Properties

Label 435.4.a.i.1.3
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 1.3
Root \(2.27711\) 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)
 
\(f(q)\) \(=\) \(q-2.27711 q^{2} -3.00000 q^{3} -2.81476 q^{4} +5.00000 q^{5} +6.83134 q^{6} -26.8439 q^{7} +24.6264 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.27711 q^{2} -3.00000 q^{3} -2.81476 q^{4} +5.00000 q^{5} +6.83134 q^{6} -26.8439 q^{7} +24.6264 q^{8} +9.00000 q^{9} -11.3856 q^{10} -58.9546 q^{11} +8.44428 q^{12} +76.8831 q^{13} +61.1265 q^{14} -15.0000 q^{15} -33.5591 q^{16} -118.899 q^{17} -20.4940 q^{18} -149.359 q^{19} -14.0738 q^{20} +80.5316 q^{21} +134.246 q^{22} -8.10284 q^{23} -73.8793 q^{24} +25.0000 q^{25} -175.072 q^{26} -27.0000 q^{27} +75.5590 q^{28} +29.0000 q^{29} +34.1567 q^{30} +151.923 q^{31} -120.594 q^{32} +176.864 q^{33} +270.747 q^{34} -134.219 q^{35} -25.3328 q^{36} -329.276 q^{37} +340.106 q^{38} -230.649 q^{39} +123.132 q^{40} +126.272 q^{41} -183.379 q^{42} -416.162 q^{43} +165.943 q^{44} +45.0000 q^{45} +18.4511 q^{46} -236.796 q^{47} +100.677 q^{48} +377.593 q^{49} -56.9278 q^{50} +356.698 q^{51} -216.408 q^{52} +470.080 q^{53} +61.4820 q^{54} -294.773 q^{55} -661.068 q^{56} +448.076 q^{57} -66.0363 q^{58} +459.022 q^{59} +42.2214 q^{60} +602.948 q^{61} -345.945 q^{62} -241.595 q^{63} +543.078 q^{64} +384.416 q^{65} -402.739 q^{66} +769.705 q^{67} +334.673 q^{68} +24.3085 q^{69} +305.632 q^{70} +494.182 q^{71} +221.638 q^{72} -908.575 q^{73} +749.799 q^{74} -75.0000 q^{75} +420.409 q^{76} +1582.57 q^{77} +525.215 q^{78} +145.802 q^{79} -167.795 q^{80} +81.0000 q^{81} -287.535 q^{82} +364.521 q^{83} -226.677 q^{84} -594.496 q^{85} +947.648 q^{86} -87.0000 q^{87} -1451.84 q^{88} +1341.18 q^{89} -102.470 q^{90} -2063.84 q^{91} +22.8076 q^{92} -455.768 q^{93} +539.210 q^{94} -746.793 q^{95} +361.781 q^{96} +441.198 q^{97} -859.822 q^{98} -530.591 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27711 −0.805081 −0.402540 0.915402i \(-0.631873\pi\)
−0.402540 + 0.915402i \(0.631873\pi\)
\(3\) −3.00000 −0.577350
\(4\) −2.81476 −0.351845
\(5\) 5.00000 0.447214
\(6\) 6.83134 0.464814
\(7\) −26.8439 −1.44943 −0.724716 0.689047i \(-0.758029\pi\)
−0.724716 + 0.689047i \(0.758029\pi\)
\(8\) 24.6264 1.08834
\(9\) 9.00000 0.333333
\(10\) −11.3856 −0.360043
\(11\) −58.9546 −1.61595 −0.807976 0.589215i \(-0.799437\pi\)
−0.807976 + 0.589215i \(0.799437\pi\)
\(12\) 8.44428 0.203138
\(13\) 76.8831 1.64027 0.820136 0.572168i \(-0.193897\pi\)
0.820136 + 0.572168i \(0.193897\pi\)
\(14\) 61.1265 1.16691
\(15\) −15.0000 −0.258199
\(16\) −33.5591 −0.524360
\(17\) −118.899 −1.69631 −0.848156 0.529747i \(-0.822287\pi\)
−0.848156 + 0.529747i \(0.822287\pi\)
\(18\) −20.4940 −0.268360
\(19\) −149.359 −1.80343 −0.901716 0.432328i \(-0.857692\pi\)
−0.901716 + 0.432328i \(0.857692\pi\)
\(20\) −14.0738 −0.157350
\(21\) 80.5316 0.836830
\(22\) 134.246 1.30097
\(23\) −8.10284 −0.0734591 −0.0367296 0.999325i \(-0.511694\pi\)
−0.0367296 + 0.999325i \(0.511694\pi\)
\(24\) −73.8793 −0.628356
\(25\) 25.0000 0.200000
\(26\) −175.072 −1.32055
\(27\) −27.0000 −0.192450
\(28\) 75.5590 0.509975
\(29\) 29.0000 0.185695
\(30\) 34.1567 0.207871
\(31\) 151.923 0.880198 0.440099 0.897949i \(-0.354943\pi\)
0.440099 + 0.897949i \(0.354943\pi\)
\(32\) −120.594 −0.666192
\(33\) 176.864 0.932971
\(34\) 270.747 1.36567
\(35\) −134.219 −0.648206
\(36\) −25.3328 −0.117282
\(37\) −329.276 −1.46305 −0.731523 0.681817i \(-0.761190\pi\)
−0.731523 + 0.681817i \(0.761190\pi\)
\(38\) 340.106 1.45191
\(39\) −230.649 −0.947012
\(40\) 123.132 0.486722
\(41\) 126.272 0.480983 0.240492 0.970651i \(-0.422691\pi\)
0.240492 + 0.970651i \(0.422691\pi\)
\(42\) −183.379 −0.673716
\(43\) −416.162 −1.47591 −0.737955 0.674850i \(-0.764208\pi\)
−0.737955 + 0.674850i \(0.764208\pi\)
\(44\) 165.943 0.568565
\(45\) 45.0000 0.149071
\(46\) 18.4511 0.0591405
\(47\) −236.796 −0.734898 −0.367449 0.930044i \(-0.619769\pi\)
−0.367449 + 0.930044i \(0.619769\pi\)
\(48\) 100.677 0.302740
\(49\) 377.593 1.10085
\(50\) −56.9278 −0.161016
\(51\) 356.698 0.979366
\(52\) −216.408 −0.577122
\(53\) 470.080 1.21831 0.609155 0.793051i \(-0.291509\pi\)
0.609155 + 0.793051i \(0.291509\pi\)
\(54\) 61.4820 0.154938
\(55\) −294.773 −0.722676
\(56\) −661.068 −1.57748
\(57\) 448.076 1.04121
\(58\) −66.0363 −0.149500
\(59\) 459.022 1.01287 0.506437 0.862277i \(-0.330962\pi\)
0.506437 + 0.862277i \(0.330962\pi\)
\(60\) 42.2214 0.0908460
\(61\) 602.948 1.26557 0.632784 0.774328i \(-0.281912\pi\)
0.632784 + 0.774328i \(0.281912\pi\)
\(62\) −345.945 −0.708630
\(63\) −241.595 −0.483144
\(64\) 543.078 1.06070
\(65\) 384.416 0.733552
\(66\) −402.739 −0.751117
\(67\) 769.705 1.40350 0.701750 0.712423i \(-0.252402\pi\)
0.701750 + 0.712423i \(0.252402\pi\)
\(68\) 334.673 0.596838
\(69\) 24.3085 0.0424116
\(70\) 305.632 0.521858
\(71\) 494.182 0.826037 0.413019 0.910723i \(-0.364474\pi\)
0.413019 + 0.910723i \(0.364474\pi\)
\(72\) 221.638 0.362781
\(73\) −908.575 −1.45672 −0.728361 0.685194i \(-0.759718\pi\)
−0.728361 + 0.685194i \(0.759718\pi\)
