Properties

Label 8013.2.a.b.1.8
Level $8013$
Weight $2$
Character 8013.1
Self dual yes
Analytic conductor $63.984$
Analytic rank $0$
Dimension $106$
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] = [8013,2,Mod(1,8013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8013, 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("8013.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8013 = 3 \cdot 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8013.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: \(63.9841271397\)
Analytic rank: \(0\)
Dimension: \(106\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.43314 q^{2} -1.00000 q^{3} +3.92015 q^{4} +4.32607 q^{5} +2.43314 q^{6} +4.27561 q^{7} -4.67199 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.43314 q^{2} -1.00000 q^{3} +3.92015 q^{4} +4.32607 q^{5} +2.43314 q^{6} +4.27561 q^{7} -4.67199 q^{8} +1.00000 q^{9} -10.5259 q^{10} +4.41643 q^{11} -3.92015 q^{12} -3.10182 q^{13} -10.4031 q^{14} -4.32607 q^{15} +3.52729 q^{16} +2.22761 q^{17} -2.43314 q^{18} +6.20974 q^{19} +16.9588 q^{20} -4.27561 q^{21} -10.7458 q^{22} +1.57714 q^{23} +4.67199 q^{24} +13.7148 q^{25} +7.54714 q^{26} -1.00000 q^{27} +16.7610 q^{28} -8.59536 q^{29} +10.5259 q^{30} -2.78902 q^{31} +0.761613 q^{32} -4.41643 q^{33} -5.42007 q^{34} +18.4966 q^{35} +3.92015 q^{36} +3.92642 q^{37} -15.1091 q^{38} +3.10182 q^{39} -20.2113 q^{40} +4.06953 q^{41} +10.4031 q^{42} -8.21929 q^{43} +17.3131 q^{44} +4.32607 q^{45} -3.83740 q^{46} -4.10099 q^{47} -3.52729 q^{48} +11.2808 q^{49} -33.3701 q^{50} -2.22761 q^{51} -12.1596 q^{52} -5.52229 q^{53} +2.43314 q^{54} +19.1058 q^{55} -19.9756 q^{56} -6.20974 q^{57} +20.9137 q^{58} -8.78197 q^{59} -16.9588 q^{60} -12.8871 q^{61} +6.78607 q^{62} +4.27561 q^{63} -8.90768 q^{64} -13.4187 q^{65} +10.7458 q^{66} +4.05528 q^{67} +8.73256 q^{68} -1.57714 q^{69} -45.0047 q^{70} -2.48373 q^{71} -4.67199 q^{72} +0.913035 q^{73} -9.55350 q^{74} -13.7148 q^{75} +24.3431 q^{76} +18.8829 q^{77} -7.54714 q^{78} -13.3802 q^{79} +15.2593 q^{80} +1.00000 q^{81} -9.90171 q^{82} +12.3204 q^{83} -16.7610 q^{84} +9.63677 q^{85} +19.9986 q^{86} +8.59536 q^{87} -20.6335 q^{88} +13.8184 q^{89} -10.5259 q^{90} -13.2622 q^{91} +6.18263 q^{92} +2.78902 q^{93} +9.97827 q^{94} +26.8637 q^{95} -0.761613 q^{96} -0.475066 q^{97} -27.4478 q^{98} +4.41643 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 106 q + 15 q^{2} - 106 q^{3} + 109 q^{4} + 16 q^{5} - 15 q^{6} + 35 q^{7} + 48 q^{8} + 106 q^{9} - 3 q^{10} + 55 q^{11} - 109 q^{12} - 8 q^{13} + 27 q^{14} - 16 q^{15} + 111 q^{16} + 28 q^{17} + 15 q^{18} + q^{19} + 54 q^{20} - 35 q^{21} + 20 q^{22} + 62 q^{23} - 48 q^{24} + 102 q^{25} + 21 q^{26} - 106 q^{27} + 79 q^{28} + 36 q^{29} + 3 q^{30} + q^{31} + 111 q^{32} - 55 q^{33} - 27 q^{34} + 72 q^{35} + 109 q^{36} + 31 q^{37} + 43 q^{38} + 8 q^{39} - 13 q^{40} + 35 q^{41} - 27 q^{42} + 98 q^{43} + 121 q^{44} + 16 q^{45} + 8 q^{46} + 75 q^{47} - 111 q^{48} + 49 q^{49} + 83 q^{50} - 28 q^{51} - 18 q^{52} + 60 q^{53} - 15 q^{54} + 14 q^{55} + 85 q^{56} - q^{57} + 65 q^{58} + 77 q^{59} - 54 q^{60} - 55 q^{61} + 83 q^{62} + 35 q^{63} + 122 q^{64} + 86 q^{65} - 20 q^{66} + 121 q^{67} + 80 q^{68} - 62 q^{69} - 11 q^{70} + 79 q^{71} + 48 q^{72} - 29 q^{73} + 91 q^{74} - 102 q^{75} - 10 q^{76} + 87 q^{77} - 21 q^{78} + 15 q^{79} + 108 q^{80} + 106 q^{81} + 21 q^{82} + 196 q^{83} - 79 q^{84} - 5 q^{85} + 65 q^{86} - 36 q^{87} + 84 q^{88} + 34 q^{89} - 3 q^{90} + 17 q^{91} + 162 q^{92} - q^{93} - 35 q^{94} + 113 q^{95} - 111 q^{96} - 63 q^{97} + 112 q^{98} + 55 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.43314 −1.72049 −0.860244 0.509883i \(-0.829689\pi\)
−0.860244 + 0.509883i \(0.829689\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.92015 1.96008
\(5\) 4.32607 1.93468 0.967338 0.253492i \(-0.0815791\pi\)
0.967338 + 0.253492i \(0.0815791\pi\)
\(6\) 2.43314 0.993324
\(7\) 4.27561 1.61603 0.808014 0.589163i \(-0.200542\pi\)
0.808014 + 0.589163i \(0.200542\pi\)
\(8\) −4.67199 −1.65180
\(9\) 1.00000 0.333333
\(10\) −10.5259 −3.32858
\(11\) 4.41643 1.33160 0.665802 0.746128i \(-0.268089\pi\)
0.665802 + 0.746128i \(0.268089\pi\)
\(12\) −3.92015 −1.13165
\(13\) −3.10182 −0.860289 −0.430145 0.902760i \(-0.641537\pi\)
−0.430145 + 0.902760i \(0.641537\pi\)
\(14\) −10.4031 −2.78036
\(15\) −4.32607 −1.11699
\(16\) 3.52729 0.881822
\(17\) 2.22761 0.540274 0.270137 0.962822i \(-0.412931\pi\)
0.270137 + 0.962822i \(0.412931\pi\)
\(18\) −2.43314 −0.573496
\(19\) 6.20974 1.42461 0.712306 0.701869i \(-0.247651\pi\)
0.712306 + 0.701869i \(0.247651\pi\)
\(20\) 16.9588 3.79211
\(21\) −4.27561 −0.933015
\(22\) −10.7458 −2.29101
\(23\) 1.57714 0.328856 0.164428 0.986389i \(-0.447422\pi\)
0.164428 + 0.986389i \(0.447422\pi\)
\(24\) 4.67199 0.953666
\(25\) 13.7148 2.74297
\(26\) 7.54714 1.48012
\(27\) −1.00000 −0.192450
\(28\) 16.7610 3.16754
\(29\) −8.59536 −1.59612 −0.798060 0.602579i \(-0.794140\pi\)
−0.798060 + 0.602579i \(0.794140\pi\)
\(30\) 10.5259 1.92176
\(31\) −2.78902 −0.500923 −0.250462 0.968127i \(-0.580582\pi\)
−0.250462 + 0.968127i \(0.580582\pi\)
\(32\) 0.761613 0.134635
\(33\) −4.41643 −0.768802
\(34\) −5.42007 −0.929534
\(35\) 18.4966 3.12649
\(36\) 3.92015 0.653359
