Properties

Label 5445.2.a.by.1.6
Level $5445$
Weight $2$
Character 5445.1
Self dual yes
Analytic conductor $43.479$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5445.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(43.4785439006\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.74043072.1
Defining polynomial: \(x^{6} - 9 x^{4} + 21 x^{2} - 12\)
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 1.6
Root \(2.38098\) of defining polynomial
Character \(\chi\) \(=\) 5445.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.38098 q^{2} +3.66908 q^{4} +1.00000 q^{5} +2.24200 q^{7} +3.97405 q^{8} +O(q^{10})\) \(q+2.38098 q^{2} +3.66908 q^{4} +1.00000 q^{5} +2.24200 q^{7} +3.97405 q^{8} +2.38098 q^{10} +5.33816 q^{14} +2.12398 q^{16} +0.509947 q^{17} +2.24200 q^{19} +3.66908 q^{20} +4.45490 q^{23} +1.00000 q^{25} +8.22607 q^{28} -3.46410 q^{29} -7.24797 q^{31} -2.89093 q^{32} +1.21417 q^{34} +2.24200 q^{35} +10.7931 q^{37} +5.33816 q^{38} +3.97405 q^{40} +7.94810 q^{41} +6.05983 q^{43} +10.6071 q^{46} +12.2214 q^{47} -1.97345 q^{49} +2.38098 q^{50} -3.79306 q^{53} +8.90981 q^{56} -8.24797 q^{58} -4.67632 q^{59} +7.79188 q^{61} -17.2573 q^{62} -11.1312 q^{64} -8.79306 q^{67} +1.87104 q^{68} +5.33816 q^{70} +16.6763 q^{71} -12.7858 q^{73} +25.6981 q^{74} +8.22607 q^{76} +6.49402 q^{79} +2.12398 q^{80} +18.9243 q^{82} -12.9880 q^{83} +0.509947 q^{85} +14.4283 q^{86} +0.180384 q^{89} +16.3454 q^{92} +29.0990 q^{94} +2.24200 q^{95} -10.6127 q^{97} -4.69874 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{4} + 6q^{5} + O(q^{10}) \) \( 6q + 6q^{4} + 6q^{5} - 6q^{16} + 6q^{20} + 24q^{23} + 6q^{25} - 6q^{31} - 6q^{34} + 30q^{37} + 12q^{47} + 12q^{49} + 12q^{53} + 48q^{56} - 12q^{58} + 36q^{59} - 18q^{67} + 36q^{71} - 6q^{80} + 12q^{82} + 60q^{86} + 12q^{89} + 18q^{92} - 18q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.38098 1.68361 0.841805 0.539782i \(-0.181494\pi\)
0.841805 + 0.539782i \(0.181494\pi\)
\(3\) 0 0
\(4\) 3.66908 1.83454
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.24200 0.847396 0.423698 0.905804i \(-0.360732\pi\)
0.423698 + 0.905804i \(0.360732\pi\)
\(8\) 3.97405 1.40504
\(9\) 0 0
\(10\) 2.38098 0.752933
\(11\) 0 0
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 5.33816 1.42668
\(15\) 0 0
\(16\) 2.12398 0.530996
\(17\) 0.509947 0.123680 0.0618402 0.998086i \(-0.480303\pi\)
0.0618402 + 0.998086i \(0.480303\pi\)
\(18\) 0 0
\(19\) 2.24200 0.514350 0.257175 0.966365i \(-0.417208\pi\)
0.257175 + 0.966365i \(0.417208\pi\)
\(20\) 3.66908 0.820431
\(21\) 0 0
\(22\) 0 0
\(23\) 4.45490 0.928912 0.464456 0.885596i \(-0.346250\pi\)
0.464456 + 0.885596i \(0.346250\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 8.22607 1.55458
\(29\) −3.46410 −0.643268 −0.321634 0.946864i \(-0.604232\pi\)
−0.321634 + 0.946864i \(0.604232\pi\)
\(30\) 0 0
\(31\) −7.24797 −1.30177 −0.650887 0.759175i \(-0.725603\pi\)
−0.650887 + 0.759175i \(0.725603\pi\)
\(32\) −2.89093 −0.511049
\(33\) 0 0
\(34\) 1.21417 0.208229
\(35\) 2.24200 0.378967
\(36\) 0 0
\(37\) 10.7931 1.77437 0.887184 0.461415i \(-0.152658\pi\)
0.887184 + 0.461415i \(0.152658\pi\)
\(38\) 5.33816 0.865964
\(39\) 0 0
\(40\) 3.97405 0.628352
\(41\) 7.94810 1.24128 0.620642 0.784094i \(-0.286872\pi\)
0.620642 + 0.784094i \(0.286872\pi\)
\(42\) 0 0
\(43\) 6.05983 0.924115 0.462058 0.886850i \(-0.347111\pi\)
0.462058 + 0.886850i \(0.347111\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 10.6071 1.56392
\(47\) 12.2214 1.78268 0.891338 0.453339i \(-0.149767\pi\)
0.891338 + 0.453339i \(0.149767\pi\)
\(48\) 0 0
\(49\) −1.97345 −0.281921
\(50\) 2.38098 0.336722
\(51\) 0 0
\(52\) 0 0
\(53\) −3.79306 −0.521017 −0.260509 0.965472i \(-0.583890\pi\)
−0.260509 + 0.965472i \(0.583890\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 8.90981 1.19062
\(57\) 0 0
\(58\) −8.24797 −1.08301
\(59\) −4.67632 −0.608805 −0.304402 0.952544i \(-0.598457\pi\)
−0.304402 + 0.952544i \(0.598457\pi\)
\(60\) 0 0
\(61\) 7.79188 0.997648 0.498824 0.866703i \(-0.333765\pi\)
0.498824 + 0.866703i \(0.333765\pi\)
\(62\) −17.2573 −2.19168
\(63\) 0 0
\(64\) −11.1312 −1.39140
\(65\) 0 0
\(66\) 0 0
\(67\) −8.79306 −1.07424 −0.537122 0.843505i \(-0.680488\pi\)
−0.537122 + 0.843505i \(0.680488\pi\)
\(68\) 1.87104 0.226896
\(69\) 0 0
\(70\) 5.33816 0.638032
