Properties

Label 6025.2.a.p.1.3
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 1.3
Character \(\chi\) \(=\) 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.49572 q^{2} -1.66439 q^{3} +4.22863 q^{4} +4.15385 q^{6} +4.24911 q^{7} -5.56203 q^{8} -0.229807 q^{9} +O(q^{10})\) \(q-2.49572 q^{2} -1.66439 q^{3} +4.22863 q^{4} +4.15385 q^{6} +4.24911 q^{7} -5.56203 q^{8} -0.229807 q^{9} -6.39942 q^{11} -7.03808 q^{12} +1.34094 q^{13} -10.6046 q^{14} +5.42403 q^{16} -1.79850 q^{17} +0.573534 q^{18} -3.80298 q^{19} -7.07217 q^{21} +15.9712 q^{22} -5.33957 q^{23} +9.25739 q^{24} -3.34661 q^{26} +5.37566 q^{27} +17.9679 q^{28} +1.62578 q^{29} -3.96508 q^{31} -2.41281 q^{32} +10.6511 q^{33} +4.48857 q^{34} -0.971768 q^{36} +10.3760 q^{37} +9.49117 q^{38} -2.23185 q^{39} +2.25683 q^{41} +17.6502 q^{42} -1.94938 q^{43} -27.0608 q^{44} +13.3261 q^{46} +11.9862 q^{47} -9.02770 q^{48} +11.0549 q^{49} +2.99341 q^{51} +5.67034 q^{52} -10.9623 q^{53} -13.4161 q^{54} -23.6337 q^{56} +6.32964 q^{57} -4.05750 q^{58} +9.06104 q^{59} +14.1035 q^{61} +9.89574 q^{62} -0.976474 q^{63} -4.82637 q^{64} -26.5823 q^{66} +4.44323 q^{67} -7.60520 q^{68} +8.88712 q^{69} -6.47202 q^{71} +1.27819 q^{72} +4.44788 q^{73} -25.8956 q^{74} -16.0814 q^{76} -27.1918 q^{77} +5.57007 q^{78} -9.81502 q^{79} -8.25777 q^{81} -5.63241 q^{82} +14.6835 q^{83} -29.9056 q^{84} +4.86511 q^{86} -2.70593 q^{87} +35.5938 q^{88} +10.4329 q^{89} +5.69780 q^{91} -22.5790 q^{92} +6.59944 q^{93} -29.9143 q^{94} +4.01585 q^{96} -5.74102 q^{97} -27.5900 q^{98} +1.47063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} + O(q^{10}) \) \( 46q + 34q^{4} - 4q^{6} + 34q^{9} - 64q^{11} - 66q^{14} + 22q^{16} - 14q^{21} - 50q^{24} - 60q^{26} - 36q^{29} - 36q^{31} + 12q^{34} - 34q^{36} - 88q^{39} - 76q^{41} - 100q^{44} - 12q^{46} + 22q^{49} - 112q^{51} - 26q^{54} - 120q^{56} - 84q^{59} - 78q^{61} + 28q^{64} - 2q^{66} - 24q^{69} - 172q^{71} - 16q^{74} - 18q^{76} - 54q^{79} - 42q^{81} + 44q^{84} - 80q^{86} - 86q^{89} - 88q^{91} + 4q^{94} - 122q^{96} - 148q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49572 −1.76474 −0.882371 0.470555i \(-0.844054\pi\)
−0.882371 + 0.470555i \(0.844054\pi\)
\(3\) −1.66439 −0.960936 −0.480468 0.877012i \(-0.659533\pi\)
−0.480468 + 0.877012i \(0.659533\pi\)
\(4\) 4.22863 2.11431
\(5\) 0 0
\(6\) 4.15385 1.69580
\(7\) 4.24911 1.60601 0.803006 0.595972i \(-0.203233\pi\)
0.803006 + 0.595972i \(0.203233\pi\)
\(8\) −5.56203 −1.96648
\(9\) −0.229807 −0.0766023
\(10\) 0 0
\(11\) −6.39942 −1.92950 −0.964749 0.263170i \(-0.915232\pi\)
−0.964749 + 0.263170i \(0.915232\pi\)
\(12\) −7.03808 −2.03172
\(13\) 1.34094 0.371910 0.185955 0.982558i \(-0.440462\pi\)
0.185955 + 0.982558i \(0.440462\pi\)
\(14\) −10.6046 −2.83419
\(15\) 0 0
\(16\) 5.42403 1.35601
\(17\) −1.79850 −0.436201 −0.218101 0.975926i \(-0.569986\pi\)
−0.218101 + 0.975926i \(0.569986\pi\)
\(18\) 0.573534 0.135183
\(19\) −3.80298 −0.872463 −0.436231 0.899835i \(-0.643687\pi\)
−0.436231 + 0.899835i \(0.643687\pi\)
\(20\) 0 0
\(21\) −7.07217 −1.54327
\(22\) 15.9712 3.40507
\(23\) −5.33957 −1.11338 −0.556688 0.830721i \(-0.687928\pi\)
−0.556688 + 0.830721i \(0.687928\pi\)
\(24\) 9.25739 1.88966
\(25\) 0 0
\(26\) −3.34661 −0.656325
\(27\) 5.37566 1.03455
\(28\) 17.9679 3.39561
\(29\) 1.62578 0.301900 0.150950 0.988541i \(-0.451767\pi\)
0.150950 + 0.988541i \(0.451767\pi\)
\(30\) 0 0
\(31\) −3.96508 −0.712149 −0.356075 0.934458i \(-0.615885\pi\)
−0.356075 + 0.934458i \(0.615885\pi\)
\(32\) −2.41281 −0.426528
\(33\) 10.6511 1.85412
\(34\) 4.48857 0.769783
\(35\) 0 0
\(36\) −0.971768 −0.161961
\(37\) 10.3760 1.70580 0.852901 0.522072i \(-0.174841\pi\)
0.852901 + 0.522072i \(0.174841\pi\)
\(38\) 9.49117 1.53967
\(39\) −2.23185 −0.357382
\(40\) 0 0
\(41\) 2.25683 0.352457 0.176228 0.984349i \(-0.443610\pi\)
0.176228 + 0.984349i \(0.443610\pi\)
\(42\) 17.6502 2.72348
\(43\) −1.94938 −0.297278 −0.148639 0.988892i \(-0.547489\pi\)
−0.148639 + 0.988892i \(0.547489\pi\)
\(44\) −27.0608 −4.07957
\(45\) 0 0
\(46\) 13.3261 1.96482
\(47\) 11.9862 1.74837 0.874186 0.485591i \(-0.161395\pi\)
0.874186 + 0.485591i \(0.161395\pi\)
\(48\) −9.02770 −1.30304
\(49\) 11.0549 1.57927
\(50\) 0 0
\(51\) 2.99341 0.419161
\(52\) 5.67034 0.786334
\(53\) −10.9623 −1.50578 −0.752892 0.658145i \(-0.771342\pi\)
−0.752892 + 0.658145i \(0.771342\pi\)
\(54\) −13.4161 −1.82571
\(55\) 0 0
\(56\) −23.6337 −3.15818
\(57\) 6.32964 0.838381
\(58\) −4.05750 −0.532776
\(59\) 9.06104 1.17965 0.589823 0.807532i \(-0.299197\pi\)
0.589823 + 0.807532i \(0.299197\pi\)
\(60\) 0 0
\(61\) 14.1035 1.80577 0.902885 0.429882i \(-0.141445\pi\)
0.902885 + 0.429882i \(0.141445\pi\)
\(62\) 9.89574 1.25676
\(63\) −0.976474 −0.123024
