Properties

Label 6017.2.a.f.1.9
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 1.9
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.57735 q^{2} -3.20978 q^{3} +4.64274 q^{4} +2.33292 q^{5} +8.27272 q^{6} +1.38140 q^{7} -6.81126 q^{8} +7.30267 q^{9} +O(q^{10})\) \(q-2.57735 q^{2} -3.20978 q^{3} +4.64274 q^{4} +2.33292 q^{5} +8.27272 q^{6} +1.38140 q^{7} -6.81126 q^{8} +7.30267 q^{9} -6.01276 q^{10} -1.00000 q^{11} -14.9022 q^{12} +0.769601 q^{13} -3.56035 q^{14} -7.48817 q^{15} +8.26953 q^{16} +6.58139 q^{17} -18.8216 q^{18} +5.77216 q^{19} +10.8311 q^{20} -4.43399 q^{21} +2.57735 q^{22} +3.17024 q^{23} +21.8626 q^{24} +0.442533 q^{25} -1.98353 q^{26} -13.8106 q^{27} +6.41348 q^{28} -8.93163 q^{29} +19.2996 q^{30} +1.12347 q^{31} -7.69095 q^{32} +3.20978 q^{33} -16.9626 q^{34} +3.22270 q^{35} +33.9044 q^{36} -1.89906 q^{37} -14.8769 q^{38} -2.47025 q^{39} -15.8901 q^{40} -9.43805 q^{41} +11.4279 q^{42} +9.02537 q^{43} -4.64274 q^{44} +17.0366 q^{45} -8.17081 q^{46} +10.6335 q^{47} -26.5433 q^{48} -5.09173 q^{49} -1.14056 q^{50} -21.1248 q^{51} +3.57306 q^{52} +6.21181 q^{53} +35.5948 q^{54} -2.33292 q^{55} -9.40907 q^{56} -18.5273 q^{57} +23.0199 q^{58} +0.0178386 q^{59} -34.7656 q^{60} -3.23513 q^{61} -2.89559 q^{62} +10.0879 q^{63} +3.28323 q^{64} +1.79542 q^{65} -8.27272 q^{66} -2.98653 q^{67} +30.5557 q^{68} -10.1758 q^{69} -8.30603 q^{70} -0.135869 q^{71} -49.7404 q^{72} +2.06341 q^{73} +4.89454 q^{74} -1.42043 q^{75} +26.7986 q^{76} -1.38140 q^{77} +6.36670 q^{78} +14.0930 q^{79} +19.2922 q^{80} +22.4210 q^{81} +24.3252 q^{82} +0.342920 q^{83} -20.5858 q^{84} +15.3539 q^{85} -23.2615 q^{86} +28.6685 q^{87} +6.81126 q^{88} +11.2035 q^{89} -43.9092 q^{90} +1.06313 q^{91} +14.7186 q^{92} -3.60610 q^{93} -27.4063 q^{94} +13.4660 q^{95} +24.6863 q^{96} +18.0597 q^{97} +13.1232 q^{98} -7.30267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + O(q^{10}) \) \( 121q + 2q^{2} + 18q^{3} + 138q^{4} + 13q^{5} + 10q^{6} + 56q^{7} + 12q^{8} + 143q^{9} + 20q^{10} - 121q^{11} + 40q^{12} + 31q^{13} + 7q^{14} + 53q^{15} + 164q^{16} - 23q^{17} + 14q^{18} + 62q^{19} + 53q^{20} + 19q^{21} - 2q^{22} + 34q^{23} + 34q^{24} + 172q^{25} + 34q^{26} + 87q^{27} + 91q^{28} - 30q^{29} + 2q^{30} + 102q^{31} + 31q^{32} - 18q^{33} + 30q^{34} + 20q^{35} + 164q^{36} + 58q^{37} + 35q^{38} + 42q^{39} + 52q^{40} - 12q^{41} + 56q^{42} + 96q^{43} - 138q^{44} + 72q^{45} + 48q^{46} + 136q^{47} + 99q^{48} + 199q^{49} - 7q^{50} + 22q^{51} + 81q^{52} + 24q^{53} + 37q^{54} - 13q^{55} + 28q^{56} + 25q^{57} + 76q^{58} + 58q^{59} + 81q^{60} + 14q^{61} - 2q^{62} + 152q^{63} + 236q^{64} - 29q^{65} - 10q^{66} + 112q^{67} - 61q^{68} + 41q^{69} + 105q^{70} + 56q^{71} + 71q^{72} + 113q^{73} - 23q^{74} + 111q^{75} + 144q^{76} - 56q^{77} + 59q^{78} + 80q^{79} + 100q^{80} + 177q^{81} + 123q^{82} + 6q^{83} + 79q^{84} + 26q^{85} + 14q^{86} + 180q^{87} - 12q^{88} + 26q^{89} + 75q^{90} + 72q^{91} + 58q^{92} + 139q^{93} + 37q^{94} + 39q^{95} + 66q^{96} + 136q^{97} + 7q^{98} - 143q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57735 −1.82246 −0.911231 0.411896i \(-0.864867\pi\)
−0.911231 + 0.411896i \(0.864867\pi\)
\(3\) −3.20978 −1.85317 −0.926583 0.376090i \(-0.877268\pi\)
−0.926583 + 0.376090i \(0.877268\pi\)
\(4\) 4.64274 2.32137
\(5\) 2.33292 1.04332 0.521658 0.853155i \(-0.325314\pi\)
0.521658 + 0.853155i \(0.325314\pi\)
\(6\) 8.27272 3.37733
\(7\) 1.38140 0.522120 0.261060 0.965323i \(-0.415928\pi\)
0.261060 + 0.965323i \(0.415928\pi\)
\(8\) −6.81126 −2.40814
\(9\) 7.30267 2.43422
\(10\) −6.01276 −1.90140
\(11\) −1.00000 −0.301511
\(12\) −14.9022 −4.30188
\(13\) 0.769601 0.213449 0.106725 0.994289i \(-0.465964\pi\)
0.106725 + 0.994289i \(0.465964\pi\)
\(14\) −3.56035 −0.951544
\(15\) −7.48817 −1.93344
\(16\) 8.26953 2.06738
\(17\) 6.58139 1.59622 0.798111 0.602510i \(-0.205833\pi\)
0.798111 + 0.602510i \(0.205833\pi\)
\(18\) −18.8216 −4.43628
\(19\) 5.77216 1.32422 0.662112 0.749405i \(-0.269660\pi\)
0.662112 + 0.749405i \(0.269660\pi\)
\(20\) 10.8311 2.42192
\(21\) −4.43399 −0.967576
\(22\) 2.57735 0.549493
\(23\) 3.17024 0.661040 0.330520 0.943799i \(-0.392776\pi\)
0.330520 + 0.943799i \(0.392776\pi\)
\(24\) 21.8626 4.46269
\(25\) 0.442533 0.0885066
\(26\) −1.98353 −0.389003
\(27\) −13.8106 −2.65786
\(28\) 6.41348 1.21203
\(29\) −8.93163 −1.65856 −0.829281 0.558832i \(-0.811250\pi\)
−0.829281 + 0.558832i \(0.811250\pi\)
\(30\) 19.2996 3.52361
\(31\) 1.12347 0.201782 0.100891 0.994897i \(-0.467831\pi\)
0.100891 + 0.994897i \(0.467831\pi\)
\(32\) −7.69095 −1.35958
\(33\) 3.20978 0.558751
\(34\) −16.9626 −2.90905
\(35\) 3.22270 0.544736
\(36\) 33.9044 5.65073
\(37\) −1.89906 −0.312203 −0.156102 0.987741i \(-0.549893\pi\)
−0.156102 + 0.987741i \(0.549893\pi\)
\(38\) −14.8769 −2.41335
\(39\) −2.47025 −0.395557
\(40\) −15.8901 −2.51245
\(41\) −9.43805 −1.47398 −0.736988 0.675906i \(-0.763753\pi\)
−0.736988 + 0.675906i \(0.763753\pi\)
\(42\) 11.4279 1.76337
\(43\) 9.02537 1.37636 0.688178 0.725542i \(-0.258411\pi\)
0.688178 + 0.725542i \(0.258411\pi\)
\(44\) −4.64274 −0.699919
\(45\) 17.0366 2.53966
\(46\) −8.17081 −1.20472
\(47\) 10.6335 1.55106 0.775530 0.631311i \(-0.217483\pi\)
