Properties

Label 8016.2.a.bb.1.7
Level $8016$
Weight $2$
Character 8016.1
Self dual yes
Analytic conductor $64.008$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - 29 x^{7} - 7 x^{6} + 266 x^{5} + 69 x^{4} - 901 x^{3} - 199 x^{2} + 875 x + 391\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2004)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-2.42964\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +3.42964 q^{5} -3.44225 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +3.42964 q^{5} -3.44225 q^{7} +1.00000 q^{9} +3.41215 q^{11} -2.00499 q^{13} -3.42964 q^{15} -3.07729 q^{17} +0.565935 q^{19} +3.44225 q^{21} -7.40517 q^{23} +6.76244 q^{25} -1.00000 q^{27} +9.73140 q^{29} +2.62390 q^{31} -3.41215 q^{33} -11.8057 q^{35} -0.527120 q^{37} +2.00499 q^{39} +3.19921 q^{41} -7.98923 q^{43} +3.42964 q^{45} +6.96499 q^{47} +4.84911 q^{49} +3.07729 q^{51} +2.40664 q^{53} +11.7025 q^{55} -0.565935 q^{57} -6.23937 q^{59} -14.3204 q^{61} -3.44225 q^{63} -6.87641 q^{65} -0.623373 q^{67} +7.40517 q^{69} +13.4942 q^{71} +8.13677 q^{73} -6.76244 q^{75} -11.7455 q^{77} +4.25787 q^{79} +1.00000 q^{81} +15.2864 q^{83} -10.5540 q^{85} -9.73140 q^{87} +3.69141 q^{89} +6.90169 q^{91} -2.62390 q^{93} +1.94095 q^{95} +10.6187 q^{97} +3.41215 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} + 9q^{5} - 2q^{7} + 9q^{9} - 7q^{11} + 6q^{13} - 9q^{15} + 7q^{17} - 2q^{19} + 2q^{21} - 19q^{23} + 22q^{25} - 9q^{27} + 13q^{29} - 12q^{31} + 7q^{33} - 4q^{35} + 15q^{37} - 6q^{39} + 18q^{41} + 6q^{43} + 9q^{45} - 25q^{47} + 19q^{49} - 7q^{51} + 17q^{53} + 3q^{55} + 2q^{57} - 3q^{59} + 14q^{61} - 2q^{63} + 14q^{65} + 4q^{67} + 19q^{69} - 17q^{71} - 20q^{73} - 22q^{75} + 14q^{77} + 8q^{79} + 9q^{81} + q^{83} + 5q^{85} - 13q^{87} + 36q^{89} + 41q^{91} + 12q^{93} - 5q^{95} + 31q^{97} - 7q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 3.42964 1.53378 0.766891 0.641777i \(-0.221803\pi\)
0.766891 + 0.641777i \(0.221803\pi\)
\(6\) 0 0
\(7\) −3.44225 −1.30105 −0.650525 0.759485i \(-0.725451\pi\)
−0.650525 + 0.759485i \(0.725451\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.41215 1.02880 0.514401 0.857549i \(-0.328014\pi\)
0.514401 + 0.857549i \(0.328014\pi\)
\(12\) 0 0
\(13\) −2.00499 −0.556085 −0.278042 0.960569i \(-0.589686\pi\)
−0.278042 + 0.960569i \(0.589686\pi\)
\(14\) 0 0
\(15\) −3.42964 −0.885530
\(16\) 0 0
\(17\) −3.07729 −0.746353 −0.373176 0.927760i \(-0.621731\pi\)
−0.373176 + 0.927760i \(0.621731\pi\)
\(18\) 0 0
\(19\) 0.565935 0.129834 0.0649172 0.997891i \(-0.479322\pi\)
0.0649172 + 0.997891i \(0.479322\pi\)
\(20\) 0 0
\(21\) 3.44225 0.751161
\(22\) 0 0
\(23\) −7.40517 −1.54409 −0.772043 0.635571i \(-0.780765\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(24\) 0 0
\(25\) 6.76244 1.35249
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 9.73140 1.80708 0.903538 0.428508i \(-0.140961\pi\)
0.903538 + 0.428508i \(0.140961\pi\)
\(30\) 0 0
\(31\) 2.62390 0.471266 0.235633 0.971842i \(-0.424284\pi\)
0.235633 + 0.971842i \(0.424284\pi\)
\(32\) 0 0
\(33\) −3.41215 −0.593980
\(34\) 0 0
\(35\) −11.8057 −1.99553
\(36\) 0 0
\(37\) −0.527120 −0.0866580 −0.0433290 0.999061i \(-0.513796\pi\)
−0.0433290 + 0.999061i \(0.513796\pi\)
\(38\) 0 0
\(39\) 2.00499 0.321056
\(40\) 0 0
\(41\) 3.19921 0.499632 0.249816 0.968293i \(-0.419630\pi\)
0.249816 + 0.968293i \(0.419630\pi\)
\(42\) 0 0
\(43\) −7.98923 −1.21835 −0.609173 0.793037i \(-0.708499\pi\)
−0.609173 + 0.793037i \(0.708499\pi\)
\(44\) 0 0
\(45\) 3.42964 0.511261
\(46\) 0 0
\(47\) 6.96499 1.01595 0.507974 0.861372i \(-0.330395\pi\)
0.507974 + 0.861372i \(0.330395\pi\)
\(48\) 0 0
\(49\) 4.84911 0.692729
\(50\) 0 0
\(51\) 3.07729 0.430907
\(52\) 0 0
\(53\) 2.40664 0.330577 0.165288 0.986245i \(-0.447144\pi\)
0.165288 + 0.986245i \(0.447144\pi\)
\(54\) 0 0
\(55\) 11.7025 1.57796
\(56\) 0 0
\(57\) −0.565935 −0.0749599
\(58\) 0 0
\(59\) −6.23937 −0.812297 −0.406149 0.913807i \(-0.633128\pi\)
−0.406149 + 0.913807i \(0.633128\pi\)
\(60\) 0 0
\(61\) −14.3204 −1.83354 −0.916769 0.399418i \(-0.869212\pi\)
−0.916769 + 0.399418i \(0.869212\pi\)
\(62\) 0 0
\(63\) −3.44225 −0.433683
\(64\) 0 0
\(65\) −6.87641 −0.852913
