Properties

Label 729.2.a.e.1.6
Level $729$
Weight $2$
Character 729.1
Self dual yes
Analytic conductor $5.821$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.7459857.1
Defining polynomial: \( x^{6} - 3x^{5} - 6x^{4} + 13x^{3} + 12x^{2} - 12x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.17298\) of defining polynomial
Character \(\chi\) \(=\) 729.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.70506 q^{2} +5.31738 q^{4} -1.67238 q^{5} +0.500591 q^{7} +8.97372 q^{8} +O(q^{10})\) \(q+2.70506 q^{2} +5.31738 q^{4} -1.67238 q^{5} +0.500591 q^{7} +8.97372 q^{8} -4.52391 q^{10} -1.91772 q^{11} +3.11244 q^{13} +1.35413 q^{14} +13.6397 q^{16} +2.66467 q^{17} +5.79664 q^{19} -8.89270 q^{20} -5.18755 q^{22} -4.64587 q^{23} -2.20313 q^{25} +8.41934 q^{26} +2.66183 q^{28} -2.61507 q^{29} -4.61460 q^{31} +18.9489 q^{32} +7.20811 q^{34} -0.837181 q^{35} -4.85867 q^{37} +15.6803 q^{38} -15.0075 q^{40} -11.5482 q^{41} -9.00434 q^{43} -10.1972 q^{44} -12.5674 q^{46} +6.83224 q^{47} -6.74941 q^{49} -5.95961 q^{50} +16.5500 q^{52} -5.43322 q^{53} +3.20716 q^{55} +4.49216 q^{56} -7.07393 q^{58} -2.19131 q^{59} +6.84034 q^{61} -12.4828 q^{62} +23.9786 q^{64} -5.20519 q^{65} +12.4836 q^{67} +14.1691 q^{68} -2.26463 q^{70} -2.83568 q^{71} +9.93497 q^{73} -13.1430 q^{74} +30.8229 q^{76} -0.959993 q^{77} +5.31121 q^{79} -22.8109 q^{80} -31.2385 q^{82} -2.72815 q^{83} -4.45636 q^{85} -24.3573 q^{86} -17.2091 q^{88} +11.2189 q^{89} +1.55806 q^{91} -24.7038 q^{92} +18.4816 q^{94} -9.69421 q^{95} -6.88914 q^{97} -18.2576 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} + 9 q^{4} - 3 q^{5} + 6 q^{7} + 6 q^{8} + 6 q^{10} - 6 q^{11} + 6 q^{13} + 24 q^{14} + 15 q^{16} - 9 q^{17} + 12 q^{19} - 21 q^{20} + 3 q^{22} - 12 q^{23} + 9 q^{25} + 24 q^{26} + 3 q^{28} + 21 q^{29} + 15 q^{31} + 30 q^{35} + 3 q^{37} + 15 q^{38} + 3 q^{40} - 12 q^{41} + 6 q^{43} - 33 q^{44} - 3 q^{46} - 15 q^{47} + 12 q^{49} - 24 q^{50} + 3 q^{52} - 9 q^{53} + 15 q^{55} + 12 q^{56} - 15 q^{58} + 6 q^{59} + 24 q^{61} - 30 q^{62} + 6 q^{64} - 15 q^{65} + 15 q^{67} + 36 q^{68} - 15 q^{70} + 12 q^{73} + 24 q^{74} + 9 q^{76} + 15 q^{77} + 24 q^{79} - 21 q^{80} - 21 q^{82} - 6 q^{83} - 18 q^{85} - 30 q^{86} - 21 q^{88} - 9 q^{89} + 18 q^{91} + 6 q^{92} - 6 q^{94} - 33 q^{95} - 21 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.70506 1.91277 0.956385 0.292110i \(-0.0943572\pi\)
0.956385 + 0.292110i \(0.0943572\pi\)
\(3\) 0 0
\(4\) 5.31738 2.65869
\(5\) −1.67238 −0.747913 −0.373957 0.927446i \(-0.621999\pi\)
−0.373957 + 0.927446i \(0.621999\pi\)
\(6\) 0 0
\(7\) 0.500591 0.189206 0.0946028 0.995515i \(-0.469842\pi\)
0.0946028 + 0.995515i \(0.469842\pi\)
\(8\) 8.97372 3.17269
\(9\) 0 0
\(10\) −4.52391 −1.43059
\(11\) −1.91772 −0.578214 −0.289107 0.957297i \(-0.593358\pi\)
−0.289107 + 0.957297i \(0.593358\pi\)
\(12\) 0 0
\(13\) 3.11244 0.863234 0.431617 0.902057i \(-0.357943\pi\)
0.431617 + 0.902057i \(0.357943\pi\)
\(14\) 1.35413 0.361907
\(15\) 0 0
\(16\) 13.6397 3.40993
\(17\) 2.66467 0.646278 0.323139 0.946352i \(-0.395262\pi\)
0.323139 + 0.946352i \(0.395262\pi\)
\(18\) 0 0
\(19\) 5.79664 1.32984 0.664920 0.746915i \(-0.268466\pi\)
0.664920 + 0.746915i \(0.268466\pi\)
\(20\) −8.89270 −1.98847
\(21\) 0 0
\(22\) −5.18755 −1.10599
\(23\) −4.64587 −0.968731 −0.484365 0.874866i \(-0.660949\pi\)
−0.484365 + 0.874866i \(0.660949\pi\)
\(24\) 0 0
\(25\) −2.20313 −0.440626
\(26\) 8.41934 1.65117
\(27\) 0 0
\(28\) 2.66183 0.503039
\(29\) −2.61507 −0.485606 −0.242803 0.970076i \(-0.578067\pi\)
−0.242803 + 0.970076i \(0.578067\pi\)
\(30\) 0 0
\(31\) −4.61460 −0.828807 −0.414404 0.910093i \(-0.636010\pi\)
−0.414404 + 0.910093i \(0.636010\pi\)
\(32\) 18.9489 3.34973
\(33\) 0 0
\(34\) 7.20811 1.23618
\(35\) −0.837181 −0.141509
\(36\) 0 0
\(37\) −4.85867 −0.798761 −0.399381 0.916785i \(-0.630775\pi\)
−0.399381 + 0.916785i \(0.630775\pi\)
\(38\) 15.6803 2.54368
\(39\) 0 0
\(40\) −15.0075 −2.37290
\(41\) −11.5482 −1.80352 −0.901760 0.432237i \(-0.857724\pi\)
−0.901760 + 0.432237i \(0.857724\pi\)
\(42\) 0 0
\(43\) −9.00434 −1.37315 −0.686574 0.727060i \(-0.740886\pi\)
−0.686574 + 0.727060i \(0.740886\pi\)
\(44\) −10.1972 −1.53729
\(45\) 0 0
\(46\) −12.5674 −1.85296
\(47\) 6.83224 0.996584 0.498292 0.867009i \(-0.333961\pi\)
0.498292 + 0.867009i \(0.333961\pi\)
\(48\) 0 0
\(49\) −6.74941 −0.964201
\(50\) −5.95961 −0.842816
\(51\) 0 0
\(52\) 16.5500 2.29507
\(53\) −5.43322 −0.746309 −0.373155 0.927769i \(-0.621724\pi\)
−0.373155 + 0.927769i \(0.621724\pi\)
\(54\) 0 0
\(55\) 3.20716 0.432454
\(56\) 4.49216 0.600291
\(57\) 0 0
\(58\) −7.07393 −0.928853
\(59\) −2.19131 −0.285285 −0.142642 0.989774i \(-0.545560\pi\)
