Properties

Label 1859.4.a.f.1.5
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $1$
Dimension $17$
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] = [1859,4,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1859.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(109.684550701\)
Analytic rank: \(1\)
Dimension: \(17\)
Coefficient field: \(\mathbb{Q}[x]/(x^{17} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + 941923 x^{9} - 2799440 x^{8} - 6021311 x^{7} + 15765187 x^{6} + \cdots + 2596992 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8}\cdot 3\cdot 5 \)
Twist minimal: no (minimal twist has level 143)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(2.79502\) of defining polynomial
Character \(\chi\) \(=\) 1859.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.79502 q^{2} +10.1456 q^{3} -0.187860 q^{4} -5.45712 q^{5} -28.3572 q^{6} -7.73594 q^{7} +22.8852 q^{8} +75.9332 q^{9} +O(q^{10})\) \(q-2.79502 q^{2} +10.1456 q^{3} -0.187860 q^{4} -5.45712 q^{5} -28.3572 q^{6} -7.73594 q^{7} +22.8852 q^{8} +75.9332 q^{9} +15.2528 q^{10} +11.0000 q^{11} -1.90595 q^{12} +21.6221 q^{14} -55.3657 q^{15} -62.4618 q^{16} -18.5218 q^{17} -212.235 q^{18} -65.8223 q^{19} +1.02517 q^{20} -78.4858 q^{21} -30.7452 q^{22} +38.8477 q^{23} +232.184 q^{24} -95.2199 q^{25} +496.457 q^{27} +1.45328 q^{28} +16.1969 q^{29} +154.748 q^{30} -100.762 q^{31} -8.49981 q^{32} +111.602 q^{33} +51.7687 q^{34} +42.2159 q^{35} -14.2648 q^{36} -327.545 q^{37} +183.975 q^{38} -124.887 q^{40} -460.876 q^{41} +219.369 q^{42} +346.386 q^{43} -2.06646 q^{44} -414.376 q^{45} -108.580 q^{46} -318.457 q^{47} -633.713 q^{48} -283.155 q^{49} +266.142 q^{50} -187.914 q^{51} -387.521 q^{53} -1387.61 q^{54} -60.0283 q^{55} -177.039 q^{56} -667.807 q^{57} -45.2707 q^{58} +93.9545 q^{59} +10.4010 q^{60} +801.303 q^{61} +281.632 q^{62} -587.415 q^{63} +523.452 q^{64} -311.929 q^{66} +344.235 q^{67} +3.47950 q^{68} +394.134 q^{69} -117.994 q^{70} -186.939 q^{71} +1737.75 q^{72} +820.160 q^{73} +915.496 q^{74} -966.063 q^{75} +12.3654 q^{76} -85.0954 q^{77} -502.726 q^{79} +340.861 q^{80} +2986.66 q^{81} +1288.16 q^{82} -199.772 q^{83} +14.7443 q^{84} +101.075 q^{85} -968.156 q^{86} +164.327 q^{87} +251.738 q^{88} -535.708 q^{89} +1158.19 q^{90} -7.29794 q^{92} -1022.29 q^{93} +890.093 q^{94} +359.200 q^{95} -86.2356 q^{96} +462.280 q^{97} +791.425 q^{98} +835.265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 17 q - 4 q^{2} - 6 q^{3} + 78 q^{4} - 16 q^{5} - 14 q^{6} + 6 q^{7} - 63 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 95 q^{12} - 60 q^{14} + 28 q^{15} + 350 q^{16} + 118 q^{17} - 478 q^{18} - 403 q^{19} - 98 q^{20} - 220 q^{21} - 44 q^{22} - 215 q^{23} - 26 q^{24} + 319 q^{25} - 384 q^{27} + 396 q^{28} - 7 q^{29} - 1269 q^{30} - 682 q^{31} - 813 q^{32} - 66 q^{33} - 738 q^{34} + 10 q^{35} + 560 q^{36} - 1084 q^{37} + 410 q^{38} + 95 q^{40} - 240 q^{41} + 393 q^{42} - 435 q^{43} + 858 q^{44} - 1242 q^{45} - 1671 q^{46} - 549 q^{47} + 894 q^{48} + 403 q^{49} + 651 q^{50} + 1552 q^{51} - 566 q^{53} - 311 q^{54} - 176 q^{55} - 1925 q^{56} + 534 q^{57} - 618 q^{58} - 2010 q^{59} + 411 q^{60} + 460 q^{61} - 823 q^{62} - 820 q^{63} + 3171 q^{64} - 154 q^{66} + 232 q^{67} + 1795 q^{68} - 1608 q^{69} - 207 q^{70} - 489 q^{71} - 2556 q^{72} - 290 q^{73} + 2653 q^{74} - 2852 q^{75} - 2421 q^{76} + 66 q^{77} - 732 q^{79} - 4915 q^{80} + 2393 q^{81} - 1772 q^{82} + 117 q^{83} - 4161 q^{84} - 4858 q^{85} - 1034 q^{86} + 3032 q^{87} - 693 q^{88} - 4113 q^{89} + 15145 q^{90} - 3554 q^{92} - 802 q^{93} + 2325 q^{94} - 3924 q^{95} - 2601 q^{96} - 2793 q^{97} - 533 q^{98} + 1485 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79502 −0.988189 −0.494094 0.869408i \(-0.664500\pi\)
−0.494094 + 0.869408i \(0.664500\pi\)
\(3\) 10.1456 1.95252 0.976261 0.216598i \(-0.0694960\pi\)
0.976261 + 0.216598i \(0.0694960\pi\)
\(4\) −0.187860 −0.0234825
\(5\) −5.45712 −0.488099 −0.244050 0.969763i \(-0.578476\pi\)
−0.244050 + 0.969763i \(0.578476\pi\)
\(6\) −28.3572 −1.92946
\(7\) −7.73594 −0.417702 −0.208851 0.977948i \(-0.566972\pi\)
−0.208851 + 0.977948i \(0.566972\pi\)
\(8\) 22.8852 1.01139
\(9\) 75.9332 2.81234
\(10\) 15.2528 0.482334
\(11\) 11.0000 0.301511
\(12\) −1.90595 −0.0458501
\(13\) 0 0
\(14\) 21.6221 0.412768
\(15\) −55.3657 −0.953025
\(16\) −62.4618 −0.975966
\(17\) −18.5218 −0.264246 −0.132123 0.991233i \(-0.542179\pi\)
−0.132123 + 0.991233i \(0.542179\pi\)
\(18\) −212.235 −2.77912
\(19\) −65.8223 −0.794773 −0.397386 0.917651i \(-0.630083\pi\)
−0.397386 + 0.917651i \(0.630083\pi\)
\(20\) 1.02517 0.0114618
\(21\) −78.4858 −0.815572
\(22\) −30.7452 −0.297950
\(23\) 38.8477 0.352188 0.176094 0.984373i \(-0.443654\pi\)
0.176094 + 0.984373i \(0.443654\pi\)
\(24\) 232.184 1.97477
\(25\) −95.2199 −0.761759
\(26\) 0 0
\(27\) 496.457 3.53864
\(28\) 1.45328 0.00980868
\(29\) 16.1969 0.103714 0.0518568 0.998655i \(-0.483486\pi\)
0.0518568 + 0.998655i \(0.483486\pi\)
\(30\) 154.748 0.941768
\(31\) −100.762 −0.583788 −0.291894 0.956451i \(-0.594285\pi\)
−0.291894 + 0.956451i \(0.594285\pi\)
\(32\) −8.49981 −0.0469552
\(33\) 111.602 0.588707
\(34\) 51.7687 0.261125
