Properties

Label 8045.2.a.d.1.16
Level $8045$
Weight $2$
Character 8045.1
Self dual yes
Analytic conductor $64.240$
Analytic rank $0$
Dimension $141$
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] = [8045,2,Mod(1,8045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8045, 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("8045.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8045 = 5 \cdot 1609 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8045.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: \(64.2396484261\)
Analytic rank: \(0\)
Dimension: \(141\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 8045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.41054 q^{2} +1.33575 q^{3} +3.81069 q^{4} -1.00000 q^{5} -3.21988 q^{6} -0.579711 q^{7} -4.36473 q^{8} -1.21576 q^{9} +O(q^{10})\) \(q-2.41054 q^{2} +1.33575 q^{3} +3.81069 q^{4} -1.00000 q^{5} -3.21988 q^{6} -0.579711 q^{7} -4.36473 q^{8} -1.21576 q^{9} +2.41054 q^{10} +5.70925 q^{11} +5.09014 q^{12} -1.30078 q^{13} +1.39741 q^{14} -1.33575 q^{15} +2.89997 q^{16} -6.86388 q^{17} +2.93064 q^{18} +5.70841 q^{19} -3.81069 q^{20} -0.774351 q^{21} -13.7624 q^{22} +4.02978 q^{23} -5.83021 q^{24} +1.00000 q^{25} +3.13557 q^{26} -5.63122 q^{27} -2.20910 q^{28} +0.140171 q^{29} +3.21988 q^{30} +6.35534 q^{31} +1.73898 q^{32} +7.62616 q^{33} +16.5456 q^{34} +0.579711 q^{35} -4.63289 q^{36} -6.11193 q^{37} -13.7603 q^{38} -1.73752 q^{39} +4.36473 q^{40} +1.11713 q^{41} +1.86660 q^{42} +3.75806 q^{43} +21.7562 q^{44} +1.21576 q^{45} -9.71393 q^{46} -9.17145 q^{47} +3.87365 q^{48} -6.66394 q^{49} -2.41054 q^{50} -9.16845 q^{51} -4.95686 q^{52} +0.869216 q^{53} +13.5743 q^{54} -5.70925 q^{55} +2.53028 q^{56} +7.62503 q^{57} -0.337886 q^{58} +10.5599 q^{59} -5.09014 q^{60} +12.3740 q^{61} -15.3198 q^{62} +0.704790 q^{63} -9.99181 q^{64} +1.30078 q^{65} -18.3831 q^{66} +3.52300 q^{67} -26.1561 q^{68} +5.38279 q^{69} -1.39741 q^{70} -2.15319 q^{71} +5.30647 q^{72} -1.33394 q^{73} +14.7330 q^{74} +1.33575 q^{75} +21.7530 q^{76} -3.30972 q^{77} +4.18835 q^{78} +6.29460 q^{79} -2.89997 q^{80} -3.87464 q^{81} -2.69288 q^{82} -12.6133 q^{83} -2.95081 q^{84} +6.86388 q^{85} -9.05894 q^{86} +0.187233 q^{87} -24.9194 q^{88} +0.459166 q^{89} -2.93064 q^{90} +0.754074 q^{91} +15.3562 q^{92} +8.48917 q^{93} +22.1081 q^{94} -5.70841 q^{95} +2.32284 q^{96} +1.65456 q^{97} +16.0637 q^{98} -6.94109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 141 q - 8 q^{2} + 11 q^{3} + 158 q^{4} - 141 q^{5} + 23 q^{6} + 29 q^{7} - 21 q^{8} + 160 q^{9} + 8 q^{10} + 32 q^{11} + 17 q^{12} + 35 q^{13} + 18 q^{14} - 11 q^{15} + 188 q^{16} - 13 q^{17} - 16 q^{18} + 152 q^{19} - 158 q^{20} + 40 q^{21} + 14 q^{22} - 77 q^{23} + 69 q^{24} + 141 q^{25} + 27 q^{26} + 38 q^{27} + 67 q^{28} + 22 q^{29} - 23 q^{30} + 86 q^{31} - 65 q^{32} + 51 q^{33} + 79 q^{34} - 29 q^{35} + 191 q^{36} + 45 q^{37} - 9 q^{38} + 55 q^{39} + 21 q^{40} + 36 q^{41} + 6 q^{42} + 132 q^{43} + 74 q^{44} - 160 q^{45} + 72 q^{46} - 16 q^{47} + 22 q^{48} + 212 q^{49} - 8 q^{50} + 82 q^{51} + 106 q^{52} - 28 q^{53} + 86 q^{54} - 32 q^{55} + 27 q^{56} + 10 q^{57} + 23 q^{58} + 71 q^{59} - 17 q^{60} + 116 q^{61} - 36 q^{62} + 45 q^{63} + 237 q^{64} - 35 q^{65} + 69 q^{66} + 99 q^{67} - 7 q^{68} + 45 q^{69} - 18 q^{70} + 34 q^{71} - 53 q^{72} + 125 q^{73} + 50 q^{74} + 11 q^{75} + 271 q^{76} - 31 q^{77} + 2 q^{78} + 101 q^{79} - 188 q^{80} + 221 q^{81} + 67 q^{82} + 67 q^{83} + 141 q^{84} + 13 q^{85} + 48 q^{86} - 21 q^{87} + 71 q^{88} + 79 q^{89} + 16 q^{90} + 228 q^{91} - 198 q^{92} - 12 q^{93} + 114 q^{94} - 152 q^{95} + 129 q^{96} + 98 q^{97} - 31 q^{98} + 195 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.41054 −1.70451 −0.852254 0.523129i \(-0.824765\pi\)
−0.852254 + 0.523129i \(0.824765\pi\)
\(3\) 1.33575 0.771198 0.385599 0.922666i \(-0.373995\pi\)
0.385599 + 0.922666i \(0.373995\pi\)
\(4\) 3.81069 1.90534
\(5\) −1.00000 −0.447214
\(6\) −3.21988 −1.31451
\(7\) −0.579711 −0.219110 −0.109555 0.993981i \(-0.534943\pi\)
−0.109555 + 0.993981i \(0.534943\pi\)
\(8\) −4.36473 −1.54317
\(9\) −1.21576 −0.405254
\(10\) 2.41054 0.762279
\(11\) 5.70925 1.72140 0.860702 0.509108i \(-0.170025\pi\)
0.860702 + 0.509108i \(0.170025\pi\)
\(12\) 5.09014 1.46940
\(13\) −1.30078 −0.360771 −0.180385 0.983596i \(-0.557734\pi\)
−0.180385 + 0.983596i \(0.557734\pi\)
\(14\) 1.39741 0.373475
\(15\) −1.33575 −0.344890
\(16\) 2.89997 0.724993
\(17\) −6.86388 −1.66474 −0.832368 0.554224i \(-0.813015\pi\)
−0.832368 + 0.554224i \(0.813015\pi\)
\(18\) 2.93064 0.690758
\(19\) 5.70841 1.30960 0.654800 0.755802i \(-0.272753\pi\)
0.654800 + 0.755802i \(0.272753\pi\)
\(20\) −3.81069 −0.852096
\(21\) −0.774351 −0.168977
\(22\) −13.7624 −2.93415
\(23\) 4.02978 0.840267 0.420134 0.907462i \(-0.361983\pi\)
0.420134 + 0.907462i \(0.361983\pi\)
\(24\) −5.83021 −1.19009
\(25\) 1.00000 0.200000
\(26\) 3.13557 0.614936
\(27\) −5.63122 −1.08373
\(28\) −2.20910 −0.417480
\(29\) 0.140171 0.0260290 0.0130145 0.999915i \(-0.495857\pi\)
0.0130145 + 0.999915i \(0.495857\pi\)
\(30\) 3.21988 0.587868
\(31\) 6.35534 1.14145 0.570726 0.821141i \(-0.306662\pi\)
0.570726 + 0.821141i \(0.306662\pi\)
\(32\) 1.73898 0.307410
\(33\) 7.62616 1.32754
\(34\) 16.5456 2.83755
\(35\) 0.579711 0.0979890
