Properties

Label 2667.2.a.j.1.7
Level $2667$
Weight $2$
Character 2667.1
Self dual yes
Analytic conductor $21.296$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2667 = 3 \cdot 7 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2667.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(21.2961022191\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: 7.7.118870813.1
Defining polynomial: \(x^{7} - 9 x^{5} - 3 x^{4} + 20 x^{3} + 7 x^{2} - 13 x - 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.301070\) of defining polynomial
Character \(\chi\) \(=\) 2667.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.09968 q^{2} +1.00000 q^{3} +2.40865 q^{4} -3.29054 q^{5} +2.09968 q^{6} +1.00000 q^{7} +0.858029 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.09968 q^{2} +1.00000 q^{3} +2.40865 q^{4} -3.29054 q^{5} +2.09968 q^{6} +1.00000 q^{7} +0.858029 q^{8} +1.00000 q^{9} -6.90907 q^{10} -3.62521 q^{11} +2.40865 q^{12} -2.16007 q^{13} +2.09968 q^{14} -3.29054 q^{15} -3.01571 q^{16} +2.19233 q^{17} +2.09968 q^{18} -6.66601 q^{19} -7.92575 q^{20} +1.00000 q^{21} -7.61177 q^{22} +2.36522 q^{23} +0.858029 q^{24} +5.82765 q^{25} -4.53544 q^{26} +1.00000 q^{27} +2.40865 q^{28} +2.06180 q^{29} -6.90907 q^{30} -2.19207 q^{31} -8.04808 q^{32} -3.62521 q^{33} +4.60319 q^{34} -3.29054 q^{35} +2.40865 q^{36} -10.1454 q^{37} -13.9965 q^{38} -2.16007 q^{39} -2.82338 q^{40} -0.647495 q^{41} +2.09968 q^{42} +3.67859 q^{43} -8.73185 q^{44} -3.29054 q^{45} +4.96620 q^{46} -8.59064 q^{47} -3.01571 q^{48} +1.00000 q^{49} +12.2362 q^{50} +2.19233 q^{51} -5.20284 q^{52} +2.84924 q^{53} +2.09968 q^{54} +11.9289 q^{55} +0.858029 q^{56} -6.66601 q^{57} +4.32912 q^{58} -0.592789 q^{59} -7.92575 q^{60} -13.5269 q^{61} -4.60265 q^{62} +1.00000 q^{63} -10.8670 q^{64} +7.10778 q^{65} -7.61177 q^{66} +0.664083 q^{67} +5.28055 q^{68} +2.36522 q^{69} -6.90907 q^{70} -5.65049 q^{71} +0.858029 q^{72} -3.24624 q^{73} -21.3021 q^{74} +5.82765 q^{75} -16.0561 q^{76} -3.62521 q^{77} -4.53544 q^{78} +4.01101 q^{79} +9.92332 q^{80} +1.00000 q^{81} -1.35953 q^{82} -3.40033 q^{83} +2.40865 q^{84} -7.21395 q^{85} +7.72385 q^{86} +2.06180 q^{87} -3.11054 q^{88} +6.31252 q^{89} -6.90907 q^{90} -2.16007 q^{91} +5.69698 q^{92} -2.19207 q^{93} -18.0376 q^{94} +21.9348 q^{95} -8.04808 q^{96} -0.0689323 q^{97} +2.09968 q^{98} -3.62521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 2q^{2} + 7q^{3} + 4q^{4} - 8q^{5} - 2q^{6} + 7q^{7} - 9q^{8} + 7q^{9} - 3q^{11} + 4q^{12} - 23q^{13} - 2q^{14} - 8q^{15} + 2q^{16} + 3q^{17} - 2q^{18} - 9q^{19} - 9q^{20} + 7q^{21} - 19q^{22} + 12q^{23} - 9q^{24} + 3q^{25} + 18q^{26} + 7q^{27} + 4q^{28} - 9q^{29} - 33q^{31} + 10q^{32} - 3q^{33} - 2q^{34} - 8q^{35} + 4q^{36} - 33q^{37} - 3q^{38} - 23q^{39} - 9q^{40} - 3q^{41} - 2q^{42} - 9q^{43} + 2q^{44} - 8q^{45} - 32q^{46} + 11q^{47} + 2q^{48} + 7q^{49} + 29q^{50} + 3q^{51} - 21q^{52} + q^{53} - 2q^{54} - 16q^{55} - 9q^{56} - 9q^{57} - 5q^{58} - 30q^{59} - 9q^{60} - 19q^{61} + 3q^{62} + 7q^{63} - 21q^{64} + 14q^{65} - 19q^{66} - 30q^{67} + 24q^{68} + 12q^{69} + 8q^{71} - 9q^{72} - 20q^{73} - 9q^{74} + 3q^{75} - 42q^{76} - 3q^{77} + 18q^{78} + 8q^{79} + 12q^{80} + 7q^{81} + 10q^{82} - 34q^{83} + 4q^{84} - 28q^{85} + 24q^{86} - 9q^{87} - q^{88} - 12q^{89} - 23q^{91} + 60q^{92} - 33q^{93} - 3q^{94} + 12q^{95} + 10q^{96} + 7q^{97} - 2q^{98} - 3q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.09968 1.48470 0.742348 0.670014i \(-0.233712\pi\)
0.742348 + 0.670014i \(0.233712\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.40865 1.20432
\(5\) −3.29054 −1.47157 −0.735787 0.677213i \(-0.763188\pi\)
−0.735787 + 0.677213i \(0.763188\pi\)
\(6\) 2.09968 0.857190
\(7\) 1.00000 0.377964
\(8\) 0.858029 0.303359
\(9\) 1.00000 0.333333
\(10\) −6.90907 −2.18484
\(11\) −3.62521 −1.09304 −0.546521 0.837445i \(-0.684048\pi\)
−0.546521 + 0.837445i \(0.684048\pi\)
\(12\) 2.40865 0.695317
\(13\) −2.16007 −0.599095 −0.299547 0.954081i \(-0.596836\pi\)
−0.299547 + 0.954081i \(0.596836\pi\)
\(14\) 2.09968 0.561163
\(15\) −3.29054 −0.849614
\(16\) −3.01571 −0.753928
\(17\) 2.19233 0.531718 0.265859 0.964012i \(-0.414344\pi\)
0.265859 + 0.964012i \(0.414344\pi\)
\(18\) 2.09968 0.494899
\(19\) −6.66601 −1.52929 −0.764643 0.644454i \(-0.777085\pi\)
−0.764643 + 0.644454i \(0.777085\pi\)
\(20\) −7.92575 −1.77225
\(21\) 1.00000 0.218218
\(22\) −7.61177 −1.62284
\(23\) 2.36522 0.493183 0.246591 0.969120i \(-0.420689\pi\)
0.246591 + 0.969120i \(0.420689\pi\)
\(24\) 0.858029 0.175145
\(25\) 5.82765 1.16553
\(26\) −4.53544 −0.889474
\(27\) 1.00000 0.192450
\(28\) 2.40865 0.455192
\(29\) 2.06180 0.382867 0.191433 0.981506i \(-0.438686\pi\)
0.191433 + 0.981506i \(0.438686\pi\)
\(30\) −6.90907 −1.26142
\(31\) −2.19207 −0.393708 −0.196854 0.980433i \(-0.563072\pi\)
−0.196854 + 0.980433i \(0.563072\pi\)
\(32\) −8.04808 −1.42271
\(33\) −3.62521 −0.631068
\(34\) 4.60319 0.789440
\(35\) −3.29054 −0.556203
\(36\) 2.40865 0.401441
\(37\) −10.1454 −1.66789 −0.833947 0.551845i \(-0.813924\pi\)
−0.833947 + 0.551845i \(0.813924\pi\)
\(38\) −13.9965 −2.27053
\(39\) −2.16007 −0.345887
\(40\) −2.82338 −0.446416
\(41\) −0.647495 −0.101122 −0.0505608 0.998721i \(-0.516101\pi\)
−0.0505608 + 0.998721i \(0.516101\pi\)
