Properties

Label 4007.2.a.b.1.14
Level $4007$
Weight $2$
Character 4007.1
Self dual yes
Analytic conductor $31.996$
Analytic rank $0$
Dimension $195$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4007,2,Mod(1,4007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4007, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4007.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(31.9960560899\)
Analytic rank: \(0\)
Dimension: \(195\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 4007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.54911 q^{2} +2.95187 q^{3} +4.49797 q^{4} +1.50040 q^{5} -7.52466 q^{6} +0.00462218 q^{7} -6.36761 q^{8} +5.71356 q^{9} +O(q^{10})\) \(q-2.54911 q^{2} +2.95187 q^{3} +4.49797 q^{4} +1.50040 q^{5} -7.52466 q^{6} +0.00462218 q^{7} -6.36761 q^{8} +5.71356 q^{9} -3.82468 q^{10} +0.915110 q^{11} +13.2774 q^{12} +3.64298 q^{13} -0.0117825 q^{14} +4.42898 q^{15} +7.23581 q^{16} -5.36049 q^{17} -14.5645 q^{18} +5.52584 q^{19} +6.74874 q^{20} +0.0136441 q^{21} -2.33272 q^{22} +2.61394 q^{23} -18.7964 q^{24} -2.74881 q^{25} -9.28636 q^{26} +8.01009 q^{27} +0.0207905 q^{28} -3.05203 q^{29} -11.2900 q^{30} +7.05511 q^{31} -5.70967 q^{32} +2.70129 q^{33} +13.6645 q^{34} +0.00693510 q^{35} +25.6994 q^{36} -4.15585 q^{37} -14.0860 q^{38} +10.7536 q^{39} -9.55394 q^{40} +9.94726 q^{41} -0.0347803 q^{42} +10.0386 q^{43} +4.11614 q^{44} +8.57260 q^{45} -6.66322 q^{46} +5.72607 q^{47} +21.3592 q^{48} -6.99998 q^{49} +7.00703 q^{50} -15.8235 q^{51} +16.3860 q^{52} -8.21492 q^{53} -20.4186 q^{54} +1.37303 q^{55} -0.0294323 q^{56} +16.3116 q^{57} +7.77997 q^{58} -13.6497 q^{59} +19.9214 q^{60} +11.3779 q^{61} -17.9843 q^{62} +0.0264091 q^{63} +0.0829690 q^{64} +5.46591 q^{65} -6.88589 q^{66} -11.5822 q^{67} -24.1113 q^{68} +7.71602 q^{69} -0.0176784 q^{70} -3.36596 q^{71} -36.3817 q^{72} -3.92477 q^{73} +10.5937 q^{74} -8.11415 q^{75} +24.8551 q^{76} +0.00422980 q^{77} -27.4122 q^{78} +10.5215 q^{79} +10.8566 q^{80} +6.50409 q^{81} -25.3567 q^{82} +15.7822 q^{83} +0.0613708 q^{84} -8.04285 q^{85} -25.5895 q^{86} -9.00921 q^{87} -5.82706 q^{88} -13.9848 q^{89} -21.8525 q^{90} +0.0168385 q^{91} +11.7574 q^{92} +20.8258 q^{93} -14.5964 q^{94} +8.29094 q^{95} -16.8542 q^{96} +14.5548 q^{97} +17.8437 q^{98} +5.22853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54911 −1.80249 −0.901247 0.433305i \(-0.857347\pi\)
−0.901247 + 0.433305i \(0.857347\pi\)
\(3\) 2.95187 1.70427 0.852133 0.523326i \(-0.175309\pi\)
0.852133 + 0.523326i \(0.175309\pi\)
\(4\) 4.49797 2.24899
\(5\) 1.50040 0.670997 0.335499 0.942041i \(-0.391095\pi\)
0.335499 + 0.942041i \(0.391095\pi\)
\(6\) −7.52466 −3.07193
\(7\) 0.00462218 0.00174702 0.000873511 1.00000i \(-0.499722\pi\)
0.000873511 1.00000i \(0.499722\pi\)
\(8\) −6.36761 −2.25129
\(9\) 5.71356 1.90452
\(10\) −3.82468 −1.20947
\(11\) 0.915110 0.275916 0.137958 0.990438i \(-0.455946\pi\)
0.137958 + 0.990438i \(0.455946\pi\)
\(12\) 13.2774 3.83287
\(13\) 3.64298 1.01038 0.505190 0.863008i \(-0.331422\pi\)
0.505190 + 0.863008i \(0.331422\pi\)
\(14\) −0.0117825 −0.00314900
\(15\) 4.42898 1.14356
\(16\) 7.23581 1.80895
\(17\) −5.36049 −1.30011 −0.650055 0.759887i \(-0.725254\pi\)
−0.650055 + 0.759887i \(0.725254\pi\)
\(18\) −14.5645 −3.43289
\(19\) 5.52584 1.26771 0.633857 0.773450i \(-0.281471\pi\)
0.633857 + 0.773450i \(0.281471\pi\)
\(20\) 6.74874 1.50906
\(21\) 0.0136441 0.00297739
\(22\) −2.33272 −0.497337
\(23\) 2.61394 0.545044 0.272522 0.962150i \(-0.412142\pi\)
0.272522 + 0.962150i \(0.412142\pi\)
\(24\) −18.7964 −3.83680
\(25\) −2.74881 −0.549763
\(26\) −9.28636 −1.82120
\(27\) 8.01009 1.54154
\(28\) 0.0207905 0.00392903
\(29\) −3.05203 −0.566748 −0.283374 0.959010i \(-0.591454\pi\)
−0.283374 + 0.959010i \(0.591454\pi\)
\(30\) −11.2900 −2.06126
\(31\) 7.05511 1.26714 0.633568 0.773687i \(-0.281590\pi\)
0.633568 + 0.773687i \(0.281590\pi\)
\(32\) −5.70967 −1.00934
\(33\) 2.70129 0.470234
\(34\) 13.6645 2.34344
\(35\) 0.00693510 0.00117225
\(36\) 25.6994 4.28324
\(37\) −4.15585 −0.683217 −0.341608 0.939842i \(-0.610972\pi\)
−0.341608 + 0.939842i \(0.610972\pi\)
\(38\) −14.0860 −2.28505
\(39\) 10.7536 1.72196
\(40\) −9.55394 −1.51061
\(41\) 9.94726 1.55350 0.776750 0.629809i \(-0.216867\pi\)
0.776750 + 0.629809i \(0.216867\pi\)
\(42\) −0.0347803 −0.00536672
\(43\) 10.0386 1.53087 0.765436 0.643512i \(-0.222523\pi\)
0.765436 + 0.643512i \(0.222523\pi\)
\(44\) 4.11614 0.620531
\(45\) 8.57260 1.27793
\(46\) −6.66322 −0.982438
\(47\) 5.72607 0.835233 0.417616 0.908623i \(-0.362866\pi\)
0.417616 + 0.908623i \(0.362866\pi\)
\(48\) 21.3592 3.08294
\(49\) −6.99998 −0.999997
\(50\) 7.00703 0.990944
\(51\) −15.8235 −2.21573
\(52\) 16.3860 2.27233
\(53\) −8.21492 −1.12841 −0.564203 0.825636i \(-0.690817\pi\)
−0.564203 + 0.825636i \(0.690817\pi\)
\(54\) −20.4186 −2.77862
\(55\) 1.37303 0.185139
\(56\) −0.0294323 −0.00393305
\(57\) 16.3116 2.16052
\(58\) 7.77997 1.02156
\(59\) −13.6497 −1.77704 −0.888519 0.458840i \(-0.848265\pi\)
−0.888519 + 0.458840i \(0.848265\pi\)
\(60\) 19.9214 2.57184
\(61\) 11.3779 1.45680 0.728398 0.685154i \(-0.240265\pi\)
0.728398 + 0.685154i \(0.240265\pi\)
