Properties

Label 6017.2.a.e.1.9
Level $6017$
Weight $2$
Character 6017.1
Self dual yes
Analytic conductor $48.046$
Analytic rank $0$
Dimension $119$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6017,2,Mod(1,6017)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6017.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6017 = 11 \cdot 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6017.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: \(48.0459868962\)
Analytic rank: \(0\)
Dimension: \(119\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 6017.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.40399 q^{2} -2.26995 q^{3} +3.77918 q^{4} -1.51011 q^{5} +5.45695 q^{6} -2.08665 q^{7} -4.27714 q^{8} +2.15269 q^{9} +O(q^{10})\) \(q-2.40399 q^{2} -2.26995 q^{3} +3.77918 q^{4} -1.51011 q^{5} +5.45695 q^{6} -2.08665 q^{7} -4.27714 q^{8} +2.15269 q^{9} +3.63028 q^{10} +1.00000 q^{11} -8.57857 q^{12} +2.52148 q^{13} +5.01629 q^{14} +3.42787 q^{15} +2.72384 q^{16} -3.45087 q^{17} -5.17506 q^{18} -2.66540 q^{19} -5.70696 q^{20} +4.73660 q^{21} -2.40399 q^{22} -7.64641 q^{23} +9.70890 q^{24} -2.71958 q^{25} -6.06161 q^{26} +1.92335 q^{27} -7.88582 q^{28} -6.54517 q^{29} -8.24058 q^{30} -4.30054 q^{31} +2.00618 q^{32} -2.26995 q^{33} +8.29587 q^{34} +3.15106 q^{35} +8.13542 q^{36} +9.17839 q^{37} +6.40760 q^{38} -5.72364 q^{39} +6.45893 q^{40} -4.82899 q^{41} -11.3868 q^{42} +0.829704 q^{43} +3.77918 q^{44} -3.25080 q^{45} +18.3819 q^{46} -0.606466 q^{47} -6.18300 q^{48} -2.64589 q^{49} +6.53785 q^{50} +7.83332 q^{51} +9.52911 q^{52} +5.23353 q^{53} -4.62371 q^{54} -1.51011 q^{55} +8.92488 q^{56} +6.05034 q^{57} +15.7345 q^{58} -4.33952 q^{59} +12.9545 q^{60} -4.40105 q^{61} +10.3385 q^{62} -4.49192 q^{63} -10.2705 q^{64} -3.80770 q^{65} +5.45695 q^{66} +1.85979 q^{67} -13.0415 q^{68} +17.3570 q^{69} -7.57513 q^{70} -8.95640 q^{71} -9.20736 q^{72} -2.96845 q^{73} -22.0648 q^{74} +6.17332 q^{75} -10.0730 q^{76} -2.08665 q^{77} +13.7596 q^{78} +13.1655 q^{79} -4.11329 q^{80} -10.8240 q^{81} +11.6088 q^{82} +3.49794 q^{83} +17.9005 q^{84} +5.21118 q^{85} -1.99460 q^{86} +14.8572 q^{87} -4.27714 q^{88} -6.65752 q^{89} +7.81489 q^{90} -5.26144 q^{91} -28.8972 q^{92} +9.76203 q^{93} +1.45794 q^{94} +4.02504 q^{95} -4.55393 q^{96} -5.12048 q^{97} +6.36071 q^{98} +2.15269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.40399 −1.69988 −0.849940 0.526880i \(-0.823362\pi\)
−0.849940 + 0.526880i \(0.823362\pi\)
\(3\) −2.26995 −1.31056 −0.655279 0.755387i \(-0.727449\pi\)
−0.655279 + 0.755387i \(0.727449\pi\)
\(4\) 3.77918 1.88959
\(5\) −1.51011 −0.675340 −0.337670 0.941265i \(-0.609639\pi\)
−0.337670 + 0.941265i \(0.609639\pi\)
\(6\) 5.45695 2.22779
\(7\) −2.08665 −0.788679 −0.394340 0.918965i \(-0.629027\pi\)
−0.394340 + 0.918965i \(0.629027\pi\)
\(8\) −4.27714 −1.51220
\(9\) 2.15269 0.717565
\(10\) 3.63028 1.14800
\(11\) 1.00000 0.301511
\(12\) −8.57857 −2.47642
\(13\) 2.52148 0.699332 0.349666 0.936874i \(-0.386295\pi\)
0.349666 + 0.936874i \(0.386295\pi\)
\(14\) 5.01629 1.34066
\(15\) 3.42787 0.885073
\(16\) 2.72384 0.680960
\(17\) −3.45087 −0.836959 −0.418480 0.908226i \(-0.637437\pi\)
−0.418480 + 0.908226i \(0.637437\pi\)
\(18\) −5.17506 −1.21977
\(19\) −2.66540 −0.611485 −0.305742 0.952114i \(-0.598905\pi\)
−0.305742 + 0.952114i \(0.598905\pi\)
\(20\) −5.70696 −1.27612
\(21\) 4.73660 1.03361
\(22\) −2.40399 −0.512533
\(23\) −7.64641 −1.59439 −0.797193 0.603724i \(-0.793683\pi\)
−0.797193 + 0.603724i \(0.793683\pi\)
\(24\) 9.70890 1.98182
\(25\) −2.71958 −0.543916
\(26\) −6.06161 −1.18878
\(27\) 1.92335 0.370148
\(28\) −7.88582 −1.49028
\(29\) −6.54517 −1.21541 −0.607704 0.794164i \(-0.707909\pi\)
−0.607704 + 0.794164i \(0.707909\pi\)
\(30\) −8.24058 −1.50452
\(31\) −4.30054 −0.772399 −0.386200 0.922415i \(-0.626212\pi\)
−0.386200 + 0.922415i \(0.626212\pi\)
\(32\) 2.00618 0.354645
\(33\) −2.26995 −0.395148
\(34\) 8.29587 1.42273
\(35\) 3.15106 0.532627
\(36\) 8.13542 1.35590
\(37\) 9.17839 1.50892 0.754459 0.656347i \(-0.227899\pi\)
0.754459 + 0.656347i \(0.227899\pi\)
\(38\) 6.40760 1.03945
\(39\) −5.72364 −0.916515
\(40\) 6.45893 1.02125
\(41\) −4.82899 −0.754161 −0.377080 0.926181i \(-0.623072\pi\)
−0.377080 + 0.926181i \(0.623072\pi\)
\(42\) −11.3868 −1.75701
\(43\) 0.829704 0.126529 0.0632643 0.997997i \(-0.479849\pi\)
0.0632643 + 0.997997i \(0.479849\pi\)
\(44\) 3.77918 0.569733
\(45\) −3.25080 −0.484600
\(46\) 18.3819 2.71027
\(47\) −0.606466 −0.0884622 −0.0442311 0.999021i \(-0.514084\pi\)
−0.0442311 + 0.999021i \(0.514084\pi\)
\(48\) −6.18300 −0.892439
\(49\) −2.64589 −0.377985
\(50\) 6.53785 0.924592
\(51\) 7.83332 1.09688
\(52\) 9.52911 1.32145
\(53\) 5.23353 0.718881 0.359440 0.933168i \(-0.382968\pi\)
0.359440 + 0.933168i \(0.382968\pi\)
\(54\) −4.62371 −0.629207
\(55\) −1.51011 −0.203623
\(56\) 8.92488 1.19264
\(57\) 6.05034 0.801387
\(58\) 15.7345 2.06605
\(59\) −4.33952 −0.564958 −0.282479 0.959274i \(-0.591157\pi\)
−0.282479 + 0.959274i \(0.591157\pi\)
\(60\) 12.9545 1.67242
\(61\) −4.40105 −0.563497 −0.281748 0.959488i \(-0.590914\pi\)
