Properties

Label 1859.2.a.s.1.20
Level $1859$
Weight $2$
Character 1859.1
Self dual yes
Analytic conductor $14.844$
Analytic rank $0$
Dimension $21$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.8441897358\)
Analytic rank: \(0\)
Dimension: \(21\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 1859.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.70607 q^{2} +0.960218 q^{3} +5.32282 q^{4} +3.57279 q^{5} +2.59842 q^{6} -3.95601 q^{7} +8.99178 q^{8} -2.07798 q^{9} +O(q^{10})\) \(q+2.70607 q^{2} +0.960218 q^{3} +5.32282 q^{4} +3.57279 q^{5} +2.59842 q^{6} -3.95601 q^{7} +8.99178 q^{8} -2.07798 q^{9} +9.66821 q^{10} -1.00000 q^{11} +5.11106 q^{12} -10.7053 q^{14} +3.43065 q^{15} +13.6867 q^{16} +2.79876 q^{17} -5.62316 q^{18} +0.00685455 q^{19} +19.0173 q^{20} -3.79863 q^{21} -2.70607 q^{22} -3.94433 q^{23} +8.63406 q^{24} +7.76481 q^{25} -4.87597 q^{27} -21.0571 q^{28} +6.09411 q^{29} +9.28359 q^{30} -0.242210 q^{31} +19.0537 q^{32} -0.960218 q^{33} +7.57365 q^{34} -14.1340 q^{35} -11.0607 q^{36} -0.801720 q^{37} +0.0185489 q^{38} +32.1257 q^{40} +6.58954 q^{41} -10.2794 q^{42} -6.24920 q^{43} -5.32282 q^{44} -7.42419 q^{45} -10.6736 q^{46} -6.29173 q^{47} +13.1423 q^{48} +8.65004 q^{49} +21.0121 q^{50} +2.68742 q^{51} +9.02538 q^{53} -13.1947 q^{54} -3.57279 q^{55} -35.5716 q^{56} +0.00658186 q^{57} +16.4911 q^{58} -4.00551 q^{59} +18.2607 q^{60} -6.32993 q^{61} -0.655437 q^{62} +8.22052 q^{63} +24.1873 q^{64} -2.59842 q^{66} -8.97718 q^{67} +14.8973 q^{68} -3.78741 q^{69} -38.2476 q^{70} -8.03382 q^{71} -18.6847 q^{72} -0.166373 q^{73} -2.16951 q^{74} +7.45591 q^{75} +0.0364855 q^{76} +3.95601 q^{77} -9.30756 q^{79} +48.8998 q^{80} +1.55195 q^{81} +17.8318 q^{82} -0.547068 q^{83} -20.2194 q^{84} +9.99939 q^{85} -16.9108 q^{86} +5.85167 q^{87} -8.99178 q^{88} -17.0658 q^{89} -20.0904 q^{90} -20.9949 q^{92} -0.232574 q^{93} -17.0259 q^{94} +0.0244899 q^{95} +18.2957 q^{96} -8.78558 q^{97} +23.4076 q^{98} +2.07798 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.70607 1.91348 0.956740 0.290943i \(-0.0939690\pi\)
0.956740 + 0.290943i \(0.0939690\pi\)
\(3\) 0.960218 0.554382 0.277191 0.960815i \(-0.410597\pi\)
0.277191 + 0.960815i \(0.410597\pi\)
\(4\) 5.32282 2.66141
\(5\) 3.57279 1.59780 0.798900 0.601464i \(-0.205416\pi\)
0.798900 + 0.601464i \(0.205416\pi\)
\(6\) 2.59842 1.06080
\(7\) −3.95601 −1.49523 −0.747616 0.664131i \(-0.768802\pi\)
−0.747616 + 0.664131i \(0.768802\pi\)
\(8\) 8.99178 3.17907
\(9\) −2.07798 −0.692661
\(10\) 9.66821 3.05736
\(11\) −1.00000 −0.301511
\(12\) 5.11106 1.47544
\(13\) 0 0
\(14\) −10.7053 −2.86110
\(15\) 3.43065 0.885791
\(16\) 13.6867 3.42169
\(17\) 2.79876 0.678800 0.339400 0.940642i \(-0.389776\pi\)
0.339400 + 0.940642i \(0.389776\pi\)
\(18\) −5.62316 −1.32539
\(19\) 0.00685455 0.00157254 0.000786271 1.00000i \(-0.499750\pi\)
0.000786271 1.00000i \(0.499750\pi\)
\(20\) 19.0173 4.25240
\(21\) −3.79863 −0.828930
\(22\) −2.70607 −0.576936
\(23\) −3.94433 −0.822449 −0.411224 0.911534i \(-0.634899\pi\)
−0.411224 + 0.911534i \(0.634899\pi\)
\(24\) 8.63406 1.76242
\(25\) 7.76481 1.55296
\(26\) 0 0
\(27\) −4.87597 −0.938381
\(28\) −21.0571 −3.97942
\(29\) 6.09411 1.13165 0.565824 0.824526i \(-0.308558\pi\)
0.565824 + 0.824526i \(0.308558\pi\)
\(30\) 9.28359 1.69494
\(31\) −0.242210 −0.0435022 −0.0217511 0.999763i \(-0.506924\pi\)
−0.0217511 + 0.999763i \(0.506924\pi\)
\(32\) 19.0537 3.36826
\(33\) −0.960218 −0.167152
\(34\) 7.57365 1.29887
\(35\) −14.1340 −2.38908
\(36\) −11.0607 −1.84345
\(37\) −0.801720 −0.131802 −0.0659010 0.997826i \(-0.520992\pi\)
−0.0659010 + 0.997826i \(0.520992\pi\)
\(38\) 0.0185489 0.00300903
\(39\) 0 0
\(40\) 32.1257 5.07952
\(41\) 6.58954 1.02911 0.514557 0.857456i \(-0.327956\pi\)
0.514557 + 0.857456i \(0.327956\pi\)
\(42\) −10.2794 −1.58614
\(43\) −6.24920 −0.952994 −0.476497 0.879176i \(-0.658094\pi\)
−0.476497 + 0.879176i \(0.658094\pi\)
\(44\) −5.32282 −0.802445
\(45\) −7.42419 −1.10673
\(46\) −10.6736 −1.57374
\(47\) −6.29173 −0.917743 −0.458872 0.888503i \(-0.651746\pi\)
−0.458872 + 0.888503i \(0.651746\pi\)
\(48\) 13.1423 1.89692
\(49\) 8.65004 1.23572
\(50\) 21.0121 2.97156
\(51\) 2.68742 0.376315
\(52\) 0 0
\(53\) 9.02538 1.23973 0.619865 0.784708i \(-0.287187\pi\)
0.619865 + 0.784708i \(0.287187\pi\)
\(54\) −13.1947 −1.79557
\(55\) −3.57279 −0.481755
\(56\) −35.5716 −4.75345
\(57\) 0.00658186 0.000871789 0
\(58\) 16.4911 2.16539
\(59\) −4.00551 −0.521472 −0.260736 0.965410i \(-0.583965\pi\)
−0.260736 + 0.965410i \(0.583965\pi\)
\(60\) 18.2607 2.35745
\(61\) −6.32993 −0.810464 −0.405232 0.914214i \(-0.632809\pi\)
−0.405232 + 0.914214i \(0.632809\pi\)
\(62\) −0.655437 −0.0832405
\(63\) 8.22052 1.03569
\(64\) 24.1873 3.02341
\(65\) 0 0
\(66\) −2.59842 −0.319843
\(67\) −8.97718 −1.09674 −0.548368 0.836237i \(-0.684751\pi\)
−0.548368 + 0.836237i \(0.684751\pi\)
\(68\) 14.8973 1.80656
\(69\) −3.78741 −0.455951
\(70\) −38.2476 −4.57146
