Properties

Label 201.4.a.e.1.1
Level $201$
Weight $4$
Character 201.1
Self dual yes
Analytic conductor $11.859$
Analytic rank $0$
Dimension $11$
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] = [201,4,Mod(1,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("201.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 201.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: \(11.8593839112\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 3 x^{10} - 74 x^{9} + 208 x^{8} + 1913 x^{7} - 4831 x^{6} - 20432 x^{5} + 42994 x^{4} + 79648 x^{3} - 112288 x^{2} - 85440 x + 3072 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-5.56558\) of defining polynomial
Character \(\chi\) \(=\) 201.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.56558 q^{2} +3.00000 q^{3} +22.9757 q^{4} -9.37616 q^{5} -16.6967 q^{6} +18.3374 q^{7} -83.3483 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-5.56558 q^{2} +3.00000 q^{3} +22.9757 q^{4} -9.37616 q^{5} -16.6967 q^{6} +18.3374 q^{7} -83.3483 q^{8} +9.00000 q^{9} +52.1838 q^{10} +63.5123 q^{11} +68.9270 q^{12} -10.7502 q^{13} -102.058 q^{14} -28.1285 q^{15} +280.076 q^{16} -79.2323 q^{17} -50.0902 q^{18} -15.5002 q^{19} -215.424 q^{20} +55.0123 q^{21} -353.483 q^{22} +13.8269 q^{23} -250.045 q^{24} -37.0876 q^{25} +59.8310 q^{26} +27.0000 q^{27} +421.315 q^{28} +244.274 q^{29} +156.551 q^{30} -210.135 q^{31} -892.001 q^{32} +190.537 q^{33} +440.974 q^{34} -171.935 q^{35} +206.781 q^{36} +403.251 q^{37} +86.2677 q^{38} -32.2505 q^{39} +781.487 q^{40} +444.299 q^{41} -306.175 q^{42} +175.855 q^{43} +1459.24 q^{44} -84.3854 q^{45} -76.9549 q^{46} -73.6213 q^{47} +840.229 q^{48} -6.73855 q^{49} +206.414 q^{50} -237.697 q^{51} -246.993 q^{52} +107.900 q^{53} -150.271 q^{54} -595.502 q^{55} -1528.39 q^{56} -46.5006 q^{57} -1359.52 q^{58} +588.147 q^{59} -646.271 q^{60} +398.852 q^{61} +1169.52 q^{62} +165.037 q^{63} +2723.89 q^{64} +100.795 q^{65} -1060.45 q^{66} +67.0000 q^{67} -1820.42 q^{68} +41.4808 q^{69} +956.916 q^{70} -2.78311 q^{71} -750.135 q^{72} +459.408 q^{73} -2244.33 q^{74} -111.263 q^{75} -356.128 q^{76} +1164.65 q^{77} +179.493 q^{78} +956.408 q^{79} -2626.04 q^{80} +81.0000 q^{81} -2472.78 q^{82} +129.779 q^{83} +1263.94 q^{84} +742.895 q^{85} -978.736 q^{86} +732.821 q^{87} -5293.65 q^{88} -1258.66 q^{89} +469.654 q^{90} -197.131 q^{91} +317.683 q^{92} -630.404 q^{93} +409.746 q^{94} +145.333 q^{95} -2676.00 q^{96} -2.29216 q^{97} +37.5039 q^{98} +571.611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9} + 29 q^{10} + 104 q^{11} + 207 q^{12} + 172 q^{13} + 143 q^{14} + 24 q^{15} + 485 q^{16} - 48 q^{17} + 27 q^{18} + 180 q^{19} - 539 q^{20} + 234 q^{21} - 144 q^{22} + 156 q^{23} + 63 q^{24} + 383 q^{25} - 252 q^{26} + 297 q^{27} + 1011 q^{28} - 4 q^{29} + 87 q^{30} + 514 q^{31} - 119 q^{32} + 312 q^{33} + 72 q^{34} - 338 q^{35} + 621 q^{36} + 854 q^{37} - 308 q^{38} + 516 q^{39} - 15 q^{40} + 674 q^{41} + 429 q^{42} + 738 q^{43} + 356 q^{44} + 72 q^{45} + 507 q^{46} + 54 q^{47} + 1455 q^{48} + 1465 q^{49} + 656 q^{50} - 144 q^{51} - 12 q^{52} - 190 q^{53} + 81 q^{54} + 262 q^{55} + 239 q^{56} + 540 q^{57} - 1466 q^{58} + 18 q^{59} - 1617 q^{60} + 328 q^{61} - 915 q^{62} + 702 q^{63} + 2253 q^{64} - 732 q^{65} - 432 q^{66} + 737 q^{67} - 5746 q^{68} + 468 q^{69} - 4451 q^{70} + 264 q^{71} + 189 q^{72} + 330 q^{73} - 5975 q^{74} + 1149 q^{75} - 178 q^{76} - 368 q^{77} - 756 q^{78} + 456 q^{79} - 8515 q^{80} + 891 q^{81} - 3629 q^{82} - 2432 q^{83} + 3033 q^{84} + 2882 q^{85} - 6225 q^{86} - 12 q^{87} - 5492 q^{88} - 2340 q^{89} + 261 q^{90} - 994 q^{91} - 2939 q^{92} + 1542 q^{93} - 3506 q^{94} - 2568 q^{95} - 357 q^{96} + 1892 q^{97} - 1078 q^{98} + 936 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.56558 −1.96773 −0.983865 0.178913i \(-0.942742\pi\)
−0.983865 + 0.178913i \(0.942742\pi\)
\(3\) 3.00000 0.577350
\(4\) 22.9757 2.87196
\(5\) −9.37616 −0.838629 −0.419315 0.907841i \(-0.637730\pi\)
−0.419315 + 0.907841i \(0.637730\pi\)
\(6\) −16.6967 −1.13607
\(7\) 18.3374 0.990128 0.495064 0.868856i \(-0.335145\pi\)
0.495064 + 0.868856i \(0.335145\pi\)
\(8\) −83.3483 −3.68351
\(9\) 9.00000 0.333333
\(10\) 52.1838 1.65020
\(11\) 63.5123 1.74088 0.870440 0.492274i \(-0.163834\pi\)
0.870440 + 0.492274i \(0.163834\pi\)
\(12\) 68.9270 1.65813
\(13\) −10.7502 −0.229351 −0.114676 0.993403i \(-0.536583\pi\)
−0.114676 + 0.993403i \(0.536583\pi\)
\(14\) −102.058 −1.94830
\(15\) −28.1285 −0.484183
\(16\) 280.076 4.37619
\(17\) −79.2323 −1.13039 −0.565196 0.824957i \(-0.691199\pi\)
−0.565196 + 0.824957i \(0.691199\pi\)
\(18\) −50.0902 −0.655910
\(19\) −15.5002 −0.187158 −0.0935788 0.995612i \(-0.529831\pi\)
−0.0935788 + 0.995612i \(0.529831\pi\)
\(20\) −215.424 −2.40851
\(21\) 55.0123 0.571651
\(22\) −353.483 −3.42558
\(23\) 13.8269 0.125353 0.0626764 0.998034i \(-0.480036\pi\)
0.0626764 + 0.998034i \(0.480036\pi\)
\(24\) −250.045 −2.12668
\(25\) −37.0876 −0.296701
\(26\) 59.8310 0.451301
\(27\) 27.0000 0.192450
\(28\) 421.315 2.84361
\(29\) 244.274 1.56415 0.782077 0.623182i \(-0.214160\pi\)
0.782077 + 0.623182i \(0.214160\pi\)
\(30\) 156.551 0.952741
\(31\) −210.135 −1.21746 −0.608730 0.793377i \(-0.708321\pi\)
−0.608730 + 0.793377i \(0.708321\pi\)
\(32\) −892.001 −4.92766