−0.281748 + 0.959488i \(0.590914\pi\)
\(62\) 10.3385 1.31299
\(63\) −4.49192 −0.565928
\(64\) −10.2705 −1.28381
\(65\) −3.80770 −0.472287
\(66\) 5.45695 0.671705
\(67\) 1.85979 0.227210 0.113605 0.993526i \(-0.463760\pi\)
0.113605 + 0.993526i \(0.463760\pi\)
\(68\) −13.0415 −1.58151
\(69\) 17.3570 2.08954
\(70\) −7.57513 −0.905401
\(71\) −8.95640 −1.06293 −0.531464 0.847081i \(-0.678358\pi\)
−0.531464 + 0.847081i \(0.678358\pi\)
\(72\) −9.20736 −1.08510
\(73\) −2.96845 −0.347431 −0.173715 0.984796i \(-0.555577\pi\)
−0.173715 + 0.984796i \(0.555577\pi\)
\(74\) −22.0648 −2.56498
\(75\) 6.17332 0.712834
\(76\) −10.0730 −1.15546
\(77\) −2.08665 −0.237796
\(78\) 13.7596 1.55797
\(79\) 13.1655 1.48124 0.740618 0.671926i \(-0.234533\pi\)
0.740618 + 0.671926i \(0.234533\pi\)
\(80\) −4.11329 −0.459880
\(81\) −10.8240 −1.20267
\(82\) 11.6088 1.28198
\(83\) 3.49794 0.383949 0.191974 0.981400i \(-0.438511\pi\)
0.191974 + 0.981400i \(0.438511\pi\)
\(84\) 17.9005 1.95310
\(85\) 5.21118 0.565232
\(86\) −1.99460 −0.215084
\(87\) 14.8572 1.59286
\(88\) −4.27714 −0.455944
\(89\) −6.65752 −0.705696 −0.352848 0.935681i \(-0.614787\pi\)
−0.352848 + 0.935681i \(0.614787\pi\)
\(90\) 7.81489 0.823761
\(91\) −5.26144 −0.551548
\(92\) −28.8972 −3.01274
\(93\) 9.76203 1.01227
\(94\) 1.45794 0.150375
\(95\) 4.02504 0.412960
\(96\) −4.55393 −0.464783
\(97\) −5.12048 −0.519906 −0.259953 0.965621i \(-0.583707\pi\)
−0.259953 + 0.965621i \(0.583707\pi\)
\(98\) 6.36071 0.642528
\(99\) 2.15269 0.216354
\(100\) −10.2778 −1.02778
\(101\) −9.99545 −0.994585 −0.497292 0.867583i \(-0.665672\pi\)
−0.497292 + 0.867583i \(0.665672\pi\)
\(102\) −18.8312 −1.86457
\(103\) 10.8870 1.07273 0.536366 0.843986i \(-0.319797\pi\)
0.536366 + 0.843986i \(0.319797\pi\)
\(104\) −10.7847 −1.05753
\(105\) −7.15277 −0.698039
\(106\) −12.5814 −1.22201
\(107\) 10.3963 1.00505 0.502526 0.864562i \(-0.332404\pi\)
0.502526 + 0.864562i \(0.332404\pi\)
\(108\) 7.26867 0.699429
\(109\) −18.4807 −1.77013 −0.885065 0.465468i \(-0.845886\pi\)
−0.885065 + 0.465468i \(0.845886\pi\)
\(110\) 3.63028 0.346134
\(111\) −20.8345 −1.97753
\(112\) −5.68370 −0.537059
\(113\) −18.0313 −1.69624 −0.848119 0.529805i \(-0.822265\pi\)
−0.848119 + 0.529805i \(0.822265\pi\)
\(114\) −14.5450 −1.36226
\(115\) 11.5469 1.07675
\(116\) −24.7354 −2.29662
\(117\) 5.42797 0.501816
\(118\) 10.4322 0.960360
\(119\) 7.20076 0.660093
\(120\) −14.6615 −1.33840
\(121\) 1.00000 0.0909091
\(122\) 10.5801 0.957876
\(123\) 10.9616 0.988372
\(124\) −16.2525 −1.45952
\(125\) 11.6574 1.04267
\(126\) 10.7985 0.962010
\(127\) −17.9343 −1.59141 −0.795706 0.605683i \(-0.792900\pi\)
−0.795706 + 0.605683i \(0.792900\pi\)
\(128\) 20.6779 1.82768
\(129\) −1.88339 −0.165823
\(130\) 9.15367 0.802830
\(131\) −12.7359 −1.11274 −0.556370 0.830935i \(-0.687806\pi\)
−0.556370 + 0.830935i \(0.687806\pi\)
\(132\) −8.57857 −0.746668
\(133\) 5.56176 0.482266
\(134\) −4.47093 −0.386229
\(135\) −2.90446 −0.249976
\(136\) 14.7598 1.26565
\(137\) −8.49771 −0.726008 −0.363004 0.931788i \(-0.618249\pi\)
−0.363004 + 0.931788i \(0.618249\pi\)
\(138\) −41.7261 −3.55196
\(139\) −8.78959 −0.745523 −0.372762 0.927927i \(-0.621589\pi\)
−0.372762 + 0.927927i \(0.621589\pi\)
\(140\) 11.9084 1.00645
\(141\) 1.37665 0.115935
\(142\) 21.5311 1.80685
\(143\) 2.52148 0.210856
\(144\) 5.86360 0.488633
\(145\) 9.88390 0.820813
\(146\) 7.13613 0.590590
\(147\) 6.00606 0.495371
\(148\) 34.6868 2.85124
\(149\) −11.3902 −0.933121 −0.466560 0.884489i \(-0.654507\pi\)
−0.466560 + 0.884489i \(0.654507\pi\)
\(150\) −14.8406 −1.21173
\(151\) −11.5394 −0.939065 −0.469533 0.882915i \(-0.655578\pi\)
−0.469533 + 0.882915i \(0.655578\pi\)
\(152\) 11.4003 0.924685
\(153\) −7.42867 −0.600572
\(154\) 5.01629 0.404224
\(155\) 6.49427 0.521632
\(156\) −21.6307 −1.73184
\(157\) −0.372088 −0.0296959 −0.0148479 0.999890i \(-0.504726\pi\)
−0.0148479 + 0.999890i \(0.504726\pi\)
\(158\) −31.6498 −2.51792
\(159\) −11.8799 −0.942135
\(160\) −3.02954 −0.239506
\(161\) 15.9554 1.25746
\(162\) 26.0208 2.04439
\(163\) −22.4248 −1.75645 −0.878224 0.478249i \(-0.841272\pi\)
−0.878224 + 0.478249i \(0.841272\pi\)
\(164\) −18.2496 −1.42505
\(165\) 3.42787 0.266859
\(166\) −8.40902 −0.652666
\(167\) 7.77964 0.602006 0.301003 0.953623i \(-0.402679\pi\)
0.301003 + 0.953623i \(0.402679\pi\)
\(168\) −20.2591 −1.56302
\(169\) −6.64216 −0.510935
\(170\) −12.5276 −0.960826
\(171\) −5.73779 −0.438780
\(172\) 3.13560 0.239087
\(173\) 20.9192 1.59045 0.795227 0.606312i \(-0.207352\pi\)
0.795227 + 0.606312i \(0.207352\pi\)
\(174\) −35.7167 −2.70768
\(175\) 5.67481 0.428975
\(176\) 2.72384 0.205317
\(177\) 9.85052 0.740410
\(178\) 16.0046 1.19960
\(179\) 7.64198 0.571188 0.285594 0.958351i \(-0.407809\pi\)
0.285594 + 0.958351i \(0.407809\pi\)
\(180\) −12.2853 −0.915695
\(181\) 9.54483 0.709461 0.354731 0.934969i \(-0.384573\pi\)
0.354731 + 0.934969i \(0.384573\pi\)
\(182\) 12.6485 0.937566
\(183\) 9.99018 0.738496
\(184\) 32.7047 2.41102
\(185\) −13.8603 −1.01903
\(186\) −23.4678 −1.72075
\(187\) −3.45087 −0.252353
