Properties

Label 177.4.a.b.1.7
Level $177$
Weight $4$
Character 177.1
Self dual yes
Analytic conductor $10.443$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.7
Root \(-4.58037\) of defining polynomial
Character \(\chi\) \(=\) 177.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.58037 q^{2} -3.00000 q^{3} +12.9798 q^{4} -17.0129 q^{5} -13.7411 q^{6} -20.9898 q^{7} +22.8093 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.58037 q^{2} -3.00000 q^{3} +12.9798 q^{4} -17.0129 q^{5} -13.7411 q^{6} -20.9898 q^{7} +22.8093 q^{8} +9.00000 q^{9} -77.9254 q^{10} -48.1602 q^{11} -38.9394 q^{12} +29.4612 q^{13} -96.1410 q^{14} +51.0387 q^{15} +0.636565 q^{16} +108.283 q^{17} +41.2233 q^{18} -111.228 q^{19} -220.824 q^{20} +62.9694 q^{21} -220.591 q^{22} -14.3946 q^{23} -68.4278 q^{24} +164.439 q^{25} +134.943 q^{26} -27.0000 q^{27} -272.443 q^{28} +292.789 q^{29} +233.776 q^{30} -216.676 q^{31} -179.558 q^{32} +144.480 q^{33} +495.978 q^{34} +357.097 q^{35} +116.818 q^{36} -168.516 q^{37} -509.464 q^{38} -88.3836 q^{39} -388.052 q^{40} -342.050 q^{41} +288.423 q^{42} +325.352 q^{43} -625.109 q^{44} -153.116 q^{45} -65.9325 q^{46} -315.587 q^{47} -1.90970 q^{48} +97.5712 q^{49} +753.191 q^{50} -324.850 q^{51} +382.400 q^{52} +256.246 q^{53} -123.670 q^{54} +819.344 q^{55} -478.762 q^{56} +333.683 q^{57} +1341.08 q^{58} +59.0000 q^{59} +662.472 q^{60} -749.020 q^{61} -992.457 q^{62} -188.908 q^{63} -827.536 q^{64} -501.221 q^{65} +661.774 q^{66} +664.622 q^{67} +1405.50 q^{68} +43.1837 q^{69} +1635.64 q^{70} +207.420 q^{71} +205.283 q^{72} +45.3093 q^{73} -771.868 q^{74} -493.317 q^{75} -1443.71 q^{76} +1010.87 q^{77} -404.830 q^{78} -813.087 q^{79} -10.8298 q^{80} +81.0000 q^{81} -1566.71 q^{82} +19.2056 q^{83} +817.329 q^{84} -1842.22 q^{85} +1490.23 q^{86} -878.367 q^{87} -1098.50 q^{88} -636.087 q^{89} -701.328 q^{90} -618.385 q^{91} -186.838 q^{92} +650.028 q^{93} -1445.50 q^{94} +1892.31 q^{95} +538.675 q^{96} -235.487 q^{97} +446.912 q^{98} -433.441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} + O(q^{10}) \) \( 7q - 21q^{3} + 26q^{4} - 2q^{5} - 59q^{7} - 21q^{8} + 63q^{9} - 71q^{10} - 5q^{11} - 78q^{12} - 67q^{13} - 65q^{14} + 6q^{15} - 94q^{16} - 23q^{17} - 176q^{19} - 207q^{20} + 177q^{21} - 704q^{22} - 218q^{23} + 63q^{24} - 183q^{25} + 58q^{26} - 189q^{27} - 938q^{28} + 168q^{29} + 213q^{30} - 604q^{31} - 448q^{32} + 15q^{33} - 610q^{34} - 336q^{35} + 234q^{36} - 505q^{37} - 453q^{38} + 201q^{39} - 1080q^{40} - 265q^{41} + 195q^{42} - 493q^{43} + 504q^{44} - 18q^{45} + 381q^{46} - 244q^{47} + 282q^{48} + 770q^{49} + 1639q^{50} + 69q^{51} + 160q^{52} + 686q^{53} - 116q^{55} + 2190q^{56} + 528q^{57} + 1584q^{58} + 413q^{59} + 621q^{60} - 838q^{61} + 286q^{62} - 531q^{63} + 205q^{64} + 490q^{65} + 2112q^{66} - 1504q^{67} + 3047q^{68} + 654q^{69} + 1530q^{70} - 1267q^{71} - 189q^{72} - 666q^{73} + 528q^{74} + 549q^{75} - 64q^{76} + 1109q^{77} - 174q^{78} - 2741q^{79} + 1213q^{80} + 567q^{81} + 953q^{82} - 2025q^{83} + 2814q^{84} - 1274q^{85} + 4394q^{86} - 504q^{87} - 1639q^{88} + 616q^{89} - 639q^{90} - 2415q^{91} + 218q^{92} + 1812q^{93} + 900q^{94} + 2554q^{95} + 1344q^{96} - 1298q^{97} - 172q^{98} - 45q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.58037 1.61941 0.809703 0.586840i \(-0.199628\pi\)
0.809703 + 0.586840i \(0.199628\pi\)
\(3\) −3.00000 −0.577350
\(4\) 12.9798 1.62247
\(5\) −17.0129 −1.52168 −0.760840 0.648939i \(-0.775213\pi\)
−0.760840 + 0.648939i \(0.775213\pi\)
\(6\) −13.7411 −0.934964
\(7\) −20.9898 −1.13334 −0.566671 0.823944i \(-0.691769\pi\)
−0.566671 + 0.823944i \(0.691769\pi\)
\(8\) 22.8093 1.00804
\(9\) 9.00000 0.333333
\(10\) −77.9254 −2.46422
\(11\) −48.1602 −1.32008 −0.660038 0.751232i \(-0.729460\pi\)
−0.660038 + 0.751232i \(0.729460\pi\)
\(12\) −38.9394 −0.936735
\(13\) 29.4612 0.628544 0.314272 0.949333i \(-0.398240\pi\)
0.314272 + 0.949333i \(0.398240\pi\)
\(14\) −96.1410 −1.83534
\(15\) 51.0387 0.878543
\(16\) 0.636565 0.00994633
\(17\) 108.283 1.54486 0.772429 0.635101i \(-0.219042\pi\)
0.772429 + 0.635101i \(0.219042\pi\)
\(18\) 41.2233 0.539802
\(19\) −111.228 −1.34302 −0.671510 0.740995i \(-0.734354\pi\)
−0.671510 + 0.740995i \(0.734354\pi\)
\(20\) −220.824 −2.46889
\(21\) 62.9694 0.654335
\(22\) −220.591 −2.13774
\(23\) −14.3946 −0.130499 −0.0652495 0.997869i \(-0.520784\pi\)
−0.0652495 + 0.997869i \(0.520784\pi\)
\(24\) −68.4278 −0.581990
\(25\) 164.439 1.31551
\(26\) 134.943 1.01787
\(27\) −27.0000 −0.192450
\(28\) −272.443 −1.83882
\(29\) 292.789 1.87481 0.937406 0.348238i \(-0.113220\pi\)
0.937406 + 0.348238i \(0.113220\pi\)
\(30\) 233.776 1.42272
\(31\) −216.676 −1.25536 −0.627680 0.778471i \(-0.715995\pi\)
−0.627680 + 0.778471i \(0.715995\pi\)
\(32\) −179.558 −0.991929
\(33\) 144.480 0.762146
\(34\) 495.978 2.50175
\(35\) 357.097 1.72458
\(36\) 116.818 0.540824
\(37\) −168.516 −0.748755 −0.374378 0.927276i \(-0.622144\pi\)
−0.374378 + 0.927276i \(0.622144\pi\)
\(38\) −509.464 −2.17489
\(39\) −88.3836 −0.362890
\(40\) −388.052 −1.53391
\(41\) −342.050 −1.30291 −0.651453 0.758689i \(-0.725840\pi\)
−0.651453 + 0.758689i \(0.725840\pi\)
\(42\) 288.423 1.05963
\(43\) 325.352 1.15385 0.576927 0.816795i \(-0.304252\pi\)
