Properties

Label 6025.2.a.p.1.8
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.88286 q^{2} -2.55671 q^{3} +1.54517 q^{4} +4.81392 q^{6} +3.51799 q^{7} +0.856390 q^{8} +3.53675 q^{9} +O(q^{10})\) \(q-1.88286 q^{2} -2.55671 q^{3} +1.54517 q^{4} +4.81392 q^{6} +3.51799 q^{7} +0.856390 q^{8} +3.53675 q^{9} -1.11714 q^{11} -3.95054 q^{12} +0.230541 q^{13} -6.62388 q^{14} -4.70279 q^{16} +4.35003 q^{17} -6.65921 q^{18} +3.14602 q^{19} -8.99446 q^{21} +2.10341 q^{22} +6.36510 q^{23} -2.18954 q^{24} -0.434076 q^{26} -1.37232 q^{27} +5.43587 q^{28} -0.0527009 q^{29} -4.55850 q^{31} +7.14193 q^{32} +2.85619 q^{33} -8.19050 q^{34} +5.46487 q^{36} +6.27282 q^{37} -5.92351 q^{38} -0.589425 q^{39} -8.79348 q^{41} +16.9353 q^{42} -2.95908 q^{43} -1.72616 q^{44} -11.9846 q^{46} -10.3334 q^{47} +12.0237 q^{48} +5.37623 q^{49} -11.1218 q^{51} +0.356224 q^{52} -6.03035 q^{53} +2.58389 q^{54} +3.01277 q^{56} -8.04344 q^{57} +0.0992284 q^{58} +6.43499 q^{59} -11.8995 q^{61} +8.58302 q^{62} +12.4423 q^{63} -4.04167 q^{64} -5.37781 q^{66} -2.08295 q^{67} +6.72152 q^{68} -16.2737 q^{69} -5.17552 q^{71} +3.02884 q^{72} -1.25992 q^{73} -11.8109 q^{74} +4.86112 q^{76} -3.93007 q^{77} +1.10981 q^{78} -0.749786 q^{79} -7.10164 q^{81} +16.5569 q^{82} -11.1374 q^{83} -13.8979 q^{84} +5.57154 q^{86} +0.134741 q^{87} -0.956703 q^{88} -8.15389 q^{89} +0.811039 q^{91} +9.83514 q^{92} +11.6547 q^{93} +19.4564 q^{94} -18.2598 q^{96} +7.78090 q^{97} -10.1227 q^{98} -3.95103 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88286 −1.33138 −0.665692 0.746227i \(-0.731863\pi\)
−0.665692 + 0.746227i \(0.731863\pi\)
\(3\) −2.55671 −1.47612 −0.738058 0.674737i \(-0.764257\pi\)
−0.738058 + 0.674737i \(0.764257\pi\)
\(4\) 1.54517 0.772583
\(5\) 0 0
\(6\) 4.81392 1.96528
\(7\) 3.51799 1.32967 0.664837 0.746988i \(-0.268501\pi\)
0.664837 + 0.746988i \(0.268501\pi\)
\(8\) 0.856390 0.302780
\(9\) 3.53675 1.17892
\(10\) 0 0
\(11\) −1.11714 −0.336829 −0.168414 0.985716i \(-0.553865\pi\)
−0.168414 + 0.985716i \(0.553865\pi\)
\(12\) −3.95054 −1.14042
\(13\) 0.230541 0.0639405 0.0319702 0.999489i \(-0.489822\pi\)
0.0319702 + 0.999489i \(0.489822\pi\)
\(14\) −6.62388 −1.77031
\(15\) 0 0
\(16\) −4.70279 −1.17570
\(17\) 4.35003 1.05504 0.527519 0.849543i \(-0.323123\pi\)
0.527519 + 0.849543i \(0.323123\pi\)
\(18\) −6.65921 −1.56959
\(19\) 3.14602 0.721746 0.360873 0.932615i \(-0.382479\pi\)
0.360873 + 0.932615i \(0.382479\pi\)
\(20\) 0 0
\(21\) −8.99446 −1.96275
\(22\) 2.10341 0.448449
\(23\) 6.36510 1.32722 0.663608 0.748081i \(-0.269024\pi\)
0.663608 + 0.748081i \(0.269024\pi\)
\(24\) −2.18954 −0.446938
\(25\) 0 0
\(26\) −0.434076 −0.0851293
\(27\) −1.37232 −0.264103
\(28\) 5.43587 1.02728
\(29\) −0.0527009 −0.00978631 −0.00489315 0.999988i \(-0.501558\pi\)
−0.00489315 + 0.999988i \(0.501558\pi\)
\(30\) 0 0
\(31\) −4.55850 −0.818730 −0.409365 0.912371i \(-0.634250\pi\)
−0.409365 + 0.912371i \(0.634250\pi\)
\(32\) 7.14193 1.26253
\(33\) 2.85619 0.497199
\(34\) −8.19050 −1.40466
\(35\) 0 0
\(36\) 5.46487 0.910811
\(37\) 6.27282 1.03125 0.515623 0.856816i \(-0.327561\pi\)
0.515623 + 0.856816i \(0.327561\pi\)
\(38\) −5.92351 −0.960921
\(39\) −0.589425 −0.0943835
\(40\) 0 0
\(41\) −8.79348 −1.37331 −0.686655 0.726983i \(-0.740922\pi\)
−0.686655 + 0.726983i \(0.740922\pi\)
\(42\) 16.9353 2.61318
\(43\) −2.95908 −0.451256 −0.225628 0.974214i \(-0.572443\pi\)
−0.225628 + 0.974214i \(0.572443\pi\)
\(44\) −1.72616 −0.260228
\(45\) 0 0
\(46\) −11.9846 −1.76703
\(47\) −10.3334 −1.50729 −0.753643 0.657284i \(-0.771705\pi\)
−0.753643 + 0.657284i \(0.771705\pi\)
\(48\) 12.0237 1.73547
\(49\) 5.37623 0.768033
\(50\) 0 0
\(51\) −11.1218 −1.55736
\(52\) 0.356224 0.0493993
\(53\) −6.03035 −0.828332 −0.414166 0.910201i \(-0.635927\pi\)
−0.414166 + 0.910201i \(0.635927\pi\)
\(54\) 2.58389 0.351622
\(55\) 0 0
\(56\) 3.01277 0.402598
\(57\) −8.04344 −1.06538
\(58\) 0.0992284 0.0130293
\(59\) 6.43499 0.837765 0.418882 0.908041i \(-0.362422\pi\)
0.418882 + 0.908041i \(0.362422\pi\)
\(60\) 0 0
\(61\) −11.8995 −1.52358 −0.761789 0.647825i \(-0.775679\pi\)
−0.761789 + 0.647825i \(0.775679\pi\)
\(62\) 8.58302 1.09004
\(63\) 12.4423 1.56758
\(64\) −4.04167 −0.505209
\(65\) 0 0
\(66\) −5.37781 −0.661962
\(67\) −2.08295 −0.254473 −0.127236 0.991872i \(-0.540611\pi\)
−0.127236 + 0.991872i \(0.540611\pi\)
\(68\) 6.72152 0.815104
\(69\) −16.2737 −1.95912
\(70\) 0 0
\(71\) −5.17552 −0.614222 −0.307111 0.951674i \(-0.599362\pi\)
−0.307111 + 0.951674i \(0.599362\pi\)
\(72\) 3.02884 0.356952
\(73\) −1.25992 −0.147463 −0.0737313 0.997278i \(-0.523491\pi\)
−0.0737313 + 0.997278i \(0.523491\pi\)
\(74\) −11.8109 −1.37298
\(75\) 0 0
\(76\) 4.86112 0.557608
