Properties

Label 5445.2.a.cc.1.2
Level $5445$
Weight $2$
Character 5445.1
Self dual yes
Analytic conductor $43.479$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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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: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 4 x^{7} - 3 x^{6} + 22 x^{5} - 3 x^{4} - 32 x^{3} + 9 x^{2} + 8 x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 495)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.13569\) of defining polynomial
Character \(\chi\) \(=\) 5445.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.13569 q^{2} -0.710206 q^{4} -1.00000 q^{5} -4.10132 q^{7} +3.07796 q^{8} +O(q^{10})\) \(q-1.13569 q^{2} -0.710206 q^{4} -1.00000 q^{5} -4.10132 q^{7} +3.07796 q^{8} +1.13569 q^{10} +2.27388 q^{13} +4.65784 q^{14} -2.07520 q^{16} -5.01888 q^{17} +7.57794 q^{19} +0.710206 q^{20} +1.97494 q^{23} +1.00000 q^{25} -2.58242 q^{26} +2.91278 q^{28} +4.00136 q^{29} -3.81490 q^{31} -3.79913 q^{32} +5.69990 q^{34} +4.10132 q^{35} -6.73089 q^{37} -8.60619 q^{38} -3.07796 q^{40} +4.02336 q^{41} -9.57903 q^{43} -2.24292 q^{46} -3.18673 q^{47} +9.82086 q^{49} -1.13569 q^{50} -1.61492 q^{52} -11.2291 q^{53} -12.6237 q^{56} -4.54431 q^{58} +9.53769 q^{59} -3.61186 q^{61} +4.33255 q^{62} +8.46503 q^{64} -2.27388 q^{65} -6.31504 q^{67} +3.56444 q^{68} -4.65784 q^{70} -12.2950 q^{71} +3.89030 q^{73} +7.64422 q^{74} -5.38189 q^{76} -17.5747 q^{79} +2.07520 q^{80} -4.56930 q^{82} +13.8475 q^{83} +5.01888 q^{85} +10.8788 q^{86} -7.85399 q^{89} -9.32590 q^{91} -1.40261 q^{92} +3.61914 q^{94} -7.57794 q^{95} +5.17866 q^{97} -11.1535 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} + 6q^{4} - 8q^{5} - 8q^{7} + 12q^{8} + O(q^{10}) \) \( 8q + 4q^{2} + 6q^{4} - 8q^{5} - 8q^{7} + 12q^{8} - 4q^{10} - 6q^{13} - 14q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 6q^{20} - 4q^{23} + 8q^{25} + 2q^{26} - 24q^{28} + 22q^{29} + 10q^{31} + 28q^{32} - 2q^{34} + 8q^{35} - 14q^{37} + 20q^{38} - 12q^{40} + 22q^{41} - 14q^{43} + 2q^{46} - 10q^{47} + 4q^{50} + 10q^{52} + 18q^{53} - 34q^{56} + 12q^{58} - 2q^{59} + 14q^{61} + 30q^{62} + 30q^{64} + 6q^{65} + 10q^{67} + 6q^{68} + 14q^{70} + 2q^{71} - 16q^{73} + 24q^{74} + 22q^{76} + 16q^{79} - 14q^{80} + 10q^{82} + 46q^{83} - 8q^{85} + 28q^{86} - 38q^{89} + 8q^{91} + 24q^{92} + 10q^{94} - 2q^{95} - 4q^{97} + 4q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.13569 −0.803055 −0.401527 0.915847i \(-0.631521\pi\)
−0.401527 + 0.915847i \(0.631521\pi\)
\(3\) 0 0
\(4\) −0.710206 −0.355103
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −4.10132 −1.55015 −0.775077 0.631866i \(-0.782289\pi\)
−0.775077 + 0.631866i \(0.782289\pi\)
\(8\) 3.07796 1.08822
\(9\) 0 0
\(10\) 1.13569 0.359137
\(11\) 0 0
\(12\) 0 0
\(13\) 2.27388 0.630660 0.315330 0.948982i \(-0.397885\pi\)
0.315330 + 0.948982i \(0.397885\pi\)
\(14\) 4.65784 1.24486
\(15\) 0 0
\(16\) −2.07520 −0.518799
\(17\) −5.01888 −1.21726 −0.608629 0.793455i \(-0.708280\pi\)
−0.608629 + 0.793455i \(0.708280\pi\)
\(18\) 0 0
\(19\) 7.57794 1.73850 0.869249 0.494375i \(-0.164603\pi\)
0.869249 + 0.494375i \(0.164603\pi\)
\(20\) 0.710206 0.158807
\(21\) 0 0
\(22\) 0 0
\(23\) 1.97494 0.411803 0.205902 0.978573i \(-0.433987\pi\)
0.205902 + 0.978573i \(0.433987\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −2.58242 −0.506455
\(27\) 0 0
\(28\) 2.91278 0.550464
\(29\) 4.00136 0.743033 0.371517 0.928426i \(-0.378838\pi\)
0.371517 + 0.928426i \(0.378838\pi\)
\(30\) 0 0
\(31\) −3.81490 −0.685176 −0.342588 0.939486i \(-0.611304\pi\)
−0.342588 + 0.939486i \(0.611304\pi\)
\(32\) −3.79913 −0.671598
\(33\) 0 0
\(34\) 5.69990 0.977525
\(35\) 4.10132 0.693250
\(36\) 0 0
\(37\) −6.73089 −1.10655 −0.553276 0.832998i \(-0.686623\pi\)
−0.553276 + 0.832998i \(0.686623\pi\)
\(38\) −8.60619 −1.39611
\(39\) 0 0
\(40\) −3.07796 −0.486668
\(41\) 4.02336 0.628344 0.314172 0.949366i \(-0.398273\pi\)
0.314172 + 0.949366i \(0.398273\pi\)
\(42\) 0 0
\(43\) −9.57903 −1.46079 −0.730394 0.683026i \(-0.760664\pi\)
−0.730394 + 0.683026i \(0.760664\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −2.24292 −0.330701
\(47\) −3.18673 −0.464832 −0.232416 0.972616i \(-0.574663\pi\)
−0.232416 + 0.972616i \(0.574663\pi\)
\(48\) 0 0
\(49\) 9.82086 1.40298
\(50\) −1.13569 −0.160611
\(51\) 0 0
\(52\) −1.61492 −0.223949
\(53\) −11.2291 −1.54244 −0.771219 0.636570i \(-0.780352\pi\)
−0.771219 + 0.636570i \(0.780352\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −12.6237 −1.68691