\(64\) −4.82637 −0.603296
\(65\) 0 0
\(66\) −26.5823 −3.27205
\(67\) 4.44323 0.542827 0.271413 0.962463i \(-0.412509\pi\)
0.271413 + 0.962463i \(0.412509\pi\)
\(68\) −7.60520 −0.922266
\(69\) 8.88712 1.06988
\(70\) 0 0
\(71\) −6.47202 −0.768087 −0.384044 0.923315i \(-0.625469\pi\)
−0.384044 + 0.923315i \(0.625469\pi\)
\(72\) 1.27819 0.150637
\(73\) 4.44788 0.520585 0.260293 0.965530i \(-0.416181\pi\)
0.260293 + 0.965530i \(0.416181\pi\)
\(74\) −25.8956 −3.01030
\(75\) 0 0
\(76\) −16.0814 −1.84466
\(77\) −27.1918 −3.09880
\(78\) 5.57007 0.630686
\(79\) −9.81502 −1.10428 −0.552138 0.833753i \(-0.686188\pi\)
−0.552138 + 0.833753i \(0.686188\pi\)
\(80\) 0 0
\(81\) −8.25777 −0.917530
\(82\) −5.63241 −0.621995
\(83\) 14.6835 1.61172 0.805861 0.592105i \(-0.201703\pi\)
0.805861 + 0.592105i \(0.201703\pi\)
\(84\) −29.9056 −3.26296
\(85\) 0 0
\(86\) 4.86511 0.524618
\(87\) −2.70593 −0.290107
\(88\) 35.5938 3.79431
\(89\) 10.4329 1.10589 0.552944 0.833219i \(-0.313504\pi\)
0.552944 + 0.833219i \(0.313504\pi\)
\(90\) 0 0
\(91\) 5.69780 0.597292
\(92\) −22.5790 −2.35403
\(93\) 6.59944 0.684330
\(94\) −29.9143 −3.08543
\(95\) 0 0
\(96\) 4.01585 0.409866
\(97\) −5.74102 −0.582913 −0.291456 0.956584i \(-0.594140\pi\)
−0.291456 + 0.956584i \(0.594140\pi\)
\(98\) −27.5900 −2.78701
\(99\) 1.47063 0.147804
\(100\) 0 0
\(101\) −1.30373 −0.129726 −0.0648630 0.997894i \(-0.520661\pi\)
−0.0648630 + 0.997894i \(0.520661\pi\)
\(102\) −7.47072 −0.739712
\(103\) −12.0003 −1.18242 −0.591212 0.806516i \(-0.701350\pi\)
−0.591212 + 0.806516i \(0.701350\pi\)
\(104\) −7.45836 −0.731352
\(105\) 0 0
\(106\) 27.3588 2.65732
\(107\) −13.1936 −1.27547 −0.637736 0.770255i \(-0.720129\pi\)
−0.637736 + 0.770255i \(0.720129\pi\)
\(108\) 22.7316 2.18735
\(109\) 3.91188 0.374690 0.187345 0.982294i \(-0.440012\pi\)
0.187345 + 0.982294i \(0.440012\pi\)
\(110\) 0 0
\(111\) −17.2697 −1.63917
\(112\) 23.0473 2.17776
\(113\) 3.69680 0.347765 0.173883 0.984766i \(-0.444369\pi\)
0.173883 + 0.984766i \(0.444369\pi\)
\(114\) −15.7970 −1.47953
\(115\) 0 0
\(116\) 6.87482 0.638311
\(117\) −0.308157 −0.0284892
\(118\) −22.6138 −2.08177
\(119\) −7.64203 −0.700544
\(120\) 0 0
\(121\) 29.9526 2.72297
\(122\) −35.1985 −3.18672
\(123\) −3.75624 −0.338689
\(124\) −16.7668 −1.50571
\(125\) 0 0
\(126\) 2.43701 0.217106
\(127\) 3.75745 0.333420 0.166710 0.986006i \(-0.446686\pi\)
0.166710 + 0.986006i \(0.446686\pi\)
\(128\) 16.8709 1.49119
\(129\) 3.24453 0.285665
\(130\) 0 0
\(131\) −13.7718 −1.20325 −0.601625 0.798778i \(-0.705480\pi\)
−0.601625 + 0.798778i \(0.705480\pi\)
\(132\) 45.0397 3.92020
\(133\) −16.1593 −1.40119
\(134\) −11.0891 −0.957949
\(135\) 0 0
\(136\) 10.0033 0.857779
\(137\) −4.69491 −0.401113 −0.200557 0.979682i \(-0.564275\pi\)
−0.200557 + 0.979682i \(0.564275\pi\)
\(138\) −22.1798 −1.88807
\(139\) −12.6737 −1.07497 −0.537483 0.843275i \(-0.680625\pi\)
−0.537483 + 0.843275i \(0.680625\pi\)
\(140\) 0 0
\(141\) −19.9498 −1.68007
\(142\) 16.1524 1.35548
\(143\) −8.58125 −0.717600
\(144\) −1.24648 −0.103873
\(145\) 0 0
\(146\) −11.1007 −0.918699
\(147\) −18.3997 −1.51758
\(148\) 43.8762 3.60660
\(149\) 0.645320 0.0528667 0.0264333 0.999651i \(-0.491585\pi\)
0.0264333 + 0.999651i \(0.491585\pi\)
\(150\) 0 0
\(151\) 8.32983 0.677872 0.338936 0.940809i \(-0.389933\pi\)
0.338936 + 0.940809i \(0.389933\pi\)
\(152\) 21.1523 1.71568
\(153\) 0.413309 0.0334140
\(154\) 67.8632 5.46858
\(155\) 0 0
\(156\) −9.43765 −0.755617
\(157\) 2.68853 0.214568 0.107284 0.994228i \(-0.465785\pi\)
0.107284 + 0.994228i \(0.465785\pi\)
\(158\) 24.4956 1.94876
\(159\) 18.2455 1.44696
\(160\) 0 0
\(161\) −22.6884 −1.78810
\(162\) 20.6091 1.61920
\(163\) 16.9173 1.32507 0.662533 0.749033i \(-0.269482\pi\)
0.662533 + 0.749033i \(0.269482\pi\)
\(164\) 9.54327 0.745204
\(165\) 0 0
\(166\) −36.6459 −2.84427
\(167\) −16.0096 −1.23886 −0.619428 0.785053i \(-0.712635\pi\)
−0.619428 + 0.785053i \(0.712635\pi\)
\(168\) 39.3356 3.03481
\(169\) −11.2019 −0.861683
\(170\) 0 0
\(171\) 0.873950 0.0668327
\(172\) −8.24320 −0.628538
\(173\) −6.85866 −0.521454 −0.260727 0.965413i \(-0.583962\pi\)
−0.260727 + 0.965413i \(0.583962\pi\)
\(174\) 6.75326 0.511963
\(175\) 0 0
\(176\) −34.7107 −2.61641
\(177\) −15.0811 −1.13356
\(178\) −26.0377 −1.95161
\(179\) 4.54167 0.339461 0.169730 0.985491i \(-0.445710\pi\)
0.169730 + 0.985491i \(0.445710\pi\)
\(180\) 0 0
\(181\) −21.3544 −1.58726 −0.793631 0.608399i \(-0.791812\pi\)
−0.793631 + 0.608399i \(0.791812\pi\)
\(182\) −14.2201 −1.05407
\(183\) −23.4738 −1.73523
\(184\) 29.6988 2.18943
\(185\) 0 0
\(186\) −16.4704 −1.20767
\(187\) 11.5094 0.841650
\(188\) 50.6853 3.69661
\(189\) 22.8417 1.66149
\(190\) 0 0
\(191\) 6.63439 0.480047 0.240024 0.970767i \(-0.422845\pi\)
