Properties

Label 35.4.a.b.1.1
Level $35$
Weight $4$
Character 35.1
Self dual yes
Analytic conductor $2.065$
Analytic rank $0$
Dimension $2$
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] = [35,4,Mod(1,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, 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("35.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 35.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: \(2.06506685020\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 35.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.58579 q^{2} +6.65685 q^{3} -1.31371 q^{4} -5.00000 q^{5} +17.2132 q^{6} -7.00000 q^{7} -24.0833 q^{8} +17.3137 q^{9} +O(q^{10})\) \(q+2.58579 q^{2} +6.65685 q^{3} -1.31371 q^{4} -5.00000 q^{5} +17.2132 q^{6} -7.00000 q^{7} -24.0833 q^{8} +17.3137 q^{9} -12.9289 q^{10} +38.2548 q^{11} -8.74517 q^{12} +19.3431 q^{13} -18.1005 q^{14} -33.2843 q^{15} -51.7645 q^{16} -87.2254 q^{17} +44.7696 q^{18} -44.2254 q^{19} +6.56854 q^{20} -46.5980 q^{21} +98.9188 q^{22} +218.167 q^{23} -160.319 q^{24} +25.0000 q^{25} +50.0172 q^{26} -64.4802 q^{27} +9.19596 q^{28} -46.9411 q^{29} -86.0660 q^{30} +194.558 q^{31} +58.8141 q^{32} +254.657 q^{33} -225.546 q^{34} +35.0000 q^{35} -22.7452 q^{36} +366.853 q^{37} -114.357 q^{38} +128.765 q^{39} +120.416 q^{40} -339.362 q^{41} -120.492 q^{42} -226.167 q^{43} -50.2557 q^{44} -86.5685 q^{45} +564.132 q^{46} +11.6762 q^{47} -344.589 q^{48} +49.0000 q^{49} +64.6447 q^{50} -580.647 q^{51} -25.4113 q^{52} -209.019 q^{53} -166.732 q^{54} -191.274 q^{55} +168.583 q^{56} -294.402 q^{57} -121.380 q^{58} -616.000 q^{59} +43.7258 q^{60} +320.735 q^{61} +503.087 q^{62} -121.196 q^{63} +566.197 q^{64} -96.7157 q^{65} +658.488 q^{66} +14.5097 q^{67} +114.589 q^{68} +1452.30 q^{69} +90.5025 q^{70} -952.000 q^{71} -416.971 q^{72} +824.489 q^{73} +948.603 q^{74} +166.421 q^{75} +58.0993 q^{76} -267.784 q^{77} +332.958 q^{78} +156.275 q^{79} +258.823 q^{80} -896.706 q^{81} -877.519 q^{82} -1036.53 q^{83} +61.2162 q^{84} +436.127 q^{85} -584.818 q^{86} -312.480 q^{87} -921.301 q^{88} -170.225 q^{89} -223.848 q^{90} -135.402 q^{91} -286.607 q^{92} +1295.15 q^{93} +30.1921 q^{94} +221.127 q^{95} +391.517 q^{96} +1059.87 q^{97} +126.704 q^{98} +662.333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 8 q^{2} + 2 q^{3} + 20 q^{4} - 10 q^{5} - 8 q^{6} - 14 q^{7} + 48 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 8 q^{2} + 2 q^{3} + 20 q^{4} - 10 q^{5} - 8 q^{6} - 14 q^{7} + 48 q^{8} + 12 q^{9} - 40 q^{10} - 14 q^{11} - 108 q^{12} + 50 q^{13} - 56 q^{14} - 10 q^{15} + 168 q^{16} - 50 q^{17} + 16 q^{18} + 36 q^{19} - 100 q^{20} - 14 q^{21} - 184 q^{22} + 244 q^{23} - 496 q^{24} + 50 q^{25} + 216 q^{26} + 86 q^{27} - 140 q^{28} - 26 q^{29} + 40 q^{30} - 120 q^{31} + 672 q^{32} + 498 q^{33} - 24 q^{34} + 70 q^{35} - 136 q^{36} + 564 q^{37} + 320 q^{38} - 14 q^{39} - 240 q^{40} - 328 q^{41} + 56 q^{42} - 260 q^{43} - 1164 q^{44} - 60 q^{45} + 704 q^{46} - 350 q^{47} - 1368 q^{48} + 98 q^{49} + 200 q^{50} - 754 q^{51} + 628 q^{52} - 56 q^{53} + 648 q^{54} + 70 q^{55} - 336 q^{56} - 668 q^{57} - 8 q^{58} - 1232 q^{59} + 540 q^{60} + 336 q^{61} - 1200 q^{62} - 84 q^{63} + 2128 q^{64} - 250 q^{65} + 1976 q^{66} - 152 q^{67} + 908 q^{68} + 1332 q^{69} + 280 q^{70} - 1904 q^{71} - 800 q^{72} + 676 q^{73} + 2016 q^{74} + 50 q^{75} + 1768 q^{76} + 98 q^{77} - 440 q^{78} + 1014 q^{79} - 840 q^{80} - 1454 q^{81} - 816 q^{82} - 376 q^{83} + 756 q^{84} + 250 q^{85} - 768 q^{86} - 410 q^{87} - 4688 q^{88} - 216 q^{89} - 80 q^{90} - 350 q^{91} + 264 q^{92} + 2760 q^{93} - 1928 q^{94} - 180 q^{95} - 2464 q^{96} + 2742 q^{97} + 392 q^{98} + 940 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.58579 0.914214 0.457107 0.889412i \(-0.348886\pi\)
0.457107 + 0.889412i \(0.348886\pi\)
\(3\) 6.65685 1.28111 0.640556 0.767911i \(-0.278704\pi\)
0.640556 + 0.767911i \(0.278704\pi\)
\(4\) −1.31371 −0.164214
\(5\) −5.00000 −0.447214
\(6\) 17.2132 1.17121
\(7\) −7.00000 −0.377964
\(8\) −24.0833 −1.06434
\(9\) 17.3137 0.641248
\(10\) −12.9289 −0.408849
\(11\) 38.2548 1.04857 0.524285 0.851543i \(-0.324333\pi\)
0.524285 + 0.851543i \(0.324333\pi\)
\(12\) −8.74517 −0.210376
\(13\) 19.3431 0.412679 0.206339 0.978480i \(-0.433845\pi\)
0.206339 + 0.978480i \(0.433845\pi\)
\(14\) −18.1005 −0.345540
\(15\) −33.2843 −0.572931
\(16\) −51.7645 −0.808820
\(17\) −87.2254 −1.24443 −0.622214 0.782847i \(-0.713767\pi\)
−0.622214 + 0.782847i \(0.713767\pi\)
\(18\) 44.7696 0.586238
\(19\) −44.2254 −0.534000 −0.267000 0.963697i \(-0.586032\pi\)
−0.267000 + 0.963697i \(0.586032\pi\)
\(20\) 6.56854 0.0734385
\(21\) −46.5980 −0.484215
\(22\) 98.9188 0.958617
\(23\) 218.167 1.97786 0.988932 0.148371i \(-0.0474028\pi\)
0.988932 + 0.148371i \(0.0474028\pi\)
\(24\) −160.319 −1.36354
\(25\) 25.0000 0.200000
\(26\) 50.0172 0.377276
\(27\) −64.4802 −0.459601
\(28\) 9.19596 0.0620669
\(29\) −46.9411 −0.300578 −0.150289 0.988642i \(-0.548020\pi\)
−0.150289 + 0.988642i \(0.548020\pi\)
\(30\) −86.0660 −0.523781
\(31\) 194.558 1.12722 0.563609 0.826042i \(-0.309413\pi\)
0.563609 + 0.826042i \(0.309413\pi\)
\(32\) 58.8141 0.324905
\(33\) 254.657 1.34334
\(34\) −225.546 −1.13767
\(35\) 35.0000 0.169031
\(36\) −22.7452 −0.105302
\(37\) 366.853 1.63001 0.815003 0.579457i \(-0.196735\pi\)
0.815003 + 0.579457i \(0.196735\pi\)
\(38\) −114.357 −0.488190