\(74\) 749.799 1.17787
\(75\) −75.0000 −0.115470
\(76\) 420.409 0.634529
\(77\) 1582.57 2.34221
\(78\) 525.215 0.762421
\(79\) 145.802 0.207645 0.103823 0.994596i \(-0.466893\pi\)
0.103823 + 0.994596i \(0.466893\pi\)
\(80\) −167.795 −0.234501
\(81\) 81.0000 0.111111
\(82\) −287.535 −0.387231
\(83\) 364.521 0.482065 0.241033 0.970517i \(-0.422514\pi\)
0.241033 + 0.970517i \(0.422514\pi\)
\(84\) −226.677 −0.294434
\(85\) −594.496 −0.758613
\(86\) 947.648 1.18823
\(87\) −87.0000 −0.107211
\(88\) −1451.84 −1.75871
\(89\) 1341.18 1.59736 0.798678 0.601759i \(-0.205533\pi\)
0.798678 + 0.601759i \(0.205533\pi\)
\(90\) −102.470 −0.120014
\(91\) −2063.84 −2.37746
\(92\) 22.8076 0.0258462
\(93\) −455.768 −0.508182
\(94\) 539.210 0.591652
\(95\) −746.793 −0.806520
\(96\) 361.781 0.384626
\(97\) 441.198 0.461823 0.230912 0.972975i \(-0.425829\pi\)
0.230912 + 0.972975i \(0.425829\pi\)
\(98\) −859.822 −0.886277
\(99\) −530.591 −0.538651
\(100\) −70.3690 −0.0703690
\(101\) 8.77903 0.00864897 0.00432449 0.999991i \(-0.498623\pi\)
0.00432449 + 0.999991i \(0.498623\pi\)
\(102\) −812.240 −0.788469
\(103\) −1307.14 −1.25045 −0.625224 0.780445i \(-0.714992\pi\)
−0.625224 + 0.780445i \(0.714992\pi\)
\(104\) 1893.36 1.78518
\(105\) 402.658 0.374242
\(106\) −1070.42 −0.980838
\(107\) 734.360 0.663488 0.331744 0.943369i \(-0.392363\pi\)
0.331744 + 0.943369i \(0.392363\pi\)
\(108\) 75.9985 0.0677126
\(109\) 735.066 0.645932 0.322966 0.946411i \(-0.395320\pi\)
0.322966 + 0.946411i \(0.395320\pi\)
\(110\) 671.231 0.581813
\(111\) 987.829 0.844690
\(112\) 900.855 0.760025
\(113\) 1335.34 1.11166 0.555831 0.831295i \(-0.312400\pi\)
0.555831 + 0.831295i \(0.312400\pi\)
\(114\) −1020.32 −0.838260
\(115\) −40.5142 −0.0328519
\(116\) −81.6280 −0.0653360
\(117\) 691.948 0.546758
\(118\) −1045.24 −0.815445
\(119\) 3191.71 2.45869
\(120\) −369.396 −0.281009
\(121\) 2144.64 1.61130
\(122\) −1372.98 −1.01888
\(123\) −378.815 −0.277696
\(124\) −427.626 −0.309693
\(125\) 125.000 0.0894427
\(126\) 550.138 0.388970
\(127\) −98.9846 −0.0691611 −0.0345806 0.999402i \(-0.511010\pi\)
−0.0345806 + 0.999402i \(0.511010\pi\)
\(128\) −271.900 −0.187756
\(129\) 1248.49 0.852117
\(130\) −875.358 −0.590569
\(131\) 458.226 0.305614 0.152807 0.988256i \(-0.451169\pi\)
0.152807 + 0.988256i \(0.451169\pi\)
\(132\) −497.829 −0.328261
\(133\) 4009.36 2.61395
\(134\) −1752.71 −1.12993
\(135\) −135.000 −0.0860663
\(136\) −2928.06 −1.84617
\(137\) −1514.86 −0.944693 −0.472346 0.881413i \(-0.656593\pi\)
−0.472346 + 0.881413i \(0.656593\pi\)
\(138\) −55.3533 −0.0341448
\(139\) −1174.64 −0.716774 −0.358387 0.933573i \(-0.616673\pi\)
−0.358387 + 0.933573i \(0.616673\pi\)
\(140\) 377.795 0.228068
\(141\) 710.387 0.424293
\(142\) −1125.31 −0.665027
\(143\) −4532.61 −2.65060
\(144\) −302.032 −0.174787
\(145\) 145.000 0.0830455
\(146\) 2068.93 1.17278
\(147\) −1132.78 −0.635579
\(148\) 926.834 0.514765
\(149\) −2868.30 −1.57705 −0.788526 0.615002i \(-0.789155\pi\)
−0.788526 + 0.615002i \(0.789155\pi\)
\(150\) 170.783 0.0929627
\(151\) −3009.92 −1.62214 −0.811072 0.584946i \(-0.801116\pi\)
−0.811072 + 0.584946i \(0.801116\pi\)
\(152\) −3678.17 −1.96276
\(153\) −1070.09 −0.565437
\(154\) −3603.69 −1.88567
\(155\) 759.614 0.393636
\(156\) 649.223 0.333201
\(157\) −1831.72 −0.931128 −0.465564 0.885014i \(-0.654148\pi\)
−0.465564 + 0.885014i \(0.654148\pi\)
\(158\) −332.007 −0.167171
\(159\) −1410.24 −0.703392
\(160\) −602.968 −0.297930
\(161\) 217.512 0.106474
\(162\) −184.446 −0.0894534
\(163\) 1791.86 0.861038 0.430519 0.902582i \(-0.358331\pi\)
0.430519 + 0.902582i \(0.358331\pi\)
\(164\) −355.424 −0.169232
\(165\) 884.319 0.417237
\(166\) −830.056 −0.388102
\(167\) 1689.71 0.782958 0.391479 0.920187i \(-0.371964\pi\)
0.391479 + 0.920187i \(0.371964\pi\)
\(168\) 1983.21 0.910759
\(169\) 3714.02 1.69049
\(170\) 1353.73 0.610745
\(171\) −1344.23 −0.601144
\(172\) 1171.40 0.519291
\(173\) −196.378 −0.0863024 −0.0431512 0.999069i \(-0.513740\pi\)
−0.0431512 + 0.999069i \(0.513740\pi\)
\(174\) 198.109 0.0863137
\(175\) −671.097 −0.289886
\(176\) 1978.46 0.847341
\(177\) −1377.07 −0.584783
\(178\) −3054.01 −1.28600
\(179\) −334.894 −0.139839 −0.0699195 0.997553i \(-0.522274\pi\)
−0.0699195 + 0.997553i \(0.522274\pi\)
\(180\) −126.664 −0.0524499
\(181\) 1111.80 0.456571 0.228286 0.973594i \(-0.426688\pi\)
0.228286 + 0.973594i \(0.426688\pi\)
\(182\) 4699.60 1.91405
\(183\) −1808.85 −0.730676
\(184\) −199.544 −0.0799488
\(185\) −1646.38 −0.654294
\(186\) 1037.84 0.409128
\(187\) 7009.65 2.74116
\(188\) 666.523 0.258570
\(189\) 724.784 0.278943
\(190\) 1700.53 0.649314
\(191\) 923.099 0.349702 0.174851 0.984595i \(-0.444056\pi\)
0.174851 + 0.984595i \(0.444056\pi\)
\(192\) −1629.23 −0.612395
\(193\) 1015.66 0.378803 0.189401 0.981900i \(-0.439345\pi\)
0.189401 + 0.981900i \(0.439345\pi\)
\(194\) −1004.66 −0.371805
\(195\) −1153.25 −0.423517
\(196\) −1062.83 −0.387330
\(197\) −3656.92 −1.32256 −0.661282 0.750137i \(-0.729987\pi\)
−0.661282 + 0.750137i \(0.729987\pi\)
\(198\) 1208.22 0.433657
