Properties

Label 6003.2.a.m.1.11
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 1.11
Root \(-2.51124\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.51124 q^{2} +4.30634 q^{4} -2.07440 q^{5} -0.329384 q^{7} +5.79178 q^{8} +O(q^{10})\) \(q+2.51124 q^{2} +4.30634 q^{4} -2.07440 q^{5} -0.329384 q^{7} +5.79178 q^{8} -5.20933 q^{10} -4.89635 q^{11} +2.21503 q^{13} -0.827164 q^{14} +5.93189 q^{16} -4.14979 q^{17} +0.434775 q^{19} -8.93309 q^{20} -12.2959 q^{22} -1.00000 q^{23} -0.696851 q^{25} +5.56247 q^{26} -1.41844 q^{28} +1.00000 q^{29} +11.0142 q^{31} +3.31286 q^{32} -10.4211 q^{34} +0.683276 q^{35} +0.655818 q^{37} +1.09182 q^{38} -12.0145 q^{40} -7.37293 q^{41} +0.463287 q^{43} -21.0853 q^{44} -2.51124 q^{46} -4.14571 q^{47} -6.89151 q^{49} -1.74996 q^{50} +9.53866 q^{52} -2.30936 q^{53} +10.1570 q^{55} -1.90772 q^{56} +2.51124 q^{58} -9.22421 q^{59} -12.4374 q^{61} +27.6594 q^{62} -3.54439 q^{64} -4.59486 q^{65} -14.6596 q^{67} -17.8704 q^{68} +1.71587 q^{70} -12.1080 q^{71} +7.93152 q^{73} +1.64692 q^{74} +1.87229 q^{76} +1.61278 q^{77} -6.32788 q^{79} -12.3051 q^{80} -18.5152 q^{82} +16.4719 q^{83} +8.60834 q^{85} +1.16343 q^{86} -28.3586 q^{88} -7.88890 q^{89} -0.729595 q^{91} -4.30634 q^{92} -10.4109 q^{94} -0.901898 q^{95} -15.8429 q^{97} -17.3062 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \) \( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.51124 1.77572 0.887858 0.460117i \(-0.152192\pi\)
0.887858 + 0.460117i \(0.152192\pi\)
\(3\) 0 0
\(4\) 4.30634 2.15317
\(5\) −2.07440 −0.927701 −0.463851 0.885913i \(-0.653533\pi\)
−0.463851 + 0.885913i \(0.653533\pi\)
\(6\) 0 0
\(7\) −0.329384 −0.124496 −0.0622478 0.998061i \(-0.519827\pi\)
−0.0622478 + 0.998061i \(0.519827\pi\)
\(8\) 5.79178 2.04770
\(9\) 0 0
\(10\) −5.20933 −1.64733
\(11\) −4.89635 −1.47630 −0.738152 0.674635i \(-0.764301\pi\)
−0.738152 + 0.674635i \(0.764301\pi\)
\(12\) 0 0
\(13\) 2.21503 0.614338 0.307169 0.951655i \(-0.400618\pi\)
0.307169 + 0.951655i \(0.400618\pi\)
\(14\) −0.827164 −0.221069
\(15\) 0 0
\(16\) 5.93189 1.48297
\(17\) −4.14979 −1.00647 −0.503236 0.864149i \(-0.667857\pi\)
−0.503236 + 0.864149i \(0.667857\pi\)
\(18\) 0 0
\(19\) 0.434775 0.0997441 0.0498721 0.998756i \(-0.484119\pi\)
0.0498721 + 0.998756i \(0.484119\pi\)
\(20\) −8.93309 −1.99750
\(21\) 0 0
\(22\) −12.2959 −2.62150
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −0.696851 −0.139370
\(26\) 5.56247 1.09089
\(27\) 0 0
\(28\) −1.41844 −0.268060
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 11.0142 1.97822 0.989108 0.147189i \(-0.0470227\pi\)
0.989108 + 0.147189i \(0.0470227\pi\)
\(32\) 3.31286 0.585636
\(33\) 0 0
\(34\) −10.4211 −1.78721
\(35\) 0.683276 0.115495
\(36\) 0 0
\(37\) 0.655818 0.107816 0.0539079 0.998546i \(-0.482832\pi\)
0.0539079 + 0.998546i \(0.482832\pi\)
\(38\) 1.09182 0.177117
\(39\) 0 0
\(40\) −12.0145 −1.89966
\(41\) −7.37293 −1.15146 −0.575729 0.817640i \(-0.695282\pi\)
−0.575729 + 0.817640i \(0.695282\pi\)
\(42\) 0 0
\(43\) 0.463287 0.0706505 0.0353253 0.999376i \(-0.488753\pi\)
0.0353253 + 0.999376i \(0.488753\pi\)
\(44\) −21.0853 −3.17873
\(45\) 0 0
\(46\) −2.51124 −0.370263
\(47\) −4.14571 −0.604714 −0.302357 0.953195i \(-0.597774\pi\)
−0.302357 + 0.953195i \(0.597774\pi\)
\(48\) 0 0
\(49\) −6.89151 −0.984501
\(50\) −1.74996 −0.247482
\(51\) 0 0
\(52\) 9.53866 1.32277
\(53\) −2.30936 −0.317215 −0.158608 0.987342i \(-0.550700\pi\)
−0.158608 + 0.987342i \(0.550700\pi\)
\(54\) 0 0
\(55\) 10.1570 1.36957
\(56\) −1.90772 −0.254930
\(57\) 0 0
\(58\) 2.51124 0.329742
\(59\) −9.22421 −1.20089 −0.600445 0.799666i \(-0.705010\pi\)
−0.600445 + 0.799666i \(0.705010\pi\)
\(60\) 0 0
\(61\) −12.4374 −1.59245 −0.796226 0.605000i \(-0.793173\pi\)
−0.796226 + 0.605000i \(0.793173\pi\)
\(62\) 27.6594 3.51275
\(63\) 0 0
\(64\) −3.54439 −0.443049
\(65\) −4.59486 −0.569922
\(66\) 0 0
\(67\) −14.6596 −1.79096 −0.895478 0.445106i \(-0.853166\pi\)
−0.895478 + 0.445106i \(0.853166\pi\)
\(68\) −17.8704 −2.16711
\(69\) 0 0
\(70\) 1.71587 0.205086
\(71\) −12.1080 −1.43695 −0.718476 0.695552i \(-0.755160\pi\)
−0.718476 + 0.695552i \(0.755160\pi\)
\(72\) 0 0
\(73\) 7.93152 0.928315 0.464157 0.885753i \(-0.346357\pi\)
0.464157 + 0.885753i \(0.346357\pi\)
\(74\) 1.64692 0.191450
\(75\) 0 0
\(76\) 1.87229 0.214766
\(77\) 1.61278 0.183793
\(78\) 0 0
\(79\) −6.32788 −0.711942 −0.355971 0.934497i \(-0.615850\pi\)
