Properties

Label 4730.2.a.bf.1.4
Level 4730
Weight 2
Character 4730.1
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 13
CM no
Inner twists 1

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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: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.30046\)
Character \(\chi\) = 4730.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.30046 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.30046 q^{6} +3.42310 q^{7} +1.00000 q^{8} -1.30880 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.30046 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.30046 q^{6} +3.42310 q^{7} +1.00000 q^{8} -1.30880 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.30046 q^{12} +2.16503 q^{13} +3.42310 q^{14} +1.30046 q^{15} +1.00000 q^{16} +6.19311 q^{17} -1.30880 q^{18} +4.97577 q^{19} -1.00000 q^{20} -4.45162 q^{21} +1.00000 q^{22} -4.95191 q^{23} -1.30046 q^{24} +1.00000 q^{25} +2.16503 q^{26} +5.60343 q^{27} +3.42310 q^{28} -8.41999 q^{29} +1.30046 q^{30} +7.34665 q^{31} +1.00000 q^{32} -1.30046 q^{33} +6.19311 q^{34} -3.42310 q^{35} -1.30880 q^{36} -4.92683 q^{37} +4.97577 q^{38} -2.81554 q^{39} -1.00000 q^{40} -6.22563 q^{41} -4.45162 q^{42} +1.00000 q^{43} +1.00000 q^{44} +1.30880 q^{45} -4.95191 q^{46} +4.34083 q^{47} -1.30046 q^{48} +4.71763 q^{49} +1.00000 q^{50} -8.05390 q^{51} +2.16503 q^{52} +0.623093 q^{53} +5.60343 q^{54} -1.00000 q^{55} +3.42310 q^{56} -6.47081 q^{57} -8.41999 q^{58} +2.83303 q^{59} +1.30046 q^{60} -4.29500 q^{61} +7.34665 q^{62} -4.48014 q^{63} +1.00000 q^{64} -2.16503 q^{65} -1.30046 q^{66} +11.2990 q^{67} +6.19311 q^{68} +6.43978 q^{69} -3.42310 q^{70} -5.78909 q^{71} -1.30880 q^{72} +10.7001 q^{73} -4.92683 q^{74} -1.30046 q^{75} +4.97577 q^{76} +3.42310 q^{77} -2.81554 q^{78} -9.34359 q^{79} -1.00000 q^{80} -3.36066 q^{81} -6.22563 q^{82} -7.05958 q^{83} -4.45162 q^{84} -6.19311 q^{85} +1.00000 q^{86} +10.9499 q^{87} +1.00000 q^{88} +8.33954 q^{89} +1.30880 q^{90} +7.41112 q^{91} -4.95191 q^{92} -9.55405 q^{93} +4.34083 q^{94} -4.97577 q^{95} -1.30046 q^{96} +2.72798 q^{97} +4.71763 q^{98} -1.30880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13q + 13q^{2} + 13q^{4} - 13q^{5} + 7q^{7} + 13q^{8} + 25q^{9} + O(q^{10}) \) \( 13q + 13q^{2} + 13q^{4} - 13q^{5} + 7q^{7} + 13q^{8} + 25q^{9} - 13q^{10} + 13q^{11} + 11q^{13} + 7q^{14} + 13q^{16} - 2q^{17} + 25q^{18} + 7q^{19} - 13q^{20} + 12q^{21} + 13q^{22} + 12q^{23} + 13q^{25} + 11q^{26} - 15q^{27} + 7q^{28} + 14q^{29} + 20q^{31} + 13q^{32} - 2q^{34} - 7q^{35} + 25q^{36} + 17q^{37} + 7q^{38} - 4q^{39} - 13q^{40} + 9q^{41} + 12q^{42} + 13q^{43} + 13q^{44} - 25q^{45} + 12q^{46} - 9q^{47} + 30q^{49} + 13q^{50} - 3q^{51} + 11q^{52} + 22q^{53} - 15q^{54} - 13q^{55} + 7q^{56} + 17q^{57} + 14q^{58} + 19q^{59} + 2q^{61} + 20q^{62} + 12q^{63} + 13q^{64} - 11q^{65} + 9q^{67} - 2q^{68} - 6q^{69} - 7q^{70} + 6q^{71} + 25q^{72} + 7q^{73} + 17q^{74} + 7q^{76} + 7q^{77} - 4q^{78} + 50q^{79} - 13q^{80} + 85q^{81} + 9q^{82} + q^{83} + 12q^{84} + 2q^{85} + 13q^{86} - 21q^{87} + 13q^{88} + 5q^{89} - 25q^{90} + 5q^{91} + 12q^{92} + 3q^{93} - 9q^{94} - 7q^{95} + 20q^{97} + 30q^{98} + 25q^{99} + O(q^{100}) \)

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
\(3\) −1.30046 −0.750823 −0.375411 0.926858i \(-0.622499\pi\)
−0.375411 + 0.926858i \(0.622499\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.30046 −0.530912
\(7\) 3.42310 1.29381 0.646905 0.762570i \(-0.276063\pi\)
0.646905 + 0.762570i \(0.276063\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.30880 −0.436265
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) −1.30046 −0.375411
\(13\) 2.16503 0.600471 0.300236 0.953865i \(-0.402935\pi\)
0.300236 + 0.953865i \(0.402935\pi\)
\(14\) 3.42310 0.914863
\(15\) 1.30046 0.335778
\(16\) 1.00000 0.250000
\(17\) 6.19311 1.50205 0.751024 0.660275i \(-0.229560\pi\)
0.751024 + 0.660275i \(0.229560\pi\)
\(18\) −1.30880 −0.308486
\(19\) 4.97577 1.14152 0.570760 0.821117i \(-0.306649\pi\)
0.570760 + 0.821117i \(0.306649\pi\)
\(20\) −1.00000 −0.223607
\(21\) −4.45162 −0.971422
\(22\) 1.00000 0.213201
\(23\) −4.95191 −1.03254 −0.516272 0.856424i \(-0.672681\pi\)
−0.516272 + 0.856424i \(0.672681\pi\)
\(24\) −1.30046 −0.265456
\(25\) 1.00000 0.200000
\(26\) 2.16503 0.424597
\(27\) 5.60343 1.07838
\(28\) 3.42310 0.646905
\(29\) −8.41999 −1.56355 −0.781777 0.623559i \(-0.785686\pi\)
−0.781777 + 0.623559i \(0.785686\pi\)
\(30\) 1.30046 0.237431
\(31\) 7.34665 1.31950 0.659749 0.751486i \(-0.270663\pi\)
0.659749 + 0.751486i \(0.270663\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.30046 −0.226382
\(34\) 6.19311 1.06211
\(35\) −3.42310 −0.578610
\(36\) −1.30880 −0.218133
\(37\) −4.92683 −0.809967 −0.404983 0.914324i \(-0.632723\pi\)
−0.404983 + 0.914324i \(0.632723\pi\)
\(38\) 4.97577 0.807177
\(39\) −2.81554 −0.450847
\(40\) −1.00000 −0.158114
\(41\) −6.22563 −0.972280 −0.486140 0.873881i \(-0.661595\pi\)
−0.486140 + 0.873881i \(0.661595\pi\)
\(42\) −4.45162 −0.686899
\(43\) 1.00000 0.152499
\(44\) 1.00000 0.150756
\(45\) 1.30880 0.195104
\(46\) −4.95191 −0.730120
\(47\) 4.34083 0.633176 0.316588 0.948563i \(-0.397463\pi\)
0.316588 + 0.948563i \(0.397463\pi\)