\(42\) 2.09968 0.323987
\(43\) 3.67859 0.560979 0.280490 0.959857i \(-0.409503\pi\)
0.280490 + 0.959857i \(0.409503\pi\)
\(44\) −8.73185 −1.31638
\(45\) −3.29054 −0.490525
\(46\) 4.96620 0.732227
\(47\) −8.59064 −1.25307 −0.626537 0.779392i \(-0.715528\pi\)
−0.626537 + 0.779392i \(0.715528\pi\)
\(48\) −3.01571 −0.435280
\(49\) 1.00000 0.142857
\(50\) 12.2362 1.73046
\(51\) 2.19233 0.306988
\(52\) −5.20284 −0.721504
\(53\) 2.84924 0.391373 0.195686 0.980667i \(-0.437307\pi\)
0.195686 + 0.980667i \(0.437307\pi\)
\(54\) 2.09968 0.285730
\(55\) 11.9289 1.60849
\(56\) 0.858029 0.114659
\(57\) −6.66601 −0.882934
\(58\) 4.32912 0.568441
\(59\) −0.592789 −0.0771745 −0.0385873 0.999255i \(-0.512286\pi\)
−0.0385873 + 0.999255i \(0.512286\pi\)
\(60\) −7.92575 −1.02321
\(61\) −13.5269 −1.73195 −0.865973 0.500091i \(-0.833300\pi\)
−0.865973 + 0.500091i \(0.833300\pi\)
\(62\) −4.60265 −0.584537
\(63\) 1.00000 0.125988
\(64\) −10.8670 −1.35837
\(65\) 7.10778 0.881612
\(66\) −7.61177 −0.936945
\(67\) 0.664083 0.0811306 0.0405653 0.999177i \(-0.487084\pi\)
0.0405653 + 0.999177i \(0.487084\pi\)
\(68\) 5.28055 0.640361
\(69\) 2.36522 0.284739
\(70\) −6.90907 −0.825792
\(71\) −5.65049 −0.670589 −0.335295 0.942113i \(-0.608836\pi\)
−0.335295 + 0.942113i \(0.608836\pi\)
\(72\) 0.858029 0.101120
\(73\) −3.24624 −0.379943 −0.189972 0.981790i \(-0.560840\pi\)
−0.189972 + 0.981790i \(0.560840\pi\)
\(74\) −21.3021 −2.47632
\(75\) 5.82765 0.672919
\(76\) −16.0561 −1.84176
\(77\) −3.62521 −0.413131
\(78\) −4.53544 −0.513538
\(79\) 4.01101 0.451274 0.225637 0.974211i \(-0.427554\pi\)
0.225637 + 0.974211i \(0.427554\pi\)
\(80\) 9.92332 1.10946
\(81\) 1.00000 0.111111
\(82\) −1.35953 −0.150135
\(83\) −3.40033 −0.373235 −0.186617 0.982433i \(-0.559752\pi\)
−0.186617 + 0.982433i \(0.559752\pi\)
\(84\) 2.40865 0.262805
\(85\) −7.21395 −0.782463
\(86\) 7.72385 0.832884
\(87\) 2.06180 0.221048
\(88\) −3.11054 −0.331584
\(89\) 6.31252 0.669126 0.334563 0.942373i \(-0.391411\pi\)
0.334563 + 0.942373i \(0.391411\pi\)
\(90\) −6.90907 −0.728280
\(91\) −2.16007 −0.226436
\(92\) 5.69698 0.593952
\(93\) −2.19207 −0.227307
\(94\) −18.0376 −1.86043
\(95\) 21.9348 2.25046
\(96\) −8.04808 −0.821404
\(97\) −0.0689323 −0.00699902 −0.00349951 0.999994i \(-0.501114\pi\)
−0.00349951 + 0.999994i \(0.501114\pi\)
\(98\) 2.09968 0.212100
\(99\) −3.62521 −0.364347
\(100\) 14.0368 1.40368
\(101\) 6.53614 0.650370 0.325185 0.945650i \(-0.394573\pi\)
0.325185 + 0.945650i \(0.394573\pi\)
\(102\) 4.60319 0.455784
\(103\) 1.42084 0.140000 0.0700000 0.997547i \(-0.477700\pi\)
0.0700000 + 0.997547i \(0.477700\pi\)
\(104\) −1.85340 −0.181741
\(105\) −3.29054 −0.321124
\(106\) 5.98248 0.581070
\(107\) 17.1418 1.65716 0.828581 0.559869i \(-0.189149\pi\)
0.828581 + 0.559869i \(0.189149\pi\)
\(108\) 2.40865 0.231772
\(109\) 14.3137 1.37100 0.685500 0.728073i \(-0.259584\pi\)
0.685500 + 0.728073i \(0.259584\pi\)
\(110\) 25.0468 2.38812
\(111\) −10.1454 −0.962959
\(112\) −3.01571 −0.284958
\(113\) 9.27873 0.872870 0.436435 0.899736i \(-0.356241\pi\)
0.436435 + 0.899736i \(0.356241\pi\)
\(114\) −13.9965 −1.31089
\(115\) −7.78285 −0.725755
\(116\) 4.96615 0.461095
\(117\) −2.16007 −0.199698
\(118\) −1.24467 −0.114581
\(119\) 2.19233 0.200971
\(120\) −2.82338 −0.257738
\(121\) 2.14215 0.194741
\(122\) −28.4022 −2.57141
\(123\) −0.647495 −0.0583826
\(124\) −5.27993 −0.474152
\(125\) −2.72342 −0.243590
\(126\) 2.09968 0.187054
\(127\) −1.00000 −0.0887357
\(128\) −6.72095 −0.594054
\(129\) 3.67859 0.323882
\(130\) 14.9241 1.30893
\(131\) 17.8118 1.55623 0.778113 0.628124i \(-0.216177\pi\)
0.778113 + 0.628124i \(0.216177\pi\)
\(132\) −8.73185 −0.760010
\(133\) −6.66601 −0.578016
\(134\) 1.39436 0.120454
\(135\) −3.29054 −0.283205
\(136\) 1.88108 0.161302
\(137\) 7.51288 0.641869 0.320934 0.947101i \(-0.396003\pi\)
0.320934 + 0.947101i \(0.396003\pi\)
\(138\) 4.96620 0.422751
\(139\) −4.67226 −0.396296 −0.198148 0.980172i \(-0.563493\pi\)
−0.198148 + 0.980172i \(0.563493\pi\)
\(140\) −7.92575 −0.669848
\(141\) −8.59064 −0.723462
\(142\) −11.8642 −0.995622
\(143\) 7.83069 0.654836
\(144\) −3.01571 −0.251309
\(145\) −6.78443 −0.563417
\(146\) −6.81605 −0.564101
\(147\) 1.00000 0.0824786
\(148\) −24.4367 −2.00868
\(149\) −12.9632 −1.06199 −0.530994 0.847375i \(-0.678181\pi\)
−0.530994 + 0.847375i \(0.678181\pi\)
\(150\) 12.2362 0.999081
\(151\) 10.9338 0.889780 0.444890 0.895585i \(-0.353243\pi\)
0.444890 + 0.895585i \(0.353243\pi\)
\(152\) −5.71963 −0.463923
\(153\) 2.19233 0.177239
\(154\) −7.61177 −0.613374
\(155\) 7.21310 0.579370
\(156\) −5.20284 −0.416561
\(157\) −20.5157 −1.63733 −0.818665 0.574271i \(-0.805285\pi\)
−0.818665 + 0.574271i \(0.805285\pi\)
\(158\) 8.42183 0.670005
\(159\) 2.84924 0.225959
\(160\) 26.4825 2.09363
\(161\) 2.36522 0.186406
\(162\) 2.09968 0.164966
\(163\) 1.33340 0.104440 0.0522199 0.998636i \(-0.483370\pi\)
0.0522199 + 0.998636i \(0.483370\pi\)
\(164\) −1.55959 −0.121783
\(165\) 11.9289 0.928663
\(166\) −7.13960 −0.554140
\(167\) 0.822111 0.0636169 0.0318084 0.999494i \(-0.489873\pi\)
0.0318084 + 0.999494i \(0.489873\pi\)
\(168\) 0.858029 0.0661984
\(169\) −8.33411 −0.641086
\(170\) −15.1470 −1.16172
\(171\) −6.66601 −0.509762
\(172\) 8.86042 0.675601
