Properties

Label 4001.2.a.b.1.15
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 1.15
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)
 
\(f(q)\) \(=\) \(q-2.55462 q^{2} +2.40673 q^{3} +4.52611 q^{4} +3.51168 q^{5} -6.14829 q^{6} +3.52515 q^{7} -6.45325 q^{8} +2.79234 q^{9} +O(q^{10})\) \(q-2.55462 q^{2} +2.40673 q^{3} +4.52611 q^{4} +3.51168 q^{5} -6.14829 q^{6} +3.52515 q^{7} -6.45325 q^{8} +2.79234 q^{9} -8.97103 q^{10} -5.09895 q^{11} +10.8931 q^{12} -0.353446 q^{13} -9.00544 q^{14} +8.45166 q^{15} +7.43343 q^{16} +1.22514 q^{17} -7.13338 q^{18} +0.445154 q^{19} +15.8942 q^{20} +8.48408 q^{21} +13.0259 q^{22} +9.35822 q^{23} -15.5312 q^{24} +7.33191 q^{25} +0.902921 q^{26} -0.499785 q^{27} +15.9552 q^{28} -6.41904 q^{29} -21.5908 q^{30} +4.59805 q^{31} -6.08311 q^{32} -12.2718 q^{33} -3.12979 q^{34} +12.3792 q^{35} +12.6384 q^{36} -0.0828449 q^{37} -1.13720 q^{38} -0.850647 q^{39} -22.6618 q^{40} +4.27416 q^{41} -21.6736 q^{42} -9.28723 q^{43} -23.0784 q^{44} +9.80581 q^{45} -23.9067 q^{46} +2.53171 q^{47} +17.8902 q^{48} +5.42670 q^{49} -18.7303 q^{50} +2.94859 q^{51} -1.59973 q^{52} -1.29833 q^{53} +1.27676 q^{54} -17.9059 q^{55} -22.7487 q^{56} +1.07136 q^{57} +16.3982 q^{58} -7.77128 q^{59} +38.2531 q^{60} +7.07624 q^{61} -11.7463 q^{62} +9.84342 q^{63} +0.673206 q^{64} -1.24119 q^{65} +31.3498 q^{66} +15.5801 q^{67} +5.54514 q^{68} +22.5227 q^{69} -31.6243 q^{70} +6.33364 q^{71} -18.0197 q^{72} +12.7305 q^{73} +0.211638 q^{74} +17.6459 q^{75} +2.01482 q^{76} -17.9746 q^{77} +2.17308 q^{78} -0.799467 q^{79} +26.1038 q^{80} -9.57986 q^{81} -10.9189 q^{82} +2.66341 q^{83} +38.3999 q^{84} +4.30232 q^{85} +23.7254 q^{86} -15.4489 q^{87} +32.9048 q^{88} -12.6340 q^{89} -25.0502 q^{90} -1.24595 q^{91} +42.3563 q^{92} +11.0663 q^{93} -6.46758 q^{94} +1.56324 q^{95} -14.6404 q^{96} +7.86963 q^{97} -13.8632 q^{98} -14.2380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55462 −1.80639 −0.903196 0.429228i \(-0.858786\pi\)
−0.903196 + 0.429228i \(0.858786\pi\)
\(3\) 2.40673 1.38952 0.694762 0.719239i \(-0.255510\pi\)
0.694762 + 0.719239i \(0.255510\pi\)
\(4\) 4.52611 2.26305
\(5\) 3.51168 1.57047 0.785236 0.619196i \(-0.212542\pi\)
0.785236 + 0.619196i \(0.212542\pi\)
\(6\) −6.14829 −2.51003
\(7\) 3.52515 1.33238 0.666191 0.745781i \(-0.267923\pi\)
0.666191 + 0.745781i \(0.267923\pi\)
\(8\) −6.45325 −2.28157
\(9\) 2.79234 0.930779
\(10\) −8.97103 −2.83689
\(11\) −5.09895 −1.53739 −0.768696 0.639615i \(-0.779094\pi\)
−0.768696 + 0.639615i \(0.779094\pi\)
\(12\) 10.8931 3.14457
\(13\) −0.353446 −0.0980281 −0.0490141 0.998798i \(-0.515608\pi\)
−0.0490141 + 0.998798i \(0.515608\pi\)
\(14\) −9.00544 −2.40681
\(15\) 8.45166 2.18221
\(16\) 7.43343 1.85836
\(17\) 1.22514 0.297141 0.148571 0.988902i \(-0.452533\pi\)
0.148571 + 0.988902i \(0.452533\pi\)
\(18\) −7.13338 −1.68135
\(19\) 0.445154 0.102125 0.0510627 0.998695i \(-0.483739\pi\)
0.0510627 + 0.998695i \(0.483739\pi\)
\(20\) 15.8942 3.55406
\(21\) 8.48408 1.85138
\(22\) 13.0259 2.77713
\(23\) 9.35822 1.95132 0.975662 0.219280i \(-0.0703710\pi\)
0.975662 + 0.219280i \(0.0703710\pi\)
\(24\) −15.5312 −3.17030
\(25\) 7.33191 1.46638
\(26\) 0.902921 0.177077
\(27\) −0.499785 −0.0961838
\(28\) 15.9552 3.01525
\(29\) −6.41904 −1.19199 −0.595993 0.802990i \(-0.703241\pi\)
−0.595993 + 0.802990i \(0.703241\pi\)
\(30\) −21.5908 −3.94193
\(31\) 4.59805 0.825834 0.412917 0.910769i \(-0.364510\pi\)
0.412917 + 0.910769i \(0.364510\pi\)
\(32\) −6.08311 −1.07535
\(33\) −12.2718 −2.13624
\(34\) −3.12979 −0.536754
\(35\) 12.3792 2.09247
\(36\) 12.6384 2.10640
\(37\) −0.0828449 −0.0136196 −0.00680981 0.999977i \(-0.502168\pi\)
−0.00680981 + 0.999977i \(0.502168\pi\)
\(38\) −1.13720 −0.184478
\(39\) −0.850647 −0.136213
\(40\) −22.6618 −3.58314
\(41\) 4.27416 0.667512 0.333756 0.942660i \(-0.391684\pi\)
0.333756 + 0.942660i \(0.391684\pi\)
\(42\) −21.6736 −3.34432
\(43\) −9.28723 −1.41629 −0.708144 0.706068i \(-0.750467\pi\)
−0.708144 + 0.706068i \(0.750467\pi\)
\(44\) −23.0784 −3.47920
\(45\) 9.80581 1.46176
\(46\) −23.9067 −3.52486
\(47\) 2.53171 0.369288 0.184644 0.982805i \(-0.440887\pi\)
0.184644 + 0.982805i \(0.440887\pi\)
\(48\) 17.8902 2.58223
\(49\) 5.42670 0.775243
\(50\) −18.7303 −2.64886
\(51\) 2.94859 0.412885
\(52\) −1.59973 −0.221843
\(53\) −1.29833 −0.178339 −0.0891694 0.996016i \(-0.528421\pi\)
−0.0891694 + 0.996016i \(0.528421\pi\)
\(54\) 1.27676 0.173746
\(55\) −17.9059 −2.41443
\(56\) −22.7487 −3.03992
\(57\) 1.07136 0.141906
\(58\) 16.3982 2.15319
\(59\) −7.77128 −1.01173 −0.505867 0.862611i \(-0.668828\pi\)
−0.505867 + 0.862611i \(0.668828\pi\)
\(60\) 38.2531 4.93846
\(61\) 7.07624 0.906020 0.453010 0.891505i \(-0.350350\pi\)
0.453010 + 0.891505i \(0.350350\pi\)
\(62\) −11.7463 −1.49178
\(63\) 9.84342 1.24015
\(64\) 0.673206 0.0841507
\(65\) −1.24119 −0.153950
\(66\) 31.3498 3.85889
\(67\) 15.5801 1.90341 0.951704 0.307017i \(-0.0993310\pi\)
0.951704 + 0.307017i \(0.0993310\pi\)
\(68\) 5.54514 0.672447
\(69\) 22.5227 2.71141
\(70\) −31.6243 −3.77982
