Properties

Label 2001.2.a.i.1.2
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.9780654445\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 5 x^{5} + 18 x^{4} + 4 x^{3} - 26 x^{2} + x + 8\)
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 1.2
Root \(2.22973\) of defining polynomial
Character \(\chi\) \(=\) 2001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.22973 q^{2} +1.00000 q^{3} +2.97167 q^{4} +0.537118 q^{5} -2.22973 q^{6} -1.88241 q^{7} -2.16657 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.22973 q^{2} +1.00000 q^{3} +2.97167 q^{4} +0.537118 q^{5} -2.22973 q^{6} -1.88241 q^{7} -2.16657 q^{8} +1.00000 q^{9} -1.19762 q^{10} +1.11723 q^{11} +2.97167 q^{12} +1.56781 q^{13} +4.19726 q^{14} +0.537118 q^{15} -1.11250 q^{16} -3.41741 q^{17} -2.22973 q^{18} -2.62638 q^{19} +1.59614 q^{20} -1.88241 q^{21} -2.49110 q^{22} +1.00000 q^{23} -2.16657 q^{24} -4.71150 q^{25} -3.49579 q^{26} +1.00000 q^{27} -5.59392 q^{28} -1.00000 q^{29} -1.19762 q^{30} -2.26219 q^{31} +6.81370 q^{32} +1.11723 q^{33} +7.61989 q^{34} -1.01108 q^{35} +2.97167 q^{36} +1.64906 q^{37} +5.85610 q^{38} +1.56781 q^{39} -1.16370 q^{40} +5.06667 q^{41} +4.19726 q^{42} -10.0332 q^{43} +3.32003 q^{44} +0.537118 q^{45} -2.22973 q^{46} -6.06906 q^{47} -1.11250 q^{48} -3.45652 q^{49} +10.5054 q^{50} -3.41741 q^{51} +4.65903 q^{52} +10.2961 q^{53} -2.22973 q^{54} +0.600081 q^{55} +4.07837 q^{56} -2.62638 q^{57} +2.22973 q^{58} -8.80232 q^{59} +1.59614 q^{60} -3.73087 q^{61} +5.04406 q^{62} -1.88241 q^{63} -12.9677 q^{64} +0.842100 q^{65} -2.49110 q^{66} -7.67562 q^{67} -10.1554 q^{68} +1.00000 q^{69} +2.25442 q^{70} -2.43146 q^{71} -2.16657 q^{72} +1.02242 q^{73} -3.67695 q^{74} -4.71150 q^{75} -7.80475 q^{76} -2.10308 q^{77} -3.49579 q^{78} +1.24162 q^{79} -0.597544 q^{80} +1.00000 q^{81} -11.2973 q^{82} +13.0672 q^{83} -5.59392 q^{84} -1.83555 q^{85} +22.3712 q^{86} -1.00000 q^{87} -2.42054 q^{88} -13.1482 q^{89} -1.19762 q^{90} -2.95127 q^{91} +2.97167 q^{92} -2.26219 q^{93} +13.5323 q^{94} -1.41068 q^{95} +6.81370 q^{96} -7.41766 q^{97} +7.70710 q^{98} +1.11723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{2} + 7q^{3} + 5q^{4} - 3q^{5} - 3q^{6} - 5q^{7} - 6q^{8} + 7q^{9} + O(q^{10}) \) \( 7q - 3q^{2} + 7q^{3} + 5q^{4} - 3q^{5} - 3q^{6} - 5q^{7} - 6q^{8} + 7q^{9} + 3q^{10} - 4q^{11} + 5q^{12} - 18q^{13} - 2q^{14} - 3q^{15} - 7q^{16} - 3q^{17} - 3q^{18} - 4q^{19} - 2q^{20} - 5q^{21} - 26q^{22} + 7q^{23} - 6q^{24} - 8q^{25} - 7q^{26} + 7q^{27} - 6q^{28} - 7q^{29} + 3q^{30} - 22q^{31} + 5q^{32} - 4q^{33} + 9q^{34} + 3q^{35} + 5q^{36} - 25q^{37} + 14q^{38} - 18q^{39} - 10q^{40} - 13q^{41} - 2q^{42} - 2q^{43} + 4q^{44} - 3q^{45} - 3q^{46} - 25q^{47} - 7q^{48} - 8q^{49} + 19q^{50} - 3q^{51} - 12q^{52} - 5q^{53} - 3q^{54} - 15q^{55} + 18q^{56} - 4q^{57} + 3q^{58} + 11q^{59} - 2q^{60} - 33q^{61} + 28q^{62} - 5q^{63} - 14q^{64} - 2q^{65} - 26q^{66} + 8q^{67} + 12q^{68} + 7q^{69} - 22q^{70} - 6q^{71} - 6q^{72} + 15q^{73} + 34q^{74} - 8q^{75} - 28q^{76} - q^{77} - 7q^{78} - 15q^{79} - 12q^{80} + 7q^{81} - 14q^{82} + 21q^{83} - 6q^{84} - 28q^{85} - 12q^{86} - 7q^{87} - 13q^{88} + 8q^{89} + 3q^{90} + 6q^{91} + 5q^{92} - 22q^{93} - 35q^{94} - 25q^{95} + 5q^{96} + 13q^{97} + q^{98} - 4q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22973 −1.57665 −0.788327 0.615257i \(-0.789052\pi\)
−0.788327 + 0.615257i \(0.789052\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.97167 1.48584
\(5\) 0.537118 0.240206 0.120103 0.992761i \(-0.461677\pi\)
0.120103 + 0.992761i \(0.461677\pi\)
\(6\) −2.22973 −0.910281
\(7\) −1.88241 −0.711485 −0.355743 0.934584i \(-0.615772\pi\)
−0.355743 + 0.934584i \(0.615772\pi\)
\(8\) −2.16657 −0.765997
\(9\) 1.00000 0.333333
\(10\) −1.19762 −0.378722
\(11\) 1.11723 0.336856 0.168428 0.985714i \(-0.446131\pi\)
0.168428 + 0.985714i \(0.446131\pi\)
\(12\) 2.97167 0.857849
\(13\) 1.56781 0.434833 0.217417 0.976079i \(-0.430237\pi\)
0.217417 + 0.976079i \(0.430237\pi\)
\(14\) 4.19726 1.12177
\(15\) 0.537118 0.138683
\(16\) −1.11250 −0.278125
\(17\) −3.41741 −0.828844 −0.414422 0.910085i \(-0.636016\pi\)
−0.414422 + 0.910085i \(0.636016\pi\)
\(18\) −2.22973 −0.525551
\(19\) −2.62638 −0.602533 −0.301266 0.953540i \(-0.597409\pi\)
−0.301266 + 0.953540i \(0.597409\pi\)
\(20\) 1.59614 0.356908
\(21\) −1.88241 −0.410776
\(22\) −2.49110 −0.531105
\(23\) 1.00000 0.208514
\(24\) −2.16657 −0.442249
\(25\) −4.71150 −0.942301
\(26\) −3.49579 −0.685581
\(27\) 1.00000 0.192450
\(28\) −5.59392 −1.05715
\(29\) −1.00000 −0.185695
\(30\) −1.19762 −0.218655
\(31\) −2.26219 −0.406301 −0.203150 0.979148i \(-0.565118\pi\)
−0.203150 + 0.979148i \(0.565118\pi\)
\(32\) 6.81370 1.20450
\(33\) 1.11723 0.194484
\(34\) 7.61989 1.30680
\(35\) −1.01108 −0.170903
\(36\) 2.97167 0.495279
\(37\) 1.64906 0.271104 0.135552 0.990770i \(-0.456719\pi\)
0.135552 + 0.990770i \(0.456719\pi\)
\(38\) 5.85610 0.949986
\(39\) 1.56781 0.251051
\(40\) −1.16370 −0.183997
\(41\) 5.06667 0.791280 0.395640 0.918406i \(-0.370523\pi\)
0.395640 + 0.918406i \(0.370523\pi\)
\(42\) 4.19726 0.647652
\(43\) −10.0332 −1.53004 −0.765021 0.644005i \(-0.777272\pi\)
−0.765021 + 0.644005i \(0.777272\pi\)
\(44\) 3.32003 0.500513
\(45\) 0.537118 0.0800688
\(46\) −2.22973 −0.328755
