Properties

Label 435.4.a.j.1.6
Level $435$
Weight $4$
Character 435.1
Self dual yes
Analytic conductor $25.666$
Analytic rank $1$
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: \(1\)
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: \( x^{7} - x^{6} - 35x^{5} + 18x^{4} + 329x^{3} - 167x^{2} - 767x + 638 \) 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 1.6
Root \(-3.52131\) 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)
 
\(f(q)\) \(=\) \(q+3.52131 q^{2} +3.00000 q^{3} +4.39964 q^{4} -5.00000 q^{5} +10.5639 q^{6} -8.86571 q^{7} -12.6780 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q+3.52131 q^{2} +3.00000 q^{3} +4.39964 q^{4} -5.00000 q^{5} +10.5639 q^{6} -8.86571 q^{7} -12.6780 q^{8} +9.00000 q^{9} -17.6066 q^{10} -61.9492 q^{11} +13.1989 q^{12} +31.6208 q^{13} -31.2189 q^{14} -15.0000 q^{15} -79.8403 q^{16} -48.6694 q^{17} +31.6918 q^{18} -127.727 q^{19} -21.9982 q^{20} -26.5971 q^{21} -218.143 q^{22} +184.026 q^{23} -38.0339 q^{24} +25.0000 q^{25} +111.347 q^{26} +27.0000 q^{27} -39.0059 q^{28} -29.0000 q^{29} -52.8197 q^{30} -251.985 q^{31} -179.719 q^{32} -185.848 q^{33} -171.380 q^{34} +44.3285 q^{35} +39.5968 q^{36} +197.740 q^{37} -449.765 q^{38} +94.8624 q^{39} +63.3899 q^{40} -163.446 q^{41} -93.6568 q^{42} -33.2231 q^{43} -272.555 q^{44} -45.0000 q^{45} +648.012 q^{46} +528.945 q^{47} -239.521 q^{48} -264.399 q^{49} +88.0328 q^{50} -146.008 q^{51} +139.120 q^{52} -240.256 q^{53} +95.0754 q^{54} +309.746 q^{55} +112.399 q^{56} -383.180 q^{57} -102.118 q^{58} -202.976 q^{59} -65.9947 q^{60} +492.192 q^{61} -887.318 q^{62} -79.7914 q^{63} +5.87624 q^{64} -158.104 q^{65} -654.428 q^{66} -229.556 q^{67} -214.128 q^{68} +552.077 q^{69} +156.095 q^{70} +21.2064 q^{71} -114.102 q^{72} -1145.48 q^{73} +696.303 q^{74} +75.0000 q^{75} -561.952 q^{76} +549.224 q^{77} +334.040 q^{78} +95.6307 q^{79} +399.201 q^{80} +81.0000 q^{81} -575.545 q^{82} +1239.97 q^{83} -117.018 q^{84} +243.347 q^{85} -116.989 q^{86} -87.0000 q^{87} +785.391 q^{88} +116.863 q^{89} -158.459 q^{90} -280.341 q^{91} +809.648 q^{92} -755.955 q^{93} +1862.58 q^{94} +638.633 q^{95} -539.156 q^{96} -275.722 q^{97} -931.032 q^{98} -557.543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - q^{2} + 21 q^{3} + 15 q^{4} - 35 q^{5} - 3 q^{6} - 37 q^{7} - 36 q^{8} + 63 q^{9} + 5 q^{10} - 11 q^{11} + 45 q^{12} - 133 q^{13} - 75 q^{14} - 105 q^{15} - 53 q^{16} + 21 q^{17} - 9 q^{18} - 170 q^{19} - 75 q^{20} - 111 q^{21} - 369 q^{22} - 68 q^{23} - 108 q^{24} + 175 q^{25} + 181 q^{26} + 189 q^{27} - 637 q^{28} - 203 q^{29} + 15 q^{30} - 480 q^{31} - 779 q^{32} - 33 q^{33} - 897 q^{34} + 185 q^{35} + 135 q^{36} - 1032 q^{37} - 194 q^{38} - 399 q^{39} + 180 q^{40} - 638 q^{41} - 225 q^{42} - 512 q^{43} + 625 q^{44} - 315 q^{45} + 16 q^{46} - 111 q^{47} - 159 q^{48} + 178 q^{49} - 25 q^{50} + 63 q^{51} - 1263 q^{52} + 410 q^{53} - 27 q^{54} + 55 q^{55} + 1174 q^{56} - 510 q^{57} + 29 q^{58} - 426 q^{59} - 225 q^{60} - 1192 q^{61} + 460 q^{62} - 333 q^{63} + 390 q^{64} + 665 q^{65} - 1107 q^{66} - 1671 q^{67} + 1509 q^{68} - 204 q^{69} + 375 q^{70} - 1324 q^{71} - 324 q^{72} - 852 q^{73} + 1780 q^{74} + 525 q^{75} - 564 q^{76} - 2107 q^{77} + 543 q^{78} + 366 q^{79} + 265 q^{80} + 567 q^{81} - 318 q^{82} + 470 q^{83} - 1911 q^{84} - 105 q^{85} - 2196 q^{86} - 609 q^{87} - 2518 q^{88} + 51 q^{89} + 45 q^{90} - 1297 q^{91} - 684 q^{92} - 1440 q^{93} - 1837 q^{94} + 850 q^{95} - 2337 q^{96} - 3322 q^{97} + 1068 q^{98} - 99 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.52131 1.24497 0.622486 0.782631i \(-0.286123\pi\)
0.622486 + 0.782631i \(0.286123\pi\)
\(3\) 3.00000 0.577350
\(4\) 4.39964 0.549955
\(5\) −5.00000 −0.447214
\(6\) 10.5639 0.718785
\(7\) −8.86571 −0.478703 −0.239352 0.970933i \(-0.576935\pi\)
−0.239352 + 0.970933i \(0.576935\pi\)
\(8\) −12.6780 −0.560293
\(9\) 9.00000 0.333333
\(10\) −17.6066 −0.556768
\(11\) −61.9492 −1.69804 −0.849018 0.528364i \(-0.822806\pi\)
−0.849018 + 0.528364i \(0.822806\pi\)
\(12\) 13.1989 0.317517
\(13\) 31.6208 0.674618 0.337309 0.941394i \(-0.390483\pi\)
0.337309 + 0.941394i \(0.390483\pi\)
\(14\) −31.2189 −0.595972
\(15\) −15.0000 −0.258199
\(16\) −79.8403 −1.24750
\(17\) −48.6694 −0.694357 −0.347178 0.937799i \(-0.612860\pi\)
−0.347178 + 0.937799i \(0.612860\pi\)
\(18\) 31.6918 0.414991
\(19\) −127.727 −1.54224 −0.771118 0.636692i \(-0.780302\pi\)
−0.771118 + 0.636692i \(0.780302\pi\)
\(20\) −21.9982 −0.245948
\(21\) −26.5971 −0.276379
\(22\) −218.143 −2.11401
\(23\) 184.026 1.66835 0.834175 0.551501i \(-0.185945\pi\)
0.834175 + 0.551501i \(0.185945\pi\)
\(24\) −38.0339 −0.323485
\(25\) 25.0000 0.200000
\(26\) 111.347 0.839881
\(27\) 27.0000 0.192450
\(28\) −39.0059 −0.263265
\(29\) −29.0000 −0.185695
\(30\) −52.8197 −0.321450
\(31\) −251.985 −1.45993 −0.729965 0.683484i \(-0.760464\pi\)
−0.729965 + 0.683484i \(0.760464\pi\)
\(32\) −179.719 −0.992815
\(33\) −185.848 −0.980361
\(34\) −171.380 −0.864455
\(35\) 44.3285 0.214083
\(36\) 39.5968 0.183318
\(37\) 197.740 0.878600 0.439300 0.898340i \(-0.355226\pi\)
0.439300 + 0.898340i \(0.355226\pi\)
\(38\) −449.765 −1.92004
\(39\) 94.8624 0.389491
\(40\) 63.3899 0.250571
\(41\) −163.446 −0.622585 −0.311293 0.950314i \(-0.600762\pi\)