\(71\) −8.03382 −0.953439 −0.476720 0.879055i \(-0.658174\pi\)
−0.476720 + 0.879055i \(0.658174\pi\)
\(72\) −18.6847 −2.20202
\(73\) −0.166373 −0.0194725 −0.00973623 0.999953i \(-0.503099\pi\)
−0.00973623 + 0.999953i \(0.503099\pi\)
\(74\) −2.16951 −0.252200
\(75\) 7.45591 0.860934
\(76\) 0.0364855 0.00418518
\(77\) 3.95601 0.450830
\(78\) 0 0
\(79\) −9.30756 −1.04718 −0.523591 0.851970i \(-0.675408\pi\)
−0.523591 + 0.851970i \(0.675408\pi\)
\(80\) 48.8998 5.46717
\(81\) 1.55195 0.172439
\(82\) 17.8318 1.96919
\(83\) −0.547068 −0.0600485 −0.0300242 0.999549i \(-0.509558\pi\)
−0.0300242 + 0.999549i \(0.509558\pi\)
\(84\) −20.2194 −2.20612
\(85\) 9.99939 1.08459
\(86\) −16.9108 −1.82354
\(87\) 5.85167 0.627365
\(88\) −8.99178 −0.958527
\(89\) −17.0658 −1.80897 −0.904487 0.426502i \(-0.859746\pi\)
−0.904487 + 0.426502i \(0.859746\pi\)
\(90\) −20.0904 −2.11771
\(91\) 0 0
\(92\) −20.9949 −2.18887
\(93\) −0.232574 −0.0241168
\(94\) −17.0259 −1.75608
\(95\) 0.0244899 0.00251261
\(96\) 18.2957 1.86730
\(97\) −8.78558 −0.892040 −0.446020 0.895023i \(-0.647159\pi\)
−0.446020 + 0.895023i \(0.647159\pi\)
\(98\) 23.4076 2.36453
\(99\) 2.07798 0.208845
\(100\) 41.3307 4.13307
\(101\) −0.664826 −0.0661527 −0.0330763 0.999453i \(-0.510530\pi\)
−0.0330763 + 0.999453i \(0.510530\pi\)
\(102\) 7.27236 0.720071
\(103\) −14.3916 −1.41804 −0.709021 0.705187i \(-0.750863\pi\)
−0.709021 + 0.705187i \(0.750863\pi\)
\(104\) 0 0
\(105\) −13.5717 −1.32446
\(106\) 24.4233 2.37220
\(107\) 7.11634 0.687962 0.343981 0.938977i \(-0.388224\pi\)
0.343981 + 0.938977i \(0.388224\pi\)
\(108\) −25.9539 −2.49741
\(109\) 7.76979 0.744211 0.372105 0.928191i \(-0.378636\pi\)
0.372105 + 0.928191i \(0.378636\pi\)
\(110\) −9.66821 −0.921828
\(111\) −0.769826 −0.0730686
\(112\) −54.1450 −5.11622
\(113\) −13.4649 −1.26667 −0.633334 0.773878i \(-0.718314\pi\)
−0.633334 + 0.773878i \(0.718314\pi\)
\(114\) 0.0178110 0.00166815
\(115\) −14.0922 −1.31411
\(116\) 32.4378 3.01178
\(117\) 0 0
\(118\) −10.8392 −0.997827
\(119\) −11.0720 −1.01496
\(120\) 30.8477 2.81599
\(121\) 1.00000 0.0909091
\(122\) −17.1292 −1.55081
\(123\) 6.32740 0.570522
\(124\) −1.28924 −0.115777
\(125\) 9.87808 0.883523
\(126\) 22.2453 1.98177
\(127\) 13.1288 1.16499 0.582495 0.812834i \(-0.302076\pi\)
0.582495 + 0.812834i \(0.302076\pi\)
\(128\) 27.3450 2.41698
\(129\) −6.00059 −0.528323
\(130\) 0 0
\(131\) 16.5571 1.44660 0.723300 0.690534i \(-0.242625\pi\)
0.723300 + 0.690534i \(0.242625\pi\)
\(132\) −5.11106 −0.444861
\(133\) −0.0271167 −0.00235132
\(134\) −24.2929 −2.09859
\(135\) −17.4208 −1.49934
\(136\) 25.1659 2.15796
\(137\) 17.9393 1.53266 0.766330 0.642447i \(-0.222081\pi\)
0.766330 + 0.642447i \(0.222081\pi\)
\(138\) −10.2490 −0.872453
\(139\) 8.20712 0.696119 0.348059 0.937473i \(-0.386841\pi\)
0.348059 + 0.937473i \(0.386841\pi\)
\(140\) −75.2327 −6.35832
\(141\) −6.04143 −0.508780
\(142\) −21.7401 −1.82439
\(143\) 0 0
\(144\) −28.4408 −2.37007
\(145\) 21.7730 1.80815
\(146\) −0.450216 −0.0372602
\(147\) 8.30592 0.685061
\(148\) −4.26741 −0.350779
\(149\) −6.02019 −0.493193 −0.246597 0.969118i \(-0.579312\pi\)
−0.246597 + 0.969118i \(0.579312\pi\)
\(150\) 20.1762 1.64738
\(151\) 9.53009 0.775547 0.387774 0.921755i \(-0.373244\pi\)
0.387774 + 0.921755i \(0.373244\pi\)
\(152\) 0.0616346 0.00499923
\(153\) −5.81578 −0.470178
\(154\) 10.7053 0.862654
\(155\) −0.865364 −0.0695077
\(156\) 0 0
\(157\) 7.58684 0.605496 0.302748 0.953071i \(-0.402096\pi\)
0.302748 + 0.953071i \(0.402096\pi\)
\(158\) −25.1869 −2.00376
\(159\) 8.66633 0.687284
\(160\) 68.0750 5.38180
\(161\) 15.6038 1.22975
\(162\) 4.19969 0.329959
\(163\) −0.420278 −0.0329187 −0.0164594 0.999865i \(-0.505239\pi\)
−0.0164594 + 0.999865i \(0.505239\pi\)
\(164\) 35.0749 2.73889
\(165\) −3.43065 −0.267076
\(166\) −1.48040 −0.114902
\(167\) 15.9576 1.23484 0.617420 0.786634i \(-0.288178\pi\)
0.617420 + 0.786634i \(0.288178\pi\)
\(168\) −34.1565 −2.63523
\(169\) 0 0
\(170\) 27.0591 2.07534
\(171\) −0.0142436 −0.00108924
\(172\) −33.2633 −2.53631
\(173\) −1.43723 −0.109270 −0.0546352 0.998506i \(-0.517400\pi\)
−0.0546352 + 0.998506i \(0.517400\pi\)
\(174\) 15.8350 1.20045
\(175\) −30.7177 −2.32204
\(176\) −13.6867 −1.03168
\(177\) −3.84616 −0.289095
\(178\) −46.1813 −3.46144
\(179\) 16.8302 1.25795 0.628973 0.777427i \(-0.283476\pi\)
0.628973 + 0.777427i \(0.283476\pi\)
\(180\) −39.5176 −2.94547
\(181\) 4.85465 0.360843 0.180422 0.983589i \(-0.442254\pi\)
0.180422 + 0.983589i \(0.442254\pi\)
\(182\) 0 0
\(183\) −6.07811 −0.449307
\(184\) −35.4665 −2.61462
\(185\) −2.86437 −0.210593
\(186\) −0.629362 −0.0461471
\(187\) −2.79876 −0.204666
\(188\) −33.4897 −2.44249
\(189\) 19.2894 1.40310
\(190\) 0.0662713 0.00480782
\(191\) 11.5662 0.836898 0.418449 0.908240i \(-0.362574\pi\)
0.418449 + 0.908240i \(0.362574\pi\)
\(192\) 23.2251 1.67612
\(193\) −26.9954 −1.94317 −0.971584 0.236693i \(-0.923936\pi\)
−0.971584 + 0.236693i \(0.923936\pi\)