\(47\) −6.06906 −0.885263 −0.442631 0.896704i \(-0.645955\pi\)
−0.442631 + 0.896704i \(0.645955\pi\)
\(48\) −1.11250 −0.160576
\(49\) −3.45652 −0.493789
\(50\) 10.5054 1.48568
\(51\) −3.41741 −0.478533
\(52\) 4.65903 0.646091
\(53\) 10.2961 1.41427 0.707137 0.707077i \(-0.249987\pi\)
0.707137 + 0.707077i \(0.249987\pi\)
\(54\) −2.22973 −0.303427
\(55\) 0.600081 0.0809150
\(56\) 4.07837 0.544995
\(57\) −2.62638 −0.347872
\(58\) 2.22973 0.292777
\(59\) −8.80232 −1.14596 −0.572982 0.819568i \(-0.694214\pi\)
−0.572982 + 0.819568i \(0.694214\pi\)
\(60\) 1.59614 0.206061
\(61\) −3.73087 −0.477689 −0.238845 0.971058i \(-0.576769\pi\)
−0.238845 + 0.971058i \(0.576769\pi\)
\(62\) 5.04406 0.640596
\(63\) −1.88241 −0.237162
\(64\) −12.9677 −1.62096
\(65\) 0.842100 0.104450
\(66\) −2.49110 −0.306634
\(67\) −7.67562 −0.937726 −0.468863 0.883271i \(-0.655336\pi\)
−0.468863 + 0.883271i \(0.655336\pi\)
\(68\) −10.1554 −1.23153
\(69\) 1.00000 0.120386
\(70\) 2.25442 0.269455
\(71\) −2.43146 −0.288561 −0.144281 0.989537i \(-0.546087\pi\)
−0.144281 + 0.989537i \(0.546087\pi\)
\(72\) −2.16657 −0.255332
\(73\) 1.02242 0.119665 0.0598326 0.998208i \(-0.480943\pi\)
0.0598326 + 0.998208i \(0.480943\pi\)
\(74\) −3.67695 −0.427437
\(75\) −4.71150 −0.544038
\(76\) −7.80475 −0.895266
\(77\) −2.10308 −0.239668
\(78\) −3.49579 −0.395821
\(79\) 1.24162 0.139693 0.0698466 0.997558i \(-0.477749\pi\)
0.0698466 + 0.997558i \(0.477749\pi\)
\(80\) −0.597544 −0.0668074
\(81\) 1.00000 0.111111
\(82\) −11.2973 −1.24758
\(83\) 13.0672 1.43432 0.717158 0.696910i \(-0.245442\pi\)
0.717158 + 0.696910i \(0.245442\pi\)
\(84\) −5.59392 −0.610346
\(85\) −1.83555 −0.199094
\(86\) 22.3712 2.41235
\(87\) −1.00000 −0.107211
\(88\) −2.42054 −0.258031
\(89\) −13.1482 −1.39370 −0.696851 0.717216i \(-0.745416\pi\)
−0.696851 + 0.717216i \(0.745416\pi\)
\(90\) −1.19762 −0.126241
\(91\) −2.95127 −0.309377
\(92\) 2.97167 0.309818
\(93\) −2.26219 −0.234578
\(94\) 13.5323 1.39575
\(95\) −1.41068 −0.144732
\(96\) 6.81370 0.695421
\(97\) −7.41766 −0.753149 −0.376575 0.926386i \(-0.622898\pi\)
−0.376575 + 0.926386i \(0.622898\pi\)
\(98\) 7.70710 0.778534
\(99\) 1.11723 0.112285
\(100\) −14.0011 −1.40011
\(101\) −2.80104 −0.278714 −0.139357 0.990242i \(-0.544504\pi\)
−0.139357 + 0.990242i \(0.544504\pi\)
\(102\) 7.61989 0.754481
\(103\) 10.0128 0.986589 0.493295 0.869862i \(-0.335792\pi\)
0.493295 + 0.869862i \(0.335792\pi\)
\(104\) −3.39677 −0.333081
\(105\) −1.01108 −0.0986710
\(106\) −22.9574 −2.22982
\(107\) −5.25354 −0.507878 −0.253939 0.967220i \(-0.581726\pi\)
−0.253939 + 0.967220i \(0.581726\pi\)
\(108\) 2.97167 0.285950
\(109\) −5.08675 −0.487223 −0.243611 0.969873i \(-0.578332\pi\)
−0.243611 + 0.969873i \(0.578332\pi\)
\(110\) −1.33802 −0.127575
\(111\) 1.64906 0.156522
\(112\) 2.09418 0.197882
\(113\) 18.3795 1.72900 0.864500 0.502633i \(-0.167635\pi\)
0.864500 + 0.502633i \(0.167635\pi\)
\(114\) 5.85610 0.548474
\(115\) 0.537118 0.0500865
\(116\) −2.97167 −0.275913
\(117\) 1.56781 0.144944
\(118\) 19.6268 1.80679
\(119\) 6.43298 0.589710
\(120\) −1.16370 −0.106231
\(121\) −9.75181 −0.886528
\(122\) 8.31882 0.753151
\(123\) 5.06667 0.456846
\(124\) −6.72249 −0.603697
\(125\) −5.21622 −0.466553
\(126\) 4.19726 0.373922
\(127\) 4.33301 0.384492 0.192246 0.981347i \(-0.438423\pi\)
0.192246 + 0.981347i \(0.438423\pi\)
\(128\) 15.2870 1.35119
\(129\) −10.0332 −0.883371
\(130\) −1.87765 −0.164681
\(131\) 19.3607 1.69155 0.845777 0.533537i \(-0.179137\pi\)
0.845777 + 0.533537i \(0.179137\pi\)
\(132\) 3.32003 0.288971
\(133\) 4.94393 0.428693
\(134\) 17.1145 1.47847
\(135\) 0.537118 0.0462277
\(136\) 7.40405 0.634892
\(137\) −10.2352 −0.874456 −0.437228 0.899351i \(-0.644040\pi\)
−0.437228 + 0.899351i \(0.644040\pi\)
\(138\) −2.22973 −0.189807
\(139\) −0.289212 −0.0245306 −0.0122653 0.999925i \(-0.503904\pi\)
−0.0122653 + 0.999925i \(0.503904\pi\)
\(140\) −3.00459 −0.253934
\(141\) −6.06906 −0.511107
\(142\) 5.42149 0.454961
\(143\) 1.75160 0.146476
\(144\) −1.11250 −0.0927083
\(145\) −0.537118 −0.0446052
\(146\) −2.27972 −0.188671
\(147\) −3.45652 −0.285089
\(148\) 4.90047 0.402816
\(149\) 20.1266 1.64884 0.824419 0.565979i \(-0.191502\pi\)
0.824419 + 0.565979i \(0.191502\pi\)
\(150\) 10.5054 0.857759
\(151\) 0.370644 0.0301626 0.0150813 0.999886i \(-0.495199\pi\)
0.0150813 + 0.999886i \(0.495199\pi\)
\(152\) 5.69023 0.461538
\(153\) −3.41741 −0.276281
\(154\) 4.68929 0.377874
\(155\) −1.21506 −0.0975961
\(156\) 4.65903 0.373021
\(157\) −7.03038 −0.561086 −0.280543 0.959842i \(-0.590514\pi\)
−0.280543 + 0.959842i \(0.590514\pi\)
\(158\) −2.76847 −0.220248
\(159\) 10.2961 0.816531
\(160\) 3.65976 0.289330
\(161\) −1.88241 −0.148355
\(162\) −2.22973 −0.175184
\(163\) −19.9434 −1.56209 −0.781044 0.624476i \(-0.785312\pi\)
−0.781044 + 0.624476i \(0.785312\pi\)
\(164\) 15.0565 1.17571
\(165\) 0.600081 0.0467163
\(166\) −29.1364 −2.26142
\(167\) −12.4215 −0.961201 −0.480601 0.876940i \(-0.659581\pi\)
−0.480601 + 0.876940i \(0.659581\pi\)
\(168\) 4.07837 0.314653
\(169\) −10.5420 −0.810920
\(170\) 4.09278 0.313902
\(171\) −2.62638 −0.200844
\(172\) −29.8153 −2.27339
\(173\) −12.5473 −0.953954 −0.476977 0.878916i \(-0.658267\pi\)
−0.476977 + 0.878916i \(0.658267\pi\)