\(66\) 0 0
\(67\) −0.623373 −0.0761572 −0.0380786 0.999275i \(-0.512124\pi\)
−0.0380786 + 0.999275i \(0.512124\pi\)
\(68\) 0 0
\(69\) 7.40517 0.891478
\(70\) 0 0
\(71\) 13.4942 1.60147 0.800735 0.599018i \(-0.204442\pi\)
0.800735 + 0.599018i \(0.204442\pi\)
\(72\) 0 0
\(73\) 8.13677 0.952336 0.476168 0.879354i \(-0.342025\pi\)
0.476168 + 0.879354i \(0.342025\pi\)
\(74\) 0 0
\(75\) −6.76244 −0.780860
\(76\) 0 0
\(77\) −11.7455 −1.33852
\(78\) 0 0
\(79\) 4.25787 0.479048 0.239524 0.970890i \(-0.423009\pi\)
0.239524 + 0.970890i \(0.423009\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 15.2864 1.67790 0.838951 0.544207i \(-0.183169\pi\)
0.838951 + 0.544207i \(0.183169\pi\)
\(84\) 0 0
\(85\) −10.5540 −1.14474
\(86\) 0 0
\(87\) −9.73140 −1.04332
\(88\) 0 0
\(89\) 3.69141 0.391289 0.195645 0.980675i \(-0.437320\pi\)
0.195645 + 0.980675i \(0.437320\pi\)
\(90\) 0 0
\(91\) 6.90169 0.723494
\(92\) 0 0
\(93\) −2.62390 −0.272086
\(94\) 0 0
\(95\) 1.94095 0.199138
\(96\) 0 0
\(97\) 10.6187 1.07816 0.539082 0.842253i \(-0.318771\pi\)
0.539082 + 0.842253i \(0.318771\pi\)
\(98\) 0 0
\(99\) 3.41215 0.342934
\(100\) 0 0
\(101\) 15.4086 1.53321 0.766604 0.642120i \(-0.221945\pi\)
0.766604 + 0.642120i \(0.221945\pi\)
\(102\) 0 0
\(103\) −0.208803 −0.0205740 −0.0102870 0.999947i \(-0.503275\pi\)
−0.0102870 + 0.999947i \(0.503275\pi\)
\(104\) 0 0
\(105\) 11.8057 1.15212
\(106\) 0 0
\(107\) 15.4023 1.48900 0.744498 0.667624i \(-0.232689\pi\)
0.744498 + 0.667624i \(0.232689\pi\)
\(108\) 0 0
\(109\) −18.6798 −1.78920 −0.894600 0.446867i \(-0.852540\pi\)
−0.894600 + 0.446867i \(0.852540\pi\)
\(110\) 0 0
\(111\) 0.527120 0.0500320
\(112\) 0 0
\(113\) 7.05501 0.663679 0.331840 0.943336i \(-0.392331\pi\)
0.331840 + 0.943336i \(0.392331\pi\)
\(114\) 0 0
\(115\) −25.3971 −2.36829
\(116\) 0 0
\(117\) −2.00499 −0.185362
\(118\) 0 0
\(119\) 10.5928 0.971042
\(120\) 0 0
\(121\) 0.642792 0.0584356
\(122\) 0 0
\(123\) −3.19921 −0.288463
\(124\) 0 0
\(125\) 6.04455 0.540641
\(126\) 0 0
\(127\) −2.32500 −0.206310 −0.103155 0.994665i \(-0.532894\pi\)
−0.103155 + 0.994665i \(0.532894\pi\)
\(128\) 0 0
\(129\) 7.98923 0.703413
\(130\) 0 0
\(131\) −10.3974 −0.908423 −0.454211 0.890894i \(-0.650079\pi\)
−0.454211 + 0.890894i \(0.650079\pi\)
\(132\) 0 0
\(133\) −1.94809 −0.168921
\(134\) 0 0
\(135\) −3.42964 −0.295177
\(136\) 0 0
\(137\) 3.14496 0.268692 0.134346 0.990934i \(-0.457107\pi\)
0.134346 + 0.990934i \(0.457107\pi\)
\(138\) 0 0
\(139\) 4.67040 0.396138 0.198069 0.980188i \(-0.436533\pi\)
0.198069 + 0.980188i \(0.436533\pi\)
\(140\) 0 0
\(141\) −6.96499 −0.586558
\(142\) 0 0
\(143\) −6.84134 −0.572102
\(144\) 0 0
\(145\) 33.3752 2.77166
\(146\) 0 0
\(147\) −4.84911 −0.399947
\(148\) 0 0
\(149\) 17.4241 1.42744 0.713721 0.700430i \(-0.247009\pi\)
0.713721 + 0.700430i \(0.247009\pi\)
\(150\) 0 0
\(151\) −2.51771 −0.204888 −0.102444 0.994739i \(-0.532666\pi\)
−0.102444 + 0.994739i \(0.532666\pi\)
\(152\) 0 0
\(153\) −3.07729 −0.248784
\(154\) 0 0
\(155\) 8.99903 0.722820
\(156\) 0 0
\(157\) −12.3224 −0.983436 −0.491718 0.870754i \(-0.663631\pi\)
−0.491718 + 0.870754i \(0.663631\pi\)
\(158\) 0 0
\(159\) −2.40664 −0.190859
\(160\) 0 0
\(161\) 25.4905 2.00893
\(162\) 0 0
\(163\) 17.4945 1.37027 0.685137 0.728414i \(-0.259742\pi\)
0.685137 + 0.728414i \(0.259742\pi\)
\(164\) 0 0
\(165\) −11.7025 −0.911036
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −8.98001 −0.690770
\(170\) 0 0
\(171\) 0.565935 0.0432781
\(172\) 0 0
\(173\) −8.48906 −0.645411 −0.322706 0.946499i \(-0.604592\pi\)
−0.322706 + 0.946499i \(0.604592\pi\)
\(174\) 0 0
\(175\) −23.2780 −1.75965
\(176\) 0 0
\(177\) 6.23937 0.468980
\(178\) 0 0
\(179\) 9.45927 0.707019 0.353510 0.935431i \(-0.384988\pi\)
0.353510 + 0.935431i \(0.384988\pi\)
\(180\) 0 0
\(181\) −2.41594 −0.179575 −0.0897877 0.995961i \(-0.528619\pi\)
−0.0897877 + 0.995961i \(0.528619\pi\)
\(182\) 0 0
\(183\) 14.3204 1.05859
\(184\) 0 0
\(185\) −1.80783 −0.132915
\(186\) 0 0
\(187\) −10.5002 −0.767850
\(188\) 0 0
\(189\) 3.44225 0.250387
\(190\) 0 0
\(191\) −5.50321 −0.398198 −0.199099 0.979979i \(-0.563802\pi\)
−0.199099 + 0.979979i \(0.563802\pi\)
