Properties

Label 8021.2.a.d.1.15
Level $8021$
Weight $2$
Character 8021.1
Self dual yes
Analytic conductor $64.048$
Analytic rank $0$
Dimension $174$
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] = [8021,2,Mod(1,8021)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8021, 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("8021.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8021 = 13 \cdot 617 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8021.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(0\)
Dimension: \(174\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 8021.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.62193 q^{2} +2.84190 q^{3} +4.87451 q^{4} +3.72911 q^{5} -7.45125 q^{6} -2.25507 q^{7} -7.53678 q^{8} +5.07638 q^{9} +O(q^{10})\) \(q-2.62193 q^{2} +2.84190 q^{3} +4.87451 q^{4} +3.72911 q^{5} -7.45125 q^{6} -2.25507 q^{7} -7.53678 q^{8} +5.07638 q^{9} -9.77745 q^{10} -3.42407 q^{11} +13.8529 q^{12} +1.00000 q^{13} +5.91264 q^{14} +10.5977 q^{15} +10.0119 q^{16} +3.16545 q^{17} -13.3099 q^{18} -4.50680 q^{19} +18.1776 q^{20} -6.40868 q^{21} +8.97767 q^{22} +8.74374 q^{23} -21.4187 q^{24} +8.90623 q^{25} -2.62193 q^{26} +5.90085 q^{27} -10.9924 q^{28} -6.67219 q^{29} -27.7865 q^{30} -5.48594 q^{31} -11.1769 q^{32} -9.73085 q^{33} -8.29958 q^{34} -8.40940 q^{35} +24.7449 q^{36} +2.43963 q^{37} +11.8165 q^{38} +2.84190 q^{39} -28.1054 q^{40} +5.37733 q^{41} +16.8031 q^{42} +10.9038 q^{43} -16.6907 q^{44} +18.9303 q^{45} -22.9255 q^{46} +10.1256 q^{47} +28.4527 q^{48} -1.91465 q^{49} -23.3515 q^{50} +8.99587 q^{51} +4.87451 q^{52} +8.19512 q^{53} -15.4716 q^{54} -12.7687 q^{55} +16.9960 q^{56} -12.8079 q^{57} +17.4940 q^{58} +4.96930 q^{59} +51.6588 q^{60} +0.209772 q^{61} +14.3837 q^{62} -11.4476 q^{63} +9.28119 q^{64} +3.72911 q^{65} +25.5136 q^{66} +11.3885 q^{67} +15.4300 q^{68} +24.8488 q^{69} +22.0489 q^{70} +6.26110 q^{71} -38.2595 q^{72} -0.932277 q^{73} -6.39653 q^{74} +25.3106 q^{75} -21.9685 q^{76} +7.72152 q^{77} -7.45125 q^{78} +2.93860 q^{79} +37.3353 q^{80} +1.54047 q^{81} -14.0990 q^{82} -6.72996 q^{83} -31.2392 q^{84} +11.8043 q^{85} -28.5890 q^{86} -18.9617 q^{87} +25.8064 q^{88} -14.5178 q^{89} -49.6340 q^{90} -2.25507 q^{91} +42.6215 q^{92} -15.5905 q^{93} -26.5486 q^{94} -16.8063 q^{95} -31.7635 q^{96} -7.80793 q^{97} +5.02007 q^{98} -17.3819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62193 −1.85398 −0.926992 0.375081i \(-0.877615\pi\)
−0.926992 + 0.375081i \(0.877615\pi\)
\(3\) 2.84190 1.64077 0.820385 0.571812i \(-0.193759\pi\)
0.820385 + 0.571812i \(0.193759\pi\)
\(4\) 4.87451 2.43726
\(5\) 3.72911 1.66771 0.833853 0.551986i \(-0.186130\pi\)
0.833853 + 0.551986i \(0.186130\pi\)
\(6\) −7.45125 −3.04196
\(7\) −2.25507 −0.852337 −0.426169 0.904644i \(-0.640137\pi\)
−0.426169 + 0.904644i \(0.640137\pi\)
\(8\) −7.53678 −2.66465
\(9\) 5.07638 1.69213
\(10\) −9.77745 −3.09190
\(11\) −3.42407 −1.03240 −0.516198 0.856469i \(-0.672653\pi\)
−0.516198 + 0.856469i \(0.672653\pi\)
\(12\) 13.8529 3.99898
\(13\) 1.00000 0.277350
\(14\) 5.91264 1.58022
\(15\) 10.5977 2.73632
\(16\) 10.0119 2.50297
\(17\) 3.16545 0.767733 0.383867 0.923389i \(-0.374592\pi\)
0.383867 + 0.923389i \(0.374592\pi\)
\(18\) −13.3099 −3.13717
\(19\) −4.50680 −1.03393 −0.516965 0.856006i \(-0.672938\pi\)
−0.516965 + 0.856006i \(0.672938\pi\)
\(20\) 18.1776 4.06463
\(21\) −6.40868 −1.39849
\(22\) 8.97767 1.91404
\(23\) 8.74374 1.82320 0.911598 0.411082i \(-0.134849\pi\)
0.911598 + 0.411082i \(0.134849\pi\)
\(24\) −21.4187 −4.37208
\(25\) 8.90623 1.78125
\(26\) −2.62193 −0.514203
\(27\) 5.90085 1.13562
\(28\) −10.9924 −2.07737
\(29\) −6.67219 −1.23899 −0.619497 0.784999i \(-0.712663\pi\)
−0.619497 + 0.784999i \(0.712663\pi\)
\(30\) −27.7865 −5.07310
\(31\) −5.48594 −0.985303 −0.492652 0.870227i \(-0.663972\pi\)
−0.492652 + 0.870227i \(0.663972\pi\)
\(32\) −11.1769 −1.97581
\(33\) −9.73085 −1.69392
\(34\) −8.29958 −1.42337
\(35\) −8.40940 −1.42145
\(36\) 24.7449 4.12415
\(37\) 2.43963 0.401072 0.200536 0.979686i \(-0.435732\pi\)
0.200536 + 0.979686i \(0.435732\pi\)
\(38\) 11.8165 1.91689
\(39\) 2.84190 0.455068
\(40\) −28.1054 −4.44386
\(41\) 5.37733 0.839798 0.419899 0.907571i \(-0.362065\pi\)
0.419899 + 0.907571i \(0.362065\pi\)
\(42\) 16.8031 2.59278
\(43\) 10.9038 1.66281 0.831407 0.555664i \(-0.187536\pi\)
0.831407 + 0.555664i \(0.187536\pi\)
\(44\) −16.6907 −2.51621
\(45\) 18.9303 2.82197
\(46\) −22.9255 −3.38018
\(47\) 10.1256 1.47697 0.738485 0.674270i \(-0.235542\pi\)
0.738485 + 0.674270i \(0.235542\pi\)
\(48\) 28.4527 4.10679
\(49\) −1.91465 −0.273521
\(50\) −23.3515 −3.30240
\(51\) 8.99587 1.25967
\(52\) 4.87451 0.675974
\(53\) 8.19512 1.12569 0.562843 0.826564i \(-0.309707\pi\)
0.562843 + 0.826564i \(0.309707\pi\)
\(54\) −15.4716 −2.10542
\(55\) −12.7687 −1.72173
\(56\) 16.9960 2.27118
\(57\) −12.8079 −1.69644
\(58\) 17.4940 2.29708
\(59\) 4.96930 0.646947 0.323474 0.946237i \(-0.395149\pi\)
0.323474 + 0.946237i \(0.395149\pi\)
\(60\) 51.6588 6.66912
