Properties

Label 619.2.a.b.1.22
Level $619$
Weight $2$
Character 619.1
Self dual yes
Analytic conductor $4.943$
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] = [619,2,Mod(1,619)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(619, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("619.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 619 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 619.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: \(4.94273988512\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) \(=\) 619.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.77256 q^{2} -2.61871 q^{3} +1.14198 q^{4} +2.86335 q^{5} -4.64183 q^{6} +2.04983 q^{7} -1.52089 q^{8} +3.85763 q^{9} +O(q^{10})\) \(q+1.77256 q^{2} -2.61871 q^{3} +1.14198 q^{4} +2.86335 q^{5} -4.64183 q^{6} +2.04983 q^{7} -1.52089 q^{8} +3.85763 q^{9} +5.07548 q^{10} -3.53364 q^{11} -2.99052 q^{12} +5.12412 q^{13} +3.63345 q^{14} -7.49829 q^{15} -4.97984 q^{16} +5.62332 q^{17} +6.83790 q^{18} +4.67171 q^{19} +3.26990 q^{20} -5.36791 q^{21} -6.26360 q^{22} -1.06415 q^{23} +3.98277 q^{24} +3.19879 q^{25} +9.08283 q^{26} -2.24589 q^{27} +2.34087 q^{28} +8.34802 q^{29} -13.2912 q^{30} -4.96773 q^{31} -5.78530 q^{32} +9.25357 q^{33} +9.96770 q^{34} +5.86939 q^{35} +4.40535 q^{36} -1.19702 q^{37} +8.28090 q^{38} -13.4186 q^{39} -4.35485 q^{40} -1.05581 q^{41} -9.51495 q^{42} +6.18169 q^{43} -4.03535 q^{44} +11.0458 q^{45} -1.88628 q^{46} +11.1882 q^{47} +13.0408 q^{48} -2.79820 q^{49} +5.67006 q^{50} -14.7258 q^{51} +5.85165 q^{52} -2.73223 q^{53} -3.98098 q^{54} -10.1181 q^{55} -3.11757 q^{56} -12.2338 q^{57} +14.7974 q^{58} -10.0977 q^{59} -8.56291 q^{60} -6.59654 q^{61} -8.80562 q^{62} +7.90749 q^{63} -0.295133 q^{64} +14.6722 q^{65} +16.4025 q^{66} -14.7096 q^{67} +6.42173 q^{68} +2.78671 q^{69} +10.4039 q^{70} +8.64906 q^{71} -5.86704 q^{72} -9.61528 q^{73} -2.12179 q^{74} -8.37671 q^{75} +5.33500 q^{76} -7.24336 q^{77} -23.7853 q^{78} +2.15346 q^{79} -14.2590 q^{80} -5.69157 q^{81} -1.87149 q^{82} -15.2974 q^{83} -6.13005 q^{84} +16.1016 q^{85} +10.9574 q^{86} -21.8610 q^{87} +5.37428 q^{88} -3.00189 q^{89} +19.5793 q^{90} +10.5036 q^{91} -1.21525 q^{92} +13.0090 q^{93} +19.8317 q^{94} +13.3767 q^{95} +15.1500 q^{96} +2.92181 q^{97} -4.95998 q^{98} -13.6315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.77256 1.25339 0.626696 0.779264i \(-0.284407\pi\)
0.626696 + 0.779264i \(0.284407\pi\)
\(3\) −2.61871 −1.51191 −0.755956 0.654623i \(-0.772828\pi\)
−0.755956 + 0.654623i \(0.772828\pi\)
\(4\) 1.14198 0.570991
\(5\) 2.86335 1.28053 0.640265 0.768154i \(-0.278824\pi\)
0.640265 + 0.768154i \(0.278824\pi\)
\(6\) −4.64183 −1.89502
\(7\) 2.04983 0.774763 0.387381 0.921920i \(-0.373380\pi\)
0.387381 + 0.921920i \(0.373380\pi\)
\(8\) −1.52089 −0.537716
\(9\) 3.85763 1.28588
\(10\) 5.07548 1.60501
\(11\) −3.53364 −1.06543 −0.532716 0.846294i \(-0.678829\pi\)
−0.532716 + 0.846294i \(0.678829\pi\)
\(12\) −2.99052 −0.863288
\(13\) 5.12412 1.42117 0.710587 0.703609i \(-0.248429\pi\)
0.710587 + 0.703609i \(0.248429\pi\)
\(14\) 3.63345 0.971081
\(15\) −7.49829 −1.93605
\(16\) −4.97984 −1.24496
\(17\) 5.62332 1.36386 0.681928 0.731419i \(-0.261142\pi\)
0.681928 + 0.731419i \(0.261142\pi\)
\(18\) 6.83790 1.61171
\(19\) 4.67171 1.07176 0.535881 0.844293i \(-0.319979\pi\)
0.535881 + 0.844293i \(0.319979\pi\)
\(20\) 3.26990 0.731171
\(21\) −5.36791 −1.17137
\(22\) −6.26360 −1.33540
\(23\) −1.06415 −0.221892 −0.110946 0.993826i \(-0.535388\pi\)
−0.110946 + 0.993826i \(0.535388\pi\)
\(24\) 3.98277 0.812980
\(25\) 3.19879 0.639759
\(26\) 9.08283 1.78129
\(27\) −2.24589 −0.432221
\(28\) 2.34087 0.442383
\(29\) 8.34802 1.55019 0.775094 0.631846i \(-0.217703\pi\)
0.775094 + 0.631846i \(0.217703\pi\)
\(30\) −13.2912 −2.42663
\(31\) −4.96773 −0.892230 −0.446115 0.894976i \(-0.647193\pi\)
−0.446115 + 0.894976i \(0.647193\pi\)
\(32\) −5.78530 −1.02271
\(33\) 9.25357 1.61084
\(34\) 9.96770 1.70945
\(35\) 5.86939 0.992108
\(36\) 4.40535 0.734224
\(37\) −1.19702 −0.196788 −0.0983940 0.995148i \(-0.531371\pi\)
−0.0983940 + 0.995148i \(0.531371\pi\)
\(38\) 8.28090 1.34334
\(39\) −13.4186 −2.14869
\(40\) −4.35485 −0.688562
\(41\) −1.05581 −0.164889 −0.0824447 0.996596i \(-0.526273\pi\)
−0.0824447 + 0.996596i \(0.526273\pi\)
\(42\) −9.51495 −1.46819
\(43\) 6.18169 0.942699 0.471350 0.881946i \(-0.343767\pi\)
0.471350 + 0.881946i \(0.343767\pi\)
\(44\) −4.03535 −0.608352
\(45\) 11.0458 1.64661
\(46\) −1.88628 −0.278117
\(47\) 11.1882 1.63196 0.815981 0.578079i \(-0.196198\pi\)
0.815981 + 0.578079i \(0.196198\pi\)
\(48\) 13.0408 1.88227
\(49\) −2.79820 −0.399743
\(50\) 5.67006 0.801868
\(51\) −14.7258 −2.06203
\(52\) 5.85165 0.811478
\(53\) −2.73223 −0.375301 −0.187650 0.982236i \(-0.560087\pi\)
−0.187650 + 0.982236i \(0.560087\pi\)
\(54\) −3.98098 −0.541743
\(55\) −10.1181 −1.36432
\(56\) −3.11757 −0.416603
\(57\) −12.2338 −1.62041
\(58\) 14.7974 1.94299
\(59\) −10.0977 −1.31461 −0.657304 0.753626i \(-0.728303\pi\)
−0.657304 + 0.753626i \(0.728303\pi\)
\(60\) −8.56291 −1.10547
