Properties

Label 5733.2.a.bd.1.3
Level $5733$
Weight $2$
Character 5733.1
Self dual yes
Analytic conductor $45.778$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(45.7782354788\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.404.1
Defining polynomial: \(x^{3} - x^{2} - 5 x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 637)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.65544\) of defining polynomial
Character \(\chi\) \(=\) 5733.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.65544 q^{2} +5.05137 q^{4} -3.65544 q^{5} +8.10275 q^{8} +O(q^{10})\) \(q+2.65544 q^{2} +5.05137 q^{4} -3.65544 q^{5} +8.10275 q^{8} -9.70682 q^{10} -0.655442 q^{11} -1.00000 q^{13} +11.4136 q^{16} -2.39593 q^{17} -2.70682 q^{19} -18.4650 q^{20} -1.74049 q^{22} -7.36226 q^{23} +8.36226 q^{25} -2.65544 q^{26} +0.208136 q^{29} -1.13642 q^{31} +14.1027 q^{32} -6.36226 q^{34} -7.44731 q^{37} -7.18780 q^{38} -29.6191 q^{40} +10.2055 q^{41} -3.10275 q^{43} -3.31088 q^{44} -19.5501 q^{46} -4.60407 q^{47} +22.2055 q^{50} -5.05137 q^{52} -5.25951 q^{53} +2.39593 q^{55} +0.552694 q^{58} -8.25951 q^{59} -1.89725 q^{61} -3.01770 q^{62} +14.6218 q^{64} +3.65544 q^{65} -12.8946 q^{67} -12.1027 q^{68} +6.75819 q^{71} +12.5367 q^{73} -19.7759 q^{74} -13.6731 q^{76} -1.51902 q^{79} -41.7219 q^{80} +27.1001 q^{82} -15.7582 q^{83} +8.75819 q^{85} -8.23917 q^{86} -5.31088 q^{88} +14.8096 q^{89} -37.1895 q^{92} -12.2258 q^{94} +9.89461 q^{95} -10.0177 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 6 q^{8} + O(q^{10}) \) \( 3 q + 2 q^{2} + 6 q^{4} - 5 q^{5} + 6 q^{8} - 14 q^{10} + 4 q^{11} - 3 q^{13} + 4 q^{16} - 4 q^{17} + 7 q^{19} - 16 q^{20} - 8 q^{22} - q^{23} + 4 q^{25} - 2 q^{26} + 7 q^{29} - 3 q^{31} + 24 q^{32} + 2 q^{34} - 10 q^{37} - 12 q^{38} - 22 q^{40} - 6 q^{41} + 9 q^{43} + 2 q^{44} - 28 q^{46} - 17 q^{47} + 30 q^{50} - 6 q^{52} - 13 q^{53} + 4 q^{55} + 14 q^{58} - 22 q^{59} - 24 q^{61} + 18 q^{62} + 20 q^{64} + 5 q^{65} - 14 q^{67} - 18 q^{68} - 4 q^{71} + 5 q^{73} - 8 q^{74} - 8 q^{76} + q^{79} - 40 q^{80} + 20 q^{82} - 23 q^{83} + 2 q^{85} - 6 q^{86} - 4 q^{88} + 11 q^{89} - 30 q^{92} - 16 q^{94} + 5 q^{95} - 3 q^{97} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.65544 1.87768 0.938841 0.344352i \(-0.111901\pi\)
0.938841 + 0.344352i \(0.111901\pi\)
\(3\) 0 0
\(4\) 5.05137 2.52569
\(5\) −3.65544 −1.63476 −0.817382 0.576096i \(-0.804575\pi\)
−0.817382 + 0.576096i \(0.804575\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.10275 2.86475
\(9\) 0 0
\(10\) −9.70682 −3.06956
\(11\) −0.655442 −0.197623 −0.0988117 0.995106i \(-0.531504\pi\)
−0.0988117 + 0.995106i \(0.531504\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 11.4136 2.85341
\(17\) −2.39593 −0.581099 −0.290549 0.956860i \(-0.593838\pi\)
−0.290549 + 0.956860i \(0.593838\pi\)
\(18\) 0 0
\(19\) −2.70682 −0.620986 −0.310493 0.950576i \(-0.600494\pi\)
−0.310493 + 0.950576i \(0.600494\pi\)
\(20\) −18.4650 −4.12890
\(21\) 0 0
\(22\) −1.74049 −0.371074
\(23\) −7.36226 −1.53514 −0.767569 0.640967i \(-0.778534\pi\)
−0.767569 + 0.640967i \(0.778534\pi\)
\(24\) 0 0
\(25\) 8.36226 1.67245
\(26\) −2.65544 −0.520775
\(27\) 0 0
\(28\) 0 0
\(29\) 0.208136 0.0386499 0.0193250 0.999813i \(-0.493848\pi\)
0.0193250 + 0.999813i \(0.493848\pi\)
\(30\) 0 0
\(31\) −1.13642 −0.204107 −0.102054 0.994779i \(-0.532541\pi\)
−0.102054 + 0.994779i \(0.532541\pi\)
\(32\) 14.1027 2.49304
\(33\) 0 0
\(34\) −6.36226 −1.09112
\(35\) 0 0
\(36\) 0 0
\(37\) −7.44731 −1.22433 −0.612165 0.790730i \(-0.709701\pi\)
−0.612165 + 0.790730i \(0.709701\pi\)
\(38\) −7.18780 −1.16601
\(39\) 0 0
\(40\) −29.6191 −4.68320
\(41\) 10.2055 1.59383 0.796915 0.604091i \(-0.206464\pi\)
0.796915 + 0.604091i \(0.206464\pi\)
\(42\) 0 0
\(43\) −3.10275 −0.473165 −0.236582 0.971611i \(-0.576027\pi\)
−0.236582 + 0.971611i \(0.576027\pi\)
\(44\) −3.31088 −0.499135
\(45\) 0 0
\(46\) −19.5501 −2.88250
\(47\) −4.60407 −0.671572 −0.335786 0.941938i \(-0.609002\pi\)
−0.335786 + 0.941938i \(0.609002\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 22.2055 3.14033
\(51\) 0 0
\(52\) −5.05137 −0.700500
\(53\) −5.25951 −0.722449 −0.361225 0.932479i \(-0.617641\pi\)
−0.361225 + 0.932479i \(0.617641\pi\)
\(54\) 0 0
\(55\) 2.39593 0.323067
\(56\) 0 0
\(57\) 0 0
\(58\) 0.552694 0.0725723
\(59\) −8.25951 −1.07530 −0.537648 0.843169i \(-0.680687\pi\)
−0.537648 + 0.843169i \(0.680687\pi\)
\(60\) 0 0
\(61\) −1.89725 −0.242918 −0.121459 0.992596i \(-0.538757\pi\)
