Properties

Label 6017.2.a.f.1.15
Level 6017
Weight 2
Character 6017.1
Self dual yes
Analytic conductor 48.046
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.29477 q^{2} +3.40179 q^{3} +3.26597 q^{4} +3.88142 q^{5} -7.80633 q^{6} +2.49357 q^{7} -2.90510 q^{8} +8.57220 q^{9} +O(q^{10})\) \(q-2.29477 q^{2} +3.40179 q^{3} +3.26597 q^{4} +3.88142 q^{5} -7.80633 q^{6} +2.49357 q^{7} -2.90510 q^{8} +8.57220 q^{9} -8.90697 q^{10} -1.00000 q^{11} +11.1101 q^{12} -3.83894 q^{13} -5.72217 q^{14} +13.2038 q^{15} +0.134602 q^{16} -0.384749 q^{17} -19.6712 q^{18} -3.93567 q^{19} +12.6766 q^{20} +8.48262 q^{21} +2.29477 q^{22} -1.53652 q^{23} -9.88255 q^{24} +10.0654 q^{25} +8.80948 q^{26} +18.9555 q^{27} +8.14392 q^{28} +9.23562 q^{29} -30.2997 q^{30} -2.04469 q^{31} +5.50132 q^{32} -3.40179 q^{33} +0.882911 q^{34} +9.67860 q^{35} +27.9965 q^{36} +4.79025 q^{37} +9.03147 q^{38} -13.0593 q^{39} -11.2759 q^{40} -8.74208 q^{41} -19.4657 q^{42} -4.80553 q^{43} -3.26597 q^{44} +33.2723 q^{45} +3.52595 q^{46} +1.56722 q^{47} +0.457889 q^{48} -0.782100 q^{49} -23.0978 q^{50} -1.30884 q^{51} -12.5378 q^{52} -1.13491 q^{53} -43.4985 q^{54} -3.88142 q^{55} -7.24408 q^{56} -13.3884 q^{57} -21.1936 q^{58} -9.39532 q^{59} +43.1231 q^{60} +13.5181 q^{61} +4.69208 q^{62} +21.3754 q^{63} -12.8935 q^{64} -14.9005 q^{65} +7.80633 q^{66} +3.81781 q^{67} -1.25658 q^{68} -5.22691 q^{69} -22.2102 q^{70} +7.77422 q^{71} -24.9031 q^{72} -2.25867 q^{73} -10.9925 q^{74} +34.2405 q^{75} -12.8538 q^{76} -2.49357 q^{77} +29.9680 q^{78} +0.175607 q^{79} +0.522448 q^{80} +38.7661 q^{81} +20.0611 q^{82} +7.26733 q^{83} +27.7039 q^{84} -1.49337 q^{85} +11.0276 q^{86} +31.4177 q^{87} +2.90510 q^{88} +13.1294 q^{89} -76.3523 q^{90} -9.57267 q^{91} -5.01821 q^{92} -6.95560 q^{93} -3.59640 q^{94} -15.2760 q^{95} +18.7144 q^{96} +1.38802 q^{97} +1.79474 q^{98} -8.57220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.29477 −1.62265 −0.811323 0.584598i \(-0.801252\pi\)
−0.811323 + 0.584598i \(0.801252\pi\)
\(3\) 3.40179 1.96403 0.982013 0.188811i \(-0.0604634\pi\)
0.982013 + 0.188811i \(0.0604634\pi\)
\(4\) 3.26597 1.63298
\(5\) 3.88142 1.73582 0.867912 0.496718i \(-0.165462\pi\)
0.867912 + 0.496718i \(0.165462\pi\)
\(6\) −7.80633 −3.18692
\(7\) 2.49357 0.942482 0.471241 0.882005i \(-0.343806\pi\)
0.471241 + 0.882005i \(0.343806\pi\)
\(8\) −2.90510 −1.02711
\(9\) 8.57220 2.85740
\(10\) −8.90697 −2.81663
\(11\) −1.00000 −0.301511
\(12\) 11.1101 3.20722
\(13\) −3.83894 −1.06473 −0.532365 0.846515i \(-0.678697\pi\)
−0.532365 + 0.846515i \(0.678697\pi\)
\(14\) −5.72217 −1.52931
\(15\) 13.2038 3.40921
\(16\) 0.134602 0.0336505
\(17\) −0.384749 −0.0933154 −0.0466577 0.998911i \(-0.514857\pi\)
−0.0466577 + 0.998911i \(0.514857\pi\)
\(18\) −19.6712 −4.63655
\(19\) −3.93567 −0.902906 −0.451453 0.892295i \(-0.649094\pi\)
−0.451453 + 0.892295i \(0.649094\pi\)
\(20\) 12.6766 2.83457
\(21\) 8.48262 1.85106
\(22\) 2.29477 0.489246
\(23\) −1.53652 −0.320386 −0.160193 0.987086i \(-0.551212\pi\)
−0.160193 + 0.987086i \(0.551212\pi\)
\(24\) −9.88255 −2.01727
\(25\) 10.0654 2.01309
\(26\) 8.80948 1.72768
\(27\) 18.9555 3.64799
\(28\) 8.14392 1.53906
\(29\) 9.23562 1.71501 0.857506 0.514474i \(-0.172013\pi\)
0.857506 + 0.514474i \(0.172013\pi\)
\(30\) −30.2997 −5.53194
\(31\) −2.04469 −0.367236 −0.183618 0.982998i \(-0.558781\pi\)
−0.183618 + 0.982998i \(0.558781\pi\)
\(32\) 5.50132 0.972505
\(33\) −3.40179 −0.592176
\(34\) 0.882911 0.151418
\(35\) 9.67860 1.63598
\(36\) 27.9965 4.66609
\(37\) 4.79025 0.787512 0.393756 0.919215i \(-0.371175\pi\)
0.393756 + 0.919215i \(0.371175\pi\)
\(38\) 9.03147 1.46510
\(39\) −13.0593 −2.09116
\(40\) −11.2759 −1.78288
\(41\) −8.74208 −1.36528 −0.682642 0.730753i \(-0.739169\pi\)
−0.682642 + 0.730753i \(0.739169\pi\)
\(42\) −19.4657 −3.00362
\(43\) −4.80553 −0.732837 −0.366418 0.930450i \(-0.619416\pi\)
−0.366418 + 0.930450i \(0.619416\pi\)
\(44\) −3.26597 −0.492363
\(45\) 33.2723 4.95995
\(46\) 3.52595 0.519873
\(47\) 1.56722 0.228602 0.114301 0.993446i \(-0.463537\pi\)
0.114301 + 0.993446i \(0.463537\pi\)
\(48\) 0.457889 0.0660906
\(49\) −0.782100 −0.111729
\(50\) −23.0978 −3.26653
\(51\) −1.30884 −0.183274
\(52\) −12.5378 −1.73869
\(53\) −1.13491 −0.155892 −0.0779461 0.996958i \(-0.524836\pi\)
−0.0779461 + 0.996958i \(0.524836\pi\)
\(54\) −43.4985 −5.91939
\(55\) −3.88142 −0.523371
\(56\) −7.24408 −0.968030
\(57\) −13.3884 −1.77333
\(58\) −21.1936 −2.78286
\(59\) −9.39532 −1.22317 −0.611583 0.791180i \(-0.709467\pi\)
−0.611583 + 0.791180i \(0.709467\pi\)
\(60\) 43.1231 5.56717
\(61\) 13.5181 1.73082 0.865409 0.501066i \(-0.167059\pi\)
0.865409 + 0.501066i \(0.167059\pi\)
\(62\) 4.69208 0.595895
\(63\) 21.3754 2.69305
\(64\) −12.8935 −1.61168
\(65\) −14.9005 −1.84818
\(66\) 7.80633 0.960893
\(67\) 3.81781 0.466420 0.233210 0.972426i \(-0.425077\pi\)
0.233210 + 0.972426i \(0.425077\pi\)
\(68\) −1.25658 −0.152383
\(69\) −5.22691 −0.629247
\(70\) −22.2102 −2.65462
\(71\) 7.77422 0.922630 0.461315 0.887236i \(-0.347378\pi\)
