Properties

Label 177.4.a.b.1.3
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(10.4433380710\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 41 x^{5} - 7 x^{4} + 484 x^{3} + 63 x^{2} - 1736 x - 44\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.61892\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61892 q^{2} -3.00000 q^{3} -1.14126 q^{4} -7.96684 q^{5} +7.85676 q^{6} +16.8751 q^{7} +23.9402 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.61892 q^{2} -3.00000 q^{3} -1.14126 q^{4} -7.96684 q^{5} +7.85676 q^{6} +16.8751 q^{7} +23.9402 q^{8} +9.00000 q^{9} +20.8645 q^{10} +62.7682 q^{11} +3.42378 q^{12} -75.2191 q^{13} -44.1946 q^{14} +23.9005 q^{15} -53.5675 q^{16} -51.9804 q^{17} -23.5703 q^{18} +24.2087 q^{19} +9.09222 q^{20} -50.6254 q^{21} -164.385 q^{22} -9.85642 q^{23} -71.8207 q^{24} -61.5295 q^{25} +196.993 q^{26} -27.0000 q^{27} -19.2589 q^{28} +160.344 q^{29} -62.5935 q^{30} -125.861 q^{31} -51.2329 q^{32} -188.305 q^{33} +136.132 q^{34} -134.441 q^{35} -10.2713 q^{36} -224.138 q^{37} -63.4006 q^{38} +225.657 q^{39} -190.728 q^{40} -467.472 q^{41} +132.584 q^{42} +90.9608 q^{43} -71.6348 q^{44} -71.7015 q^{45} +25.8132 q^{46} +437.881 q^{47} +160.702 q^{48} -58.2301 q^{49} +161.141 q^{50} +155.941 q^{51} +85.8445 q^{52} -353.688 q^{53} +70.7108 q^{54} -500.064 q^{55} +403.994 q^{56} -72.6261 q^{57} -419.929 q^{58} +59.0000 q^{59} -27.2767 q^{60} -697.325 q^{61} +329.620 q^{62} +151.876 q^{63} +562.715 q^{64} +599.258 q^{65} +493.154 q^{66} -292.026 q^{67} +59.3231 q^{68} +29.5693 q^{69} +352.091 q^{70} +223.496 q^{71} +215.462 q^{72} +122.800 q^{73} +586.998 q^{74} +184.589 q^{75} -27.6284 q^{76} +1059.22 q^{77} -590.978 q^{78} -440.541 q^{79} +426.763 q^{80} +81.0000 q^{81} +1224.27 q^{82} -662.365 q^{83} +57.7767 q^{84} +414.119 q^{85} -238.219 q^{86} -481.033 q^{87} +1502.68 q^{88} +1012.63 q^{89} +187.781 q^{90} -1269.33 q^{91} +11.2487 q^{92} +377.583 q^{93} -1146.77 q^{94} -192.867 q^{95} +153.699 q^{96} -397.912 q^{97} +152.500 q^{98} +564.914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} - 71q^{10} - 5q^{11} - 78q^{12} - 67q^{13} - 65q^{14} + 6q^{15} - 94q^{16} - 23q^{17} - 176q^{19} - 207q^{20} + 177q^{21} - 704q^{22} - 218q^{23} + 63q^{24} - 183q^{25} + 58q^{26} - 189q^{27} - 938q^{28} + 168q^{29} + 213q^{30} - 604q^{31} - 448q^{32} + 15q^{33} - 610q^{34} - 336q^{35} + 234q^{36} - 505q^{37} - 453q^{38} + 201q^{39} - 1080q^{40} - 265q^{41} + 195q^{42} - 493q^{43} + 504q^{44} - 18q^{45} + 381q^{46} - 244q^{47} + 282q^{48} + 770q^{49} + 1639q^{50} + 69q^{51} + 160q^{52} + 686q^{53} - 116q^{55} + 2190q^{56} + 528q^{57} + 1584q^{58} + 413q^{59} + 621q^{60} - 838q^{61} + 286q^{62} - 531q^{63} + 205q^{64} + 490q^{65} + 2112q^{66} - 1504q^{67} + 3047q^{68} + 654q^{69} + 1530q^{70} - 1267q^{71} - 189q^{72} - 666q^{73} + 528q^{74} + 549q^{75} - 64q^{76} + 1109q^{77} - 174q^{78} - 2741q^{79} + 1213q^{80} + 567q^{81} + 953q^{82} - 2025q^{83} + 2814q^{84} - 1274q^{85} + 4394q^{86} - 504q^{87} - 1639q^{88} + 616q^{89} - 639q^{90} - 2415q^{91} + 218q^{92} + 1812q^{93} + 900q^{94} + 2554q^{95} + 1344q^{96} - 1298q^{97} - 172q^{98} - 45q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61892 −0.925928 −0.462964 0.886377i \(-0.653214\pi\)
−0.462964 + 0.886377i \(0.653214\pi\)
\(3\) −3.00000 −0.577350
\(4\) −1.14126 −0.142657
\(5\) −7.96684 −0.712575 −0.356288 0.934376i \(-0.615958\pi\)
−0.356288 + 0.934376i \(0.615958\pi\)
\(6\) 7.85676 0.534585
\(7\) 16.8751 0.911171 0.455586 0.890192i \(-0.349430\pi\)
0.455586 + 0.890192i \(0.349430\pi\)
\(8\) 23.9402 1.05802
\(9\) 9.00000 0.333333
\(10\) 20.8645 0.659793
\(11\) 62.7682 1.72048 0.860242 0.509886i \(-0.170313\pi\)
0.860242 + 0.509886i \(0.170313\pi\)
\(12\) 3.42378 0.0823633
\(13\) −75.2191 −1.60477 −0.802385 0.596807i \(-0.796436\pi\)
−0.802385 + 0.596807i \(0.796436\pi\)
\(14\) −44.1946 −0.843679
\(15\) 23.9005 0.411406
\(16\) −53.5675 −0.836991
\(17\) −51.9804 −0.741593 −0.370797 0.928714i \(-0.620915\pi\)
−0.370797 + 0.928714i \(0.620915\pi\)
\(18\) −23.5703 −0.308643
\(19\) 24.2087 0.292308 0.146154 0.989262i \(-0.453310\pi\)
0.146154 + 0.989262i \(0.453310\pi\)
\(20\) 9.09222 0.101654
\(21\) −50.6254 −0.526065
\(22\) −164.385 −1.59304
\(23\) −9.85642 −0.0893568 −0.0446784 0.999001i \(-0.514226\pi\)
−0.0446784 + 0.999001i \(0.514226\pi\)
\(24\) −71.8207 −0.610847
\(25\) −61.5295 −0.492236
\(26\) 196.993 1.48590
\(27\) −27.0000 −0.192450
\(28\) −19.2589 −0.129985
\(29\) 160.344 1.02673 0.513365 0.858170i \(-0.328399\pi\)
0.513365 + 0.858170i \(0.328399\pi\)
\(30\) −62.5935 −0.380932
\(31\) −125.861 −0.729203 −0.364602 0.931164i \(-0.618795\pi\)
−0.364602 + 0.931164i \(0.618795\pi\)
\(32\) −51.2329 −0.283025
\(33\) −188.305 −0.993322
\(34\) 136.132 0.686662
\(35\) −134.441 −0.649278
\(36\) −10.2713 −0.0475525
\(37\) −224.138 −0.995892 −0.497946 0.867208i \(-0.665912\pi\)
−0.497946 + 0.867208i \(0.665912\pi\)
\(38\) −63.4006 −0.270656
\(39\) 225.657 0.926515
\(40\) −190.728 −0.753918
\(41\) −467.472 −1.78066 −0.890328 0.455319i \(-0.849525\pi\)
−0.890328 + 0.455319i \(0.849525\pi\)
\(42\) 132.584 0.487098
\(43\) 90.9608 0.322591 0.161295 0.986906i \(-0.448433\pi\)
0.161295 + 0.986906i \(0.448433\pi\)
