Properties

Label 4026.2.a.u.1.2
Level 4026
Weight 2
Character 4026.1
Self dual yes
Analytic conductor 32.148
Analytic rank 0
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4026.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.9176805.1
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 1.2
Root \(1.62906\) of \(x^{5} - x^{4} - 12 x^{3} + 7 x^{2} + 30 x - 20\)
Character \(\chi\) \(=\) 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.62906 q^{5} -1.00000 q^{6} -4.09482 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.62906 q^{5} -1.00000 q^{6} -4.09482 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.62906 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.05318 q^{13} +4.09482 q^{14} -1.62906 q^{15} +1.00000 q^{16} -6.07005 q^{17} -1.00000 q^{18} +8.57070 q^{19} -1.62906 q^{20} -4.09482 q^{21} +1.00000 q^{22} -8.01687 q^{23} -1.00000 q^{24} -2.34617 q^{25} -2.05318 q^{26} +1.00000 q^{27} -4.09482 q^{28} +1.71712 q^{29} +1.62906 q^{30} -4.38782 q^{31} -1.00000 q^{32} -1.00000 q^{33} +6.07005 q^{34} +6.67070 q^{35} +1.00000 q^{36} +3.63917 q^{37} -8.57070 q^{38} +2.05318 q^{39} +1.62906 q^{40} +2.67070 q^{41} +4.09482 q^{42} -1.73399 q^{43} -1.00000 q^{44} -1.62906 q^{45} +8.01687 q^{46} +9.02841 q^{47} +1.00000 q^{48} +9.76758 q^{49} +2.34617 q^{50} -6.07005 q^{51} +2.05318 q^{52} -8.44100 q^{53} -1.00000 q^{54} +1.62906 q^{55} +4.09482 q^{56} +8.57070 q^{57} -1.71712 q^{58} +6.78574 q^{59} -1.62906 q^{60} -1.00000 q^{61} +4.38782 q^{62} -4.09482 q^{63} +1.00000 q^{64} -3.34475 q^{65} +1.00000 q^{66} -8.71870 q^{67} -6.07005 q^{68} -8.01687 q^{69} -6.67070 q^{70} -4.87030 q^{71} -1.00000 q^{72} -13.8572 q^{73} -3.63917 q^{74} -2.34617 q^{75} +8.57070 q^{76} +4.09482 q^{77} -2.05318 q^{78} +15.9806 q^{79} -1.62906 q^{80} +1.00000 q^{81} -2.67070 q^{82} -14.6824 q^{83} -4.09482 q^{84} +9.88846 q^{85} +1.73399 q^{86} +1.71712 q^{87} +1.00000 q^{88} +11.8389 q^{89} +1.62906 q^{90} -8.40741 q^{91} -8.01687 q^{92} -4.38782 q^{93} -9.02841 q^{94} -13.9622 q^{95} -1.00000 q^{96} +4.94164 q^{97} -9.76758 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} + 5q^{3} + 5q^{4} - q^{5} - 5q^{6} - 3q^{7} - 5q^{8} + 5q^{9} + q^{10} - 5q^{11} + 5q^{12} + 2q^{13} + 3q^{14} - q^{15} + 5q^{16} + 6q^{17} - 5q^{18} + 7q^{19} - q^{20} - 3q^{21} + 5q^{22} - 12q^{23} - 5q^{24} - 2q^{26} + 5q^{27} - 3q^{28} + 4q^{29} + q^{30} - q^{31} - 5q^{32} - 5q^{33} - 6q^{34} + 17q^{35} + 5q^{36} + 3q^{37} - 7q^{38} + 2q^{39} + q^{40} - 3q^{41} + 3q^{42} + 24q^{43} - 5q^{44} - q^{45} + 12q^{46} + 18q^{47} + 5q^{48} + 26q^{49} + 6q^{51} + 2q^{52} - 13q^{53} - 5q^{54} + q^{55} + 3q^{56} + 7q^{57} - 4q^{58} - 16q^{59} - q^{60} - 5q^{61} + q^{62} - 3q^{63} + 5q^{64} + 4q^{65} + 5q^{66} + 18q^{67} + 6q^{68} - 12q^{69} - 17q^{70} - 31q^{71} - 5q^{72} + 8q^{73} - 3q^{74} + 7q^{76} + 3q^{77} - 2q^{78} + 32q^{79} - q^{80} + 5q^{81} + 3q^{82} + 8q^{83} - 3q^{84} + 29q^{85} - 24q^{86} + 4q^{87} + 5q^{88} + q^{89} + q^{90} - 3q^{91} - 12q^{92} - q^{93} - 18q^{94} + 33q^{95} - 5q^{96} - 4q^{97} - 26q^{98} - 5q^{99} + O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −1.62906 −0.728536 −0.364268 0.931294i \(-0.618681\pi\)
−0.364268 + 0.931294i \(0.618681\pi\)
\(6\) −1.00000 −0.408248
\(7\) −4.09482 −1.54770 −0.773849 0.633370i \(-0.781671\pi\)
−0.773849 + 0.633370i \(0.781671\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.62906 0.515153
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) 2.05318 0.569450 0.284725 0.958609i \(-0.408098\pi\)
0.284725 + 0.958609i \(0.408098\pi\)
\(14\) 4.09482 1.09439
\(15\) −1.62906 −0.420621
\(16\) 1.00000 0.250000
\(17\) −6.07005 −1.47220 −0.736102 0.676870i \(-0.763336\pi\)
−0.736102 + 0.676870i \(0.763336\pi\)
\(18\) −1.00000 −0.235702
\(19\) 8.57070 1.96625 0.983127 0.182926i \(-0.0585568\pi\)
0.983127 + 0.182926i \(0.0585568\pi\)
\(20\) −1.62906 −0.364268
\(21\) −4.09482 −0.893564
\(22\) 1.00000 0.213201
\(23\) −8.01687 −1.67163 −0.835817 0.549008i \(-0.815006\pi\)
−0.835817 + 0.549008i \(0.815006\pi\)
\(24\) −1.00000 −0.204124
\(25\) −2.34617 −0.469235
\(26\) −2.05318 −0.402662
\(27\) 1.00000 0.192450
\(28\) −4.09482 −0.773849
\(29\) 1.71712 0.318861 0.159430 0.987209i \(-0.449034\pi\)
0.159430 + 0.987209i \(0.449034\pi\)
\(30\) 1.62906 0.297424
\(31\) −4.38782 −0.788075 −0.394038 0.919094i \(-0.628922\pi\)
−0.394038 + 0.919094i \(0.628922\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) 6.07005 1.04101
\(35\) 6.67070 1.12755
\(36\) 1.00000 0.166667
\(37\) 3.63917 0.598275 0.299138 0.954210i \(-0.403301\pi\)
0.299138 + 0.954210i \(0.403301\pi\)
\(38\) −8.57070 −1.39035
\(39\) 2.05318 0.328772
\(40\) 1.62906 0.257577
\(41\) 2.67070 0.417093 0.208547 0.978012i \(-0.433127\pi\)
0.208547 + 0.978012i \(0.433127\pi\)
\(42\) 4.09482 0.631845
\(43\) −1.73399 −0.264431 −0.132216 0.991221i \(-0.542209\pi\)
−0.132216 + 0.991221i \(0.542209\pi\)
\(44\) −1.00000 −0.150756
\(45\) −1.62906 −0.242845
\(46\) 8.01687 1.18202
\(47\) 9.02841 1.31693 0.658465 0.752612i \(-0.271206\pi\)
0.658465 + 0.752612i \(0.271206\pi\)
\(48\) 1.00000 0.144338
\(49\) 9.76758 1.39537
\(50\) 2.34617 0.331799
\(51\) −6.07005 −0.849978
\(52\) 2.05318 0.284725