\(62\) −17.9843 −2.28400
\(63\) 0.0264091 0.00332724
\(64\) 0.0829690 0.0103711
\(65\) 5.46591 0.677962
\(66\) −6.88589 −0.847594
\(67\) −11.5822 −1.41499 −0.707495 0.706719i \(-0.750175\pi\)
−0.707495 + 0.706719i \(0.750175\pi\)
\(68\) −24.1113 −2.92393
\(69\) 7.71602 0.928899
\(70\) −0.0176784 −0.00211297
\(71\) −3.36596 −0.399466 −0.199733 0.979850i \(-0.564007\pi\)
−0.199733 + 0.979850i \(0.564007\pi\)
\(72\) −36.3817 −4.28763
\(73\) −3.92477 −0.459359 −0.229680 0.973266i \(-0.573768\pi\)
−0.229680 + 0.973266i \(0.573768\pi\)
\(74\) 10.5937 1.23149
\(75\) −8.11415 −0.936942
\(76\) 24.8551 2.85107
\(77\) 0.00422980 0.000482031 0
\(78\) −27.4122 −3.10382
\(79\) 10.5215 1.18376 0.591878 0.806027i \(-0.298387\pi\)
0.591878 + 0.806027i \(0.298387\pi\)
\(80\) 10.8566 1.21380
\(81\) 6.50409 0.722677
\(82\) −25.3567 −2.80018
\(83\) 15.7822 1.73232 0.866159 0.499768i \(-0.166581\pi\)
0.866159 + 0.499768i \(0.166581\pi\)
\(84\) 0.0613708 0.00669610
\(85\) −8.04285 −0.872370
\(86\) −25.5895 −2.75939
\(87\) −9.00921 −0.965888
\(88\) −5.82706 −0.621167
\(89\) −13.9848 −1.48239 −0.741194 0.671291i \(-0.765740\pi\)
−0.741194 + 0.671291i \(0.765740\pi\)
\(90\) −21.8525 −2.30346
\(91\) 0.0168385 0.00176516
\(92\) 11.7574 1.22580
\(93\) 20.8258 2.15954
\(94\) −14.5964 −1.50550
\(95\) 8.29094 0.850633
\(96\) −16.8542 −1.72018
\(97\) 14.5548 1.47782 0.738910 0.673805i \(-0.235341\pi\)
0.738910 + 0.673805i \(0.235341\pi\)
\(98\) 17.8437 1.80249
\(99\) 5.22853 0.525487
\(100\) −12.3641 −1.23641
\(101\) −15.2426 −1.51670 −0.758348 0.651850i \(-0.773993\pi\)
−0.758348 + 0.651850i \(0.773993\pi\)
\(102\) 40.3358 3.99384
\(103\) 8.46423 0.834005 0.417003 0.908905i \(-0.363081\pi\)
0.417003 + 0.908905i \(0.363081\pi\)
\(104\) −23.1971 −2.27466
\(105\) 0.0204716 0.00199782
\(106\) 20.9408 2.03395
\(107\) 19.5701 1.89191 0.945957 0.324291i \(-0.105126\pi\)
0.945957 + 0.324291i \(0.105126\pi\)
\(108\) 36.0292 3.46691
\(109\) −7.54636 −0.722810 −0.361405 0.932409i \(-0.617703\pi\)
−0.361405 + 0.932409i \(0.617703\pi\)
\(110\) −3.50000 −0.333712
\(111\) −12.2675 −1.16438
\(112\) 0.0334452 0.00316028
\(113\) 11.2685 1.06005 0.530023 0.847983i \(-0.322183\pi\)
0.530023 + 0.847983i \(0.322183\pi\)
\(114\) −41.5801 −3.89433
\(115\) 3.92194 0.365723
\(116\) −13.7279 −1.27461
\(117\) 20.8144 1.92429
\(118\) 34.7946 3.20310
\(119\) −0.0247772 −0.00227132
\(120\) −28.2020 −2.57448
\(121\) −10.1626 −0.923870
\(122\) −29.0036 −2.62587
\(123\) 29.3630 2.64758
\(124\) 31.7337 2.84977
\(125\) −11.6263 −1.03989
\(126\) −0.0673198 −0.00599733
\(127\) 1.93886 0.172046 0.0860230 0.996293i \(-0.472584\pi\)
0.0860230 + 0.996293i \(0.472584\pi\)
\(128\) 11.2078 0.990643
\(129\) 29.6327 2.60901
\(130\) −13.9332 −1.22202
\(131\) 0.526451 0.0459962 0.0229981 0.999736i \(-0.492679\pi\)
0.0229981 + 0.999736i \(0.492679\pi\)
\(132\) 12.1503 1.05755
\(133\) 0.0255414 0.00221472
\(134\) 29.5243 2.55051
\(135\) 12.0183 1.03437
\(136\) 34.1335 2.92692
\(137\) 7.77265 0.664063 0.332031 0.943268i \(-0.392266\pi\)
0.332031 + 0.943268i \(0.392266\pi\)
\(138\) −19.6690 −1.67434
\(139\) −7.75632 −0.657883 −0.328941 0.944350i \(-0.606692\pi\)
−0.328941 + 0.944350i \(0.606692\pi\)
\(140\) 0.0311939 0.00263637
\(141\) 16.9026 1.42346
\(142\) 8.58020 0.720035
\(143\) 3.33372 0.278780
\(144\) 41.3422 3.44519
\(145\) −4.57925 −0.380286
\(146\) 10.0047 0.827993
\(147\) −20.6631 −1.70426
\(148\) −18.6929 −1.53655
\(149\) −9.34367 −0.765463 −0.382732 0.923860i \(-0.625017\pi\)
−0.382732 + 0.923860i \(0.625017\pi\)
\(150\) 20.6839 1.68883
\(151\) 2.86280 0.232971 0.116486 0.993192i \(-0.462837\pi\)
0.116486 + 0.993192i \(0.462837\pi\)
\(152\) −35.1864 −2.85399
\(153\) −30.6275 −2.47608
\(154\) −0.0107822 −0.000868858 0
\(155\) 10.5855 0.850244
\(156\) 48.3694 3.87266
\(157\) 10.3224 0.823815 0.411908 0.911226i \(-0.364863\pi\)
0.411908 + 0.911226i \(0.364863\pi\)
\(158\) −26.8204 −2.13371
\(159\) −24.2494 −1.92310
\(160\) −8.56676 −0.677262
\(161\) 0.0120821 0.000952203 0
\(162\) −16.5797 −1.30262
\(163\) −0.192412 −0.0150709 −0.00753545 0.999972i \(-0.502399\pi\)
−0.00753545 + 0.999972i \(0.502399\pi\)
\(164\) 44.7425 3.49380
\(165\) 4.05300 0.315526
\(166\) −40.2305 −3.12249
\(167\) 17.6694 1.36730 0.683651 0.729809i \(-0.260391\pi\)
0.683651 + 0.729809i \(0.260391\pi\)
\(168\) −0.0868804 −0.00670297
\(169\) 0.271286 0.0208682
\(170\) 20.5021 1.57244
\(171\) 31.5722 2.41439
\(172\) 45.1533 3.44291
\(173\) −18.2056 −1.38414 −0.692071 0.721829i \(-0.743302\pi\)
−0.692071 + 0.721829i \(0.743302\pi\)
\(174\) 22.9655 1.74101
\(175\) −0.0127055 −0.000960447 0
\(176\) 6.62156 0.499119
\(177\) −40.2922 −3.02854
\(178\) 35.6489 2.67200
\(179\) 9.83691 0.735245 0.367623 0.929975i \(-0.380172\pi\)
0.367623 + 0.929975i \(0.380172\pi\)
\(180\) 38.5593 2.87404
\(181\) −4.34576 −0.323018 −0.161509 0.986871i \(-0.551636\pi\)
−0.161509 + 0.986871i \(0.551636\pi\)
\(182\) −0.0429233 −0.00318168
\(183\) 33.5862 2.48277
\(184\) −16.6445 −1.22705
\(185\) −6.23541 −0.458437
\(186\) −53.0873 −3.89255
\(187\) −4.90544 −0.358721
\(188\) 25.7557 1.87843
\(189\) 0.0370241 0.00269311
