Properties

Label 4015.2.a.c.1.12
Level $4015$
Weight $2$
Character 4015.1
Self dual yes
Analytic conductor $32.060$
Analytic rank $1$
Dimension $23$
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] = [4015,2,Mod(1,4015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4015, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4015.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: \(32.0599364115\)
Analytic rank: \(1\)
Dimension: \(23\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 4015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.197331 q^{2} +2.44280 q^{3} -1.96106 q^{4} +1.00000 q^{5} -0.482041 q^{6} -1.78119 q^{7} +0.781640 q^{8} +2.96728 q^{9} +O(q^{10})\) \(q-0.197331 q^{2} +2.44280 q^{3} -1.96106 q^{4} +1.00000 q^{5} -0.482041 q^{6} -1.78119 q^{7} +0.781640 q^{8} +2.96728 q^{9} -0.197331 q^{10} -1.00000 q^{11} -4.79048 q^{12} +5.00904 q^{13} +0.351485 q^{14} +2.44280 q^{15} +3.76788 q^{16} -6.94282 q^{17} -0.585537 q^{18} -4.83335 q^{19} -1.96106 q^{20} -4.35110 q^{21} +0.197331 q^{22} -0.570816 q^{23} +1.90939 q^{24} +1.00000 q^{25} -0.988439 q^{26} -0.0799170 q^{27} +3.49303 q^{28} -3.97018 q^{29} -0.482041 q^{30} -5.21743 q^{31} -2.30680 q^{32} -2.44280 q^{33} +1.37003 q^{34} -1.78119 q^{35} -5.81902 q^{36} +3.33047 q^{37} +0.953769 q^{38} +12.2361 q^{39} +0.781640 q^{40} +1.30184 q^{41} +0.858607 q^{42} +4.44442 q^{43} +1.96106 q^{44} +2.96728 q^{45} +0.112640 q^{46} -10.7328 q^{47} +9.20419 q^{48} -3.82735 q^{49} -0.197331 q^{50} -16.9599 q^{51} -9.82304 q^{52} -10.1135 q^{53} +0.0157701 q^{54} -1.00000 q^{55} -1.39225 q^{56} -11.8069 q^{57} +0.783440 q^{58} -0.898038 q^{59} -4.79048 q^{60} +13.2417 q^{61} +1.02956 q^{62} -5.28531 q^{63} -7.08056 q^{64} +5.00904 q^{65} +0.482041 q^{66} -4.29196 q^{67} +13.6153 q^{68} -1.39439 q^{69} +0.351485 q^{70} -2.39877 q^{71} +2.31935 q^{72} +1.00000 q^{73} -0.657206 q^{74} +2.44280 q^{75} +9.47849 q^{76} +1.78119 q^{77} -2.41456 q^{78} +8.48581 q^{79} +3.76788 q^{80} -9.09708 q^{81} -0.256893 q^{82} +7.45000 q^{83} +8.53278 q^{84} -6.94282 q^{85} -0.877022 q^{86} -9.69837 q^{87} -0.781640 q^{88} -9.68874 q^{89} -0.585537 q^{90} -8.92207 q^{91} +1.11940 q^{92} -12.7452 q^{93} +2.11791 q^{94} -4.83335 q^{95} -5.63506 q^{96} +14.8362 q^{97} +0.755255 q^{98} -2.96728 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.197331 −0.139534 −0.0697670 0.997563i \(-0.522226\pi\)
−0.0697670 + 0.997563i \(0.522226\pi\)
\(3\) 2.44280 1.41035 0.705176 0.709032i \(-0.250868\pi\)
0.705176 + 0.709032i \(0.250868\pi\)
\(4\) −1.96106 −0.980530
\(5\) 1.00000 0.447214
\(6\) −0.482041 −0.196792
\(7\) −1.78119 −0.673228 −0.336614 0.941643i \(-0.609282\pi\)
−0.336614 + 0.941643i \(0.609282\pi\)
\(8\) 0.781640 0.276351
\(9\) 2.96728 0.989095
\(10\) −0.197331 −0.0624015
\(11\) −1.00000 −0.301511
\(12\) −4.79048 −1.38289
\(13\) 5.00904 1.38926 0.694629 0.719368i \(-0.255568\pi\)
0.694629 + 0.719368i \(0.255568\pi\)
\(14\) 0.351485 0.0939382
\(15\) 2.44280 0.630729
\(16\) 3.76788 0.941970
\(17\) −6.94282 −1.68388 −0.841940 0.539571i \(-0.818587\pi\)
−0.841940 + 0.539571i \(0.818587\pi\)
\(18\) −0.585537 −0.138012
\(19\) −4.83335 −1.10885 −0.554423 0.832235i \(-0.687061\pi\)
−0.554423 + 0.832235i \(0.687061\pi\)
\(20\) −1.96106 −0.438506
\(21\) −4.35110 −0.949488
\(22\) 0.197331 0.0420711
\(23\) −0.570816 −0.119023 −0.0595117 0.998228i \(-0.518954\pi\)
−0.0595117 + 0.998228i \(0.518954\pi\)
\(24\) 1.90939 0.389753
\(25\) 1.00000 0.200000
\(26\) −0.988439 −0.193849
\(27\) −0.0799170 −0.0153800
\(28\) 3.49303 0.660120
\(29\) −3.97018 −0.737244 −0.368622 0.929579i \(-0.620170\pi\)
−0.368622 + 0.929579i \(0.620170\pi\)
\(30\) −0.482041 −0.0880082
\(31\) −5.21743 −0.937079 −0.468539 0.883443i \(-0.655220\pi\)
−0.468539 + 0.883443i \(0.655220\pi\)
\(32\) −2.30680 −0.407788
\(33\) −2.44280 −0.425237
\(34\) 1.37003 0.234959
\(35\) −1.78119 −0.301077
\(36\) −5.81902 −0.969837
\(37\) 3.33047 0.547527 0.273763 0.961797i \(-0.411731\pi\)
0.273763 + 0.961797i \(0.411731\pi\)
\(38\) 0.953769 0.154722
\(39\) 12.2361 1.95934
\(40\) 0.781640 0.123588
\(41\) 1.30184 0.203313 0.101656 0.994820i \(-0.467586\pi\)
0.101656 + 0.994820i \(0.467586\pi\)
\(42\) 0.858607 0.132486
\(43\) 4.44442 0.677768 0.338884 0.940828i \(-0.389951\pi\)
0.338884 + 0.940828i \(0.389951\pi\)
\(44\) 1.96106 0.295641
\(45\) 2.96728 0.442337
\(46\) 0.112640 0.0166078
\(47\) −10.7328 −1.56554 −0.782769 0.622312i \(-0.786193\pi\)
−0.782769 + 0.622312i \(0.786193\pi\)
\(48\) 9.20419 1.32851
\(49\) −3.82735 −0.546765
\(50\) −0.197331 −0.0279068
\(51\) −16.9599 −2.37487
\(52\) −9.82304 −1.36221
\(53\) −10.1135 −1.38920 −0.694599 0.719397i \(-0.744418\pi\)
−0.694599 + 0.719397i \(0.744418\pi\)
\(54\) 0.0157701 0.00214604
\(55\) −1.00000 −0.134840
\(56\) −1.39225 −0.186047
\(57\) −11.8069 −1.56386
\(58\) 0.783440 0.102871
\(59\) −0.898038 −0.116915 −0.0584573 0.998290i \(-0.518618\pi\)
−0.0584573 + 0.998290i \(0.518618\pi\)
\(60\) −4.79048 −0.618449
\(61\) 13.2417 1.69543 0.847713 0.530455i \(-0.177979\pi\)
0.847713 + 0.530455i \(0.177979\pi\)
\(62\) 1.02956 0.130754
\(63\) −5.28531 −0.665886