\(57\) 0 0
\(58\) −4.54431 −0.596697
\(59\) 9.53769 1.24170 0.620851 0.783929i \(-0.286787\pi\)
0.620851 + 0.783929i \(0.286787\pi\)
\(60\) 0 0
\(61\) −3.61186 −0.462452 −0.231226 0.972900i \(-0.574274\pi\)
−0.231226 + 0.972900i \(0.574274\pi\)
\(62\) 4.33255 0.550234
\(63\) 0 0
\(64\) 8.46503 1.05813
\(65\) −2.27388 −0.282040
\(66\) 0 0
\(67\) −6.31504 −0.771505 −0.385752 0.922602i \(-0.626058\pi\)
−0.385752 + 0.922602i \(0.626058\pi\)
\(68\) 3.56444 0.432252
\(69\) 0 0
\(70\) −4.65784 −0.556718
\(71\) −12.2950 −1.45915 −0.729574 0.683901i \(-0.760282\pi\)
−0.729574 + 0.683901i \(0.760282\pi\)
\(72\) 0 0
\(73\) 3.89030 0.455325 0.227663 0.973740i \(-0.426892\pi\)
0.227663 + 0.973740i \(0.426892\pi\)
\(74\) 7.64422 0.888622
\(75\) 0 0
\(76\) −5.38189 −0.617345
\(77\) 0 0
\(78\) 0 0
\(79\) −17.5747 −1.97731 −0.988656 0.150196i \(-0.952009\pi\)
−0.988656 + 0.150196i \(0.952009\pi\)
\(80\) 2.07520 0.232014
\(81\) 0 0
\(82\) −4.56930 −0.504594
\(83\) 13.8475 1.51996 0.759982 0.649944i \(-0.225208\pi\)
0.759982 + 0.649944i \(0.225208\pi\)
\(84\) 0 0
\(85\) 5.01888 0.544374
\(86\) 10.8788 1.17309
\(87\) 0 0
\(88\) 0 0
\(89\) −7.85399 −0.832522 −0.416261 0.909245i \(-0.636660\pi\)
−0.416261 + 0.909245i \(0.636660\pi\)
\(90\) 0 0
\(91\) −9.32590 −0.977620
\(92\) −1.40261 −0.146232
\(93\) 0 0
\(94\) 3.61914 0.373286
\(95\) −7.57794 −0.777480
\(96\) 0 0
\(97\) 5.17866 0.525813 0.262907 0.964821i \(-0.415319\pi\)
0.262907 + 0.964821i \(0.415319\pi\)
\(98\) −11.1535 −1.12667
\(99\) 0 0
\(100\) −0.710206 −0.0710206
\(101\) −3.99265 −0.397284 −0.198642 0.980072i \(-0.563653\pi\)
−0.198642 + 0.980072i \(0.563653\pi\)
\(102\) 0 0
\(103\) −0.940967 −0.0927162 −0.0463581 0.998925i \(-0.514762\pi\)
−0.0463581 + 0.998925i \(0.514762\pi\)
\(104\) 6.99889 0.686298
\(105\) 0 0
\(106\) 12.7528 1.23866
\(107\) 14.5295 1.40462 0.702308 0.711873i \(-0.252153\pi\)
0.702308 + 0.711873i \(0.252153\pi\)
\(108\) 0 0
\(109\) −7.70193 −0.737711 −0.368855 0.929487i \(-0.620250\pi\)
−0.368855 + 0.929487i \(0.620250\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 8.51105 0.804219
\(113\) 0.675502 0.0635459 0.0317729 0.999495i \(-0.489885\pi\)
0.0317729 + 0.999495i \(0.489885\pi\)
\(114\) 0 0
\(115\) −1.97494 −0.184164
\(116\) −2.84179 −0.263853
\(117\) 0 0
\(118\) −10.8319 −0.997155
\(119\) 20.5841 1.88694
\(120\) 0 0
\(121\) 0 0
\(122\) 4.10196 0.371374
\(123\) 0 0
\(124\) 2.70936 0.243308
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.41105 0.391418 0.195709 0.980662i \(-0.437299\pi\)
0.195709 + 0.980662i \(0.437299\pi\)
\(128\) −2.01540 −0.178138
\(129\) 0 0
\(130\) 2.58242 0.226493
\(131\) 21.4004 1.86976 0.934882 0.354959i \(-0.115505\pi\)
0.934882 + 0.354959i \(0.115505\pi\)
\(132\) 0 0
\(133\) −31.0796 −2.69494
\(134\) 7.17193 0.619561
\(135\) 0 0
\(136\) −15.4479 −1.32465
\(137\) 3.82130 0.326475 0.163238 0.986587i \(-0.447806\pi\)
0.163238 + 0.986587i \(0.447806\pi\)
\(138\) 0 0
\(139\) −6.29721 −0.534122 −0.267061 0.963680i \(-0.586053\pi\)
−0.267061 + 0.963680i \(0.586053\pi\)
\(140\) −2.91278 −0.246175
\(141\) 0 0
\(142\) 13.9633 1.17178
\(143\) 0 0
\(144\) 0 0
\(145\) −4.00136 −0.332295
\(146\) −4.41818 −0.365651
\(147\) 0 0
\(148\) 4.78032 0.392940
\(149\) 22.4959 1.84293 0.921467 0.388457i \(-0.126992\pi\)
0.921467 + 0.388457i \(0.126992\pi\)
\(150\) 0 0
\(151\) 2.99699 0.243892 0.121946 0.992537i \(-0.461087\pi\)
0.121946 + 0.992537i \(0.461087\pi\)
\(152\) 23.3246 1.89187
\(153\) 0 0
\(154\) 0 0
\(155\) 3.81490 0.306420
\(156\) 0 0
\(157\) −10.1899 −0.813244 −0.406622 0.913597i \(-0.633293\pi\)
−0.406622 + 0.913597i \(0.633293\pi\)
\(158\) 19.9595 1.58789
\(159\) 0 0
\(160\) 3.79913 0.300348
\(161\) −8.09986 −0.638359
\(162\) 0 0
\(163\) −19.8034 −1.55112 −0.775561 0.631273i \(-0.782533\pi\)
−0.775561 + 0.631273i \(0.782533\pi\)
\(164\) −2.85741 −0.223127
\(165\) 0 0
\(166\) −15.7265 −1.22061
\(167\) 4.96739 0.384388 0.192194 0.981357i \(-0.438440\pi\)
0.192194 + 0.981357i \(0.438440\pi\)
\(168\) 0 0
\(169\) −7.82948 −0.602268
\(170\) −5.69990 −0.437162
\(171\) 0 0
\(172\) 6.80308 0.518730
\(173\) 16.2510 1.23554 0.617768 0.786360i \(-0.288037\pi\)
0.617768 + 0.786360i \(0.288037\pi\)
\(174\) 0 0
\(175\) −4.10132 −0.310031
\(176\) 0 0
\(177\) 0 0
\(178\) 8.91971 0.668561
\(179\) −3.18448 −0.238019 −0.119010 0.992893i \(-0.537972\pi\)
−0.119010 + 0.992893i \(0.537972\pi\)
\(180\) 0 0
\(181\) 1.50099 0.111568 0.0557838 0.998443i \(-0.482234\pi\)
0.0557838 + 0.998443i \(0.482234\pi\)
