Properties

Label 8281.2.a.bh.1.3
Level $8281$
Weight $2$
Character 8281.1
Self dual yes
Analytic conductor $66.124$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8281 = 7^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8281.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(66.1241179138\)
Analytic rank: \(0\)
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 \(\chi\) \(=\) 8281.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.65544 q^{2} -2.39593 q^{3} +5.05137 q^{4} +3.65544 q^{5} -6.36226 q^{6} +8.10275 q^{8} +2.74049 q^{9} +O(q^{10})\) \(q+2.65544 q^{2} -2.39593 q^{3} +5.05137 q^{4} +3.65544 q^{5} -6.36226 q^{6} +8.10275 q^{8} +2.74049 q^{9} +9.70682 q^{10} -0.655442 q^{11} -12.1027 q^{12} -8.75819 q^{15} +11.4136 q^{16} -2.39593 q^{17} +7.27721 q^{18} -2.70682 q^{19} +18.4650 q^{20} -1.74049 q^{22} +7.36226 q^{23} -19.4136 q^{24} +8.36226 q^{25} +0.621770 q^{27} -0.208136 q^{29} -23.2569 q^{30} -1.13642 q^{31} +14.1027 q^{32} +1.57040 q^{33} -6.36226 q^{34} +13.8432 q^{36} +7.44731 q^{37} -7.18780 q^{38} +29.6191 q^{40} -10.2055 q^{41} -3.10275 q^{43} -3.31088 q^{44} +10.0177 q^{45} +19.5501 q^{46} +4.60407 q^{47} -27.3463 q^{48} +22.2055 q^{50} +5.74049 q^{51} +5.25951 q^{53} +1.65107 q^{54} -2.39593 q^{55} +6.48535 q^{57} -0.552694 q^{58} +8.25951 q^{59} -44.2409 q^{60} +1.89725 q^{61} -3.01770 q^{62} +14.6218 q^{64} +4.17009 q^{66} +12.8946 q^{67} -12.1027 q^{68} -17.6395 q^{69} +6.75819 q^{71} +22.2055 q^{72} +12.5367 q^{73} +19.7759 q^{74} -20.0354 q^{75} -13.6731 q^{76} -1.51902 q^{79} +41.7219 q^{80} -9.71119 q^{81} -27.1001 q^{82} +15.7582 q^{83} -8.75819 q^{85} -8.23917 q^{86} +0.498680 q^{87} -5.31088 q^{88} -14.8096 q^{89} +26.6014 q^{90} +37.1895 q^{92} +2.72279 q^{93} +12.2258 q^{94} -9.89461 q^{95} -33.7892 q^{96} -10.0177 q^{97} -1.79623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} - 4 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} + 11 q^{9} + O(q^{10}) \) \( 3 q + 2 q^{2} - 4 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} + 6 q^{8} + 11 q^{9} + 14 q^{10} + 4 q^{11} - 18 q^{12} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 8 q^{18} + 7 q^{19} + 16 q^{20} - 8 q^{22} + q^{23} - 28 q^{24} + 4 q^{25} - 22 q^{27} - 7 q^{29} - 24 q^{30} - 3 q^{31} + 24 q^{32} - 10 q^{33} + 2 q^{34} + 26 q^{36} + 10 q^{37} - 12 q^{38} + 22 q^{40} + 6 q^{41} + 9 q^{43} + 2 q^{44} + 3 q^{45} + 28 q^{46} + 17 q^{47} - 16 q^{48} + 30 q^{50} + 20 q^{51} + 13 q^{53} + 28 q^{54} - 4 q^{55} - 4 q^{57} - 14 q^{58} + 22 q^{59} - 42 q^{60} + 24 q^{61} + 18 q^{62} + 20 q^{64} + 30 q^{66} + 14 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{71} + 30 q^{72} + 5 q^{73} + 8 q^{74} - 6 q^{75} - 8 q^{76} + q^{79} + 40 q^{80} + 15 q^{81} - 20 q^{82} + 23 q^{83} - 2 q^{85} - 6 q^{86} - 20 q^{87} - 4 q^{88} - 11 q^{89} + 40 q^{90} + 30 q^{92} + 38 q^{93} + 16 q^{94} - 5 q^{95} - 52 q^{96} - 3 q^{97} + 30 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.65544 1.87768 0.938841 0.344352i \(-0.111901\pi\)
0.938841 + 0.344352i \(0.111901\pi\)
\(3\) −2.39593 −1.38329 −0.691646 0.722237i \(-0.743114\pi\)
−0.691646 + 0.722237i \(0.743114\pi\)
\(4\) 5.05137 2.52569
\(5\) 3.65544 1.63476 0.817382 0.576096i \(-0.195425\pi\)
0.817382 + 0.576096i \(0.195425\pi\)
\(6\) −6.36226 −2.59738
\(7\) 0 0
\(8\) 8.10275 2.86475
\(9\) 2.74049 0.913496
\(10\) 9.70682 3.06956
\(11\) −0.655442 −0.197623 −0.0988117 0.995106i \(-0.531504\pi\)
−0.0988117 + 0.995106i \(0.531504\pi\)
\(12\) −12.1027 −3.49376
\(13\) 0 0
\(14\) 0 0
\(15\) −8.75819 −2.26136
\(16\) 11.4136 2.85341
\(17\) −2.39593 −0.581099 −0.290549 0.956860i \(-0.593838\pi\)
−0.290549 + 0.956860i \(0.593838\pi\)
\(18\) 7.27721 1.71526
\(19\) −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 \(-0.221466\pi\)
0.767569 + 0.640967i \(0.221466\pi\)
\(24\) −19.4136 −3.96279
\(25\) 8.36226 1.67245
\(26\) 0 0
\(27\) 0.621770 0.119660
\(28\) 0 0
\(29\) −0.208136 −0.0386499 −0.0193250 0.999813i \(-0.506152\pi\)
−0.0193250 + 0.999813i \(0.506152\pi\)
\(30\) −23.2569 −4.24610
\(31\) −1.13642 −0.204107 −0.102054 0.994779i \(-0.532541\pi\)
−0.102054 + 0.994779i \(0.532541\pi\)
\(32\) 14.1027 2.49304
\(33\) 1.57040 0.273371
\(34\) −6.36226 −1.09112
\(35\) 0 0
\(36\) 13.8432 2.30721
\(37\) 7.44731 1.22433 0.612165 0.790730i \(-0.290299\pi\)
