Properties

Label 8033.2.a.b.1.5
Level $8033$
Weight $2$
Character 8033.1
Self dual yes
Analytic conductor $64.144$
Analytic rank $1$
Dimension $153$
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] = [8033,2,Mod(1,8033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8033, 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("8033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8033 = 29 \cdot 277 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8033.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: \(64.1438279437\)
Analytic rank: \(1\)
Dimension: \(153\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 8033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.62862 q^{2} +3.02798 q^{3} +4.90963 q^{4} +2.24361 q^{5} -7.95940 q^{6} -3.55148 q^{7} -7.64830 q^{8} +6.16867 q^{9} +O(q^{10})\) \(q-2.62862 q^{2} +3.02798 q^{3} +4.90963 q^{4} +2.24361 q^{5} -7.95940 q^{6} -3.55148 q^{7} -7.64830 q^{8} +6.16867 q^{9} -5.89760 q^{10} +4.02450 q^{11} +14.8663 q^{12} -2.03015 q^{13} +9.33547 q^{14} +6.79362 q^{15} +10.2852 q^{16} -7.13861 q^{17} -16.2151 q^{18} -4.32009 q^{19} +11.0153 q^{20} -10.7538 q^{21} -10.5789 q^{22} -4.46785 q^{23} -23.1589 q^{24} +0.0337976 q^{25} +5.33650 q^{26} +9.59469 q^{27} -17.4364 q^{28} -1.00000 q^{29} -17.8578 q^{30} -0.124315 q^{31} -11.7392 q^{32} +12.1861 q^{33} +18.7647 q^{34} -7.96814 q^{35} +30.2859 q^{36} +1.06662 q^{37} +11.3559 q^{38} -6.14727 q^{39} -17.1598 q^{40} +0.321628 q^{41} +28.2676 q^{42} +4.21144 q^{43} +19.7588 q^{44} +13.8401 q^{45} +11.7443 q^{46} -6.24344 q^{47} +31.1434 q^{48} +5.61299 q^{49} -0.0888409 q^{50} -21.6156 q^{51} -9.96730 q^{52} +1.21606 q^{53} -25.2208 q^{54} +9.02943 q^{55} +27.1627 q^{56} -13.0811 q^{57} +2.62862 q^{58} +2.09684 q^{59} +33.3541 q^{60} +5.39164 q^{61} +0.326777 q^{62} -21.9079 q^{63} +10.2875 q^{64} -4.55488 q^{65} -32.0327 q^{66} +11.1623 q^{67} -35.0479 q^{68} -13.5286 q^{69} +20.9452 q^{70} -1.49342 q^{71} -47.1798 q^{72} -13.6425 q^{73} -2.80373 q^{74} +0.102338 q^{75} -21.2100 q^{76} -14.2929 q^{77} +16.1588 q^{78} +6.70219 q^{79} +23.0760 q^{80} +10.5465 q^{81} -0.845437 q^{82} +4.10285 q^{83} -52.7972 q^{84} -16.0163 q^{85} -11.0703 q^{86} -3.02798 q^{87} -30.7806 q^{88} -12.0251 q^{89} -36.3804 q^{90} +7.21004 q^{91} -21.9355 q^{92} -0.376424 q^{93} +16.4116 q^{94} -9.69260 q^{95} -35.5461 q^{96} +12.4420 q^{97} -14.7544 q^{98} +24.8259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62862 −1.85871 −0.929356 0.369184i \(-0.879637\pi\)
−0.929356 + 0.369184i \(0.879637\pi\)
\(3\) 3.02798 1.74821 0.874103 0.485741i \(-0.161450\pi\)
0.874103 + 0.485741i \(0.161450\pi\)
\(4\) 4.90963 2.45481
\(5\) 2.24361 1.00337 0.501687 0.865049i \(-0.332713\pi\)
0.501687 + 0.865049i \(0.332713\pi\)
\(6\) −7.95940 −3.24941
\(7\) −3.55148 −1.34233 −0.671166 0.741307i \(-0.734206\pi\)
−0.671166 + 0.741307i \(0.734206\pi\)
\(8\) −7.64830 −2.70408
\(9\) 6.16867 2.05622
\(10\) −5.89760 −1.86498
\(11\) 4.02450 1.21343 0.606717 0.794918i \(-0.292486\pi\)
0.606717 + 0.794918i \(0.292486\pi\)
\(12\) 14.8663 4.29152
\(13\) −2.03015 −0.563063 −0.281532 0.959552i \(-0.590842\pi\)
−0.281532 + 0.959552i \(0.590842\pi\)
\(14\) 9.33547 2.49501
\(15\) 6.79362 1.75410
\(16\) 10.2852 2.57130
\(17\) −7.13861 −1.73137 −0.865683 0.500592i \(-0.833116\pi\)
−0.865683 + 0.500592i \(0.833116\pi\)
\(18\) −16.2151 −3.82193
\(19\) −4.32009 −0.991096 −0.495548 0.868581i \(-0.665033\pi\)
−0.495548 + 0.868581i \(0.665033\pi\)
\(20\) 11.0153 2.46310
\(21\) −10.7538 −2.34667
\(22\) −10.5789 −2.25542
\(23\) −4.46785 −0.931612 −0.465806 0.884887i \(-0.654235\pi\)
−0.465806 + 0.884887i \(0.654235\pi\)
\(24\) −23.1589 −4.72729
\(25\) 0.0337976 0.00675952
\(26\) 5.33650 1.04657
\(27\) 9.59469 1.84650
\(28\) −17.4364 −3.29518
\(29\) −1.00000 −0.185695
\(30\) −17.8578 −3.26038
\(31\) −0.124315 −0.0223277 −0.0111638 0.999938i \(-0.503554\pi\)
−0.0111638 + 0.999938i \(0.503554\pi\)
\(32\) −11.7392 −2.07522
\(33\) 12.1861 2.12133
\(34\) 18.7647 3.21811
\(35\) −7.96814 −1.34686
\(36\) 30.2859 5.04765
\(37\) 1.06662 0.175351 0.0876754 0.996149i \(-0.472056\pi\)
0.0876754 + 0.996149i \(0.472056\pi\)
\(38\) 11.3559 1.84216
\(39\) −6.14727 −0.984351
\(40\) −17.1598 −2.71320
\(41\) 0.321628 0.0502299 0.0251149 0.999685i \(-0.492005\pi\)
0.0251149 + 0.999685i \(0.492005\pi\)
\(42\) 28.2676 4.36179
\(43\) 4.21144 0.642238 0.321119 0.947039i \(-0.395941\pi\)
0.321119 + 0.947039i \(0.395941\pi\)
\(44\) 19.7588 2.97875
\(45\) 13.8401 2.06316
\(46\) 11.7443 1.73160
\(47\) −6.24344 −0.910699 −0.455350 0.890313i \(-0.650486\pi\)
−0.455350 + 0.890313i \(0.650486\pi\)
\(48\) 31.1434 4.49516
\(49\) 5.61299 0.801856
\(50\) −0.0888409 −0.0125640
\(51\) −21.6156 −3.02678
\(52\) −9.96730 −1.38222
\(53\) 1.21606 0.167038 0.0835190 0.996506i \(-0.473384\pi\)
0.0835190 + 0.996506i \(0.473384\pi\)
\(54\) −25.2208 −3.43211
\(55\) 9.02943 1.21753
\(56\) 27.1627 3.62977
\(57\) −13.0811 −1.73264
\(58\) 2.62862 0.345154
\(59\) 2.09684 0.272986 0.136493 0.990641i \(-0.456417\pi\)
0.136493 + 0.990641i \(0.456417\pi\)
