Properties

Label 1045.4.a.c.1.15
Level $1045$
Weight $4$
Character 1045.1
Self dual yes
Analytic conductor $61.657$
Analytic rank $1$
Dimension $20$
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] = [1045,4,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.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: \(61.6569959560\)
Analytic rank: \(1\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} - 105 x^{18} + 103 x^{17} + 4500 x^{16} - 4345 x^{15} - 101844 x^{14} + 95592 x^{13} + 1317797 x^{12} - 1160501 x^{11} - 9914845 x^{10} + 7570653 x^{9} + \cdots + 150528 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Root \(-1.78835\) of defining polynomial
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.78835 q^{2} -7.45188 q^{3} -4.80180 q^{4} -5.00000 q^{5} -13.3266 q^{6} -20.9424 q^{7} -22.8941 q^{8} +28.5305 q^{9} +O(q^{10})\) \(q+1.78835 q^{2} -7.45188 q^{3} -4.80180 q^{4} -5.00000 q^{5} -13.3266 q^{6} -20.9424 q^{7} -22.8941 q^{8} +28.5305 q^{9} -8.94175 q^{10} -11.0000 q^{11} +35.7825 q^{12} +37.7596 q^{13} -37.4524 q^{14} +37.2594 q^{15} -2.52827 q^{16} +119.316 q^{17} +51.0225 q^{18} +19.0000 q^{19} +24.0090 q^{20} +156.060 q^{21} -19.6719 q^{22} -24.1294 q^{23} +170.604 q^{24} +25.0000 q^{25} +67.5274 q^{26} -11.4052 q^{27} +100.561 q^{28} +1.45246 q^{29} +66.6329 q^{30} -7.62072 q^{31} +178.631 q^{32} +81.9707 q^{33} +213.378 q^{34} +104.712 q^{35} -136.998 q^{36} -402.545 q^{37} +33.9787 q^{38} -281.380 q^{39} +114.471 q^{40} +278.512 q^{41} +279.090 q^{42} -228.717 q^{43} +52.8198 q^{44} -142.653 q^{45} -43.1519 q^{46} +409.518 q^{47} +18.8404 q^{48} +95.5842 q^{49} +44.7088 q^{50} -889.125 q^{51} -181.314 q^{52} +45.2974 q^{53} -20.3964 q^{54} +55.0000 q^{55} +479.458 q^{56} -141.586 q^{57} +2.59751 q^{58} -203.531 q^{59} -178.912 q^{60} -196.662 q^{61} -13.6285 q^{62} -597.497 q^{63} +339.682 q^{64} -188.798 q^{65} +146.592 q^{66} -81.1892 q^{67} -572.930 q^{68} +179.810 q^{69} +187.262 q^{70} +257.755 q^{71} -653.181 q^{72} +544.148 q^{73} -719.892 q^{74} -186.297 q^{75} -91.2342 q^{76} +230.366 q^{77} -503.206 q^{78} +77.8441 q^{79} +12.6414 q^{80} -685.334 q^{81} +498.076 q^{82} -819.324 q^{83} -749.371 q^{84} -596.578 q^{85} -409.027 q^{86} -10.8236 q^{87} +251.835 q^{88} +992.947 q^{89} -255.113 q^{90} -790.776 q^{91} +115.865 q^{92} +56.7887 q^{93} +732.362 q^{94} -95.0000 q^{95} -1331.14 q^{96} +1227.59 q^{97} +170.938 q^{98} -313.836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - q^{2} - 8 q^{3} + 51 q^{4} - 100 q^{5} - 54 q^{6} + 49 q^{7} + 9 q^{8} + 146 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - q^{2} - 8 q^{3} + 51 q^{4} - 100 q^{5} - 54 q^{6} + 49 q^{7} + 9 q^{8} + 146 q^{9} + 5 q^{10} - 220 q^{11} - 59 q^{12} + 60 q^{13} - 89 q^{14} + 40 q^{15} + 275 q^{16} - 155 q^{17} + 45 q^{18} + 380 q^{19} - 255 q^{20} + 105 q^{21} + 11 q^{22} - 154 q^{23} - 397 q^{24} + 500 q^{25} + 176 q^{26} - 206 q^{27} + 155 q^{28} - 305 q^{29} + 270 q^{30} - 759 q^{31} - 254 q^{32} + 88 q^{33} - 565 q^{34} - 245 q^{35} + 705 q^{36} + 698 q^{37} - 19 q^{38} - 758 q^{39} - 45 q^{40} + 547 q^{41} + 106 q^{42} - 925 q^{43} - 561 q^{44} - 730 q^{45} - 254 q^{46} - 681 q^{47} - 540 q^{48} + 213 q^{49} - 25 q^{50} - 899 q^{51} + 889 q^{52} - 419 q^{53} - 2241 q^{54} + 1100 q^{55} - 2473 q^{56} - 152 q^{57} - 1440 q^{58} - 2829 q^{59} + 295 q^{60} - 959 q^{61} + 1575 q^{62} - 426 q^{63} + 93 q^{64} - 300 q^{65} + 594 q^{66} - 1020 q^{67} - 4218 q^{68} - 572 q^{69} + 445 q^{70} + 106 q^{71} + 210 q^{72} + 558 q^{73} - 3439 q^{74} - 200 q^{75} + 969 q^{76} - 539 q^{77} - 3599 q^{78} + 536 q^{79} - 1375 q^{80} - 2128 q^{81} - 1255 q^{82} - 4179 q^{83} - 2024 q^{84} + 775 q^{85} - 1119 q^{86} - 557 q^{87} - 99 q^{88} - 4120 q^{89} - 225 q^{90} - 111 q^{91} - 2831 q^{92} + 801 q^{93} + 1213 q^{94} - 1900 q^{95} - 6147 q^{96} + 1414 q^{97} - 7869 q^{98} - 1606 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.78835 0.632277 0.316139 0.948713i \(-0.397614\pi\)
0.316139 + 0.948713i \(0.397614\pi\)
\(3\) −7.45188 −1.43411 −0.717057 0.697014i \(-0.754511\pi\)
−0.717057 + 0.697014i \(0.754511\pi\)
\(4\) −4.80180 −0.600225
\(5\) −5.00000 −0.447214
\(6\) −13.3266 −0.906758
\(7\) −20.9424 −1.13078 −0.565392 0.824823i \(-0.691275\pi\)
−0.565392 + 0.824823i \(0.691275\pi\)
\(8\) −22.8941 −1.01179
\(9\) 28.5305 1.05669
\(10\) −8.94175 −0.282763
\(11\) −11.0000 −0.301511
\(12\) 35.7825 0.860792
\(13\) 37.7596 0.805586 0.402793 0.915291i \(-0.368039\pi\)
0.402793 + 0.915291i \(0.368039\pi\)
\(14\) −37.4524 −0.714969
\(15\) 37.2594 0.641356
\(16\) −2.52827 −0.0395042
\(17\) 119.316 1.70225 0.851126 0.524962i \(-0.175921\pi\)
0.851126 + 0.524962i \(0.175921\pi\)
\(18\) 51.0225 0.668118
\(19\) 19.0000 0.229416
\(20\) 24.0090 0.268429
\(21\) 156.060 1.62167
\(22\) −19.6719 −0.190639
\(23\) −24.1294 −0.218754 −0.109377 0.994000i \(-0.534886\pi\)
−0.109377 + 0.994000i \(0.534886\pi\)
\(24\) 170.604 1.45102
\(25\) 25.0000 0.200000
\(26\) 67.5274 0.509354
\(27\) −11.4052 −0.0812935
\(28\) 100.561 0.678725
\(29\) 1.45246 0.00930051 0.00465026 0.999989i \(-0.498520\pi\)
0.00465026 + 0.999989i \(0.498520\pi\)
\(30\) 66.6329 0.405515
\(31\) −7.62072 −0.0441523 −0.0220762 0.999756i \(-0.507028\pi\)
−0.0220762 + 0.999756i \(0.507028\pi\)
\(32\) 178.631 0.986809