−0.142642 + 0.989774i \(0.545560\pi\)
\(60\) 0 0
\(61\) 6.84034 0.875815 0.437908 0.899020i \(-0.355720\pi\)
0.437908 + 0.899020i \(0.355720\pi\)
\(62\) −12.4828 −1.58532
\(63\) 0 0
\(64\) 23.9786 2.99733
\(65\) −5.20519 −0.645624
\(66\) 0 0
\(67\) 12.4836 1.52511 0.762557 0.646921i \(-0.223944\pi\)
0.762557 + 0.646921i \(0.223944\pi\)
\(68\) 14.1691 1.71825
\(69\) 0 0
\(70\) −2.26463 −0.270675
\(71\) −2.83568 −0.336534 −0.168267 0.985741i \(-0.553817\pi\)
−0.168267 + 0.985741i \(0.553817\pi\)
\(72\) 0 0
\(73\) 9.93497 1.16280 0.581400 0.813618i \(-0.302505\pi\)
0.581400 + 0.813618i \(0.302505\pi\)
\(74\) −13.1430 −1.52785
\(75\) 0 0
\(76\) 30.8229 3.53563
\(77\) −0.959993 −0.109401
\(78\) 0 0
\(79\) 5.31121 0.597558 0.298779 0.954322i \(-0.403421\pi\)
0.298779 + 0.954322i \(0.403421\pi\)
\(80\) −22.8109 −2.55033
\(81\) 0 0
\(82\) −31.2385 −3.44972
\(83\) −2.72815 −0.299453 −0.149727 0.988727i \(-0.547839\pi\)
−0.149727 + 0.988727i \(0.547839\pi\)
\(84\) 0 0
\(85\) −4.45636 −0.483360
\(86\) −24.3573 −2.62652
\(87\) 0 0
\(88\) −17.2091 −1.83449
\(89\) 11.2189 1.18920 0.594600 0.804021i \(-0.297310\pi\)
0.594600 + 0.804021i \(0.297310\pi\)
\(90\) 0 0
\(91\) 1.55806 0.163329
\(92\) −24.7038 −2.57555
\(93\) 0 0
\(94\) 18.4816 1.90624
\(95\) −9.69421 −0.994605
\(96\) 0 0
\(97\) −6.88914 −0.699486 −0.349743 0.936846i \(-0.613731\pi\)
−0.349743 + 0.936846i \(0.613731\pi\)
\(98\) −18.2576 −1.84429
\(99\) 0 0
\(100\) −11.7149 −1.17149
\(101\) 3.72965 0.371114 0.185557 0.982634i \(-0.440591\pi\)
0.185557 + 0.982634i \(0.440591\pi\)
\(102\) 0 0
\(103\) 7.68080 0.756811 0.378406 0.925640i \(-0.376472\pi\)
0.378406 + 0.925640i \(0.376472\pi\)
\(104\) 27.9301 2.73877
\(105\) 0 0
\(106\) −14.6972 −1.42752
\(107\) −10.7658 −1.04077 −0.520383 0.853933i \(-0.674211\pi\)
−0.520383 + 0.853933i \(0.674211\pi\)
\(108\) 0 0
\(109\) 12.2298 1.17141 0.585703 0.810526i \(-0.300819\pi\)
0.585703 + 0.810526i \(0.300819\pi\)
\(110\) 8.67558 0.827184
\(111\) 0 0
\(112\) 6.82793 0.645179
\(113\) −1.94395 −0.182871 −0.0914357 0.995811i \(-0.529146\pi\)
−0.0914357 + 0.995811i \(0.529146\pi\)
\(114\) 0 0
\(115\) 7.76968 0.724526
\(116\) −13.9053 −1.29108
\(117\) 0 0
\(118\) −5.92764 −0.545684
\(119\) 1.33391 0.122279
\(120\) 0 0
\(121\) −7.32236 −0.665669
\(122\) 18.5036 1.67523
\(123\) 0 0
\(124\) −24.5376 −2.20354
\(125\) 12.0464 1.07746
\(126\) 0 0
\(127\) 2.34433 0.208026 0.104013 0.994576i \(-0.466832\pi\)
0.104013 + 0.994576i \(0.466832\pi\)
\(128\) 26.9659 2.38347
\(129\) 0 0
\(130\) −14.0804 −1.23493
\(131\) −17.1024 −1.49424 −0.747121 0.664688i \(-0.768565\pi\)
−0.747121 + 0.664688i \(0.768565\pi\)
\(132\) 0 0
\(133\) 2.90174 0.251613
\(134\) 33.7689 2.91719
\(135\) 0 0
\(136\) 23.9120 2.05044
\(137\) 13.9272 1.18988 0.594939 0.803771i \(-0.297176\pi\)
0.594939 + 0.803771i \(0.297176\pi\)
\(138\) 0 0
\(139\) 7.91664 0.671480 0.335740 0.941955i \(-0.391014\pi\)
0.335740 + 0.941955i \(0.391014\pi\)
\(140\) −4.45161 −0.376229
\(141\) 0 0
\(142\) −7.67071 −0.643712
\(143\) −5.96877 −0.499134
\(144\) 0 0
\(145\) 4.37340 0.363191
\(146\) 26.8747 2.22417
\(147\) 0 0
\(148\) −25.8354 −2.12366
\(149\) 0.728134 0.0596511 0.0298255 0.999555i \(-0.490505\pi\)
0.0298255 + 0.999555i \(0.490505\pi\)
\(150\) 0 0
\(151\) 4.34209 0.353354 0.176677 0.984269i \(-0.443465\pi\)
0.176677 + 0.984269i \(0.443465\pi\)
\(152\) 52.0174 4.21917
\(153\) 0 0
\(154\) −2.59684 −0.209260
\(155\) 7.71739 0.619876
\(156\) 0 0
\(157\) −15.5233 −1.23889 −0.619446 0.785040i \(-0.712643\pi\)
−0.619446 + 0.785040i \(0.712643\pi\)
\(158\) 14.3672 1.14299
\(159\) 0 0
\(160\) −31.6899 −2.50531
\(161\) −2.32568 −0.183289
\(162\) 0 0
\(163\) 8.49738 0.665566 0.332783 0.943003i \(-0.392012\pi\)
0.332783 + 0.943003i \(0.392012\pi\)
\(164\) −61.4059 −4.79500
\(165\) 0 0
\(166\) −7.37982 −0.572785
\(167\) 23.1419 1.79078 0.895389 0.445285i \(-0.146898\pi\)
0.895389 + 0.445285i \(0.146898\pi\)
\(168\) 0 0
\(169\) −3.31275 −0.254827
\(170\) −12.0547 −0.924556
\(171\) 0 0
\(172\) −47.8794 −3.65077
\(173\) −2.57848 −0.196038 −0.0980190 0.995185i \(-0.531251\pi\)
−0.0980190 + 0.995185i \(0.531251\pi\)
\(174\) 0 0
\(175\) −1.10287 −0.0833689
\(176\) −26.1572 −1.97167
\(177\) 0 0
\(178\) 30.3478 2.27467
\(179\) −8.89613 −0.664928 −0.332464 0.943116i \(-0.607880\pi\)
−0.332464 + 0.943116i \(0.607880\pi\)
\(180\) 0 0
\(181\) 7.91183 0.588082 0.294041 0.955793i \(-0.405000\pi\)
0.294041 + 0.955793i \(0.405000\pi\)
\(182\) 4.21465 0.312410
\(183\) 0 0
\(184\) −41.6907 −3.07348
\(185\) 8.12557 0.597404
\(186\) 0 0
\(187\) −5.11009 −0.373687
\(188\) 36.3296 2.64961
\(189\) 0 0