\(192\) 0 0
\(193\) −15.1701 −1.09197 −0.545983 0.837796i \(-0.683844\pi\)
−0.545983 + 0.837796i \(0.683844\pi\)
\(194\) 0 0
\(195\) 6.87641 0.492430
\(196\) 0 0
\(197\) 7.92869 0.564896 0.282448 0.959283i \(-0.408854\pi\)
0.282448 + 0.959283i \(0.408854\pi\)
\(198\) 0 0
\(199\) 22.8595 1.62047 0.810233 0.586107i \(-0.199340\pi\)
0.810233 + 0.586107i \(0.199340\pi\)
\(200\) 0 0
\(201\) 0.623373 0.0439694
\(202\) 0 0
\(203\) −33.4979 −2.35109
\(204\) 0 0
\(205\) 10.9721 0.766327
\(206\) 0 0
\(207\) −7.40517 −0.514695
\(208\) 0 0
\(209\) 1.93106 0.133574
\(210\) 0 0
\(211\) 9.58607 0.659932 0.329966 0.943993i \(-0.392963\pi\)
0.329966 + 0.943993i \(0.392963\pi\)
\(212\) 0 0
\(213\) −13.4942 −0.924609
\(214\) 0 0
\(215\) −27.4002 −1.86868
\(216\) 0 0
\(217\) −9.03212 −0.613141
\(218\) 0 0
\(219\) −8.13677 −0.549832
\(220\) 0 0
\(221\) 6.16995 0.415035
\(222\) 0 0
\(223\) −11.0930 −0.742842 −0.371421 0.928464i \(-0.621129\pi\)
−0.371421 + 0.928464i \(0.621129\pi\)
\(224\) 0 0
\(225\) 6.76244 0.450830
\(226\) 0 0
\(227\) 13.3442 0.885686 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(228\) 0 0
\(229\) 8.71943 0.576196 0.288098 0.957601i \(-0.406977\pi\)
0.288098 + 0.957601i \(0.406977\pi\)
\(230\) 0 0
\(231\) 11.7455 0.772797
\(232\) 0 0
\(233\) 23.4773 1.53805 0.769026 0.639218i \(-0.220742\pi\)
0.769026 + 0.639218i \(0.220742\pi\)
\(234\) 0 0
\(235\) 23.8874 1.55824
\(236\) 0 0
\(237\) −4.25787 −0.276579
\(238\) 0 0
\(239\) 23.7397 1.53559 0.767797 0.640693i \(-0.221353\pi\)
0.767797 + 0.640693i \(0.221353\pi\)
\(240\) 0 0
\(241\) 2.51503 0.162007 0.0810037 0.996714i \(-0.474187\pi\)
0.0810037 + 0.996714i \(0.474187\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 16.6307 1.06250
\(246\) 0 0
\(247\) −1.13470 −0.0721989
\(248\) 0 0
\(249\) −15.2864 −0.968737
\(250\) 0 0
\(251\) −9.11605 −0.575400 −0.287700 0.957721i \(-0.592891\pi\)
−0.287700 + 0.957721i \(0.592891\pi\)
\(252\) 0 0
\(253\) −25.2676 −1.58856
\(254\) 0 0
\(255\) 10.5540 0.660918
\(256\) 0 0
\(257\) 29.6735 1.85098 0.925490 0.378773i \(-0.123654\pi\)
0.925490 + 0.378773i \(0.123654\pi\)
\(258\) 0 0
\(259\) 1.81448 0.112746
\(260\) 0 0
\(261\) 9.73140 0.602359
\(262\) 0 0
\(263\) 6.20229 0.382450 0.191225 0.981546i \(-0.438754\pi\)
0.191225 + 0.981546i \(0.438754\pi\)
\(264\) 0 0
\(265\) 8.25390 0.507033
\(266\) 0 0
\(267\) −3.69141 −0.225911
\(268\) 0 0
\(269\) −5.92390 −0.361186 −0.180593 0.983558i \(-0.557802\pi\)
−0.180593 + 0.983558i \(0.557802\pi\)
\(270\) 0 0
\(271\) 5.59031 0.339587 0.169793 0.985480i \(-0.445690\pi\)
0.169793 + 0.985480i \(0.445690\pi\)
\(272\) 0 0
\(273\) −6.90169 −0.417709
\(274\) 0 0
\(275\) 23.0745 1.39144
\(276\) 0 0
\(277\) −30.4989 −1.83250 −0.916251 0.400606i \(-0.868800\pi\)
−0.916251 + 0.400606i \(0.868800\pi\)
\(278\) 0 0
\(279\) 2.62390 0.157089
\(280\) 0 0
\(281\) −26.0428 −1.55359 −0.776793 0.629756i \(-0.783155\pi\)
−0.776793 + 0.629756i \(0.783155\pi\)
\(282\) 0 0
\(283\) 7.81579 0.464601 0.232300 0.972644i \(-0.425375\pi\)
0.232300 + 0.972644i \(0.425375\pi\)
\(284\) 0 0
\(285\) −1.94095 −0.114972
\(286\) 0 0
\(287\) −11.0125 −0.650046
\(288\) 0 0
\(289\) −7.53028 −0.442957
\(290\) 0 0
\(291\) −10.6187 −0.622478
\(292\) 0 0
\(293\) 15.2331 0.889929 0.444965 0.895548i \(-0.353216\pi\)
0.444965 + 0.895548i \(0.353216\pi\)
\(294\) 0 0
\(295\) −21.3988 −1.24589
\(296\) 0 0
\(297\) −3.41215 −0.197993
\(298\) 0 0
\(299\) 14.8473 0.858642
\(300\) 0 0
\(301\) 27.5010 1.58513
\(302\) 0 0
\(303\) −15.4086 −0.885198
\(304\) 0 0
\(305\) −49.1138 −2.81225
\(306\) 0 0
\(307\) −22.5939 −1.28950 −0.644750 0.764394i \(-0.723038\pi\)
−0.644750 + 0.764394i \(0.723038\pi\)
\(308\) 0 0
\(309\) 0.208803 0.0118784
\(310\) 0 0
\(311\) 18.3609 1.04115 0.520576 0.853815i \(-0.325717\pi\)
0.520576 + 0.853815i \(0.325717\pi\)
\(312\) 0 0
\(313\) −11.7189 −0.662389 −0.331194 0.943563i \(-0.607452\pi\)
−0.331194 + 0.943563i \(0.607452\pi\)
\(314\) 0 0
\(315\) −11.8057 −0.665176
\(316\) 0 0
\(317\) 5.56779 0.312718 0.156359 0.987700i \(-0.450024\pi\)
0.156359 + 0.987700i \(0.450024\pi\)
\(318\) 0 0
\(319\) 33.2050 1.85912
\(320\) 0 0
\(321\) −15.4023 −0.859673
\(322\) 0 0
