Properties

Label 4730.2.a.bb.1.4
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 11
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
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 1.4
Root \(1.48284\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.48284 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.48284 q^{6} +4.82678 q^{7} -1.00000 q^{8} -0.801199 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.48284 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.48284 q^{6} +4.82678 q^{7} -1.00000 q^{8} -0.801199 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.48284 q^{12} +3.11595 q^{13} -4.82678 q^{14} +1.48284 q^{15} +1.00000 q^{16} +7.03311 q^{17} +0.801199 q^{18} +6.23135 q^{19} -1.00000 q^{20} -7.15731 q^{21} +1.00000 q^{22} +1.11595 q^{23} +1.48284 q^{24} +1.00000 q^{25} -3.11595 q^{26} +5.63655 q^{27} +4.82678 q^{28} +3.16385 q^{29} -1.48284 q^{30} -4.13157 q^{31} -1.00000 q^{32} +1.48284 q^{33} -7.03311 q^{34} -4.82678 q^{35} -0.801199 q^{36} +3.75260 q^{37} -6.23135 q^{38} -4.62044 q^{39} +1.00000 q^{40} -5.76616 q^{41} +7.15731 q^{42} +1.00000 q^{43} -1.00000 q^{44} +0.801199 q^{45} -1.11595 q^{46} +10.3447 q^{47} -1.48284 q^{48} +16.2978 q^{49} -1.00000 q^{50} -10.4289 q^{51} +3.11595 q^{52} -10.1774 q^{53} -5.63655 q^{54} +1.00000 q^{55} -4.82678 q^{56} -9.24006 q^{57} -3.16385 q^{58} +9.27380 q^{59} +1.48284 q^{60} +11.2530 q^{61} +4.13157 q^{62} -3.86721 q^{63} +1.00000 q^{64} -3.11595 q^{65} -1.48284 q^{66} -11.3564 q^{67} +7.03311 q^{68} -1.65477 q^{69} +4.82678 q^{70} +1.75115 q^{71} +0.801199 q^{72} +6.29746 q^{73} -3.75260 q^{74} -1.48284 q^{75} +6.23135 q^{76} -4.82678 q^{77} +4.62044 q^{78} -9.80398 q^{79} -1.00000 q^{80} -5.95448 q^{81} +5.76616 q^{82} -7.75457 q^{83} -7.15731 q^{84} -7.03311 q^{85} -1.00000 q^{86} -4.69147 q^{87} +1.00000 q^{88} -11.1654 q^{89} -0.801199 q^{90} +15.0400 q^{91} +1.11595 q^{92} +6.12644 q^{93} -10.3447 q^{94} -6.23135 q^{95} +1.48284 q^{96} -0.459065 q^{97} -16.2978 q^{98} +0.801199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + O(q^{10}) \) \( 11q - 11q^{2} - q^{3} + 11q^{4} - 11q^{5} + q^{6} + 6q^{7} - 11q^{8} + 12q^{9} + 11q^{10} - 11q^{11} - q^{12} + 4q^{13} - 6q^{14} + q^{15} + 11q^{16} - 10q^{17} - 12q^{18} + 14q^{19} - 11q^{20} - 2q^{21} + 11q^{22} - 18q^{23} + q^{24} + 11q^{25} - 4q^{26} + 2q^{27} + 6q^{28} - 6q^{29} - q^{30} + 13q^{31} - 11q^{32} + q^{33} + 10q^{34} - 6q^{35} + 12q^{36} + q^{37} - 14q^{38} + 12q^{39} + 11q^{40} + 12q^{41} + 2q^{42} + 11q^{43} - 11q^{44} - 12q^{45} + 18q^{46} - 5q^{47} - q^{48} + 31q^{49} - 11q^{50} + q^{51} + 4q^{52} - 27q^{53} - 2q^{54} + 11q^{55} - 6q^{56} - 5q^{57} + 6q^{58} + 11q^{59} + q^{60} + 36q^{61} - 13q^{62} + 17q^{63} + 11q^{64} - 4q^{65} - q^{66} + 18q^{67} - 10q^{68} + 14q^{69} + 6q^{70} - 14q^{71} - 12q^{72} - 11q^{73} - q^{74} - q^{75} + 14q^{76} - 6q^{77} - 12q^{78} + 28q^{79} - 11q^{80} + 7q^{81} - 12q^{82} - 4q^{83} - 2q^{84} + 10q^{85} - 11q^{86} + 38q^{87} + 11q^{88} - 7q^{89} + 12q^{90} + 14q^{91} - 18q^{92} - 3q^{93} + 5q^{94} - 14q^{95} + q^{96} - q^{97} - 31q^{98} - 12q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.48284 −0.856115 −0.428058 0.903751i \(-0.640802\pi\)
−0.428058 + 0.903751i \(0.640802\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.48284 0.605365
\(7\) 4.82678 1.82435 0.912175 0.409801i \(-0.134402\pi\)
0.912175 + 0.409801i \(0.134402\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.801199 −0.267066
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) −1.48284 −0.428058
\(13\) 3.11595 0.864209 0.432105 0.901823i \(-0.357771\pi\)
0.432105 + 0.901823i \(0.357771\pi\)
\(14\) −4.82678 −1.29001
\(15\) 1.48284 0.382866
\(16\) 1.00000 0.250000
\(17\) 7.03311 1.70578 0.852890 0.522091i \(-0.174848\pi\)
0.852890 + 0.522091i \(0.174848\pi\)
\(18\) 0.801199 0.188844
\(19\) 6.23135 1.42957 0.714785 0.699345i \(-0.246525\pi\)
0.714785 + 0.699345i \(0.246525\pi\)
\(20\) −1.00000 −0.223607
\(21\) −7.15731 −1.56185
\(22\) 1.00000 0.213201
\(23\) 1.11595 0.232692 0.116346 0.993209i \(-0.462882\pi\)
0.116346 + 0.993209i \(0.462882\pi\)
\(24\) 1.48284 0.302682
\(25\) 1.00000 0.200000
\(26\) −3.11595 −0.611088
\(27\) 5.63655 1.08476
\(28\) 4.82678 0.912175
\(29\) 3.16385 0.587512 0.293756 0.955880i \(-0.405095\pi\)
0.293756 + 0.955880i \(0.405095\pi\)
\(30\) −1.48284 −0.270727
\(31\) −4.13157 −0.742052 −0.371026 0.928623i \(-0.620994\pi\)
−0.371026 + 0.928623i \(0.620994\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.48284 0.258129
\(34\) −7.03311 −1.20617
\(35\) −4.82678 −0.815874
\(36\) −0.801199 −0.133533
\(37\) 3.75260 0.616924 0.308462 0.951237i \(-0.400186\pi\)
0.308462 + 0.951237i \(0.400186\pi\)
\(38\) −6.23135 −1.01086
\(39\) −4.62044 −0.739863
\(40\) 1.00000 0.158114
\(41\) −5.76616 −0.900524 −0.450262 0.892897i \(-0.648669\pi\)
−0.450262 + 0.892897i \(0.648669\pi\)
\(42\) 7.15731 1.10440
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) 0.801199 0.119436
\(46\) −1.11595 −0.164538
\(47\) 10.3447 1.50893 0.754464 0.656342i \(-0.227897\pi\)
0.754464 + 0.656342i \(0.227897\pi\)
\(48\) −1.48284 −0.214029
\(49\) 16.2978 2.32825
\(50\) −1.00000 −0.141421
\(51\) −10.4289 −1.46034