\(174\) 2.22973 0.169035
\(175\) 8.86900 0.670433
\(176\) −1.24291 −0.0936881
\(177\) −8.80232 −0.661623
\(178\) 29.3168 2.19739
\(179\) −23.4139 −1.75003 −0.875017 0.484092i \(-0.839150\pi\)
−0.875017 + 0.484092i \(0.839150\pi\)
\(180\) 1.59614 0.118969
\(181\) −10.0534 −0.747263 −0.373632 0.927577i \(-0.621888\pi\)
−0.373632 + 0.927577i \(0.621888\pi\)
\(182\) 6.58052 0.487781
\(183\) −3.73087 −0.275794
\(184\) −2.16657 −0.159721
\(185\) 0.885740 0.0651209
\(186\) 5.04406 0.369848
\(187\) −3.81802 −0.279201
\(188\) −18.0353 −1.31536
\(189\) −1.88241 −0.136925
\(190\) 3.14542 0.228193
\(191\) −20.7174 −1.49905 −0.749527 0.661973i \(-0.769719\pi\)
−0.749527 + 0.661973i \(0.769719\pi\)
\(192\) −12.9677 −0.935862
\(193\) 8.55796 0.616015 0.308008 0.951384i \(-0.400338\pi\)
0.308008 + 0.951384i \(0.400338\pi\)
\(194\) 16.5393 1.18746
\(195\) 0.842100 0.0603041
\(196\) −10.2717 −0.733690
\(197\) 5.84888 0.416715 0.208358 0.978053i \(-0.433188\pi\)
0.208358 + 0.978053i \(0.433188\pi\)
\(198\) −2.49110 −0.177035
\(199\) 9.16433 0.649642 0.324821 0.945775i \(-0.394696\pi\)
0.324821 + 0.945775i \(0.394696\pi\)
\(200\) 10.2078 0.721800
\(201\) −7.67562 −0.541396
\(202\) 6.24555 0.439436
\(203\) 1.88241 0.132119
\(204\) −10.1554 −0.711023
\(205\) 2.72140 0.190071
\(206\) −22.3258 −1.55551
\(207\) 1.00000 0.0695048
\(208\) −1.74419 −0.120938
\(209\) −2.93426 −0.202967
\(210\) 2.25442 0.155570
\(211\) −0.0926588 −0.00637889 −0.00318945 0.999995i \(-0.501015\pi\)
−0.00318945 + 0.999995i \(0.501015\pi\)
\(212\) 30.5966 2.10138
\(213\) −2.43146 −0.166601
\(214\) 11.7139 0.800749
\(215\) −5.38899 −0.367526
\(216\) −2.16657 −0.147416
\(217\) 4.25837 0.289077
\(218\) 11.3421 0.768182
\(219\) 1.02242 0.0690888
\(220\) 1.78325 0.120226
\(221\) −5.35786 −0.360409
\(222\) −3.67695 −0.246781
\(223\) −12.8223 −0.858643 −0.429322 0.903152i \(-0.641247\pi\)
−0.429322 + 0.903152i \(0.641247\pi\)
\(224\) −12.8262 −0.856987
\(225\) −4.71150 −0.314100
\(226\) −40.9813 −2.72603
\(227\) 14.6393 0.971643 0.485821 0.874058i \(-0.338521\pi\)
0.485821 + 0.874058i \(0.338521\pi\)
\(228\) −7.80475 −0.516882
\(229\) −24.1483 −1.59577 −0.797883 0.602812i \(-0.794047\pi\)
−0.797883 + 0.602812i \(0.794047\pi\)
\(230\) −1.19762 −0.0789691
\(231\) −2.10308 −0.138372
\(232\) 2.16657 0.142242
\(233\) 16.5564 1.08465 0.542324 0.840170i \(-0.317545\pi\)
0.542324 + 0.840170i \(0.317545\pi\)
\(234\) −3.49579 −0.228527
\(235\) −3.25980 −0.212646
\(236\) −26.1576 −1.70272
\(237\) 1.24162 0.0806519
\(238\) −14.3438 −0.929769
\(239\) −18.3128 −1.18455 −0.592277 0.805735i \(-0.701771\pi\)
−0.592277 + 0.805735i \(0.701771\pi\)
\(240\) −0.597544 −0.0385713
\(241\) 16.0413 1.03331 0.516655 0.856194i \(-0.327177\pi\)
0.516655 + 0.856194i \(0.327177\pi\)
\(242\) 21.7439 1.39775
\(243\) 1.00000 0.0641500
\(244\) −11.0869 −0.709768
\(245\) −1.85656 −0.118611
\(246\) −11.2973 −0.720288
\(247\) −4.11767 −0.262001
\(248\) 4.90118 0.311225
\(249\) 13.0672 0.828103
\(250\) 11.6307 0.735593
\(251\) −16.2544 −1.02597 −0.512983 0.858399i \(-0.671460\pi\)
−0.512983 + 0.858399i \(0.671460\pi\)
\(252\) −5.59392 −0.352384
\(253\) 1.11723 0.0702393
\(254\) −9.66141 −0.606211
\(255\) −1.83555 −0.114947
\(256\) −8.15037 −0.509398
\(257\) 2.52528 0.157523 0.0787613 0.996894i \(-0.474904\pi\)
0.0787613 + 0.996894i \(0.474904\pi\)
\(258\) 22.3712 1.39277
\(259\) −3.10421 −0.192886
\(260\) 2.50245 0.155195
\(261\) −1.00000 −0.0618984
\(262\) −43.1691 −2.66699
\(263\) −28.6908 −1.76915 −0.884575 0.466399i \(-0.845551\pi\)
−0.884575 + 0.466399i \(0.845551\pi\)
\(264\) −2.42054 −0.148974
\(265\) 5.53020 0.339717
\(266\) −11.0236 −0.675901
\(267\) −13.1482 −0.804655
\(268\) −22.8094 −1.39331
\(269\) −18.4710 −1.12620 −0.563099 0.826389i \(-0.690391\pi\)
−0.563099 + 0.826389i \(0.690391\pi\)
\(270\) −1.19762 −0.0728851
\(271\) −7.71437 −0.468614 −0.234307 0.972163i \(-0.575282\pi\)
−0.234307 + 0.972163i \(0.575282\pi\)
\(272\) 3.80187 0.230522
\(273\) −2.95127 −0.178619
\(274\) 22.8218 1.37871
\(275\) −5.26381 −0.317420
\(276\) 2.97167 0.178874
\(277\) −0.702588 −0.0422144 −0.0211072 0.999777i \(-0.506719\pi\)
−0.0211072 + 0.999777i \(0.506719\pi\)
\(278\) 0.644863 0.0386763
\(279\) −2.26219 −0.135434
\(280\) 2.19057 0.130911
\(281\) 2.46040 0.146775 0.0733876 0.997303i \(-0.476619\pi\)
0.0733876 + 0.997303i \(0.476619\pi\)
\(282\) 13.5323 0.805838
\(283\) −15.1893 −0.902908 −0.451454 0.892294i \(-0.649095\pi\)
−0.451454 + 0.892294i \(0.649095\pi\)
\(284\) −7.22551 −0.428755
\(285\) −1.41068 −0.0835612
\(286\) −3.90559 −0.230942
\(287\) −9.53756 −0.562984
\(288\) 6.81370 0.401501
\(289\) −5.32130 −0.313018
\(290\) 1.19762 0.0703270
\(291\) −7.41766 −0.434831
\(292\) 3.03830 0.177803
\(293\) 8.84429 0.516689 0.258344 0.966053i \(-0.416823\pi\)
0.258344 + 0.966053i \(0.416823\pi\)
\(294\) 7.70710 0.449487
\(295\) −4.72788 −0.275268
\(296\) −3.57280 −0.207665
\(297\) 1.11723 0.0648280
\(298\) −44.8769 −2.59965
\(299\) 1.56781 0.0906690
\(300\) −14.0011 −0.808351
\(301\) 18.8865 1.08860
\(302\) −0.826433 −0.0475559
\(303\) −2.80104 −0.160916
\(304\) 2.92185 0.167579
\(305\) −2.00392 −0.114744
\(306\) 7.61989 0.435600
\(307\) 5.52326 0.315229 0.157614 0.987501i \(-0.449620\pi\)