\(33\) 190.537 1.00510
\(34\) 440.974 2.22431
\(35\) −171.935 −0.830351
\(36\) 206.781 0.957320
\(37\) 403.251 1.79173 0.895866 0.444324i \(-0.146556\pi\)
0.895866 + 0.444324i \(0.146556\pi\)
\(38\) 86.2677 0.368275
\(39\) −32.2505 −0.132416
\(40\) 781.487 3.08910
\(41\) 444.299 1.69239 0.846194 0.532875i \(-0.178888\pi\)
0.846194 + 0.532875i \(0.178888\pi\)
\(42\) −306.175 −1.12485
\(43\) 175.855 0.623667 0.311833 0.950137i \(-0.399057\pi\)
0.311833 + 0.950137i \(0.399057\pi\)
\(44\) 1459.24 4.99974
\(45\) −84.3854 −0.279543
\(46\) −76.9549 −0.246660
\(47\) −73.6213 −0.228485 −0.114242 0.993453i \(-0.536444\pi\)
−0.114242 + 0.993453i \(0.536444\pi\)
\(48\) 840.229 2.52660
\(49\) −6.73855 −0.0196459
\(50\) 206.414 0.583827
\(51\) −237.697 −0.652632
\(52\) −246.993 −0.658687
\(53\) 107.900 0.279647 0.139823 0.990176i \(-0.455347\pi\)
0.139823 + 0.990176i \(0.455347\pi\)
\(54\) −150.271 −0.378690
\(55\) −595.502 −1.45995
\(56\) −1528.39 −3.64715
\(57\) −46.5006 −0.108055
\(58\) −1359.52 −3.07783
\(59\) 588.147 1.29780 0.648900 0.760874i \(-0.275229\pi\)
0.648900 + 0.760874i \(0.275229\pi\)
\(60\) −646.271 −1.39055
\(61\) 398.852 0.837176 0.418588 0.908176i \(-0.362525\pi\)
0.418588 + 0.908176i \(0.362525\pi\)
\(62\) 1169.52 2.39563
\(63\) 165.037 0.330043
\(64\) 2723.89 5.32010
\(65\) 100.795 0.192341
\(66\) −1060.45 −1.97776
\(67\) 67.0000 0.122169
\(68\) −1820.42 −3.24644
\(69\) 41.4808 0.0723725
\(70\) 956.916 1.63391
\(71\) −2.78311 −0.00465204 −0.00232602 0.999997i \(-0.500740\pi\)
−0.00232602 + 0.999997i \(0.500740\pi\)
\(72\) −750.135 −1.22784
\(73\) 459.408 0.736571 0.368285 0.929713i \(-0.379945\pi\)
0.368285 + 0.929713i \(0.379945\pi\)
\(74\) −2244.33 −3.52564
\(75\) −111.263 −0.171300
\(76\) −356.128 −0.537509
\(77\) 1164.65 1.72370
\(78\) 179.493 0.260559
\(79\) 956.408 1.36208 0.681040 0.732246i \(-0.261528\pi\)
0.681040 + 0.732246i \(0.261528\pi\)
\(80\) −2626.04 −3.67000
\(81\) 81.0000 0.111111
\(82\) −2472.78 −3.33016
\(83\) 129.779 0.171628 0.0858141 0.996311i \(-0.472651\pi\)
0.0858141 + 0.996311i \(0.472651\pi\)
\(84\) 1263.94 1.64176
\(85\) 742.895 0.947980
\(86\) −978.736 −1.22721
\(87\) 732.821 0.903065
\(88\) −5293.65 −6.41255
\(89\) −1258.66 −1.49907 −0.749537 0.661963i \(-0.769724\pi\)
−0.749537 + 0.661963i \(0.769724\pi\)
\(90\) 469.654 0.550065
\(91\) −197.131 −0.227087
\(92\) 317.683 0.360008
\(93\) −630.404 −0.702901
\(94\) 409.746 0.449596
\(95\) 145.333 0.156956
\(96\) −2676.00 −2.84498
\(97\) −2.29216 −0.00239931 −0.00119966 0.999999i \(-0.500382\pi\)
−0.00119966 + 0.999999i \(0.500382\pi\)
\(98\) 37.5039 0.0386579
\(99\) 571.611 0.580294
\(100\) −852.113 −0.852113
\(101\) −593.678 −0.584883 −0.292442 0.956283i \(-0.594468\pi\)
−0.292442 + 0.956283i \(0.594468\pi\)
\(102\) 1322.92 1.28420
\(103\) −736.895 −0.704936 −0.352468 0.935824i \(-0.614657\pi\)
−0.352468 + 0.935824i \(0.614657\pi\)
\(104\) 896.010 0.844817
\(105\) −515.804 −0.479403
\(106\) −600.529 −0.550269
\(107\) 848.945 0.767015 0.383508 0.923538i \(-0.374716\pi\)
0.383508 + 0.923538i \(0.374716\pi\)
\(108\) 620.343 0.552709
\(109\) 915.296 0.804307 0.402153 0.915572i \(-0.368262\pi\)
0.402153 + 0.915572i \(0.368262\pi\)
\(110\) 3314.31 2.87279
\(111\) 1209.75 1.03446
\(112\) 5135.88 4.33299
\(113\) 476.132 0.396379 0.198189 0.980164i \(-0.436494\pi\)
0.198189 + 0.980164i \(0.436494\pi\)
\(114\) 258.803 0.212624
\(115\) −129.644 −0.105125
\(116\) 5612.35 4.49219
\(117\) −96.7516 −0.0764503
\(118\) −3273.38 −2.55372
\(119\) −1452.92 −1.11923
\(120\) 2344.46 1.78349
\(121\) 2702.82 2.03067
\(122\) −2219.84 −1.64734
\(123\) 1332.90 0.977101
\(124\) −4827.98 −3.49650
\(125\) 1519.76 1.08745
\(126\) −918.526 −0.649435
\(127\) −2247.08 −1.57005 −0.785025 0.619464i \(-0.787350\pi\)
−0.785025 + 0.619464i \(0.787350\pi\)
\(128\) −8024.03 −5.54086
\(129\) 527.566 0.360074
\(130\) −560.985 −0.378474
\(131\) −223.337 −0.148955 −0.0744774 0.997223i \(-0.523729\pi\)
−0.0744774 + 0.997223i \(0.523729\pi\)
\(132\) 4377.72 2.88660
\(133\) −284.234 −0.185310
\(134\) −372.894 −0.240396
\(135\) −253.156 −0.161394
\(136\) 6603.88 4.16381
\(137\) 472.494 0.294656 0.147328 0.989088i \(-0.452933\pi\)
0.147328 + 0.989088i \(0.452933\pi\)
\(138\) −230.865 −0.142409
\(139\) −1016.47 −0.620255 −0.310128 0.950695i \(-0.600372\pi\)
−0.310128 + 0.950695i \(0.600372\pi\)
\(140\) −3950.32 −2.38473
\(141\) −220.864 −0.131916
\(142\) 15.4896 0.00915395
\(143\) −682.769 −0.399273
\(144\) 2520.69 1.45873
\(145\) −2290.35 −1.31175
\(146\) −2556.87 −1.44937
\(147\) −20.2157 −0.0113426
\(148\) 9264.97 5.14578
\(149\) −674.161 −0.370667 −0.185334 0.982676i \(-0.559337\pi\)
−0.185334 + 0.982676i \(0.559337\pi\)
\(150\) 619.242 0.337073
\(151\) 470.825 0.253743 0.126871 0.991919i \(-0.459506\pi\)
0.126871 + 0.991919i \(0.459506\pi\)
\(152\) 1291.92 0.689397
\(153\) −713.091 −0.376797
\(154\) −6481.97 −3.39177
\(155\) 1970.26 1.02100
\(156\) −740.978 −0.380293
\(157\) −1549.13 −0.787478 −0.393739 0.919222i \(-0.628819\pi\)
−0.393739 + 0.919222i \(0.628819\pi\)
\(158\) −5322.96 −2.68020
\(159\) 323.701 0.161454
\(160\) 8363.54 4.13248
\(161\) 253.550 0.124115
\(162\) −450.812 −0.218637
\(163\) −2870.76 −1.37948 −0.689741 0.724057i \(-0.742275\pi\)
−0.689741 + 0.724057i \(0.742275\pi\)