\(60\) 33.3541 4.30600
\(61\) 5.39164 0.690328 0.345164 0.938542i \(-0.387823\pi\)
0.345164 + 0.938542i \(0.387823\pi\)
\(62\) 0.326777 0.0415007
\(63\) −21.9079 −2.76014
\(64\) 10.2875 1.28594
\(65\) −4.55488 −0.564963
\(66\) −32.0327 −3.94295
\(67\) 11.1623 1.36369 0.681847 0.731495i \(-0.261177\pi\)
0.681847 + 0.731495i \(0.261177\pi\)
\(68\) −35.0479 −4.25018
\(69\) −13.5286 −1.62865
\(70\) 20.9452 2.50343
\(71\) −1.49342 −0.177237 −0.0886183 0.996066i \(-0.528245\pi\)
−0.0886183 + 0.996066i \(0.528245\pi\)
\(72\) −47.1798 −5.56020
\(73\) −13.6425 −1.59673 −0.798365 0.602173i \(-0.794302\pi\)
−0.798365 + 0.602173i \(0.794302\pi\)
\(74\) −2.80373 −0.325927
\(75\) 0.102338 0.0118170
\(76\) −21.2100 −2.43296
\(77\) −14.2929 −1.62883
\(78\) 16.1588 1.82962
\(79\) 6.70219 0.754055 0.377028 0.926202i \(-0.376946\pi\)
0.377028 + 0.926202i \(0.376946\pi\)
\(80\) 23.0760 2.57997
\(81\) 10.5465 1.17183
\(82\) −0.845437 −0.0933629
\(83\) 4.10285 0.450346 0.225173 0.974319i \(-0.427705\pi\)
0.225173 + 0.974319i \(0.427705\pi\)
\(84\) −52.7972 −5.76065
\(85\) −16.0163 −1.73721
\(86\) −11.0703 −1.19374
\(87\) −3.02798 −0.324634
\(88\) −30.7806 −3.28122
\(89\) −12.0251 −1.27465 −0.637326 0.770594i \(-0.719960\pi\)
−0.637326 + 0.770594i \(0.719960\pi\)
\(90\) −36.3804 −3.83483
\(91\) 7.21004 0.755818
\(92\) −21.9355 −2.28693
\(93\) −0.376424 −0.0390334
\(94\) 16.4116 1.69273
\(95\) −9.69260 −0.994440
\(96\) −35.5461 −3.62791
\(97\) 12.4420 1.26329 0.631646 0.775257i \(-0.282379\pi\)
0.631646 + 0.775257i \(0.282379\pi\)
\(98\) −14.7544 −1.49042
\(99\) 24.8259 2.49509
\(100\) 0.165934 0.0165934
\(101\) −7.91237 −0.787310 −0.393655 0.919258i \(-0.628790\pi\)
−0.393655 + 0.919258i \(0.628790\pi\)
\(102\) 56.8190 5.62592
\(103\) −0.883298 −0.0870340 −0.0435170 0.999053i \(-0.513856\pi\)
−0.0435170 + 0.999053i \(0.513856\pi\)
\(104\) 15.5272 1.52257
\(105\) −24.1274 −2.35459
\(106\) −3.19654 −0.310476
\(107\) −8.42006 −0.813998 −0.406999 0.913429i \(-0.633425\pi\)
−0.406999 + 0.913429i \(0.633425\pi\)
\(108\) 47.1063 4.53281
\(109\) −4.73249 −0.453291 −0.226645 0.973977i \(-0.572776\pi\)
−0.226645 + 0.973977i \(0.572776\pi\)
\(110\) −23.7349 −2.26303
\(111\) 3.22970 0.306549
\(112\) −36.5276 −3.45153
\(113\) −5.21987 −0.491044 −0.245522 0.969391i \(-0.578959\pi\)
−0.245522 + 0.969391i \(0.578959\pi\)
\(114\) 34.3853 3.22048
\(115\) −10.0241 −0.934755
\(116\) −4.90963 −0.455847
\(117\) −12.5234 −1.15778
\(118\) −5.51180 −0.507402
\(119\) 25.3526 2.32407
\(120\) −51.9596 −4.74324
\(121\) 5.19664 0.472421
\(122\) −14.1725 −1.28312
\(123\) 0.973884 0.0878121
\(124\) −0.610342 −0.0548103
\(125\) −11.1422 −0.996592
\(126\) 57.5875 5.13030
\(127\) −15.1814 −1.34713 −0.673565 0.739128i \(-0.735238\pi\)
−0.673565 + 0.739128i \(0.735238\pi\)
\(128\) −3.56358 −0.314979
\(129\) 12.7522 1.12276
\(130\) 11.9730 1.05010
\(131\) 18.5401 1.61986 0.809928 0.586529i \(-0.199506\pi\)
0.809928 + 0.586529i \(0.199506\pi\)
\(132\) 59.8293 5.20748
\(133\) 15.3427 1.33038
\(134\) −29.3415 −2.53472
\(135\) 21.5268 1.85273
\(136\) 54.5982 4.68175
\(137\) 4.91278 0.419727 0.209864 0.977731i \(-0.432698\pi\)
0.209864 + 0.977731i \(0.432698\pi\)
\(138\) 35.5614 3.02719
\(139\) −9.83617 −0.834293 −0.417146 0.908839i \(-0.636970\pi\)
−0.417146 + 0.908839i \(0.636970\pi\)
\(140\) −39.1206 −3.30629
\(141\) −18.9050 −1.59209
\(142\) 3.92563 0.329432
\(143\) −8.17036 −0.683240
\(144\) 63.4459 5.28716
\(145\) −2.24361 −0.186322
\(146\) 35.8608 2.96786
\(147\) 16.9960 1.40181
\(148\) 5.23669 0.430453
\(149\) 7.43738 0.609294 0.304647 0.952465i \(-0.401462\pi\)
0.304647 + 0.952465i \(0.401462\pi\)
\(150\) −0.269009 −0.0219645
\(151\) −11.2375 −0.914496 −0.457248 0.889339i \(-0.651165\pi\)
−0.457248 + 0.889339i \(0.651165\pi\)
\(152\) 33.0413 2.68000
\(153\) −44.0357 −3.56008
\(154\) 37.5707 3.02753
\(155\) −0.278915 −0.0224030
\(156\) −30.1808 −2.41640
\(157\) −17.0684 −1.36220 −0.681102 0.732188i \(-0.738499\pi\)
−0.681102 + 0.732188i \(0.738499\pi\)
\(158\) −17.6175 −1.40157
\(159\) 3.68219 0.292017
\(160\) −26.3383 −2.08222
\(161\) 15.8675 1.25053
\(162\) −27.7227 −2.17810
\(163\) 7.59726 0.595063 0.297532 0.954712i \(-0.403837\pi\)
0.297532 + 0.954712i \(0.403837\pi\)
\(164\) 1.57907 0.123305
\(165\) 27.3409 2.12849
\(166\) −10.7848 −0.837065
\(167\) −20.7071 −1.60236 −0.801182 0.598420i \(-0.795795\pi\)
−0.801182 + 0.598420i \(0.795795\pi\)
\(168\) 82.2483 6.34559
\(169\) −8.87848 −0.682960
\(170\) 42.1006 3.22897
\(171\) −26.6492 −2.03792
\(172\) 20.6766 1.57657
\(173\) 18.0870 1.37513 0.687564 0.726124i \(-0.258680\pi\)
0.687564 + 0.726124i \(0.258680\pi\)
\(174\) 7.95940 0.603401
\(175\) −0.120031 −0.00907352
\(176\) 41.3928 3.12010
\(177\) 6.34920 0.477235
\(178\) 31.6093 2.36921
\(179\) −3.80591 −0.284467 −0.142233 0.989833i \(-0.545428\pi\)
−0.142233 + 0.989833i \(0.545428\pi\)
\(180\) 67.9498 5.06468
\(181\) −8.75462 −0.650725 −0.325363 0.945589i \(-0.605486\pi\)
−0.325363 + 0.945589i \(0.605486\pi\)
\(182\) −18.9524 −1.40485
\(183\) 16.3258 1.20684
\(184\) 34.1715 2.51915
\(185\) 2.39308 0.175942