\(64\) −7.08056 −0.885069
\(65\) 5.00904 0.621295
\(66\) 0.482041 0.0593351
\(67\) −4.29196 −0.524347 −0.262173 0.965021i \(-0.584439\pi\)
−0.262173 + 0.965021i \(0.584439\pi\)
\(68\) 13.6153 1.65110
\(69\) −1.39439 −0.167865
\(70\) 0.351485 0.0420104
\(71\) −2.39877 −0.284682 −0.142341 0.989818i \(-0.545463\pi\)
−0.142341 + 0.989818i \(0.545463\pi\)
\(72\) 2.31935 0.273338
\(73\) 1.00000 0.117041
\(74\) −0.657206 −0.0763986
\(75\) 2.44280 0.282071
\(76\) 9.47849 1.08726
\(77\) 1.78119 0.202986
\(78\) −2.41456 −0.273395
\(79\) 8.48581 0.954728 0.477364 0.878706i \(-0.341592\pi\)
0.477364 + 0.878706i \(0.341592\pi\)
\(80\) 3.76788 0.421262
\(81\) −9.09708 −1.01079
\(82\) −0.256893 −0.0283691
\(83\) 7.45000 0.817744 0.408872 0.912592i \(-0.365922\pi\)
0.408872 + 0.912592i \(0.365922\pi\)
\(84\) 8.53278 0.931002
\(85\) −6.94282 −0.753054
\(86\) −0.877022 −0.0945718
\(87\) −9.69837 −1.03977
\(88\) −0.781640 −0.0833231
\(89\) −9.68874 −1.02700 −0.513502 0.858088i \(-0.671652\pi\)
−0.513502 + 0.858088i \(0.671652\pi\)
\(90\) −0.585537 −0.0617210
\(91\) −8.92207 −0.935287
\(92\) 1.11940 0.116706
\(93\) −12.7452 −1.32161
\(94\) 2.11791 0.218446
\(95\) −4.83335 −0.495891
\(96\) −5.63506 −0.575125
\(97\) 14.8362 1.50639 0.753194 0.657799i \(-0.228512\pi\)
0.753194 + 0.657799i \(0.228512\pi\)
\(98\) 0.755255 0.0762923
\(99\) −2.96728 −0.298223
\(100\) −1.96106 −0.196106
\(101\) −18.1023 −1.80125 −0.900623 0.434602i \(-0.856889\pi\)
−0.900623 + 0.434602i \(0.856889\pi\)
\(102\) 3.34672 0.331375
\(103\) 11.0685 1.09061 0.545305 0.838238i \(-0.316414\pi\)
0.545305 + 0.838238i \(0.316414\pi\)
\(104\) 3.91527 0.383924
\(105\) −4.35110 −0.424624
\(106\) 1.99571 0.193840
\(107\) 11.4458 1.10651 0.553253 0.833013i \(-0.313386\pi\)
0.553253 + 0.833013i \(0.313386\pi\)
\(108\) 0.156722 0.0150806
\(109\) −4.52758 −0.433664 −0.216832 0.976209i \(-0.569572\pi\)
−0.216832 + 0.976209i \(0.569572\pi\)
\(110\) 0.197331 0.0188148
\(111\) 8.13569 0.772206
\(112\) −6.71132 −0.634160
\(113\) −15.4078 −1.44944 −0.724720 0.689043i \(-0.758031\pi\)
−0.724720 + 0.689043i \(0.758031\pi\)
\(114\) 2.32987 0.218212
\(115\) −0.570816 −0.0532289
\(116\) 7.78577 0.722890
\(117\) 14.8633 1.37411
\(118\) 0.177211 0.0163136
\(119\) 12.3665 1.13363
\(120\) 1.90939 0.174303
\(121\) 1.00000 0.0909091
\(122\) −2.61300 −0.236570
\(123\) 3.18013 0.286743
\(124\) 10.2317 0.918834
\(125\) 1.00000 0.0894427
\(126\) 1.04295 0.0929138
\(127\) −11.9381 −1.05933 −0.529666 0.848206i \(-0.677683\pi\)
−0.529666 + 0.848206i \(0.677683\pi\)
\(128\) 6.01081 0.531286
\(129\) 10.8568 0.955892
\(130\) −0.988439 −0.0866919
\(131\) 6.02423 0.526340 0.263170 0.964750i \(-0.415232\pi\)
0.263170 + 0.964750i \(0.415232\pi\)
\(132\) 4.79048 0.416958
\(133\) 8.60913 0.746506
\(134\) 0.846937 0.0731642
\(135\) −0.0799170 −0.00687816
\(136\) −5.42678 −0.465343
\(137\) −17.4750 −1.49299 −0.746493 0.665393i \(-0.768264\pi\)
−0.746493 + 0.665393i \(0.768264\pi\)
\(138\) 0.275157 0.0234229
\(139\) 11.2114 0.950936 0.475468 0.879733i \(-0.342279\pi\)
0.475468 + 0.879733i \(0.342279\pi\)
\(140\) 3.49303 0.295215
\(141\) −26.2181 −2.20796
\(142\) 0.473352 0.0397228
\(143\) −5.00904 −0.418877
\(144\) 11.1804 0.931698
\(145\) −3.97018 −0.329706
\(146\) −0.197331 −0.0163312
\(147\) −9.34947 −0.771131
\(148\) −6.53126 −0.536866
\(149\) −12.6487 −1.03622 −0.518109 0.855314i \(-0.673364\pi\)
−0.518109 + 0.855314i \(0.673364\pi\)
\(150\) −0.482041 −0.0393585
\(151\) −3.11872 −0.253798 −0.126899 0.991916i \(-0.540502\pi\)
−0.126899 + 0.991916i \(0.540502\pi\)
\(152\) −3.77794 −0.306431
\(153\) −20.6013 −1.66552
\(154\) −0.351485 −0.0283234
\(155\) −5.21743 −0.419074
\(156\) −23.9957 −1.92120
\(157\) −18.7273 −1.49460 −0.747301 0.664485i \(-0.768651\pi\)
−0.747301 + 0.664485i \(0.768651\pi\)
\(158\) −1.67451 −0.133217
\(159\) −24.7053 −1.95926
\(160\) −2.30680 −0.182368
\(161\) 1.01673 0.0801298
\(162\) 1.79513 0.141039
\(163\) −17.6943 −1.38593 −0.692963 0.720973i \(-0.743695\pi\)
−0.692963 + 0.720973i \(0.743695\pi\)
\(164\) −2.55298 −0.199354
\(165\) −2.44280 −0.190172
\(166\) −1.47012 −0.114103
\(167\) −20.7265 −1.60386 −0.801932 0.597415i \(-0.796194\pi\)
−0.801932 + 0.597415i \(0.796194\pi\)
\(168\) −3.40100 −0.262393
\(169\) 12.0905 0.930039
\(170\) 1.37003 0.105077
\(171\) −14.3419 −1.09675
\(172\) −8.71578 −0.664572
\(173\) 11.0769 0.842158 0.421079 0.907024i \(-0.361651\pi\)
0.421079 + 0.907024i \(0.361651\pi\)
\(174\) 1.91379 0.145084
\(175\) −1.78119 −0.134646
\(176\) −3.76788 −0.284015
\(177\) −2.19373 −0.164891
\(178\) 1.91189 0.143302
\(179\) −3.70277 −0.276758 −0.138379 0.990379i \(-0.544189\pi\)
−0.138379 + 0.990379i \(0.544189\pi\)
\(180\) −5.81902 −0.433724
\(181\) 4.23567 0.314835 0.157418 0.987532i \(-0.449683\pi\)
0.157418 + 0.987532i \(0.449683\pi\)
\(182\) 1.76060 0.130504
\(183\) 32.3469 2.39115
\(184\) −0.446173 −0.0328923
\(185\) 3.33047 0.244861
\(186\) 2.51501 0.184410
\(187\) 6.94282 0.507709
\(188\) 21.0476 1.53506
\(189\) 0.142348 0.0103543
\(190\) 0.953769 0.0691937
\(191\) 0.744661 0.0538817 0.0269409 0.999637i \(-0.491423\pi\)
0.0269409 + 0.999637i \(0.491423\pi\)