\(61\) 0.209772 0.0268585 0.0134293 0.999910i \(-0.495725\pi\)
0.0134293 + 0.999910i \(0.495725\pi\)
\(62\) 14.3837 1.82674
\(63\) −11.4476 −1.44226
\(64\) 9.28119 1.16015
\(65\) 3.72911 0.462539
\(66\) 25.5136 3.14051
\(67\) 11.3885 1.39133 0.695665 0.718366i \(-0.255110\pi\)
0.695665 + 0.718366i \(0.255110\pi\)
\(68\) 15.4300 1.87116
\(69\) 24.8488 2.99145
\(70\) 22.0489 2.63534
\(71\) 6.26110 0.743056 0.371528 0.928422i \(-0.378834\pi\)
0.371528 + 0.928422i \(0.378834\pi\)
\(72\) −38.2595 −4.50893
\(73\) −0.932277 −0.109115 −0.0545574 0.998511i \(-0.517375\pi\)
−0.0545574 + 0.998511i \(0.517375\pi\)
\(74\) −6.39653 −0.743582
\(75\) 25.3106 2.92261
\(76\) −21.9685 −2.51995
\(77\) 7.72152 0.879949
\(78\) −7.45125 −0.843688
\(79\) 2.93860 0.330618 0.165309 0.986242i \(-0.447138\pi\)
0.165309 + 0.986242i \(0.447138\pi\)
\(80\) 37.3353 4.17421
\(81\) 1.54047 0.171164
\(82\) −14.0990 −1.55697
\(83\) −6.72996 −0.738709 −0.369354 0.929289i \(-0.620421\pi\)
−0.369354 + 0.929289i \(0.620421\pi\)
\(84\) −31.2392 −3.40848
\(85\) 11.8043 1.28035
\(86\) −28.5890 −3.08283
\(87\) −18.9617 −2.03290
\(88\) 25.8064 2.75097
\(89\) −14.5178 −1.53888 −0.769440 0.638719i \(-0.779465\pi\)
−0.769440 + 0.638719i \(0.779465\pi\)
\(90\) −49.6340 −5.23189
\(91\) −2.25507 −0.236396
\(92\) 42.6215 4.44360
\(93\) −15.5905 −1.61666
\(94\) −26.5486 −2.73828
\(95\) −16.8063 −1.72429
\(96\) −31.7635 −3.24184
\(97\) −7.80793 −0.792775 −0.396388 0.918083i \(-0.629736\pi\)
−0.396388 + 0.918083i \(0.629736\pi\)
\(98\) 5.02007 0.507104
\(99\) −17.3819 −1.74694
\(100\) 43.4135 4.34135
\(101\) 4.41878 0.439685 0.219842 0.975535i \(-0.429446\pi\)
0.219842 + 0.975535i \(0.429446\pi\)
\(102\) −23.5865 −2.33542
\(103\) 7.91310 0.779701 0.389850 0.920878i \(-0.372527\pi\)
0.389850 + 0.920878i \(0.372527\pi\)
\(104\) −7.53678 −0.739042
\(105\) −23.8987 −2.33227
\(106\) −21.4870 −2.08701
\(107\) −8.25216 −0.797766 −0.398883 0.917002i \(-0.630602\pi\)
−0.398883 + 0.917002i \(0.630602\pi\)
\(108\) 28.7638 2.76780
\(109\) −5.79536 −0.555094 −0.277547 0.960712i \(-0.589521\pi\)
−0.277547 + 0.960712i \(0.589521\pi\)
\(110\) 33.4787 3.19206
\(111\) 6.93317 0.658067
\(112\) −22.5775 −2.13337
\(113\) −3.66565 −0.344836 −0.172418 0.985024i \(-0.555158\pi\)
−0.172418 + 0.985024i \(0.555158\pi\)
\(114\) 33.5813 3.14518
\(115\) 32.6063 3.04056
\(116\) −32.5237 −3.01975
\(117\) 5.07638 0.469311
\(118\) −13.0291 −1.19943
\(119\) −7.13831 −0.654368
\(120\) −79.8727 −7.29135
\(121\) 0.724242 0.0658402
\(122\) −0.550007 −0.0497953
\(123\) 15.2818 1.37792
\(124\) −26.7413 −2.40144
\(125\) 14.5667 1.30289
\(126\) 30.0148 2.67393
\(127\) 7.88873 0.700011 0.350006 0.936748i \(-0.386180\pi\)
0.350006 + 0.936748i \(0.386180\pi\)
\(128\) −1.98093 −0.175091
\(129\) 30.9875 2.72829
\(130\) −9.77745 −0.857539
\(131\) −2.79361 −0.244079 −0.122040 0.992525i \(-0.538943\pi\)
−0.122040 + 0.992525i \(0.538943\pi\)
\(132\) −47.4332 −4.12853
\(133\) 10.1632 0.881257
\(134\) −29.8599 −2.57950
\(135\) 22.0049 1.89388
\(136\) −23.8573 −2.04574
\(137\) −7.62769 −0.651677 −0.325839 0.945425i \(-0.605647\pi\)
−0.325839 + 0.945425i \(0.605647\pi\)
\(138\) −65.1518 −5.54609
\(139\) 12.2502 1.03905 0.519526 0.854455i \(-0.326108\pi\)
0.519526 + 0.854455i \(0.326108\pi\)
\(140\) −40.9918 −3.46444
\(141\) 28.7759 2.42337
\(142\) −16.4162 −1.37761
\(143\) −3.42407 −0.286335
\(144\) 50.8240 4.23533
\(145\) −24.8813 −2.06628
\(146\) 2.44436 0.202297
\(147\) −5.44123 −0.448785
\(148\) 11.8920 0.977516
\(149\) 13.1013 1.07330 0.536650 0.843805i \(-0.319690\pi\)
0.536650 + 0.843805i \(0.319690\pi\)
\(150\) −66.3625 −5.41848
\(151\) −6.88641 −0.560408 −0.280204 0.959940i \(-0.590402\pi\)
−0.280204 + 0.959940i \(0.590402\pi\)
\(152\) 33.9667 2.75507
\(153\) 16.0690 1.29910
\(154\) −20.2453 −1.63141
\(155\) −20.4576 −1.64320
\(156\) 13.8529 1.10912
\(157\) 3.22834 0.257649 0.128825 0.991667i \(-0.458880\pi\)
0.128825 + 0.991667i \(0.458880\pi\)
\(158\) −7.70480 −0.612961
\(159\) 23.2897 1.84699
\(160\) −41.6797 −3.29507
\(161\) −19.7178 −1.55398
\(162\) −4.03901 −0.317335
\(163\) 22.7189 1.77948 0.889739 0.456470i \(-0.150886\pi\)
0.889739 + 0.456470i \(0.150886\pi\)
\(164\) 26.2119 2.04680
\(165\) −36.2874 −2.82497
\(166\) 17.6455 1.36955
\(167\) −8.42879 −0.652239 −0.326120 0.945328i \(-0.605741\pi\)
−0.326120 + 0.945328i \(0.605741\pi\)
\(168\) 48.3008 3.72649
\(169\) 1.00000 0.0769231
\(170\) −30.9500 −2.37376
\(171\) −22.8782 −1.74954
\(172\) 53.1507 4.05271
\(173\) −12.3806 −0.941281 −0.470640 0.882325i \(-0.655977\pi\)
−0.470640 + 0.882325i \(0.655977\pi\)
\(174\) 49.7162 3.76897
\(175\) −20.0842 −1.51822
\(176\) −34.2813 −2.58405
\(177\) 14.1222 1.06149
\(178\) 38.0646 2.85306
\(179\) −5.19884 −0.388579 −0.194290 0.980944i \(-0.562240\pi\)
−0.194290 + 0.980944i \(0.562240\pi\)
\(180\) 92.2762 6.87786
\(181\) −17.3678 −1.29093 −0.645467 0.763788i \(-0.723337\pi\)
−0.645467 + 0.763788i \(0.723337\pi\)
\(182\) 5.91264 0.438274
\(183\) 0.596149 0.0440686
\(184\) −65.8996 −4.85818
\(185\) 9.09763 0.668871
\(186\) 40.8771 2.99725
