Properties

Label 6037.2.a.b.1.10
Level $6037$
Weight $2$
Character 6037.1
Self dual yes
Analytic conductor $48.206$
Analytic rank $0$
Dimension $259$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6037 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6037.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.2056877002\)
Analytic rank: \(0\)
Dimension: \(259\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6037.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.58711 q^{2} -3.26786 q^{3} +4.69312 q^{4} +2.66521 q^{5} +8.45431 q^{6} +2.69955 q^{7} -6.96738 q^{8} +7.67894 q^{9} +O(q^{10})\) \(q-2.58711 q^{2} -3.26786 q^{3} +4.69312 q^{4} +2.66521 q^{5} +8.45431 q^{6} +2.69955 q^{7} -6.96738 q^{8} +7.67894 q^{9} -6.89517 q^{10} +1.78104 q^{11} -15.3365 q^{12} +0.833324 q^{13} -6.98403 q^{14} -8.70953 q^{15} +8.63912 q^{16} +5.88299 q^{17} -19.8662 q^{18} +3.75980 q^{19} +12.5081 q^{20} -8.82177 q^{21} -4.60774 q^{22} +5.86102 q^{23} +22.7685 q^{24} +2.10333 q^{25} -2.15590 q^{26} -15.2901 q^{27} +12.6693 q^{28} -4.40811 q^{29} +22.5325 q^{30} -8.58372 q^{31} -8.41557 q^{32} -5.82020 q^{33} -15.2199 q^{34} +7.19486 q^{35} +36.0382 q^{36} +7.29770 q^{37} -9.72700 q^{38} -2.72319 q^{39} -18.5695 q^{40} -10.9515 q^{41} +22.8228 q^{42} +1.81334 q^{43} +8.35863 q^{44} +20.4660 q^{45} -15.1631 q^{46} -5.45378 q^{47} -28.2315 q^{48} +0.287576 q^{49} -5.44153 q^{50} -19.2248 q^{51} +3.91089 q^{52} -1.35833 q^{53} +39.5572 q^{54} +4.74684 q^{55} -18.8088 q^{56} -12.2865 q^{57} +11.4043 q^{58} +6.16715 q^{59} -40.8749 q^{60} -13.5682 q^{61} +22.2070 q^{62} +20.7297 q^{63} +4.49371 q^{64} +2.22098 q^{65} +15.0575 q^{66} +1.49479 q^{67} +27.6096 q^{68} -19.1530 q^{69} -18.6139 q^{70} +13.0574 q^{71} -53.5021 q^{72} +5.94246 q^{73} -18.8799 q^{74} -6.87339 q^{75} +17.6452 q^{76} +4.80801 q^{77} +7.04519 q^{78} +15.6967 q^{79} +23.0251 q^{80} +26.9293 q^{81} +28.3328 q^{82} +15.5119 q^{83} -41.4016 q^{84} +15.6794 q^{85} -4.69131 q^{86} +14.4051 q^{87} -12.4092 q^{88} +4.85742 q^{89} -52.9476 q^{90} +2.24960 q^{91} +27.5064 q^{92} +28.0504 q^{93} +14.1095 q^{94} +10.0206 q^{95} +27.5009 q^{96} -11.1935 q^{97} -0.743990 q^{98} +13.6765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + O(q^{10}) \) \( 259q + 47q^{2} + 29q^{3} + 273q^{4} + 38q^{5} + 24q^{6} + 42q^{7} + 141q^{8} + 286q^{9} + 18q^{10} + 108q^{11} + 46q^{12} + 33q^{13} + 35q^{14} + 40q^{15} + 301q^{16} + 67q^{17} + 117q^{18} + 69q^{19} + 103q^{20} + 24q^{21} + 42q^{22} + 162q^{23} + 45q^{24} + 291q^{25} + 41q^{26} + 101q^{27} + 87q^{28} + 78q^{29} + 48q^{30} + 25q^{31} + 314q^{32} + 67q^{33} + 9q^{34} + 252q^{35} + 337q^{36} + 49q^{37} + 59q^{38} + 93q^{39} + 44q^{40} + 60q^{41} + 38q^{42} + 178q^{43} + 171q^{44} + 67q^{45} + 43q^{46} + 185q^{47} + 67q^{48} + 273q^{49} + 204q^{50} + 145q^{51} + 83q^{52} + 112q^{53} + 60q^{54} + 57q^{55} + 93q^{56} + 109q^{57} + 63q^{58} + 228q^{59} + 53q^{60} + 20q^{61} + 126q^{62} + 153q^{63} + 345q^{64} + 113q^{65} + 5q^{66} + 208q^{67} + 166q^{68} + 10q^{69} + 69q^{70} + 150q^{71} + 331q^{72} + 75q^{73} + 84q^{74} + 72q^{75} + 102q^{76} + 166q^{77} + 69q^{78} + 52q^{79} + 180q^{80} + 327q^{81} + 43q^{82} + 434q^{83} + 75q^{85} + 133q^{86} + 144q^{87} + 111q^{88} + 78q^{89} - 8q^{90} + 35q^{91} + 372q^{92} + 160q^{93} + 36q^{94} + 154q^{95} + 60q^{96} + 35q^{97} + 254q^{98} + 234q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58711 −1.82936 −0.914680 0.404178i \(-0.867557\pi\)
−0.914680 + 0.404178i \(0.867557\pi\)
\(3\) −3.26786 −1.88670 −0.943351 0.331796i \(-0.892345\pi\)
−0.943351 + 0.331796i \(0.892345\pi\)
\(4\) 4.69312 2.34656
\(5\) 2.66521 1.19192 0.595958 0.803015i \(-0.296772\pi\)
0.595958 + 0.803015i \(0.296772\pi\)
\(6\) 8.45431 3.45146
\(7\) 2.69955 1.02033 0.510167 0.860075i \(-0.329584\pi\)
0.510167 + 0.860075i \(0.329584\pi\)
\(8\) −6.96738 −2.46334
\(9\) 7.67894 2.55965
\(10\) −6.89517 −2.18045
\(11\) 1.78104 0.537004 0.268502 0.963279i \(-0.413471\pi\)
0.268502 + 0.963279i \(0.413471\pi\)
\(12\) −15.3365 −4.42726
\(13\) 0.833324 0.231123 0.115561 0.993300i \(-0.463133\pi\)
0.115561 + 0.993300i \(0.463133\pi\)
\(14\) −6.98403 −1.86656
\(15\) −8.70953 −2.24879
\(16\) 8.63912 2.15978
\(17\) 5.88299 1.42683 0.713417 0.700740i \(-0.247147\pi\)
0.713417 + 0.700740i \(0.247147\pi\)
\(18\) −19.8662 −4.68252
\(19\) 3.75980 0.862558 0.431279 0.902219i \(-0.358063\pi\)
0.431279 + 0.902219i \(0.358063\pi\)
\(20\) 12.5081 2.79690
\(21\) −8.82177 −1.92507
\(22\) −4.60774 −0.982374
\(23\) 5.86102 1.22211 0.611053 0.791589i \(-0.290746\pi\)
0.611053 + 0.791589i \(0.290746\pi\)
\(24\) 22.7685 4.64759
\(25\) 2.10333 0.420665
\(26\) −2.15590 −0.422807
\(27\) −15.2901 −2.94259
\(28\) 12.6693 2.39428
\(29\) −4.40811 −0.818566 −0.409283 0.912407i \(-0.634221\pi\)
−0.409283 + 0.912407i \(0.634221\pi\)
\(30\) 22.5325 4.11385
\(31\) −8.58372 −1.54168 −0.770841 0.637028i \(-0.780164\pi\)
−0.770841 + 0.637028i \(0.780164\pi\)
\(32\) −8.41557 −1.48768
\(33\) −5.82020 −1.01317
\(34\) −15.2199 −2.61019
\(35\) 7.19486 1.21615
\(36\) 36.0382 6.00636
\(37\) 7.29770 1.19973 0.599867 0.800099i \(-0.295220\pi\)
0.599867 + 0.800099i \(0.295220\pi\)
\(38\) −9.72700 −1.57793