−0.121459 + 0.992596i \(0.538757\pi\)
\(62\) −3.01770 −0.383248
\(63\) 0 0
\(64\) 14.6218 1.82772
\(65\) 3.65544 0.453402
\(66\) 0 0
\(67\) −12.8946 −1.57533 −0.787664 0.616105i \(-0.788710\pi\)
−0.787664 + 0.616105i \(0.788710\pi\)
\(68\) −12.1027 −1.46767
\(69\) 0 0
\(70\) 0 0
\(71\) 6.75819 0.802050 0.401025 0.916067i \(-0.368654\pi\)
0.401025 + 0.916067i \(0.368654\pi\)
\(72\) 0 0
\(73\) 12.5367 1.46731 0.733656 0.679521i \(-0.237812\pi\)
0.733656 + 0.679521i \(0.237812\pi\)
\(74\) −19.7759 −2.29890
\(75\) 0 0
\(76\) −13.6731 −1.56842
\(77\) 0 0
\(78\) 0 0
\(79\) −1.51902 −0.170903 −0.0854516 0.996342i \(-0.527233\pi\)
−0.0854516 + 0.996342i \(0.527233\pi\)
\(80\) −41.7219 −4.66465
\(81\) 0 0
\(82\) 27.1001 2.99271
\(83\) −15.7582 −1.72969 −0.864843 0.502042i \(-0.832582\pi\)
−0.864843 + 0.502042i \(0.832582\pi\)
\(84\) 0 0
\(85\) 8.75819 0.949959
\(86\) −8.23917 −0.888453
\(87\) 0 0
\(88\) −5.31088 −0.566142
\(89\) 14.8096 1.56981 0.784905 0.619616i \(-0.212712\pi\)
0.784905 + 0.619616i \(0.212712\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −37.1895 −3.87728
\(93\) 0 0
\(94\) −12.2258 −1.26100
\(95\) 9.89461 1.01517
\(96\) 0 0
\(97\) −10.0177 −1.01714 −0.508572 0.861020i \(-0.669826\pi\)
−0.508572 + 0.861020i \(0.669826\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 42.2409 4.22409
\(101\) 3.01770 0.300273 0.150136 0.988665i \(-0.452029\pi\)
0.150136 + 0.988665i \(0.452029\pi\)
\(102\) 0 0
\(103\) −5.03804 −0.496413 −0.248207 0.968707i \(-0.579841\pi\)
−0.248207 + 0.968707i \(0.579841\pi\)
\(104\) −8.10275 −0.794540
\(105\) 0 0
\(106\) −13.9663 −1.35653
\(107\) −11.8432 −1.14493 −0.572465 0.819929i \(-0.694013\pi\)
−0.572465 + 0.819929i \(0.694013\pi\)
\(108\) 0 0
\(109\) 3.55005 0.340034 0.170017 0.985441i \(-0.445618\pi\)
0.170017 + 0.985441i \(0.445618\pi\)
\(110\) 6.36226 0.606618
\(111\) 0 0
\(112\) 0 0
\(113\) 9.46501 0.890393 0.445197 0.895433i \(-0.353134\pi\)
0.445197 + 0.895433i \(0.353134\pi\)
\(114\) 0 0
\(115\) 26.9123 2.50959
\(116\) 1.05137 0.0976176
\(117\) 0 0
\(118\) −21.9327 −2.01906
\(119\) 0 0
\(120\) 0 0
\(121\) −10.5704 −0.960945
\(122\) −5.03804 −0.456123
\(123\) 0 0
\(124\) −5.74049 −0.515511
\(125\) −12.2905 −1.09930
\(126\) 0 0
\(127\) 5.46765 0.485175 0.242588 0.970130i \(-0.422004\pi\)
0.242588 + 0.970130i \(0.422004\pi\)
\(128\) 10.6218 0.938841
\(129\) 0 0
\(130\) 9.70682 0.851344
\(131\) −9.82991 −0.858843 −0.429421 0.903104i \(-0.641282\pi\)
−0.429421 + 0.903104i \(0.641282\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −34.2409 −2.95796
\(135\) 0 0
\(136\) −19.4136 −1.66471
\(137\) −17.5501 −1.49940 −0.749701 0.661777i \(-0.769803\pi\)
−0.749701 + 0.661777i \(0.769803\pi\)
\(138\) 0 0
\(139\) −4.91495 −0.416881 −0.208440 0.978035i \(-0.566839\pi\)
−0.208440 + 0.978035i \(0.566839\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 17.9460 1.50599
\(143\) 0.655442 0.0548108
\(144\) 0 0
\(145\) −0.760830 −0.0631835
\(146\) 33.2905 2.75515
\(147\) 0 0
\(148\) −37.6191 −3.09227
\(149\) 10.3419 0.847243 0.423621 0.905839i \(-0.360759\pi\)
0.423621 + 0.905839i \(0.360759\pi\)
\(150\) 0 0
\(151\) 5.07171 0.412730 0.206365 0.978475i \(-0.433837\pi\)
0.206365 + 0.978475i \(0.433837\pi\)
\(152\) −21.9327 −1.77897
\(153\) 0 0
\(154\) 0 0
\(155\) 4.15412 0.333667
\(156\) 0 0
\(157\) −12.6014 −1.00570 −0.502852 0.864373i \(-0.667716\pi\)
−0.502852 + 0.864373i \(0.667716\pi\)
\(158\) −4.03367 −0.320902
\(159\) 0 0
\(160\) −51.5518 −4.07553
\(161\) 0 0
\(162\) 0 0
\(163\) 3.20814 0.251281 0.125640 0.992076i \(-0.459901\pi\)
0.125640 + 0.992076i \(0.459901\pi\)
\(164\) 51.5518 4.02552
\(165\) 0 0
\(166\) −41.8450 −3.24780
\(167\) −8.12045 −0.628379 −0.314190 0.949360i \(-0.601733\pi\)
−0.314190 + 0.949360i \(0.601733\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 23.2569 1.78372
\(171\) 0 0
\(172\) −15.6731 −1.19507
\(173\) 10.3286 0.785268 0.392634 0.919695i \(-0.371564\pi\)
0.392634 + 0.919695i \(0.371564\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −7.48098 −0.563900
\(177\) 0 0
\(178\) 39.3259 2.94760
\(179\) 2.37823 0.177757 0.0888786 0.996042i \(-0.471672\pi\)
0.0888786 + 0.996042i \(0.471672\pi\)
\(180\) 0 0
\(181\) 21.8096 1.62109 0.810546 0.585675i \(-0.199170\pi\)
0.810546 + 0.585675i \(0.199170\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −59.6545 −4.39779
\(185\) 27.2232 2.00149
\(186\) 0 0
\(187\) 1.57040 0.114839