\(44\) −71.6348 −0.245440
\(45\) −71.7015 −0.237525
\(46\) 25.8132 0.0827379
\(47\) 437.881 1.35897 0.679484 0.733691i \(-0.262204\pi\)
0.679484 + 0.733691i \(0.262204\pi\)
\(48\) 160.702 0.483237
\(49\) −58.2301 −0.169767
\(50\) 161.141 0.455775
\(51\) 155.941 0.428159
\(52\) 85.8445 0.228932
\(53\) −353.688 −0.916655 −0.458328 0.888783i \(-0.651551\pi\)
−0.458328 + 0.888783i \(0.651551\pi\)
\(54\) 70.7108 0.178195
\(55\) −500.064 −1.22597
\(56\) 403.994 0.964036
\(57\) −72.6261 −0.168764
\(58\) −419.929 −0.950678
\(59\) 59.0000 0.130189
\(60\) −27.2767 −0.0586901
\(61\) −697.325 −1.46366 −0.731831 0.681487i \(-0.761334\pi\)
−0.731831 + 0.681487i \(0.761334\pi\)
\(62\) 329.620 0.675190
\(63\) 151.876 0.303724
\(64\) 562.715 1.09905
\(65\) 599.258 1.14352
\(66\) 493.154 0.919744
\(67\) −292.026 −0.532487 −0.266244 0.963906i \(-0.585783\pi\)
−0.266244 + 0.963906i \(0.585783\pi\)
\(68\) 59.3231 0.105794
\(69\) 29.5693 0.0515902
\(70\) 352.091 0.601185
\(71\) 223.496 0.373579 0.186789 0.982400i \(-0.440192\pi\)
0.186789 + 0.982400i \(0.440192\pi\)
\(72\) 215.462 0.352673
\(73\) 122.800 0.196885 0.0984426 0.995143i \(-0.468614\pi\)
0.0984426 + 0.995143i \(0.468614\pi\)
\(74\) 586.998 0.922124
\(75\) 184.589 0.284193
\(76\) −27.6284 −0.0416999
\(77\) 1059.22 1.56766
\(78\) −590.978 −0.857886
\(79\) −440.541 −0.627401 −0.313701 0.949522i \(-0.601569\pi\)
−0.313701 + 0.949522i \(0.601569\pi\)
\(80\) 426.763 0.596420
\(81\) 81.0000 0.111111
\(82\) 1224.27 1.64876
\(83\) −662.365 −0.875951 −0.437976 0.898987i \(-0.644304\pi\)
−0.437976 + 0.898987i \(0.644304\pi\)
\(84\) 57.7767 0.0750471
\(85\) 414.119 0.528441
\(86\) −238.219 −0.298696
\(87\) −481.033 −0.592783
\(88\) 1502.68 1.82030
\(89\) 1012.63 1.20606 0.603029 0.797720i \(-0.293960\pi\)
0.603029 + 0.797720i \(0.293960\pi\)
\(90\) 187.781 0.219931
\(91\) −1269.33 −1.46222
\(92\) 11.2487 0.0127474
\(93\) 377.583 0.421006
\(94\) −1146.77 −1.25831
\(95\) −192.867 −0.208292
\(96\) 153.699 0.163404
\(97\) −397.912 −0.416513 −0.208257 0.978074i \(-0.566779\pi\)
−0.208257 + 0.978074i \(0.566779\pi\)
\(98\) 152.500 0.157192
\(99\) 564.914 0.573495
\(100\) 70.2212 0.0702212
\(101\) −961.752 −0.947504 −0.473752 0.880658i \(-0.657101\pi\)
−0.473752 + 0.880658i \(0.657101\pi\)
\(102\) −408.397 −0.396445
\(103\) −1085.47 −1.03839 −0.519197 0.854654i \(-0.673769\pi\)
−0.519197 + 0.854654i \(0.673769\pi\)
\(104\) −1800.76 −1.69788
\(105\) 403.324 0.374861
\(106\) 926.279 0.848757
\(107\) 39.2036 0.0354201 0.0177101 0.999843i \(-0.494362\pi\)
0.0177101 + 0.999843i \(0.494362\pi\)
\(108\) 30.8140 0.0274544
\(109\) −210.156 −0.184672 −0.0923361 0.995728i \(-0.529433\pi\)
−0.0923361 + 0.995728i \(0.529433\pi\)
\(110\) 1309.63 1.13516
\(111\) 672.413 0.574978
\(112\) −903.958 −0.762643
\(113\) −889.542 −0.740540 −0.370270 0.928924i \(-0.620735\pi\)
−0.370270 + 0.928924i \(0.620735\pi\)
\(114\) 190.202 0.156264
\(115\) 78.5245 0.0636734
\(116\) −182.994 −0.146471
\(117\) −676.972 −0.534923
\(118\) −154.516 −0.120546
\(119\) −877.175 −0.675719
\(120\) 572.183 0.435275
\(121\) 2608.84 1.96006
\(122\) 1826.24 1.35524
\(123\) 1402.42 1.02806
\(124\) 143.640 0.104026
\(125\) 1486.05 1.06333
\(126\) −397.751 −0.281226
\(127\) −2040.11 −1.42543 −0.712717 0.701451i \(-0.752536\pi\)
−0.712717 + 0.701451i \(0.752536\pi\)
\(128\) −1063.84 −0.734618
\(129\) −272.883 −0.186248
\(130\) −1569.41 −1.05882
\(131\) −2233.61 −1.48971 −0.744853 0.667228i \(-0.767481\pi\)
−0.744853 + 0.667228i \(0.767481\pi\)
\(132\) 214.904 0.141705
\(133\) 408.525 0.266343
\(134\) 764.792 0.493045
\(135\) 215.105 0.137135
\(136\) −1244.42 −0.784620
\(137\) −2125.70 −1.32563 −0.662815 0.748784i \(-0.730638\pi\)
−0.662815 + 0.748784i \(0.730638\pi\)
\(138\) −77.4395 −0.0477688
\(139\) 2710.99 1.65427 0.827133 0.562006i \(-0.189970\pi\)
0.827133 + 0.562006i \(0.189970\pi\)
\(140\) 153.432 0.0926244
\(141\) −1313.64 −0.784600
\(142\) −585.318 −0.345907
\(143\) −4721.36 −2.76098
\(144\) −482.107 −0.278997
\(145\) −1277.44 −0.731622
\(146\) −321.603 −0.182301
\(147\) 174.690 0.0980150
\(148\) 255.799 0.142071
\(149\) 1041.19 0.572470 0.286235 0.958160i \(-0.407596\pi\)
0.286235 + 0.958160i \(0.407596\pi\)
\(150\) −483.423 −0.263142
\(151\) 1448.13 0.780444 0.390222 0.920721i \(-0.372398\pi\)
0.390222 + 0.920721i \(0.372398\pi\)
\(152\) 579.562 0.309267
\(153\) −467.823 −0.247198
\(154\) −2774.02 −1.45154
\(155\) 1002.71 0.519612
\(156\) −257.533 −0.132174
\(157\) −2438.90 −1.23978 −0.619891 0.784688i \(-0.712823\pi\)
−0.619891 + 0.784688i \(0.712823\pi\)
\(158\) 1153.74 0.580928
\(159\) 1061.06 0.529231
\(160\) 408.164 0.201676
\(161\) −166.328 −0.0814193
\(162\) −212.133 −0.102881
\(163\) 3332.07 1.60115 0.800575 0.599232i \(-0.204527\pi\)
0.800575 + 0.599232i \(0.204527\pi\)
\(164\) 533.507 0.254024
\(165\) 1500.19 0.707817
\(166\) 1734.68 0.811068
\(167\) −2643.67 −1.22499 −0.612494 0.790475i \(-0.709834\pi\)
−0.612494 + 0.790475i \(0.709834\pi\)
\(168\) −1211.98 −0.556586
\(169\) 3460.91 1.57529
\(170\) −1084.54 −0.489299
\(171\) 217.878 0.0974361
\(172\) −103.810 −0.0460200
\(173\) −1207.93 −0.530849 −0.265424 0.964132i \(-0.585512\pi\)
−0.265424 + 0.964132i \(0.585512\pi\)
\(174\) 1259.79 0.548874
