Properties

Label 1155.2.a.u.1.1
Level 1155
Weight 2
Character 1155.1
Self dual yes
Analytic conductor 9.223
Analytic rank 0
Dimension 4
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.13448.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.58874\) of \(x^{4} - 7 x^{2} + 2\)
Character \(\chi\) \(=\) 1155.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.58874 q^{2} +1.00000 q^{3} +4.70156 q^{4} -1.00000 q^{5} -2.58874 q^{6} -1.00000 q^{7} -6.99364 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.58874 q^{2} +1.00000 q^{3} +4.70156 q^{4} -1.00000 q^{5} -2.58874 q^{6} -1.00000 q^{7} -6.99364 q^{8} +1.00000 q^{9} +2.58874 q^{10} -1.00000 q^{11} +4.70156 q^{12} -2.40490 q^{13} +2.58874 q^{14} -1.00000 q^{15} +8.70156 q^{16} -3.70156 q^{17} -2.58874 q^{18} +4.15641 q^{19} -4.70156 q^{20} -1.00000 q^{21} +2.58874 q^{22} -0.0692417 q^{23} -6.99364 q^{24} +1.00000 q^{25} +6.22565 q^{26} +1.00000 q^{27} -4.70156 q^{28} +0.703336 q^{29} +2.58874 q^{30} +5.22742 q^{31} -8.53879 q^{32} -1.00000 q^{33} +9.58237 q^{34} +1.00000 q^{35} +4.70156 q^{36} +7.95005 q^{37} -10.7598 q^{38} -2.40490 q^{39} +6.99364 q^{40} +2.31773 q^{41} +2.58874 q^{42} +4.24849 q^{43} -4.70156 q^{44} -1.00000 q^{45} +0.179249 q^{46} +13.3532 q^{47} +8.70156 q^{48} +1.00000 q^{49} -2.58874 q^{50} -3.70156 q^{51} -11.3068 q^{52} -8.51136 q^{53} -2.58874 q^{54} +1.00000 q^{55} +6.99364 q^{56} +4.15641 q^{57} -1.82075 q^{58} -4.47414 q^{59} -4.70156 q^{60} +5.02107 q^{61} -13.5324 q^{62} -1.00000 q^{63} +4.70156 q^{64} +2.40490 q^{65} +2.58874 q^{66} +4.72263 q^{67} -17.4031 q^{68} -0.0692417 q^{69} -2.58874 q^{70} +4.40490 q^{71} -6.99364 q^{72} -14.2129 q^{73} -20.5806 q^{74} +1.00000 q^{75} +19.5416 q^{76} +1.00000 q^{77} +6.22565 q^{78} -4.40490 q^{79} -8.70156 q^{80} +1.00000 q^{81} -6.00000 q^{82} +5.56308 q^{83} -4.70156 q^{84} +3.70156 q^{85} -10.9982 q^{86} +0.703336 q^{87} +6.99364 q^{88} +15.1968 q^{89} +2.58874 q^{90} +2.40490 q^{91} -0.325544 q^{92} +5.22742 q^{93} -34.5679 q^{94} -4.15641 q^{95} -8.53879 q^{96} -8.24494 q^{97} -2.58874 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{3} + 6q^{4} - 4q^{5} - 4q^{7} + 4q^{9} + O(q^{10}) \) \( 4q + 4q^{3} + 6q^{4} - 4q^{5} - 4q^{7} + 4q^{9} - 4q^{11} + 6q^{12} + 8q^{13} - 4q^{15} + 22q^{16} - 2q^{17} + 10q^{19} - 6q^{20} - 4q^{21} - 2q^{23} + 4q^{25} + 20q^{26} + 4q^{27} - 6q^{28} - 2q^{29} + 24q^{31} - 4q^{33} + 4q^{35} + 6q^{36} + 8q^{37} + 16q^{38} + 8q^{39} + 6q^{43} - 6q^{44} - 4q^{45} - 12q^{46} + 4q^{47} + 22q^{48} + 4q^{49} - 2q^{51} + 12q^{52} + 14q^{53} + 4q^{55} + 10q^{57} - 20q^{58} - 2q^{59} - 6q^{60} + 6q^{61} + 8q^{62} - 4q^{63} + 6q^{64} - 8q^{65} - 8q^{67} - 44q^{68} - 2q^{69} + 4q^{73} - 36q^{74} + 4q^{75} + 56q^{76} + 4q^{77} + 20q^{78} - 22q^{80} + 4q^{81} - 24q^{82} + 6q^{83} - 6q^{84} + 2q^{85} - 36q^{86} - 2q^{87} + 18q^{89} - 8q^{91} - 44q^{92} + 24q^{93} - 36q^{94} - 10q^{95} - 6q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58874 −1.83051 −0.915257 0.402871i \(-0.868012\pi\)
−0.915257 + 0.402871i \(0.868012\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.70156 2.35078
\(5\) −1.00000 −0.447214
\(6\) −2.58874 −1.05685
\(7\) −1.00000 −0.377964
\(8\) −6.99364 −2.47262
\(9\) 1.00000 0.333333
\(10\) 2.58874 0.818631
\(11\) −1.00000 −0.301511
\(12\) 4.70156 1.35722
\(13\) −2.40490 −0.666999 −0.333499 0.942750i \(-0.608229\pi\)
−0.333499 + 0.942750i \(0.608229\pi\)
\(14\) 2.58874 0.691869
\(15\) −1.00000 −0.258199
\(16\) 8.70156 2.17539
\(17\) −3.70156 −0.897761 −0.448880 0.893592i \(-0.648177\pi\)
−0.448880 + 0.893592i \(0.648177\pi\)
\(18\) −2.58874 −0.610171
\(19\) 4.15641 0.953545 0.476773 0.879027i \(-0.341807\pi\)
0.476773 + 0.879027i \(0.341807\pi\)
\(20\) −4.70156 −1.05130
\(21\) −1.00000 −0.218218
\(22\) 2.58874 0.551921
\(23\) −0.0692417 −0.0144379 −0.00721895 0.999974i \(-0.502298\pi\)
−0.00721895 + 0.999974i \(0.502298\pi\)
\(24\) −6.99364 −1.42757
\(25\) 1.00000 0.200000
\(26\) 6.22565 1.22095
\(27\) 1.00000 0.192450
\(28\) −4.70156 −0.888512
\(29\) 0.703336 0.130606 0.0653031 0.997865i \(-0.479199\pi\)
0.0653031 + 0.997865i \(0.479199\pi\)
\(30\) 2.58874 0.472637
\(31\) 5.22742 0.938873 0.469436 0.882966i \(-0.344457\pi\)
0.469436 + 0.882966i \(0.344457\pi\)
\(32\) −8.53879 −1.50946
\(33\) −1.00000 −0.174078
\(34\) 9.58237 1.64336
\(35\) 1.00000 0.169031
\(36\) 4.70156 0.783594
\(37\) 7.95005 1.30698 0.653490 0.756935i \(-0.273304\pi\)
0.653490 + 0.756935i \(0.273304\pi\)
\(38\) −10.7598 −1.74548
\(39\) −2.40490 −0.385092
\(40\) 6.99364 1.10579
\(41\) 2.31773 0.361969 0.180984 0.983486i \(-0.442072\pi\)
0.180984 + 0.983486i \(0.442072\pi\)
\(42\) 2.58874 0.399451
\(43\) 4.24849 0.647889 0.323944 0.946076i \(-0.394991\pi\)
0.323944 + 0.946076i \(0.394991\pi\)
\(44\) −4.70156 −0.708787
\(45\) −1.00000 −0.149071
\(46\) 0.179249 0.0264288
\(47\) 13.3532 1.94776 0.973881 0.227061i \(-0.0729117\pi\)
0.973881 + 0.227061i \(0.0729117\pi\)
\(48\) 8.70156 1.25596
\(49\) 1.00000 0.142857
\(50\) −2.58874 −0.366103
\(51\) −3.70156 −0.518322
\(52\) −11.3068 −1.56797
\(53\) −8.51136 −1.16912 −0.584562 0.811349i \(-0.698734\pi\)
−0.584562 + 0.811349i \(0.698734\pi\)
\(54\) −2.58874 −0.352283
