Properties

Label 177.4.a.c.1.5
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $0$
Dimension $8$
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: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 2 x^{7} - 49 x^{6} + 89 x^{5} + 648 x^{4} - 1023 x^{3} - 1476 x^{2} + 1940 x - 384\)
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 1.5
Root \(0.780043\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.780043 q^{2} -3.00000 q^{3} -7.39153 q^{4} -21.9196 q^{5} -2.34013 q^{6} +32.1153 q^{7} -12.0061 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+0.780043 q^{2} -3.00000 q^{3} -7.39153 q^{4} -21.9196 q^{5} -2.34013 q^{6} +32.1153 q^{7} -12.0061 q^{8} +9.00000 q^{9} -17.0983 q^{10} -35.3089 q^{11} +22.1746 q^{12} +34.5155 q^{13} +25.0513 q^{14} +65.7589 q^{15} +49.7670 q^{16} -27.9810 q^{17} +7.02038 q^{18} +74.3473 q^{19} +162.020 q^{20} -96.3458 q^{21} -27.5424 q^{22} +128.081 q^{23} +36.0182 q^{24} +355.471 q^{25} +26.9235 q^{26} -27.0000 q^{27} -237.381 q^{28} +42.7099 q^{29} +51.2948 q^{30} -211.536 q^{31} +134.869 q^{32} +105.927 q^{33} -21.8263 q^{34} -703.955 q^{35} -66.5238 q^{36} -165.794 q^{37} +57.9940 q^{38} -103.546 q^{39} +263.168 q^{40} +377.795 q^{41} -75.1538 q^{42} -393.343 q^{43} +260.987 q^{44} -197.277 q^{45} +99.9085 q^{46} +261.503 q^{47} -149.301 q^{48} +688.391 q^{49} +277.282 q^{50} +83.9429 q^{51} -255.122 q^{52} -113.158 q^{53} -21.0611 q^{54} +773.957 q^{55} -385.578 q^{56} -223.042 q^{57} +33.3155 q^{58} -59.0000 q^{59} -486.059 q^{60} +337.123 q^{61} -165.007 q^{62} +289.037 q^{63} -292.933 q^{64} -756.567 q^{65} +82.6272 q^{66} +183.638 q^{67} +206.822 q^{68} -384.242 q^{69} -549.115 q^{70} -168.306 q^{71} -108.054 q^{72} +805.659 q^{73} -129.326 q^{74} -1066.41 q^{75} -549.540 q^{76} -1133.95 q^{77} -80.7706 q^{78} +797.644 q^{79} -1090.88 q^{80} +81.0000 q^{81} +294.696 q^{82} +251.649 q^{83} +712.143 q^{84} +613.333 q^{85} -306.824 q^{86} -128.130 q^{87} +423.920 q^{88} +653.582 q^{89} -153.884 q^{90} +1108.47 q^{91} -946.713 q^{92} +634.607 q^{93} +203.983 q^{94} -1629.67 q^{95} -404.606 q^{96} -1574.87 q^{97} +536.974 q^{98} -317.780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + 29q^{10} - 27q^{11} - 114q^{12} + 89q^{13} - 37q^{14} + 36q^{15} + 362q^{16} + 79q^{17} + 18q^{18} + 288q^{19} + 457q^{20} - 159q^{21} + 596q^{22} + 202q^{23} - 9q^{24} + 264q^{25} + 270q^{26} - 216q^{27} + 702q^{28} - 114q^{29} - 87q^{30} + 538q^{31} + 316q^{32} + 81q^{33} + 498q^{34} - 196q^{35} + 342q^{36} + 395q^{37} + 397q^{38} - 267q^{39} + 918q^{40} - 39q^{41} + 111q^{42} + 527q^{43} + 64q^{44} - 108q^{45} - 539q^{46} + 860q^{47} - 1086q^{48} + 347q^{49} - 591q^{50} - 237q^{51} - 644q^{52} - 812q^{53} - 54q^{54} + 536q^{55} - 2218q^{56} - 864q^{57} - 1154q^{58} - 472q^{59} - 1371q^{60} - 460q^{61} - 2014q^{62} + 477q^{63} - 451q^{64} - 986q^{65} - 1788q^{66} + 1934q^{67} - 69q^{68} - 606q^{69} - 1028q^{70} - 1687q^{71} + 27q^{72} + 1980q^{73} - 2400q^{74} - 792q^{75} - 940q^{76} - 821q^{77} - 810q^{78} + 3319q^{79} - 2119q^{80} + 648q^{81} + 429q^{82} + 2057q^{83} - 2106q^{84} + 566q^{85} - 6690q^{86} + 342q^{87} + 1189q^{88} + 1668q^{89} + 261q^{90} + 2427q^{91} - 980q^{92} - 1614q^{93} + 332q^{94} + 2146q^{95} - 948q^{96} + 1956q^{97} - 2026q^{98} - 243q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.780043 0.275787 0.137893 0.990447i \(-0.455967\pi\)
0.137893 + 0.990447i \(0.455967\pi\)
\(3\) −3.00000 −0.577350
\(4\) −7.39153 −0.923942
\(5\) −21.9196 −1.96055 −0.980276 0.197633i \(-0.936675\pi\)
−0.980276 + 0.197633i \(0.936675\pi\)
\(6\) −2.34013 −0.159226
\(7\) 32.1153 1.73406 0.867031 0.498255i \(-0.166026\pi\)
0.867031 + 0.498255i \(0.166026\pi\)
\(8\) −12.0061 −0.530598
\(9\) 9.00000 0.333333
\(10\) −17.0983 −0.540694
\(11\) −35.3089 −0.967820 −0.483910 0.875118i \(-0.660784\pi\)
−0.483910 + 0.875118i \(0.660784\pi\)
\(12\) 22.1746 0.533438
\(13\) 34.5155 0.736375 0.368187 0.929752i \(-0.379978\pi\)
0.368187 + 0.929752i \(0.379978\pi\)
\(14\) 25.0513 0.478231
\(15\) 65.7589 1.13193
\(16\) 49.7670 0.777610
\(17\) −27.9810 −0.399199 −0.199599 0.979878i \(-0.563964\pi\)
−0.199599 + 0.979878i \(0.563964\pi\)
\(18\) 7.02038 0.0919289
\(19\) 74.3473 0.897707 0.448853 0.893605i \(-0.351833\pi\)
0.448853 + 0.893605i \(0.351833\pi\)
\(20\) 162.020 1.81144
\(21\) −96.3458 −1.00116
\(22\) −27.5424 −0.266912
\(23\) 128.081 1.16116 0.580580 0.814203i \(-0.302826\pi\)
0.580580 + 0.814203i \(0.302826\pi\)
\(24\) 36.0182 0.306341
\(25\) 355.471 2.84377
\(26\) 26.9235 0.203082
\(27\) −27.0000 −0.192450
\(28\) −237.381 −1.60217
\(29\) 42.7099 0.273484 0.136742 0.990607i \(-0.456337\pi\)
0.136742 + 0.990607i \(0.456337\pi\)
\(30\) 51.2948 0.312170
\(31\) −211.536 −1.22558 −0.612790 0.790246i \(-0.709953\pi\)
−0.612790 + 0.790246i \(0.709953\pi\)
\(32\) 134.869 0.745052
\(33\) 105.927 0.558771
\(34\) −21.8263 −0.110094
\(35\) −703.955 −3.39972
\(36\) −66.5238 −0.307981
\(37\) −165.794 −0.736658 −0.368329 0.929695i \(-0.620070\pi\)
−0.368329 + 0.929695i \(0.620070\pi\)
\(38\) 57.9940 0.247576
\(39\) −103.546 −0.425146
\(40\) 263.168 1.04026
\(41\) 377.795 1.43906 0.719532 0.694459i \(-0.244356\pi\)
0.719532 + 0.694459i \(0.244356\pi\)
\(42\) −75.1538 −0.276107