\(36\) −4.63289 −0.772148
\(37\) −6.11193 −1.00480 −0.502398 0.864637i \(-0.667549\pi\)
−0.502398 + 0.864637i \(0.667549\pi\)
\(38\) −13.7603 −2.23222
\(39\) −1.73752 −0.278225
\(40\) 4.36473 0.690125
\(41\) 1.11713 0.174466 0.0872329 0.996188i \(-0.472198\pi\)
0.0872329 + 0.996188i \(0.472198\pi\)
\(42\) 1.86660 0.288023
\(43\) 3.75806 0.573099 0.286549 0.958065i \(-0.407492\pi\)
0.286549 + 0.958065i \(0.407492\pi\)
\(44\) 21.7562 3.27987
\(45\) 1.21576 0.181235
\(46\) −9.71393 −1.43224
\(47\) −9.17145 −1.33779 −0.668897 0.743355i \(-0.733233\pi\)
−0.668897 + 0.743355i \(0.733233\pi\)
\(48\) 3.87365 0.559113
\(49\) −6.66394 −0.951991
\(50\) −2.41054 −0.340901
\(51\) −9.16845 −1.28384
\(52\) −4.95686 −0.687392
\(53\) 0.869216 0.119396 0.0596980 0.998216i \(-0.480986\pi\)
0.0596980 + 0.998216i \(0.480986\pi\)
\(54\) 13.5743 1.84722
\(55\) −5.70925 −0.769836
\(56\) 2.53028 0.338123
\(57\) 7.62503 1.00996
\(58\) −0.337886 −0.0443666
\(59\) 10.5599 1.37478 0.687391 0.726288i \(-0.258756\pi\)
0.687391 + 0.726288i \(0.258756\pi\)
\(60\) −5.09014 −0.657135
\(61\) 12.3740 1.58433 0.792167 0.610305i \(-0.208953\pi\)
0.792167 + 0.610305i \(0.208953\pi\)
\(62\) −15.3198 −1.94561
\(63\) 0.704790 0.0887952
\(64\) −9.99181 −1.24898
\(65\) 1.30078 0.161341
\(66\) −18.3831 −2.26281
\(67\) 3.52300 0.430403 0.215201 0.976570i \(-0.430959\pi\)
0.215201 + 0.976570i \(0.430959\pi\)
\(68\) −26.1561 −3.17189
\(69\) 5.38279 0.648012
\(70\) −1.39741 −0.167023
\(71\) −2.15319 −0.255537 −0.127768 0.991804i \(-0.540781\pi\)
−0.127768 + 0.991804i \(0.540781\pi\)
\(72\) 5.30647 0.625374
\(73\) −1.33394 −0.156126 −0.0780632 0.996948i \(-0.524874\pi\)
−0.0780632 + 0.996948i \(0.524874\pi\)
\(74\) 14.7330 1.71268
\(75\) 1.33575 0.154240
\(76\) 21.7530 2.49524
\(77\) −3.30972 −0.377177
\(78\) 4.18835 0.474237
\(79\) 6.29460 0.708198 0.354099 0.935208i \(-0.384788\pi\)
0.354099 + 0.935208i \(0.384788\pi\)
\(80\) −2.89997 −0.324227
\(81\) −3.87464 −0.430516
\(82\) −2.69288 −0.297378
\(83\) −12.6133 −1.38449 −0.692246 0.721662i \(-0.743378\pi\)
−0.692246 + 0.721662i \(0.743378\pi\)
\(84\) −2.95081 −0.321960
\(85\) 6.86388 0.744492
\(86\) −9.05894 −0.976851
\(87\) 0.187233 0.0200735
\(88\) −24.9194 −2.65641
\(89\) 0.459166 0.0486715 0.0243357 0.999704i \(-0.492253\pi\)
0.0243357 + 0.999704i \(0.492253\pi\)
\(90\) −2.93064 −0.308916
\(91\) 0.754074 0.0790484
\(92\) 15.3562 1.60100
\(93\) 8.48917 0.880286
\(94\) 22.1081 2.28028
\(95\) −5.70841 −0.585671
\(96\) 2.32284 0.237074
\(97\) 1.65456 0.167995 0.0839973 0.996466i \(-0.473231\pi\)
0.0839973 + 0.996466i \(0.473231\pi\)
\(98\) 16.0637 1.62268
\(99\) −6.94109 −0.697606
\(100\) 3.81069 0.381069
\(101\) −17.9101 −1.78212 −0.891060 0.453885i \(-0.850038\pi\)
−0.891060 + 0.453885i \(0.850038\pi\)
\(102\) 22.1009 2.18832
\(103\) 2.57010 0.253240 0.126620 0.991951i \(-0.459587\pi\)
0.126620 + 0.991951i \(0.459587\pi\)
\(104\) 5.67754 0.556729
\(105\) 0.774351 0.0755689
\(106\) −2.09528 −0.203511
\(107\) 16.4936 1.59450 0.797250 0.603650i \(-0.206287\pi\)
0.797250 + 0.603650i \(0.206287\pi\)
\(108\) −21.4588 −2.06488
\(109\) −5.84389 −0.559743 −0.279872 0.960037i \(-0.590292\pi\)
−0.279872 + 0.960037i \(0.590292\pi\)
\(110\) 13.7624 1.31219
\(111\) −8.16404 −0.774896
\(112\) −1.68114 −0.158853
\(113\) 15.5070 1.45878 0.729389 0.684099i \(-0.239804\pi\)
0.729389 + 0.684099i \(0.239804\pi\)
\(114\) −18.3804 −1.72148
\(115\) −4.02978 −0.375779
\(116\) 0.534146 0.0495942
\(117\) 1.58143 0.146204
\(118\) −25.4550 −2.34332
\(119\) 3.97906 0.364760
\(120\) 5.83021 0.532223
\(121\) 21.5956 1.96323
\(122\) −29.8281 −2.70051
\(123\) 1.49221 0.134548
\(124\) 24.2182 2.17486
\(125\) −1.00000 −0.0894427
\(126\) −1.69892 −0.151352
\(127\) 15.4325 1.36941 0.684707 0.728819i \(-0.259930\pi\)
0.684707 + 0.728819i \(0.259930\pi\)
\(128\) 20.6077 1.82148
\(129\) 5.01984 0.441972
\(130\) −3.13557 −0.275008
\(131\) 0.915298 0.0799699 0.0399850 0.999200i \(-0.487269\pi\)
0.0399850 + 0.999200i \(0.487269\pi\)
\(132\) 29.0609 2.52943
\(133\) −3.30923 −0.286946
\(134\) −8.49232 −0.733624
\(135\) 5.63122 0.484658
\(136\) 29.9590 2.56896
\(137\) −6.65133 −0.568262 −0.284131 0.958785i \(-0.591705\pi\)
−0.284131 + 0.958785i \(0.591705\pi\)
\(138\) −12.9754 −1.10454
\(139\) −12.4453 −1.05560 −0.527799 0.849369i \(-0.676983\pi\)
−0.527799 + 0.849369i \(0.676983\pi\)
\(140\) 2.20910 0.186703
\(141\) −12.2508 −1.03170
\(142\) 5.19035 0.435564
\(143\) −7.42646 −0.621032
\(144\) −3.52567 −0.293806
\(145\) −0.140171 −0.0116405
\(146\) 3.21552 0.266119
\(147\) −8.90138 −0.734173
\(148\) −23.2907 −1.91448
\(149\) −5.49516 −0.450181 −0.225090 0.974338i \(-0.572268\pi\)
−0.225090 + 0.974338i \(0.572268\pi\)
\(150\) −3.21988 −0.262902
\(151\) −15.8564 −1.29038 −0.645189 0.764023i \(-0.723221\pi\)
−0.645189 + 0.764023i \(0.723221\pi\)
\(152\) −24.9157 −2.02093
\(153\) 8.34484 0.674640
\(154\) 7.97819 0.642901
\(155\) −6.35534 −0.510473
\(156\) −6.62114 −0.530115
\(157\) −16.1043 −1.28526 −0.642631 0.766176i \(-0.722157\pi\)
−0.642631 + 0.766176i \(0.722157\pi\)
\(158\) −15.1734 −1.20713
\(159\) 1.16106 0.0920779
\(160\) −1.73898 −0.137478
\(161\) −2.33611 −0.184111
\(162\) 9.33996 0.733817
\(163\) 10.0309 0.785679 0.392839 0.919607i \(-0.371493\pi\)
