Properties

Label 6025.2.a.p.1.7
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 1.7
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.92263 q^{2} +0.557567 q^{3} +1.69651 q^{4} -1.07200 q^{6} -0.976687 q^{7} +0.583491 q^{8} -2.68912 q^{9} +O(q^{10})\) \(q-1.92263 q^{2} +0.557567 q^{3} +1.69651 q^{4} -1.07200 q^{6} -0.976687 q^{7} +0.583491 q^{8} -2.68912 q^{9} +5.68399 q^{11} +0.945921 q^{12} -0.519007 q^{13} +1.87781 q^{14} -4.51487 q^{16} +2.78999 q^{17} +5.17019 q^{18} -2.82159 q^{19} -0.544569 q^{21} -10.9282 q^{22} +7.25155 q^{23} +0.325336 q^{24} +0.997860 q^{26} -3.17207 q^{27} -1.65696 q^{28} -2.98708 q^{29} -4.59370 q^{31} +7.51345 q^{32} +3.16920 q^{33} -5.36412 q^{34} -4.56213 q^{36} -9.40071 q^{37} +5.42487 q^{38} -0.289381 q^{39} +1.99776 q^{41} +1.04700 q^{42} -5.68341 q^{43} +9.64296 q^{44} -13.9421 q^{46} +1.33825 q^{47} -2.51734 q^{48} -6.04608 q^{49} +1.55561 q^{51} -0.880503 q^{52} +2.40587 q^{53} +6.09872 q^{54} -0.569888 q^{56} -1.57322 q^{57} +5.74306 q^{58} +5.64524 q^{59} -11.4529 q^{61} +8.83199 q^{62} +2.62643 q^{63} -5.41586 q^{64} -6.09321 q^{66} +5.66108 q^{67} +4.73325 q^{68} +4.04323 q^{69} -10.9432 q^{71} -1.56908 q^{72} +15.5123 q^{73} +18.0741 q^{74} -4.78686 q^{76} -5.55147 q^{77} +0.556374 q^{78} -15.9163 q^{79} +6.29872 q^{81} -3.84096 q^{82} -6.63802 q^{83} -0.923868 q^{84} +10.9271 q^{86} -1.66550 q^{87} +3.31656 q^{88} +13.2676 q^{89} +0.506907 q^{91} +12.3024 q^{92} -2.56129 q^{93} -2.57295 q^{94} +4.18925 q^{96} +1.00517 q^{97} +11.6244 q^{98} -15.2849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92263 −1.35951 −0.679753 0.733441i \(-0.737913\pi\)
−0.679753 + 0.733441i \(0.737913\pi\)
\(3\) 0.557567 0.321912 0.160956 0.986962i \(-0.448542\pi\)
0.160956 + 0.986962i \(0.448542\pi\)
\(4\) 1.69651 0.848257
\(5\) 0 0
\(6\) −1.07200 −0.437641
\(7\) −0.976687 −0.369153 −0.184576 0.982818i \(-0.559091\pi\)
−0.184576 + 0.982818i \(0.559091\pi\)
\(8\) 0.583491 0.206295
\(9\) −2.68912 −0.896373
\(10\) 0 0
\(11\) 5.68399 1.71379 0.856893 0.515494i \(-0.172392\pi\)
0.856893 + 0.515494i \(0.172392\pi\)
\(12\) 0.945921 0.273064
\(13\) −0.519007 −0.143947 −0.0719733 0.997407i \(-0.522930\pi\)
−0.0719733 + 0.997407i \(0.522930\pi\)
\(14\) 1.87781 0.501866
\(15\) 0 0
\(16\) −4.51487 −1.12872
\(17\) 2.78999 0.676671 0.338336 0.941025i \(-0.390136\pi\)
0.338336 + 0.941025i \(0.390136\pi\)
\(18\) 5.17019 1.21862
\(19\) −2.82159 −0.647316 −0.323658 0.946174i \(-0.604913\pi\)
−0.323658 + 0.946174i \(0.604913\pi\)
\(20\) 0 0
\(21\) −0.544569 −0.118835
\(22\) −10.9282 −2.32990
\(23\) 7.25155 1.51205 0.756027 0.654541i \(-0.227138\pi\)
0.756027 + 0.654541i \(0.227138\pi\)
\(24\) 0.325336 0.0664089
\(25\) 0 0
\(26\) 0.997860 0.195696
\(27\) −3.17207 −0.610464
\(28\) −1.65696 −0.313137
\(29\) −2.98708 −0.554687 −0.277344 0.960771i \(-0.589454\pi\)
−0.277344 + 0.960771i \(0.589454\pi\)
\(30\) 0 0
\(31\) −4.59370 −0.825052 −0.412526 0.910946i \(-0.635353\pi\)
−0.412526 + 0.910946i \(0.635353\pi\)
\(32\) 7.51345 1.32820
\(33\) 3.16920 0.551688
\(34\) −5.36412 −0.919939
\(35\) 0 0
\(36\) −4.56213 −0.760355
\(37\) −9.40071 −1.54547 −0.772734 0.634731i \(-0.781111\pi\)
−0.772734 + 0.634731i \(0.781111\pi\)
\(38\) 5.42487 0.880030
\(39\) −0.289381 −0.0463381
\(40\) 0 0
\(41\) 1.99776 0.311998 0.155999 0.987757i \(-0.450140\pi\)
0.155999 + 0.987757i \(0.450140\pi\)
\(42\) 1.04700 0.161556
\(43\) −5.68341 −0.866712 −0.433356 0.901223i \(-0.642671\pi\)
−0.433356 + 0.901223i \(0.642671\pi\)
\(44\) 9.64296 1.45373
\(45\) 0 0
\(46\) −13.9421 −2.05565
\(47\) 1.33825 0.195203 0.0976016 0.995226i \(-0.468883\pi\)
0.0976016 + 0.995226i \(0.468883\pi\)
\(48\) −2.51734 −0.363347
\(49\) −6.04608 −0.863726
\(50\) 0 0
\(51\) 1.55561 0.217828
\(52\) −0.880503 −0.122104
\(53\) 2.40587 0.330471 0.165236 0.986254i \(-0.447162\pi\)
0.165236 + 0.986254i \(0.447162\pi\)
\(54\) 6.09872 0.829930
\(55\) 0 0
\(56\) −0.569888 −0.0761545
\(57\) −1.57322 −0.208379
\(58\) 5.74306 0.754101
\(59\) 5.64524 0.734947 0.367474 0.930034i \(-0.380223\pi\)
0.367474 + 0.930034i \(0.380223\pi\)
\(60\) 0 0
\(61\) −11.4529 −1.46639 −0.733196 0.680017i \(-0.761972\pi\)
−0.733196 + 0.680017i \(0.761972\pi\)
\(62\) 8.83199 1.12166
\(63\) 2.62643 0.330899
\(64\) −5.41586 −0.676982
\(65\) 0 0
\(66\) −6.09321 −0.750023
\(67\) 5.66108 0.691611 0.345805 0.938306i \(-0.387606\pi\)
0.345805 + 0.938306i \(0.387606\pi\)
\(68\) 4.73325 0.573991
\(69\) 4.04323 0.486748
\(70\) 0 0
\(71\) −10.9432 −1.29872 −0.649360 0.760481i \(-0.724963\pi\)
−0.649360 + 0.760481i \(0.724963\pi\)
\(72\) −1.56908 −0.184918
\(73\) 15.5123 1.81558 0.907789 0.419427i \(-0.137769\pi\)
0.907789 + 0.419427i \(0.137769\pi\)