\(53\) −8.44100 −1.15946 −0.579730 0.814809i \(-0.696842\pi\)
−0.579730 + 0.814809i \(0.696842\pi\)
\(54\) −1.00000 −0.136083
\(55\) 1.62906 0.219662
\(56\) 4.09482 0.547194
\(57\) 8.57070 1.13522
\(58\) −1.71712 −0.225468
\(59\) 6.78574 0.883429 0.441714 0.897156i \(-0.354370\pi\)
0.441714 + 0.897156i \(0.354370\pi\)
\(60\) −1.62906 −0.210310
\(61\) −1.00000 −0.128037
\(62\) 4.38782 0.557253
\(63\) −4.09482 −0.515899
\(64\) 1.00000 0.125000
\(65\) −3.34475 −0.414865
\(66\) 1.00000 0.123091
\(67\) −8.71870 −1.06516 −0.532580 0.846380i \(-0.678777\pi\)
−0.532580 + 0.846380i \(0.678777\pi\)
\(68\) −6.07005 −0.736102
\(69\) −8.01687 −0.965118
\(70\) −6.67070 −0.797301
\(71\) −4.87030 −0.577998 −0.288999 0.957329i \(-0.593322\pi\)
−0.288999 + 0.957329i \(0.593322\pi\)
\(72\) −1.00000 −0.117851
\(73\) −13.8572 −1.62187 −0.810933 0.585139i \(-0.801040\pi\)
−0.810933 + 0.585139i \(0.801040\pi\)
\(74\) −3.63917 −0.423045
\(75\) −2.34617 −0.270913
\(76\) 8.57070 0.983127
\(77\) 4.09482 0.466648
\(78\) −2.05318 −0.232477
\(79\) 15.9806 1.79795 0.898977 0.437996i \(-0.144311\pi\)
0.898977 + 0.437996i \(0.144311\pi\)
\(80\) −1.62906 −0.182134
\(81\) 1.00000 0.111111
\(82\) −2.67070 −0.294929
\(83\) −14.6824 −1.61160 −0.805801 0.592186i \(-0.798265\pi\)
−0.805801 + 0.592186i \(0.798265\pi\)
\(84\) −4.09482 −0.446782
\(85\) 9.88846 1.07255
\(86\) 1.73399 0.186981
\(87\) 1.71712 0.184094
\(88\) 1.00000 0.106600
\(89\) 11.8389 1.25492 0.627462 0.778647i \(-0.284094\pi\)
0.627462 + 0.778647i \(0.284094\pi\)
\(90\) 1.62906 0.171718
\(91\) −8.40741 −0.881336
\(92\) −8.01687 −0.835817
\(93\) −4.38782 −0.454995
\(94\) −9.02841 −0.931209
\(95\) −13.9622 −1.43249
\(96\) −1.00000 −0.102062
\(97\) 4.94164 0.501748 0.250874 0.968020i \(-0.419282\pi\)
0.250874 + 0.968020i \(0.419282\pi\)
\(98\) −9.76758 −0.986674
\(99\) −1.00000 −0.100504
\(100\) −2.34617 −0.234617
\(101\) 8.66695 0.862394 0.431197 0.902258i \(-0.358091\pi\)
0.431197 + 0.902258i \(0.358091\pi\)
\(102\) 6.07005 0.601025
\(103\) 2.92477 0.288186 0.144093 0.989564i \(-0.453974\pi\)
0.144093 + 0.989564i \(0.453974\pi\)
\(104\) −2.05318 −0.201331
\(105\) 6.67070 0.650994
\(106\) 8.44100 0.819862
\(107\) 11.9162 1.15199 0.575993 0.817454i \(-0.304615\pi\)
0.575993 + 0.817454i \(0.304615\pi\)
\(108\) 1.00000 0.0962250
\(109\) 15.1581 1.45188 0.725942 0.687756i \(-0.241404\pi\)
0.725942 + 0.687756i \(0.241404\pi\)
\(110\) −1.62906 −0.155324
\(111\) 3.63917 0.345414
\(112\) −4.09482 −0.386924
\(113\) 15.9090 1.49659 0.748295 0.663366i \(-0.230873\pi\)
0.748295 + 0.663366i \(0.230873\pi\)
\(114\) −8.57070 −0.802720
\(115\) 13.0599 1.21785
\(116\) 1.71712 0.159430
\(117\) 2.05318 0.189817
\(118\) −6.78574 −0.624678
\(119\) 24.8558 2.27853
\(120\) 1.62906 0.148712
\(121\) 1.00000 0.0909091
\(122\) 1.00000 0.0905357
\(123\) 2.67070 0.240809
\(124\) −4.38782 −0.394038
\(125\) 11.9673 1.07039
\(126\) 4.09482 0.364796
\(127\) 12.6938 1.12639 0.563195 0.826324i \(-0.309572\pi\)
0.563195 + 0.826324i \(0.309572\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.73399 −0.152669
\(130\) 3.34475 0.293354
\(131\) −10.9774 −0.959104 −0.479552 0.877514i \(-0.659201\pi\)
−0.479552 + 0.877514i \(0.659201\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −35.0955 −3.04317
\(134\) 8.71870 0.753181
\(135\) −1.62906 −0.140207
\(136\) 6.07005 0.520503
\(137\) −2.77547 −0.237125 −0.118562 0.992947i \(-0.537829\pi\)
−0.118562 + 0.992947i \(0.537829\pi\)
\(138\) 8.01687 0.682442
\(139\) 17.0533 1.44645 0.723223 0.690615i \(-0.242660\pi\)
0.723223 + 0.690615i \(0.242660\pi\)
\(140\) 6.67070 0.563777
\(141\) 9.02841 0.760329
\(142\) 4.87030 0.408706
\(143\) −2.05318 −0.171696
\(144\) 1.00000 0.0833333
\(145\) −2.79728 −0.232302
\(146\) 13.8572 1.14683
\(147\) 9.76758 0.805616
\(148\) 3.63917 0.299138
\(149\) −0.367193 −0.0300816 −0.0150408 0.999887i \(-0.504788\pi\)
−0.0150408 + 0.999887i \(0.504788\pi\)
\(150\) 2.34617 0.191564
\(151\) −2.81051 −0.228716 −0.114358 0.993440i \(-0.536481\pi\)
−0.114358 + 0.993440i \(0.536481\pi\)
\(152\) −8.57070 −0.695176
\(153\) −6.07005 −0.490735
\(154\) −4.09482 −0.329970
\(155\) 7.14800 0.574141
\(156\) 2.05318 0.164386
\(157\) −2.35423 −0.187888 −0.0939440 0.995577i \(-0.529947\pi\)
−0.0939440 + 0.995577i \(0.529947\pi\)
\(158\) −15.9806 −1.27135
\(159\) −8.44100 −0.669415
\(160\) 1.62906 0.128788
\(161\) 32.8277 2.58718
\(162\) −1.00000 −0.0785674
\(163\) 23.6811 1.85485 0.927424 0.374013i \(-0.122018\pi\)
0.927424 + 0.374013i \(0.122018\pi\)
\(164\) 2.67070 0.208547
\(165\) 1.62906 0.126822
\(166\) 14.6824 1.13958
\(167\) 1.19754 0.0926686 0.0463343 0.998926i \(-0.485246\pi\)
0.0463343 + 0.998926i \(0.485246\pi\)
\(168\) 4.09482 0.315922
\(169\) −8.78445 −0.675727
\(170\) −9.88846 −0.758410
\(171\) 8.57070 0.655418
\(172\) −1.73399 −0.132216
\(173\) 3.99416 0.303670 0.151835 0.988406i \(-0.451482\pi\)
0.151835 + 0.988406i \(0.451482\pi\)
\(174\) −1.71712 −0.130174
\(175\) 9.60717 0.726234
\(176\) −1.00000 −0.0753778
\(177\) 6.78574 0.510048
\(178\) −11.8389 −0.887365
\(179\) −10.2150 −0.763508 −0.381754 0.924264i \(-0.624680\pi\)
−0.381754 + 0.924264i \(0.624680\pi\)
\(180\) −1.62906 −0.121423