\(187\) −10.8387 −0.792604
\(188\) 49.3574 3.59976
\(189\) −13.3068 −0.967930
\(190\) 44.0650 3.19681
\(191\) 20.5368 1.48599 0.742994 0.669298i \(-0.233405\pi\)
0.742994 + 0.669298i \(0.233405\pi\)
\(192\) 26.3762 1.90354
\(193\) 19.6316 1.41312 0.706558 0.707655i \(-0.250247\pi\)
0.706558 + 0.707655i \(0.250247\pi\)
\(194\) 20.4718 1.46979
\(195\) 10.5977 0.758919
\(196\) −9.33298 −0.666642
\(197\) −15.6084 −1.11205 −0.556025 0.831166i \(-0.687674\pi\)
−0.556025 + 0.831166i \(0.687674\pi\)
\(198\) 45.5740 3.23880
\(199\) −18.8218 −1.33424 −0.667120 0.744951i \(-0.732473\pi\)
−0.667120 + 0.744951i \(0.732473\pi\)
\(200\) −67.1242 −4.74640
\(201\) 32.3650 2.28285
\(202\) −11.5857 −0.815169
\(203\) 15.0463 1.05604
\(204\) 43.8505 3.07015
\(205\) 20.0526 1.40054
\(206\) −20.7476 −1.44555
\(207\) 44.3865 3.08508
\(208\) 10.0119 0.694198
\(209\) 15.4316 1.06743
\(210\) 62.6606 4.32399
\(211\) −12.9645 −0.892512 −0.446256 0.894905i \(-0.647243\pi\)
−0.446256 + 0.894905i \(0.647243\pi\)
\(212\) 39.9472 2.74359
\(213\) 17.7934 1.21918
\(214\) 21.6366 1.47905
\(215\) 40.6614 2.77309
\(216\) −44.4734 −3.02603
\(217\) 12.3712 0.839811
\(218\) 15.1950 1.02914
\(219\) −2.64943 −0.179032
\(220\) −62.2413 −4.19631
\(221\) 3.16545 0.212931
\(222\) −18.1783 −1.22005
\(223\) −15.5035 −1.03819 −0.519097 0.854715i \(-0.673732\pi\)
−0.519097 + 0.854715i \(0.673732\pi\)
\(224\) 25.2046 1.68405
\(225\) 45.2114 3.01409
\(226\) 9.61108 0.639320
\(227\) 10.7779 0.715354 0.357677 0.933845i \(-0.383569\pi\)
0.357677 + 0.933845i \(0.383569\pi\)
\(228\) −62.4321 −4.13467
\(229\) −5.41258 −0.357673 −0.178837 0.983879i \(-0.557233\pi\)
−0.178837 + 0.983879i \(0.557233\pi\)
\(230\) −85.4915 −5.63714
\(231\) 21.9438 1.44379
\(232\) 50.2868 3.30149
\(233\) 16.4092 1.07500 0.537502 0.843263i \(-0.319368\pi\)
0.537502 + 0.843263i \(0.319368\pi\)
\(234\) −13.3099 −0.870096
\(235\) 37.7594 2.46315
\(236\) 24.2229 1.57678
\(237\) 8.35119 0.542468
\(238\) 18.7161 1.21319
\(239\) 28.8550 1.86648 0.933238 0.359260i \(-0.116971\pi\)
0.933238 + 0.359260i \(0.116971\pi\)
\(240\) 106.103 6.84892
\(241\) 8.34062 0.537267 0.268633 0.963242i \(-0.413428\pi\)
0.268633 + 0.963242i \(0.413428\pi\)
\(242\) −1.89891 −0.122067
\(243\) −13.3247 −0.854779
\(244\) 1.02254 0.0654611
\(245\) −7.13993 −0.456153
\(246\) −40.0679 −2.55463
\(247\) −4.50680 −0.286761
\(248\) 41.3463 2.62549
\(249\) −19.1258 −1.21205
\(250\) −38.1929 −2.41553
\(251\) −13.2856 −0.838579 −0.419290 0.907852i \(-0.637721\pi\)
−0.419290 + 0.907852i \(0.637721\pi\)
\(252\) −55.8015 −3.51516
\(253\) −29.9392 −1.88226
\(254\) −20.6837 −1.29781
\(255\) 33.5465 2.10077
\(256\) −13.3685 −0.835533
\(257\) 0.256572 0.0160045 0.00800227 0.999968i \(-0.497453\pi\)
0.00800227 + 0.999968i \(0.497453\pi\)
\(258\) −81.2470 −5.05822
\(259\) −5.50154 −0.341849
\(260\) 18.1776 1.12733
\(261\) −33.8705 −2.09653
\(262\) 7.32465 0.452519
\(263\) 15.8266 0.975911 0.487955 0.872869i \(-0.337743\pi\)
0.487955 + 0.872869i \(0.337743\pi\)
\(264\) 73.3392 4.51372
\(265\) 30.5605 1.87731
\(266\) −26.6471 −1.63384
\(267\) −41.2580 −2.52495
\(268\) 55.5135 3.39103
\(269\) −5.84510 −0.356382 −0.178191 0.983996i \(-0.557025\pi\)
−0.178191 + 0.983996i \(0.557025\pi\)
\(270\) −57.6953 −3.51122
\(271\) 30.8508 1.87405 0.937027 0.349257i \(-0.113566\pi\)
0.937027 + 0.349257i \(0.113566\pi\)
\(272\) 31.6920 1.92161
\(273\) −6.40868 −0.387871
\(274\) 19.9993 1.20820
\(275\) −30.4955 −1.83895
\(276\) 121.126 7.29092
\(277\) 21.8280 1.31152 0.655759 0.754970i \(-0.272349\pi\)
0.655759 + 0.754970i \(0.272349\pi\)
\(278\) −32.1193 −1.92639
\(279\) −27.8487 −1.66726
\(280\) 63.3798 3.78767
\(281\) −10.8601 −0.647860 −0.323930 0.946081i \(-0.605004\pi\)
−0.323930 + 0.946081i \(0.605004\pi\)
\(282\) −75.4484 −4.49289
\(283\) −19.5384 −1.16144 −0.580719 0.814104i \(-0.697229\pi\)
−0.580719 + 0.814104i \(0.697229\pi\)
\(284\) 30.5198 1.81102
\(285\) −47.7618 −2.82917
\(286\) 8.97767 0.530860
\(287\) −12.1263 −0.715791
\(288\) −56.7379 −3.34331
\(289\) −6.97995 −0.410585
\(290\) 65.2370 3.83085
\(291\) −22.1893 −1.30076
\(292\) −4.54440 −0.265941
\(293\) 9.35072 0.546275 0.273137 0.961975i \(-0.411939\pi\)
0.273137 + 0.961975i \(0.411939\pi\)
\(294\) 14.2665 0.832041
\(295\) 18.5310 1.07892
\(296\) −18.3869 −1.06872
\(297\) −20.2049 −1.17241
\(298\) −34.3507 −1.98988
\(299\) 8.74374 0.505664
\(300\) 123.377 7.12316
\(301\) −24.5889 −1.41728
\(302\) 18.0557 1.03899
\(303\) 12.5577 0.721422
\(304\) −45.1215 −2.58789
\(305\) 0.782261 0.0447921
\(306\) −42.1318 −2.40851
\(307\) 16.2060 0.924926 0.462463 0.886639i \(-0.346966\pi\)
0.462463 + 0.886639i \(0.346966\pi\)
\(308\) 37.6387 2.14466
\(309\) 22.4882 1.27931
\(310\) 53.6385 3.04646
\(311\) −6.74254 −0.382335 −0.191167 0.981557i \(-0.561227\pi\)
−0.191167 + 0.981557i \(0.561227\pi\)
\(312\) −21.4187 −1.21260
\(313\) 34.6469 1.95836 0.979179 0.202998i \(-0.0650685\pi\)
0.979179 + 0.202998i \(0.0650685\pi\)
\(314\) −8.46448 −0.477678
\(315\) −42.6893 −2.40527
\(316\) 14.3242 0.805801