\(194\) −23.7744 −1.70690
\(195\) 0 0
\(196\) 46.0426 3.28876
\(197\) −16.7441 −1.19297 −0.596483 0.802626i \(-0.703436\pi\)
−0.596483 + 0.802626i \(0.703436\pi\)
\(198\) 5.62316 0.399621
\(199\) 24.3915 1.72907 0.864535 0.502572i \(-0.167613\pi\)
0.864535 + 0.502572i \(0.167613\pi\)
\(200\) 69.8194 4.93698
\(201\) −8.62005 −0.608011
\(202\) −1.79907 −0.126582
\(203\) −24.1084 −1.69208
\(204\) 14.3047 1.00153
\(205\) 23.5430 1.64432
\(206\) −38.9446 −2.71340
\(207\) 8.19624 0.569678
\(208\) 0 0
\(209\) −0.00685455 −0.000474139 0
\(210\) −36.7260 −2.53434
\(211\) 20.9742 1.44392 0.721961 0.691934i \(-0.243241\pi\)
0.721961 + 0.691934i \(0.243241\pi\)
\(212\) 48.0404 3.29943
\(213\) −7.71422 −0.528570
\(214\) 19.2573 1.31640
\(215\) −22.3271 −1.52269
\(216\) −43.8436 −2.98318
\(217\) 0.958185 0.0650458
\(218\) 21.0256 1.42403
\(219\) −0.159754 −0.0107952
\(220\) −19.0173 −1.28215
\(221\) 0 0
\(222\) −2.08320 −0.139815
\(223\) 2.16005 0.144647 0.0723237 0.997381i \(-0.476959\pi\)
0.0723237 + 0.997381i \(0.476959\pi\)
\(224\) −75.3769 −5.03633
\(225\) −16.1351 −1.07568
\(226\) −36.4369 −2.42375
\(227\) 19.0617 1.26517 0.632586 0.774490i \(-0.281994\pi\)
0.632586 + 0.774490i \(0.281994\pi\)
\(228\) 0.0350340 0.00232019
\(229\) −18.7054 −1.23609 −0.618043 0.786144i \(-0.712074\pi\)
−0.618043 + 0.786144i \(0.712074\pi\)
\(230\) −38.1346 −2.51452
\(231\) 3.79863 0.249932
\(232\) 54.7969 3.59759
\(233\) 29.4725 1.93081 0.965404 0.260758i \(-0.0839725\pi\)
0.965404 + 0.260758i \(0.0839725\pi\)
\(234\) 0 0
\(235\) −22.4790 −1.46637
\(236\) −21.3206 −1.38785
\(237\) −8.93728 −0.580539
\(238\) −29.9615 −1.94211
\(239\) 0.858675 0.0555431 0.0277715 0.999614i \(-0.491159\pi\)
0.0277715 + 0.999614i \(0.491159\pi\)
\(240\) 46.9545 3.03090
\(241\) −6.76007 −0.435454 −0.217727 0.976010i \(-0.569864\pi\)
−0.217727 + 0.976010i \(0.569864\pi\)
\(242\) 2.70607 0.173953
\(243\) 16.1181 1.03398
\(244\) −33.6931 −2.15698
\(245\) 30.9048 1.97443
\(246\) 17.1224 1.09168
\(247\) 0 0
\(248\) −2.17790 −0.138297
\(249\) −0.525304 −0.0332898
\(250\) 26.7308 1.69060
\(251\) 24.1131 1.52200 0.761002 0.648749i \(-0.224707\pi\)
0.761002 + 0.648749i \(0.224707\pi\)
\(252\) 43.7563 2.75639
\(253\) 3.94433 0.247978
\(254\) 35.5274 2.22919
\(255\) 9.60159 0.601275
\(256\) 25.6229 1.60143
\(257\) 11.8561 0.739563 0.369781 0.929119i \(-0.379433\pi\)
0.369781 + 0.929119i \(0.379433\pi\)
\(258\) −16.2380 −1.01094
\(259\) 3.17161 0.197075
\(260\) 0 0
\(261\) −12.6634 −0.783848
\(262\) 44.8046 2.76804
\(263\) 11.5619 0.712939 0.356470 0.934307i \(-0.383980\pi\)
0.356470 + 0.934307i \(0.383980\pi\)
\(264\) −8.63406 −0.531390
\(265\) 32.2458 1.98084
\(266\) −0.0733797 −0.00449920
\(267\) −16.3869 −1.00286
\(268\) −47.7839 −2.91887
\(269\) 24.0669 1.46739 0.733693 0.679481i \(-0.237795\pi\)
0.733693 + 0.679481i \(0.237795\pi\)
\(270\) −47.1419 −2.86897
\(271\) −18.6610 −1.13357 −0.566787 0.823864i \(-0.691814\pi\)
−0.566787 + 0.823864i \(0.691814\pi\)
\(272\) 38.3060 2.32264
\(273\) 0 0
\(274\) 48.5451 2.93272
\(275\) −7.76481 −0.468236
\(276\) −20.1597 −1.21347
\(277\) 0.407769 0.0245005 0.0122502 0.999925i \(-0.496101\pi\)
0.0122502 + 0.999925i \(0.496101\pi\)
\(278\) 22.2090 1.33201
\(279\) 0.503307 0.0301322
\(280\) −127.090 −7.59506
\(281\) 30.5675 1.82350 0.911752 0.410741i \(-0.134730\pi\)
0.911752 + 0.410741i \(0.134730\pi\)
\(282\) −16.3485 −0.973541
\(283\) 14.5967 0.867683 0.433841 0.900989i \(-0.357158\pi\)
0.433841 + 0.900989i \(0.357158\pi\)
\(284\) −42.7626 −2.53749
\(285\) 0.0235156 0.00139294
\(286\) 0 0
\(287\) −26.0683 −1.53876
\(288\) −39.5933 −2.33306
\(289\) −9.16691 −0.539230
\(290\) 58.9191 3.45985
\(291\) −8.43607 −0.494531
\(292\) −0.885572 −0.0518242
\(293\) 29.1102 1.70064 0.850319 0.526268i \(-0.176409\pi\)
0.850319 + 0.526268i \(0.176409\pi\)
\(294\) 22.4764 1.31085
\(295\) −14.3108 −0.833208
\(296\) −7.20889 −0.419008
\(297\) 4.87597 0.282932
\(298\) −16.2911 −0.943715
\(299\) 0 0
\(300\) 39.6864 2.29130
\(301\) 24.7219 1.42495
\(302\) 25.7891 1.48399
\(303\) −0.638378 −0.0366738
\(304\) 0.0938165 0.00538075
\(305\) −22.6155 −1.29496
\(306\) −15.7379 −0.899677
\(307\) −24.4200 −1.39372 −0.696861 0.717207i \(-0.745420\pi\)
−0.696861 + 0.717207i \(0.745420\pi\)
\(308\) 21.0571 1.19984
\(309\) −13.8190 −0.786137
\(310\) −2.34174 −0.133002
\(311\) 26.3470 1.49400 0.747002 0.664822i \(-0.231493\pi\)
0.747002 + 0.664822i \(0.231493\pi\)
\(312\) 0 0
\(313\) −29.2630 −1.65404 −0.827021 0.562171i \(-0.809966\pi\)
−0.827021 + 0.562171i \(0.809966\pi\)
\(314\) 20.5305 1.15860
\(315\) 29.3702 1.65482
\(316\) −49.5424 −2.78698
\(317\) 16.1999 0.909875 0.454937 0.890523i \(-0.349662\pi\)
0.454937 + 0.890523i \(0.349662\pi\)
\(318\) 23.4517 1.31511
\(319\) −6.09411 −0.341205
\(320\) 86.4160 4.83080
\(321\) 6.83323 0.381394
\(322\) 42.2250 2.35311
\(323\) 0.0191843 0.00106744
\(324\) 8.26076 0.458931
\(325\) 0 0
\(326\) −1.13730 −0.0629893