0.461315 + 0.887236i \(0.347378\pi\)
\(72\) −24.9031 −2.93486
\(73\) −2.25867 −0.264358 −0.132179 0.991226i \(-0.542197\pi\)
−0.132179 + 0.991226i \(0.542197\pi\)
\(74\) −10.9925 −1.27785
\(75\) 34.2405 3.95375
\(76\) −12.8538 −1.47443
\(77\) −2.49357 −0.284169
\(78\) 29.9680 3.39321
\(79\) 0.175607 0.0197574 0.00987869 0.999951i \(-0.496855\pi\)
0.00987869 + 0.999951i \(0.496855\pi\)
\(80\) 0.522448 0.0584114
\(81\) 38.7661 4.30734
\(82\) 20.0611 2.21537
\(83\) 7.26733 0.797693 0.398846 0.917018i \(-0.369411\pi\)
0.398846 + 0.917018i \(0.369411\pi\)
\(84\) 27.7039 3.02275
\(85\) −1.49337 −0.161979
\(86\) 11.0276 1.18914
\(87\) 31.4177 3.36833
\(88\) 2.90510 0.309685
\(89\) 13.1294 1.39172 0.695858 0.718180i \(-0.255024\pi\)
0.695858 + 0.718180i \(0.255024\pi\)
\(90\) −76.3523 −8.04824
\(91\) −9.57267 −1.00349
\(92\) −5.01821 −0.523185
\(93\) −6.95560 −0.721262
\(94\) −3.59640 −0.370940
\(95\) −15.2760 −1.56729
\(96\) 18.7144 1.91003
\(97\) 1.38802 0.140932 0.0704659 0.997514i \(-0.477551\pi\)
0.0704659 + 0.997514i \(0.477551\pi\)
\(98\) 1.79474 0.181296
\(99\) −8.57220 −0.861539
\(100\) 32.8733 3.28733
\(101\) −12.3538 −1.22925 −0.614623 0.788821i \(-0.710692\pi\)
−0.614623 + 0.788821i \(0.710692\pi\)
\(102\) 3.00348 0.297389
\(103\) −15.3186 −1.50939 −0.754693 0.656078i \(-0.772214\pi\)
−0.754693 + 0.656078i \(0.772214\pi\)
\(104\) 11.1525 1.09359
\(105\) 32.9246 3.21311
\(106\) 2.60436 0.252958
\(107\) 13.0770 1.26420 0.632102 0.774885i \(-0.282192\pi\)
0.632102 + 0.774885i \(0.282192\pi\)
\(108\) 61.9080 5.95710
\(109\) −4.82160 −0.461826 −0.230913 0.972974i \(-0.574171\pi\)
−0.230913 + 0.972974i \(0.574171\pi\)
\(110\) 8.90697 0.849246
\(111\) 16.2954 1.54669
\(112\) 0.335640 0.0317150
\(113\) −6.17374 −0.580777 −0.290389 0.956909i \(-0.593785\pi\)
−0.290389 + 0.956909i \(0.593785\pi\)
\(114\) 30.7232 2.87749
\(115\) −5.96387 −0.556134
\(116\) 30.1632 2.80059
\(117\) −32.9082 −3.04236
\(118\) 21.5601 1.98477
\(119\) −0.959400 −0.0879481
\(120\) −38.3583 −3.50162
\(121\) 1.00000 0.0909091
\(122\) −31.0210 −2.80851
\(123\) −29.7388 −2.68145
\(124\) −6.67787 −0.599691
\(125\) 19.6611 1.75854
\(126\) −49.0516 −4.36987
\(127\) −16.3730 −1.45287 −0.726433 0.687237i \(-0.758823\pi\)
−0.726433 + 0.687237i \(0.758823\pi\)
\(128\) 18.5849 1.64269
\(129\) −16.3474 −1.43931
\(130\) 34.1933 2.99895
\(131\) 12.8407 1.12190 0.560949 0.827851i \(-0.310436\pi\)
0.560949 + 0.827851i \(0.310436\pi\)
\(132\) −11.1101 −0.967014
\(133\) −9.81389 −0.850972
\(134\) −8.76099 −0.756835
\(135\) 73.5742 6.33226
\(136\) 1.11774 0.0958450
\(137\) 3.33500 0.284928 0.142464 0.989800i \(-0.454497\pi\)
0.142464 + 0.989800i \(0.454497\pi\)
\(138\) 11.9946 1.02104
\(139\) 21.1148 1.79094 0.895469 0.445124i \(-0.146841\pi\)
0.895469 + 0.445124i \(0.146841\pi\)
\(140\) 31.6100 2.67153
\(141\) 5.33135 0.448980
\(142\) −17.8400 −1.49710
\(143\) 3.83894 0.321028
\(144\) 1.15384 0.0961531
\(145\) 35.8473 2.97696
\(146\) 5.18314 0.428959
\(147\) −2.66054 −0.219438
\(148\) 15.6448 1.28599
\(149\) 2.53645 0.207794 0.103897 0.994588i \(-0.466869\pi\)
0.103897 + 0.994588i \(0.466869\pi\)
\(150\) −78.5741 −6.41555
\(151\) 11.8290 0.962633 0.481316 0.876547i \(-0.340159\pi\)
0.481316 + 0.876547i \(0.340159\pi\)
\(152\) 11.4335 0.927382
\(153\) −3.29815 −0.266640
\(154\) 5.72217 0.461106
\(155\) −7.93628 −0.637458
\(156\) −42.6512 −3.41483
\(157\) −0.934206 −0.0745578 −0.0372789 0.999305i \(-0.511869\pi\)
−0.0372789 + 0.999305i \(0.511869\pi\)
\(158\) −0.402978 −0.0320592
\(159\) −3.86074 −0.306177
\(160\) 21.3529 1.68810
\(161\) −3.83141 −0.301958
\(162\) −88.9592 −6.98929
\(163\) 11.2630 0.882190 0.441095 0.897460i \(-0.354590\pi\)
0.441095 + 0.897460i \(0.354590\pi\)
\(164\) −28.5513 −2.22949
\(165\) −13.2038 −1.02791
\(166\) −16.6768 −1.29437
\(167\) 19.1049 1.47838 0.739189 0.673498i \(-0.235209\pi\)
0.739189 + 0.673498i \(0.235209\pi\)
\(168\) −24.6429 −1.90124
\(169\) 1.73744 0.133649
\(170\) 3.42695 0.262835
\(171\) −33.7374 −2.57996
\(172\) −15.6947 −1.19671
\(173\) −24.3308 −1.84983 −0.924917 0.380170i \(-0.875865\pi\)
−0.924917 + 0.380170i \(0.875865\pi\)
\(174\) −72.0964 −5.46561
\(175\) 25.0989 1.89730
\(176\) −0.134602 −0.0101460
\(177\) −31.9609 −2.40233
\(178\) −30.1290 −2.25826
\(179\) −5.61541 −0.419716 −0.209858 0.977732i \(-0.567300\pi\)
−0.209858 + 0.977732i \(0.567300\pi\)
\(180\) 108.666 8.09951
\(181\) −5.22545 −0.388404 −0.194202 0.980962i \(-0.562212\pi\)
−0.194202 + 0.980962i \(0.562212\pi\)
\(182\) 21.9671 1.62831
\(183\) 45.9859 3.39937
\(184\) 4.46374 0.329071
\(185\) 18.5930 1.36698
\(186\) 15.9615 1.17035
\(187\) 0.384749 0.0281357
\(188\) 5.11847 0.373303
\(189\) 47.2669 3.43816
\(190\) 35.0549 2.54315
\(191\) −20.4724 −1.48133 −0.740665 0.671874i \(-0.765490\pi\)
−0.740665 + 0.671874i \(0.765490\pi\)
\(192\) −43.8609 −3.16539
\(193\) 20.9183 1.50574 0.752868 0.658172i \(-0.228670\pi\)
0.752868 + 0.658172i \(0.228670\pi\)
\(194\) −3.18518 −0.228682
\(195\) −50.6885 −3.62988
\(196\) −2.55431 −0.182451
