Properties

Label 177.4.a.c.1.1
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 1.1
Root \(-5.19624\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.19624 q^{2} -3.00000 q^{3} +19.0009 q^{4} -8.30102 q^{5} +15.5887 q^{6} +21.5539 q^{7} -57.1634 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-5.19624 q^{2} -3.00000 q^{3} +19.0009 q^{4} -8.30102 q^{5} +15.5887 q^{6} +21.5539 q^{7} -57.1634 q^{8} +9.00000 q^{9} +43.1341 q^{10} -28.3746 q^{11} -57.0027 q^{12} -28.2089 q^{13} -111.999 q^{14} +24.9031 q^{15} +145.027 q^{16} +21.8166 q^{17} -46.7662 q^{18} -122.388 q^{19} -157.727 q^{20} -64.6617 q^{21} +147.441 q^{22} +82.1571 q^{23} +171.490 q^{24} -56.0930 q^{25} +146.580 q^{26} -27.0000 q^{27} +409.544 q^{28} +86.9209 q^{29} -129.402 q^{30} +131.178 q^{31} -296.290 q^{32} +85.1239 q^{33} -113.364 q^{34} -178.919 q^{35} +171.008 q^{36} +280.467 q^{37} +635.957 q^{38} +84.6266 q^{39} +474.515 q^{40} +381.788 q^{41} +335.998 q^{42} +452.501 q^{43} -539.144 q^{44} -74.7092 q^{45} -426.908 q^{46} -158.067 q^{47} -435.082 q^{48} +121.570 q^{49} +291.473 q^{50} -65.4499 q^{51} -535.994 q^{52} -162.922 q^{53} +140.298 q^{54} +235.539 q^{55} -1232.09 q^{56} +367.164 q^{57} -451.662 q^{58} -59.0000 q^{59} +473.181 q^{60} -368.344 q^{61} -681.632 q^{62} +193.985 q^{63} +379.374 q^{64} +234.162 q^{65} -442.324 q^{66} +177.950 q^{67} +414.536 q^{68} -246.471 q^{69} +929.708 q^{70} +58.9220 q^{71} -514.470 q^{72} +880.299 q^{73} -1457.37 q^{74} +168.279 q^{75} -2325.48 q^{76} -611.584 q^{77} -439.740 q^{78} -825.284 q^{79} -1203.88 q^{80} +81.0000 q^{81} -1983.86 q^{82} +1426.68 q^{83} -1228.63 q^{84} -181.100 q^{85} -2351.30 q^{86} -260.763 q^{87} +1621.99 q^{88} +1556.78 q^{89} +388.207 q^{90} -608.011 q^{91} +1561.06 q^{92} -393.534 q^{93} +821.356 q^{94} +1015.94 q^{95} +888.869 q^{96} +1811.25 q^{97} -631.708 q^{98} -255.372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + 29q^{10} - 27q^{11} - 114q^{12} + 89q^{13} - 37q^{14} + 36q^{15} + 362q^{16} + 79q^{17} + 18q^{18} + 288q^{19} + 457q^{20} - 159q^{21} + 596q^{22} + 202q^{23} - 9q^{24} + 264q^{25} + 270q^{26} - 216q^{27} + 702q^{28} - 114q^{29} - 87q^{30} + 538q^{31} + 316q^{32} + 81q^{33} + 498q^{34} - 196q^{35} + 342q^{36} + 395q^{37} + 397q^{38} - 267q^{39} + 918q^{40} - 39q^{41} + 111q^{42} + 527q^{43} + 64q^{44} - 108q^{45} - 539q^{46} + 860q^{47} - 1086q^{48} + 347q^{49} - 591q^{50} - 237q^{51} - 644q^{52} - 812q^{53} - 54q^{54} + 536q^{55} - 2218q^{56} - 864q^{57} - 1154q^{58} - 472q^{59} - 1371q^{60} - 460q^{61} - 2014q^{62} + 477q^{63} - 451q^{64} - 986q^{65} - 1788q^{66} + 1934q^{67} - 69q^{68} - 606q^{69} - 1028q^{70} - 1687q^{71} + 27q^{72} + 1980q^{73} - 2400q^{74} - 792q^{75} - 940q^{76} - 821q^{77} - 810q^{78} + 3319q^{79} - 2119q^{80} + 648q^{81} + 429q^{82} + 2057q^{83} - 2106q^{84} + 566q^{85} - 6690q^{86} + 342q^{87} + 1189q^{88} + 1668q^{89} + 261q^{90} + 2427q^{91} - 980q^{92} - 1614q^{93} + 332q^{94} + 2146q^{95} - 948q^{96} + 1956q^{97} - 2026q^{98} - 243q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.19624 −1.83715 −0.918574 0.395249i \(-0.870658\pi\)
−0.918574 + 0.395249i \(0.870658\pi\)
\(3\) −3.00000 −0.577350
\(4\) 19.0009 2.37511
\(5\) −8.30102 −0.742466 −0.371233 0.928540i \(-0.621065\pi\)
−0.371233 + 0.928540i \(0.621065\pi\)
\(6\) 15.5887 1.06068
\(7\) 21.5539 1.16380 0.581900 0.813260i \(-0.302309\pi\)
0.581900 + 0.813260i \(0.302309\pi\)
\(8\) −57.1634 −2.52629
\(9\) 9.00000 0.333333
\(10\) 43.1341 1.36402
\(11\) −28.3746 −0.777752 −0.388876 0.921290i \(-0.627137\pi\)
−0.388876 + 0.921290i \(0.627137\pi\)
\(12\) −57.0027 −1.37127
\(13\) −28.2089 −0.601826 −0.300913 0.953652i \(-0.597291\pi\)
−0.300913 + 0.953652i \(0.597291\pi\)
\(14\) −111.999 −2.13807
\(15\) 24.9031 0.428663
\(16\) 145.027 2.26605
\(17\) 21.8166 0.311254 0.155627 0.987816i \(-0.450260\pi\)
0.155627 + 0.987816i \(0.450260\pi\)
\(18\) −46.7662 −0.612383
\(19\) −122.388 −1.47777 −0.738887 0.673830i \(-0.764648\pi\)
−0.738887 + 0.673830i \(0.764648\pi\)
\(20\) −157.727 −1.76344
\(21\) −64.6617 −0.671921
\(22\) 147.441 1.42885
\(23\) 82.1571 0.744823 0.372412 0.928068i \(-0.378531\pi\)
0.372412 + 0.928068i \(0.378531\pi\)
\(24\) 171.490 1.45855
\(25\) −56.0930 −0.448744
\(26\) 146.580 1.10564
\(27\) −27.0000 −0.192450
\(28\) 409.544 2.76416
\(29\) 86.9209 0.556580 0.278290 0.960497i \(-0.410232\pi\)
0.278290 + 0.960497i \(0.410232\pi\)
\(30\) −129.402 −0.787518
\(31\) 131.178 0.760009 0.380004 0.924985i \(-0.375922\pi\)
0.380004 + 0.924985i \(0.375922\pi\)
\(32\) −296.290 −1.63678
\(33\) 85.1239 0.449035
\(34\) −113.364 −0.571819
\(35\) −178.919 −0.864083
\(36\) 171.008 0.791705
\(37\) 280.467 1.24617 0.623087 0.782152i \(-0.285878\pi\)
0.623087 + 0.782152i \(0.285878\pi\)
\(38\) 635.957 2.71489
\(39\) 84.6266 0.347464
\(40\) 474.515 1.87568
\(41\) 381.788 1.45427 0.727137 0.686493i \(-0.240851\pi\)
0.727137 + 0.686493i \(0.240851\pi\)
\(42\) 335.998 1.23442
\(43\) 452.501 1.60478 0.802392 0.596798i \(-0.203560\pi\)
0.802392 + 0.596798i \(0.203560\pi\)
\(44\) −539.144 −1.84725
\(45\) −74.7092 −0.247489
\(46\) −426.908 −1.36835
\(47\) −158.067 −0.490564 −0.245282 0.969452i \(-0.578881\pi\)
