Properties

Label 547.2.a.b.1.18
Level $547$
Weight $2$
Character 547.1
Self dual yes
Analytic conductor $4.368$
Analytic rank $1$
Dimension $18$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.36781699056\)
Analytic rank: \(1\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} - 137 x^{10} - 7703 x^{9} + 2068 x^{8} + 11068 x^{7} - 4274 x^{6} - 9021 x^{5} + 4048 x^{4} + 3834 x^{3} - 1851 x^{2} - 654 x + 328\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Root \(-2.50138\) of defining polynomial
Character \(\chi\) \(=\) 547.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.50138 q^{2} -3.08733 q^{3} +4.25691 q^{4} -3.57921 q^{5} -7.72259 q^{6} +1.44216 q^{7} +5.64540 q^{8} +6.53160 q^{9} +O(q^{10})\) \(q+2.50138 q^{2} -3.08733 q^{3} +4.25691 q^{4} -3.57921 q^{5} -7.72259 q^{6} +1.44216 q^{7} +5.64540 q^{8} +6.53160 q^{9} -8.95298 q^{10} -5.34528 q^{11} -13.1425 q^{12} -5.39279 q^{13} +3.60739 q^{14} +11.0502 q^{15} +5.60749 q^{16} -5.31413 q^{17} +16.3380 q^{18} +2.56610 q^{19} -15.2364 q^{20} -4.45242 q^{21} -13.3706 q^{22} -6.63074 q^{23} -17.4292 q^{24} +7.81075 q^{25} -13.4894 q^{26} -10.9032 q^{27} +6.13915 q^{28} +5.19544 q^{29} +27.6408 q^{30} +4.77081 q^{31} +2.73566 q^{32} +16.5026 q^{33} -13.2927 q^{34} -5.16179 q^{35} +27.8045 q^{36} -3.44033 q^{37} +6.41880 q^{38} +16.6493 q^{39} -20.2061 q^{40} +8.38934 q^{41} -11.1372 q^{42} +5.49566 q^{43} -22.7544 q^{44} -23.3780 q^{45} -16.5860 q^{46} -0.427891 q^{47} -17.3122 q^{48} -4.92018 q^{49} +19.5377 q^{50} +16.4065 q^{51} -22.9566 q^{52} -3.73075 q^{53} -27.2731 q^{54} +19.1319 q^{55} +8.14157 q^{56} -7.92240 q^{57} +12.9958 q^{58} +2.87686 q^{59} +47.0398 q^{60} -3.71286 q^{61} +11.9336 q^{62} +9.41961 q^{63} -4.37204 q^{64} +19.3019 q^{65} +41.2794 q^{66} +6.57367 q^{67} -22.6218 q^{68} +20.4713 q^{69} -12.9116 q^{70} -11.1354 q^{71} +36.8735 q^{72} -0.468824 q^{73} -8.60558 q^{74} -24.1144 q^{75} +10.9237 q^{76} -7.70874 q^{77} +41.6463 q^{78} +5.80618 q^{79} -20.0704 q^{80} +14.0670 q^{81} +20.9849 q^{82} +0.338379 q^{83} -18.9536 q^{84} +19.0204 q^{85} +13.7467 q^{86} -16.0400 q^{87} -30.1763 q^{88} +1.79829 q^{89} -58.4773 q^{90} -7.77726 q^{91} -28.2265 q^{92} -14.7291 q^{93} -1.07032 q^{94} -9.18462 q^{95} -8.44588 q^{96} -11.5278 q^{97} -12.3072 q^{98} -34.9132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} + O(q^{10}) \) \( 18q - 4q^{2} - 10q^{3} + 16q^{4} - 27q^{5} - 3q^{6} - 11q^{7} - 12q^{8} + 14q^{9} - 5q^{10} + 2q^{11} - 32q^{12} - 25q^{13} - 7q^{14} + 9q^{15} + 8q^{16} - 30q^{17} - 10q^{18} + 4q^{19} - 41q^{20} - 16q^{21} - 24q^{22} - 26q^{23} - 12q^{24} + 31q^{25} - 18q^{26} - 37q^{27} - 16q^{28} - 18q^{29} + 8q^{30} - 5q^{31} - 28q^{32} - 10q^{33} + 5q^{34} - 9q^{35} + 31q^{36} - 18q^{37} - 45q^{38} + 7q^{39} + 7q^{40} - 17q^{41} + 4q^{42} + 8q^{43} + 12q^{44} - 44q^{45} + 30q^{46} - 52q^{47} - 7q^{48} + 29q^{49} + 13q^{50} + 19q^{51} - 14q^{52} - 60q^{53} + 11q^{54} + 11q^{55} + 7q^{56} + 4q^{57} + 14q^{58} - 8q^{59} + 86q^{60} - 26q^{61} + 4q^{62} - q^{63} + 44q^{64} - 6q^{65} + 18q^{66} + 12q^{67} - 61q^{68} - 38q^{69} + 35q^{70} - q^{71} + 28q^{72} - 2q^{73} + 16q^{74} - 17q^{75} + 66q^{76} - 73q^{77} + 115q^{78} + 18q^{79} - 32q^{80} + 18q^{81} + 44q^{82} - 43q^{83} + 41q^{84} + 51q^{85} + 4q^{86} + 3q^{87} - 17q^{88} - 28q^{89} + 58q^{90} - q^{91} - 68q^{92} - 60q^{93} + 78q^{94} - 18q^{95} + 29q^{96} - 34q^{97} + 34q^{98} + 15q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.50138 1.76874 0.884372 0.466782i \(-0.154587\pi\)
0.884372 + 0.466782i \(0.154587\pi\)
\(3\) −3.08733 −1.78247 −0.891235 0.453541i \(-0.850160\pi\)
−0.891235 + 0.453541i \(0.850160\pi\)
\(4\) 4.25691 2.12846
\(5\) −3.57921 −1.60067 −0.800336 0.599552i \(-0.795346\pi\)
−0.800336 + 0.599552i \(0.795346\pi\)
\(6\) −7.72259 −3.15273
\(7\) 1.44216 0.545085 0.272542 0.962144i \(-0.412135\pi\)
0.272542 + 0.962144i \(0.412135\pi\)
\(8\) 5.64540 1.99595
\(9\) 6.53160 2.17720
\(10\) −8.95298 −2.83118
\(11\) −5.34528 −1.61166 −0.805831 0.592145i \(-0.798281\pi\)
−0.805831 + 0.592145i \(0.798281\pi\)
\(12\) −13.1425 −3.79391
\(13\) −5.39279 −1.49569 −0.747845 0.663873i \(-0.768911\pi\)
−0.747845 + 0.663873i \(0.768911\pi\)
\(14\) 3.60739 0.964116
\(15\) 11.0502 2.85315
\(16\) 5.60749 1.40187
\(17\) −5.31413 −1.28887 −0.644433 0.764661i \(-0.722907\pi\)
−0.644433 + 0.764661i \(0.722907\pi\)
\(18\) 16.3380 3.85091
\(19\) 2.56610 0.588704 0.294352 0.955697i \(-0.404896\pi\)
0.294352 + 0.955697i \(0.404896\pi\)
\(20\) −15.2364 −3.40696
\(21\) −4.45242 −0.971598
\(22\) −13.3706 −2.85062
\(23\) −6.63074 −1.38260 −0.691302 0.722566i \(-0.742963\pi\)
−0.691302 + 0.722566i \(0.742963\pi\)
\(24\) −17.4292 −3.55772
\(25\) 7.81075 1.56215
\(26\) −13.4894 −2.64549
\(27\) −10.9032 −2.09832
\(28\) 6.13915 1.16019
\(29\) 5.19544 0.964768 0.482384 0.875960i \(-0.339771\pi\)
0.482384 + 0.875960i \(0.339771\pi\)
\(30\) 27.6408 5.04649
\(31\) 4.77081 0.856864 0.428432 0.903574i \(-0.359066\pi\)
0.428432 + 0.903574i \(0.359066\pi\)
\(32\) 2.73566 0.483601
\(33\) 16.5026 2.87274
\(34\) −13.2927 −2.27967
\(35\) −5.16179 −0.872502
\(36\) 27.8045 4.63408
\(37\) −3.44033 −0.565586 −0.282793 0.959181i \(-0.591261\pi\)