\(186\) 0.989475 0.0725518
\(187\) −28.7294 −2.10090
\(188\) −30.6530 −2.23560
\(189\) −34.0753 −2.47861
\(190\) 25.4781 1.84838
\(191\) −2.89359 −0.209373 −0.104687 0.994505i \(-0.533384\pi\)
−0.104687 + 0.994505i \(0.533384\pi\)
\(192\) 31.1505 2.24809
\(193\) 11.0955 0.798670 0.399335 0.916805i \(-0.369241\pi\)
0.399335 + 0.916805i \(0.369241\pi\)
\(194\) −32.7052 −2.34810
\(195\) −13.7921 −0.987672
\(196\) 27.5577 1.96841
\(197\) −1.72833 −0.123139 −0.0615693 0.998103i \(-0.519611\pi\)
−0.0615693 + 0.998103i \(0.519611\pi\)
\(198\) −65.2577 −4.63766
\(199\) −23.6554 −1.67689 −0.838444 0.544988i \(-0.816534\pi\)
−0.838444 + 0.544988i \(0.816534\pi\)
\(200\) −0.258494 −0.0182783
\(201\) 33.7993 2.38402
\(202\) 20.7986 1.46338
\(203\) 3.55148 0.249265
\(204\) −106.124 −7.43019
\(205\) 0.721609 0.0503993
\(206\) 2.32185 0.161771
\(207\) −27.5607 −1.91560
\(208\) −20.8805 −1.44780
\(209\) −17.3862 −1.20263
\(210\) 63.4216 4.37651
\(211\) 1.76161 0.121274 0.0606372 0.998160i \(-0.480687\pi\)
0.0606372 + 0.998160i \(0.480687\pi\)
\(212\) 5.97038 0.410047
\(213\) −4.52205 −0.309846
\(214\) 22.1331 1.51299
\(215\) 9.44883 0.644405
\(216\) −73.3830 −4.99308
\(217\) 0.441503 0.0299712
\(218\) 12.4399 0.842537
\(219\) −41.3092 −2.79141
\(220\) 44.3311 2.98880
\(221\) 14.4925 0.974869
\(222\) −8.48964 −0.569787
\(223\) −24.0428 −1.61002 −0.805012 0.593258i \(-0.797841\pi\)
−0.805012 + 0.593258i \(0.797841\pi\)
\(224\) 41.6916 2.78564
\(225\) 0.208486 0.0138991
\(226\) 13.7210 0.912710
\(227\) 16.4501 1.09183 0.545916 0.837840i \(-0.316182\pi\)
0.545916 + 0.837840i \(0.316182\pi\)
\(228\) −64.2236 −4.25331
\(229\) −12.5342 −0.828283 −0.414142 0.910212i \(-0.635918\pi\)
−0.414142 + 0.910212i \(0.635918\pi\)
\(230\) 26.3496 1.73744
\(231\) −43.2787 −2.84753
\(232\) 7.64830 0.502135
\(233\) −27.1534 −1.77888 −0.889441 0.457051i \(-0.848906\pi\)
−0.889441 + 0.457051i \(0.848906\pi\)
\(234\) 32.9191 2.15199
\(235\) −14.0079 −0.913772
\(236\) 10.2947 0.670129
\(237\) 20.2941 1.31824
\(238\) −66.6423 −4.31978
\(239\) −7.94928 −0.514196 −0.257098 0.966385i \(-0.582766\pi\)
−0.257098 + 0.966385i \(0.582766\pi\)
\(240\) 69.8736 4.51032
\(241\) 24.5705 1.58273 0.791364 0.611346i \(-0.209371\pi\)
0.791364 + 0.611346i \(0.209371\pi\)
\(242\) −13.6600 −0.878096
\(243\) 3.15059 0.202110
\(244\) 26.4709 1.69463
\(245\) 12.5934 0.804561
\(246\) −2.55997 −0.163218
\(247\) 8.77044 0.558050
\(248\) 0.950800 0.0603758
\(249\) 12.4234 0.787298
\(250\) 29.2887 1.85238
\(251\) 1.28499 0.0811075 0.0405538 0.999177i \(-0.487088\pi\)
0.0405538 + 0.999177i \(0.487088\pi\)
\(252\) −107.560 −6.77562
\(253\) −17.9809 −1.13045
\(254\) 39.9060 2.50393
\(255\) −48.4970 −3.03700
\(256\) −11.2078 −0.700489
\(257\) −22.6435 −1.41246 −0.706231 0.707982i \(-0.749606\pi\)
−0.706231 + 0.707982i \(0.749606\pi\)
\(258\) −33.5205 −2.08690
\(259\) −3.78807 −0.235379
\(260\) −22.3628 −1.38688
\(261\) −6.16867 −0.381831
\(262\) −48.7348 −3.01085
\(263\) 19.1202 1.17900 0.589501 0.807767i \(-0.299324\pi\)
0.589501 + 0.807767i \(0.299324\pi\)
\(264\) −93.2031 −5.73625
\(265\) 2.72836 0.167602
\(266\) −40.3301 −2.47279
\(267\) −36.4116 −2.22836
\(268\) 54.8028 3.34762
\(269\) −14.6549 −0.893527 −0.446763 0.894652i \(-0.647423\pi\)
−0.446763 + 0.894652i \(0.647423\pi\)
\(270\) −56.5856 −3.44369
\(271\) −25.1373 −1.52698 −0.763490 0.645820i \(-0.776516\pi\)
−0.763490 + 0.645820i \(0.776516\pi\)
\(272\) −73.4219 −4.45186
\(273\) 21.8319 1.32133
\(274\) −12.9138 −0.780153
\(275\) 0.136019 0.00820223
\(276\) −66.4203 −3.99803
\(277\) −1.00000 −0.0600842
\(278\) 25.8555 1.55071
\(279\) −0.766860 −0.0459107
\(280\) 60.9427 3.64202
\(281\) −13.9716 −0.833474 −0.416737 0.909027i \(-0.636826\pi\)
−0.416737 + 0.909027i \(0.636826\pi\)
\(282\) 49.6941 2.95924
\(283\) −5.60095 −0.332942 −0.166471 0.986046i \(-0.553237\pi\)
−0.166471 + 0.986046i \(0.553237\pi\)
\(284\) −7.33214 −0.435083
\(285\) −29.3490 −1.73849
\(286\) 21.4767 1.26995
\(287\) −1.14225 −0.0674252
\(288\) −72.4154 −4.26712
\(289\) 33.9597 1.99763
\(290\) 5.89760 0.346319
\(291\) 37.6741 2.20850
\(292\) −66.9795 −3.91968
\(293\) −26.9202 −1.57269 −0.786346 0.617786i \(-0.788030\pi\)
−0.786346 + 0.617786i \(0.788030\pi\)
\(294\) −44.6761 −2.60556
\(295\) 4.70450 0.273907
\(296\) −8.15780 −0.474163
\(297\) 38.6139 2.24060
\(298\) −19.5500 −1.13250
\(299\) 9.07043 0.524556
\(300\) 0.502444 0.0290086
\(301\) −14.9568 −0.862097
\(302\) 29.5391 1.69979
\(303\) −23.9585 −1.37638
\(304\) −44.4329 −2.54840
\(305\) 12.0967 0.692658
\(306\) 115.753 6.61716
\(307\) −9.42974 −0.538184 −0.269092 0.963115i \(-0.586724\pi\)
−0.269092 + 0.963115i \(0.586724\pi\)
\(308\) −70.1730 −3.99848
\(309\) −2.67461 −0.152153
\(310\) 0.733161 0.0416408
\(311\) 4.35408 0.246897 0.123449 0.992351i \(-0.460605\pi\)
0.123449 + 0.992351i \(0.460605\pi\)
\(312\) 47.0161 2.66176
\(313\) 17.4888 0.988528 0.494264 0.869312i \(-0.335438\pi\)
0.494264 + 0.869312i \(0.335438\pi\)
\(314\) 44.8662 2.53195
\(315\) −49.1528 −2.76945
\(316\) 32.9053 1.85107
\(317\) −0.666177 −0.0374162 −0.0187081 0.999825i \(-0.505955\pi\)