\(188\) −23.2569 −1.69618
\(189\) 0 0
\(190\) 26.2746 1.90616
\(191\) 25.0868 1.81522 0.907608 0.419819i \(-0.137907\pi\)
0.907608 + 0.419819i \(0.137907\pi\)
\(192\) 0 0
\(193\) 11.3109 0.814175 0.407088 0.913389i \(-0.366544\pi\)
0.407088 + 0.913389i \(0.366544\pi\)
\(194\) −26.6014 −1.90987
\(195\) 0 0
\(196\) 0 0
\(197\) 16.7919 1.19637 0.598185 0.801358i \(-0.295889\pi\)
0.598185 + 0.801358i \(0.295889\pi\)
\(198\) 0 0
\(199\) 20.5341 1.45562 0.727811 0.685777i \(-0.240538\pi\)
0.727811 + 0.685777i \(0.240538\pi\)
\(200\) 67.7573 4.79116
\(201\) 0 0
\(202\) 8.01333 0.563816
\(203\) 0 0
\(204\) 0 0
\(205\) −37.3056 −2.60554
\(206\) −13.3782 −0.932105
\(207\) 0 0
\(208\) −11.4136 −0.791393
\(209\) 1.77416 0.122721
\(210\) 0 0
\(211\) −15.7785 −1.08624 −0.543119 0.839655i \(-0.682757\pi\)
−0.543119 + 0.839655i \(0.682757\pi\)
\(212\) −26.5678 −1.82468
\(213\) 0 0
\(214\) −31.4490 −2.14981
\(215\) 11.3419 0.773512
\(216\) 0 0
\(217\) 0 0
\(218\) 9.42697 0.638475
\(219\) 0 0
\(220\) 12.1027 0.815967
\(221\) 2.39593 0.161168
\(222\) 0 0
\(223\) −8.44731 −0.565673 −0.282837 0.959168i \(-0.591275\pi\)
−0.282837 + 0.959168i \(0.591275\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 25.1338 1.67187
\(227\) −6.68912 −0.443972 −0.221986 0.975050i \(-0.571254\pi\)
−0.221986 + 0.975050i \(0.571254\pi\)
\(228\) 0 0
\(229\) 8.63510 0.570624 0.285312 0.958435i \(-0.407903\pi\)
0.285312 + 0.958435i \(0.407903\pi\)
\(230\) 71.4641 4.71220
\(231\) 0 0
\(232\) 1.68648 0.110723
\(233\) 4.16745 0.273019 0.136510 0.990639i \(-0.456412\pi\)
0.136510 + 0.990639i \(0.456412\pi\)
\(234\) 0 0
\(235\) 16.8299 1.09786
\(236\) −41.7219 −2.71586
\(237\) 0 0
\(238\) 0 0
\(239\) 1.79450 0.116077 0.0580384 0.998314i \(-0.481515\pi\)
0.0580384 + 0.998314i \(0.481515\pi\)
\(240\) 0 0
\(241\) 13.8609 0.892862 0.446431 0.894818i \(-0.352695\pi\)
0.446431 + 0.894818i \(0.352695\pi\)
\(242\) −28.0691 −1.80435
\(243\) 0 0
\(244\) −9.58373 −0.613535
\(245\) 0 0
\(246\) 0 0
\(247\) 2.70682 0.172231
\(248\) −9.20814 −0.584717
\(249\) 0 0
\(250\) −32.6368 −2.06413
\(251\) −14.7449 −0.930687 −0.465344 0.885130i \(-0.654069\pi\)
−0.465344 + 0.885130i \(0.654069\pi\)
\(252\) 0 0
\(253\) 4.82554 0.303379
\(254\) 14.5190 0.911004
\(255\) 0 0
\(256\) −1.03804 −0.0648776
\(257\) −23.7068 −1.47879 −0.739395 0.673272i \(-0.764888\pi\)
−0.739395 + 0.673272i \(0.764888\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 18.4650 1.14515
\(261\) 0 0
\(262\) −26.1027 −1.61263
\(263\) −11.3756 −0.701449 −0.350725 0.936479i \(-0.614065\pi\)
−0.350725 + 0.936479i \(0.614065\pi\)
\(264\) 0 0
\(265\) 19.2258 1.18103
\(266\) 0 0
\(267\) 0 0
\(268\) −65.1355 −3.97878
\(269\) 11.1054 0.677107 0.338554 0.940947i \(-0.390062\pi\)
0.338554 + 0.940947i \(0.390062\pi\)
\(270\) 0 0
\(271\) −12.7245 −0.772959 −0.386480 0.922298i \(-0.626309\pi\)
−0.386480 + 0.922298i \(0.626309\pi\)
\(272\) −27.3463 −1.65811
\(273\) 0 0
\(274\) −46.6032 −2.81540
\(275\) −5.48098 −0.330515
\(276\) 0 0
\(277\) −3.00000 −0.180253 −0.0901263 0.995930i \(-0.528727\pi\)
−0.0901263 + 0.995930i \(0.528727\pi\)
\(278\) −13.0514 −0.782769
\(279\) 0 0
\(280\) 0 0
\(281\) −3.44731 −0.205649 −0.102825 0.994700i \(-0.532788\pi\)
−0.102825 + 0.994700i \(0.532788\pi\)
\(282\) 0 0
\(283\) −12.4783 −0.741760 −0.370880 0.928681i \(-0.620944\pi\)
−0.370880 + 0.928681i \(0.620944\pi\)
\(284\) 34.1382 2.02573
\(285\) 0 0
\(286\) 1.74049 0.102917
\(287\) 0 0
\(288\) 0 0
\(289\) −11.2595 −0.662324
\(290\) −2.02034 −0.118638
\(291\) 0 0
\(292\) 63.3277 3.70597
\(293\) 13.5341 0.790670 0.395335 0.918537i \(-0.370629\pi\)
0.395335 + 0.918537i \(0.370629\pi\)
\(294\) 0 0
\(295\) 30.1922 1.75786
\(296\) −60.3436 −3.50740
\(297\) 0 0
\(298\) 27.4624 1.59085
\(299\) 7.36226 0.425770
\(300\) 0 0
\(301\) 0 0
\(302\) 13.4676 0.774976
\(303\) 0 0
\(304\) −30.8946 −1.77193
\(305\) 6.93529 0.397114
\(306\) 0 0
\(307\) 28.2365 1.61154 0.805772 0.592226i \(-0.201751\pi\)
0.805772 + 0.592226i \(0.201751\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 11.0310 0.626521
\(311\) 24.7042 1.40085 0.700423 0.713728i \(-0.252995\pi\)
0.700423 + 0.713728i \(0.252995\pi\)
\(312\) 0 0
\(313\) −20.8122 −1.17638 −0.588188 0.808724i \(-0.700158\pi\)
−0.588188 + 0.808724i \(0.700158\pi\)
\(314\) −33.4624 −1.88839
\(315\) 0 0
\(316\) −7.67314 −0.431648
\(317\) −26.1382 −1.46806 −0.734032 0.679114i \(-0.762364\pi\)
−0.734032 + 0.679114i \(0.762364\pi\)
\(318\) 0 0