0.612165 + 0.790730i \(0.290299\pi\)
\(38\) −7.18780 −1.16601
\(39\) 0 0
\(40\) 29.6191 4.68320
\(41\) −10.2055 −1.59383 −0.796915 0.604091i \(-0.793536\pi\)
−0.796915 + 0.604091i \(0.793536\pi\)
\(42\) 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
\(45\) 10.0177 1.49335
\(46\) 19.5501 2.88250
\(47\) 4.60407 0.671572 0.335786 0.941938i \(-0.390998\pi\)
0.335786 + 0.941938i \(0.390998\pi\)
\(48\) −27.3463 −3.94710
\(49\) 0 0
\(50\) 22.2055 3.14033
\(51\) 5.74049 0.803829
\(52\) 0 0
\(53\) 5.25951 0.722449 0.361225 0.932479i \(-0.382359\pi\)
0.361225 + 0.932479i \(0.382359\pi\)
\(54\) 1.65107 0.224683
\(55\) −2.39593 −0.323067
\(56\) 0 0
\(57\) 6.48535 0.859005
\(58\) −0.552694 −0.0725723
\(59\) 8.25951 1.07530 0.537648 0.843169i \(-0.319313\pi\)
0.537648 + 0.843169i \(0.319313\pi\)
\(60\) −44.2409 −5.71148
\(61\) 1.89725 0.242918 0.121459 0.992596i \(-0.461243\pi\)
0.121459 + 0.992596i \(0.461243\pi\)
\(62\) −3.01770 −0.383248
\(63\) 0 0
\(64\) 14.6218 1.82772
\(65\) 0 0
\(66\) 4.17009 0.513303
\(67\) 12.8946 1.57533 0.787664 0.616105i \(-0.211290\pi\)
0.787664 + 0.616105i \(0.211290\pi\)
\(68\) −12.1027 −1.46767
\(69\) −17.6395 −2.12354
\(70\) 0 0
\(71\) 6.75819 0.802050 0.401025 0.916067i \(-0.368654\pi\)
0.401025 + 0.916067i \(0.368654\pi\)
\(72\) 22.2055 2.61694
\(73\) 12.5367 1.46731 0.733656 0.679521i \(-0.237812\pi\)
0.733656 + 0.679521i \(0.237812\pi\)
\(74\) 19.7759 2.29890
\(75\) −20.0354 −2.31349
\(76\) −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
\(81\) −9.71119 −1.07902
\(82\) −27.1001 −2.99271
\(83\) 15.7582 1.72969 0.864843 0.502042i \(-0.167418\pi\)
0.864843 + 0.502042i \(0.167418\pi\)
\(84\) 0 0
\(85\) −8.75819 −0.949959
\(86\) −8.23917 −0.888453
\(87\) 0.498680 0.0534641
\(88\) −5.31088 −0.566142
\(89\) −14.8096 −1.56981 −0.784905 0.619616i \(-0.787288\pi\)
−0.784905 + 0.619616i \(0.787288\pi\)
\(90\) 26.6014 2.80404
\(91\) 0 0
\(92\) 37.1895 3.87728
\(93\) 2.72279 0.282340
\(94\) 12.2258 1.26100
\(95\) −9.89461 −1.01517
\(96\) −33.7892 −3.44860
\(97\) −10.0177 −1.01714 −0.508572 0.861020i \(-0.669826\pi\)
−0.508572 + 0.861020i \(0.669826\pi\)
\(98\) 0 0
\(99\) −1.79623 −0.180528
\(100\) 42.2409 4.22409
\(101\) 3.01770 0.300273 0.150136 0.988665i \(-0.452029\pi\)
0.150136 + 0.988665i \(0.452029\pi\)
\(102\) 15.2435 1.50934
\(103\) 5.03804 0.496413 0.248207 0.968707i \(-0.420159\pi\)
0.248207 + 0.968707i \(0.420159\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 13.9663 1.35653
\(107\) 11.8432 1.14493 0.572465 0.819929i \(-0.305987\pi\)
0.572465 + 0.819929i \(0.305987\pi\)
\(108\) 3.14079 0.302223
\(109\) −3.55005 −0.340034 −0.170017 0.985441i \(-0.554382\pi\)
−0.170017 + 0.985441i \(0.554382\pi\)
\(110\) −6.36226 −0.606618
\(111\) −17.8432 −1.69361
\(112\) 0 0
\(113\) −9.46501 −0.890393 −0.445197 0.895433i \(-0.646866\pi\)
−0.445197 + 0.895433i \(0.646866\pi\)
\(114\) 17.2215 1.61294
\(115\) 26.9123 2.50959
\(116\) −1.05137 −0.0976176
\(117\) 0 0
\(118\) 21.9327 2.01906
\(119\) 0 0
\(120\) −70.9654 −6.47823
\(121\) −10.5704 −0.960945
\(122\) 5.03804 0.456123
\(123\) 24.4517 2.20473
\(124\) −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
\(129\) 7.43397 0.654525
\(130\) 0 0
\(131\) −9.82991 −0.858843 −0.429421 0.903104i \(-0.641282\pi\)
−0.429421 + 0.903104i \(0.641282\pi\)
\(132\) 7.93265 0.690449
\(133\) 0 0
\(134\) 34.2409 2.95796
\(135\) 2.27284 0.195615
\(136\) −19.4136 −1.66471
\(137\) −17.5501 −1.49940 −0.749701 0.661777i \(-0.769803\pi\)
−0.749701 + 0.661777i \(0.769803\pi\)
\(138\) −46.8406 −3.98734
\(139\) 4.91495 0.416881 0.208440 0.978035i \(-0.433161\pi\)
0.208440 + 0.978035i \(0.433161\pi\)
\(140\) 0 0
\(141\) −11.0310 −0.928981
\(142\) 17.9460 1.50599
\(143\) 0 0
\(144\) 31.2789 2.60658
\(145\) −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 \(0.360759\pi\)
\(150\) −53.2029 −4.34400
\(151\) −5.07171 −0.412730 −0.206365 0.978475i \(-0.566163\pi\)
−0.206365 + 0.978475i \(0.566163\pi\)
\(152\) −21.9327 −1.77897
\(153\) −6.56603 −0.530832
\(154\) 0 0
\(155\) −4.15412 −0.333667
\(156\) 0 0
\(157\) 12.6014 1.00570 0.502852 0.864373i \(-0.332284\pi\)
0.502852 + 0.864373i \(0.332284\pi\)
\(158\) −4.03367 −0.320902
\(159\) −12.6014 −0.999358
\(160\) 51.5518 4.07553
\(161\) 0 0
\(162\) −25.7875 −2.02606
\(163\) −3.20814 −0.251281 −0.125640 0.992076i \(-0.540099\pi\)