\(77\) −3.93007 −0.447873
\(78\) 1.10981 0.125661
\(79\) −0.749786 −0.0843575 −0.0421788 0.999110i \(-0.513430\pi\)
−0.0421788 + 0.999110i \(0.513430\pi\)
\(80\) 0 0
\(81\) −7.10164 −0.789071
\(82\) 16.5569 1.82840
\(83\) −11.1374 −1.22249 −0.611244 0.791442i \(-0.709331\pi\)
−0.611244 + 0.791442i \(0.709331\pi\)
\(84\) −13.8979 −1.51639
\(85\) 0 0
\(86\) 5.57154 0.600795
\(87\) 0.134741 0.0144457
\(88\) −0.956703 −0.101985
\(89\) −8.15389 −0.864310 −0.432155 0.901799i \(-0.642247\pi\)
−0.432155 + 0.901799i \(0.642247\pi\)
\(90\) 0 0
\(91\) 0.811039 0.0850200
\(92\) 9.83514 1.02538
\(93\) 11.6547 1.20854
\(94\) 19.4564 2.00678
\(95\) 0 0
\(96\) −18.2598 −1.86364
\(97\) 7.78090 0.790031 0.395016 0.918674i \(-0.370739\pi\)
0.395016 + 0.918674i \(0.370739\pi\)
\(98\) −10.1227 −1.02255
\(99\) −3.95103 −0.397094
\(100\) 0 0
\(101\) 6.17087 0.614025 0.307012 0.951706i \(-0.400671\pi\)
0.307012 + 0.951706i \(0.400671\pi\)
\(102\) 20.9407 2.07344
\(103\) −12.4124 −1.22303 −0.611513 0.791235i \(-0.709439\pi\)
−0.611513 + 0.791235i \(0.709439\pi\)
\(104\) 0.197433 0.0193599
\(105\) 0 0
\(106\) 11.3543 1.10283
\(107\) −7.65910 −0.740433 −0.370216 0.928946i \(-0.620716\pi\)
−0.370216 + 0.928946i \(0.620716\pi\)
\(108\) −2.12046 −0.204041
\(109\) −0.837327 −0.0802014 −0.0401007 0.999196i \(-0.512768\pi\)
−0.0401007 + 0.999196i \(0.512768\pi\)
\(110\) 0 0
\(111\) −16.0378 −1.52224
\(112\) −16.5444 −1.56330
\(113\) −14.1036 −1.32676 −0.663378 0.748285i \(-0.730878\pi\)
−0.663378 + 0.748285i \(0.730878\pi\)
\(114\) 15.1447 1.41843
\(115\) 0 0
\(116\) −0.0814316 −0.00756073
\(117\) 0.815365 0.0753805
\(118\) −12.1162 −1.11539
\(119\) 15.3033 1.40286
\(120\) 0 0
\(121\) −9.75201 −0.886546
\(122\) 22.4052 2.02847
\(123\) 22.4824 2.02717
\(124\) −7.04363 −0.632537
\(125\) 0 0
\(126\) −23.4270 −2.08705
\(127\) −16.6119 −1.47407 −0.737033 0.675857i \(-0.763774\pi\)
−0.737033 + 0.675857i \(0.763774\pi\)
\(128\) −6.67395 −0.589900
\(129\) 7.56551 0.666106
\(130\) 0 0
\(131\) −1.55100 −0.135512 −0.0677558 0.997702i \(-0.521584\pi\)
−0.0677558 + 0.997702i \(0.521584\pi\)
\(132\) 4.41328 0.384127
\(133\) 11.0676 0.959687
\(134\) 3.92190 0.338801
\(135\) 0 0
\(136\) 3.72532 0.319444
\(137\) 1.06515 0.0910016 0.0455008 0.998964i \(-0.485512\pi\)
0.0455008 + 0.998964i \(0.485512\pi\)
\(138\) 30.6411 2.60835
\(139\) 10.1224 0.858570 0.429285 0.903169i \(-0.358766\pi\)
0.429285 + 0.903169i \(0.358766\pi\)
\(140\) 0 0
\(141\) 26.4196 2.22493
\(142\) 9.74479 0.817765
\(143\) −0.257545 −0.0215370
\(144\) −16.6326 −1.38605
\(145\) 0 0
\(146\) 2.37226 0.196329
\(147\) −13.7455 −1.13371
\(148\) 9.69255 0.796723
\(149\) −18.6972 −1.53173 −0.765867 0.642999i \(-0.777690\pi\)
−0.765867 + 0.642999i \(0.777690\pi\)
\(150\) 0 0
\(151\) 4.48916 0.365323 0.182661 0.983176i \(-0.441529\pi\)
0.182661 + 0.983176i \(0.441529\pi\)
\(152\) 2.69422 0.218530
\(153\) 15.3850 1.24380
\(154\) 7.39977 0.596291
\(155\) 0 0
\(156\) −0.910759 −0.0729191
\(157\) 2.73158 0.218003 0.109002 0.994042i \(-0.465235\pi\)
0.109002 + 0.994042i \(0.465235\pi\)
\(158\) 1.41174 0.112312
\(159\) 15.4178 1.22271
\(160\) 0 0
\(161\) 22.3923 1.76476
\(162\) 13.3714 1.05056
\(163\) 19.3913 1.51884 0.759421 0.650600i \(-0.225483\pi\)
0.759421 + 0.650600i \(0.225483\pi\)
\(164\) −13.5874 −1.06100
\(165\) 0 0
\(166\) 20.9702 1.62760
\(167\) 14.3680 1.11183 0.555913 0.831241i \(-0.312369\pi\)
0.555913 + 0.831241i \(0.312369\pi\)
\(168\) −7.70277 −0.594281
\(169\) −12.9469 −0.995912
\(170\) 0 0
\(171\) 11.1267 0.850879
\(172\) −4.57227 −0.348632
\(173\) 15.0237 1.14223 0.571114 0.820871i \(-0.306512\pi\)
0.571114 + 0.820871i \(0.306512\pi\)
\(174\) −0.253698 −0.0192328
\(175\) 0 0
\(176\) 5.25366 0.396009
\(177\) −16.4524 −1.23664
\(178\) 15.3526 1.15073
\(179\) −12.9071 −0.964719 −0.482360 0.875973i \(-0.660220\pi\)
−0.482360 + 0.875973i \(0.660220\pi\)
\(180\) 0 0
\(181\) 21.0476 1.56446 0.782229 0.622991i \(-0.214083\pi\)
0.782229 + 0.622991i \(0.214083\pi\)
\(182\) −1.52707 −0.113194
\(183\) 30.4236 2.24898
\(184\) 5.45101 0.401854
\(185\) 0 0
\(186\) −21.9443 −1.60903
\(187\) −4.85957 −0.355367
\(188\) −15.9669 −1.16450
\(189\) −4.82780 −0.351171
\(190\) 0 0
\(191\) −12.3891 −0.896442 −0.448221 0.893923i \(-0.647942\pi\)
−0.448221 + 0.893923i \(0.647942\pi\)
\(192\) 10.3334 0.745747
\(193\) 12.3460 0.888684 0.444342 0.895857i \(-0.353438\pi\)
0.444342 + 0.895857i \(0.353438\pi\)
\(194\) −14.6504 −1.05183
\(195\) 0 0
\(196\) 8.30717 0.593369
\(197\) −7.55643 −0.538373 −0.269187 0.963088i \(-0.586755\pi\)
−0.269187 + 0.963088i \(0.586755\pi\)
\(198\) 7.43924 0.528684
\(199\) −19.3457 −1.37138 −0.685689 0.727895i \(-0.740499\pi\)
