Properties

Label 6007.2.a.c.1.7
Level $6007$
Weight $2$
Character 6007.1
Self dual yes
Analytic conductor $47.966$
Analytic rank $0$
Dimension $261$
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] = [6007,2,Mod(1,6007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6007, 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("6007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6007 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6007.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: \(47.9661364942\)
Analytic rank: \(0\)
Dimension: \(261\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 6007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.63601 q^{2} +0.145552 q^{3} +4.94856 q^{4} +0.530894 q^{5} -0.383678 q^{6} +0.464377 q^{7} -7.77243 q^{8} -2.97881 q^{9} +O(q^{10})\) \(q-2.63601 q^{2} +0.145552 q^{3} +4.94856 q^{4} +0.530894 q^{5} -0.383678 q^{6} +0.464377 q^{7} -7.77243 q^{8} -2.97881 q^{9} -1.39944 q^{10} +3.49469 q^{11} +0.720274 q^{12} +5.14638 q^{13} -1.22410 q^{14} +0.0772729 q^{15} +10.5911 q^{16} -1.13332 q^{17} +7.85219 q^{18} -4.89648 q^{19} +2.62716 q^{20} +0.0675912 q^{21} -9.21205 q^{22} -7.53211 q^{23} -1.13130 q^{24} -4.71815 q^{25} -13.5659 q^{26} -0.870231 q^{27} +2.29800 q^{28} +3.17919 q^{29} -0.203692 q^{30} -0.803639 q^{31} -12.3734 q^{32} +0.508661 q^{33} +2.98744 q^{34} +0.246535 q^{35} -14.7408 q^{36} -2.21469 q^{37} +12.9072 q^{38} +0.749068 q^{39} -4.12633 q^{40} +7.88114 q^{41} -0.178171 q^{42} -4.69155 q^{43} +17.2937 q^{44} -1.58143 q^{45} +19.8547 q^{46} +6.42226 q^{47} +1.54156 q^{48} -6.78435 q^{49} +12.4371 q^{50} -0.164957 q^{51} +25.4671 q^{52} +5.01065 q^{53} +2.29394 q^{54} +1.85531 q^{55} -3.60934 q^{56} -0.712695 q^{57} -8.38038 q^{58} +8.41858 q^{59} +0.382389 q^{60} -8.02261 q^{61} +2.11840 q^{62} -1.38329 q^{63} +11.4342 q^{64} +2.73218 q^{65} -1.34084 q^{66} +6.98917 q^{67} -5.60829 q^{68} -1.09632 q^{69} -0.649869 q^{70} -5.36420 q^{71} +23.1526 q^{72} +0.136320 q^{73} +5.83796 q^{74} -0.686739 q^{75} -24.2305 q^{76} +1.62286 q^{77} -1.97455 q^{78} -11.6822 q^{79} +5.62275 q^{80} +8.80978 q^{81} -20.7748 q^{82} +5.50982 q^{83} +0.334479 q^{84} -0.601672 q^{85} +12.3670 q^{86} +0.462739 q^{87} -27.1623 q^{88} +15.4879 q^{89} +4.16868 q^{90} +2.38986 q^{91} -37.2731 q^{92} -0.116972 q^{93} -16.9292 q^{94} -2.59951 q^{95} -1.80098 q^{96} +10.1553 q^{97} +17.8836 q^{98} -10.4100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.63601 −1.86394 −0.931971 0.362533i \(-0.881912\pi\)
−0.931971 + 0.362533i \(0.881912\pi\)
\(3\) 0.145552 0.0840347 0.0420174 0.999117i \(-0.486622\pi\)
0.0420174 + 0.999117i \(0.486622\pi\)
\(4\) 4.94856 2.47428
\(5\) 0.530894 0.237423 0.118711 0.992929i \(-0.462124\pi\)
0.118711 + 0.992929i \(0.462124\pi\)
\(6\) −0.383678 −0.156636
\(7\) 0.464377 0.175518 0.0877590 0.996142i \(-0.472029\pi\)
0.0877590 + 0.996142i \(0.472029\pi\)
\(8\) −7.77243 −2.74797
\(9\) −2.97881 −0.992938
\(10\) −1.39944 −0.442543
\(11\) 3.49469 1.05369 0.526845 0.849961i \(-0.323375\pi\)
0.526845 + 0.849961i \(0.323375\pi\)
\(12\) 0.720274 0.207925
\(13\) 5.14638 1.42735 0.713674 0.700478i \(-0.247030\pi\)
0.713674 + 0.700478i \(0.247030\pi\)
\(14\) −1.22410 −0.327155
\(15\) 0.0772729 0.0199518
\(16\) 10.5911 2.64777
\(17\) −1.13332 −0.274870 −0.137435 0.990511i \(-0.543886\pi\)
−0.137435 + 0.990511i \(0.543886\pi\)
\(18\) 7.85219 1.85078
\(19\) −4.89648 −1.12333 −0.561665 0.827365i \(-0.689839\pi\)
−0.561665 + 0.827365i \(0.689839\pi\)
\(20\) 2.62716 0.587450
\(21\) 0.0675912 0.0147496
\(22\) −9.21205 −1.96402
\(23\) −7.53211 −1.57055 −0.785276 0.619145i \(-0.787479\pi\)
−0.785276 + 0.619145i \(0.787479\pi\)
\(24\) −1.13130 −0.230925
\(25\) −4.71815 −0.943630
\(26\) −13.5659 −2.66049
\(27\) −0.870231 −0.167476
\(28\) 2.29800 0.434281
\(29\) 3.17919 0.590361 0.295180 0.955442i \(-0.404620\pi\)
0.295180 + 0.955442i \(0.404620\pi\)
\(30\) −0.203692 −0.0371889
\(31\) −0.803639 −0.144338 −0.0721689 0.997392i \(-0.522992\pi\)
−0.0721689 + 0.997392i \(0.522992\pi\)
\(32\) −12.3734 −2.18733
\(33\) 0.508661 0.0885466
\(34\) 2.98744 0.512342
\(35\) 0.246535 0.0416720
\(36\) −14.7408 −2.45681
\(37\) −2.21469 −0.364093 −0.182047 0.983290i \(-0.558272\pi\)
−0.182047 + 0.983290i \(0.558272\pi\)
\(38\) 12.9072 2.09382
\(39\) 0.749068 0.119947
\(40\) −4.12633 −0.652431
\(41\) 7.88114 1.23083 0.615413 0.788205i \(-0.288989\pi\)
0.615413 + 0.788205i \(0.288989\pi\)
\(42\) −0.178171 −0.0274924
\(43\) −4.69155 −0.715455 −0.357727 0.933826i \(-0.616448\pi\)
−0.357727 + 0.933826i \(0.616448\pi\)
\(44\) 17.2937 2.60712
\(45\) −1.58143 −0.235746
\(46\) 19.8547 2.92742
\(47\) 6.42226 0.936783 0.468391 0.883521i \(-0.344834\pi\)
0.468391 + 0.883521i \(0.344834\pi\)
\(48\) 1.54156 0.222505
\(49\) −6.78435 −0.969193
\(50\) 12.4371 1.75887
\(51\) −0.164957 −0.0230986
\(52\) 25.4671 3.53166
\(53\) 5.01065 0.688266 0.344133 0.938921i \(-0.388173\pi\)
0.344133 + 0.938921i \(0.388173\pi\)
\(54\) 2.29394 0.312166
\(55\) 1.85531 0.250170
\(56\) −3.60934 −0.482318
\(57\) −0.712695 −0.0943988
\(58\) −8.38038 −1.10040
\(59\) 8.41858 1.09601 0.548003 0.836476i \(-0.315388\pi\)