−0.311293 + 0.950314i \(0.600762\pi\)
\(42\) −93.6568 −0.344085
\(43\) −33.2231 −0.117825 −0.0589124 0.998263i \(-0.518763\pi\)
−0.0589124 + 0.998263i \(0.518763\pi\)
\(44\) −272.555 −0.933844
\(45\) −45.0000 −0.149071
\(46\) 648.012 2.07705
\(47\) 528.945 1.64159 0.820793 0.571226i \(-0.193532\pi\)
0.820793 + 0.571226i \(0.193532\pi\)
\(48\) −239.521 −0.720247
\(49\) −264.399 −0.770843
\(50\) 88.0328 0.248994
\(51\) −146.008 −0.400887
\(52\) 139.120 0.371010
\(53\) −240.256 −0.622673 −0.311336 0.950300i \(-0.600777\pi\)
−0.311336 + 0.950300i \(0.600777\pi\)
\(54\) 95.0754 0.239595
\(55\) 309.746 0.759385
\(56\) 112.399 0.268214
\(57\) −383.180 −0.890411
\(58\) −102.118 −0.231186
\(59\) −202.976 −0.447885 −0.223942 0.974602i \(-0.571893\pi\)
−0.223942 + 0.974602i \(0.571893\pi\)
\(60\) −65.9947 −0.141998
\(61\) 492.192 1.03309 0.516547 0.856259i \(-0.327217\pi\)
0.516547 + 0.856259i \(0.327217\pi\)
\(62\) −887.318 −1.81757
\(63\) −79.7914 −0.159568
\(64\) 5.87624 0.0114770
\(65\) −158.104 −0.301698
\(66\) −654.428 −1.22052
\(67\) −229.556 −0.418577 −0.209289 0.977854i \(-0.567115\pi\)
−0.209289 + 0.977854i \(0.567115\pi\)
\(68\) −214.128 −0.381865
\(69\) 552.077 0.963222
\(70\) 156.095 0.266527
\(71\) 21.2064 0.0354471 0.0177235 0.999843i \(-0.494358\pi\)
0.0177235 + 0.999843i \(0.494358\pi\)
\(72\) −114.102 −0.186764
\(73\) −1145.48 −1.83656 −0.918279 0.395934i \(-0.870421\pi\)
−0.918279 + 0.395934i \(0.870421\pi\)
\(74\) 696.303 1.09383
\(75\) 75.0000 0.115470
\(76\) −561.952 −0.848161
\(77\) 549.224 0.812855
\(78\) 334.040 0.484905
\(79\) 95.6307 0.136194 0.0680968 0.997679i \(-0.478307\pi\)
0.0680968 + 0.997679i \(0.478307\pi\)
\(80\) 399.201 0.557901
\(81\) 81.0000 0.111111
\(82\) −575.545 −0.775101
\(83\) 1239.97 1.63982 0.819908 0.572496i \(-0.194025\pi\)
0.819908 + 0.572496i \(0.194025\pi\)
\(84\) −117.018 −0.151996
\(85\) 243.347 0.310526
\(86\) −116.989 −0.146689
\(87\) −87.0000 −0.107211
\(88\) 785.391 0.951397
\(89\) 116.863 0.139185 0.0695927 0.997575i \(-0.477830\pi\)
0.0695927 + 0.997575i \(0.477830\pi\)
\(90\) −158.459 −0.185589
\(91\) −280.341 −0.322942
\(92\) 809.648 0.917518
\(93\) −755.955 −0.842891
\(94\) 1862.58 2.04373
\(95\) 638.633 0.689709
\(96\) −539.156 −0.573202
\(97\) −275.722 −0.288611 −0.144306 0.989533i \(-0.546095\pi\)
−0.144306 + 0.989533i \(0.546095\pi\)
\(98\) −931.032 −0.959678
\(99\) −557.543 −0.566012
\(100\) 109.991 0.109991
\(101\) −1909.39 −1.88111 −0.940553 0.339648i \(-0.889692\pi\)
−0.940553 + 0.339648i \(0.889692\pi\)
\(102\) −514.141 −0.499093
\(103\) 1501.97 1.43683 0.718415 0.695614i \(-0.244868\pi\)
0.718415 + 0.695614i \(0.244868\pi\)
\(104\) −400.888 −0.377984
\(105\) 132.986 0.123601
\(106\) −846.016 −0.775210
\(107\) 1434.61 1.29616 0.648080 0.761572i \(-0.275572\pi\)
0.648080 + 0.761572i \(0.275572\pi\)
\(108\) 118.790 0.105839
\(109\) −347.951 −0.305758 −0.152879 0.988245i \(-0.548855\pi\)
−0.152879 + 0.988245i \(0.548855\pi\)
\(110\) 1090.71 0.945413
\(111\) 593.219 0.507260
\(112\) 707.840 0.597184
\(113\) −1812.68 −1.50905 −0.754524 0.656272i \(-0.772132\pi\)
−0.754524 + 0.656272i \(0.772132\pi\)
\(114\) −1349.30 −1.10854
\(115\) −920.129 −0.746108
\(116\) −127.590 −0.102124
\(117\) 284.587 0.224873
\(118\) −714.742 −0.557604
\(119\) 431.489 0.332391
\(120\) 190.170 0.144667
\(121\) 2506.71 1.88333
\(122\) 1733.16 1.28617
\(123\) −490.338 −0.359450
\(124\) −1108.64 −0.802897
\(125\) −125.000 −0.0894427
\(126\) −280.970 −0.198657
\(127\) 550.739 0.384804 0.192402 0.981316i \(-0.438372\pi\)
0.192402 + 0.981316i \(0.438372\pi\)
\(128\) 1458.44 1.00710
\(129\) −99.6692 −0.0680262
\(130\) −556.734 −0.375606
\(131\) −124.824 −0.0832515 −0.0416257 0.999133i \(-0.513254\pi\)
−0.0416257 + 0.999133i \(0.513254\pi\)
\(132\) −817.664 −0.539155
\(133\) 1132.39 0.738273
\(134\) −808.337 −0.521117
\(135\) −135.000 −0.0860663
\(136\) 617.030 0.389043
\(137\) −549.879 −0.342915 −0.171458 0.985192i \(-0.554848\pi\)
−0.171458 + 0.985192i \(0.554848\pi\)
\(138\) 1944.04 1.19918
\(139\) −2243.32 −1.36889 −0.684445 0.729065i \(-0.739955\pi\)
−0.684445 + 0.729065i \(0.739955\pi\)
\(140\) 195.030 0.117736
\(141\) 1586.83 0.947770
\(142\) 74.6745 0.0441306
\(143\) −1958.88 −1.14553
\(144\) −718.563 −0.415835
\(145\) 145.000 0.0830455
\(146\) −4033.61 −2.28646
\(147\) −793.198 −0.445047
\(148\) 869.984 0.483191
\(149\) −614.305 −0.337757 −0.168879 0.985637i \(-0.554015\pi\)
−0.168879 + 0.985637i \(0.554015\pi\)
\(150\) 264.098 0.143757
\(151\) −1121.72 −0.604531 −0.302266 0.953224i \(-0.597743\pi\)
−0.302266 + 0.953224i \(0.597743\pi\)
\(152\) 1619.32 0.864104
\(153\) −438.025 −0.231452
\(154\) 1933.99 1.01198
\(155\) 1259.92 0.652901
\(156\) 417.361 0.214203
\(157\) 3238.34 1.64616 0.823082 0.567923i \(-0.192253\pi\)
0.823082 + 0.567923i \(0.192253\pi\)
\(158\) 336.746 0.169557
\(159\) −720.767 −0.359500
\(160\) 898.594 0.444001
\(161\) −1631.52 −0.798644
\(162\) 285.226 0.138330
\(163\) −2973.43 −1.42881 −0.714407 0.699730i \(-0.753303\pi\)
−0.714407 + 0.699730i \(0.753303\pi\)
\(164\) −719.105 −0.342394
\(165\) 929.238 0.438431
\(166\) 4366.33 2.04152
\(167\) 4133.13 1.91515 0.957577 0.288176i \(-0.0930489\pi\)
0.957577 + 0.288176i \(0.0930489\pi\)
\(168\) 337.198 0.154853
\(169\) −1197.12 −0.544890