−0.245282 + 0.969452i \(0.578881\pi\)
\(48\) −435.082 −1.30831
\(49\) 121.570 0.354432
\(50\) 291.473 0.824409
\(51\) −65.4499 −0.179702
\(52\) −535.994 −1.42940
\(53\) −162.922 −0.422245 −0.211123 0.977460i \(-0.567712\pi\)
−0.211123 + 0.977460i \(0.567712\pi\)
\(54\) 140.298 0.353559
\(55\) 235.539 0.577455
\(56\) −1232.09 −2.94010
\(57\) 367.164 0.853193
\(58\) −451.662 −1.02252
\(59\) −59.0000 −0.130189
\(60\) 473.181 1.01812
\(61\) −368.344 −0.773141 −0.386570 0.922260i \(-0.626340\pi\)
−0.386570 + 0.922260i \(0.626340\pi\)
\(62\) −681.632 −1.39625
\(63\) 193.985 0.387934
\(64\) 379.374 0.740965
\(65\) 234.162 0.446835
\(66\) −442.324 −0.824945
\(67\) 177.950 0.324478 0.162239 0.986752i \(-0.448128\pi\)
0.162239 + 0.986752i \(0.448128\pi\)
\(68\) 414.536 0.739263
\(69\) −246.471 −0.430024
\(70\) 929.708 1.58745
\(71\) 58.9220 0.0984894 0.0492447 0.998787i \(-0.484319\pi\)
0.0492447 + 0.998787i \(0.484319\pi\)
\(72\) −514.470 −0.842096
\(73\) 880.299 1.41139 0.705693 0.708518i \(-0.250636\pi\)
0.705693 + 0.708518i \(0.250636\pi\)
\(74\) −1457.37 −2.28941
\(75\) 168.279 0.259082
\(76\) −2325.48 −3.50988
\(77\) −611.584 −0.905148
\(78\) −439.740 −0.638343
\(79\) −825.284 −1.17534 −0.587669 0.809101i \(-0.699954\pi\)
−0.587669 + 0.809101i \(0.699954\pi\)
\(80\) −1203.88 −1.68247
\(81\) 81.0000 0.111111
\(82\) −1983.86 −2.67172
\(83\) 1426.68 1.88673 0.943367 0.331752i \(-0.107640\pi\)
0.943367 + 0.331752i \(0.107640\pi\)
\(84\) −1228.63 −1.59589
\(85\) −181.100 −0.231095
\(86\) −2351.30 −2.94823
\(87\) −260.763 −0.321341
\(88\) 1621.99 1.96483
\(89\) 1556.78 1.85413 0.927067 0.374896i \(-0.122322\pi\)
0.927067 + 0.374896i \(0.122322\pi\)
\(90\) 388.207 0.454673
\(91\) −608.011 −0.700405
\(92\) 1561.06 1.76904
\(93\) −393.534 −0.438791
\(94\) 821.356 0.901238
\(95\) 1015.94 1.09720
\(96\) 888.869 0.944998
\(97\) 1811.25 1.89593 0.947964 0.318377i \(-0.103138\pi\)
0.947964 + 0.318377i \(0.103138\pi\)
\(98\) −631.708 −0.651144
\(99\) −255.372 −0.259251
\(100\) −1065.82 −1.06582
\(101\) 1132.95 1.11617 0.558085 0.829784i \(-0.311536\pi\)
0.558085 + 0.829784i \(0.311536\pi\)
\(102\) 340.093 0.330140
\(103\) 1479.79 1.41561 0.707805 0.706408i \(-0.249685\pi\)
0.707805 + 0.706408i \(0.249685\pi\)
\(104\) 1612.51 1.52038
\(105\) 536.758 0.498878
\(106\) 846.580 0.775727
\(107\) 293.850 0.265491 0.132746 0.991150i \(-0.457621\pi\)
0.132746 + 0.991150i \(0.457621\pi\)
\(108\) −513.025 −0.457091
\(109\) −801.451 −0.704267 −0.352133 0.935950i \(-0.614544\pi\)
−0.352133 + 0.935950i \(0.614544\pi\)
\(110\) −1223.91 −1.06087
\(111\) −841.401 −0.719479
\(112\) 3125.90 2.63723
\(113\) −1834.04 −1.52683 −0.763415 0.645908i \(-0.776479\pi\)
−0.763415 + 0.645908i \(0.776479\pi\)
\(114\) −1907.87 −1.56744
\(115\) −681.988 −0.553006
\(116\) 1651.58 1.32194
\(117\) −253.880 −0.200609
\(118\) 306.578 0.239176
\(119\) 470.233 0.362237
\(120\) −1423.54 −1.08293
\(121\) −525.880 −0.395102
\(122\) 1914.00 1.42037
\(123\) −1145.36 −0.839625
\(124\) 2492.50 1.80511
\(125\) 1503.26 1.07564
\(126\) −1007.99 −0.712691
\(127\) 745.001 0.520537 0.260268 0.965536i \(-0.416189\pi\)
0.260268 + 0.965536i \(0.416189\pi\)
\(128\) 398.999 0.275522
\(129\) −1357.50 −0.926522
\(130\) −1216.76 −0.820902
\(131\) −2205.52 −1.47097 −0.735485 0.677541i \(-0.763046\pi\)
−0.735485 + 0.677541i \(0.763046\pi\)
\(132\) 1617.43 1.06651
\(133\) −2637.93 −1.71983
\(134\) −924.669 −0.596114
\(135\) 224.128 0.142888
\(136\) −1247.11 −0.786316
\(137\) 744.233 0.464118 0.232059 0.972702i \(-0.425454\pi\)
0.232059 + 0.972702i \(0.425454\pi\)
\(138\) 1280.72 0.790018
\(139\) 267.712 0.163360 0.0816801 0.996659i \(-0.473971\pi\)
0.0816801 + 0.996659i \(0.473971\pi\)
\(140\) −3399.63 −2.05229
\(141\) 474.202 0.283227
\(142\) −306.173 −0.180940
\(143\) 800.416 0.468071
\(144\) 1305.25 0.755351
\(145\) −721.533 −0.413242
\(146\) −4574.24 −2.59292
\(147\) −364.711 −0.204631
\(148\) 5329.13 2.95981
\(149\) −2478.30 −1.36262 −0.681308 0.731997i \(-0.738589\pi\)
−0.681308 + 0.731997i \(0.738589\pi\)
\(150\) −874.418 −0.475973
\(151\) 1902.48 1.02531 0.512655 0.858595i \(-0.328662\pi\)
0.512655 + 0.858595i \(0.328662\pi\)
\(152\) 6996.10 3.73328
\(153\) 196.350 0.103751
\(154\) 3177.94 1.66289
\(155\) −1088.91 −0.564281
\(156\) 1607.98 0.825267
\(157\) −3638.32 −1.84949 −0.924745 0.380588i \(-0.875722\pi\)
−0.924745 + 0.380588i \(0.875722\pi\)
\(158\) 4288.37 2.15927
\(159\) 488.765 0.243783
\(160\) 2459.51 1.21526
\(161\) 1770.81 0.866826
\(162\) −420.895 −0.204128
\(163\) 1188.42 0.571068 0.285534 0.958369i \(-0.407829\pi\)
0.285534 + 0.958369i \(0.407829\pi\)
\(164\) 7254.31 3.45407
\(165\) −706.616 −0.333394
\(166\) −7413.39 −3.46621
\(167\) 1667.69 0.772752 0.386376 0.922341i \(-0.373727\pi\)
0.386376 + 0.922341i \(0.373727\pi\)
\(168\) 3696.28 1.69746
\(169\) −1401.26 −0.637806
\(170\) 941.041 0.424556
\(171\) −1101.49 −0.492591
\(172\) 8597.92 3.81154
\(173\) 1854.57 0.815032 0.407516 0.913198i \(-0.366395\pi\)
0.407516 + 0.913198i \(0.366395\pi\)
\(174\) 1354.99 0.590352
\(175\) −1209.02 −0.522249
\(176\) −4115.10 −1.76243
\(177\) 177.000 0.0751646
\(178\) −8089.38 −3.40632