−0.355971 + 0.934497i \(0.615850\pi\)
\(80\) −12.3051 −1.37576
\(81\) 0 0
\(82\) −18.5152 −2.04467
\(83\) 16.4719 1.80803 0.904014 0.427502i \(-0.140606\pi\)
0.904014 + 0.427502i \(0.140606\pi\)
\(84\) 0 0
\(85\) 8.60834 0.933706
\(86\) 1.16343 0.125455
\(87\) 0 0
\(88\) −28.3586 −3.02303
\(89\) −7.88890 −0.836222 −0.418111 0.908396i \(-0.637308\pi\)
−0.418111 + 0.908396i \(0.637308\pi\)
\(90\) 0 0
\(91\) −0.729595 −0.0764823
\(92\) −4.30634 −0.448967
\(93\) 0 0
\(94\) −10.4109 −1.07380
\(95\) −0.901898 −0.0925328
\(96\) 0 0
\(97\) −15.8429 −1.60861 −0.804303 0.594219i \(-0.797461\pi\)
−0.804303 + 0.594219i \(0.797461\pi\)
\(98\) −17.3062 −1.74819
\(99\) 0 0
\(100\) −3.00088 −0.300088
\(101\) 12.1067 1.20466 0.602332 0.798246i \(-0.294239\pi\)
0.602332 + 0.798246i \(0.294239\pi\)
\(102\) 0 0
\(103\) −11.8721 −1.16979 −0.584895 0.811109i \(-0.698864\pi\)
−0.584895 + 0.811109i \(0.698864\pi\)
\(104\) 12.8290 1.25798
\(105\) 0 0
\(106\) −5.79937 −0.563284
\(107\) 3.91344 0.378327 0.189163 0.981946i \(-0.439422\pi\)
0.189163 + 0.981946i \(0.439422\pi\)
\(108\) 0 0
\(109\) 6.10250 0.584514 0.292257 0.956340i \(-0.405594\pi\)
0.292257 + 0.956340i \(0.405594\pi\)
\(110\) 25.5067 2.43197
\(111\) 0 0
\(112\) −1.95387 −0.184624
\(113\) 3.69220 0.347333 0.173666 0.984805i \(-0.444439\pi\)
0.173666 + 0.984805i \(0.444439\pi\)
\(114\) 0 0
\(115\) 2.07440 0.193439
\(116\) 4.30634 0.399834
\(117\) 0 0
\(118\) −23.1642 −2.13244
\(119\) 1.36688 0.125301
\(120\) 0 0
\(121\) 12.9742 1.17947
\(122\) −31.2334 −2.82774
\(123\) 0 0
\(124\) 47.4311 4.25944
\(125\) 11.8176 1.05700
\(126\) 0 0
\(127\) −11.0829 −0.983444 −0.491722 0.870752i \(-0.663632\pi\)
−0.491722 + 0.870752i \(0.663632\pi\)
\(128\) −15.5265 −1.37237
\(129\) 0 0
\(130\) −11.5388 −1.01202
\(131\) −16.7632 −1.46461 −0.732304 0.680977i \(-0.761555\pi\)
−0.732304 + 0.680977i \(0.761555\pi\)
\(132\) 0 0
\(133\) −0.143208 −0.0124177
\(134\) −36.8138 −3.18023
\(135\) 0 0
\(136\) −24.0347 −2.06096
\(137\) −1.30482 −0.111478 −0.0557391 0.998445i \(-0.517752\pi\)
−0.0557391 + 0.998445i \(0.517752\pi\)
\(138\) 0 0
\(139\) 0.506684 0.0429764 0.0214882 0.999769i \(-0.493160\pi\)
0.0214882 + 0.999769i \(0.493160\pi\)
\(140\) 2.94242 0.248680
\(141\) 0 0
\(142\) −30.4061 −2.55162
\(143\) −10.8455 −0.906949
\(144\) 0 0
\(145\) −2.07440 −0.172270
\(146\) 19.9180 1.64842
\(147\) 0 0
\(148\) 2.82418 0.232146
\(149\) 12.4088 1.01657 0.508286 0.861188i \(-0.330279\pi\)
0.508286 + 0.861188i \(0.330279\pi\)
\(150\) 0 0
\(151\) 17.4673 1.42147 0.710736 0.703459i \(-0.248362\pi\)
0.710736 + 0.703459i \(0.248362\pi\)
\(152\) 2.51812 0.204247
\(153\) 0 0
\(154\) 4.05008 0.326365
\(155\) −22.8480 −1.83519
\(156\) 0 0
\(157\) 0.289576 0.0231107 0.0115553 0.999933i \(-0.496322\pi\)
0.0115553 + 0.999933i \(0.496322\pi\)
\(158\) −15.8908 −1.26421
\(159\) 0 0
\(160\) −6.87221 −0.543296
\(161\) 0.329384 0.0259591
\(162\) 0 0
\(163\) 16.7973 1.31566 0.657832 0.753165i \(-0.271474\pi\)
0.657832 + 0.753165i \(0.271474\pi\)
\(164\) −31.7504 −2.47929
\(165\) 0 0
\(166\) 41.3650 3.21055
\(167\) −10.5399 −0.815598 −0.407799 0.913072i \(-0.633704\pi\)
−0.407799 + 0.913072i \(0.633704\pi\)
\(168\) 0 0
\(169\) −8.09366 −0.622589
\(170\) 21.6176 1.65800
\(171\) 0 0
\(172\) 1.99507 0.152123
\(173\) 22.2051 1.68822 0.844112 0.536168i \(-0.180128\pi\)
0.844112 + 0.536168i \(0.180128\pi\)
\(174\) 0 0
\(175\) 0.229532 0.0173510
\(176\) −29.0446 −2.18932
\(177\) 0 0
\(178\) −19.8109 −1.48489
\(179\) −5.20296 −0.388887 −0.194444 0.980914i \(-0.562290\pi\)
−0.194444 + 0.980914i \(0.562290\pi\)
\(180\) 0 0
\(181\) 25.8911 1.92447 0.962235 0.272218i \(-0.0877573\pi\)
0.962235 + 0.272218i \(0.0877573\pi\)
\(182\) −1.83219 −0.135811
\(183\) 0 0
\(184\) −5.79178 −0.426976
\(185\) −1.36043 −0.100021
\(186\) 0 0
\(187\) 20.3188 1.48586
\(188\) −17.8529 −1.30205
\(189\) 0 0
\(190\) −2.26488 −0.164312
\(191\) 18.1086 1.31029 0.655147 0.755501i \(-0.272607\pi\)
0.655147 + 0.755501i \(0.272607\pi\)
\(192\) 0 0
\(193\) 21.6895 1.56124 0.780622 0.625003i \(-0.214902\pi\)
0.780622 + 0.625003i \(0.214902\pi\)
\(194\) −39.7855 −2.85643
\(195\) 0 0
\(196\) −29.6772 −2.11980
\(197\) 12.8759 0.917368 0.458684 0.888600i \(-0.348321\pi\)
0.458684 + 0.888600i \(0.348321\pi\)
\(198\) 0 0
\(199\) 9.73022 0.689757 0.344878 0.938647i \(-0.387920\pi\)
0.344878 + 0.938647i \(0.387920\pi\)
\(200\) −4.03601 −0.285389
\(201\) 0 0
