Properties

Label 1045.4.a.b.1.18
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: \( x^{20} - 8 x^{19} - 82 x^{18} + 700 x^{17} + 2826 x^{16} - 25467 x^{15} - 53768 x^{14} + 498499 x^{13} + 623613 x^{12} - 5673747 x^{11} - 4539454 x^{10} + 37893109 x^{9} + \cdots + 17756160 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3}\cdot 7 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Root \(4.30367\) 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)
 
\(f(q)\) \(=\) \(q+3.30367 q^{2} -7.25904 q^{3} +2.91425 q^{4} +5.00000 q^{5} -23.9815 q^{6} -9.92986 q^{7} -16.8016 q^{8} +25.6936 q^{9} +O(q^{10})\) \(q+3.30367 q^{2} -7.25904 q^{3} +2.91425 q^{4} +5.00000 q^{5} -23.9815 q^{6} -9.92986 q^{7} -16.8016 q^{8} +25.6936 q^{9} +16.5184 q^{10} +11.0000 q^{11} -21.1547 q^{12} +57.0738 q^{13} -32.8050 q^{14} -36.2952 q^{15} -78.8212 q^{16} +50.0959 q^{17} +84.8833 q^{18} +19.0000 q^{19} +14.5713 q^{20} +72.0813 q^{21} +36.3404 q^{22} -40.7075 q^{23} +121.964 q^{24} +25.0000 q^{25} +188.553 q^{26} +9.48305 q^{27} -28.9381 q^{28} +99.7381 q^{29} -119.907 q^{30} -61.4620 q^{31} -125.986 q^{32} -79.8494 q^{33} +165.500 q^{34} -49.6493 q^{35} +74.8777 q^{36} -107.743 q^{37} +62.7698 q^{38} -414.301 q^{39} -84.0082 q^{40} +95.4636 q^{41} +238.133 q^{42} -480.111 q^{43} +32.0568 q^{44} +128.468 q^{45} -134.484 q^{46} -311.050 q^{47} +572.166 q^{48} -244.398 q^{49} +82.5918 q^{50} -363.648 q^{51} +166.328 q^{52} +193.574 q^{53} +31.3289 q^{54} +55.0000 q^{55} +166.838 q^{56} -137.922 q^{57} +329.502 q^{58} +341.118 q^{59} -105.773 q^{60} -408.667 q^{61} -203.050 q^{62} -255.134 q^{63} +214.352 q^{64} +285.369 q^{65} -263.796 q^{66} -520.416 q^{67} +145.992 q^{68} +295.497 q^{69} -164.025 q^{70} -881.595 q^{71} -431.695 q^{72} +1023.02 q^{73} -355.947 q^{74} -181.476 q^{75} +55.3708 q^{76} -109.229 q^{77} -1368.71 q^{78} -78.3320 q^{79} -394.106 q^{80} -762.566 q^{81} +315.380 q^{82} +902.858 q^{83} +210.063 q^{84} +250.479 q^{85} -1586.13 q^{86} -724.003 q^{87} -184.818 q^{88} -995.340 q^{89} +424.417 q^{90} -566.735 q^{91} -118.632 q^{92} +446.155 q^{93} -1027.61 q^{94} +95.0000 q^{95} +914.538 q^{96} -410.183 q^{97} -807.410 q^{98} +282.630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 12 q^{2} - 21 q^{3} + 72 q^{4} + 100 q^{5} - 45 q^{6} - 131 q^{7} - 108 q^{8} + 159 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 12 q^{2} - 21 q^{3} + 72 q^{4} + 100 q^{5} - 45 q^{6} - 131 q^{7} - 108 q^{8} + 159 q^{9} - 60 q^{10} + 220 q^{11} - 196 q^{12} - 223 q^{13} - 11 q^{14} - 105 q^{15} + 380 q^{16} - 471 q^{17} + 113 q^{18} + 380 q^{19} + 360 q^{20} - 57 q^{21} - 132 q^{22} - 653 q^{23} - 486 q^{24} + 500 q^{25} - 145 q^{26} - 177 q^{27} - 747 q^{28} + 51 q^{29} - 225 q^{30} - 90 q^{31} - 381 q^{32} - 231 q^{33} + 517 q^{34} - 655 q^{35} + 875 q^{36} - 96 q^{37} - 228 q^{38} + 97 q^{39} - 540 q^{40} - 1284 q^{41} - 638 q^{42} - 1592 q^{43} + 792 q^{44} + 795 q^{45} - 35 q^{46} - 2030 q^{47} - 1471 q^{48} + 765 q^{49} - 300 q^{50} - 185 q^{51} - 3242 q^{52} - 943 q^{53} - 730 q^{54} + 1100 q^{55} + 887 q^{56} - 399 q^{57} - 492 q^{58} - 515 q^{59} - 980 q^{60} + 446 q^{61} - 770 q^{62} - 3980 q^{63} + 2526 q^{64} - 1115 q^{65} - 495 q^{66} - 1719 q^{67} - 1808 q^{68} + 317 q^{69} - 55 q^{70} - 90 q^{71} + 1058 q^{72} - 3763 q^{73} - 1313 q^{74} - 525 q^{75} + 1368 q^{76} - 1441 q^{77} + 4286 q^{78} + 2 q^{79} + 1900 q^{80} + 308 q^{81} - 3830 q^{82} - 3436 q^{83} + 5734 q^{84} - 2355 q^{85} + 1922 q^{86} - 2719 q^{87} - 1188 q^{88} + 1700 q^{89} + 565 q^{90} + 2007 q^{91} - 3980 q^{92} - 2276 q^{93} + 2700 q^{94} + 1900 q^{95} - 6252 q^{96} - 1956 q^{97} - 2356 q^{98} + 1749 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.30367 1.16802 0.584012 0.811745i \(-0.301482\pi\)
0.584012 + 0.811745i \(0.301482\pi\)
\(3\) −7.25904 −1.39700 −0.698501 0.715609i \(-0.746149\pi\)
−0.698501 + 0.715609i \(0.746149\pi\)
\(4\) 2.91425 0.364282
\(5\) 5.00000 0.447214
\(6\) −23.9815 −1.63173
\(7\) −9.92986 −0.536162 −0.268081 0.963396i \(-0.586390\pi\)
−0.268081 + 0.963396i \(0.586390\pi\)
\(8\) −16.8016 −0.742535
\(9\) 25.6936 0.951616
\(10\) 16.5184 0.522357
\(11\) 11.0000 0.301511
\(12\) −21.1547 −0.508902
\(13\) 57.0738 1.21765 0.608824 0.793305i \(-0.291642\pi\)
0.608824 + 0.793305i \(0.291642\pi\)
\(14\) −32.8050 −0.626251
\(15\) −36.2952 −0.624758
\(16\) −78.8212 −1.23158
\(17\) 50.0959 0.714708 0.357354 0.933969i \(-0.383679\pi\)
0.357354 + 0.933969i \(0.383679\pi\)
\(18\) 84.8833 1.11151
\(19\) 19.0000 0.229416
\(20\) 14.5713 0.162912
\(21\) 72.0813 0.749020
\(22\) 36.3404 0.352173
\(23\) −40.7075 −0.369048 −0.184524 0.982828i \(-0.559074\pi\)
−0.184524 + 0.982828i \(0.559074\pi\)
\(24\) 121.964 1.03732
\(25\) 25.0000 0.200000
\(26\) 188.553 1.42224
\(27\) 9.48305 0.0675931
\(28\) −28.9381 −0.195314
\(29\) 99.7381 0.638652 0.319326 0.947645i \(-0.396544\pi\)
0.319326 + 0.947645i \(0.396544\pi\)
\(30\) −119.907 −0.729733
\(31\) −61.4620 −0.356093 −0.178047 0.984022i \(-0.556978\pi\)
−0.178047 + 0.984022i \(0.556978\pi\)
\(32\) −125.986 −0.695982
\(33\) −79.8494 −0.421212
\(34\) 165.500 0.834797
\(35\) −49.6493 −0.239779
\(36\) 74.8777 0.346656
\(37\) −107.743 −0.478724 −0.239362 0.970930i \(-0.576938\pi\)
−0.239362 + 0.970930i \(0.576938\pi\)
