Properties

Label 177.4.a.c.1.8
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 1.8
Root \(5.26363\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.26363 q^{2} -3.00000 q^{3} +19.7058 q^{4} +11.8799 q^{5} -15.7909 q^{6} -3.36662 q^{7} +61.6149 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+5.26363 q^{2} -3.00000 q^{3} +19.7058 q^{4} +11.8799 q^{5} -15.7909 q^{6} -3.36662 q^{7} +61.6149 q^{8} +9.00000 q^{9} +62.5311 q^{10} -3.40311 q^{11} -59.1173 q^{12} -54.8553 q^{13} -17.7206 q^{14} -35.6396 q^{15} +166.672 q^{16} +68.7547 q^{17} +47.3727 q^{18} +8.88097 q^{19} +234.102 q^{20} +10.0999 q^{21} -17.9127 q^{22} +80.8007 q^{23} -184.845 q^{24} +16.1310 q^{25} -288.738 q^{26} -27.0000 q^{27} -66.3419 q^{28} -235.255 q^{29} -187.593 q^{30} +145.469 q^{31} +384.378 q^{32} +10.2093 q^{33} +361.899 q^{34} -39.9950 q^{35} +177.352 q^{36} -309.554 q^{37} +46.7461 q^{38} +164.566 q^{39} +731.976 q^{40} +37.6647 q^{41} +53.1619 q^{42} -465.320 q^{43} -67.0609 q^{44} +106.919 q^{45} +425.305 q^{46} +271.410 q^{47} -500.015 q^{48} -331.666 q^{49} +84.9076 q^{50} -206.264 q^{51} -1080.97 q^{52} -82.0797 q^{53} -142.118 q^{54} -40.4284 q^{55} -207.434 q^{56} -26.6429 q^{57} -1238.29 q^{58} -59.0000 q^{59} -702.306 q^{60} -736.743 q^{61} +765.695 q^{62} -30.2996 q^{63} +689.850 q^{64} -651.673 q^{65} +53.7381 q^{66} +768.441 q^{67} +1354.86 q^{68} -242.402 q^{69} -210.519 q^{70} -164.728 q^{71} +554.534 q^{72} +445.018 q^{73} -1629.38 q^{74} -48.3930 q^{75} +175.006 q^{76} +11.4570 q^{77} +866.213 q^{78} +602.572 q^{79} +1980.03 q^{80} +81.0000 q^{81} +198.253 q^{82} -779.626 q^{83} +199.026 q^{84} +816.795 q^{85} -2449.27 q^{86} +705.764 q^{87} -209.682 q^{88} +1393.87 q^{89} +562.780 q^{90} +184.677 q^{91} +1592.24 q^{92} -436.407 q^{93} +1428.60 q^{94} +105.505 q^{95} -1153.13 q^{96} -269.591 q^{97} -1745.77 q^{98} -30.6280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + 29q^{10} - 27q^{11} - 114q^{12} + 89q^{13} - 37q^{14} + 36q^{15} + 362q^{16} + 79q^{17} + 18q^{18} + 288q^{19} + 457q^{20} - 159q^{21} + 596q^{22} + 202q^{23} - 9q^{24} + 264q^{25} + 270q^{26} - 216q^{27} + 702q^{28} - 114q^{29} - 87q^{30} + 538q^{31} + 316q^{32} + 81q^{33} + 498q^{34} - 196q^{35} + 342q^{36} + 395q^{37} + 397q^{38} - 267q^{39} + 918q^{40} - 39q^{41} + 111q^{42} + 527q^{43} + 64q^{44} - 108q^{45} - 539q^{46} + 860q^{47} - 1086q^{48} + 347q^{49} - 591q^{50} - 237q^{51} - 644q^{52} - 812q^{53} - 54q^{54} + 536q^{55} - 2218q^{56} - 864q^{57} - 1154q^{58} - 472q^{59} - 1371q^{60} - 460q^{61} - 2014q^{62} + 477q^{63} - 451q^{64} - 986q^{65} - 1788q^{66} + 1934q^{67} - 69q^{68} - 606q^{69} - 1028q^{70} - 1687q^{71} + 27q^{72} + 1980q^{73} - 2400q^{74} - 792q^{75} - 940q^{76} - 821q^{77} - 810q^{78} + 3319q^{79} - 2119q^{80} + 648q^{81} + 429q^{82} + 2057q^{83} - 2106q^{84} + 566q^{85} - 6690q^{86} + 342q^{87} + 1189q^{88} + 1668q^{89} + 261q^{90} + 2427q^{91} - 980q^{92} - 1614q^{93} + 332q^{94} + 2146q^{95} - 948q^{96} + 1956q^{97} - 2026q^{98} - 243q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.26363 1.86097 0.930487 0.366325i \(-0.119384\pi\)
0.930487 + 0.366325i \(0.119384\pi\)
\(3\) −3.00000 −0.577350
\(4\) 19.7058 2.46322
\(5\) 11.8799 1.06257 0.531283 0.847194i \(-0.321710\pi\)
0.531283 + 0.847194i \(0.321710\pi\)
\(6\) −15.7909 −1.07443
\(7\) −3.36662 −0.181781 −0.0908903 0.995861i \(-0.528971\pi\)
−0.0908903 + 0.995861i \(0.528971\pi\)
\(8\) 61.6149 2.72302
\(9\) 9.00000 0.333333
\(10\) 62.5311 1.97741
\(11\) −3.40311 −0.0932796 −0.0466398 0.998912i \(-0.514851\pi\)
−0.0466398 + 0.998912i \(0.514851\pi\)
\(12\) −59.1173 −1.42214
\(13\) −54.8553 −1.17032 −0.585158 0.810919i \(-0.698968\pi\)
−0.585158 + 0.810919i \(0.698968\pi\)
\(14\) −17.7206 −0.338289
\(15\) −35.6396 −0.613473
\(16\) 166.672 2.60424
\(17\) 68.7547 0.980909 0.490455 0.871467i \(-0.336831\pi\)
0.490455 + 0.871467i \(0.336831\pi\)
\(18\) 47.3727 0.620325
\(19\) 8.88097 0.107233 0.0536167 0.998562i \(-0.482925\pi\)
0.0536167 + 0.998562i \(0.482925\pi\)
\(20\) 234.102 2.61734
\(21\) 10.0999 0.104951
\(22\) −17.9127 −0.173591
\(23\) 80.8007 0.732526 0.366263 0.930511i \(-0.380637\pi\)
0.366263 + 0.930511i \(0.380637\pi\)
\(24\) −184.845 −1.57214
\(25\) 16.1310 0.129048
\(26\) −288.738 −2.17793
\(27\) −27.0000 −0.192450
\(28\) −66.3419 −0.447766
\(29\) −235.255 −1.50640 −0.753202 0.657789i \(-0.771492\pi\)
−0.753202 + 0.657789i \(0.771492\pi\)
\(30\) −187.593 −1.14166
\(31\) 145.469 0.842807 0.421404 0.906873i \(-0.361538\pi\)
0.421404 + 0.906873i \(0.361538\pi\)
\(32\) 384.378 2.12341
\(33\) 10.2093 0.0538550
\(34\) 361.899 1.82545
\(35\) −39.9950 −0.193154
\(36\) 177.352 0.821074
\(37\) −309.554 −1.37542 −0.687709 0.725987i \(-0.741383\pi\)
−0.687709 + 0.725987i \(0.741383\pi\)
\(38\) 46.7461 0.199558
\(39\) 164.566 0.675683
\(40\) 731.976 2.89339
\(41\) 37.6647 0.143469 0.0717346 0.997424i \(-0.477147\pi\)
0.0717346 + 0.997424i \(0.477147\pi\)
\(42\) 53.1619 0.195311
\(43\) −465.320 −1.65025 −0.825124 0.564952i \(-0.808895\pi\)
−0.825124 + 0.564952i \(0.808895\pi\)
\(44\) −67.0609 −0.229768
\(45\) 106.919 0.354189
\(46\) 425.305 1.36321
\(47\) 271.410 0.842324 0.421162 0.906986i \(-0.361622\pi\)