0.548003 + 0.836476i \(0.315388\pi\)
\(60\) 0.382389 0.0493662
\(61\) −8.02261 −1.02719 −0.513595 0.858033i \(-0.671686\pi\)
−0.513595 + 0.858033i \(0.671686\pi\)
\(62\) 2.11840 0.269037
\(63\) −1.38329 −0.174279
\(64\) 11.4342 1.42928
\(65\) 2.73218 0.338885
\(66\) −1.34084 −0.165046
\(67\) 6.98917 0.853863 0.426931 0.904284i \(-0.359595\pi\)
0.426931 + 0.904284i \(0.359595\pi\)
\(68\) −5.60829 −0.680105
\(69\) −1.09632 −0.131981
\(70\) −0.649869 −0.0776742
\(71\) −5.36420 −0.636613 −0.318306 0.947988i \(-0.603114\pi\)
−0.318306 + 0.947988i \(0.603114\pi\)
\(72\) 23.1526 2.72856
\(73\) 0.136320 0.0159551 0.00797754 0.999968i \(-0.497461\pi\)
0.00797754 + 0.999968i \(0.497461\pi\)
\(74\) 5.83796 0.678649
\(75\) −0.686739 −0.0792977
\(76\) −24.2305 −2.77943
\(77\) 1.62286 0.184942
\(78\) −1.97455 −0.223574
\(79\) −11.6822 −1.31435 −0.657173 0.753740i \(-0.728248\pi\)
−0.657173 + 0.753740i \(0.728248\pi\)
\(80\) 5.62275 0.628642
\(81\) 8.80978 0.978864
\(82\) −20.7748 −2.29419
\(83\) 5.50982 0.604781 0.302390 0.953184i \(-0.402215\pi\)
0.302390 + 0.953184i \(0.402215\pi\)
\(84\) 0.334479 0.0364947
\(85\) −0.601672 −0.0652604
\(86\) 12.3670 1.33357
\(87\) 0.462739 0.0496108
\(88\) −27.1623 −2.89551
\(89\) 15.4879 1.64171 0.820855 0.571137i \(-0.193497\pi\)
0.820855 + 0.571137i \(0.193497\pi\)
\(90\) 4.16868 0.439417
\(91\) 2.38986 0.250526
\(92\) −37.2731 −3.88598
\(93\) −0.116972 −0.0121294
\(94\) −16.9292 −1.74611
\(95\) −2.59951 −0.266704
\(96\) −1.80098 −0.183812
\(97\) 10.1553 1.03112 0.515559 0.856854i \(-0.327584\pi\)
0.515559 + 0.856854i \(0.327584\pi\)
\(98\) 17.8836 1.80652
\(99\) −10.4100 −1.04625
\(100\) −23.3480 −2.33480
\(101\) −11.0329 −1.09782 −0.548909 0.835882i \(-0.684957\pi\)
−0.548909 + 0.835882i \(0.684957\pi\)
\(102\) 0.434829 0.0430545
\(103\) 11.5710 1.14013 0.570063 0.821601i \(-0.306919\pi\)
0.570063 + 0.821601i \(0.306919\pi\)
\(104\) −39.9999 −3.92231
\(105\) 0.0358838 0.00350190
\(106\) −13.2081 −1.28289
\(107\) 3.42860 0.331455 0.165727 0.986172i \(-0.447003\pi\)
0.165727 + 0.986172i \(0.447003\pi\)
\(108\) −4.30639 −0.414382
\(109\) 16.8798 1.61679 0.808396 0.588639i \(-0.200336\pi\)
0.808396 + 0.588639i \(0.200336\pi\)
\(110\) −4.89062 −0.466303
\(111\) −0.322354 −0.0305965
\(112\) 4.91826 0.464732
\(113\) −0.114943 −0.0108129 −0.00540647 0.999985i \(-0.501721\pi\)
−0.00540647 + 0.999985i \(0.501721\pi\)
\(114\) 1.87867 0.175954
\(115\) −3.99875 −0.372885
\(116\) 15.7324 1.46072
\(117\) −15.3301 −1.41727
\(118\) −22.1915 −2.04289
\(119\) −0.526287 −0.0482447
\(120\) −0.600598 −0.0548268
\(121\) 1.21289 0.110263
\(122\) 21.1477 1.91462
\(123\) 1.14712 0.103432
\(124\) −3.97685 −0.357132
\(125\) −5.15931 −0.461462
\(126\) 3.64638 0.324845
\(127\) 2.21966 0.196963 0.0984813 0.995139i \(-0.468602\pi\)
0.0984813 + 0.995139i \(0.468602\pi\)
\(128\) −5.39393 −0.476761
\(129\) −0.682867 −0.0601230
\(130\) −7.20206 −0.631662
\(131\) −9.03676 −0.789545 −0.394773 0.918779i \(-0.629177\pi\)
−0.394773 + 0.918779i \(0.629177\pi\)
\(132\) 2.51714 0.219089
\(133\) −2.27382 −0.197165
\(134\) −18.4235 −1.59155
\(135\) −0.462000 −0.0397627
\(136\) 8.80863 0.755334
\(137\) 21.0127 1.79524 0.897618 0.440774i \(-0.145296\pi\)
0.897618 + 0.440774i \(0.145296\pi\)
\(138\) 2.88990 0.246005
\(139\) 8.17664 0.693533 0.346767 0.937951i \(-0.387280\pi\)
0.346767 + 0.937951i \(0.387280\pi\)
\(140\) 1.21999 0.103108
\(141\) 0.934776 0.0787223
\(142\) 14.1401 1.18661
\(143\) 17.9850 1.50398
\(144\) −31.5489 −2.62908
\(145\) 1.68781 0.140165
\(146\) −0.359342 −0.0297393
\(147\) −0.987479 −0.0814459
\(148\) −10.9595 −0.900868
\(149\) 10.3436 0.847378 0.423689 0.905808i \(-0.360735\pi\)
0.423689 + 0.905808i \(0.360735\pi\)
\(150\) 1.81025 0.147806
\(151\) 2.24726 0.182880 0.0914398 0.995811i \(-0.470853\pi\)
0.0914398 + 0.995811i \(0.470853\pi\)
\(152\) 38.0576 3.08688
\(153\) 3.37594 0.272929
\(154\) −4.27787 −0.344720
\(155\) −0.426647 −0.0342691
\(156\) 3.70681 0.296782
\(157\) −11.7734 −0.939617 −0.469809 0.882768i \(-0.655677\pi\)
−0.469809 + 0.882768i \(0.655677\pi\)
\(158\) 30.7943 2.44986
\(159\) 0.729313 0.0578383
\(160\) −6.56896 −0.519322
\(161\) −3.49774 −0.275660
\(162\) −23.2227 −1.82455
\(163\) −6.22278 −0.487406 −0.243703 0.969850i \(-0.578362\pi\)
−0.243703 + 0.969850i \(0.578362\pi\)
\(164\) 39.0002 3.04541
\(165\) 0.270045 0.0210230
\(166\) −14.5239 −1.12728
\(167\) 7.95673 0.615711 0.307855 0.951433i \(-0.400389\pi\)
0.307855 + 0.951433i \(0.400389\pi\)
\(168\) −0.525348 −0.0405315
\(169\) 13.4852 1.03732
\(170\) 1.58601 0.121642
\(171\) 14.5857 1.11540
\(172\) −23.2164 −1.77023
\(173\) 11.0349 0.838967 0.419483 0.907763i \(-0.362211\pi\)
0.419483 + 0.907763i \(0.362211\pi\)
\(174\) −1.21978 −0.0924716
\(175\) −2.19100 −0.165624
\(176\) 37.0126 2.78993
\(177\) 1.22535 0.0921026
\(178\) −40.8262 −3.06005
\(179\) 23.3320 1.74391 0.871956 0.489584i \(-0.162851\pi\)
0.871956 + 0.489584i \(0.162851\pi\)
\(180\) −7.82582 −0.583302
\(181\) 8.44649 0.627823 0.313911 0.949452i \(-0.398360\pi\)
0.313911 + 0.949452i \(0.398360\pi\)
\(182\) −6.29970 −0.466965
\(183\) −1.16771 −0.0863196
\(184\) 58.5428 4.31583
\(185\) −1.17577 −0.0864441