\(319\) −0.136421 −0.00763813
\(320\) −53.4490 −2.98789
\(321\) 0 0
\(322\) 0 0
\(323\) 6.48535 0.360854
\(324\) 0 0
\(325\) −8.36226 −0.463855
\(326\) 8.51902 0.471825
\(327\) 0 0
\(328\) 82.6926 4.56593
\(329\) 0 0
\(330\) 0 0
\(331\) −24.1382 −1.32675 −0.663376 0.748286i \(-0.730877\pi\)
−0.663376 + 0.748286i \(0.730877\pi\)
\(332\) −79.6005 −4.36865
\(333\) 0 0
\(334\) −21.5634 −1.17990
\(335\) 47.1355 2.57529
\(336\) 0 0
\(337\) −30.5297 −1.66306 −0.831530 0.555480i \(-0.812534\pi\)
−0.831530 + 0.555480i \(0.812534\pi\)
\(338\) 2.65544 0.144437
\(339\) 0 0
\(340\) 44.2409 2.39930
\(341\) 0.744859 0.0403364
\(342\) 0 0
\(343\) 0 0
\(344\) −25.1408 −1.35550
\(345\) 0 0
\(346\) 27.4270 1.47448
\(347\) 24.9974 1.34193 0.670964 0.741490i \(-0.265880\pi\)
0.670964 + 0.741490i \(0.265880\pi\)
\(348\) 0 0
\(349\) −1.83887 −0.0984324 −0.0492162 0.998788i \(-0.515672\pi\)
−0.0492162 + 0.998788i \(0.515672\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −9.24354 −0.492682
\(353\) 23.2569 1.23784 0.618919 0.785455i \(-0.287571\pi\)
0.618919 + 0.785455i \(0.287571\pi\)
\(354\) 0 0
\(355\) −24.7042 −1.31116
\(356\) 74.8087 3.96485
\(357\) 0 0
\(358\) 6.31525 0.333772
\(359\) 21.4473 1.13195 0.565973 0.824424i \(-0.308501\pi\)
0.565973 + 0.824424i \(0.308501\pi\)
\(360\) 0 0
\(361\) −11.6731 −0.614376
\(362\) 57.9140 3.04389
\(363\) 0 0
\(364\) 0 0
\(365\) −45.8273 −2.39871
\(366\) 0 0
\(367\) −1.12045 −0.0584870 −0.0292435 0.999572i \(-0.509310\pi\)
−0.0292435 + 0.999572i \(0.509310\pi\)
\(368\) −84.0301 −4.38037
\(369\) 0 0
\(370\) 72.2896 3.75816
\(371\) 0 0
\(372\) 0 0
\(373\) 15.6058 0.808038 0.404019 0.914751i \(-0.367613\pi\)
0.404019 + 0.914751i \(0.367613\pi\)
\(374\) 4.17009 0.215630
\(375\) 0 0
\(376\) −37.3056 −1.92389
\(377\) −0.208136 −0.0107196
\(378\) 0 0
\(379\) 12.7849 0.656714 0.328357 0.944554i \(-0.393505\pi\)
0.328357 + 0.944554i \(0.393505\pi\)
\(380\) 49.9814 2.56399
\(381\) 0 0
\(382\) 66.6165 3.40840
\(383\) −34.0354 −1.73913 −0.869564 0.493820i \(-0.835600\pi\)
−0.869564 + 0.493820i \(0.835600\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 30.0354 1.52876
\(387\) 0 0
\(388\) −50.6032 −2.56899
\(389\) 24.6705 1.25084 0.625422 0.780287i \(-0.284927\pi\)
0.625422 + 0.780287i \(0.284927\pi\)
\(390\) 0 0
\(391\) 17.6395 0.892066
\(392\) 0 0
\(393\) 0 0
\(394\) 44.5898 2.24640
\(395\) 5.55269 0.279386
\(396\) 0 0
\(397\) −4.97966 −0.249922 −0.124961 0.992162i \(-0.539881\pi\)
−0.124961 + 0.992162i \(0.539881\pi\)
\(398\) 54.5271 2.73320
\(399\) 0 0
\(400\) 95.4438 4.77219
\(401\) −0.689115 −0.0344128 −0.0172064 0.999852i \(-0.505477\pi\)
−0.0172064 + 0.999852i \(0.505477\pi\)
\(402\) 0 0
\(403\) 1.13642 0.0566092
\(404\) 15.2435 0.758394
\(405\) 0 0
\(406\) 0 0
\(407\) 4.88128 0.241956
\(408\) 0 0
\(409\) 19.9770 0.987800 0.493900 0.869519i \(-0.335571\pi\)
0.493900 + 0.869519i \(0.335571\pi\)
\(410\) −99.0629 −4.89237
\(411\) 0 0
\(412\) −25.4490 −1.25378
\(413\) 0 0
\(414\) 0 0
\(415\) 57.6032 2.82763
\(416\) −14.1027 −0.691444
\(417\) 0 0
\(418\) 4.71119 0.230432
\(419\) −19.6661 −0.960754 −0.480377 0.877062i \(-0.659500\pi\)
−0.480377 + 0.877062i \(0.659500\pi\)
\(420\) 0 0
\(421\) 14.9283 0.727560 0.363780 0.931485i \(-0.381486\pi\)
0.363780 + 0.931485i \(0.381486\pi\)
\(422\) −41.8990 −2.03961
\(423\) 0 0
\(424\) −42.6165 −2.06964
\(425\) −20.0354 −0.971860
\(426\) 0 0
\(427\) 0 0
\(428\) −59.8246 −2.89173
\(429\) 0 0
\(430\) 30.1178 1.45241
\(431\) 32.6838 1.57433 0.787163 0.616746i \(-0.211549\pi\)
0.787163 + 0.616746i \(0.211549\pi\)
\(432\) 0 0
\(433\) −8.96196 −0.430684 −0.215342 0.976539i \(-0.569087\pi\)
−0.215342 + 0.976539i \(0.569087\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 17.9327 0.858818
\(437\) 19.9283 0.953299
\(438\) 0 0
\(439\) −7.93265 −0.378605 −0.189302 0.981919i \(-0.560623\pi\)
−0.189302 + 0.981919i \(0.560623\pi\)
\(440\) 19.4136 0.925509
\(441\) 0 0
\(442\) 6.36226 0.302622
\(443\) 8.91058 0.423355 0.211677 0.977340i \(-0.432107\pi\)
0.211677 + 0.977340i \(0.432107\pi\)
\(444\) 0 0
\(445\) −54.1355 −2.56627
\(446\) −22.4313 −1.06215
\(447\) 0 0
\(448\) 0 0
\(449\) 8.45168 0.398859 0.199430 0.979912i \(-0.436091\pi\)
0.199430 + 0.979912i \(0.436091\pi\)
\(450\) 0 0
\(451\) −6.68912 −0.314978
\(452\) 47.8113 2.24885
\(453\) 0 0
\(454\) −17.7626 −0.833638
\(455\) 0 0
\(456\) 0 0
\(457\) 23.1692 1.08381 0.541904 0.840440i \(-0.317703\pi\)
0.541904 + 0.840440i \(0.317703\pi\)