\(39\) 128.765 0.528688
\(40\) 120.416 0.475987
\(41\) −339.362 −1.29267 −0.646336 0.763053i \(-0.723699\pi\)
−0.646336 + 0.763053i \(0.723699\pi\)
\(42\) −120.492 −0.442676
\(43\) −226.167 −0.802095 −0.401047 0.916057i \(-0.631354\pi\)
−0.401047 + 0.916057i \(0.631354\pi\)
\(44\) −50.2557 −0.172189
\(45\) −86.5685 −0.286775
\(46\) 564.132 1.80819
\(47\) 11.6762 0.0362372 0.0181186 0.999836i \(-0.494232\pi\)
0.0181186 + 0.999836i \(0.494232\pi\)
\(48\) −344.589 −1.03619
\(49\) 49.0000 0.142857
\(50\) 64.6447 0.182843
\(51\) −580.647 −1.59425
\(52\) −25.4113 −0.0677674
\(53\) −209.019 −0.541717 −0.270859 0.962619i \(-0.587308\pi\)
−0.270859 + 0.962619i \(0.587308\pi\)
\(54\) −166.732 −0.420173
\(55\) −191.274 −0.468935
\(56\) 168.583 0.402283
\(57\) −294.402 −0.684114
\(58\) −121.380 −0.274792
\(59\) −616.000 −1.35926 −0.679630 0.733555i \(-0.737860\pi\)
−0.679630 + 0.733555i \(0.737860\pi\)
\(60\) 43.7258 0.0940830
\(61\) 320.735 0.673212 0.336606 0.941646i \(-0.390721\pi\)
0.336606 + 0.941646i \(0.390721\pi\)
\(62\) 503.087 1.03052
\(63\) −121.196 −0.242369
\(64\) 566.197 1.10585
\(65\) −96.7157 −0.184556
\(66\) 658.488 1.22810
\(67\) 14.5097 0.0264573 0.0132286 0.999912i \(-0.495789\pi\)
0.0132286 + 0.999912i \(0.495789\pi\)
\(68\) 114.589 0.204352
\(69\) 1452.30 2.53387
\(70\) 90.5025 0.154530
\(71\) −952.000 −1.59129 −0.795645 0.605763i \(-0.792868\pi\)
−0.795645 + 0.605763i \(0.792868\pi\)
\(72\) −416.971 −0.682506
\(73\) 824.489 1.32191 0.660953 0.750427i \(-0.270152\pi\)
0.660953 + 0.750427i \(0.270152\pi\)
\(74\) 948.603 1.49017
\(75\) 166.421 0.256222
\(76\) 58.0993 0.0876901
\(77\) −267.784 −0.396322
\(78\) 332.958 0.483334
\(79\) 156.275 0.222561 0.111280 0.993789i \(-0.464505\pi\)
0.111280 + 0.993789i \(0.464505\pi\)
\(80\) 258.823 0.361715
\(81\) −896.706 −1.23005
\(82\) −877.519 −1.18178
\(83\) −1036.53 −1.37077 −0.685384 0.728182i \(-0.740366\pi\)
−0.685384 + 0.728182i \(0.740366\pi\)
\(84\) 61.2162 0.0795147
\(85\) 436.127 0.556525
\(86\) −584.818 −0.733286
\(87\) −312.480 −0.385074
\(88\) −921.301 −1.11603
\(89\) −170.225 −0.202740 −0.101370 0.994849i \(-0.532323\pi\)
−0.101370 + 0.994849i \(0.532323\pi\)
\(90\) −223.848 −0.262174
\(91\) −135.402 −0.155978
\(92\) −286.607 −0.324792
\(93\) 1295.15 1.44409
\(94\) 30.1921 0.0331285
\(95\) 221.127 0.238812
\(96\) 391.517 0.416240
\(97\) 1059.87 1.10942 0.554710 0.832044i \(-0.312829\pi\)
0.554710 + 0.832044i \(0.312829\pi\)
\(98\) 126.704 0.130602
\(99\) 662.333 0.672394
\(100\) −32.8427 −0.0328427
\(101\) −241.833 −0.238251 −0.119125 0.992879i \(-0.538009\pi\)
−0.119125 + 0.992879i \(0.538009\pi\)
\(102\) −1501.43 −1.45749
\(103\) −1679.58 −1.60673 −0.803367 0.595484i \(-0.796960\pi\)
−0.803367 + 0.595484i \(0.796960\pi\)
\(104\) −465.846 −0.439230
\(105\) 232.990 0.216547
\(106\) −540.479 −0.495245
\(107\) 1506.88 1.36146 0.680728 0.732537i \(-0.261664\pi\)
0.680728 + 0.732537i \(0.261664\pi\)
\(108\) 84.7082 0.0754727
\(109\) −1252.41 −1.10054 −0.550271 0.834986i \(-0.685476\pi\)
−0.550271 + 0.834986i \(0.685476\pi\)
\(110\) −494.594 −0.428706
\(111\) 2442.09 2.08822
\(112\) 362.352 0.305705
\(113\) 1370.20 1.14069 0.570345 0.821405i \(-0.306810\pi\)
0.570345 + 0.821405i \(0.306810\pi\)
\(114\) −761.261 −0.625426
\(115\) −1090.83 −0.884528
\(116\) 61.6670 0.0493589
\(117\) 334.902 0.264630
\(118\) −1592.84 −1.24265
\(119\) 610.578 0.470349
\(120\) 801.594 0.609793
\(121\) 132.432 0.0994984
\(122\) 829.352 0.615459
\(123\) −2259.09 −1.65606
\(124\) −255.593 −0.185104
\(125\) −125.000 −0.0894427
\(126\) −313.387 −0.221577
\(127\) 1213.49 0.847873 0.423936 0.905692i \(-0.360648\pi\)
0.423936 + 0.905692i \(0.360648\pi\)
\(128\) 993.551 0.686081
\(129\) −1505.56 −1.02757
\(130\) −250.086 −0.168723
\(131\) −1982.42 −1.32217 −0.661087 0.750309i \(-0.729904\pi\)
−0.661087 + 0.750309i \(0.729904\pi\)
\(132\) −334.545 −0.220594
\(133\) 309.578 0.201833
\(134\) 37.5189 0.0241876
\(135\) 322.401 0.205540
\(136\) 2100.67 1.32449
\(137\) 2210.95 1.37879 0.689394 0.724386i \(-0.257877\pi\)
0.689394 + 0.724386i \(0.257877\pi\)
\(138\) 3755.34 2.31649
\(139\) 528.039 0.322213 0.161107 0.986937i \(-0.448494\pi\)
0.161107 + 0.986937i \(0.448494\pi\)
\(140\) −45.9798 −0.0277572
\(141\) 77.7267 0.0464239
\(142\) −2461.67 −1.45478
\(143\) 739.969 0.432722
\(144\) −896.235 −0.518655
\(145\) 234.706 0.134422
\(146\) 2131.95 1.20851
\(147\) 326.186 0.183016
\(148\) −481.938 −0.267669
\(149\) −328.372 −0.180545 −0.0902727 0.995917i \(-0.528774\pi\)
−0.0902727 + 0.995917i \(0.528774\pi\)
\(150\) 430.330 0.234242
\(151\) 1029.43 0.554793 0.277396 0.960756i \(-0.410528\pi\)
0.277396 + 0.960756i \(0.410528\pi\)
\(152\) 1065.09 0.568358
\(153\) −1510.20 −0.797987
\(154\) −692.432 −0.362323
\(155\) −972.792 −0.504107
\(156\) −169.159 −0.0868177
\(157\) 525.098 0.266926 0.133463 0.991054i \(-0.457390\pi\)
0.133463 + 0.991054i \(0.457390\pi\)
\(158\) 404.094 0.203468
\(159\) −1391.41 −0.694001
\(160\) −294.071 −0.145302
\(161\) −1527.17 −0.747562
\(162\) −2318.69 −1.12453
\(163\) 1002.63 0.481790 0.240895 0.970551i \(-0.422559\pi\)
0.240895 + 0.970551i \(0.422559\pi\)
\(164\) 445.823 0.212274
\(165\) −1273.28 −0.600758
\(166\) −2680.24 −1.25317
\(167\) −359.422 −0.166544 −0.0832722 0.996527i \(-0.526537\pi\)
−0.0832722 + 0.996527i \(0.526537\pi\)
\(168\) 1122.23 0.515369
\(169\) −1822.84 −0.829696
\(170\) 1127.73 0.508783