\(186\) 0.308339 0.0226085
\(187\) −3.96060 −0.289628
\(188\) 31.7809 2.31786
\(189\) −0.404116 −0.0293951
\(190\) 6.85235 0.497122
\(191\) −1.43300 −0.103688 −0.0518442 0.998655i \(-0.516510\pi\)
−0.0518442 + 0.998655i \(0.516510\pi\)
\(192\) 1.66428 0.120109
\(193\) −0.640689 −0.0461178 −0.0230589 0.999734i \(-0.507341\pi\)
−0.0230589 + 0.999734i \(0.507341\pi\)
\(194\) −26.7696 −1.92194
\(195\) 0.397676 0.0284781
\(196\) −33.5728 −2.39805
\(197\) 6.86801 0.489325 0.244663 0.969608i \(-0.421323\pi\)
0.244663 + 0.969608i \(0.421323\pi\)
\(198\) 27.4410 1.95015
\(199\) −5.01432 −0.355455 −0.177728 0.984080i \(-0.556875\pi\)
−0.177728 + 0.984080i \(0.556875\pi\)
\(200\) 36.6715 2.59307
\(201\) 1.01729 0.0717542
\(202\) 29.0829 2.04627
\(203\) 1.47634 0.103619
\(204\) −0.816300 −0.0571524
\(205\) 4.18405 0.292227
\(206\) −30.5013 −2.12513
\(207\) 22.4368 1.55946
\(208\) 54.5058 3.77930
\(209\) −17.1117 −1.18364
\(210\) −0.0945900 −0.00652733
\(211\) −6.15793 −0.423929 −0.211965 0.977277i \(-0.567986\pi\)
−0.211965 + 0.977277i \(0.567986\pi\)
\(212\) 24.7955 1.70296
\(213\) −0.780772 −0.0534976
\(214\) −9.03782 −0.617813
\(215\) −2.49071 −0.169865
\(216\) 6.76381 0.460219
\(217\) −0.373192 −0.0253339
\(218\) −44.4954 −3.01361
\(219\) 0.0198417 0.00134078
\(220\) 9.18111 0.618991
\(221\) −5.83248 −0.392335
\(222\) 0.849729 0.0570301
\(223\) −1.59962 −0.107119 −0.0535593 0.998565i \(-0.517057\pi\)
−0.0535593 + 0.998565i \(0.517057\pi\)
\(224\) −5.74592 −0.383916
\(225\) 14.0545 0.936967
\(226\) 0.302992 0.0201547
\(227\) 2.71787 0.180391 0.0901956 0.995924i \(-0.471251\pi\)
0.0901956 + 0.995924i \(0.471251\pi\)
\(228\) −3.52681 −0.233569
\(229\) 21.1403 1.39699 0.698495 0.715615i \(-0.253853\pi\)
0.698495 + 0.715615i \(0.253853\pi\)
\(230\) 10.5407 0.695036
\(231\) 0.236211 0.0155415
\(232\) −24.7100 −1.62229
\(233\) −5.27553 −0.345611 −0.172806 0.984956i \(-0.555283\pi\)
−0.172806 + 0.984956i \(0.555283\pi\)
\(234\) 40.4103 2.64171
\(235\) 3.40954 0.222414
\(236\) 41.6598 2.71182
\(237\) −1.70037 −0.110451
\(238\) 1.38730 0.0899252
\(239\) −13.2777 −0.858863 −0.429432 0.903099i \(-0.641286\pi\)
−0.429432 + 0.903099i \(0.641286\pi\)
\(240\) 0.818405 0.0528278
\(241\) 3.64256 0.234638 0.117319 0.993094i \(-0.462570\pi\)
0.117319 + 0.993094i \(0.462570\pi\)
\(242\) −3.19719 −0.205523
\(243\) 3.89298 0.249735
\(244\) −39.7003 −2.54155
\(245\) −3.60177 −0.230109
\(246\) −3.02382 −0.192792
\(247\) −25.1992 −1.60338
\(248\) 6.24623 0.396636
\(249\) 0.801967 0.0508226
\(250\) 13.6000 0.860139
\(251\) 0.0182307 0.00115071 0.000575356 1.00000i \(-0.499817\pi\)
0.000575356 1.00000i \(0.499817\pi\)
\(252\) −6.84531 −0.431214
\(253\) −26.3224 −1.65488
\(254\) −5.85104 −0.367127
\(255\) −0.0875748 −0.00548415
\(256\) −8.64996 −0.540623
\(257\) 22.0359 1.37456 0.687281 0.726392i \(-0.258804\pi\)
0.687281 + 0.726392i \(0.258804\pi\)
\(258\) 1.80004 0.112066
\(259\) −1.02845 −0.0639050
\(260\) 13.5204 0.838497
\(261\) −9.47022 −0.586192
\(262\) 23.8210 1.47167
\(263\) −10.5274 −0.649146 −0.324573 0.945861i \(-0.605221\pi\)
−0.324573 + 0.945861i \(0.605221\pi\)
\(264\) −3.95353 −0.243323
\(265\) 2.66013 0.163410
\(266\) 5.99380 0.367504
\(267\) 2.25430 0.137961
\(268\) 34.5863 2.11269
\(269\) −24.6221 −1.50124 −0.750619 0.660735i \(-0.770245\pi\)
−0.750619 + 0.660735i \(0.770245\pi\)
\(270\) 1.21784 0.0741153
\(271\) −5.27947 −0.320705 −0.160353 0.987060i \(-0.551263\pi\)
−0.160353 + 0.987060i \(0.551263\pi\)
\(272\) −12.0031 −0.727794
\(273\) 0.347850 0.0210528
\(274\) −55.3897 −3.34622
\(275\) −16.4885 −0.994294
\(276\) −5.42518 −0.326558
\(277\) 17.1113 1.02812 0.514058 0.857756i \(-0.328142\pi\)
0.514058 + 0.857756i \(0.328142\pi\)
\(278\) −21.5537 −1.29271
\(279\) 2.39389 0.143319
\(280\) −1.91618 −0.114513
\(281\) −8.24845 −0.492061 −0.246031 0.969262i \(-0.579126\pi\)
−0.246031 + 0.969262i \(0.579126\pi\)
\(282\) −2.46408 −0.146734
\(283\) −2.56891 −0.152706 −0.0763528 0.997081i \(-0.524328\pi\)
−0.0763528 + 0.997081i \(0.524328\pi\)
\(284\) −26.5450 −1.57516
\(285\) −0.378366 −0.0224124
\(286\) −47.4087 −2.80334
\(287\) 3.65982 0.216032
\(288\) 36.8580 2.17188
\(289\) −15.7156 −0.924446
\(290\) −4.44909 −0.261260
\(291\) 1.47813 0.0866497
\(292\) 0.674588 0.0394773
\(293\) 15.7408 0.919585 0.459792 0.888026i \(-0.347924\pi\)
0.459792 + 0.888026i \(0.347924\pi\)
\(294\) 2.60301 0.151810
\(295\) 4.46937 0.260217
\(296\) 17.2135 1.00052
\(297\) −3.04119 −0.176468
\(298\) −27.2658 −1.57946
\(299\) −38.7631 −2.24173
\(300\) −3.39836 −0.196205
\(301\) −2.17865 −0.125575
\(302\) −5.92381 −0.340877
\(303\) −1.60587 −0.0922548
\(304\) −51.8591 −2.97433
\(305\) −4.25915 −0.243878
\(306\) −8.89903 −0.508724
\(307\) −13.1574 −0.750934 −0.375467 0.926836i \(-0.622518\pi\)
−0.375467 + 0.926836i \(0.622518\pi\)
\(308\) 8.03080 0.457597
\(309\) 1.68419 0.0958102
\(310\) 1.12465 0.0638756
\(311\) 3.66100 0.207596 0.103798 0.994598i \(-0.466900\pi\)
0.103798 + 0.994598i \(0.466900\pi\)
\(312\) −5.82208 −0.329610
\(313\) −17.5814 −0.993762 −0.496881 0.867819i \(-0.665521\pi\)
−0.496881 + 0.867819i \(0.665521\pi\)
\(314\) 31.0347 1.75139
\(315\) −0.734382 −0.0413777