\(71\) 16.6763 1.97911 0.989557 0.144140i \(-0.0460415\pi\)
0.989557 + 0.144140i \(0.0460415\pi\)
\(72\) 0 0
\(73\) −12.7858 −1.49647 −0.748234 0.663435i \(-0.769098\pi\)
−0.748234 + 0.663435i \(0.769098\pi\)
\(74\) 25.6981 2.98734
\(75\) 0 0
\(76\) 8.22607 0.943595
\(77\) 0 0
\(78\) 0 0
\(79\) 6.49402 0.730634 0.365317 0.930883i \(-0.380961\pi\)
0.365317 + 0.930883i \(0.380961\pi\)
\(80\) 2.12398 0.237469
\(81\) 0 0
\(82\) 18.9243 2.08984
\(83\) −12.9880 −1.42562 −0.712811 0.701356i \(-0.752578\pi\)
−0.712811 + 0.701356i \(0.752578\pi\)
\(84\) 0 0
\(85\) 0.509947 0.0553115
\(86\) 14.4283 1.55585
\(87\) 0 0
\(88\) 0 0
\(89\) 0.180384 0.0191206 0.00956031 0.999954i \(-0.496957\pi\)
0.00956031 + 0.999954i \(0.496957\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 16.3454 1.70413
\(93\) 0 0
\(94\) 29.0990 3.00133
\(95\) 2.24200 0.230024
\(96\) 0 0
\(97\) −10.6127 −1.07755 −0.538777 0.842448i \(-0.681114\pi\)
−0.538777 + 0.842448i \(0.681114\pi\)
\(98\) −4.69874 −0.474644
\(99\) 0 0
\(100\) 3.66908 0.366908
\(101\) 12.4321 1.23704 0.618520 0.785769i \(-0.287733\pi\)
0.618520 + 0.785769i \(0.287733\pi\)
\(102\) 0 0
\(103\) −2.06364 −0.203336 −0.101668 0.994818i \(-0.532418\pi\)
−0.101668 + 0.994818i \(0.532418\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −9.03122 −0.877189
\(107\) −6.29181 −0.608252 −0.304126 0.952632i \(-0.598364\pi\)
−0.304126 + 0.952632i \(0.598364\pi\)
\(108\) 0 0
\(109\) −0.666164 −0.0638069 −0.0319035 0.999491i \(-0.510157\pi\)
−0.0319035 + 0.999491i \(0.510157\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 4.76197 0.449963
\(113\) −6.70287 −0.630553 −0.315277 0.949000i \(-0.602097\pi\)
−0.315277 + 0.949000i \(0.602097\pi\)
\(114\) 0 0
\(115\) 4.45490 0.415422
\(116\) −12.7101 −1.18010
\(117\) 0 0
\(118\) −11.1342 −1.02499
\(119\) 1.14330 0.104806
\(120\) 0 0
\(121\) 0 0
\(122\) 18.5523 1.67965
\(123\) 0 0
\(124\) −26.5934 −2.38815
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −12.0784 −1.07178 −0.535891 0.844287i \(-0.680024\pi\)
−0.535891 + 0.844287i \(0.680024\pi\)
\(128\) −20.7214 −1.83153
\(129\) 0 0
\(130\) 0 0
\(131\) −3.61562 −0.315898 −0.157949 0.987447i \(-0.550488\pi\)
−0.157949 + 0.987447i \(0.550488\pi\)
\(132\) 0 0
\(133\) 5.02655 0.435858
\(134\) −20.9361 −1.80861
\(135\) 0 0
\(136\) 2.02655 0.173776
\(137\) −6.88325 −0.588076 −0.294038 0.955794i \(-0.594999\pi\)
−0.294038 + 0.955794i \(0.594999\pi\)
\(138\) 0 0
\(139\) −20.7042 −1.75610 −0.878052 0.478566i \(-0.841157\pi\)
−0.878052 + 0.478566i \(0.841157\pi\)
\(140\) 8.22607 0.695230
\(141\) 0 0
\(142\) 39.7060 3.33206
\(143\) 0 0
\(144\) 0 0
\(145\) −3.46410 −0.287678
\(146\) −30.4428 −2.51947
\(147\) 0 0
\(148\) 39.6006 3.25515
\(149\) 7.63566 0.625538 0.312769 0.949829i \(-0.398743\pi\)
0.312769 + 0.949829i \(0.398743\pi\)
\(150\) 0 0
\(151\) −6.29181 −0.512020 −0.256010 0.966674i \(-0.582408\pi\)
−0.256010 + 0.966674i \(0.582408\pi\)
\(152\) 8.90981 0.722681
\(153\) 0 0
\(154\) 0 0
\(155\) −7.24797 −0.582171
\(156\) 0 0
\(157\) 24.5596 1.96007 0.980034 0.198832i \(-0.0637149\pi\)
0.980034 + 0.198832i \(0.0637149\pi\)
\(158\) 15.4621 1.23010
\(159\) 0 0
\(160\) −2.89093 −0.228548
\(161\) 9.98789 0.787156
\(162\) 0 0
\(163\) −10.6127 −0.831249 −0.415625 0.909536i \(-0.636437\pi\)
−0.415625 + 0.909536i \(0.636437\pi\)
\(164\) 29.1622 2.27719
\(165\) 0 0
\(166\) −30.9243 −2.40019
\(167\) −6.14029 −0.475150 −0.237575 0.971369i \(-0.576352\pi\)
−0.237575 + 0.971369i \(0.576352\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 1.21417 0.0931230
\(171\) 0 0
\(172\) 22.2340 1.69533
\(173\) −16.6037 −1.26235 −0.631176 0.775639i \(-0.717428\pi\)
−0.631176 + 0.775639i \(0.717428\pi\)
\(174\) 0 0
\(175\) 2.24200 0.169479
\(176\) 0 0
\(177\) 0 0
\(178\) 0.429490 0.0321917
\(179\) 19.4057 1.45045 0.725227 0.688510i \(-0.241735\pi\)
0.725227 + 0.688510i \(0.241735\pi\)
\(180\) 0 0
\(181\) 10.5596 0.784887 0.392443 0.919776i \(-0.371630\pi\)
0.392443 + 0.919776i \(0.371630\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 17.7040 1.30516
\(185\) 10.7931 0.793522
\(186\) 0 0
\(187\) 0 0
\(188\) 44.8413 3.27039
\(189\) 0 0
\(190\) 5.33816 0.387271
\(191\) 8.90981 0.644691 0.322346 0.946622i \(-0.395529\pi\)
0.322346 + 0.946622i \(0.395529\pi\)
\(192\) 0 0
\(193\) 17.6742 1.27222 0.636110 0.771599i \(-0.280543\pi\)
0.636110 + 0.771599i \(0.280543\pi\)