\(197\) 0.277697 0.0197851 0.00989254 0.999951i \(-0.496851\pi\)
0.00989254 + 0.999951i \(0.496851\pi\)
\(198\) 19.6712 1.39797
\(199\) 6.96795 0.493945 0.246972 0.969023i \(-0.420564\pi\)
0.246972 + 0.969023i \(0.420564\pi\)
\(200\) −29.2411 −2.06766
\(201\) 12.9874 0.916061
\(202\) 28.3490 1.99463
\(203\) 23.0297 1.61637
\(204\) −4.27462 −0.299283
\(205\) −33.9317 −2.36989
\(206\) 35.1526 2.44920
\(207\) −13.1713 −0.915471
\(208\) −0.516729 −0.0358287
\(209\) 3.93567 0.272236
\(210\) −75.5544 −5.21375
\(211\) −0.833253 −0.0573635 −0.0286817 0.999589i \(-0.509131\pi\)
−0.0286817 + 0.999589i \(0.509131\pi\)
\(212\) −3.70659 −0.254569
\(213\) 26.4463 1.81207
\(214\) −30.0088 −2.05136
\(215\) −18.6523 −1.27208
\(216\) −55.0676 −3.74688
\(217\) −5.09857 −0.346113
\(218\) 11.0645 0.749380
\(219\) −7.68354 −0.519206
\(220\) −12.6766 −0.854655
\(221\) 1.47703 0.0993557
\(222\) −37.3943 −2.50974
\(223\) 23.8089 1.59436 0.797182 0.603738i \(-0.206323\pi\)
0.797182 + 0.603738i \(0.206323\pi\)
\(224\) 13.7179 0.916568
\(225\) 86.2829 5.75219
\(226\) 14.1673 0.942396
\(227\) −7.45079 −0.494526 −0.247263 0.968948i \(-0.579531\pi\)
−0.247263 + 0.968948i \(0.579531\pi\)
\(228\) −43.7259 −2.89582
\(229\) −9.43985 −0.623803 −0.311901 0.950115i \(-0.600966\pi\)
−0.311901 + 0.950115i \(0.600966\pi\)
\(230\) 13.6857 0.902408
\(231\) −8.48262 −0.558115
\(232\) −26.8304 −1.76150
\(233\) −29.3067 −1.91995 −0.959974 0.280089i \(-0.909636\pi\)
−0.959974 + 0.280089i \(0.909636\pi\)
\(234\) 75.5166 4.93668
\(235\) 6.08303 0.396813
\(236\) −30.6848 −1.99741
\(237\) 0.597380 0.0388040
\(238\) 2.20160 0.142709
\(239\) −15.4508 −0.999430 −0.499715 0.866190i \(-0.666562\pi\)
−0.499715 + 0.866190i \(0.666562\pi\)
\(240\) 1.77726 0.114722
\(241\) −13.3069 −0.857175 −0.428588 0.903500i \(-0.640989\pi\)
−0.428588 + 0.903500i \(0.640989\pi\)
\(242\) −2.29477 −0.147513
\(243\) 75.0077 4.81175
\(244\) 44.1497 2.82640
\(245\) −3.03566 −0.193941
\(246\) 68.2436 4.35105
\(247\) 15.1088 0.961351
\(248\) 5.94001 0.377191
\(249\) 24.7220 1.56669
\(250\) −45.1176 −2.85349
\(251\) 21.1815 1.33696 0.668481 0.743729i \(-0.266945\pi\)
0.668481 + 0.743729i \(0.266945\pi\)
\(252\) 69.8113 4.39770
\(253\) 1.53652 0.0966000
\(254\) 37.5722 2.35749
\(255\) −5.08015 −0.318131
\(256\) −16.8611 −1.05382
\(257\) −23.0580 −1.43832 −0.719158 0.694846i \(-0.755472\pi\)
−0.719158 + 0.694846i \(0.755472\pi\)
\(258\) 37.5136 2.33549
\(259\) 11.9448 0.742216
\(260\) −48.6646 −3.01805
\(261\) 79.1697 4.90048
\(262\) −29.4665 −1.82044
\(263\) 11.6442 0.718011 0.359005 0.933336i \(-0.383116\pi\)
0.359005 + 0.933336i \(0.383116\pi\)
\(264\) 9.88255 0.608229
\(265\) −4.40507 −0.270602
\(266\) 22.5206 1.38083
\(267\) 44.6636 2.73337
\(268\) 12.4688 0.761655
\(269\) −18.9028 −1.15252 −0.576262 0.817265i \(-0.695489\pi\)
−0.576262 + 0.817265i \(0.695489\pi\)
\(270\) −168.836 −10.2750
\(271\) 17.8487 1.08423 0.542117 0.840303i \(-0.317623\pi\)
0.542117 + 0.840303i \(0.317623\pi\)
\(272\) −0.0517881 −0.00314012
\(273\) −32.5642 −1.97088
\(274\) −7.65306 −0.462338
\(275\) −10.0654 −0.606968
\(276\) −17.0709 −1.02755
\(277\) −14.5671 −0.875250 −0.437625 0.899158i \(-0.644180\pi\)
−0.437625 + 0.899158i \(0.644180\pi\)
\(278\) −48.4537 −2.90606
\(279\) −17.5275 −1.04934
\(280\) −28.1173 −1.68033
\(281\) 13.8882 0.828502 0.414251 0.910163i \(-0.364044\pi\)
0.414251 + 0.910163i \(0.364044\pi\)
\(282\) −12.2342 −0.728537
\(283\) 24.8296 1.47597 0.737983 0.674819i \(-0.235778\pi\)
0.737983 + 0.674819i \(0.235778\pi\)
\(284\) 25.3903 1.50664
\(285\) −51.9658 −3.07819
\(286\) −8.80948 −0.520915
\(287\) −21.7990 −1.28675
\(288\) 47.1584 2.77884
\(289\) −16.8520 −0.991292
\(290\) −82.2614 −4.83055
\(291\) 4.72175 0.276794
\(292\) −7.37675 −0.431692
\(293\) 2.17646 0.127150 0.0635750 0.997977i \(-0.479750\pi\)
0.0635750 + 0.997977i \(0.479750\pi\)
\(294\) 6.10533 0.356070
\(295\) −36.4672 −2.12320
\(296\) −13.9162 −0.808860
\(297\) −18.9555 −1.09991
\(298\) −5.82056 −0.337176
\(299\) 5.89859 0.341124
\(300\) 111.828 6.45641
\(301\) −11.9829 −0.690685
\(302\) −27.1449 −1.56201
\(303\) −42.0250 −2.41427
\(304\) −0.529750 −0.0303833
\(305\) 52.4695 3.00440
\(306\) 7.56849 0.432662
\(307\) −11.6506 −0.664932 −0.332466 0.943115i \(-0.607881\pi\)
−0.332466 + 0.943115i \(0.607881\pi\)
\(308\) −8.14392 −0.464043
\(309\) −52.1107 −2.96447
\(310\) 18.2119 1.03437
\(311\) −22.8376 −1.29500 −0.647500 0.762065i \(-0.724185\pi\)
−0.647500 + 0.762065i \(0.724185\pi\)
\(312\) 37.9385 2.14784
\(313\) 21.5645 1.21890 0.609450 0.792825i \(-0.291390\pi\)
0.609450 + 0.792825i \(0.291390\pi\)
\(314\) 2.14379 0.120981
\(315\) 82.9669 4.67466
\(316\) 0.573528 0.0322635
\(317\) −7.46570 −0.419316 −0.209658 0.977775i \(-0.567235\pi\)
−0.209658 + 0.977775i \(0.567235\pi\)
\(318\) 8.85951 0.496816
\(319\) −9.23562 −0.517096
\(320\) −50.0450 −2.79760
\(321\) 44.4854 2.48293
\(322\) 8.79221 0.489971
\(323\) 1.51425 0.0842550
\(324\) 126.609 7.03381
\(325\) −38.6405 −2.14339
\(326\) −25.8461 −1.43148
