Properties

Label 435.4.a.i.1.7
Level $435$
Weight $4$
Character 435.1
Self dual yes
Analytic conductor $25.666$
Analytic rank $0$
Dimension $7$
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] = [435,4,Mod(1,435)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(435, 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("435.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 435.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: \(25.6658308525\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-4.88324\) of defining polynomial
Character \(\chi\) \(=\) 435.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.88324 q^{2} -3.00000 q^{3} +15.8460 q^{4} +5.00000 q^{5} -14.6497 q^{6} +5.48750 q^{7} +38.3141 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+4.88324 q^{2} -3.00000 q^{3} +15.8460 q^{4} +5.00000 q^{5} -14.6497 q^{6} +5.48750 q^{7} +38.3141 q^{8} +9.00000 q^{9} +24.4162 q^{10} +50.1324 q^{11} -47.5381 q^{12} -20.7349 q^{13} +26.7968 q^{14} -15.0000 q^{15} +60.3288 q^{16} -18.8027 q^{17} +43.9492 q^{18} +78.8346 q^{19} +79.2302 q^{20} -16.4625 q^{21} +244.809 q^{22} -6.33763 q^{23} -114.942 q^{24} +25.0000 q^{25} -101.254 q^{26} -27.0000 q^{27} +86.9552 q^{28} +29.0000 q^{29} -73.2486 q^{30} +310.950 q^{31} -11.9130 q^{32} -150.397 q^{33} -91.8182 q^{34} +27.4375 q^{35} +142.614 q^{36} -338.745 q^{37} +384.969 q^{38} +62.2047 q^{39} +191.571 q^{40} +353.526 q^{41} -80.3904 q^{42} +507.609 q^{43} +794.400 q^{44} +45.0000 q^{45} -30.9482 q^{46} -112.771 q^{47} -180.986 q^{48} -312.887 q^{49} +122.081 q^{50} +56.4081 q^{51} -328.566 q^{52} -144.849 q^{53} -131.848 q^{54} +250.662 q^{55} +210.249 q^{56} -236.504 q^{57} +141.614 q^{58} -342.739 q^{59} -237.691 q^{60} +357.486 q^{61} +1518.44 q^{62} +49.3875 q^{63} -540.804 q^{64} -103.675 q^{65} -734.426 q^{66} -183.087 q^{67} -297.949 q^{68} +19.0129 q^{69} +133.984 q^{70} -594.034 q^{71} +344.827 q^{72} -622.609 q^{73} -1654.17 q^{74} -75.0000 q^{75} +1249.22 q^{76} +275.102 q^{77} +303.761 q^{78} -1275.18 q^{79} +301.644 q^{80} +81.0000 q^{81} +1726.35 q^{82} -739.108 q^{83} -260.866 q^{84} -94.0136 q^{85} +2478.78 q^{86} -87.0000 q^{87} +1920.78 q^{88} +906.113 q^{89} +219.746 q^{90} -113.783 q^{91} -100.426 q^{92} -932.849 q^{93} -550.688 q^{94} +394.173 q^{95} +35.7390 q^{96} +76.0665 q^{97} -1527.90 q^{98} +451.192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19} + 110 q^{20} + 150 q^{21} + 61 q^{22} + 34 q^{23} + 99 q^{24} + 175 q^{25} - 241 q^{26} - 189 q^{27} - 57 q^{28} + 203 q^{29} + 30 q^{30} + 524 q^{31} - 6 q^{32} - 228 q^{33} + 255 q^{34} - 250 q^{35} + 198 q^{36} - 28 q^{37} + 222 q^{38} - 90 q^{39} - 165 q^{40} + 1532 q^{41} - 267 q^{42} - 464 q^{43} + 1475 q^{44} + 315 q^{45} + 72 q^{46} - 360 q^{47} - 414 q^{48} + 569 q^{49} - 50 q^{50} + 420 q^{51} - 205 q^{52} + 282 q^{53} + 54 q^{54} + 380 q^{55} + 1102 q^{56} - 270 q^{57} - 58 q^{58} + 766 q^{59} - 330 q^{60} + 1200 q^{61} + 2856 q^{62} - 450 q^{63} + 701 q^{64} + 150 q^{65} - 183 q^{66} + 1546 q^{67} + 1801 q^{68} - 102 q^{69} + 445 q^{70} + 1802 q^{71} - 297 q^{72} - 220 q^{73} + 1594 q^{74} - 525 q^{75} + 1960 q^{76} + 3222 q^{77} + 723 q^{78} + 1298 q^{79} + 690 q^{80} + 567 q^{81} + 856 q^{82} + 1652 q^{83} + 171 q^{84} - 700 q^{85} + 7628 q^{86} - 609 q^{87} + 550 q^{88} + 2846 q^{89} - 90 q^{90} - 816 q^{91} + 472 q^{92} - 1572 q^{93} + 745 q^{94} + 450 q^{95} + 18 q^{96} + 1110 q^{97} - 761 q^{98} + 684 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.88324 1.72649 0.863243 0.504788i \(-0.168429\pi\)
0.863243 + 0.504788i \(0.168429\pi\)
\(3\) −3.00000 −0.577350
\(4\) 15.8460 1.98076
\(5\) 5.00000 0.447214
\(6\) −14.6497 −0.996787
\(7\) 5.48750 0.296297 0.148149 0.988965i \(-0.452669\pi\)
0.148149 + 0.988965i \(0.452669\pi\)
\(8\) 38.3141 1.69326
\(9\) 9.00000 0.333333
\(10\) 24.4162 0.772108
\(11\) 50.1324 1.37413 0.687067 0.726594i \(-0.258898\pi\)
0.687067 + 0.726594i \(0.258898\pi\)
\(12\) −47.5381 −1.14359
\(13\) −20.7349 −0.442371 −0.221186 0.975232i \(-0.570993\pi\)
−0.221186 + 0.975232i \(0.570993\pi\)
\(14\) 26.7968 0.511553
\(15\) −15.0000 −0.258199
\(16\) 60.3288 0.942637
\(17\) −18.8027 −0.268255 −0.134127 0.990964i \(-0.542823\pi\)
−0.134127 + 0.990964i \(0.542823\pi\)
\(18\) 43.9492 0.575496
\(19\) 78.8346 0.951890 0.475945 0.879475i \(-0.342106\pi\)
0.475945 + 0.879475i \(0.342106\pi\)
\(20\) 79.2302 0.885821
\(21\) −16.4625 −0.171067
\(22\) 244.809 2.37243
\(23\) −6.33763 −0.0574559 −0.0287280 0.999587i \(-0.509146\pi\)
−0.0287280 + 0.999587i \(0.509146\pi\)
\(24\) −114.942 −0.977605
\(25\) 25.0000 0.200000
\(26\) −101.254 −0.763748
\(27\) −27.0000 −0.192450
\(28\) 86.9552 0.586892
\(29\) 29.0000 0.185695
\(30\) −73.2486 −0.445777
\(31\) 310.950 1.80156 0.900778 0.434280i \(-0.142997\pi\)
0.900778 + 0.434280i \(0.142997\pi\)
\(32\) −11.9130 −0.0658106
\(33\) −150.397 −0.793357
\(34\) −91.8182 −0.463138
\(35\) 27.4375 0.132508
\(36\) 142.614 0.660252
\(37\) −338.745 −1.50512 −0.752558 0.658525i \(-0.771180\pi\)
−0.752558 + 0.658525i \(0.771180\pi\)
\(38\) 384.969 1.64343
\(39\) 62.2047 0.255403
\(40\) 191.571 0.757250
\(41\) 353.526 1.34662 0.673312 0.739359i \(-0.264871\pi\)
0.673312 + 0.739359i \(0.264871\pi\)
\(42\) −80.3904 −0.295345