−0.125640 + 0.992076i \(0.540099\pi\)
\(164\) −51.5518 −4.02552
\(165\) 5.74049 0.446896
\(166\) 41.8450 3.24780
\(167\) 8.12045 0.628379 0.314190 0.949360i \(-0.398267\pi\)
0.314190 + 0.949360i \(0.398267\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −23.2569 −1.78372
\(171\) −7.41800 −0.567269
\(172\) −15.6731 −1.19507
\(173\) 10.3286 0.785268 0.392634 0.919695i \(-0.371564\pi\)
0.392634 + 0.919695i \(0.371564\pi\)
\(174\) 1.32422 0.100389
\(175\) 0 0
\(176\) −7.48098 −0.563900
\(177\) −19.7892 −1.48745
\(178\) −39.3259 −2.94760
\(179\) −2.37823 −0.177757 −0.0888786 0.996042i \(-0.528328\pi\)
−0.0888786 + 0.996042i \(0.528328\pi\)
\(180\) 50.6032 3.77174
\(181\) −21.8096 −1.62109 −0.810546 0.585675i \(-0.800830\pi\)
−0.810546 + 0.585675i \(0.800830\pi\)
\(182\) 0 0
\(183\) −4.54569 −0.336027
\(184\) 59.6545 4.39779
\(185\) 27.2232 2.00149
\(186\) 7.23021 0.530144
\(187\) 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 \(-0.862093\pi\)
−0.907608 + 0.419819i \(0.862093\pi\)
\(192\) −35.0328 −2.52827
\(193\) −11.3109 −0.814175 −0.407088 0.913389i \(-0.633456\pi\)
−0.407088 + 0.913389i \(0.633456\pi\)
\(194\) −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 \(0.295889\pi\)
\(198\) −4.76979 −0.338974
\(199\) −20.5341 −1.45562 −0.727811 0.685777i \(-0.759462\pi\)
−0.727811 + 0.685777i \(0.759462\pi\)
\(200\) 67.7573 4.79116
\(201\) −30.8946 −2.17914
\(202\) 8.01333 0.563816
\(203\) 0 0
\(204\) 28.9974 2.03022
\(205\) −37.3056 −2.60554
\(206\) 13.3782 0.932105
\(207\) 20.1762 1.40234
\(208\) 0 0
\(209\) 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
\(213\) −16.1922 −1.10947
\(214\) 31.4490 2.14981
\(215\) −11.3419 −0.773512
\(216\) 5.03804 0.342795
\(217\) 0 0
\(218\) −9.42697 −0.638475
\(219\) −30.0371 −2.02972
\(220\) −12.1027 −0.815967
\(221\) 0 0
\(222\) −47.3817 −3.18005
\(223\) −8.44731 −0.565673 −0.282837 0.959168i \(-0.591275\pi\)
−0.282837 + 0.959168i \(0.591275\pi\)
\(224\) 0 0
\(225\) 22.9167 1.52778
\(226\) −25.1338 −1.67187
\(227\) 6.68912 0.443972 0.221986 0.975050i \(-0.428746\pi\)
0.221986 + 0.975050i \(0.428746\pi\)
\(228\) 32.7599 2.16958
\(229\) 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 \(-0.543588\pi\)
−0.136510 + 0.990639i \(0.543588\pi\)
\(234\) 0 0
\(235\) 16.8299 1.09786
\(236\) 41.7219 2.71586
\(237\) 3.63947 0.236409
\(238\) 0 0
\(239\) 1.79450 0.116077 0.0580384 0.998314i \(-0.481515\pi\)
0.0580384 + 0.998314i \(0.481515\pi\)
\(240\) −99.9628 −6.45257
\(241\) 13.8609 0.892862 0.446431 0.894818i \(-0.352695\pi\)
0.446431 + 0.894818i \(0.352695\pi\)
\(242\) −28.0691 −1.80435
\(243\) 21.4020 1.37294
\(244\) 9.58373 0.613535
\(245\) 0 0
\(246\) 64.9300 4.13979
\(247\) 0 0
\(248\) −9.20814 −0.584717
\(249\) −37.7556 −2.39266
\(250\) 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
\(255\) 20.9840 1.31407
\(256\) −1.03804 −0.0648776
\(257\) −23.7068 −1.47879 −0.739395 0.673272i \(-0.764888\pi\)
−0.739395 + 0.673272i \(0.764888\pi\)
\(258\) 19.7405 1.22899
\(259\) 0 0
\(260\) 0 0
\(261\) −0.570395 −0.0353066
\(262\) −26.1027 −1.61263
\(263\) 11.3756 0.701449 0.350725 0.936479i \(-0.385935\pi\)
0.350725 + 0.936479i \(0.385935\pi\)
\(264\) 12.7245 0.783140
\(265\) 19.2258 1.18103
\(266\) 0 0
\(267\) 35.4827 2.17151
\(268\) 65.1355 3.97878
\(269\) 11.1054 0.677107 0.338554 0.940947i \(-0.390062\pi\)
0.338554 + 0.940947i \(0.390062\pi\)
\(270\) 6.03540 0.367303
\(271\) −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
\(276\) −89.1036 −5.36340
\(277\) −3.00000 −0.180253 −0.0901263 0.995930i \(-0.528727\pi\)
−0.0901263 + 0.995930i \(0.528727\pi\)
\(278\) 13.0514 0.782769
\(279\) −3.11435 −0.186451
\(280\) 0 0
\(281\) −3.44731 −0.205649 −0.102825 0.994700i \(-0.532788\pi\)
−0.102825 + 0.994700i \(0.532788\pi\)
\(282\) −29.2923 −1.74433
\(283\) 12.4783 0.741760 0.370880 0.928681i \(-0.379056\pi\)
0.370880 + 0.928681i \(0.379056\pi\)
\(284\) 34.1382 2.02573
\(285\) 23.7068 1.40427
\(286\) 0 0
\(287\) 0 0
\(288\) 38.6484 2.27738
\(289\) −11.2595 −0.662324
\(290\) −2.02034 −0.118638
\(291\) 24.0017 1.40701
\(292\) 63.3277 3.70597
\(293\) −13.5341 −0.790670 −0.395335 0.918537i \(-0.629371\pi\)
−0.395335 + 0.918537i \(0.629371\pi\)
\(294\) 0 0
\(295\) 30.1922 1.75786
\(296\) 60.3436 3.50740
\(297\) −0.407534 −0.0236475
\(298\) 27.4624 1.59085
