Properties

Label 177.4.a.a.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: \(x^{7} - x^{6} - 34 x^{5} + 25 x^{4} + 315 x^{3} - 146 x^{2} - 736 x + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.46227\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.46227 q^{2} +3.00000 q^{3} -1.93724 q^{4} -11.2702 q^{5} -7.38680 q^{6} +18.6588 q^{7} +24.4681 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.46227 q^{2} +3.00000 q^{3} -1.93724 q^{4} -11.2702 q^{5} -7.38680 q^{6} +18.6588 q^{7} +24.4681 q^{8} +9.00000 q^{9} +27.7502 q^{10} -16.5085 q^{11} -5.81171 q^{12} +24.7044 q^{13} -45.9430 q^{14} -33.8105 q^{15} -44.7492 q^{16} -125.357 q^{17} -22.1604 q^{18} -104.913 q^{19} +21.8330 q^{20} +55.9764 q^{21} +40.6484 q^{22} +116.317 q^{23} +73.4044 q^{24} +2.01688 q^{25} -60.8289 q^{26} +27.0000 q^{27} -36.1465 q^{28} -295.871 q^{29} +83.2506 q^{30} -62.8500 q^{31} -85.5606 q^{32} -49.5255 q^{33} +308.663 q^{34} -210.288 q^{35} -17.4351 q^{36} +318.173 q^{37} +258.325 q^{38} +74.1133 q^{39} -275.760 q^{40} -488.331 q^{41} -137.829 q^{42} -127.236 q^{43} +31.9809 q^{44} -101.432 q^{45} -286.404 q^{46} -221.541 q^{47} -134.248 q^{48} +5.15084 q^{49} -4.96610 q^{50} -376.072 q^{51} -47.8584 q^{52} -40.8953 q^{53} -66.4812 q^{54} +186.054 q^{55} +456.546 q^{56} -314.740 q^{57} +728.514 q^{58} -59.0000 q^{59} +65.4990 q^{60} -237.039 q^{61} +154.754 q^{62} +167.929 q^{63} +568.667 q^{64} -278.423 q^{65} +121.945 q^{66} +532.451 q^{67} +242.847 q^{68} +348.952 q^{69} +517.785 q^{70} +634.893 q^{71} +220.213 q^{72} +375.980 q^{73} -783.427 q^{74} +6.05065 q^{75} +203.242 q^{76} -308.029 q^{77} -182.487 q^{78} -323.957 q^{79} +504.332 q^{80} +81.0000 q^{81} +1202.40 q^{82} +1174.38 q^{83} -108.440 q^{84} +1412.80 q^{85} +313.290 q^{86} -887.613 q^{87} -403.933 q^{88} -1444.33 q^{89} +249.752 q^{90} +460.955 q^{91} -225.334 q^{92} -188.550 q^{93} +545.494 q^{94} +1182.39 q^{95} -256.682 q^{96} -1046.28 q^{97} -12.6827 q^{98} -148.577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 8q^{2} + 21q^{3} + 22q^{4} - 28q^{5} - 24q^{6} - 59q^{7} - 117q^{8} + 63q^{9} - 79q^{10} - 131q^{11} + 66q^{12} - 123q^{13} - 117q^{14} - 84q^{15} + 202q^{16} - 235q^{17} - 72q^{18} - 80q^{19} + 61q^{20} - 177q^{21} + 688q^{22} - 274q^{23} - 351q^{24} + 193q^{25} - 180q^{26} + 189q^{27} - 118q^{28} - 406q^{29} - 237q^{30} - 346q^{31} - 854q^{32} - 393q^{33} + 178q^{34} - 424q^{35} + 198q^{36} - 157q^{37} - 129q^{38} - 369q^{39} - 590q^{40} - 825q^{41} - 351q^{42} - 815q^{43} - 1690q^{44} - 252q^{45} + 1457q^{46} - 1196q^{47} + 606q^{48} + 914q^{49} + 713q^{50} - 705q^{51} + 1030q^{52} - 900q^{53} - 216q^{54} - 1044q^{55} + 2172q^{56} - 240q^{57} + 1242q^{58} - 413q^{59} + 183q^{60} + 420q^{61} + 646q^{62} - 531q^{63} + 3541q^{64} + 190q^{65} + 2064q^{66} + 1316q^{67} - 611q^{68} - 822q^{69} + 4658q^{70} - 173q^{71} - 1053q^{72} - 418q^{73} + 660q^{74} + 579q^{75} + 1540q^{76} - 753q^{77} - 540q^{78} + 2635q^{79} + 6155q^{80} + 567q^{81} - 125q^{82} + 457q^{83} - 354q^{84} + 1270q^{85} + 3482q^{86} - 1218q^{87} + 7685q^{88} + 592q^{89} - 711q^{90} + 3179q^{91} - 3500q^{92} - 1038q^{93} + 2064q^{94} - 2250q^{95} - 2562q^{96} - 1906q^{97} + 2994q^{98} - 1179q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46227 −0.870543 −0.435272 0.900299i \(-0.643348\pi\)
−0.435272 + 0.900299i \(0.643348\pi\)
\(3\) 3.00000 0.577350
\(4\) −1.93724 −0.242155
\(5\) −11.2702 −1.00804 −0.504018 0.863693i \(-0.668145\pi\)
−0.504018 + 0.863693i \(0.668145\pi\)
\(6\) −7.38680 −0.502608
\(7\) 18.6588 1.00748 0.503740 0.863855i \(-0.331957\pi\)
0.503740 + 0.863855i \(0.331957\pi\)
\(8\) 24.4681 1.08135
\(9\) 9.00000 0.333333
\(10\) 27.7502 0.877538
\(11\) −16.5085 −0.452500 −0.226250 0.974069i \(-0.572647\pi\)
−0.226250 + 0.974069i \(0.572647\pi\)
\(12\) −5.81171 −0.139808
\(13\) 24.7044 0.527060 0.263530 0.964651i \(-0.415113\pi\)
0.263530 + 0.964651i \(0.415113\pi\)
\(14\) −45.9430 −0.877055
\(15\) −33.8105 −0.581989
\(16\) −44.7492 −0.699206
\(17\) −125.357 −1.78845 −0.894223 0.447621i \(-0.852271\pi\)
−0.894223 + 0.447621i \(0.852271\pi\)
\(18\) −22.1604 −0.290181
\(19\) −104.913 −1.26678 −0.633388 0.773834i \(-0.718336\pi\)
−0.633388 + 0.773834i \(0.718336\pi\)
\(20\) 21.8330 0.244100
\(21\) 55.9764 0.581669
\(22\) 40.6484 0.393921
\(23\) 116.317 1.05451 0.527257 0.849706i \(-0.323221\pi\)
0.527257 + 0.849706i \(0.323221\pi\)
\(24\) 73.4044 0.624317
\(25\) 2.01688 0.0161351
\(26\) −60.8289 −0.458828
\(27\) 27.0000 0.192450
\(28\) −36.1465 −0.243966
\(29\) −295.871 −1.89455 −0.947274 0.320425i \(-0.896174\pi\)
−0.947274 + 0.320425i \(0.896174\pi\)
\(30\) 83.2506 0.506647
\(31\) −62.8500 −0.364135 −0.182068 0.983286i \(-0.558279\pi\)
−0.182068 + 0.983286i \(0.558279\pi\)
\(32\) −85.5606 −0.472660
\(33\) −49.5255 −0.261251
\(34\) 308.663 1.55692
\(35\) −210.288 −1.01558
\(36\) −17.4351 −0.0807182
\(37\) 318.173 1.41371 0.706856 0.707358i \(-0.250113\pi\)
0.706856 + 0.707358i \(0.250113\pi\)
\(38\) 258.325 1.10278
\(39\) 74.1133 0.304298
\(40\) −275.760 −1.09004
\(41\) −488.331 −1.86011 −0.930055 0.367421i \(-0.880241\pi\)
−0.930055 + 0.367421i \(0.880241\pi\)
\(42\) −137.829 −0.506368
\(43\) −127.236 −0.451241 −0.225620 0.974215i \(-0.572441\pi\)