\(170\) 856.901 0.386596
\(171\) −1149.54 −0.514079
\(172\) −146.170 −0.0647984
\(173\) 347.755 0.152829 0.0764143 0.997076i \(-0.475653\pi\)
0.0764143 + 0.997076i \(0.475653\pi\)
\(174\) −306.354 −0.133475
\(175\) −221.643 −0.0957406
\(176\) 4946.04 2.11831
\(177\) −608.928 −0.258587
\(178\) 411.513 0.173282
\(179\) 789.082 0.329490 0.164745 0.986336i \(-0.447320\pi\)
0.164745 + 0.986336i \(0.447320\pi\)
\(180\) −197.984 −0.0819825
\(181\) −4547.86 −1.86762 −0.933812 0.357763i \(-0.883539\pi\)
−0.933812 + 0.357763i \(0.883539\pi\)
\(182\) −987.168 −0.402054
\(183\) 1476.58 0.596458
\(184\) −2333.08 −0.934764
\(185\) −988.699 −0.392922
\(186\) −2661.95 −1.04938
\(187\) 3015.03 1.17904
\(188\) 2327.17 0.902799
\(189\) −239.374 −0.0921265
\(190\) 2248.83 0.858669
\(191\) −1121.45 −0.424843 −0.212421 0.977178i \(-0.568135\pi\)
−0.212421 + 0.977178i \(0.568135\pi\)
\(192\) 17.6287 0.00662627
\(193\) −3950.05 −1.47322 −0.736608 0.676320i \(-0.763574\pi\)
−0.736608 + 0.676320i \(0.763574\pi\)
\(194\) −970.902 −0.359313
\(195\) −474.312 −0.174186
\(196\) −1163.26 −0.423930
\(197\) −436.434 −0.157841 −0.0789205 0.996881i \(-0.525147\pi\)
−0.0789205 + 0.996881i \(0.525147\pi\)
\(198\) −1963.28 −0.704669
\(199\) 775.787 0.276352 0.138176 0.990408i \(-0.455876\pi\)
0.138176 + 0.990408i \(0.455876\pi\)
\(200\) −316.949 −0.112059
\(201\) −688.667 −0.241666
\(202\) −6723.57 −2.34192
\(203\) 257.105 0.0888929
\(204\) −642.384 −0.220470
\(205\) 817.231 0.278429
\(206\) 5288.91 1.78881
\(207\) 1656.23 0.556116
\(208\) −2524.61 −0.841589
\(209\) 7912.57 2.61877
\(210\) 468.284 0.153879
\(211\) 2474.44 0.807335 0.403667 0.914906i \(-0.367735\pi\)
0.403667 + 0.914906i \(0.367735\pi\)
\(212\) −1057.04 −0.342442
\(213\) 63.6193 0.0204654
\(214\) 5051.71 1.61368
\(215\) 166.115 0.0526929
\(216\) −342.305 −0.107828
\(217\) 2234.02 0.698873
\(218\) −1225.24 −0.380660
\(219\) −3436.45 −1.06034
\(220\) 1362.77 0.417628
\(221\) −1538.97 −0.468426
\(222\) 2088.91 0.631525
\(223\) −1035.62 −0.310987 −0.155494 0.987837i \(-0.549697\pi\)
−0.155494 + 0.987837i \(0.549697\pi\)
\(224\) 1593.33 0.475264
\(225\) 225.000 0.0666667
\(226\) −6383.01 −1.87872
\(227\) −1068.43 −0.312398 −0.156199 0.987726i \(-0.549924\pi\)
−0.156199 + 0.987726i \(0.549924\pi\)
\(228\) −1685.85 −0.489686
\(229\) −638.809 −0.184339 −0.0921696 0.995743i \(-0.529380\pi\)
−0.0921696 + 0.995743i \(0.529380\pi\)
\(230\) −3240.06 −0.928884
\(231\) 1647.67 0.469302
\(232\) 367.661 0.104044
\(233\) 4199.81 1.18085 0.590427 0.807091i \(-0.298959\pi\)
0.590427 + 0.807091i \(0.298959\pi\)
\(234\) 1002.12 0.279960
\(235\) −2644.72 −0.734139
\(236\) −893.022 −0.246317
\(237\) 286.892 0.0786314
\(238\) 1519.41 0.413817
\(239\) 1481.20 0.400882 0.200441 0.979706i \(-0.435763\pi\)
0.200441 + 0.979706i \(0.435763\pi\)
\(240\) 1197.60 0.322104
\(241\) 7144.57 1.90964 0.954818 0.297191i \(-0.0960498\pi\)
0.954818 + 0.297191i \(0.0960498\pi\)
\(242\) 8826.90 2.34469
\(243\) 243.000 0.0641500
\(244\) 2165.47 0.568156
\(245\) 1322.00 0.344732
\(246\) −1726.64 −0.447505
\(247\) −4038.82 −1.04042
\(248\) 3194.66 0.817988
\(249\) 3719.92 0.946748
\(250\) −440.164 −0.111354
\(251\) −5209.72 −1.31010 −0.655049 0.755587i \(-0.727352\pi\)
−0.655049 + 0.755587i \(0.727352\pi\)
\(252\) −351.054 −0.0877551
\(253\) −11400.3 −2.83292
\(254\) 1939.32 0.479071
\(255\) 730.041 0.179282
\(256\) 5088.62 1.24234
\(257\) 3431.65 0.832919 0.416460 0.909154i \(-0.363271\pi\)
0.416460 + 0.909154i \(0.363271\pi\)
\(258\) −350.966 −0.0846907
\(259\) −1753.10 −0.420589
\(260\) −695.602 −0.165921
\(261\) −261.000 −0.0618984
\(262\) −439.545 −0.103646
\(263\) −1738.29 −0.407558 −0.203779 0.979017i \(-0.565322\pi\)
−0.203779 + 0.979017i \(0.565322\pi\)
\(264\) 2356.17 0.549290
\(265\) 1201.28 0.278468
\(266\) 3987.49 0.919130
\(267\) 350.590 0.0803587
\(268\) −1009.96 −0.230199
\(269\) 2829.31 0.641287 0.320643 0.947200i \(-0.396101\pi\)
0.320643 + 0.947200i \(0.396101\pi\)
\(270\) −475.377 −0.107150
\(271\) −1399.29 −0.313657 −0.156828 0.987626i \(-0.550127\pi\)
−0.156828 + 0.987626i \(0.550127\pi\)
\(272\) 3885.78 0.866213
\(273\) −841.022 −0.186451
\(274\) −1936.30 −0.426920
\(275\) −1548.73 −0.339607
\(276\) 2428.94 0.529729
\(277\) −3526.40 −0.764912 −0.382456 0.923974i \(-0.624922\pi\)
−0.382456 + 0.923974i \(0.624922\pi\)
\(278\) −7899.42 −1.70423
\(279\) −2267.86 −0.486643
\(280\) −561.996 −0.119949
\(281\) −857.124 −0.181963 −0.0909817 0.995853i \(-0.529000\pi\)
−0.0909817 + 0.995853i \(0.529000\pi\)
\(282\) 5587.74 1.17995
\(283\) −7197.47 −1.51182 −0.755910 0.654676i \(-0.772805\pi\)
−0.755910 + 0.654676i \(0.772805\pi\)
\(284\) 93.3008 0.0194943
\(285\) 1915.90 0.398204
\(286\) −6897.85 −1.42615
\(287\) 1449.07 0.298034
\(288\) −1617.47 −0.330938
\(289\) −2544.29 −0.517869
\(290\) 510.590 0.103389
\(291\) −827.165 −0.166630
\(292\) −5039.72 −1.01003
\(293\) 2936.05 0.585412 0.292706 0.956202i \(-0.405444\pi\)
0.292706 + 0.956202i \(0.405444\pi\)
\(294\) −2793.10 −0.554071
\(295\) 1014.88 0.200300
\(296\) −2506.94 −0.492274
\(297\) −1672.63 −0.326787
\(298\) −2163.16 −0.420498
\(299\) 5819.04 1.12550
\(300\) 329.973 0.0635034
\(301\) 294.546 0.0564031
\(302\) −3949.93 −0.752625
\(303\) −5728.18 −1.08606
\(304\) 10197.7 1.92395