\(299\) 0 0
\(300\) −101.206 −5.84315
\(301\) 0 0
\(302\) −13.4676 −0.774976
\(303\) −7.23021 −0.415365
\(304\) −30.8946 −1.77193
\(305\) 6.93529 0.397114
\(306\) −17.4357 −0.996733
\(307\) 28.2365 1.61154 0.805772 0.592226i \(-0.201751\pi\)
0.805772 + 0.592226i \(0.201751\pi\)
\(308\) 0 0
\(309\) −12.0708 −0.686684
\(310\) −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 \(-0.299842\pi\)
0.588188 + 0.808724i \(0.299842\pi\)
\(314\) 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 \(0.762364\pi\)
\(318\) −33.4624 −1.87648
\(319\) 0.136421 0.00763813
\(320\) 53.4490 2.98789
\(321\) −28.3756 −1.58377
\(322\) 0 0
\(323\) 6.48535 0.360854
\(324\) −49.0548 −2.72527
\(325\) 0 0
\(326\) −8.51902 −0.471825
\(327\) 8.50569 0.470366
\(328\) −82.6926 −4.56593
\(329\) 0 0
\(330\) 15.2435 0.839129
\(331\) 24.1382 1.32675 0.663376 0.748286i \(-0.269123\pi\)
0.663376 + 0.748286i \(0.269123\pi\)
\(332\) 79.6005 4.36865
\(333\) 20.4093 1.11842
\(334\) 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 \(0.812534\pi\)
\(338\) 0 0
\(339\) 22.6775 1.23167
\(340\) −44.2409 −2.39930
\(341\) 0.744859 0.0403364
\(342\) −19.6981 −1.06515
\(343\) 0 0
\(344\) −25.1408 −1.35550
\(345\) −64.4801 −3.47149
\(346\) 27.4270 1.47448
\(347\) −24.9974 −1.34193 −0.670964 0.741490i \(-0.734120\pi\)
−0.670964 + 0.741490i \(0.734120\pi\)
\(348\) 2.51902 0.135034
\(349\) −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 \(-0.712429\pi\)
−0.618919 + 0.785455i \(0.712429\pi\)
\(354\) −52.5491 −2.79296
\(355\) 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 \(0.308501\pi\)
\(360\) 81.1709 4.27808
\(361\) −11.6731 −0.614376
\(362\) −57.9140 −3.04389
\(363\) 25.3259 1.32927
\(364\) 0 0
\(365\) 45.8273 2.39871
\(366\) −12.0708 −0.630951
\(367\) 1.12045 0.0584870 0.0292435 0.999572i \(-0.490690\pi\)
0.0292435 + 0.999572i \(0.490690\pi\)
\(368\) 84.0301 4.38037
\(369\) −27.9681 −1.45596
\(370\) 72.2896 3.75816
\(371\) 0 0
\(372\) 13.7538 0.713102
\(373\) 15.6058 0.808038 0.404019 0.914751i \(-0.367613\pi\)
0.404019 + 0.914751i \(0.367613\pi\)
\(374\) 4.17009 0.215630
\(375\) −29.4473 −1.52065
\(376\) 37.3056 1.92389
\(377\) 0 0
\(378\) 0 0
\(379\) −12.7849 −0.656714 −0.328357 0.944554i \(-0.606495\pi\)
−0.328357 + 0.944554i \(0.606495\pi\)
\(380\) −49.9814 −2.56399
\(381\) −13.1001 −0.671139
\(382\) −66.6165 −3.40840
\(383\) 34.0354 1.73913 0.869564 0.493820i \(-0.164400\pi\)
0.869564 + 0.493820i \(0.164400\pi\)
\(384\) −25.4490 −1.29869
\(385\) 0 0
\(386\) −30.0354 −1.52876
\(387\) −8.50305 −0.432234
\(388\) −50.6032 −2.56899
\(389\) −24.6705 −1.25084 −0.625422 0.780287i \(-0.715073\pi\)
−0.625422 + 0.780287i \(0.715073\pi\)
\(390\) 0 0
\(391\) −17.6395 −0.892066
\(392\) 0 0
\(393\) 23.5518 1.18803
\(394\) 44.5898 2.24640
\(395\) −5.55269 −0.279386
\(396\) −9.07344 −0.455958
\(397\) −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 \(0.505477\pi\)
\(402\) −82.0389 −4.09173
\(403\) 0 0
\(404\) 15.2435 0.758394
\(405\) −35.4987 −1.76394
\(406\) 0 0
\(407\) −4.88128 −0.241956
\(408\) 46.5137 2.30277
\(409\) 19.9770 0.987800 0.493900 0.869519i \(-0.335571\pi\)
0.493900 + 0.869519i \(0.335571\pi\)
\(410\) −99.0629 −4.89237
\(411\) 42.0487 2.07411
\(412\) 25.4490 1.25378
\(413\) 0 0
\(414\) 53.5767 2.63315
\(415\) 57.6032 2.82763
\(416\) 0 0
\(417\) −11.7759 −0.576668
\(418\) 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 \(-0.618514\pi\)
−0.363780 + 0.931485i \(0.618514\pi\)
\(422\) −41.8990 −2.03961
\(423\) 12.6174 0.613479
\(424\) 42.6165 2.06964
\(425\) −20.0354 −0.971860
\(426\) −42.9974 −2.08323
\(427\) 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 \(0.211549\pi\)
\(432\) 7.09665 0.341438
\(433\) 8.96196 0.430684 0.215342 0.976539i \(-0.430913\pi\)
0.215342 + 0.976539i \(0.430913\pi\)
\(434\) 0 0
\(435\) 1.82290 0.0874012
\(436\) −17.9327 −0.858818
\(437\) −19.9283 −0.953299
\(438\) −79.7619 −3.81117
\(439\) 7.93265 0.378605 0.189302 0.981919i \(-0.439377\pi\)
0.189302 + 0.981919i \(0.439377\pi\)
\(440\) −19.4136 −0.925509
\(441\) 0 0
\(442\) 0 0
\(443\) −8.91058 −0.423355 −0.211677 0.977340i \(-0.567893\pi\)
−0.211677 + 0.977340i \(0.567893\pi\)
\(444\) −90.1329 −4.27752
\(445\) −54.1355 −2.56627
\(446\) −22.4313 −1.06215
\(447\) −24.7785 −1.17198
\(448\) 0 0
\(449\) 8.45168 0.398859 0.199430 0.979912i \(-0.436091\pi\)