\(55\) 1.00000 0.134840
\(56\) 6.99364 0.934564
\(57\) 4.15641 0.550530
\(58\) −1.82075 −0.239076
\(59\) −4.47414 −0.582483 −0.291242 0.956650i \(-0.594068\pi\)
−0.291242 + 0.956650i \(0.594068\pi\)
\(60\) −4.70156 −0.606969
\(61\) 5.02107 0.642882 0.321441 0.946930i \(-0.395833\pi\)
0.321441 + 0.946930i \(0.395833\pi\)
\(62\) −13.5324 −1.71862
\(63\) −1.00000 −0.125988
\(64\) 4.70156 0.587695
\(65\) 2.40490 0.298291
\(66\) 2.58874 0.318652
\(67\) 4.72263 0.576961 0.288481 0.957486i \(-0.406850\pi\)
0.288481 + 0.957486i \(0.406850\pi\)
\(68\) −17.4031 −2.11044
\(69\) −0.0692417 −0.00833572
\(70\) −2.58874 −0.309413
\(71\) 4.40490 0.522765 0.261383 0.965235i \(-0.415822\pi\)
0.261383 + 0.965235i \(0.415822\pi\)
\(72\) −6.99364 −0.824208
\(73\) −14.2129 −1.66350 −0.831748 0.555153i \(-0.812660\pi\)
−0.831748 + 0.555153i \(0.812660\pi\)
\(74\) −20.5806 −2.39245
\(75\) 1.00000 0.115470
\(76\) 19.5416 2.24158
\(77\) 1.00000 0.113961
\(78\) 6.22565 0.704916
\(79\) −4.40490 −0.495590 −0.247795 0.968813i \(-0.579706\pi\)
−0.247795 + 0.968813i \(0.579706\pi\)
\(80\) −8.70156 −0.972864
\(81\) 1.00000 0.111111
\(82\) −6.00000 −0.662589
\(83\) 5.56308 0.610627 0.305314 0.952252i \(-0.401239\pi\)
0.305314 + 0.952252i \(0.401239\pi\)
\(84\) −4.70156 −0.512982
\(85\) 3.70156 0.401491
\(86\) −10.9982 −1.18597
\(87\) 0.703336 0.0754055
\(88\) 6.99364 0.745524
\(89\) 15.1968 1.61085 0.805427 0.592695i \(-0.201936\pi\)
0.805427 + 0.592695i \(0.201936\pi\)
\(90\) 2.58874 0.272877
\(91\) 2.40490 0.252102
\(92\) −0.325544 −0.0339403
\(93\) 5.22742 0.542058
\(94\) −34.5679 −3.56540
\(95\) −4.15641 −0.426438
\(96\) −8.53879 −0.871487
\(97\) −8.24494 −0.837147 −0.418574 0.908183i \(-0.637470\pi\)
−0.418574 + 0.908183i \(0.637470\pi\)
\(98\) −2.58874 −0.261502
\(99\) −1.00000 −0.100504
\(100\) 4.70156 0.470156
\(101\) 11.0354 1.09807 0.549034 0.835800i \(-0.314996\pi\)
0.549034 + 0.835800i \(0.314996\pi\)
\(102\) 9.58237 0.948796
\(103\) −2.84182 −0.280013 −0.140006 0.990151i \(-0.544712\pi\)
−0.140006 + 0.990151i \(0.544712\pi\)
\(104\) 16.8190 1.64924
\(105\) 1.00000 0.0975900
\(106\) 22.0337 2.14010
\(107\) −15.3567 −1.48459 −0.742295 0.670073i \(-0.766263\pi\)
−0.742295 + 0.670073i \(0.766263\pi\)
\(108\) 4.70156 0.452408
\(109\) 12.8597 1.23174 0.615870 0.787848i \(-0.288805\pi\)
0.615870 + 0.787848i \(0.288805\pi\)
\(110\) −2.58874 −0.246826
\(111\) 7.95005 0.754586
\(112\) −8.70156 −0.822220
\(113\) 16.5114 1.55326 0.776629 0.629958i \(-0.216928\pi\)
0.776629 + 0.629958i \(0.216928\pi\)
\(114\) −10.7598 −1.00775
\(115\) 0.0692417 0.00645682
\(116\) 3.30678 0.307026
\(117\) −2.40490 −0.222333
\(118\) 11.5824 1.06624
\(119\) 3.70156 0.339322
\(120\) 6.99364 0.638429
\(121\) 1.00000 0.0909091
\(122\) −12.9982 −1.17680
\(123\) 2.31773 0.208983
\(124\) 24.5771 2.20708
\(125\) −1.00000 −0.0894427
\(126\) 2.58874 0.230623
\(127\) −0.248490 −0.0220500 −0.0110250 0.999939i \(-0.503509\pi\)
−0.0110250 + 0.999939i \(0.503509\pi\)
\(128\) 4.90647 0.433675
\(129\) 4.24849 0.374059
\(130\) −6.22565 −0.546026
\(131\) 12.6178 1.10242 0.551212 0.834365i \(-0.314166\pi\)
0.551212 + 0.834365i \(0.314166\pi\)
\(132\) −4.70156 −0.409218
\(133\) −4.15641 −0.360406
\(134\) −12.2256 −1.05614
\(135\) −1.00000 −0.0860663
\(136\) 25.8874 2.21982
\(137\) 9.40312 0.803363 0.401682 0.915779i \(-0.368426\pi\)
0.401682 + 0.915779i \(0.368426\pi\)
\(138\) 0.179249 0.0152587
\(139\) 22.4934 1.90787 0.953934 0.300016i \(-0.0969921\pi\)
0.953934 + 0.300016i \(0.0969921\pi\)
\(140\) 4.70156 0.397355
\(141\) 13.3532 1.12454
\(142\) −11.4031 −0.956929
\(143\) 2.40490 0.201108
\(144\) 8.70156 0.725130
\(145\) −0.703336 −0.0584088
\(146\) 36.7935 3.04505
\(147\) 1.00000 0.0824786
\(148\) 37.3777 3.07243
\(149\) −13.9001 −1.13874 −0.569370 0.822081i \(-0.692813\pi\)
−0.569370 + 0.822081i \(0.692813\pi\)
\(150\) −2.58874 −0.211370
\(151\) 2.95183 0.240216 0.120108 0.992761i \(-0.461676\pi\)
0.120108 + 0.992761i \(0.461676\pi\)
\(152\) −29.0684 −2.35776
\(153\) −3.70156 −0.299254
\(154\) −2.58874 −0.208606
\(155\) −5.22742 −0.419877
\(156\) −11.3068 −0.905267
\(157\) 5.15463 0.411385 0.205692 0.978617i \(-0.434055\pi\)
0.205692 + 0.978617i \(0.434055\pi\)
\(158\) 11.4031 0.907184
\(159\) −8.51136 −0.674995
\(160\) 8.53879 0.675051
\(161\) 0.0692417 0.00545701
\(162\) −2.58874 −0.203390
\(163\) 2.32128 0.181817 0.0909083 0.995859i \(-0.471023\pi\)
0.0909083 + 0.995859i \(0.471023\pi\)
\(164\) 10.8970 0.850910
\(165\) 1.00000 0.0778499
\(166\) −14.4014 −1.11776
\(167\) 17.7581 1.37416 0.687081 0.726581i \(-0.258892\pi\)
0.687081 + 0.726581i \(0.258892\pi\)
\(168\) 6.99364 0.539571
\(169\) −7.21647 −0.555113
\(170\) −9.58237 −0.734934
\(171\) 4.15641 0.317848
\(172\) 19.9745 1.52304
\(173\) 20.2094 1.53649 0.768245 0.640156i \(-0.221130\pi\)
0.768245 + 0.640156i \(0.221130\pi\)
\(174\) −1.82075 −0.138031
\(175\) −1.00000 −0.0755929
\(176\) −8.70156 −0.655905
\(177\) −4.47414 −0.336297
\(178\) −39.3404 −2.94869
\(179\) −5.95005 −0.444728 −0.222364 0.974964i \(-0.571377\pi\)
−0.222364 + 0.974964i \(0.571377\pi\)
\(180\) −4.70156 −0.350434
\(181\) −5.54161 −0.411904 −0.205952 0.978562i \(-0.566029\pi\)
−0.205952 + 0.978562i \(0.566029\pi\)