\(327\) 7.46069 0.412577
\(328\) 59.2517 3.27163
\(329\) 24.8902 1.37224
\(330\) −9.28359 −0.511045
\(331\) −9.41075 −0.517262 −0.258631 0.965976i \(-0.583271\pi\)
−0.258631 + 0.965976i \(0.583271\pi\)
\(332\) −2.91194 −0.159814
\(333\) 1.66596 0.0912940
\(334\) 43.1825 2.36284
\(335\) −32.0736 −1.75237
\(336\) −51.9909 −2.83634
\(337\) −34.4623 −1.87728 −0.938640 0.344900i \(-0.887913\pi\)
−0.938640 + 0.344900i \(0.887913\pi\)
\(338\) 0 0
\(339\) −12.9292 −0.702218
\(340\) 53.2249 2.88653
\(341\) 0.242210 0.0131164
\(342\) −0.0385443 −0.00208424
\(343\) −6.52758 −0.352456
\(344\) −56.1914 −3.02964
\(345\) −13.5316 −0.728518
\(346\) −3.88924 −0.209087
\(347\) −17.3788 −0.932945 −0.466473 0.884536i \(-0.654475\pi\)
−0.466473 + 0.884536i \(0.654475\pi\)
\(348\) 31.1474 1.66967
\(349\) −1.75565 −0.0939780 −0.0469890 0.998895i \(-0.514963\pi\)
−0.0469890 + 0.998895i \(0.514963\pi\)
\(350\) −83.1242 −4.44318
\(351\) 0 0
\(352\) −19.0537 −1.01557
\(353\) 9.12962 0.485921 0.242960 0.970036i \(-0.421882\pi\)
0.242960 + 0.970036i \(0.421882\pi\)
\(354\) −10.4080 −0.553178
\(355\) −28.7031 −1.52340
\(356\) −90.8383 −4.81442
\(357\) −10.6315 −0.562678
\(358\) 45.5436 2.40706
\(359\) 5.56656 0.293792 0.146896 0.989152i \(-0.453072\pi\)
0.146896 + 0.989152i \(0.453072\pi\)
\(360\) −66.7566 −3.51838
\(361\) −19.0000 −0.999998
\(362\) 13.1370 0.690467
\(363\) 0.960218 0.0503984
\(364\) 0 0
\(365\) −0.594415 −0.0311131
\(366\) −16.4478 −0.859740
\(367\) −10.8050 −0.564017 −0.282009 0.959412i \(-0.591001\pi\)
−0.282009 + 0.959412i \(0.591001\pi\)
\(368\) −53.9850 −2.81416
\(369\) −13.6930 −0.712827
\(370\) −7.75120 −0.402966
\(371\) −35.7045 −1.85369
\(372\) −1.23795 −0.0641847
\(373\) 3.71923 0.192574 0.0962872 0.995354i \(-0.469303\pi\)
0.0962872 + 0.995354i \(0.469303\pi\)
\(374\) −7.57365 −0.391624
\(375\) 9.48511 0.489809
\(376\) −56.5738 −2.91757
\(377\) 0 0
\(378\) 52.1985 2.68480
\(379\) −6.49327 −0.333537 −0.166768 0.985996i \(-0.553333\pi\)
−0.166768 + 0.985996i \(0.553333\pi\)
\(380\) 0.130355 0.00668707
\(381\) 12.6065 0.645850
\(382\) 31.2988 1.60139
\(383\) −4.15841 −0.212485 −0.106242 0.994340i \(-0.533882\pi\)
−0.106242 + 0.994340i \(0.533882\pi\)
\(384\) 26.2572 1.33993
\(385\) 14.1340 0.720335
\(386\) −73.0514 −3.71822
\(387\) 12.9857 0.660101
\(388\) −46.7640 −2.37408
\(389\) 12.5597 0.636803 0.318402 0.947956i \(-0.396854\pi\)
0.318402 + 0.947956i \(0.396854\pi\)
\(390\) 0 0
\(391\) −11.0392 −0.558278
\(392\) 77.7792 3.92844
\(393\) 15.8984 0.801969
\(394\) −45.3106 −2.28272
\(395\) −33.2539 −1.67319
\(396\) 11.0607 0.555822
\(397\) −18.0947 −0.908147 −0.454073 0.890964i \(-0.650030\pi\)
−0.454073 + 0.890964i \(0.650030\pi\)
\(398\) 66.0052 3.30854
\(399\) −0.0260379 −0.00130353
\(400\) 106.275 5.31375
\(401\) 8.08415 0.403703 0.201852 0.979416i \(-0.435304\pi\)
0.201852 + 0.979416i \(0.435304\pi\)
\(402\) −23.3265 −1.16342
\(403\) 0 0
\(404\) −3.53875 −0.176059
\(405\) 5.54480 0.275523
\(406\) −65.2389 −3.23775
\(407\) 0.801720 0.0397398
\(408\) 24.1647 1.19633
\(409\) 18.9341 0.936233 0.468116 0.883667i \(-0.344933\pi\)
0.468116 + 0.883667i \(0.344933\pi\)
\(410\) 63.7091 3.14637
\(411\) 17.2257 0.849679
\(412\) −76.6036 −3.77399
\(413\) 15.8458 0.779722
\(414\) 22.1796 1.09007
\(415\) −1.95456 −0.0959454
\(416\) 0 0
\(417\) 7.88062 0.385916
\(418\) −0.0185489 −0.000907256 0
\(419\) −22.2827 −1.08858 −0.544292 0.838896i \(-0.683202\pi\)
−0.544292 + 0.838896i \(0.683202\pi\)
\(420\) −72.2397 −3.52494
\(421\) −16.8899 −0.823161 −0.411581 0.911373i \(-0.635023\pi\)
−0.411581 + 0.911373i \(0.635023\pi\)
\(422\) 56.7576 2.76292
\(423\) 13.0741 0.635685
\(424\) 81.1542 3.94119
\(425\) 21.7319 1.05415
\(426\) −20.8752 −1.01141
\(427\) 25.0413 1.21183
\(428\) 37.8790 1.83095
\(429\) 0 0
\(430\) −60.4186 −2.91364
\(431\) 12.8476 0.618846 0.309423 0.950924i \(-0.399864\pi\)
0.309423 + 0.950924i \(0.399864\pi\)
\(432\) −66.7361 −3.21084
\(433\) 12.3159 0.591865 0.295933 0.955209i \(-0.404370\pi\)
0.295933 + 0.955209i \(0.404370\pi\)
\(434\) 2.59292 0.124464
\(435\) 20.9068 1.00240
\(436\) 41.3572 1.98065
\(437\) −0.0270366 −0.00129333
\(438\) −0.432306 −0.0206564
\(439\) −5.79480 −0.276571 −0.138285 0.990392i \(-0.544159\pi\)
−0.138285 + 0.990392i \(0.544159\pi\)
\(440\) −32.1257 −1.53153
\(441\) −17.9746 −0.855935
\(442\) 0 0
\(443\) −25.9984 −1.23522 −0.617612 0.786483i \(-0.711900\pi\)
−0.617612 + 0.786483i \(0.711900\pi\)
\(444\) −4.09764 −0.194465
\(445\) −60.9726 −2.89038
\(446\) 5.84524 0.276780
\(447\) −5.78069 −0.273417
\(448\) −95.6852 −4.52070
\(449\) −23.8705 −1.12652 −0.563258 0.826281i \(-0.690452\pi\)
−0.563258 + 0.826281i \(0.690452\pi\)
\(450\) −43.6628 −2.05828
\(451\) −6.58954 −0.310290
\(452\) −71.6711 −3.37112
\(453\) 9.15096 0.429949
\(454\) 51.5824 2.42088
\(455\) 0 0
\(456\) 0.0591826 0.00277148
\(457\) −6.67322 −0.312160 −0.156080 0.987744i \(-0.549886\pi\)
−0.156080 + 0.987744i \(0.549886\pi\)
