Properties

Label 4001.2.a.b.1.99
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $0$
Dimension $184$
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] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, 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("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.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: \(31.9481458487\)
Analytic rank: \(0\)
Dimension: \(184\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.99
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.273610 q^{2} -1.75031 q^{3} -1.92514 q^{4} -3.00014 q^{5} -0.478902 q^{6} +1.86672 q^{7} -1.07396 q^{8} +0.0635960 q^{9} +O(q^{10})\) \(q+0.273610 q^{2} -1.75031 q^{3} -1.92514 q^{4} -3.00014 q^{5} -0.478902 q^{6} +1.86672 q^{7} -1.07396 q^{8} +0.0635960 q^{9} -0.820867 q^{10} +3.70792 q^{11} +3.36959 q^{12} -5.97047 q^{13} +0.510753 q^{14} +5.25118 q^{15} +3.55643 q^{16} -4.58955 q^{17} +0.0174005 q^{18} +1.73061 q^{19} +5.77568 q^{20} -3.26735 q^{21} +1.01452 q^{22} -8.34614 q^{23} +1.87976 q^{24} +4.00084 q^{25} -1.63358 q^{26} +5.13963 q^{27} -3.59370 q^{28} +3.53627 q^{29} +1.43677 q^{30} -7.77624 q^{31} +3.12098 q^{32} -6.49003 q^{33} -1.25575 q^{34} -5.60043 q^{35} -0.122431 q^{36} -11.3660 q^{37} +0.473511 q^{38} +10.4502 q^{39} +3.22202 q^{40} -4.43689 q^{41} -0.893978 q^{42} -9.20892 q^{43} -7.13827 q^{44} -0.190797 q^{45} -2.28358 q^{46} +0.180289 q^{47} -6.22487 q^{48} -3.51534 q^{49} +1.09467 q^{50} +8.03316 q^{51} +11.4940 q^{52} +0.827330 q^{53} +1.40625 q^{54} -11.1243 q^{55} -2.00478 q^{56} -3.02911 q^{57} +0.967558 q^{58} -2.17404 q^{59} -10.1093 q^{60} -1.81133 q^{61} -2.12765 q^{62} +0.118716 q^{63} -6.25893 q^{64} +17.9123 q^{65} -1.77573 q^{66} -7.78855 q^{67} +8.83552 q^{68} +14.6084 q^{69} -1.53233 q^{70} -0.381705 q^{71} -0.0682993 q^{72} -6.72766 q^{73} -3.10984 q^{74} -7.00272 q^{75} -3.33166 q^{76} +6.92167 q^{77} +2.85927 q^{78} -3.55275 q^{79} -10.6698 q^{80} -9.18674 q^{81} -1.21398 q^{82} -6.70350 q^{83} +6.29010 q^{84} +13.7693 q^{85} -2.51965 q^{86} -6.18958 q^{87} -3.98214 q^{88} +6.69890 q^{89} -0.0522039 q^{90} -11.1452 q^{91} +16.0675 q^{92} +13.6109 q^{93} +0.0493287 q^{94} -5.19207 q^{95} -5.46270 q^{96} +16.9117 q^{97} -0.961831 q^{98} +0.235809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18} + 86 q^{19} + 26 q^{20} + 22 q^{21} + 54 q^{22} + 55 q^{23} + 72 q^{24} + 241 q^{25} + 32 q^{26} + 97 q^{27} + 75 q^{28} + 27 q^{29} - 10 q^{30} + 276 q^{31} + 20 q^{33} + 122 q^{34} + 30 q^{35} + 278 q^{36} + 42 q^{37} + 14 q^{38} + 113 q^{39} + 115 q^{40} + 39 q^{41} + 15 q^{42} + 65 q^{43} + 32 q^{44} + 54 q^{45} + 65 q^{46} + 82 q^{47} + 117 q^{48} + 297 q^{49} + 4 q^{50} + 45 q^{51} + 136 q^{52} + 21 q^{53} + 93 q^{54} + 252 q^{55} + 74 q^{56} + 14 q^{57} + 54 q^{58} + 95 q^{59} + 58 q^{60} + 131 q^{61} + 14 q^{62} + 88 q^{63} + 368 q^{64} - 9 q^{65} + 52 q^{66} + 90 q^{67} + 27 q^{68} + 101 q^{69} + 18 q^{70} + 117 q^{71} - 15 q^{72} + 72 q^{73} + 7 q^{74} + 150 q^{75} + 148 q^{76} + 7 q^{77} + 22 q^{78} + 287 q^{79} + 43 q^{80} + 244 q^{81} + 86 q^{82} + 25 q^{83} + 14 q^{84} + 41 q^{85} + 25 q^{86} + 82 q^{87} + 115 q^{88} + 48 q^{89} + 78 q^{90} + 272 q^{91} + 69 q^{92} + 44 q^{93} + 161 q^{94} + 37 q^{95} + 129 q^{96} + 106 q^{97} - 46 q^{98} + 53 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.273610 0.193471 0.0967356 0.995310i \(-0.469160\pi\)
0.0967356 + 0.995310i \(0.469160\pi\)
\(3\) −1.75031 −1.01054 −0.505272 0.862960i \(-0.668608\pi\)
−0.505272 + 0.862960i \(0.668608\pi\)
\(4\) −1.92514 −0.962569
\(5\) −3.00014 −1.34170 −0.670852 0.741592i \(-0.734071\pi\)
−0.670852 + 0.741592i \(0.734071\pi\)
\(6\) −0.478902 −0.195511
\(7\) 1.86672 0.705555 0.352778 0.935707i \(-0.385237\pi\)
0.352778 + 0.935707i \(0.385237\pi\)
\(8\) −1.07396 −0.379700
\(9\) 0.0635960 0.0211987
\(10\) −0.820867 −0.259581
\(11\) 3.70792 1.11798 0.558991 0.829174i \(-0.311189\pi\)
0.558991 + 0.829174i \(0.311189\pi\)
\(12\) 3.36959 0.972718
\(13\) −5.97047 −1.65591 −0.827956 0.560793i \(-0.810496\pi\)
−0.827956 + 0.560793i \(0.810496\pi\)
\(14\) 0.510753 0.136505
\(15\) 5.25118 1.35585
\(16\) 3.55643 0.889108
\(17\) −4.58955 −1.11313 −0.556565 0.830804i \(-0.687881\pi\)
−0.556565 + 0.830804i \(0.687881\pi\)
\(18\) 0.0174005 0.00410133
\(19\) 1.73061 0.397029 0.198514 0.980098i \(-0.436388\pi\)
0.198514 + 0.980098i \(0.436388\pi\)
\(20\) 5.77568 1.29148
\(21\) −3.26735 −0.712994
\(22\) 1.01452 0.216297
\(23\) −8.34614 −1.74029 −0.870146 0.492795i \(-0.835975\pi\)
−0.870146 + 0.492795i \(0.835975\pi\)
\(24\) 1.87976 0.383704
\(25\) 4.00084 0.800167
\(26\) −1.63358 −0.320371
\(27\) 5.13963 0.989122
\(28\) −3.59370 −0.679145
\(29\) 3.53627 0.656669 0.328335 0.944561i \(-0.393513\pi\)
0.328335 + 0.944561i \(0.393513\pi\)
\(30\) 1.43677 0.262318
\(31\) −7.77624 −1.39665 −0.698327 0.715779i \(-0.746072\pi\)
−0.698327 + 0.715779i \(0.746072\pi\)
\(32\) 3.12098 0.551717
\(33\) −6.49003 −1.12977
\(34\) −1.25575 −0.215359
\(35\) −5.60043 −0.946646
\(36\) −0.122431 −0.0204052
\(37\) −11.3660 −1.86856 −0.934278 0.356547i \(-0.883954\pi\)
−0.934278 + 0.356547i \(0.883954\pi\)
\(38\) 0.473511 0.0768136
\(39\) 10.4502 1.67337
\(40\) 3.22202 0.509445
\(41\) −4.43689 −0.692926 −0.346463 0.938064i \(-0.612617\pi\)
