Properties

Label 8034.2.a.w.1.7
Level 8034
Weight 2
Character 8034.1
Self dual yes
Analytic conductor 64.152
Analytic rank 1
Dimension 12
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8034.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} - 2790 x^{3} - 352 x^{2} + 1768 x + 768\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.02386\) of defining polynomial
Character \(\chi\) \(=\) 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.812175 q^{5} -1.00000 q^{6} -2.80411 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.812175 q^{5} -1.00000 q^{6} -2.80411 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.812175 q^{10} +4.04933 q^{11} +1.00000 q^{12} +1.00000 q^{13} +2.80411 q^{14} -0.812175 q^{15} +1.00000 q^{16} +2.29591 q^{17} -1.00000 q^{18} -1.01847 q^{19} -0.812175 q^{20} -2.80411 q^{21} -4.04933 q^{22} -8.19340 q^{23} -1.00000 q^{24} -4.34037 q^{25} -1.00000 q^{26} +1.00000 q^{27} -2.80411 q^{28} +6.94281 q^{29} +0.812175 q^{30} +1.13390 q^{31} -1.00000 q^{32} +4.04933 q^{33} -2.29591 q^{34} +2.27743 q^{35} +1.00000 q^{36} +5.96324 q^{37} +1.01847 q^{38} +1.00000 q^{39} +0.812175 q^{40} -10.6535 q^{41} +2.80411 q^{42} -8.47462 q^{43} +4.04933 q^{44} -0.812175 q^{45} +8.19340 q^{46} -4.10776 q^{47} +1.00000 q^{48} +0.863023 q^{49} +4.34037 q^{50} +2.29591 q^{51} +1.00000 q^{52} +12.4604 q^{53} -1.00000 q^{54} -3.28876 q^{55} +2.80411 q^{56} -1.01847 q^{57} -6.94281 q^{58} +0.884938 q^{59} -0.812175 q^{60} -4.79433 q^{61} -1.13390 q^{62} -2.80411 q^{63} +1.00000 q^{64} -0.812175 q^{65} -4.04933 q^{66} +0.580237 q^{67} +2.29591 q^{68} -8.19340 q^{69} -2.27743 q^{70} -8.92029 q^{71} -1.00000 q^{72} +15.9992 q^{73} -5.96324 q^{74} -4.34037 q^{75} -1.01847 q^{76} -11.3547 q^{77} -1.00000 q^{78} -9.00058 q^{79} -0.812175 q^{80} +1.00000 q^{81} +10.6535 q^{82} -4.73672 q^{83} -2.80411 q^{84} -1.86468 q^{85} +8.47462 q^{86} +6.94281 q^{87} -4.04933 q^{88} +10.1598 q^{89} +0.812175 q^{90} -2.80411 q^{91} -8.19340 q^{92} +1.13390 q^{93} +4.10776 q^{94} +0.827178 q^{95} -1.00000 q^{96} +4.77835 q^{97} -0.863023 q^{98} +4.04933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{2} + 12q^{3} + 12q^{4} - 4q^{5} - 12q^{6} - 12q^{8} + 12q^{9} + O(q^{10}) \) \( 12q - 12q^{2} + 12q^{3} + 12q^{4} - 4q^{5} - 12q^{6} - 12q^{8} + 12q^{9} + 4q^{10} - 9q^{11} + 12q^{12} + 12q^{13} - 4q^{15} + 12q^{16} - 20q^{17} - 12q^{18} + 4q^{19} - 4q^{20} + 9q^{22} - 30q^{23} - 12q^{24} + 14q^{25} - 12q^{26} + 12q^{27} - 29q^{29} + 4q^{30} + 6q^{31} - 12q^{32} - 9q^{33} + 20q^{34} - 22q^{35} + 12q^{36} + 7q^{37} - 4q^{38} + 12q^{39} + 4q^{40} - 8q^{41} - 8q^{43} - 9q^{44} - 4q^{45} + 30q^{46} - 16q^{47} + 12q^{48} + 10q^{49} - 14q^{50} - 20q^{51} + 12q^{52} - 9q^{53} - 12q^{54} - 20q^{55} + 4q^{57} + 29q^{58} - 29q^{59} - 4q^{60} - 26q^{61} - 6q^{62} + 12q^{64} - 4q^{65} + 9q^{66} + 12q^{67} - 20q^{68} - 30q^{69} + 22q^{70} - 35q^{71} - 12q^{72} + 18q^{73} - 7q^{74} + 14q^{75} + 4q^{76} - 25q^{77} - 12q^{78} - 37q^{79} - 4q^{80} + 12q^{81} + 8q^{82} - 24q^{83} - 17q^{85} + 8q^{86} - 29q^{87} + 9q^{88} + 15q^{89} + 4q^{90} - 30q^{92} + 6q^{93} + 16q^{94} - 54q^{95} - 12q^{96} - 11q^{97} - 10q^{98} - 9q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −0.812175 −0.363216 −0.181608 0.983371i \(-0.558130\pi\)
−0.181608 + 0.983371i \(0.558130\pi\)
\(6\) −1.00000 −0.408248
\(7\) −2.80411 −1.05985 −0.529927 0.848043i \(-0.677781\pi\)
−0.529927 + 0.848043i \(0.677781\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0.812175 0.256832
\(11\) 4.04933 1.22092 0.610459 0.792048i \(-0.290985\pi\)
0.610459 + 0.792048i \(0.290985\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350
\(14\) 2.80411 0.749429
\(15\) −0.812175 −0.209703
\(16\) 1.00000 0.250000
\(17\) 2.29591 0.556841 0.278420 0.960459i \(-0.410189\pi\)
0.278420 + 0.960459i \(0.410189\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.01847 −0.233654 −0.116827 0.993152i \(-0.537272\pi\)
−0.116827 + 0.993152i \(0.537272\pi\)
\(20\) −0.812175 −0.181608
\(21\) −2.80411 −0.611907
\(22\) −4.04933 −0.863319
\(23\) −8.19340 −1.70844 −0.854221 0.519910i \(-0.825965\pi\)
−0.854221 + 0.519910i \(0.825965\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.34037 −0.868074
\(26\) −1.00000 −0.196116
\(27\) 1.00000 0.192450
\(28\) −2.80411 −0.529927
\(29\) 6.94281 1.28925 0.644624 0.764500i \(-0.277014\pi\)
0.644624 + 0.764500i \(0.277014\pi\)
\(30\) 0.812175 0.148282
\(31\) 1.13390 0.203655 0.101827 0.994802i \(-0.467531\pi\)
0.101827 + 0.994802i \(0.467531\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.04933 0.704897
\(34\) −2.29591 −0.393746
\(35\) 2.27743 0.384955
\(36\) 1.00000 0.166667
\(37\) 5.96324 0.980351 0.490175 0.871624i \(-0.336933\pi\)
0.490175 + 0.871624i \(0.336933\pi\)
\(38\) 1.01847 0.165218
\(39\) 1.00000 0.160128
\(40\) 0.812175 0.128416
\(41\) −10.6535 −1.66379 −0.831896 0.554932i \(-0.812744\pi\)
−0.831896 + 0.554932i \(0.812744\pi\)
\(42\) 2.80411 0.432683
\(43\) −8.47462 −1.29237 −0.646184 0.763182i \(-0.723636\pi\)
−0.646184 + 0.763182i \(0.723636\pi\)
\(44\) 4.04933 0.610459
\(45\) −0.812175 −0.121072
\(46\) 8.19340 1.20805
\(47\) −4.10776 −0.599179 −0.299589 0.954068i \(-0.596850\pi\)
−0.299589 + 0.954068i \(0.596850\pi\)