\(323\) −1.74155 −0.0969023
\(324\) 0 0
\(325\) −13.5586 −0.752098
\(326\) 0 0
\(327\) 18.6798 1.03300
\(328\) 0 0
\(329\) −23.9753 −1.32180
\(330\) 0 0
\(331\) 13.9422 0.766334 0.383167 0.923679i \(-0.374833\pi\)
0.383167 + 0.923679i \(0.374833\pi\)
\(332\) 0 0
\(333\) −0.527120 −0.0288860
\(334\) 0 0
\(335\) −2.13795 −0.116809
\(336\) 0 0
\(337\) −20.7120 −1.12825 −0.564127 0.825688i \(-0.690787\pi\)
−0.564127 + 0.825688i \(0.690787\pi\)
\(338\) 0 0
\(339\) −7.05501 −0.383176
\(340\) 0 0
\(341\) 8.95315 0.484840
\(342\) 0 0
\(343\) 7.40392 0.399774
\(344\) 0 0
\(345\) 25.3971 1.36733
\(346\) 0 0
\(347\) −0.782314 −0.0419968 −0.0209984 0.999780i \(-0.506684\pi\)
−0.0209984 + 0.999780i \(0.506684\pi\)
\(348\) 0 0
\(349\) 8.12106 0.434710 0.217355 0.976093i \(-0.430257\pi\)
0.217355 + 0.976093i \(0.430257\pi\)
\(350\) 0 0
\(351\) 2.00499 0.107019
\(352\) 0 0
\(353\) 24.1568 1.28574 0.642869 0.765976i \(-0.277744\pi\)
0.642869 + 0.765976i \(0.277744\pi\)
\(354\) 0 0
\(355\) 46.2804 2.45631
\(356\) 0 0
\(357\) −10.5928 −0.560631
\(358\) 0 0
\(359\) −18.9721 −1.00131 −0.500654 0.865647i \(-0.666907\pi\)
−0.500654 + 0.865647i \(0.666907\pi\)
\(360\) 0 0
\(361\) −18.6797 −0.983143
\(362\) 0 0
\(363\) −0.642792 −0.0337378
\(364\) 0 0
\(365\) 27.9062 1.46068
\(366\) 0 0
\(367\) −24.9269 −1.30117 −0.650587 0.759432i \(-0.725477\pi\)
−0.650587 + 0.759432i \(0.725477\pi\)
\(368\) 0 0
\(369\) 3.19921 0.166544
\(370\) 0 0
\(371\) −8.28425 −0.430097
\(372\) 0 0
\(373\) −2.81458 −0.145733 −0.0728666 0.997342i \(-0.523215\pi\)
−0.0728666 + 0.997342i \(0.523215\pi\)
\(374\) 0 0
\(375\) −6.04455 −0.312139
\(376\) 0 0
\(377\) −19.5114 −1.00489
\(378\) 0 0
\(379\) −0.592271 −0.0304229 −0.0152114 0.999884i \(-0.504842\pi\)
−0.0152114 + 0.999884i \(0.504842\pi\)
\(380\) 0 0
\(381\) 2.32500 0.119113
\(382\) 0 0
\(383\) −30.2931 −1.54790 −0.773952 0.633244i \(-0.781723\pi\)
−0.773952 + 0.633244i \(0.781723\pi\)
\(384\) 0 0
\(385\) −40.2828 −2.05300
\(386\) 0 0
\(387\) −7.98923 −0.406115
\(388\) 0 0
\(389\) 27.8198 1.41052 0.705261 0.708948i \(-0.250830\pi\)
0.705261 + 0.708948i \(0.250830\pi\)
\(390\) 0 0
\(391\) 22.7879 1.15243
\(392\) 0 0
\(393\) 10.3974 0.524478
\(394\) 0 0
\(395\) 14.6030 0.734756
\(396\) 0 0
\(397\) −0.292346 −0.0146724 −0.00733622 0.999973i \(-0.502335\pi\)
−0.00733622 + 0.999973i \(0.502335\pi\)
\(398\) 0 0
\(399\) 1.94809 0.0975266
\(400\) 0 0
\(401\) 2.65795 0.132732 0.0663659 0.997795i \(-0.478860\pi\)
0.0663659 + 0.997795i \(0.478860\pi\)
\(402\) 0 0
\(403\) −5.26090 −0.262064
\(404\) 0 0
\(405\) 3.42964 0.170420
\(406\) 0 0
\(407\) −1.79861 −0.0891540
\(408\) 0 0
\(409\) 33.7254 1.66761 0.833807 0.552056i \(-0.186156\pi\)
0.833807 + 0.552056i \(0.186156\pi\)
\(410\) 0 0
\(411\) −3.14496 −0.155130
\(412\) 0 0
\(413\) 21.4775 1.05684
\(414\) 0 0
\(415\) 52.4269 2.57354
\(416\) 0 0
\(417\) −4.67040 −0.228710
\(418\) 0 0
\(419\) 23.3953 1.14293 0.571466 0.820625i \(-0.306375\pi\)
0.571466 + 0.820625i \(0.306375\pi\)
\(420\) 0 0
\(421\) 29.0353 1.41510 0.707548 0.706665i \(-0.249801\pi\)
0.707548 + 0.706665i \(0.249801\pi\)
\(422\) 0 0
\(423\) 6.96499 0.338649
\(424\) 0 0
\(425\) −20.8100 −1.00943
\(426\) 0 0
\(427\) 49.2944 2.38552
\(428\) 0 0
\(429\) 6.84134 0.330303
\(430\) 0 0
\(431\) −17.9561 −0.864917 −0.432458 0.901654i \(-0.642354\pi\)
−0.432458 + 0.901654i \(0.642354\pi\)
\(432\) 0 0
\(433\) −9.77953 −0.469974 −0.234987 0.971998i \(-0.575505\pi\)
−0.234987 + 0.971998i \(0.575505\pi\)
\(434\) 0 0
\(435\) −33.3752 −1.60022
\(436\) 0 0
\(437\) −4.19085 −0.200475
\(438\) 0 0
\(439\) 26.6654 1.27267 0.636335 0.771413i \(-0.280450\pi\)
0.636335 + 0.771413i \(0.280450\pi\)
\(440\) 0 0
\(441\) 4.84911 0.230910
\(442\) 0 0
\(443\) −33.8389 −1.60774 −0.803868 0.594807i \(-0.797228\pi\)
−0.803868 + 0.594807i \(0.797228\pi\)
\(444\) 0 0
\(445\) 12.6602 0.600152
\(446\) 0 0
\(447\) −17.4241 −0.824134
\(448\) 0 0
\(449\) 12.1207 0.572011 0.286006 0.958228i \(-0.407672\pi\)
0.286006 + 0.958228i \(0.407672\pi\)
\(450\) 0 0
\(451\) 10.9162 0.514023
\(452\) 0 0
\(453\) 2.51771 0.118292
\(454\) 0 0
\(455\) 23.6703 1.10968
\(456\) 0 0
\(457\) 33.2110 1.55355 0.776773 0.629780i \(-0.216855\pi\)