\(175\) −1038.32 −0.448512
\(176\) −3362.33 −1.44003
\(177\) −177.000 −0.0751646
\(178\) −2652.01 −1.11672
\(179\) −1379.61 −0.576074 −0.288037 0.957619i \(-0.593003\pi\)
−0.288037 + 0.957619i \(0.593003\pi\)
\(180\) 81.8300 0.0338847
\(181\) −2223.79 −0.913221 −0.456611 0.889667i \(-0.650937\pi\)
−0.456611 + 0.889667i \(0.650937\pi\)
\(182\) 3324.28 1.35391
\(183\) 2091.98 0.845045
\(184\) −235.965 −0.0945411
\(185\) 1785.67 0.709648
\(186\) −988.860 −0.389821
\(187\) −3262.71 −1.27590
\(188\) −499.735 −0.193867
\(189\) −455.628 −0.175355
\(190\) 505.102 0.192863
\(191\) −1419.51 −0.537762 −0.268881 0.963173i \(-0.586654\pi\)
−0.268881 + 0.963173i \(0.586654\pi\)
\(192\) −1688.14 −0.634538
\(193\) 2797.83 1.04348 0.521741 0.853104i \(-0.325283\pi\)
0.521741 + 0.853104i \(0.325283\pi\)
\(194\) 1042.10 0.385661
\(195\) −1797.77 −0.660212
\(196\) 66.4556 0.0242185
\(197\) 4134.50 1.49528 0.747641 0.664103i \(-0.231186\pi\)
0.747641 + 0.664103i \(0.231186\pi\)
\(198\) −1479.46 −0.531015
\(199\) −5049.42 −1.79871 −0.899357 0.437214i \(-0.855965\pi\)
−0.899357 + 0.437214i \(0.855965\pi\)
\(200\) −1473.03 −0.520795
\(201\) 876.078 0.307432
\(202\) 2518.75 0.877320
\(203\) 2705.83 0.935527
\(204\) −177.969 −0.0610801
\(205\) 3724.28 1.26885
\(206\) 2842.76 0.961479
\(207\) −88.7078 −0.0297856
\(208\) 4029.29 1.34318
\(209\) 1519.54 0.502911
\(210\) −1056.27 −0.347094
\(211\) 4910.79 1.60224 0.801121 0.598503i \(-0.204237\pi\)
0.801121 + 0.598503i \(0.204237\pi\)
\(212\) 403.649 0.130768
\(213\) −670.488 −0.215686
\(214\) −102.671 −0.0327965
\(215\) −724.670 −0.229870
\(216\) −646.386 −0.203616
\(217\) −2123.92 −0.664429
\(218\) 550.381 0.170993
\(219\) −368.399 −0.113672
\(220\) 570.702 0.174894
\(221\) 3909.91 1.19009
\(222\) −1760.99 −0.532388
\(223\) −47.4526 −0.0142496 −0.00712480 0.999975i \(-0.502268\pi\)
−0.00712480 + 0.999975i \(0.502268\pi\)
\(224\) −864.562 −0.257884
\(225\) −553.766 −0.164079
\(226\) 2329.64 0.685687
\(227\) 3097.71 0.905737 0.452869 0.891577i \(-0.350401\pi\)
0.452869 + 0.891577i \(0.350401\pi\)
\(228\) 82.8852 0.0240755
\(229\) 2273.82 0.656149 0.328074 0.944652i \(-0.393600\pi\)
0.328074 + 0.944652i \(0.393600\pi\)
\(230\) −205.649 −0.0589570
\(231\) −3177.66 −0.905086
\(232\) 3838.68 1.08630
\(233\) −3433.68 −0.965442 −0.482721 0.875774i \(-0.660351\pi\)
−0.482721 + 0.875774i \(0.660351\pi\)
\(234\) 1772.93 0.495301
\(235\) −3488.52 −0.968367
\(236\) −67.3343 −0.0185724
\(237\) 1321.62 0.362230
\(238\) 2297.25 0.625667
\(239\) 5489.29 1.48566 0.742830 0.669480i \(-0.233483\pi\)
0.742830 + 0.669480i \(0.233483\pi\)
\(240\) −1280.29 −0.344343
\(241\) 71.4197 0.0190894 0.00954470 0.999954i \(-0.496962\pi\)
0.00954470 + 0.999954i \(0.496962\pi\)
\(242\) −6832.35 −1.81488
\(243\) −243.000 −0.0641500
\(244\) 795.829 0.208802
\(245\) 463.909 0.120972
\(246\) −3672.82 −0.951912
\(247\) −1820.96 −0.469088
\(248\) −3013.14 −0.771511
\(249\) 1987.09 0.505731
\(250\) −3891.85 −0.984568
\(251\) 7078.52 1.78005 0.890024 0.455913i \(-0.150687\pi\)
0.890024 + 0.455913i \(0.150687\pi\)
\(252\) −173.330 −0.0433284
\(253\) −618.670 −0.153737
\(254\) 5342.88 1.31985
\(255\) −1242.36 −0.305096
\(256\) −1715.60 −0.418848
\(257\) −5131.54 −1.24551 −0.622756 0.782416i \(-0.713987\pi\)
−0.622756 + 0.782416i \(0.713987\pi\)
\(258\) 714.657 0.172452
\(259\) −3782.35 −0.907428
\(260\) −683.909 −0.163132
\(261\) 1443.10 0.342243
\(262\) 5849.65 1.37936
\(263\) −2899.64 −0.679846 −0.339923 0.940453i \(-0.610401\pi\)
−0.339923 + 0.940453i \(0.610401\pi\)
\(264\) −4508.05 −1.05095
\(265\) 2817.77 0.653186
\(266\) −1069.89 −0.246614
\(267\) −3037.90 −0.696317
\(268\) 333.277 0.0759632
\(269\) 2624.44 0.594852 0.297426 0.954745i \(-0.403872\pi\)
0.297426 + 0.954745i \(0.403872\pi\)
\(270\) −563.342 −0.126977
\(271\) 8503.68 1.90613 0.953066 0.302762i \(-0.0979088\pi\)
0.953066 + 0.302762i \(0.0979088\pi\)
\(272\) 2784.46 0.620707
\(273\) 3807.99 0.844213
\(274\) 5567.05 1.22744
\(275\) −3862.10 −0.846884
\(276\) −33.7462 −0.00735972
\(277\) −3533.33 −0.766415 −0.383208 0.923662i \(-0.625181\pi\)
−0.383208 + 0.923662i \(0.625181\pi\)
\(278\) −7099.86 −1.53173
\(279\) −1132.75 −0.243068
\(280\) −3218.56 −0.686948
\(281\) −2767.76 −0.587584 −0.293792 0.955869i \(-0.594917\pi\)
−0.293792 + 0.955869i \(0.594917\pi\)
\(282\) 3440.32 0.726483
\(283\) −3853.33 −0.809388 −0.404694 0.914452i \(-0.632622\pi\)
−0.404694 + 0.914452i \(0.632622\pi\)
\(284\) −255.067 −0.0532938
\(285\) 578.600 0.120257
\(286\) 12364.9 2.55647
\(287\) −7888.66 −1.62248
\(288\) −461.096 −0.0943416
\(289\) −2211.04 −0.450039
\(290\) 3345.50 0.677430
\(291\) 1193.73 0.240474
\(292\) −140.146 −0.0280871
\(293\) 6720.24 1.33993 0.669967 0.742391i \(-0.266308\pi\)
0.669967 + 0.742391i \(0.266308\pi\)
\(294\) −457.500 −0.0907548
\(295\) −470.043 −0.0927694
\(296\) −5365.90 −1.05367
\(297\) −1694.74 −0.331107
\(298\) −2726.80 −0.530066
\(299\) 741.391 0.143397
\(300\) −210.663 −0.0405422
\(301\) 1534.98 0.293935
\(302\) −3792.53 −0.722635
\(303\) 2885.26 0.547042
\(304\) −1296.80 −0.244659
\(305\) 5555.47 1.04297
\(306\) 1225.19 0.228887
\(307\) −3154.37 −0.586416 −0.293208 0.956049i \(-0.594723\pi\)
−0.293208 + 0.956049i \(0.594723\pi\)