\(43\) 507.609 1.80022 0.900112 0.435658i \(-0.143484\pi\)
0.900112 + 0.435658i \(0.143484\pi\)
\(44\) 794.400 2.72183
\(45\) 45.0000 0.149071
\(46\) −30.9482 −0.0991969
\(47\) −112.771 −0.349986 −0.174993 0.984570i \(-0.555990\pi\)
−0.174993 + 0.984570i \(0.555990\pi\)
\(48\) −180.986 −0.544232
\(49\) −312.887 −0.912208
\(50\) 122.081 0.345297
\(51\) 56.4081 0.154877
\(52\) −328.566 −0.876230
\(53\) −144.849 −0.375406 −0.187703 0.982226i \(-0.560104\pi\)
−0.187703 + 0.982226i \(0.560104\pi\)
\(54\) −131.848 −0.332262
\(55\) 250.662 0.614532
\(56\) 210.249 0.501709
\(57\) −236.504 −0.549574
\(58\) 141.614 0.320600
\(59\) −342.739 −0.756285 −0.378142 0.925747i \(-0.623437\pi\)
−0.378142 + 0.925747i \(0.623437\pi\)
\(60\) −237.691 −0.511429
\(61\) 357.486 0.750350 0.375175 0.926954i \(-0.377583\pi\)
0.375175 + 0.926954i \(0.377583\pi\)
\(62\) 1518.44 3.11036
\(63\) 49.3875 0.0987657
\(64\) −540.804 −1.05626
\(65\) −103.675 −0.197834
\(66\) −734.426 −1.36972
\(67\) −183.087 −0.333844 −0.166922 0.985970i \(-0.553383\pi\)
−0.166922 + 0.985970i \(0.553383\pi\)
\(68\) −297.949 −0.531347
\(69\) 19.0129 0.0331722
\(70\) 133.984 0.228773
\(71\) −594.034 −0.992942 −0.496471 0.868053i \(-0.665371\pi\)
−0.496471 + 0.868053i \(0.665371\pi\)
\(72\) 344.827 0.564421
\(73\) −622.609 −0.998231 −0.499115 0.866536i \(-0.666342\pi\)
−0.499115 + 0.866536i \(0.666342\pi\)
\(74\) −1654.17 −2.59856
\(75\) −75.0000 −0.115470
\(76\) 1249.22 1.88546
\(77\) 275.102 0.407152
\(78\) 303.761 0.440950
\(79\) −1275.18 −1.81607 −0.908034 0.418897i \(-0.862417\pi\)
−0.908034 + 0.418897i \(0.862417\pi\)
\(80\) 301.644 0.421560
\(81\) 81.0000 0.111111
\(82\) 1726.35 2.32493
\(83\) −739.108 −0.977441 −0.488720 0.872440i \(-0.662536\pi\)
−0.488720 + 0.872440i \(0.662536\pi\)
\(84\) −260.866 −0.338842
\(85\) −94.0136 −0.119967
\(86\) 2478.78 3.10806
\(87\) −87.0000 −0.107211
\(88\) 1920.78 2.32677
\(89\) 906.113 1.07919 0.539594 0.841925i \(-0.318578\pi\)
0.539594 + 0.841925i \(0.318578\pi\)
\(90\) 219.746 0.257369
\(91\) −113.783 −0.131073
\(92\) −100.426 −0.113806
\(93\) −932.849 −1.04013
\(94\) −550.688 −0.604246
\(95\) 394.173 0.425698
\(96\) 35.7390 0.0379958
\(97\) 76.0665 0.0796225 0.0398112 0.999207i \(-0.487324\pi\)
0.0398112 + 0.999207i \(0.487324\pi\)
\(98\) −1527.90 −1.57491
\(99\) 451.192 0.458045
\(100\) 396.151 0.396151
\(101\) 653.553 0.643871 0.321935 0.946762i \(-0.395667\pi\)
0.321935 + 0.946762i \(0.395667\pi\)
\(102\) 275.455 0.267393
\(103\) 969.801 0.927741 0.463871 0.885903i \(-0.346460\pi\)
0.463871 + 0.885903i \(0.346460\pi\)
\(104\) −794.440 −0.749050
\(105\) −82.3125 −0.0765036
\(106\) −707.332 −0.648133
\(107\) −1267.53 −1.14520 −0.572601 0.819835i \(-0.694065\pi\)
−0.572601 + 0.819835i \(0.694065\pi\)
\(108\) −427.843 −0.381197
\(109\) −808.142 −0.710146 −0.355073 0.934838i \(-0.615544\pi\)
−0.355073 + 0.934838i \(0.615544\pi\)
\(110\) 1224.04 1.06098
\(111\) 1016.23 0.868980
\(112\) 331.054 0.279301
\(113\) −1220.10 −1.01572 −0.507862 0.861438i \(-0.669564\pi\)
−0.507862 + 0.861438i \(0.669564\pi\)
\(114\) −1154.91 −0.948832
\(115\) −31.6881 −0.0256951
\(116\) 459.535 0.367817
\(117\) −186.614 −0.147457
\(118\) −1673.68 −1.30572
\(119\) −103.180 −0.0794831
\(120\) −574.712 −0.437198
\(121\) 1182.26 0.888247
\(122\) 1745.69 1.29547
\(123\) −1060.58 −0.777473
\(124\) 4927.32 3.56844
\(125\) 125.000 0.0894427
\(126\) 241.171 0.170518
\(127\) 814.733 0.569258 0.284629 0.958638i \(-0.408130\pi\)
0.284629 + 0.958638i \(0.408130\pi\)
\(128\) −2545.57 −1.75781
\(129\) −1522.83 −1.03936
\(130\) −506.268 −0.341559
\(131\) −1493.91 −0.996363 −0.498181 0.867073i \(-0.665999\pi\)
−0.498181 + 0.867073i \(0.665999\pi\)
\(132\) −2383.20 −1.57145
\(133\) 432.605 0.282042
\(134\) −894.056 −0.576378
\(135\) −135.000 −0.0860663
\(136\) −720.410 −0.454225
\(137\) −1608.72 −1.00323 −0.501615 0.865091i \(-0.667261\pi\)
−0.501615 + 0.865091i \(0.667261\pi\)
\(138\) 92.8445 0.0572714
\(139\) 51.5725 0.0314700 0.0157350 0.999876i \(-0.494991\pi\)
0.0157350 + 0.999876i \(0.494991\pi\)
\(140\) 434.776 0.262466
\(141\) 338.313 0.202064
\(142\) −2900.81 −1.71430
\(143\) −1039.49 −0.607878
\(144\) 542.959 0.314212
\(145\) 145.000 0.0830455
\(146\) −3040.35 −1.72343
\(147\) 938.662 0.526664
\(148\) −5367.77 −2.98127
\(149\) −608.330 −0.334472 −0.167236 0.985917i \(-0.553484\pi\)
−0.167236 + 0.985917i \(0.553484\pi\)
\(150\) −366.243 −0.199357
\(151\) −341.568 −0.184082 −0.0920412 0.995755i \(-0.529339\pi\)
−0.0920412 + 0.995755i \(0.529339\pi\)
\(152\) 3020.48 1.61180
\(153\) −169.224 −0.0894182
\(154\) 1343.39 0.702943
\(155\) 1554.75 0.805680
\(156\) 985.699 0.505891
\(157\) −358.378 −0.182176 −0.0910882 0.995843i \(-0.529035\pi\)
−0.0910882 + 0.995843i \(0.529035\pi\)
\(158\) −6227.03 −3.13542
\(159\) 434.547 0.216741
\(160\) −59.5650 −0.0294314
\(161\) −34.7777 −0.0170240
\(162\) 395.543 0.191832
\(163\) −1667.36 −0.801213 −0.400606 0.916250i \(-0.631201\pi\)
−0.400606 + 0.916250i \(0.631201\pi\)
\(164\) 5602.00 2.66733
\(165\) −751.986 −0.354800
\(166\) −3609.24 −1.68754
\(167\) −1832.30 −0.849029 −0.424514 0.905421i \(-0.639555\pi\)
−0.424514 + 0.905421i \(0.639555\pi\)
\(168\) −630.746 −0.289662
\(169\) −1767.06 −0.804308
\(170\) −459.091 −0.207122