\(179\) 3650.51 1.52431 0.762155 0.647394i \(-0.224141\pi\)
0.762155 + 0.647394i \(0.224141\pi\)
\(180\) −1419.54 −0.587814
\(181\) 912.195 0.374602 0.187301 0.982303i \(-0.440026\pi\)
0.187301 + 0.982303i \(0.440026\pi\)
\(182\) 3159.37 1.28675
\(183\) 1105.03 0.446373
\(184\) −4696.38 −1.88164
\(185\) −2328.16 −0.925243
\(186\) 2044.90 0.806124
\(187\) −619.039 −0.242078
\(188\) −3003.42 −1.16514
\(189\) −581.955 −0.223974
\(190\) −5279.09 −2.01571
\(191\) 2060.65 0.780646 0.390323 0.920678i \(-0.372363\pi\)
0.390323 + 0.920678i \(0.372363\pi\)
\(192\) −1138.12 −0.427796
\(193\) −1917.94 −0.715318 −0.357659 0.933852i \(-0.616425\pi\)
−0.357659 + 0.933852i \(0.616425\pi\)
\(194\) −9411.71 −3.48310
\(195\) −702.487 −0.257980
\(196\) 2309.94 0.841817
\(197\) −2490.32 −0.900651 −0.450325 0.892864i \(-0.648692\pi\)
−0.450325 + 0.892864i \(0.648692\pi\)
\(198\) 1326.97 0.476282
\(199\) 3412.12 1.21547 0.607735 0.794140i \(-0.292078\pi\)
0.607735 + 0.794140i \(0.292078\pi\)
\(200\) 3206.46 1.13366
\(201\) −533.849 −0.187337
\(202\) −5887.10 −2.05057
\(203\) 1873.48 0.647748
\(204\) −1243.61 −0.426814
\(205\) −3169.23 −1.07975
\(206\) −7689.34 −2.60069
\(207\) 739.414 0.248274
\(208\) −4091.06 −1.36377
\(209\) 3472.71 1.14934
\(210\) −2789.12 −0.916514
\(211\) 892.077 0.291057 0.145529 0.989354i \(-0.453512\pi\)
0.145529 + 0.989354i \(0.453512\pi\)
\(212\) −3095.66 −1.00288
\(213\) −176.766 −0.0568629
\(214\) −1526.92 −0.487747
\(215\) −3756.22 −1.19150
\(216\) 1543.41 0.486184
\(217\) 2827.40 0.884499
\(218\) 4164.53 1.29384
\(219\) −2640.90 −0.814864
\(220\) 4475.45 1.37152
\(221\) −615.423 −0.187320
\(222\) 4372.12 1.32179
\(223\) −2891.35 −0.868246 −0.434123 0.900854i \(-0.642942\pi\)
−0.434123 + 0.900854i \(0.642942\pi\)
\(224\) −6386.20 −1.90489
\(225\) −504.837 −0.149581
\(226\) 9530.10 2.80501
\(227\) −1746.45 −0.510643 −0.255321 0.966856i \(-0.582181\pi\)
−0.255321 + 0.966856i \(0.582181\pi\)
\(228\) 6976.44 2.02643
\(229\) −1195.00 −0.344837 −0.172418 0.985024i \(-0.555158\pi\)
−0.172418 + 0.985024i \(0.555158\pi\)
\(230\) 3543.77 1.01595
\(231\) 1834.75 0.522588
\(232\) −4968.69 −1.40608
\(233\) −4741.93 −1.33328 −0.666640 0.745380i \(-0.732268\pi\)
−0.666640 + 0.745380i \(0.732268\pi\)
\(234\) 1319.22 0.368548
\(235\) 1312.12 0.364227
\(236\) −1121.05 −0.309213
\(237\) 2475.85 0.678582
\(238\) −2443.45 −0.665483
\(239\) −2889.11 −0.781928 −0.390964 0.920406i \(-0.627858\pi\)
−0.390964 + 0.920406i \(0.627858\pi\)
\(240\) 3611.63 0.971373
\(241\) 2648.11 0.707799 0.353899 0.935284i \(-0.384856\pi\)
0.353899 + 0.935284i \(0.384856\pi\)
\(242\) 2732.60 0.725860
\(243\) −243.000 −0.0641500
\(244\) −6998.87 −1.83630
\(245\) −1009.16 −0.263154
\(246\) 5951.58 1.54252
\(247\) 3452.42 0.889362
\(248\) −7498.58 −1.92000
\(249\) −4280.05 −1.08931
\(250\) −7811.29 −1.97612
\(251\) 2327.49 0.585299 0.292650 0.956220i \(-0.405463\pi\)
0.292650 + 0.956220i \(0.405463\pi\)
\(252\) 3685.89 0.921386
\(253\) −2331.18 −0.579288
\(254\) −3871.21 −0.956303
\(255\) 543.301 0.133423
\(256\) −5108.29 −1.24714
\(257\) −4224.97 −1.02547 −0.512737 0.858546i \(-0.671368\pi\)
−0.512737 + 0.858546i \(0.671368\pi\)
\(258\) 7053.91 1.70216
\(259\) 6045.15 1.45030
\(260\) 4449.30 1.06128
\(261\) 782.288 0.185527
\(262\) 11460.4 2.70239
\(263\) 3245.27 0.760881 0.380441 0.924805i \(-0.375772\pi\)
0.380441 + 0.924805i \(0.375772\pi\)
\(264\) −4865.97 −1.13439
\(265\) 1352.42 0.313503
\(266\) 13707.3 3.15959
\(267\) −4670.33 −1.07048
\(268\) 3381.21 0.770672
\(269\) −4695.98 −1.06438 −0.532191 0.846624i \(-0.678631\pi\)
−0.532191 + 0.846624i \(0.678631\pi\)
\(270\) −1164.62 −0.262506
\(271\) 1442.96 0.323444 0.161722 0.986836i \(-0.448295\pi\)
0.161722 + 0.986836i \(0.448295\pi\)
\(272\) 3164.01 0.705317
\(273\) 1824.03 0.404379
\(274\) −3867.21 −0.852653
\(275\) 1591.62 0.349012
\(276\) −4683.18 −1.02136
\(277\) 6781.78 1.47104 0.735519 0.677504i \(-0.236938\pi\)
0.735519 + 0.677504i \(0.236938\pi\)
\(278\) −1391.10 −0.300117
\(279\) 1180.60 0.253336
\(280\) 10227.6 2.18292
\(281\) 916.383 0.194544 0.0972719 0.995258i \(-0.468988\pi\)
0.0972719 + 0.995258i \(0.468988\pi\)
\(282\) −2464.07 −0.520330
\(283\) −1693.18 −0.355651 −0.177825 0.984062i \(-0.556906\pi\)
−0.177825 + 0.984062i \(0.556906\pi\)
\(284\) 1119.57 0.233924
\(285\) −3047.83 −0.633467
\(286\) −4159.15 −0.859916
\(287\) 8229.01 1.69248
\(288\) −2666.61 −0.545595
\(289\) −4437.03 −0.903121
\(290\) 3749.26 0.759186
\(291\) −5433.76 −1.09461
\(292\) 16726.5 3.35220
\(293\) −4712.00 −0.939515 −0.469757 0.882796i \(-0.655659\pi\)
−0.469757 + 0.882796i \(0.655659\pi\)
\(294\) 1895.12 0.375938
\(295\) 489.760 0.0966609
\(296\) −16032.4 −3.14820
\(297\) 766.115 0.149678
\(298\) 12877.8 2.50333
\(299\) −2317.56 −0.448254
\(300\) 3197.45 0.615350
\(301\) 9753.15 1.86765
\(302\) −9885.75 −1.88364
\(303\) −3398.86 −0.644421
\(304\) −17749.6 −3.34871
\(305\) 3057.63 0.574031
\(306\) −1020.28 −0.190606
\(307\) 7720.48 1.43528 0.717640 0.696414i \(-0.245222\pi\)
0.717640 + 0.696414i \(0.245222\pi\)
\(308\) −11620.6 −2.14983
\(309\) −4439.37 −0.817303
\(310\) 5658.25 1.03667
\(311\) 5773.53 1.05269 0.526345 0.850271i \(-0.323562\pi\)