\(458\) 22.9300 1.07145
\(459\) 0 0
\(460\) 135.944 6.33843
\(461\) −2.27284 −0.105857 −0.0529284 0.998598i \(-0.516856\pi\)
−0.0529284 + 0.998598i \(0.516856\pi\)
\(462\) 0 0
\(463\) −4.10976 −0.190997 −0.0954983 0.995430i \(-0.530444\pi\)
−0.0954983 + 0.995430i \(0.530444\pi\)
\(464\) 2.37559 0.110284
\(465\) 0 0
\(466\) 11.0664 0.512643
\(467\) −32.9150 −1.52312 −0.761561 0.648093i \(-0.775567\pi\)
−0.761561 + 0.648093i \(0.775567\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 44.6908 2.06143
\(471\) 0 0
\(472\) −66.9247 −3.08046
\(473\) 2.03367 0.0935084
\(474\) 0 0
\(475\) −22.6351 −1.03857
\(476\) 0 0
\(477\) 0 0
\(478\) 4.76520 0.217955
\(479\) 9.31525 0.425625 0.212812 0.977093i \(-0.431738\pi\)
0.212812 + 0.977093i \(0.431738\pi\)
\(480\) 0 0
\(481\) 7.44731 0.339568
\(482\) 36.8069 1.67651
\(483\) 0 0
\(484\) −53.3950 −2.42705
\(485\) 36.6191 1.66279
\(486\) 0 0
\(487\) 20.2409 0.917203 0.458601 0.888642i \(-0.348351\pi\)
0.458601 + 0.888642i \(0.348351\pi\)
\(488\) −15.3730 −0.695901
\(489\) 0 0
\(490\) 0 0
\(491\) 4.36226 0.196866 0.0984330 0.995144i \(-0.468617\pi\)
0.0984330 + 0.995144i \(0.468617\pi\)
\(492\) 0 0
\(493\) −0.498680 −0.0224594
\(494\) 7.18780 0.323394
\(495\) 0 0
\(496\) −12.9707 −0.582401
\(497\) 0 0
\(498\) 0 0
\(499\) 9.69348 0.433940 0.216970 0.976178i \(-0.430383\pi\)
0.216970 + 0.976178i \(0.430383\pi\)
\(500\) −62.0841 −2.77649
\(501\) 0 0
\(502\) −39.1541 −1.74753
\(503\) −2.64843 −0.118088 −0.0590439 0.998255i \(-0.518805\pi\)
−0.0590439 + 0.998255i \(0.518805\pi\)
\(504\) 0 0
\(505\) −11.0310 −0.490875
\(506\) 12.8139 0.569649
\(507\) 0 0
\(508\) 27.6191 1.22540
\(509\) 13.9416 0.617951 0.308976 0.951070i \(-0.400014\pi\)
0.308976 + 0.951070i \(0.400014\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −24.0000 −1.06066
\(513\) 0 0
\(514\) −62.9521 −2.77670
\(515\) 18.4163 0.811518
\(516\) 0 0
\(517\) 3.01770 0.132718
\(518\) 0 0
\(519\) 0 0
\(520\) 29.6191 1.29888
\(521\) 14.6218 0.640591 0.320296 0.947318i \(-0.396218\pi\)
0.320296 + 0.947318i \(0.396218\pi\)
\(522\) 0 0
\(523\) 16.5190 0.722326 0.361163 0.932503i \(-0.382380\pi\)
0.361163 + 0.932503i \(0.382380\pi\)
\(524\) −49.6545 −2.16917
\(525\) 0 0
\(526\) −30.2072 −1.31710
\(527\) 2.72279 0.118607
\(528\) 0 0
\(529\) 31.2029 1.35665
\(530\) 51.0531 2.21761
\(531\) 0 0
\(532\) 0 0
\(533\) −10.2055 −0.442049
\(534\) 0 0
\(535\) 43.2923 1.87169
\(536\) −104.482 −4.51293
\(537\) 0 0
\(538\) 29.4897 1.27139
\(539\) 0 0
\(540\) 0 0
\(541\) −43.1018 −1.85309 −0.926546 0.376181i \(-0.877237\pi\)
−0.926546 + 0.376181i \(0.877237\pi\)
\(542\) −33.7892 −1.45137
\(543\) 0 0
\(544\) −33.7892 −1.44870
\(545\) −12.9770 −0.555874
\(546\) 0 0
\(547\) −13.5057 −0.577462 −0.288731 0.957410i \(-0.593233\pi\)
−0.288731 + 0.957410i \(0.593233\pi\)
\(548\) −88.6519 −3.78702
\(549\) 0 0
\(550\) −14.5544 −0.620603
\(551\) −0.563387 −0.0240011
\(552\) 0 0
\(553\) 0 0
\(554\) −7.96633 −0.338457
\(555\) 0 0
\(556\) −24.8273 −1.05291
\(557\) −1.35157 −0.0572677 −0.0286338 0.999590i \(-0.509116\pi\)
−0.0286338 + 0.999590i \(0.509116\pi\)
\(558\) 0 0
\(559\) 3.10275 0.131232
\(560\) 0 0
\(561\) 0 0
\(562\) −9.15412 −0.386143
\(563\) −31.7626 −1.33863 −0.669316 0.742978i \(-0.733413\pi\)
−0.669316 + 0.742978i \(0.733413\pi\)
\(564\) 0 0
\(565\) −34.5988 −1.45558
\(566\) −33.1355 −1.39279
\(567\) 0 0
\(568\) 54.7599 2.29768
\(569\) −30.3730 −1.27330 −0.636650 0.771153i \(-0.719680\pi\)
−0.636650 + 0.771153i \(0.719680\pi\)
\(570\) 0 0
\(571\) −0.432244 −0.0180888 −0.00904442 0.999959i \(-0.502879\pi\)
−0.00904442 + 0.999959i \(0.502879\pi\)
\(572\) 3.31088 0.138435
\(573\) 0 0
\(574\) 0 0
\(575\) −61.5651 −2.56744
\(576\) 0 0
\(577\) 18.1382 0.755101 0.377551 0.925989i \(-0.376766\pi\)
0.377551 + 0.925989i \(0.376766\pi\)
\(578\) −29.8990 −1.24363
\(579\) 0 0
\(580\) −3.84324 −0.159582
\(581\) 0 0
\(582\) 0 0
\(583\) 3.44731 0.142773
\(584\) 101.582 4.20349
\(585\) 0 0
\(586\) 35.9390 1.48463
\(587\) −19.3065 −0.796865 −0.398433 0.917198i \(-0.630446\pi\)
−0.398433 + 0.917198i \(0.630446\pi\)
\(588\) 0 0
\(589\) 3.07608 0.126748
\(590\) 80.1736 3.30069
\(591\) 0 0
\(592\) −85.0008 −3.49351
\(593\) −8.20113 −0.336780 −0.168390 0.985720i \(-0.553857\pi\)
−0.168390 + 0.985720i \(0.553857\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 52.2409 2.13987
\(597\) 0 0
\(598\) 19.5501 0.799461
\(599\) −23.4783 −0.959299 −0.479649 0.877460i \(-0.659236\pi\)