\(171\) 709.512 0.317297
\(172\) 8043.60 3.56580
\(173\) 2034.77 0.894224 0.447112 0.894478i \(-0.352453\pi\)
0.447112 + 0.894478i \(0.352453\pi\)
\(174\) −424.842 −0.185099
\(175\) 137.188 0.0592594
\(176\) 3024.43 1.29531
\(177\) 1028.22 0.436641
\(178\) 4424.77 1.86320
\(179\) −332.198 −0.138713 −0.0693566 0.997592i \(-0.522095\pi\)
−0.0693566 + 0.997592i \(0.522095\pi\)
\(180\) 713.072 0.295274
\(181\) −843.391 −0.346347 −0.173173 0.984891i \(-0.555402\pi\)
−0.173173 + 0.984891i \(0.555402\pi\)
\(182\) −555.629 −0.226296
\(183\) −1072.46 −0.433215
\(184\) −242.821 −0.0972879
\(185\) −1693.72 −0.673109
\(186\) −4555.33 −1.79577
\(187\) −942.625 −0.368618
\(188\) −1786.97 −0.693236
\(189\) −148.163 −0.0570224
\(190\) 1924.84 0.734962
\(191\) 2438.81 0.923908 0.461954 0.886904i \(-0.347148\pi\)
0.461954 + 0.886904i \(0.347148\pi\)
\(192\) 1622.41 0.609831
\(193\) 4095.03 1.52729 0.763645 0.645637i \(-0.223408\pi\)
0.763645 + 0.645637i \(0.223408\pi\)
\(194\) 371.451 0.137467
\(195\) 311.024 0.114220
\(196\) −4958.03 −1.80686
\(197\) 3226.76 1.16699 0.583495 0.812117i \(-0.301685\pi\)
0.583495 + 0.812117i \(0.301685\pi\)
\(198\) 2203.28 0.790809
\(199\) −4218.74 −1.50281 −0.751404 0.659842i \(-0.770623\pi\)
−0.751404 + 0.659842i \(0.770623\pi\)
\(200\) 957.853 0.338652
\(201\) 549.260 0.192745
\(202\) 3191.46 1.11163
\(203\) 159.138 0.0550210
\(204\) 893.846 0.306773
\(205\) 1767.63 0.602228
\(206\) 4735.77 1.60173
\(207\) −57.0387 −0.0191520
\(208\) −1250.91 −0.416996
\(209\) 3952.17 1.30803
\(210\) −401.952 −0.132082
\(211\) −2798.33 −0.913010 −0.456505 0.889721i \(-0.650899\pi\)
−0.456505 + 0.889721i \(0.650899\pi\)
\(212\) −2295.28 −0.743588
\(213\) 1782.10 0.573276
\(214\) −6189.64 −1.97717
\(215\) 2538.05 0.805085
\(216\) −1034.48 −0.325868
\(217\) 1706.34 0.533796
\(218\) −3946.35 −1.22606
\(219\) 1867.83 0.576329
\(220\) 3972.00 1.21724
\(221\) 389.872 0.118668
\(222\) 4962.52 1.50028
\(223\) 2496.01 0.749529 0.374764 0.927120i \(-0.377724\pi\)
0.374764 + 0.927120i \(0.377724\pi\)
\(224\) −65.3725 −0.0194995
\(225\) 225.000 0.0666667
\(226\) −5958.02 −1.75364
\(227\) 3409.57 0.996920 0.498460 0.866913i \(-0.333899\pi\)
0.498460 + 0.866913i \(0.333899\pi\)
\(228\) −3747.65 −1.08857
\(229\) 4794.47 1.38353 0.691763 0.722125i \(-0.256834\pi\)
0.691763 + 0.722125i \(0.256834\pi\)
\(230\) −154.741 −0.0443622
\(231\) −825.305 −0.235069
\(232\) 1111.11 0.314431
\(233\) 1989.36 0.559345 0.279672 0.960095i \(-0.409774\pi\)
0.279672 + 0.960095i \(0.409774\pi\)
\(234\) −911.282 −0.254583
\(235\) −563.855 −0.156518
\(236\) −5431.06 −1.49802
\(237\) 3825.55 1.04851
\(238\) −503.852 −0.137226
\(239\) 2574.69 0.696832 0.348416 0.937340i \(-0.386720\pi\)
0.348416 + 0.937340i \(0.386720\pi\)
\(240\) −904.932 −0.243388
\(241\) −3683.44 −0.984528 −0.492264 0.870446i \(-0.663831\pi\)
−0.492264 + 0.870446i \(0.663831\pi\)
\(242\) 5773.24 1.53355
\(243\) −243.000 −0.0641500
\(244\) 5664.73 1.48626
\(245\) −1564.44 −0.407952
\(246\) −5179.06 −1.34230
\(247\) −1634.63 −0.421089
\(248\) 11913.8 3.05050
\(249\) 2217.32 0.564326
\(250\) 610.405 0.154422
\(251\) 4631.27 1.16463 0.582317 0.812962i \(-0.302146\pi\)
0.582317 + 0.812962i \(0.302146\pi\)
\(252\) 782.597 0.195631
\(253\) −317.720 −0.0789522
\(254\) 3978.54 0.982817
\(255\) 282.041 0.0692630
\(256\) −8104.22 −1.97857
\(257\) −1609.98 −0.390770 −0.195385 0.980727i \(-0.562596\pi\)
−0.195385 + 0.980727i \(0.562596\pi\)
\(258\) −7436.33 −1.79444
\(259\) −1858.86 −0.445962
\(260\) −1642.83 −0.391862
\(261\) 261.000 0.0618984
\(262\) −7295.12 −1.72021
\(263\) −2868.22 −0.672479 −0.336239 0.941777i \(-0.609155\pi\)
−0.336239 + 0.941777i \(0.609155\pi\)
\(264\) −5762.34 −1.34336
\(265\) −724.244 −0.167887
\(266\) 2112.52 0.486942
\(267\) −2718.34 −0.623070
\(268\) −2901.20 −0.661264
\(269\) −554.047 −0.125579 −0.0627896 0.998027i \(-0.520000\pi\)
−0.0627896 + 0.998027i \(0.520000\pi\)
\(270\) −659.238 −0.148592
\(271\) −1826.02 −0.409309 −0.204655 0.978834i \(-0.565607\pi\)
−0.204655 + 0.978834i \(0.565607\pi\)
\(272\) −1134.35 −0.252867
\(273\) 341.348 0.0756752
\(274\) −7855.79 −1.73206
\(275\) 1253.31 0.274827
\(276\) 301.279 0.0657060
\(277\) 1470.00 0.318859 0.159429 0.987209i \(-0.449035\pi\)
0.159429 + 0.987209i \(0.449035\pi\)
\(278\) 251.841 0.0543325
\(279\) 2798.55 0.600519
\(280\) 1051.24 0.224371
\(281\) 7826.43 1.66151 0.830757 0.556635i \(-0.187908\pi\)
0.830757 + 0.556635i \(0.187908\pi\)
\(282\) 1652.06 0.348861
\(283\) −6796.87 −1.42767 −0.713837 0.700312i \(-0.753044\pi\)
−0.713837 + 0.700312i \(0.753044\pi\)
\(284\) −9413.10 −1.96678
\(285\) −1182.52 −0.245777
\(286\) −5076.08 −1.04949
\(287\) 1939.98 0.399001
\(288\) −107.217 −0.0219369
\(289\) −4559.46 −0.928039
\(290\) 708.070 0.143377
\(291\) −228.199 −0.0459701
\(292\) −9865.89 −1.97725
\(293\) 3631.49 0.724074 0.362037 0.932164i \(-0.382081\pi\)
0.362037 + 0.932164i \(0.382081\pi\)
\(294\) 4583.71 0.909277
\(295\) −1713.69 −0.338221
\(296\) −12978.7 −2.54856
\(297\) −1353.57 −0.264452
\(298\) −2970.62 −0.577461
\(299\) 131.410 0.0254169
\(300\) −1188.45 −0.228718
\(301\) 2785.50 0.533401
\(302\) −1667.96 −0.317816
\(303\) −1960.66 −0.371739
\(304\) 4756.00 0.897287
\(305\) 1787.43 0.335567
\(306\) −826.364 −0.154379
