Properties

Label 1183.2.a.m.1.1
Level $1183$
Weight $2$
Character 1183.1
Self dual yes
Analytic conductor $9.446$
Analytic rank $1$
Dimension $6$
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] = [1183,2,Mod(1,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, 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("1183.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.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: \(9.44630255912\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.7674048.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.70320\) of defining polynomial
Character \(\chi\) \(=\) 1183.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.70320 q^{2} -0.345949 q^{3} +5.30727 q^{4} -3.25812 q^{5} +0.935168 q^{6} +1.00000 q^{7} -8.94020 q^{8} -2.88032 q^{9} +O(q^{10})\) \(q-2.70320 q^{2} -0.345949 q^{3} +5.30727 q^{4} -3.25812 q^{5} +0.935168 q^{6} +1.00000 q^{7} -8.94020 q^{8} -2.88032 q^{9} +8.80735 q^{10} +1.84603 q^{11} -1.83605 q^{12} -2.70320 q^{14} +1.12715 q^{15} +13.5526 q^{16} +2.15314 q^{17} +7.78607 q^{18} +2.40096 q^{19} -17.2917 q^{20} -0.345949 q^{21} -4.99017 q^{22} +1.81263 q^{23} +3.09285 q^{24} +5.61537 q^{25} +2.03429 q^{27} +5.30727 q^{28} -2.73406 q^{29} -3.04689 q^{30} -1.74236 q^{31} -18.7549 q^{32} -0.638632 q^{33} -5.82036 q^{34} -3.25812 q^{35} -15.2866 q^{36} +5.93565 q^{37} -6.49025 q^{38} +29.1283 q^{40} +4.22131 q^{41} +0.935168 q^{42} -8.68223 q^{43} +9.79737 q^{44} +9.38444 q^{45} -4.89989 q^{46} -5.87774 q^{47} -4.68850 q^{48} +1.00000 q^{49} -15.1794 q^{50} -0.744877 q^{51} -9.30628 q^{53} -5.49909 q^{54} -6.01459 q^{55} -8.94020 q^{56} -0.830609 q^{57} +7.39071 q^{58} +10.7523 q^{59} +5.98206 q^{60} +10.1101 q^{61} +4.70994 q^{62} -2.88032 q^{63} +23.5929 q^{64} +1.72635 q^{66} +0.826916 q^{67} +11.4273 q^{68} -0.627077 q^{69} +8.80735 q^{70} +2.35425 q^{71} +25.7506 q^{72} -3.19482 q^{73} -16.0452 q^{74} -1.94263 q^{75} +12.7425 q^{76} +1.84603 q^{77} +0.801911 q^{79} -44.1559 q^{80} +7.93720 q^{81} -11.4110 q^{82} -9.97031 q^{83} -1.83605 q^{84} -7.01520 q^{85} +23.4698 q^{86} +0.945847 q^{87} -16.5039 q^{88} -15.1135 q^{89} -25.3680 q^{90} +9.62010 q^{92} +0.602768 q^{93} +15.8887 q^{94} -7.82261 q^{95} +6.48823 q^{96} -9.23171 q^{97} -2.70320 q^{98} -5.31715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{2} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} + 12 q^{10} - 4 q^{11} + 2 q^{12} - 4 q^{14} - 20 q^{15} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 2 q^{19} - 26 q^{20} - 6 q^{22} - 12 q^{23} - 2 q^{24} + 10 q^{25} + 6 q^{27} + 4 q^{28} - 8 q^{29} + 8 q^{30} + 14 q^{31} - 8 q^{32} - 16 q^{33} + 2 q^{34} - 6 q^{35} - 10 q^{36} - 12 q^{37} - 2 q^{38} + 46 q^{40} - 28 q^{41} - 4 q^{42} + 2 q^{43} + 20 q^{44} - 16 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} + 6 q^{49} - 32 q^{50} - 26 q^{51} - 22 q^{53} - 14 q^{54} + 6 q^{55} - 12 q^{56} - 4 q^{58} + 2 q^{59} - 14 q^{61} - 4 q^{62} + 4 q^{63} + 26 q^{64} - 26 q^{66} - 24 q^{67} + 8 q^{68} + 4 q^{69} + 12 q^{70} - 4 q^{71} - 8 q^{72} - 36 q^{73} - 6 q^{74} + 46 q^{75} + 26 q^{76} - 4 q^{77} - 28 q^{79} - 36 q^{80} - 2 q^{81} + 14 q^{82} - 26 q^{83} + 2 q^{84} + 20 q^{85} + 24 q^{86} + 2 q^{87} - 14 q^{88} - 42 q^{89} - 12 q^{90} + 12 q^{92} - 4 q^{94} - 22 q^{95} + 42 q^{96} - 24 q^{97} - 4 q^{98} - 16 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70320 −1.91145 −0.955724 0.294264i \(-0.904925\pi\)
−0.955724 + 0.294264i \(0.904925\pi\)
\(3\) −0.345949 −0.199734 −0.0998669 0.995001i \(-0.531842\pi\)
−0.0998669 + 0.995001i \(0.531842\pi\)
\(4\) 5.30727 2.65363
\(5\) −3.25812 −1.45708 −0.728539 0.685005i \(-0.759800\pi\)
−0.728539 + 0.685005i \(0.759800\pi\)
\(6\) 0.935168 0.381781
\(7\) 1.00000 0.377964
\(8\) −8.94020 −3.16084
\(9\) −2.88032 −0.960106
\(10\) 8.80735 2.78513
\(11\) 1.84603 0.556598 0.278299 0.960494i \(-0.410229\pi\)
0.278299 + 0.960494i \(0.410229\pi\)
\(12\) −1.83605 −0.530021
\(13\) 0 0
\(14\) −2.70320 −0.722460
\(15\) 1.12715 0.291028
\(16\) 13.5526 3.38814
\(17\) 2.15314 0.522213 0.261107 0.965310i \(-0.415913\pi\)
0.261107 + 0.965310i \(0.415913\pi\)
\(18\) 7.78607 1.83519
\(19\) 2.40096 0.550817 0.275408 0.961327i \(-0.411187\pi\)
0.275408 + 0.961327i \(0.411187\pi\)
\(20\) −17.2917 −3.86655
\(21\) −0.345949 −0.0754923
\(22\) −4.99017 −1.06391
\(23\) 1.81263 0.377959 0.188979 0.981981i \(-0.439482\pi\)
0.188979 + 0.981981i \(0.439482\pi\)
\(24\) 3.09285 0.631326
\(25\) 5.61537 1.12307
\(26\) 0 0
\(27\) 2.03429 0.391500
\(28\) 5.30727 1.00298
\(29\) −2.73406 −0.507703 −0.253851 0.967243i \(-0.581697\pi\)
−0.253851 + 0.967243i \(0.581697\pi\)
\(30\) −3.04689 −0.556284
\(31\) −1.74236 −0.312937 −0.156468 0.987683i \(-0.550011\pi\)
−0.156468 + 0.987683i \(0.550011\pi\)
\(32\) −18.7549 −3.31542
\(33\) −0.638632 −0.111172
\(34\) −5.82036 −0.998183
\(35\) −3.25812 −0.550723
\(36\) −15.2866 −2.54777
\(37\) 5.93565 0.975815 0.487908 0.872895i \(-0.337760\pi\)
0.487908 + 0.872895i \(0.337760\pi\)
\(38\) −6.49025 −1.05286
\(39\) 0 0
\(40\) 29.1283 4.60558
\(41\) 4.22131 0.659259 0.329629 0.944110i \(-0.393076\pi\)
0.329629 + 0.944110i \(0.393076\pi\)
\(42\) 0.935168 0.144300
\(43\) −8.68223 −1.32403 −0.662014 0.749492i \(-0.730298\pi\)