\(194\) −25.2686 −1.81418
\(195\) 0 0
\(196\) −7.24073 −0.517195
\(197\) 13.8564 0.987228 0.493614 0.869681i \(-0.335676\pi\)
0.493614 + 0.869681i \(0.335676\pi\)
\(198\) 0 0
\(199\) 14.1047 0.999853 0.499927 0.866068i \(-0.333360\pi\)
0.499927 + 0.866068i \(0.333360\pi\)
\(200\) 3.97405 0.281008
\(201\) 0 0
\(202\) 29.6006 2.08269
\(203\) −7.76651 −0.545102
\(204\) 0 0
\(205\) 7.94810 0.555119
\(206\) −4.91349 −0.342339
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −9.08974 −0.625764 −0.312882 0.949792i \(-0.601294\pi\)
−0.312882 + 0.949792i \(0.601294\pi\)
\(212\) −13.9170 −0.955827
\(213\) 0 0
\(214\) −14.9807 −1.02406
\(215\) 6.05983 0.413277
\(216\) 0 0
\(217\) −16.2499 −1.10312
\(218\) −1.58612 −0.107426
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 5.70287 0.381892 0.190946 0.981600i \(-0.438844\pi\)
0.190946 + 0.981600i \(0.438844\pi\)
\(224\) −6.48146 −0.433061
\(225\) 0 0
\(226\) −15.9594 −1.06160
\(227\) −7.16018 −0.475238 −0.237619 0.971358i \(-0.576367\pi\)
−0.237619 + 0.971358i \(0.576367\pi\)
\(228\) 0 0
\(229\) −14.7029 −0.971593 −0.485797 0.874072i \(-0.661470\pi\)
−0.485797 + 0.874072i \(0.661470\pi\)
\(230\) 10.6071 0.699408
\(231\) 0 0
\(232\) −13.7665 −0.903816
\(233\) −14.3664 −0.941171 −0.470586 0.882354i \(-0.655957\pi\)
−0.470586 + 0.882354i \(0.655957\pi\)
\(234\) 0 0
\(235\) 12.2214 0.797237
\(236\) −17.1578 −1.11688
\(237\) 0 0
\(238\) 2.72218 0.176453
\(239\) −1.33233 −0.0861811 −0.0430906 0.999071i \(-0.513720\pi\)
−0.0430906 + 0.999071i \(0.513720\pi\)
\(240\) 0 0
\(241\) 6.56978 0.423197 0.211598 0.977357i \(-0.432133\pi\)
0.211598 + 0.977357i \(0.432133\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 28.5890 1.83022
\(245\) −1.97345 −0.126079
\(246\) 0 0
\(247\) 0 0
\(248\) −28.8038 −1.82904
\(249\) 0 0
\(250\) 2.38098 0.150587
\(251\) 6.18038 0.390102 0.195051 0.980793i \(-0.437513\pi\)
0.195051 + 0.980793i \(0.437513\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −28.7584 −1.80446
\(255\) 0 0
\(256\) −27.0748 −1.69218
\(257\) −2.46938 −0.154036 −0.0770178 0.997030i \(-0.524540\pi\)
−0.0770178 + 0.997030i \(0.524540\pi\)
\(258\) 0 0
\(259\) 24.1980 1.50359
\(260\) 0 0
\(261\) 0 0
\(262\) −8.60873 −0.531849
\(263\) 22.0365 1.35883 0.679414 0.733755i \(-0.262234\pi\)
0.679414 + 0.733755i \(0.262234\pi\)
\(264\) 0 0
\(265\) −3.79306 −0.233006
\(266\) 11.9681 0.733814
\(267\) 0 0
\(268\) −32.2624 −1.97074
\(269\) −13.5861 −0.828361 −0.414180 0.910195i \(-0.635932\pi\)
−0.414180 + 0.910195i \(0.635932\pi\)
\(270\) 0 0
\(271\) −21.7240 −1.31964 −0.659821 0.751423i \(-0.729368\pi\)
−0.659821 + 0.751423i \(0.729368\pi\)
\(272\) 1.08312 0.0656737
\(273\) 0 0
\(274\) −16.3889 −0.990090
\(275\) 0 0
\(276\) 0 0
\(277\) −13.8057 −0.829505 −0.414753 0.909934i \(-0.636132\pi\)
−0.414753 + 0.909934i \(0.636132\pi\)
\(278\) −49.2962 −2.95659
\(279\) 0 0
\(280\) 8.90981 0.532463
\(281\) −28.4203 −1.69541 −0.847706 0.530467i \(-0.822017\pi\)
−0.847706 + 0.530467i \(0.822017\pi\)
\(282\) 0 0
\(283\) 9.17020 0.545112 0.272556 0.962140i \(-0.412131\pi\)
0.272556 + 0.962140i \(0.412131\pi\)
\(284\) 61.1867 3.63076
\(285\) 0 0
\(286\) 0 0
\(287\) 17.8196 1.05186
\(288\) 0 0
\(289\) −16.7400 −0.984703
\(290\) −8.24797 −0.484337
\(291\) 0 0
\(292\) −46.9122 −2.74533
\(293\) 19.0019 1.11010 0.555051 0.831817i \(-0.312699\pi\)
0.555051 + 0.831817i \(0.312699\pi\)
\(294\) 0 0
\(295\) −4.67632 −0.272266
\(296\) 42.8922 2.49306
\(297\) 0 0
\(298\) 18.1804 1.05316
\(299\) 0 0
\(300\) 0 0
\(301\) 13.5861 0.783091
\(302\) −14.9807 −0.862041
\(303\) 0 0
\(304\) 4.76197 0.273117
\(305\) 7.79188 0.446162
\(306\) 0 0
\(307\) 4.68621 0.267456 0.133728 0.991018i \(-0.457305\pi\)
0.133728 + 0.991018i \(0.457305\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −17.2573 −0.980148
\(311\) −19.4057 −1.10040 −0.550199 0.835033i \(-0.685448\pi\)
−0.550199 + 0.835033i \(0.685448\pi\)
\(312\) 0 0
\(313\) −17.1722 −0.970633 −0.485316 0.874339i \(-0.661296\pi\)
−0.485316 + 0.874339i \(0.661296\pi\)
\(314\) 58.4759 3.29999
\(315\) 0 0
\(316\) 23.8271 1.34038
\(317\) −19.1457 −1.07533 −0.537665 0.843159i \(-0.680693\pi\)
−0.537665 + 0.843159i \(0.680693\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −11.1312 −0.622254
\(321\) 0 0
\(322\) 23.7810 1.32526
\(323\) 1.14330 0.0636149
\(324\) 0 0
\(325\) 0 0