\(52\) 3.11595 0.432105
\(53\) −10.1774 −1.39797 −0.698987 0.715134i \(-0.746366\pi\)
−0.698987 + 0.715134i \(0.746366\pi\)
\(54\) −5.63655 −0.767038
\(55\) 1.00000 0.134840
\(56\) −4.82678 −0.645005
\(57\) −9.24006 −1.22388
\(58\) −3.16385 −0.415434
\(59\) 9.27380 1.20735 0.603673 0.797232i \(-0.293703\pi\)
0.603673 + 0.797232i \(0.293703\pi\)
\(60\) 1.48284 0.191433
\(61\) 11.2530 1.44080 0.720400 0.693559i \(-0.243958\pi\)
0.720400 + 0.693559i \(0.243958\pi\)
\(62\) 4.13157 0.524710
\(63\) −3.86721 −0.487223
\(64\) 1.00000 0.125000
\(65\) −3.11595 −0.386486
\(66\) −1.48284 −0.182524
\(67\) −11.3564 −1.38740 −0.693701 0.720263i \(-0.744021\pi\)
−0.693701 + 0.720263i \(0.744021\pi\)
\(68\) 7.03311 0.852890
\(69\) −1.65477 −0.199211
\(70\) 4.82678 0.576910
\(71\) 1.75115 0.207823 0.103912 0.994587i \(-0.466864\pi\)
0.103912 + 0.994587i \(0.466864\pi\)
\(72\) 0.801199 0.0944222
\(73\) 6.29746 0.737062 0.368531 0.929615i \(-0.379861\pi\)
0.368531 + 0.929615i \(0.379861\pi\)
\(74\) −3.75260 −0.436231
\(75\) −1.48284 −0.171223
\(76\) 6.23135 0.714785
\(77\) −4.82678 −0.550062
\(78\) 4.62044 0.523162
\(79\) −9.80398 −1.10303 −0.551517 0.834164i \(-0.685951\pi\)
−0.551517 + 0.834164i \(0.685951\pi\)
\(80\) −1.00000 −0.111803
\(81\) −5.95448 −0.661609
\(82\) 5.76616 0.636766
\(83\) −7.75457 −0.851174 −0.425587 0.904917i \(-0.639932\pi\)
−0.425587 + 0.904917i \(0.639932\pi\)
\(84\) −7.15731 −0.780927
\(85\) −7.03311 −0.762848
\(86\) −1.00000 −0.107833
\(87\) −4.69147 −0.502978
\(88\) 1.00000 0.106600
\(89\) −11.1654 −1.18353 −0.591764 0.806111i \(-0.701568\pi\)
−0.591764 + 0.806111i \(0.701568\pi\)
\(90\) −0.801199 −0.0844538
\(91\) 15.0400 1.57662
\(92\) 1.11595 0.116346
\(93\) 6.12644 0.635282
\(94\) −10.3447 −1.06697
\(95\) −6.23135 −0.639323
\(96\) 1.48284 0.151341
\(97\) −0.459065 −0.0466110 −0.0233055 0.999728i \(-0.507419\pi\)
−0.0233055 + 0.999728i \(0.507419\pi\)
\(98\) −16.2978 −1.64632
\(99\) 0.801199 0.0805236
\(100\) 1.00000 0.100000
\(101\) −5.99326 −0.596351 −0.298176 0.954511i \(-0.596378\pi\)
−0.298176 + 0.954511i \(0.596378\pi\)
\(102\) 10.4289 1.03262
\(103\) 12.0077 1.18315 0.591575 0.806250i \(-0.298506\pi\)
0.591575 + 0.806250i \(0.298506\pi\)
\(104\) −3.11595 −0.305544
\(105\) 7.15731 0.698482
\(106\) 10.1774 0.988517
\(107\) 2.10185 0.203193 0.101597 0.994826i \(-0.467605\pi\)
0.101597 + 0.994826i \(0.467605\pi\)
\(108\) 5.63655 0.542378
\(109\) 7.83137 0.750109 0.375055 0.927003i \(-0.377624\pi\)
0.375055 + 0.927003i \(0.377624\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −5.56449 −0.528158
\(112\) 4.82678 0.456088
\(113\) −2.25538 −0.212169 −0.106084 0.994357i \(-0.533831\pi\)
−0.106084 + 0.994357i \(0.533831\pi\)
\(114\) 9.24006 0.865411
\(115\) −1.11595 −0.104063
\(116\) 3.16385 0.293756
\(117\) −2.49650 −0.230801
\(118\) −9.27380 −0.853723
\(119\) 33.9472 3.11194
\(120\) −1.48284 −0.135364
\(121\) 1.00000 0.0909091
\(122\) −11.2530 −1.01880
\(123\) 8.55027 0.770952
\(124\) −4.13157 −0.371026
\(125\) −1.00000 −0.0894427
\(126\) 3.86721 0.344518
\(127\) −20.9378 −1.85793 −0.928963 0.370173i \(-0.879298\pi\)
−0.928963 + 0.370173i \(0.879298\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.48284 −0.130556
\(130\) 3.11595 0.273287
\(131\) 1.76078 0.153840 0.0769200 0.997037i \(-0.475491\pi\)
0.0769200 + 0.997037i \(0.475491\pi\)
\(132\) 1.48284 0.129064
\(133\) 30.0773 2.60803
\(134\) 11.3564 0.981041
\(135\) −5.63655 −0.485117
\(136\) −7.03311 −0.603084
\(137\) 9.43115 0.805758 0.402879 0.915253i \(-0.368010\pi\)
0.402879 + 0.915253i \(0.368010\pi\)
\(138\) 1.65477 0.140863
\(139\) 16.0028 1.35734 0.678670 0.734444i \(-0.262557\pi\)
0.678670 + 0.734444i \(0.262557\pi\)
\(140\) −4.82678 −0.407937
\(141\) −15.3395 −1.29182
\(142\) −1.75115 −0.146953
\(143\) −3.11595 −0.260569
\(144\) −0.801199 −0.0667666
\(145\) −3.16385 −0.262744
\(146\) −6.29746 −0.521182
\(147\) −24.1669 −1.99325
\(148\) 3.75260 0.308462
\(149\) 4.39902 0.360382 0.180191 0.983632i \(-0.442328\pi\)
0.180191 + 0.983632i \(0.442328\pi\)
\(150\) 1.48284 0.121073
\(151\) −18.2702 −1.48680 −0.743402 0.668845i \(-0.766789\pi\)
−0.743402 + 0.668845i \(0.766789\pi\)
\(152\) −6.23135 −0.505429
\(153\) −5.63492 −0.455556
\(154\) 4.82678 0.388953
\(155\) 4.13157 0.331856
\(156\) −4.62044 −0.369931
\(157\) −8.48633 −0.677283 −0.338641 0.940916i \(-0.609967\pi\)
−0.338641 + 0.940916i \(0.609967\pi\)
\(158\) 9.80398 0.779963
\(159\) 15.0914 1.19683
\(160\) 1.00000 0.0790569
\(161\) 5.38644 0.424511
\(162\) 5.95448 0.467828
\(163\) −5.34228 −0.418440 −0.209220 0.977869i \(-0.567092\pi\)
−0.209220 + 0.977869i \(0.567092\pi\)
\(164\) −5.76616 −0.450262
\(165\) −1.48284 −0.115439
\(166\) 7.75457 0.601871
\(167\) −24.0863 −1.86385 −0.931925 0.362651i \(-0.881872\pi\)
−0.931925 + 0.362651i \(0.881872\pi\)
\(168\) 7.15731 0.552199
\(169\) −3.29085 −0.253142
\(170\) 7.03311 0.539415
\(171\) −4.99255 −0.381790
\(172\) 1.00000 0.0762493
\(173\) −21.9002 −1.66504 −0.832522 0.553992i \(-0.813104\pi\)
−0.832522 + 0.553992i \(0.813104\pi\)
\(174\) 4.69147 0.355659
\(175\) 4.82678 0.364870
\(176\) −1.00000 −0.0753778
\(177\) −13.7515 −1.03363
\(178\) 11.1654 0.836880
\(179\) 6.07104 0.453770 0.226885 0.973921i \(-0.427146\pi\)