\(182\) −6.22565 −0.461476
\(183\) 5.02107 0.371168
\(184\) 0.484251 0.0356995
\(185\) −7.95005 −0.584499
\(186\) −13.5324 −0.992246
\(187\) 3.70156 0.270685
\(188\) 62.7808 4.57876
\(189\) −1.00000 −0.0727393
\(190\) 10.7598 0.780601
\(191\) 25.8966 1.87381 0.936905 0.349585i \(-0.113677\pi\)
0.936905 + 0.349585i \(0.113677\pi\)
\(192\) 4.70156 0.339306
\(193\) −1.31596 −0.0947248 −0.0473624 0.998878i \(-0.515082\pi\)
−0.0473624 + 0.998878i \(0.515082\pi\)
\(194\) 21.3440 1.53241
\(195\) 2.40490 0.172218
\(196\) 4.70156 0.335826
\(197\) −4.44212 −0.316488 −0.158244 0.987400i \(-0.550583\pi\)
−0.158244 + 0.987400i \(0.550583\pi\)
\(198\) 2.58874 0.183974
\(199\) −25.7453 −1.82504 −0.912520 0.409033i \(-0.865866\pi\)
−0.912520 + 0.409033i \(0.865866\pi\)
\(200\) −6.99364 −0.494525
\(201\) 4.72263 0.333109
\(202\) −28.5679 −2.01003
\(203\) −0.703336 −0.0493645
\(204\) −17.4031 −1.21846
\(205\) −2.31773 −0.161877
\(206\) 7.35672 0.512567
\(207\) −0.0692417 −0.00481263
\(208\) −20.9264 −1.45098
\(209\) −4.15641 −0.287505
\(210\) −2.58874 −0.178640
\(211\) −24.2129 −1.66689 −0.833443 0.552605i \(-0.813634\pi\)
−0.833443 + 0.552605i \(0.813634\pi\)
\(212\) −40.0167 −2.74836
\(213\) 4.40490 0.301819
\(214\) 39.7545 2.71756
\(215\) −4.24849 −0.289745
\(216\) −6.99364 −0.475857
\(217\) −5.22742 −0.354861
\(218\) −33.2905 −2.25472
\(219\) −14.2129 −0.960420
\(220\) 4.70156 0.316979
\(221\) 8.90188 0.598805
\(222\) −20.5806 −1.38128
\(223\) 8.38697 0.561633 0.280817 0.959761i \(-0.409395\pi\)
0.280817 + 0.959761i \(0.409395\pi\)
\(224\) 8.53879 0.570522
\(225\) 1.00000 0.0666667
\(226\) −42.7436 −2.84326
\(227\) 2.79542 0.185538 0.0927692 0.995688i \(-0.470428\pi\)
0.0927692 + 0.995688i \(0.470428\pi\)
\(228\) 19.5416 1.29417
\(229\) 9.95360 0.657752 0.328876 0.944373i \(-0.393330\pi\)
0.328876 + 0.944373i \(0.393330\pi\)
\(230\) −0.179249 −0.0118193
\(231\) 1.00000 0.0657952
\(232\) −4.91887 −0.322940
\(233\) −2.77612 −0.181870 −0.0909350 0.995857i \(-0.528986\pi\)
−0.0909350 + 0.995857i \(0.528986\pi\)
\(234\) 6.22565 0.406983
\(235\) −13.3532 −0.871065
\(236\) −21.0354 −1.36929
\(237\) −4.40490 −0.286129
\(238\) −9.58237 −0.621133
\(239\) −14.6034 −0.944618 −0.472309 0.881433i \(-0.656579\pi\)
−0.472309 + 0.881433i \(0.656579\pi\)
\(240\) −8.70156 −0.561683
\(241\) 10.5385 0.678842 0.339421 0.940635i \(-0.389769\pi\)
0.339421 + 0.940635i \(0.389769\pi\)
\(242\) −2.58874 −0.166410
\(243\) 1.00000 0.0641500
\(244\) 23.6069 1.51127
\(245\) −1.00000 −0.0638877
\(246\) −6.00000 −0.382546
\(247\) −9.99573 −0.636013
\(248\) −36.5587 −2.32148
\(249\) 5.56308 0.352546
\(250\) 2.58874 0.163726
\(251\) −19.3904 −1.22391 −0.611955 0.790892i \(-0.709617\pi\)
−0.611955 + 0.790892i \(0.709617\pi\)
\(252\) −4.70156 −0.296171
\(253\) 0.0692417 0.00435319
\(254\) 0.643276 0.0403627
\(255\) 3.70156 0.231801
\(256\) −22.1047 −1.38154
\(257\) 2.71771 0.169526 0.0847631 0.996401i \(-0.472987\pi\)
0.0847631 + 0.996401i \(0.472987\pi\)
\(258\) −10.9982 −0.684720
\(259\) −7.95005 −0.493992
\(260\) 11.3068 0.701216
\(261\) 0.703336 0.0435354
\(262\) −32.6642 −2.01800
\(263\) −14.4548 −0.891324 −0.445662 0.895201i \(-0.647032\pi\)
−0.445662 + 0.895201i \(0.647032\pi\)
\(264\) 6.99364 0.430428
\(265\) 8.51136 0.522849
\(266\) 10.7598 0.659729
\(267\) 15.1968 0.930027
\(268\) 22.2037 1.35631
\(269\) −17.2677 −1.05283 −0.526414 0.850228i \(-0.676464\pi\)
−0.526414 + 0.850228i \(0.676464\pi\)
\(270\) 2.58874 0.157546
\(271\) 15.7051 0.954017 0.477009 0.878899i \(-0.341721\pi\)
0.477009 + 0.878899i \(0.341721\pi\)
\(272\) −32.2094 −1.95298
\(273\) 2.40490 0.145551
\(274\) −24.3422 −1.47057
\(275\) −1.00000 −0.0603023
\(276\) −0.325544 −0.0195955
\(277\) 15.9837 0.960369 0.480184 0.877168i \(-0.340570\pi\)
0.480184 + 0.877168i \(0.340570\pi\)
\(278\) −58.2296 −3.49238
\(279\) 5.22742 0.312958
\(280\) −6.99364 −0.417950
\(281\) −5.50302 −0.328283 −0.164141 0.986437i \(-0.552485\pi\)
−0.164141 + 0.986437i \(0.552485\pi\)
\(282\) −34.5679 −2.05849
\(283\) −8.09208 −0.481024 −0.240512 0.970646i \(-0.577315\pi\)
−0.240512 + 0.970646i \(0.577315\pi\)
\(284\) 20.7099 1.22891
\(285\) −4.15641 −0.246204
\(286\) −6.22565 −0.368130
\(287\) −2.31773 −0.136811
\(288\) −8.53879 −0.503153
\(289\) −3.29844 −0.194026
\(290\) 1.82075 0.106918
\(291\) −8.24494 −0.483327
\(292\) −66.8229 −3.91052
\(293\) 6.51490 0.380605 0.190302 0.981726i \(-0.439053\pi\)
0.190302 + 0.981726i \(0.439053\pi\)
\(294\) −2.58874 −0.150978
\(295\) 4.47414 0.260494
\(296\) −55.5998 −3.23167
\(297\) −1.00000 −0.0580259
\(298\) 35.9837 2.08448
\(299\) 0.166519 0.00963006
\(300\) 4.70156 0.271445
\(301\) −4.24849 −0.244879
\(302\) −7.64150 −0.439719
\(303\) 11.0354 0.633970
\(304\) 36.1672 2.07433
\(305\) −5.02107 −0.287505
\(306\) 9.58237 0.547788
\(307\) −22.5679 −1.28802 −0.644008 0.765019i \(-0.722730\pi\)
−0.644008 + 0.765019i \(0.722730\pi\)
\(308\) 4.70156 0.267896
\(309\) −2.84182 −0.161665
\(310\) 13.5324 0.768590
\(311\) 0.0513177 0.00290996 0.00145498 0.999999i \(-0.499537\pi\)
0.00145498 + 0.999999i \(0.499537\pi\)
\(312\) 16.8190 0.952187
\(313\) −3.44224 −0.194567 −0.0972835 0.995257i \(-0.531015\pi\)
−0.0972835 + 0.995257i \(0.531015\pi\)