\(190\) −21.1345 −1.53326
\(191\) 23.3581 1.69013 0.845065 0.534663i \(-0.179561\pi\)
0.845065 + 0.534663i \(0.179561\pi\)
\(192\) 0.244914 0.0176751
\(193\) 4.53940 0.326753 0.163376 0.986564i \(-0.447761\pi\)
0.163376 + 0.986564i \(0.447761\pi\)
\(194\) −37.1019 −2.66376
\(195\) 16.1347 1.15543
\(196\) −31.4857 −2.24898
\(197\) −24.8451 −1.77014 −0.885072 0.465455i \(-0.845891\pi\)
−0.885072 + 0.465455i \(0.845891\pi\)
\(198\) −13.3281 −0.947188
\(199\) 4.05814 0.287674 0.143837 0.989601i \(-0.454056\pi\)
0.143837 + 0.989601i \(0.454056\pi\)
\(200\) 17.5034 1.23768
\(201\) −34.1892 −2.41152
\(202\) 38.8551 2.73383
\(203\) −0.0141070 −0.000990120 0
\(204\) −71.1736 −4.98315
\(205\) 14.9248 1.04239
\(206\) −21.5763 −1.50329
\(207\) 14.9349 1.03805
\(208\) 26.3599 1.82773
\(209\) 5.05675 0.349783
\(210\) −0.0521843 −0.00360106
\(211\) 23.1060 1.59068 0.795341 0.606162i \(-0.207292\pi\)
0.795341 + 0.606162i \(0.207292\pi\)
\(212\) −36.9505 −2.53777
\(213\) −9.93588 −0.680796
\(214\) −49.8864 −3.41017
\(215\) 15.0619 1.02721
\(216\) −51.0051 −3.47046
\(217\) 0.0326100 0.00221371
\(218\) 19.2365 1.30286
\(219\) −11.5854 −0.782870
\(220\) 6.17583 0.416375
\(221\) −19.5281 −1.31360
\(222\) 31.2713 2.09879
\(223\) −2.62407 −0.175720 −0.0878602 0.996133i \(-0.528003\pi\)
−0.0878602 + 0.996133i \(0.528003\pi\)
\(224\) −0.0263911 −0.00176333
\(225\) −15.7055 −1.04703
\(226\) −28.7245 −1.91073
\(227\) −19.3383 −1.28353 −0.641764 0.766903i \(-0.721797\pi\)
−0.641764 + 0.766903i \(0.721797\pi\)
\(228\) 73.3691 4.85898
\(229\) 21.3270 1.40933 0.704665 0.709541i \(-0.251097\pi\)
0.704665 + 0.709541i \(0.251097\pi\)
\(230\) −9.99747 −0.659213
\(231\) 0.0124859 0.000821509 0
\(232\) 19.4341 1.27591
\(233\) 7.33932 0.480815 0.240407 0.970672i \(-0.422719\pi\)
0.240407 + 0.970672i \(0.422719\pi\)
\(234\) −53.0582 −3.46852
\(235\) 8.59137 0.560439
\(236\) −61.3959 −3.99653
\(237\) 31.0580 2.01743
\(238\) 0.0631598 0.00409404
\(239\) 0.513609 0.0332226 0.0166113 0.999862i \(-0.494712\pi\)
0.0166113 + 0.999862i \(0.494712\pi\)
\(240\) 32.0473 2.06864
\(241\) −15.1014 −0.972765 −0.486382 0.873746i \(-0.661684\pi\)
−0.486382 + 0.873746i \(0.661684\pi\)
\(242\) 25.9055 1.66527
\(243\) −4.83101 −0.309909
\(244\) 51.1777 3.27631
\(245\) −10.5027 −0.670995
\(246\) −74.8497 −4.77224
\(247\) 20.1305 1.28087
\(248\) −44.9242 −2.85269
\(249\) 46.5870 2.95233
\(250\) 29.6367 1.87439
\(251\) −27.2410 −1.71943 −0.859717 0.510770i \(-0.829360\pi\)
−0.859717 + 0.510770i \(0.829360\pi\)
\(252\) 0.118788 0.00748291
\(253\) 2.39204 0.150386
\(254\) −4.94237 −0.310112
\(255\) −23.7415 −1.48675
\(256\) −28.7360 −1.79600
\(257\) −24.9546 −1.55662 −0.778312 0.627878i \(-0.783924\pi\)
−0.778312 + 0.627878i \(0.783924\pi\)
\(258\) −75.5370 −4.70273
\(259\) −0.0192091 −0.00119359
\(260\) 24.5855 1.52473
\(261\) −17.4380 −1.07938
\(262\) −1.34198 −0.0829080
\(263\) 8.68790 0.535719 0.267859 0.963458i \(-0.413684\pi\)
0.267859 + 0.963458i \(0.413684\pi\)
\(264\) −17.2008 −1.05863
\(265\) −12.3256 −0.757158
\(266\) −0.0651080 −0.00399203
\(267\) −41.2814 −2.52638
\(268\) −52.0964 −3.18229
\(269\) −14.2432 −0.868423 −0.434211 0.900811i \(-0.642973\pi\)
−0.434211 + 0.900811i \(0.642973\pi\)
\(270\) −30.6360 −1.86445
\(271\) −13.4489 −0.816961 −0.408481 0.912767i \(-0.633941\pi\)
−0.408481 + 0.912767i \(0.633941\pi\)
\(272\) −38.7875 −2.35184
\(273\) 0.0497052 0.00300829
\(274\) −19.8134 −1.19697
\(275\) −2.51547 −0.151688
\(276\) 34.7064 2.08908
\(277\) −7.90622 −0.475038 −0.237519 0.971383i \(-0.576334\pi\)
−0.237519 + 0.971383i \(0.576334\pi\)
\(278\) 19.7717 1.18583
\(279\) 40.3098 2.41329
\(280\) −0.0441600 −0.00263907
\(281\) 5.65916 0.337597 0.168799 0.985651i \(-0.446011\pi\)
0.168799 + 0.985651i \(0.446011\pi\)
\(282\) −43.0867 −2.56578
\(283\) −9.12743 −0.542570 −0.271285 0.962499i \(-0.587449\pi\)
−0.271285 + 0.962499i \(0.587449\pi\)
\(284\) −15.1400 −0.898393
\(285\) 24.4738 1.44970
\(286\) −8.49804 −0.502499
\(287\) 0.0459780 0.00271400
\(288\) −32.6226 −1.92230
\(289\) 11.7348 0.690285
\(290\) 11.6730 0.685464
\(291\) 42.9640 2.51860
\(292\) −17.6535 −1.03309
\(293\) 9.36213 0.546941 0.273471 0.961880i \(-0.411828\pi\)
0.273471 + 0.961880i \(0.411828\pi\)
\(294\) 52.6724 3.07192
\(295\) −20.4799 −1.19239
\(296\) 26.4628 1.53812
\(297\) 7.33011 0.425336
\(298\) 23.8181 1.37974
\(299\) 9.52252 0.550701
\(300\) −36.4972 −2.10717
\(301\) 0.0464002 0.00267447
\(302\) −7.29759 −0.419929
\(303\) −44.9942 −2.58485
\(304\) 39.9839 2.29324
\(305\) 17.0714 0.977506
\(306\) 78.0729 4.46313
\(307\) −29.5506 −1.68654 −0.843270 0.537490i \(-0.819373\pi\)
−0.843270 + 0.537490i \(0.819373\pi\)
\(308\) 0.0190255 0.00108408
\(309\) 24.9853 1.42137
\(310\) −26.9835 −1.53256
\(311\) 5.32872 0.302164 0.151082 0.988521i \(-0.451724\pi\)
0.151082 + 0.988521i \(0.451724\pi\)
\(312\) −68.4748 −3.87662
\(313\) 13.3000 0.751761 0.375880 0.926668i \(-0.377340\pi\)
0.375880 + 0.926668i \(0.377340\pi\)
\(314\) −26.3129 −1.48492
\(315\) 0.0396241 0.00223257
\(316\) 47.3252 2.66225
\(317\) −24.4974 −1.37591 −0.687955 0.725754i \(-0.741491\pi\)
−0.687955 + 0.725754i \(0.741491\pi\)