\(164\) 10208.1 4.86047
\(165\) −1786.51 −0.842905
\(166\) −722.298 −0.337718
\(167\) 1972.94 0.914194 0.457097 0.889417i \(-0.348889\pi\)
0.457097 + 0.889417i \(0.348889\pi\)
\(168\) −4585.18 −2.10568
\(169\) −2081.43 −0.947398
\(170\) −4134.64 −1.86537
\(171\) −139.502 −0.0623858
\(172\) 4040.39 1.79115
\(173\) −1043.63 −0.458645 −0.229323 0.973350i \(-0.573651\pi\)
−0.229323 + 0.973350i \(0.573651\pi\)
\(174\) −4078.57 −1.77699
\(175\) −680.092 −0.293772
\(176\) 17788.3 7.61843
\(177\) 1764.44 0.749285
\(178\) 7005.17 2.94977
\(179\) −2507.53 −1.04705 −0.523525 0.852010i \(-0.675383\pi\)
−0.523525 + 0.852010i \(0.675383\pi\)
\(180\) −1938.81 −0.802837
\(181\) −274.593 −0.112764 −0.0563821 0.998409i \(-0.517957\pi\)
−0.0563821 + 0.998409i \(0.517957\pi\)
\(182\) 1097.15 0.446846
\(183\) 1196.55 0.483344
\(184\) −1152.45 −0.461738
\(185\) −3780.95 −1.50260
\(186\) 3508.56 1.38312
\(187\) −5032.23 −1.96788
\(188\) −1691.50 −0.656199
\(189\) 495.111 0.190550
\(190\) −808.860 −0.308847
\(191\) 2152.11 0.815293 0.407647 0.913140i \(-0.366349\pi\)
0.407647 + 0.913140i \(0.366349\pi\)
\(192\) 8171.67 3.07156
\(193\) −1602.82 −0.597788 −0.298894 0.954286i \(-0.596618\pi\)
−0.298894 + 0.954286i \(0.596618\pi\)
\(194\) 12.7572 0.00472120
\(195\) 302.386 0.111048
\(196\) −154.823 −0.0564223
\(197\) 3809.99 1.37792 0.688960 0.724799i \(-0.258068\pi\)
0.688960 + 0.724799i \(0.258068\pi\)
\(198\) −3181.35 −1.14186
\(199\) −1597.86 −0.569193 −0.284596 0.958647i \(-0.591860\pi\)
−0.284596 + 0.958647i \(0.591860\pi\)
\(200\) 3091.19 1.09290
\(201\) 201.000 0.0705346
\(202\) 3304.16 1.15089
\(203\) 4479.35 1.54871
\(204\) −5461.25 −1.87433
\(205\) −4165.82 −1.41929
\(206\) 4101.25 1.38712
\(207\) 124.442 0.0417843
\(208\) −3010.87 −1.00368
\(209\) −984.455 −0.325819
\(210\) 2870.75 0.943336
\(211\) 1005.09 0.327929 0.163965 0.986466i \(-0.447572\pi\)
0.163965 + 0.986466i \(0.447572\pi\)
\(212\) 2479.09 0.803134
\(213\) −8.34933 −0.00268585
\(214\) −4724.87 −1.50928
\(215\) −1648.85 −0.523025
\(216\) −2250.41 −0.708892
\(217\) −3853.33 −1.20544
\(218\) −5094.15 −1.58266
\(219\) 1378.22 0.425259
\(220\) −13682.1 −4.19293
\(221\) 851.762 0.259257
\(222\) −6732.98 −2.03553
\(223\) 5789.03 1.73839 0.869197 0.494465i \(-0.164636\pi\)
0.869197 + 0.494465i \(0.164636\pi\)
\(224\) −16357.0 −4.87901
\(225\) −333.788 −0.0989003
\(226\) −2649.95 −0.779966
\(227\) −5509.30 −1.61086 −0.805429 0.592692i \(-0.798065\pi\)
−0.805429 + 0.592692i \(0.798065\pi\)
\(228\) −1068.38 −0.310331
\(229\) 5909.75 1.70536 0.852679 0.522434i \(-0.174976\pi\)
0.852679 + 0.522434i \(0.174976\pi\)
\(230\) 721.541 0.206857
\(231\) 3493.96 0.995176
\(232\) −20359.8 −5.76158
\(233\) −4435.64 −1.24716 −0.623580 0.781760i \(-0.714322\pi\)
−0.623580 + 0.781760i \(0.714322\pi\)
\(234\) 538.479 0.150434
\(235\) 690.286 0.191614
\(236\) 13513.1 3.72723
\(237\) 2869.22 0.786397
\(238\) 8086.33 2.20235
\(239\) 6913.28 1.87106 0.935529 0.353250i \(-0.114924\pi\)
0.935529 + 0.353250i \(0.114924\pi\)
\(240\) −7878.12 −2.11888
\(241\) 613.868 0.164078 0.0820388 0.996629i \(-0.473857\pi\)
0.0820388 + 0.996629i \(0.473857\pi\)
\(242\) −15042.7 −3.99580
\(243\) 243.000 0.0641500
\(244\) 9163.89 2.40434
\(245\) 63.1817 0.0164756
\(246\) −7418.35 −1.92267
\(247\) 166.630 0.0429248
\(248\) 17514.4 4.48453
\(249\) 389.338 0.0990896
\(250\) −8458.34 −2.13981
\(251\) −6522.04 −1.64011 −0.820054 0.572286i \(-0.806057\pi\)
−0.820054 + 0.572286i \(0.806057\pi\)
\(252\) 3791.83 0.947870
\(253\) 878.181 0.218224
\(254\) 12506.3 3.08944
\(255\) 2228.69 0.547316
\(256\) 22867.2 5.58282
\(257\) 3709.96 0.900471 0.450235 0.892910i \(-0.351340\pi\)
0.450235 + 0.892910i \(0.351340\pi\)
\(258\) −2936.21 −0.708529
\(259\) 7394.59 1.77404
\(260\) 2315.84 0.552394
\(261\) 2198.46 0.521385
\(262\) 1243.00 0.293103
\(263\) −5209.27 −1.22136 −0.610679 0.791878i \(-0.709104\pi\)
−0.610679 + 0.791878i \(0.709104\pi\)
\(264\) −15880.9 −3.70229
\(265\) −1011.69 −0.234520
\(266\) 1581.93 0.364640
\(267\) −3775.98 −0.865491
\(268\) 1539.37 0.350866
\(269\) −5274.71 −1.19556 −0.597779 0.801661i \(-0.703950\pi\)
−0.597779 + 0.801661i \(0.703950\pi\)
\(270\) 1408.96 0.317580
\(271\) 5396.33 1.20961 0.604804 0.796374i \(-0.293251\pi\)
0.604804 + 0.796374i \(0.293251\pi\)
\(272\) −22191.1 −4.94681
\(273\) −591.392 −0.131109
\(274\) −2629.70 −0.579803
\(275\) −2355.52 −0.516521
\(276\) 953.049 0.207851
\(277\) −6909.29 −1.49870 −0.749349 0.662176i \(-0.769633\pi\)
−0.749349 + 0.662176i \(0.769633\pi\)
\(278\) 5657.22 1.22050
\(279\) −1891.21 −0.405820
\(280\) 14330.5 3.05861
\(281\) 7176.10 1.52345 0.761727 0.647899i \(-0.224352\pi\)
0.761727 + 0.647899i \(0.224352\pi\)
\(282\) 1229.24 0.259574
\(283\) −3277.87 −0.688513 −0.344256 0.938876i \(-0.611869\pi\)
−0.344256 + 0.938876i \(0.611869\pi\)
\(284\) −63.9439 −0.0133605
\(285\) 435.998 0.0906185
\(286\) 3800.01 0.785661
\(287\) 8147.31 1.67568
\(288\) −8028.01 −1.64255
\(289\) 1364.76 0.277786
\(290\) 12747.1 2.58116
\(291\) −6.87647 −0.00138524
\(292\) 10555.2 2.11540
\(293\) −4245.73 −0.846547 −0.423274 0.906002i \(-0.639119\pi\)
−0.423274 + 0.906002i \(0.639119\pi\)
\(294\) 112.512 0.0223191
\(295\) −5514.56 −1.08837
\(296\) −33610.3 −6.59987
\(297\) 1714.83 0.335033
\(298\) 3752.10 0.729373