\(43\) −393.343 −1.39498 −0.697491 0.716594i \(-0.745700\pi\)
−0.697491 + 0.716594i \(0.745700\pi\)
\(44\) 260.987 0.894209
\(45\) −197.277 −0.653517
\(46\) 99.9085 0.320233
\(47\) 261.503 0.811577 0.405789 0.913967i \(-0.366997\pi\)
0.405789 + 0.913967i \(0.366997\pi\)
\(48\) −149.301 −0.448953
\(49\) 688.391 2.00697
\(50\) 277.282 0.784273
\(51\) 83.9429 0.230478
\(52\) −255.122 −0.680367
\(53\) −113.158 −0.293273 −0.146636 0.989190i \(-0.546845\pi\)
−0.146636 + 0.989190i \(0.546845\pi\)
\(54\) −21.0611 −0.0530752
\(55\) 773.957 1.89746
\(56\) −385.578 −0.920089
\(57\) −223.042 −0.518291
\(58\) 33.3155 0.0754232
\(59\) −59.0000 −0.130189
\(60\) −486.059 −1.04583
\(61\) 337.123 0.707610 0.353805 0.935319i \(-0.384888\pi\)
0.353805 + 0.935319i \(0.384888\pi\)
\(62\) −165.007 −0.337998
\(63\) 289.037 0.578021
\(64\) −292.933 −0.572135
\(65\) −756.567 −1.44370
\(66\) 82.6272 0.154102
\(67\) 183.638 0.334850 0.167425 0.985885i \(-0.446455\pi\)
0.167425 + 0.985885i \(0.446455\pi\)
\(68\) 206.822 0.368837
\(69\) −384.242 −0.670396
\(70\) −549.115 −0.937597
\(71\) −168.306 −0.281327 −0.140664 0.990057i \(-0.544924\pi\)
−0.140664 + 0.990057i \(0.544924\pi\)
\(72\) −108.054 −0.176866
\(73\) 805.659 1.29172 0.645858 0.763457i \(-0.276500\pi\)
0.645858 + 0.763457i \(0.276500\pi\)
\(74\) −129.326 −0.203161
\(75\) −1066.41 −1.64185
\(76\) −549.540 −0.829429
\(77\) −1133.95 −1.67826
\(78\) −80.7706 −0.117250
\(79\) 797.644 1.13597 0.567987 0.823038i \(-0.307722\pi\)
0.567987 + 0.823038i \(0.307722\pi\)
\(80\) −1090.88 −1.52454
\(81\) 81.0000 0.111111
\(82\) 294.696 0.396875
\(83\) 251.649 0.332796 0.166398 0.986059i \(-0.446786\pi\)
0.166398 + 0.986059i \(0.446786\pi\)
\(84\) 712.143 0.925014
\(85\) 613.333 0.782650
\(86\) −306.824 −0.384717
\(87\) −128.130 −0.157896
\(88\) 423.920 0.513523
\(89\) 653.582 0.778422 0.389211 0.921149i \(-0.372748\pi\)
0.389211 + 0.921149i \(0.372748\pi\)
\(90\) −153.884 −0.180231
\(91\) 1108.47 1.27692
\(92\) −946.713 −1.07284
\(93\) 634.607 0.707589
\(94\) 203.983 0.223822
\(95\) −1629.67 −1.76000
\(96\) −404.606 −0.430156
\(97\) −1574.87 −1.64849 −0.824246 0.566231i \(-0.808401\pi\)
−0.824246 + 0.566231i \(0.808401\pi\)
\(98\) 536.974 0.553495
\(99\) −317.780 −0.322607
\(100\) −2627.47 −2.62747
\(101\) 1309.13 1.28973 0.644867 0.764295i \(-0.276913\pi\)
0.644867 + 0.764295i \(0.276913\pi\)
\(102\) 65.4790 0.0635627
\(103\) 855.586 0.818479 0.409240 0.912427i \(-0.365794\pi\)
0.409240 + 0.912427i \(0.365794\pi\)
\(104\) −414.395 −0.390719
\(105\) 2111.87 1.96283
\(106\) −88.2681 −0.0808807
\(107\) 661.333 0.597509 0.298755 0.954330i \(-0.403429\pi\)
0.298755 + 0.954330i \(0.403429\pi\)
\(108\) 199.571 0.177813
\(109\) 979.622 0.860832 0.430416 0.902631i \(-0.358367\pi\)
0.430416 + 0.902631i \(0.358367\pi\)
\(110\) 603.720 0.523295
\(111\) 497.382 0.425310
\(112\) 1598.28 1.34842
\(113\) 1814.46 1.51053 0.755267 0.655417i \(-0.227507\pi\)
0.755267 + 0.655417i \(0.227507\pi\)
\(114\) −173.982 −0.142938
\(115\) −2807.48 −2.27652
\(116\) −315.692 −0.252683
\(117\) 310.639 0.245458
\(118\) −46.0225 −0.0359044
\(119\) −898.616 −0.692235
\(120\) −789.505 −0.600597
\(121\) −84.2847 −0.0633244
\(122\) 262.970 0.195149
\(123\) −1133.38 −0.830844
\(124\) 1563.57 1.13236
\(125\) −5051.83 −3.61480
\(126\) 225.461 0.159410
\(127\) −2057.03 −1.43726 −0.718629 0.695393i \(-0.755230\pi\)
−0.718629 + 0.695393i \(0.755230\pi\)
\(128\) −1307.45 −0.902839
\(129\) 1180.03 0.805393
\(130\) −590.154 −0.398154
\(131\) 2007.37 1.33881 0.669407 0.742896i \(-0.266548\pi\)
0.669407 + 0.742896i \(0.266548\pi\)
\(132\) −782.960 −0.516272
\(133\) 2387.68 1.55668
\(134\) 143.245 0.0923471
\(135\) 591.830 0.377308
\(136\) 335.941 0.211814
\(137\) −1424.64 −0.888434 −0.444217 0.895919i \(-0.646518\pi\)
−0.444217 + 0.895919i \(0.646518\pi\)
\(138\) −299.725 −0.184886
\(139\) 455.829 0.278150 0.139075 0.990282i \(-0.455587\pi\)
0.139075 + 0.990282i \(0.455587\pi\)
\(140\) 5203.31 3.14114
\(141\) −784.509 −0.468564
\(142\) −131.286 −0.0775863
\(143\) −1218.70 −0.712678
\(144\) 447.903 0.259203
\(145\) −936.185 −0.536179
\(146\) 628.449 0.356238
\(147\) −2065.17 −1.15872
\(148\) 1225.47 0.680629
\(149\) 2370.80 1.30351 0.651756 0.758429i \(-0.274033\pi\)
0.651756 + 0.758429i \(0.274033\pi\)
\(150\) −831.847 −0.452800
\(151\) 413.879 0.223053 0.111526 0.993761i \(-0.464426\pi\)
0.111526 + 0.993761i \(0.464426\pi\)
\(152\) −892.617 −0.476321
\(153\) −251.829 −0.133066
\(154\) −884.532 −0.462842
\(155\) 4636.79 2.40281
\(156\) 765.367 0.392810
\(157\) −833.858 −0.423880 −0.211940 0.977283i \(-0.567978\pi\)
−0.211940 + 0.977283i \(0.567978\pi\)
\(158\) 622.196 0.313286
\(159\) 339.474 0.169321
\(160\) −2956.28 −1.46071
\(161\) 4113.35 2.01352
\(162\) 63.1834 0.0306430
\(163\) 3278.36 1.57534 0.787672 0.616095i \(-0.211286\pi\)
0.787672 + 0.616095i \(0.211286\pi\)
\(164\) −2792.48 −1.32961
\(165\) −2321.87 −1.09550
\(166\) 196.297 0.0917808
\(167\) 938.229 0.434745 0.217372 0.976089i \(-0.430251\pi\)
0.217372 + 0.976089i \(0.430251\pi\)
\(168\) 1156.73 0.531213
\(169\) −1005.68 −0.457752
\(170\) 478.426 0.215845
\(171\) 669.125 0.299236
\(172\) 2907.41 1.28888
\(173\) −1635.88 −0.718924 −0.359462 0.933160i \(-0.617040\pi\)