−0.662014 + 0.749492i \(0.730298\pi\)
\(44\) 9.79737 1.47701
\(45\) 9.38444 1.39895
\(46\) −4.89989 −0.722449
\(47\) −5.87774 −0.857357 −0.428678 0.903457i \(-0.641021\pi\)
−0.428678 + 0.903457i \(0.641021\pi\)
\(48\) −4.68850 −0.676727
\(49\) 1.00000 0.142857
\(50\) −15.1794 −2.14670
\(51\) −0.744877 −0.104304
\(52\) 0 0
\(53\) −9.30628 −1.27832 −0.639158 0.769076i \(-0.720717\pi\)
−0.639158 + 0.769076i \(0.720717\pi\)
\(54\) −5.49909 −0.748331
\(55\) −6.01459 −0.811007
\(56\) −8.94020 −1.19468
\(57\) −0.830609 −0.110017
\(58\) 7.39071 0.970447
\(59\) 10.7523 1.39982 0.699912 0.714229i \(-0.253222\pi\)
0.699912 + 0.714229i \(0.253222\pi\)
\(60\) 5.98206 0.772281
\(61\) 10.1101 1.29446 0.647231 0.762294i \(-0.275927\pi\)
0.647231 + 0.762294i \(0.275927\pi\)
\(62\) 4.70994 0.598163
\(63\) −2.88032 −0.362886
\(64\) 23.5929 2.94911
\(65\) 0 0
\(66\) 1.72635 0.212499
\(67\) 0.826916 0.101024 0.0505119 0.998723i \(-0.483915\pi\)
0.0505119 + 0.998723i \(0.483915\pi\)
\(68\) 11.4273 1.38576
\(69\) −0.627077 −0.0754912
\(70\) 8.80735 1.05268
\(71\) 2.35425 0.279398 0.139699 0.990194i \(-0.455387\pi\)
0.139699 + 0.990194i \(0.455387\pi\)
\(72\) 25.7506 3.03474
\(73\) −3.19482 −0.373925 −0.186963 0.982367i \(-0.559864\pi\)
−0.186963 + 0.982367i \(0.559864\pi\)
\(74\) −16.0452 −1.86522
\(75\) −1.94263 −0.224316
\(76\) 12.7425 1.46167
\(77\) 1.84603 0.210374
\(78\) 0 0
\(79\) 0.801911 0.0902220 0.0451110 0.998982i \(-0.485636\pi\)
0.0451110 + 0.998982i \(0.485636\pi\)
\(80\) −44.1559 −4.93678
\(81\) 7.93720 0.881911
\(82\) −11.4110 −1.26014
\(83\) −9.97031 −1.09438 −0.547192 0.837007i \(-0.684303\pi\)
−0.547192 + 0.837007i \(0.684303\pi\)
\(84\) −1.83605 −0.200329
\(85\) −7.01520 −0.760905
\(86\) 23.4698 2.53081
\(87\) 0.945847 0.101405
\(88\) −16.5039 −1.75932
\(89\) −15.1135 −1.60202 −0.801012 0.598648i \(-0.795705\pi\)
−0.801012 + 0.598648i \(0.795705\pi\)
\(90\) −25.3680 −2.67402
\(91\) 0 0
\(92\) 9.62010 1.00296
\(93\) 0.602768 0.0625041
\(94\) 15.8887 1.63879
\(95\) −7.82261 −0.802583
\(96\) 6.48823 0.662202
\(97\) −9.23171 −0.937338 −0.468669 0.883374i \(-0.655266\pi\)
−0.468669 + 0.883374i \(0.655266\pi\)
\(98\) −2.70320 −0.273064
\(99\) −5.31715 −0.534394
\(100\) 29.8023 2.98023
\(101\) 14.8234 1.47498 0.737491 0.675357i \(-0.236011\pi\)
0.737491 + 0.675357i \(0.236011\pi\)
\(102\) 2.01355 0.199371
\(103\) −4.28286 −0.422003 −0.211001 0.977486i \(-0.567672\pi\)
−0.211001 + 0.977486i \(0.567672\pi\)
\(104\) 0 0
\(105\) 1.12715 0.109998
\(106\) 25.1567 2.44343
\(107\) −19.1258 −1.84896 −0.924479 0.381233i \(-0.875500\pi\)
−0.924479 + 0.381233i \(0.875500\pi\)
\(108\) 10.7965 1.03890
\(109\) −4.27153 −0.409139 −0.204569 0.978852i \(-0.565579\pi\)
−0.204569 + 0.978852i \(0.565579\pi\)
\(110\) 16.2586 1.55020
\(111\) −2.05343 −0.194903
\(112\) 13.5526 1.28060
\(113\) 2.74976 0.258676 0.129338 0.991601i \(-0.458715\pi\)
0.129338 + 0.991601i \(0.458715\pi\)
\(114\) 2.24530 0.210291
\(115\) −5.90576 −0.550715
\(116\) −14.5104 −1.34726
\(117\) 0 0
\(118\) −29.0655 −2.67569
\(119\) 2.15314 0.197378
\(120\) −10.0769 −0.919891
\(121\) −7.59218 −0.690198
\(122\) −27.3295 −2.47430
\(123\) −1.46036 −0.131676
\(124\) −9.24717 −0.830420
\(125\) −2.00495 −0.179329
\(126\) 7.78607 0.693638
\(127\) −9.73438 −0.863786 −0.431893 0.901925i \(-0.642154\pi\)
−0.431893 + 0.901925i \(0.642154\pi\)
\(128\) −26.2666 −2.32166
\(129\) 3.00361 0.264453
\(130\) 0 0
\(131\) −18.6615 −1.63046 −0.815230 0.579138i \(-0.803389\pi\)
−0.815230 + 0.579138i \(0.803389\pi\)
\(132\) −3.38939 −0.295009
\(133\) 2.40096 0.208189
\(134\) −2.23532 −0.193102
\(135\) −6.62797 −0.570445
\(136\) −19.2495 −1.65063
\(137\) −8.42156 −0.719502 −0.359751 0.933048i \(-0.617138\pi\)
−0.359751 + 0.933048i \(0.617138\pi\)
\(138\) 1.69511 0.144298
\(139\) −17.6362 −1.49588 −0.747941 0.663765i \(-0.768957\pi\)
−0.747941 + 0.663765i \(0.768957\pi\)
\(140\) −17.2917 −1.46142
\(141\) 2.03340 0.171243
\(142\) −6.36399 −0.534054
\(143\) 0 0
\(144\) −39.0357 −3.25298
\(145\) 8.90791 0.739762
\(146\) 8.63623 0.714739
\(147\) −0.345949 −0.0285334
\(148\) 31.5021 2.58946
\(149\) 4.02104 0.329416 0.164708 0.986342i \(-0.447332\pi\)
0.164708 + 0.986342i \(0.447332\pi\)
\(150\) 5.25132 0.428768
\(151\) −18.9010 −1.53814 −0.769069 0.639165i \(-0.779280\pi\)
−0.769069 + 0.639165i \(0.779280\pi\)
\(152\) −21.4650 −1.74104
\(153\) −6.20173 −0.501380
\(154\) −4.99017 −0.402120
\(155\) 5.67682 0.455973
\(156\) 0 0
\(157\) −11.5735 −0.923670 −0.461835 0.886966i \(-0.652809\pi\)
−0.461835 + 0.886966i \(0.652809\pi\)
\(158\) −2.16772 −0.172455
\(159\) 3.21950 0.255323
\(160\) 61.1056 4.83082
\(161\) 1.81263 0.142855
\(162\) −21.4558 −1.68573
\(163\) −4.40542 −0.345059 −0.172529 0.985004i \(-0.555194\pi\)
−0.172529 + 0.985004i \(0.555194\pi\)
\(164\) 22.4037 1.74943
\(165\) 2.08074 0.161985
\(166\) 26.9517 2.09186
\(167\) 9.01909 0.697918 0.348959 0.937138i \(-0.386535\pi\)
0.348959 + 0.937138i \(0.386535\pi\)
\(168\) 3.09285 0.238619
\(169\) 0 0
\(170\) 18.9635 1.45443
\(171\) −6.91552 −0.528843
\(172\) −46.0789 −3.51349
\(173\) 6.09200 0.463166 0.231583 0.972815i \(-0.425609\pi\)
0.231583 + 0.972815i \(0.425609\pi\)
\(174\) −2.55681 −0.193831
\(175\) 5.61537 0.424482
\(176\) 25.0184 1.88583
\(177\) −3.71974 −0.279592