0.157614 + 0.987501i \(0.449620\pi\)
\(308\) −6.24966 −0.356108
\(309\) 10.0128 0.569608
\(310\) 2.70925 0.153875
\(311\) 0.0662747 0.00375809 0.00187905 0.999998i \(-0.499402\pi\)
0.00187905 + 0.999998i \(0.499402\pi\)
\(312\) −3.39677 −0.192304
\(313\) 17.7785 1.00490 0.502450 0.864606i \(-0.332432\pi\)
0.502450 + 0.864606i \(0.332432\pi\)
\(314\) 15.6758 0.884638
\(315\) −1.01108 −0.0569677
\(316\) 3.68969 0.207561
\(317\) −8.12451 −0.456318 −0.228159 0.973624i \(-0.573271\pi\)
−0.228159 + 0.973624i \(0.573271\pi\)
\(318\) −22.9574 −1.28739
\(319\) −1.11723 −0.0625526
\(320\) −6.96517 −0.389365
\(321\) −5.25354 −0.293224
\(322\) 4.19726 0.233904
\(323\) 8.97542 0.499406
\(324\) 2.97167 0.165093
\(325\) −7.38676 −0.409744
\(326\) 44.4683 2.46287
\(327\) −5.08675 −0.281298
\(328\) −10.9773 −0.606118
\(329\) 11.4245 0.629851
\(330\) −1.33802 −0.0736554
\(331\) 20.2364 1.11229 0.556146 0.831085i \(-0.312280\pi\)
0.556146 + 0.831085i \(0.312280\pi\)
\(332\) 38.8316 2.13116
\(333\) 1.64906 0.0903680
\(334\) 27.6964 1.51548
\(335\) −4.12271 −0.225248
\(336\) 2.09418 0.114247
\(337\) 19.0760 1.03914 0.519568 0.854429i \(-0.326093\pi\)
0.519568 + 0.854429i \(0.326093\pi\)
\(338\) 23.5057 1.27854
\(339\) 18.3795 0.998238
\(340\) −5.45466 −0.295821
\(341\) −2.52737 −0.136865
\(342\) 5.85610 0.316662
\(343\) 19.6835 1.06281
\(344\) 21.7375 1.17201
\(345\) 0.537118 0.0289174
\(346\) 27.9770 1.50405
\(347\) −29.5028 −1.58379 −0.791897 0.610655i \(-0.790906\pi\)
−0.791897 + 0.610655i \(0.790906\pi\)
\(348\) −2.97167 −0.159298
\(349\) −11.6279 −0.622426 −0.311213 0.950340i \(-0.600735\pi\)
−0.311213 + 0.950340i \(0.600735\pi\)
\(350\) −19.7754 −1.05704
\(351\) 1.56781 0.0836837
\(352\) 7.61244 0.405744
\(353\) −0.349829 −0.0186195 −0.00930975 0.999957i \(-0.502963\pi\)
−0.00930975 + 0.999957i \(0.502963\pi\)
\(354\) 19.6268 1.04315
\(355\) −1.30598 −0.0693143
\(356\) −39.0721 −2.07082
\(357\) 6.43298 0.340469
\(358\) 52.2065 2.75920
\(359\) −17.4984 −0.923528 −0.461764 0.887003i \(-0.652783\pi\)
−0.461764 + 0.887003i \(0.652783\pi\)
\(360\) −1.16370 −0.0613325
\(361\) −12.1021 −0.636954
\(362\) 22.4163 1.17818
\(363\) −9.75181 −0.511837
\(364\) −8.77022 −0.459684
\(365\) 0.549160 0.0287444
\(366\) 8.31882 0.434832
\(367\) −33.9848 −1.77399 −0.886997 0.461775i \(-0.847213\pi\)
−0.886997 + 0.461775i \(0.847213\pi\)
\(368\) −1.11250 −0.0579931
\(369\) 5.06667 0.263760
\(370\) −1.97496 −0.102673
\(371\) −19.3814 −1.00623
\(372\) −6.72249 −0.348545
\(373\) 19.9955 1.03533 0.517664 0.855584i \(-0.326802\pi\)
0.517664 + 0.855584i \(0.326802\pi\)
\(374\) 8.51313 0.440203
\(375\) −5.21622 −0.269365
\(376\) 13.1490 0.678109
\(377\) −1.56781 −0.0807465
\(378\) 4.19726 0.215884
\(379\) 23.0774 1.18541 0.592704 0.805420i \(-0.298060\pi\)
0.592704 + 0.805420i \(0.298060\pi\)
\(380\) −4.19207 −0.215049
\(381\) 4.33301 0.221987
\(382\) 46.1940 2.36349
\(383\) 32.8565 1.67889 0.839445 0.543444i \(-0.182880\pi\)
0.839445 + 0.543444i \(0.182880\pi\)
\(384\) 15.2870 0.780110
\(385\) −1.12960 −0.0575698
\(386\) −19.0819 −0.971243
\(387\) −10.0332 −0.510014
\(388\) −22.0429 −1.11906
\(389\) 13.9353 0.706547 0.353274 0.935520i \(-0.385068\pi\)
0.353274 + 0.935520i \(0.385068\pi\)
\(390\) −1.87765 −0.0950786
\(391\) −3.41741 −0.172826
\(392\) 7.48879 0.378241
\(393\) 19.3607 0.976619
\(394\) −13.0414 −0.657016
\(395\) 0.666896 0.0335552
\(396\) 3.32003 0.166838
\(397\) 13.9272 0.698988 0.349494 0.936939i \(-0.386353\pi\)
0.349494 + 0.936939i \(0.386353\pi\)
\(398\) −20.4339 −1.02426
\(399\) 4.94393 0.247506
\(400\) 5.24155 0.262077
\(401\) 5.07639 0.253503 0.126752 0.991935i \(-0.459545\pi\)
0.126752 + 0.991935i \(0.459545\pi\)
\(402\) 17.1145 0.853595
\(403\) −3.54669 −0.176673
\(404\) −8.32378 −0.414124
\(405\) 0.537118 0.0266896
\(406\) −4.19726 −0.208307
\(407\) 1.84237 0.0913230
\(408\) 7.40405 0.366555
\(409\) −20.8607 −1.03150 −0.515748 0.856740i \(-0.672486\pi\)
−0.515748 + 0.856740i \(0.672486\pi\)
\(410\) −6.06797 −0.299676
\(411\) −10.2352 −0.504868
\(412\) 29.7547 1.46591
\(413\) 16.5696 0.815336
\(414\) −2.22973 −0.109585
\(415\) 7.01865 0.344532
\(416\) 10.6826 0.523758
\(417\) −0.289212 −0.0141628
\(418\) 6.54259 0.320008
\(419\) 3.26760 0.159633 0.0798163 0.996810i \(-0.474567\pi\)
0.0798163 + 0.996810i \(0.474567\pi\)
\(420\) −3.00459 −0.146609
\(421\) −1.97217 −0.0961175 −0.0480587 0.998845i \(-0.515303\pi\)
−0.0480587 + 0.998845i \(0.515303\pi\)
\(422\) 0.206604 0.0100573
\(423\) −6.06906 −0.295088
\(424\) −22.3071 −1.08333
\(425\) 16.1011 0.781020
\(426\) 5.42149 0.262672
\(427\) 7.02304 0.339869
\(428\) −15.6118 −0.754625
\(429\) 1.75160 0.0845681
\(430\) 12.0160 0.579461
\(431\) −3.63225 −0.174959 −0.0874797 0.996166i \(-0.527881\pi\)
−0.0874797 + 0.996166i \(0.527881\pi\)
\(432\) −1.11250 −0.0535252
\(433\) −1.31543 −0.0632156 −0.0316078 0.999500i \(-0.510063\pi\)
−0.0316078 + 0.999500i \(0.510063\pi\)
\(434\) −9.49500 −0.455774
\(435\) −0.537118 −0.0257528
\(436\) −15.1162 −0.723934
\(437\) −2.62638 −0.125637
\(438\) −2.27972 −0.108929
\(439\) 17.1910 0.820480 0.410240 0.911978i \(-0.365445\pi\)
0.410240 + 0.911978i \(0.365445\pi\)
\(440\) −1.30012 −0.0619806
\(441\) −3.45652 −0.164596
\(442\) 11.9466 0.568240