−0.282793 + 0.959181i \(0.591261\pi\)
\(38\) 6.41880 1.04127
\(39\) 16.6493 2.66602
\(40\) −20.2061 −3.19486
\(41\) 8.38934 1.31019 0.655097 0.755545i \(-0.272628\pi\)
0.655097 + 0.755545i \(0.272628\pi\)
\(42\) −11.1372 −1.71851
\(43\) 5.49566 0.838080 0.419040 0.907968i \(-0.362367\pi\)
0.419040 + 0.907968i \(0.362367\pi\)
\(44\) −22.7544 −3.43035
\(45\) −23.3780 −3.48498
\(46\) −16.5860 −2.44547
\(47\) −0.427891 −0.0624143 −0.0312072 0.999513i \(-0.509935\pi\)
−0.0312072 + 0.999513i \(0.509935\pi\)
\(48\) −17.3122 −2.49879
\(49\) −4.92018 −0.702882
\(50\) 19.5377 2.76304
\(51\) 16.4065 2.29737
\(52\) −22.9566 −3.18351
\(53\) −3.73075 −0.512458 −0.256229 0.966616i \(-0.582480\pi\)
−0.256229 + 0.966616i \(0.582480\pi\)
\(54\) −27.2731 −3.71140
\(55\) 19.1319 2.57974
\(56\) 8.14157 1.08796
\(57\) −7.92240 −1.04935
\(58\) 12.9958 1.70643
\(59\) 2.87686 0.374535 0.187268 0.982309i \(-0.440037\pi\)
0.187268 + 0.982309i \(0.440037\pi\)
\(60\) 47.0398 6.07281
\(61\) −3.71286 −0.475383 −0.237691 0.971341i \(-0.576391\pi\)
−0.237691 + 0.971341i \(0.576391\pi\)
\(62\) 11.9336 1.51557
\(63\) 9.41961 1.18676
\(64\) −4.37204 −0.546505
\(65\) 19.3019 2.39411
\(66\) 41.2794 5.08114
\(67\) 6.57367 0.803101 0.401551 0.915837i \(-0.368471\pi\)
0.401551 + 0.915837i \(0.368471\pi\)
\(68\) −22.6218 −2.74330
\(69\) 20.4713 2.46445
\(70\) −12.9116 −1.54323
\(71\) −11.1354 −1.32153 −0.660764 0.750594i \(-0.729768\pi\)
−0.660764 + 0.750594i \(0.729768\pi\)
\(72\) 36.8735 4.34559
\(73\) −0.468824 −0.0548717 −0.0274359 0.999624i \(-0.508734\pi\)
−0.0274359 + 0.999624i \(0.508734\pi\)
\(74\) −8.60558 −1.00038
\(75\) −24.1144 −2.78449
\(76\) 10.9237 1.25303
\(77\) −7.70874 −0.878493
\(78\) 41.6463 4.71551
\(79\) 5.80618 0.653246 0.326623 0.945155i \(-0.394089\pi\)
0.326623 + 0.945155i \(0.394089\pi\)
\(80\) −20.0704 −2.24394
\(81\) 14.0670 1.56300
\(82\) 20.9849 2.31740
\(83\) 0.338379 0.0371420 0.0185710 0.999828i \(-0.494088\pi\)
0.0185710 + 0.999828i \(0.494088\pi\)
\(84\) −18.9536 −2.06800
\(85\) 19.0204 2.06305
\(86\) 13.7467 1.48235
\(87\) −16.0400 −1.71967
\(88\) −30.1763 −3.21680
\(89\) 1.79829 0.190618 0.0953091 0.995448i \(-0.469616\pi\)
0.0953091 + 0.995448i \(0.469616\pi\)
\(90\) −58.4773 −6.16405
\(91\) −7.77726 −0.815278
\(92\) −28.2265 −2.94281
\(93\) −14.7291 −1.52733
\(94\) −1.07032 −0.110395
\(95\) −9.18462 −0.942322
\(96\) −8.44588 −0.862004
\(97\) −11.5278 −1.17047 −0.585234 0.810864i \(-0.698997\pi\)
−0.585234 + 0.810864i \(0.698997\pi\)
\(98\) −12.3072 −1.24322
\(99\) −34.9132 −3.50891
\(100\) 33.2497 3.32497
\(101\) −6.15589 −0.612534 −0.306267 0.951946i \(-0.599080\pi\)
−0.306267 + 0.951946i \(0.599080\pi\)
\(102\) 41.0389 4.06345
\(103\) 16.0271 1.57920 0.789601 0.613621i \(-0.210288\pi\)
0.789601 + 0.613621i \(0.210288\pi\)
\(104\) −30.4445 −2.98533
\(105\) 15.9362 1.55521
\(106\) −9.33203 −0.906407
\(107\) 0.286864 0.0277322 0.0138661 0.999904i \(-0.495586\pi\)
0.0138661 + 0.999904i \(0.495586\pi\)
\(108\) −46.4140 −4.46619
\(109\) −15.7934 −1.51273 −0.756366 0.654149i \(-0.773027\pi\)
−0.756366 + 0.654149i \(0.773027\pi\)
\(110\) 47.8562 4.56291
\(111\) 10.6214 1.00814
\(112\) 8.08689 0.764139
\(113\) −12.9488 −1.21812 −0.609058 0.793126i \(-0.708452\pi\)
−0.609058 + 0.793126i \(0.708452\pi\)
\(114\) −19.8169 −1.85603
\(115\) 23.7328 2.21310
\(116\) 22.1165 2.05347
\(117\) −35.2235 −3.25642
\(118\) 7.19613 0.662458
\(119\) −7.66382 −0.702541
\(120\) 62.3829 5.69475
\(121\) 17.5720 1.59746
\(122\) −9.28727 −0.840830
\(123\) −25.9006 −2.33538
\(124\) 20.3089 1.82380
\(125\) −10.0603 −0.899818
\(126\) 23.5620 2.09907
\(127\) −2.62312 −0.232764 −0.116382 0.993205i \(-0.537130\pi\)
−0.116382 + 0.993205i \(0.537130\pi\)
\(128\) −16.4075 −1.45023
\(129\) −16.9669 −1.49385
\(130\) 48.2815 4.23457
\(131\) 1.96563 0.171738 0.0858691 0.996306i \(-0.472633\pi\)
0.0858691 + 0.996306i \(0.472633\pi\)
\(132\) 70.2503 6.11450
\(133\) 3.70073 0.320894
\(134\) 16.4433 1.42048
\(135\) 39.0249 3.35873
\(136\) −30.0004 −2.57251
\(137\) −13.8493 −1.18323 −0.591614 0.806221i \(-0.701509\pi\)
−0.591614 + 0.806221i \(0.701509\pi\)
\(138\) 51.2065 4.35899
\(139\) 3.30984 0.280737 0.140368 0.990099i \(-0.455171\pi\)
0.140368 + 0.990099i \(0.455171\pi\)
\(140\) −21.9733 −1.85708
\(141\) 1.32104 0.111252
\(142\) −27.8539 −2.33744
\(143\) 28.8260 2.41055
\(144\) 36.6259 3.05216
\(145\) −18.5956 −1.54428
\(146\) −1.17271 −0.0970541
\(147\) 15.1902 1.25287
\(148\) −14.6452 −1.20383
\(149\) 1.24371 0.101889 0.0509443 0.998701i \(-0.483777\pi\)
0.0509443 + 0.998701i \(0.483777\pi\)
\(150\) −60.3192 −4.92505
\(151\) −19.7224 −1.60499 −0.802494 0.596660i \(-0.796494\pi\)
−0.802494 + 0.596660i \(0.796494\pi\)
\(152\) 14.4867 1.17502
\(153\) −34.7098 −2.80612
\(154\) −19.2825 −1.55383
\(155\) −17.0758 −1.37156
\(156\) 70.8747 5.67452
\(157\) −11.3800 −0.908221 −0.454110 0.890945i \(-0.650043\pi\)
−0.454110 + 0.890945i \(0.650043\pi\)
\(158\) 14.5235 1.15543
\(159\) 11.5181 0.913441
\(160\) −9.79150 −0.774086
\(161\) −9.56258 −0.753637
\(162\) 35.1870 2.76455
\(163\) 2.36146 0.184964 0.0924819 0.995714i \(-0.470520\pi\)
0.0924819 + 0.995714i \(0.470520\pi\)
\(164\) 35.7127 2.78869
\(165\) −59.0664 −4.59832
\(166\) 0.846416 0.0656946