\(39\) −2.72319 −0.436060
\(40\) −18.5695 −2.93610
\(41\) −10.9515 −1.71034 −0.855171 0.518346i \(-0.826548\pi\)
−0.855171 + 0.518346i \(0.826548\pi\)
\(42\) 22.8228 3.52164
\(43\) 1.81334 0.276532 0.138266 0.990395i \(-0.455847\pi\)
0.138266 + 0.990395i \(0.455847\pi\)
\(44\) 8.35863 1.26011
\(45\) 20.4660 3.05088
\(46\) −15.1631 −2.23567
\(47\) −5.45378 −0.795515 −0.397758 0.917491i \(-0.630211\pi\)
−0.397758 + 0.917491i \(0.630211\pi\)
\(48\) −28.2315 −4.07486
\(49\) 0.287576 0.0410823
\(50\) −5.44153 −0.769548
\(51\) −19.2248 −2.69201
\(52\) 3.91089 0.542343
\(53\) −1.35833 −0.186581 −0.0932905 0.995639i \(-0.529739\pi\)
−0.0932905 + 0.995639i \(0.529739\pi\)
\(54\) 39.5572 5.38305
\(55\) 4.74684 0.640064
\(56\) −18.8088 −2.51343
\(57\) −12.2865 −1.62739
\(58\) 11.4043 1.49745
\(59\) 6.16715 0.802895 0.401447 0.915882i \(-0.368507\pi\)
0.401447 + 0.915882i \(0.368507\pi\)
\(60\) −40.8749 −5.27692
\(61\) −13.5682 −1.73723 −0.868613 0.495491i \(-0.834988\pi\)
−0.868613 + 0.495491i \(0.834988\pi\)
\(62\) 22.2070 2.82029
\(63\) 20.7297 2.61169
\(64\) 4.49371 0.561714
\(65\) 2.22098 0.275479
\(66\) 15.0575 1.85345
\(67\) 1.49479 0.182617 0.0913087 0.995823i \(-0.470895\pi\)
0.0913087 + 0.995823i \(0.470895\pi\)
\(68\) 27.6096 3.34815
\(69\) −19.1530 −2.30575
\(70\) −18.6139 −2.22478
\(71\) 13.0574 1.54963 0.774813 0.632190i \(-0.217844\pi\)
0.774813 + 0.632190i \(0.217844\pi\)
\(72\) −53.5021 −6.30528
\(73\) 5.94246 0.695513 0.347756 0.937585i \(-0.386944\pi\)
0.347756 + 0.937585i \(0.386944\pi\)
\(74\) −18.8799 −2.19475
\(75\) −6.87339 −0.793670
\(76\) 17.6452 2.02404
\(77\) 4.80801 0.547924
\(78\) 7.04519 0.797710
\(79\) 15.6967 1.76602 0.883011 0.469352i \(-0.155512\pi\)
0.883011 + 0.469352i \(0.155512\pi\)
\(80\) 23.0251 2.57428
\(81\) 26.9293 2.99214
\(82\) 28.3328 3.12883
\(83\) 15.5119 1.70266 0.851328 0.524634i \(-0.175798\pi\)
0.851328 + 0.524634i \(0.175798\pi\)
\(84\) −41.4016 −4.51728
\(85\) 15.6794 1.70067
\(86\) −4.69131 −0.505877
\(87\) 14.4051 1.54439
\(88\) −12.4092 −1.32282
\(89\) 4.85742 0.514885 0.257442 0.966294i \(-0.417120\pi\)
0.257442 + 0.966294i \(0.417120\pi\)
\(90\) −52.9476 −5.58117
\(91\) 2.24960 0.235822
\(92\) 27.5064 2.86775
\(93\) 28.0504 2.90869
\(94\) 14.1095 1.45528
\(95\) 10.0206 1.02810
\(96\) 27.5009 2.80680
\(97\) −11.1935 −1.13653 −0.568263 0.822847i \(-0.692384\pi\)
−0.568263 + 0.822847i \(0.692384\pi\)
\(98\) −0.743990 −0.0751544
\(99\) 13.6765 1.37454
\(100\) 9.87116 0.987116
\(101\) −6.38725 −0.635555 −0.317778 0.948165i \(-0.602937\pi\)
−0.317778 + 0.948165i \(0.602937\pi\)
\(102\) 49.7366 4.92466
\(103\) 7.55629 0.744543 0.372272 0.928124i \(-0.378579\pi\)
0.372272 + 0.928124i \(0.378579\pi\)
\(104\) −5.80609 −0.569334
\(105\) −23.5118 −2.29452
\(106\) 3.51414 0.341324
\(107\) 20.2302 1.95573 0.977863 0.209246i \(-0.0671010\pi\)
0.977863 + 0.209246i \(0.0671010\pi\)
\(108\) −71.7584 −6.90496
\(109\) 5.37553 0.514882 0.257441 0.966294i \(-0.417121\pi\)
0.257441 + 0.966294i \(0.417121\pi\)
\(110\) −12.2806 −1.17091
\(111\) −23.8479 −2.26354
\(112\) 23.3218 2.20370
\(113\) −9.18266 −0.863832 −0.431916 0.901914i \(-0.642162\pi\)
−0.431916 + 0.901914i \(0.642162\pi\)
\(114\) 31.7865 2.97708
\(115\) 15.6208 1.45665
\(116\) −20.6878 −1.92081
\(117\) 6.39905 0.591592
\(118\) −15.9551 −1.46878
\(119\) 15.8814 1.45585
\(120\) 60.6827 5.53954
\(121\) −7.82790 −0.711627
\(122\) 35.1023 3.17801
\(123\) 35.7881 3.22691
\(124\) −40.2844 −3.61765
\(125\) −7.72023 −0.690519
\(126\) −53.6299 −4.77773
\(127\) 13.3228 1.18220 0.591102 0.806597i \(-0.298693\pi\)
0.591102 + 0.806597i \(0.298693\pi\)
\(128\) 5.20542 0.460098
\(129\) −5.92576 −0.521734
\(130\) −5.74592 −0.503950
\(131\) −8.33750 −0.728451 −0.364226 0.931311i \(-0.618666\pi\)
−0.364226 + 0.931311i \(0.618666\pi\)
\(132\) −27.3149 −2.37746
\(133\) 10.1498 0.880097
\(134\) −3.86717 −0.334073
\(135\) −40.7514 −3.50732
\(136\) −40.9890 −3.51478
\(137\) −0.0440816 −0.00376615 −0.00188307 0.999998i \(-0.500599\pi\)
−0.00188307 + 0.999998i \(0.500599\pi\)
\(138\) 49.5509 4.21805
\(139\) −8.15248 −0.691484 −0.345742 0.938330i \(-0.612373\pi\)
−0.345742 + 0.938330i \(0.612373\pi\)
\(140\) 33.7663 2.85378
\(141\) 17.8222 1.50090
\(142\) −33.7808 −2.83482
\(143\) 1.48418 0.124114
\(144\) 66.3393 5.52828
\(145\) −11.7485 −0.975663
\(146\) −15.3738 −1.27234
\(147\) −0.939760 −0.0775101
\(148\) 34.2490 2.81525
\(149\) 13.9625 1.14385 0.571926 0.820305i \(-0.306197\pi\)
0.571926 + 0.820305i \(0.306197\pi\)
\(150\) 17.7822 1.45191
\(151\) −11.1285 −0.905627 −0.452814 0.891605i \(-0.649580\pi\)
−0.452814 + 0.891605i \(0.649580\pi\)
\(152\) −26.1960 −2.12477
\(153\) 45.1751 3.65219
\(154\) −12.4388 −1.00235
\(155\) −22.8774 −1.83756
\(156\) −12.7803 −1.02324
\(157\) 9.71956 0.775705 0.387853 0.921721i \(-0.373217\pi\)
0.387853 + 0.921721i \(0.373217\pi\)
\(158\) −40.6092 −3.23069
\(159\) 4.43884 0.352023
\(160\) −22.4292 −1.77319
\(161\) 15.8221 1.24696
\(162\) −69.6689 −5.47371
\(163\) −14.0085 −1.09723 −0.548616 0.836075i \(-0.684845\pi\)
−0.548616 + 0.836075i \(0.684845\pi\)
\(164\) −51.3968 −4.01342
\(165\) −15.5120 −1.20761
\(166\) −40.1310 −3.11477
\(167\) −14.4959 −1.12173 −0.560864 0.827908i \(-0.689531\pi\)