\(202\) 30.4029 2.13914
\(203\) −0.329384 −0.0231183
\(204\) 0 0
\(205\) 15.2944 1.06821
\(206\) −29.8136 −2.07721
\(207\) 0 0
\(208\) 13.1393 0.911047
\(209\) −2.12881 −0.147253
\(210\) 0 0
\(211\) 21.1320 1.45479 0.727394 0.686220i \(-0.240731\pi\)
0.727394 + 0.686220i \(0.240731\pi\)
\(212\) −9.94490 −0.683018
\(213\) 0 0
\(214\) 9.82760 0.671801
\(215\) −0.961043 −0.0655426
\(216\) 0 0
\(217\) −3.62792 −0.246279
\(218\) 15.3249 1.03793
\(219\) 0 0
\(220\) 43.7395 2.94892
\(221\) −9.19190 −0.618314
\(222\) 0 0
\(223\) 18.3905 1.23152 0.615759 0.787934i \(-0.288849\pi\)
0.615759 + 0.787934i \(0.288849\pi\)
\(224\) −1.09120 −0.0729092
\(225\) 0 0
\(226\) 9.27201 0.616765
\(227\) −20.9143 −1.38813 −0.694066 0.719912i \(-0.744182\pi\)
−0.694066 + 0.719912i \(0.744182\pi\)
\(228\) 0 0
\(229\) 6.61855 0.437366 0.218683 0.975796i \(-0.429824\pi\)
0.218683 + 0.975796i \(0.429824\pi\)
\(230\) 5.20933 0.343493
\(231\) 0 0
\(232\) 5.79178 0.380249
\(233\) 17.6336 1.15522 0.577608 0.816314i \(-0.303986\pi\)
0.577608 + 0.816314i \(0.303986\pi\)
\(234\) 0 0
\(235\) 8.59988 0.560994
\(236\) −39.7226 −2.58572
\(237\) 0 0
\(238\) 3.43256 0.222500
\(239\) 3.61613 0.233908 0.116954 0.993137i \(-0.462687\pi\)
0.116954 + 0.993137i \(0.462687\pi\)
\(240\) 0 0
\(241\) −27.5459 −1.77439 −0.887193 0.461398i \(-0.847348\pi\)
−0.887193 + 0.461398i \(0.847348\pi\)
\(242\) 32.5814 2.09441
\(243\) 0 0
\(244\) −53.5599 −3.42882
\(245\) 14.2958 0.913323
\(246\) 0 0
\(247\) 0.963037 0.0612766
\(248\) 63.7921 4.05080
\(249\) 0 0
\(250\) 29.6768 1.87692
\(251\) −8.21398 −0.518462 −0.259231 0.965815i \(-0.583469\pi\)
−0.259231 + 0.965815i \(0.583469\pi\)
\(252\) 0 0
\(253\) 4.89635 0.307831
\(254\) −27.8317 −1.74632
\(255\) 0 0
\(256\) −31.9022 −1.99388
\(257\) −10.5170 −0.656034 −0.328017 0.944672i \(-0.606380\pi\)
−0.328017 + 0.944672i \(0.606380\pi\)
\(258\) 0 0
\(259\) −0.216016 −0.0134226
\(260\) −19.7870 −1.22714
\(261\) 0 0
\(262\) −42.0965 −2.60073
\(263\) 2.77438 0.171076 0.0855378 0.996335i \(-0.472739\pi\)
0.0855378 + 0.996335i \(0.472739\pi\)
\(264\) 0 0
\(265\) 4.79055 0.294281
\(266\) −0.359630 −0.0220503
\(267\) 0 0
\(268\) −63.1293 −3.85623
\(269\) −23.7005 −1.44505 −0.722524 0.691346i \(-0.757018\pi\)
−0.722524 + 0.691346i \(0.757018\pi\)
\(270\) 0 0
\(271\) 7.94842 0.482832 0.241416 0.970422i \(-0.422388\pi\)
0.241416 + 0.970422i \(0.422388\pi\)
\(272\) −24.6161 −1.49257
\(273\) 0 0
\(274\) −3.27672 −0.197954
\(275\) 3.41202 0.205753
\(276\) 0 0
\(277\) −3.94280 −0.236900 −0.118450 0.992960i \(-0.537793\pi\)
−0.118450 + 0.992960i \(0.537793\pi\)
\(278\) 1.27241 0.0763139
\(279\) 0 0
\(280\) 3.95739 0.236499
\(281\) −19.7692 −1.17933 −0.589667 0.807647i \(-0.700741\pi\)
−0.589667 + 0.807647i \(0.700741\pi\)
\(282\) 0 0
\(283\) −19.5488 −1.16205 −0.581027 0.813885i \(-0.697349\pi\)
−0.581027 + 0.813885i \(0.697349\pi\)
\(284\) −52.1411 −3.09400
\(285\) 0 0
\(286\) −27.2358 −1.61048
\(287\) 2.42853 0.143352
\(288\) 0 0
\(289\) 0.220779 0.0129870
\(290\) −5.20933 −0.305902
\(291\) 0 0
\(292\) 34.1558 1.99882
\(293\) −10.8038 −0.631162 −0.315581 0.948899i \(-0.602199\pi\)
−0.315581 + 0.948899i \(0.602199\pi\)
\(294\) 0 0
\(295\) 19.1347 1.11407
\(296\) 3.79836 0.220775
\(297\) 0 0
\(298\) 31.1616 1.80514
\(299\) −2.21503 −0.128098
\(300\) 0 0
\(301\) −0.152599 −0.00879568
\(302\) 43.8647 2.52413
\(303\) 0 0
\(304\) 2.57904 0.147918
\(305\) 25.8003 1.47732
\(306\) 0 0
\(307\) 4.16574 0.237751 0.118876 0.992909i \(-0.462071\pi\)
0.118876 + 0.992909i \(0.462071\pi\)
\(308\) 6.94518 0.395738
\(309\) 0 0
\(310\) −57.3768 −3.25879
\(311\) 8.17076 0.463321 0.231661 0.972797i \(-0.425584\pi\)
0.231661 + 0.972797i \(0.425584\pi\)
\(312\) 0 0
\(313\) 13.6902 0.773819 0.386909 0.922118i \(-0.373543\pi\)
0.386909 + 0.922118i \(0.373543\pi\)
\(314\) 0.727195 0.0410380
\(315\) 0 0
\(316\) −27.2500 −1.53293
\(317\) 19.5419 1.09758 0.548792 0.835959i \(-0.315088\pi\)
0.548792 + 0.835959i \(0.315088\pi\)
\(318\) 0 0
\(319\) −4.89635 −0.274143
\(320\) 7.35250 0.411017
\(321\) 0 0
\(322\) 0.827164 0.0460961
\(323\) −1.80422 −0.100390
\(324\) 0 0
\(325\) −1.54354 −0.0856204
\(326\) 42.1820 2.33625
\(327\) 0 0
\(328\) −42.7024 −2.35785
\(329\) 1.36553 0.0752843
\(330\) 0 0
\(331\) −11.9595 −0.657352 −0.328676 0.944443i \(-0.606602\pi\)
−0.328676 + 0.944443i \(0.606602\pi\)
\(332\) 70.9337 3.89299
\(333\) 0 0
\(334\) −26.4681 −1.44827