\(182\) 10.5913 0.785083
\(183\) 0 0
\(184\) 6.07877 0.448133
\(185\) 6.73089 0.494865
\(186\) 0 0
\(187\) 0 0
\(188\) 2.26323 0.165063
\(189\) 0 0
\(190\) 8.60619 0.624359
\(191\) −10.4428 −0.755613 −0.377807 0.925885i \(-0.623322\pi\)
−0.377807 + 0.925885i \(0.623322\pi\)
\(192\) 0 0
\(193\) −6.02750 −0.433869 −0.216935 0.976186i \(-0.569606\pi\)
−0.216935 + 0.976186i \(0.569606\pi\)
\(194\) −5.88136 −0.422257
\(195\) 0 0
\(196\) −6.97483 −0.498202
\(197\) −9.07040 −0.646239 −0.323120 0.946358i \(-0.604732\pi\)
−0.323120 + 0.946358i \(0.604732\pi\)
\(198\) 0 0
\(199\) 17.3143 1.22738 0.613689 0.789548i \(-0.289685\pi\)
0.613689 + 0.789548i \(0.289685\pi\)
\(200\) 3.07796 0.217644
\(201\) 0 0
\(202\) 4.53442 0.319041
\(203\) −16.4109 −1.15182
\(204\) 0 0
\(205\) −4.02336 −0.281004
\(206\) 1.06865 0.0744562
\(207\) 0 0
\(208\) −4.71874 −0.327186
\(209\) 0 0
\(210\) 0 0
\(211\) 15.7153 1.08189 0.540945 0.841058i \(-0.318067\pi\)
0.540945 + 0.841058i \(0.318067\pi\)
\(212\) 7.97498 0.547724
\(213\) 0 0
\(214\) −16.5010 −1.12798
\(215\) 9.57903 0.653285
\(216\) 0 0
\(217\) 15.6461 1.06213
\(218\) 8.74701 0.592422
\(219\) 0 0
\(220\) 0 0
\(221\) −11.4123 −0.767676
\(222\) 0 0
\(223\) 1.08382 0.0725778 0.0362889 0.999341i \(-0.488446\pi\)
0.0362889 + 0.999341i \(0.488446\pi\)
\(224\) 15.5815 1.04108
\(225\) 0 0
\(226\) −0.767162 −0.0510308
\(227\) −1.99171 −0.132195 −0.0660974 0.997813i \(-0.521055\pi\)
−0.0660974 + 0.997813i \(0.521055\pi\)
\(228\) 0 0
\(229\) 8.13974 0.537889 0.268945 0.963156i \(-0.413325\pi\)
0.268945 + 0.963156i \(0.413325\pi\)
\(230\) 2.24292 0.147894
\(231\) 0 0
\(232\) 12.3160 0.808585
\(233\) 24.4296 1.60043 0.800217 0.599710i \(-0.204717\pi\)
0.800217 + 0.599710i \(0.204717\pi\)
\(234\) 0 0
\(235\) 3.18673 0.207879
\(236\) −6.77372 −0.440932
\(237\) 0 0
\(238\) −23.3771 −1.51531
\(239\) −0.0709845 −0.00459161 −0.00229580 0.999997i \(-0.500731\pi\)
−0.00229580 + 0.999997i \(0.500731\pi\)
\(240\) 0 0
\(241\) 12.6653 0.815842 0.407921 0.913017i \(-0.366254\pi\)
0.407921 + 0.913017i \(0.366254\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 2.56517 0.164218
\(245\) −9.82086 −0.627431
\(246\) 0 0
\(247\) 17.2313 1.09640
\(248\) −11.7421 −0.745624
\(249\) 0 0
\(250\) 1.13569 0.0718274
\(251\) 7.65705 0.483309 0.241654 0.970362i \(-0.422310\pi\)
0.241654 + 0.970362i \(0.422310\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −5.00959 −0.314330
\(255\) 0 0
\(256\) −14.6412 −0.915075
\(257\) 23.1101 1.44157 0.720784 0.693160i \(-0.243782\pi\)
0.720784 + 0.693160i \(0.243782\pi\)
\(258\) 0 0
\(259\) 27.6056 1.71533
\(260\) 1.61492 0.100153
\(261\) 0 0
\(262\) −24.3043 −1.50152
\(263\) −9.67819 −0.596783 −0.298391 0.954444i \(-0.596450\pi\)
−0.298391 + 0.954444i \(0.596450\pi\)
\(264\) 0 0
\(265\) 11.2291 0.689799
\(266\) 35.2968 2.16418
\(267\) 0 0
\(268\) 4.48498 0.273964
\(269\) 1.82359 0.111186 0.0555931 0.998454i \(-0.482295\pi\)
0.0555931 + 0.998454i \(0.482295\pi\)
\(270\) 0 0
\(271\) 14.7934 0.898635 0.449318 0.893372i \(-0.351667\pi\)
0.449318 + 0.893372i \(0.351667\pi\)
\(272\) 10.4152 0.631512
\(273\) 0 0
\(274\) −4.33981 −0.262178
\(275\) 0 0
\(276\) 0 0
\(277\) −16.9801 −1.02024 −0.510118 0.860104i \(-0.670398\pi\)
−0.510118 + 0.860104i \(0.670398\pi\)
\(278\) 7.15169 0.428930
\(279\) 0 0
\(280\) 12.6237 0.754410
\(281\) 4.60152 0.274504 0.137252 0.990536i \(-0.456173\pi\)
0.137252 + 0.990536i \(0.456173\pi\)
\(282\) 0 0
\(283\) −13.7869 −0.819545 −0.409772 0.912188i \(-0.634392\pi\)
−0.409772 + 0.912188i \(0.634392\pi\)
\(284\) 8.73198 0.518148
\(285\) 0 0
\(286\) 0 0
\(287\) −16.5011 −0.974030
\(288\) 0 0
\(289\) 8.18917 0.481716
\(290\) 4.54431 0.266851
\(291\) 0 0
\(292\) −2.76291 −0.161687
\(293\) 31.4245 1.83584 0.917919 0.396769i \(-0.129869\pi\)
0.917919 + 0.396769i \(0.129869\pi\)
\(294\) 0 0
\(295\) −9.53769 −0.555306
\(296\) −20.7174 −1.20417
\(297\) 0 0
\(298\) −25.5484 −1.47998
\(299\) 4.49077 0.259708
\(300\) 0 0
\(301\) 39.2867 2.26445
\(302\) −3.40366 −0.195858
\(303\) 0 0
\(304\) −15.7257 −0.901931
\(305\) 3.61186 0.206815
\(306\) 0 0
\(307\) −20.1733 −1.15135 −0.575676 0.817678i \(-0.695261\pi\)
−0.575676 + 0.817678i \(0.695261\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.33255 −0.246072
\(311\) 18.5810 1.05363 0.526816 0.849979i \(-0.323386\pi\)
0.526816 + 0.849979i \(0.323386\pi\)
\(312\) 0 0
\(313\) 11.4086 0.644854 0.322427 0.946594i \(-0.395501\pi\)
0.322427 + 0.946594i \(0.395501\pi\)
\(314\) 11.5726 0.653079
\(315\) 0 0