\(299\) −148.642 −0.0287498
\(300\) −2556.34 −0.491968
\(301\) 3224.73 0.617510
\(302\) −2620.41 −0.499297
\(303\) −1781.03 −0.337682
\(304\) −4341.24 −0.819038
\(305\) −3739.70 −0.702080
\(306\) 3968.77 0.741435
\(307\) −214.823 −0.0399368 −0.0199684 0.999801i \(-0.506357\pi\)
−0.0199684 + 0.999801i \(0.506357\pi\)
\(308\) 26758.7 4.95038
\(309\) −2210.69 −0.406995
\(310\) −10965.6 −2.00905
\(311\) −494.235 −0.0901141 −0.0450570 0.998984i \(-0.514347\pi\)
−0.0450570 + 0.998984i \(0.514347\pi\)
\(312\) 2688.03 0.487755
\(313\) −265.923 −0.0480220 −0.0240110 0.999712i \(-0.507644\pi\)
−0.0240110 + 0.999712i \(0.507644\pi\)
\(314\) 8621.81 1.54954
\(315\) −1547.41 −0.276784
\(316\) 21974.1 3.91184
\(317\) −678.113 −0.120147 −0.0600735 0.998194i \(-0.519134\pi\)
−0.0600735 + 0.998194i \(0.519134\pi\)
\(318\) −1801.59 −0.317698
\(319\) 15514.4 2.72301
\(320\) −25539.6 −4.46159
\(321\) 2546.84 0.442836
\(322\) −1411.16 −0.244225
\(323\) 1228.12 0.211561
\(324\) 1861.03 0.319107
\(325\) 398.698 0.0680487
\(326\) 15977.5 2.71445
\(327\) 2745.89 0.464367
\(328\) −37031.6 −6.23393
\(329\) −1350.03 −0.226229
\(330\) 9942.94 1.65861
\(331\) 4855.63 0.806313 0.403157 0.915131i \(-0.367913\pi\)
0.403157 + 0.915131i \(0.367913\pi\)
\(332\) 2981.77 0.492910
\(333\) 3629.26 0.597244
\(334\) −10980.5 −1.79889
\(335\) −628.203 −0.102455
\(336\) 15407.6 2.50165
\(337\) 7662.97 1.23866 0.619331 0.785130i \(-0.287404\pi\)
0.619331 + 0.785130i \(0.287404\pi\)
\(338\) 11584.4 1.86422
\(339\) 1428.40 0.228849
\(340\) 17068.5 2.72256
\(341\) −13346.1 −2.11945
\(342\) 776.409 0.122758
\(343\) −6413.31 −1.00958
\(344\) −14657.2 −2.29728
\(345\) −388.931 −0.0606937
\(346\) 5808.40 0.902490
\(347\) 1372.20 0.212287 0.106143 0.994351i \(-0.466150\pi\)
0.106143 + 0.994351i \(0.466150\pi\)
\(348\) 16837.1 2.59357
\(349\) −1713.78 −0.262855 −0.131428 0.991326i \(-0.541956\pi\)
−0.131428 + 0.991326i \(0.541956\pi\)
\(350\) 3785.10 0.578064
\(351\) −290.255 −0.0441386
\(352\) −56653.1 −8.57846
\(353\) −9043.82 −1.36361 −0.681804 0.731535i \(-0.738804\pi\)
−0.681804 + 0.731535i \(0.738804\pi\)
\(354\) −9820.14 −1.47439
\(355\) 26.0949 0.00390133
\(356\) −28918.5 −4.30528
\(357\) −4358.75 −0.646190
\(358\) 13955.9 2.06031
\(359\) 2963.70 0.435706 0.217853 0.975982i \(-0.430095\pi\)
0.217853 + 0.975982i \(0.430095\pi\)
\(360\) 7033.39 1.02970
\(361\) −6618.74 −0.964972
\(362\) 1528.27 0.221890
\(363\) 8108.45 1.17241
\(364\) −4529.21 −0.652185
\(365\) −4307.48 −0.617710
\(366\) −6659.52 −0.951090
\(367\) −637.767 −0.0907117 −0.0453558 0.998971i \(-0.514442\pi\)
−0.0453558 + 0.998971i \(0.514442\pi\)
\(368\) 3872.60 0.548568
\(369\) 3998.70 0.564129
\(370\) 21043.2 2.95671
\(371\) 1978.62 0.276886
\(372\) −14484.0 −2.01870
\(373\) 3834.52 0.532289 0.266144 0.963933i \(-0.414250\pi\)
0.266144 + 0.963933i \(0.414250\pi\)
\(374\) 28007.3 3.87225
\(375\) 4559.28 0.627840
\(376\) 6136.22 0.841626
\(377\) −2625.99 −0.358740
\(378\) −2755.58 −0.374951
\(379\) −566.636 −0.0767972 −0.0383986 0.999263i \(-0.512226\pi\)
−0.0383986 + 0.999263i \(0.512226\pi\)
\(380\) 3339.11 0.450771
\(381\) −6741.25 −0.906469
\(382\) −11977.7 −1.60428
\(383\) −9217.20 −1.22971 −0.614853 0.788642i \(-0.710784\pi\)
−0.614853 + 0.788642i \(0.710784\pi\)
\(384\) −24072.1 −3.19902
\(385\) −10920.0 −1.44554
\(386\) 8920.60 1.17629
\(387\) 1582.70 0.207889
\(388\) −52.6639 −0.00689073
\(389\) −12751.8 −1.66206 −0.831031 0.556226i \(-0.812249\pi\)
−0.831031 + 0.556226i \(0.812249\pi\)
\(390\) −1682.95 −0.218512
\(391\) −1095.54 −0.141698
\(392\) 561.647 0.0723660
\(393\) −670.012 −0.0859991
\(394\) −21204.8 −2.71137
\(395\) −8967.43 −1.14228
\(396\) 13133.2 1.66658
\(397\) 2193.72 0.277329 0.138664 0.990339i \(-0.455719\pi\)
0.138664 + 0.990339i \(0.455719\pi\)
\(398\) 8893.02 1.12002
\(399\) −852.702 −0.106989
\(400\) −10387.4 −1.29842
\(401\) 1852.85 0.230741 0.115371 0.993323i \(-0.463194\pi\)
0.115371 + 0.993323i \(0.463194\pi\)
\(402\) −1118.68 −0.138793
\(403\) 2258.98 0.279226
\(404\) −13640.2 −1.67976
\(405\) −759.469 −0.0931810
\(406\) −24930.2 −3.04745
\(407\) 25611.4 3.11919
\(408\) 19811.7 2.40398
\(409\) −9730.07 −1.17633 −0.588167 0.808739i \(-0.700150\pi\)
−0.588167 + 0.808739i \(0.700150\pi\)
\(410\) 23185.2 2.79277
\(411\) 1417.48 0.170120
\(412\) −16930.7 −2.02455
\(413\) 10785.1 1.28499
\(414\) −692.594 −0.0822201
\(415\) −1216.83 −0.143933
\(416\) 9589.17 1.13016
\(417\) −3049.40 −0.358105
\(418\) 5479.06 0.641124
\(419\) −13507.7 −1.57493 −0.787465 0.616359i \(-0.788607\pi\)
−0.787465 + 0.616359i \(0.788607\pi\)
\(420\) −11851.0 −1.37683
\(421\) 5819.08 0.673645 0.336823 0.941568i \(-0.390648\pi\)
0.336823 + 0.941568i \(0.390648\pi\)
\(422\) −5593.90 −0.645277
\(423\) −662.592 −0.0761615
\(424\) −8993.32 −1.03008
\(425\) 2938.54 0.335388
\(426\) 46.4689 0.00528503
\(427\) 7313.92 0.828911
\(428\) 19505.1 2.20284
\(429\) −2048.31 −0.230520
\(430\) 9176.79 1.02917
\(431\) 10170.6 1.13667 0.568333 0.822799i \(-0.307589\pi\)
0.568333 + 0.822799i \(0.307589\pi\)
\(432\) 7562.06 0.842199
\(433\) 780.624 0.0866383 0.0433192 0.999061i \(-0.486207\pi\)
0.0433192 + 0.999061i \(0.486207\pi\)
\(434\) 21446.0 2.37198
\(435\) −6871.05 −0.757337
\(436\) 21029.5 2.30994
\(437\) −214.320 −0.0234607