0.421162 + 0.906986i \(0.361622\pi\)
\(48\) −500.015 −1.50356
\(49\) −331.666 −0.966956
\(50\) 84.9076 0.240155
\(51\) −206.264 −0.566328
\(52\) −1080.97 −2.88275
\(53\) −82.0797 −0.212727 −0.106363 0.994327i \(-0.533921\pi\)
−0.106363 + 0.994327i \(0.533921\pi\)
\(54\) −142.118 −0.358145
\(55\) −40.4284 −0.0991158
\(56\) −207.434 −0.494992
\(57\) −26.6429 −0.0619112
\(58\) −1238.29 −2.80338
\(59\) −59.0000 −0.130189
\(60\) −702.306 −1.51112
\(61\) −736.743 −1.54640 −0.773199 0.634164i \(-0.781345\pi\)
−0.773199 + 0.634164i \(0.781345\pi\)
\(62\) 765.695 1.56844
\(63\) −30.2996 −0.0605935
\(64\) 689.850 1.34736
\(65\) −651.673 −1.24354
\(66\) 53.7381 0.100223
\(67\) 768.441 1.40119 0.700597 0.713557i \(-0.252917\pi\)
0.700597 + 0.713557i \(0.252917\pi\)
\(68\) 1354.86 2.41620
\(69\) −242.402 −0.422924
\(70\) −210.519 −0.359454
\(71\) −164.728 −0.275347 −0.137674 0.990478i \(-0.543963\pi\)
−0.137674 + 0.990478i \(0.543963\pi\)
\(72\) 554.534 0.907673
\(73\) 445.018 0.713499 0.356749 0.934200i \(-0.383885\pi\)
0.356749 + 0.934200i \(0.383885\pi\)
\(74\) −1629.38 −2.55961
\(75\) −48.3930 −0.0745059
\(76\) 175.006 0.264140
\(77\) 11.4570 0.0169564
\(78\) 866.213 1.25743
\(79\) 602.572 0.858160 0.429080 0.903266i \(-0.358838\pi\)
0.429080 + 0.903266i \(0.358838\pi\)
\(80\) 1980.03 2.76718
\(81\) 81.0000 0.111111
\(82\) 198.253 0.266992
\(83\) −779.626 −1.03102 −0.515512 0.856882i \(-0.672398\pi\)
−0.515512 + 0.856882i \(0.672398\pi\)
\(84\) 199.026 0.258518
\(85\) 816.795 1.04228
\(86\) −2449.27 −3.07107
\(87\) 705.764 0.869723
\(88\) −209.682 −0.254002
\(89\) 1393.87 1.66011 0.830056 0.557681i \(-0.188309\pi\)
0.830056 + 0.557681i \(0.188309\pi\)
\(90\) 562.780 0.659136
\(91\) 184.677 0.212741
\(92\) 1592.24 1.80437
\(93\) −436.407 −0.486595
\(94\) 1428.60 1.56754
\(95\) 105.505 0.113943
\(96\) −1153.13 −1.22595
\(97\) −269.591 −0.282194 −0.141097 0.989996i \(-0.545063\pi\)
−0.141097 + 0.989996i \(0.545063\pi\)
\(98\) −1745.77 −1.79948
\(99\) −30.6280 −0.0310932
\(100\) 317.874 0.317874
\(101\) 936.949 0.923069 0.461534 0.887122i \(-0.347299\pi\)
0.461534 + 0.887122i \(0.347299\pi\)
\(102\) −1085.70 −1.05392
\(103\) 1461.76 1.39836 0.699182 0.714943i \(-0.253547\pi\)
0.699182 + 0.714943i \(0.253547\pi\)
\(104\) −3379.90 −3.18679
\(105\) 119.985 0.111517
\(106\) −432.037 −0.395879
\(107\) 830.314 0.750182 0.375091 0.926988i \(-0.377611\pi\)
0.375091 + 0.926988i \(0.377611\pi\)
\(108\) −532.056 −0.474047
\(109\) 1476.02 1.29703 0.648517 0.761200i \(-0.275390\pi\)
0.648517 + 0.761200i \(0.275390\pi\)
\(110\) −212.800 −0.184452
\(111\) 928.663 0.794097
\(112\) −561.120 −0.473401
\(113\) −2355.58 −1.96101 −0.980507 0.196482i \(-0.937048\pi\)
−0.980507 + 0.196482i \(0.937048\pi\)
\(114\) −140.238 −0.115215
\(115\) 959.900 0.778358
\(116\) −4635.88 −3.71061
\(117\) −493.698 −0.390106
\(118\) −310.554 −0.242278
\(119\) −231.471 −0.178310
\(120\) −2195.93 −1.67050
\(121\) −1319.42 −0.991299
\(122\) −3877.94 −2.87781
\(123\) −112.994 −0.0828320
\(124\) 2866.58 2.07602
\(125\) −1293.35 −0.925445
\(126\) −159.486 −0.112763
\(127\) 2512.25 1.75533 0.877663 0.479279i \(-0.159102\pi\)
0.877663 + 0.479279i \(0.159102\pi\)
\(128\) 556.092 0.384001
\(129\) 1395.96 0.952771
\(130\) −3430.16 −2.31419
\(131\) −907.845 −0.605487 −0.302744 0.953072i \(-0.597903\pi\)
−0.302744 + 0.953072i \(0.597903\pi\)
\(132\) 201.183 0.132657
\(133\) −29.8989 −0.0194929
\(134\) 4044.79 2.60758
\(135\) −320.756 −0.204491
\(136\) 4236.31 2.67103
\(137\) 326.883 0.203850 0.101925 0.994792i \(-0.467500\pi\)
0.101925 + 0.994792i \(0.467500\pi\)
\(138\) −1275.91 −0.787051
\(139\) 3008.75 1.83597 0.917983 0.396620i \(-0.129817\pi\)
0.917983 + 0.396620i \(0.129817\pi\)
\(140\) −788.132 −0.475781
\(141\) −814.230 −0.486316
\(142\) −867.069 −0.512414
\(143\) 186.678 0.109167
\(144\) 1500.04 0.868081
\(145\) −2794.79 −1.60065
\(146\) 2342.41 1.32780
\(147\) 994.998 0.558272
\(148\) −6100.01 −3.38796
\(149\) −144.752 −0.0795873 −0.0397937 0.999208i \(-0.512670\pi\)
−0.0397937 + 0.999208i \(0.512670\pi\)
\(150\) −254.723 −0.138654
\(151\) −767.404 −0.413579 −0.206789 0.978385i \(-0.566302\pi\)
−0.206789 + 0.978385i \(0.566302\pi\)
\(152\) 547.200 0.291998
\(153\) 618.792 0.326970
\(154\) 60.3052 0.0315554
\(155\) 1728.15 0.895539
\(156\) 3242.90 1.66436
\(157\) 3523.01 1.79087 0.895436 0.445190i \(-0.146864\pi\)
0.895436 + 0.445190i \(0.146864\pi\)
\(158\) 3171.71 1.59701
\(159\) 246.239 0.122818
\(160\) 4566.36 2.25626
\(161\) −272.025 −0.133159
\(162\) 426.354 0.206775
\(163\) −1448.84 −0.696209 −0.348104 0.937456i \(-0.613175\pi\)
−0.348104 + 0.937456i \(0.613175\pi\)
\(164\) 742.212 0.353397
\(165\) 121.285 0.0572245
\(166\) −4103.66 −1.91871
\(167\) −584.113 −0.270659 −0.135329 0.990801i \(-0.543209\pi\)
−0.135329 + 0.990801i \(0.543209\pi\)
\(168\) 622.302 0.285784
\(169\) 812.102 0.369641
\(170\) 4299.31 1.93966
\(171\) 79.9287 0.0357445
\(172\) −9169.49 −4.06493
\(173\) 2756.29 1.21131 0.605656 0.795727i \(-0.292911\pi\)
0.605656 + 0.795727i \(0.292911\pi\)
\(174\) 3714.88 1.61853
\(175\) −54.3070 −0.0234584
\(176\) −567.201 −0.242923
\(177\) 177.000 0.0751646
\(178\) 7336.81 3.08942