\(326\) −25.2686 −1.39950
\(327\) 0 0
\(328\) 31.5861 1.74405
\(329\) 27.4004 1.51063
\(330\) 0 0
\(331\) 19.5104 1.07239 0.536194 0.844094i \(-0.319861\pi\)
0.536194 + 0.844094i \(0.319861\pi\)
\(332\) −47.6541 −2.61536
\(333\) 0 0
\(334\) −14.6199 −0.799966
\(335\) −8.79306 −0.480416
\(336\) 0 0
\(337\) 12.0784 0.657950 0.328975 0.944339i \(-0.393297\pi\)
0.328975 + 0.944339i \(0.393297\pi\)
\(338\) −30.9528 −1.68361
\(339\) 0 0
\(340\) 1.87104 0.101471
\(341\) 0 0
\(342\) 0 0
\(343\) −20.1184 −1.08629
\(344\) 24.0821 1.29842
\(345\) 0 0
\(346\) −39.5330 −2.12531
\(347\) −8.73601 −0.468974 −0.234487 0.972119i \(-0.575341\pi\)
−0.234487 + 0.972119i \(0.575341\pi\)
\(348\) 0 0
\(349\) 8.10431 0.433814 0.216907 0.976192i \(-0.430403\pi\)
0.216907 + 0.976192i \(0.430403\pi\)
\(350\) 5.33816 0.285337
\(351\) 0 0
\(352\) 0 0
\(353\) −1.24402 −0.0662126 −0.0331063 0.999452i \(-0.510540\pi\)
−0.0331063 + 0.999452i \(0.510540\pi\)
\(354\) 0 0
\(355\) 16.6763 0.885087
\(356\) 0.661842 0.0350775
\(357\) 0 0
\(358\) 46.2047 2.44200
\(359\) 19.9162 1.05114 0.525569 0.850751i \(-0.323852\pi\)
0.525569 + 0.850751i \(0.323852\pi\)
\(360\) 0 0
\(361\) −13.9734 −0.735445
\(362\) 25.1422 1.32144
\(363\) 0 0
\(364\) 0 0
\(365\) −12.7858 −0.669241
\(366\) 0 0
\(367\) 14.1804 0.740210 0.370105 0.928990i \(-0.379322\pi\)
0.370105 + 0.928990i \(0.379322\pi\)
\(368\) 9.46214 0.493248
\(369\) 0 0
\(370\) 25.6981 1.33598
\(371\) −8.50404 −0.441508
\(372\) 0 0
\(373\) −34.2779 −1.77484 −0.887421 0.460960i \(-0.847505\pi\)
−0.887421 + 0.460960i \(0.847505\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 48.5685 2.50473
\(377\) 0 0
\(378\) 0 0
\(379\) −26.7173 −1.37238 −0.686189 0.727423i \(-0.740718\pi\)
−0.686189 + 0.727423i \(0.740718\pi\)
\(380\) 8.22607 0.421988
\(381\) 0 0
\(382\) 21.2141 1.08541
\(383\) 0.360767 0.0184343 0.00921717 0.999958i \(-0.497066\pi\)
0.00921717 + 0.999958i \(0.497066\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 42.0821 2.14192
\(387\) 0 0
\(388\) −38.9388 −1.97682
\(389\) 19.9469 1.01135 0.505674 0.862725i \(-0.331244\pi\)
0.505674 + 0.862725i \(0.331244\pi\)
\(390\) 0 0
\(391\) 2.27176 0.114888
\(392\) −7.84257 −0.396110
\(393\) 0 0
\(394\) 32.9919 1.66211
\(395\) 6.49402 0.326749
\(396\) 0 0
\(397\) 18.1457 0.910706 0.455353 0.890311i \(-0.349513\pi\)
0.455353 + 0.890311i \(0.349513\pi\)
\(398\) 33.5830 1.68336
\(399\) 0 0
\(400\) 2.12398 0.106199
\(401\) −1.94689 −0.0972231 −0.0486116 0.998818i \(-0.515480\pi\)
−0.0486116 + 0.998818i \(0.515480\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 45.6143 2.26940
\(405\) 0 0
\(406\) −18.4919 −0.917739
\(407\) 0 0
\(408\) 0 0
\(409\) −35.3438 −1.74764 −0.873819 0.486252i \(-0.838364\pi\)
−0.873819 + 0.486252i \(0.838364\pi\)
\(410\) 18.9243 0.934604
\(411\) 0 0
\(412\) −7.57165 −0.373028
\(413\) −10.4843 −0.515898
\(414\) 0 0
\(415\) −12.9880 −0.637557
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −28.7584 −1.40494 −0.702469 0.711714i \(-0.747919\pi\)
−0.702469 + 0.711714i \(0.747919\pi\)
\(420\) 0 0
\(421\) 22.3421 1.08889 0.544444 0.838797i \(-0.316741\pi\)
0.544444 + 0.838797i \(0.316741\pi\)
\(422\) −21.6425 −1.05354
\(423\) 0 0
\(424\) −15.0738 −0.732049
\(425\) 0.509947 0.0247361
\(426\) 0 0
\(427\) 17.4694 0.845402
\(428\) −23.0851 −1.11586
\(429\) 0 0
\(430\) 14.4283 0.695797
\(431\) −38.2566 −1.84276 −0.921379 0.388666i \(-0.872936\pi\)
−0.921379 + 0.388666i \(0.872936\pi\)
\(432\) 0 0
\(433\) −16.6127 −0.798354 −0.399177 0.916874i \(-0.630704\pi\)
−0.399177 + 0.916874i \(0.630704\pi\)
\(434\) −38.6908 −1.85722
\(435\) 0 0
\(436\) −2.44421 −0.117056
\(437\) 9.98789 0.477785
\(438\) 0 0
\(439\) −23.9660 −1.14384 −0.571918 0.820310i \(-0.693801\pi\)
−0.571918 + 0.820310i \(0.693801\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −13.2254 −0.628356 −0.314178 0.949364i \(-0.601729\pi\)
−0.314178 + 0.949364i \(0.601729\pi\)
\(444\) 0 0
\(445\) 0.180384 0.00855100
\(446\) 13.5784 0.642958
\(447\) 0 0
\(448\) −24.9562 −1.17907
\(449\) 28.7584 1.35719 0.678596 0.734512i \(-0.262589\pi\)
0.678596 + 0.734512i \(0.262589\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −24.5934 −1.15677
\(453\) 0 0
\(454\) −17.0483 −0.800115
\(455\) 0 0
\(456\) 0 0
\(457\) −26.9960 −1.26282 −0.631409 0.775450i \(-0.717523\pi\)
−0.631409 + 0.775450i \(0.717523\pi\)
