Properties

Label 637.2.a.i.1.1
Level $637$
Weight $2$
Character 637.1
Self dual yes
Analytic conductor $5.086$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.08647060876\)
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: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.65544\) of defining polynomial
Character \(\chi\) \(=\) 637.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65544 q^{2} +2.39593 q^{3} +5.05137 q^{4} +3.65544 q^{5} -6.36226 q^{6} -8.10275 q^{8} +2.74049 q^{9} +O(q^{10})\) \(q-2.65544 q^{2} +2.39593 q^{3} +5.05137 q^{4} +3.65544 q^{5} -6.36226 q^{6} -8.10275 q^{8} +2.74049 q^{9} -9.70682 q^{10} +0.655442 q^{11} +12.1027 q^{12} -1.00000 q^{13} +8.75819 q^{15} +11.4136 q^{16} +2.39593 q^{17} -7.27721 q^{18} -2.70682 q^{19} +18.4650 q^{20} -1.74049 q^{22} +7.36226 q^{23} -19.4136 q^{24} +8.36226 q^{25} +2.65544 q^{26} -0.621770 q^{27} -0.208136 q^{29} -23.2569 q^{30} -1.13642 q^{31} -14.1027 q^{32} +1.57040 q^{33} -6.36226 q^{34} +13.8432 q^{36} -7.44731 q^{37} +7.18780 q^{38} -2.39593 q^{39} -29.6191 q^{40} -10.2055 q^{41} -3.10275 q^{43} +3.31088 q^{44} +10.0177 q^{45} -19.5501 q^{46} +4.60407 q^{47} +27.3463 q^{48} -22.2055 q^{50} +5.74049 q^{51} -5.05137 q^{52} +5.25951 q^{53} +1.65107 q^{54} +2.39593 q^{55} -6.48535 q^{57} +0.552694 q^{58} +8.25951 q^{59} +44.2409 q^{60} -1.89725 q^{61} +3.01770 q^{62} +14.6218 q^{64} -3.65544 q^{65} -4.17009 q^{66} -12.8946 q^{67} +12.1027 q^{68} +17.6395 q^{69} -6.75819 q^{71} -22.2055 q^{72} +12.5367 q^{73} +19.7759 q^{74} +20.0354 q^{75} -13.6731 q^{76} +6.36226 q^{78} -1.51902 q^{79} +41.7219 q^{80} -9.71119 q^{81} +27.1001 q^{82} +15.7582 q^{83} +8.75819 q^{85} +8.23917 q^{86} -0.498680 q^{87} -5.31088 q^{88} -14.8096 q^{89} -26.6014 q^{90} +37.1895 q^{92} -2.72279 q^{93} -12.2258 q^{94} -9.89461 q^{95} -33.7892 q^{96} -10.0177 q^{97} +1.79623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} + O(q^{10}) \) \( 3 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 5 q^{5} + 2 q^{6} - 6 q^{8} + 11 q^{9} - 14 q^{10} - 4 q^{11} + 18 q^{12} - 3 q^{13} + 2 q^{15} + 4 q^{16} + 4 q^{17} + 8 q^{18} + 7 q^{19} + 16 q^{20} - 8 q^{22} + q^{23} - 28 q^{24} + 4 q^{25} + 2 q^{26} + 22 q^{27} - 7 q^{29} - 24 q^{30} - 3 q^{31} - 24 q^{32} - 10 q^{33} + 2 q^{34} + 26 q^{36} - 10 q^{37} + 12 q^{38} - 4 q^{39} - 22 q^{40} + 6 q^{41} + 9 q^{43} - 2 q^{44} + 3 q^{45} - 28 q^{46} + 17 q^{47} + 16 q^{48} - 30 q^{50} + 20 q^{51} - 6 q^{52} + 13 q^{53} + 28 q^{54} + 4 q^{55} + 4 q^{57} + 14 q^{58} + 22 q^{59} + 42 q^{60} - 24 q^{61} - 18 q^{62} + 20 q^{64} - 5 q^{65} - 30 q^{66} - 14 q^{67} + 18 q^{68} + 2 q^{69} + 4 q^{71} - 30 q^{72} + 5 q^{73} + 8 q^{74} + 6 q^{75} - 8 q^{76} - 2 q^{78} + q^{79} + 40 q^{80} + 15 q^{81} + 20 q^{82} + 23 q^{83} + 2 q^{85} + 6 q^{86} + 20 q^{87} - 4 q^{88} - 11 q^{89} - 40 q^{90} + 30 q^{92} - 38 q^{93} - 16 q^{94} - 5 q^{95} - 52 q^{96} - 3 q^{97} - 30 q^{99} + O(q^{100}) \)

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 \(-0.888099\pi\)
−0.938841 + 0.344352i \(0.888099\pi\)
\(3\) 2.39593 1.38329 0.691646 0.722237i \(-0.256886\pi\)
0.691646 + 0.722237i \(0.256886\pi\)
\(4\) 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 \(-0.468496\pi\)
