Properties

Label 1339.2.a.g.1.19
Level $1339$
Weight $2$
Character 1339.1
Self dual yes
Analytic conductor $10.692$
Analytic rank $0$
Dimension $30$
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] = [1339,2,Mod(1,1339)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1339, 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("1339.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1339 = 13 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1339.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: \(10.6919688306\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) \(=\) 1339.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.903670 q^{2} +2.25573 q^{3} -1.18338 q^{4} +1.13079 q^{5} +2.03843 q^{6} +2.22819 q^{7} -2.87673 q^{8} +2.08831 q^{9} +O(q^{10})\) \(q+0.903670 q^{2} +2.25573 q^{3} -1.18338 q^{4} +1.13079 q^{5} +2.03843 q^{6} +2.22819 q^{7} -2.87673 q^{8} +2.08831 q^{9} +1.02186 q^{10} +2.22736 q^{11} -2.66938 q^{12} -1.00000 q^{13} +2.01355 q^{14} +2.55075 q^{15} -0.232853 q^{16} +3.96482 q^{17} +1.88714 q^{18} +4.47586 q^{19} -1.33815 q^{20} +5.02618 q^{21} +2.01280 q^{22} +0.0963147 q^{23} -6.48911 q^{24} -3.72132 q^{25} -0.903670 q^{26} -2.05653 q^{27} -2.63679 q^{28} -3.60531 q^{29} +2.30504 q^{30} +7.04913 q^{31} +5.54303 q^{32} +5.02431 q^{33} +3.58289 q^{34} +2.51961 q^{35} -2.47126 q^{36} -4.21245 q^{37} +4.04470 q^{38} -2.25573 q^{39} -3.25297 q^{40} +4.72050 q^{41} +4.54201 q^{42} +6.32020 q^{43} -2.63581 q^{44} +2.36143 q^{45} +0.0870367 q^{46} +4.12572 q^{47} -0.525252 q^{48} -2.03519 q^{49} -3.36285 q^{50} +8.94357 q^{51} +1.18338 q^{52} -6.20318 q^{53} -1.85842 q^{54} +2.51867 q^{55} -6.40988 q^{56} +10.0963 q^{57} -3.25802 q^{58} -8.61233 q^{59} -3.01851 q^{60} +1.39069 q^{61} +6.37009 q^{62} +4.65314 q^{63} +5.47478 q^{64} -1.13079 q^{65} +4.54032 q^{66} +1.77035 q^{67} -4.69189 q^{68} +0.217260 q^{69} +2.27689 q^{70} +8.33313 q^{71} -6.00749 q^{72} -10.8259 q^{73} -3.80667 q^{74} -8.39429 q^{75} -5.29664 q^{76} +4.96297 q^{77} -2.03843 q^{78} -4.74504 q^{79} -0.263307 q^{80} -10.9039 q^{81} +4.26578 q^{82} -10.3415 q^{83} -5.94788 q^{84} +4.48337 q^{85} +5.71137 q^{86} -8.13261 q^{87} -6.40749 q^{88} +1.80124 q^{89} +2.13396 q^{90} -2.22819 q^{91} -0.113977 q^{92} +15.9009 q^{93} +3.72829 q^{94} +5.06124 q^{95} +12.5036 q^{96} -10.1464 q^{97} -1.83914 q^{98} +4.65141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.903670 0.638991 0.319496 0.947588i \(-0.396486\pi\)
0.319496 + 0.947588i \(0.396486\pi\)
\(3\) 2.25573 1.30235 0.651173 0.758930i \(-0.274277\pi\)
0.651173 + 0.758930i \(0.274277\pi\)
\(4\) −1.18338 −0.591690
\(5\) 1.13079 0.505704 0.252852 0.967505i \(-0.418632\pi\)
0.252852 + 0.967505i \(0.418632\pi\)
\(6\) 2.03843 0.832188
\(7\) 2.22819 0.842175 0.421088 0.907020i \(-0.361648\pi\)
0.421088 + 0.907020i \(0.361648\pi\)
\(8\) −2.87673 −1.01708
\(9\) 2.08831 0.696103
\(10\) 1.02186 0.323140
\(11\) 2.22736 0.671573 0.335787 0.941938i \(-0.390998\pi\)
0.335787 + 0.941938i \(0.390998\pi\)
\(12\) −2.66938 −0.770585
\(13\) −1.00000 −0.277350
\(14\) 2.01355 0.538143
\(15\) 2.55075 0.658601
\(16\) −0.232853 −0.0582132
\(17\) 3.96482 0.961611 0.480806 0.876827i \(-0.340344\pi\)
0.480806 + 0.876827i \(0.340344\pi\)
\(18\) 1.88714 0.444804
\(19\) 4.47586 1.02683 0.513416 0.858140i \(-0.328380\pi\)
0.513416 + 0.858140i \(0.328380\pi\)
\(20\) −1.33815 −0.299220
\(21\) 5.02618 1.09680
\(22\) 2.01280 0.429130
\(23\) 0.0963147 0.0200830 0.0100415 0.999950i \(-0.496804\pi\)
0.0100415 + 0.999950i \(0.496804\pi\)
\(24\) −6.48911 −1.32458
\(25\) −3.72132 −0.744264
\(26\) −0.903670 −0.177224
\(27\) −2.05653 −0.395779
\(28\) −2.63679 −0.498307
\(29\) −3.60531 −0.669490 −0.334745 0.942309i \(-0.608650\pi\)
−0.334745 + 0.942309i \(0.608650\pi\)
\(30\) 2.30504 0.420840
\(31\) 7.04913 1.26606 0.633030 0.774127i \(-0.281811\pi\)
0.633030 + 0.774127i \(0.281811\pi\)
\(32\) 5.54303 0.979879
\(33\) 5.02431 0.874620
\(34\) 3.58289 0.614461
\(35\) 2.51961 0.425891
\(36\) −2.47126 −0.411877
\(37\) −4.21245 −0.692522 −0.346261 0.938138i \(-0.612549\pi\)
−0.346261 + 0.938138i \(0.612549\pi\)
\(38\) 4.04470 0.656137
\(39\) −2.25573 −0.361206
\(40\) −3.25297 −0.514339
\(41\) 4.72050 0.737218 0.368609 0.929585i \(-0.379834\pi\)
0.368609 + 0.929585i \(0.379834\pi\)
\(42\) 4.54201 0.700848
\(43\) 6.32020 0.963821 0.481910 0.876220i \(-0.339943\pi\)
0.481910 + 0.876220i \(0.339943\pi\)
\(44\) −2.63581 −0.397363
\(45\) 2.36143 0.352022
\(46\) 0.0870367 0.0128329
\(47\) 4.12572 0.601797 0.300899 0.953656i \(-0.402713\pi\)
0.300899 + 0.953656i \(0.402713\pi\)
\(48\) −0.525252 −0.0758137
\(49\) −2.03519 −0.290741
\(50\) −3.36285 −0.475578
\(51\) 8.94357 1.25235
\(52\) 1.18338 0.164105
\(53\) −6.20318 −0.852073 −0.426036 0.904706i \(-0.640090\pi\)
−0.426036 + 0.904706i \(0.640090\pi\)
\(54\) −1.85842 −0.252899
\(55\) 2.51867 0.339617
\(56\) −6.40988 −0.856557
\(57\) 10.0963 1.33729
\(58\) −3.25802 −0.427798
\(59\) −8.61233 −1.12123 −0.560615 0.828077i \(-0.689435\pi\)
−0.560615 + 0.828077i \(0.689435\pi\)
\(60\) −3.01851 −0.389687
\(61\) 1.39069 0.178059 0.0890297 0.996029i \(-0.471623\pi\)
