Properties

Label 9075.2.a.db.1.4
Level $9075$
Weight $2$
Character 9075.1
Self dual yes
Analytic conductor $72.464$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9075.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.4642398343\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{3}, \sqrt{11})\)
Defining polynomial: \(x^{4} - 7 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.52434\) of defining polynomial
Character \(\chi\) \(=\) 9075.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.52434 q^{2} +1.00000 q^{3} +4.37228 q^{4} +2.52434 q^{6} +0.792287 q^{7} +5.98844 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.52434 q^{2} +1.00000 q^{3} +4.37228 q^{4} +2.52434 q^{6} +0.792287 q^{7} +5.98844 q^{8} +1.00000 q^{9} +4.37228 q^{12} -0.147477 q^{13} +2.00000 q^{14} +6.37228 q^{16} +6.63325 q^{17} +2.52434 q^{18} -4.40387 q^{19} +0.792287 q^{21} -8.00000 q^{23} +5.98844 q^{24} -0.372281 q^{26} +1.00000 q^{27} +3.46410 q^{28} +10.0974 q^{29} +2.37228 q^{31} +4.10891 q^{32} +16.7446 q^{34} +4.37228 q^{36} -5.00000 q^{37} -11.1168 q^{38} -0.147477 q^{39} +6.92820 q^{41} +2.00000 q^{42} +9.94987 q^{43} -20.1947 q^{46} +8.74456 q^{47} +6.37228 q^{48} -6.37228 q^{49} +6.63325 q^{51} -0.644810 q^{52} +1.25544 q^{53} +2.52434 q^{54} +4.74456 q^{56} -4.40387 q^{57} +25.4891 q^{58} +4.00000 q^{59} +5.98844 q^{61} +5.98844 q^{62} +0.792287 q^{63} -2.37228 q^{64} +11.1168 q^{67} +29.0024 q^{68} -8.00000 q^{69} +10.7446 q^{71} +5.98844 q^{72} -5.19615 q^{73} -12.6217 q^{74} -19.2549 q^{76} -0.372281 q^{78} -6.78073 q^{79} +1.00000 q^{81} +17.4891 q^{82} +8.51278 q^{83} +3.46410 q^{84} +25.1168 q^{86} +10.0974 q^{87} +5.48913 q^{89} -0.116844 q^{91} -34.9783 q^{92} +2.37228 q^{93} +22.0742 q^{94} +4.10891 q^{96} +9.37228 q^{97} -16.0858 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{3} + 6 q^{4} + 4 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{3} + 6 q^{4} + 4 q^{9} + 6 q^{12} + 8 q^{14} + 14 q^{16} - 32 q^{23} + 10 q^{26} + 4 q^{27} - 2 q^{31} + 44 q^{34} + 6 q^{36} - 20 q^{37} - 10 q^{38} + 8 q^{42} + 12 q^{47} + 14 q^{48} - 14 q^{49} + 28 q^{53} - 4 q^{56} + 56 q^{58} + 16 q^{59} + 2 q^{64} + 10 q^{67} - 32 q^{69} + 20 q^{71} + 10 q^{78} + 4 q^{81} + 24 q^{82} + 66 q^{86} - 24 q^{89} + 34 q^{91} - 48 q^{92} - 2 q^{93} + 26 q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.52434 1.78498 0.892488 0.451071i \(-0.148958\pi\)
0.892488 + 0.451071i \(0.148958\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.37228 2.18614
\(5\) 0 0
\(6\) 2.52434 1.03056
\(7\) 0.792287 0.299456 0.149728 0.988727i \(-0.452160\pi\)
0.149728 + 0.988727i \(0.452160\pi\)
\(8\) 5.98844 2.11723
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0
\(12\) 4.37228 1.26217
\(13\) −0.147477 −0.0409027 −0.0204514 0.999791i \(-0.506510\pi\)
−0.0204514 + 0.999791i \(0.506510\pi\)
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) 6.37228 1.59307
\(17\) 6.63325 1.60880 0.804400 0.594089i \(-0.202487\pi\)
0.804400 + 0.594089i \(0.202487\pi\)
\(18\) 2.52434 0.594992
\(19\) −4.40387 −1.01032 −0.505158 0.863027i \(-0.668566\pi\)
−0.505158 + 0.863027i \(0.668566\pi\)
\(20\) 0 0
\(21\) 0.792287 0.172891
\(22\) 0 0
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 5.98844 1.22239
\(25\) 0 0
\(26\) −0.372281 −0.0730104
\(27\) 1.00000 0.192450
\(28\) 3.46410 0.654654
\(29\) 10.0974 1.87503 0.937516 0.347943i \(-0.113120\pi\)
0.937516 + 0.347943i \(0.113120\pi\)
\(30\) 0 0
\(31\) 2.37228 0.426074 0.213037 0.977044i \(-0.431664\pi\)
0.213037 + 0.977044i \(0.431664\pi\)
\(32\) 4.10891 0.726360
\(33\) 0 0
\(34\) 16.7446 2.87167
\(35\) 0 0
\(36\) 4.37228 0.728714
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) −11.1168 −1.80339
\(39\) −0.147477 −0.0236152
\(40\) 0 0
\(41\) 6.92820 1.08200 0.541002 0.841021i \(-0.318045\pi\)
0.541002 + 0.841021i \(0.318045\pi\)
\(42\) 2.00000 0.308607
\(43\) 9.94987 1.51734 0.758671 0.651474i \(-0.225849\pi\)
0.758671 + 0.651474i \(0.225849\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −20.1947 −2.97755
\(47\) 8.74456 1.27553 0.637763 0.770233i \(-0.279860\pi\)
0.637763 + 0.770233i \(0.279860\pi\)
\(48\) 6.37228 0.919760
\(49\) −6.37228 −0.910326
\(50\) 0 0
\(51\) 6.63325 0.928841
\(52\) −0.644810 −0.0894191
\(53\) 1.25544 0.172448 0.0862238 0.996276i \(-0.472520\pi\)
0.0862238 + 0.996276i \(0.472520\pi\)
\(54\) 2.52434 0.343519
\(55\) 0 0
\(56\) 4.74456 0.634019
\(57\) −4.40387 −0.583306
\(58\) 25.4891 3.34689
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 5.98844 0.766741 0.383371 0.923595i \(-0.374763\pi\)
0.383371 + 0.923595i \(0.374763\pi\)
\(62\) 5.98844 0.760533
