Properties

Label 7098.2.a.cg.1.3
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7098.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.6778153547\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.24698 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.24698 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.24698 q^{10} +0.198062 q^{11} +1.00000 q^{12} +1.00000 q^{14} +4.24698 q^{15} +1.00000 q^{16} -0.664874 q^{17} -1.00000 q^{18} +2.91185 q^{19} +4.24698 q^{20} -1.00000 q^{21} -0.198062 q^{22} +1.96077 q^{23} -1.00000 q^{24} +13.0368 q^{25} +1.00000 q^{27} -1.00000 q^{28} +4.65279 q^{29} -4.24698 q^{30} +6.67994 q^{31} -1.00000 q^{32} +0.198062 q^{33} +0.664874 q^{34} -4.24698 q^{35} +1.00000 q^{36} -4.96077 q^{37} -2.91185 q^{38} -4.24698 q^{40} +10.0707 q^{41} +1.00000 q^{42} -2.85086 q^{43} +0.198062 q^{44} +4.24698 q^{45} -1.96077 q^{46} +10.6039 q^{47} +1.00000 q^{48} +1.00000 q^{49} -13.0368 q^{50} -0.664874 q^{51} -14.5036 q^{53} -1.00000 q^{54} +0.841166 q^{55} +1.00000 q^{56} +2.91185 q^{57} -4.65279 q^{58} -5.05861 q^{59} +4.24698 q^{60} -0.878002 q^{61} -6.67994 q^{62} -1.00000 q^{63} +1.00000 q^{64} -0.198062 q^{66} -6.03684 q^{67} -0.664874 q^{68} +1.96077 q^{69} +4.24698 q^{70} -10.9879 q^{71} -1.00000 q^{72} +4.84117 q^{73} +4.96077 q^{74} +13.0368 q^{75} +2.91185 q^{76} -0.198062 q^{77} +0.423272 q^{79} +4.24698 q^{80} +1.00000 q^{81} -10.0707 q^{82} +11.0881 q^{83} -1.00000 q^{84} -2.82371 q^{85} +2.85086 q^{86} +4.65279 q^{87} -0.198062 q^{88} -15.6407 q^{89} -4.24698 q^{90} +1.96077 q^{92} +6.67994 q^{93} -10.6039 q^{94} +12.3666 q^{95} -1.00000 q^{96} +1.47889 q^{97} -1.00000 q^{98} +0.198062 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3q^{2} + 3q^{3} + 3q^{4} + 8q^{5} - 3q^{6} - 3q^{7} - 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - 3q^{2} + 3q^{3} + 3q^{4} + 8q^{5} - 3q^{6} - 3q^{7} - 3q^{8} + 3q^{9} - 8q^{10} + 5q^{11} + 3q^{12} + 3q^{14} + 8q^{15} + 3q^{16} - 3q^{17} - 3q^{18} + 5q^{19} + 8q^{20} - 3q^{21} - 5q^{22} - 7q^{23} - 3q^{24} + 11q^{25} + 3q^{27} - 3q^{28} - 4q^{29} - 8q^{30} - 4q^{31} - 3q^{32} + 5q^{33} + 3q^{34} - 8q^{35} + 3q^{36} - 2q^{37} - 5q^{38} - 8q^{40} + 18q^{41} + 3q^{42} + 5q^{43} + 5q^{44} + 8q^{45} + 7q^{46} + 23q^{47} + 3q^{48} + 3q^{49} - 11q^{50} - 3q^{51} - 12q^{53} - 3q^{54} + 11q^{55} + 3q^{56} + 5q^{57} + 4q^{58} + 16q^{59} + 8q^{60} + 17q^{61} + 4q^{62} - 3q^{63} + 3q^{64} - 5q^{66} + 10q^{67} - 3q^{68} - 7q^{69} + 8q^{70} - 14q^{71} - 3q^{72} + 23q^{73} + 2q^{74} + 11q^{75} + 5q^{76} - 5q^{77} + 4q^{79} + 8q^{80} + 3q^{81} - 18q^{82} + 37q^{83} - 3q^{84} - q^{85} - 5q^{86} - 4q^{87} - 5q^{88} - 10q^{89} - 8q^{90} - 7q^{92} - 4q^{93} - 23q^{94} + 11q^{95} - 3q^{96} + 20q^{97} - 3q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 4.24698 1.89931 0.949654 0.313302i \(-0.101435\pi\)
0.949654 + 0.313302i \(0.101435\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −4.24698 −1.34301
\(11\) 0.198062 0.0597180 0.0298590 0.999554i \(-0.490494\pi\)
0.0298590 + 0.999554i \(0.490494\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 1.00000 0.267261
\(15\) 4.24698 1.09657
\(16\) 1.00000 0.250000
\(17\) −0.664874 −0.161256 −0.0806279 0.996744i \(-0.525693\pi\)
−0.0806279 + 0.996744i \(0.525693\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.91185 0.668025 0.334013 0.942569i \(-0.391597\pi\)
0.334013 + 0.942569i \(0.391597\pi\)
\(20\) 4.24698 0.949654
\(21\) −1.00000 −0.218218
\(22\) −0.198062 −0.0422270
\(23\) 1.96077 0.408849 0.204425 0.978882i \(-0.434468\pi\)
0.204425 + 0.978882i \(0.434468\pi\)
\(24\) −1.00000 −0.204124
\(25\) 13.0368 2.60737
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) 4.65279 0.864002 0.432001 0.901873i \(-0.357808\pi\)
0.432001 + 0.901873i \(0.357808\pi\)
\(30\) −4.24698 −0.775389
\(31\) 6.67994 1.19975 0.599876 0.800093i \(-0.295216\pi\)
0.599876 + 0.800093i \(0.295216\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.198062 0.0344782
\(34\) 0.664874 0.114025
\(35\) −4.24698 −0.717871
\(36\) 1.00000 0.166667
\(37\) −4.96077 −0.815546 −0.407773 0.913083i \(-0.633694\pi\)
−0.407773 + 0.913083i \(0.633694\pi\)
\(38\) −2.91185 −0.472365
\(39\) 0 0
\(40\) −4.24698 −0.671506
\(41\) 10.0707 1.57278 0.786389 0.617732i \(-0.211948\pi\)
0.786389 + 0.617732i \(0.211948\pi\)
\(42\) 1.00000 0.154303
\(43\) −2.85086 −0.434751 −0.217376 0.976088i \(-0.569750\pi\)
−0.217376 + 0.976088i \(0.569750\pi\)
\(44\) 0.198062 0.0298590
\(45\) 4.24698 0.633102
\(46\) −1.96077 −0.289100
\(47\) 10.6039 1.54673 0.773367 0.633958i \(-0.218571\pi\)
0.773367 + 0.633958i \(0.218571\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) −13.0368 −1.84369
\(51\) −0.664874 −0.0931010
\(52\) 0 0
\(53\) −14.5036 −1.99223 −0.996115 0.0880662i \(-0.971931\pi\)
−0.996115 + 0.0880662i \(0.971931\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0.841166 0.113423
\(56\) 1.00000 0.133631
\(57\) 2.91185 0.385684
\(58\) −4.65279 −0.610942
\(59\) −5.05861 −0.658574 −0.329287 0.944230i \(-0.606808\pi\)
−0.329287 + 0.944230i \(0.606808\pi\)