\(35\) 42.2159 0.203880
\(36\) −14.2648 −0.0660408
\(37\) −327.545 −1.45536 −0.727678 0.685919i \(-0.759400\pi\)
−0.727678 + 0.685919i \(0.759400\pi\)
\(38\) 183.975 0.785385
\(39\) 0 0
\(40\) −124.887 −0.493661
\(41\) −460.876 −1.75553 −0.877765 0.479092i \(-0.840966\pi\)
−0.877765 + 0.479092i \(0.840966\pi\)
\(42\) 219.369 0.805939
\(43\) 346.386 1.22845 0.614225 0.789131i \(-0.289469\pi\)
0.614225 + 0.789131i \(0.289469\pi\)
\(44\) −2.06646 −0.00708024
\(45\) −414.376 −1.37270
\(46\) −108.580 −0.348028
\(47\) −318.457 −0.988334 −0.494167 0.869367i \(-0.664527\pi\)
−0.494167 + 0.869367i \(0.664527\pi\)
\(48\) −633.713 −1.90560
\(49\) −283.155 −0.825525
\(50\) 266.142 0.752762
\(51\) −187.914 −0.515947
\(52\) 0 0
\(53\) −387.521 −1.00434 −0.502170 0.864769i \(-0.667465\pi\)
−0.502170 + 0.864769i \(0.667465\pi\)
\(54\) −1387.61 −3.49684
\(55\) −60.0283 −0.147167
\(56\) −177.039 −0.422461
\(57\) −667.807 −1.55181
\(58\) −45.2707 −0.102489
\(59\) 93.9545 0.207319 0.103660 0.994613i \(-0.466945\pi\)
0.103660 + 0.994613i \(0.466945\pi\)
\(60\) 10.4010 0.0223794
\(61\) 801.303 1.68191 0.840954 0.541107i \(-0.181994\pi\)
0.840954 + 0.541107i \(0.181994\pi\)
\(62\) 281.632 0.576893
\(63\) −587.415 −1.17472
\(64\) 523.452 1.02237
\(65\) 0 0
\(66\) −311.929 −0.581754
\(67\) 344.235 0.627687 0.313843 0.949475i \(-0.398383\pi\)
0.313843 + 0.949475i \(0.398383\pi\)
\(68\) 3.47950 0.00620517
\(69\) 394.134 0.687654
\(70\) −117.994 −0.201472
\(71\) −186.939 −0.312473 −0.156237 0.987720i \(-0.549936\pi\)
−0.156237 + 0.987720i \(0.549936\pi\)
\(72\) 1737.75 2.84439
\(73\) 820.160 1.31497 0.657483 0.753469i \(-0.271621\pi\)
0.657483 + 0.753469i \(0.271621\pi\)
\(74\) 915.496 1.43817
\(75\) −966.063 −1.48735
\(76\) 12.3654 0.0186633
\(77\) −85.0954 −0.125942
\(78\) 0 0
\(79\) −502.726 −0.715963 −0.357981 0.933729i \(-0.616535\pi\)
−0.357981 + 0.933729i \(0.616535\pi\)
\(80\) 340.861 0.476368
\(81\) 2986.66 4.09692
\(82\) 1288.16 1.73479
\(83\) −199.772 −0.264191 −0.132096 0.991237i \(-0.542171\pi\)
−0.132096 + 0.991237i \(0.542171\pi\)
\(84\) 14.7443 0.0191517
\(85\) 101.075 0.128978
\(86\) −968.156 −1.21394
\(87\) 164.327 0.202503
\(88\) 251.738 0.304947
\(89\) −535.708 −0.638033 −0.319017 0.947749i \(-0.603353\pi\)
−0.319017 + 0.947749i \(0.603353\pi\)
\(90\) 1158.19 1.35649
\(91\) 0 0
\(92\) −7.29794 −0.00827025
\(93\) −1022.29 −1.13986
\(94\) 890.093 0.976660
\(95\) 359.200 0.387928
\(96\) −86.2356 −0.0916811
\(97\) 462.280 0.483891 0.241945 0.970290i \(-0.422214\pi\)
0.241945 + 0.970290i \(0.422214\pi\)
\(98\) 791.425 0.815775
\(99\) 835.265 0.847953
\(100\) 17.8880 0.0178880
\(101\) −1430.27 −1.40908 −0.704541 0.709663i \(-0.748847\pi\)
−0.704541 + 0.709663i \(0.748847\pi\)
\(102\) 525.225 0.509853
\(103\) −170.160 −0.162780 −0.0813901 0.996682i \(-0.525936\pi\)
−0.0813901 + 0.996682i \(0.525936\pi\)
\(104\) 0 0
\(105\) 428.306 0.398080
\(106\) 1083.13 0.992478
\(107\) 47.2612 0.0427002 0.0213501 0.999772i \(-0.493204\pi\)
0.0213501 + 0.999772i \(0.493204\pi\)
\(108\) −93.2645 −0.0830961
\(109\) 1320.38 1.16027 0.580136 0.814520i \(-0.303000\pi\)
0.580136 + 0.814520i \(0.303000\pi\)
\(110\) 167.780 0.145429
\(111\) −3323.15 −2.84161
\(112\) 483.201 0.407663
\(113\) −1997.52 −1.66293 −0.831465 0.555577i \(-0.812497\pi\)
−0.831465 + 0.555577i \(0.812497\pi\)
\(114\) 1866.53 1.53348
\(115\) −211.997 −0.171903
\(116\) −3.04275 −0.00243545
\(117\) 0 0
\(118\) −262.605 −0.204870
\(119\) 143.283 0.110376
\(120\) −1267.06 −0.963884
\(121\) 121.000 0.0909091
\(122\) −2239.66 −1.66204
\(123\) −4675.86 −3.42771
\(124\) 18.9292 0.0137088
\(125\) 1201.77 0.859913
\(126\) 1641.84 1.16084
\(127\) −1184.44 −0.827576 −0.413788 0.910373i \(-0.635795\pi\)
−0.413788 + 0.910373i \(0.635795\pi\)
\(128\) −1395.06 −0.963336
\(129\) 3514.29 2.39858
\(130\) 0 0
\(131\) 499.167 0.332919 0.166460 0.986048i \(-0.446766\pi\)
0.166460 + 0.986048i \(0.446766\pi\)
\(132\) −20.9655 −0.0138243
\(133\) 509.198 0.331978
\(134\) −962.144 −0.620273
\(135\) −2709.22 −1.72721
\(136\) −423.875 −0.267257
\(137\) 2929.03 1.82660 0.913299 0.407290i \(-0.133526\pi\)
0.913299 + 0.407290i \(0.133526\pi\)
\(138\) −1101.61 −0.679532
\(139\) −1710.17 −1.04356 −0.521780 0.853080i \(-0.674732\pi\)
−0.521780 + 0.853080i \(0.674732\pi\)
\(140\) −7.93069 −0.00478761
\(141\) −3230.93 −1.92974
\(142\) 522.499 0.308783
\(143\) 0 0
\(144\) −4742.93 −2.74475
\(145\) −88.3885 −0.0506225
\(146\) −2292.36 −1.29943
\(147\) −2872.78 −1.61186
\(148\) 61.5327 0.0341754
\(149\) 8.91668 0.00490257 0.00245128 0.999997i \(-0.499220\pi\)
0.00245128 + 0.999997i \(0.499220\pi\)
\(150\) 2700.17 1.46978
\(151\) 1112.51 0.599568 0.299784 0.954007i \(-0.403085\pi\)
0.299784 + 0.954007i \(0.403085\pi\)
\(152\) −1506.36 −0.803828
\(153\) −1406.42 −0.743151
\(154\) 237.843 0.124454
\(155\) 549.871 0.284946
\(156\) 0 0
\(157\) −2750.70 −1.39828 −0.699140 0.714985i \(-0.746434\pi\)
−0.699140 + 0.714985i \(0.746434\pi\)
\(158\) 1405.13 0.707506
\(159\) −3931.63 −1.96100
\(160\) 46.3844 0.0229188
\(161\) −300.524 −0.147109
\(162\) −8347.77 −4.04853
\(163\) −3606.84 −1.73319 −0.866593 0.499016i \(-0.833695\pi\)
−0.866593 + 0.499016i \(0.833695\pi\)