0.775530 + 0.631311i \(0.217483\pi\)
\(48\) −26.5433 −3.83120
\(49\) −5.09173 −0.727390
\(50\) −1.14056 −0.161300
\(51\) −21.1248 −2.95806
\(52\) 3.57306 0.495494
\(53\) 6.21181 0.853258 0.426629 0.904427i \(-0.359701\pi\)
0.426629 + 0.904427i \(0.359701\pi\)
\(54\) 35.5948 4.84384
\(55\) −2.33292 −0.314571
\(56\) −9.40907 −1.25734
\(57\) −18.5273 −2.45401
\(58\) 23.0199 3.02267
\(59\) 0.0178386 0.00232238 0.00116119 0.999999i \(-0.499630\pi\)
0.00116119 + 0.999999i \(0.499630\pi\)
\(60\) −34.7656 −4.48822
\(61\) −3.23513 −0.414216 −0.207108 0.978318i \(-0.566405\pi\)
−0.207108 + 0.978318i \(0.566405\pi\)
\(62\) −2.89559 −0.367740
\(63\) 10.0879 1.27096
\(64\) 3.28323 0.410404
\(65\) 1.79542 0.222695
\(66\) −8.27272 −1.01830
\(67\) −2.98653 −0.364862 −0.182431 0.983219i \(-0.558397\pi\)
−0.182431 + 0.983219i \(0.558397\pi\)
\(68\) 30.5557 3.70542
\(69\) −10.1758 −1.22502
\(70\) −8.30603 −0.992761
\(71\) −0.135869 −0.0161247 −0.00806234 0.999967i \(-0.502566\pi\)
−0.00806234 + 0.999967i \(0.502566\pi\)
\(72\) −49.7404 −5.86196
\(73\) 2.06341 0.241504 0.120752 0.992683i \(-0.461469\pi\)
0.120752 + 0.992683i \(0.461469\pi\)
\(74\) 4.89454 0.568979
\(75\) −1.42043 −0.164017
\(76\) 26.7986 3.07401
\(77\) −1.38140 −0.157425
\(78\) 6.36670 0.720887
\(79\) 14.0930 1.58559 0.792794 0.609490i \(-0.208626\pi\)
0.792794 + 0.609490i \(0.208626\pi\)
\(80\) 19.2922 2.15693
\(81\) 22.4210 2.49123
\(82\) 24.3252 2.68627
\(83\) 0.342920 0.0376404 0.0188202 0.999823i \(-0.494009\pi\)
0.0188202 + 0.999823i \(0.494009\pi\)
\(84\) −20.5858 −2.24610
\(85\) 15.3539 1.66536
\(86\) −23.2615 −2.50836
\(87\) 28.6685 3.07359
\(88\) 6.81126 0.726082
\(89\) 11.2035 1.18756 0.593782 0.804626i \(-0.297634\pi\)
0.593782 + 0.804626i \(0.297634\pi\)
\(90\) −43.9092 −4.62844
\(91\) 1.06313 0.111446
\(92\) 14.7186 1.53452
\(93\) −3.60610 −0.373936
\(94\) −27.4063 −2.82675
\(95\) 13.4660 1.38158
\(96\) 24.6863 2.51953
\(97\) 18.0597 1.83368 0.916840 0.399254i \(-0.130731\pi\)
0.916840 + 0.399254i \(0.130731\pi\)
\(98\) 13.1232 1.32564
\(99\) −7.30267 −0.733946
\(100\) 2.05456 0.205456
\(101\) −6.00007 −0.597029 −0.298514 0.954405i \(-0.596491\pi\)
−0.298514 + 0.954405i \(0.596491\pi\)
\(102\) 54.4460 5.39096
\(103\) 13.0078 1.28170 0.640851 0.767666i \(-0.278582\pi\)
0.640851 + 0.767666i \(0.278582\pi\)
\(104\) −5.24195 −0.514016
\(105\) −10.3442 −1.00949
\(106\) −16.0100 −1.55503
\(107\) −1.32107 −0.127713 −0.0638564 0.997959i \(-0.520340\pi\)
−0.0638564 + 0.997959i \(0.520340\pi\)
\(108\) −64.1191 −6.16986
\(109\) 7.22114 0.691660 0.345830 0.938297i \(-0.387597\pi\)
0.345830 + 0.938297i \(0.387597\pi\)
\(110\) 6.01276 0.573294
\(111\) 6.09555 0.578564
\(112\) 11.4235 1.07942
\(113\) −13.4355 −1.26391 −0.631953 0.775007i \(-0.717746\pi\)
−0.631953 + 0.775007i \(0.717746\pi\)
\(114\) 47.7515 4.47233
\(115\) 7.39592 0.689673
\(116\) −41.4672 −3.85013
\(117\) 5.62015 0.519583
\(118\) −0.0459762 −0.00423245
\(119\) 9.09154 0.833420
\(120\) 51.0038 4.65599
\(121\) 1.00000 0.0909091
\(122\) 8.33807 0.754894
\(123\) 30.2941 2.73152
\(124\) 5.21600 0.468410
\(125\) −10.6322 −0.950975
\(126\) −26.0001 −2.31627
\(127\) 3.00645 0.266779 0.133389 0.991064i \(-0.457414\pi\)
0.133389 + 0.991064i \(0.457414\pi\)
\(128\) 6.91987 0.611636
\(129\) −28.9694 −2.55062
\(130\) −4.62743 −0.405853
\(131\) −14.8214 −1.29495 −0.647475 0.762087i \(-0.724175\pi\)
−0.647475 + 0.762087i \(0.724175\pi\)
\(132\) 14.9022 1.29707
\(133\) 7.97366 0.691404
\(134\) 7.69732 0.664947
\(135\) −32.2191 −2.77298
\(136\) −44.8276 −3.84393
\(137\) 10.3194 0.881650 0.440825 0.897593i \(-0.354686\pi\)
0.440825 + 0.897593i \(0.354686\pi\)
\(138\) 26.2265 2.23255
\(139\) 11.9377 1.01254 0.506272 0.862374i \(-0.331023\pi\)
0.506272 + 0.862374i \(0.331023\pi\)
\(140\) 14.9622 1.26453
\(141\) −34.1313 −2.87437
\(142\) 0.350182 0.0293866
\(143\) −0.769601 −0.0643573
\(144\) 60.3897 5.03247
\(145\) −20.8368 −1.73040
\(146\) −5.31813 −0.440132
\(147\) 16.3433 1.34798
\(148\) −8.81682 −0.724739
\(149\) 17.1702 1.40664 0.703320 0.710873i \(-0.251700\pi\)
0.703320 + 0.710873i \(0.251700\pi\)
\(150\) 3.66095 0.298916
\(151\) 8.12230 0.660983 0.330492 0.943809i \(-0.392785\pi\)
0.330492 + 0.943809i \(0.392785\pi\)
\(152\) −39.3157 −3.18892
\(153\) 48.0618 3.88556
\(154\) 3.56035 0.286901
\(155\) 2.62098 0.210522
\(156\) −11.4687 −0.918232
\(157\) 21.2969 1.69968 0.849839 0.527042i \(-0.176699\pi\)
0.849839 + 0.527042i \(0.176699\pi\)
\(158\) −36.3226 −2.88967
\(159\) −19.9385 −1.58123
\(160\) −17.9424 −1.41847
\(161\) 4.37936 0.345142
\(162\) −57.7869 −4.54016
\(163\) −6.83850 −0.535632 −0.267816 0.963470i \(-0.586302\pi\)
−0.267816 + 0.963470i \(0.586302\pi\)
\(164\) −43.8184 −3.42164
\(165\) 7.48817 0.582953
\(166\) −0.883825 −0.0685982
\(167\) 2.08895 0.161648 0.0808241 0.996728i \(-0.474245\pi\)
0.0808241 + 0.996728i \(0.474245\pi\)
\(168\) 30.2010 2.33006
\(169\) −12.4077 −0.954440
\(170\) −39.5723 −3.03506
\(171\) 42.1522 3.22346
\(172\) 41.9024 3.19503
\(173\) −13.1599 −1.00053 −0.500265 0.865872i \(-0.666764\pi\)
−0.500265 + 0.865872i \(0.666764\pi\)
\(174\) −73.8889 −5.60150
\(175\) 0.611315 0.0462111