0.0890297 + 0.996029i \(0.471623\pi\)
\(62\) 6.37009 0.809002
\(63\) 4.65314 0.586241
\(64\) 5.47478 0.684347
\(65\) −1.13079 −0.140257
\(66\) 4.54032 0.558875
\(67\) 1.77035 0.216283 0.108141 0.994136i \(-0.465510\pi\)
0.108141 + 0.994136i \(0.465510\pi\)
\(68\) −4.69189 −0.568976
\(69\) 0.217260 0.0261550
\(70\) 2.27689 0.272141
\(71\) 8.33313 0.988961 0.494480 0.869189i \(-0.335358\pi\)
0.494480 + 0.869189i \(0.335358\pi\)
\(72\) −6.00749 −0.707990
\(73\) −10.8259 −1.26708 −0.633540 0.773710i \(-0.718399\pi\)
−0.633540 + 0.773710i \(0.718399\pi\)
\(74\) −3.80667 −0.442516
\(75\) −8.39429 −0.969289
\(76\) −5.29664 −0.607566
\(77\) 4.96297 0.565582
\(78\) −2.03843 −0.230807
\(79\) −4.74504 −0.533858 −0.266929 0.963716i \(-0.586009\pi\)
−0.266929 + 0.963716i \(0.586009\pi\)
\(80\) −0.263307 −0.0294386
\(81\) −10.9039 −1.21154
\(82\) 4.26578 0.471076
\(83\) −10.3415 −1.13513 −0.567565 0.823329i \(-0.692114\pi\)
−0.567565 + 0.823329i \(0.692114\pi\)
\(84\) −5.94788 −0.648967
\(85\) 4.48337 0.486290
\(86\) 5.71137 0.615873
\(87\) −8.13261 −0.871907
\(88\) −6.40749 −0.683041
\(89\) 1.80124 0.190931 0.0954655 0.995433i \(-0.469566\pi\)
0.0954655 + 0.995433i \(0.469566\pi\)
\(90\) 2.13396 0.224939
\(91\) −2.22819 −0.233577
\(92\) −0.113977 −0.0118829
\(93\) 15.9009 1.64885
\(94\) 3.72829 0.384543
\(95\) 5.06124 0.519273
\(96\) 12.5036 1.27614
\(97\) −10.1464 −1.03021 −0.515107 0.857126i \(-0.672248\pi\)
−0.515107 + 0.857126i \(0.672248\pi\)
\(98\) −1.83914 −0.185781
\(99\) 4.65141 0.467484
\(100\) 4.40373 0.440373
\(101\) −1.09105 −0.108564 −0.0542818 0.998526i \(-0.517287\pi\)
−0.0542818 + 0.998526i \(0.517287\pi\)
\(102\) 8.08204 0.800241
\(103\) 1.00000 0.0985329
\(104\) 2.87673 0.282086
\(105\) 5.68354 0.554657
\(106\) −5.60563 −0.544467
\(107\) 5.80619 0.561305 0.280653 0.959809i \(-0.409449\pi\)
0.280653 + 0.959809i \(0.409449\pi\)
\(108\) 2.43365 0.234178
\(109\) 16.7131 1.60082 0.800412 0.599450i \(-0.204614\pi\)
0.800412 + 0.599450i \(0.204614\pi\)
\(110\) 2.27604 0.217012
\(111\) −9.50214 −0.901903
\(112\) −0.518839 −0.0490257
\(113\) −8.03065 −0.755460 −0.377730 0.925916i \(-0.623295\pi\)
−0.377730 + 0.925916i \(0.623295\pi\)
\(114\) 9.12374 0.854517
\(115\) 0.108911 0.0101560
\(116\) 4.26646 0.396130
\(117\) −2.08831 −0.193064
\(118\) −7.78271 −0.716456
\(119\) 8.83437 0.809845
\(120\) −7.33781 −0.669847
\(121\) −6.03888 −0.548989
\(122\) 1.25672 0.113778
\(123\) 10.6482 0.960113
\(124\) −8.34179 −0.749115
\(125\) −9.86196 −0.882080
\(126\) 4.20491 0.374603
\(127\) −12.8089 −1.13660 −0.568301 0.822820i \(-0.692399\pi\)
−0.568301 + 0.822820i \(0.692399\pi\)
\(128\) −6.13867 −0.542587
\(129\) 14.2566 1.25523
\(130\) −1.02186 −0.0896230
\(131\) 10.2802 0.898184 0.449092 0.893486i \(-0.351748\pi\)
0.449092 + 0.893486i \(0.351748\pi\)
\(132\) −5.94567 −0.517504
\(133\) 9.97304 0.864772
\(134\) 1.59981 0.138203
\(135\) −2.32549 −0.200147
\(136\) −11.4057 −0.978032
\(137\) −10.2616 −0.876704 −0.438352 0.898803i \(-0.644438\pi\)
−0.438352 + 0.898803i \(0.644438\pi\)
\(138\) 0.196331 0.0167128
\(139\) 3.75566 0.318551 0.159275 0.987234i \(-0.449084\pi\)
0.159275 + 0.987234i \(0.449084\pi\)
\(140\) −2.98165 −0.251995
\(141\) 9.30649 0.783748
\(142\) 7.53041 0.631938
\(143\) −2.22736 −0.186261
\(144\) −0.486269 −0.0405224
\(145\) −4.07684 −0.338563
\(146\) −9.78308 −0.809654
\(147\) −4.59082 −0.378645
\(148\) 4.98493 0.409758
\(149\) −11.1166 −0.910707 −0.455353 0.890311i \(-0.650487\pi\)
−0.455353 + 0.890311i \(0.650487\pi\)
\(150\) −7.58567 −0.619367
\(151\) −3.13721 −0.255303 −0.127651 0.991819i \(-0.540744\pi\)
−0.127651 + 0.991819i \(0.540744\pi\)
\(152\) −12.8758 −1.04437
\(153\) 8.27978 0.669381
\(154\) 4.48488 0.361402
\(155\) 7.97106 0.640251
\(156\) 2.66938 0.213722
\(157\) −4.44102 −0.354432 −0.177216 0.984172i \(-0.556709\pi\)
−0.177216 + 0.984172i \(0.556709\pi\)
\(158\) −4.28795 −0.341131
\(159\) −13.9927 −1.10969
\(160\) 6.26799 0.495528
\(161\) 0.214607 0.0169134
\(162\) −9.85352 −0.774166
\(163\) −18.9769 −1.48639 −0.743193 0.669077i \(-0.766689\pi\)
−0.743193 + 0.669077i \(0.766689\pi\)
\(164\) −5.58614 −0.436205
\(165\) 5.68143 0.442299
\(166\) −9.34532 −0.725338
\(167\) 6.23721 0.482649 0.241325 0.970444i \(-0.422418\pi\)
0.241325 + 0.970444i \(0.422418\pi\)
\(168\) −14.4590 −1.11553
\(169\) 1.00000 0.0769231
\(170\) 4.05149 0.310735
\(171\) 9.34697 0.714781
\(172\) −7.47919 −0.570283
\(173\) −6.83448 −0.519616 −0.259808 0.965660i \(-0.583659\pi\)
−0.259808 + 0.965660i \(0.583659\pi\)
\(174\) −7.34920 −0.557141
\(175\) −8.29179 −0.626801
\(176\) −0.518646 −0.0390944
\(177\) −19.4271 −1.46023
\(178\) 1.62773 0.122003
\(179\) 5.66656 0.423539 0.211769 0.977320i \(-0.432077\pi\)
0.211769 + 0.977320i \(0.432077\pi\)
\(180\) −2.79447 −0.208288
\(181\) −2.76231 −0.205321 −0.102661 0.994716i \(-0.532736\pi\)
−0.102661 + 0.994716i \(0.532736\pi\)
\(182\) −2.01355 −0.149254
\(183\) 3.13701 0.231895
\(184\) −0.277071 −0.0204259
\(185\) −4.76338 −0.350211
\(186\) 14.3692 1.05360
\(187\) 8.83108 0.645792
\(188\) −4.88229 −0.356077
\(189\) −4.58232 −0.333315
\(190\) 4.57369 0.331811