0.0988117 + 0.995106i \(0.468496\pi\)
\(12\) 12.1027 3.49376
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 8.75819 2.26136
\(16\) 11.4136 2.85341
\(17\) 2.39593 0.581099 0.290549 0.956860i \(-0.406162\pi\)
0.290549 + 0.956860i \(0.406162\pi\)
\(18\) −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
\(26\) 2.65544 0.520775
\(27\) −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 \(-0.709701\pi\)
−0.612165 + 0.790730i \(0.709701\pi\)
\(38\) 7.18780 1.16601
\(39\) −2.39593 −0.383656
\(40\) −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
\(52\) −5.05137 −0.700500
\(53\) 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 \(-0.538757\pi\)
−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
\(66\) −4.17009 −0.513303
\(67\) −12.8946 −1.57533 −0.787664 0.616105i \(-0.788710\pi\)
−0.787664 + 0.616105i \(0.788710\pi\)
\(68\) 12.1027 1.46767
\(69\) 17.6395 2.12354
\(70\) 0 0
\(71\) −6.75819 −0.802050 −0.401025 0.916067i \(-0.631346\pi\)
−0.401025 + 0.916067i \(0.631346\pi\)
\(72\) −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
\(78\) 6.36226 0.720384
\(79\) −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 \(-0.547971\pi\)
−0.150136 + 0.988665i \(0.547971\pi\)
\(102\) −15.2435 −1.50934
\(103\) −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 \(-0.305987\pi\)
0.572465 + 0.819929i \(0.305987\pi\)
\(108\) −3.14079 −0.302223
\(109\) 3.55005 0.340034 0.170017 0.985441i \(-0.445618\pi\)
0.170017 + 0.985441i \(0.445618\pi\)
\(110\) −6.36226 −0.606618
\(111\) −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
\(117\) −2.74049 −0.253358
\(118\) −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
\(130\) 9.70682 0.851344
\(131\) 9.82991 0.858843 0.429421 0.903104i \(-0.358718\pi\)
0.429421 + 0.903104i \(0.358718\pi\)
\(132\) 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 \(-0.230197\pi\)
0.749701 + 0.661777i \(0.230197\pi\)
\(138\) −46.8406 −3.98734
\(139\) −4.91495 −0.416881 −0.208440 0.978035i \(-0.566839\pi\)
−0.208440 + 0.978035i \(0.566839\pi\)
\(140\) 0 0
\(141\) 11.0310 0.928981
\(142\) 17.9460 1.50599
\(143\) −0.655442 −0.0548108
\(144\) 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 \(-0.639241\pi\)
−0.423621 + 0.905839i \(0.639241\pi\)
\(150\) −53.2029 −4.34400
\(151\) 5.07171 0.412730 0.206365 0.978475i \(-0.433837\pi\)
0.206365 + 0.978475i \(0.433837\pi\)
\(152\) 21.9327 1.77897
\(153\) 6.56603 0.530832
\(154\) 0 0
\(155\) −4.15412 −0.333667
\(156\) −12.1027 −0.968995
\(157\) −12.6014 −1.00570 −0.502852 0.864373i \(-0.667716\pi\)
−0.502852 + 0.864373i \(0.667716\pi\)
\(158\) 4.03367 0.320902
\(159\) 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 \(-0.459901\pi\)
0.125640 + 0.992076i \(0.459901\pi\)
\(164\) −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
\(169\) 1.00000 0.0769231
\(170\) −23.2569 −1.78372
\(171\) −7.41800 −0.567269
\(172\) −15.6731 −1.19507
\(173\) −10.3286 −0.785268 −0.392634 0.919695i \(-0.628436\pi\)
−0.392634 + 0.919695i \(0.628436\pi\)
\(174\) 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 \(-0.199170\pi\)
0.810546 + 0.585675i \(0.199170\pi\)
\(182\) 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 \(-0.366544\pi\)