\(327\) −16.4021 −0.907038
\(328\) 25.3966 1.40229
\(329\) 3.90797 0.215453
\(330\) 30.2997 1.66794
\(331\) −17.8599 −0.981671 −0.490835 0.871252i \(-0.663308\pi\)
−0.490835 + 0.871252i \(0.663308\pi\)
\(332\) 23.7348 1.30262
\(333\) 41.0630 2.25024
\(334\) −43.8412 −2.39889
\(335\) 14.8185 0.809623
\(336\) 1.14178 0.0622891
\(337\) −3.85714 −0.210112 −0.105056 0.994466i \(-0.533502\pi\)
−0.105056 + 0.994466i \(0.533502\pi\)
\(338\) −3.98703 −0.216866
\(339\) −21.0018 −1.14066
\(340\) −4.87731 −0.264509
\(341\) 2.04469 0.110726
\(342\) 77.4196 4.18637
\(343\) −19.4052 −1.04778
\(344\) 13.9606 0.752703
\(345\) −20.2879 −1.09226
\(346\) 55.8335 3.00163
\(347\) −7.65766 −0.411084 −0.205542 0.978648i \(-0.565896\pi\)
−0.205542 + 0.978648i \(0.565896\pi\)
\(348\) 102.609 5.50043
\(349\) −20.8804 −1.11770 −0.558850 0.829269i \(-0.688757\pi\)
−0.558850 + 0.829269i \(0.688757\pi\)
\(350\) −57.5961 −3.07864
\(351\) −72.7690 −3.88412
\(352\) −5.50132 −0.293221
\(353\) −31.5101 −1.67711 −0.838557 0.544815i \(-0.816600\pi\)
−0.838557 + 0.544815i \(0.816600\pi\)
\(354\) 73.3430 3.89814
\(355\) 30.1750 1.60152
\(356\) 42.8802 2.27265
\(357\) −3.26368 −0.172732
\(358\) 12.8861 0.681051
\(359\) −21.7079 −1.14570 −0.572850 0.819661i \(-0.694162\pi\)
−0.572850 + 0.819661i \(0.694162\pi\)
\(360\) −96.6595 −5.09440
\(361\) −3.51046 −0.184761
\(362\) 11.9912 0.630243
\(363\) 3.40179 0.178548
\(364\) −31.2640 −1.63868
\(365\) −8.76686 −0.458879
\(366\) −105.527 −5.51598
\(367\) −22.1398 −1.15569 −0.577845 0.816147i \(-0.696106\pi\)
−0.577845 + 0.816147i \(0.696106\pi\)
\(368\) −0.206819 −0.0107812
\(369\) −74.9389 −3.90116
\(370\) −42.6666 −2.21813
\(371\) −2.82999 −0.146926
\(372\) −22.7167 −1.17781
\(373\) −22.1036 −1.14448 −0.572240 0.820086i \(-0.693925\pi\)
−0.572240 + 0.820086i \(0.693925\pi\)
\(374\) −0.882911 −0.0456542
\(375\) 66.8829 3.45382
\(376\) −4.55292 −0.234799
\(377\) −35.4550 −1.82602
\(378\) −108.467 −5.57892
\(379\) −14.6258 −0.751278 −0.375639 0.926766i \(-0.622577\pi\)
−0.375639 + 0.926766i \(0.622577\pi\)
\(380\) −49.8909 −2.55935
\(381\) −55.6975 −2.85347
\(382\) 46.9794 2.40368
\(383\) −10.0580 −0.513940 −0.256970 0.966419i \(-0.582724\pi\)
−0.256970 + 0.966419i \(0.582724\pi\)
\(384\) 63.2219 3.22628
\(385\) −9.67860 −0.493267
\(386\) −48.0028 −2.44328
\(387\) −41.1940 −2.09401
\(388\) 4.53322 0.230139
\(389\) 9.82753 0.498276 0.249138 0.968468i \(-0.419853\pi\)
0.249138 + 0.968468i \(0.419853\pi\)
\(390\) 116.319 5.89002
\(391\) 0.591174 0.0298970
\(392\) 2.27208 0.114757
\(393\) 43.6814 2.20344
\(394\) −0.637250 −0.0321042
\(395\) 0.681606 0.0342953
\(396\) −27.9965 −1.40688
\(397\) −2.24596 −0.112721 −0.0563606 0.998410i \(-0.517950\pi\)
−0.0563606 + 0.998410i \(0.517950\pi\)
\(398\) −15.9898 −0.801498
\(399\) −33.3848 −1.67133
\(400\) 1.35483 0.0677414
\(401\) 7.15542 0.357325 0.178662 0.983910i \(-0.442823\pi\)
0.178662 + 0.983910i \(0.442823\pi\)
\(402\) −29.8031 −1.48644
\(403\) 7.84942 0.391007
\(404\) −40.3470 −2.00734
\(405\) 150.467 7.47679
\(406\) −52.8478 −2.62279
\(407\) −4.79025 −0.237444
\(408\) 3.80231 0.188242
\(409\) 14.1397 0.699162 0.349581 0.936906i \(-0.386324\pi\)
0.349581 + 0.936906i \(0.386324\pi\)
\(410\) 77.8654 3.84550
\(411\) 11.3450 0.559607
\(412\) −50.0300 −2.46480
\(413\) −23.4279 −1.15281
\(414\) 30.2252 1.48549
\(415\) 28.2076 1.38465
\(416\) −21.1192 −1.03545
\(417\) 71.8283 3.51745
\(418\) −9.03147 −0.441743
\(419\) −17.2268 −0.841584 −0.420792 0.907157i \(-0.638248\pi\)
−0.420792 + 0.907157i \(0.638248\pi\)
\(420\) 107.531 5.24696
\(421\) 17.0202 0.829513 0.414756 0.909932i \(-0.363867\pi\)
0.414756 + 0.909932i \(0.363867\pi\)
\(422\) 1.91212 0.0930807
\(423\) 13.4345 0.653208
\(424\) 3.29703 0.160118
\(425\) −3.87267 −0.187852
\(426\) −60.6881 −2.94035
\(427\) 33.7084 1.63126
\(428\) 42.7091 2.06442
\(429\) 13.0593 0.630508
\(430\) 42.8027 2.06413
\(431\) −24.8064 −1.19488 −0.597442 0.801912i \(-0.703816\pi\)
−0.597442 + 0.801912i \(0.703816\pi\)
\(432\) 2.55145 0.122757
\(433\) 12.5758 0.604356 0.302178 0.953252i \(-0.402286\pi\)
0.302178 + 0.953252i \(0.402286\pi\)
\(434\) 11.7000 0.561620
\(435\) 121.945 5.84683
\(436\) −15.7472 −0.754154
\(437\) 6.04723 0.289278
\(438\) 17.6320 0.842488
\(439\) 1.56351 0.0746222 0.0373111 0.999304i \(-0.488121\pi\)
0.0373111 + 0.999304i \(0.488121\pi\)
\(440\) 11.2759 0.537558
\(441\) −6.70432 −0.319253
\(442\) −3.38944 −0.161219
\(443\) −24.4177 −1.16012 −0.580061 0.814573i \(-0.696971\pi\)
−0.580061 + 0.814573i \(0.696971\pi\)
\(444\) 53.2204 2.52573
\(445\) 50.9608 2.41577
\(446\) −54.6360 −2.58709
\(447\) 8.62847 0.408113
\(448\) −32.1508 −1.51898
\(449\) 7.71052 0.363882 0.181941 0.983309i \(-0.441762\pi\)
0.181941 + 0.983309i \(0.441762\pi\)
\(450\) −197.999 −9.33378
\(451\) 8.74208 0.411649
\(452\) −20.1632 −0.948399
\(453\) 40.2399 1.89064
\(454\) 17.0978 0.802442
\(455\) −37.1555 −1.74188
\(456\) 38.8945 1.82140
\(457\) −30.8822 −1.44461 −0.722304 0.691576i \(-0.756917\pi\)