\(335\) 30.4099 1.66147
\(336\) 0 0
\(337\) −14.1312 −0.769773 −0.384887 0.922964i \(-0.625759\pi\)
−0.384887 + 0.922964i \(0.625759\pi\)
\(338\) −20.3251 −1.10554
\(339\) 0 0
\(340\) 37.0705 2.01043
\(341\) −53.9295 −2.92045
\(342\) 0 0
\(343\) 4.57565 0.247062
\(344\) 2.68326 0.144671
\(345\) 0 0
\(346\) 55.7624 2.99781
\(347\) 5.12769 0.275269 0.137635 0.990483i \(-0.456050\pi\)
0.137635 + 0.990483i \(0.456050\pi\)
\(348\) 0 0
\(349\) −24.1423 −1.29231 −0.646154 0.763207i \(-0.723624\pi\)
−0.646154 + 0.763207i \(0.723624\pi\)
\(350\) 0.576411 0.0308104
\(351\) 0 0
\(352\) −16.2209 −0.864577
\(353\) −15.5988 −0.830241 −0.415121 0.909766i \(-0.636261\pi\)
−0.415121 + 0.909766i \(0.636261\pi\)
\(354\) 0 0
\(355\) 25.1168 1.33306
\(356\) −33.9723 −1.80053
\(357\) 0 0
\(358\) −13.0659 −0.690554
\(359\) −16.0554 −0.847370 −0.423685 0.905810i \(-0.639264\pi\)
−0.423685 + 0.905810i \(0.639264\pi\)
\(360\) 0 0
\(361\) −18.8110 −0.990051
\(362\) 65.0189 3.41732
\(363\) 0 0
\(364\) −3.14189 −0.164680
\(365\) −16.4532 −0.861199
\(366\) 0 0
\(367\) 24.1708 1.26170 0.630852 0.775903i \(-0.282706\pi\)
0.630852 + 0.775903i \(0.282706\pi\)
\(368\) −5.93189 −0.309221
\(369\) 0 0
\(370\) −3.41637 −0.177609
\(371\) 0.760668 0.0394919
\(372\) 0 0
\(373\) 0.418763 0.0216827 0.0108414 0.999941i \(-0.496549\pi\)
0.0108414 + 0.999941i \(0.496549\pi\)
\(374\) 51.0255 2.63847
\(375\) 0 0
\(376\) −24.0111 −1.23828
\(377\) 2.21503 0.114080
\(378\) 0 0
\(379\) −12.9349 −0.664419 −0.332209 0.943206i \(-0.607794\pi\)
−0.332209 + 0.943206i \(0.607794\pi\)
\(380\) −3.88388 −0.199239
\(381\) 0 0
\(382\) 45.4752 2.32671
\(383\) −19.4317 −0.992912 −0.496456 0.868062i \(-0.665366\pi\)
−0.496456 + 0.868062i \(0.665366\pi\)
\(384\) 0 0
\(385\) −3.34556 −0.170505
\(386\) 54.4676 2.77233
\(387\) 0 0
\(388\) −68.2251 −3.46361
\(389\) −12.7146 −0.644655 −0.322327 0.946628i \(-0.604465\pi\)
−0.322327 + 0.946628i \(0.604465\pi\)
\(390\) 0 0
\(391\) 4.14979 0.209864
\(392\) −39.9141 −2.01597
\(393\) 0 0
\(394\) 32.3344 1.62899
\(395\) 13.1266 0.660470
\(396\) 0 0
\(397\) −3.82487 −0.191965 −0.0959824 0.995383i \(-0.530599\pi\)
−0.0959824 + 0.995383i \(0.530599\pi\)
\(398\) 24.4349 1.22481
\(399\) 0 0
\(400\) −4.13365 −0.206682
\(401\) 25.7050 1.28364 0.641822 0.766853i \(-0.278179\pi\)
0.641822 + 0.766853i \(0.278179\pi\)
\(402\) 0 0
\(403\) 24.3968 1.21529
\(404\) 52.1356 2.59385
\(405\) 0 0
\(406\) −0.827164 −0.0410515
\(407\) −3.21111 −0.159169
\(408\) 0 0
\(409\) −3.42184 −0.169199 −0.0845996 0.996415i \(-0.526961\pi\)
−0.0845996 + 0.996415i \(0.526961\pi\)
\(410\) 38.4081 1.89684
\(411\) 0 0
\(412\) −51.1252 −2.51876
\(413\) 3.03831 0.149505
\(414\) 0 0
\(415\) −34.1694 −1.67731
\(416\) 7.33807 0.359779
\(417\) 0 0
\(418\) −5.34595 −0.261479
\(419\) 6.84345 0.334324 0.167162 0.985929i \(-0.446540\pi\)
0.167162 + 0.985929i \(0.446540\pi\)
\(420\) 0 0
\(421\) 30.2672 1.47513 0.737567 0.675273i \(-0.235974\pi\)
0.737567 + 0.675273i \(0.235974\pi\)
\(422\) 53.0676 2.58329
\(423\) 0 0
\(424\) −13.3753 −0.649563
\(425\) 2.89179 0.140272
\(426\) 0 0
\(427\) 4.09670 0.198253
\(428\) 16.8526 0.814602
\(429\) 0 0
\(430\) −2.41341 −0.116385
\(431\) 23.8381 1.14824 0.574120 0.818771i \(-0.305344\pi\)
0.574120 + 0.818771i \(0.305344\pi\)
\(432\) 0 0
\(433\) −32.3113 −1.55278 −0.776392 0.630250i \(-0.782952\pi\)
−0.776392 + 0.630250i \(0.782952\pi\)
\(434\) −9.11059 −0.437322
\(435\) 0 0
\(436\) 26.2795 1.25856
\(437\) −0.434775 −0.0207981
\(438\) 0 0
\(439\) −3.14005 −0.149866 −0.0749332 0.997189i \(-0.523874\pi\)
−0.0749332 + 0.997189i \(0.523874\pi\)
\(440\) 58.8271 2.80447
\(441\) 0 0
\(442\) −23.0831 −1.09795
\(443\) −20.0935 −0.954673 −0.477336 0.878721i \(-0.658398\pi\)
−0.477336 + 0.878721i \(0.658398\pi\)
\(444\) 0 0
\(445\) 16.3648 0.775764
\(446\) 46.1830 2.18683
\(447\) 0 0
\(448\) 1.16747 0.0551577
\(449\) 26.5247 1.25178 0.625890 0.779911i \(-0.284736\pi\)
0.625890 + 0.779911i \(0.284736\pi\)
\(450\) 0 0
\(451\) 36.1004 1.69990
\(452\) 15.8999 0.747867
\(453\) 0 0
\(454\) −52.5209 −2.46493
\(455\) 1.51347 0.0709528
\(456\) 0 0
\(457\) 24.8925 1.16442 0.582211 0.813038i \(-0.302188\pi\)
0.582211 + 0.813038i \(0.302188\pi\)
\(458\) 16.6208 0.776638
\(459\) 0 0
\(460\) 8.93309 0.416507
\(461\) −14.3135 −0.666645 −0.333323 0.942813i \(-0.608170\pi\)
−0.333323 + 0.942813i \(0.608170\pi\)
\(462\) 0 0