\(178\) 40.8547 3.06219
\(179\) 3.87964 0.289978 0.144989 0.989433i \(-0.453685\pi\)
0.144989 + 0.989433i \(0.453685\pi\)
\(180\) 49.8057 3.71230
\(181\) 6.58392 0.489379 0.244690 0.969601i \(-0.421314\pi\)
0.244690 + 0.969601i \(0.421314\pi\)
\(182\) 0 0
\(183\) −3.49757 −0.258548
\(184\) −16.2052 −1.19467
\(185\) −19.3391 −1.42184
\(186\) −1.62940 −0.119473
\(187\) 3.97476 0.290663
\(188\) −31.1948 −2.27511
\(189\) 2.03429 0.147973
\(190\) 21.1460 1.53410
\(191\) −13.7434 −0.994435 −0.497218 0.867626i \(-0.665645\pi\)
−0.497218 + 0.867626i \(0.665645\pi\)
\(192\) −8.16195 −0.589038
\(193\) −22.7530 −1.63780 −0.818899 0.573937i \(-0.805415\pi\)
−0.818899 + 0.573937i \(0.805415\pi\)
\(194\) 24.9551 1.79167
\(195\) 0 0
\(196\) 5.30727 0.379091
\(197\) −14.5272 −1.03502 −0.517509 0.855678i \(-0.673141\pi\)
−0.517509 + 0.855678i \(0.673141\pi\)
\(198\) 14.3733 1.02147
\(199\) 23.8404 1.69000 0.845001 0.534765i \(-0.179600\pi\)
0.845001 + 0.534765i \(0.179600\pi\)
\(200\) −50.2025 −3.54985
\(201\) −0.286071 −0.0201779
\(202\) −40.0705 −2.81935
\(203\) −2.73406 −0.191894
\(204\) −3.95326 −0.276784
\(205\) −13.7536 −0.960591
\(206\) 11.5774 0.806637
\(207\) −5.22095 −0.362881
\(208\) 0 0
\(209\) 4.43223 0.306584
\(210\) −3.04689 −0.210256
\(211\) 4.31527 0.297076 0.148538 0.988907i \(-0.452543\pi\)
0.148538 + 0.988907i \(0.452543\pi\)
\(212\) −49.3909 −3.39218
\(213\) −0.814450 −0.0558052
\(214\) 51.7007 3.53419
\(215\) 28.2878 1.92921
\(216\) −18.1870 −1.23747
\(217\) −1.74236 −0.118279
\(218\) 11.5468 0.782047
\(219\) 1.10525 0.0746856
\(220\) −31.9210 −2.15212
\(221\) 0 0
\(222\) 5.55083 0.372548
\(223\) −23.3947 −1.56662 −0.783312 0.621629i \(-0.786471\pi\)
−0.783312 + 0.621629i \(0.786471\pi\)
\(224\) −18.7549 −1.25311
\(225\) −16.1741 −1.07827
\(226\) −7.43315 −0.494446
\(227\) 26.7229 1.77366 0.886829 0.462097i \(-0.152903\pi\)
0.886829 + 0.462097i \(0.152903\pi\)
\(228\) −4.40826 −0.291944
\(229\) 3.00670 0.198688 0.0993442 0.995053i \(-0.468326\pi\)
0.0993442 + 0.995053i \(0.468326\pi\)
\(230\) 15.9644 1.05266
\(231\) −0.638632 −0.0420189
\(232\) 24.4431 1.60477
\(233\) −11.7148 −0.767462 −0.383731 0.923445i \(-0.625361\pi\)
−0.383731 + 0.923445i \(0.625361\pi\)
\(234\) 0 0
\(235\) 19.1504 1.24924
\(236\) 57.0651 3.71462
\(237\) −0.277420 −0.0180204
\(238\) −5.82036 −0.377278
\(239\) 1.42797 0.0923677 0.0461838 0.998933i \(-0.485294\pi\)
0.0461838 + 0.998933i \(0.485294\pi\)
\(240\) 15.2757 0.986043
\(241\) −2.67969 −0.172614 −0.0863069 0.996269i \(-0.527507\pi\)
−0.0863069 + 0.996269i \(0.527507\pi\)
\(242\) 20.5232 1.31928
\(243\) −8.84874 −0.567647
\(244\) 53.6569 3.43503
\(245\) −3.25812 −0.208154
\(246\) 3.94764 0.251692
\(247\) 0 0
\(248\) 15.5770 0.989143
\(249\) 3.44922 0.218586
\(250\) 5.41978 0.342777
\(251\) 10.9339 0.690143 0.345072 0.938576i \(-0.387855\pi\)
0.345072 + 0.938576i \(0.387855\pi\)
\(252\) −15.2866 −0.962967
\(253\) 3.34616 0.210371
\(254\) 26.3139 1.65108
\(255\) 2.42690 0.151978
\(256\) 23.8178 1.48861
\(257\) 4.15138 0.258956 0.129478 0.991582i \(-0.458670\pi\)
0.129478 + 0.991582i \(0.458670\pi\)
\(258\) −8.11935 −0.505488
\(259\) 5.93565 0.368823
\(260\) 0 0
\(261\) 7.87497 0.487448
\(262\) 50.4456 3.11654
\(263\) 4.05360 0.249955 0.124978 0.992160i \(-0.460114\pi\)
0.124978 + 0.992160i \(0.460114\pi\)
\(264\) 5.70949 0.351395
\(265\) 30.3210 1.86260
\(266\) −6.49025 −0.397943
\(267\) 5.22849 0.319979
\(268\) 4.38866 0.268080
\(269\) 4.00022 0.243898 0.121949 0.992536i \(-0.461086\pi\)
0.121949 + 0.992536i \(0.461086\pi\)
\(270\) 17.9167 1.09038
\(271\) 2.78502 0.169178 0.0845888 0.996416i \(-0.473042\pi\)
0.0845888 + 0.996416i \(0.473042\pi\)
\(272\) 29.1806 1.76933
\(273\) 0 0
\(274\) 22.7651 1.37529
\(275\) 10.3661 0.625101
\(276\) −3.32807 −0.200326
\(277\) 16.6924 1.00295 0.501474 0.865173i \(-0.332791\pi\)
0.501474 + 0.865173i \(0.332791\pi\)
\(278\) 47.6741 2.85930
\(279\) 5.01855 0.300453
\(280\) 29.1283 1.74075
\(281\) −13.3731 −0.797774 −0.398887 0.917000i \(-0.630603\pi\)
−0.398887 + 0.917000i \(0.630603\pi\)
\(282\) −5.49668 −0.327322
\(283\) −18.8862 −1.12267 −0.561335 0.827589i \(-0.689712\pi\)
−0.561335 + 0.827589i \(0.689712\pi\)
\(284\) 12.4946 0.741419
\(285\) 2.70623 0.160303
\(286\) 0 0
\(287\) 4.22131 0.249176
\(288\) 54.0200 3.18316
\(289\) −12.3640 −0.727293
\(290\) −24.0798 −1.41402
\(291\) 3.19370 0.187218
\(292\) −16.9558 −0.992262
\(293\) −3.41790 −0.199676 −0.0998380 0.995004i \(-0.531832\pi\)
−0.0998380 + 0.995004i \(0.531832\pi\)
\(294\) 0.935168 0.0545401
\(295\) −35.0322 −2.03965
\(296\) −53.0659 −3.08439
\(297\) 3.75536 0.217908
\(298\) −10.8697 −0.629663
\(299\) 0 0
\(300\) −10.3101 −0.595252
\(301\) −8.68223 −0.500435
\(302\) 51.0930 2.94007
\(303\) −5.12814 −0.294604
\(304\) 32.5391 1.86625
\(305\) −32.9399 −1.88613
\(306\) 16.7645 0.958362
\(307\) 16.3679 0.934165 0.467083 0.884214i \(-0.345305\pi\)
0.467083 + 0.884214i \(0.345305\pi\)
\(308\) 9.79737 0.558257
\(309\) 1.48165 0.0842883
\(310\) −15.3456 −0.871569
\(311\) 23.6979 1.34378 0.671891 0.740650i \(-0.265482\pi\)
0.671891 + 0.740650i \(0.265482\pi\)
\(312\) 0 0
\(313\) −5.18025 −0.292805 −0.146403 0.989225i \(-0.546769\pi\)
−0.146403 + 0.989225i \(0.546769\pi\)
\(314\) 31.2856 1.76555
\(315\) 9.38444 0.528753