\(171\) −765.706 −0.342427
\(172\) 297.117 0.131715
\(173\) 3293.65 1.44747 0.723733 0.690080i \(-0.242425\pi\)
0.723733 + 0.690080i \(0.242425\pi\)
\(174\) −808.007 −0.352039
\(175\) −175.000 −0.0755929
\(176\) −1980.24 −0.848104
\(177\) −4100.62 −1.74137
\(178\) −440.167 −0.185348
\(179\) 2978.82 1.24384 0.621921 0.783080i \(-0.286353\pi\)
0.621921 + 0.783080i \(0.286353\pi\)
\(180\) 113.726 0.0470923
\(181\) 1462.31 0.600514 0.300257 0.953858i \(-0.402928\pi\)
0.300257 + 0.953858i \(0.402928\pi\)
\(182\) −350.121 −0.142597
\(183\) 2135.09 0.862460
\(184\) −5254.16 −2.10512
\(185\) −1834.26 −0.728961
\(186\) 3348.97 1.32021
\(187\) −3336.79 −1.30487
\(188\) −15.3391 −0.00595064
\(189\) 451.362 0.173713
\(190\) 571.787 0.218325
\(191\) −374.923 −0.142034 −0.0710169 0.997475i \(-0.522624\pi\)
−0.0710169 + 0.997475i \(0.522624\pi\)
\(192\) 3769.09 1.41672
\(193\) 733.028 0.273391 0.136696 0.990613i \(-0.456352\pi\)
0.136696 + 0.990613i \(0.456352\pi\)
\(194\) 2740.61 1.01425
\(195\) −643.823 −0.236436
\(196\) −64.3717 −0.0234591
\(197\) −2093.24 −0.757043 −0.378521 0.925593i \(-0.623567\pi\)
−0.378521 + 0.925593i \(0.623567\pi\)
\(198\) 1712.65 0.614711
\(199\) 2865.04 1.02059 0.510295 0.860000i \(-0.329536\pi\)
0.510295 + 0.860000i \(0.329536\pi\)
\(200\) −602.082 −0.212868
\(201\) 96.5887 0.0338948
\(202\) −625.330 −0.217812
\(203\) 328.588 0.113608
\(204\) 762.801 0.261798
\(205\) 1696.81 0.578100
\(206\) −4343.03 −1.46890
\(207\) 3777.27 1.26830
\(208\) −1001.29 −0.333783
\(209\) −1691.84 −0.559936
\(210\) 602.462 0.197971
\(211\) 5643.65 1.84135 0.920674 0.390331i \(-0.127640\pi\)
0.920674 + 0.390331i \(0.127640\pi\)
\(212\) 274.590 0.0889573
\(213\) −6337.33 −2.03862
\(214\) 3896.47 1.24466
\(215\) 1130.83 0.358708
\(216\) 1552.89 0.489172
\(217\) −1361.91 −0.426048
\(218\) −3238.46 −1.00613
\(219\) 5488.51 1.69351
\(220\) 251.279 0.0770054
\(221\) −1687.21 −0.513549
\(222\) 6314.71 1.90908
\(223\) −6369.16 −1.91260 −0.956302 0.292381i \(-0.905552\pi\)
−0.956302 + 0.292381i \(0.905552\pi\)
\(224\) −411.699 −0.122803
\(225\) 432.843 0.128250
\(226\) 3543.05 1.04283
\(227\) −1015.67 −0.296972 −0.148486 0.988914i \(-0.547440\pi\)
−0.148486 + 0.988914i \(0.547440\pi\)
\(228\) 386.758 0.112341
\(229\) 4108.35 1.18554 0.592768 0.805373i \(-0.298035\pi\)
0.592768 + 0.805373i \(0.298035\pi\)
\(230\) −2820.66 −0.808647
\(231\) −1782.60 −0.507733
\(232\) 1130.50 0.319917
\(233\) 608.431 0.171071 0.0855357 0.996335i \(-0.472740\pi\)
0.0855357 + 0.996335i \(0.472740\pi\)
\(234\) 865.984 0.241928
\(235\) −58.3810 −0.0162058
\(236\) 809.244 0.223209
\(237\) 1040.30 0.285126
\(238\) 1578.82 0.430000
\(239\) −5054.44 −1.36797 −0.683985 0.729496i \(-0.739755\pi\)
−0.683985 + 0.729496i \(0.739755\pi\)
\(240\) 1722.94 0.463398
\(241\) 4.86782 0.00130109 0.000650547 1.00000i \(-0.499793\pi\)
0.000650547 1.00000i \(0.499793\pi\)
\(242\) 342.442 0.0909628
\(243\) −4228.27 −1.11623
\(244\) −421.352 −0.110551
\(245\) −245.000 −0.0638877
\(246\) −5841.52 −1.51399
\(247\) −855.458 −0.220370
\(248\) −4685.60 −1.19974
\(249\) −6900.02 −1.75611
\(250\) −323.223 −0.0817697
\(251\) −547.921 −0.137787 −0.0688934 0.997624i \(-0.521947\pi\)
−0.0688934 + 0.997624i \(0.521947\pi\)
\(252\) 159.216 0.0398003
\(253\) 8345.92 2.07393
\(254\) 3137.83 0.775137
\(255\) 2903.23 0.712971
\(256\) −1960.46 −0.478629
\(257\) −1774.61 −0.430729 −0.215364 0.976534i \(-0.569094\pi\)
−0.215364 + 0.976534i \(0.569094\pi\)
\(258\) −3893.05 −0.939421
\(259\) −2567.97 −0.616084
\(260\) 127.056 0.0303065
\(261\) −812.725 −0.192745
\(262\) −5126.11 −1.20875
\(263\) −1199.09 −0.281138 −0.140569 0.990071i \(-0.544893\pi\)
−0.140569 + 0.990071i \(0.544893\pi\)
\(264\) −6132.97 −1.42977
\(265\) 1045.10 0.242263
\(266\) 800.502 0.184519
\(267\) −1133.17 −0.259733
\(268\) −19.0615 −0.00434464
\(269\) 3250.29 0.736706 0.368353 0.929686i \(-0.379922\pi\)
0.368353 + 0.929686i \(0.379922\pi\)
\(270\) 833.661 0.187907
\(271\) −896.143 −0.200874 −0.100437 0.994943i \(-0.532024\pi\)
−0.100437 + 0.994943i \(0.532024\pi\)
\(272\) 4515.18 1.00652
\(273\) −901.352 −0.199825
\(274\) 5717.04 1.26051
\(275\) 956.371 0.209714
\(276\) −1907.90 −0.416095
\(277\) −386.562 −0.0838492 −0.0419246 0.999121i \(-0.513349\pi\)
−0.0419246 + 0.999121i \(0.513349\pi\)
\(278\) 1365.40 0.294572
\(279\) 3368.53 0.722826
\(280\) −842.914 −0.179906
\(281\) −3335.10 −0.708025 −0.354013 0.935241i \(-0.615183\pi\)
−0.354013 + 0.935241i \(0.615183\pi\)
\(282\) 200.985 0.0424414
\(283\) 5412.26 1.13684 0.568419 0.822739i \(-0.307555\pi\)
0.568419 + 0.822739i \(0.307555\pi\)
\(284\) 1250.65 0.261311
\(285\) 1472.01 0.305945
\(286\) 1913.40 0.395601
\(287\) 2375.54 0.488584
\(288\) 1018.29 0.208345
\(289\) 2695.27 0.548600
\(290\) 606.899 0.122891
\(291\) 7055.42 1.42129
\(292\) −1083.14 −0.217075
\(293\) 282.211 0.0562695 0.0281347 0.999604i \(-0.491043\pi\)
0.0281347 + 0.999604i \(0.491043\pi\)
\(294\) 843.447 0.167316
\(295\) 3080.00 0.607880
\(296\) −8835.01 −1.73488
\(297\) −2466.68 −0.481924
\(298\) −849.099 −0.165057
\(299\) 4220.03 0.816222
\(300\) −218.629 −0.0420752
\(301\) 1583.17 0.303163
\(302\) 2661.88 0.507199
\(303\) −1609.85 −0.305226
\(304\) 2289.31 0.431910
\(305\) −1603.68 −0.301069
\(306\) −3905.04 −0.729531
\(307\) 1919.67 0.356878 0.178439 0.983951i \(-0.442895\pi\)
0.178439 + 0.983951i \(0.442895\pi\)