−0.0187081 + 0.999825i \(0.505955\pi\)
\(318\) −9.67908 −0.542776
\(319\) −4.02450 −0.225329
\(320\) 23.0813 1.29028
\(321\) −25.4958 −1.42304
\(322\) −41.7095 −2.32438
\(323\) 30.8394 1.71595
\(324\) 51.7794 2.87664
\(325\) −0.0686143 −0.00380604
\(326\) −19.9703 −1.10605
\(327\) −14.3299 −0.792445
\(328\) −2.45991 −0.135826
\(329\) 22.1734 1.22246
\(330\) −71.8689 −3.95625
\(331\) −33.4301 −1.83749 −0.918743 0.394855i \(-0.870795\pi\)
−0.918743 + 0.394855i \(0.870795\pi\)
\(332\) 20.1435 1.10552
\(333\) 6.57961 0.360560
\(334\) 54.4311 2.97834
\(335\) 25.0439 1.36830
\(336\) −110.605 −6.03399
\(337\) −26.2482 −1.42983 −0.714916 0.699210i \(-0.753535\pi\)
−0.714916 + 0.699210i \(0.753535\pi\)
\(338\) 23.3381 1.26943
\(339\) −15.8057 −0.858447
\(340\) −78.6339 −4.26452
\(341\) −0.500307 −0.0270932
\(342\) 70.0506 3.78790
\(343\) 4.92593 0.265975
\(344\) −32.2103 −1.73666
\(345\) −30.3529 −1.63414
\(346\) −47.5438 −2.55597
\(347\) 2.19961 0.118081 0.0590407 0.998256i \(-0.481196\pi\)
0.0590407 + 0.998256i \(0.481196\pi\)
\(348\) −14.8663 −0.796915
\(349\) 6.65676 0.356328 0.178164 0.984001i \(-0.442984\pi\)
0.178164 + 0.984001i \(0.442984\pi\)
\(350\) 0.315516 0.0168651
\(351\) −19.4787 −1.03970
\(352\) −47.2445 −2.51814
\(353\) −23.3662 −1.24366 −0.621828 0.783154i \(-0.713610\pi\)
−0.621828 + 0.783154i \(0.713610\pi\)
\(354\) −16.6896 −0.887043
\(355\) −3.35066 −0.177835
\(356\) −59.0385 −3.12904
\(357\) 76.7672 4.06295
\(358\) 10.0043 0.528742
\(359\) 26.2202 1.38385 0.691924 0.721970i \(-0.256763\pi\)
0.691924 + 0.721970i \(0.256763\pi\)
\(360\) −105.853 −5.57896
\(361\) −0.336842 −0.0177285
\(362\) 23.0125 1.20951
\(363\) 15.7353 0.825890
\(364\) 35.3986 1.85539
\(365\) −30.6084 −1.60212
\(366\) −42.9142 −2.24316
\(367\) −23.2231 −1.21223 −0.606117 0.795376i \(-0.707274\pi\)
−0.606117 + 0.795376i \(0.707274\pi\)
\(368\) −45.9527 −2.39545
\(369\) 1.98402 0.103284
\(370\) −6.29048 −0.327026
\(371\) −4.31879 −0.224221
\(372\) −1.84810 −0.0958197
\(373\) 5.29004 0.273908 0.136954 0.990577i \(-0.456269\pi\)
0.136954 + 0.990577i \(0.456269\pi\)
\(374\) 75.5185 3.90497
\(375\) −33.7385 −1.74225
\(376\) 47.7517 2.46260
\(377\) 2.03015 0.104558
\(378\) 89.5709 4.60703
\(379\) 4.89341 0.251358 0.125679 0.992071i \(-0.459889\pi\)
0.125679 + 0.992071i \(0.459889\pi\)
\(380\) −47.5871 −2.44117
\(381\) −45.9689 −2.35506
\(382\) 7.60615 0.389164
\(383\) −1.22634 −0.0626630 −0.0313315 0.999509i \(-0.509975\pi\)
−0.0313315 + 0.999509i \(0.509975\pi\)
\(384\) −10.7904 −0.550647
\(385\) −32.0678 −1.63433
\(386\) −29.1658 −1.48450
\(387\) 25.9790 1.32059
\(388\) 61.0855 3.10115
\(389\) 9.73216 0.493440 0.246720 0.969087i \(-0.420647\pi\)
0.246720 + 0.969087i \(0.420647\pi\)
\(390\) 36.2541 1.83580
\(391\) 31.8942 1.61296
\(392\) −42.9298 −2.16828
\(393\) 56.1391 2.83184
\(394\) 4.54313 0.228879
\(395\) 15.0371 0.756599
\(396\) 121.886 6.12499
\(397\) 8.41018 0.422095 0.211047 0.977476i \(-0.432313\pi\)
0.211047 + 0.977476i \(0.432313\pi\)
\(398\) 62.1810 3.11685
\(399\) 46.4574 2.32578
\(400\) 0.347614 0.0173807
\(401\) 27.1012 1.35337 0.676685 0.736273i \(-0.263416\pi\)
0.676685 + 0.736273i \(0.263416\pi\)
\(402\) −88.8454 −4.43121
\(403\) 0.252379 0.0125719
\(404\) −38.8468 −1.93270
\(405\) 23.6623 1.17579
\(406\) −9.33547 −0.463312
\(407\) 4.29260 0.212777
\(408\) 165.322 8.18467
\(409\) −31.1136 −1.53847 −0.769234 0.638967i \(-0.779362\pi\)
−0.769234 + 0.638967i \(0.779362\pi\)
\(410\) −1.89683 −0.0936779
\(411\) 14.8758 0.733770
\(412\) −4.33667 −0.213652
\(413\) −7.44689 −0.366437
\(414\) 72.4466 3.56056
\(415\) 9.20521 0.451866
\(416\) 23.8324 1.16848
\(417\) −29.7837 −1.45852
\(418\) 45.7017 2.23534
\(419\) 12.4010 0.605826 0.302913 0.953018i \(-0.402041\pi\)
0.302913 + 0.953018i \(0.402041\pi\)
\(420\) −118.456 −5.78008
\(421\) 9.86836 0.480954 0.240477 0.970655i \(-0.422696\pi\)
0.240477 + 0.970655i \(0.422696\pi\)
\(422\) −4.63060 −0.225414
\(423\) −38.5137 −1.87260
\(424\) −9.30075 −0.451685
\(425\) −0.241268 −0.0117032
\(426\) 11.8867 0.575915
\(427\) −19.1483 −0.926650
\(428\) −41.3393 −1.99821
\(429\) −24.7397 −1.19444
\(430\) −24.8374 −1.19776
\(431\) 31.8135 1.53240 0.766200 0.642602i \(-0.222145\pi\)
0.766200 + 0.642602i \(0.222145\pi\)
\(432\) 98.6831 4.74789
\(433\) −24.7488 −1.18935 −0.594677 0.803965i \(-0.702720\pi\)
−0.594677 + 0.803965i \(0.702720\pi\)
\(434\) −1.16054 −0.0557078
\(435\) −6.79362 −0.325729
\(436\) −23.2348 −1.11274
\(437\) 19.3015 0.923317
\(438\) 108.586 5.18844
\(439\) 5.10896 0.243837 0.121919 0.992540i \(-0.461095\pi\)
0.121919 + 0.992540i \(0.461095\pi\)
\(440\) −69.0597 −3.29229
\(441\) 34.6247 1.64880
\(442\) −38.0951 −1.81200
\(443\) 35.0742 1.66642 0.833212 0.552954i \(-0.186499\pi\)
0.833212 + 0.552954i \(0.186499\pi\)
\(444\) 15.8566 0.752521
\(445\) −26.9796 −1.27895
\(446\) 63.1993 2.99257
\(447\) 22.5202 1.06517
\(448\) −36.5360 −1.72616
\(449\) 10.5709 0.498870 0.249435 0.968392i \(-0.419755\pi\)
0.249435 + 0.968392i \(0.419755\pi\)
\(450\) −0.548031 −0.0258344
\(451\) 1.29439 0.0609506
\(452\) −25.6276 −1.20542