\(74\) 18.0741 2.10107
\(75\) 0 0
\(76\) −4.78686 −0.549091
\(77\) −5.55147 −0.632649
\(78\) 0.556374 0.0629969
\(79\) −15.9163 −1.79073 −0.895363 0.445337i \(-0.853084\pi\)
−0.895363 + 0.445337i \(0.853084\pi\)
\(80\) 0 0
\(81\) 6.29872 0.699857
\(82\) −3.84096 −0.424163
\(83\) −6.63802 −0.728618 −0.364309 0.931278i \(-0.618695\pi\)
−0.364309 + 0.931278i \(0.618695\pi\)
\(84\) −0.923868 −0.100802
\(85\) 0 0
\(86\) 10.9271 1.17830
\(87\) −1.66550 −0.178560
\(88\) 3.31656 0.353546
\(89\) 13.2676 1.40636 0.703182 0.711009i \(-0.251762\pi\)
0.703182 + 0.711009i \(0.251762\pi\)
\(90\) 0 0
\(91\) 0.506907 0.0531383
\(92\) 12.3024 1.28261
\(93\) −2.56129 −0.265594
\(94\) −2.57295 −0.265380
\(95\) 0 0
\(96\) 4.18925 0.427564
\(97\) 1.00517 0.102060 0.0510298 0.998697i \(-0.483750\pi\)
0.0510298 + 0.998697i \(0.483750\pi\)
\(98\) 11.6244 1.17424
\(99\) −15.2849 −1.53619
\(100\) 0 0
\(101\) −7.10243 −0.706718 −0.353359 0.935488i \(-0.614961\pi\)
−0.353359 + 0.935488i \(0.614961\pi\)
\(102\) −2.99086 −0.296139
\(103\) 5.52638 0.544531 0.272265 0.962222i \(-0.412227\pi\)
0.272265 + 0.962222i \(0.412227\pi\)
\(104\) −0.302836 −0.0296955
\(105\) 0 0
\(106\) −4.62559 −0.449277
\(107\) 7.01208 0.677884 0.338942 0.940807i \(-0.389931\pi\)
0.338942 + 0.940807i \(0.389931\pi\)
\(108\) −5.38146 −0.517831
\(109\) −7.33345 −0.702417 −0.351209 0.936297i \(-0.614229\pi\)
−0.351209 + 0.936297i \(0.614229\pi\)
\(110\) 0 0
\(111\) −5.24153 −0.497504
\(112\) 4.40961 0.416669
\(113\) 0.394108 0.0370746 0.0185373 0.999828i \(-0.494099\pi\)
0.0185373 + 0.999828i \(0.494099\pi\)
\(114\) 3.02473 0.283292
\(115\) 0 0
\(116\) −5.06763 −0.470517
\(117\) 1.39567 0.129030
\(118\) −10.8537 −0.999165
\(119\) −2.72494 −0.249795
\(120\) 0 0
\(121\) 21.3077 1.93706
\(122\) 22.0197 1.99357
\(123\) 1.11389 0.100436
\(124\) −7.79327 −0.699857
\(125\) 0 0
\(126\) −5.04965 −0.449859
\(127\) −9.43489 −0.837211 −0.418605 0.908168i \(-0.637481\pi\)
−0.418605 + 0.908168i \(0.637481\pi\)
\(128\) −4.61419 −0.407841
\(129\) −3.16888 −0.279005
\(130\) 0 0
\(131\) 9.36627 0.818335 0.409167 0.912459i \(-0.365819\pi\)
0.409167 + 0.912459i \(0.365819\pi\)
\(132\) 5.37660 0.467973
\(133\) 2.75581 0.238959
\(134\) −10.8842 −0.940249
\(135\) 0 0
\(136\) 1.62793 0.139594
\(137\) −5.32866 −0.455258 −0.227629 0.973748i \(-0.573097\pi\)
−0.227629 + 0.973748i \(0.573097\pi\)
\(138\) −7.77364 −0.661736
\(139\) 7.74702 0.657093 0.328547 0.944488i \(-0.393441\pi\)
0.328547 + 0.944488i \(0.393441\pi\)
\(140\) 0 0
\(141\) 0.746162 0.0628382
\(142\) 21.0398 1.76562
\(143\) −2.95003 −0.246694
\(144\) 12.1410 1.01175
\(145\) 0 0
\(146\) −29.8245 −2.46829
\(147\) −3.37110 −0.278043
\(148\) −15.9484 −1.31095
\(149\) −19.8084 −1.62277 −0.811383 0.584515i \(-0.801285\pi\)
−0.811383 + 0.584515i \(0.801285\pi\)
\(150\) 0 0
\(151\) 19.6869 1.60209 0.801047 0.598601i \(-0.204276\pi\)
0.801047 + 0.598601i \(0.204276\pi\)
\(152\) −1.64637 −0.133538
\(153\) −7.50261 −0.606550
\(154\) 10.6734 0.860090
\(155\) 0 0
\(156\) −0.490940 −0.0393066
\(157\) −21.5455 −1.71952 −0.859758 0.510701i \(-0.829386\pi\)
−0.859758 + 0.510701i \(0.829386\pi\)
\(158\) 30.6012 2.43450
\(159\) 1.34143 0.106382
\(160\) 0 0
\(161\) −7.08250 −0.558179
\(162\) −12.1101 −0.951460
\(163\) 12.5163 0.980349 0.490175 0.871624i \(-0.336933\pi\)
0.490175 + 0.871624i \(0.336933\pi\)
\(164\) 3.38923 0.264654
\(165\) 0 0
\(166\) 12.7625 0.990560
\(167\) 7.38516 0.571481 0.285740 0.958307i \(-0.407761\pi\)
0.285740 + 0.958307i \(0.407761\pi\)
\(168\) −0.317751 −0.0245150
\(169\) −12.7306 −0.979279
\(170\) 0 0
\(171\) 7.58758 0.580237
\(172\) −9.64199 −0.735195
\(173\) 17.6215 1.33974 0.669868 0.742480i \(-0.266351\pi\)
0.669868 + 0.742480i \(0.266351\pi\)
\(174\) 3.20214 0.242754
\(175\) 0 0
\(176\) −25.6624 −1.93438
\(177\) 3.14760 0.236588
\(178\) −25.5088 −1.91196
\(179\) −2.22554 −0.166345 −0.0831723 0.996535i \(-0.526505\pi\)
−0.0831723 + 0.996535i \(0.526505\pi\)
\(180\) 0 0
\(181\) −18.6828 −1.38868 −0.694341 0.719646i \(-0.744304\pi\)
−0.694341 + 0.719646i \(0.744304\pi\)
\(182\) −0.974596 −0.0722419
\(183\) −6.38576 −0.472049
\(184\) 4.23122 0.311930
\(185\) 0 0
\(186\) 4.92443 0.361077
\(187\) 15.8583 1.15967
\(188\) 2.27035 0.165583
\(189\) 3.09812 0.225355
\(190\) 0 0
\(191\) −13.4719 −0.974793 −0.487396 0.873181i \(-0.662053\pi\)
−0.487396 + 0.873181i \(0.662053\pi\)
\(192\) −3.01971 −0.217928
\(193\) −9.23670 −0.664872 −0.332436 0.943126i \(-0.607871\pi\)
−0.332436 + 0.943126i \(0.607871\pi\)
\(194\) −1.93257 −0.138751
\(195\) 0 0
\(196\) −10.2573 −0.732662
\(197\) 25.8626 1.84263 0.921315 0.388816i \(-0.127116\pi\)
0.921315 + 0.388816i \(0.127116\pi\)
\(198\) 29.3873 2.08846