0.240024 + 0.970767i \(0.422845\pi\)
\(192\) 8.03296 0.579729
\(193\) 11.4179 0.821878 0.410939 0.911663i \(-0.365201\pi\)
0.410939 + 0.911663i \(0.365201\pi\)
\(194\) 14.3280 1.02869
\(195\) 0 0
\(196\) 46.7470 3.33907
\(197\) 22.5597 1.60731 0.803657 0.595093i \(-0.202885\pi\)
0.803657 + 0.595093i \(0.202885\pi\)
\(198\) −3.67029 −0.260836
\(199\) −24.5485 −1.74019 −0.870097 0.492881i \(-0.835944\pi\)
−0.870097 + 0.492881i \(0.835944\pi\)
\(200\) 0 0
\(201\) −7.39526 −0.521622
\(202\) 3.25375 0.228933
\(203\) 6.90812 0.484855
\(204\) 12.6580 0.886239
\(205\) 0 0
\(206\) 29.9494 2.08667
\(207\) 1.22707 0.0852872
\(208\) 7.27330 0.504313
\(209\) 24.3369 1.68342
\(210\) 0 0
\(211\) −5.29691 −0.364654 −0.182327 0.983238i \(-0.558363\pi\)
−0.182327 + 0.983238i \(0.558363\pi\)
\(212\) −46.3553 −3.18370
\(213\) 10.7720 0.738083
\(214\) 32.9275 2.25088
\(215\) 0 0
\(216\) −29.8996 −2.03441
\(217\) −16.8480 −1.14372
\(218\) −9.76296 −0.661231
\(219\) −7.40301 −0.500249
\(220\) 0 0
\(221\) −2.41169 −0.162228
\(222\) 43.1004 2.89271
\(223\) 9.77130 0.654335 0.327167 0.944966i \(-0.393906\pi\)
0.327167 + 0.944966i \(0.393906\pi\)
\(224\) −10.2523 −0.685008
\(225\) 0 0
\(226\) −9.22618 −0.613716
\(227\) −6.78250 −0.450170 −0.225085 0.974339i \(-0.572266\pi\)
−0.225085 + 0.974339i \(0.572266\pi\)
\(228\) 26.7657 1.77260
\(229\) 5.63514 0.372381 0.186190 0.982514i \(-0.440386\pi\)
0.186190 + 0.982514i \(0.440386\pi\)
\(230\) 0 0
\(231\) 45.2578 2.97774
\(232\) −9.04265 −0.593679
\(233\) 1.29396 0.0847702 0.0423851 0.999101i \(-0.486504\pi\)
0.0423851 + 0.999101i \(0.486504\pi\)
\(234\) 0.769075 0.0502760
\(235\) 0 0
\(236\) 38.3157 2.49414
\(237\) 16.3360 1.06114
\(238\) 19.0724 1.23628
\(239\) −0.893288 −0.0577820 −0.0288910 0.999583i \(-0.509198\pi\)
−0.0288910 + 0.999583i \(0.509198\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −74.7534 −4.80533
\(243\) −2.38283 −0.152858
\(244\) 59.6385 3.81796
\(245\) 0 0
\(246\) 9.37452 0.597698
\(247\) −5.09957 −0.324478
\(248\) 22.0539 1.40042
\(249\) −24.4390 −1.54876
\(250\) 0 0
\(251\) 15.9569 1.00719 0.503595 0.863940i \(-0.332010\pi\)
0.503595 + 0.863940i \(0.332010\pi\)
\(252\) −4.12914 −0.260112
\(253\) 34.1702 2.14826
\(254\) −9.37754 −0.588399
\(255\) 0 0
\(256\) −32.4523 −2.02827
\(257\) −1.49006 −0.0929473 −0.0464736 0.998920i \(-0.514798\pi\)
−0.0464736 + 0.998920i \(0.514798\pi\)
\(258\) −8.09744 −0.504124
\(259\) 44.0887 2.73954
\(260\) 0 0
\(261\) −0.373616 −0.0231262
\(262\) 34.3707 2.12343
\(263\) −17.3437 −1.06946 −0.534731 0.845023i \(-0.679587\pi\)
−0.534731 + 0.845023i \(0.679587\pi\)
\(264\) −59.2420 −3.64609
\(265\) 0 0
\(266\) 40.3290 2.47273
\(267\) −17.3644 −1.06269
\(268\) 18.7888 1.14771
\(269\) −17.9557 −1.09478 −0.547388 0.836879i \(-0.684378\pi\)
−0.547388 + 0.836879i \(0.684378\pi\)
\(270\) 0 0
\(271\) −14.3727 −0.873078 −0.436539 0.899685i \(-0.643796\pi\)
−0.436539 + 0.899685i \(0.643796\pi\)
\(272\) −9.75514 −0.591492
\(273\) −9.48336 −0.573959
\(274\) 11.7172 0.707861
\(275\) 0 0
\(276\) 37.5803 2.26207
\(277\) −1.25592 −0.0754612 −0.0377306 0.999288i \(-0.512013\pi\)
−0.0377306 + 0.999288i \(0.512013\pi\)
\(278\) 31.6299 1.89704
\(279\) 0.911203 0.0545523
\(280\) 0 0
\(281\) 22.3278 1.33197 0.665983 0.745967i \(-0.268012\pi\)
0.665983 + 0.745967i \(0.268012\pi\)
\(282\) 49.7891 2.96490
\(283\) 10.3956 0.617952 0.308976 0.951070i \(-0.400014\pi\)
0.308976 + 0.951070i \(0.400014\pi\)
\(284\) −27.3678 −1.62398
\(285\) 0 0
\(286\) 21.4164 1.26638
\(287\) 9.58949 0.566050
\(288\) 0.554479 0.0326730
\(289\) −13.7654 −0.809728
\(290\) 0 0
\(291\) 9.55530 0.560142
\(292\) 18.8084 1.10068
\(293\) −23.3313 −1.36303 −0.681514 0.731805i \(-0.738678\pi\)
−0.681514 + 0.731805i \(0.738678\pi\)
\(294\) 45.9204 2.67813
\(295\) 0 0
\(296\) −57.7116 −3.35442
\(297\) −34.4011 −1.99615
\(298\) −1.61054 −0.0932960
\(299\) −7.16004 −0.414076
\(300\) 0 0
\(301\) −8.28312 −0.477431
\(302\) −20.7889 −1.19627
\(303\) 2.16991 0.124658
\(304\) −20.6275 −1.18307
\(305\) 0 0
\(306\) −1.03150 −0.0589671
\(307\) 15.6330 0.892220 0.446110 0.894978i \(-0.352809\pi\)
0.446110 + 0.894978i \(0.352809\pi\)
\(308\) −114.984 −6.55183
\(309\) 19.9732 1.13623
\(310\) 0 0
\(311\) −26.6480 −1.51107 −0.755535 0.655108i \(-0.772623\pi\)
−0.755535 + 0.655108i \(0.772623\pi\)
\(312\) 12.4136 0.702782
\(313\) −2.78211 −0.157254 −0.0786272 0.996904i \(-0.525054\pi\)
−0.0786272 + 0.996904i \(0.525054\pi\)
\(314\) −6.70982 −0.378657
\(315\) 0 0
\(316\) −41.5040 −2.33478
\(317\) −19.6989 −1.10640 −0.553200 0.833049i \(-0.686593\pi\)
−0.553200 + 0.833049i \(0.686593\pi\)
\(318\) −45.5356 −2.55351
\(319\) −10.4041 −0.582516
\(320\) 0 0
\(321\) 21.9593 1.22565
\(322\) 56.6239 3.15553