\(453\) −34.0270 −1.59873
\(454\) −43.2411 −2.02940
\(455\) 16.1765 0.758368
\(456\) 100.048 4.68520
\(457\) 29.0183 1.35742 0.678709 0.734407i \(-0.262540\pi\)
0.678709 + 0.734407i \(0.262540\pi\)
\(458\) 32.9476 1.53954
\(459\) −68.4927 −3.19696
\(460\) −49.2147 −2.29465
\(461\) 26.0885 1.21506 0.607532 0.794295i \(-0.292160\pi\)
0.607532 + 0.794295i \(0.292160\pi\)
\(462\) 113.763 5.29275
\(463\) 9.98755 0.464161 0.232080 0.972697i \(-0.425447\pi\)
0.232080 + 0.972697i \(0.425447\pi\)
\(464\) −10.2852 −0.477478
\(465\) −0.844550 −0.0391651
\(466\) 71.3760 3.30643
\(467\) −41.8477 −1.93648 −0.968240 0.250024i \(-0.919562\pi\)
−0.968240 + 0.250024i \(0.919562\pi\)
\(468\) −61.4850 −2.84214
\(469\) −39.6427 −1.83053
\(470\) 36.8213 1.69844
\(471\) −51.6827 −2.38141
\(472\) −16.0373 −0.738175
\(473\) 16.9489 0.779313
\(474\) −53.3454 −2.45024
\(475\) −0.146009 −0.00669933
\(476\) 124.472 5.70516
\(477\) 7.50145 0.343468
\(478\) 20.8956 0.955743
\(479\) 19.6771 0.899071 0.449536 0.893262i \(-0.351589\pi\)
0.449536 + 0.893262i \(0.351589\pi\)
\(480\) −79.7518 −3.64015
\(481\) −2.16540 −0.0987336
\(482\) −64.5865 −2.94184
\(483\) 48.0464 2.18619
\(484\) 25.5135 1.15971
\(485\) 27.9150 1.26756
\(486\) −8.28169 −0.375665
\(487\) −41.0333 −1.85940 −0.929699 0.368320i \(-0.879933\pi\)
−0.929699 + 0.368320i \(0.879933\pi\)
\(488\) −41.2368 −1.86670
\(489\) 23.0044 1.04029
\(490\) −33.1032 −1.49545
\(491\) 29.0552 1.31124 0.655621 0.755090i \(-0.272407\pi\)
0.655621 + 0.755090i \(0.272407\pi\)
\(492\) 4.78141 0.215562
\(493\) 7.13861 0.321507
\(494\) −23.0541 −1.03725
\(495\) 55.6996 2.50351
\(496\) −1.27861 −0.0574111
\(497\) 5.30385 0.237910
\(498\) −32.6562 −1.46336
\(499\) 42.2250 1.89025 0.945125 0.326708i \(-0.105939\pi\)
0.945125 + 0.326708i \(0.105939\pi\)
\(500\) −54.7042 −2.44645
\(501\) −62.7008 −2.80126
\(502\) −3.37773 −0.150756
\(503\) 36.1451 1.61163 0.805815 0.592168i \(-0.201728\pi\)
0.805815 + 0.592168i \(0.201728\pi\)
\(504\) 167.558 7.46363
\(505\) −17.7523 −0.789967
\(506\) 47.2649 2.10118
\(507\) −26.8839 −1.19395
\(508\) −74.5349 −3.30695
\(509\) 19.2978 0.855362 0.427681 0.903930i \(-0.359331\pi\)
0.427681 + 0.903930i \(0.359331\pi\)
\(510\) 127.480 5.64491
\(511\) 48.4509 2.14334
\(512\) 36.5882 1.61699
\(513\) −41.4499 −1.83006
\(514\) 59.5210 2.62536
\(515\) −1.98178 −0.0873276
\(516\) 62.6083 2.75618
\(517\) −25.1267 −1.10507
\(518\) 9.95737 0.437502
\(519\) 54.7671 2.40401
\(520\) 34.8370 1.52771
\(521\) 11.0548 0.484318 0.242159 0.970237i \(-0.422144\pi\)
0.242159 + 0.970237i \(0.422144\pi\)
\(522\) 16.2151 0.709715
\(523\) 29.3926 1.28525 0.642623 0.766182i \(-0.277846\pi\)
0.642623 + 0.766182i \(0.277846\pi\)
\(524\) 91.0250 3.97645
\(525\) −0.363453 −0.0158624
\(526\) −50.2597 −2.19143
\(527\) 0.887437 0.0386574
\(528\) 125.337 5.45457
\(529\) −3.03829 −0.132100
\(530\) −7.17181 −0.311523
\(531\) 12.9347 0.561320
\(532\) 75.3269 3.26584
\(533\) −0.652954 −0.0282826
\(534\) 95.7122 4.14187
\(535\) −18.8913 −0.816744
\(536\) −85.3727 −3.68754
\(537\) −11.5242 −0.497307
\(538\) 38.5222 1.66081
\(539\) 22.5895 0.972999
\(540\) 105.688 4.54810
\(541\) 39.5024 1.69834 0.849171 0.528118i \(-0.177102\pi\)
0.849171 + 0.528118i \(0.177102\pi\)
\(542\) 66.0762 2.83822
\(543\) −26.5088 −1.13760
\(544\) 83.8017 3.59297
\(545\) −10.6179 −0.454820
\(546\) −57.3876 −2.45596
\(547\) −33.4027 −1.42820 −0.714098 0.700046i \(-0.753163\pi\)
−0.714098 + 0.700046i \(0.753163\pi\)
\(548\) 24.1199 1.03035
\(549\) 33.2593 1.41947
\(550\) −0.357541 −0.0152456
\(551\) 4.32009 0.184042
\(552\) 103.471 4.40400
\(553\) −23.8027 −1.01219
\(554\) 2.62862 0.111679
\(555\) 7.24619 0.307584
\(556\) −48.2919 −2.04803
\(557\) −7.42457 −0.314589 −0.157294 0.987552i \(-0.550277\pi\)
−0.157294 + 0.987552i \(0.550277\pi\)
\(558\) 2.01578 0.0853348
\(559\) −8.54986 −0.361621
\(560\) −81.9538 −3.46318
\(561\) −86.9919 −3.67280
\(562\) 36.7259 1.54919
\(563\) −12.5824 −0.530284 −0.265142 0.964209i \(-0.585419\pi\)
−0.265142 + 0.964209i \(0.585419\pi\)
\(564\) −92.8166 −3.90828
\(565\) −11.7114 −0.492701
\(566\) 14.7228 0.618844
\(567\) −37.4557 −1.57299
\(568\) 11.4221 0.479262
\(569\) 19.6994 0.825843 0.412921 0.910767i \(-0.364508\pi\)
0.412921 + 0.910767i \(0.364508\pi\)
\(570\) 77.1473 3.23135
\(571\) −10.4133 −0.435784 −0.217892 0.975973i \(-0.569918\pi\)
−0.217892 + 0.975973i \(0.569918\pi\)
\(572\) −40.1134 −1.67723
\(573\) −8.76175 −0.366027
\(574\) 3.00255 0.125324
\(575\) −0.151003 −0.00629725
\(576\) 63.4605 2.64419
\(577\) −31.9524 −1.33020 −0.665098 0.746756i \(-0.731610\pi\)
−0.665098 + 0.746756i \(0.731610\pi\)
\(578\) −89.2670 −3.71302
\(579\) 33.5969 1.39624
\(580\) −11.0153 −0.457386
\(581\) −14.5712 −0.604514
\(582\) −99.0308 −4.10496
\(583\) 4.89402 0.202690
\(584\) 104.342 4.31769
\(585\) −28.0976 −1.16169
\(586\) 70.7628 2.92318
\(587\) −31.7717 −1.31136 −0.655680 0.755039i \(-0.727618\pi\)
−0.655680 + 0.755039i \(0.727618\pi\)
\(588\) 83.4442 3.44118
\(589\) 0.537053 0.0221289
\(590\) −12.3663 −0.509114
\(591\) −5.23336 −0.215272