0.776773 + 0.629780i \(0.216855\pi\)
\(458\) 0 0
\(459\) 3.07729 0.143636
\(460\) 0 0
\(461\) −8.65829 −0.403257 −0.201628 0.979462i \(-0.564623\pi\)
−0.201628 + 0.979462i \(0.564623\pi\)
\(462\) 0 0
\(463\) 9.11138 0.423442 0.211721 0.977330i \(-0.432093\pi\)
0.211721 + 0.977330i \(0.432093\pi\)
\(464\) 0 0
\(465\) −8.99903 −0.417320
\(466\) 0 0
\(467\) 5.77095 0.267048 0.133524 0.991046i \(-0.457371\pi\)
0.133524 + 0.991046i \(0.457371\pi\)
\(468\) 0 0
\(469\) 2.14581 0.0990843
\(470\) 0 0
\(471\) 12.3224 0.567787
\(472\) 0 0
\(473\) −27.2605 −1.25344
\(474\) 0 0
\(475\) 3.82710 0.175600
\(476\) 0 0
\(477\) 2.40664 0.110192
\(478\) 0 0
\(479\) 13.0611 0.596777 0.298388 0.954445i \(-0.403551\pi\)
0.298388 + 0.954445i \(0.403551\pi\)
\(480\) 0 0
\(481\) 1.05687 0.0481892
\(482\) 0 0
\(483\) −25.4905 −1.15986
\(484\) 0 0
\(485\) 36.4183 1.65367
\(486\) 0 0
\(487\) −4.46374 −0.202272 −0.101136 0.994873i \(-0.532248\pi\)
−0.101136 + 0.994873i \(0.532248\pi\)
\(488\) 0 0
\(489\) −17.4945 −0.791128
\(490\) 0 0
\(491\) 32.0860 1.44802 0.724010 0.689790i \(-0.242297\pi\)
0.724010 + 0.689790i \(0.242297\pi\)
\(492\) 0 0
\(493\) −29.9464 −1.34872
\(494\) 0 0
\(495\) 11.7025 0.525987
\(496\) 0 0
\(497\) −46.4506 −2.08359
\(498\) 0 0
\(499\) 1.83022 0.0819321 0.0409660 0.999161i \(-0.486956\pi\)
0.0409660 + 0.999161i \(0.486956\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) 38.9557 1.73695 0.868475 0.495734i \(-0.165101\pi\)
0.868475 + 0.495734i \(0.165101\pi\)
\(504\) 0 0
\(505\) 52.8458 2.35161
\(506\) 0 0
\(507\) 8.98001 0.398816
\(508\) 0 0
\(509\) −29.2174 −1.29504 −0.647520 0.762049i \(-0.724194\pi\)
−0.647520 + 0.762049i \(0.724194\pi\)
\(510\) 0 0
\(511\) −28.0088 −1.23904
\(512\) 0 0
\(513\) −0.565935 −0.0249866
\(514\) 0 0
\(515\) −0.716119 −0.0315560
\(516\) 0 0
\(517\) 23.7656 1.04521
\(518\) 0 0
\(519\) 8.48906 0.372629
\(520\) 0 0
\(521\) −4.48938 −0.196683 −0.0983416 0.995153i \(-0.531354\pi\)
−0.0983416 + 0.995153i \(0.531354\pi\)
\(522\) 0 0
\(523\) 5.38078 0.235285 0.117643 0.993056i \(-0.462466\pi\)
0.117643 + 0.993056i \(0.462466\pi\)
\(524\) 0 0
\(525\) 23.2780 1.01594
\(526\) 0 0
\(527\) −8.07450 −0.351731
\(528\) 0 0
\(529\) 31.8366 1.38420
\(530\) 0 0
\(531\) −6.23937 −0.270766
\(532\) 0 0
\(533\) −6.41438 −0.277838
\(534\) 0 0
\(535\) 52.8244 2.28380
\(536\) 0 0
\(537\) −9.45927 −0.408198
\(538\) 0 0
\(539\) 16.5459 0.712682
\(540\) 0 0
\(541\) 6.00067 0.257989 0.128995 0.991645i \(-0.458825\pi\)
0.128995 + 0.991645i \(0.458825\pi\)
\(542\) 0 0
\(543\) 2.41594 0.103678
\(544\) 0 0
\(545\) −64.0650 −2.74424
\(546\) 0 0
\(547\) 3.34004 0.142810 0.0714050 0.997447i \(-0.477252\pi\)
0.0714050 + 0.997447i \(0.477252\pi\)
\(548\) 0 0
\(549\) −14.3204 −0.611179
\(550\) 0 0
\(551\) 5.50734 0.234621
\(552\) 0 0
\(553\) −14.6567 −0.623265
\(554\) 0 0
\(555\) 1.80783 0.0767382
\(556\) 0 0
\(557\) −14.2270 −0.602816 −0.301408 0.953495i \(-0.597457\pi\)
−0.301408 + 0.953495i \(0.597457\pi\)
\(558\) 0 0
\(559\) 16.0183 0.677504
\(560\) 0 0
\(561\) 10.5002 0.443318
\(562\) 0 0
\(563\) −19.8750 −0.837633 −0.418817 0.908071i \(-0.637555\pi\)
−0.418817 + 0.908071i \(0.637555\pi\)
\(564\) 0 0
\(565\) 24.1962 1.01794
\(566\) 0 0
\(567\) −3.44225 −0.144561
\(568\) 0 0
\(569\) 38.8695 1.62950 0.814748 0.579816i \(-0.196876\pi\)
0.814748 + 0.579816i \(0.196876\pi\)
\(570\) 0 0
\(571\) 45.0691 1.88608 0.943042 0.332674i \(-0.107951\pi\)
0.943042 + 0.332674i \(0.107951\pi\)
\(572\) 0 0
\(573\) 5.50321 0.229900
\(574\) 0 0
\(575\) −50.0771 −2.08836
\(576\) 0 0
\(577\) 33.1251 1.37902 0.689509 0.724277i \(-0.257827\pi\)
0.689509 + 0.724277i \(0.257827\pi\)
\(578\) 0 0
\(579\) 15.1701 0.630447
\(580\) 0 0
\(581\) −52.6197 −2.18303
\(582\) 0 0
\(583\) 8.21181 0.340099
\(584\) 0 0
\(585\) −6.87641 −0.284304
\(586\) 0 0
\(587\) −14.4500 −0.596415 −0.298207 0.954501i \(-0.596389\pi\)
−0.298207 + 0.954501i \(0.596389\pi\)
\(588\) 0 0
\(589\) 1.48496 0.0611866
\(590\) 0 0
\(591\) −7.92869 −0.326143
\(592\) 0 0
\(593\) −29.0136 −1.19145 −0.595724 0.803189i \(-0.703135\pi\)
−0.595724 + 0.803189i \(0.703135\pi\)
\(594\) 0 0
\(595\) 36.3296 1.48937
