Properties

Label 1617.2.a.t.1.2
Level $1617$
Weight $2$
Character 1617.1
Self dual yes
Analytic conductor $12.912$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1617.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.9118100068\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \( x^{3} - 4x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 231)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.86081\) of defining polynomial
Character \(\chi\) \(=\) 1617.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.46260 q^{2} -1.00000 q^{3} +0.139194 q^{4} -2.39821 q^{5} -1.46260 q^{6} -2.72161 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.46260 q^{2} -1.00000 q^{3} +0.139194 q^{4} -2.39821 q^{5} -1.46260 q^{6} -2.72161 q^{8} +1.00000 q^{9} -3.50761 q^{10} -1.00000 q^{11} -0.139194 q^{12} -5.04502 q^{13} +2.39821 q^{15} -4.25901 q^{16} +6.36842 q^{17} +1.46260 q^{18} +5.32340 q^{19} -0.333816 q^{20} -1.46260 q^{22} +4.92520 q^{23} +2.72161 q^{24} +0.751399 q^{25} -7.37883 q^{26} -1.00000 q^{27} +5.04502 q^{29} +3.50761 q^{30} +7.57201 q^{31} -0.786003 q^{32} +1.00000 q^{33} +9.31444 q^{34} +0.139194 q^{36} +4.24860 q^{37} +7.78600 q^{38} +5.04502 q^{39} +6.52699 q^{40} +0.646809 q^{41} -10.5180 q^{43} -0.139194 q^{44} -2.39821 q^{45} +7.20359 q^{46} -0.526989 q^{47} +4.25901 q^{48} +1.09899 q^{50} -6.36842 q^{51} -0.702237 q^{52} +3.72161 q^{53} -1.46260 q^{54} +2.39821 q^{55} -5.32340 q^{57} +7.37883 q^{58} -7.97021 q^{59} +0.333816 q^{60} +2.00000 q^{61} +11.0748 q^{62} +7.36842 q^{64} +12.0990 q^{65} +1.46260 q^{66} +8.76663 q^{67} +0.886447 q^{68} -4.92520 q^{69} -11.4432 q^{71} -2.72161 q^{72} +13.0450 q^{73} +6.21400 q^{74} -0.751399 q^{75} +0.740987 q^{76} +7.37883 q^{78} +11.4432 q^{79} +10.2140 q^{80} +1.00000 q^{81} +0.946021 q^{82} -13.1648 q^{83} -15.2728 q^{85} -15.3836 q^{86} -5.04502 q^{87} +2.72161 q^{88} -11.8504 q^{89} -3.50761 q^{90} +0.685559 q^{92} -7.57201 q^{93} -0.770774 q^{94} -12.7666 q^{95} +0.786003 q^{96} +1.87122 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 4 q^{5} - 2 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{2} - 3 q^{3} + 6 q^{4} - 4 q^{5} - 2 q^{6} + 3 q^{8} + 3 q^{9} + 11 q^{10} - 3 q^{11} - 6 q^{12} + 4 q^{13} + 4 q^{15} - 4 q^{16} - 8 q^{17} + 2 q^{18} + 8 q^{19} + 3 q^{20} - 2 q^{22} + 10 q^{23} - 3 q^{24} + 15 q^{25} + q^{26} - 3 q^{27} - 4 q^{29} - 11 q^{30} + 2 q^{31} + 8 q^{32} + 3 q^{33} + 4 q^{34} + 6 q^{36} + 13 q^{38} - 4 q^{39} + 18 q^{40} - 14 q^{41} - 14 q^{43} - 6 q^{44} - 4 q^{45} + 28 q^{46} + 4 q^{48} - 19 q^{50} + 8 q^{51} + 29 q^{52} - 2 q^{54} + 4 q^{55} - 8 q^{57} - q^{58} - 3 q^{60} + 6 q^{61} + 38 q^{62} - 5 q^{64} + 14 q^{65} + 2 q^{66} - 4 q^{67} - 42 q^{68} - 10 q^{69} - 12 q^{71} + 3 q^{72} + 20 q^{73} + 29 q^{74} - 15 q^{75} + 11 q^{76} - q^{78} + 12 q^{79} + 41 q^{80} + 3 q^{81} + 6 q^{82} - 6 q^{83} - 6 q^{85} + 24 q^{86} + 4 q^{87} - 3 q^{88} - 26 q^{89} + 11 q^{90} + 26 q^{92} - 2 q^{93} - 35 q^{94} - 8 q^{95} - 8 q^{96} + 4 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.46260 1.03421 0.517107 0.855921i \(-0.327009\pi\)
0.517107 + 0.855921i \(0.327009\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.139194 0.0695971
\(5\) −2.39821 −1.07251 −0.536255 0.844056i \(-0.680162\pi\)
−0.536255 + 0.844056i \(0.680162\pi\)
\(6\) −1.46260 −0.597103
\(7\) 0 0
\(8\) −2.72161 −0.962235
\(9\) 1.00000 0.333333
\(10\) −3.50761 −1.10921
\(11\) −1.00000 −0.301511
\(12\) −0.139194 −0.0401819
\(13\) −5.04502 −1.39924 −0.699618 0.714517i \(-0.746646\pi\)
−0.699618 + 0.714517i \(0.746646\pi\)
\(14\) 0 0
\(15\) 2.39821 0.619214
\(16\) −4.25901 −1.06475
\(17\) 6.36842 1.54457 0.772284 0.635277i \(-0.219114\pi\)
0.772284 + 0.635277i \(0.219114\pi\)
\(18\) 1.46260 0.344738
\(19\) 5.32340 1.22127 0.610636 0.791911i \(-0.290914\pi\)
0.610636 + 0.791911i \(0.290914\pi\)
\(20\) −0.333816 −0.0746436
\(21\) 0 0
\(22\) −1.46260 −0.311827
\(23\) 4.92520 1.02697 0.513487 0.858097i \(-0.328353\pi\)
0.513487 + 0.858097i \(0.328353\pi\)
\(24\) 2.72161 0.555547
\(25\) 0.751399 0.150280
\(26\) −7.37883 −1.44711
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 5.04502 0.936836 0.468418 0.883507i \(-0.344824\pi\)
0.468418 + 0.883507i \(0.344824\pi\)
\(30\) 3.50761 0.640400
\(31\) 7.57201 1.35997 0.679986 0.733225i \(-0.261986\pi\)
0.679986 + 0.733225i \(0.261986\pi\)
\(32\) −0.786003 −0.138947
\(33\) 1.00000 0.174078
\(34\) 9.31444 1.59741
\(35\) 0 0
\(36\) 0.139194 0.0231990
\(37\) 4.24860 0.698466 0.349233 0.937036i \(-0.386442\pi\)
0.349233 + 0.937036i \(0.386442\pi\)
\(38\) 7.78600 1.26306
\(39\) 5.04502 0.807849
\(40\) 6.52699 1.03201
\(41\) 0.646809 0.101015 0.0505073 0.998724i \(-0.483916\pi\)
0.0505073 + 0.998724i \(0.483916\pi\)
\(42\) 0 0
\(43\) −10.5180 −1.60398 −0.801992 0.597335i \(-0.796226\pi\)
−0.801992 + 0.597335i \(0.796226\pi\)
\(44\) −0.139194 −0.0209843
\(45\) −2.39821 −0.357504
\(46\) 7.20359 1.06211
\(47\) −0.526989 −0.0768693 −0.0384347 0.999261i \(-0.512237\pi\)