\(308\) −1208.85 −0.223638
\(309\) 3256.41 0.599518
\(310\) −2626.03 −0.481124
\(311\) 4204.57 0.766622 0.383311 0.923619i \(-0.374784\pi\)
0.383311 + 0.923619i \(0.374784\pi\)
\(312\) 5402.28 0.980270
\(313\) −6497.54 −1.17336 −0.586682 0.809818i \(-0.699566\pi\)
−0.586682 + 0.809818i \(0.699566\pi\)
\(314\) 6387.29 1.14795
\(315\) −1209.97 −0.216426
\(316\) 502.771 0.0895034
\(317\) 5621.97 0.996092 0.498046 0.867151i \(-0.334051\pi\)
0.498046 + 0.867151i \(0.334051\pi\)
\(318\) −2778.84 −0.490030
\(319\) 10064.5 1.76647
\(320\) −4483.05 −0.783157
\(321\) −117.611 −0.0204498
\(322\) 435.601 0.0753884
\(323\) −1258.38 −0.216774
\(324\) −92.4420 −0.0158508
\(325\) 4628.19 0.789926
\(326\) −8726.41 −1.48255
\(327\) 630.467 0.106620
\(328\) −11191.4 −1.88397
\(329\) 7389.29 1.23825
\(330\) −3928.88 −0.655387
\(331\) −7641.62 −1.26895 −0.634473 0.772945i \(-0.718783\pi\)
−0.634473 + 0.772945i \(0.718783\pi\)
\(332\) 755.930 0.124961
\(333\) −2017.24 −0.331964
\(334\) 6923.55 1.13425
\(335\) 2326.52 0.379437
\(336\) 2711.87 0.440312
\(337\) 7138.77 1.15393 0.576964 0.816770i \(-0.304237\pi\)
0.576964 + 0.816770i \(0.304237\pi\)
\(338\) −9063.84 −1.45860
\(339\) 2668.63 0.427551
\(340\) −472.617 −0.0753861
\(341\) −7900.07 −1.25458
\(342\) −570.606 −0.0902188
\(343\) −6770.81 −1.06586
\(344\) 2177.62 0.341307
\(345\) −235.573 −0.0367619
\(346\) 3163.46 0.491528
\(347\) 3416.69 0.528580 0.264290 0.964443i \(-0.414862\pi\)
0.264290 + 0.964443i \(0.414862\pi\)
\(348\) 548.983 0.0845649
\(349\) 8930.15 1.36968 0.684842 0.728691i \(-0.259871\pi\)
0.684842 + 0.728691i \(0.259871\pi\)
\(350\) 2719.27 0.415289
\(351\) 2030.91 0.308838
\(352\) −3215.80 −0.486939
\(353\) 9550.53 1.44001 0.720005 0.693969i \(-0.244139\pi\)
0.720005 + 0.693969i \(0.244139\pi\)
\(354\) 463.549 0.0695970
\(355\) −1780.56 −0.266203
\(356\) −1155.68 −0.172053
\(357\) 2631.53 0.390126
\(358\) 3613.10 0.533403
\(359\) −7990.13 −1.17466 −0.587330 0.809347i \(-0.699821\pi\)
−0.587330 + 0.809347i \(0.699821\pi\)
\(360\) −1716.55 −0.251306
\(361\) −6272.94 −0.914556
\(362\) 5823.93 0.845577
\(363\) −7826.53 −1.13164
\(364\) 1448.64 0.208597
\(365\) −978.325 −0.140296
\(366\) −5478.72 −0.782451
\(367\) −9255.46 −1.31643 −0.658216 0.752829i \(-0.728689\pi\)
−0.658216 + 0.752829i \(0.728689\pi\)
\(368\) 527.983 0.0747908
\(369\) −4207.25 −0.593552
\(370\) −4676.52 −0.657083
\(371\) −5968.52 −0.835230
\(372\) −430.920 −0.0600596
\(373\) −5532.87 −0.768047 −0.384023 0.923323i \(-0.625462\pi\)
−0.384023 + 0.923323i \(0.625462\pi\)
\(374\) 8544.78 1.18139
\(375\) −4458.15 −0.613914
\(376\) 10483.0 1.43781
\(377\) −12060.9 −1.64767
\(378\) 1193.25 0.162366
\(379\) 12355.4 1.67456 0.837278 0.546778i \(-0.184146\pi\)
0.837278 + 0.546778i \(0.184146\pi\)
\(380\) 220.111 0.0297143
\(381\) 6120.32 0.822975
\(382\) 3717.59 0.497929
\(383\) −12814.3 −1.70961 −0.854807 0.518946i \(-0.826325\pi\)
−0.854807 + 0.518946i \(0.826325\pi\)
\(384\) 3191.52 0.424132
\(385\) −8438.64 −1.11707
\(386\) −7327.28 −0.966188
\(387\) 818.648 0.107530
\(388\) 454.120 0.0594187
\(389\) −1715.48 −0.223595 −0.111797 0.993731i \(-0.535661\pi\)
−0.111797 + 0.993731i \(0.535661\pi\)
\(390\) 4708.22 0.611308
\(391\) 512.340 0.0662664
\(392\) −1394.04 −0.179617
\(393\) 6700.84 0.860083
\(394\) −10827.9 −1.38452
\(395\) 3509.71 0.447071
\(396\) −644.713 −0.0818132
\(397\) 1097.81 0.138785 0.0693924 0.997589i \(-0.477894\pi\)
0.0693924 + 0.997589i \(0.477894\pi\)
\(398\) 13224.0 1.66548
\(399\) −1225.57 −0.153773
\(400\) 3295.98 0.411998
\(401\) −3949.81 −0.491880 −0.245940 0.969285i \(-0.579097\pi\)
−0.245940 + 0.969285i \(0.579097\pi\)
\(402\) −2294.38 −0.284660
\(403\) 9467.15 1.17020
\(404\) 1097.61 0.135168
\(405\) −645.314 −0.0791750
\(406\) −7086.35 −0.866230
\(407\) −14068.7 −1.71342
\(408\) 3733.26 0.453000
\(409\) −1709.43 −0.206665 −0.103332 0.994647i \(-0.532951\pi\)
−0.103332 + 0.994647i \(0.532951\pi\)
\(410\) −9753.58 −1.17487
\(411\) 6377.11 0.765352
\(412\) 1238.80 0.148135
\(413\) 995.633 0.118624
\(414\) 232.319 0.0275793
\(415\) 5276.95 0.624181
\(416\) 3853.69 0.454190
\(417\) −8132.97 −0.955091
\(418\) −3979.54 −0.465660
\(419\) −280.723 −0.0327308 −0.0163654 0.999866i \(-0.505209\pi\)
−0.0163654 + 0.999866i \(0.505209\pi\)
\(420\) −460.297 −0.0534767
\(421\) −11642.2 −1.34776 −0.673878 0.738842i \(-0.735373\pi\)
−0.673878 + 0.738842i \(0.735373\pi\)
\(422\) −12861.0 −1.48356
\(423\) 3940.93 0.452989
\(424\) −8467.36 −0.969838
\(425\) 3198.33 0.365039
\(426\) 1755.95 0.199709
\(427\) −11767.5 −1.33365
\(428\) −44.7414 −0.00505294
\(429\) 14164.1 1.59405
\(430\) 1897.85 0.212843
\(431\) −1887.48 −0.210943 −0.105472 0.994422i \(-0.533635\pi\)
−0.105472 + 0.994422i \(0.533635\pi\)
\(432\) 1446.32 0.161079
\(433\) −2668.89 −0.296210 −0.148105 0.988972i \(-0.547317\pi\)
−0.148105 + 0.988972i \(0.547317\pi\)
\(434\) 5562.38 0.615213
\(435\) 3832.31 0.422402
\(436\) 239.842 0.0263448
\(437\) −238.611 −0.0261197
\(438\) 964.808 0.105252
\(439\) 11389.6 1.23826 0.619131 0.785287i \(-0.287485\pi\)
0.619131 + 0.785287i \(0.287485\pi\)
\(440\) −11971.6 −1.29710
\(441\) −524.071 −0.0565890
\(442\) −10239.8 −1.10193
\(443\) 14630.8 1.56914 0.784569 0.620041i \(-0.212884\pi\)