\(71\) 6.33364 0.751665 0.375832 0.926688i \(-0.377357\pi\)
0.375832 + 0.926688i \(0.377357\pi\)
\(72\) −18.0197 −2.12364
\(73\) 12.7305 1.49000 0.744999 0.667066i \(-0.232450\pi\)
0.744999 + 0.667066i \(0.232450\pi\)
\(74\) 0.211638 0.0246024
\(75\) 17.6459 2.03758
\(76\) 2.01482 0.231115
\(77\) −17.9746 −2.04839
\(78\) 2.17308 0.246053
\(79\) −0.799467 −0.0899471 −0.0449736 0.998988i \(-0.514320\pi\)
−0.0449736 + 0.998988i \(0.514320\pi\)
\(80\) 26.1038 2.91850
\(81\) −9.57986 −1.06443
\(82\) −10.9189 −1.20579
\(83\) 2.66341 0.292347 0.146174 0.989259i \(-0.453304\pi\)
0.146174 + 0.989259i \(0.453304\pi\)
\(84\) 38.3999 4.18977
\(85\) 4.30232 0.466652
\(86\) 23.7254 2.55837
\(87\) −15.4489 −1.65629
\(88\) 32.9048 3.50767
\(89\) −12.6340 −1.33920 −0.669599 0.742723i \(-0.733534\pi\)
−0.669599 + 0.742723i \(0.733534\pi\)
\(90\) −25.0502 −2.64052
\(91\) −1.24595 −0.130611
\(92\) 42.3563 4.41595
\(93\) 11.0663 1.14752
\(94\) −6.46758 −0.667080
\(95\) 1.56324 0.160385
\(96\) −14.6404 −1.49423
\(97\) 7.86963 0.799040 0.399520 0.916725i \(-0.369177\pi\)
0.399520 + 0.916725i \(0.369177\pi\)
\(98\) −13.8632 −1.40039
\(99\) −14.2380 −1.43097
\(100\) 33.1850 3.31850
\(101\) −11.6404 −1.15827 −0.579133 0.815233i \(-0.696609\pi\)
−0.579133 + 0.815233i \(0.696609\pi\)
\(102\) −7.53254 −0.745833
\(103\) 15.0025 1.47824 0.739119 0.673575i \(-0.235242\pi\)
0.739119 + 0.673575i \(0.235242\pi\)
\(104\) 2.28087 0.223658
\(105\) 29.7934 2.90754
\(106\) 3.31674 0.322150
\(107\) −9.94886 −0.961792 −0.480896 0.876778i \(-0.659689\pi\)
−0.480896 + 0.876778i \(0.659689\pi\)
\(108\) −2.26208 −0.217669
\(109\) 11.2873 1.08113 0.540563 0.841304i \(-0.318211\pi\)
0.540563 + 0.841304i \(0.318211\pi\)
\(110\) 45.7428 4.36141
\(111\) −0.199385 −0.0189248
\(112\) 26.2040 2.47604
\(113\) 14.6614 1.37923 0.689615 0.724176i \(-0.257780\pi\)
0.689615 + 0.724176i \(0.257780\pi\)
\(114\) −2.73693 −0.256337
\(115\) 32.8631 3.06450
\(116\) −29.0533 −2.69753
\(117\) −0.986939 −0.0912426
\(118\) 19.8527 1.82759
\(119\) 4.31882 0.395906
\(120\) −54.5407 −4.97886
\(121\) 14.9993 1.36357
\(122\) −18.0771 −1.63663
\(123\) 10.2867 0.927524
\(124\) 20.8113 1.86891
\(125\) 8.18894 0.732441
\(126\) −25.1462 −2.24021
\(127\) 0.785559 0.0697070 0.0348535 0.999392i \(-0.488904\pi\)
0.0348535 + 0.999392i \(0.488904\pi\)
\(128\) 10.4464 0.923343
\(129\) −22.3518 −1.96797
\(130\) 3.17077 0.278095
\(131\) −8.11721 −0.709204 −0.354602 0.935017i \(-0.615384\pi\)
−0.354602 + 0.935017i \(0.615384\pi\)
\(132\) −55.5434 −4.83443
\(133\) 1.56924 0.136070
\(134\) −39.8012 −3.43830
\(135\) −1.75509 −0.151054
\(136\) −7.90617 −0.677949
\(137\) 5.38620 0.460174 0.230087 0.973170i \(-0.426099\pi\)
0.230087 + 0.973170i \(0.426099\pi\)
\(138\) −57.5370 −4.89788
\(139\) −5.75940 −0.488506 −0.244253 0.969712i \(-0.578543\pi\)
−0.244253 + 0.969712i \(0.578543\pi\)
\(140\) 56.0297 4.73537
\(141\) 6.09314 0.513135
\(142\) −16.1801 −1.35780
\(143\) 1.80220 0.150708
\(144\) 20.7566 1.72972
\(145\) −22.5416 −1.87198
\(146\) −32.5218 −2.69152
\(147\) 13.0606 1.07722
\(148\) −0.374965 −0.0308219
\(149\) −16.8085 −1.37701 −0.688503 0.725234i \(-0.741732\pi\)
−0.688503 + 0.725234i \(0.741732\pi\)
\(150\) −45.0787 −3.68066
\(151\) −2.73254 −0.222371 −0.111186 0.993800i \(-0.535465\pi\)
−0.111186 + 0.993800i \(0.535465\pi\)
\(152\) −2.87269 −0.233006
\(153\) 3.42102 0.276573
\(154\) 45.9183 3.70020
\(155\) 16.1469 1.29695
\(156\) −3.85012 −0.308256
\(157\) 6.77702 0.540865 0.270433 0.962739i \(-0.412833\pi\)
0.270433 + 0.962739i \(0.412833\pi\)
\(158\) 2.04234 0.162480
\(159\) −3.12472 −0.247806
\(160\) −21.3620 −1.68881
\(161\) 32.9892 2.59991
\(162\) 24.4730 1.92278
\(163\) −15.2624 −1.19544 −0.597720 0.801705i \(-0.703927\pi\)
−0.597720 + 0.801705i \(0.703927\pi\)
\(164\) 19.3453 1.51061
\(165\) −43.0946 −3.35491
\(166\) −6.80402 −0.528094
\(167\) 13.2940 1.02872 0.514360 0.857574i \(-0.328029\pi\)
0.514360 + 0.857574i \(0.328029\pi\)
\(168\) −54.7499 −4.22405
\(169\) −12.8751 −0.990390
\(170\) −10.9908 −0.842957
\(171\) 1.24302 0.0950562
\(172\) −42.0350 −3.20514
\(173\) 5.89000 0.447808 0.223904 0.974611i \(-0.428120\pi\)
0.223904 + 0.974611i \(0.428120\pi\)
\(174\) 39.4661 2.99192
\(175\) 25.8461 1.95378
\(176\) −37.9027 −2.85702
\(177\) −18.7034 −1.40583
\(178\) 32.2750 2.41912
\(179\) 13.4178 1.00290 0.501448 0.865188i \(-0.332801\pi\)
0.501448 + 0.865188i \(0.332801\pi\)
\(180\) 44.3821 3.30805
\(181\) 12.2281 0.908908 0.454454 0.890770i \(-0.349834\pi\)
0.454454 + 0.890770i \(0.349834\pi\)
\(182\) 3.18293 0.235935
\(183\) 17.0306 1.25894
\(184\) −60.3910 −4.45208
\(185\) −0.290925 −0.0213892
\(186\) −28.2701 −2.07287
\(187\) −6.24695 −0.456822
\(188\) 11.4588 0.835719
\(189\) −1.76182 −0.128154
\(190\) −3.99349 −0.289718
\(191\) −25.3620 −1.83513 −0.917565 0.397585i \(-0.869848\pi\)
−0.917565 + 0.397585i \(0.869848\pi\)
\(192\) 1.62022 0.116930
\(193\) −15.3996 −1.10849 −0.554244 0.832354i \(-0.686993\pi\)
−0.554244 + 0.832354i \(0.686993\pi\)
\(194\) −20.1039 −1.44338