\(181\) −9.65733 −0.717824 −0.358912 0.933371i \(-0.616852\pi\)
−0.358912 + 0.933371i \(0.616852\pi\)
\(182\) 8.40741 0.623199
\(183\) −1.00000 −0.0739221
\(184\) 8.01687 0.591012
\(185\) −5.92841 −0.435865
\(186\) 4.38782 0.321730
\(187\) 6.07005 0.443886
\(188\) 9.02841 0.658465
\(189\) −4.09482 −0.297855
\(190\) 13.9622 1.01292
\(191\) −17.8595 −1.29227 −0.646136 0.763222i \(-0.723616\pi\)
−0.646136 + 0.763222i \(0.723616\pi\)
\(192\) 1.00000 0.0721688
\(193\) 16.6298 1.19704 0.598521 0.801107i \(-0.295755\pi\)
0.598521 + 0.801107i \(0.295755\pi\)
\(194\) −4.94164 −0.354789
\(195\) −3.34475 −0.239522
\(196\) 9.76758 0.697684
\(197\) −6.83671 −0.487095 −0.243548 0.969889i \(-0.578311\pi\)
−0.243548 + 0.969889i \(0.578311\pi\)
\(198\) 1.00000 0.0710669
\(199\) 16.8268 1.19282 0.596409 0.802681i \(-0.296594\pi\)
0.596409 + 0.802681i \(0.296594\pi\)
\(200\) 2.34617 0.165900
\(201\) −8.71870 −0.614970
\(202\) −8.66695 −0.609804
\(203\) −7.03129 −0.493500
\(204\) −6.07005 −0.424989
\(205\) −4.35072 −0.303868
\(206\) −2.92477 −0.203778
\(207\) −8.01687 −0.557211
\(208\) 2.05318 0.142362
\(209\) −8.57070 −0.592848
\(210\) −6.67070 −0.460322
\(211\) 23.2247 1.59885 0.799427 0.600764i \(-0.205137\pi\)
0.799427 + 0.600764i \(0.205137\pi\)
\(212\) −8.44100 −0.579730
\(213\) −4.87030 −0.333707
\(214\) −11.9162 −0.814578
\(215\) 2.82477 0.192648
\(216\) −1.00000 −0.0680414
\(217\) 17.9673 1.21970
\(218\) −15.1581 −1.02664
\(219\) −13.8572 −0.936384
\(220\) 1.62906 0.109831
\(221\) −12.4629 −0.838346
\(222\) −3.63917 −0.244245
\(223\) 11.6012 0.776871 0.388436 0.921476i \(-0.373016\pi\)
0.388436 + 0.921476i \(0.373016\pi\)
\(224\) 4.09482 0.273597
\(225\) −2.34617 −0.156412
\(226\) −15.9090 −1.05825
\(227\) 21.9215 1.45498 0.727492 0.686116i \(-0.240686\pi\)
0.727492 + 0.686116i \(0.240686\pi\)
\(228\) 8.57070 0.567608
\(229\) −15.0052 −0.991573 −0.495787 0.868444i \(-0.665120\pi\)
−0.495787 + 0.868444i \(0.665120\pi\)
\(230\) −13.0599 −0.861147
\(231\) 4.09482 0.269420
\(232\) −1.71712 −0.112734
\(233\) 16.4547 1.07799 0.538993 0.842310i \(-0.318805\pi\)
0.538993 + 0.842310i \(0.318805\pi\)
\(234\) −2.05318 −0.134221
\(235\) −14.7078 −0.959431
\(236\) 6.78574 0.441714
\(237\) 15.9806 1.03805
\(238\) −24.8558 −1.61116
\(239\) 28.5650 1.84772 0.923859 0.382734i \(-0.125017\pi\)
0.923859 + 0.382734i \(0.125017\pi\)
\(240\) −1.62906 −0.105155
\(241\) 24.8317 1.59955 0.799775 0.600300i \(-0.204952\pi\)
0.799775 + 0.600300i \(0.204952\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −15.9119 −1.01658
\(246\) −2.67070 −0.170278
\(247\) 17.5972 1.11968
\(248\) 4.38782 0.278627
\(249\) −14.6824 −0.930459
\(250\) −11.9673 −0.756881
\(251\) −10.4083 −0.656968 −0.328484 0.944510i \(-0.606538\pi\)
−0.328484 + 0.944510i \(0.606538\pi\)
\(252\) −4.09482 −0.257950
\(253\) 8.01687 0.504017
\(254\) −12.6938 −0.796478
\(255\) 9.88846 0.619240
\(256\) 1.00000 0.0625000
\(257\) −18.3426 −1.14418 −0.572089 0.820191i \(-0.693867\pi\)
−0.572089 + 0.820191i \(0.693867\pi\)
\(258\) 1.73399 0.107954
\(259\) −14.9017 −0.925949
\(260\) −3.34475 −0.207432
\(261\) 1.71712 0.106287
\(262\) 10.9774 0.678189
\(263\) −9.55996 −0.589492 −0.294746 0.955576i \(-0.595235\pi\)
−0.294746 + 0.955576i \(0.595235\pi\)
\(264\) 1.00000 0.0615457
\(265\) 13.7509 0.844709
\(266\) 35.0955 2.15184
\(267\) 11.8389 0.724530
\(268\) −8.71870 −0.532580
\(269\) −5.13997 −0.313390 −0.156695 0.987647i \(-0.550084\pi\)
−0.156695 + 0.987647i \(0.550084\pi\)
\(270\) 1.62906 0.0991412
\(271\) −11.4849 −0.697655 −0.348828 0.937187i \(-0.613420\pi\)
−0.348828 + 0.937187i \(0.613420\pi\)
\(272\) −6.07005 −0.368051
\(273\) −8.40741 −0.508840
\(274\) 2.77547 0.167672
\(275\) 2.34617 0.141480
\(276\) −8.01687 −0.482559
\(277\) −22.0520 −1.32498 −0.662490 0.749071i \(-0.730500\pi\)
−0.662490 + 0.749071i \(0.730500\pi\)
\(278\) −17.0533 −1.02279
\(279\) −4.38782 −0.262692
\(280\) −6.67070 −0.398651
\(281\) 10.0948 0.602207 0.301103 0.953592i \(-0.402645\pi\)
0.301103 + 0.953592i \(0.402645\pi\)
\(282\) −9.02841 −0.537634
\(283\) 17.7154 1.05307 0.526534 0.850154i \(-0.323491\pi\)
0.526534 + 0.850154i \(0.323491\pi\)
\(284\) −4.87030 −0.288999
\(285\) −13.9622 −0.827047
\(286\) 2.05318 0.121407
\(287\) −10.9360 −0.645534
\(288\) −1.00000 −0.0589256
\(289\) 19.8456 1.16739
\(290\) 2.79728 0.164262
\(291\) 4.94164 0.289684
\(292\) −13.8572 −0.810933
\(293\) −23.9789 −1.40086 −0.700430 0.713721i \(-0.747009\pi\)
−0.700430 + 0.713721i \(0.747009\pi\)
\(294\) −9.76758 −0.569657
\(295\) −11.0544 −0.643610
\(296\) −3.63917 −0.211522
\(297\) −1.00000 −0.0580259
\(298\) 0.367193 0.0212709
\(299\) −16.4601 −0.951911
\(300\) −2.34617 −0.135456
\(301\) 7.10038 0.409259
\(302\) 2.81051 0.161727
\(303\) 8.66695 0.497903
\(304\) 8.57070 0.491563
\(305\) 1.62906 0.0932795
\(306\) 6.07005 0.347002
\(307\) −2.95252 −0.168509 −0.0842545 0.996444i \(-0.526851\pi\)
−0.0842545 + 0.996444i \(0.526851\pi\)
\(308\) 4.09482 0.233324
\(309\) 2.92477 0.166384
\(310\) −7.14800 −0.405979
\(311\) −18.0561 −1.02387 −0.511933 0.859026i \(-0.671070\pi\)
−0.511933 + 0.859026i \(0.671070\pi\)
\(312\) −2.05318 −0.116238
\(313\) 29.2592 1.65383 0.826914 0.562329i \(-0.190094\pi\)