\(199\) 4.26338 0.302223 0.151112 0.988517i \(-0.451715\pi\)
0.151112 + 0.988517i \(0.451715\pi\)
\(200\) 0 0
\(201\) 3.15643 0.222638
\(202\) 13.6554 0.960788
\(203\) 2.91744 0.204764
\(204\) 2.63911 0.184774
\(205\) 0 0
\(206\) −10.6252 −0.740293
\(207\) −19.5003 −1.35536
\(208\) 2.34325 0.162475
\(209\) −16.0379 −1.10936
\(210\) 0 0
\(211\) 6.03303 0.415331 0.207665 0.978200i \(-0.433413\pi\)
0.207665 + 0.978200i \(0.433413\pi\)
\(212\) 4.08159 0.280324
\(213\) −6.10158 −0.418073
\(214\) −13.4817 −0.921587
\(215\) 0 0
\(216\) −1.85087 −0.125936
\(217\) 4.48660 0.304570
\(218\) 14.0995 0.954941
\(219\) 8.64915 0.584456
\(220\) 0 0
\(221\) −1.44802 −0.0974046
\(222\) 10.0775 0.676360
\(223\) −21.1766 −1.41809 −0.709046 0.705162i \(-0.750874\pi\)
−0.709046 + 0.705162i \(0.750874\pi\)
\(224\) −7.33828 −0.490310
\(225\) 0 0
\(226\) −0.757725 −0.0504031
\(227\) 3.50318 0.232514 0.116257 0.993219i \(-0.462910\pi\)
0.116257 + 0.993219i \(0.462910\pi\)
\(228\) −2.66900 −0.176759
\(229\) −19.3330 −1.27756 −0.638781 0.769389i \(-0.720561\pi\)
−0.638781 + 0.769389i \(0.720561\pi\)
\(230\) 0 0
\(231\) −3.09532 −0.203657
\(232\) −1.74294 −0.114429
\(233\) −23.0684 −1.51126 −0.755632 0.654997i \(-0.772670\pi\)
−0.755632 + 0.654997i \(0.772670\pi\)
\(234\) −2.68336 −0.175417
\(235\) 0 0
\(236\) 9.57722 0.623424
\(237\) −8.87442 −0.576456
\(238\) 5.23906 0.339598
\(239\) −3.13382 −0.202710 −0.101355 0.994850i \(-0.532318\pi\)
−0.101355 + 0.994850i \(0.532318\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −40.9669 −2.63345
\(243\) 13.0282 0.835757
\(244\) −19.4300 −1.24388
\(245\) 0 0
\(246\) −2.14159 −0.136543
\(247\) 1.46442 0.0931790
\(248\) −2.68038 −0.170204
\(249\) −3.70114 −0.234551
\(250\) 0 0
\(251\) 8.51378 0.537385 0.268693 0.963226i \(-0.413408\pi\)
0.268693 + 0.963226i \(0.413408\pi\)
\(252\) 4.45577 0.280687
\(253\) 41.2177 2.59134
\(254\) 18.1398 1.13819
\(255\) 0 0
\(256\) 19.7031 1.23144
\(257\) 0.300229 0.0187278 0.00936389 0.999956i \(-0.497019\pi\)
0.00936389 + 0.999956i \(0.497019\pi\)
\(258\) 6.09260 0.379309
\(259\) 9.18155 0.570514
\(260\) 0 0
\(261\) 8.03262 0.497207
\(262\) −18.0079 −1.11253
\(263\) −15.5157 −0.956740 −0.478370 0.878158i \(-0.658772\pi\)
−0.478370 + 0.878158i \(0.658772\pi\)
\(264\) 1.84920 0.113811
\(265\) 0 0
\(266\) −5.29840 −0.324866
\(267\) 7.39759 0.452725
\(268\) 9.60410 0.586664
\(269\) −28.6731 −1.74823 −0.874115 0.485718i \(-0.838558\pi\)
−0.874115 + 0.485718i \(0.838558\pi\)
\(270\) 0 0
\(271\) −6.01685 −0.365498 −0.182749 0.983160i \(-0.558500\pi\)
−0.182749 + 0.983160i \(0.558500\pi\)
\(272\) −12.5964 −0.763771
\(273\) 0.282635 0.0171058
\(274\) 10.2451 0.618927
\(275\) 0 0
\(276\) 6.85940 0.412887
\(277\) 22.1758 1.33241 0.666207 0.745767i \(-0.267917\pi\)
0.666207 + 0.745767i \(0.267917\pi\)
\(278\) −14.8947 −0.893322
\(279\) 12.3530 0.739555
\(280\) 0 0
\(281\) −17.6552 −1.05322 −0.526610 0.850107i \(-0.676537\pi\)
−0.526610 + 0.850107i \(0.676537\pi\)
\(282\) −1.43460 −0.0854289
\(283\) 3.73383 0.221953 0.110977 0.993823i \(-0.464602\pi\)
0.110977 + 0.993823i \(0.464602\pi\)
\(284\) −18.5653 −1.10165
\(285\) 0 0
\(286\) 5.67182 0.335382
\(287\) −1.95119 −0.115175
\(288\) −20.2046 −1.19056
\(289\) −9.21597 −0.542116
\(290\) 0 0
\(291\) 0.560451 0.0328542
\(292\) 26.3168 1.54008
\(293\) −30.3941 −1.77564 −0.887821 0.460190i \(-0.847781\pi\)
−0.887821 + 0.460190i \(0.847781\pi\)
\(294\) 6.48138 0.378002
\(295\) 0 0
\(296\) −5.48523 −0.318823
\(297\) −18.0300 −1.04621
\(298\) 38.0842 2.20616
\(299\) −3.76361 −0.217655
\(300\) 0 0
\(301\) 5.55091 0.319949
\(302\) −37.8506 −2.17806
\(303\) −3.96008 −0.227501
\(304\) 12.7391 0.730637
\(305\) 0 0
\(306\) 14.4248 0.824608
\(307\) 5.88448 0.335845 0.167923 0.985800i \(-0.446294\pi\)
0.167923 + 0.985800i \(0.446294\pi\)
\(308\) −9.41815 −0.536649
\(309\) 3.08133 0.175291
\(310\) 0 0
\(311\) −8.56865 −0.485883 −0.242942 0.970041i \(-0.578112\pi\)
−0.242942 + 0.970041i \(0.578112\pi\)
\(312\) −0.168852 −0.00955933
\(313\) −6.68268 −0.377728 −0.188864 0.982003i \(-0.560480\pi\)
−0.188864 + 0.982003i \(0.560480\pi\)
\(314\) 41.4240 2.33769
\(315\) 0 0
\(316\) −27.0023 −1.51900
\(317\) 18.7500 1.05311 0.526553 0.850142i \(-0.323484\pi\)
0.526553 + 0.850142i \(0.323484\pi\)
\(318\) −2.57908 −0.144628
\(319\) −16.9785 −0.950615
\(320\) 0 0
\(321\) 3.90971 0.218219
\(322\) 13.6170 0.758848
\(323\) −7.87219 −0.438020
\(324\) 10.6859 0.593659
\(325\) 0 0
\(326\) −24.0642 −1.33279
\(327\) −4.08889 −0.226116
\(328\) 1.16568 0.0643637
\(329\) −1.30705 −0.0720598
\(330\) 0 0
\(331\) −10.1395 −0.557317 −0.278659 0.960390i \(-0.589890\pi\)
−0.278659 + 0.960390i \(0.589890\pi\)
\(332\) −11.2615 −0.618055