\(37\) 3.92642 0.645499 0.322749 0.946484i \(-0.395393\pi\)
0.322749 + 0.946484i \(0.395393\pi\)
\(38\) −15.1091 −2.45103
\(39\) 3.10182 0.496688
\(40\) −20.2113 −3.19569
\(41\) 4.06953 0.635553 0.317777 0.948166i \(-0.397064\pi\)
0.317777 + 0.948166i \(0.397064\pi\)
\(42\) 10.4031 1.60524
\(43\) −8.21929 −1.25343 −0.626715 0.779249i \(-0.715601\pi\)
−0.626715 + 0.779249i \(0.715601\pi\)
\(44\) 17.3131 2.61005
\(45\) 4.32607 0.644892
\(46\) −3.83740 −0.565793
\(47\) −4.10099 −0.598191 −0.299095 0.954223i \(-0.596685\pi\)
−0.299095 + 0.954223i \(0.596685\pi\)
\(48\) −3.52729 −0.509120
\(49\) 11.2808 1.61155
\(50\) −33.3701 −4.71924
\(51\) −2.22761 −0.311927
\(52\) −12.1596 −1.68623
\(53\) −5.52229 −0.758545 −0.379273 0.925285i \(-0.623826\pi\)
−0.379273 + 0.925285i \(0.623826\pi\)
\(54\) 2.43314 0.331108
\(55\) 19.1058 2.57622
\(56\) −19.9756 −2.66935
\(57\) −6.20974 −0.822500
\(58\) 20.9137 2.74610
\(59\) −8.78197 −1.14331 −0.571657 0.820492i \(-0.693699\pi\)
−0.571657 + 0.820492i \(0.693699\pi\)
\(60\) −16.9588 −2.18938
\(61\) −12.8871 −1.65003 −0.825015 0.565111i \(-0.808833\pi\)
−0.825015 + 0.565111i \(0.808833\pi\)
\(62\) 6.78607 0.861832
\(63\) 4.27561 0.538676
\(64\) −8.90768 −1.11346
\(65\) −13.4187 −1.66438
\(66\) 10.7458 1.32271
\(67\) 4.05528 0.495431 0.247716 0.968833i \(-0.420320\pi\)
0.247716 + 0.968833i \(0.420320\pi\)
\(68\) 8.73256 1.05898
\(69\) −1.57714 −0.189865
\(70\) −45.0047 −5.37909
\(71\) −2.48373 −0.294764 −0.147382 0.989080i \(-0.547085\pi\)
−0.147382 + 0.989080i \(0.547085\pi\)
\(72\) −4.67199 −0.550599
\(73\) 0.913035 0.106863 0.0534314 0.998572i \(-0.482984\pi\)
0.0534314 + 0.998572i \(0.482984\pi\)
\(74\) −9.55350 −1.11057
\(75\) −13.7148 −1.58365
\(76\) 24.3431 2.79235
\(77\) 18.8829 2.15191
\(78\) −7.54714 −0.854546
\(79\) −13.3802 −1.50539 −0.752697 0.658367i \(-0.771248\pi\)
−0.752697 + 0.658367i \(0.771248\pi\)
\(80\) 15.2593 1.70604
\(81\) 1.00000 0.111111
\(82\) −9.90171 −1.09346
\(83\) 12.3204 1.35234 0.676171 0.736745i \(-0.263638\pi\)
0.676171 + 0.736745i \(0.263638\pi\)
\(84\) −16.7610 −1.82878
\(85\) 9.63677 1.04525
\(86\) 19.9986 2.15651
\(87\) 8.59536 0.921520
\(88\) −20.6335 −2.19954
\(89\) 13.8184 1.46475 0.732374 0.680903i \(-0.238412\pi\)
0.732374 + 0.680903i \(0.238412\pi\)
\(90\) −10.5259 −1.10953
\(91\) −13.2622 −1.39025
\(92\) 6.18263 0.644583
\(93\) 2.78902 0.289208
\(94\) 9.97827 1.02918
\(95\) 26.8637 2.75616
\(96\) −0.761613 −0.0777318
\(97\) −0.475066 −0.0482357 −0.0241178 0.999709i \(-0.507678\pi\)
−0.0241178 + 0.999709i \(0.507678\pi\)
\(98\) −27.4478 −2.77265
\(99\) 4.41643 0.443868
\(100\) 53.7642 5.37642
\(101\) −0.687244 −0.0683834 −0.0341917 0.999415i \(-0.510886\pi\)
−0.0341917 + 0.999415i \(0.510886\pi\)
\(102\) 5.42007 0.536667
\(103\) −6.80191 −0.670212 −0.335106 0.942180i \(-0.608772\pi\)
−0.335106 + 0.942180i \(0.608772\pi\)
\(104\) 14.4917 1.42102
\(105\) −18.4966 −1.80508
\(106\) 13.4365 1.30507
\(107\) 7.16048 0.692230 0.346115 0.938192i \(-0.387501\pi\)
0.346115 + 0.938192i \(0.387501\pi\)
\(108\) −3.92015 −0.377217
\(109\) 15.8253 1.51579 0.757894 0.652378i \(-0.226229\pi\)
0.757894 + 0.652378i \(0.226229\pi\)
\(110\) −46.4870 −4.43236
\(111\) −3.92642 −0.372679
\(112\) 15.0813 1.42505
\(113\) 4.14186 0.389633 0.194817 0.980840i \(-0.437589\pi\)
0.194817 + 0.980840i \(0.437589\pi\)
\(114\) 15.1091 1.41510
\(115\) 6.82281 0.636230
\(116\) −33.6951 −3.12851
\(117\) −3.10182 −0.286763
\(118\) 21.3677 1.96706
\(119\) 9.52438 0.873098
\(120\) 20.2113 1.84503
\(121\) 8.50488 0.773171
\(122\) 31.3562 2.83885
\(123\) −4.06953 −0.366937
\(124\) −10.9334 −0.981847
\(125\) 37.7010 3.37208
\(126\) −10.4031 −0.926786
\(127\) 13.3891 1.18809 0.594045 0.804431i \(-0.297530\pi\)
0.594045 + 0.804431i \(0.297530\pi\)
\(128\) 20.1504 1.78106
\(129\) 8.21929 0.723668
\(130\) 32.6494 2.86355
\(131\) −2.23789 −0.195526 −0.0977629 0.995210i \(-0.531169\pi\)
−0.0977629 + 0.995210i \(0.531169\pi\)
\(132\) −17.3131 −1.50691
\(133\) 26.5504 2.30222
\(134\) −9.86704 −0.852383
\(135\) −4.32607 −0.372328
\(136\) −10.4074 −0.892423
\(137\) −5.49567 −0.469527 −0.234763 0.972053i \(-0.575432\pi\)
−0.234763 + 0.972053i \(0.575432\pi\)
\(138\) 3.83740 0.326661
\(139\) −12.3433 −1.04695 −0.523474 0.852041i \(-0.675364\pi\)
−0.523474 + 0.852041i \(0.675364\pi\)
\(140\) 72.5094 6.12816
\(141\) 4.10099 0.345366
\(142\) 6.04324 0.507138
\(143\) −13.6990 −1.14557
\(144\) 3.52729 0.293941
\(145\) −37.1841 −3.08797
\(146\) −2.22154 −0.183856
\(147\) −11.2808 −0.930428
\(148\) 15.3921 1.26523
\(149\) 15.6789 1.28446 0.642232 0.766510i \(-0.278009\pi\)
0.642232 + 0.766510i \(0.278009\pi\)
\(150\) 33.3701 2.72465
\(151\) −5.53514 −0.450444 −0.225222 0.974308i \(-0.572311\pi\)
−0.225222 + 0.974308i \(0.572311\pi\)
\(152\) −29.0119 −2.35317
\(153\) 2.22761 0.180091
\(154\) −45.9448 −3.70234
\(155\) −12.0655 −0.969123
\(156\) 12.1596 0.973547
\(157\) −2.45042 −0.195565 −0.0977823 0.995208i \(-0.531175\pi\)
−0.0977823 + 0.995208i \(0.531175\pi\)
\(158\) 32.5559 2.59001
\(159\) 5.52229 0.437946
\(160\) 3.29479 0.260476
\(161\) 6.74324 0.531441
\(162\) −2.43314 −0.191165
\(163\) 16.7975 1.31568 0.657840 0.753158i \(-0.271470\pi\)
0.657840 + 0.753158i \(0.271470\pi\)