\(38\) 62.7698 0.267963
\(39\) −414.301 −1.70106
\(40\) −84.0082 −0.332072
\(41\) 95.4636 0.363632 0.181816 0.983333i \(-0.441803\pi\)
0.181816 + 0.983333i \(0.441803\pi\)
\(42\) 238.133 0.874874
\(43\) −480.111 −1.70270 −0.851351 0.524596i \(-0.824216\pi\)
−0.851351 + 0.524596i \(0.824216\pi\)
\(44\) 32.0568 0.109835
\(45\) 128.468 0.425575
\(46\) −134.484 −0.431057
\(47\) −311.050 −0.965346 −0.482673 0.875801i \(-0.660334\pi\)
−0.482673 + 0.875801i \(0.660334\pi\)
\(48\) 572.166 1.72052
\(49\) −244.398 −0.712530
\(50\) 82.5918 0.233605
\(51\) −363.648 −0.998449
\(52\) 166.328 0.443567
\(53\) 193.574 0.501688 0.250844 0.968028i \(-0.419292\pi\)
0.250844 + 0.968028i \(0.419292\pi\)
\(54\) 31.3289 0.0789504
\(55\) 55.0000 0.134840
\(56\) 166.838 0.398119
\(57\) −137.922 −0.320494
\(58\) 329.502 0.745961
\(59\) 341.118 0.752707 0.376354 0.926476i \(-0.377178\pi\)
0.376354 + 0.926476i \(0.377178\pi\)
\(60\) −105.773 −0.227588
\(61\) −408.667 −0.857777 −0.428889 0.903357i \(-0.641095\pi\)
−0.428889 + 0.903357i \(0.641095\pi\)
\(62\) −203.050 −0.415926
\(63\) −255.134 −0.510220
\(64\) 214.352 0.418656
\(65\) 285.369 0.544549
\(66\) −263.796 −0.491986
\(67\) −520.416 −0.948940 −0.474470 0.880272i \(-0.657360\pi\)
−0.474470 + 0.880272i \(0.657360\pi\)
\(68\) 145.992 0.260355
\(69\) 295.497 0.515561
\(70\) −164.025 −0.280068
\(71\) −881.595 −1.47361 −0.736804 0.676107i \(-0.763666\pi\)
−0.736804 + 0.676107i \(0.763666\pi\)
\(72\) −431.695 −0.706608
\(73\) 1023.02 1.64022 0.820110 0.572206i \(-0.193912\pi\)
0.820110 + 0.572206i \(0.193912\pi\)
\(74\) −355.947 −0.559162
\(75\) −181.476 −0.279400
\(76\) 55.3708 0.0835720
\(77\) −109.229 −0.161659
\(78\) −1368.71 −1.98688
\(79\) −78.3320 −0.111557 −0.0557787 0.998443i \(-0.517764\pi\)
−0.0557787 + 0.998443i \(0.517764\pi\)
\(80\) −394.106 −0.550780
\(81\) −762.566 −1.04604
\(82\) 315.380 0.424731
\(83\) 902.858 1.19399 0.596997 0.802243i \(-0.296360\pi\)
0.596997 + 0.802243i \(0.296360\pi\)
\(84\) 210.063 0.272854
\(85\) 250.479 0.319627
\(86\) −1586.13 −1.98880
\(87\) −724.003 −0.892198
\(88\) −184.818 −0.223883
\(89\) −995.340 −1.18546 −0.592729 0.805402i \(-0.701950\pi\)
−0.592729 + 0.805402i \(0.701950\pi\)
\(90\) 424.417 0.497083
\(91\) −566.735 −0.652857
\(92\) −118.632 −0.134437
\(93\) 446.155 0.497463
\(94\) −1027.61 −1.12755
\(95\) 95.0000 0.102598
\(96\) 914.538 0.972288
\(97\) −410.183 −0.429358 −0.214679 0.976685i \(-0.568871\pi\)
−0.214679 + 0.976685i \(0.568871\pi\)
\(98\) −807.410 −0.832253
\(99\) 282.630 0.286923
\(100\) 72.8564 0.0728564
\(101\) 775.920 0.764425 0.382213 0.924074i \(-0.375162\pi\)
0.382213 + 0.924074i \(0.375162\pi\)
\(102\) −1201.37 −1.16621
\(103\) −1437.83 −1.37547 −0.687737 0.725960i \(-0.741396\pi\)
−0.687737 + 0.725960i \(0.741396\pi\)
\(104\) −958.934 −0.904146
\(105\) 360.406 0.334972
\(106\) 639.505 0.585983
\(107\) −1562.36 −1.41158 −0.705789 0.708422i \(-0.749407\pi\)
−0.705789 + 0.708422i \(0.749407\pi\)
\(108\) 27.6360 0.0246229
\(109\) −1203.46 −1.05752 −0.528762 0.848770i \(-0.677344\pi\)
−0.528762 + 0.848770i \(0.677344\pi\)
\(110\) 181.702 0.157496
\(111\) 782.109 0.668779
\(112\) 782.683 0.660327
\(113\) −1652.95 −1.37608 −0.688038 0.725675i \(-0.741528\pi\)
−0.688038 + 0.725675i \(0.741528\pi\)
\(114\) −455.648 −0.374345
\(115\) −203.538 −0.165043
\(116\) 290.662 0.232649
\(117\) 1466.43 1.15873
\(118\) 1126.94 0.879181
\(119\) −497.445 −0.383200
\(120\) 609.819 0.463905
\(121\) 121.000 0.0909091
\(122\) −1350.10 −1.00191
\(123\) −692.974 −0.507995
\(124\) −179.116 −0.129718
\(125\) 125.000 0.0894427
\(126\) −842.880 −0.595950
\(127\) −820.257 −0.573119 −0.286559 0.958062i \(-0.592512\pi\)
−0.286559 + 0.958062i \(0.592512\pi\)
\(128\) 1716.04 1.18498
\(129\) 3485.14 2.37868
\(130\) 942.766 0.636046
\(131\) −224.528 −0.149749 −0.0748744 0.997193i \(-0.523856\pi\)
−0.0748744 + 0.997193i \(0.523856\pi\)
\(132\) −232.701 −0.153440
\(133\) −188.667 −0.123004
\(134\) −1719.29 −1.10839
\(135\) 47.4152 0.0302285
\(136\) −841.693 −0.530696
\(137\) −2474.25 −1.54299 −0.771493 0.636237i \(-0.780490\pi\)
−0.771493 + 0.636237i \(0.780490\pi\)
\(138\) 976.227 0.602188
\(139\) 697.199 0.425437 0.212718 0.977114i \(-0.431768\pi\)
0.212718 + 0.977114i \(0.431768\pi\)
\(140\) −144.691 −0.0873471
\(141\) 2257.92 1.34859
\(142\) −2912.50 −1.72121
\(143\) 627.812 0.367135
\(144\) −2025.20 −1.17199
\(145\) 498.691 0.285614
\(146\) 3379.74 1.91582
\(147\) 1774.09 0.995406
\(148\) −313.990 −0.174391
\(149\) 3320.36 1.82560 0.912801 0.408405i \(-0.133915\pi\)
0.912801 + 0.408405i \(0.133915\pi\)
\(150\) −599.537 −0.326347
\(151\) −480.979 −0.259215 −0.129608 0.991565i \(-0.541372\pi\)
−0.129608 + 0.991565i \(0.541372\pi\)
\(152\) −319.231 −0.170349
\(153\) 1287.14 0.680127
\(154\) −360.855 −0.188822
\(155\) −307.310 −0.159250
\(156\) −1207.38 −0.619664
\(157\) −1113.11 −0.565832 −0.282916 0.959145i \(-0.591302\pi\)
−0.282916 + 0.959145i \(0.591302\pi\)
\(158\) −258.783 −0.130302
\(159\) −1405.16 −0.700859
\(160\) −629.931 −0.311253
\(161\) 404.220 0.197870
\(162\) −2519.27 −1.22180
\(163\) 1089.57 0.523568 0.261784 0.965127i \(-0.415689\pi\)
0.261784 + 0.965127i \(0.415689\pi\)
\(164\) 278.205 0.132464
\(165\) −399.247 −0.188372
\(166\) 2982.75 1.39461