\(188\) −2.29195 −0.167157
\(189\) −4.01335 −0.291928
\(190\) −9.67616 −0.701983
\(191\) −15.1850 −1.09875 −0.549373 0.835577i \(-0.685133\pi\)
−0.549373 + 0.835577i \(0.685133\pi\)
\(192\) 23.3136 1.68251
\(193\) 9.37732 0.674994 0.337497 0.941327i \(-0.390420\pi\)
0.337497 + 0.941327i \(0.390420\pi\)
\(194\) 12.3096 0.883778
\(195\) 8.64330 0.618959
\(196\) −9.99931 −0.714236
\(197\) −24.6276 −1.75464 −0.877322 0.479902i \(-0.840672\pi\)
−0.877322 + 0.479902i \(0.840672\pi\)
\(198\) −5.17506 −0.367775
\(199\) −4.21845 −0.299038 −0.149519 0.988759i \(-0.547772\pi\)
−0.149519 + 0.988759i \(0.547772\pi\)
\(200\) 11.6320 0.822508
\(201\) −4.22164 −0.297772
\(202\) 24.0290 1.69067
\(203\) 13.6575 0.958567
\(204\) 29.6035 2.07266
\(205\) 7.29228 0.509315
\(206\) −26.1723 −1.82351
\(207\) −16.4604 −1.14408
\(208\) 6.86810 0.476217
\(209\) −2.66540 −0.184370
\(210\) 17.1952 1.18658
\(211\) 23.3921 1.61038 0.805189 0.593019i \(-0.202064\pi\)
0.805189 + 0.593019i \(0.202064\pi\)
\(212\) 19.7785 1.35839
\(213\) 20.3306 1.39303
\(214\) −24.9927 −1.70847
\(215\) −1.25294 −0.0854499
\(216\) −8.22642 −0.559737
\(217\) 8.97372 0.609176
\(218\) 44.4275 3.00901
\(219\) 6.73824 0.455328
\(220\) −5.70696 −0.384763
\(221\) −8.70129 −0.585312
\(222\) 50.0861 3.36156
\(223\) 20.2933 1.35894 0.679471 0.733702i \(-0.262209\pi\)
0.679471 + 0.733702i \(0.262209\pi\)
\(224\) −4.18619 −0.279701
\(225\) −5.85442 −0.390295
\(226\) 43.3470 2.88340
\(227\) −22.0826 −1.46568 −0.732838 0.680403i \(-0.761805\pi\)
−0.732838 + 0.680403i \(0.761805\pi\)
\(228\) 22.8653 1.51429
\(229\) −16.7997 −1.11016 −0.555078 0.831798i \(-0.687312\pi\)
−0.555078 + 0.831798i \(0.687312\pi\)
\(230\) −27.7586 −1.83035
\(231\) 4.73660 0.311645
\(232\) 27.9946 1.83793
\(233\) 9.29069 0.608653 0.304327 0.952568i \(-0.401569\pi\)
0.304327 + 0.952568i \(0.401569\pi\)
\(234\) −13.0488 −0.853026
\(235\) 0.915828 0.0597421
\(236\) −16.3998 −1.06754
\(237\) −29.8851 −1.94125
\(238\) −17.3106 −1.12208
\(239\) −25.8064 −1.66928 −0.834638 0.550799i \(-0.814323\pi\)
−0.834638 + 0.550799i \(0.814323\pi\)
\(240\) 9.33698 0.602699
\(241\) −23.9305 −1.54150 −0.770750 0.637138i \(-0.780118\pi\)
−0.770750 + 0.637138i \(0.780118\pi\)
\(242\) −2.40399 −0.154534
\(243\) 18.7999 1.20602
\(244\) −16.6324 −1.06478
\(245\) 3.99558 0.255268
\(246\) −26.3516 −1.68011
\(247\) −6.72074 −0.427631
\(248\) 18.3940 1.16802
\(249\) −7.94016 −0.503187
\(250\) −28.0243 −1.77241
\(251\) 17.0822 1.07822 0.539110 0.842235i \(-0.318761\pi\)
0.539110 + 0.842235i \(0.318761\pi\)
\(252\) −16.9758 −1.06937
\(253\) −7.64641 −0.480726
\(254\) 43.1139 2.70521
\(255\) −11.8291 −0.740770
\(256\) −29.1685 −1.82303
\(257\) −30.5627 −1.90645 −0.953223 0.302268i \(-0.902256\pi\)
−0.953223 + 0.302268i \(0.902256\pi\)
\(258\) 4.52766 0.281880
\(259\) −19.1521 −1.19005
\(260\) −14.3900 −0.892428
\(261\) −14.0897 −0.872133
\(262\) 30.6170 1.89152
\(263\) −20.5830 −1.26920 −0.634600 0.772841i \(-0.718835\pi\)
−0.634600 + 0.772841i \(0.718835\pi\)
\(264\) 9.70890 0.597542
\(265\) −7.90319 −0.485489
\(266\) −13.3704 −0.819793
\(267\) 15.1123 0.924856
\(268\) 7.02849 0.429333
\(269\) −18.2785 −1.11446 −0.557230 0.830358i \(-0.688136\pi\)
−0.557230 + 0.830358i \(0.688136\pi\)
\(270\) 6.98229 0.424929
\(271\) −5.31546 −0.322891 −0.161446 0.986882i \(-0.551616\pi\)
−0.161446 + 0.986882i \(0.551616\pi\)
\(272\) −9.39963 −0.569936
\(273\) 11.9432 0.722837
\(274\) 20.4284 1.23413
\(275\) −2.71958 −0.163997
\(276\) 65.5952 3.94837
\(277\) 1.32154 0.0794034 0.0397017 0.999212i \(-0.487359\pi\)
0.0397017 + 0.999212i \(0.487359\pi\)
\(278\) 21.1301 1.26730
\(279\) −9.25774 −0.554246
\(280\) −13.4775 −0.805436
\(281\) 28.2381 1.68454 0.842271 0.539055i \(-0.181218\pi\)
0.842271 + 0.539055i \(0.181218\pi\)
\(282\) −3.30946 −0.197075
\(283\) 8.30176 0.493488 0.246744 0.969081i \(-0.420639\pi\)
0.246744 + 0.969081i \(0.420639\pi\)
\(284\) −33.8478 −2.00850
\(285\) −9.13665 −0.541209
\(286\) −6.06161 −0.358430
\(287\) 10.0764 0.594791
\(288\) 4.31868 0.254481
\(289\) −5.09149 −0.299499
\(290\) −23.7608 −1.39528
\(291\) 11.6233 0.681368
\(292\) −11.2183 −0.656501
\(293\) −30.3495 −1.77304 −0.886518 0.462693i \(-0.846883\pi\)
−0.886518 + 0.462693i \(0.846883\pi\)
\(294\) −14.4385 −0.842071
\(295\) 6.55314 0.381539
\(296\) −39.2572 −2.28178
\(297\) 1.92335 0.111604
\(298\) 27.3819 1.58619
\(299\) −19.2802 −1.11501
\(300\) 23.3301 1.34696
\(301\) −1.73130 −0.0997906
\(302\) 27.7407 1.59630
\(303\) 22.6892 1.30346
\(304\) −7.26013 −0.416397
\(305\) 6.64605 0.380552
\(306\) 17.8585 1.02090
\(307\) 20.6568 1.17895 0.589473 0.807788i \(-0.299335\pi\)
0.589473 + 0.807788i \(0.299335\pi\)
\(308\) −7.88582 −0.449337
\(309\) −24.7131 −1.40588
\(310\) −15.6122 −0.886712
\(311\) −30.1829 −1.71151 −0.855757 0.517379i \(-0.826908\pi\)
−0.855757 + 0.517379i \(0.826908\pi\)
\(312\) 24.4808 1.38595
\(313\) −30.0485 −1.69844 −0.849221 0.528037i \(-0.822928\pi\)
−0.849221 + 0.528037i \(0.822928\pi\)
\(314\) 0.894497 0.0504794
\(315\) 6.78327 0.382194
\(316\) 49.7548 2.79893