\(596\) 0 0
\(597\) −22.8595 −0.935577
\(598\) 0 0
\(599\) −22.5523 −0.921461 −0.460731 0.887540i \(-0.652413\pi\)
−0.460731 + 0.887540i \(0.652413\pi\)
\(600\) 0 0
\(601\) 21.5721 0.879943 0.439972 0.898012i \(-0.354989\pi\)
0.439972 + 0.898012i \(0.354989\pi\)
\(602\) 0 0
\(603\) −0.623373 −0.0253857
\(604\) 0 0
\(605\) 2.20454 0.0896275
\(606\) 0 0
\(607\) −16.5729 −0.672674 −0.336337 0.941742i \(-0.609188\pi\)
−0.336337 + 0.941742i \(0.609188\pi\)
\(608\) 0 0
\(609\) 33.4979 1.35741
\(610\) 0 0
\(611\) −13.9647 −0.564953
\(612\) 0 0
\(613\) −28.6472 −1.15705 −0.578524 0.815665i \(-0.696371\pi\)
−0.578524 + 0.815665i \(0.696371\pi\)
\(614\) 0 0
\(615\) −10.9721 −0.442439
\(616\) 0 0
\(617\) 22.2824 0.897054 0.448527 0.893769i \(-0.351949\pi\)
0.448527 + 0.893769i \(0.351949\pi\)
\(618\) 0 0
\(619\) −1.46731 −0.0589760 −0.0294880 0.999565i \(-0.509388\pi\)
−0.0294880 + 0.999565i \(0.509388\pi\)
\(620\) 0 0
\(621\) 7.40517 0.297159
\(622\) 0 0
\(623\) −12.7068 −0.509086
\(624\) 0 0
\(625\) −13.0816 −0.523263
\(626\) 0 0
\(627\) −1.93106 −0.0771190
\(628\) 0 0
\(629\) 1.62210 0.0646775
\(630\) 0 0
\(631\) −21.5061 −0.856144 −0.428072 0.903745i \(-0.640807\pi\)
−0.428072 + 0.903745i \(0.640807\pi\)
\(632\) 0 0
\(633\) −9.58607 −0.381012
\(634\) 0 0
\(635\) −7.97391 −0.316435
\(636\) 0 0
\(637\) −9.72242 −0.385216
\(638\) 0 0
\(639\) 13.4942 0.533824
\(640\) 0 0
\(641\) 2.14974 0.0849096 0.0424548 0.999098i \(-0.486482\pi\)
0.0424548 + 0.999098i \(0.486482\pi\)
\(642\) 0 0
\(643\) −24.0361 −0.947890 −0.473945 0.880554i \(-0.657170\pi\)
−0.473945 + 0.880554i \(0.657170\pi\)
\(644\) 0 0
\(645\) 27.4002 1.07888
\(646\) 0 0
\(647\) 36.1627 1.42170 0.710851 0.703343i \(-0.248310\pi\)
0.710851 + 0.703343i \(0.248310\pi\)
\(648\) 0 0
\(649\) −21.2897 −0.835694
\(650\) 0 0
\(651\) 9.03212 0.353997
\(652\) 0 0
\(653\) −15.4966 −0.606428 −0.303214 0.952923i \(-0.598060\pi\)
−0.303214 + 0.952923i \(0.598060\pi\)
\(654\) 0 0
\(655\) −35.6593 −1.39332
\(656\) 0 0
\(657\) 8.13677 0.317445
\(658\) 0 0
\(659\) 24.9559 0.972142 0.486071 0.873919i \(-0.338430\pi\)
0.486071 + 0.873919i \(0.338430\pi\)
\(660\) 0 0
\(661\) −8.12692 −0.316100 −0.158050 0.987431i \(-0.550521\pi\)
−0.158050 + 0.987431i \(0.550521\pi\)
\(662\) 0 0
\(663\) −6.16995 −0.239621
\(664\) 0 0
\(665\) −6.68126 −0.259088
\(666\) 0 0
\(667\) −72.0627 −2.79028
\(668\) 0 0
\(669\) 11.0930 0.428880
\(670\) 0 0
\(671\) −48.8634 −1.88635
\(672\) 0 0
\(673\) −40.7000 −1.56887 −0.784434 0.620212i \(-0.787046\pi\)
−0.784434 + 0.620212i \(0.787046\pi\)
\(674\) 0 0
\(675\) −6.76244 −0.260287
\(676\) 0 0
\(677\) −0.855237 −0.0328694 −0.0164347 0.999865i \(-0.505232\pi\)
−0.0164347 + 0.999865i \(0.505232\pi\)
\(678\) 0 0
\(679\) −36.5522 −1.40274
\(680\) 0 0
\(681\) −13.3442 −0.511351
\(682\) 0 0
\(683\) 17.1386 0.655791 0.327895 0.944714i \(-0.393661\pi\)
0.327895 + 0.944714i \(0.393661\pi\)
\(684\) 0 0
\(685\) 10.7861 0.412116
\(686\) 0 0
\(687\) −8.71943 −0.332667
\(688\) 0 0
\(689\) −4.82529 −0.183829
\(690\) 0 0
\(691\) 49.0132 1.86455 0.932275 0.361749i \(-0.117820\pi\)
0.932275 + 0.361749i \(0.117820\pi\)
\(692\) 0 0
\(693\) −11.7455 −0.446174
\(694\) 0 0
\(695\) 16.0178 0.607589
\(696\) 0 0
\(697\) −9.84489 −0.372902
\(698\) 0 0
\(699\) −23.4773 −0.887995
\(700\) 0 0
\(701\) −19.8877 −0.751148 −0.375574 0.926792i \(-0.622554\pi\)
−0.375574 + 0.926792i \(0.622554\pi\)
\(702\) 0 0
\(703\) −0.298316 −0.0112512
\(704\) 0 0
\(705\) −23.8874 −0.899652
\(706\) 0 0
\(707\) −53.0401 −1.99478
\(708\) 0 0
\(709\) 19.6916 0.739532 0.369766 0.929125i \(-0.379438\pi\)
0.369766 + 0.929125i \(0.379438\pi\)
\(710\) 0 0
\(711\) 4.25787 0.159683
\(712\) 0 0
\(713\) −19.4304 −0.727675
\(714\) 0 0
\(715\) −23.4634 −0.877480
\(716\) 0 0
\(717\) −23.7397 −0.886576
\(718\) 0 0
\(719\) 14.0200 0.522859 0.261429 0.965223i \(-0.415806\pi\)
0.261429 + 0.965223i \(0.415806\pi\)
\(720\) 0 0
\(721\) 0.718752 0.0267677
\(722\) 0 0
\(723\) −2.51503 −0.0935350
\(724\) 0 0
\(725\) 65.8080 2.44405
\(726\) 0 0
\(727\) −6.39045 −0.237009 −0.118504 0.992954i \(-0.537810\pi\)
−0.118504 + 0.992954i \(0.537810\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 24.5852 0.909316