0.784569 + 0.620041i \(0.212884\pi\)
\(444\) −767.397 −0.0820249
\(445\) −8067.50 −0.859407
\(446\) 124.274 0.0131941
\(447\) −3123.58 −0.330515
\(448\) 9495.88 1.00142
\(449\) 10838.9 1.13924 0.569620 0.821908i \(-0.307090\pi\)
0.569620 + 0.821908i \(0.307090\pi\)
\(450\) 1450.27 0.151925
\(451\) −29342.4 −3.06359
\(452\) 1015.20 0.105644
\(453\) −4344.39 −0.450589
\(454\) −8112.66 −0.838648
\(455\) 10112.6 1.04194
\(456\) −1738.68 −0.178556
\(457\) −7768.54 −0.795179 −0.397590 0.917563i \(-0.630153\pi\)
−0.397590 + 0.917563i \(0.630153\pi\)
\(458\) −5954.95 −0.607547
\(459\) 1403.47 0.142720
\(460\) −89.6168 −0.00908349
\(461\) 7262.50 0.733727 0.366864 0.930275i \(-0.380432\pi\)
0.366864 + 0.930275i \(0.380432\pi\)
\(462\) 8322.05 0.838045
\(463\) 8935.85 0.896942 0.448471 0.893797i \(-0.351969\pi\)
0.448471 + 0.893797i \(0.351969\pi\)
\(464\) −8589.23 −0.859364
\(465\) −3008.14 −0.299998
\(466\) 8992.53 0.893929
\(467\) 17921.0 1.77577 0.887885 0.460065i \(-0.152174\pi\)
0.887885 + 0.460065i \(0.152174\pi\)
\(468\) 772.600 0.0763108
\(469\) −4927.97 −0.485187
\(470\) 9136.16 0.896638
\(471\) 7316.71 0.715788
\(472\) 1412.47 0.137742
\(473\) 5709.45 0.555012
\(474\) −3461.22 −0.335399
\(475\) −1489.55 −0.143885
\(476\) 1001.08 0.0963963
\(477\) −3183.19 −0.305552
\(478\) −14376.0 −1.37561
\(479\) 1733.15 0.165323 0.0826616 0.996578i \(-0.473658\pi\)
0.0826616 + 0.996578i \(0.473658\pi\)
\(480\) −1224.49 −0.116438
\(481\) 16859.4 1.59818
\(482\) −187.042 −0.0176754
\(483\) 498.985 0.0470075
\(484\) −2977.37 −0.279618
\(485\) 3170.10 0.296797
\(486\) 636.398 0.0593983
\(487\) −2597.17 −0.241661 −0.120831 0.992673i \(-0.538556\pi\)
−0.120831 + 0.992673i \(0.538556\pi\)
\(488\) −16694.1 −1.54858
\(489\) −9996.20 −0.924425
\(490\) −1214.94 −0.112011
\(491\) 7523.32 0.691492 0.345746 0.938328i \(-0.387626\pi\)
0.345746 + 0.938328i \(0.387626\pi\)
\(492\) −1600.52 −0.146661
\(493\) −8334.75 −0.761416
\(494\) 4768.94 0.434341
\(495\) −4500.57 −0.408658
\(496\) 6742.05 0.610337
\(497\) 3771.52 0.340394
\(498\) −5204.04 −0.468270
\(499\) 9392.79 0.842643 0.421322 0.906911i \(-0.361566\pi\)
0.421322 + 0.906911i \(0.361566\pi\)
\(500\) −1695.97 −0.151692
\(501\) 7931.00 0.707248
\(502\) −18538.1 −1.64820
\(503\) 2687.97 0.238272 0.119136 0.992878i \(-0.461988\pi\)
0.119136 + 0.992878i \(0.461988\pi\)
\(504\) 3635.95 0.321345
\(505\) 7662.12 0.675168
\(506\) 1620.25 0.142349
\(507\) −10382.7 −0.909493
\(508\) 2328.29 0.203349
\(509\) 10267.4 0.894098 0.447049 0.894510i \(-0.352475\pi\)
0.447049 + 0.894510i \(0.352475\pi\)
\(510\) 3253.63 0.282497
\(511\) 2072.26 0.179396
\(512\) 13003.8 1.12244
\(513\) −653.635 −0.0562547
\(514\) 13439.1 1.15325
\(515\) 8647.77 0.739935
\(516\) 311.430 0.0265696
\(517\) 27485.0 2.33808
\(518\) 9905.67 0.840213
\(519\) 3623.78 0.306486
\(520\) 14346.4 1.20987
\(521\) −14725.4 −1.23826 −0.619128 0.785290i \(-0.712514\pi\)
−0.619128 + 0.785290i \(0.712514\pi\)
\(522\) −3779.36 −0.316893
\(523\) 5672.69 0.474282 0.237141 0.971475i \(-0.423790\pi\)
0.237141 + 0.971475i \(0.423790\pi\)
\(524\) 2549.13 0.212518
\(525\) 3114.96 0.258948
\(526\) 7593.93 0.629488
\(527\) 6542.30 0.540772
\(528\) 10087.0 0.831402
\(529\) −12069.9 −0.992015
\(530\) −7379.52 −0.604803
\(531\) 531.000 0.0433963
\(532\) −466.233 −0.0379958
\(533\) 35162.8 2.85755
\(534\) 7956.03 0.644740
\(535\) −312.328 −0.0252395
\(536\) −6991.17 −0.563381
\(537\) 4138.84 0.332596
\(538\) −6873.20 −0.550790
\(539\) −3655.00 −0.292081
\(540\) −245.490 −0.0195634
\(541\) −13483.4 −1.07153 −0.535766 0.844367i \(-0.679977\pi\)
−0.535766 + 0.844367i \(0.679977\pi\)
\(542\) −22270.5 −1.76494
\(543\) 6671.37 0.527248
\(544\) 2663.11 0.209889
\(545\) 1674.28 0.131593
\(546\) −9972.83 −0.781681
\(547\) 3503.56 0.273860 0.136930 0.990581i \(-0.456277\pi\)
0.136930 + 0.990581i \(0.456277\pi\)
\(548\) 2425.98 0.189111
\(549\) −6275.93 −0.487887
\(550\) 10114.5 0.784154
\(551\) 3881.72 0.300122
\(552\) 707.895 0.0545833
\(553\) −7434.18 −0.571670
\(554\) 9253.50 0.709645
\(555\) −5357.00 −0.409715
\(556\) −3093.94 −0.235993
\(557\) 785.734 0.0597713 0.0298856 0.999553i \(-0.490486\pi\)
0.0298856 + 0.999553i \(0.490486\pi\)
\(558\) 2966.58 0.225063
\(559\) −6841.99 −0.517684
\(560\) 7201.68 0.543440
\(561\) 9788.14 0.736641
\(562\) 7248.55 0.544060
\(563\) −711.755 −0.0532805 −0.0266402 0.999645i \(-0.508481\pi\)
−0.0266402 + 0.999645i \(0.508481\pi\)
\(564\) 1499.21 0.111929
\(565\) 7086.83 0.527691
\(566\) 10091.6 0.749435
\(567\) 1366.89 0.101241
\(568\) 5350.54 0.395253
\(569\) −12752.6 −0.939574 −0.469787 0.882780i \(-0.655669\pi\)
−0.469787 + 0.882780i \(0.655669\pi\)
\(570\) −1515.31 −0.111350
\(571\) 568.844 0.0416907 0.0208454 0.999783i \(-0.493364\pi\)
0.0208454 + 0.999783i \(0.493364\pi\)
\(572\) 5388.30 0.393874
\(573\) 4258.54 0.310477
\(574\) 20659.8 1.50230
\(575\) 606.461 0.0439846
\(576\) 5064.43 0.366351
\(577\) −4814.50 −0.347366 −0.173683 0.984802i \(-0.555567\pi\)
−0.173683 + 0.984802i \(0.555567\pi\)
\(578\) 5790.54 0.416704
\(579\) −8393.48 −0.602454
\(580\) 1457.89 0.104371
\(581\) −11177.5 −0.798142
\(582\) −3126.29 −0.222662
\(583\) −22200.3 −1.57709
\(584\) 2939.85 0.208308