\(190\) −26.2235 −1.90245
\(191\) −15.8973 −1.15029 −0.575146 0.818051i \(-0.695055\pi\)
−0.575146 + 0.818051i \(0.695055\pi\)
\(192\) 0 0
\(193\) −4.58478 −0.330020 −0.165010 0.986292i \(-0.552766\pi\)
−0.165010 + 0.986292i \(0.552766\pi\)
\(194\) −18.6356 −1.33796
\(195\) 0 0
\(196\) −35.8891 −2.56351
\(197\) 2.99417 0.213326 0.106663 0.994295i \(-0.465983\pi\)
0.106663 + 0.994295i \(0.465983\pi\)
\(198\) 0 0
\(199\) 14.8885 1.05542 0.527709 0.849425i \(-0.323051\pi\)
0.527709 + 0.849425i \(0.323051\pi\)
\(200\) −19.7703 −1.39797
\(201\) 0 0
\(202\) 10.0889 0.709855
\(203\) −1.30908 −0.0918795
\(204\) 0 0
\(205\) 19.3130 1.34888
\(206\) 20.7771 1.44761
\(207\) 0 0
\(208\) 42.4528 2.94357
\(209\) −11.1163 −0.768932
\(210\) 0 0
\(211\) 13.8790 0.955467 0.477733 0.878505i \(-0.341458\pi\)
0.477733 + 0.878505i \(0.341458\pi\)
\(212\) −28.8904 −1.98420
\(213\) 0 0
\(214\) −29.1221 −1.99074
\(215\) 15.0587 1.02700
\(216\) 0 0
\(217\) −2.31003 −0.156815
\(218\) 33.0825 2.24063
\(219\) 0 0
\(220\) 17.0537 1.14976
\(221\) 8.29362 0.557889
\(222\) 0 0
\(223\) −6.81198 −0.456164 −0.228082 0.973642i \(-0.573245\pi\)
−0.228082 + 0.973642i \(0.573245\pi\)
\(224\) 9.48567 0.633788
\(225\) 0 0
\(226\) −5.25851 −0.349791
\(227\) −9.74084 −0.646522 −0.323261 0.946310i \(-0.604779\pi\)
−0.323261 + 0.946310i \(0.604779\pi\)
\(228\) 0 0
\(229\) −14.0448 −0.928109 −0.464055 0.885807i \(-0.653606\pi\)
−0.464055 + 0.885807i \(0.653606\pi\)
\(230\) 21.0175 1.38585
\(231\) 0 0
\(232\) −23.4669 −1.54068
\(233\) 5.32333 0.348743 0.174372 0.984680i \(-0.444211\pi\)
0.174372 + 0.984680i \(0.444211\pi\)
\(234\) 0 0
\(235\) −11.4261 −0.745359
\(236\) −11.6520 −0.758483
\(237\) 0 0
\(238\) 3.60832 0.233892
\(239\) 17.7735 1.14967 0.574836 0.818268i \(-0.305066\pi\)
0.574836 + 0.818268i \(0.305066\pi\)
\(240\) 0 0
\(241\) −2.00679 −0.129269 −0.0646344 0.997909i \(-0.520588\pi\)
−0.0646344 + 0.997909i \(0.520588\pi\)
\(242\) −19.8075 −1.27327
\(243\) 0 0
\(244\) 36.3726 2.32852
\(245\) 11.2876 0.721139
\(246\) 0 0
\(247\) 18.0417 1.14796
\(248\) −41.4101 −2.62955
\(249\) 0 0
\(250\) 32.5863 2.06094
\(251\) 23.5643 1.48737 0.743683 0.668533i \(-0.233077\pi\)
0.743683 + 0.668533i \(0.233077\pi\)
\(252\) 0 0
\(253\) 8.90947 0.560133
\(254\) 6.34157 0.397906
\(255\) 0 0
\(256\) 24.9871 1.56170
\(257\) 5.87457 0.366445 0.183223 0.983071i \(-0.441347\pi\)
0.183223 + 0.983071i \(0.441347\pi\)
\(258\) 0 0
\(259\) −2.43221 −0.151130
\(260\) −27.6779 −1.71651
\(261\) 0 0
\(262\) −46.2631 −2.85814
\(263\) 21.9781 1.35523 0.677615 0.735417i \(-0.263014\pi\)
0.677615 + 0.735417i \(0.263014\pi\)
\(264\) 0 0
\(265\) 9.08643 0.558175
\(266\) 7.84941 0.481278
\(267\) 0 0
\(268\) 66.3800 4.05480
\(269\) −30.6026 −1.86587 −0.932937 0.360041i \(-0.882763\pi\)
−0.932937 + 0.360041i \(0.882763\pi\)
\(270\) 0 0
\(271\) −16.0823 −0.976928 −0.488464 0.872584i \(-0.662443\pi\)
−0.488464 + 0.872584i \(0.662443\pi\)
\(272\) 36.3454 2.20376
\(273\) 0 0
\(274\) 37.6739 2.27596
\(275\) 4.22498 0.254776
\(276\) 0 0
\(277\) −20.8136 −1.25057 −0.625283 0.780398i \(-0.715017\pi\)
−0.625283 + 0.780398i \(0.715017\pi\)
\(278\) 21.4150 1.28439
\(279\) 0 0
\(280\) −7.51263 −0.448965
\(281\) 12.2603 0.731387 0.365693 0.930735i \(-0.380832\pi\)
0.365693 + 0.930735i \(0.380832\pi\)
\(282\) 0 0
\(283\) 4.57258 0.271812 0.135906 0.990722i \(-0.456606\pi\)
0.135906 + 0.990722i \(0.456606\pi\)
\(284\) −15.0784 −0.894738
\(285\) 0 0
\(286\) −16.1459 −0.954728
\(287\) −5.78091 −0.341236
\(288\) 0 0
\(289\) −9.89952 −0.582325
\(290\) 11.8303 0.694702
\(291\) 0 0
\(292\) 52.8280 3.09152
\(293\) 26.1234 1.52615 0.763073 0.646312i \(-0.223690\pi\)
0.763073 + 0.646312i \(0.223690\pi\)
\(294\) 0 0
\(295\) 3.66472 0.213368
\(296\) −43.6004 −2.53422
\(297\) 0 0
\(298\) 1.96965 0.114099
\(299\) −14.4600 −0.836241
\(300\) 0 0
\(301\) −4.50749 −0.259807
\(302\) 11.7456 0.675885
\(303\) 0 0
\(304\) 79.0646 4.53466
\(305\) −11.4397 −0.655034
\(306\) 0 0
\(307\) 3.29277 0.187928 0.0939641 0.995576i \(-0.470046\pi\)
0.0939641 + 0.995576i \(0.470046\pi\)
\(308\) −5.10464 −0.290864
\(309\) 0 0
\(310\) 20.8760 1.18568
\(311\) 34.7926 1.97291 0.986455 0.164034i \(-0.0524505\pi\)
0.986455 + 0.164034i \(0.0524505\pi\)
\(312\) 0 0
\(313\) 10.6278 0.600721 0.300360 0.953826i \(-0.402893\pi\)
0.300360 + 0.953826i \(0.402893\pi\)
\(314\) −41.9914 −2.36971
\(315\) 0 0
\(316\) 28.2417 1.58872
\(317\) −15.5002 −0.870579 −0.435290 0.900290i \(-0.643354\pi\)
−0.435290 + 0.900290i \(0.643354\pi\)
\(318\) 0 0
\(319\) 5.01497 0.280784
\(320\) −40.1015 −2.24174
\(321\) 0 0
\(322\) −6.29112 −0.350590
\(323\) 15.4461 0.859446
\(324\) 0 0