\(308\) 351.790 0.0650815
\(309\) −11180.7 −2.05841
\(310\) −2515.43 −0.460861
\(311\) 1213.31 0.221223 0.110612 0.993864i \(-0.464719\pi\)
0.110612 + 0.993864i \(0.464719\pi\)
\(312\) −3101.07 −0.562703
\(313\) −1434.00 −0.258960 −0.129480 0.991582i \(-0.541331\pi\)
−0.129480 + 0.991582i \(0.541331\pi\)
\(314\) 1357.79 0.244028
\(315\) 605.980 0.108391
\(316\) −205.300 −0.0365475
\(317\) 6496.95 1.15112 0.575560 0.817760i \(-0.304784\pi\)
0.575560 + 0.817760i \(0.304784\pi\)
\(318\) −3597.89 −0.634465
\(319\) −1795.72 −0.315176
\(320\) −2830.98 −0.494553
\(321\) 10031.1 1.74418
\(322\) −3948.92 −0.683432
\(323\) 3857.58 0.664524
\(324\) 1178.01 0.201991
\(325\) 483.579 0.0825357
\(326\) 2592.58 0.440459
\(327\) −8337.11 −1.40992
\(328\) 8172.96 1.37584
\(329\) −81.7333 −0.0136964
\(330\) −3292.44 −0.549221
\(331\) −9683.88 −1.60808 −0.804039 0.594576i \(-0.797320\pi\)
−0.804039 + 0.594576i \(0.797320\pi\)
\(332\) 1361.70 0.225099
\(333\) 6351.58 1.04524
\(334\) −929.389 −0.152257
\(335\) −72.5483 −0.0118321
\(336\) 2412.12 0.391643
\(337\) 29.1319 0.00470895 0.00235447 0.999997i \(-0.499251\pi\)
0.00235447 + 0.999997i \(0.499251\pi\)
\(338\) −4713.48 −0.758520
\(339\) 9121.24 1.46135
\(340\) −572.944 −0.0913889
\(341\) 7442.80 1.18197
\(342\) −1979.95 −0.313051
\(343\) −343.000 −0.0539949
\(344\) 5446.83 0.853701
\(345\) −7261.51 −1.13318
\(346\) 8516.68 1.32329
\(347\) −7848.58 −1.21422 −0.607110 0.794618i \(-0.707671\pi\)
−0.607110 + 0.794618i \(0.707671\pi\)
\(348\) 410.508 0.0632343
\(349\) −10269.6 −1.57513 −0.787567 0.616229i \(-0.788659\pi\)
−0.787567 + 0.616229i \(0.788659\pi\)
\(350\) −452.513 −0.0691080
\(351\) −1247.25 −0.189668
\(352\) 2249.93 0.340686
\(353\) 2799.93 0.422168 0.211084 0.977468i \(-0.432301\pi\)
0.211084 + 0.977468i \(0.432301\pi\)
\(354\) −10603.3 −1.59198
\(355\) 4760.00 0.711647
\(356\) 223.627 0.0332927
\(357\) 4064.53 0.602570
\(358\) 7702.60 1.13714
\(359\) −3163.29 −0.465048 −0.232524 0.972591i \(-0.574698\pi\)
−0.232524 + 0.972591i \(0.574698\pi\)
\(360\) 2084.85 0.305226
\(361\) −4903.11 −0.714844
\(362\) 3781.23 0.548998
\(363\) 881.583 0.127469
\(364\) 177.879 0.0256137
\(365\) −4122.45 −0.591175
\(366\) 5520.88 0.788472
\(367\) 3182.85 0.452706 0.226353 0.974045i \(-0.427320\pi\)
0.226353 + 0.974045i \(0.427320\pi\)
\(368\) −11293.3 −1.59974
\(369\) −5875.62 −0.828923
\(370\) −4743.02 −0.666426
\(371\) 1463.14 0.204750
\(372\) −1701.45 −0.237139
\(373\) −2615.14 −0.363021 −0.181510 0.983389i \(-0.558099\pi\)
−0.181510 + 0.983389i \(0.558099\pi\)
\(374\) −8628.23 −1.19293
\(375\) −832.107 −0.114586
\(376\) −281.201 −0.0385687
\(377\) −907.989 −0.124042
\(378\) 1167.12 0.158811
\(379\) −672.434 −0.0911362 −0.0455681 0.998961i \(-0.514510\pi\)
−0.0455681 + 0.998961i \(0.514510\pi\)
\(380\) −290.496 −0.0392162
\(381\) 8078.03 1.08622
\(382\) −969.470 −0.129849
\(383\) 1169.86 0.156075 0.0780377 0.996950i \(-0.475135\pi\)
0.0780377 + 0.996950i \(0.475135\pi\)
\(384\) 6613.92 0.878946
\(385\) 1338.92 0.177241
\(386\) 1895.45 0.249938
\(387\) −3915.78 −0.514342
\(388\) −1392.36 −0.182182
\(389\) −1122.22 −0.146269 −0.0731347 0.997322i \(-0.523300\pi\)
−0.0731347 + 0.997322i \(0.523300\pi\)
\(390\) −1664.79 −0.216153
\(391\) −19029.7 −2.46131
\(392\) −1180.08 −0.152049
\(393\) −13196.7 −1.69385
\(394\) −5412.68 −0.692099
\(395\) −781.375 −0.0995323
\(396\) −870.113 −0.110416
\(397\) −1985.93 −0.251060 −0.125530 0.992090i \(-0.540063\pi\)
−0.125530 + 0.992090i \(0.540063\pi\)
\(398\) 7408.38 0.933037
\(399\) 2060.81 0.258571
\(400\) −1294.11 −0.161764
\(401\) −4172.38 −0.519597 −0.259799 0.965663i \(-0.583656\pi\)
−0.259799 + 0.965663i \(0.583656\pi\)
\(402\) 249.758 0.0309870
\(403\) 3763.37 0.465178
\(404\) 317.699 0.0391240
\(405\) 4483.53 0.550095
\(406\) 849.658 0.103862
\(407\) 14033.9 1.70918
\(408\) 13983.9 1.69682
\(409\) −11700.8 −1.41459 −0.707295 0.706919i \(-0.750085\pi\)
−0.707295 + 0.706919i \(0.750085\pi\)
\(410\) 4387.59 0.528507
\(411\) 14718.0 1.76638
\(412\) 2206.47 0.263848
\(413\) 4312.00 0.513752
\(414\) 9767.22 1.15950
\(415\) 5182.64 0.613026
\(416\) 1137.65 0.134082
\(417\) 3515.08 0.412791
\(418\) −4374.72 −0.511901
\(419\) 2733.20 0.318677 0.159339 0.987224i \(-0.449064\pi\)
0.159339 + 0.987224i \(0.449064\pi\)
\(420\) −306.081 −0.0355600
\(421\) 13549.4 1.56854 0.784272 0.620417i \(-0.213037\pi\)
0.784272 + 0.620417i \(0.213037\pi\)
\(422\) 14593.3 1.68339
\(423\) 202.158 0.0232370
\(424\) 5033.87 0.576571
\(425\) −2180.63 −0.248885
\(426\) −16387.0 −1.86374
\(427\) −2245.15 −0.254450
\(428\) −1979.60 −0.223569
\(429\) 4925.86 0.554366
\(430\) 2924.09 0.327935
\(431\) −6429.25 −0.718530 −0.359265 0.933236i \(-0.616973\pi\)
−0.359265 + 0.933236i \(0.616973\pi\)
\(432\) 3337.79 0.371735
\(433\) 8022.03 0.890333 0.445166 0.895448i \(-0.353145\pi\)
0.445166 + 0.895448i \(0.353145\pi\)
\(434\) −3521.61 −0.389499
\(435\) 1562.40 0.172210
\(436\) 1645.30 0.180724
\(437\) −9648.50 −1.05618
\(438\) 14192.1 1.54823
\(439\) −5569.88 −0.605549 −0.302774 0.953062i \(-0.597913\pi\)
−0.302774 + 0.953062i \(0.597913\pi\)
\(440\) 4606.51 0.499106
\(441\) 848.372 0.0916069
\(442\) −4362.77 −0.469493
\(443\) −5486.21 −0.588392 −0.294196 0.955745i \(-0.595052\pi\)
−0.294196 + 0.955745i \(0.595052\pi\)
\(444\) −3208.19 −0.342914
\(445\) 851.127 0.0906681
\(446\) −16469.3 −1.74853
\(447\) −2185.92 −0.231299