\(191\) −5.53593 −0.400566 −0.200283 0.979738i \(-0.564186\pi\)
−0.200283 + 0.979738i \(0.564186\pi\)
\(192\) 12.3496 0.891256
\(193\) 12.8074 0.921899 0.460950 0.887426i \(-0.347509\pi\)
0.460950 + 0.887426i \(0.347509\pi\)
\(194\) −9.16904 −0.658299
\(195\) −2.55075 −0.182663
\(196\) 2.40840 0.172028
\(197\) 0.250974 0.0178812 0.00894058 0.999960i \(-0.497154\pi\)
0.00894058 + 0.999960i \(0.497154\pi\)
\(198\) 4.20334 0.298718
\(199\) 6.22262 0.441110 0.220555 0.975375i \(-0.429213\pi\)
0.220555 + 0.975375i \(0.429213\pi\)
\(200\) 10.7052 0.756973
\(201\) 3.99343 0.281675
\(202\) −0.985950 −0.0693712
\(203\) −8.03331 −0.563828
\(204\) −10.5836 −0.741003
\(205\) 5.33788 0.372814
\(206\) 0.903670 0.0629617
\(207\) 0.201135 0.0139798
\(208\) 0.232853 0.0161454
\(209\) 9.96933 0.689593
\(210\) 5.13605 0.354421
\(211\) 4.89217 0.336791 0.168395 0.985720i \(-0.446141\pi\)
0.168395 + 0.985720i \(0.446141\pi\)
\(212\) 7.34072 0.504163
\(213\) 18.7973 1.28797
\(214\) 5.24688 0.358669
\(215\) 7.14680 0.487408
\(216\) 5.91606 0.402537
\(217\) 15.7068 1.06624
\(218\) 15.1031 1.02291
\(219\) −24.4204 −1.65018
\(220\) −2.98054 −0.200948
\(221\) −3.96482 −0.266703
\(222\) −8.58680 −0.576308
\(223\) 1.67018 0.111843 0.0559216 0.998435i \(-0.482190\pi\)
0.0559216 + 0.998435i \(0.482190\pi\)
\(224\) 12.3509 0.825230
\(225\) −7.77127 −0.518084
\(226\) −7.25706 −0.482733
\(227\) −8.25340 −0.547798 −0.273899 0.961759i \(-0.588313\pi\)
−0.273899 + 0.961759i \(0.588313\pi\)
\(228\) −11.9478 −0.791261
\(229\) 3.90549 0.258082 0.129041 0.991639i \(-0.458810\pi\)
0.129041 + 0.991639i \(0.458810\pi\)
\(230\) 0.0984201 0.00648963
\(231\) 11.1951 0.736584
\(232\) 10.3715 0.680922
\(233\) −26.3188 −1.72420 −0.862100 0.506738i \(-0.830851\pi\)
−0.862100 + 0.506738i \(0.830851\pi\)
\(234\) −1.88714 −0.123366
\(235\) 4.66531 0.304331
\(236\) 10.1917 0.663420
\(237\) −10.7035 −0.695268
\(238\) 7.98336 0.517484
\(239\) 17.1497 1.10932 0.554660 0.832077i \(-0.312849\pi\)
0.554660 + 0.832077i \(0.312849\pi\)
\(240\) −0.593949 −0.0383392
\(241\) −15.7608 −1.01524 −0.507622 0.861580i \(-0.669475\pi\)
−0.507622 + 0.861580i \(0.669475\pi\)
\(242\) −5.45716 −0.350800
\(243\) −18.4266 −1.18207
\(244\) −1.64571 −0.105356
\(245\) −2.30136 −0.147029
\(246\) 9.62243 0.613504
\(247\) −4.47586 −0.284792
\(248\) −20.2784 −1.28768
\(249\) −23.3277 −1.47833
\(250\) −8.91196 −0.563642
\(251\) 26.6394 1.68146 0.840732 0.541452i \(-0.182125\pi\)
0.840732 + 0.541452i \(0.182125\pi\)
\(252\) −5.50644 −0.346873
\(253\) 0.214527 0.0134872
\(254\) −11.5750 −0.726280
\(255\) 10.1133 0.633318
\(256\) −16.4969 −1.03106
\(257\) −26.6341 −1.66139 −0.830695 0.556728i \(-0.812056\pi\)
−0.830695 + 0.556728i \(0.812056\pi\)
\(258\) 12.8833 0.802080
\(259\) −9.38612 −0.583225
\(260\) 1.33815 0.0829886
\(261\) −7.52901 −0.466034
\(262\) 9.28990 0.573932
\(263\) 18.4550 1.13799 0.568993 0.822342i \(-0.307333\pi\)
0.568993 + 0.822342i \(0.307333\pi\)
\(264\) −14.4536 −0.889555
\(265\) −7.01448 −0.430896
\(266\) 9.01234 0.552582
\(267\) 4.06311 0.248658
\(268\) −2.09500 −0.127972
\(269\) −9.81711 −0.598560 −0.299280 0.954165i \(-0.596746\pi\)
−0.299280 + 0.954165i \(0.596746\pi\)
\(270\) −2.10148 −0.127892
\(271\) −11.4232 −0.693907 −0.346954 0.937882i \(-0.612784\pi\)
−0.346954 + 0.937882i \(0.612784\pi\)
\(272\) −0.923220 −0.0559784
\(273\) −5.02618 −0.304198
\(274\) −9.27306 −0.560206
\(275\) −8.28871 −0.499828
\(276\) −0.257101 −0.0154757
\(277\) 23.8560 1.43337 0.716683 0.697399i \(-0.245659\pi\)
0.716683 + 0.697399i \(0.245659\pi\)
\(278\) 3.39388 0.203551
\(279\) 14.7208 0.881309
\(280\) −7.24821 −0.433164
\(281\) 17.9354 1.06994 0.534968 0.844872i \(-0.320323\pi\)
0.534968 + 0.844872i \(0.320323\pi\)
\(282\) 8.41000 0.500808
\(283\) −11.0837 −0.658856 −0.329428 0.944181i \(-0.606856\pi\)
−0.329428 + 0.944181i \(0.606856\pi\)
\(284\) −9.86126 −0.585158
\(285\) 11.4168 0.676272
\(286\) −2.01280 −0.119019
\(287\) 10.5182 0.620867
\(288\) 11.5756 0.682097
\(289\) −1.28017 −0.0753040
\(290\) −3.68412 −0.216339
\(291\) −22.8876 −1.34170
\(292\) 12.8112 0.749719
\(293\) 11.2580 0.657699 0.328849 0.944382i \(-0.393339\pi\)
0.328849 + 0.944382i \(0.393339\pi\)
\(294\) −4.14859 −0.241951
\(295\) −9.73871 −0.567010
\(296\) 12.1181 0.704348
\(297\) −4.58062 −0.265794
\(298\) −10.0457 −0.581934
\(299\) −0.0963147 −0.00557002
\(300\) 9.93363 0.573518
\(301\) 14.0826 0.811706
\(302\) −2.83501 −0.163136
\(303\) −2.46111 −0.141387
\(304\) −1.04222 −0.0597751
\(305\) 1.57257 0.0900452
\(306\) 7.48219 0.427728
\(307\) 2.03265 0.116009 0.0580047 0.998316i \(-0.481526\pi\)
0.0580047 + 0.998316i \(0.481526\pi\)
\(308\) −5.87307 −0.334649
\(309\) 2.25573 0.128324
\(310\) 7.20321 0.409115
\(311\) −9.81849 −0.556755 −0.278378 0.960472i \(-0.589797\pi\)
−0.278378 + 0.960472i \(0.589797\pi\)
\(312\) 6.48911 0.367374
\(313\) 11.5664 0.653773 0.326887 0.945064i \(-0.394000\pi\)
0.326887 + 0.945064i \(0.394000\pi\)
\(314\) −4.01322 −0.226479
\(315\) 5.26172 0.296464
\(316\) 5.61518 0.315879
\(317\) −3.10943 −0.174643 −0.0873215 0.996180i \(-0.527831\pi\)
−0.0873215 + 0.996180i \(0.527831\pi\)
\(318\) −12.6448 −0.709084