\(325\) −6.85710 −0.380363
\(326\) 22.9860 1.27308
\(327\) 0 0
\(328\) −103.630 −5.72201
\(329\) 3.42016 0.188559
\(330\) 0 0
\(331\) −14.5703 −0.800855 −0.400427 0.916328i \(-0.631138\pi\)
−0.400427 + 0.916328i \(0.631138\pi\)
\(332\) −14.5066 −0.796153
\(333\) 0 0
\(334\) 62.6005 3.42534
\(335\) −20.8774 −1.14065
\(336\) 0 0
\(337\) −20.6148 −1.12296 −0.561479 0.827491i \(-0.689768\pi\)
−0.561479 + 0.827491i \(0.689768\pi\)
\(338\) −8.96120 −0.487425
\(339\) 0 0
\(340\) −23.6961 −1.28510
\(341\) 8.84951 0.479228
\(342\) 0 0
\(343\) −6.88283 −0.371638
\(344\) −80.8024 −4.35657
\(345\) 0 0
\(346\) −6.97495 −0.374976
\(347\) −21.1835 −1.13719 −0.568596 0.822617i \(-0.692513\pi\)
−0.568596 + 0.822617i \(0.692513\pi\)
\(348\) 0 0
\(349\) −4.62597 −0.247623 −0.123811 0.992306i \(-0.539512\pi\)
−0.123811 + 0.992306i \(0.539512\pi\)
\(350\) −2.98333 −0.159466
\(351\) 0 0
\(352\) −36.3387 −1.93686
\(353\) −13.6434 −0.726165 −0.363083 0.931757i \(-0.618276\pi\)
−0.363083 + 0.931757i \(0.618276\pi\)
\(354\) 0 0
\(355\) 4.74236 0.251698
\(356\) 59.6551 3.16171
\(357\) 0 0
\(358\) −24.0646 −1.27185
\(359\) −28.2447 −1.49070 −0.745349 0.666675i \(-0.767717\pi\)
−0.745349 + 0.666675i \(0.767717\pi\)
\(360\) 0 0
\(361\) 14.6010 0.768473
\(362\) 21.4020 1.12486
\(363\) 0 0
\(364\) 8.28478 0.434240
\(365\) −16.6151 −0.869674
\(366\) 0 0
\(367\) 34.8802 1.82073 0.910366 0.413804i \(-0.135800\pi\)
0.910366 + 0.413804i \(0.135800\pi\)
\(368\) −63.3684 −3.30331
\(369\) 0 0
\(370\) 21.9802 1.14270
\(371\) −2.71982 −0.141206
\(372\) 0 0
\(373\) 3.05944 0.158412 0.0792059 0.996858i \(-0.474762\pi\)
0.0792059 + 0.996858i \(0.474762\pi\)
\(374\) −13.8231 −0.714777
\(375\) 0 0
\(376\) 61.3106 3.16185
\(377\) −8.13924 −0.419192
\(378\) 0 0
\(379\) −7.67705 −0.394344 −0.197172 0.980369i \(-0.563176\pi\)
−0.197172 + 0.980369i \(0.563176\pi\)
\(380\) −51.5477 −2.64434
\(381\) 0 0
\(382\) −43.0034 −2.20024
\(383\) 10.3619 0.529470 0.264735 0.964321i \(-0.414715\pi\)
0.264735 + 0.964321i \(0.414715\pi\)
\(384\) 0 0
\(385\) 1.60548 0.0818227
\(386\) −12.4021 −0.631252
\(387\) 0 0
\(388\) −36.6322 −1.85972
\(389\) −0.426951 −0.0216473 −0.0108236 0.999941i \(-0.503445\pi\)
−0.0108236 + 0.999941i \(0.503445\pi\)
\(390\) 0 0
\(391\) −12.3797 −0.626069
\(392\) −60.5673 −3.05911
\(393\) 0 0
\(394\) 8.09942 0.408043
\(395\) −8.88239 −0.446922
\(396\) 0 0
\(397\) −27.0891 −1.35956 −0.679781 0.733416i \(-0.737925\pi\)
−0.679781 + 0.733416i \(0.737925\pi\)
\(398\) 40.2743 2.01877
\(399\) 0 0
\(400\) −30.0501 −1.50250
\(401\) 29.3605 1.46619 0.733096 0.680125i \(-0.238075\pi\)
0.733096 + 0.680125i \(0.238075\pi\)
\(402\) 0 0
\(403\) −14.3627 −0.715455
\(404\) 19.8319 0.986675
\(405\) 0 0
\(406\) −3.54115 −0.175744
\(407\) 9.31757 0.461855
\(408\) 0 0
\(409\) −20.1839 −0.998031 −0.499015 0.866593i \(-0.666305\pi\)
−0.499015 + 0.866593i \(0.666305\pi\)
\(410\) 52.2428 2.58009
\(411\) 0 0
\(412\) 40.8417 2.01213
\(413\) −1.09695 −0.0539775
\(414\) 0 0
\(415\) 4.56252 0.223965
\(416\) 58.9773 2.89160
\(417\) 0 0
\(418\) −30.0704 −1.47079
\(419\) 24.3703 1.19057 0.595284 0.803515i \(-0.297040\pi\)
0.595284 + 0.803515i \(0.297040\pi\)
\(420\) 0 0
\(421\) −26.1745 −1.27567 −0.637835 0.770173i \(-0.720170\pi\)
−0.637835 + 0.770173i \(0.720170\pi\)
\(422\) 37.5435 1.82759
\(423\) 0 0
\(424\) −48.7561 −2.36781
\(425\) −5.87062 −0.284767
\(426\) 0 0
\(427\) 3.42421 0.165709
\(428\) −57.2456 −2.76707
\(429\) 0 0
\(430\) 40.7348 1.96441
\(431\) 31.9185 1.53746 0.768731 0.639572i \(-0.220889\pi\)
0.768731 + 0.639572i \(0.220889\pi\)
\(432\) 0 0
\(433\) 0.0123080 0.000591484 0 0.000295742 1.00000i \(-0.499906\pi\)
0.000295742 1.00000i \(0.499906\pi\)
\(434\) −6.24878 −0.299951
\(435\) 0 0
\(436\) 65.0306 3.11440
\(437\) −26.9304 −1.28826
\(438\) 0 0
\(439\) 5.30480 0.253185 0.126592 0.991955i \(-0.459596\pi\)
0.126592 + 0.991955i \(0.459596\pi\)
\(440\) 28.7802 1.37204
\(441\) 0 0
\(442\) 22.4348 1.06711
\(443\) 40.6963 1.93354 0.966771 0.255645i \(-0.0822879\pi\)
0.966771 + 0.255645i \(0.0822879\pi\)
\(444\) 0 0
\(445\) −18.7623 −0.889419
\(446\) −18.4268 −0.872536
\(447\) 0 0
\(448\) 12.0035 0.567111
\(449\) 15.4280 0.728093 0.364047 0.931381i \(-0.381395\pi\)
0.364047 + 0.931381i \(0.381395\pi\)
\(450\) 0 0
\(451\) 22.1461 1.04282
\(452\) −10.3367 −0.486198
\(453\) 0 0
\(454\) −26.3496 −1.23665
\(455\) −2.60567 −0.122156
\(456\) 0 0
\(457\) 2.38875 0.111741 0.0558704 0.998438i \(-0.482207\pi\)
0.0558704 + 0.998438i \(0.482207\pi\)
\(458\) −37.9922 −1.77526
\(459\) 0 0
\(460\) 41.3143 1.92629
\(461\) 32.4839 1.51292 0.756462 0.654037i \(-0.226926\pi\)
0.756462 + 0.654037i \(0.226926\pi\)