\(176\) −8.26953 −0.623339
\(177\) −0.0572578 −0.00430376
\(178\) −28.8752 −2.16429
\(179\) 7.31004 0.546378 0.273189 0.961960i \(-0.411922\pi\)
0.273189 + 0.961960i \(0.411922\pi\)
\(180\) 79.0964 5.89549
\(181\) −19.8789 −1.47759 −0.738794 0.673931i \(-0.764604\pi\)
−0.738794 + 0.673931i \(0.764604\pi\)
\(182\) −2.74005 −0.203106
\(183\) 10.3841 0.767612
\(184\) −21.5933 −1.59188
\(185\) −4.43036 −0.325726
\(186\) 9.29419 0.681483
\(187\) −6.58139 −0.481279
\(188\) 49.3687 3.60058
\(189\) −19.0780 −1.38772
\(190\) −34.7066 −2.51788
\(191\) 19.0651 1.37950 0.689751 0.724046i \(-0.257720\pi\)
0.689751 + 0.724046i \(0.257720\pi\)
\(192\) −10.5384 −0.760546
\(193\) −0.281245 −0.0202444 −0.0101222 0.999949i \(-0.503222\pi\)
−0.0101222 + 0.999949i \(0.503222\pi\)
\(194\) −46.5461 −3.34181
\(195\) −5.76290 −0.412690
\(196\) −23.6396 −1.68854
\(197\) −16.5147 −1.17663 −0.588313 0.808633i \(-0.700208\pi\)
−0.588313 + 0.808633i \(0.700208\pi\)
\(198\) 18.8216 1.33759
\(199\) −5.90149 −0.418345 −0.209173 0.977879i \(-0.567077\pi\)
−0.209173 + 0.977879i \(0.567077\pi\)
\(200\) −3.01421 −0.213137
\(201\) 9.58608 0.676150
\(202\) 15.4643 1.08806
\(203\) −12.3382 −0.865969
\(204\) −98.0769 −6.86676
\(205\) −22.0183 −1.53782
\(206\) −33.5258 −2.33585
\(207\) 23.1512 1.60912
\(208\) 6.36424 0.441281
\(209\) −5.77216 −0.399269
\(210\) 26.6605 1.83975
\(211\) 14.0450 0.966895 0.483447 0.875373i \(-0.339384\pi\)
0.483447 + 0.875373i \(0.339384\pi\)
\(212\) 28.8398 1.98073
\(213\) 0.436109 0.0298817
\(214\) 3.40486 0.232752
\(215\) 21.0555 1.43597
\(216\) 94.0678 6.40050
\(217\) 1.55197 0.105354
\(218\) −18.6114 −1.26052
\(219\) −6.62309 −0.447547
\(220\) −10.8311 −0.730236
\(221\) 5.06505 0.340712
\(222\) −15.7104 −1.05441
\(223\) −12.8365 −0.859597 −0.429799 0.902925i \(-0.641415\pi\)
−0.429799 + 0.902925i \(0.641415\pi\)
\(224\) −10.6243 −0.709865
\(225\) 3.23167 0.215445
\(226\) 34.6280 2.30342
\(227\) −9.41289 −0.624756 −0.312378 0.949958i \(-0.601126\pi\)
−0.312378 + 0.949958i \(0.601126\pi\)
\(228\) −86.0176 −5.69665
\(229\) −6.80902 −0.449953 −0.224976 0.974364i \(-0.572230\pi\)
−0.224976 + 0.974364i \(0.572230\pi\)
\(230\) −19.0619 −1.25690
\(231\) 4.43399 0.291735
\(232\) 60.8356 3.99405
\(233\) 8.45611 0.553978 0.276989 0.960873i \(-0.410663\pi\)
0.276989 + 0.960873i \(0.410663\pi\)
\(234\) −14.4851 −0.946920
\(235\) 24.8072 1.61824
\(236\) 0.0828197 0.00539110
\(237\) −45.2354 −2.93836
\(238\) −23.4321 −1.51888
\(239\) −17.5385 −1.13447 −0.567234 0.823556i \(-0.691987\pi\)
−0.567234 + 0.823556i \(0.691987\pi\)
\(240\) −61.9236 −3.99715
\(241\) −2.59226 −0.166982 −0.0834911 0.996509i \(-0.526607\pi\)
−0.0834911 + 0.996509i \(0.526607\pi\)
\(242\) −2.57735 −0.165678
\(243\) −30.5346 −1.95880
\(244\) −15.0199 −0.961549
\(245\) −11.8786 −0.758898
\(246\) −78.0784 −4.97810
\(247\) 4.44226 0.282654
\(248\) −7.65227 −0.485920
\(249\) −1.10070 −0.0697539
\(250\) 27.4030 1.73312
\(251\) −8.47328 −0.534829 −0.267414 0.963582i \(-0.586169\pi\)
−0.267414 + 0.963582i \(0.586169\pi\)
\(252\) 46.8355 2.95036
\(253\) −3.17024 −0.199311
\(254\) −7.74866 −0.486194
\(255\) −49.2826 −3.08619
\(256\) −24.4014 −1.52509
\(257\) −21.4980 −1.34101 −0.670505 0.741905i \(-0.733923\pi\)
−0.670505 + 0.741905i \(0.733923\pi\)
\(258\) 74.6644 4.64840
\(259\) −2.62336 −0.163008
\(260\) 8.33567 0.516956
\(261\) −65.2248 −4.03731
\(262\) 38.1999 2.36000
\(263\) 8.59907 0.530241 0.265121 0.964215i \(-0.414588\pi\)
0.265121 + 0.964215i \(0.414588\pi\)
\(264\) −21.8626 −1.34555
\(265\) 14.4917 0.890217
\(266\) −20.5509 −1.26006
\(267\) −35.9606 −2.20075
\(268\) −13.8657 −0.846979
\(269\) 14.4973 0.883916 0.441958 0.897036i \(-0.354284\pi\)
0.441958 + 0.897036i \(0.354284\pi\)
\(270\) 83.0400 5.05366
\(271\) −24.2610 −1.47375 −0.736874 0.676030i \(-0.763699\pi\)
−0.736874 + 0.676030i \(0.763699\pi\)
\(272\) 54.4250 3.30000
\(273\) −3.41240 −0.206528
\(274\) −26.5968 −1.60677
\(275\) −0.442533 −0.0266857
\(276\) −47.2433 −2.84371
\(277\) −12.3393 −0.741399 −0.370699 0.928753i \(-0.620882\pi\)
−0.370699 + 0.928753i \(0.620882\pi\)
\(278\) −30.7677 −1.84532
\(279\) 8.20437 0.491183
\(280\) −21.9506 −1.31180
\(281\) −1.43908 −0.0858486 −0.0429243 0.999078i \(-0.513667\pi\)
−0.0429243 + 0.999078i \(0.513667\pi\)
\(282\) 87.9683 5.23843
\(283\) 20.0728 1.19321 0.596603 0.802537i \(-0.296517\pi\)
0.596603 + 0.802537i \(0.296517\pi\)
\(284\) −0.630804 −0.0374313
\(285\) −43.2229 −2.56030
\(286\) 1.98353 0.117289
\(287\) −13.0377 −0.769593
\(288\) −56.1645 −3.30953
\(289\) 26.3147 1.54793
\(290\) 53.7038 3.15359
\(291\) −57.9675 −3.39811
\(292\) 9.57987 0.560620
\(293\) −28.5544 −1.66817 −0.834084 0.551637i \(-0.814003\pi\)
−0.834084 + 0.551637i \(0.814003\pi\)
\(294\) −42.1225 −2.45663
\(295\) 0.0416160 0.00242298
\(296\) 12.9350 0.751830
\(297\) 13.8106 0.801374
\(298\) −44.2537 −2.56355
\(299\) 2.43982 0.141098
\(300\) −6.59469 −0.380745
\(301\) 12.4676 0.718623
\(302\) −20.9340 −1.20462
\(303\) 19.2589 1.10639
\(304\) 47.7330 2.73768
\(305\) −7.54732 −0.432158
\(306\) −123.872 −7.08129
\(307\) 12.5858 0.718308 0.359154 0.933278i \(-0.383065\pi\)