\(173\) −22.8603 −1.73804 −0.869020 0.494777i \(-0.835250\pi\)
−0.869020 + 0.494777i \(0.835250\pi\)
\(174\) 4.32912 0.328189
\(175\) 5.82765 0.440529
\(176\) 10.9326 0.824075
\(177\) −0.592789 −0.0445567
\(178\) 13.2543 0.993449
\(179\) 1.52134 0.113710 0.0568552 0.998382i \(-0.481893\pi\)
0.0568552 + 0.998382i \(0.481893\pi\)
\(180\) −7.92575 −0.590751
\(181\) 14.4514 1.07417 0.537084 0.843529i \(-0.319526\pi\)
0.537084 + 0.843529i \(0.319526\pi\)
\(182\) −4.53544 −0.336189
\(183\) −13.5269 −0.999939
\(184\) 2.02943 0.149611
\(185\) 33.3838 2.45443
\(186\) −4.60265 −0.337483
\(187\) −7.94766 −0.581190
\(188\) −20.6918 −1.50911
\(189\) 1.00000 0.0727393
\(190\) 46.0559 3.34125
\(191\) 6.46436 0.467744 0.233872 0.972267i \(-0.424860\pi\)
0.233872 + 0.972267i \(0.424860\pi\)
\(192\) −10.8670 −0.784255
\(193\) −21.4158 −1.54154 −0.770771 0.637112i \(-0.780129\pi\)
−0.770771 + 0.637112i \(0.780129\pi\)
\(194\) −0.144736 −0.0103914
\(195\) 7.10778 0.508999
\(196\) 2.40865 0.172046
\(197\) 15.2826 1.08884 0.544419 0.838814i \(-0.316750\pi\)
0.544419 + 0.838814i \(0.316750\pi\)
\(198\) −7.61177 −0.540945
\(199\) −9.68248 −0.686373 −0.343186 0.939267i \(-0.611506\pi\)
−0.343186 + 0.939267i \(0.611506\pi\)
\(200\) 5.00030 0.353574
\(201\) 0.664083 0.0468408
\(202\) 13.7238 0.965603
\(203\) 2.06180 0.144710
\(204\) 5.28055 0.369713
\(205\) 2.13061 0.148808
\(206\) 2.98332 0.207857
\(207\) 2.36522 0.164394
\(208\) 6.51414 0.451674
\(209\) 24.1657 1.67157
\(210\) −6.90907 −0.476771
\(211\) −22.7122 −1.56357 −0.781785 0.623549i \(-0.785690\pi\)
−0.781785 + 0.623549i \(0.785690\pi\)
\(212\) 6.86281 0.471340
\(213\) −5.65049 −0.387165
\(214\) 35.9923 2.46038
\(215\) −12.1045 −0.825523
\(216\) 0.858029 0.0583815
\(217\) −2.19207 −0.148808
\(218\) 30.0541 2.03552
\(219\) −3.24624 −0.219360
\(220\) 28.7325 1.93715
\(221\) −4.73558 −0.318550
\(222\) −21.3021 −1.42970
\(223\) 6.33989 0.424551 0.212275 0.977210i \(-0.431913\pi\)
0.212275 + 0.977210i \(0.431913\pi\)
\(224\) −8.04808 −0.537735
\(225\) 5.82765 0.388510
\(226\) 19.4824 1.29595
\(227\) −15.7349 −1.04436 −0.522181 0.852835i \(-0.674881\pi\)
−0.522181 + 0.852835i \(0.674881\pi\)
\(228\) −16.0561 −1.06334
\(229\) −0.365275 −0.0241380 −0.0120690 0.999927i \(-0.503842\pi\)
−0.0120690 + 0.999927i \(0.503842\pi\)
\(230\) −16.3415 −1.07753
\(231\) −3.62521 −0.238521
\(232\) 1.76908 0.116146
\(233\) −4.21293 −0.275998 −0.137999 0.990432i \(-0.544067\pi\)
−0.137999 + 0.990432i \(0.544067\pi\)
\(234\) −4.53544 −0.296491
\(235\) 28.2678 1.84399
\(236\) −1.42782 −0.0929431
\(237\) 4.01101 0.260543
\(238\) 4.60319 0.298380
\(239\) −3.38821 −0.219165 −0.109582 0.993978i \(-0.534951\pi\)
−0.109582 + 0.993978i \(0.534951\pi\)
\(240\) 9.92332 0.640547
\(241\) −10.0609 −0.648077 −0.324039 0.946044i \(-0.605041\pi\)
−0.324039 + 0.946044i \(0.605041\pi\)
\(242\) 4.49782 0.289131
\(243\) 1.00000 0.0641500
\(244\) −32.5816 −2.08582
\(245\) −3.29054 −0.210225
\(246\) −1.35953 −0.0866805
\(247\) 14.3990 0.916188
\(248\) −1.88086 −0.119435
\(249\) −3.40033 −0.215487
\(250\) −5.71830 −0.361657
\(251\) 1.13195 0.0714479 0.0357240 0.999362i \(-0.488626\pi\)
0.0357240 + 0.999362i \(0.488626\pi\)
\(252\) 2.40865 0.151731
\(253\) −8.57442 −0.539069
\(254\) −2.09968 −0.131746
\(255\) −7.21395 −0.451755
\(256\) 7.62208 0.476380
\(257\) −29.2462 −1.82433 −0.912165 0.409824i \(-0.865590\pi\)
−0.912165 + 0.409824i \(0.865590\pi\)
\(258\) 7.72385 0.480866
\(259\) −10.1454 −0.630404
\(260\) 17.1202 1.06175
\(261\) 2.06180 0.127622
\(262\) 37.3991 2.31052
\(263\) 26.3656 1.62577 0.812887 0.582422i \(-0.197895\pi\)
0.812887 + 0.582422i \(0.197895\pi\)
\(264\) −3.11054 −0.191440
\(265\) −9.37552 −0.575934
\(266\) −13.9965 −0.858179
\(267\) 6.31252 0.386320
\(268\) 1.59954 0.0977076
\(269\) −22.2274 −1.35523 −0.677613 0.735419i \(-0.736986\pi\)
−0.677613 + 0.735419i \(0.736986\pi\)
\(270\) −6.90907 −0.420473
\(271\) −26.8490 −1.63096 −0.815482 0.578783i \(-0.803528\pi\)
−0.815482 + 0.578783i \(0.803528\pi\)
\(272\) −6.61144 −0.400877
\(273\) −2.16007 −0.130733
\(274\) 15.7746 0.952981
\(275\) −21.1265 −1.27397
\(276\) 5.69698 0.342918
\(277\) 2.10995 0.126775 0.0633873 0.997989i \(-0.479810\pi\)
0.0633873 + 0.997989i \(0.479810\pi\)
\(278\) −9.81024 −0.588379
\(279\) −2.19207 −0.131236
\(280\) −2.82338 −0.168729
\(281\) 19.6051 1.16954 0.584772 0.811198i \(-0.301184\pi\)
0.584772 + 0.811198i \(0.301184\pi\)
\(282\) −18.0376 −1.07412
\(283\) −5.28771 −0.314322 −0.157161 0.987573i \(-0.550234\pi\)
−0.157161 + 0.987573i \(0.550234\pi\)
\(284\) −13.6100 −0.807607
\(285\) 21.9348 1.29930
\(286\) 16.4419 0.972232
\(287\) −0.647495 −0.0382204
\(288\) −8.04808 −0.474238
\(289\) −12.1937 −0.717276
\(290\) −14.2451 −0.836503
\(291\) −0.0689323 −0.00404089
\(292\) −7.81904 −0.457575
\(293\) 9.05623 0.529071 0.264535 0.964376i \(-0.414781\pi\)
0.264535 + 0.964376i \(0.414781\pi\)
\(294\) 2.09968 0.122456
\(295\) 1.95059 0.113568
\(296\) −8.70505 −0.505971
\(297\) −3.62521 −0.210356
\(298\) −27.2186 −1.57673
\(299\) −5.10903 −0.295463
\(300\) 14.0368 0.810413
\(301\) 3.67859 0.212030
\(302\) 22.9575 1.32105
\(303\) 6.53614 0.375492
\(304\) 20.1027 1.15297
\(305\) 44.5109 2.54869
\(306\) 4.60319 0.263147