−0.359462 + 0.933160i \(0.617040\pi\)
\(174\) −99.9466 −0.0435456
\(175\) 11416.0 4.93126
\(176\) −1757.22 −0.752587
\(177\) 177.000 0.0751646
\(178\) 509.822 0.214678
\(179\) −1356.18 −0.566287 −0.283144 0.959078i \(-0.591377\pi\)
−0.283144 + 0.959078i \(0.591377\pi\)
\(180\) 1458.18 0.603812
\(181\) −2778.89 −1.14118 −0.570590 0.821235i \(-0.693285\pi\)
−0.570590 + 0.821235i \(0.693285\pi\)
\(182\) 864.657 0.352157
\(183\) −1011.37 −0.408539
\(184\) −1537.74 −0.616109
\(185\) 3634.14 1.44426
\(186\) 495.021 0.195143
\(187\) 987.976 0.386353
\(188\) −1932.91 −0.749850
\(189\) −867.112 −0.333720
\(190\) −1271.21 −0.485385
\(191\) −3200.32 −1.21239 −0.606197 0.795315i \(-0.707306\pi\)
−0.606197 + 0.795315i \(0.707306\pi\)
\(192\) 878.799 0.330322
\(193\) 945.056 0.352470 0.176235 0.984348i \(-0.443608\pi\)
0.176235 + 0.984348i \(0.443608\pi\)
\(194\) −1228.47 −0.454632
\(195\) 2269.70 0.833521
\(196\) −5088.26 −1.85432
\(197\) −135.114 −0.0488653 −0.0244327 0.999701i \(-0.507778\pi\)
−0.0244327 + 0.999701i \(0.507778\pi\)
\(198\) −247.882 −0.0889706
\(199\) −1993.07 −0.709976 −0.354988 0.934871i \(-0.615515\pi\)
−0.354988 + 0.934871i \(0.615515\pi\)
\(200\) −4267.80 −1.50889
\(201\) −550.913 −0.193326
\(202\) 1021.18 0.355691
\(203\) 1371.64 0.474238
\(204\) −620.467 −0.212948
\(205\) −8281.12 −2.82136
\(206\) 667.393 0.225726
\(207\) 1152.73 0.387053
\(208\) 1717.73 0.572612
\(209\) −2625.12 −0.868819
\(210\) 1647.34 0.541322
\(211\) 1231.14 0.401684 0.200842 0.979624i \(-0.435632\pi\)
0.200842 + 0.979624i \(0.435632\pi\)
\(212\) 836.412 0.270967
\(213\) 504.917 0.162424
\(214\) 515.868 0.164785
\(215\) 8621.93 2.73493
\(216\) 324.163 0.102114
\(217\) −6793.53 −2.12523
\(218\) 764.147 0.237406
\(219\) −2416.98 −0.745773
\(220\) −5720.73 −1.75314
\(221\) −965.777 −0.293960
\(222\) 387.979 0.117295
\(223\) 4085.96 1.22698 0.613489 0.789703i \(-0.289765\pi\)
0.613489 + 0.789703i \(0.289765\pi\)
\(224\) 4331.35 1.29197
\(225\) 3199.24 0.947922
\(226\) 1415.36 0.416585
\(227\) 5198.03 1.51985 0.759924 0.650012i \(-0.225236\pi\)
0.759924 + 0.650012i \(0.225236\pi\)
\(228\) 1648.62 0.478871
\(229\) −1237.19 −0.357014 −0.178507 0.983939i \(-0.557127\pi\)
−0.178507 + 0.983939i \(0.557127\pi\)
\(230\) −2189.96 −0.627833
\(231\) 3401.86 0.968944
\(232\) −512.777 −0.145110
\(233\) −5514.40 −1.55047 −0.775236 0.631671i \(-0.782369\pi\)
−0.775236 + 0.631671i \(0.782369\pi\)
\(234\) 242.312 0.0676941
\(235\) −5732.05 −1.59114
\(236\) 436.100 0.120287
\(237\) −2392.93 −0.655855
\(238\) −700.959 −0.190909
\(239\) −3600.71 −0.974522 −0.487261 0.873256i \(-0.662004\pi\)
−0.487261 + 0.873256i \(0.662004\pi\)
\(240\) 3272.63 0.880196
\(241\) 6157.76 1.64588 0.822938 0.568131i \(-0.192333\pi\)
0.822938 + 0.568131i \(0.192333\pi\)
\(242\) −65.7457 −0.0174640
\(243\) −243.000 −0.0641500
\(244\) −2491.86 −0.653790
\(245\) −15089.3 −3.93477
\(246\) −884.088 −0.229136
\(247\) 2566.13 0.661049
\(248\) 2539.71 0.650289
\(249\) −754.948 −0.192140
\(250\) −3940.65 −0.996913
\(251\) 6014.95 1.51259 0.756296 0.654230i \(-0.227007\pi\)
0.756296 + 0.654230i \(0.227007\pi\)
\(252\) −2136.43 −0.534057
\(253\) −4522.39 −1.12379
\(254\) −1604.57 −0.396377
\(255\) −1840.00 −0.451863
\(256\) 1323.60 0.323144
\(257\) −3933.41 −0.954706 −0.477353 0.878712i \(-0.658404\pi\)
−0.477353 + 0.878712i \(0.658404\pi\)
\(258\) 920.472 0.222117
\(259\) −5324.52 −1.27741
\(260\) 5592.19 1.33390
\(261\) 384.389 0.0911612
\(262\) 1565.83 0.369227
\(263\) 1974.57 0.462955 0.231477 0.972840i \(-0.425644\pi\)
0.231477 + 0.972840i \(0.425644\pi\)
\(264\) −1271.76 −0.296483
\(265\) 2480.38 0.574977
\(266\) 1862.49 0.429311
\(267\) −1960.75 −0.449422
\(268\) −1357.36 −0.309381
\(269\) 334.493 0.0758155 0.0379078 0.999281i \(-0.487931\pi\)
0.0379078 + 0.999281i \(0.487931\pi\)
\(270\) 461.653 0.104057
\(271\) −4193.71 −0.940036 −0.470018 0.882657i \(-0.655753\pi\)
−0.470018 + 0.882657i \(0.655753\pi\)
\(272\) −1392.53 −0.310421
\(273\) −3325.42 −0.737230
\(274\) −1111.28 −0.245018
\(275\) −12551.3 −2.75225
\(276\) 2840.14 0.619407
\(277\) 2515.63 0.545666 0.272833 0.962061i \(-0.412039\pi\)
0.272833 + 0.962061i \(0.412039\pi\)
\(278\) 355.566 0.0767101
\(279\) −1903.82 −0.408526
\(280\) 8451.72 1.80388
\(281\) −616.348 −0.130848 −0.0654239 0.997858i \(-0.520840\pi\)
−0.0654239 + 0.997858i \(0.520840\pi\)
\(282\) −611.950 −0.129224
\(283\) −3782.80 −0.794573 −0.397286 0.917695i \(-0.630048\pi\)
−0.397286 + 0.917695i \(0.630048\pi\)
\(284\) 1244.04 0.259930
\(285\) 4889.00 1.01614
\(286\) −950.640 −0.196547
\(287\) 12133.0 2.49543
\(288\) 1213.82 0.248351
\(289\) −4130.07 −0.840640
\(290\) −730.264 −0.147871
\(291\) 4724.61 0.951758
\(292\) −5955.06 −1.19347
\(293\) 1298.66 0.258938 0.129469 0.991583i \(-0.458673\pi\)
0.129469 + 0.991583i \(0.458673\pi\)
\(294\) −1610.92 −0.319561
\(295\) 1293.26 0.255242
\(296\) 1990.53 0.390869
\(297\) 953.339 0.186257
\(298\) 1849.32 0.359491
\(299\) 4420.77 0.855049
\(300\) 7882.42 1.51697
\(301\) −12632.3 −2.41898
\(302\) 322.843 0.0615150
\(303\) −3927.38 −0.744628
\(304\) 3700.04 0.698066
\(305\) −7389.62 −1.38731
\(306\) −196.437 −0.0366979
\(307\) −2669.82 −0.496335 −0.248167 0.968717i \(-0.579828\pi\)