\(443\) −9.59576 −0.455908 −0.227954 0.973672i \(-0.573204\pi\)
−0.227954 + 0.973672i \(0.573204\pi\)
\(444\) 4.90047 0.232566
\(445\) −7.06211 −0.334776
\(446\) 28.5902 1.35378
\(447\) 20.1266 0.951958
\(448\) 24.4105 1.15329
\(449\) 19.5494 0.922594 0.461297 0.887246i \(-0.347384\pi\)
0.461297 + 0.887246i \(0.347384\pi\)
\(450\) 10.5054 0.495227
\(451\) 5.66061 0.266548
\(452\) 54.6179 2.56901
\(453\) 0.370644 0.0174144
\(454\) −32.6416 −1.53194
\(455\) −1.58518 −0.0743144
\(456\) 5.69023 0.266469
\(457\) −12.3018 −0.575453 −0.287726 0.957713i \(-0.592899\pi\)
−0.287726 + 0.957713i \(0.592899\pi\)
\(458\) 53.8441 2.51597
\(459\) −3.41741 −0.159511
\(460\) 1.59614 0.0744204
\(461\) −33.7959 −1.57403 −0.787016 0.616933i \(-0.788375\pi\)
−0.787016 + 0.616933i \(0.788375\pi\)
\(462\) 4.68929 0.218165
\(463\) 32.9615 1.53185 0.765925 0.642930i \(-0.222282\pi\)
0.765925 + 0.642930i \(0.222282\pi\)
\(464\) 1.11250 0.0516465
\(465\) −1.21506 −0.0563471
\(466\) −36.9163 −1.71011
\(467\) −11.5793 −0.535826 −0.267913 0.963443i \(-0.586334\pi\)
−0.267913 + 0.963443i \(0.586334\pi\)
\(468\) 4.65903 0.215364
\(469\) 14.4487 0.667178
\(470\) 7.26845 0.335269
\(471\) −7.03038 −0.323943
\(472\) 19.0708 0.877805
\(473\) −11.2093 −0.515404
\(474\) −2.76847 −0.127160
\(475\) 12.3742 0.567767
\(476\) 19.1167 0.876213
\(477\) 10.2961 0.471424
\(478\) 40.8324 1.86763
\(479\) 14.2331 0.650326 0.325163 0.945658i \(-0.394581\pi\)
0.325163 + 0.945658i \(0.394581\pi\)
\(480\) 3.65976 0.167044
\(481\) 2.58542 0.117885
\(482\) −35.7676 −1.62917
\(483\) −1.88241 −0.0856527
\(484\) −28.9792 −1.31724
\(485\) −3.98416 −0.180911
\(486\) −2.22973 −0.101142
\(487\) 25.8118 1.16964 0.584821 0.811162i \(-0.301165\pi\)
0.584821 + 0.811162i \(0.301165\pi\)
\(488\) 8.08318 0.365909
\(489\) −19.9434 −0.901872
\(490\) 4.13962 0.187009
\(491\) −35.5608 −1.60484 −0.802419 0.596761i \(-0.796454\pi\)
−0.802419 + 0.596761i \(0.796454\pi\)
\(492\) 15.0565 0.678799
\(493\) 3.41741 0.153912
\(494\) 9.18128 0.413085
\(495\) 0.600081 0.0269717
\(496\) 2.51668 0.113002
\(497\) 4.57701 0.205307
\(498\) −29.1364 −1.30563
\(499\) 15.5456 0.695918 0.347959 0.937510i \(-0.386875\pi\)
0.347959 + 0.937510i \(0.386875\pi\)
\(500\) −15.5009 −0.693222
\(501\) −12.4215 −0.554950
\(502\) 36.2428 1.61759
\(503\) 19.4816 0.868641 0.434321 0.900758i \(-0.356989\pi\)
0.434321 + 0.900758i \(0.356989\pi\)
\(504\) 4.07837 0.181665
\(505\) −1.50449 −0.0669489
\(506\) −2.49110 −0.110743
\(507\) −10.5420 −0.468185
\(508\) 12.8763 0.571293
\(509\) 21.8713 0.969428 0.484714 0.874673i \(-0.338924\pi\)
0.484714 + 0.874673i \(0.338924\pi\)
\(510\) 4.09278 0.181231
\(511\) −1.92462 −0.0851401
\(512\) −12.4009 −0.548046
\(513\) −2.62638 −0.115957
\(514\) −5.63068 −0.248359
\(515\) 5.37805 0.236985
\(516\) −29.8153 −1.31254
\(517\) −6.78050 −0.298206
\(518\) 6.92154 0.304115
\(519\) −12.5473 −0.550765
\(520\) −1.82447 −0.0800082
\(521\) 27.2480 1.19375 0.596877 0.802333i \(-0.296408\pi\)
0.596877 + 0.802333i \(0.296408\pi\)
\(522\) 2.22973 0.0975924
\(523\) 16.5965 0.725715 0.362858 0.931845i \(-0.381801\pi\)
0.362858 + 0.931845i \(0.381801\pi\)
\(524\) 57.5337 2.51337
\(525\) 8.86900 0.387075
\(526\) 63.9726 2.78934
\(527\) 7.73083 0.336760
\(528\) −1.24291 −0.0540908
\(529\) 1.00000 0.0434783
\(530\) −12.3308 −0.535617
\(531\) −8.80232 −0.381988
\(532\) 14.6917 0.636968
\(533\) 7.94359 0.344075
\(534\) 29.3168 1.26866
\(535\) −2.82177 −0.121996
\(536\) 16.6297 0.718295
\(537\) −23.4139 −1.01038
\(538\) 41.1853 1.77563
\(539\) −3.86171 −0.166336
\(540\) 1.59614 0.0686869
\(541\) −32.7816 −1.40939 −0.704696 0.709509i \(-0.748917\pi\)
−0.704696 + 0.709509i \(0.748917\pi\)
\(542\) 17.2009 0.738843
\(543\) −10.0534 −0.431433
\(544\) −23.2852 −0.998346
\(545\) −2.73219 −0.117034
\(546\) 6.58052 0.281620
\(547\) 32.1520 1.37472 0.687359 0.726318i \(-0.258770\pi\)
0.687359 + 0.726318i \(0.258770\pi\)
\(548\) −30.4158 −1.29930
\(549\) −3.73087 −0.159230
\(550\) 11.7369 0.500461
\(551\) 2.62638 0.111888
\(552\) −2.16657 −0.0922152
\(553\) −2.33724 −0.0993896
\(554\) 1.56658 0.0665575
\(555\) 0.885740 0.0375976
\(556\) −0.859444 −0.0364485
\(557\) −4.00666 −0.169768 −0.0848839 0.996391i \(-0.527052\pi\)
−0.0848839 + 0.996391i \(0.527052\pi\)
\(558\) 5.04406 0.213532
\(559\) −15.7301 −0.665313
\(560\) 1.12482 0.0475325
\(561\) −3.81802 −0.161197
\(562\) −5.48602 −0.231414
\(563\) 2.38095 0.100345 0.0501726 0.998741i \(-0.484023\pi\)
0.0501726 + 0.998741i \(0.484023\pi\)
\(564\) −18.0353 −0.759421
\(565\) 9.87196 0.415317
\(566\) 33.8679 1.42357
\(567\) −1.88241 −0.0790539
\(568\) 5.26792 0.221037
\(569\) 42.7445 1.79194 0.895971 0.444113i \(-0.146481\pi\)
0.895971 + 0.444113i \(0.146481\pi\)
\(570\) 3.14542 0.131747
\(571\) −29.5201 −1.23538 −0.617688 0.786423i \(-0.711930\pi\)
−0.617688 + 0.786423i \(0.711930\pi\)
\(572\) 5.20519 0.217640
\(573\) −20.7174 −0.865480
\(574\) 21.2661 0.887631
\(575\) −4.71150 −0.196483
\(576\) −12.9677 −0.540320
\(577\) 31.3969 1.30707 0.653535 0.756896i \(-0.273285\pi\)
0.653535 + 0.756896i \(0.273285\pi\)
\(578\) 11.8650 0.493521
\(579\) 8.55796 0.355657
\(580\) −1.59614 −0.0662761
\(581\) −24.5980 −1.02049
\(582\) 16.5393 0.685578
\(583\) 11.5030 0.476406
\(584\) −2.21514 −0.0916633