\(63\) 0.792287 0.0998188
\(64\) −2.37228 −0.296535
\(65\) 0 0
\(66\) 0 0
\(67\) 11.1168 1.35814 0.679069 0.734074i \(-0.262384\pi\)
0.679069 + 0.734074i \(0.262384\pi\)
\(68\) 29.0024 3.51706
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 10.7446 1.27514 0.637572 0.770390i \(-0.279939\pi\)
0.637572 + 0.770390i \(0.279939\pi\)
\(72\) 5.98844 0.705744
\(73\) −5.19615 −0.608164 −0.304082 0.952646i \(-0.598350\pi\)
−0.304082 + 0.952646i \(0.598350\pi\)
\(74\) −12.6217 −1.46724
\(75\) 0 0
\(76\) −19.2549 −2.20869
\(77\) 0 0
\(78\) −0.372281 −0.0421526
\(79\) −6.78073 −0.762891 −0.381446 0.924391i \(-0.624574\pi\)
−0.381446 + 0.924391i \(0.624574\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 17.4891 1.93135
\(83\) 8.51278 0.934399 0.467199 0.884152i \(-0.345263\pi\)
0.467199 + 0.884152i \(0.345263\pi\)
\(84\) 3.46410 0.377964
\(85\) 0 0
\(86\) 25.1168 2.70842
\(87\) 10.0974 1.08255
\(88\) 0 0
\(89\) 5.48913 0.581846 0.290923 0.956746i \(-0.406038\pi\)
0.290923 + 0.956746i \(0.406038\pi\)
\(90\) 0 0
\(91\) −0.116844 −0.0122486
\(92\) −34.9783 −3.64673
\(93\) 2.37228 0.245994
\(94\) 22.0742 2.27678
\(95\) 0 0
\(96\) 4.10891 0.419364
\(97\) 9.37228 0.951611 0.475805 0.879551i \(-0.342157\pi\)
0.475805 + 0.879551i \(0.342157\pi\)
\(98\) −16.0858 −1.62491
\(99\) 0 0
\(100\) 0 0
\(101\) −13.2665 −1.32007 −0.660033 0.751237i \(-0.729458\pi\)
−0.660033 + 0.751237i \(0.729458\pi\)
\(102\) 16.7446 1.65796
\(103\) −3.74456 −0.368963 −0.184481 0.982836i \(-0.559061\pi\)
−0.184481 + 0.982836i \(0.559061\pi\)
\(104\) −0.883156 −0.0866006
\(105\) 0 0
\(106\) 3.16915 0.307815
\(107\) −8.21782 −0.794447 −0.397223 0.917722i \(-0.630026\pi\)
−0.397223 + 0.917722i \(0.630026\pi\)
\(108\) 4.37228 0.420723
\(109\) −2.67181 −0.255913 −0.127957 0.991780i \(-0.540842\pi\)
−0.127957 + 0.991780i \(0.540842\pi\)
\(110\) 0 0
\(111\) −5.00000 −0.474579
\(112\) 5.04868 0.477055
\(113\) −16.2337 −1.52714 −0.763568 0.645727i \(-0.776554\pi\)
−0.763568 + 0.645727i \(0.776554\pi\)
\(114\) −11.1168 −1.04119
\(115\) 0 0
\(116\) 44.1485 4.09908
\(117\) −0.147477 −0.0136342
\(118\) 10.0974 0.929537
\(119\) 5.25544 0.481765
\(120\) 0 0
\(121\) 0 0
\(122\) 15.1168 1.36861
\(123\) 6.92820 0.624695
\(124\) 10.3723 0.931458
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −10.2448 −0.909081 −0.454541 0.890726i \(-0.650197\pi\)
−0.454541 + 0.890726i \(0.650197\pi\)
\(128\) −14.2063 −1.25567
\(129\) 9.94987 0.876038
\(130\) 0 0
\(131\) −18.6101 −1.62597 −0.812987 0.582282i \(-0.802160\pi\)
−0.812987 + 0.582282i \(0.802160\pi\)
\(132\) 0 0
\(133\) −3.48913 −0.302546
\(134\) 28.0627 2.42425
\(135\) 0 0
\(136\) 39.7228 3.40620
\(137\) 0.744563 0.0636123 0.0318061 0.999494i \(-0.489874\pi\)
0.0318061 + 0.999494i \(0.489874\pi\)
\(138\) −20.1947 −1.71909
\(139\) −10.3923 −0.881464 −0.440732 0.897639i \(-0.645281\pi\)
−0.440732 + 0.897639i \(0.645281\pi\)
\(140\) 0 0
\(141\) 8.74456 0.736425
\(142\) 27.1229 2.27610
\(143\) 0 0
\(144\) 6.37228 0.531023
\(145\) 0 0
\(146\) −13.1168 −1.08556
\(147\) −6.37228 −0.525577
\(148\) −21.8614 −1.79700
\(149\) −1.28962 −0.105650 −0.0528249 0.998604i \(-0.516823\pi\)
−0.0528249 + 0.998604i \(0.516823\pi\)
\(150\) 0 0
\(151\) −23.8063 −1.93733 −0.968664 0.248375i \(-0.920103\pi\)
−0.968664 + 0.248375i \(0.920103\pi\)
\(152\) −26.3723 −2.13907
\(153\) 6.63325 0.536266
\(154\) 0 0
\(155\) 0 0
\(156\) −0.644810 −0.0516261
\(157\) −8.37228 −0.668181 −0.334090 0.942541i \(-0.608429\pi\)
−0.334090 + 0.942541i \(0.608429\pi\)
\(158\) −17.1168 −1.36174
\(159\) 1.25544 0.0995627
\(160\) 0 0
\(161\) −6.33830 −0.499528
\(162\) 2.52434 0.198331
\(163\) −14.3723 −1.12572 −0.562862 0.826551i \(-0.690300\pi\)
−0.562862 + 0.826551i \(0.690300\pi\)
\(164\) 30.2921 2.36541
\(165\) 0 0
\(166\) 21.4891 1.66788
\(167\) 5.04868 0.390678 0.195339 0.980736i \(-0.437419\pi\)
0.195339 + 0.980736i \(0.437419\pi\)
\(168\) 4.74456 0.366051
\(169\) −12.9783 −0.998327
\(170\) 0 0
\(171\) −4.40387 −0.336772
\(172\) 43.5036 3.31712
\(173\) −6.92820 −0.526742 −0.263371 0.964695i \(-0.584834\pi\)
−0.263371 + 0.964695i \(0.584834\pi\)
\(174\) 25.4891 1.93233
\(175\) 0 0
\(176\) 0 0
\(177\) 4.00000 0.300658
\(178\) 13.8564 1.03858
\(179\) 19.4891 1.45669 0.728343 0.685213i \(-0.240291\pi\)
0.728343 + 0.685213i \(0.240291\pi\)
\(180\) 0 0
\(181\) 13.8614 1.03031 0.515155 0.857097i \(-0.327734\pi\)
0.515155 + 0.857097i \(0.327734\pi\)
\(182\) −0.294954 −0.0218634
\(183\) 5.98844 0.442678
\(184\) −47.9075 −3.53179
\(185\) 0 0
\(186\) 5.98844 0.439094
\(187\) 0 0
\(188\) 38.2337 2.78848
\(189\) 0.792287 0.0576304
\(190\) 0 0