\(458\) −50.6181 −2.36523
\(459\) −13.6467 −0.636973
\(460\) −75.0104 −3.49738
\(461\) −16.3391 −0.760989 −0.380495 0.924783i \(-0.624246\pi\)
−0.380495 + 0.924783i \(0.624246\pi\)
\(462\) 10.2794 0.478240
\(463\) −31.3751 −1.45812 −0.729062 0.684447i \(-0.760044\pi\)
−0.729062 + 0.684447i \(0.760044\pi\)
\(464\) 83.4085 3.87214
\(465\) −0.830938 −0.0385338
\(466\) 79.7547 3.69456
\(467\) −5.90578 −0.273287 −0.136643 0.990620i \(-0.543631\pi\)
−0.136643 + 0.990620i \(0.543631\pi\)
\(468\) 0 0
\(469\) 35.5138 1.63988
\(470\) −60.8298 −2.80587
\(471\) 7.28502 0.335676
\(472\) −36.0166 −1.65780
\(473\) 6.24920 0.287338
\(474\) −24.1849 −1.11085
\(475\) 0.0532243 0.00244210
\(476\) −58.9340 −2.70123
\(477\) −18.7546 −0.858713
\(478\) 2.32363 0.106281
\(479\) −5.29228 −0.241811 −0.120905 0.992664i \(-0.538580\pi\)
−0.120905 + 0.992664i \(0.538580\pi\)
\(480\) 65.3668 2.98357
\(481\) 0 0
\(482\) −18.2932 −0.833234
\(483\) 14.9830 0.681752
\(484\) 5.32282 0.241946
\(485\) −31.3890 −1.42530
\(486\) 43.6168 1.97850
\(487\) 15.4866 0.701763 0.350881 0.936420i \(-0.385882\pi\)
0.350881 + 0.936420i \(0.385882\pi\)
\(488\) −56.9173 −2.57653
\(489\) −0.403558 −0.0182495
\(490\) 83.6305 3.77804
\(491\) −31.9189 −1.44048 −0.720240 0.693725i \(-0.755968\pi\)
−0.720240 + 0.693725i \(0.755968\pi\)
\(492\) 33.6796 1.51839
\(493\) 17.0560 0.768162
\(494\) 0 0
\(495\) 7.42419 0.333692
\(496\) −3.31506 −0.148851
\(497\) 31.7819 1.42561
\(498\) −1.42151 −0.0636994
\(499\) 5.83312 0.261126 0.130563 0.991440i \(-0.458321\pi\)
0.130563 + 0.991440i \(0.458321\pi\)
\(500\) 52.5792 2.35141
\(501\) 15.3228 0.684573
\(502\) 65.2517 2.91233
\(503\) 0.285275 0.0127198 0.00635990 0.999980i \(-0.497976\pi\)
0.00635990 + 0.999980i \(0.497976\pi\)
\(504\) 73.9171 3.29253
\(505\) −2.37528 −0.105699
\(506\) 10.6736 0.474500
\(507\) 0 0
\(508\) 69.8821 3.10052
\(509\) −34.6860 −1.53743 −0.768714 0.639592i \(-0.779103\pi\)
−0.768714 + 0.639592i \(0.779103\pi\)
\(510\) 25.9826 1.15053
\(511\) 0.658173 0.0291159
\(512\) 14.6475 0.647332
\(513\) −0.0334226 −0.00147564
\(514\) 32.0834 1.41514
\(515\) −51.4180 −2.26575
\(516\) −31.9401 −1.40608
\(517\) 6.29173 0.276710
\(518\) 8.58261 0.377098
\(519\) −1.38005 −0.0605775
\(520\) 0 0
\(521\) 36.6073 1.60379 0.801897 0.597463i \(-0.203824\pi\)
0.801897 + 0.597463i \(0.203824\pi\)
\(522\) −34.2682 −1.49988
\(523\) −1.29679 −0.0567048 −0.0283524 0.999598i \(-0.509026\pi\)
−0.0283524 + 0.999598i \(0.509026\pi\)
\(524\) 88.1303 3.84999
\(525\) −29.4957 −1.28730
\(526\) 31.2874 1.36420
\(527\) −0.677888 −0.0295293
\(528\) −13.1423 −0.571943
\(529\) −7.44230 −0.323578
\(530\) 87.2593 3.79030
\(531\) 8.32337 0.361203
\(532\) −0.144337 −0.00625781
\(533\) 0 0
\(534\) −44.3441 −1.91896
\(535\) 25.4252 1.09923
\(536\) −80.7208 −3.48661
\(537\) 16.1606 0.697383
\(538\) 65.1268 2.80781
\(539\) −8.65004 −0.372584
\(540\) −92.7277 −3.99037
\(541\) 23.0243 0.989893 0.494947 0.868923i \(-0.335188\pi\)
0.494947 + 0.868923i \(0.335188\pi\)
\(542\) −50.4980 −2.16907
\(543\) 4.66152 0.200045
\(544\) 53.3270 2.28637
\(545\) 27.7598 1.18910
\(546\) 0 0
\(547\) 16.9199 0.723441 0.361721 0.932287i \(-0.382189\pi\)
0.361721 + 0.932287i \(0.382189\pi\)
\(548\) 95.4878 4.07904
\(549\) 13.1535 0.561377
\(550\) −21.0121 −0.895960
\(551\) 0.0417724 0.00177956
\(552\) −34.0556 −1.44950
\(553\) 36.8208 1.56578
\(554\) 1.10345 0.0468811
\(555\) −2.75042 −0.116749
\(556\) 43.6850 1.85266
\(557\) 9.45511 0.400626 0.200313 0.979732i \(-0.435804\pi\)
0.200313 + 0.979732i \(0.435804\pi\)
\(558\) 1.36199 0.0576574
\(559\) 0 0
\(560\) −193.448 −8.17469
\(561\) −2.68742 −0.113463
\(562\) 82.7178 3.48924
\(563\) −41.4269 −1.74593 −0.872967 0.487779i \(-0.837807\pi\)
−0.872967 + 0.487779i \(0.837807\pi\)
\(564\) −32.1574 −1.35407
\(565\) −48.1071 −2.02388
\(566\) 39.4997 1.66029
\(567\) −6.13955 −0.257837
\(568\) −72.2383 −3.03105
\(569\) −9.18281 −0.384963 −0.192482 0.981301i \(-0.561654\pi\)
−0.192482 + 0.981301i \(0.561654\pi\)
\(570\) 0.0636349 0.00266537
\(571\) −17.2362 −0.721311 −0.360655 0.932699i \(-0.617447\pi\)
−0.360655 + 0.932699i \(0.617447\pi\)
\(572\) 0 0
\(573\) 11.1060 0.463961
\(574\) −70.5427 −2.94440
\(575\) −30.6269 −1.27723
\(576\) −50.2607 −2.09420
\(577\) 23.4108 0.974603 0.487301 0.873234i \(-0.337981\pi\)
0.487301 + 0.873234i \(0.337981\pi\)
\(578\) −24.8063 −1.03181
\(579\) −25.9214 −1.07726
\(580\) 115.893 4.81221
\(581\) 2.16421 0.0897864
\(582\) −22.8286 −0.946276
\(583\) −9.02538 −0.373793
\(584\) −1.49599 −0.0619044
\(585\) 0 0
\(586\) 78.7743 3.25414
\(587\) 23.3954 0.965633 0.482817 0.875721i \(-0.339614\pi\)
0.482817 + 0.875721i \(0.339614\pi\)
\(588\) 44.2109 1.82323
\(589\) −0.00166024 −6.84090e−5 0
\(590\) −38.7261 −1.59433
\(591\) −16.0780 −0.661359
\(592\) −10.9729 −0.450985
\(593\) 37.8389 1.55386 0.776929 0.629588i \(-0.216776\pi\)
0.776929 + 0.629588i \(0.216776\pi\)
\(594\) 13.1947 0.541386
\(595\) −39.5577 −1.62171
