Properties

Label 6001.2.a.d.1.12
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.40063 q^{2} +1.09881 q^{3} +3.76301 q^{4} +3.50161 q^{5} -2.63784 q^{6} -0.487426 q^{7} -4.23233 q^{8} -1.79261 q^{9} +O(q^{10})\) \(q-2.40063 q^{2} +1.09881 q^{3} +3.76301 q^{4} +3.50161 q^{5} -2.63784 q^{6} -0.487426 q^{7} -4.23233 q^{8} -1.79261 q^{9} -8.40605 q^{10} +6.01034 q^{11} +4.13484 q^{12} -4.55832 q^{13} +1.17013 q^{14} +3.84760 q^{15} +2.63423 q^{16} +1.00000 q^{17} +4.30340 q^{18} +6.87329 q^{19} +13.1766 q^{20} -0.535589 q^{21} -14.4286 q^{22} -2.75110 q^{23} -4.65053 q^{24} +7.26125 q^{25} +10.9428 q^{26} -5.26618 q^{27} -1.83419 q^{28} +1.62719 q^{29} -9.23666 q^{30} +7.48845 q^{31} +2.14086 q^{32} +6.60422 q^{33} -2.40063 q^{34} -1.70677 q^{35} -6.74563 q^{36} +10.9773 q^{37} -16.5002 q^{38} -5.00874 q^{39} -14.8200 q^{40} -2.87672 q^{41} +1.28575 q^{42} +4.13799 q^{43} +22.6170 q^{44} -6.27703 q^{45} +6.60437 q^{46} +1.97939 q^{47} +2.89452 q^{48} -6.76242 q^{49} -17.4315 q^{50} +1.09881 q^{51} -17.1530 q^{52} +7.66192 q^{53} +12.6421 q^{54} +21.0458 q^{55} +2.06295 q^{56} +7.55244 q^{57} -3.90628 q^{58} -7.29041 q^{59} +14.4786 q^{60} +1.41542 q^{61} -17.9770 q^{62} +0.873766 q^{63} -10.4079 q^{64} -15.9615 q^{65} -15.8543 q^{66} -4.20163 q^{67} +3.76301 q^{68} -3.02294 q^{69} +4.09732 q^{70} -3.65362 q^{71} +7.58694 q^{72} +2.06241 q^{73} -26.3524 q^{74} +7.97874 q^{75} +25.8643 q^{76} -2.92959 q^{77} +12.0241 q^{78} +4.26027 q^{79} +9.22405 q^{80} -0.408689 q^{81} +6.90593 q^{82} -12.4415 q^{83} -2.01543 q^{84} +3.50161 q^{85} -9.93377 q^{86} +1.78797 q^{87} -25.4378 q^{88} +1.52336 q^{89} +15.0688 q^{90} +2.22184 q^{91} -10.3524 q^{92} +8.22839 q^{93} -4.75179 q^{94} +24.0676 q^{95} +2.35240 q^{96} -4.02291 q^{97} +16.2340 q^{98} -10.7742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40063 −1.69750 −0.848750 0.528794i \(-0.822644\pi\)
−0.848750 + 0.528794i \(0.822644\pi\)
\(3\) 1.09881 0.634399 0.317199 0.948359i \(-0.397258\pi\)
0.317199 + 0.948359i \(0.397258\pi\)
\(4\) 3.76301 1.88151
\(5\) 3.50161 1.56597 0.782983 0.622043i \(-0.213697\pi\)
0.782983 + 0.622043i \(0.213697\pi\)
\(6\) −2.63784 −1.07689
\(7\) −0.487426 −0.184230 −0.0921148 0.995748i \(-0.529363\pi\)
−0.0921148 + 0.995748i \(0.529363\pi\)
\(8\) −4.23233 −1.49636
\(9\) −1.79261 −0.597538
\(10\) −8.40605 −2.65823
\(11\) 6.01034 1.81218 0.906092 0.423080i \(-0.139051\pi\)
0.906092 + 0.423080i \(0.139051\pi\)
\(12\) 4.13484 1.19362
\(13\) −4.55832 −1.26425 −0.632126 0.774866i \(-0.717817\pi\)
−0.632126 + 0.774866i \(0.717817\pi\)
\(14\) 1.17013 0.312730
\(15\) 3.84760 0.993447
\(16\) 2.63423 0.658558
\(17\) 1.00000 0.242536
\(18\) 4.30340 1.01432
\(19\) 6.87329 1.57684 0.788420 0.615137i \(-0.210899\pi\)
0.788420 + 0.615137i \(0.210899\pi\)
\(20\) 13.1766 2.94637
\(21\) −0.535589 −0.116875
\(22\) −14.4286 −3.07618
\(23\) −2.75110 −0.573645 −0.286822 0.957984i \(-0.592599\pi\)
−0.286822 + 0.957984i \(0.592599\pi\)
\(24\) −4.65053 −0.949286
\(25\) 7.26125 1.45225
\(26\) 10.9428 2.14607
\(27\) −5.26618 −1.01348
\(28\) −1.83419 −0.346629
\(29\) 1.62719 0.302161 0.151081 0.988521i \(-0.451725\pi\)
0.151081 + 0.988521i \(0.451725\pi\)
\(30\) −9.23666 −1.68638
\(31\) 7.48845 1.34497 0.672483 0.740113i \(-0.265228\pi\)
0.672483 + 0.740113i \(0.265228\pi\)
\(32\) 2.14086 0.378453
\(33\) 6.60422 1.14965
\(34\) −2.40063 −0.411704
\(35\) −1.70677 −0.288497
\(36\) −6.74563 −1.12427
\(37\) 10.9773 1.80466 0.902330 0.431047i \(-0.141856\pi\)
0.902330 + 0.431047i \(0.141856\pi\)
\(38\) −16.5002 −2.67669
\(39\) −5.00874 −0.802040
\(40\) −14.8200 −2.34324
\(41\) −2.87672 −0.449268 −0.224634 0.974443i \(-0.572119\pi\)
−0.224634 + 0.974443i \(0.572119\pi\)
\(42\) 1.28575 0.198395
\(43\) 4.13799 0.631037 0.315519 0.948919i \(-0.397822\pi\)
0.315519 + 0.948919i \(0.397822\pi\)
\(44\) 22.6170 3.40964
\(45\) −6.27703 −0.935725
\(46\) 6.60437 0.973762
\(47\) 1.97939 0.288724 0.144362 0.989525i \(-0.453887\pi\)
0.144362 + 0.989525i \(0.453887\pi\)
\(48\) 2.89452 0.417789
\(49\) −6.76242 −0.966059
\(50\) −17.4315 −2.46519
\(51\) 1.09881 0.153864
\(52\) −17.1530 −2.37870
\(53\) 7.66192 1.05245 0.526223 0.850347i \(-0.323608\pi\)
0.526223 + 0.850347i \(0.323608\pi\)
\(54\) 12.6421 1.72038
\(55\) 21.0458 2.83782
\(56\) 2.06295 0.275673
\(57\) 7.55244 1.00035
\(58\) −3.90628 −0.512919
\(59\) −7.29041 −0.949131 −0.474566 0.880220i \(-0.657395\pi\)
−0.474566 + 0.880220i \(0.657395\pi\)
\(60\) 14.4786 1.86918
\(61\) 1.41542 0.181226 0.0906129 0.995886i \(-0.471117\pi\)
0.0906129 + 0.995886i \(0.471117\pi\)
\(62\) −17.9770 −2.28308
\(63\) 0.873766 0.110084
\(64\) −10.4079 −1.30098
\(65\) −15.9615 −1.97978
\(66\) −15.8543 −1.95153
\(67\) −4.20163 −0.513310 −0.256655 0.966503i \(-0.582620\pi\)
−0.256655 + 0.966503i \(0.582620\pi\)
\(68\) 3.76301 0.456332
\(69\) −3.02294 −0.363919
\(70\) 4.09732 0.489724
\(71\) −3.65362 −0.433605 −0.216802 0.976216i \(-0.569563\pi\)
−0.216802 + 0.976216i \(0.569563\pi\)
\(72\) 7.58694 0.894130