0.576927 + 0.816795i \(0.304252\pi\)
\(44\) −625.109 −2.14179
\(45\) −153.116 −0.507227
\(46\) −65.9325 −0.211331
\(47\) −315.587 −0.979426 −0.489713 0.871884i \(-0.662898\pi\)
−0.489713 + 0.871884i \(0.662898\pi\)
\(48\) −1.90970 −0.00574252
\(49\) 97.5712 0.284464
\(50\) 753.191 2.13035
\(51\) −324.850 −0.891924
\(52\) 382.400 1.01980
\(53\) 256.246 0.664115 0.332058 0.943259i \(-0.392257\pi\)
0.332058 + 0.943259i \(0.392257\pi\)
\(54\) −123.670 −0.311655
\(55\) 819.344 2.00873
\(56\) −478.762 −1.14245
\(57\) 333.683 0.775393
\(58\) 1341.08 3.03608
\(59\) 59.0000 0.130189
\(60\) 662.472 1.42541
\(61\) −749.020 −1.57217 −0.786083 0.618120i \(-0.787894\pi\)
−0.786083 + 0.618120i \(0.787894\pi\)
\(62\) −992.457 −2.03294
\(63\) −188.908 −0.377781
\(64\) −827.536 −1.61628
\(65\) −501.221 −0.956443
\(66\) 661.774 1.23422
\(67\) 664.622 1.21189 0.605944 0.795507i \(-0.292796\pi\)
0.605944 + 0.795507i \(0.292796\pi\)
\(68\) 1405.50 2.50649
\(69\) 43.1837 0.0753436
\(70\) 1635.64 2.79280
\(71\) 207.420 0.346708 0.173354 0.984860i \(-0.444540\pi\)
0.173354 + 0.984860i \(0.444540\pi\)
\(72\) 205.283 0.336012
\(73\) 45.3093 0.0726445 0.0363222 0.999340i \(-0.488436\pi\)
0.0363222 + 0.999340i \(0.488436\pi\)
\(74\) −771.868 −1.21254
\(75\) −493.317 −0.759511
\(76\) −1443.71 −2.17901
\(77\) 1010.87 1.49610
\(78\) −404.830 −0.587666
\(79\) −813.087 −1.15797 −0.578984 0.815339i \(-0.696551\pi\)
−0.578984 + 0.815339i \(0.696551\pi\)
\(80\) −10.8298 −0.0151351
\(81\) 81.0000 0.111111
\(82\) −1566.71 −2.10993
\(83\) 19.2056 0.0253986 0.0126993 0.999919i \(-0.495958\pi\)
0.0126993 + 0.999919i \(0.495958\pi\)
\(84\) 817.329 1.06164
\(85\) −1842.22 −2.35078
\(86\) 1490.23 1.86856
\(87\) −878.367 −1.08242
\(88\) −1098.50 −1.33068
\(89\) −636.087 −0.757585 −0.378792 0.925482i \(-0.623661\pi\)
−0.378792 + 0.925482i \(0.623661\pi\)
\(90\) −701.328 −0.821406
\(91\) −618.385 −0.712355
\(92\) −186.838 −0.211731
\(93\) 650.028 0.724783
\(94\) −1445.50 −1.58609
\(95\) 1892.31 2.04365
\(96\) 538.675 0.572691
\(97\) −235.487 −0.246495 −0.123248 0.992376i \(-0.539331\pi\)
−0.123248 + 0.992376i \(0.539331\pi\)
\(98\) 446.912 0.460663
\(99\) −433.441 −0.440025
\(100\) 2134.38 2.13438
\(101\) 1807.59 1.78081 0.890406 0.455167i \(-0.150420\pi\)
0.890406 + 0.455167i \(0.150420\pi\)
\(102\) −1487.93 −1.44439
\(103\) −1437.56 −1.37522 −0.687609 0.726081i \(-0.741340\pi\)
−0.687609 + 0.726081i \(0.741340\pi\)
\(104\) 671.989 0.633595
\(105\) −1071.29 −0.995689
\(106\) 1173.70 1.07547
\(107\) −430.727 −0.389158 −0.194579 0.980887i \(-0.562334\pi\)
−0.194579 + 0.980887i \(0.562334\pi\)
\(108\) −350.454 −0.312245
\(109\) 459.238 0.403551 0.201775 0.979432i \(-0.435329\pi\)
0.201775 + 0.979432i \(0.435329\pi\)
\(110\) 3752.90 3.25295
\(111\) 505.549 0.432294
\(112\) −13.3614 −0.0112726
\(113\) −1009.57 −0.840460 −0.420230 0.907418i \(-0.638051\pi\)
−0.420230 + 0.907418i \(0.638051\pi\)
\(114\) 1528.39 1.25568
\(115\) 244.893 0.198578
\(116\) 3800.34 3.04183
\(117\) 265.151 0.209515
\(118\) 270.242 0.210829
\(119\) −2272.85 −1.75085
\(120\) 1164.16 0.885603
\(121\) 988.402 0.742601
\(122\) −3430.79 −2.54598
\(123\) 1026.15 0.752233
\(124\) −2812.41 −2.03679
\(125\) −670.969 −0.480107
\(126\) −865.269 −0.611780
\(127\) 392.027 0.273912 0.136956 0.990577i \(-0.456268\pi\)
0.136956 + 0.990577i \(0.456268\pi\)
\(128\) −2353.96 −1.62549
\(129\) −976.057 −0.666178
\(130\) −2295.78 −1.54887
\(131\) 1782.88 1.18909 0.594546 0.804062i \(-0.297332\pi\)
0.594546 + 0.804062i \(0.297332\pi\)
\(132\) 1875.33 1.23656
\(133\) 2334.65 1.52210
\(134\) 3044.21 1.96254
\(135\) 459.348 0.292848
\(136\) 2469.86 1.55727
\(137\) −776.765 −0.484405 −0.242203 0.970226i \(-0.577870\pi\)
−0.242203 + 0.970226i \(0.577870\pi\)
\(138\) 197.797 0.122012
\(139\) −555.020 −0.338678 −0.169339 0.985558i \(-0.554163\pi\)
−0.169339 + 0.985558i \(0.554163\pi\)
\(140\) 4635.05 2.79809
\(141\) 946.760 0.565472
\(142\) 950.062 0.561461
\(143\) −1418.86 −0.829726
\(144\) 5.72909 0.00331544
\(145\) −4981.19 −2.85287
\(146\) 207.533 0.117641
\(147\) −292.713 −0.164235
\(148\) −2187.31 −1.21484
\(149\) 2066.64 1.13628 0.568141 0.822932i \(-0.307663\pi\)
0.568141 + 0.822932i \(0.307663\pi\)
\(150\) −2259.57 −1.22996
\(151\) −922.182 −0.496994 −0.248497 0.968633i \(-0.579937\pi\)
−0.248497 + 0.968633i \(0.579937\pi\)
\(152\) −2537.02 −1.35381
\(153\) 974.551 0.514953
\(154\) 4630.17 2.42279
\(155\) 3686.29 1.91026
\(156\) −1147.20 −0.588779
\(157\) −2147.92 −1.09187 −0.545933 0.837829i \(-0.683825\pi\)
−0.545933 + 0.837829i \(0.683825\pi\)
\(158\) −3724.24 −1.87522
\(159\) −768.739 −0.383427
\(160\) 3054.81 1.50940
\(161\) 302.139 0.147900
\(162\) 371.010 0.179934
\(163\) 202.941 0.0975188 0.0487594 0.998811i \(-0.484473\pi\)
0.0487594 + 0.998811i \(0.484473\pi\)
\(164\) −4439.73 −2.11393
\(165\) −2458.03 −1.15974
\(166\) 87.9686 0.0411307
\(167\) −1984.16 −0.919395 −0.459697 0.888076i \(-0.652042\pi\)
−0.459697 + 0.888076i \(0.652042\pi\)
\(168\) 1436.28 0.659594
\(169\) −1329.04 −0.604933
\(170\) −8438.03 −3.80687
\(171\) −1001.05 −0.447673
\(172\) 4223.00 1.87210
\(173\) −1484.23 −0.652279 −0.326139 0.945322i \(-0.605748\pi\)