−0.248167 + 0.968717i \(0.579828\pi\)
\(308\) 8381.65 1.55061
\(309\) −2566.76 −0.472549
\(310\) 3616.89 0.662664
\(311\) 3834.46 0.699139 0.349570 0.936910i \(-0.386328\pi\)
0.349570 + 0.936910i \(0.386328\pi\)
\(312\) 1243.18 0.225582
\(313\) 6620.03 1.19548 0.597741 0.801689i \(-0.296065\pi\)
0.597741 + 0.801689i \(0.296065\pi\)
\(314\) −650.445 −0.116900
\(315\) −6335.60 −1.13324
\(316\) −5895.81 −1.04957
\(317\) −2662.49 −0.471736 −0.235868 0.971785i \(-0.575793\pi\)
−0.235868 + 0.971785i \(0.575793\pi\)
\(318\) 264.804 0.0466965
\(319\) −1508.04 −0.264683
\(320\) 6420.98 1.12170
\(321\) −1984.00 −0.344972
\(322\) 3208.59 0.555303
\(323\) −2080.31 −0.358364
\(324\) −598.714 −0.102660
\(325\) 12269.2 2.09408
\(326\) 2557.26 0.434459
\(327\) −2938.86 −0.497002
\(328\) −4535.82 −0.763564
\(329\) 8398.24 1.40732
\(330\) −1811.16 −0.302124
\(331\) −6571.43 −1.09123 −0.545617 0.838035i \(-0.683705\pi\)
−0.545617 + 0.838035i \(0.683705\pi\)
\(332\) −1860.07 −0.307484
\(333\) −1492.15 −0.245553
\(334\) 731.859 0.119897
\(335\) −4025.27 −0.656490
\(336\) −4794.85 −0.778513
\(337\) 5603.74 0.905802 0.452901 0.891561i \(-0.350389\pi\)
0.452901 + 0.891561i \(0.350389\pi\)
\(338\) −784.474 −0.126242
\(339\) −5443.39 −0.872107
\(340\) −4533.47 −0.723123
\(341\) 7469.09 1.18614
\(342\) 521.946 0.0825252
\(343\) 11092.3 1.74615
\(344\) 4722.49 0.740174
\(345\) 8422.45 1.31435
\(346\) −1276.06 −0.198270
\(347\) 653.011 0.101024 0.0505122 0.998723i \(-0.483915\pi\)
0.0505122 + 0.998723i \(0.483915\pi\)
\(348\) 947.075 0.145887
\(349\) 1891.17 0.290063 0.145031 0.989427i \(-0.453672\pi\)
0.145031 + 0.989427i \(0.453672\pi\)
\(350\) 8904.99 1.35998
\(351\) −931.918 −0.141715
\(352\) −4762.06 −0.721076
\(353\) −10774.6 −1.62457 −0.812285 0.583261i \(-0.801776\pi\)
−0.812285 + 0.583261i \(0.801776\pi\)
\(354\) 138.068 0.0207294
\(355\) 3689.20 0.551557
\(356\) −4830.97 −0.719216
\(357\) 2695.85 0.399662
\(358\) −1057.88 −0.156175
\(359\) 2797.37 0.411253 0.205626 0.978631i \(-0.434077\pi\)
0.205626 + 0.978631i \(0.434077\pi\)
\(360\) 2368.52 0.346755
\(361\) −1331.48 −0.194122
\(362\) −2167.66 −0.314722
\(363\) 252.854 0.0365603
\(364\) −8193.32 −1.17980
\(365\) −17659.8 −2.53248
\(366\) −788.911 −0.112670
\(367\) 3198.93 0.454994 0.227497 0.973779i \(-0.426946\pi\)
0.227497 + 0.973779i \(0.426946\pi\)
\(368\) 6374.20 0.902930
\(369\) 3400.15 0.479688
\(370\) 2834.79 0.398307
\(371\) −3634.10 −0.508553
\(372\) −4690.72 −0.653771
\(373\) 263.678 0.0366025 0.0183013 0.999833i \(-0.494174\pi\)
0.0183013 + 0.999833i \(0.494174\pi\)
\(374\) 770.663 0.106551
\(375\) 15155.5 2.08700
\(376\) −3139.62 −0.430621
\(377\) 1474.15 0.201387
\(378\) −676.384 −0.0920356
\(379\) 1657.03 0.224580 0.112290 0.993675i \(-0.464181\pi\)
0.112290 + 0.993675i \(0.464181\pi\)
\(380\) 12045.7 1.62614
\(381\) 6171.09 0.829802
\(382\) −2496.39 −0.334362
\(383\) 12320.1 1.64367 0.821837 0.569723i \(-0.192949\pi\)
0.821837 + 0.569723i \(0.192949\pi\)
\(384\) 3922.35 0.521254
\(385\) 24855.9 3.29032
\(386\) 737.184 0.0972064
\(387\) −3540.08 −0.464994
\(388\) 11640.7 1.52311
\(389\) −4911.58 −0.640172 −0.320086 0.947389i \(-0.603712\pi\)
−0.320086 + 0.947389i \(0.603712\pi\)
\(390\) 1770.46 0.229874
\(391\) −3583.82 −0.463534
\(392\) −8264.85 −1.06489
\(393\) −6022.11 −0.772965
\(394\) −105.395 −0.0134764
\(395\) −17484.1 −2.22714
\(396\) 2348.88 0.298070
\(397\) 15177.7 1.91875 0.959377 0.282126i \(-0.0910397\pi\)
0.959377 + 0.282126i \(0.0910397\pi\)
\(398\) −1554.68 −0.195802
\(399\) −7163.05 −0.898749
\(400\) 17690.7 2.21134
\(401\) −6165.32 −0.767785 −0.383892 0.923378i \(-0.625417\pi\)
−0.383892 + 0.923378i \(0.625417\pi\)
\(402\) −429.736 −0.0533166
\(403\) −7301.26 −0.902486
\(404\) −9676.47 −1.19164
\(405\) −1775.49 −0.217839
\(406\) 1069.94 0.130788
\(407\) 5853.99 0.712953
\(408\) −1007.82 −0.122291
\(409\) −7801.41 −0.943166 −0.471583 0.881822i \(-0.656317\pi\)
−0.471583 + 0.881822i \(0.656317\pi\)
\(410\) −6459.63 −0.778093
\(411\) 4273.93 0.512938
\(412\) −6324.09 −0.756227
\(413\) −1894.80 −0.225756
\(414\) 899.176 0.106744
\(415\) −5516.06 −0.652465
\(416\) 4655.06 0.548638
\(417\) −1367.49 −0.160590
\(418\) −2047.70 −0.239609
\(419\) −8108.97 −0.945463 −0.472732 0.881207i \(-0.656732\pi\)
−0.472732 + 0.881207i \(0.656732\pi\)
\(420\) −15609.9 −1.81354
\(421\) 9487.25 1.09829 0.549145 0.835727i \(-0.314953\pi\)
0.549145 + 0.835727i \(0.314953\pi\)
\(422\) 960.343 0.110779
\(423\) 2353.53 0.270526
\(424\) 1358.58 0.155610
\(425\) −9946.41 −1.13523
\(426\) 393.857 0.0447945
\(427\) 10826.8 1.22704
\(428\) −4888.27 −0.552064
\(429\) 3656.11 0.411465
\(430\) 6725.47 0.754258
\(431\) 11388.1 1.27273 0.636366 0.771387i \(-0.280437\pi\)
0.636366 + 0.771387i \(0.280437\pi\)
\(432\) −1343.71 −0.149651
\(433\) 15467.8 1.71671 0.858353 0.513060i \(-0.171488\pi\)
0.858353 + 0.513060i \(0.171488\pi\)
\(434\) −5299.24 −0.586110
\(435\) 2808.56 0.309563
\(436\) −7240.91 −0.795359
\(437\) 9522.46 1.04238
\(438\) −1885.35 −0.205674
\(439\) 8989.92 0.977370 0.488685 0.872460i \(-0.337477\pi\)
0.488685 + 0.872460i \(0.337477\pi\)
\(440\) −9292.17 −1.00679
\(441\) 6195.51 0.668990
\(442\) −753.347 −0.0810703