\(305\) −2460.96 −0.462014
\(306\) −1542.42 −0.288152
\(307\) −3828.27 −0.711698 −0.355849 0.934544i \(-0.615808\pi\)
−0.355849 + 0.934544i \(0.615808\pi\)
\(308\) 2416.39 0.447034
\(309\) 4505.91 0.829555
\(310\) 4436.59 0.812843
\(311\) −8035.81 −1.46517 −0.732587 0.680673i \(-0.761687\pi\)
−0.732587 + 0.680673i \(0.761687\pi\)
\(312\) −1202.66 −0.218229
\(313\) −1288.78 −0.232736 −0.116368 0.993206i \(-0.537125\pi\)
−0.116368 + 0.993206i \(0.537125\pi\)
\(314\) 11403.2 2.04943
\(315\) 398.957 0.0713608
\(316\) 420.741 0.0749004
\(317\) 8166.90 1.44700 0.723499 0.690325i \(-0.242532\pi\)
0.723499 + 0.690325i \(0.242532\pi\)
\(318\) −2538.05 −0.447568
\(319\) 1796.53 0.315317
\(320\) −29.3812 −0.00513269
\(321\) 4303.83 0.748338
\(322\) −5745.09 −0.994289
\(323\) 6216.38 1.07086
\(324\) 356.371 0.0611062
\(325\) 790.520 0.134924
\(326\) −10470.4 −1.77883
\(327\) −1043.85 −0.176530
\(328\) 2072.17 0.348830
\(329\) −4689.47 −0.785832
\(330\) 3272.14 0.545834
\(331\) −5018.85 −0.833417 −0.416708 0.909040i \(-0.636816\pi\)
−0.416708 + 0.909040i \(0.636816\pi\)
\(332\) 5455.44 0.901825
\(333\) 1779.66 0.292867
\(334\) 14554.0 2.38431
\(335\) 1147.78 0.187194
\(336\) 2123.52 0.344785
\(337\) −3702.30 −0.598448 −0.299224 0.954183i \(-0.596728\pi\)
−0.299224 + 0.954183i \(0.596728\pi\)
\(338\) −4215.45 −0.678373
\(339\) −5438.03 −0.871249
\(340\) 1070.64 0.170775
\(341\) 15610.3 2.47901
\(342\) −4047.89 −0.640014
\(343\) 5385.02 0.847708
\(344\) 421.201 0.0660164
\(345\) −2760.39 −0.430766
\(346\) 1224.56 0.190267
\(347\) 1084.12 0.167719 0.0838594 0.996478i \(-0.473275\pi\)
0.0838594 + 0.996478i \(0.473275\pi\)
\(348\) −382.769 −0.0589614
\(349\) −3145.52 −0.482453 −0.241226 0.970469i \(-0.577550\pi\)
−0.241226 + 0.970469i \(0.577550\pi\)
\(350\) −780.473 −0.119194
\(351\) 853.762 0.129830
\(352\) 11133.4 1.68584
\(353\) −7477.34 −1.12742 −0.563709 0.825974i \(-0.690626\pi\)
−0.563709 + 0.825974i \(0.690626\pi\)
\(354\) −2144.23 −0.321933
\(355\) −106.032 −0.0158524
\(356\) 514.157 0.0765458
\(357\) 1294.47 0.191906
\(358\) 2778.60 0.410206
\(359\) 3987.75 0.586255 0.293128 0.956073i \(-0.405304\pi\)
0.293128 + 0.956073i \(0.405304\pi\)
\(360\) 570.509 0.0835235
\(361\) 9455.09 1.37849
\(362\) −16014.5 −2.32514
\(363\) 7520.12 1.08734
\(364\) −1233.40 −0.177604
\(365\) 5727.42 0.821334
\(366\) 5199.49 0.742573
\(367\) 6261.36 0.890573 0.445286 0.895388i \(-0.353102\pi\)
0.445286 + 0.895388i \(0.353102\pi\)
\(368\) −14692.7 −2.08127
\(369\) −1471.02 −0.207528
\(370\) −3481.52 −0.489177
\(371\) 2130.04 0.298075
\(372\) −3325.93 −0.463553
\(373\) −9332.46 −1.29549 −0.647743 0.761859i \(-0.724287\pi\)
−0.647743 + 0.761859i \(0.724287\pi\)
\(374\) 10616.9 1.46788
\(375\) −375.000 −0.0516398
\(376\) −6705.95 −0.919769
\(377\) −917.004 −0.125273
\(378\) −842.911 −0.114695
\(379\) −4570.38 −0.619432 −0.309716 0.950829i \(-0.600234\pi\)
−0.309716 + 0.950829i \(0.600234\pi\)
\(380\) 2809.76 0.379309
\(381\) 1652.22 0.222167
\(382\) −3948.96 −0.528918
\(383\) 2266.02 0.302320 0.151160 0.988509i \(-0.451699\pi\)
0.151160 + 0.988509i \(0.451699\pi\)
\(384\) 4375.33 0.581452
\(385\) −2746.12 −0.363520
\(386\) −13909.4 −1.83411
\(387\) −299.008 −0.0392750
\(388\) −1213.08 −0.158723
\(389\) 3874.40 0.504987 0.252494 0.967599i \(-0.418749\pi\)
0.252494 + 0.967599i \(0.418749\pi\)
\(390\) −1670.20 −0.216856
\(391\) −8956.43 −1.15843
\(392\) 3352.05 0.431898
\(393\) −374.473 −0.0480653
\(394\) −1536.82 −0.196508
\(395\) −478.154 −0.0609076
\(396\) −2452.99 −0.311281
\(397\) −10370.5 −1.31104 −0.655519 0.755179i \(-0.727550\pi\)
−0.655519 + 0.755179i \(0.727550\pi\)
\(398\) 2731.79 0.344051
\(399\) 3397.16 0.426242
\(400\) −1996.01 −0.249501
\(401\) −10537.9 −1.31231 −0.656155 0.754626i \(-0.727818\pi\)
−0.656155 + 0.754626i \(0.727818\pi\)
\(402\) −2425.01 −0.300867
\(403\) −7967.97 −0.984895
\(404\) −8400.65 −1.03452
\(405\) −405.000 −0.0496904
\(406\) 905.349 0.110669
\(407\) −12249.8 −1.49189
\(408\) 1851.09 0.224614
\(409\) −4052.17 −0.489894 −0.244947 0.969536i \(-0.578771\pi\)
−0.244947 + 0.969536i \(0.578771\pi\)
\(410\) 2877.73 0.346636
\(411\) −1649.64 −0.197982
\(412\) 6608.14 0.790193
\(413\) 1799.52 0.214404
\(414\) 5832.11 0.692349
\(415\) −6199.86 −0.733348
\(416\) −5682.85 −0.669771
\(417\) −6729.95 −0.790329
\(418\) 27862.6 3.26030
\(419\) −12386.0 −1.44414 −0.722071 0.691819i \(-0.756810\pi\)
−0.722071 + 0.691819i \(0.756810\pi\)
\(420\) 585.089 0.0679748
\(421\) −16516.0 −1.91198 −0.955989 0.293402i \(-0.905213\pi\)
−0.955989 + 0.293402i \(0.905213\pi\)
\(422\) 8713.29 1.00511
\(423\) 4760.50 0.547195
\(424\) 3045.96 0.348879
\(425\) −1216.74 −0.138871
\(426\) 224.024 0.0254788
\(427\) −4363.63 −0.494546
\(428\) 6311.78 0.712830
\(429\) −5876.65 −0.661370
\(430\) 584.944 0.0656012
\(431\) 11987.2 1.33969 0.669843 0.742503i \(-0.266361\pi\)
0.669843 + 0.742503i \(0.266361\pi\)
\(432\) −2155.69 −0.240082
\(433\) −14217.4 −1.57793 −0.788965 0.614439i \(-0.789383\pi\)
−0.788965 + 0.614439i \(0.789383\pi\)
\(434\) 7866.70 0.870078
\(435\) 435.000 0.0479463
\(436\) −1530.86 −0.168153
\(437\) −23505.0 −2.57299
\(438\) −12100.8 −1.32009
\(439\) 685.738 0.0745524 0.0372762 0.999305i \(-0.488132\pi\)
0.0372762 + 0.999305i \(0.488132\pi\)
\(440\) −3926.96 −0.425478