\(33\) 81.9707 0.432402
\(34\) 213.378 1.07629
\(35\) 104.712 0.505702
\(36\) −136.998 −0.634249
\(37\) −402.545 −1.78860 −0.894298 0.447473i \(-0.852324\pi\)
−0.894298 + 0.447473i \(0.852324\pi\)
\(38\) 33.9787 0.145054
\(39\) −281.380 −1.15530
\(40\) 114.471 0.452485
\(41\) 278.512 1.06088 0.530441 0.847722i \(-0.322026\pi\)
0.530441 + 0.847722i \(0.322026\pi\)
\(42\) 279.090 1.02535
\(43\) −228.717 −0.811141 −0.405571 0.914064i \(-0.632927\pi\)
−0.405571 + 0.914064i \(0.632927\pi\)
\(44\) 52.8198 0.180975
\(45\) −142.653 −0.472564
\(46\) −43.1519 −0.138313
\(47\) 409.518 1.27094 0.635472 0.772124i \(-0.280806\pi\)
0.635472 + 0.772124i \(0.280806\pi\)
\(48\) 18.8404 0.0566536
\(49\) 95.5842 0.278671
\(50\) 44.7088 0.126455
\(51\) −889.125 −2.44122
\(52\) −181.314 −0.483533
\(53\) 45.2974 0.117398 0.0586988 0.998276i \(-0.481305\pi\)
0.0586988 + 0.998276i \(0.481305\pi\)
\(54\) −20.3964 −0.0514000
\(55\) 55.0000 0.134840
\(56\) 479.458 1.14411
\(57\) −141.586 −0.329009
\(58\) 2.59751 0.00588050
\(59\) −203.531 −0.449109 −0.224555 0.974462i \(-0.572093\pi\)
−0.224555 + 0.974462i \(0.572093\pi\)
\(60\) −178.912 −0.384958
\(61\) −196.662 −0.412787 −0.206394 0.978469i \(-0.566173\pi\)
−0.206394 + 0.978469i \(0.566173\pi\)
\(62\) −13.6285 −0.0279165
\(63\) −597.497 −1.19488
\(64\) 339.682 0.663441
\(65\) −188.798 −0.360269
\(66\) 146.592 0.273398
\(67\) −81.1892 −0.148042 −0.0740212 0.997257i \(-0.523583\pi\)
−0.0740212 + 0.997257i \(0.523583\pi\)
\(68\) −572.930 −1.02173
\(69\) 179.810 0.313718
\(70\) 187.262 0.319744
\(71\) 257.755 0.430844 0.215422 0.976521i \(-0.430887\pi\)
0.215422 + 0.976521i \(0.430887\pi\)
\(72\) −653.181 −1.06914
\(73\) 544.148 0.872435 0.436217 0.899841i \(-0.356318\pi\)
0.436217 + 0.899841i \(0.356318\pi\)
\(74\) −719.892 −1.13089
\(75\) −186.297 −0.286823
\(76\) −91.2342 −0.137701
\(77\) 230.366 0.340944
\(78\) −503.206 −0.730472
\(79\) 77.8441 0.110863 0.0554313 0.998463i \(-0.482347\pi\)
0.0554313 + 0.998463i \(0.482347\pi\)
\(80\) 12.6414 0.0176668
\(81\) −685.334 −0.940101
\(82\) 498.076 0.670772
\(83\) −819.324 −1.08352 −0.541762 0.840532i \(-0.682242\pi\)
−0.541762 + 0.840532i \(0.682242\pi\)
\(84\) −749.371 −0.973369
\(85\) −596.578 −0.761270
\(86\) −409.027 −0.512866
\(87\) −10.8236 −0.0133380
\(88\) 251.835 0.305065
\(89\) 992.947 1.18261 0.591304 0.806448i \(-0.298613\pi\)
0.591304 + 0.806448i \(0.298613\pi\)
\(90\) −255.113 −0.298792
\(91\) −790.776 −0.910944
\(92\) 115.865 0.131301
\(93\) 56.7887 0.0633195
\(94\) 732.362 0.803589
\(95\) −95.0000 −0.102598
\(96\) −1331.14 −1.41520
\(97\) 1227.59 1.28498 0.642491 0.766294i \(-0.277901\pi\)
0.642491 + 0.766294i \(0.277901\pi\)
\(98\) 170.938 0.176197
\(99\) −313.836 −0.318603
\(100\) −120.045 −0.120045
\(101\) −602.090 −0.593171 −0.296585 0.955006i \(-0.595848\pi\)
−0.296585 + 0.955006i \(0.595848\pi\)
\(102\) −1590.07 −1.54353
\(103\) −646.684 −0.618638 −0.309319 0.950958i \(-0.600101\pi\)
−0.309319 + 0.950958i \(0.600101\pi\)
\(104\) −864.472 −0.815081
\(105\) −780.301 −0.725234
\(106\) 81.0076 0.0742279
\(107\) −417.116 −0.376861 −0.188431 0.982087i \(-0.560340\pi\)
−0.188431 + 0.982087i \(0.560340\pi\)
\(108\) 54.7653 0.0487944
\(109\) 540.431 0.474898 0.237449 0.971400i \(-0.423689\pi\)
0.237449 + 0.971400i \(0.423689\pi\)
\(110\) 98.3593 0.0852563
\(111\) 2999.72 2.56505
\(112\) 52.9481 0.0446707
\(113\) −367.393 −0.305853 −0.152927 0.988238i \(-0.548870\pi\)
−0.152927 + 0.988238i \(0.548870\pi\)
\(114\) −253.205 −0.208025
\(115\) 120.647 0.0978296
\(116\) −6.97442 −0.00558240
\(117\) 1077.30 0.851251
\(118\) −363.984 −0.283962
\(119\) −2498.75 −1.92488
\(120\) −853.021 −0.648915
\(121\) 121.000 0.0909091
\(122\) −351.701 −0.260996
\(123\) −2075.43 −1.52143
\(124\) 36.5932 0.0265013
\(125\) −125.000 −0.0894427
\(126\) −1068.53 −0.755497
\(127\) 1067.02 0.745535 0.372768 0.927925i \(-0.378409\pi\)
0.372768 + 0.927925i \(0.378409\pi\)
\(128\) −821.581 −0.567330
\(129\) 1704.37 1.16327
\(130\) −337.637 −0.227790
\(131\) 2114.17 1.41005 0.705023 0.709185i \(-0.250937\pi\)
0.705023 + 0.709185i \(0.250937\pi\)
\(132\) −393.607 −0.259539
\(133\) −397.906 −0.259420
\(134\) −145.195 −0.0936039
\(135\) 57.0258 0.0363556
\(136\) −2731.62 −1.72231
\(137\) 736.727 0.459437 0.229718 0.973257i \(-0.426220\pi\)
0.229718 + 0.973257i \(0.426220\pi\)
\(138\) 321.562 0.198357
\(139\) −1707.49 −1.04193 −0.520963 0.853579i \(-0.674427\pi\)
−0.520963 + 0.853579i \(0.674427\pi\)
\(140\) −502.806 −0.303535
\(141\) −3051.68 −1.82268
\(142\) 460.957 0.272413
\(143\) −415.355 −0.242893
\(144\) −72.1329 −0.0417436
\(145\) −7.26230 −0.00415932
\(146\) 973.128 0.551621
\(147\) −712.282 −0.399646
\(148\) 1932.94 1.07356
\(149\) −393.039 −0.216101 −0.108050 0.994145i \(-0.534461\pi\)
−0.108050 + 0.994145i \(0.534461\pi\)
\(150\) −333.164 −0.181352
\(151\) −2977.78 −1.60483 −0.802413 0.596769i \(-0.796451\pi\)
−0.802413 + 0.596769i \(0.796451\pi\)
\(152\) −434.988 −0.232120
\(153\) 3404.13 1.79874
\(154\) 411.976 0.215571
\(155\) 38.1036 0.0197455
\(156\) 1351.13 0.693442
\(157\) 2358.06 1.19868 0.599342 0.800493i \(-0.295429\pi\)
0.599342 + 0.800493i \(0.295429\pi\)
\(158\) 139.213 0.0700959
\(159\) −337.551 −0.168362
\(160\) −893.157 −0.441314
\(161\) 505.328 0.247363
\(162\) −1225.62 −0.594405
\(163\) 1274.77 0.612565 0.306282 0.951941i \(-0.400915\pi\)