\(191\) −17.4891 −1.26547 −0.632734 0.774369i \(-0.718067\pi\)
−0.632734 + 0.774369i \(0.718067\pi\)
\(192\) −2.37228 −0.171205
\(193\) −21.1345 −1.52129 −0.760646 0.649167i \(-0.775118\pi\)
−0.760646 + 0.649167i \(0.775118\pi\)
\(194\) 23.6588 1.69860
\(195\) 0 0
\(196\) −27.8614 −1.99010
\(197\) 8.51278 0.606510 0.303255 0.952909i \(-0.401927\pi\)
0.303255 + 0.952909i \(0.401927\pi\)
\(198\) 0 0
\(199\) 16.8614 1.19527 0.597637 0.801767i \(-0.296107\pi\)
0.597637 + 0.801767i \(0.296107\pi\)
\(200\) 0 0
\(201\) 11.1168 0.784122
\(202\) −33.4891 −2.35629
\(203\) 8.00000 0.561490
\(204\) 29.0024 2.03058
\(205\) 0 0
\(206\) −9.45254 −0.658590
\(207\) −8.00000 −0.556038
\(208\) −0.939764 −0.0651609
\(209\) 0 0
\(210\) 0 0
\(211\) 4.55134 0.313327 0.156664 0.987652i \(-0.449926\pi\)
0.156664 + 0.987652i \(0.449926\pi\)
\(212\) 5.48913 0.376995
\(213\) 10.7446 0.736205
\(214\) −20.7446 −1.41807
\(215\) 0 0
\(216\) 5.98844 0.407462
\(217\) 1.87953 0.127591
\(218\) −6.74456 −0.456799
\(219\) −5.19615 −0.351123
\(220\) 0 0
\(221\) −0.978251 −0.0658043
\(222\) −12.6217 −0.847112
\(223\) 23.8614 1.59788 0.798939 0.601412i \(-0.205395\pi\)
0.798939 + 0.601412i \(0.205395\pi\)
\(224\) 3.25544 0.217513
\(225\) 0 0
\(226\) −40.9793 −2.72590
\(227\) −17.3205 −1.14960 −0.574801 0.818293i \(-0.694921\pi\)
−0.574801 + 0.818293i \(0.694921\pi\)
\(228\) −19.2549 −1.27519
\(229\) −10.4891 −0.693141 −0.346570 0.938024i \(-0.612654\pi\)
−0.346570 + 0.938024i \(0.612654\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 60.4674 3.96988
\(233\) 15.1460 0.992249 0.496125 0.868251i \(-0.334756\pi\)
0.496125 + 0.868251i \(0.334756\pi\)
\(234\) −0.372281 −0.0243368
\(235\) 0 0
\(236\) 17.4891 1.13845
\(237\) −6.78073 −0.440456
\(238\) 13.2665 0.859939
\(239\) 13.2665 0.858138 0.429069 0.903272i \(-0.358842\pi\)
0.429069 + 0.903272i \(0.358842\pi\)
\(240\) 0 0
\(241\) −14.0039 −0.902069 −0.451035 0.892506i \(-0.648945\pi\)
−0.451035 + 0.892506i \(0.648945\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 26.1831 1.67620
\(245\) 0 0
\(246\) 17.4891 1.11507
\(247\) 0.649468 0.0413247
\(248\) 14.2063 0.902099
\(249\) 8.51278 0.539475
\(250\) 0 0
\(251\) −0.510875 −0.0322461 −0.0161231 0.999870i \(-0.505132\pi\)
−0.0161231 + 0.999870i \(0.505132\pi\)
\(252\) 3.46410 0.218218
\(253\) 0 0
\(254\) −25.8614 −1.62269
\(255\) 0 0
\(256\) −31.1168 −1.94480
\(257\) −17.4891 −1.09094 −0.545471 0.838130i \(-0.683649\pi\)
−0.545471 + 0.838130i \(0.683649\pi\)
\(258\) 25.1168 1.56371
\(259\) −3.96143 −0.246152
\(260\) 0 0
\(261\) 10.0974 0.625010
\(262\) −46.9783 −2.90233
\(263\) −5.04868 −0.311315 −0.155657 0.987811i \(-0.549750\pi\)
−0.155657 + 0.987811i \(0.549750\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −8.80773 −0.540037
\(267\) 5.48913 0.335929
\(268\) 48.6060 2.96908
\(269\) −2.74456 −0.167339 −0.0836695 0.996494i \(-0.526664\pi\)
−0.0836695 + 0.996494i \(0.526664\pi\)
\(270\) 0 0
\(271\) −10.3923 −0.631288 −0.315644 0.948878i \(-0.602220\pi\)
−0.315644 + 0.948878i \(0.602220\pi\)
\(272\) 42.2689 2.56293
\(273\) −0.116844 −0.00707172
\(274\) 1.87953 0.113546
\(275\) 0 0
\(276\) −34.9783 −2.10544
\(277\) 20.5446 1.23440 0.617201 0.786805i \(-0.288266\pi\)
0.617201 + 0.786805i \(0.288266\pi\)
\(278\) −26.2337 −1.57339
\(279\) 2.37228 0.142025
\(280\) 0 0
\(281\) −8.51278 −0.507830 −0.253915 0.967227i \(-0.581718\pi\)
−0.253915 + 0.967227i \(0.581718\pi\)
\(282\) 22.0742 1.31450
\(283\) −28.3576 −1.68569 −0.842843 0.538160i \(-0.819120\pi\)
−0.842843 + 0.538160i \(0.819120\pi\)
\(284\) 46.9783 2.78765
\(285\) 0 0
\(286\) 0 0
\(287\) 5.48913 0.324013
\(288\) 4.10891 0.242120
\(289\) 27.0000 1.58824
\(290\) 0 0
\(291\) 9.37228 0.549413
\(292\) −22.7190 −1.32953
\(293\) −32.7615 −1.91395 −0.956973 0.290176i \(-0.906286\pi\)
−0.956973 + 0.290176i \(0.906286\pi\)
\(294\) −16.0858 −0.938142
\(295\) 0 0
\(296\) −29.9422 −1.74035
\(297\) 0 0
\(298\) −3.25544 −0.188582
\(299\) 1.17981 0.0682304
\(300\) 0 0
\(301\) 7.88316 0.454378
\(302\) −60.0951 −3.45808
\(303\) −13.2665 −0.762140
\(304\) −28.0627 −1.60950
\(305\) 0 0
\(306\) 16.7446 0.957223
\(307\) −26.4781 −1.51118 −0.755592 0.655042i \(-0.772651\pi\)
−0.755592 + 0.655042i \(0.772651\pi\)
\(308\) 0 0
\(309\) −3.74456 −0.213021
\(310\) 0 0
\(311\) −10.2337 −0.580299 −0.290150 0.956981i \(-0.593705\pi\)
−0.290150 + 0.956981i \(0.593705\pi\)
\(312\) −0.883156 −0.0499989
\(313\) 25.9783 1.46838 0.734189 0.678945i \(-0.237563\pi\)
0.734189 + 0.678945i \(0.237563\pi\)
\(314\) −21.1345 −1.19269
\(315\) 0 0
\(316\) −29.6472 −1.66779
\(317\) 18.9783 1.06592 0.532962 0.846139i \(-0.321079\pi\)
0.532962 + 0.846139i \(0.321079\pi\)