\(438\) −7670.62 −0.836795
\(439\) −9387.18 −1.02056 −0.510280 0.860008i \(-0.670458\pi\)
−0.510280 + 0.860008i \(0.670458\pi\)
\(440\) 49634.1 5.37776
\(441\) −60.6470 −0.00654864
\(442\) −4740.55 −0.510147
\(443\) −16622.6 −1.78276 −0.891381 0.453254i \(-0.850263\pi\)
−0.891381 + 0.453254i \(0.850263\pi\)
\(444\) 27794.9 2.97092
\(445\) 11801.4 1.25717
\(446\) −32219.3 −3.42069
\(447\) −2022.48 −0.214005
\(448\) 49949.2 5.26758
\(449\) 986.558 0.103694 0.0518469 0.998655i \(-0.483489\pi\)
0.0518469 + 0.998655i \(0.483489\pi\)
\(450\) 1857.73 0.194609
\(451\) 28218.5 2.94625
\(452\) 10939.5 1.13838
\(453\) 1412.47 0.146498
\(454\) 30662.4 3.16973
\(455\) 1848.33 0.190442
\(456\) 3875.75 0.398023
\(457\) 6599.18 0.675485 0.337742 0.941239i \(-0.390337\pi\)
0.337742 + 0.941239i \(0.390337\pi\)
\(458\) −32891.2 −3.35569
\(459\) −2139.27 −0.217544
\(460\) −2978.65 −0.301913
\(461\) −17494.0 −1.76741 −0.883704 0.468047i \(-0.844958\pi\)
−0.883704 + 0.468047i \(0.844958\pi\)
\(462\) −19445.9 −1.95824
\(463\) 1622.80 0.162890 0.0814450 0.996678i \(-0.474047\pi\)
0.0814450 + 0.996678i \(0.474047\pi\)
\(464\) 68415.3 6.84504
\(465\) 5910.77 0.589473
\(466\) 24686.9 2.45407
\(467\) 3130.69 0.310217 0.155108 0.987897i \(-0.450427\pi\)
0.155108 + 0.987897i \(0.450427\pi\)
\(468\) −2222.93 −0.219562
\(469\) 1228.61 0.120963
\(470\) −3841.84 −0.377044
\(471\) −4647.39 −0.454651
\(472\) −49021.1 −4.78046
\(473\) 11169.0 1.08573
\(474\) −15968.9 −1.54742
\(475\) 574.866 0.0555298
\(476\) −33381.8 −3.21439
\(477\) 971.104 0.0932155
\(478\) −38476.4 −3.68174
\(479\) 498.066 0.0475099 0.0237549 0.999718i \(-0.492438\pi\)
0.0237549 + 0.999718i \(0.492438\pi\)
\(480\) 25090.6 2.38589
\(481\) −4335.02 −0.410936
\(482\) −3416.53 −0.322860
\(483\) 760.651 0.0716580
\(484\) 62099.0 5.83199
\(485\) 21.4916 0.00201213
\(486\) −1352.44 −0.126230
\(487\) −8164.16 −0.759658 −0.379829 0.925057i \(-0.624017\pi\)
−0.379829 + 0.925057i \(0.624017\pi\)
\(488\) −33243.6 −3.08375
\(489\) −8612.29 −0.796444
\(490\) −351.643 −0.0324196
\(491\) 6914.18 0.635505 0.317752 0.948174i \(-0.397072\pi\)
0.317752 + 0.948174i \(0.397072\pi\)
\(492\) 30624.2 2.80619
\(493\) −19354.4 −1.76811
\(494\) −927.393 −0.0844644
\(495\) −5359.52 −0.486651
\(496\) −58853.7 −5.32784
\(497\) −51.0351 −0.00460611
\(498\) −2166.89 −0.194982
\(499\) −10976.7 −0.984743 −0.492372 0.870385i \(-0.663870\pi\)
−0.492372 + 0.870385i \(0.663870\pi\)
\(500\) 34917.5 3.12312
\(501\) 5918.81 0.527810
\(502\) 36298.9 3.22729
\(503\) 4883.56 0.432897 0.216449 0.976294i \(-0.430553\pi\)
0.216449 + 0.976294i \(0.430553\pi\)
\(504\) −13755.6 −1.21572
\(505\) 5566.42 0.490500
\(506\) −4887.58 −0.429406
\(507\) −6244.30 −0.546981
\(508\) −51628.3 −4.50912
\(509\) −3071.69 −0.267486 −0.133743 0.991016i \(-0.542700\pi\)
−0.133743 + 0.991016i \(0.542700\pi\)
\(510\) −12403.9 −1.07697
\(511\) 8424.36 0.729299
\(512\) −63077.2 −5.44462
\(513\) −418.506 −0.0360185
\(514\) −20648.1 −1.77188
\(515\) 6909.25 0.591180
\(516\) 12121.2 1.03412
\(517\) −4675.86 −0.397764
\(518\) −41155.2 −3.49084
\(519\) −3130.89 −0.264799
\(520\) −8401.13 −0.708488
\(521\) −10466.6 −0.880134 −0.440067 0.897965i \(-0.645045\pi\)
−0.440067 + 0.897965i \(0.645045\pi\)
\(522\) −12235.7 −1.02594
\(523\) 17015.5 1.42263 0.711317 0.702872i \(-0.248099\pi\)
0.711317 + 0.702872i \(0.248099\pi\)
\(524\) −5131.33 −0.427792
\(525\) −2040.27 −0.169609
\(526\) 28992.6 2.40330
\(527\) 16649.4 1.37621
\(528\) 53364.9 4.39850
\(529\) −11975.8 −0.984287
\(530\) 5630.65 0.461472
\(531\) 5293.32 0.432600
\(532\) −6530.47 −0.532203
\(533\) −4776.30 −0.388151
\(534\) 21015.5 1.70305
\(535\) −7959.85 −0.643241
\(536\) −5584.34 −0.450012
\(537\) −7522.60 −0.604514
\(538\) 29356.8 2.35253
\(539\) −427.981 −0.0342012
\(540\) −5816.44 −0.463518
\(541\) 196.265 0.0155972 0.00779861 0.999970i \(-0.497518\pi\)
0.00779861 + 0.999970i \(0.497518\pi\)
\(542\) −30033.7 −2.38018
\(543\) −823.779 −0.0651045
\(544\) 70675.3 5.57018
\(545\) −8581.96 −0.674515
\(546\) 3291.44 0.257987
\(547\) −15657.7 −1.22390 −0.611952 0.790895i \(-0.709615\pi\)
−0.611952 + 0.790895i \(0.709615\pi\)
\(548\) 10855.9 0.846240
\(549\) 3589.66 0.279059
\(550\) 13109.8 1.01637
\(551\) −3786.29 −0.292743
\(552\) −3457.36 −0.266585
\(553\) 17538.1 1.34863
\(554\) 38454.2 2.94903
\(555\) −11342.8 −0.867526
\(556\) −23354.0 −1.78135
\(557\) 10543.5 0.802050 0.401025 0.916067i \(-0.368654\pi\)
0.401025 + 0.916067i \(0.368654\pi\)
\(558\) 10525.7 0.798544
\(559\) −1890.48 −0.143039
\(560\) −48154.9 −3.63378
\(561\) −15096.7 −1.13615
\(562\) −39939.2 −2.99774
\(563\) 3882.05 0.290602 0.145301 0.989387i \(-0.453585\pi\)
0.145301 + 0.989387i \(0.453585\pi\)
\(564\) −5074.50 −0.378856
\(565\) −4464.29 −0.332415
\(566\) 18243.2 1.35481
\(567\) 1485.33 0.110014
\(568\) 231.968 0.0171358
\(569\) −8596.23 −0.633344 −0.316672 0.948535i \(-0.602565\pi\)
−0.316672 + 0.948535i \(0.602565\pi\)
\(570\) −2426.58 −0.178313
\(571\) 9931.35 0.727871 0.363935 0.931424i \(-0.381433\pi\)
0.363935 + 0.931424i \(0.381433\pi\)
\(572\) −15687.1 −1.14670
\(573\) 6456.32 0.470710
\(574\) −45344.5 −3.29729
\(575\) −512.808 −0.0371923
\(576\) 24515.0 1.77337
\(577\) 19338.0 1.39524 0.697619 0.716469i \(-0.254243\pi\)