\(458\) −35.0073 −1.63578
\(459\) 0 0
\(460\) 16.3454 0.762108
\(461\) −31.1675 −1.45162 −0.725808 0.687897i \(-0.758534\pi\)
−0.725808 + 0.687897i \(0.758534\pi\)
\(462\) 0 0
\(463\) 1.73756 0.0807512 0.0403756 0.999185i \(-0.487145\pi\)
0.0403756 + 0.999185i \(0.487145\pi\)
\(464\) −7.35769 −0.341572
\(465\) 0 0
\(466\) −34.2060 −1.58456
\(467\) 29.0781 1.34557 0.672787 0.739836i \(-0.265097\pi\)
0.672787 + 0.739836i \(0.265097\pi\)
\(468\) 0 0
\(469\) −19.7140 −0.910309
\(470\) 29.0990 1.34224
\(471\) 0 0
\(472\) −18.5839 −0.855394
\(473\) 0 0
\(474\) 0 0
\(475\) 2.24200 0.102870
\(476\) 4.19486 0.192271
\(477\) 0 0
\(478\) −3.17225 −0.145095
\(479\) 19.7553 0.902644 0.451322 0.892361i \(-0.350953\pi\)
0.451322 + 0.892361i \(0.350953\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 15.6425 0.712497
\(483\) 0 0
\(484\) 0 0
\(485\) −10.6127 −0.481897
\(486\) 0 0
\(487\) 40.0821 1.81629 0.908146 0.418654i \(-0.137498\pi\)
0.908146 + 0.418654i \(0.137498\pi\)
\(488\) 30.9653 1.40173
\(489\) 0 0
\(490\) −4.69874 −0.212267
\(491\) −12.5836 −0.567891 −0.283945 0.958840i \(-0.591643\pi\)
−0.283945 + 0.958840i \(0.591643\pi\)
\(492\) 0 0
\(493\) −1.76651 −0.0795595
\(494\) 0 0
\(495\) 0 0
\(496\) −15.3946 −0.691236
\(497\) 37.3883 1.67709
\(498\) 0 0
\(499\) −10.7400 −0.480786 −0.240393 0.970676i \(-0.577276\pi\)
−0.240393 + 0.970676i \(0.577276\pi\)
\(500\) 3.66908 0.164086
\(501\) 0 0
\(502\) 14.7154 0.656780
\(503\) −23.4514 −1.04565 −0.522823 0.852441i \(-0.675121\pi\)
−0.522823 + 0.852441i \(0.675121\pi\)
\(504\) 0 0
\(505\) 12.4321 0.553221
\(506\) 0 0
\(507\) 0 0
\(508\) −44.3165 −1.96623
\(509\) 44.8115 1.98623 0.993117 0.117126i \(-0.0373683\pi\)
0.993117 + 0.117126i \(0.0373683\pi\)
\(510\) 0 0
\(511\) −28.6658 −1.26810
\(512\) −23.0219 −1.01743
\(513\) 0 0
\(514\) −5.87955 −0.259336
\(515\) −2.06364 −0.0909347
\(516\) 0 0
\(517\) 0 0
\(518\) 57.6151 2.53146
\(519\) 0 0
\(520\) 0 0
\(521\) 40.7584 1.78566 0.892828 0.450397i \(-0.148718\pi\)
0.892828 + 0.450397i \(0.148718\pi\)
\(522\) 0 0
\(523\) −13.4933 −0.590020 −0.295010 0.955494i \(-0.595323\pi\)
−0.295010 + 0.955494i \(0.595323\pi\)
\(524\) −13.2660 −0.579528
\(525\) 0 0
\(526\) 52.4685 2.28773
\(527\) −3.69608 −0.161004
\(528\) 0 0
\(529\) −3.15383 −0.137123
\(530\) −9.03122 −0.392291
\(531\) 0 0
\(532\) 18.4428 0.799598
\(533\) 0 0
\(534\) 0 0
\(535\) −6.29181 −0.272019
\(536\) −34.9441 −1.50935
\(537\) 0 0
\(538\) −32.3483 −1.39464
\(539\) 0 0
\(540\) 0 0
\(541\) 8.66495 0.372535 0.186268 0.982499i \(-0.440361\pi\)
0.186268 + 0.982499i \(0.440361\pi\)
\(542\) −51.7246 −2.22176
\(543\) 0 0
\(544\) −1.47422 −0.0632067
\(545\) −0.666164 −0.0285353
\(546\) 0 0
\(547\) −9.37241 −0.400735 −0.200368 0.979721i \(-0.564214\pi\)
−0.200368 + 0.979721i \(0.564214\pi\)
\(548\) −25.2552 −1.07885
\(549\) 0 0
\(550\) 0 0
\(551\) −7.76651 −0.330864
\(552\) 0 0
\(553\) 14.5596 0.619136
\(554\) −32.8712 −1.39656
\(555\) 0 0
\(556\) −75.9652 −3.22164
\(557\) 39.7865 1.68581 0.842904 0.538065i \(-0.180844\pi\)
0.842904 + 0.538065i \(0.180844\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 4.76197 0.201230
\(561\) 0 0
\(562\) −67.6682 −2.85441
\(563\) 8.50404 0.358402 0.179201 0.983812i \(-0.442649\pi\)
0.179201 + 0.983812i \(0.442649\pi\)
\(564\) 0 0
\(565\) −6.70287 −0.281992
\(566\) 21.8341 0.917755
\(567\) 0 0
\(568\) 66.2725 2.78073
\(569\) 46.0438 1.93026 0.965129 0.261776i \(-0.0843081\pi\)
0.965129 + 0.261776i \(0.0843081\pi\)
\(570\) 0 0
\(571\) −0.829214 −0.0347015 −0.0173508 0.999849i \(-0.505523\pi\)
−0.0173508 + 0.999849i \(0.505523\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 42.4282 1.77092
\(575\) 4.45490 0.185782
\(576\) 0 0
\(577\) −14.6127 −0.608334 −0.304167 0.952619i \(-0.598378\pi\)
−0.304167 + 0.952619i \(0.598378\pi\)
\(578\) −39.8575 −1.65786
\(579\) 0 0
\(580\) −12.7101 −0.527757
\(581\) −29.1191 −1.20807
\(582\) 0 0
\(583\) 0 0
\(584\) −50.8115 −2.10259
\(585\) 0 0
\(586\) 45.2431 1.86898
\(587\) −3.13122 −0.129239 −0.0646196 0.997910i \(-0.520583\pi\)
−0.0646196 + 0.997910i \(0.520583\pi\)
\(588\) 0 0
\(589\) −16.2499 −0.669566
\(590\) −11.1342 −0.458389
\(591\) 0 0
\(592\) 22.9243 0.942182
\(593\) −21.0877 −0.865966 −0.432983 0.901402i \(-0.642539\pi\)
−0.432983 + 0.901402i \(0.642539\pi\)
\(594\) 0 0
\(595\) 1.14330 0.0468707