\(48\) 1.00000 0.144338
\(49\) 0.863023 0.123289
\(50\) 4.34037 0.613821
\(51\) 2.29591 0.321492
\(52\) 1.00000 0.138675
\(53\) 12.4604 1.71157 0.855784 0.517334i \(-0.173075\pi\)
0.855784 + 0.517334i \(0.173075\pi\)
\(54\) −1.00000 −0.136083
\(55\) −3.28876 −0.443456
\(56\) 2.80411 0.374715
\(57\) −1.01847 −0.134900
\(58\) −6.94281 −0.911636
\(59\) 0.884938 0.115209 0.0576045 0.998339i \(-0.481654\pi\)
0.0576045 + 0.998339i \(0.481654\pi\)
\(60\) −0.812175 −0.104851
\(61\) −4.79433 −0.613851 −0.306926 0.951733i \(-0.599300\pi\)
−0.306926 + 0.951733i \(0.599300\pi\)
\(62\) −1.13390 −0.144006
\(63\) −2.80411 −0.353284
\(64\) 1.00000 0.125000
\(65\) −0.812175 −0.100738
\(66\) −4.04933 −0.498438
\(67\) 0.580237 0.0708873 0.0354436 0.999372i \(-0.488716\pi\)
0.0354436 + 0.999372i \(0.488716\pi\)
\(68\) 2.29591 0.278420
\(69\) −8.19340 −0.986369
\(70\) −2.27743 −0.272204
\(71\) −8.92029 −1.05864 −0.529322 0.848421i \(-0.677554\pi\)
−0.529322 + 0.848421i \(0.677554\pi\)
\(72\) −1.00000 −0.117851
\(73\) 15.9992 1.87256 0.936282 0.351249i \(-0.114243\pi\)
0.936282 + 0.351249i \(0.114243\pi\)
\(74\) −5.96324 −0.693213
\(75\) −4.34037 −0.501183
\(76\) −1.01847 −0.116827
\(77\) −11.3547 −1.29399
\(78\) −1.00000 −0.113228
\(79\) −9.00058 −1.01264 −0.506322 0.862344i \(-0.668995\pi\)
−0.506322 + 0.862344i \(0.668995\pi\)
\(80\) −0.812175 −0.0908039
\(81\) 1.00000 0.111111
\(82\) 10.6535 1.17648
\(83\) −4.73672 −0.519923 −0.259962 0.965619i \(-0.583710\pi\)
−0.259962 + 0.965619i \(0.583710\pi\)
\(84\) −2.80411 −0.305953
\(85\) −1.86468 −0.202253
\(86\) 8.47462 0.913842
\(87\) 6.94281 0.744348
\(88\) −4.04933 −0.431660
\(89\) 10.1598 1.07694 0.538469 0.842645i \(-0.319003\pi\)
0.538469 + 0.842645i \(0.319003\pi\)
\(90\) 0.812175 0.0856107
\(91\) −2.80411 −0.293950
\(92\) −8.19340 −0.854221
\(93\) 1.13390 0.117580
\(94\) 4.10776 0.423683
\(95\) 0.827178 0.0848667
\(96\) −1.00000 −0.102062
\(97\) 4.77835 0.485168 0.242584 0.970130i \(-0.422005\pi\)
0.242584 + 0.970130i \(0.422005\pi\)
\(98\) −0.863023 −0.0871785
\(99\) 4.04933 0.406973
\(100\) −4.34037 −0.434037
\(101\) −15.0451 −1.49704 −0.748522 0.663110i \(-0.769236\pi\)
−0.748522 + 0.663110i \(0.769236\pi\)
\(102\) −2.29591 −0.227329
\(103\) −1.00000 −0.0985329
\(104\) −1.00000 −0.0980581
\(105\) 2.27743 0.222254
\(106\) −12.4604 −1.21026
\(107\) 0.0930370 0.00899423 0.00449712 0.999990i \(-0.498569\pi\)
0.00449712 + 0.999990i \(0.498569\pi\)
\(108\) 1.00000 0.0962250
\(109\) −7.16487 −0.686270 −0.343135 0.939286i \(-0.611489\pi\)
−0.343135 + 0.939286i \(0.611489\pi\)
\(110\) 3.28876 0.313571
\(111\) 5.96324 0.566006
\(112\) −2.80411 −0.264963
\(113\) −5.38039 −0.506145 −0.253072 0.967447i \(-0.581441\pi\)
−0.253072 + 0.967447i \(0.581441\pi\)
\(114\) 1.01847 0.0953888
\(115\) 6.65447 0.620533
\(116\) 6.94281 0.644624
\(117\) 1.00000 0.0924500
\(118\) −0.884938 −0.0814651
\(119\) −6.43799 −0.590170
\(120\) 0.812175 0.0741411
\(121\) 5.39704 0.490640
\(122\) 4.79433 0.434058
\(123\) −10.6535 −0.960591
\(124\) 1.13390 0.101827
\(125\) 7.58601 0.678514
\(126\) 2.80411 0.249810
\(127\) −10.4196 −0.924593 −0.462296 0.886725i \(-0.652974\pi\)
−0.462296 + 0.886725i \(0.652974\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −8.47462 −0.746148
\(130\) 0.812175 0.0712324
\(131\) 10.0961 0.882104 0.441052 0.897482i \(-0.354605\pi\)
0.441052 + 0.897482i \(0.354605\pi\)
\(132\) 4.04933 0.352449
\(133\) 2.85591 0.247639
\(134\) −0.580237 −0.0501249
\(135\) −0.812175 −0.0699009
\(136\) −2.29591 −0.196873
\(137\) 6.33088 0.540883 0.270442 0.962736i \(-0.412830\pi\)
0.270442 + 0.962736i \(0.412830\pi\)
\(138\) 8.19340 0.697468
\(139\) −7.51896 −0.637750 −0.318875 0.947797i \(-0.603305\pi\)
−0.318875 + 0.947797i \(0.603305\pi\)
\(140\) 2.27743 0.192478
\(141\) −4.10776 −0.345936
\(142\) 8.92029 0.748574
\(143\) 4.04933 0.338622
\(144\) 1.00000 0.0833333
\(145\) −5.63878 −0.468275
\(146\) −15.9992 −1.32410
\(147\) 0.863023 0.0711810
\(148\) 5.96324 0.490175
\(149\) 5.49662 0.450300 0.225150 0.974324i \(-0.427713\pi\)
0.225150 + 0.974324i \(0.427713\pi\)
\(150\) 4.34037 0.354390
\(151\) 6.71314 0.546308 0.273154 0.961970i \(-0.411933\pi\)
0.273154 + 0.961970i \(0.411933\pi\)
\(152\) 1.01847 0.0826091
\(153\) 2.29591 0.185614
\(154\) 11.3547 0.914992
\(155\) −0.920926 −0.0739706
\(156\) 1.00000 0.0800641
\(157\) −8.77574 −0.700381 −0.350190 0.936679i \(-0.613883\pi\)
−0.350190 + 0.936679i \(0.613883\pi\)
\(158\) 9.00058 0.716048
\(159\) 12.4604 0.988174
\(160\) 0.812175 0.0642080
\(161\) 22.9752 1.81070
\(162\) −1.00000 −0.0785674
\(163\) 19.3491 1.51554 0.757769 0.652523i \(-0.226289\pi\)
0.757769 + 0.652523i \(0.226289\pi\)
\(164\) −10.6535 −0.831896
\(165\) −3.28876 −0.256030
\(166\) 4.73672 0.367641
\(167\) −10.1438 −0.784952 −0.392476 0.919762i \(-0.628381\pi\)
−0.392476 + 0.919762i \(0.628381\pi\)
\(168\) 2.80411 0.216342
\(169\) 1.00000 0.0769231
\(170\) 1.86468 0.143015
\(171\) −1.01847 −0.0778846
\(172\) −8.47462 −0.646184
\(173\) −15.1679 −1.15319 −0.576596 0.817029i \(-0.695619\pi\)
−0.576596 + 0.817029i \(0.695619\pi\)
\(174\) −6.94281 −0.526333
\(175\) 12.1709 0.920032
\(176\) 4.04933 0.305229
\(177\) 0.884938 0.0665160
\(178\) −10.1598 −0.761510
\(179\) −20.7858 −1.55360 −0.776802 0.629745i \(-0.783159\pi\)