\(199\) −3408.89 −1.21432 −0.607160 0.794580i \(-0.707691\pi\)
−0.607160 + 0.794580i \(0.707691\pi\)
\(200\) 615.661 0.217669
\(201\) −2309.12 −0.810311
\(202\) −19.9908 −0.00696312
\(203\) −778.472 −0.269153
\(204\) −1004.02 −0.344585
\(205\) 631.358 0.215102
\(206\) 2976.50 1.00671
\(207\) −72.9256 −0.0244864
\(208\) −2580.13 −0.860094
\(209\) 8805.38 2.91426
\(210\) −916.897 −0.301295
\(211\) 982.934 0.320701 0.160351 0.987060i \(-0.448738\pi\)
0.160351 + 0.987060i \(0.448738\pi\)
\(212\) −1323.16 −0.428656
\(213\) −1482.55 −0.476913
\(214\) −1672.22 −0.534162
\(215\) −2080.81 −0.660047
\(216\) −664.913 −0.209452
\(217\) −4078.19 −1.27579
\(218\) −1673.83 −0.520027
\(219\) 2725.73 0.841039
\(220\) 829.715 0.254270
\(221\) −9141.34 −2.78241
\(222\) −2249.40 −0.680044
\(223\) 987.852 0.296643 0.148322 0.988939i \(-0.452613\pi\)
0.148322 + 0.988939i \(0.452613\pi\)
\(224\) 3237.20 0.965600
\(225\) 225.000 0.0666667
\(226\) −3040.71 −0.894978
\(227\) 3532.07 1.03274 0.516369 0.856366i \(-0.327283\pi\)
0.516369 + 0.856366i \(0.327283\pi\)
\(228\) −1261.23 −0.366345
\(229\) −121.305 −0.0350047 −0.0175023 0.999847i \(-0.505571\pi\)
−0.0175023 + 0.999847i \(0.505571\pi\)
\(230\) 92.2554 0.0264484
\(231\) −4747.71 −1.35228
\(232\) 714.166 0.202100
\(233\) 681.137 0.191514 0.0957570 0.995405i \(-0.469473\pi\)
0.0957570 + 0.995405i \(0.469473\pi\)
\(234\) −1575.64 −0.440184
\(235\) −1183.98 −0.328656
\(236\) −1292.04 −0.356374
\(237\) −437.405 −0.119884
\(238\) −7267.89 −1.97944
\(239\) 3861.30 1.04505 0.522525 0.852624i \(-0.324990\pi\)
0.522525 + 0.852624i \(0.324990\pi\)
\(240\) 503.386 0.135389
\(241\) −1335.54 −0.356970 −0.178485 0.983943i \(-0.557120\pi\)
−0.178485 + 0.983943i \(0.557120\pi\)
\(242\) −4883.59 −1.29723
\(243\) −243.000 −0.0641500
\(244\) −1697.15 −0.445284
\(245\) 1887.97 0.492317
\(246\) 862.604 0.223568
\(247\) −11483.2 −2.95812
\(248\) 3741.31 0.957958
\(249\) −1093.56 −0.278321
\(250\) −284.639 −0.0720086
\(251\) 3078.19 0.774079 0.387040 0.922063i \(-0.373498\pi\)
0.387040 + 0.922063i \(0.373498\pi\)
\(252\) 680.031 0.169992
\(253\) 477.700 0.118706
\(254\) 225.399 0.0556803
\(255\) 1783.49 0.437986
\(256\) −3725.47 −0.909540
\(257\) −1535.42 −0.372672 −0.186336 0.982486i \(-0.559661\pi\)
−0.186336 + 0.982486i \(0.559661\pi\)
\(258\) −2842.94 −0.686023
\(259\) 8839.05 2.12059
\(260\) −1082.04 −0.258097
\(261\) 261.000 0.0618984
\(262\) −1043.43 −0.246044
\(263\) −1460.46 −0.342418 −0.171209 0.985235i \(-0.554767\pi\)
−0.171209 + 0.985235i \(0.554767\pi\)
\(264\) 4355.52 1.01539
\(265\) 2350.40 0.544845
\(266\) −9129.77 −2.10444
\(267\) −4023.54 −0.922234
\(268\) −2166.54 −0.493814
\(269\) 4489.02 1.01747 0.508737 0.860922i \(-0.330113\pi\)
0.508737 + 0.860922i \(0.330113\pi\)
\(270\) 307.410 0.0692903
\(271\) 5678.26 1.27280 0.636402 0.771357i \(-0.280422\pi\)
0.636402 + 0.771357i \(0.280422\pi\)
\(272\) 3990.15 0.889478
\(273\) 6191.52 1.37263
\(274\) 3449.50 0.760554
\(275\) −1473.86 −0.323191
\(276\) −68.4227 −0.0149223
\(277\) −8342.92 −1.80967 −0.904833 0.425766i \(-0.860005\pi\)
−0.904833 + 0.425766i \(0.860005\pi\)
\(278\) 2674.78 0.577061
\(279\) 1367.30 0.293399
\(280\) −3305.34 −0.705471
\(281\) 4551.39 0.966238 0.483119 0.875555i \(-0.339504\pi\)
0.483119 + 0.875555i \(0.339504\pi\)
\(282\) −1617.63 −0.341591
\(283\) −5634.41 −1.18350 −0.591751 0.806121i \(-0.701563\pi\)
−0.591751 + 0.806121i \(0.701563\pi\)
\(284\) −1391.00 −0.290637
\(285\) 2240.38 0.465644
\(286\) 10321.3 2.13395
\(287\) −3389.62 −0.697153
\(288\) −1085.34 −0.222064
\(289\) 9224.02 1.87747
\(290\) −330.181 −0.0668583
\(291\) −1323.59 −0.266634
\(292\) 2557.42 0.512540
\(293\) −4203.48 −0.838122 −0.419061 0.907958i \(-0.637641\pi\)
−0.419061 + 0.907958i \(0.637641\pi\)
\(294\) 2579.47 0.511692
\(295\) 2295.11 0.452971
\(296\) −8108.90 −1.59230
\(297\) 1591.77 0.310990
\(298\) 6531.45 1.26965
\(299\) −622.972 −0.120493
\(300\) 211.107 0.0406275
\(301\) 11171.4 2.13923
\(302\) 6853.93 1.30596
\(303\) −26.3371 −0.00499349
\(304\) 5012.34 0.945649
\(305\) 3014.74 0.565979
\(306\) 2436.72 0.455223
\(307\) 419.382 0.0779655 0.0389827 0.999240i \(-0.487588\pi\)
0.0389827 + 0.999240i \(0.487588\pi\)
\(308\) −4454.55 −0.824096
\(309\) 3921.41 0.721946
\(310\) −1729.73 −0.316909
\(311\) 7213.66 1.31527 0.657636 0.753336i \(-0.271557\pi\)
0.657636 + 0.753336i \(0.271557\pi\)
\(312\) −5680.07 −1.03068
\(313\) 1775.17 0.320571 0.160286 0.987071i \(-0.448758\pi\)
0.160286 + 0.987071i \(0.448758\pi\)
\(314\) 4171.03 0.749633
\(315\) −1207.97 −0.216069
\(316\) −410.397 −0.0730589
\(317\) 4522.95 0.801369 0.400685 0.916216i \(-0.368772\pi\)
0.400685 + 0.916216i \(0.368772\pi\)
\(318\) 3211.27 0.566287
\(319\) −1709.68 −0.300075
\(320\) 2715.39 0.474359
\(321\) −2203.08 −0.383065
\(322\) −495.298 −0.0857202
\(323\) 17758.6 3.05918
\(324\) −227.995 −0.0390939
\(325\) 1922.08 0.328055
\(326\) −4080.26 −0.693205
\(327\) −2205.20 −0.372929
\(328\) 3109.62 0.523476
\(329\) 6356.51 1.06518
\(330\) −2013.69 −0.335910
\(331\) −4817.66 −0.800007 −0.400004 0.916514i \(-0.630991\pi\)
