Properties

Label 799.2.a.g.1.1
Level $799$
Weight $2$
Character 799.1
Self dual yes
Analytic conductor $6.380$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [799,2,Mod(1,799)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(799, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("799.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 799.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: \(6.38004712150\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 4 x^{19} - 24 x^{18} + 108 x^{17} + 221 x^{16} - 1200 x^{15} - 931 x^{14} + 7128 x^{13} + 1280 x^{12} - 24559 x^{11} + 3411 x^{10} + 49829 x^{9} - 15132 x^{8} - 58070 x^{7} + \cdots + 63 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.74861\) of defining polynomial
Character \(\chi\) \(=\) 799.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.74861 q^{2} +0.350871 q^{3} +5.55484 q^{4} +4.31399 q^{5} -0.964407 q^{6} -1.95626 q^{7} -9.77085 q^{8} -2.87689 q^{9} +O(q^{10})\) \(q-2.74861 q^{2} +0.350871 q^{3} +5.55484 q^{4} +4.31399 q^{5} -0.964407 q^{6} -1.95626 q^{7} -9.77085 q^{8} -2.87689 q^{9} -11.8575 q^{10} +0.406909 q^{11} +1.94903 q^{12} +1.40203 q^{13} +5.37700 q^{14} +1.51365 q^{15} +15.7465 q^{16} -1.00000 q^{17} +7.90744 q^{18} -1.50045 q^{19} +23.9635 q^{20} -0.686397 q^{21} -1.11843 q^{22} +5.78890 q^{23} -3.42831 q^{24} +13.6105 q^{25} -3.85363 q^{26} -2.06203 q^{27} -10.8667 q^{28} +6.87157 q^{29} -4.16044 q^{30} -1.67590 q^{31} -23.7394 q^{32} +0.142773 q^{33} +2.74861 q^{34} -8.43930 q^{35} -15.9807 q^{36} +8.97370 q^{37} +4.12416 q^{38} +0.491932 q^{39} -42.1513 q^{40} +11.7431 q^{41} +1.88663 q^{42} -6.25773 q^{43} +2.26032 q^{44} -12.4109 q^{45} -15.9114 q^{46} +1.00000 q^{47} +5.52501 q^{48} -3.17303 q^{49} -37.4099 q^{50} -0.350871 q^{51} +7.78805 q^{52} -2.13587 q^{53} +5.66771 q^{54} +1.75540 q^{55} +19.1144 q^{56} -0.526467 q^{57} -18.8872 q^{58} +13.8777 q^{59} +8.40811 q^{60} +1.07857 q^{61} +4.60638 q^{62} +5.62795 q^{63} +33.7571 q^{64} +6.04834 q^{65} -0.392426 q^{66} -10.7462 q^{67} -5.55484 q^{68} +2.03116 q^{69} +23.1963 q^{70} +9.62778 q^{71} +28.1097 q^{72} -2.68137 q^{73} -24.6652 q^{74} +4.77553 q^{75} -8.33478 q^{76} -0.796022 q^{77} -1.35213 q^{78} +13.5667 q^{79} +67.9304 q^{80} +7.90716 q^{81} -32.2773 q^{82} -0.391596 q^{83} -3.81282 q^{84} -4.31399 q^{85} +17.2000 q^{86} +2.41104 q^{87} -3.97585 q^{88} -2.71107 q^{89} +34.1126 q^{90} -2.74274 q^{91} +32.1564 q^{92} -0.588024 q^{93} -2.74861 q^{94} -6.47294 q^{95} -8.32946 q^{96} -12.3441 q^{97} +8.72142 q^{98} -1.17063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.74861 −1.94356 −0.971779 0.235892i \(-0.924199\pi\)
−0.971779 + 0.235892i \(0.924199\pi\)
\(3\) 0.350871 0.202576 0.101288 0.994857i \(-0.467704\pi\)
0.101288 + 0.994857i \(0.467704\pi\)
\(4\) 5.55484 2.77742
\(5\) 4.31399 1.92927 0.964637 0.263582i \(-0.0849039\pi\)
0.964637 + 0.263582i \(0.0849039\pi\)
\(6\) −0.964407 −0.393718
\(7\) −1.95626 −0.739398 −0.369699 0.929152i \(-0.620539\pi\)
−0.369699 + 0.929152i \(0.620539\pi\)
\(8\) −9.77085 −3.45452
\(9\) −2.87689 −0.958963
\(10\) −11.8575 −3.74966
\(11\) 0.406909 0.122688 0.0613439 0.998117i \(-0.480461\pi\)
0.0613439 + 0.998117i \(0.480461\pi\)
\(12\) 1.94903 0.562637
\(13\) 1.40203 0.388853 0.194427 0.980917i \(-0.437715\pi\)
0.194427 + 0.980917i \(0.437715\pi\)
\(14\) 5.37700 1.43706
\(15\) 1.51365 0.390824
\(16\) 15.7465 3.93664
\(17\) −1.00000 −0.242536
\(18\) 7.90744 1.86380
\(19\) −1.50045 −0.344228 −0.172114 0.985077i \(-0.555060\pi\)
−0.172114 + 0.985077i \(0.555060\pi\)
\(20\) 23.9635 5.35840
\(21\) −0.686397 −0.149784
\(22\) −1.11843 −0.238451
\(23\) 5.78890 1.20707 0.603534 0.797337i \(-0.293759\pi\)
0.603534 + 0.797337i \(0.293759\pi\)
\(24\) −3.42831 −0.699801
\(25\) 13.6105 2.72210
\(26\) −3.85363 −0.755759
\(27\) −2.06203 −0.396838
\(28\) −10.8667 −2.05362
\(29\) 6.87157 1.27602 0.638009 0.770029i \(-0.279758\pi\)
0.638009 + 0.770029i \(0.279758\pi\)
\(30\) −4.16044 −0.759589
\(31\) −1.67590 −0.301000 −0.150500 0.988610i \(-0.548088\pi\)
−0.150500 + 0.988610i \(0.548088\pi\)
\(32\) −23.7394 −4.19657
\(33\) 0.142773 0.0248536
\(34\) 2.74861 0.471382
\(35\) −8.43930 −1.42650
\(36\) −15.9807 −2.66344
\(37\) 8.97370 1.47527 0.737634 0.675201i \(-0.235943\pi\)
0.737634 + 0.675201i \(0.235943\pi\)
\(38\) 4.12416 0.669027
\(39\) 0.491932 0.0787721
\(40\) −42.1513 −6.66471
\(41\) 11.7431 1.83397 0.916985 0.398921i \(-0.130615\pi\)
0.916985 + 0.398921i \(0.130615\pi\)
\(42\) 1.88663 0.291114
\(43\) −6.25773 −0.954295 −0.477148 0.878823i \(-0.658329\pi\)
−0.477148 + 0.878823i \(0.658329\pi\)
\(44\) 2.26032 0.340755
\(45\) −12.4109 −1.85010
\(46\) −15.9114 −2.34601
\(47\) 1.00000 0.145865
\(48\) 5.52501 0.797467
\(49\) −3.17303 −0.453291
\(50\) −37.4099 −5.29056
\(51\) −0.350871 −0.0491318
\(52\) 7.78805 1.08001
\(53\) −2.13587 −0.293384 −0.146692 0.989182i \(-0.546863\pi\)
−0.146692 + 0.989182i \(0.546863\pi\)
\(54\) 5.66771 0.771278
\(55\) 1.75540 0.236698
\(56\) 19.1144 2.55426
\(57\) −0.526467 −0.0697322
\(58\) −18.8872 −2.48002
\(59\) 13.8777 1.80673 0.903364 0.428875i \(-0.141090\pi\)