\(179\) −3014.07 −1.25856 −0.629280 0.777179i \(-0.716650\pi\)
−0.629280 + 0.777179i \(0.716650\pi\)
\(180\) 2106.92 0.872446
\(181\) −1361.03 −0.558921 −0.279461 0.960157i \(-0.590156\pi\)
−0.279461 + 0.960157i \(0.590156\pi\)
\(182\) 972.071 0.395905
\(183\) 2210.23 0.892813
\(184\) 4978.52 1.99468
\(185\) −3677.46 −1.46147
\(186\) −2297.09 −0.905540
\(187\) −233.979 −0.0914988
\(188\) 5348.34 2.07483
\(189\) 90.8988 0.0349837
\(190\) 555.337 0.212044
\(191\) 182.879 0.0692810 0.0346405 0.999400i \(-0.488971\pi\)
0.0346405 + 0.999400i \(0.488971\pi\)
\(192\) −2069.55 −0.777901
\(193\) 4052.56 1.51145 0.755725 0.654889i \(-0.227285\pi\)
0.755725 + 0.654889i \(0.227285\pi\)
\(194\) −1419.03 −0.525155
\(195\) 1955.02 0.717958
\(196\) −6535.73 −2.38183
\(197\) 1243.86 0.449856 0.224928 0.974375i \(-0.427785\pi\)
0.224928 + 0.974375i \(0.427785\pi\)
\(198\) −161.214 −0.0578636
\(199\) −191.567 −0.0682404 −0.0341202 0.999418i \(-0.510863\pi\)
−0.0341202 + 0.999418i \(0.510863\pi\)
\(200\) 993.910 0.351400
\(201\) −2305.32 −0.808980
\(202\) 4931.75 1.71781
\(203\) 792.014 0.273835
\(204\) −4064.59 −1.39499
\(205\) 447.451 0.152446
\(206\) 7694.17 2.60232
\(207\) 727.206 0.244175
\(208\) −9142.81 −3.04779
\(209\) −30.2229 −0.0100027
\(210\) 631.556 0.207531
\(211\) 3016.73 0.984268 0.492134 0.870520i \(-0.336217\pi\)
0.492134 + 0.870520i \(0.336217\pi\)
\(212\) −1617.44 −0.523993
\(213\) 494.185 0.158972
\(214\) 4370.46 1.39607
\(215\) −5527.94 −1.75350
\(216\) −1663.60 −0.524045
\(217\) −489.740 −0.153206
\(218\) 7769.20 2.41375
\(219\) −1335.05 −0.411939
\(220\) −796.674 −0.244144
\(221\) −3771.56 −1.14797
\(222\) 4888.14 1.47779
\(223\) −3416.65 −1.02599 −0.512995 0.858392i \(-0.671464\pi\)
−0.512995 + 0.858392i \(0.671464\pi\)
\(224\) −1294.06 −0.385994
\(225\) 145.179 0.0430160
\(226\) −12398.9 −3.64940
\(227\) 442.483 0.129377 0.0646886 0.997906i \(-0.479395\pi\)
0.0646886 + 0.997906i \(0.479395\pi\)
\(228\) −525.019 −0.152501
\(229\) −5469.58 −1.57834 −0.789170 0.614175i \(-0.789489\pi\)
−0.789170 + 0.614175i \(0.789489\pi\)
\(230\) 5052.56 1.44850
\(231\) −34.3709 −0.00978979
\(232\) −14495.2 −4.10197
\(233\) 3053.40 0.858519 0.429259 0.903181i \(-0.358775\pi\)
0.429259 + 0.903181i \(0.358775\pi\)
\(234\) −2598.64 −0.725976
\(235\) 3224.31 0.895025
\(236\) −1162.64 −0.320684
\(237\) −1807.72 −0.495459
\(238\) −1218.38 −0.331830
\(239\) −4582.19 −1.24015 −0.620077 0.784541i \(-0.712899\pi\)
−0.620077 + 0.784541i \(0.712899\pi\)
\(240\) −5940.10 −1.59763
\(241\) 6410.62 1.71346 0.856731 0.515764i \(-0.172492\pi\)
0.856731 + 0.515764i \(0.172492\pi\)
\(242\) −6944.93 −1.84478
\(243\) −243.000 −0.0641500
\(244\) −14518.1 −3.80912
\(245\) −3940.14 −1.02746
\(246\) −594.759 −0.154148
\(247\) −487.168 −0.125497
\(248\) 8963.06 2.29498
\(249\) 2338.88 0.595262
\(250\) −6807.70 −1.72223
\(251\) 1936.29 0.486922 0.243461 0.969911i \(-0.421717\pi\)
0.243461 + 0.969911i \(0.421717\pi\)
\(252\) −597.077 −0.149255
\(253\) −274.973 −0.0683297
\(254\) 13223.6 3.26661
\(255\) −2450.39 −0.601761
\(256\) −2591.74 −0.632749
\(257\) −341.077 −0.0827852 −0.0413926 0.999143i \(-0.513179\pi\)
−0.0413926 + 0.999143i \(0.513179\pi\)
\(258\) 7347.81 1.77308
\(259\) 1042.15 0.250024
\(260\) −12841.7 −3.06312
\(261\) −2117.29 −0.502135
\(262\) −4778.56 −1.12680
\(263\) 5497.72 1.28899 0.644494 0.764609i \(-0.277068\pi\)
0.644494 + 0.764609i \(0.277068\pi\)
\(264\) 629.046 0.146648
\(265\) −975.095 −0.226036
\(266\) −157.377 −0.0362758
\(267\) −4181.61 −0.958466
\(268\) 15142.7 3.45145
\(269\) 104.441 0.0236725 0.0118363 0.999930i \(-0.496232\pi\)
0.0118363 + 0.999930i \(0.496232\pi\)
\(270\) −1688.34 −0.380552
\(271\) 4199.52 0.941339 0.470669 0.882310i \(-0.344012\pi\)
0.470669 + 0.882310i \(0.344012\pi\)
\(272\) 11459.4 2.55453
\(273\) −554.031 −0.122826
\(274\) 1720.59 0.379360
\(275\) −54.8955 −0.0120375
\(276\) −4776.72 −1.04176
\(277\) 1330.67 0.288636 0.144318 0.989531i \(-0.453901\pi\)
0.144318 + 0.989531i \(0.453901\pi\)
\(278\) 15837.0 3.41668
\(279\) 1309.22 0.280936
\(280\) −2464.29 −0.525962
\(281\) −4164.03 −0.884004 −0.442002 0.897014i \(-0.645732\pi\)
−0.442002 + 0.897014i \(0.645732\pi\)
\(282\) −4285.80 −0.905021
\(283\) −985.954 −0.207099 −0.103549 0.994624i \(-0.533020\pi\)
−0.103549 + 0.994624i \(0.533020\pi\)
\(284\) −3246.10 −0.678242
\(285\) −316.514 −0.0657848
\(286\) 982.605 0.203156
\(287\) −126.803 −0.0260799
\(288\) 3459.40 0.707803
\(289\) −185.798 −0.0378175
\(290\) −14710.8 −2.97878
\(291\) 808.773 0.162925
\(292\) 8769.43 1.75751
\(293\) −1679.74 −0.334920 −0.167460 0.985879i \(-0.553557\pi\)
−0.167460 + 0.985879i \(0.553557\pi\)
\(294\) 5237.30 1.03893
\(295\) −700.912 −0.138334
\(296\) −19073.2 −3.74529
\(297\) 91.8839 0.0179517
\(298\) −761.918 −0.148110
\(299\) −4432.34 −0.857288
\(300\) −953.622 −0.183525
\(301\) 1566.56 0.299983
\(302\) −4039.33 −0.769660
\(303\) −2810.85 −0.532934
\(304\) 1480.20 0.279262
\(305\) −8752.40 −1.64315
\(306\) 3257.09 0.608482
\(307\) −2907.22 −0.540469 −0.270234 0.962795i \(-0.587101\pi\)
−0.270234 + 0.962795i \(0.587101\pi\)
\(308\) 225.769 0.0417674
\(309\) −4385.28 −0.807346
\(310\) 9096.35 1.66657