\(314\) −13.3440 −0.753045
\(315\) 1.00000 0.0563436
\(316\) −20.7099 −1.16502
\(317\) 31.6582 1.77810 0.889050 0.457810i \(-0.151366\pi\)
0.889050 + 0.457810i \(0.151366\pi\)
\(318\) 22.0337 1.23559
\(319\) −0.703336 −0.0393792
\(320\) −4.70156 −0.262825
\(321\) −15.3567 −0.857129
\(322\) −0.179249 −0.00998914
\(323\) −15.3852 −0.856055
\(324\) 4.70156 0.261198
\(325\) −2.40490 −0.133400
\(326\) −6.00918 −0.332818
\(327\) 12.8597 0.711145
\(328\) −16.2094 −0.895013
\(329\) −13.3532 −0.736184
\(330\) −2.58874 −0.142505
\(331\) −3.55953 −0.195650 −0.0978248 0.995204i \(-0.531188\pi\)
−0.0978248 + 0.995204i \(0.531188\pi\)
\(332\) 26.1552 1.43545
\(333\) 7.95005 0.435660
\(334\) −45.9710 −2.51542
\(335\) −4.72263 −0.258025
\(336\) −8.70156 −0.474709
\(337\) 4.23221 0.230543 0.115272 0.993334i \(-0.463226\pi\)
0.115272 + 0.993334i \(0.463226\pi\)
\(338\) 18.6815 1.01614
\(339\) 16.5114 0.896774
\(340\) 17.4031 0.943817
\(341\) −5.22742 −0.283081
\(342\) −10.7598 −0.581826
\(343\) −1.00000 −0.0539949
\(344\) −29.7124 −1.60198
\(345\) 0.0692417 0.00372785
\(346\) −52.3168 −2.81257
\(347\) 15.6160 0.838313 0.419157 0.907914i \(-0.362326\pi\)
0.419157 + 0.907914i \(0.362326\pi\)
\(348\) 3.30678 0.177262
\(349\) 2.24357 0.120096 0.0600479 0.998195i \(-0.480875\pi\)
0.0600479 + 0.998195i \(0.480875\pi\)
\(350\) 2.58874 0.138374
\(351\) −2.40490 −0.128364
\(352\) 8.53879 0.455119
\(353\) 11.9965 0.638507 0.319253 0.947669i \(-0.396568\pi\)
0.319253 + 0.947669i \(0.396568\pi\)
\(354\) 11.5824 0.615596
\(355\) −4.40490 −0.233788
\(356\) 71.4486 3.78677
\(357\) 3.70156 0.195907
\(358\) 15.4031 0.814080
\(359\) 24.6743 1.30226 0.651131 0.758966i \(-0.274295\pi\)
0.651131 + 0.758966i \(0.274295\pi\)
\(360\) 6.99364 0.368597
\(361\) −1.72428 −0.0907514
\(362\) 14.3458 0.753997
\(363\) 1.00000 0.0524864
\(364\) 11.3068 0.592636
\(365\) 14.2129 0.743938
\(366\) −12.9982 −0.679428
\(367\) 22.2808 1.16305 0.581524 0.813529i \(-0.302457\pi\)
0.581524 + 0.813529i \(0.302457\pi\)
\(368\) −0.602511 −0.0314081
\(369\) 2.31773 0.120656
\(370\) 20.5806 1.06993
\(371\) 8.51136 0.441888
\(372\) 24.5771 1.27426
\(373\) 13.6389 0.706195 0.353097 0.935587i \(-0.385128\pi\)
0.353097 + 0.935587i \(0.385128\pi\)
\(374\) −9.58237 −0.495493
\(375\) −1.00000 −0.0516398
\(376\) −93.3872 −4.81608
\(377\) −1.69145 −0.0871141
\(378\) 2.58874 0.133150
\(379\) 14.1985 0.729330 0.364665 0.931139i \(-0.381183\pi\)
0.364665 + 0.931139i \(0.381183\pi\)
\(380\) −19.5416 −1.00246
\(381\) −0.248490 −0.0127305
\(382\) −67.0394 −3.43003
\(383\) −10.1244 −0.517332 −0.258666 0.965967i \(-0.583283\pi\)
−0.258666 + 0.965967i \(0.583283\pi\)
\(384\) 4.90647 0.250382
\(385\) −1.00000 −0.0509647
\(386\) 3.40667 0.173395
\(387\) 4.24849 0.215963
\(388\) −38.7641 −1.96795
\(389\) −20.9342 −1.06141 −0.530703 0.847558i \(-0.678072\pi\)
−0.530703 + 0.847558i \(0.678072\pi\)
\(390\) −6.22565 −0.315248
\(391\) 0.256303 0.0129618
\(392\) −6.99364 −0.353232
\(393\) 12.6178 0.636485
\(394\) 11.4995 0.579335
\(395\) 4.40490 0.221634
\(396\) −4.70156 −0.236262
\(397\) −24.5679 −1.23303 −0.616513 0.787345i \(-0.711455\pi\)
−0.616513 + 0.787345i \(0.711455\pi\)
\(398\) 66.6479 3.34076
\(399\) −4.15641 −0.208081
\(400\) 8.70156 0.435078
\(401\) −38.4180 −1.91850 −0.959252 0.282551i \(-0.908819\pi\)
−0.959252 + 0.282551i \(0.908819\pi\)
\(402\) −12.2256 −0.609760
\(403\) −12.5714 −0.626227
\(404\) 51.8838 2.58132
\(405\) −1.00000 −0.0496904
\(406\) 1.82075 0.0903624
\(407\) −7.95005 −0.394069
\(408\) 25.8874 1.28162
\(409\) −1.17748 −0.0582224 −0.0291112 0.999576i \(-0.509268\pi\)
−0.0291112 + 0.999576i \(0.509268\pi\)
\(410\) 6.00000 0.296319
\(411\) 9.40312 0.463822
\(412\) −13.3610 −0.658249
\(413\) 4.47414 0.220158
\(414\) 0.179249 0.00880959
\(415\) −5.56308 −0.273081
\(416\) 20.5349 1.00681
\(417\) 22.4934 1.10151
\(418\) 10.7598 0.526281
\(419\) −37.2585 −1.82020 −0.910098 0.414393i \(-0.863994\pi\)
−0.910098 + 0.414393i \(0.863994\pi\)
\(420\) 4.70156 0.229413
\(421\) 3.10469 0.151313 0.0756566 0.997134i \(-0.475895\pi\)
0.0756566 + 0.997134i \(0.475895\pi\)
\(422\) 62.6809 3.05126
\(423\) 13.3532 0.649254
\(424\) 59.5253 2.89081
\(425\) −3.70156 −0.179552
\(426\) −11.4031 −0.552483
\(427\) −5.02107 −0.242986
\(428\) −72.2006 −3.48995
\(429\) 2.40490 0.116110
\(430\) 10.9982 0.530382
\(431\) −13.5452 −0.652447 −0.326224 0.945293i \(-0.605776\pi\)
−0.326224 + 0.945293i \(0.605776\pi\)
\(432\) 8.70156 0.418654
\(433\) −33.7904 −1.62386 −0.811931 0.583754i \(-0.801583\pi\)
−0.811931 + 0.583754i \(0.801583\pi\)
\(434\) 13.5324 0.649577
\(435\) −0.703336 −0.0337224
\(436\) 60.4609 2.89555
\(437\) −0.287797 −0.0137672
\(438\) 36.7935 1.75806
\(439\) 11.6052 0.553887 0.276943 0.960886i \(-0.410679\pi\)
0.276943 + 0.960886i \(0.410679\pi\)
\(440\) −6.99364 −0.333408
\(441\) 1.00000 0.0476190
\(442\) −23.0446 −1.09612
\(443\) −24.7226 −1.17461 −0.587304 0.809367i \(-0.699811\pi\)
−0.587304 + 0.809367i \(0.699811\pi\)
\(444\) 37.3777 1.77387
\(445\) −15.1968 −0.720396
\(446\) −21.7117 −1.02808
\(447\) −13.9001 −0.657452
\(448\) −4.70156 −0.222128
\(449\) 31.5275 1.48788 0.743938 0.668249i \(-0.232956\pi\)
0.743938 + 0.668249i \(0.232956\pi\)