\(316\) 4.25596 0.239416
\(317\) −6.06537 −0.340665 −0.170332 0.985387i \(-0.554484\pi\)
−0.170332 + 0.985387i \(0.554484\pi\)
\(318\) −8.70294 −0.488037
\(319\) −5.04715 −0.282586
\(320\) −76.8686 −4.29709
\(321\) 6.61655 0.369300
\(322\) −4.89989 −0.273060
\(323\) 5.16959 0.287644
\(324\) 42.1248 2.34027
\(325\) 0 0
\(326\) 11.9087 0.659562
\(327\) 1.47773 0.0817188
\(328\) −37.7394 −2.08381
\(329\) −5.87774 −0.324050
\(330\) −5.62465 −0.309627
\(331\) −17.2749 −0.949512 −0.474756 0.880118i \(-0.657464\pi\)
−0.474756 + 0.880118i \(0.657464\pi\)
\(332\) −52.9151 −2.90410
\(333\) −17.0966 −0.936886
\(334\) −24.3804 −1.33403
\(335\) −2.69419 −0.147200
\(336\) −4.68850 −0.255779
\(337\) 8.35464 0.455106 0.227553 0.973766i \(-0.426927\pi\)
0.227553 + 0.973766i \(0.426927\pi\)
\(338\) 0 0
\(339\) −0.951279 −0.0516664
\(340\) −37.2315 −2.01916
\(341\) −3.21644 −0.174180
\(342\) 18.6940 1.01086
\(343\) 1.00000 0.0539949
\(344\) 77.6208 4.18504
\(345\) 2.04309 0.109997
\(346\) −16.4679 −0.885318
\(347\) 28.8220 1.54725 0.773623 0.633646i \(-0.218443\pi\)
0.773623 + 0.633646i \(0.218443\pi\)
\(348\) 5.01986 0.269093
\(349\) 11.7221 0.627467 0.313734 0.949511i \(-0.398420\pi\)
0.313734 + 0.949511i \(0.398420\pi\)
\(350\) −15.1794 −0.811376
\(351\) 0 0
\(352\) −34.6220 −1.84536
\(353\) 17.8362 0.949326 0.474663 0.880168i \(-0.342570\pi\)
0.474663 + 0.880168i \(0.342570\pi\)
\(354\) 10.0552 0.534426
\(355\) −7.67043 −0.407104
\(356\) −80.2113 −4.25119
\(357\) −0.744877 −0.0394231
\(358\) −10.4874 −0.554278
\(359\) 5.68162 0.299864 0.149932 0.988696i \(-0.452094\pi\)
0.149932 + 0.988696i \(0.452094\pi\)
\(360\) −83.8987 −4.42185
\(361\) −13.2354 −0.696601
\(362\) −17.7976 −0.935423
\(363\) 2.62651 0.137856
\(364\) 0 0
\(365\) 10.4091 0.544838
\(366\) 9.45462 0.494201
\(367\) −19.6316 −1.02476 −0.512381 0.858758i \(-0.671236\pi\)
−0.512381 + 0.858758i \(0.671236\pi\)
\(368\) 24.5658 1.28058
\(369\) −12.1587 −0.632958
\(370\) 52.2773 2.71777
\(371\) −9.30628 −0.483158
\(372\) 3.19905 0.165863
\(373\) 32.0645 1.66024 0.830119 0.557586i \(-0.188272\pi\)
0.830119 + 0.557586i \(0.188272\pi\)
\(374\) −10.7445 −0.555587
\(375\) 0.693612 0.0358180
\(376\) 52.5482 2.70997
\(377\) 0 0
\(378\) −5.49909 −0.282843
\(379\) −19.0231 −0.977150 −0.488575 0.872522i \(-0.662483\pi\)
−0.488575 + 0.872522i \(0.662483\pi\)
\(380\) −41.5167 −2.12976
\(381\) 3.36760 0.172527
\(382\) 37.1510 1.90081
\(383\) −0.699829 −0.0357596 −0.0178798 0.999840i \(-0.505692\pi\)
−0.0178798 + 0.999840i \(0.505692\pi\)
\(384\) 9.08689 0.463714
\(385\) −6.01459 −0.306532
\(386\) 61.5059 3.13057
\(387\) 25.0076 1.27121
\(388\) −48.9951 −2.48735
\(389\) −20.0547 −1.01681 −0.508407 0.861117i \(-0.669765\pi\)
−0.508407 + 0.861117i \(0.669765\pi\)
\(390\) 0 0
\(391\) 3.90284 0.197375
\(392\) −8.94020 −0.451548
\(393\) 6.45592 0.325658
\(394\) 39.2698 1.97838
\(395\) −2.61272 −0.131460
\(396\) −28.2195 −1.41809
\(397\) −22.2803 −1.11822 −0.559108 0.829095i \(-0.688856\pi\)
−0.559108 + 0.829095i \(0.688856\pi\)
\(398\) −64.4453 −3.23035
\(399\) −0.830609 −0.0415824
\(400\) 76.1027 3.80513
\(401\) 4.80749 0.240074 0.120037 0.992769i \(-0.461699\pi\)
0.120037 + 0.992769i \(0.461699\pi\)
\(402\) 0.773306 0.0385690
\(403\) 0 0
\(404\) 78.6717 3.91406
\(405\) −25.8604 −1.28501
\(406\) 7.39071 0.366795
\(407\) 10.9574 0.543137
\(408\) 6.65935 0.329687
\(409\) −36.8035 −1.81981 −0.909907 0.414811i \(-0.863848\pi\)
−0.909907 + 0.414811i \(0.863848\pi\)
\(410\) 37.1786 1.83612
\(411\) 2.91343 0.143709
\(412\) −22.7303 −1.11984
\(413\) 10.7523 0.529084
\(414\) 14.1132 0.693628
\(415\) 32.4845 1.59460
\(416\) 0 0
\(417\) 6.10122 0.298778
\(418\) −11.9812 −0.586019
\(419\) 29.2667 1.42977 0.714887 0.699240i \(-0.246478\pi\)
0.714887 + 0.699240i \(0.246478\pi\)
\(420\) 5.98206 0.291895
\(421\) −7.53862 −0.367410 −0.183705 0.982981i \(-0.558809\pi\)
−0.183705 + 0.982981i \(0.558809\pi\)
\(422\) −11.6650 −0.567845
\(423\) 16.9298 0.823154
\(424\) 83.2000 4.04055
\(425\) 12.0907 0.586484
\(426\) 2.20162 0.106669
\(427\) 10.1101 0.489261
\(428\) −101.506 −4.90646
\(429\) 0 0
\(430\) −76.4674 −3.68759
\(431\) −31.2261 −1.50411 −0.752055 0.659101i \(-0.770937\pi\)
−0.752055 + 0.659101i \(0.770937\pi\)
\(432\) 27.5699 1.32646
\(433\) 5.88404 0.282769 0.141384 0.989955i \(-0.454845\pi\)
0.141384 + 0.989955i \(0.454845\pi\)
\(434\) 4.70994 0.226084
\(435\) −3.08169 −0.147755
\(436\) −22.6702 −1.08570
\(437\) 4.35204 0.208186
\(438\) −2.98770 −0.142758
\(439\) −9.95642 −0.475194 −0.237597 0.971364i \(-0.576360\pi\)
−0.237597 + 0.971364i \(0.576360\pi\)
\(440\) 53.7716 2.56346
\(441\) −2.88032 −0.137158
\(442\) 0 0
\(443\) −35.8813 −1.70477 −0.852385 0.522915i \(-0.824845\pi\)
−0.852385 + 0.522915i \(0.824845\pi\)
\(444\) −10.8981 −0.517202
\(445\) 49.2416 2.33427
\(446\) 63.2404 2.99452
\(447\) −1.39108 −0.0657956
\(448\) 23.5929 1.11466
\(449\) 3.99528 0.188549 0.0942744 0.995546i \(-0.469947\pi\)
0.0942744 + 0.995546i \(0.469947\pi\)
\(450\) 43.7217 2.06106
\(451\) 7.79266 0.366942
\(452\) 14.5937 0.686432
\(453\) 6.53877 0.307218
\(454\) −72.2371 −3.39026
\(455\) 0 0
\(456\) 7.42580 0.347745
\(457\) 41.2222 1.92829 0.964147 0.265369i \(-0.0854937\pi\)
0.964147 + 0.265369i \(0.0854937\pi\)