\(319\) −8.03032 −0.449612
\(320\) 6.19081 0.346077
\(321\) 13.0972 0.731013
\(322\) 0.193934 0.0108075
\(323\) 17.7460 0.987413
\(324\) 12.9034 0.716858
\(325\) 3.72132 0.206422
\(326\) −17.1489 −0.949788
\(327\) 37.7002 2.08483
\(328\) −13.5796 −0.749807
\(329\) 9.19286 0.506819
\(330\) 5.13414 0.282625
\(331\) −0.0569490 −0.00313020 −0.00156510 0.999999i \(-0.500498\pi\)
−0.00156510 + 0.999999i \(0.500498\pi\)
\(332\) 12.2379 0.671644
\(333\) −8.79690 −0.482067
\(334\) 5.63638 0.308409
\(335\) 2.00189 0.109375
\(336\) −1.17036 −0.0638484
\(337\) −1.80926 −0.0985565 −0.0492783 0.998785i \(-0.515692\pi\)
−0.0492783 + 0.998785i \(0.515692\pi\)
\(338\) 0.903670 0.0491532
\(339\) −18.1150 −0.983870
\(340\) −5.30553 −0.287733
\(341\) 15.7009 0.850252
\(342\) 8.44658 0.456739
\(343\) −20.1321 −1.08703
\(344\) −18.1815 −0.980279
\(345\) 0.245675 0.0132267
\(346\) −6.17612 −0.332030
\(347\) −12.2642 −0.658377 −0.329188 0.944264i \(-0.606775\pi\)
−0.329188 + 0.944264i \(0.606775\pi\)
\(348\) 9.62396 0.515899
\(349\) −18.1887 −0.973618 −0.486809 0.873508i \(-0.661839\pi\)
−0.486809 + 0.873508i \(0.661839\pi\)
\(350\) −7.49305 −0.400520
\(351\) 2.05653 0.109769
\(352\) 12.3463 0.658060
\(353\) 6.08261 0.323744 0.161872 0.986812i \(-0.448247\pi\)
0.161872 + 0.986812i \(0.448247\pi\)
\(354\) −17.5557 −0.933073
\(355\) 9.42300 0.500121
\(356\) −2.13155 −0.112972
\(357\) 19.9279 1.05470
\(358\) 5.12071 0.270638
\(359\) −1.98443 −0.104734 −0.0523670 0.998628i \(-0.516677\pi\)
−0.0523670 + 0.998628i \(0.516677\pi\)
\(360\) −6.79320 −0.358033
\(361\) 1.03329 0.0543836
\(362\) −2.49622 −0.131198
\(363\) −13.6221 −0.714974
\(364\) 2.63679 0.138205
\(365\) −12.2418 −0.640767
\(366\) 2.83483 0.148179
\(367\) 24.7346 1.29113 0.645567 0.763704i \(-0.276621\pi\)
0.645567 + 0.763704i \(0.276621\pi\)
\(368\) −0.0224271 −0.00116910
\(369\) 9.85786 0.513180
\(370\) −4.30453 −0.223782
\(371\) −13.8219 −0.717595
\(372\) −18.8168 −0.975607
\(373\) 6.09102 0.315381 0.157691 0.987489i \(-0.449595\pi\)
0.157691 + 0.987489i \(0.449595\pi\)
\(374\) 7.98038 0.412656
\(375\) −22.2459 −1.14877
\(376\) −11.8686 −0.612074
\(377\) 3.60531 0.185683
\(378\) −4.14091 −0.212985
\(379\) 4.59817 0.236192 0.118096 0.993002i \(-0.462321\pi\)
0.118096 + 0.993002i \(0.462321\pi\)
\(380\) −5.98937 −0.307248
\(381\) −28.8933 −1.48025
\(382\) −5.00265 −0.255958
\(383\) −1.09401 −0.0559012 −0.0279506 0.999609i \(-0.508898\pi\)
−0.0279506 + 0.999609i \(0.508898\pi\)
\(384\) −13.8472 −0.706635
\(385\) 5.61206 0.286017
\(386\) 11.5737 0.589086
\(387\) 13.1985 0.670919
\(388\) 12.0071 0.609568
\(389\) 26.9512 1.36648 0.683240 0.730193i \(-0.260570\pi\)
0.683240 + 0.730193i \(0.260570\pi\)
\(390\) −2.30504 −0.116720
\(391\) 0.381871 0.0193120
\(392\) 5.85467 0.295706
\(393\) 23.1893 1.16975
\(394\) 0.226798 0.0114259
\(395\) −5.36563 −0.269974
\(396\) −5.50438 −0.276606
\(397\) −35.0178 −1.75749 −0.878747 0.477288i \(-0.841620\pi\)
−0.878747 + 0.477288i \(0.841620\pi\)
\(398\) 5.62319 0.281865
\(399\) 22.4965 1.12623
\(400\) 0.866519 0.0433260
\(401\) −11.8182 −0.590173 −0.295087 0.955471i \(-0.595348\pi\)
−0.295087 + 0.955471i \(0.595348\pi\)
\(402\) 3.60874 0.179988
\(403\) −7.04913 −0.351142
\(404\) 1.29113 0.0642360
\(405\) −12.3300 −0.612682
\(406\) −7.25947 −0.360281
\(407\) −9.38262 −0.465079
\(408\) −25.7282 −1.27374
\(409\) −2.64552 −0.130813 −0.0654063 0.997859i \(-0.520834\pi\)
−0.0654063 + 0.997859i \(0.520834\pi\)
\(410\) 4.82369 0.238225
\(411\) −23.1473 −1.14177
\(412\) −1.18338 −0.0583009
\(413\) −19.1899 −0.944272
\(414\) 0.181760 0.00893300
\(415\) −11.6941 −0.574039
\(416\) −5.54303 −0.271769
\(417\) 8.47175 0.414863
\(418\) 9.00899 0.440644
\(419\) 17.6740 0.863430 0.431715 0.902010i \(-0.357909\pi\)
0.431715 + 0.902010i \(0.357909\pi\)
\(420\) −6.72579 −0.328185
\(421\) 27.6691 1.34851 0.674254 0.738499i \(-0.264465\pi\)
0.674254 + 0.738499i \(0.264465\pi\)
\(422\) 4.42091 0.215207
\(423\) 8.61577 0.418913
\(424\) 17.8449 0.866623
\(425\) −14.7544 −0.715692
\(426\) 16.9865 0.823001
\(427\) 3.09871 0.149957
\(428\) −6.87092 −0.332119
\(429\) −5.02431 −0.242576
\(430\) 6.45835 0.311449
\(431\) 34.0927 1.64219 0.821095 0.570792i \(-0.193364\pi\)
0.821095 + 0.570792i \(0.193364\pi\)
\(432\) 0.478868 0.0230395
\(433\) 16.1001 0.773721 0.386860 0.922138i \(-0.373560\pi\)
0.386860 + 0.922138i \(0.373560\pi\)
\(434\) 14.1937 0.681321
\(435\) −9.19625 −0.440926
\(436\) −19.7779 −0.947191
\(437\) 0.431091 0.0206219
\(438\) −22.0680 −1.05445
\(439\) 12.3597 0.589897 0.294948 0.955513i \(-0.404698\pi\)
0.294948 + 0.955513i \(0.404698\pi\)
\(440\) −7.24551 −0.345416
\(441\) −4.25010 −0.202386
\(442\) −3.58289 −0.170421
\(443\) −14.9741 −0.711440 −0.355720 0.934593i \(-0.615764\pi\)
−0.355720 + 0.934593i \(0.615764\pi\)
\(444\) 11.2446 0.533647
\(445\) 2.03682 0.0965545
\(446\) 1.50929 0.0714669
\(447\) −25.0760 −1.18605
\(448\) 12.1988 0.576340
\(449\) −9.90349 −0.467375 −0.233687 0.972312i \(-0.575079\pi\)
−0.233687 + 0.972312i \(0.575079\pi\)
\(450\) −7.02266 −0.331052
\(451\) 10.5142 0.495096
\(452\) 9.50331 0.446998
\(453\) −7.07670 −0.332492