\(317\) 1.99174 0.111867 0.0559336 0.998434i \(-0.482186\pi\)
0.0559336 + 0.998434i \(0.482186\pi\)
\(318\) −61.0639 −3.42430
\(319\) 22.8460 1.27913
\(320\) 34.6105 1.93479
\(321\) −23.4518 −1.30895
\(322\) 51.6986 2.88105
\(323\) −14.2660 −0.793783
\(324\) 7.50905 0.417170
\(325\) 8.90623 0.494029
\(326\) −59.5672 −3.29912
\(327\) −16.4698 −0.910782
\(328\) −40.5278 −2.23777
\(329\) −22.8340 −1.25888
\(330\) 95.1429 5.23744
\(331\) 19.7267 1.08427 0.542137 0.840290i \(-0.317615\pi\)
0.542137 + 0.840290i \(0.317615\pi\)
\(332\) −32.8053 −1.80042
\(333\) 12.3845 0.678665
\(334\) 22.0997 1.20924
\(335\) 42.4690 2.32033
\(336\) −64.1629 −3.50037
\(337\) 2.12506 0.115759 0.0578797 0.998324i \(-0.481566\pi\)
0.0578797 + 0.998324i \(0.481566\pi\)
\(338\) −2.62193 −0.142614
\(339\) −10.4174 −0.565796
\(340\) 57.5401 3.12055
\(341\) 18.7842 1.01722
\(342\) 59.9851 3.24362
\(343\) 20.1032 1.08547
\(344\) −82.1795 −4.43082
\(345\) 92.6638 4.98885
\(346\) 32.4611 1.74512
\(347\) 5.78773 0.310702 0.155351 0.987859i \(-0.450349\pi\)
0.155351 + 0.987859i \(0.450349\pi\)
\(348\) −92.4289 −4.95471
\(349\) 30.6998 1.64332 0.821661 0.569977i \(-0.193048\pi\)
0.821661 + 0.569977i \(0.193048\pi\)
\(350\) 52.6593 2.81476
\(351\) 5.90085 0.314964
\(352\) 38.2703 2.03981
\(353\) 1.95836 0.104233 0.0521165 0.998641i \(-0.483403\pi\)
0.0521165 + 0.998641i \(0.483403\pi\)
\(354\) −37.0275 −1.96799
\(355\) 23.3483 1.23920
\(356\) −70.7671 −3.75065
\(357\) −20.2863 −1.07367
\(358\) 13.6310 0.720420
\(359\) 12.5648 0.663143 0.331572 0.943430i \(-0.392421\pi\)
0.331572 + 0.943430i \(0.392421\pi\)
\(360\) −142.674 −7.51957
\(361\) 1.31123 0.0690123
\(362\) 45.5370 2.39337
\(363\) 2.05822 0.108029
\(364\) −10.9924 −0.576157
\(365\) −3.47656 −0.181971
\(366\) −1.56306 −0.0817025
\(367\) −3.61386 −0.188642 −0.0943210 0.995542i \(-0.530068\pi\)
−0.0943210 + 0.995542i \(0.530068\pi\)
\(368\) 87.5412 4.56340
\(369\) 27.2974 1.42104
\(370\) −23.8533 −1.24008
\(371\) −18.4806 −0.959465
\(372\) −75.9959 −3.94021
\(373\) −5.72676 −0.296520 −0.148260 0.988948i \(-0.547367\pi\)
−0.148260 + 0.988948i \(0.547367\pi\)
\(374\) 28.4183 1.46948
\(375\) 41.3971 2.13774
\(376\) −76.3143 −3.93561
\(377\) −6.67219 −0.343635
\(378\) 34.8896 1.79453
\(379\) 20.7953 1.06818 0.534090 0.845427i \(-0.320654\pi\)
0.534090 + 0.845427i \(0.320654\pi\)
\(380\) −81.9227 −4.20255
\(381\) 22.4190 1.14856
\(382\) −53.8460 −2.75500
\(383\) −4.63341 −0.236756 −0.118378 0.992969i \(-0.537769\pi\)
−0.118378 + 0.992969i \(0.537769\pi\)
\(384\) −5.62960 −0.287284
\(385\) 28.7944 1.46750
\(386\) −51.4728 −2.61990
\(387\) 55.3518 2.81369
\(388\) −38.0599 −1.93220
\(389\) −10.1357 −0.513898 −0.256949 0.966425i \(-0.582717\pi\)
−0.256949 + 0.966425i \(0.582717\pi\)
\(390\) −27.7865 −1.40702
\(391\) 27.6778 1.39973
\(392\) 14.4303 0.728839
\(393\) −7.93916 −0.400478
\(394\) 40.9240 2.06172
\(395\) 10.9583 0.551374
\(396\) −84.7281 −4.25775
\(397\) −12.0080 −0.602662 −0.301331 0.953520i \(-0.597431\pi\)
−0.301331 + 0.953520i \(0.597431\pi\)
\(398\) 49.3493 2.47366
\(399\) 28.8826 1.44594
\(400\) 89.1679 4.45840
\(401\) −18.6946 −0.933563 −0.466781 0.884373i \(-0.654587\pi\)
−0.466781 + 0.884373i \(0.654587\pi\)
\(402\) −84.8588 −4.23237
\(403\) −5.48594 −0.273274
\(404\) 21.5394 1.07163
\(405\) 5.74458 0.285451
\(406\) −39.4503 −1.95788
\(407\) −8.35345 −0.414065
\(408\) −67.7998 −3.35659
\(409\) 2.78300 0.137611 0.0688053 0.997630i \(-0.478081\pi\)
0.0688053 + 0.997630i \(0.478081\pi\)
\(410\) −52.5766 −2.59657
\(411\) −21.6771 −1.06925
\(412\) 38.5725 1.90033
\(413\) −11.2061 −0.551417
\(414\) −116.378 −5.71968
\(415\) −25.0967 −1.23195
\(416\) −11.1769 −0.547990
\(417\) 34.8139 1.70485
\(418\) −40.4605 −1.97899
\(419\) 22.7358 1.11072 0.555359 0.831610i \(-0.312581\pi\)
0.555359 + 0.831610i \(0.312581\pi\)
\(420\) −116.494 −5.68434
\(421\) 37.4428 1.82485 0.912426 0.409243i \(-0.134207\pi\)
0.912426 + 0.409243i \(0.134207\pi\)
\(422\) 33.9920 1.65470
\(423\) 51.4013 2.49922
\(424\) −61.7648 −2.99956
\(425\) 28.1922 1.36752
\(426\) −46.6531 −2.26035
\(427\) −0.473050 −0.0228925
\(428\) −40.2253 −1.94436
\(429\) −9.73085 −0.469810
\(430\) −106.611 −5.14126
\(431\) −36.3309 −1.75000 −0.875000 0.484123i \(-0.839139\pi\)
−0.875000 + 0.484123i \(0.839139\pi\)
\(432\) 59.0785 2.84242
\(433\) 28.8949 1.38860 0.694300 0.719686i \(-0.255714\pi\)
0.694300 + 0.719686i \(0.255714\pi\)
\(434\) −32.4364 −1.55700
\(435\) −70.7101 −3.39029
\(436\) −28.2495 −1.35291
\(437\) −39.4063 −1.88506
\(438\) 6.94663 0.331923
\(439\) 36.2964 1.73233 0.866166 0.499757i \(-0.166577\pi\)
0.866166 + 0.499757i \(0.166577\pi\)
\(440\) 96.2349 4.58782
\(441\) −9.71948 −0.462832
\(442\) −8.29958 −0.394771
\(443\) −11.6530 −0.553653 −0.276826 0.960920i \(-0.589283\pi\)
−0.276826 + 0.960920i \(0.589283\pi\)
\(444\) 33.7958 1.60388
\(445\) −54.1383 −2.56640
\(446\) 40.6492 1.92480
\(447\) 37.2325 1.76104
\(448\) −20.9298 −0.988838
\(449\) 32.7532 1.54572 0.772861 0.634576i \(-0.218825\pi\)
0.772861 + 0.634576i \(0.218825\pi\)
\(450\) −118.541 −5.58808