\(311\) −1187.35 −0.216490 −0.108245 0.994124i \(-0.534523\pi\)
−0.108245 + 0.994124i \(0.534523\pi\)
\(312\) 10139.7 1.83990
\(313\) 3620.47 0.653806 0.326903 0.945058i \(-0.393995\pi\)
0.326903 + 0.945058i \(0.393995\pi\)
\(314\) 18543.8 3.33277
\(315\) −359.955 −0.0643846
\(316\) 11874.1 2.11384
\(317\) −3700.69 −0.655683 −0.327842 0.944733i \(-0.606321\pi\)
−0.327842 + 0.944733i \(0.606321\pi\)
\(318\) 1296.11 0.228561
\(319\) 800.597 0.140517
\(320\) 8195.32 1.43166
\(321\) −2490.94 −0.433118
\(322\) −1431.84 −0.247805
\(323\) 610.608 0.105186
\(324\) 1596.17 0.273691
\(325\) −884.871 −0.151027
\(326\) −7626.16 −1.29563
\(327\) −4428.05 −0.748843
\(328\) 2320.71 0.390669
\(329\) −913.735 −0.153118
\(330\) 638.400 0.106493
\(331\) −1595.64 −0.264967 −0.132484 0.991185i \(-0.542295\pi\)
−0.132484 + 0.991185i \(0.542295\pi\)
\(332\) −15363.1 −2.53964
\(333\) −2785.99 −0.458472
\(334\) −3074.55 −0.503689
\(335\) 9128.97 1.48886
\(336\) 1683.36 0.273318
\(337\) −5677.39 −0.917707 −0.458853 0.888512i \(-0.651740\pi\)
−0.458853 + 0.888512i \(0.651740\pi\)
\(338\) 4274.60 0.687893
\(339\) 7066.75 1.13219
\(340\) 16095.6 2.56737
\(341\) −495.047 −0.0786167
\(342\) 420.715 0.0665195
\(343\) 2271.34 0.357554
\(344\) −28670.6 −4.49365
\(345\) −2879.70 −0.449385
\(346\) 14508.1 2.25422
\(347\) 4193.13 0.648700 0.324350 0.945937i \(-0.394854\pi\)
0.324350 + 0.945937i \(0.394854\pi\)
\(348\) 13907.6 2.14232
\(349\) 3131.79 0.480346 0.240173 0.970730i \(-0.422796\pi\)
0.240173 + 0.970730i \(0.422796\pi\)
\(350\) −285.852 −0.0436555
\(351\) 1481.09 0.225228
\(352\) −1308.08 −0.198071
\(353\) 3984.82 0.600823 0.300412 0.953810i \(-0.402876\pi\)
0.300412 + 0.953810i \(0.402876\pi\)
\(354\) 931.662 0.139879
\(355\) −1956.95 −0.292575
\(356\) 27467.3 4.08922
\(357\) 694.413 0.102947
\(358\) −15864.9 −2.34215
\(359\) −4378.11 −0.643643 −0.321822 0.946800i \(-0.604295\pi\)
−0.321822 + 0.946800i \(0.604295\pi\)
\(360\) 6587.78 0.964463
\(361\) −6780.13 −0.988501
\(362\) −7163.97 −1.04014
\(363\) 3958.26 0.572327
\(364\) 3639.20 0.524028
\(365\) 5286.75 0.758140
\(366\) 11633.8 1.66150
\(367\) −8615.60 −1.22542 −0.612712 0.790306i \(-0.709922\pi\)
−0.612712 + 0.790306i \(0.709922\pi\)
\(368\) 13467.2 1.90768
\(369\) 338.982 0.0478231
\(370\) −19356.8 −2.71976
\(371\) 276.331 0.0386695
\(372\) −8599.75 −1.19859
\(373\) −8463.20 −1.17482 −0.587410 0.809290i \(-0.699852\pi\)
−0.587410 + 0.809290i \(0.699852\pi\)
\(374\) −1231.58 −0.170277
\(375\) 3880.04 0.534306
\(376\) 16722.9 2.29366
\(377\) 12905.0 1.76297
\(378\) 478.457 0.0651037
\(379\) 5731.49 0.776800 0.388400 0.921491i \(-0.373028\pi\)
0.388400 + 0.921491i \(0.373028\pi\)
\(380\) 2079.05 0.280666
\(381\) −7536.75 −1.01344
\(382\) 962.608 0.128930
\(383\) −12082.4 −1.61197 −0.805983 0.591939i \(-0.798363\pi\)
−0.805983 + 0.591939i \(0.798363\pi\)
\(384\) −1668.28 −0.221703
\(385\) 136.107 0.0180173
\(386\) 21331.2 2.81277
\(387\) −4187.88 −0.550082
\(388\) −5312.50 −0.695106
\(389\) −14859.0 −1.93671 −0.968357 0.249571i \(-0.919711\pi\)
−0.968357 + 0.249571i \(0.919711\pi\)
\(390\) 10290.5 1.33610
\(391\) 5555.42 0.718541
\(392\) −20435.5 −2.63304
\(393\) 2723.54 0.349578
\(394\) 6547.24 0.837171
\(395\) 7158.47 0.911852
\(396\) −603.548 −0.0765894
\(397\) 11650.0 1.47279 0.736396 0.676551i \(-0.236526\pi\)
0.736396 + 0.676551i \(0.236526\pi\)
\(398\) −1008.34 −0.126994
\(399\) 89.6966 0.0112543
\(400\) 2688.58 0.336072
\(401\) −5665.33 −0.705518 −0.352759 0.935714i \(-0.614757\pi\)
−0.352759 + 0.935714i \(0.614757\pi\)
\(402\) −12134.4 −1.50549
\(403\) −7979.75 −0.986352
\(404\) 18463.3 2.27372
\(405\) 962.268 0.118063
\(406\) 4168.87 0.509599
\(407\) 1053.45 0.128298
\(408\) −12708.9 −1.54212
\(409\) −7654.36 −0.925388 −0.462694 0.886518i \(-0.653117\pi\)
−0.462694 + 0.886518i \(0.653117\pi\)
\(410\) 2355.22 0.283697
\(411\) −980.649 −0.117693
\(412\) 28805.1 3.44448
\(413\) 198.631 0.0236658
\(414\) 3827.74 0.454404
\(415\) −9261.84 −1.09553
\(416\) −21085.2 −2.48506
\(417\) −9026.26 −1.06000
\(418\) −159.082 −0.0186147
\(419\) 8887.25 1.03621 0.518103 0.855318i \(-0.326638\pi\)
0.518103 + 0.855318i \(0.326638\pi\)
\(420\) 2364.40 0.274692
\(421\) −8283.80 −0.958974 −0.479487 0.877549i \(-0.659177\pi\)
−0.479487 + 0.877549i \(0.659177\pi\)
\(422\) 15879.0 1.83170
\(423\) 2442.69 0.280775
\(424\) −5057.33 −0.579258
\(425\) 1109.08 0.126584
\(426\) 2601.21 0.295842
\(427\) 2480.33 0.281105
\(428\) 16362.0 1.84787
\(429\) −560.035 −0.0630274
\(430\) −29097.0 −3.26321
\(431\) −5882.75 −0.657453 −0.328726 0.944425i \(-0.606619\pi\)
−0.328726 + 0.944425i \(0.606619\pi\)
\(432\) −4500.13 −0.501187
\(433\) −14513.8 −1.61083 −0.805415 0.592711i \(-0.798058\pi\)
−0.805415 + 0.592711i \(0.798058\pi\)
\(434\) −2577.81 −0.285112
\(435\) 8384.38 0.924139
\(436\) 29086.1 3.19488
\(437\) 717.588 0.0785512
\(438\) −7027.23 −0.766607
\(439\) 3287.31 0.357392 0.178696 0.983904i \(-0.442812\pi\)
0.178696 + 0.983904i \(0.442812\pi\)
\(440\) −2490.99 −0.269894
\(441\) −2984.99 −0.322319
\(442\) −19852.1 −2.13635
\(443\) 12974.8 1.39153 0.695767 0.718267i \(-0.255064\pi\)
0.695767 + 0.718267i \(0.255064\pi\)
\(444\) 18300.0 1.95604
\(445\) 16559.0 1.76398