\(318\) 3.16915 0.177717
\(319\) 0 0
\(320\) 0 0
\(321\) −8.21782 −0.458674
\(322\) −16.0000 −0.891645
\(323\) −29.2119 −1.62540
\(324\) 4.37228 0.242905
\(325\) 0 0
\(326\) −36.2805 −2.00939
\(327\) −2.67181 −0.147752
\(328\) 41.4891 2.29085
\(329\) 6.92820 0.381964
\(330\) 0 0
\(331\) 1.23369 0.0678096 0.0339048 0.999425i \(-0.489206\pi\)
0.0339048 + 0.999425i \(0.489206\pi\)
\(332\) 37.2203 2.04273
\(333\) −5.00000 −0.273998
\(334\) 12.7446 0.697351
\(335\) 0 0
\(336\) 5.04868 0.275428
\(337\) 10.5947 0.577129 0.288565 0.957460i \(-0.406822\pi\)
0.288565 + 0.957460i \(0.406822\pi\)
\(338\) −32.7615 −1.78199
\(339\) −16.2337 −0.881693
\(340\) 0 0
\(341\) 0 0
\(342\) −11.1168 −0.601130
\(343\) −10.5947 −0.572059
\(344\) 59.5842 3.21257
\(345\) 0 0
\(346\) −17.4891 −0.940221
\(347\) −2.17448 −0.116732 −0.0583661 0.998295i \(-0.518589\pi\)
−0.0583661 + 0.998295i \(0.518589\pi\)
\(348\) 44.1485 2.36661
\(349\) 8.66025 0.463573 0.231786 0.972767i \(-0.425543\pi\)
0.231786 + 0.972767i \(0.425543\pi\)
\(350\) 0 0
\(351\) −0.147477 −0.00787173
\(352\) 0 0
\(353\) 16.2337 0.864032 0.432016 0.901866i \(-0.357802\pi\)
0.432016 + 0.901866i \(0.357802\pi\)
\(354\) 10.0974 0.536668
\(355\) 0 0
\(356\) 24.0000 1.27200
\(357\) 5.25544 0.278147
\(358\) 49.1971 2.60015
\(359\) 6.63325 0.350090 0.175045 0.984560i \(-0.443993\pi\)
0.175045 + 0.984560i \(0.443993\pi\)
\(360\) 0 0
\(361\) 0.394031 0.0207385
\(362\) 34.9909 1.83908
\(363\) 0 0
\(364\) −0.510875 −0.0267771
\(365\) 0 0
\(366\) 15.1168 0.790170
\(367\) 15.0000 0.782994 0.391497 0.920179i \(-0.371957\pi\)
0.391497 + 0.920179i \(0.371957\pi\)
\(368\) −50.9783 −2.65743
\(369\) 6.92820 0.360668
\(370\) 0 0
\(371\) 0.994667 0.0516405
\(372\) 10.3723 0.537778
\(373\) 26.0357 1.34808 0.674038 0.738697i \(-0.264558\pi\)
0.674038 + 0.738697i \(0.264558\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 52.3663 2.70058
\(377\) −1.48913 −0.0766939
\(378\) 2.00000 0.102869
\(379\) −5.00000 −0.256833 −0.128416 0.991720i \(-0.540989\pi\)
−0.128416 + 0.991720i \(0.540989\pi\)
\(380\) 0 0
\(381\) −10.2448 −0.524858
\(382\) −44.1485 −2.25883
\(383\) 10.2337 0.522917 0.261459 0.965215i \(-0.415797\pi\)
0.261459 + 0.965215i \(0.415797\pi\)
\(384\) −14.2063 −0.724960
\(385\) 0 0
\(386\) −53.3505 −2.71547
\(387\) 9.94987 0.505781
\(388\) 40.9783 2.08036
\(389\) 32.7446 1.66022 0.830108 0.557603i \(-0.188279\pi\)
0.830108 + 0.557603i \(0.188279\pi\)
\(390\) 0 0
\(391\) −53.0660 −2.68366
\(392\) −38.1600 −1.92737
\(393\) −18.6101 −0.938757
\(394\) 21.4891 1.08261
\(395\) 0 0
\(396\) 0 0
\(397\) 2.62772 0.131881 0.0659407 0.997824i \(-0.478995\pi\)
0.0659407 + 0.997824i \(0.478995\pi\)
\(398\) 42.5639 2.13353
\(399\) −3.48913 −0.174675
\(400\) 0 0
\(401\) −30.9783 −1.54698 −0.773490 0.633808i \(-0.781491\pi\)
−0.773490 + 0.633808i \(0.781491\pi\)
\(402\) 28.0627 1.39964
\(403\) −0.349857 −0.0174276
\(404\) −58.0049 −2.88585
\(405\) 0 0
\(406\) 20.1947 1.00225
\(407\) 0 0
\(408\) 39.7228 1.96657
\(409\) 38.3075 1.89418 0.947092 0.320962i \(-0.104006\pi\)
0.947092 + 0.320962i \(0.104006\pi\)
\(410\) 0 0
\(411\) 0.744563 0.0367266
\(412\) −16.3723 −0.806604
\(413\) 3.16915 0.155944
\(414\) −20.1947 −0.992515
\(415\) 0 0
\(416\) −0.605969 −0.0297101
\(417\) −10.3923 −0.508913
\(418\) 0 0
\(419\) −2.23369 −0.109123 −0.0545614 0.998510i \(-0.517376\pi\)
−0.0545614 + 0.998510i \(0.517376\pi\)
\(420\) 0 0
\(421\) 18.0000 0.877266 0.438633 0.898666i \(-0.355463\pi\)
0.438633 + 0.898666i \(0.355463\pi\)
\(422\) 11.4891 0.559282
\(423\) 8.74456 0.425175
\(424\) 7.51811 0.365112
\(425\) 0 0
\(426\) 27.1229 1.31411
\(427\) 4.74456 0.229605
\(428\) −35.9306 −1.73677
\(429\) 0 0
\(430\) 0 0
\(431\) 23.6588 1.13960 0.569802 0.821782i \(-0.307020\pi\)
0.569802 + 0.821782i \(0.307020\pi\)
\(432\) 6.37228 0.306587
\(433\) −40.0951 −1.92685 −0.963424 0.267983i \(-0.913643\pi\)
−0.963424 + 0.267983i \(0.913643\pi\)
\(434\) 4.74456 0.227746
\(435\) 0 0
\(436\) −11.6819 −0.559463
\(437\) 35.2309 1.68532
\(438\) −13.1168 −0.626747
\(439\) 7.13058 0.340324 0.170162 0.985416i \(-0.445571\pi\)
0.170162 + 0.985416i \(0.445571\pi\)
\(440\) 0 0
\(441\) −6.37228 −0.303442
\(442\) −2.46943 −0.117459
\(443\) −9.25544 −0.439739 −0.219870 0.975529i \(-0.570563\pi\)
−0.219870 + 0.975529i \(0.570563\pi\)
\(444\) −21.8614 −1.03750
\(445\) 0 0
\(446\) 60.2343 2.85217
\(447\) −1.28962 −0.0609969
\(448\) −1.87953 −0.0887993
\(449\) 12.7446 0.601453 0.300727 0.953710i \(-0.402771\pi\)
0.300727 + 0.953710i \(0.402771\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −70.9783 −3.33854
\(453\) −23.8063 −1.11852