\(195\) −2.98720 −0.213918
\(196\) 24.5618 1.75442
\(197\) 21.6149 1.54000 0.769998 0.638046i \(-0.220257\pi\)
0.769998 + 0.638046i \(0.220257\pi\)
\(198\) 36.3727 2.58490
\(199\) 0.935357 0.0663057 0.0331529 0.999450i \(-0.489445\pi\)
0.0331529 + 0.999450i \(0.489445\pi\)
\(200\) −47.3147 −3.34565
\(201\) 37.4970 2.64483
\(202\) 29.7369 2.09228
\(203\) −22.6281 −1.58818
\(204\) 13.3456 0.934381
\(205\) 15.0095 1.04831
\(206\) −38.3257 −2.67028
\(207\) 26.1313 1.81625
\(208\) −2.62731 −0.182171
\(209\) −2.26982 −0.157007
\(210\) −76.1110 −5.25216
\(211\) 19.6612 1.35353 0.676765 0.736199i \(-0.263381\pi\)
0.676765 + 0.736199i \(0.263381\pi\)
\(212\) −5.87636 −0.403590
\(213\) 15.2433 1.04446
\(214\) 25.4156 1.73737
\(215\) −32.6138 −2.22424
\(216\) 3.22524 0.219450
\(217\) 16.2088 1.10033
\(218\) −28.8348 −1.95294
\(219\) 30.6390 2.07039
\(220\) −81.0440 −5.46398
\(221\) −0.433022 −0.0291282
\(222\) 0.509354 0.0341856
\(223\) −10.0202 −0.671004 −0.335502 0.942040i \(-0.608906\pi\)
−0.335502 + 0.942040i \(0.608906\pi\)
\(224\) −21.4439 −1.43278
\(225\) 20.4732 1.36488
\(226\) −37.4544 −2.49143
\(227\) −6.75105 −0.448083 −0.224041 0.974580i \(-0.571925\pi\)
−0.224041 + 0.974580i \(0.571925\pi\)
\(228\) 4.84911 0.321140
\(229\) 14.7685 0.975932 0.487966 0.872863i \(-0.337739\pi\)
0.487966 + 0.872863i \(0.337739\pi\)
\(230\) −83.9529 −5.53569
\(231\) −43.2599 −2.84629
\(232\) 41.4237 2.71960
\(233\) 9.02909 0.591515 0.295758 0.955263i \(-0.404428\pi\)
0.295758 + 0.955263i \(0.404428\pi\)
\(234\) 2.52126 0.164820
\(235\) 8.89057 0.579957
\(236\) −35.1737 −2.28961
\(237\) −1.92410 −0.124984
\(238\) −11.0330 −0.715161
\(239\) −7.53759 −0.487566 −0.243783 0.969830i \(-0.578388\pi\)
−0.243783 + 0.969830i \(0.578388\pi\)
\(240\) 62.8248 4.05533
\(241\) −0.590570 −0.0380419 −0.0190210 0.999819i \(-0.506055\pi\)
−0.0190210 + 0.999819i \(0.506055\pi\)
\(242\) −38.3176 −2.46315
\(243\) −21.5568 −1.38287
\(244\) 32.0278 2.05037
\(245\) 19.0569 1.21750
\(246\) −26.2788 −1.67547
\(247\) −0.157338 −0.0100112
\(248\) −29.6724 −1.88420
\(249\) 6.41011 0.406224
\(250\) −20.9197 −1.32308
\(251\) 5.33818 0.336943 0.168471 0.985707i \(-0.446117\pi\)
0.168471 + 0.985707i \(0.446117\pi\)
\(252\) 44.5524 2.80654
\(253\) −47.7171 −2.99995
\(254\) −2.00681 −0.125918
\(255\) 10.3545 0.648425
\(256\) −28.0331 −1.75207
\(257\) 14.8048 0.923496 0.461748 0.887011i \(-0.347222\pi\)
0.461748 + 0.887011i \(0.347222\pi\)
\(258\) 57.1005 3.55492
\(259\) −0.292041 −0.0181465
\(260\) −5.61775 −0.348398
\(261\) −17.9241 −1.10948
\(262\) 20.7364 1.28110
\(263\) −9.17985 −0.566054 −0.283027 0.959112i \(-0.591339\pi\)
−0.283027 + 0.959112i \(0.591339\pi\)
\(264\) 79.1929 4.87399
\(265\) −4.55931 −0.280076
\(266\) −4.00881 −0.245796
\(267\) −30.4065 −1.86085
\(268\) 70.5170 4.30751
\(269\) −21.5102 −1.31150 −0.655751 0.754977i \(-0.727648\pi\)
−0.655751 + 0.754977i \(0.727648\pi\)
\(270\) 4.48359 0.272863
\(271\) −30.7485 −1.86784 −0.933920 0.357481i \(-0.883636\pi\)
−0.933920 + 0.357481i \(0.883636\pi\)
\(272\) 9.10703 0.552195
\(273\) −2.99866 −0.181487
\(274\) −13.7597 −0.831255
\(275\) −37.3851 −2.25440
\(276\) 101.940 6.13607
\(277\) −0.316138 −0.0189949 −0.00949745 0.999955i \(-0.503023\pi\)
−0.00949745 + 0.999955i \(0.503023\pi\)
\(278\) 14.7131 0.882434
\(279\) 12.8393 0.768669
\(280\) −79.8862 −4.77412
\(281\) −24.1824 −1.44260 −0.721302 0.692621i \(-0.756456\pi\)
−0.721302 + 0.692621i \(0.756456\pi\)
\(282\) −15.5657 −0.926924
\(283\) 14.5123 0.862666 0.431333 0.902193i \(-0.358043\pi\)
0.431333 + 0.902193i \(0.358043\pi\)
\(284\) 28.6667 1.70106
\(285\) 3.76229 0.222859
\(286\) −4.60395 −0.272237
\(287\) 15.0671 0.889381
\(288\) −16.9861 −1.00092
\(289\) −15.4990 −0.911707
\(290\) 57.5854 3.38153
\(291\) 18.9401 1.11029
\(292\) 57.6198 3.37194
\(293\) −12.8933 −0.753232 −0.376616 0.926369i \(-0.622912\pi\)
−0.376616 + 0.926369i \(0.622912\pi\)
\(294\) −33.3649 −1.94588
\(295\) −27.2903 −1.58890
\(296\) 0.534619 0.0310741
\(297\) 2.54838 0.147872
\(298\) 42.9394 2.48741
\(299\) −3.30762 −0.191285
\(300\) 79.8673 4.61114
\(301\) −32.7389 −1.88704
\(302\) 6.98062 0.401690
\(303\) −28.0153 −1.60944
\(304\) 3.30902 0.189785
\(305\) 24.8495 1.42288
\(306\) −8.73942 −0.499599
\(307\) −26.2910 −1.50050 −0.750252 0.661151i \(-0.770068\pi\)
−0.750252 + 0.661151i \(0.770068\pi\)
\(308\) −81.3549 −4.63562
\(309\) 36.1069 2.05405
\(310\) −41.2492 −2.34280
\(311\) −35.0596 −1.98805 −0.994024 0.109159i \(-0.965184\pi\)
−0.994024 + 0.109159i \(0.965184\pi\)
\(312\) 5.48944 0.310778
\(313\) 2.41352 0.136420 0.0682102 0.997671i \(-0.478271\pi\)
0.0682102 + 0.997671i \(0.478271\pi\)
\(314\) −17.3127 −0.977015
\(315\) 34.5670 1.94763
\(316\) −3.61847 −0.203555
\(317\) −17.0471 −0.957460 −0.478730 0.877962i \(-0.658903\pi\)
−0.478730 + 0.877962i \(0.658903\pi\)
\(318\) 7.98248 0.447635
\(319\) 32.7304 1.83255
\(320\) 2.36409 0.132156
\(321\) −23.9442 −1.33643
\(322\) −84.2749 −4.69646
\(323\) 0.545378 0.0303457
\(324\) −43.3595 −2.40886
\(325\) −2.59143 −0.143747