−0.346463 + 0.938064i \(0.612617\pi\)
\(42\) −0.893978 −0.137944
\(43\) −9.20892 −1.40435 −0.702173 0.712006i \(-0.747787\pi\)
−0.702173 + 0.712006i \(0.747787\pi\)
\(44\) −7.13827 −1.07613
\(45\) −0.190797 −0.0284423
\(46\) −2.28358 −0.336696
\(47\) 0.180289 0.0262978 0.0131489 0.999914i \(-0.495814\pi\)
0.0131489 + 0.999914i \(0.495814\pi\)
\(48\) −6.22487 −0.898482
\(49\) −3.51534 −0.502192
\(50\) 1.09467 0.154809
\(51\) 8.03316 1.12487
\(52\) 11.4940 1.59393
\(53\) 0.827330 0.113642 0.0568212 0.998384i \(-0.481903\pi\)
0.0568212 + 0.998384i \(0.481903\pi\)
\(54\) 1.40625 0.191367
\(55\) −11.1243 −1.50000
\(56\) −2.00478 −0.267900
\(57\) −3.02911 −0.401215
\(58\) 0.967558 0.127047
\(59\) −2.17404 −0.283036 −0.141518 0.989936i \(-0.545198\pi\)
−0.141518 + 0.989936i \(0.545198\pi\)
\(60\) −10.1093 −1.30510
\(61\) −1.81133 −0.231918 −0.115959 0.993254i \(-0.536994\pi\)
−0.115959 + 0.993254i \(0.536994\pi\)
\(62\) −2.12765 −0.270212
\(63\) 0.118716 0.0149568
\(64\) −6.25893 −0.782366
\(65\) 17.9123 2.22174
\(66\) −1.77573 −0.218578
\(67\) −7.78855 −0.951522 −0.475761 0.879574i \(-0.657827\pi\)
−0.475761 + 0.879574i \(0.657827\pi\)
\(68\) 8.83552 1.07146
\(69\) 14.6084 1.75864
\(70\) −1.53233 −0.183149
\(71\) −0.381705 −0.0453000 −0.0226500 0.999743i \(-0.507210\pi\)
−0.0226500 + 0.999743i \(0.507210\pi\)
\(72\) −0.0682993 −0.00804915
\(73\) −6.72766 −0.787413 −0.393706 0.919236i \(-0.628807\pi\)
−0.393706 + 0.919236i \(0.628807\pi\)
\(74\) −3.10984 −0.361512
\(75\) −7.00272 −0.808604
\(76\) −3.33166 −0.382168
\(77\) 6.92167 0.788797
\(78\) 2.85927 0.323749
\(79\) −3.55275 −0.399716 −0.199858 0.979825i \(-0.564048\pi\)
−0.199858 + 0.979825i \(0.564048\pi\)
\(80\) −10.6698 −1.19292
\(81\) −9.18674 −1.02075
\(82\) −1.21398 −0.134061
\(83\) −6.70350 −0.735804 −0.367902 0.929865i \(-0.619924\pi\)
−0.367902 + 0.929865i \(0.619924\pi\)
\(84\) 6.29010 0.686306
\(85\) 13.7693 1.49349
\(86\) −2.51965 −0.271701
\(87\) −6.18958 −0.663593
\(88\) −3.98214 −0.424498
\(89\) 6.69890 0.710082 0.355041 0.934851i \(-0.384467\pi\)
0.355041 + 0.934851i \(0.384467\pi\)
\(90\) −0.0522039 −0.00550277
\(91\) −11.1452 −1.16834
\(92\) 16.0675 1.67515
\(93\) 13.6109 1.41138
\(94\) 0.0493287 0.00508787
\(95\) −5.19207 −0.532695
\(96\) −5.46270 −0.557534
\(97\) 16.9117 1.71712 0.858561 0.512711i \(-0.171359\pi\)
0.858561 + 0.512711i \(0.171359\pi\)
\(98\) −0.961831 −0.0971597
\(99\) 0.235809 0.0236997
\(100\) −7.70216 −0.770216
\(101\) 11.8744 1.18154 0.590772 0.806839i \(-0.298823\pi\)
0.590772 + 0.806839i \(0.298823\pi\)
\(102\) 2.19795 0.217629
\(103\) 14.8105 1.45933 0.729663 0.683807i \(-0.239677\pi\)
0.729663 + 0.683807i \(0.239677\pi\)
\(104\) 6.41202 0.628750
\(105\) 9.80251 0.956627
\(106\) 0.226365 0.0219865
\(107\) −9.58696 −0.926806 −0.463403 0.886148i \(-0.653372\pi\)
−0.463403 + 0.886148i \(0.653372\pi\)
\(108\) −9.89449 −0.952098
\(109\) 9.92829 0.950958 0.475479 0.879727i \(-0.342275\pi\)
0.475479 + 0.879727i \(0.342275\pi\)
\(110\) −3.04371 −0.290207
\(111\) 19.8940 1.88826
\(112\) 6.63887 0.627315
\(113\) −18.6924 −1.75843 −0.879215 0.476425i \(-0.841932\pi\)
−0.879215 + 0.476425i \(0.841932\pi\)
\(114\) −0.828792 −0.0776235
\(115\) 25.0396 2.33495
\(116\) −6.80781 −0.632089
\(117\) −0.379698 −0.0351031
\(118\) −0.594839 −0.0547594
\(119\) −8.56743 −0.785375
\(120\) −5.63954 −0.514817
\(121\) 2.74870 0.249882
\(122\) −0.495599 −0.0448694
\(123\) 7.76595 0.700233
\(124\) 14.9703 1.34438
\(125\) 2.99763 0.268116
\(126\) 0.0324819 0.00289372
\(127\) −8.12664 −0.721122 −0.360561 0.932736i \(-0.617415\pi\)
−0.360561 + 0.932736i \(0.617415\pi\)
\(128\) −7.95447 −0.703083
\(129\) 16.1185 1.41915
\(130\) 4.90096 0.429843
\(131\) −9.79055 −0.855404 −0.427702 0.903920i \(-0.640677\pi\)
−0.427702 + 0.903920i \(0.640677\pi\)
\(132\) 12.4942 1.08748
\(133\) 3.23057 0.280126
\(134\) −2.13102 −0.184092
\(135\) −15.4196 −1.32711
\(136\) 4.92897 0.422656
\(137\) 2.83725 0.242402 0.121201 0.992628i \(-0.461325\pi\)
0.121201 + 0.992628i \(0.461325\pi\)
\(138\) 3.99699 0.340246
\(139\) 17.4355 1.47886 0.739431 0.673232i \(-0.235095\pi\)
0.739431 + 0.673232i \(0.235095\pi\)
\(140\) 10.7816 0.911212
\(141\) −0.315562 −0.0265751
\(142\) −0.104438 −0.00876425
\(143\) −22.1381 −1.85128
\(144\) 0.226175 0.0188479
\(145\) −10.6093 −0.881055
\(146\) −1.84075 −0.152342
\(147\) 6.15295 0.507487
\(148\) 21.8811 1.79861
\(149\) −8.42407 −0.690126 −0.345063 0.938579i \(-0.612143\pi\)
−0.345063 + 0.938579i \(0.612143\pi\)
\(150\) −1.91601 −0.156442
\(151\) 7.91976 0.644501 0.322251 0.946654i \(-0.395561\pi\)
0.322251 + 0.946654i \(0.395561\pi\)
\(152\) −1.85860 −0.150752
\(153\) −0.291877 −0.0235969
\(154\) 1.89383 0.152610
\(155\) 23.3298 1.87390
\(156\) −20.1181 −1.61074
\(157\) −15.0434 −1.20059 −0.600296 0.799778i \(-0.704951\pi\)
−0.600296 + 0.799778i \(0.704951\pi\)
\(158\) −0.972067 −0.0773335
\(159\) −1.44809 −0.114841
\(160\) −9.36339 −0.740241
\(161\) −15.5799 −1.22787
\(162\) −2.51358 −0.197486
\(163\) −1.50863 −0.118165 −0.0590826 0.998253i \(-0.518818\pi\)
−0.0590826 + 0.998253i \(0.518818\pi\)
\(164\) 8.54163 0.666989
\(165\) 19.4710 1.51581
\(166\) −1.83414 −0.142357
\(167\) −1.91199 −0.147954 −0.0739772 0.997260i \(-0.523569\pi\)
−0.0739772 + 0.997260i \(0.523569\pi\)