\(317\) −8.02485 −0.450721 −0.225360 0.974275i \(-0.572356\pi\)
−0.225360 + 0.974275i \(0.572356\pi\)
\(318\) 28.5591 1.60152
\(319\) −6.54517 −0.366459
\(320\) 15.5096 0.867011
\(321\) −23.5992 −1.31718
\(322\) −38.3566 −2.13753
\(323\) 9.19796 0.511788
\(324\) −40.9058 −2.27255
\(325\) −6.85736 −0.380378
\(326\) 53.9091 2.98575
\(327\) 41.9503 2.31986
\(328\) 20.6542 1.14044
\(329\) 1.26548 0.0697683
\(330\) −8.24058 −0.453629
\(331\) 18.3426 1.00820 0.504099 0.863646i \(-0.331825\pi\)
0.504099 + 0.863646i \(0.331825\pi\)
\(332\) 13.2193 0.725506
\(333\) 19.7583 1.08275
\(334\) −18.7022 −1.02334
\(335\) −2.80848 −0.153444
\(336\) 12.9017 0.703848
\(337\) −9.26795 −0.504857 −0.252429 0.967616i \(-0.581229\pi\)
−0.252429 + 0.967616i \(0.581229\pi\)
\(338\) 15.9677 0.868528
\(339\) 40.9302 2.22302
\(340\) 19.6940 1.06806
\(341\) −4.30054 −0.232887
\(342\) 13.7936 0.745873
\(343\) 20.1276 1.08679
\(344\) −3.54876 −0.191336
\(345\) −26.2109 −1.41115
\(346\) −50.2895 −2.70358
\(347\) −19.1148 −1.02614 −0.513068 0.858348i \(-0.671491\pi\)
−0.513068 + 0.858348i \(0.671491\pi\)
\(348\) 56.1482 3.00986
\(349\) 31.9173 1.70849 0.854246 0.519869i \(-0.174019\pi\)
0.854246 + 0.519869i \(0.174019\pi\)
\(350\) −13.6422 −0.729206
\(351\) 4.84967 0.258856
\(352\) 2.00618 0.106930
\(353\) −15.1290 −0.805234 −0.402617 0.915369i \(-0.631899\pi\)
−0.402617 + 0.915369i \(0.631899\pi\)
\(354\) −23.6806 −1.25861
\(355\) 13.5251 0.717838
\(356\) −25.1600 −1.33348
\(357\) −16.3454 −0.865090
\(358\) −18.3713 −0.970951
\(359\) −18.0070 −0.950372 −0.475186 0.879885i \(-0.657619\pi\)
−0.475186 + 0.879885i \(0.657619\pi\)
\(360\) 13.9041 0.732810
\(361\) −11.8956 −0.626086
\(362\) −22.9457 −1.20600
\(363\) −2.26995 −0.119142
\(364\) −19.8839 −1.04220
\(365\) 4.48267 0.234634
\(366\) −24.0163 −1.25535
\(367\) 17.0362 0.889283 0.444641 0.895709i \(-0.353331\pi\)
0.444641 + 0.895709i \(0.353331\pi\)
\(368\) −20.8276 −1.08571
\(369\) −10.3953 −0.541159
\(370\) 33.3202 1.73223
\(371\) −10.9205 −0.566966
\(372\) 36.8925 1.91278
\(373\) −28.6584 −1.48388 −0.741938 0.670469i \(-0.766093\pi\)
−0.741938 + 0.670469i \(0.766093\pi\)
\(374\) 8.29587 0.428969
\(375\) −26.4617 −1.36648
\(376\) 2.59394 0.133772
\(377\) −16.5035 −0.849973
\(378\) 9.64807 0.496243
\(379\) 23.3996 1.20196 0.600978 0.799265i \(-0.294778\pi\)
0.600978 + 0.799265i \(0.294778\pi\)
\(380\) 15.2113 0.780325
\(381\) 40.7101 2.08564
\(382\) 36.5045 1.86773
\(383\) −30.3914 −1.55293 −0.776464 0.630161i \(-0.782989\pi\)
−0.776464 + 0.630161i \(0.782989\pi\)
\(384\) −46.9379 −2.39529
\(385\) 3.15106 0.160593
\(386\) −22.5430 −1.14741
\(387\) 1.78610 0.0907925
\(388\) −19.3512 −0.982410
\(389\) 25.0239 1.26876 0.634381 0.773020i \(-0.281255\pi\)
0.634381 + 0.773020i \(0.281255\pi\)
\(390\) −20.7784 −1.05216
\(391\) 26.3868 1.33444
\(392\) 11.3168 0.571587
\(393\) 28.9099 1.45831
\(394\) 59.2046 2.98268
\(395\) −19.8813 −1.00034
\(396\) 8.13542 0.408820
\(397\) −28.9668 −1.45380 −0.726902 0.686741i \(-0.759041\pi\)
−0.726902 + 0.686741i \(0.759041\pi\)
\(398\) 10.1411 0.508328
\(399\) −12.6249 −0.632037
\(400\) −7.40771 −0.370385
\(401\) −7.85044 −0.392032 −0.196016 0.980601i \(-0.562801\pi\)
−0.196016 + 0.980601i \(0.562801\pi\)
\(402\) 10.1488 0.506176
\(403\) −10.8437 −0.540163
\(404\) −37.7746 −1.87936
\(405\) 16.3454 0.812208
\(406\) −32.8325 −1.62945
\(407\) 9.17839 0.454956
\(408\) −33.5042 −1.65870
\(409\) 7.27346 0.359650 0.179825 0.983699i \(-0.442447\pi\)
0.179825 + 0.983699i \(0.442447\pi\)
\(410\) −17.5306 −0.865774
\(411\) 19.2894 0.951476
\(412\) 41.1441 2.02702
\(413\) 9.05506 0.445571
\(414\) 39.5706 1.94479
\(415\) −5.28226 −0.259296
\(416\) 5.05852 0.248015
\(417\) 19.9520 0.977052
\(418\) 6.40760 0.313406
\(419\) 13.7486 0.671661 0.335831 0.941922i \(-0.390983\pi\)
0.335831 + 0.941922i \(0.390983\pi\)
\(420\) −27.0316 −1.31901
\(421\) 10.2897 0.501487 0.250744 0.968053i \(-0.419325\pi\)
0.250744 + 0.968053i \(0.419325\pi\)
\(422\) −56.2344 −2.73745
\(423\) −1.30554 −0.0634773
\(424\) −22.3845 −1.08709
\(425\) 9.38492 0.455236
\(426\) −48.8746 −2.36798
\(427\) 9.18345 0.444418
\(428\) 39.2896 1.89914
\(429\) −5.72364 −0.276340
\(430\) 3.01206 0.145254
\(431\) 9.22181 0.444199 0.222099 0.975024i \(-0.428709\pi\)
0.222099 + 0.975024i \(0.428709\pi\)
\(432\) 5.23889 0.252056
\(433\) −12.1809 −0.585375 −0.292688 0.956208i \(-0.594550\pi\)
−0.292688 + 0.956208i \(0.594550\pi\)
\(434\) −21.5727 −1.03553
\(435\) −22.4360 −1.07572
\(436\) −69.8419 −3.34482
\(437\) 20.3808 0.974943
\(438\) −16.1987 −0.774003
\(439\) −14.9755 −0.714741 −0.357370 0.933963i \(-0.616327\pi\)
−0.357370 + 0.933963i \(0.616327\pi\)
\(440\) 6.45893 0.307917
\(441\) −5.69580 −0.271228
\(442\) 20.9178 0.994960
\(443\) −29.7636 −1.41411 −0.707055 0.707158i \(-0.749977\pi\)
−0.707055 + 0.707158i \(0.749977\pi\)
\(444\) −78.7375 −3.73671
\(445\) 10.0536 0.476585
\(446\) −48.7850 −2.31004
\(447\) 25.8552 1.22291
\(448\) 21.4310 1.01252
\(449\) 40.6067 1.91635 0.958175 0.286182i \(-0.0923863\pi\)
0.958175 + 0.286182i \(0.0923863\pi\)
\(450\) 14.0740 0.663454
\(451\) −4.82899 −0.227388