0.306282 + 0.951941i \(0.400915\pi\)
\(164\) −1337.36 −0.636769
\(165\) −409.853 −0.193376
\(166\) −1465.24 −0.685087
\(167\) 2396.90 1.11065 0.555323 0.831635i \(-0.312595\pi\)
0.555323 + 0.831635i \(0.312595\pi\)
\(168\) −3572.86 −1.64079
\(169\) −771.214 −0.351031
\(170\) −1066.89 −0.481334
\(171\) 542.080 0.242420
\(172\) 1098.26 0.486868
\(173\) 3707.72 1.62944 0.814719 0.579856i \(-0.196891\pi\)
0.814719 + 0.579856i \(0.196891\pi\)
\(174\) −19.3563 −0.00843332
\(175\) −523.560 −0.226157
\(176\) 27.8110 0.0119110
\(177\) 1516.69 0.644074
\(178\) 1775.74 0.747737
\(179\) −3584.65 −1.49681 −0.748406 0.663241i \(-0.769180\pi\)
−0.748406 + 0.663241i \(0.769180\pi\)
\(180\) 684.989 0.283645
\(181\) −4671.14 −1.91825 −0.959124 0.282986i \(-0.908675\pi\)
−0.959124 + 0.282986i \(0.908675\pi\)
\(182\) −1414.19 −0.575969
\(183\) 1465.50 0.591984
\(184\) 552.422 0.221332
\(185\) 2012.73 0.799884
\(186\) 101.558 0.0400355
\(187\) −1312.47 −0.513248
\(188\) −1966.42 −0.762852
\(189\) 238.851 0.0919253
\(190\) −169.893 −0.0648703
\(191\) −4407.46 −1.66970 −0.834850 0.550477i \(-0.814446\pi\)
−0.834850 + 0.550477i \(0.814446\pi\)
\(192\) −2531.27 −0.951451
\(193\) −609.803 −0.227433 −0.113717 0.993513i \(-0.536276\pi\)
−0.113717 + 0.993513i \(0.536276\pi\)
\(194\) 2195.37 0.812465
\(195\) 1406.90 0.516667
\(196\) −458.976 −0.167265
\(197\) 869.384 0.314422 0.157211 0.987565i \(-0.449750\pi\)
0.157211 + 0.987565i \(0.449750\pi\)
\(198\) −561.248 −0.201445
\(199\) −1594.47 −0.567986 −0.283993 0.958826i \(-0.591659\pi\)
−0.283993 + 0.958826i \(0.591659\pi\)
\(200\) −572.353 −0.202357
\(201\) 605.012 0.212310
\(202\) −1076.75 −0.375048
\(203\) −30.4180 −0.0105169
\(204\) 4269.40 1.46528
\(205\) −1392.56 −0.474441
\(206\) −1156.50 −0.391151
\(207\) −688.425 −0.231154
\(208\) −95.4665 −0.0318241
\(209\) −209.000 −0.0691714
\(210\) −1395.45 −0.458549
\(211\) −3299.68 −1.07658 −0.538292 0.842758i \(-0.680930\pi\)
−0.538292 + 0.842758i \(0.680930\pi\)
\(212\) −217.509 −0.0704650
\(213\) −1920.76 −0.617879
\(214\) −745.950 −0.238281
\(215\) 1143.59 0.362753
\(216\) 261.111 0.0822516
\(217\) 159.596 0.0499267
\(218\) 966.480 0.300267
\(219\) −4054.93 −1.25117
\(220\) −264.099 −0.0809344
\(221\) 4505.30 1.37131
\(222\) 5364.55 1.62182
\(223\) −2928.53 −0.879413 −0.439707 0.898141i \(-0.644918\pi\)
−0.439707 + 0.898141i \(0.644918\pi\)
\(224\) −3740.97 −1.11587
\(225\) 713.263 0.211337
\(226\) −657.027 −0.193384
\(227\) −4913.12 −1.43654 −0.718272 0.695762i \(-0.755067\pi\)
−0.718272 + 0.695762i \(0.755067\pi\)
\(228\) 679.867 0.197479
\(229\) 5249.74 1.51490 0.757451 0.652892i \(-0.226444\pi\)
0.757451 + 0.652892i \(0.226444\pi\)
\(230\) 215.759 0.0618554
\(231\) −1716.66 −0.488953
\(232\) −33.2528 −0.00941013
\(233\) −6568.13 −1.84675 −0.923374 0.383901i \(-0.874580\pi\)
−0.923374 + 0.383901i \(0.874580\pi\)
\(234\) 1926.59 0.538227
\(235\) −2047.59 −0.568383
\(236\) 977.314 0.269567
\(237\) −580.085 −0.158990
\(238\) −4468.65 −1.21706
\(239\) 6260.32 1.69434 0.847168 0.531324i \(-0.178305\pi\)
0.847168 + 0.531324i \(0.178305\pi\)
\(240\) −94.2019 −0.0253363
\(241\) 2113.07 0.564792 0.282396 0.959298i \(-0.408871\pi\)
0.282396 + 0.959298i \(0.408871\pi\)
\(242\) 216.390 0.0574798
\(243\) 5414.96 1.42951
\(244\) 944.333 0.247765
\(245\) −477.921 −0.124626
\(246\) −3711.60 −0.961964
\(247\) 717.432 0.184814
\(248\) 174.470 0.0446727
\(249\) 6105.50 1.55390
\(250\) −223.544 −0.0565526
\(251\) −969.609 −0.243829 −0.121915 0.992541i \(-0.538903\pi\)
−0.121915 + 0.992541i \(0.538903\pi\)
\(252\) 2869.06 0.717199
\(253\) 265.424 0.0659567
\(254\) 1908.21 0.471385
\(255\) 4445.63 1.09175
\(256\) −4186.73 −1.02215
\(257\) −951.570 −0.230962 −0.115481 0.993310i \(-0.536841\pi\)
−0.115481 + 0.993310i \(0.536841\pi\)
\(258\) 3048.02 0.735509
\(259\) 8430.26 2.02251
\(260\) 906.570 0.216243
\(261\) 41.4394 0.00982772
\(262\) 3780.88 0.891540
\(263\) 6299.17 1.47689 0.738447 0.674311i \(-0.235559\pi\)
0.738447 + 0.674311i \(0.235559\pi\)
\(264\) −1876.65 −0.437498
\(265\) −226.487 −0.0525018
\(266\) −711.595 −0.164025
\(267\) −7399.32 −1.69600
\(268\) 389.855 0.0888588
\(269\) 5074.67 1.15022 0.575108 0.818077i \(-0.304960\pi\)
0.575108 + 0.818077i \(0.304960\pi\)
\(270\) 101.982 0.0229868
\(271\) −8433.87 −1.89048 −0.945242 0.326370i \(-0.894175\pi\)
−0.945242 + 0.326370i \(0.894175\pi\)
\(272\) −301.662 −0.0672461
\(273\) 5892.77 1.30640
\(274\) 1317.53 0.290491
\(275\) −275.000 −0.0603023
\(276\) −863.410 −0.188301
\(277\) −3816.53 −0.827845 −0.413922 0.910312i \(-0.635841\pi\)
−0.413922 + 0.910312i \(0.635841\pi\)
\(278\) −3053.60 −0.658787
\(279\) −217.423 −0.0466551
\(280\) −2397.29 −0.511662
\(281\) −4097.68 −0.869918 −0.434959 0.900450i \(-0.643237\pi\)
−0.434959 + 0.900450i \(0.643237\pi\)
\(282\) −5457.47 −1.15244
\(283\) 5871.93 1.23339 0.616696 0.787201i \(-0.288471\pi\)
0.616696 + 0.787201i \(0.288471\pi\)
\(284\) −1237.69 −0.258603
\(285\) 707.929 0.147137
\(286\) −742.801 −0.153576
\(287\) −5832.70 −1.19963
\(288\) 5096.45 1.04275
\(289\) 9323.20 1.89766
\(290\) −12.9875 −0.00262984
\(291\) −9147.87 −1.84281
\(292\) −2612.89 −0.523657
\(293\) −3042.30 −0.606598 −0.303299 0.952895i \(-0.598088\pi\)
−0.303299 + 0.952895i \(0.598088\pi\)
\(294\) −1273.81 −0.252687