−0.225620 + 0.974215i \(0.572441\pi\)
\(44\) 31.9809 0.109575
\(45\) −101.432 −0.336012
\(46\) −286.404 −0.918000
\(47\) −221.541 −0.687555 −0.343778 0.939051i \(-0.611707\pi\)
−0.343778 + 0.939051i \(0.611707\pi\)
\(48\) −134.248 −0.403687
\(49\) 5.15084 0.0150170
\(50\) −4.96610 −0.0140463
\(51\) −376.072 −1.03256
\(52\) −47.8584 −0.127630
\(53\) −40.8953 −0.105989 −0.0529944 0.998595i \(-0.516877\pi\)
−0.0529944 + 0.998595i \(0.516877\pi\)
\(54\) −66.4812 −0.167536
\(55\) 186.054 0.456136
\(56\) 456.546 1.08944
\(57\) −314.740 −0.731374
\(58\) 728.514 1.64929
\(59\) −59.0000 −0.130189
\(60\) 65.4990 0.140931
\(61\) −237.039 −0.497536 −0.248768 0.968563i \(-0.580026\pi\)
−0.248768 + 0.968563i \(0.580026\pi\)
\(62\) 154.754 0.316996
\(63\) 167.929 0.335827
\(64\) 568.667 1.11068
\(65\) −278.423 −0.531295
\(66\) 121.945 0.227430
\(67\) 532.451 0.970884 0.485442 0.874269i \(-0.338659\pi\)
0.485442 + 0.874269i \(0.338659\pi\)
\(68\) 242.847 0.433081
\(69\) 348.952 0.608824
\(70\) 517.785 0.884103
\(71\) 634.893 1.06124 0.530619 0.847610i \(-0.321960\pi\)
0.530619 + 0.847610i \(0.321960\pi\)
\(72\) 220.213 0.360450
\(73\) 375.980 0.602809 0.301405 0.953496i \(-0.402544\pi\)
0.301405 + 0.953496i \(0.402544\pi\)
\(74\) −783.427 −1.23070
\(75\) 6.05065 0.00931558
\(76\) 203.242 0.306756
\(77\) −308.029 −0.455885
\(78\) −182.487 −0.264905
\(79\) −323.957 −0.461367 −0.230683 0.973029i \(-0.574096\pi\)
−0.230683 + 0.973029i \(0.574096\pi\)
\(80\) 504.332 0.704825
\(81\) 81.0000 0.111111
\(82\) 1202.40 1.61931
\(83\) 1174.38 1.55308 0.776538 0.630070i \(-0.216974\pi\)
0.776538 + 0.630070i \(0.216974\pi\)
\(84\) −108.440 −0.140854
\(85\) 1412.80 1.80282
\(86\) 313.290 0.392824
\(87\) −887.613 −1.09382
\(88\) −403.933 −0.489311
\(89\) −1444.33 −1.72021 −0.860107 0.510113i \(-0.829604\pi\)
−0.860107 + 0.510113i \(0.829604\pi\)
\(90\) 249.752 0.292513
\(91\) 460.955 0.531003
\(92\) −225.334 −0.255355
\(93\) −188.550 −0.210234
\(94\) 545.494 0.598547
\(95\) 1182.39 1.27696
\(96\) −256.682 −0.272890
\(97\) −1046.28 −1.09519 −0.547595 0.836744i \(-0.684456\pi\)
−0.547595 + 0.836744i \(0.684456\pi\)
\(98\) −12.6827 −0.0130730
\(99\) −148.577 −0.150833
\(100\) −3.90718 −0.00390718
\(101\) −1182.97 −1.16545 −0.582724 0.812670i \(-0.698013\pi\)
−0.582724 + 0.812670i \(0.698013\pi\)
\(102\) 925.989 0.898888
\(103\) 1084.27 1.03725 0.518625 0.855002i \(-0.326444\pi\)
0.518625 + 0.855002i \(0.326444\pi\)
\(104\) 604.472 0.569936
\(105\) −630.864 −0.586343
\(106\) 100.695 0.0922678
\(107\) −555.182 −0.501603 −0.250801 0.968039i \(-0.580694\pi\)
−0.250801 + 0.968039i \(0.580694\pi\)
\(108\) −52.3054 −0.0466027
\(109\) −1089.62 −0.957491 −0.478746 0.877954i \(-0.658908\pi\)
−0.478746 + 0.877954i \(0.658908\pi\)
\(110\) −458.114 −0.397086
\(111\) 954.519 0.816207
\(112\) −834.967 −0.704437
\(113\) 514.974 0.428714 0.214357 0.976755i \(-0.431234\pi\)
0.214357 + 0.976755i \(0.431234\pi\)
\(114\) 774.974 0.636692
\(115\) −1310.92 −1.06299
\(116\) 573.173 0.458774
\(117\) 222.340 0.175687
\(118\) 145.274 0.113335
\(119\) −2339.02 −1.80183
\(120\) −827.281 −0.629334
\(121\) −1058.47 −0.795243
\(122\) 583.653 0.433127
\(123\) −1464.99 −1.07393
\(124\) 121.755 0.0881771
\(125\) 1386.04 0.991771
\(126\) −413.487 −0.292352
\(127\) 2240.79 1.56565 0.782827 0.622240i \(-0.213777\pi\)
0.782827 + 0.622240i \(0.213777\pi\)
\(128\) −715.725 −0.494233
\(129\) −381.709 −0.260524
\(130\) 685.553 0.462515
\(131\) 943.152 0.629035 0.314517 0.949252i \(-0.398157\pi\)
0.314517 + 0.949252i \(0.398157\pi\)
\(132\) 95.9427 0.0632632
\(133\) −1957.56 −1.27625
\(134\) −1311.04 −0.845196
\(135\) −304.295 −0.193996
\(136\) −3067.26 −1.93394
\(137\) 1837.48 1.14588 0.572942 0.819596i \(-0.305802\pi\)
0.572942 + 0.819596i \(0.305802\pi\)
\(138\) −859.213 −0.530007
\(139\) −404.410 −0.246774 −0.123387 0.992359i \(-0.539376\pi\)
−0.123387 + 0.992359i \(0.539376\pi\)
\(140\) 407.378 0.245926
\(141\) −664.623 −0.396960
\(142\) −1563.28 −0.923853
\(143\) −407.834 −0.238495
\(144\) −402.743 −0.233069
\(145\) 3334.52 1.90977
\(146\) −925.762 −0.524772
\(147\) 15.4525 0.00867008
\(148\) −616.377 −0.342337
\(149\) 2398.95 1.31899 0.659496 0.751708i \(-0.270770\pi\)
0.659496 + 0.751708i \(0.270770\pi\)
\(150\) −14.8983 −0.00810961
\(151\) −1819.90 −0.980805 −0.490403 0.871496i \(-0.663150\pi\)
−0.490403 + 0.871496i \(0.663150\pi\)
\(152\) −2567.03 −1.36983
\(153\) −1128.22 −0.596149
\(154\) 758.450 0.396868
\(155\) 708.331 0.367061
\(156\) −143.575 −0.0736872
\(157\) −3018.40 −1.53436 −0.767181 0.641430i \(-0.778341\pi\)
−0.767181 + 0.641430i \(0.778341\pi\)
\(158\) 797.668 0.401640
\(159\) −122.686 −0.0611926
\(160\) 964.283 0.476458
\(161\) 2170.34 1.06240
\(162\) −199.444 −0.0967270
\(163\) 1249.65 0.600493 0.300246 0.953862i \(-0.402931\pi\)
0.300246 + 0.953862i \(0.402931\pi\)
\(164\) 946.013 0.450434
\(165\) 558.162 0.263350
\(166\) −2891.65 −1.35202
\(167\) −2805.96 −1.30019 −0.650095 0.759853i \(-0.725271\pi\)
−0.650095 + 0.759853i \(0.725271\pi\)
\(168\) 1369.64 0.628987
\(169\) −1586.69 −0.722208
\(170\) −3478.69 −1.56943
\(171\) −944.219 −0.422259
\(172\) 246.487 0.109270
\(173\) 1191.77 0.523751 0.261875 0.965102i \(-0.415659\pi\)