\(454\) −7.45836 −0.350038
\(455\) −2.51961 −0.118121
\(456\) −29.0443 −1.36013
\(457\) 34.1375 1.59689 0.798443 0.602071i \(-0.205658\pi\)
0.798443 + 0.602071i \(0.205658\pi\)
\(458\) 3.52927 0.164912
\(459\) −8.15376 −0.380585
\(460\) −0.128884 −0.00600923
\(461\) −19.8327 −0.923700 −0.461850 0.886958i \(-0.652814\pi\)
−0.461850 + 0.886958i \(0.652814\pi\)
\(462\) 10.1167 0.470671
\(463\) 5.86990 0.272797 0.136399 0.990654i \(-0.456447\pi\)
0.136399 + 0.990654i \(0.456447\pi\)
\(464\) 0.839507 0.0389731
\(465\) 17.9806 0.833828
\(466\) −23.7835 −1.10175
\(467\) 29.6514 1.37210 0.686051 0.727554i \(-0.259343\pi\)
0.686051 + 0.727554i \(0.259343\pi\)
\(468\) 2.47126 0.114234
\(469\) 3.94467 0.182148
\(470\) 4.21590 0.194465
\(471\) −10.0177 −0.461593
\(472\) 24.7753 1.14038
\(473\) 14.0773 0.647276
\(474\) −9.67245 −0.444270
\(475\) −16.6561 −0.764234
\(476\) −10.4544 −0.479177
\(477\) −12.9542 −0.593131
\(478\) 15.4976 0.708845
\(479\) −0.439562 −0.0200841 −0.0100421 0.999950i \(-0.503197\pi\)
−0.0100421 + 0.999950i \(0.503197\pi\)
\(480\) 14.1389 0.645349
\(481\) 4.21245 0.192071
\(482\) −14.2426 −0.648732
\(483\) 0.484095 0.0220271
\(484\) 7.14629 0.324831
\(485\) −11.4735 −0.520983
\(486\) −16.6516 −0.755332
\(487\) −26.9021 −1.21905 −0.609525 0.792767i \(-0.708640\pi\)
−0.609525 + 0.792767i \(0.708640\pi\)
\(488\) −4.00063 −0.181100
\(489\) −42.8067 −1.93579
\(490\) −2.07967 −0.0939500
\(491\) −14.8866 −0.671821 −0.335911 0.941894i \(-0.609044\pi\)
−0.335911 + 0.941894i \(0.609044\pi\)
\(492\) −12.6008 −0.568089
\(493\) −14.2944 −0.643789
\(494\) −4.04470 −0.181980
\(495\) 5.25976 0.236408
\(496\) −1.64141 −0.0737014
\(497\) 18.5678 0.832878
\(498\) −21.0805 −0.944640
\(499\) −16.8021 −0.752166 −0.376083 0.926586i \(-0.622729\pi\)
−0.376083 + 0.926586i \(0.622729\pi\)
\(500\) 11.6704 0.521918
\(501\) 14.0694 0.628576
\(502\) 24.0732 1.07444
\(503\) −38.4444 −1.71415 −0.857075 0.515191i \(-0.827721\pi\)
−0.857075 + 0.515191i \(0.827721\pi\)
\(504\) −13.3858 −0.596252
\(505\) −1.23375 −0.0549010
\(506\) 0.193862 0.00861821
\(507\) 2.25573 0.100180
\(508\) 15.1578 0.672516
\(509\) −35.7475 −1.58448 −0.792240 0.610210i \(-0.791085\pi\)
−0.792240 + 0.610210i \(0.791085\pi\)
\(510\) 9.13907 0.404685
\(511\) −24.1222 −1.06710
\(512\) −2.63042 −0.116249
\(513\) −9.20471 −0.406398
\(514\) −24.0684 −1.06161
\(515\) 1.13079 0.0498285
\(516\) −16.8710 −0.742706
\(517\) 9.18944 0.404151
\(518\) −8.48196 −0.372676
\(519\) −15.4167 −0.676720
\(520\) 3.25297 0.142652
\(521\) 27.9008 1.22236 0.611179 0.791492i \(-0.290696\pi\)
0.611179 + 0.791492i \(0.290696\pi\)
\(522\) −6.80374 −0.297792
\(523\) 15.9778 0.698662 0.349331 0.936999i \(-0.386409\pi\)
0.349331 + 0.936999i \(0.386409\pi\)
\(524\) −12.1654 −0.531446
\(525\) −18.7040 −0.816311
\(526\) 16.6773 0.727163
\(527\) 27.9485 1.21746
\(528\) −1.16992 −0.0509144
\(529\) −22.9907 −0.999597
\(530\) −6.33878 −0.275339
\(531\) −17.9852 −0.780491
\(532\) −11.8019 −0.511677
\(533\) −4.72050 −0.204468
\(534\) 3.67171 0.158890
\(535\) 6.56556 0.283854
\(536\) −5.09281 −0.219976
\(537\) 12.7822 0.551594
\(538\) −8.87143 −0.382475
\(539\) −4.53308 −0.195254
\(540\) 2.75194 0.118425
\(541\) 32.4710 1.39604 0.698018 0.716080i \(-0.254065\pi\)
0.698018 + 0.716080i \(0.254065\pi\)
\(542\) −10.3228 −0.443401
\(543\) −6.23103 −0.267399
\(544\) 21.9771 0.942262
\(545\) 18.8990 0.809542
\(546\) −4.54201 −0.194380
\(547\) 26.7174 1.14235 0.571176 0.820827i \(-0.306487\pi\)
0.571176 + 0.820827i \(0.306487\pi\)
\(548\) 12.1433 0.518737
\(549\) 2.90419 0.123948
\(550\) −7.49026 −0.319386
\(551\) −16.1369 −0.687454
\(552\) −0.624997 −0.0266016
\(553\) −10.5728 −0.449602
\(554\) 21.5579 0.915909
\(555\) −10.7449 −0.456096
\(556\) −4.44437 −0.188483
\(557\) 31.4267 1.33159 0.665795 0.746135i \(-0.268092\pi\)
0.665795 + 0.746135i \(0.268092\pi\)
\(558\) 13.3027 0.563149
\(559\) −6.32020 −0.267316
\(560\) −0.586697 −0.0247925
\(561\) 19.9205 0.841045
\(562\) 16.2077 0.683681
\(563\) 9.77243 0.411859 0.205929 0.978567i \(-0.433978\pi\)
0.205929 + 0.978567i \(0.433978\pi\)
\(564\) −11.0131 −0.463736
\(565\) −9.08096 −0.382039
\(566\) −10.0160 −0.421003
\(567\) −24.2959 −1.02033
\(568\) −23.9721 −1.00585
\(569\) 31.6223 1.32568 0.662839 0.748762i \(-0.269352\pi\)
0.662839 + 0.748762i \(0.269352\pi\)
\(570\) 10.3170 0.432132
\(571\) 11.6719 0.488455 0.244227 0.969718i \(-0.421466\pi\)
0.244227 + 0.969718i \(0.421466\pi\)
\(572\) 2.63581 0.110209
\(573\) −12.4875 −0.521675
\(574\) 9.50494 0.396729
\(575\) −0.358418 −0.0149471
\(576\) 11.4330 0.476376
\(577\) −37.4894 −1.56070 −0.780352 0.625341i \(-0.784960\pi\)
−0.780352 + 0.625341i \(0.784960\pi\)
\(578\) −1.15685 −0.0481186
\(579\) 28.8901 1.20063
\(580\) 4.82445 0.200325
\(581\) −23.0428 −0.955978
\(582\) −20.6829 −0.857332
\(583\) −13.8167 −0.572229
\(584\) 31.1433 1.28872
\(585\) −2.36143 −0.0976333
\(586\) 10.1735 0.420264
\(587\) 35.1772 1.45192 0.725960 0.687737i \(-0.241396\pi\)
0.725960 + 0.687737i \(0.241396\pi\)
\(588\) 5.43269 0.224040
\(589\) 31.5509 1.30003
\(590\) −8.80059 −0.362314
\(591\) 0.566129 0.0232874
\(592\) 0.980880 0.0403139