−0.400004 + 0.916514i \(0.630991\pi\)
\(332\) −1026.04 −0.169612
\(333\) −2963.49 −0.487682
\(334\) −3847.67 −0.630345
\(335\) 3848.53 0.627664
\(336\) −2702.56 −0.438801
\(337\) 1947.15 0.314742 0.157371 0.987540i \(-0.449698\pi\)
0.157371 + 0.987540i \(0.449698\pi\)
\(338\) −8457.24 −1.36099
\(339\) −4006.01 −0.641819
\(340\) 1673.36 0.266914
\(341\) −8956.54 −1.42236
\(342\) 3060.96 0.483970
\(343\) −928.613 −0.146182
\(344\) −10248.6 −1.60630
\(345\) 121.543 0.0189671
\(346\) 447.174 0.0694804
\(347\) 6797.20 1.05156 0.525782 0.850619i \(-0.323773\pi\)
0.525782 + 0.850619i \(0.323773\pi\)
\(348\) 244.884 0.0377217
\(349\) −9920.99 −1.52166 −0.760829 0.648953i \(-0.775207\pi\)
−0.760829 + 0.648953i \(0.775207\pi\)
\(350\) 1528.16 0.233382
\(351\) −2075.84 −0.315671
\(352\) 7109.55 1.07653
\(353\) −2488.63 −0.375231 −0.187616 0.982243i \(-0.560076\pi\)
−0.187616 + 0.982243i \(0.560076\pi\)
\(354\) 3135.73 0.470798
\(355\) 2470.91 0.369415
\(356\) −3775.09 −0.562021
\(357\) −9575.14 −1.41952
\(358\) 762.592 0.112582
\(359\) 7951.79 1.16902 0.584512 0.811385i \(-0.301286\pi\)
0.584512 + 0.811385i \(0.301286\pi\)
\(360\) 1108.19 0.162241
\(361\) 15449.0 2.25237
\(362\) −2531.69 −0.367577
\(363\) −6433.93 −0.930286
\(364\) 5809.21 0.836499
\(365\) −4542.88 −0.651466
\(366\) 4118.94 0.588253
\(367\) 8545.32 1.21543 0.607714 0.794156i \(-0.292087\pi\)
0.607714 + 0.794156i \(0.292087\pi\)
\(368\) 271.924 0.0385190
\(369\) 1136.45 0.160328
\(370\) 3749.00 0.526760
\(371\) −12618.8 −1.76586
\(372\) 1282.88 0.178801
\(373\) −10494.4 −1.45678 −0.728391 0.685162i \(-0.759731\pi\)
−0.728391 + 0.685162i \(0.759731\pi\)
\(374\) −15961.8 −2.20685
\(375\) −375.000 −0.0516398
\(376\) −5831.43 −0.799822
\(377\) 2229.61 0.304591
\(378\) −1650.42 −0.224572
\(379\) 3861.31 0.523330 0.261665 0.965159i \(-0.415728\pi\)
0.261665 + 0.965159i \(0.415728\pi\)
\(380\) 2102.04 0.283770
\(381\) 296.954 0.0399302
\(382\) −2102.00 −0.281539
\(383\) 5649.95 0.753784 0.376892 0.926257i \(-0.376993\pi\)
0.376892 + 0.926257i \(0.376993\pi\)
\(384\) 815.700 0.108401
\(385\) 7912.85 1.04747
\(386\) −2312.77 −0.304967
\(387\) −3745.46 −0.491970
\(388\) −1241.87 −0.162490
\(389\) 2257.79 0.294279 0.147139 0.989116i \(-0.452993\pi\)
0.147139 + 0.989116i \(0.452993\pi\)
\(390\) 2626.07 0.340965
\(391\) 963.422 0.124610
\(392\) 9298.77 1.19811
\(393\) −1374.68 −0.176446
\(394\) 8327.23 1.06477
\(395\) 729.009 0.0928618
\(396\) 1493.49 0.189522
\(397\) 221.335 0.0279811 0.0139905 0.999902i \(-0.495547\pi\)
0.0139905 + 0.999902i \(0.495547\pi\)
\(398\) 7762.42 0.977625
\(399\) −12028.1 −1.50917
\(400\) −838.977 −0.104872
\(401\) 3656.31 0.455330 0.227665 0.973739i \(-0.426891\pi\)
0.227665 + 0.973739i \(0.426891\pi\)
\(402\) 5258.12 0.652366
\(403\) 11680.3 1.44376
\(404\) −24.7109 −0.00304310
\(405\) 405.000 0.0496904
\(406\) 1772.67 0.216690
\(407\) 19412.4 2.36421
\(408\) 8784.19 1.06589
\(409\) −1114.22 −0.134706 −0.0673530 0.997729i \(-0.521455\pi\)
−0.0673530 + 0.997729i \(0.521455\pi\)
\(410\) −1437.67 −0.173175
\(411\) 4544.57 0.545419
\(412\) 3679.28 0.439964
\(413\) −12321.9 −1.46809
\(414\) 166.060 0.0197135
\(415\) 1822.61 0.215586
\(416\) −9271.62 −1.09274
\(417\) 3523.92 0.413829
\(418\) −20050.8 −2.34622
\(419\) −2992.41 −0.348899 −0.174450 0.984666i \(-0.555815\pi\)
−0.174450 + 0.984666i \(0.555815\pi\)
\(420\) −1133.39 −0.131675
\(421\) −7412.33 −0.858087 −0.429044 0.903284i \(-0.641149\pi\)
−0.429044 + 0.903284i \(0.641149\pi\)
\(422\) −2238.25 −0.258190
\(423\) −2131.16 −0.244966
\(424\) 11576.4 1.32594
\(425\) −2972.48 −0.339262
\(426\) 3375.93 0.383953
\(427\) −16185.5 −1.83436
\(428\) −2067.05 −0.233445
\(429\) 13597.8 1.53033
\(430\) 4738.24 0.531391
\(431\) 2761.79 0.308656 0.154328 0.988020i \(-0.450679\pi\)
0.154328 + 0.988020i \(0.450679\pi\)
\(432\) 906.095 0.100913
\(433\) −15263.4 −1.69402 −0.847012 0.531573i \(-0.821601\pi\)
−0.847012 + 0.531573i \(0.821601\pi\)
\(434\) 9286.50 1.02711
\(435\) −435.000 −0.0479463
\(436\) −2069.03 −0.227268
\(437\) 1210.23 0.132479
\(438\) −6206.78 −0.677104
\(439\) −9343.27 −1.01579 −0.507893 0.861420i \(-0.669575\pi\)
−0.507893 + 0.861420i \(0.669575\pi\)
\(440\) −7259.20 −0.786520
\(441\) 3398.34 0.366952
\(442\) 20815.9 2.24007
\(443\) −8167.05 −0.875911 −0.437955 0.898997i \(-0.644297\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(444\) −2780.50 −0.297200
\(445\) 6705.89 0.714359
\(446\) −2249.45 −0.238822
\(447\) 8604.91 0.910511
\(448\) −14578.3 −1.53741
\(449\) 4390.88 0.461511 0.230756 0.973012i \(-0.425880\pi\)
0.230756 + 0.973012i \(0.425880\pi\)
\(450\) −512.350 −0.0536721
\(451\) −7444.29 −0.777246
\(452\) −3758.65 −0.391133
\(453\) 9029.76 0.936546
\(454\) −8042.91 −0.831438
\(455\) −10319.2 −1.06323
\(456\) 11034.5 1.13320
\(457\) 16232.1 1.66150 0.830748 0.556648i \(-0.187913\pi\)
0.830748 + 0.556648i \(0.187913\pi\)
\(458\) 276.226 0.0281816
\(459\) 3210.28 0.326455
\(460\) 114.038 0.0115588
\(461\) 14847.4 1.50002 0.750011 0.661425i \(-0.230048\pi\)