0.226885 + 0.973921i \(0.427146\pi\)
\(180\) 0.801199 0.0597179
\(181\) 10.3540 0.769606 0.384803 0.922999i \(-0.374269\pi\)
0.384803 + 0.922999i \(0.374269\pi\)
\(182\) −15.0400 −1.11484
\(183\) −16.6864 −1.23349
\(184\) −1.11595 −0.0822690
\(185\) −3.75260 −0.275897
\(186\) −6.12644 −0.449212
\(187\) −7.03311 −0.514312
\(188\) 10.3447 0.754464
\(189\) 27.2064 1.97897
\(190\) 6.23135 0.452069
\(191\) −15.9490 −1.15403 −0.577015 0.816733i \(-0.695783\pi\)
−0.577015 + 0.816733i \(0.695783\pi\)
\(192\) −1.48284 −0.107014
\(193\) −2.80456 −0.201877 −0.100938 0.994893i \(-0.532185\pi\)
−0.100938 + 0.994893i \(0.532185\pi\)
\(194\) 0.459065 0.0329590
\(195\) 4.62044 0.330877
\(196\) 16.2978 1.16413
\(197\) 15.2867 1.08914 0.544568 0.838717i \(-0.316694\pi\)
0.544568 + 0.838717i \(0.316694\pi\)
\(198\) −0.801199 −0.0569388
\(199\) −10.4346 −0.739686 −0.369843 0.929094i \(-0.620589\pi\)
−0.369843 + 0.929094i \(0.620589\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 16.8396 1.18778
\(202\) 5.99326 0.421684
\(203\) 15.2712 1.07183
\(204\) −10.4289 −0.730172
\(205\) 5.76616 0.402726
\(206\) −12.0077 −0.836614
\(207\) −0.894099 −0.0621442
\(208\) 3.11595 0.216052
\(209\) −6.23135 −0.431031
\(210\) −7.15731 −0.493902
\(211\) 18.4743 1.27183 0.635913 0.771761i \(-0.280624\pi\)
0.635913 + 0.771761i \(0.280624\pi\)
\(212\) −10.1774 −0.698987
\(213\) −2.59666 −0.177921
\(214\) −2.10185 −0.143679
\(215\) −1.00000 −0.0681994
\(216\) −5.63655 −0.383519
\(217\) −19.9422 −1.35376
\(218\) −7.83137 −0.530407
\(219\) −9.33810 −0.631010
\(220\) 1.00000 0.0674200
\(221\) 21.9148 1.47415
\(222\) 5.56449 0.373464
\(223\) 5.99924 0.401739 0.200870 0.979618i \(-0.435623\pi\)
0.200870 + 0.979618i \(0.435623\pi\)
\(224\) −4.82678 −0.322503
\(225\) −0.801199 −0.0534133
\(226\) 2.25538 0.150026
\(227\) −9.51703 −0.631668 −0.315834 0.948815i \(-0.602284\pi\)
−0.315834 + 0.948815i \(0.602284\pi\)
\(228\) −9.24006 −0.611938
\(229\) 21.3780 1.41270 0.706349 0.707863i \(-0.250341\pi\)
0.706349 + 0.707863i \(0.250341\pi\)
\(230\) 1.11595 0.0735836
\(231\) 7.15731 0.470917
\(232\) −3.16385 −0.207717
\(233\) −26.2946 −1.72262 −0.861308 0.508083i \(-0.830354\pi\)
−0.861308 + 0.508083i \(0.830354\pi\)
\(234\) 2.49650 0.163201
\(235\) −10.3447 −0.674813
\(236\) 9.27380 0.603673
\(237\) 14.5377 0.944325
\(238\) −33.9472 −2.20047
\(239\) −10.0042 −0.647115 −0.323558 0.946209i \(-0.604879\pi\)
−0.323558 + 0.946209i \(0.604879\pi\)
\(240\) 1.48284 0.0957166
\(241\) 9.71227 0.625622 0.312811 0.949815i \(-0.398729\pi\)
0.312811 + 0.949815i \(0.398729\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −8.08014 −0.518341
\(244\) 11.2530 0.720400
\(245\) −16.2978 −1.04123
\(246\) −8.55027 −0.545145
\(247\) 19.4166 1.23545
\(248\) 4.13157 0.262355
\(249\) 11.4987 0.728704
\(250\) 1.00000 0.0632456
\(251\) 25.5642 1.61360 0.806798 0.590828i \(-0.201199\pi\)
0.806798 + 0.590828i \(0.201199\pi\)
\(252\) −3.86721 −0.243611
\(253\) −1.11595 −0.0701592
\(254\) 20.9378 1.31375
\(255\) 10.4289 0.653086
\(256\) 1.00000 0.0625000
\(257\) 4.82868 0.301205 0.150603 0.988594i \(-0.451879\pi\)
0.150603 + 0.988594i \(0.451879\pi\)
\(258\) 1.48284 0.0923173
\(259\) 18.1130 1.12548
\(260\) −3.11595 −0.193243
\(261\) −2.53488 −0.156905
\(262\) −1.76078 −0.108781
\(263\) −10.2445 −0.631701 −0.315850 0.948809i \(-0.602290\pi\)
−0.315850 + 0.948809i \(0.602290\pi\)
\(264\) −1.48284 −0.0912622
\(265\) 10.1774 0.625193
\(266\) −30.0773 −1.84416
\(267\) 16.5564 1.01324
\(268\) −11.3564 −0.693701
\(269\) −13.6765 −0.833870 −0.416935 0.908936i \(-0.636896\pi\)
−0.416935 + 0.908936i \(0.636896\pi\)
\(270\) 5.63655 0.343030
\(271\) −11.1336 −0.676318 −0.338159 0.941089i \(-0.609804\pi\)
−0.338159 + 0.941089i \(0.609804\pi\)
\(272\) 7.03311 0.426445
\(273\) −22.3018 −1.34977
\(274\) −9.43115 −0.569757
\(275\) −1.00000 −0.0603023
\(276\) −1.65477 −0.0996055
\(277\) 20.9792 1.26052 0.630258 0.776386i \(-0.282949\pi\)
0.630258 + 0.776386i \(0.282949\pi\)
\(278\) −16.0028 −0.959784
\(279\) 3.31021 0.198177
\(280\) 4.82678 0.288455
\(281\) −4.12104 −0.245841 −0.122920 0.992417i \(-0.539226\pi\)
−0.122920 + 0.992417i \(0.539226\pi\)
\(282\) 15.3395 0.913452
\(283\) 28.9926 1.72343 0.861716 0.507391i \(-0.169390\pi\)
0.861716 + 0.507391i \(0.169390\pi\)
\(284\) 1.75115 0.103912
\(285\) 9.24006 0.547334
\(286\) 3.11595 0.184250
\(287\) −27.8320 −1.64287
\(288\) 0.801199 0.0472111
\(289\) 32.4646 1.90968
\(290\) 3.16385 0.185788
\(291\) 0.680718 0.0399044
\(292\) 6.29746 0.368531
\(293\) −9.42775 −0.550775 −0.275388 0.961333i \(-0.588806\pi\)
−0.275388 + 0.961333i \(0.588806\pi\)
\(294\) 24.1669 1.40944
\(295\) −9.27380 −0.539942
\(296\) −3.75260 −0.218115
\(297\) −5.63655 −0.327066
\(298\) −4.39902 −0.254828
\(299\) 3.47725 0.201094
\(300\) −1.48284 −0.0856115
\(301\) 4.82678 0.278211
\(302\) 18.2702 1.05133
\(303\) 8.88701 0.510545
\(304\) 6.23135 0.357392
\(305\) −11.2530 −0.644345
\(306\) 5.63492 0.322127
\(307\) 20.6914 1.18092 0.590460 0.807067i \(-0.298946\pi\)
0.590460 + 0.807067i \(0.298946\pi\)
\(308\) −4.82678 −0.275031
\(309\) −17.8054 −1.01291
\(310\) −4.13157 −0.234657
\(311\) 32.6114 1.84922 0.924612 0.380911i \(-0.124389\pi\)
