Properties

Label 2151.4.a.c.1.2
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $28$
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] = [2151,4,Mod(1,2151)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2151, 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("2151.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.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: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: no (minimal twist has level 717)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 2151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.27604 q^{2} +10.2845 q^{4} +1.46589 q^{5} -24.3497 q^{7} -9.76851 q^{8} +O(q^{10})\) \(q-4.27604 q^{2} +10.2845 q^{4} +1.46589 q^{5} -24.3497 q^{7} -9.76851 q^{8} -6.26822 q^{10} +39.8171 q^{11} -56.6674 q^{13} +104.120 q^{14} -40.5053 q^{16} -98.8941 q^{17} -20.1280 q^{19} +15.0760 q^{20} -170.259 q^{22} -217.605 q^{23} -122.851 q^{25} +242.312 q^{26} -250.424 q^{28} +158.291 q^{29} -275.269 q^{31} +251.350 q^{32} +422.875 q^{34} -35.6941 q^{35} -341.944 q^{37} +86.0679 q^{38} -14.3196 q^{40} +409.072 q^{41} +100.252 q^{43} +409.498 q^{44} +930.486 q^{46} -254.372 q^{47} +249.909 q^{49} +525.316 q^{50} -582.794 q^{52} -509.753 q^{53} +58.3677 q^{55} +237.861 q^{56} -676.857 q^{58} -808.008 q^{59} -24.1394 q^{61} +1177.06 q^{62} -750.740 q^{64} -83.0684 q^{65} +242.006 q^{67} -1017.07 q^{68} +152.629 q^{70} +4.86949 q^{71} +45.9729 q^{73} +1462.16 q^{74} -207.006 q^{76} -969.536 q^{77} -208.443 q^{79} -59.3765 q^{80} -1749.21 q^{82} +200.204 q^{83} -144.968 q^{85} -428.680 q^{86} -388.954 q^{88} +713.266 q^{89} +1379.84 q^{91} -2237.95 q^{92} +1087.71 q^{94} -29.5055 q^{95} -1598.60 q^{97} -1068.62 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 13 q^{2} + 99 q^{4} + 74 q^{5} - 82 q^{7} + 135 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 13 q^{2} + 99 q^{4} + 74 q^{5} - 82 q^{7} + 135 q^{8} - 68 q^{10} + 258 q^{11} - 134 q^{13} + 292 q^{14} + 327 q^{16} + 364 q^{17} - 278 q^{19} + 986 q^{20} - 179 q^{22} + 668 q^{23} + 490 q^{25} + 760 q^{26} - 802 q^{28} + 714 q^{29} - 608 q^{31} + 918 q^{32} - 228 q^{34} + 934 q^{35} - 1080 q^{37} + 1395 q^{38} - 563 q^{40} + 1796 q^{41} - 1934 q^{43} + 3157 q^{44} - 940 q^{46} + 2032 q^{47} + 762 q^{49} + 1754 q^{50} - 2328 q^{52} + 1790 q^{53} - 478 q^{55} + 3557 q^{56} - 2626 q^{58} + 3622 q^{59} + 324 q^{61} + 796 q^{62} + 2023 q^{64} + 2200 q^{65} - 2444 q^{67} - 357 q^{68} + 4305 q^{70} + 1298 q^{71} - 1368 q^{73} - 813 q^{74} + 1390 q^{76} + 1408 q^{77} - 1378 q^{79} + 7684 q^{80} + 9001 q^{82} + 3524 q^{83} + 60 q^{85} + 2543 q^{86} + 1749 q^{88} + 7854 q^{89} + 850 q^{91} + 496 q^{92} + 6634 q^{94} + 3696 q^{95} - 1746 q^{97} + 4632 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.27604 −1.51181 −0.755903 0.654683i \(-0.772802\pi\)
−0.755903 + 0.654683i \(0.772802\pi\)
\(3\) 0 0
\(4\) 10.2845 1.28556
\(5\) 1.46589 0.131114 0.0655568 0.997849i \(-0.479118\pi\)
0.0655568 + 0.997849i \(0.479118\pi\)
\(6\) 0 0
\(7\) −24.3497 −1.31476 −0.657381 0.753558i \(-0.728336\pi\)
−0.657381 + 0.753558i \(0.728336\pi\)
\(8\) −9.76851 −0.431711
\(9\) 0 0
\(10\) −6.26822 −0.198218
\(11\) 39.8171 1.09139 0.545696 0.837983i \(-0.316265\pi\)
0.545696 + 0.837983i \(0.316265\pi\)
\(12\) 0 0
\(13\) −56.6674 −1.20898 −0.604489 0.796614i \(-0.706623\pi\)
−0.604489 + 0.796614i \(0.706623\pi\)
\(14\) 104.120 1.98767
\(15\) 0 0
\(16\) −40.5053 −0.632896
\(17\) −98.8941 −1.41090 −0.705451 0.708759i \(-0.749256\pi\)
−0.705451 + 0.708759i \(0.749256\pi\)
\(18\) 0 0
\(19\) −20.1280 −0.243035 −0.121518 0.992589i \(-0.538776\pi\)
−0.121518 + 0.992589i \(0.538776\pi\)
\(20\) 15.0760 0.168554
\(21\) 0 0
\(22\) −170.259 −1.64997
\(23\) −217.605 −1.97277 −0.986386 0.164447i \(-0.947416\pi\)
−0.986386 + 0.164447i \(0.947416\pi\)
\(24\) 0 0
\(25\) −122.851 −0.982809