0.697619 + 0.716469i \(0.254243\pi\)
\(578\) −7595.70 −0.546608
\(579\) −4808.45 −0.345133
\(580\) −52622.3 −3.76728
\(581\) 2379.82 0.169934
\(582\) 38.2716 0.00272579
\(583\) 6853.01 0.486831
\(584\) −38290.9 −2.71317
\(585\) 907.159 0.0641135
\(586\) 23630.0 1.66578
\(587\) −17190.3 −1.20872 −0.604360 0.796712i \(-0.706571\pi\)
−0.604360 + 0.796712i \(0.706571\pi\)
\(588\) −464.468 −0.0325754
\(589\) 3257.13 0.227857
\(590\) 30691.7 2.14162
\(591\) 11430.0 0.795543
\(592\) 112941. 7.84097
\(593\) −2497.07 −0.172921 −0.0864607 0.996255i \(-0.527556\pi\)
−0.0864607 + 0.996255i \(0.527556\pi\)
\(594\) −9544.04 −0.659254
\(595\) 13622.8 0.938622
\(596\) −15489.3 −1.06454
\(597\) −4793.58 −0.328624
\(598\) 827.279 0.0565718
\(599\) 16534.3 1.12784 0.563918 0.825831i \(-0.309293\pi\)
0.563918 + 0.825831i \(0.309293\pi\)
\(600\) 9273.57 0.630987
\(601\) 14103.7 0.957238 0.478619 0.878023i \(-0.341137\pi\)
0.478619 + 0.878023i \(0.341137\pi\)
\(602\) −17947.5 −1.21509
\(603\) 603.000 0.0407231
\(604\) 10817.5 0.728739
\(605\) −25342.0 −1.70298
\(606\) 9912.49 0.664468
\(607\) 7489.59 0.500812 0.250406 0.968141i \(-0.419436\pi\)
0.250406 + 0.968141i \(0.419436\pi\)
\(608\) 13826.2 0.922248
\(609\) 13438.1 0.894150
\(610\) 20813.6 1.38150
\(611\) 791.443 0.0524032
\(612\) −16383.8 −1.08215
\(613\) 17712.9 1.16708 0.583539 0.812085i \(-0.301668\pi\)
0.583539 + 0.812085i \(0.301668\pi\)
\(614\) 1195.62 0.0785849
\(615\) −12497.5 −0.819425
\(616\) −97071.9 −6.34925
\(617\) −15231.7 −0.993847 −0.496924 0.867794i \(-0.665537\pi\)
−0.496924 + 0.867794i \(0.665537\pi\)
\(618\) 12303.7 0.800856
\(619\) −1777.52 −0.115420 −0.0577098 0.998333i \(-0.518380\pi\)
−0.0577098 + 0.998333i \(0.518380\pi\)
\(620\) 45267.9 2.93227
\(621\) 373.327 0.0241242
\(622\) 2750.70 0.177320
\(623\) −23080.6 −1.48428
\(624\) −9032.62 −0.579478
\(625\) −9613.56 −0.615268
\(626\) 1480.02 0.0944943
\(627\) −2953.36 −0.188112
\(628\) −35592.3 −2.26161
\(629\) −31950.5 −2.02536
\(630\) 8612.25 0.544635
\(631\) −29832.3 −1.88210 −0.941049 0.338271i \(-0.890158\pi\)
−0.941049 + 0.338271i \(0.890158\pi\)
\(632\) −79715.0 −5.01724
\(633\) 3015.26 0.189330
\(634\) 3774.09 0.236417
\(635\) 21069.0 1.31669
\(636\) 7437.26 0.463689
\(637\) 72.4406 0.00450581
\(638\) −86346.6 −5.35814
\(639\) −25.0480 −0.00155068
\(640\) 75234.6 4.64673
\(641\) −12016.1 −0.740418 −0.370209 0.928949i \(-0.620714\pi\)
−0.370209 + 0.928949i \(0.620714\pi\)
\(642\) −14174.6 −0.871382
\(643\) −14193.2 −0.870490 −0.435245 0.900312i \(-0.643338\pi\)
−0.435245 + 0.900312i \(0.643338\pi\)
\(644\) 5825.49 0.356454
\(645\) −4946.54 −0.301969
\(646\) −6835.19 −0.416296
\(647\) 26400.1 1.60416 0.802082 0.597214i \(-0.203726\pi\)
0.802082 + 0.597214i \(0.203726\pi\)
\(648\) −6751.22 −0.409279
\(649\) 37354.6 2.25932
\(650\) −2218.99 −0.133901
\(651\) −11560.0 −0.695962
\(652\) −65957.7 −3.96181
\(653\) −9641.82 −0.577815 −0.288908 0.957357i \(-0.593292\pi\)
−0.288908 + 0.957357i \(0.593292\pi\)
\(654\) −15282.5 −0.913748
\(655\) 2094.05 0.124918
\(656\) 124438. 7.40622
\(657\) 4134.67 0.245524
\(658\) 7513.68 0.445158
\(659\) −9945.53 −0.587895 −0.293948 0.955822i \(-0.594969\pi\)
−0.293948 + 0.955822i \(0.594969\pi\)
\(660\) −41046.2 −2.42079
\(661\) −16881.2 −0.993348 −0.496674 0.867937i \(-0.665446\pi\)
−0.496674 + 0.867937i \(0.665446\pi\)
\(662\) −27024.4 −1.58661
\(663\) 2555.29 0.149682
\(664\) −10816.9 −0.632195
\(665\) 2665.03 0.155406
\(666\) −20198.9 −1.17521
\(667\) 3377.56 0.196071
\(668\) 45329.6 2.62553
\(669\) 17367.1 1.00366
\(670\) 3496.31 0.201604
\(671\) 25332.0 1.45742
\(672\) −49071.0 −2.81690
\(673\) 18318.3 1.04921 0.524606 0.851345i \(-0.324213\pi\)
0.524606 + 0.851345i \(0.324213\pi\)
\(674\) −42648.9 −2.43735
\(675\) −1001.37 −0.0571001
\(676\) −47822.4 −2.72089
\(677\) 5568.23 0.316107 0.158054 0.987431i \(-0.449478\pi\)
0.158054 + 0.987431i \(0.449478\pi\)
\(678\) −7949.86 −0.450313
\(679\) −42.0323 −0.00237563
\(680\) −61919.1 −3.49189
\(681\) −16527.9 −0.930029
\(682\) 74279.0 4.17051
\(683\) 12021.4 0.673476 0.336738 0.941598i \(-0.390676\pi\)
0.336738 + 0.941598i \(0.390676\pi\)
\(684\) −3205.15 −0.179170
\(685\) −4430.18 −0.247107
\(686\) 35693.8 1.98658
\(687\) 17729.2 0.984589
\(688\) 49252.9 2.72929
\(689\) −1159.95 −0.0641372
\(690\) 2164.62 0.119429
\(691\) 21089.9 1.16107 0.580534 0.814236i \(-0.302844\pi\)
0.580534 + 0.814236i \(0.302844\pi\)
\(692\) −23978.1 −1.31721
\(693\) 10481.9 0.574565
\(694\) −7637.09 −0.417723
\(695\) 9530.55 0.520164
\(696\) −61079.4 −3.32645
\(697\) −35202.9 −1.91306
\(698\) 9538.16 0.517228
\(699\) −13306.9 −0.720048
\(700\) −15625.6 −0.843701
\(701\) 23160.3 1.24786 0.623932 0.781479i \(-0.285534\pi\)
0.623932 + 0.781479i \(0.285534\pi\)
\(702\) 1615.44 0.0868529
\(703\) −6250.48 −0.335336
\(704\) 173001. 9.26166
\(705\) 2070.86 0.110628
\(706\) 50334.1 2.68321
\(707\) −10886.5 −0.579109
\(708\) 40539.2 2.15192
\(709\) −9142.60 −0.484284 −0.242142 0.970241i \(-0.577850\pi\)
−0.242142 + 0.970241i \(0.577850\pi\)
\(710\) −145.233 −0.00767677
\(711\) 8607.67 0.454027
\(712\) 104907. 5.52185
\(713\) −2905.52 −0.152612
\(714\) 24259.0 1.27153
\(715\) 6401.75 0.334842
\(716\) −57612.3 −3.00708
\(717\) 20739.8 1.08026
\(718\) −16494.7 −0.857351