\(448\) −3963.38 −0.417973
\(449\) −7232.67 −0.760203 −0.380101 0.924945i \(-0.624111\pi\)
−0.380101 + 0.924945i \(0.624111\pi\)
\(450\) 1119.24 0.117248
\(451\) −12982.3 −1.35546
\(452\) −1800.05 −0.187317
\(453\) 6852.76 0.710752
\(454\) −2626.32 −0.271496
\(455\) 677.010 0.0697554
\(456\) 7090.16 0.728130
\(457\) −2900.51 −0.296893 −0.148446 0.988920i \(-0.547427\pi\)
−0.148446 + 0.988920i \(0.547427\pi\)
\(458\) 10623.3 1.08383
\(459\) 5624.31 0.571940
\(460\) 1433.04 0.145251
\(461\) 6073.57 0.613611 0.306805 0.951772i \(-0.400740\pi\)
0.306805 + 0.951772i \(0.400740\pi\)
\(462\) −4609.42 −0.464176
\(463\) −18922.8 −1.89939 −0.949693 0.313183i \(-0.898605\pi\)
−0.949693 + 0.313183i \(0.898605\pi\)
\(464\) 2429.88 0.243113
\(465\) −6475.74 −0.645817
\(466\) 1573.27 0.156396
\(467\) −6776.71 −0.671496 −0.335748 0.941952i \(-0.608989\pi\)
−0.335748 + 0.941952i \(0.608989\pi\)
\(468\) −439.963 −0.0434558
\(469\) −101.568 −0.00999991
\(470\) −150.961 −0.0148155
\(471\) 3495.50 0.341962
\(472\) 14835.3 1.44672
\(473\) −8651.96 −0.841052
\(474\) 2689.99 0.260666
\(475\) −1105.63 −0.106800
\(476\) −802.121 −0.0772377
\(477\) −3618.90 −0.347375
\(478\) −13069.7 −1.25062
\(479\) 2397.32 0.228677 0.114338 0.993442i \(-0.463525\pi\)
0.114338 + 0.993442i \(0.463525\pi\)
\(480\) −1957.59 −0.186148
\(481\) 7096.09 0.672669
\(482\) 12.5871 0.00118948
\(483\) −10166.1 −0.957711
\(484\) −173.977 −0.0163390
\(485\) −5299.37 −0.496148
\(486\) −10933.4 −1.02047
\(487\) 5586.17 0.519781 0.259890 0.965638i \(-0.416314\pi\)
0.259890 + 0.965638i \(0.416314\pi\)
\(488\) −7724.35 −0.716526
\(489\) 6674.33 0.617227
\(490\) −633.518 −0.0584070
\(491\) 537.392 0.0493934 0.0246967 0.999695i \(-0.492138\pi\)
0.0246967 + 0.999695i \(0.492138\pi\)
\(492\) 2967.78 0.271947
\(493\) 4094.46 0.374047
\(494\) −2212.03 −0.201466
\(495\) −3311.67 −0.300704
\(496\) −10071.2 −0.911716
\(497\) 6664.00 0.601451
\(498\) −17842.0 −1.60546
\(499\) 598.965 0.0537342 0.0268671 0.999639i \(-0.491447\pi\)
0.0268671 + 0.999639i \(0.491447\pi\)
\(500\) 164.214 0.0146877
\(501\) −2392.62 −0.213362
\(502\) −1416.81 −0.125966
\(503\) 4426.76 0.392405 0.196202 0.980563i \(-0.437139\pi\)
0.196202 + 0.980563i \(0.437139\pi\)
\(504\) 2918.79 0.257963
\(505\) 1209.17 0.106549
\(506\) 21580.8 1.89601
\(507\) −12134.4 −1.06293
\(508\) −1594.17 −0.139232
\(509\) 17727.7 1.54374 0.771872 0.635779i \(-0.219321\pi\)
0.771872 + 0.635779i \(0.219321\pi\)
\(510\) 7507.14 0.651808
\(511\) −5771.43 −0.499634
\(512\) −13017.7 −1.12365
\(513\) 2851.66 0.245427
\(514\) −4588.77 −0.393778
\(515\) 8397.88 0.718553
\(516\) 1977.86 0.168741
\(517\) 446.671 0.0379972
\(518\) −6640.22 −0.563233
\(519\) 21925.4 1.85437
\(520\) 2329.23 0.196430
\(521\) 8662.79 0.728453 0.364226 0.931310i \(-0.381333\pi\)
0.364226 + 0.931310i \(0.381333\pi\)
\(522\) −2101.53 −0.176210
\(523\) −7770.40 −0.649667 −0.324833 0.945771i \(-0.605308\pi\)
−0.324833 + 0.945771i \(0.605308\pi\)
\(524\) 2604.32 0.217119
\(525\) −1164.95 −0.0968430
\(526\) −3100.60 −0.257020
\(527\) −16970.4 −1.40274
\(528\) −13182.2 −1.08652
\(529\) 35429.6 2.91194
\(530\) 2702.40 0.221480
\(531\) −10665.2 −0.871624
\(532\) −406.695 −0.0331437
\(533\) −6564.34 −0.533458
\(534\) −2930.12 −0.237451
\(535\) −7534.41 −0.608861
\(536\) −349.440 −0.0281595
\(537\) 19829.6 1.59350
\(538\) 8404.56 0.673506
\(539\) 1874.49 0.149796
\(540\) −423.541 −0.0337524
\(541\) 21641.0 1.71981 0.859906 0.510453i \(-0.170522\pi\)
0.859906 + 0.510453i \(0.170522\pi\)
\(542\) −2317.23 −0.183642
\(543\) 9734.41 0.769325
\(544\) −5130.09 −0.404321
\(545\) 6262.05 0.492177
\(546\) −2330.70 −0.182683
\(547\) 7489.29 0.585409 0.292705 0.956203i \(-0.405445\pi\)
0.292705 + 0.956203i \(0.405445\pi\)
\(548\) −2904.54 −0.226416
\(549\) 5553.11 0.431696
\(550\) 2472.97 0.191723
\(551\) 2075.99 0.160508
\(552\) −34976.2 −2.69689
\(553\) −1093.93 −0.0841201
\(554\) −999.566 −0.0766561
\(555\) −12210.4 −0.933881
\(556\) −693.689 −0.0529118
\(557\) 25297.9 1.92443 0.962214 0.272295i \(-0.0877826\pi\)
0.962214 + 0.272295i \(0.0877826\pi\)
\(558\) 8710.29 0.660817
\(559\) −4374.77 −0.331007
\(560\) −1811.76 −0.136716
\(561\) −22212.5 −1.67168
\(562\) −8623.85 −0.647286
\(563\) 15661.3 1.17237 0.586186 0.810177i \(-0.300629\pi\)
0.586186 + 0.810177i \(0.300629\pi\)
\(564\) −102.110 −0.00762343
\(565\) −6851.02 −0.510132
\(566\) 13994.9 1.03931
\(567\) 6276.94 0.464915
\(568\) 22927.3 1.69367
\(569\) −9982.75 −0.735498 −0.367749 0.929925i \(-0.619871\pi\)
−0.367749 + 0.929925i \(0.619871\pi\)
\(570\) 3806.30 0.279699
\(571\) −11583.6 −0.848966 −0.424483 0.905436i \(-0.639544\pi\)
−0.424483 + 0.905436i \(0.639544\pi\)
\(572\) −972.103 −0.0710589
\(573\) −2495.81 −0.181961
\(574\) 6142.63 0.446670
\(575\) 5454.16 0.395573
\(576\) 9802.97 0.709127
\(577\) −595.378 −0.0429565 −0.0214783 0.999769i \(-0.506837\pi\)
−0.0214783 + 0.999769i \(0.506837\pi\)
\(578\) 6969.39 0.501537
\(579\) 4879.66 0.350245
\(580\) −308.335 −0.0220740
\(581\) 7255.70 0.518102
\(582\) 18243.8 1.29936
\(583\) −7996.00 −0.568028
\(584\) −19856.4 −1.40696
\(585\) −1674.51 −0.118346
\(586\) 729.738 0.0514423
\(587\) −15750.3 −1.10747 −0.553736 0.832693i \(-0.686798\pi\)
−0.553736 + 0.832693i \(0.686798\pi\)
\(588\) −428.513 −0.0300537
\(589\) −8604.42 −0.601934
\(590\) 7964.22 0.555732
\(591\) −13934.4 −0.969856
\(592\) −18990.0 −1.31838