\(323\) 6.83967 0.380569
\(324\) −34.9190 −1.93995
\(325\) 0 0
\(326\) −42.2209 −2.33840
\(327\) −6.51089 −0.360053
\(328\) −12.5525 −0.693098
\(329\) 50.9308 2.80791
\(330\) 0 0
\(331\) 15.0620 0.827882 0.413941 0.910304i \(-0.364152\pi\)
0.413941 + 0.910304i \(0.364152\pi\)
\(332\) 62.0910 3.40768
\(333\) −2.38448 −0.130668
\(334\) 39.9554 2.18626
\(335\) 0 0
\(336\) −38.3597 −2.09269
\(337\) 16.6018 0.904359 0.452180 0.891927i \(-0.350647\pi\)
0.452180 + 0.891927i \(0.350647\pi\)
\(338\) 27.9568 1.52065
\(339\) −6.15291 −0.334180
\(340\) 0 0
\(341\) 25.3742 1.37409
\(342\) −2.18114 −0.117942
\(343\) 17.2297 0.930316
\(344\) 10.8425 0.584589
\(345\) 0 0
\(346\) 17.1173 0.920232
\(347\) −15.8055 −0.848486 −0.424243 0.905549i \(-0.639460\pi\)
−0.424243 + 0.905549i \(0.639460\pi\)
\(348\) −11.4424 −0.613376
\(349\) −8.70148 −0.465779 −0.232890 0.972503i \(-0.574818\pi\)
−0.232890 + 0.972503i \(0.574818\pi\)
\(350\) 0 0
\(351\) 7.20844 0.384758
\(352\) 15.4406 0.822985
\(353\) 21.5327 1.14607 0.573035 0.819531i \(-0.305766\pi\)
0.573035 + 0.819531i \(0.305766\pi\)
\(354\) 37.6382 2.00045
\(355\) 0 0
\(356\) 44.1169 2.33819
\(357\) 12.7193 0.673178
\(358\) −11.3348 −0.599060
\(359\) 10.5631 0.557498 0.278749 0.960364i \(-0.410080\pi\)
0.278749 + 0.960364i \(0.410080\pi\)
\(360\) 0 0
\(361\) −4.53736 −0.238809
\(362\) 53.2947 2.80111
\(363\) −49.8528 −2.61660
\(364\) 24.0939 1.26286
\(365\) 0 0
\(366\) 58.5840 3.06223
\(367\) −29.8064 −1.55588 −0.777939 0.628339i \(-0.783735\pi\)
−0.777939 + 0.628339i \(0.783735\pi\)
\(368\) −28.9620 −1.50975
\(369\) −0.518634 −0.0269990
\(370\) 0 0
\(371\) −46.5798 −2.41830
\(372\) 27.9066 1.44689
\(373\) −18.0975 −0.937051 −0.468526 0.883450i \(-0.655215\pi\)
−0.468526 + 0.883450i \(0.655215\pi\)
\(374\) −28.7242 −1.48529
\(375\) 0 0
\(376\) −66.6678 −3.43813
\(377\) 2.18008 0.112280
\(378\) −57.0066 −2.93210
\(379\) 20.2276 1.03902 0.519512 0.854463i \(-0.326114\pi\)
0.519512 + 0.854463i \(0.326114\pi\)
\(380\) 0 0
\(381\) −6.25386 −0.320395
\(382\) −16.5576 −0.847160
\(383\) −4.68748 −0.239519 −0.119760 0.992803i \(-0.538212\pi\)
−0.119760 + 0.992803i \(0.538212\pi\)
\(384\) −28.0797 −1.43294
\(385\) 0 0
\(386\) −28.4959 −1.45040
\(387\) 0.447981 0.0227721
\(388\) −24.2766 −1.23246
\(389\) −15.4056 −0.781094 −0.390547 0.920583i \(-0.627714\pi\)
−0.390547 + 0.920583i \(0.627714\pi\)
\(390\) 0 0
\(391\) 9.60323 0.485656
\(392\) −61.4877 −3.10560
\(393\) 22.9217 1.15625
\(394\) −56.3028 −2.83649
\(395\) 0 0
\(396\) 6.21875 0.312504
\(397\) −38.1510 −1.91474 −0.957372 0.288857i \(-0.906725\pi\)
−0.957372 + 0.288857i \(0.906725\pi\)
\(398\) 61.2661 3.07099
\(399\) 26.8953 1.34645
\(400\) 0 0
\(401\) 32.9356 1.64472 0.822362 0.568965i \(-0.192656\pi\)
0.822362 + 0.568965i \(0.192656\pi\)
\(402\) 18.4565 0.920528
\(403\) −5.31694 −0.264856
\(404\) −5.51299 −0.274281
\(405\) 0 0
\(406\) −17.2407 −0.855644
\(407\) −66.4004 −3.29134
\(408\) −16.6494 −0.824271
\(409\) −19.1149 −0.945169 −0.472584 0.881285i \(-0.656679\pi\)
−0.472584 + 0.881285i \(0.656679\pi\)
\(410\) 0 0
\(411\) 7.81416 0.385444
\(412\) −50.7448 −2.50002
\(413\) 38.5013 1.89453
\(414\) −3.06242 −0.150510
\(415\) 0 0
\(416\) −3.23543 −0.158630
\(417\) 21.0939 1.03297
\(418\) −60.7380 −2.97079
\(419\) 0.832487 0.0406696 0.0203348 0.999793i \(-0.493527\pi\)
0.0203348 + 0.999793i \(0.493527\pi\)
\(420\) 0 0
\(421\) 2.06135 0.100464 0.0502321 0.998738i \(-0.484004\pi\)
0.0502321 + 0.998738i \(0.484004\pi\)
\(422\) 13.2196 0.643521
\(423\) −2.75452 −0.133929
\(424\) 60.9725 2.96109
\(425\) 0 0
\(426\) −26.8838 −1.30253
\(427\) 59.9273 2.90009
\(428\) −55.7908 −2.69675
\(429\) 14.2825 0.689568
\(430\) 0 0
\(431\) −16.1802 −0.779375 −0.389688 0.920947i \(-0.627417\pi\)
−0.389688 + 0.920947i \(0.627417\pi\)
\(432\) 29.1577 1.40285
\(433\) −21.6854 −1.04213 −0.521066 0.853517i \(-0.674465\pi\)
−0.521066 + 0.853517i \(0.674465\pi\)
\(434\) 42.0480 2.01837
\(435\) 0 0
\(436\) 16.5419 0.792212
\(437\) 20.3063 0.971380
\(438\) 18.4759 0.882810
\(439\) −26.9940 −1.28836 −0.644178 0.764876i \(-0.722800\pi\)
−0.644178 + 0.764876i \(0.722800\pi\)
\(440\) 0 0
\(441\) −2.54049 −0.120976
\(442\) 6.01890 0.286290
\(443\) 26.0917 1.23965 0.619826 0.784739i \(-0.287203\pi\)
0.619826 + 0.784739i \(0.287203\pi\)
\(444\) −73.0271 −3.46571
\(445\) 0 0
\(446\) −24.3864 −1.15473
\(447\) −1.07406 −0.0508015
\(448\) −20.5078 −0.968900
\(449\) −21.4983 −1.01457 −0.507285 0.861778i \(-0.669351\pi\)
−0.507285 + 0.861778i \(0.669351\pi\)
\(450\) 0 0
\(451\) −14.4424 −0.680065
\(452\) 15.6324 0.735285
\(453\) −13.8641 −0.651391
\(454\) 16.9272 0.794434
\(455\) 0 0
\(456\) −35.2056 −1.64866
\(457\) 17.4405 0.815831 0.407915 0.913020i \(-0.366256\pi\)