\(168\) 3.50899 0.270724
\(169\) 22.6466 1.74204
\(170\) 3.76741 0.288947
\(171\) 0.110060 0.00841648
\(172\) 17.7284 1.35178
\(173\) −6.19158 −0.470737 −0.235368 0.971906i \(-0.575630\pi\)
−0.235368 + 0.971906i \(0.575630\pi\)
\(174\) −1.69353 −0.128386
\(175\) 7.46845 0.564562
\(176\) 13.1870 0.994006
\(177\) 3.80526 0.286021
\(178\) 1.83288 0.137380
\(179\) 0.988273 0.0738670 0.0369335 0.999318i \(-0.488241\pi\)
0.0369335 + 0.999318i \(0.488241\pi\)
\(180\) 0.367310 0.0273777
\(181\) 17.2474 1.28199 0.640993 0.767547i \(-0.278523\pi\)
0.640993 + 0.767547i \(0.278523\pi\)
\(182\) −3.04944 −0.226040
\(183\) 3.17040 0.234363
\(184\) 8.96338 0.660789
\(185\) 34.0995 2.50705
\(186\) 3.72406 0.273061
\(187\) −17.0177 −1.24446
\(188\) −0.347081 −0.0253135
\(189\) 9.59426 0.697880
\(190\) −1.42060 −0.103061
\(191\) −18.6835 −1.35189 −0.675945 0.736952i \(-0.736264\pi\)
−0.675945 + 0.736952i \(0.736264\pi\)
\(192\) 10.9551 0.790616
\(193\) 9.46633 0.681401 0.340701 0.940172i \(-0.389336\pi\)
0.340701 + 0.940172i \(0.389336\pi\)
\(194\) 4.62720 0.332214
\(195\) −31.3521 −2.24517
\(196\) 6.76752 0.483394
\(197\) −4.19098 −0.298595 −0.149298 0.988792i \(-0.547701\pi\)
−0.149298 + 0.988792i \(0.547701\pi\)
\(198\) 0.0645197 0.00458521
\(199\) 14.5931 1.03448 0.517239 0.855841i \(-0.326960\pi\)
0.517239 + 0.855841i \(0.326960\pi\)
\(200\) −4.29672 −0.303824
\(201\) 13.6324 0.961555
\(202\) 3.24894 0.228595
\(203\) 6.60124 0.463316
\(204\) −15.4649 −1.08276
\(205\) 13.3113 0.929702
\(206\) 4.05231 0.282338
\(207\) −0.530781 −0.0368919
\(208\) −21.2336 −1.47228
\(209\) 6.41696 0.443871
\(210\) 2.68206 0.185080
\(211\) −22.0389 −1.51722 −0.758609 0.651546i \(-0.774121\pi\)
−0.758609 + 0.651546i \(0.774121\pi\)
\(212\) −1.59272 −0.109389
\(213\) 0.668103 0.0457777
\(214\) −2.62308 −0.179310
\(215\) 27.6280 1.88422
\(216\) −5.51973 −0.375570
\(217\) −14.5161 −0.985417
\(218\) 2.71648 0.183983
\(219\) 11.7755 0.795715
\(220\) 21.4158 1.44385
\(221\) 27.4018 1.84325
\(222\) 5.44319 0.365323
\(223\) −20.6864 −1.38526 −0.692631 0.721292i \(-0.743548\pi\)
−0.692631 + 0.721292i \(0.743548\pi\)
\(224\) 5.82601 0.389267
\(225\) 0.254437 0.0169625
\(226\) −5.11441 −0.340206
\(227\) 5.37200 0.356552 0.178276 0.983981i \(-0.442948\pi\)
0.178276 + 0.983981i \(0.442948\pi\)
\(228\) 5.83145 0.386197
\(229\) 22.0031 1.45400 0.727001 0.686636i \(-0.240913\pi\)
0.727001 + 0.686636i \(0.240913\pi\)
\(230\) 6.85107 0.451746
\(231\) −12.1151 −0.797114
\(232\) −3.79780 −0.249338
\(233\) −7.68655 −0.503563 −0.251781 0.967784i \(-0.581016\pi\)
−0.251781 + 0.967784i \(0.581016\pi\)
\(234\) −0.103889 −0.00679144
\(235\) −0.540891 −0.0352839
\(236\) 4.18533 0.272442
\(237\) 6.21843 0.403930
\(238\) −2.34413 −0.151947
\(239\) 10.7005 0.692156 0.346078 0.938206i \(-0.387513\pi\)
0.346078 + 0.938206i \(0.387513\pi\)
\(240\) 18.6755 1.20550
\(241\) 22.6716 1.46041 0.730203 0.683230i \(-0.239426\pi\)
0.730203 + 0.683230i \(0.239426\pi\)
\(242\) 0.752072 0.0483450
\(243\) 0.660799 0.0423902
\(244\) 3.48707 0.223237
\(245\) 10.5465 0.673792
\(246\) 2.12484 0.135475
\(247\) −10.3326 −0.657445
\(248\) 8.35134 0.530310
\(249\) 11.7332 0.743562
\(250\) 0.820181 0.0518728
\(251\) 7.98553 0.504042 0.252021 0.967722i \(-0.418905\pi\)
0.252021 + 0.967722i \(0.418905\pi\)
\(252\) −0.228545 −0.0143970
\(253\) −30.9469 −1.94561
\(254\) −2.22353 −0.139516
\(255\) −24.1006 −1.50924
\(256\) 10.3414 0.646340
\(257\) −1.90960 −0.119117 −0.0595587 0.998225i \(-0.518969\pi\)
−0.0595587 + 0.998225i \(0.518969\pi\)
\(258\) 4.41017 0.274565
\(259\) −21.2171 −1.31837
\(260\) −34.4836 −2.13858
\(261\) 0.224893 0.0139205
\(262\) −2.67879 −0.165496
\(263\) 11.5263 0.710742 0.355371 0.934725i \(-0.384355\pi\)
0.355371 + 0.934725i \(0.384355\pi\)
\(264\) 6.97000 0.428974
\(265\) −2.48210 −0.152474
\(266\) 0.883914 0.0541962
\(267\) −11.7252 −0.717569
\(268\) 14.9940 0.915906
\(269\) −17.1075 −1.04306 −0.521532 0.853232i \(-0.674639\pi\)
−0.521532 + 0.853232i \(0.674639\pi\)
\(270\) −4.21895 −0.256757
\(271\) 3.84391 0.233501 0.116750 0.993161i \(-0.462752\pi\)
0.116750 + 0.993161i \(0.462752\pi\)
\(272\) −16.3224 −0.989693
\(273\) 19.5076 1.18066
\(274\) 0.776298 0.0468979
\(275\) 14.8348 0.894572
\(276\) −28.1231 −1.69281
\(277\) 9.85454 0.592102 0.296051 0.955172i \(-0.404330\pi\)
0.296051 + 0.955172i \(0.404330\pi\)
\(278\) 4.77053 0.286117
\(279\) −0.494538 −0.0296072
\(280\) 6.01461 0.359442
\(281\) 26.8883 1.60402 0.802011 0.597309i \(-0.203764\pi\)
0.802011 + 0.597309i \(0.203764\pi\)
\(282\) −0.0863407 −0.00514151
\(283\) 3.29380 0.195796 0.0978980 0.995196i \(-0.468788\pi\)
0.0978980 + 0.995196i \(0.468788\pi\)
\(284\) 0.734834 0.0436044
\(285\) 9.08774 0.538311
\(286\) −6.05719 −0.358169
\(287\) −8.28245 −0.488898
\(288\) 0.198482 0.0116957
\(289\) 4.06400 0.239059
\(290\) −2.90281 −0.170459
\(291\) −29.6008 −1.73523
\(292\) 12.9517 0.757939
\(293\) −2.01585 −0.117768 −0.0588838 0.998265i \(-0.518754\pi\)
−0.0588838 + 0.998265i \(0.518754\pi\)
\(294\) 1.68351 0.0981841
\(295\) 6.52243 0.379751
\(296\) 12.2065 0.709491
\(297\) 19.0573 1.10582
\(298\) −2.30490 −0.133520
\(299\) 49.8304 2.88177
\(300\) 13.4812 0.778337
\(301\) −17.1905 −0.990844
\(302\) 2.16692 0.124692
\(303\) −20.7839 −1.19400
\(304\) 6.15479 0.353001