\(192\) −17.2964 −1.24826
\(193\) 2.39299 0.172251 0.0861255 0.996284i \(-0.472551\pi\)
0.0861255 + 0.996284i \(0.472551\pi\)
\(194\) −2.92764 −0.210192
\(195\) 12.2361 0.876246
\(196\) 7.50567 0.536119
\(197\) −3.10788 −0.221427 −0.110714 0.993852i \(-0.535314\pi\)
−0.110714 + 0.993852i \(0.535314\pi\)
\(198\) 0.585537 0.0416123
\(199\) −8.87127 −0.628868 −0.314434 0.949279i \(-0.601815\pi\)
−0.314434 + 0.949279i \(0.601815\pi\)
\(200\) 0.781640 0.0552703
\(201\) −10.4844 −0.739514
\(202\) 3.57214 0.251335
\(203\) 7.07166 0.496333
\(204\) 33.2595 2.32863
\(205\) 1.30184 0.0909243
\(206\) −2.18416 −0.152177
\(207\) −1.69377 −0.117725
\(208\) 18.8735 1.30864
\(209\) 4.83335 0.334330
\(210\) 0.858607 0.0592495
\(211\) −11.5535 −0.795377 −0.397688 0.917521i \(-0.630187\pi\)
−0.397688 + 0.917521i \(0.630187\pi\)
\(212\) 19.8332 1.36215
\(213\) −5.85973 −0.401502
\(214\) −2.25861 −0.154395
\(215\) 4.44442 0.303107
\(216\) −0.0624663 −0.00425029
\(217\) 9.29325 0.630867
\(218\) 0.893432 0.0605109
\(219\) 2.44280 0.165069
\(220\) 1.96106 0.132215
\(221\) −34.7769 −2.33935
\(222\) −1.60542 −0.107749
\(223\) −24.6790 −1.65263 −0.826314 0.563209i \(-0.809566\pi\)
−0.826314 + 0.563209i \(0.809566\pi\)
\(224\) 4.10885 0.274534
\(225\) 2.96728 0.197819
\(226\) 3.04043 0.202246
\(227\) 24.6063 1.63318 0.816589 0.577219i \(-0.195862\pi\)
0.816589 + 0.577219i \(0.195862\pi\)
\(228\) 23.1541 1.53342
\(229\) −22.0208 −1.45518 −0.727588 0.686014i \(-0.759359\pi\)
−0.727588 + 0.686014i \(0.759359\pi\)
\(230\) 0.112640 0.00742724
\(231\) 4.35110 0.286282
\(232\) −3.10325 −0.203739
\(233\) −11.7764 −0.771497 −0.385748 0.922604i \(-0.626057\pi\)
−0.385748 + 0.922604i \(0.626057\pi\)
\(234\) −2.93298 −0.191735
\(235\) −10.7328 −0.700130
\(236\) 1.76111 0.114638
\(237\) 20.7292 1.34650
\(238\) −2.44029 −0.158181
\(239\) −9.10364 −0.588866 −0.294433 0.955672i \(-0.595131\pi\)
−0.294433 + 0.955672i \(0.595131\pi\)
\(240\) 9.20419 0.594128
\(241\) 28.1635 1.81417 0.907085 0.420948i \(-0.138302\pi\)
0.907085 + 0.420948i \(0.138302\pi\)
\(242\) −0.197331 −0.0126849
\(243\) −21.9826 −1.41019
\(244\) −25.9678 −1.66242
\(245\) −3.82735 −0.244521
\(246\) −0.627538 −0.0400104
\(247\) −24.2105 −1.54047
\(248\) −4.07815 −0.258963
\(249\) 18.1989 1.15331
\(250\) −0.197331 −0.0124803
\(251\) 31.2318 1.97134 0.985668 0.168699i \(-0.0539567\pi\)
0.985668 + 0.168699i \(0.0539567\pi\)
\(252\) 10.3648 0.652921
\(253\) 0.570816 0.0358869
\(254\) 2.35575 0.147813
\(255\) −16.9599 −1.06207
\(256\) 12.9750 0.810937
\(257\) 19.5259 1.21799 0.608997 0.793173i \(-0.291572\pi\)
0.608997 + 0.793173i \(0.291572\pi\)
\(258\) −2.14239 −0.133380
\(259\) −5.93222 −0.368610
\(260\) −9.82304 −0.609199
\(261\) −11.7807 −0.729205
\(262\) −1.18877 −0.0734423
\(263\) 20.8901 1.28814 0.644070 0.764966i \(-0.277244\pi\)
0.644070 + 0.764966i \(0.277244\pi\)
\(264\) −1.90939 −0.117515
\(265\) −10.1135 −0.621268
\(266\) −1.69885 −0.104163
\(267\) −23.6677 −1.44844
\(268\) 8.41680 0.514138
\(269\) 16.8032 1.02451 0.512256 0.858833i \(-0.328810\pi\)
0.512256 + 0.858833i \(0.328810\pi\)
\(270\) 0.0157701 0.000959738 0
\(271\) 29.2510 1.77687 0.888437 0.458999i \(-0.151792\pi\)
0.888437 + 0.458999i \(0.151792\pi\)
\(272\) −26.1597 −1.58616
\(273\) −21.7949 −1.31908
\(274\) 3.44835 0.208322
\(275\) −1.00000 −0.0603023
\(276\) 2.73448 0.164597
\(277\) −16.9208 −1.01667 −0.508336 0.861159i \(-0.669739\pi\)
−0.508336 + 0.861159i \(0.669739\pi\)
\(278\) −2.21235 −0.132688
\(279\) −15.4816 −0.926860
\(280\) −1.39225 −0.0832029
\(281\) −18.2585 −1.08921 −0.544607 0.838692i \(-0.683321\pi\)
−0.544607 + 0.838692i \(0.683321\pi\)
\(282\) 5.17364 0.308086
\(283\) −16.7785 −0.997380 −0.498690 0.866780i \(-0.666185\pi\)
−0.498690 + 0.866780i \(0.666185\pi\)
\(284\) 4.70414 0.279139
\(285\) −11.8069 −0.699381
\(286\) 0.988439 0.0584476
\(287\) −2.31882 −0.136876
\(288\) −6.84493 −0.403341
\(289\) 31.2027 1.83545
\(290\) 0.783440 0.0460052
\(291\) 36.2419 2.12454
\(292\) −1.96106 −0.114762
\(293\) −24.9399 −1.45700 −0.728502 0.685044i \(-0.759783\pi\)
−0.728502 + 0.685044i \(0.759783\pi\)
\(294\) 1.84494 0.107599
\(295\) −0.898038 −0.0522858
\(296\) 2.60323 0.151310
\(297\) 0.0799170 0.00463725
\(298\) 2.49597 0.144588
\(299\) −2.85924 −0.165354
\(300\) −4.79048 −0.276579
\(301\) −7.91637 −0.456292
\(302\) 0.615419 0.0354134
\(303\) −44.2203 −2.54039
\(304\) −18.2115 −1.04450
\(305\) 13.2417 0.758218
\(306\) 4.06528 0.232396
\(307\) −5.36373 −0.306124 −0.153062 0.988217i \(-0.548913\pi\)
−0.153062 + 0.988217i \(0.548913\pi\)
\(308\) −3.49303 −0.199034
\(309\) 27.0381 1.53815
\(310\) 1.02956 0.0584751
\(311\) −5.05281 −0.286519 −0.143259 0.989685i \(-0.545758\pi\)
−0.143259 + 0.989685i \(0.545758\pi\)
\(312\) 9.56423 0.541468
\(313\) −23.2503 −1.31418 −0.657092 0.753810i \(-0.728214\pi\)
−0.657092 + 0.753810i \(0.728214\pi\)
\(314\) 3.69548 0.208548
\(315\) −5.28531 −0.297793
\(316\) −16.6412 −0.936140
\(317\) 28.4200 1.59623 0.798113 0.602507i \(-0.205832\pi\)
0.798113 + 0.602507i \(0.205832\pi\)
\(318\) 4.87512 0.273383
\(319\) 3.97018 0.222288
\(320\) −7.08056 −0.395815
\(321\) 27.9598 1.56057