\(451\) −18.4124 −0.867004
\(452\) −17.8683 −0.840453
\(453\) −19.5705 −0.919500
\(454\) −28.2589 −1.32625
\(455\) −8.40940 −0.394239
\(456\) 96.5299 4.52043
\(457\) −28.2760 −1.32270 −0.661348 0.750079i \(-0.730015\pi\)
−0.661348 + 0.750079i \(0.730015\pi\)
\(458\) 14.1914 0.663121
\(459\) 18.6788 0.871853
\(460\) 158.940 7.41062
\(461\) −3.69114 −0.171914 −0.0859569 0.996299i \(-0.527395\pi\)
−0.0859569 + 0.996299i \(0.527395\pi\)
\(462\) −57.5350 −2.67677
\(463\) −41.2551 −1.91729 −0.958643 0.284611i \(-0.908136\pi\)
−0.958643 + 0.284611i \(0.908136\pi\)
\(464\) −66.8011 −3.10116
\(465\) −58.1385 −2.69611
\(466\) −43.0238 −1.99304
\(467\) −7.99468 −0.369950 −0.184975 0.982743i \(-0.559220\pi\)
−0.184975 + 0.982743i \(0.559220\pi\)
\(468\) 24.7449 1.14383
\(469\) −25.6819 −1.18588
\(470\) −99.0025 −4.56665
\(471\) 9.17461 0.422743
\(472\) −37.4525 −1.72389
\(473\) −37.3353 −1.71668
\(474\) −21.8962 −1.00573
\(475\) −40.1386 −1.84168
\(476\) −34.7958 −1.59486
\(477\) 41.6015 1.90480
\(478\) −75.6558 −3.46042
\(479\) −24.5744 −1.12283 −0.561416 0.827534i \(-0.689743\pi\)
−0.561416 + 0.827534i \(0.689743\pi\)
\(480\) −118.449 −5.40645
\(481\) 2.43963 0.111237
\(482\) −21.8685 −0.996084
\(483\) −56.0359 −2.54972
\(484\) 3.53033 0.160469
\(485\) −29.1166 −1.32212
\(486\) 34.9364 1.58475
\(487\) 12.3170 0.558136 0.279068 0.960271i \(-0.409975\pi\)
0.279068 + 0.960271i \(0.409975\pi\)
\(488\) −1.58100 −0.0715686
\(489\) 64.5646 2.91971
\(490\) 18.7204 0.845701
\(491\) −8.87011 −0.400302 −0.200151 0.979765i \(-0.564143\pi\)
−0.200151 + 0.979765i \(0.564143\pi\)
\(492\) 74.4915 3.35834
\(493\) −21.1205 −0.951217
\(494\) 11.8165 0.531650
\(495\) −64.8188 −2.91339
\(496\) −54.9244 −2.46618
\(497\) −14.1192 −0.633335
\(498\) 50.1466 2.24712
\(499\) 14.1052 0.631435 0.315717 0.948853i \(-0.397755\pi\)
0.315717 + 0.948853i \(0.397755\pi\)
\(500\) 71.0057 3.17547
\(501\) −23.9538 −1.07017
\(502\) 34.8339 1.55471
\(503\) 30.3883 1.35495 0.677473 0.735547i \(-0.263075\pi\)
0.677473 + 0.735547i \(0.263075\pi\)
\(504\) 86.2780 3.84313
\(505\) 16.4781 0.733265
\(506\) 78.4984 3.48968
\(507\) 2.84190 0.126213
\(508\) 38.4537 1.70611
\(509\) −11.2447 −0.498412 −0.249206 0.968451i \(-0.580170\pi\)
−0.249206 + 0.968451i \(0.580170\pi\)
\(510\) −87.9567 −3.89479
\(511\) 2.10235 0.0930026
\(512\) 39.0132 1.72416
\(513\) −26.5939 −1.17415
\(514\) −0.672715 −0.0296722
\(515\) 29.5088 1.30031
\(516\) 151.049 6.64956
\(517\) −34.6707 −1.52482
\(518\) 14.4246 0.633782
\(519\) −35.1844 −1.54443
\(520\) −28.1054 −1.23250
\(521\) −43.8867 −1.92271 −0.961355 0.275310i \(-0.911219\pi\)
−0.961355 + 0.275310i \(0.911219\pi\)
\(522\) 88.8062 3.88694
\(523\) −34.1115 −1.49159 −0.745795 0.666175i \(-0.767930\pi\)
−0.745795 + 0.666175i \(0.767930\pi\)
\(524\) −13.6175 −0.594883
\(525\) −57.0772 −2.49105
\(526\) −41.4963 −1.80932
\(527\) −17.3654 −0.756450
\(528\) −97.4239 −4.23983
\(529\) 53.4530 2.32404
\(530\) −80.1274 −3.48051
\(531\) 25.2260 1.09472
\(532\) 49.5405 2.14785
\(533\) 5.37733 0.232918
\(534\) 108.176 4.68122
\(535\) −30.7732 −1.33044
\(536\) −85.8328 −3.70741
\(537\) −14.7746 −0.637569
\(538\) 15.3255 0.660727
\(539\) 6.55589 0.282382
\(540\) 107.263 4.61587
\(541\) 22.9599 0.987125 0.493563 0.869710i \(-0.335694\pi\)
0.493563 + 0.869710i \(0.335694\pi\)
\(542\) −80.8887 −3.47447
\(543\) −49.3574 −2.11813
\(544\) −35.3797 −1.51689
\(545\) −21.6115 −0.925735
\(546\) 16.8031 0.719107
\(547\) −7.53017 −0.321967 −0.160984 0.986957i \(-0.551467\pi\)
−0.160984 + 0.986957i \(0.551467\pi\)
\(548\) −37.1813 −1.58831
\(549\) 1.06488 0.0454480
\(550\) 79.9571 3.40938
\(551\) 30.0702 1.28103
\(552\) −187.280 −7.97116
\(553\) −6.62675 −0.281798
\(554\) −57.2315 −2.43153
\(555\) 25.8545 1.09746
\(556\) 59.7140 2.53244
\(557\) 21.2656 0.901053 0.450527 0.892763i \(-0.351236\pi\)
0.450527 + 0.892763i \(0.351236\pi\)
\(558\) 73.0173 3.09107
\(559\) 10.9038 0.461182
\(560\) −84.1938 −3.55784
\(561\) −30.8025 −1.30048
\(562\) 28.4745 1.20112
\(563\) −14.5870 −0.614769 −0.307385 0.951585i \(-0.599454\pi\)
−0.307385 + 0.951585i \(0.599454\pi\)
\(564\) 140.269 5.90637
\(565\) −13.6696 −0.575084
\(566\) 51.2284 2.15329
\(567\) −3.47388 −0.145889
\(568\) −47.1885 −1.97999
\(569\) −37.5624 −1.57470 −0.787349 0.616507i \(-0.788547\pi\)
−0.787349 + 0.616507i \(0.788547\pi\)
\(570\) 125.228 5.24523
\(571\) 8.33478 0.348800 0.174400 0.984675i \(-0.444202\pi\)
0.174400 + 0.984675i \(0.444202\pi\)
\(572\) −16.6907 −0.697872
\(573\) 58.3634 2.43817
\(574\) 31.7942 1.32707
\(575\) 77.8737 3.24756
\(576\) 47.1148 1.96312
\(577\) −13.4895 −0.561577 −0.280788 0.959770i \(-0.590596\pi\)
−0.280788 + 0.959770i \(0.590596\pi\)
\(578\) 18.3009 0.761219
\(579\) 55.7911 2.31860
\(580\) −121.284 −5.03605
\(581\) 15.1765 0.629629
\(582\) 58.1789 2.41159
\(583\) −28.0607 −1.16215
\(584\) 7.02636 0.290753
\(585\) 18.9303 0.782673
\(586\) −24.5169 −1.01279
\(587\) 3.80675 0.157121 0.0785607 0.996909i \(-0.474968\pi\)
0.0785607 + 0.996909i \(0.474968\pi\)
\(588\) −26.5234 −1.09381
\(589\) 24.7240 1.01874