\(719\) −4851.00 −0.251616 −0.125808 0.992055i \(-0.540152\pi\)
−0.125808 + 0.992055i \(0.540152\pi\)
\(720\) −23634.4 −1.22333
\(721\) −13512.8 −0.697977
\(722\) 36837.1 1.89880
\(723\) 1841.60 0.0947303
\(724\) −6308.96 −0.323854
\(725\) −9059.53 −0.464086
\(726\) −45128.2 −2.30698
\(727\) 393.072 0.0200526 0.0100263 0.999950i \(-0.496808\pi\)
0.0100263 + 0.999950i \(0.496808\pi\)
\(728\) 16430.5 0.836477
\(729\) 729.000 0.0370370
\(730\) 23973.6 1.21549
\(731\) −13933.4 −0.704988
\(732\) 27491.7 1.38814
\(733\) 9672.93 0.487419 0.243709 0.969848i \(-0.421636\pi\)
0.243709 + 0.969848i \(0.421636\pi\)
\(734\) 3549.54 0.178496
\(735\) 189.545 0.00951222
\(736\) −12333.6 −0.617695
\(737\) 4255.33 0.212682
\(738\) −22255.1 −1.11005
\(739\) −16379.8 −0.815344 −0.407672 0.913128i \(-0.633659\pi\)
−0.407672 + 0.913128i \(0.633659\pi\)
\(740\) −86869.9 −4.31540
\(741\) 499.890 0.0247826
\(742\) −11012.2 −0.544837
\(743\) 1918.02 0.0947043 0.0473522 0.998878i \(-0.484922\pi\)
0.0473522 + 0.998878i \(0.484922\pi\)
\(744\) 52543.1 2.58914
\(745\) 6321.04 0.310852
\(746\) −21341.3 −1.04740
\(747\) 1168.02 0.0572094
\(748\) −115619. −5.65167
\(749\) 15567.5 0.759444
\(750\) −25375.0 −1.23542
\(751\) 18041.6 0.876627 0.438313 0.898822i \(-0.355576\pi\)
0.438313 + 0.898822i \(0.355576\pi\)
\(752\) −20619.6 −0.999893
\(753\) −19566.1 −0.946917
\(754\) 14615.1 0.705904
\(755\) −4414.53 −0.212796
\(756\) 11375.5 0.547253
\(757\) −4736.09 −0.227393 −0.113696 0.993516i \(-0.536269\pi\)
−0.113696 + 0.993516i \(0.536269\pi\)
\(758\) 3153.66 0.151116
\(759\) 2634.54 0.125992
\(760\) −12113.2 −0.578148
\(761\) −37890.8 −1.80491 −0.902457 0.430781i \(-0.858238\pi\)
−0.902457 + 0.430781i \(0.858238\pi\)
\(762\) 37519.0 1.78369
\(763\) 16784.2 0.796367
\(764\) 49446.1 2.34149
\(765\) 6686.06 0.315993
\(766\) 51299.1 2.41973
\(767\) −6322.69 −0.297652
\(768\) 68601.7 3.22324
\(769\) −10807.3 −0.506791 −0.253395 0.967363i \(-0.581547\pi\)
−0.253395 + 0.967363i \(0.581547\pi\)
\(770\) 60776.0 2.84443
\(771\) 11129.9 0.519887
\(772\) −36825.8 −1.71682
\(773\) 35806.3 1.66606 0.833029 0.553230i \(-0.186605\pi\)
0.833029 + 0.553230i \(0.186605\pi\)
\(774\) −8808.63 −0.409069
\(775\) 7793.39 0.361222
\(776\) 191.048 0.00883790
\(777\) 22183.8 1.02425
\(778\) 70971.2 3.27049
\(779\) −6886.74 −0.316743
\(780\) 6947.53 0.318925
\(781\) −176.762 −0.00809864
\(782\) 6097.32 0.278823
\(783\) 6595.39 0.301022
\(784\) −1887.31 −0.0859744
\(785\) 14524.9 0.660402
\(786\) 3729.01 0.169223
\(787\) 19577.1 0.886722 0.443361 0.896343i \(-0.353786\pi\)
0.443361 + 0.896343i \(0.353786\pi\)
\(788\) 87537.0 3.95733
\(789\) −15627.8 −0.705152
\(790\) 49909.0 2.24770
\(791\) 8731.05 0.392466
\(792\) −47642.8 −2.13752
\(793\) −4287.73 −0.192007
\(794\) −12209.3 −0.545708
\(795\) −3035.08 −0.135400
\(796\) −36711.9 −1.63470
\(797\) 24351.5 1.08228 0.541139 0.840933i \(-0.317993\pi\)
0.541139 + 0.840933i \(0.317993\pi\)
\(798\) 4745.78 0.210525
\(799\) 5833.19 0.258277
\(800\) 33082.2 1.46204
\(801\) −11327.9 −0.499691
\(802\) −10312.2 −0.454036
\(803\) 29178.1 1.28228
\(804\) 4618.11 0.202572
\(805\) −2377.33 −0.104087
\(806\) −12572.6 −0.549441
\(807\) −15824.1 −0.690255
\(808\) 49482.1 2.15442
\(809\) −19396.6 −0.842953 −0.421476 0.906839i \(-0.638488\pi\)
−0.421476 + 0.906839i \(0.638488\pi\)
\(810\) 4226.89 0.183355
\(811\) −24238.5 −1.04948 −0.524739 0.851263i \(-0.675837\pi\)
−0.524739 + 0.851263i \(0.675837\pi\)
\(812\) 102916. 4.44784
\(813\) 16189.0 0.698368
\(814\) −142542. −6.13773
\(815\) 26916.7 1.15687
\(816\) −66573.3 −2.85604
\(817\) −2725.79 −0.116724
\(818\) 54153.5 2.31471
\(819\) −1774.18 −0.0756957
\(820\) −95712.6 −4.07613
\(821\) −13774.7 −0.585554 −0.292777 0.956181i \(-0.594579\pi\)
−0.292777 + 0.956181i \(0.594579\pi\)
\(822\) −7889.10 −0.334749
\(823\) −29087.7 −1.23200 −0.615998 0.787748i \(-0.711247\pi\)
−0.615998 + 0.787748i \(0.711247\pi\)
\(824\) 61419.0 2.59664
\(825\) −7066.56 −0.298213
\(826\) −60025.4 −2.52851
\(827\) 24698.3 1.03850 0.519252 0.854621i \(-0.326211\pi\)
0.519252 + 0.854621i \(0.326211\pi\)
\(828\) 2859.15 0.120003
\(829\) −9009.94 −0.377477 −0.188738 0.982027i \(-0.560440\pi\)
−0.188738 + 0.982027i \(0.560440\pi\)
\(830\) 6772.38 0.283220
\(831\) −20727.9 −0.865273
\(832\) −29282.3 −1.22017
\(833\) 533.911 0.0222076
\(834\) 16971.7 0.704653
\(835\) −18498.6 −0.766670
\(836\) −22618.5 −0.935739
\(837\) −5673.63 −0.234300
\(838\) 75178.4 3.09904
\(839\) −18900.3 −0.777726 −0.388863 0.921296i \(-0.627132\pi\)
−0.388863 + 0.921296i \(0.627132\pi\)
\(840\) 42991.4 1.76589
\(841\) 35280.6 1.44658
\(842\) −32386.5 −1.32555
\(843\) 21528.3 0.879566
\(844\) 23092.6 0.941800
\(845\) 19515.9 0.794516
\(846\) 3687.71 0.149865
\(847\) 49562.7 2.01062
\(848\) 30220.4 1.22379
\(849\) −9833.61 −0.397513
\(850\) −16354.7 −0.659953
\(851\) 5575.73 0.224599
\(852\) −191.832 −0.00771366
\(853\) 15100.3 0.606123 0.303062 0.952971i \(-0.401991\pi\)
0.303062 + 0.952971i \(0.401991\pi\)
\(854\) −40706.2 −1.63107
\(855\) 1307.99 0.0523186
\(856\) −70758.2 −2.82531
\(857\) −36278.5 −1.44603 −0.723016 0.690831i \(-0.757245\pi\)
−0.723016 + 0.690831i \(0.757245\pi\)
\(858\) 11400.0 0.453602
\(859\) 22352.9 0.887861 0.443931 0.896061i \(-0.353584\pi\)
0.443931 + 0.896061i \(0.353584\pi\)