\(592\) 10.9704 0.450879
\(593\) −15.4064 −0.632665 −0.316333 0.948648i \(-0.602452\pi\)
−0.316333 + 0.948648i \(0.602452\pi\)
\(594\) −101.501 −4.16464
\(595\) 56.8814 2.33191
\(596\) 36.5148 1.49570
\(597\) −71.6282 −2.93155
\(598\) −23.8427 −0.974999
\(599\) −21.0518 −0.860155 −0.430078 0.902792i \(-0.641514\pi\)
−0.430078 + 0.902792i \(0.641514\pi\)
\(600\) −0.782715 −0.0319542
\(601\) −27.4790 −1.12089 −0.560446 0.828191i \(-0.689370\pi\)
−0.560446 + 0.828191i \(0.689370\pi\)
\(602\) 39.3158 1.60239
\(603\) 68.8567 2.80406
\(604\) −55.1720 −2.24492
\(605\) 11.6592 0.474015
\(606\) 62.9778 2.55830
\(607\) −47.2220 −1.91668 −0.958341 0.285625i \(-0.907799\pi\)
−0.958341 + 0.285625i \(0.907799\pi\)
\(608\) 50.7145 2.05674
\(609\) 10.7538 0.435766
\(610\) −31.7977 −1.28745
\(611\) 12.6751 0.512781
\(612\) −216.199 −8.73933
\(613\) 18.0691 0.729803 0.364902 0.931046i \(-0.381103\pi\)
0.364902 + 0.931046i \(0.381103\pi\)
\(614\) 24.7872 1.00033
\(615\) 2.18502 0.0881084
\(616\) 109.317 4.40449
\(617\) 7.74046 0.311619 0.155810 0.987787i \(-0.450201\pi\)
0.155810 + 0.987787i \(0.450201\pi\)
\(618\) 7.03053 0.282809
\(619\) −9.02740 −0.362842 −0.181421 0.983406i \(-0.558070\pi\)
−0.181421 + 0.983406i \(0.558070\pi\)
\(620\) −1.36937 −0.0549952
\(621\) −42.8676 −1.72022
\(622\) −11.4452 −0.458912
\(623\) 42.7067 1.71101
\(624\) −63.2258 −2.53106
\(625\) −25.1678 −1.00671
\(626\) −45.9715 −1.83739
\(627\) −52.6451 −2.10244
\(628\) −83.7994 −3.34396
\(629\) −7.61416 −0.303596
\(630\) 129.204 5.14761
\(631\) 41.0017 1.63225 0.816126 0.577874i \(-0.196117\pi\)
0.816126 + 0.577874i \(0.196117\pi\)
\(632\) −51.2603 −2.03903
\(633\) 5.33413 0.212013
\(634\) 1.75112 0.0695460
\(635\) −34.0611 −1.35168
\(636\) 18.0782 0.716847
\(637\) −11.3952 −0.451495
\(638\) 10.5789 0.418822
\(639\) −9.21243 −0.364438
\(640\) −7.99528 −0.316041
\(641\) 46.1016 1.82090 0.910451 0.413616i \(-0.135734\pi\)
0.910451 + 0.413616i \(0.135734\pi\)
\(642\) 67.0186 2.64501
\(643\) 4.40584 0.173749 0.0868747 0.996219i \(-0.472312\pi\)
0.0868747 + 0.996219i \(0.472312\pi\)
\(644\) 77.9034 3.06982
\(645\) 28.6109 1.12655
\(646\) −81.0650 −3.18946
\(647\) −14.6659 −0.576576 −0.288288 0.957544i \(-0.593086\pi\)
−0.288288 + 0.957544i \(0.593086\pi\)
\(648\) −80.6628 −3.16874
\(649\) 8.43875 0.331250
\(650\) 0.180361 0.00707433
\(651\) 1.33686 0.0523958
\(652\) 37.2997 1.46077
\(653\) 13.8140 0.540583 0.270292 0.962779i \(-0.412880\pi\)
0.270292 + 0.962779i \(0.412880\pi\)
\(654\) 37.6678 1.47293
\(655\) 41.5968 1.62532
\(656\) 3.30800 0.129156
\(657\) −84.1560 −3.28324
\(658\) −58.2855 −2.27220
\(659\) 25.8540 1.00713 0.503565 0.863957i \(-0.332021\pi\)
0.503565 + 0.863957i \(0.332021\pi\)
\(660\) 134.234 5.22505
\(661\) 12.5580 0.488450 0.244225 0.969719i \(-0.421467\pi\)
0.244225 + 0.969719i \(0.421467\pi\)
\(662\) 87.8750 3.41536
\(663\) 43.8829 1.70427
\(664\) −31.3798 −1.21777
\(665\) 34.4231 1.33487
\(666\) −17.2953 −0.670178
\(667\) 4.46785 0.172996
\(668\) −101.664 −3.93351
\(669\) −72.8011 −2.81465
\(670\) −65.8309 −2.54327
\(671\) 21.6987 0.837668
\(672\) 126.241 4.86987
\(673\) −9.30043 −0.358505 −0.179253 0.983803i \(-0.557368\pi\)
−0.179253 + 0.983803i \(0.557368\pi\)
\(674\) 68.9966 2.65765
\(675\) 0.324277 0.0124814
\(676\) −43.5900 −1.67654
\(677\) 16.2598 0.624914 0.312457 0.949932i \(-0.398848\pi\)
0.312457 + 0.949932i \(0.398848\pi\)
\(678\) 41.5471 1.59561
\(679\) −44.1875 −1.69576
\(680\) 122.497 4.69755
\(681\) 49.8107 1.90875
\(682\) 1.31512 0.0503584
\(683\) −15.2953 −0.585260 −0.292630 0.956226i \(-0.594530\pi\)
−0.292630 + 0.956226i \(0.594530\pi\)
\(684\) −130.838 −5.00270
\(685\) 11.0224 0.421144
\(686\) −12.9484 −0.494372
\(687\) −37.9533 −1.44801
\(688\) 43.3154 1.65138
\(689\) −2.46878 −0.0940530
\(690\) 79.7861 3.03741
\(691\) 28.1357 1.07033 0.535167 0.844746i \(-0.320249\pi\)
0.535167 + 0.844746i \(0.320249\pi\)
\(692\) 88.8004 3.37568
\(693\) −88.1685 −3.34924
\(694\) −5.78194 −0.219480
\(695\) −22.0686 −0.837108
\(696\) 23.1589 0.877836
\(697\) −2.29598 −0.0869663
\(698\) −17.4981 −0.662312
\(699\) −82.2201 −3.10985
\(700\) −0.589309 −0.0222738
\(701\) −18.8307 −0.711226 −0.355613 0.934633i \(-0.615728\pi\)
−0.355613 + 0.934633i \(0.615728\pi\)
\(702\) 51.2020 1.93249
\(703\) −4.60788 −0.173789
\(704\) 41.4023 1.56041
\(705\) −42.4155 −1.59746
\(706\) 61.4207 2.31160
\(707\) 28.1006 1.05683
\(708\) 31.1722 1.17152
\(709\) 35.6439 1.33864 0.669318 0.742976i \(-0.266586\pi\)
0.669318 + 0.742976i \(0.266586\pi\)
\(710\) 8.80760 0.330543
\(711\) 41.3436 1.55051
\(712\) 91.9712 3.44676
\(713\) 0.555422 0.0208007
\(714\) −201.792 −7.55186
\(715\) −18.3311 −0.685545
\(716\) −18.6856 −0.698313
\(717\) −24.0703 −0.898921
\(718\) −68.9228 −2.57218
\(719\) −2.69021 −0.100328 −0.0501639 0.998741i \(-0.515974\pi\)
−0.0501639 + 0.998741i \(0.515974\pi\)
\(720\) 142.348 5.30500
\(721\) 3.13701 0.116829
\(722\) 0.885429 0.0329523
\(723\) 74.3991 2.76693
\(724\) −42.9819 −1.59741
\(725\) −0.0337976 −0.00125521
\(726\) −41.3621 −1.53509
\(727\) −5.04604 −0.187147 −0.0935737 0.995612i \(-0.529829\pi\)