\(593\) −417.878 −0.0289379 −0.0144690 0.999895i \(-0.504606\pi\)
−0.0144690 + 0.999895i \(0.504606\pi\)
\(594\) −6378.31 −0.440581
\(595\) −3052.89 −0.210347
\(596\) 431.385 0.0296480
\(597\) 19072.2 1.30749
\(598\) 10912.1 0.746201
\(599\) −19997.3 −1.36406 −0.682028 0.731326i \(-0.738902\pi\)
−0.682028 + 0.731326i \(0.738902\pi\)
\(600\) −4007.97 −0.272708
\(601\) −15992.6 −1.08545 −0.542723 0.839912i \(-0.682607\pi\)
−0.542723 + 0.839912i \(0.682607\pi\)
\(602\) 4093.73 0.277156
\(603\) 251.216 0.0169657
\(604\) −1352.37 −0.0911045
\(605\) −662.162 −0.0444970
\(606\) −4162.73 −0.279042
\(607\) 14159.2 0.946793 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(608\) −2601.08 −0.173499
\(609\) 2187.36 0.145544
\(610\) −4146.76 −0.275242
\(611\) 225.854 0.0149543
\(612\) 1983.96 0.131040
\(613\) −4629.41 −0.305025 −0.152512 0.988302i \(-0.548736\pi\)
−0.152512 + 0.988302i \(0.548736\pi\)
\(614\) 4963.87 0.326263
\(615\) 11295.4 0.740611
\(616\) 6449.11 0.421821
\(617\) −23165.3 −1.51151 −0.755753 0.654857i \(-0.772729\pi\)
−0.755753 + 0.654857i \(0.772729\pi\)
\(618\) −28910.9 −1.88182
\(619\) 12370.6 0.803258 0.401629 0.915803i \(-0.368444\pi\)
0.401629 + 0.915803i \(0.368444\pi\)
\(620\) 1277.97 0.0827812
\(621\) −14067.4 −0.909028
\(622\) 3137.36 0.202245
\(623\) 1191.58 0.0766285
\(624\) −6665.43 −0.427613
\(625\) 625.000 0.0400000
\(626\) −3708.02 −0.236745
\(627\) −11262.3 −0.717341
\(628\) −689.826 −0.0438329
\(629\) −31998.9 −2.02842
\(630\) 1566.93 0.0990923
\(631\) 13980.2 0.882002 0.441001 0.897507i \(-0.354623\pi\)
0.441001 + 0.897507i \(0.354623\pi\)
\(632\) −3763.61 −0.236880
\(633\) 37568.9 2.35897
\(634\) 16799.7 1.05237
\(635\) −6067.45 −0.379180
\(636\) 1827.91 0.113964
\(637\) 947.814 0.0589541
\(638\) −4643.36 −0.288139
\(639\) −16482.7 −1.02041
\(640\) −4967.75 −0.306825
\(641\) −16060.9 −0.989655 −0.494828 0.868991i \(-0.664769\pi\)
−0.494828 + 0.868991i \(0.664769\pi\)
\(642\) 25938.3 1.59455
\(643\) −4502.17 −0.276125 −0.138063 0.990424i \(-0.544087\pi\)
−0.138063 + 0.990424i \(0.544087\pi\)
\(644\) 2006.25 0.122760
\(645\) 7527.79 0.459545
\(646\) 9974.87 0.607517
\(647\) 29414.8 1.78735 0.893675 0.448715i \(-0.148118\pi\)
0.893675 + 0.448715i \(0.148118\pi\)
\(648\) 21595.6 1.30919
\(649\) −23565.0 −1.42528
\(650\) 1250.43 0.0754553
\(651\) −9066.03 −0.545815
\(652\) −1317.16 −0.0791164
\(653\) 13013.6 0.779882 0.389941 0.920840i \(-0.372495\pi\)
0.389941 + 0.920840i \(0.372495\pi\)
\(654\) −21558.0 −1.28897
\(655\) 9912.09 0.591294
\(656\) 17566.9 1.04554
\(657\) 14275.0 0.847671
\(658\) −211.345 −0.0125214
\(659\) 23474.2 1.38759 0.693797 0.720171i \(-0.255937\pi\)
0.693797 + 0.720171i \(0.255937\pi\)
\(660\) 1672.72 0.0986526
\(661\) −9266.36 −0.545264 −0.272632 0.962118i \(-0.587894\pi\)
−0.272632 + 0.962118i \(0.587894\pi\)
\(662\) −25040.4 −1.47013
\(663\) −11231.5 −0.657914
\(664\) 24963.0 1.45896
\(665\) −1547.89 −0.0902625
\(666\) 16423.8 0.955572
\(667\) −10241.0 −0.594501
\(668\) 472.176 0.0273489
\(669\) −42398.6 −2.45026
\(670\) −187.595 −0.0108170
\(671\) 12269.7 0.705909
\(672\) −2740.62 −0.157324
\(673\) −25067.2 −1.43576 −0.717882 0.696164i \(-0.754888\pi\)
−0.717882 + 0.696164i \(0.754888\pi\)
\(674\) 75.3288 0.00430498
\(675\) −1612.01 −0.0919202
\(676\) 2394.68 0.136247
\(677\) −22409.6 −1.27219 −0.636093 0.771613i \(-0.719450\pi\)
−0.636093 + 0.771613i \(0.719450\pi\)
\(678\) 23585.6 1.33599
\(679\) −7419.11 −0.419322
\(680\) −10503.4 −0.592332
\(681\) −6761.20 −0.380455
\(682\) 19245.5 1.08057
\(683\) −8757.53 −0.490626 −0.245313 0.969444i \(-0.578891\pi\)
−0.245313 + 0.969444i \(0.578891\pi\)
\(684\) 1005.91 0.0562311
\(685\) −11054.7 −0.616613
\(686\) −886.925 −0.0493629
\(687\) 27348.7 1.51880
\(688\) 11707.4 0.648750
\(689\) −4043.09 −0.223555
\(690\) −18776.7 −1.03597
\(691\) 8468.42 0.466214 0.233107 0.972451i \(-0.425111\pi\)
0.233107 + 0.972451i \(0.425111\pi\)
\(692\) −4326.90 −0.237694
\(693\) −4636.33 −0.254141
\(694\) −20294.8 −1.11006
\(695\) −2640.19 −0.144098
\(696\) 7525.54 0.409849
\(697\) 29601.0 1.60864
\(698\) −26555.1 −1.44001
\(699\) 4050.23 0.219162
\(700\) 229.899 0.0124134
\(701\) 15996.9 0.861906 0.430953 0.902374i \(-0.358177\pi\)
0.430953 + 0.902374i \(0.358177\pi\)
\(702\) −3225.12 −0.173397
\(703\) −16224.2 −0.870423
\(704\) 21659.8 1.15956
\(705\) −388.633 −0.0207614
\(706\) 7240.03 0.385952
\(707\) 1692.83 0.0900503
\(708\) 5387.02 0.285956
\(709\) 19903.0 1.05426 0.527131 0.849784i \(-0.323268\pi\)
0.527131 + 0.849784i \(0.323268\pi\)
\(710\) 12308.3 0.650597
\(711\) 2705.70 0.142717
\(712\) 4099.58 0.215784
\(713\) 42446.1 2.22948
\(714\) 10510.0 0.550878
\(715\) −3699.84 −0.193519
\(716\) −3913.30 −0.204256
\(717\) −33646.7 −1.75252
\(718\) −8179.59 −0.425153
\(719\) −11073.1 −0.574347 −0.287174 0.957879i \(-0.592716\pi\)
−0.287174 + 0.957879i \(0.592716\pi\)
\(720\) 4481.18 0.231949
\(721\) 11757.0 0.607288
\(722\) −12678.4 −0.653520
\(723\) 32.4043 0.00166685
\(724\) −1921.06 −0.0986125
\(725\) −1173.53 −0.0601155
\(726\) 2279.58 0.116533
\(727\) 31652.7 1.61476 0.807382 0.590029i \(-0.200884\pi\)
0.807382 + 0.590029i \(0.200884\pi\)
\(728\) 3260.92 0.166013
\(729\) −3935.94 −0.199967
\(730\) −10659.8 −0.540460
\(731\) 19727.5 0.998149
\(732\) −2804.88 −0.141628
\(733\) 16958.3 0.854528 0.427264 0.904127i \(-0.359477\pi\)
0.427264 + 0.904127i \(0.359477\pi\)