\(590\) −48.5870 −2.00030
\(591\) −44.3573 −1.82462
\(592\) 24.4252 1.00387
\(593\) 28.0179 1.15056 0.575279 0.817957i \(-0.304893\pi\)
0.575279 + 0.817957i \(0.304893\pi\)
\(594\) 52.9758 2.17363
\(595\) −26.6195 −1.09129
\(596\) 63.8625 2.61591
\(597\) −53.4895 −2.18918
\(598\) −22.9255 −0.937492
\(599\) 0.655518 0.0267837 0.0133919 0.999910i \(-0.495737\pi\)
0.0133919 + 0.999910i \(0.495737\pi\)
\(600\) −190.760 −7.78775
\(601\) −12.9947 −0.530066 −0.265033 0.964239i \(-0.585383\pi\)
−0.265033 + 0.964239i \(0.585383\pi\)
\(602\) 64.4702 2.62761
\(603\) 57.8124 2.35430
\(604\) −33.5679 −1.36586
\(605\) 2.70077 0.109802
\(606\) −32.9254 −1.33750
\(607\) 29.0475 1.17900 0.589500 0.807768i \(-0.299325\pi\)
0.589500 + 0.807768i \(0.299325\pi\)
\(608\) 50.3718 2.04285
\(609\) 42.7599 1.73272
\(610\) −2.05103 −0.0830439
\(611\) 10.1256 0.409638
\(612\) 78.3286 3.16624
\(613\) −16.6481 −0.672411 −0.336206 0.941789i \(-0.609144\pi\)
−0.336206 + 0.941789i \(0.609144\pi\)
\(614\) −42.4910 −1.71480
\(615\) 56.9875 2.29796
\(616\) −58.1954 −2.34476
\(617\) −1.00000 −0.0402585
\(618\) −58.9625 −2.37182
\(619\) −40.7759 −1.63892 −0.819460 0.573136i \(-0.805727\pi\)
−0.819460 + 0.573136i \(0.805727\pi\)
\(620\) −99.7210 −4.00489
\(621\) 51.5955 2.07046
\(622\) 17.6785 0.708842
\(623\) 32.7386 1.31165
\(624\) 28.4527 1.13902
\(625\) 9.78973 0.391589
\(626\) −90.8417 −3.63077
\(627\) 43.8550 1.75140
\(628\) 15.7366 0.627958
\(629\) 7.72251 0.307917
\(630\) 111.928 4.45933
\(631\) −34.7951 −1.38517 −0.692586 0.721335i \(-0.743529\pi\)
−0.692586 + 0.721335i \(0.743529\pi\)
\(632\) −22.1476 −0.880982
\(633\) −36.8437 −1.46441
\(634\) −5.22220 −0.207400
\(635\) 29.4179 1.16741
\(636\) 113.526 4.50160
\(637\) −1.91465 −0.0758611
\(638\) −59.9007 −2.37149
\(639\) 31.7837 1.25734
\(640\) −7.38710 −0.292001
\(641\) −13.6626 −0.539639 −0.269820 0.962911i \(-0.586964\pi\)
−0.269820 + 0.962911i \(0.586964\pi\)
\(642\) 61.4889 2.42677
\(643\) −16.0964 −0.634779 −0.317389 0.948295i \(-0.602806\pi\)
−0.317389 + 0.948295i \(0.602806\pi\)
\(644\) −96.1146 −3.78744
\(645\) 115.556 4.54999
\(646\) 37.4045 1.47166
\(647\) −13.3231 −0.523787 −0.261893 0.965097i \(-0.584347\pi\)
−0.261893 + 0.965097i \(0.584347\pi\)
\(648\) −11.6102 −0.456091
\(649\) −17.0152 −0.667905
\(650\) −23.3515 −0.915921
\(651\) 35.1576 1.37794
\(652\) 110.743 4.33705
\(653\) −44.7546 −1.75138 −0.875692 0.482870i \(-0.839594\pi\)
−0.875692 + 0.482870i \(0.839594\pi\)
\(654\) 43.1827 1.68858
\(655\) −10.4177 −0.407052
\(656\) 53.8371 2.10199
\(657\) −4.73259 −0.184636
\(658\) 59.8690 2.33394
\(659\) −4.17416 −0.162602 −0.0813011 0.996690i \(-0.525908\pi\)
−0.0813011 + 0.996690i \(0.525908\pi\)
\(660\) −176.883 −6.88517
\(661\) −45.7584 −1.77980 −0.889898 0.456159i \(-0.849225\pi\)
−0.889898 + 0.456159i \(0.849225\pi\)
\(662\) −51.7219 −2.01023
\(663\) 8.99587 0.349371
\(664\) 50.7222 1.96840
\(665\) 37.8995 1.46968
\(666\) −32.4712 −1.25823
\(667\) −58.3399 −2.25893
\(668\) −41.0863 −1.58968
\(669\) −44.0595 −1.70344
\(670\) −111.351 −4.30185
\(671\) −0.718272 −0.0277286
\(672\) 71.6289 2.76315
\(673\) 34.7819 1.34074 0.670372 0.742025i \(-0.266134\pi\)
0.670372 + 0.742025i \(0.266134\pi\)
\(674\) −5.57176 −0.214616
\(675\) 52.5543 2.02282
\(676\) 4.87451 0.187481
\(677\) 40.7997 1.56806 0.784030 0.620723i \(-0.213161\pi\)
0.784030 + 0.620723i \(0.213161\pi\)
\(678\) 27.3137 1.04898
\(679\) 17.6075 0.675712
\(680\) −88.9662 −3.41170
\(681\) 30.6296 1.17373
\(682\) −49.2509 −1.88591
\(683\) 15.2793 0.584648 0.292324 0.956319i \(-0.405571\pi\)
0.292324 + 0.956319i \(0.405571\pi\)
\(684\) −111.520 −4.26408
\(685\) −28.4444 −1.08681
\(686\) −52.7091 −2.01244
\(687\) −15.3820 −0.586860
\(688\) 109.167 4.16197
\(689\) 8.19512 0.312209
\(690\) −242.958 −9.24926
\(691\) 14.2108 0.540603 0.270302 0.962776i \(-0.412877\pi\)
0.270302 + 0.962776i \(0.412877\pi\)
\(692\) −60.3495 −2.29414
\(693\) 39.1974 1.48898
\(694\) −15.1750 −0.576036
\(695\) 45.6825 1.73283
\(696\) 142.910 5.41698
\(697\) 17.0217 0.644741
\(698\) −80.4926 −3.04669
\(699\) 46.6333 1.76383
\(700\) −97.9006 −3.70030
\(701\) 1.49731 0.0565528 0.0282764 0.999600i \(-0.490998\pi\)
0.0282764 + 0.999600i \(0.490998\pi\)
\(702\) −15.4716 −0.583938
\(703\) −10.9949 −0.414681
\(704\) −31.7794 −1.19773
\(705\) 107.308 4.04147
\(706\) −5.13468 −0.193246
\(707\) −9.96466 −0.374760
\(708\) 68.8390 2.58713
\(709\) 36.4475 1.36881 0.684407 0.729100i \(-0.260061\pi\)
0.684407 + 0.729100i \(0.260061\pi\)
\(710\) −61.2176 −2.29746
\(711\) 14.9174 0.559447
\(712\) 109.417 4.10058
\(713\) −47.9676 −1.79640
\(714\) 53.1893 1.99056
\(715\) −12.7687 −0.477523
\(716\) −25.3418 −0.947068
\(717\) 82.0030 3.06246
\(718\) −32.9439 −1.22946
\(719\) −23.9022 −0.891400 −0.445700 0.895182i \(-0.647045\pi\)
−0.445700 + 0.895182i \(0.647045\pi\)
\(720\) 189.528 7.06329
\(721\) −17.8446 −0.664568
\(722\) −3.43796 −0.127948
\(723\) 23.7032 0.881531
\(724\) −84.6594 −3.14634
\(725\) −59.4240 −2.20695
\(726\) −5.39651 −0.200283