\(441\) −2379.59 −0.256948
\(442\) −5419.18 −0.583177
\(443\) −13828.1 −1.48305 −0.741527 0.670923i \(-0.765898\pi\)
−0.741527 + 0.670923i \(0.765898\pi\)
\(444\) 2609.95 0.278971
\(445\) −584.317 −0.0622456
\(446\) −3646.74 −0.387170
\(447\) −1842.92 −0.195004
\(448\) −52.0970 −0.00549409
\(449\) −4346.88 −0.456887 −0.228443 0.973557i \(-0.573364\pi\)
−0.228443 + 0.973557i \(0.573364\pi\)
\(450\) 792.295 0.0829981
\(451\) 10125.4 1.05717
\(452\) −7975.14 −0.829909
\(453\) −3365.16 −0.349026
\(454\) −3762.29 −0.388927
\(455\) 1401.70 0.144424
\(456\) 4857.95 0.498891
\(457\) 2375.45 0.243149 0.121574 0.992582i \(-0.461206\pi\)
0.121574 + 0.992582i \(0.461206\pi\)
\(458\) −2249.45 −0.229497
\(459\) −1314.07 −0.133629
\(460\) −4048.24 −0.410326
\(461\) −5656.94 −0.571519 −0.285759 0.958301i \(-0.592246\pi\)
−0.285759 + 0.958301i \(0.592246\pi\)
\(462\) 5801.96 0.584268
\(463\) −11017.3 −1.10587 −0.552935 0.833225i \(-0.686492\pi\)
−0.552935 + 0.833225i \(0.686492\pi\)
\(464\) 2315.37 0.231656
\(465\) 3779.77 0.376952
\(466\) 14788.9 1.47013
\(467\) −4441.89 −0.440142 −0.220071 0.975484i \(-0.570629\pi\)
−0.220071 + 0.975484i \(0.570629\pi\)
\(468\) 1252.08 0.123670
\(469\) 2035.17 0.200374
\(470\) −9312.90 −0.913983
\(471\) 9715.02 0.950413
\(472\) 2573.32 0.250947
\(473\) 2058.14 0.200071
\(474\) 1010.24 0.0978939
\(475\) −3193.17 −0.308447
\(476\) 1898.40 0.182800
\(477\) −2162.30 −0.207558
\(478\) 5215.76 0.499087
\(479\) −6919.43 −0.660035 −0.330017 0.943975i \(-0.607055\pi\)
−0.330017 + 0.943975i \(0.607055\pi\)
\(480\) 2695.78 0.256344
\(481\) 6252.69 0.592720
\(482\) 25158.3 2.37744
\(483\) −4894.56 −0.461097
\(484\) 11028.6 1.03575
\(485\) 1378.61 0.129071
\(486\) 855.679 0.0798650
\(487\) 4439.83 0.413116 0.206558 0.978434i \(-0.433774\pi\)
0.206558 + 0.978434i \(0.433774\pi\)
\(488\) −6240.01 −0.578836
\(489\) −8920.28 −0.824926
\(490\) 4655.16 0.429181
\(491\) 12089.1 1.11115 0.555575 0.831466i \(-0.312498\pi\)
0.555575 + 0.831466i \(0.312498\pi\)
\(492\) −2157.31 −0.197681
\(493\) 1411.41 0.128939
\(494\) −14221.9 −1.29529
\(495\) 2787.72 0.253128
\(496\) 20118.6 1.82127
\(497\) −188.010 −0.0169686
\(498\) 13099.0 1.17867
\(499\) 7312.25 0.655994 0.327997 0.944679i \(-0.393626\pi\)
0.327997 + 0.944679i \(0.393626\pi\)
\(500\) −549.955 −0.0491895
\(501\) 12399.4 1.10572
\(502\) −18345.0 −1.63103
\(503\) 7487.34 0.663706 0.331853 0.943331i \(-0.392326\pi\)
0.331853 + 0.943331i \(0.392326\pi\)
\(504\) 1011.59 0.0894046
\(505\) 9546.96 0.841256
\(506\) −40143.9 −3.52690
\(507\) −3591.37 −0.314593
\(508\) 2423.05 0.211625
\(509\) −16901.9 −1.47184 −0.735919 0.677070i \(-0.763250\pi\)
−0.735919 + 0.677070i \(0.763250\pi\)
\(510\) 2570.70 0.223201
\(511\) 10155.5 0.879166
\(512\) 6251.09 0.539574
\(513\) −3448.62 −0.296804
\(514\) 12083.9 1.03696
\(515\) −7509.85 −0.642570
\(516\) −438.509 −0.0374114
\(517\) −32767.7 −2.78747
\(518\) −6173.22 −0.523621
\(519\) 1043.27 0.0882356
\(520\) 2004.44 0.169039
\(521\) −8351.65 −0.702289 −0.351144 0.936321i \(-0.614207\pi\)
−0.351144 + 0.936321i \(0.614207\pi\)
\(522\) −919.063 −0.0770618
\(523\) 5420.89 0.453230 0.226615 0.973984i \(-0.427234\pi\)
0.226615 + 0.973984i \(0.427234\pi\)
\(524\) −549.182 −0.0457846
\(525\) −664.928 −0.0552759
\(526\) −6121.07 −0.507398
\(527\) 12264.0 1.01371
\(528\) 14838.1 1.22301
\(529\) 21698.5 1.78339
\(530\) 4230.08 0.346685
\(531\) −1826.78 −0.149295
\(532\) 4982.10 0.406018
\(533\) −5168.30 −0.420007
\(534\) 1234.54 0.100044
\(535\) −7173.05 −0.579660
\(536\) 2910.30 0.234526
\(537\) 2367.25 0.190231
\(538\) 9962.89 0.798384
\(539\) 16379.3 1.30892
\(540\) −593.952 −0.0473326
\(541\) 14428.9 1.14667 0.573333 0.819323i \(-0.305650\pi\)
0.573333 + 0.819323i \(0.305650\pi\)
\(542\) −4927.34 −0.390494
\(543\) −13643.6 −1.07827
\(544\) 8746.81 0.689368
\(545\) 1739.75 0.136739
\(546\) −2961.50 −0.232126
\(547\) 4990.35 0.390077 0.195038 0.980796i \(-0.437517\pi\)
0.195038 + 0.980796i \(0.437517\pi\)
\(548\) −2419.27 −0.188588
\(549\) 4429.73 0.344365
\(550\) −5453.57 −0.422801
\(551\) 3704.07 0.286386
\(552\) −6999.23 −0.539686
\(553\) −847.834 −0.0651963
\(554\) −12417.5 −0.952294
\(555\) −2966.10 −0.226854
\(556\) −9869.80 −0.752828
\(557\) 23481.4 1.78625 0.893123 0.449812i \(-0.148509\pi\)
0.893123 + 0.449812i \(0.148509\pi\)
\(558\) −7985.86 −0.605857
\(559\) −1050.54 −0.0794868
\(560\) −3539.20 −0.267069
\(561\) 9045.10 0.680721
\(562\) −3018.20 −0.226539
\(563\) 8869.38 0.663943 0.331972 0.943289i \(-0.392286\pi\)
0.331972 + 0.943289i \(0.392286\pi\)
\(564\) 6981.51 0.521231
\(565\) 9063.39 0.674867
\(566\) −25344.5 −1.88217
\(567\) −718.122 −0.0531892
\(568\) −268.855 −0.0198607
\(569\) 25722.7 1.89517 0.947585 0.319503i \(-0.103516\pi\)
0.947585 + 0.319503i \(0.103516\pi\)
\(570\) 6746.48 0.495753
\(571\) 26056.8 1.90971 0.954853 0.297078i \(-0.0960122\pi\)
0.954853 + 0.297078i \(0.0960122\pi\)
\(572\) −8618.40 −0.629988
\(573\) −3364.34 −0.245283
\(574\) 5102.61 0.371043
\(575\) 4600.64 0.333670
\(576\) 52.8862 0.00382568
\(577\) −25737.2 −1.85694 −0.928471 0.371406i \(-0.878876\pi\)
−0.928471 + 0.371406i \(0.878876\pi\)
\(578\) −8959.23 −0.644732
\(579\) −11850.1 −0.850562
\(580\) 637.948 0.0456713
\(581\) −10993.2 −0.784985