\(443\) 12756.2 1.36809 0.684045 0.729439i \(-0.260219\pi\)
0.684045 + 0.729439i \(0.260219\pi\)
\(444\) −3676.41 −0.392961
\(445\) −14326.3 −1.52614
\(446\) 3187.22 0.338384
\(447\) −7112.39 −0.752583
\(448\) −9407.62 −0.992116
\(449\) −7974.32 −0.838154 −0.419077 0.907951i \(-0.637646\pi\)
−0.419077 + 0.907951i \(0.637646\pi\)
\(450\) 2495.54 0.261424
\(451\) −13339.5 −1.39275
\(452\) −13411.7 −1.39565
\(453\) −1241.64 −0.128780
\(454\) 4054.69 0.419154
\(455\) −24297.4 −2.50347
\(456\) 2677.85 0.275004
\(457\) −2012.86 −0.206034 −0.103017 0.994680i \(-0.532850\pi\)
−0.103017 + 0.994680i \(0.532850\pi\)
\(458\) −965.065 −0.0984596
\(459\) 755.486 0.0768259
\(460\) 20751.6 2.10337
\(461\) −12665.8 −1.27962 −0.639810 0.768533i \(-0.720987\pi\)
−0.639810 + 0.768533i \(0.720987\pi\)
\(462\) 2653.60 0.267222
\(463\) −3474.03 −0.348709 −0.174354 0.984683i \(-0.555784\pi\)
−0.174354 + 0.984683i \(0.555784\pi\)
\(464\) 2125.54 0.212664
\(465\) −13910.4 −1.38726
\(466\) −4301.46 −0.427600
\(467\) 317.104 0.0314214 0.0157107 0.999877i \(-0.494999\pi\)
0.0157107 + 0.999877i \(0.494999\pi\)
\(468\) −2296.10 −0.226789
\(469\) 5897.58 0.580650
\(470\) −4471.24 −0.438815
\(471\) 2501.57 0.244727
\(472\) 708.357 0.0690779
\(473\) 13888.5 1.35009
\(474\) −1866.59 −0.180876
\(475\) 26428.3 2.55287
\(476\) 6642.15 0.639585
\(477\) −1018.42 −0.0977576
\(478\) −2808.71 −0.268760
\(479\) 19601.8 1.86979 0.934895 0.354923i \(-0.115493\pi\)
0.934895 + 0.354923i \(0.115493\pi\)
\(480\) 8868.83 0.843343
\(481\) −5722.46 −0.542457
\(482\) 4803.31 0.453911
\(483\) −12340.0 −1.16251
\(484\) 622.993 0.0585080
\(485\) 34520.6 3.23196
\(486\) −189.550 −0.0176917
\(487\) −13669.1 −1.27189 −0.635943 0.771736i \(-0.719389\pi\)
−0.635943 + 0.771736i \(0.719389\pi\)
\(488\) −4047.52 −0.375456
\(489\) −9835.09 −0.909525
\(490\) −11770.3 −1.08516
\(491\) −13294.5 −1.22194 −0.610970 0.791653i \(-0.709221\pi\)
−0.610970 + 0.791653i \(0.709221\pi\)
\(492\) 8377.45 0.767651
\(493\) −1195.06 −0.109174
\(494\) 2001.69 0.182308
\(495\) 6965.62 0.632487
\(496\) −10527.5 −0.953023
\(497\) −5405.19 −0.487839
\(498\) −588.892 −0.0529897
\(499\) 4779.40 0.428768 0.214384 0.976749i \(-0.431226\pi\)
0.214384 + 0.976749i \(0.431226\pi\)
\(500\) 37340.8 3.33986
\(501\) −2814.69 −0.251000
\(502\) 4691.92 0.417152
\(503\) −6846.81 −0.606927 −0.303463 0.952843i \(-0.598143\pi\)
−0.303463 + 0.952843i \(0.598143\pi\)
\(504\) −3470.20 −0.306696
\(505\) −28695.6 −2.52859
\(506\) −3527.65 −0.309928
\(507\) 3017.04 0.264283
\(508\) 15204.6 1.32794
\(509\) 2306.50 0.200852 0.100426 0.994945i \(-0.467979\pi\)
0.100426 + 0.994945i \(0.467979\pi\)
\(510\) −1435.28 −0.124618
\(511\) 25874.0 2.23992
\(512\) 11492.1 0.991958
\(513\) −2007.38 −0.172764
\(514\) −3068.23 −0.263295
\(515\) −18754.1 −1.60467
\(516\) −8722.22 −0.744136
\(517\) −9233.37 −0.785461
\(518\) −4153.35 −0.352293
\(519\) 4907.65 0.415071
\(520\) 9083.38 0.766024
\(521\) −2031.49 −0.170828 −0.0854139 0.996346i \(-0.527221\pi\)
−0.0854139 + 0.996346i \(0.527221\pi\)
\(522\) 299.840 0.0251411
\(523\) −16135.1 −1.34902 −0.674512 0.738264i \(-0.735646\pi\)
−0.674512 + 0.738264i \(0.735646\pi\)
\(524\) −14837.5 −1.23699
\(525\) −34248.1 −2.84707
\(526\) 1540.25 0.127677
\(527\) 5918.98 0.489250
\(528\) 5271.65 0.434506
\(529\) 4237.69 0.348293
\(530\) 1934.81 0.158571
\(531\) −531.000 −0.0433963
\(532\) −17648.6 −1.43828
\(533\) 13039.8 1.05969
\(534\) −1529.47 −0.123945
\(535\) −14496.2 −1.17145
\(536\) −2204.76 −0.177670
\(537\) 4068.53 0.326946
\(538\) 260.919 0.0209089
\(539\) −24306.3 −1.94239
\(540\) −4374.53 −0.348611
\(541\) 4833.44 0.384114 0.192057 0.981384i \(-0.438484\pi\)
0.192057 + 0.981384i \(0.438484\pi\)
\(542\) −3271.27 −0.259249
\(543\) 8336.68 0.658860
\(544\) −3773.76 −0.297424
\(545\) −21473.0 −1.68771
\(546\) −2593.97 −0.203318
\(547\) −6411.62 −0.501172 −0.250586 0.968094i \(-0.580623\pi\)
−0.250586 + 0.968094i \(0.580623\pi\)
\(548\) 10530.3 0.820861
\(549\) 3034.11 0.235870
\(550\) −9790.52 −0.759035
\(551\) 3175.36 0.245508
\(552\) 4613.23 0.355711
\(553\) 25616.5 1.96985
\(554\) 1962.30 0.150488
\(555\) −10902.4 −0.833842
\(556\) −3369.27 −0.256995
\(557\) −4099.19 −0.311828 −0.155914 0.987771i \(-0.549832\pi\)
−0.155914 + 0.987771i \(0.549832\pi\)
\(558\) −1485.06 −0.112666
\(559\) −13576.4 −1.02723
\(560\) −35033.8 −2.64365
\(561\) −2963.93 −0.223061
\(562\) −480.777 −0.0360861
\(563\) −4795.83 −0.359006 −0.179503 0.983757i \(-0.557449\pi\)
−0.179503 + 0.983757i \(0.557449\pi\)
\(564\) 5798.72 0.432926
\(565\) −39772.4 −2.96148
\(566\) −2950.74 −0.219133
\(567\) 2601.34 0.192674
\(568\) 2020.69 0.149271
\(569\) 14582.8 1.07441 0.537207 0.843451i \(-0.319480\pi\)
0.537207 + 0.843451i \(0.319480\pi\)
\(570\) 3813.63 0.280237
\(571\) −17268.6 −1.26562 −0.632809 0.774308i \(-0.718098\pi\)
−0.632809 + 0.774308i \(0.718098\pi\)
\(572\) 9008.08 0.658473
\(573\) 9600.96 0.699976
\(574\) 9464.24 0.688205
\(575\) 45529.0 3.30207
\(576\) −2636.40 −0.190712
\(577\) −10005.8 −0.721918 −0.360959 0.932582i \(-0.617551\pi\)
−0.360959 + 0.932582i \(0.617551\pi\)
\(578\) −3221.63 −0.231837
\(579\) −2835.17 −0.203498
\(580\) 6919.85 0.495398
\(581\) 8081.78 0.577089
\(582\) 3685.40 0.262482