\(60\) 4.24698 0.548283
\(61\) −0.878002 −0.112417 −0.0562083 0.998419i \(-0.517901\pi\)
−0.0562083 + 0.998419i \(0.517901\pi\)
\(62\) −6.67994 −0.848353
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.198062 −0.0243798
\(67\) −6.03684 −0.737517 −0.368758 0.929525i \(-0.620217\pi\)
−0.368758 + 0.929525i \(0.620217\pi\)
\(68\) −0.664874 −0.0806279
\(69\) 1.96077 0.236049
\(70\) 4.24698 0.507611
\(71\) −10.9879 −1.30403 −0.652013 0.758208i \(-0.726075\pi\)
−0.652013 + 0.758208i \(0.726075\pi\)
\(72\) −1.00000 −0.117851
\(73\) 4.84117 0.566616 0.283308 0.959029i \(-0.408568\pi\)
0.283308 + 0.959029i \(0.408568\pi\)
\(74\) 4.96077 0.576678
\(75\) 13.0368 1.50536
\(76\) 2.91185 0.334013
\(77\) −0.198062 −0.0225713
\(78\) 0 0
\(79\) 0.423272 0.0476218 0.0238109 0.999716i \(-0.492420\pi\)
0.0238109 + 0.999716i \(0.492420\pi\)
\(80\) 4.24698 0.474827
\(81\) 1.00000 0.111111
\(82\) −10.0707 −1.11212
\(83\) 11.0881 1.21708 0.608541 0.793522i \(-0.291755\pi\)
0.608541 + 0.793522i \(0.291755\pi\)
\(84\) −1.00000 −0.109109
\(85\) −2.82371 −0.306274
\(86\) 2.85086 0.307416
\(87\) 4.65279 0.498832
\(88\) −0.198062 −0.0211135
\(89\) −15.6407 −1.65791 −0.828956 0.559314i \(-0.811065\pi\)
−0.828956 + 0.559314i \(0.811065\pi\)
\(90\) −4.24698 −0.447671
\(91\) 0 0
\(92\) 1.96077 0.204425
\(93\) 6.67994 0.692677
\(94\) −10.6039 −1.09371
\(95\) 12.3666 1.26878
\(96\) −1.00000 −0.102062
\(97\) 1.47889 0.150159 0.0750795 0.997178i \(-0.476079\pi\)
0.0750795 + 0.997178i \(0.476079\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0.198062 0.0199060
\(100\) 13.0368 1.30368
\(101\) −18.6407 −1.85482 −0.927410 0.374046i \(-0.877970\pi\)
−0.927410 + 0.374046i \(0.877970\pi\)
\(102\) 0.664874 0.0658324
\(103\) 12.5700 1.23856 0.619281 0.785170i \(-0.287424\pi\)
0.619281 + 0.785170i \(0.287424\pi\)
\(104\) 0 0
\(105\) −4.24698 −0.414463
\(106\) 14.5036 1.40872
\(107\) 5.98792 0.578874 0.289437 0.957197i \(-0.406532\pi\)
0.289437 + 0.957197i \(0.406532\pi\)
\(108\) 1.00000 0.0962250
\(109\) −0.850855 −0.0814971 −0.0407486 0.999169i \(-0.512974\pi\)
−0.0407486 + 0.999169i \(0.512974\pi\)
\(110\) −0.841166 −0.0802021
\(111\) −4.96077 −0.470856
\(112\) −1.00000 −0.0944911
\(113\) −15.0030 −1.41136 −0.705681 0.708530i \(-0.749359\pi\)
−0.705681 + 0.708530i \(0.749359\pi\)
\(114\) −2.91185 −0.272720
\(115\) 8.32736 0.776530
\(116\) 4.65279 0.432001
\(117\) 0 0
\(118\) 5.05861 0.465682
\(119\) 0.664874 0.0609489
\(120\) −4.24698 −0.387694
\(121\) −10.9608 −0.996434
\(122\) 0.878002 0.0794906
\(123\) 10.0707 0.908043
\(124\) 6.67994 0.599876
\(125\) 34.1323 3.05288
\(126\) 1.00000 0.0890871
\(127\) −5.11529 −0.453909 −0.226954 0.973905i \(-0.572877\pi\)
−0.226954 + 0.973905i \(0.572877\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.85086 −0.251004
\(130\) 0 0
\(131\) −5.97046 −0.521642 −0.260821 0.965387i \(-0.583993\pi\)
−0.260821 + 0.965387i \(0.583993\pi\)
\(132\) 0.198062 0.0172391
\(133\) −2.91185 −0.252490
\(134\) 6.03684 0.521503
\(135\) 4.24698 0.365522
\(136\) 0.664874 0.0570125
\(137\) 13.0271 1.11298 0.556492 0.830853i \(-0.312147\pi\)
0.556492 + 0.830853i \(0.312147\pi\)
\(138\) −1.96077 −0.166912
\(139\) 4.36227 0.370003 0.185002 0.982738i \(-0.440771\pi\)
0.185002 + 0.982738i \(0.440771\pi\)
\(140\) −4.24698 −0.358935
\(141\) 10.6039 0.893007
\(142\) 10.9879 0.922086
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 19.7603 1.64100
\(146\) −4.84117 −0.400658
\(147\) 1.00000 0.0824786
\(148\) −4.96077 −0.407773
\(149\) 3.80194 0.311467 0.155733 0.987799i \(-0.450226\pi\)
0.155733 + 0.987799i \(0.450226\pi\)
\(150\) −13.0368 −1.06445
\(151\) 14.7342 1.19905 0.599527 0.800354i \(-0.295355\pi\)
0.599527 + 0.800354i \(0.295355\pi\)
\(152\) −2.91185 −0.236183
\(153\) −0.664874 −0.0537519
\(154\) 0.198062 0.0159603
\(155\) 28.3696 2.27870
\(156\) 0 0
\(157\) 1.15346 0.0920559 0.0460279 0.998940i \(-0.485344\pi\)
0.0460279 + 0.998940i \(0.485344\pi\)
\(158\) −0.423272 −0.0336737
\(159\) −14.5036 −1.15021
\(160\) −4.24698 −0.335753
\(161\) −1.96077 −0.154530
\(162\) −1.00000 −0.0785674
\(163\) 12.0532 0.944082 0.472041 0.881577i \(-0.343517\pi\)
0.472041 + 0.881577i \(0.343517\pi\)
\(164\) 10.0707 0.786389
\(165\) 0.841166 0.0654847
\(166\) −11.0881 −0.860607
\(167\) 17.8291 1.37966 0.689828 0.723973i \(-0.257686\pi\)
0.689828 + 0.723973i \(0.257686\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) 2.82371 0.216569
\(171\) 2.91185 0.222675
\(172\) −2.85086 −0.217376
\(173\) 16.7332 1.27220 0.636100 0.771607i \(-0.280547\pi\)
0.636100 + 0.771607i \(0.280547\pi\)
\(174\) −4.65279 −0.352727
\(175\) −13.0368 −0.985492
\(176\) 0.198062 0.0149295
\(177\) −5.05861 −0.380228
\(178\) 15.6407 1.17232
\(179\) 3.67025 0.274327 0.137164 0.990548i \(-0.456201\pi\)
0.137164 + 0.990548i \(0.456201\pi\)
\(180\) 4.24698 0.316551
\(181\) −14.6189 −1.08662 −0.543309 0.839533i \(-0.682829\pi\)
−0.543309 + 0.839533i \(0.682829\pi\)
\(182\) 0 0
\(183\) −0.878002 −0.0649038
\(184\) −1.96077 −0.144550
\(185\) −21.0683 −1.54897
\(186\) −6.67994 −0.489797