\(582\) −2912.71 −0.207449
\(583\) 14883.7 1.05732
\(584\) 14522.4 1.02901
\(585\) −1422.94 −0.100566
\(586\) 10338.7 0.728822
\(587\) −6862.44 −0.482527 −0.241263 0.970460i \(-0.577562\pi\)
−0.241263 + 0.970460i \(0.577562\pi\)
\(588\) −3489.79 −0.244756
\(589\) 32185.2 2.25156
\(590\) 3573.71 0.249368
\(591\) −1309.30 −0.0911295
\(592\) −15787.6 −1.09606
\(593\) 4016.32 0.278129 0.139065 0.990283i \(-0.455590\pi\)
0.139065 + 0.990283i \(0.455590\pi\)
\(594\) −5889.85 −0.406841
\(595\) −2157.44 −0.148650
\(596\) −2702.72 −0.185751
\(597\) 2327.36 0.159552
\(598\) 20490.7 1.40121
\(599\) −1729.64 −0.117982 −0.0589911 0.998259i \(-0.518788\pi\)
−0.0589911 + 0.998259i \(0.518788\pi\)
\(600\) −950.848 −0.0646970
\(601\) 2597.41 0.176291 0.0881453 0.996108i \(-0.471906\pi\)
0.0881453 + 0.996108i \(0.471906\pi\)
\(602\) 1037.19 0.0702203
\(603\) −2066.00 −0.139526
\(604\) −4935.17 −0.332465
\(605\) −12533.5 −0.842249
\(606\) −20170.7 −1.35211
\(607\) −13844.6 −0.925755 −0.462877 0.886422i \(-0.653183\pi\)
−0.462877 + 0.886422i \(0.653183\pi\)
\(608\) 22954.9 1.53116
\(609\) 771.316 0.0513224
\(610\) −8665.82 −0.575195
\(611\) 16725.7 1.10744
\(612\) −1927.15 −0.127288
\(613\) 1127.16 0.0742667 0.0371334 0.999310i \(-0.488177\pi\)
0.0371334 + 0.999310i \(0.488177\pi\)
\(614\) −13480.6 −0.886044
\(615\) 2451.69 0.160751
\(616\) −6963.05 −0.455437
\(617\) 29575.8 1.92978 0.964892 0.262645i \(-0.0845949\pi\)
0.964892 + 0.262645i \(0.0845949\pi\)
\(618\) 15866.7 1.03277
\(619\) 12535.0 0.813935 0.406967 0.913443i \(-0.366586\pi\)
0.406967 + 0.913443i \(0.366586\pi\)
\(620\) 5543.22 0.359066
\(621\) 4968.70 0.321074
\(622\) −28296.6 −1.82410
\(623\) −1036.08 −0.0666285
\(624\) −7573.84 −0.485892
\(625\) 625.000 0.0400000
\(626\) −4538.20 −0.289749
\(627\) 23737.7 1.51195
\(628\) 14247.5 0.905316
\(629\) −9623.88 −0.610062
\(630\) 1404.85 0.0888423
\(631\) 15162.1 0.956569 0.478284 0.878205i \(-0.341259\pi\)
0.478284 + 0.878205i \(0.341259\pi\)
\(632\) −1212.40 −0.0763083
\(633\) 7423.33 0.466115
\(634\) 28758.2 1.80147
\(635\) −2753.69 −0.172090
\(636\) −3171.12 −0.197709
\(637\) −8360.52 −0.520025
\(638\) 6326.14 0.392561
\(639\) 190.858 0.0118157
\(640\) −7292.21 −0.450391
\(641\) −10138.5 −0.624722 −0.312361 0.949964i \(-0.601120\pi\)
−0.312361 + 0.949964i \(0.601120\pi\)
\(642\) 15155.1 0.931660
\(643\) 29580.6 1.81423 0.907113 0.420888i \(-0.138282\pi\)
0.907113 + 0.420888i \(0.138282\pi\)
\(644\) −7178.10 −0.439219
\(645\) 498.346 0.0304223
\(646\) 21889.8 1.33319
\(647\) 30140.7 1.83146 0.915728 0.401798i \(-0.131615\pi\)
0.915728 + 0.401798i \(0.131615\pi\)
\(648\) −1026.92 −0.0622548
\(649\) 12574.2 0.760525
\(650\) 2783.67 0.167976
\(651\) 6702.07 0.403495
\(652\) −13082.0 −0.785784
\(653\) −10094.0 −0.604911 −0.302456 0.953163i \(-0.597806\pi\)
−0.302456 + 0.953163i \(0.597806\pi\)
\(654\) −3675.73 −0.219774
\(655\) 624.121 0.0372312
\(656\) 13049.6 0.776678
\(657\) −10309.4 −0.612186
\(658\) −16513.1 −0.978339
\(659\) 16019.7 0.946947 0.473473 0.880808i \(-0.343000\pi\)
0.473473 + 0.880808i \(0.343000\pi\)
\(660\) 4088.32 0.241118
\(661\) −26006.5 −1.53031 −0.765157 0.643844i \(-0.777338\pi\)
−0.765157 + 0.643844i \(0.777338\pi\)
\(662\) −17672.9 −1.03758
\(663\) −4616.90 −0.270446
\(664\) −15720.3 −0.918777
\(665\) −5661.93 −0.330166
\(666\) 6266.73 0.364611
\(667\) −5336.75 −0.309805
\(668\) 18184.3 1.05325
\(669\) −3106.85 −0.179549
\(670\) 4041.69 0.233051
\(671\) −30490.9 −1.75423
\(672\) 4780.00 0.274394
\(673\) 30662.4 1.75624 0.878119 0.478443i \(-0.158799\pi\)
0.878119 + 0.478443i \(0.158799\pi\)
\(674\) −13036.9 −0.745051
\(675\) 675.000 0.0384900
\(676\) −5266.92 −0.299665
\(677\) −4128.37 −0.234366 −0.117183 0.993110i \(-0.537386\pi\)
−0.117183 + 0.993110i \(0.537386\pi\)
\(678\) −19149.0 −1.08468
\(679\) 2444.47 0.138159
\(680\) −3085.15 −0.173985
\(681\) −3205.30 −0.180363
\(682\) 54968.7 3.08630
\(683\) −19130.6 −1.07176 −0.535881 0.844294i \(-0.680020\pi\)
−0.535881 + 0.844294i \(0.680020\pi\)
\(684\) −5057.56 −0.282720
\(685\) 2749.40 0.153356
\(686\) 18962.4 1.05537
\(687\) −1916.43 −0.106428
\(688\) 2652.54 0.146987
\(689\) −7597.08 −0.420066
\(690\) −9720.19 −0.536292
\(691\) 27493.6 1.51361 0.756807 0.653638i \(-0.226758\pi\)
0.756807 + 0.653638i \(0.226758\pi\)
\(692\) 1530.00 0.0840489
\(693\) 4943.01 0.270952
\(694\) 3817.51 0.208805
\(695\) 11216.6 0.612186
\(696\) 1102.98 0.0600697
\(697\) 7954.83 0.432296
\(698\) −11076.4 −0.600640
\(699\) 12599.4 0.681766
\(700\) −975.149 −0.0526531
\(701\) 13029.3 0.702010 0.351005 0.936374i \(-0.385840\pi\)
0.351005 + 0.936374i \(0.385840\pi\)
\(702\) 3006.36 0.161635
\(703\) −25256.6 −1.35501
\(704\) −364.029 −0.0194884
\(705\) −7934.17 −0.423856
\(706\) −26330.0 −1.40360
\(707\) 16928.1 0.900491
\(708\) −2679.07 −0.142211
\(709\) −33140.8 −1.75547 −0.877735 0.479146i \(-0.840946\pi\)
−0.877735 + 0.479146i \(0.840946\pi\)
\(710\) −373.373 −0.0197358
\(711\) 860.676 0.0453979
\(712\) −1481.59 −0.0779846
\(713\) −46371.7 −2.43567
\(714\) 4558.22 0.238918
\(715\) 9794.42 0.512295
\(716\) 3471.68 0.181205
\(717\) 4443.59 0.231449
\(718\) 14042.1 0.729871
\(719\) 23672.8 1.22788 0.613940 0.789353i \(-0.289584\pi\)
0.613940 + 0.789353i \(0.289584\pi\)
\(720\) 3592.81 0.185967