\(326\) 38.9896 2.15943
\(327\) 27.1654 1.50225
\(328\) −27.5822 −1.52297
\(329\) 8.92468 0.492033
\(330\) 110.091 6.06029
\(331\) −2.47954 −0.136288 −0.0681440 0.997675i \(-0.521708\pi\)
−0.0681440 + 0.997675i \(0.521708\pi\)
\(332\) 12.0549 0.661598
\(333\) −0.231331 −0.0126769
\(334\) −33.9612 −1.85827
\(335\) 54.7122 2.98925
\(336\) 63.0658 3.44052
\(337\) 22.4278 1.22172 0.610861 0.791738i \(-0.290823\pi\)
0.610861 + 0.791738i \(0.290823\pi\)
\(338\) 32.8910 1.78903
\(339\) 35.2860 1.91647
\(340\) 19.4728 1.05606
\(341\) −23.4452 −1.26963
\(342\) −3.17545 −0.171709
\(343\) −5.54612 −0.299462
\(344\) 59.9328 3.23136
\(345\) 79.0925 4.25820
\(346\) −15.0467 −0.808918
\(347\) 5.51687 0.296161 0.148081 0.988975i \(-0.452691\pi\)
0.148081 + 0.988975i \(0.452691\pi\)
\(348\) −69.9233 −3.74828
\(349\) −31.8235 −1.70347 −0.851737 0.523969i \(-0.824451\pi\)
−0.851737 + 0.523969i \(0.824451\pi\)
\(350\) −66.0271 −3.52930
\(351\) 0.176647 0.00942872
\(352\) 31.0175 1.65324
\(353\) 8.64697 0.460232 0.230116 0.973163i \(-0.426089\pi\)
0.230116 + 0.973163i \(0.426089\pi\)
\(354\) 47.7801 2.53948
\(355\) 22.2417 1.18047
\(356\) −57.1827 −3.03068
\(357\) 10.3942 0.550121
\(358\) −34.2776 −1.81163
\(359\) −1.07069 −0.0565090 −0.0282545 0.999601i \(-0.508995\pi\)
−0.0282545 + 0.999601i \(0.508995\pi\)
\(360\) −63.2794 −3.33511
\(361\) −18.8018 −0.989570
\(362\) −31.2382 −1.64185
\(363\) 36.0992 1.89472
\(364\) −5.63930 −0.295580
\(365\) 44.7056 2.34000
\(366\) −43.5068 −2.27414
\(367\) 14.4814 0.755923 0.377961 0.925821i \(-0.376625\pi\)
0.377961 + 0.925821i \(0.376625\pi\)
\(368\) 69.5637 3.62626
\(369\) 11.9349 0.621306
\(370\) 0.743204 0.0386374
\(371\) −4.57680 −0.237616
\(372\) 50.0870 2.59689
\(373\) −4.76462 −0.246703 −0.123351 0.992363i \(-0.539364\pi\)
−0.123351 + 0.992363i \(0.539364\pi\)
\(374\) 15.9586 0.825201
\(375\) 19.7086 1.01775
\(376\) −16.3378 −0.842557
\(377\) 2.26878 0.116848
\(378\) 4.50079 0.231496
\(379\) 28.7046 1.47446 0.737229 0.675643i \(-0.236134\pi\)
0.737229 + 0.675643i \(0.236134\pi\)
\(380\) 7.07539 0.362960
\(381\) 1.89063 0.0968597
\(382\) 64.7904 3.31497
\(383\) 10.3699 0.529876 0.264938 0.964265i \(-0.414648\pi\)
0.264938 + 0.964265i \(0.414648\pi\)
\(384\) 25.1417 1.28301
\(385\) −63.1210 −3.21694
\(386\) 39.3402 2.00236
\(387\) −25.9331 −1.31825
\(388\) 35.6188 1.80827
\(389\) 26.5424 1.34575 0.672876 0.739755i \(-0.265059\pi\)
0.672876 + 0.739755i \(0.265059\pi\)
\(390\) 7.63118 0.386420
\(391\) 11.4652 0.579819
\(392\) −35.0199 −1.76877
\(393\) −19.5359 −0.985457
\(394\) −55.2179 −2.78184
\(395\) −2.80748 −0.141259
\(396\) −64.4427 −3.23837
\(397\) −18.8686 −0.946989 −0.473494 0.880797i \(-0.657008\pi\)
−0.473494 + 0.880797i \(0.657008\pi\)
\(398\) −2.38949 −0.119774
\(399\) 3.77672 0.189073
\(400\) 54.5013 2.72506
\(401\) −18.8086 −0.939258 −0.469629 0.882864i \(-0.655612\pi\)
−0.469629 + 0.882864i \(0.655612\pi\)
\(402\) −95.7907 −4.77761
\(403\) −1.62516 −0.0809550
\(404\) −52.6858 −2.62122
\(405\) −33.6414 −1.67166
\(406\) 57.8063 2.86888
\(407\) 0.422422 0.0209387
\(408\) −19.0280 −0.942026
\(409\) −16.2427 −0.803148 −0.401574 0.915826i \(-0.631537\pi\)
−0.401574 + 0.915826i \(0.631537\pi\)
\(410\) −38.3436 −1.89366
\(411\) 12.9631 0.639424
\(412\) 67.9028 3.34533
\(413\) −27.3950 −1.34802
\(414\) −66.7557 −3.28086
\(415\) 9.35306 0.459124
\(416\) 2.15005 0.105415
\(417\) −13.8613 −0.678791
\(418\) 5.79854 0.283616
\(419\) −5.03656 −0.246052 −0.123026 0.992403i \(-0.539260\pi\)
−0.123026 + 0.992403i \(0.539260\pi\)
\(420\) 134.848 6.57992
\(421\) −25.8441 −1.25956 −0.629782 0.776772i \(-0.716856\pi\)
−0.629782 + 0.776772i \(0.716856\pi\)
\(422\) −50.2269 −2.44501
\(423\) 7.06940 0.343726
\(424\) 8.37843 0.406893
\(425\) 8.98266 0.435723
\(426\) −38.9410 −1.88670
\(427\) 24.9448 1.20717
\(428\) −45.0296 −2.17659
\(429\) 4.33741 0.209412
\(430\) 83.3160 4.01785
\(431\) 31.3134 1.50831 0.754157 0.656695i \(-0.228046\pi\)
0.754157 + 0.656695i \(0.228046\pi\)
\(432\) −3.71512 −0.178744
\(433\) −9.53010 −0.457988 −0.228994 0.973428i \(-0.573544\pi\)
−0.228994 + 0.973428i \(0.573544\pi\)
\(434\) −41.4075 −1.98762
\(435\) −54.2516 −2.60116
\(436\) 51.0874 2.44664
\(437\) 4.16585 0.199280
\(438\) −78.2710 −3.73993
\(439\) 28.4026 1.35558 0.677791 0.735254i \(-0.262937\pi\)
0.677791 + 0.735254i \(0.262937\pi\)
\(440\) 115.551 5.50869
\(441\) 15.1532 0.721580
\(442\) 1.10621 0.0526170
\(443\) −26.2582 −1.24756 −0.623782 0.781598i \(-0.714405\pi\)
−0.623782 + 0.781598i \(0.714405\pi\)
\(444\) −0.902438 −0.0428278
\(445\) −44.3665 −2.10317
\(446\) 25.5979 1.21210
\(447\) −40.4535 −1.91338
\(448\) 2.37315 0.112121
\(449\) −19.5626 −0.923215 −0.461608 0.887084i \(-0.652727\pi\)
−0.461608 + 0.887084i \(0.652727\pi\)
\(450\) −52.3013 −2.46551
\(451\) −21.7937 −1.02623
\(452\) 66.3591 3.12127
\(453\) −6.57649 −0.308990
\(454\) 17.2464 0.809413
\(455\) −4.37538 −0.205121
\(456\) −6.91379 −0.323768
\(457\) 5.10525 0.238813 0.119407 0.992845i \(-0.461901\pi\)
0.119407 + 0.992845i \(0.461901\pi\)