−0.560864 + 0.827908i \(0.689531\pi\)
\(168\) 61.4646 4.74210
\(169\) −12.3056 −0.946582
\(170\) −40.5642 −3.11113
\(171\) 28.8713 2.20784
\(172\) 8.51024 0.648900
\(173\) −8.85267 −0.673056 −0.336528 0.941673i \(-0.609253\pi\)
−0.336528 + 0.941673i \(0.609253\pi\)
\(174\) −37.2676 −2.82525
\(175\) 5.67804 0.429219
\(176\) 15.3866 1.15981
\(177\) −20.1534 −1.51482
\(178\) −12.5666 −0.941910
\(179\) 15.2719 1.14148 0.570739 0.821131i \(-0.306657\pi\)
0.570739 + 0.821131i \(0.306657\pi\)
\(180\) 96.0492 7.15908
\(181\) 11.4202 0.848860 0.424430 0.905461i \(-0.360475\pi\)
0.424430 + 0.905461i \(0.360475\pi\)
\(182\) −5.81996 −0.431404
\(183\) 44.3389 3.27763
\(184\) −40.8360 −3.01047
\(185\) 19.4499 1.42998
\(186\) −72.5694 −5.32105
\(187\) 10.4778 0.766215
\(188\) −25.5952 −1.86672
\(189\) −41.2765 −3.00242
\(190\) −25.9245 −1.88076
\(191\) 21.7398 1.57304 0.786519 0.617566i \(-0.211881\pi\)
0.786519 + 0.617566i \(0.211881\pi\)
\(192\) −14.6848 −1.05979
\(193\) 13.6555 0.982947 0.491473 0.870893i \(-0.336459\pi\)
0.491473 + 0.870893i \(0.336459\pi\)
\(194\) 28.9587 2.07911
\(195\) −7.25787 −0.519747
\(196\) 1.34963 0.0964021
\(197\) 3.84837 0.274185 0.137092 0.990558i \(-0.456224\pi\)
0.137092 + 0.990558i \(0.456224\pi\)
\(198\) −35.3826 −2.51453
\(199\) 6.90982 0.489824 0.244912 0.969545i \(-0.421241\pi\)
0.244912 + 0.969545i \(0.421241\pi\)
\(200\) −14.6547 −1.03624
\(201\) −4.88476 −0.344545
\(202\) 16.5245 1.16266
\(203\) −11.8999 −0.835211
\(204\) −90.2243 −6.31696
\(205\) −29.1881 −2.03859
\(206\) −19.5489 −1.36204
\(207\) 45.0064 3.12816
\(208\) 7.19919 0.499174
\(209\) 6.69636 0.463197
\(210\) 60.8276 4.19750
\(211\) −22.2344 −1.53068 −0.765341 0.643625i \(-0.777430\pi\)
−0.765341 + 0.643625i \(0.777430\pi\)
\(212\) −6.37480 −0.437823
\(213\) −42.6698 −2.92368
\(214\) −52.3376 −3.57773
\(215\) 4.83294 0.329604
\(216\) 106.532 7.24860
\(217\) −23.1722 −1.57303
\(218\) −13.9071 −0.941905
\(219\) −19.4192 −1.31223
\(220\) 22.2775 1.50195
\(221\) 4.90244 0.329774
\(222\) 61.6971 4.14084
\(223\) −2.65269 −0.177637 −0.0888185 0.996048i \(-0.528309\pi\)
−0.0888185 + 0.996048i \(0.528309\pi\)
\(224\) −22.7183 −1.51793
\(225\) 16.1513 1.07675
\(226\) 23.7565 1.58026
\(227\) 7.90391 0.524601 0.262301 0.964986i \(-0.415519\pi\)
0.262301 + 0.964986i \(0.415519\pi\)
\(228\) −57.6621 −3.81877
\(229\) 24.0296 1.58792 0.793961 0.607969i \(-0.208016\pi\)
0.793961 + 0.607969i \(0.208016\pi\)
\(230\) −40.4127 −2.66474
\(231\) −15.7119 −1.03377
\(232\) 30.7130 2.01641
\(233\) −2.81518 −0.184429 −0.0922143 0.995739i \(-0.529394\pi\)
−0.0922143 + 0.995739i \(0.529394\pi\)
\(234\) −16.5550 −1.08224
\(235\) −14.5354 −0.948188
\(236\) 28.9432 1.88404
\(237\) −51.2948 −3.33196
\(238\) −41.0869 −2.66327
\(239\) 26.2813 1.70000 0.849999 0.526784i \(-0.176602\pi\)
0.849999 + 0.526784i \(0.176602\pi\)
\(240\) −75.2428 −4.85690
\(241\) −22.9326 −1.47722 −0.738610 0.674133i \(-0.764518\pi\)
−0.738610 + 0.674133i \(0.764518\pi\)
\(242\) 20.2516 1.30182
\(243\) −42.1308 −2.70269
\(244\) −63.6770 −4.07650
\(245\) 0.766450 0.0489667
\(246\) −92.5877 −5.90318
\(247\) 3.13313 0.199357
\(248\) 59.8061 3.79769
\(249\) −50.6909 −3.21240
\(250\) 19.9731 1.26321
\(251\) −2.89924 −0.182998 −0.0914991 0.995805i \(-0.529166\pi\)
−0.0914991 + 0.995805i \(0.529166\pi\)
\(252\) 97.2869 6.12850
\(253\) 10.4387 0.656276
\(254\) −34.4674 −2.16268
\(255\) −51.2381 −3.20865
\(256\) −22.4544 −1.40340
\(257\) 14.4049 0.898555 0.449277 0.893392i \(-0.351681\pi\)
0.449277 + 0.893392i \(0.351681\pi\)
\(258\) 15.3306 0.954440
\(259\) 19.7005 1.22413
\(260\) 10.4233 0.646428
\(261\) −33.8496 −2.09524
\(262\) 21.5700 1.33260
\(263\) 29.5009 1.81910 0.909551 0.415592i \(-0.136425\pi\)
0.909551 + 0.415592i \(0.136425\pi\)
\(264\) 40.5516 2.49578
\(265\) −3.62023 −0.222389
\(266\) −26.2585 −1.61001
\(267\) −15.8734 −0.971435
\(268\) 7.01521 0.428522
\(269\) 16.0481 0.978470 0.489235 0.872152i \(-0.337276\pi\)
0.489235 + 0.872152i \(0.337276\pi\)
\(270\) 105.428 6.41615
\(271\) −12.7876 −0.776790 −0.388395 0.921493i \(-0.626970\pi\)
−0.388395 + 0.921493i \(0.626970\pi\)
\(272\) 50.8239 3.08165
\(273\) −7.35139 −0.444927
\(274\) 0.114044 0.00688964
\(275\) 3.74611 0.225899
\(276\) −89.8873 −5.41058
\(277\) 4.98817 0.299710 0.149855 0.988708i \(-0.452119\pi\)
0.149855 + 0.988708i \(0.452119\pi\)
\(278\) 21.0913 1.26497
\(279\) −65.9138 −3.94616
\(280\) −50.1294 −2.99580
\(281\) −13.6316 −0.813190 −0.406595 0.913608i \(-0.633284\pi\)
−0.406595 + 0.913608i \(0.633284\pi\)
\(282\) −46.1079 −2.74569
\(283\) −12.9069 −0.767236 −0.383618 0.923492i \(-0.625322\pi\)
−0.383618 + 0.923492i \(0.625322\pi\)
\(284\) 61.2798 3.63629
\(285\) −32.7461 −1.93971
\(286\) −3.83974 −0.227049
\(287\) −29.5642 −1.74512
\(288\) −64.6226 −3.80792
\(289\) 17.6095 1.03586
\(290\) 30.3947 1.78484
\(291\) 36.5788 2.14428
\(292\) 27.8887 1.63206
\(293\) −7.69534 −0.449567 −0.224783 0.974409i \(-0.572167\pi\)
−0.224783 + 0.974409i \(0.572167\pi\)
\(294\) 2.43126 0.141794
\(295\) 16.4367 0.956984
\(296\) −50.8459 −2.95536
\(297\) −27.2323 −1.58018
\(298\) −36.1224 −2.09252
\(299\) 4.88413 0.282456
\(300\) −32.2576 −1.86239
\(301\) 4.89521 0.282155