\(73\) 2.06241 0.241387 0.120693 0.992690i \(-0.461488\pi\)
0.120693 + 0.992690i \(0.461488\pi\)
\(74\) −26.3524 −3.06341
\(75\) 7.97874 0.921305
\(76\) 25.8643 2.96683
\(77\) −2.92959 −0.333858
\(78\) 12.0241 1.36146
\(79\) 4.26027 0.479318 0.239659 0.970857i \(-0.422964\pi\)
0.239659 + 0.970857i \(0.422964\pi\)
\(80\) 9.22405 1.03128
\(81\) −0.408689 −0.0454099
\(82\) 6.90593 0.762632
\(83\) −12.4415 −1.36563 −0.682816 0.730590i \(-0.739245\pi\)
−0.682816 + 0.730590i \(0.739245\pi\)
\(84\) −2.01543 −0.219901
\(85\) 3.50161 0.379803
\(86\) −9.93377 −1.07119
\(87\) 1.78797 0.191691
\(88\) −25.4378 −2.71167
\(89\) 1.52336 0.161476 0.0807378 0.996735i \(-0.474272\pi\)
0.0807378 + 0.996735i \(0.474272\pi\)
\(90\) 15.0688 1.58839
\(91\) 2.22184 0.232913
\(92\) −10.3524 −1.07932
\(93\) 8.22839 0.853245
\(94\) −4.75179 −0.490110
\(95\) 24.0676 2.46928
\(96\) 2.35240 0.240090
\(97\) −4.02291 −0.408464 −0.204232 0.978922i \(-0.565470\pi\)
−0.204232 + 0.978922i \(0.565470\pi\)
\(98\) 16.2340 1.63989
\(99\) −10.7742 −1.08285
\(100\) 27.3242 2.73242
\(101\) −12.6927 −1.26297 −0.631487 0.775386i \(-0.717555\pi\)
−0.631487 + 0.775386i \(0.717555\pi\)
\(102\) −2.63784 −0.261185
\(103\) −3.53486 −0.348300 −0.174150 0.984719i \(-0.555718\pi\)
−0.174150 + 0.984719i \(0.555718\pi\)
\(104\) 19.2924 1.89177
\(105\) −1.87542 −0.183022
\(106\) −18.3934 −1.78653
\(107\) −8.31837 −0.804168 −0.402084 0.915603i \(-0.631714\pi\)
−0.402084 + 0.915603i \(0.631714\pi\)
\(108\) −19.8167 −1.90686
\(109\) 9.57657 0.917269 0.458635 0.888625i \(-0.348339\pi\)
0.458635 + 0.888625i \(0.348339\pi\)
\(110\) −50.5232 −4.81720
\(111\) 12.0620 1.14487
\(112\) −1.28399 −0.121326
\(113\) 8.72160 0.820459 0.410230 0.911982i \(-0.365449\pi\)
0.410230 + 0.911982i \(0.365449\pi\)
\(114\) −18.1306 −1.69809
\(115\) −9.63328 −0.898308
\(116\) 6.12313 0.568519
\(117\) 8.17132 0.755439
\(118\) 17.5016 1.61115
\(119\) −0.487426 −0.0446822
\(120\) −16.2843 −1.48655
\(121\) 25.1242 2.28401
\(122\) −3.39789 −0.307631
\(123\) −3.16097 −0.285015
\(124\) 28.1791 2.53056
\(125\) 7.91800 0.708207
\(126\) −2.09759 −0.186868
\(127\) −16.5734 −1.47066 −0.735328 0.677712i \(-0.762972\pi\)
−0.735328 + 0.677712i \(0.762972\pi\)
\(128\) 20.7037 1.82996
\(129\) 4.54687 0.400329
\(130\) 38.3175 3.36067
\(131\) 22.3423 1.95206 0.976028 0.217643i \(-0.0698368\pi\)
0.976028 + 0.217643i \(0.0698368\pi\)
\(132\) 24.8518 2.16307
\(133\) −3.35022 −0.290501
\(134\) 10.0865 0.871344
\(135\) −18.4401 −1.58707
\(136\) −4.23233 −0.362920
\(137\) 13.5185 1.15496 0.577480 0.816405i \(-0.304036\pi\)
0.577480 + 0.816405i \(0.304036\pi\)
\(138\) 7.25696 0.617753
\(139\) −10.7700 −0.913498 −0.456749 0.889596i \(-0.650986\pi\)
−0.456749 + 0.889596i \(0.650986\pi\)
\(140\) −6.42260 −0.542809
\(141\) 2.17498 0.183166
\(142\) 8.77098 0.736044
\(143\) −27.3971 −2.29106
\(144\) −4.72217 −0.393514
\(145\) 5.69778 0.473175
\(146\) −4.95108 −0.409754
\(147\) −7.43062 −0.612867
\(148\) 41.3078 3.39548
\(149\) 16.5397 1.35499 0.677494 0.735528i \(-0.263066\pi\)
0.677494 + 0.735528i \(0.263066\pi\)
\(150\) −19.1540 −1.56392
\(151\) 2.99218 0.243500 0.121750 0.992561i \(-0.461149\pi\)
0.121750 + 0.992561i \(0.461149\pi\)
\(152\) −29.0901 −2.35951
\(153\) −1.79261 −0.144924
\(154\) 7.03286 0.566724
\(155\) 26.2216 2.10617
\(156\) −18.8479 −1.50904
\(157\) −5.68083 −0.453380 −0.226690 0.973967i \(-0.572790\pi\)
−0.226690 + 0.973967i \(0.572790\pi\)
\(158\) −10.2273 −0.813642
\(159\) 8.41900 0.667670
\(160\) 7.49643 0.592645
\(161\) 1.34096 0.105682
\(162\) 0.981110 0.0770833
\(163\) 6.78133 0.531154 0.265577 0.964090i \(-0.414437\pi\)
0.265577 + 0.964090i \(0.414437\pi\)
\(164\) −10.8251 −0.845300
\(165\) 23.1254 1.80031
\(166\) 29.8674 2.31816
\(167\) 1.05966 0.0819987 0.0409994 0.999159i \(-0.486946\pi\)
0.0409994 + 0.999159i \(0.486946\pi\)
\(168\) 2.26679 0.174887
\(169\) 7.77832 0.598332
\(170\) −8.40605 −0.644715
\(171\) −12.3212 −0.942222
\(172\) 15.5713 1.18730
\(173\) −8.21664 −0.624699 −0.312350 0.949967i \(-0.601116\pi\)
−0.312350 + 0.949967i \(0.601116\pi\)
\(174\) −4.29226 −0.325395
\(175\) −3.53932 −0.267547
\(176\) 15.8326 1.19343
\(177\) −8.01079 −0.602128
\(178\) −3.65702 −0.274105
\(179\) 8.38918 0.627037 0.313518 0.949582i \(-0.398492\pi\)
0.313518 + 0.949582i \(0.398492\pi\)
\(180\) −23.6205 −1.76057
\(181\) 0.124965 0.00928854 0.00464427 0.999989i \(-0.498522\pi\)
0.00464427 + 0.999989i \(0.498522\pi\)
\(182\) −5.33382 −0.395369
\(183\) 1.55528 0.114969
\(184\) 11.6436 0.858376
\(185\) 38.4382 2.82604
\(186\) −19.7533 −1.44838
\(187\) 6.01034 0.439519
\(188\) 7.44848 0.543237
\(189\) 2.56687 0.186712
\(190\) −57.7772 −4.19160
\(191\) 10.3647 0.749965 0.374982 0.927032i \(-0.377649\pi\)
0.374982 + 0.927032i \(0.377649\pi\)
\(192\) −11.4363 −0.825342
\(193\) −10.5637 −0.760394 −0.380197 0.924905i \(-0.624144\pi\)
−0.380197 + 0.924905i \(0.624144\pi\)
\(194\) 9.65750 0.693368
\(195\) −17.5386 −1.25597
\(196\) −25.4471 −1.81765
\(197\) 7.75272 0.552359 0.276179 0.961106i \(-0.410932\pi\)