\(305\) 5.43426 0.311165
\(306\) −0.0798604 −0.00456532
\(307\) 3.49294 0.199353 0.0996763 0.995020i \(-0.468219\pi\)
0.0996763 + 0.995020i \(0.468219\pi\)
\(308\) −13.3252 −0.759272
\(309\) −25.9231 −1.47471
\(310\) 6.38326 0.362545
\(311\) 2.08613 0.118293 0.0591467 0.998249i \(-0.481162\pi\)
0.0591467 + 0.998249i \(0.481162\pi\)
\(312\) −11.2230 −0.635380
\(313\) 19.4399 1.09881 0.549405 0.835556i \(-0.314854\pi\)
0.549405 + 0.835556i \(0.314854\pi\)
\(314\) −4.11601 −0.232280
\(315\) −0.356165 −0.0200676
\(316\) 6.83954 0.384754
\(317\) 1.15367 0.0647964 0.0323982 0.999475i \(-0.489686\pi\)
0.0323982 + 0.999475i \(0.489686\pi\)
\(318\) −0.396210 −0.0222184
\(319\) 13.1122 0.734144
\(320\) 18.7777 1.04970
\(321\) 16.7802 0.936578
\(322\) −4.26282 −0.237558
\(323\) −7.94272 −0.441945
\(324\) 17.6857 0.982542
\(325\) −23.8869 −1.32501
\(326\) −0.412776 −0.0228616
\(327\) −17.3776 −0.960985
\(328\) 4.76503 0.263105
\(329\) 0.336549 0.0185546
\(330\) 5.32745 0.293266
\(331\) −21.7620 −1.19615 −0.598075 0.801440i \(-0.704067\pi\)
−0.598075 + 0.801440i \(0.704067\pi\)
\(332\) 12.9052 0.708262
\(333\) −0.722831 −0.0396109
\(334\) −0.523139 −0.0286249
\(335\) 23.3667 1.27666
\(336\) −11.6201 −0.633929
\(337\) −1.23573 −0.0673147 −0.0336573 0.999433i \(-0.510715\pi\)
−0.0336573 + 0.999433i \(0.510715\pi\)
\(338\) 6.19632 0.337035
\(339\) 32.7175 1.77697
\(340\) −26.5078 −1.43759
\(341\) −28.8337 −1.56143
\(342\) 0.0301134 0.00162835
\(343\) −19.6292 −1.05988
\(344\) 9.88996 0.533231
\(345\) −43.8271 −2.35957
\(346\) −1.69407 −0.0910740
\(347\) −26.1681 −1.40478 −0.702389 0.711793i \(-0.747883\pi\)
−0.702389 + 0.711793i \(0.747883\pi\)
\(348\) 11.9158 0.638754
\(349\) −32.5117 −1.74031 −0.870155 0.492778i \(-0.835982\pi\)
−0.870155 + 0.492778i \(0.835982\pi\)
\(350\) 2.04344 0.109226
\(351\) −30.6860 −1.63790
\(352\) 11.5724 0.616810
\(353\) −25.4204 −1.35299 −0.676495 0.736447i \(-0.736502\pi\)
−0.676495 + 0.736447i \(0.736502\pi\)
\(354\) 1.04115 0.0553367
\(355\) 1.14517 0.0607792
\(356\) −12.8963 −0.683503
\(357\) 14.9957 0.793656
\(358\) 0.270401 0.0142911
\(359\) 18.8771 0.996293 0.498147 0.867093i \(-0.334014\pi\)
0.498147 + 0.867093i \(0.334014\pi\)
\(360\) 0.204907 0.0107996
\(361\) −16.0050 −0.842368
\(362\) 4.71904 0.248027
\(363\) −4.81109 −0.252517
\(364\) 21.4561 1.12460
\(365\) 20.1839 1.05647
\(366\) 0.867453 0.0453425
\(367\) 22.6084 1.18015 0.590075 0.807349i \(-0.299098\pi\)
0.590075 + 0.807349i \(0.299098\pi\)
\(368\) −29.6825 −1.54731
\(369\) −0.282169 −0.0146891
\(370\) 9.32995 0.485041
\(371\) 1.54440 0.0801810
\(372\) −26.2028 −1.35855
\(373\) −4.22807 −0.218921 −0.109461 0.993991i \(-0.534912\pi\)
−0.109461 + 0.993991i \(0.534912\pi\)
\(374\) −4.65621 −0.240767
\(375\) −5.24679 −0.270943
\(376\) −0.193622 −0.00998529
\(377\) −21.1132 −1.08739
\(378\) 2.62508 0.135020
\(379\) −0.0938411 −0.00482029 −0.00241015 0.999997i \(-0.500767\pi\)
−0.00241015 + 0.999997i \(0.500767\pi\)
\(380\) 9.99544 0.512755
\(381\) 14.2242 0.728726
\(382\) −5.11198 −0.261552
\(383\) 11.0532 0.564791 0.282396 0.959298i \(-0.408871\pi\)
0.282396 + 0.959298i \(0.408871\pi\)
\(384\) 13.9228 0.710496
\(385\) −20.7660 −1.05833
\(386\) 2.59008 0.131831
\(387\) −0.585650 −0.0297703
\(388\) −32.5573 −1.65285
\(389\) −4.14102 −0.209958 −0.104979 0.994474i \(-0.533478\pi\)
−0.104979 + 0.994474i \(0.533478\pi\)
\(390\) −8.57822 −0.434375
\(391\) 38.3051 1.93717
\(392\) 3.77532 0.190683
\(393\) 17.1365 0.864424
\(394\) −1.14669 −0.0577695
\(395\) 10.6587 0.536300
\(396\) −0.453965 −0.0228126
\(397\) 33.3372 1.67314 0.836572 0.547857i \(-0.184556\pi\)
0.836572 + 0.547857i \(0.184556\pi\)
\(398\) 3.99282 0.200142
\(399\) −5.65450 −0.283079
\(400\) 14.2287 0.711435
\(401\) −26.5022 −1.32346 −0.661729 0.749743i \(-0.730177\pi\)
−0.661729 + 0.749743i \(0.730177\pi\)
\(402\) 3.72995 0.186033
\(403\) 46.4279 2.31274
\(404\) −22.8598 −1.13732
\(405\) 27.5615 1.36954
\(406\) 1.80616 0.0896383
\(407\) −42.1442 −2.08901
\(408\) −8.62725 −0.427112
\(409\) 30.1507 1.49086 0.745428 0.666586i \(-0.232245\pi\)
0.745428 + 0.666586i \(0.232245\pi\)
\(410\) 3.64210 0.179870
\(411\) −4.96607 −0.244958
\(412\) −28.5123 −1.40470
\(413\) −4.05834 −0.199698
\(414\) −0.145227 −0.00713751
\(415\) 20.1114 0.987231
\(416\) −18.6338 −0.913595
\(417\) −30.5176 −1.49446
\(418\) 1.75574 0.0858762
\(419\) −4.34784 −0.212406 −0.106203 0.994344i \(-0.533869\pi\)
−0.106203 + 0.994344i \(0.533869\pi\)
\(420\) −18.8712 −0.920819
\(421\) 25.6692 1.25104 0.625520 0.780208i \(-0.284887\pi\)
0.625520 + 0.780208i \(0.284887\pi\)
\(422\) −6.03004 −0.293538
\(423\) 0.0114656 0.000557479 0
\(424\) −0.888515 −0.0431501
\(425\) −18.3620 −0.890690
\(426\) 0.182799 0.00885666
\(427\) −3.38126 −0.163631
\(428\) 18.4562 0.892115
\(429\) 38.7486 1.87080
\(430\) 7.55929 0.364541
\(431\) 17.4951 0.842708 0.421354 0.906896i \(-0.361555\pi\)
0.421354 + 0.906896i \(0.361555\pi\)
\(432\) 18.2787 0.879436
\(433\) 0.996301 0.0478792 0.0239396 0.999713i \(-0.492379\pi\)
0.0239396 + 0.999713i \(0.492379\pi\)
\(434\) −3.97174 −0.190650
\(435\) 18.5696 0.890345
\(436\) −19.1133 −0.915363
\(437\) −14.4439 −0.690946
\(438\) 3.22189 0.153948
\(439\) 23.5023 1.12171 0.560853 0.827916i \(-0.310473\pi\)
0.560853 + 0.827916i \(0.310473\pi\)