\(167\) 3.39282 0.262544 0.131272 0.991346i \(-0.458094\pi\)
0.131272 + 0.991346i \(0.458094\pi\)
\(168\) −25.1357 −1.93926
\(169\) 16.0822 1.23709
\(170\) 47.5773 3.64901
\(171\) 16.7607 1.28173
\(172\) 23.3945 1.78382
\(173\) −24.1775 −1.83819 −0.919093 0.394042i \(-0.871077\pi\)
−0.919093 + 0.394042i \(0.871077\pi\)
\(174\) −40.1222 −3.04166
\(175\) 11.2643 0.851505
\(176\) −29.9736 −2.25934
\(177\) −8.88182 −0.667598
\(178\) 4.49821 0.337155
\(179\) −9.73639 −0.727732 −0.363866 0.931451i \(-0.618543\pi\)
−0.363866 + 0.931451i \(0.618543\pi\)
\(180\) −99.5180 −7.41764
\(181\) −8.08741 −0.601133 −0.300566 0.953761i \(-0.597176\pi\)
−0.300566 + 0.953761i \(0.597176\pi\)
\(182\) −19.4539 −1.44202
\(183\) 11.4628 0.847355
\(184\) −37.4332 −2.75961
\(185\) 12.3137 0.905318
\(186\) −36.8430 −2.70146
\(187\) 28.4055 2.07722
\(188\) −1.82150 −0.132846
\(189\) −15.7242 −1.14377
\(190\) −22.9742 −1.66673
\(191\) 23.4764 1.69869 0.849347 0.527835i \(-0.176996\pi\)
0.849347 + 0.527835i \(0.176996\pi\)
\(192\) 13.4979 0.974129
\(193\) 0.846561 0.0609368 0.0304684 0.999536i \(-0.490300\pi\)
0.0304684 + 0.999536i \(0.490300\pi\)
\(194\) −28.8354 −2.07026
\(195\) −59.5914 −4.26743
\(196\) −20.9448 −1.49605
\(197\) 24.5035 1.74580 0.872900 0.487900i \(-0.162237\pi\)
0.872900 + 0.487900i \(0.162237\pi\)
\(198\) −87.3314 −6.20637
\(199\) −6.60963 −0.468544 −0.234272 0.972171i \(-0.575271\pi\)
−0.234272 + 0.972171i \(0.575271\pi\)
\(200\) 44.0949 3.11798
\(201\) −20.2951 −1.43150
\(202\) −15.3982 −1.08342
\(203\) 7.49265 0.525881
\(204\) 69.8409 4.88984
\(205\) −30.0272 −2.09719
\(206\) 40.0900 2.79320
\(207\) −43.3093 −3.01021
\(208\) −30.2400 −2.09677
\(209\) −13.7165 −0.948792
\(210\) 39.8624 2.75077
\(211\) 1.49983 0.103253 0.0516264 0.998666i \(-0.483559\pi\)
0.0516264 + 0.998666i \(0.483559\pi\)
\(212\) −15.8815 −1.09074
\(213\) 34.3786 2.35558
\(214\) 0.717556 0.0490511
\(215\) −19.6701 −1.34149
\(216\) −61.5531 −4.18816
\(217\) 6.88027 0.467063
\(218\) −39.5053 −2.67564
\(219\) 1.44741 0.0978072
\(220\) 81.4428 5.49087
\(221\) 28.6580 1.92774
\(222\) 26.5682 1.78314
\(223\) 22.0562 1.47699 0.738497 0.674257i \(-0.235536\pi\)
0.738497 + 0.674257i \(0.235536\pi\)
\(224\) 3.94526 0.263604
\(225\) 51.0167 3.40111
\(226\) −32.3898 −2.15454
\(227\) 9.69637 0.643571 0.321785 0.946813i \(-0.395717\pi\)
0.321785 + 0.946813i \(0.395717\pi\)
\(228\) −33.7250 −2.23349
\(229\) 12.6579 0.836460 0.418230 0.908341i \(-0.362651\pi\)
0.418230 + 0.908341i \(0.362651\pi\)
\(230\) 59.3648 3.91440
\(231\) 23.7994 1.56589
\(232\) 29.3303 1.92563
\(233\) 12.4477 0.815473 0.407736 0.913100i \(-0.366318\pi\)
0.407736 + 0.913100i \(0.366318\pi\)
\(234\) −88.1075 −5.75977
\(235\) 1.53151 0.0999049
\(236\) 12.2466 0.797183
\(237\) −17.9256 −1.16439
\(238\) −19.1701 −1.24262
\(239\) 1.95816 0.126663 0.0633314 0.997993i \(-0.479827\pi\)
0.0633314 + 0.997993i \(0.479827\pi\)
\(240\) 61.9639 3.99975
\(241\) −17.4587 −1.12462 −0.562308 0.826928i \(-0.690086\pi\)
−0.562308 + 0.826928i \(0.690086\pi\)
\(242\) 43.9543 2.82549
\(243\) −10.7199 −0.687679
\(244\) −15.8053 −1.01183
\(245\) 17.6104 1.12508
\(246\) −64.7874 −4.13069
\(247\) −13.8384 −0.880519
\(248\) 26.9332 1.71026
\(249\) −1.04469 −0.0662044
\(250\) −25.1646 −1.59155
\(251\) 3.61597 0.228238 0.114119 0.993467i \(-0.463595\pi\)
0.114119 + 0.993467i \(0.463595\pi\)
\(252\) 40.0985 2.52597
\(253\) 35.4432 2.22829
\(254\) −6.56142 −0.411700
\(255\) −58.7222 −3.67733
\(256\) −32.2973 −2.01858
\(257\) −10.0934 −0.629606 −0.314803 0.949157i \(-0.601939\pi\)
−0.314803 + 0.949157i \(0.601939\pi\)
\(258\) −42.4407 −2.64224
\(259\) −4.96150 −0.308293
\(260\) 82.1666 5.09576
\(261\) 33.9345 2.10049
\(262\) 4.91680 0.303761
\(263\) −5.71252 −0.352249 −0.176124 0.984368i \(-0.556356\pi\)
−0.176124 + 0.984368i \(0.556356\pi\)
\(264\) 93.1641 5.73385
\(265\) 13.3531 0.820277
\(266\) 9.25693 0.567579
\(267\) −5.55191 −0.339771
\(268\) 27.9835 1.70937
\(269\) −11.2319 −0.684820 −0.342410 0.939551i \(-0.611243\pi\)
−0.342410 + 0.939551i \(0.611243\pi\)
\(270\) 97.6162 5.94073
\(271\) −25.7123 −1.56191 −0.780954 0.624588i \(-0.785267\pi\)
−0.780954 + 0.624588i \(0.785267\pi\)
\(272\) −29.7989 −1.80682
\(273\) 24.0110 1.45321
\(274\) −34.6425 −2.09283
\(275\) −41.7507 −2.51766
\(276\) 87.1444 5.24548
\(277\) 10.7925 0.648461 0.324231 0.945978i \(-0.394895\pi\)
0.324231 + 0.945978i \(0.394895\pi\)
\(278\) 8.27916 0.496551
\(279\) 31.1611 1.86556
\(280\) −29.1404 −1.74147
\(281\) 0.316572 0.0188851 0.00944256 0.999955i \(-0.496994\pi\)
0.00944256 + 0.999955i \(0.496994\pi\)
\(282\) 3.30443 0.196776
\(283\) −30.9827 −1.84173 −0.920864 0.389883i \(-0.872515\pi\)
−0.920864 + 0.389883i \(0.872515\pi\)
\(284\) −47.4024 −2.81281
\(285\) 28.3559 1.67966
\(286\) 72.1047 4.26364
\(287\) 12.0988 0.714167
\(288\) 17.8682 1.05290
\(289\) 11.2400 0.661175
\(290\) −46.5146 −2.73143
\(291\) 35.5900 2.08632
\(292\) −1.99574 −0.116792
\(293\) −21.7659 −1.27158 −0.635789 0.771863i \(-0.719325\pi\)
−0.635789 + 0.771863i \(0.719325\pi\)
\(294\) 37.9965 2.21600
\(295\) −10.2969 −0.599508
\(296\) −19.4220 −1.12888
\(297\) 58.2807 3.38179
\(298\) 3.11099 0.180215
\(299\) 35.7582 2.06795
\(300\) −102.653 −5.92666