0.276179 + 0.961106i \(0.410932\pi\)
\(198\) 25.8649 1.83814
\(199\) 23.9183 1.69552 0.847760 0.530379i \(-0.177950\pi\)
0.847760 + 0.530379i \(0.177950\pi\)
\(200\) −30.7320 −2.17308
\(201\) −4.61679 −0.325644
\(202\) 30.4705 2.14390
\(203\) −0.793134 −0.0556671
\(204\) 4.13484 0.289497
\(205\) −10.0731 −0.703538
\(206\) 8.48589 0.591240
\(207\) 4.93167 0.342775
\(208\) −12.0077 −0.832584
\(209\) 41.3108 2.85753
\(210\) 4.50219 0.310680
\(211\) 23.0644 1.58782 0.793908 0.608037i \(-0.208043\pi\)
0.793908 + 0.608037i \(0.208043\pi\)
\(212\) 28.8319 1.98018
\(213\) −4.01464 −0.275078
\(214\) 19.9693 1.36507
\(215\) 14.4896 0.988183
\(216\) 22.2882 1.51652
\(217\) −3.65006 −0.247782
\(218\) −22.9898 −1.55706
\(219\) 2.26620 0.153136
\(220\) 79.1957 5.33937
\(221\) −4.55832 −0.306626
\(222\) −28.9563 −1.94342
\(223\) 10.5482 0.706360 0.353180 0.935555i \(-0.385100\pi\)
0.353180 + 0.935555i \(0.385100\pi\)
\(224\) −1.04351 −0.0697223
\(225\) −13.0166 −0.867775
\(226\) −20.9373 −1.39273
\(227\) −2.92631 −0.194226 −0.0971129 0.995273i \(-0.530961\pi\)
−0.0971129 + 0.995273i \(0.530961\pi\)
\(228\) 28.4199 1.88216
\(229\) 9.67358 0.639248 0.319624 0.947544i \(-0.396443\pi\)
0.319624 + 0.947544i \(0.396443\pi\)
\(230\) 23.1259 1.52488
\(231\) −3.21907 −0.211799
\(232\) −6.88681 −0.452141
\(233\) −18.7384 −1.22759 −0.613797 0.789464i \(-0.710359\pi\)
−0.613797 + 0.789464i \(0.710359\pi\)
\(234\) −19.6163 −1.28236
\(235\) 6.93106 0.452133
\(236\) −27.4339 −1.78580
\(237\) 4.68123 0.304079
\(238\) 1.17013 0.0758481
\(239\) −28.2400 −1.82669 −0.913347 0.407183i \(-0.866511\pi\)
−0.913347 + 0.407183i \(0.866511\pi\)
\(240\) 10.1355 0.654243
\(241\) −8.08882 −0.521047 −0.260523 0.965468i \(-0.583895\pi\)
−0.260523 + 0.965468i \(0.583895\pi\)
\(242\) −60.3137 −3.87711
\(243\) 15.3495 0.984668
\(244\) 5.32624 0.340977
\(245\) −23.6793 −1.51282
\(246\) 7.58831 0.483813
\(247\) −31.3307 −1.99352
\(248\) −31.6936 −2.01255
\(249\) −13.6709 −0.866356
\(250\) −19.0082 −1.20218
\(251\) 5.95958 0.376165 0.188083 0.982153i \(-0.439773\pi\)
0.188083 + 0.982153i \(0.439773\pi\)
\(252\) 3.28799 0.207124
\(253\) −16.5351 −1.03955
\(254\) 39.7867 2.49644
\(255\) 3.84760 0.240946
\(256\) −28.8861 −1.80538
\(257\) 13.3879 0.835117 0.417558 0.908650i \(-0.362886\pi\)
0.417558 + 0.908650i \(0.362886\pi\)
\(258\) −10.9153 −0.679559
\(259\) −5.35062 −0.332472
\(260\) −60.0632 −3.72496
\(261\) −2.91692 −0.180553
\(262\) −53.6356 −3.31362
\(263\) −13.2960 −0.819864 −0.409932 0.912116i \(-0.634448\pi\)
−0.409932 + 0.912116i \(0.634448\pi\)
\(264\) −27.9513 −1.72028
\(265\) 26.8290 1.64809
\(266\) 8.04262 0.493125
\(267\) 1.67388 0.102440
\(268\) −15.8108 −0.965797
\(269\) −7.95143 −0.484807 −0.242403 0.970176i \(-0.577936\pi\)
−0.242403 + 0.970176i \(0.577936\pi\)
\(270\) 44.2678 2.69405
\(271\) −30.8478 −1.87387 −0.936935 0.349504i \(-0.886350\pi\)
−0.936935 + 0.349504i \(0.886350\pi\)
\(272\) 2.63423 0.159724
\(273\) 2.44139 0.147759
\(274\) −32.4528 −1.96055
\(275\) 43.6425 2.63174
\(276\) −11.3754 −0.684716
\(277\) −25.6404 −1.54058 −0.770290 0.637693i \(-0.779889\pi\)
−0.770290 + 0.637693i \(0.779889\pi\)
\(278\) 25.8547 1.55066
\(279\) −13.4239 −0.803668
\(280\) 7.22363 0.431695
\(281\) 27.0485 1.61358 0.806791 0.590838i \(-0.201203\pi\)
0.806791 + 0.590838i \(0.201203\pi\)
\(282\) −5.22132 −0.310925
\(283\) −4.26410 −0.253474 −0.126737 0.991936i \(-0.540450\pi\)
−0.126737 + 0.991936i \(0.540450\pi\)
\(284\) −13.7486 −0.815830
\(285\) 26.4457 1.56651
\(286\) 65.7701 3.88907
\(287\) 1.40219 0.0827684
\(288\) −3.83773 −0.226140
\(289\) 1.00000 0.0588235
\(290\) −13.6782 −0.803214
\(291\) −4.42042 −0.259129
\(292\) 7.76088 0.454171
\(293\) 3.58060 0.209181 0.104591 0.994515i \(-0.466647\pi\)
0.104591 + 0.994515i \(0.466647\pi\)
\(294\) 17.8381 1.04034
\(295\) −25.5282 −1.48631
\(296\) −46.4597 −2.70041
\(297\) −31.6515 −1.83661
\(298\) −39.7058 −2.30009
\(299\) 12.5404 0.725231
\(300\) 30.0241 1.73344
\(301\) −2.01696 −0.116256
\(302\) −7.18311 −0.413341
\(303\) −13.9469 −0.801229
\(304\) 18.1058 1.03844
\(305\) 4.95624 0.283793
\(306\) 4.30340 0.246009
\(307\) −10.7728 −0.614837 −0.307418 0.951574i \(-0.599465\pi\)
−0.307418 + 0.951574i \(0.599465\pi\)
\(308\) −11.0241 −0.628156
\(309\) −3.88415 −0.220961
\(310\) −62.9483 −3.57522
\(311\) 25.1093 1.42382 0.711909 0.702271i \(-0.247831\pi\)
0.711909 + 0.702271i \(0.247831\pi\)
\(312\) 21.1986 1.20014
\(313\) 27.2336 1.53933 0.769666 0.638447i \(-0.220423\pi\)
0.769666 + 0.638447i \(0.220423\pi\)
\(314\) 13.6376 0.769612
\(315\) 3.05959 0.172388
\(316\) 16.0315 0.901840
\(317\) −1.32101 −0.0741952 −0.0370976 0.999312i \(-0.511811\pi\)
−0.0370976 + 0.999312i \(0.511811\pi\)
\(318\) −20.2109 −1.13337
\(319\) 9.77996 0.547572
\(320\) −36.4442 −2.03729
\(321\) −9.14032 −0.510163
\(322\) −3.21914 −0.179396
\(323\) 6.87329 0.382440
\(324\) −1.53790 −0.0854390
\(325\) −33.0991 −1.83601
\(326\) −16.2794 −0.901635
\(327\) 10.5228 0.581915
\(328\) 12.1752 0.672265