\(164\) 86.5802 0.0412242
\(165\) −609.023 −0.287348
\(166\) 558.368 0.261071
\(167\) −2248.35 −1.04181 −0.520906 0.853614i \(-0.674406\pi\)
−0.520906 + 0.853614i \(0.674406\pi\)
\(168\) −1796.17 −0.824864
\(169\) 0 0
\(170\) −282.508 −0.127455
\(171\) −4998.10 −2.23517
\(172\) −65.0721 −0.0288471
\(173\) 226.145 0.0993843 0.0496922 0.998765i \(-0.484176\pi\)
0.0496922 + 0.998765i \(0.484176\pi\)
\(174\) −459.299 −0.200111
\(175\) 736.616 0.318188
\(176\) −687.080 −0.294265
\(177\) 953.224 0.404795
\(178\) 1497.32 0.630497
\(179\) 3424.30 1.42986 0.714929 0.699197i \(-0.246459\pi\)
0.714929 + 0.699197i \(0.246459\pi\)
\(180\) 77.8448 0.0322345
\(181\) −2211.50 −0.908173 −0.454087 0.890958i \(-0.650034\pi\)
−0.454087 + 0.890958i \(0.650034\pi\)
\(182\) 0 0
\(183\) 8129.70 3.28396
\(184\) 889.040 0.356200
\(185\) 1787.45 0.710358
\(186\) 2857.33 1.12640
\(187\) −203.739 −0.0796733
\(188\) 59.8253 0.0232086
\(189\) −3840.56 −1.47809
\(190\) −1003.97 −0.383346
\(191\) −2358.91 −0.893636 −0.446818 0.894625i \(-0.647443\pi\)
−0.446818 + 0.894625i \(0.647443\pi\)
\(192\) 5310.73 1.99619
\(193\) −2383.69 −0.889025 −0.444512 0.895773i \(-0.646623\pi\)
−0.444512 + 0.895773i \(0.646623\pi\)
\(194\) −1292.08 −0.478176
\(195\) 0 0
\(196\) 53.1936 0.0193854
\(197\) 407.461 0.147363 0.0736813 0.997282i \(-0.476525\pi\)
0.0736813 + 0.997282i \(0.476525\pi\)
\(198\) −2334.58 −0.837938
\(199\) −3844.74 −1.36958 −0.684790 0.728740i \(-0.740106\pi\)
−0.684790 + 0.728740i \(0.740106\pi\)
\(200\) −2179.13 −0.770439
\(201\) 3492.47 1.22557
\(202\) 3997.64 1.39244
\(203\) −125.298 −0.0433213
\(204\) 35.3016 0.0121157
\(205\) 2515.05 0.856873
\(206\) 475.600 0.160858
\(207\) 2949.83 0.990472
\(208\) 0 0
\(209\) −724.046 −0.239633
\(210\) −1197.12 −0.393378
\(211\) 4758.95 1.55270 0.776349 0.630303i \(-0.217069\pi\)
0.776349 + 0.630303i \(0.217069\pi\)
\(212\) 72.7997 0.0235844
\(213\) −1896.61 −0.610111
\(214\) −132.096 −0.0421958
\(215\) −1890.27 −0.599606
\(216\) 11361.5 3.57896
\(217\) 779.491 0.243849
\(218\) −3690.49 −1.14657
\(219\) 8321.02 2.56750
\(220\) 11.2769 0.00345586
\(221\) 0 0
\(222\) 9288.26 2.80805
\(223\) −3483.52 −1.04607 −0.523035 0.852311i \(-0.675200\pi\)
−0.523035 + 0.852311i \(0.675200\pi\)
\(224\) 65.7540 0.0196133
\(225\) −7230.35 −2.14233
\(226\) 5583.12 1.64329
\(227\) −2480.99 −0.725414 −0.362707 0.931903i \(-0.618147\pi\)
−0.362707 + 0.931903i \(0.618147\pi\)
\(228\) 125.454 0.0364404
\(229\) −4432.17 −1.27898 −0.639490 0.768800i \(-0.720854\pi\)
−0.639490 + 0.768800i \(0.720854\pi\)
\(230\) 592.535 0.169872
\(231\) −863.344 −0.245904
\(232\) 370.670 0.104895
\(233\) 634.737 0.178468 0.0892338 0.996011i \(-0.471558\pi\)
0.0892338 + 0.996011i \(0.471558\pi\)
\(234\) 0 0
\(235\) 1737.86 0.482405
\(236\) −17.6503 −0.00486837
\(237\) −5100.45 −1.39793
\(238\) −400.480 −0.109072
\(239\) 3562.16 0.964086 0.482043 0.876147i \(-0.339895\pi\)
0.482043 + 0.876147i \(0.339895\pi\)
\(240\) 3458.24 0.930120
\(241\) −2783.75 −0.744055 −0.372027 0.928222i \(-0.621337\pi\)
−0.372027 + 0.928222i \(0.621337\pi\)
\(242\) −338.197 −0.0898354
\(243\) 16897.1 4.46070
\(244\) −150.533 −0.0394954
\(245\) 1545.21 0.402938
\(246\) 13069.1 3.38722
\(247\) 0 0
\(248\) −2305.97 −0.590440
\(249\) −2026.81 −0.515839
\(250\) −3358.96 −0.849757
\(251\) −5789.65 −1.45593 −0.727967 0.685613i \(-0.759534\pi\)
−0.727967 + 0.685613i \(0.759534\pi\)
\(252\) 110.352 0.0275854
\(253\) 427.325 0.106189
\(254\) 3310.54 0.817802
\(255\) 1025.47 0.251833
\(256\) −288.393 −0.0704084
\(257\) −4982.51 −1.20934 −0.604670 0.796476i \(-0.706695\pi\)
−0.604670 + 0.796476i \(0.706695\pi\)
\(258\) −9822.53 −2.37025
\(259\) 2533.87 0.607904
\(260\) 0 0
\(261\) 1229.88 0.291678
\(262\) −1395.18 −0.328987
\(263\) −2717.14 −0.637057 −0.318529 0.947913i \(-0.603189\pi\)
−0.318529 + 0.947913i \(0.603189\pi\)
\(264\) 2554.03 0.595415
\(265\) 2114.75 0.490218
\(266\) −1423.22 −0.328057
\(267\) −5435.08 −1.24577
\(268\) −64.6680 −0.0147397
\(269\) 4736.82 1.07364 0.536820 0.843697i \(-0.319625\pi\)
0.536820 + 0.843697i \(0.319625\pi\)
\(270\) 7572.33 1.70681
\(271\) −2289.85 −0.513279 −0.256640 0.966507i \(-0.582615\pi\)
−0.256640 + 0.966507i \(0.582615\pi\)
\(272\) 1156.90 0.257895
\(273\) 0 0
\(274\) −8186.70 −1.80502
\(275\) −1047.42 −0.229679
\(276\) −74.0420 −0.0161478
\(277\) 1780.05 0.386111 0.193055 0.981188i \(-0.438160\pi\)
0.193055 + 0.981188i \(0.438160\pi\)
\(278\) 4779.96 1.03123
\(279\) −7651.20 −1.64181
\(280\) 966.122 0.206203
\(281\) 3675.35 0.780261 0.390130 0.920760i \(-0.372430\pi\)
0.390130 + 0.920760i \(0.372430\pi\)
\(282\) 9030.53 1.90695
\(283\) −3837.92 −0.806150 −0.403075 0.915167i \(-0.632059\pi\)
−0.403075 + 0.915167i \(0.632059\pi\)
\(284\) 35.1184 0.00733766
\(285\) 3644.30 0.757438
\(286\) 0 0
\(287\) 3565.31 0.733287
\(288\) −645.418 −0.132054
\(289\) −4569.94 −0.930174
\(290\) 247.048 0.0500246
\(291\) 4690.11 0.944808
\(292\) −154.075 −0.0308787
\(293\) 7896.16 1.57440 0.787199 0.616699i \(-0.211531\pi\)
0.787199 + 0.616699i \(0.211531\pi\)
\(294\) 8029.48 1.59282
\(295\) −512.720 −0.101192
\(296\) −7495.96 −1.47194
\(297\) 5461.03 1.06694