−0.0384347 + 0.999261i \(0.512237\pi\)
\(48\) 4.25901 0.614736
\(49\) 0 0
\(50\) 1.09899 0.155421
\(51\) −6.36842 −0.891757
\(52\) −0.702237 −0.0973827
\(53\) 3.72161 0.511203 0.255601 0.966782i \(-0.417727\pi\)
0.255601 + 0.966782i \(0.417727\pi\)
\(54\) −1.46260 −0.199034
\(55\) 2.39821 0.323374
\(56\) 0 0
\(57\) −5.32340 −0.705102
\(58\) 7.37883 0.968888
\(59\) −7.97021 −1.03763 −0.518817 0.854886i \(-0.673627\pi\)
−0.518817 + 0.854886i \(0.673627\pi\)
\(60\) 0.333816 0.0430955
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 11.0748 1.40650
\(63\) 0 0
\(64\) 7.36842 0.921053
\(65\) 12.0990 1.50070
\(66\) 1.46260 0.180033
\(67\) 8.76663 1.07101 0.535507 0.844531i \(-0.320121\pi\)
0.535507 + 0.844531i \(0.320121\pi\)
\(68\) 0.886447 0.107497
\(69\) −4.92520 −0.592924
\(70\) 0 0
\(71\) −11.4432 −1.35806 −0.679030 0.734110i \(-0.737600\pi\)
−0.679030 + 0.734110i \(0.737600\pi\)
\(72\) −2.72161 −0.320745
\(73\) 13.0450 1.52680 0.763402 0.645924i \(-0.223528\pi\)
0.763402 + 0.645924i \(0.223528\pi\)
\(74\) 6.21400 0.722363
\(75\) −0.751399 −0.0867641
\(76\) 0.740987 0.0849970
\(77\) 0 0
\(78\) 7.37883 0.835488
\(79\) 11.4432 1.28746 0.643732 0.765251i \(-0.277385\pi\)
0.643732 + 0.765251i \(0.277385\pi\)
\(80\) 10.2140 1.14196
\(81\) 1.00000 0.111111
\(82\) 0.946021 0.104471
\(83\) −13.1648 −1.44503 −0.722514 0.691356i \(-0.757014\pi\)
−0.722514 + 0.691356i \(0.757014\pi\)
\(84\) 0 0
\(85\) −15.2728 −1.65657
\(86\) −15.3836 −1.65886
\(87\) −5.04502 −0.540882
\(88\) 2.72161 0.290125
\(89\) −11.8504 −1.25614 −0.628070 0.778157i \(-0.716155\pi\)
−0.628070 + 0.778157i \(0.716155\pi\)
\(90\) −3.50761 −0.369735
\(91\) 0 0
\(92\) 0.685559 0.0714744
\(93\) −7.57201 −0.785180
\(94\) −0.770774 −0.0794993
\(95\) −12.7666 −1.30983
\(96\) 0.786003 0.0802211
\(97\) 1.87122 0.189993 0.0949967 0.995478i \(-0.469716\pi\)
0.0949967 + 0.995478i \(0.469716\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 0.104590 0.0104590
\(101\) −4.51803 −0.449560 −0.224780 0.974409i \(-0.572166\pi\)
−0.224780 + 0.974409i \(0.572166\pi\)
\(102\) −9.31444 −0.922267
\(103\) 10.6468 1.04906 0.524531 0.851392i \(-0.324241\pi\)
0.524531 + 0.851392i \(0.324241\pi\)
\(104\) 13.7306 1.34639
\(105\) 0 0
\(106\) 5.44322 0.528693
\(107\) 15.9702 1.54390 0.771949 0.635684i \(-0.219282\pi\)
0.771949 + 0.635684i \(0.219282\pi\)
\(108\) −0.139194 −0.0133940
\(109\) 12.7756 1.22368 0.611840 0.790982i \(-0.290430\pi\)
0.611840 + 0.790982i \(0.290430\pi\)
\(110\) 3.50761 0.334438
\(111\) −4.24860 −0.403259
\(112\) 0 0
\(113\) 18.7368 1.76261 0.881307 0.472544i \(-0.156664\pi\)
0.881307 + 0.472544i \(0.156664\pi\)
\(114\) −7.78600 −0.729226
\(115\) −11.8116 −1.10144
\(116\) 0.702237 0.0652010
\(117\) −5.04502 −0.466412
\(118\) −11.6572 −1.07313
\(119\) 0 0
\(120\) −6.52699 −0.595830
\(121\) 1.00000 0.0909091
\(122\) 2.92520 0.264835
\(123\) −0.646809 −0.0583208
\(124\) 1.05398 0.0946501
\(125\) 10.1890 0.911334
\(126\) 0 0
\(127\) −2.27839 −0.202174 −0.101087 0.994878i \(-0.532232\pi\)
−0.101087 + 0.994878i \(0.532232\pi\)
\(128\) 12.3490 1.09151
\(129\) 10.5180 0.926061
\(130\) 17.6960 1.55204
\(131\) −4.00000 −0.349482 −0.174741 0.984614i \(-0.555909\pi\)
−0.174741 + 0.984614i \(0.555909\pi\)
\(132\) 0.139194 0.0121153
\(133\) 0 0
\(134\) 12.8221 1.10766
\(135\) 2.39821 0.206405
\(136\) −17.3324 −1.48624
\(137\) −4.77559 −0.408006 −0.204003 0.978970i \(-0.565395\pi\)
−0.204003 + 0.978970i \(0.565395\pi\)
\(138\) −7.20359 −0.613210
\(139\) 15.4432 1.30988 0.654939 0.755682i \(-0.272694\pi\)
0.654939 + 0.755682i \(0.272694\pi\)
\(140\) 0 0
\(141\) 0.526989 0.0443805
\(142\) −16.7368 −1.40452
\(143\) 5.04502 0.421885
\(144\) −4.25901 −0.354918
\(145\) −12.0990 −1.00477
\(146\) 19.0796 1.57904
\(147\) 0 0
\(148\) 0.591380 0.0486112
\(149\) −9.84143 −0.806241 −0.403121 0.915147i \(-0.632075\pi\)
−0.403121 + 0.915147i \(0.632075\pi\)
\(150\) −1.09899 −0.0897326
\(151\) −4.12878 −0.335996 −0.167998 0.985787i \(-0.553730\pi\)
−0.167998 + 0.985787i \(0.553730\pi\)
\(152\) −14.4882 −1.17515
\(153\) 6.36842 0.514856
\(154\) 0 0
\(155\) −18.1592 −1.45859
\(156\) 0.702237 0.0562239
\(157\) 0.946021 0.0755007 0.0377504 0.999287i \(-0.487981\pi\)
0.0377504 + 0.999287i \(0.487981\pi\)
\(158\) 16.7368 1.33151
\(159\) −3.72161 −0.295143
\(160\) 1.88500 0.149022
\(161\) 0 0
\(162\) 1.46260 0.114913
\(163\) 8.76663 0.686655 0.343328 0.939216i \(-0.388446\pi\)
0.343328 + 0.939216i \(0.388446\pi\)
\(164\) 0.0900320 0.00703032
\(165\) −2.39821 −0.186700
\(166\) −19.2549 −1.49447
\(167\) 24.3684 1.88568 0.942842 0.333239i \(-0.108142\pi\)
0.942842 + 0.333239i \(0.108142\pi\)
\(168\) 0 0
\(169\) 12.4522 0.957860
\(170\) −22.3380 −1.71324
\(171\) 5.32340 0.407091
\(172\) −1.46405 −0.111633
\(173\) −12.3476 −0.938770 −0.469385 0.882994i \(-0.655524\pi\)
−0.469385 + 0.882994i \(0.655524\pi\)
\(174\) −7.37883 −0.559388
\(175\) 0 0
\(176\) 4.25901 0.321035
\(177\) 7.97021 0.599078
\(178\) −17.3324 −1.29912