\(727\) 33.4843 1.24187 0.620933 0.783864i \(-0.286754\pi\)
0.620933 + 0.783864i \(0.286754\pi\)
\(728\) 16.9960 0.629913
\(729\) −42.4888 −1.57366
\(730\) 9.11529 0.337372
\(731\) 34.5154 1.27660
\(732\) 2.90594 0.107407
\(733\) −37.7822 −1.39552 −0.697759 0.716332i \(-0.745820\pi\)
−0.697759 + 0.716332i \(0.745820\pi\)
\(734\) 9.47528 0.349739
\(735\) −20.2909 −0.748442
\(736\) −97.7275 −3.60228
\(737\) −38.9951 −1.43640
\(738\) −71.5718 −2.63459
\(739\) 18.4077 0.677139 0.338569 0.940941i \(-0.390057\pi\)
0.338569 + 0.940941i \(0.390057\pi\)
\(740\) 44.3465 1.63021
\(741\) −12.8079 −0.470508
\(742\) 48.4548 1.77883
\(743\) −22.2932 −0.817857 −0.408929 0.912566i \(-0.634098\pi\)
−0.408929 + 0.912566i \(0.634098\pi\)
\(744\) 117.502 4.30783
\(745\) 48.8561 1.78995
\(746\) 15.0152 0.549744
\(747\) −34.1638 −1.24999
\(748\) −52.8334 −1.93178
\(749\) 18.6092 0.679966
\(750\) −108.540 −3.96333
\(751\) 41.3400 1.50852 0.754260 0.656576i \(-0.227996\pi\)
0.754260 + 0.656576i \(0.227996\pi\)
\(752\) 101.376 3.69681
\(753\) −37.7563 −1.37592
\(754\) 17.4940 0.637094
\(755\) −25.6801 −0.934596
\(756\) −64.8644 −2.35910
\(757\) −13.7432 −0.499504 −0.249752 0.968310i \(-0.580349\pi\)
−0.249752 + 0.968310i \(0.580349\pi\)
\(758\) −54.5237 −1.98039
\(759\) −85.0840 −3.08835
\(760\) 126.666 4.59464
\(761\) 10.2563 0.371791 0.185895 0.982570i \(-0.440481\pi\)
0.185895 + 0.982570i \(0.440481\pi\)
\(762\) −58.7809 −2.12941
\(763\) 13.0689 0.473128
\(764\) 100.107 3.62174
\(765\) 59.9230 2.16652
\(766\) 12.1485 0.438942
\(767\) 4.96930 0.179431
\(768\) −37.9920 −1.37092
\(769\) 3.08183 0.111134 0.0555669 0.998455i \(-0.482303\pi\)
0.0555669 + 0.998455i \(0.482303\pi\)
\(770\) −75.4968 −2.72072
\(771\) 0.729152 0.0262598
\(772\) 95.6947 3.44413
\(773\) 13.8242 0.497222 0.248611 0.968603i \(-0.420026\pi\)
0.248611 + 0.968603i \(0.420026\pi\)
\(774\) −145.129 −5.21654
\(775\) −48.8590 −1.75507
\(776\) 58.8466 2.11247
\(777\) −15.6348 −0.560895
\(778\) 26.5750 0.952759
\(779\) −24.2346 −0.868293
\(780\) 51.6588 1.84968
\(781\) −21.4384 −0.767128
\(782\) −72.5694 −2.59507
\(783\) −39.3716 −1.40703
\(784\) −19.1692 −0.684614
\(785\) 12.0388 0.429684
\(786\) 20.8159 0.742479
\(787\) 28.5067 1.01615 0.508077 0.861312i \(-0.330357\pi\)
0.508077 + 0.861312i \(0.330357\pi\)
\(788\) −76.0832 −2.71035
\(789\) 44.9776 1.60125
\(790\) −28.7320 −1.02224
\(791\) 8.26631 0.293916
\(792\) 131.003 4.65500
\(793\) 0.209772 0.00744921
\(794\) 31.4840 1.11733
\(795\) 86.8497 3.08024
\(796\) −91.7469 −3.25188
\(797\) 40.0833 1.41982 0.709912 0.704290i \(-0.248735\pi\)
0.709912 + 0.704290i \(0.248735\pi\)
\(798\) −75.7283 −2.68075
\(799\) 32.0520 1.13392
\(800\) −99.5436 −3.51940
\(801\) −73.6977 −2.60398
\(802\) 49.0159 1.73081
\(803\) 3.19218 0.112650
\(804\) 157.764 5.56390
\(805\) −73.5296 −2.59158
\(806\) 14.3837 0.506646
\(807\) −16.6112 −0.584741
\(808\) −33.3033 −1.17161
\(809\) −23.9235 −0.841107 −0.420553 0.907268i \(-0.638164\pi\)
−0.420553 + 0.907268i \(0.638164\pi\)
\(810\) −15.0619 −0.529221
\(811\) −36.5835 −1.28462 −0.642311 0.766444i \(-0.722024\pi\)
−0.642311 + 0.766444i \(0.722024\pi\)
\(812\) 73.3433 2.57384
\(813\) 87.6748 3.07489
\(814\) 21.9022 0.767670
\(815\) 84.7210 2.96765
\(816\) 90.0654 3.15292
\(817\) −49.1412 −1.71923
\(818\) −7.29684 −0.255128
\(819\) −11.4476 −0.400011
\(820\) 97.7469 3.41347
\(821\) −28.2665 −0.986509 −0.493254 0.869885i \(-0.664193\pi\)
−0.493254 + 0.869885i \(0.664193\pi\)
\(822\) 56.8358 1.98238
\(823\) −34.0266 −1.18609 −0.593047 0.805168i \(-0.702075\pi\)
−0.593047 + 0.805168i \(0.702075\pi\)
\(824\) −59.6392 −2.07763
\(825\) −86.6651 −3.01729
\(826\) 29.3817 1.02232
\(827\) −0.299380 −0.0104105 −0.00520524 0.999986i \(-0.501657\pi\)
−0.00520524 + 0.999986i \(0.501657\pi\)
\(828\) 216.363 7.51913
\(829\) 6.31373 0.219285 0.109642 0.993971i \(-0.465029\pi\)
0.109642 + 0.993971i \(0.465029\pi\)
\(830\) 65.8018 2.28402
\(831\) 62.0330 2.15190
\(832\) 9.28119 0.321768
\(833\) −6.06072 −0.209991
\(834\) −91.2797 −3.16076
\(835\) −31.4318 −1.08774
\(836\) 75.2215 2.60159
\(837\) −32.3717 −1.11893
\(838\) −59.6118 −2.05926
\(839\) −50.6110 −1.74729 −0.873643 0.486568i \(-0.838249\pi\)
−0.873643 + 0.486568i \(0.838249\pi\)
\(840\) 180.119 6.21469
\(841\) 15.5181 0.535107
\(842\) −98.1724 −3.38325
\(843\) −30.8633 −1.06299
\(844\) −63.1956 −2.17528
\(845\) 3.72911 0.128285
\(846\) −134.771 −4.63351
\(847\) −1.63322 −0.0561180
\(848\) 82.0485 2.81756
\(849\) −55.5262 −1.90565
\(850\) −73.9179 −2.53536
\(851\) 21.3315 0.731233
\(852\) 86.7342 2.97147
\(853\) −55.9334 −1.91512 −0.957562 0.288228i \(-0.906934\pi\)
−0.957562 + 0.288228i \(0.906934\pi\)
\(854\) 1.24030 0.0424423
\(855\) −85.3152 −2.91772
\(856\) 62.1947 2.12577
\(857\) −26.7680 −0.914378 −0.457189 0.889370i \(-0.651144\pi\)
−0.457189 + 0.889370i \(0.651144\pi\)
\(858\) 25.5136 0.871020
\(859\) 54.1769 1.84849 0.924246 0.381798i \(-0.124695\pi\)
0.924246 + 0.381798i \(0.124695\pi\)
\(860\) 198.205 6.75872
\(861\) −34.4616 −1.17445
\(862\) 95.2572 3.24447