0.924612 + 0.380911i \(0.124389\pi\)
\(312\) 4.62044 0.261581
\(313\) 30.0632 1.69927 0.849636 0.527370i \(-0.176822\pi\)
0.849636 + 0.527370i \(0.176822\pi\)
\(314\) 8.48633 0.478911
\(315\) 3.86721 0.217893
\(316\) −9.80398 −0.551517
\(317\) −5.56557 −0.312593 −0.156297 0.987710i \(-0.549956\pi\)
−0.156297 + 0.987710i \(0.549956\pi\)
\(318\) −15.0914 −0.846285
\(319\) −3.16385 −0.177142
\(320\) −1.00000 −0.0559017
\(321\) −3.11669 −0.173957
\(322\) −5.38644 −0.300175
\(323\) 43.8257 2.43853
\(324\) −5.95448 −0.330805
\(325\) 3.11595 0.172842
\(326\) 5.34228 0.295882
\(327\) −11.6126 −0.642180
\(328\) 5.76616 0.318383
\(329\) 49.9315 2.75281
\(330\) 1.48284 0.0816274
\(331\) −6.80814 −0.374209 −0.187105 0.982340i \(-0.559910\pi\)
−0.187105 + 0.982340i \(0.559910\pi\)
\(332\) −7.75457 −0.425587
\(333\) −3.00658 −0.164760
\(334\) 24.0863 1.31794
\(335\) 11.3564 0.620465
\(336\) −7.15731 −0.390464
\(337\) −17.6757 −0.962854 −0.481427 0.876486i \(-0.659881\pi\)
−0.481427 + 0.876486i \(0.659881\pi\)
\(338\) 3.29085 0.178999
\(339\) 3.34436 0.181641
\(340\) −7.03311 −0.381424
\(341\) 4.13157 0.223737
\(342\) 4.99255 0.269966
\(343\) 44.8783 2.42320
\(344\) −1.00000 −0.0539164
\(345\) 1.65477 0.0890899
\(346\) 21.9002 1.17736
\(347\) −1.50630 −0.0808623 −0.0404311 0.999182i \(-0.512873\pi\)
−0.0404311 + 0.999182i \(0.512873\pi\)
\(348\) −4.69147 −0.251489
\(349\) 6.73446 0.360487 0.180244 0.983622i \(-0.442311\pi\)
0.180244 + 0.983622i \(0.442311\pi\)
\(350\) −4.82678 −0.258002
\(351\) 17.5632 0.937455
\(352\) 1.00000 0.0533002
\(353\) 2.06180 0.109739 0.0548693 0.998494i \(-0.482526\pi\)
0.0548693 + 0.998494i \(0.482526\pi\)
\(354\) 13.7515 0.730885
\(355\) −1.75115 −0.0929413
\(356\) −11.1654 −0.591764
\(357\) −50.3382 −2.66418
\(358\) −6.07104 −0.320864
\(359\) 14.9385 0.788422 0.394211 0.919020i \(-0.371018\pi\)
0.394211 + 0.919020i \(0.371018\pi\)
\(360\) −0.801199 −0.0422269
\(361\) 19.8297 1.04367
\(362\) −10.3540 −0.544194
\(363\) −1.48284 −0.0778287
\(364\) 15.0400 0.788310
\(365\) −6.29746 −0.329624
\(366\) 16.6864 0.872210
\(367\) 14.7313 0.768966 0.384483 0.923132i \(-0.374380\pi\)
0.384483 + 0.923132i \(0.374380\pi\)
\(368\) 1.11595 0.0581729
\(369\) 4.61985 0.240500
\(370\) 3.75260 0.195088
\(371\) −49.1241 −2.55039
\(372\) 6.12644 0.317641
\(373\) −13.7561 −0.712263 −0.356131 0.934436i \(-0.615904\pi\)
−0.356131 + 0.934436i \(0.615904\pi\)
\(374\) 7.03311 0.363673
\(375\) 1.48284 0.0765733
\(376\) −10.3447 −0.533486
\(377\) 9.85841 0.507734
\(378\) −27.2064 −1.39935
\(379\) −19.6061 −1.00710 −0.503550 0.863966i \(-0.667973\pi\)
−0.503550 + 0.863966i \(0.667973\pi\)
\(380\) −6.23135 −0.319661
\(381\) 31.0472 1.59060
\(382\) 15.9490 0.816023
\(383\) 32.1235 1.64143 0.820716 0.571336i \(-0.193575\pi\)
0.820716 + 0.571336i \(0.193575\pi\)
\(384\) 1.48284 0.0756706
\(385\) 4.82678 0.245995
\(386\) 2.80456 0.142749
\(387\) −0.801199 −0.0407273
\(388\) −0.459065 −0.0233055
\(389\) −23.0968 −1.17105 −0.585527 0.810653i \(-0.699112\pi\)
−0.585527 + 0.810653i \(0.699112\pi\)
\(390\) −4.62044 −0.233965
\(391\) 7.84860 0.396921
\(392\) −16.2978 −0.823162
\(393\) −2.61095 −0.131705
\(394\) −15.2867 −0.770135
\(395\) 9.80398 0.493292
\(396\) 0.801199 0.0402618
\(397\) 36.8054 1.84721 0.923604 0.383348i \(-0.125229\pi\)
0.923604 + 0.383348i \(0.125229\pi\)
\(398\) 10.4346 0.523037
\(399\) −44.5997 −2.23278
\(400\) 1.00000 0.0500000
\(401\) −6.49490 −0.324340 −0.162170 0.986763i \(-0.551849\pi\)
−0.162170 + 0.986763i \(0.551849\pi\)
\(402\) −16.8396 −0.839884
\(403\) −12.8738 −0.641288
\(404\) −5.99326 −0.298176
\(405\) 5.95448 0.295881
\(406\) −15.2712 −0.757897
\(407\) −3.75260 −0.186010
\(408\) 10.4289 0.516310
\(409\) 18.1660 0.898249 0.449125 0.893469i \(-0.351736\pi\)
0.449125 + 0.893469i \(0.351736\pi\)
\(410\) −5.76616 −0.284771
\(411\) −13.9848 −0.689821
\(412\) 12.0077 0.591575
\(413\) 44.7626 2.20262
\(414\) 0.894099 0.0439426
\(415\) 7.75457 0.380657
\(416\) −3.11595 −0.152772
\(417\) −23.7295 −1.16204
\(418\) 6.23135 0.304785
\(419\) −8.59949 −0.420113 −0.210056 0.977689i \(-0.567365\pi\)
−0.210056 + 0.977689i \(0.567365\pi\)
\(420\) 7.15731 0.349241
\(421\) −30.7705 −1.49966 −0.749831 0.661630i \(-0.769865\pi\)
−0.749831 + 0.661630i \(0.769865\pi\)
\(422\) −18.4743 −0.899317
\(423\) −8.28816 −0.402984
\(424\) 10.1774 0.494259
\(425\) 7.03311 0.341156
\(426\) 2.59666 0.125809
\(427\) 54.3157 2.62852
\(428\) 2.10185 0.101597
\(429\) 4.62044 0.223077
\(430\) 1.00000 0.0482243
\(431\) 29.0510 1.39934 0.699669 0.714467i \(-0.253331\pi\)
0.699669 + 0.714467i \(0.253331\pi\)
\(432\) 5.63655 0.271189
\(433\) −10.6572 −0.512152 −0.256076 0.966657i \(-0.582430\pi\)
−0.256076 + 0.966657i \(0.582430\pi\)
\(434\) 19.9422 0.957255
\(435\) 4.69147 0.224939
\(436\) 7.83137 0.375055
\(437\) 6.95388 0.332649
\(438\) 9.33810 0.446192
\(439\) 8.49937 0.405653 0.202826 0.979215i \(-0.434987\pi\)
0.202826 + 0.979215i \(0.434987\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −13.0578 −0.621798
\(442\) −21.9148 −1.04238
\(443\) 12.7886 0.607604 0.303802 0.952735i \(-0.401744\pi\)
0.303802 + 0.952735i \(0.401744\pi\)
\(444\) −5.56449 −0.264079
\(445\) 11.1654 0.529290