\(179\) −5.59283 −0.418028 −0.209014 0.977913i \(-0.567025\pi\)
−0.209014 + 0.977913i \(0.567025\pi\)
\(180\) −0.333816 −0.0248812
\(181\) −13.5720 −1.00880 −0.504400 0.863470i \(-0.668286\pi\)
−0.504400 + 0.863470i \(0.668286\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) −13.4045 −0.988191
\(185\) −10.1890 −0.749112
\(186\) −11.0748 −0.812044
\(187\) −6.36842 −0.465705
\(188\) −0.0733538 −0.00534988
\(189\) 0 0
\(190\) −18.6724 −1.35464
\(191\) −9.42240 −0.681781 −0.340890 0.940103i \(-0.610729\pi\)
−0.340890 + 0.940103i \(0.610729\pi\)
\(192\) −7.36842 −0.531770
\(193\) −10.1288 −0.729086 −0.364543 0.931187i \(-0.618775\pi\)
−0.364543 + 0.931187i \(0.618775\pi\)
\(194\) 2.73684 0.196494
\(195\) −12.0990 −0.866427
\(196\) 0 0
\(197\) −2.25756 −0.160845 −0.0804224 0.996761i \(-0.525627\pi\)
−0.0804224 + 0.996761i \(0.525627\pi\)
\(198\) −1.46260 −0.103942
\(199\) −3.07480 −0.217967 −0.108984 0.994044i \(-0.534760\pi\)
−0.108984 + 0.994044i \(0.534760\pi\)
\(200\) −2.04502 −0.144604
\(201\) −8.76663 −0.618350
\(202\) −6.60806 −0.464941
\(203\) 0 0
\(204\) −0.886447 −0.0620637
\(205\) −1.55118 −0.108339
\(206\) 15.5720 1.08495
\(207\) 4.92520 0.342325
\(208\) 21.4868 1.48984
\(209\) −5.32340 −0.368228
\(210\) 0 0
\(211\) −14.6468 −1.00833 −0.504164 0.863608i \(-0.668199\pi\)
−0.504164 + 0.863608i \(0.668199\pi\)
\(212\) 0.518027 0.0355782
\(213\) 11.4432 0.784077
\(214\) 23.3580 1.59672
\(215\) 25.2244 1.72029
\(216\) 2.72161 0.185182
\(217\) 0 0
\(218\) 18.6856 1.26555
\(219\) −13.0450 −0.881500
\(220\) 0.333816 0.0225059
\(221\) −32.1288 −2.16122
\(222\) −6.21400 −0.417056
\(223\) 1.90997 0.127901 0.0639505 0.997953i \(-0.479630\pi\)
0.0639505 + 0.997953i \(0.479630\pi\)
\(224\) 0 0
\(225\) 0.751399 0.0500933
\(226\) 27.4045 1.82292
\(227\) 3.20359 0.212629 0.106315 0.994333i \(-0.466095\pi\)
0.106315 + 0.994333i \(0.466095\pi\)
\(228\) −0.740987 −0.0490730
\(229\) 18.3088 1.20988 0.604941 0.796270i \(-0.293197\pi\)
0.604941 + 0.796270i \(0.293197\pi\)
\(230\) −17.2757 −1.13913
\(231\) 0 0
\(232\) −13.7306 −0.901456
\(233\) −16.5872 −1.08667 −0.543333 0.839517i \(-0.682838\pi\)
−0.543333 + 0.839517i \(0.682838\pi\)
\(234\) −7.37883 −0.482369
\(235\) 1.26383 0.0824432
\(236\) −1.10941 −0.0722162
\(237\) −11.4432 −0.743317
\(238\) 0 0
\(239\) 2.91623 0.188635 0.0943177 0.995542i \(-0.469933\pi\)
0.0943177 + 0.995542i \(0.469933\pi\)
\(240\) −10.2140 −0.659311
\(241\) 6.09899 0.392871 0.196435 0.980517i \(-0.437063\pi\)
0.196435 + 0.980517i \(0.437063\pi\)
\(242\) 1.46260 0.0940194
\(243\) −1.00000 −0.0641500
\(244\) 0.278388 0.0178220
\(245\) 0 0
\(246\) −0.946021 −0.0603161
\(247\) −26.8567 −1.70885
\(248\) −20.6081 −1.30861
\(249\) 13.1648 0.834288
\(250\) 14.9025 0.942514
\(251\) −1.62262 −0.102419 −0.0512093 0.998688i \(-0.516308\pi\)
−0.0512093 + 0.998688i \(0.516308\pi\)
\(252\) 0 0
\(253\) −4.92520 −0.309644
\(254\) −3.33237 −0.209091
\(255\) 15.2728 0.956419
\(256\) 3.32485 0.207803
\(257\) 6.89541 0.430124 0.215062 0.976600i \(-0.431005\pi\)
0.215062 + 0.976600i \(0.431005\pi\)
\(258\) 15.3836 0.957744
\(259\) 0 0
\(260\) 1.68411 0.104444
\(261\) 5.04502 0.312279
\(262\) −5.85039 −0.361439
\(263\) 5.08377 0.313478 0.156739 0.987640i \(-0.449902\pi\)
0.156739 + 0.987640i \(0.449902\pi\)
\(264\) −2.72161 −0.167504
\(265\) −8.92520 −0.548270
\(266\) 0 0
\(267\) 11.8504 0.725232
\(268\) 1.22026 0.0745394
\(269\) 0.886447 0.0540476 0.0270238 0.999635i \(-0.491397\pi\)
0.0270238 + 0.999635i \(0.491397\pi\)
\(270\) 3.50761 0.213467
\(271\) 25.3234 1.53829 0.769144 0.639076i \(-0.220683\pi\)
0.769144 + 0.639076i \(0.220683\pi\)
\(272\) −27.1232 −1.64458
\(273\) 0 0
\(274\) −6.98477 −0.421965
\(275\) −0.751399 −0.0453111
\(276\) −0.685559 −0.0412658
\(277\) −24.8269 −1.49170 −0.745851 0.666113i \(-0.767957\pi\)
−0.745851 + 0.666113i \(0.767957\pi\)
\(278\) 22.5872 1.35469
\(279\) 7.57201 0.453324
\(280\) 0 0
\(281\) 1.90101 0.113404 0.0567022 0.998391i \(-0.481941\pi\)
0.0567022 + 0.998391i \(0.481941\pi\)
\(282\) 0.770774 0.0458989
\(283\) 22.3178 1.32666 0.663328 0.748329i \(-0.269143\pi\)
0.663328 + 0.748329i \(0.269143\pi\)
\(284\) −1.59283 −0.0945171
\(285\) 12.7666 0.756230
\(286\) 7.37883 0.436320
\(287\) 0 0
\(288\) −0.786003 −0.0463157
\(289\) 23.5568 1.38569
\(290\) −17.6960 −1.03914
\(291\) −1.87122 −0.109693
\(292\) 1.81579 0.106261
\(293\) −12.0900 −0.706307 −0.353154 0.935565i \(-0.614891\pi\)
−0.353154 + 0.935565i \(0.614891\pi\)
\(294\) 0 0
\(295\) 19.1142 1.11287
\(296\) −11.5630 −0.672088
\(297\) 1.00000 0.0580259
\(298\) −14.3941 −0.833826
\(299\) −24.8477 −1.43698
\(300\) −0.104590 −0.00603853
\(301\) 0 0
\(302\) −6.03875 −0.347491
\(303\) 4.51803 0.259554
\(304\) −22.6724 −1.30035
\(305\) −4.79641 −0.274642
\(306\) 9.31444 0.532471
\(307\) 13.5928 0.775784 0.387892 0.921705i \(-0.373203\pi\)
0.387892 + 0.921705i \(0.373203\pi\)
\(308\) 0 0
\(309\) −10.6468 −0.605676
\(310\) −26.5597 −1.50849
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −13.7306 −0.777341