−0.685689 + 0.727895i \(0.740499\pi\)
\(200\) 0 0
\(201\) 5.32549 0.375631
\(202\) −11.6189 −0.817503
\(203\) −0.185401 −0.0130126
\(204\) −17.1850 −1.20319
\(205\) 0 0
\(206\) 23.3707 1.62832
\(207\) 22.5118 1.56468
\(208\) −1.08419 −0.0751747
\(209\) −3.51453 −0.243105
\(210\) 0 0
\(211\) 24.8658 1.71183 0.855915 0.517116i \(-0.172994\pi\)
0.855915 + 0.517116i \(0.172994\pi\)
\(212\) −9.31788 −0.639955
\(213\) 13.2323 0.906662
\(214\) 14.4210 0.985800
\(215\) 0 0
\(216\) −1.17524 −0.0799650
\(217\) −16.0367 −1.08864
\(218\) 1.57657 0.106779
\(219\) 3.22125 0.217672
\(220\) 0 0
\(221\) 1.00286 0.0674596
\(222\) 30.1969 2.02668
\(223\) 1.62890 0.109079 0.0545396 0.998512i \(-0.482631\pi\)
0.0545396 + 0.998512i \(0.482631\pi\)
\(224\) 25.1252 1.67875
\(225\) 0 0
\(226\) 26.5551 1.76642
\(227\) −11.5071 −0.763751 −0.381876 0.924214i \(-0.624722\pi\)
−0.381876 + 0.924214i \(0.624722\pi\)
\(228\) −12.4285 −0.823094
\(229\) 21.7531 1.43749 0.718743 0.695276i \(-0.244718\pi\)
0.718743 + 0.695276i \(0.244718\pi\)
\(230\) 0 0
\(231\) 10.0480 0.661112
\(232\) −0.0451325 −0.00296309
\(233\) −6.93311 −0.454203 −0.227102 0.973871i \(-0.572925\pi\)
−0.227102 + 0.973871i \(0.572925\pi\)
\(234\) −1.53522 −0.100360
\(235\) 0 0
\(236\) 9.94313 0.647243
\(237\) 1.91698 0.124521
\(238\) −28.8141 −1.86774
\(239\) 13.0493 0.844087 0.422044 0.906576i \(-0.361313\pi\)
0.422044 + 0.906576i \(0.361313\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 18.3617 1.18033
\(243\) 22.2738 1.42886
\(244\) −18.3867 −1.17709
\(245\) 0 0
\(246\) −42.3312 −2.69894
\(247\) 0.725285 0.0461488
\(248\) −3.90385 −0.247895
\(249\) 28.4751 1.80453
\(250\) 0 0
\(251\) −28.8117 −1.81858 −0.909291 0.416162i \(-0.863375\pi\)
−0.909291 + 0.416162i \(0.863375\pi\)
\(252\) 19.2253 1.21108
\(253\) −7.11068 −0.447045
\(254\) 31.2778 1.96255
\(255\) 0 0
\(256\) 20.6495 1.29059
\(257\) 15.3709 0.958809 0.479404 0.877594i \(-0.340853\pi\)
0.479404 + 0.877594i \(0.340853\pi\)
\(258\) −14.2448 −0.886842
\(259\) 22.0677 1.37122
\(260\) 0 0
\(261\) −0.186390 −0.0115372
\(262\) 2.92032 0.180418
\(263\) 7.75814 0.478387 0.239194 0.970972i \(-0.423117\pi\)
0.239194 + 0.970972i \(0.423117\pi\)
\(264\) 2.44601 0.150542
\(265\) 0 0
\(266\) −20.8388 −1.27771
\(267\) 20.8471 1.27582
\(268\) −3.21850 −0.196601
\(269\) −26.5185 −1.61686 −0.808430 0.588592i \(-0.799682\pi\)
−0.808430 + 0.588592i \(0.799682\pi\)
\(270\) 0 0
\(271\) −25.7841 −1.56627 −0.783137 0.621849i \(-0.786382\pi\)
−0.783137 + 0.621849i \(0.786382\pi\)
\(272\) −20.4573 −1.24041
\(273\) −2.07359 −0.125499
\(274\) −2.00552 −0.121158
\(275\) 0 0
\(276\) −25.1456 −1.51359
\(277\) 16.8051 1.00972 0.504860 0.863201i \(-0.331544\pi\)
0.504860 + 0.863201i \(0.331544\pi\)
\(278\) −19.0591 −1.14309
\(279\) −16.1223 −0.965215
\(280\) 0 0
\(281\) 7.13034 0.425360 0.212680 0.977122i \(-0.431781\pi\)
0.212680 + 0.977122i \(0.431781\pi\)
\(282\) −49.7444 −2.96223
\(283\) −1.50077 −0.0892114 −0.0446057 0.999005i \(-0.514203\pi\)
−0.0446057 + 0.999005i \(0.514203\pi\)
\(284\) −7.99704 −0.474537
\(285\) 0 0
\(286\) 0.484922 0.0286740
\(287\) −30.9354 −1.82606
\(288\) 25.2592 1.48841
\(289\) 1.92276 0.113103
\(290\) 0 0
\(291\) −19.8935 −1.16618
\(292\) −1.94679 −0.113927
\(293\) 27.0432 1.57988 0.789939 0.613186i \(-0.210112\pi\)
0.789939 + 0.613186i \(0.210112\pi\)
\(294\) 25.8808 1.50940
\(295\) 0 0
\(296\) 5.37198 0.312240
\(297\) 1.53307 0.0889575
\(298\) 35.2042 2.03933
\(299\) 1.46741 0.0848628
\(300\) 0 0
\(301\) −10.4100 −0.600023
\(302\) −8.45247 −0.486385
\(303\) −15.7771 −0.906371
\(304\) −14.7951 −0.848555
\(305\) 0 0
\(306\) −28.9678 −1.65598
\(307\) −1.85072 −0.105626 −0.0528130 0.998604i \(-0.516819\pi\)
−0.0528130 + 0.998604i \(0.516819\pi\)
\(308\) −6.07261 −0.346019
\(309\) 31.7347 1.80533
\(310\) 0 0
\(311\) 0.609280 0.0345491 0.0172745 0.999851i \(-0.494501\pi\)
0.0172745 + 0.999851i \(0.494501\pi\)
\(312\) −0.504778 −0.0285774
\(313\) −22.9454 −1.29695 −0.648476 0.761236i \(-0.724593\pi\)
−0.648476 + 0.761236i \(0.724593\pi\)
\(314\) −5.14318 −0.290246
\(315\) 0 0
\(316\) −1.15854 −0.0651732
\(317\) −2.44078 −0.137088 −0.0685439 0.997648i \(-0.521835\pi\)
−0.0685439 + 0.997648i \(0.521835\pi\)
\(318\) −29.0296 −1.62790
\(319\) 0.0588740 0.00329631
\(320\) 0 0
\(321\) 19.5821 1.09296
\(322\) −42.1617 −2.34958
\(323\) 13.6853 0.761469
\(324\) −10.9732 −0.609623
\(325\) 0 0
\(326\) −36.5111 −2.02216
\(327\) 2.14080 0.118387
\(328\) −7.53065 −0.415810
\(329\) −36.3529 −2.00420
\(330\) 0 0
\(331\) 6.91377 0.380015 0.190008 0.981783i \(-0.439149\pi\)
0.190008 + 0.981783i \(0.439149\pi\)
\(332\) −17.2091 −0.944473
\(333\) 22.1854 1.21575
\(334\) −27.0529 −1.48027