\(583\) 3995.48 0.283835
\(584\) −9672.79 −0.685382
\(585\) −6809.10 −0.481234
\(586\) 1013.01 0.0714116
\(587\) −1313.62 −0.0923662 −0.0461831 0.998933i \(-0.514706\pi\)
−0.0461831 + 0.998933i \(0.514706\pi\)
\(588\) 15264.8 1.07059
\(589\) −15727.1 −1.10021
\(590\) 1008.80 0.0703924
\(591\) 405.342 0.0282124
\(592\) −8251.07 −0.572833
\(593\) 18128.5 1.25539 0.627697 0.778458i \(-0.283998\pi\)
0.627697 + 0.778458i \(0.283998\pi\)
\(594\) 743.645 0.0513672
\(595\) 19697.3 1.35716
\(596\) −17523.8 −1.20437
\(597\) 5979.22 0.409905
\(598\) 3448.39 0.235811
\(599\) 636.072 0.0433876 0.0216938 0.999765i \(-0.493094\pi\)
0.0216938 + 0.999765i \(0.493094\pi\)
\(600\) 12803.4 0.871161
\(601\) 12022.0 0.815950 0.407975 0.912993i \(-0.366235\pi\)
0.407975 + 0.912993i \(0.366235\pi\)
\(602\) −9853.74 −0.667123
\(603\) 1652.74 0.111617
\(604\) −3059.20 −0.206088
\(605\) 1847.49 0.124151
\(606\) −3063.53 −0.205359
\(607\) 4317.86 0.288726 0.144363 0.989525i \(-0.453887\pi\)
0.144363 + 0.989525i \(0.453887\pi\)
\(608\) 10027.1 0.668838
\(609\) −4114.92 −0.273801
\(610\) −5764.22 −0.382600
\(611\) 9025.90 0.597625
\(612\) 1861.40 0.122946
\(613\) 7724.56 0.508959 0.254480 0.967078i \(-0.418096\pi\)
0.254480 + 0.967078i \(0.418096\pi\)
\(614\) −2082.57 −0.136883
\(615\) 24843.4 1.62891
\(616\) 13614.3 0.890480
\(617\) −13543.2 −0.883676 −0.441838 0.897095i \(-0.645673\pi\)
−0.441838 + 0.897095i \(0.645673\pi\)
\(618\) −2002.18 −0.130323
\(619\) 24983.1 1.62222 0.811112 0.584891i \(-0.198863\pi\)
0.811112 + 0.584891i \(0.198863\pi\)
\(620\) −34273.0 −2.22006
\(621\) −3458.18 −0.223465
\(622\) 2991.04 0.192813
\(623\) 20990.0 1.34983
\(624\) −5153.20 −0.330598
\(625\) 66300.6 4.24324
\(626\) 5163.90 0.329698
\(627\) 7875.35 0.501613
\(628\) 6163.49 0.391640
\(629\) 4639.07 0.294073
\(630\) −4942.03 −0.312532
\(631\) 2921.67 0.184327 0.0921633 0.995744i \(-0.470622\pi\)
0.0921633 + 0.995744i \(0.470622\pi\)
\(632\) −9576.55 −0.602745
\(633\) −3693.43 −0.231912
\(634\) −2076.85 −0.130098
\(635\) 45089.3 2.81782
\(636\) −2509.24 −0.156443
\(637\) 23760.1 1.47788
\(638\) −1176.33 −0.0729960
\(639\) −1514.75 −0.0937757
\(640\) 28658.8 1.77006
\(641\) 7252.88 0.446914 0.223457 0.974714i \(-0.428266\pi\)
0.223457 + 0.974714i \(0.428266\pi\)
\(642\) −1547.60 −0.0951388
\(643\) 21945.7 1.34596 0.672981 0.739659i \(-0.265013\pi\)
0.672981 + 0.739659i \(0.265013\pi\)
\(644\) −30404.0 −1.86038
\(645\) −25865.8 −1.57901
\(646\) −1622.73 −0.0988319
\(647\) −4657.90 −0.283031 −0.141515 0.989936i \(-0.545197\pi\)
−0.141515 + 0.989936i \(0.545197\pi\)
\(648\) −972.490 −0.0589553
\(649\) 2083.22 0.125999
\(650\) 9570.53 0.577519
\(651\) 20380.6 1.22700
\(652\) −24232.1 −1.45553
\(653\) −6157.88 −0.369030 −0.184515 0.982830i \(-0.559071\pi\)
−0.184515 + 0.982830i \(0.559071\pi\)
\(654\) −2292.44 −0.137066
\(655\) −44000.8 −2.62482
\(656\) 18801.7 1.11903
\(657\) 7250.94 0.430572
\(658\) 6550.98 0.388121
\(659\) −5471.34 −0.323419 −0.161709 0.986838i \(-0.551701\pi\)
−0.161709 + 0.986838i \(0.551701\pi\)
\(660\) 17162.2 1.01218
\(661\) 14162.9 0.833396 0.416698 0.909045i \(-0.363187\pi\)
0.416698 + 0.909045i \(0.363187\pi\)
\(662\) −5126.00 −0.300948
\(663\) 2897.33 0.169718
\(664\) −3021.31 −0.176581
\(665\) −52337.1 −3.05195
\(666\) −1163.94 −0.0677202
\(667\) 5470.32 0.317558
\(668\) −6934.95 −0.401679
\(669\) −12257.9 −0.708397
\(670\) −3139.88 −0.181051
\(671\) −11903.4 −0.684839
\(672\) −12994.0 −0.745917
\(673\) −9280.39 −0.531550 −0.265775 0.964035i \(-0.585628\pi\)
−0.265775 + 0.964035i \(0.585628\pi\)
\(674\) 4371.16 0.249808
\(675\) −9597.71 −0.547283
\(676\) 7433.53 0.422936
\(677\) 17040.6 0.967391 0.483695 0.875236i \(-0.339294\pi\)
0.483695 + 0.875236i \(0.339294\pi\)
\(678\) −4246.08 −0.240516
\(679\) −50577.4 −2.85859
\(680\) −7363.70 −0.415272
\(681\) −15594.1 −0.877485
\(682\) 5826.21 0.327122
\(683\) 20830.7 1.16700 0.583502 0.812112i \(-0.301682\pi\)
0.583502 + 0.812112i \(0.301682\pi\)
\(684\) −4945.86 −0.276476
\(685\) 31227.7 1.74182
\(686\) 8652.47 0.481564
\(687\) 3711.58 0.206122
\(688\) −19575.5 −1.08475
\(689\) −3905.71 −0.215959
\(690\) 6569.87 0.362479
\(691\) 13181.3 0.725671 0.362835 0.931853i \(-0.381809\pi\)
0.362835 + 0.931853i \(0.381809\pi\)
\(692\) 12091.7 0.664244
\(693\) −10205.6 −0.559420
\(694\) 509.376 0.0278612
\(695\) −9991.60 −0.545328
\(696\) 1538.33 0.0837792
\(697\) −10571.1 −0.574473
\(698\) 1475.19 0.0799955
\(699\) 16543.2 0.895166
\(700\) −84382.0 −4.55620
\(701\) −2796.51 −0.150675 −0.0753373 0.997158i \(-0.524003\pi\)
−0.0753373 + 0.997158i \(0.524003\pi\)
\(702\) −726.936 −0.0390832
\(703\) −12326.3 −0.661303
\(704\) 10343.1 0.553723
\(705\) 17196.2 0.918645
\(706\) −8404.63 −0.448035
\(707\) 42043.0 2.23648
\(708\) −1308.30 −0.0694477
\(709\) −8280.22 −0.438604 −0.219302 0.975657i \(-0.570378\pi\)
−0.219302 + 0.975657i \(0.570378\pi\)
\(710\) 2877.74 0.152112
\(711\) 7178.79 0.378658
\(712\) −7846.94 −0.413029
\(713\) −27093.7 −1.42309
\(714\) 2102.88 0.110222
\(715\) 26713.5 1.39724
\(716\) 10024.2 0.523216
\(717\) 10802.1 0.562641
\(718\) 2182.07 0.113418
\(719\) −30936.1 −1.60462 −0.802310 0.596907i \(-0.796396\pi\)
−0.802310 + 0.596907i \(0.796396\pi\)
\(720\) −9817.88 −0.508182