−0.326139 + 0.945322i \(0.605748\pi\)
\(174\) −4023.25 −1.75288
\(175\) −3451.54 −1.49092
\(176\) −30.6571 −0.0131299
\(177\) −177.000 −0.0751646
\(178\) −2913.51 −1.22684
\(179\) −546.514 −0.228203 −0.114102 0.993469i \(-0.536399\pi\)
−0.114102 + 0.993469i \(0.536399\pi\)
\(180\) −1987.41 −0.822962
\(181\) −4561.98 −1.87342 −0.936710 0.350106i \(-0.886145\pi\)
−0.936710 + 0.350106i \(0.886145\pi\)
\(182\) −2832.43 −1.15359
\(183\) 2247.06 0.907691
\(184\) −328.330 −0.131548
\(185\) 2866.95 1.13937
\(186\) 2977.37 1.17372
\(187\) −5214.95 −2.03933
\(188\) −4096.25 −1.58909
\(189\) 566.724 0.218112
\(190\) 8667.46 3.30949
\(191\) −837.383 −0.317230 −0.158615 0.987341i \(-0.550703\pi\)
−0.158615 + 0.987341i \(0.550703\pi\)
\(192\) 2482.61 0.933161
\(193\) −3423.57 −1.27686 −0.638430 0.769680i \(-0.720416\pi\)
−0.638430 + 0.769680i \(0.720416\pi\)
\(194\) −1078.62 −0.399176
\(195\) 1503.66 0.552203
\(196\) 1266.45 0.461535
\(197\) 3978.23 1.43877 0.719383 0.694613i \(-0.244425\pi\)
0.719383 + 0.694613i \(0.244425\pi\)
\(198\) −1985.32 −0.712579
\(199\) 2224.15 0.792290 0.396145 0.918188i \(-0.370348\pi\)
0.396145 + 0.918188i \(0.370348\pi\)
\(200\) 3750.73 1.32608
\(201\) −1993.87 −0.699684
\(202\) 8279.44 2.88386
\(203\) −6145.58 −2.12480
\(204\) −4216.49 −1.44712
\(205\) 5819.26 1.98261
\(206\) −6584.58 −2.22703
\(207\) −129.551 −0.0434997
\(208\) 18.7540 0.00625171
\(209\) 5356.74 1.77289
\(210\) −4906.91 −1.61242
\(211\) 1783.56 0.581921 0.290961 0.956735i \(-0.406025\pi\)
0.290961 + 0.956735i \(0.406025\pi\)
\(212\) 3326.02 1.07751
\(213\) −622.261 −0.200172
\(214\) −1972.89 −0.630205
\(215\) −5535.19 −1.75580
\(216\) −615.850 −0.193997
\(217\) 4547.98 1.42275
\(218\) 2103.48 0.653513
\(219\) −135.928 −0.0419413
\(220\) 10634.9 3.25912
\(221\) 3190.16 0.971011
\(222\) 2315.60 0.700059
\(223\) 477.801 0.143479 0.0717397 0.997423i \(-0.477145\pi\)
0.0717397 + 0.997423i \(0.477145\pi\)
\(224\) 3768.89 1.12420
\(225\) 1479.95 0.438504
\(226\) −4624.18 −1.36105
\(227\) 2763.61 0.808050 0.404025 0.914748i \(-0.367611\pi\)
0.404025 + 0.914748i \(0.367611\pi\)
\(228\) 4331.14 1.25805
\(229\) 2794.53 0.806408 0.403204 0.915110i \(-0.367896\pi\)
0.403204 + 0.915110i \(0.367896\pi\)
\(230\) 1121.70 0.321578
\(231\) −3032.61 −0.863772
\(232\) 6678.30 1.88988
\(233\) 6224.12 1.75002 0.875012 0.484102i \(-0.160854\pi\)
0.875012 + 0.484102i \(0.160854\pi\)
\(234\) 1214.49 0.339289
\(235\) 5369.04 1.49037
\(236\) 765.807 0.211228
\(237\) 2439.26 0.668553
\(238\) −10410.5 −2.83534
\(239\) −2721.14 −0.736468 −0.368234 0.929733i \(-0.620037\pi\)
−0.368234 + 0.929733i \(0.620037\pi\)
\(240\) 32.4895 0.00873828
\(241\) 2695.03 0.720340 0.360170 0.932887i \(-0.382719\pi\)
0.360170 + 0.932887i \(0.382719\pi\)
\(242\) 4527.24 1.20257
\(243\) −243.000 −0.0641500
\(244\) −9722.12 −2.55080
\(245\) −1659.97 −0.432863
\(246\) 4700.14 1.21817
\(247\) −3276.90 −0.844147
\(248\) −4942.22 −1.26545
\(249\) −57.6167 −0.0146639
\(250\) −3073.29 −0.777487
\(251\) −1146.02 −0.288191 −0.144096 0.989564i \(-0.546027\pi\)
−0.144096 + 0.989564i \(0.546027\pi\)
\(252\) −2451.99 −0.612939
\(253\) 693.245 0.172269
\(254\) 1795.63 0.443574
\(255\) 5526.65 1.35722
\(256\) −4161.69 −1.01604
\(257\) −964.525 −0.234107 −0.117053 0.993126i \(-0.537345\pi\)
−0.117053 + 0.993126i \(0.537345\pi\)
\(258\) −4470.70 −1.07881
\(259\) 3537.12 0.848596
\(260\) −6505.74 −1.55180
\(261\) 2635.10 0.624938
\(262\) 8166.26 1.92562
\(263\) −5111.64 −1.19847 −0.599234 0.800574i \(-0.704528\pi\)
−0.599234 + 0.800574i \(0.704528\pi\)
\(264\) 3295.49 0.768271
\(265\) −4359.49 −1.01057
\(266\) 10693.5 2.46490
\(267\) 1908.26 0.437392
\(268\) 8626.65 1.96626
\(269\) −4488.46 −1.01735 −0.508673 0.860960i \(-0.669864\pi\)
−0.508673 + 0.860960i \(0.669864\pi\)
\(270\) 2103.99 0.474239
\(271\) 4399.29 0.986118 0.493059 0.869996i \(-0.335879\pi\)
0.493059 + 0.869996i \(0.335879\pi\)
\(272\) 68.9295 0.0153657
\(273\) 1855.15 0.411278
\(274\) −3557.87 −0.784448
\(275\) −7919.40 −1.73657
\(276\) 560.515 0.122243
\(277\) −4750.92 −1.03052 −0.515262 0.857033i \(-0.672305\pi\)
−0.515262 + 0.857033i \(0.672305\pi\)
\(278\) −2542.20 −0.548456
\(279\) −1950.08 −0.418453
\(280\) 8145.12 1.73844
\(281\) 8074.21 1.71412 0.857058 0.515219i \(-0.172289\pi\)
0.857058 + 0.515219i \(0.172289\pi\)
\(282\) 4336.51 0.915728
\(283\) 1950.54 0.409708 0.204854 0.978793i \(-0.434328\pi\)
0.204854 + 0.978793i \(0.434328\pi\)
\(284\) 2692.27 0.562525
\(285\) −5676.92 −1.17990
\(286\) −6498.89 −1.34366
\(287\) 7179.55 1.47664
\(288\) −1616.03 −0.330643
\(289\) 6812.30 1.38659
\(290\) −22815.7 −4.61995
\(291\) 706.460 0.142314
\(292\) 588.105 0.117864
\(293\) −7662.67 −1.52784 −0.763921 0.645309i \(-0.776728\pi\)
−0.763921 + 0.645309i \(0.776728\pi\)
\(294\) −1340.74 −0.265964
\(295\) −1003.76 −0.198106
\(296\) −3843.74 −0.754772
\(297\) 1300.32 0.254049
\(298\) 9465.98 1.84010
\(299\) −424.082 −0.0820243
\(300\) −6403.14 −1.23229
\(301\) −6829.07 −1.30771
\(302\) −4223.93 −0.804835
\(303\) −5422.77 −1.02815
\(304\) −70.8037 −0.0133581
\(305\) 12743.0 2.39234
\(306\) 4463.80 0.833917
\(307\) −1433.79 −0.266550 −0.133275 0.991079i \(-0.542549\pi\)
−0.133275 + 0.991079i \(0.542549\pi\)