0.359154 + 0.933278i \(0.383065\pi\)
\(308\) −6.41348 −0.365442
\(309\) −41.7523 −2.37521
\(310\) −6.75519 −0.383669
\(311\) −21.5978 −1.22470 −0.612350 0.790587i \(-0.709776\pi\)
−0.612350 + 0.790587i \(0.709776\pi\)
\(312\) 16.8255 0.952557
\(313\) 20.0110 1.13109 0.565544 0.824718i \(-0.308666\pi\)
0.565544 + 0.824718i \(0.308666\pi\)
\(314\) −54.8896 −3.09760
\(315\) 23.5343 1.32601
\(316\) 65.4301 3.68073
\(317\) −10.0061 −0.561998 −0.280999 0.959708i \(-0.590666\pi\)
−0.280999 + 0.959708i \(0.590666\pi\)
\(318\) 51.3886 2.88173
\(319\) 8.93163 0.500075
\(320\) 7.65953 0.428181
\(321\) 4.24034 0.236673
\(322\) −11.2872 −0.629009
\(323\) 37.9888 2.11376
\(324\) 104.095 5.78305
\(325\) 0.340574 0.0188916
\(326\) 17.6252 0.976170
\(327\) −23.1783 −1.28176
\(328\) 64.2850 3.54955
\(329\) 14.6892 0.809840
\(330\) −19.2996 −1.06241
\(331\) 29.7987 1.63788 0.818942 0.573876i \(-0.194561\pi\)
0.818942 + 0.573876i \(0.194561\pi\)
\(332\) 1.59209 0.0873772
\(333\) −13.8682 −0.759973
\(334\) −5.38397 −0.294598
\(335\) −6.96734 −0.380666
\(336\) −36.6670 −2.00035
\(337\) −20.0353 −1.09139 −0.545697 0.837982i \(-0.683735\pi\)
−0.545697 + 0.837982i \(0.683735\pi\)
\(338\) 31.9790 1.73943
\(339\) 43.1250 2.34223
\(340\) 71.2840 3.86592
\(341\) −1.12347 −0.0608396
\(342\) −108.641 −5.87463
\(343\) −16.7035 −0.901905
\(344\) −61.4741 −3.31446
\(345\) −23.7393 −1.27808
\(346\) 33.9177 1.82343
\(347\) −23.9790 −1.28726 −0.643629 0.765337i \(-0.722572\pi\)
−0.643629 + 0.765337i \(0.722572\pi\)
\(348\) 133.100 7.13493
\(349\) −6.11350 −0.327248 −0.163624 0.986523i \(-0.552318\pi\)
−0.163624 + 0.986523i \(0.552318\pi\)
\(350\) −1.57557 −0.0842180
\(351\) −10.6287 −0.567317
\(352\) 7.69095 0.409929
\(353\) 13.1569 0.700269 0.350134 0.936699i \(-0.386136\pi\)
0.350134 + 0.936699i \(0.386136\pi\)
\(354\) 0.147573 0.00784344
\(355\) −0.316972 −0.0168231
\(356\) 52.0147 2.75677
\(357\) −29.1818 −1.54447
\(358\) −18.8405 −0.995754
\(359\) 0.957506 0.0505352 0.0252676 0.999681i \(-0.491956\pi\)
0.0252676 + 0.999681i \(0.491956\pi\)
\(360\) −116.041 −6.11587
\(361\) 14.3178 0.753569
\(362\) 51.2349 2.69285
\(363\) −3.20978 −0.168470
\(364\) 4.93582 0.258707
\(365\) 4.81378 0.251965
\(366\) −26.7634 −1.39894
\(367\) 26.5373 1.38524 0.692618 0.721304i \(-0.256457\pi\)
0.692618 + 0.721304i \(0.256457\pi\)
\(368\) 26.2163 1.36662
\(369\) −68.9230 −3.58799
\(370\) 11.4186 0.593624
\(371\) 8.58100 0.445503
\(372\) −16.7422 −0.868042
\(373\) 22.3055 1.15493 0.577467 0.816414i \(-0.304041\pi\)
0.577467 + 0.816414i \(0.304041\pi\)
\(374\) 16.9626 0.877113
\(375\) 34.1271 1.76231
\(376\) −72.4277 −3.73517
\(377\) −6.87379 −0.354018
\(378\) 49.1707 2.52907
\(379\) −29.1644 −1.49807 −0.749037 0.662528i \(-0.769483\pi\)
−0.749037 + 0.662528i \(0.769483\pi\)
\(380\) 62.5191 3.20716
\(381\) −9.65002 −0.494386
\(382\) −49.1375 −2.51409
\(383\) 12.9243 0.660402 0.330201 0.943911i \(-0.392883\pi\)
0.330201 + 0.943911i \(0.392883\pi\)
\(384\) −22.2112 −1.13346
\(385\) −3.22270 −0.164244
\(386\) 0.724866 0.0368947
\(387\) 65.9093 3.35036
\(388\) 83.8462 4.25665
\(389\) 10.7342 0.544247 0.272123 0.962262i \(-0.412274\pi\)
0.272123 + 0.962262i \(0.412274\pi\)
\(390\) 14.8530 0.752112
\(391\) 20.8646 1.05517
\(392\) 34.6811 1.75166
\(393\) 47.5733 2.39976
\(394\) 42.5643 2.14436
\(395\) 32.8779 1.65427
\(396\) −33.9044 −1.70376
\(397\) 10.5470 0.529339 0.264669 0.964339i \(-0.414737\pi\)
0.264669 + 0.964339i \(0.414737\pi\)
\(398\) 15.2102 0.762419
\(399\) −25.5937 −1.28129
\(400\) 3.65954 0.182977
\(401\) −5.88750 −0.294008 −0.147004 0.989136i \(-0.546963\pi\)
−0.147004 + 0.989136i \(0.546963\pi\)
\(402\) −24.7067 −1.23226
\(403\) 0.864628 0.0430702
\(404\) −27.8567 −1.38592
\(405\) 52.3066 2.59913
\(406\) 31.7997 1.57819
\(407\) 1.89906 0.0941328
\(408\) 143.887 7.12344
\(409\) −18.4142 −0.910524 −0.455262 0.890357i \(-0.650454\pi\)
−0.455262 + 0.890357i \(0.650454\pi\)
\(410\) 56.7488 2.80262
\(411\) −33.1231 −1.63384
\(412\) 60.3920 2.97530
\(413\) 0.0246422 0.00121256
\(414\) −59.6688 −2.93256
\(415\) 0.800007 0.0392708
\(416\) −5.91897 −0.290201
\(417\) −38.3174 −1.87641
\(418\) 14.8769 0.727652
\(419\) 8.10769 0.396086 0.198043 0.980193i \(-0.436541\pi\)
0.198043 + 0.980193i \(0.436541\pi\)
\(420\) −48.0252 −2.34339
\(421\) 28.3488 1.38163 0.690817 0.723030i \(-0.257251\pi\)
0.690817 + 0.723030i \(0.257251\pi\)
\(422\) −36.1988 −1.76213
\(423\) 77.6532 3.77563
\(424\) −42.3102 −2.05477
\(425\) 2.91248 0.141276
\(426\) −1.12401 −0.0544583
\(427\) −4.46901 −0.216271
\(428\) −6.13338 −0.296468
\(429\) 2.47025 0.119265
\(430\) −54.2674 −2.61701
\(431\) 11.6853 0.562859 0.281429 0.959582i \(-0.409191\pi\)
0.281429 + 0.959582i \(0.409191\pi\)
\(432\) −114.207 −5.49480
\(433\) 19.4370 0.934082 0.467041 0.884236i \(-0.345320\pi\)
0.467041 + 0.884236i \(0.345320\pi\)
\(434\) −3.99997 −0.192004
\(435\) 66.8815 3.20672
\(436\) 33.5258 1.60560
\(437\) 18.2991 0.875365
\(438\) 17.0700 0.815638
\(439\) 30.4812 1.45479 0.727394 0.686220i \(-0.240731\pi\)
0.727394 + 0.686220i \(0.240731\pi\)
\(440\) 15.8901 0.757533
\(441\) −37.1833 −1.77063
\(442\) −13.0544 −0.620935