\(335\) 0 0
\(336\) 42.2991 2.30761
\(337\) 14.0181 0.763616 0.381808 0.924242i \(-0.375302\pi\)
0.381808 + 0.924242i \(0.375302\pi\)
\(338\) 24.3771 1.32594
\(339\) 36.0588 1.95845
\(340\) 0 0
\(341\) 5.09246 0.275772
\(342\) −20.9500 −1.13285
\(343\) −5.71239 −0.308440
\(344\) −2.53413 −0.136631
\(345\) 0 0
\(346\) −28.2874 −1.52074
\(347\) −25.2046 −1.35305 −0.676526 0.736419i \(-0.736515\pi\)
−0.676526 + 0.736419i \(0.736515\pi\)
\(348\) 0.208197 0.0111605
\(349\) 0.543622 0.0290994 0.0145497 0.999894i \(-0.495369\pi\)
0.0145497 + 0.999894i \(0.495369\pi\)
\(350\) 0 0
\(351\) −0.316375 −0.0168869
\(352\) −7.97850 −0.425256
\(353\) −7.06140 −0.375840 −0.187920 0.982184i \(-0.560175\pi\)
−0.187920 + 0.982184i \(0.560175\pi\)
\(354\) 30.9776 1.64644
\(355\) 0 0
\(356\) −12.5991 −0.667751
\(357\) −39.1262 −2.07078
\(358\) 24.3022 1.28441
\(359\) −32.0985 −1.69409 −0.847047 0.531519i \(-0.821622\pi\)
−0.847047 + 0.531519i \(0.821622\pi\)
\(360\) 0 0
\(361\) −9.10258 −0.479083
\(362\) −39.6298 −2.08289
\(363\) 24.9330 1.30864
\(364\) 1.25319 0.0656850
\(365\) 0 0
\(366\) −57.2834 −2.99425
\(367\) 15.2909 0.798176 0.399088 0.916913i \(-0.369327\pi\)
0.399088 + 0.916913i \(0.369327\pi\)
\(368\) −29.9338 −1.56041
\(369\) −31.1004 −1.61902
\(370\) 0 0
\(371\) −21.2147 −1.10141
\(372\) 18.0085 0.933698
\(373\) −15.6074 −0.808122 −0.404061 0.914732i \(-0.632402\pi\)
−0.404061 + 0.914732i \(0.632402\pi\)
\(374\) 9.14990 0.473130
\(375\) 0 0
\(376\) −8.84945 −0.456375
\(377\) −0.0121497 −0.000625741 0
\(378\) 9.09008 0.467543
\(379\) 18.5818 0.954484 0.477242 0.878772i \(-0.341637\pi\)
0.477242 + 0.878772i \(0.341637\pi\)
\(380\) 0 0
\(381\) 42.4717 2.17589
\(382\) 23.3269 1.19351
\(383\) −31.3371 −1.60125 −0.800626 0.599165i \(-0.795499\pi\)
−0.800626 + 0.599165i \(0.795499\pi\)
\(384\) 17.0633 0.870760
\(385\) 0 0
\(386\) −23.2458 −1.18318
\(387\) −10.4655 −0.531993
\(388\) 12.0228 0.610364
\(389\) −24.3977 −1.23701 −0.618506 0.785780i \(-0.712262\pi\)
−0.618506 + 0.785780i \(0.712262\pi\)
\(390\) 0 0
\(391\) 27.6884 1.40026
\(392\) 4.60415 0.232545
\(393\) 3.96545 0.200031
\(394\) 14.2277 0.716781
\(395\) 0 0
\(396\) −6.10500 −0.306788
\(397\) −9.32624 −0.468071 −0.234035 0.972228i \(-0.575193\pi\)
−0.234035 + 0.972228i \(0.575193\pi\)
\(398\) 36.4252 1.82583
\(399\) −28.2967 −1.41661
\(400\) 0 0
\(401\) −10.9440 −0.546518 −0.273259 0.961940i \(-0.588102\pi\)
−0.273259 + 0.961940i \(0.588102\pi\)
\(402\) −10.0272 −0.500109
\(403\) −1.05092 −0.0523500
\(404\) 9.53502 0.474385
\(405\) 0 0
\(406\) 0.349084 0.0173248
\(407\) −7.00759 −0.347353
\(408\) −9.52456 −0.471536
\(409\) 29.3280 1.45017 0.725087 0.688657i \(-0.241799\pi\)
0.725087 + 0.688657i \(0.241799\pi\)
\(410\) 0 0
\(411\) −2.72327 −0.134329
\(412\) −19.1791 −0.944888
\(413\) 22.6382 1.11395
\(414\) −42.3866 −2.08319
\(415\) 0 0
\(416\) 1.64650 0.0807265
\(417\) −25.8800 −1.26735
\(418\) 6.61737 0.323666
\(419\) 28.6323 1.39878 0.699391 0.714740i \(-0.253455\pi\)
0.699391 + 0.714740i \(0.253455\pi\)
\(420\) 0 0
\(421\) −0.0637058 −0.00310483 −0.00155241 0.999999i \(-0.500494\pi\)
−0.00155241 + 0.999999i \(0.500494\pi\)
\(422\) −46.8188 −2.27910
\(423\) −36.5468 −1.77697
\(424\) −5.16433 −0.250802
\(425\) 0 0
\(426\) −24.9146 −1.20712
\(427\) −41.8624 −2.02586
\(428\) −11.8346 −0.572046
\(429\) 0.658468 0.0317911
\(430\) 0 0
\(431\) −25.7098 −1.23840 −0.619199 0.785234i \(-0.712543\pi\)
−0.619199 + 0.785234i \(0.712543\pi\)
\(432\) 6.45374 0.310506
\(433\) −22.4971 −1.08114 −0.540570 0.841299i \(-0.681791\pi\)
−0.540570 + 0.841299i \(0.681791\pi\)
\(434\) 30.1949 1.44940
\(435\) 0 0
\(436\) −1.29381 −0.0619622
\(437\) 20.0247 0.957912
\(438\) −6.06516 −0.289805
\(439\) −17.3064 −0.825989 −0.412995 0.910733i \(-0.635517\pi\)
−0.412995 + 0.910733i \(0.635517\pi\)
\(440\) 0 0
\(441\) 19.0144 0.905448
\(442\) −1.88824 −0.0898146
\(443\) −35.4484 −1.68421 −0.842103 0.539317i \(-0.818682\pi\)
−0.842103 + 0.539317i \(0.818682\pi\)
\(444\) −24.7810 −1.17605
\(445\) 0 0
\(446\) −3.06699 −0.145226
\(447\) 47.8032 2.26102
\(448\) −14.2185 −0.671763
\(449\) 15.9564 0.753031 0.376516 0.926410i \(-0.377122\pi\)
0.376516 + 0.926410i \(0.377122\pi\)
\(450\) 0 0
\(451\) 9.82351 0.462571
\(452\) −21.7924 −1.02503
\(453\) −11.4775 −0.539259
\(454\) 21.6662 1.01685
\(455\) 0 0
\(456\) −6.88832 −0.322575
\(457\) 8.07516 0.377740 0.188870 0.982002i \(-0.439518\pi\)
0.188870 + 0.982002i \(0.439518\pi\)
\(458\) −40.9581 −1.91384
\(459\) −5.96963 −0.278638
\(460\) 0 0
\(461\) −27.1354 −1.26382 −0.631912 0.775040i \(-0.717730\pi\)
−0.631912 + 0.775040i \(0.717730\pi\)
\(462\) −18.9191 −0.880194
\(463\) 29.4190 1.36721 0.683607 0.729850i \(-0.260410\pi\)