0.903364 + 0.428875i \(0.141090\pi\)
\(60\) 8.40811 1.08548
\(61\) 1.07857 0.138097 0.0690484 0.997613i \(-0.478004\pi\)
0.0690484 + 0.997613i \(0.478004\pi\)
\(62\) 4.60638 0.585011
\(63\) 5.62795 0.709055
\(64\) 33.7571 4.21964
\(65\) 6.04834 0.750204
\(66\) −0.392426 −0.0483043
\(67\) −10.7462 −1.31286 −0.656430 0.754387i \(-0.727934\pi\)
−0.656430 + 0.754387i \(0.727934\pi\)
\(68\) −5.55484 −0.673623
\(69\) 2.03116 0.244523
\(70\) 23.1963 2.77249
\(71\) 9.62778 1.14261 0.571304 0.820739i \(-0.306438\pi\)
0.571304 + 0.820739i \(0.306438\pi\)
\(72\) 28.1097 3.31275
\(73\) −2.68137 −0.313831 −0.156915 0.987612i \(-0.550155\pi\)
−0.156915 + 0.987612i \(0.550155\pi\)
\(74\) −24.6652 −2.86727
\(75\) 4.77553 0.551431
\(76\) −8.33478 −0.956065
\(77\) −0.796022 −0.0907151
\(78\) −1.35213 −0.153098
\(79\) 13.5667 1.52638 0.763188 0.646177i \(-0.223633\pi\)
0.763188 + 0.646177i \(0.223633\pi\)
\(80\) 67.9304 7.59485
\(81\) 7.90716 0.878573
\(82\) −32.2773 −3.56443
\(83\) −0.391596 −0.0429833 −0.0214916 0.999769i \(-0.506842\pi\)
−0.0214916 + 0.999769i \(0.506842\pi\)
\(84\) −3.81282 −0.416013
\(85\) −4.31399 −0.467918
\(86\) 17.2000 1.85473
\(87\) 2.41104 0.258490
\(88\) −3.97585 −0.423827
\(89\) −2.71107 −0.287373 −0.143687 0.989623i \(-0.545896\pi\)
−0.143687 + 0.989623i \(0.545896\pi\)
\(90\) 34.1126 3.59578
\(91\) −2.74274 −0.287517
\(92\) 32.1564 3.35253
\(93\) −0.588024 −0.0609753
\(94\) −2.74861 −0.283497
\(95\) −6.47294 −0.664110
\(96\) −8.32946 −0.850122
\(97\) −12.3441 −1.25335 −0.626675 0.779281i \(-0.715584\pi\)
−0.626675 + 0.779281i \(0.715584\pi\)
\(98\) 8.72142 0.880997
\(99\) −1.17063 −0.117653
\(100\) 75.6041 7.56041
\(101\) 7.41866 0.738184 0.369092 0.929393i \(-0.379669\pi\)
0.369092 + 0.929393i \(0.379669\pi\)
\(102\) 0.964407 0.0954905
\(103\) −3.56783 −0.351549 −0.175774 0.984431i \(-0.556243\pi\)
−0.175774 + 0.984431i \(0.556243\pi\)
\(104\) −13.6990 −1.34330
\(105\) −2.96111 −0.288974
\(106\) 5.87067 0.570210
\(107\) −11.4161 −1.10363 −0.551816 0.833966i \(-0.686065\pi\)
−0.551816 + 0.833966i \(0.686065\pi\)
\(108\) −11.4543 −1.10219
\(109\) −1.04844 −0.100422 −0.0502112 0.998739i \(-0.515989\pi\)
−0.0502112 + 0.998739i \(0.515989\pi\)
\(110\) −4.82491 −0.460037
\(111\) 3.14861 0.298853
\(112\) −30.8044 −2.91074
\(113\) −2.05435 −0.193257 −0.0966283 0.995321i \(-0.530806\pi\)
−0.0966283 + 0.995321i \(0.530806\pi\)
\(114\) 1.44705 0.135529
\(115\) 24.9732 2.32877
\(116\) 38.1704 3.54404
\(117\) −4.03348 −0.372896
\(118\) −38.1444 −3.51148
\(119\) 1.95626 0.179330
\(120\) −14.7897 −1.35011
\(121\) −10.8344 −0.984948
\(122\) −2.96457 −0.268399
\(123\) 4.12033 0.371518
\(124\) −9.30934 −0.836003
\(125\) 37.1456 3.32240
\(126\) −15.4690 −1.37809
\(127\) −12.6407 −1.12168 −0.560842 0.827923i \(-0.689522\pi\)
−0.560842 + 0.827923i \(0.689522\pi\)
\(128\) −45.3062 −4.00454
\(129\) −2.19566 −0.193317
\(130\) −16.6245 −1.45807
\(131\) −16.9115 −1.47757 −0.738783 0.673943i \(-0.764599\pi\)
−0.738783 + 0.673943i \(0.764599\pi\)
\(132\) 0.793080 0.0690288
\(133\) 2.93528 0.254521
\(134\) 29.5372 2.55162
\(135\) −8.89558 −0.765610
\(136\) 9.77085 0.837844
\(137\) 5.38302 0.459902 0.229951 0.973202i \(-0.426143\pi\)
0.229951 + 0.973202i \(0.426143\pi\)
\(138\) −5.58285 −0.475244
\(139\) 1.65232 0.140148 0.0700741 0.997542i \(-0.477676\pi\)
0.0700741 + 0.997542i \(0.477676\pi\)
\(140\) −46.8789 −3.96199
\(141\) 0.350871 0.0295487
\(142\) −26.4630 −2.22072
\(143\) 0.570499 0.0477075
\(144\) −45.3011 −3.77509
\(145\) 29.6439 2.46179
\(146\) 7.37004 0.609949
\(147\) −1.11333 −0.0918256
\(148\) 49.8475 4.09744
\(149\) −1.20271 −0.0985296 −0.0492648 0.998786i \(-0.515688\pi\)
−0.0492648 + 0.998786i \(0.515688\pi\)
\(150\) −13.1261 −1.07174
\(151\) −0.365814 −0.0297696 −0.0148848 0.999889i \(-0.504738\pi\)
−0.0148848 + 0.999889i \(0.504738\pi\)
\(152\) 14.6607 1.18914
\(153\) 2.87689 0.232583
\(154\) 2.18795 0.176310
\(155\) −7.22980 −0.580712
\(156\) 2.73260 0.218783
\(157\) −13.4026 −1.06965 −0.534823 0.844964i \(-0.679622\pi\)
−0.534823 + 0.844964i \(0.679622\pi\)
\(158\) −37.2896 −2.96660
\(159\) −0.749416 −0.0594325
\(160\) −102.411 −8.09633
\(161\) −11.3246 −0.892504
\(162\) −21.7337 −1.70756
\(163\) 8.48728 0.664775 0.332387 0.943143i \(-0.392146\pi\)
0.332387 + 0.943143i \(0.392146\pi\)
\(164\) 65.2312 5.09370
\(165\) 0.615920 0.0479493
\(166\) 1.07634 0.0835405
\(167\) 5.56470 0.430609 0.215305 0.976547i \(-0.430926\pi\)
0.215305 + 0.976547i \(0.430926\pi\)
\(168\) 6.70668 0.517432
\(169\) −11.0343 −0.848793
\(170\) 11.8575 0.909425
\(171\) 4.31664 0.330102
\(172\) −34.7607 −2.65048
\(173\) 18.9290 1.43914 0.719571 0.694419i \(-0.244339\pi\)
0.719571 + 0.694419i \(0.244339\pi\)
\(174\) −6.62699 −0.502391
\(175\) −26.6257 −2.01271
\(176\) 6.40742 0.482977
\(177\) 4.86930 0.365999
\(178\) 7.45167 0.558526
\(179\) 10.7361 0.802451 0.401226 0.915979i \(-0.368584\pi\)
0.401226 + 0.915979i \(0.368584\pi\)
\(180\) −68.9404 −5.13851
\(181\) 17.1488 1.27466 0.637330 0.770591i \(-0.280039\pi\)
0.637330 + 0.770591i \(0.280039\pi\)
\(182\) 7.53871 0.558806
\(183\) 0.378440 0.0279751
\(184\) −56.5624 −4.16984
\(185\) 38.7124 2.84620