−0.722304 + 0.691576i \(0.756917\pi\)
\(458\) 21.6623 1.01221
\(459\) −7.29311 −0.340413
\(460\) −19.4778 −0.908157
\(461\) −35.7065 −1.66302 −0.831509 0.555512i \(-0.812522\pi\)
−0.831509 + 0.555512i \(0.812522\pi\)
\(462\) 19.4657 0.905624
\(463\) −18.0308 −0.837965 −0.418982 0.907994i \(-0.637613\pi\)
−0.418982 + 0.907994i \(0.637613\pi\)
\(464\) 1.24314 0.0577111
\(465\) −26.9976 −1.25198
\(466\) 67.2522 3.11540
\(467\) 28.4992 1.31879 0.659393 0.751799i \(-0.270813\pi\)
0.659393 + 0.751799i \(0.270813\pi\)
\(468\) −107.477 −4.96812
\(469\) 9.51998 0.439592
\(470\) −13.9591 −0.643887
\(471\) −3.17798 −0.146433
\(472\) 27.2943 1.25632
\(473\) 4.80553 0.220959
\(474\) −1.37085 −0.0629652
\(475\) −39.6143 −1.81763
\(476\) −3.13337 −0.143618
\(477\) −9.72870 −0.445447
\(478\) 35.4561 1.62172
\(479\) −36.5478 −1.66991 −0.834955 0.550318i \(-0.814507\pi\)
−0.834955 + 0.550318i \(0.814507\pi\)
\(480\) 72.6383 3.31547
\(481\) −18.3895 −0.838488
\(482\) 30.5363 1.39089
\(483\) −13.0337 −0.593053
\(484\) 3.26597 0.148453
\(485\) 5.38748 0.244633
\(486\) −172.125 −7.80777
\(487\) 38.8696 1.76135 0.880675 0.473721i \(-0.157089\pi\)
0.880675 + 0.473721i \(0.157089\pi\)
\(488\) −39.2715 −1.77774
\(489\) 38.3146 1.73264
\(490\) 6.96614 0.314698
\(491\) 37.0059 1.67005 0.835027 0.550209i \(-0.185452\pi\)
0.835027 + 0.550209i \(0.185452\pi\)
\(492\) −97.1258 −4.37877
\(493\) −3.55340 −0.160037
\(494\) −34.6712 −1.55993
\(495\) −33.2723 −1.49548
\(496\) −0.275219 −0.0123577
\(497\) 19.3856 0.869562
\(498\) −56.7312 −2.54218
\(499\) 22.4957 1.00705 0.503524 0.863981i \(-0.332037\pi\)
0.503524 + 0.863981i \(0.332037\pi\)
\(500\) 64.2123 2.87166
\(501\) 64.9908 2.90357
\(502\) −48.6066 −2.16942
\(503\) −12.8176 −0.571509 −0.285754 0.958303i \(-0.592244\pi\)
−0.285754 + 0.958303i \(0.592244\pi\)
\(504\) −62.0977 −2.76605
\(505\) −47.9502 −2.13375
\(506\) −3.52595 −0.156748
\(507\) 5.91042 0.262491
\(508\) −53.4736 −2.37251
\(509\) 9.11722 0.404114 0.202057 0.979374i \(-0.435237\pi\)
0.202057 + 0.979374i \(0.435237\pi\)
\(510\) 11.6578 0.516215
\(511\) −5.63216 −0.249152
\(512\) 1.52256 0.0672881
\(513\) −74.6027 −3.29379
\(514\) 52.9127 2.33388
\(515\) −59.4579 −2.62003
\(516\) −53.3902 −2.35037
\(517\) −1.56722 −0.0689261
\(518\) −27.4106 −1.20435
\(519\) −82.7682 −3.63312
\(520\) 43.2875 1.89828
\(521\) −15.6808 −0.686986 −0.343493 0.939155i \(-0.611610\pi\)
−0.343493 + 0.939155i \(0.611610\pi\)
\(522\) −181.676 −7.95175
\(523\) −3.13344 −0.137016 −0.0685078 0.997651i \(-0.521824\pi\)
−0.0685078 + 0.997651i \(0.521824\pi\)
\(524\) 41.9373 1.83204
\(525\) 85.3812 3.72634
\(526\) −26.7207 −1.16508
\(527\) 0.786691 0.0342688
\(528\) −0.457889 −0.0199271
\(529\) −20.6391 −0.897353
\(530\) 10.1086 0.439091
\(531\) −80.5386 −3.49508
\(532\) −32.0518 −1.38962
\(533\) 33.5603 1.45366
\(534\) −102.493 −4.43529
\(535\) 50.7574 2.19444
\(536\) −11.0911 −0.479063
\(537\) −19.1025 −0.824333
\(538\) 43.3775 1.87014
\(539\) 0.782100 0.0336874
\(540\) 240.291 10.3405
\(541\) 25.8455 1.11119 0.555593 0.831455i \(-0.312491\pi\)
0.555593 + 0.831455i \(0.312491\pi\)
\(542\) −40.9588 −1.75933
\(543\) −17.7759 −0.762837
\(544\) −2.11663 −0.0907497
\(545\) −18.7147 −0.801649
\(546\) 74.7274 3.19804
\(547\) 1.00000 0.0427569
\(548\) 10.8920 0.465283
\(549\) 115.880 4.94564
\(550\) 23.0978 0.984895
\(551\) −36.3484 −1.54849
\(552\) 15.1847 0.646304
\(553\) 0.437890 0.0186210
\(554\) 33.4280 1.42022
\(555\) 63.2495 2.68479
\(556\) 68.9604 2.92457
\(557\) 28.1466 1.19261 0.596304 0.802758i \(-0.296635\pi\)
0.596304 + 0.802758i \(0.296635\pi\)
\(558\) 40.2215 1.70271
\(559\) 18.4481 0.780273
\(560\) 1.30276 0.0550517
\(561\) 1.30884 0.0552592
\(562\) −31.8703 −1.34437
\(563\) 19.7853 0.833851 0.416926 0.908941i \(-0.363108\pi\)
0.416926 + 0.908941i \(0.363108\pi\)
\(564\) 17.4120 0.733177
\(565\) −23.9629 −1.00813
\(566\) −56.9782 −2.39497
\(567\) 96.6660 4.05959
\(568\) −22.5849 −0.947641
\(569\) −12.0280 −0.504240 −0.252120 0.967696i \(-0.581128\pi\)
−0.252120 + 0.967696i \(0.581128\pi\)
\(570\) 119.250 4.99482
\(571\) 14.3454 0.600338 0.300169 0.953886i \(-0.402957\pi\)
0.300169 + 0.953886i \(0.402957\pi\)
\(572\) 12.5378 0.524233
\(573\) −69.6429 −2.90937
\(574\) 50.0237 2.08795
\(575\) −15.4657 −0.644964
\(576\) −110.525 −4.60522
\(577\) −6.41702 −0.267144 −0.133572 0.991039i \(-0.542645\pi\)
−0.133572 + 0.991039i \(0.542645\pi\)
\(578\) 38.6714 1.60852
\(579\) 71.1599 2.95730
\(580\) 117.076 4.86132
\(581\) 18.1216 0.751811
\(582\) −10.8353 −0.449138
\(583\) 1.13491 0.0470033
\(584\) 6.56167 0.271524
\(585\) −127.730 −5.28100
\(586\) −4.99447 −0.206320
\(587\) −2.72214 −0.112355 −0.0561773 0.998421i \(-0.517891\pi\)
−0.0561773 + 0.998421i \(0.517891\pi\)
\(588\) −8.68925 −0.358338
\(589\) 8.04722 0.331580
\(590\) 83.6838 3.44521
\(591\) 0.944668 0.0388584
\(592\) 0.644778 0.0265002
\(593\) −27.0454 −1.11062 −0.555311 0.831643i \(-0.687401\pi\)
−0.555311 + 0.831643i \(0.687401\pi\)
\(594\) 43.4985 1.78476
\(595\) −3.72384 −0.152662