\(734\) 8230.16 0.413870
\(735\) −1630.93 −0.0818473
\(736\) 12831.3 0.642618
\(737\) 555.065 0.0277423
\(738\) −15193.1 −0.757813
\(739\) −11616.6 −0.578245 −0.289123 0.957292i \(-0.593364\pi\)
−0.289123 + 0.957292i \(0.593364\pi\)
\(740\) 2409.69 0.119705
\(741\) −5694.66 −0.282319
\(742\) 3783.36 0.187185
\(743\) 15928.0 0.786464 0.393232 0.919439i \(-0.371357\pi\)
0.393232 + 0.919439i \(0.371357\pi\)
\(744\) −31191.4 −1.53700
\(745\) 1641.86 0.0807423
\(746\) −6762.19 −0.331879
\(747\) −17946.1 −0.879003
\(748\) 4383.57 0.214277
\(749\) −10548.2 −0.514582
\(750\) −2151.65 −0.104756
\(751\) 25571.9 1.24252 0.621260 0.783604i \(-0.286621\pi\)
0.621260 + 0.783604i \(0.286621\pi\)
\(752\) −604.412 −0.0293094
\(753\) −3647.43 −0.176520
\(754\) −2347.87 −0.113401
\(755\) −5147.14 −0.248111
\(756\) −592.958 −0.0285260
\(757\) 6202.41 0.297794 0.148897 0.988853i \(-0.452428\pi\)
0.148897 + 0.988853i \(0.452428\pi\)
\(758\) −1738.77 −0.0833179
\(759\) 55557.6 2.65693
\(760\) −5325.46 −0.254177
\(761\) −29199.1 −1.39089 −0.695444 0.718580i \(-0.744792\pi\)
−0.695444 + 0.718580i \(0.744792\pi\)
\(762\) 20888.1 0.993037
\(763\) 8766.87 0.415966
\(764\) 492.539 0.0233239
\(765\) 7550.98 0.356871
\(766\) 3025.00 0.142686
\(767\) −11915.4 −0.560938
\(768\) −13050.5 −0.613177
\(769\) 21838.2 1.02407 0.512033 0.858966i \(-0.328892\pi\)
0.512033 + 0.858966i \(0.328892\pi\)
\(770\) 3462.16 0.162036
\(771\) −11813.3 −0.551812
\(772\) −962.985 −0.0448945
\(773\) −25544.8 −1.18859 −0.594296 0.804246i \(-0.702569\pi\)
−0.594296 + 0.804246i \(0.702569\pi\)
\(774\) −10125.4 −0.470218
\(775\) 4863.96 0.225443
\(776\) −25525.2 −1.18080
\(777\) −17094.6 −0.789273
\(778\) −2901.82 −0.133721
\(779\) 15008.4 0.690286
\(780\) 845.795 0.0388261
\(781\) −36418.6 −1.66858
\(782\) −49206.6 −2.25016
\(783\) 3026.77 0.138146
\(784\) −2536.46 −0.115546
\(785\) −2625.49 −0.119373
\(786\) −34123.8 −1.54854
\(787\) −37223.2 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(788\) 2749.91 0.124317
\(789\) −7982.19 −0.360169
\(790\) −2020.47 −0.0909938
\(791\) −9591.42 −0.431140
\(792\) −15951.1 −0.715655
\(793\) 6204.03 0.277820
\(794\) −5135.18 −0.229522
\(795\) 6957.06 0.310366
\(796\) −3763.83 −0.167595
\(797\) −40384.6 −1.79485 −0.897425 0.441168i \(-0.854564\pi\)
−0.897425 + 0.441168i \(0.854564\pi\)
\(798\) 5328.83 0.236389
\(799\) −1018.46 −0.0450945
\(800\) 1470.35 0.0649811
\(801\) −2947.23 −0.130007
\(802\) −10788.9 −0.475023
\(803\) 31540.7 1.38611
\(804\) −126.889 −0.00556598
\(805\) 7635.83 0.334320
\(806\) 9731.28 0.425272
\(807\) 21636.7 0.943803
\(808\) 5824.14 0.253580
\(809\) −1955.76 −0.0849948 −0.0424974 0.999097i \(-0.513531\pi\)
−0.0424974 + 0.999097i \(0.513531\pi\)
\(810\) 11593.4 0.502904
\(811\) −34301.8 −1.48520 −0.742600 0.669735i \(-0.766408\pi\)
−0.742600 + 0.669735i \(0.766408\pi\)
\(812\) −431.669 −0.0186559
\(813\) −5965.49 −0.257342
\(814\) 36288.7 1.56255
\(815\) −5013.13 −0.215463
\(816\) 30056.9 1.28946
\(817\) 10002.3 0.428319
\(818\) −30255.8 −1.29324
\(819\) −2344.31 −0.100021
\(820\) −2229.12 −0.0949319
\(821\) −13665.6 −0.580918 −0.290459 0.956887i \(-0.593808\pi\)
−0.290459 + 0.956887i \(0.593808\pi\)
\(822\) 38057.5 1.61485
\(823\) −21519.5 −0.911449 −0.455724 0.890121i \(-0.650620\pi\)
−0.455724 + 0.890121i \(0.650620\pi\)
\(824\) 40449.7 1.71011
\(825\) 6366.42 0.268667
\(826\) 11149.9 0.469679
\(827\) 35220.6 1.48094 0.740471 0.672088i \(-0.234602\pi\)
0.740471 + 0.672088i \(0.234602\pi\)
\(828\) −4962.23 −0.208272
\(829\) 31365.5 1.31408 0.657039 0.753857i \(-0.271809\pi\)
0.657039 + 0.753857i \(0.271809\pi\)
\(830\) 13401.2 0.560437
\(831\) −2573.28 −0.107420
\(832\) 10952.0 0.456362
\(833\) −4274.04 −0.177775
\(834\) 9089.24 0.377380
\(835\) 1797.11 0.0744810
\(836\) 2222.58 0.0919491
\(837\) −12545.2 −0.518070
\(838\) 7067.48 0.291339
\(839\) −28287.1 −1.16398 −0.581990 0.813196i \(-0.697726\pi\)
−0.581990 + 0.813196i \(0.697726\pi\)
\(840\) −5611.16 −0.230480
\(841\) −22185.5 −0.909653
\(842\) 35035.8 1.43398
\(843\) −22201.2 −0.907060
\(844\) −7414.11 −0.302374
\(845\) 9114.21 0.371051
\(846\) 522.738 0.0212436
\(847\) −927.026 −0.0376068
\(848\) 10819.8 0.438152
\(849\) 36028.6 1.45642
\(850\) −5638.66 −0.227534
\(851\) 80035.0 3.22393
\(852\) 8325.40 0.334769
\(853\) 9405.41 0.377533 0.188766 0.982022i \(-0.439551\pi\)
0.188766 + 0.982022i \(0.439551\pi\)
\(854\) −5805.47 −0.232622
\(855\) 3828.53 0.153138
\(856\) −36290.6 −1.44905
\(857\) −27966.9 −1.11474 −0.557369 0.830265i \(-0.688189\pi\)
−0.557369 + 0.830265i \(0.688189\pi\)
\(858\) 12737.2 0.506809
\(859\) 6281.11 0.249486 0.124743 0.992189i \(-0.460189\pi\)
0.124743 + 0.992189i \(0.460189\pi\)
\(860\) −1485.58 −0.0589047
\(861\) 15813.6 0.625931
\(862\) −16624.7 −0.656890
\(863\) −4757.13 −0.187642 −0.0938208 0.995589i \(-0.529908\pi\)
−0.0938208 + 0.995589i \(0.529908\pi\)
\(864\) −3792.35 −0.149327
\(865\) −16468.3 −0.647327
\(866\) 20743.3 0.813954
\(867\) 17942.0 0.702818
\(868\) 1789.15 0.0699629
\(869\) 5978.28 0.233371
\(870\) 4040.04 0.157437
\(871\) 280.663 0.0109184
\(872\) 30162.1 1.17135
\(873\) 18350.3 0.711414
\(874\) −24949.0 −0.965574
\(875\) 875.000 0.0338062
\(876\) −7210.30 −0.278097
\(877\) −30240.5 −1.16437 −0.582184 0.813057i \(-0.697802\pi\)
−0.582184 + 0.813057i \(0.697802\pi\)
\(878\) −14402.5 −0.553601
\(879\) 1878.64 0.0720875
\(880\) 9901.21 0.379284