\(26\) 242.312 1.82774
\(27\) 0 0
\(28\) −250.424 −1.69020
\(29\) 158.291 1.01358 0.506790 0.862069i \(-0.330832\pi\)
0.506790 + 0.862069i \(0.330832\pi\)
\(30\) 0 0
\(31\) −275.269 −1.59483 −0.797415 0.603431i \(-0.793800\pi\)
−0.797415 + 0.603431i \(0.793800\pi\)
\(32\) 251.350 1.38853
\(33\) 0 0
\(34\) 422.875 2.13301
\(35\) −35.6941 −0.172383
\(36\) 0 0
\(37\) −341.944 −1.51933 −0.759665 0.650315i \(-0.774637\pi\)
−0.759665 + 0.650315i \(0.774637\pi\)
\(38\) 86.0679 0.367423
\(39\) 0 0
\(40\) −14.3196 −0.0566032
\(41\) 409.072 1.55820 0.779102 0.626897i \(-0.215675\pi\)
0.779102 + 0.626897i \(0.215675\pi\)
\(42\) 0 0
\(43\) 100.252 0.355541 0.177771 0.984072i \(-0.443112\pi\)
0.177771 + 0.984072i \(0.443112\pi\)
\(44\) 409.498 1.40305
\(45\) 0 0
\(46\) 930.486 2.98245
\(47\) −254.372 −0.789447 −0.394724 0.918800i \(-0.629160\pi\)
−0.394724 + 0.918800i \(0.629160\pi\)
\(48\) 0 0
\(49\) 249.909 0.728598
\(50\) 525.316 1.48582
\(51\) 0 0
\(52\) −582.794 −1.55421
\(53\) −509.753 −1.32113 −0.660566 0.750768i \(-0.729684\pi\)
−0.660566 + 0.750768i \(0.729684\pi\)
\(54\) 0 0
\(55\) 58.3677 0.143096
\(56\) 237.861 0.567597
\(57\) 0 0
\(58\) −676.857 −1.53234
\(59\) −808.008 −1.78294 −0.891472 0.453076i \(-0.850327\pi\)
−0.891472 + 0.453076i \(0.850327\pi\)
\(60\) 0 0
\(61\) −24.1394 −0.0506677 −0.0253339 0.999679i \(-0.508065\pi\)
−0.0253339 + 0.999679i \(0.508065\pi\)
\(62\) 1177.06 2.41108
\(63\) 0 0
\(64\) −750.740 −1.46629
\(65\) −83.0684 −0.158513
\(66\) 0 0
\(67\) 242.006 0.441280 0.220640 0.975355i \(-0.429185\pi\)
0.220640 + 0.975355i \(0.429185\pi\)
\(68\) −1017.07 −1.81380
\(69\) 0 0
\(70\) 152.629 0.260610
\(71\) 4.86949 0.00813947 0.00406974 0.999992i \(-0.498705\pi\)
0.00406974 + 0.999992i \(0.498705\pi\)
\(72\) 0 0
\(73\) 45.9729 0.0737086 0.0368543 0.999321i \(-0.488266\pi\)
0.0368543 + 0.999321i \(0.488266\pi\)
\(74\) 1462.16 2.29693
\(75\) 0 0
\(76\) −207.006 −0.312437
\(77\) −969.536 −1.43492
\(78\) 0 0
\(79\) −208.443 −0.296856 −0.148428 0.988923i \(-0.547421\pi\)
−0.148428 + 0.988923i \(0.547421\pi\)
\(80\) −59.3765 −0.0829812
\(81\) 0 0
\(82\) −1749.21 −2.35570
\(83\) 200.204 0.264762 0.132381 0.991199i \(-0.457738\pi\)
0.132381 + 0.991199i \(0.457738\pi\)
\(84\) 0 0
\(85\) −144.968 −0.184988
\(86\) −428.680 −0.537509
\(87\) 0 0
\(88\) −388.954 −0.471166
\(89\) 713.266 0.849506 0.424753 0.905309i \(-0.360361\pi\)
0.424753 + 0.905309i \(0.360361\pi\)
\(90\) 0 0
\(91\) 1379.84 1.58952
\(92\) −2237.95 −2.53612
\(93\) 0 0
\(94\) 1087.71 1.19349
\(95\) −29.5055 −0.0318652
\(96\) 0 0
\(97\) −1598.60 −1.67333 −0.836664 0.547716i \(-0.815497\pi\)
−0.836664 + 0.547716i \(0.815497\pi\)
\(98\) −1068.62 −1.10150
\(99\) 0 0
\(100\) −1263.46 −1.26346
\(101\) 151.191 0.148951 0.0744757 0.997223i \(-0.476272\pi\)
0.0744757 + 0.997223i \(0.476272\pi\)
\(102\) 0 0
\(103\) 1815.75 1.73700 0.868501 0.495688i \(-0.165084\pi\)
0.868501 + 0.495688i \(0.165084\pi\)
\(104\) 553.556 0.521929
\(105\) 0 0
\(106\) 2179.72 1.99730
\(107\) −704.181 −0.636222 −0.318111 0.948053i \(-0.603048\pi\)
−0.318111 + 0.948053i \(0.603048\pi\)
\(108\) 0 0
\(109\) 1508.90 1.32593 0.662966 0.748650i \(-0.269297\pi\)
0.662966 + 0.748650i \(0.269297\pi\)
\(110\) −249.582 −0.216334
\(111\) 0 0
\(112\) 986.294 0.832107
\(113\) −713.075 −0.593632 −0.296816 0.954935i \(-0.595925\pi\)
−0.296816 + 0.954935i \(0.595925\pi\)
\(114\) 0 0
\(115\) −318.986 −0.258657
\(116\) 1627.94 1.30302
\(117\) 0 0
\(118\) 3455.07 2.69547
\(119\) 2408.04 1.85500
\(120\) 0 0
\(121\) 254.403 0.191137
\(122\) 103.221 0.0765998
\(123\) 0 0
\(124\) −2831.00 −2.05025
\(125\) −363.324 −0.259973
\(126\) 0 0
\(127\) −1501.02 −1.04877 −0.524387 0.851480i \(-0.675705\pi\)
−0.524387 + 0.851480i \(0.675705\pi\)
\(128\) 1199.39 0.828219
\(129\) 0 0
\(130\) 355.203 0.239642
\(131\) 193.574 0.129104 0.0645522 0.997914i \(-0.479438\pi\)
0.0645522 + 0.997914i \(0.479438\pi\)