\(458\) −37.7280 −1.76292
\(459\) −0.612310 −0.0285802
\(460\) 148.742 6.93513
\(461\) −38.1937 −1.77886 −0.889430 0.457072i \(-0.848898\pi\)
−0.889430 + 0.457072i \(0.848898\pi\)
\(462\) 110.513 5.14152
\(463\) −3.88947 −0.180759 −0.0903796 0.995907i \(-0.528808\pi\)
−0.0903796 + 0.995907i \(0.528808\pi\)
\(464\) −47.7155 −2.21514
\(465\) 38.8612 1.80214
\(466\) −23.0659 −1.06851
\(467\) 10.8376 0.501504 0.250752 0.968051i \(-0.419322\pi\)
0.250752 + 0.968051i \(0.419322\pi\)
\(468\) −4.46699 −0.206487
\(469\) 54.9221 2.53607
\(470\) −22.7121 −1.04763
\(471\) 16.3104 0.751546
\(472\) 50.1501 2.30834
\(473\) 47.3551 2.17739
\(474\) 4.91535 0.225770
\(475\) 3.26383 0.149755
\(476\) 19.5475 0.895956
\(477\) −3.62537 −0.165994
\(478\) 19.2557 0.880735
\(479\) 6.20721 0.283615 0.141807 0.989894i \(-0.454709\pi\)
0.141807 + 0.989894i \(0.454709\pi\)
\(480\) −51.4124 −2.34664
\(481\) 0.0292812 0.00133511
\(482\) 1.50868 0.0687187
\(483\) 79.3959 3.61264
\(484\) 67.8884 3.08584
\(485\) 27.6356 1.25487
\(486\) 55.0694 2.49800
\(487\) −15.1882 −0.688244 −0.344122 0.938925i \(-0.611823\pi\)
−0.344122 + 0.938925i \(0.611823\pi\)
\(488\) −45.6648 −2.06715
\(489\) −36.7324 −1.66109
\(490\) −48.6831 −2.19928
\(491\) −5.62931 −0.254047 −0.127024 0.991900i \(-0.540542\pi\)
−0.127024 + 0.991900i \(0.540542\pi\)
\(492\) 46.5589 2.09904
\(493\) −7.86425 −0.354188
\(494\) 0.401939 0.0180841
\(495\) −49.9993 −2.24730
\(496\) 34.1793 1.53469
\(497\) 22.3270 1.00150
\(498\) −16.3754 −0.733800
\(499\) 38.9865 1.74527 0.872637 0.488369i \(-0.162408\pi\)
0.872637 + 0.488369i \(0.162408\pi\)
\(500\) 37.0640 1.65755
\(501\) 31.9950 1.42943
\(502\) −13.6370 −0.608651
\(503\) −30.5385 −1.36165 −0.680823 0.732448i \(-0.738378\pi\)
−0.680823 + 0.732448i \(0.738378\pi\)
\(504\) −63.5221 −2.82950
\(505\) −40.8775 −1.81902
\(506\) 121.899 5.41908
\(507\) −30.9868 −1.37617
\(508\) 3.55552 0.157751
\(509\) −17.2270 −0.763572 −0.381786 0.924251i \(-0.624691\pi\)
−0.381786 + 0.924251i \(0.624691\pi\)
\(510\) −26.4519 −1.17131
\(511\) 44.8771 1.98525
\(512\) 50.7212 2.24158
\(513\) −0.222482 −0.00982280
\(514\) −37.8206 −1.66820
\(515\) 52.6840 2.32153
\(516\) −101.167 −4.45362
\(517\) −12.9091 −0.567741
\(518\) 0.746055 0.0327798
\(519\) 14.1756 0.622241
\(520\) 8.00970 0.351249
\(521\) 34.3181 1.50350 0.751751 0.659447i \(-0.229209\pi\)
0.751751 + 0.659447i \(0.229209\pi\)
\(522\) 45.7894 2.00415
\(523\) 27.8798 1.21910 0.609549 0.792748i \(-0.291351\pi\)
0.609549 + 0.792748i \(0.291351\pi\)
\(524\) −36.7394 −1.60497
\(525\) 62.2046 2.71483
\(526\) 23.4511 1.02252
\(527\) 5.63328 0.245389
\(528\) −91.2214 −3.96990
\(529\) 64.5763 2.80766
\(530\) 11.6473 0.505928
\(531\) −21.7001 −0.941702
\(532\) 7.10253 0.307934
\(533\) −1.51068 −0.0654349
\(534\) 77.6772 3.36142
\(535\) −34.9372 −1.51047
\(536\) −100.542 −4.34276
\(537\) 32.2931 1.39355
\(538\) 54.9505 2.36909
\(539\) −27.6705 −1.19185
\(540\) −7.94372 −0.341843
\(541\) −42.1269 −1.81118 −0.905588 0.424158i \(-0.860570\pi\)
−0.905588 + 0.424158i \(0.860570\pi\)
\(542\) 78.5510 3.37405
\(543\) 29.4297 1.26295
\(544\) −7.45269 −0.319531
\(545\) 39.6373 1.69788
\(546\) 7.66045 0.327837
\(547\) −40.3783 −1.72645 −0.863226 0.504817i \(-0.831560\pi\)
−0.863226 + 0.504817i \(0.831560\pi\)
\(548\) 24.3785 1.04140
\(549\) 19.7593 0.843305
\(550\) 95.5048 4.07234
\(551\) −2.85746 −0.121732
\(552\) −145.345 −6.18628
\(553\) −2.81824 −0.119844
\(554\) 0.807614 0.0343122
\(555\) −0.700177 −0.0297209
\(556\) −26.0677 −1.10552
\(557\) −14.4863 −0.613802 −0.306901 0.951741i \(-0.599292\pi\)
−0.306901 + 0.951741i \(0.599292\pi\)
\(558\) −32.7996 −1.38852
\(559\) 3.28253 0.138836
\(560\) 92.0200 3.88856
\(561\) −15.0347 −0.634766
\(562\) 61.7770 2.60591
\(563\) −16.6356 −0.701108 −0.350554 0.936543i \(-0.614007\pi\)
−0.350554 + 0.936543i \(0.614007\pi\)
\(564\) 27.5782 1.16125
\(565\) 51.4862 2.16604
\(566\) −37.0735 −1.55831
\(567\) −33.7705 −1.41823
\(568\) −40.8726 −1.71498
\(569\) −30.2930 −1.26995 −0.634974 0.772534i \(-0.718989\pi\)
−0.634974 + 0.772534i \(0.718989\pi\)
\(570\) −9.61125 −0.402571
\(571\) 31.3960 1.31388 0.656940 0.753943i \(-0.271850\pi\)
0.656940 + 0.753943i \(0.271850\pi\)
\(572\) 8.15695 0.341059
\(573\) −61.0395 −2.54996
\(574\) −38.4907 −1.60657
\(575\) 68.6137 2.86139
\(576\) 1.87982 0.0783258
\(577\) 36.1967 1.50689 0.753445 0.657511i \(-0.228391\pi\)
0.753445 + 0.657511i \(0.228391\pi\)
\(578\) 39.5942 1.64690
\(579\) −37.0627 −1.54027
\(580\) −102.026 −4.23639
\(581\) 9.38893 0.389519
\(582\) −48.3847 −2.00561
\(583\) 6.62010 0.274177
\(584\) −82.1534 −3.39953
\(585\) −3.46582 −0.143294
\(586\) 32.9374 1.36063
\(587\) −10.1363 −0.418370 −0.209185 0.977876i \(-0.567081\pi\)
−0.209185 + 0.977876i \(0.567081\pi\)
\(588\) 59.1136 2.43781
\(589\) 2.04684 0.0843386
\(590\) 69.7164 2.87018
\(591\) 52.0211 2.13986
\(592\) −0.615822 −0.0253101
\(593\) −29.0057 −1.19112 −0.595560 0.803311i \(-0.703070\pi\)
−0.595560 + 0.803311i \(0.703070\pi\)
\(594\) −6.51016 −0.267115
\(595\) 15.1663 0.621759