\(298\) −24.9223 −0.00484466
\(299\) 0 0
\(300\) 181.485 0.0349267
\(301\) −2679.62 −0.513126
\(302\) −3109.49 −0.592487
\(303\) −14511.0 −2.75126
\(304\) 4111.38 0.775671
\(305\) −4372.81 −0.820938
\(306\) 3930.96 0.734373
\(307\) 1002.68 0.186405 0.0932023 0.995647i \(-0.470290\pi\)
0.0932023 + 0.995647i \(0.470290\pi\)
\(308\) 15.9860 0.00295743
\(309\) −1726.37 −0.317832
\(310\) −1536.90 −0.281581
\(311\) −5246.74 −0.956641 −0.478321 0.878185i \(-0.658754\pi\)
−0.478321 + 0.878185i \(0.658754\pi\)
\(312\) 0 0
\(313\) −1548.16 −0.279576 −0.139788 0.990181i \(-0.544642\pi\)
−0.139788 + 0.990181i \(0.544642\pi\)
\(314\) 7688.27 1.38176
\(315\) 3205.59 0.573380
\(316\) 94.4421 0.0168126
\(317\) 8289.92 1.46880 0.734398 0.678719i \(-0.237465\pi\)
0.734398 + 0.678719i \(0.237465\pi\)
\(318\) 10989.0 1.93784
\(319\) 178.166 0.0312708
\(320\) −2856.54 −0.499017
\(321\) 479.494 0.0833730
\(322\) 839.970 0.145372
\(323\) 1219.15 0.210016
\(324\) −561.074 −0.0962061
\(325\) 0 0
\(326\) 10081.2 1.71271
\(327\) 13396.1 2.26545
\(328\) −10547.3 −1.77553
\(329\) 2463.56 0.412829
\(330\) 1702.23 0.283954
\(331\) 6815.21 1.13172 0.565858 0.824503i \(-0.308545\pi\)
0.565858 + 0.824503i \(0.308545\pi\)
\(332\) 37.5293 0.00620387
\(333\) −24871.6 −4.09296
\(334\) 6284.19 1.02951
\(335\) −1878.53 −0.306373
\(336\) 4902.37 0.795970
\(337\) 11413.6 1.84492 0.922460 0.386094i \(-0.126176\pi\)
0.922460 + 0.386094i \(0.126176\pi\)
\(338\) 0 0
\(339\) −20266.1 −3.24691
\(340\) −18.9880 −0.00302874
\(341\) −1108.38 −0.176019
\(342\) 13969.8 2.20877
\(343\) 4843.90 0.762525
\(344\) 7927.13 1.24245
\(345\) −2150.83 −0.335643
\(346\) −632.080 −0.0982105
\(347\) 7866.47 1.21699 0.608493 0.793559i \(-0.291774\pi\)
0.608493 + 0.793559i \(0.291774\pi\)
\(348\) −30.8706 −0.00475528
\(349\) −2589.45 −0.397164 −0.198582 0.980084i \(-0.563634\pi\)
−0.198582 + 0.980084i \(0.563634\pi\)
\(350\) −2058.86 −0.314430
\(351\) 0 0
\(352\) −93.4979 −0.0141575
\(353\) −5349.76 −0.806626 −0.403313 0.915062i \(-0.632141\pi\)
−0.403313 + 0.915062i \(0.632141\pi\)
\(354\) −2664.28 −0.400014
\(355\) 1020.15 0.152518
\(356\) 100.638 0.0149826
\(357\) 1453.70 0.215512
\(358\) −9571.00 −1.41297
\(359\) −7919.96 −1.16434 −0.582172 0.813066i \(-0.697797\pi\)
−0.582172 + 0.813066i \(0.697797\pi\)
\(360\) −9483.10 −1.38834
\(361\) −2526.42 −0.368337
\(362\) 6181.18 0.897447
\(363\) 1227.62 0.177502
\(364\) 0 0
\(365\) −4475.71 −0.641834
\(366\) −22722.7 −3.24517
\(367\) 8311.54 1.18218 0.591089 0.806607i \(-0.298698\pi\)
0.591089 + 0.806607i \(0.298698\pi\)
\(368\) −2426.50 −0.343723
\(369\) −34995.8 −4.93715
\(370\) −4995.97 −0.701968
\(371\) 2997.84 0.419515
\(372\) 192.048 0.0267667
\(373\) −13584.3 −1.88570 −0.942851 0.333214i \(-0.891867\pi\)
−0.942851 + 0.333214i \(0.891867\pi\)
\(374\) 569.456 0.0787322
\(375\) 12192.6 1.67900
\(376\) −7287.96 −0.999595
\(377\) 0 0
\(378\) 10734.5 1.46064
\(379\) 13192.4 1.78798 0.893992 0.448083i \(-0.147893\pi\)
0.893992 + 0.448083i \(0.147893\pi\)
\(380\) −67.4794 −0.00910952
\(381\) −12016.9 −1.61586
\(382\) 6593.20 0.883082
\(383\) −1397.19 −0.186405 −0.0932024 0.995647i \(-0.529710\pi\)
−0.0932024 + 0.995647i \(0.529710\pi\)
\(384\) −14153.7 −1.88094
\(385\) 464.375 0.0614721
\(386\) 6662.46 0.878524
\(387\) 26302.2 3.45482
\(388\) −86.8440 −0.0113630
\(389\) 3634.88 0.473768 0.236884 0.971538i \(-0.423874\pi\)
0.236884 + 0.971538i \(0.423874\pi\)
\(390\) 0 0
\(391\) −719.529 −0.0930643
\(392\) −6480.07 −0.834932
\(393\) 5064.35 0.650032
\(394\) −1138.86 −0.145622
\(395\) 2743.43 0.349461
\(396\) −156.913 −0.0199121
\(397\) 4666.40 0.589924 0.294962 0.955509i \(-0.404693\pi\)
0.294962 + 0.955509i \(0.404693\pi\)
\(398\) 10746.1 1.35340
\(399\) 5166.12 0.648194
\(400\) 5947.61 0.743451
\(401\) −6638.07 −0.826657 −0.413329 0.910582i \(-0.635634\pi\)
−0.413329 + 0.910582i \(0.635634\pi\)
\(402\) −9761.53 −1.21110
\(403\) 0 0
\(404\) 268.691 0.0330888
\(405\) −16298.5 −1.99971
\(406\) 350.212 0.0428096
\(407\) −3603.00 −0.438806
\(408\) −4300.47 −0.521825
\(409\) −9754.31 −1.17927 −0.589633 0.807672i \(-0.700727\pi\)
−0.589633 + 0.807672i \(0.700727\pi\)
\(410\) −7029.62 −0.846752
\(411\) 29716.8 3.56647
\(412\) 31.9663 0.00382249
\(413\) −726.826 −0.0865975
\(414\) −8244.85 −0.978773
\(415\) 1090.18 0.128952
\(416\) 0 0
\(417\) −17350.7 −2.03757
\(418\) 2023.72 0.236803
\(419\) −3199.32 −0.373024 −0.186512 0.982453i \(-0.559718\pi\)
−0.186512 + 0.982453i \(0.559718\pi\)
\(420\) −80.4616 −0.00934792
\(421\) −7448.14 −0.862233 −0.431116 0.902296i \(-0.641880\pi\)
−0.431116 + 0.902296i \(0.641880\pi\)
\(422\) −13301.4 −1.53436
\(423\) −24181.4 −2.77953
\(424\) −8868.50 −1.01578
\(425\) 1763.64 0.201292
\(426\) 5301.07 0.602905
\(427\) −6198.84 −0.702536
\(428\) −8.87850 −0.00100271
\(429\) 0 0
\(430\) 5283.34 0.592524
\(431\) −935.516 −0.104553 −0.0522763 0.998633i \(-0.516648\pi\)
−0.0522763 + 0.998633i \(0.516648\pi\)
\(432\) −31009.6 −3.45359
\(433\) 5279.36 0.585935 0.292967 0.956122i \(-0.405357\pi\)
0.292967 + 0.956122i \(0.405357\pi\)
\(434\) −2178.69 −0.240969
\(435\) −896.754 −0.0988415
\(436\) −248.047 −0.0272461
\(437\) −2557.05 −0.279909
\(438\) −23257.4 −2.53717