\(48\) −1.30046 −0.187706
\(49\) 4.71763 0.673947
\(50\) 1.00000 0.141421
\(51\) −8.05390 −1.12777
\(52\) 2.16503 0.300236
\(53\) 0.623093 0.0855884 0.0427942 0.999084i \(-0.486374\pi\)
0.0427942 + 0.999084i \(0.486374\pi\)
\(54\) 5.60343 0.762530
\(55\) −1.00000 −0.134840
\(56\) 3.42310 0.457431
\(57\) −6.47081 −0.857079
\(58\) −8.41999 −1.10560
\(59\) 2.83303 0.368829 0.184415 0.982849i \(-0.440961\pi\)
0.184415 + 0.982849i \(0.440961\pi\)
\(60\) 1.30046 0.167889
\(61\) −4.29500 −0.549919 −0.274959 0.961456i \(-0.588664\pi\)
−0.274959 + 0.961456i \(0.588664\pi\)
\(62\) 7.34665 0.933026
\(63\) −4.48014 −0.564445
\(64\) 1.00000 0.125000
\(65\) −2.16503 −0.268539
\(66\) −1.30046 −0.160076
\(67\) 11.2990 1.38039 0.690194 0.723624i \(-0.257525\pi\)
0.690194 + 0.723624i \(0.257525\pi\)
\(68\) 6.19311 0.751024
\(69\) 6.43978 0.775258
\(70\) −3.42310 −0.409139
\(71\) −5.78909 −0.687039 −0.343520 0.939146i \(-0.611619\pi\)
−0.343520 + 0.939146i \(0.611619\pi\)
\(72\) −1.30880 −0.154243
\(73\) 10.7001 1.25235 0.626174 0.779684i \(-0.284620\pi\)
0.626174 + 0.779684i \(0.284620\pi\)
\(74\) −4.92683 −0.572733
\(75\) −1.30046 −0.150165
\(76\) 4.97577 0.570760
\(77\) 3.42310 0.390099
\(78\) −2.81554 −0.318797
\(79\) −9.34359 −1.05124 −0.525618 0.850721i \(-0.676166\pi\)
−0.525618 + 0.850721i \(0.676166\pi\)
\(80\) −1.00000 −0.111803
\(81\) −3.36066 −0.373407
\(82\) −6.22563 −0.687506
\(83\) −7.05958 −0.774890 −0.387445 0.921893i \(-0.626642\pi\)
−0.387445 + 0.921893i \(0.626642\pi\)
\(84\) −4.45162 −0.485711
\(85\) −6.19311 −0.671737
\(86\) 1.00000 0.107833
\(87\) 10.9499 1.17395
\(88\) 1.00000 0.106600
\(89\) 8.33954 0.883990 0.441995 0.897018i \(-0.354271\pi\)
0.441995 + 0.897018i \(0.354271\pi\)
\(90\) 1.30880 0.137959
\(91\) 7.41112 0.776896
\(92\) −4.95191 −0.516272
\(93\) −9.55405 −0.990708
\(94\) 4.34083 0.447723
\(95\) −4.97577 −0.510503
\(96\) −1.30046 −0.132728
\(97\) 2.72798 0.276984 0.138492 0.990364i \(-0.455774\pi\)
0.138492 + 0.990364i \(0.455774\pi\)
\(98\) 4.71763 0.476552
\(99\) −1.30880 −0.131539
\(100\) 1.00000 0.100000
\(101\) 12.4002 1.23386 0.616932 0.787016i \(-0.288375\pi\)
0.616932 + 0.787016i \(0.288375\pi\)
\(102\) −8.05390 −0.797455
\(103\) 6.32565 0.623285 0.311643 0.950199i \(-0.399121\pi\)
0.311643 + 0.950199i \(0.399121\pi\)
\(104\) 2.16503 0.212299
\(105\) 4.45162 0.434433
\(106\) 0.623093 0.0605201
\(107\) 3.29446 0.318488 0.159244 0.987239i \(-0.449094\pi\)
0.159244 + 0.987239i \(0.449094\pi\)
\(108\) 5.60343 0.539190
\(109\) 3.61019 0.345794 0.172897 0.984940i \(-0.444687\pi\)
0.172897 + 0.984940i \(0.444687\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 6.40716 0.608141
\(112\) 3.42310 0.323453
\(113\) −12.0417 −1.13279 −0.566394 0.824135i \(-0.691662\pi\)
−0.566394 + 0.824135i \(0.691662\pi\)
\(114\) −6.47081 −0.606047
\(115\) 4.95191 0.461768
\(116\) −8.41999 −0.781777
\(117\) −2.83358 −0.261965
\(118\) 2.83303 0.260802
\(119\) 21.1996 1.94337
\(120\) 1.30046 0.118715
\(121\) 1.00000 0.0909091
\(122\) −4.29500 −0.388851
\(123\) 8.09620 0.730010
\(124\) 7.34665 0.659749
\(125\) −1.00000 −0.0894427
\(126\) −4.48014 −0.399123
\(127\) 15.6355 1.38743 0.693715 0.720249i \(-0.255973\pi\)
0.693715 + 0.720249i \(0.255973\pi\)
\(128\) 1.00000 0.0883883
\(129\) −1.30046 −0.114499
\(130\) −2.16503 −0.189886
\(131\) −8.49576 −0.742278 −0.371139 0.928577i \(-0.621033\pi\)
−0.371139 + 0.928577i \(0.621033\pi\)
\(132\) −1.30046 −0.113191
\(133\) 17.0326 1.47691
\(134\) 11.2990 0.976082
\(135\) −5.60343 −0.482266
\(136\) 6.19311 0.531054
\(137\) −12.2600 −1.04744 −0.523720 0.851891i \(-0.675456\pi\)
−0.523720 + 0.851891i \(0.675456\pi\)
\(138\) 6.43978 0.548190
\(139\) 4.33409 0.367613 0.183806 0.982962i \(-0.441158\pi\)
0.183806 + 0.982962i \(0.441158\pi\)
\(140\) −3.42310 −0.289305
\(141\) −5.64509 −0.475403
\(142\) −5.78909 −0.485810
\(143\) 2.16503 0.181049
\(144\) −1.30880 −0.109066
\(145\) 8.41999 0.699242
\(146\) 10.7001 0.885543
\(147\) −6.13510 −0.506014
\(148\) −4.92683 −0.404983
\(149\) 2.58758 0.211983 0.105991 0.994367i \(-0.466198\pi\)
0.105991 + 0.994367i \(0.466198\pi\)
\(150\) −1.30046 −0.106182
\(151\) 6.91199 0.562490 0.281245 0.959636i \(-0.409253\pi\)
0.281245 + 0.959636i \(0.409253\pi\)
\(152\) 4.97577 0.403588
\(153\) −8.10551 −0.655292
\(154\) 3.42310 0.275841
\(155\) −7.34665 −0.590097
\(156\) −2.81554 −0.225424
\(157\) 14.8219 1.18292 0.591459 0.806335i \(-0.298552\pi\)
0.591459 + 0.806335i \(0.298552\pi\)
\(158\) −9.34359 −0.743336
\(159\) −0.810309 −0.0642617
\(160\) −1.00000 −0.0790569
\(161\) −16.9509 −1.33592
\(162\) −3.36066 −0.264039
\(163\) −2.87721 −0.225360 −0.112680 0.993631i \(-0.535944\pi\)
−0.112680 + 0.993631i \(0.535944\pi\)
\(164\) −6.22563 −0.486140
\(165\) 1.30046 0.101241
\(166\) −7.05958 −0.547930
\(167\) 25.2030 1.95027 0.975134 0.221616i \(-0.0711332\pi\)
0.975134 + 0.221616i \(0.0711332\pi\)
\(168\) −4.45162 −0.343450
\(169\) −8.31264 −0.639434
\(170\) −6.19311 −0.474989
\(171\) −6.51227 −0.498006
\(172\) 1.00000 0.0762493
\(173\) 8.32115 0.632645 0.316323 0.948652i \(-0.397552\pi\)
0.316323 + 0.948652i \(0.397552\pi\)
\(174\) 10.9499 0.830109
\(175\) 3.42310 0.258762
\(176\) 1.00000 0.0753778