\(301\) 7.92561 0.456825
\(302\) −49.3333 −2.83881
\(303\) 19.0053 1.09182
\(304\) 14.3894 0.825287
\(305\) 13.2891 0.760932
\(306\) −86.8224 −4.96331
\(307\) 3.11297 0.177667 0.0888334 0.996046i \(-0.471686\pi\)
0.0888334 + 0.996046i \(0.471686\pi\)
\(308\) −32.8155 −1.86983
\(309\) −49.4811 −2.81488
\(310\) −42.7130 −2.42593
\(311\) 27.3164 1.54897 0.774485 0.632592i \(-0.218009\pi\)
0.774485 + 0.632592i \(0.218009\pi\)
\(312\) 93.9921 5.32125
\(313\) 13.8638 0.783630 0.391815 0.920044i \(-0.371847\pi\)
0.391815 + 0.920044i \(0.371847\pi\)
\(314\) −28.4657 −1.60641
\(315\) −33.7148 −1.89961
\(316\) 24.7164 1.39041
\(317\) −14.2600 −0.800923 −0.400461 0.916314i \(-0.631150\pi\)
−0.400461 + 0.916314i \(0.631150\pi\)
\(318\) 28.8111 1.61564
\(319\) −27.7711 −1.55488
\(320\) 15.6485 0.874776
\(321\) −0.885643 −0.0494318
\(322\) −23.9197 −1.33299
\(323\) −13.6366 −0.758761
\(324\) 59.8821 3.32678
\(325\) −42.1217 −2.33649
\(326\) 5.90692 0.327154
\(327\) 48.7594 2.69640
\(328\) 47.3612 2.61508
\(329\) −0.617087 −0.0340211
\(330\) −147.748 −8.13324
\(331\) −14.0211 −0.770667 −0.385334 0.922777i \(-0.625914\pi\)
−0.385334 + 0.922777i \(0.625914\pi\)
\(332\) 1.44045 0.0790550
\(333\) −22.4709 −1.23140
\(334\) 8.48675 0.464374
\(335\) −23.5285 −1.28550
\(336\) −24.9669 −1.36206
\(337\) −2.77663 −0.151253 −0.0756263 0.997136i \(-0.524096\pi\)
−0.0756263 + 0.997136i \(0.524096\pi\)
\(338\) 40.2276 2.18809
\(339\) 39.9771 2.17126
\(340\) 80.9682 4.39112
\(341\) −25.5013 −1.38098
\(342\) 41.9250 2.26705
\(343\) −17.1908 −0.928216
\(344\) 31.0252 1.67277
\(345\) −73.2710 −3.94478
\(346\) −60.4773 −3.25128
\(347\) 34.2051 1.83623 0.918114 0.396317i \(-0.129712\pi\)
0.918114 + 0.396317i \(0.129712\pi\)
\(348\) −68.2810 −3.66025
\(349\) 31.8576 1.70530 0.852649 0.522485i \(-0.174995\pi\)
0.852649 + 0.522485i \(0.174995\pi\)
\(350\) 28.1764 1.50609
\(351\) 58.7987 3.13844
\(352\) −14.6229 −0.779402
\(353\) 19.7596 1.05170 0.525849 0.850578i \(-0.323748\pi\)
0.525849 + 0.850578i \(0.323748\pi\)
\(354\) −22.2168 −1.18081
\(355\) 39.8559 2.11533
\(356\) 7.65516 0.405723
\(357\) 23.6607 1.25226
\(358\) −24.3544 −1.28717
\(359\) 6.12948 0.323501 0.161751 0.986832i \(-0.448286\pi\)
0.161751 + 0.986832i \(0.448286\pi\)
\(360\) −131.978 −6.95586
\(361\) −12.4151 −0.653428
\(362\) −20.2297 −1.06325
\(363\) −54.2506 −2.84742
\(364\) −33.1071 −1.73528
\(365\) 1.67802 0.0878316
\(366\) 28.6729 1.49876
\(367\) −13.4451 −0.701828 −0.350914 0.936408i \(-0.614129\pi\)
−0.350914 + 0.936408i \(0.614129\pi\)
\(368\) −37.1818 −1.93823
\(369\) 54.7958 2.85256
\(370\) 30.8012 1.60128
\(371\) −5.38034 −0.279333
\(372\) −62.7004 −3.25086
\(373\) 12.5335 0.648963 0.324481 0.945892i \(-0.394810\pi\)
0.324481 + 0.945892i \(0.394810\pi\)
\(374\) 71.0531 3.67407
\(375\) 31.0594 1.60390
\(376\) −2.41562 −0.124576
\(377\) −28.0179 −1.44299
\(378\) −39.3322 −2.02303
\(379\) −8.91515 −0.457940 −0.228970 0.973433i \(-0.573536\pi\)
−0.228970 + 0.973433i \(0.573536\pi\)
\(380\) −39.0981 −2.00569
\(381\) 8.09843 0.414895
\(382\) 58.7235 3.00455
\(383\) −8.41053 −0.429758 −0.214879 0.976641i \(-0.568936\pi\)
−0.214879 + 0.976641i \(0.568936\pi\)
\(384\) 50.6553 2.58499
\(385\) 27.5912 1.40618
\(386\) 2.11757 0.107782
\(387\) 35.8954 1.82467
\(388\) −49.0727 −2.49129
\(389\) −6.85721 −0.347674 −0.173837 0.984774i \(-0.555617\pi\)
−0.173837 + 0.984774i \(0.555617\pi\)
\(390\) −149.061 −7.54799
\(391\) 35.2366 1.78199
\(392\) −27.7764 −1.40292
\(393\) −6.06855 −0.306118
\(394\) 61.2925 3.08787
\(395\) −20.7815 −1.04563
\(396\) −148.623 −7.46857
\(397\) −7.82424 −0.392688 −0.196344 0.980535i \(-0.562907\pi\)
−0.196344 + 0.980535i \(0.562907\pi\)
\(398\) −16.5332 −0.828735
\(399\) −11.4254 −0.571983
\(400\) 43.7987 2.18993
\(401\) −16.2178 −0.809879 −0.404939 0.914344i \(-0.632707\pi\)
−0.404939 + 0.914344i \(0.632707\pi\)
\(402\) −50.7657 −2.53197
\(403\) −25.7280 −1.28160
\(404\) −26.2051 −1.30375
\(405\) −50.3488 −2.50185
\(406\) 18.7420 0.930148
\(407\) 18.3895 0.911535
\(408\) 92.6212 4.58543
\(409\) 10.0577 0.497322 0.248661 0.968591i \(-0.420009\pi\)
0.248661 + 0.968591i \(0.420009\pi\)
\(410\) −75.1095 −3.70939
\(411\) 42.7574 2.10907
\(412\) 68.2262 3.36126
\(413\) 4.14889 0.204154
\(414\) −108.333 −5.32429
\(415\) −1.21113 −0.0594521
\(416\) −14.7528 −0.723317
\(417\) −10.2186 −0.500405
\(418\) −34.3103 −1.67817
\(419\) 29.3701 1.43482 0.717412 0.696649i \(-0.245327\pi\)
0.717412 + 0.696649i \(0.245327\pi\)
\(420\) 67.8388 3.31020
\(421\) −28.4591 −1.38701 −0.693507 0.720450i \(-0.743935\pi\)
−0.693507 + 0.720450i \(0.743935\pi\)
\(422\) 3.75166 0.182628
\(423\) −2.79481 −0.135889
\(424\) −21.0616 −1.02284
\(425\) −41.5074 −2.01340
\(426\) 85.9941 4.16643
\(427\) −5.35453 −0.259124
\(428\) 1.22115 0.0590267
\(429\) −88.9952 −4.29673
\(430\) −49.2025 −2.37275
\(431\) −16.8736 −0.812772 −0.406386 0.913701i \(-0.633211\pi\)
−0.406386 + 0.913701i \(0.633211\pi\)
\(432\) −61.1396 −2.94158
\(433\) −17.5129 −0.841615 −0.420807 0.907150i \(-0.638253\pi\)
−0.420807 + 0.907150i \(0.638253\pi\)
\(434\) 17.2102 0.826116
\(435\) 57.4106 2.75263
\(436\) −67.2310 −3.21978
\(437\) −17.0151 −0.813945
\(438\) 3.62054 0.172996