\(61\) −6.59654 −0.844601 −0.422300 0.906456i \(-0.638777\pi\)
−0.422300 + 0.906456i \(0.638777\pi\)
\(62\) −8.80562 −1.11831
\(63\) 7.90749 0.996250
\(64\) −0.295133 −0.0368917
\(65\) 14.6722 1.81986
\(66\) 16.4025 2.01901
\(67\) −14.7096 −1.79706 −0.898530 0.438913i \(-0.855364\pi\)
−0.898530 + 0.438913i \(0.855364\pi\)
\(68\) 6.42173 0.778749
\(69\) 2.78671 0.335481
\(70\) 10.4039 1.24350
\(71\) 8.64906 1.02646 0.513228 0.858253i \(-0.328450\pi\)
0.513228 + 0.858253i \(0.328450\pi\)
\(72\) −5.86704 −0.691437
\(73\) −9.61528 −1.12538 −0.562692 0.826667i \(-0.690234\pi\)
−0.562692 + 0.826667i \(0.690234\pi\)
\(74\) −2.12179 −0.246653
\(75\) −8.37671 −0.967259
\(76\) 5.33500 0.611967
\(77\) −7.24336 −0.825457
\(78\) −23.7853 −2.69315
\(79\) 2.15346 0.242283 0.121142 0.992635i \(-0.461344\pi\)
0.121142 + 0.992635i \(0.461344\pi\)
\(80\) −14.2590 −1.59421
\(81\) −5.69157 −0.632397
\(82\) −1.87149 −0.206671
\(83\) −15.2974 −1.67911 −0.839554 0.543277i \(-0.817183\pi\)
−0.839554 + 0.543277i \(0.817183\pi\)
\(84\) −6.13005 −0.668843
\(85\) 16.1016 1.74646
\(86\) 10.9574 1.18157
\(87\) −21.8610 −2.34375
\(88\) 5.37428 0.572900
\(89\) −3.00189 −0.318200 −0.159100 0.987262i \(-0.550859\pi\)
−0.159100 + 0.987262i \(0.550859\pi\)
\(90\) 19.5793 2.06384
\(91\) 10.5036 1.10107
\(92\) −1.21525 −0.126698
\(93\) 13.0090 1.34897
\(94\) 19.8317 2.04549
\(95\) 13.3767 1.37243
\(96\) 15.1500 1.54624
\(97\) 2.92181 0.296665 0.148333 0.988938i \(-0.452609\pi\)
0.148333 + 0.988938i \(0.452609\pi\)
\(98\) −4.95998 −0.501034
\(99\) −13.6315 −1.37001
\(100\) 3.65296 0.365296
\(101\) 1.50237 0.149492 0.0747459 0.997203i \(-0.476185\pi\)
0.0747459 + 0.997203i \(0.476185\pi\)
\(102\) −26.1025 −2.58453
\(103\) −6.10995 −0.602031 −0.301016 0.953619i \(-0.597326\pi\)
−0.301016 + 0.953619i \(0.597326\pi\)
\(104\) −7.79323 −0.764189
\(105\) −15.3702 −1.49998
\(106\) −4.84306 −0.470399
\(107\) 14.3894 1.39108 0.695538 0.718490i \(-0.255166\pi\)
0.695538 + 0.718490i \(0.255166\pi\)
\(108\) −2.56476 −0.246795
\(109\) −6.64977 −0.636933 −0.318466 0.947934i \(-0.603168\pi\)
−0.318466 + 0.947934i \(0.603168\pi\)
\(110\) −17.9349 −1.71003
\(111\) 3.13463 0.297526
\(112\) −10.2078 −0.964549
\(113\) 0.748342 0.0703980 0.0351990 0.999380i \(-0.488793\pi\)
0.0351990 + 0.999380i \(0.488793\pi\)
\(114\) −21.6853 −2.03101
\(115\) −3.04705 −0.284139
\(116\) 9.53328 0.885143
\(117\) 19.7670 1.82746
\(118\) −17.8988 −1.64772
\(119\) 11.5269 1.05666
\(120\) 11.4041 1.04105
\(121\) 1.48660 0.135145
\(122\) −11.6928 −1.05862
\(123\) 2.76485 0.249298
\(124\) −5.67306 −0.509455
\(125\) −5.15749 −0.461300
\(126\) 14.0165 1.24869
\(127\) −15.3680 −1.36369 −0.681846 0.731496i \(-0.738823\pi\)
−0.681846 + 0.731496i \(0.738823\pi\)
\(128\) 11.0475 0.976467
\(129\) −16.1880 −1.42528
\(130\) 26.0073 2.28099
\(131\) −14.3661 −1.25517 −0.627584 0.778549i \(-0.715956\pi\)
−0.627584 + 0.778549i \(0.715956\pi\)
\(132\) 10.5674 0.919775
\(133\) 9.57620 0.830362
\(134\) −26.0736 −2.25242
\(135\) −6.43077 −0.553473
\(136\) −8.55246 −0.733368
\(137\) −18.9233 −1.61672 −0.808362 0.588686i \(-0.799646\pi\)
−0.808362 + 0.588686i \(0.799646\pi\)
\(138\) 4.93962 0.420489
\(139\) 14.9651 1.26932 0.634661 0.772791i \(-0.281140\pi\)
0.634661 + 0.772791i \(0.281140\pi\)
\(140\) 6.70273 0.566484
\(141\) −29.2985 −2.46738
\(142\) 15.3310 1.28655
\(143\) −18.1068 −1.51416
\(144\) −19.2104 −1.60087
\(145\) 23.9033 1.98506
\(146\) −17.0437 −1.41055
\(147\) 7.32766 0.604375
\(148\) −1.36697 −0.112364
\(149\) −8.62743 −0.706786 −0.353393 0.935475i \(-0.614972\pi\)
−0.353393 + 0.935475i \(0.614972\pi\)
\(150\) −14.8482 −1.21235
\(151\) 6.43359 0.523558 0.261779 0.965128i \(-0.415691\pi\)
0.261779 + 0.965128i \(0.415691\pi\)
\(152\) −7.10516 −0.576305
\(153\) 21.6927 1.75375
\(154\) −12.8393 −1.03462
\(155\) −14.2244 −1.14253
\(156\) −15.3238 −1.22688
\(157\) 16.5731 1.32268 0.661338 0.750088i \(-0.269989\pi\)
0.661338 + 0.750088i \(0.269989\pi\)
\(158\) 3.81715 0.303676
\(159\) 7.15492 0.567422
\(160\) −16.5654 −1.30961
\(161\) −2.18134 −0.171913
\(162\) −10.0887 −0.792641
\(163\) 9.34785 0.732180 0.366090 0.930579i \(-0.380696\pi\)
0.366090 + 0.930579i \(0.380696\pi\)
\(164\) −1.20571 −0.0941504
\(165\) 26.4962 2.06273
\(166\) −27.1156 −2.10458
\(167\) 5.82612 0.450839 0.225419 0.974262i \(-0.427625\pi\)
0.225419 + 0.974262i \(0.427625\pi\)
\(168\) 8.16400 0.629867
\(169\) 13.2566 1.01974
\(170\) 28.5410 2.18900
\(171\) 18.0217 1.37816
\(172\) 7.05938 0.538273
\(173\) 18.4409 1.40204 0.701019 0.713143i \(-0.252729\pi\)
0.701019 + 0.713143i \(0.252729\pi\)
\(174\) −38.7500 −2.93763
\(175\) 6.55698 0.495661
\(176\) 17.5970 1.32642
\(177\) 26.4429 1.98757
\(178\) −5.32105 −0.398829
\(179\) 12.2662 0.916817 0.458409 0.888741i \(-0.348420\pi\)
0.458409 + 0.888741i \(0.348420\pi\)
\(180\) 12.6141 0.940197
\(181\) −2.30343 −0.171212 −0.0856061 0.996329i \(-0.527283\pi\)
−0.0856061 + 0.996329i \(0.527283\pi\)
\(182\) 18.6182 1.38008
\(183\) 17.2744 1.27696
\(184\) 1.61846 0.119315
\(185\) −3.42748 −0.251993
\(186\) 23.0593 1.69079
\(187\) −19.8708 −1.45310
\(188\) 12.7767 0.931835