0.392839 + 0.919607i \(0.371493\pi\)
\(164\) 4.25702 0.332418
\(165\) −7.62616 −0.593696
\(166\) 30.4049 2.35987
\(167\) −7.43019 −0.574966 −0.287483 0.957786i \(-0.592818\pi\)
−0.287483 + 0.957786i \(0.592818\pi\)
\(168\) 3.37983 0.260760
\(169\) −11.3080 −0.869845
\(170\) −16.5456 −1.26899
\(171\) −6.94007 −0.530720
\(172\) 14.3208 1.09195
\(173\) 1.24346 0.0945388 0.0472694 0.998882i \(-0.484948\pi\)
0.0472694 + 0.998882i \(0.484948\pi\)
\(174\) −0.451333 −0.0342155
\(175\) −0.579711 −0.0438220
\(176\) 16.5567 1.24801
\(177\) 14.1054 1.06023
\(178\) −1.10684 −0.0829609
\(179\) 25.9239 1.93764 0.968821 0.247764i \(-0.0796956\pi\)
0.968821 + 0.247764i \(0.0796956\pi\)
\(180\) 4.63289 0.345315
\(181\) 16.8986 1.25607 0.628033 0.778187i \(-0.283860\pi\)
0.628033 + 0.778187i \(0.283860\pi\)
\(182\) −1.81772 −0.134739
\(183\) 16.5287 1.22183
\(184\) −17.5889 −1.29667
\(185\) 6.11193 0.449358
\(186\) −20.4634 −1.50045
\(187\) −39.1876 −2.86568
\(188\) −34.9495 −2.54896
\(189\) 3.26448 0.237456
\(190\) 13.7603 0.998280
\(191\) 1.13415 0.0820642 0.0410321 0.999158i \(-0.486935\pi\)
0.0410321 + 0.999158i \(0.486935\pi\)
\(192\) −13.3466 −0.963208
\(193\) 10.1469 0.730386 0.365193 0.930932i \(-0.381003\pi\)
0.365193 + 0.930932i \(0.381003\pi\)
\(194\) −3.98837 −0.286348
\(195\) 1.73752 0.124426
\(196\) −25.3942 −1.81387
\(197\) −13.6503 −0.972543 −0.486272 0.873808i \(-0.661643\pi\)
−0.486272 + 0.873808i \(0.661643\pi\)
\(198\) 16.7318 1.18907
\(199\) −11.7669 −0.834135 −0.417068 0.908875i \(-0.636942\pi\)
−0.417068 + 0.908875i \(0.636942\pi\)
\(200\) −4.36473 −0.308633
\(201\) 4.70586 0.331926
\(202\) 43.1729 3.03764
\(203\) −0.0812584 −0.00570322
\(204\) −34.9381 −2.44616
\(205\) −1.11713 −0.0780235
\(206\) −6.19532 −0.431649
\(207\) −4.89925 −0.340521
\(208\) −3.77222 −0.261556
\(209\) 32.5908 2.25435
\(210\) −1.86660 −0.128808
\(211\) 27.5331 1.89546 0.947728 0.319080i \(-0.103374\pi\)
0.947728 + 0.319080i \(0.103374\pi\)
\(212\) 3.31231 0.227490
\(213\) −2.87613 −0.197070
\(214\) −39.7585 −2.71784
\(215\) −3.75806 −0.256298
\(216\) 24.5788 1.67237
\(217\) −3.68426 −0.250104
\(218\) 14.0869 0.954086
\(219\) −1.78182 −0.120404
\(220\) −21.7562 −1.46680
\(221\) 8.92837 0.600587
\(222\) 19.6797 1.32082
\(223\) −5.28037 −0.353599 −0.176800 0.984247i \(-0.556574\pi\)
−0.176800 + 0.984247i \(0.556574\pi\)
\(224\) −1.00810 −0.0673567
\(225\) −1.21576 −0.0810508
\(226\) −37.3803 −2.48650
\(227\) 11.7070 0.777023 0.388511 0.921444i \(-0.372989\pi\)
0.388511 + 0.921444i \(0.372989\pi\)
\(228\) 29.0566 1.92432
\(229\) 21.7015 1.43408 0.717039 0.697033i \(-0.245497\pi\)
0.717039 + 0.697033i \(0.245497\pi\)
\(230\) 9.71393 0.640518
\(231\) −4.42097 −0.290878
\(232\) −0.611807 −0.0401671
\(233\) −4.91197 −0.321794 −0.160897 0.986971i \(-0.551439\pi\)
−0.160897 + 0.986971i \(0.551439\pi\)
\(234\) −3.81211 −0.249205
\(235\) 9.17145 0.598279
\(236\) 40.2405 2.61943
\(237\) 8.40804 0.546161
\(238\) −9.59168 −0.621736
\(239\) −25.4102 −1.64365 −0.821824 0.569741i \(-0.807043\pi\)
−0.821824 + 0.569741i \(0.807043\pi\)
\(240\) −3.87365 −0.250043
\(241\) −0.552882 −0.0356143 −0.0178071 0.999841i \(-0.505668\pi\)
−0.0178071 + 0.999841i \(0.505668\pi\)
\(242\) −52.0570 −3.34635
\(243\) 11.7181 0.751716
\(244\) 47.1536 3.01870
\(245\) 6.66394 0.425743
\(246\) −3.59702 −0.229338
\(247\) −7.42537 −0.472465
\(248\) −27.7393 −1.76145
\(249\) −16.8483 −1.06772
\(250\) 2.41054 0.152456
\(251\) −1.11420 −0.0703277 −0.0351639 0.999382i \(-0.511195\pi\)
−0.0351639 + 0.999382i \(0.511195\pi\)
\(252\) 2.68573 0.169185
\(253\) 23.0070 1.44644
\(254\) −37.2006 −2.33418
\(255\) 9.16845 0.574151
\(256\) −29.6919 −1.85575
\(257\) 14.6434 0.913430 0.456715 0.889613i \(-0.349026\pi\)
0.456715 + 0.889613i \(0.349026\pi\)
\(258\) −12.1005 −0.753345
\(259\) 3.54315 0.220161
\(260\) 4.95686 0.307411
\(261\) −0.170414 −0.0105484
\(262\) −2.20636 −0.136309
\(263\) 20.0453 1.23604 0.618022 0.786161i \(-0.287934\pi\)
0.618022 + 0.786161i \(0.287934\pi\)
\(264\) −33.2861 −2.04862
\(265\) −0.869216 −0.0533955
\(266\) 7.97702 0.489102
\(267\) 0.613332 0.0375353
\(268\) 13.4250 0.820065
\(269\) 9.60367 0.585546 0.292773 0.956182i \(-0.405422\pi\)
0.292773 + 0.956182i \(0.405422\pi\)
\(270\) −13.5743 −0.826103
\(271\) 6.36441 0.386610 0.193305 0.981139i \(-0.438079\pi\)
0.193305 + 0.981139i \(0.438079\pi\)
\(272\) −19.9051 −1.20692
\(273\) 1.00726 0.0609620
\(274\) 16.0333 0.968606
\(275\) 5.70925 0.344281
\(276\) 20.5122 1.23469
\(277\) 12.2752 0.737547 0.368774 0.929519i \(-0.379778\pi\)
0.368774 + 0.929519i \(0.379778\pi\)
\(278\) 29.9999 1.79928
\(279\) −7.72657 −0.462578
\(280\) −2.53028 −0.151213
\(281\) −10.2846 −0.613529 −0.306764 0.951785i \(-0.599246\pi\)
−0.306764 + 0.951785i \(0.599246\pi\)
\(282\) 29.5310 1.75855
\(283\) 11.0051 0.654188 0.327094 0.944992i \(-0.393931\pi\)
0.327094 + 0.944992i \(0.393931\pi\)
\(284\) −8.20515 −0.486886
\(285\) −7.62503 −0.451668
\(286\) 17.9018 1.05855
\(287\) −0.647610 −0.0382272
\(288\) −2.11418 −0.124579
\(289\) 30.1128 1.77134
\(290\) 0.337886 0.0198414
\(291\) 2.21008 0.129557
\(292\) −5.08325 −0.297475
\(293\) 4.93739 0.288445 0.144223 0.989545i \(-0.453932\pi\)
0.144223 + 0.989545i \(0.453932\pi\)
\(294\) 21.4571 1.25140
\(295\) −10.5599 −0.614821
\(296\) 26.6769 1.55057