\(318\) 61.8145 3.46638
\(319\) −2.79294 −0.156375
\(320\) 0.124486 0.00695900
\(321\) 57.7685 3.22432
\(322\) −0.0307986 −0.00171634
\(323\) −29.6212 −1.64817
\(324\) 29.2552 1.62529
\(325\) −10.0139 −0.555469
\(326\) 0.490481 0.0271652
\(327\) −22.2759 −1.23186
\(328\) −63.3403 −3.49738
\(329\) 0.0264669 0.00145917
\(330\) −10.3316 −0.568733
\(331\) −13.0062 −0.714884 −0.357442 0.933935i \(-0.616351\pi\)
−0.357442 + 0.933935i \(0.616351\pi\)
\(332\) 70.9878 3.89596
\(333\) −23.7447 −1.30120
\(334\) −45.0414 −2.46456
\(335\) −17.3779 −0.949454
\(336\) 0.0987262 0.00538595
\(337\) 31.6916 1.72635 0.863175 0.504904i \(-0.168472\pi\)
0.863175 + 0.504904i \(0.168472\pi\)
\(338\) −0.691539 −0.0376148
\(339\) 33.2631 1.80660
\(340\) −36.1765 −1.96195
\(341\) 6.45620 0.349623
\(342\) −80.4811 −4.35192
\(343\) −0.0647105 −0.00349404
\(344\) −63.9219 −3.44644
\(345\) 11.5771 0.623289
\(346\) 46.4080 2.49491
\(347\) −27.7317 −1.48872 −0.744358 0.667781i \(-0.767244\pi\)
−0.744358 + 0.667781i \(0.767244\pi\)
\(348\) −40.5232 −2.17227
\(349\) 9.51397 0.509271 0.254636 0.967037i \(-0.418044\pi\)
0.254636 + 0.967037i \(0.418044\pi\)
\(350\) 0.0323878 0.00173120
\(351\) 29.1806 1.55754
\(352\) −5.22498 −0.278492
\(353\) 34.0646 1.81308 0.906539 0.422123i \(-0.138715\pi\)
0.906539 + 0.422123i \(0.138715\pi\)
\(354\) 102.709 5.45893
\(355\) −5.05027 −0.268040
\(356\) −62.9033 −3.33387
\(357\) −0.0731391 −0.00387093
\(358\) −25.0754 −1.32528
\(359\) 3.16457 0.167020 0.0835098 0.996507i \(-0.473387\pi\)
0.0835098 + 0.996507i \(0.473387\pi\)
\(360\) −54.5870 −2.87699
\(361\) 11.5349 0.607100
\(362\) 11.0778 0.582238
\(363\) −29.9986 −1.57452
\(364\) 0.0757392 0.00396981
\(365\) −5.88870 −0.308229
\(366\) −85.6151 −4.47517
\(367\) −5.00040 −0.261019 −0.130509 0.991447i \(-0.541661\pi\)
−0.130509 + 0.991447i \(0.541661\pi\)
\(368\) 18.9140 0.985959
\(369\) 56.8342 2.95867
\(370\) 15.8948 0.826330
\(371\) −0.0379709 −0.00197135
\(372\) 93.6739 4.85676
\(373\) 37.1857 1.92540 0.962702 0.270565i \(-0.0872104\pi\)
0.962702 + 0.270565i \(0.0872104\pi\)
\(374\) 12.5045 0.646593
\(375\) −34.3193 −1.77224
\(376\) −36.4614 −1.88035
\(377\) −11.1185 −0.572631
\(378\) −0.0943786 −0.00485431
\(379\) 8.28572 0.425609 0.212805 0.977095i \(-0.431740\pi\)
0.212805 + 0.977095i \(0.431740\pi\)
\(380\) 37.2924 1.91306
\(381\) 5.72327 0.293212
\(382\) −59.5424 −3.04645
\(383\) −32.2768 −1.64927 −0.824633 0.565667i \(-0.808619\pi\)
−0.824633 + 0.565667i \(0.808619\pi\)
\(384\) 33.0841 1.68832
\(385\) 0.00634638 0.000323441 0
\(386\) −11.5714 −0.588970
\(387\) 57.3561 2.91558
\(388\) 65.4672 3.32360
\(389\) −19.7935 −1.00357 −0.501786 0.864992i \(-0.667324\pi\)
−0.501786 + 0.864992i \(0.667324\pi\)
\(390\) −41.1291 −2.08265
\(391\) −14.0120 −0.708617
\(392\) 44.5731 2.25128
\(393\) 1.55402 0.0783898
\(394\) 63.3331 3.19067
\(395\) 15.7863 0.794297
\(396\) 23.5178 1.18181
\(397\) −5.23152 −0.262563 −0.131281 0.991345i \(-0.541909\pi\)
−0.131281 + 0.991345i \(0.541909\pi\)
\(398\) −10.3447 −0.518531
\(399\) 0.0753951 0.00377448
\(400\) −19.8899 −0.994495
\(401\) −4.10787 −0.205137 −0.102569 0.994726i \(-0.532706\pi\)
−0.102569 + 0.994726i \(0.532706\pi\)
\(402\) 87.1520 4.34675
\(403\) 25.7016 1.28029
\(404\) −68.5608 −3.41103
\(405\) 9.75871 0.484914
\(406\) 0.0359604 0.00178469
\(407\) −3.80306 −0.188510
\(408\) 100.758 4.98826
\(409\) 1.33455 0.0659893 0.0329947 0.999456i \(-0.489496\pi\)
0.0329947 + 0.999456i \(0.489496\pi\)
\(410\) −38.0450 −1.87891
\(411\) 22.9439 1.13174
\(412\) 38.0719 1.87567
\(413\) −0.0630914 −0.00310452
\(414\) −38.0707 −1.87107
\(415\) 23.6795 1.16238
\(416\) −20.8002 −1.01981
\(417\) −22.8957 −1.12121
\(418\) −12.8902 −0.630481
\(419\) −16.9558 −0.828343 −0.414171 0.910199i \(-0.635929\pi\)
−0.414171 + 0.910199i \(0.635929\pi\)
\(420\) 0.0920805 0.00449307
\(421\) −40.4275 −1.97032 −0.985159 0.171644i \(-0.945092\pi\)
−0.985159 + 0.171644i \(0.945092\pi\)
\(422\) −58.8998 −2.86720
\(423\) 32.7162 1.59072
\(424\) 52.3094 2.54037
\(425\) 14.7350 0.714752
\(426\) 25.3277 1.22713
\(427\) 0.0525909 0.00254505
\(428\) 88.0258 4.25489
\(429\) 9.84073 0.475115
\(430\) −38.3944 −1.85154
\(431\) −13.0345 −0.627849 −0.313924 0.949448i \(-0.601644\pi\)
−0.313924 + 0.949448i \(0.601644\pi\)
\(432\) 57.9595 2.78858
\(433\) 5.87320 0.282248 0.141124 0.989992i \(-0.454928\pi\)
0.141124 + 0.989992i \(0.454928\pi\)
\(434\) −0.0831266 −0.00399020
\(435\) −13.5174 −0.648108
\(436\) −33.9433 −1.62559
\(437\) 14.4442 0.690960
\(438\) 29.5325 1.41112
\(439\) 20.3681 0.972117 0.486059 0.873926i \(-0.338434\pi\)
0.486059 + 0.873926i \(0.338434\pi\)
\(440\) −8.74290 −0.416801
\(441\) −39.9948 −1.90451
\(442\) 49.7794 2.36777
\(443\) 4.33123 0.205783 0.102891 0.994693i \(-0.467191\pi\)
0.102891 + 0.994693i \(0.467191\pi\)
\(444\) −55.1790 −2.61868
\(445\) −20.9828 −0.994678
\(446\) 6.68904 0.316735
\(447\) −27.5813 −1.30455
\(448\) 0.000383498 0 1.81186e−5 0
\(449\) −1.05155 −0.0496258 −0.0248129 0.999692i \(-0.507899\pi\)
−0.0248129 + 0.999692i \(0.507899\pi\)
\(450\) 40.0351 1.88727
\(451\) 9.10283 0.428635
\(452\) 50.6852 2.38403
\(453\) 8.45062 0.397045