\(189\) −4.60369 −0.334869
\(190\) 23.7111 1.72019
\(191\) 19.8066 1.43315 0.716577 0.697508i \(-0.245708\pi\)
0.716577 + 0.697508i \(0.245708\pi\)
\(192\) 0.772868 0.0557770
\(193\) 5.55014 0.399508 0.199754 0.979846i \(-0.435986\pi\)
0.199754 + 0.979846i \(0.435986\pi\)
\(194\) 5.17910 0.371838
\(195\) −38.4221 −2.75146
\(196\) −3.19549 −0.228249
\(197\) 4.81650 0.343162 0.171581 0.985170i \(-0.445113\pi\)
0.171581 + 0.985170i \(0.445113\pi\)
\(198\) −24.1627 −1.71717
\(199\) −23.4188 −1.66011 −0.830056 0.557681i \(-0.811691\pi\)
−0.830056 + 0.557681i \(0.811691\pi\)
\(200\) −4.86502 −0.344009
\(201\) 38.5201 2.71700
\(202\) 2.66305 0.187372
\(203\) 17.1120 1.20103
\(204\) −16.8166 −1.17740
\(205\) −3.02315 −0.211146
\(206\) −10.8303 −0.754581
\(207\) −4.10512 −0.285325
\(208\) −25.5173 −1.76931
\(209\) −16.5081 −1.14189
\(210\) −27.2447 −1.88006
\(211\) 21.7797 1.49937 0.749687 0.661793i \(-0.230204\pi\)
0.749687 + 0.661793i \(0.230204\pi\)
\(212\) −3.12016 −0.214293
\(213\) −22.6494 −1.55191
\(214\) 25.5061 1.74356
\(215\) 17.7004 1.20716
\(216\) 3.41575 0.232413
\(217\) −10.1830 −0.691267
\(218\) −11.7871 −0.798326
\(219\) 25.1796 1.70148
\(220\) −11.5546 −0.779013
\(221\) 28.8146 1.93828
\(222\) 5.55634 0.372917
\(223\) −15.6515 −1.04810 −0.524049 0.851688i \(-0.675579\pi\)
−0.524049 + 0.851688i \(0.675579\pi\)
\(224\) −11.8589 −0.792355
\(225\) 12.3398 0.822651
\(226\) 1.32648 0.0882363
\(227\) 12.2763 0.814807 0.407404 0.913248i \(-0.366434\pi\)
0.407404 + 0.913248i \(0.366434\pi\)
\(228\) −13.9708 −0.925240
\(229\) −0.387189 −0.0255862 −0.0127931 0.999918i \(-0.504072\pi\)
−0.0127931 + 0.999918i \(0.504072\pi\)
\(230\) −5.40109 −0.356137
\(231\) 18.9682 1.24802
\(232\) −12.6964 −0.833561
\(233\) −9.67415 −0.633775 −0.316887 0.948463i \(-0.602638\pi\)
−0.316887 + 0.948463i \(0.602638\pi\)
\(234\) 35.0382 2.29052
\(235\) 32.0357 2.08978
\(236\) −11.5314 −0.750629
\(237\) −5.63929 −0.366311
\(238\) 20.4321 1.32442
\(239\) −5.72187 −0.370117 −0.185058 0.982728i \(-0.559247\pi\)
−0.185058 + 0.982728i \(0.559247\pi\)
\(240\) 37.3403 2.41030
\(241\) −4.51000 −0.290515 −0.145257 0.989394i \(-0.546401\pi\)
−0.145257 + 0.989394i \(0.546401\pi\)
\(242\) 2.63509 0.169390
\(243\) 21.6422 1.38835
\(244\) −7.53313 −0.482259
\(245\) −8.01223 −0.511883
\(246\) 4.90088 0.312468
\(247\) 23.9384 1.52316
\(248\) 7.55538 0.479767
\(249\) 40.0594 2.53866
\(250\) −9.14198 −0.578190
\(251\) 23.1844 1.46338 0.731692 0.681636i \(-0.238731\pi\)
0.731692 + 0.681636i \(0.238731\pi\)
\(252\) 9.03021 0.568850
\(253\) 3.76034 0.236410
\(254\) −27.2408 −1.70924
\(255\) −42.1653 −2.64049
\(256\) 20.1726 1.26079
\(257\) 6.28231 0.391880 0.195940 0.980616i \(-0.437224\pi\)
0.195940 + 0.980616i \(0.437224\pi\)
\(258\) −28.6943 −1.78643
\(259\) −2.45368 −0.152464
\(260\) 16.7553 1.03912
\(261\) 32.2036 1.99335
\(262\) −25.4648 −1.57322
\(263\) −29.6312 −1.82714 −0.913568 0.406685i \(-0.866685\pi\)
−0.913568 + 0.406685i \(0.866685\pi\)
\(264\) −14.0737 −0.866175
\(265\) −7.82335 −0.480584
\(266\) 16.9744 1.04077
\(267\) 7.86108 0.481091
\(268\) −16.7981 −1.02610
\(269\) 4.54785 0.277287 0.138644 0.990342i \(-0.455726\pi\)
0.138644 + 0.990342i \(0.455726\pi\)
\(270\) −11.3990 −0.693718
\(271\) −30.0453 −1.82512 −0.912560 0.408943i \(-0.865898\pi\)
−0.912560 + 0.408943i \(0.865898\pi\)
\(272\) −28.0033 −1.69795
\(273\) −27.5058 −1.66473
\(274\) −33.5427 −2.02639
\(275\) −11.3034 −0.681619
\(276\) 3.18237 0.191556
\(277\) −26.4968 −1.59204 −0.796018 0.605273i \(-0.793064\pi\)
−0.796018 + 0.605273i \(0.793064\pi\)
\(278\) 26.5266 1.59096
\(279\) −19.1637 −1.14730
\(280\) −8.92670 −0.533473
\(281\) 10.2039 0.608716 0.304358 0.952558i \(-0.401558\pi\)
0.304358 + 0.952558i \(0.401558\pi\)
\(282\) −51.9335 −3.09260
\(283\) −3.47496 −0.206565 −0.103282 0.994652i \(-0.532935\pi\)
−0.103282 + 0.994652i \(0.532935\pi\)
\(284\) 9.87707 0.586096
\(285\) −35.0298 −2.07499
\(286\) −32.0954 −1.89784
\(287\) −2.16423 −0.127750
\(288\) −22.3176 −1.31508
\(289\) 14.6218 0.860103
\(290\) 42.3702 2.48806
\(291\) −7.65138 −0.448532
\(292\) −10.9805 −0.642584
\(293\) −13.5197 −0.789830 −0.394915 0.918718i \(-0.629226\pi\)
−0.394915 + 0.918718i \(0.629226\pi\)
\(294\) 12.9887 0.757519
\(295\) −28.9133 −1.68340
\(296\) 1.82053 0.105816
\(297\) 7.93616 0.460503
\(298\) −15.2927 −0.885880
\(299\) −5.45285 −0.315347
\(300\) −9.56605 −0.552296
\(301\) 12.6714 0.730368
\(302\) 11.4039 0.656223
\(303\) −3.93428 −0.226018
\(304\) −23.2644 −1.33430
\(305\) −18.8882 −1.08154
\(306\) 38.4517 2.19814
\(307\) 7.10925 0.405747 0.202873 0.979205i \(-0.434972\pi\)
0.202873 + 0.979205i \(0.434972\pi\)
\(308\) −8.27178 −0.471328
\(309\) 16.0002 0.910218
\(310\) −25.2136 −1.43204
\(311\) 10.0199 0.568177 0.284088 0.958798i \(-0.408309\pi\)
0.284088 + 0.958798i \(0.408309\pi\)
\(312\) 20.4082 1.15539
\(313\) −15.6347 −0.883726 −0.441863 0.897083i \(-0.645682\pi\)
−0.441863 + 0.897083i \(0.645682\pi\)
\(314\) 29.3769 1.65783
\(315\) 22.6419 1.27573
\(316\) 2.45921 0.138342
\(317\) −25.7276 −1.44501 −0.722503 0.691368i \(-0.757008\pi\)