\(177\) −3.68425 −0.276925
\(178\) 8.33954 0.625075
\(179\) 16.8744 1.26125 0.630627 0.776086i \(-0.282798\pi\)
0.630627 + 0.776086i \(0.282798\pi\)
\(180\) 1.30880 0.0975519
\(181\) 3.36414 0.250055 0.125027 0.992153i \(-0.460098\pi\)
0.125027 + 0.992153i \(0.460098\pi\)
\(182\) 7.41112 0.549349
\(183\) 5.58549 0.412891
\(184\) −4.95191 −0.365060
\(185\) 4.92683 0.362228
\(186\) −9.55405 −0.700537
\(187\) 6.19311 0.452885
\(188\) 4.34083 0.316588
\(189\) 19.1811 1.39522
\(190\) −4.97577 −0.360980
\(191\) 13.3995 0.969556 0.484778 0.874637i \(-0.338900\pi\)
0.484778 + 0.874637i \(0.338900\pi\)
\(192\) −1.30046 −0.0938528
\(193\) 8.68042 0.624830 0.312415 0.949946i \(-0.398862\pi\)
0.312415 + 0.949946i \(0.398862\pi\)
\(194\) 2.72798 0.195857
\(195\) 2.81554 0.201625
\(196\) 4.71763 0.336973
\(197\) −2.92760 −0.208583 −0.104291 0.994547i \(-0.533257\pi\)
−0.104291 + 0.994547i \(0.533257\pi\)
\(198\) −1.30880 −0.0930121
\(199\) −7.46077 −0.528880 −0.264440 0.964402i \(-0.585187\pi\)
−0.264440 + 0.964402i \(0.585187\pi\)
\(200\) 1.00000 0.0707107
\(201\) −14.6939 −1.03643
\(202\) 12.4002 0.872474
\(203\) −28.8225 −2.02294
\(204\) −8.05390 −0.563886
\(205\) 6.22563 0.434817
\(206\) 6.32565 0.440729
\(207\) 6.48104 0.450464
\(208\) 2.16503 0.150118
\(209\) 4.97577 0.344181
\(210\) 4.45162 0.307191
\(211\) 9.23358 0.635666 0.317833 0.948147i \(-0.397045\pi\)
0.317833 + 0.948147i \(0.397045\pi\)
\(212\) 0.623093 0.0427942
\(213\) 7.52850 0.515845
\(214\) 3.29446 0.225205
\(215\) −1.00000 −0.0681994
\(216\) 5.60343 0.381265
\(217\) 25.1483 1.70718
\(218\) 3.61019 0.244513
\(219\) −13.9150 −0.940291
\(220\) −1.00000 −0.0674200
\(221\) 13.4083 0.901937
\(222\) 6.40716 0.430021
\(223\) −15.0062 −1.00489 −0.502444 0.864610i \(-0.667566\pi\)
−0.502444 + 0.864610i \(0.667566\pi\)
\(224\) 3.42310 0.228716
\(225\) −1.30880 −0.0872531
\(226\) −12.0417 −0.801002
\(227\) −9.38383 −0.622827 −0.311413 0.950275i \(-0.600802\pi\)
−0.311413 + 0.950275i \(0.600802\pi\)
\(228\) −6.47081 −0.428540
\(229\) 0.644040 0.0425593 0.0212797 0.999774i \(-0.493226\pi\)
0.0212797 + 0.999774i \(0.493226\pi\)
\(230\) 4.95191 0.326519
\(231\) −4.45162 −0.292895
\(232\) −8.41999 −0.552800
\(233\) −6.49014 −0.425183 −0.212592 0.977141i \(-0.568190\pi\)
−0.212592 + 0.977141i \(0.568190\pi\)
\(234\) −2.83358 −0.185237
\(235\) −4.34083 −0.283165
\(236\) 2.83303 0.184415
\(237\) 12.1510 0.789292
\(238\) 21.1996 1.37417
\(239\) 14.7664 0.955157 0.477578 0.878589i \(-0.341515\pi\)
0.477578 + 0.878589i \(0.341515\pi\)
\(240\) 1.30046 0.0839445
\(241\) 18.0201 1.16078 0.580388 0.814340i \(-0.302901\pi\)
0.580388 + 0.814340i \(0.302901\pi\)
\(242\) 1.00000 0.0642824
\(243\) −12.4399 −0.798018
\(244\) −4.29500 −0.274959
\(245\) −4.71763 −0.301398
\(246\) 8.09620 0.516195
\(247\) 10.7727 0.685450
\(248\) 7.34665 0.466513
\(249\) 9.18072 0.581805
\(250\) −1.00000 −0.0632456
\(251\) −31.1292 −1.96486 −0.982429 0.186636i \(-0.940241\pi\)
−0.982429 + 0.186636i \(0.940241\pi\)
\(252\) −4.48014 −0.282223
\(253\) −4.95191 −0.311324
\(254\) 15.6355 0.981062
\(255\) 8.05390 0.504355
\(256\) 1.00000 0.0625000
\(257\) −1.37282 −0.0856344 −0.0428172 0.999083i \(-0.513633\pi\)
−0.0428172 + 0.999083i \(0.513633\pi\)
\(258\) −1.30046 −0.0809633
\(259\) −16.8651 −1.04794
\(260\) −2.16503 −0.134269
\(261\) 11.0201 0.682124
\(262\) −8.49576 −0.524870
\(263\) 21.9517 1.35360 0.676801 0.736166i \(-0.263366\pi\)
0.676801 + 0.736166i \(0.263366\pi\)
\(264\) −1.30046 −0.0800380
\(265\) −0.623093 −0.0382763
\(266\) 17.0326 1.04433
\(267\) −10.8453 −0.663719
\(268\) 11.2990 0.690194
\(269\) −12.2234 −0.745276 −0.372638 0.927977i \(-0.621547\pi\)
−0.372638 + 0.927977i \(0.621547\pi\)
\(270\) −5.60343 −0.341014
\(271\) 9.73963 0.591640 0.295820 0.955244i \(-0.404407\pi\)
0.295820 + 0.955244i \(0.404407\pi\)
\(272\) 6.19311 0.375512
\(273\) −9.63789 −0.583311
\(274\) −12.2600 −0.740651
\(275\) 1.00000 0.0603023
\(276\) 6.43978 0.387629
\(277\) −16.9494 −1.01839 −0.509195 0.860651i \(-0.670057\pi\)
−0.509195 + 0.860651i \(0.670057\pi\)
\(278\) 4.33409 0.259942
\(279\) −9.61527 −0.575651
\(280\) −3.42310 −0.204569
\(281\) 6.37151 0.380092 0.190046 0.981775i \(-0.439136\pi\)
0.190046 + 0.981775i \(0.439136\pi\)
\(282\) −5.64509 −0.336160
\(283\) −19.9176 −1.18398 −0.591990 0.805945i \(-0.701658\pi\)
−0.591990 + 0.805945i \(0.701658\pi\)
\(284\) −5.78909 −0.343520
\(285\) 6.47081 0.383298
\(286\) 2.16503 0.128021
\(287\) −21.3110 −1.25795
\(288\) −1.30880 −0.0771216
\(289\) 21.3546 1.25615
\(290\) 8.41999 0.494439
\(291\) −3.54763 −0.207966
\(292\) 10.7001 0.626174
\(293\) 13.4631 0.786525 0.393263 0.919426i \(-0.371346\pi\)
0.393263 + 0.919426i \(0.371346\pi\)
\(294\) −6.13510 −0.357806
\(295\) −2.83303 −0.164945
\(296\) −4.92683 −0.286366
\(297\) 5.60343 0.325144
\(298\) 2.58758 0.149895
\(299\) −10.7210 −0.620014
\(300\) −1.30046 −0.0750823
\(301\) 3.42310 0.197304
\(302\) 6.91199 0.397740
\(303\) −16.1260 −0.926413
\(304\) 4.97577 0.285380
\(305\) 4.29500 0.245931
\(306\) −8.10551 −0.463361
\(307\) 7.49575 0.427805 0.213902 0.976855i \(-0.431383\pi\)
0.213902 + 0.976855i \(0.431383\pi\)
\(308\) 3.42310 0.195049
\(309\) −8.22628 −0.467977
\(310\) −7.34665 −0.417262