0.750011 + 0.661425i \(0.230048\pi\)
\(462\) 10811.1 1.08869
\(463\) 9208.48 0.924307 0.462154 0.886800i \(-0.347077\pi\)
0.462154 + 0.886800i \(0.347077\pi\)
\(464\) −973.213 −0.0973713
\(465\) −2278.84 −0.227266
\(466\) −1551.02 −0.154184
\(467\) −8652.79 −0.857394 −0.428697 0.903448i \(-0.641027\pi\)
−0.428697 + 0.903448i \(0.641027\pi\)
\(468\) −1947.67 −0.192374
\(469\) −20661.9 −2.03428
\(470\) 2696.05 0.264595
\(471\) 5495.16 0.537587
\(472\) 11304.1 1.10236
\(473\) 24534.7 2.38500
\(474\) 996.021 0.0965164
\(475\) −3733.97 −0.360687
\(476\) −8983.91 −0.865077
\(477\) 4230.72 0.406103
\(478\) −8792.62 −0.841350
\(479\) −9373.99 −0.894173 −0.447086 0.894491i \(-0.647538\pi\)
−0.447086 + 0.894491i \(0.647538\pi\)
\(480\) 1808.90 0.172010
\(481\) −25315.8 −2.39979
\(482\) 3041.18 0.287390
\(483\) −652.535 −0.0614728
\(484\) −6036.65 −0.566929
\(485\) 2205.99 0.206534
\(486\) 553.338 0.0516460
\(487\) −6481.75 −0.603114 −0.301557 0.953448i \(-0.597506\pi\)
−0.301557 + 0.953448i \(0.597506\pi\)
\(488\) 14848.5 1.37737
\(489\) −5375.57 −0.497120
\(490\) −4299.11 −0.396355
\(491\) −1108.08 −0.101847 −0.0509235 0.998703i \(-0.516216\pi\)
−0.0509235 + 0.998703i \(0.516216\pi\)
\(492\) 1066.27 0.0977059
\(493\) −3448.08 −0.314997
\(494\) 26148.5 2.38153
\(495\) −2652.96 −0.240892
\(496\) −5098.38 −0.461541
\(497\) −13265.8 −1.19729
\(498\) 2490.17 0.224071
\(499\) 4054.00 0.363691 0.181845 0.983327i \(-0.441793\pi\)
0.181845 + 0.983327i \(0.441793\pi\)
\(500\) −351.845 −0.0314700
\(501\) −5069.14 −0.452041
\(502\) −7009.40 −0.623196
\(503\) −2816.84 −0.249695 −0.124847 0.992176i \(-0.539844\pi\)
−0.124847 + 0.992176i \(0.539844\pi\)
\(504\) −5949.62 −0.525827
\(505\) 43.8952 0.00386794
\(506\) −1087.78 −0.0955683
\(507\) −11142.1 −0.976008
\(508\) 278.618 0.0243340
\(509\) −830.334 −0.0723063 −0.0361532 0.999346i \(-0.511510\pi\)
−0.0361532 + 0.999346i \(0.511510\pi\)
\(510\) −4061.20 −0.352614
\(511\) 24389.7 2.11142
\(512\) 10658.5 0.920009
\(513\) 4032.68 0.347071
\(514\) 3496.31 0.300031
\(515\) −6535.69 −0.559217
\(516\) −3514.19 −0.299813
\(517\) 13960.2 1.18756
\(518\) −20127.5 −1.70724
\(519\) 589.133 0.0498267
\(520\) 9466.78 0.798358
\(521\) −14425.9 −1.21307 −0.606536 0.795056i \(-0.707441\pi\)
−0.606536 + 0.795056i \(0.707441\pi\)
\(522\) −594.326 −0.0498333
\(523\) 18615.3 1.55638 0.778192 0.628027i \(-0.216137\pi\)
0.778192 + 0.628027i \(0.216137\pi\)
\(524\) −1289.80 −0.107529
\(525\) 2013.29 0.167366
\(526\) 3325.63 0.275674
\(527\) −18063.5 −1.49309
\(528\) −5935.38 −0.489213
\(529\) −12101.3 −0.994604
\(530\) −5352.12 −0.438644
\(531\) 4131.20 0.337625
\(532\) −11285.4 −0.919706
\(533\) 9708.16 0.788944
\(534\) 9162.04 0.742473
\(535\) 3671.80 0.296721
\(536\) 18955.1 1.52749
\(537\) 1004.68 0.0807360
\(538\) −10222.0 −0.819148
\(539\) −22260.8 −1.77893
\(540\) 379.992 0.0302820
\(541\) 5586.54 0.443963 0.221982 0.975051i \(-0.428748\pi\)
0.221982 + 0.975051i \(0.428748\pi\)
\(542\) −12930.0 −1.02471
\(543\) −3335.40 −0.263602
\(544\) 14338.5 1.13007
\(545\) 3675.33 0.288869
\(546\) −14098.8 −1.10508
\(547\) −4779.89 −0.373626 −0.186813 0.982396i \(-0.559816\pi\)
−0.186813 + 0.982396i \(0.559816\pi\)
\(548\) 4263.96 0.332385
\(549\) 5426.54 0.421856
\(550\) 3356.16 0.260194
\(551\) −4331.40 −0.334889
\(552\) 598.632 0.0461585
\(553\) −3913.88 −0.300968
\(554\) 18997.8 1.45693
\(555\) 4939.15 0.377757
\(556\) 3306.32 0.252193
\(557\) −11829.0 −0.899837 −0.449919 0.893070i \(-0.648547\pi\)
−0.449919 + 0.893070i \(0.648547\pi\)
\(558\) −3113.51 −0.236210
\(559\) −31995.8 −2.42089
\(560\) 4504.27 0.339893
\(561\) −21029.0 −1.58261
\(562\) −10364.0 −0.777900
\(563\) −22516.9 −1.68557 −0.842783 0.538254i \(-0.819084\pi\)
−0.842783 + 0.538254i \(0.819084\pi\)
\(564\) −1999.57 −0.149285
\(565\) 6676.68 0.497151
\(566\) 12830.2 0.952815
\(567\) −2174.35 −0.161048
\(568\) 12169.9 0.899013
\(569\) −6879.75 −0.506879 −0.253439 0.967351i \(-0.581562\pi\)
−0.253439 + 0.967351i \(0.581562\pi\)
\(570\) −5101.60 −0.374881
\(571\) −3088.90 −0.226386 −0.113193 0.993573i \(-0.536108\pi\)
−0.113193 + 0.993573i \(0.536108\pi\)
\(572\) 12758.2 0.932601
\(573\) −2769.30 −0.201901
\(574\) 7718.55 0.561265
\(575\) −202.571 −0.0146918
\(576\) 4887.70 0.353566
\(577\) 760.799 0.0548916 0.0274458 0.999623i \(-0.491263\pi\)
0.0274458 + 0.999623i \(0.491263\pi\)
\(578\) −21004.1 −1.51152
\(579\) −3046.98 −0.218702
\(580\) −408.140 −0.0292191
\(581\) −9785.16 −0.698721
\(582\) 3013.97 0.214662
\(583\) −27713.4 −1.96873
\(584\) −22375.0 −1.58542
\(585\) 3459.74 0.244517
\(586\) 9571.79 0.674756
\(587\) −3106.07 −0.218401 −0.109200 0.994020i \(-0.534829\pi\)
−0.109200 + 0.994020i \(0.534829\pi\)
\(588\) 3188.50 0.223625
\(589\) −22691.0 −1.58738
\(590\) −5226.22 −0.364678
\(591\) 10970.8 0.763583
\(592\) 11050.2 0.767163
\(593\) −7836.74 −0.542692 −0.271346 0.962482i \(-0.587469\pi\)
−0.271346 + 0.962482i \(0.587469\pi\)
\(594\) −3624.65 −0.250372
\(595\) 15958.6 1.09956
\(596\) 8073.59 0.554877
\(597\) 10226.7 0.701088
\(598\) 1418.58 0.0970066