\(307\) −9080.77 −1.68817 −0.844083 0.536213i \(-0.819854\pi\)
−0.844083 + 0.536213i \(0.819854\pi\)
\(308\) 4359.27 0.806469
\(309\) −2909.40 −0.535632
\(310\) 7592.21 1.39100
\(311\) 2657.69 0.484577 0.242289 0.970204i \(-0.422102\pi\)
0.242289 + 0.970204i \(0.422102\pi\)
\(312\) 2383.32 0.432464
\(313\) −530.474 −0.0957960 −0.0478980 0.998852i \(-0.515252\pi\)
−0.0478980 + 0.998852i \(0.515252\pi\)
\(314\) −1750.05 −0.314525
\(315\) 246.938 0.0441694
\(316\) −20206.6 −3.59719
\(317\) 2393.66 0.424106 0.212053 0.977258i \(-0.431985\pi\)
0.212053 + 0.977258i \(0.431985\pi\)
\(318\) 2122.00 0.374200
\(319\) 1453.84 0.255170
\(320\) −2704.02 −0.472373
\(321\) 3802.58 0.661182
\(322\) −169.828 −0.0293918
\(323\) −1482.31 −0.255349
\(324\) 1283.53 0.220084
\(325\) −518.373 −0.0884743
\(326\) −8142.12 −1.38328
\(327\) 2424.43 0.410003
\(328\) 13545.1 2.28019
\(329\) −618.830 −0.103700
\(330\) −3672.13 −0.612558
\(331\) −7984.54 −1.32589 −0.662945 0.748668i \(-0.730694\pi\)
−0.662945 + 0.748668i \(0.730694\pi\)
\(332\) −11711.9 −1.93607
\(333\) −3048.70 −0.501706
\(334\) −8947.57 −1.46584
\(335\) −915.433 −0.149300
\(336\) −993.163 −0.161254
\(337\) 9704.45 1.56865 0.784325 0.620350i \(-0.213010\pi\)
0.784325 + 0.620350i \(0.213010\pi\)
\(338\) −8629.00 −1.38863
\(339\) 3660.29 0.586429
\(340\) −1489.74 −0.237626
\(341\) 15588.7 2.47558
\(342\) 3464.72 0.547808
\(343\) −3599.18 −0.566582
\(344\) 19448.6 3.04825
\(345\) 95.0644 0.0148351
\(346\) 9936.27 1.54387
\(347\) 5514.04 0.853053 0.426526 0.904475i \(-0.359737\pi\)
0.426526 + 0.904475i \(0.359737\pi\)
\(348\) −1378.61 −0.212359
\(349\) 2521.06 0.386674 0.193337 0.981132i \(-0.438069\pi\)
0.193337 + 0.981132i \(0.438069\pi\)
\(350\) 669.920 0.102311
\(351\) 559.842 0.0851344
\(352\) −597.227 −0.0904326
\(353\) 5721.03 0.862606 0.431303 0.902207i \(-0.358054\pi\)
0.431303 + 0.902207i \(0.358054\pi\)
\(354\) 5021.03 0.753855
\(355\) −2970.17 −0.444057
\(356\) 14358.3 2.13761
\(357\) 309.540 0.0458896
\(358\) −1622.20 −0.239486
\(359\) 6403.95 0.941470 0.470735 0.882275i \(-0.343989\pi\)
0.470735 + 0.882275i \(0.343989\pi\)
\(360\) 1724.14 0.252417
\(361\) −644.098 −0.0939055
\(362\) −4118.48 −0.597963
\(363\) −3546.77 −0.512830
\(364\) −1803.01 −0.259624
\(365\) −3113.04 −0.446422
\(366\) −5237.06 −0.747939
\(367\) 13350.7 1.89891 0.949456 0.313899i \(-0.101635\pi\)
0.949456 + 0.313899i \(0.101635\pi\)
\(368\) −382.341 −0.0541601
\(369\) 3181.74 0.448874
\(370\) −8270.87 −1.16211
\(371\) −794.858 −0.111232
\(372\) −14782.0 −2.06024
\(373\) −1367.05 −0.189767 −0.0948837 0.995488i \(-0.530248\pi\)
−0.0948837 + 0.995488i \(0.530248\pi\)
\(374\) −4603.07 −0.636414
\(375\) −375.000 −0.0516398
\(376\) −4320.72 −0.592617
\(377\) −601.312 −0.0821463
\(378\) −723.513 −0.0984484
\(379\) 9882.96 1.33945 0.669727 0.742607i \(-0.266411\pi\)
0.669727 + 0.742607i \(0.266411\pi\)
\(380\) 6246.09 0.843204
\(381\) −2444.20 −0.328662
\(382\) 11909.3 1.59511
\(383\) 13225.8 1.76450 0.882252 0.470777i \(-0.156026\pi\)
0.882252 + 0.470777i \(0.156026\pi\)
\(384\) 7636.72 1.01487
\(385\) 1375.51 0.182084
\(386\) 19997.0 2.63684
\(387\) 4568.48 0.600075
\(388\) 1205.35 0.157713
\(389\) −8442.16 −1.10035 −0.550173 0.835051i \(-0.685438\pi\)
−0.550173 + 0.835051i \(0.685438\pi\)
\(390\) 1518.80 0.197199
\(391\) 119.165 0.0154128
\(392\) −11988.0 −1.54461
\(393\) 4481.73 0.575250
\(394\) 15757.0 2.01479
\(395\) −6375.92 −0.812170
\(396\) 7149.60 0.907275
\(397\) −2268.55 −0.286789 −0.143394 0.989666i \(-0.545802\pi\)
−0.143394 + 0.989666i \(0.545802\pi\)
\(398\) −20601.1 −2.59458
\(399\) −1297.82 −0.162837
\(400\) 1508.22 0.188527
\(401\) 8294.00 1.03287 0.516437 0.856325i \(-0.327258\pi\)
0.516437 + 0.856325i \(0.327258\pi\)
\(402\) 2682.17 0.332772
\(403\) −6447.51 −0.796957
\(404\) 10356.2 1.27535
\(405\) 405.000 0.0496904
\(406\) 777.107 0.0949930
\(407\) −16982.1 −2.06823
\(408\) 2161.23 0.262247
\(409\) 9913.01 1.19845 0.599226 0.800580i \(-0.295475\pi\)
0.599226 + 0.800580i \(0.295475\pi\)
\(410\) 8631.77 1.03974
\(411\) 4826.17 0.579216
\(412\) 15367.5 1.83763
\(413\) −1880.78 −0.224085
\(414\) −278.534 −0.0330656
\(415\) −3695.54 −0.437125
\(416\) 247.015 0.0291127
\(417\) −154.718 −0.0181692
\(418\) 19299.4 2.25829
\(419\) −13332.1 −1.55446 −0.777228 0.629219i \(-0.783375\pi\)
−0.777228 + 0.629219i \(0.783375\pi\)
\(420\) −1304.33 −0.151535
\(421\) −2848.13 −0.329714 −0.164857 0.986317i \(-0.552716\pi\)
−0.164857 + 0.986317i \(0.552716\pi\)
\(422\) −13664.9 −1.57630
\(423\) −1014.94 −0.116662
\(424\) −5549.76 −0.635661
\(425\) −470.068 −0.0536509
\(426\) 8702.44 0.989752
\(427\) 1961.70 0.222326
\(428\) −20085.3 −2.26836
\(429\) 3118.47 0.350958
\(430\) 12393.9 1.38997
\(431\) 12669.7 1.41595 0.707977 0.706235i \(-0.249608\pi\)
0.707977 + 0.706235i \(0.249608\pi\)
\(432\) −1628.88 −0.181411
\(433\) −14545.6 −1.61436 −0.807178 0.590308i \(-0.799006\pi\)
−0.807178 + 0.590308i \(0.799006\pi\)
\(434\) 8332.45 0.921591
\(435\) −435.000 −0.0479463
\(436\) −12805.9 −1.40663
\(437\) −499.625 −0.0546917
\(438\) 9121.05 0.995024
\(439\) 11489.4 1.24911 0.624557 0.780979i \(-0.285280\pi\)
0.624557 + 0.780979i \(0.285280\pi\)
\(440\) 9603.90 1.04056
\(441\) −2815.99 −0.304069
\(442\) 1903.84 0.204879