\(302\) 28.7907 1.65672
\(303\) 20.8727 1.19910
\(304\) 32.4814 1.86294
\(305\) −36.1620 −2.07063
\(306\) −116.873 −6.68117
\(307\) −8.54169 −0.487500 −0.243750 0.969838i \(-0.578378\pi\)
−0.243750 + 0.969838i \(0.578378\pi\)
\(308\) 22.5646 1.28574
\(309\) −24.6929 −1.40473
\(310\) 59.1862 3.36155
\(311\) 13.0024 0.737296 0.368648 0.929569i \(-0.379821\pi\)
0.368648 + 0.929569i \(0.379821\pi\)
\(312\) 18.9735 1.07416
\(313\) −0.527559 −0.0298194 −0.0149097 0.999889i \(-0.504746\pi\)
−0.0149097 + 0.999889i \(0.504746\pi\)
\(314\) −25.1455 −1.41904
\(315\) 55.2489 3.11292
\(316\) 73.6667 4.14408
\(317\) 8.85398 0.497289 0.248644 0.968595i \(-0.420015\pi\)
0.248644 + 0.968595i \(0.420015\pi\)
\(318\) −11.4837 −0.643977
\(319\) −7.85103 −0.439573
\(320\) 11.9767 0.669516
\(321\) −66.1095 −3.68987
\(322\) −40.9335 −2.28113
\(323\) 22.1189 1.23073
\(324\) 126.382 7.02124
\(325\) 1.75275 0.0972253
\(326\) 36.2415 2.00723
\(327\) −17.5665 −0.971430
\(328\) 76.3035 4.21316
\(329\) −14.7228 −0.811692
\(330\) 40.1313 2.20915
\(331\) 4.38103 0.240803 0.120402 0.992725i \(-0.461582\pi\)
0.120402 + 0.992725i \(0.461582\pi\)
\(332\) 72.7993 3.99538
\(333\) 56.0386 3.07090
\(334\) 37.5025 2.05205
\(335\) 3.98392 0.217665
\(336\) −76.2123 −4.15772
\(337\) −14.5867 −0.794589 −0.397294 0.917691i \(-0.630051\pi\)
−0.397294 + 0.917691i \(0.630051\pi\)
\(338\) 31.8358 1.73164
\(339\) 30.0077 1.62979
\(340\) 73.5852 3.99072
\(341\) −15.2880 −0.827889
\(342\) −74.6931 −4.03894
\(343\) −18.1205 −0.978417
\(344\) −12.6343 −0.681194
\(345\) −51.0467 −2.74826
\(346\) 22.9028 1.23126
\(347\) −4.34547 −0.233277 −0.116638 0.993174i \(-0.537212\pi\)
−0.116638 + 0.993174i \(0.537212\pi\)
\(348\) 67.6049 3.62401
\(349\) −20.7044 −1.10828 −0.554142 0.832422i \(-0.686953\pi\)
−0.554142 + 0.832422i \(0.686953\pi\)
\(350\) −14.6897 −0.785197
\(351\) −12.7416 −0.680099
\(352\) −14.9885 −0.798888
\(353\) −18.4882 −0.984030 −0.492015 0.870587i \(-0.663739\pi\)
−0.492015 + 0.870587i \(0.663739\pi\)
\(354\) 52.1390 2.77116
\(355\) 34.8006 1.84703
\(356\) 22.7964 1.20821
\(357\) −51.8984 −2.74675
\(358\) −39.5101 −2.08817
\(359\) −0.00828583 −0.000437310 0 −0.000218655 1.00000i \(-0.500070\pi\)
−0.000218655 1.00000i \(0.500070\pi\)
\(360\) −142.594 −7.51537
\(361\) −4.86390 −0.255995
\(362\) −29.5454 −1.55287
\(363\) 25.5805 1.34263
\(364\) 10.5576 0.553371
\(365\) 15.8379 0.828993
\(366\) −114.710 −5.99596
\(367\) −17.8359 −0.931029 −0.465514 0.885040i \(-0.654131\pi\)
−0.465514 + 0.885040i \(0.654131\pi\)
\(368\) 50.6341 2.63948
\(369\) −84.0961 −4.37787
\(370\) −50.3189 −2.61596
\(371\) −3.66688 −0.190375
\(372\) 131.644 6.82542
\(373\) −7.06112 −0.365611 −0.182805 0.983149i \(-0.558518\pi\)
−0.182805 + 0.983149i \(0.558518\pi\)
\(374\) −27.1073 −1.40168
\(375\) 25.2287 1.30280
\(376\) 37.9986 1.95963
\(377\) −3.67339 −0.189189
\(378\) 106.787 5.49252
\(379\) −16.1473 −0.829432 −0.414716 0.909951i \(-0.636119\pi\)
−0.414716 + 0.909951i \(0.636119\pi\)
\(380\) 47.0281 2.41249
\(381\) −43.5370 −2.23047
\(382\) −56.2432 −2.87765
\(383\) 32.7186 1.67184 0.835922 0.548849i \(-0.184934\pi\)
0.835922 + 0.548849i \(0.184934\pi\)
\(384\) −17.0106 −0.868069
\(385\) 12.8143 0.653079
\(386\) −35.3283 −1.79816
\(387\) 13.9246 0.707825
\(388\) −52.5323 −2.66692
\(389\) 34.3002 1.73909 0.869545 0.493853i \(-0.164412\pi\)
0.869545 + 0.493853i \(0.164412\pi\)
\(390\) 18.7769 0.950804
\(391\) 34.4803 1.74374
\(392\) −2.00365 −0.101200
\(393\) 27.2458 1.37437
\(394\) −9.95614 −0.501583
\(395\) 41.8351 2.10495
\(396\) 64.1854 3.22544
\(397\) 7.76342 0.389635 0.194817 0.980840i \(-0.437589\pi\)
0.194817 + 0.980840i \(0.437589\pi\)
\(398\) −17.8764 −0.896064
\(399\) −33.1681 −1.66048
\(400\) 18.1709 0.908545
\(401\) −25.1007 −1.25347 −0.626735 0.779233i \(-0.715609\pi\)
−0.626735 + 0.779233i \(0.715609\pi\)
\(402\) 12.6374 0.630296
\(403\) −7.15302 −0.356317
\(404\) −29.9761 −1.49137
\(405\) 71.7721 3.56638
\(406\) 30.7864 1.52790
\(407\) 12.9975 0.644262
\(408\) 133.947 6.63135
\(409\) 38.2637 1.89202 0.946009 0.324141i \(-0.105075\pi\)
0.946009 + 0.324141i \(0.105075\pi\)
\(410\) 75.5127 3.72931
\(411\) 0.144053 0.00710560
\(412\) 35.4626 1.74712
\(413\) 16.6485 0.819221
\(414\) −116.436 −5.72253
\(415\) 41.3425 2.02942
\(416\) −7.01290 −0.343836
\(417\) 26.6412 1.30462
\(418\) −17.3242 −0.847354
\(419\) −3.99514 −0.195175 −0.0975877 0.995227i \(-0.531113\pi\)
−0.0975877 + 0.995227i \(0.531113\pi\)
\(420\) −110.344 −5.38423
\(421\) 18.7870 0.915624 0.457812 0.889049i \(-0.348633\pi\)
0.457812 + 0.889049i \(0.348633\pi\)
\(422\) 57.5228 2.80017
\(423\) −41.8792 −2.03624
\(424\) 9.46401 0.459613
\(425\) 12.3738 0.600220
\(426\) 110.391 5.34847
\(427\) −36.6280 −1.77255
\(428\) 94.9427 4.58923
\(429\) −4.85011 −0.234166
\(430\) −12.5033 −0.602964
\(431\) 38.7169 1.86493 0.932463 0.361266i \(-0.117656\pi\)
0.932463 + 0.361266i \(0.117656\pi\)
\(432\) −132.093 −6.35535
\(433\) 17.3288 0.832769 0.416385 0.909189i \(-0.363297\pi\)
0.416385 + 0.909189i \(0.363297\pi\)
\(434\) 59.9489 2.87764
\(435\) 38.3926 1.84079
\(436\) 25.2280 1.20820
\(437\) 22.0363 1.05414
\(438\) 50.2394 2.40053
\(439\) 0.353601 0.0168765 0.00843823 0.999964i \(-0.497314\pi\)