\(452\) −68.1434 −3.20520
\(453\) 26.1940 1.23070
\(454\) 53.0865 2.49147
\(455\) 7.94533 0.372483
\(456\) −25.8781 −1.21185
\(457\) 25.2577 1.18150 0.590752 0.806853i \(-0.298831\pi\)
0.590752 + 0.806853i \(0.298831\pi\)
\(458\) 40.3864 1.88713
\(459\) −6.63722 −0.309799
\(460\) 43.6378 2.03462
\(461\) 33.0679 1.54013 0.770064 0.637967i \(-0.220224\pi\)
0.770064 + 0.637967i \(0.220224\pi\)
\(462\) −11.3868 −0.529760
\(463\) −10.5726 −0.491350 −0.245675 0.969352i \(-0.579010\pi\)
−0.245675 + 0.969352i \(0.579010\pi\)
\(464\) −17.8280 −0.827644
\(465\) −14.7417 −0.683630
\(466\) −22.3347 −1.03464
\(467\) −13.2070 −0.611146 −0.305573 0.952169i \(-0.598848\pi\)
−0.305573 + 0.952169i \(0.598848\pi\)
\(468\) 20.5133 0.948226
\(469\) −3.88073 −0.179196
\(470\) −2.20164 −0.101554
\(471\) 0.844623 0.0389182
\(472\) 18.5607 0.854327
\(473\) 0.829704 0.0381498
\(474\) 71.8436 3.29989
\(475\) 7.24877 0.332596
\(476\) 27.2130 1.24730
\(477\) 11.2662 0.515843
\(478\) 62.0383 2.83757
\(479\) −35.2765 −1.61183 −0.805913 0.592034i \(-0.798325\pi\)
−0.805913 + 0.592034i \(0.798325\pi\)
\(480\) 6.87691 0.313887
\(481\) 23.1431 1.05523
\(482\) 57.5288 2.62036
\(483\) −36.2180 −1.64798
\(484\) 3.77918 0.171781
\(485\) 7.73247 0.351114
\(486\) −45.1949 −2.05008
\(487\) 29.2891 1.32721 0.663607 0.748081i \(-0.269025\pi\)
0.663607 + 0.748081i \(0.269025\pi\)
\(488\) 18.8239 0.852117
\(489\) 50.9033 2.30193
\(490\) −9.60534 −0.433925
\(491\) −8.88302 −0.400885 −0.200443 0.979705i \(-0.564238\pi\)
−0.200443 + 0.979705i \(0.564238\pi\)
\(492\) 41.4258 1.86762
\(493\) 22.5865 1.01725
\(494\) 16.1566 0.726921
\(495\) −3.25080 −0.146112
\(496\) −11.7140 −0.525973
\(497\) 18.6889 0.838310
\(498\) 19.0881 0.855358
\(499\) 26.4315 1.18324 0.591618 0.806218i \(-0.298489\pi\)
0.591618 + 0.806218i \(0.298489\pi\)
\(500\) 44.0554 1.97022
\(501\) −17.6594 −0.788965
\(502\) −41.0655 −1.83284
\(503\) 15.3632 0.685013 0.342507 0.939515i \(-0.388724\pi\)
0.342507 + 0.939515i \(0.388724\pi\)
\(504\) 19.2125 0.855795
\(505\) 15.0942 0.671683
\(506\) 18.3819 0.817176
\(507\) 15.0774 0.669611
\(508\) −67.7770 −3.00712
\(509\) 15.2410 0.675547 0.337774 0.941227i \(-0.390326\pi\)
0.337774 + 0.941227i \(0.390326\pi\)
\(510\) 28.4372 1.25922
\(511\) 6.19411 0.274011
\(512\) 28.7650 1.27124
\(513\) −5.12649 −0.226340
\(514\) 73.4724 3.24073
\(515\) −16.4406 −0.724458
\(516\) −7.11767 −0.313338
\(517\) −0.606466 −0.0266724
\(518\) 46.0415 2.02295
\(519\) −47.4855 −2.08438
\(520\) 16.2860 0.714190
\(521\) −37.5200 −1.64378 −0.821890 0.569646i \(-0.807080\pi\)
−0.821890 + 0.569646i \(0.807080\pi\)
\(522\) 33.8716 1.48252
\(523\) 36.1966 1.58277 0.791384 0.611319i \(-0.209361\pi\)
0.791384 + 0.611319i \(0.209361\pi\)
\(524\) −48.1312 −2.10262
\(525\) −12.8816 −0.562198
\(526\) 49.4813 2.15749
\(527\) 14.8406 0.646467
\(528\) −6.18300 −0.269080
\(529\) 35.4676 1.54207
\(530\) 18.9992 0.825272
\(531\) −9.34166 −0.405394
\(532\) 21.0189 0.911284
\(533\) −12.1762 −0.527408
\(534\) −36.3298 −1.57214
\(535\) −15.6996 −0.678751
\(536\) −7.95458 −0.343586
\(537\) −17.3469 −0.748576
\(538\) 43.9414 1.89445
\(539\) −2.64589 −0.113967
\(540\) −10.9765 −0.472352
\(541\) −13.5138 −0.581003 −0.290501 0.956875i \(-0.593822\pi\)
−0.290501 + 0.956875i \(0.593822\pi\)
\(542\) 12.7783 0.548876
\(543\) −21.6663 −0.929791
\(544\) −6.92306 −0.296824
\(545\) 27.9078 1.19544
\(546\) −28.7114 −1.22874
\(547\) −1.00000 −0.0427569
\(548\) −32.1144 −1.37186
\(549\) −9.47411 −0.404345
\(550\) 6.53785 0.278775
\(551\) 17.4455 0.743203
\(552\) −74.2383 −3.15979
\(553\) −27.4718 −1.16822
\(554\) −3.17696 −0.134976
\(555\) 31.4624 1.33550
\(556\) −33.2174 −1.40873
\(557\) 19.9686 0.846096 0.423048 0.906107i \(-0.360960\pi\)
0.423048 + 0.906107i \(0.360960\pi\)
\(558\) 22.2555 0.942152
\(559\) 2.09208 0.0884855
\(560\) 8.58299 0.362698
\(561\) 7.83332 0.330723
\(562\) −67.8841 −2.86352
\(563\) 33.3850 1.40701 0.703506 0.710690i \(-0.251617\pi\)
0.703506 + 0.710690i \(0.251617\pi\)
\(564\) 5.20261 0.219070
\(565\) 27.2291 1.14554
\(566\) −19.9574 −0.838871
\(567\) 22.5859 0.948518
\(568\) 38.3077 1.60736
\(569\) 38.8166 1.62728 0.813638 0.581371i \(-0.197484\pi\)
0.813638 + 0.581371i \(0.197484\pi\)
\(570\) 21.9644 0.919989
\(571\) 13.4426 0.562557 0.281279 0.959626i \(-0.409242\pi\)
0.281279 + 0.959626i \(0.409242\pi\)
\(572\) 9.52911 0.398432
\(573\) 34.4692 1.43997
\(574\) −24.2236 −1.01107
\(575\) 20.7950 0.867213
\(576\) −22.1093 −0.921220
\(577\) −12.4689 −0.519087 −0.259544 0.965731i \(-0.583572\pi\)
−0.259544 + 0.965731i \(0.583572\pi\)
\(578\) 12.2399 0.509113
\(579\) −21.2861 −0.884620
\(580\) 37.3530 1.55100
\(581\) −7.29897 −0.302812
\(582\) −27.9422 −1.15824
\(583\) 5.23353 0.216751
\(584\) 12.6965 0.525383
\(585\) −8.19680 −0.338896
\(586\) 72.9600 3.01395
\(587\) 29.6787 1.22497 0.612485 0.790482i \(-0.290170\pi\)
0.612485 + 0.790482i \(0.290170\pi\)
\(588\) 22.6980 0.936049
\(589\) 11.4627 0.472311
\(590\) −15.7537 −0.648570
\(591\) 55.9035 2.29956
\(592\) 25.0005 1.02751
\(593\) −28.0727 −1.15281 −0.576405 0.817165i \(-0.695545\pi\)