\(585\) 5393.32 0.381173
\(586\) −17599.8 −1.24068
\(587\) −3790.32 −0.266513 −0.133256 0.991082i \(-0.542543\pi\)
−0.133256 + 0.991082i \(0.542543\pi\)
\(588\) −199.367 −0.0139826
\(589\) −3046.93 −0.213152
\(590\) 1231.01 0.0858978
\(591\) −12403.5 −0.863302
\(592\) 12006.5 0.833553
\(593\) 15605.2 1.08065 0.540326 0.841456i \(-0.318301\pi\)
0.540326 + 0.841456i \(0.318301\pi\)
\(594\) 4438.39 0.306581
\(595\) 6988.31 0.481500
\(596\) −1188.27 −0.0816670
\(597\) 15148.3 1.03849
\(598\) −1941.64 −0.132775
\(599\) −26016.3 −1.77462 −0.887310 0.461174i \(-0.847428\pi\)
−0.887310 + 0.461174i \(0.847428\pi\)
\(600\) 4419.09 0.300681
\(601\) −15990.4 −1.08530 −0.542648 0.839960i \(-0.682578\pi\)
−0.542648 + 0.839960i \(0.682578\pi\)
\(602\) −4019.98 −0.272163
\(603\) −2628.23 −0.177496
\(604\) −1652.69 −0.111336
\(605\) −20784.2 −1.39669
\(606\) −7556.25 −0.506521
\(607\) 8461.94 0.565831 0.282915 0.959145i \(-0.408698\pi\)
0.282915 + 0.959145i \(0.408698\pi\)
\(608\) −1240.28 −0.0827304
\(609\) −8117.49 −0.540127
\(610\) −14549.3 −0.965714
\(611\) −32937.0 −2.18083
\(612\) 533.908 0.0352646
\(613\) −3306.42 −0.217855 −0.108927 0.994050i \(-0.534742\pi\)
−0.108927 + 0.994050i \(0.534742\pi\)
\(614\) 8261.05 0.542979
\(615\) −11172.8 −0.732572
\(616\) 25358.0 1.65861
\(617\) −2038.03 −0.132979 −0.0664894 0.997787i \(-0.521180\pi\)
−0.0664894 + 0.997787i \(0.521180\pi\)
\(618\) −8528.29 −0.555110
\(619\) −1376.65 −0.0893896 −0.0446948 0.999001i \(-0.514232\pi\)
−0.0446948 + 0.999001i \(0.514232\pi\)
\(620\) −1144.36 −0.0741266
\(621\) 266.123 0.0171967
\(622\) −11011.4 −0.709837
\(623\) 17088.3 1.09892
\(624\) −12087.9 −0.775485
\(625\) −4147.92 −0.265467
\(626\) 17016.5 1.08645
\(627\) −4558.61 −0.290356
\(628\) 2783.42 0.176864
\(629\) 11650.8 0.738547
\(630\) 3168.82 0.200395
\(631\) −12856.2 −0.811091 −0.405546 0.914075i \(-0.632918\pi\)
−0.405546 + 0.914075i \(0.632918\pi\)
\(632\) −10546.6 −0.663802
\(633\) −14732.4 −0.925054
\(634\) −14723.5 −0.922309
\(635\) 16253.2 1.01573
\(636\) −1210.95 −0.0754987
\(637\) 4380.01 0.272437
\(638\) −26358.2 −1.63563
\(639\) 2011.46 0.124526
\(640\) 8475.44 0.523471
\(641\) 6936.45 0.427416 0.213708 0.976898i \(-0.431446\pi\)
0.213708 + 0.976898i \(0.431446\pi\)
\(642\) 308.013 0.0189351
\(643\) −30055.9 −1.84337 −0.921685 0.387938i \(-0.873187\pi\)
−0.921685 + 0.387938i \(0.873187\pi\)
\(644\) 189.824 0.0116151
\(645\) 2174.01 0.132716
\(646\) 3295.59 0.200717
\(647\) −22193.5 −1.34856 −0.674280 0.738476i \(-0.735546\pi\)
−0.674280 + 0.738476i \(0.735546\pi\)
\(648\) 1939.16 0.117558
\(649\) 3703.32 0.223988
\(650\) −12120.9 −0.731415
\(651\) 6371.76 0.383608
\(652\) −3802.75 −0.228416
\(653\) −4334.02 −0.259729 −0.129865 0.991532i \(-0.541454\pi\)
−0.129865 + 0.991532i \(0.541454\pi\)
\(654\) −1651.14 −0.0987229
\(655\) 17794.8 1.06153
\(656\) 25041.3 1.49039
\(657\) 1105.20 0.0656284
\(658\) −19352.0 −1.14653
\(659\) 10735.4 0.634584 0.317292 0.948328i \(-0.397226\pi\)
0.317292 + 0.948328i \(0.397226\pi\)
\(660\) −1712.11 −0.100975
\(661\) −31199.2 −1.83587 −0.917934 0.396734i \(-0.870144\pi\)
−0.917934 + 0.396734i \(0.870144\pi\)
\(662\) 20012.8 1.17495
\(663\) −11729.7 −0.687097
\(664\) −15857.2 −0.926773
\(665\) −3254.65 −0.189789
\(666\) 5282.98 0.307375
\(667\) −1580.42 −0.0917453
\(668\) 3017.11 0.174754
\(669\) 142.358 0.00822701
\(670\) −6092.97 −0.351332
\(671\) −43769.8 −2.51821
\(672\) 2593.69 0.148889
\(673\) 4517.81 0.258765 0.129383 0.991595i \(-0.458700\pi\)
0.129383 + 0.991595i \(0.458700\pi\)
\(674\) −18695.9 −1.06845
\(675\) 1661.30 0.0947309
\(676\) −3949.79 −0.224726
\(677\) 4980.54 0.282744 0.141372 0.989957i \(-0.454849\pi\)
0.141372 + 0.989957i \(0.454849\pi\)
\(678\) −6988.92 −0.395882
\(679\) −6714.81 −0.379515
\(680\) 9914.10 0.559101
\(681\) −9293.14 −0.522928
\(682\) 20689.6 1.16165
\(683\) −11878.0 −0.665446 −0.332723 0.943025i \(-0.607967\pi\)
−0.332723 + 0.943025i \(0.607967\pi\)
\(684\) −248.656 −0.0139000
\(685\) 16935.1 0.944611
\(686\) 17732.2 0.986908
\(687\) −6821.45 −0.378828
\(688\) −4872.54 −0.270006
\(689\) 26604.1 1.47102
\(690\) 616.948 0.0340388
\(691\) 3069.47 0.168984 0.0844921 0.996424i \(-0.473073\pi\)
0.0844921 + 0.996424i \(0.473073\pi\)
\(692\) 1378.56 0.0757295
\(693\) 9532.99 0.522552
\(694\) −8948.03 −0.489427
\(695\) −21598.0 −1.17879
\(696\) −11516.0 −0.627175
\(697\) 24299.4 1.32052
\(698\) −23387.3 −1.26823
\(699\) 10301.0 0.557398
\(700\) 1184.99 0.0639835
\(701\) −14816.8 −0.798321 −0.399161 0.916881i \(-0.630698\pi\)
−0.399161 + 0.916881i \(0.630698\pi\)
\(702\) −5318.80 −0.285962
\(703\) −5426.08 −0.291107
\(704\) 35320.6 1.89090
\(705\) 10465.6 0.559087
\(706\) −25012.1 −1.33335
\(707\) −16229.7 −0.863338
\(708\) 202.003 0.0107228
\(709\) 29464.2 1.56072 0.780361 0.625329i \(-0.215035\pi\)
0.780361 + 0.625329i \(0.215035\pi\)
\(710\) 4663.13 0.246485
\(711\) −3964.87 −0.209134
\(712\) 24242.7 1.27603
\(713\) 1240.54 0.0651592
\(714\) −6891.75 −0.361229
\(715\) 37614.3 1.96741
\(716\) 1574.50 0.0821812
\(717\) −16467.9 −0.857746
\(718\) 20925.5 1.08765
\(719\) 16747.1 0.868654 0.434327 0.900755i \(-0.356986\pi\)
0.434327 + 0.900755i \(0.356986\pi\)
\(720\) 3840.87 0.198807
\(721\) −18317.5 −0.946156