\(167\) −1285.41 −0.595616 −0.297808 0.954626i \(-0.596256\pi\)
−0.297808 + 0.954626i \(0.596256\pi\)
\(168\) −1211.08 −0.556173
\(169\) 1060.42 0.482667
\(170\) 827.502 0.373332
\(171\) 488.179 0.218316
\(172\) −1399.17 −0.620264
\(173\) −1399.78 −0.615163 −0.307581 0.951522i \(-0.599520\pi\)
−0.307581 + 0.951522i \(0.599520\pi\)
\(174\) −2391.87 −1.04211
\(175\) −248.247 −0.107232
\(176\) −867.033 −0.371336
\(177\) −2476.19 −1.05153
\(178\) −3288.28 −1.38464
\(179\) 225.412 0.0941234 0.0470617 0.998892i \(-0.485014\pi\)
0.0470617 + 0.998892i \(0.485014\pi\)
\(180\) 374.389 0.155029
\(181\) 243.788 0.100114 0.0500571 0.998746i \(-0.484060\pi\)
0.0500571 + 0.998746i \(0.484060\pi\)
\(182\) −1872.31 −0.762553
\(183\) 2966.53 1.19832
\(184\) 683.953 0.274031
\(185\) −538.714 −0.214092
\(186\) 1473.95 0.581049
\(187\) 551.055 0.215493
\(188\) −906.478 −0.351658
\(189\) −94.1654 −0.0362409
\(190\) 313.849 0.119837
\(191\) 2583.89 0.978868 0.489434 0.872040i \(-0.337203\pi\)
0.489434 + 0.872040i \(0.337203\pi\)
\(192\) −1555.99 −0.584864
\(193\) −324.276 −0.120943 −0.0604713 0.998170i \(-0.519260\pi\)
−0.0604713 + 0.998170i \(0.519260\pi\)
\(194\) −1355.11 −0.501501
\(195\) −2071.50 −0.760736
\(196\) −712.237 −0.259562
\(197\) −2961.19 −1.07094 −0.535472 0.844553i \(-0.679866\pi\)
−0.535472 + 0.844553i \(0.679866\pi\)
\(198\) 933.717 0.335133
\(199\) −1551.15 −0.552555 −0.276278 0.961078i \(-0.589101\pi\)
−0.276278 + 0.961078i \(0.589101\pi\)
\(200\) −420.041 −0.148507
\(201\) 3777.72 1.32567
\(202\) 2563.39 0.892868
\(203\) −990.386 −0.342421
\(204\) −1059.76 −0.363717
\(205\) 477.318 0.162621
\(206\) −4750.12 −1.60659
\(207\) −1045.92 −0.351192
\(208\) −4498.62 −1.49963
\(209\) 209.000 0.0691714
\(210\) 1190.66 0.391255
\(211\) 2329.33 0.759989 0.379994 0.924989i \(-0.375926\pi\)
0.379994 + 0.924989i \(0.375926\pi\)
\(212\) 564.124 0.182756
\(213\) 6399.53 2.05863
\(214\) −5161.52 −1.64876
\(215\) −2400.55 −0.761472
\(216\) −159.331 −0.0501902
\(217\) 610.309 0.190924
\(218\) −3975.82 −1.23521
\(219\) −7426.18 −2.29139
\(220\) 160.284 0.0491197
\(221\) 2859.16 0.870263
\(222\) 2583.83 0.781151
\(223\) 192.527 0.0578141 0.0289070 0.999582i \(-0.490797\pi\)
0.0289070 + 0.999582i \(0.490797\pi\)
\(224\) 1251.03 0.373159
\(225\) 642.341 0.190323
\(226\) −5460.81 −1.60729
\(227\) 189.492 0.0554053 0.0277026 0.999616i \(-0.491181\pi\)
0.0277026 + 0.999616i \(0.491181\pi\)
\(228\) −401.939 −0.116750
\(229\) −3616.47 −1.04360 −0.521798 0.853069i \(-0.674738\pi\)
−0.521798 + 0.853069i \(0.674738\pi\)
\(230\) −672.422 −0.192775
\(231\) 792.894 0.225838
\(232\) −1675.76 −0.474221
\(233\) 3665.01 1.03048 0.515242 0.857045i \(-0.327702\pi\)
0.515242 + 0.857045i \(0.327702\pi\)
\(234\) 4844.61 1.35343
\(235\) −1555.25 −0.431716
\(236\) 994.103 0.274198
\(237\) 568.615 0.155846
\(238\) −1643.40 −0.447587
\(239\) −191.701 −0.0518833 −0.0259416 0.999663i \(-0.508258\pi\)
−0.0259416 + 0.999663i \(0.508258\pi\)
\(240\) 2860.83 0.769440
\(241\) −130.956 −0.0350025 −0.0175012 0.999847i \(-0.505571\pi\)
−0.0175012 + 0.999847i \(0.505571\pi\)
\(242\) 399.744 0.106184
\(243\) 5279.45 1.39373
\(244\) −1190.96 −0.312473
\(245\) −1221.99 −0.318653
\(246\) −2289.36 −0.593350
\(247\) 1084.40 0.279348
\(248\) 1032.66 0.264412
\(249\) −6553.88 −1.66801
\(250\) 412.959 0.104471
\(251\) −3751.83 −0.943481 −0.471740 0.881737i \(-0.656374\pi\)
−0.471740 + 0.881737i \(0.656374\pi\)
\(252\) −743.526 −0.185864
\(253\) −447.783 −0.111272
\(254\) −2709.86 −0.669417
\(255\) −1818.24 −0.446520
\(256\) 3954.41 0.965433
\(257\) −793.367 −0.192564 −0.0962818 0.995354i \(-0.530695\pi\)
−0.0962818 + 0.995354i \(0.530695\pi\)
\(258\) 11513.8 2.77836
\(259\) 1069.87 0.256674
\(260\) 831.638 0.198369
\(261\) 2562.63 0.607751
\(262\) −741.767 −0.174910
\(263\) −4848.74 −1.13683 −0.568414 0.822742i \(-0.692443\pi\)
−0.568414 + 0.822742i \(0.692443\pi\)
\(264\) 1341.60 0.312765
\(265\) 967.870 0.224361
\(266\) −623.295 −0.143672
\(267\) 7225.21 1.65609
\(268\) −1516.63 −0.345681
\(269\) 3140.99 0.711930 0.355965 0.934499i \(-0.384152\pi\)
0.355965 + 0.934499i \(0.384152\pi\)
\(270\) 156.644 0.0353077
\(271\) 3402.74 0.762738 0.381369 0.924423i \(-0.375453\pi\)
0.381369 + 0.924423i \(0.375453\pi\)
\(272\) −3948.62 −0.880221
\(273\) 4113.95 0.912043
\(274\) −8174.10 −1.80225
\(275\) 275.000 0.0603023
\(276\) 861.154 0.187809
\(277\) 7059.57 1.53130 0.765648 0.643260i \(-0.222419\pi\)
0.765648 + 0.643260i \(0.222419\pi\)
\(278\) 2303.32 0.496920
\(279\) −1579.18 −0.338864
\(280\) 834.190 0.178044
\(281\) 7065.36 1.49994 0.749971 0.661470i \(-0.230067\pi\)
0.749971 + 0.661470i \(0.230067\pi\)
\(282\) 7459.44 1.57519
\(283\) −5348.00 −1.12334 −0.561671 0.827361i \(-0.689841\pi\)
−0.561671 + 0.827361i \(0.689841\pi\)
\(284\) −2569.19 −0.536808
\(285\) −689.609 −0.143329
\(286\) 2074.09 0.428822
\(287\) −947.940 −0.194966
\(288\) −3237.04 −0.662307
\(289\) −2403.40 −0.489192
\(290\) 1647.51 0.333604
\(291\) 2977.53 0.599815
\(292\) 2981.35 0.597502
\(293\) 5155.07 1.02786 0.513929 0.857833i \(-0.328189\pi\)
0.513929 + 0.857833i \(0.328189\pi\)
\(294\) 5861.02 1.16266
\(295\) 1705.59 0.336621
\(296\) 1810.26 0.355469
\(297\) 104.314 0.0203801
\(298\) 10969.4 2.13235
\(299\) −2323.33 −0.449371
\(300\) −528.867 −0.101780