\(295\) 1017.65 0.200848
\(296\) 9215.91 1.80968
\(297\) 125.457 0.0245109
\(298\) −702.892 −0.136636
\(299\) −911.117 −0.176225
\(300\) 894.561 0.172158
\(301\) 4789.89 0.917225
\(302\) −5325.32 −1.01470
\(303\) 4486.71 0.850675
\(304\) −48.0372 −0.00906289
\(305\) 983.311 0.184604
\(306\) 6087.78 1.13731
\(307\) 6735.16 1.25210 0.626052 0.779781i \(-0.284670\pi\)
0.626052 + 0.779781i \(0.284670\pi\)
\(308\) −1106.17 −0.204643
\(309\) 4819.01 0.887197
\(310\) 68.1426 0.0124846
\(311\) 5200.28 0.948169 0.474085 0.880479i \(-0.342779\pi\)
0.474085 + 0.880479i \(0.342779\pi\)
\(312\) 6441.94 1.16892
\(313\) 5226.57 0.943845 0.471922 0.881640i \(-0.343560\pi\)
0.471922 + 0.881640i \(0.343560\pi\)
\(314\) 4217.03 0.757901
\(315\) 2987.49 0.534368
\(316\) −373.792 −0.0665425
\(317\) 6376.16 1.12972 0.564860 0.825187i \(-0.308930\pi\)
0.564860 + 0.825187i \(0.308930\pi\)
\(318\) −603.659 −0.106451
\(319\) −15.9771 −0.00280421
\(320\) −1698.41 −0.296700
\(321\) 3108.30 0.540462
\(322\) 903.703 0.156402
\(323\) 2267.00 0.390523
\(324\) 3290.84 0.564273
\(325\) 943.990 0.161117
\(326\) 2279.74 0.387311
\(327\) −4027.23 −0.681059
\(328\) −6376.27 −1.07339
\(329\) −8576.29 −1.43716
\(330\) −732.961 −0.122267
\(331\) −4935.60 −0.819593 −0.409796 0.912177i \(-0.634400\pi\)
−0.409796 + 0.912177i \(0.634400\pi\)
\(332\) 3934.23 0.650358
\(333\) −11484.8 −1.88998
\(334\) 4286.50 0.702236
\(335\) 405.946 0.0662066
\(336\) −394.563 −0.0640630
\(337\) −5097.13 −0.823911 −0.411956 0.911204i \(-0.635154\pi\)
−0.411956 + 0.911204i \(0.635154\pi\)
\(338\) −1379.20 −0.221949
\(339\) 2737.77 0.438628
\(340\) 2864.65 0.456933
\(341\) 83.8279 0.0133124
\(342\) 969.428 0.153277
\(343\) 5181.48 0.815667
\(344\) 5236.28 0.820702
\(345\) −899.048 −0.140299
\(346\) 6630.70 1.03026
\(347\) 954.649 0.147690 0.0738448 0.997270i \(-0.476473\pi\)
0.0738448 + 0.997270i \(0.476473\pi\)
\(348\) 51.9726 0.00800581
\(349\) 3972.22 0.609249 0.304625 0.952472i \(-0.401469\pi\)
0.304625 + 0.952472i \(0.401469\pi\)
\(350\) −936.309 −0.142994
\(351\) −430.654 −0.0654889
\(352\) −1964.95 −0.297534
\(353\) 1495.63 0.225508 0.112754 0.993623i \(-0.464033\pi\)
0.112754 + 0.993623i \(0.464033\pi\)
\(354\) 2712.37 0.407233
\(355\) −1288.78 −0.192679
\(356\) −4767.94 −0.709832
\(357\) 18620.4 2.76050
\(358\) −6410.61 −0.946400
\(359\) 319.114 0.0469142 0.0234571 0.999725i \(-0.492533\pi\)
0.0234571 + 0.999725i \(0.492533\pi\)
\(360\) 3265.90 0.478134
\(361\) 361.000 0.0526316
\(362\) −8353.63 −1.21286
\(363\) −901.677 −0.130374
\(364\) 3797.15 0.546772
\(365\) −2720.74 −0.390165
\(366\) 2620.83 0.374298
\(367\) −4571.59 −0.650231 −0.325116 0.945674i \(-0.605403\pi\)
−0.325116 + 0.945674i \(0.605403\pi\)
\(368\) 61.0057 0.00864169
\(369\) 7946.07 1.12102
\(370\) 3599.46 0.505749
\(371\) −948.636 −0.132751
\(372\) −272.688 −0.0380060
\(373\) −3209.95 −0.445590 −0.222795 0.974865i \(-0.571518\pi\)
−0.222795 + 0.974865i \(0.571518\pi\)
\(374\) −2347.16 −0.324515
\(375\) 931.485 0.128271
\(376\) −9375.55 −1.28592
\(377\) 54.8442 0.00749237
\(378\) 427.150 0.0581223
\(379\) −12645.1 −1.71381 −0.856905 0.515475i \(-0.827616\pi\)
−0.856905 + 0.515475i \(0.827616\pi\)
\(380\) 456.171 0.0615818
\(381\) −7951.33 −1.06918
\(382\) −7882.09 −1.05571
\(383\) 4590.06 0.612379 0.306189 0.951971i \(-0.400946\pi\)
0.306189 + 0.951971i \(0.400946\pi\)
\(384\) 6122.33 0.813616
\(385\) −1151.83 −0.152475
\(386\) −1090.54 −0.143801
\(387\) −6525.42 −0.857121
\(388\) −5894.66 −0.771278
\(389\) 8744.77 1.13979 0.569894 0.821718i \(-0.306984\pi\)
0.569894 + 0.821718i \(0.306984\pi\)
\(390\) 2516.03 0.326677
\(391\) −2879.01 −0.372373
\(392\) −2188.32 −0.281956
\(393\) −15754.5 −2.02217
\(394\) 1554.76 0.198802
\(395\) −389.221 −0.0495793
\(396\) 1506.98 0.191233
\(397\) −6465.26 −0.817335 −0.408668 0.912683i \(-0.634007\pi\)
−0.408668 + 0.912683i \(0.634007\pi\)
\(398\) −2851.48 −0.359125
\(399\) 2965.14 0.372037
\(400\) −63.2068 −0.00790085
\(401\) −123.393 −0.0153664 −0.00768320 0.999970i \(-0.502446\pi\)
−0.00768320 + 0.999970i \(0.502446\pi\)
\(402\) 1081.97 0.134239
\(403\) −287.755 −0.0355685
\(404\) 2891.12 0.356036
\(405\) 3426.67 0.420426
\(406\) −54.3980 −0.00664958
\(407\) 4428.00 0.539282
\(408\) 20355.7 2.47000
\(409\) −13319.8 −1.61033 −0.805163 0.593054i \(-0.797922\pi\)
−0.805163 + 0.593054i \(0.797922\pi\)
\(410\) −2490.38 −0.299978
\(411\) −5490.00 −0.658885
\(412\) 3105.25 0.371322
\(413\) 4262.42 0.507845
\(414\) −1231.14 −0.146153
\(415\) 4096.62 0.484566
\(416\) 6745.05 0.794960
\(417\) 12724.0 1.49424
\(418\) −373.765 −0.0437355
\(419\) 3291.83 0.383810 0.191905 0.981413i \(-0.438533\pi\)
0.191905 + 0.981413i \(0.438533\pi\)
\(420\) 3746.85 0.435304
\(421\) −5041.47 −0.583626 −0.291813 0.956475i \(-0.594258\pi\)
−0.291813 + 0.956475i \(0.594258\pi\)
\(422\) −5900.98 −0.680700
\(423\) 11683.8 1.34299
\(424\) −1037.04 −0.118781
\(425\) 2982.89 0.340450
\(426\) −3434.99 −0.390671
\(427\) 4118.58 0.466773
\(428\) 2002.91 0.226202
\(429\) 3095.18 0.348337
\(430\) 2045.13 0.229361
\(431\) −1674.46 −0.187137 −0.0935684 0.995613i \(-0.529827\pi\)
−0.0935684 + 0.995613i \(0.529827\pi\)
\(432\) 28.8353 0.00321144
\(433\) −2752.16 −0.305451 −0.152726 0.988269i \(-0.548805\pi\)
−0.152726 + 0.988269i \(0.548805\pi\)
\(434\) 285.414 0.0315675
