Properties

Label 1849.4.a.c.1.6
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
Dimension $6$
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] = [1849,4,Mod(1,1849)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1849.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.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: \(109.094531601\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 32x^{4} - 16x^{3} + 251x^{2} + 276x + 60 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(4.31455\) of defining polynomial
Character \(\chi\) \(=\) 1849.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} -8.51910 q^{5} +23.5469 q^{6} -9.84502 q^{7} -16.6183 q^{8} +23.4681 q^{9} +O(q^{10})\) \(q+3.31455 q^{2} +7.10409 q^{3} +2.98627 q^{4} -8.51910 q^{5} +23.5469 q^{6} -9.84502 q^{7} -16.6183 q^{8} +23.4681 q^{9} -28.2370 q^{10} +0.597776 q^{11} +21.2147 q^{12} +34.9021 q^{13} -32.6318 q^{14} -60.5204 q^{15} -78.9723 q^{16} +91.3552 q^{17} +77.7863 q^{18} +24.0324 q^{19} -25.4403 q^{20} -69.9399 q^{21} +1.98136 q^{22} +127.719 q^{23} -118.058 q^{24} -52.4250 q^{25} +115.685 q^{26} -25.0908 q^{27} -29.3999 q^{28} -285.724 q^{29} -200.598 q^{30} -192.699 q^{31} -128.812 q^{32} +4.24666 q^{33} +302.802 q^{34} +83.8707 q^{35} +70.0821 q^{36} -363.399 q^{37} +79.6565 q^{38} +247.948 q^{39} +141.573 q^{40} +191.586 q^{41} -231.820 q^{42} +1.78512 q^{44} -199.927 q^{45} +423.330 q^{46} -458.267 q^{47} -561.027 q^{48} -246.076 q^{49} -173.765 q^{50} +648.995 q^{51} +104.227 q^{52} -583.068 q^{53} -83.1648 q^{54} -5.09252 q^{55} +163.607 q^{56} +170.728 q^{57} -947.047 q^{58} +416.589 q^{59} -180.730 q^{60} +30.9376 q^{61} -638.710 q^{62} -231.044 q^{63} +204.825 q^{64} -297.334 q^{65} +14.0758 q^{66} +16.1466 q^{67} +272.811 q^{68} +907.324 q^{69} +277.994 q^{70} +219.461 q^{71} -390.000 q^{72} -1031.07 q^{73} -1204.50 q^{74} -372.432 q^{75} +71.7670 q^{76} -5.88512 q^{77} +821.836 q^{78} +445.438 q^{79} +672.773 q^{80} -811.887 q^{81} +635.022 q^{82} +298.511 q^{83} -208.859 q^{84} -778.264 q^{85} -2029.81 q^{87} -9.93402 q^{88} -846.185 q^{89} -662.669 q^{90} -343.612 q^{91} +381.402 q^{92} -1368.95 q^{93} -1518.95 q^{94} -204.734 q^{95} -915.091 q^{96} -259.068 q^{97} -815.631 q^{98} +14.0287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} - 7 q^{3} + 22 q^{4} - 43 q^{5} - 3 q^{6} - 8 q^{7} - 54 q^{8} + 81 q^{9} + 57 q^{10} - 28 q^{11} + 157 q^{12} + 56 q^{13} - 184 q^{14} - 124 q^{15} - 54 q^{16} + 19 q^{17} + 81 q^{18} + 75 q^{19} - 135 q^{20} - 18 q^{21} + 504 q^{22} + 131 q^{23} - 567 q^{24} + 105 q^{25} - 44 q^{26} - 238 q^{27} + 404 q^{28} - 515 q^{29} + 396 q^{30} + 237 q^{31} - 558 q^{32} - 540 q^{33} + 107 q^{34} + 198 q^{35} + 73 q^{36} - 269 q^{37} + 527 q^{38} - 290 q^{39} + 613 q^{40} + 471 q^{41} - 362 q^{42} - 428 q^{44} - 334 q^{45} + 67 q^{46} + 415 q^{47} + 989 q^{48} + 350 q^{49} - 1335 q^{50} + 1241 q^{51} - 8 q^{52} + 450 q^{53} + 402 q^{54} + 1732 q^{55} - 780 q^{56} - 1000 q^{57} - 1055 q^{58} + 356 q^{59} - 2732 q^{60} + 1328 q^{61} - 1603 q^{62} + 2290 q^{63} + 466 q^{64} + 62 q^{65} + 156 q^{66} - 632 q^{67} + 571 q^{68} + 1130 q^{69} + 1902 q^{70} + 144 q^{71} - 567 q^{72} - 864 q^{73} + 1207 q^{74} + 2494 q^{75} - 1005 q^{76} - 2660 q^{77} + 2222 q^{78} - 1613 q^{79} - 2399 q^{80} - 102 q^{81} - 1673 q^{82} - 682 q^{83} + 3758 q^{84} - 84 q^{85} + 449 q^{87} + 608 q^{88} - 3378 q^{89} + 930 q^{90} + 3900 q^{91} + 3491 q^{92} - 1879 q^{93} - 3197 q^{94} - 79 q^{95} - 591 q^{96} - 55 q^{97} - 2398 q^{98} - 1612 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.31455 1.17187 0.585936 0.810357i \(-0.300727\pi\)
0.585936 + 0.810357i \(0.300727\pi\)
\(3\) 7.10409 1.36718 0.683592 0.729865i \(-0.260417\pi\)
0.683592 + 0.729865i \(0.260417\pi\)
\(4\) 2.98627 0.373283
\(5\) −8.51910 −0.761971 −0.380986 0.924581i \(-0.624415\pi\)
−0.380986 + 0.924581i \(0.624415\pi\)
\(6\) 23.5469 1.60216
\(7\) −9.84502 −0.531581 −0.265791 0.964031i \(-0.585633\pi\)
−0.265791 + 0.964031i \(0.585633\pi\)
\(8\) −16.6183 −0.734432
\(9\) 23.4681 0.869190
\(10\) −28.2370 −0.892933
\(11\) 0.597776 0.0163851 0.00819256 0.999966i \(-0.497392\pi\)
0.00819256 + 0.999966i \(0.497392\pi\)
\(12\) 21.2147 0.510347
\(13\) 34.9021 0.744623 0.372311 0.928108i \(-0.378565\pi\)
0.372311 + 0.928108i \(0.378565\pi\)
\(14\) −32.6318 −0.622945
\(15\) −60.5204 −1.04175
\(16\) −78.9723 −1.23394
\(17\) 91.3552 1.30335 0.651673 0.758500i \(-0.274067\pi\)
0.651673 + 0.758500i \(0.274067\pi\)
\(18\) 77.7863 1.01858
\(19\) 24.0324 0.290179 0.145089 0.989419i \(-0.453653\pi\)
0.145089 + 0.989419i \(0.453653\pi\)
\(20\) −25.4403 −0.284431
\(21\) −69.9399 −0.726769
\(22\) 1.98136 0.0192013
\(23\) 127.719 1.15788 0.578938 0.815371i \(-0.303467\pi\)
0.578938 + 0.815371i \(0.303467\pi\)
\(24\) −118.058 −1.00410
\(25\) −52.4250 −0.419400
\(26\) 115.685 0.872602
\(27\) −25.0908 −0.178842
\(28\) −29.3999 −0.198430
\(29\) −285.724 −1.82957 −0.914786 0.403939i \(-0.867641\pi\)
−0.914786 + 0.403939i \(0.867641\pi\)
\(30\) −200.598 −1.22080
\(31\) −192.699 −1.11644 −0.558221 0.829692i \(-0.688516\pi\)
−0.558221 + 0.829692i \(0.688516\pi\)
\(32\) −128.812 −0.711591
\(33\) 4.24666 0.0224015
\(34\) 302.802 1.52735
\(35\) 83.8707 0.405050
\(36\) 70.0821 0.324454