\(446\) −5.99924 −0.284072
\(447\) −6.52302 −0.308528
\(448\) 4.82678 0.228044
\(449\) −10.0081 −0.472312 −0.236156 0.971715i \(-0.575888\pi\)
−0.236156 + 0.971715i \(0.575888\pi\)
\(450\) 0.801199 0.0377689
\(451\) 5.76616 0.271518
\(452\) −2.25538 −0.106084
\(453\) 27.0916 1.27288
\(454\) 9.51703 0.446656
\(455\) −15.0400 −0.705086
\(456\) 9.24006 0.432706
\(457\) −23.1307 −1.08201 −0.541004 0.841020i \(-0.681956\pi\)
−0.541004 + 0.841020i \(0.681956\pi\)
\(458\) −21.3780 −0.998929
\(459\) 39.6425 1.85035
\(460\) −1.11595 −0.0520315
\(461\) −7.38407 −0.343910 −0.171955 0.985105i \(-0.555008\pi\)
−0.171955 + 0.985105i \(0.555008\pi\)
\(462\) −7.15731 −0.332988
\(463\) −26.1690 −1.21618 −0.608088 0.793870i \(-0.708063\pi\)
−0.608088 + 0.793870i \(0.708063\pi\)
\(464\) 3.16385 0.146878
\(465\) −6.12644 −0.284107
\(466\) 26.2946 1.21807
\(467\) −2.76399 −0.127902 −0.0639512 0.997953i \(-0.520370\pi\)
−0.0639512 + 0.997953i \(0.520370\pi\)
\(468\) −2.49650 −0.115401
\(469\) −54.8147 −2.53111
\(470\) 10.3447 0.477165
\(471\) 12.5838 0.579832
\(472\) −9.27380 −0.426861
\(473\) −1.00000 −0.0459800
\(474\) −14.5377 −0.667738
\(475\) 6.23135 0.285914
\(476\) 33.9472 1.55597
\(477\) 8.15413 0.373352
\(478\) 10.0042 0.457579
\(479\) 36.2872 1.65800 0.829001 0.559247i \(-0.188910\pi\)
0.829001 + 0.559247i \(0.188910\pi\)
\(480\) −1.48284 −0.0676819
\(481\) 11.6929 0.533151
\(482\) −9.71227 −0.442382
\(483\) −7.98721 −0.363431
\(484\) 1.00000 0.0454545
\(485\) 0.459065 0.0208451
\(486\) 8.08014 0.366523
\(487\) 12.2972 0.557240 0.278620 0.960401i \(-0.410123\pi\)
0.278620 + 0.960401i \(0.410123\pi\)
\(488\) −11.2530 −0.509400
\(489\) 7.92173 0.358233
\(490\) 16.2978 0.736258
\(491\) 20.5937 0.929383 0.464691 0.885473i \(-0.346165\pi\)
0.464691 + 0.885473i \(0.346165\pi\)
\(492\) 8.55027 0.385476
\(493\) 22.2517 1.00217
\(494\) −19.4166 −0.873593
\(495\) −0.801199 −0.0360112
\(496\) −4.13157 −0.185513
\(497\) 8.45240 0.379142
\(498\) −11.4987 −0.515271
\(499\) 10.9689 0.491038 0.245519 0.969392i \(-0.421042\pi\)
0.245519 + 0.969392i \(0.421042\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 35.7159 1.59567
\(502\) −25.5642 −1.14098
\(503\) 6.60727 0.294603 0.147302 0.989092i \(-0.452941\pi\)
0.147302 + 0.989092i \(0.452941\pi\)
\(504\) 3.86721 0.172259
\(505\) 5.99326 0.266696
\(506\) 1.11595 0.0496101
\(507\) 4.87979 0.216719
\(508\) −20.9378 −0.928963
\(509\) 28.0503 1.24331 0.621654 0.783292i \(-0.286461\pi\)
0.621654 + 0.783292i \(0.286461\pi\)
\(510\) −10.4289 −0.461801
\(511\) 30.3964 1.34466
\(512\) −1.00000 −0.0441942
\(513\) 35.1233 1.55073
\(514\) −4.82868 −0.212984
\(515\) −12.0077 −0.529121
\(516\) −1.48284 −0.0652782
\(517\) −10.3447 −0.454959
\(518\) −18.1130 −0.795838
\(519\) 32.4744 1.42547
\(520\) 3.11595 0.136643
\(521\) 37.5182 1.64370 0.821851 0.569702i \(-0.192941\pi\)
0.821851 + 0.569702i \(0.192941\pi\)
\(522\) 2.53488 0.110948
\(523\) 6.94141 0.303527 0.151763 0.988417i \(-0.451505\pi\)
0.151763 + 0.988417i \(0.451505\pi\)
\(524\) 1.76078 0.0769200
\(525\) −7.15731 −0.312371
\(526\) 10.2445 0.446680
\(527\) −29.0578 −1.26578
\(528\) 1.48284 0.0645321
\(529\) −21.7547 −0.945855
\(530\) −10.1774 −0.442078
\(531\) −7.43017 −0.322442
\(532\) 30.0773 1.30402
\(533\) −17.9671 −0.778241
\(534\) −16.5564 −0.716466
\(535\) −2.10185 −0.0908708
\(536\) 11.3564 0.490521
\(537\) −9.00235 −0.388480
\(538\) 13.6765 0.589635
\(539\) −16.2978 −0.701995
\(540\) −5.63655 −0.242559
\(541\) 21.3494 0.917884 0.458942 0.888466i \(-0.348229\pi\)
0.458942 + 0.888466i \(0.348229\pi\)
\(542\) 11.1336 0.478229
\(543\) −15.3533 −0.658872
\(544\) −7.03311 −0.301542
\(545\) −7.83137 −0.335459
\(546\) 22.3018 0.954431
\(547\) −9.21096 −0.393832 −0.196916 0.980420i \(-0.563093\pi\)
−0.196916 + 0.980420i \(0.563093\pi\)
\(548\) 9.43115 0.402879
\(549\) −9.01590 −0.384789
\(550\) 1.00000 0.0426401
\(551\) 19.7151 0.839890
\(552\) 1.65477 0.0704317
\(553\) −47.3216 −2.01232
\(554\) −20.9792 −0.891319
\(555\) 5.56449 0.236199
\(556\) 16.0028 0.678670
\(557\) 0.983118 0.0416560 0.0208280 0.999783i \(-0.493370\pi\)
0.0208280 + 0.999783i \(0.493370\pi\)
\(558\) −3.31021 −0.140132
\(559\) 3.11595 0.131791
\(560\) −4.82678 −0.203969
\(561\) 10.4289 0.440310
\(562\) 4.12104 0.173836
\(563\) −5.42395 −0.228592 −0.114296 0.993447i \(-0.536461\pi\)
−0.114296 + 0.993447i \(0.536461\pi\)
\(564\) −15.3395 −0.645908
\(565\) 2.25538 0.0948847
\(566\) −28.9926 −1.21865
\(567\) −28.7410 −1.20701
\(568\) −1.75115 −0.0734765
\(569\) −34.1852 −1.43312 −0.716559 0.697527i \(-0.754284\pi\)
−0.716559 + 0.697527i \(0.754284\pi\)
\(570\) −9.24006 −0.387024
\(571\) 21.9627 0.919111 0.459556 0.888149i \(-0.348009\pi\)
0.459556 + 0.888149i \(0.348009\pi\)
\(572\) −3.11595 −0.130284
\(573\) 23.6498 0.987983
\(574\) 27.8320 1.16168
\(575\) 1.11595 0.0465384
\(576\) −0.801199 −0.0333833
\(577\) −13.5274 −0.563153 −0.281577 0.959539i \(-0.590857\pi\)
−0.281577 + 0.959539i \(0.590857\pi\)
\(578\) −32.4646 −1.35035
\(579\) 4.15871 0.172830
\(580\) −3.16385 −0.131372
\(581\) −37.4296 −1.55284
\(582\) −0.680718 −0.0282167
\(583\) 10.1774 0.421505
\(584\) −6.29746 −0.260591
\(585\) 2.49650 0.103217
\(586\) 9.42775 0.389457