\(333\) 25.2796 1.38531
\(334\) −14.1989 −0.776932
\(335\) 0 0
\(336\) 2.45865 0.134131
\(337\) −22.7996 −1.24197 −0.620986 0.783822i \(-0.713268\pi\)
−0.620986 + 0.783822i \(0.713268\pi\)
\(338\) 24.4763 1.33134
\(339\) 0.219742 0.0119347
\(340\) 0 0
\(341\) −26.1105 −1.41396
\(342\) −14.5881 −0.788835
\(343\) 12.7419 0.688000
\(344\) −3.31622 −0.178799
\(345\) 0 0
\(346\) −33.8796 −1.82138
\(347\) 33.0431 1.77385 0.886924 0.461916i \(-0.152838\pi\)
0.886924 + 0.461916i \(0.152838\pi\)
\(348\) −2.82554 −0.151465
\(349\) −10.7629 −0.576126 −0.288063 0.957611i \(-0.593011\pi\)
−0.288063 + 0.957611i \(0.593011\pi\)
\(350\) 0 0
\(351\) 1.64632 0.0878743
\(352\) 42.7063 2.27626
\(353\) −12.8113 −0.681879 −0.340940 0.940085i \(-0.610745\pi\)
−0.340940 + 0.940085i \(0.610745\pi\)
\(354\) −6.05167 −0.321643
\(355\) 0 0
\(356\) 22.5087 1.19296
\(357\) −1.51934 −0.0804120
\(358\) 4.27889 0.226146
\(359\) 12.7434 0.672570 0.336285 0.941760i \(-0.390830\pi\)
0.336285 + 0.941760i \(0.390830\pi\)
\(360\) 0 0
\(361\) −11.0387 −0.580982
\(362\) 35.9202 1.88792
\(363\) 11.8805 0.623563
\(364\) 0.859975 0.0450750
\(365\) 0 0
\(366\) 12.2775 0.641753
\(367\) −1.03639 −0.0540989 −0.0270495 0.999634i \(-0.508611\pi\)
−0.0270495 + 0.999634i \(0.508611\pi\)
\(368\) −32.7398 −1.70668
\(369\) −5.37222 −0.279666
\(370\) 0 0
\(371\) −2.34978 −0.121994
\(372\) −4.34527 −0.225292
\(373\) 14.7553 0.763999 0.381999 0.924163i \(-0.375236\pi\)
0.381999 + 0.924163i \(0.375236\pi\)
\(374\) −30.4896 −1.57658
\(375\) 0 0
\(376\) 0.780855 0.0402695
\(377\) 1.55032 0.0798454
\(378\) −5.95654 −0.306371
\(379\) 23.1923 1.19131 0.595653 0.803242i \(-0.296893\pi\)
0.595653 + 0.803242i \(0.296893\pi\)
\(380\) 0 0
\(381\) −5.26058 −0.269508
\(382\) 25.9015 1.32524
\(383\) 12.7484 0.651415 0.325707 0.945471i \(-0.394398\pi\)
0.325707 + 0.945471i \(0.394398\pi\)
\(384\) −2.57272 −0.131289
\(385\) 0 0
\(386\) 17.7588 0.903898
\(387\) 15.2834 0.776897
\(388\) 1.70529 0.0865728
\(389\) 31.6959 1.60705 0.803523 0.595274i \(-0.202957\pi\)
0.803523 + 0.595274i \(0.202957\pi\)
\(390\) 0 0
\(391\) 20.2317 1.02316
\(392\) −3.52784 −0.178183
\(393\) 5.22233 0.263432
\(394\) −49.7242 −2.50507
\(395\) 0 0
\(396\) −25.9311 −1.30309
\(397\) −18.0796 −0.907389 −0.453694 0.891157i \(-0.649894\pi\)
−0.453694 + 0.891157i \(0.649894\pi\)
\(398\) −8.19692 −0.410874
\(399\) 1.53655 0.0769236
\(400\) 0 0
\(401\) 24.8583 1.24136 0.620682 0.784063i \(-0.286856\pi\)
0.620682 + 0.784063i \(0.286856\pi\)
\(402\) −6.06866 −0.302677
\(403\) 2.38416 0.118764
\(404\) −12.0494 −0.599479
\(405\) 0 0
\(406\) −5.60917 −0.278378
\(407\) −53.4335 −2.64860
\(408\) 0.907683 0.0449370
\(409\) 4.25506 0.210399 0.105200 0.994451i \(-0.466452\pi\)
0.105200 + 0.994451i \(0.466452\pi\)
\(410\) 0 0
\(411\) −2.97109 −0.146553
\(412\) 9.37559 0.461902
\(413\) −5.51363 −0.271308
\(414\) 37.4919 1.84263
\(415\) 0 0
\(416\) −3.89953 −0.191190
\(417\) 4.31948 0.211526
\(418\) 30.8349 1.50818
\(419\) 16.7521 0.818396 0.409198 0.912446i \(-0.365809\pi\)
0.409198 + 0.912446i \(0.365809\pi\)
\(420\) 0 0
\(421\) 20.9251 1.01982 0.509912 0.860226i \(-0.329678\pi\)
0.509912 + 0.860226i \(0.329678\pi\)
\(422\) −11.5993 −0.564645
\(423\) −3.59870 −0.174975
\(424\) 1.40380 0.0681746
\(425\) 0 0
\(426\) 11.7311 0.568373
\(427\) 11.1859 0.541323
\(428\) 11.8961 0.575020
\(429\) −1.64484 −0.0794136
\(430\) 0 0
\(431\) −27.7303 −1.33572 −0.667861 0.744286i \(-0.732790\pi\)
−0.667861 + 0.744286i \(0.732790\pi\)
\(432\) 14.3215 0.689042
\(433\) −28.0853 −1.34969 −0.674847 0.737958i \(-0.735790\pi\)
−0.674847 + 0.737958i \(0.735790\pi\)
\(434\) −8.62609 −0.414065
\(435\) 0 0
\(436\) −12.4413 −0.595831
\(437\) −20.4609 −0.978777
\(438\) −16.6291 −0.794571
\(439\) −10.0542 −0.479863 −0.239931 0.970790i \(-0.577125\pi\)
−0.239931 + 0.970790i \(0.577125\pi\)
\(440\) 0 0
\(441\) 16.2586 0.774221
\(442\) 2.78402 0.132422
\(443\) −4.38230 −0.208209 −0.104105 0.994566i \(-0.533198\pi\)
−0.104105 + 0.994566i \(0.533198\pi\)
\(444\) −8.89233 −0.422011
\(445\) 0 0
\(446\) 40.7149 1.92791
\(447\) −11.0445 −0.522387
\(448\) 5.28960 0.249910
\(449\) 7.51495 0.354652 0.177326 0.984152i \(-0.443255\pi\)
0.177326 + 0.984152i \(0.443255\pi\)
\(450\) 0 0
\(451\) 11.3552 0.534698
\(452\) 0.668610 0.0314488
\(453\) 10.9768 0.515733
\(454\) −6.73533 −0.316105
\(455\) 0 0
\(456\) −0.917963 −0.0429875
\(457\) −27.0931 −1.26736 −0.633682 0.773594i \(-0.718457\pi\)
−0.633682 + 0.773594i \(0.718457\pi\)
\(458\) 37.1703 1.73685
\(459\) −8.85003 −0.413084
\(460\) 0 0
\(461\) 8.28811 0.386016 0.193008 0.981197i \(-0.438176\pi\)
0.193008 + 0.981197i \(0.438176\pi\)
\(462\) 5.95116 0.276873