\(435\) 54.1178 0.00596494
\(436\) −2595.04 −0.285046
\(437\) −458.459 −0.0501855
\(438\) −7251.63 −0.791088
\(439\) 3465.38 0.376751 0.188375 0.982097i \(-0.439678\pi\)
0.188375 + 0.982097i \(0.439678\pi\)
\(440\) −1259.18 −0.136429
\(441\) 2727.07 0.294468
\(442\) 8057.06 0.867049
\(443\) −1779.53 −0.190853 −0.0954267 0.995436i \(-0.530422\pi\)
−0.0954267 + 0.995436i \(0.530422\pi\)
\(444\) −14404.1 −1.53961
\(445\) −4964.74 −0.528879
\(446\) −5237.25 −0.556033
\(447\) 2928.88 0.309913
\(448\) −7113.75 −0.750208
\(449\) 1657.89 0.174255 0.0871275 0.996197i \(-0.472231\pi\)
0.0871275 + 0.996197i \(0.472231\pi\)
\(450\) 1275.56 0.133624
\(451\) −3063.63 −0.319868
\(452\) 1764.15 0.183581
\(453\) 22190.1 2.30150
\(454\) −8786.39 −0.908294
\(455\) 3953.88 0.407386
\(456\) 3241.48 0.332886
\(457\) −2508.32 −0.256749 −0.128374 0.991726i \(-0.540976\pi\)
−0.128374 + 0.991726i \(0.540976\pi\)
\(458\) 9388.38 0.957839
\(459\) −1360.81 −0.138382
\(460\) −579.323 −0.0587198
\(461\) −7503.96 −0.758122 −0.379061 0.925372i \(-0.623753\pi\)
−0.379061 + 0.925372i \(0.623753\pi\)
\(462\) −3069.99 −0.309154
\(463\) −12437.1 −1.24839 −0.624193 0.781271i \(-0.714572\pi\)
−0.624193 + 0.781271i \(0.714572\pi\)
\(464\) −3.67221 −0.000367410 0
\(465\) −283.943 −0.0283173
\(466\) −11746.1 −1.16766
\(467\) −8190.30 −0.811567 −0.405784 0.913969i \(-0.633001\pi\)
−0.405784 + 0.913969i \(0.633001\pi\)
\(468\) −5172.98 −0.510943
\(469\) 1700.30 0.167404
\(470\) −3661.81 −0.359376
\(471\) −17572.0 −1.71905
\(472\) 4659.65 0.454402
\(473\) 2515.89 0.244568
\(474\) −1037.40 −0.100526
\(475\) 475.000 0.0458831
\(476\) 11998.5 1.15536
\(477\) 1292.36 0.124052
\(478\) 11195.6 1.07129
\(479\) −12906.5 −1.23113 −0.615567 0.788085i \(-0.711073\pi\)
−0.615567 + 0.788085i \(0.711073\pi\)
\(480\) 6655.70 0.632895
\(481\) −15199.9 −1.44087
\(482\) 3778.91 0.357105
\(483\) −3765.64 −0.354747
\(484\) −581.018 −0.0545659
\(485\) −6137.96 −0.574661
\(486\) 9683.85 0.903845
\(487\) 12808.3 1.19179 0.595893 0.803064i \(-0.296798\pi\)
0.595893 + 0.803064i \(0.296798\pi\)
\(488\) 4502.41 0.417652
\(489\) −9499.47 −0.878488
\(490\) −854.690 −0.0787979
\(491\) −16694.4 −1.53443 −0.767217 0.641387i \(-0.778359\pi\)
−0.767217 + 0.641387i \(0.778359\pi\)
\(492\) 9965.83 0.913199
\(493\) 173.301 0.0158318
\(494\) 1283.02 0.116854
\(495\) 1569.18 0.142483
\(496\) 19.2672 0.00174420
\(497\) −5398.01 −0.487191
\(498\) 10918.8 0.982494
\(499\) 16314.1 1.46357 0.731785 0.681536i \(-0.238688\pi\)
0.731785 + 0.681536i \(0.238688\pi\)
\(500\) 600.225 0.0536858
\(501\) −17861.4 −1.59279
\(502\) −1734.00 −0.154168
\(503\) −9513.14 −0.843281 −0.421640 0.906763i \(-0.638545\pi\)
−0.421640 + 0.906763i \(0.638545\pi\)
\(504\) 13679.2 1.20897
\(505\) 3010.45 0.265274
\(506\) 474.670 0.0417029
\(507\) 5746.99 0.503418
\(508\) −5123.63 −0.447489
\(509\) −5737.09 −0.499592 −0.249796 0.968299i \(-0.580364\pi\)
−0.249796 + 0.968299i \(0.580364\pi\)
\(510\) 7950.34 0.690288
\(511\) −11395.8 −0.986535
\(512\) −914.689 −0.0789530
\(513\) −216.698 −0.0186500
\(514\) −1701.74 −0.146032
\(515\) 3233.42 0.276663
\(516\) −8184.07 −0.698224
\(517\) −4504.70 −0.383204
\(518\) 15076.3 1.27879
\(519\) −27629.5 −2.33680
\(520\) 4322.36 0.364515
\(521\) −14832.1 −1.24723 −0.623614 0.781732i \(-0.714336\pi\)
−0.623614 + 0.781732i \(0.714336\pi\)
\(522\) 74.1082 0.00621384
\(523\) −11485.4 −0.960269 −0.480134 0.877195i \(-0.659412\pi\)
−0.480134 + 0.877195i \(0.659412\pi\)
\(524\) −10151.8 −0.846345
\(525\) 3901.51 0.324335
\(526\) 11265.1 0.933807
\(527\) −909.270 −0.0751583
\(528\) −207.244 −0.0170817
\(529\) −11584.8 −0.952147
\(530\) −405.038 −0.0331957
\(531\) −5806.83 −0.474567
\(532\) 1910.66 0.155710
\(533\) 10516.5 0.854633
\(534\) −13232.6 −1.07234
\(535\) 2085.58 0.168537
\(536\) 1858.75 0.149787
\(537\) 26712.4 2.14660
\(538\) 9075.30 0.727256
\(539\) −1051.43 −0.0840225
\(540\) −273.827 −0.0218215
\(541\) −13934.3 −1.10736 −0.553679 0.832730i \(-0.686777\pi\)
−0.553679 + 0.832730i \(0.686777\pi\)
\(542\) −15082.7 −1.19531
\(543\) 34808.8 2.75099
\(544\) 21313.5 1.67980
\(545\) −2702.16 −0.212381
\(546\) 10538.3 0.826006
\(547\) 11970.4 0.935681 0.467841 0.883813i \(-0.345032\pi\)
0.467841 + 0.883813i \(0.345032\pi\)
\(548\) −3537.62 −0.275766
\(549\) −5610.87 −0.436186
\(550\) −491.796 −0.0381278
\(551\) 27.5967 0.00213368
\(552\) −4116.58 −0.317415
\(553\) −1630.24 −0.125362
\(554\) −6825.29 −0.523427
\(555\) −14998.6 −1.14713
\(556\) 8199.05 0.625391
\(557\) −868.155 −0.0660411 −0.0330205 0.999455i \(-0.510513\pi\)
−0.0330205 + 0.999455i \(0.510513\pi\)
\(558\) −388.828 −0.0294990
\(559\) −8636.27 −0.653445
\(560\) −264.740 −0.0199774
\(561\) 9780.38 0.736057
\(562\) −7328.09 −0.550030
\(563\) −4001.26 −0.299526 −0.149763 0.988722i \(-0.547851\pi\)
−0.149763 + 0.988722i \(0.547851\pi\)
\(564\) 14653.6 1.09402
\(565\) 1836.96 0.136782
\(566\) 10501.1 0.779846
\(567\) 14352.5 1.06305
\(568\) −5901.07 −0.435922
\(569\) 6500.31 0.478923 0.239461 0.970906i \(-0.423029\pi\)
0.239461 + 0.970906i \(0.423029\pi\)
\(570\) 1266.02 0.0930314
\(571\) −7316.14 −0.536202 −0.268101 0.963391i \(-0.586396\pi\)
−0.268101 + 0.963391i \(0.586396\pi\)
\(572\) 1994.45 0.145791
\(573\) 32843.9 2.39454
\(574\) −10430.9 −0.758498
\(575\) −603.235 −0.0437507
\(576\) 9691.29 0.701048