\(596\) 8.28395 0.339324
\(597\) 23.7035 0.970120
\(598\) −13.5359 −0.553524
\(599\) −46.5407 −1.90160 −0.950800 0.309805i \(-0.899736\pi\)
−0.950800 + 0.309805i \(0.899736\pi\)
\(600\) −99.4721 −4.06093
\(601\) −24.2496 −0.989160 −0.494580 0.869132i \(-0.664678\pi\)
−0.494580 + 0.869132i \(0.664678\pi\)
\(602\) 27.4981 1.12074
\(603\) 32.7270 1.33275
\(604\) 38.6332 1.57196
\(605\) 3.88142 0.157802
\(606\) 96.4376 3.91751
\(607\) −19.7787 −0.802794 −0.401397 0.915904i \(-0.631475\pi\)
−0.401397 + 0.915904i \(0.631475\pi\)
\(608\) −21.6514 −0.878080
\(609\) 78.3423 3.17459
\(610\) −120.405 −4.87507
\(611\) −6.01645 −0.243399
\(612\) −10.7716 −0.435418
\(613\) 22.1445 0.894408 0.447204 0.894432i \(-0.352420\pi\)
0.447204 + 0.894432i \(0.352420\pi\)
\(614\) 26.7353 1.07895
\(615\) −115.429 −4.65453
\(616\) 7.24408 0.291872
\(617\) −32.3709 −1.30320 −0.651601 0.758562i \(-0.725902\pi\)
−0.651601 + 0.758562i \(0.725902\pi\)
\(618\) 119.582 4.81029
\(619\) −16.0701 −0.645910 −0.322955 0.946414i \(-0.604676\pi\)
−0.322955 + 0.946414i \(0.604676\pi\)
\(620\) −25.9196 −1.04096
\(621\) −29.1254 −1.16876
\(622\) 52.4070 2.10133
\(623\) 32.7391 1.31167
\(624\) −1.75781 −0.0703686
\(625\) 25.9857 1.03943
\(626\) −49.4856 −1.97784
\(627\) 13.3884 0.534679
\(628\) −3.05109 −0.121752
\(629\) −1.84305 −0.0734870
\(630\) −190.390 −7.58532
\(631\) 38.9934 1.55230 0.776151 0.630547i \(-0.217170\pi\)
0.776151 + 0.630547i \(0.217170\pi\)
\(632\) −0.510157 −0.0202930
\(633\) −2.83455 −0.112663
\(634\) 17.1321 0.680401
\(635\) −63.5504 −2.52192
\(636\) −12.6090 −0.499981
\(637\) 3.00243 0.118961
\(638\) 21.1936 0.839064
\(639\) 66.6422 2.63632
\(640\) 72.1358 2.85142
\(641\) −6.83403 −0.269928 −0.134964 0.990851i \(-0.543092\pi\)
−0.134964 + 0.990851i \(0.543092\pi\)
\(642\) −102.084 −4.02892
\(643\) −35.0196 −1.38104 −0.690520 0.723314i \(-0.742618\pi\)
−0.690520 + 0.723314i \(0.742618\pi\)
\(644\) −12.5133 −0.493092
\(645\) −63.4513 −2.49839
\(646\) −3.47485 −0.136716
\(647\) 36.9174 1.45137 0.725686 0.688026i \(-0.241522\pi\)
0.725686 + 0.688026i \(0.241522\pi\)
\(648\) −112.619 −4.42410
\(649\) 9.39532 0.368799
\(650\) 88.6711 3.47797
\(651\) −17.3443 −0.679776
\(652\) 36.7847 1.44060
\(653\) −20.5073 −0.802514 −0.401257 0.915966i \(-0.631427\pi\)
−0.401257 + 0.915966i \(0.631427\pi\)
\(654\) 37.6390 1.47180
\(655\) 49.8402 1.94742
\(656\) −1.17670 −0.0459425
\(657\) −19.3618 −0.755376
\(658\) −8.96788 −0.349604
\(659\) −16.3098 −0.635339 −0.317669 0.948202i \(-0.602900\pi\)
−0.317669 + 0.948202i \(0.602900\pi\)
\(660\) −43.1231 −1.67857
\(661\) −38.6304 −1.50255 −0.751274 0.659991i \(-0.770560\pi\)
−0.751274 + 0.659991i \(0.770560\pi\)
\(662\) 40.9844 1.59291
\(663\) 5.02455 0.195137
\(664\) −21.1123 −0.819317
\(665\) −38.0918 −1.47714
\(666\) −94.2301 −3.65134
\(667\) −14.1907 −0.549466
\(668\) 62.3958 2.41417
\(669\) 80.9931 3.13138
\(670\) −34.0051 −1.31373
\(671\) −13.5181 −0.521861
\(672\) 46.6656 1.80016
\(673\) −26.1730 −1.00889 −0.504447 0.863443i \(-0.668304\pi\)
−0.504447 + 0.863443i \(0.668304\pi\)
\(674\) 8.85126 0.340938
\(675\) 190.795 7.34371
\(676\) 5.67443 0.218247
\(677\) −30.7469 −1.18170 −0.590849 0.806782i \(-0.701207\pi\)
−0.590849 + 0.806782i \(0.701207\pi\)
\(678\) 48.1943 1.85089
\(679\) 3.46112 0.132826
\(680\) 4.33840 0.166370
\(681\) −25.3461 −0.971263
\(682\) −4.69208 −0.179669
\(683\) −51.5321 −1.97182 −0.985910 0.167279i \(-0.946502\pi\)
−0.985910 + 0.167279i \(0.946502\pi\)
\(684\) −110.185 −4.21304
\(685\) 12.9445 0.494586
\(686\) 44.5305 1.70018
\(687\) −32.1124 −1.22517
\(688\) −0.646835 −0.0246604
\(689\) 4.35686 0.165983
\(690\) 46.5559 1.77235
\(691\) 24.2843 0.923820 0.461910 0.886927i \(-0.347164\pi\)
0.461910 + 0.886927i \(0.347164\pi\)
\(692\) −79.4634 −3.02075
\(693\) −21.3754 −0.811985
\(694\) 17.5726 0.667045
\(695\) 81.9556 3.10875
\(696\) −91.2715 −3.45964
\(697\) 3.36351 0.127402
\(698\) 47.9156 1.81363
\(699\) −99.6955 −3.77083
\(700\) 81.9720 3.09825
\(701\) 7.92748 0.299417 0.149708 0.988730i \(-0.452167\pi\)
0.149708 + 0.988730i \(0.452167\pi\)
\(702\) 166.988 6.30255
\(703\) −18.8529 −0.711049
\(704\) 12.8935 0.485941
\(705\) 20.6932 0.779351
\(706\) 72.3084 2.72136
\(707\) −30.8050 −1.15854
\(708\) −104.383 −3.92297
\(709\) 0.355524 0.0133520 0.00667599 0.999978i \(-0.497875\pi\)
0.00667599 + 0.999978i \(0.497875\pi\)
\(710\) −69.2447 −2.59871
\(711\) 1.50534 0.0564548
\(712\) −38.1423 −1.42944
\(713\) 3.14169 0.117657
\(714\) 7.48940 0.280284
\(715\) 14.9005 0.557248
\(716\) −18.3398 −0.685389
\(717\) −52.5605 −1.96291
\(718\) 49.8146 1.85907
\(719\) −25.6548 −0.956761 −0.478381 0.878153i \(-0.658776\pi\)
−0.478381 + 0.878153i \(0.658776\pi\)
\(720\) 4.47853 0.166905
\(721\) −38.1980 −1.42257
\(722\) 8.05570 0.299802
\(723\) −45.2675 −1.68351
\(724\) −17.0661 −0.634258
\(725\) 92.9605 3.45247
\(726\) −7.80633 −0.289720
\(727\) 37.4547 1.38912 0.694560 0.719435i \(-0.255599\pi\)
0.694560 + 0.719435i \(0.255599\pi\)
\(728\) 27.8096 1.03069
\(729\) 138.863 5.14306