\(443\) −11125.7 −1.19322 −0.596611 0.802531i \(-0.703486\pi\)
−0.596611 + 0.802531i \(0.703486\pi\)
\(444\) 16103.3 1.72124
\(445\) 4530.57 0.482628
\(446\) 12188.6 1.29405
\(447\) 1824.99 0.193107
\(448\) −2967.66 −0.312966
\(449\) −6676.79 −0.701776 −0.350888 0.936418i \(-0.614120\pi\)
−0.350888 + 0.936418i \(0.614120\pi\)
\(450\) 1098.73 0.115099
\(451\) 17723.1 1.85044
\(452\) −19333.7 −2.01190
\(453\) 1024.70 0.106280
\(454\) 16649.7 1.72117
\(455\) −568.914 −0.0586178
\(456\) −9061.44 −0.930572
\(457\) −10826.9 −1.10823 −0.554114 0.832441i \(-0.686943\pi\)
−0.554114 + 0.832441i \(0.686943\pi\)
\(458\) 23412.6 2.38864
\(459\) 507.673 0.0516256
\(460\) −502.132 −0.0508957
\(461\) −4114.21 −0.415657 −0.207829 0.978165i \(-0.566640\pi\)
−0.207829 + 0.978165i \(0.566640\pi\)
\(462\) −4030.16 −0.405844
\(463\) −6107.19 −0.613014 −0.306507 0.951868i \(-0.599160\pi\)
−0.306507 + 0.951868i \(0.599160\pi\)
\(464\) 1749.54 0.175043
\(465\) −4664.25 −0.465160
\(466\) 9714.53 0.965701
\(467\) −1409.31 −0.139647 −0.0698235 0.997559i \(-0.522244\pi\)
−0.0698235 + 0.997559i \(0.522244\pi\)
\(468\) −2957.10 −0.292077
\(469\) −1004.69 −0.0989172
\(470\) −2753.44 −0.270227
\(471\) 1075.13 0.105180
\(472\) −13131.7 −1.28059
\(473\) 25447.7 2.47375
\(474\) 18681.1 1.81023
\(475\) 1970.87 0.190378
\(476\) −1634.99 −0.157437
\(477\) −1303.64 −0.125135
\(478\) 12572.8 1.20307
\(479\) 12633.9 1.20513 0.602566 0.798069i \(-0.294145\pi\)
0.602566 + 0.798069i \(0.294145\pi\)
\(480\) 178.695 0.0169922
\(481\) 7023.84 0.665821
\(482\) −17987.1 −1.69977
\(483\) 104.333 0.00982883
\(484\) 18734.1 1.75940
\(485\) 380.332 0.0356083
\(486\) −1186.63 −0.110754
\(487\) −17024.7 −1.58411 −0.792056 0.610449i \(-0.790989\pi\)
−0.792056 + 0.610449i \(0.790989\pi\)
\(488\) 13696.7 1.27054
\(489\) 5002.08 0.462580
\(490\) −7639.52 −0.704323
\(491\) −3792.47 −0.348578 −0.174289 0.984695i \(-0.555763\pi\)
−0.174289 + 0.984695i \(0.555763\pi\)
\(492\) −16806.0 −1.53998
\(493\) −545.279 −0.0498136
\(494\) −7982.29 −0.727004
\(495\) 2255.96 0.204844
\(496\) 18759.2 1.69821
\(497\) −3259.76 −0.294206
\(498\) 10827.7 0.974301
\(499\) 6484.19 0.581708 0.290854 0.956767i \(-0.406061\pi\)
0.290854 + 0.956767i \(0.406061\pi\)
\(500\) 1980.76 0.177164
\(501\) 5496.91 0.490187
\(502\) 22615.6 2.01073
\(503\) −8781.60 −0.778434 −0.389217 0.921146i \(-0.627254\pi\)
−0.389217 + 0.921146i \(0.627254\pi\)
\(504\) 1892.24 0.167236
\(505\) 3267.76 0.287948
\(506\) −1551.51 −0.136310
\(507\) 5301.19 0.464367
\(508\) 12910.3 1.12756
\(509\) 21343.3 1.85860 0.929299 0.369328i \(-0.120412\pi\)
0.929299 + 0.369328i \(0.120412\pi\)
\(510\) 1377.27 0.119582
\(511\) −3416.57 −0.295773
\(512\) −19210.3 −1.65817
\(513\) −2128.54 −0.183191
\(514\) −7861.93 −0.674659
\(515\) 4849.01 0.414898
\(516\) −24130.8 −2.05872
\(517\) −5653.48 −0.480928
\(518\) −9077.28 −0.769947
\(519\) −6104.31 −0.516280
\(520\) −3972.20 −0.334985
\(521\) 7007.06 0.589223 0.294611 0.955617i \(-0.404810\pi\)
0.294611 + 0.955617i \(0.404810\pi\)
\(522\) 1274.53 0.106867
\(523\) −5901.85 −0.493441 −0.246721 0.969087i \(-0.579353\pi\)
−0.246721 + 0.969087i \(0.579353\pi\)
\(524\) −23672.6 −1.97355
\(525\) −411.563 −0.0342134
\(526\) −14006.2 −1.16103
\(527\) −5846.70 −0.483276
\(528\) −9073.28 −0.747848
\(529\) −12126.8 −0.996699
\(530\) −3536.66 −0.289854
\(531\) −3084.65 −0.252095
\(532\) 6855.08 0.558657
\(533\) −7330.34 −0.595707
\(534\) −13274.3 −1.07572
\(535\) −6337.64 −0.512149
\(536\) −7014.80 −0.565286
\(537\) 996.595 0.0800861
\(538\) −2705.54 −0.216811
\(539\) −15685.8 −1.25350
\(540\) −2139.22 −0.170476
\(541\) 7826.71 0.621990 0.310995 0.950412i \(-0.399338\pi\)
0.310995 + 0.950412i \(0.399338\pi\)
\(542\) −8916.90 −0.706667
\(543\) 2530.17 0.199963
\(544\) 223.997 0.0176540
\(545\) −4040.71 −0.317587
\(546\) 1666.89 0.130652
\(547\) 4256.78 0.332737 0.166368 0.986064i \(-0.446796\pi\)
0.166368 + 0.986064i \(0.446796\pi\)
\(548\) −25491.9 −1.98716
\(549\) 3217.37 0.250117
\(550\) 6120.21 0.474485
\(551\) 2286.20 0.176762
\(552\) 728.462 0.0561692
\(553\) −6997.57 −0.538096
\(554\) 7178.38 0.550506
\(555\) 5081.17 0.388620
\(556\) 817.221 0.0623343
\(557\) −11138.6 −0.847324 −0.423662 0.905820i \(-0.639256\pi\)
−0.423662 + 0.905820i \(0.639256\pi\)
\(558\) 13666.0 1.03679
\(559\) −10525.2 −0.796368
\(560\) 1655.27 0.124907
\(561\) 2827.88 0.212822
\(562\) 38218.3 2.86858
\(563\) 16458.1 1.23202 0.616009 0.787739i \(-0.288748\pi\)
0.616009 + 0.787739i \(0.288748\pi\)
\(564\) 5360.92 0.400240
\(565\) −6100.48 −0.454246
\(566\) −33190.7 −2.46486
\(567\) 444.488 0.0329219
\(568\) −22759.9 −1.68131
\(569\) 2449.68 0.180485 0.0902423 0.995920i \(-0.471236\pi\)
0.0902423 + 0.995920i \(0.471236\pi\)
\(570\) −5774.53 −0.424331
\(571\) 156.880 0.0114978 0.00574888 0.999983i \(-0.498170\pi\)
0.00574888 + 0.999983i \(0.498170\pi\)
\(572\) −16471.8 −1.20406
\(573\) −7316.44 −0.533419
\(574\) 9473.37 0.688869
\(575\) −158.441 −0.0114912
\(576\) −4867.24 −0.352086
\(577\) −20318.3 −1.46597 −0.732984 0.680246i \(-0.761873\pi\)
−0.732984 + 0.680246i \(0.761873\pi\)
\(578\) −22264.9 −1.60225
\(579\) −12285.1 −0.881781
\(580\) 2297.68 0.164493
\(581\) −4055.85 −0.289613
\(582\) −1114.35 −0.0793667
\(583\) −7261.62 −0.515859