−0.722503 + 0.691368i \(0.757008\pi\)
\(318\) 12.6825 0.711202
\(319\) −29.4989 −1.65162
\(320\) −0.845071 −0.0472409
\(321\) −37.6816 −2.10318
\(322\) −3.86656 −0.215475
\(323\) 26.2705 1.46173
\(324\) −6.49967 −0.361093
\(325\) 16.3910 0.909209
\(326\) 16.5697 0.917709
\(327\) 17.4138 0.962986
\(328\) 1.60577 0.0886638
\(329\) 22.9338 1.26438
\(330\) 46.9663 2.58541
\(331\) −8.78459 −0.482845 −0.241422 0.970420i \(-0.577614\pi\)
−0.241422 + 0.970420i \(0.577614\pi\)
\(332\) −17.4693 −0.958755
\(333\) −4.61764 −0.253045
\(334\) 10.3272 0.565078
\(335\) −42.1187 −2.30119
\(336\) 26.7313 1.45831
\(337\) −33.9248 −1.84800 −0.924001 0.382391i \(-0.875101\pi\)
−0.924001 + 0.382391i \(0.875101\pi\)
\(338\) 23.4981 1.27813
\(339\) −1.95969 −0.106436
\(340\) 18.3877 0.997212
\(341\) 17.5542 0.950611
\(342\) 31.9447 1.72737
\(343\) −20.0846 −1.08447
\(344\) −9.40168 −0.506905
\(345\) 7.97934 0.429593
\(346\) 32.6877 1.75730
\(347\) −7.68216 −0.412400 −0.206200 0.978510i \(-0.566110\pi\)
−0.206200 + 0.978510i \(0.566110\pi\)
\(348\) −24.9649 −1.33826
\(349\) 31.7792 1.70110 0.850550 0.525895i \(-0.176269\pi\)
0.850550 + 0.525895i \(0.176269\pi\)
\(350\) 11.6227 0.621258
\(351\) −11.5082 −0.614262
\(352\) 20.4432 1.08962
\(353\) 26.2450 1.39688 0.698439 0.715669i \(-0.253878\pi\)
0.698439 + 0.715669i \(0.253878\pi\)
\(354\) 46.8718 2.49121
\(355\) 24.7653 1.31441
\(356\) −3.42811 −0.181689
\(357\) −30.1855 −1.59758
\(358\) 21.7426 1.14913
\(359\) −30.5776 −1.61382 −0.806911 0.590673i \(-0.798862\pi\)
−0.806911 + 0.590673i \(0.798862\pi\)
\(360\) −16.7994 −0.885407
\(361\) 2.82484 0.148676
\(362\) −4.08297 −0.214596
\(363\) −3.89296 −0.204328
\(364\) 11.9949 0.628703
\(365\) −27.5320 −1.44109
\(366\) 30.6200 1.60053
\(367\) −22.2568 −1.16179 −0.580897 0.813977i \(-0.697298\pi\)
−0.580897 + 0.813977i \(0.697298\pi\)
\(368\) 5.29932 0.276246
\(369\) −4.07292 −0.212028
\(370\) −6.07542 −0.315846
\(371\) −5.60061 −0.290769
\(372\) 14.8561 0.770252
\(373\) −7.73776 −0.400646 −0.200323 0.979730i \(-0.564199\pi\)
−0.200323 + 0.979730i \(0.564199\pi\)
\(374\) −35.2222 −1.82130
\(375\) 13.5060 0.697445
\(376\) −17.0160 −0.877532
\(377\) 42.7762 2.20309
\(378\) −8.16033 −0.419722
\(379\) −7.45714 −0.383047 −0.191524 0.981488i \(-0.561343\pi\)
−0.191524 + 0.981488i \(0.561343\pi\)
\(380\) 15.2760 0.783642
\(381\) 40.2444 2.06178
\(382\) 35.1084 1.79630
\(383\) −15.2271 −0.778068 −0.389034 0.921223i \(-0.627191\pi\)
−0.389034 + 0.921223i \(0.627191\pi\)
\(384\) −28.9301 −1.47633
\(385\) −20.7403 −1.05702
\(386\) 9.83797 0.500740
\(387\) 23.8467 1.21220
\(388\) 3.33666 0.169393
\(389\) 26.8823 1.36299 0.681494 0.731823i \(-0.261330\pi\)
0.681494 + 0.731823i \(0.261330\pi\)
\(390\) −68.1056 −3.44866
\(391\) −5.98409 −0.302628
\(392\) 4.25576 0.214948
\(393\) 37.6205 1.89770
\(394\) 8.53756 0.430116
\(395\) 6.16612 0.310251
\(396\) −15.5669 −0.782266
\(397\) −8.28463 −0.415794 −0.207897 0.978151i \(-0.566662\pi\)
−0.207897 + 0.978151i \(0.566662\pi\)
\(398\) −41.5112 −2.08077
\(399\) −25.0773 −1.25543
\(400\) −15.9295 −0.796474
\(401\) −8.88838 −0.443865 −0.221932 0.975062i \(-0.571236\pi\)
−0.221932 + 0.975062i \(0.571236\pi\)
\(402\) 68.2793 3.40546
\(403\) −25.4552 −1.26802
\(404\) 1.71568 0.0853584
\(405\) −16.2970 −0.809803
\(406\) 30.3321 1.50536
\(407\) 4.22982 0.209664
\(408\) 22.3964 1.10879
\(409\) 14.7487 0.729278 0.364639 0.931149i \(-0.381192\pi\)
0.364639 + 0.931149i \(0.381192\pi\)
\(410\) −5.35873 −0.264649
\(411\) 49.5545 2.44434
\(412\) −6.97745 −0.343754
\(413\) −20.6986 −1.01851
\(414\) −7.27658 −0.357625
\(415\) −43.8019 −2.15015
\(416\) −29.6446 −1.45344
\(417\) −39.1892 −1.91910
\(418\) −29.2617 −1.43124
\(419\) −8.87226 −0.433438 −0.216719 0.976234i \(-0.569536\pi\)
−0.216719 + 0.976234i \(0.569536\pi\)
\(420\) −17.5525 −0.856474
\(421\) 30.8807 1.50503 0.752516 0.658574i \(-0.228840\pi\)
0.752516 + 0.658574i \(0.228840\pi\)
\(422\) 38.6058 1.87930
\(423\) 43.1598 2.09850
\(424\) 4.15543 0.201805
\(425\) 17.9878 0.872539
\(426\) −40.1475 −1.94515
\(427\) −13.5218 −0.654365
\(428\) 16.4324 0.794291
\(429\) 47.4164 2.28928
\(430\) 31.3750 1.51304
\(431\) 32.0482 1.54371 0.771853 0.635801i \(-0.219330\pi\)
0.771853 + 0.635801i \(0.219330\pi\)
\(432\) 11.1842 0.538099
\(433\) 2.86180 0.137529 0.0687647 0.997633i \(-0.478094\pi\)
0.0687647 + 0.997633i \(0.478094\pi\)
\(434\) −18.0500 −0.866428
\(435\) −62.5958 −3.00124
\(436\) −7.59392 −0.363683
\(437\) −4.97142 −0.237815
\(438\) 44.6325 2.13262
\(439\) −25.1526 −1.20047 −0.600234 0.799824i \(-0.704926\pi\)
−0.600234 + 0.799824i \(0.704926\pi\)
\(440\) 15.3885 0.733616
\(441\) −10.7944 −0.514020
\(442\) 51.0757 2.42942
\(443\) 23.2449 1.10440 0.552199 0.833712i \(-0.313789\pi\)
0.552199 + 0.833712i \(0.313789\pi\)
\(444\) 3.57969 0.169885
\(445\) −8.59548 −0.407465
\(446\) −27.7432 −1.31368
\(447\) 22.5927 1.06860
\(448\) −0.604973 −0.0285823
\(449\) 2.42638 0.114508 0.0572539 0.998360i \(-0.481766\pi\)
0.0572539 + 0.998360i \(0.481766\pi\)
\(450\) 21.8730 1.03110
\(451\) 3.73084 0.175678
\(452\) 0.854592 0.0401966