\(463\) −39.3319 −1.82791 −0.913955 0.405815i \(-0.866988\pi\)
−0.913955 + 0.405815i \(0.866988\pi\)
\(464\) 13.4863 0.626085
\(465\) 0 0
\(466\) 44.3521 2.05457
\(467\) −1.62543 −0.0752160 −0.0376080 0.999293i \(-0.511974\pi\)
−0.0376080 + 0.999293i \(0.511974\pi\)
\(468\) 2.36778 0.109451
\(469\) −5.52910 −0.255310
\(470\) 0 0
\(471\) −12.0131 −0.553532
\(472\) 3.29395 0.151616
\(473\) −32.3044 −1.48536
\(474\) 17.0622 0.783695
\(475\) 0 0
\(476\) −4.62291 −0.211891
\(477\) −6.46966 −0.296225
\(478\) 6.02518 0.275585
\(479\) 27.2783 1.24638 0.623189 0.782071i \(-0.285837\pi\)
0.623189 + 0.782071i \(0.285837\pi\)
\(480\) 0 0
\(481\) 4.87903 0.222465
\(482\) −1.92263 −0.0875735
\(483\) −3.94897 −0.179684
\(484\) 36.1488 1.64313
\(485\) 0 0
\(486\) −25.0484 −1.13622
\(487\) 16.1457 0.731631 0.365815 0.930687i \(-0.380790\pi\)
0.365815 + 0.930687i \(0.380790\pi\)
\(488\) −6.68266 −0.302510
\(489\) 6.97866 0.315586
\(490\) 0 0
\(491\) −13.9774 −0.630791 −0.315395 0.948960i \(-0.602137\pi\)
−0.315395 + 0.948960i \(0.602137\pi\)
\(492\) 1.88972 0.0851953
\(493\) −8.33392 −0.375341
\(494\) −2.81555 −0.126677
\(495\) 0 0
\(496\) 20.7399 0.931251
\(497\) 10.6881 0.479427
\(498\) 7.11594 0.318873
\(499\) 13.5580 0.606937 0.303469 0.952841i \(-0.401855\pi\)
0.303469 + 0.952841i \(0.401855\pi\)
\(500\) 0 0
\(501\) 4.11772 0.183966
\(502\) −16.3689 −0.730578
\(503\) −28.0739 −1.25175 −0.625876 0.779923i \(-0.715258\pi\)
−0.625876 + 0.779923i \(0.715258\pi\)
\(504\) 1.53250 0.0682629
\(505\) 0 0
\(506\) −79.2465 −3.52294
\(507\) −7.09818 −0.315241
\(508\) −16.0064 −0.710170
\(509\) −39.5857 −1.75460 −0.877302 0.479939i \(-0.840659\pi\)
−0.877302 + 0.479939i \(0.840659\pi\)
\(510\) 0 0
\(511\) −15.1507 −0.670226
\(512\) −28.6534 −1.26632
\(513\) 8.95026 0.395164
\(514\) −0.577230 −0.0254605
\(515\) 0 0
\(516\) −5.37606 −0.236668
\(517\) 7.60657 0.334537
\(518\) −17.6527 −0.775617
\(519\) 9.82516 0.431277
\(520\) 0 0
\(521\) 13.3893 0.586597 0.293299 0.956021i \(-0.405247\pi\)
0.293299 + 0.956021i \(0.405247\pi\)
\(522\) −15.4438 −0.675955
\(523\) −11.5484 −0.504976 −0.252488 0.967600i \(-0.581249\pi\)
−0.252488 + 0.967600i \(0.581249\pi\)
\(524\) 15.8900 0.694158
\(525\) 0 0
\(526\) 29.8310 1.30069
\(527\) −12.8164 −0.558289
\(528\) −14.3085 −0.622699
\(529\) 29.5850 1.28631
\(530\) 0 0
\(531\) −15.1807 −0.658787
\(532\) 4.67526 0.202698
\(533\) −1.03685 −0.0449110
\(534\) −14.2228 −0.615483
\(535\) 0 0
\(536\) 3.30319 0.142676
\(537\) −1.24089 −0.0535482
\(538\) 55.1279 2.37673
\(539\) −34.3659 −1.48024
\(540\) 0 0
\(541\) −24.7679 −1.06486 −0.532428 0.846476i \(-0.678720\pi\)
−0.532428 + 0.846476i \(0.678720\pi\)
\(542\) 11.5682 0.496897
\(543\) −10.4169 −0.447033
\(544\) 20.9624 0.898757
\(545\) 0 0
\(546\) −0.543403 −0.0232555
\(547\) −34.4650 −1.47362 −0.736808 0.676102i \(-0.763668\pi\)
−0.736808 + 0.676102i \(0.763668\pi\)
\(548\) −9.04015 −0.386176
\(549\) 30.7982 1.31443
\(550\) 0 0
\(551\) 8.42831 0.359058
\(552\) 2.35919 0.100414
\(553\) 15.5453 0.661052
\(554\) −42.6359 −1.81142
\(555\) 0 0
\(556\) 13.1429 0.557384
\(557\) 3.13055 0.132646 0.0663228 0.997798i \(-0.478873\pi\)
0.0663228 + 0.997798i \(0.478873\pi\)
\(558\) −23.7503 −1.00543
\(559\) 2.94973 0.124760
\(560\) 0 0
\(561\) 8.84204 0.373311
\(562\) 33.9444 1.43186
\(563\) −41.5012 −1.74907 −0.874533 0.484966i \(-0.838832\pi\)
−0.874533 + 0.484966i \(0.838832\pi\)
\(564\) 1.26587 0.0533029
\(565\) 0 0
\(566\) −7.17878 −0.301747
\(567\) −6.15187 −0.258354
\(568\) −6.38527 −0.267920
\(569\) 9.52061 0.399125 0.199562 0.979885i \(-0.436048\pi\)
0.199562 + 0.979885i \(0.436048\pi\)
\(570\) 0 0
\(571\) −12.5830 −0.526583 −0.263292 0.964716i \(-0.584808\pi\)
−0.263292 + 0.964716i \(0.584808\pi\)
\(572\) −5.00477 −0.209260
\(573\) −7.51149 −0.313797
\(574\) 3.75141 0.156581
\(575\) 0 0
\(576\) 14.5639 0.606829
\(577\) 4.59818 0.191425 0.0957123 0.995409i \(-0.469487\pi\)
0.0957123 + 0.995409i \(0.469487\pi\)
\(578\) 17.7189 0.737010
\(579\) −5.15008 −0.214030
\(580\) 0 0
\(581\) 6.48327 0.268971
\(582\) −1.07754 −0.0446655
\(583\) 13.6749 0.566357
\(584\) 9.05130 0.374545
\(585\) 0 0
\(586\) 58.4366 2.41400
\(587\) 11.2149 0.462887 0.231443 0.972848i \(-0.425655\pi\)
0.231443 + 0.972848i \(0.425655\pi\)
\(588\) −5.71912 −0.235852
\(589\) 12.9615 0.534070
\(590\) 0 0
\(591\) 14.4201 0.593164
\(592\) 42.4430 1.74439
\(593\) −15.2963 −0.628144 −0.314072 0.949399i \(-0.601693\pi\)
−0.314072 + 0.949399i \(0.601693\pi\)
\(594\) 34.6650 1.42232
\(595\) 0 0
\(596\) −33.6052 −1.37652
\(597\) 2.37712 0.0972892
\(598\) 7.23603 0.295903
\(599\) 26.5049 1.08296 0.541480 0.840713i \(-0.317864\pi\)
0.541480 + 0.840713i \(0.317864\pi\)
\(600\) 0 0