0.407088 + 0.913389i \(0.366544\pi\)
\(194\) 26.6014 1.90987
\(195\) −8.75819 −0.627187
\(196\) 0 0
\(197\) −16.7919 −1.19637 −0.598185 0.801358i \(-0.704111\pi\)
−0.598185 + 0.801358i \(0.704111\pi\)
\(198\) −4.76979 −0.338974
\(199\) 20.5341 1.45562 0.727811 0.685777i \(-0.240538\pi\)
0.727811 + 0.685777i \(0.240538\pi\)
\(200\) −67.7573 −4.79116
\(201\) −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
\(208\) −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
\(213\) −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
\(221\) −2.39593 −0.161168
\(222\) 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 \(0.543588\pi\)
\(234\) 7.27721 0.475726
\(235\) 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 \(-0.518485\pi\)
−0.0580384 + 0.998314i \(0.518485\pi\)
\(240\) 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
\(247\) 2.70682 0.172231
\(248\) 9.20814 0.584717
\(249\) 37.7556 2.39266
\(250\) −32.6368 −2.06413
\(251\) 14.7449 0.930687 0.465344 0.885130i \(-0.345931\pi\)
0.465344 + 0.885130i \(0.345931\pi\)
\(252\) 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 \(-0.235112\pi\)
0.739395 + 0.673272i \(0.235112\pi\)
\(258\) 19.7405 1.22899
\(259\) 0 0
\(260\) −18.4650 −1.14515
\(261\) −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 \(-0.609938\pi\)
−0.338554 + 0.940947i \(0.609938\pi\)
\(270\) 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 \(-0.467212\pi\)
0.102825 + 0.994700i \(0.467212\pi\)
\(282\) −29.2923 −1.74433
\(283\) −12.4783 −0.741760 −0.370880 0.928681i \(-0.620944\pi\)
−0.370880 + 0.928681i \(0.620944\pi\)
\(284\) −34.1382 −2.02573
\(285\) −23.7068 −1.40427
\(286\) 1.74049 0.102917
\(287\) 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
\(299\) −7.36226 −0.425770
\(300\) 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 \(-0.747005\pi\)
−0.700423 + 0.713728i \(0.747005\pi\)
\(312\) 19.4136 1.09908
\(313\) −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 \(-0.237636\pi\)
0.734032 + 0.679114i \(0.237636\pi\)
\(318\) −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
\(325\) −8.36226 −0.463855
\(326\) −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 \(-0.730877\pi\)
−0.663376 + 0.748286i \(0.730877\pi\)
\(332\) 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 \(0.812534\pi\)
\(338\) −2.65544 −0.144437
\(339\) −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
\(351\) 0.621770 0.0331876
\(352\) −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 \(-0.691499\pi\)
−0.565973 + 0.824424i \(0.691499\pi\)
\(360\) −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 \(-0.509310\pi\)
−0.0292435 + 0.999572i \(0.509310\pi\)
\(368\) 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
\(377\) 0.208136 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
\(381\) 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 \(0.715073\pi\)
\(390\) 23.2569 1.17766
\(391\) 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 \(-0.494523\pi\)
0.0172064 + 0.999852i \(0.494523\pi\)
\(402\) 82.0389 4.09173
\(403\) 1.13642 0.0566092
\(404\) −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
\(416\) 14.1027 0.691444