0.683607 + 0.729850i \(0.260410\pi\)
\(464\) 0.247841 0.0115057
\(465\) 0 0
\(466\) 13.0541 0.604719
\(467\) 2.70008 0.124945 0.0624724 0.998047i \(-0.480101\pi\)
0.0624724 + 0.998047i \(0.480101\pi\)
\(468\) 1.25987 0.0582377
\(469\) −7.32779 −0.338366
\(470\) 0 0
\(471\) −6.98384 −0.321798
\(472\) 5.51086 0.253658
\(473\) 3.30570 0.151996
\(474\) −3.60941 −0.165786
\(475\) 0 0
\(476\) 23.6462 1.08382
\(477\) −21.3278 −0.976535
\(478\) −24.5700 −1.12380
\(479\) −24.4078 −1.11522 −0.557609 0.830103i \(-0.688281\pi\)
−0.557609 + 0.830103i \(0.688281\pi\)
\(480\) 0 0
\(481\) 1.44614 0.0659383
\(482\) −1.88286 −0.0857620
\(483\) −57.2507 −2.60500
\(484\) −15.0685 −0.684930
\(485\) 0 0
\(486\) −41.9384 −1.90237
\(487\) −19.3677 −0.877633 −0.438817 0.898577i \(-0.644602\pi\)
−0.438817 + 0.898577i \(0.644602\pi\)
\(488\) −10.1906 −0.461308
\(489\) −49.5778 −2.24199
\(490\) 0 0
\(491\) 14.3025 0.645462 0.322731 0.946491i \(-0.395399\pi\)
0.322731 + 0.946491i \(0.395399\pi\)
\(492\) 34.7390 1.56615
\(493\) −0.229250 −0.0103249
\(494\) −1.36561 −0.0614417
\(495\) 0 0
\(496\) 21.4377 0.962580
\(497\) −18.2074 −0.816715
\(498\) −53.6146 −2.40253
\(499\) −22.6504 −1.01397 −0.506987 0.861954i \(-0.669241\pi\)
−0.506987 + 0.861954i \(0.669241\pi\)
\(500\) 0 0
\(501\) −36.7347 −1.64118
\(502\) 54.2485 2.42123
\(503\) −33.2011 −1.48036 −0.740181 0.672407i \(-0.765260\pi\)
−0.740181 + 0.672407i \(0.765260\pi\)
\(504\) 10.6554 0.474630
\(505\) 0 0
\(506\) 13.3884 0.595188
\(507\) 33.1013 1.47008
\(508\) −25.6681 −1.13884
\(509\) 26.1038 1.15703 0.578515 0.815671i \(-0.303632\pi\)
0.578515 + 0.815671i \(0.303632\pi\)
\(510\) 0 0
\(511\) −4.43239 −0.196077
\(512\) −25.5322 −1.12837
\(513\) −4.31734 −0.190615
\(514\) −28.9412 −1.27654
\(515\) 0 0
\(516\) 11.6900 0.514622
\(517\) 11.5438 0.507698
\(518\) −41.5504 −1.82562
\(519\) −38.4111 −1.68606
\(520\) 0 0
\(521\) 11.1582 0.488849 0.244425 0.969668i \(-0.421401\pi\)
0.244425 + 0.969668i \(0.421401\pi\)
\(522\) 0.350946 0.0153605
\(523\) 21.4491 0.937902 0.468951 0.883224i \(-0.344632\pi\)
0.468951 + 0.883224i \(0.344632\pi\)
\(524\) −2.39655 −0.104694
\(525\) 0 0
\(526\) −14.6075 −0.636917
\(527\) −19.8296 −0.863791
\(528\) −13.4321 −0.584556
\(529\) 17.5145 0.761501
\(530\) 0 0
\(531\) 22.7590 0.987655
\(532\) 17.1013 0.741437
\(533\) −2.02725 −0.0878102
\(534\) −39.2522 −1.69861
\(535\) 0 0
\(536\) −1.78382 −0.0770491
\(537\) 32.9996 1.42404
\(538\) 49.9306 2.15266
\(539\) −6.00598 −0.258696
\(540\) 0 0
\(541\) 37.9845 1.63308 0.816541 0.577288i \(-0.195889\pi\)
0.816541 + 0.577288i \(0.195889\pi\)
\(542\) 48.5479 2.08531
\(543\) −53.8126 −2.30932
\(544\) 31.0676 1.33201
\(545\) 0 0
\(546\) 3.90428 0.167088
\(547\) 12.5760 0.537711 0.268856 0.963180i \(-0.413355\pi\)
0.268856 + 0.963180i \(0.413355\pi\)
\(548\) 1.64583 0.0703063
\(549\) −42.0857 −1.79617
\(550\) 0 0
\(551\) −0.165798 −0.00706322
\(552\) −13.9366 −0.593183
\(553\) −2.63774 −0.112168
\(554\) −31.6417 −1.34433
\(555\) 0 0
\(556\) 15.6408 0.663316
\(557\) −17.7488 −0.752039 −0.376020 0.926612i \(-0.622707\pi\)
−0.376020 + 0.926612i \(0.622707\pi\)
\(558\) 30.3560 1.28507
\(559\) −0.682189 −0.0288535
\(560\) 0 0
\(561\) 12.4245 0.524563
\(562\) −13.4254 −0.566318
\(563\) 19.5515 0.823999 0.411999 0.911184i \(-0.364831\pi\)
0.411999 + 0.911184i \(0.364831\pi\)
\(564\) 40.8226 1.71894
\(565\) 0 0
\(566\) 2.82574 0.118775
\(567\) −24.9835 −1.04921
\(568\) −4.43227 −0.185974
\(569\) 41.0771 1.72204 0.861021 0.508570i \(-0.169826\pi\)
0.861021 + 0.508570i \(0.169826\pi\)
\(570\) 0 0
\(571\) −34.8425 −1.45811 −0.729057 0.684453i \(-0.760041\pi\)
−0.729057 + 0.684453i \(0.760041\pi\)
\(572\) −0.397950 −0.0166391
\(573\) 31.6752 1.32325
\(574\) 58.2470 2.43118
\(575\) 0 0
\(576\) −14.2944 −0.595599
\(577\) −2.25604 −0.0939202 −0.0469601 0.998897i \(-0.514953\pi\)
−0.0469601 + 0.998897i \(0.514953\pi\)
\(578\) −3.62029 −0.150584
\(579\) −31.5651 −1.31180
\(580\) 0 0
\(581\) −39.1812 −1.62551
\(582\) 37.4567 1.55263
\(583\) 6.73671 0.279006
\(584\) −1.07898 −0.0446487
\(585\) 0 0
\(586\) −50.9185 −2.10342
\(587\) 27.6141 1.13976 0.569879 0.821729i \(-0.306990\pi\)
0.569879 + 0.821729i \(0.306990\pi\)
\(588\) −21.2390 −0.875882
\(589\) −14.3411 −0.590915
\(590\) 0 0
\(591\) 19.3196 0.794701
\(592\) −29.4998 −1.21243
\(593\) −32.2396 −1.32392 −0.661961 0.749538i \(-0.730276\pi\)
−0.661961 + 0.749538i \(0.730276\pi\)
\(594\) −2.88655 −0.118437
\(595\) 0 0
\(596\) −28.8903 −1.18339
\(597\) 49.4612 2.02431
\(598\) −2.76294 −0.112985
\(599\) 23.7981 0.972365 0.486183 0.873857i \(-0.338389\pi\)
0.486183 + 0.873857i \(0.338389\pi\)
\(600\) 0 0