\(322\) −0.200633 −0.0111808
\(323\) 33.5571 1.86716
\(324\) 17.8399 0.991106
\(325\) 5.00904 0.277852
\(326\) 3.49164 0.193384
\(327\) −11.0600 −0.611619
\(328\) 1.01757 0.0561858
\(329\) 19.1172 1.05396
\(330\) 0.482041 0.0265355
\(331\) 29.6745 1.63106 0.815528 0.578717i \(-0.196447\pi\)
0.815528 + 0.578717i \(0.196447\pi\)
\(332\) −14.6099 −0.801822
\(333\) 9.88247 0.541556
\(334\) 4.08998 0.223794
\(335\) −4.29196 −0.234495
\(336\) −16.3944 −0.894389
\(337\) −14.0488 −0.765285 −0.382642 0.923897i \(-0.624986\pi\)
−0.382642 + 0.923897i \(0.624986\pi\)
\(338\) −2.38583 −0.129772
\(339\) −37.6381 −2.04422
\(340\) 13.6153 0.738392
\(341\) 5.21743 0.282540
\(342\) 2.83011 0.153035
\(343\) 19.2856 1.04132
\(344\) 3.47394 0.187302
\(345\) −1.39439 −0.0750715
\(346\) −2.18581 −0.117510
\(347\) 22.0207 1.18213 0.591067 0.806623i \(-0.298707\pi\)
0.591067 + 0.806623i \(0.298707\pi\)
\(348\) 19.0191 1.01953
\(349\) −24.3363 −1.30269 −0.651346 0.758781i \(-0.725795\pi\)
−0.651346 + 0.758781i \(0.725795\pi\)
\(350\) 0.351485 0.0187876
\(351\) −0.400308 −0.0213668
\(352\) 2.30680 0.122953
\(353\) −11.4548 −0.609675 −0.304837 0.952404i \(-0.598602\pi\)
−0.304837 + 0.952404i \(0.598602\pi\)
\(354\) 0.432891 0.0230079
\(355\) −2.39877 −0.127314
\(356\) 19.0002 1.00701
\(357\) 30.2089 1.59883
\(358\) 0.730671 0.0386171
\(359\) 17.4891 0.923041 0.461520 0.887130i \(-0.347304\pi\)
0.461520 + 0.887130i \(0.347304\pi\)
\(360\) 2.31935 0.122240
\(361\) 4.36126 0.229540
\(362\) −0.835830 −0.0439302
\(363\) 2.44280 0.128214
\(364\) 17.4967 0.917077
\(365\) 1.00000 0.0523424
\(366\) −6.38304 −0.333647
\(367\) 19.0440 0.994091 0.497045 0.867725i \(-0.334418\pi\)
0.497045 + 0.867725i \(0.334418\pi\)
\(368\) −2.15077 −0.112116
\(369\) 3.86292 0.201096
\(370\) −0.657206 −0.0341665
\(371\) 18.0141 0.935246
\(372\) 24.9940 1.29588
\(373\) 7.73068 0.400279 0.200140 0.979767i \(-0.435860\pi\)
0.200140 + 0.979767i \(0.435860\pi\)
\(374\) −1.37003 −0.0708427
\(375\) 2.44280 0.126146
\(376\) −8.38918 −0.432639
\(377\) −19.8868 −1.02422
\(378\) −0.0280896 −0.00144477
\(379\) 7.51613 0.386078 0.193039 0.981191i \(-0.438166\pi\)
0.193039 + 0.981191i \(0.438166\pi\)
\(380\) 9.47849 0.486236
\(381\) −29.1623 −1.49403
\(382\) −0.146945 −0.00751834
\(383\) −2.81371 −0.143774 −0.0718870 0.997413i \(-0.522902\pi\)
−0.0718870 + 0.997413i \(0.522902\pi\)
\(384\) 14.6832 0.749300
\(385\) 1.78119 0.0907780
\(386\) −0.472211 −0.0240349
\(387\) 13.1879 0.670377
\(388\) −29.0947 −1.47706
\(389\) −18.0770 −0.916542 −0.458271 0.888813i \(-0.651531\pi\)
−0.458271 + 0.888813i \(0.651531\pi\)
\(390\) −2.41456 −0.122266
\(391\) 3.96307 0.200421
\(392\) −2.99161 −0.151099
\(393\) 14.7160 0.742325
\(394\) 0.613281 0.0308967
\(395\) 8.48581 0.426967
\(396\) 5.81902 0.292417
\(397\) 10.2941 0.516646 0.258323 0.966059i \(-0.416830\pi\)
0.258323 + 0.966059i \(0.416830\pi\)
\(398\) 1.75058 0.0877485
\(399\) 21.0304 1.05284
\(400\) 3.76788 0.188394
\(401\) −17.8361 −0.890692 −0.445346 0.895358i \(-0.646919\pi\)
−0.445346 + 0.895358i \(0.646919\pi\)
\(402\) 2.06890 0.103187
\(403\) −26.1343 −1.30184
\(404\) 35.4997 1.76618
\(405\) −9.09708 −0.452037
\(406\) −1.39546 −0.0692554
\(407\) −3.33047 −0.165086
\(408\) −13.2566 −0.656298
\(409\) 13.4983 0.667450 0.333725 0.942670i \(-0.391694\pi\)
0.333725 + 0.942670i \(0.391694\pi\)
\(410\) −0.256893 −0.0126870
\(411\) −42.6879 −2.10564
\(412\) −21.7060 −1.06938
\(413\) 1.59958 0.0787101
\(414\) 0.334234 0.0164267
\(415\) 7.45000 0.365706
\(416\) −11.5549 −0.566523
\(417\) 27.3872 1.34116
\(418\) −0.953769 −0.0466504
\(419\) 4.54853 0.222210 0.111105 0.993809i \(-0.464561\pi\)
0.111105 + 0.993809i \(0.464561\pi\)
\(420\) 8.53278 0.416357
\(421\) 3.75818 0.183163 0.0915813 0.995798i \(-0.470808\pi\)
0.0915813 + 0.995798i \(0.470808\pi\)
\(422\) 2.27987 0.110982
\(423\) −31.8472 −1.54847
\(424\) −7.90513 −0.383907
\(425\) −6.94282 −0.336776
\(426\) 1.15631 0.0560232
\(427\) −23.5860 −1.14141
\(428\) −22.4459 −1.08496
\(429\) −12.2361 −0.590765
\(430\) −0.877022 −0.0422938
\(431\) 15.2119 0.732732 0.366366 0.930471i \(-0.380602\pi\)
0.366366 + 0.930471i \(0.380602\pi\)
\(432\) −0.301118 −0.0144875
\(433\) −8.94042 −0.429649 −0.214825 0.976653i \(-0.568918\pi\)
−0.214825 + 0.976653i \(0.568918\pi\)
\(434\) −1.83385 −0.0880275
\(435\) −9.69837 −0.465001
\(436\) 8.87886 0.425220
\(437\) 2.75895 0.131979
\(438\) −0.482041 −0.0230328
\(439\) 36.9901 1.76544 0.882720 0.469900i \(-0.155710\pi\)
0.882720 + 0.469900i \(0.155710\pi\)
\(440\) −0.781640 −0.0372632
\(441\) −11.3568 −0.540802
\(442\) 6.86255 0.326418
\(443\) −4.88064 −0.231886 −0.115943 0.993256i \(-0.536989\pi\)
−0.115943 + 0.993256i \(0.536989\pi\)
\(444\) −15.9546 −0.757171
\(445\) −9.68874 −0.459290
\(446\) 4.86993 0.230598
\(447\) −30.8982 −1.46143
\(448\) 12.6118 0.595853
\(449\) 30.5866 1.44347 0.721736 0.692168i \(-0.243344\pi\)
0.721736 + 0.692168i \(0.243344\pi\)
\(450\) −0.585537 −0.0276025
\(451\) −1.30184 −0.0613011
\(452\) 30.2156 1.42122
\(453\) −7.61841 −0.357944
\(454\) −4.85559 −0.227884
\(455\) −8.92207 −0.418273
\(456\) −9.22876 −0.432176