\(164\) 15.9532 1.24573
\(165\) −19.1058 −1.48738
\(166\) −29.9773 −2.32669
\(167\) 11.4013 0.882256 0.441128 0.897444i \(-0.354579\pi\)
0.441128 + 0.897444i \(0.354579\pi\)
\(168\) 19.9756 1.54115
\(169\) −3.37873 −0.259902
\(170\) −23.4476 −1.79835
\(171\) 6.20974 0.474871
\(172\) −32.2208 −2.45682
\(173\) 15.4104 1.17163 0.585816 0.810444i \(-0.300774\pi\)
0.585816 + 0.810444i \(0.300774\pi\)
\(174\) −20.9137 −1.58546
\(175\) 58.6393 4.43272
\(176\) 15.5780 1.17424
\(177\) 8.78197 0.660093
\(178\) −33.6221 −2.52008
\(179\) −7.82666 −0.584992 −0.292496 0.956267i \(-0.594486\pi\)
−0.292496 + 0.956267i \(0.594486\pi\)
\(180\) 16.9588 1.26404
\(181\) 5.73370 0.426182 0.213091 0.977032i \(-0.431647\pi\)
0.213091 + 0.977032i \(0.431647\pi\)
\(182\) 32.2687 2.39191
\(183\) 12.8871 0.952645
\(184\) −7.36838 −0.543204
\(185\) 16.9859 1.24883
\(186\) −6.78607 −0.497579
\(187\) 9.83807 0.719431
\(188\) −16.0765 −1.17250
\(189\) −4.27561 −0.311005
\(190\) −65.3632 −4.74194
\(191\) 26.7017 1.93207 0.966033 0.258417i \(-0.0832010\pi\)
0.966033 + 0.258417i \(0.0832010\pi\)
\(192\) 8.90768 0.642857
\(193\) 5.01994 0.361343 0.180672 0.983543i \(-0.442173\pi\)
0.180672 + 0.983543i \(0.442173\pi\)
\(194\) 1.15590 0.0829889
\(195\) 13.4187 0.960931
\(196\) 44.2226 3.15876
\(197\) 5.40340 0.384976 0.192488 0.981299i \(-0.438344\pi\)
0.192488 + 0.981299i \(0.438344\pi\)
\(198\) −10.7458 −0.763670
\(199\) −6.84587 −0.485291 −0.242645 0.970115i \(-0.578015\pi\)
−0.242645 + 0.970115i \(0.578015\pi\)
\(200\) −64.0756 −4.53083
\(201\) −4.05528 −0.286037
\(202\) 1.67216 0.117653
\(203\) −36.7504 −2.57937
\(204\) −8.73256 −0.611401
\(205\) 17.6050 1.22959
\(206\) 16.5500 1.15309
\(207\) 1.57714 0.109619
\(208\) −10.9410 −0.758622
\(209\) 27.4249 1.89702
\(210\) 45.0047 3.10562
\(211\) −2.07753 −0.143023 −0.0715117 0.997440i \(-0.522782\pi\)
−0.0715117 + 0.997440i \(0.522782\pi\)
\(212\) −21.6482 −1.48681
\(213\) 2.48373 0.170182
\(214\) −17.4224 −1.19097
\(215\) −35.5572 −2.42498
\(216\) 4.67199 0.317889
\(217\) −11.9248 −0.809506
\(218\) −38.5051 −2.60789
\(219\) −0.913035 −0.0616972
\(220\) 74.8975 5.04959
\(221\) −6.90963 −0.464792
\(222\) 9.55350 0.641189
\(223\) −16.3319 −1.09367 −0.546834 0.837241i \(-0.684167\pi\)
−0.546834 + 0.837241i \(0.684167\pi\)
\(224\) 3.25636 0.217575
\(225\) 13.7148 0.914323
\(226\) −10.0777 −0.670359
\(227\) 10.2045 0.677299 0.338650 0.940913i \(-0.390030\pi\)
0.338650 + 0.940913i \(0.390030\pi\)
\(228\) −24.3431 −1.61216
\(229\) 13.8003 0.911952 0.455976 0.889992i \(-0.349290\pi\)
0.455976 + 0.889992i \(0.349290\pi\)
\(230\) −16.6008 −1.09463
\(231\) −18.8829 −1.24241
\(232\) 40.1575 2.63647
\(233\) 18.9576 1.24195 0.620976 0.783829i \(-0.286736\pi\)
0.620976 + 0.783829i \(0.286736\pi\)
\(234\) 7.54714 0.493372
\(235\) −17.7411 −1.15730
\(236\) −34.4266 −2.24098
\(237\) 13.3802 0.869140
\(238\) −23.1741 −1.50215
\(239\) −4.74569 −0.306973 −0.153487 0.988151i \(-0.549050\pi\)
−0.153487 + 0.988151i \(0.549050\pi\)
\(240\) −15.2593 −0.984982
\(241\) −2.14957 −0.138466 −0.0692329 0.997601i \(-0.522055\pi\)
−0.0692329 + 0.997601i \(0.522055\pi\)
\(242\) −20.6935 −1.33023
\(243\) −1.00000 −0.0641500
\(244\) −50.5196 −3.23418
\(245\) 48.8017 3.11782
\(246\) 9.90171 0.631310
\(247\) −19.2615 −1.22558
\(248\) 13.0303 0.827424
\(249\) −12.3204 −0.780775
\(250\) −91.7316 −5.80161
\(251\) −1.07911 −0.0681129 −0.0340564 0.999420i \(-0.510843\pi\)
−0.0340564 + 0.999420i \(0.510843\pi\)
\(252\) 16.7610 1.05585
\(253\) 6.96533 0.437907
\(254\) −32.5775 −2.04410
\(255\) −9.63677 −0.603478
\(256\) −31.2132 −1.95083
\(257\) 19.0965 1.19121 0.595603 0.803279i \(-0.296913\pi\)
0.595603 + 0.803279i \(0.296913\pi\)
\(258\) −19.9986 −1.24506
\(259\) 16.7878 1.04314
\(260\) −52.6032 −3.26231
\(261\) −8.59536 −0.532040
\(262\) 5.44510 0.336400
\(263\) 21.0525 1.29815 0.649077 0.760723i \(-0.275155\pi\)
0.649077 + 0.760723i \(0.275155\pi\)
\(264\) 20.6335 1.26991
\(265\) −23.8898 −1.46754
\(266\) −64.6008 −3.96093
\(267\) −13.8184 −0.845673
\(268\) 15.8973 0.971082
\(269\) 2.84626 0.173539 0.0867697 0.996228i \(-0.472346\pi\)
0.0867697 + 0.996228i \(0.472346\pi\)
\(270\) 10.5259 0.640586
\(271\) 0.859074 0.0521850 0.0260925 0.999660i \(-0.491694\pi\)
0.0260925 + 0.999660i \(0.491694\pi\)
\(272\) 7.85741 0.476425
\(273\) 13.2622 0.802663
\(274\) 13.3717 0.807814
\(275\) 60.5707 3.65255
\(276\) −6.18263 −0.372150
\(277\) −14.5325 −0.873173 −0.436586 0.899662i \(-0.643813\pi\)
−0.436586 + 0.899662i \(0.643813\pi\)
\(278\) 30.0330 1.80126
\(279\) −2.78902 −0.166974
\(280\) −86.4158 −5.16433
\(281\) 28.0433 1.67292 0.836462 0.548025i \(-0.184620\pi\)
0.836462 + 0.548025i \(0.184620\pi\)
\(282\) −9.97827 −0.594197
\(283\) −3.01509 −0.179229 −0.0896143 0.995977i \(-0.528563\pi\)
−0.0896143 + 0.995977i \(0.528563\pi\)
\(284\) −9.73658 −0.577760
\(285\) −26.8637 −1.59127
\(286\) 33.3315 1.97093
\(287\) 17.3997 1.02707
\(288\) 0.761613 0.0448785
\(289\) −12.0378 −0.708104
\(290\) 90.4740 5.31282
\(291\) 0.475066 0.0278489
\(292\) 3.57924 0.209459
\(293\) −28.0077 −1.63623 −0.818113 0.575057i \(-0.804980\pi\)
−0.818113 + 0.575057i \(0.804980\pi\)
\(294\) 27.4478 1.60079
\(295\) −37.9914 −2.21194
\(296\) −18.3442 −1.06623
\(297\) −4.41643 −0.256267