\(881\) 44875.5 1.71611 0.858056 0.513556i \(-0.171672\pi\)
0.858056 + 0.513556i \(0.171672\pi\)
\(882\) 2193.71 0.0837483
\(883\) 4892.13 0.186448 0.0932238 0.995645i \(-0.470283\pi\)
0.0932238 + 0.995645i \(0.470283\pi\)
\(884\) 2216.51 0.0843317
\(885\) 20503.1 0.778762
\(886\) −14186.2 −0.537916
\(887\) 1761.40 0.0666765 0.0333382 0.999444i \(-0.489386\pi\)
0.0333382 + 0.999444i \(0.489386\pi\)
\(888\) −58813.4 −2.22258
\(889\) −8494.43 −0.320466
\(890\) 2200.83 0.0828900
\(891\) −34303.3 −1.28979
\(892\) 8367.22 0.314075
\(893\) −516.384 −0.0193507
\(894\) −5652.33 −0.211457
\(895\) −14894.1 −0.556263
\(896\) −6954.86 −0.259314
\(897\) 28092.1 1.04567
\(898\) −18702.2 −0.694988
\(899\) −9132.79 −0.338816
\(900\) −568.629 −0.0210603
\(901\) 18231.8 0.674128
\(902\) −33569.3 −1.23918
\(903\) 10538.9 0.388386
\(904\) −32999.0 −1.21408
\(905\) −7311.57 −0.268558
\(906\) 17719.8 0.649779
\(907\) 23689.1 0.867238 0.433619 0.901096i \(-0.357236\pi\)
0.433619 + 0.901096i \(0.357236\pi\)
\(908\) 1334.30 0.0487669
\(909\) −4187.03 −0.152778
\(910\) 1750.60 0.0637714
\(911\) −13877.3 −0.504692 −0.252346 0.967637i \(-0.581202\pi\)
−0.252346 + 0.967637i \(0.581202\pi\)
\(912\) 15239.6 0.553325
\(913\) −39652.2 −1.43735
\(914\) −7500.09 −0.271423
\(915\) −10675.4 −0.385704
\(916\) −5397.18 −0.194681
\(917\) 13876.9 0.499735
\(918\) 14543.3 0.522875
\(919\) 14331.6 0.514426 0.257213 0.966355i \(-0.417196\pi\)
0.257213 + 0.966355i \(0.417196\pi\)
\(920\) 26270.8 0.941438
\(921\) 12779.0 0.457201
\(922\) 15705.0 0.560971
\(923\) −18414.7 −0.656692
\(924\) 2341.81 0.0833767
\(925\) 9171.32 0.326001
\(926\) −48930.2 −1.73644
\(927\) −29079.7 −1.03032
\(928\) −2760.80 −0.0976592
\(929\) 16668.4 0.588668 0.294334 0.955703i \(-0.404902\pi\)
0.294334 + 0.955703i \(0.404902\pi\)
\(930\) −16744.9 −0.590415
\(931\) −2167.04 −0.0762857
\(932\) −799.300 −0.0280922
\(933\) 8076.82 0.283412
\(934\) −17523.1 −0.613891
\(935\) 16684.0 0.583555
\(936\) −8065.52 −0.281656
\(937\) 30384.9 1.05937 0.529685 0.848194i \(-0.322310\pi\)
0.529685 + 0.848194i \(0.322310\pi\)
\(938\) −262.632 −0.00914206
\(939\) −9545.94 −0.331757
\(940\) 76.6956 0.00266121
\(941\) −1196.35 −0.0414452 −0.0207226 0.999785i \(-0.506597\pi\)
−0.0207226 + 0.999785i \(0.506597\pi\)
\(942\) 9038.63 0.312627
\(943\) −74037.5 −2.55673
\(944\) 31886.9 1.09940
\(945\) −2256.81 −0.0776867
\(946\) −22372.1 −0.768901
\(947\) 1788.41 0.0613681 0.0306840 0.999529i \(-0.490231\pi\)
0.0306840 + 0.999529i \(0.490231\pi\)
\(948\) −1366.65 −0.0468215
\(949\) 15948.2 0.545523
\(950\) −2858.94 −0.0976380
\(951\) 43249.2 1.47471
\(952\) −14704.7 −0.500612
\(953\) 8578.60 0.291593 0.145796 0.989315i \(-0.453426\pi\)
0.145796 + 0.989315i \(0.453426\pi\)
\(954\) −9357.70 −0.317575
\(955\) 1874.61 0.0635194
\(956\) 6640.06 0.224639
\(957\) −11953.9 −0.403776
\(958\) 6198.95 0.209059
\(959\) −15476.6 −0.521133
\(960\) −18845.4 −0.633577
\(961\) 8061.99 0.270618
\(962\) 18349.0 0.614963
\(963\) 26089.7 0.873031
\(964\) −6.39489 −0.000213657 0
\(965\) −3665.14 −0.122264
\(966\) −26287.4 −0.875552
\(967\) −55459.3 −1.84431 −0.922156 0.386818i \(-0.873574\pi\)
−0.922156 + 0.386818i \(0.873574\pi\)
\(968\) −3189.40 −0.105900
\(969\) 25679.3 0.851330
\(970\) −13703.0 −0.453585
\(971\) 22047.3 0.728662 0.364331 0.931270i \(-0.381298\pi\)
0.364331 + 0.931270i \(0.381298\pi\)
\(972\) 5554.72 0.183300
\(973\) −3696.27 −0.121785
\(974\) 14444.6 0.475191
\(975\) 3219.11 0.105738
\(976\) −16602.7 −0.544507
\(977\) 14402.3 0.471617 0.235809 0.971800i \(-0.424226\pi\)
0.235809 + 0.971800i \(0.424226\pi\)
\(978\) 17258.4 0.564277
\(979\) −6511.94 −0.212587
\(980\) 321.859 0.0104912
\(981\) −21683.9 −0.705721
\(982\) 1389.58 0.0451561
\(983\) 7817.11 0.253639 0.126819 0.991926i \(-0.459523\pi\)
0.126819 + 0.991926i \(0.459523\pi\)
\(984\) 54406.2 1.76261
\(985\) 10466.2 0.338560
\(986\) 10587.4 0.341959
\(987\) −544.087 −0.0175466
\(988\) 1123.82 0.0361878
\(989\) −49342.0 −1.58643
\(990\) −8563.26 −0.274907
\(991\) 24501.6 0.785386 0.392693 0.919670i \(-0.371543\pi\)
0.392693 + 0.919670i \(0.371543\pi\)
\(992\) 11442.8 0.366239
\(993\) −64464.2 −2.06013
\(994\) 17231.7 0.549855
\(995\) −14325.2 −0.456421
\(996\) 9064.61 0.288377
\(997\) −50696.0 −1.61039 −0.805195 0.593010i \(-0.797940\pi\)
−0.805195 + 0.593010i \(0.797940\pi\)
\(998\) 1548.80 0.0491245
\(999\) −23654.8 −0.749152
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 35.4.a.b.1.1 2
3.2 odd 2 315.4.a.f.1.2 2
4.3 odd 2 560.4.a.r.1.1 2
5.2 odd 4 175.4.b.c.99.3 4
5.3 odd 4 175.4.b.c.99.2 4
5.4 even 2 175.4.a.c.1.2 2
7.2 even 3 245.4.e.h.116.2 4
7.3 odd 6 245.4.e.i.226.2 4
7.4 even 3 245.4.e.h.226.2 4
7.5 odd 6 245.4.e.i.116.2 4
7.6 odd 2 245.4.a.k.1.1 2
8.3 odd 2 2240.4.a.bo.1.2 2
8.5 even 2 2240.4.a.bn.1.1 2
15.14 odd 2 1575.4.a.z.1.1 2
21.20 even 2 2205.4.a.u.1.2 2
35.34 odd 2 1225.4.a.m.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.4.a.b.1.1 2 1.1 even 1 trivial
175.4.a.c.1.2 2 5.4 even 2
175.4.b.c.99.2 4 5.3 odd 4
175.4.b.c.99.3 4 5.2 odd 4
245.4.a.k.1.1 2 7.6 odd 2
245.4.e.h.116.2 4 7.2 even 3
245.4.e.h.226.2 4 7.4 even 3
245.4.e.i.116.2 4 7.5 odd 6
245.4.e.i.226.2 4 7.3 odd 6
315.4.a.f.1.2 2 3.2 odd 2
560.4.a.r.1.1 2 4.3 odd 2
1225.4.a.m.1.2 2 35.34 odd 2
1575.4.a.z.1.1 2 15.14 odd 2
2205.4.a.u.1.2 2 21.20 even 2
2240.4.a.bn.1.1 2 8.5 even 2
2240.4.a.bo.1.2 2 8.3 odd 2