\(417\) −11.7759 −0.576668
\(418\) 4.71119 0.230432
\(419\) 19.6661 0.960754 0.480377 0.877062i \(-0.340500\pi\)
0.480377 + 0.877062i \(0.340500\pi\)
\(420\) 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
\(423\) 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
\(429\) −1.57040 −0.0758194
\(430\) 30.1178 1.45241
\(431\) −32.6838 −1.57433 −0.787163 0.616746i \(-0.788451\pi\)
−0.787163 + 0.616746i \(0.788451\pi\)
\(432\) −7.09665 −0.341438
\(433\) −8.96196 −0.430684 −0.215342 0.976539i \(-0.569087\pi\)
−0.215342 + 0.976539i \(0.569087\pi\)
\(434\) 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 \(-0.560623\pi\)
−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 \(-0.567893\pi\)
−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 \(-0.563909\pi\)
−0.199430 + 0.979912i \(0.563909\pi\)
\(450\) −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 \(-0.317703\pi\)
0.541904 + 0.840440i \(0.317703\pi\)
\(458\) −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 \(-0.530444\pi\)
−0.0954983 + 0.995430i \(0.530444\pi\)
\(464\) −2.37559 −0.110284
\(465\) −9.95299 −0.461559
\(466\) 11.0664 0.512643
\(467\) 32.9150 1.52312 0.761561 0.648093i \(-0.224433\pi\)
0.761561 + 0.648093i \(0.224433\pi\)
\(468\) −13.8432 −0.639904
\(469\) 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
\(481\) 7.44731 0.339568
\(482\) −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 \(-0.348351\pi\)
0.458601 + 0.888642i \(0.348351\pi\)
\(488\) 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
\(494\) −7.18780 −0.323394
\(495\) 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 \(-0.430383\pi\)
0.216970 + 0.976178i \(0.430383\pi\)
\(500\) 62.0841 2.77649
\(501\) 19.4560 0.869232
\(502\) −39.1541 −1.74753
\(503\) 2.64843 0.118088 0.0590439 0.998255i \(-0.481195\pi\)
0.0590439 + 0.998255i \(0.481195\pi\)
\(504\) 0 0
\(505\) −11.0310 −0.490875
\(506\) −12.8139 −0.569649
\(507\) 2.39593 0.106407
\(508\) 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
\(520\) 29.6191 1.29888
\(521\) −14.6218 −0.640591 −0.320296 0.947318i \(-0.603782\pi\)
−0.320296 + 0.947318i \(0.603782\pi\)
\(522\) 1.51465 0.0662945
\(523\) 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
\(528\) 17.9239 0.780038
\(529\) 31.2029 1.35665
\(530\) −51.0531 −2.21761
\(531\) 22.6351 0.982280
\(532\) 0 0
\(533\) 10.2055 0.442049
\(534\) 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 \(-0.877237\pi\)
−0.926546 + 0.376181i \(0.877237\pi\)
\(542\) 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 \(-0.490884\pi\)
0.0286338 + 0.999590i \(0.490884\pi\)
\(558\) 8.26998 0.350096
\(559\) 3.10275 0.131232
\(560\) 0 0
\(561\) 3.76256 0.158855
\(562\) −9.15412 −0.386143
\(563\) 31.7626 1.33863 0.669316 0.742978i \(-0.266587\pi\)
0.669316 + 0.742978i \(0.266587\pi\)
\(564\) 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 \(0.502879\pi\)
\(572\) −3.31088 −0.138435
\(573\) −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
\(585\) −10.0177 −0.414181
\(586\) 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
\(598\) 19.5501 0.799461
\(599\) 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 \(-0.558511\pi\)
−0.182783 + 0.983153i \(0.558511\pi\)