\(593\) 34.4406 1.41431 0.707154 0.707060i \(-0.249979\pi\)
0.707154 + 0.707060i \(0.249979\pi\)
\(594\) −4.13937 −0.169840
\(595\) 9.98979 0.409542
\(596\) 13.1551 0.538856
\(597\) 14.0365 0.574477
\(598\) −0.0870367 −0.00355920
\(599\) 12.8653 0.525660 0.262830 0.964842i \(-0.415344\pi\)
0.262830 + 0.964842i \(0.415344\pi\)
\(600\) 24.1481 0.985840
\(601\) −35.2591 −1.43825 −0.719125 0.694881i \(-0.755457\pi\)
−0.719125 + 0.694881i \(0.755457\pi\)
\(602\) 12.7260 0.518673
\(603\) 3.69704 0.150555
\(604\) 3.71251 0.151060
\(605\) −6.82869 −0.277626
\(606\) −2.22403 −0.0903452
\(607\) 22.7548 0.923587 0.461794 0.886987i \(-0.347206\pi\)
0.461794 + 0.886987i \(0.347206\pi\)
\(608\) 24.8098 1.00617
\(609\) −18.1210 −0.734299
\(610\) 1.42109 0.0575381
\(611\) −4.12572 −0.166909
\(612\) −9.79813 −0.396066
\(613\) −41.4744 −1.67514 −0.837568 0.546333i \(-0.816023\pi\)
−0.837568 + 0.546333i \(0.816023\pi\)
\(614\) 1.83684 0.0741290
\(615\) 12.0408 0.485532
\(616\) −14.2771 −0.575240
\(617\) 31.4984 1.26808 0.634038 0.773302i \(-0.281396\pi\)
0.634038 + 0.773302i \(0.281396\pi\)
\(618\) 2.03843 0.0819979
\(619\) −45.2965 −1.82062 −0.910310 0.413926i \(-0.864157\pi\)
−0.910310 + 0.413926i \(0.864157\pi\)
\(620\) −9.43280 −0.378830
\(621\) −0.198074 −0.00794842
\(622\) −8.87268 −0.355762
\(623\) 4.01350 0.160797
\(624\) 0.525252 0.0210269
\(625\) 7.45482 0.298193
\(626\) 10.4522 0.417756
\(627\) 22.4881 0.898088
\(628\) 5.25542 0.209714
\(629\) −16.7016 −0.665937
\(630\) 4.75486 0.189438
\(631\) −9.56661 −0.380841 −0.190420 0.981703i \(-0.560985\pi\)
−0.190420 + 0.981703i \(0.560985\pi\)
\(632\) 13.6502 0.542975
\(633\) 11.0354 0.438618
\(634\) −2.80990 −0.111595
\(635\) −14.4841 −0.574784
\(636\) 16.5587 0.656594
\(637\) 2.03519 0.0806370
\(638\) −7.25676 −0.287298
\(639\) 17.4022 0.688419
\(640\) −6.94153 −0.274388
\(641\) 32.6148 1.28821 0.644103 0.764939i \(-0.277231\pi\)
0.644103 + 0.764939i \(0.277231\pi\)
\(642\) 11.8355 0.467111
\(643\) −38.8264 −1.53116 −0.765582 0.643338i \(-0.777549\pi\)
−0.765582 + 0.643338i \(0.777549\pi\)
\(644\) −0.253962 −0.0100075
\(645\) 16.1212 0.634773
\(646\) 16.0365 0.630948
\(647\) 2.11253 0.0830521 0.0415260 0.999137i \(-0.486778\pi\)
0.0415260 + 0.999137i \(0.486778\pi\)
\(648\) 31.3675 1.23223
\(649\) −19.1827 −0.752988
\(650\) 3.36285 0.131902
\(651\) 35.4302 1.38862
\(652\) 22.4569 0.879479
\(653\) 18.1623 0.710746 0.355373 0.934725i \(-0.384354\pi\)
0.355373 + 0.934725i \(0.384354\pi\)
\(654\) 34.0685 1.33219
\(655\) 11.6247 0.454215
\(656\) −1.09918 −0.0429158
\(657\) −22.6079 −0.882019
\(658\) 8.30732 0.323853
\(659\) 26.4829 1.03163 0.515813 0.856701i \(-0.327490\pi\)
0.515813 + 0.856701i \(0.327490\pi\)
\(660\) −6.72329 −0.261704
\(661\) 7.52159 0.292556 0.146278 0.989244i \(-0.453271\pi\)
0.146278 + 0.989244i \(0.453271\pi\)
\(662\) −0.0514631 −0.00200017
\(663\) −8.94357 −0.347339
\(664\) 29.7497 1.15451
\(665\) 11.2774 0.437318
\(666\) −7.94950 −0.308037
\(667\) −0.347245 −0.0134454
\(668\) −7.38098 −0.285579
\(669\) 3.76746 0.145659
\(670\) 1.80905 0.0698896
\(671\) 3.09756 0.119580
\(672\) 27.8603 1.07473
\(673\) −32.7473 −1.26231 −0.631157 0.775655i \(-0.717420\pi\)
−0.631157 + 0.775655i \(0.717420\pi\)
\(674\) −1.63497 −0.0629768
\(675\) 7.65299 0.294564
\(676\) −1.18338 −0.0455146
\(677\) 45.9277 1.76514 0.882572 0.470177i \(-0.155810\pi\)
0.882572 + 0.470177i \(0.155810\pi\)
\(678\) −16.3700 −0.628685
\(679\) −22.6082 −0.867621
\(680\) −12.8974 −0.494594
\(681\) −18.6174 −0.713422
\(682\) 14.1885 0.543304
\(683\) 47.3508 1.81183 0.905914 0.423461i \(-0.139185\pi\)
0.905914 + 0.423461i \(0.139185\pi\)
\(684\) −11.0610 −0.422929
\(685\) −11.6036 −0.443352
\(686\) −18.1928 −0.694603
\(687\) 8.80972 0.336112
\(688\) −1.47167 −0.0561071
\(689\) 6.20318 0.236323
\(690\) 0.222009 0.00845173
\(691\) 26.9497 1.02521 0.512607 0.858623i \(-0.328680\pi\)
0.512607 + 0.858623i \(0.328680\pi\)
\(692\) 8.08779 0.307452
\(693\) 10.3642 0.393704
\(694\) −11.0828 −0.420697
\(695\) 4.24685 0.161092
\(696\) 23.3953 0.886796
\(697\) 18.7160 0.708917
\(698\) −16.4366 −0.622134
\(699\) −59.3680 −2.24550
\(700\) 9.81234 0.370872
\(701\) 42.6310 1.61015 0.805076 0.593171i \(-0.202124\pi\)
0.805076 + 0.593171i \(0.202124\pi\)
\(702\) 1.85842 0.0701416
\(703\) −18.8543 −0.711104
\(704\) 12.1943 0.459589
\(705\) 10.5237 0.396344
\(706\) 5.49667 0.206870
\(707\) −2.43106 −0.0914296
\(708\) 22.9896 0.864002
\(709\) 19.3382 0.726260 0.363130 0.931738i \(-0.381708\pi\)
0.363130 + 0.931738i \(0.381708\pi\)
\(710\) 8.51529 0.319573
\(711\) −9.90910 −0.371620
\(712\) −5.18167 −0.194191
\(713\) 0.678934 0.0254263
\(714\) 18.0083 0.673943
\(715\) −2.51867 −0.0941928
\(716\) −6.70570 −0.250604
\(717\) 38.6850 1.44472
\(718\) −1.79327 −0.0669241
\(719\) −0.129535 −0.00483084 −0.00241542 0.999997i \(-0.500769\pi\)
−0.00241542 + 0.999997i \(0.500769\pi\)
\(720\) −0.549866 −0.0204923
\(721\) 2.22819 0.0829820
\(722\) 0.933753 0.0347507
\(723\) −35.5521 −1.32220
\(724\) 3.26887 0.121486
\(725\) 13.4165 0.498277
\(726\) −12.3099 −0.456862
\(727\) 34.8868 1.29388 0.646939 0.762541i \(-0.276049\pi\)