\(187\) −0.131687 −0.00962987
\(188\) 10.6039 0.773367
\(189\) −1.00000 −0.0727393
\(190\) −12.3666 −0.897166
\(191\) −24.7928 −1.79395 −0.896973 0.442084i \(-0.854239\pi\)
−0.896973 + 0.442084i \(0.854239\pi\)
\(192\) 1.00000 0.0721688
\(193\) 18.9487 1.36396 0.681978 0.731372i \(-0.261120\pi\)
0.681978 + 0.731372i \(0.261120\pi\)
\(194\) −1.47889 −0.106178
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 4.58642 0.326769 0.163384 0.986562i \(-0.447759\pi\)
0.163384 + 0.986562i \(0.447759\pi\)
\(198\) −0.198062 −0.0140757
\(199\) −17.8998 −1.26888 −0.634441 0.772972i \(-0.718769\pi\)
−0.634441 + 0.772972i \(0.718769\pi\)
\(200\) −13.0368 −0.921843
\(201\) −6.03684 −0.425806
\(202\) 18.6407 1.31156
\(203\) −4.65279 −0.326562
\(204\) −0.664874 −0.0465505
\(205\) 42.7700 2.98719
\(206\) −12.5700 −0.875795
\(207\) 1.96077 0.136283
\(208\) 0 0
\(209\) 0.576728 0.0398931
\(210\) 4.24698 0.293069
\(211\) 1.95108 0.134318 0.0671590 0.997742i \(-0.478607\pi\)
0.0671590 + 0.997742i \(0.478607\pi\)
\(212\) −14.5036 −0.996115
\(213\) −10.9879 −0.752880
\(214\) −5.98792 −0.409326
\(215\) −12.1075 −0.825726
\(216\) −1.00000 −0.0680414
\(217\) −6.67994 −0.453464
\(218\) 0.850855 0.0576272
\(219\) 4.84117 0.327136
\(220\) 0.841166 0.0567114
\(221\) 0 0
\(222\) 4.96077 0.332945
\(223\) 18.9051 1.26598 0.632991 0.774159i \(-0.281827\pi\)
0.632991 + 0.774159i \(0.281827\pi\)
\(224\) 1.00000 0.0668153
\(225\) 13.0368 0.869122
\(226\) 15.0030 0.997984
\(227\) 21.1468 1.40356 0.701780 0.712394i \(-0.252389\pi\)
0.701780 + 0.712394i \(0.252389\pi\)
\(228\) 2.91185 0.192842
\(229\) −22.3884 −1.47946 −0.739732 0.672902i \(-0.765048\pi\)
−0.739732 + 0.672902i \(0.765048\pi\)
\(230\) −8.32736 −0.549090
\(231\) −0.198062 −0.0130315
\(232\) −4.65279 −0.305471
\(233\) −23.5894 −1.54539 −0.772697 0.634776i \(-0.781093\pi\)
−0.772697 + 0.634776i \(0.781093\pi\)
\(234\) 0 0
\(235\) 45.0344 2.93772
\(236\) −5.05861 −0.329287
\(237\) 0.423272 0.0274944
\(238\) −0.664874 −0.0430974
\(239\) 15.9323 1.03057 0.515287 0.857018i \(-0.327685\pi\)
0.515287 + 0.857018i \(0.327685\pi\)
\(240\) 4.24698 0.274141
\(241\) −10.3569 −0.667146 −0.333573 0.942724i \(-0.608254\pi\)
−0.333573 + 0.942724i \(0.608254\pi\)
\(242\) 10.9608 0.704585
\(243\) 1.00000 0.0641500
\(244\) −0.878002 −0.0562083
\(245\) 4.24698 0.271330
\(246\) −10.0707 −0.642084
\(247\) 0 0
\(248\) −6.67994 −0.424177
\(249\) 11.0881 0.702683
\(250\) −34.1323 −2.15871
\(251\) 24.3424 1.53648 0.768240 0.640162i \(-0.221133\pi\)
0.768240 + 0.640162i \(0.221133\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 0.388355 0.0244157
\(254\) 5.11529 0.320962
\(255\) −2.82371 −0.176827
\(256\) 1.00000 0.0625000
\(257\) 22.6015 1.40984 0.704921 0.709286i \(-0.250982\pi\)
0.704921 + 0.709286i \(0.250982\pi\)
\(258\) 2.85086 0.177486
\(259\) 4.96077 0.308247
\(260\) 0 0
\(261\) 4.65279 0.288001
\(262\) 5.97046 0.368856
\(263\) −12.3110 −0.759126 −0.379563 0.925166i \(-0.623926\pi\)
−0.379563 + 0.925166i \(0.623926\pi\)
\(264\) −0.198062 −0.0121899
\(265\) −61.5967 −3.78386
\(266\) 2.91185 0.178537
\(267\) −15.6407 −0.957196
\(268\) −6.03684 −0.368758
\(269\) 5.67563 0.346049 0.173025 0.984918i \(-0.444646\pi\)
0.173025 + 0.984918i \(0.444646\pi\)
\(270\) −4.24698 −0.258463
\(271\) −14.4698 −0.878978 −0.439489 0.898248i \(-0.644840\pi\)
−0.439489 + 0.898248i \(0.644840\pi\)
\(272\) −0.664874 −0.0403139
\(273\) 0 0
\(274\) −13.0271 −0.786999
\(275\) 2.58211 0.155707
\(276\) 1.96077 0.118025
\(277\) 27.6383 1.66063 0.830313 0.557298i \(-0.188162\pi\)
0.830313 + 0.557298i \(0.188162\pi\)
\(278\) −4.36227 −0.261632
\(279\) 6.67994 0.399918
\(280\) 4.24698 0.253806
\(281\) −4.25368 −0.253754 −0.126877 0.991918i \(-0.540495\pi\)
−0.126877 + 0.991918i \(0.540495\pi\)
\(282\) −10.6039 −0.631452
\(283\) 10.8388 0.644298 0.322149 0.946689i \(-0.395595\pi\)
0.322149 + 0.946689i \(0.395595\pi\)
\(284\) −10.9879 −0.652013
\(285\) 12.3666 0.732533
\(286\) 0 0
\(287\) −10.0707 −0.594454
\(288\) −1.00000 −0.0589256
\(289\) −16.5579 −0.973997
\(290\) −19.7603 −1.16037
\(291\) 1.47889 0.0866943
\(292\) 4.84117 0.283308
\(293\) 15.6160 0.912294 0.456147 0.889904i \(-0.349229\pi\)
0.456147 + 0.889904i \(0.349229\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −21.4838 −1.25083
\(296\) 4.96077 0.288339
\(297\) 0.198062 0.0114927
\(298\) −3.80194 −0.220240
\(299\) 0 0
\(300\) 13.0368 0.752682
\(301\) 2.85086 0.164321
\(302\) −14.7342 −0.847860
\(303\) −18.6407 −1.07088
\(304\) 2.91185 0.167006
\(305\) −3.72886 −0.213514
\(306\) 0.664874 0.0380083
\(307\) 11.2838 0.644001 0.322001 0.946739i \(-0.395645\pi\)
0.322001 + 0.946739i \(0.395645\pi\)
\(308\) −0.198062 −0.0112856
\(309\) 12.5700 0.715084
\(310\) −28.3696 −1.61128
\(311\) 31.8732 1.80736 0.903682 0.428204i \(-0.140853\pi\)
0.903682 + 0.428204i \(0.140853\pi\)
\(312\) 0 0
\(313\) 4.55927 0.257705 0.128853 0.991664i \(-0.458871\pi\)
0.128853 + 0.991664i \(0.458871\pi\)
\(314\) −1.15346 −0.0650933
\(315\) −4.24698 −0.239290
\(316\) 0.423272 0.0238109
\(317\) 22.1239 1.24260 0.621301 0.783572i \(-0.286604\pi\)