\(311\) 3.71197 0.210486 0.105243 0.994447i \(-0.466438\pi\)
0.105243 + 0.994447i \(0.466438\pi\)
\(312\) −2.81554 −0.159399
\(313\) −24.8649 −1.40545 −0.702724 0.711462i \(-0.748033\pi\)
−0.702724 + 0.711462i \(0.748033\pi\)
\(314\) 14.8219 0.836449
\(315\) 4.48014 0.252427
\(316\) −9.34359 −0.525618
\(317\) −30.2711 −1.70020 −0.850098 0.526624i \(-0.823457\pi\)
−0.850098 + 0.526624i \(0.823457\pi\)
\(318\) −0.810309 −0.0454399
\(319\) −8.41999 −0.471429
\(320\) −1.00000 −0.0559017
\(321\) −4.28433 −0.239128
\(322\) −16.9509 −0.944637
\(323\) 30.8155 1.71462
\(324\) −3.36066 −0.186703
\(325\) 2.16503 0.120094
\(326\) −2.87721 −0.159354
\(327\) −4.69492 −0.259630
\(328\) −6.22563 −0.343753
\(329\) 14.8591 0.819210
\(330\) 1.30046 0.0715881
\(331\) −28.0973 −1.54437 −0.772183 0.635400i \(-0.780835\pi\)
−0.772183 + 0.635400i \(0.780835\pi\)
\(332\) −7.05958 −0.387445
\(333\) 6.44822 0.353360
\(334\) 25.2030 1.37905
\(335\) −11.2990 −0.617329
\(336\) −4.45162 −0.242856
\(337\) 21.0302 1.14559 0.572795 0.819699i \(-0.305859\pi\)
0.572795 + 0.819699i \(0.305859\pi\)
\(338\) −8.31264 −0.452148
\(339\) 15.6598 0.850523
\(340\) −6.19311 −0.335868
\(341\) 7.34665 0.397843
\(342\) −6.51227 −0.352143
\(343\) −7.81279 −0.421851
\(344\) 1.00000 0.0539164
\(345\) −6.43978 −0.346706
\(346\) 8.32115 0.447348
\(347\) 22.0487 1.18364 0.591818 0.806071i \(-0.298410\pi\)
0.591818 + 0.806071i \(0.298410\pi\)
\(348\) 10.9499 0.586976
\(349\) −2.14153 −0.114634 −0.0573168 0.998356i \(-0.518255\pi\)
−0.0573168 + 0.998356i \(0.518255\pi\)
\(350\) 3.42310 0.182973
\(351\) 12.1316 0.647537
\(352\) 1.00000 0.0533002
\(353\) −4.04206 −0.215137 −0.107569 0.994198i \(-0.534306\pi\)
−0.107569 + 0.994198i \(0.534306\pi\)
\(354\) −3.68425 −0.195816
\(355\) 5.78909 0.307253
\(356\) 8.33954 0.441995
\(357\) −27.5693 −1.45912
\(358\) 16.8744 0.891842
\(359\) 22.3355 1.17882 0.589411 0.807833i \(-0.299360\pi\)
0.589411 + 0.807833i \(0.299360\pi\)
\(360\) 1.30880 0.0689796
\(361\) 5.75831 0.303069
\(362\) 3.36414 0.176815
\(363\) −1.30046 −0.0682566
\(364\) 7.41112 0.388448
\(365\) −10.7001 −0.560067
\(366\) 5.58549 0.291958
\(367\) −1.19297 −0.0622726 −0.0311363 0.999515i \(-0.509913\pi\)
−0.0311363 + 0.999515i \(0.509913\pi\)
\(368\) −4.95191 −0.258136
\(369\) 8.14808 0.424172
\(370\) 4.92683 0.256134
\(371\) 2.13291 0.110735
\(372\) −9.55405 −0.495354
\(373\) −10.6679 −0.552362 −0.276181 0.961106i \(-0.589069\pi\)
−0.276181 + 0.961106i \(0.589069\pi\)
\(374\) 6.19311 0.320238
\(375\) 1.30046 0.0671556
\(376\) 4.34083 0.223861
\(377\) −18.2295 −0.938869
\(378\) 19.1811 0.986570
\(379\) −12.0989 −0.621479 −0.310740 0.950495i \(-0.600577\pi\)
−0.310740 + 0.950495i \(0.600577\pi\)
\(380\) −4.97577 −0.255252
\(381\) −20.3335 −1.04171
\(382\) 13.3995 0.685580
\(383\) 9.76694 0.499067 0.249534 0.968366i \(-0.419723\pi\)
0.249534 + 0.968366i \(0.419723\pi\)
\(384\) −1.30046 −0.0663640
\(385\) −3.42310 −0.174457
\(386\) 8.68042 0.441822
\(387\) −1.30880 −0.0665299
\(388\) 2.72798 0.138492
\(389\) 27.6691 1.40288 0.701439 0.712729i \(-0.252541\pi\)
0.701439 + 0.712729i \(0.252541\pi\)
\(390\) 2.81554 0.142570
\(391\) −30.6677 −1.55093
\(392\) 4.71763 0.238276
\(393\) 11.0484 0.557319
\(394\) −2.92760 −0.147490
\(395\) 9.34359 0.470127
\(396\) −1.30880 −0.0657695
\(397\) −5.32288 −0.267148 −0.133574 0.991039i \(-0.542645\pi\)
−0.133574 + 0.991039i \(0.542645\pi\)
\(398\) −7.46077 −0.373974
\(399\) −22.1502 −1.10890
\(400\) 1.00000 0.0500000
\(401\) −24.3895 −1.21795 −0.608976 0.793189i \(-0.708419\pi\)
−0.608976 + 0.793189i \(0.708419\pi\)
\(402\) −14.6939 −0.732865
\(403\) 15.9057 0.792320
\(404\) 12.4002 0.616932
\(405\) 3.36066 0.166993
\(406\) −28.8225 −1.43044
\(407\) −4.92683 −0.244214
\(408\) −8.05390 −0.398728
\(409\) 15.8080 0.781655 0.390828 0.920464i \(-0.372189\pi\)
0.390828 + 0.920464i \(0.372189\pi\)
\(410\) 6.22563 0.307462
\(411\) 15.9436 0.786441
\(412\) 6.32565 0.311643
\(413\) 9.69775 0.477195
\(414\) 6.48104 0.318526
\(415\) 7.05958 0.346541
\(416\) 2.16503 0.106149
\(417\) −5.63633 −0.276012
\(418\) 4.97577 0.243373
\(419\) −22.0577 −1.07759 −0.538795 0.842437i \(-0.681120\pi\)
−0.538795 + 0.842437i \(0.681120\pi\)
\(420\) 4.45162 0.217217
\(421\) −1.98468 −0.0967272 −0.0483636 0.998830i \(-0.515401\pi\)
−0.0483636 + 0.998830i \(0.515401\pi\)
\(422\) 9.23358 0.449484
\(423\) −5.68127 −0.276233
\(424\) 0.623093 0.0302601
\(425\) 6.19311 0.300410
\(426\) 7.52850 0.364757
\(427\) −14.7022 −0.711491
\(428\) 3.29446 0.159244
\(429\) −2.81554 −0.135936
\(430\) −1.00000 −0.0482243
\(431\) 8.17853 0.393946 0.196973 0.980409i \(-0.436889\pi\)
0.196973 + 0.980409i \(0.436889\pi\)
\(432\) 5.60343 0.269595
\(433\) 36.1824 1.73882 0.869409 0.494094i \(-0.164500\pi\)
0.869409 + 0.494094i \(0.164500\pi\)
\(434\) 25.1483 1.20716
\(435\) −10.9499 −0.525007
\(436\) 3.61019 0.172897
\(437\) −24.6396 −1.17867
\(438\) −13.9150 −0.664886
\(439\) −16.7014 −0.797113 −0.398557 0.917144i \(-0.630489\pi\)
−0.398557 + 0.917144i \(0.630489\pi\)
\(440\) −1.00000 −0.0476731
\(441\) −6.17441 −0.294020
\(442\) 13.4083 0.637766
\(443\) 5.77900 0.274569 0.137284 0.990532i \(-0.456163\pi\)
0.137284 + 0.990532i \(0.456163\pi\)