0.199430 + 0.979912i \(0.436091\pi\)
\(450\) 60.8539 2.86868
\(451\) 6.68912 0.314978
\(452\) −47.8113 −2.24885
\(453\) 12.1515 0.570926
\(454\) 17.7626 0.833638
\(455\) 0 0
\(456\) 52.5491 2.46084
\(457\) −23.1692 −1.08381 −0.541904 0.840440i \(-0.682297\pi\)
−0.541904 + 0.840440i \(0.682297\pi\)
\(458\) 22.9300 1.07145
\(459\) −1.48972 −0.0695341
\(460\) 135.944 6.33843
\(461\) 2.27284 0.105857 0.0529284 0.998598i \(-0.483144\pi\)
0.0529284 + 0.998598i \(0.483144\pi\)
\(462\) 0 0
\(463\) 4.10976 0.190997 0.0954983 0.995430i \(-0.469556\pi\)
0.0954983 + 0.995430i \(0.469556\pi\)
\(464\) −2.37559 −0.110284
\(465\) 9.95299 0.461559
\(466\) −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
\(471\) −30.1922 −1.39118
\(472\) 66.9247 3.08046
\(473\) 2.03367 0.0935084
\(474\) 9.66441 0.443901
\(475\) −22.6351 −1.03857
\(476\) 0 0
\(477\) 14.4136 0.659955
\(478\) 4.76520 0.217955
\(479\) −9.31525 −0.425625 −0.212812 0.977093i \(-0.568262\pi\)
−0.212812 + 0.977093i \(0.568262\pi\)
\(480\) −123.515 −5.63764
\(481\) 0 0
\(482\) 36.8069 1.67651
\(483\) 0 0
\(484\) −53.3950 −2.42705
\(485\) −36.6191 −1.66279
\(486\) 56.8319 2.57795
\(487\) −20.2409 −0.917203 −0.458601 0.888642i \(-0.651649\pi\)
−0.458601 + 0.888642i \(0.651649\pi\)
\(488\) 15.3730 0.695901
\(489\) 7.68648 0.347594
\(490\) 0 0
\(491\) −4.36226 −0.196866 −0.0984330 0.995144i \(-0.531383\pi\)
−0.0984330 + 0.995144i \(0.531383\pi\)
\(492\) 123.515 5.56847
\(493\) 0.498680 0.0224594
\(494\) 0 0
\(495\) −6.56603 −0.295121
\(496\) −12.9707 −0.582401
\(497\) 0 0
\(498\) −100.258 −4.49265
\(499\) −9.69348 −0.433940 −0.216970 0.976178i \(-0.569617\pi\)
−0.216970 + 0.976178i \(0.569617\pi\)
\(500\) 62.0841 2.77649
\(501\) −19.4560 −0.869232
\(502\) −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 \(-0.599986\pi\)
−0.308976 + 0.951070i \(0.599986\pi\)
\(510\) 55.7219 2.46741
\(511\) 0 0
\(512\) −24.0000 −1.06066
\(513\) −1.68302 −0.0743070
\(514\) −62.9521 −2.77670
\(515\) 18.4163 0.811518
\(516\) 37.5518 1.65313
\(517\) −3.01770 −0.132718
\(518\) 0 0
\(519\) −24.7466 −1.08625
\(520\) 0 0
\(521\) 14.6218 0.640591 0.320296 0.947318i \(-0.396218\pi\)
0.320296 + 0.947318i \(0.396218\pi\)
\(522\) −1.51465 −0.0662945
\(523\) −16.5190 −0.722326 −0.361163 0.932503i \(-0.617620\pi\)
−0.361163 + 0.932503i \(0.617620\pi\)
\(524\) −49.6545 −2.16917
\(525\) 0 0
\(526\) 30.2072 1.31710
\(527\) 2.72279 0.118607
\(528\) 17.9239 0.780038
\(529\) 31.2029 1.35665
\(530\) 51.0531 2.21761
\(531\) 22.6351 0.982280
\(532\) 0 0
\(533\) 0 0
\(534\) 94.2223 4.07740
\(535\) 43.2923 1.87169
\(536\) 104.482 4.51293
\(537\) 5.69808 0.245890
\(538\) 29.4897 1.27139
\(539\) 0 0
\(540\) 11.4810 0.494063
\(541\) 43.1018 1.85309 0.926546 0.376181i \(-0.122763\pi\)
0.926546 + 0.376181i \(0.122763\pi\)
\(542\) −33.7892 −1.45137
\(543\) 52.2542 2.24244
\(544\) −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
\(549\) 5.19940 0.221905
\(550\) −14.5544 −0.620603
\(551\) 0.563387 0.0240011
\(552\) −142.928 −6.08343
\(553\) 0 0
\(554\) −7.96633 −0.338457
\(555\) −65.2249 −2.76864
\(556\) 24.8273 1.05291
\(557\) −1.35157 −0.0572677 −0.0286338 0.999590i \(-0.509116\pi\)
−0.0286338 + 0.999590i \(0.509116\pi\)
\(558\) −8.26998 −0.350096
\(559\) 0 0
\(560\) 0 0
\(561\) −3.76256 −0.158855
\(562\) −9.15412 −0.386143
\(563\) −31.7626 −1.33863 −0.669316 0.742978i \(-0.733413\pi\)
−0.669316 + 0.742978i \(0.733413\pi\)
\(564\) −55.7219 −2.34631
\(565\) −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 \(-0.280320\pi\)
0.636650 + 0.771153i \(0.280320\pi\)
\(570\) 62.9521 2.63677
\(571\) −0.432244 −0.0180888 −0.00904442 0.999959i \(-0.502879\pi\)
−0.00904442 + 0.999959i \(0.502879\pi\)
\(572\) 0 0
\(573\) 60.1062 2.51097
\(574\) 0 0
\(575\) 61.5651 2.56744
\(576\) 40.0708 1.66962
\(577\) 18.1382 0.755101 0.377551 0.925989i \(-0.376766\pi\)
0.377551 + 0.925989i \(0.376766\pi\)
\(578\) −29.8990 −1.24363
\(579\) 27.1001 1.12624
\(580\) −3.84324 −0.159582
\(581\) 0 0
\(582\) 63.7352 2.64191
\(583\) −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 \(-0.369554\pi\)
0.398433 + 0.917198i \(0.369554\pi\)
\(588\) 0 0
\(589\) 3.07608 0.126748
\(590\) 80.1736 3.30069
\(591\) −40.2322 −1.65493
\(592\) 85.0008 3.49351
\(593\) 8.20113 0.336780 0.168390 0.985720i \(-0.446143\pi\)