\(440\) 11.9470 0.569550
\(441\) −0.223562 −0.0106458
\(442\) 7.49740 0.356615
\(443\) −39.0629 −1.85593 −0.927967 0.372662i \(-0.878445\pi\)
−0.927967 + 0.372662i \(0.878445\pi\)
\(444\) −38.2987 −1.81758
\(445\) −20.0976 −0.952720
\(446\) −5.65999 −0.268008
\(447\) 14.7448 0.697403
\(448\) −11.6837 −0.552003
\(449\) −30.3220 −1.43099 −0.715493 0.698620i \(-0.753798\pi\)
−0.715493 + 0.698620i \(0.753798\pi\)
\(450\) 0.0696165 0.00328175
\(451\) −16.4517 −0.774679
\(452\) 35.9854 1.69261
\(453\) −13.8621 −0.651297
\(454\) 1.46983 0.0689825
\(455\) 33.4372 1.56756
\(456\) 3.25312 0.152342
\(457\) 13.1097 0.613245 0.306623 0.951831i \(-0.400801\pi\)
0.306623 + 0.951831i \(0.400801\pi\)
\(458\) 6.02025 0.281308
\(459\) −23.5886 −1.10102
\(460\) −48.2047 −2.24755
\(461\) −32.8530 −1.53011 −0.765057 0.643962i \(-0.777289\pi\)
−0.765057 + 0.643962i \(0.777289\pi\)
\(462\) −3.31480 −0.154219
\(463\) −3.20561 −0.148977 −0.0744886 0.997222i \(-0.523732\pi\)
−0.0744886 + 0.997222i \(0.523732\pi\)
\(464\) 12.5765 0.583850
\(465\) −40.8345 −1.89365
\(466\) −2.10311 −0.0974249
\(467\) 16.8311 0.778851 0.389426 0.921058i \(-0.372674\pi\)
0.389426 + 0.921058i \(0.372674\pi\)
\(468\) 0.730972 0.0337892
\(469\) −14.5391 −0.671352
\(470\) −0.147993 −0.00682641
\(471\) 26.3306 1.21325
\(472\) 2.33483 0.107469
\(473\) −34.1460 −1.57003
\(474\) 1.70142 0.0781489
\(475\) 6.92388 0.317689
\(476\) 16.4935 0.755977
\(477\) 0.0526149 0.00240907
\(478\) 2.92775 0.133912
\(479\) −1.33542 −0.0610171 −0.0305085 0.999535i \(-0.509713\pi\)
−0.0305085 + 0.999535i \(0.509713\pi\)
\(480\) 16.3889 0.748046
\(481\) 67.8603 3.09416
\(482\) 6.20316 0.282546
\(483\) 27.2698 1.24082
\(484\) −5.29163 −0.240529
\(485\) −50.7374 −2.30387
\(486\) 0.180801 0.00820129
\(487\) 2.38892 0.108252 0.0541261 0.998534i \(-0.482763\pi\)
0.0541261 + 0.998534i \(0.482763\pi\)
\(488\) 1.94529 0.0880593
\(489\) 2.64058 0.119411
\(490\) 2.88563 0.130359
\(491\) −27.3128 −1.23261 −0.616304 0.787508i \(-0.711371\pi\)
−0.616304 + 0.787508i \(0.711371\pi\)
\(492\) −14.9505 −0.674022
\(493\) −16.2299 −0.730958
\(494\) −2.82708 −0.127197
\(495\) −0.707461 −0.0317980
\(496\) −27.6557 −1.24178
\(497\) −0.712537 −0.0319617
\(498\) 3.21032 0.143858
\(499\) −28.1844 −1.26171 −0.630853 0.775902i \(-0.717295\pi\)
−0.630853 + 0.775902i \(0.717295\pi\)
\(500\) −5.77085 −0.258080
\(501\) 3.34658 0.149514
\(502\) 2.18492 0.0975177
\(503\) 29.3083 1.30679 0.653395 0.757017i \(-0.273344\pi\)
0.653395 + 0.757017i \(0.273344\pi\)
\(504\) −0.127496 −0.00567912
\(505\) −35.6247 −1.58528
\(506\) −8.46736 −0.376420
\(507\) −39.6386 −1.76041
\(508\) 15.6449 0.694130
\(509\) −7.79102 −0.345331 −0.172665 0.984981i \(-0.555238\pi\)
−0.172665 + 0.984981i \(0.555238\pi\)
\(510\) −6.59415 −0.291994
\(511\) −12.5587 −0.555563
\(512\) 18.7385 0.828131
\(513\) 8.89468 0.392710
\(514\) −0.522484 −0.0230458
\(515\) −44.4337 −1.95798
\(516\) −31.0303 −1.36603
\(517\) 0.668497 0.0294005
\(518\) −5.80521 −0.255066
\(519\) 10.8372 0.475700
\(520\) −19.2370 −0.843596
\(521\) −14.4354 −0.632428 −0.316214 0.948688i \(-0.602412\pi\)
−0.316214 + 0.948688i \(0.602412\pi\)
\(522\) 0.0615328 0.00269322
\(523\) −9.85239 −0.430815 −0.215407 0.976524i \(-0.569108\pi\)
−0.215407 + 0.976524i \(0.569108\pi\)
\(524\) 18.8482 0.823386
\(525\) −13.0721 −0.570515
\(526\) 3.15370 0.137508
\(527\) 35.6895 1.55466
\(528\) −23.0813 −1.00449
\(529\) 46.6581 2.02861
\(530\) −0.679127 −0.0294994
\(531\) −0.138260 −0.00599999
\(532\) −6.21929 −0.269640
\(533\) 26.4904 1.14743
\(534\) −3.20812 −0.138829
\(535\) 28.7622 1.24350
\(536\) 8.36455 0.361294
\(537\) −1.72979 −0.0746459
\(538\) −4.68078 −0.201803
\(539\) −13.0346 −0.561441
\(540\) 29.6848 1.27743
\(541\) −31.4079 −1.35033 −0.675166 0.737666i \(-0.735928\pi\)
−0.675166 + 0.737666i \(0.735928\pi\)
\(542\) 1.05173 0.0451757
\(543\) −30.1883 −1.29550
\(544\) −14.3239 −0.614133
\(545\) −29.7863 −1.27590
\(546\) 5.33747 0.228423
\(547\) −17.2727 −0.738527 −0.369264 0.929325i \(-0.620390\pi\)
−0.369264 + 0.929325i \(0.620390\pi\)
\(548\) −5.46209 −0.233329
\(549\) −0.115194 −0.00491635
\(550\) 4.05894 0.173074
\(551\) 6.11990 0.260717
\(552\) −15.6887 −0.667757
\(553\) −6.63200 −0.282022
\(554\) 2.69630 0.114555
\(555\) −59.6848 −2.53348
\(556\) −33.5658 −1.42351
\(557\) 5.57348 0.236156 0.118078 0.993004i \(-0.462327\pi\)
0.118078 + 0.993004i \(0.462327\pi\)
\(558\) −0.135310 −0.00572814
\(559\) 54.9816 2.32547
\(560\) −19.9175 −0.841670
\(561\) 29.7863 1.25758
\(562\) 7.35690 0.310332
\(563\) 10.7904 0.454763 0.227381 0.973806i \(-0.426984\pi\)
0.227381 + 0.973806i \(0.426984\pi\)
\(564\) 0.607500 0.0255804
\(565\) 56.0797 2.35929
\(566\) 0.901214 0.0378809
\(567\) −17.1491 −0.720195
\(568\) 0.409934 0.0172004
\(569\) −26.7148 −1.11994 −0.559971 0.828512i \(-0.689188\pi\)
−0.559971 + 0.828512i \(0.689188\pi\)
\(570\) 2.48649 0.104148
\(571\) −17.6386 −0.738154 −0.369077 0.929399i \(-0.620326\pi\)
−0.369077 + 0.929399i \(0.620326\pi\)
\(572\) 42.6188 1.78198
\(573\) 32.7020 1.36614
\(574\) −2.26616 −0.0945876
\(575\) −33.3915 −1.39252
\(576\) −0.398043 −0.0165851
\(577\) −25.1722 −1.04793 −0.523967 0.851738i \(-0.675549\pi\)
−0.523967 + 0.851738i \(0.675549\pi\)
\(578\) 1.11195 0.0462510
\(579\) −16.5690 −0.688586
\(580\) 20.4244 0.848076