\(313\) −14.9252 −0.843622 −0.421811 0.906684i \(-0.638605\pi\)
−0.421811 + 0.906684i \(0.638605\pi\)
\(314\) 1.38365 0.0780838
\(315\) 0 0
\(316\) 1.59283 0.0896037
\(317\) 3.97918 0.223493 0.111746 0.993737i \(-0.464356\pi\)
0.111746 + 0.993737i \(0.464356\pi\)
\(318\) −5.44322 −0.305241
\(319\) −5.04502 −0.282467
\(320\) −17.6710 −0.987839
\(321\) −15.9702 −0.891370
\(322\) 0 0
\(323\) 33.9017 1.88634
\(324\) 0.139194 0.00773301
\(325\) −3.79082 −0.210277
\(326\) 12.8221 0.710148
\(327\) −12.7756 −0.706492
\(328\) −1.76036 −0.0971997
\(329\) 0 0
\(330\) −3.50761 −0.193088
\(331\) 23.4432 1.28856 0.644278 0.764791i \(-0.277158\pi\)
0.644278 + 0.764791i \(0.277158\pi\)
\(332\) −1.83247 −0.100570
\(333\) 4.24860 0.232822
\(334\) 35.6412 1.95020
\(335\) −21.0242 −1.14867
\(336\) 0 0
\(337\) 11.1648 0.608187 0.304094 0.952642i \(-0.401646\pi\)
0.304094 + 0.952642i \(0.401646\pi\)
\(338\) 18.2125 0.990632
\(339\) −18.7368 −1.01765
\(340\) −2.12588 −0.115292
\(341\) −7.57201 −0.410047
\(342\) 7.78600 0.421019
\(343\) 0 0
\(344\) 28.6260 1.54341
\(345\) 11.8116 0.635918
\(346\) −18.0596 −0.970889
\(347\) −22.5872 −1.21255 −0.606273 0.795256i \(-0.707336\pi\)
−0.606273 + 0.795256i \(0.707336\pi\)
\(348\) −0.702237 −0.0376438
\(349\) −27.9315 −1.49514 −0.747568 0.664185i \(-0.768779\pi\)
−0.747568 + 0.664185i \(0.768779\pi\)
\(350\) 0 0
\(351\) 5.04502 0.269283
\(352\) 0.786003 0.0418941
\(353\) 16.5478 0.880751 0.440376 0.897814i \(-0.354845\pi\)
0.440376 + 0.897814i \(0.354845\pi\)
\(354\) 11.6572 0.619574
\(355\) 27.4432 1.45654
\(356\) −1.64951 −0.0874236
\(357\) 0 0
\(358\) −8.18006 −0.432330
\(359\) 22.0305 1.16272 0.581362 0.813645i \(-0.302520\pi\)
0.581362 + 0.813645i \(0.302520\pi\)
\(360\) 6.52699 0.344003
\(361\) 9.33863 0.491507
\(362\) −19.8504 −1.04331
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) −31.2847 −1.63751
\(366\) −2.92520 −0.152902
\(367\) 19.3836 1.01182 0.505909 0.862587i \(-0.331157\pi\)
0.505909 + 0.862587i \(0.331157\pi\)
\(368\) −20.9765 −1.09347
\(369\) 0.646809 0.0336715
\(370\) −14.9025 −0.774742
\(371\) 0 0
\(372\) −1.05398 −0.0546463
\(373\) 29.2549 1.51476 0.757380 0.652975i \(-0.226479\pi\)
0.757380 + 0.652975i \(0.226479\pi\)
\(374\) −9.31444 −0.481638
\(375\) −10.1890 −0.526159
\(376\) 1.43426 0.0739663
\(377\) −25.4522 −1.31085
\(378\) 0 0
\(379\) 12.5270 0.643468 0.321734 0.946830i \(-0.395734\pi\)
0.321734 + 0.946830i \(0.395734\pi\)
\(380\) −1.77704 −0.0911602
\(381\) 2.27839 0.116725
\(382\) −13.7812 −0.705107
\(383\) 17.5928 0.898952 0.449476 0.893293i \(-0.351611\pi\)
0.449476 + 0.893293i \(0.351611\pi\)
\(384\) −12.3490 −0.630185
\(385\) 0 0
\(386\) −14.8143 −0.754030
\(387\) −10.5180 −0.534661
\(388\) 0.260463 0.0132230
\(389\) 20.0900 1.01861 0.509303 0.860588i \(-0.329903\pi\)
0.509303 + 0.860588i \(0.329903\pi\)
\(390\) −17.6960 −0.896070
\(391\) 31.3657 1.58623
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) −3.30191 −0.166348
\(395\) −27.4432 −1.38082
\(396\) −0.139194 −0.00699477
\(397\) 35.1053 1.76188 0.880941 0.473226i \(-0.156910\pi\)
0.880941 + 0.473226i \(0.156910\pi\)
\(398\) −4.49720 −0.225424
\(399\) 0 0
\(400\) −3.20022 −0.160011
\(401\) 9.57201 0.478003 0.239002 0.971019i \(-0.423180\pi\)
0.239002 + 0.971019i \(0.423180\pi\)
\(402\) −12.8221 −0.639506
\(403\) −38.2009 −1.90292
\(404\) −0.628883 −0.0312881
\(405\) −2.39821 −0.119168
\(406\) 0 0
\(407\) −4.24860 −0.210595
\(408\) 17.3324 0.858080
\(409\) −38.1801 −1.88788 −0.943941 0.330113i \(-0.892913\pi\)
−0.943941 + 0.330113i \(0.892913\pi\)
\(410\) −2.26875 −0.112046
\(411\) 4.77559 0.235563
\(412\) 1.48197 0.0730116
\(413\) 0 0
\(414\) 7.20359 0.354037
\(415\) 31.5720 1.54981
\(416\) 3.96540 0.194420
\(417\) −15.4432 −0.756258
\(418\) −7.78600 −0.380826
\(419\) −7.17380 −0.350463 −0.175231 0.984527i \(-0.556067\pi\)
−0.175231 + 0.984527i \(0.556067\pi\)
\(420\) 0 0
\(421\) 15.1530 0.738511 0.369255 0.929328i \(-0.379613\pi\)
0.369255 + 0.929328i \(0.379613\pi\)
\(422\) −21.4224 −1.04283
\(423\) −0.526989 −0.0256231
\(424\) −10.1288 −0.491897
\(425\) 4.78522 0.232117
\(426\) 16.7368 0.810903
\(427\) 0 0
\(428\) 2.22296 0.107451
\(429\) −5.04502 −0.243576
\(430\) 36.8932 1.77915
\(431\) 5.56304 0.267962 0.133981 0.990984i \(-0.457224\pi\)
0.133981 + 0.990984i \(0.457224\pi\)
\(432\) 4.25901 0.204912
\(433\) 25.6412 1.23224 0.616119 0.787653i \(-0.288704\pi\)
0.616119 + 0.787653i \(0.288704\pi\)
\(434\) 0 0
\(435\) 12.0990 0.580102
\(436\) 1.77829 0.0851645
\(437\) 26.2188 1.25422
\(438\) −19.0796 −0.911659
\(439\) −23.6710 −1.12976 −0.564878 0.825175i \(-0.691077\pi\)
−0.564878 + 0.825175i \(0.691077\pi\)
\(440\) −6.52699 −0.311162
\(441\) 0 0
\(442\) −46.9915 −2.23516
\(443\) −18.0305 −0.856653 −0.428326 0.903624i \(-0.640897\pi\)
−0.428326 + 0.903624i \(0.640897\pi\)
\(444\) −0.591380 −0.0280657
\(445\) 28.4197 1.34722
\(446\) 2.79352 0.132277
\(447\) 9.84143 0.465484
\(448\) 0 0
\(449\) −34.9765 −1.65064 −0.825321 0.564664i \(-0.809006\pi\)