\(596\) −32.0444 −1.31259
\(597\) 23.4212 0.958566
\(598\) 0 0
\(599\) 24.6076 1.00544 0.502720 0.864449i \(-0.332333\pi\)
0.502720 + 0.864449i \(0.332333\pi\)
\(600\) 67.0419 2.73697
\(601\) 31.6065 1.28926 0.644628 0.764496i \(-0.277012\pi\)
0.644628 + 0.764496i \(0.277012\pi\)
\(602\) 66.8992 2.72661
\(603\) 18.6544 0.759666
\(604\) 50.7269 2.06405
\(605\) 3.57279 0.145254
\(606\) −1.72750 −0.0701747
\(607\) 4.05847 0.164728 0.0823640 0.996602i \(-0.473753\pi\)
0.0823640 + 0.996602i \(0.473753\pi\)
\(608\) 0.130605 0.00529673
\(609\) −23.1493 −0.938056
\(610\) −61.1991 −2.47788
\(611\) 0 0
\(612\) −30.9563 −1.25134
\(613\) −30.8970 −1.24792 −0.623959 0.781457i \(-0.714477\pi\)
−0.623959 + 0.781457i \(0.714477\pi\)
\(614\) −66.0822 −2.66686
\(615\) 22.6064 0.911580
\(616\) 35.5716 1.43322
\(617\) 33.9704 1.36759 0.683797 0.729672i \(-0.260327\pi\)
0.683797 + 0.729672i \(0.260327\pi\)
\(618\) −37.3953 −1.50426
\(619\) 10.1642 0.408535 0.204267 0.978915i \(-0.434519\pi\)
0.204267 + 0.978915i \(0.434519\pi\)
\(620\) −4.60617 −0.184988
\(621\) 19.2324 0.771770
\(622\) 71.2970 2.85875
\(623\) 67.5126 2.70484
\(624\) 0 0
\(625\) −3.53176 −0.141271
\(626\) −79.1877 −3.16498
\(627\) −0.00658186 −0.000262854 0
\(628\) 40.3834 1.61147
\(629\) −2.24383 −0.0894672
\(630\) 79.4778 3.16647
\(631\) −0.696721 −0.0277360 −0.0138680 0.999904i \(-0.504414\pi\)
−0.0138680 + 0.999904i \(0.504414\pi\)
\(632\) −83.6915 −3.32907
\(633\) 20.1398 0.800485
\(634\) 43.8380 1.74103
\(635\) 46.9063 1.86142
\(636\) 46.1293 1.82914
\(637\) 0 0
\(638\) −16.4911 −0.652888
\(639\) 16.6941 0.660410
\(640\) 97.6979 3.86185
\(641\) −40.2357 −1.58922 −0.794608 0.607123i \(-0.792323\pi\)
−0.794608 + 0.607123i \(0.792323\pi\)
\(642\) 18.4912 0.729790
\(643\) 17.1540 0.676486 0.338243 0.941059i \(-0.390167\pi\)
0.338243 + 0.941059i \(0.390167\pi\)
\(644\) 83.0562 3.27287
\(645\) −21.4388 −0.844154
\(646\) 0.0519140 0.00204253
\(647\) −27.6409 −1.08668 −0.543338 0.839514i \(-0.682840\pi\)
−0.543338 + 0.839514i \(0.682840\pi\)
\(648\) 13.9548 0.548197
\(649\) 4.00551 0.157230
\(650\) 0 0
\(651\) 0.920066 0.0360602
\(652\) −2.23706 −0.0876101
\(653\) −31.7645 −1.24304 −0.621520 0.783398i \(-0.713485\pi\)
−0.621520 + 0.783398i \(0.713485\pi\)
\(654\) 20.1891 0.789458
\(655\) 59.1549 2.31138
\(656\) 90.1894 3.52131
\(657\) 0.345720 0.0134878
\(658\) 67.3546 2.62575
\(659\) 23.2018 0.903813 0.451907 0.892065i \(-0.350744\pi\)
0.451907 + 0.892065i \(0.350744\pi\)
\(660\) −18.2607 −0.710799
\(661\) −31.7645 −1.23550 −0.617749 0.786376i \(-0.711955\pi\)
−0.617749 + 0.786376i \(0.711955\pi\)
\(662\) −25.4661 −0.989770
\(663\) 0 0
\(664\) −4.91911 −0.190898
\(665\) −0.0968822 −0.00375693
\(666\) 4.50820 0.174689
\(667\) −24.0371 −0.930722
\(668\) 84.9396 3.28641
\(669\) 2.07412 0.0801899
\(670\) −86.7933 −3.35312
\(671\) 6.32993 0.244364
\(672\) −72.3782 −2.79205
\(673\) −17.8907 −0.689635 −0.344817 0.938670i \(-0.612059\pi\)
−0.344817 + 0.938670i \(0.612059\pi\)
\(674\) −93.2573 −3.59214
\(675\) −37.8610 −1.45727
\(676\) 0 0
\(677\) 6.49534 0.249636 0.124818 0.992180i \(-0.460165\pi\)
0.124818 + 0.992180i \(0.460165\pi\)
\(678\) −34.9874 −1.34368
\(679\) 34.7559 1.33381
\(680\) 89.9123 3.44798
\(681\) 18.3034 0.701388
\(682\) 0.655437 0.0250980
\(683\) −18.8733 −0.722169 −0.361084 0.932533i \(-0.617593\pi\)
−0.361084 + 0.932533i \(0.617593\pi\)
\(684\) −0.0758162 −0.00289891
\(685\) 64.0934 2.44888
\(686\) −17.6641 −0.674418
\(687\) −17.9612 −0.685264
\(688\) −85.5312 −3.26085
\(689\) 0 0
\(690\) −36.6175 −1.39400
\(691\) −15.6086 −0.593781 −0.296890 0.954912i \(-0.595950\pi\)
−0.296890 + 0.954912i \(0.595950\pi\)
\(692\) −7.65010 −0.290813
\(693\) −8.22052 −0.312272
\(694\) −47.0284 −1.78517
\(695\) 29.3223 1.11226
\(696\) 52.6169 1.99444
\(697\) 18.4426 0.698563
\(698\) −4.75092 −0.179825
\(699\) 28.3000 1.07041
\(700\) −163.505 −6.17990
\(701\) −28.0280 −1.05860 −0.529301 0.848434i \(-0.677546\pi\)
−0.529301 + 0.848434i \(0.677546\pi\)
\(702\) 0 0
\(703\) −0.00549543 −0.000207264 0
\(704\) −24.1873 −0.911593
\(705\) −21.5848 −0.812929
\(706\) 24.7054 0.929800
\(707\) 2.63006 0.0989136
\(708\) −20.4724 −0.769400
\(709\) −23.0101 −0.864161 −0.432081 0.901835i \(-0.642220\pi\)
−0.432081 + 0.901835i \(0.642220\pi\)
\(710\) −77.6727 −2.91501
\(711\) 19.3409 0.725342
\(712\) −153.452 −5.75086
\(713\) 0.955354 0.0357783
\(714\) −28.7695 −1.07667
\(715\) 0 0
\(716\) 89.5839 3.34791
\(717\) 0.824515 0.0307921
\(718\) 15.0635 0.562165
\(719\) −10.3567 −0.386239 −0.193120 0.981175i \(-0.561861\pi\)
−0.193120 + 0.981175i \(0.561861\pi\)
\(720\) −101.613 −3.78689
\(721\) 56.9332 2.12030
\(722\) −51.4152 −1.91348
\(723\) −6.49114 −0.241408
\(724\) 25.8404 0.960351
\(725\) 47.3196 1.75741
\(726\) 2.59842 0.0964363
\(727\) 4.61443 0.171140 0.0855699 0.996332i \(-0.472729\pi\)
0.0855699 + 0.996332i \(0.472729\pi\)
\(728\) 0 0
\(729\) 10.8210 0.400779
\(730\) −1.60853 −0.0595343