\(329\) −0.964807 −0.0531916
\(330\) −55.5155 −3.05602
\(331\) 6.96486 0.382823 0.191412 0.981510i \(-0.438693\pi\)
0.191412 + 0.981510i \(0.438693\pi\)
\(332\) −46.8175 −2.56945
\(333\) −19.6781 −1.07835
\(334\) −2.54384 −0.139193
\(335\) −14.7124 −0.803827
\(336\) −1.41087 −0.0769690
\(337\) −14.4699 −0.788224 −0.394112 0.919062i \(-0.628948\pi\)
−0.394112 + 0.919062i \(0.628948\pi\)
\(338\) −18.6729 −1.01567
\(339\) 9.58339 0.520498
\(340\) 13.1766 0.714601
\(341\) 45.0081 2.43733
\(342\) 29.5785 1.59942
\(343\) 6.70815 0.362206
\(344\) −17.5133 −0.944256
\(345\) −10.5852 −0.569885
\(346\) 19.7251 1.06043
\(347\) −5.14523 −0.276210 −0.138105 0.990418i \(-0.544101\pi\)
−0.138105 + 0.990418i \(0.544101\pi\)
\(348\) 6.72816 0.360667
\(349\) 2.65429 0.142081 0.0710404 0.997473i \(-0.477368\pi\)
0.0710404 + 0.997473i \(0.477368\pi\)
\(350\) 8.49658 0.454161
\(351\) 24.0049 1.28129
\(352\) 12.8673 0.685827
\(353\) −1.00000 −0.0532246
\(354\) 19.2309 1.02211
\(355\) −12.7935 −0.679010
\(356\) 5.73241 0.303817
\(357\) −0.535589 −0.0283464
\(358\) −20.1393 −1.06439
\(359\) −15.4706 −0.816507 −0.408253 0.912869i \(-0.633862\pi\)
−0.408253 + 0.912869i \(0.633862\pi\)
\(360\) 26.5665 1.40018
\(361\) 28.2421 1.48643
\(362\) −0.299993 −0.0157673
\(363\) 27.6067 1.44898
\(364\) 8.36082 0.438226
\(365\) 7.22175 0.378004
\(366\) −3.73364 −0.195161
\(367\) 18.1620 0.948051 0.474026 0.880511i \(-0.342800\pi\)
0.474026 + 0.880511i \(0.342800\pi\)
\(368\) −7.24705 −0.377778
\(369\) 5.15685 0.268455
\(370\) −92.2759 −4.79719
\(371\) −3.73462 −0.193892
\(372\) 30.9635 1.60538
\(373\) 23.9183 1.23844 0.619222 0.785216i \(-0.287448\pi\)
0.619222 + 0.785216i \(0.287448\pi\)
\(374\) −14.4286 −0.746084
\(375\) 8.70038 0.449286
\(376\) −8.37746 −0.432034
\(377\) −7.41726 −0.382008
\(378\) −6.16210 −0.316944
\(379\) −23.3987 −1.20191 −0.600956 0.799282i \(-0.705213\pi\)
−0.600956 + 0.799282i \(0.705213\pi\)
\(380\) 90.5665 4.64596
\(381\) −18.2111 −0.932982
\(382\) −24.8818 −1.27306
\(383\) −8.14655 −0.416269 −0.208135 0.978100i \(-0.566739\pi\)
−0.208135 + 0.978100i \(0.566739\pi\)
\(384\) 22.7494 1.16093
\(385\) −10.2583 −0.522810
\(386\) 25.3596 1.29077
\(387\) −7.41782 −0.377069
\(388\) −15.1383 −0.768528
\(389\) −31.5196 −1.59811 −0.799055 0.601258i \(-0.794666\pi\)
−0.799055 + 0.601258i \(0.794666\pi\)
\(390\) 42.1037 2.13200
\(391\) −2.75110 −0.139129
\(392\) 28.6208 1.44557
\(393\) 24.5500 1.23838
\(394\) −18.6114 −0.937628
\(395\) 14.9178 0.750596
\(396\) −40.5435 −2.03739
\(397\) −23.9201 −1.20052 −0.600258 0.799807i \(-0.704935\pi\)
−0.600258 + 0.799807i \(0.704935\pi\)
\(398\) −57.4188 −2.87815
\(399\) −3.68125 −0.184293
\(400\) 19.1278 0.956391
\(401\) 27.8501 1.39077 0.695383 0.718640i \(-0.255235\pi\)
0.695383 + 0.718640i \(0.255235\pi\)
\(402\) 11.0832 0.552780
\(403\) −34.1348 −1.70038
\(404\) −47.7629 −2.37629
\(405\) −1.43107 −0.0711103
\(406\) 1.90402 0.0944948
\(407\) 65.9774 3.27038
\(408\) −4.65053 −0.230236
\(409\) 5.65405 0.279575 0.139787 0.990182i \(-0.455358\pi\)
0.139787 + 0.990182i \(0.455358\pi\)
\(410\) 24.1819 1.19426
\(411\) 14.8542 0.732706
\(412\) −13.3017 −0.655329
\(413\) 3.55353 0.174858
\(414\) −11.8391 −0.581860
\(415\) −43.5653 −2.13853
\(416\) −9.75871 −0.478460
\(417\) −11.8342 −0.579522
\(418\) −99.1718 −4.85065
\(419\) 12.0032 0.586395 0.293198 0.956052i \(-0.405281\pi\)
0.293198 + 0.956052i \(0.405281\pi\)
\(420\) −7.05723 −0.344357
\(421\) −35.1370 −1.71247 −0.856236 0.516585i \(-0.827203\pi\)
−0.856236 + 0.516585i \(0.827203\pi\)
\(422\) −55.3690 −2.69532
\(423\) −3.54829 −0.172524
\(424\) −32.4278 −1.57483
\(425\) 7.26125 0.352222
\(426\) 9.63765 0.466946
\(427\) −0.689911 −0.0333871
\(428\) −31.3021 −1.51305
\(429\) −30.1042 −1.45344
\(430\) −34.7841 −1.67744
\(431\) 34.7262 1.67270 0.836350 0.548195i \(-0.184685\pi\)
0.836350 + 0.548195i \(0.184685\pi\)
\(432\) −13.8723 −0.667433
\(433\) −2.03217 −0.0976601 −0.0488300 0.998807i \(-0.515549\pi\)
−0.0488300 + 0.998807i \(0.515549\pi\)
\(434\) 8.76244 0.420611
\(435\) 6.26078 0.300181
\(436\) 36.0368 1.72585
\(437\) −18.9091 −0.904546
\(438\) −5.44030 −0.259948
\(439\) 3.08615 0.147294 0.0736469 0.997284i \(-0.476536\pi\)
0.0736469 + 0.997284i \(0.476536\pi\)
\(440\) −89.0730 −4.24639
\(441\) 12.1224 0.577257
\(442\) 10.9428 0.520498
\(443\) −24.7452 −1.17568 −0.587841 0.808977i \(-0.700022\pi\)
−0.587841 + 0.808977i \(0.700022\pi\)
\(444\) 45.3894 2.15409
\(445\) 5.33420 0.252865
\(446\) −25.3223 −1.19905
\(447\) 18.1741 0.859603
\(448\) 5.07306 0.239679
\(449\) 39.7187 1.87444 0.937220 0.348740i \(-0.113390\pi\)
0.937220 + 0.348740i \(0.113390\pi\)
\(450\) 31.2481 1.47305
\(451\) −17.2901 −0.814157
\(452\) 32.8195 1.54370
\(453\) 3.28784 0.154476
\(454\) 7.02497 0.329698
\(455\) 7.78002 0.364733
\(456\) −31.9645 −1.49687
\(457\) −2.21351 −0.103544 −0.0517719 0.998659i \(-0.516487\pi\)
−0.0517719 + 0.998659i \(0.516487\pi\)
\(458\) −23.2227 −1.08512
\(459\) −5.26618 −0.245804
\(460\) −36.2501 −1.69017