0.826914 + 0.562329i \(0.190094\pi\)
\(314\) 2.35423 0.132857
\(315\) 6.67070 0.375851
\(316\) 15.9806 0.898977
\(317\) −17.1452 −0.962968 −0.481484 0.876455i \(-0.659902\pi\)
−0.481484 + 0.876455i \(0.659902\pi\)
\(318\) 8.44100 0.473348
\(319\) −1.71712 −0.0961401
\(320\) −1.62906 −0.0910670
\(321\) 11.9162 0.665100
\(322\) −32.8277 −1.82942
\(323\) −52.0246 −2.89473
\(324\) 1.00000 0.0555556
\(325\) −4.81712 −0.267206
\(326\) −23.6811 −1.31158
\(327\) 15.1581 0.838246
\(328\) −2.67070 −0.147465
\(329\) −36.9697 −2.03821
\(330\) −1.62906 −0.0896766
\(331\) 8.59927 0.472659 0.236329 0.971673i \(-0.424056\pi\)
0.236329 + 0.971673i \(0.424056\pi\)
\(332\) −14.6824 −0.805801
\(333\) 3.63917 0.199425
\(334\) −1.19754 −0.0655266
\(335\) 14.2033 0.776007
\(336\) −4.09482 −0.223391
\(337\) 6.29714 0.343027 0.171514 0.985182i \(-0.445134\pi\)
0.171514 + 0.985182i \(0.445134\pi\)
\(338\) 8.78445 0.477811
\(339\) 15.9090 0.864057
\(340\) 9.88846 0.536277
\(341\) 4.38782 0.237614
\(342\) −8.57070 −0.463450
\(343\) −11.3327 −0.611911
\(344\) 1.73399 0.0934905
\(345\) 13.0599 0.703124
\(346\) −3.99416 −0.214727
\(347\) 22.5634 1.21127 0.605634 0.795743i \(-0.292919\pi\)
0.605634 + 0.795743i \(0.292919\pi\)
\(348\) 1.71712 0.0920471
\(349\) −34.5368 −1.84871 −0.924355 0.381533i \(-0.875396\pi\)
−0.924355 + 0.381533i \(0.875396\pi\)
\(350\) −9.60717 −0.513525
\(351\) 2.05318 0.109591
\(352\) 1.00000 0.0533002
\(353\) −7.43073 −0.395498 −0.197749 0.980253i \(-0.563363\pi\)
−0.197749 + 0.980253i \(0.563363\pi\)
\(354\) −6.78574 −0.360658
\(355\) 7.93399 0.421093
\(356\) 11.8389 0.627462
\(357\) 24.8558 1.31551
\(358\) 10.2150 0.539882
\(359\) 20.8794 1.10197 0.550987 0.834514i \(-0.314251\pi\)
0.550987 + 0.834514i \(0.314251\pi\)
\(360\) 1.62906 0.0858588
\(361\) 54.4569 2.86615
\(362\) 9.65733 0.507578
\(363\) 1.00000 0.0524864
\(364\) −8.40741 −0.440668
\(365\) 22.5742 1.18159
\(366\) 1.00000 0.0522708
\(367\) −29.7949 −1.55528 −0.777639 0.628711i \(-0.783583\pi\)
−0.777639 + 0.628711i \(0.783583\pi\)
\(368\) −8.01687 −0.417908
\(369\) 2.67070 0.139031
\(370\) 5.92841 0.308203
\(371\) 34.5644 1.79449
\(372\) −4.38782 −0.227498
\(373\) 33.9622 1.75849 0.879247 0.476366i \(-0.158046\pi\)
0.879247 + 0.476366i \(0.158046\pi\)
\(374\) −6.07005 −0.313875
\(375\) 11.9673 0.617991
\(376\) −9.02841 −0.465605
\(377\) 3.52555 0.181575
\(378\) 4.09482 0.210615
\(379\) 20.1239 1.03370 0.516848 0.856077i \(-0.327105\pi\)
0.516848 + 0.856077i \(0.327105\pi\)
\(380\) −13.9622 −0.716244
\(381\) 12.6938 0.650322
\(382\) 17.8595 0.913774
\(383\) −19.6855 −1.00588 −0.502942 0.864320i \(-0.667749\pi\)
−0.502942 + 0.864320i \(0.667749\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −6.67070 −0.339970
\(386\) −16.6298 −0.846437
\(387\) −1.73399 −0.0881437
\(388\) 4.94164 0.250874
\(389\) −11.7682 −0.596674 −0.298337 0.954461i \(-0.596432\pi\)
−0.298337 + 0.954461i \(0.596432\pi\)
\(390\) 3.34475 0.169368
\(391\) 48.6629 2.46099
\(392\) −9.76758 −0.493337
\(393\) −10.9774 −0.553739
\(394\) 6.83671 0.344428
\(395\) −26.0333 −1.30988
\(396\) −1.00000 −0.0502519
\(397\) −22.3152 −1.11997 −0.559984 0.828503i \(-0.689193\pi\)
−0.559984 + 0.828503i \(0.689193\pi\)
\(398\) −16.8268 −0.843449
\(399\) −35.0955 −1.75697
\(400\) −2.34617 −0.117309
\(401\) 7.01767 0.350446 0.175223 0.984529i \(-0.443935\pi\)
0.175223 + 0.984529i \(0.443935\pi\)
\(402\) 8.71870 0.434849
\(403\) −9.00898 −0.448769
\(404\) 8.66695 0.431197
\(405\) −1.62906 −0.0809485
\(406\) 7.03129 0.348957
\(407\) −3.63917 −0.180387
\(408\) 6.07005 0.300512
\(409\) −5.33129 −0.263615 −0.131808 0.991275i \(-0.542078\pi\)
−0.131808 + 0.991275i \(0.542078\pi\)
\(410\) 4.35072 0.214867
\(411\) −2.77547 −0.136904
\(412\) 2.92477 0.144093
\(413\) −27.7864 −1.36728
\(414\) 8.01687 0.394008
\(415\) 23.9185 1.17411
\(416\) −2.05318 −0.100665
\(417\) 17.0533 0.835106
\(418\) 8.57070 0.419207
\(419\) −10.8315 −0.529155 −0.264577 0.964364i \(-0.585232\pi\)
−0.264577 + 0.964364i \(0.585232\pi\)
\(420\) 6.67070 0.325497
\(421\) −30.1117 −1.46756 −0.733778 0.679389i \(-0.762245\pi\)
−0.733778 + 0.679389i \(0.762245\pi\)
\(422\) −23.2247 −1.13056
\(423\) 9.02841 0.438976
\(424\) 8.44100 0.409931
\(425\) 14.2414 0.690809
\(426\) 4.87030 0.235967
\(427\) 4.09482 0.198162
\(428\) 11.9162 0.575993
\(429\) −2.05318 −0.0991285
\(430\) −2.82477 −0.136222
\(431\) −12.9374 −0.623172 −0.311586 0.950218i \(-0.600860\pi\)
−0.311586 + 0.950218i \(0.600860\pi\)
\(432\) 1.00000 0.0481125
\(433\) 25.0904 1.20577 0.602885 0.797828i \(-0.294018\pi\)
0.602885 + 0.797828i \(0.294018\pi\)
\(434\) −17.9673 −0.862460
\(435\) −2.79728 −0.134119
\(436\) 15.1581 0.725942
\(437\) −68.7102 −3.28686
\(438\) 13.8572 0.662124
\(439\) −9.17005 −0.437663 −0.218831 0.975763i \(-0.570224\pi\)
−0.218831 + 0.975763i \(0.570224\pi\)
\(440\) −1.62906 −0.0776622
\(441\) 9.76758 0.465123
\(442\) 12.4629 0.592800
\(443\) −32.2319 −1.53138 −0.765692 0.643207i \(-0.777603\pi\)
−0.765692 + 0.643207i \(0.777603\pi\)
\(444\) 3.63917 0.172707
\(445\) −19.2863 −0.914257
\(446\) −11.6012 −0.549331
\(447\) −0.367193 −0.0173676
\(448\) −4.09482 −0.193462