\(444\) 6.40716 0.304071
\(445\) −8.33954 −0.395332
\(446\) −15.0062 −0.710563
\(447\) −3.36505 −0.159162
\(448\) 3.42310 0.161726
\(449\) 20.4579 0.965469 0.482735 0.875767i \(-0.339644\pi\)
0.482735 + 0.875767i \(0.339644\pi\)
\(450\) −1.30880 −0.0616973
\(451\) −6.22563 −0.293153
\(452\) −12.0417 −0.566394
\(453\) −8.98878 −0.422330
\(454\) −9.38383 −0.440405
\(455\) −7.41112 −0.347439
\(456\) −6.47081 −0.303023
\(457\) 31.2053 1.45972 0.729862 0.683595i \(-0.239584\pi\)
0.729862 + 0.683595i \(0.239584\pi\)
\(458\) 0.644040 0.0300940
\(459\) 34.7026 1.61978
\(460\) 4.95191 0.230884
\(461\) 28.2199 1.31433 0.657165 0.753747i \(-0.271756\pi\)
0.657165 + 0.753747i \(0.271756\pi\)
\(462\) −4.45162 −0.207108
\(463\) 39.3122 1.82699 0.913497 0.406845i \(-0.133371\pi\)
0.913497 + 0.406845i \(0.133371\pi\)
\(464\) −8.41999 −0.390888
\(465\) 9.55405 0.443058
\(466\) −6.49014 −0.300650
\(467\) −11.9611 −0.553493 −0.276746 0.960943i \(-0.589256\pi\)
−0.276746 + 0.960943i \(0.589256\pi\)
\(468\) −2.83358 −0.130982
\(469\) 38.6775 1.78596
\(470\) −4.34083 −0.200228
\(471\) −19.2753 −0.888161
\(472\) 2.83303 0.130401
\(473\) 1.00000 0.0459800
\(474\) 12.1510 0.558114
\(475\) 4.97577 0.228304
\(476\) 21.1996 0.971684
\(477\) −0.815502 −0.0373393
\(478\) 14.7664 0.675398
\(479\) 25.2739 1.15479 0.577397 0.816464i \(-0.304069\pi\)
0.577397 + 0.816464i \(0.304069\pi\)
\(480\) 1.30046 0.0593577
\(481\) −10.6667 −0.486362
\(482\) 18.0201 0.820793
\(483\) 22.0440 1.00304
\(484\) 1.00000 0.0454545
\(485\) −2.72798 −0.123871
\(486\) −12.4399 −0.564284
\(487\) 5.91495 0.268032 0.134016 0.990979i \(-0.457213\pi\)
0.134016 + 0.990979i \(0.457213\pi\)
\(488\) −4.29500 −0.194426
\(489\) 3.74170 0.169206
\(490\) −4.71763 −0.213121
\(491\) −28.8499 −1.30198 −0.650989 0.759087i \(-0.725646\pi\)
−0.650989 + 0.759087i \(0.725646\pi\)
\(492\) 8.09620 0.365005
\(493\) −52.1459 −2.34853
\(494\) 10.7727 0.484687
\(495\) 1.30880 0.0588260
\(496\) 7.34665 0.329874
\(497\) −19.8167 −0.888899
\(498\) 9.18072 0.411398
\(499\) 11.3045 0.506059 0.253030 0.967459i \(-0.418573\pi\)
0.253030 + 0.967459i \(0.418573\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −32.7756 −1.46431
\(502\) −31.1292 −1.38936
\(503\) −38.4606 −1.71487 −0.857437 0.514589i \(-0.827945\pi\)
−0.857437 + 0.514589i \(0.827945\pi\)
\(504\) −4.48014 −0.199561
\(505\) −12.4002 −0.551801
\(506\) −4.95191 −0.220139
\(507\) 10.8103 0.480102
\(508\) 15.6355 0.693715
\(509\) 14.8900 0.659986 0.329993 0.943983i \(-0.392954\pi\)
0.329993 + 0.943983i \(0.392954\pi\)
\(510\) 8.05390 0.356633
\(511\) 36.6274 1.62030
\(512\) 1.00000 0.0441942
\(513\) 27.8814 1.23099
\(514\) −1.37282 −0.0605526
\(515\) −6.32565 −0.278742
\(516\) −1.30046 −0.0572497
\(517\) 4.34083 0.190910
\(518\) −16.8651 −0.741008
\(519\) −10.8213 −0.475004
\(520\) −2.16503 −0.0949429
\(521\) 24.1955 1.06002 0.530012 0.847990i \(-0.322187\pi\)
0.530012 + 0.847990i \(0.322187\pi\)
\(522\) 11.0201 0.482335
\(523\) 20.6699 0.903834 0.451917 0.892060i \(-0.350740\pi\)
0.451917 + 0.892060i \(0.350740\pi\)
\(524\) −8.49576 −0.371139
\(525\) −4.45162 −0.194284
\(526\) 21.9517 0.957141
\(527\) 45.4986 1.98195
\(528\) −1.30046 −0.0565954
\(529\) 1.52143 0.0661491
\(530\) −0.623093 −0.0270654
\(531\) −3.70786 −0.160907
\(532\) 17.0326 0.738456
\(533\) −13.4787 −0.583826
\(534\) −10.8453 −0.469320
\(535\) −3.29446 −0.142432
\(536\) 11.2990 0.488041
\(537\) −21.9446 −0.946979
\(538\) −12.2234 −0.526990
\(539\) 4.71763 0.203203
\(540\) −5.60343 −0.241133
\(541\) 3.27057 0.140613 0.0703063 0.997525i \(-0.477602\pi\)
0.0703063 + 0.997525i \(0.477602\pi\)
\(542\) 9.73963 0.418353
\(543\) −4.37494 −0.187747
\(544\) 6.19311 0.265527
\(545\) −3.61019 −0.154644
\(546\) −9.63789 −0.412463
\(547\) −3.76828 −0.161120 −0.0805600 0.996750i \(-0.525671\pi\)
−0.0805600 + 0.996750i \(0.525671\pi\)
\(548\) −12.2600 −0.523720
\(549\) 5.62128 0.239910
\(550\) 1.00000 0.0426401
\(551\) −41.8960 −1.78483
\(552\) 6.43978 0.274095
\(553\) −31.9841 −1.36010
\(554\) −16.9494 −0.720110
\(555\) −6.40716 −0.271969
\(556\) 4.33409 0.183806
\(557\) −35.9041 −1.52131 −0.760653 0.649158i \(-0.775121\pi\)
−0.760653 + 0.649158i \(0.775121\pi\)
\(558\) −9.61527 −0.407047
\(559\) 2.16503 0.0915710
\(560\) −3.42310 −0.144652
\(561\) −8.05390 −0.340036
\(562\) 6.37151 0.268766
\(563\) −30.6715 −1.29265 −0.646325 0.763062i \(-0.723695\pi\)
−0.646325 + 0.763062i \(0.723695\pi\)
\(564\) −5.64509 −0.237701
\(565\) 12.0417 0.506598
\(566\) −19.9176 −0.837200
\(567\) −11.5039 −0.483118
\(568\) −5.78909 −0.242905
\(569\) −19.9792 −0.837570 −0.418785 0.908085i \(-0.637544\pi\)
−0.418785 + 0.908085i \(0.637544\pi\)
\(570\) 6.47081 0.271032
\(571\) −12.3359 −0.516241 −0.258121 0.966113i \(-0.583103\pi\)
−0.258121 + 0.966113i \(0.583103\pi\)
\(572\) 2.16503 0.0905245
\(573\) −17.4256 −0.727965
\(574\) −21.3110 −0.889502
\(575\) −4.95191 −0.206509
\(576\) −1.30880 −0.0545332
\(577\) −23.3094 −0.970385 −0.485192 0.874407i \(-0.661250\pi\)
−0.485192 + 0.874407i \(0.661250\pi\)
\(578\) 21.3546 0.888232
\(579\) −11.2886 −0.469137
\(580\) 8.41999 0.349621
\(581\) −24.1657 −1.00256
\(582\) −3.54763 −0.147054
\(583\) 0.623093 0.0258059
\(584\) 10.7001 0.442772