\(596\) −76.0770 −3.11624
\(597\) 2.25115 0.0921335
\(598\) 8.44973 0.345535
\(599\) −6.04943 −0.247173 −0.123587 0.992334i \(-0.539440\pi\)
−0.123587 + 0.992334i \(0.539440\pi\)
\(600\) −113.874 −4.64887
\(601\) −13.7169 −0.559526 −0.279763 0.960069i \(-0.590256\pi\)
−0.279763 + 0.960069i \(0.590256\pi\)
\(602\) 83.6356 3.40873
\(603\) 43.5048 1.77165
\(604\) −12.3678 −0.503238
\(605\) 52.6728 2.14145
\(606\) 71.5687 2.90728
\(607\) −14.0943 −0.572069 −0.286035 0.958219i \(-0.592337\pi\)
−0.286035 + 0.958219i \(0.592337\pi\)
\(608\) −2.70792 −0.109821
\(609\) −54.4597 −2.20682
\(610\) −63.4812 −2.57028
\(611\) −0.894823 −0.0362007
\(612\) 15.4839 0.625899
\(613\) −24.6314 −0.994854 −0.497427 0.867506i \(-0.665722\pi\)
−0.497427 + 0.867506i \(0.665722\pi\)
\(614\) 67.1636 2.71050
\(615\) 36.1238 1.45665
\(616\) 115.995 4.67355
\(617\) 10.3455 0.416492 0.208246 0.978076i \(-0.433224\pi\)
0.208246 + 0.978076i \(0.433224\pi\)
\(618\) −92.2395 −3.71042
\(619\) 10.9672 0.440809 0.220404 0.975409i \(-0.429262\pi\)
0.220404 + 0.975409i \(0.429262\pi\)
\(620\) 73.0826 2.93507
\(621\) −4.67710 −0.187686
\(622\) 89.5642 3.59120
\(623\) −44.5367 −1.78432
\(624\) −6.32322 −0.253132
\(625\) −7.90260 −0.316104
\(626\) −6.16564 −0.246429
\(627\) −5.46284 −0.218165
\(628\) 30.6735 1.22401
\(629\) −0.101497 −0.00404695
\(630\) −88.3056 −3.51818
\(631\) 0.888044 0.0353525 0.0176762 0.999844i \(-0.494373\pi\)
0.0176762 + 0.999844i \(0.494373\pi\)
\(632\) 5.15917 0.205221
\(633\) 47.3191 1.88076
\(634\) 43.5489 1.72955
\(635\) 2.75863 0.109473
\(636\) −14.1428 −0.560799
\(637\) −1.91804 −0.0759956
\(638\) −83.6138 −3.31030
\(639\) 17.6857 0.699634
\(640\) 36.6846 1.45008
\(641\) 0.884608 0.0349399 0.0174700 0.999847i \(-0.494439\pi\)
0.0174700 + 0.999847i \(0.494439\pi\)
\(642\) 61.1684 2.41413
\(643\) 22.1672 0.874188 0.437094 0.899416i \(-0.356008\pi\)
0.437094 + 0.899416i \(0.356008\pi\)
\(644\) 149.312 5.88373
\(645\) −78.4925 −3.09064
\(646\) −1.39324 −0.0548162
\(647\) 9.43374 0.370879 0.185439 0.982656i \(-0.440629\pi\)
0.185439 + 0.982656i \(0.440629\pi\)
\(648\) 61.8213 2.42857
\(649\) 39.6254 1.55543
\(650\) 6.62014 0.259663
\(651\) 39.0102 1.52893
\(652\) −69.0791 −2.70535
\(653\) 17.8173 0.697245 0.348622 0.937263i \(-0.386650\pi\)
0.348622 + 0.937263i \(0.386650\pi\)
\(654\) −69.3974 −2.71365
\(655\) −28.5051 −1.11379
\(656\) 31.7717 1.24048
\(657\) 35.5480 1.38686
\(658\) −22.7992 −0.888805
\(659\) 31.2464 1.21719 0.608593 0.793483i \(-0.291734\pi\)
0.608593 + 0.793483i \(0.291734\pi\)
\(660\) −195.051 −7.59234
\(661\) 16.8636 0.655919 0.327960 0.944692i \(-0.393639\pi\)
0.327960 + 0.944692i \(0.393639\pi\)
\(662\) 6.33430 0.246190
\(663\) −1.04217 −0.0404744
\(664\) −17.1877 −0.667011
\(665\) 5.51066 0.213694
\(666\) 0.590964 0.0228994
\(667\) −60.0708 −2.32595
\(668\) 60.1701 2.32805
\(669\) −24.1160 −0.932377
\(670\) −139.769 −5.39976
\(671\) −36.0814 −1.39291
\(672\) −51.6096 −1.99088
\(673\) 13.7763 0.531036 0.265518 0.964106i \(-0.414457\pi\)
0.265518 + 0.964106i \(0.414457\pi\)
\(674\) −57.2947 −2.20691
\(675\) −3.66438 −0.141042
\(676\) −58.2740 −2.24131
\(677\) 25.7184 0.988438 0.494219 0.869338i \(-0.335454\pi\)
0.494219 + 0.869338i \(0.335454\pi\)
\(678\) −90.1426 −3.46190
\(679\) 27.7416 1.06463
\(680\) −27.7640 −1.06470
\(681\) −16.2479 −0.622622
\(682\) 59.8938 2.29345
\(683\) −49.8079 −1.90584 −0.952922 0.303214i \(-0.901940\pi\)
−0.952922 + 0.303214i \(0.901940\pi\)
\(684\) 5.62605 0.215117
\(685\) 18.9146 0.722691
\(686\) 14.1682 0.540946
\(687\) 35.5438 1.35608
\(688\) −69.0359 −2.63197
\(689\) 0.458888 0.0174822
\(690\) −202.052 −7.69198
\(691\) 9.33284 0.355038 0.177519 0.984117i \(-0.443193\pi\)
0.177519 + 0.984117i \(0.443193\pi\)
\(692\) 26.6588 1.01341
\(693\) −50.1911 −1.90660
\(694\) −14.0935 −0.534983
\(695\) −20.2252 −0.767185
\(696\) 99.6956 3.77895
\(697\) 5.23647 0.198345
\(698\) 81.2972 3.07714
\(699\) 21.7306 0.821925
\(700\) 116.982 4.42151
\(701\) −35.9991 −1.35967 −0.679834 0.733366i \(-0.737948\pi\)
−0.679834 + 0.733366i \(0.737948\pi\)
\(702\) −0.451267 −0.0170320
\(703\) −0.0368788 −0.00139091
\(704\) −3.43264 −0.129373
\(705\) 21.3972 0.805865
\(706\) −22.0898 −0.831359
\(707\) −41.0343 −1.54325
\(708\) −84.6534 −3.18147
\(709\) −28.6493 −1.07595 −0.537973 0.842962i \(-0.680810\pi\)
−0.537973 + 0.842962i \(0.680810\pi\)
\(710\) −56.8193 −2.13239
\(711\) −2.23238 −0.0837209
\(712\) 81.5302 3.05547
\(713\) 43.0296 1.61147
\(714\) −26.5534 −0.993734
\(715\) 6.32876 0.236682
\(716\) 60.7306 2.26961
\(717\) −18.1409 −0.677485
\(718\) 2.73522 0.102077
\(719\) −16.0244 −0.597608 −0.298804 0.954315i \(-0.596588\pi\)
−0.298804 + 0.954315i \(0.596588\pi\)
\(720\) 72.8907 2.71648
\(721\) 52.8860 1.96958
\(722\) 48.0316 1.78755
\(723\) −1.42134 −0.0528602
\(724\) 55.3457 2.05691
\(725\) −47.0639 −1.74791
\(726\) −92.2199 −3.42260
\(727\) −25.9717 −0.963237 −0.481618 0.876381i \(-0.659951\pi\)
−0.481618 + 0.876381i \(0.659951\pi\)
\(728\) 8.04043 0.297998
\(729\) −23.1417 −0.857099