\(307\) 23.4922 1.34077 0.670386 0.742012i \(-0.266128\pi\)
0.670386 + 0.742012i \(0.266128\pi\)
\(308\) −8.73185 −0.497544
\(309\) 1.42084 0.0808290
\(310\) 15.1452 0.860189
\(311\) −0.106610 −0.00604531 −0.00302265 0.999995i \(-0.500962\pi\)
−0.00302265 + 0.999995i \(0.500962\pi\)
\(312\) −1.85340 −0.104928
\(313\) 23.6312 1.33572 0.667858 0.744289i \(-0.267211\pi\)
0.667858 + 0.744289i \(0.267211\pi\)
\(314\) −43.0763 −2.43094
\(315\) −3.29054 −0.185401
\(316\) 9.66112 0.543480
\(317\) 8.87083 0.498236 0.249118 0.968473i \(-0.419859\pi\)
0.249118 + 0.968473i \(0.419859\pi\)
\(318\) 5.98248 0.335481
\(319\) −7.47446 −0.418489
\(320\) 35.7582 1.99894
\(321\) 17.1418 0.956763
\(322\) 4.96620 0.276756
\(323\) −14.6141 −0.813150
\(324\) 2.40865 0.133814
\(325\) −12.5881 −0.698263
\(326\) 2.79971 0.155061
\(327\) 14.3137 0.791547
\(328\) −0.555570 −0.0306762
\(329\) −8.59064 −0.473617
\(330\) 25.0468 1.37878
\(331\) −27.3847 −1.50520 −0.752599 0.658480i \(-0.771200\pi\)
−0.752599 + 0.658480i \(0.771200\pi\)
\(332\) −8.19020 −0.449496
\(333\) −10.1454 −0.555964
\(334\) 1.72617 0.0944518
\(335\) −2.18519 −0.119390
\(336\) −3.01571 −0.164521
\(337\) 18.4898 1.00720 0.503601 0.863936i \(-0.332008\pi\)
0.503601 + 0.863936i \(0.332008\pi\)
\(338\) −17.4990 −0.951818
\(339\) 9.27873 0.503952
\(340\) −17.3759 −0.942339
\(341\) 7.94673 0.430339
\(342\) −13.9965 −0.756842
\(343\) 1.00000 0.0539949
\(344\) 3.15634 0.170178
\(345\) −7.78285 −0.419015
\(346\) −47.9994 −2.58046
\(347\) 24.2408 1.30132 0.650658 0.759371i \(-0.274493\pi\)
0.650658 + 0.759371i \(0.274493\pi\)
\(348\) 4.96615 0.266214
\(349\) −7.74084 −0.414358 −0.207179 0.978303i \(-0.566428\pi\)
−0.207179 + 0.978303i \(0.566428\pi\)
\(350\) 12.2362 0.654052
\(351\) −2.16007 −0.115296
\(352\) 29.1760 1.55508
\(353\) −10.6201 −0.565253 −0.282626 0.959230i \(-0.591206\pi\)
−0.282626 + 0.959230i \(0.591206\pi\)
\(354\) −1.24467 −0.0661532
\(355\) 18.5932 0.986822
\(356\) 15.2046 0.805845
\(357\) 2.19233 0.116030
\(358\) 3.19433 0.168825
\(359\) 11.5939 0.611900 0.305950 0.952048i \(-0.401026\pi\)
0.305950 + 0.952048i \(0.401026\pi\)
\(360\) −2.82338 −0.148805
\(361\) 25.4357 1.33872
\(362\) 30.3434 1.59481
\(363\) 2.14215 0.112434
\(364\) −5.20284 −0.272703
\(365\) 10.6819 0.559115
\(366\) −28.4022 −1.48461
\(367\) −19.5505 −1.02053 −0.510263 0.860018i \(-0.670452\pi\)
−0.510263 + 0.860018i \(0.670452\pi\)
\(368\) −7.13282 −0.371824
\(369\) −0.647495 −0.0337072
\(370\) 70.0953 3.64408
\(371\) 2.84924 0.147925
\(372\) −5.27993 −0.273752
\(373\) 3.95621 0.204845 0.102423 0.994741i \(-0.467341\pi\)
0.102423 + 0.994741i \(0.467341\pi\)
\(374\) −16.6875 −0.862891
\(375\) −2.72342 −0.140637
\(376\) −7.37102 −0.380131
\(377\) −4.45362 −0.229373
\(378\) 2.09968 0.107996
\(379\) −26.2433 −1.34803 −0.674014 0.738718i \(-0.735431\pi\)
−0.674014 + 0.738718i \(0.735431\pi\)
\(380\) 52.8331 2.71028
\(381\) −1.00000 −0.0512316
\(382\) 13.5731 0.694459
\(383\) 2.25979 0.115470 0.0577349 0.998332i \(-0.481612\pi\)
0.0577349 + 0.998332i \(0.481612\pi\)
\(384\) −6.72095 −0.342977
\(385\) 11.9289 0.607953
\(386\) −44.9663 −2.28872
\(387\) 3.67859 0.186993
\(388\) −0.166034 −0.00842909
\(389\) −4.79264 −0.242997 −0.121498 0.992592i \(-0.538770\pi\)
−0.121498 + 0.992592i \(0.538770\pi\)
\(390\) 14.9241 0.755709
\(391\) 5.18535 0.262234
\(392\) 0.858029 0.0433370
\(393\) 17.8118 0.898488
\(394\) 32.0885 1.61659
\(395\) −13.1984 −0.664083
\(396\) −8.73185 −0.438792
\(397\) 34.5066 1.73184 0.865919 0.500185i \(-0.166735\pi\)
0.865919 + 0.500185i \(0.166735\pi\)
\(398\) −20.3301 −1.01906
\(399\) −6.66601 −0.333718
\(400\) −17.5745 −0.878725
\(401\) −2.10653 −0.105195 −0.0525975 0.998616i \(-0.516750\pi\)
−0.0525975 + 0.998616i \(0.516750\pi\)
\(402\) 1.39436 0.0695444
\(403\) 4.73502 0.235868
\(404\) 15.7433 0.783257
\(405\) −3.29054 −0.163508
\(406\) 4.32912 0.214850
\(407\) 36.7792 1.82308
\(408\) 1.88108 0.0931276
\(409\) 36.8469 1.82196 0.910981 0.412449i \(-0.135327\pi\)
0.910981 + 0.412449i \(0.135327\pi\)
\(410\) 4.47359 0.220935
\(411\) 7.51288 0.370583
\(412\) 3.42231 0.168605
\(413\) −0.592789 −0.0291692
\(414\) 4.96620 0.244076
\(415\) 11.1889 0.549243
\(416\) 17.3844 0.852340
\(417\) −4.67226 −0.228801
\(418\) 50.7401 2.48178
\(419\) −23.4163 −1.14396 −0.571981 0.820267i \(-0.693825\pi\)
−0.571981 + 0.820267i \(0.693825\pi\)
\(420\) −7.92575 −0.386737
\(421\) 7.19583 0.350703 0.175352 0.984506i \(-0.443894\pi\)
0.175352 + 0.984506i \(0.443894\pi\)
\(422\) −47.6882 −2.32143
\(423\) −8.59064 −0.417691
\(424\) 2.44473 0.118727
\(425\) 12.7761 0.619734
\(426\) −11.8642 −0.574823
\(427\) −13.5269 −0.654614
\(428\) 41.2886 1.99576
\(429\) 7.83069 0.378069
\(430\) −25.4156 −1.22565
\(431\) −18.8941 −0.910098 −0.455049 0.890466i \(-0.650378\pi\)
−0.455049 + 0.890466i \(0.650378\pi\)
\(432\) −3.01571 −0.145093
\(433\) 18.2660 0.877810 0.438905 0.898534i \(-0.355367\pi\)
0.438905 + 0.898534i \(0.355367\pi\)
\(434\) −4.60265 −0.220934
\(435\) −6.78443 −0.325289
\(436\) 34.4766 1.65113
\(437\) −15.7666 −0.754218
\(438\) −6.81605 −0.325684
\(439\) −31.3238 −1.49501 −0.747503 0.664259i \(-0.768747\pi\)
−0.747503 + 0.664259i \(0.768747\pi\)
\(440\) 10.2353 0.487951
\(441\) 1.00000 0.0476190
\(442\) −9.94319 −0.472950