\(453\) −16.8477 −0.791573
\(454\) 21.7605 1.02127
\(455\) 30.0754 1.40996
\(456\) 18.6063 0.871322
\(457\) 27.2030 1.27250 0.636252 0.771481i \(-0.280484\pi\)
0.636252 + 0.771481i \(0.280484\pi\)
\(458\) −0.686318 −0.0320695
\(459\) −12.6294 −0.589488
\(460\) −3.47968 −0.162241
\(461\) −23.3601 −1.08799 −0.543995 0.839089i \(-0.683089\pi\)
−0.543995 + 0.839089i \(0.683089\pi\)
\(462\) 33.6224 1.56426
\(463\) 30.9316 1.43751 0.718756 0.695262i \(-0.244712\pi\)
0.718756 + 0.695262i \(0.244712\pi\)
\(464\) −41.5718 −1.92992
\(465\) 37.2495 1.72740
\(466\) −17.1480 −0.794368
\(467\) −22.6883 −1.04989 −0.524944 0.851137i \(-0.675914\pi\)
−0.524944 + 0.851137i \(0.675914\pi\)
\(468\) 22.5735 1.04346
\(469\) −30.1521 −1.39229
\(470\) 56.7853 2.61931
\(471\) −43.4001 −1.99977
\(472\) 15.3575 0.706886
\(473\) −21.8439 −1.00438
\(474\) −9.99599 −0.459131
\(475\) 14.9438 0.685670
\(476\) 13.1635 0.603346
\(477\) −10.5399 −0.482591
\(478\) −10.1424 −0.463902
\(479\) 20.3393 0.929324 0.464662 0.885488i \(-0.346176\pi\)
0.464662 + 0.885488i \(0.346176\pi\)
\(480\) 43.3799 1.98001
\(481\) −6.13365 −0.279670
\(482\) −7.99426 −0.364129
\(483\) 5.71228 0.259918
\(484\) 1.69767 0.0771667
\(485\) 8.36618 0.379889
\(486\) 38.3622 1.74015
\(487\) −6.65399 −0.301521 −0.150761 0.988570i \(-0.548172\pi\)
−0.150761 + 0.988570i \(0.548172\pi\)
\(488\) 10.0326 0.454156
\(489\) −24.4793 −1.10699
\(490\) −14.2022 −0.641589
\(491\) −5.39859 −0.243635 −0.121817 0.992553i \(-0.538872\pi\)
−0.121817 + 0.992553i \(0.538872\pi\)
\(492\) 3.15741 0.142347
\(493\) 46.9436 2.11423
\(494\) 42.4323 1.90912
\(495\) −39.0317 −1.75435
\(496\) 24.7385 1.11079
\(497\) 17.7291 0.795259
\(498\) 71.0079 3.18194
\(499\) 17.6044 0.788082 0.394041 0.919093i \(-0.371077\pi\)
0.394041 + 0.919093i \(0.371077\pi\)
\(500\) −5.88976 −0.263398
\(501\) −15.2569 −0.681628
\(502\) 41.0957 1.83419
\(503\) −15.7102 −0.700485 −0.350242 0.936659i \(-0.613901\pi\)
−0.350242 + 0.936659i \(0.613901\pi\)
\(504\) −12.0264 −0.535700
\(505\) 4.30183 0.191429
\(506\) 6.66544 0.296315
\(507\) −34.7151 −1.54175
\(508\) −17.5500 −0.778656
\(509\) 31.5509 1.39847 0.699234 0.714893i \(-0.253525\pi\)
0.699234 + 0.714893i \(0.253525\pi\)
\(510\) −74.7407 −3.30957
\(511\) −19.7097 −0.871906
\(512\) 13.6623 0.603793
\(513\) −10.4921 −0.463239
\(514\) 11.1358 0.491179
\(515\) −17.4949 −0.770919
\(516\) −18.4865 −0.813821
\(517\) −39.5349 −1.73874
\(518\) −4.34930 −0.191097
\(519\) −48.2914 −2.11976
\(520\) −22.3148 −0.978567
\(521\) 13.8794 0.608067 0.304034 0.952661i \(-0.401666\pi\)
0.304034 + 0.952661i \(0.401666\pi\)
\(522\) 57.0829 2.49845
\(523\) −36.7351 −1.60631 −0.803156 0.595769i \(-0.796847\pi\)
−0.803156 + 0.595769i \(0.796847\pi\)
\(524\) −16.4058 −0.716690
\(525\) −17.1708 −0.749396
\(526\) −52.5232 −2.29012
\(527\) −27.9351 −1.21687
\(528\) −46.0813 −2.00543
\(529\) −21.8676 −0.950764
\(530\) −13.8674 −0.602360
\(531\) −38.9532 −1.69042
\(532\) 10.9358 0.474129
\(533\) −5.41008 −0.234337
\(534\) 13.9343 0.602995
\(535\) 41.2019 1.78131
\(536\) 22.3717 0.966308
\(537\) −32.1216 −1.38615
\(538\) 8.06135 0.347550
\(539\) 9.88782 0.425898
\(540\) −7.34383 −0.316028
\(541\) 41.6749 1.79174 0.895872 0.444312i \(-0.146552\pi\)
0.895872 + 0.444312i \(0.146552\pi\)
\(542\) −53.2572 −2.28759
\(543\) 6.03200 0.258858
\(544\) −32.5326 −1.39482
\(545\) −19.0406 −0.815612
\(546\) −48.7558 −2.08655
\(547\) −14.3379 −0.613044 −0.306522 0.951864i \(-0.599165\pi\)
−0.306522 + 0.951864i \(0.599165\pi\)
\(548\) −21.6100 −0.923135
\(549\) −25.4470 −1.08605
\(550\) −20.0360 −0.854336
\(551\) 38.9995 1.66143
\(552\) −4.23829 −0.180393
\(553\) 4.41423 0.187712
\(554\) −46.9672 −1.99544
\(555\) 8.97556 0.380991
\(556\) 17.0898 0.724771
\(557\) −23.1687 −0.981688 −0.490844 0.871248i \(-0.663311\pi\)
−0.490844 + 0.871248i \(0.663311\pi\)
\(558\) −33.9688 −1.43802
\(559\) 31.6757 1.33974
\(560\) −29.2286 −1.23513
\(561\) 52.0358 2.19695
\(562\) 18.0871 0.762959
\(563\) 24.3544 1.02642 0.513208 0.858264i \(-0.328457\pi\)
0.513208 + 0.858264i \(0.328457\pi\)
\(564\) −33.4584 −1.40885
\(565\) 2.14277 0.0901469
\(566\) −6.15959 −0.258907
\(567\) −11.6667 −0.489957
\(568\) −13.1543 −0.551942
\(569\) 5.41237 0.226899 0.113449 0.993544i \(-0.463810\pi\)
0.113449 + 0.993544i \(0.463810\pi\)
\(570\) −62.0925 −2.60077
\(571\) −1.81071 −0.0757760 −0.0378880 0.999282i \(-0.512063\pi\)
−0.0378880 + 0.999282i \(0.512063\pi\)
\(572\) −20.6776 −0.864574
\(573\) −51.8677 −2.16680
\(574\) −3.83623 −0.160121
\(575\) −3.40401 −0.141957
\(576\) −1.13852 −0.0474382
\(577\) 10.7228 0.446395 0.223198 0.974773i \(-0.428350\pi\)
0.223198 + 0.974773i \(0.428350\pi\)
\(578\) 25.9180 1.07805
\(579\) −14.5342 −0.604020
\(580\) 27.2972 1.13345
\(581\) −31.3571 −1.30091
\(582\) −13.5625 −0.562186
\(583\) 9.65472 0.399858
\(584\) 14.6238 0.605137
\(585\) 56.5998 2.34011
\(586\) −23.9646 −0.989967
\(587\) 12.1605 0.501919 0.250960 0.967998i \(-0.419254\pi\)
0.250960 + 0.967998i \(0.419254\pi\)
\(588\) 8.36806 0.345093
\(589\) −23.2078 −0.956259
\(590\) −51.2506 −2.10995
\(591\) −12.6130 −0.518830