\(461\) −10.1273 −0.471676 −0.235838 0.971792i \(-0.575783\pi\)
−0.235838 + 0.971792i \(0.575783\pi\)
\(462\) 7.72778 0.359529
\(463\) −32.0874 −1.49123 −0.745613 0.666379i \(-0.767843\pi\)
−0.745613 + 0.666379i \(0.767843\pi\)
\(464\) 4.28640 0.198991
\(465\) 28.8126 1.33615
\(466\) 44.9840 2.08384
\(467\) 0.0194297 0.000899101 0 0.000449551 1.00000i \(-0.499857\pi\)
0.000449551 1.00000i \(0.499857\pi\)
\(468\) 30.7488 1.42136
\(469\) 2.04798 0.0945670
\(470\) −16.6389 −0.767495
\(471\) −6.24216 −0.287624
\(472\) 30.8555 1.42024
\(473\) 24.8707 1.14356
\(474\) −11.2379 −0.516174
\(475\) 49.9086 2.28997
\(476\) −1.83419 −0.0840699
\(477\) −13.7349 −0.628876
\(478\) 67.7937 3.10081
\(479\) −30.2491 −1.38212 −0.691059 0.722798i \(-0.742856\pi\)
−0.691059 + 0.722798i \(0.742856\pi\)
\(480\) 8.23716 0.375973
\(481\) −50.0382 −2.28154
\(482\) 19.4183 0.884477
\(483\) 1.47346 0.0670447
\(484\) 94.5425 4.29739
\(485\) −14.0866 −0.639641
\(486\) −36.8483 −1.67147
\(487\) 30.2718 1.37175 0.685873 0.727721i \(-0.259421\pi\)
0.685873 + 0.727721i \(0.259421\pi\)
\(488\) −5.99052 −0.271178
\(489\) 7.45139 0.336964
\(490\) 56.8452 2.56801
\(491\) 2.46502 0.111245 0.0556224 0.998452i \(-0.482286\pi\)
0.0556224 + 0.998452i \(0.482286\pi\)
\(492\) −11.8948 −0.536258
\(493\) 1.62719 0.0732849
\(494\) 75.2133 3.38401
\(495\) −37.7271 −1.69571
\(496\) 19.7263 0.885738
\(497\) 1.78087 0.0798828
\(498\) 32.8186 1.47064
\(499\) 26.1103 1.16886 0.584428 0.811445i \(-0.301319\pi\)
0.584428 + 0.811445i \(0.301319\pi\)
\(500\) 29.7955 1.33250
\(501\) 1.16436 0.0520199
\(502\) −14.3067 −0.638541
\(503\) 34.7378 1.54888 0.774441 0.632647i \(-0.218031\pi\)
0.774441 + 0.632647i \(0.218031\pi\)
\(504\) −3.69807 −0.164725
\(505\) −44.4450 −1.97777
\(506\) 39.6945 1.76464
\(507\) 8.54690 0.379581
\(508\) −62.3661 −2.76705
\(509\) 27.7376 1.22945 0.614724 0.788742i \(-0.289267\pi\)
0.614724 + 0.788742i \(0.289267\pi\)
\(510\) −9.23666 −0.409006
\(511\) −1.00527 −0.0444706
\(512\) 27.9374 1.23467
\(513\) −36.1960 −1.59809
\(514\) −32.1394 −1.41761
\(515\) −12.3777 −0.545427
\(516\) 17.1099 0.753222
\(517\) 11.8968 0.523222
\(518\) 12.8449 0.564370
\(519\) −9.02853 −0.396309
\(520\) 67.5542 2.96245
\(521\) −18.2058 −0.797611 −0.398806 0.917036i \(-0.630575\pi\)
−0.398806 + 0.917036i \(0.630575\pi\)
\(522\) 7.00245 0.306489
\(523\) −24.5032 −1.07145 −0.535724 0.844393i \(-0.679961\pi\)
−0.535724 + 0.844393i \(0.679961\pi\)
\(524\) 84.0744 3.67281
\(525\) −3.88904 −0.169732
\(526\) 31.9187 1.39172
\(527\) 7.48845 0.326202
\(528\) 17.3971 0.757110
\(529\) −15.4314 −0.670932
\(530\) −64.4065 −2.79764
\(531\) 13.0689 0.567142
\(532\) −12.6069 −0.546579
\(533\) 13.1130 0.567988
\(534\) −4.01837 −0.173892
\(535\) −29.1277 −1.25930
\(536\) 17.7827 0.768095
\(537\) 9.21812 0.397791
\(538\) 19.0884 0.822960
\(539\) −40.6444 −1.75068
\(540\) −69.3902 −2.98608
\(541\) 29.1054 1.25134 0.625669 0.780088i \(-0.284826\pi\)
0.625669 + 0.780088i \(0.284826\pi\)
\(542\) 74.0541 3.18089
\(543\) 0.137312 0.00589264
\(544\) 2.14086 0.0917884
\(545\) 33.5334 1.43641
\(546\) −5.86086 −0.250822
\(547\) 14.9512 0.639268 0.319634 0.947541i \(-0.396440\pi\)
0.319634 + 0.947541i \(0.396440\pi\)
\(548\) 50.8702 2.17307
\(549\) −2.53730 −0.108289
\(550\) −104.769 −4.46739
\(551\) 11.1841 0.476460
\(552\) 12.7941 0.544553
\(553\) −2.07657 −0.0883045
\(554\) 61.5530 2.61514
\(555\) 42.2364 1.79283
\(556\) −40.5276 −1.71875
\(557\) 2.28629 0.0968733 0.0484366 0.998826i \(-0.484576\pi\)
0.0484366 + 0.998826i \(0.484576\pi\)
\(558\) 32.2258 1.36423
\(559\) −18.8623 −0.797790
\(560\) −4.49604 −0.189992
\(561\) 6.60422 0.278831
\(562\) −64.9335 −2.73905
\(563\) 27.5689 1.16189 0.580946 0.813942i \(-0.302683\pi\)
0.580946 + 0.813942i \(0.302683\pi\)
\(564\) 8.18448 0.344629
\(565\) 30.5396 1.28481
\(566\) 10.2365 0.430273
\(567\) 0.199205 0.00836584
\(568\) 15.4633 0.648827
\(569\) −4.68379 −0.196355 −0.0981774 0.995169i \(-0.531301\pi\)
−0.0981774 + 0.995169i \(0.531301\pi\)
\(570\) −63.4862 −2.65915
\(571\) −39.4381 −1.65043 −0.825216 0.564818i \(-0.808947\pi\)
−0.825216 + 0.564818i \(0.808947\pi\)
\(572\) −103.095 −4.31064
\(573\) 11.3889 0.475777
\(574\) −3.36613 −0.140499
\(575\) −19.9764 −0.833075
\(576\) 18.6573 0.777387
\(577\) −39.4245 −1.64126 −0.820632 0.571457i \(-0.806378\pi\)
−0.820632 + 0.571457i \(0.806378\pi\)
\(578\) −2.40063 −0.0998529
\(579\) −11.6075 −0.482393
\(580\) 21.4408 0.890281
\(581\) 6.06431 0.251590
\(582\) 10.6118 0.439872
\(583\) 46.0507 1.90723
\(584\) −8.72881 −0.361201
\(585\) 28.6127 1.18299
\(586\) −8.59569 −0.355085
\(587\) 11.7564 0.485239 0.242620 0.970122i \(-0.421993\pi\)
0.242620 + 0.970122i \(0.421993\pi\)
\(588\) −27.9615 −1.15311
\(589\) 51.4703 2.12080
\(590\) 61.2836 2.52301
\(591\) 8.51877 0.350416
\(592\) 28.9168 1.18847
\(593\) 25.4062 1.04331 0.521654 0.853157i \(-0.325315\pi\)
0.521654 + 0.853157i \(0.325315\pi\)
\(594\) 75.9835 3.11764
\(595\) −1.70677 −0.0699709
\(596\) 62.2393 2.54942
\(597\) 26.2817 1.07564