\(601\) −4.30453 −0.175586 −0.0877928 0.996139i \(-0.527981\pi\)
−0.0877928 + 0.996139i \(0.527981\pi\)
\(602\) −10.6724 −0.434973
\(603\) −15.2233 −0.619941
\(604\) 33.3991 1.35899
\(605\) 0 0
\(606\) 7.61378 0.309289
\(607\) 5.46958 0.222004 0.111002 0.993820i \(-0.464594\pi\)
0.111002 + 0.993820i \(0.464594\pi\)
\(608\) −21.1998 −0.859767
\(609\) 1.62667 0.0659160
\(610\) 0 0
\(611\) −0.694559 −0.0280989
\(612\) −12.7283 −0.514510
\(613\) −34.9065 −1.40986 −0.704930 0.709277i \(-0.749021\pi\)
−0.704930 + 0.709277i \(0.749021\pi\)
\(614\) −11.3137 −0.456584
\(615\) 0 0
\(616\) −3.23924 −0.130513
\(617\) 24.0459 0.968052 0.484026 0.875054i \(-0.339174\pi\)
0.484026 + 0.875054i \(0.339174\pi\)
\(618\) −5.92427 −0.238309
\(619\) −36.3148 −1.45961 −0.729807 0.683653i \(-0.760390\pi\)
−0.729807 + 0.683653i \(0.760390\pi\)
\(620\) 0 0
\(621\) −23.0024 −0.923055
\(622\) 16.4744 0.660562
\(623\) −12.9583 −0.519164
\(624\) 1.30652 0.0523026
\(625\) 0 0
\(626\) 12.8483 0.513523
\(627\) −8.94218 −0.357116
\(628\) −36.5522 −1.45859
\(629\) −26.2279 −1.04577
\(630\) 0 0
\(631\) −19.2957 −0.768150 −0.384075 0.923302i \(-0.625480\pi\)
−0.384075 + 0.923302i \(0.625480\pi\)
\(632\) −9.28704 −0.369419
\(633\) 3.36382 0.133700
\(634\) −36.0494 −1.43171
\(635\) 0 0
\(636\) 2.27576 0.0902397
\(637\) 3.13796 0.124330
\(638\) 32.6435 1.29237
\(639\) 29.4276 1.16414
\(640\) 0 0
\(641\) −29.0190 −1.14618 −0.573091 0.819492i \(-0.694256\pi\)
−0.573091 + 0.819492i \(0.694256\pi\)
\(642\) −7.51693 −0.296670
\(643\) −29.2586 −1.15385 −0.576924 0.816798i \(-0.695747\pi\)
−0.576924 + 0.816798i \(0.695747\pi\)
\(644\) −12.0156 −0.473479
\(645\) 0 0
\(646\) 15.1353 0.595491
\(647\) −32.7993 −1.28947 −0.644736 0.764405i \(-0.723033\pi\)
−0.644736 + 0.764405i \(0.723033\pi\)
\(648\) 3.67525 0.144377
\(649\) 32.0874 1.25954
\(650\) 0 0
\(651\) 2.50158 0.0980448
\(652\) 21.2340 0.831588
\(653\) −15.9479 −0.624092 −0.312046 0.950067i \(-0.601014\pi\)
−0.312046 + 0.950067i \(0.601014\pi\)
\(654\) 7.86144 0.307407
\(655\) 0 0
\(656\) −9.01963 −0.352157
\(657\) −41.7144 −1.62743
\(658\) 2.51297 0.0979658
\(659\) −19.1492 −0.745947 −0.372973 0.927842i \(-0.621662\pi\)
−0.372973 + 0.927842i \(0.621662\pi\)
\(660\) 0 0
\(661\) −2.28059 −0.0887045 −0.0443523 0.999016i \(-0.514122\pi\)
−0.0443523 + 0.999016i \(0.514122\pi\)
\(662\) 19.4945 0.757676
\(663\) −0.807370 −0.0313557
\(664\) −3.87323 −0.150310
\(665\) 0 0
\(666\) −48.6034 −1.88334
\(667\) −21.6610 −0.838717
\(668\) 12.5290 0.484763
\(669\) −11.8074 −0.456500
\(670\) 0 0
\(671\) −65.0981 −2.51308
\(672\) −4.09159 −0.157836
\(673\) −24.0503 −0.927073 −0.463536 0.886078i \(-0.653420\pi\)
−0.463536 + 0.886078i \(0.653420\pi\)
\(674\) 43.8352 1.68847
\(675\) 0 0
\(676\) −21.5977 −0.830681
\(677\) −47.6572 −1.83161 −0.915807 0.401619i \(-0.868448\pi\)
−0.915807 + 0.401619i \(0.868448\pi\)
\(678\) −0.422483 −0.0162254
\(679\) −0.981737 −0.0376756
\(680\) 0 0
\(681\) 1.95326 0.0748491
\(682\) 50.2009 1.92229
\(683\) −30.1166 −1.15238 −0.576190 0.817316i \(-0.695461\pi\)
−0.576190 + 0.817316i \(0.695461\pi\)
\(684\) 12.8724 0.492190
\(685\) 0 0
\(686\) −24.4981 −0.935340
\(687\) −10.7795 −0.411262
\(688\) 25.6599 0.978273
\(689\) −1.24866 −0.0475702
\(690\) 0 0
\(691\) 6.81543 0.259271 0.129636 0.991562i \(-0.458619\pi\)
0.129636 + 0.991562i \(0.458619\pi\)
\(692\) 29.8951 1.13644
\(693\) 14.9286 0.567090
\(694\) −63.5297 −2.41156
\(695\) 0 0
\(696\) −0.971804 −0.0368361
\(697\) 5.57373 0.211120
\(698\) 20.6931 0.783247
\(699\) −12.8622 −0.486493
\(700\) 0 0
\(701\) 38.7899 1.46507 0.732537 0.680727i \(-0.238336\pi\)
0.732537 + 0.680727i \(0.238336\pi\)
\(702\) −3.16528 −0.119466
\(703\) 26.5249 1.00041
\(704\) −30.7837 −1.16020
\(705\) 0 0
\(706\) 24.6315 0.927019
\(707\) 6.93685 0.260887
\(708\) 5.33995 0.200687
\(709\) −8.72623 −0.327720 −0.163860 0.986484i \(-0.552395\pi\)
−0.163860 + 0.986484i \(0.552395\pi\)
\(710\) 0 0
\(711\) 42.8009 1.60516
\(712\) 7.74154 0.290127
\(713\) −33.3114 −1.24752
\(714\) 2.92113 0.109321
\(715\) 0 0
\(716\) −3.77566 −0.141103
\(717\) −1.74732 −0.0652547
\(718\) −24.5008 −0.914362
\(719\) −22.6803 −0.845832 −0.422916 0.906169i \(-0.638994\pi\)
−0.422916 + 0.906169i \(0.638994\pi\)
\(720\) 0 0
\(721\) −5.39755 −0.201015
\(722\) 21.2233 0.789848
\(723\) 0.557567 0.0207361
\(724\) −31.6956 −1.17796
\(725\) 0 0
\(726\) −22.8418 −0.847738
\(727\) −7.41044 −0.274838 −0.137419 0.990513i \(-0.543881\pi\)
−0.137419 + 0.990513i \(0.543881\pi\)
\(728\) 0.295776 0.0109622
\(729\) −11.6321 −0.430818
\(730\) 0 0
\(731\) −15.8567 −0.586479
\(732\) −10.8335 −0.400419
\(733\) −9.84342 −0.363575 −0.181787 0.983338i \(-0.558188\pi\)
−0.181787 + 0.983338i \(0.558188\pi\)