\(37\) −363.399 −1.61466 −0.807329 0.590101i \(-0.799088\pi\)
−0.807329 + 0.590101i \(0.799088\pi\)
\(38\) 79.6565 0.340053
\(39\) 247.948 1.01804
\(40\) 141.573 0.559616
\(41\) 191.586 0.729774 0.364887 0.931052i \(-0.381108\pi\)
0.364887 + 0.931052i \(0.381108\pi\)
\(42\) −231.820 −0.851680
\(43\) 0 0
\(44\) 1.78512 0.00611629
\(45\) −199.927 −0.662297
\(46\) 423.330 1.35688
\(47\) −458.267 −1.42223 −0.711117 0.703073i \(-0.751811\pi\)
−0.711117 + 0.703073i \(0.751811\pi\)
\(48\) −561.027 −1.68703
\(49\) −246.076 −0.717422
\(50\) −173.765 −0.491483
\(51\) 648.995 1.78191
\(52\) 104.227 0.277955
\(53\) −583.068 −1.51114 −0.755572 0.655066i \(-0.772641\pi\)
−0.755572 + 0.655066i \(0.772641\pi\)
\(54\) −83.1648 −0.209580
\(55\) −5.09252 −0.0124850
\(56\) 163.607 0.390410
\(57\) 170.728 0.396728
\(58\) −947.047 −2.14402
\(59\) 416.589 0.919243 0.459621 0.888115i \(-0.347985\pi\)
0.459621 + 0.888115i \(0.347985\pi\)
\(60\) −180.730 −0.388869
\(61\) 30.9376 0.0649369 0.0324685 0.999473i \(-0.489663\pi\)
0.0324685 + 0.999473i \(0.489663\pi\)
\(62\) −638.710 −1.30833
\(63\) −231.044 −0.462045
\(64\) 204.825 0.400049
\(65\) −297.334 −0.567381
\(66\) 14.0758 0.0262516
\(67\) 16.1466 0.0294421 0.0147210 0.999892i \(-0.495314\pi\)
0.0147210 + 0.999892i \(0.495314\pi\)
\(68\) 272.811 0.486517
\(69\) 907.324 1.58303
\(70\) 277.994 0.474666
\(71\) 219.461 0.366835 0.183418 0.983035i \(-0.441284\pi\)
0.183418 + 0.983035i \(0.441284\pi\)
\(72\) −390.000 −0.638360
\(73\) −1031.07 −1.65311 −0.826557 0.562853i \(-0.809704\pi\)
−0.826557 + 0.562853i \(0.809704\pi\)
\(74\) −1204.50 −1.89217
\(75\) −372.432 −0.573396
\(76\) 71.7670 0.108319
\(77\) −5.88512 −0.00871002
\(78\) 821.836 1.19301
\(79\) 445.438 0.634375 0.317188 0.948363i \(-0.397262\pi\)
0.317188 + 0.948363i \(0.397262\pi\)
\(80\) 672.773 0.940229
\(81\) −811.887 −1.11370
\(82\) 635.022 0.855201
\(83\) 298.511 0.394769 0.197384 0.980326i \(-0.436755\pi\)
0.197384 + 0.980326i \(0.436755\pi\)
\(84\) −208.859 −0.271291
\(85\) −778.264 −0.993112
\(86\) 0 0
\(87\) −2029.81 −2.50136
\(88\) −9.93402 −0.0120338
\(89\) −846.185 −1.00781 −0.503907 0.863758i \(-0.668105\pi\)
−0.503907 + 0.863758i \(0.668105\pi\)
\(90\) −662.669 −0.776128
\(91\) −343.612 −0.395827
\(92\) 381.402 0.432216
\(93\) −1368.95 −1.52638
\(94\) −1518.95 −1.66668
\(95\) −204.734 −0.221108
\(96\) −915.091 −0.972876
\(97\) −259.068 −0.271179 −0.135590 0.990765i \(-0.543293\pi\)
−0.135590 + 0.990765i \(0.543293\pi\)
\(98\) −815.631 −0.840726
\(99\) 14.0287 0.0142418
\(100\) −156.555 −0.156555
\(101\) −1182.01 −1.16450 −0.582252 0.813009i \(-0.697828\pi\)
−0.582252 + 0.813009i \(0.697828\pi\)
\(102\) 2151.13 2.08817
\(103\) 319.565 0.305706 0.152853 0.988249i \(-0.451154\pi\)
0.152853 + 0.988249i \(0.451154\pi\)
\(104\) −580.013 −0.546874
\(105\) 595.825 0.553777
\(106\) −1932.61 −1.77087
\(107\) 1647.14 1.48818 0.744089 0.668081i \(-0.232884\pi\)
0.744089 + 0.668081i \(0.232884\pi\)
\(108\) −74.9279 −0.0667587
\(109\) −560.538 −0.492567 −0.246283 0.969198i \(-0.579209\pi\)
−0.246283 + 0.969198i \(0.579209\pi\)
\(110\) −16.8794 −0.0146308
\(111\) −2581.62 −2.20753
\(112\) 777.484 0.655941
\(113\) 65.6852 0.0546827 0.0273414 0.999626i \(-0.491296\pi\)
0.0273414 + 0.999626i \(0.491296\pi\)
\(114\) 565.887 0.464914
\(115\) −1088.05 −0.882269
\(116\) −853.248 −0.682949
\(117\) 819.086 0.647218
\(118\) 1380.81 1.07723
\(119\) −899.393 −0.692834
\(120\) 1005.75 0.765097
\(121\) −1330.64 −0.999732
\(122\) 102.544 0.0760977
\(123\) 1361.05 0.997734
\(124\) −575.450 −0.416749
\(125\) 1511.50 1.08154
\(126\) −765.808 −0.541457
\(127\) −1906.92 −1.33238 −0.666189 0.745783i \(-0.732076\pi\)
−0.666189 + 0.745783i \(0.732076\pi\)
\(128\) 1709.40 1.18040
\(129\) 0 0
\(130\) −985.530 −0.664898
\(131\) 1536.09 1.02449 0.512246 0.858839i \(-0.328814\pi\)
0.512246 + 0.858839i \(0.328814\pi\)
\(132\) 12.6817 0.00836209
\(133\) −236.599 −0.154254
\(134\) 53.5187 0.0345023
\(135\) 213.751 0.136272
\(136\) −1518.17 −0.957218
\(137\) 1695.38 1.05727 0.528634 0.848850i \(-0.322704\pi\)
0.528634 + 0.848850i \(0.322704\pi\)
\(138\) 3007.38 1.85511
\(139\) 947.580 0.578221 0.289110 0.957296i \(-0.406641\pi\)
0.289110 + 0.957296i \(0.406641\pi\)
\(140\) 250.460 0.151198
\(141\) −3255.57 −1.94446
\(142\) 727.417 0.429884
\(143\) 20.8636 0.0122007
\(144\) −1853.33 −1.07253
\(145\) 2434.11 1.39408
\(146\) −3417.53 −1.93724
\(147\) −1748.14 −0.980847
\(148\) −1085.21 −0.602725
\(149\) −3084.10 −1.69570 −0.847850 0.530236i \(-0.822103\pi\)
−0.847850 + 0.530236i \(0.822103\pi\)
\(150\) −1234.45 −0.671947
\(151\) 2346.83 1.26478 0.632391 0.774649i \(-0.282074\pi\)
0.632391 + 0.774649i \(0.282074\pi\)
\(152\) −399.377 −0.213117
\(153\) 2143.93 1.13285
\(154\) −19.5066 −0.0102070
\(155\) 1641.62 0.850697
\(156\) 740.438 0.380016
\(157\) −1582.73 −0.804556 −0.402278 0.915517i \(-0.631782\pi\)
−0.402278 + 0.915517i \(0.631782\pi\)
\(158\) 1476.43 0.743406
\(159\) −4142.17 −2.06601
\(160\) 1097.36 0.542212
\(161\) −1257.39 −0.615505
\(162\) −2691.04 −1.30511
\(163\) 820.887 0.394459 0.197229 0.980357i \(-0.436806\pi\)
0.197229 + 0.980357i \(0.436806\pi\)
\(164\) 572.127 0.272412
\(165\) −36.1777 −0.0170693
\(166\) 989.430 0.462618
\(167\) 1690.58 0.783358 0.391679 0.920102i \(-0.371894\pi\)