\(598\) −30.1049 −1.23108
\(599\) 27.7028 1.13191 0.565954 0.824437i \(-0.308508\pi\)
0.565954 + 0.824437i \(0.308508\pi\)
\(600\) −33.7687 −1.37860
\(601\) 40.0846 1.63508 0.817542 0.575869i \(-0.195336\pi\)
0.817542 + 0.575869i \(0.195336\pi\)
\(602\) 4.84197 0.197344
\(603\) 7.53190 0.306723
\(604\) 11.2596 0.458147
\(605\) 87.9749 3.57669
\(606\) 33.4813 1.36009
\(607\) 25.7499 1.04516 0.522578 0.852591i \(-0.324970\pi\)
0.522578 + 0.852591i \(0.324970\pi\)
\(608\) 14.7147 0.596761
\(609\) −0.871504 −0.0353151
\(610\) −11.8981 −0.481739
\(611\) −9.02272 −0.365020
\(612\) −6.74563 −0.272676
\(613\) 5.55352 0.224305 0.112152 0.993691i \(-0.464226\pi\)
0.112152 + 0.993691i \(0.464226\pi\)
\(614\) 25.8615 1.04369
\(615\) −11.0685 −0.446324
\(616\) 12.3990 0.499570
\(617\) 25.6171 1.03131 0.515653 0.856797i \(-0.327549\pi\)
0.515653 + 0.856797i \(0.327549\pi\)
\(618\) 9.32439 0.375082
\(619\) −27.7032 −1.11349 −0.556743 0.830685i \(-0.687949\pi\)
−0.556743 + 0.830685i \(0.687949\pi\)
\(620\) 98.6722 3.96277
\(621\) 14.4878 0.581375
\(622\) −60.2781 −2.41693
\(623\) −0.742524 −0.0297486
\(624\) −13.1942 −0.528190
\(625\) −8.58052 −0.343221
\(626\) −65.3777 −2.61302
\(627\) 45.3927 1.81281
\(628\) −21.3770 −0.853037
\(629\) 10.9773 0.437694
\(630\) −7.34492 −0.292629
\(631\) −42.3152 −1.68454 −0.842272 0.539053i \(-0.818782\pi\)
−0.842272 + 0.539053i \(0.818782\pi\)
\(632\) −18.0309 −0.717230
\(633\) 25.3434 1.00731
\(634\) 3.17125 0.125946
\(635\) −58.0337 −2.30300
\(636\) 31.6808 1.25623
\(637\) 30.8253 1.22134
\(638\) −23.4780 −0.929504
\(639\) 6.54953 0.259095
\(640\) 72.4962 2.86566
\(641\) −7.04179 −0.278134 −0.139067 0.990283i \(-0.544410\pi\)
−0.139067 + 0.990283i \(0.544410\pi\)
\(642\) 21.9425 0.866001
\(643\) −39.6442 −1.56342 −0.781708 0.623645i \(-0.785651\pi\)
−0.781708 + 0.623645i \(0.785651\pi\)
\(644\) 5.04604 0.198842
\(645\) 15.9213 0.626902
\(646\) −16.5002 −0.649192
\(647\) −19.5614 −0.769038 −0.384519 0.923117i \(-0.625633\pi\)
−0.384519 + 0.923117i \(0.625633\pi\)
\(648\) 1.72971 0.0679493
\(649\) −43.8178 −1.72000
\(650\) 79.4587 3.11663
\(651\) −4.01073 −0.157193
\(652\) 25.5182 0.999370
\(653\) 3.79297 0.148431 0.0742153 0.997242i \(-0.476355\pi\)
0.0742153 + 0.997242i \(0.476355\pi\)
\(654\) −25.2614 −0.987800
\(655\) 78.2340 3.05685
\(656\) −7.57795 −0.295869
\(657\) −3.69711 −0.144238
\(658\) 2.31614 0.0902927
\(659\) −1.99727 −0.0778025 −0.0389013 0.999243i \(-0.512386\pi\)
−0.0389013 + 0.999243i \(0.512386\pi\)
\(660\) 87.0211 3.38729
\(661\) 12.3236 0.479331 0.239665 0.970856i \(-0.422962\pi\)
0.239665 + 0.970856i \(0.422962\pi\)
\(662\) −16.7200 −0.649842
\(663\) −5.00874 −0.194523
\(664\) 52.6566 2.04347
\(665\) −11.7311 −0.454914
\(666\) 47.2398 1.83050
\(667\) −4.47656 −0.173333
\(668\) 3.98750 0.154281
\(669\) 11.5905 0.448114
\(670\) 35.3191 1.36450
\(671\) 8.50714 0.328415
\(672\) −1.14662 −0.0442317
\(673\) −0.917475 −0.0353661 −0.0176830 0.999844i \(-0.505629\pi\)
−0.0176830 + 0.999844i \(0.505629\pi\)
\(674\) 34.7368 1.33801
\(675\) −38.2390 −1.47182
\(676\) 29.2699 1.12577
\(677\) 42.5417 1.63501 0.817505 0.575922i \(-0.195357\pi\)
0.817505 + 0.575922i \(0.195357\pi\)
\(678\) −23.0062 −0.883546
\(679\) 1.96087 0.0752512
\(680\) −14.8200 −0.568320
\(681\) −3.21546 −0.123217
\(682\) −108.048 −4.13736
\(683\) −19.7735 −0.756613 −0.378307 0.925680i \(-0.623494\pi\)
−0.378307 + 0.925680i \(0.623494\pi\)
\(684\) −46.3647 −1.77280
\(685\) 47.3364 1.80863
\(686\) −16.1038 −0.614845
\(687\) 10.6294 0.405538
\(688\) 10.9004 0.415575
\(689\) −34.9255 −1.33056
\(690\) 25.4110 0.967380
\(691\) 14.1800 0.539433 0.269716 0.962940i \(-0.413070\pi\)
0.269716 + 0.962940i \(0.413070\pi\)
\(692\) −30.9193 −1.17538
\(693\) 5.25163 0.199493
\(694\) 12.3518 0.468867
\(695\) −37.7122 −1.43051
\(696\) −7.56730 −0.286838
\(697\) −2.87672 −0.108964
\(698\) −6.37196 −0.241182
\(699\) −20.5900 −0.778785
\(700\) −13.3185 −0.503392
\(701\) 16.0119 0.604762 0.302381 0.953187i \(-0.402219\pi\)
0.302381 + 0.953187i \(0.402219\pi\)
\(702\) −57.6269 −2.17499
\(703\) 75.4502 2.84566
\(704\) −62.5548 −2.35762
\(705\) 7.61592 0.286832
\(706\) 2.40063 0.0903488
\(707\) 6.18676 0.232677
\(708\) −30.1447 −1.13291
\(709\) 13.8289 0.519355 0.259678 0.965695i \(-0.416384\pi\)
0.259678 + 0.965695i \(0.416384\pi\)
\(710\) 30.7125 1.15262
\(711\) −7.63703 −0.286411
\(712\) −6.44736 −0.241625
\(713\) −20.6015 −0.771532
\(714\) 1.28575 0.0481179
\(715\) −95.9337 −3.58772
\(716\) 31.5686 1.17977
\(717\) −31.0304 −1.15885
\(718\) 37.1391 1.38602
\(719\) 43.4883 1.62184 0.810920 0.585157i \(-0.198967\pi\)
0.810920 + 0.585157i \(0.198967\pi\)
\(720\) −16.5352 −0.616229
\(721\) 1.72298 0.0641672
\(722\) −67.7987 −2.52321
\(723\) −8.88809 −0.330552
\(724\) 0.470243 0.0174764
\(725\) 11.8154 0.438814
\(726\) −66.2734 −2.45964
\(727\) 10.7642 0.399222 0.199611 0.979875i \(-0.436032\pi\)
0.199611 + 0.979875i \(0.436032\pi\)
\(728\) −9.40359 −0.348520
\(729\) 18.0922 0.670082
\(730\) −17.3367 −0.641661