\(443\) −16.2171 −0.770496 −0.385248 0.922813i \(-0.625884\pi\)
−0.385248 + 0.922813i \(0.625884\pi\)
\(444\) 28.3001 1.34306
\(445\) 26.1368 1.23900
\(446\) 33.0842 1.56658
\(447\) −55.1127 −2.60674
\(448\) 4.53546 0.214280
\(449\) 36.5803 1.72633 0.863167 0.504919i \(-0.168478\pi\)
0.863167 + 0.504919i \(0.168478\pi\)
\(450\) −8.32916 −0.392640
\(451\) 9.43805 0.444421
\(452\) −62.3775 −2.93399
\(453\) −26.0708 −1.22491
\(454\) 24.2603 1.13859
\(455\) 2.48020 0.116273
\(456\) 126.195 5.90960
\(457\) −4.51917 −0.211398 −0.105699 0.994398i \(-0.533708\pi\)
−0.105699 + 0.994398i \(0.533708\pi\)
\(458\) 17.5492 0.820022
\(459\) −90.8932 −4.24253
\(460\) 34.3373 1.60098
\(461\) −18.8411 −0.877517 −0.438758 0.898605i \(-0.644582\pi\)
−0.438758 + 0.898605i \(0.644582\pi\)
\(462\) −11.4279 −0.531676
\(463\) −3.54446 −0.164725 −0.0823626 0.996602i \(-0.526247\pi\)
−0.0823626 + 0.996602i \(0.526247\pi\)
\(464\) −73.8603 −3.42888
\(465\) −8.41277 −0.390133
\(466\) −21.7944 −1.00960
\(467\) 9.96830 0.461278 0.230639 0.973039i \(-0.425918\pi\)
0.230639 + 0.973039i \(0.425918\pi\)
\(468\) 26.0929 1.20614
\(469\) −4.12559 −0.190502
\(470\) −63.9369 −2.94919
\(471\) −68.3583 −3.14979
\(472\) −0.121503 −0.00559263
\(473\) −9.02537 −0.414987
\(474\) 116.588 5.35504
\(475\) 2.55437 0.117203
\(476\) 42.2096 1.93467
\(477\) 45.3628 2.07702
\(478\) 45.2028 2.06753
\(479\) −40.2592 −1.83949 −0.919745 0.392515i \(-0.871605\pi\)
−0.919745 + 0.392515i \(0.871605\pi\)
\(480\) 57.5911 2.62866
\(481\) −1.46152 −0.0666395
\(482\) 6.68116 0.304319
\(483\) −14.0568 −0.639606
\(484\) 4.64274 0.211033
\(485\) 42.1318 1.91311
\(486\) 78.6985 3.56984
\(487\) 12.9893 0.588601 0.294301 0.955713i \(-0.404913\pi\)
0.294301 + 0.955713i \(0.404913\pi\)
\(488\) 22.0353 0.997492
\(489\) 21.9501 0.992616
\(490\) 30.6154 1.38306
\(491\) 42.8913 1.93566 0.967829 0.251609i \(-0.0809597\pi\)
0.967829 + 0.251609i \(0.0809597\pi\)
\(492\) 140.647 6.34087
\(493\) −58.7825 −2.64743
\(494\) −11.4493 −0.515127
\(495\) −17.0366 −0.765737
\(496\) 9.29060 0.417160
\(497\) −0.187689 −0.00841902
\(498\) 2.83688 0.127124
\(499\) 35.8763 1.60604 0.803021 0.595951i \(-0.203225\pi\)
0.803021 + 0.595951i \(0.203225\pi\)
\(500\) −49.3626 −2.20756
\(501\) −6.70508 −0.299561
\(502\) 21.8386 0.974705
\(503\) 5.08196 0.226594 0.113297 0.993561i \(-0.463859\pi\)
0.113297 + 0.993561i \(0.463859\pi\)
\(504\) −68.7114 −3.06065
\(505\) −13.9977 −0.622889
\(506\) 8.17081 0.363237
\(507\) 39.8260 1.76874
\(508\) 13.9581 0.619292
\(509\) 19.8926 0.881722 0.440861 0.897575i \(-0.354673\pi\)
0.440861 + 0.897575i \(0.354673\pi\)
\(510\) 127.018 5.62447
\(511\) 2.85040 0.126094
\(512\) 49.0512 2.16778
\(513\) −79.7171 −3.51960
\(514\) 55.4080 2.44394
\(515\) 30.3463 1.33722
\(516\) −134.497 −5.92092
\(517\) −10.6335 −0.467662
\(518\) 6.76132 0.297075
\(519\) 42.2404 1.85415
\(520\) −12.2291 −0.536281
\(521\) −28.8343 −1.26325 −0.631627 0.775273i \(-0.717612\pi\)
−0.631627 + 0.775273i \(0.717612\pi\)
\(522\) 168.107 7.35785
\(523\) −35.2451 −1.54116 −0.770581 0.637342i \(-0.780034\pi\)
−0.770581 + 0.637342i \(0.780034\pi\)
\(524\) −68.8118 −3.00606
\(525\) −1.96219 −0.0856368
\(526\) −22.1628 −0.966345
\(527\) 7.39403 0.322089
\(528\) 26.5433 1.15515
\(529\) −12.9496 −0.563026
\(530\) −37.3501 −1.62239
\(531\) 0.130269 0.00565320
\(532\) 37.0196 1.60500
\(533\) −7.26354 −0.314619
\(534\) 92.6831 4.01079
\(535\) −3.08196 −0.133245
\(536\) 20.3420 0.878640
\(537\) −23.4636 −1.01253
\(538\) −37.3646 −1.61090
\(539\) 5.09173 0.219316
\(540\) −149.585 −6.43711
\(541\) −9.89636 −0.425478 −0.212739 0.977109i \(-0.568238\pi\)
−0.212739 + 0.977109i \(0.568238\pi\)
\(542\) 62.5290 2.68585
\(543\) 63.8069 2.73822
\(544\) −50.6172 −2.17019
\(545\) 16.8464 0.721619
\(546\) 8.79496 0.376390
\(547\) 1.00000 0.0427569
\(548\) 47.9105 2.04663
\(549\) −23.6251 −1.00830
\(550\) 1.14056 0.0486338
\(551\) −51.5548 −2.19631
\(552\) 69.3097 2.95002
\(553\) 19.4681 0.827867
\(554\) 31.8028 1.35117
\(555\) 14.2205 0.603625
\(556\) 55.4236 2.35049
\(557\) −18.3965 −0.779485 −0.389743 0.920924i \(-0.627436\pi\)
−0.389743 + 0.920924i \(0.627436\pi\)
\(558\) −21.1455 −0.895162
\(559\) 6.94594 0.293782
\(560\) 26.6502 1.12618
\(561\) 21.1248 0.891890
\(562\) 3.70902 0.156456
\(563\) −45.7526 −1.92824 −0.964121 0.265462i \(-0.914476\pi\)
−0.964121 + 0.265462i \(0.914476\pi\)
\(564\) −158.463 −6.67248
\(565\) −31.3440 −1.31865
\(566\) −51.7347 −2.17457
\(567\) 30.9724 1.30072
\(568\) 0.925439 0.0388305
\(569\) −2.85684 −0.119765 −0.0598824 0.998205i \(-0.519073\pi\)
−0.0598824 + 0.998205i \(0.519073\pi\)
\(570\) 111.401 4.66605
\(571\) −5.83956 −0.244378 −0.122189 0.992507i \(-0.538991\pi\)
−0.122189 + 0.992507i \(0.538991\pi\)
\(572\) −3.57306 −0.149397
\(573\) −61.1948 −2.55645
\(574\) 33.6028 1.40255
\(575\) 1.40293 0.0585064
\(576\) 23.9764 0.999015
\(577\) 18.5549 0.772451 0.386226 0.922404i \(-0.373779\pi\)
0.386226 + 0.922404i \(0.373779\pi\)
\(578\) −67.8223 −2.82103
\(579\) 0.902733 0.0375163
\(580\) −96.7398 −4.01690
\(581\) 0.473710 0.0196528
\(582\) 149.403 6.19293
\(583\) −6.21181 −0.257267
\(584\) −14.0544 −0.581576
\(585\) 13.1114 0.542089