\(446\) −17984.0 −1.90934
\(447\) 434.255 0.0459498
\(448\) −2322.47 −0.244925
\(449\) 15485.8 1.62766 0.813831 0.581101i \(-0.197378\pi\)
0.813831 + 0.581101i \(0.197378\pi\)
\(450\) 764.169 0.0800517
\(451\) −128.177 −0.0133827
\(452\) −46418.6 −4.83042
\(453\) 2302.21 0.238780
\(454\) 2329.06 0.240767
\(455\) 2193.94 0.226051
\(456\) −1641.60 −0.168585
\(457\) 4088.09 0.418452 0.209226 0.977867i \(-0.432906\pi\)
0.209226 + 0.977867i \(0.432906\pi\)
\(458\) −28789.8 −2.93725
\(459\) −1856.38 −0.188776
\(460\) 18915.6 1.91727
\(461\) −7983.57 −0.806577 −0.403289 0.915073i \(-0.632133\pi\)
−0.403289 + 0.915073i \(0.632133\pi\)
\(462\) −180.916 −0.0182185
\(463\) 9829.43 0.986635 0.493318 0.869849i \(-0.335784\pi\)
0.493318 + 0.869849i \(0.335784\pi\)
\(464\) −39210.3 −3.92304
\(465\) −5184.46 −0.517040
\(466\) 16072.0 1.59768
\(467\) −7096.19 −0.703153 −0.351577 0.936159i \(-0.614354\pi\)
−0.351577 + 0.936159i \(0.614354\pi\)
\(468\) −9728.70 −0.960917
\(469\) −2587.05 −0.254710
\(470\) 16971.6 1.66562
\(471\) −10569.0 −1.03396
\(472\) −3635.28 −0.354507
\(473\) 1583.53 0.153934
\(474\) −9515.14 −0.922036
\(475\) 143.259 0.0138383
\(476\) −4561.32 −0.439218
\(477\) −738.717 −0.0709089
\(478\) −24118.9 −2.30790
\(479\) −8405.79 −0.801817 −0.400909 0.916118i \(-0.631305\pi\)
−0.400909 + 0.916118i \(0.631305\pi\)
\(480\) −13699.1 −1.30265
\(481\) 16980.7 1.60967
\(482\) 33743.1 3.18871
\(483\) 816.076 0.0768794
\(484\) −26000.2 −2.44179
\(485\) −3202.70 −0.299850
\(486\) −1279.06 −0.119382
\(487\) −33.3955 −0.00310738 −0.00155369 0.999999i \(-0.500495\pi\)
−0.00155369 + 0.999999i \(0.500495\pi\)
\(488\) −45394.3 −4.21087
\(489\) 4346.53 0.401956
\(490\) −20739.4 −1.91207
\(491\) −3539.38 −0.325316 −0.162658 0.986683i \(-0.552007\pi\)
−0.162658 + 0.986683i \(0.552007\pi\)
\(492\) −2226.64 −0.204034
\(493\) −16174.9 −1.47765
\(494\) −2564.27 −0.233547
\(495\) −363.856 −0.0330386
\(496\) 24245.6 2.19487
\(497\) 554.578 0.0500528
\(498\) 12311.0 1.10777
\(499\) 3739.04 0.335435 0.167718 0.985835i \(-0.446360\pi\)
0.167718 + 0.985835i \(0.446360\pi\)
\(500\) −25486.4 −2.27958
\(501\) 1752.34 0.156265
\(502\) 10191.9 0.906148
\(503\) 18545.4 1.64393 0.821965 0.569539i \(-0.192878\pi\)
0.821965 + 0.569539i \(0.192878\pi\)
\(504\) −1866.91 −0.164997
\(505\) 11130.8 0.980822
\(506\) −1447.36 −0.127160
\(507\) −2436.31 −0.213413
\(508\) 49505.9 4.32376
\(509\) 18221.3 1.58673 0.793363 0.608749i \(-0.208328\pi\)
0.793363 + 0.608749i \(0.208328\pi\)
\(510\) −12897.9 −1.11986
\(511\) −1498.21 −0.129700
\(512\) −18090.7 −1.56153
\(513\) −239.786 −0.0206371
\(514\) −1795.30 −0.154061
\(515\) 17365.5 1.48586
\(516\) 27508.5 2.34689
\(517\) −923.637 −0.0785716
\(518\) 5485.50 0.465288
\(519\) −8268.88 −0.699351
\(520\) −40152.7 −3.38618
\(521\) 15891.9 1.33634 0.668172 0.744007i \(-0.267077\pi\)
0.668172 + 0.744007i \(0.267077\pi\)
\(522\) −11144.6 −0.934459
\(523\) 15241.9 1.27434 0.637170 0.770723i \(-0.280105\pi\)
0.637170 + 0.770723i \(0.280105\pi\)
\(524\) −17889.8 −1.49145
\(525\) 162.921 0.0135437
\(526\) 28938.0 2.39877
\(527\) 10001.7 0.826717
\(528\) 1701.60 0.140251
\(529\) −5638.25 −0.463405
\(530\) −5132.54 −0.420647
\(531\) −531.000 −0.0433963
\(532\) −589.180 −0.0480154
\(533\) −2066.11 −0.167904
\(534\) −22010.4 −1.78368
\(535\) 9864.01 0.797118
\(536\) 47347.4 3.81548
\(537\) 9042.21 0.726629
\(538\) 549.741 0.0440539
\(539\) 1128.69 0.0901972
\(540\) −6320.75 −0.503707
\(541\) 14342.6 1.13981 0.569904 0.821711i \(-0.306980\pi\)
0.569904 + 0.821711i \(0.306980\pi\)
\(542\) 22104.7 1.75181
\(543\) 4083.10 0.322693
\(544\) 26427.8 2.08287
\(545\) 17534.9 1.37819
\(546\) −2916.21 −0.228576
\(547\) 4343.76 0.339536 0.169768 0.985484i \(-0.445698\pi\)
0.169768 + 0.985484i \(0.445698\pi\)
\(548\) 6441.48 0.502129
\(549\) −6630.69 −0.515466
\(550\) −288.950 −0.0224016
\(551\) −2089.29 −0.161537
\(552\) −14935.6 −1.15163
\(553\) −2028.63 −0.155997
\(554\) 7004.15 0.537144
\(555\) 11032.4 0.843782
\(556\) 59289.9 4.52239
\(557\) −7199.47 −0.547669 −0.273834 0.961777i \(-0.588292\pi\)
−0.273834 + 0.961777i \(0.588292\pi\)
\(558\) 6891.26 0.522814
\(559\) 25525.3 1.93131
\(560\) −6666.03 −0.503020
\(561\) 701.938 0.0528268
\(562\) −21917.9 −1.64511
\(563\) 9629.26 0.720826 0.360413 0.932793i \(-0.382636\pi\)
0.360413 + 0.932793i \(0.382636\pi\)
\(564\) −16045.0 −1.19790
\(565\) −27984.0 −2.08371
\(566\) −5189.69 −0.385405
\(567\) −272.696 −0.0201978
\(568\) −10149.7 −0.749776
\(569\) 17896.5 1.31856 0.659279 0.751899i \(-0.270862\pi\)
0.659279 + 0.751899i \(0.270862\pi\)
\(570\) −1666.01 −0.122424
\(571\) −14247.6 −1.04421 −0.522105 0.852881i \(-0.674853\pi\)
−0.522105 + 0.852881i \(0.674853\pi\)
\(572\) 3678.64 0.268902
\(573\) −548.638 −0.0399994
\(574\) −667.443 −0.0485340
\(575\) 1303.40 0.0945311
\(576\) 6208.65 0.449121
\(577\) −14178.5 −1.02298 −0.511490 0.859289i \(-0.670906\pi\)
−0.511490 + 0.859289i \(0.670906\pi\)
\(578\) −977.969 −0.0703774
\(579\) −12157.7 −0.872636
\(580\) −55073.6 −3.94277
\(581\) 2624.71 0.187420
\(582\) 4257.08 0.303199
\(583\) 279.326 0.0198430
\(584\) 27419.7 1.94287
\(585\) −5865.06 −0.414513
\(586\) −8841.54 −0.623278