0.621301 + 0.783572i \(0.286604\pi\)
\(318\) 14.5036 0.813324
\(319\) 0.921543 0.0515965
\(320\) 4.24698 0.237413
\(321\) 5.98792 0.334213
\(322\) 1.96077 0.109270
\(323\) −1.93602 −0.107723
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −12.0532 −0.667567
\(327\) −0.850855 −0.0470524
\(328\) −10.0707 −0.556061
\(329\) −10.6039 −0.584611
\(330\) −0.841166 −0.0463047
\(331\) −7.59286 −0.417341 −0.208671 0.977986i \(-0.566914\pi\)
−0.208671 + 0.977986i \(0.566914\pi\)
\(332\) 11.0881 0.608541
\(333\) −4.96077 −0.271849
\(334\) −17.8291 −0.975564
\(335\) −25.6383 −1.40077
\(336\) −1.00000 −0.0545545
\(337\) 20.7603 1.13089 0.565443 0.824787i \(-0.308705\pi\)
0.565443 + 0.824787i \(0.308705\pi\)
\(338\) 0 0
\(339\) −15.0030 −0.814850
\(340\) −2.82371 −0.153137
\(341\) 1.32304 0.0716469
\(342\) −2.91185 −0.157455
\(343\) −1.00000 −0.0539949
\(344\) 2.85086 0.153708
\(345\) 8.32736 0.448330
\(346\) −16.7332 −0.899581
\(347\) −25.5381 −1.37096 −0.685478 0.728093i \(-0.740407\pi\)
−0.685478 + 0.728093i \(0.740407\pi\)
\(348\) 4.65279 0.249416
\(349\) −3.42327 −0.183244 −0.0916218 0.995794i \(-0.529205\pi\)
−0.0916218 + 0.995794i \(0.529205\pi\)
\(350\) 13.0368 0.696848
\(351\) 0 0
\(352\) −0.198062 −0.0105568
\(353\) −3.18359 −0.169445 −0.0847226 0.996405i \(-0.527000\pi\)
−0.0847226 + 0.996405i \(0.527000\pi\)
\(354\) 5.05861 0.268862
\(355\) −46.6655 −2.47675
\(356\) −15.6407 −0.828956
\(357\) 0.664874 0.0351889
\(358\) −3.67025 −0.193979
\(359\) −22.7429 −1.20032 −0.600161 0.799879i \(-0.704897\pi\)
−0.600161 + 0.799879i \(0.704897\pi\)
\(360\) −4.24698 −0.223835
\(361\) −10.5211 −0.553742
\(362\) 14.6189 0.768354
\(363\) −10.9608 −0.575291
\(364\) 0 0
\(365\) 20.5603 1.07618
\(366\) 0.878002 0.0458939
\(367\) −27.0315 −1.41103 −0.705515 0.708695i \(-0.749284\pi\)
−0.705515 + 0.708695i \(0.749284\pi\)
\(368\) 1.96077 0.102212
\(369\) 10.0707 0.524259
\(370\) 21.0683 1.09529
\(371\) 14.5036 0.752992
\(372\) 6.67994 0.346339
\(373\) −13.2338 −0.685222 −0.342611 0.939477i \(-0.611311\pi\)
−0.342611 + 0.939477i \(0.611311\pi\)
\(374\) 0.131687 0.00680935
\(375\) 34.1323 1.76258
\(376\) −10.6039 −0.546853
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) −14.7095 −0.755575 −0.377788 0.925892i \(-0.623315\pi\)
−0.377788 + 0.925892i \(0.623315\pi\)
\(380\) 12.3666 0.634392
\(381\) −5.11529 −0.262064
\(382\) 24.7928 1.26851
\(383\) −15.5754 −0.795866 −0.397933 0.917415i \(-0.630272\pi\)
−0.397933 + 0.917415i \(0.630272\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −0.841166 −0.0428698
\(386\) −18.9487 −0.964463
\(387\) −2.85086 −0.144917
\(388\) 1.47889 0.0750795
\(389\) −18.8847 −0.957493 −0.478746 0.877953i \(-0.658909\pi\)
−0.478746 + 0.877953i \(0.658909\pi\)
\(390\) 0 0
\(391\) −1.30367 −0.0659293
\(392\) −1.00000 −0.0505076
\(393\) −5.97046 −0.301170
\(394\) −4.58642 −0.231060
\(395\) 1.79763 0.0904484
\(396\) 0.198062 0.00995300
\(397\) −28.6233 −1.43656 −0.718280 0.695754i \(-0.755070\pi\)
−0.718280 + 0.695754i \(0.755070\pi\)
\(398\) 17.8998 0.897235
\(399\) −2.91185 −0.145775
\(400\) 13.0368 0.651842
\(401\) −22.6601 −1.13159 −0.565795 0.824546i \(-0.691431\pi\)
−0.565795 + 0.824546i \(0.691431\pi\)
\(402\) 6.03684 0.301090
\(403\) 0 0
\(404\) −18.6407 −0.927410
\(405\) 4.24698 0.211034
\(406\) 4.65279 0.230914
\(407\) −0.982542 −0.0487028
\(408\) 0.664874 0.0329162
\(409\) −11.0325 −0.545523 −0.272762 0.962082i \(-0.587937\pi\)
−0.272762 + 0.962082i \(0.587937\pi\)
\(410\) −42.7700 −2.11226
\(411\) 13.0271 0.642582
\(412\) 12.5700 0.619281
\(413\) 5.05861 0.248918
\(414\) −1.96077 −0.0963667
\(415\) 47.0911 2.31161
\(416\) 0 0
\(417\) 4.36227 0.213621
\(418\) −0.576728 −0.0282087
\(419\) 16.0508 0.784135 0.392067 0.919937i \(-0.371760\pi\)
0.392067 + 0.919937i \(0.371760\pi\)
\(420\) −4.24698 −0.207231
\(421\) −25.2838 −1.23226 −0.616129 0.787645i \(-0.711300\pi\)
−0.616129 + 0.787645i \(0.711300\pi\)
\(422\) −1.95108 −0.0949772
\(423\) 10.6039 0.515578
\(424\) 14.5036 0.704359
\(425\) −8.66786 −0.420453
\(426\) 10.9879 0.532366
\(427\) 0.878002 0.0424895
\(428\) 5.98792 0.289437
\(429\) 0 0
\(430\) 12.1075 0.583877
\(431\) 36.0116 1.73462 0.867309 0.497770i \(-0.165848\pi\)
0.867309 + 0.497770i \(0.165848\pi\)
\(432\) 1.00000 0.0481125
\(433\) 27.9299 1.34223 0.671113 0.741355i \(-0.265817\pi\)
0.671113 + 0.741355i \(0.265817\pi\)
\(434\) 6.67994 0.320647
\(435\) 19.7603 0.947435
\(436\) −0.850855 −0.0407486
\(437\) 5.70948 0.273121
\(438\) −4.84117 −0.231320
\(439\) −28.4969 −1.36008 −0.680042 0.733173i \(-0.738039\pi\)
−0.680042 + 0.733173i \(0.738039\pi\)
\(440\) −0.841166 −0.0401010
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 33.9366 1.61238 0.806188 0.591659i \(-0.201527\pi\)
0.806188 + 0.591659i \(0.201527\pi\)
\(444\) −4.96077 −0.235428
\(445\) −66.4258 −3.14888
\(446\) −18.9051 −0.895185
\(447\) 3.80194 0.179825
\(448\) −1.00000 −0.0472456
\(449\) 3.59312 0.169570 0.0847850 0.996399i \(-0.472980\pi\)
0.0847850 + 0.996399i \(0.472980\pi\)
\(450\) −13.0368 −0.614562