\(730\) −114.206 −4.22696
\(731\) −11.3782 −0.420838
\(732\) 77.0823 2.84904
\(733\) −2.78609 −0.102906 −0.0514532 0.998675i \(-0.516385\pi\)
−0.0514532 + 0.998675i \(0.516385\pi\)
\(734\) −36.9945 −1.36549
\(735\) 45.8647 1.69174
\(736\) −56.9271 −2.09836
\(737\) −79.4420 −2.92628
\(738\) −30.4892 −1.12232
\(739\) −30.7886 −1.13258 −0.566288 0.824208i \(-0.691621\pi\)
−0.566288 + 0.824208i \(0.691621\pi\)
\(740\) −1.31676 −0.0484050
\(741\) −0.378669 −0.0139108
\(742\) 11.6920 0.429227
\(743\) −14.2263 −0.521911 −0.260955 0.965351i \(-0.584038\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(744\) −71.4133 −2.61814
\(745\) −59.0261 −2.16255
\(746\) 12.1718 0.445642
\(747\) 7.43715 0.272111
\(748\) −28.2744 −1.03381
\(749\) −35.0712 −1.28148
\(750\) −50.3480 −1.83845
\(751\) 25.4622 0.929129 0.464564 0.885539i \(-0.346211\pi\)
0.464564 + 0.885539i \(0.346211\pi\)
\(752\) 18.8193 0.686270
\(753\) 12.8475 0.468190
\(754\) −5.79588 −0.211074
\(755\) −9.59582 −0.349228
\(756\) −7.97419 −0.290018
\(757\) −3.16487 −0.115029 −0.0575145 0.998345i \(-0.518318\pi\)
−0.0575145 + 0.998345i \(0.518318\pi\)
\(758\) −73.3296 −2.66345
\(759\) −114.842 −4.16850
\(760\) −10.0880 −0.365930
\(761\) 32.0100 1.16036 0.580181 0.814488i \(-0.302982\pi\)
0.580181 + 0.814488i \(0.302982\pi\)
\(762\) −4.82984 −0.174967
\(763\) 39.7894 1.44047
\(764\) −114.791 −4.15300
\(765\) 12.0135 0.434350
\(766\) −26.4912 −0.957164
\(767\) 2.74673 0.0991785
\(768\) −67.4681 −2.43455
\(769\) 6.79258 0.244947 0.122473 0.992472i \(-0.460917\pi\)
0.122473 + 0.992472i \(0.460917\pi\)
\(770\) 161.250 5.81106
\(771\) 35.6310 1.28322
\(772\) −69.7003 −2.50857
\(773\) −33.1736 −1.19317 −0.596587 0.802549i \(-0.703477\pi\)
−0.596587 + 0.802549i \(0.703477\pi\)
\(774\) 66.2493 2.38128
\(775\) 33.7125 1.21099
\(776\) −50.7847 −1.82307
\(777\) −0.702863 −0.0252151
\(778\) −67.8059 −2.43096
\(779\) 1.90266 0.0681699
\(780\) −13.5204 −0.484108
\(781\) −32.2949 −1.15560
\(782\) −29.2892 −1.04738
\(783\) 3.20814 0.114650
\(784\) 40.3390 1.44068
\(785\) 23.7988 0.849414
\(786\) 49.9069 1.78012
\(787\) −39.5558 −1.41001 −0.705006 0.709202i \(-0.749056\pi\)
−0.705006 + 0.709202i \(0.749056\pi\)
\(788\) 97.8313 3.48510
\(789\) −22.0934 −0.786546
\(790\) 7.17205 0.255170
\(791\) 51.6837 1.83766
\(792\) 91.8814 3.26486
\(793\) −2.50107 −0.0888155
\(794\) 48.2022 1.71063
\(795\) −10.9730 −0.389173
\(796\) 4.23353 0.150053
\(797\) −10.3530 −0.366722 −0.183361 0.983046i \(-0.558698\pi\)
−0.183361 + 0.983046i \(0.558698\pi\)
\(798\) −9.64811 −0.341540
\(799\) 3.10172 0.109731
\(800\) −44.6008 −1.57688
\(801\) −35.2783 −1.24650
\(802\) 48.0490 1.69667
\(803\) −64.9124 −2.29071
\(804\) 169.715 5.98540
\(805\) 115.847 4.08309
\(806\) 4.15167 0.146236
\(807\) −51.7692 −1.82236
\(808\) 75.1186 2.64266
\(809\) 1.86785 0.0656700 0.0328350 0.999461i \(-0.489546\pi\)
0.0328350 + 0.999461i \(0.489546\pi\)
\(810\) 85.9412 3.01967
\(811\) 51.6194 1.81260 0.906302 0.422632i \(-0.138894\pi\)
0.906302 + 0.422632i \(0.138894\pi\)
\(812\) −102.417 −3.59414
\(813\) −74.0034 −2.59541
\(814\) −1.07913 −0.0378235
\(815\) −53.5966 −1.87741
\(816\) 21.9181 0.767288
\(817\) −4.13425 −0.144639
\(818\) 41.4939 1.45080
\(819\) −3.47911 −0.121570
\(820\) 67.9346 2.37238
\(821\) 15.8072 0.551674 0.275837 0.961204i \(-0.411045\pi\)
0.275837 + 0.961204i \(0.411045\pi\)
\(822\) −33.1159 −1.15505
\(823\) −0.0293980 −0.00102475 −0.000512376 1.00000i \(-0.500163\pi\)
−0.000512376 1.00000i \(0.500163\pi\)
\(824\) −96.8148 −3.37270
\(825\) −89.9757 −3.13255
\(826\) 69.9838 2.43505
\(827\) 44.2492 1.53870 0.769349 0.638829i \(-0.220581\pi\)
0.769349 + 0.638829i \(0.220581\pi\)
\(828\) 118.273 4.11027
\(829\) 43.2558 1.50234 0.751168 0.660111i \(-0.229491\pi\)
0.751168 + 0.660111i \(0.229491\pi\)
\(830\) −23.8936 −0.829357
\(831\) −0.760858 −0.0263939
\(832\) −0.237942 −0.00824914
\(833\) 6.64850 0.230357
\(834\) 35.4104 1.22616
\(835\) 46.6843 1.61558
\(836\) −10.2734 −0.355314
\(837\) −2.29804 −0.0794318
\(838\) 12.8665 0.444466
\(839\) −7.67883 −0.265103 −0.132551 0.991176i \(-0.542317\pi\)
−0.132551 + 0.991176i \(0.542317\pi\)
\(840\) −192.264 −6.63375
\(841\) 12.2041 0.420831
\(842\) 66.0219 2.27527
\(843\) −58.2005 −2.00453
\(844\) 88.9885 3.06311
\(845\) −45.2132 −1.55538
\(846\) −18.0597 −0.620904
\(847\) 52.8748 1.81680
\(848\) −9.65102 −0.331417
\(849\) 34.9271 1.19870
\(850\) −22.9473 −0.787086
\(851\) −0.775281 −0.0265763
\(852\) 68.9930 2.36366
\(853\) −30.2289 −1.03502 −0.517508 0.855678i \(-0.673140\pi\)
−0.517508 + 0.855678i \(0.673140\pi\)
\(854\) −63.7247 −2.18061
\(855\) 4.36509 0.149283
\(856\) 64.2025 2.19440
\(857\) −3.54349 −0.121043 −0.0605216 0.998167i \(-0.519276\pi\)
−0.0605216 + 0.998167i \(0.519276\pi\)
\(858\) −11.0804 −0.378280
\(859\) 20.8200 0.710370 0.355185 0.934796i \(-0.384418\pi\)
0.355185 + 0.934796i \(0.384418\pi\)
\(860\) −147.613 −5.03358
\(861\) 36.2623 1.23582
\(862\) −79.9940 −2.72461
\(863\) −44.3342 −1.50915 −0.754576 0.656212i \(-0.772158\pi\)
−0.754576 + 0.656212i \(0.772158\pi\)