\(602\) 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 \(-0.156145\pi\)
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
\(612\) 33.1675 1.34071
\(613\) −21.4490 −0.866318 −0.433159 0.901317i \(-0.642601\pi\)
−0.433159 + 0.901317i \(0.642601\pi\)
\(614\) −74.9805 −3.02597
\(615\) −89.3817 −3.60422
\(616\) 0 0
\(617\) −12.1294 −0.488312 −0.244156 0.969736i \(-0.578511\pi\)
−0.244156 + 0.969736i \(0.578511\pi\)
\(618\) 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
\(624\) −27.3463 −1.09473
\(625\) 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 \(-0.575167\pi\)
−0.233956 + 0.972247i \(0.575167\pi\)
\(632\) 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 \(-0.203267\pi\)
0.802943 + 0.596056i \(0.203267\pi\)
\(648\) 78.6873 3.09113
\(649\) 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 \(-0.863473\pi\)
−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
\(663\) −5.74049 −0.222942
\(664\) −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
\(676\) 5.05137 0.194284
\(677\) −20.7803 −0.798650 −0.399325 0.916809i \(-0.630756\pi\)
−0.399325 + 0.916809i \(0.630756\pi\)
\(678\) 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 \(-0.323043\pi\)
0.527731 + 0.849412i \(0.323043\pi\)
\(684\) −37.4711 −1.43274
\(685\) 64.1532 2.45117
\(686\) 0 0
\(687\) 20.6891 0.789339
\(688\) −35.4136 −1.35013
\(689\) −5.25951 −0.200371
\(690\) −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 \(0.629130\pi\)
\(702\) −1.65107 −0.0623157
\(703\) 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 \(-0.440238\pi\)
0.186646 + 0.982427i \(0.440238\pi\)
\(710\) 65.6005 2.46194
\(711\) −4.16286 −0.156119
\(712\) 119.998 4.49712
\(713\) −8.36663 −0.313333
\(714\) 0 0
\(715\) −2.39593 −0.0896028
\(716\) −12.0133 −0.448959
\(717\) −4.29951 −0.160568
\(718\) 56.9521 2.12543
\(719\) −11.9797 −0.446766 −0.223383 0.974731i \(-0.571710\pi\)
−0.223383 + 0.974731i \(0.571710\pi\)
\(720\) 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 \(-0.352039\pi\)
0.448274 + 0.893896i \(0.352039\pi\)
\(728\) 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 \(-0.206951\pi\)
0.795989 + 0.605311i \(0.206951\pi\)
\(740\) −137.515 −5.05514
\(741\) 6.48535 0.238245
\(742\) 0 0
\(743\) 22.6572 0.831211 0.415606 0.909545i \(-0.363570\pi\)
0.415606 + 0.909545i \(0.363570\pi\)
\(744\) 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
\(754\) −0.552694 −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
\(759\) 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
\(767\) −8.25951 −0.298234
\(768\) −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
\(780\) −44.2409 −1.58408
\(781\) −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
\(793\) 1.89725 0.0673734
\(794\) 13.2232 0.469274
\(795\) 46.0638 1.63371
\(796\) 103.725 3.67645
\(797\) −17.8920 −0.633766 −0.316883 0.948465i \(-0.602636\pi\)
−0.316883 + 0.948465i \(0.602636\pi\)
\(798\) 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
\(806\) −3.01770 −0.106294
\(807\) −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 \(-0.397851\pi\)
0.315430 + 0.948949i \(0.397851\pi\)
\(822\) −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 \(-0.651643\pi\)