0.646939 + 0.762541i \(0.276049\pi\)
\(728\) 6.40988 0.237566
\(729\) −8.85381 −0.327919
\(730\) −11.0626 −0.409445
\(731\) 25.0585 0.926821
\(732\) −3.71228 −0.137210
\(733\) 24.4474 0.902986 0.451493 0.892275i \(-0.350892\pi\)
0.451493 + 0.892275i \(0.350892\pi\)
\(734\) 22.3519 0.825024
\(735\) −5.19125 −0.191482
\(736\) 0.533875 0.0196789
\(737\) 3.94320 0.145250
\(738\) 8.90826 0.327918
\(739\) −12.6222 −0.464315 −0.232158 0.972678i \(-0.574579\pi\)
−0.232158 + 0.972678i \(0.574579\pi\)
\(740\) 5.63689 0.207216
\(741\) −10.0963 −0.370897
\(742\) −12.4904 −0.458537
\(743\) 10.9176 0.400528 0.200264 0.979742i \(-0.435820\pi\)
0.200264 + 0.979742i \(0.435820\pi\)
\(744\) −45.7426 −1.67700
\(745\) −12.5705 −0.460548
\(746\) 5.50428 0.201526
\(747\) −21.5963 −0.790167
\(748\) −10.4505 −0.382109
\(749\) 12.9373 0.472717
\(750\) −20.1030 −0.734056
\(751\) 19.2343 0.701869 0.350934 0.936400i \(-0.385864\pi\)
0.350934 + 0.936400i \(0.385864\pi\)
\(752\) −0.960684 −0.0350325
\(753\) 60.0912 2.18985
\(754\) 3.25802 0.118650
\(755\) −3.54752 −0.129108
\(756\) 5.42263 0.197219
\(757\) 40.5213 1.47277 0.736386 0.676562i \(-0.236531\pi\)
0.736386 + 0.676562i \(0.236531\pi\)
\(758\) 4.15523 0.150925
\(759\) 0.483915 0.0175650
\(760\) −14.5598 −0.528140
\(761\) −23.5856 −0.854977 −0.427489 0.904021i \(-0.640602\pi\)
−0.427489 + 0.904021i \(0.640602\pi\)
\(762\) −26.1100 −0.945867
\(763\) 37.2399 1.34817
\(764\) 6.55110 0.237011
\(765\) 9.36267 0.338508
\(766\) −0.988623 −0.0357204
\(767\) 8.61233 0.310973
\(768\) −37.2125 −1.34279
\(769\) −36.8906 −1.33031 −0.665154 0.746706i \(-0.731634\pi\)
−0.665154 + 0.746706i \(0.731634\pi\)
\(770\) 5.07145 0.182762
\(771\) −60.0793 −2.16370
\(772\) −15.1561 −0.545479
\(773\) −9.44627 −0.339759 −0.169879 0.985465i \(-0.554338\pi\)
−0.169879 + 0.985465i \(0.554338\pi\)
\(774\) 11.9271 0.428711
\(775\) −26.2321 −0.942283
\(776\) 29.1885 1.04781
\(777\) −21.1725 −0.759561
\(778\) 24.3550 0.873170
\(779\) 21.1283 0.756999
\(780\) 3.01851 0.108080
\(781\) 18.5609 0.664160
\(782\) 0.345085 0.0123402
\(783\) 7.41442 0.264970
\(784\) 0.473898 0.0169249
\(785\) −5.02185 −0.179238
\(786\) 20.9555 0.747458
\(787\) −17.1347 −0.610786 −0.305393 0.952226i \(-0.598788\pi\)
−0.305393 + 0.952226i \(0.598788\pi\)
\(788\) −0.296997 −0.0105801
\(789\) 41.6295 1.48205
\(790\) −4.84876 −0.172511
\(791\) −17.8938 −0.636230
\(792\) −13.3808 −0.475467
\(793\) −1.39069 −0.0493848
\(794\) −31.6446 −1.12302
\(795\) −15.8228 −0.561176
\(796\) −7.36372 −0.261000
\(797\) 0.489636 0.0173438 0.00867190 0.999962i \(-0.497240\pi\)
0.00867190 + 0.999962i \(0.497240\pi\)
\(798\) 20.3294 0.719653
\(799\) 16.3577 0.578695
\(800\) −20.6274 −0.729288
\(801\) 3.76155 0.132908
\(802\) −10.6798 −0.377116
\(803\) −24.1132 −0.850937
\(804\) −4.72574 −0.166664
\(805\) 0.242675 0.00855317
\(806\) −6.37009 −0.224377
\(807\) −22.1447 −0.779531
\(808\) 3.13865 0.110417
\(809\) 17.5604 0.617390 0.308695 0.951161i \(-0.400108\pi\)
0.308695 + 0.951161i \(0.400108\pi\)
\(810\) −11.1422 −0.391498
\(811\) −31.6346 −1.11084 −0.555421 0.831569i \(-0.687443\pi\)
−0.555421 + 0.831569i \(0.687443\pi\)
\(812\) 9.50646 0.333611
\(813\) −25.7675 −0.903707
\(814\) −8.47880 −0.297182
\(815\) −21.4588 −0.751670
\(816\) −2.08253 −0.0729033
\(817\) 28.2883 0.989682
\(818\) −2.39068 −0.0835881
\(819\) −4.65314 −0.162594
\(820\) −6.31674 −0.220590
\(821\) 16.9989 0.593267 0.296633 0.954991i \(-0.404136\pi\)
0.296633 + 0.954991i \(0.404136\pi\)
\(822\) −20.9175 −0.729582
\(823\) −16.0717 −0.560225 −0.280113 0.959967i \(-0.590372\pi\)
−0.280113 + 0.959967i \(0.590372\pi\)
\(824\) −2.87673 −0.100216
\(825\) −18.6971 −0.650948
\(826\) −17.3413 −0.603382
\(827\) 25.5240 0.887555 0.443778 0.896137i \(-0.353638\pi\)
0.443778 + 0.896137i \(0.353638\pi\)
\(828\) −0.238019 −0.00827173
\(829\) −9.24249 −0.321005 −0.160503 0.987035i \(-0.551311\pi\)
−0.160503 + 0.987035i \(0.551311\pi\)
\(830\) −10.5676 −0.366806
\(831\) 53.8126 1.86674
\(832\) −5.47478 −0.189804
\(833\) −8.06915 −0.279580
\(834\) 7.65567 0.265094
\(835\) 7.05295 0.244078
\(836\) −11.7975 −0.408025
\(837\) −14.4967 −0.501080
\(838\) 15.9714 0.551724
\(839\) 40.6143 1.40216 0.701081 0.713081i \(-0.252701\pi\)
0.701081 + 0.713081i \(0.252701\pi\)
\(840\) −16.3500 −0.564129
\(841\) −16.0017 −0.551783
\(842\) 25.0037 0.861686
\(843\) 40.4574 1.39343
\(844\) −5.78930 −0.199276
\(845\) 1.13079 0.0389003
\(846\) 7.78582 0.267682
\(847\) −13.4558 −0.462345
\(848\) 1.44443 0.0496019
\(849\) −25.0018 −0.858058
\(850\) −13.3331 −0.457321
\(851\) −0.405721 −0.0139079
\(852\) −22.2443 −0.762078
\(853\) −39.7341 −1.36047 −0.680235 0.732994i \(-0.738122\pi\)
−0.680235 + 0.732994i \(0.738122\pi\)
\(854\) 2.80021 0.0958214
\(855\) 10.5694 0.361467
\(856\) −16.7028 −0.570890
\(857\) 20.5365 0.701512 0.350756 0.936467i \(-0.385925\pi\)
0.350756 + 0.936467i \(0.385925\pi\)
\(858\) −4.54032 −0.155004
\(859\) −15.2790 −0.521312 −0.260656 0.965432i \(-0.583939\pi\)
−0.260656 + 0.965432i \(0.583939\pi\)
\(860\) −8.45738 −0.288394
\(861\) 23.7261 0.808583
\(862\) 30.8086 1.04934
\(863\) 20.3166 0.691584 0.345792 0.938311i \(-0.387610\pi\)