0.407915 + 0.913020i \(0.366256\pi\)
\(458\) −14.0637 −0.657156
\(459\) −9.66814 −0.451270
\(460\) 0 0
\(461\) −4.48673 −0.208968 −0.104484 0.994527i \(-0.533319\pi\)
−0.104484 + 0.994527i \(0.533319\pi\)
\(462\) −112.951 −5.25495
\(463\) −5.29000 −0.245847 −0.122924 0.992416i \(-0.539227\pi\)
−0.122924 + 0.992416i \(0.539227\pi\)
\(464\) 8.81829 0.409379
\(465\) 0 0
\(466\) −3.22937 −0.149598
\(467\) 35.3907 1.63768 0.818842 0.574018i \(-0.194616\pi\)
0.818842 + 0.574018i \(0.194616\pi\)
\(468\) −1.30308 −0.0602350
\(469\) 18.8798 0.871786
\(470\) 0 0
\(471\) −4.47476 −0.206186
\(472\) −50.3978 −2.31975
\(473\) 12.4749 0.573597
\(474\) −40.7701 −1.87263
\(475\) 0 0
\(476\) −32.3153 −1.48117
\(477\) 2.51920 0.115346
\(478\) 2.22940 0.101970
\(479\) −38.1256 −1.74200 −0.871002 0.491279i \(-0.836529\pi\)
−0.871002 + 0.491279i \(0.836529\pi\)
\(480\) 0 0
\(481\) 13.9136 0.634405
\(482\) −2.49572 −0.113677
\(483\) 37.7623 1.71824
\(484\) 126.658 5.75720
\(485\) 0 0
\(486\) 5.94688 0.269756
\(487\) −8.85116 −0.401084 −0.200542 0.979685i \(-0.564270\pi\)
−0.200542 + 0.979685i \(0.564270\pi\)
\(488\) −78.4442 −3.55100
\(489\) −28.1570 −1.27330
\(490\) 0 0
\(491\) 6.67644 0.301304 0.150652 0.988587i \(-0.451863\pi\)
0.150652 + 0.988587i \(0.451863\pi\)
\(492\) −15.8837 −0.716094
\(493\) −2.92397 −0.131689
\(494\) 12.7271 0.572619
\(495\) 0 0
\(496\) −21.5067 −0.965680
\(497\) −27.5003 −1.23356
\(498\) 60.9930 2.73316
\(499\) −23.1701 −1.03724 −0.518619 0.855006i \(-0.673554\pi\)
−0.518619 + 0.855006i \(0.673554\pi\)
\(500\) 0 0
\(501\) 26.6461 1.19046
\(502\) −39.8240 −1.77743
\(503\) 2.36856 0.105609 0.0528044 0.998605i \(-0.483184\pi\)
0.0528044 + 0.998605i \(0.483184\pi\)
\(504\) 5.43118 0.241924
\(505\) 0 0
\(506\) −85.2792 −3.79112
\(507\) 18.6443 0.828022
\(508\) 15.8888 0.704954
\(509\) 11.4066 0.505590 0.252795 0.967520i \(-0.418650\pi\)
0.252795 + 0.967520i \(0.418650\pi\)
\(510\) 0 0
\(511\) 18.8995 0.836066
\(512\) 47.2501 2.08818
\(513\) −20.4435 −0.902603
\(514\) 3.71877 0.164028
\(515\) 0 0
\(516\) 13.7199 0.603985
\(517\) −76.7050 −3.37348
\(518\) −110.033 −4.83458
\(519\) 11.4155 0.501084
\(520\) 0 0
\(521\) −8.79487 −0.385310 −0.192655 0.981267i \(-0.561710\pi\)
−0.192655 + 0.981267i \(0.561710\pi\)
\(522\) 0.932441 0.0408118
\(523\) 9.06170 0.396241 0.198120 0.980178i \(-0.436516\pi\)
0.198120 + 0.980178i \(0.436516\pi\)
\(524\) −58.2359 −2.54405
\(525\) 0 0
\(526\) 43.2852 1.88732
\(527\) 7.13121 0.310640
\(528\) 57.7721 2.51421
\(529\) 5.51097 0.239608
\(530\) 0 0
\(531\) −2.08229 −0.0903636
\(532\) −68.3315 −2.96254
\(533\) 3.02627 0.131082
\(534\) 43.3368 1.87537
\(535\) 0 0
\(536\) −24.7134 −1.06746
\(537\) −7.55911 −0.326200
\(538\) 44.8123 1.93200
\(539\) −70.7450 −3.04720
\(540\) 0 0
\(541\) −39.4094 −1.69434 −0.847171 0.531320i \(-0.821696\pi\)
−0.847171 + 0.531320i \(0.821696\pi\)
\(542\) 35.8702 1.54076
\(543\) 35.5421 1.52526
\(544\) 4.33944 0.186052
\(545\) 0 0
\(546\) 23.6678 1.01289
\(547\) 12.2963 0.525753 0.262877 0.964829i \(-0.415329\pi\)
0.262877 + 0.964829i \(0.415329\pi\)
\(548\) −19.8530 −0.848079
\(549\) −3.24109 −0.138326
\(550\) 0 0
\(551\) −6.18281 −0.263397
\(552\) −49.4304 −2.10390
\(553\) −41.7050 −1.77348
\(554\) 3.13444 0.133169
\(555\) 0 0
\(556\) −53.5922 −2.27281
\(557\) 16.8825 0.715333 0.357667 0.933849i \(-0.383572\pi\)
0.357667 + 0.933849i \(0.383572\pi\)
\(558\) −2.27411 −0.0962707
\(559\) −2.61400 −0.110561
\(560\) 0 0
\(561\) −19.1561 −0.808772
\(562\) −55.7240 −2.35058
\(563\) −3.43922 −0.144946 −0.0724729 0.997370i \(-0.523089\pi\)
−0.0724729 + 0.997370i \(0.523089\pi\)
\(564\) −84.3601 −3.55220
\(565\) 0 0
\(566\) −25.9444 −1.09053
\(567\) −35.0881 −1.47356
\(568\) 35.9976 1.51042
\(569\) −18.8153 −0.788779 −0.394390 0.918943i \(-0.629044\pi\)
−0.394390 + 0.918943i \(0.629044\pi\)
\(570\) 0 0
\(571\) −28.5582 −1.19512 −0.597562 0.801823i \(-0.703864\pi\)
−0.597562 + 0.801823i \(0.703864\pi\)
\(572\) −36.2869 −1.51723
\(573\) −11.0422 −0.461295
\(574\) −23.9327 −0.998932
\(575\) 0 0
\(576\) 1.10913 0.0462139
\(577\) −10.0008 −0.416337 −0.208169 0.978093i \(-0.566750\pi\)
−0.208169 + 0.978093i \(0.566750\pi\)
\(578\) 34.3546 1.42896
\(579\) −19.0038 −0.789772
\(580\) 0 0
\(581\) 62.3917 2.58844
\(582\) −23.8474 −0.988505
\(583\) 70.1522 2.90541
\(584\) −24.7393 −1.02372
\(585\) 0 0
\(586\) 58.2284 2.40539
\(587\) −26.7660 −1.10475 −0.552376 0.833595i \(-0.686279\pi\)
−0.552376 + 0.833595i \(0.686279\pi\)
\(588\) −77.8053 −3.20864
\(589\) 15.0791 0.621324
\(590\) 0 0
\(591\) −37.5482 −1.54453
\(592\) 56.2797 2.31308
\(593\) −18.5431 −0.761472 −0.380736 0.924684i \(-0.624329\pi\)
−0.380736 + 0.924684i \(0.624329\pi\)
\(594\) 85.8556 3.52270