0.261875 + 0.965102i \(0.415659\pi\)
\(174\) 2185.54 0.952215
\(175\) 37.6326 0.0162558
\(176\) 738.743 0.316391
\(177\) −177.000 −0.0751646
\(178\) 3556.34 1.49752
\(179\) 3035.70 1.26759 0.633796 0.773500i \(-0.281496\pi\)
0.633796 + 0.773500i \(0.281496\pi\)
\(180\) 196.497 0.0813668
\(181\) 2731.80 1.12184 0.560920 0.827870i \(-0.310448\pi\)
0.560920 + 0.827870i \(0.310448\pi\)
\(182\) −1135.00 −0.462261
\(183\) −711.117 −0.287253
\(184\) 2846.07 1.14030
\(185\) −3585.87 −1.42507
\(186\) 464.261 0.183017
\(187\) 2069.46 0.809273
\(188\) 429.178 0.166495
\(189\) 503.788 0.193890
\(190\) −2911.36 −1.11164
\(191\) 1111.96 0.421248 0.210624 0.977567i \(-0.432450\pi\)
0.210624 + 0.977567i \(0.432450\pi\)
\(192\) 1706.00 0.641250
\(193\) −2285.89 −0.852549 −0.426274 0.904594i \(-0.640174\pi\)
−0.426274 + 0.904594i \(0.640174\pi\)
\(194\) 2576.21 0.953410
\(195\) −835.270 −0.306743
\(196\) −9.97839 −0.00363644
\(197\) 625.776 0.226318 0.113159 0.993577i \(-0.463903\pi\)
0.113159 + 0.993577i \(0.463903\pi\)
\(198\) 365.835 0.131307
\(199\) −4797.28 −1.70890 −0.854448 0.519537i \(-0.826104\pi\)
−0.854448 + 0.519537i \(0.826104\pi\)
\(200\) 49.3493 0.0174476
\(201\) 1597.35 0.560540
\(202\) 2912.80 1.01457
\(203\) −5520.60 −1.90872
\(204\) 728.540 0.250039
\(205\) 5503.58 1.87506
\(206\) −2669.77 −0.902970
\(207\) 1046.86 0.351505
\(208\) −1105.50 −0.368524
\(209\) 1731.96 0.573217
\(210\) 1553.36 0.510437
\(211\) −3653.40 −1.19199 −0.595997 0.802987i \(-0.703243\pi\)
−0.595997 + 0.802987i \(0.703243\pi\)
\(212\) 79.2239 0.0256657
\(213\) 1904.68 0.612706
\(214\) 1367.01 0.436667
\(215\) 1433.97 0.454866
\(216\) 660.640 0.208106
\(217\) −1172.71 −0.366859
\(218\) 2682.93 0.833538
\(219\) 1127.94 0.348032
\(220\) −360.430 −0.110456
\(221\) −3096.88 −0.942619
\(222\) −2350.28 −0.710543
\(223\) −3631.49 −1.09051 −0.545253 0.838272i \(-0.683566\pi\)
−0.545253 + 0.838272i \(0.683566\pi\)
\(224\) −1596.46 −0.476196
\(225\) 18.1519 0.00537835
\(226\) −1268.00 −0.373214
\(227\) −3959.13 −1.15761 −0.578803 0.815467i \(-0.696480\pi\)
−0.578803 + 0.815467i \(0.696480\pi\)
\(228\) 609.726 0.177106
\(229\) 2725.06 0.786362 0.393181 0.919461i \(-0.371375\pi\)
0.393181 + 0.919461i \(0.371375\pi\)
\(230\) 3227.83 0.925376
\(231\) −924.087 −0.263206
\(232\) −7239.41 −2.04867
\(233\) 1249.69 0.351374 0.175687 0.984446i \(-0.443785\pi\)
0.175687 + 0.984446i \(0.443785\pi\)
\(234\) −547.461 −0.152943
\(235\) 2496.81 0.693080
\(236\) 114.297 0.0315259
\(237\) −971.870 −0.266370
\(238\) 5759.28 1.56857
\(239\) 4000.87 1.08282 0.541412 0.840757i \(-0.317890\pi\)
0.541412 + 0.840757i \(0.317890\pi\)
\(240\) 1512.99 0.406931
\(241\) 1847.78 0.493884 0.246942 0.969030i \(-0.420574\pi\)
0.246942 + 0.969030i \(0.420574\pi\)
\(242\) 2606.23 0.692294
\(243\) 243.000 0.0641500
\(244\) 459.201 0.120481
\(245\) −58.0508 −0.0151377
\(246\) 3607.20 0.934906
\(247\) −2591.82 −0.667667
\(248\) −1537.82 −0.393758
\(249\) 3523.15 0.896669
\(250\) −3412.81 −0.863379
\(251\) 2059.75 0.517970 0.258985 0.965881i \(-0.416612\pi\)
0.258985 + 0.965881i \(0.416612\pi\)
\(252\) −325.319 −0.0813220
\(253\) −1920.22 −0.477168
\(254\) −5517.42 −1.36297
\(255\) 4238.39 1.04086
\(256\) −2787.03 −0.680426
\(257\) 464.966 0.112855 0.0564275 0.998407i \(-0.482029\pi\)
0.0564275 + 0.998407i \(0.482029\pi\)
\(258\) 939.869 0.226797
\(259\) 5936.73 1.42429
\(260\) 539.372 0.128656
\(261\) −2662.84 −0.631516
\(262\) −2322.29 −0.547602
\(263\) −2946.12 −0.690742 −0.345371 0.938466i \(-0.612247\pi\)
−0.345371 + 0.938466i \(0.612247\pi\)
\(264\) −1211.80 −0.282504
\(265\) 460.897 0.106840
\(266\) 4820.03 1.11103
\(267\) −4333.00 −0.993166
\(268\) −1031.48 −0.235104
\(269\) 4266.67 0.967076 0.483538 0.875323i \(-0.339351\pi\)
0.483538 + 0.875323i \(0.339351\pi\)
\(270\) 749.255 0.168882
\(271\) −1985.24 −0.444999 −0.222499 0.974933i \(-0.571422\pi\)
−0.222499 + 0.974933i \(0.571422\pi\)
\(272\) 5609.64 1.25049
\(273\) 1382.87 0.306574
\(274\) −4524.36 −0.997542
\(275\) −33.2957 −0.00730112
\(276\) −676.002 −0.147430
\(277\) −763.770 −0.165670 −0.0828349 0.996563i \(-0.526397\pi\)
−0.0828349 + 0.996563i \(0.526397\pi\)
\(278\) 995.766 0.214828
\(279\) −565.650 −0.121378
\(280\) −5145.36 −1.09819
\(281\) 1976.32 0.419564 0.209782 0.977748i \(-0.432725\pi\)
0.209782 + 0.977748i \(0.432725\pi\)
\(282\) 1636.48 0.345571
\(283\) 4445.80 0.933835 0.466918 0.884301i \(-0.345364\pi\)
0.466918 + 0.884301i \(0.345364\pi\)
\(284\) −1229.94 −0.256984
\(285\) 3547.17 0.737251
\(286\) 1004.20 0.207620
\(287\) −9111.67 −1.87402
\(288\) −770.045 −0.157553
\(289\) 10801.4 2.19854
\(290\) −8210.48 −1.66254
\(291\) −3138.83 −0.632308
\(292\) −728.362 −0.145973
\(293\) 152.195 0.0303459 0.0151729 0.999885i \(-0.495170\pi\)
0.0151729 + 0.999885i \(0.495170\pi\)
\(294\) −38.0482 −0.00754768
\(295\) 664.940 0.131235
\(296\) 7785.10 1.52872
\(297\) −445.730 −0.0870837
\(298\) −5906.86 −1.14824
\(299\) 2873.55 0.555792
\(300\) −11.7215 −0.00225581
\(301\) −2374.08 −0.454616
\(302\) 4481.09 0.853833
\(303\) −3548.92 −0.672872
\(304\) 4694.79 0.885738
\(305\) 2671.47 0.501534
\(306\) 2777.97 0.518973
\(307\) 1890.01 0.351363 0.175682 0.984447i \(-0.443787\pi\)
0.175682 + 0.984447i \(0.443787\pi\)
\(308\) 596.725 0.110395