\(439\) 375.139 0.0407845 0.0203923 0.999792i \(-0.493508\pi\)
0.0203923 + 0.999792i \(0.493508\pi\)
\(440\) −1373.76 −0.148844
\(441\) −21500.9 −2.32166
\(442\) 0 0
\(443\) −16515.4 −1.77126 −0.885631 0.464389i \(-0.846274\pi\)
−0.885631 + 0.464389i \(0.846274\pi\)
\(444\) 624.287 0.0667282
\(445\) 2923.42 0.311424
\(446\) 9736.51 1.03372
\(447\) 90.4651 0.00957237
\(448\) −4049.39 −0.427044
\(449\) 6135.87 0.644921 0.322461 0.946583i \(-0.395490\pi\)
0.322461 + 0.946583i \(0.395490\pi\)
\(450\) 20209.0 2.11702
\(451\) −5069.63 −0.529312
\(452\) 375.255 0.0390498
\(453\) 11287.1 1.17067
\(454\) 6934.42 0.716846
\(455\) 0 0
\(456\) −15282.9 −1.56949
\(457\) −2609.05 −0.267059 −0.133530 0.991045i \(-0.542631\pi\)
−0.133530 + 0.991045i \(0.542631\pi\)
\(458\) 12388.0 1.26387
\(459\) −9195.26 −0.935072
\(460\) 39.8257 0.00403670
\(461\) 8234.09 0.831887 0.415943 0.909391i \(-0.363451\pi\)
0.415943 + 0.909391i \(0.363451\pi\)
\(462\) 2413.06 0.243000
\(463\) −15472.8 −1.55309 −0.776546 0.630060i \(-0.783030\pi\)
−0.776546 + 0.630060i \(0.783030\pi\)
\(464\) −1011.69 −0.101221
\(465\) 5578.77 0.556364
\(466\) −1774.10 −0.176360
\(467\) 6389.68 0.633146 0.316573 0.948568i \(-0.397468\pi\)
0.316573 + 0.948568i \(0.397468\pi\)
\(468\) 0 0
\(469\) −2662.98 −0.262186
\(470\) −4857.34 −0.476707
\(471\) −27907.5 −2.73017
\(472\) 2150.17 0.209681
\(473\) 3810.25 0.370392
\(474\) 14255.9 1.38142
\(475\) 6267.59 0.605425
\(476\) −26.9172 −0.00259191
\(477\) −29425.7 −2.82455
\(478\) −9956.30 −0.952700
\(479\) −14490.9 −1.38227 −0.691134 0.722726i \(-0.742889\pi\)
−0.691134 + 0.722726i \(0.742889\pi\)
\(480\) 470.598 0.0447495
\(481\) 0 0
\(482\) 7780.64 0.735267
\(483\) −3049.00 −0.287234
\(484\) −22.7311 −0.00213477
\(485\) −2522.72 −0.236187
\(486\) −47227.7 −4.40801
\(487\) 7754.32 0.721524 0.360762 0.932658i \(-0.382517\pi\)
0.360762 + 0.932658i \(0.382517\pi\)
\(488\) 18338.0 1.70107
\(489\) −36593.5 −3.38408
\(490\) −4318.90 −0.398179
\(491\) −7089.28 −0.651599 −0.325799 0.945439i \(-0.605633\pi\)
−0.325799 + 0.945439i \(0.605633\pi\)
\(492\) 878.408 0.0804912
\(493\) −299.995 −0.0274059
\(494\) 0 0
\(495\) −4558.14 −0.413885
\(496\) 6293.79 0.569757
\(497\) 1446.15 0.130521
\(498\) 5664.98 0.509746
\(499\) 8769.38 0.786716 0.393358 0.919385i \(-0.371313\pi\)
0.393358 + 0.919385i \(0.371313\pi\)
\(500\) −225.764 −0.0201929
\(501\) −22810.9 −2.03416
\(502\) 16182.2 1.43874
\(503\) −5128.57 −0.454616 −0.227308 0.973823i \(-0.572992\pi\)
−0.227308 + 0.973823i \(0.572992\pi\)
\(504\) −13443.1 −1.18810
\(505\) 7805.15 0.687772
\(506\) −1194.38 −0.104934
\(507\) 0 0
\(508\) 222.509 0.0194336
\(509\) 13058.9 1.13718 0.568589 0.822622i \(-0.307489\pi\)
0.568589 + 0.822622i \(0.307489\pi\)
\(510\) −2866.21 −0.248859
\(511\) −6344.71 −0.549263
\(512\) 11966.5 1.03291
\(513\) −32678.0 −2.81241
\(514\) 13926.2 1.19506
\(515\) 928.582 0.0794529
\(516\) −660.196 −0.0563246
\(517\) −3503.02 −0.297994
\(518\) −7082.23 −0.600724
\(519\) 2294.38 0.194050
\(520\) 0 0
\(521\) −2189.22 −0.184091 −0.0920457 0.995755i \(-0.529341\pi\)
−0.0920457 + 0.995755i \(0.529341\pi\)
\(522\) −3437.55 −0.288233
\(523\) −6183.03 −0.516950 −0.258475 0.966018i \(-0.583220\pi\)
−0.258475 + 0.966018i \(0.583220\pi\)
\(524\) −93.7735 −0.00781778
\(525\) 7473.41 0.621269
\(526\) 7594.46 0.629533
\(527\) 1866.29 0.154264
\(528\) −6970.84 −0.574559
\(529\) −10657.9 −0.875964
\(530\) −5910.76 −0.484428
\(531\) 7134.26 0.583052
\(532\) −95.6580 −0.00779567
\(533\) 0 0
\(534\) 15191.2 1.23106
\(535\) −257.910 −0.0208419
\(536\) 7877.90 0.634839
\(537\) 34741.6 2.79183
\(538\) −13239.5 −1.06096
\(539\) −3114.71 −0.248905
\(540\) 508.955 0.0405591
\(541\) −2056.64 −0.163442 −0.0817208 0.996655i \(-0.526042\pi\)
−0.0817208 + 0.996655i \(0.526042\pi\)
\(542\) 6400.19 0.507217
\(543\) −22437.0 −1.77323
\(544\) 157.431 0.0124077
\(545\) −7205.47 −0.566328
\(546\) 0 0
\(547\) −14278.7 −1.11611 −0.558055 0.829804i \(-0.688452\pi\)
−0.558055 + 0.829804i \(0.688452\pi\)
\(548\) −550.248 −0.0428931
\(549\) 60845.5 4.73010
\(550\) 2927.56 0.226966
\(551\) −1066.12 −0.0824287
\(552\) 9019.84 0.695489
\(553\) 3889.06 0.299059
\(554\) −4975.27 −0.381550
\(555\) 18134.8 1.38699
\(556\) 321.273 0.0245054
\(557\) −3547.29 −0.269845 −0.134922 0.990856i \(-0.543078\pi\)
−0.134922 + 0.990856i \(0.543078\pi\)
\(558\) 21385.3 1.62242
\(559\) 0 0
\(560\) −2636.88 −0.198980
\(561\) −2067.06 −0.155564
\(562\) −10272.7 −0.771045
\(563\) −7881.91 −0.590023 −0.295011 0.955494i \(-0.595323\pi\)
−0.295011 + 0.955494i \(0.595323\pi\)
\(564\) 606.964 0.0453152
\(565\) 10900.7 0.811675
\(566\) 10727.1 0.796628
\(567\) −23104.6 −1.71129
\(568\) −4278.15 −0.316034
\(569\) −10336.6 −0.761567 −0.380784 0.924664i \(-0.624346\pi\)
−0.380784 + 0.924664i \(0.624346\pi\)
\(570\) −10185.9 −0.748492
\(571\) 25104.0 1.83988 0.919940 0.392059i \(-0.128237\pi\)
0.919940 + 0.392059i \(0.128237\pi\)
\(572\) 0 0
\(573\) −23932.5 −1.74484
\(574\) −9965.11 −0.724627
\(575\) −3699.08 −0.268282
\(576\) 39747.4 2.87524
\(577\) −5486.30 −0.395836 −0.197918 0.980219i \(-0.563418\pi\)
−0.197918 + 0.980219i \(0.563418\pi\)
\(578\) 12773.1 0.919188