−0.776802 + 0.629745i \(0.783159\pi\)
\(180\) −0.812175 −0.0605359
\(181\) 8.49683 0.631565 0.315782 0.948832i \(-0.397733\pi\)
0.315782 + 0.948832i \(0.397733\pi\)
\(182\) 2.80411 0.207854
\(183\) −4.79433 −0.354407
\(184\) 8.19340 0.604025
\(185\) −4.84319 −0.356079
\(186\) −1.13390 −0.0831417
\(187\) 9.29690 0.679857
\(188\) −4.10776 −0.299589
\(189\) −2.80411 −0.203969
\(190\) −0.827178 −0.0600098
\(191\) −24.5573 −1.77690 −0.888452 0.458970i \(-0.848218\pi\)
−0.888452 + 0.458970i \(0.848218\pi\)
\(192\) 1.00000 0.0721688
\(193\) 20.6351 1.48535 0.742675 0.669652i \(-0.233557\pi\)
0.742675 + 0.669652i \(0.233557\pi\)
\(194\) −4.77835 −0.343066
\(195\) −0.812175 −0.0581610
\(196\) 0.863023 0.0616445
\(197\) 12.8639 0.916515 0.458258 0.888819i \(-0.348474\pi\)
0.458258 + 0.888819i \(0.348474\pi\)
\(198\) −4.04933 −0.287773
\(199\) 23.5266 1.66776 0.833879 0.551948i \(-0.186115\pi\)
0.833879 + 0.551948i \(0.186115\pi\)
\(200\) 4.34037 0.306911
\(201\) 0.580237 0.0409268
\(202\) 15.0451 1.05857
\(203\) −19.4684 −1.36641
\(204\) 2.29591 0.160746
\(205\) 8.65247 0.604315
\(206\) 1.00000 0.0696733
\(207\) −8.19340 −0.569481
\(208\) 1.00000 0.0693375
\(209\) −4.12413 −0.285272
\(210\) −2.27743 −0.157157
\(211\) 5.66546 0.390027 0.195013 0.980801i \(-0.437525\pi\)
0.195013 + 0.980801i \(0.437525\pi\)
\(212\) 12.4604 0.855784
\(213\) −8.92029 −0.611208
\(214\) −0.0930370 −0.00635988
\(215\) 6.88287 0.469408
\(216\) −1.00000 −0.0680414
\(217\) −3.17958 −0.215844
\(218\) 7.16487 0.485266
\(219\) 15.9992 1.08113
\(220\) −3.28876 −0.221728
\(221\) 2.29591 0.154440
\(222\) −5.96324 −0.400227
\(223\) 2.11119 0.141376 0.0706878 0.997498i \(-0.477481\pi\)
0.0706878 + 0.997498i \(0.477481\pi\)
\(224\) 2.80411 0.187357
\(225\) −4.34037 −0.289358
\(226\) 5.38039 0.357898
\(227\) 16.6256 1.10348 0.551739 0.834017i \(-0.313964\pi\)
0.551739 + 0.834017i \(0.313964\pi\)
\(228\) −1.01847 −0.0674500
\(229\) −22.6417 −1.49620 −0.748101 0.663585i \(-0.769034\pi\)
−0.748101 + 0.663585i \(0.769034\pi\)
\(230\) −6.65447 −0.438783
\(231\) −11.3547 −0.747088
\(232\) −6.94281 −0.455818
\(233\) −0.805363 −0.0527611 −0.0263806 0.999652i \(-0.508398\pi\)
−0.0263806 + 0.999652i \(0.508398\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 3.33622 0.217631
\(236\) 0.884938 0.0576045
\(237\) −9.00058 −0.584651
\(238\) 6.43799 0.417313
\(239\) −27.6450 −1.78821 −0.894103 0.447861i \(-0.852186\pi\)
−0.894103 + 0.447861i \(0.852186\pi\)
\(240\) −0.812175 −0.0524257
\(241\) 5.25526 0.338521 0.169260 0.985571i \(-0.445862\pi\)
0.169260 + 0.985571i \(0.445862\pi\)
\(242\) −5.39704 −0.346935
\(243\) 1.00000 0.0641500
\(244\) −4.79433 −0.306926
\(245\) −0.700926 −0.0447805
\(246\) 10.6535 0.679240
\(247\) −1.01847 −0.0648039
\(248\) −1.13390 −0.0720028
\(249\) −4.73672 −0.300178
\(250\) −7.58601 −0.479782
\(251\) −11.7511 −0.741721 −0.370860 0.928689i \(-0.620937\pi\)
−0.370860 + 0.928689i \(0.620937\pi\)
\(252\) −2.80411 −0.176642
\(253\) −33.1777 −2.08587
\(254\) 10.4196 0.653786
\(255\) −1.86468 −0.116771
\(256\) 1.00000 0.0625000
\(257\) 4.55065 0.283862 0.141931 0.989877i \(-0.454669\pi\)
0.141931 + 0.989877i \(0.454669\pi\)
\(258\) 8.47462 0.527607
\(259\) −16.7216 −1.03903
\(260\) −0.812175 −0.0503689
\(261\) 6.94281 0.429749
\(262\) −10.0961 −0.623742
\(263\) 2.07134 0.127724 0.0638620 0.997959i \(-0.479658\pi\)
0.0638620 + 0.997959i \(0.479658\pi\)
\(264\) −4.04933 −0.249219
\(265\) −10.1200 −0.621668
\(266\) −2.85591 −0.175107
\(267\) 10.1598 0.621771
\(268\) 0.580237 0.0354436
\(269\) −16.0087 −0.976067 −0.488034 0.872825i \(-0.662286\pi\)
−0.488034 + 0.872825i \(0.662286\pi\)
\(270\) 0.812175 0.0494274
\(271\) −22.3206 −1.35588 −0.677940 0.735118i \(-0.737127\pi\)
−0.677940 + 0.735118i \(0.737127\pi\)
\(272\) 2.29591 0.139210
\(273\) −2.80411 −0.169712
\(274\) −6.33088 −0.382462
\(275\) −17.5756 −1.05985
\(276\) −8.19340 −0.493185
\(277\) 1.43459 0.0861962 0.0430981 0.999071i \(-0.486277\pi\)
0.0430981 + 0.999071i \(0.486277\pi\)
\(278\) 7.51896 0.450958
\(279\) 1.13390 0.0678849
\(280\) −2.27743 −0.136102
\(281\) −27.6330 −1.64845 −0.824223 0.566266i \(-0.808388\pi\)
−0.824223 + 0.566266i \(0.808388\pi\)
\(282\) 4.10776 0.244614
\(283\) −29.2077 −1.73621 −0.868107 0.496376i \(-0.834664\pi\)
−0.868107 + 0.496376i \(0.834664\pi\)
\(284\) −8.92029 −0.529322
\(285\) 0.827178 0.0489978
\(286\) −4.04933 −0.239442
\(287\) 29.8735 1.76338
\(288\) −1.00000 −0.0589256
\(289\) −11.7288 −0.689928
\(290\) 5.63878 0.331120
\(291\) 4.77835 0.280112
\(292\) 15.9992 0.936282
\(293\) −25.8130 −1.50801 −0.754005 0.656868i \(-0.771881\pi\)
−0.754005 + 0.656868i \(0.771881\pi\)
\(294\) −0.863023 −0.0503325
\(295\) −0.718724 −0.0418457
\(296\) −5.96324 −0.346606
\(297\) 4.04933 0.234966
\(298\) −5.49662 −0.318410
\(299\) −8.19340 −0.473837
\(300\) −4.34037 −0.250592
\(301\) 23.7637 1.36972
\(302\) −6.71314 −0.386298
\(303\) −15.0451 −0.864319
\(304\) −1.01847 −0.0584134
\(305\) 3.89384 0.222960
\(306\) −2.29591 −0.131249
\(307\) −4.20527 −0.240008 −0.120004 0.992773i \(-0.538291\pi\)
−0.120004 + 0.992773i \(0.538291\pi\)
\(308\) −11.3547 −0.646997
\(309\) −1.00000 −0.0568880
\(310\) 0.920926 0.0523051
\(311\) 6.72177 0.381156 0.190578 0.981672i \(-0.438964\pi\)