\(454\) −43.7228 −2.05201
\(455\) 0 0
\(456\) −26.3723 −1.23500
\(457\) −19.6048 −0.917074 −0.458537 0.888675i \(-0.651626\pi\)
−0.458537 + 0.888675i \(0.651626\pi\)
\(458\) −26.4781 −1.23724
\(459\) 6.63325 0.309614
\(460\) 0 0
\(461\) 1.87953 0.0875383 0.0437692 0.999042i \(-0.486063\pi\)
0.0437692 + 0.999042i \(0.486063\pi\)
\(462\) 0 0
\(463\) −26.9783 −1.25379 −0.626893 0.779106i \(-0.715674\pi\)
−0.626893 + 0.779106i \(0.715674\pi\)
\(464\) 64.3432 2.98706
\(465\) 0 0
\(466\) 38.2337 1.77114
\(467\) 1.48913 0.0689085 0.0344543 0.999406i \(-0.489031\pi\)
0.0344543 + 0.999406i \(0.489031\pi\)
\(468\) −0.644810 −0.0298064
\(469\) 8.80773 0.406703
\(470\) 0 0
\(471\) −8.37228 −0.385774
\(472\) 23.9538 1.10256
\(473\) 0 0
\(474\) −17.1168 −0.786203
\(475\) 0 0
\(476\) 22.9783 1.05321
\(477\) 1.25544 0.0574825
\(478\) 33.4891 1.53176
\(479\) 2.87419 0.131325 0.0656626 0.997842i \(-0.479084\pi\)
0.0656626 + 0.997842i \(0.479084\pi\)
\(480\) 0 0
\(481\) 0.737384 0.0336218
\(482\) −35.3505 −1.61017
\(483\) −6.33830 −0.288402
\(484\) 0 0
\(485\) 0 0
\(486\) 2.52434 0.114506
\(487\) 35.9783 1.63033 0.815165 0.579229i \(-0.196646\pi\)
0.815165 + 0.579229i \(0.196646\pi\)
\(488\) 35.8614 1.62337
\(489\) −14.3723 −0.649937
\(490\) 0 0
\(491\) −6.63325 −0.299354 −0.149677 0.988735i \(-0.547823\pi\)
−0.149677 + 0.988735i \(0.547823\pi\)
\(492\) 30.2921 1.36567
\(493\) 66.9783 3.01655
\(494\) 1.63948 0.0737636
\(495\) 0 0
\(496\) 15.1168 0.678766
\(497\) 8.51278 0.381850
\(498\) 21.4891 0.962951
\(499\) −14.1168 −0.631957 −0.315978 0.948766i \(-0.602333\pi\)
−0.315978 + 0.948766i \(0.602333\pi\)
\(500\) 0 0
\(501\) 5.04868 0.225558
\(502\) −1.28962 −0.0575586
\(503\) −3.16915 −0.141305 −0.0706527 0.997501i \(-0.522508\pi\)
−0.0706527 + 0.997501i \(0.522508\pi\)
\(504\) 4.74456 0.211340
\(505\) 0 0
\(506\) 0 0
\(507\) −12.9783 −0.576384
\(508\) −44.7933 −1.98738
\(509\) −30.9783 −1.37309 −0.686543 0.727089i \(-0.740873\pi\)
−0.686543 + 0.727089i \(0.740873\pi\)
\(510\) 0 0
\(511\) −4.11684 −0.182118
\(512\) −50.1369 −2.21576
\(513\) −4.40387 −0.194435
\(514\) −44.1485 −1.94731
\(515\) 0 0
\(516\) 43.5036 1.91514
\(517\) 0 0
\(518\) −10.0000 −0.439375
\(519\) −6.92820 −0.304114
\(520\) 0 0
\(521\) −36.7446 −1.60981 −0.804904 0.593405i \(-0.797783\pi\)
−0.804904 + 0.593405i \(0.797783\pi\)
\(522\) 25.4891 1.11563
\(523\) 27.0680 1.18360 0.591801 0.806084i \(-0.298417\pi\)
0.591801 + 0.806084i \(0.298417\pi\)
\(524\) −81.3687 −3.55461
\(525\) 0 0
\(526\) −12.7446 −0.555689
\(527\) 15.7359 0.685468
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) −15.2554 −0.661407
\(533\) −1.02175 −0.0442569
\(534\) 13.8564 0.599625
\(535\) 0 0
\(536\) 66.5725 2.87550
\(537\) 19.4891 0.841018
\(538\) −6.92820 −0.298696
\(539\) 0 0
\(540\) 0 0
\(541\) 23.5113 1.01083 0.505415 0.862876i \(-0.331339\pi\)
0.505415 + 0.862876i \(0.331339\pi\)
\(542\) −26.2337 −1.12683
\(543\) 13.8614 0.594850
\(544\) 27.2554 1.16857
\(545\) 0 0
\(546\) −0.294954 −0.0126229
\(547\) 0.884861 0.0378339 0.0189170 0.999821i \(-0.493978\pi\)
0.0189170 + 0.999821i \(0.493978\pi\)
\(548\) 3.25544 0.139065
\(549\) 5.98844 0.255580
\(550\) 0 0
\(551\) −44.4674 −1.89437
\(552\) −47.9075 −2.03908
\(553\) −5.37228 −0.228453
\(554\) 51.8614 2.20338
\(555\) 0 0
\(556\) −45.4381 −1.92700
\(557\) −6.33830 −0.268562 −0.134281 0.990943i \(-0.542873\pi\)
−0.134281 + 0.990943i \(0.542873\pi\)
\(558\) 5.98844 0.253511
\(559\) −1.46738 −0.0620634
\(560\) 0 0
\(561\) 0 0
\(562\) −21.4891 −0.906464
\(563\) −43.8535 −1.84820 −0.924102 0.382145i \(-0.875186\pi\)
−0.924102 + 0.382145i \(0.875186\pi\)
\(564\) 38.2337 1.60993
\(565\) 0 0
\(566\) −71.5842 −3.00891
\(567\) 0.792287 0.0332729
\(568\) 64.3432 2.69978
\(569\) 23.0689 0.967098 0.483549 0.875317i \(-0.339347\pi\)
0.483549 + 0.875317i \(0.339347\pi\)
\(570\) 0 0
\(571\) −3.37153 −0.141094 −0.0705470 0.997508i \(-0.522474\pi\)
−0.0705470 + 0.997508i \(0.522474\pi\)
\(572\) 0 0
\(573\) −17.4891 −0.730619
\(574\) 13.8564 0.578355
\(575\) 0 0
\(576\) −2.37228 −0.0988451
\(577\) 24.0951 1.00309 0.501546 0.865131i \(-0.332765\pi\)
0.501546 + 0.865131i \(0.332765\pi\)
\(578\) 68.1571 2.83496
\(579\) −21.1345 −0.878318
\(580\) 0 0
\(581\) 6.74456 0.279812
\(582\) 23.6588 0.980689
\(583\) 0 0
\(584\) −31.1168 −1.28762
\(585\) 0 0
\(586\) −82.7011 −3.41635
\(587\) −34.7446 −1.43406 −0.717031 0.697041i \(-0.754499\pi\)
−0.717031 + 0.697041i \(0.754499\pi\)
\(588\) −27.8614 −1.14899
\(589\) −10.4472 −0.430470
\(590\) 0 0
\(591\) 8.51278 0.350169
\(592\) −31.8614 −1.30950
\(593\) 24.5437 1.00789 0.503944 0.863736i \(-0.331882\pi\)