\(450\) −2.58874 −0.122034
\(451\) −2.31773 −0.109138
\(452\) 77.6292 3.65137
\(453\) 2.95183 0.138689
\(454\) −7.23660 −0.339631
\(455\) −2.40490 −0.112743
\(456\) −29.0684 −1.36125
\(457\) −13.3874 −0.626235 −0.313118 0.949714i \(-0.601373\pi\)
−0.313118 + 0.949714i \(0.601373\pi\)
\(458\) −25.7673 −1.20402
\(459\) −3.70156 −0.172774
\(460\) 0.325544 0.0151786
\(461\) 3.87070 0.180276 0.0901382 0.995929i \(-0.471269\pi\)
0.0901382 + 0.995929i \(0.471269\pi\)
\(462\) −2.58874 −0.120439
\(463\) 29.2484 1.35929 0.679643 0.733543i \(-0.262135\pi\)
0.679643 + 0.733543i \(0.262135\pi\)
\(464\) 6.12012 0.284119
\(465\) −5.22742 −0.242416
\(466\) 7.18666 0.332915
\(467\) 14.2551 0.659645 0.329823 0.944043i \(-0.393011\pi\)
0.329823 + 0.944043i \(0.393011\pi\)
\(468\) −11.3068 −0.522656
\(469\) −4.72263 −0.218071
\(470\) 34.5679 1.59450
\(471\) 5.15463 0.237513
\(472\) 31.2905 1.44026
\(473\) −4.24849 −0.195346
\(474\) 11.4031 0.523763
\(475\) 4.15641 0.190709
\(476\) 17.4031 0.797671
\(477\) −8.51136 −0.389708
\(478\) 37.8045 1.72914
\(479\) −32.2339 −1.47280 −0.736401 0.676545i \(-0.763476\pi\)
−0.736401 + 0.676545i \(0.763476\pi\)
\(480\) 8.53879 0.389741
\(481\) −19.1191 −0.871754
\(482\) −27.2813 −1.24263
\(483\) 0.0692417 0.00315061
\(484\) 4.70156 0.213707
\(485\) 8.24494 0.374384
\(486\) −2.58874 −0.117428
\(487\) 5.27382 0.238980 0.119490 0.992835i \(-0.461874\pi\)
0.119490 + 0.992835i \(0.461874\pi\)
\(488\) −35.1155 −1.58960
\(489\) 2.32128 0.104972
\(490\) 2.58874 0.116947
\(491\) 35.6647 1.60953 0.804764 0.593595i \(-0.202292\pi\)
0.804764 + 0.593595i \(0.202292\pi\)
\(492\) 10.8970 0.491273
\(493\) −2.60344 −0.117253
\(494\) 25.8763 1.16423
\(495\) 1.00000 0.0449467
\(496\) 45.4867 2.04242
\(497\) −4.40490 −0.197587
\(498\) −14.4014 −0.645340
\(499\) −39.0083 −1.74625 −0.873127 0.487494i \(-0.837911\pi\)
−0.873127 + 0.487494i \(0.837911\pi\)
\(500\) −4.70156 −0.210260
\(501\) 17.7581 0.793372
\(502\) 50.1966 2.24039
\(503\) −32.6821 −1.45722 −0.728612 0.684926i \(-0.759834\pi\)
−0.728612 + 0.684926i \(0.759834\pi\)
\(504\) 6.99364 0.311521
\(505\) −11.0354 −0.491071
\(506\) −0.179249 −0.00796857
\(507\) −7.21647 −0.320495
\(508\) −1.16829 −0.0518346
\(509\) 3.25808 0.144412 0.0722058 0.997390i \(-0.476996\pi\)
0.0722058 + 0.997390i \(0.476996\pi\)
\(510\) −9.58237 −0.424315
\(511\) 14.2129 0.628743
\(512\) 47.4103 2.09526
\(513\) 4.15641 0.183510
\(514\) −7.03544 −0.310320
\(515\) 2.84182 0.125226
\(516\) 19.9745 0.879330
\(517\) −13.3532 −0.587272
\(518\) 20.5806 0.904260
\(519\) 20.2094 0.887093
\(520\) −16.8190 −0.737561
\(521\) 7.75506 0.339755 0.169878 0.985465i \(-0.445663\pi\)
0.169878 + 0.985465i \(0.445663\pi\)
\(522\) −1.82075 −0.0796921
\(523\) 27.1647 1.18783 0.593916 0.804527i \(-0.297581\pi\)
0.593916 + 0.804527i \(0.297581\pi\)
\(524\) 59.3235 2.59156
\(525\) −1.00000 −0.0436436
\(526\) 37.4198 1.63158
\(527\) −19.3496 −0.842883
\(528\) −8.70156 −0.378687
\(529\) −22.9952 −0.999792
\(530\) −22.0337 −0.957082
\(531\) −4.47414 −0.194161
\(532\) −19.5416 −0.847236
\(533\) −5.57391 −0.241433
\(534\) −39.3404 −1.70243
\(535\) 15.3567 0.663929
\(536\) −33.0284 −1.42661
\(537\) −5.95005 −0.256764
\(538\) 44.7014 1.92722
\(539\) −1.00000 −0.0430730
\(540\) −4.70156 −0.202323
\(541\) 36.2087 1.55673 0.778366 0.627811i \(-0.216049\pi\)
0.778366 + 0.627811i \(0.216049\pi\)
\(542\) −40.6564 −1.74634
\(543\) −5.54161 −0.237813
\(544\) 31.6069 1.35513
\(545\) −12.8597 −0.550851
\(546\) −6.22565 −0.266433
\(547\) −11.1160 −0.475288 −0.237644 0.971352i \(-0.576375\pi\)
−0.237644 + 0.971352i \(0.576375\pi\)
\(548\) 44.2094 1.88853
\(549\) 5.02107 0.214294
\(550\) 2.58874 0.110384
\(551\) 2.92335 0.124539
\(552\) 0.484251 0.0206111
\(553\) 4.40490 0.187315
\(554\) −41.3777 −1.75797
\(555\) −7.95005 −0.337461
\(556\) 105.754 4.48498
\(557\) 34.4772 1.46084 0.730422 0.682996i \(-0.239323\pi\)
0.730422 + 0.682996i \(0.239323\pi\)
\(558\) −13.5324 −0.572873
\(559\) −10.2172 −0.432141
\(560\) 8.70156 0.367708
\(561\) 3.70156 0.156280
\(562\) 14.2459 0.600926
\(563\) 16.2129 0.683293 0.341647 0.939829i \(-0.389015\pi\)
0.341647 + 0.939829i \(0.389015\pi\)
\(564\) 62.7808 2.64355
\(565\) −16.5114 −0.694638
\(566\) 20.9483 0.880522
\(567\) −1.00000 −0.0419961
\(568\) −30.8062 −1.29260
\(569\) 3.64807 0.152935 0.0764675 0.997072i \(-0.475636\pi\)
0.0764675 + 0.997072i \(0.475636\pi\)
\(570\) 10.7598 0.450680
\(571\) −36.7563 −1.53820 −0.769102 0.639126i \(-0.779296\pi\)
−0.769102 + 0.639126i \(0.779296\pi\)
\(572\) 11.3068 0.472760
\(573\) 25.8966 1.08184
\(574\) 6.00000 0.250435
\(575\) −0.0692417 −0.00288758
\(576\) 4.70156 0.195898
\(577\) −2.17433 −0.0905186 −0.0452593 0.998975i \(-0.514411\pi\)
−0.0452593 + 0.998975i \(0.514411\pi\)
\(578\) 8.53879 0.355167
\(579\) −1.31596 −0.0546894
\(580\) −3.30678 −0.137306
\(581\) −5.56308 −0.230795
\(582\) 21.3440 0.884737
\(583\) 8.51136 0.352504
\(584\) 99.4000 4.11320
\(585\) 2.40490 0.0994303
\(586\) −16.8654 −0.696702
\(587\) 13.9501 0.575780 0.287890 0.957663i \(-0.407046\pi\)
0.287890 + 0.957663i \(0.407046\pi\)
\(588\) 4.70156 0.193889
\(589\) 21.7273 0.895258
\(590\) −11.5824 −0.476839
\(591\) −4.44212 −0.182724