\(308\) 13120.9 2.42738
\(309\) 4312.69 0.793982
\(310\) 16884.6 3.09348
\(311\) 8645.17 1.57628 0.788140 0.615497i \(-0.211045\pi\)
0.788140 + 0.615497i \(0.211045\pi\)
\(312\) −2015.97 −0.365806
\(313\) 6474.17 1.16914 0.584571 0.811342i \(-0.301263\pi\)
0.584571 + 0.811342i \(0.301263\pi\)
\(314\) −9838.29 −1.76817
\(315\) 3213.87 0.574861
\(316\) −10553.7 −1.87877
\(317\) 5278.69 0.935270 0.467635 0.883922i \(-0.345106\pi\)
0.467635 + 0.883922i \(0.345106\pi\)
\(318\) −3521.11 −0.620924
\(319\) −14100.8 −2.47490
\(320\) 14078.8 2.45946
\(321\) 1292.18 0.224681
\(322\) 1383.91 0.239510
\(323\) −12044.1 −2.07478
\(324\) 1051.36 0.180275
\(325\) 4844.57 0.826856
\(326\) 929.545 0.157923
\(327\) −1377.72 −0.232990
\(328\) −7801.90 −1.31338
\(329\) 6624.09 1.11002
\(330\) −11258.7 −1.87809
\(331\) 7562.70 1.25584 0.627921 0.778277i \(-0.283906\pi\)
0.627921 + 0.778277i \(0.283906\pi\)
\(332\) 249.284 0.0412086
\(333\) −1516.65 −0.249585
\(334\) −9088.19 −1.48887
\(335\) −11307.2 −1.84411
\(336\) 40.0841 0.00650824
\(337\) 1241.33 0.200652 0.100326 0.994955i \(-0.468011\pi\)
0.100326 + 0.994955i \(0.468011\pi\)
\(338\) −6087.48 −0.979631
\(339\) 3028.70 0.485240
\(340\) −23911.6 −3.81408
\(341\) 10435.2 1.65717
\(342\) −4585.18 −0.724965
\(343\) 5151.50 0.810947
\(344\) 7421.05 1.16313
\(345\) −734.680 −0.114649
\(346\) −6798.34 −1.05630
\(347\) 10314.8 1.59576 0.797879 0.602818i \(-0.205956\pi\)
0.797879 + 0.602818i \(0.205956\pi\)
\(348\) −11401.0 −1.75620
\(349\) 6190.01 0.949409 0.474704 0.880145i \(-0.342555\pi\)
0.474704 + 0.880145i \(0.342555\pi\)
\(350\) −15809.3 −2.41441
\(351\) −795.453 −0.120963
\(352\) 8647.56 1.30942
\(353\) 2309.30 0.348191 0.174096 0.984729i \(-0.444300\pi\)
0.174096 + 0.984729i \(0.444300\pi\)
\(354\) −810.725 −0.121722
\(355\) −3528.82 −0.527579
\(356\) −8256.27 −1.22916
\(357\) 6818.54 1.01086
\(358\) −2503.24 −0.369554
\(359\) 12546.4 1.84449 0.922244 0.386608i \(-0.126353\pi\)
0.922244 + 0.386608i \(0.126353\pi\)
\(360\) −3492.47 −0.511303
\(361\) 5512.60 0.803703
\(362\) −20895.5 −3.03383
\(363\) −2965.20 −0.428741
\(364\) −8026.50 −1.15578
\(365\) −770.842 −0.110542
\(366\) 10292.4 1.46992
\(367\) −9343.94 −1.32902 −0.664509 0.747280i \(-0.731359\pi\)
−0.664509 + 0.747280i \(0.731359\pi\)
\(368\) −9.16309 −0.00129799
\(369\) −3078.45 −0.434302
\(370\) 13131.7 1.84509
\(371\) −5378.55 −0.752670
\(372\) 8437.23 1.17594
\(373\) −8906.58 −1.23637 −0.618184 0.786033i \(-0.712131\pi\)
−0.618184 + 0.786033i \(0.712131\pi\)
\(374\) −23886.4 −3.30250
\(375\) 2012.91 0.277190
\(376\) −7198.30 −0.987297
\(377\) 8625.92 1.17840
\(378\) 2595.81 0.353211
\(379\) 3568.77 0.483681 0.241841 0.970316i \(-0.422249\pi\)
0.241841 + 0.970316i \(0.422249\pi\)
\(380\) 24561.7 3.31576
\(381\) −1176.08 −0.158143
\(382\) −3835.52 −0.513724
\(383\) −9195.63 −1.22683 −0.613414 0.789762i \(-0.710204\pi\)
−0.613414 + 0.789762i \(0.710204\pi\)
\(384\) 7061.87 0.938475
\(385\) −17197.9 −2.27658
\(386\) −15681.2 −2.06775
\(387\) 2928.17 0.384618
\(388\) −3056.57 −0.399932
\(389\) −7464.36 −0.972900 −0.486450 0.873708i \(-0.661708\pi\)
−0.486450 + 0.873708i \(0.661708\pi\)
\(390\) 6887.33 0.894240
\(391\) −1558.69 −0.201602
\(392\) 2225.53 0.286750
\(393\) −5348.64 −0.686523
\(394\) 18221.8 2.32995
\(395\) 13833.0 1.76206
\(396\) −5625.98 −0.713929
\(397\) 9258.84 1.17050 0.585249 0.810853i \(-0.300997\pi\)
0.585249 + 0.810853i \(0.300997\pi\)
\(398\) 10187.4 1.28304
\(399\) −7003.94 −0.878786
\(400\) 104.676 0.0130845
\(401\) −9944.75 −1.23845 −0.619224 0.785215i \(-0.712553\pi\)
−0.619224 + 0.785215i \(0.712553\pi\)
\(402\) −9132.64 −1.13307
\(403\) −6383.54 −0.789049
\(404\) 23462.1 2.88932
\(405\) −1378.05 −0.169076
\(406\) −28149.0 −3.44092
\(407\) 8115.78 0.988414
\(408\) −7409.59 −0.899092
\(409\) −2770.27 −0.334917 −0.167459 0.985879i \(-0.553556\pi\)
−0.167459 + 0.985879i \(0.553556\pi\)
\(410\) 26654.3 3.21064
\(411\) 2330.29 0.279671
\(412\) −18659.3 −2.23125
\(413\) −1238.40 −0.147549
\(414\) −593.392 −0.0704436
\(415\) −326.743 −0.0386486
\(416\) −5290.01 −0.623471
\(417\) 1665.06 0.195536
\(418\) 24535.9 2.87103
\(419\) −10519.7 −1.22654 −0.613272 0.789872i \(-0.710147\pi\)
−0.613272 + 0.789872i \(0.710147\pi\)
\(420\) −13905.1 −1.61548
\(421\) −15029.7 −1.73991 −0.869957 0.493127i \(-0.835854\pi\)
−0.869957 + 0.493127i \(0.835854\pi\)
\(422\) 8169.37 0.942366
\(423\) −2840.28 −0.326475
\(424\) 5844.79 0.669453
\(425\) 17806.0 2.03228
\(426\) −2850.19 −0.324160
\(427\) 15721.8 1.78180
\(428\) −5590.74 −0.631399
\(429\) 4256.57 0.479042
\(430\) −25353.2 −2.84335
\(431\) −5056.76 −0.565140 −0.282570 0.959247i \(-0.591187\pi\)
−0.282570 + 0.959247i \(0.591187\pi\)
\(432\) −17.1873 −0.00191417
\(433\) −10275.6 −1.14045 −0.570226 0.821488i \(-0.693144\pi\)
−0.570226 + 0.821488i \(0.693144\pi\)
\(434\) 20831.5 2.30401
\(435\) 14943.6 1.64710
\(436\) 5960.82 0.654751
\(437\) 1601.08 0.175263
\(438\) −622.600 −0.0679200
\(439\) −1490.51 −0.162046 −0.0810232 0.996712i \(-0.525819\pi\)
−0.0810232 + 0.996712i \(0.525819\pi\)
\(440\) 18688.6 2.02488
\(441\) 878.140 0.0948213
\(442\) 14612.1 1.57246
\(443\) −1892.30 −0.202948 −0.101474 0.994838i \(-0.532356\pi\)