\(587\) −17769.4 −1.24944 −0.624720 0.780848i \(-0.714787\pi\)
−0.624720 + 0.780848i \(0.714787\pi\)
\(588\) 19607.2 1.37515
\(589\) 1291.91 0.0903771
\(590\) −3689.34 −0.257437
\(591\) −3731.59 −0.259725
\(592\) −51593.9 −3.58192
\(593\) −12282.0 −0.850527 −0.425263 0.905070i \(-0.639819\pi\)
−0.425263 + 0.905070i \(0.639819\pi\)
\(594\) 483.643 0.0334076
\(595\) −2749.84 −0.189466
\(596\) −2852.44 −0.196041
\(597\) 574.702 0.0393986
\(598\) −23330.2 −1.59539
\(599\) 22571.6 1.53965 0.769827 0.638253i \(-0.220343\pi\)
0.769827 + 0.638253i \(0.220343\pi\)
\(600\) −2981.73 −0.202881
\(601\) −5500.85 −0.373352 −0.186676 0.982422i \(-0.559771\pi\)
−0.186676 + 0.982422i \(0.559771\pi\)
\(602\) 8245.77 0.558260
\(603\) 6915.97 0.467065
\(604\) −15122.3 −1.01874
\(605\) −15674.5 −1.05332
\(606\) −14795.3 −0.991776
\(607\) 377.433 0.0252381 0.0126190 0.999920i \(-0.495983\pi\)
0.0126190 + 0.999920i \(0.495983\pi\)
\(608\) 3413.65 0.227700
\(609\) −2376.04 −0.158099
\(610\) −46069.4 −3.05786
\(611\) −14888.3 −0.985786
\(612\) 12193.8 0.805399
\(613\) 12016.8 0.791766 0.395883 0.918301i \(-0.370439\pi\)
0.395883 + 0.918301i \(0.370439\pi\)
\(614\) −15302.5 −1.00580
\(615\) −1342.35 −0.0880145
\(616\) 705.920 0.0461726
\(617\) −15545.9 −1.01435 −0.507176 0.861843i \(-0.669311\pi\)
−0.507176 + 0.861843i \(0.669311\pi\)
\(618\) −23082.5 −1.50245
\(619\) 2904.00 0.188565 0.0942825 0.995545i \(-0.469944\pi\)
0.0942825 + 0.995545i \(0.469944\pi\)
\(620\) 34054.6 2.20591
\(621\) −2181.62 −0.140975
\(622\) −6249.76 −0.402882
\(623\) −4692.63 −0.301776
\(624\) 27428.4 1.75964
\(625\) −17381.2 −1.11239
\(626\) 19056.8 1.21672
\(627\) 90.6686 0.00577505
\(628\) 69423.7 4.41132
\(629\) −21283.3 −1.34916
\(630\) −1894.67 −0.119818
\(631\) −16236.4 −1.02434 −0.512172 0.858883i \(-0.671159\pi\)
−0.512172 + 0.858883i \(0.671159\pi\)
\(632\) 37127.4 2.33679
\(633\) −9050.20 −0.568267
\(634\) −19479.1 −1.22021
\(635\) 29845.2 1.86515
\(636\) 4852.33 0.302527
\(637\) 18193.6 1.13164
\(638\) 4214.05 0.261498
\(639\) −1482.56 −0.0917825
\(640\) 6606.30 0.408026
\(641\) −28390.2 −1.74937 −0.874684 0.484694i \(-0.838931\pi\)
−0.874684 + 0.484694i \(0.838931\pi\)
\(642\) −13111.4 −0.806021
\(643\) 23941.9 1.46839 0.734196 0.678937i \(-0.237559\pi\)
0.734196 + 0.678937i \(0.237559\pi\)
\(644\) −5360.47 −0.328000
\(645\) 16583.8 1.01238
\(646\) 3214.01 0.195749
\(647\) 3874.64 0.235437 0.117718 0.993047i \(-0.462442\pi\)
0.117718 + 0.993047i \(0.462442\pi\)
\(648\) 4990.80 0.302558
\(649\) 200.783 0.0121440
\(650\) −4657.63 −0.281057
\(651\) 1469.22 0.0884535
\(652\) −28550.6 −1.71492
\(653\) −23410.1 −1.40292 −0.701460 0.712709i \(-0.747468\pi\)
−0.701460 + 0.712709i \(0.747468\pi\)
\(654\) −23307.6 −1.39358
\(655\) −10785.1 −0.643371
\(656\) 6277.63 0.373629
\(657\) 4005.16 0.237833
\(658\) −4809.56 −0.284949
\(659\) 22240.7 1.31468 0.657342 0.753593i \(-0.271681\pi\)
0.657342 + 0.753593i \(0.271681\pi\)
\(660\) 2390.02 0.140957
\(661\) 30096.9 1.77100 0.885502 0.464635i \(-0.153815\pi\)
0.885502 + 0.464635i \(0.153815\pi\)
\(662\) −8398.84 −0.493097
\(663\) 11314.7 0.662783
\(664\) −48036.5 −2.80750
\(665\) −355.194 −0.0207125
\(666\) −14664.4 −0.853205
\(667\) −19008.7 −1.10348
\(668\) −11510.4 −0.666693
\(669\) 10249.9 0.592355
\(670\) 48051.5 2.77073
\(671\) 2507.21 0.144247
\(672\) 3882.17 0.222854
\(673\) 17650.2 1.01094 0.505471 0.862844i \(-0.331319\pi\)
0.505471 + 0.862844i \(0.331319\pi\)
\(674\) −29883.7 −1.70783
\(675\) −435.537 −0.0248353
\(676\) 16003.1 0.910509
\(677\) −8151.07 −0.462734 −0.231367 0.972866i \(-0.574320\pi\)
−0.231367 + 0.972866i \(0.574320\pi\)
\(678\) 37196.7 2.10698
\(679\) 907.611 0.0512974
\(680\) 50326.7 2.83815
\(681\) −1327.45 −0.0746959
\(682\) −2605.74 −0.146304
\(683\) −23902.8 −1.33912 −0.669558 0.742760i \(-0.733516\pi\)
−0.669558 + 0.742760i \(0.733516\pi\)
\(684\) 1575.06 0.0880465
\(685\) 3883.32 0.216605
\(686\) 11955.5 0.665399
\(687\) 16408.7 0.911255
\(688\) −77555.6 −4.29764
\(689\) 4502.50 0.248958
\(690\) −15157.7 −0.836294
\(691\) −25203.7 −1.38754 −0.693772 0.720194i \(-0.744053\pi\)
−0.693772 + 0.720194i \(0.744053\pi\)
\(692\) 54314.9 2.98373
\(693\) 103.113 0.00565214
\(694\) 22071.1 1.20721
\(695\) 35743.6 1.95084
\(696\) 43485.6 2.36827
\(697\) 2589.62 0.140730
\(698\) 16484.6 0.893912
\(699\) −9160.20 −0.495666
\(700\) −1070.16 −0.0577833
\(701\) −6102.41 −0.328794 −0.164397 0.986394i \(-0.552568\pi\)
−0.164397 + 0.986394i \(0.552568\pi\)
\(702\) 7795.92 0.419143
\(703\) −2749.14 −0.147491
\(704\) −2347.63 −0.125682
\(705\) −9672.93 −0.516743
\(706\) 20974.6 1.11812
\(707\) −3154.35 −0.167796
\(708\) 3487.92 0.185147
\(709\) −483.971 −0.0256360 −0.0128180 0.999918i \(-0.504080\pi\)
−0.0128180 + 0.999918i \(0.504080\pi\)
\(710\) −10300.7 −0.544474
\(711\) 5423.15 0.286053
\(712\) 85883.1 4.52051
\(713\) 11754.0 0.617378
\(714\) 3655.13 0.191582
\(715\) 2217.71 0.115997
\(716\) −59394.6 −3.10011
\(717\) 13746.6 0.716004
\(718\) −23044.8 −1.19780
\(719\) 21253.9 1.10242 0.551208 0.834368i \(-0.314167\pi\)
0.551208 + 0.834368i \(0.314167\pi\)
\(720\) 17820.3 0.922394
\(721\) −4921.20 −0.254195
\(722\) −35688.1 −1.83957
\(723\) −19231.9 −0.989267