\(439\) −1.19663 −0.0571120 −0.0285560 0.999592i \(-0.509091\pi\)
−0.0285560 + 0.999592i \(0.509091\pi\)
\(440\) 108.007 5.14904
\(441\) −32.1366 −1.53032
\(442\) 71.6846 3.40969
\(443\) −1.77986 −0.0845637 −0.0422819 0.999106i \(-0.513463\pi\)
−0.0422819 + 0.999106i \(0.513463\pi\)
\(444\) 45.2145 2.14578
\(445\) −6.43646 −0.305117
\(446\) 55.1710 2.61242
\(447\) −3.83974 −0.181614
\(448\) −6.30518 −0.297892
\(449\) 35.7981 1.68942 0.844708 0.535227i \(-0.179774\pi\)
0.844708 + 0.535227i \(0.179774\pi\)
\(450\) 127.612 6.01570
\(451\) −44.8433 −2.11159
\(452\) −55.1217 −2.59271
\(453\) 60.8896 2.86084
\(454\) 24.2543 1.13831
\(455\) 27.8364 1.30499
\(456\) −44.7251 −2.09445
\(457\) −9.01813 −0.421850 −0.210925 0.977502i \(-0.567648\pi\)
−0.210925 + 0.977502i \(0.567648\pi\)
\(458\) 31.6623 1.47948
\(459\) 57.9411 2.70446
\(460\) 101.029 4.71048
\(461\) −30.8599 −1.43729 −0.718646 0.695377i \(-0.755238\pi\)
−0.718646 + 0.695377i \(0.755238\pi\)
\(462\) 59.5315 2.76965
\(463\) −1.05816 −0.0491767 −0.0245884 0.999698i \(-0.507828\pi\)
−0.0245884 + 0.999698i \(0.507828\pi\)
\(464\) 29.1333 1.35248
\(465\) 52.7185 2.44476
\(466\) 31.1363 1.44236
\(467\) −34.1893 −1.58209 −0.791047 0.611755i \(-0.790464\pi\)
−0.791047 + 0.611755i \(0.790464\pi\)
\(468\) −149.944 −6.93114
\(469\) 9.48027 0.437758
\(470\) 3.83090 0.176706
\(471\) 35.1337 1.61888
\(472\) 16.2410 0.747555
\(473\) −29.3758 −1.35070
\(474\) −44.8388 −2.05951
\(475\) 20.0432 0.919644
\(476\) −32.6242 −1.49533
\(477\) −24.3678 −1.11572
\(478\) 4.89811 0.224034
\(479\) −30.8709 −1.41053 −0.705265 0.708944i \(-0.749172\pi\)
−0.705265 + 0.708944i \(0.749172\pi\)
\(480\) 30.2296 1.37979
\(481\) 18.5530 0.845942
\(482\) −43.6710 −1.98916
\(483\) 29.5228 1.34334
\(484\) 74.8026 3.40012
\(485\) 41.2603 1.87354
\(486\) −26.8144 −1.21633
\(487\) −23.2537 −1.05373 −0.526863 0.849950i \(-0.676632\pi\)
−0.526863 + 0.849950i \(0.676632\pi\)
\(488\) −20.9606 −0.948841
\(489\) −7.29061 −0.329693
\(490\) 44.0502 1.98999
\(491\) −9.10242 −0.410786 −0.205393 0.978680i \(-0.565847\pi\)
−0.205393 + 0.978680i \(0.565847\pi\)
\(492\) −110.257 −4.97076
\(493\) −27.6092 −1.24346
\(494\) −34.6152 −1.55741
\(495\) 124.962 5.61662
\(496\) 26.7523 1.20121
\(497\) −16.0590 −0.720345
\(498\) −2.61316 −0.117099
\(499\) 25.0594 1.12181 0.560907 0.827879i \(-0.310452\pi\)
0.560907 + 0.827879i \(0.310452\pi\)
\(500\) −42.8257 −1.91522
\(501\) −10.4748 −0.467978
\(502\) 9.04493 0.403695
\(503\) −7.25454 −0.323464 −0.161732 0.986835i \(-0.551708\pi\)
−0.161732 + 0.986835i \(0.551708\pi\)
\(504\) 53.1775 2.36871
\(505\) 22.0332 0.980467
\(506\) 88.6569 3.94128
\(507\) −49.6509 −2.20507
\(508\) −11.1664 −0.495428
\(509\) 1.63509 0.0724740 0.0362370 0.999343i \(-0.488463\pi\)
0.0362370 + 0.999343i \(0.488463\pi\)
\(510\) −146.887 −6.50425
\(511\) −0.676119 −0.0299098
\(512\) −47.9729 −2.12012
\(513\) −27.9788 −1.23529
\(514\) −25.2473 −1.11361
\(515\) −57.3645 −2.52778
\(516\) −72.2266 −3.17960
\(517\) 2.28720 0.100591
\(518\) −12.4106 −0.545291
\(519\) 74.6441 3.27651
\(520\) 108.967 4.77853
\(521\) 32.4953 1.42365 0.711823 0.702359i \(-0.247870\pi\)
0.711823 + 0.702359i \(0.247870\pi\)
\(522\) 84.8832 3.71524
\(523\) 42.1414 1.84272 0.921358 0.388714i \(-0.127081\pi\)
0.921358 + 0.388714i \(0.127081\pi\)
\(524\) 8.36753 0.365537
\(525\) −34.7767 −1.51778
\(526\) −14.2892 −0.623038
\(527\) −25.3527 −1.10438
\(528\) 92.5383 4.02721
\(529\) 20.9667 0.911595
\(530\) 33.4013 1.45086
\(531\) 18.7905 0.815439
\(532\) 15.7537 0.683008
\(533\) −45.2419 −1.95964
\(534\) −13.8874 −0.600969
\(535\) −1.02675 −0.0443901
\(536\) 37.1110 1.60295
\(537\) 30.0595 1.29716
\(538\) −28.0952 −1.21127
\(539\) 26.2997 1.13281
\(540\) 166.126 7.14891
\(541\) 43.3831 1.86519 0.932593 0.360930i \(-0.117541\pi\)
0.932593 + 0.360930i \(0.117541\pi\)
\(542\) −64.3162 −2.76262
\(543\) 24.9685 1.07150
\(544\) −14.5377 −0.623297
\(545\) 56.5278 2.42139
\(546\) 60.0606 2.57036
\(547\) −1.00000 −0.0427569
\(548\) −58.9554 −2.51845
\(549\) −24.2509 −1.03500
\(550\) −104.434 −4.45310
\(551\) 13.3320 0.567963
\(552\) 115.569 4.91893
\(553\) 8.37344 0.356075
\(554\) 26.9963 1.14696
\(555\) −38.0163 −1.61370
\(556\) 14.0897 0.597536
\(557\) −26.5599 −1.12538 −0.562689 0.826669i \(-0.690233\pi\)
−0.562689 + 0.826669i \(0.690233\pi\)
\(558\) 77.9457 3.29971
\(559\) −29.6369 −1.25351
\(560\) −28.9447 −1.22314
\(561\) −87.6972 −3.70258
\(562\) 0.791868 0.0334029
\(563\) −41.6328 −1.75461 −0.877306 0.479931i \(-0.840662\pi\)
−0.877306 + 0.479931i \(0.840662\pi\)
\(564\) 5.62356 0.236794
\(565\) 46.3463 1.94980
\(566\) −77.4995 −3.25755
\(567\) 20.2869 0.851969
\(568\) −62.8638 −2.63771
\(569\) 15.6265 0.655097 0.327549 0.944834i \(-0.393777\pi\)
0.327549 + 0.944834i \(0.393777\pi\)
\(570\) 70.9290 2.97089
\(571\) 37.2288 1.55798 0.778988 0.627038i \(-0.215733\pi\)
0.778988 + 0.627038i \(0.215733\pi\)
\(572\) 122.710 5.13075
\(573\) −72.4794 −3.02787
\(574\) 30.2636 1.26318
\(575\) −51.7911 −2.15984
\(576\) −28.5564 −1.18985
\(577\) −9.81210 −0.408483 −0.204242 0.978921i \(-0.565473\pi\)
−0.204242 + 0.978921i \(0.565473\pi\)
\(578\) 28.1155 1.16945
\(579\) −2.61361 −0.108618
\(580\) −79.1597 −3.28693
\(581\) 0.487997 0.0202455