\(732\) 0 0
\(733\) 27.2071 1.00492 0.502459 0.864601i \(-0.332429\pi\)
0.502459 + 0.864601i \(0.332429\pi\)
\(734\) 0 0
\(735\) −16.6307 −0.613432
\(736\) 0 0
\(737\) −2.12705 −0.0783507
\(738\) 0 0
\(739\) 31.7809 1.16908 0.584540 0.811365i \(-0.301275\pi\)
0.584540 + 0.811365i \(0.301275\pi\)
\(740\) 0 0
\(741\) 1.13470 0.0416841
\(742\) 0 0
\(743\) 25.6426 0.940735 0.470368 0.882471i \(-0.344121\pi\)
0.470368 + 0.882471i \(0.344121\pi\)
\(744\) 0 0
\(745\) 59.7586 2.18938
\(746\) 0 0
\(747\) 15.2864 0.559301
\(748\) 0 0
\(749\) −53.0186 −1.93726
\(750\) 0 0
\(751\) 13.3662 0.487739 0.243870 0.969808i \(-0.421583\pi\)
0.243870 + 0.969808i \(0.421583\pi\)
\(752\) 0 0
\(753\) 9.11605 0.332207
\(754\) 0 0
\(755\) −8.63483 −0.314254
\(756\) 0 0
\(757\) 46.5562 1.69211 0.846057 0.533092i \(-0.178970\pi\)
0.846057 + 0.533092i \(0.178970\pi\)
\(758\) 0 0
\(759\) 25.2676 0.917155
\(760\) 0 0
\(761\) 30.9214 1.12090 0.560450 0.828188i \(-0.310628\pi\)
0.560450 + 0.828188i \(0.310628\pi\)
\(762\) 0 0
\(763\) 64.3006 2.32784
\(764\) 0 0
\(765\) −10.5540 −0.381581
\(766\) 0 0
\(767\) 12.5099 0.451706
\(768\) 0 0
\(769\) −28.7870 −1.03809 −0.519044 0.854748i \(-0.673712\pi\)
−0.519044 + 0.854748i \(0.673712\pi\)
\(770\) 0 0
\(771\) −29.6735 −1.06866
\(772\) 0 0
\(773\) 49.9587 1.79689 0.898445 0.439086i \(-0.144698\pi\)
0.898445 + 0.439086i \(0.144698\pi\)
\(774\) 0 0
\(775\) 17.7440 0.637382
\(776\) 0 0
\(777\) −1.81448 −0.0650941
\(778\) 0 0
\(779\) 1.81054 0.0648694
\(780\) 0 0
\(781\) 46.0444 1.64760
\(782\) 0 0
\(783\) −9.73140 −0.347772
\(784\) 0 0
\(785\) −42.2615 −1.50838
\(786\) 0 0
\(787\) −20.4420 −0.728680 −0.364340 0.931266i \(-0.618705\pi\)
−0.364340 + 0.931266i \(0.618705\pi\)
\(788\) 0 0
\(789\) −6.20229 −0.220807
\(790\) 0 0
\(791\) −24.2851 −0.863480
\(792\) 0 0
\(793\) 28.7123 1.01960
\(794\) 0 0
\(795\) −8.25390 −0.292736
\(796\) 0 0
\(797\) −43.6420 −1.54588 −0.772939 0.634481i \(-0.781214\pi\)
−0.772939 + 0.634481i \(0.781214\pi\)
\(798\) 0 0
\(799\) −21.4333 −0.758256
\(800\) 0 0
\(801\) 3.69141 0.130430
\(802\) 0 0
\(803\) 27.7639 0.979767
\(804\) 0 0
\(805\) 87.4232 3.08126
\(806\) 0 0
\(807\) 5.92390 0.208531
\(808\) 0 0
\(809\) −34.1990 −1.20237 −0.601187 0.799108i \(-0.705305\pi\)
−0.601187 + 0.799108i \(0.705305\pi\)
\(810\) 0 0
\(811\) −18.4143 −0.646613 −0.323306 0.946294i \(-0.604794\pi\)
−0.323306 + 0.946294i \(0.604794\pi\)
\(812\) 0 0
\(813\) −5.59031 −0.196061
\(814\) 0 0
\(815\) 59.9998 2.10170
\(816\) 0 0
\(817\) −4.52139 −0.158183
\(818\) 0 0
\(819\) 6.90169 0.241165
\(820\) 0 0
\(821\) 13.9748 0.487724 0.243862 0.969810i \(-0.421586\pi\)
0.243862 + 0.969810i \(0.421586\pi\)
\(822\) 0 0
\(823\) 38.7321 1.35012 0.675058 0.737765i \(-0.264119\pi\)
0.675058 + 0.737765i \(0.264119\pi\)
\(824\) 0 0
\(825\) −23.0745 −0.803351
\(826\) 0 0
\(827\) −15.2856 −0.531531 −0.265766 0.964038i \(-0.585625\pi\)
−0.265766 + 0.964038i \(0.585625\pi\)
\(828\) 0 0
\(829\) 15.8583 0.550783 0.275391 0.961332i \(-0.411193\pi\)
0.275391 + 0.961332i \(0.411193\pi\)
\(830\) 0 0
\(831\) 30.4989 1.05800
\(832\) 0 0
\(833\) −14.9221 −0.517021
\(834\) 0 0
\(835\) −3.42964 −0.118688
\(836\) 0 0
\(837\) −2.62390 −0.0906952
\(838\) 0 0
\(839\) −11.9835 −0.413716 −0.206858 0.978371i \(-0.566324\pi\)
−0.206858 + 0.978371i \(0.566324\pi\)
\(840\) 0 0
\(841\) 65.7002 2.26552
\(842\) 0 0
\(843\) 26.0428 0.896963
\(844\) 0 0
\(845\) −30.7982 −1.05949
\(846\) 0 0
\(847\) −2.21265 −0.0760276
\(848\) 0 0
\(849\) −7.81579 −0.268237
\(850\) 0 0
\(851\) 3.90341 0.133807
\(852\) 0 0
\(853\) −41.5858 −1.42387 −0.711936 0.702245i \(-0.752181\pi\)
−0.711936 + 0.702245i \(0.752181\pi\)
\(854\) 0 0
\(855\) 1.94095 0.0663793
\(856\) 0 0
\(857\) 20.9894 0.716985 0.358492 0.933533i \(-0.383291\pi\)
0.358492 + 0.933533i \(0.383291\pi\)
\(858\) 0 0
\(859\) −4.03076 −0.137528 −0.0687638 0.997633i \(-0.521905\pi\)
−0.0687638 + 0.997633i \(0.521905\pi\)
\(860\) 0 0
\(861\) 11.0125 0.375304
\(862\) 0 0
\(863\) 13.1107 0.446292 0.223146 0.974785i \(-0.428367\pi\)
0.223146 + 0.974785i \(0.428367\pi\)
\(864\) 0 0
\(865\) −29.1144 −0.989921
\(866\) 0 0