0.391679 + 0.920102i \(0.371894\pi\)
\(168\) 1162.28 0.533762
\(169\) −978.845 −0.445537
\(170\) −2579.60 −1.16380
\(171\) 563.994 0.252221
\(172\) 0 0
\(173\) 1390.24 0.610973 0.305486 0.952196i \(-0.401181\pi\)
0.305486 + 0.952196i \(0.401181\pi\)
\(174\) −6727.91 −2.93127
\(175\) 516.125 0.222945
\(176\) −47.2078 −0.0202183
\(177\) 2959.49 1.25677
\(178\) −2804.73 −1.18103
\(179\) −693.895 −0.289744 −0.144872 0.989450i \(-0.546277\pi\)
−0.144872 + 0.989450i \(0.546277\pi\)
\(180\) −597.036 −0.247225
\(181\) −2355.50 −0.967309 −0.483655 0.875259i \(-0.660691\pi\)
−0.483655 + 0.875259i \(0.660691\pi\)
\(182\) −1138.92 −0.463859
\(183\) 219.783 0.0887807
\(184\) −2122.46 −0.850381
\(185\) 3095.83 1.23032
\(186\) −4537.46 −1.78872
\(187\) 54.6100 0.0213555
\(188\) −1368.51 −0.530897
\(189\) 247.020 0.0950689
\(190\) −678.602 −0.259110
\(191\) 2168.09 0.821349 0.410674 0.911782i \(-0.365293\pi\)
0.410674 + 0.911782i \(0.365293\pi\)
\(192\) 1455.10 0.546940
\(193\) 1305.00 0.486717 0.243358 0.969936i \(-0.421751\pi\)
0.243358 + 0.969936i \(0.421751\pi\)
\(194\) −858.695 −0.317787
\(195\) −2112.29 −0.775714
\(196\) −734.847 −0.267802
\(197\) −4800.27 −1.73607 −0.868033 0.496507i \(-0.834616\pi\)
−0.868033 + 0.496507i \(0.834616\pi\)
\(198\) 46.4988 0.0166895
\(199\) 2113.34 0.752816 0.376408 0.926454i \(-0.377159\pi\)
0.376408 + 0.926454i \(0.377159\pi\)
\(200\) 871.213 0.308020
\(201\) 114.707 0.0402527
\(202\) −3917.85 −1.36465
\(203\) 2812.96 0.972566
\(204\) 1938.07 0.665158
\(205\) −1632.14 −0.556067
\(206\) 1059.22 0.358248
\(207\) 2997.31 1.00641
\(208\) −2756.30 −0.918822
\(209\) 14.3660 0.00475462
\(210\) 1974.89 0.648955
\(211\) −5564.31 −1.81546 −0.907732 0.419551i \(-0.862188\pi\)
−0.907732 + 0.419551i \(0.862188\pi\)
\(212\) −1741.20 −0.564085
\(213\) 1559.07 0.501531
\(214\) 5459.53 1.74395
\(215\) 0 0
\(216\) 416.966 0.131347
\(217\) 1897.12 0.593480
\(218\) −1857.93 −0.577225
\(219\) −7324.80 −2.26011
\(220\) −15.2076 −0.00466044
\(221\) 3188.49 0.970501
\(222\) −8556.91 −2.58695
\(223\) 1709.75 0.513422 0.256711 0.966488i \(-0.417361\pi\)
0.256711 + 0.966488i \(0.417361\pi\)
\(224\) 1268.15 0.378268
\(225\) −1230.32 −0.364538
\(226\) 217.717 0.0640811
\(227\) −347.506 −0.101607 −0.0508035 0.998709i \(-0.516178\pi\)
−0.0508035 + 0.998709i \(0.516178\pi\)
\(228\) 509.840 0.148092
\(229\) 713.508 0.205895 0.102947 0.994687i \(-0.467173\pi\)
0.102947 + 0.994687i \(0.467173\pi\)
\(230\) −3606.39 −1.03391
\(231\) −41.8084 −0.0119082
\(232\) 4748.24 1.34370
\(233\) 6539.93 1.83882 0.919410 0.393300i \(-0.128667\pi\)
0.919410 + 0.393300i \(0.128667\pi\)
\(234\) 2714.91 0.758457
\(235\) 3904.02 1.08370
\(236\) 1244.05 0.343138
\(237\) 3164.43 0.867307
\(238\) −2981.09 −0.811913
\(239\) −2561.41 −0.693238 −0.346619 0.938006i \(-0.612670\pi\)
−0.346619 + 0.938006i \(0.612670\pi\)
\(240\) 4779.44 1.28547
\(241\) 4656.80 1.24469 0.622346 0.782742i \(-0.286180\pi\)
0.622346 + 0.782742i \(0.286180\pi\)
\(242\) −4410.49 −1.17156
\(243\) −5090.27 −1.34379
\(244\) 92.3879 0.0242399
\(245\) 2096.34 0.546655
\(246\) 4511.26 1.16922
\(247\) 838.779 0.216074
\(248\) 3202.32 0.819950
\(249\) 2120.65 0.539721
\(250\) 5009.95 1.26743
\(251\) 6104.04 1.53499 0.767497 0.641053i \(-0.221502\pi\)
0.767497 + 0.641053i \(0.221502\pi\)
\(252\) −689.959 −0.172474
\(253\) 76.3471 0.0189720
\(254\) −6320.60 −1.56138
\(255\) −5528.86 −1.35777
\(256\) 4027.29 0.983225
\(257\) −682.439 −0.165640 −0.0828199 0.996565i \(-0.526393\pi\)
−0.0828199 + 0.996565i \(0.526393\pi\)
\(258\) 0 0
\(259\) 3577.67 0.858322
\(260\) −887.919 −0.211794
\(261\) −6705.40 −1.59024
\(262\) 5091.44 1.20057
\(263\) −1671.87 −0.391984 −0.195992 0.980605i \(-0.562793\pi\)
−0.195992 + 0.980605i \(0.562793\pi\)
\(264\) −70.5722 −0.0164523
\(265\) 4967.22 1.15145
\(266\) −784.220 −0.180766
\(267\) −6011.38 −1.37787
\(268\) 48.2180 0.0109902
\(269\) −261.999 −0.0593843 −0.0296921 0.999559i \(-0.509453\pi\)
−0.0296921 + 0.999559i \(0.509453\pi\)
\(270\) 708.489 0.159694
\(271\) 4620.04 1.03560 0.517800 0.855502i \(-0.326751\pi\)
0.517800 + 0.855502i \(0.326751\pi\)
\(272\) −7214.53 −1.60825
\(273\) −2441.05 −0.541168
\(274\) 5619.41 1.23898
\(275\) −31.3384 −0.00687192
\(276\) 2709.51 0.590918
\(277\) −5163.93 −1.12011 −0.560055 0.828456i \(-0.689220\pi\)
−0.560055 + 0.828456i \(0.689220\pi\)
\(278\) 3140.81 0.677601
\(279\) −4522.28 −0.970400
\(280\) −1393.79 −0.297481
\(281\) −5275.67 −1.12000 −0.560000 0.828493i \(-0.689199\pi\)
−0.560000 + 0.828493i \(0.689199\pi\)
\(282\) −10790.8 −2.27865
\(283\) −5028.34 −1.05620 −0.528098 0.849183i \(-0.677095\pi\)
−0.528098 + 0.849183i \(0.677095\pi\)
\(284\) 655.371 0.136933
\(285\) −1454.45 −0.302295
\(286\) 69.1537 0.0142977
\(287\) −1886.17 −0.387934
\(288\) −3022.97 −0.618508
\(289\) 3432.77 0.698711
\(290\) 8067.99 1.63368
\(291\) −1840.44 −0.370751
\(292\) −3079.04 −0.617080
\(293\) 8840.69 1.76273 0.881363 0.472439i \(-0.156626\pi\)
0.881363 + 0.472439i \(0.156626\pi\)
\(294\) −5794.32 −1.14943
\(295\) −3548.96 −0.700436
\(296\) 6039.06 1.18586
\(297\) −14.9987 −0.00293035
\(298\) −10222.4 −1.98714
\(299\) 4457.64 0.862181
\(300\) −1112.18 −0.214039
\(301\) 0 0
\(302\) 7778.68 1.48216
\(303\) −8397.14 −1.59209