\(316\) 12.4817 0.702149
\(317\) −25.4611 −1.43004 −0.715018 0.699106i \(-0.753581\pi\)
−0.715018 + 0.699106i \(0.753581\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −8.46503 −0.473210
\(321\) 0 0
\(322\) 9.19894 0.512637
\(323\) −38.0328 −2.11620
\(324\) 0 0
\(325\) 2.27388 0.126132
\(326\) 22.4905 1.24564
\(327\) 0 0
\(328\) 12.3837 0.683777
\(329\) 13.0698 0.720561
\(330\) 0 0
\(331\) 31.1055 1.70971 0.854857 0.518864i \(-0.173645\pi\)
0.854857 + 0.518864i \(0.173645\pi\)
\(332\) −9.83460 −0.539744
\(333\) 0 0
\(334\) −5.64142 −0.308684
\(335\) 6.31504 0.345027
\(336\) 0 0
\(337\) 26.6950 1.45417 0.727084 0.686548i \(-0.240875\pi\)
0.727084 + 0.686548i \(0.240875\pi\)
\(338\) 8.89188 0.483654
\(339\) 0 0
\(340\) −3.56444 −0.193309
\(341\) 0 0
\(342\) 0 0
\(343\) −11.5692 −0.624680
\(344\) −29.4838 −1.58966
\(345\) 0 0
\(346\) −18.4561 −0.992204
\(347\) 6.79251 0.364641 0.182321 0.983239i \(-0.441639\pi\)
0.182321 + 0.983239i \(0.441639\pi\)
\(348\) 0 0
\(349\) 7.84626 0.420001 0.210000 0.977701i \(-0.432653\pi\)
0.210000 + 0.977701i \(0.432653\pi\)
\(350\) 4.65784 0.248972
\(351\) 0 0
\(352\) 0 0
\(353\) −18.4136 −0.980056 −0.490028 0.871707i \(-0.663014\pi\)
−0.490028 + 0.871707i \(0.663014\pi\)
\(354\) 0 0
\(355\) 12.2950 0.652551
\(356\) 5.57795 0.295631
\(357\) 0 0
\(358\) 3.61659 0.191142
\(359\) −25.4119 −1.34119 −0.670595 0.741823i \(-0.733961\pi\)
−0.670595 + 0.741823i \(0.733961\pi\)
\(360\) 0 0
\(361\) 38.4251 2.02237
\(362\) −1.70466 −0.0895949
\(363\) 0 0
\(364\) 6.62331 0.347156
\(365\) −3.89030 −0.203628
\(366\) 0 0
\(367\) −3.48293 −0.181808 −0.0909038 0.995860i \(-0.528976\pi\)
−0.0909038 + 0.995860i \(0.528976\pi\)
\(368\) −4.09839 −0.213643
\(369\) 0 0
\(370\) −7.64422 −0.397404
\(371\) 46.0542 2.39102
\(372\) 0 0
\(373\) −12.8348 −0.664561 −0.332281 0.943181i \(-0.607818\pi\)
−0.332281 + 0.943181i \(0.607818\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −9.80861 −0.505840
\(377\) 9.09859 0.468601
\(378\) 0 0
\(379\) −24.0638 −1.23607 −0.618037 0.786149i \(-0.712072\pi\)
−0.618037 + 0.786149i \(0.712072\pi\)
\(380\) 5.38189 0.276085
\(381\) 0 0
\(382\) 11.8598 0.606799
\(383\) −3.17618 −0.162295 −0.0811477 0.996702i \(-0.525859\pi\)
−0.0811477 + 0.996702i \(0.525859\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6.84538 0.348421
\(387\) 0 0
\(388\) −3.67791 −0.186718
\(389\) −14.9001 −0.755463 −0.377731 0.925915i \(-0.623296\pi\)
−0.377731 + 0.925915i \(0.623296\pi\)
\(390\) 0 0
\(391\) −9.91198 −0.501270
\(392\) 30.2282 1.52675
\(393\) 0 0
\(394\) 10.3012 0.518965
\(395\) 17.5747 0.884281
\(396\) 0 0
\(397\) 10.8837 0.546237 0.273119 0.961980i \(-0.411945\pi\)
0.273119 + 0.961980i \(0.411945\pi\)
\(398\) −19.6637 −0.985651
\(399\) 0 0
\(400\) −2.07520 −0.103760
\(401\) −33.2847 −1.66216 −0.831080 0.556153i \(-0.812277\pi\)
−0.831080 + 0.556153i \(0.812277\pi\)
\(402\) 0 0
\(403\) −8.67461 −0.432113
\(404\) 2.83561 0.141077
\(405\) 0 0
\(406\) 18.6377 0.924972
\(407\) 0 0
\(408\) 0 0
\(409\) −2.77694 −0.137311 −0.0686554 0.997640i \(-0.521871\pi\)
−0.0686554 + 0.997640i \(0.521871\pi\)
\(410\) 4.56930 0.225661
\(411\) 0 0
\(412\) 0.668280 0.0329238
\(413\) −39.1172 −1.92483
\(414\) 0 0
\(415\) −13.8475 −0.679749
\(416\) −8.63876 −0.423550
\(417\) 0 0
\(418\) 0 0
\(419\) 29.5565 1.44393 0.721965 0.691930i \(-0.243239\pi\)
0.721965 + 0.691930i \(0.243239\pi\)
\(420\) 0 0
\(421\) 0.291904 0.0142265 0.00711326 0.999975i \(-0.497736\pi\)
0.00711326 + 0.999975i \(0.497736\pi\)
\(422\) −17.8478 −0.868816
\(423\) 0 0
\(424\) −34.5627 −1.67851
\(425\) −5.01888 −0.243451
\(426\) 0 0
\(427\) 14.8134 0.716872
\(428\) −10.3189 −0.498783
\(429\) 0 0
\(430\) −10.8788 −0.524623
\(431\) −4.49580 −0.216555 −0.108277 0.994121i \(-0.534534\pi\)
−0.108277 + 0.994121i \(0.534534\pi\)
\(432\) 0 0
\(433\) −6.56823 −0.315649 −0.157824 0.987467i \(-0.550448\pi\)
−0.157824 + 0.987467i \(0.550448\pi\)
\(434\) −17.7692 −0.852948
\(435\) 0 0
\(436\) 5.46995 0.261963
\(437\) 14.9660 0.715919
\(438\) 0 0
\(439\) 26.7142 1.27500 0.637500 0.770451i \(-0.279969\pi\)
0.637500 + 0.770451i \(0.279969\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.9609 0.616486
\(443\) 23.1670 1.10070 0.550349 0.834935i \(-0.314495\pi\)
0.550349 + 0.834935i \(0.314495\pi\)
\(444\) 0 0
\(445\) 7.85399 0.372315
\(446\) −1.23088 −0.0582839
\(447\) 0 0
\(448\) −34.7178 −1.64026
\(449\) 29.0593 1.37139 0.685696 0.727888i \(-0.259498\pi\)
0.685696 + 0.727888i \(0.259498\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.479745 −0.0225653