\(443\) −7.54570 −0.358507 −0.179254 0.983803i \(-0.557368\pi\)
−0.179254 + 0.983803i \(0.557368\pi\)
\(444\) −24.4367 −1.15971
\(445\) −20.7716 −0.984669
\(446\) 13.3117 0.630329
\(447\) −12.9632 −0.613140
\(448\) −10.8670 −0.513415
\(449\) −24.4439 −1.15358 −0.576790 0.816892i \(-0.695695\pi\)
−0.576790 + 0.816892i \(0.695695\pi\)
\(450\) 12.2362 0.576820
\(451\) 2.34730 0.110530
\(452\) 22.3492 1.05122
\(453\) 10.9338 0.513715
\(454\) −33.0382 −1.55056
\(455\) 7.10778 0.333218
\(456\) −5.71963 −0.267846
\(457\) 10.3236 0.482915 0.241458 0.970411i \(-0.422375\pi\)
0.241458 + 0.970411i \(0.422375\pi\)
\(458\) −0.766959 −0.0358377
\(459\) 2.19233 0.102329
\(460\) −18.7462 −0.874044
\(461\) −0.224984 −0.0104785 −0.00523927 0.999986i \(-0.501668\pi\)
−0.00523927 + 0.999986i \(0.501668\pi\)
\(462\) −7.61177 −0.354132
\(463\) −21.4269 −0.995795 −0.497897 0.867236i \(-0.665894\pi\)
−0.497897 + 0.867236i \(0.665894\pi\)
\(464\) −6.21779 −0.288654
\(465\) 7.21310 0.334500
\(466\) −8.84580 −0.409774
\(467\) 14.8070 0.685186 0.342593 0.939484i \(-0.388695\pi\)
0.342593 + 0.939484i \(0.388695\pi\)
\(468\) −5.20284 −0.240501
\(469\) 0.664083 0.0306645
\(470\) 59.3534 2.73777
\(471\) −20.5157 −0.945313
\(472\) −0.508630 −0.0234116
\(473\) −13.3357 −0.613174
\(474\) 8.42183 0.386828
\(475\) −38.8472 −1.78243
\(476\) 5.28055 0.242034
\(477\) 2.84924 0.130458
\(478\) −7.11414 −0.325393
\(479\) −10.2074 −0.466390 −0.233195 0.972430i \(-0.574918\pi\)
−0.233195 + 0.972430i \(0.574918\pi\)
\(480\) 26.4825 1.20876
\(481\) 21.9147 0.999226
\(482\) −21.1246 −0.962198
\(483\) 2.36522 0.107621
\(484\) 5.15968 0.234531
\(485\) 0.226825 0.0102996
\(486\) 2.09968 0.0952433
\(487\) 16.1543 0.732023 0.366011 0.930610i \(-0.380723\pi\)
0.366011 + 0.930610i \(0.380723\pi\)
\(488\) −11.6065 −0.525402
\(489\) 1.33340 0.0602984
\(490\) −6.90907 −0.312120
\(491\) −12.4633 −0.562459 −0.281229 0.959641i \(-0.590742\pi\)
−0.281229 + 0.959641i \(0.590742\pi\)
\(492\) −1.55959 −0.0703116
\(493\) 4.52015 0.203577
\(494\) 30.2333 1.36026
\(495\) 11.9289 0.536164
\(496\) 6.61066 0.296827
\(497\) −5.65049 −0.253459
\(498\) −7.13960 −0.319933
\(499\) −13.4987 −0.604283 −0.302142 0.953263i \(-0.597702\pi\)
−0.302142 + 0.953263i \(0.597702\pi\)
\(500\) −6.55976 −0.293361
\(501\) 0.822111 0.0367292
\(502\) 2.37673 0.106078
\(503\) 22.8347 1.01815 0.509074 0.860723i \(-0.329988\pi\)
0.509074 + 0.860723i \(0.329988\pi\)
\(504\) 0.858029 0.0382197
\(505\) −21.5074 −0.957068
\(506\) −18.0035 −0.800354
\(507\) −8.33411 −0.370131
\(508\) −2.40865 −0.106866
\(509\) −27.5341 −1.22043 −0.610214 0.792237i \(-0.708916\pi\)
−0.610214 + 0.792237i \(0.708916\pi\)
\(510\) −15.1470 −0.670719
\(511\) −3.24624 −0.143605
\(512\) 29.4458 1.30133
\(513\) −6.66601 −0.294311
\(514\) −61.4077 −2.70858
\(515\) −4.67534 −0.206020
\(516\) 8.86042 0.390058
\(517\) 31.1429 1.36966
\(518\) −21.3021 −0.935959
\(519\) −22.8603 −1.00346
\(520\) 6.09869 0.267445
\(521\) 21.7185 0.951504 0.475752 0.879580i \(-0.342176\pi\)
0.475752 + 0.879580i \(0.342176\pi\)
\(522\) 4.32912 0.189480
\(523\) −25.3129 −1.10685 −0.553427 0.832898i \(-0.686680\pi\)
−0.553427 + 0.832898i \(0.686680\pi\)
\(524\) 42.9024 1.87420
\(525\) 5.82765 0.254340
\(526\) 55.3593 2.41378
\(527\) −4.80575 −0.209342
\(528\) 10.9326 0.475780
\(529\) −17.4057 −0.756771
\(530\) −19.6856 −0.855087
\(531\) −0.592789 −0.0257248
\(532\) −16.0561 −0.696119
\(533\) 1.39863 0.0605815
\(534\) 13.2543 0.573568
\(535\) −56.4058 −2.43864
\(536\) 0.569803 0.0246117
\(537\) 1.52134 0.0656508
\(538\) −46.6703 −2.01210
\(539\) −3.62521 −0.156149
\(540\) −7.92575 −0.341070
\(541\) −0.966528 −0.0415543 −0.0207771 0.999784i \(-0.506614\pi\)
−0.0207771 + 0.999784i \(0.506614\pi\)
\(542\) −56.3744 −2.42149
\(543\) 14.4514 0.620171
\(544\) −17.6441 −0.756483
\(545\) −47.0997 −2.01753
\(546\) −4.53544 −0.194099
\(547\) −6.92682 −0.296170 −0.148085 0.988975i \(-0.547311\pi\)
−0.148085 + 0.988975i \(0.547311\pi\)
\(548\) 18.0959 0.773018
\(549\) −13.5269 −0.577315
\(550\) −44.3588 −1.89146
\(551\) −13.7440 −0.585513
\(552\) 2.02943 0.0863782
\(553\) 4.01101 0.170566
\(554\) 4.43021 0.188222
\(555\) 33.3838 1.41706
\(556\) −11.2538 −0.477268
\(557\) −41.5856 −1.76204 −0.881019 0.473080i \(-0.843142\pi\)
−0.881019 + 0.473080i \(0.843142\pi\)
\(558\) −4.60265 −0.194846
\(559\) −7.94600 −0.336080
\(560\) 9.92332 0.419337
\(561\) −7.94766 −0.335550
\(562\) 41.1645 1.73642
\(563\) −31.7414 −1.33774 −0.668871 0.743378i \(-0.733222\pi\)
−0.668871 + 0.743378i \(0.733222\pi\)
\(564\) −20.6918 −0.871283
\(565\) −30.5320 −1.28449
\(566\) −11.1025 −0.466673
\(567\) 1.00000 0.0419961
\(568\) −4.84828 −0.203429
\(569\) −0.333729 −0.0139906 −0.00699532 0.999976i \(-0.502227\pi\)
−0.00699532 + 0.999976i \(0.502227\pi\)
\(570\) 46.0559 1.92907
\(571\) 12.9921 0.543704 0.271852 0.962339i \(-0.412364\pi\)
0.271852 + 0.962339i \(0.412364\pi\)
\(572\) 18.8614 0.788634
\(573\) 6.46436 0.270052
\(574\) −1.35953 −0.0567457
\(575\) 13.7837 0.574819
\(576\) −10.8670 −0.452790
\(577\) 32.0896 1.33591 0.667954 0.744203i \(-0.267170\pi\)
0.667954 + 0.744203i \(0.267170\pi\)
\(578\) −25.6028 −1.06494
\(579\) −21.4158 −0.890010
\(580\) −16.3413 −0.678536
\(581\) −3.40033 −0.141070