\(731\) 4.13799 0.153049
\(732\) 5.85253 0.216316
\(733\) −45.4987 −1.68053 −0.840266 0.542174i \(-0.817601\pi\)
−0.840266 + 0.542174i \(0.817601\pi\)
\(734\) −43.6003 −1.60932
\(735\) −26.0191 −0.959729
\(736\) −5.88971 −0.217098
\(737\) −25.2532 −0.930213
\(738\) −12.3797 −0.455702
\(739\) 42.8420 1.57597 0.787984 0.615695i \(-0.211125\pi\)
0.787984 + 0.615695i \(0.211125\pi\)
\(740\) 144.644 5.31720
\(741\) −34.4265 −1.26469
\(742\) 8.96542 0.329131
\(743\) −49.1350 −1.80259 −0.901294 0.433208i \(-0.857381\pi\)
−0.901294 + 0.433208i \(0.857381\pi\)
\(744\) −34.8253 −1.27676
\(745\) 57.9157 2.12187
\(746\) −57.4190 −2.10226
\(747\) 22.3028 0.816018
\(748\) 22.6170 0.826958
\(749\) 4.05459 0.148151
\(750\) −20.8864 −0.762663
\(751\) −0.825863 −0.0301362 −0.0150681 0.999886i \(-0.504797\pi\)
−0.0150681 + 0.999886i \(0.504797\pi\)
\(752\) 5.21419 0.190142
\(753\) 6.54845 0.238639
\(754\) 17.8061 0.648459
\(755\) 10.4774 0.381313
\(756\) 9.65916 0.351300
\(757\) −8.31401 −0.302178 −0.151089 0.988520i \(-0.548278\pi\)
−0.151089 + 0.988520i \(0.548278\pi\)
\(758\) 56.1716 2.04024
\(759\) −18.1689 −0.659489
\(760\) −101.862 −3.69492
\(761\) 16.9711 0.615201 0.307600 0.951516i \(-0.400474\pi\)
0.307600 + 0.951516i \(0.400474\pi\)
\(762\) 43.7180 1.58374
\(763\) −4.66787 −0.168988
\(764\) 39.0025 1.41106
\(765\) −6.27703 −0.226947
\(766\) 19.5568 0.706617
\(767\) 33.2321 1.19994
\(768\) −31.7404 −1.14533
\(769\) −4.43102 −0.159787 −0.0798934 0.996803i \(-0.525458\pi\)
−0.0798934 + 0.996803i \(0.525458\pi\)
\(770\) 24.6263 0.887470
\(771\) 14.7108 0.529797
\(772\) −39.7515 −1.43069
\(773\) 23.1401 0.832291 0.416146 0.909298i \(-0.363381\pi\)
0.416146 + 0.909298i \(0.363381\pi\)
\(774\) 17.8074 0.640074
\(775\) 54.3755 1.95323
\(776\) 17.0263 0.611208
\(777\) −5.87932 −0.210920
\(778\) 75.6669 2.71279
\(779\) −19.7725 −0.708424
\(780\) −65.9980 −2.36311
\(781\) −21.9595 −0.785772
\(782\) 6.60437 0.236172
\(783\) −8.56907 −0.306233
\(784\) −17.8138 −0.636207
\(785\) −19.8920 −0.709977
\(786\) −58.9353 −2.10215
\(787\) 46.8869 1.67134 0.835668 0.549235i \(-0.185081\pi\)
0.835668 + 0.549235i \(0.185081\pi\)
\(788\) 29.1736 1.03927
\(789\) −14.6098 −0.520121
\(790\) −35.8121 −1.27414
\(791\) −4.25113 −0.151153
\(792\) 45.6001 1.62033
\(793\) −6.45194 −0.229115
\(794\) 57.4232 2.03787
\(795\) 29.4800 1.04555
\(796\) 90.0047 3.19013
\(797\) 40.2857 1.42699 0.713496 0.700659i \(-0.247111\pi\)
0.713496 + 0.700659i \(0.247111\pi\)
\(798\) 8.83732 0.312838
\(799\) 1.97939 0.0700259
\(800\) 15.5453 0.549609
\(801\) −2.73079 −0.0964879
\(802\) −66.8576 −2.36082
\(803\) 12.3958 0.437438
\(804\) −17.3730 −0.612700
\(805\) 4.69551 0.165495
\(806\) 81.9449 2.88639
\(807\) −8.73711 −0.307561
\(808\) 53.7199 1.88986
\(809\) −10.4878 −0.368731 −0.184366 0.982858i \(-0.559023\pi\)
−0.184366 + 0.982858i \(0.559023\pi\)
\(810\) 3.43546 0.120710
\(811\) −50.9633 −1.78956 −0.894781 0.446504i \(-0.852669\pi\)
−0.894781 + 0.446504i \(0.852669\pi\)
\(812\) −2.98457 −0.104738
\(813\) −33.8959 −1.18878
\(814\) −158.387 −5.55146
\(815\) 23.7455 0.831770
\(816\) 2.89452 0.101329
\(817\) 28.4416 0.995045
\(818\) −13.5733 −0.474578
\(819\) −3.98291 −0.139174
\(820\) −37.9053 −1.32371
\(821\) −1.48936 −0.0519791 −0.0259896 0.999662i \(-0.508274\pi\)
−0.0259896 + 0.999662i \(0.508274\pi\)
\(822\) −35.6595 −1.24377
\(823\) −44.9827 −1.56800 −0.783999 0.620763i \(-0.786823\pi\)
−0.783999 + 0.620763i \(0.786823\pi\)
\(824\) 14.9607 0.521182
\(825\) 47.9549 1.66958
\(826\) −8.53071 −0.296821
\(827\) −25.5840 −0.889644 −0.444822 0.895619i \(-0.646733\pi\)
−0.444822 + 0.895619i \(0.646733\pi\)
\(828\) 18.5579 0.644932
\(829\) 18.2673 0.634451 0.317226 0.948350i \(-0.397249\pi\)
0.317226 + 0.948350i \(0.397249\pi\)
\(830\) 104.584 3.63016
\(831\) −28.1739 −0.977343
\(832\) 47.4424 1.64477
\(833\) −6.76242 −0.234304
\(834\) 28.4094 0.983738
\(835\) 3.71050 0.128407
\(836\) 155.453 5.37645
\(837\) −39.4355 −1.36309
\(838\) −28.8152 −0.995406
\(839\) −12.0792 −0.417021 −0.208511 0.978020i \(-0.566862\pi\)
−0.208511 + 0.978020i \(0.566862\pi\)
\(840\) 7.93740 0.273866
\(841\) −26.3523 −0.908698
\(842\) 84.3508 2.90692
\(843\) 29.7212 1.02365
\(844\) 86.7915 2.98749
\(845\) 27.2366 0.936968
\(846\) 8.51813 0.292859
\(847\) −12.2462 −0.420783
\(848\) 20.1833 0.693097
\(849\) −4.68544 −0.160804
\(850\) −17.4315 −0.597897
\(851\) −30.1997 −1.03523
\(852\) −15.1071 −0.517562
\(853\) −0.897418 −0.0307270 −0.0153635 0.999882i \(-0.504891\pi\)
−0.0153635 + 0.999882i \(0.504891\pi\)
\(854\) 1.65622 0.0566747
\(855\) −43.1438 −1.47549
\(856\) 35.2061 1.20332
\(857\) 0.295836 0.0101056 0.00505279 0.999987i \(-0.498392\pi\)
0.00505279 + 0.999987i \(0.498392\pi\)
\(858\) 72.2690 2.46722
\(859\) 12.8220 0.437482 0.218741 0.975783i \(-0.429805\pi\)
0.218741 + 0.975783i \(0.429805\pi\)
\(860\) 54.5246 1.85927
\(861\) 1.54074 0.0525082
\(862\) −83.3646 −2.83941
\(863\) −37.2757 −1.26888 −0.634439 0.772973i \(-0.718769\pi\)
−0.634439 + 0.772973i \(0.718769\pi\)