\(449\) −1.29157 −0.0609528 −0.0304764 0.999535i \(-0.509702\pi\)
−0.0304764 + 0.999535i \(0.509702\pi\)
\(450\) 2.34617 0.110600
\(451\) −2.67070 −0.125758
\(452\) 15.9090 0.748295
\(453\) −2.81051 −0.132049
\(454\) −21.9215 −1.02883
\(455\) 13.6961 0.642085
\(456\) −8.57070 −0.401360
\(457\) −21.1257 −0.988219 −0.494110 0.869400i \(-0.664506\pi\)
−0.494110 + 0.869400i \(0.664506\pi\)
\(458\) 15.0052 0.701148
\(459\) −6.07005 −0.283326
\(460\) 13.0599 0.608923
\(461\) 6.07148 0.282777 0.141389 0.989954i \(-0.454843\pi\)
0.141389 + 0.989954i \(0.454843\pi\)
\(462\) −4.09482 −0.190508
\(463\) −8.79221 −0.408609 −0.204304 0.978907i \(-0.565493\pi\)
−0.204304 + 0.978907i \(0.565493\pi\)
\(464\) 1.71712 0.0797151
\(465\) 7.14800 0.331481
\(466\) −16.4547 −0.762251
\(467\) 41.2298 1.90789 0.953943 0.299989i \(-0.0969829\pi\)
0.953943 + 0.299989i \(0.0969829\pi\)
\(468\) 2.05318 0.0949083
\(469\) 35.7015 1.64854
\(470\) 14.7078 0.678420
\(471\) −2.35423 −0.108477
\(472\) −6.78574 −0.312339
\(473\) 1.73399 0.0797290
\(474\) −15.9806 −0.734012
\(475\) −20.1084 −0.922634
\(476\) 24.8558 1.13926
\(477\) −8.44100 −0.386487
\(478\) −28.5650 −1.30653
\(479\) 18.4907 0.844860 0.422430 0.906396i \(-0.361177\pi\)
0.422430 + 0.906396i \(0.361177\pi\)
\(480\) 1.62906 0.0743559
\(481\) 7.47187 0.340688
\(482\) −24.8317 −1.13105
\(483\) 32.8277 1.49371
\(484\) 1.00000 0.0454545
\(485\) −8.05022 −0.365542
\(486\) −1.00000 −0.0453609
\(487\) −10.4782 −0.474814 −0.237407 0.971410i \(-0.576297\pi\)
−0.237407 + 0.971410i \(0.576297\pi\)
\(488\) 1.00000 0.0452679
\(489\) 23.6811 1.07090
\(490\) 15.9119 0.718828
\(491\) 41.7373 1.88358 0.941789 0.336205i \(-0.109144\pi\)
0.941789 + 0.336205i \(0.109144\pi\)
\(492\) 2.67070 0.120404
\(493\) −10.4230 −0.469428
\(494\) −17.5972 −0.791735
\(495\) 1.62906 0.0732207
\(496\) −4.38782 −0.197019
\(497\) 19.9430 0.894566
\(498\) 14.6824 0.657934
\(499\) 17.5898 0.787427 0.393714 0.919233i \(-0.371190\pi\)
0.393714 + 0.919233i \(0.371190\pi\)
\(500\) 11.9673 0.535195
\(501\) 1.19754 0.0535022
\(502\) 10.4083 0.464547
\(503\) 16.0760 0.716794 0.358397 0.933569i \(-0.383323\pi\)
0.358397 + 0.933569i \(0.383323\pi\)
\(504\) 4.09482 0.182398
\(505\) −14.1190 −0.628285
\(506\) −8.01687 −0.356394
\(507\) −8.78445 −0.390131
\(508\) 12.6938 0.563195
\(509\) −30.2149 −1.33925 −0.669627 0.742698i \(-0.733546\pi\)
−0.669627 + 0.742698i \(0.733546\pi\)
\(510\) −9.88846 −0.437869
\(511\) 56.7429 2.51016
\(512\) −1.00000 −0.0441942
\(513\) 8.57070 0.378406
\(514\) 18.3426 0.809057
\(515\) −4.76462 −0.209954
\(516\) −1.73399 −0.0763347
\(517\) −9.02841 −0.397069
\(518\) 14.9017 0.654745
\(519\) 3.99416 0.175324
\(520\) 3.34475 0.146677
\(521\) 39.7338 1.74077 0.870385 0.492372i \(-0.163870\pi\)
0.870385 + 0.492372i \(0.163870\pi\)
\(522\) −1.71712 −0.0751562
\(523\) 3.06186 0.133886 0.0669430 0.997757i \(-0.478675\pi\)
0.0669430 + 0.997757i \(0.478675\pi\)
\(524\) −10.9774 −0.479552
\(525\) 9.60717 0.419291
\(526\) 9.55996 0.416834
\(527\) 26.6343 1.16021
\(528\) −1.00000 −0.0435194
\(529\) 41.2703 1.79436
\(530\) −13.7509 −0.597299
\(531\) 6.78574 0.294476
\(532\) −35.0955 −1.52158
\(533\) 5.48343 0.237514
\(534\) −11.8389 −0.512320
\(535\) −19.4122 −0.839264
\(536\) 8.71870 0.376591
\(537\) −10.2150 −0.440812
\(538\) 5.13997 0.221600
\(539\) −9.76758 −0.420719
\(540\) −1.62906 −0.0701034
\(541\) −26.9818 −1.16004 −0.580018 0.814604i \(-0.696955\pi\)
−0.580018 + 0.814604i \(0.696955\pi\)
\(542\) 11.4849 0.493317
\(543\) −9.65733 −0.414436
\(544\) 6.07005 0.260251
\(545\) −24.6934 −1.05775
\(546\) 8.40741 0.359804
\(547\) 14.6014 0.624312 0.312156 0.950031i \(-0.398949\pi\)
0.312156 + 0.950031i \(0.398949\pi\)
\(548\) −2.77547 −0.118562
\(549\) −1.00000 −0.0426790
\(550\) −2.34617 −0.100041
\(551\) 14.7169 0.626961
\(552\) 8.01687 0.341221
\(553\) −65.4376 −2.78269
\(554\) 22.0520 0.936902
\(555\) −5.92841 −0.251647
\(556\) 17.0533 0.723223
\(557\) 25.3341 1.07344 0.536721 0.843760i \(-0.319663\pi\)
0.536721 + 0.843760i \(0.319663\pi\)
\(558\) 4.38782 0.185751
\(559\) −3.56019 −0.150580
\(560\) 6.67070 0.281889
\(561\) 6.07005 0.256278
\(562\) −10.0948 −0.425824
\(563\) −1.15888 −0.0488408 −0.0244204 0.999702i \(-0.507774\pi\)
−0.0244204 + 0.999702i \(0.507774\pi\)
\(564\) 9.02841 0.380165
\(565\) −25.9166 −1.09032
\(566\) −17.7154 −0.744632
\(567\) −4.09482 −0.171966
\(568\) 4.87030 0.204353
\(569\) 4.79768 0.201129 0.100565 0.994931i \(-0.467935\pi\)
0.100565 + 0.994931i \(0.467935\pi\)
\(570\) 13.9622 0.584810
\(571\) −17.3259 −0.725065 −0.362533 0.931971i \(-0.618088\pi\)
−0.362533 + 0.931971i \(0.618088\pi\)
\(572\) −2.05318 −0.0858478
\(573\) −17.8595 −0.746093
\(574\) 10.9360 0.456462
\(575\) 18.8090 0.784389
\(576\) 1.00000 0.0416667
\(577\) −14.0342 −0.584253 −0.292127 0.956380i \(-0.594363\pi\)
−0.292127 + 0.956380i \(0.594363\pi\)
\(578\) −19.8456 −0.825466
\(579\) 16.6298 0.691113
\(580\) −2.79728 −0.116151
\(581\) 60.1218 2.49427
\(582\) −4.94164 −0.204838
\(583\) 8.44100 0.349590
\(584\) 13.8572 0.573416
\(585\) −3.34475 −0.138288
\(586\) 23.9789 0.990558
\(587\) −13.5554 −0.559490 −0.279745 0.960074i \(-0.590250\pi\)
−0.279745 + 0.960074i \(0.590250\pi\)
\(588\) 9.76758 0.402808