\(730\) 20.1179 0.744598
\(731\) 1.84893 0.0683850
\(732\) 150.188 5.55112
\(733\) −0.881589 −0.0325622 −0.0162811 0.999867i \(-0.505183\pi\)
−0.0162811 + 0.999867i \(0.505183\pi\)
\(734\) 50.8058 1.87528
\(735\) −10.3267 −0.380906
\(736\) −8.45287 −0.311577
\(737\) −3.81781 −0.140631
\(738\) 171.968 6.33021
\(739\) −18.9331 −0.696466 −0.348233 0.937408i \(-0.613218\pi\)
−0.348233 + 0.937408i \(0.613218\pi\)
\(740\) 60.7240 2.23226
\(741\) 51.3971 1.88812
\(742\) 6.49417 0.238408
\(743\) −4.13373 −0.151652 −0.0758259 0.997121i \(-0.524159\pi\)
−0.0758259 + 0.997121i \(0.524159\pi\)
\(744\) 20.2067 0.740814
\(745\) 9.84502 0.360694
\(746\) 50.7226 1.85709
\(747\) 62.2970 2.27933
\(748\) 1.25658 0.0459451
\(749\) 32.6085 1.19149
\(750\) −153.481 −5.60432
\(751\) 19.7061 0.719085 0.359543 0.933129i \(-0.382933\pi\)
0.359543 + 0.933129i \(0.382933\pi\)
\(752\) 0.210951 0.00769258
\(753\) 72.0550 2.62583
\(754\) 81.3610 2.96299
\(755\) 45.9134 1.67096
\(756\) 154.372 5.61446
\(757\) 16.6576 0.605429 0.302715 0.953081i \(-0.402107\pi\)
0.302715 + 0.953081i \(0.402107\pi\)
\(758\) 33.5629 1.21906
\(759\) 5.22691 0.189725
\(760\) 44.3783 1.60977
\(761\) −29.8931 −1.08362 −0.541812 0.840500i \(-0.682261\pi\)
−0.541812 + 0.840500i \(0.682261\pi\)
\(762\) 127.813 4.63017
\(763\) −12.0230 −0.435262
\(764\) −66.8622 −2.41899
\(765\) −12.8015 −0.462840
\(766\) 23.0808 0.833943
\(767\) 36.0680 1.30234
\(768\) −57.3580 −2.06973
\(769\) −3.67393 −0.132485 −0.0662427 0.997804i \(-0.521101\pi\)
−0.0662427 + 0.997804i \(0.521101\pi\)
\(770\) 22.2102 0.800398
\(771\) −78.4385 −2.82489
\(772\) 68.3186 2.45884
\(773\) 12.8806 0.463284 0.231642 0.972801i \(-0.425590\pi\)
0.231642 + 0.972801i \(0.425590\pi\)
\(774\) 94.5308 3.39784
\(775\) −20.5806 −0.739278
\(776\) −4.03233 −0.144752
\(777\) 40.6339 1.45773
\(778\) −22.5519 −0.808525
\(779\) 34.4060 1.23272
\(780\) −165.547 −5.92754
\(781\) −7.77422 −0.278183
\(782\) −1.35661 −0.0485122
\(783\) 175.066 6.25634
\(784\) −0.105272 −0.00375973
\(785\) −3.62605 −0.129419
\(786\) −100.239 −3.57540
\(787\) 45.3111 1.61517 0.807583 0.589754i \(-0.200775\pi\)
0.807583 + 0.589754i \(0.200775\pi\)
\(788\) 0.906949 0.0323087
\(789\) 39.6111 1.41019
\(790\) −1.56413 −0.0556492
\(791\) −15.3947 −0.547372
\(792\) 24.9031 0.884893
\(793\) −51.8952 −1.84285
\(794\) 5.15395 0.182907
\(795\) −14.9852 −0.531469
\(796\) 22.7571 0.806603
\(797\) −5.84557 −0.207061 −0.103530 0.994626i \(-0.533014\pi\)
−0.103530 + 0.994626i \(0.533014\pi\)
\(798\) 76.6105 2.71198
\(799\) −0.602985 −0.0213321
\(800\) 55.3731 1.95774
\(801\) 112.548 3.97669
\(802\) −16.4200 −0.579812
\(803\) 2.25867 0.0797069
\(804\) 42.4164 1.49591
\(805\) −14.8713 −0.524146
\(806\) −18.0126 −0.634467
\(807\) −64.3034 −2.26359
\(808\) 35.8889 1.26257
\(809\) 13.0053 0.457242 0.228621 0.973515i \(-0.426578\pi\)
0.228621 + 0.973515i \(0.426578\pi\)
\(810\) −345.288 −12.1322
\(811\) 13.4655 0.472838 0.236419 0.971651i \(-0.424026\pi\)
0.236419 + 0.971651i \(0.424026\pi\)
\(812\) 75.2142 2.63950
\(813\) 60.7178 2.12947
\(814\) 10.9925 0.385287
\(815\) 43.7166 1.53133
\(816\) −0.176172 −0.00616727
\(817\) 18.9130 0.661683
\(818\) −32.4473 −1.13449
\(819\) −82.0588 −2.86737
\(820\) −110.820 −3.86999
\(821\) 37.2586 1.30034 0.650168 0.759791i \(-0.274699\pi\)
0.650168 + 0.759791i \(0.274699\pi\)
\(822\) −26.0341 −0.908045
\(823\) −9.63528 −0.335865 −0.167932 0.985799i \(-0.553709\pi\)
−0.167932 + 0.985799i \(0.553709\pi\)
\(824\) 44.5020 1.55030
\(825\) −34.2405 −1.19210
\(826\) 53.7616 1.87061
\(827\) 2.81571 0.0979120 0.0489560 0.998801i \(-0.484411\pi\)
0.0489560 + 0.998801i \(0.484411\pi\)
\(828\) −43.0171 −1.49495
\(829\) 35.6028 1.23654 0.618268 0.785968i \(-0.287835\pi\)
0.618268 + 0.785968i \(0.287835\pi\)
\(830\) −64.7298 −2.24681
\(831\) −49.5541 −1.71901
\(832\) 49.4972 1.71601
\(833\) 0.300913 0.0104260
\(834\) −164.829 −5.70758
\(835\) 74.1540 2.56621
\(836\) 12.8538 0.444557
\(837\) −38.7580 −1.33967
\(838\) 39.5315 1.36559
\(839\) 47.8060 1.65045 0.825223 0.564808i \(-0.191050\pi\)
0.825223 + 0.564808i \(0.191050\pi\)
\(840\) −95.6493 −3.30021
\(841\) 56.2967 1.94127
\(842\) −39.0574 −1.34601
\(843\) 47.2449 1.62720
\(844\) −2.72137 −0.0936736
\(845\) 6.74374 0.231992
\(846\) −30.8291 −1.05993
\(847\) 2.49357 0.0856801
\(848\) −0.152762 −0.00524586
\(849\) 84.4652 2.89884
\(850\) 8.88688 0.304817
\(851\) −7.36030 −0.252308
\(852\) 86.3727 2.95908
\(853\) 8.48535 0.290533 0.145266 0.989393i \(-0.453596\pi\)
0.145266 + 0.989393i \(0.453596\pi\)
\(854\) −77.3530 −2.64697
\(855\) −130.949 −4.47836
\(856\) −37.9901 −1.29847
\(857\) −21.2334 −0.725320 −0.362660 0.931922i \(-0.618131\pi\)
−0.362660 + 0.931922i \(0.618131\pi\)
\(858\) −29.9680 −1.02309
\(859\) −0.364795 −0.0124467 −0.00622333 0.999981i \(-0.501981\pi\)
−0.00622333 + 0.999981i \(0.501981\pi\)
\(860\) −60.9178 −2.07728
\(861\) −74.1557 −2.52722
\(862\) 56.9250 1.93887
\(863\) 51.2218 1.74361 0.871806 0.489852i \(-0.162949\pi\)
0.871806 + 0.489852i \(0.162949\pi\)