\(587\) −41.1694 −1.69924 −0.849621 0.527394i \(-0.823169\pi\)
−0.849621 + 0.527394i \(0.823169\pi\)
\(588\) −24.1669 −0.996627
\(589\) −25.7452 −1.06081
\(590\) 9.27380 0.381796
\(591\) −22.6677 −0.932426
\(592\) 3.75260 0.154231
\(593\) 7.26639 0.298395 0.149197 0.988807i \(-0.452331\pi\)
0.149197 + 0.988807i \(0.452331\pi\)
\(594\) 5.63655 0.231271
\(595\) −33.9472 −1.39170
\(596\) 4.39902 0.180191
\(597\) 15.4727 0.633257
\(598\) −3.47725 −0.142195
\(599\) −1.35091 −0.0551967 −0.0275984 0.999619i \(-0.508786\pi\)
−0.0275984 + 0.999619i \(0.508786\pi\)
\(600\) 1.48284 0.0605365
\(601\) −9.92951 −0.405033 −0.202516 0.979279i \(-0.564912\pi\)
−0.202516 + 0.979279i \(0.564912\pi\)
\(602\) −4.82678 −0.196725
\(603\) 9.09872 0.370528
\(604\) −18.2702 −0.743402
\(605\) −1.00000 −0.0406558
\(606\) −8.88701 −0.361010
\(607\) −23.4087 −0.950131 −0.475066 0.879950i \(-0.657576\pi\)
−0.475066 + 0.879950i \(0.657576\pi\)
\(608\) −6.23135 −0.252714
\(609\) −22.6447 −0.917609
\(610\) 11.2530 0.455621
\(611\) 32.2335 1.30403
\(612\) −5.63492 −0.227778
\(613\) −7.18631 −0.290252 −0.145126 0.989413i \(-0.546359\pi\)
−0.145126 + 0.989413i \(0.546359\pi\)
\(614\) −20.6914 −0.835036
\(615\) −8.55027 −0.344780
\(616\) 4.82678 0.194476
\(617\) −7.29957 −0.293869 −0.146935 0.989146i \(-0.546941\pi\)
−0.146935 + 0.989146i \(0.546941\pi\)
\(618\) 17.8054 0.716238
\(619\) 35.5846 1.43027 0.715133 0.698989i \(-0.246366\pi\)
0.715133 + 0.698989i \(0.246366\pi\)
\(620\) 4.13157 0.165928
\(621\) 6.29011 0.252414
\(622\) −32.6114 −1.30760
\(623\) −53.8928 −2.15917
\(624\) −4.62044 −0.184966
\(625\) 1.00000 0.0400000
\(626\) −30.0632 −1.20157
\(627\) 9.24006 0.369013
\(628\) −8.48633 −0.338641
\(629\) 26.3925 1.05234
\(630\) −3.86721 −0.154073
\(631\) −18.0131 −0.717090 −0.358545 0.933513i \(-0.616727\pi\)
−0.358545 + 0.933513i \(0.616727\pi\)
\(632\) 9.80398 0.389982
\(633\) −27.3944 −1.08883
\(634\) 5.56557 0.221037
\(635\) 20.9378 0.830889
\(636\) 15.0914 0.598414
\(637\) 50.7831 2.01210
\(638\) 3.16385 0.125258
\(639\) −1.40302 −0.0555026
\(640\) 1.00000 0.0395285
\(641\) −9.51890 −0.375974 −0.187987 0.982172i \(-0.560196\pi\)
−0.187987 + 0.982172i \(0.560196\pi\)
\(642\) 3.11669 0.123006
\(643\) −35.6561 −1.40614 −0.703069 0.711122i \(-0.748187\pi\)
−0.703069 + 0.711122i \(0.748187\pi\)
\(644\) 5.38644 0.212256
\(645\) 1.48284 0.0583866
\(646\) −43.8257 −1.72430
\(647\) 20.4070 0.802281 0.401141 0.916017i \(-0.368614\pi\)
0.401141 + 0.916017i \(0.368614\pi\)
\(648\) 5.95448 0.233914
\(649\) −9.27380 −0.364029
\(650\) −3.11595 −0.122218
\(651\) 29.5709 1.15898
\(652\) −5.34228 −0.209220
\(653\) −35.5748 −1.39215 −0.696074 0.717970i \(-0.745072\pi\)
−0.696074 + 0.717970i \(0.745072\pi\)
\(654\) 11.6126 0.454090
\(655\) −1.76078 −0.0687993
\(656\) −5.76616 −0.225131
\(657\) −5.04552 −0.196845
\(658\) −49.9315 −1.94653
\(659\) 22.8345 0.889507 0.444754 0.895653i \(-0.353291\pi\)
0.444754 + 0.895653i \(0.353291\pi\)
\(660\) −1.48284 −0.0577193
\(661\) −0.0985728 −0.00383404 −0.00191702 0.999998i \(-0.500610\pi\)
−0.00191702 + 0.999998i \(0.500610\pi\)
\(662\) 6.80814 0.264606
\(663\) −32.4961 −1.26204
\(664\) 7.75457 0.300936
\(665\) −30.0773 −1.16635
\(666\) 3.00658 0.116503
\(667\) 3.53070 0.136709
\(668\) −24.0863 −0.931925
\(669\) −8.89589 −0.343935
\(670\) −11.3564 −0.438735
\(671\) −11.2530 −0.434417
\(672\) 7.15731 0.276099
\(673\) −1.64560 −0.0634332 −0.0317166 0.999497i \(-0.510097\pi\)
−0.0317166 + 0.999497i \(0.510097\pi\)
\(674\) 17.6757 0.680841
\(675\) 5.63655 0.216951
\(676\) −3.29085 −0.126571
\(677\) −12.0789 −0.464231 −0.232116 0.972688i \(-0.574565\pi\)
−0.232116 + 0.972688i \(0.574565\pi\)
\(678\) −3.34436 −0.128439
\(679\) −2.21581 −0.0850348
\(680\) 7.03311 0.269707
\(681\) 14.1122 0.540780
\(682\) −4.13157 −0.158206
\(683\) 21.7046 0.830503 0.415251 0.909707i \(-0.363694\pi\)
0.415251 + 0.909707i \(0.363694\pi\)
\(684\) −4.99255 −0.190895
\(685\) −9.43115 −0.360346
\(686\) −44.8783 −1.71346
\(687\) −31.7001 −1.20943
\(688\) 1.00000 0.0381246
\(689\) −31.7123 −1.20814
\(690\) −1.65477 −0.0629961
\(691\) −21.4673 −0.816656 −0.408328 0.912835i \(-0.633888\pi\)
−0.408328 + 0.912835i \(0.633888\pi\)
\(692\) −21.9002 −0.832522
\(693\) 3.86721 0.146903
\(694\) 1.50630 0.0571783
\(695\) −16.0028 −0.607021
\(696\) 4.69147 0.177830
\(697\) −40.5541 −1.53609
\(698\) −6.73446 −0.254903
\(699\) 38.9906 1.47476
\(700\) 4.82678 0.182435
\(701\) −15.7822 −0.596085 −0.298042 0.954553i \(-0.596334\pi\)
−0.298042 + 0.954553i \(0.596334\pi\)
\(702\) −17.5632 −0.662881
\(703\) 23.3838 0.881935
\(704\) −1.00000 −0.0376889
\(705\) 15.3395 0.577718
\(706\) −2.06180 −0.0775969
\(707\) −28.9281 −1.08795
\(708\) −13.7515 −0.516814
\(709\) −49.3521 −1.85346 −0.926729 0.375731i \(-0.877392\pi\)
−0.926729 + 0.375731i \(0.877392\pi\)
\(710\) 1.75115 0.0657194
\(711\) 7.85495 0.294583
\(712\) 11.1654 0.418440
\(713\) −4.61063 −0.172669
\(714\) 50.3382 1.88386
\(715\) 3.11595 0.116530
\(716\) 6.07104 0.226885
\(717\) 14.8345 0.554005
\(718\) −14.9385 −0.557499
\(719\) −39.6827 −1.47991 −0.739957 0.672654i \(-0.765154\pi\)
−0.739957 + 0.672654i \(0.765154\pi\)
\(720\) 0.801199 0.0298589
\(721\) 57.9583 2.15848