\(458\) −8.12770 −0.379783
\(459\) 4.38011 0.204446
\(460\) −31.3435 −1.46140
\(461\) −24.7266 −1.15163 −0.575816 0.817579i \(-0.695316\pi\)
−0.575816 + 0.817579i \(0.695316\pi\)
\(462\) 1.72635 0.0803169
\(463\) 24.4057 1.13423 0.567115 0.823639i \(-0.308060\pi\)
0.567115 + 0.823639i \(0.308060\pi\)
\(464\) −37.0536 −1.72017
\(465\) −1.96389 −0.0910733
\(466\) 31.6674 1.46696
\(467\) −4.44860 −0.205857 −0.102928 0.994689i \(-0.532821\pi\)
−0.102928 + 0.994689i \(0.532821\pi\)
\(468\) 0 0
\(469\) 0.826916 0.0381834
\(470\) −51.7673 −2.38785
\(471\) 4.00386 0.184488
\(472\) −96.1273 −4.42462
\(473\) −16.0276 −0.736951
\(474\) 0.749922 0.0344450
\(475\) 13.4823 0.618608
\(476\) 11.4273 0.523769
\(477\) 26.8051 1.22732
\(478\) −3.86008 −0.176556
\(479\) 31.6766 1.44734 0.723671 0.690145i \(-0.242453\pi\)
0.723671 + 0.690145i \(0.242453\pi\)
\(480\) −21.1394 −0.964879
\(481\) 0 0
\(482\) 7.24372 0.329942
\(483\) −0.627077 −0.0285330
\(484\) −40.2938 −1.83153
\(485\) 30.0780 1.36577
\(486\) 23.9199 1.08503
\(487\) −26.9156 −1.21966 −0.609832 0.792531i \(-0.708763\pi\)
−0.609832 + 0.792531i \(0.708763\pi\)
\(488\) −90.3860 −4.09158
\(489\) 1.52405 0.0689200
\(490\) 8.80735 0.397875
\(491\) 9.72716 0.438980 0.219490 0.975615i \(-0.429561\pi\)
0.219490 + 0.975615i \(0.429561\pi\)
\(492\) −7.75052 −0.349421
\(493\) −5.88682 −0.265129
\(494\) 0 0
\(495\) 17.3239 0.778653
\(496\) −23.6134 −1.06027
\(497\) 2.35425 0.105602
\(498\) −9.32392 −0.417815
\(499\) 7.87525 0.352545 0.176272 0.984341i \(-0.443596\pi\)
0.176272 + 0.984341i \(0.443596\pi\)
\(500\) −10.6408 −0.475872
\(501\) −3.12015 −0.139398
\(502\) −29.5565 −1.31917
\(503\) −9.75206 −0.434823 −0.217411 0.976080i \(-0.569761\pi\)
−0.217411 + 0.976080i \(0.569761\pi\)
\(504\) 25.7506 1.14702
\(505\) −48.2964 −2.14916
\(506\) −9.04533 −0.402114
\(507\) 0 0
\(508\) −51.6630 −2.29217
\(509\) −23.0256 −1.02059 −0.510295 0.859999i \(-0.670464\pi\)
−0.510295 + 0.859999i \(0.670464\pi\)
\(510\) −6.56039 −0.290499
\(511\) −3.19482 −0.141331
\(512\) −11.8512 −0.523752
\(513\) 4.88424 0.215645
\(514\) −11.2220 −0.494981
\(515\) 13.9541 0.614891
\(516\) 15.9410 0.701762
\(517\) −10.8505 −0.477203
\(518\) −16.0452 −0.704987
\(519\) −2.10752 −0.0925100
\(520\) 0 0
\(521\) 0.486481 0.0213131 0.0106566 0.999943i \(-0.496608\pi\)
0.0106566 + 0.999943i \(0.496608\pi\)
\(522\) −21.2876 −0.931733
\(523\) −34.6270 −1.51413 −0.757065 0.653339i \(-0.773368\pi\)
−0.757065 + 0.653339i \(0.773368\pi\)
\(524\) −99.0414 −4.32664
\(525\) −1.94263 −0.0847834
\(526\) −10.9577 −0.477777
\(527\) −3.75154 −0.163420
\(528\) −8.65510 −0.376665
\(529\) −19.7144 −0.857147
\(530\) −81.9636 −3.56027
\(531\) −30.9699 −1.34398
\(532\) 12.7425 0.552458
\(533\) 0 0
\(534\) −14.1336 −0.611622
\(535\) 62.3141 2.69408
\(536\) −7.39279 −0.319320
\(537\) −1.34216 −0.0579185
\(538\) −10.8134 −0.466198
\(539\) 1.84603 0.0795140
\(540\) −35.1764 −1.51375
\(541\) −22.5384 −0.969002 −0.484501 0.874791i \(-0.660999\pi\)
−0.484501 + 0.874791i \(0.660999\pi\)
\(542\) −7.52844 −0.323374
\(543\) −2.27770 −0.0977456
\(544\) −40.3818 −1.73136
\(545\) 13.9172 0.596146
\(546\) 0 0
\(547\) 39.3716 1.68341 0.841704 0.539940i \(-0.181553\pi\)
0.841704 + 0.539940i \(0.181553\pi\)
\(548\) −44.6955 −1.90930
\(549\) −29.1202 −1.24282
\(550\) −28.0217 −1.19485
\(551\) −6.56436 −0.279651
\(552\) 5.60619 0.238615
\(553\) 0.801911 0.0341007
\(554\) −45.1227 −1.91708
\(555\) 6.69034 0.283989
\(556\) −93.6000 −3.96952
\(557\) −0.726975 −0.0308029 −0.0154015 0.999881i \(-0.504903\pi\)
−0.0154015 + 0.999881i \(0.504903\pi\)
\(558\) −13.5661 −0.574300
\(559\) 0 0
\(560\) −44.1559 −1.86593
\(561\) −1.37506 −0.0580552
\(562\) 36.1502 1.52490
\(563\) 41.6077 1.75355 0.876777 0.480897i \(-0.159689\pi\)
0.876777 + 0.480897i \(0.159689\pi\)
\(564\) 10.7918 0.454417
\(565\) −8.95907 −0.376911
\(566\) 51.0532 2.14593
\(567\) 7.93720 0.333331
\(568\) −21.0474 −0.883130
\(569\) −25.3888 −1.06435 −0.532177 0.846633i \(-0.678626\pi\)
−0.532177 + 0.846633i \(0.678626\pi\)
\(570\) −7.31546 −0.306411
\(571\) 16.9992 0.711393 0.355697 0.934602i \(-0.384244\pi\)
0.355697 + 0.934602i \(0.384244\pi\)
\(572\) 0 0
\(573\) 4.75451 0.198622
\(574\) −11.4110 −0.476288
\(575\) 10.1786 0.424476
\(576\) −67.9551 −2.83146
\(577\) −15.9759 −0.665084 −0.332542 0.943088i \(-0.607906\pi\)
−0.332542 + 0.943088i \(0.607906\pi\)
\(578\) 33.4223 1.39018
\(579\) 7.87139 0.327124
\(580\) 47.2767 1.96306
\(581\) −9.97031 −0.413638
\(582\) −8.63320 −0.357858
\(583\) −17.1796 −0.711508
\(584\) 28.5623 1.18192
\(585\) 0 0
\(586\) 9.23926 0.381670
\(587\) −15.9815 −0.659627 −0.329814 0.944046i \(-0.606986\pi\)
−0.329814 + 0.944046i \(0.606986\pi\)
\(588\) −1.83605 −0.0757172
\(589\) −4.18333 −0.172371
\(590\) 94.6989 3.89869
\(591\) 5.02566 0.206728
\(592\) 80.4433 3.30620
\(593\) 29.0532 1.19307 0.596536 0.802586i \(-0.296543\pi\)
0.596536 + 0.802586i \(0.296543\pi\)
\(594\) −10.1515 −0.416520
\(595\) −7.01520 −0.287595
\(596\) 21.3407 0.874151
\(597\) −8.24757 −0.337551
\(598\) 0 0
\(599\) 3.45554 0.141190 0.0705948 0.997505i \(-0.477510\pi\)
0.0705948 + 0.997505i \(0.477510\pi\)
\(600\) 17.3675 0.709026
\(601\) 15.5304 0.633497 0.316748 0.948510i \(-0.397409\pi\)
0.316748 + 0.948510i \(0.397409\pi\)