\(454\) 49.2955 2.31355
\(455\) 0.0252644 0.00118441
\(456\) −103.866 −4.86396
\(457\) −29.4666 −1.37839 −0.689195 0.724576i \(-0.742036\pi\)
−0.689195 + 0.724576i \(0.742036\pi\)
\(458\) −54.3650 −2.54031
\(459\) −42.9380 −2.00417
\(460\) 17.6408 0.822506
\(461\) −15.9660 −0.743609 −0.371804 0.928311i \(-0.621261\pi\)
−0.371804 + 0.928311i \(0.621261\pi\)
\(462\) −0.0318278 −0.00148076
\(463\) 28.6875 1.33322 0.666611 0.745406i \(-0.267744\pi\)
0.666611 + 0.745406i \(0.267744\pi\)
\(464\) −22.0839 −1.02522
\(465\) 31.2469 1.44904
\(466\) −18.7088 −0.866666
\(467\) 31.6695 1.46549 0.732744 0.680504i \(-0.238239\pi\)
0.732744 + 0.680504i \(0.238239\pi\)
\(468\) 93.6225 4.32770
\(469\) −0.0535350 −0.00247202
\(470\) −21.9004 −1.01019
\(471\) 30.4704 1.40400
\(472\) 86.9159 4.00063
\(473\) 9.18642 0.422392
\(474\) −79.1704 −3.63641
\(475\) −15.1895 −0.696942
\(476\) −0.111447 −0.00510816
\(477\) −46.9365 −2.14907
\(478\) −1.30925 −0.0598835
\(479\) 14.5936 0.666800 0.333400 0.942786i \(-0.391804\pi\)
0.333400 + 0.942786i \(0.391804\pi\)
\(480\) −25.2880 −1.15423
\(481\) −15.1397 −0.690309
\(482\) 38.4951 1.75340
\(483\) 0.0356648 0.00162281
\(484\) −45.7110 −2.07777
\(485\) 21.8380 0.991613
\(486\) 12.3148 0.558610
\(487\) 15.9608 0.723253 0.361627 0.932323i \(-0.382222\pi\)
0.361627 + 0.932323i \(0.382222\pi\)
\(488\) −72.4503 −3.27967
\(489\) −0.567977 −0.0256848
\(490\) 26.7727 1.20947
\(491\) −1.62149 −0.0731767 −0.0365883 0.999330i \(-0.511649\pi\)
−0.0365883 + 0.999330i \(0.511649\pi\)
\(492\) 132.074 5.95436
\(493\) 16.3604 0.736834
\(494\) −51.3149 −2.30877
\(495\) 7.84487 0.352601
\(496\) 51.0495 2.29219
\(497\) −0.0155581 −0.000697875 0
\(498\) −118.755 −5.32156
\(499\) 24.3963 1.09213 0.546065 0.837743i \(-0.316125\pi\)
0.546065 + 0.837743i \(0.316125\pi\)
\(500\) −52.2947 −2.33869
\(501\) 52.1580 2.33025
\(502\) 69.4403 3.09927
\(503\) 17.5035 0.780441 0.390220 0.920722i \(-0.372399\pi\)
0.390220 + 0.920722i \(0.372399\pi\)
\(504\) −0.168163 −0.00749058
\(505\) −22.8699 −1.01770
\(506\) −6.09758 −0.271070
\(507\) 0.800803 0.0355649
\(508\) 8.72094 0.386929
\(509\) −13.5323 −0.599808 −0.299904 0.953969i \(-0.596955\pi\)
−0.299904 + 0.953969i \(0.596955\pi\)
\(510\) 60.5197 2.67986
\(511\) −0.0181410 −0.000802510 0
\(512\) 50.8356 2.24664
\(513\) 44.2625 1.95424
\(514\) 63.6120 2.80581
\(515\) 12.6997 0.559615
\(516\) 133.287 5.86763
\(517\) 5.23998 0.230454
\(518\) 0.0489661 0.00215145
\(519\) −53.7405 −2.35895
\(520\) −34.8048 −1.52629
\(521\) 27.0095 1.18331 0.591655 0.806191i \(-0.298475\pi\)
0.591655 + 0.806191i \(0.298475\pi\)
\(522\) 44.4513 1.94558
\(523\) −25.7344 −1.12529 −0.562643 0.826700i \(-0.690216\pi\)
−0.562643 + 0.826700i \(0.690216\pi\)
\(524\) 2.36796 0.103445
\(525\) −0.0375051 −0.00163686
\(526\) −22.1464 −0.965630
\(527\) −37.8188 −1.64741
\(528\) 19.5460 0.850631
\(529\) −16.1673 −0.702927
\(530\) 31.4194 1.36477
\(531\) −77.9883 −3.38440
\(532\) 0.114885 0.00498088
\(533\) 36.2376 1.56963
\(534\) 105.231 4.55379
\(535\) 29.3629 1.26947
\(536\) 73.7509 3.18555
\(537\) 29.0373 1.25305
\(538\) 36.3075 1.56533
\(539\) −6.40575 −0.275915
\(540\) 54.0580 2.32629
\(541\) −33.8268 −1.45433 −0.727164 0.686464i \(-0.759162\pi\)
−0.727164 + 0.686464i \(0.759162\pi\)
\(542\) 34.2827 1.47257
\(543\) −12.8281 −0.550508
\(544\) 30.6066 1.31225
\(545\) −11.3225 −0.485003
\(546\) −0.126704 −0.00542243
\(547\) 11.9447 0.510720 0.255360 0.966846i \(-0.417806\pi\)
0.255360 + 0.966846i \(0.417806\pi\)
\(548\) 34.9612 1.49347
\(549\) 65.0085 2.77450
\(550\) 6.41220 0.273417
\(551\) −16.8650 −0.718474
\(552\) −49.1326 −2.09122
\(553\) 0.0486321 0.00206805
\(554\) 20.1538 0.856254
\(555\) −18.4062 −0.781298
\(556\) −34.8877 −1.47957
\(557\) 35.8936 1.52086 0.760429 0.649421i \(-0.224989\pi\)
0.760429 + 0.649421i \(0.224989\pi\)
\(558\) −102.754 −4.34993
\(559\) 36.5704 1.54676
\(560\) 0.0501811 0.00212054
\(561\) −14.4802 −0.611356
\(562\) −14.4258 −0.608517
\(563\) −40.3092 −1.69883 −0.849415 0.527725i \(-0.823045\pi\)
−0.849415 + 0.527725i \(0.823045\pi\)
\(564\) 76.0276 3.20134
\(565\) 16.9071 0.711288
\(566\) 23.2668 0.977979
\(567\) 0.0300631 0.00126253
\(568\) 21.4331 0.899314
\(569\) 33.1670 1.39043 0.695217 0.718800i \(-0.255308\pi\)
0.695217 + 0.718800i \(0.255308\pi\)
\(570\) −62.3865 −2.61308
\(571\) −2.25230 −0.0942560 −0.0471280 0.998889i \(-0.515007\pi\)
−0.0471280 + 0.998889i \(0.515007\pi\)
\(572\) 14.9950 0.626972
\(573\) 68.9501 2.88043
\(574\) −0.117203 −0.00489197
\(575\) −7.18523 −0.299645
\(576\) 0.474048 0.0197520
\(577\) −8.30809 −0.345870 −0.172935 0.984933i \(-0.555325\pi\)
−0.172935 + 0.984933i \(0.555325\pi\)
\(578\) −29.9134 −1.24423
\(579\) 13.3997 0.556874
\(580\) −20.5973 −0.855258
\(581\) 0.0729481 0.00302640
\(582\) −109.520 −4.53976
\(583\) −7.51756 −0.311345
\(584\) 24.9914 1.03415
\(585\) 31.2298 1.29119
\(586\) −23.8651 −0.985859
\(587\) −1.82503 −0.0753272 −0.0376636 0.999290i \(-0.511992\pi\)
−0.0376636 + 0.999290i \(0.511992\pi\)
\(588\) −92.9419 −3.83286
\(589\) 38.9854 1.60637
\(590\) 52.2056 2.14927
\(591\) −73.3397 −3.01679
\(592\) −30.0709 −1.23591