−0.101474 + 0.994838i \(0.532356\pi\)
\(444\) 6561.92 0.701385
\(445\) 10821.7 1.15280
\(446\) 2188.50 0.232351
\(447\) −6199.92 −0.656032
\(448\) 17369.8 1.83180
\(449\) −6571.09 −0.690665 −0.345333 0.938480i \(-0.612234\pi\)
−0.345333 + 0.938480i \(0.612234\pi\)
\(450\) 6778.72 0.710115
\(451\) 16473.2 1.71994
\(452\) −13103.9 −1.36362
\(453\) 2766.55 0.286940
\(454\) 12658.4 1.30856
\(455\) 10520.5 1.08398
\(456\) 7611.07 0.781625
\(457\) −5361.76 −0.548824 −0.274412 0.961612i \(-0.588483\pi\)
−0.274412 + 0.961612i \(0.588483\pi\)
\(458\) 12800.0 1.30590
\(459\) −2923.65 −0.297308
\(460\) 3178.67 0.322187
\(461\) −1940.27 −0.196025 −0.0980125 0.995185i \(-0.531249\pi\)
−0.0980125 + 0.995185i \(0.531249\pi\)
\(462\) −13890.5 −1.39880
\(463\) −9369.84 −0.940504 −0.470252 0.882532i \(-0.655837\pi\)
−0.470252 + 0.882532i \(0.655837\pi\)
\(464\) 186.379 0.0186475
\(465\) −11058.9 −1.10289
\(466\) 28508.8 2.83400
\(467\) −10643.9 −1.05469 −0.527344 0.849652i \(-0.676812\pi\)
−0.527344 + 0.849652i \(0.676812\pi\)
\(468\) 3441.60 0.339932
\(469\) −13950.3 −1.37348
\(470\) 24592.2 2.41352
\(471\) 6443.77 0.630389
\(472\) 1345.75 0.131235
\(473\) −15669.0 −1.52318
\(474\) 11172.7 1.08266
\(475\) −18290.2 −1.76676
\(476\) −29501.1 −2.84071
\(477\) 2306.22 0.221372
\(478\) −12463.8 −1.19264
\(479\) −787.956 −0.0751620 −0.0375810 0.999294i \(-0.511965\pi\)
−0.0375810 + 0.999294i \(0.511965\pi\)
\(480\) −9164.43 −0.871452
\(481\) −4964.70 −0.470625
\(482\) 12344.2 1.16652
\(483\) −906.417 −0.0853901
\(484\) 12829.2 1.20485
\(485\) 4006.31 0.375087
\(486\) −1113.03 −0.103885
\(487\) −11562.0 −1.07582 −0.537908 0.843004i \(-0.680785\pi\)
−0.537908 + 0.843004i \(0.680785\pi\)
\(488\) −17084.6 −1.58480
\(489\) −608.823 −0.0563025
\(490\) −7603.27 −0.700981
\(491\) −784.077 −0.0720670 −0.0360335 0.999351i \(-0.511472\pi\)
−0.0360335 + 0.999351i \(0.511472\pi\)
\(492\) 13319.2 1.22048
\(493\) 31704.2 2.89632
\(494\) −15009.4 −1.36702
\(495\) 7374.10 0.669578
\(496\) −137.928 −0.0124862
\(497\) −4353.71 −0.392939
\(498\) −263.906 −0.0237468
\(499\) 1378.28 0.123648 0.0618238 0.998087i \(-0.480308\pi\)
0.0618238 + 0.998087i \(0.480308\pi\)
\(500\) −8709.04 −0.778960
\(501\) 5952.48 0.530813
\(502\) −5249.18 −0.466698
\(503\) −1919.94 −0.170190 −0.0850952 0.996373i \(-0.527119\pi\)
−0.0850952 + 0.996373i \(0.527119\pi\)
\(504\) −4308.85 −0.380817
\(505\) −30752.4 −2.70983
\(506\) 3175.32 0.278973
\(507\) 3987.11 0.349258
\(508\) 5088.43 0.444414
\(509\) −20478.5 −1.78329 −0.891646 0.452734i \(-0.850449\pi\)
−0.891646 + 0.452734i \(0.850449\pi\)
\(510\) 25314.1 2.19789
\(511\) −951.032 −0.0823311
\(512\) −230.457 −0.0198923
\(513\) 3003.15 0.258464
\(514\) −4417.88 −0.379113
\(515\) 24457.1 2.09264
\(516\) −12669.0 −1.08086
\(517\) 15198.7 1.29292
\(518\) 16201.3 1.37422
\(519\) 4452.70 0.376593
\(520\) −11432.5 −0.964129
\(521\) 15109.6 1.27056 0.635280 0.772282i \(-0.280885\pi\)
0.635280 + 0.772282i \(0.280885\pi\)
\(522\) 12069.7 1.01203
\(523\) −1296.32 −0.108383 −0.0541914 0.998531i \(-0.517258\pi\)
−0.0541914 + 0.998531i \(0.517258\pi\)
\(524\) 23141.4 1.92927
\(525\) 10354.6 0.860785
\(526\) −23413.2 −1.94081
\(527\) −23462.4 −1.93935
\(528\) 91.9713 0.00758056
\(529\) −11959.8 −0.982970
\(530\) −19968.1 −1.63652
\(531\) 531.000 0.0433963
\(532\) 30303.2 2.46957
\(533\) −10077.2 −0.818934
\(534\) 8740.54 0.708315
\(535\) 7327.92 0.592175
\(536\) 15159.5 1.22163
\(537\) 1639.54 0.131753
\(538\) −20558.8 −1.64750
\(539\) −4699.04 −0.375514
\(540\) 5962.24 0.475137
\(541\) −15541.1 −1.23505 −0.617525 0.786551i \(-0.711865\pi\)
−0.617525 + 0.786551i \(0.711865\pi\)
\(542\) 20150.4 1.59692
\(543\) 13685.9 1.08162
\(544\) −19443.2 −1.53239
\(545\) −7812.98 −0.614076
\(546\) 8497.29 0.666027
\(547\) −10003.4 −0.781926 −0.390963 0.920406i \(-0.627858\pi\)
−0.390963 + 0.920406i \(0.627858\pi\)
\(548\) −10082.2 −0.785934
\(549\) −6741.18 −0.524056
\(550\) −36273.8 −2.81222
\(551\) −32566.3 −2.51791
\(552\) 984.989 0.0759491
\(553\) 17066.5 1.31237
\(554\) −21761.0 −1.66883
\(555\) −8600.86 −0.657813
\(556\) −7204.04 −0.549495
\(557\) −8031.77 −0.610982 −0.305491 0.952195i \(-0.598821\pi\)
−0.305491 + 0.952195i \(0.598821\pi\)
\(558\) −8932.11 −0.677646
\(559\) 9585.27 0.725248
\(560\) 227.316 0.0171533
\(561\) 15644.8 1.17741
\(562\) 36982.9 2.77585
\(563\) −8865.46 −0.663649 −0.331825 0.943341i \(-0.607664\pi\)
−0.331825 + 0.943341i \(0.607664\pi\)
\(564\) 12288.7 0.917463
\(565\) 17175.6 1.27891
\(566\) 8934.18 0.663483
\(567\) −1700.17 −0.125927
\(568\) 4731.11 0.349494
\(569\) 20450.1 1.50670 0.753351 0.657619i \(-0.228436\pi\)
0.753351 + 0.657619i \(0.228436\pi\)
\(570\) −26002.4 −1.91074
\(571\) −10105.3 −0.740618 −0.370309 0.928909i \(-0.620748\pi\)
−0.370309 + 0.928909i \(0.620748\pi\)
\(572\) −18416.5 −1.34621
\(573\) 2512.15 0.183153
\(574\) 32885.0 2.39128
\(575\) −2367.03 −0.171673
\(576\) −7447.83 −0.538761
\(577\) 17381.4 1.25407 0.627033 0.778993i \(-0.284269\pi\)
0.627033 + 0.778993i \(0.284269\pi\)
\(578\) 31202.8 2.24544
\(579\) 10270.7 0.737196
\(580\) −64654.8 −4.62870
\(581\) −403.121 −0.0287853
\(582\) 3235.85 0.230464
\(583\) −12340.9 −0.876683
\(584\) 1033.47 0.0732283