\(451\) 1.99462 0.0939231
\(452\) −15.0030 −0.705681
\(453\) 14.7342 0.692275
\(454\) −21.1468 −0.992466
\(455\) 0 0
\(456\) −2.91185 −0.136360
\(457\) −16.2591 −0.760567 −0.380283 0.924870i \(-0.624174\pi\)
−0.380283 + 0.924870i \(0.624174\pi\)
\(458\) 22.3884 1.04614
\(459\) −0.664874 −0.0310337
\(460\) 8.32736 0.388265
\(461\) 33.7372 1.57130 0.785649 0.618672i \(-0.212329\pi\)
0.785649 + 0.618672i \(0.212329\pi\)
\(462\) 0.198062 0.00921469
\(463\) −13.6606 −0.634860 −0.317430 0.948282i \(-0.602820\pi\)
−0.317430 + 0.948282i \(0.602820\pi\)
\(464\) 4.65279 0.216000
\(465\) 28.3696 1.31561
\(466\) 23.5894 1.09276
\(467\) 1.33081 0.0615827 0.0307914 0.999526i \(-0.490197\pi\)
0.0307914 + 0.999526i \(0.490197\pi\)
\(468\) 0 0
\(469\) 6.03684 0.278755
\(470\) −45.0344 −2.07728
\(471\) 1.15346 0.0531485
\(472\) 5.05861 0.232841
\(473\) −0.564647 −0.0259625
\(474\) −0.423272 −0.0194415
\(475\) 37.9614 1.74179
\(476\) 0.664874 0.0304745
\(477\) −14.5036 −0.664076
\(478\) −15.9323 −0.728726
\(479\) 39.4416 1.80213 0.901066 0.433682i \(-0.142786\pi\)
0.901066 + 0.433682i \(0.142786\pi\)
\(480\) −4.24698 −0.193847
\(481\) 0 0
\(482\) 10.3569 0.471744
\(483\) −1.96077 −0.0892182
\(484\) −10.9608 −0.498217
\(485\) 6.28083 0.285198
\(486\) −1.00000 −0.0453609
\(487\) −14.7549 −0.668610 −0.334305 0.942465i \(-0.608502\pi\)
−0.334305 + 0.942465i \(0.608502\pi\)
\(488\) 0.878002 0.0397453
\(489\) 12.0532 0.545066
\(490\) −4.24698 −0.191859
\(491\) −20.5187 −0.925997 −0.462998 0.886359i \(-0.653226\pi\)
−0.462998 + 0.886359i \(0.653226\pi\)
\(492\) 10.0707 0.454022
\(493\) −3.09352 −0.139325
\(494\) 0 0
\(495\) 0.841166 0.0378076
\(496\) 6.67994 0.299938
\(497\) 10.9879 0.492876
\(498\) −11.0881 −0.496872
\(499\) −43.8678 −1.96379 −0.981897 0.189415i \(-0.939341\pi\)
−0.981897 + 0.189415i \(0.939341\pi\)
\(500\) 34.1323 1.52644
\(501\) 17.8291 0.796545
\(502\) −24.3424 −1.08646
\(503\) 8.50498 0.379218 0.189609 0.981860i \(-0.439278\pi\)
0.189609 + 0.981860i \(0.439278\pi\)
\(504\) 1.00000 0.0445435
\(505\) −79.1667 −3.52287
\(506\) −0.388355 −0.0172645
\(507\) 0 0
\(508\) −5.11529 −0.226954
\(509\) 35.7512 1.58464 0.792322 0.610103i \(-0.208872\pi\)
0.792322 + 0.610103i \(0.208872\pi\)
\(510\) 2.82371 0.125036
\(511\) −4.84117 −0.214161
\(512\) −1.00000 −0.0441942
\(513\) 2.91185 0.128561
\(514\) −22.6015 −0.996909
\(515\) 53.3846 2.35241
\(516\) −2.85086 −0.125502
\(517\) 2.10023 0.0923679
\(518\) −4.96077 −0.217964
\(519\) 16.7332 0.734505
\(520\) 0 0
\(521\) 15.5157 0.679756 0.339878 0.940469i \(-0.389614\pi\)
0.339878 + 0.940469i \(0.389614\pi\)
\(522\) −4.65279 −0.203647
\(523\) 44.6413 1.95203 0.976014 0.217708i \(-0.0698581\pi\)
0.976014 + 0.217708i \(0.0698581\pi\)
\(524\) −5.97046 −0.260821
\(525\) −13.0368 −0.568974
\(526\) 12.3110 0.536783
\(527\) −4.44132 −0.193467
\(528\) 0.198062 0.00861955
\(529\) −19.1554 −0.832842
\(530\) 61.5967 2.67559
\(531\) −5.05861 −0.219525
\(532\) −2.91185 −0.126245
\(533\) 0 0
\(534\) 15.6407 0.676840
\(535\) 25.4306 1.09946
\(536\) 6.03684 0.260752
\(537\) 3.67025 0.158383
\(538\) −5.67563 −0.244694
\(539\) 0.198062 0.00853115
\(540\) 4.24698 0.182761
\(541\) −24.7530 −1.06422 −0.532108 0.846677i \(-0.678600\pi\)
−0.532108 + 0.846677i \(0.678600\pi\)
\(542\) 14.4698 0.621531
\(543\) −14.6189 −0.627359
\(544\) 0.664874 0.0285063
\(545\) −3.61356 −0.154788
\(546\) 0 0
\(547\) 0.242668 0.0103757 0.00518786 0.999987i \(-0.498349\pi\)
0.00518786 + 0.999987i \(0.498349\pi\)
\(548\) 13.0271 0.556492
\(549\) −0.878002 −0.0374722
\(550\) −2.58211 −0.110101
\(551\) 13.5483 0.577175
\(552\) −1.96077 −0.0834560
\(553\) −0.423272 −0.0179993
\(554\) −27.6383 −1.17424
\(555\) −21.0683 −0.894299
\(556\) 4.36227 0.185002
\(557\) −46.9197 −1.98805 −0.994027 0.109138i \(-0.965191\pi\)
−0.994027 + 0.109138i \(0.965191\pi\)
\(558\) −6.67994 −0.282784
\(559\) 0 0
\(560\) −4.24698 −0.179468
\(561\) −0.131687 −0.00555981
\(562\) 4.25368 0.179431
\(563\) 0.718578 0.0302844 0.0151422 0.999885i \(-0.495180\pi\)
0.0151422 + 0.999885i \(0.495180\pi\)
\(564\) 10.6039 0.446504
\(565\) −63.7174 −2.68061
\(566\) −10.8388 −0.455588
\(567\) −1.00000 −0.0419961
\(568\) 10.9879 0.461043
\(569\) −0.486189 −0.0203821 −0.0101911 0.999948i \(-0.503244\pi\)
−0.0101911 + 0.999948i \(0.503244\pi\)
\(570\) −12.3666 −0.517979
\(571\) −27.3260 −1.14356 −0.571779 0.820407i \(-0.693747\pi\)
−0.571779 + 0.820407i \(0.693747\pi\)
\(572\) 0 0
\(573\) −24.7928 −1.03574
\(574\) 10.0707 0.420342
\(575\) 25.5623 1.06602
\(576\) 1.00000 0.0416667
\(577\) −36.6276 −1.52483 −0.762413 0.647091i \(-0.775985\pi\)
−0.762413 + 0.647091i \(0.775985\pi\)
\(578\) 16.5579 0.688720
\(579\) 18.9487 0.787481
\(580\) 19.7603 0.820502
\(581\) −11.0881 −0.460014
\(582\) −1.47889 −0.0613021
\(583\) −2.87263 −0.118972
\(584\) −4.84117 −0.200329
\(585\) 0 0
\(586\) −15.6160 −0.645089
\(587\) 8.96077 0.369851 0.184925 0.982753i \(-0.440796\pi\)
0.184925 + 0.982753i \(0.440796\pi\)
\(588\) 1.00000 0.0412393
\(589\) 19.4510 0.801465
\(590\) 21.4838 0.884474
\(591\) 4.58642 0.188660