−0.825321 + 0.564664i \(0.809006\pi\)
\(450\) 1.09899 0.0518071
\(451\) −0.646809 −0.0304570
\(452\) 2.60806 0.122673
\(453\) 4.12878 0.193987
\(454\) 4.68556 0.219904
\(455\) 0 0
\(456\) 14.4882 0.678474
\(457\) 4.53595 0.212183 0.106091 0.994356i \(-0.466166\pi\)
0.106091 + 0.994356i \(0.466166\pi\)
\(458\) 26.7785 1.25128
\(459\) −6.36842 −0.297252
\(460\) −1.64411 −0.0766571
\(461\) 2.79641 0.130242 0.0651210 0.997877i \(-0.479257\pi\)
0.0651210 + 0.997877i \(0.479257\pi\)
\(462\) 0 0
\(463\) 38.3595 1.78272 0.891358 0.453301i \(-0.149754\pi\)
0.891358 + 0.453301i \(0.149754\pi\)
\(464\) −21.4868 −0.997499
\(465\) 18.1592 0.842115
\(466\) −24.2605 −1.12384
\(467\) 20.4674 0.947119 0.473560 0.880762i \(-0.342969\pi\)
0.473560 + 0.880762i \(0.342969\pi\)
\(468\) −0.702237 −0.0324609
\(469\) 0 0
\(470\) 1.84848 0.0852638
\(471\) −0.946021 −0.0435904
\(472\) 21.6918 0.998447
\(473\) 10.5180 0.483619
\(474\) −16.7368 −0.768749
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 3.72161 0.170401
\(478\) 4.26528 0.195089
\(479\) 11.6137 0.530641 0.265321 0.964160i \(-0.414522\pi\)
0.265321 + 0.964160i \(0.414522\pi\)
\(480\) −1.88500 −0.0860380
\(481\) −21.4343 −0.977318
\(482\) 8.92038 0.406312
\(483\) 0 0
\(484\) 0.139194 0.00632701
\(485\) −4.48757 −0.203770
\(486\) −1.46260 −0.0663448
\(487\) 32.4793 1.47178 0.735888 0.677103i \(-0.236765\pi\)
0.735888 + 0.677103i \(0.236765\pi\)
\(488\) −5.44322 −0.246403
\(489\) −8.76663 −0.396441
\(490\) 0 0
\(491\) 26.6766 1.20390 0.601949 0.798535i \(-0.294391\pi\)
0.601949 + 0.798535i \(0.294391\pi\)
\(492\) −0.0900320 −0.00405895
\(493\) 32.1288 1.44701
\(494\) −39.2805 −1.76731
\(495\) 2.39821 0.107791
\(496\) −32.2493 −1.44804
\(497\) 0 0
\(498\) 19.2549 0.862831
\(499\) −41.2459 −1.84642 −0.923210 0.384296i \(-0.874444\pi\)
−0.923210 + 0.384296i \(0.874444\pi\)
\(500\) 1.41825 0.0634262
\(501\) −24.3684 −1.08870
\(502\) −2.37324 −0.105923
\(503\) −30.5180 −1.36073 −0.680366 0.732873i \(-0.738179\pi\)
−0.680366 + 0.732873i \(0.738179\pi\)
\(504\) 0 0
\(505\) 10.8352 0.482159
\(506\) −7.20359 −0.320238
\(507\) −12.4522 −0.553021
\(508\) −0.317138 −0.0140707
\(509\) 18.9944 0.841912 0.420956 0.907081i \(-0.361695\pi\)
0.420956 + 0.907081i \(0.361695\pi\)
\(510\) 22.3380 0.989142
\(511\) 0 0
\(512\) −19.8352 −0.876599
\(513\) −5.32340 −0.235034
\(514\) 10.0852 0.444840
\(515\) −25.5333 −1.12513
\(516\) 1.46405 0.0644511
\(517\) 0.526989 0.0231770
\(518\) 0 0
\(519\) 12.3476 0.541999
\(520\) −32.9288 −1.44402
\(521\) −25.2430 −1.10592 −0.552958 0.833209i \(-0.686501\pi\)
−0.552958 + 0.833209i \(0.686501\pi\)
\(522\) 7.37883 0.322963
\(523\) 2.93416 0.128302 0.0641509 0.997940i \(-0.479566\pi\)
0.0641509 + 0.997940i \(0.479566\pi\)
\(524\) −0.556777 −0.0243229
\(525\) 0 0
\(526\) 7.43551 0.324204
\(527\) 48.2217 2.10057
\(528\) −4.25901 −0.185350
\(529\) 1.25756 0.0546767
\(530\) −13.0540 −0.567029
\(531\) −7.97021 −0.345878
\(532\) 0 0
\(533\) −3.26316 −0.141343
\(534\) 17.3324 0.750045
\(535\) −38.2999 −1.65585
\(536\) −23.8594 −1.03057
\(537\) 5.59283 0.241348
\(538\) 1.29652 0.0558968
\(539\) 0 0
\(540\) 0.333816 0.0143652
\(541\) 8.90437 0.382829 0.191414 0.981509i \(-0.438693\pi\)
0.191414 + 0.981509i \(0.438693\pi\)
\(542\) 37.0380 1.59092
\(543\) 13.5720 0.582430
\(544\) −5.00560 −0.214613
\(545\) −30.6385 −1.31241
\(546\) 0 0
\(547\) −29.4737 −1.26020 −0.630102 0.776513i \(-0.716987\pi\)
−0.630102 + 0.776513i \(0.716987\pi\)
\(548\) −0.664734 −0.0283960
\(549\) 2.00000 0.0853579
\(550\) −1.09899 −0.0468613
\(551\) 26.8567 1.14413
\(552\) 13.4045 0.570532
\(553\) 0 0
\(554\) −36.3117 −1.54274
\(555\) 10.1890 0.432500
\(556\) 2.14961 0.0911636
\(557\) 14.8954 0.631139 0.315569 0.948903i \(-0.397804\pi\)
0.315569 + 0.948903i \(0.397804\pi\)
\(558\) 11.0748 0.468834
\(559\) 53.0636 2.24435
\(560\) 0 0
\(561\) 6.36842 0.268875
\(562\) 2.78041 0.117284
\(563\) 7.81164 0.329222 0.164611 0.986359i \(-0.447363\pi\)
0.164611 + 0.986359i \(0.447363\pi\)
\(564\) 0.0733538 0.00308875
\(565\) −44.9348 −1.89042
\(566\) 32.6420 1.37205
\(567\) 0 0
\(568\) 31.1440 1.30677
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 18.6724 0.782103
\(571\) 25.5512 1.06928 0.534642 0.845079i \(-0.320447\pi\)
0.534642 + 0.845079i \(0.320447\pi\)
\(572\) 0.702237 0.0293620
\(573\) 9.42240 0.393626
\(574\) 0 0
\(575\) 3.70079 0.154334
\(576\) 7.36842 0.307018
\(577\) 29.5124 1.22862 0.614309 0.789065i \(-0.289435\pi\)
0.614309 + 0.789065i \(0.289435\pi\)
\(578\) 34.4541 1.43310
\(579\) 10.1288 0.420938
\(580\) −1.68411 −0.0699288
\(581\) 0 0
\(582\) −2.73684 −0.113446
\(583\) −3.72161 −0.154133
\(584\) −35.5035 −1.46914
\(585\) 12.0990 0.500232
\(586\) −17.6829 −0.730472
\(587\) −31.3955 −1.29583 −0.647916 0.761712i \(-0.724359\pi\)
−0.647916 + 0.761712i \(0.724359\pi\)
\(588\) 0 0
\(589\) 40.3088 1.66090
\(590\) 27.9564 1.15095
\(591\) 2.25756 0.0928638
\(592\) −18.0948 −0.743694