0.00843823 + 0.999964i \(0.497314\pi\)
\(440\) −33.0731 −1.57670
\(441\) 2.20828 0.105156
\(442\) −12.6831 −0.603275
\(443\) 24.8597 1.18112 0.590561 0.806993i \(-0.298907\pi\)
0.590561 + 0.806993i \(0.298907\pi\)
\(444\) −111.921 −5.31154
\(445\) 12.9460 0.613700
\(446\) 6.86278 0.324962
\(447\) −45.6275 −2.15811
\(448\) 12.1310 0.573136
\(449\) −29.2334 −1.37961 −0.689804 0.723997i \(-0.742303\pi\)
−0.689804 + 0.723997i \(0.742303\pi\)
\(450\) −41.7852 −1.96977
\(451\) −19.5051 −0.918460
\(452\) −43.0953 −2.02703
\(453\) 36.3665 1.70865
\(454\) −20.4483 −0.959685
\(455\) 5.99565 0.281081
\(456\) 85.6049 4.00882
\(457\) 34.5762 1.61741 0.808704 0.588216i \(-0.200169\pi\)
0.808704 + 0.588216i \(0.200169\pi\)
\(458\) −62.1671 −2.90488
\(459\) −89.9517 −4.19859
\(460\) 73.3104 3.41811
\(461\) −18.0049 −0.838571 −0.419286 0.907854i \(-0.637719\pi\)
−0.419286 + 0.907854i \(0.637719\pi\)
\(462\) 40.6484 1.89114
\(463\) −31.9655 −1.48556 −0.742782 0.669533i \(-0.766494\pi\)
−0.742782 + 0.669533i \(0.766494\pi\)
\(464\) −38.0823 −1.76792
\(465\) 74.7602 3.46692
\(466\) 7.28317 0.337386
\(467\) −37.9096 −1.75425 −0.877123 0.480266i \(-0.840540\pi\)
−0.877123 + 0.480266i \(0.840540\pi\)
\(468\) 30.0315 1.38821
\(469\) 4.03525 0.186331
\(470\) 37.6047 1.73458
\(471\) −31.7622 −1.46352
\(472\) −42.9689 −1.97780
\(473\) 3.22964 0.148499
\(474\) 132.705 6.09535
\(475\) 7.90809 0.362848
\(476\) 74.5334 3.41623
\(477\) −10.4305 −0.477581
\(478\) −67.9926 −3.10991
\(479\) −5.03277 −0.229953 −0.114977 0.993368i \(-0.536679\pi\)
−0.114977 + 0.993368i \(0.536679\pi\)
\(480\) 73.2957 3.34547
\(481\) 6.08135 0.277286
\(482\) 59.3291 2.70237
\(483\) −51.7045 −2.35264
\(484\) −36.7372 −1.66987
\(485\) −29.8329 −1.35464
\(486\) 108.997 4.94420
\(487\) 16.6581 0.754849 0.377424 0.926040i \(-0.376810\pi\)
0.377424 + 0.926040i \(0.376810\pi\)
\(488\) 94.5347 4.27938
\(489\) 45.7779 2.07015
\(490\) −1.98289 −0.0895778
\(491\) 3.05886 0.138044 0.0690221 0.997615i \(-0.478012\pi\)
0.0690221 + 0.997615i \(0.478012\pi\)
\(492\) 167.958 7.57213
\(493\) −25.9329 −1.16796
\(494\) −8.10575 −0.364695
\(495\) 36.4507 1.63834
\(496\) −74.1558 −3.32969
\(497\) 35.2491 1.58114
\(498\) 131.143 5.87665
\(499\) −14.9054 −0.667258 −0.333629 0.942704i \(-0.608273\pi\)
−0.333629 + 0.942704i \(0.608273\pi\)
\(500\) −36.2320 −1.62034
\(501\) 47.3707 2.11637
\(502\) 7.50063 0.334770
\(503\) −20.2347 −0.902220 −0.451110 0.892468i \(-0.648972\pi\)
−0.451110 + 0.892468i \(0.648972\pi\)
\(504\) −144.432 −6.43350
\(505\) −17.0233 −0.757529
\(506\) −27.0060 −1.20057
\(507\) 40.2129 1.78592
\(508\) 62.5253 2.77411
\(509\) 31.5475 1.39832 0.699159 0.714966i \(-0.253558\pi\)
0.699159 + 0.714966i \(0.253558\pi\)
\(510\) 132.558 5.86978
\(511\) 16.0420 0.709655
\(512\) 47.6811 2.10723
\(513\) −57.4879 −2.53815
\(514\) −37.2671 −1.64378
\(515\) 20.1391 0.887434
\(516\) −27.8103 −1.22428
\(517\) −9.71340 −0.427195
\(518\) −50.9673 −2.23938
\(519\) 28.9293 1.26986
\(520\) −15.4744 −0.678599
\(521\) −4.88434 −0.213987 −0.106993 0.994260i \(-0.534122\pi\)
−0.106993 + 0.994260i \(0.534122\pi\)
\(522\) 87.5726 3.83295
\(523\) 18.5613 0.811630 0.405815 0.913955i \(-0.366988\pi\)
0.405815 + 0.913955i \(0.366988\pi\)
\(524\) −39.1289 −1.70935
\(525\) −18.5551 −0.809809
\(526\) −76.3219 −3.32779
\(527\) −50.4979 −2.19972
\(528\) −50.2814 −2.18822
\(529\) 11.3515 0.493544
\(530\) 9.36592 0.406830
\(531\) 47.3572 2.05513
\(532\) 47.6341 2.06520
\(533\) −9.12618 −0.395299
\(534\) 41.0661 1.77710
\(535\) 53.9176 2.33106
\(536\) −10.4148 −0.449849
\(537\) −49.9066 −2.15363
\(538\) −41.5182 −1.78997
\(539\) 0.512185 0.0220614
\(540\) −191.251 −8.23013
\(541\) −7.28670 −0.313280 −0.156640 0.987656i \(-0.550066\pi\)
−0.156640 + 0.987656i \(0.550066\pi\)
\(542\) 33.0828 1.42103
\(543\) −37.3198 −1.60155
\(544\) −49.5087 −2.12267
\(545\) 14.3269 0.613697
\(546\) 19.0188 0.813931
\(547\) 7.29380 0.311860 0.155930 0.987768i \(-0.450163\pi\)
0.155930 + 0.987768i \(0.450163\pi\)
\(548\) −0.206880 −0.00883749
\(549\) −104.189 −4.44668
\(550\) −9.69158 −0.413250
\(551\) −16.5736 −0.706060
\(552\) 133.446 5.67985
\(553\) 42.3742 1.80193
\(554\) −12.9049 −0.548278
\(555\) −63.5596 −2.69795
\(556\) −38.2605 −1.62261
\(557\) 4.00018 0.169493 0.0847465 0.996403i \(-0.472992\pi\)
0.0847465 + 0.996403i \(0.472992\pi\)
\(558\) 170.526 7.21895
\(559\) 1.51110 0.0639129
\(560\) 62.1573 2.62663
\(561\) −34.2402 −1.44562
\(562\) 35.2663 1.48762
\(563\) −14.4938 −0.610840 −0.305420 0.952218i \(-0.598797\pi\)
−0.305420 + 0.952218i \(0.598797\pi\)
\(564\) 83.6417 3.52195
\(565\) −24.4737 −1.02962
\(566\) 33.3915 1.40355
\(567\) 72.6970 3.05299
\(568\) −90.9758 −3.81726
\(569\) −25.7920 −1.08125 −0.540627 0.841262i \(-0.681813\pi\)
−0.540627 + 0.841262i \(0.681813\pi\)
\(570\) 84.7177 3.54843
\(571\) 6.09385 0.255020 0.127510 0.991837i \(-0.459302\pi\)
0.127510 + 0.991837i \(0.459302\pi\)
\(572\) 6.96545 0.291240
\(573\) −71.0428 −2.96785
\(574\) 76.4858 3.19246
\(575\) 12.3276 0.514098
\(576\) 34.5069 1.43779
\(577\) 2.74582 0.114310 0.0571550 0.998365i \(-0.481797\pi\)
0.0571550 + 0.998365i \(0.481797\pi\)
\(578\) −45.5578 −1.89495