−0.0935737 + 0.995612i \(0.529829\pi\)
\(728\) −55.1445 −2.04379
\(729\) −22.0996 −0.818504
\(730\) 80.4578 2.97788
\(731\) −30.0638 −1.11195
\(732\) 80.1535 2.96256
\(733\) −15.3664 −0.567570 −0.283785 0.958888i \(-0.591590\pi\)
−0.283785 + 0.958888i \(0.591590\pi\)
\(734\) 61.0445 2.25319
\(735\) 38.1325 1.40654
\(736\) 52.4491 1.93330
\(737\) 44.9228 1.65475
\(738\) −5.21522 −0.191975
\(739\) 9.10492 0.334930 0.167465 0.985878i \(-0.446442\pi\)
0.167465 + 0.985878i \(0.446442\pi\)
\(740\) 11.7491 0.431906
\(741\) 26.5567 0.975586
\(742\) 11.3525 0.416762
\(743\) 22.2951 0.817929 0.408964 0.912550i \(-0.365890\pi\)
0.408964 + 0.912550i \(0.365890\pi\)
\(744\) 2.87900 0.105549
\(745\) 16.6866 0.611350
\(746\) −13.9055 −0.509116
\(747\) 25.3091 0.926013
\(748\) −141.050 −5.15731
\(749\) 29.9036 1.09266
\(750\) 88.6855 3.23834
\(751\) −10.5708 −0.385733 −0.192866 0.981225i \(-0.561778\pi\)
−0.192866 + 0.981225i \(0.561778\pi\)
\(752\) −64.2149 −2.34168
\(753\) 3.89091 0.141793
\(754\) −5.33650 −0.194344
\(755\) −25.2126 −0.917581
\(756\) −167.297 −6.08453
\(757\) 9.60956 0.349265 0.174633 0.984634i \(-0.444126\pi\)
0.174633 + 0.984634i \(0.444126\pi\)
\(758\) −12.8629 −0.467202
\(759\) −54.4458 −1.97626
\(760\) 74.1319 2.68905
\(761\) −15.0353 −0.545029 −0.272514 0.962152i \(-0.587855\pi\)
−0.272514 + 0.962152i \(0.587855\pi\)
\(762\) 120.835 4.37738
\(763\) 16.8073 0.608467
\(764\) −14.2065 −0.513972
\(765\) −98.7991 −3.57209
\(766\) 3.22357 0.116472
\(767\) −4.25691 −0.153708
\(768\) −33.9371 −1.22460
\(769\) 39.4562 1.42283 0.711414 0.702773i \(-0.248055\pi\)
0.711414 + 0.702773i \(0.248055\pi\)
\(770\) 84.2940 3.03774
\(771\) −68.5640 −2.46927
\(772\) 54.4747 1.96059
\(773\) 50.1342 1.80320 0.901601 0.432569i \(-0.142393\pi\)
0.901601 + 0.432569i \(0.142393\pi\)
\(774\) −68.2888 −2.45459
\(775\) −0.00420156 −0.000150924 0
\(776\) −95.1600 −3.41605
\(777\) −11.4702 −0.411491
\(778\) −25.5821 −0.917164
\(779\) −1.38946 −0.0497826
\(780\) −67.7140 −2.42455
\(781\) −6.01028 −0.215065
\(782\) −83.8377 −2.99803
\(783\) −9.59469 −0.342886
\(784\) 57.7306 2.06181
\(785\) −38.2948 −1.36680
\(786\) −147.568 −5.26358
\(787\) 49.0931 1.74998 0.874990 0.484142i \(-0.160868\pi\)
0.874990 + 0.484142i \(0.160868\pi\)
\(788\) −8.48547 −0.302283
\(789\) 57.8957 2.06114
\(790\) −39.5268 −1.40630
\(791\) 18.5383 0.659145
\(792\) −189.875 −6.74693
\(793\) −10.9459 −0.388699
\(794\) −22.1071 −0.784553
\(795\) 8.26142 0.293002
\(796\) −116.139 −4.11645
\(797\) −26.4428 −0.936651 −0.468325 0.883556i \(-0.655142\pi\)
−0.468325 + 0.883556i \(0.655142\pi\)
\(798\) −122.119 −4.32295
\(799\) 44.5694 1.57675
\(800\) −0.396757 −0.0140275
\(801\) −74.1786 −2.62097
\(802\) −71.2387 −2.51553
\(803\) −54.9042 −1.93753
\(804\) 165.942 5.85232
\(805\) 35.6005 1.25475
\(806\) −0.663408 −0.0233675
\(807\) −44.3749 −1.56207
\(808\) 60.5162 2.12895
\(809\) 52.2726 1.83781 0.918903 0.394484i \(-0.129077\pi\)
0.918903 + 0.394484i \(0.129077\pi\)
\(810\) −62.1991 −2.18545
\(811\) −10.3865 −0.364721 −0.182360 0.983232i \(-0.558374\pi\)
−0.182360 + 0.983232i \(0.558374\pi\)
\(812\) 17.4364 0.611899
\(813\) −76.1151 −2.66947
\(814\) −11.2836 −0.395490
\(815\) 17.0453 0.597071
\(816\) −222.320 −7.78276
\(817\) −18.1938 −0.636520
\(818\) 81.7857 2.85957
\(819\) 44.4764 1.55413
\(820\) 3.54283 0.123721
\(821\) −32.2228 −1.12458 −0.562291 0.826939i \(-0.690080\pi\)
−0.562291 + 0.826939i \(0.690080\pi\)
\(822\) −39.1028 −1.36387
\(823\) −30.1346 −1.05043 −0.525213 0.850971i \(-0.676014\pi\)
−0.525213 + 0.850971i \(0.676014\pi\)
\(824\) 6.75573 0.235347
\(825\) 0.411862 0.0143392
\(826\) 19.5750 0.681102
\(827\) −29.0327 −1.00957 −0.504784 0.863246i \(-0.668428\pi\)
−0.504784 + 0.863246i \(0.668428\pi\)
\(828\) −135.313 −4.70245
\(829\) −7.90200 −0.274448 −0.137224 0.990540i \(-0.543818\pi\)
−0.137224 + 0.990540i \(0.543818\pi\)
\(830\) −24.1970 −0.839889
\(831\) −3.02798 −0.105040
\(832\) −20.8853 −0.724067
\(833\) −40.0689 −1.38831
\(834\) 78.2900 2.71096
\(835\) −46.4587 −1.60777
\(836\) −85.3598 −2.95223
\(837\) −1.19277 −0.0412280
\(838\) −32.5974 −1.12606
\(839\) 37.8130 1.30545 0.652725 0.757595i \(-0.273626\pi\)
0.652725 + 0.757595i \(0.273626\pi\)
\(840\) 184.533 6.36700
\(841\) 1.00000 0.0344828
\(842\) −25.9401 −0.893956
\(843\) −42.3056 −1.45708
\(844\) 8.64886 0.297706
\(845\) −19.9199 −0.685264
\(846\) 101.238 3.48063
\(847\) −18.4557 −0.634147
\(848\) 12.5074 0.429504
\(849\) −16.9596 −0.582051
\(850\) 0.634200 0.0217529
\(851\) −4.76549 −0.163359
\(852\) −22.2016 −0.760614
\(853\) 10.5224 0.360279 0.180139 0.983641i \(-0.442345\pi\)
0.180139 + 0.983641i \(0.442345\pi\)
\(854\) 50.3335 1.72238
\(855\) −59.7905 −2.04479
\(856\) 64.3991 2.20112
\(857\) 16.1404 0.551346 0.275673 0.961251i \(-0.411099\pi\)
0.275673 + 0.961251i \(0.411099\pi\)
\(858\) 65.0312 2.22013
\(859\) 19.5149 0.665841 0.332921 0.942955i \(-0.391966\pi\)
0.332921 + 0.942955i \(0.391966\pi\)
\(860\) 46.3902 1.58189
\(861\) −3.45873 −0.117873
\(862\) −83.6254 −2.84829
\(863\) −17.7448 −0.604040 −0.302020 0.953302i \(-0.597661\pi\)