\(577\) −4347.60 −0.313679 −0.156839 0.987624i \(-0.550131\pi\)
−0.156839 + 0.987624i \(0.550131\pi\)
\(578\) 16673.1 1.19985
\(579\) 4544.18 0.326165
\(580\) 34.8721 0.00249653
\(581\) 17158.6 1.22523
\(582\) −16359.6 −1.16517
\(583\) −498.271 −0.0353967
\(584\) −12457.8 −0.882717
\(585\) −5386.50 −0.380691
\(586\) −5440.70 −0.383538
\(587\) 898.208 0.0631567 0.0315784 0.999501i \(-0.489947\pi\)
0.0315784 + 0.999501i \(0.489947\pi\)
\(588\) 3420.24 0.239878
\(589\) −144.794 −0.0101292
\(590\) 1819.92 0.126991
\(591\) −6478.55 −0.450917
\(592\) 1017.74 0.0706571
\(593\) −23375.2 −1.61873 −0.809364 0.587307i \(-0.800188\pi\)
−0.809364 + 0.587307i \(0.800188\pi\)
\(594\) 224.361 0.0154977
\(595\) 12493.8 0.860831
\(596\) 1887.30 0.129709
\(597\) 11881.8 0.814557
\(598\) −1629.40 −0.111423
\(599\) 18358.9 1.25229 0.626147 0.779705i \(-0.284631\pi\)
0.626147 + 0.779705i \(0.284631\pi\)
\(600\) 4265.10 0.290204
\(601\) 12042.5 0.817342 0.408671 0.912682i \(-0.365992\pi\)
0.408671 + 0.912682i \(0.365992\pi\)
\(602\) 8566.01 0.579941
\(603\) −2316.37 −0.156434
\(604\) 14298.7 0.963257
\(605\) −605.000 −0.0406558
\(606\) 8023.80 0.537862
\(607\) −22486.3 −1.50361 −0.751804 0.659387i \(-0.770816\pi\)
−0.751804 + 0.659387i \(0.770816\pi\)
\(608\) 3394.00 0.226389
\(609\) 226.671 0.0150824
\(610\) 1758.50 0.116721
\(611\) 15463.2 1.02385
\(612\) −16346.0 −1.07965
\(613\) 2950.06 0.194375 0.0971874 0.995266i \(-0.469015\pi\)
0.0971874 + 0.995266i \(0.469015\pi\)
\(614\) 12044.8 0.791677
\(615\) 10377.2 0.680403
\(616\) −5274.03 −0.344962
\(617\) 7637.57 0.498342 0.249171 0.968459i \(-0.419842\pi\)
0.249171 + 0.968459i \(0.419842\pi\)
\(618\) 8618.08 0.560955
\(619\) 790.824 0.0513504 0.0256752 0.999670i \(-0.491826\pi\)
0.0256752 + 0.999670i \(0.491826\pi\)
\(620\) −182.966 −0.0118518
\(621\) 275.200 0.0177832
\(622\) 9299.92 0.599506
\(623\) −20794.7 −1.33727
\(624\) 711.405 0.0456394
\(625\) 625.000 0.0400000
\(626\) 9346.94 0.596772
\(627\) 1557.44 0.0991998
\(628\) −11322.9 −0.719481
\(629\) −48029.9 −3.04464
\(630\) 5342.67 0.337869
\(631\) 11969.8 0.755164 0.377582 0.925976i \(-0.376756\pi\)
0.377582 + 0.925976i \(0.376756\pi\)
\(632\) −1782.17 −0.112169
\(633\) 24588.8 1.54395
\(634\) 11402.8 0.714296
\(635\) −5335.11 −0.333413
\(636\) 1620.85 0.101055
\(637\) 3609.22 0.224494
\(638\) −28.5726 −0.00177304
\(639\) 7353.89 0.455266
\(640\) 4107.91 0.253718
\(641\) −23883.4 −1.47167 −0.735833 0.677163i \(-0.763209\pi\)
−0.735833 + 0.677163i \(0.763209\pi\)
\(642\) 5558.73 0.341722
\(643\) −10055.6 −0.616725 −0.308363 0.951269i \(-0.599781\pi\)
−0.308363 + 0.951269i \(0.599781\pi\)
\(644\) −2426.49 −0.148473
\(645\) −8521.87 −0.520230
\(646\) 4054.18 0.246919
\(647\) 22455.5 1.36448 0.682239 0.731129i \(-0.261006\pi\)
0.682239 + 0.731129i \(0.261006\pi\)
\(648\) 15690.1 0.951182
\(649\) 2238.84 0.135411
\(650\) 1688.18 0.101871
\(651\) −1189.29 −0.0716006
\(652\) −6121.22 −0.367677
\(653\) −9295.71 −0.557074 −0.278537 0.960425i \(-0.589849\pi\)
−0.278537 + 0.960425i \(0.589849\pi\)
\(654\) −7202.09 −0.430618
\(655\) −10570.9 −0.630591
\(656\) −704.153 −0.0419094
\(657\) 15524.8 0.921889
\(658\) −15337.4 −0.908685
\(659\) −30903.1 −1.82673 −0.913365 0.407142i \(-0.866525\pi\)
−0.913365 + 0.407142i \(0.866525\pi\)
\(660\) 1968.03 0.116069
\(661\) 8031.50 0.472601 0.236300 0.971680i \(-0.424065\pi\)
0.236300 + 0.971680i \(0.424065\pi\)
\(662\) −8826.58 −0.518210
\(663\) −33573.0 −1.96662
\(664\) 18757.7 1.09629
\(665\) 1989.53 0.116016
\(666\) −20538.9 −1.19499
\(667\) −35.0470 −0.00203452
\(668\) −11509.4 −0.666637
\(669\) 21823.1 1.26118
\(670\) 725.974 0.0418609
\(671\) 2163.28 0.124460
\(672\) 27877.3 1.60028
\(673\) 2762.96 0.158253 0.0791265 0.996865i \(-0.474787\pi\)
0.0791265 + 0.996865i \(0.474787\pi\)
\(674\) −9115.45 −0.520941
\(675\) −285.129 −0.0162587
\(676\) 3703.22 0.210697
\(677\) −12500.7 −0.709662 −0.354831 0.934930i \(-0.615462\pi\)
−0.354831 + 0.934930i \(0.615462\pi\)
\(678\) 4896.08 0.277335
\(679\) −25708.7 −1.45304
\(680\) 13658.1 0.770242
\(681\) 36612.0 2.06017
\(682\) 149.914 0.00841714
\(683\) 24987.8 1.39990 0.699951 0.714191i \(-0.253205\pi\)
0.699951 + 0.714191i \(0.253205\pi\)
\(684\) −2602.96 −0.145507
\(685\) −3683.63 −0.205466
\(686\) 9266.30 0.515728
\(687\) −39120.4 −2.17254
\(688\) 578.260 0.0320435
\(689\) 1710.41 0.0945740
\(690\) −1607.81 −0.0887078
\(691\) −10223.2 −0.562823 −0.281411 0.959587i \(-0.590803\pi\)
−0.281411 + 0.959587i \(0.590803\pi\)
\(692\) −17803.7 −0.978030
\(693\) 6572.47 0.360271
\(694\) 1707.25 0.0933807
\(695\) 8537.47 0.465964
\(696\) 247.796 0.0134952
\(697\) 33230.8 1.80589
\(698\) 7103.72 0.385215
\(699\) 48944.9 2.64845
\(700\) 2514.03 0.135745
\(701\) −6778.24 −0.365208 −0.182604 0.983187i \(-0.558453\pi\)
−0.182604 + 0.983187i \(0.558453\pi\)
\(702\) −770.160 −0.0414072
\(703\) −7648.36 −0.410332
\(704\) −3736.50 −0.200035
\(705\) 15258.4 0.815127
\(706\) 2674.71 0.142584
\(707\) 12609.2 0.670748
\(708\) −7282.83 −0.386590
\(709\) 35011.7 1.85457 0.927285 0.374355i \(-0.122136\pi\)
0.927285 + 0.374355i \(0.122136\pi\)
\(710\) −2304.78 −0.121827
\(711\) 2220.93 0.117147
\(712\) −22732.6 −1.19655
\(713\) 183.884 0.00965847
\(714\) 33299.8 1.74540
\(715\) 2076.78 0.108625
\(716\) 17212.8 0.898424
\(717\) −46651.2 −2.42987