\(582\) −0.144736 −0.00599949
\(583\) −10.3291 −0.427787
\(584\) −2.78537 −0.115259
\(585\) 7.10778 0.293871
\(586\) 19.0152 0.785509
\(587\) −40.9497 −1.69017 −0.845087 0.534629i \(-0.820451\pi\)
−0.845087 + 0.534629i \(0.820451\pi\)
\(588\) 2.40865 0.0993310
\(589\) 14.6124 0.602093
\(590\) 4.09562 0.168614
\(591\) 15.2826 0.628640
\(592\) 30.5956 1.25747
\(593\) 42.4563 1.74347 0.871735 0.489978i \(-0.162995\pi\)
0.871735 + 0.489978i \(0.162995\pi\)
\(594\) −7.61177 −0.312315
\(595\) −7.21395 −0.295743
\(596\) −31.2238 −1.27898
\(597\) −9.68248 −0.396277
\(598\) −10.7273 −0.438673
\(599\) 26.8144 1.09560 0.547802 0.836608i \(-0.315465\pi\)
0.547802 + 0.836608i \(0.315465\pi\)
\(600\) 5.00030 0.204136
\(601\) −32.3520 −1.31967 −0.659833 0.751412i \(-0.729373\pi\)
−0.659833 + 0.751412i \(0.729373\pi\)
\(602\) 7.72385 0.314801
\(603\) 0.664083 0.0270435
\(604\) 26.3357 1.07158
\(605\) −7.04882 −0.286575
\(606\) 13.7238 0.557491
\(607\) −5.75375 −0.233538 −0.116769 0.993159i \(-0.537254\pi\)
−0.116769 + 0.993159i \(0.537254\pi\)
\(608\) 53.6486 2.17574
\(609\) 2.06180 0.0835483
\(610\) 93.4585 3.78402
\(611\) 18.5564 0.750710
\(612\) 5.28055 0.213454
\(613\) −28.0175 −1.13162 −0.565808 0.824537i \(-0.691436\pi\)
−0.565808 + 0.824537i \(0.691436\pi\)
\(614\) 49.3261 1.99064
\(615\) 2.13061 0.0859144
\(616\) −3.11054 −0.125327
\(617\) −1.13222 −0.0455814 −0.0227907 0.999740i \(-0.507255\pi\)
−0.0227907 + 0.999740i \(0.507255\pi\)
\(618\) 2.98332 0.120007
\(619\) 14.6756 0.589862 0.294931 0.955519i \(-0.404703\pi\)
0.294931 + 0.955519i \(0.404703\pi\)
\(620\) 17.3738 0.697750
\(621\) 2.36522 0.0949130
\(622\) −0.223847 −0.00897545
\(623\) 6.31252 0.252906
\(624\) 6.51414 0.260774
\(625\) −20.1767 −0.807070
\(626\) 49.6180 1.98313
\(627\) 24.1657 0.965084
\(628\) −49.4151 −1.97188
\(629\) −22.2421 −0.886849
\(630\) −6.90907 −0.275264
\(631\) −33.4295 −1.33081 −0.665404 0.746483i \(-0.731741\pi\)
−0.665404 + 0.746483i \(0.731741\pi\)
\(632\) 3.44157 0.136898
\(633\) −22.7122 −0.902727
\(634\) 18.6259 0.739729
\(635\) 3.29054 0.130581
\(636\) 6.86281 0.272128
\(637\) −2.16007 −0.0855850
\(638\) −15.6940 −0.621329
\(639\) −5.65049 −0.223530
\(640\) 22.1156 0.874194
\(641\) 13.4509 0.531278 0.265639 0.964073i \(-0.414417\pi\)
0.265639 + 0.964073i \(0.414417\pi\)
\(642\) 35.9923 1.42050
\(643\) 11.7618 0.463838 0.231919 0.972735i \(-0.425499\pi\)
0.231919 + 0.972735i \(0.425499\pi\)
\(644\) 5.69698 0.224493
\(645\) −12.1045 −0.476616
\(646\) −30.6849 −1.20728
\(647\) 8.12298 0.319347 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(648\) 0.858029 0.0337066
\(649\) 2.14898 0.0843550
\(650\) −26.4310 −1.03671
\(651\) −2.19207 −0.0859141
\(652\) 3.21169 0.125779
\(653\) −29.8203 −1.16696 −0.583479 0.812128i \(-0.698309\pi\)
−0.583479 + 0.812128i \(0.698309\pi\)
\(654\) 30.0541 1.17521
\(655\) −58.6105 −2.29010
\(656\) 1.95266 0.0762384
\(657\) −3.24624 −0.126648
\(658\) −18.0376 −0.703178
\(659\) 7.08303 0.275916 0.137958 0.990438i \(-0.455946\pi\)
0.137958 + 0.990438i \(0.455946\pi\)
\(660\) 28.7325 1.11841
\(661\) 36.2548 1.41015 0.705075 0.709133i \(-0.250913\pi\)
0.705075 + 0.709133i \(0.250913\pi\)
\(662\) −57.4990 −2.23476
\(663\) −4.73558 −0.183915
\(664\) −2.91758 −0.113224
\(665\) 21.9348 0.850594
\(666\) −21.3021 −0.825439
\(667\) 4.87661 0.188823
\(668\) 1.98018 0.0766153
\(669\) 6.33989 0.245114
\(670\) −4.58820 −0.177258
\(671\) 49.0379 1.89309
\(672\) −8.04808 −0.310461
\(673\) 22.9499 0.884656 0.442328 0.896853i \(-0.354153\pi\)
0.442328 + 0.896853i \(0.354153\pi\)
\(674\) 38.8226 1.49539
\(675\) 5.82765 0.224306
\(676\) −20.0739 −0.772075
\(677\) 3.57237 0.137297 0.0686486 0.997641i \(-0.478131\pi\)
0.0686486 + 0.997641i \(0.478131\pi\)
\(678\) 19.4824 0.748215
\(679\) −0.0689323 −0.00264538
\(680\) −6.18978 −0.237367
\(681\) −15.7349 −0.602962
\(682\) 16.6856 0.638923
\(683\) −22.1918 −0.849145 −0.424573 0.905394i \(-0.639576\pi\)
−0.424573 + 0.905394i \(0.639576\pi\)
\(684\) −16.0561 −0.613919
\(685\) −24.7214 −0.944558
\(686\) 2.09968 0.0801661
\(687\) −0.365275 −0.0139361
\(688\) −11.0936 −0.422938
\(689\) −6.15454 −0.234469
\(690\) −16.3415 −0.622110
\(691\) −27.5328 −1.04740 −0.523698 0.851904i \(-0.675448\pi\)
−0.523698 + 0.851904i \(0.675448\pi\)
\(692\) −55.0625 −2.09316
\(693\) −3.62521 −0.137710
\(694\) 50.8979 1.93206
\(695\) 15.3742 0.583178
\(696\) 1.76908 0.0670570
\(697\) −1.41952 −0.0537683
\(698\) −16.2533 −0.615195
\(699\) −4.21293 −0.159348
\(700\) 14.0368 0.530540
\(701\) −33.7129 −1.27332 −0.636659 0.771146i \(-0.719684\pi\)
−0.636659 + 0.771146i \(0.719684\pi\)
\(702\) −4.53544 −0.171179
\(703\) 67.6293 2.55069
\(704\) 39.3950 1.48475
\(705\) 28.2678 1.06463
\(706\) −22.2989 −0.839229
\(707\) 6.53614 0.245817
\(708\) −1.42782 −0.0536607
\(709\) −43.1638 −1.62105 −0.810525 0.585704i \(-0.800818\pi\)
−0.810525 + 0.585704i \(0.800818\pi\)
\(710\) 39.0396 1.46513
\(711\) 4.01101 0.150425
\(712\) 5.41633 0.202986
\(713\) −5.18474 −0.194170
\(714\) 4.60319 0.172270
\(715\) −25.7672 −0.963639
\(716\) 3.66438 0.136944
\(717\) −3.38821 −0.126535
\(718\) 24.3434 0.908486
\(719\) 13.6734 0.509931 0.254965 0.966950i \(-0.417936\pi\)
0.254965 + 0.966950i \(0.417936\pi\)
\(720\) 9.92332 0.369820