\(602\) 23.4698 0.956556
\(603\) −2.38178 −0.0969936
\(604\) −100.313 −4.08166
\(605\) 24.7363 1.00567
\(606\) 13.8624 0.563120
\(607\) 15.4784 0.628250 0.314125 0.949382i \(-0.398289\pi\)
0.314125 + 0.949382i \(0.398289\pi\)
\(608\) −45.0296 −1.82619
\(609\) 0.945847 0.0383276
\(610\) 89.0429 3.60524
\(611\) 0 0
\(612\) −32.9142 −1.33048
\(613\) −7.13223 −0.288068 −0.144034 0.989573i \(-0.546007\pi\)
−0.144034 + 0.989573i \(0.546007\pi\)
\(614\) −44.2456 −1.78561
\(615\) 4.75803 0.191862
\(616\) −16.5039 −0.664959
\(617\) 4.96685 0.199958 0.0999789 0.994990i \(-0.468122\pi\)
0.0999789 + 0.994990i \(0.468122\pi\)
\(618\) −4.00520 −0.161113
\(619\) 42.3570 1.70247 0.851235 0.524784i \(-0.175854\pi\)
0.851235 + 0.524784i \(0.175854\pi\)
\(620\) 30.1284 1.20999
\(621\) 3.68741 0.147971
\(622\) −64.0600 −2.56857
\(623\) −15.1135 −0.605508
\(624\) 0 0
\(625\) −21.5445 −0.861779
\(626\) 14.0032 0.559682
\(627\) −1.53333 −0.0612352
\(628\) −61.4239 −2.45108
\(629\) 12.7803 0.509583
\(630\) −25.3680 −1.01068
\(631\) −6.26775 −0.249515 −0.124758 0.992187i \(-0.539815\pi\)
−0.124758 + 0.992187i \(0.539815\pi\)
\(632\) −7.16924 −0.285177
\(633\) −1.49286 −0.0593361
\(634\) 16.3959 0.651163
\(635\) 31.7158 1.25860
\(636\) 17.0868 0.677534
\(637\) 0 0
\(638\) 13.6434 0.540149
\(639\) −6.78098 −0.268251
\(640\) 85.5797 3.38283
\(641\) −31.5637 −1.24669 −0.623345 0.781947i \(-0.714227\pi\)
−0.623345 + 0.781947i \(0.714227\pi\)
\(642\) −17.8858 −0.705897
\(643\) −18.2504 −0.719725 −0.359863 0.933005i \(-0.617176\pi\)
−0.359863 + 0.933005i \(0.617176\pi\)
\(644\) 9.62010 0.379085
\(645\) −9.78613 −0.385329
\(646\) −13.9744 −0.549816
\(647\) 23.0273 0.905298 0.452649 0.891689i \(-0.350479\pi\)
0.452649 + 0.891689i \(0.350479\pi\)
\(648\) −70.9601 −2.78758
\(649\) 19.8490 0.779140
\(650\) 0 0
\(651\) 0.602768 0.0236243
\(652\) −23.3807 −0.915660
\(653\) 28.8124 1.12752 0.563759 0.825939i \(-0.309355\pi\)
0.563759 + 0.825939i \(0.309355\pi\)
\(654\) −3.99460 −0.156201
\(655\) 60.8014 2.37571
\(656\) 57.2096 2.23366
\(657\) 9.20210 0.359008
\(658\) 15.8887 0.619406
\(659\) −31.2228 −1.21627 −0.608134 0.793835i \(-0.708082\pi\)
−0.608134 + 0.793835i \(0.708082\pi\)
\(660\) 11.0431 0.429850
\(661\) 26.5582 1.03299 0.516496 0.856289i \(-0.327236\pi\)
0.516496 + 0.856289i \(0.327236\pi\)
\(662\) 46.6973 1.81494
\(663\) 0 0
\(664\) 89.1366 3.45917
\(665\) −7.82261 −0.303348
\(666\) 46.2154 1.79081
\(667\) −4.95584 −0.191891
\(668\) 47.8667 1.85202
\(669\) 8.09337 0.312908
\(670\) 7.28293 0.281364
\(671\) 18.6635 0.720495
\(672\) 6.48823 0.250289
\(673\) −19.7386 −0.760867 −0.380434 0.924808i \(-0.624225\pi\)
−0.380434 + 0.924808i \(0.624225\pi\)
\(674\) −22.5842 −0.869912
\(675\) 11.4233 0.439683
\(676\) 0 0
\(677\) −13.1440 −0.505163 −0.252582 0.967576i \(-0.581280\pi\)
−0.252582 + 0.967576i \(0.581280\pi\)
\(678\) 2.57149 0.0987576
\(679\) −9.23171 −0.354280
\(680\) 62.7172 2.40510
\(681\) −9.24475 −0.354260
\(682\) 8.69468 0.332936
\(683\) −6.76255 −0.258762 −0.129381 0.991595i \(-0.541299\pi\)
−0.129381 + 0.991595i \(0.541299\pi\)
\(684\) −36.7025 −1.40336
\(685\) 27.4385 1.04837
\(686\) −2.70320 −0.103209
\(687\) −1.04017 −0.0396848
\(688\) −117.666 −4.48599
\(689\) 0 0
\(690\) −5.52288 −0.210253
\(691\) 9.17090 0.348877 0.174439 0.984668i \(-0.444189\pi\)
0.174439 + 0.984668i \(0.444189\pi\)
\(692\) 32.3319 1.22907
\(693\) −5.31715 −0.201982
\(694\) −77.9115 −2.95748
\(695\) 57.4609 2.17962
\(696\) −8.45605 −0.320526
\(697\) 9.08908 0.344273
\(698\) −31.6870 −1.19937
\(699\) 4.05272 0.153288
\(700\) 29.8023 1.12642
\(701\) −47.4700 −1.79292 −0.896459 0.443127i \(-0.853869\pi\)
−0.896459 + 0.443127i \(0.853869\pi\)
\(702\) 0 0
\(703\) 14.2512 0.537495
\(704\) 43.5532 1.64147
\(705\) −6.62507 −0.249515
\(706\) −48.2148 −1.81459
\(707\) 14.8234 0.557491
\(708\) −19.7416 −0.741936
\(709\) 34.9719 1.31340 0.656699 0.754153i \(-0.271952\pi\)
0.656699 + 0.754153i \(0.271952\pi\)
\(710\) 20.7347 0.778158
\(711\) −2.30976 −0.0866227
\(712\) 135.117 5.06374
\(713\) −3.15825 −0.118277
\(714\) 2.01355 0.0753552
\(715\) 0 0
\(716\) 20.5903 0.769496
\(717\) −0.494005 −0.0184490
\(718\) −15.3585 −0.573175
\(719\) −8.36101 −0.311813 −0.155907 0.987772i \(-0.549830\pi\)
−0.155907 + 0.987772i \(0.549830\pi\)
\(720\) 127.183 4.73984
\(721\) −4.28286 −0.159502
\(722\) 35.7779 1.33152
\(723\) 0.927035 0.0344768
\(724\) 34.9427 1.29863
\(725\) −15.3528 −0.570188
\(726\) −7.09997 −0.263505
\(727\) 27.4014 1.01626 0.508131 0.861280i \(-0.330337\pi\)
0.508131 + 0.861280i \(0.330337\pi\)
\(728\) 0 0
\(729\) −20.7504 −0.768532
\(730\) −28.1379 −1.04143
\(731\) −18.6941 −0.691425
\(732\) −18.5625 −0.686092
\(733\) −12.1569 −0.449026 −0.224513 0.974471i \(-0.572079\pi\)
−0.224513 + 0.974471i \(0.572079\pi\)
\(734\) 53.0681 1.95878
\(735\) 1.12715 0.0415754
\(736\) −33.9956 −1.25309
\(737\) 1.52651 0.0562297
\(738\) 32.8674 1.20987
\(739\) 48.4439 1.78204 0.891019 0.453966i \(-0.149991\pi\)
0.891019 + 0.453966i \(0.149991\pi\)
\(740\) −102.638 −3.77304
\(741\) 0 0
\(742\) 25.1567 0.923531
\(743\) −16.9906 −0.623326 −0.311663 0.950193i \(-0.600886\pi\)
−0.311663 + 0.950193i \(0.600886\pi\)
\(744\) −5.38886 −0.197565
\(745\) −13.1010 −0.479985
\(746\) −86.6767 −3.17346