\(592\) 69.1779 2.84319
\(593\) −10.9483 −0.449592 −0.224796 0.974406i \(-0.572172\pi\)
−0.224796 + 0.974406i \(0.572172\pi\)
\(594\) 2.58874 0.106217
\(595\) −3.70156 −0.151749
\(596\) −65.3522 −2.67693
\(597\) −25.7453 −1.05369
\(598\) −0.431075 −0.0176280
\(599\) −41.1998 −1.68338 −0.841689 0.539963i \(-0.818438\pi\)
−0.841689 + 0.539963i \(0.818438\pi\)
\(600\) −6.99364 −0.285514
\(601\) 21.5110 0.877450 0.438725 0.898621i \(-0.355430\pi\)
0.438725 + 0.898621i \(0.355430\pi\)
\(602\) 10.9982 0.448254
\(603\) 4.72263 0.192320
\(604\) 13.8782 0.564696
\(605\) −1.00000 −0.0406558
\(606\) −28.5679 −1.16049
\(607\) −13.8580 −0.562478 −0.281239 0.959638i \(-0.590745\pi\)
−0.281239 + 0.959638i \(0.590745\pi\)
\(608\) −35.4907 −1.43934
\(609\) −0.703336 −0.0285006
\(610\) 12.9982 0.526283
\(611\) −32.1130 −1.29915
\(612\) −17.4031 −0.703480
\(613\) −32.0223 −1.29337 −0.646684 0.762758i \(-0.723845\pi\)
−0.646684 + 0.762758i \(0.723845\pi\)
\(614\) 58.4223 2.35773
\(615\) −2.31773 −0.0934600
\(616\) −6.99364 −0.281782
\(617\) −3.39958 −0.136862 −0.0684309 0.997656i \(-0.521799\pi\)
−0.0684309 + 0.997656i \(0.521799\pi\)
\(618\) 7.35672 0.295931
\(619\) −1.91638 −0.0770259 −0.0385129 0.999258i \(-0.512262\pi\)
−0.0385129 + 0.999258i \(0.512262\pi\)
\(620\) −24.5771 −0.987038
\(621\) −0.0692417 −0.00277857
\(622\) −0.132848 −0.00532672
\(623\) −15.1968 −0.608846
\(624\) −20.9264 −0.837725
\(625\) 1.00000 0.0400000
\(626\) 8.91106 0.356158
\(627\) −4.15641 −0.165991
\(628\) 24.2348 0.967075
\(629\) −29.4276 −1.17336
\(630\) −2.58874 −0.103138
\(631\) −37.4019 −1.48895 −0.744473 0.667653i \(-0.767299\pi\)
−0.744473 + 0.667653i \(0.767299\pi\)
\(632\) 30.8062 1.22541
\(633\) −24.2129 −0.962377
\(634\) −81.9547 −3.25484
\(635\) 0.248490 0.00986104
\(636\) −40.0167 −1.58676
\(637\) −2.40490 −0.0952855
\(638\) 1.82075 0.0720842
\(639\) 4.40490 0.174255
\(640\) −4.90647 −0.193945
\(641\) 8.52928 0.336886 0.168443 0.985711i \(-0.446126\pi\)
0.168443 + 0.985711i \(0.446126\pi\)
\(642\) 39.7545 1.56899
\(643\) 36.3615 1.43396 0.716979 0.697095i \(-0.245524\pi\)
0.716979 + 0.697095i \(0.245524\pi\)
\(644\) 0.325544 0.0128282
\(645\) −4.24849 −0.167284
\(646\) 39.8282 1.56702
\(647\) 42.2551 1.66122 0.830609 0.556856i \(-0.187993\pi\)
0.830609 + 0.556856i \(0.187993\pi\)
\(648\) −6.99364 −0.274736
\(649\) 4.47414 0.175625
\(650\) 6.22565 0.244190
\(651\) −5.22742 −0.204879
\(652\) 10.9136 0.427411
\(653\) −21.8110 −0.853532 −0.426766 0.904362i \(-0.640347\pi\)
−0.426766 + 0.904362i \(0.640347\pi\)
\(654\) −33.2905 −1.30176
\(655\) −12.6178 −0.493019
\(656\) 20.1679 0.787424
\(657\) −14.2129 −0.554499
\(658\) 34.5679 1.34760
\(659\) −46.8164 −1.82371 −0.911853 0.410516i \(-0.865348\pi\)
−0.911853 + 0.410516i \(0.865348\pi\)
\(660\) 4.70156 0.183008
\(661\) −17.1113 −0.665551 −0.332775 0.943006i \(-0.607985\pi\)
−0.332775 + 0.943006i \(0.607985\pi\)
\(662\) 9.21469 0.358139
\(663\) 8.90188 0.345720
\(664\) −38.9061 −1.50985
\(665\) 4.15641 0.161179
\(666\) −20.5806 −0.797482
\(667\) −0.0487002 −0.00188568
\(668\) 83.4907 3.23035
\(669\) 8.38697 0.324259
\(670\) 12.2256 0.472318
\(671\) −5.02107 −0.193836
\(672\) 8.53879 0.329391
\(673\) −48.3707 −1.86455 −0.932277 0.361746i \(-0.882181\pi\)
−0.932277 + 0.361746i \(0.882181\pi\)
\(674\) −10.9561 −0.422013
\(675\) 1.00000 0.0384900
\(676\) −33.9287 −1.30495
\(677\) 26.6463 1.02410 0.512050 0.858956i \(-0.328886\pi\)
0.512050 + 0.858956i \(0.328886\pi\)
\(678\) −42.7436 −1.64156
\(679\) 8.24494 0.316412
\(680\) −25.8874 −0.992736
\(681\) 2.79542 0.107121
\(682\) 13.5324 0.518183
\(683\) 5.94514 0.227484 0.113742 0.993510i \(-0.463716\pi\)
0.113742 + 0.993510i \(0.463716\pi\)
\(684\) 19.5416 0.747192
\(685\) −9.40312 −0.359275
\(686\) 2.58874 0.0988385
\(687\) 9.95360 0.379754
\(688\) 36.9685 1.40941
\(689\) 20.4689 0.779805
\(690\) −0.179249 −0.00682388
\(691\) 7.72867 0.294012 0.147006 0.989136i \(-0.453036\pi\)
0.147006 + 0.989136i \(0.453036\pi\)
\(692\) 95.0156 3.61195
\(693\) 1.00000 0.0379869
\(694\) −40.4258 −1.53454
\(695\) −22.4934 −0.853225
\(696\) −4.91887 −0.186449
\(697\) −8.57923 −0.324961
\(698\) −5.80802 −0.219837
\(699\) −2.77612 −0.105003
\(700\) −4.70156 −0.177702
\(701\) −4.70334 −0.177643 −0.0888213 0.996048i \(-0.528310\pi\)
−0.0888213 + 0.996048i \(0.528310\pi\)
\(702\) 6.22565 0.234972
\(703\) 33.0437 1.24627
\(704\) −4.70156 −0.177197
\(705\) −13.3532 −0.502910
\(706\) −31.0557 −1.16880
\(707\) −11.0354 −0.415031
\(708\) −21.0354 −0.790560
\(709\) 21.8822 0.821803 0.410901 0.911680i \(-0.365214\pi\)
0.410901 + 0.911680i \(0.365214\pi\)
\(710\) 11.4031 0.427952
\(711\) −4.40490 −0.165197
\(712\) −106.281 −3.98304
\(713\) −0.361956 −0.0135553
\(714\) −9.58237 −0.358611
\(715\) −2.40490 −0.0899381
\(716\) −27.9745 −1.04546
\(717\) −14.6034 −0.545375
\(718\) −63.8754 −2.38381
\(719\) −19.2875 −0.719302 −0.359651 0.933087i \(-0.617104\pi\)
−0.359651 + 0.933087i \(0.617104\pi\)
\(720\) −8.70156 −0.324288
\(721\) 2.84182 0.105835
\(722\) 4.46370 0.166122
\(723\) 10.5385 0.391930
\(724\) −26.0542 −0.968297
\(725\) 0.703336 0.0261212
\(726\) −2.58874 −0.0960771
\(727\) 35.4877 1.31616 0.658082 0.752946i \(-0.271368\pi\)