0.503944 + 0.863736i \(0.331882\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −5.63858 −0.230965
\(597\) 16.8614 0.690091
\(598\) 2.97825 0.121790
\(599\) −33.2554 −1.35878 −0.679390 0.733777i \(-0.737756\pi\)
−0.679390 + 0.733777i \(0.737756\pi\)
\(600\) 0 0
\(601\) −11.0371 −0.450213 −0.225107 0.974334i \(-0.572273\pi\)
−0.225107 + 0.974334i \(0.572273\pi\)
\(602\) 19.8997 0.811053
\(603\) 11.1168 0.452713
\(604\) −104.088 −4.23527
\(605\) 0 0
\(606\) −33.4891 −1.36040
\(607\) −33.7562 −1.37012 −0.685060 0.728487i \(-0.740224\pi\)
−0.685060 + 0.728487i \(0.740224\pi\)
\(608\) −18.0951 −0.733853
\(609\) 8.00000 0.324176
\(610\) 0 0
\(611\) −1.28962 −0.0521725
\(612\) 29.0024 1.17235
\(613\) 14.9985 0.605786 0.302893 0.953025i \(-0.402048\pi\)
0.302893 + 0.953025i \(0.402048\pi\)
\(614\) −66.8397 −2.69743
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) −9.45254 −0.380237
\(619\) −48.4891 −1.94894 −0.974471 0.224512i \(-0.927921\pi\)
−0.974471 + 0.224512i \(0.927921\pi\)
\(620\) 0 0
\(621\) −8.00000 −0.321029
\(622\) −25.8333 −1.03582
\(623\) 4.34896 0.174238
\(624\) −0.939764 −0.0376207
\(625\) 0 0
\(626\) 65.5779 2.62102
\(627\) 0 0
\(628\) −36.6060 −1.46074
\(629\) −33.1662 −1.32242
\(630\) 0 0
\(631\) −36.4891 −1.45261 −0.726305 0.687373i \(-0.758764\pi\)
−0.726305 + 0.687373i \(0.758764\pi\)
\(632\) −40.6060 −1.61522
\(633\) 4.55134 0.180900
\(634\) 47.9075 1.90265
\(635\) 0 0
\(636\) 5.48913 0.217658
\(637\) 0.939764 0.0372348
\(638\) 0 0
\(639\) 10.7446 0.425048
\(640\) 0 0
\(641\) 28.9783 1.14457 0.572286 0.820054i \(-0.306057\pi\)
0.572286 + 0.820054i \(0.306057\pi\)
\(642\) −20.7446 −0.818723
\(643\) 9.23369 0.364141 0.182071 0.983285i \(-0.441720\pi\)
0.182071 + 0.983285i \(0.441720\pi\)
\(644\) −27.7128 −1.09204
\(645\) 0 0
\(646\) −73.7408 −2.90129
\(647\) −2.00000 −0.0786281 −0.0393141 0.999227i \(-0.512517\pi\)
−0.0393141 + 0.999227i \(0.512517\pi\)
\(648\) 5.98844 0.235248
\(649\) 0 0
\(650\) 0 0
\(651\) 1.87953 0.0736645
\(652\) −62.8397 −2.46099
\(653\) −45.4891 −1.78013 −0.890064 0.455837i \(-0.849340\pi\)
−0.890064 + 0.455837i \(0.849340\pi\)
\(654\) −6.74456 −0.263733
\(655\) 0 0
\(656\) 44.1485 1.72371
\(657\) −5.19615 −0.202721
\(658\) 17.4891 0.681797
\(659\) −12.2718 −0.478043 −0.239021 0.971014i \(-0.576827\pi\)
−0.239021 + 0.971014i \(0.576827\pi\)
\(660\) 0 0
\(661\) −3.00000 −0.116686 −0.0583432 0.998297i \(-0.518582\pi\)
−0.0583432 + 0.998297i \(0.518582\pi\)
\(662\) 3.11425 0.121039
\(663\) −0.978251 −0.0379921
\(664\) 50.9783 1.97834
\(665\) 0 0
\(666\) −12.6217 −0.489081
\(667\) −80.7788 −3.12777
\(668\) 22.0742 0.854078
\(669\) 23.8614 0.922535
\(670\) 0 0
\(671\) 0 0
\(672\) 3.25544 0.125581
\(673\) 28.8550 1.11228 0.556138 0.831090i \(-0.312282\pi\)
0.556138 + 0.831090i \(0.312282\pi\)
\(674\) 26.7446 1.03016
\(675\) 0 0
\(676\) −56.7446 −2.18248
\(677\) −10.9822 −0.422081 −0.211040 0.977477i \(-0.567685\pi\)
−0.211040 + 0.977477i \(0.567685\pi\)
\(678\) −40.9793 −1.57380
\(679\) 7.42554 0.284966
\(680\) 0 0
\(681\) −17.3205 −0.663723
\(682\) 0 0
\(683\) −18.0000 −0.688751 −0.344375 0.938832i \(-0.611909\pi\)
−0.344375 + 0.938832i \(0.611909\pi\)
\(684\) −19.2549 −0.736231
\(685\) 0 0
\(686\) −26.7446 −1.02111
\(687\) −10.4891 −0.400185
\(688\) 63.4034 2.41723
\(689\) −0.185148 −0.00705357
\(690\) 0 0
\(691\) −2.25544 −0.0858009 −0.0429004 0.999079i \(-0.513660\pi\)
−0.0429004 + 0.999079i \(0.513660\pi\)
\(692\) −30.2921 −1.15153
\(693\) 0 0
\(694\) −5.48913 −0.208364
\(695\) 0 0
\(696\) 60.4674 2.29201
\(697\) 45.9565 1.74073
\(698\) 21.8614 0.827466
\(699\) 15.1460 0.572875
\(700\) 0 0
\(701\) −4.05401 −0.153118 −0.0765589 0.997065i \(-0.524393\pi\)
−0.0765589 + 0.997065i \(0.524393\pi\)
\(702\) −0.372281 −0.0140509
\(703\) 22.0193 0.830475
\(704\) 0 0
\(705\) 0 0
\(706\) 40.9793 1.54228
\(707\) −10.5109 −0.395302
\(708\) 17.4891 0.657282
\(709\) 31.0000 1.16423 0.582115 0.813107i \(-0.302225\pi\)
0.582115 + 0.813107i \(0.302225\pi\)
\(710\) 0 0
\(711\) −6.78073 −0.254297
\(712\) 32.8713 1.23190
\(713\) −18.9783 −0.710741
\(714\) 13.2665 0.496486
\(715\) 0 0
\(716\) 85.2119 3.18452
\(717\) 13.2665 0.495446
\(718\) 16.7446 0.624902
\(719\) 14.0000 0.522112 0.261056 0.965324i \(-0.415929\pi\)
0.261056 + 0.965324i \(0.415929\pi\)
\(720\) 0 0
\(721\) −2.96677 −0.110488
\(722\) 0.994667 0.0370177
\(723\) −14.0039 −0.520810
\(724\) 60.6060 2.25240
\(725\) 0 0
\(726\) 0 0
\(727\) −21.4674 −0.796181 −0.398090 0.917346i \(-0.630327\pi\)
−0.398090 + 0.917346i \(0.630327\pi\)
\(728\) −0.699713 −0.0259331
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 66.0000 2.44110