\(579\) −44.6244 −1.85453
\(580\) −55.1373 −2.28945
\(581\) 41.8753 1.73728
\(582\) −94.6331 −3.92267
\(583\) −2.41924 −0.100195
\(584\) −41.4034 −1.71329
\(585\) 17.0548 0.705128
\(586\) 19.9087 0.822419
\(587\) −6.17044 −0.254681 −0.127341 0.991859i \(-0.540644\pi\)
−0.127341 + 0.991859i \(0.540644\pi\)
\(588\) −4.41041 −0.181882
\(589\) −32.2731 −1.32979
\(590\) −42.5236 −1.75067
\(591\) −12.5759 −0.517305
\(592\) 63.0458 2.59116
\(593\) −5.34173 −0.219359 −0.109679 0.993967i \(-0.534982\pi\)
−0.109679 + 0.993967i \(0.534982\pi\)
\(594\) 70.4530 2.89072
\(595\) 42.3273 1.73525
\(596\) 65.5276 2.68412
\(597\) −22.5803 −0.924152
\(598\) −12.6358 −0.516715
\(599\) −21.3099 −0.870700 −0.435350 0.900261i \(-0.643375\pi\)
−0.435350 + 0.900261i \(0.643375\pi\)
\(600\) 47.8895 1.95508
\(601\) −0.757251 −0.0308889 −0.0154444 0.999881i \(-0.504916\pi\)
−0.0154444 + 0.999881i \(0.504916\pi\)
\(602\) −12.6644 −0.516164
\(603\) 11.4784 0.467436
\(604\) −52.2275 −2.12511
\(605\) −20.8630 −0.848200
\(606\) −53.9998 −2.19359
\(607\) 23.4434 0.951539 0.475770 0.879570i \(-0.342170\pi\)
0.475770 + 0.879570i \(0.342170\pi\)
\(608\) −31.6409 −1.28321
\(609\) 38.8874 1.57580
\(610\) 93.5549 3.78793
\(611\) −4.54477 −0.183862
\(612\) 212.012 8.57008
\(613\) 16.8473 0.680454 0.340227 0.940343i \(-0.389496\pi\)
0.340227 + 0.940343i \(0.389496\pi\)
\(614\) 22.0982 0.891813
\(615\) 95.3828 3.84620
\(616\) −33.4992 −1.34972
\(617\) 12.3191 0.495949 0.247975 0.968767i \(-0.420235\pi\)
0.247975 + 0.968767i \(0.420235\pi\)
\(618\) 63.8832 2.56976
\(619\) −37.2520 −1.49728 −0.748642 0.662975i \(-0.769294\pi\)
−0.748642 + 0.662975i \(0.769294\pi\)
\(620\) −107.366 −4.31193
\(621\) −89.6157 −3.59616
\(622\) −33.6385 −1.34878
\(623\) 13.1128 0.525355
\(624\) −23.5260 −0.941793
\(625\) −31.0927 −1.24371
\(626\) 1.36485 0.0545505
\(627\) −21.8828 −0.873914
\(628\) 45.6150 1.82024
\(629\) 42.9323 1.71182
\(630\) −142.935 −5.69466
\(631\) −3.03001 −0.120623 −0.0603114 0.998180i \(-0.519209\pi\)
−0.0603114 + 0.998180i \(0.519209\pi\)
\(632\) −109.365 −4.35032
\(633\) 72.6591 2.88794
\(634\) −22.9062 −0.909721
\(635\) 35.5079 1.40909
\(636\) 20.8320 0.826042
\(637\) 0.239644 0.00949505
\(638\) 20.3114 0.804138
\(639\) 100.267 3.96649
\(640\) 13.8735 0.548399
\(641\) −19.3417 −0.763951 −0.381975 0.924172i \(-0.624756\pi\)
−0.381975 + 0.924172i \(0.624756\pi\)
\(642\) 171.032 6.75011
\(643\) −8.14343 −0.321146 −0.160573 0.987024i \(-0.551334\pi\)
−0.160573 + 0.987024i \(0.551334\pi\)
\(644\) 74.2551 2.92606
\(645\) −15.7934 −0.621864
\(646\) −57.2239 −2.25144
\(647\) 3.17502 0.124823 0.0624116 0.998050i \(-0.480121\pi\)
0.0624116 + 0.998050i \(0.480121\pi\)
\(648\) −187.627 −7.37067
\(649\) 10.9839 0.431158
\(650\) −4.53456 −0.177860
\(651\) 75.7236 2.96784
\(652\) −65.7436 −2.57472
\(653\) 18.5415 0.725586 0.362793 0.931870i \(-0.381823\pi\)
0.362793 + 0.931870i \(0.381823\pi\)
\(654\) 45.4464 1.77709
\(655\) −22.2212 −0.868253
\(656\) −94.6117 −3.69396
\(657\) 45.6318 1.78027
\(658\) 38.0893 1.48488
\(659\) 22.8098 0.888542 0.444271 0.895892i \(-0.353463\pi\)
0.444271 + 0.895892i \(0.353463\pi\)
\(660\) −72.7998 −2.83373
\(661\) 10.6933 0.415922 0.207961 0.978137i \(-0.433317\pi\)
0.207961 + 0.978137i \(0.433317\pi\)
\(662\) −11.3342 −0.440516
\(663\) −16.0205 −0.622185
\(664\) −108.078 −4.19422
\(665\) 27.0512 1.04900
\(666\) −144.978 −5.61778
\(667\) −25.8360 −1.00038
\(668\) −68.0311 −2.63220
\(669\) 8.66862 0.335148
\(670\) −10.3068 −0.398187
\(671\) −24.1655 −0.932897
\(672\) 74.2402 2.86388
\(673\) −28.0836 −1.08254 −0.541272 0.840847i \(-0.682057\pi\)
−0.541272 + 0.840847i \(0.682057\pi\)
\(674\) 37.7374 1.45359
\(675\) −32.1601 −1.23784
\(676\) −57.7515 −2.22121
\(677\) 6.95352 0.267246 0.133623 0.991032i \(-0.457339\pi\)
0.133623 + 0.991032i \(0.457339\pi\)
\(678\) −77.6331 −2.98148
\(679\) −30.2174 −1.15964
\(680\) −109.244 −4.18933
\(681\) −25.8289 −0.989766
\(682\) 39.5516 1.51451
\(683\) −15.0221 −0.574803 −0.287402 0.957810i \(-0.592791\pi\)
−0.287402 + 0.957810i \(0.592791\pi\)
\(684\) 135.496 5.18083
\(685\) −0.117487 −0.00448894
\(686\) 46.8797 1.78988
\(687\) −78.5255 −2.99593
\(688\) 15.6657 0.597249
\(689\) −1.13193 −0.0431231
\(690\) 132.063 5.02756
\(691\) 15.2745 0.581069 0.290534 0.956865i \(-0.406167\pi\)
0.290534 + 0.956865i \(0.406167\pi\)
\(692\) −41.5466 −1.57937
\(693\) 36.9204 1.40249
\(694\) 11.2422 0.426748
\(695\) −21.7280 −0.824191
\(696\) −100.366 −3.80436
\(697\) −64.4277 −2.44037
\(698\) 53.5646 2.02745
\(699\) 9.19963 0.347962
\(700\) 26.6477 1.00719
\(701\) 33.3521 1.25969 0.629845 0.776721i \(-0.283118\pi\)
0.629845 + 0.776721i \(0.283118\pi\)
\(702\) 32.9640 1.24415
\(703\) 27.4379 1.03484
\(704\) 8.00348 0.301643
\(705\) 47.4999 1.78895
\(706\) 47.8310 1.80014
\(707\) −17.2427 −0.648479
\(708\) −94.5824 −3.55462
\(709\) 0.766159 0.0287737 0.0143869 0.999897i \(-0.495420\pi\)
0.0143869 + 0.999897i \(0.495420\pi\)
\(710\) −90.0329 −3.37888
\(711\) 120.534 4.52039
\(712\) −33.8435 −1.26834
\(713\) −50.3093 −1.88410
\(714\) 134.267 5.02480
\(715\) 3.95566 0.147933
\(716\) 71.6730 2.67855
\(717\) −85.8838 −3.20739
\(718\) 0.0214363 0.000799997 0