\(592\) 5.96095 0.244993
\(593\) −42.9648 −1.76435 −0.882177 0.470918i \(-0.843923\pi\)
−0.882177 + 0.470918i \(0.843923\pi\)
\(594\) 14.0673 0.577190
\(595\) 33.0055 1.35309
\(596\) −9.85236 −0.403569
\(597\) 61.3269 2.50994
\(598\) −9.66553 −0.395253
\(599\) 22.5413 0.921012 0.460506 0.887656i \(-0.347668\pi\)
0.460506 + 0.887656i \(0.347668\pi\)
\(600\) 12.7401 0.520111
\(601\) 1.68713 0.0688197 0.0344098 0.999408i \(-0.489045\pi\)
0.0344098 + 0.999408i \(0.489045\pi\)
\(602\) 22.4609 0.915438
\(603\) −56.7441 −2.31080
\(604\) 7.34704 0.298947
\(605\) 4.25665 0.173057
\(606\) −6.97376 −0.283289
\(607\) 30.1716 1.22463 0.612313 0.790615i \(-0.290239\pi\)
0.612313 + 0.790615i \(0.290239\pi\)
\(608\) −27.0272 −1.09610
\(609\) −44.8114 −1.81585
\(610\) −33.4806 −1.35559
\(611\) 57.3295 2.31930
\(612\) 24.7727 1.00138
\(613\) −27.4753 −1.10972 −0.554858 0.831945i \(-0.687227\pi\)
−0.554858 + 0.831945i \(0.687227\pi\)
\(614\) 12.6016 0.508559
\(615\) 7.91675 0.319234
\(616\) 11.0164 0.443862
\(617\) 31.5957 1.27199 0.635997 0.771691i \(-0.280589\pi\)
0.635997 + 0.771691i \(0.280589\pi\)
\(618\) 28.3613 1.14086
\(619\) 1.00000 0.0401934
\(620\) −16.2440 −0.652373
\(621\) 2.38997 0.0959063
\(622\) 17.7609 0.712148
\(623\) −6.15337 −0.246530
\(624\) 66.8223 2.67503
\(625\) −30.7617 −1.23047
\(626\) −27.7135 −1.10765
\(627\) 43.2299 1.72644
\(628\) 18.9262 0.755236
\(629\) −6.73120 −0.268391
\(630\) 40.1343 1.59899
\(631\) −19.8225 −0.789122 −0.394561 0.918870i \(-0.629103\pi\)
−0.394561 + 0.918870i \(0.629103\pi\)
\(632\) −3.27518 −0.130280
\(633\) −57.0346 −2.26692
\(634\) −45.6038 −1.81116
\(635\) −44.0041 −1.74625
\(636\) 8.17079 0.323993
\(637\) −14.3383 −0.568104
\(638\) −52.2886 −2.07013
\(639\) 33.3649 1.31990
\(640\) 31.6328 1.25040
\(641\) 0.200424 0.00791629 0.00395814 0.999992i \(-0.498740\pi\)
0.00395814 + 0.999992i \(0.498740\pi\)
\(642\) −66.7931 −2.63611
\(643\) 20.3895 0.804084 0.402042 0.915621i \(-0.368301\pi\)
0.402042 + 0.915621i \(0.368301\pi\)
\(644\) −2.49105 −0.0981610
\(645\) −46.3521 −1.82511
\(646\) 46.5661 1.83212
\(647\) −9.68654 −0.380817 −0.190409 0.981705i \(-0.560981\pi\)
−0.190409 + 0.981705i \(0.560981\pi\)
\(648\) 8.65626 0.340050
\(649\) 35.6816 1.40063
\(650\) 29.0541 1.13959
\(651\) 26.6663 1.04513
\(652\) 10.6751 0.418068
\(653\) 47.7775 1.86968 0.934839 0.355073i \(-0.115544\pi\)
0.934839 + 0.355073i \(0.115544\pi\)
\(654\) 30.8671 1.20700
\(655\) −41.1351 −1.60728
\(656\) 5.25775 0.205281
\(657\) −37.0922 −1.44711
\(658\) 40.6517 1.58477
\(659\) 41.6564 1.62270 0.811352 0.584558i \(-0.198732\pi\)
0.811352 + 0.584558i \(0.198732\pi\)
\(660\) 30.2582 1.17780
\(661\) −6.19890 −0.241109 −0.120555 0.992707i \(-0.538467\pi\)
−0.120555 + 0.992707i \(0.538467\pi\)
\(662\) −15.5712 −0.605194
\(663\) −75.4569 −2.93050
\(664\) 23.2657 0.902884
\(665\) 27.4201 1.06330
\(666\) −8.18507 −0.317165
\(667\) −8.88358 −0.343974
\(668\) 6.65332 0.257425
\(669\) 40.9866 1.58463
\(670\) −74.6580 −2.88429
\(671\) 23.3098 0.899865
\(672\) 31.0550 1.19797
\(673\) −2.62521 −0.101195 −0.0505973 0.998719i \(-0.516112\pi\)
−0.0505973 + 0.998719i \(0.516112\pi\)
\(674\) −60.1338 −2.31627
\(675\) −7.18413 −0.276517
\(676\) 15.1388 0.582261
\(677\) 9.70520 0.373001 0.186501 0.982455i \(-0.440285\pi\)
0.186501 + 0.982455i \(0.440285\pi\)
\(678\) −3.47367 −0.133406
\(679\) 5.98922 0.229845
\(680\) −24.4887 −0.939100
\(681\) −32.1481 −1.23192
\(682\) 31.1159 1.19149
\(683\) 25.9542 0.993109 0.496554 0.868006i \(-0.334598\pi\)
0.496554 + 0.868006i \(0.334598\pi\)
\(684\) 20.5805 0.786914
\(685\) −54.1840 −2.07026
\(686\) −35.6013 −1.35926
\(687\) 1.01394 0.0386841
\(688\) −30.7838 −1.17362
\(689\) −14.0003 −0.533368
\(690\) 14.1439 0.538448
\(691\) 2.19332 0.0834379 0.0417189 0.999129i \(-0.486717\pi\)
0.0417189 + 0.999129i \(0.486717\pi\)
\(692\) 21.0592 0.800551
\(693\) −27.9422 −1.06144
\(694\) −13.6171 −0.516899
\(695\) 42.8503 1.62540
\(696\) 33.2482 1.26027
\(697\) −5.93715 −0.224885
\(698\) 56.3306 2.13214
\(699\) 25.3338 0.958211
\(700\) 7.48795 0.283018
\(701\) −47.1625 −1.78130 −0.890652 0.454685i \(-0.849752\pi\)
−0.890652 + 0.454685i \(0.849752\pi\)
\(702\) −20.3990 −0.769911
\(703\) −5.59210 −0.210910
\(704\) 1.04289 0.0393056
\(705\) −83.8921 −3.15956
\(706\) 46.5209 1.75084
\(707\) 3.07961 0.115821
\(708\) 30.1973 1.13489
\(709\) 4.76966 0.179128 0.0895642 0.995981i \(-0.471453\pi\)
0.0895642 + 0.995981i \(0.471453\pi\)
\(710\) 43.8981 1.64747
\(711\) 8.30726 0.311547
\(712\) 4.56556 0.171101
\(713\) 5.28643 0.197978
\(714\) −53.5057 −2.00240
\(715\) −51.8461 −1.93893
\(716\) 14.0078 0.523494
\(717\) 14.9839 0.559584
\(718\) −54.2007 −2.02275
\(719\) 40.2443 1.50086 0.750430 0.660950i \(-0.229847\pi\)
0.750430 + 0.660950i \(0.229847\pi\)
\(720\) −55.0062 −2.04996
\(721\) −12.5244 −0.466431
\(722\) 5.00720 0.186349
\(723\) 11.8104 0.439233
\(724\) −2.63047 −0.0977606
\(725\) 26.7036 0.991746
\(726\) −6.90052 −0.256102
\(727\) −10.1045 −0.374756 −0.187378 0.982288i \(-0.559999\pi\)
−0.187378 + 0.982288i \(0.559999\pi\)
\(728\) −15.9748 −0.592065
\(729\) −39.6000 −1.46667