0.190578 + 0.981672i \(0.438964\pi\)
\(312\) −1.00000 −0.0566139
\(313\) −20.8705 −1.17967 −0.589835 0.807524i \(-0.700807\pi\)
−0.589835 + 0.807524i \(0.700807\pi\)
\(314\) 8.77574 0.495244
\(315\) 2.27743 0.128318
\(316\) −9.00058 −0.506322
\(317\) −11.3847 −0.639431 −0.319715 0.947514i \(-0.603587\pi\)
−0.319715 + 0.947514i \(0.603587\pi\)
\(318\) −12.4604 −0.698745
\(319\) 28.1137 1.57407
\(320\) −0.812175 −0.0454019
\(321\) 0.0930370 0.00519282
\(322\) −22.9752 −1.28036
\(323\) −2.33833 −0.130108
\(324\) 1.00000 0.0555556
\(325\) −4.34037 −0.240761
\(326\) −19.3491 −1.07165
\(327\) −7.16487 −0.396218
\(328\) 10.6535 0.588239
\(329\) 11.5186 0.635042
\(330\) 3.28876 0.181040
\(331\) −1.90596 −0.104761 −0.0523805 0.998627i \(-0.516681\pi\)
−0.0523805 + 0.998627i \(0.516681\pi\)
\(332\) −4.73672 −0.259962
\(333\) 5.96324 0.326784
\(334\) 10.1438 0.555045
\(335\) −0.471254 −0.0257474
\(336\) −2.80411 −0.152977
\(337\) 22.3056 1.21506 0.607532 0.794295i \(-0.292159\pi\)
0.607532 + 0.794295i \(0.292159\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −5.38039 −0.292223
\(340\) −1.86468 −0.101127
\(341\) 4.59154 0.248646
\(342\) 1.01847 0.0550727
\(343\) 17.2087 0.929185
\(344\) 8.47462 0.456921
\(345\) 6.65447 0.358265
\(346\) 15.1679 0.815430
\(347\) −34.3314 −1.84301 −0.921503 0.388371i \(-0.873038\pi\)
−0.921503 + 0.388371i \(0.873038\pi\)
\(348\) 6.94281 0.372174
\(349\) −25.3383 −1.35633 −0.678165 0.734910i \(-0.737224\pi\)
−0.678165 + 0.734910i \(0.737224\pi\)
\(350\) −12.1709 −0.650561
\(351\) 1.00000 0.0533761
\(352\) −4.04933 −0.215830
\(353\) −9.54966 −0.508277 −0.254139 0.967168i \(-0.581792\pi\)
−0.254139 + 0.967168i \(0.581792\pi\)
\(354\) −0.884938 −0.0470339
\(355\) 7.24483 0.384516
\(356\) 10.1598 0.538469
\(357\) −6.43799 −0.340735
\(358\) 20.7858 1.09856
\(359\) −3.57808 −0.188844 −0.0944218 0.995532i \(-0.530100\pi\)
−0.0944218 + 0.995532i \(0.530100\pi\)
\(360\) 0.812175 0.0428054
\(361\) −17.9627 −0.945406
\(362\) −8.49683 −0.446584
\(363\) 5.39704 0.283271
\(364\) −2.80411 −0.146975
\(365\) −12.9941 −0.680145
\(366\) 4.79433 0.250604
\(367\) −3.17092 −0.165521 −0.0827604 0.996569i \(-0.526374\pi\)
−0.0827604 + 0.996569i \(0.526374\pi\)
\(368\) −8.19340 −0.427110
\(369\) −10.6535 −0.554597
\(370\) 4.84319 0.251786
\(371\) −34.9403 −1.81401
\(372\) 1.13390 0.0587901
\(373\) 26.5049 1.37237 0.686185 0.727427i \(-0.259284\pi\)
0.686185 + 0.727427i \(0.259284\pi\)
\(374\) −9.29690 −0.480731
\(375\) 7.58601 0.391740
\(376\) 4.10776 0.211842
\(377\) 6.94281 0.357573
\(378\) 2.80411 0.144228
\(379\) −26.3016 −1.35102 −0.675512 0.737349i \(-0.736078\pi\)
−0.675512 + 0.737349i \(0.736078\pi\)
\(380\) 0.827178 0.0424333
\(381\) −10.4196 −0.533814
\(382\) 24.5573 1.25646
\(383\) −10.3778 −0.530279 −0.265140 0.964210i \(-0.585418\pi\)
−0.265140 + 0.964210i \(0.585418\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 9.22204 0.469999
\(386\) −20.6351 −1.05030
\(387\) −8.47462 −0.430789
\(388\) 4.77835 0.242584
\(389\) −11.6907 −0.592743 −0.296372 0.955073i \(-0.595777\pi\)
−0.296372 + 0.955073i \(0.595777\pi\)
\(390\) 0.812175 0.0411261
\(391\) −18.8113 −0.951330
\(392\) −0.863023 −0.0435893
\(393\) 10.0961 0.509283
\(394\) −12.8639 −0.648074
\(395\) 7.31005 0.367808
\(396\) 4.04933 0.203486
\(397\) −10.2444 −0.514151 −0.257075 0.966391i \(-0.582759\pi\)
−0.257075 + 0.966391i \(0.582759\pi\)
\(398\) −23.5266 −1.17928
\(399\) 2.85591 0.142974
\(400\) −4.34037 −0.217019
\(401\) −29.0137 −1.44887 −0.724437 0.689341i \(-0.757900\pi\)
−0.724437 + 0.689341i \(0.757900\pi\)
\(402\) −0.580237 −0.0289396
\(403\) 1.13390 0.0564837
\(404\) −15.0451 −0.748522
\(405\) −0.812175 −0.0403573
\(406\) 19.4684 0.966200
\(407\) 24.1471 1.19693
\(408\) −2.29591 −0.113665
\(409\) 29.3234 1.44995 0.724973 0.688777i \(-0.241852\pi\)
0.724973 + 0.688777i \(0.241852\pi\)
\(410\) −8.65247 −0.427315
\(411\) 6.33088 0.312279
\(412\) −1.00000 −0.0492665
\(413\) −2.48146 −0.122105
\(414\) 8.19340 0.402684
\(415\) 3.84705 0.188844
\(416\) −1.00000 −0.0490290
\(417\) −7.51896 −0.368205
\(418\) 4.12413 0.201718
\(419\) −10.6366 −0.519632 −0.259816 0.965658i \(-0.583662\pi\)
−0.259816 + 0.965658i \(0.583662\pi\)
\(420\) 2.27743 0.111127
\(421\) −6.31510 −0.307779 −0.153889 0.988088i \(-0.549180\pi\)
−0.153889 + 0.988088i \(0.549180\pi\)
\(422\) −5.66546 −0.275790
\(423\) −4.10776 −0.199726
\(424\) −12.4604 −0.605131
\(425\) −9.96512 −0.483379
\(426\) 8.92029 0.432190
\(427\) 13.4438 0.650592
\(428\) 0.0930370 0.00449712
\(429\) 4.04933 0.195503
\(430\) −6.88287 −0.331921
\(431\) −32.7901 −1.57944 −0.789721 0.613466i \(-0.789775\pi\)
−0.789721 + 0.613466i \(0.789775\pi\)
\(432\) 1.00000 0.0481125
\(433\) −23.0398 −1.10722 −0.553611 0.832776i \(-0.686750\pi\)
−0.553611 + 0.832776i \(0.686750\pi\)
\(434\) 3.17958 0.152625
\(435\) −5.63878 −0.270359
\(436\) −7.16487 −0.343135
\(437\) 8.34476 0.399184
\(438\) −15.9992 −0.764471
\(439\) 37.5925 1.79419 0.897096 0.441837i \(-0.145673\pi\)
0.897096 + 0.441837i \(0.145673\pi\)
\(440\) 3.28876 0.156785
\(441\) 0.863023 0.0410963
\(442\) −2.29591 −0.109205
\(443\) 34.6459 1.64607 0.823037 0.567988i \(-0.192278\pi\)
0.823037 + 0.567988i \(0.192278\pi\)