\(722\) 16428.3 0.846813
\(723\) −214.259 −0.0110213
\(724\) 2537.92 0.130278
\(725\) −9865.90 −0.505394
\(726\) 20497.1 1.04782
\(727\) 13485.0 0.687936 0.343968 0.938981i \(-0.388229\pi\)
0.343968 + 0.938981i \(0.388229\pi\)
\(728\) −30388.1 −1.54706
\(729\) 729.000 0.0370370
\(730\) 2562.15 0.129904
\(731\) −4728.18 −0.239231
\(732\) −2387.49 −0.120552
\(733\) −25581.8 −1.28906 −0.644532 0.764577i \(-0.722948\pi\)
−0.644532 + 0.764577i \(0.722948\pi\)
\(734\) 24239.3 1.21892
\(735\) −1391.73 −0.0698431
\(736\) 504.973 0.0252902
\(737\) −18329.9 −0.916135
\(738\) 11018.5 0.549587
\(739\) −8290.39 −0.412675 −0.206338 0.978481i \(-0.566155\pi\)
−0.206338 + 0.978481i \(0.566155\pi\)
\(740\) −2037.91 −0.101237
\(741\) 5462.87 0.270828
\(742\) 15631.1 0.773363
\(743\) −29226.2 −1.44308 −0.721539 0.692374i \(-0.756565\pi\)
−0.721539 + 0.692374i \(0.756565\pi\)
\(744\) 9039.42 0.445432
\(745\) −8295.02 −0.407928
\(746\) 14490.2 0.711156
\(747\) −5961.28 −0.291984
\(748\) 3723.60 0.182016
\(749\) 661.565 0.0322738
\(750\) 11675.5 0.568440
\(751\) 4511.16 0.219194 0.109597 0.993976i \(-0.465044\pi\)
0.109597 + 0.993976i \(0.465044\pi\)
\(752\) −23456.2 −1.13744
\(753\) −21235.6 −1.02771
\(754\) 31586.6 1.52562
\(755\) −11537.0 −0.556125
\(756\) 519.990 0.0250157
\(757\) −14064.1 −0.675256 −0.337628 0.941280i \(-0.609625\pi\)
−0.337628 + 0.941280i \(0.609625\pi\)
\(758\) −32357.9 −1.55052
\(759\) 1856.01 0.0887600
\(760\) −4617.27 −0.220376
\(761\) −31754.7 −1.51262 −0.756312 0.654211i \(-0.773001\pi\)
−0.756312 + 0.654211i \(0.773001\pi\)
\(762\) −16028.6 −0.762016
\(763\) −3546.40 −0.168268
\(764\) 1620.03 0.0767157
\(765\) 3727.07 0.176147
\(766\) 33559.7 1.58298
\(767\) −4437.92 −0.208923
\(768\) 5146.81 0.241822
\(769\) 23548.0 1.10424 0.552121 0.833764i \(-0.313819\pi\)
0.552121 + 0.833764i \(0.313819\pi\)
\(770\) 22100.1 1.03433
\(771\) 15394.6 0.719096
\(772\) −3193.04 −0.148860
\(773\) −14079.0 −0.655092 −0.327546 0.944835i \(-0.606222\pi\)
−0.327546 + 0.944835i \(0.606222\pi\)
\(774\) −2143.97 −0.0995652
\(775\) 7744.17 0.358940
\(776\) −9526.09 −0.440679
\(777\) 11347.1 0.523904
\(778\) 4492.71 0.207033
\(779\) −11316.9 −0.520501
\(780\) 2051.73 0.0941841
\(781\) 14028.4 0.642736
\(782\) −1341.78 −0.0613579
\(783\) −4329.29 −0.197594
\(784\) 3119.24 0.142093
\(785\) 19430.3 0.883438
\(786\) −17549.0 −0.796375
\(787\) −11840.6 −0.536305 −0.268152 0.963377i \(-0.586413\pi\)
−0.268152 + 0.963377i \(0.586413\pi\)
\(788\) −4718.53 −0.213313
\(789\) 8698.92 0.392509
\(790\) −9191.66 −0.413955
\(791\) −15011.1 −0.674759
\(792\) 13524.2 0.606768
\(793\) 52452.1 2.34884
\(794\) −2875.08 −0.128505
\(795\) −8453.31 −0.377117
\(796\) 5762.70 0.256600
\(797\) 4057.07 0.180312 0.0901561 0.995928i \(-0.471263\pi\)
0.0901561 + 0.995928i \(0.471263\pi\)
\(798\) 3209.68 0.142383
\(799\) −22761.2 −1.00780
\(800\) 3152.34 0.139315
\(801\) 9113.71 0.402019
\(802\) 10344.2 0.455446
\(803\) 7707.91 0.338738
\(804\) −999.832 −0.0438574
\(805\) 1325.11 0.0580174
\(806\) −24793.7 −1.08352
\(807\) −7873.33 −0.343438
\(808\) −23024.6 −1.00248
\(809\) 23041.8 1.00137 0.500684 0.865630i \(-0.333082\pi\)
0.500684 + 0.865630i \(0.333082\pi\)
\(810\) 1690.02 0.0733104
\(811\) 34179.5 1.47991 0.739953 0.672659i \(-0.234848\pi\)
0.739953 + 0.672659i \(0.234848\pi\)
\(812\) −3088.05 −0.133460
\(813\) −25511.0 −1.10051
\(814\) 36844.8 1.58650
\(815\) −26546.0 −1.14094
\(816\) −8353.37 −0.358366
\(817\) 2202.04 0.0942959
\(818\) 4476.86 0.191357
\(819\) −11424.0 −0.487407
\(820\) −4250.36 −0.181011
\(821\) 5743.98 0.244173 0.122087 0.992519i \(-0.461041\pi\)
0.122087 + 0.992519i \(0.461041\pi\)
\(822\) −16701.1 −0.708661
\(823\) 28540.8 1.20883 0.604416 0.796669i \(-0.293406\pi\)
0.604416 + 0.796669i \(0.293406\pi\)
\(824\) −25986.4 −1.09864
\(825\) 11586.3 0.488949
\(826\) −2607.48 −0.109838
\(827\) 33133.5 1.39319 0.696594 0.717466i \(-0.254698\pi\)
0.696594 + 0.717466i \(0.254698\pi\)
\(828\) 101.239 0.00424913
\(829\) 24606.9 1.03092 0.515460 0.856914i \(-0.327621\pi\)
0.515460 + 0.856914i \(0.327621\pi\)
\(830\) −13819.9 −0.577947
\(831\) 10600.0 0.442490
\(832\) −42326.9 −1.76373
\(833\) 3026.82 0.125898
\(834\) 21299.6 0.884346
\(835\) 21061.7 0.872897
\(836\) −1734.18 −0.0717440
\(837\) 3398.25 0.140335
\(838\) 735.190 0.0303063
\(839\) −9141.86 −0.376177 −0.188088 0.982152i \(-0.560229\pi\)
−0.188088 + 0.982152i \(0.560229\pi\)
\(840\) 9655.67 0.396610
\(841\) 1321.26 0.0541743
\(842\) 30490.0 1.24793
\(843\) 8303.29 0.339242
\(844\) −5604.49 −0.228572
\(845\) −27572.5 −1.12251
\(846\) −10321.0 −0.419435
\(847\) 44024.6 1.78595
\(848\) 18946.1 0.767233
\(849\) 11560.0 0.467300
\(850\) −8376.16 −0.338000
\(851\) 2209.19 0.0889897
\(852\) 765.200 0.0307692
\(853\) −1471.84 −0.0590794 −0.0295397 0.999564i \(-0.509404\pi\)
−0.0295397 + 0.999564i \(0.509404\pi\)
\(854\) 30818.0 1.23486
\(855\) −1735.80 −0.0694305
\(856\) 938.542 0.0374751
\(857\) 35038.0 1.39659 0.698294 0.715811i \(-0.253943\pi\)
0.698294 + 0.715811i \(0.253943\pi\)
\(858\) −37094.6 −1.47598
\(859\) 6739.91 0.267710 0.133855 0.991001i \(-0.457264\pi\)
0.133855 + 0.991001i \(0.457264\pi\)
\(860\) 827.036 0.0327927
\(861\) 23666.0 0.936741