\(592\) −4.96077 −0.203886
\(593\) 15.2489 0.626197 0.313099 0.949721i \(-0.398633\pi\)
0.313099 + 0.949721i \(0.398633\pi\)
\(594\) −0.198062 −0.00812659
\(595\) 2.82371 0.115761
\(596\) 3.80194 0.155733
\(597\) −17.8998 −0.732589
\(598\) 0 0
\(599\) 9.64204 0.393963 0.196982 0.980407i \(-0.436886\pi\)
0.196982 + 0.980407i \(0.436886\pi\)
\(600\) −13.0368 −0.532227
\(601\) −8.21446 −0.335075 −0.167537 0.985866i \(-0.553581\pi\)
−0.167537 + 0.985866i \(0.553581\pi\)
\(602\) −2.85086 −0.116192
\(603\) −6.03684 −0.245839
\(604\) 14.7342 0.599527
\(605\) −46.5502 −1.89253
\(606\) 18.6407 0.757227
\(607\) 28.5448 1.15860 0.579299 0.815115i \(-0.303326\pi\)
0.579299 + 0.815115i \(0.303326\pi\)
\(608\) −2.91185 −0.118091
\(609\) −4.65279 −0.188541
\(610\) 3.72886 0.150977
\(611\) 0 0
\(612\) −0.664874 −0.0268760
\(613\) −3.14244 −0.126922 −0.0634610 0.997984i \(-0.520214\pi\)
−0.0634610 + 0.997984i \(0.520214\pi\)
\(614\) −11.2838 −0.455378
\(615\) 42.7700 1.72465
\(616\) 0.198062 0.00798016
\(617\) −19.3690 −0.779766 −0.389883 0.920864i \(-0.627484\pi\)
−0.389883 + 0.920864i \(0.627484\pi\)
\(618\) −12.5700 −0.505641
\(619\) 14.9004 0.598896 0.299448 0.954113i \(-0.403197\pi\)
0.299448 + 0.954113i \(0.403197\pi\)
\(620\) 28.3696 1.13935
\(621\) 1.96077 0.0786830
\(622\) −31.8732 −1.27800
\(623\) 15.6407 0.626632
\(624\) 0 0
\(625\) 79.7749 3.19100
\(626\) −4.55927 −0.182225
\(627\) 0.576728 0.0230323
\(628\) 1.15346 0.0460279
\(629\) 3.29829 0.131511
\(630\) 4.24698 0.169204
\(631\) 0.809707 0.0322339 0.0161170 0.999870i \(-0.494870\pi\)
0.0161170 + 0.999870i \(0.494870\pi\)
\(632\) −0.423272 −0.0168368
\(633\) 1.95108 0.0775486
\(634\) −22.1239 −0.878653
\(635\) −21.7245 −0.862112
\(636\) −14.5036 −0.575107
\(637\) 0 0
\(638\) −0.921543 −0.0364842
\(639\) −10.9879 −0.434675
\(640\) −4.24698 −0.167877
\(641\) 30.4868 1.20416 0.602078 0.798437i \(-0.294340\pi\)
0.602078 + 0.798437i \(0.294340\pi\)
\(642\) −5.98792 −0.236324
\(643\) 1.37004 0.0540292 0.0270146 0.999635i \(-0.491400\pi\)
0.0270146 + 0.999635i \(0.491400\pi\)
\(644\) −1.96077 −0.0772652
\(645\) −12.1075 −0.476733
\(646\) 1.93602 0.0761716
\(647\) −41.9995 −1.65117 −0.825586 0.564276i \(-0.809155\pi\)
−0.825586 + 0.564276i \(0.809155\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −1.00192 −0.0393288
\(650\) 0 0
\(651\) −6.67994 −0.261807
\(652\) 12.0532 0.472041
\(653\) 14.8226 0.580055 0.290027 0.957018i \(-0.406336\pi\)
0.290027 + 0.957018i \(0.406336\pi\)
\(654\) 0.850855 0.0332711
\(655\) −25.3564 −0.990757
\(656\) 10.0707 0.393194
\(657\) 4.84117 0.188872
\(658\) 10.6039 0.413382
\(659\) 21.5120 0.837989 0.418994 0.907989i \(-0.362383\pi\)
0.418994 + 0.907989i \(0.362383\pi\)
\(660\) 0.841166 0.0327424
\(661\) −12.5224 −0.487066 −0.243533 0.969893i \(-0.578306\pi\)
−0.243533 + 0.969893i \(0.578306\pi\)
\(662\) 7.59286 0.295105
\(663\) 0 0
\(664\) −11.0881 −0.430304
\(665\) −12.3666 −0.479556
\(666\) 4.96077 0.192226
\(667\) 9.12306 0.353246
\(668\) 17.8291 0.689828
\(669\) 18.9051 0.730915
\(670\) 25.6383 0.990495
\(671\) −0.173899 −0.00671330
\(672\) 1.00000 0.0385758
\(673\) −35.4040 −1.36472 −0.682362 0.731014i \(-0.739047\pi\)
−0.682362 + 0.731014i \(0.739047\pi\)
\(674\) −20.7603 −0.799658
\(675\) 13.0368 0.501788
\(676\) 0 0
\(677\) 0.301274 0.0115789 0.00578945 0.999983i \(-0.498157\pi\)
0.00578945 + 0.999983i \(0.498157\pi\)
\(678\) 15.0030 0.576186
\(679\) −1.47889 −0.0567547
\(680\) 2.82371 0.108284
\(681\) 21.1468 0.810345
\(682\) −1.32304 −0.0506620
\(683\) −29.3293 −1.12225 −0.561127 0.827730i \(-0.689632\pi\)
−0.561127 + 0.827730i \(0.689632\pi\)
\(684\) 2.91185 0.111338
\(685\) 55.3260 2.11390
\(686\) 1.00000 0.0381802
\(687\) −22.3884 −0.854169
\(688\) −2.85086 −0.108688
\(689\) 0 0
\(690\) −8.32736 −0.317017
\(691\) 0.896789 0.0341154 0.0170577 0.999855i \(-0.494570\pi\)
0.0170577 + 0.999855i \(0.494570\pi\)
\(692\) 16.7332 0.636100
\(693\) −0.198062 −0.00752376
\(694\) 25.5381 0.969413
\(695\) 18.5265 0.702750
\(696\) −4.65279 −0.176364
\(697\) −6.69574 −0.253619
\(698\) 3.42327 0.129573
\(699\) −23.5894 −0.892233
\(700\) −13.0368 −0.492746
\(701\) −4.67994 −0.176759 −0.0883794 0.996087i \(-0.528169\pi\)
−0.0883794 + 0.996087i \(0.528169\pi\)
\(702\) 0 0
\(703\) −14.4450 −0.544805
\(704\) 0.198062 0.00746475
\(705\) 45.0344 1.69610
\(706\) 3.18359 0.119816
\(707\) 18.6407 0.701056
\(708\) −5.05861 −0.190114
\(709\) 38.2180 1.43531 0.717654 0.696400i \(-0.245216\pi\)
0.717654 + 0.696400i \(0.245216\pi\)
\(710\) 46.6655 1.75132
\(711\) 0.423272 0.0158739
\(712\) 15.6407 0.586160
\(713\) 13.0978 0.490518
\(714\) −0.664874 −0.0248823
\(715\) 0 0
\(716\) 3.67025 0.137164
\(717\) 15.9323 0.595003
\(718\) 22.7429 0.848756
\(719\) −1.42088 −0.0529898 −0.0264949 0.999649i \(-0.508435\pi\)
−0.0264949 + 0.999649i \(0.508435\pi\)
\(720\) 4.24698 0.158276
\(721\) −12.5700 −0.468132
\(722\) 10.5211 0.391555
\(723\) −10.3569 −0.385177
\(724\) −14.6189 −0.543309
\(725\) 60.6577 2.25277
\(726\) 10.9608 0.406792
\(727\) −30.8079 −1.14260 −0.571301 0.820741i \(-0.693561\pi\)