\(132\) 0 0
\(133\) 490.111 0.319534
\(134\) −1034.83 −0.667131
\(135\) 0 0
\(136\) 966.048 0.609102
\(137\) 51.7070 0.0322455 0.0161227 0.999870i \(-0.494868\pi\)
0.0161227 + 0.999870i \(0.494868\pi\)
\(138\) 0 0
\(139\) −3064.21 −1.86981 −0.934903 0.354902i \(-0.884514\pi\)
−0.934903 + 0.354902i \(0.884514\pi\)
\(140\) −367.096 −0.221609
\(141\) 0 0
\(142\) −20.8221 −0.0123053
\(143\) −2256.33 −1.31947
\(144\) 0 0
\(145\) 232.038 0.132894
\(146\) −196.582 −0.111433
\(147\) 0 0
\(148\) −3516.71 −1.95319
\(149\) −630.884 −0.346873 −0.173436 0.984845i \(-0.555487\pi\)
−0.173436 + 0.984845i \(0.555487\pi\)
\(150\) 0 0
\(151\) −299.797 −0.161571 −0.0807853 0.996732i \(-0.525743\pi\)
−0.0807853 + 0.996732i \(0.525743\pi\)
\(152\) 196.620 0.104921
\(153\) 0 0
\(154\) 4145.77 2.16932
\(155\) −403.515 −0.209104
\(156\) 0 0
\(157\) 3810.32 1.93692 0.968461 0.249166i \(-0.0801564\pi\)
0.968461 + 0.249166i \(0.0801564\pi\)
\(158\) 891.309 0.448789
\(159\) 0 0
\(160\) 368.453 0.182055
\(161\) 5298.62 2.59373
\(162\) 0 0
\(163\) −3956.66 −1.90129 −0.950644 0.310284i \(-0.899576\pi\)
−0.950644 + 0.310284i \(0.899576\pi\)
\(164\) 4207.10 2.00317
\(165\) 0 0
\(166\) −856.079 −0.400269
\(167\) 664.588 0.307948 0.153974 0.988075i \(-0.450793\pi\)
0.153974 + 0.988075i \(0.450793\pi\)
\(168\) 0 0
\(169\) 1014.19 0.461626
\(170\) 619.890 0.279667
\(171\) 0 0
\(172\) 1031.04 0.457069
\(173\) −2287.00 −1.00507 −0.502536 0.864556i \(-0.667600\pi\)
−0.502536 + 0.864556i \(0.667600\pi\)
\(174\) 0 0
\(175\) 2991.39 1.29216
\(176\) −1612.81 −0.690738
\(177\) 0 0
\(178\) −3049.95 −1.28429
\(179\) 2687.63 1.12225 0.561124 0.827731i \(-0.310369\pi\)
0.561124 + 0.827731i \(0.310369\pi\)
\(180\) 0 0
\(181\) −445.211 −0.182830 −0.0914150 0.995813i \(-0.529139\pi\)
−0.0914150 + 0.995813i \(0.529139\pi\)
\(182\) −5900.23 −2.40304
\(183\) 0 0
\(184\) 2125.68 0.851668
\(185\) −501.253 −0.199205
\(186\) 0 0
\(187\) −3937.68 −1.53985
\(188\) −2616.09 −1.01488
\(189\) 0 0
\(190\) 126.166 0.0481741
\(191\) 146.088 0.0553431 0.0276715 0.999617i \(-0.491191\pi\)
0.0276715 + 0.999617i \(0.491191\pi\)
\(192\) 0 0
\(193\) 1155.84 0.431085 0.215543 0.976494i \(-0.430848\pi\)
0.215543 + 0.976494i \(0.430848\pi\)
\(194\) 6835.66 2.52975
\(195\) 0 0
\(196\) 2570.19 0.936657
\(197\) −2980.18 −1.07781 −0.538906 0.842366i \(-0.681162\pi\)
−0.538906 + 0.842366i \(0.681162\pi\)
\(198\) 0 0
\(199\) −2147.13 −0.764856 −0.382428 0.923985i \(-0.624912\pi\)
−0.382428 + 0.923985i \(0.624912\pi\)
\(200\) 1200.07 0.424290
\(201\) 0 0
\(202\) −646.499 −0.225186
\(203\) −3854.34 −1.33262
\(204\) 0 0
\(205\) 599.657 0.204302
\(206\) −7764.21 −2.62601
\(207\) 0 0
\(208\) 2295.33 0.765157
\(209\) −801.438 −0.265247
\(210\) 0 0
\(211\) −2889.67 −0.942811 −0.471405 0.881917i \(-0.656253\pi\)
−0.471405 + 0.881917i \(0.656253\pi\)
\(212\) −5242.55 −1.69839
\(213\) 0 0
\(214\) 3011.10 0.961845
\(215\) 146.959 0.0466163
\(216\) 0 0
\(217\) 6702.72 2.09682
\(218\) −6452.12 −2.00455
\(219\) 0 0
\(220\) 600.281 0.183959
\(221\) 5604.07 1.70575
\(222\) 0 0
\(223\) −3236.20 −0.971803 −0.485901 0.874014i \(-0.661509\pi\)
−0.485901 + 0.874014i \(0.661509\pi\)
\(224\) −6120.31 −1.82558
\(225\) 0 0
\(226\) 3049.13 0.897457
\(227\) 847.513 0.247803 0.123902 0.992294i \(-0.460459\pi\)
0.123902 + 0.992294i \(0.460459\pi\)
\(228\) 0 0
\(229\) −3025.55 −0.873075 −0.436537 0.899686i \(-0.643795\pi\)
−0.436537 + 0.899686i \(0.643795\pi\)
\(230\) 1363.99 0.391040
\(231\) 0 0
\(232\) −1546.26 −0.437574
\(233\) −5012.85 −1.40945 −0.704727 0.709478i \(-0.748931\pi\)
−0.704727 + 0.709478i \(0.748931\pi\)
\(234\) 0 0
\(235\) −372.883 −0.103507
\(236\) −8309.94 −2.29208
\(237\) 0 0
\(238\) −10296.9 −2.80440
\(239\) 239.000 0.0646846
\(240\) 0 0
\(241\) −4683.07 −1.25171 −0.625856 0.779938i \(-0.715250\pi\)
−0.625856 + 0.779938i \(0.715250\pi\)
\(242\) −1087.84 −0.288962