\(722\) −19.8297 −0.737985
\(723\) −14.4017 −0.535605
\(724\) 10.3540 0.384803
\(725\) 3.16385 0.117502
\(726\) 1.48284 0.0550332
\(727\) −25.7743 −0.955917 −0.477959 0.878382i \(-0.658623\pi\)
−0.477959 + 0.878382i \(0.658623\pi\)
\(728\) −15.0400 −0.557419
\(729\) 29.8450 1.10537
\(730\) 6.29746 0.233079
\(731\) 7.03311 0.260129
\(732\) −16.6864 −0.616745
\(733\) −8.72247 −0.322172 −0.161086 0.986940i \(-0.551500\pi\)
−0.161086 + 0.986940i \(0.551500\pi\)
\(734\) −14.7313 −0.543741
\(735\) 24.1669 0.891410
\(736\) −1.11595 −0.0411345
\(737\) 11.3564 0.418317
\(738\) −4.61985 −0.170059
\(739\) 49.5319 1.82206 0.911030 0.412341i \(-0.135289\pi\)
0.911030 + 0.412341i \(0.135289\pi\)
\(740\) −3.75260 −0.137948
\(741\) −28.7916 −1.05769
\(742\) 49.1241 1.80340
\(743\) 33.6058 1.23288 0.616439 0.787403i \(-0.288575\pi\)
0.616439 + 0.787403i \(0.288575\pi\)
\(744\) −6.12644 −0.224606
\(745\) −4.39902 −0.161168
\(746\) 13.7561 0.503646
\(747\) 6.21295 0.227320
\(748\) −7.03311 −0.257156
\(749\) 10.1452 0.370696
\(750\) −1.48284 −0.0541455
\(751\) −12.0723 −0.440525 −0.220263 0.975441i \(-0.570691\pi\)
−0.220263 + 0.975441i \(0.570691\pi\)
\(752\) 10.3447 0.377232
\(753\) −37.9074 −1.38142
\(754\) −9.85841 −0.359022
\(755\) 18.2702 0.664919
\(756\) 27.2064 0.989486
\(757\) 11.3058 0.410917 0.205459 0.978666i \(-0.434131\pi\)
0.205459 + 0.978666i \(0.434131\pi\)
\(758\) 19.6061 0.712127
\(759\) 1.65477 0.0600644
\(760\) 6.23135 0.226035
\(761\) 11.6839 0.423540 0.211770 0.977320i \(-0.432077\pi\)
0.211770 + 0.977320i \(0.432077\pi\)
\(762\) −31.0472 −1.12472
\(763\) 37.8003 1.36846
\(764\) −15.9490 −0.577015
\(765\) 5.63492 0.203731
\(766\) −32.1235 −1.16067
\(767\) 28.8967 1.04340
\(768\) −1.48284 −0.0535072
\(769\) −39.7026 −1.43171 −0.715856 0.698248i \(-0.753963\pi\)
−0.715856 + 0.698248i \(0.753963\pi\)
\(770\) −4.82678 −0.173945
\(771\) −7.16014 −0.257866
\(772\) −2.80456 −0.100938
\(773\) 31.8511 1.14560 0.572802 0.819694i \(-0.305856\pi\)
0.572802 + 0.819694i \(0.305856\pi\)
\(774\) 0.801199 0.0287985
\(775\) −4.13157 −0.148410
\(776\) 0.459065 0.0164795
\(777\) −26.8585 −0.963545
\(778\) 23.0968 0.828060
\(779\) −35.9310 −1.28736
\(780\) 4.62044 0.165438
\(781\) −1.75115 −0.0626610
\(782\) −7.84860 −0.280665
\(783\) 17.8332 0.637307
\(784\) 16.2978 0.582063
\(785\) 8.48633 0.302890
\(786\) 2.61095 0.0931294
\(787\) 21.4486 0.764560 0.382280 0.924047i \(-0.375139\pi\)
0.382280 + 0.924047i \(0.375139\pi\)
\(788\) 15.2867 0.544568
\(789\) 15.1909 0.540809
\(790\) −9.80398 −0.348810
\(791\) −10.8862 −0.387070
\(792\) −0.801199 −0.0284694
\(793\) 35.0638 1.24515
\(794\) −36.8054 −1.30617
\(795\) −15.0914 −0.535237
\(796\) −10.4346 −0.369843
\(797\) −24.7674 −0.877306 −0.438653 0.898657i \(-0.644544\pi\)
−0.438653 + 0.898657i \(0.644544\pi\)
\(798\) 44.5997 1.57881
\(799\) 72.7553 2.57390
\(800\) −1.00000 −0.0353553
\(801\) 8.94569 0.316080
\(802\) 6.49490 0.229343
\(803\) −6.29746 −0.222233
\(804\) 16.8396 0.593888
\(805\) −5.38644 −0.189847
\(806\) 12.8738 0.453459
\(807\) 20.2800 0.713889
\(808\) 5.99326 0.210842
\(809\) −19.4659 −0.684385 −0.342192 0.939630i \(-0.611169\pi\)
−0.342192 + 0.939630i \(0.611169\pi\)
\(810\) −5.95448 −0.209219
\(811\) 15.6211 0.548532 0.274266 0.961654i \(-0.411565\pi\)
0.274266 + 0.961654i \(0.411565\pi\)
\(812\) 15.2712 0.535914
\(813\) 16.5093 0.579006
\(814\) 3.75260 0.131529
\(815\) 5.34228 0.187132
\(816\) −10.4289 −0.365086
\(817\) 6.23135 0.218007
\(818\) −18.1660 −0.635158
\(819\) −12.0500 −0.421062
\(820\) 5.76616 0.201363
\(821\) −37.8925 −1.32246 −0.661229 0.750185i \(-0.729965\pi\)
−0.661229 + 0.750185i \(0.729965\pi\)
\(822\) 13.9848 0.487777
\(823\) −2.27751 −0.0793890 −0.0396945 0.999212i \(-0.512638\pi\)
−0.0396945 + 0.999212i \(0.512638\pi\)
\(824\) −12.0077 −0.418307
\(825\) 1.48284 0.0516257
\(826\) −44.7626 −1.55749
\(827\) −17.0461 −0.592749 −0.296375 0.955072i \(-0.595778\pi\)
−0.296375 + 0.955072i \(0.595778\pi\)
\(828\) −0.894099 −0.0310721
\(829\) 49.9099 1.73344 0.866721 0.498793i \(-0.166223\pi\)
0.866721 + 0.498793i \(0.166223\pi\)
\(830\) −7.75457 −0.269165
\(831\) −31.1086 −1.07915
\(832\) 3.11595 0.108026
\(833\) 114.624 3.97149
\(834\) 23.7295 0.821686
\(835\) 24.0863 0.833539
\(836\) −6.23135 −0.215516
\(837\) −23.2878 −0.804945
\(838\) 8.59949 0.297064
\(839\) 18.6811 0.644944 0.322472 0.946579i \(-0.395486\pi\)
0.322472 + 0.946579i \(0.395486\pi\)
\(840\) −7.15731 −0.246951
\(841\) −18.9900 −0.654829
\(842\) 30.7705 1.06042
\(843\) 6.11082 0.210468
\(844\) 18.4743 0.635913
\(845\) 3.29085 0.113209
\(846\) 8.28816 0.284953
\(847\) 4.82678 0.165850
\(848\) −10.1774 −0.349494
\(849\) −42.9913 −1.47546
\(850\) −7.03311 −0.241234
\(851\) 4.18772 0.143553
\(852\) −2.59666 −0.0889603
\(853\) −19.1968 −0.657287 −0.328644 0.944454i \(-0.606591\pi\)
−0.328644 + 0.944454i \(0.606591\pi\)
\(854\) −54.3157 −1.85865
\(855\) 4.99255 0.170742
\(856\) −2.10185 −0.0718397
\(857\) −20.8282 −0.711478 −0.355739 0.934585i \(-0.615771\pi\)
−0.355739 + 0.934585i \(0.615771\pi\)
\(858\) −4.62044 −0.157739
\(859\) −44.8598 −1.53060 −0.765298 0.643676i \(-0.777408\pi\)
−0.765298 + 0.643676i \(0.777408\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 41.2703 1.40649