\(301\) 4767.44 0.912925
\(302\) −1589.00 −0.302770
\(303\) −5632.44 −1.06790
\(304\) −1497.60 −0.282544
\(305\) −2043.33 −0.383610
\(306\) 4252.31 0.794406
\(307\) 343.562 0.0638701 0.0319351 0.999490i \(-0.489833\pi\)
0.0319351 + 0.999490i \(0.489833\pi\)
\(308\) −318.320 −0.0588894
\(309\) 10437.3 1.92154
\(310\) −1015.25 −0.186008
\(311\) −2132.90 −0.388893 −0.194447 0.980913i \(-0.562291\pi\)
−0.194447 + 0.980913i \(0.562291\pi\)
\(312\) 6960.93 1.26309
\(313\) −2932.08 −0.529492 −0.264746 0.964318i \(-0.585288\pi\)
−0.264746 + 0.964318i \(0.585288\pi\)
\(314\) −3677.34 −0.660906
\(315\) −1275.67 −0.228178
\(316\) −228.279 −0.0406383
\(317\) −521.450 −0.0923898 −0.0461949 0.998932i \(-0.514710\pi\)
−0.0461949 + 0.998932i \(0.514710\pi\)
\(318\) −4642.19 −0.818620
\(319\) 1097.12 0.192561
\(320\) 1071.76 0.187229
\(321\) 11341.2 1.97198
\(322\) 1335.41 0.231117
\(323\) 951.822 0.163965
\(324\) −2222.31 −0.381054
\(325\) 1426.85 0.243530
\(326\) 3599.58 0.611540
\(327\) 8735.93 1.47736
\(328\) −1603.94 −0.270009
\(329\) 3088.68 0.517582
\(330\) −1318.98 −0.220023
\(331\) −1301.60 −0.216141 −0.108070 0.994143i \(-0.534467\pi\)
−0.108070 + 0.994143i \(0.534467\pi\)
\(332\) 2631.16 0.434950
\(333\) −2768.30 −0.455562
\(334\) −4246.57 −0.695694
\(335\) −2602.08 −0.424379
\(336\) −5681.53 −0.922478
\(337\) −3908.83 −0.631832 −0.315916 0.948787i \(-0.602312\pi\)
−0.315916 + 0.948787i \(0.602312\pi\)
\(338\) 3503.28 0.563767
\(339\) 11998.8 1.92238
\(340\) 729.961 0.116434
\(341\) −676.082 −0.107366
\(342\) 1612.78 0.254998
\(343\) 5832.78 0.918194
\(344\) 8066.65 1.26432
\(345\) 1477.49 0.230566
\(346\) −4624.41 −0.718525
\(347\) −7032.79 −1.08801 −0.544006 0.839081i \(-0.683093\pi\)
−0.544006 + 0.839081i \(0.683093\pi\)
\(348\) −2109.93 −0.325011
\(349\) −7182.01 −1.10156 −0.550780 0.834651i \(-0.685670\pi\)
−0.550780 + 0.834651i \(0.685670\pi\)
\(350\) −820.126 −0.125250
\(351\) 541.234 0.0823046
\(352\) −1385.85 −0.209846
\(353\) 110.537 0.0166666 0.00833330 0.999965i \(-0.497347\pi\)
0.00833330 + 0.999965i \(0.497347\pi\)
\(354\) −8180.51 −1.22822
\(355\) −4407.98 −0.659017
\(356\) −2900.67 −0.431841
\(357\) 3610.97 0.535331
\(358\) 744.688 0.109938
\(359\) 9563.33 1.40594 0.702971 0.711218i \(-0.251856\pi\)
0.702971 + 0.711218i \(0.251856\pi\)
\(360\) −2158.48 −0.316005
\(361\) 361.000 0.0526316
\(362\) 805.397 0.116936
\(363\) −878.344 −0.127000
\(364\) −1651.61 −0.237824
\(365\) 5115.12 0.733528
\(366\) 9800.43 1.39966
\(367\) −6333.20 −0.900791 −0.450396 0.892829i \(-0.648717\pi\)
−0.450396 + 0.892829i \(0.648717\pi\)
\(368\) 3208.61 0.454512
\(369\) 2452.80 0.346038
\(370\) −1779.73 −0.250065
\(371\) −1922.16 −0.268986
\(372\) 1300.21 0.181217
\(373\) −7815.40 −1.08490 −0.542448 0.840089i \(-0.682502\pi\)
−0.542448 + 0.840089i \(0.682502\pi\)
\(374\) 1820.50 0.251701
\(375\) −907.380 −0.124952
\(376\) 5226.15 0.716803
\(377\) 5692.43 0.777653
\(378\) −311.092 −0.0423302
\(379\) −3004.64 −0.407224 −0.203612 0.979052i \(-0.565268\pi\)
−0.203612 + 0.979052i \(0.565268\pi\)
\(380\) 276.854 0.0373745
\(381\) 5954.28 0.800648
\(382\) 8536.33 1.14334
\(383\) 13591.9 1.81335 0.906677 0.421826i \(-0.138611\pi\)
0.906677 + 0.421826i \(0.138611\pi\)
\(384\) −12456.8 −1.65542
\(385\) −546.143 −0.0722961
\(386\) −1071.30 −0.141264
\(387\) −12335.8 −1.62032
\(388\) −1195.38 −0.156407
\(389\) −5797.55 −0.755648 −0.377824 0.925877i \(-0.623328\pi\)
−0.377824 + 0.925877i \(0.623328\pi\)
\(390\) −6843.57 −0.888558
\(391\) −2039.28 −0.263762
\(392\) 4106.28 0.529078
\(393\) 1629.86 0.209200
\(394\) −9782.80 −1.25089
\(395\) −391.660 −0.0498900
\(396\) 823.655 0.104521
\(397\) 4511.41 0.570331 0.285165 0.958478i \(-0.407951\pi\)
0.285165 + 0.958478i \(0.407951\pi\)
\(398\) −5124.51 −0.645398
\(399\) 1369.54 0.171837
\(400\) −1970.53 −0.246316
\(401\) 5389.27 0.671140 0.335570 0.942015i \(-0.391071\pi\)
0.335570 + 0.942015i \(0.391071\pi\)
\(402\) 12480.4 1.54842
\(403\) −3507.87 −0.433596
\(404\) 2261.23 0.278466
\(405\) −3812.83 −0.467805
\(406\) −3271.91 −0.399956
\(407\) −1185.17 −0.144341
\(408\) 6109.88 0.741383
\(409\) 9962.17 1.20440 0.602198 0.798347i \(-0.294292\pi\)
0.602198 + 0.798347i \(0.294292\pi\)
\(410\) 1576.90 0.189945
\(411\) 17960.7 2.15556
\(412\) −4190.21 −0.501060
\(413\) −3387.25 −0.403573
\(414\) −3455.39 −0.410201
\(415\) 4514.29 0.533970
\(416\) −7190.51 −0.847461
\(417\) −5061.00 −0.594336
\(418\) 690.468 0.0807940
\(419\) 16460.3 1.91919 0.959594 0.281387i \(-0.0907946\pi\)
0.959594 + 0.281387i \(0.0907946\pi\)
\(420\) 1050.32 0.122024
\(421\) 15275.0 1.76830 0.884151 0.467200i \(-0.154737\pi\)
0.884151 + 0.467200i \(0.154737\pi\)
\(422\) 7695.34 0.887686
\(423\) −7992.00 −0.918639
\(424\) −3252.36 −0.372520
\(425\) 1252.40 0.142942
\(426\) 21142.0 2.40453
\(427\) 4058.01 0.459908
\(428\) −4553.11 −0.514212
\(429\) −4557.31 −0.512888
\(430\) −7930.65 −0.889418
\(431\) 5924.25 0.662090 0.331045 0.943615i \(-0.392599\pi\)
0.331045 + 0.943615i \(0.392599\pi\)
\(432\) −747.465 −0.0832463
\(433\) 1296.43 0.143886 0.0719429 0.997409i \(-0.477080\pi\)
0.0719429 + 0.997409i \(0.477080\pi\)
\(434\) 2016.26 0.223004
\(435\) −3620.01 −0.399003
\(436\) −3507.18 −0.385237
\(437\) −773.443 −0.0846654
\(438\) −24533.7 −2.67640