\(593\) 33.7979 1.38792 0.693958 0.720016i \(-0.255866\pi\)
0.693958 + 0.720016i \(0.255866\pi\)
\(594\) −18.6853 −0.766666
\(595\) −0.0371755 −0.00152405
\(596\) −42.0276 −1.72152
\(597\) 11.9791 0.490273
\(598\) −24.2740 −0.992636
\(599\) 1.51681 0.0619750 0.0309875 0.999520i \(-0.490135\pi\)
0.0309875 + 0.999520i \(0.490135\pi\)
\(600\) 51.6678 2.10933
\(601\) −2.02529 −0.0826132 −0.0413066 0.999147i \(-0.513152\pi\)
−0.0413066 + 0.999147i \(0.513152\pi\)
\(602\) −0.118279 −0.00482071
\(603\) −66.1755 −2.69488
\(604\) 12.8768 0.523949
\(605\) −15.2479 −0.619914
\(606\) 114.695 4.65918
\(607\) 44.6349 1.81168 0.905838 0.423625i \(-0.139243\pi\)
0.905838 + 0.423625i \(0.139243\pi\)
\(608\) −31.5507 −1.27955
\(609\) −0.0416422 −0.00168743
\(610\) −43.5169 −1.76195
\(611\) 20.8599 0.843903
\(612\) −137.762 −5.56868
\(613\) −9.40983 −0.380060 −0.190030 0.981778i \(-0.560858\pi\)
−0.190030 + 0.981778i \(0.560858\pi\)
\(614\) 75.3277 3.03998
\(615\) 44.0562 1.77652
\(616\) −0.0269338 −0.00108519
\(617\) −7.61987 −0.306765 −0.153382 0.988167i \(-0.549017\pi\)
−0.153382 + 0.988167i \(0.549017\pi\)
\(618\) −63.6904 −2.56200
\(619\) 14.9861 0.602340 0.301170 0.953570i \(-0.402623\pi\)
0.301170 + 0.953570i \(0.402623\pi\)
\(620\) 47.6131 1.91219
\(621\) 20.9379 0.840208
\(622\) −13.5835 −0.544649
\(623\) −0.0646404 −0.00258976
\(624\) 77.8111 3.11494
\(625\) −3.69996 −0.147998
\(626\) −33.9032 −1.35504
\(627\) 14.9269 0.596122
\(628\) 46.4298 1.85275
\(629\) 22.2774 0.888257
\(630\) −0.101006 −0.00402419
\(631\) −19.7105 −0.784661 −0.392330 0.919824i \(-0.628331\pi\)
−0.392330 + 0.919824i \(0.628331\pi\)
\(632\) −66.9965 −2.66498
\(633\) 68.2060 2.71095
\(634\) 62.4465 2.48007
\(635\) 2.90906 0.115442
\(636\) −109.073 −4.32503
\(637\) −25.5008 −1.01038
\(638\) 7.11952 0.281865
\(639\) −19.2316 −0.760791
\(640\) 16.8162 0.664719
\(641\) 10.0432 0.396683 0.198342 0.980133i \(-0.436444\pi\)
0.198342 + 0.980133i \(0.436444\pi\)
\(642\) −147.258 −5.81183
\(643\) 38.9922 1.53770 0.768852 0.639427i \(-0.220828\pi\)
0.768852 + 0.639427i \(0.220828\pi\)
\(644\) 0.0543450 0.00214149
\(645\) 44.4607 1.75064
\(646\) 75.5078 2.97081
\(647\) 2.04625 0.0804465 0.0402233 0.999191i \(-0.487193\pi\)
0.0402233 + 0.999191i \(0.487193\pi\)
\(648\) −41.4155 −1.62696
\(649\) −12.4910 −0.490313
\(650\) 25.5265 1.00123
\(651\) 0.0962607 0.00377275
\(652\) −0.865466 −0.0338943
\(653\) 21.1787 0.828786 0.414393 0.910098i \(-0.363994\pi\)
0.414393 + 0.910098i \(0.363994\pi\)
\(654\) 56.7837 2.22042
\(655\) 0.789885 0.0308634
\(656\) 71.9765 2.81021
\(657\) −22.4244 −0.874859
\(658\) −0.0674672 −0.00263015
\(659\) 2.78147 0.108351 0.0541754 0.998531i \(-0.482747\pi\)
0.0541754 + 0.998531i \(0.482747\pi\)
\(660\) 18.2303 0.709613
\(661\) −16.9081 −0.657650 −0.328825 0.944391i \(-0.606653\pi\)
−0.328825 + 0.944391i \(0.606653\pi\)
\(662\) 33.1542 1.28857
\(663\) −57.6446 −2.23873
\(664\) −100.495 −3.89995
\(665\) 0.0383223 0.00148607
\(666\) 60.5279 2.34541
\(667\) −7.97782 −0.308902
\(668\) 79.4767 3.07505
\(669\) −7.74591 −0.299474
\(670\) 44.2981 1.71139
\(671\) 10.4121 0.401953
\(672\) −0.0779033 −0.00300519
\(673\) −25.3185 −0.975957 −0.487978 0.872856i \(-0.662266\pi\)
−0.487978 + 0.872856i \(0.662266\pi\)
\(674\) −80.7854 −3.11174
\(675\) −22.0182 −0.847483
\(676\) 1.22024 0.0469322
\(677\) −17.5217 −0.673412 −0.336706 0.941610i \(-0.609313\pi\)
−0.336706 + 0.941610i \(0.609313\pi\)
\(678\) −84.7912 −3.25639
\(679\) 0.0672751 0.00258178
\(680\) 51.2138 1.96396
\(681\) −57.0842 −2.18747
\(682\) −16.4576 −0.630193
\(683\) −39.1442 −1.49781 −0.748905 0.662678i \(-0.769420\pi\)
−0.748905 + 0.662678i \(0.769420\pi\)
\(684\) 142.011 5.42993
\(685\) 11.6621 0.445584
\(686\) 0.164954 0.00629798
\(687\) 62.9547 2.40187
\(688\) 72.6374 2.76928
\(689\) −29.9268 −1.14012
\(690\) −29.5113 −1.12347
\(691\) −10.7767 −0.409963 −0.204982 0.978766i \(-0.565713\pi\)
−0.204982 + 0.978766i \(0.565713\pi\)
\(692\) −81.8881 −3.11292
\(693\) 0.0241672 0.000918038 0
\(694\) 70.6912 2.68340
\(695\) −11.6376 −0.441438
\(696\) 57.3671 2.17450
\(697\) −53.3222 −2.01972
\(698\) −24.2522 −0.917958
\(699\) 21.6648 0.819436
\(700\) −0.0571491 −0.00216003
\(701\) −36.6735 −1.38514 −0.692569 0.721351i \(-0.743521\pi\)
−0.692569 + 0.721351i \(0.743521\pi\)
\(702\) −74.3846 −2.80746
\(703\) −22.9645 −0.866124
\(704\) 0.0759257 0.00286156
\(705\) 25.3606 0.955137
\(706\) −86.8346 −3.26806
\(707\) −0.0704541 −0.00264970
\(708\) −181.233 −6.81115
\(709\) 28.6805 1.07712 0.538560 0.842587i \(-0.318969\pi\)
0.538560 + 0.842587i \(0.318969\pi\)
\(710\) 12.8737 0.483141
\(711\) 60.1150 2.25449
\(712\) 89.0499 3.33729
\(713\) 18.4416 0.690644
\(714\) 0.186440 0.00697733
\(715\) 5.00190 0.187061
\(716\) 44.2461 1.65356
\(717\) 1.51611 0.0566201
\(718\) −8.06685 −0.301052
\(719\) −27.3469 −1.01987 −0.509933 0.860214i \(-0.670330\pi\)
−0.509933 + 0.860214i \(0.670330\pi\)
\(720\) 62.0297 2.31171
\(721\) 0.0391232 0.00145702
\(722\) −29.4038 −1.09429
\(723\) −44.5773 −1.65785
\(724\) −19.5471 −0.726462
\(725\) 8.38946 0.311577
\(726\) 76.4699 2.83806
\(727\) −19.8403 −0.735836 −0.367918 0.929858i \(-0.619929\pi\)