−0.302020 + 0.953302i \(0.597661\pi\)
\(864\) −112.634 −3.83189
\(865\) 40.5802 1.37977
\(866\) 65.0552 2.21067
\(867\) 102.829 3.49227
\(868\) 2.16761 0.0735736
\(869\) 26.9730 0.914996
\(870\) 17.8578 0.605437
\(871\) −22.6612 −0.767846
\(872\) 36.1955 1.22573
\(873\) 76.7506 2.59761
\(874\) −50.7363 −1.71618
\(875\) 39.5714 1.33776
\(876\) −202.813 −6.85240
\(877\) 13.1896 0.445382 0.222691 0.974889i \(-0.428516\pi\)
0.222691 + 0.974889i \(0.428516\pi\)
\(878\) −13.4295 −0.453224
\(879\) −81.5138 −2.74939
\(880\) 92.8694 3.13063
\(881\) 47.5500 1.60200 0.801000 0.598665i \(-0.204302\pi\)
0.801000 + 0.598665i \(0.204302\pi\)
\(882\) −91.0151 −3.06464
\(883\) 29.6255 0.996976 0.498488 0.866897i \(-0.333889\pi\)
0.498488 + 0.866897i \(0.333889\pi\)
\(884\) 71.1526 2.39312
\(885\) 14.2451 0.478845
\(886\) −92.1966 −3.09740
\(887\) −11.4122 −0.383185 −0.191593 0.981475i \(-0.561365\pi\)
−0.191593 + 0.981475i \(0.561365\pi\)
\(888\) −24.7017 −0.828934
\(889\) 53.9163 1.80830
\(890\) 70.9189 2.37721
\(891\) 42.4445 1.42194
\(892\) −118.041 −3.95231
\(893\) 26.9722 0.902590
\(894\) −59.1971 −1.97985
\(895\) −8.53898 −0.285427
\(896\) 12.6560 0.422806
\(897\) 27.4651 0.917032
\(898\) −27.7868 −0.927256
\(899\) 0.124315 0.00414615
\(900\) 1.02359 0.0341197
\(901\) −8.68094 −0.289204
\(902\) −3.40246 −0.113290
\(903\) −45.2890 −1.50712
\(904\) 39.9231 1.32782
\(905\) −19.6420 −0.652921
\(906\) 89.4439 2.97158
\(907\) 19.6318 0.651863 0.325932 0.945393i \(-0.394322\pi\)
0.325932 + 0.945393i \(0.394322\pi\)
\(908\) 80.7640 2.68025
\(909\) −48.8088 −1.61889
\(910\) −42.5219 −1.40959
\(911\) −54.5174 −1.80624 −0.903120 0.429388i \(-0.858729\pi\)
−0.903120 + 0.429388i \(0.858729\pi\)
\(912\) −134.542 −4.45513
\(913\) 16.5119 0.546465
\(914\) −76.2780 −2.52305
\(915\) 36.6287 1.21091
\(916\) −61.5382 −2.03328
\(917\) −65.8448 −2.17439
\(918\) 180.041 5.94224
\(919\) −38.4425 −1.26810 −0.634050 0.773292i \(-0.718609\pi\)
−0.634050 + 0.773292i \(0.718609\pi\)
\(920\) 76.6675 2.52765
\(921\) −28.5531 −0.940856
\(922\) −68.5767 −2.25845
\(923\) 3.03187 0.0997954
\(924\) −212.483 −6.99016
\(925\) 0.0360491 0.00118529
\(926\) −26.2534 −0.862741
\(927\) −5.44878 −0.178961
\(928\) 11.7392 0.385359
\(929\) 8.01060 0.262819 0.131410 0.991328i \(-0.458050\pi\)
0.131410 + 0.991328i \(0.458050\pi\)
\(930\) 2.22000 0.0727966
\(931\) −24.2486 −0.794716
\(932\) −133.313 −4.36682
\(933\) 13.1841 0.431628
\(934\) 110.002 3.59936
\(935\) −64.4575 −2.10799
\(936\) 95.7823 3.13074
\(937\) −10.8673 −0.355020 −0.177510 0.984119i \(-0.556804\pi\)
−0.177510 + 0.984119i \(0.556804\pi\)
\(938\) 104.206 3.40243
\(939\) 52.9559 1.72815
\(940\) −68.7734 −2.24314
\(941\) 19.2075 0.626146 0.313073 0.949729i \(-0.398642\pi\)
0.313073 + 0.949729i \(0.398642\pi\)
\(942\) 135.854 4.42637
\(943\) −1.43699 −0.0467947
\(944\) 21.5664 0.701927
\(945\) −76.4518 −2.48698
\(946\) −44.5523 −1.44852
\(947\) 31.1723 1.01296 0.506481 0.862251i \(-0.330946\pi\)
0.506481 + 0.862251i \(0.330946\pi\)
\(948\) 99.6365 3.23604
\(949\) 27.6963 0.899060
\(950\) 0.383801 0.0124521
\(951\) −2.01717 −0.0654113
\(952\) −193.904 −6.28447
\(953\) 48.6926 1.57731 0.788654 0.614837i \(-0.210778\pi\)
0.788654 + 0.614837i \(0.210778\pi\)
\(954\) −19.7184 −0.638408
\(955\) −6.49210 −0.210079
\(956\) −39.0280 −1.26226
\(957\) −12.1861 −0.393922
\(958\) −51.7237 −1.67112
\(959\) −17.4476 −0.563414
\(960\) 69.8897 2.25568
\(961\) −30.9845 −0.999501
\(962\) 5.69200 0.183517
\(963\) −51.9406 −1.67376
\(964\) 120.632 3.88530
\(965\) 24.8940 0.801365
\(966\) −126.296 −4.06350
\(967\) 46.2894 1.48857 0.744284 0.667864i \(-0.232791\pi\)
0.744284 + 0.667864i \(0.232791\pi\)
\(968\) −39.7454 −1.27747
\(969\) 93.3811 2.99983
\(970\) −73.3779 −2.35602
\(971\) −15.6421 −0.501979 −0.250989 0.967990i \(-0.580756\pi\)
−0.250989 + 0.967990i \(0.580756\pi\)
\(972\) 15.4682 0.496143
\(973\) 34.9329 1.11990
\(974\) 107.861 3.45609
\(975\) −0.207763 −0.00665373
\(976\) 55.4540 1.77504
\(977\) −28.5396 −0.913062 −0.456531 0.889707i \(-0.650908\pi\)
−0.456531 + 0.889707i \(0.650908\pi\)
\(978\) −60.4696 −1.93361
\(979\) −48.3949 −1.54671
\(980\) 61.8288 1.97505
\(981\) −29.1932 −0.932067
\(982\) −76.3749 −2.43722
\(983\) 26.6019 0.848469 0.424234 0.905552i \(-0.360543\pi\)
0.424234 + 0.905552i \(0.360543\pi\)
\(984\) −7.44855 −0.237451
\(985\) −3.87771 −0.123554
\(986\) −18.7647 −0.597589
\(987\) 67.1407 2.13711
\(988\) 43.0596 1.36991
\(989\) −18.8161 −0.598317
\(990\) −146.413 −4.65331
\(991\) −24.0184 −0.762969 −0.381485 0.924375i \(-0.624587\pi\)
−0.381485 + 0.924375i \(0.624587\pi\)
\(992\) 1.45936 0.0463349
\(993\) −101.226 −3.21231
\(994\) −13.9418 −0.442207
\(995\) −53.0736 −1.68255
\(996\) 60.9941 1.93267
\(997\) −0.274695 −0.00869969 −0.00434984 0.999991i \(-0.501385\pi\)
−0.00434984 + 0.999991i \(0.501385\pi\)
\(998\) −110.993 −3.51343
\(999\) 10.2339 0.323785
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 8033.2.a.b.1.5 153
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8033.2.a.b.1.5 153 1.1 even 1 trivial