\(585\) 0.842100 0.0348166
\(586\) −19.7203 −0.814640
\(587\) 44.3332 1.82983 0.914913 0.403652i \(-0.132259\pi\)
0.914913 + 0.403652i \(0.132259\pi\)
\(588\) −10.2717 −0.423596
\(589\) 5.94136 0.244810
\(590\) 10.5419 0.434002
\(591\) 5.84888 0.240591
\(592\) −1.83458 −0.0754008
\(593\) −7.80918 −0.320685 −0.160342 0.987061i \(-0.551260\pi\)
−0.160342 + 0.987061i \(0.551260\pi\)
\(594\) −2.49110 −0.102211
\(595\) 3.45527 0.141652
\(596\) 59.8098 2.44991
\(597\) 9.16433 0.375071
\(598\) −3.49579 −0.142954
\(599\) −26.4951 −1.08256 −0.541280 0.840843i \(-0.682060\pi\)
−0.541280 + 0.840843i \(0.682060\pi\)
\(600\) 10.2078 0.416731
\(601\) 44.4503 1.81317 0.906583 0.422027i \(-0.138681\pi\)
0.906583 + 0.422027i \(0.138681\pi\)
\(602\) −42.1118 −1.71635
\(603\) −7.67562 −0.312575
\(604\) 1.10143 0.0448166
\(605\) −5.23787 −0.212950
\(606\) 6.24555 0.253708
\(607\) −31.2745 −1.26939 −0.634697 0.772761i \(-0.718875\pi\)
−0.634697 + 0.772761i \(0.718875\pi\)
\(608\) −17.8954 −0.725753
\(609\) 1.88241 0.0762792
\(610\) 4.46819 0.180912
\(611\) −9.51515 −0.384942
\(612\) −10.1554 −0.410509
\(613\) 8.39427 0.339041 0.169521 0.985527i \(-0.445778\pi\)
0.169521 + 0.985527i \(0.445778\pi\)
\(614\) −12.3153 −0.497007
\(615\) 2.72140 0.109737
\(616\) 4.55646 0.183585
\(617\) 9.87343 0.397489 0.198745 0.980051i \(-0.436314\pi\)
0.198745 + 0.980051i \(0.436314\pi\)
\(618\) −22.3258 −0.898074
\(619\) 36.9182 1.48387 0.741935 0.670472i \(-0.233908\pi\)
0.741935 + 0.670472i \(0.233908\pi\)
\(620\) −3.61077 −0.145012
\(621\) 1.00000 0.0401286
\(622\) −0.147774 −0.00592521
\(623\) 24.7503 0.991599
\(624\) −1.74419 −0.0698236
\(625\) 20.7558 0.830232
\(626\) −39.6411 −1.58438
\(627\) −2.93426 −0.117183
\(628\) −20.8920 −0.833682
\(629\) −5.63552 −0.224703
\(630\) 2.25442 0.0898184
\(631\) 15.9457 0.634788 0.317394 0.948294i \(-0.397192\pi\)
0.317394 + 0.948294i \(0.397192\pi\)
\(632\) −2.69005 −0.107005
\(633\) −0.0926588 −0.00368286
\(634\) 18.1154 0.719455
\(635\) 2.32734 0.0923575
\(636\) 30.5966 1.21323
\(637\) −5.41918 −0.214716
\(638\) 2.49110 0.0986238
\(639\) −2.43146 −0.0961871
\(640\) 8.21090 0.324564
\(641\) −2.07492 −0.0819542 −0.0409771 0.999160i \(-0.513047\pi\)
−0.0409771 + 0.999160i \(0.513047\pi\)
\(642\) 11.7139 0.462312
\(643\) 7.94610 0.313364 0.156682 0.987649i \(-0.449920\pi\)
0.156682 + 0.987649i \(0.449920\pi\)
\(644\) −5.59392 −0.220431
\(645\) −5.38899 −0.212191
\(646\) −20.0127 −0.787390
\(647\) 16.9460 0.666217 0.333109 0.942888i \(-0.391902\pi\)
0.333109 + 0.942888i \(0.391902\pi\)
\(648\) −2.16657 −0.0851108
\(649\) −9.83417 −0.386025
\(650\) 16.4704 0.646024
\(651\) 4.25837 0.166899
\(652\) −59.2653 −2.32101
\(653\) 21.8874 0.856520 0.428260 0.903656i \(-0.359127\pi\)
0.428260 + 0.903656i \(0.359127\pi\)
\(654\) 11.3421 0.443510
\(655\) 10.3990 0.406322
\(656\) −5.63667 −0.220075
\(657\) 1.02242 0.0398884
\(658\) −25.4734 −0.993057
\(659\) 28.5542 1.11231 0.556157 0.831077i \(-0.312275\pi\)
0.556157 + 0.831077i \(0.312275\pi\)
\(660\) 1.78325 0.0694128
\(661\) −17.1280 −0.666202 −0.333101 0.942891i \(-0.608095\pi\)
−0.333101 + 0.942891i \(0.608095\pi\)
\(662\) −45.1215 −1.75370
\(663\) −5.35786 −0.208082
\(664\) −28.3111 −1.09868
\(665\) 2.65547 0.102975
\(666\) −3.67695 −0.142479
\(667\) −1.00000 −0.0387202
\(668\) −36.9125 −1.42819
\(669\) −12.8223 −0.495738
\(670\) 9.19251 0.355138
\(671\) −4.16822 −0.160912
\(672\) −12.8262 −0.494781
\(673\) 5.47704 0.211124 0.105562 0.994413i \(-0.466336\pi\)
0.105562 + 0.994413i \(0.466336\pi\)
\(674\) −42.5342 −1.63836
\(675\) −4.71150 −0.181346
\(676\) −31.3273 −1.20490
\(677\) −42.4886 −1.63297 −0.816485 0.577367i \(-0.804080\pi\)
−0.816485 + 0.577367i \(0.804080\pi\)
\(678\) −40.9813 −1.57388
\(679\) 13.9631 0.535855
\(680\) 3.97685 0.152505
\(681\) 14.6393 0.560978
\(682\) 5.63535 0.215789
\(683\) −25.1897 −0.963857 −0.481929 0.876210i \(-0.660064\pi\)
−0.481929 + 0.876210i \(0.660064\pi\)
\(684\) −7.80475 −0.298422
\(685\) −5.49753 −0.210050
\(686\) −43.8888 −1.67568
\(687\) −24.1483 −0.921316
\(688\) 11.1619 0.425543
\(689\) 16.1423 0.614973
\(690\) −1.19762 −0.0455928
\(691\) 5.79765 0.220553 0.110277 0.993901i \(-0.464826\pi\)
0.110277 + 0.993901i \(0.464826\pi\)
\(692\) −37.2865 −1.41742
\(693\) −2.10308 −0.0798893
\(694\) 65.7832 2.49710
\(695\) −0.155341 −0.00589241
\(696\) 2.16657 0.0821235
\(697\) −17.3149 −0.655848
\(698\) 25.9270 0.981351
\(699\) 16.5564 0.626221
\(700\) 26.3558 0.996154
\(701\) 13.4101 0.506494 0.253247 0.967402i \(-0.418501\pi\)
0.253247 + 0.967402i \(0.418501\pi\)
\(702\) −3.49579 −0.131940
\(703\) −4.33106 −0.163349
\(704\) −14.4878 −0.546030
\(705\) −3.25980 −0.122771
\(706\) 0.780022 0.0293565
\(707\) 5.27271 0.198301
\(708\) −26.1576 −0.983064
\(709\) −18.0256 −0.676965 −0.338482 0.940973i \(-0.609914\pi\)
−0.338482 + 0.940973i \(0.609914\pi\)
\(710\) 2.91198 0.109285
\(711\) 1.24162 0.0465644
\(712\) 28.4864 1.06757
\(713\) −2.26219 −0.0847196
\(714\) −14.3438 −0.536802
\(715\) 0.940816 0.0351845
\(716\) −69.5784 −2.60027
\(717\) −18.3128 −0.683902
\(718\) 39.0165 1.45608
\(719\) −20.6072 −0.768518 −0.384259 0.923225i \(-0.625543\pi\)
−0.384259 + 0.923225i \(0.625543\pi\)
\(720\) −0.597544 −0.0222691
\(721\) −18.8482 −0.701944