\(863\) −15.5228 −0.528403 −0.264201 0.964468i \(-0.585108\pi\)
−0.264201 + 0.964468i \(0.585108\pi\)
\(864\) −65.9529 −2.24376
\(865\) −46.1686 −1.56978
\(866\) −75.7604 −2.57444
\(867\) −19.8363 −0.673676
\(868\) 60.3035 2.04683
\(869\) −10.0620 −0.341329
\(870\) 185.397 6.28554
\(871\) 11.3885 0.385885
\(872\) 43.6783 1.47913
\(873\) −39.6360 −1.34148
\(874\) 103.321 3.49487
\(875\) −32.8490 −1.11050
\(876\) −12.9147 −0.436348
\(877\) 48.2164 1.62815 0.814076 0.580758i \(-0.197244\pi\)
0.814076 + 0.580758i \(0.197244\pi\)
\(878\) −95.1665 −3.21172
\(879\) 26.5738 0.896311
\(880\) −127.839 −4.30944
\(881\) −22.8612 −0.770214 −0.385107 0.922872i \(-0.625836\pi\)
−0.385107 + 0.922872i \(0.625836\pi\)
\(882\) 25.4838 0.858084
\(883\) −12.1253 −0.408048 −0.204024 0.978966i \(-0.565402\pi\)
−0.204024 + 0.978966i \(0.565402\pi\)
\(884\) 15.4300 0.518967
\(885\) 52.6633 1.77026
\(886\) 30.5535 1.02646
\(887\) −40.5122 −1.36027 −0.680133 0.733089i \(-0.738078\pi\)
−0.680133 + 0.733089i \(0.738078\pi\)
\(888\) −52.2537 −1.75352
\(889\) −17.7897 −0.596646
\(890\) 141.947 4.75807
\(891\) −5.27468 −0.176708
\(892\) −75.5723 −2.53035
\(893\) −45.6340 −1.52708
\(894\) −97.6211 −3.26494
\(895\) −19.3870 −0.648036
\(896\) 4.46714 0.149237
\(897\) 24.8488 0.829678
\(898\) −85.8767 −2.86574
\(899\) 36.6032 1.22079
\(900\) 220.383 7.34611
\(901\) 25.9412 0.864227
\(902\) 48.2759 1.60741
\(903\) −69.8790 −2.32543
\(904\) 27.6272 0.918867
\(905\) −64.7662 −2.15290
\(906\) 51.3124 1.70474
\(907\) 8.51435 0.282714 0.141357 0.989959i \(-0.454853\pi\)
0.141357 + 0.989959i \(0.454853\pi\)
\(908\) 52.5370 1.74350
\(909\) 22.4314 0.744002
\(910\) 22.0489 0.730913
\(911\) 29.3978 0.973994 0.486997 0.873404i \(-0.338092\pi\)
0.486997 + 0.873404i \(0.338092\pi\)
\(912\) −128.231 −4.24614
\(913\) 23.0438 0.762640
\(914\) 74.1377 2.45226
\(915\) 2.22310 0.0734935
\(916\) −26.3837 −0.871742
\(917\) 6.29980 0.208038
\(918\) −48.9745 −1.61640
\(919\) 38.3293 1.26437 0.632184 0.774818i \(-0.282159\pi\)
0.632184 + 0.774818i \(0.282159\pi\)
\(920\) −245.747 −8.10203
\(921\) 46.0558 1.51759
\(922\) 9.67792 0.318725
\(923\) 6.26110 0.206087
\(924\) 106.965 3.51890
\(925\) 21.7279 0.714408
\(926\) 108.168 3.55462
\(927\) 40.1699 1.31935
\(928\) 74.5741 2.44801
\(929\) −44.0705 −1.44591 −0.722954 0.690897i \(-0.757216\pi\)
−0.722954 + 0.690897i \(0.757216\pi\)
\(930\) 152.435 4.99854
\(931\) 8.62894 0.282802
\(932\) 79.9870 2.62006
\(933\) −19.1616 −0.627323
\(934\) 20.9615 0.685881
\(935\) −40.4187 −1.32183
\(936\) −38.2595 −1.25055
\(937\) −18.8931 −0.617210 −0.308605 0.951190i \(-0.599862\pi\)
−0.308605 + 0.951190i \(0.599862\pi\)
\(938\) 67.3363 2.19861
\(939\) 98.4629 3.21322
\(940\) 184.059 6.00334
\(941\) −46.8173 −1.52620 −0.763100 0.646280i \(-0.776324\pi\)
−0.763100 + 0.646280i \(0.776324\pi\)
\(942\) −24.0552 −0.783760
\(943\) 47.0180 1.53112
\(944\) 49.7519 1.61929
\(945\) −49.6226 −1.61422
\(946\) 97.8907 3.18270
\(947\) −10.9288 −0.355138 −0.177569 0.984108i \(-0.556823\pi\)
−0.177569 + 0.984108i \(0.556823\pi\)
\(948\) 40.7080 1.32213
\(949\) −0.932277 −0.0302630
\(950\) 105.240 3.41445
\(951\) 5.66031 0.183548
\(952\) 53.7998 1.74366
\(953\) −13.1711 −0.426654 −0.213327 0.976981i \(-0.568430\pi\)
−0.213327 + 0.976981i \(0.568430\pi\)
\(954\) −109.076 −3.53148
\(955\) 76.5838 2.47819
\(956\) 140.654 4.54908
\(957\) 64.9261 2.09876
\(958\) 64.4323 2.08171
\(959\) 17.2010 0.555449
\(960\) 98.3596 3.17454
\(961\) −0.904506 −0.0291776
\(962\) −6.39653 −0.206232
\(963\) −41.8911 −1.34992
\(964\) 40.6565 1.30946
\(965\) 73.2085 2.35666
\(966\) 146.922 4.72714
\(967\) −46.1107 −1.48282 −0.741410 0.671053i \(-0.765842\pi\)
−0.741410 + 0.671053i \(0.765842\pi\)
\(968\) −5.45845 −0.175441
\(969\) −40.5426 −1.30242
\(970\) 76.3417 2.45118
\(971\) 34.7972 1.11670 0.558348 0.829607i \(-0.311435\pi\)
0.558348 + 0.829607i \(0.311435\pi\)
\(972\) −64.9514 −2.08332
\(973\) −27.6252 −0.885623
\(974\) −32.2943 −1.03478
\(975\) 25.3106 0.810587
\(976\) 2.10021 0.0672259
\(977\) −23.8448 −0.762862 −0.381431 0.924397i \(-0.624569\pi\)
−0.381431 + 0.924397i \(0.624569\pi\)
\(978\) −169.284 −5.41310
\(979\) 49.7098 1.58873
\(980\) −34.8037 −1.11176
\(981\) −29.4194 −0.939290
\(982\) 23.2568 0.742154
\(983\) −16.4683 −0.525257 −0.262629 0.964897i \(-0.584589\pi\)
−0.262629 + 0.964897i \(0.584589\pi\)
\(984\) −115.176 −3.67167
\(985\) −58.2052 −1.85457
\(986\) 55.3763 1.76354
\(987\) −64.8917 −2.06553
\(988\) −21.9685 −0.698910
\(989\) 95.3400 3.03164
\(990\) 169.950 5.40137
\(991\) 30.4390 0.966927 0.483464 0.875365i \(-0.339379\pi\)
0.483464 + 0.875365i \(0.339379\pi\)
\(992\) 61.3155 1.94677
\(993\) 56.0611 1.77905
\(994\) 37.0197 1.17419
\(995\) −70.1883 −2.22512
\(996\) −93.2292 −2.95408
\(997\) 10.2714 0.325298 0.162649 0.986684i \(-0.447996\pi\)
0.162649 + 0.986684i \(0.447996\pi\)
\(998\) −36.9828 −1.17067
\(999\) 14.3959 0.455465
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 8021.2.a.d.1.15 174
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8021.2.a.d.1.15 174 1.1 even 1 trivial