\(586\) 73.5948 3.04017
\(587\) 19.1370 0.789867 0.394933 0.918710i \(-0.370768\pi\)
0.394933 + 0.918710i \(0.370768\pi\)
\(588\) 75.8778 3.12915
\(589\) 6.48487 0.267205
\(590\) −0.107259 −0.00441578
\(591\) 53.0087 2.18048
\(592\) −15.7043 −0.645443
\(593\) 30.5384 1.25406 0.627031 0.778994i \(-0.284270\pi\)
0.627031 + 0.778994i \(0.284270\pi\)
\(594\) −35.5948 −1.46047
\(595\) 21.2099 0.869520
\(596\) 79.7169 3.26533
\(597\) 18.9425 0.775264
\(598\) −6.28827 −0.257146
\(599\) 10.7649 0.439842 0.219921 0.975518i \(-0.429420\pi\)
0.219921 + 0.975518i \(0.429420\pi\)
\(600\) 9.67493 0.394977
\(601\) −16.7367 −0.682703 −0.341351 0.939936i \(-0.610885\pi\)
−0.341351 + 0.939936i \(0.610885\pi\)
\(602\) −32.1335 −1.30966
\(603\) −21.8096 −0.888157
\(604\) 37.7097 1.53439
\(605\) 2.33292 0.0948468
\(606\) −49.6369 −2.01636
\(607\) −42.9376 −1.74278 −0.871391 0.490590i \(-0.836781\pi\)
−0.871391 + 0.490590i \(0.836781\pi\)
\(608\) −44.3934 −1.80039
\(609\) 39.6027 1.60478
\(610\) 19.4521 0.787592
\(611\) 8.18358 0.331072
\(612\) 223.138 9.01982
\(613\) −21.5216 −0.869251 −0.434625 0.900611i \(-0.643119\pi\)
−0.434625 + 0.900611i \(0.643119\pi\)
\(614\) −32.4380 −1.30909
\(615\) 70.6737 2.84984
\(616\) 9.40907 0.379102
\(617\) −39.9130 −1.60683 −0.803417 0.595416i \(-0.796987\pi\)
−0.803417 + 0.595416i \(0.796987\pi\)
\(618\) 107.610 4.32872
\(619\) 11.6150 0.466848 0.233424 0.972375i \(-0.425007\pi\)
0.233424 + 0.972375i \(0.425007\pi\)
\(620\) 12.1685 0.488700
\(621\) −43.7830 −1.75695
\(622\) 55.6652 2.23197
\(623\) 15.4765 0.620051
\(624\) −20.4278 −0.817766
\(625\) −27.0168 −1.08067
\(626\) −51.5754 −2.06137
\(627\) 18.5273 0.739911
\(628\) 98.8759 3.94558
\(629\) −12.4984 −0.498346
\(630\) −60.6562 −2.41660
\(631\) −29.6275 −1.17945 −0.589726 0.807604i \(-0.700764\pi\)
−0.589726 + 0.807604i \(0.700764\pi\)
\(632\) −95.9911 −3.81832
\(633\) −45.0812 −1.79182
\(634\) 25.7892 1.02422
\(635\) 7.01381 0.278335
\(636\) −92.5693 −3.67061
\(637\) −3.91861 −0.155261
\(638\) −23.0199 −0.911368
\(639\) −0.992207 −0.0392511
\(640\) 16.1435 0.638129
\(641\) 21.7058 0.857329 0.428665 0.903464i \(-0.358984\pi\)
0.428665 + 0.903464i \(0.358984\pi\)
\(642\) −10.9289 −0.431327
\(643\) 10.8110 0.426346 0.213173 0.977014i \(-0.431620\pi\)
0.213173 + 0.977014i \(0.431620\pi\)
\(644\) 20.3322 0.801202
\(645\) −67.5835 −2.66110
\(646\) −97.9106 −3.85224
\(647\) −16.1537 −0.635068 −0.317534 0.948247i \(-0.602855\pi\)
−0.317534 + 0.948247i \(0.602855\pi\)
\(648\) −152.715 −5.99923
\(649\) −0.0178386 −0.000700225 0
\(650\) −0.877779 −0.0344293
\(651\) −4.98147 −0.195239
\(652\) −31.7493 −1.24340
\(653\) 34.9183 1.36646 0.683229 0.730204i \(-0.260575\pi\)
0.683229 + 0.730204i \(0.260575\pi\)
\(654\) 59.7385 2.33596
\(655\) −34.5771 −1.35104
\(656\) −78.0482 −3.04727
\(657\) 15.0684 0.587875
\(658\) −37.8591 −1.47590
\(659\) −7.20066 −0.280498 −0.140249 0.990116i \(-0.544790\pi\)
−0.140249 + 0.990116i \(0.544790\pi\)
\(660\) 34.7656 1.35325
\(661\) 13.2807 0.516561 0.258281 0.966070i \(-0.416844\pi\)
0.258281 + 0.966070i \(0.416844\pi\)
\(662\) −76.8017 −2.98498
\(663\) −16.2577 −0.631396
\(664\) −2.33572 −0.0906434
\(665\) 18.6019 0.721352
\(666\) 35.7432 1.38502
\(667\) −28.3154 −1.09638
\(668\) 9.69846 0.375245
\(669\) 41.2024 1.59298
\(670\) 17.9573 0.693750
\(671\) 3.23513 0.124891
\(672\) 34.1016 1.31550
\(673\) 24.7329 0.953383 0.476692 0.879071i \(-0.341836\pi\)
0.476692 + 0.879071i \(0.341836\pi\)
\(674\) 51.6381 1.98903
\(675\) −6.11166 −0.235238
\(676\) −57.6057 −2.21561
\(677\) −29.8588 −1.14757 −0.573783 0.819008i \(-0.694525\pi\)
−0.573783 + 0.819008i \(0.694525\pi\)
\(678\) −111.148 −4.26862
\(679\) 24.9476 0.957402
\(680\) −104.579 −4.01043
\(681\) 30.2133 1.15778
\(682\) 2.89559 0.110878
\(683\) 13.4527 0.514753 0.257376 0.966311i \(-0.417142\pi\)
0.257376 + 0.966311i \(0.417142\pi\)
\(684\) 195.702 7.48283
\(685\) 24.0745 0.919839
\(686\) 43.0508 1.64369
\(687\) 21.8554 0.833837
\(688\) 74.6355 2.84545
\(689\) 4.78062 0.182127
\(690\) 61.1844 2.32925
\(691\) −35.2201 −1.33983 −0.669917 0.742436i \(-0.733670\pi\)
−0.669917 + 0.742436i \(0.733670\pi\)
\(692\) −61.0981 −2.32260
\(693\) −10.0879 −0.383208
\(694\) 61.8022 2.34598
\(695\) 27.8498 1.05640
\(696\) −195.269 −7.40165
\(697\) −62.1155 −2.35279
\(698\) 15.7566 0.596397
\(699\) −27.1422 −1.02661
\(700\) 2.83818 0.107273
\(701\) −21.2554 −0.802805 −0.401402 0.915902i \(-0.631477\pi\)
−0.401402 + 0.915902i \(0.631477\pi\)
\(702\) 27.3938 1.03391
\(703\) −10.9617 −0.413427
\(704\) −3.28323 −0.123741
\(705\) −79.6257 −2.99888
\(706\) −33.9098 −1.27621
\(707\) −8.28849 −0.311721
\(708\) −0.265833 −0.00999061
\(709\) −17.9272 −0.673271 −0.336636 0.941635i \(-0.609289\pi\)
−0.336636 + 0.941635i \(0.609289\pi\)
\(710\) 0.816948 0.0306595
\(711\) 102.917 3.85968
\(712\) −76.3097 −2.85983
\(713\) 3.56168 0.133386
\(714\) 75.2118 2.81473
\(715\) −1.79542 −0.0671450
\(716\) 33.9386 1.26835
\(717\) 56.2946 2.10236
\(718\) −2.46783 −0.0920985
\(719\) −31.9946 −1.19320 −0.596599 0.802540i \(-0.703482\pi\)
−0.596599 + 0.802540i \(0.703482\pi\)
\(720\) 140.884 5.25045
\(721\) 17.9690 0.669202
\(722\) −36.9020 −1.37335