\(585\) 2.83358 0.117154
\(586\) 13.4631 0.556157
\(587\) 8.90757 0.367655 0.183827 0.982959i \(-0.441151\pi\)
0.183827 + 0.982959i \(0.441151\pi\)
\(588\) −6.13510 −0.253007
\(589\) 36.5553 1.50623
\(590\) −2.83303 −0.116634
\(591\) 3.80723 0.156609
\(592\) −4.92683 −0.202492
\(593\) −43.9580 −1.80514 −0.902570 0.430544i \(-0.858322\pi\)
−0.902570 + 0.430544i \(0.858322\pi\)
\(594\) 5.60343 0.229912
\(595\) −21.1996 −0.869100
\(596\) 2.58758 0.105991
\(597\) 9.70245 0.397095
\(598\) −10.7210 −0.438416
\(599\) 9.49400 0.387915 0.193957 0.981010i \(-0.437868\pi\)
0.193957 + 0.981010i \(0.437868\pi\)
\(600\) −1.30046 −0.0530912
\(601\) −5.61247 −0.228938 −0.114469 0.993427i \(-0.536517\pi\)
−0.114469 + 0.993427i \(0.536517\pi\)
\(602\) 3.42310 0.139515
\(603\) −14.7881 −0.602216
\(604\) 6.91199 0.281245
\(605\) −1.00000 −0.0406558
\(606\) −16.1260 −0.655073
\(607\) −36.3459 −1.47524 −0.737618 0.675219i \(-0.764049\pi\)
−0.737618 + 0.675219i \(0.764049\pi\)
\(608\) 4.97577 0.201794
\(609\) 37.4826 1.51887
\(610\) 4.29500 0.173900
\(611\) 9.39803 0.380204
\(612\) −8.10551 −0.327646
\(613\) −16.1489 −0.652247 −0.326124 0.945327i \(-0.605743\pi\)
−0.326124 + 0.945327i \(0.605743\pi\)
\(614\) 7.49575 0.302504
\(615\) −8.09620 −0.326470
\(616\) 3.42310 0.137921
\(617\) 3.11745 0.125504 0.0627518 0.998029i \(-0.480012\pi\)
0.0627518 + 0.998029i \(0.480012\pi\)
\(618\) −8.22628 −0.330909
\(619\) −11.3967 −0.458072 −0.229036 0.973418i \(-0.573557\pi\)
−0.229036 + 0.973418i \(0.573557\pi\)
\(620\) −7.34665 −0.295049
\(621\) −27.7477 −1.11348
\(622\) 3.71197 0.148836
\(623\) 28.5471 1.14372
\(624\) −2.81554 −0.112712
\(625\) 1.00000 0.0400000
\(626\) −24.8649 −0.993802
\(627\) −6.47081 −0.258419
\(628\) 14.8219 0.591459
\(629\) −30.5124 −1.21661
\(630\) 4.48014 0.178493
\(631\) −30.4536 −1.21234 −0.606169 0.795336i \(-0.707294\pi\)
−0.606169 + 0.795336i \(0.707294\pi\)
\(632\) −9.34359 −0.371668
\(633\) −12.0079 −0.477272
\(634\) −30.2711 −1.20222
\(635\) −15.6355 −0.620478
\(636\) −0.810309 −0.0321309
\(637\) 10.2138 0.404686
\(638\) −8.41999 −0.333351
\(639\) 7.57675 0.299731
\(640\) −1.00000 −0.0395285
\(641\) −0.916790 −0.0362110 −0.0181055 0.999836i \(-0.505763\pi\)
−0.0181055 + 0.999836i \(0.505763\pi\)
\(642\) −4.28433 −0.169089
\(643\) −40.7833 −1.60833 −0.804167 0.594403i \(-0.797388\pi\)
−0.804167 + 0.594403i \(0.797388\pi\)
\(644\) −16.9509 −0.667959
\(645\) 1.30046 0.0512057
\(646\) 30.8155 1.21242
\(647\) −44.1766 −1.73676 −0.868380 0.495900i \(-0.834838\pi\)
−0.868380 + 0.495900i \(0.834838\pi\)
\(648\) −3.36066 −0.132019
\(649\) 2.83303 0.111206
\(650\) 2.16503 0.0849195
\(651\) −32.7045 −1.28179
\(652\) −2.87721 −0.112680
\(653\) −8.78419 −0.343752 −0.171876 0.985119i \(-0.554983\pi\)
−0.171876 + 0.985119i \(0.554983\pi\)
\(654\) −4.69492 −0.183586
\(655\) 8.49576 0.331957
\(656\) −6.22563 −0.243070
\(657\) −14.0042 −0.546356
\(658\) 14.8591 0.579269
\(659\) −38.3196 −1.49272 −0.746361 0.665542i \(-0.768201\pi\)
−0.746361 + 0.665542i \(0.768201\pi\)
\(660\) 1.30046 0.0506204
\(661\) 39.8144 1.54860 0.774301 0.632818i \(-0.218102\pi\)
0.774301 + 0.632818i \(0.218102\pi\)
\(662\) −28.0973 −1.09203
\(663\) −17.4369 −0.677195
\(664\) −7.05958 −0.273965
\(665\) −17.0326 −0.660495
\(666\) 6.44822 0.249864
\(667\) 41.6951 1.61444
\(668\) 25.2030 0.975134
\(669\) 19.5150 0.754493
\(670\) −11.2990 −0.436517
\(671\) −4.29500 −0.165807
\(672\) −4.45162 −0.171725
\(673\) −32.1996 −1.24120 −0.620602 0.784126i \(-0.713112\pi\)
−0.620602 + 0.784126i \(0.713112\pi\)
\(674\) 21.0302 0.810055
\(675\) 5.60343 0.215676
\(676\) −8.31264 −0.319717
\(677\) 29.3103 1.12649 0.563244 0.826291i \(-0.309553\pi\)
0.563244 + 0.826291i \(0.309553\pi\)
\(678\) 15.6598 0.601410
\(679\) 9.33814 0.358365
\(680\) −6.19311 −0.237495
\(681\) 12.2033 0.467632
\(682\) 7.34665 0.281318
\(683\) −49.4801 −1.89330 −0.946652 0.322259i \(-0.895558\pi\)
−0.946652 + 0.322259i \(0.895558\pi\)
\(684\) −6.51227 −0.249003
\(685\) 12.2600 0.468429
\(686\) −7.81279 −0.298294
\(687\) −0.837550 −0.0319545
\(688\) 1.00000 0.0381246
\(689\) 1.34902 0.0513934
\(690\) −6.43978 −0.245158
\(691\) 41.1902 1.56695 0.783474 0.621424i \(-0.213446\pi\)
0.783474 + 0.621424i \(0.213446\pi\)
\(692\) 8.32115 0.316323
\(693\) −4.48014 −0.170187
\(694\) 22.0487 0.836958
\(695\) −4.33409 −0.164401
\(696\) 10.9499 0.415054
\(697\) −38.5560 −1.46041
\(698\) −2.14153 −0.0810582
\(699\) 8.44018 0.319237
\(700\) 3.42310 0.129381
\(701\) 9.87256 0.372882 0.186441 0.982466i \(-0.440305\pi\)
0.186441 + 0.982466i \(0.440305\pi\)
\(702\) 12.1316 0.457878
\(703\) −24.5148 −0.924593
\(704\) 1.00000 0.0376889
\(705\) 5.64509 0.212606
\(706\) −4.04206 −0.152125
\(707\) 42.4471 1.59639
\(708\) −3.68425 −0.138463
\(709\) −4.94667 −0.185776 −0.0928880 0.995677i \(-0.529610\pi\)
−0.0928880 + 0.995677i \(0.529610\pi\)
\(710\) 5.78909 0.217261
\(711\) 12.2289 0.458618
\(712\) 8.33954 0.312537
\(713\) −36.3800 −1.36244
\(714\) −27.5693 −1.03176
\(715\) −2.16503 −0.0809675
\(716\) 16.8744 0.630627
\(717\) −19.2031 −0.717153
\(718\) 22.3355 0.833553
\(719\) 35.1117 1.30944 0.654722 0.755870i \(-0.272786\pi\)
0.654722 + 0.755870i \(0.272786\pi\)
\(720\) 1.30880 0.0487760