\(732\) 26.1831 0.967757
\(733\) −13.8564 −0.511798 −0.255899 0.966704i \(-0.582371\pi\)
−0.255899 + 0.966704i \(0.582371\pi\)
\(734\) 37.8651 1.39763
\(735\) 0 0
\(736\) −32.8713 −1.21165
\(737\) 0 0
\(738\) 17.4891 0.643784
\(739\) 33.6087 1.23632 0.618158 0.786054i \(-0.287879\pi\)
0.618158 + 0.786054i \(0.287879\pi\)
\(740\) 0 0
\(741\) 0.649468 0.0238588
\(742\) 2.51087 0.0921771
\(743\) −41.9740 −1.53988 −0.769938 0.638119i \(-0.779713\pi\)
−0.769938 + 0.638119i \(0.779713\pi\)
\(744\) 14.2063 0.520827
\(745\) 0 0
\(746\) 65.7228 2.40628
\(747\) 8.51278 0.311466
\(748\) 0 0
\(749\) −6.51087 −0.237902
\(750\) 0 0
\(751\) 29.2337 1.06675 0.533376 0.845878i \(-0.320923\pi\)
0.533376 + 0.845878i \(0.320923\pi\)
\(752\) 55.7228 2.03200
\(753\) −0.510875 −0.0186173
\(754\) −3.75906 −0.136897
\(755\) 0 0
\(756\) 3.46410 0.125988
\(757\) −32.3505 −1.17580 −0.587900 0.808934i \(-0.700045\pi\)
−0.587900 + 0.808934i \(0.700045\pi\)
\(758\) −12.6217 −0.458440
\(759\) 0 0
\(760\) 0 0
\(761\) 18.6101 0.674617 0.337308 0.941394i \(-0.390484\pi\)
0.337308 + 0.941394i \(0.390484\pi\)
\(762\) −25.8614 −0.936860
\(763\) −2.11684 −0.0766349
\(764\) −76.4674 −2.76649
\(765\) 0 0
\(766\) 25.8333 0.933395
\(767\) −0.589907 −0.0213003
\(768\) −31.1168 −1.12283
\(769\) 29.3523 1.05847 0.529235 0.848475i \(-0.322479\pi\)
0.529235 + 0.848475i \(0.322479\pi\)
\(770\) 0 0
\(771\) −17.4891 −0.629855
\(772\) −92.4058 −3.32576
\(773\) −0.510875 −0.0183749 −0.00918744 0.999958i \(-0.502924\pi\)
−0.00918744 + 0.999958i \(0.502924\pi\)
\(774\) 25.1168 0.902806
\(775\) 0 0
\(776\) 56.1253 2.01478
\(777\) −3.96143 −0.142116
\(778\) 82.6583 2.96344
\(779\) −30.5109 −1.09317
\(780\) 0 0
\(781\) 0 0
\(782\) −133.957 −4.79027
\(783\) 10.0974 0.360850
\(784\) −40.6060 −1.45021
\(785\) 0 0
\(786\) −46.9783 −1.67566
\(787\) −13.4140 −0.478157 −0.239078 0.971000i \(-0.576845\pi\)
−0.239078 + 0.971000i \(0.576845\pi\)
\(788\) 37.2203 1.32592
\(789\) −5.04868 −0.179738
\(790\) 0 0
\(791\) −12.8617 −0.457311
\(792\) 0 0
\(793\) −0.883156 −0.0313618
\(794\) 6.63325 0.235405
\(795\) 0 0
\(796\) 73.7228 2.61304
\(797\) 29.7228 1.05284 0.526418 0.850226i \(-0.323535\pi\)
0.526418 + 0.850226i \(0.323535\pi\)
\(798\) −8.80773 −0.311790
\(799\) 58.0049 2.05206
\(800\) 0 0
\(801\) 5.48913 0.193949
\(802\) −78.1996 −2.76132
\(803\) 0 0
\(804\) 48.6060 1.71420
\(805\) 0 0
\(806\) −0.883156 −0.0311078
\(807\) −2.74456 −0.0966132
\(808\) −79.4456 −2.79489
\(809\) −20.4897 −0.720378 −0.360189 0.932879i \(-0.617288\pi\)
−0.360189 + 0.932879i \(0.617288\pi\)
\(810\) 0 0
\(811\) −4.95610 −0.174032 −0.0870161 0.996207i \(-0.527733\pi\)
−0.0870161 + 0.996207i \(0.527733\pi\)
\(812\) 34.9783 1.22750
\(813\) −10.3923 −0.364474
\(814\) 0 0
\(815\) 0 0
\(816\) 42.2689 1.47971
\(817\) −43.8179 −1.53299
\(818\) 96.7011 3.38107
\(819\) −0.116844 −0.00408286
\(820\) 0 0
\(821\) −46.0280 −1.60639 −0.803194 0.595718i \(-0.796868\pi\)
−0.803194 + 0.595718i \(0.796868\pi\)
\(822\) 1.87953 0.0655561
\(823\) −2.35053 −0.0819344 −0.0409672 0.999160i \(-0.513044\pi\)
−0.0409672 + 0.999160i \(0.513044\pi\)
\(824\) −22.4241 −0.781180
\(825\) 0 0
\(826\) 8.00000 0.278356
\(827\) −16.1407 −0.561267 −0.280633 0.959815i \(-0.590545\pi\)
−0.280633 + 0.959815i \(0.590545\pi\)
\(828\) −34.9783 −1.21558
\(829\) 41.4674 1.44022 0.720111 0.693859i \(-0.244091\pi\)
0.720111 + 0.693859i \(0.244091\pi\)
\(830\) 0 0
\(831\) 20.5446 0.712683
\(832\) 0.349857 0.0121291
\(833\) −42.2689 −1.46453
\(834\) −26.2337 −0.908398
\(835\) 0 0
\(836\) 0 0
\(837\) 2.37228 0.0819980
\(838\) −5.63858 −0.194782
\(839\) 23.2554 0.802867 0.401433 0.915888i \(-0.368512\pi\)
0.401433 + 0.915888i \(0.368512\pi\)
\(840\) 0 0
\(841\) 72.9565 2.51574
\(842\) 45.4381 1.56590
\(843\) −8.51278 −0.293196
\(844\) 19.8997 0.684978
\(845\) 0 0
\(846\) 22.0742 0.758928
\(847\) 0 0
\(848\) 8.00000 0.274721
\(849\) −28.3576 −0.973231
\(850\) 0 0
\(851\) 40.0000 1.37118
\(852\) 46.9783 1.60945
\(853\) 10.4472 0.357706 0.178853 0.983876i \(-0.442761\pi\)
0.178853 + 0.983876i \(0.442761\pi\)
\(854\) 11.9769 0.409840
\(855\) 0 0
\(856\) −49.2119 −1.68203
\(857\) −42.5639 −1.45395 −0.726977 0.686661i \(-0.759075\pi\)
−0.726977 + 0.686661i \(0.759075\pi\)
\(858\) 0 0
\(859\) −10.2554 −0.349911 −0.174956 0.984576i \(-0.555978\pi\)
−0.174956 + 0.984576i \(0.555978\pi\)
\(860\) 0 0
\(861\) 5.48913 0.187069
\(862\) 59.7228 2.03417
\(863\) 20.2337 0.688763 0.344381 0.938830i \(-0.388089\pi\)
0.344381 + 0.938830i \(0.388089\pi\)
\(864\) 4.10891 0.139788
\(865\) 0 0
\(866\) −101.214 −3.43938
\(867\) 27.0000 0.916968
\(868\) 8.21782 0.278931
\(869\) 0 0