\(462\) 0 0
\(463\) 33.8785 1.57447 0.787234 0.616654i \(-0.211512\pi\)
0.787234 + 0.616654i \(0.211512\pi\)
\(464\) −35.6689 −1.65589
\(465\) 0 0
\(466\) 14.4000 0.667065
\(467\) −13.8027 −0.638711 −0.319356 0.947635i \(-0.603466\pi\)
−0.319356 + 0.947635i \(0.603466\pi\)
\(468\) 0 0
\(469\) 6.24918 0.288560
\(470\) −30.9084 −1.42570
\(471\) 0 0
\(472\) −19.6642 −0.905119
\(473\) 17.2678 0.793973
\(474\) 0 0
\(475\) −12.7707 −0.585962
\(476\) 7.09291 0.325103
\(477\) 0 0
\(478\) 48.0785 2.19906
\(479\) 5.89112 0.269172 0.134586 0.990902i \(-0.457030\pi\)
0.134586 + 0.990902i \(0.457030\pi\)
\(480\) 0 0
\(481\) −15.1223 −0.689518
\(482\) −5.42850 −0.247262
\(483\) 0 0
\(484\) −38.9357 −1.76981
\(485\) 11.5213 0.523155
\(486\) 0 0
\(487\) 29.0299 1.31547 0.657736 0.753249i \(-0.271514\pi\)
0.657736 + 0.753249i \(0.271514\pi\)
\(488\) 61.3832 2.77869
\(489\) 0 0
\(490\) 30.5337 1.37937
\(491\) 4.38351 0.197825 0.0989125 0.995096i \(-0.468464\pi\)
0.0989125 + 0.995096i \(0.468464\pi\)
\(492\) 0 0
\(493\) −6.96830 −0.313837
\(494\) 48.8038 2.19579
\(495\) 0 0
\(496\) −62.9420 −2.82618
\(497\) −1.41952 −0.0636741
\(498\) 0 0
\(499\) 35.3435 1.58219 0.791096 0.611691i \(-0.209511\pi\)
0.791096 + 0.611691i \(0.209511\pi\)
\(500\) 64.0553 2.86464
\(501\) 0 0
\(502\) 63.7430 2.84499
\(503\) −8.37659 −0.373494 −0.186747 0.982408i \(-0.559794\pi\)
−0.186747 + 0.982408i \(0.559794\pi\)
\(504\) 0 0
\(505\) −6.23740 −0.277561
\(506\) 24.1007 1.07141
\(507\) 0 0
\(508\) 12.4657 0.553076
\(509\) −3.84297 −0.170337 −0.0851683 0.996367i \(-0.527143\pi\)
−0.0851683 + 0.996367i \(0.527143\pi\)
\(510\) 0 0
\(511\) 4.97336 0.220008
\(512\) 13.6601 0.603699
\(513\) 0 0
\(514\) 15.8911 0.700925
\(515\) −12.8452 −0.566029
\(516\) 0 0
\(517\) −13.1023 −0.576239
\(518\) −6.57928 −0.289077
\(519\) 0 0
\(520\) −46.7099 −2.04836
\(521\) 19.6523 0.860983 0.430491 0.902595i \(-0.358340\pi\)
0.430491 + 0.902595i \(0.358340\pi\)
\(522\) 0 0
\(523\) −39.6103 −1.73204 −0.866018 0.500012i \(-0.833329\pi\)
−0.866018 + 0.500012i \(0.833329\pi\)
\(524\) −90.9398 −3.97272
\(525\) 0 0
\(526\) 59.4523 2.59224
\(527\) −12.2964 −0.535640
\(528\) 0 0
\(529\) −1.41591 −0.0615611
\(530\) 24.5794 1.06766
\(531\) 0 0
\(532\) 15.4297 0.668961
\(533\) −35.9429 −1.55686
\(534\) 0 0
\(535\) 18.0045 0.778402
\(536\) 112.024 4.83871
\(537\) 0 0
\(538\) −82.7820 −3.56899
\(539\) 12.9435 0.557514
\(540\) 0 0
\(541\) −41.8257 −1.79823 −0.899115 0.437713i \(-0.855788\pi\)
−0.899115 + 0.437713i \(0.855788\pi\)
\(542\) −43.5036 −1.86864
\(543\) 0 0
\(544\) 50.4927 2.16486
\(545\) −20.4530 −0.876110
\(546\) 0 0
\(547\) −17.0343 −0.728335 −0.364168 0.931333i \(-0.618646\pi\)
−0.364168 + 0.931333i \(0.618646\pi\)
\(548\) 74.0559 3.16351
\(549\) 0 0
\(550\) 11.4288 0.487328
\(551\) −15.1586 −0.645779
\(552\) 0 0
\(553\) 2.65875 0.113061
\(554\) −56.3021 −2.39205
\(555\) 0 0
\(556\) 42.0957 1.78526
\(557\) −33.7680 −1.43080 −0.715398 0.698717i \(-0.753755\pi\)
−0.715398 + 0.698717i \(0.753755\pi\)
\(558\) 0 0
\(559\) −28.0254 −1.18535
\(560\) −11.4189 −0.482538
\(561\) 0 0
\(562\) 33.1648 1.39897
\(563\) −22.7113 −0.957166 −0.478583 0.878042i \(-0.658849\pi\)
−0.478583 + 0.878042i \(0.658849\pi\)
\(564\) 0 0
\(565\) 3.25103 0.136772
\(566\) 12.3691 0.519913
\(567\) 0 0
\(568\) −25.4466 −1.06772
\(569\) 10.8714 0.455755 0.227877 0.973690i \(-0.426821\pi\)
0.227877 + 0.973690i \(0.426821\pi\)
\(570\) 0 0
\(571\) 14.8837 0.622864 0.311432 0.950268i \(-0.399191\pi\)
0.311432 + 0.950268i \(0.399191\pi\)
\(572\) −31.7382 −1.32704
\(573\) 0 0
\(574\) −15.6377 −0.652706
\(575\) 10.2354 0.426848
\(576\) 0 0
\(577\) −37.1163 −1.54517 −0.772586 0.634910i \(-0.781037\pi\)
−0.772586 + 0.634910i \(0.781037\pi\)
\(578\) −26.7789 −1.11385
\(579\) 0 0
\(580\) 23.2550 0.965613
\(581\) −1.36569 −0.0566583
\(582\) 0 0
\(583\) 10.4194 0.431526
\(584\) 89.1536 3.68920
\(585\) 0 0
\(586\) 70.6655 2.91917
\(587\) 14.6432 0.604390 0.302195 0.953246i \(-0.402281\pi\)
0.302195 + 0.953246i \(0.402281\pi\)
\(588\) 0 0
\(589\) −26.7492 −1.10218
\(590\) 9.91330 0.408124
\(591\) 0 0
\(592\) −66.2710 −2.72372
\(593\) −36.4392 −1.49638 −0.748189 0.663485i \(-0.769076\pi\)
−0.748189 + 0.663485i \(0.769076\pi\)
\(594\) 0 0
\(595\) −2.23081 −0.0914544
\(596\) 3.87176 0.158594
\(597\) 0 0
\(598\) −39.1151 −1.59954
\(599\) −27.4949 −1.12341 −0.561705 0.827337i \(-0.689855\pi\)
−0.561705 + 0.827337i \(0.689855\pi\)
\(600\) 0 0
\(601\) 45.1770 1.84281 0.921404 0.388606i \(-0.127043\pi\)
0.921404 + 0.388606i \(0.127043\pi\)
\(602\) −12.1931 −0.496952
\(603\) 0 0
\(604\) 23.0885 0.939459
\(605\) 12.2458 0.497863
\(606\) 0 0