\(243\) 0 0
\(244\) −248.261 −0.0651364
\(245\) 366.341 0.0955292
\(246\) 0 0
\(247\) 1140.60 0.293824
\(248\) 2688.97 0.688506
\(249\) 0 0
\(250\) 1553.58 0.393029
\(251\) 6402.32 1.61000 0.805002 0.593272i \(-0.202164\pi\)
0.805002 + 0.593272i \(0.202164\pi\)
\(252\) 0 0
\(253\) −8664.40 −2.15307
\(254\) 6418.42 1.58554
\(255\) 0 0
\(256\) 877.292 0.214183
\(257\) 1188.16 0.288386 0.144193 0.989550i \(-0.453941\pi\)
0.144193 + 0.989550i \(0.453941\pi\)
\(258\) 0 0
\(259\) 8326.24 1.99756
\(260\) −854.315 −0.203778
\(261\) 0 0
\(262\) −827.731 −0.195181
\(263\) −1198.30 −0.280953 −0.140476 0.990084i \(-0.544863\pi\)
−0.140476 + 0.990084i \(0.544863\pi\)
\(264\) 0 0
\(265\) −747.244 −0.173218
\(266\) −2095.73 −0.483073
\(267\) 0 0
\(268\) 2488.91 0.567292
\(269\) −5118.04 −1.16005 −0.580023 0.814600i \(-0.696956\pi\)
−0.580023 + 0.814600i \(0.696956\pi\)
\(270\) 0 0
\(271\) 1236.70 0.277211 0.138605 0.990348i \(-0.455738\pi\)
0.138605 + 0.990348i \(0.455738\pi\)
\(272\) 4005.74 0.892954
\(273\) 0 0
\(274\) −221.101 −0.0487489
\(275\) −4891.58 −1.07263
\(276\) 0 0
\(277\) −2314.81 −0.502106 −0.251053 0.967973i \(-0.580777\pi\)
−0.251053 + 0.967973i \(0.580777\pi\)
\(278\) 13102.7 2.82679
\(279\) 0 0
\(280\) 348.679 0.0744197
\(281\) −1811.91 −0.384659 −0.192330 0.981330i \(-0.561604\pi\)
−0.192330 + 0.981330i \(0.561604\pi\)
\(282\) 0 0
\(283\) 4717.55 0.990916 0.495458 0.868632i \(-0.335000\pi\)
0.495458 + 0.868632i \(0.335000\pi\)
\(284\) 50.0802 0.0104638
\(285\) 0 0
\(286\) 9648.16 1.99478
\(287\) −9960.80 −2.04867
\(288\) 0 0
\(289\) 4867.04 0.990645
\(290\) −992.201 −0.200910
\(291\) 0 0
\(292\) 472.808 0.0947568
\(293\) −3604.11 −0.718615 −0.359308 0.933219i \(-0.616987\pi\)
−0.359308 + 0.933219i \(0.616987\pi\)
\(294\) 0 0
\(295\) −1184.45 −0.233768
\(296\) 3340.28 0.655912
\(297\) 0 0
\(298\) 2697.68 0.524405
\(299\) 12331.1 2.38504
\(300\) 0 0
\(301\) −2441.11 −0.467452
\(302\) 1281.94 0.244264
\(303\) 0 0
\(304\) 815.290 0.153816
\(305\) −35.3858 −0.00664322
\(306\) 0 0
\(307\) 3983.31 0.740520 0.370260 0.928928i \(-0.379269\pi\)
0.370260 + 0.928928i \(0.379269\pi\)
\(308\) −9971.17 −1.84468
\(309\) 0 0
\(310\) 1725.45 0.316125
\(311\) 7594.07 1.38463 0.692316 0.721595i \(-0.256591\pi\)
0.692316 + 0.721595i \(0.256591\pi\)
\(312\) 0 0
\(313\) −6738.10 −1.21681 −0.608403 0.793628i \(-0.708189\pi\)
−0.608403 + 0.793628i \(0.708189\pi\)
\(314\) −16293.1 −2.92825
\(315\) 0 0
\(316\) −2143.73 −0.381626
\(317\) 10590.1 1.87634 0.938168 0.346180i \(-0.112521\pi\)
0.938168 + 0.346180i \(0.112521\pi\)
\(318\) 0 0
\(319\) 6302.68 1.10621
\(320\) −1100.51 −0.192250
\(321\) 0 0
\(322\) −22657.1 −3.92121
\(323\) 1990.54 0.342899
\(324\) 0 0
\(325\) 6961.65 1.18819
\(326\) 16918.8 2.87438
\(327\) 0 0
\(328\) −3996.03 −0.672694
\(329\) 6193.90 1.03794
\(330\) 0 0
\(331\) −3791.26 −0.629567 −0.314784 0.949163i \(-0.601932\pi\)
−0.314784 + 0.949163i \(0.601932\pi\)
\(332\) 2058.99 0.340367
\(333\) 0 0
\(334\) −2841.80 −0.465558
\(335\) 354.756 0.0578579
\(336\) 0 0
\(337\) 9258.31 1.49653 0.748267 0.663397i \(-0.230886\pi\)
0.748267 + 0.663397i \(0.230886\pi\)
\(338\) −4336.72 −0.697889
\(339\) 0 0
\(340\) −1490.92 −0.237814
\(341\) −10960.4 −1.74059
\(342\) 0 0
\(343\) 2266.73 0.356828
\(344\) −979.311 −0.153491
\(345\) 0 0
\(346\) 9779.30 1.51948
\(347\) 10437.4 1.61472 0.807360 0.590060i \(-0.200896\pi\)
0.807360 + 0.590060i \(0.200896\pi\)
\(348\) 0 0
\(349\) 943.111 0.144652 0.0723261 0.997381i \(-0.476958\pi\)
0.0723261 + 0.997381i \(0.476958\pi\)
\(350\) −12791.3 −1.95350
\(351\) 0 0
\(352\) 10008.0 1.51543
\(353\) −10865.4 −1.63826 −0.819132 0.573604i \(-0.805545\pi\)
−0.819132 + 0.573604i \(0.805545\pi\)
\(354\) 0 0
\(355\) 7.13816 0.00106720
\(356\) 7335.57 1.09209
\(357\) 0 0
\(358\) −11492.4 −1.69662
\(359\) −667.485 −0.0981296 −0.0490648 0.998796i \(-0.515624\pi\)