−0.571301 + 0.820741i \(0.693561\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −20.5603 −0.760972
\(731\) 1.89546 0.0701061
\(732\) −0.878002 −0.0324519
\(733\) 18.3502 0.677780 0.338890 0.940826i \(-0.389949\pi\)
0.338890 + 0.940826i \(0.389949\pi\)
\(734\) 27.0315 0.997749
\(735\) 4.24698 0.156652
\(736\) −1.96077 −0.0722750
\(737\) −1.19567 −0.0440430
\(738\) −10.0707 −0.370707
\(739\) 5.93794 0.218431 0.109215 0.994018i \(-0.465166\pi\)
0.109215 + 0.994018i \(0.465166\pi\)
\(740\) −21.0683 −0.774486
\(741\) 0 0
\(742\) −14.5036 −0.532446
\(743\) −1.76377 −0.0647066 −0.0323533 0.999476i \(-0.510300\pi\)
−0.0323533 + 0.999476i \(0.510300\pi\)
\(744\) −6.67994 −0.244898
\(745\) 16.1468 0.591571
\(746\) 13.2338 0.484525
\(747\) 11.0881 0.405694
\(748\) −0.131687 −0.00481494
\(749\) −5.98792 −0.218794
\(750\) −34.1323 −1.24633
\(751\) 12.2440 0.446790 0.223395 0.974728i \(-0.428286\pi\)
0.223395 + 0.974728i \(0.428286\pi\)
\(752\) 10.6039 0.386684
\(753\) 24.3424 0.887087
\(754\) 0 0
\(755\) 62.5760 2.27737
\(756\) −1.00000 −0.0363696
\(757\) 19.9912 0.726591 0.363296 0.931674i \(-0.381651\pi\)
0.363296 + 0.931674i \(0.381651\pi\)
\(758\) 14.7095 0.534272
\(759\) 0.388355 0.0140964
\(760\) −12.3666 −0.448583
\(761\) 1.78448 0.0646873 0.0323437 0.999477i \(-0.489703\pi\)
0.0323437 + 0.999477i \(0.489703\pi\)
\(762\) 5.11529 0.185308
\(763\) 0.850855 0.0308030
\(764\) −24.7928 −0.896973
\(765\) −2.82371 −0.102091
\(766\) 15.5754 0.562762
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −3.72050 −0.134165 −0.0670823 0.997747i \(-0.521369\pi\)
−0.0670823 + 0.997747i \(0.521369\pi\)
\(770\) 0.841166 0.0303135
\(771\) 22.6015 0.813973
\(772\) 18.9487 0.681978
\(773\) −7.26444 −0.261284 −0.130642 0.991430i \(-0.541704\pi\)
−0.130642 + 0.991430i \(0.541704\pi\)
\(774\) 2.85086 0.102472
\(775\) 87.0853 3.12820
\(776\) −1.47889 −0.0530892
\(777\) 4.96077 0.177967
\(778\) 18.8847 0.677050
\(779\) 29.3244 1.05065
\(780\) 0 0
\(781\) −2.17629 −0.0778739
\(782\) 1.30367 0.0466190
\(783\) 4.65279 0.166277
\(784\) 1.00000 0.0357143
\(785\) 4.89871 0.174842
\(786\) 5.97046 0.212959
\(787\) 15.9748 0.569439 0.284720 0.958611i \(-0.408100\pi\)
0.284720 + 0.958611i \(0.408100\pi\)
\(788\) 4.58642 0.163384
\(789\) −12.3110 −0.438282
\(790\) −1.79763 −0.0639567
\(791\) 15.0030 0.533445
\(792\) −0.198062 −0.00703784
\(793\) 0 0
\(794\) 28.6233 1.01580
\(795\) −61.5967 −2.18461
\(796\) −17.8998 −0.634441
\(797\) −30.3588 −1.07536 −0.537682 0.843148i \(-0.680700\pi\)
−0.537682 + 0.843148i \(0.680700\pi\)
\(798\) 2.91185 0.103079
\(799\) −7.05025 −0.249420
\(800\) −13.0368 −0.460922
\(801\) −15.6407 −0.552637
\(802\) 22.6601 0.800156
\(803\) 0.958852 0.0338372
\(804\) −6.03684 −0.212903
\(805\) −8.32736 −0.293501
\(806\) 0 0
\(807\) 5.67563 0.199792
\(808\) 18.6407 0.655778
\(809\) −16.8595 −0.592748 −0.296374 0.955072i \(-0.595777\pi\)
−0.296374 + 0.955072i \(0.595777\pi\)
\(810\) −4.24698 −0.149224
\(811\) 25.1612 0.883530 0.441765 0.897131i \(-0.354352\pi\)
0.441765 + 0.897131i \(0.354352\pi\)
\(812\) −4.65279 −0.163281
\(813\) −14.4698 −0.507478
\(814\) 0.982542 0.0344381
\(815\) 51.1898 1.79310
\(816\) −0.664874 −0.0232753
\(817\) −8.30127 −0.290425
\(818\) 11.0325 0.385743
\(819\) 0 0
\(820\) 42.7700 1.49359
\(821\) 24.8394 0.866900 0.433450 0.901178i \(-0.357296\pi\)
0.433450 + 0.901178i \(0.357296\pi\)
\(822\) −13.0271 −0.454374
\(823\) −17.4252 −0.607404 −0.303702 0.952767i \(-0.598223\pi\)
−0.303702 + 0.952767i \(0.598223\pi\)
\(824\) −12.5700 −0.437898
\(825\) 2.58211 0.0898974
\(826\) −5.05861 −0.176011
\(827\) −42.9517 −1.49358 −0.746788 0.665062i \(-0.768405\pi\)
−0.746788 + 0.665062i \(0.768405\pi\)
\(828\) 1.96077 0.0681415
\(829\) −37.5230 −1.30323 −0.651614 0.758550i \(-0.725908\pi\)
−0.651614 + 0.758550i \(0.725908\pi\)
\(830\) −47.0911 −1.63456
\(831\) 27.6383 0.958763
\(832\) 0 0
\(833\) −0.664874 −0.0230365
\(834\) −4.36227 −0.151053
\(835\) 75.7198 2.62039
\(836\) 0.576728 0.0199466
\(837\) 6.67994 0.230892
\(838\) −16.0508 −0.554467
\(839\) 1.56406 0.0539972 0.0269986 0.999635i \(-0.491405\pi\)
0.0269986 + 0.999635i \(0.491405\pi\)
\(840\) 4.24698 0.146535
\(841\) −7.35152 −0.253501
\(842\) 25.2838 0.871338
\(843\) −4.25368 −0.146505
\(844\) 1.95108 0.0671590
\(845\) 0 0
\(846\) −10.6039 −0.364569
\(847\) 10.9608 0.376617
\(848\) −14.5036 −0.498057
\(849\) 10.8388 0.371986
\(850\) 8.66786 0.297305
\(851\) −9.72694 −0.333435
\(852\) −10.9879 −0.376440
\(853\) −16.9256 −0.579521 −0.289761 0.957099i \(-0.593576\pi\)
−0.289761 + 0.957099i \(0.593576\pi\)
\(854\) −0.878002 −0.0300446
\(855\) 12.3666 0.422928
\(856\) −5.98792 −0.204663
\(857\) −10.5362 −0.359909 −0.179954 0.983675i \(-0.557595\pi\)
−0.179954 + 0.983675i \(0.557595\pi\)
\(858\) 0 0
\(859\) 41.4607 1.41462 0.707310 0.706903i \(-0.249908\pi\)
0.707310 + 0.706903i \(0.249908\pi\)
\(860\) −12.1075 −0.412863
\(861\) −10.0707 −0.343208
\(862\) −36.0116 −1.22656
\(863\) 5.30798 0.180686 0.0903428 0.995911i \(-0.471204\pi\)