\(316\) −57.8098 −3.25206
\(317\) −8.63558 −0.485023 −0.242511 0.970149i \(-0.577971\pi\)
−0.242511 + 0.970149i \(0.577971\pi\)
\(318\) −1.92248 −0.107807
\(319\) 11.1103 0.622057
\(320\) 6.07035 0.339343
\(321\) 0.499041 0.0278537
\(322\) 9.22008 0.513815
\(323\) 5.54927 0.308770
\(324\) 43.5957 2.42198
\(325\) −24.2814 −1.34689
\(326\) 16.4033 0.908496
\(327\) 2.45690 0.135867
\(328\) −61.2556 −3.38227
\(329\) 2.98235 0.164422
\(330\) −0.711842 −0.0391856
\(331\) 16.1864 0.889686 0.444843 0.895608i \(-0.353259\pi\)
0.444843 + 0.895608i \(0.353259\pi\)
\(332\) 27.2656 1.49640
\(333\) 6.59716 0.361522
\(334\) −20.9740 −1.14765
\(335\) 3.71051 0.202727
\(336\) 0.715865 0.0390537
\(337\) 16.1610 0.880346 0.440173 0.897913i \(-0.354917\pi\)
0.440173 + 0.897913i \(0.354917\pi\)
\(338\) −35.5472 −1.93351
\(339\) −0.0167303 −0.000908663 0
\(340\) −2.97741 −0.161472
\(341\) −2.80847 −0.152087
\(342\) −38.4481 −2.07904
\(343\) −6.40114 −0.345629
\(344\) 36.4647 1.96605
\(345\) −0.582028 −0.0313353
\(346\) −29.0881 −1.56378
\(347\) 10.1340 0.544021 0.272010 0.962294i \(-0.412312\pi\)
0.272010 + 0.962294i \(0.412312\pi\)
\(348\) 2.28989 0.122751
\(349\) −11.5947 −0.620648 −0.310324 0.950631i \(-0.600438\pi\)
−0.310324 + 0.950631i \(0.600438\pi\)
\(350\) 5.77551 0.308714
\(351\) −4.47854 −0.239047
\(352\) −43.2412 −2.30476
\(353\) −14.2967 −0.760936 −0.380468 0.924794i \(-0.624237\pi\)
−0.380468 + 0.924794i \(0.624237\pi\)
\(354\) −3.23002 −0.171674
\(355\) −2.84782 −0.151147
\(356\) 76.6426 4.06205
\(357\) −0.0766024 −0.00405423
\(358\) −61.5033 −3.25055
\(359\) −4.18574 −0.220915 −0.110457 0.993881i \(-0.535232\pi\)
−0.110457 + 0.993881i \(0.535232\pi\)
\(360\) 12.2916 0.647823
\(361\) 4.97556 0.261872
\(362\) −22.2651 −1.17023
\(363\) 0.176539 0.00926589
\(364\) 11.8264 0.619870
\(365\) 0.0723716 0.00378810
\(366\) 3.07810 0.160895
\(367\) 4.59241 0.239722 0.119861 0.992791i \(-0.461755\pi\)
0.119861 + 0.992791i \(0.461755\pi\)
\(368\) −79.7733 −4.15847
\(369\) −23.4764 −1.22213
\(370\) 3.09934 0.161127
\(371\) 2.32683 0.120803
\(372\) −0.578841 −0.0300115
\(373\) 29.4920 1.52704 0.763519 0.645786i \(-0.223470\pi\)
0.763519 + 0.645786i \(0.223470\pi\)
\(374\) 10.4402 0.539849
\(375\) −0.750950 −0.0387789
\(376\) −49.9165 −2.57425
\(377\) 16.3613 0.842651
\(378\) 1.06525 0.0547907
\(379\) 13.3926 0.687931 0.343965 0.938982i \(-0.388230\pi\)
0.343965 + 0.938982i \(0.388230\pi\)
\(380\) −12.8638 −0.659901
\(381\) 0.323076 0.0165517
\(382\) 3.77741 0.193269
\(383\) 3.52042 0.179885 0.0899425 0.995947i \(-0.471332\pi\)
0.0899425 + 0.995947i \(0.471332\pi\)
\(384\) −0.785100 −0.0400645
\(385\) 0.861565 0.0439094
\(386\) 1.68886 0.0859609
\(387\) 13.9753 0.710402
\(388\) 50.2542 2.55127
\(389\) 11.3354 0.574727 0.287364 0.957822i \(-0.407221\pi\)
0.287364 + 0.957822i \(0.407221\pi\)
\(390\) −1.04828 −0.0530816
\(391\) 8.53627 0.431698
\(392\) 52.7309 2.66331
\(393\) −1.31532 −0.0663492
\(394\) −18.1041 −0.912074
\(395\) −6.20199 −0.312056
\(396\) −51.5147 −2.58871
\(397\) 20.5737 1.03256 0.516282 0.856419i \(-0.327316\pi\)
0.516282 + 0.856419i \(0.327316\pi\)
\(398\) 13.2178 0.662548
\(399\) −0.330959 −0.0165687
\(400\) −49.9704 −2.49852
\(401\) 23.1609 1.15660 0.578299 0.815825i \(-0.303717\pi\)
0.578299 + 0.815825i \(0.303717\pi\)
\(402\) −2.68159 −0.133746
\(403\) −4.13583 −0.206020
\(404\) −54.5971 −2.71631
\(405\) 4.67706 0.232405
\(406\) −3.89166 −0.193140
\(407\) −7.73968 −0.383642
\(408\) 1.28212 0.0634743
\(409\) 1.59562 0.0788985 0.0394492 0.999222i \(-0.487440\pi\)
0.0394492 + 0.999222i \(0.487440\pi\)
\(410\) −11.0292 −0.544693
\(411\) 3.05845 0.150862
\(412\) 57.2598 2.82099
\(413\) 3.90940 0.192369
\(414\) −59.1435 −2.90675
\(415\) 2.92513 0.143589
\(416\) −63.6782 −3.12208
\(417\) 1.19013 0.0582809
\(418\) 45.1067 2.20624
\(419\) 26.5678 1.29792 0.648961 0.760822i \(-0.275204\pi\)
0.648961 + 0.760822i \(0.275204\pi\)
\(420\) 0.177573 0.00866467
\(421\) 8.94543 0.435974 0.217987 0.975952i \(-0.430051\pi\)
0.217987 + 0.975952i \(0.430051\pi\)
\(422\) 16.2324 0.790179
\(423\) −19.1307 −0.930167
\(424\) −38.9449 −1.89133
\(425\) 5.34717 0.259376
\(426\) 2.05812 0.0997164
\(427\) −3.72552 −0.180290
\(428\) 16.9666 0.820112
\(429\) 2.61776 0.126387
\(430\) 6.56555 0.316619
\(431\) −12.0067 −0.578343 −0.289171 0.957277i \(-0.593380\pi\)
−0.289171 + 0.957277i \(0.593380\pi\)
\(432\) −9.21670 −0.443439
\(433\) −12.8340 −0.616762 −0.308381 0.951263i \(-0.599787\pi\)
−0.308381 + 0.951263i \(0.599787\pi\)
\(434\) 0.983737 0.0472209
\(435\) 0.245665 0.0117787
\(436\) 83.5307 4.00039
\(437\) 36.8808 1.76425
\(438\) −0.0523031 −0.00249914
\(439\) −17.0890 −0.815616 −0.407808 0.913068i \(-0.633707\pi\)
−0.407808 + 0.913068i \(0.633707\pi\)
\(440\) −14.4203 −0.687460
\(441\) 20.2093 0.962349
\(442\) 15.3745 0.731290
\(443\) −14.2718 −0.678072 −0.339036 0.940773i \(-0.610101\pi\)
−0.339036 + 0.940773i \(0.610101\pi\)
\(444\) −1.59519 −0.0757043
\(445\) 8.22241 0.389780
\(446\) 4.21662 0.199663
\(447\) 1.50553 0.0712092
\(448\) 5.30979 0.250864
\(449\) −39.1732 −1.84870 −0.924348 0.381550i \(-0.875390\pi\)
−0.924348 + 0.381550i \(0.875390\pi\)