−0.0490648 + 0.998796i \(0.515624\pi\)
\(360\) 0 0
\(361\) −6453.86 −0.940934
\(362\) 1903.74 0.276404
\(363\) 0 0
\(364\) 14190.9 2.04342
\(365\) 67.3915 0.00966420
\(366\) 0 0
\(367\) −8566.53 −1.21844 −0.609222 0.792999i \(-0.708518\pi\)
−0.609222 + 0.792999i \(0.708518\pi\)
\(368\) 8814.16 1.24856
\(369\) 0 0
\(370\) 2143.38 0.301159
\(371\) 12412.4 1.73697
\(372\) 0 0
\(373\) 4410.94 0.612305 0.306152 0.951983i \(-0.400958\pi\)
0.306152 + 0.951983i \(0.400958\pi\)
\(374\) 16837.6 2.32795
\(375\) 0 0
\(376\) 2484.84 0.340813
\(377\) −8969.92 −1.22540
\(378\) 0 0
\(379\) −8965.78 −1.21515 −0.607574 0.794263i \(-0.707857\pi\)
−0.607574 + 0.794263i \(0.707857\pi\)
\(380\) −303.449 −0.0409647
\(381\) 0 0
\(382\) −624.676 −0.0836680
\(383\) 11564.1 1.54282 0.771408 0.636341i \(-0.219553\pi\)
0.771408 + 0.636341i \(0.219553\pi\)
\(384\) 0 0
\(385\) −1421.24 −0.188138
\(386\) −4942.43 −0.651718
\(387\) 0 0
\(388\) −16440.7 −2.15116
\(389\) 3853.49 0.502261 0.251131 0.967953i \(-0.419198\pi\)
0.251131 + 0.967953i \(0.419198\pi\)
\(390\) 0 0
\(391\) 21519.8 2.78339
\(392\) −2441.24 −0.314544
\(393\) 0 0
\(394\) 12743.3 1.62944
\(395\) −305.555 −0.0389219
\(396\) 0 0
\(397\) 9911.16 1.25296 0.626482 0.779436i \(-0.284494\pi\)
0.626482 + 0.779436i \(0.284494\pi\)
\(398\) 9181.22 1.15631
\(399\) 0 0
\(400\) 4976.13 0.622016
\(401\) 4926.69 0.613534 0.306767 0.951785i \(-0.400753\pi\)
0.306767 + 0.951785i \(0.400753\pi\)
\(402\) 0 0
\(403\) 15598.8 1.92811
\(404\) 1554.92 0.191486
\(405\) 0 0
\(406\) 16481.3 2.01466
\(407\) −13615.2 −1.65818
\(408\) 0 0
\(409\) 8904.87 1.07657 0.538285 0.842763i \(-0.319072\pi\)
0.538285 + 0.842763i \(0.319072\pi\)
\(410\) −2564.16 −0.308865
\(411\) 0 0
\(412\) 18674.0 2.23302
\(413\) 19674.8 2.34415
\(414\) 0 0
\(415\) 293.478 0.0347139
\(416\) −14243.4 −1.67870
\(417\) 0 0
\(418\) 3426.98 0.401002
\(419\) 12060.5 1.40620 0.703098 0.711093i \(-0.251800\pi\)
0.703098 + 0.711093i \(0.251800\pi\)
\(420\) 0 0
\(421\) −10986.1 −1.27180 −0.635902 0.771769i \(-0.719372\pi\)
−0.635902 + 0.771769i \(0.719372\pi\)
\(422\) 12356.3 1.42535
\(423\) 0 0
\(424\) 4979.53 0.570347
\(425\) 12149.3 1.38665
\(426\) 0 0
\(427\) 587.787 0.0666160
\(428\) −7242.14 −0.817902
\(429\) 0 0
\(430\) −628.400 −0.0704748
\(431\) −13635.0 −1.52384 −0.761920 0.647672i \(-0.775743\pi\)
−0.761920 + 0.647672i \(0.775743\pi\)
\(432\) 0 0
\(433\) −3364.17 −0.373375 −0.186688 0.982419i \(-0.559775\pi\)
−0.186688 + 0.982419i \(0.559775\pi\)
\(434\) −28661.1 −3.16999
\(435\) 0 0
\(436\) 15518.3 1.70456
\(437\) 4379.94 0.479453
\(438\) 0 0
\(439\) −5135.11 −0.558281 −0.279141 0.960250i \(-0.590050\pi\)
−0.279141 + 0.960250i \(0.590050\pi\)
\(440\) −570.166 −0.0617763
\(441\) 0 0
\(442\) −23963.2 −2.57876
\(443\) 5446.13 0.584093 0.292047 0.956404i \(-0.405664\pi\)
0.292047 + 0.956404i \(0.405664\pi\)
\(444\) 0 0
\(445\) 1045.57 0.111382
\(446\) 13838.1 1.46918
\(447\) 0 0
\(448\) 18280.3 1.92782
\(449\) 6622.05 0.696022 0.348011 0.937490i \(-0.386857\pi\)
0.348011 + 0.937490i \(0.386857\pi\)
\(450\) 0 0
\(451\) 16288.1 1.70061
\(452\) −7333.60 −0.763150
\(453\) 0 0
\(454\) −3623.99 −0.374631
\(455\) 2022.69 0.208407
\(456\) 0 0
\(457\) −7790.53 −0.797430 −0.398715 0.917075i \(-0.630544\pi\)
−0.398715 + 0.917075i \(0.630544\pi\)
\(458\) 12937.4 1.31992
\(459\) 0 0
\(460\) −3280.60 −0.332519
\(461\) −1328.81 −0.134249 −0.0671244 0.997745i \(-0.521382\pi\)
−0.0671244 + 0.997745i \(0.521382\pi\)
\(462\) 0 0
\(463\) 13716.6 1.37682 0.688409 0.725323i \(-0.258310\pi\)
0.688409 + 0.725323i \(0.258310\pi\)
\(464\) −6411.62 −0.641491
\(465\) 0 0
\(466\) 21435.1 2.13082
\(467\) 9312.55 0.922770 0.461385 0.887200i \(-0.347353\pi\)
0.461385 + 0.887200i \(0.347353\pi\)
\(468\) 0 0
\(469\) −5892.79 −0.580179
\(470\) 1594.46 0.156483
\(471\) 0 0
\(472\) 7893.03 0.769717
\(473\) 3991.74 0.388035
\(474\) 0 0