\(463\) −11.6147 −0.539782 −0.269891 0.962891i \(-0.586988\pi\)
−0.269891 + 0.962891i \(0.586988\pi\)
\(464\) 5.93189 0.275381
\(465\) 0 0
\(466\) 44.2823 2.05134
\(467\) −7.84693 −0.363113 −0.181556 0.983381i \(-0.558113\pi\)
−0.181556 + 0.983381i \(0.558113\pi\)
\(468\) 0 0
\(469\) 4.82865 0.222966
\(470\) 21.5964 0.996167
\(471\) 0 0
\(472\) −53.4246 −2.45907
\(473\) −2.26841 −0.104302
\(474\) 0 0
\(475\) −0.302973 −0.0139014
\(476\) 5.88624 0.269795
\(477\) 0 0
\(478\) 9.08098 0.415354
\(479\) 9.05712 0.413831 0.206915 0.978359i \(-0.433658\pi\)
0.206915 + 0.978359i \(0.433658\pi\)
\(480\) 0 0
\(481\) 1.45265 0.0662353
\(482\) −69.1744 −3.15081
\(483\) 0 0
\(484\) 55.8713 2.53961
\(485\) 32.8646 1.49231
\(486\) 0 0
\(487\) 20.1934 0.915052 0.457526 0.889196i \(-0.348736\pi\)
0.457526 + 0.889196i \(0.348736\pi\)
\(488\) −72.0350 −3.26087
\(489\) 0 0
\(490\) 35.9001 1.62180
\(491\) −1.20309 −0.0542945 −0.0271472 0.999631i \(-0.508642\pi\)
−0.0271472 + 0.999631i \(0.508642\pi\)
\(492\) 0 0
\(493\) −4.14979 −0.186897
\(494\) 2.41842 0.108810
\(495\) 0 0
\(496\) 65.3353 2.93364
\(497\) 3.98818 0.178894
\(498\) 0 0
\(499\) 13.6638 0.611674 0.305837 0.952084i \(-0.401064\pi\)
0.305837 + 0.952084i \(0.401064\pi\)
\(500\) 50.8905 2.27589
\(501\) 0 0
\(502\) −20.6273 −0.920642
\(503\) 17.6204 0.785656 0.392828 0.919612i \(-0.371497\pi\)
0.392828 + 0.919612i \(0.371497\pi\)
\(504\) 0 0
\(505\) −25.1142 −1.11757
\(506\) 12.2959 0.546620
\(507\) 0 0
\(508\) −47.7266 −2.11752
\(509\) −38.6815 −1.71453 −0.857264 0.514877i \(-0.827838\pi\)
−0.857264 + 0.514877i \(0.827838\pi\)
\(510\) 0 0
\(511\) −2.61252 −0.115571
\(512\) −49.0610 −2.16821
\(513\) 0 0
\(514\) −26.4108 −1.16493
\(515\) 24.6274 1.08521
\(516\) 0 0
\(517\) 20.2988 0.892742
\(518\) −0.542470 −0.0238347
\(519\) 0 0
\(520\) −26.6124 −1.16703
\(521\) −3.48891 −0.152852 −0.0764259 0.997075i \(-0.524351\pi\)
−0.0764259 + 0.997075i \(0.524351\pi\)
\(522\) 0 0
\(523\) 1.19981 0.0524641 0.0262321 0.999656i \(-0.491649\pi\)
0.0262321 + 0.999656i \(0.491649\pi\)
\(524\) −72.1881 −3.15355
\(525\) 0 0
\(526\) 6.96714 0.303782
\(527\) −45.7068 −1.99102
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 12.0302 0.522560
\(531\) 0 0
\(532\) −0.616703 −0.0267374
\(533\) −16.3312 −0.707385
\(534\) 0 0
\(535\) −8.11805 −0.350974
\(536\) −84.9053 −3.66735
\(537\) 0 0
\(538\) −59.5178 −2.56600
\(539\) 33.7432 1.45342
\(540\) 0 0
\(541\) −23.3264 −1.00288 −0.501439 0.865193i \(-0.667196\pi\)
−0.501439 + 0.865193i \(0.667196\pi\)
\(542\) 19.9604 0.857373
\(543\) 0 0
\(544\) −13.7477 −0.589427
\(545\) −12.6590 −0.542254
\(546\) 0 0
\(547\) 4.42366 0.189142 0.0945711 0.995518i \(-0.469852\pi\)
0.0945711 + 0.995518i \(0.469852\pi\)
\(548\) −5.61900 −0.240032
\(549\) 0 0
\(550\) 8.56842 0.365359
\(551\) 0.434775 0.0185220
\(552\) 0 0
\(553\) 2.08431 0.0886337
\(554\) −9.90134 −0.420668
\(555\) 0 0
\(556\) 2.18196 0.0925355
\(557\) −2.29640 −0.0973014 −0.0486507 0.998816i \(-0.515492\pi\)
−0.0486507 + 0.998816i \(0.515492\pi\)
\(558\) 0 0
\(559\) 1.02619 0.0434033
\(560\) 4.05312 0.171276
\(561\) 0 0
\(562\) −49.6453 −2.09416
\(563\) −9.63174 −0.405929 −0.202965 0.979186i \(-0.565058\pi\)
−0.202965 + 0.979186i \(0.565058\pi\)
\(564\) 0 0
\(565\) −7.65911 −0.322221
\(566\) −49.0917 −2.06348
\(567\) 0 0
\(568\) −70.1268 −2.94245
\(569\) 19.6362 0.823191 0.411596 0.911367i \(-0.364972\pi\)
0.411596 + 0.911367i \(0.364972\pi\)
\(570\) 0 0
\(571\) −0.0358829 −0.00150165 −0.000750827 1.00000i \(-0.500239\pi\)
−0.000750827 1.00000i \(0.500239\pi\)
\(572\) −46.7046 −1.95282
\(573\) 0 0
\(574\) 6.09863 0.254552
\(575\) 0.696851 0.0290607
\(576\) 0 0
\(577\) 20.4917 0.853082 0.426541 0.904468i \(-0.359732\pi\)
0.426541 + 0.904468i \(0.359732\pi\)
\(578\) 0.554430 0.0230613
\(579\) 0 0
\(580\) −8.93309 −0.370926
\(581\) −5.42560 −0.225092
\(582\) 0 0
\(583\) 11.3074 0.468306
\(584\) 45.9377 1.90091
\(585\) 0 0
\(586\) −27.1309 −1.12077
\(587\) −39.7227 −1.63953 −0.819766 0.572698i \(-0.805897\pi\)
−0.819766 + 0.572698i \(0.805897\pi\)
\(588\) 0 0
\(589\) 4.78871 0.197316
\(590\) 48.0519 1.97827
\(591\) 0 0
\(592\) 3.89024 0.159888
\(593\) −18.9906 −0.779849 −0.389925 0.920847i \(-0.627499\pi\)
−0.389925 + 0.920847i \(0.627499\pi\)
\(594\) 0 0
\(595\) −2.83545 −0.116242
\(596\) 53.4367 2.18885
\(597\) 0 0
\(598\) −5.56247 −0.227466
\(599\) 15.1699 0.619823 0.309912 0.950765i \(-0.399700\pi\)