\(734\) 1.99259 0.0735478
\(735\) 0 0
\(736\) 54.4842 2.00831
\(737\) 32.1775 1.18527
\(738\) 10.3288 0.380208
\(739\) −25.0992 −0.923289 −0.461645 0.887065i \(-0.652740\pi\)
−0.461645 + 0.887065i \(0.652740\pi\)
\(740\) 0 0
\(741\) 0.816514 0.0299954
\(742\) 4.51776 0.165852
\(743\) 45.4541 1.66755 0.833774 0.552106i \(-0.186176\pi\)
0.833774 + 0.552106i \(0.186176\pi\)
\(744\) −1.49449 −0.0547908
\(745\) 0 0
\(746\) −28.3690 −1.03866
\(747\) 17.8504 0.653113
\(748\) 26.9038 0.983699
\(749\) −6.84861 −0.250243
\(750\) 0 0
\(751\) 0.291173 0.0106251 0.00531253 0.999986i \(-0.498309\pi\)
0.00531253 + 0.999986i \(0.498309\pi\)
\(752\) −6.04200 −0.220329
\(753\) 4.74701 0.172991
\(754\) −2.98069 −0.108550
\(755\) 0 0
\(756\) 5.25600 0.191159
\(757\) 8.45373 0.307256 0.153628 0.988129i \(-0.450904\pi\)
0.153628 + 0.988129i \(0.450904\pi\)
\(758\) −44.5902 −1.61959
\(759\) 22.9817 0.834181
\(760\) 0 0
\(761\) −18.3586 −0.665498 −0.332749 0.943015i \(-0.607976\pi\)
−0.332749 + 0.943015i \(0.607976\pi\)
\(762\) 10.1142 0.366398
\(763\) 7.16249 0.259299
\(764\) −22.8553 −0.826875
\(765\) 0 0
\(766\) −24.5106 −0.885602
\(767\) −2.92992 −0.105793
\(768\) 10.9858 0.396416
\(769\) −45.6484 −1.64612 −0.823061 0.567953i \(-0.807736\pi\)
−0.823061 + 0.567953i \(0.807736\pi\)
\(770\) 0 0
\(771\) 0.167398 0.00602869
\(772\) −15.6702 −0.563983
\(773\) 47.5774 1.71124 0.855620 0.517604i \(-0.173176\pi\)
0.855620 + 0.517604i \(0.173176\pi\)
\(774\) −29.3843 −1.05620
\(775\) 0 0
\(776\) 0.586509 0.0210544
\(777\) 5.11933 0.183655
\(778\) −60.9395 −2.18479
\(779\) −5.63685 −0.201961
\(780\) 0 0
\(781\) −62.2011 −2.22573
\(782\) −38.8982 −1.39100
\(783\) 9.47522 0.338617
\(784\) 27.2973 0.974902
\(785\) 0 0
\(786\) −10.0406 −0.358137
\(787\) −48.3487 −1.72345 −0.861723 0.507378i \(-0.830615\pi\)
−0.861723 + 0.507378i \(0.830615\pi\)
\(788\) 43.8762 1.56302
\(789\) −8.65106 −0.307986
\(790\) 0 0
\(791\) −0.384920 −0.0136862
\(792\) −8.91862 −0.316909
\(793\) 5.94413 0.211082
\(794\) 34.7604 1.23360
\(795\) 0 0
\(796\) 7.23289 0.256363
\(797\) 26.2387 0.929422 0.464711 0.885463i \(-0.346158\pi\)
0.464711 + 0.885463i \(0.346158\pi\)
\(798\) −2.95421 −0.104578
\(799\) 3.73369 0.132088
\(800\) 0 0
\(801\) −35.6782 −1.26063
\(802\) −47.7933 −1.68764
\(803\) 88.1717 3.11151
\(804\) 5.35493 0.188854
\(805\) 0 0
\(806\) −4.58386 −0.161460
\(807\) −15.9872 −0.562776
\(808\) −4.14421 −0.145793
\(809\) 8.43180 0.296446 0.148223 0.988954i \(-0.452645\pi\)
0.148223 + 0.988954i \(0.452645\pi\)
\(810\) 0 0
\(811\) 30.9938 1.08834 0.544170 0.838975i \(-0.316845\pi\)
0.544170 + 0.838975i \(0.316845\pi\)
\(812\) 4.94948 0.173693
\(813\) −3.35480 −0.117658
\(814\) 102.733 3.60079
\(815\) 0 0
\(816\) −7.02335 −0.245867
\(817\) 16.0362 0.561037
\(818\) −8.18092 −0.286039
\(819\) −1.36313 −0.0476317
\(820\) 0 0
\(821\) 30.6989 1.07140 0.535699 0.844409i \(-0.320048\pi\)
0.535699 + 0.844409i \(0.320048\pi\)
\(822\) 5.71231 0.199240
\(823\) 20.4776 0.713804 0.356902 0.934142i \(-0.383833\pi\)
0.356902 + 0.934142i \(0.383833\pi\)
\(824\) 3.22460 0.112334
\(825\) 0 0
\(826\) 10.6007 0.368845
\(827\) −27.5776 −0.958967 −0.479484 0.877551i \(-0.659176\pi\)
−0.479484 + 0.877551i \(0.659176\pi\)
\(828\) −33.0825 −1.14970
\(829\) −13.2760 −0.461094 −0.230547 0.973061i \(-0.574052\pi\)
−0.230547 + 0.973061i \(0.574052\pi\)
\(830\) 0 0
\(831\) 12.3645 0.428919
\(832\) 2.81087 0.0974493
\(833\) −16.8685 −0.584459
\(834\) −8.30478 −0.287571
\(835\) 0 0
\(836\) −27.2084 −0.941024
\(837\) 14.5715 0.503665
\(838\) −32.2082 −1.11261
\(839\) 10.9056 0.376504 0.188252 0.982121i \(-0.439718\pi\)
0.188252 + 0.982121i \(0.439718\pi\)
\(840\) 0 0
\(841\) −20.0773 −0.692322
\(842\) −40.2312 −1.38646
\(843\) −9.84395 −0.339043
\(844\) 10.2351 0.352307
\(845\) 0 0
\(846\) 6.91898 0.237879
\(847\) −20.8109 −0.715073
\(848\) −10.8622 −0.373008
\(849\) 2.08186 0.0714493
\(850\) 0 0
\(851\) −68.1697 −2.33683
\(852\) −10.3514 −0.354634
\(853\) −8.12490 −0.278191 −0.139096 0.990279i \(-0.544420\pi\)
−0.139096 + 0.990279i \(0.544420\pi\)
\(854\) −21.5063 −0.735932
\(855\) 0 0
\(856\) 4.09149 0.139844
\(857\) −34.5296 −1.17951 −0.589755 0.807582i \(-0.700776\pi\)
−0.589755 + 0.807582i \(0.700776\pi\)
\(858\) 3.16242 0.107963
\(859\) −29.8705 −1.01917 −0.509584 0.860421i \(-0.670201\pi\)
−0.509584 + 0.860421i \(0.670201\pi\)
\(860\) 0 0
\(861\) −1.08792 −0.0370761
\(862\) 53.3152 1.81592
\(863\) 13.2136 0.449797 0.224899 0.974382i \(-0.427795\pi\)
0.224899 + 0.974382i \(0.427795\pi\)
\(864\) −23.8332 −0.810820
\(865\) 0 0
\(866\) 53.9977 1.83492
\(867\) −5.13852 −0.174513
\(868\) 7.61159 0.258354
\(869\) −90.4682 −3.06892
\(870\) 0 0
\(871\) −2.93814 −0.0995550