\(579\) −24184.0 −1.73584
\(580\) 16.6047 0.00118874
\(581\) 1545.43 0.110353
\(582\) −13108.9 −0.933648
\(583\) −4262.73 −0.302820
\(584\) 18769.6 1.32995
\(585\) 0 0
\(586\) −22069.9 −1.55580
\(587\) −4796.54 −0.337265 −0.168632 0.985679i \(-0.553935\pi\)
−0.168632 + 0.985679i \(0.553935\pi\)
\(588\) 539.681 0.0378504
\(589\) 6632.40 0.463979
\(590\) 1433.06 0.0999971
\(591\) 4133.94 0.287729
\(592\) 20459.1 1.42038
\(593\) 5888.68 0.407790 0.203895 0.978993i \(-0.434640\pi\)
0.203895 + 0.978993i \(0.434640\pi\)
\(594\) −15263.7 −1.05434
\(595\) −781.914 −0.0538745
\(596\) −1.67509 −0.000115125 0
\(597\) −39007.2 −2.67414
\(598\) 0 0
\(599\) 16087.2 1.09734 0.548668 0.836041i \(-0.315135\pi\)
0.548668 + 0.836041i \(0.315135\pi\)
\(600\) −22108.6 −1.50430
\(601\) 1577.34 0.107057 0.0535283 0.998566i \(-0.482953\pi\)
0.0535283 + 0.998566i \(0.482953\pi\)
\(602\) 7489.60 0.507065
\(603\) 26138.9 1.76527
\(604\) −208.996 −0.0140794
\(605\) −660.311 −0.0443727
\(606\) 40558.4 2.71877
\(607\) 29401.1 1.96599 0.982993 0.183641i \(-0.0587884\pi\)
0.982993 + 0.183641i \(0.0587884\pi\)
\(608\) 559.477 0.0373187
\(609\) −1271.23 −0.0845858
\(610\) 12222.1 0.811242
\(611\) 0 0
\(612\) 264.210 0.0174511
\(613\) −21093.0 −1.38978 −0.694891 0.719115i \(-0.744547\pi\)
−0.694891 + 0.719115i \(0.744547\pi\)
\(614\) −2802.52 −0.184203
\(615\) 25516.7 1.67306
\(616\) −1947.43 −0.127377
\(617\) 17937.2 1.17038 0.585189 0.810897i \(-0.301020\pi\)
0.585189 + 0.810897i \(0.301020\pi\)
\(618\) 4825.25 0.314078
\(619\) −18166.1 −1.17958 −0.589789 0.807557i \(-0.700789\pi\)
−0.589789 + 0.807557i \(0.700789\pi\)
\(620\) −103.299 −0.00669126
\(621\) 19286.2 1.24626
\(622\) 14664.7 0.945342
\(623\) 4144.21 0.266508
\(624\) 0 0
\(625\) 5344.31 0.342036
\(626\) 4327.15 0.276274
\(627\) −7345.88 −0.467889
\(628\) 516.747 0.0328351
\(629\) 6066.72 0.384572
\(630\) −8959.70 −0.566608
\(631\) −8878.70 −0.560151 −0.280076 0.959978i \(-0.590360\pi\)
−0.280076 + 0.959978i \(0.590360\pi\)
\(632\) −11505.0 −0.724120
\(633\) 48282.4 3.03168
\(634\) −23170.5 −1.45145
\(635\) 6463.63 0.403939
\(636\) 738.596 0.0460491
\(637\) 0 0
\(638\) −497.978 −0.0309015
\(639\) −14194.9 −0.878781
\(640\) 7613.00 0.470204
\(641\) −2369.01 −0.145975 −0.0729876 0.997333i \(-0.523253\pi\)
−0.0729876 + 0.997333i \(0.523253\pi\)
\(642\) −1340.19 −0.0823883
\(643\) 5914.40 0.362739 0.181369 0.983415i \(-0.441947\pi\)
0.181369 + 0.983415i \(0.441947\pi\)
\(644\) 56.4565 0.00345450
\(645\) −19177.9 −1.17074
\(646\) −3407.54 −0.207535
\(647\) 2640.30 0.160434 0.0802170 0.996777i \(-0.474439\pi\)
0.0802170 + 0.996777i \(0.474439\pi\)
\(648\) 68350.3 4.14360
\(649\) 1033.50 0.0625091
\(650\) 0 0
\(651\) 7908.40 0.476121
\(652\) 677.581 0.0406996
\(653\) 13149.0 0.787993 0.393997 0.919112i \(-0.371092\pi\)
0.393997 + 0.919112i \(0.371092\pi\)
\(654\) −37442.3 −2.23870
\(655\) −2724.01 −0.162498
\(656\) 28787.1 1.71334
\(657\) 62277.4 3.69813
\(658\) −6885.71 −0.407953
\(659\) 18288.3 1.08105 0.540525 0.841328i \(-0.318226\pi\)
0.540525 + 0.841328i \(0.318226\pi\)
\(660\) 114.411 0.00674765
\(661\) −6578.84 −0.387122 −0.193561 0.981088i \(-0.562004\pi\)
−0.193561 + 0.981088i \(0.562004\pi\)
\(662\) −19048.7 −1.11835
\(663\) 0 0
\(664\) −4571.84 −0.267201
\(665\) −2778.75 −0.162038
\(666\) 69516.6 4.04461
\(667\) 629.214 0.0365266
\(668\) 422.376 0.0244644
\(669\) −35342.4 −2.04248
\(670\) 5250.53 0.302755
\(671\) 8814.34 0.507114
\(672\) 667.114 0.0382954
\(673\) 13014.3 0.745417 0.372709 0.927948i \(-0.378429\pi\)
0.372709 + 0.927948i \(0.378429\pi\)
\(674\) −31901.2 −1.82313
\(675\) −47272.6 −2.69559
\(676\) 0 0
\(677\) 15153.5 0.860261 0.430131 0.902767i \(-0.358468\pi\)
0.430131 + 0.902767i \(0.358468\pi\)
\(678\) 56644.1 3.20856
\(679\) −3576.17 −0.202122
\(680\) 2313.13 0.130448
\(681\) −25171.1 −1.41639
\(682\) 3097.96 0.173940
\(683\) 5526.04 0.309587 0.154794 0.987947i \(-0.450529\pi\)
0.154794 + 0.987947i \(0.450529\pi\)
\(684\) 938.944 0.0524875
\(685\) −15984.1 −0.891561
\(686\) −13538.8 −0.753519
\(687\) −44967.1 −2.49724
\(688\) −21635.9 −1.19893
\(689\) 0 0
\(690\) 6011.62 0.331679
\(691\) 12665.8 0.697295 0.348648 0.937254i \(-0.386641\pi\)
0.348648 + 0.937254i \(0.386641\pi\)
\(692\) −42.4836 −0.00233379
\(693\) −6461.57 −0.354191
\(694\) −21986.9 −1.20261
\(695\) 9332.60 0.509361
\(696\) 3760.67 0.204810
\(697\) 8536.23 0.463892
\(698\) 7237.57 0.392473
\(699\) 6439.78 0.348462
\(700\) −138.381 −0.00747185
\(701\) 31069.9 1.67403 0.837013 0.547182i \(-0.184300\pi\)
0.837013 + 0.547182i \(0.184300\pi\)
\(702\) 0 0
\(703\) 21559.8 1.15668
\(704\) 5757.97 0.308255
\(705\) 17631.6 0.941906
\(706\) 14952.7 0.797099
\(707\) 11064.5 0.588576
\(708\) −179.073 −0.00950561
\(709\) −3060.38 −0.162108 −0.0810542 0.996710i \(-0.525829\pi\)
−0.0810542 + 0.996710i \(0.525829\pi\)
\(710\) −2851.34 −0.150717
\(711\) −38173.6 −2.01353
\(712\) −12259.8 −0.645303
\(713\) −3914.38 −0.205603
\(714\) −4063.11 −0.212966
\(715\) 0 0
\(716\) −643.290 −0.0335767
\(717\) 36140.2 1.88240
\(718\) 22136.5 1.15059
\(719\) 5162.79 0.267788 0.133894 0.990996i \(-0.457252\pi\)
0.133894 + 0.990996i \(0.457252\pi\)