\(607\) 17.1372 0.695576 0.347788 0.937573i \(-0.386933\pi\)
0.347788 + 0.937573i \(0.386933\pi\)
\(608\) 109.840 4.45460
\(609\) 0 0
\(610\) −30.9451 −1.25293
\(611\) 21.2649 0.860286
\(612\) 0 0
\(613\) −0.468761 −0.0189331 −0.00946653 0.999955i \(-0.503013\pi\)
−0.00946653 + 0.999955i \(0.503013\pi\)
\(614\) 8.90715 0.359463
\(615\) 0 0
\(616\) −8.61470 −0.347096
\(617\) 2.13485 0.0859458 0.0429729 0.999076i \(-0.486317\pi\)
0.0429729 + 0.999076i \(0.486317\pi\)
\(618\) 0 0
\(619\) 8.53760 0.343155 0.171578 0.985171i \(-0.445114\pi\)
0.171578 + 0.985171i \(0.445114\pi\)
\(620\) 41.0363 1.64806
\(621\) 0 0
\(622\) 94.1163 3.77372
\(623\) 5.61608 0.225004
\(624\) 0 0
\(625\) −9.13058 −0.365223
\(626\) 28.7490 1.14904
\(627\) 0 0
\(628\) −82.5430 −3.29383
\(629\) −12.9468 −0.516222
\(630\) 0 0
\(631\) −11.8708 −0.472569 −0.236284 0.971684i \(-0.575930\pi\)
−0.236284 + 0.971684i \(0.575930\pi\)
\(632\) 47.6613 1.89587
\(633\) 0 0
\(634\) −41.9291 −1.66522
\(635\) −3.92063 −0.155585
\(636\) 0 0
\(637\) −21.0071 −0.832331
\(638\) 13.5658 0.537076
\(639\) 0 0
\(640\) −45.0973 −1.78263
\(641\) −5.30366 −0.209482 −0.104741 0.994500i \(-0.533401\pi\)
−0.104741 + 0.994500i \(0.533401\pi\)
\(642\) 0 0
\(643\) −0.823869 −0.0324902 −0.0162451 0.999868i \(-0.505171\pi\)
−0.0162451 + 0.999868i \(0.505171\pi\)
\(644\) −12.3665 −0.487309
\(645\) 0 0
\(646\) 41.7828 1.64392
\(647\) 40.8373 1.60548 0.802740 0.596329i \(-0.203374\pi\)
0.802740 + 0.596329i \(0.203374\pi\)
\(648\) 0 0
\(649\) 4.20232 0.164955
\(650\) −18.5489 −0.727547
\(651\) 0 0
\(652\) 45.1838 1.76953
\(653\) −1.06936 −0.0418472 −0.0209236 0.999781i \(-0.506661\pi\)
−0.0209236 + 0.999781i \(0.506661\pi\)
\(654\) 0 0
\(655\) 28.6018 1.11756
\(656\) −157.514 −6.14988
\(657\) 0 0
\(658\) 9.25175 0.360671
\(659\) 28.6643 1.11660 0.558301 0.829638i \(-0.311453\pi\)
0.558301 + 0.829638i \(0.311453\pi\)
\(660\) 0 0
\(661\) −4.49572 −0.174863 −0.0874316 0.996171i \(-0.527866\pi\)
−0.0874316 + 0.996171i \(0.527866\pi\)
\(662\) −39.4135 −1.53185
\(663\) 0 0
\(664\) −24.4816 −0.950072
\(665\) −4.85283 −0.188185
\(666\) 0 0
\(667\) 12.1493 0.470422
\(668\) 123.054 4.76112
\(669\) 0 0
\(670\) −56.4747 −2.18181
\(671\) −13.1178 −0.506409
\(672\) 0 0
\(673\) 18.0586 0.696107 0.348054 0.937475i \(-0.386843\pi\)
0.348054 + 0.937475i \(0.386843\pi\)
\(674\) −55.7643 −2.14796
\(675\) 0 0
\(676\) −17.6151 −0.677505
\(677\) −15.7392 −0.604906 −0.302453 0.953164i \(-0.597805\pi\)
−0.302453 + 0.953164i \(0.597805\pi\)
\(678\) 0 0
\(679\) −3.44864 −0.132347
\(680\) −39.9901 −1.53355
\(681\) 0 0
\(682\) 23.9385 0.916652
\(683\) 2.76118 0.105654 0.0528268 0.998604i \(-0.483177\pi\)
0.0528268 + 0.998604i \(0.483177\pi\)
\(684\) 0 0
\(685\) −23.2916 −0.889925
\(686\) −18.6185 −0.710858
\(687\) 0 0
\(688\) −122.817 −4.68234
\(689\) −16.9105 −0.644240
\(690\) 0 0
\(691\) −34.5255 −1.31341 −0.656707 0.754146i \(-0.728051\pi\)
−0.656707 + 0.754146i \(0.728051\pi\)
\(692\) −13.7107 −0.521204
\(693\) 0 0
\(694\) −57.3029 −2.17519
\(695\) −13.2397 −0.502209
\(696\) 0 0
\(697\) −30.7721 −1.16557
\(698\) −12.5136 −0.473645
\(699\) 0 0
\(700\) −5.86436 −0.221652
\(701\) 20.7410 0.783378 0.391689 0.920098i \(-0.371891\pi\)
0.391689 + 0.920098i \(0.371891\pi\)
\(702\) 0 0
\(703\) −28.1640 −1.06222
\(704\) −45.9842 −1.73310
\(705\) 0 0
\(706\) −36.9063 −1.38899
\(707\) 1.86703 0.0702168
\(708\) 0 0
\(709\) 27.7071 1.04056 0.520281 0.853995i \(-0.325827\pi\)
0.520281 + 0.853995i \(0.325827\pi\)
\(710\) 12.8284 0.481441
\(711\) 0 0
\(712\) 100.675 3.77296
\(713\) 21.4388 0.802891
\(714\) 0 0
\(715\) 9.98209 0.373309
\(716\) −47.3041 −1.76784
\(717\) 0 0
\(718\) −76.4037 −2.85136
\(719\) −33.1314 −1.23559 −0.617797 0.786337i \(-0.711975\pi\)
−0.617797 + 0.786337i \(0.711975\pi\)
\(720\) 0 0
\(721\) 3.84494 0.143193
\(722\) 39.4966 1.46991
\(723\) 0 0
\(724\) 42.0702 1.56353
\(725\) 5.76134 0.213971
\(726\) 0 0
\(727\) −0.0826055 −0.00306367 −0.00153183 0.999999i \(-0.500488\pi\)
−0.00153183 + 0.999999i \(0.500488\pi\)
\(728\) 13.9816 0.518191
\(729\) 0 0
\(730\) −44.9449 −1.66349
\(731\) −23.9936 −0.887435
\(732\) 0 0
\(733\) −31.9175 −1.17890 −0.589450 0.807805i \(-0.700655\pi\)
−0.589450 + 0.807805i \(0.700655\pi\)
\(734\) 94.3532 3.48264
\(735\) 0 0
\(736\) −88.0342 −3.24498
\(737\) −23.9400 −0.881842
\(738\) 0 0
\(739\) −35.7919 −1.31663 −0.658314 0.752744i \(-0.728730\pi\)
−0.658314 + 0.752744i \(0.728730\pi\)
\(740\) 43.2067 1.58831
\(741\) 0 0
\(742\) −7.35729 −0.270095
\(743\) −19.7789 −0.725616 −0.362808 0.931864i \(-0.618182\pi\)
−0.362808 + 0.931864i \(0.618182\pi\)
\(744\) 0 0
\(745\) −1.21772 −0.0446138