\(593\) 7.90997 0.324823 0.162412 0.986723i \(-0.448073\pi\)
0.162412 + 0.986723i \(0.448073\pi\)
\(594\) 1.46260 0.0600111
\(595\) 0 0
\(596\) −1.36987 −0.0561120
\(597\) 3.07480 0.125843
\(598\) −36.3422 −1.48614
\(599\) 27.4432 1.12130 0.560650 0.828053i \(-0.310551\pi\)
0.560650 + 0.828053i \(0.310551\pi\)
\(600\) 2.04502 0.0834874
\(601\) −31.9910 −1.30494 −0.652471 0.757814i \(-0.726268\pi\)
−0.652471 + 0.757814i \(0.726268\pi\)
\(602\) 0 0
\(603\) 8.76663 0.357005
\(604\) −0.574702 −0.0233843
\(605\) −2.39821 −0.0975010
\(606\) 6.60806 0.268434
\(607\) −7.41344 −0.300902 −0.150451 0.988617i \(-0.548073\pi\)
−0.150451 + 0.988617i \(0.548073\pi\)
\(608\) −4.18421 −0.169692
\(609\) 0 0
\(610\) −7.01523 −0.284038
\(611\) 2.65867 0.107558
\(612\) 0.886447 0.0358325
\(613\) −33.9917 −1.37291 −0.686456 0.727171i \(-0.740835\pi\)
−0.686456 + 0.727171i \(0.740835\pi\)
\(614\) 19.8809 0.802326
\(615\) 1.55118 0.0625497
\(616\) 0 0
\(617\) −44.0305 −1.77260 −0.886300 0.463112i \(-0.846733\pi\)
−0.886300 + 0.463112i \(0.846733\pi\)
\(618\) −15.5720 −0.626398
\(619\) −40.0096 −1.60812 −0.804061 0.594546i \(-0.797332\pi\)
−0.804061 + 0.594546i \(0.797332\pi\)
\(620\) −2.52766 −0.101513
\(621\) −4.92520 −0.197641
\(622\) −11.7008 −0.469159
\(623\) 0 0
\(624\) −21.4868 −0.860160
\(625\) −28.1924 −1.12770
\(626\) −21.8296 −0.872485
\(627\) 5.32340 0.212596
\(628\) 0.131681 0.00525463
\(629\) 27.0569 1.07883
\(630\) 0 0
\(631\) 28.5568 1.13683 0.568414 0.822743i \(-0.307557\pi\)
0.568414 + 0.822743i \(0.307557\pi\)
\(632\) −31.1440 −1.23884
\(633\) 14.6468 0.582158
\(634\) 5.81994 0.231139
\(635\) 5.46405 0.216834
\(636\) −0.518027 −0.0205411
\(637\) 0 0
\(638\) −7.37883 −0.292131
\(639\) −11.4432 −0.452687
\(640\) −29.6156 −1.17066
\(641\) −31.1053 −1.22858 −0.614292 0.789079i \(-0.710558\pi\)
−0.614292 + 0.789079i \(0.710558\pi\)
\(642\) −23.3580 −0.921867
\(643\) 5.48197 0.216188 0.108094 0.994141i \(-0.465525\pi\)
0.108094 + 0.994141i \(0.465525\pi\)
\(644\) 0 0
\(645\) −25.2244 −0.993210
\(646\) 49.5845 1.95088
\(647\) 9.26383 0.364199 0.182099 0.983280i \(-0.441711\pi\)
0.182099 + 0.983280i \(0.441711\pi\)
\(648\) −2.72161 −0.106915
\(649\) 7.97021 0.312858
\(650\) −5.54445 −0.217471
\(651\) 0 0
\(652\) 1.22026 0.0477892
\(653\) −29.9821 −1.17329 −0.586645 0.809844i \(-0.699551\pi\)
−0.586645 + 0.809844i \(0.699551\pi\)
\(654\) −18.6856 −0.730663
\(655\) 9.59283 0.374823
\(656\) −2.75477 −0.107556
\(657\) 13.0450 0.508935
\(658\) 0 0
\(659\) 23.9702 0.933747 0.466873 0.884324i \(-0.345380\pi\)
0.466873 + 0.884324i \(0.345380\pi\)
\(660\) −0.333816 −0.0129938
\(661\) 40.4585 1.57365 0.786826 0.617175i \(-0.211723\pi\)
0.786826 + 0.617175i \(0.211723\pi\)
\(662\) 34.2880 1.33264
\(663\) 32.1288 1.24778
\(664\) 35.8296 1.39046
\(665\) 0 0
\(666\) 6.21400 0.240788
\(667\) 24.8477 0.962107
\(668\) 3.39194 0.131238
\(669\) −1.90997 −0.0738436
\(670\) −30.7499 −1.18797
\(671\) −2.00000 −0.0772091
\(672\) 0 0
\(673\) 21.8712 0.843073 0.421537 0.906811i \(-0.361491\pi\)
0.421537 + 0.906811i \(0.361491\pi\)
\(674\) 16.3297 0.628995
\(675\) −0.751399 −0.0289214
\(676\) 1.73327 0.0666643
\(677\) 1.26316 0.0485472 0.0242736 0.999705i \(-0.492273\pi\)
0.0242736 + 0.999705i \(0.492273\pi\)
\(678\) −27.4045 −1.05246
\(679\) 0 0
\(680\) 41.5666 1.59401
\(681\) −3.20359 −0.122762
\(682\) −11.0748 −0.424076
\(683\) 37.6441 1.44041 0.720206 0.693760i \(-0.244047\pi\)
0.720206 + 0.693760i \(0.244047\pi\)
\(684\) 0.740987 0.0283323
\(685\) 11.4529 0.437591
\(686\) 0 0
\(687\) −18.3088 −0.698526
\(688\) 44.7964 1.70785
\(689\) −18.7756 −0.715293
\(690\) 17.2757 0.657674
\(691\) −14.3892 −0.547393 −0.273696 0.961816i \(-0.588246\pi\)
−0.273696 + 0.961816i \(0.588246\pi\)
\(692\) −1.71871 −0.0653357
\(693\) 0 0
\(694\) −33.0361 −1.25403
\(695\) −37.0361 −1.40486
\(696\) 13.7306 0.520456
\(697\) 4.11915 0.156024
\(698\) −40.8525 −1.54629
\(699\) 16.5872 0.627387
\(700\) 0 0
\(701\) −39.2936 −1.48410 −0.742050 0.670345i \(-0.766146\pi\)
−0.742050 + 0.670345i \(0.766146\pi\)
\(702\) 7.37883 0.278496
\(703\) 22.6170 0.853017
\(704\) −7.36842 −0.277708
\(705\) −1.26383 −0.0475986
\(706\) 24.2028 0.910885
\(707\) 0 0
\(708\) 1.10941 0.0416941
\(709\) −49.2430 −1.84936 −0.924680 0.380745i \(-0.875667\pi\)
−0.924680 + 0.380745i \(0.875667\pi\)
\(710\) 40.1384 1.50637
\(711\) 11.4432 0.429154
\(712\) 32.2522 1.20870
\(713\) 37.2936 1.39666
\(714\) 0 0
\(715\) −12.0990 −0.452477
\(716\) −0.778489 −0.0290935
\(717\) −2.91623 −0.108909
\(718\) 32.2217 1.20250
\(719\) 7.41344 0.276475 0.138237 0.990399i \(-0.455856\pi\)
0.138237 + 0.990399i \(0.455856\pi\)
\(720\) 10.2140 0.380653
\(721\) 0 0
\(722\) 13.6587 0.508323
\(723\) −6.09899 −0.226824
\(724\) −1.88914 −0.0702095
\(725\) 3.79082 0.140787
\(726\) −1.46260 −0.0542821
\(727\) −18.9557 −0.703026 −0.351513 0.936183i \(-0.614333\pi\)
−0.351513 + 0.936183i \(0.614333\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −45.7569 −1.69354
\(731\) −66.9832 −2.47746
\(732\) −0.278388 −0.0102895