\(595\) 0 0
\(596\) 2.72882 0.111777
\(597\) 40.8582 1.67221
\(598\) 17.8695 0.730737
\(599\) −0.913482 −0.0373239 −0.0186619 0.999826i \(-0.505941\pi\)
−0.0186619 + 0.999826i \(0.505941\pi\)
\(600\) 0 0
\(601\) 16.1779 0.659912 0.329956 0.943996i \(-0.392966\pi\)
0.329956 + 0.943996i \(0.392966\pi\)
\(602\) 20.6724 0.842542
\(603\) −1.02108 −0.0415818
\(604\) 35.2237 1.43323
\(605\) 0 0
\(606\) −5.41550 −0.219990
\(607\) −16.6396 −0.675380 −0.337690 0.941257i \(-0.609646\pi\)
−0.337690 + 0.941257i \(0.609646\pi\)
\(608\) 9.17584 0.372130
\(609\) −11.4978 −0.465914
\(610\) 0 0
\(611\) 16.0728 0.650237
\(612\) 1.74773 0.0706477
\(613\) −9.20938 −0.371963 −0.185982 0.982553i \(-0.559546\pi\)
−0.185982 + 0.982553i \(0.559546\pi\)
\(614\) −39.0155 −1.57454
\(615\) 0 0
\(616\) 151.242 6.09371
\(617\) 14.7257 0.592836 0.296418 0.955058i \(-0.404208\pi\)
0.296418 + 0.955058i \(0.404208\pi\)
\(618\) −49.8475 −2.00516
\(619\) 2.38884 0.0960155 0.0480077 0.998847i \(-0.484713\pi\)
0.0480077 + 0.998847i \(0.484713\pi\)
\(620\) 0 0
\(621\) −28.7037 −1.15184
\(622\) 66.5060 2.66665
\(623\) 44.3306 1.77607
\(624\) −12.1056 −0.484612
\(625\) 0 0
\(626\) 6.94338 0.277513
\(627\) −40.5060 −1.61765
\(628\) 11.3688 0.453664
\(629\) −18.6613 −0.744073
\(630\) 0 0
\(631\) −9.31118 −0.370672 −0.185336 0.982675i \(-0.559337\pi\)
−0.185336 + 0.982675i \(0.559337\pi\)
\(632\) 54.5914 2.17153
\(633\) 8.81612 0.350409
\(634\) 49.1629 1.95251
\(635\) 0 0
\(636\) 77.1533 3.05933
\(637\) 14.8240 0.587347
\(638\) 25.9657 1.02799
\(639\) 1.48731 0.0588373
\(640\) 0 0
\(641\) 8.83364 0.348908 0.174454 0.984665i \(-0.444184\pi\)
0.174454 + 0.984665i \(0.444184\pi\)
\(642\) −54.8043 −2.16295
\(643\) 7.12073 0.280814 0.140407 0.990094i \(-0.455159\pi\)
0.140407 + 0.990094i \(0.455159\pi\)
\(644\) −95.9407 −3.78059
\(645\) 0 0
\(646\) −17.0699 −0.671607
\(647\) 25.6415 1.00807 0.504036 0.863683i \(-0.331848\pi\)
0.504036 + 0.863683i \(0.331848\pi\)
\(648\) 45.9300 1.80430
\(649\) −57.9854 −2.27613
\(650\) 0 0
\(651\) 28.0417 1.09904
\(652\) 71.5370 2.80160
\(653\) −1.15251 −0.0451011 −0.0225506 0.999746i \(-0.507179\pi\)
−0.0225506 + 0.999746i \(0.507179\pi\)
\(654\) 16.2494 0.635401
\(655\) 0 0
\(656\) 12.2411 0.477934
\(657\) −1.02215 −0.0398780
\(658\) −127.109 −4.95523
\(659\) 40.1918 1.56565 0.782826 0.622241i \(-0.213777\pi\)
0.782826 + 0.622241i \(0.213777\pi\)
\(660\) 0 0
\(661\) −37.9960 −1.47787 −0.738937 0.673774i \(-0.764672\pi\)
−0.738937 + 0.673774i \(0.764672\pi\)
\(662\) −37.5905 −1.46100
\(663\) 4.01399 0.155890
\(664\) −81.6700 −3.16941
\(665\) 0 0
\(666\) 5.95099 0.230596
\(667\) −8.68097 −0.336129
\(668\) −67.6984 −2.61933
\(669\) −16.2633 −0.628774
\(670\) 0 0
\(671\) −90.2544 −3.48423
\(672\) 17.0638 0.658249
\(673\) −10.4706 −0.403611 −0.201805 0.979426i \(-0.564681\pi\)
−0.201805 + 0.979426i \(0.564681\pi\)
\(674\) −41.4336 −1.59596
\(675\) 0 0
\(676\) −47.3686 −1.82187
\(677\) −9.18573 −0.353036 −0.176518 0.984297i \(-0.556483\pi\)
−0.176518 + 0.984297i \(0.556483\pi\)
\(678\) 15.3560 0.589742
\(679\) −24.3942 −0.936164
\(680\) 0 0
\(681\) 11.2887 0.432584
\(682\) −63.3270 −2.42492
\(683\) −17.9966 −0.688620 −0.344310 0.938856i \(-0.611887\pi\)
−0.344310 + 0.938856i \(0.611887\pi\)
\(684\) 3.69561 0.141305
\(685\) 0 0
\(686\) −43.0005 −1.64177
\(687\) −9.37907 −0.357834
\(688\) −10.5735 −0.403111
\(689\) −14.6998 −0.560016
\(690\) 0 0
\(691\) 49.5109 1.88349 0.941743 0.336335i \(-0.109187\pi\)
0.941743 + 0.336335i \(0.109187\pi\)
\(692\) −29.0027 −1.10252
\(693\) 6.24887 0.237375
\(694\) 39.4462 1.49736
\(695\) 0 0
\(696\) 15.0505 0.570487
\(697\) −4.05891 −0.153742
\(698\) 21.7165 0.821980
\(699\) −2.15366 −0.0814587
\(700\) 0 0
\(701\) −7.77497 −0.293657 −0.146828 0.989162i \(-0.546906\pi\)
−0.146828 + 0.989162i \(0.546906\pi\)
\(702\) −17.9903 −0.678998
\(703\) −39.4597 −1.48825
\(704\) 30.8860 1.16406
\(705\) 0 0
\(706\) −53.7396 −2.02252
\(707\) −5.53969 −0.208341
\(708\) −63.7723 −2.39671
\(709\) 0.260823 0.00979541 0.00489770 0.999988i \(-0.498441\pi\)
0.00489770 + 0.999988i \(0.498441\pi\)
\(710\) 0 0
\(711\) 2.25556 0.0845901
\(712\) −58.0282 −2.17470
\(713\) 21.1718 0.792890
\(714\) −31.7439 −1.18799
\(715\) 0 0
\(716\) 19.2050 0.717726
\(717\) 1.48678 0.0555248
\(718\) −26.3625 −0.983840
\(719\) 18.5739 0.692688 0.346344 0.938108i \(-0.387423\pi\)
0.346344 + 0.938108i \(0.387423\pi\)
\(720\) 0 0
\(721\) −50.9905 −1.89899
\(722\) 11.3240 0.421435
\(723\) −1.66439 −0.0618993
\(724\) −90.2999 −3.35597
\(725\) 0 0
\(726\) 124.419 4.61762
\(727\) 4.70298 0.174424 0.0872119 0.996190i \(-0.472204\pi\)
0.0872119 + 0.996190i \(0.472204\pi\)
\(728\) −31.6913 −1.17456
\(729\) 28.7393 1.06442
\(730\) 0 0