\(475\) 2472.74 0.238857
\(476\) 24765.5 2.38471
\(477\) 0 0
\(478\) −1021.97 −0.0977907
\(479\) −13199.4 −1.25907 −0.629536 0.776971i \(-0.716755\pi\)
−0.629536 + 0.776971i \(0.716755\pi\)
\(480\) 0 0
\(481\) 19377.1 1.83684
\(482\) 20025.0 1.89235
\(483\) 0 0
\(484\) 2616.41 0.245718
\(485\) −2343.37 −0.219396
\(486\) 0 0
\(487\) −6626.32 −0.616565 −0.308282 0.951295i \(-0.599754\pi\)
−0.308282 + 0.951295i \(0.599754\pi\)
\(488\) 235.806 0.0218738
\(489\) 0 0
\(490\) −1566.49 −0.144422
\(491\) −636.455 −0.0584986 −0.0292493 0.999572i \(-0.509312\pi\)
−0.0292493 + 0.999572i \(0.509312\pi\)
\(492\) 0 0
\(493\) −15654.0 −1.43006
\(494\) −4877.24 −0.444206
\(495\) 0 0
\(496\) 11149.9 1.00936
\(497\) −118.571 −0.0107015
\(498\) 0 0
\(499\) −13771.2 −1.23544 −0.617719 0.786399i \(-0.711943\pi\)
−0.617719 + 0.786399i \(0.711943\pi\)
\(500\) −3736.59 −0.334211
\(501\) 0 0
\(502\) −27376.6 −2.43401
\(503\) −15036.3 −1.33288 −0.666438 0.745560i \(-0.732182\pi\)
−0.666438 + 0.745560i \(0.732182\pi\)
\(504\) 0 0
\(505\) 221.630 0.0195295
\(506\) 37049.3 3.25502
\(507\) 0 0
\(508\) −15437.2 −1.34826
\(509\) −2199.22 −0.191510 −0.0957551 0.995405i \(-0.530527\pi\)
−0.0957551 + 0.995405i \(0.530527\pi\)
\(510\) 0 0
\(511\) −1119.43 −0.0969092
\(512\) −13346.4 −1.15202
\(513\) 0 0
\(514\) −5080.60 −0.435984
\(515\) 2661.70 0.227744
\(516\) 0 0
\(517\) −10128.4 −0.861597
\(518\) −35603.3 −3.01992
\(519\) 0 0
\(520\) 811.455 0.0684320
\(521\) 12525.5 1.05327 0.526634 0.850092i \(-0.323454\pi\)
0.526634 + 0.850092i \(0.323454\pi\)
\(522\) 0 0
\(523\) 6134.01 0.512852 0.256426 0.966564i \(-0.417455\pi\)
0.256426 + 0.966564i \(0.417455\pi\)
\(524\) 1990.81 0.165971
\(525\) 0 0
\(526\) 5123.99 0.424747
\(527\) 27222.5 2.25015
\(528\) 0 0
\(529\) 35184.9 2.89183
\(530\) 3195.24 0.261873
\(531\) 0 0
\(532\) 5040.53 0.410780
\(533\) −23181.1 −1.88383
\(534\) 0 0
\(535\) −1032.26 −0.0834174
\(536\) −2364.04 −0.190506
\(537\) 0 0
\(538\) 21884.9 1.75376
\(539\) 9950.67 0.795187
\(540\) 0 0
\(541\) −8024.28 −0.637691 −0.318846 0.947807i \(-0.603295\pi\)
−0.318846 + 0.947807i \(0.603295\pi\)
\(542\) −5288.17 −0.419089
\(543\) 0 0
\(544\) −24857.1 −1.95908
\(545\) 2211.89 0.173848
\(546\) 0 0
\(547\) 24001.4 1.87610 0.938049 0.346502i \(-0.112631\pi\)
0.938049 + 0.346502i \(0.112631\pi\)
\(548\) 531.780 0.0414535
\(549\) 0 0
\(550\) 20916.6 1.62161
\(551\) −3186.07 −0.246336
\(552\) 0 0
\(553\) 5075.52 0.390295
\(554\) 9898.21 0.759088
\(555\) 0 0
\(556\) −31513.8 −2.40375
\(557\) 9564.09 0.727547 0.363773 0.931488i \(-0.381488\pi\)
0.363773 + 0.931488i \(0.381488\pi\)
\(558\) 0 0
\(559\) −5681.01 −0.429841
\(560\) 1445.80 0.109101
\(561\) 0 0
\(562\) 7747.77 0.581530
\(563\) −10937.5 −0.818759 −0.409379 0.912364i \(-0.634255\pi\)
−0.409379 + 0.912364i \(0.634255\pi\)
\(564\) 0 0
\(565\) −1045.29 −0.0778332
\(566\) −20172.4 −1.49807
\(567\) 0 0
\(568\) −47.5677 −0.00351390
\(569\) 7816.61 0.575904 0.287952 0.957645i \(-0.407026\pi\)
0.287952 + 0.957645i \(0.407026\pi\)
\(570\) 0 0
\(571\) 9864.06 0.722939 0.361469 0.932384i \(-0.382275\pi\)
0.361469 + 0.932384i \(0.382275\pi\)
\(572\) −23205.2 −1.69626
\(573\) 0 0
\(574\) 42592.7 3.09719
\(575\) 26733.0 1.93886
\(576\) 0 0
\(577\) 23145.5 1.66995 0.834974 0.550290i \(-0.185483\pi\)
0.834974 + 0.550290i \(0.185483\pi\)
\(578\) −20811.6 −1.49766
\(579\) 0 0
\(580\) 2386.38 0.170844
\(581\) −4874.91 −0.348099
\(582\) 0 0
\(583\) −20296.9 −1.44187
\(584\) −449.087 −0.0318208
\(585\) 0 0
\(586\) 15411.3 1.08641
\(587\) 17074.8 1.20060 0.600300 0.799775i \(-0.295048\pi\)
0.600300 + 0.799775i \(0.295048\pi\)
\(588\) 0 0
\(589\) 5540.60 0.387600
\(590\) 5064.77 0.353412
\(591\) 0 0
\(592\) 13850.5 0.961577
\(593\) −9165.65 −0.634718 −0.317359 0.948305i \(-0.602796\pi\)
−0.317359 + 0.948305i \(0.602796\pi\)
\(594\) 0 0
\(595\) 3529.94 0.243216
\(596\) −6488.31 −0.445926