\(589\) −37.6067 −1.54956
\(590\) 11.0544 0.455101
\(591\) −6.83671 −0.281225
\(592\) 3.63917 0.149569
\(593\) 42.8640 1.76022 0.880108 0.474774i \(-0.157470\pi\)
0.880108 + 0.474774i \(0.157470\pi\)
\(594\) 1.00000 0.0410305
\(595\) −40.4915 −1.65999
\(596\) −0.367193 −0.0150408
\(597\) 16.8268 0.688673
\(598\) 16.4601 0.673103
\(599\) −31.2808 −1.27810 −0.639050 0.769165i \(-0.720672\pi\)
−0.639050 + 0.769165i \(0.720672\pi\)
\(600\) 2.34617 0.0957821
\(601\) −34.6508 −1.41344 −0.706718 0.707496i \(-0.749825\pi\)
−0.706718 + 0.707496i \(0.749825\pi\)
\(602\) −7.10038 −0.289390
\(603\) −8.71870 −0.355053
\(604\) −2.81051 −0.114358
\(605\) −1.62906 −0.0662306
\(606\) −8.66695 −0.352071
\(607\) 43.1308 1.75062 0.875312 0.483558i \(-0.160656\pi\)
0.875312 + 0.483558i \(0.160656\pi\)
\(608\) −8.57070 −0.347588
\(609\) −7.03129 −0.284922
\(610\) −1.62906 −0.0659586
\(611\) 18.5370 0.749925
\(612\) −6.07005 −0.245367
\(613\) 6.58820 0.266095 0.133047 0.991110i \(-0.457524\pi\)
0.133047 + 0.991110i \(0.457524\pi\)
\(614\) 2.95252 0.119154
\(615\) −4.35072 −0.175438
\(616\) −4.09482 −0.164985
\(617\) 11.8746 0.478053 0.239027 0.971013i \(-0.423172\pi\)
0.239027 + 0.971013i \(0.423172\pi\)
\(618\) −2.92477 −0.117651
\(619\) −46.6701 −1.87583 −0.937915 0.346864i \(-0.887246\pi\)
−0.937915 + 0.346864i \(0.887246\pi\)
\(620\) 7.14800 0.287071
\(621\) −8.01687 −0.321706
\(622\) 18.0561 0.723982
\(623\) −48.4783 −1.94224
\(624\) 2.05318 0.0821930
\(625\) −7.76460 −0.310584
\(626\) −29.2592 −1.16943
\(627\) −8.57070 −0.342281
\(628\) −2.35423 −0.0939440
\(629\) −22.0899 −0.880784
\(630\) −6.67070 −0.265767
\(631\) 5.51443 0.219526 0.109763 0.993958i \(-0.464991\pi\)
0.109763 + 0.993958i \(0.464991\pi\)
\(632\) −15.9806 −0.635673
\(633\) 23.2247 0.923098
\(634\) 17.1452 0.680921
\(635\) −20.6789 −0.820616
\(636\) −8.44100 −0.334707
\(637\) 20.0546 0.794592
\(638\) 1.71712 0.0679813
\(639\) −4.87030 −0.192666
\(640\) 1.62906 0.0643941
\(641\) 6.83870 0.270112 0.135056 0.990838i \(-0.456879\pi\)
0.135056 + 0.990838i \(0.456879\pi\)
\(642\) −11.9162 −0.470297
\(643\) 40.8072 1.60928 0.804639 0.593764i \(-0.202359\pi\)
0.804639 + 0.593764i \(0.202359\pi\)
\(644\) 32.8277 1.29359
\(645\) 2.82477 0.111225
\(646\) 52.0246 2.04688
\(647\) 23.8536 0.937782 0.468891 0.883256i \(-0.344654\pi\)
0.468891 + 0.883256i \(0.344654\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −6.78574 −0.266364
\(650\) 4.81712 0.188943
\(651\) 17.9673 0.704195
\(652\) 23.6811 0.927424
\(653\) 21.7971 0.852987 0.426494 0.904491i \(-0.359749\pi\)
0.426494 + 0.904491i \(0.359749\pi\)
\(654\) −15.1581 −0.592729
\(655\) 17.8829 0.698742
\(656\) 2.67070 0.104273
\(657\) −13.8572 −0.540622
\(658\) 36.9697 1.44123
\(659\) 11.2826 0.439509 0.219755 0.975555i \(-0.429474\pi\)
0.219755 + 0.975555i \(0.429474\pi\)
\(660\) 1.62906 0.0634110
\(661\) −3.85315 −0.149870 −0.0749352 0.997188i \(-0.523875\pi\)
−0.0749352 + 0.997188i \(0.523875\pi\)
\(662\) −8.59927 −0.334220
\(663\) −12.4629 −0.484019
\(664\) 14.6824 0.569788
\(665\) 57.1726 2.21706
\(666\) −3.63917 −0.141015
\(667\) −13.7659 −0.533018
\(668\) 1.19754 0.0463343
\(669\) 11.6012 0.448527
\(670\) −14.2033 −0.548720
\(671\) 1.00000 0.0386046
\(672\) 4.09482 0.157961
\(673\) −11.9556 −0.460856 −0.230428 0.973089i \(-0.574013\pi\)
−0.230428 + 0.973089i \(0.574013\pi\)
\(674\) −6.29714 −0.242557
\(675\) −2.34617 −0.0903043
\(676\) −8.78445 −0.337864
\(677\) 36.0169 1.38424 0.692121 0.721782i \(-0.256677\pi\)
0.692121 + 0.721782i \(0.256677\pi\)
\(678\) −15.9090 −0.610981
\(679\) −20.2352 −0.776554
\(680\) −9.88846 −0.379205
\(681\) 21.9215 0.840035
\(682\) −4.38782 −0.168018
\(683\) −0.0656507 −0.00251205 −0.00125603 0.999999i \(-0.500400\pi\)
−0.00125603 + 0.999999i \(0.500400\pi\)
\(684\) 8.57070 0.327709
\(685\) 4.52140 0.172754
\(686\) 11.3327 0.432686
\(687\) −15.0052 −0.572485
\(688\) −1.73399 −0.0661078
\(689\) −17.3309 −0.660254
\(690\) −13.0599 −0.497184
\(691\) −11.9959 −0.456346 −0.228173 0.973621i \(-0.573275\pi\)
−0.228173 + 0.973621i \(0.573275\pi\)
\(692\) 3.99416 0.151835
\(693\) 4.09482 0.155549
\(694\) −22.5634 −0.856496
\(695\) −27.7809 −1.05379
\(696\) −1.71712 −0.0650871
\(697\) −16.2113 −0.614047
\(698\) 34.5368 1.30724
\(699\) 16.4547 0.622376
\(700\) 9.60717 0.363117
\(701\) 9.81687 0.370778 0.185389 0.982665i \(-0.440645\pi\)
0.185389 + 0.982665i \(0.440645\pi\)
\(702\) −2.05318 −0.0774923
\(703\) 31.1902 1.17636
\(704\) −1.00000 −0.0376889
\(705\) −14.7078 −0.553928
\(706\) 7.43073 0.279659
\(707\) −35.4896 −1.33472
\(708\) 6.78574 0.255024
\(709\) 23.1199 0.868287 0.434143 0.900844i \(-0.357051\pi\)
0.434143 + 0.900844i \(0.357051\pi\)
\(710\) −7.93399 −0.297757
\(711\) 15.9806 0.599318
\(712\) −11.8389 −0.443682
\(713\) 35.1766 1.31737
\(714\) −24.8558 −0.930205
\(715\) 3.34475 0.125086
\(716\) −10.2150 −0.381754
\(717\) 28.5650 1.06678
\(718\) −20.8794 −0.779214
\(719\) −31.3915 −1.17071 −0.585353 0.810779i \(-0.699044\pi\)
−0.585353 + 0.810779i \(0.699044\pi\)
\(720\) −1.62906 −0.0607114
\(721\) −11.9764 −0.446025
\(722\) −54.4569 −2.02668
\(723\) 24.8317 0.923501
\(724\) −9.65733 −0.358912
\(725\) −4.02865 −0.149620