\(297\) −32.1501 −1.86554
\(298\) 13.2463 0.767336
\(299\) −5.24184 −0.303144
\(300\) 5.09014 0.293880
\(301\) −2.17859 −0.125572
\(302\) 38.2225 2.19946
\(303\) −23.9235 −1.37437
\(304\) 16.5542 0.949451
\(305\) −12.3740 −0.708536
\(306\) −20.1155 −1.14993
\(307\) 20.4369 1.16640 0.583199 0.812329i \(-0.301801\pi\)
0.583199 + 0.812329i \(0.301801\pi\)
\(308\) −12.6123 −0.718652
\(309\) 3.43302 0.195298
\(310\) 15.3198 0.870105
\(311\) −7.90496 −0.448249 −0.224124 0.974561i \(-0.571952\pi\)
−0.224124 + 0.974561i \(0.571952\pi\)
\(312\) 7.58380 0.429348
\(313\) 24.8828 1.40646 0.703230 0.710963i \(-0.251741\pi\)
0.703230 + 0.710963i \(0.251741\pi\)
\(314\) 38.8200 2.19074
\(315\) −0.704790 −0.0397104
\(316\) 23.9868 1.34936
\(317\) −23.2173 −1.30402 −0.652008 0.758212i \(-0.726073\pi\)
−0.652008 + 0.758212i \(0.726073\pi\)
\(318\) −2.79877 −0.156947
\(319\) 0.800269 0.0448065
\(320\) 9.99181 0.558559
\(321\) 22.0314 1.22967
\(322\) 5.63127 0.313818
\(323\) −39.1819 −2.18014
\(324\) −14.7650 −0.820281
\(325\) −1.30078 −0.0721541
\(326\) −24.1798 −1.33920
\(327\) −7.80600 −0.431673
\(328\) −4.87596 −0.269230
\(329\) 5.31679 0.293124
\(330\) 18.3831 1.01196
\(331\) 10.5504 0.579901 0.289951 0.957042i \(-0.406361\pi\)
0.289951 + 0.957042i \(0.406361\pi\)
\(332\) −48.0654 −2.63793
\(333\) 7.43065 0.407197
\(334\) 17.9108 0.980033
\(335\) −3.52300 −0.192482
\(336\) −2.24560 −0.122507
\(337\) −28.9734 −1.57828 −0.789142 0.614211i \(-0.789475\pi\)
−0.789142 + 0.614211i \(0.789475\pi\)
\(338\) 27.2583 1.48266
\(339\) 20.7136 1.12501
\(340\) 26.1561 1.41851
\(341\) 36.2842 1.96490
\(342\) 16.7293 0.904616
\(343\) 7.92113 0.427701
\(344\) −16.4029 −0.884386
\(345\) −5.38279 −0.289800
\(346\) −2.99741 −0.161142
\(347\) −28.3134 −1.51994 −0.759971 0.649957i \(-0.774787\pi\)
−0.759971 + 0.649957i \(0.774787\pi\)
\(348\) 0.713488 0.0382470
\(349\) 36.0563 1.93005 0.965025 0.262156i \(-0.0844336\pi\)
0.965025 + 0.262156i \(0.0844336\pi\)
\(350\) 1.39741 0.0746949
\(351\) 7.32496 0.390977
\(352\) 9.92825 0.529178
\(353\) 34.5113 1.83685 0.918426 0.395592i \(-0.129461\pi\)
0.918426 + 0.395592i \(0.129461\pi\)
\(354\) −34.0016 −1.80717
\(355\) 2.15319 0.114280
\(356\) 1.74974 0.0927359
\(357\) 5.31505 0.281302
\(358\) −62.4905 −3.30272
\(359\) −8.45269 −0.446116 −0.223058 0.974805i \(-0.571604\pi\)
−0.223058 + 0.974805i \(0.571604\pi\)
\(360\) −5.30647 −0.279676
\(361\) 13.5860 0.715051
\(362\) −40.7348 −2.14097
\(363\) 28.8464 1.51404
\(364\) 2.87354 0.150615
\(365\) 1.33394 0.0698219
\(366\) −39.8430 −2.08263
\(367\) 25.5447 1.33342 0.666710 0.745317i \(-0.267702\pi\)
0.666710 + 0.745317i \(0.267702\pi\)
\(368\) 11.6862 0.609188
\(369\) −1.35816 −0.0707030
\(370\) −14.7330 −0.765934
\(371\) −0.503894 −0.0261609
\(372\) 32.3496 1.67725
\(373\) 30.0540 1.55614 0.778069 0.628178i \(-0.216199\pi\)
0.778069 + 0.628178i \(0.216199\pi\)
\(374\) 94.4632 4.88458
\(375\) −1.33575 −0.0689780
\(376\) 40.0309 2.06444
\(377\) −0.182331 −0.00939050
\(378\) −7.86915 −0.404745
\(379\) −2.24607 −0.115373 −0.0576864 0.998335i \(-0.518372\pi\)
−0.0576864 + 0.998335i \(0.518372\pi\)
\(380\) −21.7530 −1.11590
\(381\) 20.6140 1.05609
\(382\) −2.73391 −0.139879
\(383\) −19.8384 −1.01369 −0.506847 0.862036i \(-0.669189\pi\)
−0.506847 + 0.862036i \(0.669189\pi\)
\(384\) 27.5268 1.40472
\(385\) 3.30972 0.168679
\(386\) −24.4594 −1.24495
\(387\) −4.56890 −0.232250
\(388\) 6.30500 0.320088
\(389\) −29.4296 −1.49214 −0.746069 0.665869i \(-0.768061\pi\)
−0.746069 + 0.665869i \(0.768061\pi\)
\(390\) −4.18835 −0.212085
\(391\) −27.6599 −1.39882
\(392\) 29.0863 1.46908
\(393\) 1.22261 0.0616727
\(394\) 32.9045 1.65771
\(395\) −6.29460 −0.316716
\(396\) −26.4503 −1.32918
\(397\) 5.48517 0.275293 0.137646 0.990481i \(-0.456046\pi\)
0.137646 + 0.990481i \(0.456046\pi\)
\(398\) 28.3646 1.42179
\(399\) −4.42031 −0.221292
\(400\) 2.89997 0.144999
\(401\) −15.2511 −0.761606 −0.380803 0.924656i \(-0.624352\pi\)
−0.380803 + 0.924656i \(0.624352\pi\)
\(402\) −11.3436 −0.565770
\(403\) −8.26687 −0.411802
\(404\) −68.2498 −3.39555
\(405\) 3.87464 0.192532
\(406\) 0.195876 0.00972118
\(407\) −34.8946 −1.72966
\(408\) 40.0179 1.98118
\(409\) 33.6003 1.66143 0.830714 0.556700i \(-0.187933\pi\)
0.830714 + 0.556700i \(0.187933\pi\)
\(410\) 2.69288 0.132992
\(411\) −8.88455 −0.438242
\(412\) 9.79386 0.482509
\(413\) −6.12168 −0.301228
\(414\) 11.8098 0.580421
\(415\) 12.6133 0.619163
\(416\) −2.26202 −0.110905
\(417\) −16.6239 −0.814076
\(418\) −78.5613 −3.84256
\(419\) 10.2645 0.501455 0.250728 0.968058i \(-0.419330\pi\)
0.250728 + 0.968058i \(0.419330\pi\)
\(420\) 2.95081 0.143985
\(421\) −3.18192 −0.155077 −0.0775386 0.996989i \(-0.524706\pi\)
−0.0775386 + 0.996989i \(0.524706\pi\)
\(422\) −66.3695 −3.23082
\(423\) 11.1503 0.542146
\(424\) −3.79389 −0.184248
\(425\) −6.86388 −0.332947
\(426\) 6.93303 0.335906
\(427\) −7.17336 −0.347143
\(428\) 62.8521 3.03807
\(429\) −9.91993 −0.478939
\(430\) 9.05894 0.436861
\(431\) 37.5920 1.81074 0.905372 0.424618i \(-0.139592\pi\)
0.905372 + 0.424618i \(0.139592\pi\)
\(432\) −16.3304 −0.785696
\(433\) −19.1518 −0.920376 −0.460188 0.887822i \(-0.652218\pi\)
−0.460188 + 0.887822i \(0.652218\pi\)
\(434\) 8.88104 0.426303
\(435\) −0.187233 −0.00897715
\(436\) −22.2692 −1.06650