\(186\) 1.61625 0.118509
\(187\) −0.406909 −0.0297562
\(188\) 5.55484 0.405128
\(189\) 4.03388 0.293421
\(190\) 17.7916 1.29074
\(191\) −15.8722 −1.14848 −0.574238 0.818689i \(-0.694702\pi\)
−0.574238 + 0.818689i \(0.694702\pi\)
\(192\) 11.8444 0.854795
\(193\) 11.7532 0.846014 0.423007 0.906126i \(-0.360975\pi\)
0.423007 + 0.906126i \(0.360975\pi\)
\(194\) 33.9290 2.43596
\(195\) 2.12219 0.151973
\(196\) −17.6257 −1.25898
\(197\) −0.777080 −0.0553647 −0.0276823 0.999617i \(-0.508813\pi\)
−0.0276823 + 0.999617i \(0.508813\pi\)
\(198\) 3.21761 0.228666
\(199\) 11.8282 0.838478 0.419239 0.907876i \(-0.362297\pi\)
0.419239 + 0.907876i \(0.362297\pi\)
\(200\) −132.986 −9.40354
\(201\) −3.77054 −0.265954
\(202\) −20.3910 −1.43470
\(203\) −13.4426 −0.943485
\(204\) −1.94903 −0.136460
\(205\) 50.6598 3.53823
\(206\) 9.80655 0.683255
\(207\) −16.6540 −1.15753
\(208\) 22.0771 1.53077
\(209\) −0.610549 −0.0422326
\(210\) 8.13892 0.561639
\(211\) 1.35124 0.0930229 0.0465115 0.998918i \(-0.485190\pi\)
0.0465115 + 0.998918i \(0.485190\pi\)
\(212\) −11.8644 −0.814852
\(213\) 3.37811 0.231464
\(214\) 31.3782 2.14497
\(215\) −26.9958 −1.84110
\(216\) 20.1478 1.37088
\(217\) 3.27850 0.222559
\(218\) 2.88175 0.195177
\(219\) −0.940817 −0.0635745
\(220\) 9.75098 0.657411
\(221\) −1.40203 −0.0943107
\(222\) −8.65430 −0.580839
\(223\) 21.2996 1.42633 0.713164 0.700998i \(-0.247262\pi\)
0.713164 + 0.700998i \(0.247262\pi\)
\(224\) 46.4405 3.10293
\(225\) −39.1559 −2.61039
\(226\) 5.64659 0.375605
\(227\) −9.21913 −0.611895 −0.305948 0.952048i \(-0.598973\pi\)
−0.305948 + 0.952048i \(0.598973\pi\)
\(228\) −2.92444 −0.193676
\(229\) 0.0267800 0.00176967 0.000884835 1.00000i \(-0.499718\pi\)
0.000884835 1.00000i \(0.499718\pi\)
\(230\) −68.6416 −4.52609
\(231\) −0.279301 −0.0183767
\(232\) −67.1411 −4.40803
\(233\) −2.88690 −0.189127 −0.0945635 0.995519i \(-0.530146\pi\)
−0.0945635 + 0.995519i \(0.530146\pi\)
\(234\) 11.0865 0.724745
\(235\) 4.31399 0.281414
\(236\) 77.0886 5.01804
\(237\) 4.76017 0.309206
\(238\) −5.37700 −0.348539
\(239\) −25.9997 −1.68178 −0.840891 0.541204i \(-0.817969\pi\)
−0.840891 + 0.541204i \(0.817969\pi\)
\(240\) 23.8348 1.53853
\(241\) −11.2112 −0.722177 −0.361088 0.932532i \(-0.617595\pi\)
−0.361088 + 0.932532i \(0.617595\pi\)
\(242\) 29.7796 1.91430
\(243\) 8.96049 0.574816
\(244\) 5.99129 0.383553
\(245\) −13.6884 −0.874522
\(246\) −11.3252 −0.722066
\(247\) −2.10368 −0.133854
\(248\) 16.3749 1.03981
\(249\) −0.137400 −0.00870737
\(250\) −102.099 −6.45728
\(251\) −20.5618 −1.29785 −0.648925 0.760852i \(-0.724781\pi\)
−0.648925 + 0.760852i \(0.724781\pi\)
\(252\) 31.2624 1.96934
\(253\) 2.35556 0.148093
\(254\) 34.7444 2.18006
\(255\) −1.51365 −0.0947887
\(256\) 57.0148 3.56342
\(257\) −15.8886 −0.991102 −0.495551 0.868579i \(-0.665034\pi\)
−0.495551 + 0.868579i \(0.665034\pi\)
\(258\) 6.03500 0.375723
\(259\) −17.5549 −1.09081
\(260\) 33.5975 2.08363
\(261\) −19.7687 −1.22365
\(262\) 46.4831 2.87174
\(263\) −8.75695 −0.539977 −0.269988 0.962864i \(-0.587020\pi\)
−0.269988 + 0.962864i \(0.587020\pi\)
\(264\) −1.39501 −0.0858571
\(265\) −9.21412 −0.566019
\(266\) −8.06794 −0.494677
\(267\) −0.951237 −0.0582148
\(268\) −59.6936 −3.64636
\(269\) 17.2294 1.05050 0.525249 0.850949i \(-0.323972\pi\)
0.525249 + 0.850949i \(0.323972\pi\)
\(270\) 24.4504 1.48801
\(271\) −13.5236 −0.821500 −0.410750 0.911748i \(-0.634733\pi\)
−0.410750 + 0.911748i \(0.634733\pi\)
\(272\) −15.7465 −0.954775
\(273\) −0.962348 −0.0582440
\(274\) −14.7958 −0.893847
\(275\) 5.53824 0.333968
\(276\) 11.2828 0.679142
\(277\) 22.7299 1.36571 0.682854 0.730555i \(-0.260739\pi\)
0.682854 + 0.730555i \(0.260739\pi\)
\(278\) −4.54159 −0.272386
\(279\) 4.82137 0.288648
\(280\) 82.4591 4.92787
\(281\) −27.2854 −1.62771 −0.813854 0.581069i \(-0.802634\pi\)
−0.813854 + 0.581069i \(0.802634\pi\)
\(282\) −0.964407 −0.0574296
\(283\) −8.24456 −0.490088 −0.245044 0.969512i \(-0.578802\pi\)
−0.245044 + 0.969512i \(0.578802\pi\)
\(284\) 53.4808 3.17350
\(285\) −2.27117 −0.134533
\(286\) −1.56808 −0.0927224
\(287\) −22.9727 −1.35603
\(288\) 68.2955 4.02435
\(289\) 1.00000 0.0588235
\(290\) −81.4793 −4.78463
\(291\) −4.33118 −0.253898
\(292\) −14.8946 −0.871640
\(293\) 10.5197 0.614570 0.307285 0.951618i \(-0.400579\pi\)
0.307285 + 0.951618i \(0.400579\pi\)
\(294\) 3.06010 0.178468
\(295\) 59.8684 3.48567
\(296\) −87.6807 −5.09634
\(297\) −0.839060 −0.0486872
\(298\) 3.30577 0.191498
\(299\) 8.11620 0.469372
\(300\) 26.5273 1.53155
\(301\) 12.2418 0.705604
\(302\) 1.00548 0.0578589
\(303\) 2.60299 0.149538
\(304\) −23.6270 −1.35510
\(305\) 4.65294 0.266427
\(306\) −7.90744 −0.452038
\(307\) −22.7339 −1.29749 −0.648746 0.761005i \(-0.724706\pi\)
−0.648746 + 0.761005i \(0.724706\pi\)
\(308\) −4.42177 −0.251954
\(309\) −1.25185 −0.0712152
\(310\) 19.8719 1.12865
\(311\) −14.6846 −0.832690 −0.416345 0.909207i \(-0.636689\pi\)
−0.416345 + 0.909207i \(0.636689\pi\)
\(312\) −4.80659 −0.272120
\(313\) −5.06283 −0.286168 −0.143084 0.989711i \(-0.545702\pi\)
−0.143084 + 0.989711i \(0.545702\pi\)
\(314\) 36.8385 2.07892
\(315\) 24.2789 1.36796
\(316\) 75.3609 4.23938