0.168390 + 0.985720i \(0.446143\pi\)
\(594\) −1.08218 −0.0444025
\(595\) 0 0
\(596\) 52.2409 2.13987
\(597\) 49.1983 2.01355
\(598\) 0 0
\(599\) 23.4783 0.959299 0.479649 0.877460i \(-0.340764\pi\)
0.479649 + 0.877460i \(0.340764\pi\)
\(600\) −162.342 −6.62758
\(601\) 8.96196 0.365566 0.182783 0.983153i \(-0.441489\pi\)
0.182783 + 0.983153i \(0.441489\pi\)
\(602\) 0 0
\(603\) 35.3375 1.43906
\(604\) −25.6191 −1.04243
\(605\) −38.6395 −1.57092
\(606\) −19.1994 −0.779922
\(607\) −43.4641 −1.76415 −0.882077 0.471106i \(-0.843855\pi\)
−0.882077 + 0.471106i \(0.843855\pi\)
\(608\) −38.1736 −1.54814
\(609\) 0 0
\(610\) 18.4163 0.745653
\(611\) 0 0
\(612\) −33.1675 −1.34071
\(613\) 21.4490 0.866318 0.433159 0.901317i \(-0.357399\pi\)
0.433159 + 0.901317i \(0.357399\pi\)
\(614\) 74.9805 3.02597
\(615\) 89.3817 3.60422
\(616\) 0 0
\(617\) 12.1294 0.488312 0.244156 0.969736i \(-0.421489\pi\)
0.244156 + 0.969736i \(0.421489\pi\)
\(618\) −32.0533 −1.28937
\(619\) 12.7245 0.511442 0.255721 0.966751i \(-0.417687\pi\)
0.255721 + 0.966751i \(0.417687\pi\)
\(620\) −20.9840 −0.842739
\(621\) 4.57763 0.183694
\(622\) 65.6005 2.63034
\(623\) 0 0
\(624\) 0 0
\(625\) 3.11608 0.124643
\(626\) 55.2656 2.20886
\(627\) −4.25077 −0.169759
\(628\) 63.6545 2.54009
\(629\) −17.8432 −0.711456
\(630\) 0 0
\(631\) 11.7538 0.467912 0.233956 0.972247i \(-0.424833\pi\)
0.233956 + 0.972247i \(0.424833\pi\)
\(632\) −12.3082 −0.489596
\(633\) 37.8043 1.50259
\(634\) −69.4084 −2.75656
\(635\) 19.9867 0.793147
\(636\) −63.6545 −2.52407
\(637\) 0 0
\(638\) 0.362259 0.0143420
\(639\) 18.5208 0.732670
\(640\) 38.8273 1.53478
\(641\) 4.68648 0.185105 0.0925523 0.995708i \(-0.470497\pi\)
0.0925523 + 0.995708i \(0.470497\pi\)
\(642\) −75.3497 −2.97382
\(643\) −0.751182 −0.0296237 −0.0148119 0.999890i \(-0.504715\pi\)
−0.0148119 + 0.999890i \(0.504715\pi\)
\(644\) 0 0
\(645\) 27.1745 1.06999
\(646\) 17.2215 0.677570
\(647\) −40.8476 −1.60589 −0.802943 0.596056i \(-0.796733\pi\)
−0.802943 + 0.596056i \(0.796733\pi\)
\(648\) −78.6873 −3.09113
\(649\) −5.41363 −0.212504
\(650\) 0 0
\(651\) 0 0
\(652\) −16.2055 −0.634656
\(653\) −46.4783 −1.81884 −0.909419 0.415881i \(-0.863473\pi\)
−0.909419 + 0.415881i \(0.863473\pi\)
\(654\) 22.5864 0.883197
\(655\) −35.9327 −1.40400
\(656\) −116.482 −4.54785
\(657\) 34.3568 1.34038
\(658\) 0 0
\(659\) 30.3596 1.18264 0.591321 0.806436i \(-0.298606\pi\)
0.591321 + 0.806436i \(0.298606\pi\)
\(660\) 28.9974 1.12872
\(661\) −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
\(666\) 54.1956 2.10004
\(667\) −1.53235 −0.0593330
\(668\) 41.0194 1.58709
\(669\) 20.2392 0.782492
\(670\) 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
\(675\) 5.19940 0.200125
\(676\) 0 0
\(677\) 20.7803 0.798650 0.399325 0.916809i \(-0.369244\pi\)
0.399325 + 0.916809i \(0.369244\pi\)
\(678\) 60.2188 2.31269
\(679\) 0 0
\(680\) −70.9654 −2.72140
\(681\) −16.0267 −0.614143
\(682\) 1.97793 0.0757388
\(683\) −27.5837 −1.05546 −0.527731 0.849412i \(-0.676957\pi\)
−0.527731 + 0.849412i \(0.676957\pi\)
\(684\) −37.4711 −1.43274
\(685\) −64.1532 −2.45117
\(686\) 0 0
\(687\) −20.6891 −0.789339
\(688\) −35.4136 −1.35013
\(689\) 0 0
\(690\) −171.223 −6.51835
\(691\) 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
\(696\) 4.04068 0.153162
\(697\) 24.4517 0.926173
\(698\) −4.88301 −0.184825
\(699\) 9.98494 0.377665
\(700\) 0 0
\(701\) −20.8973 −0.789278 −0.394639 0.918836i \(-0.629130\pi\)
−0.394639 + 0.918836i \(0.629130\pi\)
\(702\) 0 0
\(703\) −20.1585 −0.760292
\(704\) −9.58373 −0.361200
\(705\) −40.3233 −1.51866
\(706\) −61.7573 −2.32427
\(707\) 0 0
\(708\) −99.9628 −3.75683
\(709\) −9.93966 −0.373292 −0.186646 0.982427i \(-0.559762\pi\)
−0.186646 + 0.982427i \(0.559762\pi\)
\(710\) 65.6005 2.46194
\(711\) −4.16286 −0.156119
\(712\) −119.998 −4.49712
\(713\) −8.36663 −0.313333
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0133 −0.448959
\(717\) −4.29951 −0.160568
\(718\) 56.9521 2.12543
\(719\) 11.9797 0.446766 0.223383 0.974731i \(-0.428290\pi\)
0.223383 + 0.974731i \(0.428290\pi\)
\(720\) 114.338 4.26114
\(721\) 0 0
\(722\) −30.9974 −1.15360
\(723\) −33.2099 −1.23509
\(724\) −110.168 −4.09437
\(725\) −1.74049 −0.0646402
\(726\) 67.2516 2.49594
\(727\) −24.1736 −0.896547 −0.448274 0.893896i \(-0.647961\pi\)
−0.448274 + 0.893896i \(0.647961\pi\)