\(437\) 23.0036 1.10041
\(438\) 4.29515 0.205230
\(439\) 8.78346 0.419212 0.209606 0.977786i \(-0.432782\pi\)
0.209606 + 0.977786i \(0.432782\pi\)
\(440\) 24.9194 1.18798
\(441\) 8.10176 0.385798
\(442\) −21.5222 −1.02371
\(443\) −31.7253 −1.50731 −0.753657 0.657268i \(-0.771712\pi\)
−0.753657 + 0.657268i \(0.771712\pi\)
\(444\) −31.1106 −1.47644
\(445\) −0.459166 −0.0217665
\(446\) 12.7285 0.602713
\(447\) −7.34018 −0.347178
\(448\) 5.79236 0.273663
\(449\) 7.74859 0.365679 0.182839 0.983143i \(-0.441471\pi\)
0.182839 + 0.983143i \(0.441471\pi\)
\(450\) 2.93064 0.138152
\(451\) 6.37796 0.300326
\(452\) 59.0925 2.77948
\(453\) −21.1803 −0.995136
\(454\) −28.2202 −1.32444
\(455\) −0.754074 −0.0353515
\(456\) −33.2812 −1.55854
\(457\) 4.64336 0.217207 0.108604 0.994085i \(-0.465362\pi\)
0.108604 + 0.994085i \(0.465362\pi\)
\(458\) −52.3124 −2.44440
\(459\) 38.6520 1.80412
\(460\) −15.3562 −0.715988
\(461\) 39.4625 1.83795 0.918976 0.394314i \(-0.129018\pi\)
0.918976 + 0.394314i \(0.129018\pi\)
\(462\) 10.6569 0.495804
\(463\) 5.01227 0.232940 0.116470 0.993194i \(-0.462842\pi\)
0.116470 + 0.993194i \(0.462842\pi\)
\(464\) 0.406491 0.0188709
\(465\) −8.48917 −0.393676
\(466\) 11.8405 0.548500
\(467\) 1.54960 0.0717067 0.0358534 0.999357i \(-0.488585\pi\)
0.0358534 + 0.999357i \(0.488585\pi\)
\(468\) 6.02635 0.278568
\(469\) −2.04232 −0.0943055
\(470\) −22.1081 −1.01977
\(471\) −21.5114 −0.991192
\(472\) −46.0911 −2.12152
\(473\) 21.4557 0.986535
\(474\) −20.2679 −0.930935
\(475\) 5.70841 0.261920
\(476\) 15.1630 0.694994
\(477\) −1.05676 −0.0483857
\(478\) 61.2522 2.80161
\(479\) −24.6773 −1.12754 −0.563768 0.825933i \(-0.690649\pi\)
−0.563768 + 0.825933i \(0.690649\pi\)
\(480\) −2.32284 −0.106023
\(481\) 7.95026 0.362501
\(482\) 1.33274 0.0607048
\(483\) −3.12046 −0.141986
\(484\) 82.2940 3.74064
\(485\) −1.65456 −0.0751295
\(486\) −28.2469 −1.28131
\(487\) 37.8051 1.71311 0.856556 0.516054i \(-0.172600\pi\)
0.856556 + 0.516054i \(0.172600\pi\)
\(488\) −54.0094 −2.44489
\(489\) 13.3988 0.605914
\(490\) −16.0637 −0.725682
\(491\) −35.2010 −1.58860 −0.794300 0.607526i \(-0.792162\pi\)
−0.794300 + 0.607526i \(0.792162\pi\)
\(492\) 5.68633 0.256360
\(493\) −0.962114 −0.0433314
\(494\) 17.8991 0.805320
\(495\) 6.94109 0.311979
\(496\) 18.4303 0.827545
\(497\) 1.24823 0.0559907
\(498\) 40.6134 1.81993
\(499\) −20.7551 −0.929125 −0.464563 0.885540i \(-0.653788\pi\)
−0.464563 + 0.885540i \(0.653788\pi\)
\(500\) −3.81069 −0.170419
\(501\) −9.92491 −0.443412
\(502\) 2.68582 0.119874
\(503\) −34.6591 −1.54537 −0.772687 0.634787i \(-0.781088\pi\)
−0.772687 + 0.634787i \(0.781088\pi\)
\(504\) −3.07622 −0.137026
\(505\) 17.9101 0.796989
\(506\) −55.4593 −2.46547
\(507\) −15.1047 −0.670822
\(508\) 58.8085 2.60921
\(509\) 35.0177 1.55213 0.776065 0.630652i \(-0.217213\pi\)
0.776065 + 0.630652i \(0.217213\pi\)
\(510\) −22.1009 −0.978644
\(511\) 0.773302 0.0342089
\(512\) 30.3582 1.34165
\(513\) −32.1453 −1.41925
\(514\) −35.2985 −1.55695
\(515\) −2.57010 −0.113252
\(516\) 19.1291 0.842110
\(517\) −52.3621 −2.30288
\(518\) −8.54090 −0.375266
\(519\) 1.66096 0.0729081
\(520\) −5.67754 −0.248977
\(521\) −15.5454 −0.681057 −0.340528 0.940234i \(-0.610606\pi\)
−0.340528 + 0.940234i \(0.610606\pi\)
\(522\) 0.410789 0.0179798
\(523\) 19.2984 0.843860 0.421930 0.906628i \(-0.361353\pi\)
0.421930 + 0.906628i \(0.361353\pi\)
\(524\) 3.48792 0.152370
\(525\) −0.774351 −0.0337954
\(526\) −48.3198 −2.10684
\(527\) −43.6223 −1.90022
\(528\) 22.1156 0.962460
\(529\) −6.76088 −0.293951
\(530\) 2.09528 0.0910130
\(531\) −12.8383 −0.557135
\(532\) −12.6104 −0.546732
\(533\) −1.45313 −0.0629422
\(534\) −1.47846 −0.0639792
\(535\) −16.4936 −0.713082
\(536\) −15.3769 −0.664183
\(537\) 34.6279 1.49430
\(538\) −23.1500 −0.998067
\(539\) −38.0461 −1.63876
\(540\) 21.4588 0.923441
\(541\) −6.66798 −0.286679 −0.143340 0.989674i \(-0.545784\pi\)
−0.143340 + 0.989674i \(0.545784\pi\)
\(542\) −15.3416 −0.658980
\(543\) 22.5724 0.968676
\(544\) −11.9361 −0.511757
\(545\) 5.84389 0.250325
\(546\) −2.42803 −0.103910
\(547\) −35.4767 −1.51687 −0.758437 0.651746i \(-0.774037\pi\)
−0.758437 + 0.651746i \(0.774037\pi\)
\(548\) −25.3462 −1.08273
\(549\) −15.0439 −0.642057
\(550\) −13.7624 −0.586829
\(551\) 0.800151 0.0340876
\(552\) −23.4945 −0.999990
\(553\) −3.64905 −0.155173
\(554\) −29.5899 −1.25715
\(555\) 8.16404 0.346544
\(556\) −47.4253 −2.01128
\(557\) 25.5149 1.08110 0.540551 0.841311i \(-0.318216\pi\)
0.540551 + 0.841311i \(0.318216\pi\)
\(558\) 18.6252 0.788467
\(559\) −4.88840 −0.206757
\(560\) 1.68114 0.0710413
\(561\) −52.3450 −2.21001
\(562\) 24.7914 1.04576
\(563\) −25.2270 −1.06319 −0.531597 0.846998i \(-0.678408\pi\)
−0.531597 + 0.846998i \(0.678408\pi\)
\(564\) −46.6840 −1.96575
\(565\) −15.5070 −0.652386
\(566\) −26.5283 −1.11507
\(567\) 2.24617 0.0943303
\(568\) 9.39811 0.394336
\(569\) −31.1301 −1.30504 −0.652520 0.757771i \(-0.726288\pi\)
−0.652520 + 0.757771i \(0.726288\pi\)
\(570\) 18.3804 0.769871
\(571\) −18.6652 −0.781113 −0.390557 0.920579i \(-0.627717\pi\)
−0.390557 + 0.920579i \(0.627717\pi\)
\(572\) −28.2999 −1.18328
\(573\) 1.51495 0.0632877
\(574\) 1.56109 0.0651586
\(575\) 4.02978 0.168053
\(576\) 12.1477 0.506152
\(577\) −44.4690 −1.85127 −0.925634 0.378421i \(-0.876467\pi\)