\(731\) −17.4900 −0.646892
\(732\) −32.3527 −1.19579
\(733\) 18.5479 0.685081 0.342541 0.939503i \(-0.388713\pi\)
0.342541 + 0.939503i \(0.388713\pi\)
\(734\) −29.2391 −1.07924
\(735\) 29.6753 1.09459
\(736\) −75.1542 −2.77022
\(737\) 8.97718 0.330679
\(738\) −37.0541 −1.36398
\(739\) −11.4875 −0.422573 −0.211286 0.977424i \(-0.567765\pi\)
−0.211286 + 0.977424i \(0.567765\pi\)
\(740\) −15.2465 −0.560474
\(741\) 0 0
\(742\) −96.6189 −3.54699
\(743\) −6.95186 −0.255039 −0.127519 0.991836i \(-0.540702\pi\)
−0.127519 + 0.991836i \(0.540702\pi\)
\(744\) −2.09125 −0.0766691
\(745\) −21.5089 −0.788023
\(746\) 10.0645 0.368487
\(747\) 1.13680 0.0415932
\(748\) −14.8973 −0.544700
\(749\) −28.1523 −1.02866
\(750\) 25.6674 0.937240
\(751\) 9.67208 0.352939 0.176470 0.984306i \(-0.443532\pi\)
0.176470 + 0.984306i \(0.443532\pi\)
\(752\) −86.1133 −3.14023
\(753\) 23.1538 0.843772
\(754\) 0 0
\(755\) 34.0490 1.23917
\(756\) 102.674 3.73421
\(757\) −6.61489 −0.240422 −0.120211 0.992748i \(-0.538357\pi\)
−0.120211 + 0.992748i \(0.538357\pi\)
\(758\) −17.5712 −0.638217
\(759\) 3.78741 0.137474
\(760\) 0.220207 0.00798776
\(761\) 22.0974 0.801031 0.400515 0.916290i \(-0.368831\pi\)
0.400515 + 0.916290i \(0.368831\pi\)
\(762\) 34.1140 1.23582
\(763\) −30.7374 −1.11277
\(764\) 61.5646 2.22733
\(765\) −20.7786 −0.751250
\(766\) −11.2529 −0.406585
\(767\) 0 0
\(768\) 24.6036 0.887806
\(769\) −2.23113 −0.0804564 −0.0402282 0.999191i \(-0.512808\pi\)
−0.0402282 + 0.999191i \(0.512808\pi\)
\(770\) 38.2476 1.37835
\(771\) 11.3844 0.410000
\(772\) −143.691 −5.17157
\(773\) 11.1675 0.401667 0.200833 0.979625i \(-0.435635\pi\)
0.200833 + 0.979625i \(0.435635\pi\)
\(774\) 35.1403 1.26309
\(775\) −1.88071 −0.0675572
\(776\) −78.9980 −2.83586
\(777\) 3.04544 0.109255
\(778\) 33.9875 1.21851
\(779\) 0.0451684 0.00161832
\(780\) 0 0
\(781\) 8.03382 0.287473
\(782\) −29.8730 −1.06825
\(783\) −29.7147 −1.06192
\(784\) 118.391 4.22825
\(785\) 27.1062 0.967461
\(786\) 43.0222 1.53455
\(787\) 14.6600 0.522572 0.261286 0.965261i \(-0.415853\pi\)
0.261286 + 0.965261i \(0.415853\pi\)
\(788\) −89.1257 −3.17497
\(789\) 11.1020 0.395241
\(790\) −89.9875 −3.20161
\(791\) 53.2672 1.89396
\(792\) 18.6847 0.663934
\(793\) 0 0
\(794\) −48.9655 −1.73772
\(795\) 30.9629 1.09814
\(796\) 129.832 4.60176
\(797\) 0.631320 0.0223625 0.0111813 0.999937i \(-0.496441\pi\)
0.0111813 + 0.999937i \(0.496441\pi\)
\(798\) −0.0704605 −0.00249427
\(799\) −17.6091 −0.622964
\(800\) 147.949 5.23078
\(801\) 35.4625 1.25300
\(802\) 21.8763 0.772479
\(803\) 0.166373 0.00587117
\(804\) −45.8829 −1.61817
\(805\) 55.7491 1.96490
\(806\) 0 0
\(807\) 23.1095 0.813492
\(808\) −5.97797 −0.210304
\(809\) 6.32576 0.222402 0.111201 0.993798i \(-0.464530\pi\)
0.111201 + 0.993798i \(0.464530\pi\)
\(810\) 15.0046 0.527208
\(811\) 51.1786 1.79712 0.898562 0.438846i \(-0.144613\pi\)
0.898562 + 0.438846i \(0.144613\pi\)
\(812\) −128.324 −4.50331
\(813\) −17.9186 −0.628433
\(814\) 2.16951 0.0760413
\(815\) −1.50156 −0.0525975
\(816\) 36.7821 1.28763
\(817\) −0.0428355 −0.00149862
\(818\) 51.2371 1.79146
\(819\) 0 0
\(820\) 125.315 4.37620
\(821\) −16.8298 −0.587364 −0.293682 0.955903i \(-0.594881\pi\)
−0.293682 + 0.955903i \(0.594881\pi\)
\(822\) 46.6139 1.62585
\(823\) 52.7955 1.84034 0.920168 0.391524i \(-0.128052\pi\)
0.920168 + 0.391524i \(0.128052\pi\)
\(824\) −129.406 −4.50806
\(825\) −7.45591 −0.259581
\(826\) 42.8799 1.49198
\(827\) −8.61118 −0.299440 −0.149720 0.988728i \(-0.547837\pi\)
−0.149720 + 0.988728i \(0.547837\pi\)
\(828\) 43.6271 1.51615
\(829\) 11.2584 0.391021 0.195510 0.980702i \(-0.437364\pi\)
0.195510 + 0.980702i \(0.437364\pi\)
\(830\) −5.28917 −0.183590
\(831\) 0.391547 0.0135826
\(832\) 0 0
\(833\) 24.2094 0.838807
\(834\) 21.3255 0.738442
\(835\) 57.0132 1.97302
\(836\) −0.0364855 −0.00126188
\(837\) 1.18101 0.0408216
\(838\) −60.2987 −2.08298
\(839\) −8.76246 −0.302514 −0.151257 0.988494i \(-0.548332\pi\)
−0.151257 + 0.988494i \(0.548332\pi\)
\(840\) −122.034 −4.21057
\(841\) 8.13815 0.280626
\(842\) −45.7051 −1.57510
\(843\) 29.3515 1.01092
\(844\) 111.642 3.84287
\(845\) 0 0
\(846\) 35.3794 1.21637
\(847\) −3.95601 −0.135930
\(848\) 123.528 4.24197
\(849\) 14.0160 0.481028
\(850\) 58.8080 2.01710
\(851\) 3.16224 0.108400
\(852\) −41.0614 −1.40674
\(853\) −21.4641 −0.734917 −0.367458 0.930040i \(-0.619772\pi\)
−0.367458 + 0.930040i \(0.619772\pi\)
\(854\) 67.7635 2.31882
\(855\) −0.0508895 −0.00174038
\(856\) 63.9885 2.18708
\(857\) −28.8303 −0.984823 −0.492412 0.870362i \(-0.663885\pi\)
−0.492412 + 0.870362i \(0.663885\pi\)
\(858\) 0 0
\(859\) −13.5007 −0.460639 −0.230320 0.973115i \(-0.573977\pi\)
−0.230320 + 0.973115i \(0.573977\pi\)
\(860\) −118.843 −4.05251
\(861\) −25.0313 −0.853063
\(862\) 34.7665 1.18415
\(863\) 37.4769 1.27573 0.637864 0.770149i \(-0.279818\pi\)
0.637864 + 0.770149i \(0.279818\pi\)
\(864\) −92.9055 −3.16071
\(865\) −5.13491 −0.174592