\(596\) 28.0159 1.14757
\(597\) 0 0
\(598\) 0 0
\(599\) 38.3897 1.56856 0.784281 0.620406i \(-0.213032\pi\)
0.784281 + 0.620406i \(0.213032\pi\)
\(600\) 0 0
\(601\) −10.0386 −0.409482 −0.204741 0.978816i \(-0.565635\pi\)
−0.204741 + 0.978816i \(0.565635\pi\)
\(602\) 32.3483 1.31842
\(603\) 0 0
\(604\) −23.0851 −0.939321
\(605\) 0 0
\(606\) 0 0
\(607\) −28.7233 −1.16584 −0.582922 0.812528i \(-0.698091\pi\)
−0.582922 + 0.812528i \(0.698091\pi\)
\(608\) −6.48146 −0.262858
\(609\) 0 0
\(610\) 18.5523 0.751162
\(611\) 0 0
\(612\) 0 0
\(613\) −31.5306 −1.27351 −0.636755 0.771066i \(-0.719724\pi\)
−0.636755 + 0.771066i \(0.719724\pi\)
\(614\) 11.1578 0.450291
\(615\) 0 0
\(616\) 0 0
\(617\) 9.17225 0.369261 0.184630 0.982808i \(-0.440891\pi\)
0.184630 + 0.982808i \(0.440891\pi\)
\(618\) 0 0
\(619\) 32.5249 1.30729 0.653643 0.756803i \(-0.273240\pi\)
0.653643 + 0.756803i \(0.273240\pi\)
\(620\) −26.5934 −1.06802
\(621\) 0 0
\(622\) −46.2047 −1.85264
\(623\) 0.404420 0.0162027
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −40.8868 −1.63417
\(627\) 0 0
\(628\) 90.1110 3.59582
\(629\) 5.50389 0.219454
\(630\) 0 0
\(631\) −13.8606 −0.551784 −0.275892 0.961189i \(-0.588973\pi\)
−0.275892 + 0.961189i \(0.588973\pi\)
\(632\) 25.8075 1.02657
\(633\) 0 0
\(634\) −45.5856 −1.81043
\(635\) −12.0784 −0.479315
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −20.7214 −0.819085
\(641\) 37.9469 1.49881 0.749406 0.662111i \(-0.230339\pi\)
0.749406 + 0.662111i \(0.230339\pi\)
\(642\) 0 0
\(643\) 14.5306 0.573032 0.286516 0.958075i \(-0.407503\pi\)
0.286516 + 0.958075i \(0.407503\pi\)
\(644\) 36.6463 1.44407
\(645\) 0 0
\(646\) 2.72218 0.107103
\(647\) 7.98792 0.314038 0.157019 0.987596i \(-0.449812\pi\)
0.157019 + 0.987596i \(0.449812\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −38.9388 −1.52496
\(653\) 47.1191 1.84391 0.921957 0.387292i \(-0.126589\pi\)
0.921957 + 0.387292i \(0.126589\pi\)
\(654\) 0 0
\(655\) −3.61562 −0.141274
\(656\) 16.8816 0.659117
\(657\) 0 0
\(658\) 65.2398 2.54331
\(659\) 6.76729 0.263616 0.131808 0.991275i \(-0.457922\pi\)
0.131808 + 0.991275i \(0.457922\pi\)
\(660\) 0 0
\(661\) −32.6127 −1.26849 −0.634243 0.773134i \(-0.718688\pi\)
−0.634243 + 0.773134i \(0.718688\pi\)
\(662\) 46.4539 1.80548
\(663\) 0 0
\(664\) −51.6151 −2.00305
\(665\) 5.02655 0.194921
\(666\) 0 0
\(667\) −15.4322 −0.597539
\(668\) −22.5292 −0.871681
\(669\) 0 0
\(670\) −20.9361 −0.808833
\(671\) 0 0
\(672\) 0 0
\(673\) −11.4629 −0.441862 −0.220931 0.975289i \(-0.570910\pi\)
−0.220931 + 0.975289i \(0.570910\pi\)
\(674\) 28.7584 1.10773
\(675\) 0 0
\(676\) −47.6980 −1.83454
\(677\) −36.6808 −1.40976 −0.704879 0.709328i \(-0.748999\pi\)
−0.704879 + 0.709328i \(0.748999\pi\)
\(678\) 0 0
\(679\) −23.7936 −0.913115
\(680\) 2.02655 0.0777148
\(681\) 0 0
\(682\) 0 0
\(683\) 38.8115 1.48508 0.742540 0.669802i \(-0.233621\pi\)
0.742540 + 0.669802i \(0.233621\pi\)
\(684\) 0 0
\(685\) −6.88325 −0.262996
\(686\) −47.9017 −1.82889
\(687\) 0 0
\(688\) 12.8710 0.490701
\(689\) 0 0
\(690\) 0 0
\(691\) −27.8712 −1.06027 −0.530135 0.847913i \(-0.677859\pi\)
−0.530135 + 0.847913i \(0.677859\pi\)
\(692\) −60.9201 −2.31584
\(693\) 0 0
\(694\) −20.8003 −0.789569
\(695\) −20.7042 −0.785353
\(696\) 0 0
\(697\) 4.05311 0.153522
\(698\) 19.2962 0.730373
\(699\) 0 0
\(700\) 8.22607 0.310916
\(701\) 6.92820 0.261675 0.130837 0.991404i \(-0.458233\pi\)
0.130837 + 0.991404i \(0.458233\pi\)
\(702\) 0 0
\(703\) 24.1980 0.912646
\(704\) 0 0
\(705\) 0 0
\(706\) −2.96199 −0.111476
\(707\) 27.8727 1.04826
\(708\) 0 0
\(709\) −12.5756 −0.472286 −0.236143 0.971718i \(-0.575883\pi\)
−0.236143 + 0.971718i \(0.575883\pi\)
\(710\) 39.7060 1.49014
\(711\) 0 0
\(712\) 0.716853 0.0268652
\(713\) −32.2890 −1.20923
\(714\) 0 0
\(715\) 0 0
\(716\) 71.2012 2.66091
\(717\) 0 0
\(718\) 47.4202 1.76971
\(719\) −28.3155 −1.05599 −0.527996 0.849247i \(-0.677056\pi\)
−0.527996 + 0.849247i \(0.677056\pi\)
\(720\) 0 0
\(721\) −4.62667 −0.172306
\(722\) −33.2705 −1.23820
\(723\) 0 0
\(724\) 38.7439 1.43991
\(725\) −3.46410 −0.128654
\(726\) 0 0
\(727\) 21.4588 0.795865 0.397932 0.917415i \(-0.369728\pi\)
0.397932 + 0.917415i \(0.369728\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −30.4428 −1.12674
\(731\) 3.09019 0.114295
\(732\) 0 0
\(733\) −26.2791 −0.970641 −0.485320 0.874336i \(-0.661297\pi\)