\(304\) −1897.89 −0.358064
\(305\) −263.560 −0.0494801
\(306\) 7106.18 1.32756
\(307\) 6565.15 1.22050 0.610249 0.792209i \(-0.291069\pi\)
0.610249 + 0.792209i \(0.291069\pi\)
\(308\) −17.5745 −0.00325131
\(309\) 2270.22 0.417956
\(310\) 5441.23 0.996908
\(311\) 1250.31 0.227969 0.113985 0.993483i \(-0.463639\pi\)
0.113985 + 0.993483i \(0.463639\pi\)
\(312\) −4120.46 −0.747677
\(313\) 2968.85 0.536132 0.268066 0.963401i \(-0.413615\pi\)
0.268066 + 0.963401i \(0.413615\pi\)
\(314\) −5246.03 −0.942837
\(315\) 1968.29 0.352065
\(316\) 1330.20 0.236802
\(317\) 1054.32 0.186803 0.0934013 0.995629i \(-0.470226\pi\)
0.0934013 + 0.995629i \(0.470226\pi\)
\(318\) −13729.4 −2.42110
\(319\) −170.799 −0.0299778
\(320\) −1744.93 −0.304826
\(321\) 11701.4 2.03461
\(322\) −4167.69 −0.721293
\(323\) 2195.48 0.378204
\(324\) −2424.51 −0.415725
\(325\) −1829.74 −0.312295
\(326\) 2720.87 0.462255
\(327\) −3982.11 −0.673429
\(328\) −3183.83 −0.535969
\(329\) 4511.64 0.756033
\(330\) −119.913 −0.0200030
\(331\) 2881.73 0.478532 0.239266 0.970954i \(-0.423093\pi\)
0.239266 + 0.970954i \(0.423093\pi\)
\(332\) 891.432 0.147361
\(333\) −8528.28 −1.40344
\(334\) 5603.51 0.917995
\(335\) −137.554 −0.0224340
\(336\) 5523.32 0.896791
\(337\) −6147.77 −0.993740 −0.496870 0.867825i \(-0.665517\pi\)
−0.496870 + 0.867825i \(0.665517\pi\)
\(338\) −3244.43 −0.522112
\(339\) 466.634 0.0747613
\(340\) −2324.10 −0.370712
\(341\) −115.191 −0.0182930
\(342\) 1869.39 0.295570
\(343\) 5799.46 0.912949
\(344\) 0 0
\(345\) −7729.58 −1.20622
\(346\) 4608.04 0.715982
\(347\) −1404.42 −0.217271 −0.108636 0.994082i \(-0.534648\pi\)
−0.108636 + 0.994082i \(0.534648\pi\)
\(348\) −6061.55 −0.933716
\(349\) 4472.14 0.685926 0.342963 0.939349i \(-0.388570\pi\)
0.342963 + 0.939349i \(0.388570\pi\)
\(350\) 1710.72 0.261263
\(351\) −875.721 −0.133170
\(352\) −77.0007 −0.0116595
\(353\) 2146.48 0.323642 0.161821 0.986820i \(-0.448263\pi\)
0.161821 + 0.986820i \(0.448263\pi\)
\(354\) 9809.38 1.47278
\(355\) −1869.61 −0.279518
\(356\) −2526.93 −0.376200
\(357\) −6389.37 −0.947231
\(358\) −2299.95 −0.339543
\(359\) 1960.49 0.288219 0.144109 0.989562i \(-0.453968\pi\)
0.144109 + 0.989562i \(0.453968\pi\)
\(360\) 3322.45 0.486412
\(361\) −6281.45 −0.915796
\(362\) −7807.43 −1.13356
\(363\) −9453.01 −1.36682
\(364\) −1026.12 −0.147756
\(365\) 8783.77 1.25963
\(366\) 728.484 0.104040
\(367\) 13485.2 1.91804 0.959021 0.283337i \(-0.0914414\pi\)
0.959021 + 0.283337i \(0.0914414\pi\)
\(368\) −10086.2 −1.42875
\(369\) 4496.16 0.634312
\(370\) 10261.3 1.44178
\(371\) 5740.32 0.803295
\(372\) −4088.05 −0.569773
\(373\) 12034.5 1.67057 0.835285 0.549817i \(-0.185303\pi\)
0.835285 + 0.549817i \(0.185303\pi\)
\(374\) 181.008 0.0250259
\(375\) 10737.8 1.47867
\(376\) 7615.60 1.04453
\(377\) −9972.36 −1.36234
\(378\) 818.760 0.111409
\(379\) −10185.1 −1.38041 −0.690204 0.723615i \(-0.742479\pi\)
−0.690204 + 0.723615i \(0.742479\pi\)
\(380\) −611.390 −0.0825359
\(381\) −13546.9 −1.82160
\(382\) 7186.26 0.962515
\(383\) −13508.3 −1.80219 −0.901097 0.433618i \(-0.857237\pi\)
−0.901097 + 0.433618i \(0.857237\pi\)
\(384\) 12143.7 1.61382
\(385\) 50.1359 0.00663679
\(386\) 4325.51 0.570369
\(387\) 0 0
\(388\) −773.646 −0.101227
\(389\) 6651.52 0.866954 0.433477 0.901165i \(-0.357286\pi\)
0.433477 + 0.901165i \(0.357286\pi\)
\(390\) −7001.30 −0.909037
\(391\) 11667.7 1.50911
\(392\) 4089.35 0.526897
\(393\) 10912.5 1.40067
\(394\) −15910.7 −2.03445
\(395\) −3794.73 −0.483376
\(396\) 41.8934 0.00531622
\(397\) −8308.29 −1.05033 −0.525165 0.851000i \(-0.675996\pi\)
−0.525165 + 0.851000i \(0.675996\pi\)
\(398\) 7004.77 0.882204
\(399\) −1680.82 −0.210893
\(400\) 4140.12 0.517515
\(401\) 2963.57 0.369061 0.184530 0.982827i \(-0.440924\pi\)
0.184530 + 0.982827i \(0.440924\pi\)
\(402\) 380.202 0.0471710
\(403\) −6725.59 −0.831328
\(404\) −3529.81 −0.434690
\(405\) 6916.54 0.848607
\(406\) 9323.70 1.13972
\(407\) −217.231 −0.0264564
\(408\) −10785.2 −1.30869
\(409\) 9951.28 1.20308 0.601540 0.798843i \(-0.294554\pi\)
0.601540 + 0.798843i \(0.294554\pi\)
\(410\) −5409.82 −0.651639
\(411\) 12044.1 1.44548
\(412\) 954.308 0.114115
\(413\) −4101.33 −0.488652
\(414\) 9934.76 1.17939
\(415\) −2543.04 −0.300802
\(416\) −4495.80 −0.529867
\(417\) 6731.70 0.790534
\(418\) 47.6168 0.00557180
\(419\) −5281.70 −0.615818 −0.307909 0.951416i \(-0.599629\pi\)
−0.307909 + 0.951416i \(0.599629\pi\)
\(420\) 1779.29 0.206716
\(421\) 1668.54 0.193159 0.0965795 0.995325i \(-0.469210\pi\)
0.0965795 + 0.995325i \(0.469210\pi\)
\(422\) −18443.2 −2.12749
\(423\) −10754.7 −1.23619
\(424\) 9689.60 1.10983
\(425\) −4789.29 −0.546623
\(426\) 5167.64 0.587730
\(427\) −304.581 −0.0345192
\(428\) 4918.80 0.555512
\(429\) 148.217 0.0166806
\(430\) 0 0
\(431\) −10348.7 −1.15657 −0.578284 0.815835i \(-0.696278\pi\)
−0.578284 + 0.815835i \(0.696278\pi\)
\(432\) 1981.48 0.220681
\(433\) −2968.27 −0.329436 −0.164718 0.986341i \(-0.552671\pi\)
−0.164718 + 0.986341i \(0.552671\pi\)
\(434\) 6288.12 0.695482
\(435\) 17292.1 1.90596
\(436\) −1673.91 −0.183867
\(437\) 3069.38 0.335991
\(438\) −24278.4 −2.64856
\(439\) −9224.53 −1.00288 −0.501438 0.865194i \(-0.667196\pi\)
−0.501438 + 0.865194i \(0.667196\pi\)
\(440\) 84.6289 0.00916937
\(441\) −5774.93 −0.623575