\(444\) 5.96324 0.283003
\(445\) −8.25154 −0.391161
\(446\) −2.11119 −0.0999676
\(447\) 5.49662 0.259981
\(448\) −2.80411 −0.132482
\(449\) −11.6519 −0.549888 −0.274944 0.961460i \(-0.588659\pi\)
−0.274944 + 0.961460i \(0.588659\pi\)
\(450\) 4.34037 0.204607
\(451\) −43.1394 −2.03135
\(452\) −5.38039 −0.253072
\(453\) 6.71314 0.315411
\(454\) −16.6256 −0.780277
\(455\) 2.27743 0.106767
\(456\) 1.01847 0.0476944
\(457\) 26.5669 1.24275 0.621374 0.783514i \(-0.286575\pi\)
0.621374 + 0.783514i \(0.286575\pi\)
\(458\) 22.6417 1.05797
\(459\) 2.29591 0.107164
\(460\) 6.65447 0.310266
\(461\) −10.3671 −0.482844 −0.241422 0.970420i \(-0.577614\pi\)
−0.241422 + 0.970420i \(0.577614\pi\)
\(462\) 11.3547 0.528271
\(463\) 29.0583 1.35046 0.675228 0.737609i \(-0.264045\pi\)
0.675228 + 0.737609i \(0.264045\pi\)
\(464\) 6.94281 0.322312
\(465\) −0.920926 −0.0427069
\(466\) 0.805363 0.0373077
\(467\) 5.95392 0.275514 0.137757 0.990466i \(-0.456011\pi\)
0.137757 + 0.990466i \(0.456011\pi\)
\(468\) 1.00000 0.0462250
\(469\) −1.62705 −0.0751301
\(470\) −3.33622 −0.153888
\(471\) −8.77574 −0.404365
\(472\) −0.884938 −0.0407326
\(473\) −34.3165 −1.57787
\(474\) 9.00058 0.413411
\(475\) 4.42055 0.202829
\(476\) −6.43799 −0.295085
\(477\) 12.4604 0.570523
\(478\) 27.6450 1.26445
\(479\) −2.33530 −0.106703 −0.0533513 0.998576i \(-0.516990\pi\)
−0.0533513 + 0.998576i \(0.516990\pi\)
\(480\) 0.812175 0.0370705
\(481\) 5.96324 0.271900
\(482\) −5.25526 −0.239370
\(483\) 22.9752 1.04541
\(484\) 5.39704 0.245320
\(485\) −3.88086 −0.176221
\(486\) −1.00000 −0.0453609
\(487\) 17.3845 0.787769 0.393884 0.919160i \(-0.371131\pi\)
0.393884 + 0.919160i \(0.371131\pi\)
\(488\) 4.79433 0.217029
\(489\) 19.3491 0.874996
\(490\) 0.700926 0.0316646
\(491\) −19.7595 −0.891733 −0.445867 0.895099i \(-0.647104\pi\)
−0.445867 + 0.895099i \(0.647104\pi\)
\(492\) −10.6535 −0.480295
\(493\) 15.9401 0.717906
\(494\) 1.01847 0.0458233
\(495\) −3.28876 −0.147819
\(496\) 1.13390 0.0509137
\(497\) 25.0135 1.12201
\(498\) 4.73672 0.212258
\(499\) −0.921867 −0.0412684 −0.0206342 0.999787i \(-0.506569\pi\)
−0.0206342 + 0.999787i \(0.506569\pi\)
\(500\) 7.58601 0.339257
\(501\) −10.1438 −0.453192
\(502\) 11.7511 0.524476
\(503\) −12.8080 −0.571078 −0.285539 0.958367i \(-0.592173\pi\)
−0.285539 + 0.958367i \(0.592173\pi\)
\(504\) 2.80411 0.124905
\(505\) 12.2193 0.543750
\(506\) 33.1777 1.47493
\(507\) 1.00000 0.0444116
\(508\) −10.4196 −0.462296
\(509\) 5.13942 0.227801 0.113900 0.993492i \(-0.463666\pi\)
0.113900 + 0.993492i \(0.463666\pi\)
\(510\) 1.86468 0.0825696
\(511\) −44.8635 −1.98464
\(512\) −1.00000 −0.0441942
\(513\) −1.01847 −0.0449667
\(514\) −4.55065 −0.200721
\(515\) 0.812175 0.0357887
\(516\) −8.47462 −0.373074
\(517\) −16.6337 −0.731548
\(518\) 16.7216 0.734704
\(519\) −15.1679 −0.665796
\(520\) 0.812175 0.0356162
\(521\) 6.97500 0.305580 0.152790 0.988259i \(-0.451174\pi\)
0.152790 + 0.988259i \(0.451174\pi\)
\(522\) −6.94281 −0.303879
\(523\) −0.406703 −0.0177839 −0.00889194 0.999960i \(-0.502830\pi\)
−0.00889194 + 0.999960i \(0.502830\pi\)
\(524\) 10.0961 0.441052
\(525\) 12.1709 0.531180
\(526\) −2.07134 −0.0903145
\(527\) 2.60334 0.113403
\(528\) 4.04933 0.176224
\(529\) 44.1318 1.91877
\(530\) 10.1200 0.439586
\(531\) 0.884938 0.0384030
\(532\) 2.85591 0.123819
\(533\) −10.6535 −0.461453
\(534\) −10.1598 −0.439658
\(535\) −0.0755623 −0.00326684
\(536\) −0.580237 −0.0250624
\(537\) −20.7858 −0.896973
\(538\) 16.0087 0.690184
\(539\) 3.49466 0.150526
\(540\) −0.812175 −0.0349504
\(541\) 43.1680 1.85594 0.927969 0.372657i \(-0.121553\pi\)
0.927969 + 0.372657i \(0.121553\pi\)
\(542\) 22.3206 0.958751
\(543\) 8.49683 0.364634
\(544\) −2.29591 −0.0984365
\(545\) 5.81913 0.249264
\(546\) 2.80411 0.120005
\(547\) −31.5402 −1.34856 −0.674280 0.738476i \(-0.735546\pi\)
−0.674280 + 0.738476i \(0.735546\pi\)
\(548\) 6.33088 0.270442
\(549\) −4.79433 −0.204617
\(550\) 17.5756 0.749425
\(551\) −7.07107 −0.301238
\(552\) 8.19340 0.348734
\(553\) 25.2386 1.07325
\(554\) −1.43459 −0.0609499
\(555\) −4.84319 −0.205582
\(556\) −7.51896 −0.318875
\(557\) −1.08304 −0.0458899 −0.0229449 0.999737i \(-0.507304\pi\)
−0.0229449 + 0.999737i \(0.507304\pi\)
\(558\) −1.13390 −0.0480019
\(559\) −8.47462 −0.358438
\(560\) 2.27743 0.0962388
\(561\) 9.29690 0.392516
\(562\) 27.6330 1.16563
\(563\) 19.7982 0.834393 0.417196 0.908816i \(-0.363013\pi\)
0.417196 + 0.908816i \(0.363013\pi\)
\(564\) −4.10776 −0.172968
\(565\) 4.36982 0.183840
\(566\) 29.2077 1.22769
\(567\) −2.80411 −0.117761
\(568\) 8.92029 0.374287
\(569\) −27.6820 −1.16049 −0.580246 0.814442i \(-0.697043\pi\)
−0.580246 + 0.814442i \(0.697043\pi\)
\(570\) −0.827178 −0.0346467
\(571\) 20.4317 0.855042 0.427521 0.904005i \(-0.359387\pi\)
0.427521 + 0.904005i \(0.359387\pi\)
\(572\) 4.04933 0.169311
\(573\) −24.5573 −1.02590
\(574\) −29.8735 −1.24689
\(575\) 35.5624 1.48305
\(576\) 1.00000 0.0416667
\(577\) −6.45607 −0.268770 −0.134385 0.990929i \(-0.542906\pi\)
−0.134385 + 0.990929i \(0.542906\pi\)
\(578\) 11.7288 0.487853
\(579\) 20.6351 0.857567
\(580\) −5.63878 −0.234137
\(581\) 13.2823 0.551042
\(582\) −4.77835 −0.198069
\(583\) 50.4562 2.08968
\(584\) −15.9992 −0.662052
\(585\) −0.812175 −0.0335793
\(586\) 25.8130 1.06632