\(599\) 9174.05 0.625779 0.312889 0.949790i \(-0.398703\pi\)
0.312889 + 0.949790i \(0.398703\pi\)
\(600\) −1846.98 −0.125671
\(601\) −8958.64 −0.608037 −0.304019 0.952666i \(-0.598329\pi\)
−0.304019 + 0.952666i \(0.598329\pi\)
\(602\) −25438.5 −1.72225
\(603\) 6927.35 0.467833
\(604\) 8472.20 0.570743
\(605\) 10723.2 0.720596
\(606\) 59.9725 0.00402016
\(607\) 14137.8 0.945362 0.472681 0.881234i \(-0.343286\pi\)
0.472681 + 0.881234i \(0.343286\pi\)
\(608\) 18011.7 1.20143
\(609\) 2335.42 0.155395
\(610\) −6864.91 −0.455659
\(611\) −18205.6 −1.20543
\(612\) 3012.05 0.198946
\(613\) 22666.7 1.49347 0.746737 0.665120i \(-0.231620\pi\)
0.746737 + 0.665120i \(0.231620\pi\)
\(614\) −954.980 −0.0627685
\(615\) −1894.08 −0.124189
\(616\) 38973.0 2.54914
\(617\) 12743.3 0.831487 0.415744 0.909482i \(-0.363521\pi\)
0.415744 + 0.909482i \(0.363521\pi\)
\(618\) −8929.50 −0.581225
\(619\) 13912.5 0.903379 0.451690 0.892175i \(-0.350821\pi\)
0.451690 + 0.892175i \(0.350821\pi\)
\(620\) −2138.13 −0.138499
\(621\) 218.777 0.0141372
\(622\) −16426.3 −1.05890
\(623\) −36002.4 −2.31526
\(624\) 7740.38 0.496575
\(625\) 625.000 0.0400000
\(626\) −4042.27 −0.258086
\(627\) −26416.1 −1.68255
\(628\) 5155.85 0.327613
\(629\) 39150.7 2.48178
\(630\) 2750.69 0.173953
\(631\) −6045.07 −0.381379 −0.190690 0.981650i \(-0.561072\pi\)
−0.190690 + 0.981650i \(0.561072\pi\)
\(632\) 3590.58 0.225990
\(633\) −2948.80 −0.185157
\(634\) −10299.3 −0.645167
\(635\) −494.923 −0.0309298
\(636\) 3969.49 0.247485
\(637\) 29030.5 1.80570
\(638\) 3893.14 0.241585
\(639\) 4447.64 0.275346
\(640\) −1359.50 −0.0839671
\(641\) −19600.7 −1.20777 −0.603885 0.797071i \(-0.706382\pi\)
−0.603885 + 0.797071i \(0.706382\pi\)
\(642\) 5016.66 0.308398
\(643\) −11909.9 −0.730454 −0.365227 0.930919i \(-0.619009\pi\)
−0.365227 + 0.930919i \(0.619009\pi\)
\(644\) −612.243 −0.0374623
\(645\) 6242.43 0.381078
\(646\) −40438.4 −2.46289
\(647\) 10476.3 0.636576 0.318288 0.947994i \(-0.396892\pi\)
0.318288 + 0.947994i \(0.396892\pi\)
\(648\) 1994.74 0.120927
\(649\) −27061.4 −1.63676
\(650\) −4376.79 −0.264110
\(651\) 12234.6 0.736576
\(652\) −5043.65 −0.302952
\(653\) 21201.7 1.27058 0.635289 0.772275i \(-0.280881\pi\)
0.635289 + 0.772275i \(0.280881\pi\)
\(654\) 5021.48 0.300238
\(655\) 2291.13 0.136675
\(656\) −4237.56 −0.252209
\(657\) −8177.18 −0.485574
\(658\) −14474.5 −0.857560
\(659\) 23605.3 1.39534 0.697671 0.716418i \(-0.254220\pi\)
0.697671 + 0.716418i \(0.254220\pi\)
\(660\) −2489.14 −0.146803
\(661\) 12258.0 0.721305 0.360652 0.932700i \(-0.382554\pi\)
0.360652 + 0.932700i \(0.382554\pi\)
\(662\) 10970.3 0.644070
\(663\) 27424.0 1.60643
\(664\) 8976.86 0.524653
\(665\) 20046.8 1.16900
\(666\) 6748.19 0.392623
\(667\) −234.982 −0.0136410
\(668\) −4756.14 −0.275480
\(669\) −2963.56 −0.171267
\(670\) −8763.53 −0.505320
\(671\) −35546.6 −2.04510
\(672\) −9711.60 −0.557490
\(673\) 9476.64 0.542790 0.271395 0.962468i \(-0.412515\pi\)
0.271395 + 0.962468i \(0.412515\pi\)
\(674\) −4433.88 −0.253393
\(675\) −675.000 −0.0384900
\(676\) −10454.1 −0.594792
\(677\) −15508.3 −0.880401 −0.440200 0.897900i \(-0.645093\pi\)
−0.440200 + 0.897900i \(0.645093\pi\)
\(678\) 9122.13 0.516716
\(679\) −11843.5 −0.669382
\(680\) −14640.3 −0.825633
\(681\) −10596.2 −0.596252
\(682\) 20395.1 1.14511
\(683\) −18286.7 −1.02448 −0.512242 0.858841i \(-0.671185\pi\)
−0.512242 + 0.858841i \(0.671185\pi\)
\(684\) 3783.68 0.211510
\(685\) −7574.28 −0.422479
\(686\) 2114.56 0.117688
\(687\) 363.916 0.0202100
\(688\) 13966.0 0.773908
\(689\) 36141.2 1.99836
\(690\) −276.766 −0.0152700
\(691\) −22335.4 −1.22964 −0.614819 0.788668i \(-0.710771\pi\)
−0.614819 + 0.788668i \(0.710771\pi\)
\(692\) 552.756 0.0303651
\(693\) 14243.1 0.780738
\(694\) −15478.0 −0.846594
\(695\) −5873.19 −0.320551
\(696\) −2142.50 −0.116683
\(697\) −15013.6 −0.815898
\(698\) 22591.2 1.22506
\(699\) −2043.41 −0.110571
\(700\) 1888.98 0.101995
\(701\) −1101.09 −0.0593259 −0.0296630 0.999560i \(-0.509443\pi\)
−0.0296630 + 0.999560i \(0.509443\pi\)
\(702\) 4726.93 0.254140
\(703\) 49180.3 2.63851
\(704\) −32016.9 −1.71404
\(705\) 3551.93 0.189750
\(706\) 5666.90 0.302091
\(707\) −235.663 −0.0125361
\(708\) 3876.11 0.205753
\(709\) −3572.01 −0.189209 −0.0946047 0.995515i \(-0.530159\pi\)
−0.0946047 + 0.995515i \(0.530159\pi\)
\(710\) −5626.54 −0.297409
\(711\) 1312.22 0.0692151
\(712\) 33028.4 1.73847
\(713\) −1231.01 −0.0646585
\(714\) 21803.7 1.14283
\(715\) −22663.1 −1.18539
\(716\) 942.647 0.0492016
\(717\) −11583.9 −0.603360
\(718\) −18107.1 −0.941158
\(719\) 16054.3 0.832719 0.416359 0.909200i \(-0.363306\pi\)
0.416359 + 0.909200i \(0.363306\pi\)
\(720\) −1510.16 −0.0781670
\(721\) 35088.6 1.81244
\(722\) −35179.1 −1.81334
\(723\) 4006.63 0.206097
\(724\) −3129.45 −0.160642
\(725\) 725.000 0.0371391
\(726\) 14650.8 0.748955
\(727\) −34377.9 −1.75379 −0.876895 0.480682i \(-0.840389\pi\)
−0.876895 + 0.480682i \(0.840389\pi\)
\(728\) −50825.0 −2.58750
\(729\) 729.000 0.0370370
\(730\) 10344.6 0.524483
\(731\) 49481.3 2.50360
\(732\) 5091.46 0.257085