\(317\) 11.0611 0.621255 0.310627 0.950532i \(-0.399461\pi\)
0.310627 + 0.950532i \(0.399461\pi\)
\(318\) 2.05985 0.115511
\(319\) 2.79611 0.156552
\(320\) 145.628 8.14083
\(321\) −4.00557 −0.223569
\(322\) 31.1269 1.73463
\(323\) 1.50045 0.0834875
\(324\) 43.9230 2.44017
\(325\) 19.0823 1.05850
\(326\) −23.3282 −1.29203
\(327\) −0.367867 −0.0203431
\(328\) −114.740 −6.33548
\(329\) −1.95626 −0.107852
\(330\) −1.69292 −0.0931923
\(331\) −30.3272 −1.66693 −0.833466 0.552570i \(-0.813647\pi\)
−0.833466 + 0.552570i \(0.813647\pi\)
\(332\) −2.17526 −0.119383
\(333\) −25.8163 −1.41473
\(334\) −15.2952 −0.836914
\(335\) −46.3591 −2.53287
\(336\) −10.8084 −0.589645
\(337\) −24.6850 −1.34468 −0.672338 0.740244i \(-0.734710\pi\)
−0.672338 + 0.740244i \(0.734710\pi\)
\(338\) 30.3290 1.64968
\(339\) −0.720811 −0.0391491
\(340\) −23.9635 −1.29960
\(341\) −0.681939 −0.0369290
\(342\) −11.8648 −0.641572
\(343\) 19.9011 1.07456
\(344\) 61.1434 3.29663
\(345\) 8.76239 0.471751
\(346\) −52.0282 −2.79706
\(347\) 27.8592 1.49556 0.747779 0.663947i \(-0.231120\pi\)
0.747779 + 0.663947i \(0.231120\pi\)
\(348\) 13.3929 0.717936
\(349\) −5.95414 −0.318718 −0.159359 0.987221i \(-0.550943\pi\)
−0.159359 + 0.987221i \(0.550943\pi\)
\(350\) 73.1836 3.91183
\(351\) −2.89103 −0.154312
\(352\) −9.65977 −0.514868
\(353\) 6.23521 0.331867 0.165933 0.986137i \(-0.446936\pi\)
0.165933 + 0.986137i \(0.446936\pi\)
\(354\) −13.3838 −0.711340
\(355\) 41.5341 2.20440
\(356\) −15.0596 −0.798156
\(357\) 0.686397 0.0363280
\(358\) −29.5092 −1.55961
\(359\) 1.35822 0.0716839 0.0358419 0.999357i \(-0.488589\pi\)
0.0358419 + 0.999357i \(0.488589\pi\)
\(360\) 121.265 6.39121
\(361\) −16.7486 −0.881507
\(362\) −47.1353 −2.47738
\(363\) −3.80149 −0.199526
\(364\) −15.2355 −0.798556
\(365\) −11.5674 −0.605466
\(366\) −1.04018 −0.0543712
\(367\) 4.33377 0.226221 0.113111 0.993582i \(-0.463919\pi\)
0.113111 + 0.993582i \(0.463919\pi\)
\(368\) 91.1551 4.75179
\(369\) −33.7837 −1.75871
\(370\) −106.405 −5.53175
\(371\) 4.17833 0.216928
\(372\) −3.26638 −0.169354
\(373\) 7.10364 0.367812 0.183906 0.982944i \(-0.441126\pi\)
0.183906 + 0.982944i \(0.441126\pi\)
\(374\) 1.11843 0.0578328
\(375\) 13.0333 0.673037
\(376\) −9.77085 −0.503893
\(377\) 9.63414 0.496183
\(378\) −11.0875 −0.570282
\(379\) 3.14399 0.161496 0.0807479 0.996735i \(-0.474269\pi\)
0.0807479 + 0.996735i \(0.474269\pi\)
\(380\) −35.9562 −1.84451
\(381\) −4.43527 −0.227226
\(382\) 43.6266 2.23213
\(383\) 27.5124 1.40582 0.702909 0.711280i \(-0.251884\pi\)
0.702909 + 0.711280i \(0.251884\pi\)
\(384\) −15.8966 −0.811222
\(385\) −3.43403 −0.175014
\(386\) −32.3049 −1.64428
\(387\) 18.0028 0.915134
\(388\) −68.5692 −3.48108
\(389\) −30.6229 −1.55264 −0.776321 0.630338i \(-0.782916\pi\)
−0.776321 + 0.630338i \(0.782916\pi\)
\(390\) −5.83306 −0.295369
\(391\) −5.78890 −0.292757
\(392\) 31.0032 1.56590
\(393\) −5.93377 −0.299319
\(394\) 2.13589 0.107604
\(395\) 58.5267 2.94480
\(396\) −6.50268 −0.326772
\(397\) −8.99118 −0.451254 −0.225627 0.974214i \(-0.572443\pi\)
−0.225627 + 0.974214i \(0.572443\pi\)
\(398\) −32.5110 −1.62963
\(399\) 1.02991 0.0515598
\(400\) 214.318 10.7159
\(401\) 35.8105 1.78829 0.894145 0.447778i \(-0.147784\pi\)
0.894145 + 0.447778i \(0.147784\pi\)
\(402\) 10.3637 0.516896
\(403\) −2.34966 −0.117045
\(404\) 41.2094 2.05025
\(405\) 34.1114 1.69501
\(406\) 36.9484 1.83372
\(407\) 3.65148 0.180997
\(408\) 3.42831 0.169727
\(409\) 27.8153 1.37538 0.687690 0.726004i \(-0.258625\pi\)
0.687690 + 0.726004i \(0.258625\pi\)
\(410\) −139.244 −6.87676
\(411\) 1.88875 0.0931650
\(412\) −19.8187 −0.976397
\(413\) −27.1485 −1.33589
\(414\) 45.7753 2.24973
\(415\) −1.68934 −0.0829266
\(416\) −33.2833 −1.63185
\(417\) 0.579753 0.0283906
\(418\) 1.67816 0.0820815
\(419\) −23.4932 −1.14772 −0.573860 0.818953i \(-0.694555\pi\)
−0.573860 + 0.818953i \(0.694555\pi\)
\(420\) −16.4485 −0.802603
\(421\) 3.66561 0.178651 0.0893254 0.996002i \(-0.471529\pi\)
0.0893254 + 0.996002i \(0.471529\pi\)
\(422\) −3.71402 −0.180795
\(423\) −2.87689 −0.139879
\(424\) 20.8693 1.01350
\(425\) −13.6105 −0.660206
\(426\) −9.28510 −0.449865
\(427\) −2.10997 −0.102109
\(428\) −63.4143 −3.06525
\(429\) 0.200172 0.00966438
\(430\) 74.2008 3.57828
\(431\) −23.0348 −1.10955 −0.554774 0.832001i \(-0.687195\pi\)
−0.554774 + 0.832001i \(0.687195\pi\)
\(432\) −32.4699 −1.56221
\(433\) −3.61439 −0.173696 −0.0868482 0.996222i \(-0.527680\pi\)
−0.0868482 + 0.996222i \(0.527680\pi\)
\(434\) −9.01130 −0.432556
\(435\) 10.4012 0.498698
\(436\) −5.82391 −0.278915
\(437\) −8.68598 −0.415507
\(438\) 2.58594 0.123561
\(439\) 2.78594 0.132966 0.0664828 0.997788i \(-0.478822\pi\)
0.0664828 + 0.997788i \(0.478822\pi\)
\(440\) −17.1518 −0.817679
\(441\) 9.12847 0.434689
\(442\) 3.85363 0.183298
\(443\) −6.60108 −0.313627 −0.156813 0.987628i \(-0.550122\pi\)
−0.156813 + 0.987628i \(0.550122\pi\)
\(444\) 17.4900 0.830041
\(445\) −11.6955 −0.554421
\(446\) −58.5442 −2.77215
\(447\) −0.421995 −0.0199597
\(448\) −66.0377 −3.11999
\(449\) −33.0598 −1.56019 −0.780094 0.625662i \(-0.784829\pi\)
−0.780094 + 0.625662i \(0.784829\pi\)