\(864\) 3.04025 0.103431
\(865\) 20.6838 0.703271
\(866\) 24.3458 0.827305
\(867\) −37.3019 −1.26684
\(868\) 73.3629 2.49010
\(869\) 4.07644 0.138284
\(870\) 138.592 4.69872
\(871\) −5.50670 −0.186588
\(872\) −72.8397 −2.46666
\(873\) 21.9747 0.743730
\(874\) −10.6422 −0.359977
\(875\) 28.8673 0.975892
\(876\) 138.675 4.68540
\(877\) −4.57800 −0.154588 −0.0772940 0.997008i \(-0.524628\pi\)
−0.0772940 + 0.997008i \(0.524628\pi\)
\(878\) −72.5580 −2.44871
\(879\) −31.0306 −1.04664
\(880\) −133.102 −4.48687
\(881\) −19.7130 −0.664147 −0.332073 0.943254i \(-0.607748\pi\)
−0.332073 + 0.943254i \(0.607748\pi\)
\(882\) −38.7107 −1.30346
\(883\) −55.6168 −1.87165 −0.935827 0.352460i \(-0.885345\pi\)
−0.935827 + 0.352460i \(0.885345\pi\)
\(884\) −1.95990 −0.0659187
\(885\) −65.6803 −2.20782
\(886\) 67.0798 2.25359
\(887\) 48.2233 1.61918 0.809590 0.586995i \(-0.199689\pi\)
0.809590 + 0.586995i \(0.199689\pi\)
\(888\) 1.28668 0.0431783
\(889\) 2.76921 0.0928765
\(890\) 113.340 3.79916
\(891\) 48.8472 1.63644
\(892\) −45.3526 −1.51852
\(893\) 1.12700 0.0377137
\(894\) 103.343 3.45632
\(895\) 47.1192 1.57502
\(896\) 36.8253 1.23025
\(897\) −7.96054 −0.265795
\(898\) 49.9750 1.66769
\(899\) −29.5151 −0.984383
\(900\) 92.6638 3.08879
\(901\) −1.59064 −0.0529918
\(902\) 55.6748 1.85377
\(903\) −78.7936 −2.62209
\(904\) −94.6138 −3.14681
\(905\) 42.9413 1.42742
\(906\) 16.8005 0.558158
\(907\) 33.4445 1.11051 0.555253 0.831682i \(-0.312622\pi\)
0.555253 + 0.831682i \(0.312622\pi\)
\(908\) −30.5560 −1.01404
\(909\) −32.5040 −1.07809
\(910\) 11.1775 0.370529
\(911\) 48.7372 1.61474 0.807368 0.590048i \(-0.200891\pi\)
0.807368 + 0.590048i \(0.200891\pi\)
\(912\) 7.96391 0.263712
\(913\) −13.5806 −0.449452
\(914\) −13.0420 −0.431391
\(915\) 59.8060 1.97713
\(916\) 66.8439 2.20859
\(917\) −28.6144 −0.944931
\(918\) 1.56422 0.0516270
\(919\) −0.445218 −0.0146864 −0.00734319 0.999973i \(-0.502337\pi\)
−0.00734319 + 0.999973i \(0.502337\pi\)
\(920\) −212.074 −6.99187
\(921\) −63.2752 −2.08499
\(922\) 97.5707 3.21332
\(923\) −2.23860 −0.0736843
\(924\) −195.799 −6.44131
\(925\) −0.607412 −0.0199716
\(926\) 9.93614 0.326522
\(927\) 41.8920 1.37591
\(928\) 39.0477 1.28180
\(929\) −22.0155 −0.722307 −0.361153 0.932506i \(-0.617617\pi\)
−0.361153 + 0.932506i \(0.617617\pi\)
\(930\) −99.2757 −3.25538
\(931\) 2.41572 0.0791720
\(932\) 40.8666 1.33863
\(933\) −84.3790 −2.76244
\(934\) −27.6860 −0.905913
\(935\) −21.9373 −0.717427
\(936\) 6.36897 0.208176
\(937\) 14.3889 0.470064 0.235032 0.971988i \(-0.424480\pi\)
0.235032 + 0.971988i \(0.424480\pi\)
\(938\) −140.305 −4.58113
\(939\) 5.80869 0.189559
\(940\) 40.2397 1.31247
\(941\) 21.1587 0.689754 0.344877 0.938648i \(-0.387921\pi\)
0.344877 + 0.938648i \(0.387921\pi\)
\(942\) −41.6671 −1.35759
\(943\) 39.9985 1.30253
\(944\) −57.7673 −1.88016
\(945\) −6.18695 −0.201262
\(946\) −120.975 −3.93322
\(947\) −44.4077 −1.44306 −0.721529 0.692384i \(-0.756560\pi\)
−0.721529 + 0.692384i \(0.756560\pi\)
\(948\) −8.70868 −0.282845
\(949\) −4.49955 −0.146062
\(950\) −8.33787 −0.270516
\(951\) −41.0277 −1.33041
\(952\) −27.8705 −0.903287
\(953\) −9.16837 −0.296993 −0.148496 0.988913i \(-0.547443\pi\)
−0.148496 + 0.988913i \(0.547443\pi\)
\(954\) 9.26145 0.299851
\(955\) −89.0633 −2.88202
\(956\) −34.1159 −1.10339
\(957\) 78.7731 2.54637
\(958\) −15.8571 −0.512319
\(959\) 18.9872 0.613128
\(960\) 5.68971 0.183635
\(961\) −9.85794 −0.317998
\(962\) −0.0748024 −0.00241173
\(963\) −27.7806 −0.895217
\(964\) −2.67298 −0.0860909
\(965\) −54.0785 −1.74085
\(966\) −202.827 −6.52584
\(967\) 0.604773 0.0194482 0.00972410 0.999953i \(-0.496905\pi\)
0.00972410 + 0.999953i \(0.496905\pi\)
\(968\) −96.7943 −3.11109
\(969\) 1.31258 0.0421661
\(970\) −70.5987 −2.26679
\(971\) −32.9034 −1.05592 −0.527960 0.849269i \(-0.677043\pi\)
−0.527960 + 0.849269i \(0.677043\pi\)
\(972\) −97.5682 −3.12950
\(973\) −20.3028 −0.650877
\(974\) 38.8002 1.24324
\(975\) −6.23687 −0.199740
\(976\) 52.6008 1.68371
\(977\) −26.9227 −0.861333 −0.430666 0.902511i \(-0.641721\pi\)
−0.430666 + 0.902511i \(0.641721\pi\)
\(978\) 93.8374 3.00059
\(979\) 64.4200 2.05887
\(980\) 86.2534 2.75526
\(981\) 31.5179 1.00629
\(982\) 14.3808 0.458909
\(983\) −7.23485 −0.230756 −0.115378 0.993322i \(-0.536808\pi\)
−0.115378 + 0.993322i \(0.536808\pi\)
\(984\) −66.3829 −2.11621
\(985\) 75.9046 2.41852
\(986\) 20.0902 0.639803
\(987\) 21.4793 0.683693
\(988\) −0.712127 −0.0226558
\(989\) −86.9119 −2.76364
\(990\) 127.729 4.05951
\(991\) 19.4088 0.616539 0.308270 0.951299i \(-0.400250\pi\)
0.308270 + 0.951299i \(0.400250\pi\)
\(992\) −27.9704 −0.888062
\(993\) −5.96759 −0.189376
\(994\) −57.0372 −1.80911
\(995\) 3.28468 0.104131
\(996\) 29.0128 0.919307
\(997\) −44.0654 −1.39557 −0.697783 0.716310i \(-0.745830\pi\)
−0.697783 + 0.716310i \(0.745830\pi\)
\(998\) −99.5958 −3.15265
\(999\) 0.0414047 0.00130999
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.1.15 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.b.1.15 184 1.1 even 1 trivial