\(298\) −38.1488 −2.20990
\(299\) −4.89200 −0.282912
\(300\) −53.7642 −3.10408
\(301\) −35.1425 −2.02558
\(302\) 13.4678 0.774982
\(303\) 0.687244 0.0394812
\(304\) 21.9035 1.25625
\(305\) −55.7506 −3.19227
\(306\) −5.42007 −0.309845
\(307\) 31.6001 1.80351 0.901756 0.432246i \(-0.142279\pi\)
0.901756 + 0.432246i \(0.142279\pi\)
\(308\) 74.0240 4.21791
\(309\) 6.80191 0.386947
\(310\) 29.3570 1.66736
\(311\) −7.14550 −0.405184 −0.202592 0.979263i \(-0.564937\pi\)
−0.202592 + 0.979263i \(0.564937\pi\)
\(312\) −14.4917 −0.820429
\(313\) 2.29485 0.129713 0.0648563 0.997895i \(-0.479341\pi\)
0.0648563 + 0.997895i \(0.479341\pi\)
\(314\) 5.96220 0.336466
\(315\) 18.4966 1.04216
\(316\) −52.4526 −2.95069
\(317\) −4.72896 −0.265605 −0.132802 0.991143i \(-0.542398\pi\)
−0.132802 + 0.991143i \(0.542398\pi\)
\(318\) −13.4365 −0.753481
\(319\) −37.9609 −2.12540
\(320\) −38.5352 −2.15418
\(321\) −7.16048 −0.399659
\(322\) −16.4072 −0.914338
\(323\) 13.8329 0.769681
\(324\) 3.92015 0.217786
\(325\) −42.5409 −2.35975
\(326\) −40.8706 −2.26361
\(327\) −15.8253 −0.875140
\(328\) −19.0128 −1.04981
\(329\) −17.5342 −0.966694
\(330\) 46.4870 2.55902
\(331\) −27.8375 −1.53009 −0.765043 0.643980i \(-0.777282\pi\)
−0.765043 + 0.643980i \(0.777282\pi\)
\(332\) 48.2979 2.65069
\(333\) 3.92642 0.215166
\(334\) −27.7408 −1.51791
\(335\) 17.5434 0.958498
\(336\) −15.0813 −0.822753
\(337\) −29.0543 −1.58269 −0.791346 0.611369i \(-0.790619\pi\)
−0.791346 + 0.611369i \(0.790619\pi\)
\(338\) 8.22090 0.447158
\(339\) −4.14186 −0.224955
\(340\) 37.7776 2.04878
\(341\) −12.3175 −0.667031
\(342\) −15.1091 −0.817009
\(343\) 18.3032 0.988281
\(344\) 38.4004 2.07041
\(345\) −6.82281 −0.367328
\(346\) −37.4956 −2.01578
\(347\) 20.9222 1.12316 0.561581 0.827421i \(-0.310193\pi\)
0.561581 + 0.827421i \(0.310193\pi\)
\(348\) 33.6951 1.80625
\(349\) 14.6284 0.783038 0.391519 0.920170i \(-0.371950\pi\)
0.391519 + 0.920170i \(0.371950\pi\)
\(350\) −142.677 −7.62643
\(351\) 3.10182 0.165563
\(352\) 3.36361 0.179281
\(353\) −23.4035 −1.24564 −0.622822 0.782363i \(-0.714014\pi\)
−0.622822 + 0.782363i \(0.714014\pi\)
\(354\) −21.3677 −1.13568
\(355\) −10.7448 −0.570273
\(356\) 54.1702 2.87102
\(357\) −9.52438 −0.504083
\(358\) 19.0433 1.00647
\(359\) 23.9181 1.26235 0.631174 0.775641i \(-0.282573\pi\)
0.631174 + 0.775641i \(0.282573\pi\)
\(360\) −20.2113 −1.06523
\(361\) 19.5609 1.02952
\(362\) −13.9509 −0.733241
\(363\) −8.50488 −0.446391
\(364\) −51.9897 −2.72500
\(365\) 3.94985 0.206745
\(366\) −31.3562 −1.63901
\(367\) −22.3516 −1.16675 −0.583373 0.812205i \(-0.698267\pi\)
−0.583373 + 0.812205i \(0.698267\pi\)
\(368\) 5.56302 0.289993
\(369\) 4.06953 0.211851
\(370\) −41.3291 −2.14860
\(371\) −23.6112 −1.22583
\(372\) 10.9334 0.566870
\(373\) −13.6008 −0.704222 −0.352111 0.935958i \(-0.614536\pi\)
−0.352111 + 0.935958i \(0.614536\pi\)
\(374\) −23.9374 −1.23777
\(375\) −37.7010 −1.94687
\(376\) 19.1598 0.988090
\(377\) 26.6613 1.37312
\(378\) 10.4031 0.535080
\(379\) 23.7741 1.22119 0.610596 0.791942i \(-0.290930\pi\)
0.610596 + 0.791942i \(0.290930\pi\)
\(380\) 105.310 5.40229
\(381\) −13.3891 −0.685945
\(382\) −64.9689 −3.32410
\(383\) 30.8995 1.57889 0.789446 0.613820i \(-0.210368\pi\)
0.789446 + 0.613820i \(0.210368\pi\)
\(384\) −20.1504 −1.02829
\(385\) 81.6889 4.16325
\(386\) −12.2142 −0.621686
\(387\) −8.21929 −0.417810
\(388\) −1.86233 −0.0945456
\(389\) 13.5985 0.689472 0.344736 0.938700i \(-0.387968\pi\)
0.344736 + 0.938700i \(0.387968\pi\)
\(390\) −32.6494 −1.65327
\(391\) 3.51325 0.177673
\(392\) −52.7040 −2.66195
\(393\) 2.23789 0.112887
\(394\) −13.1472 −0.662347
\(395\) −57.8838 −2.91245
\(396\) 17.3131 0.870015
\(397\) −13.2920 −0.667105 −0.333553 0.942731i \(-0.608248\pi\)
−0.333553 + 0.942731i \(0.608248\pi\)
\(398\) 16.6569 0.834936
\(399\) −26.5504 −1.32918
\(400\) 48.3762 2.41881
\(401\) −38.1202 −1.90363 −0.951816 0.306670i \(-0.900785\pi\)
−0.951816 + 0.306670i \(0.900785\pi\)
\(402\) 9.86704 0.492123
\(403\) 8.65104 0.430939
\(404\) −2.69410 −0.134037
\(405\) 4.32607 0.214964
\(406\) 89.4188 4.43778
\(407\) 17.3408 0.859549
\(408\) 10.4074 0.515241
\(409\) −32.4502 −1.60456 −0.802281 0.596947i \(-0.796380\pi\)
−0.802281 + 0.596947i \(0.796380\pi\)
\(410\) −42.8355 −2.11549
\(411\) 5.49567 0.271081
\(412\) −26.6645 −1.31367
\(413\) −37.5483 −1.84763
\(414\) −3.83740 −0.188598
\(415\) 53.2989 2.61634
\(416\) −2.36239 −0.115825
\(417\) 12.3433 0.604456
\(418\) −66.7285 −3.26380
\(419\) −28.2342 −1.37933 −0.689665 0.724128i \(-0.742242\pi\)
−0.689665 + 0.724128i \(0.742242\pi\)
\(420\) −72.5094 −3.53809
\(421\) 22.3706 1.09028 0.545138 0.838346i \(-0.316477\pi\)
0.545138 + 0.838346i \(0.316477\pi\)
\(422\) 5.05492 0.246070
\(423\) −4.10099 −0.199397
\(424\) 25.8001 1.25296
\(425\) 30.5513 1.48195
\(426\) −6.04324 −0.292796
\(427\) −55.1004 −2.66650
\(428\) 28.0702 1.35682
\(429\) 13.6990 0.661393
\(430\) 86.5154 4.17214
\(431\) −28.5174 −1.37364 −0.686818 0.726829i \(-0.740993\pi\)
−0.686818 + 0.726829i \(0.740993\pi\)
\(432\) −3.52729 −0.169707
\(433\) −26.3546 −1.26652 −0.633261 0.773938i \(-0.718284\pi\)
−0.633261 + 0.773938i \(0.718284\pi\)
\(434\) 29.0146 1.39274
\(435\) 37.1841 1.78284
\(436\) 62.0375 2.97106