\(309\) 3252.82 0.598856
\(310\) −1744.10 −0.319543
\(311\) −8583.58 −1.56505 −0.782524 0.622620i \(-0.786068\pi\)
−0.782524 + 0.622620i \(0.786068\pi\)
\(312\) 1813.42 0.329053
\(313\) 8124.32 1.46714 0.733568 0.679616i \(-0.237853\pi\)
0.733568 + 0.679616i \(0.237853\pi\)
\(314\) 7432.12 1.33573
\(315\) −1892.59 −0.338525
\(316\) 627.581 0.111722
\(317\) 3908.89 0.692572 0.346286 0.938129i \(-0.387443\pi\)
0.346286 + 0.938129i \(0.387443\pi\)
\(318\) 302.086 0.0532708
\(319\) 4884.39 0.857284
\(320\) −6408.97 −1.11960
\(321\) −1665.55 −0.289600
\(322\) −5343.96 −0.924867
\(323\) 13151.6 2.26556
\(324\) −156.916 −0.0269061
\(325\) 49.8259 0.00850414
\(326\) −3076.98 −0.522755
\(327\) −3268.86 −0.552808
\(328\) −11948.5 −2.01143
\(329\) −4133.69 −0.692699
\(330\) −1374.34 −0.229258
\(331\) −865.302 −0.143690 −0.0718448 0.997416i \(-0.522889\pi\)
−0.0718448 + 0.997416i \(0.522889\pi\)
\(332\) −2275.06 −0.376085
\(333\) 2863.56 0.471237
\(334\) 6909.02 1.13187
\(335\) −6000.81 −0.978685
\(336\) −2504.90 −0.406707
\(337\) 508.758 0.0822369 0.0411184 0.999154i \(-0.486908\pi\)
0.0411184 + 0.999154i \(0.486908\pi\)
\(338\) 3906.86 0.628713
\(339\) 1544.92 0.247518
\(340\) −2736.93 −0.436561
\(341\) 1037.56 0.164771
\(342\) 2324.92 0.367595
\(343\) −6303.86 −0.992351
\(344\) −3113.23 −0.487949
\(345\) −3932.75 −0.613716
\(346\) −2934.47 −0.455948
\(347\) 8339.96 1.29024 0.645119 0.764082i \(-0.276808\pi\)
0.645119 + 0.764082i \(0.276808\pi\)
\(348\) 1719.52 0.264873
\(349\) 3274.69 0.502264 0.251132 0.967953i \(-0.419197\pi\)
0.251132 + 0.967953i \(0.419197\pi\)
\(350\) −92.6615 −0.0141513
\(351\) 667.020 0.101433
\(352\) 1412.48 0.213879
\(353\) −1578.59 −0.238017 −0.119008 0.992893i \(-0.537972\pi\)
−0.119008 + 0.992893i \(0.537972\pi\)
\(354\) 435.821 0.0654340
\(355\) −7155.35 −1.06977
\(356\) 2798.02 0.416558
\(357\) −7017.05 −1.04028
\(358\) −7474.71 −1.10349
\(359\) 3661.78 0.538333 0.269166 0.963094i \(-0.413252\pi\)
0.269166 + 0.963094i \(0.413252\pi\)
\(360\) −2481.84 −0.363346
\(361\) 4147.79 0.604723
\(362\) −6726.42 −0.976610
\(363\) −3175.41 −0.459134
\(364\) −892.980 −0.128585
\(365\) −4237.36 −0.607653
\(366\) 1750.96 0.250066
\(367\) −4573.82 −0.650548 −0.325274 0.945620i \(-0.605457\pi\)
−0.325274 + 0.945620i \(0.605457\pi\)
\(368\) −5205.10 −0.737323
\(369\) −4394.98 −0.620036
\(370\) 8829.36 1.24059
\(371\) −763.057 −0.106782
\(372\) 365.266 0.0509091
\(373\) −1200.09 −0.166591 −0.0832954 0.996525i \(-0.526545\pi\)
−0.0832954 + 0.996525i \(0.526545\pi\)
\(374\) −5095.57 −0.704507
\(375\) 4158.12 0.572599
\(376\) −5420.70 −0.743487
\(377\) −7309.33 −0.998540
\(378\) −1240.46 −0.168789
\(379\) 13056.0 1.76950 0.884752 0.466062i \(-0.154328\pi\)
0.884752 + 0.466062i \(0.154328\pi\)
\(380\) −2290.57 −0.309221
\(381\) 6722.37 0.903930
\(382\) −2737.94 −0.366715
\(383\) 6014.50 0.802420 0.401210 0.915986i \(-0.368590\pi\)
0.401210 + 0.915986i \(0.368590\pi\)
\(384\) −2147.18 −0.285345
\(385\) 3471.54 0.459548
\(386\) 5628.47 0.742181
\(387\) −1145.13 −0.150414
\(388\) 2026.89 0.265205
\(389\) −6419.19 −0.836673 −0.418336 0.908292i \(-0.637387\pi\)
−0.418336 + 0.908292i \(0.637387\pi\)
\(390\) 2056.66 0.267033
\(391\) −14581.2 −1.88594
\(392\) 126.031 0.0162386
\(393\) 2829.46 0.363173
\(394\) −1540.83 −0.197020
\(395\) 3651.05 0.465074
\(396\) 287.828 0.0365250
\(397\) 10002.4 1.26450 0.632252 0.774763i \(-0.282131\pi\)
0.632252 + 0.774763i \(0.282131\pi\)
\(398\) 11812.2 1.48767
\(399\) −5872.67 −0.736845
\(400\) −90.2539 −0.0112817
\(401\) −4714.22 −0.587075 −0.293537 0.955948i \(-0.594832\pi\)
−0.293537 + 0.955948i \(0.594832\pi\)
\(402\) −3933.11 −0.487974
\(403\) −1552.67 −0.191921
\(404\) 2291.70 0.282219
\(405\) −912.884 −0.112004
\(406\) 13593.2 1.66162
\(407\) −5252.56 −0.639705
\(408\) −9201.77 −1.11656
\(409\) −14797.6 −1.78898 −0.894489 0.447090i \(-0.852460\pi\)
−0.894489 + 0.447090i \(0.852460\pi\)
\(410\) −13551.3 −1.63232
\(411\) 5512.43 0.661577
\(412\) −2100.50 −0.251175
\(413\) −1100.87 −0.131163
\(414\) −2577.64 −0.306000
\(415\) −13235.5 −1.56556
\(416\) −2113.73 −0.249120
\(417\) −1213.23 −0.142475
\(418\) −4264.55 −0.499010
\(419\) 12527.3 1.46062 0.730311 0.683115i \(-0.239375\pi\)
0.730311 + 0.683115i \(0.239375\pi\)
\(420\) 1222.13 0.141986
\(421\) −3127.91 −0.362103 −0.181051 0.983474i \(-0.557950\pi\)
−0.181051 + 0.983474i \(0.557950\pi\)
\(422\) 8995.65 1.03768
\(423\) −1993.87 −0.229185
\(424\) −1000.63 −0.114611
\(425\) −252.831 −0.0288567
\(426\) −4689.83 −0.533387
\(427\) −4422.86 −0.501258
\(428\) 1075.52 0.121465
\(429\) −1223.50 −0.137695
\(430\) −3530.83 −0.395981
\(431\) 780.300 0.0872058 0.0436029 0.999049i \(-0.486116\pi\)
0.0436029 + 0.999049i \(0.486116\pi\)
\(432\) −1208.23 −0.134562
\(433\) 7622.27 0.845965 0.422983 0.906138i \(-0.360983\pi\)
0.422983 + 0.906138i \(0.360983\pi\)
\(434\) 2887.52 0.319367
\(435\) 10003.6 1.10261
\(436\) 2110.85 0.231861
\(437\) −12203.2 −1.33583
\(438\) −2777.29 −0.302977
\(439\) 10167.2 1.10536 0.552682 0.833392i \(-0.313604\pi\)
0.552682 + 0.833392i \(0.313604\pi\)
\(440\) 4552.39 0.493243
\(441\) 46.3575 0.00500567
\(442\) 7625.35 0.820590
\(443\) −14545.0 −1.55994 −0.779969 0.625819i \(-0.784765\pi\)