\(601\) 8.59760 0.350703 0.175352 0.984506i \(-0.443894\pi\)
0.175352 + 0.984506i \(0.443894\pi\)
\(602\) 19.6006 0.798861
\(603\) −7.36687 −0.300002
\(604\) 6.93650 0.282242
\(605\) 0 0
\(606\) 29.7061 1.20673
\(607\) 13.7016 0.556130 0.278065 0.960562i \(-0.410307\pi\)
0.278065 + 0.960562i \(0.410307\pi\)
\(608\) 22.4686 0.911223
\(609\) 0.474016 0.0192081
\(610\) 0 0
\(611\) −2.38228 −0.0963766
\(612\) 23.7723 0.960940
\(613\) −44.7325 −1.80673 −0.903365 0.428873i \(-0.858911\pi\)
−0.903365 + 0.428873i \(0.858911\pi\)
\(614\) 3.48464 0.140629
\(615\) 0 0
\(616\) −3.36567 −0.135607
\(617\) −11.8716 −0.477931 −0.238965 0.971028i \(-0.576808\pi\)
−0.238965 + 0.971028i \(0.576808\pi\)
\(618\) −59.7521 −2.40358
\(619\) −30.7196 −1.23472 −0.617362 0.786679i \(-0.711799\pi\)
−0.617362 + 0.786679i \(0.711799\pi\)
\(620\) 0 0
\(621\) −8.73495 −0.350522
\(622\) −1.14719 −0.0459981
\(623\) −28.6853 −1.14925
\(624\) 2.77194 0.110967
\(625\) 0 0
\(626\) 43.2030 1.72674
\(627\) 8.98562 0.358851
\(628\) 4.22074 0.168426
\(629\) 27.2870 1.08800
\(630\) 0 0
\(631\) −22.5309 −0.896943 −0.448471 0.893797i \(-0.648031\pi\)
−0.448471 + 0.893797i \(0.648031\pi\)
\(632\) −0.642109 −0.0255417
\(633\) −63.5745 −2.52686
\(634\) 4.59565 0.182517
\(635\) 0 0
\(636\) 23.8231 0.944647
\(637\) 1.23944 0.0491084
\(638\) −0.110852 −0.00438866
\(639\) −18.3045 −0.724117
\(640\) 0 0
\(641\) 31.9732 1.26287 0.631433 0.775430i \(-0.282467\pi\)
0.631433 + 0.775430i \(0.282467\pi\)
\(642\) −36.8703 −1.45516
\(643\) −1.68365 −0.0663968 −0.0331984 0.999449i \(-0.510569\pi\)
−0.0331984 + 0.999449i \(0.510569\pi\)
\(644\) 34.5999 1.36343
\(645\) 0 0
\(646\) −25.7675 −1.01381
\(647\) −4.78774 −0.188225 −0.0941127 0.995562i \(-0.530001\pi\)
−0.0941127 + 0.995562i \(0.530001\pi\)
\(648\) −6.08177 −0.238915
\(649\) −7.18876 −0.282183
\(650\) 0 0
\(651\) 41.0012 1.60697
\(652\) 29.9627 1.17343
\(653\) 17.3077 0.677301 0.338650 0.940912i \(-0.390030\pi\)
0.338650 + 0.940912i \(0.390030\pi\)
\(654\) −4.03083 −0.157618
\(655\) 0 0
\(656\) 41.3539 1.61460
\(657\) −4.45603 −0.173846
\(658\) 68.4474 2.66836
\(659\) −6.27035 −0.244258 −0.122129 0.992514i \(-0.538972\pi\)
−0.122129 + 0.992514i \(0.538972\pi\)
\(660\) 0 0
\(661\) −6.20469 −0.241334 −0.120667 0.992693i \(-0.538503\pi\)
−0.120667 + 0.992693i \(0.538503\pi\)
\(662\) −13.0177 −0.505946
\(663\) −2.56402 −0.0995781
\(664\) −9.53795 −0.370144
\(665\) 0 0
\(666\) −41.7721 −1.61863
\(667\) −0.335446 −0.0129885
\(668\) 22.2009 0.858977
\(669\) −4.16462 −0.161013
\(670\) 0 0
\(671\) 13.2934 0.513185
\(672\) −64.2378 −2.47803
\(673\) −32.2078 −1.24152 −0.620759 0.784001i \(-0.713176\pi\)
−0.620759 + 0.784001i \(0.713176\pi\)
\(674\) −26.3942 −1.01667
\(675\) 0 0
\(676\) −20.0050 −0.769424
\(677\) 16.1123 0.619245 0.309622 0.950860i \(-0.399797\pi\)
0.309622 + 0.950860i \(0.399797\pi\)
\(678\) −67.8937 −2.60744
\(679\) 27.3731 1.05048
\(680\) 0 0
\(681\) 29.4202 1.12739
\(682\) −9.58839 −0.367158
\(683\) 15.1853 0.581048 0.290524 0.956868i \(-0.406170\pi\)
0.290524 + 0.956868i \(0.406170\pi\)
\(684\) 17.1926 0.657374
\(685\) 0 0
\(686\) 10.7556 0.410652
\(687\) −55.6163 −2.12189
\(688\) 13.9160 0.530541
\(689\) −1.39024 −0.0529639
\(690\) 0 0
\(691\) 15.7865 0.600547 0.300274 0.953853i \(-0.402922\pi\)
0.300274 + 0.953853i \(0.402922\pi\)
\(692\) 23.2140 0.882465
\(693\) −13.8997 −0.528005
\(694\) 47.4567 1.80143
\(695\) 0 0
\(696\) 0.115391 0.00437387
\(697\) −38.2519 −1.44889
\(698\) −1.02357 −0.0387425
\(699\) 17.7259 0.670456
\(700\) 0 0
\(701\) 10.3713 0.391717 0.195859 0.980632i \(-0.437251\pi\)
0.195859 + 0.980632i \(0.437251\pi\)
\(702\) 0.595691 0.0224829
\(703\) 19.7344 0.744297
\(704\) 4.51509 0.170169
\(705\) 0 0
\(706\) 13.2956 0.500387
\(707\) 21.7090 0.816453
\(708\) −25.4217 −0.955405
\(709\) 17.6528 0.662966 0.331483 0.943461i \(-0.392451\pi\)
0.331483 + 0.943461i \(0.392451\pi\)
\(710\) 0 0
\(711\) −2.65181 −0.0994506
\(712\) −6.98291 −0.261696
\(713\) −29.0153 −1.08663
\(714\) 73.6692 2.75700
\(715\) 0 0
\(716\) −19.9435 −0.745325
\(717\) −33.3632 −1.24597
\(718\) 60.4370 2.25549
\(719\) −20.1461 −0.751324 −0.375662 0.926757i \(-0.622585\pi\)
−0.375662 + 0.926757i \(0.622585\pi\)
\(720\) 0 0
\(721\) −43.6665 −1.62623
\(722\) 17.1389 0.637843
\(723\) −2.55671 −0.0950850
\(724\) 32.5221 1.20867
\(725\) 0 0
\(726\) −46.9454 −1.74231
\(727\) 49.4317 1.83332 0.916661 0.399666i \(-0.130874\pi\)
0.916661 + 0.399666i \(0.130874\pi\)
\(728\) 0.694566 0.0257423
\(729\) −35.6426 −1.32010
\(730\) 0 0
\(731\) −12.8721 −0.476092
\(732\) 47.0095 1.73752
\(733\) 31.2375 1.15378 0.576891 0.816821i \(-0.304266\pi\)
0.576891 + 0.816821i \(0.304266\pi\)
\(734\) −28.7905 −1.06268