0.309912 + 0.950765i \(0.399700\pi\)
\(600\) 0 0
\(601\) −15.7115 −0.640885 −0.320442 0.947268i \(-0.603832\pi\)
−0.320442 + 0.947268i \(0.603832\pi\)
\(602\) −0.383214 −0.0156186
\(603\) 0 0
\(604\) 75.2203 3.06067
\(605\) −26.9137 −1.09420
\(606\) 0 0
\(607\) 16.9322 0.687257 0.343628 0.939106i \(-0.388344\pi\)
0.343628 + 0.939106i \(0.388344\pi\)
\(608\) 1.44035 0.0584138
\(609\) 0 0
\(610\) 64.7907 2.62330
\(611\) −9.18286 −0.371499
\(612\) 0 0
\(613\) −41.5232 −1.67710 −0.838552 0.544821i \(-0.816598\pi\)
−0.838552 + 0.544821i \(0.816598\pi\)
\(614\) 10.4612 0.422179
\(615\) 0 0
\(616\) 9.34087 0.376355
\(617\) 15.0521 0.605975 0.302988 0.952994i \(-0.402016\pi\)
0.302988 + 0.952994i \(0.402016\pi\)
\(618\) 0 0
\(619\) −33.7558 −1.35676 −0.678381 0.734711i \(-0.737318\pi\)
−0.678381 + 0.734711i \(0.737318\pi\)
\(620\) −98.3912 −3.95149
\(621\) 0 0
\(622\) 20.5188 0.822727
\(623\) 2.59848 0.104106
\(624\) 0 0
\(625\) −21.0301 −0.841206
\(626\) 34.3795 1.37408
\(627\) 0 0
\(628\) 1.24701 0.0497612
\(629\) −2.72151 −0.108514
\(630\) 0 0
\(631\) 25.8463 1.02893 0.514463 0.857513i \(-0.327991\pi\)
0.514463 + 0.857513i \(0.327991\pi\)
\(632\) −36.6497 −1.45785
\(633\) 0 0
\(634\) 49.0745 1.94900
\(635\) 22.9903 0.912342
\(636\) 0 0
\(637\) −15.2649 −0.604816
\(638\) −12.2959 −0.486800
\(639\) 0 0
\(640\) 32.2083 1.27315
\(641\) −11.5642 −0.456757 −0.228378 0.973572i \(-0.573342\pi\)
−0.228378 + 0.973572i \(0.573342\pi\)
\(642\) 0 0
\(643\) −19.5700 −0.771766 −0.385883 0.922548i \(-0.626103\pi\)
−0.385883 + 0.922548i \(0.626103\pi\)
\(644\) 1.41844 0.0558944
\(645\) 0 0
\(646\) −4.53085 −0.178264
\(647\) −7.87567 −0.309624 −0.154812 0.987944i \(-0.549477\pi\)
−0.154812 + 0.987944i \(0.549477\pi\)
\(648\) 0 0
\(649\) 45.1649 1.77288
\(650\) −3.87621 −0.152038
\(651\) 0 0
\(652\) 72.3348 2.83285
\(653\) 11.7165 0.458503 0.229251 0.973367i \(-0.426372\pi\)
0.229251 + 0.973367i \(0.426372\pi\)
\(654\) 0 0
\(655\) 34.7737 1.35872
\(656\) −43.7355 −1.70758
\(657\) 0 0
\(658\) 3.42919 0.133684
\(659\) −23.7139 −0.923761 −0.461881 0.886942i \(-0.652825\pi\)
−0.461881 + 0.886942i \(0.652825\pi\)
\(660\) 0 0
\(661\) 9.06231 0.352483 0.176242 0.984347i \(-0.443606\pi\)
0.176242 + 0.984347i \(0.443606\pi\)
\(662\) −30.0332 −1.16727
\(663\) 0 0
\(664\) 95.4018 3.70231
\(665\) 0.297071 0.0115199
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) −45.3882 −1.75612
\(669\) 0 0
\(670\) 76.3667 2.95030
\(671\) 60.8980 2.35094
\(672\) 0 0
\(673\) 12.5398 0.483374 0.241687 0.970354i \(-0.422299\pi\)
0.241687 + 0.970354i \(0.422299\pi\)
\(674\) −35.4868 −1.36690
\(675\) 0 0
\(676\) −34.8541 −1.34054
\(677\) 13.0087 0.499964 0.249982 0.968250i \(-0.419575\pi\)
0.249982 + 0.968250i \(0.419575\pi\)
\(678\) 0 0
\(679\) 5.21842 0.200265
\(680\) 49.8577 1.91195
\(681\) 0 0
\(682\) −135.430 −5.18589
\(683\) 24.1598 0.924449 0.462225 0.886763i \(-0.347051\pi\)
0.462225 + 0.886763i \(0.347051\pi\)
\(684\) 0 0
\(685\) 2.70672 0.103419
\(686\) 11.4906 0.438712
\(687\) 0 0
\(688\) 2.74817 0.104773
\(689\) −5.11530 −0.194877
\(690\) 0 0
\(691\) −8.79410 −0.334543 −0.167272 0.985911i \(-0.553496\pi\)
−0.167272 + 0.985911i \(0.553496\pi\)
\(692\) 95.6228 3.63503
\(693\) 0 0
\(694\) 12.8769 0.488800
\(695\) −1.05107 −0.0398693
\(696\) 0 0
\(697\) 30.5961 1.15891
\(698\) −60.6272 −2.29477
\(699\) 0 0
\(700\) 0.988443 0.0373596
\(701\) 17.1365 0.647238 0.323619 0.946188i \(-0.395100\pi\)
0.323619 + 0.946188i \(0.395100\pi\)
\(702\) 0 0
\(703\) 0.285133 0.0107540
\(704\) 17.3546 0.654075
\(705\) 0 0
\(706\) −39.1724 −1.47427
\(707\) −3.98776 −0.149975
\(708\) 0 0
\(709\) 11.6715 0.438331 0.219166 0.975688i \(-0.429666\pi\)
0.219166 + 0.975688i \(0.429666\pi\)
\(710\) 63.0744 2.36714
\(711\) 0 0
\(712\) −45.6908 −1.71234
\(713\) −11.0142 −0.412487
\(714\) 0 0
\(715\) 22.4980 0.841378
\(716\) −22.4057 −0.837341
\(717\) 0 0
\(718\) −40.3189 −1.50469
\(719\) 43.8644 1.63587 0.817933 0.575313i \(-0.195120\pi\)
0.817933 + 0.575313i \(0.195120\pi\)
\(720\) 0 0
\(721\) 3.91047 0.145634
\(722\) −47.2389 −1.75805
\(723\) 0 0
\(724\) 111.496 4.14371
\(725\) −0.696851 −0.0258804
\(726\) 0 0
\(727\) 50.0227 1.85524 0.927620 0.373526i \(-0.121851\pi\)
0.927620 + 0.373526i \(0.121851\pi\)
\(728\) −4.22566 −0.156613
\(729\) 0 0
\(730\) −41.3179 −1.52925
\(731\) −1.92254 −0.0711078
\(732\) 0 0
\(733\) −8.42563 −0.311208 −0.155604 0.987820i \(-0.549732\pi\)