\(450\) 107.624 5.07345
\(451\) 4.77839 0.225006
\(452\) −11.4116 −0.536754
\(453\) −0.128354 −0.00603059
\(454\) 25.3398 1.18925
\(455\) −11.8321 −0.554699
\(456\) 5.14403 0.240891
\(457\) −3.88614 −0.181786 −0.0908930 0.995861i \(-0.528972\pi\)
−0.0908930 + 0.995861i \(0.528972\pi\)
\(458\) −0.0736076 −0.00343946
\(459\) 2.06203 0.0962474
\(460\) 138.722 6.46796
\(461\) 15.6610 0.729407 0.364703 0.931124i \(-0.381170\pi\)
0.364703 + 0.931124i \(0.381170\pi\)
\(462\) 0.767689 0.0357161
\(463\) −30.0299 −1.39561 −0.697804 0.716288i \(-0.745840\pi\)
−0.697804 + 0.716288i \(0.745840\pi\)
\(464\) 108.203 5.02322
\(465\) −2.53673 −0.117638
\(466\) 7.93495 0.367579
\(467\) −37.6970 −1.74441 −0.872204 0.489142i \(-0.837310\pi\)
−0.872204 + 0.489142i \(0.837310\pi\)
\(468\) −22.4053 −1.03569
\(469\) 21.0225 0.970727
\(470\) −11.8575 −0.546944
\(471\) −4.70259 −0.216684
\(472\) −135.597 −6.24137
\(473\) −2.54633 −0.117080
\(474\) −13.0838 −0.600961
\(475\) −20.4219 −0.937022
\(476\) 10.8667 0.498076
\(477\) 6.14466 0.281345
\(478\) 71.4630 3.26864
\(479\) 3.47398 0.158730 0.0793651 0.996846i \(-0.474711\pi\)
0.0793651 + 0.996846i \(0.474711\pi\)
\(480\) −35.9332 −1.64012
\(481\) 12.5814 0.573662
\(482\) 30.8152 1.40359
\(483\) −3.97348 −0.180800
\(484\) −60.1835 −2.73561
\(485\) −53.2521 −2.41805
\(486\) −24.6289 −1.11719
\(487\) 7.00218 0.317299 0.158650 0.987335i \(-0.449286\pi\)
0.158650 + 0.987335i \(0.449286\pi\)
\(488\) −10.5386 −0.477058
\(489\) 2.97794 0.134667
\(490\) 37.6241 1.69968
\(491\) 1.89534 0.0855356 0.0427678 0.999085i \(-0.486382\pi\)
0.0427678 + 0.999085i \(0.486382\pi\)
\(492\) 22.8878 1.03186
\(493\) −6.87157 −0.309480
\(494\) 5.78219 0.260153
\(495\) −5.05010 −0.226985
\(496\) −26.3896 −1.18493
\(497\) −18.8345 −0.844842
\(498\) 0.377658 0.0169233
\(499\) 35.0912 1.57090 0.785449 0.618926i \(-0.212432\pi\)
0.785449 + 0.618926i \(0.212432\pi\)
\(500\) 206.338 9.22770
\(501\) 1.95249 0.0872309
\(502\) 56.5164 2.52245
\(503\) −27.6667 −1.23360 −0.616799 0.787121i \(-0.711571\pi\)
−0.616799 + 0.787121i \(0.711571\pi\)
\(504\) −54.9899 −2.44944
\(505\) 32.0040 1.42416
\(506\) −6.47450 −0.287827
\(507\) −3.87162 −0.171945
\(508\) −70.2172 −3.11538
\(509\) −9.29983 −0.412208 −0.206104 0.978530i \(-0.566078\pi\)
−0.206104 + 0.978530i \(0.566078\pi\)
\(510\) 4.16044 0.184227
\(511\) 5.24547 0.232046
\(512\) −66.0987 −2.92118
\(513\) 3.09399 0.136603
\(514\) 43.6714 1.92626
\(515\) −15.3916 −0.678233
\(516\) −12.1965 −0.536922
\(517\) 0.406909 0.0178959
\(518\) 48.2516 2.12005
\(519\) 6.64163 0.291535
\(520\) −59.0974 −2.59159
\(521\) −14.5550 −0.637665 −0.318832 0.947811i \(-0.603291\pi\)
−0.318832 + 0.947811i \(0.603291\pi\)
\(522\) 54.3365 2.37824
\(523\) −12.3264 −0.538994 −0.269497 0.963001i \(-0.586857\pi\)
−0.269497 + 0.963001i \(0.586857\pi\)
\(524\) −93.9408 −4.10382
\(525\) −9.34220 −0.407727
\(526\) 24.0694 1.04948
\(527\) 1.67590 0.0730032
\(528\) 2.24818 0.0978395
\(529\) 10.5113 0.457014
\(530\) 25.3260 1.10009
\(531\) −39.9247 −1.73259
\(532\) 16.3050 0.706913
\(533\) 16.4642 0.713145
\(534\) 2.61458 0.113144
\(535\) −49.2487 −2.12921
\(536\) 105.000 4.53530
\(537\) 3.76698 0.162557
\(538\) −47.3570 −2.04170
\(539\) −1.29114 −0.0556132
\(540\) −49.4135 −2.12642
\(541\) 31.7045 1.36308 0.681541 0.731780i \(-0.261310\pi\)
0.681541 + 0.731780i \(0.261310\pi\)
\(542\) 37.1710 1.59663
\(543\) 6.01702 0.258215
\(544\) 23.7394 1.01782
\(545\) −4.52296 −0.193742
\(546\) 2.64512 0.113201
\(547\) 26.0380 1.11330 0.556652 0.830745i \(-0.312086\pi\)
0.556652 + 0.830745i \(0.312086\pi\)
\(548\) 29.9018 1.27734
\(549\) −3.10293 −0.132430
\(550\) −15.2224 −0.649087
\(551\) −10.3105 −0.439241
\(552\) −19.8461 −0.844708
\(553\) −26.5401 −1.12860
\(554\) −62.4755 −2.65433
\(555\) 13.5831 0.576570
\(556\) 9.17839 0.389251
\(557\) 24.3865 1.03329 0.516645 0.856200i \(-0.327181\pi\)
0.516645 + 0.856200i \(0.327181\pi\)
\(558\) −13.2521 −0.561004
\(559\) −8.77353 −0.371081
\(560\) −132.890 −5.61562
\(561\) −0.142773 −0.00602787
\(562\) 74.9967 3.16355
\(563\) −9.89978 −0.417226 −0.208613 0.977998i \(-0.566895\pi\)
−0.208613 + 0.977998i \(0.566895\pi\)
\(564\) 1.94903 0.0820691
\(565\) −8.86242 −0.372845
\(566\) 22.6610 0.952515
\(567\) −15.4685 −0.649615
\(568\) −94.0716 −3.94716
\(569\) −0.423335 −0.0177471 −0.00887357 0.999961i \(-0.502825\pi\)
−0.00887357 + 0.999961i \(0.502825\pi\)
\(570\) 6.24255 0.261472
\(571\) 6.43127 0.269140 0.134570 0.990904i \(-0.457035\pi\)
0.134570 + 0.990904i \(0.457035\pi\)
\(572\) 3.16903 0.132504
\(573\) −5.56912 −0.232653
\(574\) 63.1428 2.63553
\(575\) 78.7897 3.28576
\(576\) −97.1154 −4.04647
\(577\) −24.7007 −1.02830 −0.514151 0.857700i \(-0.671893\pi\)
−0.514151 + 0.857700i \(0.671893\pi\)
\(578\) −2.74861 −0.114327
\(579\) 4.12386 0.171382
\(580\) 164.667 6.83742
\(581\) 0.766066 0.0317818
\(582\) 11.9047 0.493466
\(583\) −0.869106 −0.0359947
\(584\) 26.1993 1.08413
\(585\) −17.4004 −0.719418
\(586\) −28.9146 −1.19445
\(587\) 41.1627 1.69897 0.849483 0.527616i \(-0.176914\pi\)
0.849483 + 0.527616i \(0.176914\pi\)
\(588\) −6.18435 −0.255038
\(589\) 2.51461 0.103613