\(721\) 1.42084 0.0529150
\(722\) 53.4067 1.98759
\(723\) −10.0609 −0.374168
\(724\) 34.8085 1.29365
\(725\) 12.0154 0.446243
\(726\) 4.49782 0.166930
\(727\) −32.4355 −1.20297 −0.601483 0.798886i \(-0.705423\pi\)
−0.601483 + 0.798886i \(0.705423\pi\)
\(728\) −1.85340 −0.0686916
\(729\) 1.00000 0.0370370
\(730\) 22.4285 0.830116
\(731\) 8.06468 0.298283
\(732\) −32.5816 −1.20425
\(733\) −42.8281 −1.58189 −0.790946 0.611886i \(-0.790411\pi\)
−0.790946 + 0.611886i \(0.790411\pi\)
\(734\) −41.0497 −1.51517
\(735\) −3.29054 −0.121373
\(736\) −19.0355 −0.701657
\(737\) −2.40744 −0.0886792
\(738\) −1.35953 −0.0500450
\(739\) 38.7706 1.42620 0.713099 0.701063i \(-0.247291\pi\)
0.713099 + 0.701063i \(0.247291\pi\)
\(740\) 80.4099 2.95593
\(741\) 14.3990 0.528961
\(742\) 5.98248 0.219624
\(743\) 13.9130 0.510418 0.255209 0.966886i \(-0.417856\pi\)
0.255209 + 0.966886i \(0.417856\pi\)
\(744\) −1.88086 −0.0689558
\(745\) 42.6560 1.56280
\(746\) 8.30678 0.304133
\(747\) −3.40033 −0.124412
\(748\) −19.1431 −0.699942
\(749\) 17.1418 0.626348
\(750\) −5.71830 −0.208803
\(751\) −0.457421 −0.0166915 −0.00834576 0.999965i \(-0.502657\pi\)
−0.00834576 + 0.999965i \(0.502657\pi\)
\(752\) 25.9069 0.944727
\(753\) 1.13195 0.0412505
\(754\) −9.35118 −0.340550
\(755\) −35.9781 −1.30938
\(756\) 2.40865 0.0876017
\(757\) −20.9802 −0.762539 −0.381269 0.924464i \(-0.624513\pi\)
−0.381269 + 0.924464i \(0.624513\pi\)
\(758\) −55.1025 −2.00141
\(759\) −8.57442 −0.311232
\(760\) 18.8207 0.682697
\(761\) −30.4760 −1.10476 −0.552378 0.833594i \(-0.686279\pi\)
−0.552378 + 0.833594i \(0.686279\pi\)
\(762\) −2.09968 −0.0760633
\(763\) 14.3137 0.518189
\(764\) 15.5704 0.563316
\(765\) −7.21395 −0.260821
\(766\) 4.74483 0.171438
\(767\) 1.28046 0.0462348
\(768\) 7.62208 0.275038
\(769\) −21.8499 −0.787927 −0.393963 0.919126i \(-0.628896\pi\)
−0.393963 + 0.919126i \(0.628896\pi\)
\(770\) 25.0468 0.902626
\(771\) −29.2462 −1.05328
\(772\) −51.5831 −1.85652
\(773\) 19.4525 0.699659 0.349830 0.936813i \(-0.386239\pi\)
0.349830 + 0.936813i \(0.386239\pi\)
\(774\) 7.72385 0.277628
\(775\) −12.7746 −0.458879
\(776\) −0.0591460 −0.00212322
\(777\) −10.1454 −0.363964
\(778\) −10.0630 −0.360776
\(779\) 4.31620 0.154644
\(780\) 17.1202 0.613000
\(781\) 20.4842 0.732982
\(782\) 10.8876 0.389338
\(783\) 2.06180 0.0736827
\(784\) −3.01571 −0.107704
\(785\) 67.5077 2.40945
\(786\) 37.3991 1.33398
\(787\) 41.2974 1.47209 0.736047 0.676930i \(-0.236690\pi\)
0.736047 + 0.676930i \(0.236690\pi\)
\(788\) 36.8103 1.31131
\(789\) 26.3656 0.938641
\(790\) −27.7124 −0.985962
\(791\) 9.27873 0.329914
\(792\) −3.11054 −0.110528
\(793\) 29.2191 1.03760
\(794\) 72.4528 2.57125
\(795\) −9.37552 −0.332516
\(796\) −23.3217 −0.826615
\(797\) −35.1784 −1.24608 −0.623042 0.782188i \(-0.714103\pi\)
−0.623042 + 0.782188i \(0.714103\pi\)
\(798\) −13.9965 −0.495470
\(799\) −18.8335 −0.666282
\(800\) −46.9014 −1.65822
\(801\) 6.31252 0.223042
\(802\) −4.42303 −0.156183
\(803\) 11.7683 0.415294
\(804\) 1.59954 0.0564115
\(805\) −7.78285 −0.274310
\(806\) 9.94203 0.350193
\(807\) −22.2274 −0.782440
\(808\) 5.60820 0.197296
\(809\) 32.9258 1.15761 0.578804 0.815466i \(-0.303520\pi\)
0.578804 + 0.815466i \(0.303520\pi\)
\(810\) −6.90907 −0.242760
\(811\) −46.5481 −1.63453 −0.817263 0.576265i \(-0.804510\pi\)
−0.817263 + 0.576265i \(0.804510\pi\)
\(812\) 4.96615 0.174278
\(813\) −26.8490 −0.941637
\(814\) 77.2245 2.70672
\(815\) −4.38760 −0.153691
\(816\) −6.61144 −0.231447
\(817\) −24.5215 −0.857899
\(818\) 77.3666 2.70506
\(819\) −2.16007 −0.0754788
\(820\) 5.13188 0.179213
\(821\) 24.6736 0.861114 0.430557 0.902563i \(-0.358317\pi\)
0.430557 + 0.902563i \(0.358317\pi\)
\(822\) 15.7746 0.550204
\(823\) −35.8137 −1.24839 −0.624193 0.781270i \(-0.714572\pi\)
−0.624193 + 0.781270i \(0.714572\pi\)
\(824\) 1.21913 0.0424703
\(825\) −21.1265 −0.735529
\(826\) −1.24467 −0.0433075
\(827\) −43.4022 −1.50924 −0.754621 0.656161i \(-0.772179\pi\)
−0.754621 + 0.656161i \(0.772179\pi\)
\(828\) 5.69698 0.197984
\(829\) −12.6369 −0.438896 −0.219448 0.975624i \(-0.570426\pi\)
−0.219448 + 0.975624i \(0.570426\pi\)
\(830\) 23.4931 0.815459
\(831\) 2.10995 0.0731933
\(832\) 23.4733 0.813792
\(833\) 2.19233 0.0759598
\(834\) −9.81024 −0.339701
\(835\) −2.70519 −0.0936170
\(836\) 58.2066 2.01312
\(837\) −2.19207 −0.0757691
\(838\) −49.1668 −1.69844
\(839\) 28.0483 0.968336 0.484168 0.874975i \(-0.339122\pi\)
0.484168 + 0.874975i \(0.339122\pi\)
\(840\) −2.82338 −0.0974159
\(841\) −24.7490 −0.853413
\(842\) 15.1089 0.520688
\(843\) 19.6051 0.675237
\(844\) −54.7056 −1.88304
\(845\) 27.4237 0.943405
\(846\) −18.0376 −0.620145
\(847\) 2.14215 0.0736050
\(848\) −8.59247 −0.295067
\(849\) −5.28771 −0.181474
\(850\) 26.8258 0.920117
\(851\) −23.9961 −0.822576
\(852\) −13.6100 −0.466272
\(853\) 19.5717 0.670121 0.335060 0.942197i \(-0.391243\pi\)
0.335060 + 0.942197i \(0.391243\pi\)
\(854\) −28.4022 −0.971903
\(855\) 21.9348 0.750153
\(856\) 14.7082 0.502715
\(857\) 5.60926 0.191609 0.0958043 0.995400i \(-0.469458\pi\)
0.0958043 + 0.995400i \(0.469458\pi\)
\(858\) 16.4419 0.561318
\(859\) 9.59070 0.327231 0.163615 0.986524i \(-0.447684\pi\)
0.163615 + 0.986524i \(0.447684\pi\)
\(860\) −29.1556 −0.994197
\(861\) −0.647495 −0.0220666