\(453\) 0 0
\(454\) 2.26197 0.106160
\(455\) 9.32590 0.437205
\(456\) 0 0
\(457\) −7.62741 −0.356795 −0.178398 0.983958i \(-0.557091\pi\)
−0.178398 + 0.983958i \(0.557091\pi\)
\(458\) −9.24423 −0.431954
\(459\) 0 0
\(460\) 1.40261 0.0653971
\(461\) −34.0138 −1.58418 −0.792091 0.610404i \(-0.791007\pi\)
−0.792091 + 0.610404i \(0.791007\pi\)
\(462\) 0 0
\(463\) 15.7564 0.732263 0.366131 0.930563i \(-0.380682\pi\)
0.366131 + 0.930563i \(0.380682\pi\)
\(464\) −8.30360 −0.385485
\(465\) 0 0
\(466\) −27.7445 −1.28524
\(467\) −10.1508 −0.469724 −0.234862 0.972029i \(-0.575464\pi\)
−0.234862 + 0.972029i \(0.575464\pi\)
\(468\) 0 0
\(469\) 25.9000 1.19595
\(470\) −3.61914 −0.166938
\(471\) 0 0
\(472\) 29.3566 1.35125
\(473\) 0 0
\(474\) 0 0
\(475\) 7.57794 0.347700
\(476\) −14.6189 −0.670057
\(477\) 0 0
\(478\) 0.0806165 0.00368731
\(479\) 4.04315 0.184736 0.0923681 0.995725i \(-0.470556\pi\)
0.0923681 + 0.995725i \(0.470556\pi\)
\(480\) 0 0
\(481\) −15.3052 −0.697858
\(482\) −14.3838 −0.655166
\(483\) 0 0
\(484\) 0 0
\(485\) −5.17866 −0.235151
\(486\) 0 0
\(487\) 7.37591 0.334234 0.167117 0.985937i \(-0.446554\pi\)
0.167117 + 0.985937i \(0.446554\pi\)
\(488\) −11.1172 −0.503250
\(489\) 0 0
\(490\) 11.1535 0.503862
\(491\) −2.19528 −0.0990717 −0.0495358 0.998772i \(-0.515774\pi\)
−0.0495358 + 0.998772i \(0.515774\pi\)
\(492\) 0 0
\(493\) −20.0823 −0.904463
\(494\) −19.5694 −0.880470
\(495\) 0 0
\(496\) 7.91667 0.355469
\(497\) 50.4258 2.26191
\(498\) 0 0
\(499\) 8.06180 0.360896 0.180448 0.983585i \(-0.442245\pi\)
0.180448 + 0.983585i \(0.442245\pi\)
\(500\) 0.710206 0.0317614
\(501\) 0 0
\(502\) −8.69605 −0.388124
\(503\) 33.3563 1.48728 0.743642 0.668579i \(-0.233097\pi\)
0.743642 + 0.668579i \(0.233097\pi\)
\(504\) 0 0
\(505\) 3.99265 0.177671
\(506\) 0 0
\(507\) 0 0
\(508\) −3.13276 −0.138994
\(509\) 16.7877 0.744100 0.372050 0.928213i \(-0.378655\pi\)
0.372050 + 0.928213i \(0.378655\pi\)
\(510\) 0 0
\(511\) −15.9554 −0.705825
\(512\) 20.6587 0.912993
\(513\) 0 0
\(514\) −26.2459 −1.15766
\(515\) 0.940967 0.0414639
\(516\) 0 0
\(517\) 0 0
\(518\) −31.3514 −1.37750
\(519\) 0 0
\(520\) −6.99889 −0.306922
\(521\) 14.7904 0.647981 0.323991 0.946060i \(-0.394975\pi\)
0.323991 + 0.946060i \(0.394975\pi\)
\(522\) 0 0
\(523\) 1.41489 0.0618688 0.0309344 0.999521i \(-0.490152\pi\)
0.0309344 + 0.999521i \(0.490152\pi\)
\(524\) −15.1987 −0.663958
\(525\) 0 0
\(526\) 10.9914 0.479249
\(527\) 19.1465 0.834036
\(528\) 0 0
\(529\) −19.0996 −0.830418
\(530\) −12.7528 −0.553946
\(531\) 0 0
\(532\) 22.0729 0.956981
\(533\) 9.14863 0.396271
\(534\) 0 0
\(535\) −14.5295 −0.628163
\(536\) −19.4374 −0.839568
\(537\) 0 0
\(538\) −2.07103 −0.0892887
\(539\) 0 0
\(540\) 0 0
\(541\) −2.52676 −0.108634 −0.0543169 0.998524i \(-0.517298\pi\)
−0.0543169 + 0.998524i \(0.517298\pi\)
\(542\) −16.8007 −0.721653
\(543\) 0 0
\(544\) 19.0674 0.817507
\(545\) 7.70193 0.329914
\(546\) 0 0
\(547\) −0.519111 −0.0221956 −0.0110978 0.999938i \(-0.503533\pi\)
−0.0110978 + 0.999938i \(0.503533\pi\)
\(548\) −2.71391 −0.115932
\(549\) 0 0
\(550\) 0 0
\(551\) 30.3220 1.29176
\(552\) 0 0
\(553\) 72.0797 3.06514
\(554\) 19.2842 0.819306
\(555\) 0 0
\(556\) 4.47231 0.189668
\(557\) −11.8026 −0.500091 −0.250045 0.968234i \(-0.580446\pi\)
−0.250045 + 0.968234i \(0.580446\pi\)
\(558\) 0 0
\(559\) −21.7815 −0.921261
\(560\) −8.51105 −0.359658
\(561\) 0 0
\(562\) −5.22591 −0.220442
\(563\) −6.73272 −0.283750 −0.141875 0.989885i \(-0.545313\pi\)
−0.141875 + 0.989885i \(0.545313\pi\)
\(564\) 0 0
\(565\) −0.675502 −0.0284186
\(566\) 15.6576 0.658140
\(567\) 0 0
\(568\) −37.8435 −1.58788
\(569\) −31.4915 −1.32019 −0.660096 0.751181i \(-0.729484\pi\)
−0.660096 + 0.751181i \(0.729484\pi\)
\(570\) 0 0
\(571\) 24.1049 1.00876 0.504380 0.863482i \(-0.331721\pi\)
0.504380 + 0.863482i \(0.331721\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 18.7402 0.782199
\(575\) 1.97494 0.0823606
\(576\) 0 0
\(577\) −34.2109 −1.42422 −0.712110 0.702068i \(-0.752260\pi\)
−0.712110 + 0.702068i \(0.752260\pi\)
\(578\) −9.30037 −0.386844
\(579\) 0 0
\(580\) 2.84179 0.117999
\(581\) −56.7932 −2.35618
\(582\) 0 0
\(583\) 0 0
\(584\) 11.9742 0.495495
\(585\) 0 0
\(586\) −35.6885 −1.47428
\(587\) 17.6006 0.726457 0.363228 0.931700i \(-0.381675\pi\)
0.363228 + 0.931700i \(0.381675\pi\)
\(588\) 0 0
\(589\) −28.9091 −1.19118
\(590\) 10.8319 0.445941
\(591\) 0 0
\(592\) 13.9679 0.574078
\(593\) 33.9143 1.39269 0.696347 0.717705i \(-0.254807\pi\)