\(597\) 0 0
\(598\) −52728.2 −3.60571
\(599\) −2460.58 −0.167840 −0.0839202 0.996472i \(-0.526744\pi\)
−0.0839202 + 0.996472i \(0.526744\pi\)
\(600\) 0 0
\(601\) 9682.17 0.657145 0.328572 0.944479i \(-0.393432\pi\)
0.328572 + 0.944479i \(0.393432\pi\)
\(602\) 10438.3 0.706697
\(603\) 0 0
\(604\) −3083.26 −0.207709
\(605\) 372.929 0.0250607
\(606\) 0 0
\(607\) −25077.7 −1.67689 −0.838445 0.544986i \(-0.816535\pi\)
−0.838445 + 0.544986i \(0.816535\pi\)
\(608\) −5059.17 −0.337461
\(609\) 0 0
\(610\) 151.311 0.0100433
\(611\) 14414.6 0.954424
\(612\) 0 0
\(613\) 2294.94 0.151210 0.0756050 0.997138i \(-0.475911\pi\)
0.0756050 + 0.997138i \(0.475911\pi\)
\(614\) −17032.8 −1.11952
\(615\) 0 0
\(616\) 9470.92 0.619471
\(617\) −255.755 −0.0166877 −0.00834385 0.999965i \(-0.502656\pi\)
−0.00834385 + 0.999965i \(0.502656\pi\)
\(618\) 0 0
\(619\) −1884.06 −0.122337 −0.0611686 0.998127i \(-0.519483\pi\)
−0.0611686 + 0.998127i \(0.519483\pi\)
\(620\) −4149.94 −0.268816
\(621\) 0 0
\(622\) −32472.5 −2.09329
\(623\) −17367.8 −1.11690
\(624\) 0 0
\(625\) 14823.8 0.948723
\(626\) 28812.4 1.83957
\(627\) 0 0
\(628\) 39187.2 2.49003
\(629\) 33816.2 2.14363
\(630\) 0 0
\(631\) −6657.49 −0.420017 −0.210008 0.977700i \(-0.567349\pi\)
−0.210008 + 0.977700i \(0.567349\pi\)
\(632\) 2036.18 0.128156
\(633\) 0 0
\(634\) −45283.6 −2.83666
\(635\) −2200.34 −0.137508
\(636\) 0 0
\(637\) −14161.7 −0.880859
\(638\) −26950.5 −1.67238
\(639\) 0 0
\(640\) 1758.18 0.108591
\(641\) −22664.8 −1.39657 −0.698287 0.715818i \(-0.746054\pi\)
−0.698287 + 0.715818i \(0.746054\pi\)
\(642\) 0 0
\(643\) −17131.7 −1.05071 −0.525356 0.850882i \(-0.676068\pi\)
−0.525356 + 0.850882i \(0.676068\pi\)
\(644\) 54493.5 3.33439
\(645\) 0 0
\(646\) −8511.61 −0.518397
\(647\) 3822.86 0.232291 0.116145 0.993232i \(-0.462946\pi\)
0.116145 + 0.993232i \(0.462946\pi\)
\(648\) 0 0
\(649\) −32172.5 −1.94589
\(650\) −29768.3 −1.79632
\(651\) 0 0
\(652\) −40692.2 −2.44422
\(653\) −1365.75 −0.0818467 −0.0409233 0.999162i \(-0.513030\pi\)
−0.0409233 + 0.999162i \(0.513030\pi\)
\(654\) 0 0
\(655\) 283.760 0.0169273
\(656\) −16569.6 −0.986181
\(657\) 0 0
\(658\) −26485.3 −1.56916
\(659\) 26622.9 1.57372 0.786858 0.617134i \(-0.211706\pi\)
0.786858 + 0.617134i \(0.211706\pi\)
\(660\) 0 0
\(661\) −13900.8 −0.817972 −0.408986 0.912541i \(-0.634118\pi\)
−0.408986 + 0.912541i \(0.634118\pi\)
\(662\) 16211.6 0.951784
\(663\) 0 0
\(664\) −1955.69 −0.114301
\(665\) 718.450 0.0418952
\(666\) 0 0
\(667\) −34444.8 −1.99956
\(668\) 6834.94 0.395886
\(669\) 0 0
\(670\) −1516.95 −0.0874699
\(671\) −961.160 −0.0552983
\(672\) 0 0
\(673\) −4959.57 −0.284067 −0.142034 0.989862i \(-0.545364\pi\)
−0.142034 + 0.989862i \(0.545364\pi\)
\(674\) −39588.8 −2.26247
\(675\) 0 0
\(676\) 10430.4 0.593448
\(677\) −6386.06 −0.362535 −0.181268 0.983434i \(-0.558020\pi\)
−0.181268 + 0.983434i \(0.558020\pi\)
\(678\) 0 0
\(679\) 38925.4 2.20003
\(680\) 1416.12 0.0798616
\(681\) 0 0
\(682\) 46867.1 2.63143
\(683\) 31804.3 1.78178 0.890891 0.454217i \(-0.150081\pi\)
0.890891 + 0.454217i \(0.150081\pi\)
\(684\) 0 0
\(685\) 75.7970 0.00422782
\(686\) −9692.64 −0.539456
\(687\) 0 0
\(688\) −4060.73 −0.225020
\(689\) 28886.4 1.59722
\(690\) 0 0
\(691\) −2521.19 −0.138799 −0.0693997 0.997589i \(-0.522108\pi\)
−0.0693997 + 0.997589i \(0.522108\pi\)
\(692\) −23520.6 −1.29208
\(693\) 0 0
\(694\) −44630.6 −2.44114
\(695\) −4491.81 −0.245157
\(696\) 0 0
\(697\) −40454.8 −2.19847
\(698\) −4032.78 −0.218686
\(699\) 0 0
\(700\) 30764.9 1.66115
\(701\) 32083.7 1.72865 0.864325 0.502934i \(-0.167746\pi\)
0.864325 + 0.502934i \(0.167746\pi\)
\(702\) 0 0
\(703\) 6882.63 0.369251
\(704\) −29892.3 −1.60030
\(705\) 0 0
\(706\) 46460.9 2.47674
\(707\) −3681.46 −0.195836
\(708\) 0 0
\(709\) −9806.75 −0.519464 −0.259732 0.965681i \(-0.583634\pi\)
−0.259732 + 0.965681i \(0.583634\pi\)
\(710\) −30.5230 −0.00161339