0.345792 + 0.938311i \(0.387610\pi\)
\(864\) −11.3994 −0.387815
\(865\) −7.72835 −0.262772
\(866\) 14.5492 0.494401
\(867\) −2.88771 −0.0980718
\(868\) −18.5871 −0.630886
\(869\) −10.5689 −0.358525
\(870\) −8.31038 −0.281748
\(871\) −1.77035 −0.0599860
\(872\) −48.0790 −1.62816
\(873\) −21.1889 −0.717136
\(874\) 0.389564 0.0131772
\(875\) −21.9743 −0.742866
\(876\) 28.8986 0.976393
\(877\) 12.5880 0.425065 0.212533 0.977154i \(-0.431829\pi\)
0.212533 + 0.977154i \(0.431829\pi\)
\(878\) 11.1691 0.376939
\(879\) 25.3950 0.856551
\(880\) −0.586478 −0.0197702
\(881\) 52.9080 1.78252 0.891259 0.453496i \(-0.149823\pi\)
0.891259 + 0.453496i \(0.149823\pi\)
\(882\) −3.84069 −0.129323
\(883\) 31.2592 1.05196 0.525978 0.850498i \(-0.323699\pi\)
0.525978 + 0.850498i \(0.323699\pi\)
\(884\) 4.69189 0.157805
\(885\) −21.9679 −0.738443
\(886\) −13.5316 −0.454604
\(887\) 34.5533 1.16018 0.580092 0.814551i \(-0.303016\pi\)
0.580092 + 0.814551i \(0.303016\pi\)
\(888\) 27.3351 0.917304
\(889\) −28.5405 −0.957219
\(890\) 1.84061 0.0616975
\(891\) −24.2869 −0.813640
\(892\) −1.97645 −0.0661765
\(893\) 18.4661 0.617945
\(894\) −22.6604 −0.757879
\(895\) 6.40768 0.214185
\(896\) −13.6781 −0.456953
\(897\) −0.217260 −0.00725409
\(898\) −8.94949 −0.298648
\(899\) −25.4143 −0.847615
\(900\) 9.19636 0.306545
\(901\) −24.5945 −0.819363
\(902\) 9.50140 0.316362
\(903\) 31.7665 1.05712
\(904\) 23.1020 0.768361
\(905\) −3.12359 −0.103832
\(906\) −6.39500 −0.212460
\(907\) −15.4038 −0.511475 −0.255737 0.966746i \(-0.582318\pi\)
−0.255737 + 0.966746i \(0.582318\pi\)
\(908\) 9.76691 0.324126
\(909\) −2.27845 −0.0755714
\(910\) −2.27689 −0.0754783
\(911\) 1.83754 0.0608805 0.0304403 0.999537i \(-0.490309\pi\)
0.0304403 + 0.999537i \(0.490309\pi\)
\(912\) −2.35095 −0.0778479
\(913\) −23.0342 −0.762322
\(914\) 30.8491 1.02040
\(915\) 3.54730 0.117270
\(916\) −4.62167 −0.152704
\(917\) 22.9062 0.756428
\(918\) −7.36832 −0.243191
\(919\) −17.2624 −0.569435 −0.284717 0.958611i \(-0.591900\pi\)
−0.284717 + 0.958611i \(0.591900\pi\)
\(920\) −0.313308 −0.0103295
\(921\) 4.58510 0.151084
\(922\) −17.9222 −0.590237
\(923\) −8.33313 −0.274288
\(924\) −13.2481 −0.435829
\(925\) 15.6759 0.515419
\(926\) 5.30446 0.174315
\(927\) 2.08831 0.0685891
\(928\) −19.9844 −0.656019
\(929\) −59.9685 −1.96750 −0.983751 0.179538i \(-0.942540\pi\)
−0.983751 + 0.179538i \(0.942540\pi\)
\(930\) 16.2485 0.532809
\(931\) −9.10920 −0.298542
\(932\) 31.1451 1.02019
\(933\) −22.1478 −0.725088
\(934\) 26.7951 0.876761
\(935\) 9.98607 0.326579
\(936\) 6.00749 0.196361
\(937\) 1.88797 0.0616772 0.0308386 0.999524i \(-0.490182\pi\)
0.0308386 + 0.999524i \(0.490182\pi\)
\(938\) 3.56468 0.116391
\(939\) 26.0907 0.851439
\(940\) −5.52083 −0.180070
\(941\) −25.2206 −0.822168 −0.411084 0.911598i \(-0.634850\pi\)
−0.411084 + 0.911598i \(0.634850\pi\)
\(942\) −9.05273 −0.294954
\(943\) 0.454653 0.0148056
\(944\) 2.00540 0.0652703
\(945\) −5.18163 −0.168559
\(946\) 12.7213 0.413604
\(947\) 27.2763 0.886361 0.443181 0.896432i \(-0.353850\pi\)
0.443181 + 0.896432i \(0.353850\pi\)
\(948\) 12.6663 0.411383
\(949\) 10.8259 0.351425
\(950\) −15.0516 −0.488339
\(951\) −7.01403 −0.227445
\(952\) −25.4141 −0.823674
\(953\) 4.84988 0.157103 0.0785515 0.996910i \(-0.474971\pi\)
0.0785515 + 0.996910i \(0.474971\pi\)
\(954\) −11.7063 −0.379005
\(955\) −6.25996 −0.202567
\(956\) −20.2946 −0.656373
\(957\) −18.1142 −0.585549
\(958\) −0.397220 −0.0128336
\(959\) −22.8647 −0.738338
\(960\) 13.9648 0.450712
\(961\) 18.6902 0.602909
\(962\) 3.80667 0.122732
\(963\) 12.1251 0.390726
\(964\) 18.6510 0.600710
\(965\) 14.4825 0.466208
\(966\) 0.437463 0.0140751
\(967\) 10.0776 0.324074 0.162037 0.986785i \(-0.448194\pi\)
0.162037 + 0.986785i \(0.448194\pi\)
\(968\) 17.3722 0.558364
\(969\) 40.0301 1.28595
\(970\) −10.3682 −0.332904
\(971\) −36.6814 −1.17716 −0.588581 0.808438i \(-0.700313\pi\)
−0.588581 + 0.808438i \(0.700313\pi\)
\(972\) 21.8057 0.699419
\(973\) 8.36831 0.268276
\(974\) −24.3106 −0.778963
\(975\) 8.39429 0.268832
\(976\) −0.323825 −0.0103654
\(977\) −50.2932 −1.60902 −0.804511 0.593937i \(-0.797573\pi\)
−0.804511 + 0.593937i \(0.797573\pi\)
\(978\) −38.6832 −1.23695
\(979\) 4.01200 0.128224
\(980\) 2.72339 0.0869954
\(981\) 34.9021 1.11434
\(982\) −13.4525 −0.429288
\(983\) −17.5930 −0.561128 −0.280564 0.959835i \(-0.590522\pi\)
−0.280564 + 0.959835i \(0.590522\pi\)
\(984\) −30.6319 −0.976508
\(985\) 0.283798 0.00904256
\(986\) −12.9175 −0.411376
\(987\) 20.7366 0.660053
\(988\) 5.29664 0.168508
\(989\) 0.608728 0.0193564
\(990\) 4.75309 0.151063
\(991\) −10.3839 −0.329856 −0.164928 0.986306i \(-0.552739\pi\)
−0.164928 + 0.986306i \(0.552739\pi\)
\(992\) 39.0735 1.24059
\(993\) −0.128462 −0.00407660
\(994\) 16.7791 0.532202
\(995\) 7.03646 0.223071
\(996\) 27.6055 0.874713
\(997\) 43.8380 1.38836 0.694182 0.719799i \(-0.255766\pi\)
0.694182 + 0.719799i \(0.255766\pi\)
\(998\) −15.1836 −0.480628
\(999\) 8.66301 0.274086
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 1339.2.a.g.1.19 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1339.2.a.g.1.19 30 1.1 even 1 trivial