\(864\) 104.280 3.54768
\(865\) −94.4379 −3.21098
\(866\) −28.8586 −0.980656
\(867\) −57.3269 −1.94692
\(868\) −16.6518 −0.565197
\(869\) −0.175607 −0.00595707
\(870\) −279.836 −9.48734
\(871\) −14.6563 −0.496611
\(872\) 14.0072 0.474345
\(873\) 11.8984 0.402699
\(874\) −13.8770 −0.469397
\(875\) 49.0263 1.65739
\(876\) −25.0942 −0.847854
\(877\) −34.6400 −1.16971 −0.584855 0.811138i \(-0.698849\pi\)
−0.584855 + 0.811138i \(0.698849\pi\)
\(878\) −3.58789 −0.121085
\(879\) 7.40386 0.249726
\(880\) −0.522448 −0.0176117
\(881\) −53.6224 −1.80658 −0.903292 0.429027i \(-0.858857\pi\)
−0.903292 + 0.429027i \(0.858857\pi\)
\(882\) 15.3849 0.518036
\(883\) −42.9478 −1.44531 −0.722655 0.691209i \(-0.757078\pi\)
−0.722655 + 0.691209i \(0.757078\pi\)
\(884\) 4.82393 0.162246
\(885\) −124.054 −4.17003
\(886\) 56.0331 1.88247
\(887\) −29.5095 −0.990832 −0.495416 0.868656i \(-0.664984\pi\)
−0.495416 + 0.868656i \(0.664984\pi\)
\(888\) −47.3399 −1.58862
\(889\) −40.8272 −1.36930
\(890\) −116.943 −3.91995
\(891\) −38.7661 −1.29871
\(892\) 77.7592 2.60357
\(893\) −6.16805 −0.206406
\(894\) −19.8004 −0.662223
\(895\) −21.7958 −0.728553
\(896\) 46.3427 1.54820
\(897\) 20.0658 0.669977
\(898\) −17.6939 −0.590452
\(899\) −18.8839 −0.629815
\(900\) 281.797 9.39323
\(901\) 0.436657 0.0145472
\(902\) −20.0611 −0.667960
\(903\) −40.7635 −1.35652
\(904\) 17.9353 0.596521
\(905\) −20.2822 −0.674202
\(906\) −92.3413 −3.06783
\(907\) −31.3851 −1.04212 −0.521062 0.853519i \(-0.674464\pi\)
−0.521062 + 0.853519i \(0.674464\pi\)
\(908\) −24.3340 −0.807553
\(909\) −105.899 −3.51245
\(910\) 85.2634 2.82645
\(911\) 36.9332 1.22365 0.611825 0.790993i \(-0.290436\pi\)
0.611825 + 0.790993i \(0.290436\pi\)
\(912\) −1.80210 −0.0596736
\(913\) −7.26733 −0.240513
\(914\) 70.8675 2.34409
\(915\) 178.491 5.90072
\(916\) −30.8302 −1.01866
\(917\) 32.0192 1.05737
\(918\) 16.7360 0.552371
\(919\) 38.1897 1.25976 0.629880 0.776692i \(-0.283104\pi\)
0.629880 + 0.776692i \(0.283104\pi\)
\(920\) 17.3256 0.571209
\(921\) −39.6328 −1.30594
\(922\) 81.9382 2.69849
\(923\) −29.8447 −0.982352
\(924\) −27.7039 −0.911393
\(925\) 48.2159 1.58533
\(926\) 41.3766 1.35972
\(927\) −131.314 −4.31292
\(928\) 50.8081 1.66786
\(929\) 43.7914 1.43675 0.718375 0.695656i \(-0.244886\pi\)
0.718375 + 0.695656i \(0.244886\pi\)
\(930\) 61.9533 2.03153
\(931\) 3.07809 0.100880
\(932\) −95.7148 −3.13524
\(933\) −77.6887 −2.54341
\(934\) −65.3991 −2.13992
\(935\) 1.49337 0.0488386
\(936\) 95.6015 3.12483
\(937\) 14.9844 0.489520 0.244760 0.969584i \(-0.421291\pi\)
0.244760 + 0.969584i \(0.421291\pi\)
\(938\) −21.8462 −0.713303
\(939\) 73.3581 2.39395
\(940\) 19.8670 0.647989
\(941\) −37.6535 −1.22747 −0.613734 0.789513i \(-0.710333\pi\)
−0.613734 + 0.789513i \(0.710333\pi\)
\(942\) 7.29273 0.237610
\(943\) 13.4324 0.437418
\(944\) −1.26463 −0.0411602
\(945\) 183.463 5.96804
\(946\) −11.0276 −0.358538
\(947\) −26.8790 −0.873451 −0.436726 0.899595i \(-0.643862\pi\)
−0.436726 + 0.899595i \(0.643862\pi\)
\(948\) 1.95102 0.0633663
\(949\) 8.67091 0.281470
\(950\) 90.9056 2.94937
\(951\) −25.3968 −0.823547
\(952\) 2.78715 0.0903322
\(953\) −5.36078 −0.173653 −0.0868264 0.996223i \(-0.527673\pi\)
−0.0868264 + 0.996223i \(0.527673\pi\)
\(954\) 22.3251 0.722803
\(955\) −79.4620 −2.57133
\(956\) −50.4618 −1.63205
\(957\) −31.4177 −1.01559
\(958\) 83.8687 2.70968
\(959\) 8.31607 0.268540
\(960\) −170.243 −5.49456
\(961\) −26.8193 −0.865138
\(962\) 42.1996 1.36057
\(963\) 112.099 3.61234
\(964\) −43.4600 −1.39975
\(965\) 81.1929 2.61369
\(966\) 29.9093 0.962316
\(967\) 61.4434 1.97589 0.987944 0.154813i \(-0.0494774\pi\)
0.987944 + 0.154813i \(0.0494774\pi\)
\(968\) −2.90510 −0.0933735
\(969\) 5.15116 0.165479
\(970\) −12.3630 −0.396953
\(971\) 7.78462 0.249820 0.124910 0.992168i \(-0.460136\pi\)
0.124910 + 0.992168i \(0.460136\pi\)
\(972\) 244.973 7.85750
\(973\) 52.6514 1.68793
\(974\) −89.1968 −2.85805
\(975\) −131.447 −4.20968
\(976\) 1.81957 0.0582430
\(977\) −29.2487 −0.935750 −0.467875 0.883795i \(-0.654980\pi\)
−0.467875 + 0.883795i \(0.654980\pi\)
\(978\) −87.9231 −2.81147
\(979\) −13.1294 −0.419618
\(980\) −9.91436 −0.316703
\(981\) −41.3318 −1.31962
\(982\) −84.9200 −2.70991
\(983\) −41.7342 −1.33111 −0.665557 0.746347i \(-0.731806\pi\)
−0.665557 + 0.746347i \(0.731806\pi\)
\(984\) 86.3941 2.75414
\(985\) 1.07786 0.0343434
\(986\) 8.15423 0.259684
\(987\) 13.2941 0.423156
\(988\) 49.3449 1.56987
\(989\) 7.38378 0.234791
\(990\) 76.3523 2.42664
\(991\) −37.9590 −1.20581 −0.602904 0.797814i \(-0.705990\pi\)
−0.602904 + 0.797814i \(0.705990\pi\)
\(992\) −11.2485 −0.357139
\(993\) −60.7558 −1.92803
\(994\) −44.4854 −1.41099
\(995\) 27.0455 0.857401
\(996\) 80.7411 2.55838
\(997\) 54.0626 1.71218 0.856090 0.516827i \(-0.172887\pi\)
0.856090 + 0.516827i \(0.172887\pi\)
\(998\) −51.6225 −1.63408
\(999\) 90.8015 2.87283
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 6017.2.a.f.1.15 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.15 121 1.1 even 1 trivial