\(439\) −10400.8 −1.13076 −0.565379 0.824831i \(-0.691270\pi\)
−0.565379 + 0.824831i \(0.691270\pi\)
\(440\) −924.090 −0.100123
\(441\) −6279.46 −0.678055
\(442\) 9445.74 1.01649
\(443\) −11481.8 −1.23142 −0.615709 0.787973i \(-0.711130\pi\)
−0.615709 + 0.787973i \(0.711130\pi\)
\(444\) 2279.26 0.243624
\(445\) −4976.70 −0.530153
\(446\) 636.045 0.0675282
\(447\) −24102.6 −2.55037
\(448\) −2128.49 −0.224468
\(449\) −8437.38 −0.886825 −0.443412 0.896318i \(-0.646232\pi\)
−0.443412 + 0.896318i \(0.646232\pi\)
\(450\) 2122.08 0.222302
\(451\) 1050.10 0.109639
\(452\) −4817.12 −0.501279
\(453\) 3491.44 0.362124
\(454\) 626.018 0.0647147
\(455\) −2833.68 −0.291967
\(456\) 2317.31 0.237978
\(457\) −8733.81 −0.893983 −0.446992 0.894538i \(-0.647505\pi\)
−0.446992 + 0.894538i \(0.647505\pi\)
\(458\) −11947.6 −1.21895
\(459\) 475.062 0.0483093
\(460\) −593.160 −0.0601223
\(461\) −6012.15 −0.607406 −0.303703 0.952767i \(-0.598223\pi\)
−0.303703 + 0.952767i \(0.598223\pi\)
\(462\) 2619.46 0.263784
\(463\) −19497.3 −1.95705 −0.978527 0.206119i \(-0.933917\pi\)
−0.978527 + 0.206119i \(0.933917\pi\)
\(464\) −7861.47 −0.786551
\(465\) 2230.77 0.222472
\(466\) 12108.0 1.20363
\(467\) −2105.61 −0.208643 −0.104321 0.994544i \(-0.533267\pi\)
−0.104321 + 0.994544i \(0.533267\pi\)
\(468\) 4273.56 0.422105
\(469\) 5167.66 0.508786
\(470\) −5138.03 −0.504255
\(471\) 8080.09 0.790469
\(472\) −5731.34 −0.558911
\(473\) −5281.22 −0.513384
\(474\) 1878.52 0.182032
\(475\) 475.000 0.0458831
\(476\) −1449.68 −0.139593
\(477\) 4973.62 0.477414
\(478\) −633.317 −0.0606009
\(479\) −10637.9 −1.01473 −0.507367 0.861730i \(-0.669381\pi\)
−0.507367 + 0.861730i \(0.669381\pi\)
\(480\) 4572.69 0.434821
\(481\) −6149.29 −0.582918
\(482\) −432.635 −0.0408838
\(483\) −2934.25 −0.276424
\(484\) 352.625 0.0331165
\(485\) −2050.91 −0.192015
\(486\) 17441.6 1.62791
\(487\) −6695.45 −0.622997 −0.311499 0.950247i \(-0.600831\pi\)
−0.311499 + 0.950247i \(0.600831\pi\)
\(488\) 6866.27 0.636929
\(489\) −7909.22 −0.731426
\(490\) −4037.05 −0.372195
\(491\) −5573.36 −0.512265 −0.256133 0.966642i \(-0.582448\pi\)
−0.256133 + 0.966642i \(0.582448\pi\)
\(492\) −2019.50 −0.185053
\(493\) 4996.47 0.456450
\(494\) 3582.51 0.326285
\(495\) 1413.15 0.128316
\(496\) 4844.50 0.438558
\(497\) 8754.12 0.790093
\(498\) −21651.9 −1.94828
\(499\) −18791.5 −1.68581 −0.842907 0.538059i \(-0.819158\pi\)
−0.842907 + 0.538059i \(0.819158\pi\)
\(500\) 364.282 0.0325824
\(501\) 9330.83 0.832077
\(502\) −12394.8 −1.10201
\(503\) −13598.0 −1.20538 −0.602690 0.797976i \(-0.705904\pi\)
−0.602690 + 0.797976i \(0.705904\pi\)
\(504\) 4286.67 0.378856
\(505\) 3879.60 0.341861
\(506\) −1479.33 −0.129969
\(507\) −7697.62 −0.674287
\(508\) −2390.44 −0.208777
\(509\) −9983.72 −0.869392 −0.434696 0.900577i \(-0.643144\pi\)
−0.434696 + 0.900577i \(0.643144\pi\)
\(510\) −6006.87 −0.521546
\(511\) −10158.5 −0.879424
\(512\) −664.221 −0.0573334
\(513\) 180.178 0.0155069
\(514\) −2621.02 −0.224919
\(515\) −7189.16 −0.615130
\(516\) 10156.6 0.866510
\(517\) −3421.55 −0.291063
\(518\) 3534.50 0.299802
\(519\) 10161.0 0.859384
\(520\) −4794.67 −0.404346
\(521\) −13869.7 −1.16630 −0.583151 0.812364i \(-0.698180\pi\)
−0.583151 + 0.812364i \(0.698180\pi\)
\(522\) 8466.10 0.709868
\(523\) 13770.6 1.15133 0.575667 0.817684i \(-0.304743\pi\)
0.575667 + 0.817684i \(0.304743\pi\)
\(524\) −654.332 −0.0545508
\(525\) 1802.03 0.149804
\(526\) −16018.6 −1.32784
\(527\) −3078.99 −0.254503
\(528\) 6293.82 0.518757
\(529\) −10509.9 −0.863804
\(530\) 3197.53 0.262060
\(531\) 8764.55 0.716288
\(532\) −549.825 −0.0448081
\(533\) 5448.47 0.442776
\(534\) 23869.7 1.93435
\(535\) −7811.79 −0.631277
\(536\) 8743.85 0.704621
\(537\) −1636.28 −0.131491
\(538\) 10376.8 0.831552
\(539\) −2688.38 −0.214836
\(540\) 138.180 0.0110117
\(541\) 17008.9 1.35170 0.675848 0.737041i \(-0.263777\pi\)
0.675848 + 0.737041i \(0.263777\pi\)
\(542\) 11241.6 0.890897
\(543\) −1769.67 −0.139860
\(544\) −6311.39 −0.497424
\(545\) −6017.28 −0.472939
\(546\) 13591.2 1.06529
\(547\) −5652.22 −0.441812 −0.220906 0.975295i \(-0.570901\pi\)
−0.220906 + 0.975295i \(0.570901\pi\)
\(548\) −7210.58 −0.562082
\(549\) −10500.1 −0.816274
\(550\) 908.510 0.0704345
\(551\) 1895.02 0.146517
\(552\) −4964.84 −0.382822
\(553\) 777.826 0.0598129
\(554\) 23322.5 1.78859
\(555\) 3910.54 0.299087
\(556\) 2031.82 0.154979
\(557\) 5392.78 0.410232 0.205116 0.978738i \(-0.434243\pi\)
0.205116 + 0.978738i \(0.434243\pi\)
\(558\) −5217.10 −0.395802
\(559\) −27401.8 −2.07329
\(560\) 3913.42 0.295307
\(561\) −4000.13 −0.301044
\(562\) 23341.6 1.75197
\(563\) 21450.9 1.60577 0.802883 0.596137i \(-0.203298\pi\)
0.802883 + 0.596137i \(0.203298\pi\)
\(564\) 6580.16 0.491267
\(565\) −8264.76 −0.615400
\(566\) −17668.0 −1.31209
\(567\) 7572.17 0.560849
\(568\) 14812.2 1.09420
\(569\) 1495.70 0.110199 0.0550994 0.998481i \(-0.482452\pi\)
0.0550994 + 0.998481i \(0.482452\pi\)
\(570\) −2278.24 −0.167412
\(571\) 15375.5 1.12688 0.563438 0.826159i \(-0.309479\pi\)
0.563438 + 0.826159i \(0.309479\pi\)
\(572\) 1829.60 0.133740
\(573\) −18756.6 −1.36748
\(574\) −3131.68 −0.227725
\(575\) −1017.69 −0.0738096
\(576\) 5507.48 0.398400
\(577\) −16691.0 −1.20425 −0.602127 0.798401i \(-0.705680\pi\)
−0.602127 + 0.798401i \(0.705680\pi\)
\(578\) −7940.05 −0.571389