0.658082 + 0.752946i \(0.271368\pi\)
\(728\) −16.8190 −0.623353
\(729\) 1.00000 0.0370370
\(730\) −36.7935 −1.36179
\(731\) −15.7261 −0.581649
\(732\) 23.6069 0.872535
\(733\) 49.4163 1.82523 0.912615 0.408819i \(-0.134059\pi\)
0.912615 + 0.408819i \(0.134059\pi\)
\(734\) −57.6791 −2.12898
\(735\) −1.00000 −0.0368856
\(736\) 0.591240 0.0217934
\(737\) −4.72263 −0.173960
\(738\) −6.00000 −0.220863
\(739\) 18.1095 0.666168 0.333084 0.942897i \(-0.391911\pi\)
0.333084 + 0.942897i \(0.391911\pi\)
\(740\) −37.3777 −1.37403
\(741\) −9.99573 −0.367202
\(742\) −22.0337 −0.808882
\(743\) −45.0972 −1.65445 −0.827227 0.561868i \(-0.810083\pi\)
−0.827227 + 0.561868i \(0.810083\pi\)
\(744\) −36.5587 −1.34031
\(745\) 13.9001 0.509260
\(746\) −35.3075 −1.29270
\(747\) 5.56308 0.203542
\(748\) 17.4031 0.636321
\(749\) 15.3567 0.561122
\(750\) 2.58874 0.0945273
\(751\) 47.9495 1.74970 0.874851 0.484391i \(-0.160959\pi\)
0.874851 + 0.484391i \(0.160959\pi\)
\(752\) 116.193 4.23714
\(753\) −19.3904 −0.706625
\(754\) 4.37872 0.159464
\(755\) −2.95183 −0.107428
\(756\) −4.70156 −0.170994
\(757\) 13.8158 0.502145 0.251073 0.967968i \(-0.419217\pi\)
0.251073 + 0.967968i \(0.419217\pi\)
\(758\) −36.7563 −1.33505
\(759\) 0.0692417 0.00251331
\(760\) 29.0684 1.05442
\(761\) 12.2221 0.443051 0.221525 0.975155i \(-0.428896\pi\)
0.221525 + 0.975155i \(0.428896\pi\)
\(762\) 0.643276 0.0233034
\(763\) −12.8597 −0.465554
\(764\) 121.754 4.40492
\(765\) 3.70156 0.133830
\(766\) 26.2094 0.946983
\(767\) 10.7598 0.388516
\(768\) −22.1047 −0.797634
\(769\) 29.3013 1.05663 0.528316 0.849048i \(-0.322823\pi\)
0.528316 + 0.849048i \(0.322823\pi\)
\(770\) 2.58874 0.0932916
\(771\) 2.71771 0.0978760
\(772\) −6.18706 −0.222677
\(773\) 43.2356 1.55508 0.777539 0.628835i \(-0.216468\pi\)
0.777539 + 0.628835i \(0.216468\pi\)
\(774\) −10.9982 −0.395323
\(775\) 5.22742 0.187775
\(776\) 57.6621 2.06995
\(777\) −7.95005 −0.285207
\(778\) 54.1931 1.94292
\(779\) 9.63344 0.345154
\(780\) 11.3068 0.404848
\(781\) −4.40490 −0.157620
\(782\) −0.663500 −0.0237267
\(783\) 0.703336 0.0251352
\(784\) 8.70156 0.310770
\(785\) −5.15463 −0.183977
\(786\) −32.6642 −1.16509
\(787\) −20.1489 −0.718230 −0.359115 0.933293i \(-0.616921\pi\)
−0.359115 + 0.933293i \(0.616921\pi\)
\(788\) −20.8849 −0.743993
\(789\) −14.4548 −0.514606
\(790\) −11.4031 −0.405705
\(791\) −16.5114 −0.587076
\(792\) 6.99364 0.248508
\(793\) −12.0752 −0.428801
\(794\) 63.5998 2.25707
\(795\) 8.51136 0.301867
\(796\) −121.043 −4.29027
\(797\) −7.08676 −0.251026 −0.125513 0.992092i \(-0.540058\pi\)
−0.125513 + 0.992092i \(0.540058\pi\)
\(798\) 10.7598 0.380894
\(799\) −49.4276 −1.74862
\(800\) −8.53879 −0.301892
\(801\) 15.1968 0.536951
\(802\) 99.4542 3.51185
\(803\) 14.2129 0.501563
\(804\) 22.2037 0.783065
\(805\) −0.0692417 −0.00244045
\(806\) 32.5441 1.14632
\(807\) −17.2677 −0.607850
\(808\) −77.1779 −2.71511
\(809\) −12.5391 −0.440852 −0.220426 0.975404i \(-0.570745\pi\)
−0.220426 + 0.975404i \(0.570745\pi\)
\(810\) 2.58874 0.0909590
\(811\) −8.27697 −0.290644 −0.145322 0.989384i \(-0.546422\pi\)
−0.145322 + 0.989384i \(0.546422\pi\)
\(812\) −3.30678 −0.116045
\(813\) 15.7051 0.550802
\(814\) 20.5806 0.721350
\(815\) −2.32128 −0.0813109
\(816\) −32.2094 −1.12755
\(817\) 17.6585 0.617791
\(818\) 3.04817 0.106577
\(819\) 2.40490 0.0840339
\(820\) −10.8970 −0.380538
\(821\) 50.1133 1.74897 0.874483 0.485056i \(-0.161201\pi\)
0.874483 + 0.485056i \(0.161201\pi\)
\(822\) −24.3422 −0.849032
\(823\) −52.3851 −1.82603 −0.913014 0.407927i \(-0.866252\pi\)
−0.913014 + 0.407927i \(0.866252\pi\)
\(824\) 19.8746 0.692366
\(825\) −1.00000 −0.0348155
\(826\) −11.5824 −0.403002
\(827\) 27.7003 0.963234 0.481617 0.876382i \(-0.340050\pi\)
0.481617 + 0.876382i \(0.340050\pi\)
\(828\) −0.325544 −0.0113134
\(829\) −7.51970 −0.261170 −0.130585 0.991437i \(-0.541686\pi\)
−0.130585 + 0.991437i \(0.541686\pi\)
\(830\) 14.4014 0.499878
\(831\) 15.9837 0.554469
\(832\) −11.3068 −0.391992
\(833\) −3.70156 −0.128252
\(834\) −58.2296 −2.01633
\(835\) −17.7581 −0.614544
\(836\) −19.5416 −0.675861
\(837\) 5.22742 0.180686
\(838\) 96.4524 3.33189
\(839\) −41.0385 −1.41681 −0.708403 0.705809i \(-0.750584\pi\)
−0.708403 + 0.705809i \(0.750584\pi\)
\(840\) −6.99364 −0.241303
\(841\) −28.5053 −0.982942
\(842\) −8.03722 −0.276981
\(843\) −5.50302 −0.189534
\(844\) −113.839 −3.91848
\(845\) 7.21647 0.248254
\(846\) −34.5679 −1.18847
\(847\) −1.00000 −0.0343604
\(848\) −74.0621 −2.54330
\(849\) −8.09208 −0.277720
\(850\) 9.58237 0.328673
\(851\) −0.550475 −0.0188700
\(852\) 20.7099 0.709509
\(853\) 42.8693 1.46782 0.733909 0.679248i \(-0.237694\pi\)
0.733909 + 0.679248i \(0.237694\pi\)
\(854\) 12.9982 0.444790
\(855\) −4.15641 −0.142146
\(856\) 107.399 3.67083
\(857\) 18.7354 0.639988 0.319994 0.947420i \(-0.396319\pi\)
0.319994 + 0.947420i \(0.396319\pi\)
\(858\) −6.22565 −0.212540
\(859\) −47.5569 −1.62262 −0.811310 0.584616i \(-0.801245\pi\)
−0.811310 + 0.584616i \(0.801245\pi\)
\(860\) −19.9745 −0.681126
\(861\) −2.31773 −0.0789881
\(862\) 35.0649 1.19431
\(863\) −49.6177 −1.68901 −0.844503 0.535551i \(-0.820104\pi\)
−0.844503 + 0.535551i \(0.820104\pi\)
\(864\) −8.53879 −0.290496