\(590\) −164.555 −6.77461
\(591\) −0.272655 −0.0112155
\(592\) 141.305 5.80759
\(593\) 30.8520 1.26694 0.633470 0.773767i \(-0.281630\pi\)
0.633470 + 0.773767i \(0.281630\pi\)
\(594\) 2.30625 0.0946264
\(595\) 8.43930 0.345977
\(596\) −6.68084 −0.273658
\(597\) 4.15017 0.169855
\(598\) −22.3083 −0.912252
\(599\) 5.72917 0.234088 0.117044 0.993127i \(-0.462658\pi\)
0.117044 + 0.993127i \(0.462658\pi\)
\(600\) −46.6610 −1.90493
\(601\) −41.5788 −1.69603 −0.848017 0.529968i \(-0.822204\pi\)
−0.848017 + 0.529968i \(0.822204\pi\)
\(602\) −33.6478 −1.37138
\(603\) 30.9157 1.25899
\(604\) −2.03204 −0.0826825
\(605\) −46.7396 −1.90023
\(606\) −7.15461 −0.290636
\(607\) −1.47724 −0.0599592 −0.0299796 0.999551i \(-0.509544\pi\)
−0.0299796 + 0.999551i \(0.509544\pi\)
\(608\) 35.6198 1.44458
\(609\) −4.71662 −0.191127
\(610\) −12.7891 −0.517816
\(611\) 1.40203 0.0567200
\(612\) 15.9807 0.645980
\(613\) 11.1506 0.450370 0.225185 0.974316i \(-0.427701\pi\)
0.225185 + 0.974316i \(0.427701\pi\)
\(614\) 62.4865 2.52175
\(615\) 17.7751 0.716759
\(616\) 7.77781 0.313377
\(617\) −26.8750 −1.08195 −0.540974 0.841039i \(-0.681944\pi\)
−0.540974 + 0.841039i \(0.681944\pi\)
\(618\) 3.44084 0.138411
\(619\) −34.5972 −1.39058 −0.695290 0.718729i \(-0.744724\pi\)
−0.695290 + 0.718729i \(0.744724\pi\)
\(620\) −40.1604 −1.61288
\(621\) −11.9369 −0.479011
\(622\) 40.3623 1.61838
\(623\) 5.30357 0.212483
\(624\) 7.74623 0.310097
\(625\) 92.1931 3.68772
\(626\) 13.9157 0.556185
\(627\) −0.214224 −0.00855529
\(628\) −74.4494 −2.97085
\(629\) −8.97370 −0.357805
\(630\) −66.7332 −2.65871
\(631\) −11.7872 −0.469241 −0.234621 0.972087i \(-0.575385\pi\)
−0.234621 + 0.972087i \(0.575385\pi\)
\(632\) −132.558 −5.27289
\(633\) 0.474110 0.0188442
\(634\) −30.4027 −1.20744
\(635\) −54.5319 −2.16403
\(636\) −4.16288 −0.165069
\(637\) −4.44869 −0.176263
\(638\) −7.68539 −0.304268
\(639\) −27.6981 −1.09572
\(640\) −195.450 −7.72586
\(641\) −18.2278 −0.719955 −0.359977 0.932961i \(-0.617216\pi\)
−0.359977 + 0.932961i \(0.617216\pi\)
\(642\) 11.0097 0.434519
\(643\) −20.4687 −0.807207 −0.403604 0.914934i \(-0.632243\pi\)
−0.403604 + 0.914934i \(0.632243\pi\)
\(644\) −62.9063 −2.47886
\(645\) −9.47205 −0.372961
\(646\) −4.12416 −0.162263
\(647\) −14.3087 −0.562533 −0.281267 0.959630i \(-0.590755\pi\)
−0.281267 + 0.959630i \(0.590755\pi\)
\(648\) −77.2597 −3.03505
\(649\) 5.64698 0.221664
\(650\) −52.4498 −2.05725
\(651\) 1.15033 0.0450850
\(652\) 47.1454 1.84636
\(653\) 25.5265 0.998927 0.499464 0.866335i \(-0.333530\pi\)
0.499464 + 0.866335i \(0.333530\pi\)
\(654\) 1.01112 0.0395380
\(655\) −72.9561 −2.85063
\(656\) 184.914 7.21968
\(657\) 7.71401 0.300952
\(658\) 5.37700 0.209617
\(659\) 13.0927 0.510018 0.255009 0.966939i \(-0.417922\pi\)
0.255009 + 0.966939i \(0.417922\pi\)
\(660\) 3.42134 0.133175
\(661\) −15.4120 −0.599458 −0.299729 0.954024i \(-0.596896\pi\)
−0.299729 + 0.954024i \(0.596896\pi\)
\(662\) 83.3575 3.23978
\(663\) −0.491932 −0.0191051
\(664\) 3.82623 0.148487
\(665\) 12.6628 0.491042
\(666\) 70.9590 2.74960
\(667\) 39.7788 1.54024
\(668\) 30.9110 1.19598
\(669\) 7.47342 0.288939
\(670\) 127.423 4.92278
\(671\) 0.438881 0.0169428
\(672\) 16.2946 0.628579
\(673\) 14.9941 0.577980 0.288990 0.957332i \(-0.406681\pi\)
0.288990 + 0.957332i \(0.406681\pi\)
\(674\) 67.8493 2.61346
\(675\) −28.0653 −1.08023
\(676\) −61.2938 −2.35745
\(677\) 42.6395 1.63877 0.819384 0.573245i \(-0.194316\pi\)
0.819384 + 0.573245i \(0.194316\pi\)
\(678\) 1.98123 0.0760885
\(679\) 24.1482 0.926724
\(680\) 42.1513 1.61643
\(681\) −3.23473 −0.123955
\(682\) 1.87438 0.0717737
\(683\) −9.51113 −0.363933 −0.181967 0.983305i \(-0.558246\pi\)
−0.181967 + 0.983305i \(0.558246\pi\)
\(684\) 23.9783 0.916831
\(685\) 23.2223 0.887277
\(686\) −54.7004 −2.08847
\(687\) 0.00939632 0.000358492 0
\(688\) −98.5377 −3.75672
\(689\) −2.99455 −0.114083
\(690\) −24.0844 −0.916876
\(691\) 37.1334 1.41262 0.706311 0.707902i \(-0.250358\pi\)
0.706311 + 0.707902i \(0.250358\pi\)
\(692\) 105.147 3.99710
\(693\) 2.29007 0.0869925
\(694\) −76.5739 −2.90671
\(695\) 7.12811 0.270384
\(696\) −23.5579 −0.892959
\(697\) −11.7431 −0.444803
\(698\) 16.3656 0.619446
\(699\) −1.01293 −0.0383125
\(700\) −147.901 −5.59015
\(701\) −34.1038 −1.28808 −0.644041 0.764991i \(-0.722743\pi\)
−0.644041 + 0.764991i \(0.722743\pi\)
\(702\) 7.94630 0.299914
\(703\) −13.4646 −0.507828
\(704\) 13.7361 0.517698
\(705\) 1.51365 0.0570075
\(706\) −17.1381 −0.645002
\(707\) −14.5128 −0.545812
\(708\) 27.0482 1.01653
\(709\) 2.08603 0.0783426 0.0391713 0.999233i \(-0.487528\pi\)
0.0391713 + 0.999233i \(0.487528\pi\)
\(710\) −114.161 −4.28439
\(711\) −39.0300 −1.46374
\(712\) 26.4895 0.992735
\(713\) −9.70160 −0.363328
\(714\) −1.88663 −0.0706055
\(715\) 2.46113 0.0920409
\(716\) 59.6371 2.22874
\(717\) −9.12256 −0.340688
\(718\) −3.73320 −0.139322
\(719\) −25.0163 −0.932949 −0.466474 0.884535i \(-0.654476\pi\)
−0.466474 + 0.884535i \(0.654476\pi\)
\(720\) −195.428 −7.28318
\(721\) 6.97961 0.259934
\(722\) 46.0354 1.71326
\(723\) −3.93369 −0.146295
\(724\) 95.2588 3.54026
\(725\) 93.5254 3.47345
\(726\) 10.4488 0.387791