\(726\) −1.00000 −0.0371135
\(727\) −33.7173 −1.25050 −0.625252 0.780423i \(-0.715004\pi\)
−0.625252 + 0.780423i \(0.715004\pi\)
\(728\) 8.40741 0.311599
\(729\) 1.00000 0.0370370
\(730\) −22.5742 −0.835509
\(731\) 10.5254 0.389297
\(732\) −1.00000 −0.0369611
\(733\) −7.27108 −0.268563 −0.134282 0.990943i \(-0.542873\pi\)
−0.134282 + 0.990943i \(0.542873\pi\)
\(734\) 29.7949 1.09975
\(735\) −15.9119 −0.586921
\(736\) 8.01687 0.295506
\(737\) 8.71870 0.321158
\(738\) −2.67070 −0.0983098
\(739\) −46.7340 −1.71914 −0.859570 0.511018i \(-0.829268\pi\)
−0.859570 + 0.511018i \(0.829268\pi\)
\(740\) −5.92841 −0.217933
\(741\) 17.5972 0.646449
\(742\) −34.5644 −1.26890
\(743\) 12.7681 0.468417 0.234209 0.972186i \(-0.424750\pi\)
0.234209 + 0.972186i \(0.424750\pi\)
\(744\) 4.38782 0.160865
\(745\) 0.598178 0.0219155
\(746\) −33.9622 −1.24344
\(747\) −14.6824 −0.537201
\(748\) 6.07005 0.221943
\(749\) −48.7949 −1.78293
\(750\) −11.9673 −0.436985
\(751\) −24.9789 −0.911492 −0.455746 0.890110i \(-0.650627\pi\)
−0.455746 + 0.890110i \(0.650627\pi\)
\(752\) 9.02841 0.329232
\(753\) −10.4083 −0.379301
\(754\) −3.52555 −0.128393
\(755\) 4.57849 0.166628
\(756\) −4.09482 −0.148927
\(757\) 37.8111 1.37427 0.687133 0.726531i \(-0.258869\pi\)
0.687133 + 0.726531i \(0.258869\pi\)
\(758\) −20.1239 −0.730933
\(759\) 8.01687 0.290994
\(760\) 13.9622 0.506461
\(761\) −44.9661 −1.63002 −0.815009 0.579448i \(-0.803268\pi\)
−0.815009 + 0.579448i \(0.803268\pi\)
\(762\) −12.6938 −0.459847
\(763\) −62.0698 −2.24708
\(764\) −17.8595 −0.646136
\(765\) 9.88846 0.357518
\(766\) 19.6855 0.711267
\(767\) 13.9324 0.503068
\(768\) 1.00000 0.0360844
\(769\) −6.76002 −0.243772 −0.121886 0.992544i \(-0.538894\pi\)
−0.121886 + 0.992544i \(0.538894\pi\)
\(770\) 6.67070 0.240395
\(771\) −18.3426 −0.660592
\(772\) 16.6298 0.598521
\(773\) 24.5654 0.883557 0.441778 0.897124i \(-0.354348\pi\)
0.441778 + 0.897124i \(0.354348\pi\)
\(774\) 1.73399 0.0623270
\(775\) 10.2946 0.369792
\(776\) −4.94164 −0.177395
\(777\) −14.9017 −0.534597
\(778\) 11.7682 0.421912
\(779\) 22.8898 0.820111
\(780\) −3.34475 −0.119761
\(781\) 4.87030 0.174273
\(782\) −48.6629 −1.74018
\(783\) 1.71712 0.0613647
\(784\) 9.76758 0.348842
\(785\) 3.83517 0.136883
\(786\) 10.9774 0.391552
\(787\) −2.60728 −0.0929393 −0.0464697 0.998920i \(-0.514797\pi\)
−0.0464697 + 0.998920i \(0.514797\pi\)
\(788\) −6.83671 −0.243548
\(789\) −9.55996 −0.340344
\(790\) 26.0333 0.926222
\(791\) −65.1445 −2.31627
\(792\) 1.00000 0.0355335
\(793\) −2.05318 −0.0729106
\(794\) 22.3152 0.791937
\(795\) 13.7509 0.487693
\(796\) 16.8268 0.596409
\(797\) −28.3841 −1.00542 −0.502708 0.864457i \(-0.667663\pi\)
−0.502708 + 0.864457i \(0.667663\pi\)
\(798\) 35.0955 1.24237
\(799\) −54.8029 −1.93879
\(800\) 2.34617 0.0829498
\(801\) 11.8389 0.418308
\(802\) −7.01767 −0.247803
\(803\) 13.8572 0.489011
\(804\) −8.71870 −0.307485
\(805\) −53.4782 −1.88486
\(806\) 9.00898 0.317328
\(807\) −5.13997 −0.180936
\(808\) −8.66695 −0.304902
\(809\) 17.8556 0.627768 0.313884 0.949461i \(-0.398370\pi\)
0.313884 + 0.949461i \(0.398370\pi\)
\(810\) 1.62906 0.0572392
\(811\) −9.73867 −0.341971 −0.170985 0.985274i \(-0.554695\pi\)
−0.170985 + 0.985274i \(0.554695\pi\)
\(812\) −7.03129 −0.246750
\(813\) −11.4849 −0.402791
\(814\) 3.63917 0.127553
\(815\) −38.5779 −1.35132
\(816\) −6.07005 −0.212494
\(817\) −14.8615 −0.519939
\(818\) 5.33129 0.186404
\(819\) −8.40741 −0.293779
\(820\) −4.35072 −0.151934
\(821\) −19.1182 −0.667228 −0.333614 0.942710i \(-0.608268\pi\)
−0.333614 + 0.942710i \(0.608268\pi\)
\(822\) 2.77547 0.0968058
\(823\) −7.34033 −0.255868 −0.127934 0.991783i \(-0.540835\pi\)
−0.127934 + 0.991783i \(0.540835\pi\)
\(824\) −2.92477 −0.101889
\(825\) 2.34617 0.0816833
\(826\) 27.7864 0.966813
\(827\) 6.86483 0.238713 0.119357 0.992851i \(-0.461917\pi\)
0.119357 + 0.992851i \(0.461917\pi\)
\(828\) −8.01687 −0.278606
\(829\) 46.2219 1.60535 0.802676 0.596415i \(-0.203409\pi\)
0.802676 + 0.596415i \(0.203409\pi\)
\(830\) −23.9185 −0.830222
\(831\) −22.0520 −0.764977
\(832\) 2.05318 0.0711812
\(833\) −59.2897 −2.05427
\(834\) −17.0533 −0.590509
\(835\) −1.95086 −0.0675125
\(836\) −8.57070 −0.296424
\(837\) −4.38782 −0.151665
\(838\) 10.8315 0.374169
\(839\) 19.6151 0.677189 0.338594 0.940932i \(-0.390049\pi\)
0.338594 + 0.940932i \(0.390049\pi\)
\(840\) −6.67070 −0.230161
\(841\) −26.0515 −0.898328
\(842\) 30.1117 1.03772
\(843\) 10.0948 0.347684
\(844\) 23.2247 0.799427
\(845\) 14.3104 0.492292
\(846\) −9.02841 −0.310403
\(847\) −4.09482 −0.140700
\(848\) −8.44100 −0.289865
\(849\) 17.7154 0.607989
\(850\) −14.2414 −0.488476
\(851\) −29.1747 −1.00010
\(852\) −4.87030 −0.166854
\(853\) −12.0272 −0.411804 −0.205902 0.978573i \(-0.566013\pi\)
−0.205902 + 0.978573i \(0.566013\pi\)
\(854\) −4.09482 −0.140122
\(855\) −13.9622 −0.477496
\(856\) −11.9162 −0.407289
\(857\) −38.8685 −1.32772 −0.663862 0.747855i \(-0.731084\pi\)
−0.663862 + 0.747855i \(0.731084\pi\)
\(858\) 2.05318 0.0700944
\(859\) 29.4503 1.00483 0.502415 0.864627i \(-0.332445\pi\)
0.502415 + 0.864627i \(0.332445\pi\)
\(860\) 2.82477 0.0963238
\(861\) −10.9360 −0.372699
\(862\) 12.9374 0.440649