\(719\) 7.74131 0.288702 0.144351 0.989527i \(-0.453891\pi\)
0.144351 + 0.989527i \(0.453891\pi\)
\(720\) 176.808 6.58924
\(721\) 20.3986 0.759683
\(722\) 12.5834 0.468306
\(723\) 74.9407 2.78708
\(724\) 53.5965 1.99190
\(725\) −9.27170 −0.344342
\(726\) −66.1795 −2.45615
\(727\) −15.7242 −0.583177 −0.291588 0.956544i \(-0.594184\pi\)
−0.291588 + 0.956544i \(0.594184\pi\)
\(728\) −15.6738 −0.580911
\(729\) 56.8900 2.10704
\(730\) −40.9743 −1.51653
\(731\) 10.6679 0.394566
\(732\) 208.088 7.69115
\(733\) 16.5868 0.612648 0.306324 0.951927i \(-0.400901\pi\)
0.306324 + 0.951927i \(0.400901\pi\)
\(734\) 46.1435 1.70319
\(735\) −2.50466 −0.0923856
\(736\) −49.3238 −1.81810
\(737\) 2.66228 0.0980662
\(738\) 217.566 8.00870
\(739\) 24.1154 0.887098 0.443549 0.896250i \(-0.353719\pi\)
0.443549 + 0.896250i \(0.353719\pi\)
\(740\) 91.2806 3.35554
\(741\) −10.2387 −0.376126
\(742\) 9.48661 0.348264
\(743\) 3.34156 0.122590 0.0612950 0.998120i \(-0.480477\pi\)
0.0612950 + 0.998120i \(0.480477\pi\)
\(744\) −195.438 −7.16511
\(745\) 37.2129 1.36338
\(746\) 18.2679 0.668834
\(747\) 119.115 4.35820
\(748\) 49.1737 1.79797
\(749\) 54.6124 1.99549
\(750\) −65.2693 −2.38330
\(751\) −9.36166 −0.341612 −0.170806 0.985305i \(-0.554637\pi\)
−0.170806 + 0.985305i \(0.554637\pi\)
\(752\) −47.1159 −1.71814
\(753\) 9.47431 0.345263
\(754\) 9.50345 0.346095
\(755\) −29.6598 −1.07943
\(756\) −193.716 −7.04537
\(757\) 16.1336 0.586384 0.293192 0.956054i \(-0.405282\pi\)
0.293192 + 0.956054i \(0.405282\pi\)
\(758\) 41.7748 1.51733
\(759\) −34.1123 −1.23820
\(760\) −69.8177 −2.53255
\(761\) 1.12341 0.0407236 0.0203618 0.999793i \(-0.493518\pi\)
0.0203618 + 0.999793i \(0.493518\pi\)
\(762\) 112.635 4.08033
\(763\) 14.5115 0.525352
\(764\) 102.028 3.69123
\(765\) 120.401 4.35311
\(766\) −84.6466 −3.05840
\(767\) 5.13924 0.185567
\(768\) 73.3779 2.64780
\(769\) −0.928771 −0.0334924 −0.0167462 0.999860i \(-0.505331\pi\)
−0.0167462 + 0.999860i \(0.505331\pi\)
\(770\) −33.1521 −1.19472
\(771\) −47.0734 −1.69531
\(772\) 64.0870 2.30654
\(773\) 53.6704 1.93039 0.965194 0.261534i \(-0.0842283\pi\)
0.965194 + 0.261534i \(0.0842283\pi\)
\(774\) −36.0243 −1.29487
\(775\) −18.0544 −0.648532
\(776\) 77.9892 2.79965
\(777\) −64.3786 −2.30957
\(778\) −88.7383 −3.18142
\(779\) −41.1756 −1.47527
\(780\) −34.0620 −1.21962
\(781\) 23.2557 0.832155
\(782\) −89.2042 −3.18994
\(783\) 67.4007 2.40870
\(784\) 2.48441 0.0887288
\(785\) 25.9046 0.924576
\(786\) −70.4879 −2.51422
\(787\) −2.19248 −0.0781535 −0.0390768 0.999236i \(-0.512442\pi\)
−0.0390768 + 0.999236i \(0.512442\pi\)
\(788\) 18.0608 0.643391
\(789\) −96.4049 −3.43211
\(790\) −108.232 −3.85071
\(791\) −24.7891 −0.881398
\(792\) −95.2894 −3.38596
\(793\) −11.3067 −0.401512
\(794\) −20.0848 −0.712782
\(795\) 11.8304 0.419582
\(796\) 32.4286 1.14940
\(797\) 20.9898 0.743498 0.371749 0.928333i \(-0.378758\pi\)
0.371749 + 0.928333i \(0.378758\pi\)
\(798\) 85.8094 3.03762
\(799\) −32.0845 −1.13507
\(800\) −17.7007 −0.625814
\(801\) 37.2998 1.31792
\(802\) 64.9382 2.29305
\(803\) 10.5838 0.373493
\(804\) −22.9248 −0.808494
\(805\) 42.1692 1.48627
\(806\) 18.5056 0.651833
\(807\) −52.4430 −1.84608
\(808\) 44.5024 1.56559
\(809\) 16.9903 0.597346 0.298673 0.954356i \(-0.403456\pi\)
0.298673 + 0.954356i \(0.403456\pi\)
\(810\) −185.682 −6.52420
\(811\) 41.4830 1.45666 0.728332 0.685224i \(-0.240296\pi\)
0.728332 + 0.685224i \(0.240296\pi\)
\(812\) −55.8478 −1.95987
\(813\) 41.7881 1.46557
\(814\) −33.6259 −1.17859
\(815\) −37.3356 −1.30781
\(816\) −166.086 −5.81416
\(817\) 6.81781 0.238525
\(818\) −98.9922 −3.46118
\(819\) 17.2746 0.603622
\(820\) −136.983 −4.78366
\(821\) 35.6149 1.24297 0.621485 0.783426i \(-0.286530\pi\)
0.621485 + 0.783426i \(0.286530\pi\)
\(822\) −0.372680 −0.0129987
\(823\) −53.5314 −1.86599 −0.932993 0.359895i \(-0.882813\pi\)
−0.932993 + 0.359895i \(0.882813\pi\)
\(824\) −52.6476 −1.83406
\(825\) −12.2418 −0.426204
\(826\) −43.0716 −1.49865
\(827\) −16.9070 −0.587914 −0.293957 0.955819i \(-0.594972\pi\)
−0.293957 + 0.955819i \(0.594972\pi\)
\(828\) 211.220 7.34041
\(829\) 6.72781 0.233666 0.116833 0.993152i \(-0.462726\pi\)
0.116833 + 0.993152i \(0.462726\pi\)
\(830\) −106.957 −3.71255
\(831\) −16.3007 −0.565464
\(832\) 3.74472 0.129825
\(833\) 1.69181 0.0586177
\(834\) −68.9236 −2.38663
\(835\) −38.6347 −1.33701
\(836\) 31.4268 1.08692
\(837\) 131.246 4.53653
\(838\) 10.3358 0.357046
\(839\) 49.9522 1.72454 0.862271 0.506447i \(-0.169041\pi\)
0.862271 + 0.506447i \(0.169041\pi\)
\(840\) 163.816 5.65219
\(841\) −9.56853 −0.329949
\(842\) −48.6041 −1.67501
\(843\) 44.5461 1.53425
\(844\) −104.349 −3.59183
\(845\) −32.7969 −1.12825
\(846\) 108.346 3.72501
\(847\) −21.1318 −0.726097
\(848\) −11.7348 −0.402974
\(849\) 42.1780 1.44755
\(850\) −32.0125 −1.09802
\(851\) 42.7720 1.46620
\(852\) −200.254 −6.86060
\(853\) 10.5211 0.360235 0.180118 0.983645i \(-0.442352\pi\)
0.180118 + 0.983645i \(0.442352\pi\)
\(854\) 94.7605 3.24264
\(855\) 76.9479 2.63156
\(856\) −140.951 −4.81762
\(857\) −13.9617 −0.476924 −0.238462 0.971152i \(-0.576643\pi\)
−0.238462 + 0.971152i \(0.576643\pi\)
\(858\) 12.5478 0.428373
\(859\) −37.0411 −1.26383 −0.631913 0.775039i \(-0.717730\pi\)