\(730\) −48.8021 −1.80625
\(731\) 34.7616 1.28571
\(732\) 19.7271 0.729134
\(733\) 19.0825 0.704827 0.352413 0.935844i \(-0.385361\pi\)
0.352413 + 0.935844i \(0.385361\pi\)
\(734\) −39.4515 −1.45618
\(735\) 20.9817 0.773921
\(736\) 6.15646 0.226930
\(737\) 51.9783 1.91464
\(738\) −7.21951 −0.265754
\(739\) 21.7844 0.801351 0.400675 0.916220i \(-0.368776\pi\)
0.400675 + 0.916220i \(0.368776\pi\)
\(740\) −3.91412 −0.143886
\(741\) −62.6876 −2.30289
\(742\) −9.92744 −0.364448
\(743\) 41.4086 1.51913 0.759567 0.650429i \(-0.225411\pi\)
0.759567 + 0.650429i \(0.225411\pi\)
\(744\) −19.7853 −0.725365
\(745\) −24.7034 −0.905061
\(746\) −13.7157 −0.502167
\(747\) −59.0117 −2.15913
\(748\) −22.6921 −0.829704
\(749\) 29.4958 1.07775
\(750\) 23.9402 0.874172
\(751\) −5.81495 −0.212191 −0.106095 0.994356i \(-0.533835\pi\)
−0.106095 + 0.994356i \(0.533835\pi\)
\(752\) −55.7153 −2.03173
\(753\) −60.7131 −2.21251
\(754\) 75.8236 2.76133
\(755\) 18.4216 0.670432
\(756\) −5.25733 −0.191207
\(757\) −41.1295 −1.49488 −0.747438 0.664332i \(-0.768716\pi\)
−0.747438 + 0.664332i \(0.768716\pi\)
\(758\) −13.2183 −0.480109
\(759\) −9.84723 −0.357432
\(760\) −20.3446 −0.737976
\(761\) −4.58159 −0.166083 −0.0830413 0.996546i \(-0.526463\pi\)
−0.0830413 + 0.996546i \(0.526463\pi\)
\(762\) 71.3357 2.58422
\(763\) −13.6309 −0.493472
\(764\) 22.6188 0.818318
\(765\) 62.1139 2.24573
\(766\) −26.9910 −0.975224
\(767\) −51.7418 −1.86829
\(768\) −52.8261 −1.90620
\(769\) −36.3140 −1.30951 −0.654757 0.755839i \(-0.727229\pi\)
−0.654757 + 0.755839i \(0.727229\pi\)
\(770\) −36.7635 −1.32486
\(771\) −16.4515 −0.592488
\(772\) 6.33816 0.228115
\(773\) −32.7511 −1.17798 −0.588988 0.808141i \(-0.700474\pi\)
−0.588988 + 0.808141i \(0.700474\pi\)
\(774\) 42.2698 1.51936
\(775\) −15.8907 −0.570812
\(776\) −4.44376 −0.159522
\(777\) 6.42547 0.230512
\(778\) 47.6507 1.70836
\(779\) −4.93242 −0.176722
\(780\) −43.8773 −1.57106
\(781\) −30.5627 −1.09362
\(782\) −10.6072 −0.379312
\(783\) −18.7487 −0.670024
\(784\) 13.9346 0.497664
\(785\) 47.4546 1.69373
\(786\) 66.6848 2.37857
\(787\) 5.41033 0.192857 0.0964286 0.995340i \(-0.469258\pi\)
0.0964286 + 0.995340i \(0.469258\pi\)
\(788\) 5.50036 0.195942
\(789\) 77.5954 2.76247
\(790\) 10.9298 0.388866
\(791\) 1.53397 0.0545418
\(792\) 20.7320 0.736680
\(793\) −33.8015 −1.20033
\(794\) −14.6850 −0.521153
\(795\) 20.4871 0.726601
\(796\) −26.7438 −0.947908
\(797\) −27.9992 −0.991781 −0.495890 0.868385i \(-0.665158\pi\)
−0.495890 + 0.868385i \(0.665158\pi\)
\(798\) −44.4511 −1.57355
\(799\) 62.9146 2.22576
\(800\) −18.5060 −0.654285
\(801\) −11.5802 −0.409166
\(802\) −15.7552 −0.556336
\(803\) 33.9769 1.19902
\(804\) 43.9892 1.55138
\(805\) −6.24594 −0.220140
\(806\) −45.1210 −1.58932
\(807\) −11.9095 −0.419234
\(808\) −2.28495 −0.0803842
\(809\) −39.7925 −1.39903 −0.699515 0.714618i \(-0.746600\pi\)
−0.699515 + 0.714618i \(0.746600\pi\)
\(810\) −28.8874 −1.01500
\(811\) −13.6384 −0.478910 −0.239455 0.970907i \(-0.576969\pi\)
−0.239455 + 0.970907i \(0.576969\pi\)
\(812\) 19.5416 0.685776
\(813\) 78.6798 2.75942
\(814\) 7.49762 0.262792
\(815\) 26.7662 0.937579
\(816\) 73.3323 2.56715
\(817\) 28.8790 1.01035
\(818\) 26.1431 0.914072
\(819\) 40.5189 1.41585
\(820\) −3.45238 −0.120562
\(821\) 31.0452 1.08348 0.541742 0.840545i \(-0.317765\pi\)
0.541742 + 0.840545i \(0.317765\pi\)
\(822\) 87.8386 3.06372
\(823\) 5.73117 0.199776 0.0998880 0.994999i \(-0.468152\pi\)
0.0998880 + 0.994999i \(0.468152\pi\)
\(824\) 9.29257 0.323722
\(825\) 29.6002 1.03055
\(826\) −36.6895 −1.27659
\(827\) 3.33423 0.115942 0.0579712 0.998318i \(-0.481537\pi\)
0.0579712 + 0.998318i \(0.481537\pi\)
\(828\) −4.68797 −0.162918
\(829\) −18.3208 −0.636306 −0.318153 0.948039i \(-0.603063\pi\)
−0.318153 + 0.948039i \(0.603063\pi\)
\(830\) −77.6416 −2.69498
\(831\) 69.3873 2.40702
\(832\) −1.51230 −0.0524295
\(833\) −15.7352 −0.545191
\(834\) −69.4653 −2.40539
\(835\) 16.6822 0.577313
\(836\) −18.8520 −0.652009
\(837\) 11.1570 0.385641
\(838\) −15.7266 −0.543268
\(839\) 18.4923 0.638426 0.319213 0.947683i \(-0.396581\pi\)
0.319213 + 0.947683i \(0.396581\pi\)
\(840\) 23.3764 0.806563
\(841\) 40.6894 1.40308
\(842\) 54.7380 1.88639
\(843\) −26.7211 −0.920325
\(844\) 24.8720 0.856129
\(845\) 37.9583 1.30580
\(846\) 76.5035 2.63025
\(847\) 3.04727 0.104705
\(848\) 13.6061 0.467235
\(849\) 9.09990 0.312308
\(850\) 31.8846 1.09363
\(851\) 1.27381 0.0436656
\(852\) −25.8652 −0.886126
\(853\) 33.9838 1.16358 0.581791 0.813338i \(-0.302352\pi\)
0.581791 + 0.813338i \(0.302352\pi\)
\(854\) −23.9682 −0.820176
\(855\) 51.6026 1.76477
\(856\) −21.8847 −0.748004
\(857\) 27.2950 0.932381 0.466190 0.884684i \(-0.345626\pi\)
0.466190 + 0.884684i \(0.345626\pi\)
\(858\) 84.0485 2.86937
\(859\) −43.5056 −1.48439 −0.742196 0.670183i \(-0.766216\pi\)
−0.742196 + 0.670183i \(0.766216\pi\)
\(860\) 20.2135 0.689275
\(861\) 5.66748 0.193147
\(862\) 56.8074 1.93487
\(863\) −4.61472 −0.157087 −0.0785434 0.996911i \(-0.525027\pi\)
−0.0785434 + 0.996911i \(0.525027\pi\)
\(864\) 12.9931 0.442036
\(865\) 52.8029 1.79535