\(585\) −4510.99 −0.318814
\(586\) −35097.9 −2.47420
\(587\) 19176.4 1.34837 0.674186 0.738561i \(-0.264495\pi\)
0.674186 + 0.738561i \(0.264495\pi\)
\(588\) −3799.36 −0.266468
\(589\) 24100.4 1.68597
\(590\) −4597.60 −0.320814
\(591\) −11934.7 −0.830672
\(592\) −107.272 −0.00744737
\(593\) −10703.5 −0.741213 −0.370606 0.928790i \(-0.620850\pi\)
−0.370606 + 0.928790i \(0.620850\pi\)
\(594\) 5955.97 0.411408
\(595\) 38667.7 2.66424
\(596\) 26824.6 1.84359
\(597\) −6672.45 −0.457429
\(598\) −1942.45 −0.132831
\(599\) −16229.7 −1.10705 −0.553527 0.832831i \(-0.686719\pi\)
−0.553527 + 0.832831i \(0.686719\pi\)
\(600\) −11252.2 −0.765614
\(601\) 5481.06 0.372009 0.186004 0.982549i \(-0.440446\pi\)
0.186004 + 0.982549i \(0.440446\pi\)
\(602\) −31279.7 −2.11772
\(603\) 5981.60 0.403963
\(604\) −11969.7 −0.806359
\(605\) −16815.6 −1.13000
\(606\) −24838.3 −1.66500
\(607\) −17029.8 −1.13874 −0.569372 0.822080i \(-0.692814\pi\)
−0.569372 + 0.822080i \(0.692814\pi\)
\(608\) 19971.9 1.33218
\(609\) 18436.7 1.22676
\(610\) 58367.7 3.87416
\(611\) −9297.56 −0.615612
\(612\) 12649.5 0.835497
\(613\) 7096.79 0.467597 0.233798 0.972285i \(-0.424884\pi\)
0.233798 + 0.972285i \(0.424884\pi\)
\(614\) −6567.29 −0.431652
\(615\) −17457.8 −1.14466
\(616\) 23057.2 1.50812
\(617\) −9243.83 −0.603148 −0.301574 0.953443i \(-0.597512\pi\)
−0.301574 + 0.953443i \(0.597512\pi\)
\(618\) 19753.7 1.28578
\(619\) 24576.0 1.59579 0.797893 0.602799i \(-0.205948\pi\)
0.797893 + 0.602799i \(0.205948\pi\)
\(620\) 47847.2 3.09934
\(621\) 388.654 0.0251145
\(622\) 39598.1 2.55263
\(623\) 13351.3 0.858603
\(624\) −56.2620 −0.00360943
\(625\) −9139.72 −0.584942
\(626\) 29654.1 1.89332
\(627\) −16070.2 −1.02358
\(628\) −27879.6 −1.77152
\(629\) −18247.5 −1.15672
\(630\) 14720.7 0.930934
\(631\) 16376.8 1.03320 0.516602 0.856226i \(-0.327197\pi\)
0.516602 + 0.856226i \(0.327197\pi\)
\(632\) −18545.9 −1.16727
\(633\) −5350.68 −0.335972
\(634\) 24178.3 1.51458
\(635\) −6669.52 −0.416806
\(636\) −9978.06 −0.622100
\(637\) 2874.56 0.178798
\(638\) −64586.7 −4.00786
\(639\) 1866.78 0.115569
\(640\) 40047.6 2.47347
\(641\) −6614.72 −0.407591 −0.203795 0.979013i \(-0.565328\pi\)
−0.203795 + 0.979013i \(0.565328\pi\)
\(642\) 5918.67 0.363849
\(643\) −18544.9 −1.13739 −0.568693 0.822550i \(-0.692551\pi\)
−0.568693 + 0.822550i \(0.692551\pi\)
\(644\) 3921.70 0.239964
\(645\) 16605.6 1.01371
\(646\) −55166.5 −3.35990
\(647\) 28164.5 1.71137 0.855687 0.517493i \(-0.173135\pi\)
0.855687 + 0.517493i \(0.173135\pi\)
\(648\) 1847.55 0.112004
\(649\) −2841.45 −0.171859
\(650\) 22189.9 1.33902
\(651\) −13644.0 −0.821427
\(652\) 2634.13 0.158222
\(653\) −11520.0 −0.690370 −0.345185 0.938535i \(-0.612184\pi\)
−0.345185 + 0.938535i \(0.612184\pi\)
\(654\) −6310.44 −0.377306
\(655\) −30332.0 −1.80942
\(656\) −217.737 −0.0129591
\(657\) 407.783 0.0242148
\(658\) 30340.8 1.79758
\(659\) −16586.2 −0.980434 −0.490217 0.871600i \(-0.663083\pi\)
−0.490217 + 0.871600i \(0.663083\pi\)
\(660\) −31904.7 −1.88165
\(661\) −15191.8 −0.893935 −0.446967 0.894550i \(-0.647496\pi\)
−0.446967 + 0.894550i \(0.647496\pi\)
\(662\) 34640.0 2.03372
\(663\) −9570.48 −0.560614
\(664\) 438.065 0.0256027
\(665\) −39719.1 −2.31615
\(666\) −6946.81 −0.404179
\(667\) −4214.57 −0.244661
\(668\) −25754.0 −1.49169
\(669\) −1433.40 −0.0828379
\(670\) −51790.9 −2.98636
\(671\) 36072.9 2.07538
\(672\) −11306.7 −0.649054
\(673\) 22990.5 1.31682 0.658410 0.752660i \(-0.271229\pi\)
0.658410 + 0.752660i \(0.271229\pi\)
\(674\) 5685.77 0.324937
\(675\) −4439.85 −0.253170
\(676\) −17250.6 −0.981487
\(677\) −18654.2 −1.05899 −0.529496 0.848313i \(-0.677619\pi\)
−0.529496 + 0.848313i \(0.677619\pi\)
\(678\) 13872.6 0.785800
\(679\) 4942.82 0.279364
\(680\) −42019.6 −2.36967
\(681\) −8290.84 −0.466528
\(682\) 47796.9 2.68363
\(683\) −13970.1 −0.782649 −0.391325 0.920253i \(-0.627983\pi\)
−0.391325 + 0.920253i \(0.627983\pi\)
\(684\) −12993.4 −0.726338
\(685\) 13215.0 0.737110
\(686\) 23595.8 1.31325
\(687\) −8383.58 −0.465580
\(688\) 207.108 0.0114766
\(689\) 7549.32 0.417426
\(690\) −3365.11 −0.185663
\(691\) −4273.34 −0.235261 −0.117631 0.993057i \(-0.537530\pi\)
−0.117631 + 0.993057i \(0.537530\pi\)
\(692\) −19265.0 −1.05830
\(693\) 9097.84 0.498699
\(694\) 47245.6 2.58418
\(695\) 9442.50 0.515359
\(696\) −20034.9 −1.09112
\(697\) −37038.3 −2.01281
\(698\) 28352.5 1.53748
\(699\) −18672.3 −1.01038
\(700\) −44800.2 −2.41898
\(701\) 13904.0 0.749141 0.374570 0.927199i \(-0.377790\pi\)
0.374570 + 0.927199i \(0.377790\pi\)
\(702\) −3643.47 −0.195889
\(703\) 18743.7 1.00559
\(704\) 39854.3 2.13362
\(705\) −16107.1 −0.860468
\(706\) 10577.4 0.563863
\(707\) −37941.0 −2.01827
\(708\) −2297.42 −0.121953
\(709\) 13659.3 0.723533 0.361766 0.932269i \(-0.382174\pi\)
0.361766 + 0.932269i \(0.382174\pi\)
\(710\) −16163.3 −0.854364
\(711\) −7317.79 −0.385989
\(712\) −14508.7 −0.763673
\(713\) 3118.96 0.163823
\(714\) 31231.4 1.63698
\(715\) 24138.9 1.26258
\(716\) −7093.64 −0.370254
\(717\) 8163.42 0.425200
\(718\) 57466.9 2.98697
\(719\) 10745.5 0.557358 0.278679 0.960384i \(-0.410103\pi\)
0.278679 + 0.960384i \(0.410103\pi\)
\(720\) −97.4684 −0.00504505
\(721\) 30174.2 1.55859