\(723\) 8.32058 0.309446
\(724\) −92.2926 −3.43003
\(725\) −3.95254 −0.146794
\(726\) 8.27272 0.307030
\(727\) 34.5436 1.28115 0.640576 0.767895i \(-0.278696\pi\)
0.640576 + 0.767895i \(0.278696\pi\)
\(728\) −7.24124 −0.268378
\(729\) 30.7463 1.13875
\(730\) −12.4068 −0.459196
\(731\) 59.3995 2.19697
\(732\) 48.2104 1.78191
\(733\) 6.05541 0.223662 0.111831 0.993727i \(-0.464329\pi\)
0.111831 + 0.993727i \(0.464329\pi\)
\(734\) −68.3960 −2.52454
\(735\) 38.1278 1.40636
\(736\) −24.3821 −0.898737
\(737\) 2.98653 0.110010
\(738\) 177.639 6.53897
\(739\) 36.5162 1.34327 0.671636 0.740881i \(-0.265592\pi\)
0.671636 + 0.740881i \(0.265592\pi\)
\(740\) −20.5690 −0.756131
\(741\) −14.2587 −0.523805
\(742\) −22.1162 −0.811913
\(743\) 46.4323 1.70344 0.851718 0.524000i \(-0.175561\pi\)
0.851718 + 0.524000i \(0.175561\pi\)
\(744\) 24.5621 0.900490
\(745\) 40.0569 1.46757
\(746\) −57.4890 −2.10482
\(747\) 2.50423 0.0916251
\(748\) −30.5557 −1.11723
\(749\) −1.82493 −0.0666814
\(750\) −87.9574 −3.21175
\(751\) 32.1893 1.17460 0.587301 0.809368i \(-0.300190\pi\)
0.587301 + 0.809368i \(0.300190\pi\)
\(752\) 87.9343 3.20663
\(753\) 27.1973 0.991126
\(754\) 17.7162 0.645185
\(755\) 18.9487 0.689614
\(756\) −88.5742 −3.22141
\(757\) 40.7272 1.48026 0.740128 0.672466i \(-0.234765\pi\)
0.740128 + 0.672466i \(0.234765\pi\)
\(758\) 75.1668 2.73018
\(759\) 10.1758 0.369356
\(760\) −91.7204 −3.32705
\(761\) 46.4901 1.68527 0.842633 0.538489i \(-0.181005\pi\)
0.842633 + 0.538489i \(0.181005\pi\)
\(762\) 24.8715 0.900999
\(763\) 9.97528 0.361129
\(764\) 88.5143 3.20233
\(765\) 112.124 4.05387
\(766\) −33.3105 −1.20356
\(767\) 0.0137286 0.000495710 0
\(768\) 78.3231 2.82624
\(769\) 21.6810 0.781839 0.390919 0.920425i \(-0.372157\pi\)
0.390919 + 0.920425i \(0.372157\pi\)
\(770\) 8.30603 0.299329
\(771\) 69.0039 2.48511
\(772\) −1.30575 −0.0469948
\(773\) −37.0840 −1.33382 −0.666910 0.745139i \(-0.732383\pi\)
−0.666910 + 0.745139i \(0.732383\pi\)
\(774\) −169.871 −6.10590
\(775\) 0.497175 0.0178590
\(776\) −123.009 −4.41576
\(777\) 8.42040 0.302080
\(778\) −27.6659 −0.991869
\(779\) −54.4779 −1.95187
\(780\) −26.7556 −0.958006
\(781\) 0.135869 0.00486178
\(782\) −53.7753 −1.92300
\(783\) 123.351 4.40822
\(784\) −42.1062 −1.50379
\(785\) 49.6841 1.77330
\(786\) −122.613 −4.37347
\(787\) −39.3274 −1.40187 −0.700934 0.713226i \(-0.747233\pi\)
−0.700934 + 0.713226i \(0.747233\pi\)
\(788\) −76.6736 −2.73138
\(789\) −27.6011 −0.982625
\(790\) −84.7379 −3.01484
\(791\) −18.5598 −0.659910
\(792\) 49.7404 1.76745
\(793\) −2.48976 −0.0884141
\(794\) −27.1833 −0.964700
\(795\) −46.5151 −1.64972
\(796\) −27.3991 −0.971134
\(797\) −16.2624 −0.576045 −0.288023 0.957624i \(-0.592998\pi\)
−0.288023 + 0.957624i \(0.592998\pi\)
\(798\) 65.9639 2.33510
\(799\) 69.9835 2.47584
\(800\) −3.40350 −0.120332
\(801\) 81.8152 2.89080
\(802\) 15.1742 0.535818
\(803\) −2.06341 −0.0728162
\(804\) 44.5057 1.56959
\(805\) 10.2167 0.360092
\(806\) −2.22845 −0.0784938
\(807\) −46.5331 −1.63804
\(808\) 40.8680 1.43773
\(809\) 11.6886 0.410951 0.205476 0.978662i \(-0.434126\pi\)
0.205476 + 0.978662i \(0.434126\pi\)
\(810\) −134.812 −4.73682
\(811\) 12.0599 0.423480 0.211740 0.977326i \(-0.432087\pi\)
0.211740 + 0.977326i \(0.432087\pi\)
\(812\) −57.2828 −2.01023
\(813\) 77.8723 2.73110
\(814\) −4.89454 −0.171553
\(815\) −15.9537 −0.558833
\(816\) −174.692 −6.11545
\(817\) 52.0959 1.82260
\(818\) 47.4599 1.65940
\(819\) 7.76368 0.271285
\(820\) −102.225 −3.56985
\(821\) −54.6082 −1.90584 −0.952919 0.303224i \(-0.901937\pi\)
−0.952919 + 0.303224i \(0.901937\pi\)
\(822\) 85.3700 2.97762
\(823\) 23.4957 0.819008 0.409504 0.912308i \(-0.365702\pi\)
0.409504 + 0.912308i \(0.365702\pi\)
\(824\) −88.5998 −3.08652
\(825\) 1.42043 0.0494531
\(826\) −0.0635116 −0.00220985
\(827\) −42.1340 −1.46514 −0.732572 0.680690i \(-0.761680\pi\)
−0.732572 + 0.680690i \(0.761680\pi\)
\(828\) 107.485 3.73536
\(829\) −9.35412 −0.324882 −0.162441 0.986718i \(-0.551937\pi\)
−0.162441 + 0.986718i \(0.551937\pi\)
\(830\) −2.06190 −0.0715695
\(831\) 39.6065 1.37394
\(832\) 2.52678 0.0876003
\(833\) −33.5107 −1.16108
\(834\) 98.7574 3.41969
\(835\) 4.87337 0.168650
\(836\) −26.7986 −0.926849
\(837\) −15.5159 −0.536308
\(838\) −20.8963 −0.721852
\(839\) 12.4421 0.429549 0.214774 0.976664i \(-0.431098\pi\)
0.214774 + 0.976664i \(0.431098\pi\)
\(840\) 70.4567 2.43099
\(841\) 50.7740 1.75083
\(842\) −73.0647 −2.51798
\(843\) 4.61914 0.159092
\(844\) 65.2070 2.24452
\(845\) −28.9462 −0.995781
\(846\) −200.140 −6.88094
\(847\) 1.38140 0.0474655
\(848\) 51.3687 1.76401
\(849\) −64.4293 −2.21121
\(850\) −7.50649 −0.257471
\(851\) −6.02046 −0.206379
\(852\) 2.02474 0.0693665
\(853\) 49.5700 1.69724 0.848622 0.529000i \(-0.177433\pi\)
0.848622 + 0.529000i \(0.177433\pi\)
\(854\) 11.5182 0.394145
\(855\) 98.3379 3.36308
\(856\) 8.99815 0.307551
\(857\) −0.171008 −0.00584153 −0.00292077 0.999996i \(-0.500930\pi\)
−0.00292077 + 0.999996i \(0.500930\pi\)
\(858\) −6.36670 −0.217356
\(859\) 38.3276 1.30772 0.653861 0.756615i \(-0.273148\pi\)
0.653861 + 0.756615i \(0.273148\pi\)
\(860\) 97.7551 3.33342
\(861\) 41.8482 1.42618