\(721\) 27477.4 1.41929
\(722\) −1038.61 −0.0535363
\(723\) −18473.3 −0.950247
\(724\) 20540.3 1.05438
\(725\) 15182.1 0.777723
\(726\) 197.237 0.0100829
\(727\) 24053.2 1.22708 0.613538 0.789665i \(-0.289746\pi\)
0.613538 + 0.789665i \(0.289746\pi\)
\(728\) −13308.4 −0.677530
\(729\) 729.000 0.0370370
\(730\) −13775.4 −0.698424
\(731\) 11006.1 0.556875
\(732\) 7475.57 0.377466
\(733\) −4234.34 −0.213368 −0.106684 0.994293i \(-0.534023\pi\)
−0.106684 + 0.994293i \(0.534023\pi\)
\(734\) 2495.30 0.125481
\(735\) 45267.8 2.27174
\(736\) 17274.1 0.865125
\(737\) −6484.04 −0.324074
\(738\) 2652.26 0.132292
\(739\) −29248.6 −1.45592 −0.727961 0.685619i \(-0.759532\pi\)
−0.727961 + 0.685619i \(0.759532\pi\)
\(740\) −26861.9 −1.33441
\(741\) −7698.40 −0.381657
\(742\) −2834.75 −0.140252
\(743\) −5051.56 −0.249426 −0.124713 0.992193i \(-0.539801\pi\)
−0.124713 + 0.992193i \(0.539801\pi\)
\(744\) −7619.13 −0.375445
\(745\) −51967.0 −2.55560
\(746\) 205.680 0.0100945
\(747\) 2264.84 0.110932
\(748\) −7302.66 −0.356967
\(749\) 21238.9 1.03612
\(750\) 11821.9 0.575568
\(751\) 12132.8 0.589526 0.294763 0.955570i \(-0.404759\pi\)
0.294763 + 0.955570i \(0.404759\pi\)
\(752\) 13014.2 0.631090
\(753\) −18044.9 −0.873295
\(754\) 1149.90 0.0555397
\(755\) −9072.07 −0.437307
\(756\) 6409.29 0.308338
\(757\) −14667.2 −0.704214 −0.352107 0.935960i \(-0.614535\pi\)
−0.352107 + 0.935960i \(0.614535\pi\)
\(758\) 1292.55 0.0619362
\(759\) 13567.2 0.648823
\(760\) 19565.8 0.933852
\(761\) −2328.04 −0.110895 −0.0554477 0.998462i \(-0.517659\pi\)
−0.0554477 + 0.998462i \(0.517659\pi\)
\(762\) 4813.71 0.228848
\(763\) 31460.8 1.49274
\(764\) 23655.3 1.12018
\(765\) 5519.99 0.260883
\(766\) 9610.19 0.453303
\(767\) −2036.41 −0.0958678
\(768\) −3970.79 −0.186567
\(769\) 25456.4 1.19373 0.596867 0.802340i \(-0.296412\pi\)
0.596867 + 0.802340i \(0.296412\pi\)
\(770\) 19388.6 0.907425
\(771\) 11800.2 0.551200
\(772\) −6985.41 −0.325661
\(773\) 2331.11 0.108466 0.0542331 0.998528i \(-0.482729\pi\)
0.0542331 + 0.998528i \(0.482729\pi\)
\(774\) −2761.42 −0.128239
\(775\) −75194.8 −3.48526
\(776\) 18908.0 0.874686
\(777\) 15973.6 0.737513
\(778\) −3831.24 −0.176551
\(779\) 28088.0 1.29186
\(780\) −16776.6 −0.770125
\(781\) 5942.69 0.272274
\(782\) −2795.54 −0.127836
\(783\) −1153.17 −0.0526320
\(784\) 34259.2 1.56064
\(785\) 18277.9 0.831038
\(786\) −4697.50 −0.213173
\(787\) −15041.1 −0.681268 −0.340634 0.940196i \(-0.610642\pi\)
−0.340634 + 0.940196i \(0.610642\pi\)
\(788\) 998.699 0.0451487
\(789\) −5923.70 −0.267287
\(790\) −13638.3 −0.614214
\(791\) 58272.0 2.61936
\(792\) 3815.28 0.171174
\(793\) 11636.0 0.521066
\(794\) 11839.2 0.529167
\(795\) −7441.15 −0.331963
\(796\) 14731.9 0.655976
\(797\) 38360.4 1.70489 0.852444 0.522818i \(-0.175119\pi\)
0.852444 + 0.522818i \(0.175119\pi\)
\(798\) −5587.48 −0.247863
\(799\) −7317.10 −0.323981
\(800\) 47941.9 2.11875
\(801\) 5882.24 0.259474
\(802\) −4809.22 −0.211745
\(803\) −28446.9 −1.25015
\(804\) 4072.09 0.178621
\(805\) −90163.1 −3.94762
\(806\) −5695.29 −0.248894
\(807\) −1003.48 −0.0437721
\(808\) −15717.5 −0.684330
\(809\) 20027.1 0.870351 0.435175 0.900346i \(-0.356686\pi\)
0.435175 + 0.900346i \(0.356686\pi\)
\(810\) −1384.96 −0.0600771
\(811\) −27584.7 −1.19436 −0.597182 0.802106i \(-0.703713\pi\)
−0.597182 + 0.802106i \(0.703713\pi\)
\(812\) −10138.5 −0.438168
\(813\) 12581.1 0.542730
\(814\) 4566.36 0.196623
\(815\) −71860.5 −3.08854
\(816\) 4177.59 0.179222
\(817\) −29244.0 −1.25228
\(818\) −6085.43 −0.260113
\(819\) 9976.27 0.425640
\(820\) 61210.2 2.60677
\(821\) −5945.56 −0.252742 −0.126371 0.991983i \(-0.540333\pi\)
−0.126371 + 0.991983i \(0.540333\pi\)
\(822\) 3333.85 0.141461
\(823\) −5880.56 −0.249069 −0.124534 0.992215i \(-0.539744\pi\)
−0.124534 + 0.992215i \(0.539744\pi\)
\(824\) −10272.2 −0.434283
\(825\) 37653.8 1.58901
\(826\) −1478.03 −0.0622604
\(827\) 37847.0 1.59138 0.795689 0.605705i \(-0.207109\pi\)
0.795689 + 0.605705i \(0.207109\pi\)
\(828\) −8520.42 −0.357615
\(829\) −38100.9 −1.59626 −0.798130 0.602485i \(-0.794177\pi\)
−0.798130 + 0.602485i \(0.794177\pi\)
\(830\) −4302.76 −0.179941
\(831\) −7546.89 −0.315041
\(832\) −10110.7 −0.421305
\(833\) −19261.8 −0.801180
\(834\) −1066.70 −0.0442886
\(835\) −20565.7 −0.852340
\(836\) 19403.6 0.802738
\(837\) 5711.47 0.235863
\(838\) −6325.34 −0.260746
\(839\) −15102.5 −0.621450 −0.310725 0.950500i \(-0.600572\pi\)
−0.310725 + 0.950500i \(0.600572\pi\)
\(840\) −25355.2 −1.04147
\(841\) −22564.9 −0.925207
\(842\) 7400.46 0.302894
\(843\) 1849.04 0.0755450
\(844\) −9100.03 −0.371133
\(845\) 22044.2 0.897447
\(846\) 1835.85 0.0746074
\(847\) −2706.83 −0.109808
\(848\) −5631.54 −0.228052
\(849\) 11348.4 0.458747
\(850\) −7758.63 −0.313081
\(851\) −21235.0 −0.855378
\(852\) −3732.11 −0.150071
\(853\) 32185.9 1.29194 0.645970 0.763363i \(-0.276453\pi\)
0.645970 + 0.763363i \(0.276453\pi\)
\(854\) 8445.36 0.338401
\(855\) −14667.0 −0.586667
\(856\) −7940.00 −0.317037
\(857\) −9750.86 −0.388661 −0.194331 0.980936i \(-0.562253\pi\)
−0.194331 + 0.980936i \(0.562253\pi\)
\(858\) 2851.92 0.113477
\(859\) 11337.4 0.450323 0.225162 0.974321i \(-0.427709\pi\)
0.225162 + 0.974321i \(0.427709\pi\)