−0.925634 + 0.378421i \(0.876467\pi\)
\(578\) −72.5881 −3.01927
\(579\) 13.5537 0.563272
\(580\) −0.534146 −0.0221792
\(581\) 7.31207 0.303356
\(582\) −5.32748 −0.220831
\(583\) 4.96257 0.205529
\(584\) 5.82231 0.240929
\(585\) −1.58143 −0.0653842
\(586\) −11.9018 −0.491657
\(587\) −1.52790 −0.0630633 −0.0315316 0.999503i \(-0.510038\pi\)
−0.0315316 + 0.999503i \(0.510038\pi\)
\(588\) −33.9204 −1.39885
\(589\) 36.2789 1.49485
\(590\) 25.4550 1.04797
\(591\) −18.2334 −0.750023
\(592\) −17.7244 −0.728469
\(593\) 43.7258 1.79560 0.897801 0.440402i \(-0.145164\pi\)
0.897801 + 0.440402i \(0.145164\pi\)
\(594\) 77.4989 3.17982
\(595\) −3.97906 −0.163126
\(596\) −20.9403 −0.857749
\(597\) −15.7177 −0.643283
\(598\) 12.6357 0.516710
\(599\) 34.3780 1.40465 0.702323 0.711858i \(-0.252146\pi\)
0.702323 + 0.711858i \(0.252146\pi\)
\(600\) −5.83021 −0.238017
\(601\) 31.5603 1.28737 0.643687 0.765289i \(-0.277404\pi\)
0.643687 + 0.765289i \(0.277404\pi\)
\(602\) 5.25156 0.214038
\(603\) −4.28312 −0.174422
\(604\) −60.4239 −2.45861
\(605\) −21.5956 −0.877985
\(606\) 57.6684 2.34262
\(607\) −4.85283 −0.196970 −0.0984852 0.995139i \(-0.531400\pi\)
−0.0984852 + 0.995139i \(0.531400\pi\)
\(608\) 9.92679 0.402584
\(609\) −0.108541 −0.00439831
\(610\) 29.8281 1.20770
\(611\) 11.9300 0.482636
\(612\) 31.7996 1.28542
\(613\) 10.0307 0.405134 0.202567 0.979268i \(-0.435072\pi\)
0.202567 + 0.979268i \(0.435072\pi\)
\(614\) −49.2640 −1.98813
\(615\) −1.49221 −0.0601716
\(616\) 14.4460 0.582047
\(617\) 24.5548 0.988540 0.494270 0.869309i \(-0.335435\pi\)
0.494270 + 0.869309i \(0.335435\pi\)
\(618\) −8.27543 −0.332887
\(619\) −8.06974 −0.324350 −0.162175 0.986762i \(-0.551851\pi\)
−0.162175 + 0.986762i \(0.551851\pi\)
\(620\) −24.2182 −0.972627
\(621\) −22.6926 −0.910622
\(622\) 19.0552 0.764044
\(623\) −0.266183 −0.0106644
\(624\) −5.03875 −0.201712
\(625\) 1.00000 0.0400000
\(626\) −59.9809 −2.39732
\(627\) 43.5333 1.73855
\(628\) −61.3685 −2.44887
\(629\) 41.9516 1.67272
\(630\) 1.69892 0.0676867
\(631\) −10.7421 −0.427637 −0.213819 0.976873i \(-0.568590\pi\)
−0.213819 + 0.976873i \(0.568590\pi\)
\(632\) −27.4742 −1.09287
\(633\) 36.7774 1.46177
\(634\) 55.9662 2.22270
\(635\) −15.4325 −0.612421
\(636\) 4.42443 0.175440
\(637\) 8.66829 0.343450
\(638\) −1.92908 −0.0763730
\(639\) 2.61777 0.103557
\(640\) −20.6077 −0.814590
\(641\) −1.84518 −0.0728802 −0.0364401 0.999336i \(-0.511602\pi\)
−0.0364401 + 0.999336i \(0.511602\pi\)
\(642\) −53.1076 −2.09599
\(643\) 33.9688 1.33960 0.669799 0.742543i \(-0.266380\pi\)
0.669799 + 0.742543i \(0.266380\pi\)
\(644\) −8.90217 −0.350795
\(645\) −5.01984 −0.197656
\(646\) 94.4493 3.71606
\(647\) −16.3951 −0.644558 −0.322279 0.946645i \(-0.604449\pi\)
−0.322279 + 0.946645i \(0.604449\pi\)
\(648\) 16.9118 0.664357
\(649\) 60.2891 2.36656
\(650\) 3.13557 0.122987
\(651\) −4.92126 −0.192879
\(652\) 38.2246 1.49699
\(653\) −44.1211 −1.72659 −0.863296 0.504697i \(-0.831604\pi\)
−0.863296 + 0.504697i \(0.831604\pi\)
\(654\) 18.8167 0.735789
\(655\) −0.915298 −0.0357636
\(656\) 3.23964 0.126487
\(657\) 1.62176 0.0632708
\(658\) −12.8163 −0.499632
\(659\) −31.5331 −1.22835 −0.614177 0.789168i \(-0.710512\pi\)
−0.614177 + 0.789168i \(0.710512\pi\)
\(660\) −29.0609 −1.13119
\(661\) 29.1323 1.13312 0.566558 0.824022i \(-0.308275\pi\)
0.566558 + 0.824022i \(0.308275\pi\)
\(662\) −25.4321 −0.988446
\(663\) 11.9261 0.463172
\(664\) 55.0537 2.13650
\(665\) 3.30923 0.128326
\(666\) −17.9119 −0.694070
\(667\) 0.564856 0.0218713
\(668\) −28.3142 −1.09551
\(669\) −7.05327 −0.272695
\(670\) 8.49232 0.328087
\(671\) 70.6465 2.72728
\(672\) −1.34658 −0.0519453
\(673\) 34.3259 1.32317 0.661584 0.749871i \(-0.269885\pi\)
0.661584 + 0.749871i \(0.269885\pi\)
\(674\) 69.8416 2.69020
\(675\) −5.63122 −0.216746
\(676\) −43.0912 −1.65735
\(677\) 37.0080 1.42233 0.711167 0.703023i \(-0.248167\pi\)
0.711167 + 0.703023i \(0.248167\pi\)
\(678\) −49.9308 −1.91758
\(679\) −0.959163 −0.0368093
\(680\) −29.9590 −1.14888
\(681\) 15.6377 0.599238
\(682\) −87.4645 −3.34919
\(683\) 26.5191 1.01472 0.507362 0.861733i \(-0.330621\pi\)
0.507362 + 0.861733i \(0.330621\pi\)
\(684\) −26.4464 −1.01120
\(685\) 6.65133 0.254134
\(686\) −19.0942 −0.729019
\(687\) 28.9879 1.10596
\(688\) 10.8983 0.415493
\(689\) −1.13066 −0.0430746
\(690\) 12.9754 0.493966
\(691\) −31.4022 −1.19460 −0.597298 0.802019i \(-0.703759\pi\)
−0.597298 + 0.802019i \(0.703759\pi\)
\(692\) 4.73845 0.180129
\(693\) 4.02382 0.152852
\(694\) 68.2505 2.59075
\(695\) 12.4453 0.472078
\(696\) −0.817224 −0.0309768
\(697\) −7.66782 −0.290440
\(698\) −86.9151 −3.28979
\(699\) −6.56119 −0.248167
\(700\) −2.20910 −0.0834960
\(701\) 9.82011 0.370900 0.185450 0.982654i \(-0.440626\pi\)
0.185450 + 0.982654i \(0.440626\pi\)
\(702\) −17.6571 −0.666424
\(703\) −34.8894 −1.31588
\(704\) −57.0458 −2.14999
\(705\) 12.2508 0.461392
\(706\) −83.1908 −3.13093
\(707\) 10.3827 0.390481
\(708\) 53.7514 2.02010
\(709\) −13.1889 −0.495321 −0.247661 0.968847i \(-0.579662\pi\)
−0.247661 + 0.968847i \(0.579662\pi\)
\(710\) −5.19035 −0.194790
\(711\) −7.65273 −0.287000
\(712\) −2.00414 −0.0751081
\(713\) 25.6106 0.959125
\(714\) −12.8121 −0.479482
\(715\) 7.42646 0.277734
\(716\) 98.7878 3.69187
\(717\) −33.9418 −1.26758