\(865\) −20.2094 −0.687139
\(866\) 87.4744 2.97250
\(867\) −3.29844 −0.112021
\(868\) −24.5771 −0.834200
\(869\) 4.40490 0.149426
\(870\) 1.82075 0.0617293
\(871\) −11.3574 −0.384832
\(872\) −89.9364 −3.04563
\(873\) −8.24494 −0.279049
\(874\) 0.745030 0.0252010
\(875\) 1.00000 0.0338062
\(876\) −66.8229 −2.25774
\(877\) 29.0962 0.982510 0.491255 0.871016i \(-0.336538\pi\)
0.491255 + 0.871016i \(0.336538\pi\)
\(878\) −30.0429 −1.01390
\(879\) 6.51490 0.219742
\(880\) 8.70156 0.293330
\(881\) 10.8454 0.365390 0.182695 0.983170i \(-0.441518\pi\)
0.182695 + 0.983170i \(0.441518\pi\)
\(882\) −2.58874 −0.0871673
\(883\) 12.4000 0.417293 0.208646 0.977991i \(-0.433094\pi\)
0.208646 + 0.977991i \(0.433094\pi\)
\(884\) 41.8527 1.40766
\(885\) 4.47414 0.150397
\(886\) 64.0004 2.15014
\(887\) 19.7823 0.664224 0.332112 0.943240i \(-0.392239\pi\)
0.332112 + 0.943240i \(0.392239\pi\)
\(888\) −55.5998 −1.86581
\(889\) 0.248490 0.00833410
\(890\) 39.3404 1.31869
\(891\) −1.00000 −0.0335013
\(892\) 39.4319 1.32028
\(893\) 55.5012 1.85728
\(894\) 35.9837 1.20348
\(895\) 5.95005 0.198888
\(896\) −4.90647 −0.163914
\(897\) 0.166519 0.00555992
\(898\) −81.6164 −2.72358
\(899\) 3.67663 0.122623
\(900\) 4.70156 0.156719
\(901\) 31.5053 1.04959
\(902\) 6.00000 0.199778
\(903\) −4.24849 −0.141381
\(904\) −115.474 −3.84062
\(905\) 5.54161 0.184209
\(906\) −7.64150 −0.253872
\(907\) −9.96278 −0.330809 −0.165404 0.986226i \(-0.552893\pi\)
−0.165404 + 0.986226i \(0.552893\pi\)
\(908\) 13.1428 0.436160
\(909\) 11.0354 0.366023
\(910\) 6.22565 0.206378
\(911\) 57.6869 1.91125 0.955627 0.294580i \(-0.0951799\pi\)
0.955627 + 0.294580i \(0.0951799\pi\)
\(912\) 36.1672 1.19762
\(913\) −5.56308 −0.184111
\(914\) 34.6564 1.14633
\(915\) −5.02107 −0.165991
\(916\) 46.7975 1.54623
\(917\) −12.6178 −0.416677
\(918\) 9.58237 0.316265
\(919\) 19.2033 0.633460 0.316730 0.948516i \(-0.397415\pi\)
0.316730 + 0.948516i \(0.397415\pi\)
\(920\) −0.484251 −0.0159653
\(921\) −22.5679 −0.743637
\(922\) −10.0202 −0.329998
\(923\) −10.5933 −0.348684
\(924\) 4.70156 0.154670
\(925\) 7.95005 0.261396
\(926\) −75.7163 −2.48819
\(927\) −2.84182 −0.0933376
\(928\) −6.00564 −0.197145
\(929\) 39.9422 1.31046 0.655231 0.755428i \(-0.272571\pi\)
0.655231 + 0.755428i \(0.272571\pi\)
\(930\) 13.5324 0.443746
\(931\) 4.15641 0.136221
\(932\) −13.0521 −0.427536
\(933\) 0.0513177 0.00168007
\(934\) −36.9026 −1.20749
\(935\) −3.70156 −0.121054
\(936\) 16.8190 0.549745
\(937\) 29.7826 0.972954 0.486477 0.873693i \(-0.338282\pi\)
0.486477 + 0.873693i \(0.338282\pi\)
\(938\) 12.2256 0.399182
\(939\) −3.44224 −0.112333
\(940\) −62.7808 −2.04768
\(941\) 26.5208 0.864554 0.432277 0.901741i \(-0.357710\pi\)
0.432277 + 0.901741i \(0.357710\pi\)
\(942\) −13.3440 −0.434771
\(943\) −0.160484 −0.00522607
\(944\) −38.9320 −1.26713
\(945\) 1.00000 0.0325300
\(946\) 10.9982 0.357583
\(947\) −34.6659 −1.12649 −0.563245 0.826290i \(-0.690447\pi\)
−0.563245 + 0.826290i \(0.690447\pi\)
\(948\) −20.7099 −0.672626
\(949\) 34.1806 1.10955
\(950\) −10.7598 −0.349096
\(951\) 31.6582 1.02659
\(952\) −25.8874 −0.839015
\(953\) −31.9451 −1.03480 −0.517402 0.855742i \(-0.673101\pi\)
−0.517402 + 0.855742i \(0.673101\pi\)
\(954\) 22.0337 0.713366
\(955\) −25.8966 −0.837993
\(956\) −68.6590 −2.22059
\(957\) −0.703336 −0.0227356
\(958\) 83.4450 2.69599
\(959\) −9.40312 −0.303643
\(960\) −4.70156 −0.151742
\(961\) −3.67405 −0.118518
\(962\) 49.4942 1.59576
\(963\) −15.3567 −0.494864
\(964\) 49.5472 1.59581
\(965\) 1.31596 0.0423622
\(966\) −0.179249 −0.00576723
\(967\) 5.97781 0.192233 0.0961167 0.995370i \(-0.469358\pi\)
0.0961167 + 0.995370i \(0.469358\pi\)
\(968\) −6.99364 −0.224784
\(969\) −15.3852 −0.494244
\(970\) −21.3440 −0.685314
\(971\) −6.61617 −0.212323 −0.106161 0.994349i \(-0.533856\pi\)
−0.106161 + 0.994349i \(0.533856\pi\)
\(972\) 4.70156 0.150803
\(973\) −22.4934 −0.721106
\(974\) −13.6525 −0.437456
\(975\) −2.40490 −0.0770184
\(976\) 43.6911 1.39852
\(977\) 14.9276 0.477577 0.238788 0.971072i \(-0.423250\pi\)
0.238788 + 0.971072i \(0.423250\pi\)
\(978\) −6.00918 −0.192152
\(979\) −15.1968 −0.485691
\(980\) −4.70156 −0.150186
\(981\) 12.8597 0.410580
\(982\) −92.3267 −2.94626
\(983\) −15.6774 −0.500030 −0.250015 0.968242i \(-0.580436\pi\)
−0.250015 + 0.968242i \(0.580436\pi\)
\(984\) −16.2094 −0.516736
\(985\) 4.44212 0.141538
\(986\) 6.73962 0.214633
\(987\) −13.3532 −0.425036
\(988\) −46.9956 −1.49513
\(989\) −0.294173 −0.00935415
\(990\) −2.58874 −0.0822755
\(991\) −33.8504 −1.07529 −0.537647 0.843170i \(-0.680687\pi\)
−0.537647 + 0.843170i \(0.680687\pi\)
\(992\) −44.6359 −1.41719
\(993\) −3.55953 −0.112958
\(994\) 11.4031 0.361685
\(995\) 25.7453 0.816182
\(996\) 26.1552 0.828758
\(997\) −6.45130 −0.204315 −0.102157 0.994768i \(-0.532575\pi\)
−0.102157 + 0.994768i \(0.532575\pi\)
\(998\) 100.982 3.19654
\(999\) 7.95005 0.251529
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 1155.2.a.u.1.1 4
3.2 odd 2 3465.2.a.bl.1.4 4
5.4 even 2 5775.2.a.bz.1.4 4
7.6 odd 2 8085.2.a.bn.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.a.u.1.1 4 1.1 even 1 trivial
3465.2.a.bl.1.4 4 3.2 odd 2
5775.2.a.bz.1.4 4 5.4 even 2
8085.2.a.bn.1.1 4 7.6 odd 2