−0.779969 + 0.625819i \(0.784765\pi\)
\(444\) −1849.13 −0.197648
\(445\) 16277.9 1.73404
\(446\) 8941.71 0.949332
\(447\) 7196.85 0.761520
\(448\) 10610.6 1.11899
\(449\) 4431.72 0.465803 0.232902 0.972500i \(-0.425178\pi\)
0.232902 + 0.972500i \(0.425178\pi\)
\(450\) −44.6949 −0.00468209
\(451\) 8061.62 0.841700
\(452\) −997.628 −0.103815
\(453\) −5459.71 −0.566268
\(454\) 9748.44 1.00775
\(455\) −5195.05 −0.535269
\(456\) −7701.10 −0.790870
\(457\) 2406.49 0.246326 0.123163 0.992386i \(-0.460696\pi\)
0.123163 + 0.992386i \(0.460696\pi\)
\(458\) −6709.82 −0.684562
\(459\) −3384.65 −0.344187
\(460\) 2539.55 0.257407
\(461\) −14856.5 −1.50094 −0.750471 0.660903i \(-0.770173\pi\)
−0.750471 + 0.660903i \(0.770173\pi\)
\(462\) 2275.35 0.229132
\(463\) 1605.14 0.161117 0.0805586 0.996750i \(-0.474330\pi\)
0.0805586 + 0.996750i \(0.474330\pi\)
\(464\) 13240.0 1.32468
\(465\) 2124.99 0.211923
\(466\) −3077.08 −0.305886
\(467\) −17904.4 −1.77412 −0.887062 0.461651i \(-0.847257\pi\)
−0.887062 + 0.461651i \(0.847257\pi\)
\(468\) −430.725 −0.0425433
\(469\) 9934.89 0.978146
\(470\) −6147.81 −0.603356
\(471\) −9055.21 −0.885865
\(472\) −1443.62 −0.140780
\(473\) 2100.48 0.204187
\(474\) 2393.00 0.231887
\(475\) −211.598 −0.0204395
\(476\) 4531.23 0.436320
\(477\) −368.058 −0.0353296
\(478\) −9851.22 −0.942645
\(479\) −10467.2 −0.998448 −0.499224 0.866473i \(-0.666382\pi\)
−0.499224 + 0.866473i \(0.666382\pi\)
\(480\) 2892.85 0.275083
\(481\) 7860.29 0.745111
\(482\) −4549.74 −0.429948
\(483\) 6511.02 0.613378
\(484\) 2050.51 0.192572
\(485\) 11791.7 1.10399
\(486\) −598.331 −0.0558454
\(487\) −15284.5 −1.42219 −0.711097 0.703093i \(-0.751802\pi\)
−0.711097 + 0.703093i \(0.751802\pi\)
\(488\) −5799.90 −0.538011
\(489\) 3748.96 0.346695
\(490\) 142.937 0.0131780
\(491\) −3589.22 −0.329897 −0.164949 0.986302i \(-0.552746\pi\)
−0.164949 + 0.986302i \(0.552746\pi\)
\(492\) 2838.04 0.260058
\(493\) 37089.6 3.38830
\(494\) 6381.76 0.581233
\(495\) 1674.48 0.152045
\(496\) 2812.49 0.254606
\(497\) 11846.3 1.06918
\(498\) −8674.94 −0.780589
\(499\) −3237.65 −0.290455 −0.145228 0.989398i \(-0.546391\pi\)
−0.145228 + 0.989398i \(0.546391\pi\)
\(500\) −2685.09 −0.240162
\(501\) −8417.88 −0.750665
\(502\) −5071.67 −0.450915
\(503\) 1612.24 0.142915 0.0714576 0.997444i \(-0.477235\pi\)
0.0714576 + 0.997444i \(0.477235\pi\)
\(504\) 4108.92 0.363146
\(505\) 13332.3 1.17481
\(506\) 4728.11 0.415395
\(507\) −4760.07 −0.416967
\(508\) −4340.94 −0.379130
\(509\) 9148.28 0.796641 0.398320 0.917246i \(-0.369593\pi\)
0.398320 + 0.917246i \(0.369593\pi\)
\(510\) −10436.1 −0.906111
\(511\) 7015.33 0.607319
\(512\) 12588.2 1.08657
\(513\) −2832.66 −0.243791
\(514\) −1144.87 −0.0982452
\(515\) −12220.0 −1.04558
\(516\) 739.460 0.0630871
\(517\) 3657.32 0.311119
\(518\) −14617.8 −1.23990
\(519\) 3575.32 0.302388
\(520\) −6812.50 −0.574515
\(521\) −1715.13 −0.144225 −0.0721124 0.997397i \(-0.522974\pi\)
−0.0721124 + 0.997397i \(0.522974\pi\)
\(522\) 6556.62 0.549762
\(523\) −7402.28 −0.618889 −0.309445 0.950918i \(-0.600143\pi\)
−0.309445 + 0.950918i \(0.600143\pi\)
\(524\) −1827.11 −0.152324
\(525\) 112.898 0.00938526
\(526\) 7254.13 0.601321
\(527\) 7878.71 0.651237
\(528\) 2216.23 0.182669
\(529\) 1362.70 0.112000
\(530\) −1134.85 −0.0930092
\(531\) −531.000 −0.0433963
\(532\) 3792.25 0.309051
\(533\) −12063.9 −0.980389
\(534\) 10669.0 0.864594
\(535\) 6257.00 0.505633
\(536\) 13028.1 1.04986
\(537\) 9107.11 0.731845
\(538\) −10505.7 −0.841882
\(539\) −85.0327 −0.00679521
\(540\) 589.491 0.0469772
\(541\) −20535.4 −1.63195 −0.815974 0.578089i \(-0.803799\pi\)
−0.815974 + 0.578089i \(0.803799\pi\)
\(542\) 4888.19 0.387391
\(543\) 8195.40 0.647694
\(544\) 10725.6 0.845327
\(545\) 12280.2 0.965185
\(546\) −3404.99 −0.266886
\(547\) −1648.99 −0.128895 −0.0644475 0.997921i \(-0.520528\pi\)
−0.0644475 + 0.997921i \(0.520528\pi\)
\(548\) −3559.63 −0.277481
\(549\) −2133.35 −0.165845
\(550\) 81.9830 0.00635594
\(551\) 31040.8 2.39997
\(552\) 8538.20 0.658351
\(553\) −6044.64 −0.464818
\(554\) 1880.61 0.144223
\(555\) −10757.6 −0.822765
\(556\) 783.439 0.0597575
\(557\) −10612.2 −0.807275 −0.403638 0.914919i \(-0.632254\pi\)
−0.403638 + 0.914919i \(0.632254\pi\)
\(558\) 1392.78 0.105665
\(559\) −3143.30 −0.237831
\(560\) 9410.22 0.710097
\(561\) 6208.38 0.467234
\(562\) −4866.23 −0.365249
\(563\) 9821.65 0.735228 0.367614 0.929979i \(-0.380175\pi\)
0.367614 + 0.929979i \(0.380175\pi\)
\(564\) 1287.53 0.0961258
\(565\) −5803.85 −0.432159
\(566\) −10946.7 −0.812944
\(567\) 1511.36 0.111942
\(568\) 15534.6 1.14757
\(569\) 18417.7 1.35696 0.678479 0.734620i \(-0.262640\pi\)
0.678479 + 0.734620i \(0.262640\pi\)
\(570\) −8734.09 −0.641808
\(571\) −18415.0 −1.34964 −0.674818 0.737984i \(-0.735778\pi\)
−0.674818 + 0.737984i \(0.735778\pi\)
\(572\) 790.070 0.0577526
\(573\) 3335.87 0.243208
\(574\) 22435.4 1.63142
\(575\) 234.598 0.0170146
\(576\) 5118.00 0.370226
\(577\) 15969.8 1.15222 0.576110 0.817372i \(-0.304570\pi\)
0.576110 + 0.817372i \(0.304570\pi\)
\(578\) −26596.0 −1.91393
\(579\) −6857.67 −0.492219
\(580\) −6459.76 −0.462460
\(581\) 21912.6 1.56469
\(582\) 7728.64 0.550451
\(583\) 675.121 0.0479599
\(584\) 9199.52 0.651847
\(585\) −2505.81 −0.177098