0.526345 + 0.850271i \(0.323562\pi\)
\(312\) −4837.54 −0.877794
\(313\) −9875.96 −1.78346 −0.891729 0.452570i \(-0.850507\pi\)
−0.891729 + 0.452570i \(0.850507\pi\)
\(314\) 18905.6 3.39779
\(315\) −1610.27 −0.288028
\(316\) −15681.1 −2.79156
\(317\) −6005.53 −1.06405 −0.532025 0.846729i \(-0.678569\pi\)
−0.532025 + 0.846729i \(0.678569\pi\)
\(318\) −2539.74 −0.447866
\(319\) −2466.35 −0.432881
\(320\) −3149.19 −0.550141
\(321\) −881.551 −0.153282
\(322\) −9201.53 −1.59249
\(323\) −2670.09 −0.459962
\(324\) 1539.07 0.263902
\(325\) 1582.32 0.270066
\(326\) −6175.31 −1.04914
\(327\) 2404.35 0.406609
\(328\) −21824.3 −3.67391
\(329\) −3406.97 −0.570918
\(330\) 3671.74 0.612493
\(331\) 6895.07 1.14498 0.572488 0.819913i \(-0.305978\pi\)
0.572488 + 0.819913i \(0.305978\pi\)
\(332\) 27108.3 4.48121
\(333\) 2524.20 0.415392
\(334\) −8665.71 −1.41966
\(335\) −1477.16 −0.240914
\(336\) −9377.71 −1.52261
\(337\) 6764.00 1.09335 0.546675 0.837345i \(-0.315893\pi\)
0.546675 + 0.837345i \(0.315893\pi\)
\(338\) 7281.28 1.17174
\(339\) 5502.12 0.881516
\(340\) −3441.07 −0.548878
\(341\) −3722.13 −0.591098
\(342\) 5723.61 0.904963
\(343\) −4772.67 −0.751312
\(344\) −25866.5 −4.05415
\(345\) 2045.96 0.319278
\(346\) −9636.81 −1.49734
\(347\) 5474.73 0.846971 0.423485 0.905903i \(-0.360807\pi\)
0.423485 + 0.905903i \(0.360807\pi\)
\(348\) −4954.73 −0.763222
\(349\) −6375.89 −0.977919 −0.488960 0.872306i \(-0.662623\pi\)
−0.488960 + 0.872306i \(0.662623\pi\)
\(350\) 6282.37 0.959448
\(351\) 761.639 0.115821
\(352\) 8407.11 1.27301
\(353\) 4971.14 0.749539 0.374770 0.927118i \(-0.377722\pi\)
0.374770 + 0.927118i \(0.377722\pi\)
\(354\) −919.734 −0.138089
\(355\) −489.113 −0.0731251
\(356\) 29580.2 4.40378
\(357\) −1410.70 −0.209138
\(358\) −18968.9 −2.80039
\(359\) 2073.46 0.304827 0.152414 0.988317i \(-0.451295\pi\)
0.152414 + 0.988317i \(0.451295\pi\)
\(360\) 4270.63 0.625228
\(361\) 8119.79 1.18382
\(362\) −4739.98 −0.688199
\(363\) 1577.64 0.228112
\(364\) −11552.8 −1.66354
\(365\) −7307.38 −1.04791
\(366\) −5742.01 −0.820053
\(367\) −6485.59 −0.922466 −0.461233 0.887279i \(-0.652593\pi\)
−0.461233 + 0.887279i \(0.652593\pi\)
\(368\) 11915.0 1.68781
\(369\) 3436.09 0.484758
\(370\) 12097.7 1.69981
\(371\) −3511.59 −0.491409
\(372\) −7477.51 −1.04218
\(373\) −2610.25 −0.362342 −0.181171 0.983452i \(-0.557989\pi\)
−0.181171 + 0.983452i \(0.557989\pi\)
\(374\) 3216.67 0.444733
\(375\) −4509.77 −0.621023
\(376\) 9035.66 1.23931
\(377\) −2451.94 −0.334964
\(378\) 3023.98 0.411473
\(379\) −5609.34 −0.760244 −0.380122 0.924936i \(-0.624118\pi\)
−0.380122 + 0.924936i \(0.624118\pi\)
\(380\) 19303.9 2.60597
\(381\) −2235.00 −0.300532
\(382\) −10707.6 −1.43416
\(383\) 2978.80 0.397414 0.198707 0.980059i \(-0.436326\pi\)
0.198707 + 0.980059i \(0.436326\pi\)
\(384\) −1197.00 −0.159073
\(385\) 5076.77 0.672042
\(386\) 9966.08 1.31415
\(387\) 4072.51 0.534928
\(388\) 34415.5 4.50305
\(389\) 10137.6 1.32132 0.660662 0.750683i \(-0.270276\pi\)
0.660662 + 0.750683i \(0.270276\pi\)
\(390\) 3650.29 0.473948
\(391\) 1792.39 0.231829
\(392\) −6949.36 −0.895397
\(393\) 6616.56 0.849265
\(394\) 12940.3 1.65463
\(395\) 6850.70 0.872649
\(396\) −4852.29 −0.615750
\(397\) 12921.9 1.63359 0.816793 0.576930i \(-0.195750\pi\)
0.816793 + 0.576930i \(0.195750\pi\)
\(398\) −17730.2 −2.23300
\(399\) 7913.80 0.992947
\(400\) −8135.02 −1.01688
\(401\) −9556.68 −1.19012 −0.595060 0.803681i \(-0.702872\pi\)
−0.595060 + 0.803681i \(0.702872\pi\)
\(402\) 2774.01 0.344167
\(403\) −3700.38 −0.457393
\(404\) 21527.1 2.65103
\(405\) −672.383 −0.0824962
\(406\) −9735.07 −1.19001
\(407\) −7958.14 −0.969215
\(408\) 3741.34 0.453980
\(409\) 8381.64 1.01331 0.506657 0.862148i \(-0.330881\pi\)
0.506657 + 0.862148i \(0.330881\pi\)
\(410\) 16468.1 1.98366
\(411\) −2232.70 −0.267958
\(412\) 28117.3 3.36224
\(413\) −1271.68 −0.151514
\(414\) −3842.17 −0.456117
\(415\) −11842.9 −1.40084
\(416\) 8358.00 0.985059
\(417\) −803.137 −0.0943161
\(418\) −18045.0 −2.11151
\(419\) −9005.40 −1.04998 −0.524991 0.851108i \(-0.675931\pi\)
−0.524991 + 0.851108i \(0.675931\pi\)
\(420\) 10198.9 1.18489
\(421\) 754.089 0.0872970 0.0436485 0.999047i \(-0.486102\pi\)
0.0436485 + 0.999047i \(0.486102\pi\)
\(422\) −4635.45 −0.534716
\(423\) −1422.61 −0.163521
\(424\) 9313.15 1.06671
\(425\) −1223.76 −0.139673
\(426\) 918.518 0.104466
\(427\) −7939.24 −0.899782
\(428\) 5583.42 0.630572
\(429\) −2401.25 −0.270241
\(430\) 19518.2 2.18896
\(431\) −2505.79 −0.280046 −0.140023 0.990148i \(-0.544718\pi\)
−0.140023 + 0.990148i \(0.544718\pi\)
\(432\) −3915.74 −0.436102
\(433\) −176.502 −0.0195893 −0.00979465 0.999952i \(-0.503118\pi\)
−0.00979465 + 0.999952i \(0.503118\pi\)
\(434\) −14691.8 −1.62496
\(435\) 2164.60 0.238585
\(436\) −15228.3 −1.67271
\(437\) −10055.0 −1.10068
\(438\) 13722.7 1.49703
\(439\) −2223.93 −0.241782 −0.120891 0.992666i \(-0.538575\pi\)
−0.120891 + 0.992666i \(0.538575\pi\)
\(440\) −13464.2 −1.45882
\(441\) 1094.13 0.118144
\(442\) 3197.88 0.344135
\(443\) −6065.11 −0.650479 −0.325239 0.945632i \(-0.605445\pi\)
−0.325239 + 0.945632i \(0.605445\pi\)
\(444\) −15987.4 −1.70885