\(442\) 10568.4 1.13730
\(443\) −10115.5 −1.08488 −0.542438 0.840096i \(-0.682499\pi\)
−0.542438 + 0.840096i \(0.682499\pi\)
\(444\) −7709.40 −0.824036
\(445\) 7208.73 0.767925
\(446\) 5667.05 0.601665
\(447\) −21909.7 −2.31833
\(448\) −2016.51 −0.212659
\(449\) −14386.0 −1.51207 −0.756034 0.654532i \(-0.772866\pi\)
−0.756034 + 0.654532i \(0.772866\pi\)
\(450\) −4077.95 −0.427192
\(451\) 114.526 0.0119574
\(452\) 196.154 0.0204121
\(453\) 16672.1 1.72919
\(454\) −1151.83 −0.119070
\(455\) 2927.26 0.301609
\(456\) −2837.21 −0.291369
\(457\) 10031.8 1.02684 0.513421 0.858137i \(-0.328378\pi\)
0.513421 + 0.858137i \(0.328378\pi\)
\(458\) 2364.96 0.241282
\(459\) −2292.18 −0.233093
\(460\) −3249.20 −0.329336
\(461\) −124.788 −0.0126072 −0.00630362 0.999980i \(-0.502007\pi\)
−0.00630362 + 0.999980i \(0.502007\pi\)
\(462\) −138.576 −0.0139549
\(463\) −15438.9 −1.54969 −0.774847 0.632148i \(-0.782173\pi\)
−0.774847 + 0.632148i \(0.782173\pi\)
\(464\) 22564.3 2.25759
\(465\) 11662.2 1.16306
\(466\) 21677.0 2.15486
\(467\) 12014.7 1.19052 0.595259 0.803534i \(-0.297049\pi\)
0.595259 + 0.803534i \(0.297049\pi\)
\(468\) 2446.01 0.241596
\(469\) −158.963 −0.0156508
\(470\) 12940.1 1.26996
\(471\) −11243.8 −1.09998
\(472\) −6923.00 −0.675121
\(473\) 0 0
\(474\) 10488.7 1.01637
\(475\) −1259.90 −0.121701
\(476\) −2685.83 −0.258623
\(477\) −13683.5 −1.31347
\(478\) −8489.93 −0.812386
\(479\) 6241.39 0.595358 0.297679 0.954666i \(-0.403788\pi\)
0.297679 + 0.954666i \(0.403788\pi\)
\(480\) 7795.75 0.741303
\(481\) −12683.4 −1.20231
\(482\) 15435.2 1.45862
\(483\) −8932.63 −0.841508
\(484\) −3973.65 −0.373183
\(485\) 2207.03 0.206631
\(486\) −16872.0 −1.57475
\(487\) 924.180 0.0859930 0.0429965 0.999075i \(-0.486310\pi\)
0.0429965 + 0.999075i \(0.486310\pi\)
\(488\) −514.130 −0.0476917
\(489\) 5831.65 0.539297
\(490\) 6948.44 0.640609
\(491\) 7044.15 0.647451 0.323725 0.946151i \(-0.395065\pi\)
0.323725 + 0.946151i \(0.395065\pi\)
\(492\) 4064.44 0.372438
\(493\) −26102.3 −2.38457
\(494\) 2780.18 0.253211
\(495\) −119.512 −0.0108518
\(496\) 15217.9 1.37763
\(497\) −2160.60 −0.195003
\(498\) 7029.00 0.632484
\(499\) 3981.76 0.357210 0.178605 0.983921i \(-0.442842\pi\)
0.178605 + 0.983921i \(0.442842\pi\)
\(500\) 4513.74 0.403722
\(501\) 12010.0 1.07099
\(502\) 20232.2 1.79882
\(503\) 11650.2 1.03272 0.516358 0.856373i \(-0.327288\pi\)
0.516358 + 0.856373i \(0.327288\pi\)
\(504\) 3839.56 0.339340
\(505\) 10069.7 0.887318
\(506\) 253.057 0.0222327
\(507\) −6953.80 −0.609131
\(508\) −5694.58 −0.497354
\(509\) 11408.7 0.993481 0.496740 0.867899i \(-0.334530\pi\)
0.496740 + 0.867899i \(0.334530\pi\)
\(510\) −18325.7 −1.59113
\(511\) 10150.9 0.878764
\(512\) −326.513 −0.0281836
\(513\) −602.991 −0.0518961
\(514\) −2261.98 −0.194108
\(515\) −2722.41 −0.232939
\(516\) 0 0
\(517\) −273.941 −0.0233035
\(518\) 11858.4 1.00584
\(519\) 9876.42 0.835312
\(520\) 4941.19 0.416703
\(521\) −15272.4 −1.28425 −0.642127 0.766598i \(-0.721948\pi\)
−0.642127 + 0.766598i \(0.721948\pi\)
\(522\) −22225.4 −1.86356
\(523\) 20831.4 1.74167 0.870835 0.491575i \(-0.163579\pi\)
0.870835 + 0.491575i \(0.163579\pi\)
\(524\) 4587.16 0.382426
\(525\) 3666.60 0.304807
\(526\) −5541.50 −0.459355
\(527\) −17604.0 −1.45511
\(528\) −335.369 −0.0276421
\(529\) 4145.03 0.340678
\(530\) 16464.1 1.34935
\(531\) 9776.57 0.798996
\(532\) −706.548 −0.0575803
\(533\) 6686.75 0.543406
\(534\) −19925.0 −1.61468
\(535\) −14032.1 −1.13395
\(536\) −268.328 −0.0216232
\(537\) −4929.50 −0.396133
\(538\) −868.410 −0.0695907
\(539\) −147.098 −0.0117550
\(540\) 638.318 0.0508682
\(541\) −1411.76 −0.112192 −0.0560962 0.998425i \(-0.517865\pi\)
−0.0560962 + 0.998425i \(0.517865\pi\)
\(542\) 15313.4 1.21359
\(543\) −16733.7 −1.32249
\(544\) −11767.6 −0.927450
\(545\) 4775.27 0.375322
\(546\) −8090.99 −0.634180
\(547\) −328.281 −0.0256605 −0.0128302 0.999918i \(-0.504084\pi\)
−0.0128302 + 0.999918i \(0.504084\pi\)
\(548\) 5062.84 0.394661
\(549\) 726.047 0.0564425
\(550\) −103.873 −0.00805301
\(551\) −6866.62 −0.530903
\(552\) −15078.2 −1.16263
\(553\) −4385.34 −0.337222
\(554\) −17116.1 −1.31262
\(555\) 21993.1 1.68208
\(556\) 2829.73 0.215840
\(557\) −1908.49 −0.145180 −0.0725901 0.997362i \(-0.523126\pi\)
−0.0725901 + 0.997362i \(0.523126\pi\)
\(558\) −14989.3 −1.13718
\(559\) 0 0
\(560\) −6623.46 −0.499808
\(561\) 387.954 0.0291969
\(562\) −17486.5 −1.31250
\(563\) 3413.23 0.255507 0.127753 0.991806i \(-0.459223\pi\)
0.127753 + 0.991806i \(0.459223\pi\)
\(564\) −9721.99 −0.725833
\(565\) −559.579 −0.0416667
\(566\) −16666.7 −1.23773
\(567\) 7993.04 0.592021
\(568\) −3647.07 −0.269415
\(569\) −15405.8 −1.13505 −0.567527 0.823355i \(-0.692100\pi\)
−0.567527 + 0.823355i \(0.692100\pi\)
\(570\) −4820.85 −0.354251
\(571\) −18819.2 −1.37926 −0.689632 0.724160i \(-0.742228\pi\)
−0.689632 + 0.724160i \(0.742228\pi\)
\(572\) 62.3044 0.00455433
\(573\) 15402.3 1.12293
\(574\) −6251.81 −0.454609
\(575\) −6695.64 −0.485613
\(576\) 4806.86 0.347719
\(577\) −8098.53 −0.584309 −0.292154 0.956371i \(-0.594372\pi\)
−0.292154 + 0.956371i \(0.594372\pi\)
\(578\) 11378.1 0.818799
\(579\) 9270.87 0.665431
\(580\) 7268.90 0.520387
\(581\) −2938.84 −0.209852
\(582\) −6100.25 −0.434473
\(583\) −348.545 −0.0247603