−0.367918 + 0.929858i \(0.619929\pi\)
\(728\) −0.107221 −0.00397388
\(729\) −33.7728 −1.25084
\(730\) 15.0110 0.555581
\(731\) −53.8118 −1.99030
\(732\) 151.070 5.58371
\(733\) 1.22594 0.0452811 0.0226405 0.999744i \(-0.492793\pi\)
0.0226405 + 0.999744i \(0.492793\pi\)
\(734\) 12.7466 0.470484
\(735\) −31.0028 −1.14355
\(736\) −14.9247 −0.550133
\(737\) −10.5990 −0.390418
\(738\) −144.877 −5.33299
\(739\) −15.8595 −0.583401 −0.291701 0.956510i \(-0.594221\pi\)
−0.291701 + 0.956510i \(0.594221\pi\)
\(740\) −28.0467 −1.03102
\(741\) 59.4227 2.18295
\(742\) 0.0967920 0.00355335
\(743\) −21.2965 −0.781291 −0.390646 0.920541i \(-0.627748\pi\)
−0.390646 + 0.920541i \(0.627748\pi\)
\(744\) −132.611 −4.86174
\(745\) −14.0192 −0.513624
\(746\) −94.7906 −3.47053
\(747\) 90.1724 3.29924
\(748\) −22.0645 −0.806758
\(749\) 0.0904567 0.00330521
\(750\) 87.4838 3.19446
\(751\) 15.1655 0.553397 0.276698 0.960957i \(-0.410760\pi\)
0.276698 + 0.960957i \(0.410760\pi\)
\(752\) 41.4328 1.51090
\(753\) −80.4119 −2.93037
\(754\) 28.3422 1.03216
\(755\) 4.29533 0.156323
\(756\) 0.166533 0.00605676
\(757\) 9.74316 0.354121 0.177061 0.984200i \(-0.443341\pi\)
0.177061 + 0.984200i \(0.443341\pi\)
\(758\) −21.1212 −0.767158
\(759\) 7.06100 0.256298
\(760\) −52.7935 −1.91502
\(761\) 3.05868 0.110877 0.0554386 0.998462i \(-0.482344\pi\)
0.0554386 + 0.998462i \(0.482344\pi\)
\(762\) −14.5893 −0.528513
\(763\) −0.0348806 −0.00126276
\(764\) 105.064 3.80108
\(765\) −45.9533 −1.66145
\(766\) 82.2772 2.97279
\(767\) −49.7255 −1.79548
\(768\) −84.8250 −3.06086
\(769\) 27.8547 1.00447 0.502233 0.864733i \(-0.332512\pi\)
0.502233 + 0.864733i \(0.332512\pi\)
\(770\) −0.0161776 −0.000583001 0
\(771\) −73.6628 −2.65290
\(772\) 20.4181 0.734863
\(773\) −37.0410 −1.33227 −0.666135 0.745831i \(-0.732053\pi\)
−0.666135 + 0.745831i \(0.732053\pi\)
\(774\) −146.207 −5.25531
\(775\) −19.3932 −0.696624
\(776\) −92.6795 −3.32700
\(777\) −0.0567028 −0.00203420
\(778\) 50.4560 1.80893
\(779\) 54.9669 1.96939
\(780\) 72.5733 2.59854
\(781\) −3.08022 −0.110219
\(782\) 35.7181 1.27728
\(783\) −24.4470 −0.873665
\(784\) −50.6505 −1.80895
\(785\) 15.4876 0.552778
\(786\) −3.96136 −0.141297
\(787\) 34.7310 1.23803 0.619013 0.785380i \(-0.287533\pi\)
0.619013 + 0.785380i \(0.287533\pi\)
\(788\) −111.753 −3.98103
\(789\) 25.6456 0.913007
\(790\) −40.2412 −1.43172
\(791\) 0.0520849 0.00185192
\(792\) −33.2933 −1.18303
\(793\) 41.4496 1.47192
\(794\) 13.3357 0.473268
\(795\) −36.3837 −1.29040
\(796\) 18.2534 0.646975
\(797\) −35.0369 −1.24107 −0.620536 0.784178i \(-0.713085\pi\)
−0.620536 + 0.784178i \(0.713085\pi\)
\(798\) −0.192191 −0.00680347
\(799\) −30.6945 −1.08589
\(800\) 15.6948 0.554896
\(801\) −79.9031 −2.82324
\(802\) 10.4714 0.369759
\(803\) −3.59159 −0.126745
\(804\) −153.782 −5.42347
\(805\) 0.0181279 0.000638926 0
\(806\) −65.5163 −2.30771
\(807\) −42.0441 −1.48002
\(808\) 97.0590 3.41452
\(809\) −27.7118 −0.974297 −0.487148 0.873319i \(-0.661963\pi\)
−0.487148 + 0.873319i \(0.661963\pi\)
\(810\) −24.8760 −0.874055
\(811\) 43.6525 1.53284 0.766422 0.642337i \(-0.222035\pi\)
0.766422 + 0.642337i \(0.222035\pi\)
\(812\) −0.0634531 −0.00222677
\(813\) −39.6994 −1.39232
\(814\) 9.69441 0.339789
\(815\) −0.288695 −0.0101125
\(816\) −114.496 −4.00815
\(817\) 55.4717 1.94071
\(818\) −3.40192 −0.118945
\(819\) 0.0962079 0.00336177
\(820\) 67.1314 2.34433
\(821\) −15.0462 −0.525117 −0.262558 0.964916i \(-0.584566\pi\)
−0.262558 + 0.964916i \(0.584566\pi\)
\(822\) −58.4866 −2.03995
\(823\) −43.6192 −1.52047 −0.760236 0.649647i \(-0.774917\pi\)
−0.760236 + 0.649647i \(0.774917\pi\)
\(824\) −53.8969 −1.87759
\(825\) −7.42534 −0.258517
\(826\) 0.160827 0.00559588
\(827\) −39.7957 −1.38383 −0.691916 0.721978i \(-0.743233\pi\)
−0.691916 + 0.721978i \(0.743233\pi\)
\(828\) 67.1767 2.33455
\(829\) 21.1635 0.735039 0.367519 0.930016i \(-0.380207\pi\)
0.367519 + 0.930016i \(0.380207\pi\)
\(830\) −60.3617 −2.09519
\(831\) −23.3382 −0.809592
\(832\) 0.302254 0.0104788
\(833\) 37.5233 1.30011
\(834\) 58.3637 2.02097
\(835\) 26.5112 0.917456
\(836\) 22.7451 0.786656
\(837\) 56.5121 1.95334
\(838\) 43.2221 1.49308
\(839\) −41.8523 −1.44490 −0.722452 0.691421i \(-0.756985\pi\)
−0.722452 + 0.691421i \(0.756985\pi\)
\(840\) −0.130355 −0.00449767
\(841\) −19.6851 −0.678797
\(842\) 103.054 3.55149
\(843\) 16.7051 0.575355
\(844\) 103.930 3.57742
\(845\) 0.407037 0.0140025
\(846\) −83.3974 −2.86726
\(847\) −0.0469733 −0.00161402
\(848\) −59.4416 −2.04123
\(849\) −26.9430 −0.924682
\(850\) −37.5611 −1.28834
\(851\) −10.8631 −0.372383
\(852\) −44.6913 −1.53110
\(853\) −14.7527 −0.505122 −0.252561 0.967581i \(-0.581273\pi\)
−0.252561 + 0.967581i \(0.581273\pi\)
\(854\) −0.134060 −0.00458744
\(855\) 47.3708 1.62005
\(856\) −124.615 −4.25925
\(857\) −21.2950 −0.727424 −0.363712 0.931511i \(-0.618491\pi\)
−0.363712 + 0.931511i \(0.618491\pi\)
\(858\) −25.0851 −0.856392
\(859\) 12.0927 0.412597 0.206298 0.978489i \(-0.433858\pi\)
0.206298 + 0.978489i \(0.433858\pi\)
\(860\) 67.7479 2.31018
\(861\) 0.135721 0.00462537
\(862\) 33.2263 1.13169