\(747\) 28.7177 1.05073
\(748\) 21.0951 0.771313
\(749\) −19.1258 −0.698841
\(750\) −1.87497 −0.0684642
\(751\) 43.0323 1.57027 0.785136 0.619323i \(-0.212593\pi\)
0.785136 + 0.619323i \(0.212593\pi\)
\(752\) −79.6585 −2.90485
\(753\) −3.78258 −0.137845
\(754\) 0 0
\(755\) 61.5817 2.24119
\(756\) 10.7965 0.392666
\(757\) 29.1785 1.06051 0.530255 0.847838i \(-0.322096\pi\)
0.530255 + 0.847838i \(0.322096\pi\)
\(758\) 51.4231 1.86777
\(759\) −1.15760 −0.0420183
\(760\) 69.9357 2.53683
\(761\) −29.4251 −1.06666 −0.533330 0.845907i \(-0.679059\pi\)
−0.533330 + 0.845907i \(0.679059\pi\)
\(762\) −9.10328 −0.329777
\(763\) −4.27153 −0.154640
\(764\) −72.9398 −2.63887
\(765\) 20.2060 0.730550
\(766\) 1.89178 0.0683526
\(767\) 0 0
\(768\) −8.23976 −0.297327
\(769\) 17.1864 0.619759 0.309879 0.950776i \(-0.399711\pi\)
0.309879 + 0.950776i \(0.399711\pi\)
\(770\) 16.2586 0.585920
\(771\) −1.43617 −0.0517223
\(772\) −120.756 −4.34612
\(773\) −21.9601 −0.789851 −0.394926 0.918713i \(-0.629230\pi\)
−0.394926 + 0.918713i \(0.629230\pi\)
\(774\) −67.6004 −2.42985
\(775\) −9.78399 −0.351451
\(776\) 82.5333 2.96277
\(777\) −2.05343 −0.0736665
\(778\) 54.2118 1.94359
\(779\) 10.1352 0.363131
\(780\) 0 0
\(781\) 4.34600 0.155512
\(782\) −10.5501 −0.377272
\(783\) −5.56188 −0.198765
\(784\) 13.5526 0.484020
\(785\) 37.7081 1.34586
\(786\) −17.4516 −0.622478
\(787\) −2.33567 −0.0832578 −0.0416289 0.999133i \(-0.513255\pi\)
−0.0416289 + 0.999133i \(0.513255\pi\)
\(788\) −77.0996 −2.74656
\(789\) −1.40234 −0.0499246
\(790\) 7.06271 0.251280
\(791\) 2.74976 0.0977704
\(792\) 47.5364 1.68913
\(793\) 0 0
\(794\) 60.2280 2.13741
\(795\) −10.4895 −0.372025
\(796\) 126.527 4.48465
\(797\) 27.8040 0.984869 0.492434 0.870350i \(-0.336107\pi\)
0.492434 + 0.870350i \(0.336107\pi\)
\(798\) 2.24530 0.0794827
\(799\) −12.6556 −0.447723
\(800\) −105.315 −3.72346
\(801\) 43.5316 1.53811
\(802\) −12.9956 −0.458890
\(803\) −5.89773 −0.208126
\(804\) −1.51825 −0.0535447
\(805\) −5.90576 −0.208151
\(806\) 0 0
\(807\) −1.38387 −0.0487147
\(808\) −132.524 −4.66218
\(809\) 15.0203 0.528087 0.264043 0.964511i \(-0.414944\pi\)
0.264043 + 0.964511i \(0.414944\pi\)
\(810\) 69.9056 2.45623
\(811\) 43.6933 1.53428 0.767139 0.641481i \(-0.221680\pi\)
0.767139 + 0.641481i \(0.221680\pi\)
\(812\) −14.5104 −0.509215
\(813\) −0.963474 −0.0337905
\(814\) −29.6199 −1.03818
\(815\) 14.3534 0.502778
\(816\) −10.0950 −0.353395
\(817\) −20.8456 −0.729297
\(818\) 99.4870 3.47848
\(819\) 0 0
\(820\) −72.9939 −2.54906
\(821\) 18.0701 0.630651 0.315326 0.948984i \(-0.397886\pi\)
0.315326 + 0.948984i \(0.397886\pi\)
\(822\) −7.87557 −0.274692
\(823\) 4.45550 0.155309 0.0776544 0.996980i \(-0.475257\pi\)
0.0776544 + 0.996980i \(0.475257\pi\)
\(824\) 38.2896 1.33388
\(825\) −3.58615 −0.124854
\(826\) −29.0655 −1.01132
\(827\) −11.8352 −0.411549 −0.205774 0.978599i \(-0.565971\pi\)
−0.205774 + 0.978599i \(0.565971\pi\)
\(828\) −27.7090 −0.962953
\(829\) −3.53894 −0.122913 −0.0614563 0.998110i \(-0.519574\pi\)
−0.0614563 + 0.998110i \(0.519574\pi\)
\(830\) −87.8120 −3.04800
\(831\) −5.77471 −0.200323
\(832\) 0 0
\(833\) 2.15314 0.0746019
\(834\) −16.4928 −0.571099
\(835\) −29.3853 −1.01692
\(836\) 23.5230 0.813561
\(837\) −3.54447 −0.122515
\(838\) −79.1137 −2.73294
\(839\) −33.4853 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(840\) −10.0769 −0.347686
\(841\) −21.5249 −0.742238
\(842\) 20.3784 0.702285
\(843\) 4.62642 0.159343
\(844\) 22.9023 0.788330
\(845\) 0 0
\(846\) −45.7645 −1.57342
\(847\) −7.59218 −0.260870
\(848\) −126.124 −4.33112
\(849\) 6.53368 0.224235
\(850\) −32.6835 −1.12103
\(851\) 10.7591 0.368818
\(852\) −4.32250 −0.148087
\(853\) −22.0871 −0.756248 −0.378124 0.925755i \(-0.623431\pi\)
−0.378124 + 0.925755i \(0.623431\pi\)
\(854\) −27.3295 −0.935196
\(855\) 22.5316 0.770565
\(856\) 170.988 5.84426
\(857\) −6.89363 −0.235482 −0.117741 0.993044i \(-0.537565\pi\)
−0.117741 + 0.993044i \(0.537565\pi\)
\(858\) 0 0
\(859\) −37.4834 −1.27892 −0.639459 0.768825i \(-0.720842\pi\)
−0.639459 + 0.768825i \(0.720842\pi\)
\(860\) 150.131 5.11942
\(861\) −1.46036 −0.0497689
\(862\) 84.4103 2.87503
\(863\) −17.5248 −0.596552 −0.298276 0.954480i \(-0.596412\pi\)
−0.298276 + 0.954480i \(0.596412\pi\)
\(864\) −38.1528 −1.29799
\(865\) −19.8485 −0.674869
\(866\) −15.9057 −0.540498
\(867\) 4.27731 0.145265
\(868\) −9.24717 −0.313869
\(869\) 1.48035 0.0502174
\(870\) 8.33040 0.282427
\(871\) 0 0
\(872\) 38.1883 1.29322
\(873\) 26.5903 0.899944
\(874\) −11.7644 −0.397937
\(875\) −2.00495 −0.0677798
\(876\) 5.86584 0.198188
\(877\) 46.7491 1.57860 0.789302 0.614005i \(-0.210443\pi\)
0.789302 + 0.614005i \(0.210443\pi\)
\(878\) 26.9142 0.908309
\(879\) 1.18242 0.0398821
\(880\) −81.5131 −2.74781
\(881\) −2.91875 −0.0983350 −0.0491675 0.998791i \(-0.515657\pi\)
−0.0491675 + 0.998791i \(0.515657\pi\)
\(882\) 7.78607 0.262171
\(883\) −28.5505 −0.960801 −0.480400 0.877049i \(-0.659509\pi\)
−0.480400 + 0.877049i \(0.659509\pi\)
\(884\) 0 0
\(885\) 12.1194 0.407388
\(886\) 96.9941 3.25858
\(887\) 0.422914 0.0142001 0.00710004 0.999975i \(-0.497740\pi\)
0.00710004 + 0.999975i \(0.497740\pi\)
\(888\) 18.3581 0.616058
\(889\) −9.73438 −0.326480
\(890\) −133.110 −4.46184
\(891\) 14.6523 0.490870