0.696347 + 0.717705i \(0.254807\pi\)
\(594\) 0 0
\(595\) −20.5841 −0.843864
\(596\) −15.9767 −0.654431
\(597\) 0 0
\(598\) −5.10012 −0.208560
\(599\) 30.1345 1.23126 0.615630 0.788035i \(-0.288901\pi\)
0.615630 + 0.788035i \(0.288901\pi\)
\(600\) 0 0
\(601\) 27.7612 1.13240 0.566202 0.824266i \(-0.308412\pi\)
0.566202 + 0.824266i \(0.308412\pi\)
\(602\) −44.6176 −1.81848
\(603\) 0 0
\(604\) −2.12848 −0.0866067
\(605\) 0 0
\(606\) 0 0
\(607\) 25.4949 1.03481 0.517404 0.855742i \(-0.326899\pi\)
0.517404 + 0.855742i \(0.326899\pi\)
\(608\) −28.7896 −1.16757
\(609\) 0 0
\(610\) −4.10196 −0.166084
\(611\) −7.24622 −0.293151
\(612\) 0 0
\(613\) −2.06728 −0.0834967 −0.0417484 0.999128i \(-0.513293\pi\)
−0.0417484 + 0.999128i \(0.513293\pi\)
\(614\) 22.9107 0.924599
\(615\) 0 0
\(616\) 0 0
\(617\) −16.7249 −0.673321 −0.336660 0.941626i \(-0.609297\pi\)
−0.336660 + 0.941626i \(0.609297\pi\)
\(618\) 0 0
\(619\) −42.2465 −1.69803 −0.849015 0.528369i \(-0.822804\pi\)
−0.849015 + 0.528369i \(0.822804\pi\)
\(620\) −2.70936 −0.108811
\(621\) 0 0
\(622\) −21.1023 −0.846125
\(623\) 32.2118 1.29054
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −12.9567 −0.517853
\(627\) 0 0
\(628\) 7.23693 0.288785
\(629\) 33.7816 1.34696
\(630\) 0 0
\(631\) 38.8620 1.54707 0.773536 0.633753i \(-0.218486\pi\)
0.773536 + 0.633753i \(0.218486\pi\)
\(632\) −54.0943 −2.15175
\(633\) 0 0
\(634\) 28.9159 1.14840
\(635\) −4.41105 −0.175047
\(636\) 0 0
\(637\) 22.3314 0.884803
\(638\) 0 0
\(639\) 0 0
\(640\) 2.01540 0.0796657
\(641\) 17.5446 0.692971 0.346486 0.938055i \(-0.387375\pi\)
0.346486 + 0.938055i \(0.387375\pi\)
\(642\) 0 0
\(643\) 36.6475 1.44524 0.722619 0.691246i \(-0.242938\pi\)
0.722619 + 0.691246i \(0.242938\pi\)
\(644\) 5.75257 0.226683
\(645\) 0 0
\(646\) 43.1935 1.69942
\(647\) 22.6182 0.889214 0.444607 0.895726i \(-0.353343\pi\)
0.444607 + 0.895726i \(0.353343\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −2.58242 −0.101291
\(651\) 0 0
\(652\) 14.0645 0.550808
\(653\) −6.34671 −0.248366 −0.124183 0.992259i \(-0.539631\pi\)
−0.124183 + 0.992259i \(0.539631\pi\)
\(654\) 0 0
\(655\) −21.4004 −0.836184
\(656\) −8.34927 −0.325984
\(657\) 0 0
\(658\) −14.8433 −0.578650
\(659\) 45.8649 1.78664 0.893321 0.449420i \(-0.148369\pi\)
0.893321 + 0.449420i \(0.148369\pi\)
\(660\) 0 0
\(661\) 46.4730 1.80759 0.903796 0.427964i \(-0.140769\pi\)
0.903796 + 0.427964i \(0.140769\pi\)
\(662\) −35.3263 −1.37299
\(663\) 0 0
\(664\) 42.6221 1.65406
\(665\) 31.0796 1.20521
\(666\) 0 0
\(667\) 7.90243 0.305983
\(668\) −3.52787 −0.136497
\(669\) 0 0
\(670\) −7.17193 −0.277076
\(671\) 0 0
\(672\) 0 0
\(673\) 11.1001 0.427879 0.213939 0.976847i \(-0.431371\pi\)
0.213939 + 0.976847i \(0.431371\pi\)
\(674\) −30.3173 −1.16778
\(675\) 0 0
\(676\) 5.56054 0.213867
\(677\) −15.9352 −0.612441 −0.306220 0.951961i \(-0.599064\pi\)
−0.306220 + 0.951961i \(0.599064\pi\)
\(678\) 0 0
\(679\) −21.2394 −0.815092
\(680\) 15.4479 0.592400
\(681\) 0 0
\(682\) 0 0
\(683\) 21.8344 0.835468 0.417734 0.908569i \(-0.362824\pi\)
0.417734 + 0.908569i \(0.362824\pi\)
\(684\) 0 0
\(685\) −3.82130 −0.146004
\(686\) 13.1391 0.501653
\(687\) 0 0
\(688\) 19.8784 0.757856
\(689\) −25.5336 −0.972753
\(690\) 0 0
\(691\) −26.9932 −1.02687 −0.513435 0.858128i \(-0.671627\pi\)
−0.513435 + 0.858128i \(0.671627\pi\)
\(692\) −11.5415 −0.438743
\(693\) 0 0
\(694\) −7.71420 −0.292827
\(695\) 6.29721 0.238867
\(696\) 0 0
\(697\) −20.1928 −0.764856
\(698\) −8.91093 −0.337284
\(699\) 0 0
\(700\) 2.91278 0.110093
\(701\) −29.8366 −1.12691 −0.563455 0.826146i \(-0.690528\pi\)
−0.563455 + 0.826146i \(0.690528\pi\)
\(702\) 0 0
\(703\) −51.0063 −1.92374
\(704\) 0 0
\(705\) 0 0
\(706\) 20.9121 0.787039
\(707\) 16.3752 0.615851
\(708\) 0 0
\(709\) 33.4225 1.25521 0.627604 0.778533i \(-0.284036\pi\)
0.627604 + 0.778533i \(0.284036\pi\)
\(710\) −13.9633 −0.524034
\(711\) 0 0
\(712\) −24.1743 −0.905968
\(713\) −7.53419 −0.282158
\(714\) 0 0
\(715\) 0 0
\(716\) 2.26164 0.0845213
\(717\) 0 0
\(718\) 28.8601 1.07705
\(719\) 11.2829 0.420782 0.210391 0.977617i \(-0.432526\pi\)
0.210391 + 0.977617i \(0.432526\pi\)
\(720\) 0 0
\(721\) 3.85921 0.143724
\(722\) −43.6391 −1.62408
\(723\) 0 0
\(724\) −1.06601 −0.0396180
\(725\) 4.00136 0.148607
\(726\) 0 0
\(727\) 43.3381 1.60732 0.803661 0.595087i \(-0.202882\pi\)
0.803661 + 0.595087i \(0.202882\pi\)
\(728\) −28.7047 −1.06387
\(729\) 0 0
\(730\) 4.41818 0.163524
\(731\) 48.0760 1.77816
\(732\) 0 0
\(733\) −52.1642 −1.92673 −0.963365 0.268195i \(-0.913573\pi\)