−0.576405 + 0.817165i \(0.695545\pi\)
\(594\) −4.62371 −0.189713
\(595\) −10.8739 −0.445787
\(596\) −43.0456 −1.76322
\(597\) 9.57568 0.391906
\(598\) 46.3496 1.89537
\(599\) −22.1345 −0.904392 −0.452196 0.891919i \(-0.649359\pi\)
−0.452196 + 0.891919i \(0.649359\pi\)
\(600\) −26.4041 −1.07794
\(601\) 37.8548 1.54413 0.772064 0.635544i \(-0.219224\pi\)
0.772064 + 0.635544i \(0.219224\pi\)
\(602\) 4.16204 0.169632
\(603\) 4.00356 0.163038
\(604\) −43.6096 −1.77445
\(605\) −1.51011 −0.0613945
\(606\) −54.5447 −2.21573
\(607\) 23.2774 0.944802 0.472401 0.881384i \(-0.343387\pi\)
0.472401 + 0.881384i \(0.343387\pi\)
\(608\) −5.34726 −0.216860
\(609\) −31.0018 −1.25626
\(610\) −15.9771 −0.646892
\(611\) −1.52919 −0.0618644
\(612\) −28.0743 −1.13484
\(613\) −22.6455 −0.914644 −0.457322 0.889301i \(-0.651191\pi\)
−0.457322 + 0.889301i \(0.651191\pi\)
\(614\) −49.6588 −2.00407
\(615\) −16.5531 −0.667487
\(616\) 8.92488 0.359594
\(617\) 30.0028 1.20787 0.603934 0.797034i \(-0.293599\pi\)
0.603934 + 0.797034i \(0.293599\pi\)
\(618\) 59.4100 2.38982
\(619\) 4.04243 0.162479 0.0812395 0.996695i \(-0.474112\pi\)
0.0812395 + 0.996695i \(0.474112\pi\)
\(620\) 24.5430 0.985671
\(621\) −14.7067 −0.590160
\(622\) 72.5594 2.90937
\(623\) 13.8919 0.556568
\(624\) −15.5903 −0.624111
\(625\) −4.00598 −0.160239
\(626\) 72.2364 2.88715
\(627\) 6.05034 0.241627
\(628\) −1.40619 −0.0561130
\(629\) −31.6735 −1.26290
\(630\) −16.3069 −0.649684
\(631\) −32.5121 −1.29429 −0.647144 0.762368i \(-0.724037\pi\)
−0.647144 + 0.762368i \(0.724037\pi\)
\(632\) −56.3107 −2.23992
\(633\) −53.0990 −2.11049
\(634\) 19.2917 0.766171
\(635\) 27.0827 1.07474
\(636\) −44.8962 −1.78025
\(637\) −6.67156 −0.264337
\(638\) 15.7345 0.622936
\(639\) −19.2804 −0.762720
\(640\) −31.2258 −1.23431
\(641\) −19.5444 −0.771959 −0.385979 0.922507i \(-0.626136\pi\)
−0.385979 + 0.922507i \(0.626136\pi\)
\(642\) 56.7323 2.23905
\(643\) 1.14866 0.0452988 0.0226494 0.999743i \(-0.492790\pi\)
0.0226494 + 0.999743i \(0.492790\pi\)
\(644\) 60.2982 2.37608
\(645\) 2.84412 0.111987
\(646\) −22.1118 −0.869978
\(647\) 23.4719 0.922775 0.461387 0.887199i \(-0.347352\pi\)
0.461387 + 0.887199i \(0.347352\pi\)
\(648\) 46.2957 1.81867
\(649\) −4.33952 −0.170341
\(650\) 16.4850 0.646596
\(651\) −20.3699 −0.798360
\(652\) −84.7475 −3.31897
\(653\) −15.9812 −0.625393 −0.312696 0.949853i \(-0.601232\pi\)
−0.312696 + 0.949853i \(0.601232\pi\)
\(654\) −100.848 −3.94348
\(655\) 19.2325 0.751477
\(656\) −13.1534 −0.513554
\(657\) −6.39016 −0.249304
\(658\) −3.04221 −0.118598
\(659\) 26.4394 1.02993 0.514966 0.857210i \(-0.327804\pi\)
0.514966 + 0.857210i \(0.327804\pi\)
\(660\) 12.9545 0.504255
\(661\) 9.92932 0.386206 0.193103 0.981179i \(-0.438145\pi\)
0.193103 + 0.981179i \(0.438145\pi\)
\(662\) −44.0954 −1.71382
\(663\) 19.7515 0.767086
\(664\) −14.9612 −0.580606
\(665\) −8.39884 −0.325693
\(666\) −47.4987 −1.84054
\(667\) 50.0470 1.93783
\(668\) 29.4006 1.13755
\(669\) −46.0649 −1.78097
\(670\) 6.75157 0.260836
\(671\) −4.40105 −0.169901
\(672\) 9.50245 0.366565
\(673\) −20.0206 −0.771736 −0.385868 0.922554i \(-0.626098\pi\)
−0.385868 + 0.922554i \(0.626098\pi\)
\(674\) 22.2801 0.858196
\(675\) −5.23070 −0.201330
\(676\) −25.1019 −0.965458
\(677\) 15.4201 0.592641 0.296321 0.955089i \(-0.404240\pi\)
0.296321 + 0.955089i \(0.404240\pi\)
\(678\) −98.3958 −3.77887
\(679\) 10.6847 0.410039
\(680\) −22.2889 −0.854741
\(681\) 50.1266 1.92085
\(682\) 10.3385 0.395880
\(683\) −42.0334 −1.60836 −0.804182 0.594384i \(-0.797396\pi\)
−0.804182 + 0.594384i \(0.797396\pi\)
\(684\) −21.6841 −0.829114
\(685\) 12.8324 0.490302
\(686\) −48.3866 −1.84741
\(687\) 38.1346 1.45493
\(688\) 2.25998 0.0861610
\(689\) 13.1962 0.502736
\(690\) 63.0108 2.39878
\(691\) 9.24275 0.351611 0.175805 0.984425i \(-0.443747\pi\)
0.175805 + 0.984425i \(0.443747\pi\)
\(692\) 79.0573 3.00531
\(693\) −4.49192 −0.170634
\(694\) 45.9518 1.74431
\(695\) 13.2732 0.503482
\(696\) −63.5464 −2.40872
\(697\) 16.6642 0.631202
\(698\) −76.7288 −2.90423
\(699\) −21.0894 −0.797676
\(700\) 21.4461 0.810588
\(701\) 45.6241 1.72320 0.861599 0.507589i \(-0.169463\pi\)
0.861599 + 0.507589i \(0.169463\pi\)
\(702\) −11.6586 −0.440025
\(703\) −24.4641 −0.922681
\(704\) −10.2705 −0.387085
\(705\) −2.07889 −0.0782955
\(706\) 36.3699 1.36880
\(707\) 20.8570 0.784409
\(708\) 37.2269 1.39907
\(709\) 6.06822 0.227897 0.113948 0.993487i \(-0.463650\pi\)
0.113948 + 0.993487i \(0.463650\pi\)
\(710\) −32.5143 −1.22024
\(711\) 28.3413 1.06288
\(712\) 28.4751 1.06715
\(713\) 32.8837 1.23150
\(714\) 39.2942 1.47055
\(715\) −3.80770 −0.142400
\(716\) 28.8804 1.07931
\(717\) 58.5793 2.18768
\(718\) 43.2886 1.61552
\(719\) −6.19591 −0.231069 −0.115534 0.993303i \(-0.536858\pi\)
−0.115534 + 0.993303i \(0.536858\pi\)
\(720\) −8.85465 −0.329993
\(721\) −22.7174 −0.846041
\(722\) 28.5970 1.06427
\(723\) 54.3212 2.02023
\(724\) 36.0716 1.34059
\(725\) 17.8001 0.661080
\(726\) 5.45695 0.202527
\(727\) 10.8056 0.400759 0.200380 0.979718i \(-0.435782\pi\)
0.200380 + 0.979718i \(0.435782\pi\)