\(863\) 52.4326 1.78483 0.892413 0.451219i \(-0.149011\pi\)
0.892413 + 0.451219i \(0.149011\pi\)
\(864\) −45.7350 −1.55594
\(865\) −27.3155 −0.928756
\(866\) −14.9714 −0.508750
\(867\) 34.6398 1.17643
\(868\) 0.146679 0.00497861
\(869\) 9.62829 0.326617
\(870\) 34.4573 1.16821
\(871\) −42.1936 −1.42968
\(872\) 48.0523 1.62725
\(873\) 83.1599 2.81454
\(874\) −36.8199 −1.24545
\(875\) −0.0537388 −0.00181670
\(876\) −52.1109 −1.76066
\(877\) 22.4194 0.757048 0.378524 0.925591i \(-0.376432\pi\)
0.378524 + 0.925591i \(0.376432\pi\)
\(878\) −51.9206 −1.75224
\(879\) 27.6358 0.932133
\(880\) 9.93496 0.334907
\(881\) 34.5366 1.16357 0.581784 0.813344i \(-0.302355\pi\)
0.581784 + 0.813344i \(0.302355\pi\)
\(882\) 101.951 3.43288
\(883\) 21.5274 0.724454 0.362227 0.932090i \(-0.382016\pi\)
0.362227 + 0.932090i \(0.382016\pi\)
\(884\) −87.8370 −2.95428
\(885\) −60.4542 −2.03214
\(886\) −11.0408 −0.370923
\(887\) 45.7201 1.53513 0.767566 0.640970i \(-0.221468\pi\)
0.767566 + 0.640970i \(0.221468\pi\)
\(888\) 78.1149 2.62136
\(889\) 0.00896177 0.000300568 0
\(890\) 53.4874 1.79290
\(891\) 5.95196 0.199398
\(892\) −11.8030 −0.395193
\(893\) 31.6413 1.05884
\(894\) 70.3079 2.35145
\(895\) 14.7593 0.493347
\(896\) 0.0518047 0.00173067
\(897\) 28.1093 0.938541
\(898\) 2.68053 0.0894503
\(899\) −21.5324 −0.718146
\(900\) −70.6430 −2.35477
\(901\) 44.0360 1.46705
\(902\) −23.2041 −0.772613
\(903\) 0.136968 0.00455800
\(904\) −71.7531 −2.38647
\(905\) −6.52036 −0.216744
\(906\) −21.5416 −0.715671
\(907\) −24.7848 −0.822966 −0.411483 0.911417i \(-0.634989\pi\)
−0.411483 + 0.911417i \(0.634989\pi\)
\(908\) −86.9831 −2.88663
\(909\) −87.0895 −2.88858
\(910\) −0.0644019 −0.00213490
\(911\) 30.7110 1.01750 0.508751 0.860914i \(-0.330107\pi\)
0.508751 + 0.860914i \(0.330107\pi\)
\(912\) 118.028 3.90828
\(913\) 14.4424 0.477974
\(914\) 75.1137 2.48454
\(915\) 50.3926 1.66593
\(916\) 95.9283 3.16956
\(917\) 0.00243335 8.03564e−5 0
\(918\) 109.454 3.61251
\(919\) −15.4383 −0.509264 −0.254632 0.967038i \(-0.581954\pi\)
−0.254632 + 0.967038i \(0.581954\pi\)
\(920\) −24.9734 −0.823349
\(921\) −87.2296 −2.87431
\(922\) 40.6990 1.34035
\(923\) −12.2621 −0.403612
\(924\) 0.0561610 0.00184756
\(925\) 11.4236 0.375607
\(926\) −73.1277 −2.40312
\(927\) 48.3609 1.58838
\(928\) 17.4261 0.572039
\(929\) 12.3132 0.403983 0.201991 0.979387i \(-0.435259\pi\)
0.201991 + 0.979387i \(0.435259\pi\)
\(930\) −79.6519 −2.61189
\(931\) −38.6808 −1.26771
\(932\) 33.0121 1.08135
\(933\) 15.7297 0.514968
\(934\) −80.7290 −2.64153
\(935\) −7.36009 −0.240701
\(936\) −132.538 −4.33214
\(937\) 10.4048 0.339910 0.169955 0.985452i \(-0.445638\pi\)
0.169955 + 0.985452i \(0.445638\pi\)
\(938\) 0.136467 0.00445580
\(939\) 39.2599 1.28120
\(940\) 38.6437 1.26042
\(941\) −25.2153 −0.821994 −0.410997 0.911637i \(-0.634819\pi\)
−0.410997 + 0.911637i \(0.634819\pi\)
\(942\) −77.6724 −2.53070
\(943\) 26.0015 0.846726
\(944\) −98.7666 −3.21458
\(945\) 0.0555508 0.00180707
\(946\) −23.4172 −0.761359
\(947\) 35.0036 1.13746 0.568732 0.822523i \(-0.307434\pi\)
0.568732 + 0.822523i \(0.307434\pi\)
\(948\) 139.698 4.53718
\(949\) −14.2978 −0.464128
\(950\) 38.7197 1.25623
\(951\) −72.3131 −2.34491
\(952\) 0.157771 0.00511340
\(953\) 12.3899 0.401348 0.200674 0.979658i \(-0.435687\pi\)
0.200674 + 0.979658i \(0.435687\pi\)
\(954\) 119.646 3.87369
\(955\) 35.0463 1.13407
\(956\) 2.31020 0.0747172
\(957\) −8.24441 −0.266504
\(958\) −37.2008 −1.20190
\(959\) 0.0359266 0.00116013
\(960\) 0.367468 0.0118600
\(961\) 18.7746 0.605632
\(962\) 38.5927 1.24428
\(963\) 111.815 3.60319
\(964\) −67.9255 −2.18773
\(965\) 6.81089 0.219250
\(966\) −0.0909137 −0.00292510
\(967\) −31.0616 −0.998872 −0.499436 0.866351i \(-0.666459\pi\)
−0.499436 + 0.866351i \(0.666459\pi\)
\(968\) 64.7113 2.07990
\(969\) −87.4381 −2.80892
\(970\) −55.6675 −1.78738
\(971\) 57.2817 1.83826 0.919128 0.393959i \(-0.128895\pi\)
0.919128 + 0.393959i \(0.128895\pi\)
\(972\) −21.7297 −0.696981
\(973\) −0.0358512 −0.00114934
\(974\) −40.6859 −1.30366
\(975\) −29.5597 −0.946667
\(976\) 82.3286 2.63527
\(977\) −2.29819 −0.0735257 −0.0367629 0.999324i \(-0.511705\pi\)
−0.0367629 + 0.999324i \(0.511705\pi\)
\(978\) 1.44784 0.0462967
\(979\) −12.7976 −0.409014
\(980\) −47.2410 −1.50906
\(981\) −43.1166 −1.37661
\(982\) 4.13335 0.131901
\(983\) −10.3094 −0.328819 −0.164409 0.986392i \(-0.552572\pi\)
−0.164409 + 0.986392i \(0.552572\pi\)
\(984\) −186.972 −5.96046
\(985\) −37.2775 −1.18776
\(986\) −41.7044 −1.32814
\(987\) 0.0781271 0.00248681
\(988\) 90.5465 2.88067
\(989\) 26.2403 0.834392
\(990\) −19.9975 −0.635561
\(991\) −25.5949 −0.813049 −0.406525 0.913640i \(-0.633259\pi\)
−0.406525 + 0.913640i \(0.633259\pi\)
\(992\) −40.2824 −1.27897
\(993\) −38.3926 −1.21835
\(994\) 0.0396593 0.00125792
\(995\) 6.08882 0.193029
\(996\) 209.547 6.63975
\(997\) −1.19929 −0.0379818 −0.0189909 0.999820i \(-0.506045\pi\)
−0.0189909 + 0.999820i \(0.506045\pi\)
\(998\) −62.1890 −1.96856
\(999\) −33.2887 −1.05321
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 4007.2.a.b.1.14 195
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4007.2.a.b.1.14 195 1.1 even 1 trivial