−0.963365 + 0.268195i \(0.913573\pi\)
\(734\) 3.95554 0.146002
\(735\) 0 0
\(736\) −7.50305 −0.276566
\(737\) 0 0
\(738\) 0 0
\(739\) 14.7098 0.541109 0.270555 0.962705i \(-0.412793\pi\)
0.270555 + 0.962705i \(0.412793\pi\)
\(740\) −4.78032 −0.175728
\(741\) 0 0
\(742\) −52.3034 −1.92012
\(743\) −2.72748 −0.100062 −0.0500308 0.998748i \(-0.515932\pi\)
−0.0500308 + 0.998748i \(0.515932\pi\)
\(744\) 0 0
\(745\) −22.4959 −0.824185
\(746\) 14.5764 0.533679
\(747\) 0 0
\(748\) 0 0
\(749\) −59.5900 −2.17737
\(750\) 0 0
\(751\) 16.7867 0.612555 0.306277 0.951942i \(-0.400916\pi\)
0.306277 + 0.951942i \(0.400916\pi\)
\(752\) 6.61309 0.241154
\(753\) 0 0
\(754\) −10.3332 −0.376313
\(755\) −2.99699 −0.109072
\(756\) 0 0
\(757\) −22.9310 −0.833442 −0.416721 0.909034i \(-0.636821\pi\)
−0.416721 + 0.909034i \(0.636821\pi\)
\(758\) 27.3291 0.992636
\(759\) 0 0
\(760\) −23.3246 −0.846071
\(761\) −7.81520 −0.283301 −0.141650 0.989917i \(-0.545241\pi\)
−0.141650 + 0.989917i \(0.545241\pi\)
\(762\) 0 0
\(763\) 31.5881 1.14357
\(764\) 7.41652 0.268320
\(765\) 0 0
\(766\) 3.60716 0.130332
\(767\) 21.6875 0.783092
\(768\) 0 0
\(769\) −38.6765 −1.39471 −0.697355 0.716726i \(-0.745640\pi\)
−0.697355 + 0.716726i \(0.745640\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.28077 0.154068
\(773\) 16.8813 0.607178 0.303589 0.952803i \(-0.401815\pi\)
0.303589 + 0.952803i \(0.401815\pi\)
\(774\) 0 0
\(775\) −3.81490 −0.137035
\(776\) 15.9397 0.572201
\(777\) 0 0
\(778\) 16.9219 0.606678
\(779\) 30.4888 1.09237
\(780\) 0 0
\(781\) 0 0
\(782\) 11.2569 0.402548
\(783\) 0 0
\(784\) −20.3802 −0.727864
\(785\) 10.1899 0.363694
\(786\) 0 0
\(787\) −27.1091 −0.966335 −0.483167 0.875528i \(-0.660514\pi\)
−0.483167 + 0.875528i \(0.660514\pi\)
\(788\) 6.44185 0.229481
\(789\) 0 0
\(790\) −19.9595 −0.710126
\(791\) −2.77045 −0.0985060
\(792\) 0 0
\(793\) −8.21293 −0.291650
\(794\) −12.3605 −0.438658
\(795\) 0 0
\(796\) −12.2967 −0.435845
\(797\) 23.5525 0.834272 0.417136 0.908844i \(-0.363034\pi\)
0.417136 + 0.908844i \(0.363034\pi\)
\(798\) 0 0
\(799\) 15.9938 0.565820
\(800\) −3.79913 −0.134320
\(801\) 0 0
\(802\) 37.8012 1.33481
\(803\) 0 0
\(804\) 0 0
\(805\) 8.09986 0.285483
\(806\) 9.85168 0.347011
\(807\) 0 0
\(808\) −12.2892 −0.432333
\(809\) 18.0138 0.633330 0.316665 0.948537i \(-0.397437\pi\)
0.316665 + 0.948537i \(0.397437\pi\)
\(810\) 0 0
\(811\) −6.25684 −0.219707 −0.109854 0.993948i \(-0.535038\pi\)
−0.109854 + 0.993948i \(0.535038\pi\)
\(812\) 11.6551 0.409013
\(813\) 0 0
\(814\) 0 0
\(815\) 19.8034 0.693683
\(816\) 0 0
\(817\) −72.5893 −2.53958
\(818\) 3.15374 0.110268
\(819\) 0 0
\(820\) 2.85741 0.0997853
\(821\) 18.9344 0.660815 0.330408 0.943838i \(-0.392814\pi\)
0.330408 + 0.943838i \(0.392814\pi\)
\(822\) 0 0
\(823\) 23.3683 0.814566 0.407283 0.913302i \(-0.366476\pi\)
0.407283 + 0.913302i \(0.366476\pi\)
\(824\) −2.89625 −0.100896
\(825\) 0 0
\(826\) 44.4250 1.54574
\(827\) −5.01148 −0.174266 −0.0871330 0.996197i \(-0.527771\pi\)
−0.0871330 + 0.996197i \(0.527771\pi\)
\(828\) 0 0
\(829\) 44.9519 1.56124 0.780622 0.625003i \(-0.214902\pi\)
0.780622 + 0.625003i \(0.214902\pi\)
\(830\) 15.7265 0.545876
\(831\) 0 0
\(832\) 19.2484 0.667320
\(833\) −49.2897 −1.70779
\(834\) 0 0
\(835\) −4.96739 −0.171903
\(836\) 0 0
\(837\) 0 0
\(838\) −33.5670 −1.15955
\(839\) 52.4551 1.81095 0.905475 0.424399i \(-0.139514\pi\)
0.905475 + 0.424399i \(0.139514\pi\)
\(840\) 0 0
\(841\) −12.9891 −0.447901
\(842\) −0.331512 −0.0114247
\(843\) 0 0
\(844\) −11.1611 −0.384182
\(845\) 7.82948 0.269342
\(846\) 0 0
\(847\) 0 0
\(848\) 23.3026 0.800215
\(849\) 0 0
\(850\) 5.69990 0.195505
\(851\) −13.2931 −0.455682
\(852\) 0 0
\(853\) 50.1056 1.71558 0.857791 0.513998i \(-0.171836\pi\)
0.857791 + 0.513998i \(0.171836\pi\)
\(854\) −16.8235 −0.575687
\(855\) 0 0
\(856\) 44.7211 1.52853
\(857\) 13.2279 0.451856 0.225928 0.974144i \(-0.427459\pi\)
0.225928 + 0.974144i \(0.427459\pi\)
\(858\) 0 0
\(859\) −50.3765 −1.71883 −0.859413 0.511283i \(-0.829171\pi\)
−0.859413 + 0.511283i \(0.829171\pi\)
\(860\) −6.80308 −0.231983
\(861\) 0 0
\(862\) 5.10584 0.173906
\(863\) −13.6184 −0.463576 −0.231788 0.972766i \(-0.574458\pi\)
−0.231788 + 0.972766i \(0.574458\pi\)
\(864\) 0 0
\(865\) −16.2510 −0.552549
\(866\) 7.45948 0.253483
\(867\) 0 0
\(868\) −11.1120 −0.377165
\(869\) 0 0
\(870\) 0 0
\(871\) −14.3596 −0.486557
\(872\) −23.7062 −0.802793
\(873\) 0 0
\(874\) −16.9967 −0.574922
\(875\) 4.10132 0.138650
\(876\) 0 0
\(877\) 20.0237 0.676152 0.338076 0.941119i \(-0.390224\pi\)