\(450\) −37.0478 −1.74645
\(451\) 27.5422 1.29691
\(452\) −0.568803 −0.0267542
\(453\) 0.327094 0.0153682
\(454\) −7.16433 −0.336239
\(455\) 1.26876 0.0594805
\(456\) 5.53937 0.259405
\(457\) −25.9395 −1.21340 −0.606699 0.794931i \(-0.707507\pi\)
−0.606699 + 0.794931i \(0.707507\pi\)
\(458\) −55.7260 −2.60391
\(459\) 0.986249 0.0460341
\(460\) −19.7880 −0.922622
\(461\) 29.5030 1.37409 0.687045 0.726615i \(-0.258908\pi\)
0.687045 + 0.726615i \(0.258908\pi\)
\(462\) −0.622654 −0.0289685
\(463\) 5.14067 0.238907 0.119454 0.992840i \(-0.461886\pi\)
0.119454 + 0.992840i \(0.461886\pi\)
\(464\) 33.6711 1.56314
\(465\) −0.0620995 −0.00287980
\(466\) 13.9064 0.644199
\(467\) −2.28720 −0.105839 −0.0529194 0.998599i \(-0.516853\pi\)
−0.0529194 + 0.998599i \(0.516853\pi\)
\(468\) −75.8619 −3.50672
\(469\) 3.24561 0.149868
\(470\) −8.98758 −0.414566
\(471\) −1.71364 −0.0789605
\(472\) −65.4328 −3.01179
\(473\) −16.3955 −0.753867
\(474\) 4.48219 0.205874
\(475\) 23.1024 1.06001
\(476\) −2.60436 −0.119371
\(477\) −14.9258 −0.683406
\(478\) 35.0002 1.60087
\(479\) 17.2926 0.790117 0.395059 0.918656i \(-0.370724\pi\)
0.395059 + 0.918656i \(0.370724\pi\)
\(480\) −0.956128 −0.0436411
\(481\) −11.3977 −0.519688
\(482\) −9.60183 −0.437352
\(483\) −0.509105 −0.0231651
\(484\) 6.00204 0.272820
\(485\) 5.39140 0.244811
\(486\) −10.2619 −0.465491
\(487\) 13.6833 0.620050 0.310025 0.950728i \(-0.399663\pi\)
0.310025 + 0.950728i \(0.399663\pi\)
\(488\) 62.3551 2.82268
\(489\) −0.905741 −0.0409590
\(490\) 9.49431 0.428909
\(491\) 11.4210 0.515424 0.257712 0.966222i \(-0.417031\pi\)
0.257712 + 0.966222i \(0.417031\pi\)
\(492\) 5.67658 0.255920
\(493\) −3.60303 −0.162272
\(494\) 66.4253 2.98861
\(495\) −5.52663 −0.248404
\(496\) −8.51142 −0.382174
\(497\) −2.49101 −0.111737
\(498\) −2.11399 −0.0947304
\(499\) 11.7922 0.527893 0.263947 0.964537i \(-0.414976\pi\)
0.263947 + 0.964537i \(0.414976\pi\)
\(500\) −25.5311 −1.14179
\(501\) 1.15812 0.0517411
\(502\) −0.0480564 −0.00214486
\(503\) −29.4568 −1.31342 −0.656708 0.754145i \(-0.728052\pi\)
−0.656708 + 0.754145i \(0.728052\pi\)
\(504\) 10.7515 0.478912
\(505\) −5.85731 −0.260647
\(506\) 69.3862 3.08459
\(507\) 1.96281 0.0871713
\(508\) 10.9841 0.487340
\(509\) −14.6039 −0.647306 −0.323653 0.946176i \(-0.604911\pi\)
−0.323653 + 0.946176i \(0.604911\pi\)
\(510\) 0.230848 0.0102221
\(511\) 0.0633040 0.00280040
\(512\) 33.5893 1.48445
\(513\) 4.26107 0.188131
\(514\) −58.0869 −2.56210
\(515\) 6.14298 0.270692
\(516\) −3.37920 −0.148761
\(517\) 22.4438 0.987079
\(518\) 2.71102 0.119115
\(519\) 1.60615 0.0705023
\(520\) −21.2357 −0.931246
\(521\) −31.4069 −1.37596 −0.687980 0.725729i \(-0.741502\pi\)
−0.687980 + 0.725729i \(0.741502\pi\)
\(522\) 24.9636 1.09263
\(523\) 36.9604 1.61616 0.808082 0.589070i \(-0.200506\pi\)
0.808082 + 0.589070i \(0.200506\pi\)
\(524\) −44.7189 −1.95355
\(525\) −0.318906 −0.0139182
\(526\) 27.7503 1.20997
\(527\) 0.910778 0.0396741
\(528\) 5.38728 0.234451
\(529\) 33.7326 1.46664
\(530\) −7.01212 −0.304587
\(531\) −25.0774 −1.08827
\(532\) −11.2521 −0.487841
\(533\) 40.5593 1.75682
\(534\) −5.94235 −0.257151
\(535\) 1.82022 0.0786950
\(536\) −54.3228 −2.34639
\(537\) 3.39602 0.146549
\(538\) 64.9043 2.79822
\(539\) −23.7092 −1.02123
\(540\) −2.28623 −0.0983839
\(541\) 34.9476 1.50251 0.751257 0.660009i \(-0.229448\pi\)
0.751257 + 0.660009i \(0.229448\pi\)
\(542\) 13.9168 0.597776
\(543\) 1.22941 0.0527589
\(544\) 14.0230 0.601231
\(545\) 8.96138 0.383864
\(546\) −0.916937 −0.0392413
\(547\) 0.0554230 0.00236972 0.00118486 0.999999i \(-0.499623\pi\)
0.00118486 + 0.999999i \(0.499623\pi\)
\(548\) 103.983 4.44191
\(549\) 23.8979 1.01994
\(550\) 43.4639 1.85331
\(551\) −15.5669 −0.663170
\(552\) 8.52104 0.362680
\(553\) −5.42493 −0.230692
\(554\) −45.1055 −1.91635
\(555\) −0.171136 −0.00726431
\(556\) 40.4625 1.71599
\(557\) 12.8773 0.545629 0.272814 0.962067i \(-0.412046\pi\)
0.272814 + 0.962067i \(0.412046\pi\)
\(558\) −6.31032 −0.267137
\(559\) −24.1445 −1.02120
\(560\) 2.61108 0.110338
\(561\) −0.576475 −0.0243388
\(562\) 21.7430 0.917174
\(563\) 8.78995 0.370452 0.185226 0.982696i \(-0.440698\pi\)
0.185226 + 0.982696i \(0.440698\pi\)
\(564\) 4.62579 0.194781
\(565\) −0.0610226 −0.00256724
\(566\) 6.77167 0.284634
\(567\) 4.09106 0.171808
\(568\) 41.6928 1.74939
\(569\) −28.2277 −1.18337 −0.591683 0.806171i \(-0.701536\pi\)
−0.591683 + 0.806171i \(0.701536\pi\)
\(570\) 0.997376 0.0417755
\(571\) −12.8869 −0.539302 −0.269651 0.962958i \(-0.586908\pi\)
−0.269651 + 0.962958i \(0.586908\pi\)
\(572\) 88.9999 3.72127
\(573\) −0.208577 −0.00871343
\(574\) −9.64733 −0.402672
\(575\) 35.5376 1.48202
\(576\) −34.0604 −1.41918
\(577\) 16.1725 0.673269 0.336634 0.941635i \(-0.390711\pi\)
0.336634 + 0.941635i \(0.390711\pi\)
\(578\) 41.4265 1.72311
\(579\) −0.0932538 −0.00387550
\(580\) 8.35223 0.346808
\(581\) 2.55863 0.106150
\(582\) −3.89638 −0.161510
\(583\) 17.5107 0.725219
\(584\) −1.05954 −0.0438440
\(585\) −8.13866 −0.336492
\(586\) −41.4928 −1.71405
\(587\) −11.6784 −0.482019 −0.241010 0.970523i \(-0.577479\pi\)
−0.241010 + 0.970523i \(0.577479\pi\)
\(588\) −4.88660 −0.201520
\(589\) 3.93501 0.162139