\(864\) −11.2741 −0.383553
\(865\) −28.7714 −0.978258
\(866\) 4.87849 0.165778
\(867\) 1.09881 0.0373176
\(868\) −13.7352 −0.466204
\(869\) 25.6057 0.868613
\(870\) −15.0298 −0.509558
\(871\) 19.1524 0.648954
\(872\) −40.5313 −1.37256
\(873\) 7.21152 0.244073
\(874\) 45.3938 1.53547
\(875\) −3.85944 −0.130473
\(876\) 8.52774 0.288126
\(877\) −17.8918 −0.604162 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(878\) −7.40869 −0.250031
\(879\) 3.93441 0.132704
\(880\) 55.4396 1.86887
\(881\) −35.1392 −1.18387 −0.591935 0.805986i \(-0.701636\pi\)
−0.591935 + 0.805986i \(0.701636\pi\)
\(882\) −29.1014 −0.979894
\(883\) 56.3684 1.89695 0.948473 0.316858i \(-0.102628\pi\)
0.948473 + 0.316858i \(0.102628\pi\)
\(884\) −17.1530 −0.576919
\(885\) −28.0506 −0.942911
\(886\) 59.4041 1.99572
\(887\) −23.9499 −0.804159 −0.402080 0.915605i \(-0.631713\pi\)
−0.402080 + 0.915605i \(0.631713\pi\)
\(888\) −51.0504 −1.71314
\(889\) 8.07832 0.270938
\(890\) −12.8054 −0.429239
\(891\) −2.45636 −0.0822911
\(892\) 39.6930 1.32902
\(893\) 13.6049 0.455272
\(894\) −43.6291 −1.45918
\(895\) 29.3756 0.981918
\(896\) −10.0915 −0.337134
\(897\) 13.7795 0.460086
\(898\) −95.3497 −3.18186
\(899\) 12.1851 0.406397
\(900\) −48.9817 −1.63272
\(901\) 7.66192 0.255256
\(902\) 41.5070 1.38203
\(903\) −2.21626 −0.0737525
\(904\) −36.9127 −1.22770
\(905\) 0.437577 0.0145455
\(906\) −7.89287 −0.262223
\(907\) 25.5554 0.848552 0.424276 0.905533i \(-0.360529\pi\)
0.424276 + 0.905533i \(0.360529\pi\)
\(908\) −11.0117 −0.365437
\(909\) 22.7532 0.754675
\(910\) −18.6769 −0.619134
\(911\) −42.8474 −1.41960 −0.709799 0.704405i \(-0.751214\pi\)
−0.709799 + 0.704405i \(0.751214\pi\)
\(912\) 19.8949 0.658786
\(913\) −74.7776 −2.47478
\(914\) 5.31382 0.175765
\(915\) 5.44597 0.180038
\(916\) 36.4018 1.20275
\(917\) −10.8902 −0.359627
\(918\) 12.6421 0.417252
\(919\) −34.1593 −1.12681 −0.563406 0.826180i \(-0.690509\pi\)
−0.563406 + 0.826180i \(0.690509\pi\)
\(920\) 40.7713 1.34419
\(921\) −11.8373 −0.390052
\(922\) 24.3119 0.800669
\(923\) 16.6544 0.548186
\(924\) −12.1134 −0.398501
\(925\) 79.7090 2.62082
\(926\) 77.0298 2.53136
\(927\) 6.33665 0.208123
\(928\) 3.48358 0.114354
\(929\) −55.8226 −1.83148 −0.915740 0.401772i \(-0.868394\pi\)
−0.915740 + 0.401772i \(0.868394\pi\)
\(930\) −69.1683 −2.26812
\(931\) −46.4800 −1.52332
\(932\) −70.5129 −2.30973
\(933\) 27.5904 0.903269
\(934\) −0.0466436 −0.00152622
\(935\) 21.0458 0.688272
\(936\) −34.5838 −1.13041
\(937\) −22.4256 −0.732612 −0.366306 0.930495i \(-0.619378\pi\)
−0.366306 + 0.930495i \(0.619378\pi\)
\(938\) −4.91644 −0.160527
\(939\) 29.9245 0.976551
\(940\) 26.0817 0.850690
\(941\) −35.9294 −1.17126 −0.585632 0.810577i \(-0.699154\pi\)
−0.585632 + 0.810577i \(0.699154\pi\)
\(942\) 14.9851 0.488241
\(943\) 7.91415 0.257720
\(944\) −19.2047 −0.625058
\(945\) 8.98817 0.292385
\(946\) −59.7053 −1.94119
\(947\) 18.5466 0.602682 0.301341 0.953516i \(-0.402566\pi\)
0.301341 + 0.953516i \(0.402566\pi\)
\(948\) 17.6155 0.572126
\(949\) −9.40114 −0.305174
\(950\) −119.812 −3.88722
\(951\) −1.45154 −0.0470693
\(952\) 2.06295 0.0668605
\(953\) −38.0129 −1.23136 −0.615680 0.787997i \(-0.711118\pi\)
−0.615680 + 0.787997i \(0.711118\pi\)
\(954\) 32.9723 1.06752
\(955\) 36.2932 1.17442
\(956\) −106.267 −3.43693
\(957\) 10.7463 0.347379
\(958\) 72.6169 2.34615
\(959\) −6.58925 −0.212778
\(960\) −40.0453 −1.29246
\(961\) 25.0769 0.808933
\(962\) 120.123 3.87292
\(963\) 14.9116 0.480521
\(964\) −30.4383 −0.980353
\(965\) −36.9901 −1.19075
\(966\) −3.53723 −0.113808
\(967\) −3.16333 −0.101726 −0.0508629 0.998706i \(-0.516197\pi\)
−0.0508629 + 0.998706i \(0.516197\pi\)
\(968\) −106.334 −3.41770
\(969\) 7.55244 0.242619
\(970\) 33.8168 1.08579
\(971\) 61.4095 1.97072 0.985362 0.170475i \(-0.0545301\pi\)
0.985362 + 0.170475i \(0.0545301\pi\)
\(972\) 57.7602 1.85266
\(973\) 5.24956 0.168293
\(974\) −72.6713 −2.32854
\(975\) −36.3697 −1.16476
\(976\) 3.72854 0.119348
\(977\) 20.0509 0.641486 0.320743 0.947166i \(-0.396067\pi\)
0.320743 + 0.947166i \(0.396067\pi\)
\(978\) −17.8880 −0.571996
\(979\) 9.15590 0.292624
\(980\) −89.1056 −2.84637
\(981\) −17.1671 −0.548103
\(982\) −5.91759 −0.188838
\(983\) −39.8828 −1.27206 −0.636031 0.771663i \(-0.719425\pi\)
−0.636031 + 0.771663i \(0.719425\pi\)
\(984\) 13.3783 0.426484
\(985\) 27.1470 0.864975
\(986\) −3.90628 −0.124401
\(987\) −1.06014 −0.0337447
\(988\) −117.898 −3.75083
\(989\) −11.3840 −0.361991
\(990\) 90.5686 2.87846
\(991\) 29.7950 0.946468 0.473234 0.880937i \(-0.343087\pi\)
0.473234 + 0.880937i \(0.343087\pi\)
\(992\) 16.0317 0.509007
\(993\) 7.65306 0.242863
\(994\) −4.27520 −0.135601
\(995\) 83.7524 2.65513
\(996\) −51.4436 −1.63005
\(997\) −22.1985 −0.703033 −0.351516 0.936182i \(-0.614334\pi\)
−0.351516 + 0.936182i \(0.614334\pi\)
\(998\) −62.6810 −1.98413
\(999\) −57.8085 −1.82898
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 6001.2.a.d.1.12 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.12 121 1.1 even 1 trivial