\(746\) 8.27598 0.303005
\(747\) 0 0
\(748\) −27.1723 −0.993517
\(749\) −5.38924 −0.196919
\(750\) 0 0
\(751\) 30.5806 1.11590 0.557950 0.829874i \(-0.311588\pi\)
0.557950 + 0.829874i \(0.311588\pi\)
\(752\) 93.1899 3.39829
\(753\) 0 0
\(754\) −22.0172 −0.801818
\(755\) −7.26165 −0.264278
\(756\) 0 0
\(757\) 25.4129 0.923647 0.461824 0.886972i \(-0.347195\pi\)
0.461824 + 0.886972i \(0.347195\pi\)
\(758\) −20.7669 −0.754289
\(759\) 0 0
\(760\) −86.9931 −3.15557
\(761\) −46.8180 −1.69715 −0.848575 0.529075i \(-0.822539\pi\)
−0.848575 + 0.529075i \(0.822539\pi\)
\(762\) 0 0
\(763\) 6.12215 0.221637
\(764\) −84.5322 −3.05827
\(765\) 0 0
\(766\) 28.0297 1.01275
\(767\) −6.82032 −0.246267
\(768\) 0 0
\(769\) 14.5654 0.525243 0.262621 0.964899i \(-0.415413\pi\)
0.262621 + 0.964899i \(0.415413\pi\)
\(770\) 4.34292 0.156508
\(771\) 0 0
\(772\) −24.3790 −0.877419
\(773\) 24.3533 0.875929 0.437964 0.898992i \(-0.355700\pi\)
0.437964 + 0.898992i \(0.355700\pi\)
\(774\) 0 0
\(775\) 10.1666 0.365194
\(776\) −61.8212 −2.21925
\(777\) 0 0
\(778\) −1.15493 −0.0414063
\(779\) −66.9405 −2.39839
\(780\) 0 0
\(781\) 5.43804 0.194589
\(782\) −33.4879 −1.19753
\(783\) 0 0
\(784\) −92.0601 −3.28786
\(785\) 25.9609 0.926583
\(786\) 0 0
\(787\) −27.5672 −0.982664 −0.491332 0.870972i \(-0.663490\pi\)
−0.491332 + 0.870972i \(0.663490\pi\)
\(788\) 15.9211 0.567166
\(789\) 0 0
\(790\) −24.0274 −0.854858
\(791\) −0.973124 −0.0346003
\(792\) 0 0
\(793\) 21.2901 0.756034
\(794\) −73.2777 −2.60053
\(795\) 0 0
\(796\) 79.1677 2.80603
\(797\) −6.61692 −0.234383 −0.117192 0.993109i \(-0.537389\pi\)
−0.117192 + 0.993109i \(0.537389\pi\)
\(798\) 0 0
\(799\) 18.2057 0.644070
\(800\) −41.7469 −1.47598
\(801\) 0 0
\(802\) 79.4220 2.80449
\(803\) −19.0525 −0.672347
\(804\) 0 0
\(805\) 3.88943 0.137084
\(806\) −38.8519 −1.36850
\(807\) 0 0
\(808\) 33.4688 1.17743
\(809\) −8.61362 −0.302839 −0.151419 0.988470i \(-0.548384\pi\)
−0.151419 + 0.988470i \(0.548384\pi\)
\(810\) 0 0
\(811\) −9.58716 −0.336651 −0.168325 0.985732i \(-0.553836\pi\)
−0.168325 + 0.985732i \(0.553836\pi\)
\(812\) −6.96088 −0.244279
\(813\) 0 0
\(814\) 25.2046 0.883422
\(815\) −14.2109 −0.497786
\(816\) 0 0
\(817\) −52.1949 −1.82607
\(818\) −54.5988 −1.90900
\(819\) 0 0
\(820\) 102.694 3.58624
\(821\) −13.8635 −0.483838 −0.241919 0.970296i \(-0.577777\pi\)
−0.241919 + 0.970296i \(0.577777\pi\)
\(822\) 0 0
\(823\) 47.8257 1.66710 0.833550 0.552444i \(-0.186305\pi\)
0.833550 + 0.552444i \(0.186305\pi\)
\(824\) 68.9253 2.40113
\(825\) 0 0
\(826\) −2.96733 −0.103246
\(827\) −42.4417 −1.47584 −0.737921 0.674887i \(-0.764192\pi\)
−0.737921 + 0.674887i \(0.764192\pi\)
\(828\) 0 0
\(829\) 26.0037 0.903146 0.451573 0.892234i \(-0.350863\pi\)
0.451573 + 0.892234i \(0.350863\pi\)
\(830\) 12.3419 0.428394
\(831\) 0 0
\(832\) 74.6319 2.58740
\(833\) −17.9850 −0.623142
\(834\) 0 0
\(835\) −38.7022 −1.33935
\(836\) −59.1096 −2.04435
\(837\) 0 0
\(838\) 65.9233 2.27728
\(839\) 1.25628 0.0433715 0.0216857 0.999765i \(-0.493097\pi\)
0.0216857 + 0.999765i \(0.493097\pi\)
\(840\) 0 0
\(841\) −22.1614 −0.764186
\(842\) −70.8038 −2.44006
\(843\) 0 0
\(844\) 73.7996 2.54029
\(845\) 5.54019 0.190588
\(846\) 0 0
\(847\) −3.66551 −0.125948
\(848\) −74.1076 −2.54487
\(849\) 0 0
\(850\) −15.8804 −0.544693
\(851\) 22.5728 0.773784
\(852\) 0 0
\(853\) 1.45435 0.0497959 0.0248979 0.999690i \(-0.492074\pi\)
0.0248979 + 0.999690i \(0.492074\pi\)
\(854\) 9.26272 0.316964
\(855\) 0 0
\(856\) −96.6089 −3.30202
\(857\) −52.3097 −1.78686 −0.893432 0.449198i \(-0.851710\pi\)
−0.893432 + 0.449198i \(0.851710\pi\)
\(858\) 0 0
\(859\) −21.0043 −0.716659 −0.358329 0.933595i \(-0.616654\pi\)
−0.358329 + 0.933595i \(0.616654\pi\)
\(860\) 80.0728 2.73046
\(861\) 0 0
\(862\) 86.3417 2.94081
\(863\) 12.9813 0.441890 0.220945 0.975286i \(-0.429086\pi\)
0.220945 + 0.975286i \(0.429086\pi\)
\(864\) 0 0
\(865\) 4.31221 0.146619
\(866\) 0.0332939 0.00113137
\(867\) 0 0
\(868\) −12.2833 −0.416922
\(869\) −10.1854 −0.345516
\(870\) 0 0
\(871\) 38.8544 1.31653
\(872\) 109.747 3.71650
\(873\) 0 0
\(874\) −72.8485 −2.46414
\(875\) 6.03032 0.203862
\(876\) 0 0
\(877\) 31.0457 1.04834 0.524169 0.851614i \(-0.324376\pi\)
0.524169 + 0.851614i \(0.324376\pi\)
\(878\) 14.3498 0.484284
\(879\) 0 0
\(880\) 43.7448 1.47464
\(881\) 19.2957 0.650087 0.325044 0.945699i \(-0.394621\pi\)
0.325044 + 0.945699i \(0.394621\pi\)
\(882\) 0 0
\(883\) −9.82388 −0.330600 −0.165300 0.986243i \(-0.552859\pi\)
−0.165300 + 0.986243i \(0.552859\pi\)
\(884\) 44.1003 1.48325
\(885\) 0 0
\(886\) 110.086 3.69842
\(887\) 44.1133 1.48118 0.740590 0.671958i \(-0.234546\pi\)