\(584\) 17134.6 1.21410
\(585\) −6977.87 −0.493162
\(586\) 29303.0 2.06569
\(587\) 3631.44 0.255342 0.127671 0.991817i \(-0.459250\pi\)
0.127671 + 0.991817i \(0.459250\pi\)
\(588\) −5220.42 −0.366134
\(589\) −4631.00 −0.323968
\(590\) −11763.2 −0.820822
\(591\) −34101.5 −2.37352
\(592\) 28698.4 1.99240
\(593\) 14298.2 0.990147 0.495073 0.868851i \(-0.335141\pi\)
0.495073 + 0.868851i \(0.335141\pi\)
\(594\) −49.7140 −0.00343399
\(595\) 7662.02 0.527920
\(596\) −9209.95 −0.632977
\(597\) 15013.3 1.02924
\(598\) 14775.1 1.01037
\(599\) −27823.6 −1.89790 −0.948949 0.315430i \(-0.897851\pi\)
−0.948949 + 0.315430i \(0.897851\pi\)
\(600\) 6189.18 0.421120
\(601\) −3557.15 −0.241430 −0.120715 0.992687i \(-0.538519\pi\)
−0.120715 + 0.992687i \(0.538519\pi\)
\(602\) 0 0
\(603\) 378.930 0.0255907
\(604\) 7008.25 0.472122
\(605\) 11335.9 0.761767
\(606\) −27832.8 −1.86572
\(607\) −19170.9 −1.28192 −0.640958 0.767576i \(-0.721463\pi\)
−0.640958 + 0.767576i \(0.721463\pi\)
\(608\) −3095.65 −0.206489
\(609\) 19983.5 1.32968
\(610\) −873.585 −0.0579843
\(611\) −15994.5 −1.05903
\(612\) 6402.36 0.422876
\(613\) 4287.83 0.282518 0.141259 0.989973i \(-0.454885\pi\)
0.141259 + 0.989973i \(0.454885\pi\)
\(614\) 21760.6 1.43027
\(615\) −11594.9 −0.760245
\(616\) 97.8006 0.00639692
\(617\) −10569.5 −0.689649 −0.344824 0.938667i \(-0.612062\pi\)
−0.344824 + 0.938667i \(0.612062\pi\)
\(618\) 7524.77 0.489791
\(619\) 19947.5 1.29525 0.647624 0.761960i \(-0.275763\pi\)
0.647624 + 0.761960i \(0.275763\pi\)
\(620\) 4902.31 0.317551
\(621\) −3204.56 −0.207077
\(622\) 4144.21 0.267150
\(623\) 8330.71 0.535735
\(624\) −19581.0 −1.25620
\(625\) −6323.50 −0.404704
\(626\) 9840.42 0.628278
\(627\) 102.057 0.00650043
\(628\) −4726.44 −0.300328
\(629\) −33198.3 −2.10446
\(630\) 6523.99 0.412575
\(631\) −8854.29 −0.558611 −0.279306 0.960202i \(-0.590104\pi\)
−0.279306 + 0.960202i \(0.590104\pi\)
\(632\) −7402.41 −0.465905
\(633\) −39529.4 −2.48207
\(634\) 3494.60 0.218909
\(635\) 16245.3 1.01523
\(636\) −12369.6 −0.771207
\(637\) −8588.55 −0.534208
\(638\) −566.122 −0.0351301
\(639\) 5150.35 0.318849
\(640\) −14562.5 −0.899429
\(641\) −10022.5 −0.617571 −0.308786 0.951132i \(-0.599923\pi\)
−0.308786 + 0.951132i \(0.599923\pi\)
\(642\) 38785.0 2.38430
\(643\) −5806.52 −0.356123 −0.178061 0.984019i \(-0.556983\pi\)
−0.178061 + 0.984019i \(0.556983\pi\)
\(644\) −3754.91 −0.229758
\(645\) 0 0
\(646\) 7277.04 0.443206
\(647\) −8583.93 −0.521591 −0.260795 0.965394i \(-0.583985\pi\)
−0.260795 + 0.965394i \(0.583985\pi\)
\(648\) 13492.2 0.817936
\(649\) 249.027 0.0150619
\(650\) −6064.77 −0.365969
\(651\) 13477.3 0.811395
\(652\) 2451.39 0.147245
\(653\) −17048.8 −1.02170 −0.510849 0.859670i \(-0.670669\pi\)
−0.510849 + 0.859670i \(0.670669\pi\)
\(654\) −13198.9 −0.789172
\(655\) −13086.1 −0.780633
\(656\) −15130.0 −0.900499
\(657\) −24197.2 −1.43687
\(658\) 14954.1 0.885974
\(659\) −2694.69 −0.159287 −0.0796437 0.996823i \(-0.525378\pi\)
−0.0796437 + 0.996823i \(0.525378\pi\)
\(660\) −108.036 −0.00637168
\(661\) −29666.8 −1.74570 −0.872848 0.487992i \(-0.837730\pi\)
−0.872848 + 0.487992i \(0.837730\pi\)
\(662\) 9551.64 0.560778
\(663\) 22651.3 1.32685
\(664\) −4960.74 −0.289931
\(665\) 2015.61 0.117537
\(666\) −28267.5 −1.64466
\(667\) −36492.2 −2.11842
\(668\) 5048.52 0.292415
\(669\) 12146.2 0.701942
\(670\) −455.931 −0.0262898
\(671\) 18.4938 0.00106400
\(672\) 9009.09 0.517162
\(673\) −17932.8 −1.02713 −0.513564 0.858051i \(-0.671675\pi\)
−0.513564 + 0.858051i \(0.671675\pi\)
\(674\) −20377.1 −1.16454
\(675\) 1315.39 0.0750062
\(676\) −2923.09 −0.166312
\(677\) −2440.74 −0.138560 −0.0692801 0.997597i \(-0.522070\pi\)
−0.0692801 + 0.997597i \(0.522070\pi\)
\(678\) 1546.68 0.0876106
\(679\) 2550.53 0.144154
\(680\) 12933.4 0.729373
\(681\) −2468.72 −0.138915
\(682\) −381.806 −0.0214371
\(683\) −12722.2 −0.712737 −0.356369 0.934345i \(-0.615985\pi\)
−0.356369 + 0.934345i \(0.615985\pi\)
\(684\) 1684.24 0.0941497
\(685\) −14443.1 −0.805608
\(686\) 19222.6 1.06986
\(687\) 5068.83 0.281496
\(688\) 0 0
\(689\) −20350.3 −1.12523
\(690\) −25620.1 −1.41354
\(691\) 5584.80 0.307461 0.153731 0.988113i \(-0.450871\pi\)
0.153731 + 0.988113i \(0.450871\pi\)
\(692\) 4151.64 0.228066
\(693\) −138.113 −0.00757066
\(694\) −4655.02 −0.254614
\(695\) −8072.53 −0.440588
\(696\) 33731.9 1.83708
\(697\) 17502.4 0.951148
\(698\) 14823.1 0.803817
\(699\) 46460.3 2.51400
\(700\) 1541.29 0.0832217
\(701\) 19891.2 1.07173 0.535864 0.844304i \(-0.319986\pi\)
0.535864 + 0.844304i \(0.319986\pi\)
\(702\) −2902.63 −0.156058
\(703\) −8733.33 −0.468540
\(704\) 122.440 0.00655486
\(705\) 27734.5 1.48162
\(706\) 7114.62 0.379266
\(707\) 11637.0 0.619028
\(708\) 8837.82 0.469132
\(709\) −14613.5 −0.774078 −0.387039 0.922063i \(-0.626502\pi\)
−0.387039 + 0.922063i \(0.626502\pi\)
\(710\) −6196.94 −0.327559
\(711\) 10453.6 0.551392
\(712\) 14062.1 0.740170
\(713\) −24611.2 −1.29270
\(714\) −21177.9 −1.11003
\(715\) −177.739 −0.00929661
\(716\) −2072.16 −0.108157
\(717\) −18196.5 −0.947783
\(718\) 6498.14 0.337755
\(719\) −11027.7 −0.571995 −0.285998 0.958230i \(-0.592325\pi\)
−0.285998 + 0.958230i \(0.592325\pi\)
\(720\) 15788.7 0.817237
\(721\) −3146.13 −0.162508
\(722\) −20820.2 −1.07320
\(723\) 33082.3 1.70172