\(587\) −7.18362 −0.296500 −0.148250 0.988950i \(-0.547364\pi\)
−0.148250 + 0.988950i \(0.547364\pi\)
\(588\) 0.863023 0.0355905
\(589\) −1.15485 −0.0475847
\(590\) 0.718724 0.0295894
\(591\) 12.8639 0.529150
\(592\) 5.96324 0.245088
\(593\) 43.5311 1.78761 0.893804 0.448458i \(-0.148027\pi\)
0.893804 + 0.448458i \(0.148027\pi\)
\(594\) −4.04933 −0.166146
\(595\) 5.22877 0.214359
\(596\) 5.49662 0.225150
\(597\) 23.5266 0.962880
\(598\) 8.19340 0.335053
\(599\) −11.6674 −0.476716 −0.238358 0.971177i \(-0.576609\pi\)
−0.238358 + 0.971177i \(0.576609\pi\)
\(600\) 4.34037 0.177195
\(601\) 43.9848 1.79418 0.897090 0.441849i \(-0.145677\pi\)
0.897090 + 0.441849i \(0.145677\pi\)
\(602\) −23.7637 −0.968538
\(603\) 0.580237 0.0236291
\(604\) 6.71314 0.273154
\(605\) −4.38334 −0.178208
\(606\) 15.0451 0.611166
\(607\) 6.80863 0.276354 0.138177 0.990408i \(-0.455876\pi\)
0.138177 + 0.990408i \(0.455876\pi\)
\(608\) 1.01847 0.0413045
\(609\) −19.4684 −0.788899
\(610\) −3.89384 −0.157657
\(611\) −4.10776 −0.166182
\(612\) 2.29591 0.0928068
\(613\) −34.8280 −1.40669 −0.703344 0.710850i \(-0.748311\pi\)
−0.703344 + 0.710850i \(0.748311\pi\)
\(614\) 4.20527 0.169711
\(615\) 8.65247 0.348901
\(616\) 11.3547 0.457496
\(617\) 36.1839 1.45671 0.728354 0.685201i \(-0.240286\pi\)
0.728354 + 0.685201i \(0.240286\pi\)
\(618\) 1.00000 0.0402259
\(619\) −13.4757 −0.541632 −0.270816 0.962631i \(-0.587294\pi\)
−0.270816 + 0.962631i \(0.587294\pi\)
\(620\) −0.920926 −0.0369853
\(621\) −8.19340 −0.328790
\(622\) −6.72177 −0.269518
\(623\) −28.4892 −1.14140
\(624\) 1.00000 0.0400320
\(625\) 15.5407 0.621628
\(626\) 20.8705 0.834153
\(627\) −4.12413 −0.164702
\(628\) −8.77574 −0.350190
\(629\) 13.6911 0.545899
\(630\) −2.27743 −0.0907348
\(631\) 15.6495 0.622998 0.311499 0.950246i \(-0.399169\pi\)
0.311499 + 0.950246i \(0.399169\pi\)
\(632\) 9.00058 0.358024
\(633\) 5.66546 0.225182
\(634\) 11.3847 0.452146
\(635\) 8.46256 0.335827
\(636\) 12.4604 0.494087
\(637\) 0.863023 0.0341942
\(638\) −28.1137 −1.11303
\(639\) −8.92029 −0.352881
\(640\) 0.812175 0.0321040
\(641\) −17.3158 −0.683934 −0.341967 0.939712i \(-0.611093\pi\)
−0.341967 + 0.939712i \(0.611093\pi\)
\(642\) −0.0930370 −0.00367188
\(643\) 44.8856 1.77011 0.885057 0.465483i \(-0.154119\pi\)
0.885057 + 0.465483i \(0.154119\pi\)
\(644\) 22.9752 0.905349
\(645\) 6.88287 0.271013
\(646\) 2.33833 0.0920002
\(647\) 34.9463 1.37388 0.686940 0.726715i \(-0.258954\pi\)
0.686940 + 0.726715i \(0.258954\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 3.58340 0.140661
\(650\) 4.34037 0.170243
\(651\) −3.17958 −0.124618
\(652\) 19.3491 0.757769
\(653\) −36.4184 −1.42516 −0.712581 0.701590i \(-0.752474\pi\)
−0.712581 + 0.701590i \(0.752474\pi\)
\(654\) 7.16487 0.280169
\(655\) −8.19983 −0.320394
\(656\) −10.6535 −0.415948
\(657\) 15.9992 0.624188
\(658\) −11.5186 −0.449042
\(659\) −27.5734 −1.07411 −0.537053 0.843549i \(-0.680462\pi\)
−0.537053 + 0.843549i \(0.680462\pi\)
\(660\) −3.28876 −0.128015
\(661\) −32.6336 −1.26930 −0.634651 0.772799i \(-0.718856\pi\)
−0.634651 + 0.772799i \(0.718856\pi\)
\(662\) 1.90596 0.0740773
\(663\) 2.29591 0.0891659
\(664\) 4.73672 0.183821
\(665\) −2.31950 −0.0899462
\(666\) −5.96324 −0.231071
\(667\) −56.8852 −2.20261
\(668\) −10.1438 −0.392476
\(669\) 2.11119 0.0816232
\(670\) 0.471254 0.0182061
\(671\) −19.4138 −0.749462
\(672\) 2.80411 0.108171
\(673\) −41.2898 −1.59161 −0.795803 0.605556i \(-0.792951\pi\)
−0.795803 + 0.605556i \(0.792951\pi\)
\(674\) −22.3056 −0.859181
\(675\) −4.34037 −0.167061
\(676\) 1.00000 0.0384615
\(677\) −8.12620 −0.312315 −0.156158 0.987732i \(-0.549911\pi\)
−0.156158 + 0.987732i \(0.549911\pi\)
\(678\) 5.38039 0.206633
\(679\) −13.3990 −0.514207
\(680\) 1.86468 0.0715073
\(681\) 16.6256 0.637094
\(682\) −4.59154 −0.175819
\(683\) −2.65217 −0.101482 −0.0507412 0.998712i \(-0.516158\pi\)
−0.0507412 + 0.998712i \(0.516158\pi\)
\(684\) −1.01847 −0.0389423
\(685\) −5.14178 −0.196457
\(686\) −17.2087 −0.657033
\(687\) −22.6417 −0.863833
\(688\) −8.47462 −0.323092
\(689\) 12.4604 0.474703
\(690\) −6.65447 −0.253331
\(691\) −5.60099 −0.213072 −0.106536 0.994309i \(-0.533976\pi\)
−0.106536 + 0.994309i \(0.533976\pi\)
\(692\) −15.1679 −0.576596
\(693\) −11.3547 −0.431331
\(694\) 34.3314 1.30320
\(695\) 6.10671 0.231641
\(696\) −6.94281 −0.263167
\(697\) −24.4594 −0.926467
\(698\) 25.3383 0.959070
\(699\) −0.805363 −0.0304616
\(700\) 12.1709 0.460016
\(701\) −3.74962 −0.141621 −0.0708106 0.997490i \(-0.522559\pi\)
−0.0708106 + 0.997490i \(0.522559\pi\)
\(702\) −1.00000 −0.0377426
\(703\) −6.07340 −0.229063
\(704\) 4.04933 0.152615
\(705\) 3.33622 0.125649
\(706\) 9.54966 0.359406
\(707\) 42.1881 1.58665
\(708\) 0.884938 0.0332580
\(709\) 18.7137 0.702809 0.351405 0.936224i \(-0.385704\pi\)
0.351405 + 0.936224i \(0.385704\pi\)
\(710\) −7.24483 −0.271894
\(711\) −9.00058 −0.337548
\(712\) −10.1598 −0.380755
\(713\) −9.29051 −0.347932
\(714\) 6.43799 0.240936
\(715\) −3.28876 −0.122993
\(716\) −20.7858 −0.776802
\(717\) −27.6450 −1.03242
\(718\) 3.57808 0.133533
\(719\) −49.5279 −1.84708 −0.923540 0.383501i \(-0.874718\pi\)
−0.923540 + 0.383501i \(0.874718\pi\)
\(720\) −0.812175 −0.0302680
\(721\) 2.80411 0.104430
\(722\) 17.9627 0.668503