\(728\) 22.5039 0.834049
\(729\) −10.2030 −0.377889
\(730\) −10.7763 −0.398849
\(731\) −2.86320 −0.105899
\(732\) 37.7547 1.39545
\(733\) 39.5114 1.45939 0.729693 0.683775i \(-0.239663\pi\)
0.729693 + 0.683775i \(0.239663\pi\)
\(734\) −40.9549 −1.51167
\(735\) −9.06978 −0.334544
\(736\) −15.3400 −0.565441
\(737\) 1.85979 0.0685063
\(738\) 24.9903 0.919905
\(739\) −40.8264 −1.50182 −0.750912 0.660403i \(-0.770386\pi\)
−0.750912 + 0.660403i \(0.770386\pi\)
\(740\) −52.3807 −1.92555
\(741\) 15.2558 0.560435
\(742\) 26.2529 0.963775
\(743\) −22.9122 −0.840568 −0.420284 0.907393i \(-0.638070\pi\)
−0.420284 + 0.907393i \(0.638070\pi\)
\(744\) −41.7535 −1.53076
\(745\) 17.2004 0.630174
\(746\) 68.8946 2.52241
\(747\) 7.52999 0.275508
\(748\) −13.0415 −0.476843
\(749\) −21.6935 −0.792663
\(750\) 63.6138 2.32285
\(751\) 18.3110 0.668179 0.334090 0.942541i \(-0.391571\pi\)
0.334090 + 0.942541i \(0.391571\pi\)
\(752\) −1.65192 −0.0602393
\(753\) −38.7758 −1.41307
\(754\) 39.6743 1.44485
\(755\) 17.4258 0.634188
\(756\) −15.1672 −0.551625
\(757\) −22.2201 −0.807603 −0.403801 0.914847i \(-0.632311\pi\)
−0.403801 + 0.914847i \(0.632311\pi\)
\(758\) −56.2524 −2.04318
\(759\) 17.3570 0.630019
\(760\) −17.2156 −0.624477
\(761\) 20.1613 0.730848 0.365424 0.930841i \(-0.380924\pi\)
0.365424 + 0.930841i \(0.380924\pi\)
\(762\) −97.8667 −3.54534
\(763\) 38.5627 1.39606
\(764\) −57.3867 −2.07618
\(765\) 11.2181 0.405590
\(766\) 73.0607 2.63979
\(767\) −10.9420 −0.395093
\(768\) 66.2111 2.38919
\(769\) −9.99809 −0.360540 −0.180270 0.983617i \(-0.557697\pi\)
−0.180270 + 0.983617i \(0.557697\pi\)
\(770\) −7.57513 −0.272989
\(771\) 69.3758 2.49851
\(772\) 35.4386 1.27546
\(773\) 3.28603 0.118190 0.0590951 0.998252i \(-0.481178\pi\)
0.0590951 + 0.998252i \(0.481178\pi\)
\(774\) −4.29377 −0.154336
\(775\) 11.6957 0.420120
\(776\) 21.9010 0.786200
\(777\) 43.4744 1.55963
\(778\) −60.1573 −2.15674
\(779\) 12.8712 0.461158
\(780\) 32.6646 1.16958
\(781\) −8.95640 −0.320485
\(782\) −63.4336 −2.26838
\(783\) −12.5886 −0.449881
\(784\) −7.20699 −0.257393
\(785\) 0.561892 0.0200548
\(786\) −69.4991 −2.47895
\(787\) −1.96656 −0.0701004 −0.0350502 0.999386i \(-0.511159\pi\)
−0.0350502 + 0.999386i \(0.511159\pi\)
\(788\) −93.0722 −3.31556
\(789\) 46.7224 1.66336
\(790\) 47.7945 1.70045
\(791\) 37.6249 1.33779
\(792\) −9.20736 −0.327169
\(793\) −11.0971 −0.394071
\(794\) 69.6361 2.47129
\(795\) 17.9399 0.636262
\(796\) −15.9423 −0.565059
\(797\) 52.4229 1.85691 0.928457 0.371440i \(-0.121136\pi\)
0.928457 + 0.371440i \(0.121136\pi\)
\(798\) 30.3503 1.07439
\(799\) 2.09284 0.0740393
\(800\) −5.45596 −0.192897
\(801\) −14.3316 −0.506382
\(802\) 18.8724 0.666408
\(803\) −2.96845 −0.104754
\(804\) −15.9544 −0.562667
\(805\) −24.0943 −0.849213
\(806\) 26.0682 0.918213
\(807\) 41.4913 1.46056
\(808\) 42.7519 1.50401
\(809\) −24.2234 −0.851650 −0.425825 0.904806i \(-0.640016\pi\)
−0.425825 + 0.904806i \(0.640016\pi\)
\(810\) −39.2942 −1.38066
\(811\) 29.6743 1.04201 0.521003 0.853555i \(-0.325558\pi\)
0.521003 + 0.853555i \(0.325558\pi\)
\(812\) 51.6141 1.81130
\(813\) 12.0658 0.423168
\(814\) −22.0648 −0.773370
\(815\) 33.8639 1.18620
\(816\) 21.3367 0.746935
\(817\) −2.21149 −0.0773704
\(818\) −17.4853 −0.611361
\(819\) −11.3263 −0.395772
\(820\) 27.5588 0.962396
\(821\) −26.5478 −0.926524 −0.463262 0.886221i \(-0.653321\pi\)
−0.463262 + 0.886221i \(0.653321\pi\)
\(822\) −46.3716 −1.61740
\(823\) −11.5568 −0.402843 −0.201422 0.979505i \(-0.564556\pi\)
−0.201422 + 0.979505i \(0.564556\pi\)
\(824\) −46.5653 −1.62218
\(825\) 6.17332 0.214928
\(826\) −21.7683 −0.757416
\(827\) −51.2010 −1.78043 −0.890217 0.455537i \(-0.849447\pi\)
−0.890217 + 0.455537i \(0.849447\pi\)
\(828\) −62.2067 −2.16183
\(829\) −20.4453 −0.710094 −0.355047 0.934848i \(-0.615535\pi\)
−0.355047 + 0.934848i \(0.615535\pi\)
\(830\) 12.6985 0.440772
\(831\) −2.99983 −0.104063
\(832\) −25.8969 −0.897812
\(833\) 9.13064 0.316358
\(834\) −47.9644 −1.66087
\(835\) −11.7481 −0.406559
\(836\) −10.0730 −0.348383
\(837\) −8.27143 −0.285902
\(838\) −33.0514 −1.14174
\(839\) 21.5997 0.745705 0.372853 0.927891i \(-0.378380\pi\)
0.372853 + 0.927891i \(0.378380\pi\)
\(840\) 30.5934 1.05557
\(841\) 13.8392 0.477215
\(842\) −24.7363 −0.852468
\(843\) −64.0991 −2.20769
\(844\) 88.4029 3.04295
\(845\) 10.0304 0.345055
\(846\) 3.13850 0.107904
\(847\) −2.08665 −0.0716981
\(848\) 14.2553 0.489529
\(849\) −18.8446 −0.646746
\(850\) −22.5613 −0.773846
\(851\) −70.1818 −2.40580
\(852\) 76.8330 2.63226
\(853\) −14.3233 −0.490422 −0.245211 0.969470i \(-0.578857\pi\)
−0.245211 + 0.969470i \(0.578857\pi\)
\(854\) −22.0769 −0.755457
\(855\) 8.66467 0.296326
\(856\) −44.4665 −1.51983
\(857\) −3.80935 −0.130125 −0.0650625 0.997881i \(-0.520725\pi\)
−0.0650625 + 0.997881i \(0.520725\pi\)
\(858\) 13.7596 0.469744
\(859\) 27.9709 0.954355 0.477178 0.878807i \(-0.341660\pi\)
0.477178 + 0.878807i \(0.341660\pi\)
\(860\) −4.73509 −0.161465
\(861\) −22.8730 −0.779509
\(862\) −22.1692 −0.755084
\(863\) −1.53959 −0.0524081 −0.0262041 0.999657i \(-0.508342\pi\)