\(586\) −374.745 −0.0264174
\(587\) −8593.97 −0.604278 −0.302139 0.953264i \(-0.597701\pi\)
−0.302139 + 0.953264i \(0.597701\pi\)
\(588\) −29.9352 −0.00209950
\(589\) 6593.80 0.461278
\(590\) −1637.26 −0.114246
\(591\) 1877.33 0.130665
\(592\) −14238.0 −0.988476
\(593\) −1632.32 −0.113038 −0.0565188 0.998402i \(-0.518000\pi\)
−0.0565188 + 0.998402i \(0.518000\pi\)
\(594\) 1097.51 0.0758102
\(595\) 26361.1 1.81630
\(596\) −4647.34 −0.319400
\(597\) −14391.8 −0.986631
\(598\) −7075.45 −0.483841
\(599\) −5743.37 −0.391766 −0.195883 0.980627i \(-0.562757\pi\)
−0.195883 + 0.980627i \(0.562757\pi\)
\(600\) 148.048 0.0100734
\(601\) 10777.0 0.731454 0.365727 0.930722i \(-0.380820\pi\)
0.365727 + 0.930722i \(0.380820\pi\)
\(602\) 5845.61 0.395763
\(603\) 4792.06 0.323628
\(604\) 3525.58 0.237507
\(605\) 11929.1 0.801633
\(606\) 8738.40 0.585764
\(607\) 2064.93 0.138077 0.0690386 0.997614i \(-0.478007\pi\)
0.0690386 + 0.997614i \(0.478007\pi\)
\(608\) 8976.44 0.598754
\(609\) −16561.8 −1.10200
\(610\) −6577.88 −0.436607
\(611\) −5473.05 −0.362383
\(612\) 2185.62 0.144360
\(613\) −7430.28 −0.489569 −0.244785 0.969577i \(-0.578717\pi\)
−0.244785 + 0.969577i \(0.578717\pi\)
\(614\) −4653.71 −0.305877
\(615\) 16510.7 1.08256
\(616\) −7536.90 −0.492971
\(617\) −26320.0 −1.71735 −0.858675 0.512520i \(-0.828712\pi\)
−0.858675 + 0.512520i \(0.828712\pi\)
\(618\) −8009.32 −0.521330
\(619\) −1075.60 −0.0698416 −0.0349208 0.999390i \(-0.511118\pi\)
−0.0349208 + 0.999390i \(0.511118\pi\)
\(620\) −1372.21 −0.0888856
\(621\) 3140.57 0.202941
\(622\) 21135.1 1.36244
\(623\) −26949.5 −1.73308
\(624\) −3316.51 −0.212767
\(625\) −15873.0 −1.01587
\(626\) −20004.3 −1.27721
\(627\) 5195.89 0.330947
\(628\) 5847.37 0.371553
\(629\) −39885.3 −2.52835
\(630\) 4660.07 0.294701
\(631\) −16073.1 −1.01404 −0.507022 0.861933i \(-0.669254\pi\)
−0.507022 + 0.861933i \(0.669254\pi\)
\(632\) −7926.62 −0.498898
\(633\) −10960.2 −0.688197
\(634\) −9624.74 −0.602913
\(635\) −25254.1 −1.57823
\(636\) 237.672 0.0148181
\(637\) 127.249 0.00791487
\(638\) −12026.7 −0.746302
\(639\) 5714.03 0.353746
\(640\) 8066.35 0.498204
\(641\) −23363.5 −1.43963 −0.719815 0.694166i \(-0.755773\pi\)
−0.719815 + 0.694166i \(0.755773\pi\)
\(642\) 4101.02 0.252110
\(643\) 24799.4 1.52098 0.760492 0.649347i \(-0.224958\pi\)
0.760492 + 0.649347i \(0.224958\pi\)
\(644\) −4204.46 −0.257266
\(645\) 4301.92 0.262617
\(646\) −32382.9 −1.97227
\(647\) 2126.66 0.129224 0.0646118 0.997910i \(-0.479419\pi\)
0.0646118 + 0.997910i \(0.479419\pi\)
\(648\) 1981.92 0.120150
\(649\) 974.002 0.0589105
\(650\) −122.685 −0.00740322
\(651\) −3518.12 −0.211806
\(652\) −2420.87 −0.145412
\(653\) −501.178 −0.0300347 −0.0150173 0.999887i \(-0.504780\pi\)
−0.0150173 + 0.999887i \(0.504780\pi\)
\(654\) 8048.80 0.481243
\(655\) −10629.5 −0.634089
\(656\) 21852.4 1.30060
\(657\) 3383.82 0.200936
\(658\) 10178.3 0.603024
\(659\) −22302.4 −1.31833 −0.659164 0.752000i \(-0.729090\pi\)
−0.659164 + 0.752000i \(0.729090\pi\)
\(660\) −1081.29 −0.0637715
\(661\) −20096.2 −1.18253 −0.591263 0.806479i \(-0.701371\pi\)
−0.591263 + 0.806479i \(0.701371\pi\)
\(662\) 2130.60 0.125088
\(663\) −9290.64 −0.544221
\(664\) 28735.0 1.67942
\(665\) 22062.0 1.28651
\(666\) −7050.85 −0.410232
\(667\) −34414.9 −1.99783
\(668\) 5435.81 0.314847
\(669\) −10894.5 −0.629604
\(670\) 14775.6 0.851987
\(671\) 3913.16 0.225135
\(672\) −4789.37 −0.274932
\(673\) −21596.5 −1.23698 −0.618488 0.785794i \(-0.712255\pi\)
−0.618488 + 0.785794i \(0.712255\pi\)
\(674\) −1252.70 −0.0715907
\(675\) 54.4558 0.00310519
\(676\) 3073.80 0.174886
\(677\) 18607.2 1.05633 0.528163 0.849143i \(-0.322881\pi\)
0.528163 + 0.849143i \(0.322881\pi\)
\(678\) −3804.01 −0.215475
\(679\) −19522.3 −1.10338
\(680\) 34568.5 1.94948
\(681\) −11877.4 −0.668345
\(682\) −2554.75 −0.143441
\(683\) −3100.05 −0.173675 −0.0868376 0.996222i \(-0.527676\pi\)
−0.0868376 + 0.996222i \(0.527676\pi\)
\(684\) 1829.18 0.102252
\(685\) −20708.7 −1.15509
\(686\) 15521.8 0.863884
\(687\) 8175.17 0.454006
\(688\) 5693.72 0.315510
\(689\) −1010.30 −0.0558624
\(690\) 9683.48 0.534266
\(691\) −9940.03 −0.547231 −0.273615 0.961839i \(-0.588220\pi\)
−0.273615 + 0.961839i \(0.588220\pi\)
\(692\) −2308.75 −0.126829
\(693\) −2772.26 −0.151962
\(694\) −20535.2 −1.12321
\(695\) 4557.77 0.248757
\(696\) −21718.2 −1.18280
\(697\) 61215.8 3.32671
\(698\) −8063.17 −0.437243
\(699\) 3749.08 0.202866
\(700\) −72.9033 −0.00393641
\(701\) 17598.8 0.948213 0.474107 0.880467i \(-0.342771\pi\)
0.474107 + 0.880467i \(0.342771\pi\)
\(702\) −1642.38 −0.0883016
\(703\) −33380.6 −1.79086
\(704\) −9387.84 −0.502582
\(705\) 7490.42 0.400150
\(706\) 3886.91 0.207204
\(707\) −22072.9 −1.17417
\(708\) 342.891 0.0182015
\(709\) −22022.9 −1.16656 −0.583279 0.812272i \(-0.698230\pi\)
−0.583279 + 0.812272i \(0.698230\pi\)
\(710\) 17618.4 0.931277
\(711\) −2915.61 −0.153789
\(712\) −35340.2 −1.86015
\(713\) −7310.54 −0.383986
\(714\) 17277.8 0.905612
\(715\) 4596.36 0.240411
\(716\) −5880.88 −0.306953
\(717\) 12002.6 0.625169
\(718\) −9016.29 −0.468642
\(719\) 30517.9 1.58293 0.791464 0.611216i \(-0.209319\pi\)
0.791464 + 0.611216i \(0.209319\pi\)
\(720\) 4538.98 0.234942
\(721\) 20231.2 1.04501