\(581\) −12.5136 −0.519150
\(582\) −8.09905 −0.335716
\(583\) 3.06768 0.127050
\(584\) 7.22520 0.298981
\(585\) 1.13915 0.0470980
\(586\) −0.551557 −0.0227846
\(587\) −6.77946 −0.279818 −0.139909 0.990164i \(-0.544681\pi\)
−0.139909 + 0.990164i \(0.544681\pi\)
\(588\) −11.8453 −0.488491
\(589\) −13.4576 −0.554512
\(590\) 1.78460 0.0734708
\(591\) 7.33553 0.301743
\(592\) −40.4223 −1.66135
\(593\) 33.0057 1.35538 0.677691 0.735347i \(-0.262981\pi\)
0.677691 + 0.735347i \(0.262981\pi\)
\(594\) 5.21427 0.213944
\(595\) 25.7035 1.05374
\(596\) 16.2175 0.664294
\(597\) −25.5425 −1.04539
\(598\) 13.6341 0.557539
\(599\) −4.88130 −0.199445 −0.0997223 0.995015i \(-0.531795\pi\)
−0.0997223 + 0.995015i \(0.531795\pi\)
\(600\) 7.52060 0.307027
\(601\) −26.7936 −1.09293 −0.546466 0.837481i \(-0.684027\pi\)
−0.546466 + 0.837481i \(0.684027\pi\)
\(602\) −4.70348 −0.191700
\(603\) −0.495321 −0.0201710
\(604\) −15.2466 −0.620377
\(605\) −8.24649 −0.335268
\(606\) −5.68666 −0.231005
\(607\) 16.7752 0.680885 0.340443 0.940265i \(-0.389423\pi\)
0.340443 + 0.940265i \(0.389423\pi\)
\(608\) 5.40120 0.219048
\(609\) −11.5542 −0.468201
\(610\) 1.48686 0.0602014
\(611\) −1.07641 −0.0435469
\(612\) 0.561904 0.0227136
\(613\) 45.3150 1.83025 0.915127 0.403166i \(-0.132090\pi\)
0.915127 + 0.403166i \(0.132090\pi\)
\(614\) 0.955702 0.0385690
\(615\) −23.2989 −0.939504
\(616\) −7.43356 −0.299507
\(617\) −20.9179 −0.842123 −0.421062 0.907032i \(-0.638342\pi\)
−0.421062 + 0.907032i \(0.638342\pi\)
\(618\) −7.09280 −0.285314
\(619\) −13.9694 −0.561479 −0.280739 0.959784i \(-0.590580\pi\)
−0.280739 + 0.959784i \(0.590580\pi\)
\(620\) −44.9131 −1.80375
\(621\) −42.8961 −1.72136
\(622\) 0.570784 0.0228863
\(623\) 12.5050 0.501002
\(624\) 37.1654 1.48781
\(625\) −28.9975 −1.15990
\(626\) 5.31895 0.212588
\(627\) −11.2317 −0.448551
\(628\) 28.9606 1.15565
\(629\) 52.1648 2.07995
\(630\) −0.0974502 −0.00388251
\(631\) −10.7231 −0.426879 −0.213439 0.976956i \(-0.568467\pi\)
−0.213439 + 0.976956i \(0.568467\pi\)
\(632\) 3.81550 0.151772
\(633\) 38.5749 1.53321
\(634\) 0.315654 0.0125362
\(635\) 24.3810 0.967532
\(636\) 2.78776 0.110542
\(637\) 20.9883 0.831585
\(638\) 3.58763 0.142036
\(639\) −0.0242749 −0.000960301 0
\(640\) 23.8645 0.943328
\(641\) −22.9098 −0.904881 −0.452441 0.891794i \(-0.649447\pi\)
−0.452441 + 0.891794i \(0.649447\pi\)
\(642\) 4.59122 0.181201
\(643\) 14.0008 0.552138 0.276069 0.961138i \(-0.410968\pi\)
0.276069 + 0.961138i \(0.410968\pi\)
\(644\) 29.9935 1.18191
\(645\) −48.3577 −1.90408
\(646\) −2.17320 −0.0855036
\(647\) −8.20116 −0.322421 −0.161210 0.986920i \(-0.551540\pi\)
−0.161210 + 0.986920i \(0.551540\pi\)
\(648\) 9.86615 0.387579
\(649\) −8.06119 −0.316429
\(650\) −6.53568 −0.256350
\(651\) 25.4077 0.995807
\(652\) 2.90433 0.113742
\(653\) 33.2558 1.30140 0.650700 0.759335i \(-0.274476\pi\)
0.650700 + 0.759335i \(0.274476\pi\)
\(654\) −4.75468 −0.185923
\(655\) 29.3730 1.14770
\(656\) −15.7795 −0.616086
\(657\) −0.427852 −0.0166921
\(658\) 0.0920831 0.00358977
\(659\) −28.3719 −1.10521 −0.552606 0.833442i \(-0.686367\pi\)
−0.552606 + 0.833442i \(0.686367\pi\)
\(660\) −37.4843 −1.45908
\(661\) −24.6344 −0.958165 −0.479083 0.877770i \(-0.659031\pi\)
−0.479083 + 0.877770i \(0.659031\pi\)
\(662\) −5.95430 −0.231420
\(663\) −47.9618 −1.86268
\(664\) 7.19925 0.279385
\(665\) −9.69215 −0.375845
\(666\) −0.197773 −0.00766356
\(667\) −29.5142 −1.14280
\(668\) 3.68085 0.142416
\(669\) 36.2076 1.39987
\(670\) 6.39336 0.246997
\(671\) −6.71629 −0.259280
\(672\) −10.1973 −0.393371
\(673\) 22.6227 0.872042 0.436021 0.899936i \(-0.356387\pi\)
0.436021 + 0.899936i \(0.356387\pi\)
\(674\) −0.338108 −0.0130235
\(675\) 20.5628 0.791463
\(676\) −43.5978 −1.67684
\(677\) −32.1683 −1.23633 −0.618165 0.786048i \(-0.712124\pi\)
−0.618165 + 0.786048i \(0.712124\pi\)
\(678\) 8.95182 0.343793
\(679\) 31.5695 1.21152
\(680\) −14.7876 −0.567079
\(681\) −9.40268 −0.360311
\(682\) −7.88918 −0.302092
\(683\) −41.6390 −1.59327 −0.796637 0.604458i \(-0.793390\pi\)
−0.796637 + 0.604458i \(0.793390\pi\)
\(684\) −0.211880 −0.00810144
\(685\) −8.51214 −0.325232
\(686\) −5.37075 −0.205056
\(687\) −38.5122 −1.46933
\(688\) −32.7509 −1.24862
\(689\) −4.93955 −0.188182
\(690\) −11.9915 −0.456509
\(691\) 20.1261 0.765632 0.382816 0.923825i \(-0.374954\pi\)
0.382816 + 0.923825i \(0.374954\pi\)
\(692\) 11.9196 0.453117
\(693\) 0.440191 0.0167215
\(694\) −7.15985 −0.271784
\(695\) −52.3090 −1.98419
\(696\) 6.64733 0.251967
\(697\) 20.3634 0.771317
\(698\) −8.89551 −0.336700
\(699\) 13.4539 0.508872
\(700\) −14.3778 −0.543430
\(701\) 33.1224 1.25101 0.625507 0.780219i \(-0.284892\pi\)
0.625507 + 0.780219i \(0.284892\pi\)
\(702\) −8.39598 −0.316886
\(703\) −19.6701 −0.741870
\(704\) −23.2076 −0.874671
\(705\) 0.946729 0.0356559
\(706\) −6.95526 −0.261765
\(707\) 22.1662 0.833644
\(708\) −7.32564 −0.275315
\(709\) 21.3873 0.803216 0.401608 0.915812i \(-0.368451\pi\)
0.401608 + 0.915812i \(0.368451\pi\)
\(710\) 0.313329 0.0117590
\(711\) −0.225941 −0.00847344
\(712\) −7.19432 −0.269619
\(713\) 64.9016 2.43059
\(714\) 4.10296 0.153549
\(715\) 66.4173 2.48387
\(716\) −1.90256 −0.0711021
\(717\) −18.7292 −0.699453
\(718\) 5.16494 0.192754
\(719\) 26.7348 0.997041 0.498520 0.866878i \(-0.333877\pi\)