\(722\) 26.9844 1.00426
\(723\) 16.0413 0.596581
\(724\) −29.8754 −1.11031
\(725\) 4.71150 0.174981
\(726\) 21.7439 0.806990
\(727\) −8.38118 −0.310841 −0.155420 0.987848i \(-0.549673\pi\)
−0.155420 + 0.987848i \(0.549673\pi\)
\(728\) 6.39413 0.236982
\(729\) 1.00000 0.0370370
\(730\) −1.22448 −0.0453199
\(731\) 34.2874 1.26817
\(732\) −11.0869 −0.409785
\(733\) −9.51389 −0.351404 −0.175702 0.984443i \(-0.556219\pi\)
−0.175702 + 0.984443i \(0.556219\pi\)
\(734\) 75.7768 2.79697
\(735\) −1.85656 −0.0684802
\(736\) 6.81370 0.251156
\(737\) −8.57539 −0.315879
\(738\) −11.2973 −0.415858
\(739\) −31.0800 −1.14330 −0.571648 0.820499i \(-0.693696\pi\)
−0.571648 + 0.820499i \(0.693696\pi\)
\(740\) 2.63213 0.0967590
\(741\) −4.11767 −0.151267
\(742\) 43.2153 1.58648
\(743\) 45.6581 1.67503 0.837517 0.546412i \(-0.184007\pi\)
0.837517 + 0.546412i \(0.184007\pi\)
\(744\) 4.90118 0.179686
\(745\) 10.8104 0.396062
\(746\) −44.5844 −1.63235
\(747\) 13.0672 0.478106
\(748\) −11.3459 −0.414847
\(749\) 9.88932 0.361348
\(750\) 11.6307 0.424695
\(751\) −30.5101 −1.11333 −0.556664 0.830737i \(-0.687919\pi\)
−0.556664 + 0.830737i \(0.687919\pi\)
\(752\) 6.75183 0.246214
\(753\) −16.2544 −0.592342
\(754\) 3.49579 0.127309
\(755\) 0.199079 0.00724524
\(756\) −5.59392 −0.203449
\(757\) −30.5168 −1.10915 −0.554576 0.832133i \(-0.687120\pi\)
−0.554576 + 0.832133i \(0.687120\pi\)
\(758\) −51.4563 −1.86898
\(759\) 1.11723 0.0405527
\(760\) 3.05632 0.110864
\(761\) −20.6725 −0.749377 −0.374689 0.927151i \(-0.622250\pi\)
−0.374689 + 0.927151i \(0.622250\pi\)
\(762\) −9.66141 −0.349996
\(763\) 9.57537 0.346652
\(764\) −61.5652 −2.22735
\(765\) −1.83555 −0.0663645
\(766\) −73.2611 −2.64703
\(767\) −13.8004 −0.498303
\(768\) −8.15037 −0.294101
\(769\) 32.3606 1.16695 0.583476 0.812130i \(-0.301692\pi\)
0.583476 + 0.812130i \(0.301692\pi\)
\(770\) 2.51870 0.0907676
\(771\) 2.52528 0.0909457
\(772\) 25.4315 0.915299
\(773\) 8.63105 0.310437 0.155219 0.987880i \(-0.450392\pi\)
0.155219 + 0.987880i \(0.450392\pi\)
\(774\) 22.3712 0.804116
\(775\) 10.6583 0.382858
\(776\) 16.0709 0.576910
\(777\) −3.10421 −0.111363
\(778\) −31.0719 −1.11398
\(779\) −13.3070 −0.476772
\(780\) 2.50245 0.0896020
\(781\) −2.71649 −0.0972037
\(782\) 7.61989 0.272487
\(783\) −1.00000 −0.0357371
\(784\) 3.84538 0.137335
\(785\) −3.77614 −0.134776
\(786\) −43.1691 −1.53979
\(787\) 17.5702 0.626310 0.313155 0.949702i \(-0.398614\pi\)
0.313155 + 0.949702i \(0.398614\pi\)
\(788\) 17.3810 0.619171
\(789\) −28.6908 −1.02142
\(790\) −1.48700 −0.0529049
\(791\) −34.5978 −1.23016
\(792\) −2.42054 −0.0860102
\(793\) −5.84931 −0.207715
\(794\) −31.0539 −1.10206
\(795\) 5.53020 0.196136
\(796\) 27.2334 0.965262
\(797\) 15.4807 0.548355 0.274178 0.961679i \(-0.411594\pi\)
0.274178 + 0.961679i \(0.411594\pi\)
\(798\) −11.0236 −0.390231
\(799\) 20.7405 0.733745
\(800\) −32.1028 −1.13501
\(801\) −13.1482 −0.464568
\(802\) −11.3190 −0.399686
\(803\) 1.14227 0.0403100
\(804\) −22.8094 −0.804427
\(805\) −1.01108 −0.0356358
\(806\) 7.90814 0.278552
\(807\) −18.4710 −0.650211
\(808\) 6.06864 0.213494
\(809\) −19.9422 −0.701131 −0.350565 0.936538i \(-0.614011\pi\)
−0.350565 + 0.936538i \(0.614011\pi\)
\(810\) −1.19762 −0.0420803
\(811\) −24.0964 −0.846139 −0.423069 0.906097i \(-0.639047\pi\)
−0.423069 + 0.906097i \(0.639047\pi\)
\(812\) 5.59392 0.196308
\(813\) −7.71437 −0.270555
\(814\) −4.10798 −0.143985
\(815\) −10.7120 −0.375223
\(816\) 3.80187 0.133092
\(817\) 26.3509 0.921901
\(818\) 46.5137 1.62631
\(819\) −2.95127 −0.103126
\(820\) 8.08710 0.282414
\(821\) 29.8257 1.04092 0.520461 0.853885i \(-0.325760\pi\)
0.520461 + 0.853885i \(0.325760\pi\)
\(822\) 22.8218 0.796001
\(823\) −4.38398 −0.152816 −0.0764080 0.997077i \(-0.524345\pi\)
−0.0764080 + 0.997077i \(0.524345\pi\)
\(824\) −21.6934 −0.755725
\(825\) −5.26381 −0.183262
\(826\) −36.9456 −1.28550
\(827\) 33.8262 1.17625 0.588126 0.808769i \(-0.299866\pi\)
0.588126 + 0.808769i \(0.299866\pi\)
\(828\) 2.97167 0.103273
\(829\) 19.9346 0.692358 0.346179 0.938169i \(-0.387479\pi\)
0.346179 + 0.938169i \(0.387479\pi\)
\(830\) −15.6497 −0.543208
\(831\) −0.702588 −0.0243725
\(832\) −20.3309 −0.704848
\(833\) 11.8124 0.409274
\(834\) 0.644863 0.0223298
\(835\) −6.67179 −0.230887
\(836\) −8.71966 −0.301576
\(837\) −2.26219 −0.0781926
\(838\) −7.28584 −0.251685
\(839\) −9.52467 −0.328828 −0.164414 0.986391i \(-0.552573\pi\)
−0.164414 + 0.986391i \(0.552573\pi\)
\(840\) 2.19057 0.0755817
\(841\) 1.00000 0.0344828
\(842\) 4.39739 0.151544
\(843\) 2.46040 0.0847408
\(844\) −0.275352 −0.00947800
\(845\) −5.66227 −0.194788
\(846\) 13.5323 0.465251
\(847\) 18.3569 0.630751
\(848\) −11.4544 −0.393345
\(849\) −15.1893 −0.521294
\(850\) −35.9011 −1.23140
\(851\) 1.64906 0.0565291
\(852\) −7.22551 −0.247542
\(853\) 45.9120 1.57200 0.785998 0.618229i \(-0.212150\pi\)
0.785998 + 0.618229i \(0.212150\pi\)
\(854\) −15.6594 −0.535855
\(855\) −1.41068 −0.0482441
\(856\) 11.3821 0.389033
\(857\) 54.7299 1.86954 0.934768 0.355258i \(-0.115607\pi\)
0.934768 + 0.355258i \(0.115607\pi\)
\(858\) −3.90559 −0.133335
\(859\) −39.0054 −1.33085 −0.665423 0.746466i \(-0.731749\pi\)
−0.665423 + 0.746466i \(0.731749\pi\)
\(860\) −16.0143 −0.546084
\(861\) −9.53756 −0.325039