\(870\) 0 0
\(871\) −1.63948 −0.0555516
\(872\) −16.0000 −0.541828
\(873\) 9.37228 0.317204
\(874\) 88.9348 3.00826
\(875\) 0 0
\(876\) −22.7190 −0.767605
\(877\) −46.3778 −1.56607 −0.783034 0.621979i \(-0.786329\pi\)
−0.783034 + 0.621979i \(0.786329\pi\)
\(878\) 18.0000 0.607471
\(879\) −32.7615 −1.10502
\(880\) 0 0
\(881\) 46.4674 1.56553 0.782763 0.622320i \(-0.213810\pi\)
0.782763 + 0.622320i \(0.213810\pi\)
\(882\) −16.0858 −0.541637
\(883\) −11.1386 −0.374844 −0.187422 0.982280i \(-0.560013\pi\)
−0.187422 + 0.982280i \(0.560013\pi\)
\(884\) −4.27719 −0.143857
\(885\) 0 0
\(886\) −23.3639 −0.784924
\(887\) 21.4843 0.721373 0.360686 0.932687i \(-0.382542\pi\)
0.360686 + 0.932687i \(0.382542\pi\)
\(888\) −29.9422 −1.00479
\(889\) −8.11684 −0.272230
\(890\) 0 0
\(891\) 0 0
\(892\) 104.329 3.49319
\(893\) −38.5099 −1.28868
\(894\) −3.25544 −0.108878
\(895\) 0 0
\(896\) −11.2554 −0.376018
\(897\) 1.17981 0.0393929
\(898\) 32.1716 1.07358
\(899\) 23.9538 0.798903
\(900\) 0 0
\(901\) 8.32763 0.277434
\(902\) 0 0
\(903\) 7.88316 0.262335
\(904\) −97.2145 −3.23330
\(905\) 0 0
\(906\) −60.0951 −1.99653
\(907\) 19.2337 0.638644 0.319322 0.947646i \(-0.396545\pi\)
0.319322 + 0.947646i \(0.396545\pi\)
\(908\) −75.7301 −2.51319
\(909\) −13.2665 −0.440022
\(910\) 0 0
\(911\) 4.51087 0.149452 0.0747260 0.997204i \(-0.476192\pi\)
0.0747260 + 0.997204i \(0.476192\pi\)
\(912\) −28.0627 −0.929248
\(913\) 0 0
\(914\) −49.4891 −1.63695
\(915\) 0 0
\(916\) −45.8614 −1.51530
\(917\) −14.7446 −0.486908
\(918\) 16.7446 0.552653
\(919\) 10.8896 0.359216 0.179608 0.983738i \(-0.442517\pi\)
0.179608 + 0.983738i \(0.442517\pi\)
\(920\) 0 0
\(921\) −26.4781 −0.872483
\(922\) 4.74456 0.156254
\(923\) −1.58457 −0.0521569
\(924\) 0 0
\(925\) 0 0
\(926\) −68.1022 −2.23798
\(927\) −3.74456 −0.122988
\(928\) 41.4891 1.36195
\(929\) 13.2554 0.434897 0.217448 0.976072i \(-0.430227\pi\)
0.217448 + 0.976072i \(0.430227\pi\)
\(930\) 0 0
\(931\) 28.0627 0.919717
\(932\) 66.2227 2.16920
\(933\) −10.2337 −0.335036
\(934\) 3.75906 0.123000
\(935\) 0 0
\(936\) −0.883156 −0.0288669
\(937\) −14.9436 −0.488188 −0.244094 0.969752i \(-0.578490\pi\)
−0.244094 + 0.969752i \(0.578490\pi\)
\(938\) 22.2337 0.725956
\(939\) 25.9783 0.847768
\(940\) 0 0
\(941\) 3.75906 0.122542 0.0612708 0.998121i \(-0.480485\pi\)
0.0612708 + 0.998121i \(0.480485\pi\)
\(942\) −21.1345 −0.688598
\(943\) −55.4256 −1.80491
\(944\) 25.4891 0.829600
\(945\) 0 0
\(946\) 0 0
\(947\) −21.4891 −0.698303 −0.349151 0.937066i \(-0.613530\pi\)
−0.349151 + 0.937066i \(0.613530\pi\)
\(948\) −29.6472 −0.962898
\(949\) 0.766312 0.0248755
\(950\) 0 0
\(951\) 18.9783 0.615412
\(952\) 31.4719 1.02001
\(953\) −25.2434 −0.817713 −0.408857 0.912599i \(-0.634072\pi\)
−0.408857 + 0.912599i \(0.634072\pi\)
\(954\) 3.16915 0.102605
\(955\) 0 0
\(956\) 58.0049 1.87601
\(957\) 0 0
\(958\) 7.25544 0.234413
\(959\) 0.589907 0.0190491
\(960\) 0 0
\(961\) −25.3723 −0.818461
\(962\) 1.86141 0.0600142
\(963\) −8.21782 −0.264816
\(964\) −61.2289 −1.97205
\(965\) 0 0
\(966\) −16.0000 −0.514792
\(967\) 7.96054 0.255994 0.127997 0.991775i \(-0.459145\pi\)
0.127997 + 0.991775i \(0.459145\pi\)
\(968\) 0 0
\(969\) −29.2119 −0.938423
\(970\) 0 0
\(971\) 49.4891 1.58818 0.794091 0.607799i \(-0.207947\pi\)
0.794091 + 0.607799i \(0.207947\pi\)
\(972\) 4.37228 0.140241
\(973\) −8.23369 −0.263960
\(974\) 90.8213 2.91010
\(975\) 0 0
\(976\) 38.1600 1.22147
\(977\) −38.7446 −1.23955 −0.619774 0.784780i \(-0.712776\pi\)
−0.619774 + 0.784780i \(0.712776\pi\)
\(978\) −36.2805 −1.16012
\(979\) 0 0
\(980\) 0 0
\(981\) −2.67181 −0.0853045
\(982\) −16.7446 −0.534340
\(983\) 37.4891 1.19572 0.597859 0.801602i \(-0.296018\pi\)
0.597859 + 0.801602i \(0.296018\pi\)
\(984\) 41.4891 1.32263
\(985\) 0 0
\(986\) 169.076 5.38447
\(987\) 6.92820 0.220527
\(988\) 2.83966 0.0903415
\(989\) −79.5990 −2.53110
\(990\) 0 0
\(991\) 46.9565 1.49162 0.745811 0.666157i \(-0.232062\pi\)
0.745811 + 0.666157i \(0.232062\pi\)
\(992\) 9.74749 0.309483
\(993\) 1.23369 0.0391499
\(994\) 21.4891 0.681594
\(995\) 0 0
\(996\) 37.2203 1.17937
\(997\) −0.552236 −0.0174895 −0.00874475 0.999962i \(-0.502784\pi\)
−0.00874475 + 0.999962i \(0.502784\pi\)
\(998\) −35.6357 −1.12803
\(999\) −5.00000 −0.158193
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 9075.2.a.db.1.4 yes 4
5.4 even 2 9075.2.a.cw.1.1 4
11.10 odd 2 inner 9075.2.a.db.1.1 yes 4
55.54 odd 2 9075.2.a.cw.1.4 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9075.2.a.cw.1.1 4 5.4 even 2
9075.2.a.cw.1.4 yes 4 55.54 odd 2
9075.2.a.db.1.1 yes 4 11.10 odd 2 inner
9075.2.a.db.1.4 yes 4 1.1 even 1 trivial