−0.0262041 + 0.999657i \(0.508342\pi\)
\(864\) 3.85857 0.131271
\(865\) −31.5901 −1.07410
\(866\) 29.2827 0.995067
\(867\) 11.5574 0.392511
\(868\) 33.9133 1.15109
\(869\) 13.1655 0.446609
\(870\) 53.9360 1.82860
\(871\) 4.68942 0.158895
\(872\) 79.0444 2.67678
\(873\) −11.0228 −0.373066
\(874\) −48.9952 −1.65729
\(875\) −24.3249 −0.822331
\(876\) 25.4650 0.860384
\(877\) 23.8958 0.806903 0.403452 0.915001i \(-0.367810\pi\)
0.403452 + 0.915001i \(0.367810\pi\)
\(878\) 36.0009 1.21497
\(879\) 68.8920 2.32367
\(880\) −4.11329 −0.138659
\(881\) −46.0867 −1.55270 −0.776351 0.630301i \(-0.782931\pi\)
−0.776351 + 0.630301i \(0.782931\pi\)
\(882\) 13.6927 0.461056
\(883\) −18.1485 −0.610745 −0.305372 0.952233i \(-0.598781\pi\)
−0.305372 + 0.952233i \(0.598781\pi\)
\(884\) −32.8837 −1.10600
\(885\) −14.8753 −0.500029
\(886\) 71.5515 2.40382
\(887\) 22.6102 0.759177 0.379588 0.925155i \(-0.376066\pi\)
0.379588 + 0.925155i \(0.376066\pi\)
\(888\) 89.1121 2.99041
\(889\) 37.4226 1.25511
\(890\) −24.1687 −0.810136
\(891\) −10.8240 −0.362617
\(892\) 76.6921 2.56784
\(893\) 1.61648 0.0540933
\(894\) −62.1557 −2.07880
\(895\) −11.5402 −0.385746
\(896\) −43.1475 −1.44146
\(897\) 43.7653 1.46128
\(898\) −97.6183 −3.25756
\(899\) 28.1478 0.938780
\(900\) −22.1249 −0.737497
\(901\) −18.0602 −0.601674
\(902\) 11.6088 0.386532
\(903\) 3.92998 0.130781
\(904\) 77.1222 2.56504
\(905\) −14.4137 −0.479128
\(906\) −62.9701 −2.09204
\(907\) −25.5160 −0.847246 −0.423623 0.905838i \(-0.639242\pi\)
−0.423623 + 0.905838i \(0.639242\pi\)
\(908\) −83.4542 −2.76953
\(909\) −21.5172 −0.713679
\(910\) −19.1005 −0.633176
\(911\) 8.30911 0.275293 0.137647 0.990481i \(-0.456046\pi\)
0.137647 + 0.990481i \(0.456046\pi\)
\(912\) 16.4802 0.545713
\(913\) 3.49794 0.115765
\(914\) −60.7192 −2.00841
\(915\) −15.0862 −0.498736
\(916\) −63.4892 −2.09774
\(917\) 26.5753 0.877595
\(918\) 15.9558 0.526621
\(919\) −40.6810 −1.34194 −0.670972 0.741483i \(-0.734123\pi\)
−0.670972 + 0.741483i \(0.734123\pi\)
\(920\) −49.3876 −1.62826
\(921\) −46.8900 −1.54508
\(922\) −79.4951 −2.61803
\(923\) −22.5833 −0.743340
\(924\) 17.9005 0.588882
\(925\) −24.9614 −0.820725
\(926\) 25.4165 0.835237
\(927\) 23.4364 0.769754
\(928\) −13.1308 −0.431038
\(929\) −53.8706 −1.76744 −0.883718 0.468019i \(-0.844968\pi\)
−0.883718 + 0.468019i \(0.844968\pi\)
\(930\) 35.4389 1.16209
\(931\) 7.05237 0.231132
\(932\) 35.1112 1.15010
\(933\) 68.5137 2.24304
\(934\) 31.7495 1.03888
\(935\) 5.21118 0.170424
\(936\) −23.2161 −0.758843
\(937\) 20.2956 0.663029 0.331514 0.943450i \(-0.392440\pi\)
0.331514 + 0.943450i \(0.392440\pi\)
\(938\) 9.32926 0.304611
\(939\) 68.2088 2.22591
\(940\) 3.46108 0.112888
\(941\) 19.0799 0.621987 0.310994 0.950412i \(-0.399338\pi\)
0.310994 + 0.950412i \(0.399338\pi\)
\(942\) −2.03047 −0.0661562
\(943\) 36.9244 1.20242
\(944\) −11.8202 −0.384714
\(945\) 6.06059 0.197151
\(946\) −1.99460 −0.0648501
\(947\) −6.78891 −0.220610 −0.110305 0.993898i \(-0.535183\pi\)
−0.110305 + 0.993898i \(0.535183\pi\)
\(948\) −112.941 −3.66816
\(949\) −7.48487 −0.242969
\(950\) −17.4260 −0.565374
\(951\) 18.2161 0.590696
\(952\) −30.7986 −0.998189
\(953\) −14.6571 −0.474790 −0.237395 0.971413i \(-0.576294\pi\)
−0.237395 + 0.971413i \(0.576294\pi\)
\(954\) −27.0838 −0.876871
\(955\) 22.9309 0.742027
\(956\) −97.5269 −3.15425
\(957\) 14.8572 0.480266
\(958\) 84.8045 2.73991
\(959\) 17.7317 0.572588
\(960\) −35.2060 −1.13627
\(961\) −12.5054 −0.403399
\(962\) −55.6358 −1.79377
\(963\) 22.3801 0.721189
\(964\) −90.4377 −2.91280
\(965\) −14.1607 −0.455851
\(966\) 87.0678 2.80136
\(967\) 32.5328 1.04618 0.523091 0.852277i \(-0.324779\pi\)
0.523091 + 0.852277i \(0.324779\pi\)
\(968\) −4.27714 −0.137472
\(969\) −20.8789 −0.670728
\(970\) −18.5888 −0.596851
\(971\) −39.3080 −1.26146 −0.630728 0.776004i \(-0.717243\pi\)
−0.630728 + 0.776004i \(0.717243\pi\)
\(972\) 71.0483 2.27888
\(973\) 18.3408 0.587979
\(974\) −70.4107 −2.25610
\(975\) 15.5659 0.498507
\(976\) −11.9878 −0.383719
\(977\) 0.321298 0.0102792 0.00513962 0.999987i \(-0.498364\pi\)
0.00513962 + 0.999987i \(0.498364\pi\)
\(978\) −122.371 −3.91300
\(979\) −6.65752 −0.212775
\(980\) 15.1000 0.482352
\(981\) −39.7833 −1.27018
\(982\) 21.3547 0.681457
\(983\) 28.6296 0.913143 0.456572 0.889687i \(-0.349077\pi\)
0.456572 + 0.889687i \(0.349077\pi\)
\(984\) −46.8842 −1.49461
\(985\) 37.1903 1.18498
\(986\) −54.2979 −1.72920
\(987\) −2.87259 −0.0914355
\(988\) −25.3989 −0.808047
\(989\) −6.34426 −0.201736
\(990\) 7.81489 0.248373
\(991\) 50.7278 1.61142 0.805711 0.592309i \(-0.201784\pi\)
0.805711 + 0.592309i \(0.201784\pi\)
\(992\) −8.62764 −0.273928
\(993\) −41.6368 −1.32130
\(994\) −44.9279 −1.42503
\(995\) 6.37030 0.201952
\(996\) −30.0073 −0.950818
\(997\) −14.1408 −0.447844 −0.223922 0.974607i \(-0.571886\pi\)
−0.223922 + 0.974607i \(0.571886\pi\)
\(998\) −63.5412 −2.01136
\(999\) 17.6532 0.558524
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 6017.2.a.e.1.9 119
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6017.2.a.e.1.9 119 1.1 even 1 trivial