−0.458585 + 0.888651i \(0.651643\pi\)
\(828\) 101.918 3.54188
\(829\) 45.1152 1.56691 0.783457 0.621446i \(-0.213454\pi\)
0.783457 + 0.621446i \(0.213454\pi\)
\(830\) −152.962 −5.30938
\(831\) −7.18780 −0.249342
\(832\) −14.6218 −0.506919
\(833\) 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
\(845\) 3.65544 0.125751
\(846\) −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 \(-0.215692\pi\)
0.779070 + 0.626937i \(0.215692\pi\)
\(858\) 4.17009 0.142365
\(859\) 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 \(-0.483946\pi\)
0.0504131 + 0.998728i \(0.483946\pi\)
\(864\) 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
\(871\) 12.8946 0.436917
\(872\) −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 \(-0.714346\pi\)
−0.623637 + 0.781714i \(0.714346\pi\)
\(878\) 21.0647 0.710899
\(879\) −32.4267 −1.09373
\(880\) 27.3463 0.921843
\(881\) 30.8946 1.04087 0.520433 0.853903i \(-0.325771\pi\)
0.520433 + 0.853903i \(0.325771\pi\)
\(882\) 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
\(885\) 72.3384 2.43163
\(886\) 23.6615 0.794925
\(887\) −51.3056 −1.72267 −0.861337 0.508034i \(-0.830372\pi\)
−0.861337 + 0.508034i \(0.830372\pi\)
\(888\) 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
\(897\) −17.6395 −0.588965
\(898\) 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
\(923\) 6.75819 0.222449
\(924\) 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
\(936\) 22.2055 0.725809
\(937\) −1.64475 −0.0537316 −0.0268658 0.999639i \(-0.508553\pi\)
−0.0268658 + 0.999639i \(0.508553\pi\)
\(938\) 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 \(-0.444649\pi\)
0.173014 + 0.984919i \(0.444649\pi\)
\(948\) −18.3843 −0.597095
\(949\) −12.5367 −0.406959
\(950\) 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
\(962\) −19.7759 −0.637600
\(963\) 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 \(-0.528262\pi\)
−0.0886696 + 0.996061i \(0.528262\pi\)
\(968\) 85.6493 2.75287
\(969\) −15.5385 −0.499167
\(970\) 97.2400 3.12219
\(971\) 39.8246 1.27803 0.639017 0.769193i \(-0.279342\pi\)
0.639017 + 0.769193i \(0.279342\pi\)
\(972\) −108.110 −3.46762
\(973\) 0 0
\(974\) −53.7485 −1.72221
\(975\) −20.0354 −0.641646
\(976\) −21.6545 −0.693145
\(977\) 1.93092 0.0617757 0.0308879 0.999523i \(-0.490167\pi\)
0.0308879 + 0.999523i \(0.490167\pi\)
\(978\) −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
\(988\) 13.6731 0.435001
\(989\) −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 \(-0.565847\pi\)
−0.205393 + 0.978680i \(0.565847\pi\)
\(998\) −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 637.2.a.i.1.1 yes 3
3.2 odd 2 5733.2.a.bd.1.3 3
7.2 even 3 637.2.e.k.508.3 6
7.3 odd 6 637.2.e.l.79.3 6
7.4 even 3 637.2.e.k.79.3 6
7.5 odd 6 637.2.e.l.508.3 6
7.6 odd 2 637.2.a.h.1.1 3
13.12 even 2 8281.2.a.bk.1.3 3
21.20 even 2 5733.2.a.be.1.3 3
91.90 odd 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 7.6 odd 2
637.2.a.i.1.1 yes 3 1.1 even 1 trivial
637.2.e.k.79.3 6 7.4 even 3
637.2.e.k.508.3 6 7.2 even 3
637.2.e.l.79.3 6 7.3 odd 6
637.2.e.l.508.3 6 7.5 odd 6
5733.2.a.bd.1.3 3 3.2 odd 2
5733.2.a.be.1.3 3 21.20 even 2
8281.2.a.bh.1.3 3 91.90 odd 2
8281.2.a.bk.1.3 3 13.12 even 2