\(724\) −26820.2 −1.37675
\(725\) −3794.90 −0.194399
\(726\) 20834.8 1.06508
\(727\) −26369.1 −1.34522 −0.672610 0.739997i \(-0.734827\pi\)
−0.672610 + 0.739997i \(0.734827\pi\)
\(728\) 11378.9 0.579297
\(729\) 729.000 0.0370370
\(730\) 27827.5 1.41088
\(731\) −31992.9 −1.61874
\(732\) 43554.3 2.19920
\(733\) −6909.57 −0.348173 −0.174086 0.984730i \(-0.555697\pi\)
−0.174086 + 0.984730i \(0.555697\pi\)
\(734\) −45349.3 −2.28048
\(735\) 11820.4 0.593201
\(736\) 31058.0 1.55545
\(737\) −2615.09 −0.130703
\(738\) 1784.28 0.0889975
\(739\) −34884.6 −1.73647 −0.868235 0.496153i \(-0.834746\pi\)
−0.868235 + 0.496153i \(0.834746\pi\)
\(740\) −72467.3 −3.59993
\(741\) 1461.50 0.0724557
\(742\) 1454.50 0.0719630
\(743\) 34839.2 1.72022 0.860112 0.510106i \(-0.170394\pi\)
0.860112 + 0.510106i \(0.170394\pi\)
\(744\) −26889.2 −1.32501
\(745\) −1719.63 −0.0845668
\(746\) −44547.1 −2.18631
\(747\) −7016.63 −0.343675
\(748\) −4610.75 −0.225382
\(749\) −2795.35 −0.136368
\(750\) 20423.1 0.994329
\(751\) 32677.5 1.58777 0.793887 0.608065i \(-0.208054\pi\)
0.793887 + 0.608065i \(0.208054\pi\)
\(752\) 45236.3 2.19362
\(753\) −5808.86 −0.281124
\(754\) 67927.0 3.28084
\(755\) −9116.65 −0.439455
\(756\) 1791.23 0.0861726
\(757\) −263.405 −0.0126468 −0.00632339 0.999980i \(-0.502013\pi\)
−0.00632339 + 0.999980i \(0.502013\pi\)
\(758\) 30168.5 1.44560
\(759\) 824.920 0.0394502
\(760\) 6500.66 0.310268
\(761\) −23504.7 −1.11964 −0.559819 0.828615i \(-0.689130\pi\)
−0.559819 + 0.828615i \(0.689130\pi\)
\(762\) −39670.7 −1.88598
\(763\) −4969.19 −0.235776
\(764\) 3603.78 0.170655
\(765\) 7351.16 0.347427
\(766\) −63597.4 −2.99983
\(767\) 3236.46 0.152362
\(768\) 7775.22 0.365318
\(769\) −14106.7 −0.661508 −0.330754 0.943717i \(-0.607303\pi\)
−0.330754 + 0.943717i \(0.607303\pi\)
\(770\) 716.418 0.0335297
\(771\) 1023.23 0.0477961
\(772\) 79858.9 3.72304
\(773\) −8023.79 −0.373345 −0.186672 0.982422i \(-0.559770\pi\)
−0.186672 + 0.982422i \(0.559770\pi\)
\(774\) −22043.4 −1.02369
\(775\) 2346.56 0.108763
\(776\) −16610.8 −0.768419
\(777\) −3126.46 −0.144351
\(778\) −78212.3 −3.60417
\(779\) 334.499 0.0153847
\(780\) 38525.2 1.76849
\(781\) 560.588 0.0256843
\(782\) 29241.7 1.33719
\(783\) 6351.88 0.289908
\(784\) −55279.3 −2.51819
\(785\) 41852.9 1.90292
\(786\) 14335.7 0.650556
\(787\) 22881.4 1.03638 0.518192 0.855264i \(-0.326605\pi\)
0.518192 + 0.855264i \(0.326605\pi\)
\(788\) 24511.3 1.10810
\(789\) −16493.2 −0.744198
\(790\) 37679.5 1.69693
\(791\) 7930.36 0.356474
\(792\) −1887.14 −0.0846673
\(793\) 40414.2 1.80978
\(794\) 61321.4 2.74083
\(795\) 2925.28 0.130502
\(796\) −3774.98 −0.168091
\(797\) −3384.94 −0.150440 −0.0752200 0.997167i \(-0.523966\pi\)
−0.0752200 + 0.997167i \(0.523966\pi\)
\(798\) 472.130 0.0209439
\(799\) 18660.7 0.826243
\(800\) 6200.40 0.274022
\(801\) 12544.8 0.553370
\(802\) −29820.2 −1.31295
\(803\) −1514.44 −0.0665549
\(804\) −45428.2 −1.99270
\(805\) −3231.62 −0.141490
\(806\) −42002.4 −1.83557
\(807\) −313.324 −0.0136673
\(808\) 57730.0 2.51353
\(809\) −19080.0 −0.829193 −0.414597 0.910005i \(-0.636077\pi\)
−0.414597 + 0.910005i \(0.636077\pi\)
\(810\) 5065.02 0.219712
\(811\) −38157.7 −1.65216 −0.826078 0.563556i \(-0.809433\pi\)
−0.826078 + 0.563556i \(0.809433\pi\)
\(812\) 15607.3 0.674516
\(813\) −12598.6 −0.543482
\(814\) 5544.95 0.238760
\(815\) −17212.0 −0.739768
\(816\) −34378.3 −1.47486
\(817\) −4132.49 −0.176962
\(818\) −40289.7 −1.72212
\(819\) 1662.09 0.0709136
\(820\) 8817.38 0.375507
\(821\) −24776.7 −1.05324 −0.526621 0.850100i \(-0.676541\pi\)
−0.526621 + 0.850100i \(0.676541\pi\)
\(822\) −5161.77 −0.219024
\(823\) −29084.0 −1.23184 −0.615921 0.787808i \(-0.711216\pi\)
−0.615921 + 0.787808i \(0.711216\pi\)
\(824\) 90066.2 3.80777
\(825\) 164.687 0.00694988
\(826\) 1045.52 0.0440414
\(827\) −7505.76 −0.315600 −0.157800 0.987471i \(-0.550440\pi\)
−0.157800 + 0.987471i \(0.550440\pi\)
\(828\) 14330.2 0.601458
\(829\) −4101.70 −0.171843 −0.0859216 0.996302i \(-0.527383\pi\)
−0.0859216 + 0.996302i \(0.527383\pi\)
\(830\) −48750.9 −2.03876
\(831\) −3992.01 −0.166644
\(832\) −37841.9 −1.57684
\(833\) −22803.6 −0.948496
\(834\) −47510.9 −1.97262
\(835\) −6939.18 −0.287593
\(836\) −595.565 −0.0246388
\(837\) −3927.67 −0.162198
\(838\) 46779.2 1.92835
\(839\) −33368.3 −1.37307 −0.686533 0.727099i \(-0.740868\pi\)
−0.686533 + 0.727099i \(0.740868\pi\)
\(840\) 7392.86 0.303664
\(841\) 30955.8 1.26925
\(842\) −43602.9 −1.78462
\(843\) 12492.1 0.510380
\(844\) 59447.1 2.42447
\(845\) 9647.66 0.392769
\(846\) 12857.4 0.522514
\(847\) 4441.98 0.180199
\(848\) −13680.3 −0.553992
\(849\) 2957.86 0.119568
\(850\) 5837.79 0.235570
\(851\) −25012.2 −1.00753
\(852\) 9738.30 0.391583
\(853\) 9085.16 0.364678 0.182339 0.983236i \(-0.441633\pi\)
0.182339 + 0.983236i \(0.441633\pi\)
\(854\) 13055.6 0.523129
\(855\) 949.542 0.0379809
\(856\) 51159.7 2.04276
\(857\) 40753.2 1.62439 0.812196 0.583385i \(-0.198272\pi\)
0.812196 + 0.583385i \(0.198272\pi\)
\(858\) −2947.82 −0.117292
\(859\) −20281.5 −0.805585 −0.402792 0.915291i \(-0.631960\pi\)
−0.402792 + 0.915291i \(0.631960\pi\)
\(860\) −108932. −4.31926
\(861\) 380.408 0.0150572
\(862\) −30964.6 −1.22350