\(724\) −7034.15 −0.361080
\(725\) 14979.1 0.767322
\(726\) −31332.5 −1.60173
\(727\) −1650.84 −0.0842178 −0.0421089 0.999113i \(-0.513408\pi\)
−0.0421089 + 0.999113i \(0.513408\pi\)
\(728\) 5710.24 0.290708
\(729\) −14240.8 −0.723506
\(730\) 29114.3 1.47612
\(731\) 0 0
\(732\) 656.332 0.0331403
\(733\) 28314.8 1.42678 0.713391 0.700767i \(-0.247159\pi\)
0.713391 + 0.700767i \(0.247159\pi\)
\(734\) 44697.4 2.24770
\(735\) 14892.6 0.747377
\(736\) −16451.7 −0.823935
\(737\) 9.65204 0.000482412 0
\(738\) 14902.8 0.743332
\(739\) 28963.4 1.44172 0.720862 0.693078i \(-0.243746\pi\)
0.720862 + 0.693078i \(0.243746\pi\)
\(740\) 9244.97 0.459259
\(741\) 5958.76 0.295413
\(742\) 19026.6 0.941359
\(743\) 15510.4 0.765844 0.382922 0.923781i \(-0.374918\pi\)
0.382922 + 0.923781i \(0.374918\pi\)
\(744\) 22749.6 1.12102
\(745\) 26273.8 1.29208
\(746\) 39889.0 1.95769
\(747\) 7005.48 0.343129
\(748\) 163.080 0.00797165
\(749\) −16216.1 −0.791087
\(750\) 35591.1 1.73281
\(751\) 2901.63 0.140988 0.0704941 0.997512i \(-0.477542\pi\)
0.0704941 + 0.997512i \(0.477542\pi\)
\(752\) 36190.4 1.75496
\(753\) 43363.6 2.09862
\(754\) −33053.9 −1.59649
\(755\) −19992.8 −0.963727
\(756\) 737.666 0.0354876
\(757\) −9260.00 −0.444598 −0.222299 0.974979i \(-0.571356\pi\)
−0.222299 + 0.974979i \(0.571356\pi\)
\(758\) −33759.2 −1.61766
\(759\) 542.377 0.0259381
\(760\) 3402.33 0.162389
\(761\) 6418.29 0.305733 0.152866 0.988247i \(-0.451150\pi\)
0.152866 + 0.988247i \(0.451150\pi\)
\(762\) −44902.1 −2.13469
\(763\) 5518.50 0.261839
\(764\) 6474.50 0.306596
\(765\) −18264.4 −0.863203
\(766\) −44773.9 −2.11194
\(767\) 14539.8 0.684489
\(768\) 28610.2 1.34425
\(769\) 5335.88 0.250217 0.125108 0.992143i \(-0.460072\pi\)
0.125108 + 0.992143i \(0.460072\pi\)
\(770\) 166.178 0.00777746
\(771\) −4848.11 −0.226460
\(772\) 3897.09 0.181683
\(773\) −20062.9 −0.933520 −0.466760 0.884384i \(-0.654579\pi\)
−0.466760 + 0.884384i \(0.654579\pi\)
\(774\) 0 0
\(775\) 10102.2 0.468236
\(776\) 4305.27 0.199162
\(777\) 25416.1 1.17348
\(778\) 22046.8 1.01596
\(779\) 4604.26 0.211765
\(780\) −6307.86 −0.289561
\(781\) 131.189 0.00601064
\(782\) 38673.4 1.76849
\(783\) 7169.04 0.327204
\(784\) 19433.2 0.885257
\(785\) 13483.4 0.613049
\(786\) 36170.1 1.64140
\(787\) 17182.2 0.778248 0.389124 0.921185i \(-0.372778\pi\)
0.389124 + 0.921185i \(0.372778\pi\)
\(788\) −14334.9 −0.648045
\(789\) −11877.1 −0.535914
\(790\) −12577.8 −0.566454
\(791\) −646.672 −0.0290683
\(792\) −233.133 −0.0104596
\(793\) 1079.79 0.0483535
\(794\) −27538.3 −1.23085
\(795\) 35287.6 1.57424
\(796\) 6310.99 0.281014
\(797\) −3342.90 −0.148572 −0.0742859 0.997237i \(-0.523668\pi\)
−0.0742859 + 0.997237i \(0.523668\pi\)
\(798\) −5571.17 −0.247140
\(799\) −41865.0 −1.85366
\(800\) 6752.95 0.298441
\(801\) −19858.4 −0.875981
\(802\) 9822.90 0.432492
\(803\) −616.348 −0.0270865
\(804\) 342.545 0.0150257
\(805\) 10711.8 0.468997
\(806\) −22292.3 −0.974210
\(807\) −1861.27 −0.0811892
\(808\) 19643.1 0.855248
\(809\) −10782.5 −0.468596 −0.234298 0.972165i \(-0.575279\pi\)
−0.234298 + 0.972165i \(0.575279\pi\)
\(810\) 22925.2 0.994458
\(811\) 22440.1 0.971612 0.485806 0.874067i \(-0.338526\pi\)
0.485806 + 0.874067i \(0.338526\pi\)
\(812\) 8400.24 0.363043
\(813\) 32821.2 1.41586
\(814\) −720.024 −0.0310035
\(815\) −6993.21 −0.300566
\(816\) −51252.7 −2.19878
\(817\) 0 0
\(818\) 32984.1 1.40985
\(819\) −8063.92 −0.344049
\(820\) −4874.01 −0.207570
\(821\) −10938.7 −0.464996 −0.232498 0.972597i \(-0.574690\pi\)
−0.232498 + 0.972597i \(0.574690\pi\)
\(822\) 39920.8 1.69392
\(823\) −37928.5 −1.60645 −0.803223 0.595678i \(-0.796883\pi\)
−0.803223 + 0.595678i \(0.796883\pi\)
\(824\) −5310.63 −0.224520
\(825\) −222.631 −0.00939517
\(826\) −13594.1 −0.572637
\(827\) 36038.1 1.51532 0.757660 0.652650i \(-0.226343\pi\)
0.757660 + 0.652650i \(0.226343\pi\)
\(828\) 8950.78 0.375678
\(829\) −29221.5 −1.22425 −0.612127 0.790760i \(-0.709686\pi\)
−0.612127 + 0.790760i \(0.709686\pi\)
\(830\) −8429.05 −0.352502
\(831\) −36685.0 −1.53139
\(832\) 7148.82 0.297886
\(833\) −22480.3 −0.935048
\(834\) 22312.6 0.926404
\(835\) −14402.2 −0.596896
\(836\) 42.9006 0.00177482
\(837\) 4834.97 0.199667
\(838\) −17506.5 −0.721660
\(839\) 6285.44 0.258638 0.129319 0.991603i \(-0.458721\pi\)
0.129319 + 0.991603i \(0.458721\pi\)
\(840\) −9901.59 −0.406711
\(841\) 57249.1 2.34733
\(842\) 5530.48 0.226357
\(843\) −37478.8 −1.53125
\(844\) −16616.5 −0.677682
\(845\) 8338.87 0.339486
\(846\) −35646.9 −1.44866
\(847\) 13100.2 0.531438
\(848\) 46046.3 1.86466
\(849\) −35721.8 −1.44401
\(850\) −15874.4 −0.640572
\(851\) −46412.8 −1.86958
\(852\) 4655.81 0.187213
\(853\) −35129.3 −1.41009 −0.705044 0.709164i \(-0.749073\pi\)
−0.705044 + 0.709164i \(0.749073\pi\)
\(854\) −1009.55 −0.0404521
\(855\) −4804.72 −0.192185
\(856\) −27372.6 −1.09296
\(857\) 32983.7 1.31470 0.657352 0.753584i \(-0.271676\pi\)
0.657352 + 0.753584i \(0.271676\pi\)
\(858\) 491.274 0.0195476
\(859\) 35152.9 1.39628 0.698139 0.715962i \(-0.254012\pi\)
0.698139 + 0.715962i \(0.254012\pi\)
\(860\) 0 0
\(861\) −13399.5 −0.530377
\(862\) −34301.4 −1.35535
\(863\) −24925.6 −0.983173 −0.491587 0.870829i \(-0.663583\pi\)
−0.491587 + 0.870829i \(0.663583\pi\)
\(864\) 3231.99 0.127262
\(865\) −11843.6 −0.465544