\(582\) 89.0243 3.69017
\(583\) 19.9419 0.825909
\(584\) −2.64670 −0.109521
\(585\) 126.072 5.21246
\(586\) −54.4449 −2.24910
\(587\) 9.72834 0.401532 0.200766 0.979639i \(-0.435657\pi\)
0.200766 + 0.979639i \(0.435657\pi\)
\(588\) 64.6634 2.66667
\(589\) 12.2424 0.504439
\(590\) −25.7565 −1.06038
\(591\) −75.6503 −3.11184
\(592\) −19.2916 −0.792880
\(593\) 28.2791 1.16128 0.580642 0.814159i \(-0.302802\pi\)
0.580642 + 0.814159i \(0.302802\pi\)
\(594\) 145.782 5.98153
\(595\) 27.4304 1.12454
\(596\) 5.29436 0.216866
\(597\) 20.4061 0.835166
\(598\) 89.4448 3.65767
\(599\) 32.5093 1.32830 0.664148 0.747601i \(-0.268795\pi\)
0.664148 + 0.747601i \(0.268795\pi\)
\(600\) −136.135 −5.55770
\(601\) 5.09124 0.207676 0.103838 0.994594i \(-0.466888\pi\)
0.103838 + 0.994594i \(0.466888\pi\)
\(602\) 19.8250 0.808006
\(603\) 42.9366 1.74851
\(604\) −83.9567 −3.41615
\(605\) −62.8940 −2.55700
\(606\) 47.5395 1.93116
\(607\) 26.8978 1.09175 0.545875 0.837867i \(-0.316197\pi\)
0.545875 + 0.837867i \(0.316197\pi\)
\(608\) 7.01998 0.284698
\(609\) −23.1323 −0.937367
\(610\) 33.2411 1.34589
\(611\) 2.30753 0.0933525
\(612\) −147.757 −5.97270
\(613\) −6.32992 −0.255663 −0.127832 0.991796i \(-0.540802\pi\)
−0.127832 + 0.991796i \(0.540802\pi\)
\(614\) 7.78674 0.314247
\(615\) 92.7039 3.73818
\(616\) −43.5190 −1.75343
\(617\) −12.5277 −0.504344 −0.252172 0.967682i \(-0.581145\pi\)
−0.252172 + 0.967682i \(0.581145\pi\)
\(618\) −123.771 −4.97880
\(619\) 30.6964 1.23379 0.616897 0.787044i \(-0.288389\pi\)
0.616897 + 0.787044i \(0.288389\pi\)
\(620\) −72.6900 −2.91930
\(621\) 72.2964 2.90115
\(622\) 68.3287 2.73973
\(623\) 2.59342 0.103903
\(624\) 93.3608 3.73742
\(625\) −3.04591 −0.121837
\(626\) 34.6788 1.38604
\(627\) 42.3474 1.69119
\(628\) −48.4436 −1.93311
\(629\) 18.2824 0.728965
\(630\) −84.3335 −3.35993
\(631\) 23.2190 0.924334 0.462167 0.886793i \(-0.347072\pi\)
0.462167 + 0.886793i \(0.347072\pi\)
\(632\) 32.7782 1.30385
\(633\) −4.63048 −0.184045
\(634\) −35.6698 −1.41663
\(635\) 9.38870 0.372579
\(636\) 49.0314 1.94422
\(637\) 26.5335 1.05129
\(638\) −69.4660 −2.75019
\(639\) −72.7319 −2.87723
\(640\) 58.7258 2.32134
\(641\) 10.2964 0.406681 0.203341 0.979108i \(-0.434820\pi\)
0.203341 + 0.979108i \(0.434820\pi\)
\(642\) −2.21533 −0.0874322
\(643\) −49.1690 −1.93903 −0.969517 0.245022i \(-0.921205\pi\)
−0.969517 + 0.245022i \(0.921205\pi\)
\(644\) −40.7071 −1.60408
\(645\) 60.7281 2.39117
\(646\) −34.1103 −1.34205
\(647\) −12.1501 −0.477668 −0.238834 0.971060i \(-0.576765\pi\)
−0.238834 + 0.971060i \(0.576765\pi\)
\(648\) 79.4140 3.11968
\(649\) −15.3776 −0.603625
\(650\) −105.363 −4.13266
\(651\) −21.2417 −0.832527
\(652\) 10.0525 0.393688
\(653\) 31.9760 1.25132 0.625658 0.780097i \(-0.284830\pi\)
0.625658 + 0.780097i \(0.284830\pi\)
\(654\) 121.966 4.76924
\(655\) −7.03541 −0.274896
\(656\) 47.0431 1.83672
\(657\) −3.06217 −0.119467
\(658\) −1.54357 −0.0601747
\(659\) −16.5352 −0.644120 −0.322060 0.946719i \(-0.604375\pi\)
−0.322060 + 0.946719i \(0.604375\pi\)
\(660\) −251.441 −9.78732
\(661\) 4.40089 0.171175 0.0855873 0.996331i \(-0.472723\pi\)
0.0855873 + 0.996331i \(0.472723\pi\)
\(662\) −35.0720 −1.36311
\(663\) −88.4766 −3.43615
\(664\) 1.91029 0.0741335
\(665\) −13.2457 −0.513645
\(666\) −56.2082 −2.17802
\(667\) −34.4496 −1.33389
\(668\) 14.4430 0.558815
\(669\) −68.0948 −2.63270
\(670\) −58.8539 −2.27372
\(671\) 19.8463 0.766156
\(672\) −12.1803 −0.469866
\(673\) −28.2504 −1.08897 −0.544487 0.838769i \(-0.683276\pi\)
−0.544487 + 0.838769i \(0.683276\pi\)
\(674\) −6.94541 −0.267527
\(675\) −85.1623 −3.27790
\(676\) 68.4604 2.63309
\(677\) 15.1494 0.582240 0.291120 0.956687i \(-0.405972\pi\)
0.291120 + 0.956687i \(0.405972\pi\)
\(678\) 99.9979 3.84040
\(679\) −16.6249 −0.638004
\(680\) 107.378 4.11775
\(681\) −29.9359 −1.14715
\(682\) −63.7886 −2.44259
\(683\) −0.816285 −0.0312343 −0.0156171 0.999878i \(-0.504971\pi\)
−0.0156171 + 0.999878i \(0.504971\pi\)
\(684\) 71.3491 2.72810
\(685\) 49.5697 1.89396
\(686\) −43.0007 −1.64178
\(687\) −39.0792 −1.49097
\(688\) 30.8168 1.17488
\(689\) 20.1191 0.766478
\(690\) −183.279 −6.97730
\(691\) 18.8709 0.717882 0.358941 0.933360i \(-0.383138\pi\)
0.358941 + 0.933360i \(0.383138\pi\)
\(692\) −102.922 −3.91250
\(693\) −50.3504 −1.91266
\(694\) 85.5601 3.24782
\(695\) −11.8466 −0.449367
\(696\) −90.5524 −3.43238
\(697\) −44.5820 −1.68866
\(698\) 79.6880 3.01623
\(699\) −38.4300 −1.45356
\(700\) 47.9514 1.81239
\(701\) 29.2476 1.10467 0.552334 0.833623i \(-0.313737\pi\)
0.552334 + 0.833623i \(0.313737\pi\)
\(702\) 147.078 5.55111
\(703\) −8.82823 −0.332963
\(704\) 23.3698 0.880782
\(705\) −4.72828 −0.178077
\(706\) 49.4263 1.86018
\(707\) −8.87778 −0.333883
\(708\) −37.8091 −1.42095
\(709\) −5.19560 −0.195125 −0.0975625 0.995229i \(-0.531105\pi\)
−0.0975625 + 0.995229i \(0.531105\pi\)
\(710\) 99.6949 3.74148
\(711\) 37.9237 1.42225
\(712\) 10.1521 0.380465
\(713\) −31.6340 −1.18470
\(714\) 59.1846 2.21493
\(715\) −103.174 −3.85850
\(716\) −41.4470 −1.54895
\(717\) −6.04548 −0.225773
\(718\) 15.3322 0.572191
\(719\) −25.5079 −0.951286 −0.475643 0.879638i \(-0.657785\pi\)
−0.475643 + 0.879638i \(0.657785\pi\)
\(720\) −131.092 −4.88550