\(722\) −10213.0 −0.526437
\(723\) 5543.35 0.285144
\(724\) −5292.14 −0.271659
\(725\) −596.737 −0.0305686
\(726\) 7818.70 0.399696
\(727\) 7485.46 0.381871 0.190936 0.981603i \(-0.438848\pi\)
0.190936 + 0.981603i \(0.438848\pi\)
\(728\) 11278.7 0.574199
\(729\) 729.000 0.0370370
\(730\) 10433.5 0.528988
\(731\) 15950.0 0.807020
\(732\) 1377.60 0.0695596
\(733\) 3904.12 0.196729 0.0983643 0.995150i \(-0.468639\pi\)
0.0983643 + 0.995150i \(0.468639\pi\)
\(734\) 11262.0 0.566330
\(735\) −174.153 −0.00873974
\(736\) −9952.17 −0.498426
\(737\) −8789.97 −0.439325
\(738\) 10821.6 0.539768
\(739\) 5176.48 0.257672 0.128836 0.991666i \(-0.458876\pi\)
0.128836 + 0.991666i \(0.458876\pi\)
\(740\) 6946.67 0.345088
\(741\) −7775.47 −0.385478
\(742\) 1878.85 0.0929580
\(743\) −25011.8 −1.23498 −0.617492 0.786577i \(-0.711851\pi\)
−0.617492 + 0.786577i \(0.711851\pi\)
\(744\) −4613.47 −0.227336
\(745\) −27036.6 −1.32959
\(746\) 2954.95 0.145025
\(747\) 10569.5 0.517692
\(748\) −4009.04 −0.195969
\(749\) −10359.0 −0.505355
\(750\) −10238.4 −0.498472
\(751\) 1794.26 0.0871817 0.0435908 0.999049i \(-0.486120\pi\)
0.0435908 + 0.999049i \(0.486120\pi\)
\(752\) 9913.79 0.480743
\(753\) 6179.26 0.299050
\(754\) 17997.5 0.869272
\(755\) 20510.6 0.988686
\(756\) −975.956 −0.0469513
\(757\) −22317.1 −1.07150 −0.535752 0.844376i \(-0.679972\pi\)
−0.535752 + 0.844376i \(0.679972\pi\)
\(758\) −32147.4 −1.54043
\(759\) −5760.67 −0.275493
\(760\) 28930.9 1.38083
\(761\) 28965.0 1.37974 0.689868 0.723935i \(-0.257669\pi\)
0.689868 + 0.723935i \(0.257669\pi\)
\(762\) −16552.3 −0.786910
\(763\) −20331.0 −0.964654
\(764\) −2154.12 −0.102007
\(765\) 12715.2 0.600939
\(766\) −14809.3 −0.698541
\(767\) −1457.56 −0.0686174
\(768\) −8361.08 −0.392844
\(769\) −31709.6 −1.48697 −0.743484 0.668753i \(-0.766828\pi\)
−0.743484 + 0.668753i \(0.766828\pi\)
\(770\) −8547.87 −0.400057
\(771\) 1394.90 0.0651569
\(772\) 4428.31 0.206449
\(773\) −17454.7 −0.812165 −0.406082 0.913836i \(-0.633105\pi\)
−0.406082 + 0.913836i \(0.633105\pi\)
\(774\) 2819.61 0.130941
\(775\) −126.761 −0.00587535
\(776\) −25600.5 −1.18428
\(777\) 17810.2 0.822312
\(778\) 15805.8 0.728360
\(779\) 51232.4 2.35634
\(780\) 1618.12 0.0742793
\(781\) −10481.1 −0.480211
\(782\) 35902.8 1.64179
\(783\) −7988.52 −0.364606
\(784\) −230.496 −0.0105000
\(785\) 34018.0 1.54669
\(786\) −6966.88 −0.316158
\(787\) −43123.6 −1.95323 −0.976614 0.214999i \(-0.931025\pi\)
−0.976614 + 0.214999i \(0.931025\pi\)
\(788\) −1212.28 −0.0548041
\(789\) −8838.35 −0.398800
\(790\) −8989.86 −0.404867
\(791\) 9608.80 0.431921
\(792\) −3635.39 −0.163104
\(793\) −5855.91 −0.262231
\(794\) −24628.7 −1.10081
\(795\) 1382.69 0.0616843
\(796\) 9293.47 0.413817
\(797\) 35425.2 1.57443 0.787217 0.616676i \(-0.211521\pi\)
0.787217 + 0.616676i \(0.211521\pi\)
\(798\) 14460.1 0.641455
\(799\) 27771.8 1.22966
\(800\) −172.566 −0.00762639
\(801\) −12999.0 −0.573405
\(802\) 11607.7 0.511074
\(803\) −6206.86 −0.272771
\(804\) −3094.45 −0.135737
\(805\) −24460.1 −1.07094
\(806\) 3823.10 0.167076
\(807\) 12800.0 0.558342
\(808\) −28945.2 −1.26026
\(809\) 23010.2 0.999995 0.499997 0.866027i \(-0.333334\pi\)
0.499997 + 0.866027i \(0.333334\pi\)
\(810\) 2247.77 0.0975042
\(811\) 21404.3 0.926767 0.463384 0.886158i \(-0.346635\pi\)
0.463384 + 0.886158i \(0.346635\pi\)
\(812\) 10694.7 0.462205
\(813\) −5955.72 −0.256920
\(814\) 12933.2 0.556891
\(815\) −14083.8 −0.605318
\(816\) 16828.9 0.721973
\(817\) 13348.8 0.571621
\(818\) 36435.5 1.55738
\(819\) 4148.60 0.177001
\(820\) −10661.7 −0.454053
\(821\) −1299.78 −0.0552531 −0.0276265 0.999618i \(-0.508795\pi\)
−0.0276265 + 0.999618i \(0.508795\pi\)
\(822\) −13573.1 −0.575931
\(823\) −15147.7 −0.641572 −0.320786 0.947152i \(-0.603947\pi\)
−0.320786 + 0.947152i \(0.603947\pi\)
\(824\) 26530.2 1.12163
\(825\) −99.8872 −0.00421530
\(826\) 2710.63 0.114183
\(827\) 1909.49 0.0802895 0.0401448 0.999194i \(-0.487218\pi\)
0.0401448 + 0.999194i \(0.487218\pi\)
\(828\) −2028.01 −0.0851185
\(829\) −32675.1 −1.36894 −0.684472 0.729039i \(-0.739967\pi\)
−0.684472 + 0.729039i \(0.739967\pi\)
\(830\) 32589.4 1.36288
\(831\) −2291.31 −0.0956495
\(832\) 14048.6 0.585393
\(833\) −645.695 −0.0268571
\(834\) 2987.30 0.124031
\(835\) 31623.7 1.31064
\(836\) −3355.22 −0.138807
\(837\) −1696.95 −0.0700779
\(838\) −30845.7 −1.27153
\(839\) 23287.4 0.958250 0.479125 0.877747i \(-0.340954\pi\)
0.479125 + 0.877747i \(0.340954\pi\)
\(840\) −15436.1 −0.634042
\(841\) 63150.7 2.58931
\(842\) 7701.76 0.315226
\(843\) 5928.97 0.242235
\(844\) 7077.51 0.288647
\(845\) 17882.3 0.728011
\(846\) 4909.44 0.199516
\(847\) −19749.8 −0.801192
\(848\) 1830.03 0.0741080
\(849\) 13337.4 0.539150
\(850\) 622.537 0.0251210
\(851\) 37009.0 1.49078
\(852\) −3689.81 −0.148370
\(853\) −6441.16 −0.258548 −0.129274 0.991609i \(-0.541265\pi\)
−0.129274 + 0.991609i \(0.541265\pi\)
\(854\) 10890.3 0.436367
\(855\) 10641.5 0.425652
\(856\) −13584.3 −0.542408
\(857\) 4466.38 0.178026 0.0890131 0.996030i \(-0.471629\pi\)
0.0890131 + 0.996030i \(0.471629\pi\)
\(858\) 3012.59 0.119869
\(859\) −43793.5 −1.73948 −0.869741 0.493509i \(-0.835714\pi\)
−0.869741 + 0.493509i \(0.835714\pi\)
\(860\) −2777.95 −0.110148
\(861\) −27335.0 −1.08197