\(437\) 9.79363 0.468493
\(438\) 2.22154 0.106149
\(439\) 15.2254 0.726667 0.363333 0.931659i \(-0.381639\pi\)
0.363333 + 0.931659i \(0.381639\pi\)
\(440\) −89.2620 −4.25540
\(441\) 11.2808 0.537183
\(442\) 16.8121 0.799669
\(443\) −10.4840 −0.498109 −0.249054 0.968490i \(-0.580120\pi\)
−0.249054 + 0.968490i \(0.580120\pi\)
\(444\) −15.3921 −0.730479
\(445\) 59.7793 2.83381
\(446\) 39.7378 1.88164
\(447\) −15.6789 −0.741585
\(448\) −38.0858 −1.79938
\(449\) −5.42350 −0.255951 −0.127975 0.991777i \(-0.540848\pi\)
−0.127975 + 0.991777i \(0.540848\pi\)
\(450\) −33.3701 −1.57308
\(451\) 17.9728 0.846306
\(452\) 16.2367 0.763710
\(453\) 5.53514 0.260064
\(454\) −24.8290 −1.16528
\(455\) −57.3730 −2.68969
\(456\) 29.0119 1.35860
\(457\) 1.72894 0.0808765 0.0404383 0.999182i \(-0.487125\pi\)
0.0404383 + 0.999182i \(0.487125\pi\)
\(458\) −33.5781 −1.56900
\(459\) −2.22761 −0.103976
\(460\) 26.7464 1.24706
\(461\) 18.0135 0.838973 0.419487 0.907762i \(-0.362210\pi\)
0.419487 + 0.907762i \(0.362210\pi\)
\(462\) 45.9448 2.13754
\(463\) 35.4777 1.64879 0.824393 0.566017i \(-0.191516\pi\)
0.824393 + 0.566017i \(0.191516\pi\)
\(464\) −30.3183 −1.40749
\(465\) 12.0655 0.559524
\(466\) −46.1264 −2.13676
\(467\) 16.8773 0.780988 0.390494 0.920606i \(-0.372304\pi\)
0.390494 + 0.920606i \(0.372304\pi\)
\(468\) −12.1596 −0.562078
\(469\) 17.3388 0.800631
\(470\) 43.1666 1.99113
\(471\) 2.45042 0.112909
\(472\) 41.0293 1.88852
\(473\) −36.2999 −1.66907
\(474\) −32.5559 −1.49534
\(475\) 85.1656 3.90767
\(476\) 37.3370 1.71134
\(477\) −5.52229 −0.252848
\(478\) 11.5469 0.528143
\(479\) −33.1887 −1.51643 −0.758215 0.652004i \(-0.773928\pi\)
−0.758215 + 0.652004i \(0.773928\pi\)
\(480\) −3.29479 −0.150386
\(481\) −12.1790 −0.555316
\(482\) 5.23019 0.238229
\(483\) −6.74324 −0.306828
\(484\) 33.3404 1.51547
\(485\) −2.05517 −0.0933204
\(486\) 2.43314 0.110369
\(487\) 38.5119 1.74514 0.872570 0.488489i \(-0.162452\pi\)
0.872570 + 0.488489i \(0.162452\pi\)
\(488\) 60.2086 2.72552
\(489\) −16.7975 −0.759608
\(490\) −118.741 −5.36418
\(491\) −17.3939 −0.784977 −0.392488 0.919757i \(-0.628386\pi\)
−0.392488 + 0.919757i \(0.628386\pi\)
\(492\) −15.9532 −0.719224
\(493\) −19.1471 −0.862342
\(494\) 46.8658 2.10859
\(495\) 19.1058 0.858741
\(496\) −9.83768 −0.441725
\(497\) −10.6194 −0.476347
\(498\) 29.9773 1.34331
\(499\) 24.7114 1.10624 0.553118 0.833103i \(-0.313438\pi\)
0.553118 + 0.833103i \(0.313438\pi\)
\(500\) 147.793 6.60953
\(501\) −11.4013 −0.509371
\(502\) 2.62562 0.117187
\(503\) −2.75301 −0.122751 −0.0613753 0.998115i \(-0.519549\pi\)
−0.0613753 + 0.998115i \(0.519549\pi\)
\(504\) −19.9756 −0.889785
\(505\) −2.97306 −0.132300
\(506\) −16.9476 −0.753413
\(507\) 3.37873 0.150055
\(508\) 52.4873 2.32875
\(509\) 37.2596 1.65150 0.825751 0.564035i \(-0.190752\pi\)
0.825751 + 0.564035i \(0.190752\pi\)
\(510\) 23.4476 1.03828
\(511\) 3.90378 0.172693
\(512\) 35.6453 1.57532
\(513\) −6.20974 −0.274167
\(514\) −46.4643 −2.04945
\(515\) −29.4255 −1.29664
\(516\) 32.2208 1.41844
\(517\) −18.1117 −0.796554
\(518\) −40.8471 −1.79472
\(519\) −15.4104 −0.676442
\(520\) 62.6919 2.74922
\(521\) −39.5184 −1.73133 −0.865666 0.500621i \(-0.833105\pi\)
−0.865666 + 0.500621i \(0.833105\pi\)
\(522\) 20.9137 0.915367
\(523\) 4.09491 0.179058 0.0895289 0.995984i \(-0.471464\pi\)
0.0895289 + 0.995984i \(0.471464\pi\)
\(524\) −8.77289 −0.383245
\(525\) −58.6393 −2.55923
\(526\) −51.2236 −2.23346
\(527\) −6.21284 −0.270636
\(528\) −15.5780 −0.677947
\(529\) −20.5126 −0.891853
\(530\) 58.1271 2.52488
\(531\) −8.78197 −0.381105
\(532\) 104.082 4.51252
\(533\) −12.6229 −0.546760
\(534\) 33.6221 1.45497
\(535\) 30.9767 1.33924
\(536\) −18.9462 −0.818352
\(537\) 7.82666 0.337745
\(538\) −6.92533 −0.298572
\(539\) 49.8211 2.14595
\(540\) −16.9588 −0.729792
\(541\) 13.3054 0.572043 0.286022 0.958223i \(-0.407667\pi\)
0.286022 + 0.958223i \(0.407667\pi\)
\(542\) −2.09024 −0.0897837
\(543\) −5.73370 −0.246057
\(544\) 1.69657 0.0727400
\(545\) 68.4612 2.93256
\(546\) −32.2687 −1.38097
\(547\) 30.5954 1.30817 0.654083 0.756423i \(-0.273055\pi\)
0.654083 + 0.756423i \(0.273055\pi\)
\(548\) −21.5439 −0.920308
\(549\) −12.8871 −0.550010
\(550\) −147.377 −6.28416
\(551\) −53.3750 −2.27385
\(552\) 7.36838 0.313619
\(553\) −57.2087 −2.43276
\(554\) 35.3595 1.50228
\(555\) −16.9859 −0.721012
\(556\) −48.3878 −2.05210
\(557\) 8.92849 0.378312 0.189156 0.981947i \(-0.439425\pi\)
0.189156 + 0.981947i \(0.439425\pi\)
\(558\) 6.78607 0.287277
\(559\) 25.4947 1.07831
\(560\) 65.2427 2.75701
\(561\) −9.83807 −0.415364
\(562\) −68.2332 −2.87824
\(563\) 17.1704 0.723648 0.361824 0.932246i \(-0.382154\pi\)
0.361824 + 0.932246i \(0.382154\pi\)
\(564\) 16.0765 0.676943
\(565\) 17.9179 0.753813
\(566\) 7.33613 0.308360
\(567\) 4.27561 0.179559
\(568\) 11.6039 0.486891
\(569\) 33.4025 1.40030 0.700152 0.713994i \(-0.253115\pi\)
0.700152 + 0.713994i \(0.253115\pi\)
\(570\) 65.3632 2.73776
\(571\) −43.8389 −1.83460 −0.917301 0.398195i \(-0.869637\pi\)
−0.917301 + 0.398195i \(0.869637\pi\)
\(572\) −53.7020 −2.24540
\(573\) −26.7017 −1.11548
\(574\) −42.3359 −1.76706
\(575\) 21.6302 0.902042
\(576\) −8.90768 −0.371153
\(577\) 23.1444 0.963513 0.481757 0.876305i \(-0.339999\pi\)