\(862\) −30.1170 −1.02579
\(863\) −37.5896 −1.27957 −0.639783 0.768556i \(-0.720976\pi\)
−0.639783 + 0.768556i \(0.720976\pi\)
\(864\) 106.217 3.61357
\(865\) −30.7011 −1.04387
\(866\) −50.0959 −1.70233
\(867\) −84.4644 −2.86856
\(868\) 7.20538 0.244566
\(869\) −14.0930 −0.478072
\(870\) −172.377 −5.84413
\(871\) −2.29843 −0.0778795
\(872\) −49.1850 −1.66562
\(873\) 131.884 4.46359
\(874\) −47.1632 −1.59532
\(875\) −14.6874 −0.496523
\(876\) −30.7493 −1.03892
\(877\) −33.8154 −1.14186 −0.570932 0.820998i \(-0.693418\pi\)
−0.570932 + 0.820998i \(0.693418\pi\)
\(878\) −78.5607 −2.65130
\(879\) 91.6534 3.09139
\(880\) −19.2922 −0.650339
\(881\) −46.6245 −1.57082 −0.785410 0.618976i \(-0.787548\pi\)
−0.785410 + 0.618976i \(0.787548\pi\)
\(882\) 95.8343 3.22691
\(883\) −18.3579 −0.617793 −0.308896 0.951096i \(-0.599960\pi\)
−0.308896 + 0.951096i \(0.599960\pi\)
\(884\) 23.5157 0.790918
\(885\) −0.133578 −0.00449018
\(886\) 41.7971 1.40420
\(887\) 16.4266 0.551552 0.275776 0.961222i \(-0.411065\pi\)
0.275776 + 0.961222i \(0.411065\pi\)
\(888\) −41.5184 −1.39327
\(889\) 4.15310 0.139291
\(890\) −67.3638 −2.25804
\(891\) −22.4210 −0.751133
\(892\) −59.5966 −1.99544
\(893\) 61.3784 2.05395
\(894\) 142.045 4.75068
\(895\) 17.0538 0.570045
\(896\) 9.55911 0.319347
\(897\) −7.83127 −0.261479
\(898\) −94.2804 −3.14618
\(899\) −10.0345 −0.334668
\(900\) 15.0038 0.500127
\(901\) 40.8824 1.36199
\(902\) −24.3252 −0.809940
\(903\) −40.0184 −1.33173
\(904\) 91.5126 3.04366
\(905\) −46.3760 −1.54159
\(906\) 67.1935 2.23236
\(907\) −23.3796 −0.776308 −0.388154 0.921594i \(-0.626887\pi\)
−0.388154 + 0.921594i \(0.626887\pi\)
\(908\) −43.7016 −1.45029
\(909\) −43.8165 −1.45330
\(910\) −6.39233 −0.211904
\(911\) 43.8123 1.45156 0.725782 0.687924i \(-0.241478\pi\)
0.725782 + 0.687924i \(0.241478\pi\)
\(912\) −153.212 −5.07337
\(913\) −0.342920 −0.0113490
\(914\) 11.6475 0.385265
\(915\) 24.2252 0.800861
\(916\) −31.6125 −1.04451
\(917\) −20.4743 −0.676120
\(918\) 234.264 7.73185
\(919\) 30.8518 1.01771 0.508853 0.860854i \(-0.330070\pi\)
0.508853 + 0.860854i \(0.330070\pi\)
\(920\) −50.3755 −1.66083
\(921\) −40.3975 −1.33114
\(922\) 48.5601 1.59924
\(923\) −0.104565 −0.00344180
\(924\) 20.5858 0.677224
\(925\) −0.840396 −0.0276320
\(926\) 9.13533 0.300205
\(927\) 94.9921 3.11995
\(928\) 68.6927 2.25495
\(929\) −35.4105 −1.16178 −0.580891 0.813981i \(-0.697296\pi\)
−0.580891 + 0.813981i \(0.697296\pi\)
\(930\) 21.6826 0.711002
\(931\) −29.3903 −0.963228
\(932\) 39.2595 1.28599
\(933\) 69.3242 2.26957
\(934\) −25.6918 −0.840662
\(935\) −15.3539 −0.502126
\(936\) −38.2803 −1.25123
\(937\) −55.4325 −1.81090 −0.905451 0.424450i \(-0.860467\pi\)
−0.905451 + 0.424450i \(0.860467\pi\)
\(938\) 10.6331 0.347183
\(939\) −64.2309 −2.09610
\(940\) 115.173 3.75654
\(941\) −20.2243 −0.659292 −0.329646 0.944105i \(-0.606929\pi\)
−0.329646 + 0.944105i \(0.606929\pi\)
\(942\) 176.183 5.74037
\(943\) −29.9208 −0.974357
\(944\) 0.147516 0.00480125
\(945\) −44.5075 −1.44783
\(946\) 23.2615 0.756298
\(947\) 7.88328 0.256172 0.128086 0.991763i \(-0.459117\pi\)
0.128086 + 0.991763i \(0.459117\pi\)
\(948\) −210.016 −6.82101
\(949\) 1.58800 0.0515488
\(950\) −6.58351 −0.213597
\(951\) 32.1173 1.04148
\(952\) −61.9248 −2.00699
\(953\) −2.41705 −0.0782960 −0.0391480 0.999233i \(-0.512464\pi\)
−0.0391480 + 0.999233i \(0.512464\pi\)
\(954\) −116.916 −3.78529
\(955\) 44.4774 1.43926
\(956\) −81.4264 −2.63352
\(957\) −28.6685 −0.926722
\(958\) 103.762 3.35240
\(959\) 14.2553 0.460327
\(960\) −24.5854 −0.793490
\(961\) −29.7378 −0.959284
\(962\) 3.76684 0.121448
\(963\) −9.64735 −0.310881
\(964\) −12.0352 −0.387627
\(965\) −0.656123 −0.0211213
\(966\) 36.2293 1.16566
\(967\) −35.2845 −1.13467 −0.567336 0.823486i \(-0.692026\pi\)
−0.567336 + 0.823486i \(0.692026\pi\)
\(968\) −6.81126 −0.218922
\(969\) −121.936 −3.91714
\(970\) −108.588 −3.48656
\(971\) 0.558831 0.0179337 0.00896687 0.999960i \(-0.497146\pi\)
0.00896687 + 0.999960i \(0.497146\pi\)
\(972\) −141.764 −4.54709
\(973\) 16.4908 0.528669
\(974\) −33.4780 −1.07270
\(975\) −1.09317 −0.0350094
\(976\) −26.7530 −0.856343
\(977\) 27.5089 0.880088 0.440044 0.897976i \(-0.354963\pi\)
0.440044 + 0.897976i \(0.354963\pi\)
\(978\) −56.5730 −1.80900
\(979\) −11.2035 −0.358064
\(980\) −55.1493 −1.76168
\(981\) 52.7336 1.68366
\(982\) −110.546 −3.52766
\(983\) 49.8167 1.58891 0.794453 0.607325i \(-0.207757\pi\)
0.794453 + 0.607325i \(0.207757\pi\)
\(984\) −206.341 −6.57790
\(985\) −38.5276 −1.22759
\(986\) 151.503 4.82485
\(987\) −47.1490 −1.50077
\(988\) 20.6242 0.656145
\(989\) 28.6125 0.909826
\(990\) 43.9092 1.39553
\(991\) −40.5386 −1.28775 −0.643876 0.765130i \(-0.722675\pi\)
−0.643876 + 0.765130i \(0.722675\pi\)
\(992\) −8.64059 −0.274339
\(993\) −95.6472 −3.03527
\(994\) 0.483742 0.0153434
\(995\) −13.7677 −0.436466
\(996\) −5.11025 −0.161924
\(997\) 44.8148 1.41930 0.709649 0.704555i \(-0.248853\pi\)
0.709649 + 0.704555i \(0.248853\pi\)
\(998\) −92.4657 −2.92695
\(999\) 26.2272 0.829792
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.1.9 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.f.1.9 121 1.1 even 1 trivial