\(590\) −11.7813 −0.485029
\(591\) 0.999655 0.0411203
\(592\) −23.4560 −0.964037
\(593\) −9.14424 −0.375509 −0.187755 0.982216i \(-0.560121\pi\)
−0.187755 + 0.982216i \(0.560121\pi\)
\(594\) 8.01662 0.328926
\(595\) −0.279403 −0.0114544
\(596\) 51.1857 2.09665
\(597\) −0.729846 −0.0298706
\(598\) 102.180 4.17845
\(599\) −11.4158 −0.466437 −0.233219 0.972424i \(-0.574926\pi\)
−0.233219 + 0.972424i \(0.574926\pi\)
\(600\) 5.33763 0.217908
\(601\) −3.06977 −0.125218 −0.0626092 0.998038i \(-0.519942\pi\)
−0.0626092 + 0.998038i \(0.519942\pi\)
\(602\) 5.74294 0.234065
\(603\) −20.8194 −0.847833
\(604\) 11.1207 0.452495
\(605\) 0.643915 0.0261789
\(606\) 4.23309 0.171958
\(607\) 21.6585 0.879092 0.439546 0.898220i \(-0.355139\pi\)
0.439546 + 0.898220i \(0.355139\pi\)
\(608\) 60.5861 2.45709
\(609\) 0.214885 0.00870759
\(610\) 11.2272 0.454575
\(611\) 33.0514 1.33712
\(612\) 16.7060 0.675302
\(613\) 35.4461 1.43165 0.715827 0.698277i \(-0.246050\pi\)
0.715827 + 0.698277i \(0.246050\pi\)
\(614\) 34.6831 1.39970
\(615\) 0.608998 0.0245572
\(616\) −12.6135 −0.508214
\(617\) −8.44095 −0.339820 −0.169910 0.985460i \(-0.554348\pi\)
−0.169910 + 0.985460i \(0.554348\pi\)
\(618\) −4.43954 −0.178585
\(619\) −25.1410 −1.01050 −0.505252 0.862972i \(-0.668600\pi\)
−0.505252 + 0.862972i \(0.668600\pi\)
\(620\) −2.11129 −0.0847913
\(621\) 6.55467 0.263030
\(622\) −9.65043 −0.386947
\(623\) 7.19221 0.288150
\(624\) 7.93345 0.317592
\(625\) 20.8517 0.834069
\(626\) 46.3449 1.85231
\(627\) −2.49065 −0.0994671
\(628\) −58.2612 −2.32487
\(629\) 2.50995 0.100078
\(630\) 1.93584 0.0771257
\(631\) 11.1522 0.443960 0.221980 0.975051i \(-0.428748\pi\)
0.221980 + 0.975051i \(0.428748\pi\)
\(632\) 90.7988 3.61178
\(633\) −0.896302 −0.0356248
\(634\) 22.7635 0.904054
\(635\) 1.17840 0.0467635
\(636\) 3.60905 0.143108
\(637\) −34.9149 −1.38338
\(638\) −29.2869 −1.15948
\(639\) 15.9789 0.632117
\(640\) −2.86361 −0.113194
\(641\) 17.5609 0.693615 0.346807 0.937936i \(-0.387266\pi\)
0.346807 + 0.937936i \(0.387266\pi\)
\(642\) −1.31548 −0.0519177
\(643\) 27.7343 1.09373 0.546867 0.837219i \(-0.315820\pi\)
0.546867 + 0.837219i \(0.315820\pi\)
\(644\) −17.3088 −0.682061
\(645\) −0.362530 −0.0142746
\(646\) −14.6280 −0.575529
\(647\) 33.4666 1.31571 0.657855 0.753145i \(-0.271464\pi\)
0.657855 + 0.753145i \(0.271464\pi\)
\(648\) −68.4734 −2.68989
\(649\) 29.4204 1.15485
\(650\) 64.0060 2.51052
\(651\) −0.0543190 −0.00212893
\(652\) −30.7938 −1.20598
\(653\) 11.9381 0.467176 0.233588 0.972336i \(-0.424953\pi\)
0.233588 + 0.972336i \(0.424953\pi\)
\(654\) −6.47641 −0.253248
\(655\) −4.79756 −0.187456
\(656\) 83.4699 3.25895
\(657\) −0.406073 −0.0158424
\(658\) −7.86151 −0.306474
\(659\) 49.1115 1.91311 0.956555 0.291551i \(-0.0941713\pi\)
0.956555 + 0.291551i \(0.0941713\pi\)
\(660\) 1.33633 0.0520167
\(661\) −25.8028 −1.00361 −0.501807 0.864980i \(-0.667331\pi\)
−0.501807 + 0.864980i \(0.667331\pi\)
\(662\) −42.6676 −1.65832
\(663\) −0.848932 −0.0329698
\(664\) −42.8246 −1.66192
\(665\) −1.20715 −0.0468115
\(666\) −17.3902 −0.673856
\(667\) −23.9460 −0.927193
\(668\) 39.3743 1.52344
\(669\) −0.232829 −0.00900168
\(670\) −9.78094 −0.377871
\(671\) −28.0366 −1.08234
\(672\) −0.836333 −0.0322622
\(673\) −2.24519 −0.0865459 −0.0432729 0.999063i \(-0.513779\pi\)
−0.0432729 + 0.999063i \(0.513779\pi\)
\(674\) −42.6006 −1.64091
\(675\) 4.10588 0.158035
\(676\) 66.7324 2.56663
\(677\) 19.4441 0.747296 0.373648 0.927570i \(-0.378107\pi\)
0.373648 + 0.927570i \(0.378107\pi\)
\(678\) 0.0441012 0.00169369
\(679\) 4.71591 0.180980
\(680\) 4.67645 0.179334
\(681\) 0.395592 0.0151591
\(682\) 7.40316 0.283482
\(683\) 21.6887 0.829893 0.414947 0.909846i \(-0.363800\pi\)
0.414947 + 0.909846i \(0.363800\pi\)
\(684\) 72.1782 2.75980
\(685\) 11.1555 0.426230
\(686\) 16.8735 0.644232
\(687\) 3.07702 0.117396
\(688\) −49.6886 −1.89436
\(689\) 25.7867 0.982396
\(690\) 1.53423 0.0584072
\(691\) −21.1301 −0.803828 −0.401914 0.915677i \(-0.631655\pi\)
−0.401914 + 0.915677i \(0.631655\pi\)
\(692\) 54.6067 2.07584
\(693\) −4.83419 −0.183636
\(694\) −26.7133 −1.01402
\(695\) 4.34093 0.164661
\(696\) −3.59660 −0.136329
\(697\) −8.93183 −0.338317
\(698\) 30.5637 1.15685
\(699\) −0.767866 −0.0290434
\(700\) −10.8423 −0.409800
\(701\) −30.7681 −1.16210 −0.581048 0.813869i \(-0.697357\pi\)
−0.581048 + 0.813869i \(0.697357\pi\)
\(702\) 11.8055 0.445569
\(703\) 10.8442 0.408997
\(704\) 39.9591 1.50601
\(705\) 0.496267 0.0186905
\(706\) 37.6862 1.41834
\(707\) −5.12344 −0.192687
\(708\) 6.06369 0.227887
\(709\) −3.23862 −0.121629 −0.0608144 0.998149i \(-0.519370\pi\)
−0.0608144 + 0.998149i \(0.519370\pi\)
\(710\) 7.50688 0.281728
\(711\) 34.7990 1.30506
\(712\) −120.378 −4.51137
\(713\) 6.05309 0.226690
\(714\) 0.201925 0.00755684
\(715\) 9.54814 0.357080
\(716\) 115.459 4.31492
\(717\) −1.93260 −0.0721744
\(718\) 11.0337 0.411773
\(719\) −2.84703 −0.106176 −0.0530882 0.998590i \(-0.516906\pi\)
−0.0530882 + 0.998590i \(0.516906\pi\)
\(720\) −16.7491 −0.624203
\(721\) 5.37332 0.200113
\(722\) −13.1156 −0.488113
\(723\) 0.530184 0.0197177
\(724\) 41.7979 1.55341
\(725\) −14.9999 −0.557082
\(726\) −0.465358 −0.0172711