\(445\) −12922.8 −1.37663
\(446\) 15024.1 1.59510
\(447\) 7434.89 0.786707
\(448\) 8176.99 0.862336
\(449\) −127.588 −0.0134104 −0.00670518 0.999978i \(-0.502134\pi\)
−0.00670518 + 0.999978i \(0.502134\pi\)
\(450\) 2623.25 0.274803
\(451\) −10833.1 −1.13106
\(452\) −34848.4 −3.62640
\(453\) −5707.44 −0.591962
\(454\) 9074.97 0.938126
\(455\) 5047.11 0.520027
\(456\) −20988.3 −2.15541
\(457\) 15246.9 1.56065 0.780327 0.625372i \(-0.215053\pi\)
0.780327 + 0.625372i \(0.215053\pi\)
\(458\) 6209.49 0.633517
\(459\) −589.049 −0.0599008
\(460\) −12958.4 −1.31345
\(461\) 8148.20 0.823210 0.411605 0.911362i \(-0.364968\pi\)
0.411605 + 0.911362i \(0.364968\pi\)
\(462\) −9533.81 −0.960071
\(463\) 6518.90 0.654340 0.327170 0.944966i \(-0.393905\pi\)
0.327170 + 0.944966i \(0.393905\pi\)
\(464\) 12605.9 1.26124
\(465\) 3266.74 0.325788
\(466\) 24640.2 2.44943
\(467\) −263.751 −0.0261348 −0.0130674 0.999915i \(-0.504160\pi\)
−0.0130674 + 0.999915i \(0.504160\pi\)
\(468\) −4823.95 −0.476468
\(469\) 3835.51 0.377628
\(470\) −6818.10 −0.669139
\(471\) 10915.0 1.06780
\(472\) 3372.64 0.328895
\(473\) −12839.5 −1.24812
\(474\) −12865.1 −1.24666
\(475\) 6865.10 0.663142
\(476\) 8934.86 0.860354
\(477\) −1466.29 −0.140748
\(478\) 15012.5 1.43652
\(479\) 3204.17 0.305642 0.152821 0.988254i \(-0.451164\pi\)
0.152821 + 0.988254i \(0.451164\pi\)
\(480\) −7378.52 −0.701629
\(481\) −7911.65 −0.749980
\(482\) −13760.2 −1.30033
\(483\) −5312.42 −0.500462
\(484\) −9992.20 −0.938411
\(485\) −15035.3 −1.40766
\(486\) 1262.69 0.117853
\(487\) 5211.90 0.484957 0.242478 0.970157i \(-0.422040\pi\)
0.242478 + 0.970157i \(0.422040\pi\)
\(488\) 21055.8 1.95318
\(489\) −3565.26 −0.329706
\(490\) 5243.82 0.483453
\(491\) −10189.9 −0.936589 −0.468295 0.883572i \(-0.655131\pi\)
−0.468295 + 0.883572i \(0.655131\pi\)
\(492\) −21762.9 −1.99421
\(493\) 1896.32 0.173237
\(494\) −17939.6 −1.63389
\(495\) 2119.85 0.192485
\(496\) 19024.4 1.72222
\(497\) 1270.00 0.114622
\(498\) 22240.2 2.00122
\(499\) −20602.0 −1.84824 −0.924120 0.382103i \(-0.875200\pi\)
−0.924120 + 0.382103i \(0.875200\pi\)
\(500\) 28563.3 2.55478
\(501\) −5003.07 −0.446149
\(502\) −12094.2 −1.07528
\(503\) −8471.66 −0.750959 −0.375480 0.926831i \(-0.622522\pi\)
−0.375480 + 0.926831i \(0.622522\pi\)
\(504\) −11088.8 −0.980032
\(505\) −9404.67 −0.828718
\(506\) 12113.4 1.06424
\(507\) 4203.78 0.368237
\(508\) 14155.7 1.23633
\(509\) 11199.1 0.975230 0.487615 0.873059i \(-0.337867\pi\)
0.487615 + 0.873059i \(0.337867\pi\)
\(510\) −2823.12 −0.245118
\(511\) 18973.9 1.64257
\(512\) 23351.9 2.01566
\(513\) 3304.47 0.284398
\(514\) 21954.0 1.88395
\(515\) −12283.8 −1.05104
\(516\) −25793.8 −2.20060
\(517\) 4485.10 0.381537
\(518\) −31412.1 −2.66441
\(519\) −5563.72 −0.470559
\(520\) −13385.5 −1.12883
\(521\) −3200.10 −0.269096 −0.134548 0.990907i \(-0.542958\pi\)
−0.134548 + 0.990907i \(0.542958\pi\)
\(522\) −4064.96 −0.340840
\(523\) 16516.2 1.38089 0.690443 0.723386i \(-0.257415\pi\)
0.690443 + 0.723386i \(0.257415\pi\)
\(524\) −41906.9 −3.49372
\(525\) 3627.07 0.301520
\(526\) −16863.2 −1.39785
\(527\) 2861.86 0.236555
\(528\) 12345.3 1.01754
\(529\) −5417.21 −0.445238
\(530\) −7027.48 −0.575951
\(531\) −531.000 −0.0433963
\(532\) −50123.2 −4.08480
\(533\) −10769.8 −0.875219
\(534\) 24268.1 1.96664
\(535\) −2439.26 −0.197118
\(536\) −10172.2 −0.819724
\(537\) −10951.5 −0.880061
\(538\) 24401.4 1.95543
\(539\) −3449.51 −0.275660
\(540\) 4258.63 0.339375
\(541\) 20852.2 1.65713 0.828566 0.559892i \(-0.189157\pi\)
0.828566 + 0.559892i \(0.189157\pi\)
\(542\) −7497.95 −0.594215
\(543\) −2736.58 −0.216276
\(544\) −6464.04 −0.509455
\(545\) 6652.86 0.522894
\(546\) −9478.11 −0.742904
\(547\) 809.628 0.0632856 0.0316428 0.999499i \(-0.489926\pi\)
0.0316428 + 0.999499i \(0.489926\pi\)
\(548\) 14141.1 1.10233
\(549\) −3315.09 −0.257714
\(550\) −8270.43 −0.641186
\(551\) −10638.1 −0.822499
\(552\) 14089.1 1.08636
\(553\) −17788.1 −1.36786
\(554\) −35239.7 −2.70251
\(555\) 6984.49 0.534189
\(556\) 5086.78 0.387999
\(557\) −21643.2 −1.64641 −0.823206 0.567743i \(-0.807817\pi\)
−0.823206 + 0.567743i \(0.807817\pi\)
\(558\) −6134.69 −0.465416
\(559\) −12764.5 −0.965800
\(560\) −25948.2 −1.95806
\(561\) 1857.12 0.139764
\(562\) −4761.74 −0.357406
\(563\) 23646.1 1.77010 0.885050 0.465496i \(-0.154124\pi\)
0.885050 + 0.465496i \(0.154124\pi\)
\(564\) 9010.27 0.672697
\(565\) 15224.4 1.13362
\(566\) 8798.17 0.653383
\(567\) 1745.87 0.129311
\(568\) −3368.18 −0.248813
\(569\) −19407.6 −1.42990 −0.714948 0.699177i \(-0.753550\pi\)
−0.714948 + 0.699177i \(0.753550\pi\)
\(570\) 15837.3 1.16377
\(571\) 16659.0 1.22094 0.610470 0.792039i \(-0.290980\pi\)
0.610470 + 0.792039i \(0.290980\pi\)
\(572\) 15208.6 1.11172
\(573\) −6181.95 −0.450706
\(574\) −42759.9 −3.10935
\(575\) −4608.44 −0.334235
\(576\) 3414.37 0.246988
\(577\) −19454.1 −1.40361 −0.701805 0.712369i \(-0.747622\pi\)
−0.701805 + 0.712369i \(0.747622\pi\)
\(578\) 23055.9 1.65917
\(579\) 5753.82 0.412989
\(580\) −13709.8 −0.981496
\(581\) 30750.6 2.19578
\(582\) 28235.1 2.01097
\(583\) 4622.84 0.328402
\(584\) −50320.8 −3.56557
\(585\) 2107.46 0.148945
\(586\) 24484.7 1.72603