\(731\) 3.50597 0.129673
\(732\) −99.2617 −3.66882
\(733\) 0.215894 0.00797424 0.00398712 0.999992i \(-0.498731\pi\)
0.00398712 + 0.999992i \(0.498731\pi\)
\(734\) 74.3884 2.74572
\(735\) 0 0
\(736\) 12.8833 0.474886
\(737\) −28.4341 −1.04738
\(738\) 1.29437 0.0476463
\(739\) 1.53528 0.0564761 0.0282381 0.999601i \(-0.491010\pi\)
0.0282381 + 0.999601i \(0.491010\pi\)
\(740\) 0 0
\(741\) 8.48767 0.311802
\(742\) 116.250 4.26768
\(743\) −19.5424 −0.716943 −0.358471 0.933541i \(-0.616702\pi\)
−0.358471 + 0.933541i \(0.616702\pi\)
\(744\) −36.7063 −1.34572
\(745\) 0 0
\(746\) 45.1662 1.65365
\(747\) −3.37437 −0.123462
\(748\) 48.6689 1.77951
\(749\) −56.0610 −2.04842
\(750\) 0 0
\(751\) 9.37833 0.342220 0.171110 0.985252i \(-0.445265\pi\)
0.171110 + 0.985252i \(0.445265\pi\)
\(752\) 65.0137 2.37081
\(753\) −26.5585 −0.967845
\(754\) −5.44087 −0.198145
\(755\) 0 0
\(756\) 96.5892 3.51291
\(757\) 28.5781 1.03869 0.519344 0.854565i \(-0.326176\pi\)
0.519344 + 0.854565i \(0.326176\pi\)
\(758\) −50.4826 −1.83361
\(759\) −56.8724 −2.06434
\(760\) 0 0
\(761\) 19.0881 0.691942 0.345971 0.938245i \(-0.387550\pi\)
0.345971 + 0.938245i \(0.387550\pi\)
\(762\) 15.6079 0.565414
\(763\) 16.6220 0.601756
\(764\) 28.0543 1.01497
\(765\) 0 0
\(766\) 11.6986 0.422689
\(767\) 12.1503 0.438722
\(768\) 54.0133 1.94904
\(769\) 37.9012 1.36675 0.683376 0.730067i \(-0.260511\pi\)
0.683376 + 0.730067i \(0.260511\pi\)
\(770\) 0 0
\(771\) 2.48004 0.0893164
\(772\) 48.2820 1.73771
\(773\) −8.00091 −0.287773 −0.143886 0.989594i \(-0.545960\pi\)
−0.143886 + 0.989594i \(0.545960\pi\)
\(774\) −1.11804 −0.0401870
\(775\) 0 0
\(776\) 31.9318 1.14628
\(777\) −73.3808 −2.63252
\(778\) 38.4480 1.37843
\(779\) −8.58266 −0.307506
\(780\) 0 0
\(781\) 41.4172 1.48202
\(782\) −23.9670 −0.857058
\(783\) 8.73965 0.312329
\(784\) 59.9621 2.14150
\(785\) 0 0
\(786\) −57.2062 −2.04048
\(787\) −11.4339 −0.407576 −0.203788 0.979015i \(-0.565325\pi\)
−0.203788 + 0.979015i \(0.565325\pi\)
\(788\) 95.3966 3.39836
\(789\) 28.8668 1.02768
\(790\) 0 0
\(791\) 15.7081 0.558515
\(792\) −8.17970 −0.290653
\(793\) 18.9120 0.671584
\(794\) 95.2143 3.37903
\(795\) 0 0
\(796\) −103.806 −3.67931
\(797\) 29.3792 1.04066 0.520332 0.853964i \(-0.325808\pi\)
0.520332 + 0.853964i \(0.325808\pi\)
\(798\) −67.1232 −2.37613
\(799\) −21.5573 −0.762642
\(800\) 0 0
\(801\) −2.39756 −0.0847135
\(802\) −82.1980 −2.90251
\(803\) −28.4639 −1.00447
\(804\) −31.2718 −1.10287
\(805\) 0 0
\(806\) 13.2696 0.467402
\(807\) 29.8852 1.05201
\(808\) 7.25139 0.255103
\(809\) 5.19954 0.182806 0.0914030 0.995814i \(-0.470865\pi\)
0.0914030 + 0.995814i \(0.470865\pi\)
\(810\) 0 0
\(811\) −9.70563 −0.340811 −0.170405 0.985374i \(-0.554508\pi\)
−0.170405 + 0.985374i \(0.554508\pi\)
\(812\) 29.2119 1.02514
\(813\) 23.9218 0.838972
\(814\) 165.717 5.80837
\(815\) 0 0
\(816\) 16.2364 0.568386
\(817\) 7.41345 0.259364
\(818\) 47.7054 1.66798
\(819\) −1.30939 −0.0457539
\(820\) 0 0
\(821\) −43.5252 −1.51904 −0.759521 0.650483i \(-0.774566\pi\)
−0.759521 + 0.650483i \(0.774566\pi\)
\(822\) −19.5020 −0.680209
\(823\) −10.3541 −0.360920 −0.180460 0.983582i \(-0.557759\pi\)
−0.180460 + 0.983582i \(0.557759\pi\)
\(824\) 66.7460 2.32521
\(825\) 0 0
\(826\) −96.0885 −3.34335
\(827\) −42.4097 −1.47473 −0.737366 0.675494i \(-0.763931\pi\)
−0.737366 + 0.675494i \(0.763931\pi\)
\(828\) 5.18882 0.180324
\(829\) 20.8325 0.723543 0.361772 0.932267i \(-0.382172\pi\)
0.361772 + 0.932267i \(0.382172\pi\)
\(830\) 0 0
\(831\) 2.09035 0.0725133
\(832\) −6.47187 −0.224372
\(833\) −19.8823 −0.688880
\(834\) −52.6445 −1.82293
\(835\) 0 0
\(836\) 102.912 3.55927
\(837\) −21.3149 −0.736751
\(838\) −2.07765 −0.0717714
\(839\) −42.8307 −1.47868 −0.739341 0.673332i \(-0.764863\pi\)
−0.739341 + 0.673332i \(0.764863\pi\)
\(840\) 0 0
\(841\) −26.3568 −0.908856
\(842\) −5.14457 −0.177293
\(843\) −37.1622 −1.27993
\(844\) −22.3986 −0.770993
\(845\) 0 0
\(846\) 6.87452 0.236351
\(847\) 127.272 4.37311
\(848\) −59.4597 −2.04185
\(849\) −17.3023 −0.593813
\(850\) 0 0
\(851\) −55.4033 −1.89920
\(852\) 45.5506 1.56054
\(853\) 14.7997 0.506733 0.253367 0.967370i \(-0.418462\pi\)
0.253367 + 0.967370i \(0.418462\pi\)
\(854\) −149.562 −5.11791
\(855\) 0 0
\(856\) 73.3832 2.50819
\(857\) −5.57859 −0.190561 −0.0952806 0.995450i \(-0.530375\pi\)
−0.0952806 + 0.995450i \(0.530375\pi\)
\(858\) −35.6452 −1.21691
\(859\) −14.4231 −0.492108 −0.246054 0.969256i \(-0.579134\pi\)
−0.246054 + 0.969256i \(0.579134\pi\)
\(860\) 0 0
\(861\) −15.9607 −0.543938
\(862\) 40.3814 1.37540
\(863\) 47.4256 1.61439 0.807194 0.590287i \(-0.200985\pi\)
0.807194 + 0.590287i \(0.200985\pi\)
\(864\) −12.9704 −0.441262
\(865\) 0 0
\(866\) 54.1206 1.83909
\(867\) 22.9110 0.778097