\(866\) −9838.48 −0.386057
\(867\) 24386.7 0.955266
\(868\) 5665.31 0.221536
\(869\) 266.272 0.0103943
\(870\) 57315.7 2.23355
\(871\) 563.549 0.0219232
\(872\) 9315.17 0.361756
\(873\) −6079.84 −0.235706
\(874\) 10173.6 0.393739
\(875\) −14880.8 −0.574927
\(876\) −21873.8 −0.843661
\(877\) 2057.63 0.0792261 0.0396131 0.999215i \(-0.487387\pi\)
0.0396131 + 0.999215i \(0.487387\pi\)
\(878\) −30575.2 −1.17524
\(879\) 62805.1 2.40997
\(880\) 402.168 0.0154058
\(881\) 17912.5 0.685004 0.342502 0.939517i \(-0.388726\pi\)
0.342502 + 0.939517i \(0.388726\pi\)
\(882\) −19141.3 −0.730750
\(883\) −27215.2 −1.03722 −0.518610 0.855011i \(-0.673550\pi\)
−0.518610 + 0.855011i \(0.673550\pi\)
\(884\) 9521.67 0.362272
\(885\) −25212.2 −0.957625
\(886\) −33528.2 −1.27133
\(887\) −25313.0 −0.958206 −0.479103 0.877759i \(-0.659038\pi\)
−0.479103 + 0.877759i \(0.659038\pi\)
\(888\) 42902.1 1.62128
\(889\) 18773.7 0.708267
\(890\) 23893.7 0.899910
\(891\) −485.327 −0.0182481
\(892\) 5105.76 0.191652
\(893\) −11013.2 −0.412703
\(894\) −72621.0 −2.71679
\(895\) 5911.36 0.220777
\(896\) −16829.1 −0.627477
\(897\) 31667.5 1.17876
\(898\) −47683.3 −1.77195
\(899\) 55058.6 2.04261
\(900\) −3674.05 −0.136076
\(901\) −53266.3 −1.96954
\(902\) 379.601 0.0140126
\(903\) 0 0
\(904\) −1091.58 −0.0401607
\(905\) 20066.7 0.737062
\(906\) 55260.5 2.02639
\(907\) 45998.9 1.68398 0.841989 0.539495i \(-0.181385\pi\)
0.841989 + 0.539495i \(0.181385\pi\)
\(908\) −1037.75 −0.0379282
\(909\) −27739.7 −1.01217
\(910\) 9702.57 0.353447
\(911\) 46592.7 1.69449 0.847247 0.531199i \(-0.178258\pi\)
0.847247 + 0.531199i \(0.178258\pi\)
\(912\) −13482.8 −0.489539
\(913\) 178.443 0.00646833
\(914\) 33250.9 1.20333
\(915\) −1872.36 −0.0676483
\(916\) 2130.72 0.0768571
\(917\) −15122.8 −0.544601
\(918\) −7597.54 −0.273155
\(919\) 33168.1 1.19055 0.595274 0.803523i \(-0.297043\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(920\) 18081.5 0.647966
\(921\) 46639.5 1.66865
\(922\) −413.615 −0.0147741
\(923\) 7659.66 0.273154
\(924\) −124.851 −0.00444513
\(925\) 19051.2 0.677188
\(926\) −51173.2 −1.81604
\(927\) 7499.60 0.265716
\(928\) 36804.6 1.30191
\(929\) −19909.9 −0.703148 −0.351574 0.936160i \(-0.614353\pi\)
−0.351574 + 0.936160i \(0.614353\pi\)
\(930\) 38655.0 1.36296
\(931\) −5913.78 −0.208181
\(932\) 19530.0 0.686401
\(933\) 8882.29 0.311675
\(934\) 39823.2 1.39514
\(935\) −465.228 −0.0162723
\(936\) −13611.8 −0.475338
\(937\) −26262.2 −0.915634 −0.457817 0.889046i \(-0.651369\pi\)
−0.457817 + 0.889046i \(0.651369\pi\)
\(938\) −526.893 −0.0183408
\(939\) 21091.0 0.732991
\(940\) 11658.4 0.404528
\(941\) 42227.8 1.46290 0.731449 0.681896i \(-0.238845\pi\)
0.731449 + 0.681896i \(0.238845\pi\)
\(942\) −37268.3 −1.28903
\(943\) 24469.1 0.844988
\(944\) −32899.0 −1.13429
\(945\) −2104.38 −0.0724398
\(946\) 0 0
\(947\) −35227.0 −1.20879 −0.604394 0.796685i \(-0.706585\pi\)
−0.604394 + 0.796685i \(0.706585\pi\)
\(948\) 9449.83 0.323751
\(949\) −35986.4 −1.23095
\(950\) −4175.99 −0.142618
\(951\) 7489.98 0.255393
\(952\) 14946.4 0.508839
\(953\) −49209.9 −1.67268 −0.836340 0.548211i \(-0.815309\pi\)
−0.836340 + 0.548211i \(0.815309\pi\)
\(954\) −45354.8 −1.53922
\(955\) −18470.2 −0.625844
\(956\) −7649.06 −0.258774
\(957\) −1213.37 −0.0409851
\(958\) 20687.4 0.697683
\(959\) −16691.0 −0.562024
\(960\) −12396.1 −0.416753
\(961\) 7341.79 0.246443
\(962\) −42039.7 −1.40895
\(963\) 38655.3 1.29351
\(964\) 13906.4 0.464623
\(965\) −11117.5 −0.370864
\(966\) −29607.7 −0.986140
\(967\) 13452.5 0.447366 0.223683 0.974662i \(-0.428192\pi\)
0.223683 + 0.974662i \(0.428192\pi\)
\(968\) 22113.0 0.734234
\(969\) 15596.9 0.517074
\(970\) 7315.30 0.242145
\(971\) 37322.8 1.23352 0.616758 0.787152i \(-0.288446\pi\)
0.616758 + 0.787152i \(0.288446\pi\)
\(972\) −15200.9 −0.501614
\(973\) −9328.95 −0.307371
\(974\) 3063.24 0.100773
\(975\) −12998.6 −0.426964
\(976\) −2443.21 −0.0801285
\(977\) −45153.4 −1.47859 −0.739297 0.673380i \(-0.764842\pi\)
−0.739297 + 0.673380i \(0.764842\pi\)
\(978\) 19329.3 0.631987
\(979\) −505.829 −0.0165132
\(980\) 6260.24 0.204057
\(981\) −13154.8 −0.428134
\(982\) 23348.2 0.758729
\(983\) 15802.7 0.512745 0.256372 0.966578i \(-0.417473\pi\)
0.256372 + 0.966578i \(0.417473\pi\)
\(984\) −22618.2 −0.732767
\(985\) 40894.0 1.32283
\(986\) −86517.6 −2.79440
\(987\) 32051.1 1.03364
\(988\) 2504.82 0.0806568
\(989\) 0 0
\(990\) −396.128 −0.0127169
\(991\) −27570.0 −0.883744 −0.441872 0.897078i \(-0.645685\pi\)
−0.441872 + 0.897078i \(0.645685\pi\)
\(992\) 24821.9 0.794451
\(993\) 20472.1 0.654241
\(994\) −7161.43 −0.228518
\(995\) −18003.7 −0.573624
\(996\) 6332.82 0.201469
\(997\) 14969.8 0.475526 0.237763 0.971323i \(-0.423586\pi\)
0.237763 + 0.971323i \(0.423586\pi\)
\(998\) 13197.7 0.418605
\(999\) 9117.97 0.288768
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 1849.4.a.c.1.6 6
43.42 odd 2 43.4.a.b.1.1 6
129.128 even 2 387.4.a.h.1.6 6
172.171 even 2 688.4.a.i.1.6 6
215.214 odd 2 1075.4.a.b.1.6 6
301.300 even 2 2107.4.a.c.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.a.b.1.1 6 43.42 odd 2
387.4.a.h.1.6 6 129.128 even 2
688.4.a.i.1.6 6 172.171 even 2
1075.4.a.b.1.6 6 215.214 odd 2
1849.4.a.c.1.6 6 1.1 even 1 trivial
2107.4.a.c.1.1 6 301.300 even 2