\(720\) 25882.7 1.33971
\(721\) 1316.35 0.0679935
\(722\) 7061.40 0.363986
\(723\) −28242.8 −1.45278
\(724\) 415.452 0.0213262
\(725\) −1542.27 −0.0790047
\(726\) −3431.22 −0.175406
\(727\) −19866.9 −1.01351 −0.506756 0.862089i \(-0.669156\pi\)
−0.506756 + 0.862089i \(0.669156\pi\)
\(728\) 0 0
\(729\) 90791.4 4.61268
\(730\) 12509.7 0.634253
\(731\) −6415.68 −0.324614
\(732\) −1527.25 −0.0771157
\(733\) 22311.4 1.12427 0.562135 0.827046i \(-0.309980\pi\)
0.562135 + 0.827046i \(0.309980\pi\)
\(734\) −23230.9 −1.16821
\(735\) 15677.1 0.786746
\(736\) −330.198 −0.0165371
\(737\) 3786.59 0.189255
\(738\) 97813.9 4.87883
\(739\) 2637.38 0.131283 0.0656413 0.997843i \(-0.479091\pi\)
0.0656413 + 0.997843i \(0.479091\pi\)
\(740\) −335.791 −0.0166810
\(741\) 0 0
\(742\) −8379.02 −0.414560
\(743\) −19802.1 −0.977752 −0.488876 0.872353i \(-0.662593\pi\)
−0.488876 + 0.872353i \(0.662593\pi\)
\(744\) −23395.4 −1.15285
\(745\) −48.6593 −0.00239294
\(746\) 37968.3 1.86343
\(747\) −15169.4 −0.742996
\(748\) 38.2745 0.00187093
\(749\) −365.610 −0.0178359
\(750\) −34078.7 −1.65917
\(751\) −19359.7 −0.940673 −0.470337 0.882487i \(-0.655867\pi\)
−0.470337 + 0.882487i \(0.655867\pi\)
\(752\) 19891.4 0.964580
\(753\) −58739.4 −2.84274
\(754\) 0 0
\(755\) −6071.10 −0.292649
\(756\) 721.488 0.0347094
\(757\) −15668.4 −0.752281 −0.376140 0.926563i \(-0.622749\pi\)
−0.376140 + 0.926563i \(0.622749\pi\)
\(758\) −36872.9 −1.76687
\(759\) 4335.47 0.207335
\(760\) 8220.38 0.392348
\(761\) −9040.74 −0.430653 −0.215326 0.976542i \(-0.569082\pi\)
−0.215326 + 0.976542i \(0.569082\pi\)
\(762\) 33587.4 1.59678
\(763\) −10214.4 −0.484647
\(764\) 443.145 0.0209848
\(765\) 7674.98 0.362731
\(766\) 3905.17 0.184203
\(767\) 0 0
\(768\) −2925.92 −0.137474
\(769\) 19880.2 0.932248 0.466124 0.884719i \(-0.345650\pi\)
0.466124 + 0.884719i \(0.345650\pi\)
\(770\) −1297.94 −0.0607461
\(771\) −50550.6 −2.36126
\(772\) 447.800 0.0208765
\(773\) −26775.9 −1.24588 −0.622938 0.782271i \(-0.714061\pi\)
−0.622938 + 0.782271i \(0.714061\pi\)
\(774\) −73515.2 −3.41402
\(775\) 9594.56 0.444706
\(776\) 10579.4 0.489404
\(777\) 25707.7 1.18695
\(778\) −10159.6 −0.468173
\(779\) 30335.9 1.39525
\(780\) 0 0
\(781\) −2056.33 −0.0942142
\(782\) 2011.10 0.0919651
\(783\) 8041.07 0.367004
\(784\) 17686.4 0.805685
\(785\) 15010.9 0.682500
\(786\) −14155.0 −0.642354
\(787\) 15119.7 0.684825 0.342413 0.939550i \(-0.388756\pi\)
0.342413 + 0.939550i \(0.388756\pi\)
\(788\) −76.5457 −0.00346044
\(789\) −27567.0 −1.24387
\(790\) −7667.95 −0.345333
\(791\) 15452.7 0.694609
\(792\) 19115.2 0.857615
\(793\) 0 0
\(794\) −13042.7 −0.582957
\(795\) 21455.4 0.957161
\(796\) 722.273 0.0321612
\(797\) 25759.8 1.14487 0.572434 0.819951i \(-0.305999\pi\)
0.572434 + 0.819951i \(0.305999\pi\)
\(798\) −14439.4 −0.640538
\(799\) 5898.38 0.261164
\(800\) 809.351 0.0357686
\(801\) −40678.0 −1.79437
\(802\) 18553.5 0.816893
\(803\) 9021.76 0.396477
\(804\) −656.096 −0.0287795
\(805\) 1639.99 0.0718040
\(806\) 0 0
\(807\) 48057.9 2.09631
\(808\) −32732.1 −1.42514
\(809\) 13250.8 0.575864 0.287932 0.957651i \(-0.407032\pi\)
0.287932 + 0.957651i \(0.407032\pi\)
\(810\) 45554.7 1.97609
\(811\) 14548.1 0.629903 0.314952 0.949108i \(-0.398012\pi\)
0.314952 + 0.949108i \(0.398012\pi\)
\(812\) 23.5386 0.00101729
\(813\) −23231.9 −1.00219
\(814\) 10070.5 0.433623
\(815\) 19682.9 0.845967
\(816\) 11737.5 0.503546
\(817\) −22799.9 −0.976339
\(818\) 27263.5 1.16534
\(819\) 0 0
\(820\) −472.478 −0.0201215
\(821\) −15581.7 −0.662369 −0.331184 0.943566i \(-0.607448\pi\)
−0.331184 + 0.943566i \(0.607448\pi\)
\(822\) −83059.0 −3.52435
\(823\) −38875.7 −1.64656 −0.823282 0.567632i \(-0.807860\pi\)
−0.823282 + 0.567632i \(0.807860\pi\)
\(824\) −3894.15 −0.164635
\(825\) −10626.7 −0.448453
\(826\) 2031.49 0.0855747
\(827\) 12788.7 0.537734 0.268867 0.963177i \(-0.413351\pi\)
0.268867 + 0.963177i \(0.413351\pi\)
\(828\) −554.156 −0.0232588
\(829\) −19014.4 −0.796620 −0.398310 0.917251i \(-0.630403\pi\)
−0.398310 + 0.917251i \(0.630403\pi\)
\(830\) −3047.08 −0.127428
\(831\) 18059.6 0.753890
\(832\) 0 0
\(833\) 5244.53 0.218142
\(834\) 48495.6 2.01351
\(835\) 12269.5 0.508508
\(836\) 136.019 0.00562718
\(837\) −50024.1 −2.06581
\(838\) 8942.17 0.368618
\(839\) −16563.8 −0.681581 −0.340790 0.940139i \(-0.610695\pi\)
−0.340790 + 0.940139i \(0.610695\pi\)
\(840\) 9801.89 0.402616
\(841\) −24126.7 −0.989244
\(842\) 20817.7 0.852049
\(843\) 37288.7 1.52348
\(844\) −894.017 −0.0364613
\(845\) 0 0
\(846\) 67587.6 2.74670
\(847\) −936.049 −0.0379729
\(848\) 24205.2 0.980202
\(849\) −38938.0 −1.57403
\(850\) −4929.41 −0.198915
\(851\) −12724.4 −0.512558
\(852\) 356.297 0.0143269
\(853\) 28302.9 1.13608 0.568038 0.823002i \(-0.307703\pi\)
0.568038 + 0.823002i \(0.307703\pi\)
\(854\) 17325.9 0.694238
\(855\) 27275.2 1.09099
\(856\) 1081.58 0.0431867
\(857\) −33103.8 −1.31949 −0.659746 0.751489i \(-0.729336\pi\)
−0.659746 + 0.751489i \(0.729336\pi\)
\(858\) 0 0
\(859\) −80.2138 −0.00318610 −0.00159305 0.999999i \(-0.500507\pi\)
−0.00159305 + 0.999999i \(0.500507\pi\)
\(860\) 355.106 0.0140803
\(861\) 36172.2 1.43176
\(862\) 2614.79 0.103318