0.338076 + 0.941119i \(0.390224\pi\)
\(878\) −30.3391 −1.02389
\(879\) 0 0
\(880\) 0 0
\(881\) 30.0543 1.01256 0.506278 0.862371i \(-0.331021\pi\)
0.506278 + 0.862371i \(0.331021\pi\)
\(882\) 0 0
\(883\) 29.0963 0.979168 0.489584 0.871956i \(-0.337149\pi\)
0.489584 + 0.871956i \(0.337149\pi\)
\(884\) 8.10509 0.272604
\(885\) 0 0
\(886\) −26.3106 −0.883921
\(887\) −18.7486 −0.629515 −0.314758 0.949172i \(-0.601923\pi\)
−0.314758 + 0.949172i \(0.601923\pi\)
\(888\) 0 0
\(889\) −18.0912 −0.606758
\(890\) −8.91971 −0.298989
\(891\) 0 0
\(892\) −0.769733 −0.0257726
\(893\) −24.1488 −0.808109
\(894\) 0 0
\(895\) 3.18448 0.106445
\(896\) 8.26581 0.276141
\(897\) 0 0
\(898\) −33.0024 −1.10130
\(899\) −15.2648 −0.509109
\(900\) 0 0
\(901\) 56.3576 1.87754
\(902\) 0 0
\(903\) 0 0
\(904\) 2.07917 0.0691520
\(905\) −1.50099 −0.0498945
\(906\) 0 0
\(907\) 38.7590 1.28697 0.643486 0.765458i \(-0.277488\pi\)
0.643486 + 0.765458i \(0.277488\pi\)
\(908\) 1.41453 0.0469427
\(909\) 0 0
\(910\) −10.5913 −0.351100
\(911\) −34.8367 −1.15419 −0.577096 0.816677i \(-0.695814\pi\)
−0.577096 + 0.816677i \(0.695814\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 8.66238 0.286526
\(915\) 0 0
\(916\) −5.78089 −0.191006
\(917\) −87.7701 −2.89842
\(918\) 0 0
\(919\) 27.3492 0.902167 0.451083 0.892482i \(-0.351038\pi\)
0.451083 + 0.892482i \(0.351038\pi\)
\(920\) −6.07877 −0.200411
\(921\) 0 0
\(922\) 38.6292 1.27218
\(923\) −27.9573 −0.920227
\(924\) 0 0
\(925\) −6.73089 −0.221310
\(926\) −17.8944 −0.588047
\(927\) 0 0
\(928\) −15.2017 −0.499020
\(929\) 44.0757 1.44608 0.723039 0.690808i \(-0.242745\pi\)
0.723039 + 0.690808i \(0.242745\pi\)
\(930\) 0 0
\(931\) 74.4218 2.43908
\(932\) −17.3500 −0.568319
\(933\) 0 0
\(934\) 11.5282 0.377214
\(935\) 0 0
\(936\) 0 0
\(937\) −20.3465 −0.664690 −0.332345 0.943158i \(-0.607840\pi\)
−0.332345 + 0.943158i \(0.607840\pi\)
\(938\) −29.4144 −0.960415
\(939\) 0 0
\(940\) −2.26323 −0.0738185
\(941\) 3.86942 0.126140 0.0630698 0.998009i \(-0.479911\pi\)
0.0630698 + 0.998009i \(0.479911\pi\)
\(942\) 0 0
\(943\) 7.94589 0.258754
\(944\) −19.7926 −0.644194
\(945\) 0 0
\(946\) 0 0
\(947\) 54.4898 1.77068 0.885340 0.464943i \(-0.153925\pi\)
0.885340 + 0.464943i \(0.153925\pi\)
\(948\) 0 0
\(949\) 8.84607 0.287155
\(950\) −8.60619 −0.279222
\(951\) 0 0
\(952\) 63.3568 2.05341
\(953\) −40.5032 −1.31203 −0.656014 0.754748i \(-0.727759\pi\)
−0.656014 + 0.754748i \(0.727759\pi\)
\(954\) 0 0
\(955\) 10.4428 0.337921
\(956\) 0.0504136 0.00163049
\(957\) 0 0
\(958\) −4.59177 −0.148353
\(959\) −15.6724 −0.506087
\(960\) 0 0
\(961\) −16.4465 −0.530533
\(962\) 17.3820 0.560418
\(963\) 0 0
\(964\) −8.99495 −0.289708
\(965\) 6.02750 0.194032
\(966\) 0 0
\(967\) −22.9360 −0.737572 −0.368786 0.929514i \(-0.620226\pi\)
−0.368786 + 0.929514i \(0.620226\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 5.88136 0.188839
\(971\) −46.3553 −1.48761 −0.743806 0.668396i \(-0.766981\pi\)
−0.743806 + 0.668396i \(0.766981\pi\)
\(972\) 0 0
\(973\) 25.8269 0.827972
\(974\) −8.37675 −0.268408
\(975\) 0 0
\(976\) 7.49533 0.239920
\(977\) −26.4057 −0.844794 −0.422397 0.906411i \(-0.638811\pi\)
−0.422397 + 0.906411i \(0.638811\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 6.97483 0.222803
\(981\) 0 0
\(982\) 2.49316 0.0795600
\(983\) −15.7849 −0.503461 −0.251730 0.967797i \(-0.581000\pi\)
−0.251730 + 0.967797i \(0.581000\pi\)
\(984\) 0 0
\(985\) 9.07040 0.289007
\(986\) 22.8073 0.726333
\(987\) 0 0
\(988\) −12.2378 −0.389335
\(989\) −18.9180 −0.601557
\(990\) 0 0
\(991\) 27.9885 0.889085 0.444542 0.895758i \(-0.353366\pi\)
0.444542 + 0.895758i \(0.353366\pi\)
\(992\) 14.4933 0.460163
\(993\) 0 0
\(994\) −57.2681 −1.81644
\(995\) −17.3143 −0.548900
\(996\) 0 0
\(997\) −39.5825 −1.25359 −0.626796 0.779184i \(-0.715634\pi\)
−0.626796 + 0.779184i \(0.715634\pi\)
\(998\) −9.15572 −0.289819
\(999\) 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.cc.1.2 8
3.2 odd 2 5445.2.a.cb.1.7 8
11.2 odd 10 495.2.n.h.136.1 yes 16
11.6 odd 10 495.2.n.h.91.1 yes 16
11.10 odd 2 5445.2.a.ca.1.7 8
33.2 even 10 495.2.n.g.136.4 yes 16
33.17 even 10 495.2.n.g.91.4 16
33.32 even 2 5445.2.a.cd.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
495.2.n.g.91.4 16 33.17 even 10
495.2.n.g.136.4 yes 16 33.2 even 10
495.2.n.h.91.1 yes 16 11.6 odd 10
495.2.n.h.136.1 yes 16 11.2 odd 10
5445.2.a.ca.1.7 8 11.10 odd 2
5445.2.a.cb.1.7 8 3.2 odd 2
5445.2.a.cc.1.2 8 1.1 even 1 trivial
5445.2.a.cd.1.2 8 33.32 even 2