\(866\) 5.07272 0.172378
\(867\) −38.2901 −1.30040
\(868\) −11.6288 −0.394707
\(869\) −7.60955 −0.258136
\(870\) −110.955 −3.76173
\(871\) −75.3735 −2.55394
\(872\) 10.1136 0.342489
\(873\) 11.2713 0.381475
\(874\) −8.81215 −0.298076
\(875\) −10.5720 −0.357398
\(876\) 28.7547 0.971530
\(877\) −13.5433 −0.457326 −0.228663 0.973506i \(-0.573435\pi\)
−0.228663 + 0.973506i \(0.573435\pi\)
\(878\) −44.5846 −1.50466
\(879\) 35.4042 1.19415
\(880\) 50.3863 1.69852
\(881\) −47.1407 −1.58821 −0.794105 0.607781i \(-0.792060\pi\)
−0.794105 + 0.607781i \(0.792060\pi\)
\(882\) −19.1338 −0.644268
\(883\) −6.77213 −0.227900 −0.113950 0.993486i \(-0.536350\pi\)
−0.113950 + 0.993486i \(0.536350\pi\)
\(884\) 32.9057 1.10674
\(885\) 75.7154 2.54515
\(886\) 41.2030 1.38424
\(887\) −50.0073 −1.67908 −0.839540 0.543298i \(-0.817175\pi\)
−0.839540 + 0.543298i \(0.817175\pi\)
\(888\) −4.76744 −0.159985
\(889\) −31.5018 −1.05654
\(890\) −15.2360 −0.510713
\(891\) 20.1119 0.673776
\(892\) −17.8737 −0.598455
\(893\) 52.2678 1.74908
\(894\) 40.0470 1.33937
\(895\) 35.1224 1.17401
\(896\) 22.6454 0.756530
\(897\) 14.2794 0.476776
\(898\) 4.30091 0.143523
\(899\) −41.4707 −1.38312
\(900\) 14.0918 0.469726
\(901\) −15.3642 −0.511856
\(902\) 6.61315 0.220194
\(903\) −33.1827 −1.10425
\(904\) −1.13815 −0.0378542
\(905\) −6.59552 −0.219243
\(906\) −29.8636 −0.992151
\(907\) 24.6019 0.816893 0.408446 0.912782i \(-0.366071\pi\)
0.408446 + 0.912782i \(0.366071\pi\)
\(908\) 14.0193 0.465247
\(909\) 5.79560 0.192228
\(910\) 53.3106 1.76723
\(911\) −1.01613 −0.0336659 −0.0168329 0.999858i \(-0.505358\pi\)
−0.0168329 + 0.999858i \(0.505358\pi\)
\(912\) 60.9226 2.01735
\(913\) 54.0555 1.78897
\(914\) 48.2191 1.59495
\(915\) 49.4628 1.63519
\(916\) −0.442163 −0.0146095
\(917\) −29.4480 −0.972458
\(918\) −22.3863 −0.738859
\(919\) −48.5457 −1.60137 −0.800687 0.599083i \(-0.795532\pi\)
−0.800687 + 0.599083i \(0.795532\pi\)
\(920\) 4.63424 0.152786
\(921\) −18.6171 −0.613453
\(922\) −41.4073 −1.36368
\(923\) 44.3188 1.45877
\(924\) 21.6614 0.712607
\(925\) −3.82900 −0.125897
\(926\) 54.8282 1.80177
\(927\) −23.5699 −0.774138
\(928\) −48.2958 −1.58539
\(929\) 2.94386 0.0965849 0.0482925 0.998833i \(-0.484622\pi\)
0.0482925 + 0.998833i \(0.484622\pi\)
\(930\) 66.0270 2.16511
\(931\) −13.0724 −0.428429
\(932\) −11.0477 −0.361880
\(933\) −26.2392 −0.859033
\(934\) −40.2164 −1.31592
\(935\) −56.8971 −1.86073
\(936\) −30.0634 −0.982653
\(937\) −5.08901 −0.166251 −0.0831254 0.996539i \(-0.526490\pi\)
−0.0831254 + 0.996539i \(0.526490\pi\)
\(938\) −53.4465 −1.74509
\(939\) 40.9427 1.33612
\(940\) 36.5841 1.19324
\(941\) 41.0134 1.33700 0.668500 0.743713i \(-0.266937\pi\)
0.668500 + 0.743713i \(0.266937\pi\)
\(942\) −76.9294 −2.50650
\(943\) 1.12354 0.0365876
\(944\) 50.2849 1.63663
\(945\) −13.1820 −0.428810
\(946\) −38.7196 −1.25888
\(947\) 2.68330 0.0871955 0.0435977 0.999049i \(-0.486118\pi\)
0.0435977 + 0.999049i \(0.486118\pi\)
\(948\) −6.43996 −0.209160
\(949\) −49.2699 −1.59937
\(950\) 26.4889 0.859413
\(951\) 67.3731 2.18472
\(952\) −17.5311 −0.568186
\(953\) −9.99036 −0.323620 −0.161810 0.986822i \(-0.551733\pi\)
−0.161810 + 0.986822i \(0.551733\pi\)
\(954\) −18.6827 −0.604876
\(955\) 56.7133 1.83520
\(956\) −6.53427 −0.211333
\(957\) 77.2489 2.49710
\(958\) 36.0526 1.16481
\(959\) −38.7895 −1.25258
\(960\) 2.21299 0.0714241
\(961\) −6.32167 −0.203925
\(962\) −10.8723 −0.350536
\(963\) 55.5090 1.78875
\(964\) −5.15034 −0.165881
\(965\) 15.8920 0.511582
\(966\) 10.1254 0.325779
\(967\) 48.6395 1.56414 0.782071 0.623190i \(-0.214164\pi\)
0.782071 + 0.623190i \(0.214164\pi\)
\(968\) −2.26095 −0.0726698
\(969\) −68.7948 −2.21001
\(970\) 14.8296 0.476150
\(971\) 39.2714 1.26028 0.630140 0.776481i \(-0.282997\pi\)
0.630140 + 0.776481i \(0.282997\pi\)
\(972\) 24.7150 0.792735
\(973\) 30.6759 0.983423
\(974\) −11.7946 −0.377924
\(975\) −42.9232 −1.37464
\(976\) 32.8497 1.05149
\(977\) −16.3579 −0.523334 −0.261667 0.965158i \(-0.584272\pi\)
−0.261667 + 0.965158i \(0.584272\pi\)
\(978\) −43.3911 −1.38749
\(979\) 10.6076 0.339021
\(980\) −9.14982 −0.292280
\(981\) −25.6524 −0.819017
\(982\) −9.56934 −0.305370
\(983\) 3.32253 0.105972 0.0529861 0.998595i \(-0.483126\pi\)
0.0529861 + 0.998595i \(0.483126\pi\)
\(984\) −4.20504 −0.134052
\(985\) 13.7914 0.439429
\(986\) 83.2105 2.64996
\(987\) −60.0570 −1.91164
\(988\) 27.3372 0.869712
\(989\) −6.57828 −0.209177
\(990\) −69.1862 −2.19888
\(991\) −7.41851 −0.235657 −0.117828 0.993034i \(-0.537593\pi\)
−0.117828 + 0.993034i \(0.537593\pi\)
\(992\) 28.7398 0.912490
\(993\) 23.0043 0.730019
\(994\) 31.4260 0.996771
\(995\) −67.0562 −2.12582
\(996\) 45.7471 1.44955
\(997\) −19.6099 −0.621050 −0.310525 0.950565i \(-0.600505\pi\)
−0.310525 + 0.950565i \(0.600505\pi\)
\(998\) 31.2050 0.987776
\(999\) 2.68836 0.0850560
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 619.2.a.b.1.22 30
3.2 odd 2 5571.2.a.g.1.9 30
4.3 odd 2 9904.2.a.n.1.25 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
619.2.a.b.1.22 30 1.1 even 1 trivial
5571.2.a.g.1.9 30 3.2 odd 2
9904.2.a.n.1.25 30 4.3 odd 2