\(728\) 0 0
\(729\) −22.1443 −0.820157
\(730\) 121.692 4.50401
\(731\) 7.43397 0.274955
\(732\) −22.9620 −0.848698
\(733\) −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
\(738\) −74.2676 −2.73383
\(739\) −43.2772 −1.59198 −0.795989 0.605311i \(-0.793049\pi\)
−0.795989 + 0.605311i \(0.793049\pi\)
\(740\) 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 \(0.636430\pi\)
\(744\) 22.0621 0.808835
\(745\) 37.8043 1.38504
\(746\) 41.4403 1.51724
\(747\) 43.1852 1.58006
\(748\) 7.93265 0.290047
\(749\) 0 0
\(750\) −78.1956 −2.85530
\(751\) 29.8679 1.08990 0.544948 0.838470i \(-0.316549\pi\)
0.544948 + 0.838470i \(0.316549\pi\)
\(752\) 52.5491 1.91627
\(753\) 35.3277 1.28741
\(754\) 0 0
\(755\) −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
\(759\) 11.5617 0.419662
\(760\) −80.1736 −2.90820
\(761\) 14.7289 0.533922 0.266961 0.963707i \(-0.413981\pi\)
0.266961 + 0.963707i \(0.413981\pi\)
\(762\) −34.7866 −1.26019
\(763\) 0 0
\(764\) −126.723 −4.58467
\(765\) −24.0017 −0.867784
\(766\) 90.3791 3.26553
\(767\) 0 0
\(768\) 2.48708 0.0897447
\(769\) −36.1692 −1.30429 −0.652147 0.758092i \(-0.726132\pi\)
−0.652147 + 0.758092i \(0.726132\pi\)
\(770\) 0 0
\(771\) 56.7999 2.04560
\(772\) −57.1355 −2.05635
\(773\) 38.9567 1.40117 0.700587 0.713567i \(-0.252921\pi\)
0.700587 + 0.713567i \(0.252921\pi\)
\(774\) −22.5794 −0.811598
\(775\) −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
\(783\) −0.129413 −0.00462484
\(784\) 0 0
\(785\) 46.0638 1.64409
\(786\) 62.5404 2.23074
\(787\) 29.1045 1.03746 0.518731 0.854937i \(-0.326405\pi\)
0.518731 + 0.854937i \(0.326405\pi\)
\(788\) 84.8220 3.02166
\(789\) −27.2551 −0.970309
\(790\) −14.7449 −0.524599
\(791\) 0 0
\(792\) −14.5544 −0.517169
\(793\) 0 0
\(794\) −13.2232 −0.469274
\(795\) −46.0638 −1.63371
\(796\) −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
\(801\) −40.5855 −1.43402
\(802\) −1.82991 −0.0646162
\(803\) −8.21710 −0.289975
\(804\) −156.060 −5.50382
\(805\) 0 0
\(806\) 0 0
\(807\) −26.6078 −0.936637
\(808\) 24.4517 0.860207
\(809\) 20.4543 0.719135 0.359568 0.933119i \(-0.382924\pi\)
0.359568 + 0.933119i \(0.382924\pi\)
\(810\) −94.2647 −3.31212
\(811\) −31.6458 −1.11123 −0.555617 0.831438i \(-0.687518\pi\)
−0.555617 + 0.831438i \(0.687518\pi\)
\(812\) 0 0
\(813\) 30.4871 1.06923
\(814\) −12.9620 −0.454316
\(815\) −11.7272 −0.410784
\(816\) 65.5198 2.29365
\(817\) 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 \(0.602149\pi\)
\(822\) 111.658 3.89452
\(823\) −23.0514 −0.803520 −0.401760 0.915745i \(-0.631601\pi\)
−0.401760 + 0.915745i \(0.631601\pi\)
\(824\) 40.8220 1.42210
\(825\) 13.1321 0.457199
\(826\) 0 0
\(827\) 26.3756 0.917169 0.458585 0.888651i \(-0.348357\pi\)
0.458585 + 0.888651i \(0.348357\pi\)
\(828\) 101.918 3.54188
\(829\) −45.1152 −1.56691 −0.783457 0.621446i \(-0.786546\pi\)
−0.783457 + 0.621446i \(0.786546\pi\)
\(830\) 152.962 5.30938
\(831\) 7.18780 0.249342
\(832\) 0 0
\(833\) 0 0
\(834\) −31.2702 −1.08280
\(835\) 29.6838 1.02725
\(836\) 8.96196 0.309956
\(837\) −0.706592 −0.0244234
\(838\) −52.2223 −1.80399
\(839\) −30.4871 −1.05253 −0.526265 0.850320i \(-0.676408\pi\)
−0.526265 + 0.850320i \(0.676408\pi\)
\(840\) 0 0
\(841\) −28.9567 −0.998506
\(842\) −39.6412 −1.36613
\(843\) 8.25951 0.284473
\(844\) −79.7033 −2.74350
\(845\) 0 0
\(846\) 33.5048 1.15192
\(847\) 0 0
\(848\) 60.0301 2.06144
\(849\) −29.8973 −1.02607
\(850\) −53.2029 −1.82484
\(851\) 54.8290 1.87951
\(852\) −81.7927 −2.80217
\(853\) −33.2746 −1.13930 −0.569650 0.821888i \(-0.692921\pi\)
−0.569650 + 0.821888i \(0.692921\pi\)
\(854\) 0 0
\(855\) −27.1161 −0.927350
\(856\) 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 \(-0.616252\pi\)
−0.357151 + 0.934046i \(0.616252\pi\)
\(860\) −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 \(0.516054\pi\)
\(864\) 8.76866 0.298316
\(865\) 37.7556 1.28373
\(866\) 23.7980 0.808688
\(867\) 26.9770 0.916188
\(868\) 0 0
\(869\) 0.995631 0.0337745
\(870\) 4.84060 0.164112
\(871\) 0 0
\(872\) −28.7652 −0.974113
\(873\) −27.4534 −0.929157
\(874\) −52.9184 −1.78999
\(875\) 0 0
\(876\) −151.729 −5.12644
\(877\) 36.9370 1.24727 0.623637 0.781714i \(-0.285654\pi\)
0.623637 + 0.781714i \(0.285654\pi\)
\(878\) 21.0647 0.710899
\(879\) 32.4267 1.09373
\(880\) −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 \(0.551896\pi\)