\(862\) −39.6716 −1.35122
\(863\) −30.6668 −1.04391 −0.521955 0.852973i \(-0.674797\pi\)
−0.521955 + 0.852973i \(0.674797\pi\)
\(864\) −8.04808 −0.273801
\(865\) 75.2229 2.55765
\(866\) 38.3528 1.30328
\(867\) −12.1937 −0.414119
\(868\) −5.27993 −0.179213
\(869\) −14.5408 −0.493262
\(870\) −14.2451 −0.482955
\(871\) −1.43446 −0.0486049
\(872\) 12.2815 0.415905
\(873\) −0.0689323 −0.00233301
\(874\) −33.1047 −1.11978
\(875\) −2.72342 −0.0920684
\(876\) −7.81904 −0.264181
\(877\) −3.44789 −0.116427 −0.0582136 0.998304i \(-0.518540\pi\)
−0.0582136 + 0.998304i \(0.518540\pi\)
\(878\) −65.7700 −2.21963
\(879\) 9.05623 0.305459
\(880\) −35.9741 −1.21269
\(881\) 37.1051 1.25010 0.625052 0.780583i \(-0.285078\pi\)
0.625052 + 0.780583i \(0.285078\pi\)
\(882\) 2.09968 0.0706998
\(883\) −18.6304 −0.626964 −0.313482 0.949594i \(-0.601496\pi\)
−0.313482 + 0.949594i \(0.601496\pi\)
\(884\) −11.4063 −0.383637
\(885\) 1.95059 0.0655685
\(886\) −15.8435 −0.532274
\(887\) −4.44415 −0.149220 −0.0746100 0.997213i \(-0.523771\pi\)
−0.0746100 + 0.997213i \(0.523771\pi\)
\(888\) −8.70505 −0.292122
\(889\) −1.00000 −0.0335389
\(890\) −43.6137 −1.46193
\(891\) −3.62521 −0.121449
\(892\) 15.2706 0.511297
\(893\) 57.2653 1.91631
\(894\) −27.2186 −0.910326
\(895\) −5.00604 −0.167333
\(896\) −6.72095 −0.224531
\(897\) −5.10903 −0.170586
\(898\) −51.3244 −1.71272
\(899\) −4.51962 −0.150738
\(900\) 14.0368 0.467892
\(901\) 6.24647 0.208100
\(902\) 4.92858 0.164104
\(903\) 3.67859 0.122416
\(904\) 7.96142 0.264793
\(905\) −47.5531 −1.58072
\(906\) 22.9575 0.762711
\(907\) 48.7902 1.62005 0.810026 0.586393i \(-0.199453\pi\)
0.810026 + 0.586393i \(0.199453\pi\)
\(908\) −37.8998 −1.25775
\(909\) 6.53614 0.216790
\(910\) 14.9241 0.494728
\(911\) 33.0894 1.09630 0.548150 0.836380i \(-0.315332\pi\)
0.548150 + 0.836380i \(0.315332\pi\)
\(912\) 20.1027 0.665669
\(913\) 12.3269 0.407961
\(914\) 21.6761 0.716983
\(915\) 44.5109 1.47148
\(916\) −0.879818 −0.0290700
\(917\) 17.8118 0.588198
\(918\) 4.60319 0.151928
\(919\) 4.96601 0.163814 0.0819068 0.996640i \(-0.473899\pi\)
0.0819068 + 0.996640i \(0.473899\pi\)
\(920\) −6.67792 −0.220164
\(921\) 23.4922 0.774095
\(922\) −0.472394 −0.0155575
\(923\) 12.2054 0.401747
\(924\) −8.73185 −0.287257
\(925\) −59.1238 −1.94398
\(926\) −44.9897 −1.47845
\(927\) 1.42084 0.0466666
\(928\) −16.5935 −0.544709
\(929\) 2.64029 0.0866251 0.0433125 0.999062i \(-0.486209\pi\)
0.0433125 + 0.999062i \(0.486209\pi\)
\(930\) 15.1452 0.496631
\(931\) −6.66601 −0.218470
\(932\) −10.1475 −0.332391
\(933\) −0.106610 −0.00349026
\(934\) 31.0899 1.01729
\(935\) 26.1521 0.855265
\(936\) −1.85340 −0.0605803
\(937\) −25.1677 −0.822194 −0.411097 0.911592i \(-0.634854\pi\)
−0.411097 + 0.911592i \(0.634854\pi\)
\(938\) 1.39436 0.0455275
\(939\) 23.6312 0.771176
\(940\) 68.0873 2.22076
\(941\) 35.0361 1.14215 0.571073 0.820899i \(-0.306527\pi\)
0.571073 + 0.820899i \(0.306527\pi\)
\(942\) −43.0763 −1.40350
\(943\) −1.53147 −0.0498715
\(944\) 1.78768 0.0581840
\(945\) −3.29054 −0.107041
\(946\) −28.0006 −0.910377
\(947\) 34.0698 1.10712 0.553560 0.832809i \(-0.313269\pi\)
0.553560 + 0.832809i \(0.313269\pi\)
\(948\) 9.66112 0.313779
\(949\) 7.01209 0.227622
\(950\) −81.5665 −2.64637
\(951\) 8.87083 0.287657
\(952\) 1.88108 0.0609663
\(953\) −26.4808 −0.857796 −0.428898 0.903353i \(-0.641098\pi\)
−0.428898 + 0.903353i \(0.641098\pi\)
\(954\) 5.98248 0.193690
\(955\) −21.2712 −0.688321
\(956\) −8.16100 −0.263945
\(957\) −7.47446 −0.241615
\(958\) −21.4323 −0.692447
\(959\) 7.51288 0.242604
\(960\) 35.7582 1.15409
\(961\) −26.1948 −0.844994
\(962\) 46.0139 1.48355
\(963\) 17.1418 0.552387
\(964\) −24.2331 −0.780495
\(965\) 70.4695 2.26849
\(966\) 4.96620 0.159785
\(967\) −10.2513 −0.329659 −0.164829 0.986322i \(-0.552707\pi\)
−0.164829 + 0.986322i \(0.552707\pi\)
\(968\) 1.83802 0.0590763
\(969\) −14.6141 −0.469472
\(970\) 0.476259 0.0152917
\(971\) 10.1088 0.324407 0.162203 0.986757i \(-0.448140\pi\)
0.162203 + 0.986757i \(0.448140\pi\)
\(972\) 2.40865 0.0772574
\(973\) −4.67226 −0.149786
\(974\) 33.9189 1.08683
\(975\) −12.5881 −0.403142
\(976\) 40.7933 1.30576
\(977\) 10.4900 0.335604 0.167802 0.985821i \(-0.446333\pi\)
0.167802 + 0.985821i \(0.446333\pi\)
\(978\) 2.79971 0.0895248
\(979\) −22.8842 −0.731383
\(980\) −7.92575 −0.253179
\(981\) 14.3137 0.457000
\(982\) −26.1688 −0.835081
\(983\) 15.4551 0.492940 0.246470 0.969150i \(-0.420729\pi\)
0.246470 + 0.969150i \(0.420729\pi\)
\(984\) −0.555570 −0.0177109
\(985\) −50.2879 −1.60230
\(986\) 9.49085 0.302250
\(987\) −8.59064 −0.273443
\(988\) 34.6822 1.10339
\(989\) 8.70067 0.276665
\(990\) 25.0468 0.796041
\(991\) 58.7140 1.86511 0.932556 0.361026i \(-0.117574\pi\)
0.932556 + 0.361026i \(0.117574\pi\)
\(992\) 17.6420 0.560134
\(993\) −27.3847 −0.869026
\(994\) −11.8642 −0.376310
\(995\) 31.8606 1.01005
\(996\) −8.19020 −0.259516
\(997\) −9.14112 −0.289502 −0.144751 0.989468i \(-0.546238\pi\)
−0.144751 + 0.989468i \(0.546238\pi\)
\(998\) −28.3428 −0.897177
\(999\) −10.1454 −0.320986
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 2667.2.a.j.1.7 7
3.2 odd 2 8001.2.a.l.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2667.2.a.j.1.7 7 1.1 even 1 trivial
8001.2.a.l.1.1 7 3.2 odd 2