\(733\) 18345.6 0.924435 0.462217 0.886767i \(-0.347054\pi\)
0.462217 + 0.886767i \(0.347054\pi\)
\(734\) −19458.7 −0.978518
\(735\) −5663.90 −0.284239
\(736\) 977.151 0.0489379
\(737\) −45377.7 −2.26799
\(738\) −2587.81 −0.129077
\(739\) −6654.19 −0.331229 −0.165614 0.986191i \(-0.552961\pi\)
−0.165614 + 0.986191i \(0.552961\pi\)
\(740\) 4634.17 0.230210
\(741\) 34449.5 1.70787
\(742\) 28734.3 1.42166
\(743\) 9867.74 0.487231 0.243615 0.969872i \(-0.421667\pi\)
0.243615 + 0.969872i \(0.421667\pi\)
\(744\) −11223.9 −0.553077
\(745\) −14341.5 −0.705279
\(746\) 23896.9 1.17283
\(747\) 3280.69 0.160688
\(748\) −19730.5 −0.964462
\(749\) −19713.1 −0.961682
\(750\) 853.917 0.0415742
\(751\) −10030.7 −0.487385 −0.243693 0.969853i \(-0.578359\pi\)
−0.243693 + 0.969853i \(0.578359\pi\)
\(752\) 7946.64 0.385351
\(753\) −9234.58 −0.446915
\(754\) −5077.08 −0.245220
\(755\) −15049.6 −0.725445
\(756\) −2040.09 −0.0981448
\(757\) 21074.4 1.01184 0.505919 0.862581i \(-0.331154\pi\)
0.505919 + 0.862581i \(0.331154\pi\)
\(758\) −8792.63 −0.421323
\(759\) −1433.10 −0.0685352
\(760\) −18390.8 −0.877771
\(761\) 7469.19 0.355792 0.177896 0.984049i \(-0.443071\pi\)
0.177896 + 0.984049i \(0.443071\pi\)
\(762\) −676.197 −0.0321470
\(763\) −19732.0 −0.936234
\(764\) −2598.30 −0.123041
\(765\) −5350.46 −0.252871
\(766\) −12865.6 −0.606857
\(767\) 35291.0 1.66139
\(768\) 11176.4 0.525123
\(769\) −5361.63 −0.251424 −0.125712 0.992067i \(-0.540122\pi\)
−0.125712 + 0.992067i \(0.540122\pi\)
\(770\) −18018.4 −0.843298
\(771\) 4606.25 0.215162
\(772\) −2858.84 −0.133280
\(773\) −24649.9 −1.14695 −0.573476 0.819222i \(-0.694405\pi\)
−0.573476 + 0.819222i \(0.694405\pi\)
\(774\) 8528.83 0.396075
\(775\) 3798.07 0.176040
\(776\) 10865.1 0.502623
\(777\) −26517.2 −1.22432
\(778\) −5141.24 −0.236918
\(779\) −18859.8 −0.867421
\(780\) 3246.11 0.149012
\(781\) −29134.3 −1.33484
\(782\) −2193.82 −0.100321
\(783\) −783.000 −0.0357371
\(784\) −12671.7 −0.577244
\(785\) −9158.59 −0.416413
\(786\) 3130.30 0.142054
\(787\) −33943.1 −1.53741 −0.768705 0.639604i \(-0.779098\pi\)
−0.768705 + 0.639604i \(0.779098\pi\)
\(788\) 10293.4 0.465337
\(789\) 4381.38 0.197695
\(790\) −1660.03 −0.0747612
\(791\) −35845.6 −1.61128
\(792\) −13066.6 −0.586238
\(793\) 46356.6 2.07588
\(794\) −504.005 −0.0225270
\(795\) −7051.20 −0.314566
\(796\) 9595.19 0.427252
\(797\) 16602.5 0.737882 0.368941 0.929453i \(-0.379720\pi\)
0.368941 + 0.929453i \(0.379720\pi\)
\(798\) 27389.3 1.21500
\(799\) 28154.8 1.24662
\(800\) −3014.84 −0.133238
\(801\) 12070.6 0.532452
\(802\) −8325.83 −0.366578
\(803\) 53564.7 2.35399
\(804\) 6499.61 0.285104
\(805\) 1087.56 0.0476166
\(806\) −26597.3 −1.16235
\(807\) −13467.1 −0.587439
\(808\) 216.196 0.00941306
\(809\) −2323.51 −0.100977 −0.0504883 0.998725i \(-0.516078\pi\)
−0.0504883 + 0.998725i \(0.516078\pi\)
\(810\) −922.231 −0.0400048
\(811\) 38440.8 1.66441 0.832206 0.554466i \(-0.187078\pi\)
0.832206 + 0.554466i \(0.187078\pi\)
\(812\) 2191.21 0.0947001
\(813\) −17034.8 −0.734854
\(814\) −44204.1 −1.90338
\(815\) 8959.29 0.385068
\(816\) −11970.4 −0.513541
\(817\) 62157.4 2.66170
\(818\) 2537.21 0.108449
\(819\) −18574.6 −0.792488
\(820\) −1777.12 −0.0756827
\(821\) 27808.5 1.18212 0.591062 0.806626i \(-0.298709\pi\)
0.591062 + 0.806626i \(0.298709\pi\)
\(822\) −10348.5 −0.439106
\(823\) −7497.23 −0.317542 −0.158771 0.987315i \(-0.550753\pi\)
−0.158771 + 0.987315i \(0.550753\pi\)
\(824\) −32190.1 −1.36092
\(825\) 4421.59 0.186594
\(826\) 28058.4 1.18193
\(827\) 33174.6 1.39491 0.697457 0.716626i \(-0.254315\pi\)
0.697457 + 0.716626i \(0.254315\pi\)
\(828\) 205.268 0.00861540
\(829\) 9823.48 0.411561 0.205780 0.978598i \(-0.434027\pi\)
0.205780 + 0.978598i \(0.434027\pi\)
\(830\) −4150.28 −0.173564
\(831\) 25028.8 1.04481
\(832\) 41753.5 1.73984
\(833\) −44895.5 −1.86739
\(834\) −8024.35 −0.333166
\(835\) 8448.57 0.350150
\(836\) −24785.0 −1.02537
\(837\) −4101.91 −0.169394
\(838\) 6814.05 0.280892
\(839\) 22580.6 0.929165 0.464583 0.885530i \(-0.346204\pi\)
0.464583 + 0.885530i \(0.346204\pi\)
\(840\) 9916.03 0.407304
\(841\) 841.000 0.0344828
\(842\) 16878.7 0.690830
\(843\) −13654.2 −0.557858
\(844\) −2766.72 −0.112837
\(845\) 18570.1 0.756012
\(846\) 4852.89 0.197217
\(847\) −57570.5 −2.33547
\(848\) −15775.4 −0.638834
\(849\) 16903.2 0.683295
\(850\) 6768.67 0.273134
\(851\) 2668.07 0.107474
\(852\) 4173.01 0.167799
\(853\) −28170.3 −1.13075 −0.565377 0.824832i \(-0.691269\pi\)
−0.565377 + 0.824832i \(0.691269\pi\)
\(854\) 36856.1 1.47680
\(855\) −6721.14 −0.268840
\(856\) 18084.7 0.722104
\(857\) 3158.13 0.125880 0.0629402 0.998017i \(-0.479952\pi\)
0.0629402 + 0.998017i \(0.479952\pi\)
\(858\) −30963.8 −1.23204
\(859\) 5122.45 0.203464 0.101732 0.994812i \(-0.467562\pi\)
0.101732 + 0.994812i \(0.467562\pi\)
\(860\) 5856.98 0.232234
\(861\) 10168.9 0.402502
\(862\) −6288.92 −0.248493
\(863\) −3587.38 −0.141502 −0.0707509 0.997494i \(-0.522540\pi\)
−0.0707509 + 0.997494i \(0.522540\pi\)
\(864\) 3256.03 0.128209
\(865\) −981.888 −0.0385956
\(866\) 34756.5 1.36383