\(718\) 570.688 0.0296628
\(719\) −25327.1 −1.31369 −0.656844 0.754026i \(-0.728109\pi\)
−0.656844 + 0.754026i \(0.728109\pi\)
\(720\) 360.664 0.0186683
\(721\) 13543.1 0.699545
\(722\) 645.595 0.0332778
\(723\) −15746.4 −0.809977
\(724\) 22429.9 1.15138
\(725\) 36.3115 0.00186010
\(726\) −1612.52 −0.0824326
\(727\) −8027.09 −0.409503 −0.204751 0.978814i \(-0.565639\pi\)
−0.204751 + 0.978814i \(0.565639\pi\)
\(728\) 18104.1 0.921680
\(729\) −21847.6 −1.10998
\(730\) −4865.64 −0.246692
\(731\) −27289.5 −1.38077
\(732\) −7037.06 −0.355324
\(733\) 23016.3 1.15979 0.579895 0.814691i \(-0.303094\pi\)
0.579895 + 0.814691i \(0.303094\pi\)
\(734\) −8175.60 −0.411127
\(735\) 3561.41 0.178727
\(736\) −4310.27 −0.215868
\(737\) 893.081 0.0446365
\(738\) 14210.4 0.708795
\(739\) −36678.1 −1.82575 −0.912874 0.408242i \(-0.866142\pi\)
−0.912874 + 0.408242i \(0.866142\pi\)
\(740\) −9664.71 −0.480111
\(741\) −5346.22 −0.265045
\(742\) −1696.49 −0.0839357
\(743\) −17081.1 −0.843397 −0.421698 0.906736i \(-0.638566\pi\)
−0.421698 + 0.906736i \(0.638566\pi\)
\(744\) −1300.13 −0.0640658
\(745\) 1965.20 0.0966432
\(746\) −5740.52 −0.281736
\(747\) −23375.7 −1.14494
\(748\) 6302.23 0.308064
\(749\) 8735.41 0.426148
\(750\) 1665.82 0.0811029
\(751\) −13376.4 −0.649948 −0.324974 0.945723i \(-0.605355\pi\)
−0.324974 + 0.945723i \(0.605355\pi\)
\(752\) −1035.37 −0.0502076
\(753\) 7225.41 0.349679
\(754\) 98.0807 0.00473725
\(755\) 14888.9 0.717700
\(756\) −1146.92 −0.0551759
\(757\) 27388.9 1.31501 0.657507 0.753448i \(-0.271611\pi\)
0.657507 + 0.753448i \(0.271611\pi\)
\(758\) −22613.8 −1.08360
\(759\) −1977.90 −0.0945894
\(760\) 2174.94 0.103807
\(761\) −7526.75 −0.358534 −0.179267 0.983800i \(-0.557373\pi\)
−0.179267 + 0.983800i \(0.557373\pi\)
\(762\) −14219.8 −0.676020
\(763\) −11317.9 −0.537007
\(764\) 21163.8 1.00220
\(765\) −17020.7 −0.804423
\(766\) 8208.64 0.387193
\(767\) −7685.23 −0.361796
\(768\) 31199.0 1.46588
\(769\) −30913.3 −1.44963 −0.724814 0.688945i \(-0.758074\pi\)
−0.724814 + 0.688945i \(0.758074\pi\)
\(770\) −2059.88 −0.0964064
\(771\) 7090.98 0.331226
\(772\) 2928.15 0.136511
\(773\) 13304.9 0.619072 0.309536 0.950888i \(-0.399826\pi\)
0.309536 + 0.950888i \(0.399826\pi\)
\(774\) −11669.7 −0.541938
\(775\) −190.518 −0.00883046
\(776\) −28104.6 −1.30013
\(777\) −62821.3 −2.90052
\(778\) 15638.7 0.720662
\(779\) 5291.72 0.243383
\(780\) −6755.65 −0.310117
\(781\) −2835.31 −0.129904
\(782\) −5148.69 −0.235443
\(783\) −16.5655 −0.000756071 0
\(784\) −241.663 −0.0110087
\(785\) −11790.3 −0.536068
\(786\) −28174.6 −1.27857
\(787\) 36927.8 1.67260 0.836298 0.548275i \(-0.184715\pi\)
0.836298 + 0.548275i \(0.184715\pi\)
\(788\) −4174.61 −0.188724
\(789\) −46940.6 −2.11804
\(790\) −696.063 −0.0313478
\(791\) 7694.08 0.345854
\(792\) 7184.99 0.322358
\(793\) −7425.88 −0.332536
\(794\) −11562.2 −0.516783
\(795\) 1687.75 0.0752937
\(796\) 7656.35 0.340920
\(797\) −20336.3 −0.903825 −0.451912 0.892062i \(-0.649258\pi\)
−0.451912 + 0.892062i \(0.649258\pi\)
\(798\) 5302.72 0.235231
\(799\) 48861.8 2.16346
\(800\) 4465.79 0.197362
\(801\) 28329.3 1.24965
\(802\) −220.669 −0.00971583
\(803\) −5985.63 −0.263049
\(804\) −2905.15 −0.127434
\(805\) −2526.64 −0.110624
\(806\) −514.607 −0.0224892
\(807\) −37815.9 −1.64954
\(808\) 13784.3 0.600162
\(809\) −13172.1 −0.572444 −0.286222 0.958163i \(-0.592399\pi\)
−0.286222 + 0.958163i \(0.592399\pi\)
\(810\) 6128.09 0.265826
\(811\) 5941.27 0.257246 0.128623 0.991694i \(-0.458944\pi\)
0.128623 + 0.991694i \(0.458944\pi\)
\(812\) 146.061 0.00631249
\(813\) 62848.2 2.71117
\(814\) 7918.81 0.340976
\(815\) −6373.87 −0.273947
\(816\) 2247.95 0.0964387
\(817\) −4345.63 −0.186089
\(818\) −23820.5 −1.01817
\(819\) −22561.2 −0.962581
\(820\) 6686.79 0.284772
\(821\) 45085.3 1.91655 0.958276 0.285844i \(-0.0922739\pi\)
0.958276 + 0.285844i \(0.0922739\pi\)
\(822\) −9818.04 −0.416598
\(823\) 35942.4 1.52233 0.761163 0.648560i \(-0.224629\pi\)
0.761163 + 0.648560i \(0.224629\pi\)
\(824\) 14805.3 0.625929
\(825\) 2049.27 0.0864804
\(826\) 7622.70 0.321099
\(827\) 2665.67 0.112085 0.0560426 0.998428i \(-0.482152\pi\)
0.0560426 + 0.998428i \(0.482152\pi\)
\(828\) 3305.68 0.138744
\(829\) −30744.8 −1.28807 −0.644036 0.764995i \(-0.722741\pi\)
−0.644036 + 0.764995i \(0.722741\pi\)
\(830\) 7326.19 0.306380
\(831\) 28440.3 1.18722
\(832\) 12826.2 0.534459
\(833\) 11404.7 0.474368
\(834\) 22755.0 0.944776
\(835\) −11984.5 −0.496696
\(836\) 1003.58 0.0415185
\(837\) 86.9155 0.00358929
\(838\) 5886.95 0.242675
\(839\) 23177.1 0.953711 0.476855 0.878982i \(-0.341777\pi\)
0.476855 + 0.878982i \(0.341777\pi\)
\(840\) 17864.3 0.733782
\(841\) −24386.9 −0.999914
\(842\) −9015.92 −0.369013
\(843\) 30535.4 1.24756
\(844\) 15844.4 0.646193
\(845\) 3856.07 0.156986
\(846\) 20894.6 0.849140
\(847\) −2534.03 −0.102798
\(848\) −114.524 −0.00463771
\(849\) −43756.9 −1.76883
\(850\) 5334.45 0.215259
\(851\) 9713.18 0.391262
\(852\) 9223.11 0.370867
\(853\) 4953.65 0.198839 0.0994195 0.995046i \(-0.468301\pi\)
0.0994195 + 0.995046i \(0.468301\pi\)
\(854\) 7365.46 0.295130
\(855\) −2710.40 −0.108414
\(856\) 9549.50 0.381303
\(857\) 34235.9 1.36462 0.682308 0.731065i \(-0.260976\pi\)
0.682308 + 0.731065i \(0.260976\pi\)
\(858\) 5535.26 0.220246
\(859\) −30624.0 −1.21639 −0.608195 0.793788i \(-0.708106\pi\)