\(457\) −20.5889 −0.963110 −0.481555 0.876416i \(-0.659928\pi\)
−0.481555 + 0.876416i \(0.659928\pi\)
\(458\) 4.34539 0.203047
\(459\) 0.554849 0.0258981
\(460\) 1.11940 0.0521925
\(461\) 0.456150 0.0212450 0.0106225 0.999944i \(-0.496619\pi\)
0.0106225 + 0.999944i \(0.496619\pi\)
\(462\) −0.858607 −0.0399460
\(463\) 31.2147 1.45067 0.725336 0.688395i \(-0.241684\pi\)
0.725336 + 0.688395i \(0.241684\pi\)
\(464\) −14.9592 −0.694462
\(465\) −12.7452 −0.591043
\(466\) 2.32385 0.107650
\(467\) 39.9991 1.85094 0.925470 0.378821i \(-0.123670\pi\)
0.925470 + 0.378821i \(0.123670\pi\)
\(468\) −29.1477 −1.34735
\(469\) 7.64481 0.353005
\(470\) 2.11791 0.0976920
\(471\) −45.7471 −2.10792
\(472\) −0.701942 −0.0323095
\(473\) −4.44442 −0.204355
\(474\) −4.09050 −0.187883
\(475\) −4.83335 −0.221769
\(476\) −24.2514 −1.11156
\(477\) −30.0097 −1.37405
\(478\) 1.79643 0.0821668
\(479\) 3.89811 0.178109 0.0890547 0.996027i \(-0.471615\pi\)
0.0890547 + 0.996027i \(0.471615\pi\)
\(480\) −5.63506 −0.257204
\(481\) 16.6825 0.760656
\(482\) −5.55753 −0.253138
\(483\) 2.48368 0.113011
\(484\) −1.96106 −0.0891391
\(485\) 14.8362 0.673677
\(486\) 4.33785 0.196769
\(487\) 12.6004 0.570980 0.285490 0.958382i \(-0.407844\pi\)
0.285490 + 0.958382i \(0.407844\pi\)
\(488\) 10.3502 0.468534
\(489\) −43.2238 −1.95465
\(490\) 0.755255 0.0341189
\(491\) 1.61450 0.0728614 0.0364307 0.999336i \(-0.488401\pi\)
0.0364307 + 0.999336i \(0.488401\pi\)
\(492\) −6.23643 −0.281160
\(493\) 27.5643 1.24143
\(494\) 4.77747 0.214949
\(495\) −2.96728 −0.133370
\(496\) −19.6587 −0.882700
\(497\) 4.27268 0.191656
\(498\) −3.59120 −0.160926
\(499\) 8.65917 0.387638 0.193819 0.981037i \(-0.437913\pi\)
0.193819 + 0.981037i \(0.437913\pi\)
\(500\) −1.96106 −0.0877013
\(501\) −50.6307 −2.26201
\(502\) −6.16301 −0.275068
\(503\) −24.8528 −1.10813 −0.554065 0.832473i \(-0.686924\pi\)
−0.554065 + 0.832473i \(0.686924\pi\)
\(504\) −4.13121 −0.184019
\(505\) −18.1023 −0.805541
\(506\) −0.112640 −0.00500744
\(507\) 29.5347 1.31168
\(508\) 23.4113 1.03871
\(509\) 13.9830 0.619784 0.309892 0.950772i \(-0.399707\pi\)
0.309892 + 0.950772i \(0.399707\pi\)
\(510\) 3.34672 0.148195
\(511\) −1.78119 −0.0787953
\(512\) −14.5820 −0.644439
\(513\) 0.386267 0.0170541
\(514\) −3.85307 −0.169952
\(515\) 11.0685 0.487736
\(516\) −21.2909 −0.937281
\(517\) 10.7328 0.472027
\(518\) 1.17061 0.0514337
\(519\) 27.0586 1.18774
\(520\) 3.91527 0.171696
\(521\) −20.0362 −0.877801 −0.438900 0.898536i \(-0.644632\pi\)
−0.438900 + 0.898536i \(0.644632\pi\)
\(522\) 2.32469 0.101749
\(523\) −13.7534 −0.601396 −0.300698 0.953719i \(-0.597220\pi\)
−0.300698 + 0.953719i \(0.597220\pi\)
\(524\) −11.8139 −0.516092
\(525\) −4.35110 −0.189898
\(526\) −4.12227 −0.179740
\(527\) 36.2237 1.57793
\(528\) −9.20419 −0.400561
\(529\) −22.6742 −0.985833
\(530\) 1.99571 0.0866881
\(531\) −2.66473 −0.115640
\(532\) −16.8830 −0.731972
\(533\) 6.52096 0.282454
\(534\) 4.67037 0.202107
\(535\) 11.4458 0.494845
\(536\) −3.35477 −0.144904
\(537\) −9.04513 −0.390326
\(538\) −3.31580 −0.142954
\(539\) 3.82735 0.164856
\(540\) 0.156722 0.00674424
\(541\) 9.38822 0.403631 0.201815 0.979424i \(-0.435316\pi\)
0.201815 + 0.979424i \(0.435316\pi\)
\(542\) −5.77213 −0.247934
\(543\) 10.3469 0.444029
\(544\) 16.0157 0.686667
\(545\) −4.52758 −0.193940
\(546\) 4.30080 0.184057
\(547\) −11.0381 −0.471954 −0.235977 0.971759i \(-0.575829\pi\)
−0.235977 + 0.971759i \(0.575829\pi\)
\(548\) 34.2694 1.46392
\(549\) 39.2919 1.67694
\(550\) 0.197331 0.00841422
\(551\) 19.1893 0.817491
\(552\) −1.08991 −0.0463897
\(553\) −15.1149 −0.642749
\(554\) 3.33900 0.141861
\(555\) 8.13569 0.345341
\(556\) −21.9862 −0.932422
\(557\) −0.509545 −0.0215901 −0.0107951 0.999942i \(-0.503436\pi\)
−0.0107951 + 0.999942i \(0.503436\pi\)
\(558\) 3.05500 0.129328
\(559\) 22.2623 0.941595
\(560\) −6.71132 −0.283605
\(561\) 16.9599 0.716049
\(562\) 3.60298 0.151982
\(563\) 1.21450 0.0511851 0.0255926 0.999672i \(-0.491853\pi\)
0.0255926 + 0.999672i \(0.491853\pi\)
\(564\) 51.4152 2.16497
\(565\) −15.4078 −0.648209
\(566\) 3.31092 0.139169
\(567\) 16.2036 0.680489
\(568\) −1.87498 −0.0786722
\(569\) −10.3628 −0.434432 −0.217216 0.976124i \(-0.569698\pi\)
−0.217216 + 0.976124i \(0.569698\pi\)
\(570\) 2.32987 0.0975875
\(571\) 6.63977 0.277866 0.138933 0.990302i \(-0.455633\pi\)
0.138933 + 0.990302i \(0.455633\pi\)
\(572\) 9.82304 0.410722
\(573\) 1.81906 0.0759923
\(574\) 0.457576 0.0190988
\(575\) −0.570816 −0.0238047
\(576\) −21.0100 −0.875418
\(577\) 29.8080 1.24093 0.620463 0.784236i \(-0.286945\pi\)
0.620463 + 0.784236i \(0.286945\pi\)
\(578\) −6.15726 −0.256108
\(579\) 5.84560 0.242935
\(580\) 7.78577 0.323286
\(581\) −13.2699 −0.550528
\(582\) −7.15165 −0.296445
\(583\) 10.1135 0.418859
\(584\) 0.781640 0.0323445
\(585\) 14.8633 0.614520
\(586\) 4.92141 0.203302
\(587\) −23.0396 −0.950948 −0.475474 0.879730i \(-0.657723\pi\)
−0.475474 + 0.879730i \(0.657723\pi\)
\(588\) 18.3349 0.756117
\(589\) 25.2177 1.03908
\(590\) 0.177211 0.00729565
\(591\) −7.59194 −0.312291
\(592\) 12.5488 0.515754
\(593\) 42.5797 1.74854 0.874270 0.485441i \(-0.161341\pi\)