0.481757 + 0.876305i \(0.339999\pi\)
\(578\) 29.2895 1.21828
\(579\) −5.01994 −0.208622
\(580\) −145.767 −6.05266
\(581\) 52.6773 2.18542
\(582\) −1.15590 −0.0479136
\(583\) −24.3888 −1.01008
\(584\) −4.26569 −0.176516
\(585\) −13.4187 −0.554794
\(586\) 68.1465 2.81511
\(587\) 22.3416 0.922135 0.461068 0.887365i \(-0.347467\pi\)
0.461068 + 0.887365i \(0.347467\pi\)
\(588\) −44.2226 −1.82371
\(589\) −17.3191 −0.713621
\(590\) 92.4381 3.80562
\(591\) −5.40340 −0.222266
\(592\) 13.8496 0.569215
\(593\) 30.0817 1.23531 0.617654 0.786450i \(-0.288083\pi\)
0.617654 + 0.786450i \(0.288083\pi\)
\(594\) 10.7458 0.440905
\(595\) 41.2031 1.68916
\(596\) 61.4636 2.51765
\(597\) 6.84587 0.280183
\(598\) 11.9029 0.486746
\(599\) −38.4851 −1.57246 −0.786230 0.617934i \(-0.787970\pi\)
−0.786230 + 0.617934i \(0.787970\pi\)
\(600\) 64.0756 2.61588
\(601\) −40.4580 −1.65031 −0.825157 0.564903i \(-0.808914\pi\)
−0.825157 + 0.564903i \(0.808914\pi\)
\(602\) 85.5064 3.48498
\(603\) 4.05528 0.165144
\(604\) −21.6986 −0.882904
\(605\) 36.7927 1.49583
\(606\) −1.67216 −0.0679268
\(607\) 4.84177 0.196521 0.0982607 0.995161i \(-0.468672\pi\)
0.0982607 + 0.995161i \(0.468672\pi\)
\(608\) 4.72942 0.191803
\(609\) 36.7504 1.48920
\(610\) 135.649 5.49226
\(611\) 12.7205 0.514617
\(612\) 8.73256 0.352993
\(613\) −9.92711 −0.400952 −0.200476 0.979699i \(-0.564249\pi\)
−0.200476 + 0.979699i \(0.564249\pi\)
\(614\) −76.8873 −3.10292
\(615\) −17.6050 −0.709904
\(616\) −88.2210 −3.55452
\(617\) −29.5188 −1.18838 −0.594190 0.804325i \(-0.702527\pi\)
−0.594190 + 0.804325i \(0.702527\pi\)
\(618\) −16.5500 −0.665737
\(619\) −3.48114 −0.139919 −0.0699595 0.997550i \(-0.522287\pi\)
−0.0699595 + 0.997550i \(0.522287\pi\)
\(620\) −47.2985 −1.89956
\(621\) −1.57714 −0.0632884
\(622\) 17.3860 0.697115
\(623\) 59.0821 2.36707
\(624\) 10.9410 0.437991
\(625\) 94.5226 3.78090
\(626\) −5.58369 −0.223169
\(627\) −27.4249 −1.09525
\(628\) −9.60601 −0.383321
\(629\) 8.74651 0.348746
\(630\) −45.0047 −1.79303
\(631\) −31.8075 −1.26624 −0.633118 0.774055i \(-0.718225\pi\)
−0.633118 + 0.774055i \(0.718225\pi\)
\(632\) 62.5123 2.48661
\(633\) 2.07753 0.0825746
\(634\) 11.5062 0.456970
\(635\) 57.9221 2.29857
\(636\) 21.6482 0.858408
\(637\) −34.9911 −1.38640
\(638\) 92.3639 3.65672
\(639\) −2.48373 −0.0982547
\(640\) 87.1718 3.44577
\(641\) −46.2740 −1.82771 −0.913856 0.406039i \(-0.866910\pi\)
−0.913856 + 0.406039i \(0.866910\pi\)
\(642\) 17.4224 0.687608
\(643\) 4.72986 0.186528 0.0932638 0.995641i \(-0.470270\pi\)
0.0932638 + 0.995641i \(0.470270\pi\)
\(644\) 26.4345 1.04167
\(645\) 35.5572 1.40006
\(646\) −33.6572 −1.32423
\(647\) −27.7209 −1.08982 −0.544911 0.838494i \(-0.683436\pi\)
−0.544911 + 0.838494i \(0.683436\pi\)
\(648\) −4.67199 −0.183533
\(649\) −38.7850 −1.52244
\(650\) 103.508 4.05991
\(651\) 11.9248 0.467369
\(652\) 65.8487 2.57883
\(653\) −25.5695 −1.00061 −0.500305 0.865849i \(-0.666779\pi\)
−0.500305 + 0.865849i \(0.666779\pi\)
\(654\) 38.5051 1.50567
\(655\) −9.68128 −0.378279
\(656\) 14.3544 0.560445
\(657\) 0.913035 0.0356209
\(658\) 42.6632 1.66318
\(659\) 47.1520 1.83678 0.918391 0.395673i \(-0.129489\pi\)
0.918391 + 0.395673i \(0.129489\pi\)
\(660\) −74.8975 −2.91538
\(661\) −18.8904 −0.734752 −0.367376 0.930072i \(-0.619744\pi\)
−0.367376 + 0.930072i \(0.619744\pi\)
\(662\) 67.7323 2.63249
\(663\) 6.90963 0.268348
\(664\) −57.5609 −2.23380
\(665\) 114.859 4.45404
\(666\) −9.55350 −0.370191
\(667\) −13.5561 −0.524894
\(668\) 44.6947 1.72929
\(669\) 16.3319 0.631429
\(670\) −42.6855 −1.64908
\(671\) −56.9152 −2.19719
\(672\) −3.25636 −0.125617
\(673\) 10.3173 0.397702 0.198851 0.980030i \(-0.436279\pi\)
0.198851 + 0.980030i \(0.436279\pi\)
\(674\) 70.6932 2.72300
\(675\) −13.7148 −0.527884
\(676\) −13.2451 −0.509428
\(677\) −37.8576 −1.45499 −0.727493 0.686115i \(-0.759315\pi\)
−0.727493 + 0.686115i \(0.759315\pi\)
\(678\) 10.0777 0.387032
\(679\) −2.03120 −0.0779503
\(680\) −45.0229 −1.72655
\(681\) −10.2045 −0.391039
\(682\) 29.9702 1.14762
\(683\) −19.5701 −0.748830 −0.374415 0.927261i \(-0.622156\pi\)
−0.374415 + 0.927261i \(0.622156\pi\)
\(684\) 24.3431 0.930783
\(685\) −23.7746 −0.908381
\(686\) −44.5342 −1.70033
\(687\) −13.8003 −0.526516
\(688\) −28.9918 −1.10530
\(689\) 17.1291 0.652569
\(690\) 16.6008 0.631983
\(691\) 29.9143 1.13799 0.568997 0.822340i \(-0.307332\pi\)
0.568997 + 0.822340i \(0.307332\pi\)
\(692\) 60.4112 2.29649
\(693\) 18.8829 0.717304
\(694\) −50.9066 −1.93239
\(695\) −53.3981 −2.02551
\(696\) −40.1575 −1.52216
\(697\) 9.06530 0.343373
\(698\) −35.5928 −1.34721
\(699\) −18.9576 −0.717041
\(700\) 229.875 8.68846
\(701\) −42.8417 −1.61811 −0.809054 0.587734i \(-0.800020\pi\)
−0.809054 + 0.587734i \(0.800020\pi\)
\(702\) −7.54714 −0.284849
\(703\) 24.3820 0.919586
\(704\) −39.3402 −1.48269
\(705\) 17.7411 0.668170
\(706\) 56.9440 2.14311
\(707\) −2.93839 −0.110510
\(708\) 34.4266 1.29383
\(709\) −1.33886 −0.0502820 −0.0251410 0.999684i \(-0.508003\pi\)
−0.0251410 + 0.999684i \(0.508003\pi\)
\(710\) 26.1435 0.981147
\(711\) −13.3802 −0.501798
\(712\) −64.5595 −2.41947
\(713\) −4.39868 −0.164732
\(714\) 23.1741 0.867269
\(715\) −59.2626 −2.21630
\(716\) −30.6817 −1.14663
\(717\) 4.74569 0.177231
\(718\) −58.1959 −2.17185