\(862\) 4943.15 0.195318
\(863\) 265.457 0.0104708 0.00523538 0.999986i \(-0.498334\pi\)
0.00523538 + 0.999986i \(0.498334\pi\)
\(864\) 1383.29 0.0544681
\(865\) 9623.34 0.378270
\(866\) 6989.62 0.274269
\(867\) 6633.13 0.259830
\(868\) 2423.94 0.0947857
\(869\) −27651.9 −1.07943
\(870\) −10036.5 −0.391114
\(871\) 21965.9 0.854520
\(872\) −5031.17 −0.195386
\(873\) −3581.20 −0.138838
\(874\) 624.903 0.0241850
\(875\) 25077.3 0.968877
\(876\) 420.439 0.0162161
\(877\) −46175.2 −1.77791 −0.888955 0.457995i \(-0.848568\pi\)
−0.888955 + 0.457995i \(0.848568\pi\)
\(878\) −29828.5 −1.14654
\(879\) −20160.7 −0.773611
\(880\) 26787.1 1.02613
\(881\) −31385.6 −1.20024 −0.600118 0.799912i \(-0.704880\pi\)
−0.600118 + 0.799912i \(0.704880\pi\)
\(882\) 1372.50 0.0523973
\(883\) 16931.3 0.645281 0.322641 0.946522i \(-0.395429\pi\)
0.322641 + 0.946522i \(0.395429\pi\)
\(884\) −4462.23 −0.169775
\(885\) 1410.13 0.0535604
\(886\) −38316.8 −1.45291
\(887\) 34774.3 1.31635 0.658177 0.752863i \(-0.271328\pi\)
0.658177 + 0.752863i \(0.271328\pi\)
\(888\) 16097.7 0.608338
\(889\) −34427.1 −1.29882
\(890\) 21128.1 0.795749
\(891\) 5084.22 0.191165
\(892\) 54.1557 0.00203281
\(893\) 10600.5 0.397237
\(894\) 8180.41 0.306034
\(895\) 10991.2 0.410496
\(896\) −17952.4 −0.669363
\(897\) −2224.17 −0.0827903
\(898\) −28386.2 −1.05485
\(899\) −20181.1 −0.748695
\(900\) 631.990 0.0234071
\(901\) 18384.8 0.679786
\(902\) 76845.4 2.83666
\(903\) −4604.93 −0.169704
\(904\) −21295.8 −0.783505
\(905\) 17716.6 0.650739
\(906\) 11377.6 0.417213
\(907\) −35925.5 −1.31520 −0.657601 0.753367i \(-0.728429\pi\)
−0.657601 + 0.753367i \(0.728429\pi\)
\(908\) −3535.29 −0.129210
\(909\) −8655.77 −0.315835
\(910\) −26484.0 −0.964764
\(911\) 48786.7 1.77429 0.887143 0.461495i \(-0.152687\pi\)
0.887143 + 0.461495i \(0.152687\pi\)
\(912\) 3890.39 0.141254
\(913\) −41575.4 −1.50706
\(914\) 20345.2 0.736279
\(915\) −16666.4 −0.602158
\(916\) −2595.02 −0.0936045
\(917\) −37692.5 −1.35738
\(918\) −3675.57 −0.132148
\(919\) −18322.3 −0.657669 −0.328834 0.944388i \(-0.606656\pi\)
−0.328834 + 0.944388i \(0.606656\pi\)
\(920\) 1879.89 0.0673677
\(921\) 9463.12 0.338567
\(922\) −19019.9 −0.679378
\(923\) −16811.2 −0.599508
\(924\) 3626.54 0.129117
\(925\) 13791.1 0.490214
\(926\) −23402.3 −0.830504
\(927\) −9769.24 −0.346132
\(928\) −8214.90 −0.290590
\(929\) 30350.8 1.07188 0.535940 0.844256i \(-0.319957\pi\)
0.535940 + 0.844256i \(0.319957\pi\)
\(930\) 7878.08 0.277777
\(931\) −1409.67 −0.0496243
\(932\) 3918.72 0.137727
\(933\) −12613.7 −0.442609
\(934\) −46933.7 −1.64424
\(935\) 25993.5 0.909174
\(936\) −16206.9 −0.565959
\(937\) 52314.3 1.82394 0.911971 0.410256i \(-0.134560\pi\)
0.911971 + 0.410256i \(0.134560\pi\)
\(938\) 12906.0 0.449248
\(939\) 19492.6 0.677442
\(940\) 3981.31 0.138145
\(941\) 38821.1 1.34488 0.672440 0.740152i \(-0.265247\pi\)
0.672440 + 0.740152i \(0.265247\pi\)
\(942\) −19161.9 −0.662768
\(943\) 4607.60 0.159114
\(944\) −3160.48 −0.108967
\(945\) 3629.92 0.124954
\(946\) −14952.6 −0.513901
\(947\) 4992.59 0.171317 0.0856586 0.996325i \(-0.472701\pi\)
0.0856586 + 0.996325i \(0.472701\pi\)
\(948\) −1508.31 −0.0516748
\(949\) −9236.88 −0.315955
\(950\) 3901.01 0.133227
\(951\) −16865.9 −0.575094
\(952\) −20999.8 −0.714923
\(953\) −18808.2 −0.639304 −0.319652 0.947535i \(-0.603566\pi\)
−0.319652 + 0.947535i \(0.603566\pi\)
\(954\) 8336.52 0.282919
\(955\) 11309.0 0.383196
\(956\) −6264.71 −0.211940
\(957\) −30193.5 −1.01987
\(958\) −4538.99 −0.153077
\(959\) −35871.5 −1.20788
\(960\) 13449.2 0.452156
\(961\) −13950.0 −0.468262
\(962\) −44153.5 −1.47980
\(963\) 352.832 0.0118067
\(964\) −81.5084 −0.00272324
\(965\) −22289.8 −0.743559
\(966\) −1306.80 −0.0435255
\(967\) 113.323 0.00376857 0.00188428 0.999998i \(-0.499400\pi\)
0.00188428 + 0.999998i \(0.499400\pi\)
\(968\) 62456.3 2.07378
\(969\) 3775.13 0.125154
\(970\) −8302.23 −0.274813
\(971\) 18935.8 0.625827 0.312913 0.949782i \(-0.398695\pi\)
0.312913 + 0.949782i \(0.398695\pi\)
\(972\) 277.326 0.00915148
\(973\) 45748.3 1.50732
\(974\) 6801.78 0.223761
\(975\) −13884.6 −0.456064
\(976\) 37353.9 1.22507
\(977\) 9255.46 0.303079 0.151540 0.988451i \(-0.451577\pi\)
0.151540 + 0.988451i \(0.451577\pi\)
\(978\) 26179.2 0.855951
\(979\) 63561.3 2.07500
\(980\) −529.441 −0.0172575
\(981\) −1891.40 −0.0615574
\(982\) −19703.0 −0.640272
\(983\) 21559.8 0.699544 0.349772 0.936835i \(-0.386259\pi\)
0.349772 + 0.936835i \(0.386259\pi\)
\(984\) 33574.2 1.08771
\(985\) −32938.9 −1.06550
\(986\) 21828.0 0.705016
\(987\) −22167.9 −0.714905
\(988\) 2078.18 0.0669188
\(989\) −896.548 −0.0288257
\(990\) 11786.6 0.378388
\(991\) 35161.9 1.12710 0.563550 0.826082i \(-0.309435\pi\)
0.563550 + 0.826082i \(0.309435\pi\)
\(992\) 6448.23 0.206383
\(993\) 22924.9 0.732627
\(994\) −9877.31 −0.315180
\(995\) 40227.9 1.28172
\(996\) −2267.79 −0.0721462
\(997\) −48076.0 −1.52716 −0.763582 0.645711i \(-0.776561\pi\)
−0.763582 + 0.645711i \(0.776561\pi\)
\(998\) −24599.0 −0.780227
\(999\) 6051.71 0.191659
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 177.4.a.b.1.3 7
3.2 odd 2 531.4.a.c.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.b.1.3 7 1.1 even 1 trivial
531.4.a.c.1.5 7 3.2 odd 2