\(733\) 3.59283 0.132704 0.0663521 0.997796i \(-0.478864\pi\)
0.0663521 + 0.997796i \(0.478864\pi\)
\(734\) 28.3505 1.04644
\(735\) 0 0
\(736\) −3.87122 −0.142695
\(737\) −8.76663 −0.322923
\(738\) 0.946021 0.0348235
\(739\) −26.7756 −0.984956 −0.492478 0.870325i \(-0.663909\pi\)
−0.492478 + 0.870325i \(0.663909\pi\)
\(740\) −1.41825 −0.0521360
\(741\) 26.8567 0.986604
\(742\) 0 0
\(743\) −33.8027 −1.24010 −0.620050 0.784562i \(-0.712888\pi\)
−0.620050 + 0.784562i \(0.712888\pi\)
\(744\) 20.6081 0.755528
\(745\) 23.6018 0.864703
\(746\) 42.7881 1.56658
\(747\) −13.1648 −0.481676
\(748\) −0.886447 −0.0324117
\(749\) 0 0
\(750\) −14.9025 −0.544161
\(751\) 35.3955 1.29160 0.645800 0.763506i \(-0.276524\pi\)
0.645800 + 0.763506i \(0.276524\pi\)
\(752\) 2.24445 0.0818468
\(753\) 1.62262 0.0591314
\(754\) −37.2263 −1.35570
\(755\) 9.90168 0.360359
\(756\) 0 0
\(757\) −29.3442 −1.06653 −0.533267 0.845947i \(-0.679036\pi\)
−0.533267 + 0.845947i \(0.679036\pi\)
\(758\) 18.3220 0.665483
\(759\) 4.92520 0.178773
\(760\) 34.7458 1.26036
\(761\) −12.9044 −0.467783 −0.233892 0.972263i \(-0.575146\pi\)
−0.233892 + 0.972263i \(0.575146\pi\)
\(762\) 3.33237 0.120719
\(763\) 0 0
\(764\) −1.31154 −0.0474500
\(765\) −15.2728 −0.552189
\(766\) 25.7312 0.929708
\(767\) 40.2099 1.45189
\(768\) −3.32485 −0.119975
\(769\) −9.78186 −0.352743 −0.176371 0.984324i \(-0.556436\pi\)
−0.176371 + 0.984324i \(0.556436\pi\)
\(770\) 0 0
\(771\) −6.89541 −0.248332
\(772\) −1.40987 −0.0507422
\(773\) −29.7223 −1.06904 −0.534518 0.845157i \(-0.679507\pi\)
−0.534518 + 0.845157i \(0.679507\pi\)
\(774\) −15.3836 −0.552954
\(775\) 5.68960 0.204376
\(776\) −5.09273 −0.182818
\(777\) 0 0
\(778\) 29.3836 1.05345
\(779\) 3.44322 0.123366
\(780\) −1.68411 −0.0603008
\(781\) 11.4432 0.409471
\(782\) 45.8755 1.64050
\(783\) −5.04502 −0.180294
\(784\) 0 0
\(785\) −2.26875 −0.0809753
\(786\) 5.85039 0.208677
\(787\) −17.0242 −0.606847 −0.303423 0.952856i \(-0.598130\pi\)
−0.303423 + 0.952856i \(0.598130\pi\)
\(788\) −0.314240 −0.0111943
\(789\) −5.08377 −0.180987
\(790\) −40.1384 −1.42806
\(791\) 0 0
\(792\) 2.72161 0.0967083
\(793\) −10.0900 −0.358308
\(794\) 51.3449 1.82216
\(795\) 8.92520 0.316544
\(796\) −0.427995 −0.0151699
\(797\) 36.4287 1.29037 0.645185 0.764027i \(-0.276780\pi\)
0.645185 + 0.764027i \(0.276780\pi\)
\(798\) 0 0
\(799\) −3.35609 −0.118730
\(800\) −0.590602 −0.0208809
\(801\) −11.8504 −0.418713
\(802\) 14.0000 0.494357
\(803\) −13.0450 −0.460349
\(804\) −1.22026 −0.0430354
\(805\) 0 0
\(806\) −55.8726 −1.96803
\(807\) −0.886447 −0.0312044
\(808\) 12.2963 0.432583
\(809\) 44.4882 1.56412 0.782062 0.623201i \(-0.214168\pi\)
0.782062 + 0.623201i \(0.214168\pi\)
\(810\) −3.50761 −0.123245
\(811\) −7.65307 −0.268736 −0.134368 0.990932i \(-0.542900\pi\)
−0.134368 + 0.990932i \(0.542900\pi\)
\(812\) 0 0
\(813\) −25.3234 −0.888131
\(814\) −6.21400 −0.217800
\(815\) −21.0242 −0.736445
\(816\) 27.1232 0.949501
\(817\) −55.9917 −1.95890
\(818\) −55.8421 −1.95247
\(819\) 0 0
\(820\) −0.215915 −0.00754009
\(821\) −44.3691 −1.54849 −0.774246 0.632885i \(-0.781871\pi\)
−0.774246 + 0.632885i \(0.781871\pi\)
\(822\) 6.98477 0.243622
\(823\) 6.61702 0.230655 0.115327 0.993328i \(-0.463208\pi\)
0.115327 + 0.993328i \(0.463208\pi\)
\(824\) −28.9765 −1.00944
\(825\) 0.751399 0.0261604
\(826\) 0 0
\(827\) 39.7126 1.38094 0.690472 0.723359i \(-0.257403\pi\)
0.690472 + 0.723359i \(0.257403\pi\)
\(828\) 0.685559 0.0238248
\(829\) 3.90997 0.135799 0.0678994 0.997692i \(-0.478370\pi\)
0.0678994 + 0.997692i \(0.478370\pi\)
\(830\) 46.1772 1.60283
\(831\) 24.8269 0.861235
\(832\) −37.1738 −1.28877
\(833\) 0 0
\(834\) −22.5872 −0.782132
\(835\) −58.4405 −2.02242
\(836\) −0.740987 −0.0256276
\(837\) −7.57201 −0.261727
\(838\) −10.4924 −0.362453
\(839\) 9.58097 0.330772 0.165386 0.986229i \(-0.447113\pi\)
0.165386 + 0.986229i \(0.447113\pi\)
\(840\) 0 0
\(841\) −3.54781 −0.122338
\(842\) 22.1627 0.763778
\(843\) −1.90101 −0.0654741
\(844\) −2.03875 −0.0701767
\(845\) −29.8629 −1.02732
\(846\) −0.770774 −0.0264998
\(847\) 0 0
\(848\) −15.8504 −0.544305
\(849\) −22.3178 −0.765945
\(850\) 6.99886 0.240059
\(851\) 20.9252 0.717307
\(852\) 1.59283 0.0545694
\(853\) 14.5568 0.498415 0.249207 0.968450i \(-0.419830\pi\)
0.249207 + 0.968450i \(0.419830\pi\)
\(854\) 0 0
\(855\) −12.7666 −0.436609
\(856\) −43.4647 −1.48559
\(857\) −10.4793 −0.357965 −0.178983 0.983852i \(-0.557281\pi\)
−0.178983 + 0.983852i \(0.557281\pi\)
\(858\) −7.37883 −0.251909
\(859\) −2.88645 −0.0984843 −0.0492421 0.998787i \(-0.515681\pi\)
−0.0492421 + 0.998787i \(0.515681\pi\)
\(860\) 3.51109 0.119727
\(861\) 0 0
\(862\) 8.13650 0.277130
\(863\) −20.5485 −0.699479 −0.349739 0.936847i \(-0.613730\pi\)
−0.349739 + 0.936847i \(0.613730\pi\)
\(864\) 0.786003 0.0267404
\(865\) 29.6121 1.00684
\(866\) 37.5028 1.27440
\(867\) −23.5568 −0.800030
\(868\) 0 0
\(869\) −11.4432 −0.388185
\(870\) 17.6960 0.599950
\(871\) −44.2278 −1.49860
\(872\) −34.7702 −1.17747