0.874270 + 0.485441i \(0.161341\pi\)
\(594\) −0.0157701 −0.000647055 0
\(595\) 12.3665 0.506977
\(596\) 24.8048 1.01604
\(597\) −21.6708 −0.886925
\(598\) 0.564217 0.0230726
\(599\) 26.9798 1.10236 0.551182 0.834385i \(-0.314177\pi\)
0.551182 + 0.834385i \(0.314177\pi\)
\(600\) 1.90939 0.0779506
\(601\) −5.95279 −0.242819 −0.121410 0.992602i \(-0.538741\pi\)
−0.121410 + 0.992602i \(0.538741\pi\)
\(602\) 1.56215 0.0636683
\(603\) −12.7355 −0.518629
\(604\) 6.11599 0.248856
\(605\) 1.00000 0.0406558
\(606\) 8.72604 0.354471
\(607\) 40.2772 1.63480 0.817401 0.576069i \(-0.195414\pi\)
0.817401 + 0.576069i \(0.195414\pi\)
\(608\) 11.1496 0.452175
\(609\) 17.2747 0.700005
\(610\) −2.61300 −0.105797
\(611\) −53.7610 −2.17494
\(612\) 40.4004 1.63309
\(613\) −38.8448 −1.56893 −0.784463 0.620176i \(-0.787061\pi\)
−0.784463 + 0.620176i \(0.787061\pi\)
\(614\) 1.05843 0.0427148
\(615\) 3.18013 0.128235
\(616\) 1.39225 0.0560954
\(617\) −31.6436 −1.27392 −0.636962 0.770895i \(-0.719809\pi\)
−0.636962 + 0.770895i \(0.719809\pi\)
\(618\) −5.33546 −0.214624
\(619\) −8.31936 −0.334383 −0.167192 0.985924i \(-0.553470\pi\)
−0.167192 + 0.985924i \(0.553470\pi\)
\(620\) 10.2317 0.410915
\(621\) 0.0456179 0.00183058
\(622\) 0.997076 0.0399791
\(623\) 17.2575 0.691408
\(624\) 46.1042 1.84564
\(625\) 1.00000 0.0400000
\(626\) 4.58800 0.183373
\(627\) 11.8069 0.471523
\(628\) 36.7254 1.46550
\(629\) −23.1229 −0.921970
\(630\) 1.04295 0.0415523
\(631\) −5.92133 −0.235724 −0.117862 0.993030i \(-0.537604\pi\)
−0.117862 + 0.993030i \(0.537604\pi\)
\(632\) 6.63285 0.263840
\(633\) −28.2230 −1.12176
\(634\) −5.60815 −0.222728
\(635\) −11.9381 −0.473748
\(636\) 48.4486 1.92111
\(637\) −19.1714 −0.759597
\(638\) −0.783440 −0.0310167
\(639\) −7.11784 −0.281577
\(640\) 6.01081 0.237598
\(641\) −49.7037 −1.96318 −0.981588 0.191010i \(-0.938824\pi\)
−0.981588 + 0.191010i \(0.938824\pi\)
\(642\) −5.51734 −0.217752
\(643\) 32.9861 1.30085 0.650423 0.759572i \(-0.274592\pi\)
0.650423 + 0.759572i \(0.274592\pi\)
\(644\) −1.99388 −0.0785697
\(645\) 10.8568 0.427488
\(646\) −6.62185 −0.260533
\(647\) −16.9040 −0.664565 −0.332282 0.943180i \(-0.607819\pi\)
−0.332282 + 0.943180i \(0.607819\pi\)
\(648\) −7.11064 −0.279332
\(649\) 0.898038 0.0352511
\(650\) −0.988439 −0.0387698
\(651\) 22.7016 0.889745
\(652\) 34.6996 1.35894
\(653\) 11.7221 0.458719 0.229360 0.973342i \(-0.426337\pi\)
0.229360 + 0.973342i \(0.426337\pi\)
\(654\) 2.18248 0.0853417
\(655\) 6.02423 0.235386
\(656\) 4.90517 0.191515
\(657\) 2.96728 0.115765
\(658\) −3.77241 −0.147064
\(659\) −30.0878 −1.17205 −0.586026 0.810292i \(-0.699309\pi\)
−0.586026 + 0.810292i \(0.699309\pi\)
\(660\) 4.79048 0.186469
\(661\) 25.3985 0.987888 0.493944 0.869494i \(-0.335555\pi\)
0.493944 + 0.869494i \(0.335555\pi\)
\(662\) −5.85569 −0.227588
\(663\) −84.9530 −3.29930
\(664\) 5.82322 0.225985
\(665\) 8.60913 0.333848
\(666\) −1.95012 −0.0755655
\(667\) 2.26624 0.0877493
\(668\) 40.6459 1.57264
\(669\) −60.2859 −2.33079
\(670\) 0.846937 0.0327200
\(671\) −13.2417 −0.511190
\(672\) 10.0371 0.387190
\(673\) −8.13256 −0.313487 −0.156744 0.987639i \(-0.550100\pi\)
−0.156744 + 0.987639i \(0.550100\pi\)
\(674\) 2.77226 0.106783
\(675\) −0.0799170 −0.00307601
\(676\) −23.7102 −0.911932
\(677\) 45.6107 1.75296 0.876480 0.481438i \(-0.159886\pi\)
0.876480 + 0.481438i \(0.159886\pi\)
\(678\) 7.42717 0.285239
\(679\) −26.4261 −1.01414
\(680\) −5.42678 −0.208108
\(681\) 60.1084 2.30336
\(682\) −1.02956 −0.0394239
\(683\) 5.02751 0.192372 0.0961862 0.995363i \(-0.469336\pi\)
0.0961862 + 0.995363i \(0.469336\pi\)
\(684\) 28.1254 1.07540
\(685\) −17.4750 −0.667684
\(686\) −3.80565 −0.145300
\(687\) −53.7925 −2.05231
\(688\) 16.7460 0.638437
\(689\) −50.6590 −1.92996
\(690\) 0.275157 0.0104750
\(691\) −34.6652 −1.31873 −0.659363 0.751825i \(-0.729174\pi\)
−0.659363 + 0.751825i \(0.729174\pi\)
\(692\) −21.7224 −0.825762
\(693\) 5.28531 0.200772
\(694\) −4.34537 −0.164948
\(695\) 11.2114 0.425272
\(696\) −7.58064 −0.287343
\(697\) −9.03842 −0.342354
\(698\) 4.80231 0.181770
\(699\) −28.7674 −1.08808
\(700\) 3.49303 0.132024
\(701\) 37.6721 1.42285 0.711427 0.702760i \(-0.248049\pi\)
0.711427 + 0.702760i \(0.248049\pi\)
\(702\) 0.0789931 0.00298140
\(703\) −16.0973 −0.607123
\(704\) 7.08056 0.266858
\(705\) −26.2181 −0.987430
\(706\) 2.26038 0.0850704
\(707\) 32.2437 1.21265
\(708\) 4.30204 0.161680
\(709\) −46.9947 −1.76492 −0.882462 0.470384i \(-0.844115\pi\)
−0.882462 + 0.470384i \(0.844115\pi\)
\(710\) 0.473352 0.0177646
\(711\) 25.1798 0.944317
\(712\) −7.57311 −0.283814
\(713\) 2.97819 0.111534
\(714\) −5.96115 −0.223091
\(715\) −5.00904 −0.187328
\(716\) 7.26135 0.271369
\(717\) −22.2384 −0.830508
\(718\) −3.45115 −0.128796
\(719\) 3.78955 0.141326 0.0706631 0.997500i \(-0.477488\pi\)
0.0706631 + 0.997500i \(0.477488\pi\)
\(720\) 11.1804 0.416668
\(721\) −19.7151 −0.734229
\(722\) −0.860612 −0.0320286
\(723\) 68.7978 2.55862
\(724\) −8.30641 −0.308705
\(725\) −3.97018 −0.147449
\(726\) −0.482041 −0.0178902
\(727\) −28.4237 −1.05418 −0.527089 0.849810i \(-0.676716\pi\)
−0.527089 + 0.849810i \(0.676716\pi\)
