −49.7450 −1.68845
\(869\) −4.47642 −0.151852
\(870\) 0 0
\(871\) 0.818584 0.0277367
\(872\) −2.09444 −0.0709266
\(873\) 0 0
\(874\) 8.22195 0.278112
\(875\) 44.4657 1.50322
\(876\) 0 0
\(877\) −41.0178 −1.38507 −0.692537 0.721383i \(-0.743507\pi\)
−0.692537 + 0.721383i \(0.743507\pi\)
\(878\) 25.2487 0.852103
\(879\) 0 0
\(880\) 3.59672 0.121245
\(881\) 12.1431 0.409111 0.204556 0.978855i \(-0.434425\pi\)
0.204556 + 0.978855i \(0.434425\pi\)
\(882\) 0 0
\(883\) 13.3621 0.449669 0.224835 0.974397i \(-0.427816\pi\)
0.224835 + 0.974397i \(0.427816\pi\)
\(884\) 1.12824 0.0379467
\(885\) 0 0
\(886\) −24.5324 −0.824181
\(887\) −5.50891 −0.184971 −0.0924856 0.995714i \(-0.529481\pi\)
−0.0924856 + 0.995714i \(0.529481\pi\)
\(888\) 0 0
\(889\) −102.815 −3.44832
\(890\) −17.4296 −0.584241
\(891\) 0 0
\(892\) 2.94119 0.0984785
\(893\) −35.6011 −1.19135
\(894\) 0 0
\(895\) 16.1016 0.538218
\(896\) 56.1046 1.87432
\(897\) 0 0
\(898\) 52.3451 1.74678
\(899\) 8.96888 0.299129
\(900\) 0 0
\(901\) 13.1964 0.439637
\(902\) 3.38509 0.112711
\(903\) 0 0
\(904\) 9.59097 0.318991
\(905\) −24.5969 −0.817630
\(906\) 0 0
\(907\) −19.7017 −0.654184 −0.327092 0.944993i \(-0.606069\pi\)
−0.327092 + 0.944993i \(0.606069\pi\)
\(908\) −15.9690 −0.529951
\(909\) 0 0
\(910\) −3.82572 −0.126821
\(911\) −43.9735 −1.45691 −0.728453 0.685096i \(-0.759760\pi\)
−0.728453 + 0.685096i \(0.759760\pi\)
\(912\) 0 0
\(913\) −1.40266 −0.0464214
\(914\) −67.7136 −2.23977
\(915\) 0 0
\(916\) −26.7929 −0.885263
\(917\) 74.4774 2.45946
\(918\) 0 0
\(919\) 27.3654 0.902703 0.451351 0.892346i \(-0.350942\pi\)
0.451351 + 0.892346i \(0.350942\pi\)
\(920\) −3.98148 −0.131266
\(921\) 0 0
\(922\) −50.4973 −1.66304
\(923\) 2.71835 0.0894757
\(924\) 0 0
\(925\) 0.300746 0.00988847
\(926\) −11.5007 −0.377937
\(927\) 0 0
\(928\) 5.67599 0.186323
\(929\) −48.2798 −1.58401 −0.792004 0.610516i \(-0.790962\pi\)
−0.792004 + 0.610516i \(0.790962\pi\)
\(930\) 0 0
\(931\) 82.7384 2.71164
\(932\) 0.721789 0.0236430
\(933\) 0 0
\(934\) −29.4007 −0.962022
\(935\) 4.27004 0.139645
\(936\) 0 0
\(937\) 24.8928 0.813213 0.406607 0.913603i \(-0.366712\pi\)
0.406607 + 0.913603i \(0.366712\pi\)
\(938\) −42.0466 −1.37287
\(939\) 0 0
\(940\) −21.7048 −0.707933
\(941\) 5.98909 0.195239 0.0976193 0.995224i \(-0.468877\pi\)
0.0976193 + 0.995224i \(0.468877\pi\)
\(942\) 0 0
\(943\) −6.77658 −0.220676
\(944\) −75.8031 −2.46718
\(945\) 0 0
\(946\) −1.48723 −0.0483541
\(947\) 45.5443 1.47999 0.739995 0.672613i \(-0.234828\pi\)
0.739995 + 0.672613i \(0.234828\pi\)
\(948\) 0 0
\(949\) −0.871236 −0.0282815
\(950\) −12.2759 −0.398283
\(951\) 0 0
\(952\) 46.0304 1.49185
\(953\) 36.5769 1.18484 0.592422 0.805628i \(-0.298172\pi\)
0.592422 + 0.805628i \(0.298172\pi\)
\(954\) 0 0
\(955\) 3.35853 0.108680
\(956\) −25.6621 −0.829971
\(957\) 0 0
\(958\) −17.1754 −0.554912
\(959\) 38.2444 1.23498
\(960\) 0 0
\(961\) 49.4407 1.59486
\(962\) 0.0607765 0.00195951
\(963\) 0 0
\(964\) 4.76988 0.153627
\(965\) 53.6442 1.72687
\(966\) 0 0
\(967\) 4.29341 0.138067 0.0690334 0.997614i \(-0.478009\pi\)
0.0690334 + 0.997614i \(0.478009\pi\)
\(968\) −17.0623 −0.548404
\(969\) 0 0
\(970\) 72.1506 2.31662
\(971\) −12.3990 −0.397902 −0.198951 0.980009i \(-0.563754\pi\)
−0.198951 + 0.980009i \(0.563754\pi\)
\(972\) 0 0
\(973\) −89.6438 −2.87385
\(974\) 18.5211 0.593453
\(975\) 0 0
\(976\) −5.40404 −0.172979
\(977\) −5.07082 −0.162230 −0.0811150 0.996705i \(-0.525848\pi\)
−0.0811150 + 0.996705i \(0.525848\pi\)
\(978\) 0 0
\(979\) −1.09701 −0.0350607
\(980\) 50.4429 1.61134
\(981\) 0 0
\(982\) 56.3697 1.79883
\(983\) −7.83628 −0.249939 −0.124969 0.992161i \(-0.539883\pi\)
−0.124969 + 0.992161i \(0.539883\pi\)
\(984\) 0 0
\(985\) −15.6779 −0.499540
\(986\) 10.4486 0.332750
\(987\) 0 0
\(988\) −0.887807 −0.0282449
\(989\) 2.97728 0.0946719
\(990\) 0 0
\(991\) 58.1336 1.84667 0.923337 0.383990i \(-0.125450\pi\)
0.923337 + 0.383990i \(0.125450\pi\)
\(992\) 50.9072 1.61631
\(993\) 0 0
\(994\) −139.628 −4.42874
\(995\) 31.1392 0.987178
\(996\) 0 0
\(997\) −62.9965 −1.99512 −0.997560 0.0698195i \(-0.977758\pi\)
−0.997560 + 0.0698195i \(0.977758\pi\)
\(998\) −3.64937 −0.115519
\(999\) 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.1.4 11
3.2 odd 2 2001.2.a.l.1.8 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.8 11 3.2 odd 2
6003.2.a.m.1.4 11 1.1 even 1 trivial