\(727\) 38.4223 1.42500 0.712502 0.701670i \(-0.247562\pi\)
0.712502 + 0.701670i \(0.247562\pi\)
\(728\) 26.7989 0.993233
\(729\) −20.5775 −0.762130
\(730\) 31.7943 1.17676
\(731\) 6.25773 0.231451
\(732\) 2.10217 0.0776985
\(733\) 9.33100 0.344648 0.172324 0.985040i \(-0.444872\pi\)
0.172324 + 0.985040i \(0.444872\pi\)
\(734\) −11.9118 −0.439674
\(735\) −4.80288 −0.177157
\(736\) −137.425 −5.06554
\(737\) −4.37274 −0.161072
\(738\) 92.8581 3.41816
\(739\) 37.2271 1.36942 0.684710 0.728816i \(-0.259929\pi\)
0.684710 + 0.728816i \(0.259929\pi\)
\(740\) 215.041 7.90508
\(741\) −0.738122 −0.0271156
\(742\) −11.4846 −0.421612
\(743\) 25.6971 0.942734 0.471367 0.881937i \(-0.343761\pi\)
0.471367 + 0.881937i \(0.343761\pi\)
\(744\) 5.74550 0.210640
\(745\) −5.18846 −0.190091
\(746\) −19.5251 −0.714865
\(747\) 1.12658 0.0412194
\(748\) −2.26032 −0.0826453
\(749\) 22.3328 0.816023
\(750\) −35.8234 −1.30809
\(751\) 3.69461 0.134818 0.0674090 0.997725i \(-0.478527\pi\)
0.0674090 + 0.997725i \(0.478527\pi\)
\(752\) 15.7465 0.574218
\(753\) −7.21455 −0.262913
\(754\) −26.4805 −0.964362
\(755\) −1.57812 −0.0574336
\(756\) 22.4075 0.814954
\(757\) −50.3992 −1.83179 −0.915895 0.401418i \(-0.868518\pi\)
−0.915895 + 0.401418i \(0.868518\pi\)
\(758\) −8.64159 −0.313877
\(759\) 0.826497 0.0299999
\(760\) 63.2462 2.29418
\(761\) −33.3475 −1.20884 −0.604422 0.796664i \(-0.706596\pi\)
−0.604422 + 0.796664i \(0.706596\pi\)
\(762\) 12.1908 0.441626
\(763\) 2.05102 0.0742521
\(764\) −88.1678 −3.18980
\(765\) 12.4109 0.448716
\(766\) −75.6207 −2.73229
\(767\) 19.4570 0.702552
\(768\) 20.0048 0.721863
\(769\) −21.3320 −0.769253 −0.384626 0.923072i \(-0.625670\pi\)
−0.384626 + 0.923072i \(0.625670\pi\)
\(770\) 9.43880 0.340151
\(771\) −5.57484 −0.200773
\(772\) 65.2872 2.34974
\(773\) −38.9994 −1.40271 −0.701355 0.712812i \(-0.747421\pi\)
−0.701355 + 0.712812i \(0.747421\pi\)
\(774\) −49.4826 −1.77862
\(775\) −22.8098 −0.819352
\(776\) 120.612 4.32972
\(777\) −6.15952 −0.220971
\(778\) 84.1703 3.01765
\(779\) −17.6201 −0.631304
\(780\) 11.7884 0.422093
\(781\) 3.91764 0.140184
\(782\) 15.9114 0.568990
\(783\) −14.1694 −0.506373
\(784\) −49.9643 −1.78444
\(785\) −57.8187 −2.06364
\(786\) 16.3096 0.581744
\(787\) −26.0410 −0.928260 −0.464130 0.885767i \(-0.653633\pi\)
−0.464130 + 0.885767i \(0.653633\pi\)
\(788\) −4.31655 −0.153771
\(789\) −3.07256 −0.109386
\(790\) −160.867 −5.72338
\(791\) 4.01884 0.142894
\(792\) 11.4381 0.406435
\(793\) 1.51219 0.0536994
\(794\) 24.7132 0.877039
\(795\) −3.23297 −0.114662
\(796\) 65.7037 2.32881
\(797\) −39.3971 −1.39552 −0.697758 0.716334i \(-0.745819\pi\)
−0.697758 + 0.716334i \(0.745819\pi\)
\(798\) −2.83081 −0.100210
\(799\) −1.00000 −0.0353775
\(800\) −323.104 −11.4235
\(801\) 7.79946 0.275580
\(802\) −98.4289 −3.47565
\(803\) −1.09108 −0.0385032
\(804\) −20.9448 −0.738665
\(805\) −48.8542 −1.72188
\(806\) 6.45828 0.227483
\(807\) 6.04532 0.212805
\(808\) −72.4866 −2.55007
\(809\) 46.8692 1.64783 0.823917 0.566710i \(-0.191784\pi\)
0.823917 + 0.566710i \(0.191784\pi\)
\(810\) −93.7588 −3.29435
\(811\) 10.8519 0.381062 0.190531 0.981681i \(-0.438979\pi\)
0.190531 + 0.981681i \(0.438979\pi\)
\(812\) −74.6714 −2.62045
\(813\) −4.74504 −0.166416
\(814\) −10.0365 −0.351779
\(815\) 36.6140 1.28253
\(816\) −5.52501 −0.193414
\(817\) 9.38945 0.328495
\(818\) −76.4534 −2.67313
\(819\) 7.89056 0.275718
\(820\) 281.407 9.82715
\(821\) 20.3411 0.709910 0.354955 0.934883i \(-0.384496\pi\)
0.354955 + 0.934883i \(0.384496\pi\)
\(822\) −5.19142 −0.181072
\(823\) −42.5915 −1.48465 −0.742324 0.670041i \(-0.766276\pi\)
−0.742324 + 0.670041i \(0.766276\pi\)
\(824\) 34.8607 1.21443
\(825\) 1.94321 0.0676538
\(826\) 74.6206 2.59638
\(827\) −18.0281 −0.626898 −0.313449 0.949605i \(-0.601485\pi\)
−0.313449 + 0.949605i \(0.601485\pi\)
\(828\) −92.5104 −3.21496
\(829\) −20.3525 −0.706870 −0.353435 0.935459i \(-0.614987\pi\)
−0.353435 + 0.935459i \(0.614987\pi\)
\(830\) 4.64334 0.161173
\(831\) 7.97527 0.276659
\(832\) 47.3284 1.64082
\(833\) 3.17303 0.109939
\(834\) −1.59351 −0.0551788
\(835\) 24.0060 0.830763
\(836\) −3.39150 −0.117298
\(837\) 3.45575 0.119448
\(838\) 64.5737 2.23066
\(839\) 52.2392 1.80350 0.901749 0.432261i \(-0.142284\pi\)
0.901749 + 0.432261i \(0.142284\pi\)
\(840\) 28.9325 0.998267
\(841\) 18.2184 0.628222
\(842\) −10.0753 −0.347218
\(843\) −9.57365 −0.329734
\(844\) 7.50590 0.258364
\(845\) −47.6019 −1.63755
\(846\) 7.90744 0.271863
\(847\) 21.1950 0.728268
\(848\) −33.6326 −1.15495
\(849\) −2.89278 −0.0992799
\(850\) 37.4099 1.28315
\(851\) 51.9478 1.78075
\(852\) 18.7649 0.642874
\(853\) 19.8078 0.678206 0.339103 0.940749i \(-0.389876\pi\)
0.339103 + 0.940749i \(0.389876\pi\)
\(854\) 5.79948 0.198454
\(855\) 18.6219 0.636857
\(856\) 111.545 3.81251
\(857\) 26.4493 0.903491 0.451745 0.892147i \(-0.350802\pi\)
0.451745 + 0.892147i \(0.350802\pi\)
\(858\) −0.550193 −0.0187833
\(859\) 10.5925 0.361412 0.180706 0.983537i \(-0.442162\pi\)
0.180706 + 0.983537i \(0.442162\pi\)
\(860\) −149.957 −5.11350
\(861\) −8.06045 −0.274699
\(862\) 63.3137 2.15647
\(863\) 51.8825 1.76610 0.883051 0.469277i \(-0.155486\pi\)