\(723\) 5.25526 0.195445
\(724\) 8.49683 0.315782
\(725\) −30.1344 −1.11916
\(726\) −5.39704 −0.200303
\(727\) 25.3400 0.939807 0.469904 0.882718i \(-0.344289\pi\)
0.469904 + 0.882718i \(0.344289\pi\)
\(728\) 2.80411 0.103927
\(729\) 1.00000 0.0370370
\(730\) 12.9941 0.480935
\(731\) −19.4570 −0.719643
\(732\) −4.79433 −0.177204
\(733\) −47.0633 −1.73832 −0.869162 0.494528i \(-0.835341\pi\)
−0.869162 + 0.494528i \(0.835341\pi\)
\(734\) 3.17092 0.117041
\(735\) −0.700926 −0.0258540
\(736\) 8.19340 0.302013
\(737\) 2.34957 0.0865475
\(738\) 10.6535 0.392159
\(739\) −48.7133 −1.79195 −0.895973 0.444108i \(-0.853521\pi\)
−0.895973 + 0.444108i \(0.853521\pi\)
\(740\) −4.84319 −0.178039
\(741\) −1.01847 −0.0374145
\(742\) 34.9403 1.28270
\(743\) 3.11576 0.114306 0.0571530 0.998365i \(-0.481798\pi\)
0.0571530 + 0.998365i \(0.481798\pi\)
\(744\) −1.13390 −0.0415709
\(745\) −4.46421 −0.163556
\(746\) −26.5049 −0.970412
\(747\) −4.73672 −0.173308
\(748\) 9.29690 0.339928
\(749\) −0.260886 −0.00953257
\(750\) −7.58601 −0.277002
\(751\) −10.5836 −0.386200 −0.193100 0.981179i \(-0.561854\pi\)
−0.193100 + 0.981179i \(0.561854\pi\)
\(752\) −4.10776 −0.149795
\(753\) −11.7511 −0.428233
\(754\) −6.94281 −0.252842
\(755\) −5.45224 −0.198428
\(756\) −2.80411 −0.101984
\(757\) −44.7518 −1.62653 −0.813266 0.581893i \(-0.802312\pi\)
−0.813266 + 0.581893i \(0.802312\pi\)
\(758\) 26.3016 0.955319
\(759\) −33.1777 −1.20428
\(760\) −0.827178 −0.0300049
\(761\) −32.1122 −1.16407 −0.582034 0.813164i \(-0.697743\pi\)
−0.582034 + 0.813164i \(0.697743\pi\)
\(762\) 10.4196 0.377464
\(763\) 20.0911 0.727346
\(764\) −24.5573 −0.888452
\(765\) −1.86468 −0.0674178
\(766\) 10.3778 0.374964
\(767\) 0.884938 0.0319532
\(768\) 1.00000 0.0360844
\(769\) −10.9588 −0.395185 −0.197593 0.980284i \(-0.563312\pi\)
−0.197593 + 0.980284i \(0.563312\pi\)
\(770\) −9.22204 −0.332339
\(771\) 4.55065 0.163888
\(772\) 20.6351 0.742675
\(773\) 2.54269 0.0914540 0.0457270 0.998954i \(-0.485440\pi\)
0.0457270 + 0.998954i \(0.485440\pi\)
\(774\) 8.47462 0.304614
\(775\) −4.92156 −0.176788
\(776\) −4.77835 −0.171533
\(777\) −16.7216 −0.599883
\(778\) 11.6907 0.419133
\(779\) 10.8503 0.388751
\(780\) −0.812175 −0.0290805
\(781\) −36.1212 −1.29252
\(782\) 18.8113 0.672692
\(783\) 6.94281 0.248116
\(784\) 0.863023 0.0308223
\(785\) 7.12744 0.254389
\(786\) −10.0961 −0.360117
\(787\) −29.6963 −1.05856 −0.529279 0.848448i \(-0.677538\pi\)
−0.529279 + 0.848448i \(0.677538\pi\)
\(788\) 12.8639 0.458258
\(789\) 2.07134 0.0737415
\(790\) −7.31005 −0.260080
\(791\) 15.0872 0.536439
\(792\) −4.04933 −0.143887
\(793\) −4.79433 −0.170252
\(794\) 10.2444 0.363559
\(795\) −10.1200 −0.358920
\(796\) 23.5266 0.833879
\(797\) 12.2889 0.435294 0.217647 0.976028i \(-0.430162\pi\)
0.217647 + 0.976028i \(0.430162\pi\)
\(798\) −2.85591 −0.101098
\(799\) −9.43107 −0.333647
\(800\) 4.34037 0.153455
\(801\) 10.1598 0.358979
\(802\) 29.0137 1.02451
\(803\) 64.7860 2.28625
\(804\) 0.580237 0.0204634
\(805\) −18.6599 −0.657674
\(806\) −1.13390 −0.0399400
\(807\) −16.0087 −0.563533
\(808\) 15.0451 0.529285
\(809\) 38.1455 1.34112 0.670562 0.741854i \(-0.266053\pi\)
0.670562 + 0.741854i \(0.266053\pi\)
\(810\) 0.812175 0.0285369
\(811\) 34.7872 1.22154 0.610771 0.791807i \(-0.290860\pi\)
0.610771 + 0.791807i \(0.290860\pi\)
\(812\) −19.4684 −0.683207
\(813\) −22.3206 −0.782817
\(814\) −24.1471 −0.846356
\(815\) −15.7148 −0.550467
\(816\) 2.29591 0.0803731
\(817\) 8.63117 0.301966
\(818\) −29.3234 −1.02527
\(819\) −2.80411 −0.0979835
\(820\) 8.65247 0.302158
\(821\) 15.0268 0.524438 0.262219 0.965008i \(-0.415546\pi\)
0.262219 + 0.965008i \(0.415546\pi\)
\(822\) −6.33088 −0.220815
\(823\) 38.1909 1.33125 0.665626 0.746286i \(-0.268165\pi\)
0.665626 + 0.746286i \(0.268165\pi\)
\(824\) 1.00000 0.0348367
\(825\) −17.5756 −0.611903
\(826\) 2.48146 0.0863411
\(827\) −19.1560 −0.666121 −0.333060 0.942905i \(-0.608081\pi\)
−0.333060 + 0.942905i \(0.608081\pi\)
\(828\) −8.19340 −0.284740
\(829\) −4.32580 −0.150241 −0.0751207 0.997174i \(-0.523934\pi\)
−0.0751207 + 0.997174i \(0.523934\pi\)
\(830\) −3.84705 −0.133533
\(831\) 1.43459 0.0497654
\(832\) 1.00000 0.0346688
\(833\) 1.98143 0.0686524
\(834\) 7.51896 0.260360
\(835\) 8.23855 0.285107
\(836\) −4.12413 −0.142636
\(837\) 1.13390 0.0391934
\(838\) 10.6366 0.367435
\(839\) 4.61218 0.159230 0.0796151 0.996826i \(-0.474631\pi\)
0.0796151 + 0.996826i \(0.474631\pi\)
\(840\) −2.27743 −0.0785787
\(841\) 19.2026 0.662160
\(842\) 6.31510 0.217633
\(843\) −27.6330 −0.951730
\(844\) 5.66546 0.195013
\(845\) −0.812175 −0.0279397
\(846\) 4.10776 0.141228
\(847\) −15.1339 −0.520007
\(848\) 12.4604 0.427892
\(849\) −29.2077 −1.00240
\(850\) 9.96512 0.341801
\(851\) −48.8592 −1.67487
\(852\) −8.92029 −0.305604
\(853\) 7.79993 0.267065 0.133532 0.991044i \(-0.457368\pi\)
0.133532 + 0.991044i \(0.457368\pi\)
\(854\) −13.4438 −0.460038
\(855\) 0.827178 0.0282889
\(856\) −0.0930370 −0.00317994
\(857\) −1.80417 −0.0616293 −0.0308146 0.999525i \(-0.509810\pi\)
−0.0308146 + 0.999525i \(0.509810\pi\)
\(858\) −4.04933 −0.138242
\(859\) −35.2598 −1.20305 −0.601525 0.798854i \(-0.705440\pi\)
−0.601525 + 0.798854i \(0.705440\pi\)
\(860\) 6.88287 0.234704
\(861\) 29.8735 1.01809