\(727\) −45.1722 −1.67535 −0.837673 0.546172i \(-0.816084\pi\)
−0.837673 + 0.546172i \(0.816084\pi\)
\(728\) −18.5750 −0.688436
\(729\) −25.8627 −0.957878
\(730\) −0.190772 −0.00706080
\(731\) 5.31702 0.196657
\(732\) −5.77848 −0.213579
\(733\) 9.18130 0.339119 0.169559 0.985520i \(-0.445766\pi\)
0.169559 + 0.985520i \(0.445766\pi\)
\(734\) −12.1056 −0.446828
\(735\) −0.524247 −0.0193371
\(736\) 93.1977 3.43531
\(737\) 24.4250 0.899707
\(738\) 61.8842 2.27799
\(739\) 38.5849 1.41937 0.709685 0.704519i \(-0.248837\pi\)
0.709685 + 0.704519i \(0.248837\pi\)
\(740\) −5.81835 −0.213887
\(741\) −3.66780 −0.134740
\(742\) −6.13356 −0.225170
\(743\) 7.31389 0.268321 0.134160 0.990960i \(-0.457166\pi\)
0.134160 + 0.990960i \(0.457166\pi\)
\(744\) 0.909153 0.0333312
\(745\) 5.49134 0.201187
\(746\) −77.7412 −2.84631
\(747\) −16.4127 −0.600510
\(748\) −19.5993 −0.716620
\(749\) 1.59216 0.0581763
\(750\) 1.97951 0.0722816
\(751\) −37.0356 −1.35145 −0.675725 0.737154i \(-0.736169\pi\)
−0.675725 + 0.737154i \(0.736169\pi\)
\(752\) 68.0188 2.48039
\(753\) 0.00265353 9.66999e−5 0
\(754\) −43.1286 −1.57065
\(755\) 1.19306 0.0434198
\(756\) −1.99979 −0.0727316
\(757\) −12.4669 −0.453118 −0.226559 0.973997i \(-0.572748\pi\)
−0.226559 + 0.973997i \(0.572748\pi\)
\(758\) −35.3030 −1.28226
\(759\) −3.83129 −0.139067
\(760\) 20.2045 0.732895
\(761\) −8.41470 −0.305033 −0.152516 0.988301i \(-0.548738\pi\)
−0.152516 + 0.988301i \(0.548738\pi\)
\(762\) −0.851633 −0.0308514
\(763\) 7.83860 0.283776
\(764\) −7.09130 −0.256554
\(765\) 1.79227 0.0647996
\(766\) −9.27987 −0.335295
\(767\) 43.3252 1.56438
\(768\) −1.25902 −0.0454311
\(769\) 19.2318 0.693517 0.346759 0.937954i \(-0.387282\pi\)
0.346759 + 0.937954i \(0.387282\pi\)
\(770\) −2.27109 −0.0818445
\(771\) 3.20738 0.115511
\(772\) −3.17048 −0.114108
\(773\) −26.0713 −0.937718 −0.468859 0.883273i \(-0.655335\pi\)
−0.468859 + 0.883273i \(0.655335\pi\)
\(774\) −36.8389 −1.32415
\(775\) 3.79169 0.136202
\(776\) −78.9316 −2.83348
\(777\) −0.149694 −0.00537024
\(778\) −29.8802 −1.07126
\(779\) −38.5899 −1.38263
\(780\) 1.96792 0.0704628
\(781\) −18.7462 −0.670793
\(782\) −22.5017 −0.804660
\(783\) −2.76663 −0.0988713
\(784\) −71.8537 −2.56620
\(785\) −6.25041 −0.223087
\(786\) 3.46721 0.123671
\(787\) 14.3786 0.512540 0.256270 0.966605i \(-0.417506\pi\)
0.256270 + 0.966605i \(0.417506\pi\)
\(788\) 33.9867 1.21073
\(789\) −1.53228 −0.0545508
\(790\) 16.3485 0.581654
\(791\) −0.0533770 −0.00189787
\(792\) 80.9113 2.87506
\(793\) −41.2874 −1.46616
\(794\) −54.2325 −1.92464
\(795\) 0.387188 0.0137321
\(796\) −24.8136 −0.879496
\(797\) 38.2513 1.35493 0.677465 0.735555i \(-0.263079\pi\)
0.677465 + 0.735555i \(0.263079\pi\)
\(798\) 0.872413 0.0308831
\(799\) −7.27846 −0.257494
\(800\) 58.3795 2.06403
\(801\) −46.1355 −1.63012
\(802\) −61.0523 −2.15583
\(803\) 0.476397 0.0168117
\(804\) 5.03412 0.177540
\(805\) −1.85693 −0.0654481
\(806\) 10.9021 0.384010
\(807\) −3.58381 −0.126156
\(808\) 85.7526 3.01677
\(809\) −47.7550 −1.67898 −0.839488 0.543378i \(-0.817145\pi\)
−0.839488 + 0.543378i \(0.817145\pi\)
\(810\) −12.3288 −0.433189
\(811\) −23.6336 −0.829888 −0.414944 0.909847i \(-0.636199\pi\)
−0.414944 + 0.909847i \(0.636199\pi\)
\(812\) 7.30577 0.256382
\(813\) −0.768440 −0.0269504
\(814\) 20.4019 0.715086
\(815\) −3.30364 −0.115721
\(816\) −1.74708 −0.0611600
\(817\) 22.9721 0.803692
\(818\) −4.20608 −0.147062
\(819\) −7.11895 −0.248756
\(820\) 20.7050 0.723050
\(821\) 54.4910 1.90175 0.950874 0.309579i \(-0.100188\pi\)
0.950874 + 0.309579i \(0.100188\pi\)
\(822\) −8.06211 −0.281198
\(823\) 10.6729 0.372036 0.186018 0.982546i \(-0.440442\pi\)
0.186018 + 0.982546i \(0.440442\pi\)
\(824\) −89.9349 −3.13303
\(825\) −2.39994 −0.0835552
\(826\) −10.3052 −0.358564
\(827\) 35.8210 1.24562 0.622809 0.782374i \(-0.285991\pi\)
0.622809 + 0.782374i \(0.285991\pi\)
\(828\) 111.030 3.85854
\(829\) 45.8189 1.59136 0.795678 0.605719i \(-0.207115\pi\)
0.795678 + 0.605719i \(0.207115\pi\)
\(830\) −7.71067 −0.267641
\(831\) 2.49058 0.0863974
\(832\) 58.8448 2.04008
\(833\) 7.68883 0.266402
\(834\) −3.13719 −0.108632
\(835\) 4.22418 0.146184
\(836\) −84.6783 −2.92866
\(837\) 0.699352 0.0241731
\(838\) −70.0330 −2.41925
\(839\) 28.6828 0.990241 0.495121 0.868824i \(-0.335124\pi\)
0.495121 + 0.868824i \(0.335124\pi\)
\(840\) −0.278904 −0.00962310
\(841\) −18.8928 −0.651474
\(842\) −23.5803 −0.812629
\(843\) −1.20058 −0.0413503
\(844\) −30.4729 −1.04892
\(845\) 7.15922 0.246285
\(846\) 50.4288 1.73378
\(847\) 0.563238 0.0193531
\(848\) 53.0683 1.82237
\(849\) −0.373911 −0.0128326
\(850\) −14.0952 −0.483461
\(851\) 16.6813 0.571828
\(852\) −3.86369 −0.132368
\(853\) −15.1726 −0.519499 −0.259749 0.965676i \(-0.583640\pi\)
−0.259749 + 0.965676i \(0.583640\pi\)
\(854\) 9.82050 0.336051
\(855\) 7.74347 0.264821
\(856\) −26.6485 −0.910828
\(857\) 31.7470 1.08446 0.542229 0.840231i \(-0.317580\pi\)
0.542229 + 0.840231i \(0.317580\pi\)
\(858\) −6.90046 −0.235578
\(859\) −9.38987 −0.320378 −0.160189 0.987086i \(-0.551210\pi\)
−0.160189 + 0.987086i \(0.551210\pi\)
\(860\) −12.3254 −0.420294
\(861\) 0.532696 0.0181542
\(862\) 31.6498 1.07800