\(860\) −37883.4 −1.50211
\(861\) 24441.9 0.967455
\(862\) −56605.5 −2.23665
\(863\) −11591.1 −0.457204 −0.228602 0.973520i \(-0.573415\pi\)
−0.228602 + 0.973520i \(0.573415\pi\)
\(864\) −24084.0 −0.948328
\(865\) 9785.23 0.384633
\(866\) −4344.62 −0.170481
\(867\) 4094.29 0.160380
\(868\) −88532.8 −3.46198
\(869\) 60743.7 2.37122
\(870\) 38241.4 1.49023
\(871\) −720.262 −0.0280197
\(872\) −76288.4 −2.96267
\(873\) −20.6294 −0.000799771 0
\(874\) 1192.82 0.0461644
\(875\) 27868.5 1.07672
\(876\) 31665.6 1.22133
\(877\) 1593.02 0.0613368 0.0306684 0.999530i \(-0.490236\pi\)
0.0306684 + 0.999530i \(0.490236\pi\)
\(878\) 52245.1 2.00819
\(879\) −12737.2 −0.488754
\(880\) −166786. −6.38904
\(881\) 33123.4 1.26669 0.633347 0.773868i \(-0.281681\pi\)
0.633347 + 0.773868i \(0.281681\pi\)
\(882\) 337.536 0.0128860
\(883\) −5020.60 −0.191344 −0.0956720 0.995413i \(-0.530500\pi\)
−0.0956720 + 0.995413i \(0.530500\pi\)
\(884\) 19569.8 0.744575
\(885\) −16543.7 −0.628373
\(886\) 92514.4 3.50799
\(887\) 16806.2 0.636185 0.318093 0.948060i \(-0.396958\pi\)
0.318093 + 0.948060i \(0.396958\pi\)
\(888\) −100831. −3.81043
\(889\) −41205.8 −1.55455
\(890\) −65681.6 −2.47377
\(891\) 5144.50 0.193431
\(892\) 133007. 4.99260
\(893\) 1141.15 0.0427626
\(894\) 11256.3 0.421104
\(895\) 23511.0 0.878087
\(896\) −147140. −5.48616
\(897\) −445.926 −0.0165987
\(898\) −5490.76 −0.204041
\(899\) −51330.3 −1.90430
\(900\) −7669.02 −0.284038
\(901\) −8549.20 −0.316110
\(902\) −157052. −5.79742
\(903\) 9674.20 0.356520
\(904\) −39684.8 −1.46006
\(905\) 2574.63 0.0945674
\(906\) −7861.24 −0.288269
\(907\) 42624.3 1.56044 0.780219 0.625506i \(-0.215107\pi\)
0.780219 + 0.625506i \(0.215107\pi\)
\(908\) −126580. −4.62632
\(909\) −5343.10 −0.194961
\(910\) −10287.0 −0.374738
\(911\) 17061.2 0.620486 0.310243 0.950657i \(-0.399590\pi\)
0.310243 + 0.950657i \(0.399590\pi\)
\(912\) −13023.7 −0.472872
\(913\) 8242.60 0.298784
\(914\) −36728.3 −1.32917
\(915\) −11219.1 −0.405346
\(916\) 135780. 4.89772
\(917\) −4095.44 −0.147484
\(918\) 11906.3 0.428068
\(919\) −40517.4 −1.45435 −0.727175 0.686452i \(-0.759167\pi\)
−0.727175 + 0.686452i \(0.759167\pi\)
\(920\) 10805.6 0.387227
\(921\) −644.470 −0.0230575
\(922\) 97364.0 3.47778
\(923\) 29.9189 0.00106695
\(924\) 80276.1 2.85811
\(925\) −14955.6 −0.531609
\(926\) −9031.84 −0.320524
\(927\) −6632.06 −0.234979
\(928\) −217892. −7.70761
\(929\) −45913.3 −1.62149 −0.810746 0.585398i \(-0.800938\pi\)
−0.810746 + 0.585398i \(0.800938\pi\)
\(930\) −32896.8 −1.15992
\(931\) 104.449 0.00367688
\(932\) −101912. −3.58179
\(933\) −1482.70 −0.0520274
\(934\) −17424.1 −0.610423
\(935\) 47183.0 1.65032
\(936\) 8064.09 0.281606
\(937\) 20590.8 0.717900 0.358950 0.933357i \(-0.383135\pi\)
0.358950 + 0.933357i \(0.383135\pi\)
\(938\) −6837.92 −0.238023
\(939\) −797.770 −0.0277255
\(940\) 15859.8 0.550307
\(941\) −403.036 −0.0139624 −0.00698120 0.999976i \(-0.502222\pi\)
−0.00698120 + 0.999976i \(0.502222\pi\)
\(942\) 25865.4 0.894630
\(943\) 6143.30 0.212146
\(944\) 164726. 5.67943
\(945\) −4642.24 −0.159801
\(946\) −62161.8 −2.13642
\(947\) 8234.78 0.282571 0.141285 0.989969i \(-0.454877\pi\)
0.141285 + 0.989969i \(0.454877\pi\)
\(948\) 65922.4 2.25850
\(949\) −4938.72 −0.168933
\(950\) −3199.46 −0.109268
\(951\) −2034.34 −0.0693669
\(952\) 121098. 4.12271
\(953\) −33516.2 −1.13924 −0.569620 0.821908i \(-0.692910\pi\)
−0.569620 + 0.821908i \(0.692910\pi\)
\(954\) −5404.76 −0.183423
\(955\) −20178.5 −0.683729
\(956\) 158837. 5.37360
\(957\) 46543.2 1.57213
\(958\) −2772.03 −0.0934866
\(959\) 8664.32 0.291747
\(960\) −76618.9 −2.57590
\(961\) 14365.5 0.482210
\(962\) 24126.9 0.808610
\(963\) 7640.51 0.255672
\(964\) 14104.0 0.471224
\(965\) 15028.3 0.501323
\(966\) −4233.47 −0.141004
\(967\) −20602.4 −0.685139 −0.342570 0.939492i \(-0.611297\pi\)
−0.342570 + 0.939492i \(0.611297\pi\)
\(968\) −225275. −7.47998
\(969\) 3684.35 0.122145
\(970\) −119.613 −0.00395934
\(971\) 4984.98 0.164754 0.0823768 0.996601i \(-0.473749\pi\)
0.0823768 + 0.996601i \(0.473749\pi\)
\(972\) 5583.09 0.184236
\(973\) −18639.4 −0.614132
\(974\) 45438.3 1.49480
\(975\) 1196.10 0.0392879
\(976\) 111709. 3.66364
\(977\) −52420.8 −1.71657 −0.858286 0.513172i \(-0.828470\pi\)
−0.858286 + 0.513172i \(0.828470\pi\)
\(978\) 47932.4 1.56719
\(979\) −79940.4 −2.60971
\(980\) 1451.64 0.0473174
\(981\) 8237.66 0.268102
\(982\) −38481.4 −1.25050
\(983\) 36852.7 1.19575 0.597873 0.801591i \(-0.296013\pi\)
0.597873 + 0.801591i \(0.296013\pi\)
\(984\) −111095. −3.59916
\(985\) −35723.0 −1.15556
\(986\) 107718. 3.47916
\(987\) −4050.08 −0.130613
\(988\) 3828.44 0.123278
\(989\) 2431.54 0.0781784
\(990\) 29828.8 0.957598
\(991\) 11437.3 0.366618 0.183309 0.983055i \(-0.441319\pi\)
0.183309 + 0.983055i \(0.441319\pi\)
\(992\) 187440. 5.99923
\(993\) 14566.9 0.465525
\(994\) 284.040 0.00906358
\(995\) 14981.8 0.477342
\(996\) 8945.32 0.284581
\(997\) 34016.8 1.08057 0.540283 0.841484i \(-0.318317\pi\)
0.540283 + 0.841484i \(0.318317\pi\)
\(998\) 61092.0 1.93771
\(999\) 10887.8 0.344819
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 201.4.a.e.1.1 11
3.2 odd 2 603.4.a.g.1.11 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.4.a.e.1.1 11 1.1 even 1 trivial
603.4.a.g.1.11 11 3.2 odd 2