\(721\) 21.6534 0.806413
\(722\) 5.75831 0.214302
\(723\) −23.4345 −0.871537
\(724\) 3.36414 0.125027
\(725\) −8.41999 −0.312711
\(726\) −1.30046 −0.0482647
\(727\) −39.3046 −1.45773 −0.728864 0.684659i \(-0.759951\pi\)
−0.728864 + 0.684659i \(0.759951\pi\)
\(728\) 7.41112 0.274674
\(729\) 26.2596 0.972577
\(730\) −10.7001 −0.396027
\(731\) 6.19311 0.229060
\(732\) 5.58549 0.206446
\(733\) −24.9663 −0.922151 −0.461075 0.887361i \(-0.652536\pi\)
−0.461075 + 0.887361i \(0.652536\pi\)
\(734\) −1.19297 −0.0440334
\(735\) 6.13510 0.226297
\(736\) −4.95191 −0.182530
\(737\) 11.2990 0.416203
\(738\) 8.14808 0.299935
\(739\) 20.2667 0.745522 0.372761 0.927927i \(-0.378411\pi\)
0.372761 + 0.927927i \(0.378411\pi\)
\(740\) 4.92683 0.181114
\(741\) −14.0095 −0.514652
\(742\) 2.13291 0.0783016
\(743\) −7.96430 −0.292182 −0.146091 0.989271i \(-0.546669\pi\)
−0.146091 + 0.989271i \(0.546669\pi\)
\(744\) −9.55405 −0.350268
\(745\) −2.58758 −0.0948016
\(746\) −10.6679 −0.390579
\(747\) 9.23956 0.338058
\(748\) 6.19311 0.226442
\(749\) 11.2773 0.412063
\(750\) 1.30046 0.0474862
\(751\) −21.5523 −0.786456 −0.393228 0.919441i \(-0.628642\pi\)
−0.393228 + 0.919441i \(0.628642\pi\)
\(752\) 4.34083 0.158294
\(753\) 40.4824 1.47526
\(754\) −18.2295 −0.663881
\(755\) −6.91199 −0.251553
\(756\) 19.1811 0.697610
\(757\) −10.2568 −0.372788 −0.186394 0.982475i \(-0.559680\pi\)
−0.186394 + 0.982475i \(0.559680\pi\)
\(758\) −12.0989 −0.439452
\(759\) 6.43978 0.233749
\(760\) −4.97577 −0.180490
\(761\) −21.6999 −0.786621 −0.393310 0.919406i \(-0.628670\pi\)
−0.393310 + 0.919406i \(0.628670\pi\)
\(762\) −20.3335 −0.736603
\(763\) 12.3581 0.447392
\(764\) 13.3995 0.484778
\(765\) 8.10551 0.293055
\(766\) 9.76694 0.352894
\(767\) 6.13360 0.221471
\(768\) −1.30046 −0.0469264
\(769\) 39.5504 1.42622 0.713112 0.701050i \(-0.247285\pi\)
0.713112 + 0.701050i \(0.247285\pi\)
\(770\) −3.42310 −0.123360
\(771\) 1.78531 0.0642962
\(772\) 8.68042 0.312415
\(773\) 5.35245 0.192514 0.0962572 0.995356i \(-0.469313\pi\)
0.0962572 + 0.995356i \(0.469313\pi\)
\(774\) −1.30880 −0.0470437
\(775\) 7.34665 0.263899
\(776\) 2.72798 0.0979286
\(777\) 21.9324 0.786820
\(778\) 27.6691 0.991985
\(779\) −30.9773 −1.10988
\(780\) 2.81554 0.100813
\(781\) −5.78909 −0.207150
\(782\) −30.6677 −1.09668
\(783\) −47.1808 −1.68611
\(784\) 4.71763 0.168487
\(785\) −14.8219 −0.529017
\(786\) 11.0484 0.394084
\(787\) −48.9484 −1.74482 −0.872411 0.488773i \(-0.837444\pi\)
−0.872411 + 0.488773i \(0.837444\pi\)
\(788\) −2.92760 −0.104291
\(789\) −28.5474 −1.01631
\(790\) 9.34359 0.332430
\(791\) −41.2200 −1.46561
\(792\) −1.30880 −0.0465061
\(793\) −9.29881 −0.330210
\(794\) −5.32288 −0.188902
\(795\) 0.810309 0.0287387
\(796\) −7.46077 −0.264440
\(797\) −21.4499 −0.759795 −0.379897 0.925029i \(-0.624041\pi\)
−0.379897 + 0.925029i \(0.624041\pi\)
\(798\) −22.1502 −0.784110
\(799\) 26.8832 0.951061
\(800\) 1.00000 0.0353553
\(801\) −10.9148 −0.385654
\(802\) −24.3895 −0.861222
\(803\) 10.7001 0.377597
\(804\) −14.6939 −0.518214
\(805\) 16.9509 0.597441
\(806\) 15.9057 0.560255
\(807\) 15.8961 0.559570
\(808\) 12.4002 0.436237
\(809\) 24.9438 0.876976 0.438488 0.898737i \(-0.355514\pi\)
0.438488 + 0.898737i \(0.355514\pi\)
\(810\) 3.36066 0.118082
\(811\) 12.0392 0.422754 0.211377 0.977405i \(-0.432205\pi\)
0.211377 + 0.977405i \(0.432205\pi\)
\(812\) −28.8225 −1.01147
\(813\) −12.6660 −0.444217
\(814\) −4.92683 −0.172685
\(815\) 2.87721 0.100784
\(816\) −8.05390 −0.281943
\(817\) 4.97577 0.174080
\(818\) 15.8080 0.552714
\(819\) −9.69965 −0.338933
\(820\) 6.22563 0.217408
\(821\) −32.9154 −1.14875 −0.574377 0.818591i \(-0.694756\pi\)
−0.574377 + 0.818591i \(0.694756\pi\)
\(822\) 15.9436 0.556098
\(823\) 32.5040 1.13302 0.566508 0.824056i \(-0.308294\pi\)
0.566508 + 0.824056i \(0.308294\pi\)
\(824\) 6.32565 0.220365
\(825\) −1.30046 −0.0452763
\(826\) 9.69775 0.337428
\(827\) −47.7989 −1.66213 −0.831065 0.556176i \(-0.812268\pi\)
−0.831065 + 0.556176i \(0.812268\pi\)
\(828\) 6.48104 0.225232
\(829\) −19.9280 −0.692128 −0.346064 0.938211i \(-0.612482\pi\)
−0.346064 + 0.938211i \(0.612482\pi\)
\(830\) 7.05958 0.245042
\(831\) 22.0420 0.764629
\(832\) 2.16503 0.0750589
\(833\) 29.2168 1.01230
\(834\) −5.63633 −0.195170
\(835\) −25.2030 −0.872186
\(836\) 4.97577 0.172091
\(837\) 41.1664 1.42292
\(838\) −22.0577 −0.761971
\(839\) −40.7524 −1.40693 −0.703465 0.710730i \(-0.748365\pi\)
−0.703465 + 0.710730i \(0.748365\pi\)
\(840\) 4.45162 0.153595
\(841\) 41.8963 1.44470
\(842\) −1.98468 −0.0683965
\(843\) −8.28591 −0.285382
\(844\) 9.23358 0.317833
\(845\) 8.31264 0.285964
\(846\) −5.68127 −0.195326
\(847\) 3.42310 0.117619
\(848\) 0.623093 0.0213971
\(849\) 25.9021 0.888959
\(850\) 6.19311 0.212422
\(851\) 24.3972 0.836327
\(852\) 7.52850 0.257922
\(853\) 16.6264 0.569278 0.284639 0.958635i \(-0.408126\pi\)
0.284639 + 0.958635i \(0.408126\pi\)
\(854\) −14.7022 −0.503100
\(855\) 6.51227 0.222715
\(856\) 3.29446 0.112602
\(857\) 11.6808 0.399007 0.199504 0.979897i \(-0.436067\pi\)
0.199504 + 0.979897i \(0.436067\pi\)
\(858\) −2.81554 −0.0961210
\(859\) 9.63507 0.328744 0.164372 0.986398i \(-0.447440\pi\)
0.164372 + 0.986398i \(0.447440\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 27.7141 0.944495