\(860\) −63729.3 −2.52692
\(861\) −36398.9 −1.44073
\(862\) 8883.24 0.351003
\(863\) 25245.6 0.995794 0.497897 0.867236i \(-0.334106\pi\)
0.497897 + 0.867236i \(0.334106\pi\)
\(864\) −3641.46 −0.143385
\(865\) 35857.9 1.40949
\(866\) 12065.5 0.473445
\(867\) 12390.2 0.485344
\(868\) 50214.6 1.96359
\(869\) −28163.9 −1.09942
\(870\) 2190.79 0.0853734
\(871\) 6338.35 0.246575
\(872\) −11761.4 −0.456756
\(873\) −14173.8 −0.549498
\(874\) 7427.92 0.287475
\(875\) −162241. −6.26828
\(876\) 17865.2 0.689051
\(877\) −9052.34 −0.348547 −0.174274 0.984697i \(-0.555758\pi\)
−0.174274 + 0.984697i \(0.555758\pi\)
\(878\) 7012.52 0.269546
\(879\) −3895.99 −0.149498
\(880\) 38517.6 1.47549
\(881\) −32080.2 −1.22680 −0.613400 0.789772i \(-0.710199\pi\)
−0.613400 + 0.789772i \(0.710199\pi\)
\(882\) 4832.77 0.184498
\(883\) −39328.6 −1.49888 −0.749440 0.662072i \(-0.769677\pi\)
−0.749440 + 0.662072i \(0.769677\pi\)
\(884\) 7138.57 0.271602
\(885\) −3879.78 −0.147364
\(886\) 9950.36 0.377301
\(887\) 50922.9 1.92765 0.963823 0.266542i \(-0.0858813\pi\)
0.963823 + 0.266542i \(0.0858813\pi\)
\(888\) −5971.59 −0.225668
\(889\) −66062.1 −2.49230
\(890\) −11175.1 −0.420888
\(891\) −2860.02 −0.107536
\(892\) −30201.5 −1.13366
\(893\) 19442.0 0.728558
\(894\) −5547.97 −0.207552
\(895\) 29726.9 1.11024
\(896\) −41989.1 −1.56558
\(897\) −13262.3 −0.493663
\(898\) −6220.31 −0.231152
\(899\) −9034.67 −0.335176
\(900\) −23647.3 −0.875824
\(901\) 3166.27 0.117074
\(902\) −10405.4 −0.384103
\(903\) 37896.9 1.39660
\(904\) −21784.5 −0.801486
\(905\) 60912.3 2.23734
\(906\) −968.529 −0.0355157
\(907\) −43998.4 −1.61074 −0.805370 0.592772i \(-0.798034\pi\)
−0.805370 + 0.592772i \(0.798034\pi\)
\(908\) −38421.4 −1.40425
\(909\) 11782.2 0.429911
\(910\) −18953.0 −0.690423
\(911\) −28063.3 −1.02061 −0.510306 0.859993i \(-0.670468\pi\)
−0.510306 + 0.859993i \(0.670468\pi\)
\(912\) −11100.1 −0.403029
\(913\) −8885.45 −0.322087
\(914\) −1570.11 −0.0568214
\(915\) 22168.9 0.800961
\(916\) 9144.77 0.329860
\(917\) 64467.2 2.32159
\(918\) 589.311 0.0211876
\(919\) 29137.9 1.04589 0.522944 0.852367i \(-0.324834\pi\)
0.522944 + 0.852367i \(0.324834\pi\)
\(920\) 33706.8 1.20791
\(921\) 8009.46 0.286559
\(922\) −9879.87 −0.352902
\(923\) −5809.16 −0.207162
\(924\) −25145.0 −0.895247
\(925\) −58934.9 −2.09488
\(926\) −2709.89 −0.0961692
\(927\) 7700.27 0.272826
\(928\) 5760.23 0.203760
\(929\) −9282.01 −0.327807 −0.163904 0.986476i \(-0.552409\pi\)
−0.163904 + 0.986476i \(0.552409\pi\)
\(930\) −10850.7 −0.382589
\(931\) 51180.0 1.80167
\(932\) 40759.8 1.43255
\(933\) −11503.4 −0.403648
\(934\) 247.354 0.00866561
\(935\) −21656.1 −0.757465
\(936\) −3729.55 −0.130240
\(937\) −26659.3 −0.929478 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(938\) 4600.36 0.160135
\(939\) −19860.1 −0.690212
\(940\) 42368.6 1.47012
\(941\) −56714.2 −1.96475 −0.982375 0.186923i \(-0.940149\pi\)
−0.982375 + 0.186923i \(0.940149\pi\)
\(942\) 1951.33 0.0674925
\(943\) 48388.2 1.67098
\(944\) −2936.26 −0.101236
\(945\) 19006.8 0.654276
\(946\) 10833.6 0.372337
\(947\) −3737.90 −0.128264 −0.0641318 0.997941i \(-0.520428\pi\)
−0.0641318 + 0.997941i \(0.520428\pi\)
\(948\) 17687.4 0.605972
\(949\) 27807.7 0.951188
\(950\) 20615.2 0.704047
\(951\) 7987.46 0.272357
\(952\) 10788.8 0.367298
\(953\) −29404.8 −0.999489 −0.499745 0.866173i \(-0.666573\pi\)
−0.499745 + 0.866173i \(0.666573\pi\)
\(954\) −794.413 −0.0269602
\(955\) 70149.9 2.37696
\(956\) 26614.8 0.900402
\(957\) 4524.11 0.152815
\(958\) 15290.3 0.515663
\(959\) −45752.8 −1.54060
\(960\) −19263.0 −0.647614
\(961\) 14956.4 0.502044
\(962\) −4463.76 −0.149602
\(963\) 5952.00 0.199170
\(964\) −45515.3 −1.52069
\(965\) −20715.3 −0.691035
\(966\) −9625.76 −0.320604
\(967\) 52879.0 1.75851 0.879253 0.476356i \(-0.158043\pi\)
0.879253 + 0.476356i \(0.158043\pi\)
\(968\) 1011.93 0.0335997
\(969\) 6240.92 0.206901
\(970\) 26927.5 0.891330
\(971\) 25027.8 0.827167 0.413584 0.910466i \(-0.364277\pi\)
0.413584 + 0.910466i \(0.364277\pi\)
\(972\) 1796.14 0.0592709
\(973\) 14639.1 0.482330
\(974\) −10662.5 −0.350769
\(975\) −36807.7 −1.20902
\(976\) 16777.6 0.550244
\(977\) −29643.3 −0.970701 −0.485350 0.874320i \(-0.661308\pi\)
−0.485350 + 0.874320i \(0.661308\pi\)
\(978\) −7671.79 −0.250835
\(979\) −23077.2 −0.753372
\(980\) 111533. 3.63550
\(981\) 8816.59 0.286944
\(982\) −10370.3 −0.336995
\(983\) −14434.3 −0.468345 −0.234173 0.972195i \(-0.575238\pi\)
−0.234173 + 0.972195i \(0.575238\pi\)
\(984\) 13607.5 0.440844
\(985\) 2961.65 0.0958030
\(986\) −932.201 −0.0301088
\(987\) −25194.7 −0.812519
\(988\) −18967.6 −0.610771
\(989\) −50379.6 −1.61980
\(990\) 5433.48 0.174432
\(991\) 15333.7 0.491516 0.245758 0.969331i \(-0.420963\pi\)
0.245758 + 0.969331i \(0.420963\pi\)
\(992\) −28529.6 −0.913120
\(993\) 19714.3 0.630024
\(994\) −4216.28 −0.134539
\(995\) 43687.4 1.39194
\(996\) 5580.22 0.177526
\(997\) 3787.12 0.120300 0.0601501 0.998189i \(-0.480842\pi\)
0.0601501 + 0.998189i \(0.480842\pi\)
\(998\) 3728.14 0.118249
\(999\) 4476.44 0.141770
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.c.1.5 8
3.2 odd 2 531.4.a.f.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.c.1.5 8 1.1 even 1 trivial
531.4.a.f.1.4 8 3.2 odd 2