−0.479649 + 0.877460i \(0.659236\pi\)
\(600\) 0 0
\(601\) −8.96196 −0.365566 −0.182783 0.983153i \(-0.558511\pi\)
−0.182783 + 0.983153i \(0.558511\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 25.6191 1.04243
\(605\) 38.6395 1.57092
\(606\) 0 0
\(607\) 43.4641 1.76415 0.882077 0.471106i \(-0.156145\pi\)
0.882077 + 0.471106i \(0.156145\pi\)
\(608\) −38.1736 −1.54814
\(609\) 0 0
\(610\) 18.4163 0.745653
\(611\) 4.60407 0.186261
\(612\) 0 0
\(613\) −21.4490 −0.866318 −0.433159 0.901317i \(-0.642601\pi\)
−0.433159 + 0.901317i \(0.642601\pi\)
\(614\) 74.9805 3.02597
\(615\) 0 0
\(616\) 0 0
\(617\) 12.1294 0.488312 0.244156 0.969736i \(-0.421489\pi\)
0.244156 + 0.969736i \(0.421489\pi\)
\(618\) 0 0
\(619\) 12.7245 0.511442 0.255721 0.966751i \(-0.417687\pi\)
0.255721 + 0.966751i \(0.417687\pi\)
\(620\) 20.9840 0.842739
\(621\) 0 0
\(622\) 65.6005 2.63034
\(623\) 0 0
\(624\) 0 0
\(625\) 3.11608 0.124643
\(626\) −55.2656 −2.20886
\(627\) 0 0
\(628\) −63.6545 −2.54009
\(629\) 17.8432 0.711456
\(630\) 0 0
\(631\) −11.7538 −0.467912 −0.233956 0.972247i \(-0.575167\pi\)
−0.233956 + 0.972247i \(0.575167\pi\)
\(632\) −12.3082 −0.489596
\(633\) 0 0
\(634\) −69.4084 −2.75656
\(635\) −19.9867 −0.793147
\(636\) 0 0
\(637\) 0 0
\(638\) −0.362259 −0.0143420
\(639\) 0 0
\(640\) −38.8273 −1.53478
\(641\) −4.68648 −0.185105 −0.0925523 0.995708i \(-0.529503\pi\)
−0.0925523 + 0.995708i \(0.529503\pi\)
\(642\) 0 0
\(643\) −0.751182 −0.0296237 −0.0148119 0.999890i \(-0.504715\pi\)
−0.0148119 + 0.999890i \(0.504715\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 17.2215 0.677570
\(647\) −40.8476 −1.60589 −0.802943 0.596056i \(-0.796733\pi\)
−0.802943 + 0.596056i \(0.796733\pi\)
\(648\) 0 0
\(649\) 5.41363 0.212504
\(650\) −22.2055 −0.870971
\(651\) 0 0
\(652\) 16.2055 0.634656
\(653\) 46.4783 1.81884 0.909419 0.415881i \(-0.136527\pi\)
0.909419 + 0.415881i \(0.136527\pi\)
\(654\) 0 0
\(655\) 35.9327 1.40400
\(656\) 116.482 4.54785
\(657\) 0 0
\(658\) 0 0
\(659\) −30.3596 −1.18264 −0.591321 0.806436i \(-0.701394\pi\)
−0.591321 + 0.806436i \(0.701394\pi\)
\(660\) 0 0
\(661\) −0.107118 −0.00416640 −0.00208320 0.999998i \(-0.500663\pi\)
−0.00208320 + 0.999998i \(0.500663\pi\)
\(662\) −64.0975 −2.49122
\(663\) 0 0
\(664\) −127.685 −4.95513
\(665\) 0 0
\(666\) 0 0
\(667\) −1.53235 −0.0593330
\(668\) −41.0194 −1.58709
\(669\) 0 0
\(670\) 125.166 4.83557
\(671\) 1.24354 0.0480063
\(672\) 0 0
\(673\) 38.5385 1.48555 0.742774 0.669542i \(-0.233510\pi\)
0.742774 + 0.669542i \(0.233510\pi\)
\(674\) −81.0699 −3.12270
\(675\) 0 0
\(676\) 5.05137 0.194284
\(677\) 20.7803 0.798650 0.399325 0.916809i \(-0.369244\pi\)
0.399325 + 0.916809i \(0.369244\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 70.9654 2.72140
\(681\) 0 0
\(682\) 1.97793 0.0757388
\(683\) −27.5837 −1.05546 −0.527731 0.849412i \(-0.676957\pi\)
−0.527731 + 0.849412i \(0.676957\pi\)
\(684\) 0 0
\(685\) 64.1532 2.45117
\(686\) 0 0
\(687\) 0 0
\(688\) −35.4136 −1.35013
\(689\) 5.25951 0.200371
\(690\) 0 0
\(691\) 43.6775 1.66157 0.830785 0.556593i \(-0.187892\pi\)
0.830785 + 0.556593i \(0.187892\pi\)
\(692\) 52.1736 1.98334
\(693\) 0 0
\(694\) 66.3791 2.51971
\(695\) 17.9663 0.681502
\(696\) 0 0
\(697\) −24.4517 −0.926173
\(698\) −4.88301 −0.184825
\(699\) 0 0
\(700\) 0 0
\(701\) 20.8973 0.789278 0.394639 0.918836i \(-0.370870\pi\)
0.394639 + 0.918836i \(0.370870\pi\)
\(702\) 0 0
\(703\) 20.1585 0.760292
\(704\) −9.58373 −0.361200
\(705\) 0 0
\(706\) 61.7573 2.32427
\(707\) 0 0
\(708\) 0 0
\(709\) 9.93966 0.373292 0.186646 0.982427i \(-0.440238\pi\)
0.186646 + 0.982427i \(0.440238\pi\)
\(710\) −65.6005 −2.46194
\(711\) 0 0
\(712\) 119.998 4.49712
\(713\) 8.36663 0.313333
\(714\) 0 0
\(715\) −2.39593 −0.0896028
\(716\) 12.0133 0.448959
\(717\) 0 0
\(718\) 56.9521 2.12543
\(719\) 11.9797 0.446766 0.223383 0.974731i \(-0.428290\pi\)
0.223383 + 0.974731i \(0.428290\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −30.9974 −1.15360
\(723\) 0 0
\(724\) 110.168 4.09437
\(725\) 1.74049 0.0646402
\(726\) 0 0
\(727\) 24.1736 0.896547 0.448274 0.893896i \(-0.352039\pi\)
0.448274 + 0.893896i \(0.352039\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −121.692 −4.50401
\(731\) 7.43397 0.274955
\(732\) 0 0
\(733\) −36.4473 −1.34621 −0.673106 0.739546i \(-0.735040\pi\)
−0.673106 + 0.739546i \(0.735040\pi\)
\(734\) −2.97529 −0.109820
\(735\) 0 0
\(736\) −103.828 −3.82715
\(737\) 8.45168 0.311321
\(738\) 0 0