\(721\) 23.1137 0.860799
\(722\) −31.0550 −1.15575
\(723\) 53.9009 2.00459
\(724\) −34.4274 −1.27948
\(725\) 40.5803 1.50711
\(726\) −135.702 −5.03636
\(727\) 18.2744 0.677761 0.338881 0.940829i \(-0.389952\pi\)
0.338881 + 0.940829i \(0.389952\pi\)
\(728\) −43.9058 −1.62726
\(729\) −9.10533 −0.337234
\(730\) 4.19737 0.155352
\(731\) −29.2046 −1.08017
\(732\) 48.7962 1.80356
\(733\) 11.4034 0.421195 0.210597 0.977573i \(-0.432459\pi\)
0.210597 + 0.977573i \(0.432459\pi\)
\(734\) −33.6313 −1.24135
\(735\) −54.3690 −2.00543
\(736\) −18.1394 −0.668629
\(737\) −35.1381 −1.29433
\(738\) 137.065 5.04544
\(739\) −22.2708 −0.819246 −0.409623 0.912255i \(-0.634340\pi\)
−0.409623 + 0.912255i \(0.634340\pi\)
\(740\) 52.4182 1.92693
\(741\) 42.7238 1.56950
\(742\) −13.4583 −0.494069
\(743\) 37.4127 1.37254 0.686270 0.727347i \(-0.259247\pi\)
0.686270 + 0.727347i \(0.259247\pi\)
\(744\) −83.1516 −3.04848
\(745\) −4.45150 −0.163090
\(746\) 31.3512 1.14785
\(747\) 2.21016 0.0808655
\(748\) 120.920 4.42127
\(749\) 0.413703 0.0151164
\(750\) 77.6914 2.83689
\(751\) 20.9303 0.763758 0.381879 0.924212i \(-0.375277\pi\)
0.381879 + 0.924212i \(0.375277\pi\)
\(752\) −2.39939 −0.0874969
\(753\) −11.1637 −0.406828
\(754\) −70.0834 −2.55229
\(755\) 70.5907 2.56906
\(756\) −66.9364 −2.43445
\(757\) 1.08103 0.0392907 0.0196454 0.999807i \(-0.493746\pi\)
0.0196454 + 0.999807i \(0.493746\pi\)
\(758\) −22.3002 −0.809980
\(759\) −109.425 −3.97186
\(760\) −51.8509 −1.88083
\(761\) −38.7659 −1.40526 −0.702631 0.711554i \(-0.747992\pi\)
−0.702631 + 0.711554i \(0.747992\pi\)
\(762\) 20.2573 0.733844
\(763\) −22.7766 −0.824567
\(764\) 99.9370 3.61560
\(765\) 124.234 4.49168
\(766\) −21.0380 −0.760132
\(767\) −15.5143 −0.560189
\(768\) 99.7123 3.59806
\(769\) −48.8853 −1.76285 −0.881424 0.472326i \(-0.843415\pi\)
−0.881424 + 0.472326i \(0.843415\pi\)
\(770\) 69.0162 2.48717
\(771\) 31.1615 1.12225
\(772\) 3.60374 0.129701
\(773\) 7.06901 0.254255 0.127127 0.991886i \(-0.459424\pi\)
0.127127 + 0.991886i \(0.459424\pi\)
\(774\) 89.7882 3.22737
\(775\) 37.2637 1.33855
\(776\) −65.0789 −2.33620
\(777\) 15.3178 0.549523
\(778\) −17.1525 −0.614947
\(779\) 21.5279 0.771316
\(780\) −253.675 −9.08304
\(781\) 59.5218 2.12986
\(782\) 88.1402 3.15189
\(783\) −56.6470 −2.02440
\(784\) −27.5898 −0.985351
\(785\) 40.7313 1.45376
\(786\) −15.1798 −0.541445
\(787\) 30.3453 1.08169 0.540847 0.841121i \(-0.318104\pi\)
0.540847 + 0.841121i \(0.318104\pi\)
\(788\) 104.309 3.71586
\(789\) 17.6364 0.627873
\(790\) −51.9826 −1.84946
\(791\) −18.6742 −0.663977
\(792\) −197.099 −7.00362
\(793\) 20.0226 0.711025
\(794\) −19.5714 −0.694564
\(795\) −41.2256 −1.46212
\(796\) −28.1366 −0.997276
\(797\) −36.9392 −1.30845 −0.654227 0.756299i \(-0.727006\pi\)
−0.654227 + 0.756299i \(0.727006\pi\)
\(798\) −28.5792 −1.01169
\(799\) 2.27387 0.0804437
\(800\) 21.3676 0.755457
\(801\) 11.7457 0.415014
\(802\) −40.5669 −1.43247
\(803\) 2.50600 0.0884347
\(804\) −86.3944 −3.04689
\(805\) 34.2265 1.20633
\(806\) −64.3555 −2.26683
\(807\) 34.6765 1.22067
\(808\) −34.7525 −1.22259
\(809\) −35.3975 −1.24451 −0.622255 0.782815i \(-0.713783\pi\)
−0.622255 + 0.782815i \(0.713783\pi\)
\(810\) −125.942 −4.42514
\(811\) −26.8628 −0.943281 −0.471641 0.881791i \(-0.656338\pi\)
−0.471641 + 0.881791i \(0.656338\pi\)
\(812\) 31.8955 1.11931
\(813\) 79.3822 2.78406
\(814\) 45.9992 1.61227
\(815\) −8.45217 −0.296066
\(816\) 91.9991 3.22061
\(817\) 14.1024 0.493381
\(818\) 25.1582 0.879636
\(819\) −50.7979 −1.77502
\(820\) −127.823 −4.46378
\(821\) 33.5285 1.17015 0.585077 0.810978i \(-0.301064\pi\)
0.585077 + 0.810978i \(0.301064\pi\)
\(822\) 106.953 3.73040
\(823\) −17.8795 −0.623240 −0.311620 0.950207i \(-0.600872\pi\)
−0.311620 + 0.950207i \(0.600872\pi\)
\(824\) 90.4797 3.15201
\(825\) 128.898 4.48765
\(826\) 10.3780 0.361096
\(827\) 23.8898 0.830729 0.415364 0.909655i \(-0.363654\pi\)
0.415364 + 0.909655i \(0.363654\pi\)
\(828\) −184.364 −6.40710
\(829\) 29.2441 1.01569 0.507844 0.861449i \(-0.330443\pi\)
0.507844 + 0.861449i \(0.330443\pi\)
\(830\) −3.02950 −0.105156
\(831\) −33.3201 −1.15586
\(832\) 23.5775 0.817402
\(833\) 26.1465 0.905921
\(834\) −25.5605 −0.885088
\(835\) −12.1436 −0.420248
\(836\) −58.3901 −2.01946
\(837\) −52.0172 −1.79798
\(838\) 73.4659 2.53784
\(839\) −50.1966 −1.73298 −0.866489 0.499196i \(-0.833629\pi\)
−0.866489 + 0.499196i \(0.833629\pi\)
\(840\) 89.9660 3.10412
\(841\) −2.00744 −0.0692221
\(842\) −71.1872 −2.45327
\(843\) −0.977363 −0.0336622
\(844\) 6.38467 0.219769
\(845\) −57.5614 −1.98017
\(846\) −6.99090 −0.240352
\(847\) 25.3416 0.870749
\(848\) −20.9201 −0.718400
\(849\) 95.6537 3.28283
\(850\) −103.826 −3.56119
\(851\) 22.8119 0.781982
\(852\) 146.347 5.01376
\(853\) 48.6698 1.66642 0.833212 0.552954i \(-0.186499\pi\)
0.833212 + 0.552954i \(0.186499\pi\)
\(854\) −13.3937 −0.458324
\(855\) −59.9903 −2.05162
\(856\) 1.61946 0.0553521
\(857\) 21.2395 0.725528 0.362764 0.931881i \(-0.381833\pi\)
0.362764 + 0.931881i \(0.381833\pi\)
\(858\) −222.611 −7.59982
\(859\) 16.2261 0.553626 0.276813 0.960924i \(-0.410722\pi\)
0.276813 + 0.960924i \(0.410722\pi\)
\(860\) −83.7340 −2.85531
\(861\) −37.3528 −1.27298
\(862\) −42.2073 −1.43759