\(868\) −71.2441 −2.41818
\(869\) 62.8105 2.13070
\(870\) 0 0
\(871\) 5.95811 0.201883
\(872\) −21.7580 −0.736819
\(873\) 1.31933 0.0446524
\(874\) −50.6788 −1.71423
\(875\) 0 0
\(876\) −31.3046 −1.05768
\(877\) 47.9886 1.62046 0.810231 0.586111i \(-0.199342\pi\)
0.810231 + 0.586111i \(0.199342\pi\)
\(878\) 67.3696 2.27361
\(879\) 38.8323 1.30978
\(880\) 0 0
\(881\) −7.04800 −0.237453 −0.118727 0.992927i \(-0.537881\pi\)
−0.118727 + 0.992927i \(0.537881\pi\)
\(882\) 6.34036 0.213491
\(883\) 20.6924 0.696355 0.348177 0.937429i \(-0.386801\pi\)
0.348177 + 0.937429i \(0.386801\pi\)
\(884\) −10.1981 −0.343000
\(885\) 0 0
\(886\) −65.1175 −2.18767
\(887\) 39.9150 1.34022 0.670108 0.742264i \(-0.266248\pi\)
0.670108 + 0.742264i \(0.266248\pi\)
\(888\) 96.0546 3.22338
\(889\) 15.9658 0.535476
\(890\) 0 0
\(891\) 52.8450 1.77037
\(892\) 41.3192 1.38347
\(893\) −45.5834 −1.52539
\(894\) 2.68056 0.0896515
\(895\) 0 0
\(896\) 71.6862 2.39487
\(897\) 11.9171 0.397900
\(898\) 53.6539 1.79045
\(899\) −6.44635 −0.214998
\(900\) 0 0
\(901\) 19.7157 0.656825
\(902\) 36.0442 1.20014
\(903\) 13.7863 0.458781
\(904\) −20.5617 −0.683872
\(905\) 0 0
\(906\) 34.6009 1.14954
\(907\) 30.9313 1.02706 0.513528 0.858073i \(-0.328338\pi\)
0.513528 + 0.858073i \(0.328338\pi\)
\(908\) −28.6806 −0.951800
\(909\) 0.299606 0.00993731
\(910\) 0 0
\(911\) 2.92318 0.0968492 0.0484246 0.998827i \(-0.484580\pi\)
0.0484246 + 0.998827i \(0.484580\pi\)
\(912\) 34.3321 1.13685
\(913\) −93.9658 −3.10982
\(914\) −43.5266 −1.43973
\(915\) 0 0
\(916\) 23.8289 0.787329
\(917\) −58.5180 −1.93243
\(918\) 24.1290 0.796375
\(919\) −50.8708 −1.67807 −0.839036 0.544076i \(-0.816880\pi\)
−0.839036 + 0.544076i \(0.816880\pi\)
\(920\) 0 0
\(921\) −26.0193 −0.857366
\(922\) 11.1976 0.368774
\(923\) −8.67859 −0.285659
\(924\) 191.378 6.29589
\(925\) 0 0
\(926\) 13.2024 0.433857
\(927\) 2.75775 0.0905764
\(928\) −3.92270 −0.128769
\(929\) 44.2087 1.45044 0.725220 0.688517i \(-0.241738\pi\)
0.725220 + 0.688517i \(0.241738\pi\)
\(930\) 0 0
\(931\) −42.0415 −1.37786
\(932\) 5.47168 0.179231
\(933\) 44.3527 1.45204
\(934\) −88.3252 −2.89009
\(935\) 0 0
\(936\) 1.71398 0.0560232
\(937\) −20.4558 −0.668261 −0.334130 0.942527i \(-0.608443\pi\)
−0.334130 + 0.942527i \(0.608443\pi\)
\(938\) −47.1186 −1.53848
\(939\) 4.63052 0.151111
\(940\) 0 0
\(941\) −0.300822 −0.00980651 −0.00490325 0.999988i \(-0.501561\pi\)
−0.00490325 + 0.999988i \(0.501561\pi\)
\(942\) 11.1678 0.363865
\(943\) −12.0505 −0.392417
\(944\) 49.1473 1.59961
\(945\) 0 0
\(946\) −31.1339 −1.01225
\(947\) −38.0133 −1.23526 −0.617632 0.786467i \(-0.711908\pi\)
−0.617632 + 0.786467i \(0.711908\pi\)
\(948\) 69.0789 2.24358
\(949\) 5.96435 0.193611
\(950\) 0 0
\(951\) 32.7866 1.06318
\(952\) 42.5052 1.37760
\(953\) −19.9585 −0.646520 −0.323260 0.946310i \(-0.604779\pi\)
−0.323260 + 0.946310i \(0.604779\pi\)
\(954\) −6.28723 −0.203557
\(955\) 0 0
\(956\) −3.77738 −0.122169
\(957\) 17.3164 0.559760
\(958\) 95.1509 3.07419
\(959\) −19.9492 −0.644192
\(960\) 0 0
\(961\) −15.2781 −0.492843
\(962\) −34.7245 −1.11956
\(963\) 3.03198 0.0977042
\(964\) 4.22863 0.136195
\(965\) 0 0
\(966\) −94.2442 −3.03226
\(967\) 11.6811 0.375640 0.187820 0.982204i \(-0.439858\pi\)
0.187820 + 0.982204i \(0.439858\pi\)
\(968\) −166.597 −5.35464
\(969\) −11.3839 −0.365703
\(970\) 0 0
\(971\) 11.1262 0.357057 0.178529 0.983935i \(-0.442866\pi\)
0.178529 + 0.983935i \(0.442866\pi\)
\(972\) −10.0761 −0.323191
\(973\) −53.8517 −1.72641
\(974\) 22.0900 0.707810
\(975\) 0 0
\(976\) 76.4979 2.44864
\(977\) 62.1661 1.98887 0.994434 0.105358i \(-0.0335987\pi\)
0.994434 + 0.105358i \(0.0335987\pi\)
\(978\) 70.2720 2.24705
\(979\) −66.7647 −2.13381
\(980\) 0 0
\(981\) −0.898977 −0.0287021
\(982\) −16.6625 −0.531723
\(983\) −39.9072 −1.27284 −0.636422 0.771341i \(-0.719586\pi\)
−0.636422 + 0.771341i \(0.719586\pi\)
\(984\) 20.8923 0.666023
\(985\) 0 0
\(986\) 7.29743 0.232397
\(987\) −84.7687 −2.69822
\(988\) −21.5642 −0.686048
\(989\) 10.4088 0.330982
\(990\) 0 0
\(991\) 28.5376 0.906527 0.453264 0.891376i \(-0.350260\pi\)
0.453264 + 0.891376i \(0.350260\pi\)
\(992\) 9.56697 0.303751
\(993\) −25.0690 −0.795541
\(994\) 68.6331 2.17691
\(995\) 0 0
\(996\) −103.344 −3.27457
\(997\) −30.6103 −0.969438 −0.484719 0.874670i \(-0.661078\pi\)
−0.484719 + 0.874670i \(0.661078\pi\)
\(998\) 57.8262 1.83046
\(999\) 55.7778 1.76473
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.1.3 46
5.2 odd 4 1205.2.b.c.724.3 46
5.3 odd 4 1205.2.b.c.724.44 yes 46
5.4 even 2 inner 6025.2.a.p.1.44 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.3 46 5.2 odd 4
1205.2.b.c.724.44 yes 46 5.3 odd 4
6025.2.a.p.1.3 46 1.1 even 1 trivial
6025.2.a.p.1.44 46 5.4 even 2 inner