\(892\) −124.162 −4.15725
\(893\) −14.1122 −0.472247
\(894\) 3.76035 0.125765
\(895\) −12.6404 −0.422521
\(896\) −26.2666 −0.877504
\(897\) 0 0
\(898\) −10.8000 −0.360401
\(899\) 4.76372 0.158879
\(900\) −85.8401 −2.86134
\(901\) −20.0377 −0.667553
\(902\) −21.0651 −0.701391
\(903\) 3.00361 0.0999539
\(904\) −24.5834 −0.817633
\(905\) −21.4512 −0.713063
\(906\) −17.6756 −0.587232
\(907\) −22.4284 −0.744723 −0.372361 0.928088i \(-0.621452\pi\)
−0.372361 + 0.928088i \(0.621452\pi\)
\(908\) 141.825 4.70664
\(909\) −42.6961 −1.41614
\(910\) 0 0
\(911\) −32.5788 −1.07938 −0.539692 0.841863i \(-0.681459\pi\)
−0.539692 + 0.841863i \(0.681459\pi\)
\(912\) −11.2569 −0.372752
\(913\) −18.4055 −0.609132
\(914\) −111.432 −3.68583
\(915\) 11.3955 0.376724
\(916\) 15.9574 0.527247
\(917\) −18.6615 −0.616256
\(918\) −11.8403 −0.390788
\(919\) −9.87913 −0.325883 −0.162941 0.986636i \(-0.552098\pi\)
−0.162941 + 0.986636i \(0.552098\pi\)
\(920\) 52.7987 1.74072
\(921\) −5.66246 −0.186584
\(922\) 66.8408 2.20129
\(923\) 0 0
\(924\) −3.38939 −0.111503
\(925\) 33.3309 1.09591
\(926\) −65.9734 −2.16802
\(927\) 12.3360 0.405168
\(928\) 51.2769 1.68325
\(929\) −29.9136 −0.981434 −0.490717 0.871319i \(-0.663265\pi\)
−0.490717 + 0.871319i \(0.663265\pi\)
\(930\) 5.30878 0.174082
\(931\) 2.40096 0.0786881
\(932\) −62.1736 −2.03656
\(933\) −8.19826 −0.268399
\(934\) 12.0255 0.393485
\(935\) −12.9502 −0.423518
\(936\) 0 0
\(937\) −31.8296 −1.03983 −0.519914 0.854219i \(-0.674036\pi\)
−0.519914 + 0.854219i \(0.674036\pi\)
\(938\) −2.23532 −0.0729856
\(939\) 1.79210 0.0584831
\(940\) 101.636 3.31501
\(941\) −42.0885 −1.37205 −0.686023 0.727580i \(-0.740645\pi\)
−0.686023 + 0.727580i \(0.740645\pi\)
\(942\) −10.8232 −0.352640
\(943\) 7.65167 0.249173
\(944\) 145.721 4.74280
\(945\) −6.62797 −0.215608
\(946\) 43.3258 1.40864
\(947\) −60.3377 −1.96071 −0.980357 0.197234i \(-0.936804\pi\)
−0.980357 + 0.197234i \(0.936804\pi\)
\(948\) −1.47234 −0.0478195
\(949\) 0 0
\(950\) −36.4452 −1.18244
\(951\) 2.09831 0.0680423
\(952\) −19.2495 −0.623880
\(953\) −17.3754 −0.562844 −0.281422 0.959584i \(-0.590806\pi\)
−0.281422 + 0.959584i \(0.590806\pi\)
\(954\) −72.4593 −2.34596
\(955\) 44.7776 1.44897
\(956\) 7.57862 0.245110
\(957\) 1.74606 0.0564421
\(958\) −85.6281 −2.76652
\(959\) −8.42156 −0.271946
\(960\) 26.5926 0.858274
\(961\) −27.9642 −0.902070
\(962\) 0 0
\(963\) 55.0883 1.77520
\(964\) −14.2218 −0.458054
\(965\) 74.1322 2.38640
\(966\) 1.69511 0.0545393
\(967\) 18.8630 0.606594 0.303297 0.952896i \(-0.401913\pi\)
0.303297 + 0.952896i \(0.401913\pi\)
\(968\) 67.8756 2.18160
\(969\) −1.78842 −0.0574522
\(970\) −81.3068 −2.61061
\(971\) −1.56446 −0.0502060 −0.0251030 0.999685i \(-0.507991\pi\)
−0.0251030 + 0.999685i \(0.507991\pi\)
\(972\) −46.9626 −1.50633
\(973\) −17.6362 −0.565390
\(974\) 72.7582 2.33132
\(975\) 0 0
\(976\) 137.017 4.38582
\(977\) −27.8755 −0.891817 −0.445909 0.895078i \(-0.647119\pi\)
−0.445909 + 0.895078i \(0.647119\pi\)
\(978\) −4.11981 −0.131737
\(979\) −27.8999 −0.891684
\(980\) −17.2917 −0.552364
\(981\) 12.3034 0.392817
\(982\) −26.2944 −0.839088
\(983\) −33.4239 −1.06606 −0.533029 0.846097i \(-0.678946\pi\)
−0.533029 + 0.846097i \(0.678946\pi\)
\(984\) 13.0559 0.416207
\(985\) 47.3313 1.50810
\(986\) 15.9132 0.506780
\(987\) 2.03340 0.0647238
\(988\) 0 0
\(989\) −15.7376 −0.500428
\(990\) −46.8300 −1.48835
\(991\) −18.9110 −0.600726 −0.300363 0.953825i \(-0.597108\pi\)
−0.300363 + 0.953825i \(0.597108\pi\)
\(992\) 32.6777 1.03752
\(993\) 5.97622 0.189650
\(994\) −6.36399 −0.201853
\(995\) −77.6750 −2.46246
\(996\) 18.3059 0.580046
\(997\) 43.5775 1.38011 0.690057 0.723755i \(-0.257585\pi\)
0.690057 + 0.723755i \(0.257585\pi\)
\(998\) −21.2884 −0.673871
\(999\) 12.0748 0.382031
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 1183.2.a.m.1.1 6
7.6 odd 2 8281.2.a.by.1.1 6
13.2 odd 12 91.2.q.a.43.1 yes 12
13.5 odd 4 1183.2.c.i.337.12 12
13.7 odd 12 91.2.q.a.36.1 12
13.8 odd 4 1183.2.c.i.337.1 12
13.12 even 2 1183.2.a.p.1.6 6
39.2 even 12 819.2.ct.a.316.6 12
39.20 even 12 819.2.ct.a.127.6 12
52.7 even 12 1456.2.cc.c.673.4 12
52.15 even 12 1456.2.cc.c.225.4 12
91.2 odd 12 637.2.k.h.459.6 12
91.20 even 12 637.2.q.h.491.1 12
91.33 even 12 637.2.u.i.361.6 12
91.41 even 12 637.2.q.h.589.1 12
91.46 odd 12 637.2.k.h.569.1 12
91.54 even 12 637.2.k.g.459.6 12
91.59 even 12 637.2.k.g.569.1 12
91.67 odd 12 637.2.u.h.30.6 12
91.72 odd 12 637.2.u.h.361.6 12
91.80 even 12 637.2.u.i.30.6 12
91.90 odd 2 8281.2.a.ch.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.q.a.36.1 12 13.7 odd 12
91.2.q.a.43.1 yes 12 13.2 odd 12
637.2.k.g.459.6 12 91.54 even 12
637.2.k.g.569.1 12 91.59 even 12
637.2.k.h.459.6 12 91.2 odd 12
637.2.k.h.569.1 12 91.46 odd 12
637.2.q.h.491.1 12 91.20 even 12
637.2.q.h.589.1 12 91.41 even 12
637.2.u.h.30.6 12 91.67 odd 12
637.2.u.h.361.6 12 91.72 odd 12
637.2.u.i.30.6 12 91.80 even 12
637.2.u.i.361.6 12 91.33 even 12
819.2.ct.a.127.6 12 39.20 even 12
819.2.ct.a.316.6 12 39.2 even 12
1183.2.a.m.1.1 6 1.1 even 1 trivial
1183.2.a.p.1.6 6 13.12 even 2
1183.2.c.i.337.1 12 13.8 odd 4
1183.2.c.i.337.12 12 13.5 odd 4
1456.2.cc.c.225.4 12 52.15 even 12
1456.2.cc.c.673.4 12 52.7 even 12
8281.2.a.by.1.1 6 7.6 odd 2
8281.2.a.ch.1.6 6 91.90 odd 2