0.0903428 + 0.995911i \(0.471204\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 71.0654 2.41630
\(866\) −27.9299 −0.949097
\(867\) −16.5579 −0.562337
\(868\) −6.67994 −0.226732
\(869\) 0.0838341 0.00284388
\(870\) −19.7603 −0.669937
\(871\) 0 0
\(872\) 0.850855 0.0288136
\(873\) 1.47889 0.0500530
\(874\) −5.70948 −0.193126
\(875\) −34.1323 −1.15388
\(876\) 4.84117 0.163568
\(877\) 29.0549 0.981114 0.490557 0.871409i \(-0.336793\pi\)
0.490557 + 0.871409i \(0.336793\pi\)
\(878\) 28.4969 0.961725
\(879\) 15.6160 0.526713
\(880\) 0.841166 0.0283557
\(881\) −16.5013 −0.555941 −0.277971 0.960590i \(-0.589662\pi\)
−0.277971 + 0.960590i \(0.589662\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 18.6189 0.626577 0.313289 0.949658i \(-0.398569\pi\)
0.313289 + 0.949658i \(0.398569\pi\)
\(884\) 0 0
\(885\) −21.4838 −0.722170
\(886\) −33.9366 −1.14012
\(887\) 47.2161 1.58536 0.792681 0.609637i \(-0.208685\pi\)
0.792681 + 0.609637i \(0.208685\pi\)
\(888\) 4.96077 0.166473
\(889\) 5.11529 0.171561
\(890\) 66.4258 2.22660
\(891\) 0.198062 0.00663534
\(892\) 18.9051 0.632991
\(893\) 30.8769 1.03326
\(894\) −3.80194 −0.127156
\(895\) 15.5875 0.521032
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −3.59312 −0.119904
\(899\) 31.0804 1.03659
\(900\) 13.0368 0.434561
\(901\) 9.64310 0.321258
\(902\) −1.99462 −0.0664137
\(903\) 2.85086 0.0948705
\(904\) 15.0030 0.498992
\(905\) −62.0863 −2.06382
\(906\) −14.7342 −0.489512
\(907\) −42.1997 −1.40122 −0.700609 0.713545i \(-0.747088\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(908\) 21.1468 0.701780
\(909\) −18.6407 −0.618273
\(910\) 0 0
\(911\) −30.3967 −1.00709 −0.503544 0.863970i \(-0.667971\pi\)
−0.503544 + 0.863970i \(0.667971\pi\)
\(912\) 2.91185 0.0964211
\(913\) 2.19614 0.0726817
\(914\) 16.2591 0.537802
\(915\) −3.72886 −0.123272
\(916\) −22.3884 −0.739732
\(917\) 5.97046 0.197162
\(918\) 0.664874 0.0219441
\(919\) 41.8944 1.38197 0.690984 0.722870i \(-0.257177\pi\)
0.690984 + 0.722870i \(0.257177\pi\)
\(920\) −8.32736 −0.274545
\(921\) 11.2838 0.371814
\(922\) −33.7372 −1.11108
\(923\) 0 0
\(924\) −0.198062 −0.00651577
\(925\) −64.6728 −2.12643
\(926\) 13.6606 0.448914
\(927\) 12.5700 0.412854
\(928\) −4.65279 −0.152735
\(929\) −21.6093 −0.708977 −0.354488 0.935060i \(-0.615345\pi\)
−0.354488 + 0.935060i \(0.615345\pi\)
\(930\) −28.3696 −0.930275
\(931\) 2.91185 0.0954322
\(932\) −23.5894 −0.772697
\(933\) 31.8732 1.04348
\(934\) −1.33081 −0.0435456
\(935\) −0.559270 −0.0182901
\(936\) 0 0
\(937\) −0.396125 −0.0129408 −0.00647041 0.999979i \(-0.502060\pi\)
−0.00647041 + 0.999979i \(0.502060\pi\)
\(938\) −6.03684 −0.197110
\(939\) 4.55927 0.148786
\(940\) 45.0344 1.46886
\(941\) −39.7875 −1.29703 −0.648517 0.761200i \(-0.724611\pi\)
−0.648517 + 0.761200i \(0.724611\pi\)
\(942\) −1.15346 −0.0375817
\(943\) 19.7463 0.643029
\(944\) −5.05861 −0.164644
\(945\) −4.24698 −0.138154
\(946\) 0.564647 0.0183583
\(947\) 15.4461 0.501931 0.250966 0.967996i \(-0.419252\pi\)
0.250966 + 0.967996i \(0.419252\pi\)
\(948\) 0.423272 0.0137472
\(949\) 0 0
\(950\) −37.9614 −1.23163
\(951\) 22.1239 0.717417
\(952\) −0.664874 −0.0215487
\(953\) −9.19998 −0.298017 −0.149008 0.988836i \(-0.547608\pi\)
−0.149008 + 0.988836i \(0.547608\pi\)
\(954\) 14.5036 0.469573
\(955\) −105.295 −3.40726
\(956\) 15.9323 0.515287
\(957\) 0.921543 0.0297892
\(958\) −39.4416 −1.27430
\(959\) −13.0271 −0.420669
\(960\) 4.24698 0.137071
\(961\) 13.6216 0.439406
\(962\) 0 0
\(963\) 5.98792 0.192958
\(964\) −10.3569 −0.333573
\(965\) 80.4747 2.59057
\(966\) 1.96077 0.0630868
\(967\) 24.3521 0.783111 0.391556 0.920154i \(-0.371937\pi\)
0.391556 + 0.920154i \(0.371937\pi\)
\(968\) 10.9608 0.352293
\(969\) −1.93602 −0.0621938
\(970\) −6.28083 −0.201665
\(971\) 27.1795 0.872233 0.436116 0.899890i \(-0.356354\pi\)
0.436116 + 0.899890i \(0.356354\pi\)
\(972\) 1.00000 0.0320750
\(973\) −4.36227 −0.139848
\(974\) 14.7549 0.472779
\(975\) 0 0
\(976\) −0.878002 −0.0281042
\(977\) 34.5532 1.10545 0.552727 0.833363i \(-0.313587\pi\)
0.552727 + 0.833363i \(0.313587\pi\)
\(978\) −12.0532 −0.385420
\(979\) −3.09783 −0.0990072
\(980\) 4.24698 0.135665
\(981\) −0.850855 −0.0271657
\(982\) 20.5187 0.654778
\(983\) −7.51094 −0.239562 −0.119781 0.992800i \(-0.538219\pi\)
−0.119781 + 0.992800i \(0.538219\pi\)
\(984\) −10.0707 −0.321042
\(985\) 19.4784 0.620634
\(986\) 3.09352 0.0985178
\(987\) −10.6039 −0.337525
\(988\) 0 0
\(989\) −5.58987 −0.177748
\(990\) −0.841166 −0.0267340
\(991\) 4.78853 0.152113 0.0760563 0.997104i \(-0.475767\pi\)
0.0760563 + 0.997104i \(0.475767\pi\)
\(992\) −6.67994 −0.212088
\(993\) −7.59286 −0.240952
\(994\) −10.9879 −0.348516
\(995\) −76.0200 −2.41000
\(996\) 11.0881 0.351341
\(997\) −41.3274 −1.30885 −0.654425 0.756127i \(-0.727089\pi\)
−0.654425 + 0.756127i \(0.727089\pi\)
\(998\) 43.8678 1.38861
\(999\) −4.96077 −0.156952
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 7098.2.a.cg.1.3 3
13.12 even 2 7098.2.a.cl.1.1 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cg.1.3 3 1.1 even 1 trivial
7098.2.a.cl.1.1 yes 3 13.12 even 2