−0.155604 + 0.987820i \(0.549732\pi\)
\(734\) 60.6987 2.24043
\(735\) 0 0
\(736\) −3.31286 −0.122114
\(737\) 71.7785 2.64399
\(738\) 0 0
\(739\) −34.3160 −1.26234 −0.631168 0.775646i \(-0.717424\pi\)
−0.631168 + 0.775646i \(0.717424\pi\)
\(740\) −5.85848 −0.215362
\(741\) 0 0
\(742\) 1.91022 0.0701264
\(743\) 26.1566 0.959594 0.479797 0.877380i \(-0.340710\pi\)
0.479797 + 0.877380i \(0.340710\pi\)
\(744\) 0 0
\(745\) −25.7409 −0.943075
\(746\) 1.05162 0.0385024
\(747\) 0 0
\(748\) 87.4998 3.19931
\(749\) −1.28903 −0.0471000
\(750\) 0 0
\(751\) −2.94242 −0.107370 −0.0536852 0.998558i \(-0.517097\pi\)
−0.0536852 + 0.998558i \(0.517097\pi\)
\(752\) −24.5919 −0.896775
\(753\) 0 0
\(754\) 5.56247 0.202573
\(755\) −36.2343 −1.31870
\(756\) 0 0
\(757\) −30.5553 −1.11055 −0.555276 0.831666i \(-0.687388\pi\)
−0.555276 + 0.831666i \(0.687388\pi\)
\(758\) −32.4826 −1.17982
\(759\) 0 0
\(760\) −5.22360 −0.189480
\(761\) −7.04354 −0.255328 −0.127664 0.991817i \(-0.540748\pi\)
−0.127664 + 0.991817i \(0.540748\pi\)
\(762\) 0 0
\(763\) −2.01007 −0.0727694
\(764\) 77.9819 2.82129
\(765\) 0 0
\(766\) −48.7977 −1.76313
\(767\) −20.4319 −0.737752
\(768\) 0 0
\(769\) −38.3769 −1.38391 −0.691954 0.721942i \(-0.743250\pi\)
−0.691954 + 0.721942i \(0.743250\pi\)
\(770\) −8.40150 −0.302769
\(771\) 0 0
\(772\) 93.4024 3.36163
\(773\) 16.3163 0.586858 0.293429 0.955981i \(-0.405204\pi\)
0.293429 + 0.955981i \(0.405204\pi\)
\(774\) 0 0
\(775\) −7.67529 −0.275705
\(776\) −91.7589 −3.29395
\(777\) 0 0
\(778\) −31.9294 −1.14472
\(779\) −3.20556 −0.114851
\(780\) 0 0
\(781\) 59.2848 2.12138
\(782\) 10.4211 0.372659
\(783\) 0 0
\(784\) −40.8797 −1.45999
\(785\) −0.600697 −0.0214398
\(786\) 0 0
\(787\) −34.1348 −1.21677 −0.608387 0.793640i \(-0.708183\pi\)
−0.608387 + 0.793640i \(0.708183\pi\)
\(788\) 55.4479 1.97525
\(789\) 0 0
\(790\) 32.9640 1.17281
\(791\) −1.21615 −0.0432414
\(792\) 0 0
\(793\) −27.5493 −0.978303
\(794\) −9.60519 −0.340875
\(795\) 0 0
\(796\) 41.9016 1.48516
\(797\) −2.65681 −0.0941091 −0.0470546 0.998892i \(-0.514983\pi\)
−0.0470546 + 0.998892i \(0.514983\pi\)
\(798\) 0 0
\(799\) 17.2038 0.608628
\(800\) −2.30857 −0.0816203
\(801\) 0 0
\(802\) 64.5514 2.27939
\(803\) −38.8355 −1.37047
\(804\) 0 0
\(805\) −0.683276 −0.0240823
\(806\) 61.2664 2.15802
\(807\) 0 0
\(808\) 70.1195 2.46679
\(809\) −1.46905 −0.0516491 −0.0258246 0.999666i \(-0.508221\pi\)
−0.0258246 + 0.999666i \(0.508221\pi\)
\(810\) 0 0
\(811\) −10.8251 −0.380119 −0.190060 0.981773i \(-0.560868\pi\)
−0.190060 + 0.981773i \(0.560868\pi\)
\(812\) −1.41844 −0.0497776
\(813\) 0 0
\(814\) −8.06389 −0.282639
\(815\) −34.8443 −1.22054
\(816\) 0 0
\(817\) 0.201425 0.00704698
\(818\) −8.59308 −0.300450
\(819\) 0 0
\(820\) 65.8631 2.30004
\(821\) 11.6328 0.405988 0.202994 0.979180i \(-0.434933\pi\)
0.202994 + 0.979180i \(0.434933\pi\)
\(822\) 0 0
\(823\) 41.5811 1.44942 0.724712 0.689051i \(-0.241973\pi\)
0.724712 + 0.689051i \(0.241973\pi\)
\(824\) −68.7604 −2.39538
\(825\) 0 0
\(826\) 7.62994 0.265479
\(827\) −26.0406 −0.905521 −0.452760 0.891632i \(-0.649561\pi\)
−0.452760 + 0.891632i \(0.649561\pi\)
\(828\) 0 0
\(829\) −7.98370 −0.277285 −0.138643 0.990342i \(-0.544274\pi\)
−0.138643 + 0.990342i \(0.544274\pi\)
\(830\) −85.8077 −2.97843
\(831\) 0 0
\(832\) −7.85092 −0.272182
\(833\) 28.5983 0.990873
\(834\) 0 0
\(835\) 21.8639 0.756632
\(836\) −9.16737 −0.317060
\(837\) 0 0
\(838\) 17.1856 0.593666
\(839\) 47.9200 1.65438 0.827191 0.561920i \(-0.189937\pi\)
0.827191 + 0.561920i \(0.189937\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 76.0084 2.61942
\(843\) 0 0
\(844\) 91.0017 3.13241
\(845\) 16.7895 0.577577
\(846\) 0 0
\(847\) −4.27350 −0.146839
\(848\) −13.6989 −0.470422
\(849\) 0 0
\(850\) 7.26198 0.249084
\(851\) −0.655818 −0.0224812
\(852\) 0 0
\(853\) −9.80607 −0.335753 −0.167877 0.985808i \(-0.553691\pi\)
−0.167877 + 0.985808i \(0.553691\pi\)
\(854\) 10.2878 0.352042
\(855\) 0 0
\(856\) 22.6658 0.774701
\(857\) −1.34916 −0.0460864 −0.0230432 0.999734i \(-0.507336\pi\)
−0.0230432 + 0.999734i \(0.507336\pi\)
\(858\) 0 0
\(859\) −0.248201 −0.00846852 −0.00423426 0.999991i \(-0.501348\pi\)
−0.00423426 + 0.999991i \(0.501348\pi\)
\(860\) −4.13858 −0.141124
\(861\) 0 0
\(862\) 59.8633 2.03895
\(863\) 47.4175 1.61411 0.807055 0.590476i \(-0.201060\pi\)
0.807055 + 0.590476i \(0.201060\pi\)
\(864\) 0 0
\(865\) −46.0623 −1.56617