\(722\) 25249.7 1.30152
\(723\) −8085.08 −0.415889
\(724\) −59213.5 −3.03957
\(725\) 48145.9 2.46634
\(726\) −13581.7 −0.694305
\(727\) 23351.2 1.19126 0.595632 0.803257i \(-0.296902\pi\)
0.595632 + 0.803257i \(0.296902\pi\)
\(728\) −14104.9 −0.718080
\(729\) 729.000 0.0370370
\(730\) −3530.74 −0.179012
\(731\) 35230.3 1.78254
\(732\) 29166.4 1.47270
\(733\) 17996.9 0.906865 0.453432 0.891291i \(-0.350199\pi\)
0.453432 + 0.891291i \(0.350199\pi\)
\(734\) −42798.7 −2.15222
\(735\) 4979.91 0.249914
\(736\) 2584.67 0.129446
\(737\) −32008.3 −1.59978
\(738\) −14100.4 −0.703311
\(739\) 13155.1 0.654829 0.327415 0.944881i \(-0.393823\pi\)
0.327415 + 0.944881i \(0.393823\pi\)
\(740\) 37212.5 1.84859
\(741\) 9830.71 0.487369
\(742\) −24635.8 −1.21888
\(743\) −25720.3 −1.26997 −0.634984 0.772525i \(-0.718993\pi\)
−0.634984 + 0.772525i \(0.718993\pi\)
\(744\) 14826.7 0.730607
\(745\) −35159.6 −1.72906
\(746\) −40795.4 −2.00218
\(747\) 172.850 0.00846621
\(748\) −67688.9 −3.30876
\(749\) 9040.87 0.441050
\(750\) 9219.86 0.448882
\(751\) −35919.3 −1.74529 −0.872645 0.488356i \(-0.837597\pi\)
−0.872645 + 0.488356i \(0.837597\pi\)
\(752\) −200.891 −0.00974170
\(753\) 3438.05 0.166387
\(754\) 39509.9 1.90831
\(755\) 15689.0 0.756266
\(756\) 7355.96 0.353881
\(757\) −29818.5 −1.43167 −0.715834 0.698271i \(-0.753953\pi\)
−0.715834 + 0.698271i \(0.753953\pi\)
\(758\) 16346.3 0.783276
\(759\) −2079.74 −0.0994593
\(760\) 43162.1 2.06007
\(761\) 35322.2 1.68256 0.841280 0.540600i \(-0.181803\pi\)
0.841280 + 0.540600i \(0.181803\pi\)
\(762\) −5386.89 −0.256097
\(763\) −9639.32 −0.457361
\(764\) −10869.1 −0.514697
\(765\) −16579.9 −0.783593
\(766\) −42119.4 −1.98673
\(767\) 1738.21 0.0818294
\(768\) 12485.1 0.586610
\(769\) −6704.62 −0.314402 −0.157201 0.987567i \(-0.550247\pi\)
−0.157201 + 0.987567i \(0.550247\pi\)
\(770\) −78772.6 −3.68671
\(771\) 2893.57 0.135161
\(772\) −44437.2 −2.07167
\(773\) 10246.4 0.476762 0.238381 0.971172i \(-0.423383\pi\)
0.238381 + 0.971172i \(0.423383\pi\)
\(774\) 13412.1 0.622853
\(775\) −35630.0 −1.65144
\(776\) −5371.28 −0.248476
\(777\) −10611.4 −0.489937
\(778\) −34189.5 −1.57552
\(779\) 38045.4 1.74983
\(780\) 19517.2 0.895934
\(781\) −9989.40 −0.457681
\(782\) −7139.39 −0.326476
\(783\) −7905.30 −0.360808
\(784\) 62.1104 0.00282937
\(785\) 36542.4 1.66147
\(786\) −24498.8 −1.11176
\(787\) 25804.8 1.16880 0.584398 0.811467i \(-0.301331\pi\)
0.584398 + 0.811467i \(0.301331\pi\)
\(788\) 51636.5 2.33436
\(789\) 15334.9 0.691936
\(790\) 63360.1 2.85348
\(791\) 21190.6 0.952528
\(792\) −9886.48 −0.443562
\(793\) −22067.0 −0.988176
\(794\) 42408.9 1.89551
\(795\) 13078.5 0.583454
\(796\) 28869.0 1.28547
\(797\) 7971.15 0.354269 0.177135 0.984187i \(-0.443317\pi\)
0.177135 + 0.984187i \(0.443317\pi\)
\(798\) −32080.6 −1.42311
\(799\) −34172.8 −1.51307
\(800\) −29526.4 −1.30489
\(801\) −5724.78 −0.252528
\(802\) −45550.7 −2.00555
\(803\) −2182.10 −0.0958963
\(804\) −25880.0 −1.13522
\(805\) −5140.26 −0.225056
\(806\) −29239.0 −1.27779
\(807\) 13465.4 0.587365
\(808\) 41229.8 1.79512
\(809\) −1869.81 −0.0812595 −0.0406297 0.999174i \(-0.512936\pi\)
−0.0406297 + 0.999174i \(0.512936\pi\)
\(810\) −6311.96 −0.273802
\(811\) −4096.49 −0.177370 −0.0886851 0.996060i \(-0.528266\pi\)
−0.0886851 + 0.996060i \(0.528266\pi\)
\(812\) −79768.3 −3.44744
\(813\) −13197.9 −0.569336
\(814\) 37173.3 1.60064
\(815\) −3452.62 −0.148393
\(816\) −206.788 −0.00887138
\(817\) −36188.2 −1.54965
\(818\) −12688.9 −0.542367
\(819\) −5565.46 −0.237452
\(820\) 75532.7 3.21673
\(821\) 32856.3 1.39670 0.698350 0.715756i \(-0.253918\pi\)
0.698350 + 0.715756i \(0.253918\pi\)
\(822\) 10673.6 0.452901
\(823\) −1727.41 −0.0731638 −0.0365819 0.999331i \(-0.511647\pi\)
−0.0365819 + 0.999331i \(0.511647\pi\)
\(824\) −32789.8 −1.38627
\(825\) 23758.2 1.00261
\(826\) −5672.32 −0.238941
\(827\) −38654.4 −1.62533 −0.812664 0.582733i \(-0.801983\pi\)
−0.812664 + 0.582733i \(0.801983\pi\)
\(828\) −1681.55 −0.0705770
\(829\) −9211.90 −0.385938 −0.192969 0.981205i \(-0.561812\pi\)
−0.192969 + 0.981205i \(0.561812\pi\)
\(830\) −1496.60 −0.0625877
\(831\) 14252.7 0.594973
\(832\) −24380.2 −1.01590
\(833\) 10565.3 0.439457
\(834\) 7626.59 0.316651
\(835\) 33756.3 1.39902
\(836\) 69529.4 2.87646
\(837\) 5850.25 0.241594
\(838\) −48184.2 −1.98627
\(839\) −44020.8 −1.81140 −0.905701 0.423917i \(-0.860655\pi\)
−0.905701 + 0.423917i \(0.860655\pi\)
\(840\) −24435.4 −1.00369
\(841\) 61336.4 2.51492
\(842\) −68841.7 −2.81763
\(843\) −24222.6 −0.989646
\(844\) 23150.2 0.944152
\(845\) 22610.8 0.920514
\(846\) −13009.5 −0.528696
\(847\) −20746.3 −0.841621
\(848\) 163.117 0.00660551
\(849\) −5851.61 −0.236545
\(850\) 81558.1 3.29108
\(851\) 2425.72 0.0977118
\(852\) −8076.82 −0.324774
\(853\) 14157.1 0.568265 0.284133 0.958785i \(-0.408294\pi\)
0.284133 + 0.958785i \(0.408294\pi\)
\(854\) 72011.5 2.88546
\(855\) 17030.8 0.681216
\(856\) −9824.56 −0.392286
\(857\) −21094.5 −0.840810 −0.420405 0.907337i \(-0.638112\pi\)
−0.420405 + 0.907337i \(0.638112\pi\)
\(858\) 19496.7 0.775764
\(859\) −37442.2 −1.48721 −0.743603 0.668622i \(-0.766885\pi\)
−0.743603 + 0.668622i \(0.766885\pi\)
\(860\) −71845.5 −2.84874