\(721\) −13316.0 −0.687815
\(722\) 33294.3 1.71619
\(723\) 21433.7 1.10253
\(724\) −20009.0 −1.02711
\(725\) −725.000 −0.0371391
\(726\) 26480.7 1.35371
\(727\) 16424.5 0.837895 0.418947 0.908010i \(-0.362399\pi\)
0.418947 + 0.908010i \(0.362399\pi\)
\(728\) 3554.16 0.180942
\(729\) 729.000 0.0370370
\(730\) 20168.0 1.02254
\(731\) 1616.95 0.0818125
\(732\) 6496.41 0.328025
\(733\) 19399.9 0.977559 0.488780 0.872407i \(-0.337442\pi\)
0.488780 + 0.872407i \(0.337442\pi\)
\(734\) 22048.2 1.10874
\(735\) 3965.99 0.199031
\(736\) −33072.9 −1.65636
\(737\) 14220.8 0.710759
\(738\) −5179.91 −0.258367
\(739\) −5065.65 −0.252156 −0.126078 0.992020i \(-0.540239\pi\)
−0.126078 + 0.992020i \(0.540239\pi\)
\(740\) −4349.92 −0.216090
\(741\) −12116.5 −0.600687
\(742\) 7500.53 0.371096
\(743\) −15186.2 −0.749833 −0.374917 0.927059i \(-0.622329\pi\)
−0.374917 + 0.927059i \(0.622329\pi\)
\(744\) 9583.98 0.472266
\(745\) 3071.53 0.151050
\(746\) −32862.5 −1.61284
\(747\) 11159.8 0.546605
\(748\) 13265.1 0.648421
\(749\) −12718.8 −0.620476
\(750\) −1320.49 −0.0642901
\(751\) −25919.9 −1.25943 −0.629713 0.776828i \(-0.716828\pi\)
−0.629713 + 0.776828i \(0.716828\pi\)
\(752\) −42231.1 −2.04789
\(753\) −15629.2 −0.756385
\(754\) −3229.06 −0.155962
\(755\) 5608.60 0.270355
\(756\) −1053.16 −0.0506655
\(757\) 25691.7 1.23353 0.616765 0.787148i \(-0.288443\pi\)
0.616765 + 0.787148i \(0.288443\pi\)
\(758\) −16093.7 −0.771175
\(759\) −34200.8 −1.63559
\(760\) −8096.58 −0.386439
\(761\) 3453.84 0.164523 0.0822613 0.996611i \(-0.473786\pi\)
0.0822613 + 0.996611i \(0.473786\pi\)
\(762\) 5817.97 0.276592
\(763\) 3084.83 0.146367
\(764\) −4933.96 −0.233645
\(765\) 2190.12 0.103509
\(766\) 7979.38 0.376379
\(767\) −6418.26 −0.302151
\(768\) 15265.9 0.717265
\(769\) 24995.5 1.17212 0.586060 0.810268i \(-0.300678\pi\)
0.586060 + 0.810268i \(0.300678\pi\)
\(770\) −9669.94 −0.452572
\(771\) 10294.9 0.480886
\(772\) −17378.8 −0.810203
\(773\) 15444.9 0.718648 0.359324 0.933213i \(-0.383007\pi\)
0.359324 + 0.933213i \(0.383007\pi\)
\(774\) −1052.90 −0.0488962
\(775\) −6299.62 −0.291986
\(776\) 3495.59 0.161707
\(777\) −5259.31 −0.242827
\(778\) 13643.0 0.628695
\(779\) 20876.4 0.960174
\(780\) −2086.80 −0.0957943
\(781\) −1313.72 −0.0601904
\(782\) −31538.4 −1.44221
\(783\) −783.000 −0.0357371
\(784\) 21109.7 0.961630
\(785\) −16191.7 −0.736187
\(786\) −1318.64 −0.0598399
\(787\) −30204.3 −1.36807 −0.684033 0.729451i \(-0.739776\pi\)
−0.684033 + 0.729451i \(0.739776\pi\)
\(788\) −1920.16 −0.0868055
\(789\) −5214.88 −0.235304
\(790\) −1683.73 −0.0758283
\(791\) 16070.7 0.722386
\(792\) 7068.52 0.317132
\(793\) 15563.5 0.696944
\(794\) −36517.9 −1.63220
\(795\) 3603.84 0.160773
\(796\) 3413.19 0.151981
\(797\) 44520.9 1.97869 0.989343 0.145606i \(-0.0465131\pi\)
0.989343 + 0.145606i \(0.0465131\pi\)
\(798\) 11962.5 0.530660
\(799\) −25743.4 −1.13985
\(800\) −4492.97 −0.198563
\(801\) 1051.77 0.0463951
\(802\) −37107.1 −1.63379
\(803\) 70961.8 3.11854
\(804\) −3029.89 −0.132905
\(805\) 8157.59 0.357164
\(806\) −28057.7 −1.22617
\(807\) 8487.93 0.370247
\(808\) 24207.2 1.05397
\(809\) −10369.6 −0.450651 −0.225326 0.974284i \(-0.572345\pi\)
−0.225326 + 0.974284i \(0.572345\pi\)
\(810\) −1426.13 −0.0618632
\(811\) 24341.6 1.05394 0.526972 0.849883i \(-0.323327\pi\)
0.526972 + 0.849883i \(0.323327\pi\)
\(812\) 1131.17 0.0488872
\(813\) −4197.88 −0.181090
\(814\) −43135.5 −1.85737
\(815\) 14867.1 0.638985
\(816\) 11657.3 0.500108
\(817\) 4243.47 0.181714
\(818\) −14268.9 −0.609905
\(819\) −2523.07 −0.107647
\(820\) 3595.52 0.153123
\(821\) −17287.1 −0.734864 −0.367432 0.930050i \(-0.619763\pi\)
−0.367432 + 0.930050i \(0.619763\pi\)
\(822\) −5808.89 −0.246482
\(823\) 5724.85 0.242474 0.121237 0.992624i \(-0.461314\pi\)
0.121237 + 0.992624i \(0.461314\pi\)
\(824\) −19042.0 −0.805046
\(825\) −4646.19 −0.196072
\(826\) 6336.69 0.266927
\(827\) 25964.5 1.09175 0.545874 0.837867i \(-0.316198\pi\)
0.545874 + 0.837867i \(0.316198\pi\)
\(828\) 7286.83 0.305839
\(829\) −13876.2 −0.581349 −0.290675 0.956822i \(-0.593880\pi\)
−0.290675 + 0.956822i \(0.593880\pi\)
\(830\) −21831.7 −0.912997
\(831\) −10579.2 −0.441622
\(832\) 185.812 0.00774262
\(833\) 12868.2 0.535240
\(834\) −23698.3 −0.983937
\(835\) −20665.6 −0.856483
\(836\) 34812.5 1.44021
\(837\) −6803.59 −0.280964
\(838\) −43615.0 −1.79792
\(839\) −20190.6 −0.830818 −0.415409 0.909635i \(-0.636362\pi\)
−0.415409 + 0.909635i \(0.636362\pi\)
\(840\) −1685.99 −0.0692525
\(841\) 841.000 0.0344828
\(842\) −58158.2 −2.38036
\(843\) −2571.37 −0.105057
\(844\) 10886.7 0.443998
\(845\) 5985.62 0.243682
\(846\) 16763.2 0.681243
\(847\) −22223.7 −0.901554
\(848\) 19182.1 0.776787
\(849\) −21592.4 −0.872849
\(850\) −4284.51 −0.172891
\(851\) 36389.2 1.46581
\(852\) 279.902 0.0112550
\(853\) −14388.2 −0.577542 −0.288771 0.957398i \(-0.593247\pi\)
−0.288771 + 0.957398i \(0.593247\pi\)
\(854\) −15365.7 −0.615696
\(855\) 5747.70 0.229903
\(856\) −18188.0 −0.726229
\(857\) −12095.7 −0.482125 −0.241063 0.970510i \(-0.577496\pi\)
−0.241063 + 0.970510i \(0.577496\pi\)
\(858\) −20693.5 −0.823387
\(859\) −16863.4 −0.669815 −0.334907 0.942251i \(-0.608705\pi\)
−0.334907 + 0.942251i \(0.608705\pi\)
\(860\) 730.848 0.0289787
\(861\) 4347.20 0.172070