\(863\) −36.4580 −1.24105 −0.620523 0.784188i \(-0.713080\pi\)
−0.620523 + 0.784188i \(0.713080\pi\)
\(864\) 10.7677 0.366325
\(865\) 5.85835 0.199190
\(866\) 33.8306 1.14961
\(867\) −2.28744 −0.0776856
\(868\) −1.84676 −0.0626831
\(869\) −40.8256 −1.38491
\(870\) −0.647576 −0.0219549
\(871\) 35.9689 1.21876
\(872\) −131.197 −4.44289
\(873\) −30.2509 −1.02384
\(874\) −97.2183 −3.28846
\(875\) −2.39586 −0.0809950
\(876\) 0.0981880 0.00331746
\(877\) 0.500309 0.0168942 0.00844712 0.999964i \(-0.497311\pi\)
0.00844712 + 0.999964i \(0.497311\pi\)
\(878\) 45.0469 1.52026
\(879\) 2.29111 0.0772771
\(880\) 19.6498 0.662394
\(881\) −49.6396 −1.67240 −0.836201 0.548423i \(-0.815228\pi\)
−0.836201 + 0.548423i \(0.815228\pi\)
\(882\) −53.2720 −1.79376
\(883\) 3.65213 0.122904 0.0614519 0.998110i \(-0.480427\pi\)
0.0614519 + 0.998110i \(0.480427\pi\)
\(884\) −28.8624 −0.970747
\(885\) 0.650528 0.0218673
\(886\) 37.6205 1.26389
\(887\) 16.4471 0.552240 0.276120 0.961123i \(-0.410951\pi\)
0.276120 + 0.961123i \(0.410951\pi\)
\(888\) 2.50547 0.0840782
\(889\) 1.03076 0.0345705
\(890\) −21.6744 −0.726527
\(891\) 30.7875 1.03142
\(892\) −7.91581 −0.265041
\(893\) −31.4465 −1.05232
\(894\) −3.96860 −0.132730
\(895\) 12.3868 0.414045
\(896\) −2.50482 −0.0836801
\(897\) −5.64206 −0.188383
\(898\) 103.261 3.44586
\(899\) −2.55492 −0.0852114
\(900\) 69.5495 2.31832
\(901\) −5.67866 −0.189184
\(902\) −72.6015 −2.41736
\(903\) −0.317108 −0.0105527
\(904\) 0.893388 0.0297136
\(905\) 4.48419 0.149060
\(906\) −0.862225 −0.0286455
\(907\) 24.4458 0.811709 0.405854 0.913938i \(-0.366974\pi\)
0.405854 + 0.913938i \(0.366974\pi\)
\(908\) 13.4495 0.446338
\(909\) 32.8650 1.09006
\(910\) −3.34447 −0.110868
\(911\) 52.9608 1.75467 0.877334 0.479880i \(-0.159320\pi\)
0.877334 + 0.479880i \(0.159320\pi\)
\(912\) −7.54822 −0.249947
\(913\) 19.2551 0.637252
\(914\) 68.3768 2.26170
\(915\) −0.619930 −0.0204943
\(916\) 104.614 3.45654
\(917\) −4.19647 −0.138579
\(918\) −2.59976 −0.0858050
\(919\) 20.5426 0.677638 0.338819 0.940852i \(-0.389973\pi\)
0.338819 + 0.940852i \(0.389973\pi\)
\(920\) 31.0800 1.02468
\(921\) −1.91510 −0.0631045
\(922\) −77.7701 −2.56122
\(923\) −27.6062 −0.908669
\(924\) 1.16890 0.0384541
\(925\) 10.4493 0.343570
\(926\) −13.5509 −0.445309
\(927\) −34.4679 −1.13207
\(928\) −39.3374 −1.29131
\(929\) 18.4959 0.606831 0.303416 0.952858i \(-0.401873\pi\)
0.303416 + 0.952858i \(0.401873\pi\)
\(930\) 0.163695 0.00536777
\(931\) 33.2195 1.08872
\(932\) −26.1062 −0.855139
\(933\) 0.532867 0.0174453
\(934\) 6.02908 0.197277
\(935\) −2.10266 −0.0687643
\(936\) 119.152 3.89461
\(937\) −30.8582 −1.00809 −0.504047 0.863676i \(-0.668156\pi\)
−0.504047 + 0.863676i \(0.668156\pi\)
\(938\) −8.55547 −0.279346
\(939\) −2.55902 −0.0835105
\(940\) 16.8723 0.550313
\(941\) 37.4581 1.22110 0.610550 0.791978i \(-0.290948\pi\)
0.610550 + 0.791978i \(0.290948\pi\)
\(942\) 4.51718 0.147178
\(943\) −59.3616 −1.93308
\(944\) 89.1620 2.90198
\(945\) −0.214542 −0.00697907
\(946\) 43.2188 1.40516
\(947\) 55.5568 1.80535 0.902676 0.430320i \(-0.141599\pi\)
0.902676 + 0.430320i \(0.141599\pi\)
\(948\) −8.41437 −0.273286
\(949\) 0.701555 0.0227735
\(950\) −60.8981 −1.97579
\(951\) −1.25693 −0.0407588
\(952\) 4.09053 0.132575
\(953\) 14.0637 0.455568 0.227784 0.973712i \(-0.426852\pi\)
0.227784 + 0.973712i \(0.426852\pi\)
\(954\) 39.3446 1.27383
\(955\) −0.760773 −0.0246180
\(956\) −65.7055 −2.12507
\(957\) 1.61713 0.0522744
\(958\) −45.5834 −1.47273
\(959\) 9.75782 0.315096
\(960\) 0.883555 0.0285166
\(961\) −30.3542 −0.979167
\(962\) 30.0443 0.968669
\(963\) −10.2132 −0.329114
\(964\) 18.0254 0.580560
\(965\) −0.340138 −0.0109494
\(966\) 1.34201 0.0431783
\(967\) 32.6962 1.05144 0.525720 0.850658i \(-0.323796\pi\)
0.525720 + 0.850658i \(0.323796\pi\)
\(968\) −9.42708 −0.302998
\(969\) 0.807711 0.0259474
\(970\) −14.2118 −0.456314
\(971\) −42.4585 −1.36256 −0.681278 0.732024i \(-0.738576\pi\)
−0.681278 + 0.732024i \(0.738576\pi\)
\(972\) 19.2646 0.617913
\(973\) 3.79704 0.121728
\(974\) −36.0694 −1.15574
\(975\) −3.53422 −0.113186
\(976\) −84.9682 −2.71977
\(977\) 21.5642 0.689898 0.344949 0.938621i \(-0.387896\pi\)
0.344949 + 0.938621i \(0.387896\pi\)
\(978\) 2.38754 0.0763452
\(979\) 54.1253 1.72985
\(980\) −17.8236 −0.569353
\(981\) −50.2818 −1.60537
\(982\) −30.1060 −0.960721
\(983\) 11.8067 0.376574 0.188287 0.982114i \(-0.439706\pi\)
0.188287 + 0.982114i \(0.439706\pi\)
\(984\) −8.91590 −0.284228
\(985\) 3.64618 0.116177
\(986\) 9.49764 0.302466
\(987\) 0.434089 0.0138172
\(988\) −124.699 −3.96722
\(989\) 35.3373 1.12366
\(990\) 14.5683 0.463010
\(991\) 16.9327 0.537886 0.268943 0.963156i \(-0.413326\pi\)
0.268943 + 0.963156i \(0.413326\pi\)
\(992\) 9.94374 0.315714
\(993\) 2.35597 0.0747646
\(994\) 6.56633 0.208271
\(995\) −2.66207 −0.0843933
\(996\) 3.96858 0.125749
\(997\) 21.6310 0.685061 0.342530 0.939507i \(-0.388716\pi\)
0.342530 + 0.939507i \(0.388716\pi\)
\(998\) −31.0845 −0.983962
\(999\) 1.92730 0.0609769
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 6007.2.a.c.1.7 261
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6007.2.a.c.1.7 261 1.1 even 1 trivial