\(861\) −21538.6 −0.852538
\(862\) −23161.8 −0.915191
\(863\) 15063.2 0.594156 0.297078 0.954853i \(-0.403988\pi\)
0.297078 + 0.954853i \(0.403988\pi\)
\(864\) 4848.08 0.190897
\(865\) 25251.1 0.992560
\(866\) −47066.2 −1.84685
\(867\) −20436.9 −0.800546
\(868\) 59031.9 2.30838
\(869\) 39158.4 1.52861
\(870\) 68447.1 2.66733
\(871\) 19580.6 0.761725
\(872\) 10474.9 0.406794
\(873\) −2119.38 −0.0821652
\(874\) 7333.52 0.283821
\(875\) 14083.5 0.544125
\(876\) −1764.31 −0.0680487
\(877\) 32525.7 1.25235 0.626177 0.779681i \(-0.284619\pi\)
0.626177 + 0.779681i \(0.284619\pi\)
\(878\) −6827.11 −0.262419
\(879\) 22988.0 0.882100
\(880\) 521.566 0.0199795
\(881\) −17706.4 −0.677123 −0.338561 0.940944i \(-0.609940\pi\)
−0.338561 + 0.940944i \(0.609940\pi\)
\(882\) 4022.21 0.153554
\(883\) 24205.7 0.922522 0.461261 0.887264i \(-0.347397\pi\)
0.461261 + 0.887264i \(0.347397\pi\)
\(884\) 41407.6 1.57544
\(885\) 3011.28 0.114376
\(886\) −8667.43 −0.328655
\(887\) 36290.4 1.37374 0.686872 0.726778i \(-0.258983\pi\)
0.686872 + 0.726778i \(0.258983\pi\)
\(888\) 11531.2 0.435768
\(889\) −8228.56 −0.310435
\(890\) 49567.3 1.86685
\(891\) −3900.97 −0.146675
\(892\) 6201.75 0.232791
\(893\) 35102.0 1.31539
\(894\) −28397.9 −1.06238
\(895\) 9297.80 0.347253
\(896\) 49409.0 1.84223
\(897\) 1272.24 0.0473568
\(898\) −30098.0 −1.11847
\(899\) −63440.4 −2.35357
\(900\) 19209.4 0.711460
\(901\) 27747.2 1.02596
\(902\) 75453.2 2.78527
\(903\) 20487.2 0.755008
\(904\) −23027.5 −0.847214
\(905\) 77612.5 2.85075
\(906\) 12671.8 0.464671
\(907\) −1572.57 −0.0575705 −0.0287852 0.999586i \(-0.509164\pi\)
−0.0287852 + 0.999586i \(0.509164\pi\)
\(908\) 35871.1 1.31104
\(909\) 16268.3 0.593604
\(910\) 48187.9 1.75540
\(911\) −23504.6 −0.854820 −0.427410 0.904058i \(-0.640574\pi\)
−0.427410 + 0.904058i \(0.640574\pi\)
\(912\) 212.411 0.00771232
\(913\) −924.944 −0.0335281
\(914\) −24558.8 −0.888768
\(915\) −38229.0 −1.38122
\(916\) 36272.4 1.30838
\(917\) −37422.3 −1.34765
\(918\) −13391.4 −0.481462
\(919\) −28818.0 −1.03440 −0.517202 0.855863i \(-0.673026\pi\)
−0.517202 + 0.855863i \(0.673026\pi\)
\(920\) 5585.84 0.200174
\(921\) 4301.37 0.153892
\(922\) −8887.17 −0.317444
\(923\) 6110.86 0.217921
\(924\) −39362.7 −1.40145
\(925\) −27710.7 −0.984995
\(926\) −42917.3 −1.52306
\(927\) −12938.1 −0.458406
\(928\) −52572.7 −1.85968
\(929\) −40908.5 −1.44474 −0.722370 0.691506i \(-0.756947\pi\)
−0.722370 + 0.691506i \(0.756947\pi\)
\(930\) −50653.7 −1.78602
\(931\) −10852.6 −0.382041
\(932\) 80787.7 2.83937
\(933\) −25935.5 −0.910065
\(934\) −48752.9 −1.70797
\(935\) 88721.4 3.10321
\(936\) 6047.90 0.211198
\(937\) 42875.5 1.49486 0.747428 0.664343i \(-0.231289\pi\)
0.747428 + 0.664343i \(0.231289\pi\)
\(938\) −63897.4 −2.22423
\(939\) −19422.5 −0.675005
\(940\) 69689.0 2.41809
\(941\) 12952.0 0.448697 0.224348 0.974509i \(-0.427975\pi\)
0.224348 + 0.974509i \(0.427975\pi\)
\(942\) 29514.9 1.02086
\(943\) 4923.66 0.170028
\(944\) 37.5574 0.00129490
\(945\) −9641.62 −0.331896
\(946\) −71769.9 −2.46664
\(947\) −11075.5 −0.380046 −0.190023 0.981780i \(-0.560856\pi\)
−0.190023 + 0.981780i \(0.560856\pi\)
\(948\) 31661.1 1.08471
\(949\) 1334.87 0.0456603
\(950\) −83775.7 −2.86110
\(951\) −15836.1 −0.539978
\(952\) −51841.9 −1.76492
\(953\) −16254.9 −0.552515 −0.276257 0.961084i \(-0.589094\pi\)
−0.276257 + 0.961084i \(0.589094\pi\)
\(954\) 10563.3 0.358491
\(955\) 14246.3 0.482722
\(956\) −35319.8 −1.19490
\(957\) 42302.3 1.42888
\(958\) −3609.13 −0.121718
\(959\) 16304.1 0.548997
\(960\) −42236.4 −1.41997
\(961\) 17157.5 0.575930
\(962\) −22740.2 −0.762133
\(963\) −3876.54 −0.129719
\(964\) 34980.9 1.16873
\(965\) 58244.9 1.94297
\(966\) −4151.73 −0.138281
\(967\) 17700.6 0.588637 0.294318 0.955707i \(-0.404907\pi\)
0.294318 + 0.955707i \(0.404907\pi\)
\(968\) 22544.7 0.748569
\(969\) 36132.3 1.19787
\(970\) 18350.4 0.607418
\(971\) 37930.1 1.25359 0.626794 0.779185i \(-0.284367\pi\)
0.626794 + 0.779185i \(0.284367\pi\)
\(972\) −3154.09 −0.104082
\(973\) 11649.8 0.383837
\(974\) −52958.0 −1.74218
\(975\) −14533.7 −0.477386
\(976\) −476.800 −0.0156373
\(977\) −14003.7 −0.458565 −0.229283 0.973360i \(-0.573638\pi\)
−0.229283 + 0.973360i \(0.573638\pi\)
\(978\) −2788.64 −0.0911766
\(979\) 30634.0 1.00007
\(980\) −21546.0 −0.702309
\(981\) 4133.15 0.134517
\(982\) −3591.36 −0.116706
\(983\) −34728.6 −1.12683 −0.563413 0.826175i \(-0.690512\pi\)
−0.563413 + 0.826175i \(0.690512\pi\)
\(984\) 23405.7 0.758279
\(985\) −67681.2 −2.18934
\(986\) 145217. 4.69031
\(987\) −19872.3 −0.640873
\(988\) −42533.5 −1.36961
\(989\) −4683.31 −0.150577
\(990\) 33776.1 1.08432
\(991\) 48169.3 1.54405 0.772023 0.635595i \(-0.219245\pi\)
0.772023 + 0.635595i \(0.219245\pi\)
\(992\) 38906.0 1.24523
\(993\) −22688.1 −0.725060
\(994\) −19941.6 −0.636327
\(995\) −37839.2 −1.20561
\(996\) −747.853 −0.0237918
\(997\) −15159.6 −0.481553 −0.240776 0.970581i \(-0.577402\pi\)
−0.240776 + 0.970581i \(0.577402\pi\)
\(998\) 6313.01 0.200235
\(999\) 4549.94 0.144098
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.4.a.b.1.7 7
3.2 odd 2 531.4.a.c.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.4.a.b.1.7 7 1.1 even 1 trivial
531.4.a.c.1.1 7 3.2 odd 2