\(862\) 8.17853 0.278562
\(863\) 13.0559 0.444427 0.222213 0.974998i \(-0.428672\pi\)
0.222213 + 0.974998i \(0.428672\pi\)
\(864\) 5.60343 0.190633
\(865\) −8.32115 −0.282928
\(866\) 36.1824 1.22953
\(867\) −27.7708 −0.943146
\(868\) 25.1483 0.853590
\(869\) −9.34359 −0.316960
\(870\) −10.9499 −0.371236
\(871\) 24.4626 0.828884
\(872\) 3.61019 0.122256
\(873\) −3.57037 −0.120839
\(874\) −24.6396 −0.833446
\(875\) −3.42310 −0.115722
\(876\) −13.9150 −0.470145
\(877\) −49.9901 −1.68805 −0.844023 0.536307i \(-0.819819\pi\)
−0.844023 + 0.536307i \(0.819819\pi\)
\(878\) −16.7014 −0.563644
\(879\) −17.5083 −0.590541
\(880\) −1.00000 −0.0337100
\(881\) −6.46920 −0.217953 −0.108976 0.994044i \(-0.534757\pi\)
−0.108976 + 0.994044i \(0.534757\pi\)
\(882\) −6.17441 −0.207903
\(883\) −4.04902 −0.136260 −0.0681302 0.997676i \(-0.521703\pi\)
−0.0681302 + 0.997676i \(0.521703\pi\)
\(884\) 13.4083 0.450969
\(885\) 3.68425 0.123845
\(886\) 5.77900 0.194149
\(887\) 21.8544 0.733798 0.366899 0.930261i \(-0.380419\pi\)
0.366899 + 0.930261i \(0.380419\pi\)
\(888\) 6.40716 0.215010
\(889\) 53.5221 1.79507
\(890\) −8.33954 −0.279542
\(891\) −3.36066 −0.112586
\(892\) −15.0062 −0.502444
\(893\) 21.5990 0.722783
\(894\) −3.36505 −0.112544
\(895\) −16.8744 −0.564050
\(896\) 3.42310 0.114358
\(897\) 13.9423 0.465520
\(898\) 20.4579 0.682690
\(899\) −61.8587 −2.06310
\(900\) −1.30880 −0.0436265
\(901\) 3.85888 0.128558
\(902\) −6.22563 −0.207291
\(903\) −4.45162 −0.148141
\(904\) −12.0417 −0.400501
\(905\) −3.36414 −0.111828
\(906\) −8.98878 −0.298632
\(907\) −51.6022 −1.71342 −0.856711 0.515797i \(-0.827496\pi\)
−0.856711 + 0.515797i \(0.827496\pi\)
\(908\) −9.38383 −0.311413
\(909\) −16.2293 −0.538292
\(910\) −7.41112 −0.245676
\(911\) −28.2551 −0.936132 −0.468066 0.883693i \(-0.655049\pi\)
−0.468066 + 0.883693i \(0.655049\pi\)
\(912\) −6.47081 −0.214270
\(913\) −7.05958 −0.233638
\(914\) 31.2053 1.03218
\(915\) −5.58549 −0.184651
\(916\) 0.644040 0.0212797
\(917\) −29.0818 −0.960367
\(918\) 34.7026 1.14536
\(919\) −7.76545 −0.256158 −0.128079 0.991764i \(-0.540881\pi\)
−0.128079 + 0.991764i \(0.540881\pi\)
\(920\) 4.95191 0.163260
\(921\) −9.74794 −0.321206
\(922\) 28.2199 0.929371
\(923\) −12.5336 −0.412547
\(924\) −4.45162 −0.146447
\(925\) −4.92683 −0.161993
\(926\) 39.3122 1.29188
\(927\) −8.27899 −0.271918
\(928\) −8.41999 −0.276400
\(929\) −5.13456 −0.168459 −0.0842297 0.996446i \(-0.526843\pi\)
−0.0842297 + 0.996446i \(0.526843\pi\)
\(930\) 9.55405 0.313290
\(931\) 23.4738 0.769324
\(932\) −6.49014 −0.212592
\(933\) −4.82727 −0.158038
\(934\) −11.9611 −0.391378
\(935\) −6.19311 −0.202536
\(936\) −2.83358 −0.0926186
\(937\) 51.9015 1.69555 0.847773 0.530359i \(-0.177943\pi\)
0.847773 + 0.530359i \(0.177943\pi\)
\(938\) 38.6775 1.26287
\(939\) 32.3359 1.05524
\(940\) −4.34083 −0.141582
\(941\) −0.710465 −0.0231605 −0.0115802 0.999933i \(-0.503686\pi\)
−0.0115802 + 0.999933i \(0.503686\pi\)
\(942\) −19.2753 −0.628025
\(943\) 30.8288 1.00392
\(944\) 2.83303 0.0922073
\(945\) −19.1811 −0.623962
\(946\) 1.00000 0.0325128
\(947\) −39.9473 −1.29811 −0.649057 0.760740i \(-0.724836\pi\)
−0.649057 + 0.760740i \(0.724836\pi\)
\(948\) 12.1510 0.394646
\(949\) 23.1660 0.751999
\(950\) 4.97577 0.161435
\(951\) 39.3665 1.27655
\(952\) 21.1996 0.687084
\(953\) −31.0993 −1.00740 −0.503702 0.863878i \(-0.668029\pi\)
−0.503702 + 0.863878i \(0.668029\pi\)
\(954\) −0.815502 −0.0264028
\(955\) −13.3995 −0.433599
\(956\) 14.7664 0.477578
\(957\) 10.9499 0.353960
\(958\) 25.2739 0.816563
\(959\) −41.9671 −1.35519
\(960\) 1.30046 0.0419723
\(961\) 22.9733 0.741074
\(962\) −10.6667 −0.343910
\(963\) −4.31178 −0.138945
\(964\) 18.0201 0.580388
\(965\) −8.68042 −0.279433
\(966\) 22.0440 0.709255
\(967\) 5.99406 0.192756 0.0963780 0.995345i \(-0.469274\pi\)
0.0963780 + 0.995345i \(0.469274\pi\)
\(968\) 1.00000 0.0321412
\(969\) −40.0744 −1.28737
\(970\) −2.72798 −0.0875900
\(971\) 1.26628 0.0406370 0.0203185 0.999794i \(-0.493532\pi\)
0.0203185 + 0.999794i \(0.493532\pi\)
\(972\) −12.4399 −0.399009
\(973\) 14.8360 0.475622
\(974\) 5.91495 0.189527
\(975\) −2.81554 −0.0901695
\(976\) −4.29500 −0.137480
\(977\) −21.1001 −0.675052 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(978\) 3.74170 0.119646
\(979\) 8.33954 0.266533
\(980\) −4.71763 −0.150699
\(981\) −4.72500 −0.150858
\(982\) −28.8499 −0.920638
\(983\) 16.1900 0.516382 0.258191 0.966094i \(-0.416874\pi\)
0.258191 + 0.966094i \(0.416874\pi\)
\(984\) 8.09620 0.258097
\(985\) 2.92760 0.0932810
\(986\) −52.1459 −1.66066
\(987\) −19.3237 −0.615081
\(988\) 10.7727 0.342725
\(989\) −4.95191 −0.157462
\(990\) 1.30880 0.0415963
\(991\) 21.8380 0.693707 0.346853 0.937919i \(-0.387250\pi\)
0.346853 + 0.937919i \(0.387250\pi\)
\(992\) 7.34665 0.233256
\(993\) 36.5395 1.15955
\(994\) −19.8167 −0.628546
\(995\) 7.46077 0.236522
\(996\) 9.18072 0.290902
\(997\) 50.9650 1.61408 0.807039 0.590498i \(-0.201069\pi\)
0.807039 + 0.590498i \(0.201069\pi\)
\(998\) 11.3045 0.357838
\(999\) −27.6072 −0.873452
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.bf.1.4 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.bf.1.4 13 1.1 even 1 trivial