0.498520 + 0.866878i \(0.333877\pi\)
\(720\) −0.678556 −0.0252883
\(721\) 27.6472 1.02964
\(722\) −4.37912 −0.162974
\(723\) −39.6824 −1.47580
\(724\) −33.2035 −1.23400
\(725\) 14.1480 0.525445
\(726\) −1.31636 −0.0488547
\(727\) 20.7270 0.768724 0.384362 0.923183i \(-0.374422\pi\)
0.384362 + 0.923183i \(0.374422\pi\)
\(728\) 11.9695 0.443618
\(729\) 26.4036 0.977912
\(730\) 5.52251 0.204397
\(731\) 42.2648 1.56322
\(732\) −6.10346 −0.225590
\(733\) −30.0368 −1.10943 −0.554717 0.832039i \(-0.687173\pi\)
−0.554717 + 0.832039i \(0.687173\pi\)
\(734\) 6.18588 0.228325
\(735\) −18.4597 −0.680897
\(736\) −26.0482 −0.960149
\(737\) −28.8793 −1.06378
\(738\) −0.0772041 −0.00284192
\(739\) −44.9552 −1.65370 −0.826852 0.562420i \(-0.809871\pi\)
−0.826852 + 0.562420i \(0.809871\pi\)
\(740\) −65.6463 −2.41320
\(741\) 18.0852 0.664376
\(742\) 0.422561 0.0155127
\(743\) 26.2207 0.961946 0.480973 0.876735i \(-0.340284\pi\)
0.480973 + 0.876735i \(0.340284\pi\)
\(744\) −14.6175 −0.535902
\(745\) 25.2734 0.925945
\(746\) −1.15684 −0.0423550
\(747\) −0.426316 −0.0155981
\(748\) 32.7615 1.19788
\(749\) −17.8962 −0.653913
\(750\) −1.43557 −0.0524197
\(751\) 39.4426 1.43928 0.719640 0.694348i \(-0.244307\pi\)
0.719640 + 0.694348i \(0.244307\pi\)
\(752\) 0.641185 0.0233816
\(753\) −13.9772 −0.509357
\(754\) −5.77678 −0.210378
\(755\) −23.7604 −0.864729
\(756\) −18.4703 −0.671757
\(757\) 13.8394 0.503000 0.251500 0.967857i \(-0.419076\pi\)
0.251500 + 0.967857i \(0.419076\pi\)
\(758\) −0.0256758 −0.000932588 0
\(759\) 54.1667 1.96613
\(760\) 5.57605 0.202264
\(761\) 46.6841 1.69230 0.846149 0.532946i \(-0.178915\pi\)
0.846149 + 0.532946i \(0.178915\pi\)
\(762\) 3.89187 0.140987
\(763\) 18.5334 0.670953
\(764\) 35.9683 1.30129
\(765\) 0.875673 0.0316600
\(766\) 3.02426 0.109271
\(767\) 12.9801 0.468683
\(768\) −18.1008 −0.653155
\(769\) −35.4819 −1.27951 −0.639755 0.768579i \(-0.720964\pi\)
−0.639755 + 0.768579i \(0.720964\pi\)
\(770\) −5.68177 −0.204757
\(771\) 3.34239 0.120373
\(772\) −18.2240 −0.655896
\(773\) 25.1072 0.903043 0.451522 0.892260i \(-0.350881\pi\)
0.451522 + 0.892260i \(0.350881\pi\)
\(774\) −0.160240 −0.00575969
\(775\) −31.1115 −1.11756
\(776\) −18.1624 −0.651992
\(777\) 37.1366 1.33227
\(778\) −1.13302 −0.0406208
\(779\) −7.67853 −0.275112
\(780\) 60.3570 2.16113
\(781\) −1.41533 −0.0506446
\(782\) 10.4806 0.374787
\(783\) 18.1751 0.649526
\(784\) −12.5021 −0.446503
\(785\) 45.1323 1.61084
\(786\) 4.68872 0.167241
\(787\) −48.6263 −1.73334 −0.866670 0.498882i \(-0.833744\pi\)
−0.866670 + 0.498882i \(0.833744\pi\)
\(788\) 8.06822 0.287418
\(789\) −20.1746 −0.718235
\(790\) 2.91634 0.103759
\(791\) −34.8935 −1.24067
\(792\) −0.253249 −0.00899879
\(793\) 10.8145 0.384035
\(794\) 9.12136 0.323705
\(795\) 4.34446 0.154082
\(796\) −28.0938 −0.995757
\(797\) 34.9647 1.23851 0.619257 0.785189i \(-0.287434\pi\)
0.619257 + 0.785189i \(0.287434\pi\)
\(798\) −1.54713 −0.0547677
\(799\) −0.827445 −0.0292729
\(800\) 12.4865 0.441466
\(801\) 0.426024 0.0150528
\(802\) −7.25127 −0.256051
\(803\) −24.9457 −0.880313
\(804\) −26.2442 −0.925563
\(805\) 46.7420 1.64744
\(806\) 12.7031 0.447448
\(807\) 29.9435 1.05406
\(808\) −12.7525 −0.448633
\(809\) −5.42646 −0.190784 −0.0953921 0.995440i \(-0.530411\pi\)
−0.0953921 + 0.995440i \(0.530411\pi\)
\(810\) 7.54109 0.264967
\(811\) 12.0367 0.422666 0.211333 0.977414i \(-0.432220\pi\)
0.211333 + 0.977414i \(0.432220\pi\)
\(812\) −12.7083 −0.445974
\(813\) −6.72805 −0.235963
\(814\) −11.5311 −0.404163
\(815\) 4.52611 0.158543
\(816\) 28.5694 1.00013
\(817\) −15.9370 −0.557566
\(818\) 8.24952 0.288438
\(819\) −0.708792 −0.0247672
\(820\) −25.6261 −0.894902
\(821\) −23.2393 −0.811056 −0.405528 0.914083i \(-0.632912\pi\)
−0.405528 + 0.914083i \(0.632912\pi\)
\(822\) −1.35876 −0.0473923
\(823\) 39.5067 1.37712 0.688558 0.725181i \(-0.258244\pi\)
0.688558 + 0.725181i \(0.258244\pi\)
\(824\) −15.9059 −0.554107
\(825\) −25.9655 −0.904004
\(826\) −1.11040 −0.0386358
\(827\) 28.1602 0.979226 0.489613 0.871940i \(-0.337138\pi\)
0.489613 + 0.871940i \(0.337138\pi\)
\(828\) 1.02183 0.0355110
\(829\) −5.43801 −0.188870 −0.0944349 0.995531i \(-0.530104\pi\)
−0.0944349 + 0.995531i \(0.530104\pi\)
\(830\) 5.50268 0.191001
\(831\) −17.2485 −0.598345
\(832\) 37.3688 1.29553
\(833\) 16.1339 0.559005
\(834\) −8.34992 −0.289134
\(835\) 5.73624 0.198511
\(836\) −12.3535 −0.427256
\(837\) −39.9670 −1.38146
\(838\) −1.18961 −0.0410944
\(839\) −18.1956 −0.628181 −0.314090 0.949393i \(-0.601700\pi\)
−0.314090 + 0.949393i \(0.601700\pi\)
\(840\) −10.5275 −0.363232
\(841\) −16.4948 −0.568786
\(842\) 7.02334 0.242040
\(843\) −47.0630 −1.62093
\(844\) 42.4278 1.46043
\(845\) −67.9429 −2.33731
\(846\) 0.00313711 0.000107856 0
\(847\) 5.13107 0.176306
\(848\) 2.94234 0.101040
\(849\) −5.76518 −0.197860
\(850\) −5.02403 −0.172323
\(851\) 94.8621 3.25183
\(852\) −1.28619 −0.0440642
\(853\) −15.7779 −0.540226 −0.270113 0.962829i \(-0.587061\pi\)
−0.270113 + 0.962829i \(0.587061\pi\)
\(854\) −0.925145 −0.0316578
\(855\) −0.330195 −0.0112924
\(856\) 10.2960 0.351909
\(857\) 50.4138 1.72210 0.861051 0.508519i \(-0.169807\pi\)
0.861051 + 0.508519i \(0.169807\pi\)
\(858\) 10.6020 0.361945
\(859\) 6.69367 0.228385 0.114193 0.993459i \(-0.463572\pi\)
0.114193 + 0.993459i \(0.463572\pi\)