\(735\) 0 0
\(736\) 45.4591 1.67564
\(737\) 2.32694 0.0857138
\(738\) 58.5577 2.15554
\(739\) −0.931126 −0.0342520 −0.0171260 0.999853i \(-0.505452\pi\)
−0.0171260 + 0.999853i \(0.505452\pi\)
\(740\) 0 0
\(741\) −1.85434 −0.0681209
\(742\) 39.9443 1.46640
\(743\) 50.7530 1.86195 0.930974 0.365085i \(-0.118960\pi\)
0.930974 + 0.365085i \(0.118960\pi\)
\(744\) 9.98100 0.365921
\(745\) 0 0
\(746\) 29.3866 1.07592
\(747\) −39.3902 −1.44121
\(748\) −7.50884 −0.274551
\(749\) −26.9446 −0.984534
\(750\) 0 0
\(751\) −10.6990 −0.390412 −0.195206 0.980762i \(-0.562538\pi\)
−0.195206 + 0.980762i \(0.562538\pi\)
\(752\) 48.5960 1.77211
\(753\) 73.6632 2.68444
\(754\) 0.0228762 0.000833101 0
\(755\) 0 0
\(756\) −7.45975 −0.271309
\(757\) 3.26326 0.118605 0.0593027 0.998240i \(-0.481112\pi\)
0.0593027 + 0.998240i \(0.481112\pi\)
\(758\) −34.9870 −1.27078
\(759\) 18.1799 0.659890
\(760\) 0 0
\(761\) −43.3419 −1.57114 −0.785572 0.618771i \(-0.787631\pi\)
−0.785572 + 0.618771i \(0.787631\pi\)
\(762\) −79.9683 −2.89695
\(763\) −2.94571 −0.106642
\(764\) −19.1432 −0.692576
\(765\) 0 0
\(766\) 59.0034 2.13188
\(767\) 1.48353 0.0535671
\(768\) −52.7946 −1.90506
\(769\) 26.6436 0.960793 0.480396 0.877051i \(-0.340493\pi\)
0.480396 + 0.877051i \(0.340493\pi\)
\(770\) 0 0
\(771\) −39.2988 −1.41531
\(772\) 19.0766 0.686582
\(773\) −40.7749 −1.46657 −0.733285 0.679922i \(-0.762014\pi\)
−0.733285 + 0.679922i \(0.762014\pi\)
\(774\) 19.7052 0.708287
\(775\) 0 0
\(776\) 6.66349 0.239205
\(777\) −56.4207 −2.02408
\(778\) 45.9375 1.64694
\(779\) −27.6644 −0.991181
\(780\) 0 0
\(781\) 5.78176 0.206888
\(782\) −52.1334 −1.86429
\(783\) 0.0723224 0.00258459
\(784\) −25.2833 −0.902976
\(785\) 0 0
\(786\) −7.46640 −0.266318
\(787\) 13.2146 0.471051 0.235525 0.971868i \(-0.424319\pi\)
0.235525 + 0.971868i \(0.424319\pi\)
\(788\) −11.6759 −0.415938
\(789\) −19.8353 −0.706155
\(790\) 0 0
\(791\) −49.6163 −1.76415
\(792\) −3.38362 −0.120232
\(793\) −2.74333 −0.0974183
\(794\) 17.5600 0.623182
\(795\) 0 0
\(796\) −29.8923 −1.05950
\(797\) −3.31174 −0.117308 −0.0586539 0.998278i \(-0.518681\pi\)
−0.0586539 + 0.998278i \(0.518681\pi\)
\(798\) 53.2788 1.88605
\(799\) −44.9507 −1.59024
\(800\) 0 0
\(801\) −28.8383 −1.01895
\(802\) 20.6061 0.727626
\(803\) 1.40750 0.0496697
\(804\) 8.22876 0.290206
\(805\) 0 0
\(806\) 1.97873 0.0696979
\(807\) 67.8000 2.38667
\(808\) 5.28467 0.185914
\(809\) 22.5759 0.793727 0.396864 0.917878i \(-0.370099\pi\)
0.396864 + 0.917878i \(0.370099\pi\)
\(810\) 0 0
\(811\) 17.1034 0.600581 0.300291 0.953848i \(-0.402916\pi\)
0.300291 + 0.953848i \(0.402916\pi\)
\(812\) −0.286475 −0.0100533
\(813\) 65.9225 2.31200
\(814\) 13.1943 0.462461
\(815\) 0 0
\(816\) 52.3033 1.83098
\(817\) −9.30932 −0.325692
\(818\) −55.2205 −1.93074
\(819\) 2.86844 0.100232
\(820\) 0 0
\(821\) −7.57786 −0.264469 −0.132235 0.991218i \(-0.542215\pi\)
−0.132235 + 0.991218i \(0.542215\pi\)
\(822\) 5.12754 0.178843
\(823\) 43.7880 1.52635 0.763177 0.646190i \(-0.223639\pi\)
0.763177 + 0.646190i \(0.223639\pi\)
\(824\) −10.6298 −0.370307
\(825\) 0 0
\(826\) −42.6246 −1.48310
\(827\) 12.9806 0.451379 0.225690 0.974199i \(-0.427536\pi\)
0.225690 + 0.974199i \(0.427536\pi\)
\(828\) 34.7844 1.20884
\(829\) −2.03755 −0.0707669 −0.0353834 0.999374i \(-0.511265\pi\)
−0.0353834 + 0.999374i \(0.511265\pi\)
\(830\) 0 0
\(831\) −42.9657 −1.49046
\(832\) −0.931769 −0.0323033
\(833\) 23.3868 0.810304
\(834\) 48.7284 1.68733
\(835\) 0 0
\(836\) −5.43053 −0.187819
\(837\) 6.25571 0.216229
\(838\) −53.9107 −1.86231
\(839\) −27.3908 −0.945635 −0.472817 0.881160i \(-0.656763\pi\)
−0.472817 + 0.881160i \(0.656763\pi\)
\(840\) 0 0
\(841\) −28.9972 −0.999904
\(842\) 0.119949 0.00413372
\(843\) −18.2302 −0.627881
\(844\) 38.4217 1.32253
\(845\) 0 0
\(846\) 68.8125 2.36582
\(847\) −34.3074 −1.17882
\(848\) 28.3595 0.973868
\(849\) 3.83703 0.131686
\(850\) 0 0
\(851\) 39.9271 1.36869
\(852\) 20.4461 0.700472
\(853\) 26.0906 0.893325 0.446663 0.894702i \(-0.352612\pi\)
0.446663 + 0.894702i \(0.352612\pi\)
\(854\) 78.8211 2.69720
\(855\) 0 0
\(856\) −6.55917 −0.224188
\(857\) 17.1819 0.586922 0.293461 0.955971i \(-0.405193\pi\)
0.293461 + 0.955971i \(0.405193\pi\)
\(858\) −1.23980 −0.0423262
\(859\) 2.77639 0.0947292 0.0473646 0.998878i \(-0.484918\pi\)
0.0473646 + 0.998878i \(0.484918\pi\)
\(860\) 0 0
\(861\) 79.0926 2.69547
\(862\) 48.4080 1.64878
\(863\) −11.5989 −0.394832 −0.197416 0.980320i \(-0.563255\pi\)
−0.197416 + 0.980320i \(0.563255\pi\)
\(864\) −9.80101 −0.333437
\(865\) 0 0
\(866\) 42.3588 1.43941
\(867\) −4.91593 −0.166954
\(868\) −24.7794 −0.841068
\(869\) 0.837613 0.0284141
\(870\) 0 0
\(871\) −0.480204 −0.0162711