\(718\) 20.3755 0.760408
\(719\) −19.4729 −0.726218 −0.363109 0.931747i \(-0.618285\pi\)
−0.363109 + 0.931747i \(0.618285\pi\)
\(720\) 3.52567 0.131394
\(721\) −1.48992 −0.0554873
\(722\) −32.7495 −1.21881
\(723\) −0.738515 −0.0274657
\(724\) 64.3955 2.39324
\(725\) 0.140171 0.00520580
\(726\) −69.5353 −2.58070
\(727\) 43.4526 1.61157 0.805783 0.592211i \(-0.201745\pi\)
0.805783 + 0.592211i \(0.201745\pi\)
\(728\) −3.29133 −0.121985
\(729\) 27.2764 1.01024
\(730\) −3.21552 −0.119012
\(731\) −25.7949 −0.954058
\(732\) 62.9856 2.32802
\(733\) 10.0034 0.369484 0.184742 0.982787i \(-0.440855\pi\)
0.184742 + 0.982787i \(0.440855\pi\)
\(734\) −61.5764 −2.27283
\(735\) 8.90138 0.328332
\(736\) 7.00769 0.258307
\(737\) 20.1137 0.740897
\(738\) 3.27389 0.120514
\(739\) 7.88510 0.290058 0.145029 0.989427i \(-0.453672\pi\)
0.145029 + 0.989427i \(0.453672\pi\)
\(740\) 23.2907 0.856182
\(741\) −9.91847 −0.364364
\(742\) 1.21465 0.0445914
\(743\) 27.1428 0.995773 0.497887 0.867242i \(-0.334110\pi\)
0.497887 + 0.867242i \(0.334110\pi\)
\(744\) −37.0529 −1.35843
\(745\) 5.49516 0.201327
\(746\) −72.4463 −2.65245
\(747\) 15.3348 0.561070
\(748\) −149.332 −5.46011
\(749\) −9.56153 −0.349371
\(750\) 3.21988 0.117574
\(751\) 52.1710 1.90375 0.951873 0.306493i \(-0.0991556\pi\)
0.951873 + 0.306493i \(0.0991556\pi\)
\(752\) −26.5969 −0.969891
\(753\) −1.48830 −0.0542366
\(754\) 0.439515 0.0160062
\(755\) 15.8564 0.577074
\(756\) 12.4399 0.452435
\(757\) −30.3129 −1.10174 −0.550871 0.834590i \(-0.685704\pi\)
−0.550871 + 0.834590i \(0.685704\pi\)
\(758\) 5.41423 0.196654
\(759\) 30.7317 1.11549
\(760\) 24.9157 0.903787
\(761\) −15.0889 −0.546973 −0.273486 0.961876i \(-0.588177\pi\)
−0.273486 + 0.961876i \(0.588177\pi\)
\(762\) −49.6909 −1.80011
\(763\) 3.38777 0.122645
\(764\) 4.32189 0.156361
\(765\) −8.34484 −0.301708
\(766\) 47.8212 1.72785
\(767\) −13.7361 −0.495981
\(768\) −39.6611 −1.43115
\(769\) 48.8197 1.76048 0.880242 0.474525i \(-0.157380\pi\)
0.880242 + 0.474525i \(0.157380\pi\)
\(770\) −7.97819 −0.287514
\(771\) 19.5600 0.704435
\(772\) 38.6665 1.39164
\(773\) −24.2575 −0.872480 −0.436240 0.899830i \(-0.643690\pi\)
−0.436240 + 0.899830i \(0.643690\pi\)
\(774\) 11.0135 0.395872
\(775\) 6.35534 0.228290
\(776\) −7.22169 −0.259244
\(777\) 4.73278 0.169787
\(778\) 70.9410 2.54336
\(779\) 6.37702 0.228480
\(780\) 6.62114 0.237075
\(781\) −12.2931 −0.439882
\(782\) 66.6753 2.38430
\(783\) −0.789331 −0.0282084
\(784\) −19.3252 −0.690187
\(785\) 16.1043 0.574787
\(786\) −2.94715 −0.105121
\(787\) −33.7528 −1.20316 −0.601579 0.798813i \(-0.705462\pi\)
−0.601579 + 0.798813i \(0.705462\pi\)
\(788\) −52.0170 −1.85303
\(789\) 26.7755 0.953234
\(790\) 15.1734 0.539844
\(791\) −8.98959 −0.319633
\(792\) 30.2960 1.07652
\(793\) −16.0959 −0.571581
\(794\) −13.2222 −0.469238
\(795\) −1.16106 −0.0411785
\(796\) −44.8401 −1.58932
\(797\) 52.6570 1.86521 0.932603 0.360905i \(-0.117532\pi\)
0.932603 + 0.360905i \(0.117532\pi\)
\(798\) 10.6553 0.377195
\(799\) 62.9517 2.22707
\(800\) 1.73898 0.0614821
\(801\) −0.558236 −0.0197243
\(802\) 36.7635 1.29816
\(803\) −7.61583 −0.268757
\(804\) 17.9326 0.632433
\(805\) 2.33611 0.0823369
\(806\) 19.9276 0.701920
\(807\) 12.8281 0.451572
\(808\) 78.1728 2.75011
\(809\) 0.0319325 0.00112269 0.000561343 1.00000i \(-0.499821\pi\)
0.000561343 1.00000i \(0.499821\pi\)
\(810\) −9.33996 −0.328173
\(811\) 22.3795 0.785851 0.392926 0.919570i \(-0.371463\pi\)
0.392926 + 0.919570i \(0.371463\pi\)
\(812\) −0.309650 −0.0108666
\(813\) 8.50129 0.298153
\(814\) 84.1146 2.94822
\(815\) −10.0309 −0.351366
\(816\) −26.5883 −0.930775
\(817\) 21.4526 0.750530
\(818\) −80.9948 −2.83192
\(819\) −0.916774 −0.0320347
\(820\) −4.25702 −0.148662
\(821\) 36.1927 1.26313 0.631567 0.775321i \(-0.282412\pi\)
0.631567 + 0.775321i \(0.282412\pi\)
\(822\) 21.4165 0.746987
\(823\) 5.49059 0.191390 0.0956949 0.995411i \(-0.469493\pi\)
0.0956949 + 0.995411i \(0.469493\pi\)
\(824\) −11.2178 −0.390791
\(825\) 7.62616 0.265509
\(826\) 14.7565 0.513446
\(827\) 43.7052 1.51978 0.759889 0.650053i \(-0.225253\pi\)
0.759889 + 0.650053i \(0.225253\pi\)
\(828\) −18.6695 −0.648811
\(829\) 52.9404 1.83870 0.919349 0.393444i \(-0.128716\pi\)
0.919349 + 0.393444i \(0.128716\pi\)
\(830\) −30.4049 −1.05537
\(831\) 16.3967 0.568795
\(832\) 12.9971 0.450594
\(833\) 45.7405 1.58481
\(834\) 40.0725 1.38760
\(835\) 7.43019 0.257132
\(836\) 124.193 4.29532
\(837\) −35.7883 −1.23702
\(838\) −24.7430 −0.854734
\(839\) 18.5850 0.641625 0.320812 0.947143i \(-0.396044\pi\)
0.320812 + 0.947143i \(0.396044\pi\)
\(840\) −3.37983 −0.116615
\(841\) −28.9804 −0.999322
\(842\) 7.67013 0.264330
\(843\) −13.7377 −0.473152
\(844\) 104.920 3.61150
\(845\) 11.3080 0.389006
\(846\) −26.8782 −0.924091
\(847\) −12.5192 −0.430164
\(848\) 2.52070 0.0865612
\(849\) 14.7002 0.504508
\(850\) 16.5456 0.567511
\(851\) −24.6297 −0.844296
\(852\) −10.9601 −0.375485
\(853\) 15.7908 0.540667 0.270333 0.962767i \(-0.412866\pi\)
0.270333 + 0.962767i \(0.412866\pi\)
\(854\) 17.2917 0.591708
\(855\) 6.94007 0.237345
\(856\) −71.9903 −2.46058
\(857\) 39.4878 1.34888 0.674438 0.738331i \(-0.264386\pi\)
0.674438 + 0.738331i \(0.264386\pi\)
\(858\) 23.9124 0.816354
\(859\) 10.1549 0.346482 0.173241 0.984879i \(-0.444576\pi\)