\(860\) −53.1878 −1.81369
\(861\) 14.4969 0.494053
\(862\) 4.78682 0.163040
\(863\) 27.9913 0.952835 0.476418 0.879219i \(-0.341935\pi\)
0.476418 + 0.879219i \(0.341935\pi\)
\(864\) 16.0407 0.545715
\(865\) 18.5756 0.631589
\(866\) 0.272597 0.00926324
\(867\) −7.11327 −0.241579
\(868\) 27.9455 0.948532
\(869\) −13.1733 −0.446875
\(870\) 5.08082 0.172256
\(871\) 46.5013 1.57564
\(872\) −10.6625 −0.361079
\(873\) 1.07552 0.0364007
\(874\) −3.95199 −0.133678
\(875\) 5.59575 0.189171
\(876\) −22.6695 −0.765931
\(877\) 32.1120 1.08435 0.542173 0.840267i \(-0.317602\pi\)
0.542173 + 0.840267i \(0.317602\pi\)
\(878\) 6.43046 0.217018
\(879\) 3.52838 0.119009
\(880\) −39.5628 −1.33366
\(881\) −26.1191 −0.879976 −0.439988 0.898004i \(-0.645017\pi\)
−0.439988 + 0.898004i \(0.645017\pi\)
\(882\) −0.0611687 −0.00205966
\(883\) 39.7046 1.33617 0.668083 0.744086i \(-0.267115\pi\)
0.668083 + 0.744086i \(0.267115\pi\)
\(884\) −52.7523 −1.77425
\(885\) −11.4163 −0.383755
\(886\) −10.6880 −0.359070
\(887\) −33.5353 −1.12601 −0.563003 0.826455i \(-0.690354\pi\)
−0.563003 + 0.826455i \(0.690354\pi\)
\(888\) −21.3653 −0.716972
\(889\) −15.1702 −0.508792
\(890\) −5.49891 −0.184324
\(891\) −34.0638 −1.14118
\(892\) 39.8241 1.33341
\(893\) 0.312009 0.0104410
\(894\) 4.03431 0.134927
\(895\) −2.96496 −0.0991076
\(896\) −14.8488 −0.496064
\(897\) −87.2189 −2.91215
\(898\) −8.29640 −0.276854
\(899\) −27.4989 −0.917140
\(900\) −0.489827 −0.0163276
\(901\) −3.79707 −0.126499
\(902\) −4.50133 −0.149878
\(903\) 30.0888 1.00129
\(904\) 20.0748 0.667677
\(905\) −51.7445 −1.72004
\(906\) −3.79279 −0.126007
\(907\) 13.3872 0.444514 0.222257 0.974988i \(-0.428658\pi\)
0.222257 + 0.974988i \(0.428658\pi\)
\(908\) −10.3418 −0.343206
\(909\) 0.755162 0.0250472
\(910\) 9.14874 0.303278
\(911\) −15.3096 −0.507228 −0.253614 0.967305i \(-0.581619\pi\)
−0.253614 + 0.967305i \(0.581619\pi\)
\(912\) −10.7728 −0.356723
\(913\) −24.8561 −0.822615
\(914\) 3.58694 0.118645
\(915\) −9.51165 −0.314445
\(916\) −42.3589 −1.39958
\(917\) −18.2763 −0.603535
\(918\) −6.45406 −0.213016
\(919\) −2.27868 −0.0751667 −0.0375833 0.999293i \(-0.511966\pi\)
−0.0375833 + 0.999293i \(0.511966\pi\)
\(920\) −26.8914 −0.886583
\(921\) −6.11374 −0.201455
\(922\) −8.98888 −0.296033
\(923\) 2.27896 0.0750129
\(924\) 23.3232 0.767277
\(925\) −45.4734 −1.49516
\(926\) −0.877085 −0.0288228
\(927\) 0.941892 0.0309358
\(928\) 11.0366 0.362296
\(929\) 54.2380 1.77949 0.889745 0.456457i \(-0.150882\pi\)
0.889745 + 0.456457i \(0.150882\pi\)
\(930\) −11.1727 −0.366367
\(931\) −6.08368 −0.199385
\(932\) 14.7977 0.484714
\(933\) −3.65137 −0.119541
\(934\) 4.60515 0.150685
\(935\) 51.0555 1.66969
\(936\) 0.407779 0.0133287
\(937\) −20.7294 −0.677201 −0.338601 0.940930i \(-0.609954\pi\)
−0.338601 + 0.940930i \(0.609954\pi\)
\(938\) −3.97803 −0.129887
\(939\) −34.0260 −1.11040
\(940\) 1.04129 0.0339632
\(941\) −45.6259 −1.48736 −0.743681 0.668535i \(-0.766922\pi\)
−0.743681 + 0.668535i \(0.766922\pi\)
\(942\) 7.20431 0.234729
\(943\) 37.0310 1.20589
\(944\) −7.73184 −0.251650
\(945\) −28.7841 −0.936348
\(946\) −9.34266 −0.303756
\(947\) 10.4299 0.338927 0.169464 0.985536i \(-0.445796\pi\)
0.169464 + 0.985536i \(0.445796\pi\)
\(948\) −11.9713 −0.388811
\(949\) 40.1673 1.30389
\(950\) 1.89444 0.0614637
\(951\) −2.01928 −0.0654796
\(952\) 9.20103 0.298207
\(953\) −18.7987 −0.608949 −0.304474 0.952521i \(-0.598481\pi\)
−0.304474 + 0.952521i \(0.598481\pi\)
\(954\) 0.0143959 0.000466085 0
\(955\) 56.0531 1.81384
\(956\) −20.5999 −0.666247
\(957\) −22.9505 −0.741884
\(958\) −0.365385 −0.0118050
\(959\) 5.29636 0.171028
\(960\) −32.8668 −1.06077
\(961\) 29.4700 0.950644
\(962\) 18.5672 0.598631
\(963\) −0.609692 −0.0196471
\(964\) −43.6459 −1.40574
\(965\) −28.4003 −0.914238
\(966\) 7.46127 0.240062
\(967\) −13.6049 −0.437505 −0.218753 0.975780i \(-0.570199\pi\)
−0.218753 + 0.975780i \(0.570199\pi\)
\(968\) −2.95198 −0.0948804
\(969\) 13.9022 0.446604
\(970\) −13.8822 −0.445732
\(971\) −7.52515 −0.241494 −0.120747 0.992683i \(-0.538529\pi\)
−0.120747 + 0.992683i \(0.538529\pi\)
\(972\) −1.27213 −0.0408035
\(973\) 32.5473 1.04342
\(974\) 0.653631 0.0209437
\(975\) 41.8095 1.33898
\(976\) −6.44189 −0.206200
\(977\) −14.2026 −0.454381 −0.227191 0.973850i \(-0.572954\pi\)
−0.227191 + 0.973850i \(0.572954\pi\)
\(978\) 0.722488 0.0231026
\(979\) 24.8390 0.793859
\(980\) −20.3035 −0.648572
\(981\) 0.631400 0.0201590
\(982\) −7.47304 −0.238474
\(983\) −40.4071 −1.28879 −0.644393 0.764695i \(-0.722890\pi\)
−0.644393 + 0.764695i \(0.722890\pi\)
\(984\) −8.34029 −0.265879
\(985\) 12.5735 0.400626
\(986\) −4.44066 −0.141419
\(987\) −0.589067 −0.0187502
\(988\) 19.8916 0.632836
\(989\) 76.8589 2.44397
\(990\) −0.193568 −0.00615199
\(991\) 48.6246 1.54461 0.772306 0.635251i \(-0.219103\pi\)
0.772306 + 0.635251i \(0.219103\pi\)
\(992\) −24.2695 −0.770558
\(993\) 38.0904 1.20876
\(994\) −0.194957 −0.00618366
\(995\) −43.7814 −1.38796
\(996\) −22.5881 −0.715730
\(997\) 49.0353 1.55296 0.776482 0.630140i \(-0.217002\pi\)
0.776482 + 0.630140i \(0.217002\pi\)
\(998\) −7.71152 −0.244104
\(999\) −58.4169 −1.84823
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 4001.2.a.b.1.99 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.99 184 1.1 even 1 trivial