\(863\) −13.8257 −0.470633 −0.235317 0.971919i \(-0.575613\pi\)
−0.235317 + 0.971919i \(0.575613\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −6.50671 −0.221235
\(866\) −25.0904 −0.852608
\(867\) 19.8456 0.673990
\(868\) 17.9673 0.609851
\(869\) −15.9806 −0.542104
\(870\) 2.79728 0.0948367
\(871\) −17.9011 −0.606555
\(872\) −15.1581 −0.513318
\(873\) 4.94164 0.167249
\(874\) 68.7102 2.32416
\(875\) −49.0041 −1.65664
\(876\) −13.8572 −0.468192
\(877\) −40.5419 −1.36900 −0.684502 0.729011i \(-0.739980\pi\)
−0.684502 + 0.729011i \(0.739980\pi\)
\(878\) 9.17005 0.309474
\(879\) −23.9789 −0.808787
\(880\) 1.62906 0.0549155
\(881\) 43.6711 1.47132 0.735658 0.677353i \(-0.236873\pi\)
0.735658 + 0.677353i \(0.236873\pi\)
\(882\) −9.76758 −0.328891
\(883\) 26.0399 0.876314 0.438157 0.898899i \(-0.355631\pi\)
0.438157 + 0.898899i \(0.355631\pi\)
\(884\) −12.4629 −0.419173
\(885\) −11.0544 −0.371588
\(886\) 32.2319 1.08285
\(887\) −17.2671 −0.579771 −0.289886 0.957061i \(-0.593617\pi\)
−0.289886 + 0.957061i \(0.593617\pi\)
\(888\) −3.63917 −0.122122
\(889\) −51.9788 −1.74331
\(890\) 19.2863 0.646478
\(891\) −1.00000 −0.0335013
\(892\) 11.6012 0.388436
\(893\) 77.3798 2.58942
\(894\) 0.367193 0.0122808
\(895\) 16.6409 0.556244
\(896\) 4.09482 0.136798
\(897\) −16.4601 −0.549586
\(898\) 1.29157 0.0431002
\(899\) −7.53439 −0.251286
\(900\) −2.34617 −0.0782058
\(901\) 51.2373 1.70696
\(902\) 2.67070 0.0889246
\(903\) 7.10038 0.236286
\(904\) −15.9090 −0.529125
\(905\) 15.7323 0.522961
\(906\) 2.81051 0.0933731
\(907\) −5.76021 −0.191265 −0.0956324 0.995417i \(-0.530487\pi\)
−0.0956324 + 0.995417i \(0.530487\pi\)
\(908\) 21.9215 0.727492
\(909\) 8.66695 0.287465
\(910\) −13.6961 −0.454023
\(911\) 4.42635 0.146651 0.0733257 0.997308i \(-0.476639\pi\)
0.0733257 + 0.997308i \(0.476639\pi\)
\(912\) 8.57070 0.283804
\(913\) 14.6824 0.485916
\(914\) 21.1257 0.698777
\(915\) 1.62906 0.0538550
\(916\) −15.0052 −0.495787
\(917\) 44.9507 1.48440
\(918\) 6.07005 0.200342
\(919\) 7.93867 0.261872 0.130936 0.991391i \(-0.458202\pi\)
0.130936 + 0.991391i \(0.458202\pi\)
\(920\) −13.0599 −0.430574
\(921\) −2.95252 −0.0972887
\(922\) −6.07148 −0.199954
\(923\) −9.99960 −0.329141
\(924\) 4.09482 0.134710
\(925\) −8.53812 −0.280732
\(926\) 8.79221 0.288930
\(927\) 2.92477 0.0960620
\(928\) −1.71712 −0.0563671
\(929\) −0.954985 −0.0313320 −0.0156660 0.999877i \(-0.504987\pi\)
−0.0156660 + 0.999877i \(0.504987\pi\)
\(930\) −7.14800 −0.234392
\(931\) 83.7150 2.74365
\(932\) 16.4547 0.538993
\(933\) −18.0561 −0.591129
\(934\) −41.2298 −1.34908
\(935\) −9.88846 −0.323387
\(936\) −2.05318 −0.0671103
\(937\) −52.6043 −1.71851 −0.859254 0.511550i \(-0.829072\pi\)
−0.859254 + 0.511550i \(0.829072\pi\)
\(938\) −35.7015 −1.16570
\(939\) 29.2592 0.954838
\(940\) −14.7078 −0.479715
\(941\) −0.177546 −0.00578784 −0.00289392 0.999996i \(-0.500921\pi\)
−0.00289392 + 0.999996i \(0.500921\pi\)
\(942\) 2.35423 0.0767049
\(943\) −21.4107 −0.697227
\(944\) 6.78574 0.220857
\(945\) 6.67070 0.216998
\(946\) −1.73399 −0.0563769
\(947\) −35.5684 −1.15582 −0.577909 0.816101i \(-0.696131\pi\)
−0.577909 + 0.816101i \(0.696131\pi\)
\(948\) 15.9806 0.519025
\(949\) −28.4514 −0.923571
\(950\) 20.1084 0.652401
\(951\) −17.1452 −0.555970
\(952\) −24.8558 −0.805581
\(953\) −34.1171 −1.10516 −0.552580 0.833460i \(-0.686357\pi\)
−0.552580 + 0.833460i \(0.686357\pi\)
\(954\) 8.44100 0.273287
\(955\) 29.0942 0.941467
\(956\) 28.5650 0.923859
\(957\) −1.71712 −0.0555065
\(958\) −18.4907 −0.597406
\(959\) 11.3651 0.366997
\(960\) −1.62906 −0.0525776
\(961\) −11.7471 −0.378938
\(962\) −7.47187 −0.240903
\(963\) 11.9162 0.383996
\(964\) 24.8317 0.799775
\(965\) −27.0910 −0.872089
\(966\) −32.8277 −1.05621
\(967\) 6.20742 0.199617 0.0998085 0.995007i \(-0.468177\pi\)
0.0998085 + 0.995007i \(0.468177\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −52.0246 −1.67127
\(970\) 8.05022 0.258477
\(971\) 17.6405 0.566110 0.283055 0.959104i \(-0.408652\pi\)
0.283055 + 0.959104i \(0.408652\pi\)
\(972\) 1.00000 0.0320750
\(973\) −69.8304 −2.23866
\(974\) 10.4782 0.335744
\(975\) −4.81712 −0.154271
\(976\) −1.00000 −0.0320092
\(977\) 29.4309 0.941578 0.470789 0.882246i \(-0.343969\pi\)
0.470789 + 0.882246i \(0.343969\pi\)
\(978\) −23.6811 −0.757238
\(979\) −11.8389 −0.378374
\(980\) −15.9119 −0.508288
\(981\) 15.1581 0.483961
\(982\) −41.7373 −1.33189
\(983\) 42.2313 1.34697 0.673485 0.739201i \(-0.264796\pi\)
0.673485 + 0.739201i \(0.264796\pi\)
\(984\) −2.67070 −0.0851388
\(985\) 11.1374 0.354867
\(986\) 10.4230 0.331936
\(987\) −36.9697 −1.17676
\(988\) 17.5972 0.559841
\(989\) 13.9012 0.442032
\(990\) −1.62906 −0.0517748
\(991\) 52.3378 1.66257 0.831283 0.555850i \(-0.187607\pi\)
0.831283 + 0.555850i \(0.187607\pi\)
\(992\) 4.38782 0.139313
\(993\) 8.59927 0.272890
\(994\) −19.9430 −0.632554
\(995\) −27.4117 −0.869011
\(996\) −14.6824 −0.465230
\(997\) 28.3257 0.897083 0.448541 0.893762i \(-0.351944\pi\)
0.448541 + 0.893762i \(0.351944\pi\)
\(998\) −17.5898 −0.556795
\(999\) 3.63917 0.115138
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 4026.2.a.u.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4026.2.a.u.1.2 5 1.1 even 1 trivial