0.883051 + 0.469277i \(0.155486\pi\)
\(864\) 48.9513 1.66536
\(865\) 81.6593 2.77650
\(866\) 9.93453 0.337589
\(867\) 0.350871 0.0119162
\(868\) 18.2115 0.618139
\(869\) 5.52043 0.187268
\(870\) −28.5888 −0.969249
\(871\) −15.0665 −0.510510
\(872\) 10.2442 0.346911
\(873\) 35.5125 1.20192
\(874\) 23.8743 0.807561
\(875\) −72.6665 −2.45658
\(876\) −5.22609 −0.176573
\(877\) 20.7211 0.699702 0.349851 0.936805i \(-0.386232\pi\)
0.349851 + 0.936805i \(0.386232\pi\)
\(878\) −7.65745 −0.258426
\(879\) 3.69108 0.124497
\(880\) 27.6415 0.931796
\(881\) 4.66339 0.157114 0.0785568 0.996910i \(-0.474969\pi\)
0.0785568 + 0.996910i \(0.474969\pi\)
\(882\) −25.0906 −0.844843
\(883\) 44.6349 1.50208 0.751042 0.660254i \(-0.229551\pi\)
0.751042 + 0.660254i \(0.229551\pi\)
\(884\) −7.78805 −0.261940
\(885\) 21.0061 0.706112
\(886\) 18.1438 0.609552
\(887\) −28.9999 −0.973722 −0.486861 0.873479i \(-0.661858\pi\)
−0.486861 + 0.873479i \(0.661858\pi\)
\(888\) −30.7646 −1.03239
\(889\) 24.7286 0.829370
\(890\) 32.1464 1.07755
\(891\) 3.21750 0.107790
\(892\) 118.316 3.96151
\(893\) −1.50045 −0.0502108
\(894\) 1.15990 0.0387928
\(895\) 46.3153 1.54815
\(896\) 88.6309 2.96095
\(897\) 2.84774 0.0950834
\(898\) 90.8683 3.03232
\(899\) −11.5160 −0.384082
\(900\) −217.505 −7.25015
\(901\) 2.13587 0.0711562
\(902\) −13.1339 −0.437312
\(903\) 4.29529 0.142938
\(904\) 20.0727 0.667608
\(905\) 73.9797 2.45917
\(906\) 0.352794 0.0117208
\(907\) −21.6716 −0.719594 −0.359797 0.933031i \(-0.617154\pi\)
−0.359797 + 0.933031i \(0.617154\pi\)
\(908\) −51.2108 −1.69949
\(909\) −21.3427 −0.707891
\(910\) 32.5219 1.07809
\(911\) −27.5487 −0.912729 −0.456364 0.889793i \(-0.650849\pi\)
−0.456364 + 0.889793i \(0.650849\pi\)
\(912\) −8.29003 −0.274510
\(913\) −0.159344 −0.00527353
\(914\) 10.6815 0.353312
\(915\) 1.63258 0.0539716
\(916\) 0.148758 0.00491511
\(917\) 33.0834 1.09251
\(918\) −5.66771 −0.187062
\(919\) 6.98726 0.230488 0.115244 0.993337i \(-0.463235\pi\)
0.115244 + 0.993337i \(0.463235\pi\)
\(920\) −244.010 −8.04476
\(921\) −7.97667 −0.262840
\(922\) −43.0460 −1.41764
\(923\) 13.4984 0.444306
\(924\) −1.55147 −0.0510397
\(925\) 122.137 4.01582
\(926\) 82.5404 2.71245
\(927\) 10.2642 0.337122
\(928\) −163.127 −5.35490
\(929\) 56.1725 1.84296 0.921479 0.388427i \(-0.126981\pi\)
0.921479 + 0.388427i \(0.126981\pi\)
\(930\) 6.97247 0.228636
\(931\) 4.76099 0.156035
\(932\) −16.0363 −0.525285
\(933\) −5.15242 −0.168683
\(934\) 103.614 3.39036
\(935\) −1.75540 −0.0574078
\(936\) 39.4106 1.28817
\(937\) −31.7554 −1.03740 −0.518702 0.854955i \(-0.673584\pi\)
−0.518702 + 0.854955i \(0.673584\pi\)
\(938\) −57.7824 −1.88666
\(939\) −1.77640 −0.0579707
\(940\) 23.9635 0.781603
\(941\) −22.6325 −0.737799 −0.368900 0.929469i \(-0.620265\pi\)
−0.368900 + 0.929469i \(0.620265\pi\)
\(942\) 12.9256 0.421138
\(943\) 67.9798 2.21373
\(944\) 218.527 7.11243
\(945\) 17.4021 0.566090
\(946\) 6.99886 0.227553
\(947\) −11.7369 −0.381397 −0.190699 0.981649i \(-0.561075\pi\)
−0.190699 + 0.981649i \(0.561075\pi\)
\(948\) 26.4420 0.858796
\(949\) −3.75936 −0.122034
\(950\) 56.1319 1.82116
\(951\) 3.88103 0.125851
\(952\) −19.1144 −0.619500
\(953\) 46.4149 1.50353 0.751764 0.659433i \(-0.229203\pi\)
0.751764 + 0.659433i \(0.229203\pi\)
\(954\) −16.8893 −0.546810
\(955\) −68.4727 −2.21572
\(956\) −144.424 −4.67102
\(957\) 0.981073 0.0317136
\(958\) −9.54860 −0.308501
\(959\) −10.5306 −0.340051
\(960\) 51.0966 1.64913
\(961\) −28.1914 −0.909399
\(962\) −34.5813 −1.11495
\(963\) 32.8427 1.05834
\(964\) −62.2764 −2.00579
\(965\) 50.7032 1.63219
\(966\) 10.9215 0.351394
\(967\) −13.5855 −0.436882 −0.218441 0.975850i \(-0.570097\pi\)
−0.218441 + 0.975850i \(0.570097\pi\)
\(968\) 105.862 3.40252
\(969\) 0.526467 0.0169125
\(970\) 146.369 4.69963
\(971\) −33.3713 −1.07094 −0.535468 0.844555i \(-0.679865\pi\)
−0.535468 + 0.844555i \(0.679865\pi\)
\(972\) 49.7741 1.59650
\(973\) −3.23238 −0.103625
\(974\) −19.2462 −0.616690
\(975\) 6.69544 0.214426
\(976\) 16.9838 0.543637
\(977\) −20.4950 −0.655692 −0.327846 0.944731i \(-0.606323\pi\)
−0.327846 + 0.944731i \(0.606323\pi\)
\(978\) −8.18519 −0.261733
\(979\) −1.10316 −0.0352572
\(980\) −76.0370 −2.42891
\(981\) 3.01625 0.0963013
\(982\) −5.20955 −0.166243
\(983\) −26.9348 −0.859088 −0.429544 0.903046i \(-0.641326\pi\)
−0.429544 + 0.903046i \(0.641326\pi\)
\(984\) −40.2591 −1.28341
\(985\) −3.35231 −0.106814
\(986\) 18.8872 0.601492
\(987\) −0.686397 −0.0218482
\(988\) −11.6856 −0.371769
\(989\) −36.2254 −1.15190
\(990\) 13.8807 0.441159
\(991\) 9.19984 0.292243 0.146121 0.989267i \(-0.453321\pi\)
0.146121 + 0.989267i \(0.453321\pi\)
\(992\) 39.7847 1.26317
\(993\) −10.6409 −0.337680
\(994\) 51.7686 1.64200
\(995\) 51.0267 1.61765
\(996\) −0.763235 −0.0241840
\(997\) −7.35984 −0.233088 −0.116544 0.993186i \(-0.537182\pi\)
−0.116544 + 0.993186i \(0.537182\pi\)
\(998\) −96.4520 −3.05313
\(999\) −18.5041 −0.585442
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 799.2.a.g.1.1 20
3.2 odd 2 7191.2.a.bb.1.20 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
799.2.a.g.1.1 20 1.1 even 1 trivial
7191.2.a.bb.1.20 20 3.2 odd 2