0.173241 + 0.984879i \(0.444576\pi\)
\(860\) −14.3208 −0.488335
\(861\) −0.865048 −0.0294808
\(862\) −90.6170 −3.08643
\(863\) −8.91836 −0.303584 −0.151792 0.988412i \(-0.548504\pi\)
−0.151792 + 0.988412i \(0.548504\pi\)
\(864\) −9.79255 −0.333149
\(865\) −1.24346 −0.0422790
\(866\) 46.1661 1.56879
\(867\) 40.2233 1.36606
\(868\) −14.0396 −0.476534
\(869\) 35.9375 1.21909
\(870\) 0.451333 0.0153016
\(871\) −4.58263 −0.155277
\(872\) 25.5070 0.863777
\(873\) −2.01154 −0.0680805
\(874\) −55.4511 −1.87566
\(875\) 0.579711 0.0195978
\(876\) −6.78997 −0.229412
\(877\) 28.2114 0.952633 0.476316 0.879274i \(-0.341972\pi\)
0.476316 + 0.879274i \(0.341972\pi\)
\(878\) −21.1728 −0.714549
\(879\) 6.59513 0.222448
\(880\) −16.5567 −0.558125
\(881\) 41.2054 1.38825 0.694123 0.719856i \(-0.255792\pi\)
0.694123 + 0.719856i \(0.255792\pi\)
\(882\) −19.5296 −0.657595
\(883\) −48.1849 −1.62155 −0.810776 0.585357i \(-0.800955\pi\)
−0.810776 + 0.585357i \(0.800955\pi\)
\(884\) 34.0233 1.14433
\(885\) −14.1054 −0.474149
\(886\) 76.4749 2.56923
\(887\) 41.4084 1.39036 0.695180 0.718836i \(-0.255325\pi\)
0.695180 + 0.718836i \(0.255325\pi\)
\(888\) 35.6338 1.19579
\(889\) −8.94639 −0.300052
\(890\) 1.10684 0.0371012
\(891\) −22.1213 −0.741092
\(892\) −20.1218 −0.673729
\(893\) −52.3544 −1.75197
\(894\) 17.6938 0.591768
\(895\) −25.9239 −0.866539
\(896\) −11.9465 −0.399104
\(897\) −7.00181 −0.233784
\(898\) −18.6783 −0.623302
\(899\) 0.890831 0.0297109
\(900\) −4.63289 −0.154430
\(901\) −5.96619 −0.198763
\(902\) −15.3743 −0.511909
\(903\) −2.91006 −0.0968406
\(904\) −67.6840 −2.25114
\(905\) −16.8986 −0.561730
\(906\) 51.0558 1.69622
\(907\) 36.4098 1.20897 0.604484 0.796617i \(-0.293379\pi\)
0.604484 + 0.796617i \(0.293379\pi\)
\(908\) 44.6118 1.48050
\(909\) 21.7744 0.722211
\(910\) 1.81772 0.0602570
\(911\) 9.79543 0.324537 0.162268 0.986747i \(-0.448119\pi\)
0.162268 + 0.986747i \(0.448119\pi\)
\(912\) 22.1124 0.732214
\(913\) −72.0126 −2.38327
\(914\) −11.1930 −0.370231
\(915\) −16.5287 −0.546421
\(916\) 82.6978 2.73241
\(917\) −0.530608 −0.0175222
\(918\) −93.1721 −3.07514
\(919\) 16.5519 0.545997 0.272999 0.962014i \(-0.411985\pi\)
0.272999 + 0.962014i \(0.411985\pi\)
\(920\) 17.5889 0.579889
\(921\) 27.2987 0.899524
\(922\) −95.1258 −3.13280
\(923\) 2.80082 0.0921902
\(924\) −16.8469 −0.554223
\(925\) −6.11193 −0.200959
\(926\) −12.0823 −0.397048
\(927\) −3.12463 −0.102626
\(928\) 0.243753 0.00800159
\(929\) 12.9098 0.423556 0.211778 0.977318i \(-0.432075\pi\)
0.211778 + 0.977318i \(0.432075\pi\)
\(930\) 20.4634 0.671023
\(931\) −38.0405 −1.24673
\(932\) −18.7180 −0.613129
\(933\) −10.5591 −0.345689
\(934\) −3.73536 −0.122225
\(935\) 39.1876 1.28157
\(936\) −6.90254 −0.225616
\(937\) 34.1648 1.11612 0.558058 0.829802i \(-0.311547\pi\)
0.558058 + 0.829802i \(0.311547\pi\)
\(938\) 4.92309 0.160744
\(939\) 33.2373 1.08466
\(940\) 34.9495 1.13993
\(941\) −10.5660 −0.344441 −0.172221 0.985058i \(-0.555094\pi\)
−0.172221 + 0.985058i \(0.555094\pi\)
\(942\) 51.8540 1.68949
\(943\) 4.50177 0.146598
\(944\) 30.6234 0.996707
\(945\) −3.26448 −0.106193
\(946\) −51.7198 −1.68156
\(947\) 1.38108 0.0448791 0.0224396 0.999748i \(-0.492857\pi\)
0.0224396 + 0.999748i \(0.492857\pi\)
\(948\) 32.0404 1.04062
\(949\) 1.73516 0.0563258
\(950\) −13.7603 −0.446444
\(951\) −31.0126 −1.00565
\(952\) −17.3676 −0.562886
\(953\) −33.2565 −1.07728 −0.538642 0.842535i \(-0.681062\pi\)
−0.538642 + 0.842535i \(0.681062\pi\)
\(954\) 2.54736 0.0824737
\(955\) −1.13415 −0.0367002
\(956\) −96.8303 −3.13172
\(957\) 1.06896 0.0345547
\(958\) 59.4856 1.92189
\(959\) 3.85585 0.124512
\(960\) 13.3466 0.430760
\(961\) 9.39030 0.302913
\(962\) −19.1644 −0.617885
\(963\) −20.0523 −0.646177
\(964\) −2.10686 −0.0678575
\(965\) −10.1469 −0.326639
\(966\) 7.52199 0.242016
\(967\) 0.916683 0.0294785 0.0147393 0.999891i \(-0.495308\pi\)
0.0147393 + 0.999891i \(0.495308\pi\)
\(968\) −94.2589 −3.02960
\(969\) −52.3373 −1.68132
\(970\) 3.98837 0.128059
\(971\) 55.9817 1.79654 0.898270 0.439444i \(-0.144825\pi\)
0.898270 + 0.439444i \(0.144825\pi\)
\(972\) 44.6540 1.43228
\(973\) 7.21469 0.231292
\(974\) −91.1306 −2.92001
\(975\) −1.73752 −0.0556451
\(976\) 35.8844 1.14863
\(977\) −8.05021 −0.257549 −0.128774 0.991674i \(-0.541104\pi\)
−0.128774 + 0.991674i \(0.541104\pi\)
\(978\) −32.2983 −1.03278
\(979\) 2.62149 0.0837833
\(980\) 25.3942 0.811187
\(981\) 7.10478 0.226838
\(982\) 84.8533 2.70778
\(983\) −20.2213 −0.644960 −0.322480 0.946576i \(-0.604517\pi\)
−0.322480 + 0.946576i \(0.604517\pi\)
\(984\) −6.51308 −0.207629
\(985\) 13.6503 0.434934
\(986\) 2.31921 0.0738587
\(987\) 7.10192 0.226057
\(988\) −28.2958 −0.900208
\(989\) 15.1441 0.481556
\(990\) −16.7318 −0.531770
\(991\) −47.8187 −1.51901 −0.759505 0.650501i \(-0.774559\pi\)
−0.759505 + 0.650501i \(0.774559\pi\)
\(992\) 11.0518 0.350894
\(993\) 14.0927 0.447219
\(994\) −3.00890 −0.0954365
\(995\) 11.7669 0.373037
\(996\) −64.2036 −2.03437
\(997\) 18.9245 0.599346 0.299673 0.954042i \(-0.403122\pi\)
0.299673 + 0.954042i \(0.403122\pi\)
\(998\) 50.0309 1.58370
\(999\) 34.4176 1.08893
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 8045.2.a.d.1.16 141
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8045.2.a.d.1.16 141 1.1 even 1 trivial