\(884\) 0 0
\(885\) −72.3384 −2.43163
\(886\) −23.6615 −0.794925
\(887\) 51.3056 1.72267 0.861337 0.508034i \(-0.169628\pi\)
0.861337 + 0.508034i \(0.169628\pi\)
\(888\) −144.579 −4.85176
\(889\) 0 0
\(890\) −143.754 −4.81864
\(891\) 6.36512 0.213240
\(892\) −42.6705 −1.42871
\(893\) −12.4624 −0.417037
\(894\) −65.7980 −2.20061
\(895\) −8.69348 −0.290591
\(896\) 0 0
\(897\) 0 0
\(898\) 22.4429 0.748931
\(899\) 0.236531 0.00788873
\(900\) 115.761 3.85869
\(901\) −12.6014 −0.419814
\(902\) 17.7626 0.591429
\(903\) 0 0
\(904\) −76.6926 −2.55076
\(905\) −79.7236 −2.65010
\(906\) 32.2676 1.07202
\(907\) −18.5385 −0.615559 −0.307780 0.951458i \(-0.599586\pi\)
−0.307780 + 0.951458i \(0.599586\pi\)
\(908\) 33.7892 1.12133
\(909\) 8.26998 0.274298
\(910\) 0 0
\(911\) 20.7272 0.686721 0.343361 0.939204i \(-0.388435\pi\)
0.343361 + 0.939204i \(0.388435\pi\)
\(912\) 74.0214 2.45109
\(913\) −10.3286 −0.341826
\(914\) −61.5244 −2.03505
\(915\) −16.6165 −0.549324
\(916\) 43.6191 1.44122
\(917\) 0 0
\(918\) −3.95586 −0.130563
\(919\) −5.13205 −0.169291 −0.0846454 0.996411i \(-0.526976\pi\)
−0.0846454 + 0.996411i \(0.526976\pi\)
\(920\) 218.064 7.18935
\(921\) −67.6528 −2.22924
\(922\) 6.03540 0.198765
\(923\) 0 0
\(924\) 0 0
\(925\) 62.2763 2.04763
\(926\) 10.9132 0.358631
\(927\) 13.8067 0.453472
\(928\) −2.93529 −0.0963557
\(929\) 19.9283 0.653826 0.326913 0.945054i \(-0.393992\pi\)
0.326913 + 0.945054i \(0.393992\pi\)
\(930\) 26.4296 0.866661
\(931\) 0 0
\(932\) −21.0514 −0.689561
\(933\) −59.1895 −1.93778
\(934\) −87.4038 −2.85994
\(935\) 5.74049 0.187734
\(936\) 0 0
\(937\) 1.64475 0.0537316 0.0268658 0.999639i \(-0.491447\pi\)
0.0268658 + 0.999639i \(0.491447\pi\)
\(938\) 0 0
\(939\) −49.8646 −1.62727
\(940\) 85.0142 2.77286
\(941\) −17.7849 −0.579770 −0.289885 0.957062i \(-0.593617\pi\)
−0.289885 + 0.957062i \(0.593617\pi\)
\(942\) −80.1736 −2.61220
\(943\) −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 \(0.555351\pi\)
\(948\) 18.3843 0.597095
\(949\) 0 0
\(950\) −60.1062 −1.95010
\(951\) 62.6252 2.03076
\(952\) 0 0
\(953\) −41.5544 −1.34608 −0.673040 0.739606i \(-0.735012\pi\)
−0.673040 + 0.739606i \(0.735012\pi\)
\(954\) 38.2746 1.23919
\(955\) −91.7033 −2.96745
\(956\) 9.06471 0.293174
\(957\) −0.326856 −0.0105658
\(958\) −24.7361 −0.799188
\(959\) 0 0
\(960\) −128.060 −4.13313
\(961\) −29.7085 −0.958340
\(962\) 0 0
\(963\) 32.4563 1.04589
\(964\) 70.0168 2.25509
\(965\) −41.3463 −1.33098
\(966\) 0 0
\(967\) 5.51465 0.177339 0.0886696 0.996061i \(-0.471738\pi\)
0.0886696 + 0.996061i \(0.471738\pi\)
\(968\) −85.6493 −2.75287
\(969\) −15.5385 −0.499167
\(970\) −97.2400 −3.12219
\(971\) −39.8246 −1.27803 −0.639017 0.769193i \(-0.720658\pi\)
−0.639017 + 0.769193i \(0.720658\pi\)
\(972\) 108.110 3.46762
\(973\) 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 \(0.509833\pi\)
\(978\) 20.4110 0.652672
\(979\) 9.70682 0.310231
\(980\) 0 0
\(981\) −9.72889 −0.310619
\(982\) −11.5837 −0.369652
\(983\) −43.0238 −1.37225 −0.686123 0.727485i \(-0.740689\pi\)
−0.686123 + 0.727485i \(0.740689\pi\)
\(984\) 198.126 6.31602
\(985\) 61.3817 1.95578
\(986\) 1.32422 0.0421717
\(987\) 0 0
\(988\) 0 0
\(989\) −22.8432 −0.726373
\(990\) −17.4357 −0.554143
\(991\) −17.6058 −0.559267 −0.279633 0.960107i \(-0.590213\pi\)
−0.279633 + 0.960107i \(0.590213\pi\)
\(992\) −16.0267 −0.508847
\(993\) −57.8334 −1.83529
\(994\) 0 0
\(995\) −75.0612 −2.37960
\(996\) −190.717 −6.04311
\(997\) 12.9707 0.410786 0.205393 0.978680i \(-0.434153\pi\)
0.205393 + 0.978680i \(0.434153\pi\)
\(998\) −25.7405 −0.814801
\(999\) 4.63051 0.146503
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 8281.2.a.bh.1.3 3
7.6 odd 2 8281.2.a.bk.1.3 3
13.12 even 2 637.2.a.h.1.1 3
39.38 odd 2 5733.2.a.be.1.3 3
91.12 odd 6 637.2.e.k.508.3 6
91.25 even 6 637.2.e.l.79.3 6
91.38 odd 6 637.2.e.k.79.3 6
91.51 even 6 637.2.e.l.508.3 6
91.90 odd 2 637.2.a.i.1.1 yes 3
273.272 even 2 5733.2.a.bd.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.a.h.1.1 3 13.12 even 2
637.2.a.i.1.1 yes 3 91.90 odd 2
637.2.e.k.79.3 6 91.38 odd 6
637.2.e.k.508.3 6 91.12 odd 6
637.2.e.l.79.3 6 91.25 even 6
637.2.e.l.508.3 6 91.51 even 6
5733.2.a.bd.1.3 3 273.272 even 2
5733.2.a.be.1.3 3 39.38 odd 2
8281.2.a.bh.1.3 3 1.1 even 1 trivial
8281.2.a.bk.1.3 3 7.6 odd 2