−0.608195 + 0.793788i \(0.708106\pi\)
\(860\) −5491.28 −0.217734
\(861\) 43464.6 1.72041
\(862\) −2994.52 −0.118322
\(863\) −9692.26 −0.382304 −0.191152 0.981560i \(-0.561222\pi\)
−0.191152 + 0.981560i \(0.561222\pi\)
\(864\) −2037.32 −0.0802211
\(865\) −18538.6 −0.728707
\(866\) −4921.82 −0.193130
\(867\) −69475.3 −2.72146
\(868\) −766.349 −0.0299673
\(869\) −856.285 −0.0334263
\(870\) 96.7815 0.00377149
\(871\) −3065.67 −0.119261
\(872\) −12372.7 −0.480496
\(873\) 35023.8 1.35782
\(874\) −819.885 −0.0317312
\(875\) 2617.80 0.101140
\(876\) 19471.0 0.750985
\(877\) −11304.4 −0.435258 −0.217629 0.976032i \(-0.569832\pi\)
−0.217629 + 0.976032i \(0.569832\pi\)
\(878\) 6197.31 0.238211
\(879\) 22670.9 0.869931
\(880\) −139.055 −0.00532675
\(881\) 48137.7 1.84086 0.920431 0.390904i \(-0.127838\pi\)
0.920431 + 0.390904i \(0.127838\pi\)
\(882\) 4876.95 0.186185
\(883\) −17405.5 −0.663355 −0.331677 0.943393i \(-0.607615\pi\)
−0.331677 + 0.943393i \(0.607615\pi\)
\(884\) −21633.6 −0.823095
\(885\) −7583.43 −0.288039
\(886\) −3182.42 −0.120672
\(887\) −9812.61 −0.371449 −0.185725 0.982602i \(-0.559463\pi\)
−0.185725 + 0.982602i \(0.559463\pi\)
\(888\) −68675.9 −2.59528
\(889\) −22346.0 −0.843039
\(890\) −8878.69 −0.334398
\(891\) 7538.67 0.283451
\(892\) 14062.2 0.527846
\(893\) 7780.84 0.291574
\(894\) 5237.86 0.195951
\(895\) 17923.2 0.669395
\(896\) 17205.9 0.641527
\(897\) 6789.53 0.252727
\(898\) 2964.88 0.110177
\(899\) −11.0688 −0.000410639 0
\(900\) −3424.95 −0.126850
\(901\) 5404.68 0.199840
\(902\) −5478.84 −0.202245
\(903\) −35693.7 −1.31541
\(904\) 8411.13 0.309458
\(905\) 23355.7 0.857867
\(906\) 39683.7 1.45519
\(907\) −15424.5 −0.564677 −0.282339 0.959315i \(-0.591110\pi\)
−0.282339 + 0.959315i \(0.591110\pi\)
\(908\) 23591.9 0.862250
\(909\) −17177.9 −0.626795
\(910\) 7070.93 0.257581
\(911\) −10631.5 −0.386650 −0.193325 0.981135i \(-0.561927\pi\)
−0.193325 + 0.981135i \(0.561927\pi\)
\(912\) 357.967 0.0129972
\(913\) 9012.56 0.326695
\(914\) −4485.75 −0.162336
\(915\) −7327.51 −0.264743
\(916\) −25208.2 −0.909283
\(917\) −44275.8 −1.59446
\(918\) −2433.61 −0.0874958
\(919\) −26902.6 −0.965654 −0.482827 0.875716i \(-0.660390\pi\)
−0.482827 + 0.875716i \(0.660390\pi\)
\(920\) −2762.11 −0.0989826
\(921\) −50189.6 −1.79566
\(922\) −13419.7 −0.479343
\(923\) 9732.73 0.347082
\(924\) 8243.08 0.293482
\(925\) −10063.6 −0.357719
\(926\) −22241.9 −0.789326
\(927\) −18450.2 −0.653705
\(928\) 259.455 0.00917783
\(929\) −40771.9 −1.43992 −0.719959 0.694017i \(-0.755839\pi\)
−0.719959 + 0.694017i \(0.755839\pi\)
\(930\) −507.790 −0.0179044
\(931\) 1816.10 0.0639315
\(932\) 31538.8 1.10846
\(933\) −38751.8 −1.35978
\(934\) −14647.1 −0.513135
\(935\) 6562.35 0.229531
\(936\) −24663.8 −0.861285
\(937\) 39610.1 1.38101 0.690504 0.723329i \(-0.257389\pi\)
0.690504 + 0.723329i \(0.257389\pi\)
\(938\) 3040.73 0.105846
\(939\) −38947.8 −1.35358
\(940\) 9832.12 0.341158
\(941\) 1106.42 0.0383298 0.0191649 0.999816i \(-0.493899\pi\)
0.0191649 + 0.999816i \(0.493899\pi\)
\(942\) −31424.8 −1.08692
\(943\) −6720.32 −0.232072
\(944\) 514.581 0.0177417
\(945\) −1194.26 −0.0411103
\(946\) 4499.30 0.154635
\(947\) −38680.7 −1.32730 −0.663650 0.748043i \(-0.730994\pi\)
−0.663650 + 0.748043i \(0.730994\pi\)
\(948\) 2785.45 0.0954297
\(949\) 20546.8 0.702822
\(950\) 849.466 0.0290109
\(951\) −47514.4 −1.62015
\(952\) 57206.7 1.94756
\(953\) −25521.3 −0.867489 −0.433745 0.901036i \(-0.642808\pi\)
−0.433745 + 0.901036i \(0.642808\pi\)
\(954\) 2311.19 0.0784355
\(955\) 22037.3 0.746713
\(956\) −30060.8 −1.01698
\(957\) 119.059 0.00402156
\(958\) −23081.3 −0.778418
\(959\) −15428.8 −0.519523
\(960\) 12656.3 0.425502
\(961\) −29732.9 −0.998051
\(962\) −27182.8 −0.911028
\(963\) −11900.5 −0.398224
\(964\) −10146.6 −0.339003
\(965\) 3049.02 0.101711
\(966\) −6734.29 −0.224298
\(967\) 16055.5 0.533931 0.266965 0.963706i \(-0.413979\pi\)
0.266965 + 0.963706i \(0.413979\pi\)
\(968\) −2770.19 −0.0919806
\(969\) −16893.4 −0.560055
\(970\) −10976.8 −0.363345
\(971\) −35027.9 −1.15767 −0.578836 0.815444i \(-0.696493\pi\)
−0.578836 + 0.815444i \(0.696493\pi\)
\(972\) −26001.6 −0.858026
\(973\) 35759.0 1.17819
\(974\) 22905.7 0.753539
\(975\) −7034.50 −0.231061
\(976\) 497.215 0.0163068
\(977\) 29736.9 0.973765 0.486882 0.873467i \(-0.338134\pi\)
0.486882 + 0.873467i \(0.338134\pi\)
\(978\) −16988.4 −0.555448
\(979\) −10922.4 −0.356570
\(980\) 2294.88 0.0748034
\(981\) 15418.8 0.501818
\(982\) −29855.4 −0.970188
\(983\) 8193.33 0.265846 0.132923 0.991126i \(-0.457564\pi\)
0.132923 + 0.991126i \(0.457564\pi\)
\(984\) 47515.2 1.53936
\(985\) −4346.92 −0.140614
\(986\) 309.923 0.0100101
\(987\) 63909.5 2.06105
\(988\) −3444.97 −0.110930
\(989\) 5518.82 0.177440
\(990\) 2806.24 0.0900891
\(991\) 54024.4 1.73173 0.865864 0.500280i \(-0.166770\pi\)
0.865864 + 0.500280i \(0.166770\pi\)
\(992\) −1361.30 −0.0435699
\(993\) 36779.5 1.17539
\(994\) −9653.54 −0.308040
\(995\) 7972.37 0.254011
\(996\) −29317.4 −0.932688
\(997\) −59848.2 −1.90111 −0.950557 0.310550i \(-0.899487\pi\)
−0.950557 + 0.310550i \(0.899487\pi\)
\(998\) 29175.4 0.925382
\(999\) 4591.09 0.145401
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 1045.4.a.c.1.15 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.4.a.c.1.15 20 1.1 even 1 trivial