\(587\) −2742.52 −0.192838 −0.0964190 0.995341i \(-0.530739\pi\)
−0.0964190 + 0.995341i \(0.530739\pi\)
\(588\) −6929.83 −0.486023
\(589\) −16054.6 −1.12312
\(590\) −2544.91 −0.177580
\(591\) 7470.97 0.519991
\(592\) 40675.4 2.82390
\(593\) 9829.13 0.680664 0.340332 0.940305i \(-0.389460\pi\)
0.340332 + 0.940305i \(0.389460\pi\)
\(594\) −3980.92 −0.274982
\(595\) −3903.42 −0.268949
\(596\) −47089.9 −3.23637
\(597\) −10236.3 −0.701752
\(598\) 12042.6 0.823509
\(599\) 25261.4 1.72312 0.861562 0.507653i \(-0.169487\pi\)
0.861562 + 0.507653i \(0.169487\pi\)
\(600\) −9619.39 −0.654517
\(601\) 23269.7 1.57935 0.789677 0.613523i \(-0.210248\pi\)
0.789677 + 0.613523i \(0.210248\pi\)
\(602\) −50679.7 −3.43115
\(603\) 1601.55 0.108159
\(604\) 36148.9 2.43523
\(605\) 4365.35 0.293350
\(606\) 17661.3 1.18390
\(607\) 11725.1 0.784029 0.392015 0.919959i \(-0.371778\pi\)
0.392015 + 0.919959i \(0.371778\pi\)
\(608\) 36262.3 2.41880
\(609\) −5620.45 −0.373977
\(610\) −15888.2 −1.05458
\(611\) 4458.90 0.295234
\(612\) 3730.82 0.246421
\(613\) −4075.52 −0.268530 −0.134265 0.990945i \(-0.542867\pi\)
−0.134265 + 0.990945i \(0.542867\pi\)
\(614\) −40117.5 −2.63682
\(615\) 9507.69 0.623393
\(616\) 34960.2 2.28667
\(617\) −2326.85 −0.151824 −0.0759121 0.997115i \(-0.524187\pi\)
−0.0759121 + 0.997115i \(0.524187\pi\)
\(618\) 23068.0 1.50151
\(619\) 27579.3 1.79080 0.895400 0.445263i \(-0.146890\pi\)
0.895400 + 0.445263i \(0.146890\pi\)
\(620\) −20690.3 −1.34023
\(621\) −2218.24 −0.143341
\(622\) −30000.6 −1.93395
\(623\) 33554.6 2.15784
\(624\) 12273.2 0.787372
\(625\) −5466.95 −0.349885
\(626\) 51317.8 3.27648
\(627\) −10418.1 −0.663573
\(628\) −69131.5 −4.39275
\(629\) 6118.84 0.387876
\(630\) 8367.37 0.529149
\(631\) −4818.78 −0.304013 −0.152007 0.988379i \(-0.548574\pi\)
−0.152007 + 0.988379i \(0.548574\pi\)
\(632\) 47176.0 2.96924
\(633\) −2676.23 −0.168042
\(634\) 31206.2 1.95482
\(635\) −6184.27 −0.386481
\(636\) 9286.98 0.579014
\(637\) −3429.36 −0.213306
\(638\) 12815.7 0.795266
\(639\) 530.298 0.0328298
\(640\) −3312.10 −0.204566
\(641\) −16896.8 −1.04116 −0.520580 0.853813i \(-0.674284\pi\)
−0.520580 + 0.853813i \(0.674284\pi\)
\(642\) 4580.75 0.281601
\(643\) −30887.2 −1.89436 −0.947180 0.320702i \(-0.896081\pi\)
−0.947180 + 0.320702i \(0.896081\pi\)
\(644\) 33646.9 2.05881
\(645\) 11268.7 0.687911
\(646\) 13874.4 0.845019
\(647\) −4782.21 −0.290585 −0.145292 0.989389i \(-0.546412\pi\)
−0.145292 + 0.989389i \(0.546412\pi\)
\(648\) −4630.23 −0.280699
\(649\) 1674.10 0.101255
\(650\) −8222.11 −0.496150
\(651\) −8482.19 −0.510666
\(652\) 22581.0 1.35635
\(653\) −33078.5 −1.98233 −0.991164 0.132639i \(-0.957655\pi\)
−0.991164 + 0.132639i \(0.957655\pi\)
\(654\) −12493.6 −0.747000
\(655\) 18308.1 1.09215
\(656\) 55369.6 3.29546
\(657\) 7922.69 0.470462
\(658\) 17703.4 1.04886
\(659\) 10359.2 0.612351 0.306175 0.951975i \(-0.400951\pi\)
0.306175 + 0.951975i \(0.400951\pi\)
\(660\) −13426.3 −0.791848
\(661\) −14606.6 −0.859502 −0.429751 0.902947i \(-0.641399\pi\)
−0.429751 + 0.902947i \(0.641399\pi\)
\(662\) −35828.4 −2.10349
\(663\) 1846.27 0.108149
\(664\) −81554.0 −4.76643
\(665\) 21897.6 1.27692
\(666\) −13116.4 −0.763136
\(667\) 7141.17 0.414553
\(668\) 31687.6 1.83538
\(669\) 8674.04 0.501282
\(670\) 7675.70 0.442594
\(671\) 10451.6 0.601312
\(672\) 19158.6 1.09979
\(673\) 4901.10 0.280719 0.140359 0.990101i \(-0.455174\pi\)
0.140359 + 0.990101i \(0.455174\pi\)
\(674\) −35147.4 −2.00865
\(675\) 1514.51 0.0863608
\(676\) −26625.2 −1.51486
\(677\) −7783.32 −0.441857 −0.220929 0.975290i \(-0.570909\pi\)
−0.220929 + 0.975290i \(0.570909\pi\)
\(678\) −28590.3 −1.61948
\(679\) 39039.6 2.20648
\(680\) 10352.3 0.583813
\(681\) 5239.35 0.294820
\(682\) 19341.1 1.08594
\(683\) −5065.20 −0.283770 −0.141885 0.989883i \(-0.545316\pi\)
−0.141885 + 0.989883i \(0.545316\pi\)
\(684\) −20929.3 −1.16996
\(685\) −6177.89 −0.344592
\(686\) 24800.0 1.38027
\(687\) 3584.99 0.199092
\(688\) 65624.9 3.63652
\(689\) 4595.83 0.254118
\(690\) −10631.3 −0.586562
\(691\) −987.814 −0.0543824 −0.0271912 0.999630i \(-0.508656\pi\)
−0.0271912 + 0.999630i \(0.508656\pi\)
\(692\) 35238.6 1.93579
\(693\) −5504.25 −0.301716
\(694\) −28448.0 −1.55601
\(695\) −2222.29 −0.121289
\(696\) 14906.1 0.811801
\(697\) 8329.32 0.452648
\(698\) 33130.7 1.79658
\(699\) 14225.8 0.769769
\(700\) −22972.5 −1.24040
\(701\) 24301.9 1.30937 0.654685 0.755902i \(-0.272801\pi\)
0.654685 + 0.755902i \(0.272801\pi\)
\(702\) −3957.66 −0.212781
\(703\) −34325.7 −1.84156
\(704\) −10764.6 −0.576287
\(705\) −3936.36 −0.210287
\(706\) −25831.3 −1.37701
\(707\) 24419.6 1.29900
\(708\) 3363.16 0.178524
\(709\) 19625.0 1.03954 0.519769 0.854307i \(-0.326018\pi\)
0.519769 + 0.854307i \(0.326018\pi\)
\(710\) 2541.55 0.134342
\(711\) −7427.56 −0.391779
\(712\) −88990.5 −4.68408
\(713\) 10777.2 0.566072
\(714\) 7330.34 0.384217
\(715\) −6644.27 −0.347527
\(716\) 69362.9 3.62041
\(717\) 8667.32 0.451446
\(718\) −10774.2 −0.560012
\(719\) −12274.5 −0.636663 −0.318331 0.947979i \(-0.603123\pi\)
−0.318331 + 0.947979i \(0.603123\pi\)
\(720\) −10834.9 −0.560822
\(721\) 31895.2 1.64749
\(722\) −42192.4 −2.17484
\(723\) −7944.32 −0.408648