\(863\) −6866.87 −0.270859 −0.135429 0.990787i \(-0.543241\pi\)
−0.135429 + 0.990787i \(0.543241\pi\)
\(864\) −4219.79 −0.166158
\(865\) −1234.10 −0.0485094
\(866\) −14755.9 −0.579014
\(867\) −46364.8 −1.81618
\(868\) −146.435 −0.00572619
\(869\) −5529.98 −0.215871
\(870\) 2506.45 0.0976741
\(871\) 0 0
\(872\) 30217.2 1.17349
\(873\) 35102.4 1.36087
\(874\) 7147.00 0.276603
\(875\) −9296.79 −0.359187
\(876\) −1563.19 −0.0602913
\(877\) 35907.6 1.38257 0.691285 0.722582i \(-0.257045\pi\)
0.691285 + 0.722582i \(0.257045\pi\)
\(878\) −1048.52 −0.0403028
\(879\) 80111.3 3.07405
\(880\) 3749.48 0.143630
\(881\) −19063.6 −0.729021 −0.364511 0.931199i \(-0.618764\pi\)
−0.364511 + 0.931199i \(0.618764\pi\)
\(882\) 60095.4 2.29424
\(883\) −18097.1 −0.689711 −0.344855 0.938656i \(-0.612072\pi\)
−0.344855 + 0.938656i \(0.612072\pi\)
\(884\) 0 0
\(885\) −5201.86 −0.197580
\(886\) 46160.8 1.75034
\(887\) −49133.2 −1.85990 −0.929949 0.367687i \(-0.880150\pi\)
−0.929949 + 0.367687i \(0.880150\pi\)
\(888\) −76051.0 −2.87399
\(889\) 9162.77 0.345680
\(890\) −8171.02 −0.307745
\(891\) 32853.2 1.23527
\(892\) 654.414 0.0245644
\(893\) 20961.6 0.785500
\(894\) −252.852 −0.00945931
\(895\) −18686.8 −0.697913
\(896\) 10792.1 0.402387
\(897\) 0 0
\(898\) −17149.9 −0.637304
\(899\) −1632.04 −0.0605467
\(900\) 1358.29 0.0503072
\(901\) 7177.57 0.265393
\(902\) 14169.7 0.523060
\(903\) −27186.4 −1.00189
\(904\) −45713.8 −1.68188
\(905\) 12068.4 0.443279
\(906\) −31547.6 −1.15684
\(907\) 6772.16 0.247923 0.123961 0.992287i \(-0.460440\pi\)
0.123961 + 0.992287i \(0.460440\pi\)
\(908\) 466.079 0.0170346
\(909\) −108605. −3.96282
\(910\) 0 0
\(911\) 16679.9 0.606620 0.303310 0.952892i \(-0.401908\pi\)
0.303310 + 0.952892i \(0.401908\pi\)
\(912\) 41712.5 1.51451
\(913\) −2197.50 −0.0796566
\(914\) 7292.34 0.263905
\(915\) −44364.7 −1.60290
\(916\) 832.629 0.0300337
\(917\) −3861.52 −0.139061
\(918\) 25700.9 0.924027
\(919\) 8903.13 0.319572 0.159786 0.987152i \(-0.448920\pi\)
0.159786 + 0.987152i \(0.448920\pi\)
\(920\) −4851.59 −0.173861
\(921\) 10172.8 0.363959
\(922\) −23014.4 −0.822061
\(923\) 0 0
\(924\) 162.188 0.00577445
\(925\) 31188.8 1.10863
\(926\) 43246.8 1.53475
\(927\) −12920.8 −0.457793
\(928\) −137.671 −0.00486989
\(929\) 42394.0 1.49720 0.748601 0.663020i \(-0.230726\pi\)
0.748601 + 0.663020i \(0.230726\pi\)
\(930\) −15592.8 −0.549793
\(931\) 18637.9 0.656105
\(932\) −119.242 −0.00419087
\(933\) −53231.3 −1.86786
\(934\) −17859.3 −0.625668
\(935\) 1111.83 0.0388885
\(936\) 0 0
\(937\) −36138.5 −1.25997 −0.629986 0.776607i \(-0.716939\pi\)
−0.629986 + 0.776607i \(0.716939\pi\)
\(938\) 7443.09 0.259089
\(939\) −15707.0 −0.545878
\(940\) −326.474 −0.0113281
\(941\) 20360.0 0.705331 0.352665 0.935750i \(-0.385275\pi\)
0.352665 + 0.935750i \(0.385275\pi\)
\(942\) 78002.1 2.69793
\(943\) −17904.0 −0.618276
\(944\) −5868.57 −0.202336
\(945\) 20958.4 0.721457
\(946\) −10649.7 −0.366017
\(947\) 55852.7 1.91655 0.958274 0.285853i \(-0.0922769\pi\)
0.958274 + 0.285853i \(0.0922769\pi\)
\(948\) 958.172 0.0328270
\(949\) 0 0
\(950\) −17518.1 −0.598274
\(951\) 84106.2 2.86786
\(952\) 3279.07 0.111634
\(953\) 38154.0 1.29688 0.648441 0.761265i \(-0.275421\pi\)
0.648441 + 0.761265i \(0.275421\pi\)
\(954\) 82245.4 2.79119
\(955\) 12872.8 0.436183
\(956\) −669.187 −0.0226392
\(957\) 1807.60 0.0610569
\(958\) 40502.4 1.36594
\(959\) −22658.8 −0.762973
\(960\) −28981.3 −0.974341
\(961\) −19638.0 −0.659192
\(962\) 0 0
\(963\) 3588.70 0.120087
\(964\) 522.956 0.0174723
\(965\) 13008.1 0.433932
\(966\) 8522.01 0.283842
\(967\) −47950.6 −1.59461 −0.797304 0.603577i \(-0.793741\pi\)
−0.797304 + 0.603577i \(0.793741\pi\)
\(968\) 2769.11 0.0919449
\(969\) 12369.0 0.410060
\(970\) 7051.04 0.233397
\(971\) 46410.1 1.53385 0.766926 0.641736i \(-0.221785\pi\)
0.766926 + 0.641736i \(0.221785\pi\)
\(972\) −3174.29 −0.104748
\(973\) 13229.8 0.435896
\(974\) −21673.5 −0.713002
\(975\) 0 0
\(976\) −50050.9 −1.64149
\(977\) 18690.8 0.612050 0.306025 0.952023i \(-0.401001\pi\)
0.306025 + 0.952023i \(0.401001\pi\)
\(978\) 102280. 3.34411
\(979\) −5892.79 −0.192374
\(980\) −290.283 −0.00946201
\(981\) 100261. 3.26308
\(982\) 19814.7 0.643903
\(983\) −44536.0 −1.44504 −0.722521 0.691349i \(-0.757017\pi\)
−0.722521 + 0.691349i \(0.757017\pi\)
\(984\) −107008. −3.46676
\(985\) −2223.56 −0.0719276
\(986\) 838.493 0.0270822
\(987\) 24994.3 0.806057
\(988\) 0 0
\(989\) 13456.3 0.432645
\(990\) 12740.1 0.408997
\(991\) 30003.5 0.961748 0.480874 0.876790i \(-0.340319\pi\)
0.480874 + 0.876790i \(0.340319\pi\)
\(992\) 856.459 0.0274119
\(993\) 69144.4 2.20970
\(994\) −4042.02 −0.128979
\(995\) 20981.2 0.668491
\(996\) 380.757 0.0121132
\(997\) 38357.3 1.21844 0.609221 0.793000i \(-0.291482\pi\)
0.609221 + 0.793000i \(0.291482\pi\)
\(998\) −24510.6 −0.777424
\(999\) −162612. −5.14997
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 1859.4.a.f.1.5 17
13.4 even 6 143.4.e.a.133.5 yes 34
13.10 even 6 143.4.e.a.100.5 34
13.12 even 2 1859.4.a.i.1.13 17
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.e.a.100.5 34 13.10 even 6
143.4.e.a.133.5 yes 34 13.4 even 6
1859.4.a.f.1.5 17 1.1 even 1 trivial
1859.4.a.i.1.13 17 13.12 even 2