\(867\) −27672.1 −1.08396
\(868\) 11479.1 0.448879
\(869\) −8595.68 −0.335545
\(870\) 990.544 0.0386007
\(871\) 59177.4 2.30212
\(872\) 18102.0 0.702996
\(873\) 3970.78 0.153941
\(874\) −2755.83 −0.106656
\(875\) −3355.48 −0.129641
\(876\) −7672.26 −0.295915
\(877\) 28862.1 1.11129 0.555646 0.831419i \(-0.312471\pi\)
0.555646 + 0.831419i \(0.312471\pi\)
\(878\) 21275.7 0.817789
\(879\) 12610.4 0.483890
\(880\) 9892.30 0.378943
\(881\) −23389.1 −0.894439 −0.447219 0.894424i \(-0.647586\pi\)
−0.447219 + 0.894424i \(0.647586\pi\)
\(882\) −7738.40 −0.295426
\(883\) 27097.2 1.03272 0.516360 0.856371i \(-0.327287\pi\)
0.516360 + 0.856371i \(0.327287\pi\)
\(884\) 25730.7 0.978978
\(885\) −6885.33 −0.261523
\(886\) 18597.3 0.705179
\(887\) −37179.8 −1.40741 −0.703707 0.710490i \(-0.748473\pi\)
−0.703707 + 0.710490i \(0.748473\pi\)
\(888\) 24326.7 0.919314
\(889\) 2657.13 0.100244
\(890\) −15270.1 −0.575117
\(891\) −4775.32 −0.179550
\(892\) −2780.57 −0.104372
\(893\) 35367.5 1.32534
\(894\) −19594.4 −0.733035
\(895\) −1674.47 −0.0625379
\(896\) 7298.85 0.272140
\(897\) 1868.92 0.0695667
\(898\) −9998.53 −0.371554
\(899\) 4405.76 0.163449
\(900\) −633.321 −0.0234563
\(901\) −55892.1 −2.06663
\(902\) 16951.5 0.625746
\(903\) −33514.2 −1.23509
\(904\) 32884.6 1.20987
\(905\) 5559.00 0.204185
\(906\) −20561.8 −0.753995
\(907\) 19859.6 0.727041 0.363521 0.931586i \(-0.381575\pi\)
0.363521 + 0.931586i \(0.381575\pi\)
\(908\) −9941.92 −0.363364
\(909\) 79.0113 0.00288299
\(910\) 23498.0 0.855990
\(911\) 25471.8 0.926366 0.463183 0.886263i \(-0.346707\pi\)
0.463183 + 0.886263i \(0.346707\pi\)
\(912\) −15037.0 −0.545971
\(913\) −21490.2 −0.778995
\(914\) −36962.2 −1.33764
\(915\) −9044.23 −0.326768
\(916\) 341.445 0.0123162
\(917\) −12300.6 −0.442967
\(918\) −7310.16 −0.262823
\(919\) −26174.7 −0.939526 −0.469763 0.882793i \(-0.655661\pi\)
−0.469763 + 0.882793i \(0.655661\pi\)
\(920\) −997.720 −0.0357542
\(921\) −1258.15 −0.0450134
\(922\) −33809.1 −1.20764
\(923\) 37994.3 1.35493
\(924\) 13363.7 0.475792
\(925\) −8231.91 −0.292609
\(926\) −20968.7 −0.744142
\(927\) −11764.2 −0.416816
\(928\) −3497.22 −0.123709
\(929\) −42691.9 −1.50772 −0.753862 0.657033i \(-0.771811\pi\)
−0.753862 + 0.657033i \(0.771811\pi\)
\(930\) 5189.18 0.182968
\(931\) −56396.8 −1.98532
\(932\) −1917.24 −0.0673832
\(933\) −21641.0 −0.759372
\(934\) 19703.4 0.690272
\(935\) 35048.3 1.22588
\(936\) 17040.2 0.595061
\(937\) −6284.51 −0.219110 −0.109555 0.993981i \(-0.534943\pi\)
−0.109555 + 0.993981i \(0.534943\pi\)
\(938\) 47049.4 1.63776
\(939\) −5325.52 −0.185082
\(940\) 3332.61 0.115636
\(941\) 32542.5 1.12737 0.563684 0.825990i \(-0.309383\pi\)
0.563684 + 0.825990i \(0.309383\pi\)
\(942\) −12513.1 −0.432801
\(943\) −1023.16 −0.0353326
\(944\) −15404.3 −0.531111
\(945\) 3623.92 0.124747
\(946\) −55868.2 −1.92012
\(947\) 19841.4 0.680845 0.340423 0.940273i \(-0.389430\pi\)
0.340423 + 0.940273i \(0.389430\pi\)
\(948\) 1231.19 0.0421806
\(949\) −69854.1 −2.38942
\(950\) 8502.66 0.290382
\(951\) −13568.8 −0.462671
\(952\) 78600.5 2.67590
\(953\) −3705.36 −0.125948 −0.0629739 0.998015i \(-0.520058\pi\)
−0.0629739 + 0.998015i \(0.520058\pi\)
\(954\) −9633.82 −0.326946
\(955\) 4615.50 0.156392
\(956\) −10868.6 −0.367695
\(957\) 5129.05 0.173248
\(958\) 21345.6 0.719881
\(959\) 40664.6 1.36927
\(960\) −8146.17 −0.273871
\(961\) −6710.48 −0.225252
\(962\) 57646.9 1.93203
\(963\) 6609.24 0.221163
\(964\) 3759.23 0.125598
\(965\) 5078.31 0.169406
\(966\) 1485.90 0.0494906
\(967\) −42598.6 −1.41663 −0.708314 0.705898i \(-0.750544\pi\)
−0.708314 + 0.705898i \(0.750544\pi\)
\(968\) 52814.9 1.75365
\(969\) −53275.9 −1.76622
\(970\) −5023.29 −0.166276
\(971\) −10608.8 −0.350620 −0.175310 0.984513i \(-0.556093\pi\)
−0.175310 + 0.984513i \(0.556093\pi\)
\(972\) 683.986 0.0225709
\(973\) 31531.8 1.03892
\(974\) 14759.7 0.485555
\(975\) −5766.24 −0.189402
\(976\) −20234.4 −0.663614
\(977\) −45196.3 −1.48000 −0.739998 0.672609i \(-0.765174\pi\)
−0.739998 + 0.672609i \(0.765174\pi\)
\(978\) 12240.8 0.400222
\(979\) −79068.6 −2.58125
\(980\) −5314.17 −0.173219
\(981\) 6615.59 0.215311
\(982\) 2523.22 0.0819951
\(983\) 30853.1 1.00108 0.500540 0.865713i \(-0.333135\pi\)
0.500540 + 0.865713i \(0.333135\pi\)
\(984\) −9328.86 −0.302229
\(985\) −18284.6 −0.591469
\(986\) 7851.66 0.253598
\(987\) −19069.5 −0.614985
\(988\) 32322.3 1.04080
\(989\) 3372.10 0.108419
\(990\) 6041.08 0.193938
\(991\) 1333.81 0.0427547 0.0213774 0.999771i \(-0.493195\pi\)
0.0213774 + 0.999771i \(0.493195\pi\)
\(992\) −18320.9 −0.586381
\(993\) 14453.0 0.461884
\(994\) 30207.6 0.963912
\(995\) −17044.4 −0.543060
\(996\) 3078.12 0.0979257
\(997\) 41309.6 1.31222 0.656112 0.754664i \(-0.272200\pi\)
0.656112 + 0.754664i \(0.272200\pi\)
\(998\) −9231.41 −0.292801
\(999\) 8890.46 0.281563
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.1.3 7
3.2 odd 2 1305.4.a.n.1.5 7
5.4 even 2 2175.4.a.n.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.4.a.i.1.3 7 1.1 even 1 trivial
1305.4.a.n.1.5 7 3.2 odd 2
2175.4.a.n.1.5 7 5.4 even 2