\(863\) 20235.1 0.798157 0.399079 0.916917i \(-0.369330\pi\)
0.399079 + 0.916917i \(0.369330\pi\)
\(864\) −10378.2 −0.408650
\(865\) 32744.4 1.28710
\(866\) −76395.3 −2.99771
\(867\) 557.393 0.0218340
\(868\) −9650.70 −0.377380
\(869\) −2050.62 −0.0800488
\(870\) 44132.3 1.71980
\(871\) −42153.0 −1.63984
\(872\) 90944.6 3.53185
\(873\) −2426.32 −0.0940646
\(874\) 3777.12 0.146182
\(875\) 4354.21 0.168228
\(876\) −26308.3 −1.01470
\(877\) 32647.0 1.25703 0.628513 0.777799i \(-0.283664\pi\)
0.628513 + 0.777799i \(0.283664\pi\)
\(878\) 17303.2 0.665096
\(879\) 5039.23 0.193366
\(880\) −6738.27 −0.258121
\(881\) −30042.8 −1.14888 −0.574442 0.818545i \(-0.694781\pi\)
−0.574442 + 0.818545i \(0.694781\pi\)
\(882\) −15711.9 −0.599826
\(883\) −21269.9 −0.810634 −0.405317 0.914176i \(-0.632839\pi\)
−0.405317 + 0.914176i \(0.632839\pi\)
\(884\) −74321.5 −2.82772
\(885\) 2102.73 0.0798674
\(886\) 68294.4 2.58961
\(887\) −1012.07 −0.0383112 −0.0191556 0.999817i \(-0.506098\pi\)
−0.0191556 + 0.999817i \(0.506098\pi\)
\(888\) 57219.5 2.16234
\(889\) −8457.80 −0.319084
\(890\) 87160.3 3.28272
\(891\) −275.652 −0.0103644
\(892\) −67327.7 −2.52724
\(893\) 2410.38 0.0903252
\(894\) 2285.76 0.0855113
\(895\) −35806.7 −1.33730
\(896\) −1872.15 −0.0698038
\(897\) 13297.0 0.494955
\(898\) 81511.5 3.02904
\(899\) −34222.3 −1.26961
\(900\) 2860.87 0.105958
\(901\) −5643.36 −0.208665
\(902\) −674.676 −0.0249049
\(903\) −4699.67 −0.173195
\(904\) −145139. −5.33988
\(905\) −16168.9 −0.593891
\(906\) 12118.0 0.444363
\(907\) −9343.76 −0.342067 −0.171033 0.985265i \(-0.554711\pi\)
−0.171033 + 0.985265i \(0.554711\pi\)
\(908\) 8719.47 0.318685
\(909\) 8432.54 0.307690
\(910\) 11548.1 0.420675
\(911\) −27773.6 −1.01008 −0.505039 0.863096i \(-0.668522\pi\)
−0.505039 + 0.863096i \(0.668522\pi\)
\(912\) −4440.61 −0.161232
\(913\) 2653.15 0.0961735
\(914\) 21518.2 0.778729
\(915\) 26257.2 0.948673
\(916\) −107782. −3.88780
\(917\) 3056.37 0.110066
\(918\) −9771.27 −0.351307
\(919\) 16876.6 0.605776 0.302888 0.953026i \(-0.402049\pi\)
0.302888 + 0.953026i \(0.402049\pi\)
\(920\) 59144.1 2.11948
\(921\) 8721.67 0.312040
\(922\) −42022.6 −1.50102
\(923\) 9036.22 0.322244
\(924\) −677.306 −0.0241144
\(925\) −4993.42 −0.177495
\(926\) 51738.4 1.83610
\(927\) 13155.8 0.466122
\(928\) −90426.8 −3.19871
\(929\) 10461.8 0.369474 0.184737 0.982788i \(-0.440857\pi\)
0.184737 + 0.982788i \(0.440857\pi\)
\(930\) −27289.1 −0.962197
\(931\) −2945.51 −0.103690
\(932\) 60169.6 2.11472
\(933\) 3562.04 0.124990
\(934\) −37351.7 −1.30855
\(935\) −2779.64 −0.0972235
\(936\) −30419.1 −1.06226
\(937\) −13284.7 −0.463173 −0.231586 0.972814i \(-0.574392\pi\)
−0.231586 + 0.972814i \(0.574392\pi\)
\(938\) −13617.3 −0.474008
\(939\) −10861.4 −0.377475
\(940\) 63537.6 2.20465
\(941\) 2290.28 0.0793422 0.0396711 0.999213i \(-0.487369\pi\)
0.0396711 + 0.999213i \(0.487369\pi\)
\(942\) −55631.5 −1.92417
\(943\) 3043.33 0.105095
\(944\) −9833.62 −0.339044
\(945\) 1079.86 0.0371725
\(946\) 8335.13 0.286468
\(947\) 18255.7 0.626431 0.313216 0.949682i \(-0.398594\pi\)
0.313216 + 0.949682i \(0.398594\pi\)
\(948\) −35622.4 −1.22043
\(949\) −24411.6 −0.835020
\(950\) 754.062 0.0257526
\(951\) 11102.1 0.378559
\(952\) −14262.1 −0.485542
\(953\) −7649.51 −0.260013 −0.130006 0.991513i \(-0.541500\pi\)
−0.130006 + 0.991513i \(0.541500\pi\)
\(954\) −3888.33 −0.131960
\(955\) 2172.58 0.0736157
\(956\) −90295.6 −3.05478
\(957\) −2401.79 −0.0811274
\(958\) −44245.0 −1.49216
\(959\) −1100.49 −0.0370560
\(960\) −24586.0 −0.826572
\(961\) −8629.73 −0.289676
\(962\) 89380.1 2.99556
\(963\) 7472.83 0.250061
\(964\) 126326. 4.22064
\(965\) 48143.9 1.60602
\(966\) 4295.52 0.143070
\(967\) 22498.5 0.748194 0.374097 0.927390i \(-0.377953\pi\)
0.374097 + 0.927390i \(0.377953\pi\)
\(968\) −81295.8 −2.69933
\(969\) −1831.82 −0.0607293
\(970\) −16857.8 −0.558013
\(971\) 16368.8 0.540988 0.270494 0.962722i \(-0.412813\pi\)
0.270494 + 0.962722i \(0.412813\pi\)
\(972\) −4788.50 −0.158016
\(973\) −10129.3 −0.333743
\(974\) −175.782 −0.00578276
\(975\) 2654.61 0.0871955
\(976\) −122794. −4.02719
\(977\) 45793.1 1.49954 0.749770 0.661699i \(-0.230164\pi\)
0.749770 + 0.661699i \(0.230164\pi\)
\(978\) 22878.5 0.748030
\(979\) −4743.49 −0.154854
\(980\) −77643.6 −2.53085
\(981\) 13284.1 0.432345
\(982\) −18630.0 −0.605404
\(983\) 29019.5 0.941587 0.470793 0.882244i \(-0.343968\pi\)
0.470793 + 0.882244i \(0.343968\pi\)
\(984\) −6962.12 −0.225553
\(985\) 14776.9 0.478002
\(986\) −85138.5 −2.74986
\(987\) 2741.20 0.0884027
\(988\) −9600.03 −0.309127
\(989\) −37598.2 −1.20885
\(990\) −1915.20 −0.0614839
\(991\) 24513.2 0.785760 0.392880 0.919590i \(-0.371479\pi\)
0.392880 + 0.919590i \(0.371479\pi\)
\(992\) 55915.1 1.78962
\(993\) 4786.91 0.152979
\(994\) 2919.09 0.0931469
\(995\) −2275.79 −0.0725100
\(996\) 46089.4 1.46626
\(997\) 29685.7 0.942983 0.471491 0.881871i \(-0.343716\pi\)
0.471491 + 0.881871i \(0.343716\pi\)
\(998\) 19680.9 0.624236
\(999\) 8357.97 0.264699
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.1.8 8
3.2 odd 2 531.4.a.f.1.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.c.1.8 8 1.1 even 1 trivial
531.4.a.f.1.1 8 3.2 odd 2