−0.631913 + 0.775039i \(0.717730\pi\)
\(860\) 22.6815 0.773434
\(861\) 96.6119 3.29252
\(862\) −100.165 −3.41162
\(863\) 45.5752 1.55140 0.775699 0.631103i \(-0.217398\pi\)
0.775699 + 0.631103i \(0.217398\pi\)
\(864\) 128.675 4.37762
\(865\) −23.5942 −0.802227
\(866\) −44.8315 −1.52344
\(867\) −57.5456 −1.95435
\(868\) −108.750 −3.69121
\(869\) 27.9565 0.948361
\(870\) −99.3258 −3.36746
\(871\) 1.24564 0.0422070
\(872\) −37.4534 −1.26833
\(873\) −85.9540 −2.90910
\(874\) −57.0101 −1.92840
\(875\) −20.8412 −0.704560
\(876\) −91.1364 −3.07921
\(877\) −31.3022 −1.05700 −0.528500 0.848933i \(-0.677245\pi\)
−0.528500 + 0.848933i \(0.677245\pi\)
\(878\) −0.914803 −0.0308731
\(879\) 25.1473 0.848198
\(880\) 41.0085 1.38240
\(881\) 31.0217 1.04515 0.522574 0.852594i \(-0.324972\pi\)
0.522574 + 0.852594i \(0.324972\pi\)
\(882\) −5.71306 −0.192369
\(883\) 48.4340 1.62993 0.814967 0.579508i \(-0.196755\pi\)
0.814967 + 0.579508i \(0.196755\pi\)
\(884\) 23.0077 0.773833
\(885\) −53.7130 −1.80554
\(886\) −64.3148 −2.16070
\(887\) −34.6113 −1.16213 −0.581067 0.813856i \(-0.697364\pi\)
−0.581067 + 0.813856i \(0.697364\pi\)
\(888\) 166.157 5.57588
\(889\) 35.9655 1.20624
\(890\) −33.4927 −1.12268
\(891\) 47.9621 1.60679
\(892\) −12.4494 −0.416836
\(893\) −20.5051 −0.686178
\(894\) 118.043 3.94796
\(895\) 40.7029 1.36055
\(896\) 14.0523 0.469454
\(897\) −15.9607 −0.532911
\(898\) 75.6298 2.52380
\(899\) 37.8380 1.26197
\(900\) 75.8000 2.52667
\(901\) −7.99104 −0.266220
\(902\) 50.4618 1.68019
\(903\) −15.9969 −0.532343
\(904\) 63.9791 2.12791
\(905\) 30.4373 1.01177
\(906\) −94.0841 −3.12573
\(907\) 2.20511 0.0732194 0.0366097 0.999330i \(-0.488344\pi\)
0.0366097 + 0.999330i \(0.488344\pi\)
\(908\) 37.0940 1.23101
\(909\) −49.0473 −1.62680
\(910\) −15.5114 −0.514198
\(911\) 27.6735 0.916864 0.458432 0.888730i \(-0.348411\pi\)
0.458432 + 0.888730i \(0.348411\pi\)
\(912\) −106.145 −3.51480
\(913\) 27.6274 0.914333
\(914\) −89.4524 −2.95882
\(915\) 118.172 3.90666
\(916\) 112.774 3.72615
\(917\) −22.5075 −0.743264
\(918\) 232.715 7.68073
\(919\) −59.5447 −1.96420 −0.982100 0.188362i \(-0.939682\pi\)
−0.982100 + 0.188362i \(0.939682\pi\)
\(920\) −108.836 −3.58823
\(921\) 27.9131 0.919767
\(922\) 46.5805 1.53405
\(923\) 10.8810 0.358154
\(924\) −73.7379 −2.42580
\(925\) 15.3495 0.504687
\(926\) 82.6983 2.71763
\(927\) 58.0243 1.90577
\(928\) 37.0968 1.21776
\(929\) −22.5651 −0.740336 −0.370168 0.928965i \(-0.620700\pi\)
−0.370168 + 0.928965i \(0.620700\pi\)
\(930\) −193.413 −6.34225
\(931\) 1.08123 0.0354359
\(932\) −13.2120 −0.432773
\(933\) −42.4900 −1.39106
\(934\) 98.0761 3.20915
\(935\) 27.9256 0.913265
\(936\) −44.5846 −1.45729
\(937\) 14.5724 0.476059 0.238029 0.971258i \(-0.423499\pi\)
0.238029 + 0.971258i \(0.423499\pi\)
\(938\) −10.4396 −0.340866
\(939\) 1.72399 0.0562604
\(940\) −68.2166 −2.22498
\(941\) −43.6673 −1.42351 −0.711756 0.702426i \(-0.752100\pi\)
−0.711756 + 0.702426i \(0.752100\pi\)
\(942\) 82.1722 2.67731
\(943\) −64.1871 −2.09022
\(944\) 53.2788 1.73408
\(945\) −110.010 −3.57864
\(946\) −8.35542 −0.271658
\(947\) −31.0708 −1.00967 −0.504833 0.863217i \(-0.668446\pi\)
−0.504833 + 0.863217i \(0.668446\pi\)
\(948\) −240.733 −7.81864
\(949\) 4.95200 0.160749
\(950\) −20.4591 −0.663780
\(951\) −28.9336 −0.938236
\(952\) −110.652 −3.58625
\(953\) −36.1505 −1.17103 −0.585515 0.810661i \(-0.699108\pi\)
−0.585515 + 0.810661i \(0.699108\pi\)
\(954\) 26.9849 0.873668
\(955\) 57.9411 1.87493
\(956\) 123.341 3.98915
\(957\) 25.6561 0.829344
\(958\) 13.0203 0.420667
\(959\) −0.119001 −0.00384273
\(960\) −39.1381 −1.26318
\(961\) 42.6802 1.37678
\(962\) −15.7331 −0.507256
\(963\) 155.346 5.00597
\(964\) −107.626 −3.46639
\(965\) 36.3948 1.17159
\(966\) 133.765 4.30382
\(967\) −38.6408 −1.24261 −0.621303 0.783571i \(-0.713396\pi\)
−0.621303 + 0.783571i \(0.713396\pi\)
\(968\) 54.5400 1.75298
\(969\) −72.2814 −2.32201
\(970\) 77.1809 2.47813
\(971\) 34.0568 1.09293 0.546467 0.837481i \(-0.315972\pi\)
0.546467 + 0.837481i \(0.315972\pi\)
\(972\) −197.725 −6.34203
\(973\) −22.0080 −0.705545
\(974\) −43.0962 −1.38089
\(975\) −5.72776 −0.183435
\(976\) −117.217 −3.75203
\(977\) −35.4380 −1.13376 −0.566881 0.823800i \(-0.691850\pi\)
−0.566881 + 0.823800i \(0.691850\pi\)
\(978\) −118.432 −3.78705
\(979\) 8.65125 0.276495
\(980\) 3.59704 0.114903
\(981\) 41.2784 1.31792
\(982\) −7.91358 −0.252533
\(983\) −20.1776 −0.643566 −0.321783 0.946814i \(-0.604282\pi\)
−0.321783 + 0.946814i \(0.604282\pi\)
\(984\) −249.350 −7.94898
\(985\) 10.2567 0.326806
\(986\) 67.0911 2.13662
\(987\) 48.1120 1.53142
\(988\) 14.7042 0.467802
\(989\) 10.6280 0.337952
\(990\) −94.3018 −2.99711
\(991\) 22.6238 0.718669 0.359334 0.933209i \(-0.383004\pi\)
0.359334 + 0.933209i \(0.383004\pi\)
\(992\) 72.2369 2.29352
\(993\) −14.3166 −0.454324
\(994\) −91.1931 −2.89247
\(995\) 18.4161 0.583829
\(996\) −237.898 −7.53810
\(997\) 25.7781 0.816401 0.408200 0.912892i \(-0.366157\pi\)
0.408200 + 0.912892i \(0.366157\pi\)
\(998\) 38.5619 1.22066
\(999\) −111.583 −3.53033
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 6037.2.a.b.1.10 259
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6037.2.a.b.1.10 259 1.1 even 1 trivial