\(724\) 17332.5 0.889722
\(725\) −4875.65 −0.249762
\(726\) −8197.80 −0.419076
\(727\) 9818.35 0.500884 0.250442 0.968132i \(-0.419424\pi\)
0.250442 + 0.968132i \(0.419424\pi\)
\(728\) 34755.9 1.76942
\(729\) 729.000 0.0370370
\(730\) 37970.9 1.92516
\(731\) 9872.04 0.499495
\(732\) 20996.6 1.06019
\(733\) −36133.7 −1.82078 −0.910388 0.413756i \(-0.864217\pi\)
−0.910388 + 0.413756i \(0.864217\pi\)
\(734\) 33700.7 1.69471
\(735\) 3027.47 0.151932
\(736\) −24342.3 −1.21912
\(737\) −5049.26 −0.252363
\(738\) −17854.7 −0.890572
\(739\) 15833.8 0.788166 0.394083 0.919075i \(-0.371062\pi\)
0.394083 + 0.919075i \(0.371062\pi\)
\(740\) −44237.2 −2.19756
\(741\) −10357.3 −0.513473
\(742\) 18247.1 0.902792
\(743\) 23888.6 1.17953 0.589764 0.807576i \(-0.299221\pi\)
0.589764 + 0.807576i \(0.299221\pi\)
\(744\) 22495.7 1.10851
\(745\) 20572.4 1.01170
\(746\) 13563.5 0.665676
\(747\) 12840.2 0.628911
\(748\) −11762.3 −0.574963
\(749\) 6333.62 0.308979
\(750\) 23433.9 1.14091
\(751\) −29824.3 −1.44914 −0.724571 0.689200i \(-0.757962\pi\)
−0.724571 + 0.689200i \(0.757962\pi\)
\(752\) −22924.1 −1.11164
\(753\) −6982.48 −0.337923
\(754\) 12740.9 0.615378
\(755\) −15792.5 −0.761257
\(756\) −11057.7 −0.531963
\(757\) 7136.54 0.342645 0.171322 0.985215i \(-0.445196\pi\)
0.171322 + 0.985215i \(0.445196\pi\)
\(758\) 29147.5 1.39668
\(759\) 6993.53 0.334452
\(760\) −58074.8 −2.77184
\(761\) −19820.8 −0.944157 −0.472079 0.881557i \(-0.656496\pi\)
−0.472079 + 0.881557i \(0.656496\pi\)
\(762\) 11613.6 0.552122
\(763\) −17274.4 −0.819626
\(764\) 39154.2 1.85412
\(765\) −1629.90 −0.0770318
\(766\) −15478.5 −0.730108
\(767\) 1664.32 0.0783510
\(768\) 15324.9 0.720037
\(769\) 23969.6 1.12401 0.562006 0.827133i \(-0.310030\pi\)
0.562006 + 0.827133i \(0.310030\pi\)
\(770\) −26380.1 −1.23464
\(771\) 12674.9 0.592057
\(772\) −36442.6 −1.69896
\(773\) 41618.3 1.93649 0.968245 0.250004i \(-0.0804320\pi\)
0.968245 + 0.250004i \(0.0804320\pi\)
\(774\) −21161.7 −0.982742
\(775\) −7358.17 −0.341049
\(776\) −103537. −4.78966
\(777\) −18135.5 −0.837331
\(778\) −52677.2 −2.42747
\(779\) −46726.2 −2.14909
\(780\) −13347.9 −0.612733
\(781\) −1671.89 −0.0766004
\(782\) −9313.70 −0.425904
\(783\) −2346.86 −0.107114
\(784\) 17631.0 0.803161
\(785\) 30201.8 1.37318
\(786\) −34381.2 −1.56023
\(787\) 17130.9 0.775920 0.387960 0.921676i \(-0.373180\pi\)
0.387960 + 0.921676i \(0.373180\pi\)
\(788\) −47318.4 −2.13915
\(789\) −9735.80 −0.439295
\(790\) −35597.9 −1.60319
\(791\) −39530.7 −1.77693
\(792\) 14597.9 0.654942
\(793\) 10390.6 0.465296
\(794\) −67145.5 −3.00114
\(795\) −4057.25 −0.181001
\(796\) 64833.3 2.88688
\(797\) −3545.01 −0.157554 −0.0787770 0.996892i \(-0.525102\pi\)
−0.0787770 + 0.996892i \(0.525102\pi\)
\(798\) −41122.0 −1.82419
\(799\) −3448.50 −0.152690
\(800\) 16619.8 0.734497
\(801\) 14011.0 0.618045
\(802\) 49658.8 2.18643
\(803\) −24978.1 −1.09771
\(804\) −10143.6 −0.444948
\(805\) −14699.5 −0.643589
\(806\) 19228.1 0.840298
\(807\) 14087.9 0.614521
\(808\) −64763.4 −2.81976
\(809\) −11108.5 −0.482763 −0.241381 0.970430i \(-0.577600\pi\)
−0.241381 + 0.970430i \(0.577600\pi\)
\(810\) 3493.86 0.151558
\(811\) −11416.7 −0.494320 −0.247160 0.968975i \(-0.579497\pi\)
−0.247160 + 0.968975i \(0.579497\pi\)
\(812\) 35597.9 1.53847
\(813\) −4328.87 −0.186741
\(814\) 41352.4 1.78059
\(815\) −9865.09 −0.423999
\(816\) −9492.02 −0.407215
\(817\) −55380.6 −2.37151
\(818\) −43553.0 −1.86161
\(819\) −5472.10 −0.233468
\(820\) −60218.2 −2.56453
\(821\) 27265.7 1.15905 0.579524 0.814955i \(-0.303238\pi\)
0.579524 + 0.814955i \(0.303238\pi\)
\(822\) 11601.6 0.492279
\(823\) 18672.1 0.790849 0.395424 0.918499i \(-0.370598\pi\)
0.395424 + 0.918499i \(0.370598\pi\)
\(824\) −84589.7 −3.57624
\(825\) −4774.85 −0.201502
\(826\) 6607.95 0.278354
\(827\) 33292.9 1.39989 0.699945 0.714197i \(-0.253208\pi\)
0.699945 + 0.714197i \(0.253208\pi\)
\(828\) 14049.5 0.589680
\(829\) 21571.9 0.903768 0.451884 0.892077i \(-0.350752\pi\)
0.451884 + 0.892077i \(0.350752\pi\)
\(830\) 61538.7 2.57354
\(831\) −20345.3 −0.849304
\(832\) −10701.7 −0.445932
\(833\) 2652.25 0.110318
\(834\) 4173.29 0.173273
\(835\) −13843.5 −0.573743
\(836\) 65984.7 2.72982
\(837\) −3541.81 −0.146264
\(838\) 46794.2 1.92897
\(839\) 24952.4 1.02676 0.513381 0.858161i \(-0.328393\pi\)
0.513381 + 0.858161i \(0.328393\pi\)
\(840\) −30682.9 −1.26031
\(841\) −16833.8 −0.690219
\(842\) −3918.43 −0.160378
\(843\) −2749.15 −0.112320
\(844\) 16950.3 0.691294
\(845\) 11631.9 0.473549
\(846\) 7392.20 0.300413
\(847\) −11334.8 −0.459820
\(848\) −23628.1 −0.956830
\(849\) 5079.54 0.205335
\(850\) 6358.95 0.256600
\(851\) 23042.3 0.928180
\(852\) −3358.71 −0.135056
\(853\) 22193.3 0.890836 0.445418 0.895323i \(-0.353055\pi\)
0.445418 + 0.895323i \(0.353055\pi\)
\(854\) 41254.2 1.65303
\(855\) 9143.50 0.365732
\(856\) −16797.5 −0.670708
\(857\) 5155.43 0.205491 0.102746 0.994708i \(-0.467237\pi\)
0.102746 + 0.994708i \(0.467237\pi\)
\(858\) 12477.5 0.496473
\(859\) −18059.6 −0.717327 −0.358664 0.933467i \(-0.616767\pi\)
−0.358664 + 0.933467i \(0.616767\pi\)
\(860\) −71371.6 −2.82994
\(861\) −24687.0 −0.977156
\(862\) 13020.7 0.514486