−0.485320 + 0.874336i \(0.661297\pi\)
\(734\) 33.7632 1.24622
\(735\) 0 0
\(736\) −12.8788 −0.474719
\(737\) 0 0
\(738\) 0 0
\(739\) −29.4699 −1.08407 −0.542035 0.840356i \(-0.682346\pi\)
−0.542035 + 0.840356i \(0.682346\pi\)
\(740\) 39.6006 1.45575
\(741\) 0 0
\(742\) −20.2480 −0.743326
\(743\) −25.4912 −0.935181 −0.467591 0.883945i \(-0.654878\pi\)
−0.467591 + 0.883945i \(0.654878\pi\)
\(744\) 0 0
\(745\) 7.63566 0.279749
\(746\) −81.6151 −2.98814
\(747\) 0 0
\(748\) 0 0
\(749\) −14.1062 −0.515430
\(750\) 0 0
\(751\) −40.6006 −1.48154 −0.740768 0.671760i \(-0.765538\pi\)
−0.740768 + 0.671760i \(0.765538\pi\)
\(752\) 25.9581 0.946594
\(753\) 0 0
\(754\) 0 0
\(755\) −6.29181 −0.228982
\(756\) 0 0
\(757\) 24.3792 0.886077 0.443038 0.896503i \(-0.353901\pi\)
0.443038 + 0.896503i \(0.353901\pi\)
\(758\) −63.6135 −2.31055
\(759\) 0 0
\(760\) 8.90981 0.323193
\(761\) −27.6114 −1.00091 −0.500457 0.865761i \(-0.666835\pi\)
−0.500457 + 0.865761i \(0.666835\pi\)
\(762\) 0 0
\(763\) −1.49354 −0.0540697
\(764\) 32.6908 1.18271
\(765\) 0 0
\(766\) 0.858981 0.0310362
\(767\) 0 0
\(768\) 0 0
\(769\) −18.0233 −0.649936 −0.324968 0.945725i \(-0.605354\pi\)
−0.324968 + 0.945725i \(0.605354\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 64.8482 2.33394
\(773\) −20.7318 −0.745672 −0.372836 0.927897i \(-0.621615\pi\)
−0.372836 + 0.927897i \(0.621615\pi\)
\(774\) 0 0
\(775\) −7.24797 −0.260355
\(776\) −42.1753 −1.51401
\(777\) 0 0
\(778\) 47.4932 1.70271
\(779\) 17.8196 0.638454
\(780\) 0 0
\(781\) 0 0
\(782\) 5.40903 0.193427
\(783\) 0 0
\(784\) −4.19157 −0.149699
\(785\) 24.5596 0.876569
\(786\) 0 0
\(787\) 19.9162 0.709937 0.354969 0.934878i \(-0.384492\pi\)
0.354969 + 0.934878i \(0.384492\pi\)
\(788\) 50.8403 1.81111
\(789\) 0 0
\(790\) 15.4621 0.550118
\(791\) −15.0278 −0.534328
\(792\) 0 0
\(793\) 0 0
\(794\) 43.2046 1.53327
\(795\) 0 0
\(796\) 51.7511 1.83427
\(797\) −4.05311 −0.143568 −0.0717842 0.997420i \(-0.522869\pi\)
−0.0717842 + 0.997420i \(0.522869\pi\)
\(798\) 0 0
\(799\) 6.23227 0.220482
\(800\) −2.89093 −0.102210
\(801\) 0 0
\(802\) −4.63552 −0.163686
\(803\) 0 0
\(804\) 0 0
\(805\) 9.98789 0.352027
\(806\) 0 0
\(807\) 0 0
\(808\) 49.4057 1.73809
\(809\) −22.1169 −0.777590 −0.388795 0.921324i \(-0.627109\pi\)
−0.388795 + 0.921324i \(0.627109\pi\)
\(810\) 0 0
\(811\) 14.1986 0.498581 0.249290 0.968429i \(-0.419803\pi\)
0.249290 + 0.968429i \(0.419803\pi\)
\(812\) −28.4959 −1.00001
\(813\) 0 0
\(814\) 0 0
\(815\) −10.6127 −0.371746
\(816\) 0 0
\(817\) 13.5861 0.475318
\(818\) −84.1529 −2.94234
\(819\) 0 0
\(820\) 29.1622 1.01839
\(821\) −38.0037 −1.32634 −0.663170 0.748469i \(-0.730789\pi\)
−0.663170 + 0.748469i \(0.730789\pi\)
\(822\) 0 0
\(823\) 1.02655 0.0357834 0.0178917 0.999840i \(-0.494305\pi\)
0.0178917 + 0.999840i \(0.494305\pi\)
\(824\) −8.20100 −0.285695
\(825\) 0 0
\(826\) −24.9629 −0.868571
\(827\) 20.2193 0.703093 0.351547 0.936170i \(-0.385656\pi\)
0.351547 + 0.936170i \(0.385656\pi\)
\(828\) 0 0
\(829\) −25.2624 −0.877401 −0.438700 0.898633i \(-0.644561\pi\)
−0.438700 + 0.898633i \(0.644561\pi\)
\(830\) −30.9243 −1.07340
\(831\) 0 0
\(832\) 0 0
\(833\) −1.00635 −0.0348681
\(834\) 0 0
\(835\) −6.14029 −0.212493
\(836\) 0 0
\(837\) 0 0
\(838\) −68.4732 −2.36537
\(839\) 20.5490 0.709432 0.354716 0.934974i \(-0.384578\pi\)
0.354716 + 0.934974i \(0.384578\pi\)
\(840\) 0 0
\(841\) −17.0000 −0.586207
\(842\) 53.1962 1.83326
\(843\) 0 0
\(844\) −33.3510 −1.14799
\(845\) −13.0000 −0.447214
\(846\) 0 0
\(847\) 0 0
\(848\) −8.05640 −0.276658
\(849\) 0 0
\(850\) 1.21417 0.0416459
\(851\) 48.0821 1.64823
\(852\) 0 0
\(853\) 9.01868 0.308794 0.154397 0.988009i \(-0.450657\pi\)
0.154397 + 0.988009i \(0.450657\pi\)
\(854\) 41.5943 1.42333
\(855\) 0 0
\(856\) −25.0039 −0.854617
\(857\) 21.6896 0.740902 0.370451 0.928852i \(-0.379203\pi\)
0.370451 + 0.928852i \(0.379203\pi\)
\(858\) 0 0
\(859\) 1.38732 0.0473348 0.0236674 0.999720i \(-0.492466\pi\)
0.0236674 + 0.999720i \(0.492466\pi\)
\(860\) 22.2340 0.758173
\(861\) 0 0
\(862\) −91.0884 −3.10248
\(863\) 43.7665 1.48983 0.744915 0.667160i \(-0.232490\pi\)
0.744915 + 0.667160i \(0.232490\pi\)
\(864\) 0 0
\(865\) −16.6037 −0.564541
\(866\) −39.5545 −1.34412
\(867\) 0 0
\(868\) −59.6223 −2.02371
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −2.64737 −0.0896512