\(863\) −12.9330 −0.440243 −0.220122 0.975472i \(-0.570645\pi\)
−0.220122 + 0.975472i \(0.570645\pi\)
\(864\) −29.8275 −1.01475
\(865\) 86.5366 2.94233
\(866\) −43.8064 −1.48860
\(867\) −34.7015 −1.17853
\(868\) 29.2887 0.994124
\(869\) −31.0357 −1.05281
\(870\) 143.606 4.86870
\(871\) −35.4504 −1.20119
\(872\) −89.1600 −3.01934
\(873\) −75.2948 −2.54834
\(874\) −42.5614 −1.43966
\(875\) −14.5085 −0.490477
\(876\) 6.16152 0.208178
\(877\) −4.82463 −0.162916 −0.0814581 0.996677i \(-0.525958\pi\)
−0.0814581 + 0.996677i \(0.525958\pi\)
\(878\) −2.99323 −0.101016
\(879\) 67.1985 2.26655
\(880\) 107.282 3.61647
\(881\) 31.5509 1.06298 0.531489 0.847065i \(-0.321633\pi\)
0.531489 + 0.847065i \(0.321633\pi\)
\(882\) −80.3860 −2.70674
\(883\) 40.4305 1.36059 0.680297 0.732937i \(-0.261851\pi\)
0.680297 + 0.732937i \(0.261851\pi\)
\(884\) 121.995 4.10312
\(885\) 31.7899 1.06861
\(886\) −4.45211 −0.149572
\(887\) 30.6420 1.02886 0.514428 0.857534i \(-0.328004\pi\)
0.514428 + 0.857534i \(0.328004\pi\)
\(888\) 59.9622 2.01220
\(889\) −3.78295 −0.126876
\(890\) −16.1000 −0.539674
\(891\) −75.1921 −2.51903
\(892\) 93.8914 3.14372
\(893\) −1.09801 −0.0367436
\(894\) −9.60466 −0.321228
\(895\) 34.8486 1.16486
\(896\) −23.6622 −0.790498
\(897\) −110.397 −3.68606
\(898\) 89.5447 2.98815
\(899\) 24.7865 0.826675
\(900\) 217.174 7.23913
\(901\) 19.8257 0.660490
\(902\) −112.170 −3.73486
\(903\) −24.4690 −0.814277
\(904\) −73.1009 −2.43130
\(905\) 28.9466 0.962216
\(906\) 152.308 5.06010
\(907\) 31.9314 1.06026 0.530132 0.847915i \(-0.322142\pi\)
0.530132 + 0.847915i \(0.322142\pi\)
\(908\) 41.2766 1.36981
\(909\) −40.2079 −1.33361
\(910\) 69.6296 2.30820
\(911\) −0.929435 −0.0307936 −0.0153968 0.999881i \(-0.504901\pi\)
−0.0153968 + 0.999881i \(0.504901\pi\)
\(912\) −44.4247 −1.47105
\(913\) −1.80873 −0.0598603
\(914\) −22.5578 −0.746145
\(915\) −41.0278 −1.35634
\(916\) 53.8838 1.78037
\(917\) 2.83475 0.0936119
\(918\) 144.933 4.78350
\(919\) −58.0653 −1.91540 −0.957698 0.287775i \(-0.907084\pi\)
−0.957698 + 0.287775i \(0.907084\pi\)
\(920\) 133.981 4.41723
\(921\) −9.61078 −0.316686
\(922\) −77.1925 −2.54220
\(923\) 60.0508 1.97660
\(924\) 101.312 3.33292
\(925\) −26.8716 −0.883531
\(926\) −2.64685 −0.0869810
\(927\) 104.683 3.43824
\(928\) 14.2129 0.466563
\(929\) −43.9547 −1.44211 −0.721054 0.692879i \(-0.756342\pi\)
−0.721054 + 0.692879i \(0.756342\pi\)
\(930\) 131.869 4.32416
\(931\) −12.6257 −0.413790
\(932\) 52.9886 1.73570
\(933\) −84.3347 −2.76099
\(934\) −85.5206 −2.79832
\(935\) −101.669 −3.32494
\(936\) −198.851 −6.49965
\(937\) −40.6735 −1.32875 −0.664373 0.747401i \(-0.731301\pi\)
−0.664373 + 0.747401i \(0.731301\pi\)
\(938\) 23.7138 0.774283
\(939\) −42.8022 −1.39680
\(940\) 6.51952 0.212643
\(941\) 32.6479 1.06429 0.532146 0.846653i \(-0.321386\pi\)
0.532146 + 0.846653i \(0.321386\pi\)
\(942\) 87.8829 2.86338
\(943\) −55.6275 −1.81148
\(944\) 16.1320 0.525051
\(945\) 56.2801 1.83079
\(946\) −73.4802 −2.38905
\(947\) 23.2833 0.756605 0.378303 0.925682i \(-0.376508\pi\)
0.378303 + 0.925682i \(0.376508\pi\)
\(948\) −76.3077 −2.47836
\(949\) 2.52827 0.0820711
\(950\) 50.1357 1.62662
\(951\) 44.0254 1.42762
\(952\) −43.2654 −1.40224
\(953\) 9.41717 0.305052 0.152526 0.988299i \(-0.451259\pi\)
0.152526 + 0.988299i \(0.451259\pi\)
\(954\) −60.9531 −1.97343
\(955\) −84.0270 −2.71905
\(956\) 8.33571 0.269596
\(957\) 85.7384 2.77153
\(958\) −77.2200 −2.49487
\(959\) −19.9729 −0.644960
\(960\) −48.3119 −1.55926
\(961\) −8.23933 −0.265785
\(962\) 46.4080 1.49626
\(963\) 1.87368 0.0603785
\(964\) −74.3203 −2.39370
\(965\) −3.03002 −0.0975398
\(966\) 73.8479 2.37602
\(967\) −14.0391 −0.451467 −0.225734 0.974189i \(-0.572478\pi\)
−0.225734 + 0.974189i \(0.572478\pi\)
\(968\) 99.2011 3.18845
\(969\) 42.1007 1.35247
\(970\) 103.208 3.31380
\(971\) 16.1363 0.517838 0.258919 0.965899i \(-0.416634\pi\)
0.258919 + 0.965899i \(0.416634\pi\)
\(972\) −45.6335 −1.46369
\(973\) 4.77331 0.153025
\(974\) −58.1664 −1.86377
\(975\) 130.044 4.16473
\(976\) −20.8198 −0.666425
\(977\) 9.00176 0.287992 0.143996 0.989578i \(-0.454005\pi\)
0.143996 + 0.989578i \(0.454005\pi\)
\(978\) −18.2366 −0.583142
\(979\) −9.61236 −0.307212
\(980\) 74.9658 2.39469
\(981\) −103.156 −3.29352
\(982\) −22.7686 −0.726576
\(983\) −50.8826 −1.62290 −0.811451 0.584421i \(-0.801322\pi\)
−0.811451 + 0.584421i \(0.801322\pi\)
\(984\) −146.220 −4.66131
\(985\) −87.7031 −2.79445
\(986\) −69.0612 −2.19936
\(987\) 1.90515 0.0606416
\(988\) −58.9090 −1.87415
\(989\) −36.4403 −1.15873
\(990\) 312.577 9.93436
\(991\) −20.2975 −0.644772 −0.322386 0.946608i \(-0.604485\pi\)
−0.322386 + 0.946608i \(0.604485\pi\)
\(992\) 13.0513 0.414380
\(993\) 43.2876 1.37369
\(994\) −40.1697 −1.27411
\(995\) 23.6573 0.749985
\(996\) −4.44715 −0.140913
\(997\) −45.1716 −1.43060 −0.715300 0.698817i \(-0.753710\pi\)
−0.715300 + 0.698817i \(0.753710\pi\)
\(998\) 62.6832 1.98420
\(999\) 37.5106 1.18678
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 547.2.a.b.1.18 18
3.2 odd 2 4923.2.a.l.1.1 18
4.3 odd 2 8752.2.a.s.1.16 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.2.a.b.1.18 18 1.1 even 1 trivial
4923.2.a.l.1.1 18 3.2 odd 2
8752.2.a.s.1.16 18 4.3 odd 2