\(739\) 43.2772 1.59198 0.795989 0.605311i \(-0.206951\pi\)
0.795989 + 0.605311i \(0.206951\pi\)
\(740\) 137.515 5.05514
\(741\) 0 0
\(742\) 0 0
\(743\) −22.6572 −0.831211 −0.415606 0.909545i \(-0.636430\pi\)
−0.415606 + 0.909545i \(0.636430\pi\)
\(744\) 0 0
\(745\) −37.8043 −1.38504
\(746\) 41.4403 1.51724
\(747\) 0 0
\(748\) 7.93265 0.290047
\(749\) 0 0
\(750\) 0 0
\(751\) 29.8679 1.08990 0.544948 0.838470i \(-0.316549\pi\)
0.544948 + 0.838470i \(0.316549\pi\)
\(752\) −52.5491 −1.91627
\(753\) 0 0
\(754\) −0.552694 −0.0201279
\(755\) −18.5394 −0.674716
\(756\) 0 0
\(757\) 2.55706 0.0929380 0.0464690 0.998920i \(-0.485203\pi\)
0.0464690 + 0.998920i \(0.485203\pi\)
\(758\) 33.9494 1.23310
\(759\) 0 0
\(760\) 80.1736 2.90820
\(761\) −14.7289 −0.533922 −0.266961 0.963707i \(-0.586019\pi\)
−0.266961 + 0.963707i \(0.586019\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 126.723 4.58467
\(765\) 0 0
\(766\) −90.3791 −3.26553
\(767\) 8.25951 0.298234
\(768\) 0 0
\(769\) −36.1692 −1.30429 −0.652147 0.758092i \(-0.726132\pi\)
−0.652147 + 0.758092i \(0.726132\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 57.1355 2.05635
\(773\) −38.9567 −1.40117 −0.700587 0.713567i \(-0.747079\pi\)
−0.700587 + 0.713567i \(0.747079\pi\)
\(774\) 0 0
\(775\) −9.50305 −0.341360
\(776\) −81.1709 −2.91387
\(777\) 0 0
\(778\) 65.5111 2.34869
\(779\) −27.6244 −0.989747
\(780\) 0 0
\(781\) −4.42960 −0.158504
\(782\) 46.8406 1.67502
\(783\) 0 0
\(784\) 0 0
\(785\) 46.0638 1.64409
\(786\) 0 0
\(787\) 29.1045 1.03746 0.518731 0.854937i \(-0.326405\pi\)
0.518731 + 0.854937i \(0.326405\pi\)
\(788\) 84.8220 3.02166
\(789\) 0 0
\(790\) 14.7449 0.524599
\(791\) 0 0
\(792\) 0 0
\(793\) 1.89725 0.0673734
\(794\) −13.2232 −0.469274
\(795\) 0 0
\(796\) 103.725 3.67645
\(797\) 17.8920 0.633766 0.316883 0.948465i \(-0.397364\pi\)
0.316883 + 0.948465i \(0.397364\pi\)
\(798\) 0 0
\(799\) 11.0310 0.390250
\(800\) 117.931 4.16948
\(801\) 0 0
\(802\) −1.82991 −0.0646162
\(803\) −8.21710 −0.289975
\(804\) 0 0
\(805\) 0 0
\(806\) 3.01770 0.106294
\(807\) 0 0
\(808\) 24.4517 0.860207
\(809\) −20.4543 −0.719135 −0.359568 0.933119i \(-0.617076\pi\)
−0.359568 + 0.933119i \(0.617076\pi\)
\(810\) 0 0
\(811\) −31.6458 −1.11123 −0.555617 0.831438i \(-0.687518\pi\)
−0.555617 + 0.831438i \(0.687518\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 12.9620 0.454316
\(815\) −11.7272 −0.410784
\(816\) 0 0
\(817\) 8.39857 0.293829
\(818\) 53.0478 1.85477
\(819\) 0 0
\(820\) −188.445 −6.58077
\(821\) −18.0761 −0.630860 −0.315430 0.948949i \(-0.602149\pi\)
−0.315430 + 0.948949i \(0.602149\pi\)
\(822\) 0 0
\(823\) −23.0514 −0.803520 −0.401760 0.915745i \(-0.631601\pi\)
−0.401760 + 0.915745i \(0.631601\pi\)
\(824\) −40.8220 −1.42210
\(825\) 0 0
\(826\) 0 0
\(827\) 26.3756 0.917169 0.458585 0.888651i \(-0.348357\pi\)
0.458585 + 0.888651i \(0.348357\pi\)
\(828\) 0 0
\(829\) 45.1152 1.56691 0.783457 0.621446i \(-0.213454\pi\)
0.783457 + 0.621446i \(0.213454\pi\)
\(830\) 152.962 5.30938
\(831\) 0 0
\(832\) −14.6218 −0.506919
\(833\) 0 0
\(834\) 0 0
\(835\) 29.6838 1.02725
\(836\) 8.96196 0.309956
\(837\) 0 0
\(838\) −52.2223 −1.80399
\(839\) 30.4871 1.05253 0.526265 0.850320i \(-0.323592\pi\)
0.526265 + 0.850320i \(0.323592\pi\)
\(840\) 0 0
\(841\) −28.9567 −0.998506
\(842\) 39.6412 1.36613
\(843\) 0 0
\(844\) −79.7033 −2.74350
\(845\) −3.65544 −0.125751
\(846\) 0 0
\(847\) 0 0
\(848\) −60.0301 −2.06144
\(849\) 0 0
\(850\) −53.2029 −1.82484
\(851\) 54.8290 1.87951
\(852\) 0 0
\(853\) −33.2746 −1.13930 −0.569650 0.821888i \(-0.692921\pi\)
−0.569650 + 0.821888i \(0.692921\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −95.9628 −3.27994
\(857\) −45.6139 −1.55814 −0.779070 0.626937i \(-0.784308\pi\)
−0.779070 + 0.626937i \(0.784308\pi\)
\(858\) 0 0
\(859\) 20.9353 0.714303 0.357151 0.934046i \(-0.383748\pi\)
0.357151 + 0.934046i \(0.383748\pi\)
\(860\) 57.2923 1.95365
\(861\) 0 0
\(862\) 86.7900 2.95608
\(863\) −2.96196 −0.100826 −0.0504131 0.998728i \(-0.516054\pi\)
−0.0504131 + 0.998728i \(0.516054\pi\)
\(864\) 0 0
\(865\) −37.7556 −1.28373
\(866\) −23.7980 −0.808688
\(867\) 0 0
\(868\) 0 0
\(869\) 0.995631 0.0337745
\(870\) 0 0
\(871\) 12.8946 0.436917
\(872\) 28.7652 0.974113
\(873\) 0 0
\(874\) 52.9184 1.78999
\(875\) 0 0
\(876\) 0 0
\(877\) −36.9370 −1.24727 −0.623637 0.781714i \(-0.714346\pi\)
−0.623637 + 0.781714i \(0.714346\pi\)
\(878\) −21.0647 −0.710899
\(879\) 0 0