\(862\) 8.09892 0.275850
\(863\) 14.2092 0.483685 0.241843 0.970316i \(-0.422248\pi\)
0.241843 + 0.970316i \(0.422248\pi\)
\(864\) 6.81370 0.231807
\(865\) −6.73938 −0.229146
\(866\) 2.93305 0.0996692
\(867\) −5.32130 −0.180721
\(868\) 12.6545 0.429521
\(869\) 1.38717 0.0470565
\(870\) 1.19762 0.0406033
\(871\) −12.0339 −0.407754
\(872\) 11.0208 0.373211
\(873\) −7.41766 −0.251050
\(874\) 5.85610 0.198086
\(875\) 9.81908 0.331946
\(876\) 3.03830 0.102655
\(877\) 17.7516 0.599431 0.299715 0.954029i \(-0.403108\pi\)
0.299715 + 0.954029i \(0.403108\pi\)
\(878\) −38.3311 −1.29361
\(879\) 8.84429 0.298311
\(880\) −0.667591 −0.0225045
\(881\) 10.8019 0.363926 0.181963 0.983305i \(-0.441755\pi\)
0.181963 + 0.983305i \(0.441755\pi\)
\(882\) 7.70710 0.259511
\(883\) −23.4523 −0.789232 −0.394616 0.918846i \(-0.629122\pi\)
−0.394616 + 0.918846i \(0.629122\pi\)
\(884\) −15.9218 −0.535509
\(885\) −4.72788 −0.158926
\(886\) 21.3959 0.718809
\(887\) −39.1075 −1.31310 −0.656550 0.754283i \(-0.727985\pi\)
−0.656550 + 0.754283i \(0.727985\pi\)
\(888\) −3.57280 −0.119895
\(889\) −8.15651 −0.273560
\(890\) 15.7466 0.527826
\(891\) 1.11723 0.0374284
\(892\) −38.1036 −1.27580
\(893\) 15.9396 0.533400
\(894\) −44.8769 −1.50091
\(895\) −12.5760 −0.420369
\(896\) −28.7764 −0.961351
\(897\) 1.56781 0.0523478
\(898\) −43.5898 −1.45461
\(899\) 2.26219 0.0754482
\(900\) −14.0011 −0.466702
\(901\) −35.1859 −1.17221
\(902\) −12.6216 −0.420253
\(903\) 18.8865 0.628505
\(904\) −39.8204 −1.32441
\(905\) −5.39986 −0.179497
\(906\) −0.826433 −0.0274564
\(907\) 0.854437 0.0283711 0.0141856 0.999899i \(-0.495484\pi\)
0.0141856 + 0.999899i \(0.495484\pi\)
\(908\) 43.5032 1.44370
\(909\) −2.80104 −0.0929047
\(910\) 3.53452 0.117168
\(911\) 27.2030 0.901276 0.450638 0.892707i \(-0.351197\pi\)
0.450638 + 0.892707i \(0.351197\pi\)
\(912\) 2.92185 0.0967520
\(913\) 14.5991 0.483158
\(914\) 27.4296 0.907290
\(915\) −2.00392 −0.0662475
\(916\) −71.7609 −2.37105
\(917\) −36.4449 −1.20352
\(918\) 7.61989 0.251494
\(919\) −46.5672 −1.53611 −0.768055 0.640384i \(-0.778775\pi\)
−0.768055 + 0.640384i \(0.778775\pi\)
\(920\) −1.16370 −0.0383661
\(921\) 5.52326 0.181997
\(922\) 75.3556 2.48170
\(923\) −3.81208 −0.125476
\(924\) −6.24966 −0.205599
\(925\) −7.76956 −0.255461
\(926\) −73.4950 −2.41520
\(927\) 10.0128 0.328863
\(928\) −6.81370 −0.223671
\(929\) 31.6499 1.03840 0.519200 0.854653i \(-0.326230\pi\)
0.519200 + 0.854653i \(0.326230\pi\)
\(930\) 2.70925 0.0888399
\(931\) 9.07814 0.297524
\(932\) 49.2003 1.61161
\(933\) 0.0662747 0.00216974
\(934\) 25.8186 0.844812
\(935\) −2.05072 −0.0670659
\(936\) −3.39677 −0.111027
\(937\) 17.7619 0.580255 0.290128 0.956988i \(-0.406302\pi\)
0.290128 + 0.956988i \(0.406302\pi\)
\(938\) −32.2166 −1.05191
\(939\) 17.7785 0.580179
\(940\) −9.68706 −0.315957
\(941\) 52.0711 1.69747 0.848734 0.528820i \(-0.177365\pi\)
0.848734 + 0.528820i \(0.177365\pi\)
\(942\) 15.6758 0.510746
\(943\) 5.06667 0.164993
\(944\) 9.79258 0.318721
\(945\) −1.01108 −0.0328903
\(946\) 24.9937 0.812614
\(947\) −7.10267 −0.230806 −0.115403 0.993319i \(-0.536816\pi\)
−0.115403 + 0.993319i \(0.536816\pi\)
\(948\) 3.68969 0.119836
\(949\) 1.60296 0.0520344
\(950\) −27.5911 −0.895172
\(951\) −8.12451 −0.263455
\(952\) −13.9375 −0.451716
\(953\) 11.9585 0.387373 0.193687 0.981063i \(-0.437956\pi\)
0.193687 + 0.981063i \(0.437956\pi\)
\(954\) −22.9574 −0.743273
\(955\) −11.1277 −0.360083
\(956\) −54.4195 −1.76005
\(957\) −1.11723 −0.0361148
\(958\) −31.7359 −1.02534
\(959\) 19.2670 0.622163
\(960\) −6.96517 −0.224800
\(961\) −25.8825 −0.834920
\(962\) −5.76478 −0.185864
\(963\) −5.25354 −0.169293
\(964\) 47.6694 1.53533
\(965\) 4.59663 0.147971
\(966\) 4.19726 0.135045
\(967\) 10.3118 0.331604 0.165802 0.986159i \(-0.446979\pi\)
0.165802 + 0.986159i \(0.446979\pi\)
\(968\) 21.1279 0.679078
\(969\) 8.97542 0.288332
\(970\) 8.88358 0.285234
\(971\) −11.4796 −0.368398 −0.184199 0.982889i \(-0.558969\pi\)
−0.184199 + 0.982889i \(0.558969\pi\)
\(972\) 2.97167 0.0953165
\(973\) 0.544416 0.0174532
\(974\) −57.5531 −1.84412
\(975\) −7.38676 −0.236566
\(976\) 4.15060 0.132857
\(977\) −12.8478 −0.411036 −0.205518 0.978653i \(-0.565888\pi\)
−0.205518 + 0.978653i \(0.565888\pi\)
\(978\) 44.4683 1.42194
\(979\) −14.6895 −0.469477
\(980\) −5.51709 −0.176237
\(981\) −5.08675 −0.162408
\(982\) 79.2909 2.53027
\(983\) 1.92074 0.0612622 0.0306311 0.999531i \(-0.490248\pi\)
0.0306311 + 0.999531i \(0.490248\pi\)
\(984\) −10.9773 −0.349943
\(985\) 3.14154 0.100098
\(986\) −7.61989 −0.242667
\(987\) 11.4245 0.363645
\(988\) −12.2364 −0.389291
\(989\) −10.0332 −0.319036
\(990\) −1.33802 −0.0425250
\(991\) −2.06517 −0.0656022 −0.0328011 0.999462i \(-0.510443\pi\)
−0.0328011 + 0.999462i \(0.510443\pi\)
\(992\) −15.4139 −0.489391
\(993\) 20.2364 0.642182
\(994\) −10.2055 −0.323698
\(995\) 4.92232 0.156048
\(996\) 38.8316 1.23043
\(997\) −40.2717 −1.27542 −0.637709 0.770277i \(-0.720118\pi\)
−0.637709 + 0.770277i \(0.720118\pi\)
\(998\) −34.6625 −1.09722
\(999\) 1.64906 0.0521740
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 2001.2.a.i.1.2 7
3.2 odd 2 6003.2.a.j.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.i.1.2 7 1.1 even 1 trivial
6003.2.a.j.1.6 7 3.2 odd 2