\(872\) −4.27901 −0.144905
\(873\) −2.70302 −0.0914835
\(874\) 39.3387 1.33065
\(875\) 0 0
\(876\) 14.6734 0.495769
\(877\) 30.5723 1.03235 0.516176 0.856482i \(-0.327355\pi\)
0.516176 + 0.856482i \(0.327355\pi\)
\(878\) 19.3306 0.652377
\(879\) −16.9467 −0.571600
\(880\) 0 0
\(881\) 23.4110 0.788736 0.394368 0.918953i \(-0.370964\pi\)
0.394368 + 0.918953i \(0.370964\pi\)
\(882\) −31.2594 −1.05256
\(883\) −25.5119 −0.858545 −0.429273 0.903175i \(-0.641230\pi\)
−0.429273 + 0.903175i \(0.641230\pi\)
\(884\) −2.45659 −0.0826241
\(885\) 0 0
\(886\) 8.42555 0.283062
\(887\) 6.77343 0.227430 0.113715 0.993513i \(-0.463725\pi\)
0.113715 + 0.993513i \(0.463725\pi\)
\(888\) −3.05839 −0.102633
\(889\) 9.21493 0.309059
\(890\) 0 0
\(891\) 35.8018 1.19941
\(892\) −35.9265 −1.20291
\(893\) −3.77598 −0.126358
\(894\) 21.2345 0.710188
\(895\) 0 0
\(896\) 4.50662 0.150556
\(897\) −2.09846 −0.0700657
\(898\) −14.4485 −0.482152
\(899\) 13.7217 0.457646
\(900\) 0 0
\(901\) 6.71234 0.223620
\(902\) −21.8320 −0.726925
\(903\) 3.09501 0.102995
\(904\) 0.229959 0.00764831
\(905\) 0 0
\(906\) −21.1043 −0.701142
\(907\) 55.9625 1.85821 0.929103 0.369822i \(-0.120581\pi\)
0.929103 + 0.369822i \(0.120581\pi\)
\(908\) 5.94320 0.197232
\(909\) 19.0993 0.633483
\(910\) 0 0
\(911\) −13.0286 −0.431656 −0.215828 0.976431i \(-0.569245\pi\)
−0.215828 + 0.976431i \(0.569245\pi\)
\(912\) 7.10290 0.235200
\(913\) −37.7304 −1.24870
\(914\) 52.0901 1.72299
\(915\) 0 0
\(916\) −32.7987 −1.08370
\(917\) −9.14791 −0.302091
\(918\) 17.0153 0.561590
\(919\) 28.4860 0.939668 0.469834 0.882755i \(-0.344314\pi\)
0.469834 + 0.882755i \(0.344314\pi\)
\(920\) 0 0
\(921\) 3.28100 0.108112
\(922\) −15.9350 −0.524791
\(923\) 5.67961 0.186947
\(924\) −5.25125 −0.172754
\(925\) 0 0
\(926\) 75.6209 2.48506
\(927\) −14.8611 −0.488103
\(928\) −22.4433 −0.736737
\(929\) −29.8029 −0.977801 −0.488900 0.872340i \(-0.662602\pi\)
−0.488900 + 0.872340i \(0.662602\pi\)
\(930\) 0 0
\(931\) 17.0595 0.559104
\(932\) −39.1359 −1.28194
\(933\) −4.77760 −0.156412
\(934\) 3.12511 0.102257
\(935\) 0 0
\(936\) 0.814362 0.0266183
\(937\) −8.54890 −0.279281 −0.139640 0.990202i \(-0.544595\pi\)
−0.139640 + 0.990202i \(0.544595\pi\)
\(938\) 10.6304 0.347096
\(939\) −3.72605 −0.121595
\(940\) 0 0
\(941\) −5.33942 −0.174060 −0.0870300 0.996206i \(-0.527738\pi\)
−0.0870300 + 0.996206i \(0.527738\pi\)
\(942\) 23.0967 0.752531
\(943\) 14.4869 0.471757
\(944\) −25.4875 −0.829547
\(945\) 0 0
\(946\) 62.1096 2.01936
\(947\) −24.4488 −0.794481 −0.397240 0.917715i \(-0.630032\pi\)
−0.397240 + 0.917715i \(0.630032\pi\)
\(948\) −15.0556 −0.488983
\(949\) −8.05100 −0.261346
\(950\) 0 0
\(951\) 10.4544 0.339007
\(952\) −1.58998 −0.0515316
\(953\) 42.1998 1.36699 0.683493 0.729957i \(-0.260460\pi\)
0.683493 + 0.729957i \(0.260460\pi\)
\(954\) 12.4388 0.402720
\(955\) 0 0
\(956\) −5.31657 −0.171950
\(957\) −9.46667 −0.306014
\(958\) −52.4462 −1.69446
\(959\) 5.20443 0.168060
\(960\) 0 0
\(961\) −9.89795 −0.319289
\(962\) −9.38059 −0.302442
\(963\) −18.8563 −0.607636
\(964\) 1.69651 0.0546410
\(965\) 0 0
\(966\) 7.59241 0.244282
\(967\) −12.1031 −0.389211 −0.194605 0.980882i \(-0.562343\pi\)
−0.194605 + 0.980882i \(0.562343\pi\)
\(968\) 12.4329 0.399607
\(969\) −4.38928 −0.141004
\(970\) 0 0
\(971\) 5.26565 0.168983 0.0844913 0.996424i \(-0.473073\pi\)
0.0844913 + 0.996424i \(0.473073\pi\)
\(972\) 22.1025 0.708937
\(973\) −7.56641 −0.242568
\(974\) −31.0422 −0.994657
\(975\) 0 0
\(976\) 51.7083 1.65514
\(977\) 9.31335 0.297961 0.148980 0.988840i \(-0.452401\pi\)
0.148980 + 0.988840i \(0.452401\pi\)
\(978\) −13.4174 −0.429041
\(979\) 75.4130 2.41021
\(980\) 0 0
\(981\) 19.7205 0.629628
\(982\) 26.8734 0.857564
\(983\) −27.0262 −0.862003 −0.431002 0.902351i \(-0.641840\pi\)
−0.431002 + 0.902351i \(0.641840\pi\)
\(984\) 0.649943 0.0207194
\(985\) 0 0
\(986\) 16.0231 0.510278
\(987\) −0.728767 −0.0231969
\(988\) 2.48441 0.0790397
\(989\) −41.2136 −1.31052
\(990\) 0 0
\(991\) −22.7776 −0.723554 −0.361777 0.932265i \(-0.617830\pi\)
−0.361777 + 0.932265i \(0.617830\pi\)
\(992\) −34.5145 −1.09584
\(993\) −5.65345 −0.179407
\(994\) −20.5493 −0.651783
\(995\) 0 0
\(996\) −6.27904 −0.198959
\(997\) 24.9695 0.790791 0.395395 0.918511i \(-0.370608\pi\)
0.395395 + 0.918511i \(0.370608\pi\)
\(998\) −26.0670 −0.825135
\(999\) 29.8197 0.943453
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.1.7 46
5.2 odd 4 1205.2.b.c.724.7 46
5.3 odd 4 1205.2.b.c.724.40 yes 46
5.4 even 2 inner 6025.2.a.p.1.40 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.7 46 5.2 odd 4
1205.2.b.c.724.40 yes 46 5.3 odd 4
6025.2.a.p.1.7 46 1.1 even 1 trivial
6025.2.a.p.1.40 46 5.4 even 2 inner