0.740590 + 0.671958i \(0.234546\pi\)
\(888\) 0 0
\(889\) 1.17355 0.0393597
\(890\) −50.7533 −1.70125
\(891\) 0 0
\(892\) −36.2219 −1.21280
\(893\) 39.6040 1.32530
\(894\) 0 0
\(895\) 14.8778 0.497308
\(896\) 13.4989 0.450965
\(897\) 0 0
\(898\) 41.7338 1.39268
\(899\) 12.0675 0.402474
\(900\) 0 0
\(901\) −14.4777 −0.482323
\(902\) 59.9067 1.99467
\(903\) 0 0
\(904\) −17.4444 −0.580194
\(905\) −13.2316 −0.439834
\(906\) 0 0
\(907\) −42.4124 −1.40828 −0.704140 0.710061i \(-0.748667\pi\)
−0.704140 + 0.710061i \(0.748667\pi\)
\(908\) −51.7957 −1.71890
\(909\) 0 0
\(910\) −7.04851 −0.233656
\(911\) 36.7104 1.21627 0.608134 0.793834i \(-0.291918\pi\)
0.608134 + 0.793834i \(0.291918\pi\)
\(912\) 0 0
\(913\) 5.23182 0.173148
\(914\) 6.46171 0.213735
\(915\) 0 0
\(916\) −74.6817 −2.46755
\(917\) −8.56130 −0.282719
\(918\) 0 0
\(919\) −14.0589 −0.463761 −0.231881 0.972744i \(-0.574488\pi\)
−0.231881 + 0.972744i \(0.574488\pi\)
\(920\) 69.7229 2.29870
\(921\) 0 0
\(922\) 87.8710 2.89388
\(923\) −8.82588 −0.290508
\(924\) 0 0
\(925\) 10.7043 0.351955
\(926\) 91.6436 3.01160
\(927\) 0 0
\(928\) −49.5528 −1.62665
\(929\) −18.5175 −0.607539 −0.303770 0.952746i \(-0.598245\pi\)
−0.303770 + 0.952746i \(0.598245\pi\)
\(930\) 0 0
\(931\) −39.1239 −1.28223
\(932\) 28.3062 0.927199
\(933\) 0 0
\(934\) −37.3371 −1.22171
\(935\) 8.54604 0.279485
\(936\) 0 0
\(937\) 4.46818 0.145969 0.0729845 0.997333i \(-0.476748\pi\)
0.0729845 + 0.997333i \(0.476748\pi\)
\(938\) 16.9044 0.551949
\(939\) 0 0
\(940\) −60.7570 −1.98168
\(941\) −2.00386 −0.0653239 −0.0326620 0.999466i \(-0.510398\pi\)
−0.0326620 + 0.999466i \(0.510398\pi\)
\(942\) 0 0
\(943\) 53.6512 1.74712
\(944\) −29.8889 −0.972801
\(945\) 0 0
\(946\) 46.7105 1.51869
\(947\) −12.5838 −0.408919 −0.204460 0.978875i \(-0.565544\pi\)
−0.204460 + 0.978875i \(0.565544\pi\)
\(948\) 0 0
\(949\) 30.9220 1.00377
\(950\) −34.5457 −1.12081
\(951\) 0 0
\(952\) 11.9701 0.387955
\(953\) −19.9641 −0.646700 −0.323350 0.946279i \(-0.604809\pi\)
−0.323350 + 0.946279i \(0.604809\pi\)
\(954\) 0 0
\(955\) 26.5865 0.860318
\(956\) 94.5084 3.05662
\(957\) 0 0
\(958\) 15.9359 0.514864
\(959\) 6.97181 0.225132
\(960\) 0 0
\(961\) −9.70544 −0.313079
\(962\) −40.9068 −1.31889
\(963\) 0 0
\(964\) −10.6709 −0.343686
\(965\) 7.66752 0.246826
\(966\) 0 0
\(967\) −32.2086 −1.03576 −0.517879 0.855454i \(-0.673278\pi\)
−0.517879 + 0.855454i \(0.673278\pi\)
\(968\) −65.7088 −2.11196
\(969\) 0 0
\(970\) 31.1659 1.00068
\(971\) −6.62934 −0.212746 −0.106373 0.994326i \(-0.533924\pi\)
−0.106373 + 0.994326i \(0.533924\pi\)
\(972\) 0 0
\(973\) 3.96300 0.127048
\(974\) 78.5278 2.51619
\(975\) 0 0
\(976\) 93.3004 2.98647
\(977\) 11.8566 0.379328 0.189664 0.981849i \(-0.439260\pi\)
0.189664 + 0.981849i \(0.439260\pi\)
\(978\) 0 0
\(979\) −21.5147 −0.687612
\(980\) 60.0205 1.91728
\(981\) 0 0
\(982\) 11.8577 0.378394
\(983\) −52.0650 −1.66062 −0.830308 0.557305i \(-0.811835\pi\)
−0.830308 + 0.557305i \(0.811835\pi\)
\(984\) 0 0
\(985\) −5.00740 −0.159549
\(986\) −18.8497 −0.600297
\(987\) 0 0
\(988\) 95.9343 3.05208
\(989\) 41.8330 1.33021
\(990\) 0 0
\(991\) 1.47115 0.0467326 0.0233663 0.999727i \(-0.492562\pi\)
0.0233663 + 0.999727i \(0.492562\pi\)
\(992\) −87.4418 −2.77628
\(993\) 0 0
\(994\) −3.83989 −0.121794
\(995\) −24.8993 −0.789361
\(996\) 0 0
\(997\) −26.4213 −0.836771 −0.418385 0.908270i \(-0.637404\pi\)
−0.418385 + 0.908270i \(0.637404\pi\)
\(998\) 95.6065 3.02637
\(999\) 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 729.2.a.e.1.6 yes 6
3.2 odd 2 729.2.a.b.1.1 6
9.2 odd 6 729.2.c.d.244.6 12
9.4 even 3 729.2.c.a.487.1 12
9.5 odd 6 729.2.c.d.487.6 12
9.7 even 3 729.2.c.a.244.1 12
27.2 odd 18 729.2.e.t.568.2 12
27.4 even 9 729.2.e.u.406.2 12
27.5 odd 18 729.2.e.s.649.1 12
27.7 even 9 729.2.e.u.325.2 12
27.11 odd 18 729.2.e.s.82.1 12
27.13 even 9 729.2.e.k.163.1 12
27.14 odd 18 729.2.e.t.163.2 12
27.16 even 9 729.2.e.l.82.2 12
27.20 odd 18 729.2.e.j.325.1 12
27.22 even 9 729.2.e.l.649.2 12
27.23 odd 18 729.2.e.j.406.1 12
27.25 even 9 729.2.e.k.568.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.b.1.1 6 3.2 odd 2
729.2.a.e.1.6 yes 6 1.1 even 1 trivial
729.2.c.a.244.1 12 9.7 even 3
729.2.c.a.487.1 12 9.4 even 3
729.2.c.d.244.6 12 9.2 odd 6
729.2.c.d.487.6 12 9.5 odd 6
729.2.e.j.325.1 12 27.20 odd 18
729.2.e.j.406.1 12 27.23 odd 18
729.2.e.k.163.1 12 27.13 even 9
729.2.e.k.568.1 12 27.25 even 9
729.2.e.l.82.2 12 27.16 even 9
729.2.e.l.649.2 12 27.22 even 9
729.2.e.s.82.1 12 27.11 odd 18
729.2.e.s.649.1 12 27.5 odd 18
729.2.e.t.163.2 12 27.14 odd 18
729.2.e.t.568.2 12 27.2 odd 18
729.2.e.u.325.2 12 27.7 even 9
729.2.e.u.406.2 12 27.4 even 9