\(880\) 27.3463 0.921843
\(881\) −30.8946 −1.04087 −0.520433 0.853903i \(-0.674229\pi\)
−0.520433 + 0.853903i \(0.674229\pi\)
\(882\) 0 0
\(883\) −9.64648 −0.324630 −0.162315 0.986739i \(-0.551896\pi\)
−0.162315 + 0.986739i \(0.551896\pi\)
\(884\) 12.1027 0.407059
\(885\) 0 0
\(886\) 23.6615 0.794925
\(887\) 51.3056 1.72267 0.861337 0.508034i \(-0.169628\pi\)
0.861337 + 0.508034i \(0.169628\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −143.754 −4.81864
\(891\) 0 0
\(892\) −42.6705 −1.42871
\(893\) 12.4624 0.417037
\(894\) 0 0
\(895\) −8.69348 −0.290591
\(896\) 0 0
\(897\) 0 0
\(898\) 22.4429 0.748931
\(899\) −0.236531 −0.00788873
\(900\) 0 0
\(901\) 12.6014 0.419814
\(902\) −17.7626 −0.591429
\(903\) 0 0
\(904\) 76.6926 2.55076
\(905\) −79.7236 −2.65010
\(906\) 0 0
\(907\) −18.5385 −0.615559 −0.307780 0.951458i \(-0.599586\pi\)
−0.307780 + 0.951458i \(0.599586\pi\)
\(908\) −33.7892 −1.12133
\(909\) 0 0
\(910\) 0 0
\(911\) −20.7272 −0.686721 −0.343361 0.939204i \(-0.611565\pi\)
−0.343361 + 0.939204i \(0.611565\pi\)
\(912\) 0 0
\(913\) 10.3286 0.341826
\(914\) 61.5244 2.03505
\(915\) 0 0
\(916\) 43.6191 1.44122
\(917\) 0 0
\(918\) 0 0
\(919\) −5.13205 −0.169291 −0.0846454 0.996411i \(-0.526976\pi\)
−0.0846454 + 0.996411i \(0.526976\pi\)
\(920\) 218.064 7.18935
\(921\) 0 0
\(922\) −6.03540 −0.198765
\(923\) −6.75819 −0.222449
\(924\) 0 0
\(925\) −62.2763 −2.04763
\(926\) −10.9132 −0.358631
\(927\) 0 0
\(928\) 2.93529 0.0963557
\(929\) −19.9283 −0.653826 −0.326913 0.945054i \(-0.606008\pi\)
−0.326913 + 0.945054i \(0.606008\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 21.0514 0.689561
\(933\) 0 0
\(934\) −87.4038 −2.85994
\(935\) −5.74049 −0.187734
\(936\) 0 0
\(937\) −1.64475 −0.0537316 −0.0268658 0.999639i \(-0.508553\pi\)
−0.0268658 + 0.999639i \(0.508553\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 85.0142 2.77286
\(941\) 17.7849 0.579770 0.289885 0.957062i \(-0.406383\pi\)
0.289885 + 0.957062i \(0.406383\pi\)
\(942\) 0 0
\(943\) −75.1355 −2.44675
\(944\) −94.2710 −3.06826
\(945\) 0 0
\(946\) 5.40030 0.175579
\(947\) −10.6484 −0.346028 −0.173014 0.984919i \(-0.555351\pi\)
−0.173014 + 0.984919i \(0.555351\pi\)
\(948\) 0 0
\(949\) −12.5367 −0.406959
\(950\) −60.1062 −1.95010
\(951\) 0 0
\(952\) 0 0
\(953\) 41.5544 1.34608 0.673040 0.739606i \(-0.264988\pi\)
0.673040 + 0.739606i \(0.264988\pi\)
\(954\) 0 0
\(955\) −91.7033 −2.96745
\(956\) 9.06471 0.293174
\(957\) 0 0
\(958\) 24.7361 0.799188
\(959\) 0 0
\(960\) 0 0
\(961\) −29.7085 −0.958340
\(962\) 19.7759 0.637600
\(963\) 0 0
\(964\) 70.0168 2.25509
\(965\) −41.3463 −1.33098
\(966\) 0 0
\(967\) −5.51465 −0.177339 −0.0886696 0.996061i \(-0.528262\pi\)
−0.0886696 + 0.996061i \(0.528262\pi\)
\(968\) −85.6493 −2.75287
\(969\) 0 0
\(970\) 97.2400 3.12219
\(971\) −39.8246 −1.27803 −0.639017 0.769193i \(-0.720658\pi\)
−0.639017 + 0.769193i \(0.720658\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 53.7485 1.72221
\(975\) 0 0
\(976\) −21.6545 −0.693145
\(977\) −1.93092 −0.0617757 −0.0308879 0.999523i \(-0.509833\pi\)
−0.0308879 + 0.999523i \(0.509833\pi\)
\(978\) 0 0
\(979\) −9.70682 −0.310231
\(980\) 0 0
\(981\) 0 0
\(982\) 11.5837 0.369652
\(983\) 43.0238 1.37225 0.686123 0.727485i \(-0.259311\pi\)
0.686123 + 0.727485i \(0.259311\pi\)
\(984\) 0 0
\(985\) −61.3817 −1.95578
\(986\) −1.32422 −0.0421717
\(987\) 0 0
\(988\) 13.6731 0.435001
\(989\) 22.8432 0.726373
\(990\) 0 0
\(991\) −17.6058 −0.559267 −0.279633 0.960107i \(-0.590213\pi\)
−0.279633 + 0.960107i \(0.590213\pi\)
\(992\) −16.0267 −0.508847
\(993\) 0 0
\(994\) 0 0
\(995\) −75.0612 −2.37960
\(996\) 0 0
\(997\) −12.9707 −0.410786 −0.205393 0.978680i \(-0.565847\pi\)
−0.205393 + 0.978680i \(0.565847\pi\)
\(998\) 25.7405 0.814801
\(999\) 0 0
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 5733.2.a.bd.1.3 3
3.2 odd 2 637.2.a.i.1.1 yes 3
7.6 odd 2 5733.2.a.be.1.3 3
21.2 odd 6 637.2.e.k.508.3 6
21.5 even 6 637.2.e.l.508.3 6
21.11 odd 6 637.2.e.k.79.3 6
21.17 even 6 637.2.e.l.79.3 6
21.20 even 2 637.2.a.h.1.1 3
39.38 odd 2 8281.2.a.bk.1.3 3
273.272 even 2 8281.2.a.bh.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.a.h.1.1 3 21.20 even 2
637.2.a.i.1.1 yes 3 3.2 odd 2
637.2.e.k.79.3 6 21.11 odd 6
637.2.e.k.508.3 6 21.2 odd 6
637.2.e.l.79.3 6 21.17 even 6
637.2.e.l.508.3 6 21.5 even 6
5733.2.a.bd.1.3 3 1.1 even 1 trivial
5733.2.a.be.1.3 3 7.6 odd 2
8281.2.a.bh.1.3 3 273.272 even 2
8281.2.a.bk.1.3 3 39.38 odd 2