\(584\) −23854.7 −1.69027
\(585\) −933.071 −0.0659448
\(586\) 17733.4 1.25010
\(587\) −9510.91 −0.668752 −0.334376 0.942440i \(-0.608525\pi\)
−0.334376 + 0.942440i \(0.608525\pi\)
\(588\) 14874.1 1.04319
\(589\) 24513.6 1.71488
\(590\) −8368.38 −0.583934
\(591\) −9680.27 −0.673762
\(592\) −20436.1 −1.41878
\(593\) −15977.2 −1.10641 −0.553207 0.833044i \(-0.686596\pi\)
−0.553207 + 0.833044i \(0.686596\pi\)
\(594\) −6609.83 −0.456574
\(595\) −515.900 −0.0355459
\(596\) −9639.62 −0.662507
\(597\) 12656.2 0.867647
\(598\) 641.707 0.0438819
\(599\) −4002.17 −0.272995 −0.136498 0.990640i \(-0.543585\pi\)
−0.136498 + 0.990640i \(0.543585\pi\)
\(600\) −2873.56 −0.195521
\(601\) −1574.81 −0.106885 −0.0534425 0.998571i \(-0.517019\pi\)
−0.0534425 + 0.998571i \(0.517019\pi\)
\(602\) 13602.3 0.920910
\(603\) −1647.78 −0.111281
\(604\) −5412.51 −0.364622
\(605\) 5911.28 0.397236
\(606\) −9574.37 −0.641802
\(607\) −8803.52 −0.588672 −0.294336 0.955702i \(-0.595098\pi\)
−0.294336 + 0.955702i \(0.595098\pi\)
\(608\) −939.156 −0.0626444
\(609\) −477.413 −0.0317664
\(610\) 8728.44 0.579351
\(611\) 2338.29 0.154824
\(612\) −2681.54 −0.177116
\(613\) 16874.2 1.11181 0.555907 0.831245i \(-0.312371\pi\)
0.555907 + 0.831245i \(0.312371\pi\)
\(614\) −44343.6 −2.91460
\(615\) −5302.90 −0.347697
\(616\) 10540.3 0.689415
\(617\) 4592.02 0.299624 0.149812 0.988715i \(-0.452133\pi\)
0.149812 + 0.988715i \(0.452133\pi\)
\(618\) −14207.3 −0.924761
\(619\) 4982.48 0.323526 0.161763 0.986830i \(-0.448282\pi\)
0.161763 + 0.986830i \(0.448282\pi\)
\(620\) 24636.6 1.59586
\(621\) 171.116 0.0110574
\(622\) 12978.1 0.836616
\(623\) 4972.30 0.319761
\(624\) 3752.74 0.240753
\(625\) 625.000 0.0400000
\(626\) −2590.43 −0.165391
\(627\) −11856.5 −0.755189
\(628\) −5678.88 −0.360847
\(629\) 6369.32 0.403755
\(630\) 1205.86 0.0762578
\(631\) 20584.3 1.29865 0.649325 0.760511i \(-0.275051\pi\)
0.649325 + 0.760511i \(0.275051\pi\)
\(632\) −48857.6 −3.07508
\(633\) 8394.99 0.527126
\(634\) 11688.8 0.732213
\(635\) 4073.66 0.254580
\(636\) 6885.84 0.429310
\(637\) 6487.69 0.403535
\(638\) 7099.45 0.440548
\(639\) −5346.31 −0.330981
\(640\) −12727.9 −0.786115
\(641\) 4840.03 0.298237 0.149118 0.988819i \(-0.452356\pi\)
0.149118 + 0.988819i \(0.452356\pi\)
\(642\) 18568.9 1.14152
\(643\) 1340.16 0.0821941 0.0410970 0.999155i \(-0.486915\pi\)
0.0410970 + 0.999155i \(0.486915\pi\)
\(644\) −551.090 −0.0337205
\(645\) −7614.14 −0.464816
\(646\) −7238.46 −0.440856
\(647\) 15752.3 0.957169 0.478585 0.878041i \(-0.341150\pi\)
0.478585 + 0.878041i \(0.341150\pi\)
\(648\) 3103.44 0.188140
\(649\) −17182.3 −1.03924
\(650\) −2531.34 −0.152750
\(651\) −5119.01 −0.308187
\(652\) −26421.1 −1.58701
\(653\) 2290.66 0.137275 0.0686373 0.997642i \(-0.478135\pi\)
0.0686373 + 0.997642i \(0.478135\pi\)
\(654\) 11839.1 0.707865
\(655\) −7469.55 −0.445587
\(656\) 21327.8 1.26938
\(657\) −5603.48 −0.332744
\(658\) −3021.90 −0.179036
\(659\) −3003.49 −0.177541 −0.0887704 0.996052i \(-0.528294\pi\)
−0.0887704 + 0.996052i \(0.528294\pi\)
\(660\) −11916.0 −0.702772
\(661\) 8104.71 0.476909 0.238454 0.971154i \(-0.423359\pi\)
0.238454 + 0.971154i \(0.423359\pi\)
\(662\) −38990.4 −2.28913
\(663\) −1169.62 −0.0685131
\(664\) −28318.3 −1.65506
\(665\) 2163.03 0.126133
\(666\) −14887.6 −0.866188
\(667\) −183.791 −0.0106693
\(668\) −29034.7 −1.68172
\(669\) −7488.02 −0.432741
\(670\) −4470.28 −0.257764
\(671\) 17921.6 1.03108
\(672\) 196.118 0.0112580
\(673\) 5747.03 0.329170 0.164585 0.986363i \(-0.447371\pi\)
0.164585 + 0.986363i \(0.447371\pi\)
\(674\) 47389.2 2.70825
\(675\) −675.000 −0.0384900
\(676\) −28001.0 −1.59314
\(677\) 25714.2 1.45979 0.729895 0.683559i \(-0.239569\pi\)
0.729895 + 0.683559i \(0.239569\pi\)
\(678\) 17874.1 1.01246
\(679\) 417.415 0.0235919
\(680\) −3602.05 −0.203136
\(681\) −10228.7 −0.575572
\(682\) 76123.2 4.27406
\(683\) 4007.09 0.224490 0.112245 0.993681i \(-0.464196\pi\)
0.112245 + 0.993681i \(0.464196\pi\)
\(684\) 11243.0 0.628487
\(685\) −8043.62 −0.448658
\(686\) −17575.7 −0.978196
\(687\) −14383.4 −0.798779
\(688\) 30623.4 1.69696
\(689\) 3003.43 0.166069
\(690\) 464.223 0.0256125
\(691\) −27863.7 −1.53399 −0.766993 0.641655i \(-0.778248\pi\)
−0.766993 + 0.641655i \(0.778248\pi\)
\(692\) 32243.1 1.77124
\(693\) 2475.91 0.135717
\(694\) 26926.4 1.47278
\(695\) 257.863 0.0140738
\(696\) −3333.33 −0.181537
\(697\) −6647.26 −0.361238
\(698\) 12311.0 0.667588
\(699\) −5968.08 −0.322938
\(700\) 2173.88 0.117378
\(701\) 12916.0 0.695906 0.347953 0.937512i \(-0.386877\pi\)
0.347953 + 0.937512i \(0.386877\pi\)
\(702\) 2733.85 0.146983
\(703\) −26704.8 −1.43271
\(704\) −27111.8 −1.45144
\(705\) 1691.56 0.0903659
\(706\) 27937.2 1.48928
\(707\) 3586.37 0.190777
\(708\) 16293.2 0.864880
\(709\) −30250.8 −1.60239 −0.801193 0.598406i \(-0.795801\pi\)
−0.801193 + 0.598406i \(0.795801\pi\)
\(710\) −14504.1 −0.766659
\(711\) −11476.7 −0.605356
\(712\) 34716.9 1.82735
\(713\) −1970.68 −0.103510
\(714\) 1511.56 0.0792277
\(715\) −5197.45 −0.271851
\(716\) −5264.03 −0.274757
\(717\) −7724.07 −0.402316
\(718\) 31272.1 1.62544
\(719\) 6161.35 0.319582 0.159791 0.987151i \(-0.448918\pi\)
0.159791 + 0.987151i \(0.448918\pi\)
\(720\) 2714.80 0.140520
\(721\) 5321.78 0.274887