\(873\) 0 0
\(874\) 23.7810 0.804404
\(875\) 2.24200 0.0757934
\(876\) 0 0
\(877\) −24.6024 −0.830765 −0.415383 0.909647i \(-0.636352\pi\)
−0.415383 + 0.909647i \(0.636352\pi\)
\(878\) −57.0627 −1.92577
\(879\) 0 0
\(880\) 0 0
\(881\) −23.8196 −0.802503 −0.401252 0.915968i \(-0.631425\pi\)
−0.401252 + 0.915968i \(0.631425\pi\)
\(882\) 0 0
\(883\) −4.92034 −0.165583 −0.0827913 0.996567i \(-0.526383\pi\)
−0.0827913 + 0.996567i \(0.526383\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −31.4893 −1.05791
\(887\) 45.1848 1.51716 0.758579 0.651581i \(-0.225894\pi\)
0.758579 + 0.651581i \(0.225894\pi\)
\(888\) 0 0
\(889\) −27.0797 −0.908223
\(890\) 0.429490 0.0143965
\(891\) 0 0
\(892\) 20.9243 0.700597
\(893\) 27.4004 0.916919
\(894\) 0 0
\(895\) 19.4057 0.648662
\(896\) −46.4573 −1.55203
\(897\) 0 0
\(898\) 68.4732 2.28498
\(899\) 25.1077 0.837388
\(900\) 0 0
\(901\) −1.93426 −0.0644396
\(902\) 0 0
\(903\) 0 0
\(904\) −26.6375 −0.885951
\(905\) 10.5596 0.351012
\(906\) 0 0
\(907\) −50.1457 −1.66506 −0.832530 0.553980i \(-0.813109\pi\)
−0.832530 + 0.553980i \(0.813109\pi\)
\(908\) −26.2713 −0.871843
\(909\) 0 0
\(910\) 0 0
\(911\) 12.0821 0.400296 0.200148 0.979766i \(-0.435858\pi\)
0.200148 + 0.979766i \(0.435858\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −64.2769 −2.12609
\(915\) 0 0
\(916\) −53.9460 −1.78243
\(917\) −8.10622 −0.267691
\(918\) 0 0
\(919\) −29.5504 −0.974777 −0.487389 0.873185i \(-0.662051\pi\)
−0.487389 + 0.873185i \(0.662051\pi\)
\(920\) 17.7040 0.583684
\(921\) 0 0
\(922\) −74.2093 −2.44395
\(923\) 0 0
\(924\) 0 0
\(925\) 10.7931 0.354874
\(926\) 4.13710 0.135953
\(927\) 0 0
\(928\) 10.0145 0.328741
\(929\) −29.2995 −0.961286 −0.480643 0.876916i \(-0.659597\pi\)
−0.480643 + 0.876916i \(0.659597\pi\)
\(930\) 0 0
\(931\) −4.42446 −0.145006
\(932\) −52.7113 −1.72662
\(933\) 0 0
\(934\) 69.2345 2.26542
\(935\) 0 0
\(936\) 0 0
\(937\) 40.4986 1.32303 0.661516 0.749931i \(-0.269913\pi\)
0.661516 + 0.749931i \(0.269913\pi\)
\(938\) −46.9388 −1.53260
\(939\) 0 0
\(940\) 44.8413 1.46256
\(941\) 11.0078 0.358843 0.179422 0.983772i \(-0.442577\pi\)
0.179422 + 0.983772i \(0.442577\pi\)
\(942\) 0 0
\(943\) 35.4080 1.15304
\(944\) −9.93242 −0.323273
\(945\) 0 0
\(946\) 0 0
\(947\) 10.0941 0.328015 0.164008 0.986459i \(-0.447558\pi\)
0.164008 + 0.986459i \(0.447558\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 5.33816 0.173193
\(951\) 0 0
\(952\) 4.54353 0.147257
\(953\) −7.23124 −0.234243 −0.117121 0.993118i \(-0.537367\pi\)
−0.117121 + 0.993118i \(0.537367\pi\)
\(954\) 0 0
\(955\) 8.90981 0.288315
\(956\) −4.88842 −0.158103
\(957\) 0 0
\(958\) 47.0371 1.51970
\(959\) −15.4322 −0.498333
\(960\) 0 0
\(961\) 21.5330 0.694613
\(962\) 0 0
\(963\) 0 0
\(964\) 24.1050 0.776371
\(965\) 17.6742 0.568954
\(966\) 0 0
\(967\) −33.1660 −1.06655 −0.533274 0.845943i \(-0.679038\pi\)
−0.533274 + 0.845943i \(0.679038\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −25.2686 −0.811326
\(971\) −5.45885 −0.175183 −0.0875914 0.996156i \(-0.527917\pi\)
−0.0875914 + 0.996156i \(0.527917\pi\)
\(972\) 0 0
\(973\) −46.4187 −1.48811
\(974\) 95.4347 3.05792
\(975\) 0 0
\(976\) 16.5498 0.529747
\(977\) 49.5885 1.58648 0.793239 0.608911i \(-0.208393\pi\)
0.793239 + 0.608911i \(0.208393\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −7.24073 −0.231297
\(981\) 0 0
\(982\) −29.9614 −0.956106
\(983\) −14.1683 −0.451899 −0.225949 0.974139i \(-0.572548\pi\)
−0.225949 + 0.974139i \(0.572548\pi\)
\(984\) 0 0
\(985\) 13.8564 0.441502
\(986\) −4.20603 −0.133947
\(987\) 0 0
\(988\) 0 0
\(989\) 26.9960 0.858422
\(990\) 0 0
\(991\) −26.2214 −0.832951 −0.416475 0.909147i \(-0.636735\pi\)
−0.416475 + 0.909147i \(0.636735\pi\)
\(992\) 20.9534 0.665270
\(993\) 0 0
\(994\) 89.0208 2.82357
\(995\) 14.1047 0.447148
\(996\) 0 0
\(997\) −15.9469 −0.505043 −0.252521 0.967591i \(-0.581260\pi\)
−0.252521 + 0.967591i \(0.581260\pi\)
\(998\) −25.5716 −0.809456
\(999\) 0 0
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 5445.2.a.by.1.6 yes 6
3.2 odd 2 5445.2.a.bw.1.1 6
11.10 odd 2 inner 5445.2.a.by.1.1 yes 6
33.32 even 2 5445.2.a.bw.1.6 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5445.2.a.bw.1.1 6 3.2 odd 2
5445.2.a.bw.1.6 yes 6 33.32 even 2
5445.2.a.by.1.1 yes 6 11.10 odd 2 inner
5445.2.a.by.1.6 yes 6 1.1 even 1 trivial