\(579\) 2353.93 0.168957
\(580\) 1453.31 0.104044
\(581\) −8965.26 −0.640175
\(582\) 9836.79 0.700598
\(583\) 2129.31 0.151264
\(584\) −17188.5 −1.21792
\(585\) 7332.16 0.518201
\(586\) 17030.7 1.20056
\(587\) −13097.7 −0.920957 −0.460478 0.887671i \(-0.652322\pi\)
−0.460478 + 0.887671i \(0.652322\pi\)
\(588\) 5170.16 0.362608
\(589\) −1167.78 −0.0816934
\(590\) 5634.71 0.393182
\(591\) 21495.4 1.49611
\(592\) 8492.41 0.589588
\(593\) 7213.10 0.499505 0.249752 0.968310i \(-0.419651\pi\)
0.249752 + 0.968310i \(0.419651\pi\)
\(594\) 344.618 0.0238044
\(595\) −2487.23 −0.171372
\(596\) 9676.38 0.665033
\(597\) 11259.9 0.771921
\(598\) −7675.53 −0.524876
\(599\) 26706.6 1.82171 0.910855 0.412727i \(-0.135424\pi\)
0.910855 + 0.412727i \(0.135424\pi\)
\(600\) 3049.09 0.207465
\(601\) 5806.31 0.394084 0.197042 0.980395i \(-0.436867\pi\)
0.197042 + 0.980395i \(0.436867\pi\)
\(602\) 15750.0 1.06632
\(603\) −13371.4 −0.903026
\(604\) −1401.69 −0.0944274
\(605\) 605.000 0.0406558
\(606\) −18607.7 −1.24734
\(607\) 3285.76 0.219712 0.109856 0.993948i \(-0.464961\pi\)
0.109856 + 0.993948i \(0.464961\pi\)
\(608\) −2393.74 −0.159669
\(609\) 7189.25 0.478363
\(610\) −6750.51 −0.448066
\(611\) −17752.8 −1.17545
\(612\) 3751.07 0.247758
\(613\) −12836.7 −0.845790 −0.422895 0.906179i \(-0.638986\pi\)
−0.422895 + 0.906179i \(0.638986\pi\)
\(614\) 1135.02 0.0746019
\(615\) −3464.87 −0.227182
\(616\) 1835.22 0.120037
\(617\) −9678.22 −0.631492 −0.315746 0.948844i \(-0.602255\pi\)
−0.315746 + 0.948844i \(0.602255\pi\)
\(618\) 34481.3 2.24441
\(619\) 23000.6 1.49349 0.746747 0.665108i \(-0.231614\pi\)
0.746747 + 0.665108i \(0.231614\pi\)
\(620\) −895.579 −0.0580118
\(621\) −386.031 −0.0249451
\(622\) −7046.41 −0.454237
\(623\) 9883.59 0.635598
\(624\) 32655.7 2.09499
\(625\) 625.000 0.0400000
\(626\) −9686.63 −0.618460
\(627\) −1517.14 −0.0966327
\(628\) −3243.88 −0.206122
\(629\) −5397.47 −0.342148
\(630\) −4214.40 −0.266517
\(631\) −25171.9 −1.58808 −0.794039 0.607866i \(-0.792026\pi\)
−0.794039 + 0.607866i \(0.792026\pi\)
\(632\) 1316.11 0.0828352
\(633\) −16908.7 −1.06171
\(634\) −1722.70 −0.107914
\(635\) −4101.29 −0.256306
\(636\) −4095.00 −0.255310
\(637\) −13948.7 −0.867611
\(638\) 3624.52 0.224916
\(639\) −22651.4 −1.40231
\(640\) 8580.19 0.529941
\(641\) −23772.4 −1.46483 −0.732414 0.680860i \(-0.761606\pi\)
−0.732414 + 0.680860i \(0.761606\pi\)
\(642\) 37467.7 2.30332
\(643\) 13205.3 0.809898 0.404949 0.914339i \(-0.367289\pi\)
0.404949 + 0.914339i \(0.367289\pi\)
\(644\) 1178.00 0.0720803
\(645\) 17425.7 1.06378
\(646\) 3144.51 0.191516
\(647\) −2137.65 −0.129891 −0.0649456 0.997889i \(-0.520687\pi\)
−0.0649456 + 0.997889i \(0.520687\pi\)
\(648\) 12812.4 0.776723
\(649\) 3752.29 0.226950
\(650\) 4713.83 0.284449
\(651\) −4430.26 −0.266721
\(652\) 3175.28 0.190726
\(653\) 28100.5 1.68401 0.842003 0.539472i \(-0.181376\pi\)
0.842003 + 0.539472i \(0.181376\pi\)
\(654\) 28860.7 1.72560
\(655\) −1122.64 −0.0669697
\(656\) −7524.55 −0.447842
\(657\) 26285.2 1.56086
\(658\) 10204.0 0.604549
\(659\) 10173.2 0.601355 0.300677 0.953726i \(-0.402787\pi\)
0.300677 + 0.953726i \(0.402787\pi\)
\(660\) −1163.51 −0.0686204
\(661\) 17788.8 1.04675 0.523377 0.852101i \(-0.324672\pi\)
0.523377 + 0.852101i \(0.324672\pi\)
\(662\) −4300.07 −0.252458
\(663\) −20754.8 −1.21576
\(664\) −15169.5 −0.886582
\(665\) −943.337 −0.0550091
\(666\) −9145.56 −0.532107
\(667\) −4060.09 −0.235693
\(668\) −3746.01 −0.216972
\(669\) −1397.56 −0.0807664
\(670\) −8596.43 −0.495685
\(671\) −4495.33 −0.258630
\(672\) −9081.24 −0.521304
\(673\) 1731.14 0.0991541 0.0495771 0.998770i \(-0.484213\pi\)
0.0495771 + 0.998770i \(0.484213\pi\)
\(674\) −12913.5 −0.737996
\(675\) 237.076 0.0135186
\(676\) 3090.33 0.175827
\(677\) −8414.86 −0.477710 −0.238855 0.971055i \(-0.576772\pi\)
−0.238855 + 0.971055i \(0.576772\pi\)
\(678\) 39640.2 2.24539
\(679\) 4073.06 0.230206
\(680\) −4208.47 −0.237334
\(681\) −1375.53 −0.0774013
\(682\) −2233.55 −0.125406
\(683\) −23096.7 −1.29396 −0.646978 0.762508i \(-0.723968\pi\)
−0.646978 + 0.762508i \(0.723968\pi\)
\(684\) 1422.68 0.0795284
\(685\) −12371.2 −0.690045
\(686\) 19269.6 1.07247
\(687\) 26252.1 1.45791
\(688\) 37842.9 2.09702
\(689\) 11048.0 0.610879
\(690\) 4881.13 0.269307
\(691\) −34725.8 −1.91177 −0.955884 0.293745i \(-0.905098\pi\)
−0.955884 + 0.293745i \(0.905098\pi\)
\(692\) −4079.31 −0.224093
\(693\) −2806.48 −0.153837
\(694\) −23234.0 −1.27082
\(695\) 3486.00 0.190261
\(696\) 12164.4 0.662488
\(697\) 4782.33 0.259891
\(698\) −23727.0 −1.28665
\(699\) −26604.4 −1.43959
\(700\) −723.454 −0.0390628
\(701\) −8117.51 −0.437367 −0.218683 0.975796i \(-0.570176\pi\)
−0.218683 + 0.975796i \(0.570176\pi\)
\(702\) 1788.06 0.0961338
\(703\) −2047.11 −0.109827
\(704\) 2357.87 0.126230
\(705\) 11289.6 0.603108
\(706\) 365.179 0.0194670
\(707\) −7704.78 −0.409856
\(708\) −7216.23 −0.383055
\(709\) 35388.5 1.87453 0.937265 0.348618i \(-0.113349\pi\)
0.937265 + 0.348618i \(0.113349\pi\)
\(710\) −14562.5 −0.769748
\(711\) −2012.63 −0.106160
\(712\) 16723.3 0.880244
\(713\) 2501.96 0.131416
\(714\) 11929.5 0.625279
\(715\) 3139.06 0.164188
\(716\) 656.908 0.0342874
\(717\) 1391.56 0.0724811
\(718\) 31594.1 1.64218
\(719\) 1660.90 0.0861490 0.0430745 0.999072i \(-0.486285\pi\)