\(862\) 42210.8 1.66787
\(863\) 6575.91 0.259382 0.129691 0.991554i \(-0.458601\pi\)
0.129691 + 0.991554i \(0.458601\pi\)
\(864\) −4852.41 −0.191067
\(865\) −1738.78 −0.0683470
\(866\) −50063.8 −1.96448
\(867\) −7632.86 −0.298992
\(868\) 9828.91 0.384349
\(869\) −5924.25 −0.231262
\(870\) 1531.77 0.0596918
\(871\) −7258.74 −0.282380
\(872\) 4411.31 0.171314
\(873\) −2481.50 −0.0962038
\(874\) −82768.4 −3.20330
\(875\) 1108.21 0.0428165
\(876\) −15119.2 −0.583138
\(877\) −2474.27 −0.0952683 −0.0476341 0.998865i \(-0.515168\pi\)
−0.0476341 + 0.998865i \(0.515168\pi\)
\(878\) 2414.70 0.0928157
\(879\) 8808.15 0.337988
\(880\) −24730.2 −0.947336
\(881\) 39922.4 1.52670 0.763349 0.645987i \(-0.223554\pi\)
0.763349 + 0.645987i \(0.223554\pi\)
\(882\) −8379.29 −0.319893
\(883\) 15872.9 0.604944 0.302472 0.953158i \(-0.402188\pi\)
0.302472 + 0.953158i \(0.402188\pi\)
\(884\) −6770.90 −0.257613
\(885\) 3044.64 0.115643
\(886\) −48693.0 −1.84636
\(887\) −48655.2 −1.84181 −0.920903 0.389792i \(-0.872547\pi\)
−0.920903 + 0.389792i \(0.872547\pi\)
\(888\) −7520.82 −0.284214
\(889\) −4882.69 −0.184207
\(890\) −2057.56 −0.0774940
\(891\) −5017.89 −0.188671
\(892\) −4556.35 −0.171029
\(893\) −67560.3 −2.53171
\(894\) −6489.48 −0.242775
\(895\) −3945.41 −0.147352
\(896\) −12930.1 −0.482104
\(897\) 17457.1 0.649807
\(898\) −15306.7 −0.568811
\(899\) 7307.56 0.271102
\(900\) 989.920 0.0366637
\(901\) 11693.1 0.432357
\(902\) 35654.6 1.31615
\(903\) 883.638 0.0325644
\(904\) 22981.1 0.845509
\(905\) 22739.3 0.835227
\(906\) −11849.8 −0.434528
\(907\) −26851.3 −0.983001 −0.491501 0.870877i \(-0.663551\pi\)
−0.491501 + 0.870877i \(0.663551\pi\)
\(908\) −4700.73 −0.171805
\(909\) −17184.5 −0.627035
\(910\) 4935.84 0.179804
\(911\) 29057.6 1.05677 0.528387 0.849003i \(-0.322797\pi\)
0.528387 + 0.849003i \(0.322797\pi\)
\(912\) 30593.2 1.11079
\(913\) −76815.3 −2.78447
\(914\) 8364.72 0.302714
\(915\) −7382.89 −0.266744
\(916\) −2810.53 −0.101378
\(917\) 1106.65 0.0398527
\(918\) −4627.27 −0.166364
\(919\) 24093.6 0.864825 0.432413 0.901676i \(-0.357662\pi\)
0.432413 + 0.901676i \(0.357662\pi\)
\(920\) 11665.4 0.418039
\(921\) −11484.8 −0.410899
\(922\) −19919.9 −0.711525
\(923\) 670.565 0.0239132
\(924\) 7249.17 0.258095
\(925\) 4943.49 0.175720
\(926\) −38795.4 −1.37678
\(927\) 13517.7 0.478944
\(928\) 5211.84 0.184361
\(929\) −53631.6 −1.89408 −0.947038 0.321123i \(-0.895940\pi\)
−0.947038 + 0.321123i \(0.895940\pi\)
\(930\) 13309.8 0.469295
\(931\) 33770.8 1.18882
\(932\) 18477.7 0.649417
\(933\) −24107.4 −0.845919
\(934\) −15641.3 −0.547964
\(935\) −15075.2 −0.527284
\(936\) −3607.99 −0.125995
\(937\) 26075.5 0.909125 0.454562 0.890715i \(-0.349796\pi\)
0.454562 + 0.890715i \(0.349796\pi\)
\(938\) 7166.48 0.249460
\(939\) −3866.34 −0.134370
\(940\) −11635.8 −0.403744
\(941\) −18872.4 −0.653796 −0.326898 0.945060i \(-0.606003\pi\)
−0.326898 + 0.945060i \(0.606003\pi\)
\(942\) 34209.6 1.18324
\(943\) −30078.3 −1.03869
\(944\) 16205.7 0.558739
\(945\) 1196.87 0.0412002
\(946\) 7247.37 0.249083
\(947\) −9904.80 −0.339876 −0.169938 0.985455i \(-0.554357\pi\)
−0.169938 + 0.985455i \(0.554357\pi\)
\(948\) 1262.22 0.0432438
\(949\) −36221.1 −1.23898
\(950\) −11244.1 −0.384008
\(951\) 24500.7 0.835425
\(952\) −5470.41 −0.186236
\(953\) 11915.9 0.405029 0.202514 0.979279i \(-0.435089\pi\)
0.202514 + 0.979279i \(0.435089\pi\)
\(954\) −7614.14 −0.258403
\(955\) 5607.23 0.189996
\(956\) 6516.74 0.220467
\(957\) 5389.58 0.182049
\(958\) −24365.5 −0.821725
\(959\) 4875.07 0.164155
\(960\) −88.1436 −0.00296336
\(961\) 33705.4 1.13140
\(962\) 22017.7 0.737919
\(963\) 12911.5 0.432053
\(964\) 31433.6 1.05021
\(965\) 19750.2 0.658842
\(966\) −17235.3 −0.574053
\(967\) 38119.9 1.26769 0.633843 0.773462i \(-0.281477\pi\)
0.633843 + 0.773462i \(0.281477\pi\)
\(968\) −31780.0 −1.05521
\(969\) 18649.1 0.618263
\(970\) 4854.51 0.160690
\(971\) −12393.2 −0.409593 −0.204797 0.978805i \(-0.565653\pi\)
−0.204797 + 0.978805i \(0.565653\pi\)
\(972\) 1069.11 0.0352797
\(973\) 19888.6 0.655292
\(974\) 15634.0 0.514318
\(975\) 2371.56 0.0778982
\(976\) −39296.8 −1.28879
\(977\) 36796.8 1.20495 0.602474 0.798138i \(-0.294182\pi\)
0.602474 + 0.798138i \(0.294182\pi\)
\(978\) −31411.1 −1.02701
\(979\) −7239.60 −0.236342
\(980\) 5816.31 0.189587
\(981\) −3131.56 −0.101919
\(982\) 42569.6 1.38335
\(983\) 17819.2 0.578174 0.289087 0.957303i \(-0.406648\pi\)
0.289087 + 0.957303i \(0.406648\pi\)
\(984\) 6216.50 0.201397
\(985\) 2182.17 0.0705886
\(986\) 4970.03 0.160525
\(987\) −14068.4 −0.453700
\(988\) −17769.4 −0.572185
\(989\) −6113.90 −0.196573
\(990\) 9816.42 0.315138
\(991\) −832.856 −0.0266968 −0.0133484 0.999911i \(-0.504249\pi\)
−0.0133484 + 0.999911i \(0.504249\pi\)
\(992\) 45286.4 1.44944
\(993\) −15056.5 −0.481173
\(994\) −662.042 −0.0211255
\(995\) −3878.94 −0.123589
\(996\) 16366.3 0.520669
\(997\) −5156.04 −0.163785 −0.0818923 0.996641i \(-0.526096\pi\)
−0.0818923 + 0.996641i \(0.526096\pi\)
\(998\) 25748.7 0.816694
\(999\) 5338.97 0.169087
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.j.1.6 7
3.2 odd 2 1305.4.a.m.1.2 7
5.4 even 2 2175.4.a.m.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.4.a.j.1.6 7 1.1 even 1 trivial
1305.4.a.m.1.2 7 3.2 odd 2
2175.4.a.m.1.2 7 5.4 even 2