\(722\) −3145.29 −0.162127
\(723\) 11050.3 0.568417
\(724\) −13364.4 −0.686029
\(725\) 725.000 0.0371391
\(726\) −17319.7 −0.885393
\(727\) −35454.3 −1.80870 −0.904352 0.426786i \(-0.859646\pi\)
−0.904352 + 0.426786i \(0.859646\pi\)
\(728\) −4359.49 −0.221941
\(729\) 729.000 0.0370370
\(730\) −15201.7 −0.770742
\(731\) −9544.43 −0.482919
\(732\) −16994.2 −0.858092
\(733\) −26681.1 −1.34446 −0.672231 0.740342i \(-0.734664\pi\)
−0.672231 + 0.740342i \(0.734664\pi\)
\(734\) 65194.7 3.27845
\(735\) 4693.31 0.235531
\(736\) 75.5001 0.00378121
\(737\) −9178.57 −0.458747
\(738\) 15537.2 0.774976
\(739\) −28886.6 −1.43791 −0.718953 0.695059i \(-0.755378\pi\)
−0.718953 + 0.695059i \(0.755378\pi\)
\(740\) −26838.8 −1.33326
\(741\) 4903.89 0.243116
\(742\) −3881.48 −0.192040
\(743\) −16398.0 −0.809669 −0.404834 0.914390i \(-0.632671\pi\)
−0.404834 + 0.914390i \(0.632671\pi\)
\(744\) −35741.3 −1.76121
\(745\) −3041.65 −0.149580
\(746\) −6675.64 −0.327631
\(747\) −6651.97 −0.325814
\(748\) −14936.9 −0.730142
\(749\) −6955.56 −0.339320
\(750\) −1831.22 −0.0891554
\(751\) −5905.21 −0.286930 −0.143465 0.989655i \(-0.545824\pi\)
−0.143465 + 0.989655i \(0.545824\pi\)
\(752\) −6803.33 −0.329910
\(753\) −13893.8 −0.672402
\(754\) −2936.35 −0.141824
\(755\) −1707.84 −0.0823241
\(756\) −2347.79 −0.112947
\(757\) −12439.0 −0.597229 −0.298614 0.954374i \(-0.596524\pi\)
−0.298614 + 0.954374i \(0.596524\pi\)
\(758\) 48260.9 2.31255
\(759\) 953.161 0.0455831
\(760\) 15102.4 0.720818
\(761\) 14270.0 0.679748 0.339874 0.940471i \(-0.389616\pi\)
0.339874 + 0.940471i \(0.389616\pi\)
\(762\) −11935.6 −0.567430
\(763\) −4434.68 −0.210414
\(764\) 38645.6 1.83004
\(765\) −846.122 −0.0399890
\(766\) 64584.6 3.04639
\(767\) 7106.66 0.334559
\(768\) 24312.7 1.14233
\(769\) −15143.9 −0.710147 −0.355074 0.934838i \(-0.615544\pi\)
−0.355074 + 0.934838i \(0.615544\pi\)
\(770\) 6716.94 0.314366
\(771\) 4829.95 0.225611
\(772\) 64890.1 3.02519
\(773\) −40617.2 −1.88991 −0.944955 0.327202i \(-0.893894\pi\)
−0.944955 + 0.327202i \(0.893894\pi\)
\(774\) 22309.0 1.03602
\(775\) 7773.74 0.360311
\(776\) 2914.42 0.134822
\(777\) 5576.59 0.257476
\(778\) −41225.1 −1.89973
\(779\) 27870.1 1.28184
\(780\) 4928.49 0.226241
\(781\) −29780.4 −1.36444
\(782\) 581.910 0.0266100
\(783\) −783.000 −0.0357371
\(784\) −18876.1 −0.859881
\(785\) −1791.89 −0.0814718
\(786\) 21885.4 0.993162
\(787\) 43878.2 1.98741 0.993703 0.112048i \(-0.0357412\pi\)
0.993703 + 0.112048i \(0.0357412\pi\)
\(788\) 51131.3 2.31152
\(789\) 8604.66 0.388256
\(790\) −31135.1 −1.40220
\(791\) −6695.27 −0.300956
\(792\) 17287.0 0.775590
\(793\) −7412.43 −0.331933
\(794\) −11077.9 −0.495137
\(795\) 2172.73 0.0969294
\(796\) −66850.4 −2.97670
\(797\) 14556.0 0.646925 0.323463 0.946241i \(-0.395153\pi\)
0.323463 + 0.946241i \(0.395153\pi\)
\(798\) −6337.55 −0.281136
\(799\) 2120.40 0.0938853
\(800\) −297.825 −0.0131621
\(801\) 8155.02 0.359730
\(802\) 40501.6 1.78324
\(803\) −31212.9 −1.37170
\(804\) 8703.59 0.381781
\(805\) −173.889 −0.00761338
\(806\) −31484.8 −1.37593
\(807\) 1662.14 0.0725032
\(808\) 25040.3 1.09024
\(809\) −14030.7 −0.609755 −0.304878 0.952392i \(-0.598616\pi\)
−0.304878 + 0.952392i \(0.598616\pi\)
\(810\) 1977.71 0.0857898
\(811\) 30195.7 1.30741 0.653707 0.756747i \(-0.273213\pi\)
0.653707 + 0.756747i \(0.273213\pi\)
\(812\) 2521.70 0.108983
\(813\) 5478.06 0.236315
\(814\) −82927.7 −3.57078
\(815\) −8336.80 −0.358313
\(816\) 3403.04 0.145993
\(817\) 40017.2 1.71362
\(818\) 48407.6 2.06911
\(819\) −1024.05 −0.0436911
\(820\) 28010.0 1.19287
\(821\) 31237.5 1.32789 0.663944 0.747782i \(-0.268881\pi\)
0.663944 + 0.747782i \(0.268881\pi\)
\(822\) 23567.4 1.00001
\(823\) −22306.9 −0.944798 −0.472399 0.881385i \(-0.656612\pi\)
−0.472399 + 0.881385i \(0.656612\pi\)
\(824\) 37157.1 1.57091
\(825\) −3759.93 −0.158671
\(826\) −9184.30 −0.386880
\(827\) 41561.9 1.74758 0.873790 0.486304i \(-0.161655\pi\)
0.873790 + 0.486304i \(0.161655\pi\)
\(828\) −903.837 −0.0379354
\(829\) 42423.6 1.77736 0.888681 0.458527i \(-0.151623\pi\)
0.888681 + 0.458527i \(0.151623\pi\)
\(830\) −18046.2 −0.754690
\(831\) −4410.01 −0.184093
\(832\) 11213.5 0.467259
\(833\) 5883.13 0.244704
\(834\) −755.524 −0.0313689
\(835\) −9161.51 −0.379697
\(836\) 62626.3 2.59088
\(837\) −8395.64 −0.346710
\(838\) −65104.0 −2.68375
\(839\) −31547.4 −1.29814 −0.649068 0.760730i \(-0.724841\pi\)
−0.649068 + 0.760730i \(0.724841\pi\)
\(840\) −3153.73 −0.129541
\(841\) 841.000 0.0344828
\(842\) −13908.1 −0.569247
\(843\) −23479.3 −0.959276
\(844\) −44342.5 −1.80845
\(845\) −8835.32 −0.359697
\(846\) −4956.19 −0.201415
\(847\) 6487.63 0.263185
\(848\) −8738.56 −0.353872
\(849\) 20390.6 0.824268
\(850\) −2295.45 −0.0926276
\(851\) 2146.84 0.0864779
\(852\) 28239.3 1.13552
\(853\) −5030.77 −0.201935 −0.100967 0.994890i \(-0.532194\pi\)
−0.100967 + 0.994890i \(0.532194\pi\)
\(854\) 9579.46 0.383844
\(855\) 3547.56 0.141899
\(856\) −48564.2 −1.93912
\(857\) −16655.5 −0.663875 −0.331937 0.943301i \(-0.607702\pi\)
−0.331937 + 0.943301i \(0.607702\pi\)
\(858\) 15228.2 0.605925
\(859\) 33206.7 1.31897 0.659486 0.751717i \(-0.270774\pi\)
0.659486 + 0.751717i \(0.270774\pi\)
\(860\) 40218.0 1.59468
\(861\) −5819.93 −0.230363
\(862\) 61869.0 2.44463