0.0430745 + 0.999072i \(0.486285\pi\)
\(720\) −10126.0 −0.524130
\(721\) 14277.5 0.737477
\(722\) 1192.63 0.0614750
\(723\) 950.612 0.0488986
\(724\) 710.462 0.0364697
\(725\) 2493.45 0.127730
\(726\) −2901.76 −0.148339
\(727\) 211.015 0.0107650 0.00538248 0.999986i \(-0.498287\pi\)
0.00538248 + 0.999986i \(0.498287\pi\)
\(728\) 9522.08 0.484769
\(729\) −17734.5 −0.901003
\(730\) 16898.7 0.856779
\(731\) −24051.6 −1.21694
\(732\) 8645.21 0.436525
\(733\) −37127.2 −1.87084 −0.935420 0.353539i \(-0.884978\pi\)
−0.935420 + 0.353539i \(0.884978\pi\)
\(734\) −20922.8 −1.05215
\(735\) 8870.46 0.445159
\(736\) 5128.58 0.256851
\(737\) −5724.58 −0.286116
\(738\) 8103.26 0.404181
\(739\) −7152.21 −0.356019 −0.178010 0.984029i \(-0.556966\pi\)
−0.178010 + 0.984029i \(0.556966\pi\)
\(740\) −1569.95 −0.0779898
\(741\) −7871.72 −0.390249
\(742\) −6350.20 −0.314182
\(743\) −3028.15 −0.149518 −0.0747590 0.997202i \(-0.523819\pi\)
−0.0747590 + 0.997202i \(0.523819\pi\)
\(744\) −7496.13 −0.369384
\(745\) 16601.8 0.816434
\(746\) −25819.5 −1.26719
\(747\) 23197.7 1.13622
\(748\) 1605.91 0.0785000
\(749\) 15514.0 0.756835
\(750\) −2997.69 −0.145947
\(751\) −10125.2 −0.491975 −0.245987 0.969273i \(-0.579112\pi\)
−0.245987 + 0.969273i \(0.579112\pi\)
\(752\) 24517.3 1.18890
\(753\) 27234.7 1.31804
\(754\) 18805.9 0.908318
\(755\) −2404.89 −0.115925
\(756\) −274.422 −0.0132019
\(757\) −11000.4 −0.528160 −0.264080 0.964501i \(-0.585068\pi\)
−0.264080 + 0.964501i \(0.585068\pi\)
\(758\) −9926.34 −0.475647
\(759\) 3250.47 0.155447
\(760\) −1596.16 −0.0761824
\(761\) 29465.0 1.40356 0.701778 0.712396i \(-0.252390\pi\)
0.701778 + 0.712396i \(0.252390\pi\)
\(762\) 19671.0 0.935177
\(763\) 11950.2 0.567005
\(764\) 7530.11 0.356584
\(765\) 6435.72 0.304162
\(766\) 44903.2 2.11804
\(767\) 19468.9 0.916533
\(768\) −28705.2 −1.34871
\(769\) −26711.0 −1.25257 −0.626284 0.779595i \(-0.715425\pi\)
−0.626284 + 0.779595i \(0.715425\pi\)
\(770\) −1804.28 −0.0844436
\(771\) 5759.08 0.269012
\(772\) −945.023 −0.0440572
\(773\) −11057.2 −0.514488 −0.257244 0.966346i \(-0.582814\pi\)
−0.257244 + 0.966346i \(0.582814\pi\)
\(774\) −40753.4 −1.89257
\(775\) −1536.55 −0.0712187
\(776\) 6891.74 0.318813
\(777\) −7766.23 −0.358574
\(778\) −19153.2 −0.882616
\(779\) 1813.81 0.0834229
\(780\) −6036.89 −0.277122
\(781\) −9697.55 −0.444309
\(782\) −6737.11 −0.308080
\(783\) 945.821 0.0431684
\(784\) 19263.7 0.877538
\(785\) −5565.54 −0.253048
\(786\) 5384.51 0.244350
\(787\) 5963.94 0.270129 0.135064 0.990837i \(-0.456876\pi\)
0.135064 + 0.990837i \(0.456876\pi\)
\(788\) −8629.65 −0.390125
\(789\) 35197.2 1.58815
\(790\) −1293.92 −0.0582727
\(791\) 16413.6 0.737800
\(792\) −4748.65 −0.213050
\(793\) −23324.2 −1.04447
\(794\) 14904.2 0.666161
\(795\) −7025.81 −0.313434
\(796\) −4520.46 −0.201286
\(797\) −2716.54 −0.120734 −0.0603668 0.998176i \(-0.519227\pi\)
−0.0603668 + 0.998176i \(0.519227\pi\)
\(798\) 4524.52 0.200710
\(799\) −15582.3 −0.689941
\(800\) −3149.65 −0.139196
\(801\) −25573.9 −1.12810
\(802\) 17804.4 0.783909
\(803\) 11253.3 0.494545
\(804\) 11009.2 0.482918
\(805\) 2021.10 0.0884900
\(806\) −11588.8 −0.506451
\(807\) −22800.5 −0.994568
\(808\) −13036.7 −0.567612
\(809\) 21072.5 0.915784 0.457892 0.889008i \(-0.348605\pi\)
0.457892 + 0.889008i \(0.348605\pi\)
\(810\) −12596.3 −0.546408
\(811\) 19349.8 0.837810 0.418905 0.908030i \(-0.362414\pi\)
0.418905 + 0.908030i \(0.362414\pi\)
\(812\) −2886.24 −0.124738
\(813\) −24700.7 −1.06555
\(814\) −3915.42 −0.168594
\(815\) 5447.84 0.234147
\(816\) 28663.1 1.22967
\(817\) −9122.11 −0.390627
\(818\) 32911.7 1.40676
\(819\) −14561.5 −0.621269
\(820\) 1391.03 0.0592399
\(821\) 27124.6 1.15305 0.576526 0.817079i \(-0.304408\pi\)
0.576526 + 0.817079i \(0.304408\pi\)
\(822\) 59336.1 2.51774
\(823\) 12546.0 0.531379 0.265690 0.964059i \(-0.414400\pi\)
0.265690 + 0.964059i \(0.414400\pi\)
\(824\) 24157.9 1.02134
\(825\) −1996.24 −0.0842424
\(826\) −11190.4 −0.471384
\(827\) −8121.61 −0.341495 −0.170747 0.985315i \(-0.554618\pi\)
−0.170747 + 0.985315i \(0.554618\pi\)
\(828\) −3048.09 −0.127933
\(829\) 17848.9 0.747792 0.373896 0.927471i \(-0.378022\pi\)
0.373896 + 0.927471i \(0.378022\pi\)
\(830\) 14913.7 0.623691
\(831\) −51245.7 −2.13922
\(832\) 12233.9 0.509776
\(833\) −12243.3 −0.509251
\(834\) −16719.9 −0.694199
\(835\) −6427.04 −0.266368
\(836\) 609.079 0.0251979
\(837\) −582.847 −0.0240695
\(838\) 54379.6 2.24166
\(839\) 1723.99 0.0709402 0.0354701 0.999371i \(-0.488707\pi\)
0.0354701 + 0.999371i \(0.488707\pi\)
\(840\) −6055.42 −0.248728
\(841\) −14441.3 −0.592124
\(842\) 50463.4 2.06542
\(843\) −51287.7 −2.09542
\(844\) 6788.26 0.276850
\(845\) 5302.10 0.215855
\(846\) −26402.9 −1.07299
\(847\) −1201.51 −0.0487420
\(848\) −15257.7 −0.617869
\(849\) 38821.3 1.56931
\(850\) 4137.51 0.166959
\(851\) 4385.94 0.176672
\(852\) 18649.9 0.749922
\(853\) −5910.96 −0.237266 −0.118633 0.992938i \(-0.537851\pi\)
−0.118633 + 0.992938i \(0.537851\pi\)
\(854\) 13406.3 0.537184
\(855\) 2440.89 0.0976337
\(856\) 26250.2 1.04815
\(857\) −20640.8 −0.822728 −0.411364 0.911471i \(-0.634948\pi\)
−0.411364 + 0.911471i \(0.634948\pi\)
\(858\) −15055.9 −0.599066
\(859\) −27701.0 −1.10029 −0.550144 0.835070i \(-0.685427\pi\)
−0.550144 + 0.835070i \(0.685427\pi\)