\(867\) 7.53028 0.255742
\(868\) 0 0
\(869\) 14.5285 0.492846
\(870\) 0 0
\(871\) 1.24986 0.0423499
\(872\) 0 0
\(873\) 10.6187 0.359388
\(874\) 0 0
\(875\) −20.8069 −0.703400
\(876\) 0 0
\(877\) −10.7825 −0.364098 −0.182049 0.983289i \(-0.558273\pi\)
−0.182049 + 0.983289i \(0.558273\pi\)
\(878\) 0 0
\(879\) −15.2331 −0.513801
\(880\) 0 0
\(881\) 31.6377 1.06590 0.532951 0.846146i \(-0.321083\pi\)
0.532951 + 0.846146i \(0.321083\pi\)
\(882\) 0 0
\(883\) 36.5870 1.23125 0.615625 0.788039i \(-0.288903\pi\)
0.615625 + 0.788039i \(0.288903\pi\)
\(884\) 0 0
\(885\) 21.3988 0.719313
\(886\) 0 0
\(887\) −53.4262 −1.79387 −0.896937 0.442157i \(-0.854213\pi\)
−0.896937 + 0.442157i \(0.854213\pi\)
\(888\) 0 0
\(889\) 8.00323 0.268420
\(890\) 0 0
\(891\) 3.41215 0.114311
\(892\) 0 0
\(893\) 3.94173 0.131905
\(894\) 0 0
\(895\) 32.4419 1.08441
\(896\) 0 0
\(897\) −14.8473 −0.495737
\(898\) 0 0
\(899\) 25.5342 0.851614
\(900\) 0 0
\(901\) −7.40592 −0.246727
\(902\) 0 0
\(903\) −27.5010 −0.915175
\(904\) 0 0
\(905\) −8.28580 −0.275429
\(906\) 0 0
\(907\) 54.6924 1.81603 0.908015 0.418938i \(-0.137597\pi\)
0.908015 + 0.418938i \(0.137597\pi\)
\(908\) 0 0
\(909\) 15.4086 0.511070
\(910\) 0 0
\(911\) 0.683962 0.0226607 0.0113303 0.999936i \(-0.496393\pi\)
0.0113303 + 0.999936i \(0.496393\pi\)
\(912\) 0 0
\(913\) 52.1596 1.72623
\(914\) 0 0
\(915\) 49.1138 1.62365
\(916\) 0 0
\(917\) 35.7904 1.18190
\(918\) 0 0
\(919\) −48.8179 −1.61035 −0.805177 0.593035i \(-0.797930\pi\)
−0.805177 + 0.593035i \(0.797930\pi\)
\(920\) 0 0
\(921\) 22.5939 0.744493
\(922\) 0 0
\(923\) −27.0558 −0.890553
\(924\) 0 0
\(925\) −3.56462 −0.117204
\(926\) 0 0
\(927\) −0.208803 −0.00685799
\(928\) 0 0
\(929\) 18.6013 0.610288 0.305144 0.952306i \(-0.401295\pi\)
0.305144 + 0.952306i \(0.401295\pi\)
\(930\) 0 0
\(931\) 2.74428 0.0899401
\(932\) 0 0
\(933\) −18.3609 −0.601110
\(934\) 0 0
\(935\) −36.0119 −1.17771
\(936\) 0 0
\(937\) 27.6778 0.904193 0.452096 0.891969i \(-0.350676\pi\)
0.452096 + 0.891969i \(0.350676\pi\)
\(938\) 0 0
\(939\) 11.7189 0.382430
\(940\) 0 0
\(941\) 4.40771 0.143687 0.0718437 0.997416i \(-0.477112\pi\)
0.0718437 + 0.997416i \(0.477112\pi\)
\(942\) 0 0
\(943\) −23.6907 −0.771474
\(944\) 0 0
\(945\) 11.8057 0.384039
\(946\) 0 0
\(947\) −16.0931 −0.522954 −0.261477 0.965210i \(-0.584210\pi\)
−0.261477 + 0.965210i \(0.584210\pi\)
\(948\) 0 0
\(949\) −16.3142 −0.529580
\(950\) 0 0
\(951\) −5.56779 −0.180548
\(952\) 0 0
\(953\) −8.08542 −0.261912 −0.130956 0.991388i \(-0.541805\pi\)
−0.130956 + 0.991388i \(0.541805\pi\)
\(954\) 0 0
\(955\) −18.8740 −0.610750
\(956\) 0 0
\(957\) −33.2050 −1.07337
\(958\) 0 0
\(959\) −10.8258 −0.349582
\(960\) 0 0
\(961\) −24.1152 −0.777908
\(962\) 0 0
\(963\) 15.4023 0.496332
\(964\) 0 0
\(965\) −52.0280 −1.67484
\(966\) 0 0
\(967\) −45.0879 −1.44993 −0.724965 0.688786i \(-0.758144\pi\)
−0.724965 + 0.688786i \(0.758144\pi\)
\(968\) 0 0
\(969\) 1.74155 0.0559466
\(970\) 0 0
\(971\) −39.5386 −1.26885 −0.634427 0.772983i \(-0.718764\pi\)
−0.634427 + 0.772983i \(0.718764\pi\)
\(972\) 0 0
\(973\) −16.0767 −0.515395
\(974\) 0 0
\(975\) 13.5586 0.434224
\(976\) 0 0
\(977\) −53.9173 −1.72497 −0.862483 0.506086i \(-0.831092\pi\)
−0.862483 + 0.506086i \(0.831092\pi\)
\(978\) 0 0
\(979\) 12.5957 0.402559
\(980\) 0 0
\(981\) −18.6798 −0.596400
\(982\) 0 0
\(983\) −32.3887 −1.03304 −0.516520 0.856275i \(-0.672773\pi\)
−0.516520 + 0.856275i \(0.672773\pi\)
\(984\) 0 0
\(985\) 27.1926 0.866428
\(986\) 0 0
\(987\) 23.9753 0.763141
\(988\) 0 0
\(989\) 59.1616 1.88123
\(990\) 0 0
\(991\) −41.4568 −1.31692 −0.658459 0.752617i \(-0.728791\pi\)
−0.658459 + 0.752617i \(0.728791\pi\)
\(992\) 0 0
\(993\) −13.9422 −0.442443
\(994\) 0 0
\(995\) 78.3999 2.48544
\(996\) 0 0
\(997\) −34.5191 −1.09323 −0.546615 0.837384i \(-0.684084\pi\)
−0.546615 + 0.837384i \(0.684084\pi\)
\(998\) 0 0
\(999\) 0.527120 0.0166773
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 8016.2.a.bb.1.7 9
4.3 odd 2 2004.2.a.d.1.7 9
12.11 even 2 6012.2.a.h.1.3 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2004.2.a.d.1.7 9 4.3 odd 2
6012.2.a.h.1.3 9 12.11 even 2
8016.2.a.bb.1.7 9 1.1 even 1 trivial