\(719\) 28.3780 1.05832 0.529160 0.848522i \(-0.322507\pi\)
0.529160 + 0.848522i \(0.322507\pi\)
\(720\) 15.2593 0.568679
\(721\) −29.0823 −1.08308
\(722\) −47.5943 −1.77128
\(723\) 2.14957 0.0799433
\(724\) 22.4770 0.835350
\(725\) −117.884 −4.37810
\(726\) 20.6935 0.768009
\(727\) −37.0819 −1.37529 −0.687646 0.726046i \(-0.741356\pi\)
−0.687646 + 0.726046i \(0.741356\pi\)
\(728\) 61.9607 2.29642
\(729\) 1.00000 0.0370370
\(730\) −9.61052 −0.355701
\(731\) −18.3093 −0.677195
\(732\) 50.5196 1.86726
\(733\) −46.2021 −1.70651 −0.853256 0.521492i \(-0.825376\pi\)
−0.853256 + 0.521492i \(0.825376\pi\)
\(734\) 54.3846 2.00737
\(735\) −48.8017 −1.80008
\(736\) 1.20117 0.0442757
\(737\) 17.9099 0.659718
\(738\) −9.90171 −0.364487
\(739\) 16.5828 0.610008 0.305004 0.952351i \(-0.401342\pi\)
0.305004 + 0.952351i \(0.401342\pi\)
\(740\) 66.5874 2.44780
\(741\) 19.2615 0.707588
\(742\) 57.4492 2.10903
\(743\) 12.5815 0.461571 0.230785 0.973005i \(-0.425870\pi\)
0.230785 + 0.973005i \(0.425870\pi\)
\(744\) −13.0303 −0.477713
\(745\) 67.8278 2.48502
\(746\) 33.0926 1.21160
\(747\) 12.3204 0.450780
\(748\) 38.5667 1.41014
\(749\) 30.6154 1.11866
\(750\) 91.7316 3.34956
\(751\) 18.2752 0.666873 0.333437 0.942773i \(-0.391792\pi\)
0.333437 + 0.942773i \(0.391792\pi\)
\(752\) −14.4654 −0.527498
\(753\) 1.07911 0.0393250
\(754\) −64.8705 −2.36244
\(755\) −23.9454 −0.871462
\(756\) −16.7610 −0.609593
\(757\) −37.5022 −1.36304 −0.681520 0.731800i \(-0.738681\pi\)
−0.681520 + 0.731800i \(0.738681\pi\)
\(758\) −57.8455 −2.10104
\(759\) −6.96533 −0.252826
\(760\) −125.507 −4.55262
\(761\) −34.5732 −1.25328 −0.626638 0.779310i \(-0.715570\pi\)
−0.626638 + 0.779310i \(0.715570\pi\)
\(762\) 32.5775 1.18016
\(763\) 67.6627 2.44956
\(764\) 104.675 3.78700
\(765\) 9.63677 0.348418
\(766\) −75.1828 −2.71646
\(767\) 27.2401 0.983581
\(768\) 31.2132 1.12631
\(769\) −42.7129 −1.54026 −0.770132 0.637884i \(-0.779810\pi\)
−0.770132 + 0.637884i \(0.779810\pi\)
\(770\) −198.760 −7.16282
\(771\) −19.0965 −0.687743
\(772\) 19.6789 0.708260
\(773\) 24.0764 0.865970 0.432985 0.901401i \(-0.357460\pi\)
0.432985 + 0.901401i \(0.357460\pi\)
\(774\) 19.9986 0.718836
\(775\) −38.2510 −1.37402
\(776\) 2.21951 0.0796756
\(777\) −16.7878 −0.602260
\(778\) −33.0870 −1.18623
\(779\) 25.2707 0.905417
\(780\) 52.6032 1.88350
\(781\) −10.9692 −0.392509
\(782\) −8.54821 −0.305683
\(783\) 8.59536 0.307173
\(784\) 39.7908 1.42110
\(785\) −10.6007 −0.378354
\(786\) −5.44510 −0.194220
\(787\) 40.7181 1.45144 0.725721 0.687989i \(-0.241506\pi\)
0.725721 + 0.687989i \(0.241506\pi\)
\(788\) 21.1821 0.754582
\(789\) −21.0525 −0.749489
\(790\) 140.839 5.01083
\(791\) 17.7090 0.629658
\(792\) −20.6335 −0.733181
\(793\) 39.9736 1.41950
\(794\) 32.3412 1.14775
\(795\) 23.8898 0.847284
\(796\) −26.8368 −0.951206
\(797\) 48.0936 1.70356 0.851782 0.523897i \(-0.175522\pi\)
0.851782 + 0.523897i \(0.175522\pi\)
\(798\) 64.6008 2.28684
\(799\) −9.13539 −0.323187
\(800\) 10.4454 0.369301
\(801\) 13.8184 0.488249
\(802\) 92.7516 3.27517
\(803\) 4.03236 0.142299
\(804\) −15.8973 −0.560655
\(805\) 29.1717 1.02817
\(806\) −21.0491 −0.741425
\(807\) −2.84626 −0.100193
\(808\) 3.21080 0.112956
\(809\) −15.9086 −0.559315 −0.279657 0.960100i \(-0.590221\pi\)
−0.279657 + 0.960100i \(0.590221\pi\)
\(810\) −10.5259 −0.369843
\(811\) −2.74419 −0.0963614 −0.0481807 0.998839i \(-0.515342\pi\)
−0.0481807 + 0.998839i \(0.515342\pi\)
\(812\) −144.067 −5.05577
\(813\) −0.859074 −0.0301290
\(814\) −42.1924 −1.47884
\(815\) 72.6670 2.54541
\(816\) −7.85741 −0.275064
\(817\) −51.0396 −1.78565
\(818\) 78.9559 2.76063
\(819\) −13.2622 −0.463418
\(820\) 69.0144 2.41009
\(821\) −1.10716 −0.0386402 −0.0193201 0.999813i \(-0.506150\pi\)
−0.0193201 + 0.999813i \(0.506150\pi\)
\(822\) −13.3717 −0.466392
\(823\) −3.11513 −0.108587 −0.0542933 0.998525i \(-0.517291\pi\)
−0.0542933 + 0.998525i \(0.517291\pi\)
\(824\) 31.7785 1.10705
\(825\) −60.5707 −2.10880
\(826\) 91.3600 3.17882
\(827\) −33.4492 −1.16314 −0.581572 0.813495i \(-0.697562\pi\)
−0.581572 + 0.813495i \(0.697562\pi\)
\(828\) 6.18263 0.214861
\(829\) −43.6230 −1.51509 −0.757544 0.652784i \(-0.773601\pi\)
−0.757544 + 0.652784i \(0.773601\pi\)
\(830\) −129.684 −4.50138
\(831\) 14.5325 0.504127
\(832\) 27.6300 0.957898
\(833\) 25.1293 0.870678
\(834\) −30.0330 −1.03996
\(835\) 49.3226 1.70688
\(836\) 107.510 3.71830
\(837\) 2.78902 0.0964027
\(838\) 68.6976 2.37312
\(839\) −1.76697 −0.0610026 −0.0305013 0.999535i \(-0.509710\pi\)
−0.0305013 + 0.999535i \(0.509710\pi\)
\(840\) 86.4158 2.98163
\(841\) 44.8803 1.54760
\(842\) −54.4307 −1.87581
\(843\) −28.0433 −0.965863
\(844\) −8.14425 −0.280337
\(845\) −14.6166 −0.502826
\(846\) 9.97827 0.343060
\(847\) 36.3636 1.24947
\(848\) −19.4787 −0.668902
\(849\) 3.01509 0.103478
\(850\) −74.3354 −2.54968
\(851\) 6.19251 0.212276
\(852\) 9.73658 0.333570
\(853\) −2.18049 −0.0746584 −0.0373292 0.999303i \(-0.511885\pi\)
−0.0373292 + 0.999303i \(0.511885\pi\)
\(854\) 134.067 4.58767
\(855\) 26.8637 0.918721
\(856\) −33.4537 −1.14342
\(857\) −26.3557 −0.900295 −0.450147 0.892954i \(-0.648629\pi\)
−0.450147 + 0.892954i \(0.648629\pi\)
\(858\) −33.3315 −1.13792
\(859\) −18.2241 −0.621799 −0.310900 0.950443i \(-0.600630\pi\)