\(863\) −3135.68 −0.123685 −0.0618423 0.998086i \(-0.519698\pi\)
−0.0618423 + 0.998086i \(0.519698\pi\)
\(864\) 7999.82 0.314999
\(865\) −15394.9 −0.605134
\(866\) 917.149 0.0359884
\(867\) 13311.1 0.521417
\(868\) 53723.1 2.10078
\(869\) 23417.1 0.914122
\(870\) −11247.8 −0.438316
\(871\) −5019.76 −0.195279
\(872\) 45813.6 1.77918
\(873\) 16301.3 0.631976
\(874\) 52248.4 2.02211
\(875\) 32401.0 1.25183
\(876\) −50179.4 −1.93539
\(877\) 24764.4 0.953516 0.476758 0.879035i \(-0.341812\pi\)
0.476758 + 0.879035i \(0.341812\pi\)
\(878\) 11556.1 0.444190
\(879\) 14136.0 0.542429
\(880\) 34159.5 1.30854
\(881\) −24195.2 −0.925265 −0.462633 0.886550i \(-0.653095\pi\)
−0.462633 + 0.886550i \(0.653095\pi\)
\(882\) −5685.37 −0.217048
\(883\) −26387.8 −1.00569 −0.502843 0.864378i \(-0.667713\pi\)
−0.502843 + 0.864378i \(0.667713\pi\)
\(884\) −11693.6 −0.444907
\(885\) −1469.28 −0.0558072
\(886\) 31515.8 1.19503
\(887\) 45619.8 1.72690 0.863452 0.504431i \(-0.168298\pi\)
0.863452 + 0.504431i \(0.168298\pi\)
\(888\) 48097.3 1.81761
\(889\) 16057.7 0.605801
\(890\) 67150.1 2.52908
\(891\) −2298.35 −0.0864169
\(892\) −54938.2 −2.06218
\(893\) 19345.5 0.724942
\(894\) −38633.5 −1.44530
\(895\) −30302.9 −1.13175
\(896\) 8599.98 0.320653
\(897\) 6952.68 0.258799
\(898\) 662.978 0.0246368
\(899\) 11402.1 0.423005
\(900\) −9592.36 −0.355273
\(901\) −3554.40 −0.131425
\(902\) 56291.3 2.07793
\(903\) −29259.4 −1.07829
\(904\) 104840. 3.85721
\(905\) −7572.15 −0.278129
\(906\) 29657.2 1.08752
\(907\) −28604.5 −1.04719 −0.523593 0.851968i \(-0.675409\pi\)
−0.523593 + 0.851968i \(0.675409\pi\)
\(908\) −33184.1 −1.21283
\(909\) 10196.6 0.372056
\(910\) −26226.0 −0.955367
\(911\) 23089.0 0.839706 0.419853 0.907592i \(-0.362082\pi\)
0.419853 + 0.907592i \(0.362082\pi\)
\(912\) 53248.7 1.93338
\(913\) −40481.6 −1.46741
\(914\) −79226.4 −2.86715
\(915\) −9172.89 −0.331417
\(916\) −22706.0 −0.819027
\(917\) −47537.5 −1.71192
\(918\) 3060.84 0.110047
\(919\) −14323.8 −0.514145 −0.257072 0.966392i \(-0.582758\pi\)
−0.257072 + 0.966392i \(0.582758\pi\)
\(920\) 38984.7 1.39705
\(921\) −23161.4 −0.828659
\(922\) −42340.0 −1.51236
\(923\) −1662.12 −0.0592735
\(924\) 34861.9 1.24121
\(925\) −15732.2 −0.559213
\(926\) −33873.8 −1.20212
\(927\) 13318.1 0.471870
\(928\) −25753.8 −0.911001
\(929\) −34587.5 −1.22151 −0.610753 0.791821i \(-0.709133\pi\)
−0.610753 + 0.791821i \(0.709133\pi\)
\(930\) −16974.7 −0.598520
\(931\) −14878.7 −0.523770
\(932\) −90101.0 −3.16669
\(933\) −17320.6 −0.607771
\(934\) 1370.51 0.0480134
\(935\) 5138.66 0.179735
\(936\) 14512.6 0.506795
\(937\) 30905.7 1.07753 0.538765 0.842456i \(-0.318891\pi\)
0.538765 + 0.842456i \(0.318891\pi\)
\(938\) −19930.2 −0.693758
\(939\) 29627.9 1.02968
\(940\) 24931.5 0.865081
\(941\) −20269.1 −0.702184 −0.351092 0.936341i \(-0.614189\pi\)
−0.351092 + 0.936341i \(0.614189\pi\)
\(942\) −56716.8 −1.96171
\(943\) 31366.6 1.08318
\(944\) −8556.61 −0.295015
\(945\) 4830.82 0.166293
\(946\) 66717.3 2.29299
\(947\) 3806.38 0.130613 0.0653066 0.997865i \(-0.479197\pi\)
0.0653066 + 0.997865i \(0.479197\pi\)
\(948\) 47043.4 1.61171
\(949\) −24832.2 −0.849408
\(950\) −35672.7 −1.21829
\(951\) 18016.6 0.614330
\(952\) −26880.1 −0.915115
\(953\) −58087.5 −1.97444 −0.987219 0.159370i \(-0.949054\pi\)
−0.987219 + 0.159370i \(0.949054\pi\)
\(954\) 7619.22 0.258576
\(955\) −17105.5 −0.579603
\(956\) −54895.6 −1.85717
\(957\) 7399.05 0.249924
\(958\) −16649.6 −0.561509
\(959\) 16041.1 0.540140
\(960\) 9447.58 0.317624
\(961\) −12583.3 −0.422387
\(962\) 41110.8 1.37782
\(963\) 2644.65 0.0884971
\(964\) 50316.4 1.68110
\(965\) 15920.9 0.531100
\(966\) 27604.6 0.919423
\(967\) −9873.60 −0.328349 −0.164175 0.986431i \(-0.552496\pi\)
−0.164175 + 0.986431i \(0.552496\pi\)
\(968\) 30061.1 0.998141
\(969\) 8010.27 0.265559
\(970\) 78126.9 2.58609
\(971\) 55181.6 1.82375 0.911875 0.410468i \(-0.134634\pi\)
0.911875 + 0.410468i \(0.134634\pi\)
\(972\) −4617.22 −0.152364
\(973\) 5770.24 0.190119
\(974\) −27082.3 −0.890937
\(975\) −4746.96 −0.155922
\(976\) −53419.9 −1.75198
\(977\) 14494.0 0.474620 0.237310 0.971434i \(-0.423734\pi\)
0.237310 + 0.971434i \(0.423734\pi\)
\(978\) 18525.9 0.605720
\(979\) −44172.9 −1.44206
\(980\) −19174.9 −0.625020
\(981\) −7213.06 −0.234756
\(982\) 52949.4 1.72065
\(983\) −38986.8 −1.26499 −0.632495 0.774564i \(-0.717969\pi\)
−0.632495 + 0.774564i \(0.717969\pi\)
\(984\) 65472.8 2.12114
\(985\) 20672.2 0.668703
\(986\) −9853.74 −0.318263
\(987\) 10220.9 0.329620
\(988\) 65599.2 2.11234
\(989\) 37176.1 1.19528
\(990\) −11015.2 −0.353623
\(991\) −48817.5 −1.56482 −0.782412 0.622762i \(-0.786011\pi\)
−0.782412 + 0.622762i \(0.786011\pi\)
\(992\) −38866.7 −1.24397
\(993\) −20685.2 −0.661052
\(994\) −6599.21 −0.210578
\(995\) −28324.1 −0.902445
\(996\) −81324.9 −2.58723
\(997\) −14978.6 −0.475806 −0.237903 0.971289i \(-0.576460\pi\)
−0.237903 + 0.971289i \(0.576460\pi\)
\(998\) 107053. 3.39549
\(999\) −7572.60 −0.239826
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.1.1 8
3.2 odd 2 531.4.a.f.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.c.1.1 8 1.1 even 1 trivial
531.4.a.f.1.8 8 3.2 odd 2