\(728\) −6.97385 −0.258468
\(729\) −26.4079 −0.978072
\(730\) −0.197331 −0.00730355
\(731\) −30.8568 −1.14128
\(732\) −63.4342 −2.34459
\(733\) −34.9522 −1.29099 −0.645494 0.763765i \(-0.723348\pi\)
−0.645494 + 0.763765i \(0.723348\pi\)
\(734\) −3.75798 −0.138710
\(735\) −9.34947 −0.344860
\(736\) 1.31676 0.0485363
\(737\) 4.29196 0.158096
\(738\) −0.762274 −0.0280597
\(739\) 34.7267 1.27744 0.638720 0.769439i \(-0.279464\pi\)
0.638720 + 0.769439i \(0.279464\pi\)
\(740\) −6.53126 −0.240094
\(741\) −59.1414 −2.17261
\(742\) −3.55474 −0.130499
\(743\) 14.3969 0.528170 0.264085 0.964499i \(-0.414930\pi\)
0.264085 + 0.964499i \(0.414930\pi\)
\(744\) −9.96212 −0.365229
\(745\) −12.6487 −0.463411
\(746\) −1.52550 −0.0558526
\(747\) 22.1063 0.808826
\(748\) −13.6153 −0.497824
\(749\) −20.3872 −0.744931
\(750\) −0.482041 −0.0176016
\(751\) −18.1726 −0.663129 −0.331565 0.943433i \(-0.607576\pi\)
−0.331565 + 0.943433i \(0.607576\pi\)
\(752\) −40.4398 −1.47469
\(753\) 76.2932 2.78028
\(754\) 3.92428 0.142914
\(755\) −3.11872 −0.113502
\(756\) −0.279152 −0.0101527
\(757\) 46.0124 1.67235 0.836174 0.548464i \(-0.184787\pi\)
0.836174 + 0.548464i \(0.184787\pi\)
\(758\) −1.48317 −0.0538710
\(759\) 1.39439 0.0506132
\(760\) −3.77794 −0.137040
\(761\) −47.6641 −1.72782 −0.863911 0.503644i \(-0.831992\pi\)
−0.863911 + 0.503644i \(0.831992\pi\)
\(762\) 5.75463 0.208468
\(763\) 8.06450 0.291954
\(764\) −1.46032 −0.0528327
\(765\) −20.6013 −0.744842
\(766\) 0.555232 0.0200614
\(767\) −4.49831 −0.162425
\(768\) 31.6953 1.14371
\(769\) −6.32788 −0.228189 −0.114095 0.993470i \(-0.536397\pi\)
−0.114095 + 0.993470i \(0.536397\pi\)
\(770\) −0.351485 −0.0126666
\(771\) 47.6980 1.71780
\(772\) −4.69279 −0.168897
\(773\) −45.8984 −1.65085 −0.825426 0.564510i \(-0.809065\pi\)
−0.825426 + 0.564510i \(0.809065\pi\)
\(774\) −2.60237 −0.0935404
\(775\) −5.21743 −0.187416
\(776\) 11.5966 0.416292
\(777\) −14.4912 −0.519870
\(778\) 3.56716 0.127889
\(779\) −6.29223 −0.225443
\(780\) −23.9957 −0.859185
\(781\) 2.39877 0.0858348
\(782\) −0.782037 −0.0279656
\(783\) 0.317285 0.0113388
\(784\) −14.4210 −0.515036
\(785\) −18.7273 −0.668407
\(786\) −2.90393 −0.103580
\(787\) −21.2751 −0.758376 −0.379188 0.925320i \(-0.623797\pi\)
−0.379188 + 0.925320i \(0.623797\pi\)
\(788\) 6.09474 0.217116
\(789\) 51.0305 1.81673
\(790\) −1.67451 −0.0595765
\(791\) 27.4442 0.975803
\(792\) −2.31935 −0.0824145
\(793\) 66.3283 2.35539
\(794\) −2.03134 −0.0720897
\(795\) −24.7053 −0.876207
\(796\) 17.3971 0.616624
\(797\) 39.1362 1.38627 0.693137 0.720806i \(-0.256228\pi\)
0.693137 + 0.720806i \(0.256228\pi\)
\(798\) −4.14995 −0.146907
\(799\) 74.5158 2.63618
\(800\) −2.30680 −0.0815577
\(801\) −28.7492 −1.01580
\(802\) 3.51962 0.124282
\(803\) −1.00000 −0.0352892
\(804\) 20.5606 0.725115
\(805\) 1.01673 0.0358351
\(806\) 5.15712 0.181652
\(807\) 41.0470 1.44492
\(808\) −14.1495 −0.497777
\(809\) 12.4942 0.439272 0.219636 0.975582i \(-0.429513\pi\)
0.219636 + 0.975582i \(0.429513\pi\)
\(810\) 1.79513 0.0630746
\(811\) −46.0695 −1.61772 −0.808860 0.588002i \(-0.799915\pi\)
−0.808860 + 0.588002i \(0.799915\pi\)
\(812\) −13.8680 −0.486670
\(813\) 71.4545 2.50602
\(814\) 0.657206 0.0230351
\(815\) −17.6943 −0.619805
\(816\) −63.9030 −2.23705
\(817\) −21.4814 −0.751541
\(818\) −2.66364 −0.0931320
\(819\) −26.4743 −0.925088
\(820\) −2.55298 −0.0891540
\(821\) −6.72168 −0.234588 −0.117294 0.993097i \(-0.537422\pi\)
−0.117294 + 0.993097i \(0.537422\pi\)
\(822\) 8.42364 0.293808
\(823\) 30.0782 1.04846 0.524230 0.851577i \(-0.324353\pi\)
0.524230 + 0.851577i \(0.324353\pi\)
\(824\) 8.65157 0.301392
\(825\) −2.44280 −0.0850475
\(826\) −0.315646 −0.0109827
\(827\) 44.4793 1.54670 0.773348 0.633982i \(-0.218581\pi\)
0.773348 + 0.633982i \(0.218581\pi\)
\(828\) 3.32159 0.115433
\(829\) 22.6261 0.785836 0.392918 0.919574i \(-0.371466\pi\)
0.392918 + 0.919574i \(0.371466\pi\)
\(830\) −1.47012 −0.0510285
\(831\) −41.3342 −1.43387
\(832\) −35.4668 −1.22959
\(833\) 26.5726 0.920686
\(834\) −5.40434 −0.187137
\(835\) −20.7265 −0.717270
\(836\) −9.47849 −0.327820
\(837\) 0.416962 0.0144123
\(838\) −0.897565 −0.0310059
\(839\) 2.13174 0.0735957 0.0367978 0.999323i \(-0.488284\pi\)
0.0367978 + 0.999323i \(0.488284\pi\)
\(840\) −3.40100 −0.117345
\(841\) −13.2377 −0.456471
\(842\) −0.741606 −0.0255574
\(843\) −44.6020 −1.53617
\(844\) 22.6571 0.779891
\(845\) 12.0905 0.415926
\(846\) 6.28445 0.216064
\(847\) −1.78119 −0.0612025
\(848\) −38.1065 −1.30858
\(849\) −40.9866 −1.40666
\(850\) 1.37003 0.0469917
\(851\) −1.90109 −0.0651685
\(852\) 11.4913 0.393685
\(853\) 19.9441 0.682871 0.341436 0.939905i \(-0.389087\pi\)
0.341436 + 0.939905i \(0.389087\pi\)
\(854\) 4.65425 0.159265
\(855\) −14.3419 −0.490483
\(856\) 8.94649 0.305785
\(857\) 41.4055 1.41439 0.707193 0.707021i \(-0.249961\pi\)
0.707193 + 0.707021i \(0.249961\pi\)
\(858\) 2.41456 0.0824318
\(859\) −28.9941 −0.989266 −0.494633 0.869102i \(-0.664697\pi\)
−0.494633 + 0.869102i \(0.664697\pi\)
\(860\) −8.71578 −0.297206
\(861\) −5.66443 −0.193043
\(862\) −3.00178 −0.102241
\(863\) −52.7790 −1.79662 −0.898310 0.439363i \(-0.855204\pi\)