\(866\) 33.3277 1.13252
\(867\) −8.80224 −0.298940
\(868\) 5.10024 0.173114
\(869\) 9.30756 0.315737
\(870\) 56.5752 1.91808
\(871\) 0 0
\(872\) 69.8642 2.36590
\(873\) 18.2563 0.617881
\(874\) −0.0731629 −0.00247477
\(875\) −39.0778 −1.32107
\(876\) −0.850342 −0.0287304
\(877\) 9.81599 0.331462 0.165731 0.986171i \(-0.447002\pi\)
0.165731 + 0.986171i \(0.447002\pi\)
\(878\) −15.6811 −0.529213
\(879\) 27.9522 0.942803
\(880\) −48.8998 −1.64841
\(881\) 37.2709 1.25569 0.627844 0.778339i \(-0.283938\pi\)
0.627844 + 0.778339i \(0.283938\pi\)
\(882\) −48.6406 −1.63781
\(883\) −36.1317 −1.21593 −0.607964 0.793965i \(-0.708013\pi\)
−0.607964 + 0.793965i \(0.708013\pi\)
\(884\) 0 0
\(885\) −13.7415 −0.461916
\(886\) −70.3536 −2.36358
\(887\) −50.2943 −1.68872 −0.844358 0.535779i \(-0.820018\pi\)
−0.844358 + 0.535779i \(0.820018\pi\)
\(888\) −6.92210 −0.232291
\(889\) −51.9376 −1.74193
\(890\) −164.996 −5.53068
\(891\) −1.55195 −0.0519924
\(892\) 11.4975 0.384966
\(893\) −0.0431270 −0.00144319
\(894\) −15.6430 −0.523179
\(895\) 60.1306 2.00994
\(896\) −108.177 −3.61395
\(897\) 0 0
\(898\) −64.5952 −2.15557
\(899\) −1.47605 −0.0492291
\(900\) −85.8844 −2.86281
\(901\) 25.2599 0.841529
\(902\) −17.8318 −0.593733
\(903\) 23.7384 0.789965
\(904\) −121.073 −4.02683
\(905\) 17.3446 0.576555
\(906\) 24.7631 0.822700
\(907\) −12.9985 −0.431609 −0.215805 0.976437i \(-0.569237\pi\)
−0.215805 + 0.976437i \(0.569237\pi\)
\(908\) 101.462 3.36714
\(909\) 1.38150 0.0458213
\(910\) 0 0
\(911\) 44.3455 1.46923 0.734616 0.678483i \(-0.237362\pi\)
0.734616 + 0.678483i \(0.237362\pi\)
\(912\) 0.0900843 0.00298299
\(913\) 0.547068 0.0181053
\(914\) −18.0582 −0.597312
\(915\) −21.7158 −0.717902
\(916\) −99.5653 −3.28973
\(917\) −65.5000 −2.16300
\(918\) −36.9289 −1.21884
\(919\) −47.6103 −1.57052 −0.785260 0.619167i \(-0.787471\pi\)
−0.785260 + 0.619167i \(0.787471\pi\)
\(920\) −126.714 −4.17764
\(921\) −23.4485 −0.772654
\(922\) −44.2148 −1.45614
\(923\) 0 0
\(924\) 20.2194 0.665171
\(925\) −6.22520 −0.204683
\(926\) −84.9032 −2.79009
\(927\) 29.9054 0.982222
\(928\) 116.116 3.81168
\(929\) −33.0705 −1.08501 −0.542503 0.840054i \(-0.682523\pi\)
−0.542503 + 0.840054i \(0.682523\pi\)
\(930\) −2.24858 −0.0737337
\(931\) 0.0592921 0.00194322
\(932\) 156.877 5.13867
\(933\) 25.2989 0.828249
\(934\) −15.9815 −0.522929
\(935\) −9.99939 −0.327015
\(936\) 0 0
\(937\) −43.8560 −1.43271 −0.716356 0.697735i \(-0.754191\pi\)
−0.716356 + 0.697735i \(0.754191\pi\)
\(938\) 96.1029 3.13787
\(939\) −28.0989 −0.916971
\(940\) −119.652 −3.90261
\(941\) 27.1576 0.885313 0.442657 0.896691i \(-0.354036\pi\)
0.442657 + 0.896691i \(0.354036\pi\)
\(942\) 19.7138 0.642310
\(943\) −25.9913 −0.846393
\(944\) −54.8223 −1.78432
\(945\) 68.9169 2.24187
\(946\) 16.9108 0.549817
\(947\) 24.4338 0.793991 0.396996 0.917821i \(-0.370053\pi\)
0.396996 + 0.917821i \(0.370053\pi\)
\(948\) −47.5715 −1.54505
\(949\) 0 0
\(950\) 0.144029 0.00467291
\(951\) 15.5554 0.504418
\(952\) −99.5565 −3.22665
\(953\) −0.830376 −0.0268985 −0.0134493 0.999910i \(-0.504281\pi\)
−0.0134493 + 0.999910i \(0.504281\pi\)
\(954\) −50.7512 −1.64313
\(955\) 41.3234 1.33720
\(956\) 4.57057 0.147823
\(957\) −5.85167 −0.189158
\(958\) −14.3213 −0.462700
\(959\) −70.9682 −2.29168
\(960\) 82.9782 2.67811
\(961\) −30.9413 −0.998108
\(962\) 0 0
\(963\) −14.7876 −0.476524
\(964\) −35.9826 −1.15892
\(965\) −96.4487 −3.10479
\(966\) 40.5452 1.30452
\(967\) −3.68739 −0.118578 −0.0592892 0.998241i \(-0.518883\pi\)
−0.0592892 + 0.998241i \(0.518883\pi\)
\(968\) 8.99178 0.289007
\(969\) 0.0184211 0.000591771 0
\(970\) −84.9409 −2.72729
\(971\) −10.8602 −0.348520 −0.174260 0.984700i \(-0.555753\pi\)
−0.174260 + 0.984700i \(0.555753\pi\)
\(972\) 85.7938 2.75184
\(973\) −32.4675 −1.04086
\(974\) 41.9077 1.34281
\(975\) 0 0
\(976\) −86.6361 −2.77316
\(977\) −30.9277 −0.989466 −0.494733 0.869045i \(-0.664734\pi\)
−0.494733 + 0.869045i \(0.664734\pi\)
\(978\) −1.09206 −0.0349201
\(979\) 17.0658 0.545426
\(980\) 164.500 5.25477
\(981\) −16.1455 −0.515485
\(982\) −86.3748 −2.75633
\(983\) −12.9691 −0.413650 −0.206825 0.978378i \(-0.566313\pi\)
−0.206825 + 0.978378i \(0.566313\pi\)
\(984\) 56.8946 1.81373
\(985\) −59.8230 −1.90612
\(986\) 46.1547 1.46986
\(987\) 23.9000 0.760745
\(988\) 0 0
\(989\) 24.6489 0.783789
\(990\) 20.0904 0.638514
\(991\) 5.95855 0.189279 0.0946397 0.995512i \(-0.469830\pi\)
0.0946397 + 0.995512i \(0.469830\pi\)
\(992\) −4.61500 −0.146527
\(993\) −9.03637 −0.286761
\(994\) 86.0041 2.72788
\(995\) 87.1458 2.76271
\(996\) −2.79610 −0.0885977
\(997\) −6.47004 −0.204908 −0.102454 0.994738i \(-0.532669\pi\)
−0.102454 + 0.994738i \(0.532669\pi\)
\(998\) 15.7848 0.499660
\(999\) 3.90916 0.123680
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 1859.2.a.s.1.20 21
13.12 even 2 1859.2.a.t.1.2 yes 21
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.2.a.s.1.20 21 1.1 even 1 trivial
1859.2.a.t.1.2 yes 21 13.12 even 2