\(860\) −6995.83 −0.277390
\(861\) 6881.13 0.272368
\(862\) 19571.8 0.773338
\(863\) 23833.0 0.940073 0.470037 0.882647i \(-0.344241\pi\)
0.470037 + 0.882647i \(0.344241\pi\)
\(864\) −1194.73 −0.0470436
\(865\) −6998.89 −0.275109
\(866\) 4282.99 0.168062
\(867\) 17446.4 0.683403
\(868\) 1778.60 0.0695501
\(869\) −861.652 −0.0336358
\(870\) −11959.3 −0.466045
\(871\) −29702.1 −1.15547
\(872\) 20220.0 0.785248
\(873\) −10539.1 −0.408584
\(874\) −2555.20 −0.0988913
\(875\) −1241.23 −0.0479558
\(876\) −21641.8 −0.834712
\(877\) 46313.1 1.78322 0.891609 0.452806i \(-0.149577\pi\)
0.891609 + 0.452806i \(0.149577\pi\)
\(878\) −34360.8 −1.32075
\(879\) −37420.9 −1.43592
\(880\) −4335.16 −0.166066
\(881\) −21314.0 −0.815080 −0.407540 0.913187i \(-0.633613\pi\)
−0.407540 + 0.913187i \(0.633613\pi\)
\(882\) −20745.3 −0.791985
\(883\) −38824.9 −1.47968 −0.739842 0.672781i \(-0.765100\pi\)
−0.739842 + 0.672781i \(0.765100\pi\)
\(884\) 8332.33 0.317021
\(885\) −12380.9 −0.470260
\(886\) −37932.2 −1.43833
\(887\) −49927.7 −1.88997 −0.944987 0.327108i \(-0.893926\pi\)
−0.944987 + 0.327108i \(0.893926\pi\)
\(888\) −13140.7 −0.496592
\(889\) 8145.05 0.307285
\(890\) −16441.4 −0.619232
\(891\) −8388.22 −0.315394
\(892\) 561.071 0.0210606
\(893\) −5909.95 −0.221466
\(894\) −79627.2 −2.97889
\(895\) 1127.06 0.0420933
\(896\) −17040.0 −0.635343
\(897\) 16865.2 0.627772
\(898\) −27874.3 −1.03583
\(899\) −6130.10 −0.227420
\(900\) 1871.94 0.0693312
\(901\) 9697.26 0.358560
\(902\) 3469.18 0.128061
\(903\) −34607.0 −1.27536
\(904\) 27772.3 1.02178
\(905\) 1218.94 0.0447724
\(906\) 11534.6 0.422970
\(907\) −9529.34 −0.348860 −0.174430 0.984670i \(-0.555808\pi\)
−0.174430 + 0.984670i \(0.555808\pi\)
\(908\) 552.227 0.0201831
\(909\) 19936.2 0.727439
\(910\) −9361.54 −0.341024
\(911\) 107.105 0.00389523 0.00194762 0.999998i \(-0.499380\pi\)
0.00194762 + 0.999998i \(0.499380\pi\)
\(912\) 10871.1 0.394715
\(913\) 9931.44 0.360003
\(914\) −28853.6 −1.04419
\(915\) 14832.6 0.535904
\(916\) −10539.3 −0.380163
\(917\) 2229.53 0.0802897
\(918\) 1569.45 0.0564265
\(919\) 32125.5 1.15313 0.576563 0.817053i \(-0.304394\pi\)
0.576563 + 0.817053i \(0.304394\pi\)
\(920\) 3419.77 0.122550
\(921\) −2493.93 −0.0892267
\(922\) −19862.2 −0.709465
\(923\) −50316.0 −1.79434
\(924\) 2310.69 0.0822687
\(925\) −2693.57 −0.0957449
\(926\) −64412.7 −2.28589
\(927\) −36943.1 −1.30892
\(928\) −12565.6 −0.444490
\(929\) 8705.07 0.307432 0.153716 0.988115i \(-0.450876\pi\)
0.153716 + 0.988115i \(0.450876\pi\)
\(930\) 7369.75 0.259853
\(931\) −4643.56 −0.163466
\(932\) 10680.8 0.375386
\(933\) 15482.8 0.543285
\(934\) −6956.26 −0.243700
\(935\) 2755.27 0.0963712
\(936\) −24638.5 −0.860399
\(937\) −13023.4 −0.454063 −0.227031 0.973887i \(-0.572902\pi\)
−0.227031 + 0.973887i \(0.572902\pi\)
\(938\) 17072.3 0.594274
\(939\) 21284.1 0.739701
\(940\) −4532.39 −0.157266
\(941\) 12077.7 0.418407 0.209203 0.977872i \(-0.432913\pi\)
0.209203 + 0.977872i \(0.432913\pi\)
\(942\) 26694.0 0.923288
\(943\) −3886.09 −0.134198
\(944\) −26887.3 −0.927020
\(945\) −470.827 −0.0162074
\(946\) −17447.4 −0.599645
\(947\) −10883.2 −0.373448 −0.186724 0.982412i \(-0.559787\pi\)
−0.186724 + 0.982412i \(0.559787\pi\)
\(948\) 1657.09 0.0567718
\(949\) 58387.9 1.99721
\(950\) 1569.24 0.0535926
\(951\) 3785.23 0.129069
\(952\) 8357.90 0.284539
\(953\) 1403.82 0.0477170 0.0238585 0.999715i \(-0.492405\pi\)
0.0238585 + 0.999715i \(0.492405\pi\)
\(954\) 16431.2 0.557631
\(955\) 12919.5 0.437763
\(956\) −558.665 −0.0189001
\(957\) −7964.03 −0.269008
\(958\) −35144.1 −1.18524
\(959\) 24568.9 0.827291
\(960\) −7779.95 −0.261559
\(961\) −26013.4 −0.873197
\(962\) −20315.2 −0.680862
\(963\) −40142.6 −1.34328
\(964\) −381.638 −0.0127508
\(965\) −1621.38 −0.0540872
\(966\) −9693.80 −0.322870
\(967\) −29281.0 −0.973748 −0.486874 0.873472i \(-0.661863\pi\)
−0.486874 + 0.873472i \(0.661863\pi\)
\(968\) −2033.00 −0.0675031
\(969\) −6909.31 −0.229060
\(970\) −6775.55 −0.224278
\(971\) −26579.6 −0.878454 −0.439227 0.898376i \(-0.644748\pi\)
−0.439227 + 0.898376i \(0.644748\pi\)
\(972\) 15385.7 0.507711
\(973\) −6923.10 −0.228103
\(974\) −22119.6 −0.727676
\(975\) −10357.5 −0.340211
\(976\) 32211.6 1.05642
\(977\) 7065.14 0.231355 0.115678 0.993287i \(-0.463096\pi\)
0.115678 + 0.993287i \(0.463096\pi\)
\(978\) −26129.5 −0.854323
\(979\) −10948.7 −0.357429
\(980\) −3561.19 −0.116080
\(981\) −30921.1 −1.00636
\(982\) −18412.6 −0.598338
\(983\) 19667.6 0.638146 0.319073 0.947730i \(-0.396628\pi\)
0.319073 + 0.947730i \(0.396628\pi\)
\(984\) 11643.1 0.377204
\(985\) −14805.9 −0.478941
\(986\) 16506.7 0.533144
\(987\) −22420.9 −0.723064
\(988\) 3160.22 0.101761
\(989\) 19544.1 0.628379
\(990\) 4668.58 0.149876
\(991\) −36972.3 −1.18513 −0.592565 0.805523i \(-0.701885\pi\)
−0.592565 + 0.805523i \(0.701885\pi\)
\(992\) 7743.36 0.247835
\(993\) 9448.38 0.301949
\(994\) 28920.8 0.922848
\(995\) −7755.77 −0.247110
\(996\) −19099.7 −0.607627
\(997\) −24394.5 −0.774905 −0.387453 0.921890i \(-0.626645\pi\)
−0.387453 + 0.921890i \(0.626645\pi\)
\(998\) −62080.8 −1.96907
\(999\) −1021.73 −0.0323585
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.b.1.18 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.4.a.b.1.18 20 1.1 even 1 trivial