\(872\) −0.717078 −0.0242833
\(873\) 27.5191 0.931381
\(874\) −37.7038 −1.27535
\(875\) 0 0
\(876\) 4.97736 0.168170
\(877\) 19.8014 0.668647 0.334323 0.942458i \(-0.391492\pi\)
0.334323 + 0.942458i \(0.391492\pi\)
\(878\) 32.5855 1.09971
\(879\) −69.1414 −2.33208
\(880\) 0 0
\(881\) 50.1717 1.69033 0.845164 0.534508i \(-0.179503\pi\)
0.845164 + 0.534508i \(0.179503\pi\)
\(882\) −35.8015 −1.20550
\(883\) 13.0038 0.437614 0.218807 0.975768i \(-0.429784\pi\)
0.218807 + 0.975768i \(0.429784\pi\)
\(884\) 1.54958 0.0521181
\(885\) 0 0
\(886\) 66.7444 2.24232
\(887\) 14.2467 0.478358 0.239179 0.970975i \(-0.423122\pi\)
0.239179 + 0.970975i \(0.423122\pi\)
\(888\) −13.7346 −0.460902
\(889\) −58.4403 −1.96003
\(890\) 0 0
\(891\) 7.93349 0.265782
\(892\) 2.51692 0.0842727
\(893\) −32.5091 −1.08788
\(894\) −90.0069 −3.01028
\(895\) 0 0
\(896\) −23.4789 −0.784374
\(897\) −3.75175 −0.125267
\(898\) −30.0438 −1.00257
\(899\) 0.240237 0.00801234
\(900\) 0 0
\(901\) −26.2322 −0.873921
\(902\) −18.4963 −0.615859
\(903\) 26.6154 0.885704
\(904\) −12.0782 −0.401715
\(905\) 0 0
\(906\) 21.6105 0.717960
\(907\) −15.5109 −0.515032 −0.257516 0.966274i \(-0.582904\pi\)
−0.257516 + 0.966274i \(0.582904\pi\)
\(908\) −17.7803 −0.590061
\(909\) 21.8248 0.723884
\(910\) 0 0
\(911\) −56.4743 −1.87108 −0.935538 0.353225i \(-0.885085\pi\)
−0.935538 + 0.353225i \(0.885085\pi\)
\(912\) 37.8267 1.25257
\(913\) 12.4420 0.411769
\(914\) −15.2044 −0.502917
\(915\) 0 0
\(916\) 33.6121 1.11058
\(917\) −5.45640 −0.180186
\(918\) 11.2400 0.370975
\(919\) 50.4305 1.66355 0.831774 0.555115i \(-0.187326\pi\)
0.831774 + 0.555115i \(0.187326\pi\)
\(920\) 0 0
\(921\) 4.73174 0.155916
\(922\) 51.0923 1.68263
\(923\) −1.19317 −0.0392736
\(924\) 15.5259 0.510764
\(925\) 0 0
\(926\) −55.3918 −1.82029
\(927\) −43.8994 −1.44185
\(928\) −0.376386 −0.0123555
\(929\) 38.0255 1.24757 0.623787 0.781594i \(-0.285593\pi\)
0.623787 + 0.781594i \(0.285593\pi\)
\(930\) 0 0
\(931\) 16.9137 0.554325
\(932\) −10.7128 −0.350909
\(933\) −1.55775 −0.0509984
\(934\) −5.08388 −0.166349
\(935\) 0 0
\(936\) 0.698271 0.0228237
\(937\) 4.68279 0.152980 0.0764900 0.997070i \(-0.475629\pi\)
0.0764900 + 0.997070i \(0.475629\pi\)
\(938\) 13.7972 0.450495
\(939\) 58.6647 1.91445
\(940\) 0 0
\(941\) −51.3443 −1.67378 −0.836889 0.547373i \(-0.815628\pi\)
−0.836889 + 0.547373i \(0.815628\pi\)
\(942\) 13.1496 0.428437
\(943\) −55.9714 −1.82268
\(944\) −30.2624 −0.984959
\(945\) 0 0
\(946\) −6.22417 −0.202365
\(947\) −29.5601 −0.960575 −0.480288 0.877111i \(-0.659468\pi\)
−0.480288 + 0.877111i \(0.659468\pi\)
\(948\) 2.96206 0.0962032
\(949\) −0.290463 −0.00942883
\(950\) 0 0
\(951\) 6.24036 0.202357
\(952\) 13.1056 0.424756
\(953\) −46.8102 −1.51633 −0.758166 0.652062i \(-0.773904\pi\)
−0.758166 + 0.652062i \(0.773904\pi\)
\(954\) 40.1574 1.30014
\(955\) 0 0
\(956\) 20.1633 0.652127
\(957\) −0.150524 −0.00486574
\(958\) 45.9564 1.48478
\(959\) 3.74717 0.121003
\(960\) 0 0
\(961\) −10.2201 −0.329681
\(962\) −2.72288 −0.0877892
\(963\) −27.0883 −0.872909
\(964\) 1.54517 0.0497664
\(965\) 0 0
\(966\) 107.795 3.46825
\(967\) −37.6906 −1.21205 −0.606024 0.795446i \(-0.707237\pi\)
−0.606024 + 0.795446i \(0.707237\pi\)
\(968\) −8.35152 −0.268428
\(969\) −34.9892 −1.12402
\(970\) 0 0
\(971\) −53.4295 −1.71464 −0.857318 0.514788i \(-0.827871\pi\)
−0.857318 + 0.514788i \(0.827871\pi\)
\(972\) 34.4167 1.10392
\(973\) 35.6104 1.14162
\(974\) 36.4667 1.16847
\(975\) 0 0
\(976\) 55.9610 1.79127
\(977\) −9.03874 −0.289175 −0.144587 0.989492i \(-0.546186\pi\)
−0.144587 + 0.989492i \(0.546186\pi\)
\(978\) 93.3481 2.98494
\(979\) 9.10900 0.291125
\(980\) 0 0
\(981\) −2.96142 −0.0945508
\(982\) −26.9296 −0.859357
\(983\) 39.4162 1.25718 0.628590 0.777737i \(-0.283632\pi\)
0.628590 + 0.777737i \(0.283632\pi\)
\(984\) 19.2537 0.613784
\(985\) 0 0
\(986\) 0.431647 0.0137464
\(987\) 92.9437 2.95843
\(988\) 1.12069 0.0356537
\(989\) −18.8349 −0.598914
\(990\) 0 0
\(991\) −50.5302 −1.60515 −0.802573 0.596554i \(-0.796536\pi\)
−0.802573 + 0.596554i \(0.796536\pi\)
\(992\) −32.5565 −1.03367
\(993\) −17.6765 −0.560946
\(994\) 34.2820 1.08736
\(995\) 0 0
\(996\) 43.9987 1.39415
\(997\) 31.8629 1.00911 0.504553 0.863380i \(-0.331657\pi\)
0.504553 + 0.863380i \(0.331657\pi\)
\(998\) 42.6476 1.34999
\(999\) −8.60832 −0.272355
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 6025.2.a.p.1.8 46
5.2 odd 4 1205.2.b.c.724.8 46
5.3 odd 4 1205.2.b.c.724.39 yes 46
5.4 even 2 inner 6025.2.a.p.1.39 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.8 46 5.2 odd 4
1205.2.b.c.724.39 yes 46 5.3 odd 4
6025.2.a.p.1.8 46 1.1 even 1 trivial
6025.2.a.p.1.39 46 5.4 even 2 inner