\(863\) −12156.5 −0.479504 −0.239752 0.970834i \(-0.577066\pi\)
−0.239752 + 0.970834i \(0.577066\pi\)
\(864\) 321.651 0.0126653
\(865\) 10173.9 0.399909
\(866\) −71029.6 −2.78716
\(867\) 13678.4 0.535804
\(868\) 27038.7 1.05732
\(869\) −63928.0 −2.49552
\(870\) −2124.21 −0.0827787
\(871\) 3796.28 0.147683
\(872\) −30963.3 −1.20246
\(873\) 684.598 0.0265408
\(874\) −2439.79 −0.0944246
\(875\) 685.938 0.0265016
\(876\) 29597.7 1.14157
\(877\) 10910.0 0.420075 0.210037 0.977693i \(-0.432641\pi\)
0.210037 + 0.977693i \(0.432641\pi\)
\(878\) 56105.7 2.15658
\(879\) −10894.5 −0.418044
\(880\) 15122.1 0.579281
\(881\) −10796.4 −0.412871 −0.206435 0.978460i \(-0.566186\pi\)
−0.206435 + 0.978460i \(0.566186\pi\)
\(882\) −13751.1 −0.524972
\(883\) −23778.3 −0.906232 −0.453116 0.891452i \(-0.649688\pi\)
−0.453116 + 0.891452i \(0.649688\pi\)
\(884\) 6177.94 0.235053
\(885\) 5141.08 0.195272
\(886\) −54329.4 −2.06008
\(887\) −26229.5 −0.992897 −0.496449 0.868066i \(-0.665363\pi\)
−0.496449 + 0.868066i \(0.665363\pi\)
\(888\) 38936.2 1.47141
\(889\) 4470.85 0.168670
\(890\) 22123.8 0.833251
\(891\) 4060.72 0.152682
\(892\) 39551.8 1.48463
\(893\) −8890.26 −0.333148
\(894\) 8911.86 0.333397
\(895\) −1660.99 −0.0620344
\(896\) −13968.8 −0.520833
\(897\) −394.230 −0.0146744
\(898\) −32604.4 −1.21161
\(899\) 9017.54 0.334540
\(900\) 3565.36 0.132050
\(901\) 2723.55 0.100704
\(902\) 86546.3 3.19476
\(903\) −8356.51 −0.307959
\(904\) −46746.9 −1.71989
\(905\) −4216.96 −0.154891
\(906\) 5003.88 0.183491
\(907\) 53019.1 1.94098 0.970491 0.241136i \(-0.0775201\pi\)
0.970491 + 0.241136i \(0.0775201\pi\)
\(908\) 54028.1 1.97465
\(909\) 5881.98 0.214624
\(910\) −2778.14 −0.101203
\(911\) −16886.9 −0.614147 −0.307074 0.951686i \(-0.599350\pi\)
−0.307074 + 0.951686i \(0.599350\pi\)
\(912\) −14268.0 −0.518049
\(913\) −37053.2 −1.34314
\(914\) −52870.3 −1.91334
\(915\) −5362.28 −0.193739
\(916\) 75973.4 2.74043
\(917\) −8197.83 −0.295219
\(918\) 2479.09 0.0891309
\(919\) −54865.8 −1.96937 −0.984687 0.174330i \(-0.944224\pi\)
−0.984687 + 0.174330i \(0.944224\pi\)
\(920\) −1214.10 −0.0435085
\(921\) 27242.3 0.974663
\(922\) −20090.7 −0.717626
\(923\) 12317.2 0.439249
\(924\) −13077.8 −0.465615
\(925\) −8468.62 −0.301023
\(926\) −29822.9 −1.05836
\(927\) 8728.21 0.309247
\(928\) −345.477 −0.0122207
\(929\) 27835.6 0.983053 0.491527 0.870863i \(-0.336439\pi\)
0.491527 + 0.870863i \(0.336439\pi\)
\(930\) −22776.6 −0.803092
\(931\) −24666.4 −0.868322
\(932\) 31523.5 1.10793
\(933\) −7973.06 −0.279771
\(934\) −6882.01 −0.241099
\(935\) −4713.13 −0.164851
\(936\) −7149.96 −0.249683
\(937\) −38996.7 −1.35962 −0.679811 0.733387i \(-0.737938\pi\)
−0.679811 + 0.733387i \(0.737938\pi\)
\(938\) −4906.13 −0.170779
\(939\) 1591.42 0.0553079
\(940\) −8934.87 −0.310025
\(941\) 15686.8 0.543437 0.271718 0.962377i \(-0.412408\pi\)
0.271718 + 0.962377i \(0.412408\pi\)
\(942\) 5250.14 0.181591
\(943\) −2240.52 −0.0773715
\(944\) −20677.0 −0.712902
\(945\) −740.813 −0.0255012
\(946\) 124267. 4.27090
\(947\) −54527.1 −1.87106 −0.935530 0.353248i \(-0.885077\pi\)
−0.935530 + 0.353248i \(0.885077\pi\)
\(948\) 60619.8 2.07684
\(949\) 12909.7 0.441589
\(950\) 9624.22 0.328685
\(951\) −7180.99 −0.244858
\(952\) −3953.25 −0.134586
\(953\) 48998.7 1.66550 0.832752 0.553647i \(-0.186764\pi\)
0.832752 + 0.553647i \(0.186764\pi\)
\(954\) −6365.99 −0.216044
\(955\) 12194.1 0.413184
\(956\) 40798.6 1.38025
\(957\) −4361.52 −0.147323
\(958\) 61694.4 2.08064
\(959\) −8827.88 −0.297254
\(960\) 8112.07 0.272725
\(961\) 66898.8 2.24560
\(962\) 34299.1 1.14953
\(963\) −11407.7 −0.381734
\(964\) −58368.0 −1.95011
\(965\) 20475.2 0.683025
\(966\) 509.484 0.0169693
\(967\) −18866.1 −0.627395 −0.313698 0.949523i \(-0.601568\pi\)
−0.313698 + 0.949523i \(0.601568\pi\)
\(968\) 45297.1 1.50403
\(969\) 4446.92 0.147426
\(970\) 1857.25 0.0614772
\(971\) 49921.4 1.64990 0.824950 0.565205i \(-0.191203\pi\)
0.824950 + 0.565205i \(0.191203\pi\)
\(972\) −3850.59 −0.127066
\(973\) 283.004 0.00932446
\(974\) −83135.6 −2.73495
\(975\) 1555.12 0.0510806
\(976\) 21566.7 0.707308
\(977\) −2591.52 −0.0848618 −0.0424309 0.999099i \(-0.513510\pi\)
−0.0424309 + 0.999099i \(0.513510\pi\)
\(978\) 24426.4 0.798639
\(979\) 45425.6 1.48295
\(980\) −24790.1 −0.808053
\(981\) −7273.28 −0.236715
\(982\) −18519.6 −0.601815
\(983\) 18566.6 0.602423 0.301211 0.953557i \(-0.402609\pi\)
0.301211 + 0.953557i \(0.402609\pi\)
\(984\) −40635.2 −1.31647
\(985\) 16133.8 0.521894
\(986\) −2662.73 −0.0860026
\(987\) 1856.49 0.0598711
\(988\) −25902.4 −0.834074
\(989\) −3217.04 −0.103434
\(990\) 11016.4 0.353660
\(991\) −34558.3 −1.10775 −0.553875 0.832600i \(-0.686851\pi\)
−0.553875 + 0.832600i \(0.686851\pi\)
\(992\) −3704.34 −0.118561
\(993\) 23953.6 0.765503
\(994\) −15918.2 −0.507943
\(995\) −21093.7 −0.672076
\(996\) 35135.8 1.11779
\(997\) −11238.6 −0.357000 −0.178500 0.983940i \(-0.557124\pi\)
−0.178500 + 0.983940i \(0.557124\pi\)
\(998\) 31663.9 1.00431
\(999\) 9146.11 0.289660
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 435.4.a.i.1.7 7
3.2 odd 2 1305.4.a.n.1.1 7
5.4 even 2 2175.4.a.n.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.4.a.i.1.7 7 1.1 even 1 trivial
1305.4.a.n.1.1 7 3.2 odd 2
2175.4.a.n.1.1 7 5.4 even 2