\(873\) 1.87122 0.0633311
\(874\) 38.3476 1.29713
\(875\) 0 0
\(876\) −1.81579 −0.0613499
\(877\) 59.1149 1.99617 0.998084 0.0618724i \(-0.0197072\pi\)
0.998084 + 0.0618724i \(0.0197072\pi\)
\(878\) −34.6212 −1.16841
\(879\) 12.0900 0.407787
\(880\) −10.2140 −0.344314
\(881\) −30.3982 −1.02414 −0.512071 0.858943i \(-0.671121\pi\)
−0.512071 + 0.858943i \(0.671121\pi\)
\(882\) 0 0
\(883\) −35.6114 −1.19842 −0.599210 0.800592i \(-0.704519\pi\)
−0.599210 + 0.800592i \(0.704519\pi\)
\(884\) −4.47214 −0.150414
\(885\) −19.1142 −0.642518
\(886\) −26.3713 −0.885962
\(887\) −22.9736 −0.771377 −0.385689 0.922629i \(-0.626036\pi\)
−0.385689 + 0.922629i \(0.626036\pi\)
\(888\) 11.5630 0.388030
\(889\) 0 0
\(890\) 41.5666 1.39332
\(891\) −1.00000 −0.0335013
\(892\) 0.265856 0.00890153
\(893\) −2.80538 −0.0938784
\(894\) 14.3941 0.481409
\(895\) 13.4128 0.448339
\(896\) 0 0
\(897\) 24.8477 0.829640
\(898\) −51.1565 −1.70712
\(899\) 38.2009 1.27407
\(900\) 0.104590 0.00348634
\(901\) 23.7008 0.789588
\(902\) −0.946021 −0.0314991
\(903\) 0 0
\(904\) −50.9944 −1.69605
\(905\) 32.5485 1.08195
\(906\) 6.03875 0.200624
\(907\) −57.1745 −1.89845 −0.949224 0.314602i \(-0.898129\pi\)
−0.949224 + 0.314602i \(0.898129\pi\)
\(908\) 0.445920 0.0147984
\(909\) −4.51803 −0.149853
\(910\) 0 0
\(911\) 6.82687 0.226184 0.113092 0.993584i \(-0.463924\pi\)
0.113092 + 0.993584i \(0.463924\pi\)
\(912\) 22.6724 0.750760
\(913\) 13.1648 0.435692
\(914\) 6.63428 0.219442
\(915\) 4.79641 0.158565
\(916\) 2.54848 0.0842043
\(917\) 0 0
\(918\) −9.31444 −0.307422
\(919\) 12.0692 0.398126 0.199063 0.979987i \(-0.436210\pi\)
0.199063 + 0.979987i \(0.436210\pi\)
\(920\) 32.1467 1.05985
\(921\) −13.5928 −0.447899
\(922\) 4.09003 0.134698
\(923\) 57.7312 1.90025
\(924\) 0 0
\(925\) 3.19239 0.104965
\(926\) 56.1045 1.84371
\(927\) 10.6468 0.349687
\(928\) −3.96540 −0.130171
\(929\) −26.8954 −0.882410 −0.441205 0.897406i \(-0.645449\pi\)
−0.441205 + 0.897406i \(0.645449\pi\)
\(930\) 26.5597 0.870926
\(931\) 0 0
\(932\) −2.30885 −0.0756288
\(933\) 8.00000 0.261908
\(934\) 29.9356 0.979523
\(935\) 15.2728 0.499474
\(936\) 13.7306 0.448798
\(937\) 14.9944 0.489846 0.244923 0.969543i \(-0.421237\pi\)
0.244923 + 0.969543i \(0.421237\pi\)
\(938\) 0 0
\(939\) 14.9252 0.487065
\(940\) 0.175918 0.00573780
\(941\) 30.1205 0.981900 0.490950 0.871188i \(-0.336650\pi\)
0.490950 + 0.871188i \(0.336650\pi\)
\(942\) −1.38365 −0.0450817
\(943\) 3.18566 0.103739
\(944\) 33.9452 1.10482
\(945\) 0 0
\(946\) 15.3836 0.500166
\(947\) −17.3532 −0.563903 −0.281951 0.959429i \(-0.590982\pi\)
−0.281951 + 0.959429i \(0.590982\pi\)
\(948\) −1.59283 −0.0517327
\(949\) −65.8123 −2.13636
\(950\) 5.85039 0.189812
\(951\) −3.97918 −0.129034
\(952\) 0 0
\(953\) −2.14064 −0.0693422 −0.0346711 0.999399i \(-0.511038\pi\)
−0.0346711 + 0.999399i \(0.511038\pi\)
\(954\) 5.44322 0.176231
\(955\) 22.5969 0.731217
\(956\) 0.405923 0.0131285
\(957\) 5.04502 0.163082
\(958\) 16.9861 0.548796
\(959\) 0 0
\(960\) 17.6710 0.570329
\(961\) 26.3353 0.849525
\(962\) −31.3497 −1.01076
\(963\) 15.9702 0.514633
\(964\) 0.848944 0.0273427
\(965\) 24.2909 0.781952
\(966\) 0 0
\(967\) −1.53326 −0.0493062 −0.0246531 0.999696i \(-0.507848\pi\)
−0.0246531 + 0.999696i \(0.507848\pi\)
\(968\) −2.72161 −0.0874759
\(969\) −33.9017 −1.08908
\(970\) −6.56351 −0.210742
\(971\) 26.5574 0.852269 0.426135 0.904660i \(-0.359875\pi\)
0.426135 + 0.904660i \(0.359875\pi\)
\(972\) −0.139194 −0.00446465
\(973\) 0 0
\(974\) 47.5041 1.52213
\(975\) 3.79082 0.121403
\(976\) −8.51803 −0.272655
\(977\) −55.9017 −1.78845 −0.894227 0.447615i \(-0.852274\pi\)
−0.894227 + 0.447615i \(0.852274\pi\)
\(978\) −12.8221 −0.410004
\(979\) 11.8504 0.378740
\(980\) 0 0
\(981\) 12.7756 0.407893
\(982\) 39.0171 1.24509
\(983\) 53.0361 1.69159 0.845794 0.533510i \(-0.179127\pi\)
0.845794 + 0.533510i \(0.179127\pi\)
\(984\) 1.76036 0.0561183
\(985\) 5.41411 0.172508
\(986\) 46.9915 1.49651
\(987\) 0 0
\(988\) −3.73829 −0.118931
\(989\) −51.8034 −1.64725
\(990\) 3.50761 0.111479
\(991\) 14.7362 0.468110 0.234055 0.972223i \(-0.424800\pi\)
0.234055 + 0.972223i \(0.424800\pi\)
\(992\) −5.95162 −0.188964
\(993\) −23.4432 −0.743948
\(994\) 0 0
\(995\) 7.37402 0.233772
\(996\) 1.83247 0.0580640
\(997\) 45.0665 1.42727 0.713635 0.700517i \(-0.247047\pi\)
0.713635 + 0.700517i \(0.247047\pi\)
\(998\) −60.3262 −1.90959
\(999\) −4.24860 −0.134420
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 1617.2.a.t.1.2 3
3.2 odd 2 4851.2.a.bi.1.2 3
7.6 odd 2 231.2.a.e.1.2 3
21.20 even 2 693.2.a.l.1.2 3
28.27 even 2 3696.2.a.bo.1.2 3
35.34 odd 2 5775.2.a.bp.1.2 3
77.76 even 2 2541.2.a.bg.1.2 3
231.230 odd 2 7623.2.a.cd.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
231.2.a.e.1.2 3 7.6 odd 2
693.2.a.l.1.2 3 21.20 even 2
1617.2.a.t.1.2 3 1.1 even 1 trivial
2541.2.a.bg.1.2 3 77.76 even 2
3696.2.a.bo.1.2 3 28.27 even 2
4851.2.a.bi.1.2 3 3.2 odd 2
5775.2.a.bp.1.2 3 35.34 odd 2
7623.2.a.cd.1.2 3 231.230 odd 2