\(862\) 32.7901 1.11683
\(863\) −43.8890 −1.49400 −0.747000 0.664824i \(-0.768506\pi\)
−0.747000 + 0.664824i \(0.768506\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 12.3190 0.418857
\(866\) 23.0398 0.782924
\(867\) −11.7288 −0.398330
\(868\) −3.17958 −0.107922
\(869\) −36.4463 −1.23636
\(870\) 5.63878 0.191172
\(871\) 0.580237 0.0196606
\(872\) 7.16487 0.242633
\(873\) 4.77835 0.161723
\(874\) −8.34476 −0.282266
\(875\) −21.2720 −0.719125
\(876\) 15.9992 0.540563
\(877\) 12.7397 0.430191 0.215095 0.976593i \(-0.430994\pi\)
0.215095 + 0.976593i \(0.430994\pi\)
\(878\) −37.5925 −1.26868
\(879\) −25.8130 −0.870650
\(880\) −3.28876 −0.110864
\(881\) −32.4436 −1.09305 −0.546526 0.837442i \(-0.684050\pi\)
−0.546526 + 0.837442i \(0.684050\pi\)
\(882\) −0.863023 −0.0290595
\(883\) 1.56011 0.0525018 0.0262509 0.999655i \(-0.491643\pi\)
0.0262509 + 0.999655i \(0.491643\pi\)
\(884\) 2.29591 0.0772199
\(885\) −0.718724 −0.0241596
\(886\) −34.6459 −1.16395
\(887\) −42.1818 −1.41633 −0.708163 0.706049i \(-0.750476\pi\)
−0.708163 + 0.706049i \(0.750476\pi\)
\(888\) −5.96324 −0.200113
\(889\) 29.2178 0.979933
\(890\) 8.25154 0.276592
\(891\) 4.04933 0.135658
\(892\) 2.11119 0.0706878
\(893\) 4.18365 0.140000
\(894\) −5.49662 −0.183834
\(895\) 16.8817 0.564293
\(896\) 2.80411 0.0936787
\(897\) −8.19340 −0.273570
\(898\) 11.6519 0.388829
\(899\) 7.87247 0.262562
\(900\) −4.34037 −0.144679
\(901\) 28.6080 0.953071
\(902\) 43.1394 1.43638
\(903\) 23.7637 0.790808
\(904\) 5.38039 0.178949
\(905\) −6.90091 −0.229394
\(906\) −6.71314 −0.223029
\(907\) 6.97762 0.231688 0.115844 0.993267i \(-0.463043\pi\)
0.115844 + 0.993267i \(0.463043\pi\)
\(908\) 16.6256 0.551739
\(909\) −15.0451 −0.499015
\(910\) −2.27743 −0.0754959
\(911\) 45.6638 1.51291 0.756454 0.654047i \(-0.226930\pi\)
0.756454 + 0.654047i \(0.226930\pi\)
\(912\) −1.01847 −0.0337250
\(913\) −19.1805 −0.634783
\(914\) −26.5669 −0.878755
\(915\) 3.89384 0.128726
\(916\) −22.6417 −0.748101
\(917\) −28.3107 −0.934901
\(918\) −2.29591 −0.0757764
\(919\) −38.2955 −1.26325 −0.631625 0.775274i \(-0.717612\pi\)
−0.631625 + 0.775274i \(0.717612\pi\)
\(920\) −6.65447 −0.219391
\(921\) −4.20527 −0.138569
\(922\) 10.3671 0.341423
\(923\) −8.92029 −0.293615
\(924\) −11.3547 −0.373544
\(925\) −25.8827 −0.851018
\(926\) −29.0583 −0.954916
\(927\) −1.00000 −0.0328443
\(928\) −6.94281 −0.227909
\(929\) 21.2377 0.696787 0.348394 0.937348i \(-0.386727\pi\)
0.348394 + 0.937348i \(0.386727\pi\)
\(930\) 0.920926 0.0301984
\(931\) −0.878966 −0.0288069
\(932\) −0.805363 −0.0263806
\(933\) 6.72177 0.220061
\(934\) −5.95392 −0.194818
\(935\) −7.55071 −0.246935
\(936\) −1.00000 −0.0326860
\(937\) 15.2350 0.497706 0.248853 0.968541i \(-0.419946\pi\)
0.248853 + 0.968541i \(0.419946\pi\)
\(938\) 1.62705 0.0531250
\(939\) −20.8705 −0.681083
\(940\) 3.33622 0.108816
\(941\) 10.3780 0.338315 0.169157 0.985589i \(-0.445895\pi\)
0.169157 + 0.985589i \(0.445895\pi\)
\(942\) 8.77574 0.285929
\(943\) 87.2881 2.84249
\(944\) 0.884938 0.0288023
\(945\) 2.27743 0.0740847
\(946\) 34.3165 1.11573
\(947\) −14.8925 −0.483943 −0.241971 0.970283i \(-0.577794\pi\)
−0.241971 + 0.970283i \(0.577794\pi\)
\(948\) −9.00058 −0.292325
\(949\) 15.9992 0.519356
\(950\) −4.42055 −0.143422
\(951\) −11.3847 −0.369176
\(952\) 6.43799 0.208656
\(953\) −13.2268 −0.428458 −0.214229 0.976783i \(-0.568724\pi\)
−0.214229 + 0.976783i \(0.568724\pi\)
\(954\) −12.4604 −0.403420
\(955\) 19.9448 0.645399
\(956\) −27.6450 −0.894103
\(957\) 28.1137 0.908787
\(958\) 2.33530 0.0754501
\(959\) −17.7525 −0.573257
\(960\) −0.812175 −0.0262128
\(961\) −29.7143 −0.958525
\(962\) −5.96324 −0.192263
\(963\) 0.0930370 0.00299808
\(964\) 5.25526 0.169260
\(965\) −16.7593 −0.539502
\(966\) −22.9752 −0.739214
\(967\) −23.5141 −0.756162 −0.378081 0.925772i \(-0.623416\pi\)
−0.378081 + 0.925772i \(0.623416\pi\)
\(968\) −5.39704 −0.173467
\(969\) −2.33833 −0.0751179
\(970\) 3.88086 0.124607
\(971\) 13.0234 0.417941 0.208971 0.977922i \(-0.432989\pi\)
0.208971 + 0.977922i \(0.432989\pi\)
\(972\) 1.00000 0.0320750
\(973\) 21.0840 0.675922
\(974\) −17.3845 −0.557036
\(975\) −4.34037 −0.139003
\(976\) −4.79433 −0.153463
\(977\) 38.2541 1.22386 0.611928 0.790913i \(-0.290394\pi\)
0.611928 + 0.790913i \(0.290394\pi\)
\(978\) −19.3491 −0.618716
\(979\) 41.1404 1.31485
\(980\) −0.700926 −0.0223902
\(981\) −7.16487 −0.228757
\(982\) 19.7595 0.630551
\(983\) 14.4742 0.461656 0.230828 0.972995i \(-0.425857\pi\)
0.230828 + 0.972995i \(0.425857\pi\)
\(984\) 10.6535 0.339620
\(985\) −10.4477 −0.332893
\(986\) −15.9401 −0.507636
\(987\) 11.5186 0.366641
\(988\) −1.01847 −0.0324019
\(989\) 69.4359 2.20793
\(990\) 3.28876 0.104524
\(991\) 55.8050 1.77270 0.886351 0.463013i \(-0.153232\pi\)
0.886351 + 0.463013i \(0.153232\pi\)
\(992\) −1.13390 −0.0360014
\(993\) −1.90596 −0.0604838
\(994\) −25.0135 −0.793379
\(995\) −19.1077 −0.605755
\(996\) −4.73672 −0.150089
\(997\) −24.8981 −0.788530 −0.394265 0.918997i \(-0.629001\pi\)
−0.394265 + 0.918997i \(0.629001\pi\)
\(998\) 0.921867 0.0291812
\(999\) 5.96324 0.188669
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 8034.2.a.w.1.7 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8034.2.a.w.1.7 12 1.1 even 1 trivial