−0.310900 + 0.950443i \(0.600630\pi\)
\(860\) −139.389 −4.75314
\(861\) −17.3997 −0.592981
\(862\) 69.3868 2.36332
\(863\) −39.2193 −1.33504 −0.667521 0.744591i \(-0.732644\pi\)
−0.667521 + 0.744591i \(0.732644\pi\)
\(864\) −0.761613 −0.0259106
\(865\) 66.6665 2.26673
\(866\) 64.1243 2.17903
\(867\) 12.0378 0.408824
\(868\) −46.7469 −1.58669
\(869\) −59.0929 −2.00459
\(870\) −90.4740 −3.06736
\(871\) −12.5787 −0.426214
\(872\) −73.9356 −2.50377
\(873\) −0.475066 −0.0160786
\(874\) −23.8292 −0.806036
\(875\) 161.195 5.44937
\(876\) −3.57924 −0.120931
\(877\) −36.0077 −1.21589 −0.607946 0.793978i \(-0.708006\pi\)
−0.607946 + 0.793978i \(0.708006\pi\)
\(878\) −37.0454 −1.25022
\(879\) 28.0077 0.944676
\(880\) 67.3915 2.27177
\(881\) −11.6095 −0.391135 −0.195567 0.980690i \(-0.562655\pi\)
−0.195567 + 0.980690i \(0.562655\pi\)
\(882\) −27.4478 −0.924217
\(883\) −14.9769 −0.504014 −0.252007 0.967725i \(-0.581091\pi\)
−0.252007 + 0.967725i \(0.581091\pi\)
\(884\) −27.0868 −0.911027
\(885\) 37.9914 1.27707
\(886\) 25.5089 0.856989
\(887\) −10.1470 −0.340704 −0.170352 0.985383i \(-0.554491\pi\)
−0.170352 + 0.985383i \(0.554491\pi\)
\(888\) 18.3442 0.615590
\(889\) 57.2466 1.91999
\(890\) −145.451 −4.87554
\(891\) 4.41643 0.147956
\(892\) −64.0237 −2.14367
\(893\) −25.4661 −0.852190
\(894\) 38.1488 1.27589
\(895\) −33.8586 −1.13177
\(896\) 86.1552 2.87824
\(897\) 4.89200 0.163339
\(898\) 13.1961 0.440360
\(899\) 23.9727 0.799533
\(900\) 53.7642 1.79214
\(901\) −12.3015 −0.409822
\(902\) −43.7303 −1.45606
\(903\) 35.1425 1.16947
\(904\) −19.3507 −0.643595
\(905\) 24.8043 0.824524
\(906\) −13.4678 −0.447436
\(907\) 25.5421 0.848111 0.424056 0.905636i \(-0.360606\pi\)
0.424056 + 0.905636i \(0.360606\pi\)
\(908\) 40.0034 1.32756
\(909\) −0.687244 −0.0227945
\(910\) 139.596 4.62757
\(911\) 17.8750 0.592226 0.296113 0.955153i \(-0.404309\pi\)
0.296113 + 0.955153i \(0.404309\pi\)
\(912\) −21.9035 −0.725299
\(913\) 54.4123 1.80078
\(914\) −4.20675 −0.139147
\(915\) 55.7506 1.84306
\(916\) 54.0994 1.78749
\(917\) −9.56836 −0.315975
\(918\) 5.42007 0.178889
\(919\) 25.8102 0.851399 0.425700 0.904865i \(-0.360028\pi\)
0.425700 + 0.904865i \(0.360028\pi\)
\(920\) −31.8761 −1.05092
\(921\) −31.6001 −1.04126
\(922\) −43.8293 −1.44344
\(923\) 7.70407 0.253582
\(924\) −74.0240 −2.43521
\(925\) 53.8502 1.77058
\(926\) −86.3220 −2.83672
\(927\) −6.80191 −0.223404
\(928\) −6.54634 −0.214894
\(929\) 51.6803 1.69558 0.847788 0.530336i \(-0.177934\pi\)
0.847788 + 0.530336i \(0.177934\pi\)
\(930\) −29.3570 −0.962653
\(931\) 70.0511 2.29583
\(932\) 74.3166 2.43432
\(933\) 7.14550 0.233933
\(934\) −41.0647 −1.34368
\(935\) 42.5602 1.39187
\(936\) 14.4917 0.473675
\(937\) 25.7958 0.842711 0.421355 0.906896i \(-0.361554\pi\)
0.421355 + 0.906896i \(0.361554\pi\)
\(938\) −42.1876 −1.37748
\(939\) −2.29485 −0.0748896
\(940\) −69.5480 −2.26841
\(941\) −3.50083 −0.114124 −0.0570619 0.998371i \(-0.518173\pi\)
−0.0570619 + 0.998371i \(0.518173\pi\)
\(942\) −5.96220 −0.194259
\(943\) 6.41821 0.209006
\(944\) −30.9765 −1.00820
\(945\) −18.4966 −0.601693
\(946\) 88.3227 2.87162
\(947\) −33.5802 −1.09121 −0.545605 0.838043i \(-0.683700\pi\)
−0.545605 + 0.838043i \(0.683700\pi\)
\(948\) 52.4526 1.70358
\(949\) −2.83207 −0.0919329
\(950\) −207.220 −6.72309
\(951\) 4.72896 0.153347
\(952\) −44.4978 −1.44218
\(953\) −34.8198 −1.12792 −0.563962 0.825801i \(-0.690724\pi\)
−0.563962 + 0.825801i \(0.690724\pi\)
\(954\) 13.4365 0.435023
\(955\) 115.513 3.73792
\(956\) −18.6038 −0.601690
\(957\) 37.9609 1.22710
\(958\) 80.7526 2.60900
\(959\) −23.4973 −0.758769
\(960\) 38.5352 1.24372
\(961\) −23.2214 −0.749076
\(962\) 29.6332 0.955414
\(963\) 7.16048 0.230743
\(964\) −8.42663 −0.271404
\(965\) 21.7166 0.699081
\(966\) 16.4072 0.527893
\(967\) −11.4674 −0.368766 −0.184383 0.982854i \(-0.559029\pi\)
−0.184383 + 0.982854i \(0.559029\pi\)
\(968\) −39.7347 −1.27712
\(969\) −13.8329 −0.444376
\(970\) 5.00050 0.160557
\(971\) 38.5464 1.23701 0.618507 0.785779i \(-0.287738\pi\)
0.618507 + 0.785779i \(0.287738\pi\)
\(972\) −3.92015 −0.125739
\(973\) −52.7753 −1.69190
\(974\) −93.7046 −3.00249
\(975\) 42.5409 1.36240
\(976\) −45.4566 −1.45503
\(977\) 40.1833 1.28558 0.642789 0.766043i \(-0.277777\pi\)
0.642789 + 0.766043i \(0.277777\pi\)
\(978\) 40.8706 1.30690
\(979\) 61.0281 1.95047
\(980\) 191.310 6.11117
\(981\) 15.8253 0.505262
\(982\) 42.3218 1.35054
\(983\) 29.9943 0.956669 0.478335 0.878178i \(-0.341241\pi\)
0.478335 + 0.878178i \(0.341241\pi\)
\(984\) 19.0128 0.606106
\(985\) 23.3755 0.744804
\(986\) 46.5875 1.48365
\(987\) 17.5342 0.558121
\(988\) −75.5080 −2.40223
\(989\) −12.9630 −0.412198
\(990\) −46.4870 −1.47745
\(991\) −45.1315 −1.43365 −0.716825 0.697253i \(-0.754406\pi\)
−0.716825 + 0.697253i \(0.754406\pi\)
\(992\) −2.12416 −0.0674420
\(993\) 27.8375 0.883395
\(994\) 25.8386 0.819549
\(995\) −29.6157 −0.938880
\(996\) −48.2979 −1.53038
\(997\) −14.5720 −0.461499 −0.230749 0.973013i \(-0.574118\pi\)
−0.230749 + 0.973013i \(0.574118\pi\)
\(998\) −60.1263 −1.90326
\(999\) −3.92642 −0.124226
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 8013.2.a.b.1.8 106
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8013.2.a.b.1.8 106 1.1 even 1 trivial