−0.898310 + 0.439363i \(0.855204\pi\)
\(864\) 0.184352 0.00627180
\(865\) 11.0769 0.376625
\(866\) 1.76422 0.0599507
\(867\) 76.2221 2.58864
\(868\) −18.2246 −0.618584
\(869\) −8.48581 −0.287861
\(870\) 1.91379 0.0648835
\(871\) −21.4986 −0.728453
\(872\) −3.53894 −0.119844
\(873\) 44.0232 1.48996
\(874\) −0.544427 −0.0184155
\(875\) −1.78119 −0.0602153
\(876\) −4.79048 −0.161855
\(877\) 37.4470 1.26450 0.632248 0.774766i \(-0.282133\pi\)
0.632248 + 0.774766i \(0.282133\pi\)
\(878\) −7.29929 −0.246339
\(879\) −60.9232 −2.05489
\(880\) −3.76788 −0.127015
\(881\) 3.87080 0.130410 0.0652052 0.997872i \(-0.479230\pi\)
0.0652052 + 0.997872i \(0.479230\pi\)
\(882\) 2.24106 0.0754603
\(883\) −44.6541 −1.50273 −0.751365 0.659887i \(-0.770604\pi\)
−0.751365 + 0.659887i \(0.770604\pi\)
\(884\) 68.1995 2.29380
\(885\) −2.19373 −0.0737414
\(886\) 0.963102 0.0323560
\(887\) −17.1112 −0.574537 −0.287269 0.957850i \(-0.592747\pi\)
−0.287269 + 0.957850i \(0.592747\pi\)
\(888\) 6.35918 0.213400
\(889\) 21.2640 0.713172
\(890\) 1.91189 0.0640866
\(891\) 9.09708 0.304763
\(892\) 48.3970 1.62045
\(893\) 51.8753 1.73594
\(894\) 6.09717 0.203920
\(895\) −3.70277 −0.123770
\(896\) −10.7064 −0.357676
\(897\) −6.98456 −0.233208
\(898\) −6.03569 −0.201414
\(899\) 20.7142 0.690856
\(900\) −5.81902 −0.193967
\(901\) 70.2163 2.33924
\(902\) 0.256893 0.00855360
\(903\) −19.3381 −0.643533
\(904\) −12.0433 −0.400555
\(905\) 4.23567 0.140799
\(906\) 1.50335 0.0499454
\(907\) −4.72103 −0.156759 −0.0783797 0.996924i \(-0.524975\pi\)
−0.0783797 + 0.996924i \(0.524975\pi\)
\(908\) −48.2545 −1.60138
\(909\) −53.7147 −1.78160
\(910\) 1.76060 0.0583634
\(911\) −12.3185 −0.408132 −0.204066 0.978957i \(-0.565416\pi\)
−0.204066 + 0.978957i \(0.565416\pi\)
\(912\) −44.4870 −1.47311
\(913\) −7.45000 −0.246559
\(914\) 4.06284 0.134387
\(915\) 32.3469 1.06935
\(916\) 43.1841 1.42684
\(917\) −10.7303 −0.354346
\(918\) −0.109489 −0.00361367
\(919\) −23.9263 −0.789255 −0.394628 0.918841i \(-0.629126\pi\)
−0.394628 + 0.918841i \(0.629126\pi\)
\(920\) −0.446173 −0.0147099
\(921\) −13.1025 −0.431743
\(922\) −0.0900125 −0.00296440
\(923\) −12.0156 −0.395497
\(924\) −8.53278 −0.280708
\(925\) 3.33047 0.109505
\(926\) −6.15964 −0.202418
\(927\) 32.8433 1.07872
\(928\) 9.15841 0.300640
\(929\) 18.0170 0.591118 0.295559 0.955325i \(-0.404494\pi\)
0.295559 + 0.955325i \(0.404494\pi\)
\(930\) 2.51501 0.0824706
\(931\) 18.4989 0.606278
\(932\) 23.0942 0.756476
\(933\) −12.3430 −0.404092
\(934\) −7.89307 −0.258269
\(935\) 6.94282 0.227054
\(936\) 11.6177 0.379737
\(937\) 22.6177 0.738888 0.369444 0.929253i \(-0.379548\pi\)
0.369444 + 0.929253i \(0.379548\pi\)
\(938\) −1.50856 −0.0492562
\(939\) −56.7959 −1.85346
\(940\) 21.0476 0.686499
\(941\) −9.04843 −0.294970 −0.147485 0.989064i \(-0.547118\pi\)
−0.147485 + 0.989064i \(0.547118\pi\)
\(942\) 9.02733 0.294126
\(943\) −0.743110 −0.0241990
\(944\) −3.38370 −0.110130
\(945\) 0.142348 0.00463057
\(946\) 0.877022 0.0285145
\(947\) −56.8462 −1.84725 −0.923627 0.383292i \(-0.874790\pi\)
−0.923627 + 0.383292i \(0.874790\pi\)
\(948\) −40.6511 −1.32029
\(949\) 5.00904 0.162600
\(950\) 0.953769 0.0309444
\(951\) 69.4245 2.25124
\(952\) 9.66615 0.313282
\(953\) −40.0370 −1.29693 −0.648463 0.761246i \(-0.724588\pi\)
−0.648463 + 0.761246i \(0.724588\pi\)
\(954\) 5.92184 0.191727
\(955\) 0.744661 0.0240966
\(956\) 17.8528 0.577401
\(957\) 9.69837 0.313504
\(958\) −0.769219 −0.0248523
\(959\) 31.1263 1.00512
\(960\) −17.2964 −0.558239
\(961\) −3.77840 −0.121884
\(962\) −3.29197 −0.106137
\(963\) 33.9629 1.09444
\(964\) −55.2303 −1.77885
\(965\) 2.39299 0.0770330
\(966\) −0.490107 −0.0157689
\(967\) 30.2212 0.971849 0.485924 0.874001i \(-0.338483\pi\)
0.485924 + 0.874001i \(0.338483\pi\)
\(968\) 0.781640 0.0251229
\(969\) 81.9733 2.63336
\(970\) −2.92764 −0.0940009
\(971\) −42.6660 −1.36922 −0.684609 0.728911i \(-0.740027\pi\)
−0.684609 + 0.728911i \(0.740027\pi\)
\(972\) 43.1092 1.38273
\(973\) −19.9696 −0.640197
\(974\) −2.48646 −0.0796712
\(975\) 12.2361 0.391869
\(976\) 49.8931 1.59704
\(977\) 49.0785 1.57016 0.785081 0.619394i \(-0.212622\pi\)
0.785081 + 0.619394i \(0.212622\pi\)
\(978\) 8.52939 0.272740
\(979\) 9.68874 0.309653
\(980\) 7.50567 0.239760
\(981\) −13.4346 −0.428935
\(982\) −0.318591 −0.0101666
\(983\) 19.4484 0.620308 0.310154 0.950686i \(-0.399619\pi\)
0.310154 + 0.950686i \(0.399619\pi\)
\(984\) 2.48572 0.0792418
\(985\) −3.10788 −0.0990254
\(986\) −5.43928 −0.173222
\(987\) 46.6995 1.48646
\(988\) 47.4782 1.51048
\(989\) −2.53695 −0.0806702
\(990\) 0.585537 0.0186096
\(991\) 7.47462 0.237439 0.118720 0.992928i \(-0.462121\pi\)
0.118720 + 0.992928i \(0.462121\pi\)
\(992\) 12.0356 0.382130
\(993\) 72.4889 2.30036
\(994\) −0.843131 −0.0267425
\(995\) −8.87127 −0.281238
\(996\) −35.6891 −1.13085
\(997\) 17.2522 0.546383 0.273192 0.961960i \(-0.411921\pi\)
0.273192 + 0.961960i \(0.411921\pi\)
\(998\) −1.70872 −0.0540887
\(999\) −0.266162 −0.00842098
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 4015.2.a.c.1.12 23
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4015.2.a.c.1.12 23 1.1 even 1 trivial