\(866\) −81.1416 −2.75731
\(867\) 0 0
\(868\) −15.6231 −0.530281
\(869\) 30.9835 1.05104
\(870\) 0 0
\(871\) −32.4714 −1.10025
\(872\) 35.3444 1.19691
\(873\) 0 0
\(874\) −1.09182 −0.0369315
\(875\) −3.89252 −0.131591
\(876\) 0 0
\(877\) −24.3089 −0.820852 −0.410426 0.911894i \(-0.634620\pi\)
−0.410426 + 0.911894i \(0.634620\pi\)
\(878\) −7.88543 −0.266120
\(879\) 0 0
\(880\) 60.2502 2.03103
\(881\) 27.4357 0.924332 0.462166 0.886793i \(-0.347072\pi\)
0.462166 + 0.886793i \(0.347072\pi\)
\(882\) 0 0
\(883\) −24.8918 −0.837676 −0.418838 0.908061i \(-0.637562\pi\)
−0.418838 + 0.908061i \(0.637562\pi\)
\(884\) −39.5835 −1.33134
\(885\) 0 0
\(886\) −50.4597 −1.69523
\(887\) −12.2114 −0.410019 −0.205009 0.978760i \(-0.565723\pi\)
−0.205009 + 0.978760i \(0.565723\pi\)
\(888\) 0 0
\(889\) 3.65052 0.122434
\(890\) 41.0959 1.37754
\(891\) 0 0
\(892\) 79.1958 2.65167
\(893\) −1.80245 −0.0603167
\(894\) 0 0
\(895\) 10.7930 0.360771
\(896\) 5.11420 0.170854
\(897\) 0 0
\(898\) 66.6101 2.22281
\(899\) 11.0142 0.367346
\(900\) 0 0
\(901\) 9.58337 0.319268
\(902\) 90.6570 3.01855
\(903\) 0 0
\(904\) 21.3844 0.711235
\(905\) −53.7086 −1.78533
\(906\) 0 0
\(907\) −22.2846 −0.739949 −0.369975 0.929042i \(-0.620634\pi\)
−0.369975 + 0.929042i \(0.620634\pi\)
\(908\) −90.0641 −2.98888
\(909\) 0 0
\(910\) 3.80070 0.125992
\(911\) −24.4401 −0.809736 −0.404868 0.914375i \(-0.632682\pi\)
−0.404868 + 0.914375i \(0.632682\pi\)
\(912\) 0 0
\(913\) −80.6522 −2.66920
\(914\) 62.5111 2.06768
\(915\) 0 0
\(916\) 28.5017 0.941723
\(917\) 5.52154 0.182337
\(918\) 0 0
\(919\) −32.0653 −1.05774 −0.528869 0.848704i \(-0.677384\pi\)
−0.528869 + 0.848704i \(0.677384\pi\)
\(920\) 12.0145 0.396106
\(921\) 0 0
\(922\) −35.9446 −1.18377
\(923\) −26.8195 −0.882774
\(924\) 0 0
\(925\) −0.457008 −0.0150263
\(926\) −29.1674 −0.958501
\(927\) 0 0
\(928\) 3.31286 0.108750
\(929\) −58.1912 −1.90919 −0.954596 0.297902i \(-0.903713\pi\)
−0.954596 + 0.297902i \(0.903713\pi\)
\(930\) 0 0
\(931\) −2.99625 −0.0981982
\(932\) 75.9364 2.48738
\(933\) 0 0
\(934\) −19.7055 −0.644785
\(935\) −42.1494 −1.37843
\(936\) 0 0
\(937\) 23.5858 0.770515 0.385258 0.922809i \(-0.374113\pi\)
0.385258 + 0.922809i \(0.374113\pi\)
\(938\) 12.1259 0.395925
\(939\) 0 0
\(940\) 37.0340 1.20792
\(941\) −20.4455 −0.666503 −0.333252 0.942838i \(-0.608146\pi\)
−0.333252 + 0.942838i \(0.608146\pi\)
\(942\) 0 0
\(943\) 7.37293 0.240096
\(944\) −54.7170 −1.78089
\(945\) 0 0
\(946\) −5.69653 −0.185210
\(947\) −7.80239 −0.253544 −0.126772 0.991932i \(-0.540462\pi\)
−0.126772 + 0.991932i \(0.540462\pi\)
\(948\) 0 0
\(949\) 17.5685 0.570299
\(950\) −0.760839 −0.0246849
\(951\) 0 0
\(952\) 7.91666 0.256580
\(953\) −23.6780 −0.767007 −0.383504 0.923539i \(-0.625283\pi\)
−0.383504 + 0.923539i \(0.625283\pi\)
\(954\) 0 0
\(955\) −37.5646 −1.21556
\(956\) 15.5723 0.503644
\(957\) 0 0
\(958\) 22.7446 0.734846
\(959\) 0.429787 0.0138786
\(960\) 0 0
\(961\) 90.3136 2.91334
\(962\) 3.64797 0.117615
\(963\) 0 0
\(964\) −118.622 −3.82056
\(965\) −44.9928 −1.44837
\(966\) 0 0
\(967\) 37.1140 1.19350 0.596752 0.802425i \(-0.296457\pi\)
0.596752 + 0.802425i \(0.296457\pi\)
\(968\) 75.1438 2.41521
\(969\) 0 0
\(970\) 82.5311 2.64991
\(971\) −3.64698 −0.117037 −0.0585185 0.998286i \(-0.518638\pi\)
−0.0585185 + 0.998286i \(0.518638\pi\)
\(972\) 0 0
\(973\) −0.166894 −0.00535037
\(974\) 50.7106 1.62487
\(975\) 0 0
\(976\) −73.7776 −2.36156
\(977\) −18.3292 −0.586403 −0.293201 0.956051i \(-0.594721\pi\)
−0.293201 + 0.956051i \(0.594721\pi\)
\(978\) 0 0
\(979\) 38.6268 1.23452
\(980\) 61.5624 1.96654
\(981\) 0 0
\(982\) −3.02124 −0.0964116
\(983\) 11.7224 0.373885 0.186943 0.982371i \(-0.440142\pi\)
0.186943 + 0.982371i \(0.440142\pi\)
\(984\) 0 0
\(985\) −26.7097 −0.851043
\(986\) −10.4211 −0.331877
\(987\) 0 0
\(988\) 4.14717 0.131939
\(989\) −0.463287 −0.0147317
\(990\) 0 0
\(991\) 31.0791 0.987260 0.493630 0.869672i \(-0.335670\pi\)
0.493630 + 0.869672i \(0.335670\pi\)
\(992\) 36.4886 1.15852
\(993\) 0 0
\(994\) 10.0153 0.317665
\(995\) −20.1844 −0.639888
\(996\) 0 0
\(997\) −46.6959 −1.47887 −0.739437 0.673226i \(-0.764908\pi\)
−0.739437 + 0.673226i \(0.764908\pi\)
\(998\) 34.3130 1.08616
\(999\) 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.1.11 11
3.2 odd 2 2001.2.a.l.1.1 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.l.1.1 11 3.2 odd 2
6003.2.a.m.1.11 11 1.1 even 1 trivial