\(862\) −29.0510 −0.989481
\(863\) 51.5633 1.75524 0.877618 0.479361i \(-0.159132\pi\)
0.877618 + 0.479361i \(0.159132\pi\)
\(864\) −5.63655 −0.191759
\(865\) 21.9002 0.744630
\(866\) 10.6572 0.362146
\(867\) −48.1397 −1.63491
\(868\) −19.9422 −0.676881
\(869\) 9.80398 0.332577
\(870\) −4.69147 −0.159056
\(871\) −35.3859 −1.19901
\(872\) −7.83137 −0.265204
\(873\) 0.367803 0.0124482
\(874\) −6.95388 −0.235218
\(875\) −4.82678 −0.163175
\(876\) −9.33810 −0.315505
\(877\) −21.6569 −0.731302 −0.365651 0.930752i \(-0.619154\pi\)
−0.365651 + 0.930752i \(0.619154\pi\)
\(878\) −8.49937 −0.286840
\(879\) 13.9798 0.471527
\(880\) 1.00000 0.0337100
\(881\) 11.2800 0.380032 0.190016 0.981781i \(-0.439146\pi\)
0.190016 + 0.981781i \(0.439146\pi\)
\(882\) 13.0578 0.439678
\(883\) −16.4809 −0.554627 −0.277314 0.960779i \(-0.589444\pi\)
−0.277314 + 0.960779i \(0.589444\pi\)
\(884\) 21.9148 0.737075
\(885\) 13.7515 0.462252
\(886\) −12.7886 −0.429641
\(887\) −18.6243 −0.625341 −0.312671 0.949862i \(-0.601224\pi\)
−0.312671 + 0.949862i \(0.601224\pi\)
\(888\) 5.56449 0.186732
\(889\) −101.062 −3.38951
\(890\) −11.1654 −0.374264
\(891\) 5.95448 0.199483
\(892\) 5.99924 0.200870
\(893\) 64.4613 2.15712
\(894\) 6.52302 0.218162
\(895\) −6.07104 −0.202932
\(896\) −4.82678 −0.161251
\(897\) −5.15618 −0.172160
\(898\) 10.0081 0.333975
\(899\) −13.0717 −0.435965
\(900\) −0.801199 −0.0267066
\(901\) −71.5788 −2.38464
\(902\) −5.76616 −0.191992
\(903\) −7.15731 −0.238181
\(904\) 2.25538 0.0750129
\(905\) −10.3540 −0.344178
\(906\) −27.0916 −0.900059
\(907\) −40.8310 −1.35577 −0.677885 0.735168i \(-0.737103\pi\)
−0.677885 + 0.735168i \(0.737103\pi\)
\(908\) −9.51703 −0.315834
\(909\) 4.80179 0.159265
\(910\) 15.0400 0.498571
\(911\) 26.0470 0.862977 0.431488 0.902118i \(-0.357989\pi\)
0.431488 + 0.902118i \(0.357989\pi\)
\(912\) −9.24006 −0.305969
\(913\) 7.75457 0.256639
\(914\) 23.1307 0.765095
\(915\) 16.6864 0.551634
\(916\) 21.3780 0.706349
\(917\) 8.49889 0.280658
\(918\) −39.6425 −1.30840
\(919\) −45.7537 −1.50928 −0.754638 0.656141i \(-0.772188\pi\)
−0.754638 + 0.656141i \(0.772188\pi\)
\(920\) 1.11595 0.0367918
\(921\) −30.6819 −1.01100
\(922\) 7.38407 0.243181
\(923\) 5.45649 0.179603
\(924\) 7.15731 0.235458
\(925\) 3.75260 0.123385
\(926\) 26.1690 0.859966
\(927\) −9.62053 −0.315980
\(928\) −3.16385 −0.103859
\(929\) 25.7773 0.845725 0.422862 0.906194i \(-0.361025\pi\)
0.422862 + 0.906194i \(0.361025\pi\)
\(930\) 6.12644 0.200894
\(931\) 101.557 3.32840
\(932\) −26.2946 −0.861308
\(933\) −48.3574 −1.58315
\(934\) 2.76399 0.0904406
\(935\) 7.03311 0.230007
\(936\) 2.49650 0.0816006
\(937\) −44.7046 −1.46044 −0.730219 0.683214i \(-0.760582\pi\)
−0.730219 + 0.683214i \(0.760582\pi\)
\(938\) 54.8147 1.78976
\(939\) −44.5788 −1.45477
\(940\) −10.3447 −0.337406
\(941\) 33.2819 1.08496 0.542480 0.840069i \(-0.317485\pi\)
0.542480 + 0.840069i \(0.317485\pi\)
\(942\) −12.5838 −0.410003
\(943\) −6.43475 −0.209544
\(944\) 9.27380 0.301837
\(945\) −27.2064 −0.885024
\(946\) 1.00000 0.0325128
\(947\) 45.2271 1.46968 0.734841 0.678239i \(-0.237257\pi\)
0.734841 + 0.678239i \(0.237257\pi\)
\(948\) 14.5377 0.472162
\(949\) 19.6226 0.636976
\(950\) −6.23135 −0.202172
\(951\) 8.25282 0.267616
\(952\) −33.9472 −1.10024
\(953\) 26.3035 0.852055 0.426027 0.904710i \(-0.359913\pi\)
0.426027 + 0.904710i \(0.359913\pi\)
\(954\) −8.15413 −0.264000
\(955\) 15.9490 0.516098
\(956\) −10.0042 −0.323558
\(957\) 4.69147 0.151654
\(958\) −36.2872 −1.17238
\(959\) 45.5221 1.46998
\(960\) 1.48284 0.0478583
\(961\) −13.9301 −0.449359
\(962\) −11.6929 −0.376995
\(963\) −1.68400 −0.0542661
\(964\) 9.71227 0.312811
\(965\) 2.80456 0.0902821
\(966\) 7.98721 0.256984
\(967\) 33.5040 1.07742 0.538708 0.842493i \(-0.318913\pi\)
0.538708 + 0.842493i \(0.318913\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −64.9864 −2.08766
\(970\) −0.459065 −0.0147397
\(971\) −23.1013 −0.741356 −0.370678 0.928761i \(-0.620875\pi\)
−0.370678 + 0.928761i \(0.620875\pi\)
\(972\) −8.08014 −0.259171
\(973\) 77.2419 2.47626
\(974\) −12.2972 −0.394028
\(975\) −4.62044 −0.147973
\(976\) 11.2530 0.360200
\(977\) 48.8724 1.56357 0.781783 0.623551i \(-0.214310\pi\)
0.781783 + 0.623551i \(0.214310\pi\)
\(978\) −7.92173 −0.253309
\(979\) 11.1654 0.356847
\(980\) −16.2978 −0.520613
\(981\) −6.27449 −0.200329
\(982\) −20.5937 −0.657173
\(983\) −33.1114 −1.05609 −0.528045 0.849216i \(-0.677075\pi\)
−0.528045 + 0.849216i \(0.677075\pi\)
\(984\) −8.55027 −0.272573
\(985\) −15.2867 −0.487076
\(986\) −22.2517 −0.708639
\(987\) −74.0402 −2.35672
\(988\) 19.4166 0.617723
\(989\) 1.11595 0.0354852
\(990\) 0.801199 0.0254638
\(991\) 45.9388 1.45929 0.729647 0.683824i \(-0.239684\pi\)
0.729647 + 0.683824i \(0.239684\pi\)
\(992\) 4.13157 0.131177
\(993\) 10.0954 0.320366
\(994\) −8.45240 −0.268094
\(995\) 10.4346 0.330798
\(996\) 11.4987 0.364352
\(997\) 2.25804 0.0715127 0.0357564 0.999361i \(-0.488616\pi\)
0.0357564 + 0.999361i \(0.488616\pi\)
\(998\) −10.9689 −0.347216
\(999\) 21.1517 0.669211
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 4730.2.a.bb.1.4 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bb.1.4 11 1.1 even 1 trivial