\(862\) −1921.31 −0.0759164
\(863\) −698.451 −0.0275499 −0.0137749 0.999905i \(-0.504385\pi\)
−0.0137749 + 0.999905i \(0.504385\pi\)
\(864\) −2310.14 −0.0909634
\(865\) −13431.5 −0.527959
\(866\) −18768.1 −0.736449
\(867\) 32404.3 1.26933
\(868\) 2271.81 0.0888367
\(869\) 5348.04 0.208769
\(870\) −24631.4 −0.959867
\(871\) 13153.9 0.511714
\(872\) −26660.9 −1.03538
\(873\) −9416.50 −0.365063
\(874\) 30047.6 1.16290
\(875\) 25861.9 0.999190
\(876\) −2185.09 −0.0842776
\(877\) 25379.0 0.977180 0.488590 0.872513i \(-0.337511\pi\)
0.488590 + 0.872513i \(0.337511\pi\)
\(878\) −25034.4 −0.962267
\(879\) 456.586 0.0175202
\(880\) −8325.76 −0.318933
\(881\) −29738.5 −1.13725 −0.568624 0.822598i \(-0.692524\pi\)
−0.568624 + 0.822598i \(0.692524\pi\)
\(882\) −114.145 −0.00435765
\(883\) 40030.7 1.52564 0.762820 0.646611i \(-0.223814\pi\)
0.762820 + 0.646611i \(0.223814\pi\)
\(884\) 5999.39 0.228259
\(885\) 1994.82 0.0757686
\(886\) 35813.6 1.35799
\(887\) −31928.0 −1.20861 −0.604304 0.796754i \(-0.706549\pi\)
−0.604304 + 0.796754i \(0.706549\pi\)
\(888\) 23355.3 0.882605
\(889\) 41810.5 1.57737
\(890\) −40080.5 −1.50955
\(891\) −1337.19 −0.0502778
\(892\) 7035.07 0.264071
\(893\) 23242.6 0.870979
\(894\) −17720.6 −0.662936
\(895\) −34212.9 −1.27778
\(896\) −13354.6 −0.497930
\(897\) 8620.66 0.320887
\(898\) −10912.1 −0.405502
\(899\) 18595.5 0.689872
\(900\) −35.1646 −0.00130239
\(901\) 5126.52 0.189555
\(902\) −19849.9 −0.732736
\(903\) −7122.23 −0.262473
\(904\) 12600.5 0.463590
\(905\) −30787.9 −1.13085
\(906\) 13443.3 0.492961
\(907\) 18316.8 0.670560 0.335280 0.942119i \(-0.391169\pi\)
0.335280 + 0.942119i \(0.391169\pi\)
\(908\) 7669.78 0.280320
\(909\) −10646.8 −0.388483
\(910\) 12791.6 0.465975
\(911\) −35873.6 −1.30466 −0.652331 0.757934i \(-0.726209\pi\)
−0.652331 + 0.757934i \(0.726209\pi\)
\(912\) 14084.4 0.511381
\(913\) −19387.3 −0.702768
\(914\) −5925.43 −0.214438
\(915\) 8014.41 0.289561
\(916\) −5279.08 −0.190421
\(917\) 17598.1 0.633740
\(918\) 8333.90 0.299629
\(919\) −14992.6 −0.538151 −0.269076 0.963119i \(-0.586718\pi\)
−0.269076 + 0.963119i \(0.586718\pi\)
\(920\) −32075.7 −1.14946
\(921\) 5670.03 0.202860
\(922\) 36580.6 1.30664
\(923\) 15684.7 0.559336
\(924\) 1790.18 0.0637364
\(925\) 641.717 0.0228103
\(926\) −3952.29 −0.140260
\(927\) 9758.46 0.345750
\(928\) 25314.9 0.895477
\(929\) −42810.8 −1.51192 −0.755962 0.654615i \(-0.772831\pi\)
−0.755962 + 0.654615i \(0.772831\pi\)
\(930\) −5232.30 −0.184488
\(931\) −540.391 −0.0190232
\(932\) −2420.95 −0.0850868
\(933\) −25750.7 −0.903581
\(934\) 44085.4 1.54445
\(935\) −23323.2 −0.815776
\(936\) 5440.25 0.189979
\(937\) −1805.57 −0.0629514 −0.0314757 0.999505i \(-0.510021\pi\)
−0.0314757 + 0.999505i \(0.510021\pi\)
\(938\) −24462.4 −0.851518
\(939\) 24373.0 0.847052
\(940\) −4836.91 −0.167833
\(941\) −48559.2 −1.68224 −0.841119 0.540850i \(-0.818103\pi\)
−0.841119 + 0.540850i \(0.818103\pi\)
\(942\) 22296.4 0.771183
\(943\) −56801.3 −1.96151
\(944\) 2640.20 0.0910289
\(945\) −5677.78 −0.195448
\(946\) −5171.95 −0.177753
\(947\) −38153.0 −1.30919 −0.654597 0.755978i \(-0.727161\pi\)
−0.654597 + 0.755978i \(0.727161\pi\)
\(948\) 1882.74 0.0645028
\(949\) 9288.37 0.317717
\(950\) 521.010 0.0177935
\(951\) 11726.7 0.399856
\(952\) −57231.4 −1.94840
\(953\) 20745.8 0.705166 0.352583 0.935781i \(-0.385303\pi\)
0.352583 + 0.935781i \(0.385303\pi\)
\(954\) 906.257 0.0307559
\(955\) −12532.0 −0.424633
\(956\) −7750.64 −0.262211
\(957\) 14653.2 0.494953
\(958\) 25772.9 0.869192
\(959\) 34285.1 1.15446
\(960\) −19226.9 −0.646402
\(961\) −25840.9 −0.867405
\(962\) −19354.1 −0.648651
\(963\) −4996.64 −0.167201
\(964\) −3579.59 −0.119596
\(965\) 25762.4 0.859399
\(966\) −16031.9 −0.533972
\(967\) −17347.2 −0.576884 −0.288442 0.957497i \(-0.593137\pi\)
−0.288442 + 0.957497i \(0.593137\pi\)
\(968\) −25898.8 −0.859936
\(969\) 39454.9 1.30802
\(970\) −29034.4 −0.961070
\(971\) 23425.2 0.774202 0.387101 0.922037i \(-0.373476\pi\)
0.387101 + 0.922037i \(0.373476\pi\)
\(972\) −470.749 −0.0155342
\(973\) −7545.81 −0.248620
\(974\) 37634.6 1.23808
\(975\) 149.478 0.00490987
\(976\) 10607.3 0.347881
\(977\) −13587.7 −0.444942 −0.222471 0.974939i \(-0.571412\pi\)
−0.222471 + 0.974939i \(0.571412\pi\)
\(978\) −9230.93 −0.301813
\(979\) 23843.8 0.778398
\(980\) 112.458 0.00366566
\(981\) −9806.57 −0.319164
\(982\) 8837.63 0.287190
\(983\) −42058.9 −1.36467 −0.682336 0.731039i \(-0.739036\pi\)
−0.682336 + 0.731039i \(0.739036\pi\)
\(984\) −35845.6 −1.16130
\(985\) −7052.61 −0.228137
\(986\) −91324.5 −2.94966
\(987\) −12401.1 −0.399930
\(988\) 5020.98 0.161679
\(989\) −14799.8 −0.475839
\(990\) −4123.03 −0.132362
\(991\) 10765.5 0.345084 0.172542 0.985002i \(-0.444802\pi\)
0.172542 + 0.985002i \(0.444802\pi\)
\(992\) 5377.48 0.172112
\(993\) −2595.90 −0.0829593
\(994\) −29168.8 −0.930764
\(995\) 54066.2 1.72263
\(996\) −6825.18 −0.217133
\(997\) 33120.6 1.05210 0.526048 0.850455i \(-0.323673\pi\)
0.526048 + 0.850455i \(0.323673\pi\)
\(998\) 7971.96 0.252854
\(999\) 8590.67 0.272069
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.a.1.3 7
3.2 odd 2 531.4.a.d.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.a.1.3 7 1.1 even 1 trivial
531.4.a.d.1.5 7 3.2 odd 2