\(711\) 0 0
\(712\) −6967.55 −0.366741
\(713\) 59899.9 3.14624
\(714\) 0 0
\(715\) −3307.55 −0.173000
\(716\) 27640.8 1.44272
\(717\) 0 0
\(718\) 2854.19 0.148353
\(719\) −24234.5 −1.25702 −0.628508 0.777803i \(-0.716334\pi\)
−0.628508 + 0.777803i \(0.716334\pi\)
\(720\) 0 0
\(721\) −44213.0 −2.28374
\(722\) 27597.0 1.42251
\(723\) 0 0
\(724\) −4578.76 −0.235039
\(725\) −19446.2 −0.996157
\(726\) 0 0
\(727\) −27192.9 −1.38725 −0.693623 0.720338i \(-0.743987\pi\)
−0.693623 + 0.720338i \(0.743987\pi\)
\(728\) −13478.9 −0.686212
\(729\) 0 0
\(730\) −288.168 −0.0146104
\(731\) −9914.32 −0.501634
\(732\) 0 0
\(733\) 31910.6 1.60797 0.803986 0.594649i \(-0.202709\pi\)
0.803986 + 0.594649i \(0.202709\pi\)
\(734\) 36630.8 1.84205
\(735\) 0 0
\(736\) −54695.1 −2.73925
\(737\) 9636.00 0.481610
\(738\) 0 0
\(739\) −7912.59 −0.393869 −0.196935 0.980417i \(-0.563099\pi\)
−0.196935 + 0.980417i \(0.563099\pi\)
\(740\) −5155.13 −0.256090
\(741\) 0 0
\(742\) −53075.6 −2.62597
\(743\) 19460.3 0.960875 0.480437 0.877029i \(-0.340478\pi\)
0.480437 + 0.877029i \(0.340478\pi\)
\(744\) 0 0
\(745\) −924.809 −0.0454797
\(746\) −18861.3 −0.925686
\(747\) 0 0
\(748\) −40497.0 −1.97957
\(749\) 17146.6 0.836481
\(750\) 0 0
\(751\) −3189.64 −0.154982 −0.0774911 0.996993i \(-0.524691\pi\)
−0.0774911 + 0.996993i \(0.524691\pi\)
\(752\) 10303.4 0.499638
\(753\) 0 0
\(754\) 38355.7 1.85256
\(755\) −439.471 −0.0211841
\(756\) 0 0
\(757\) 27847.0 1.33701 0.668506 0.743707i \(-0.266934\pi\)
0.668506 + 0.743707i \(0.266934\pi\)
\(758\) 38338.0 1.83707
\(759\) 0 0
\(760\) 288.225 0.0137566
\(761\) −8994.13 −0.428432 −0.214216 0.976786i \(-0.568720\pi\)
−0.214216 + 0.976786i \(0.568720\pi\)
\(762\) 0 0
\(763\) −36741.3 −1.74328
\(764\) 1502.43 0.0711468
\(765\) 0 0
\(766\) −49448.5 −2.33244
\(767\) 45787.7 2.15554
\(768\) 0 0
\(769\) −9288.68 −0.435577 −0.217788 0.975996i \(-0.569884\pi\)
−0.217788 + 0.975996i \(0.569884\pi\)
\(770\) 6077.26 0.284428
\(771\) 0 0
\(772\) 11887.3 0.554186
\(773\) 16998.7 0.790946 0.395473 0.918478i \(-0.370581\pi\)
0.395473 + 0.918478i \(0.370581\pi\)
\(774\) 0 0
\(775\) 33817.1 1.56741
\(776\) 15615.9 0.722395
\(777\) 0 0
\(778\) −16477.6 −0.759322
\(779\) −8233.80 −0.378699
\(780\) 0 0
\(781\) 193.889 0.00888336
\(782\) −92019.6 −4.20795
\(783\) 0 0
\(784\) −10122.7 −0.461127
\(785\) 5585.53 0.253957
\(786\) 0 0
\(787\) 30289.1 1.37191 0.685954 0.727645i \(-0.259385\pi\)
0.685954 + 0.727645i \(0.259385\pi\)
\(788\) −30649.6 −1.38559
\(789\) 0 0
\(790\) 1306.56 0.0588424
\(791\) 17363.2 0.780485
\(792\) 0 0
\(793\) 1367.92 0.0612561
\(794\) −42380.5 −1.89424
\(795\) 0 0
\(796\) −22082.2 −0.983268
\(797\) 12794.7 0.568645 0.284323 0.958729i \(-0.408231\pi\)
0.284323 + 0.958729i \(0.408231\pi\)
\(798\) 0 0
\(799\) 25155.9 1.11383
\(800\) −30878.7 −1.36466
\(801\) 0 0
\(802\) −21066.7 −0.927545
\(803\) 1830.51 0.0804450
\(804\) 0 0
\(805\) 7767.22 0.340073
\(806\) −66700.9 −2.91494
\(807\) 0 0
\(808\) −1476.91 −0.0643040
\(809\) −36851.2 −1.60151 −0.800753 0.598995i \(-0.795567\pi\)
−0.800753 + 0.598995i \(0.795567\pi\)
\(810\) 0 0
\(811\) −12988.3 −0.562370 −0.281185 0.959654i \(-0.590727\pi\)
−0.281185 + 0.959654i \(0.590727\pi\)
\(812\) −39639.8 −1.71316
\(813\) 0 0
\(814\) 58219.1 2.50685
\(815\) −5800.05 −0.249285
\(816\) 0 0
\(817\) −2017.87 −0.0864091
\(818\) −38077.5 −1.62757
\(819\) 0 0
\(820\) 6167.16 0.262642
\(821\) −19988.9 −0.849717 −0.424859 0.905260i \(-0.639676\pi\)
−0.424859 + 0.905260i \(0.639676\pi\)
\(822\) 0 0
\(823\) 7405.51 0.313657 0.156829 0.987626i \(-0.449873\pi\)
0.156829 + 0.987626i \(0.449873\pi\)
\(824\) −17737.2 −0.749883
\(825\) 0 0
\(826\) −84130.0 −3.54390
\(827\) 20628.9 0.867396 0.433698 0.901058i \(-0.357208\pi\)
0.433698 + 0.901058i \(0.357208\pi\)
\(828\) 0 0
\(829\) 16056.1 0.672678 0.336339 0.941741i \(-0.390811\pi\)
0.336339 + 0.941741i \(0.390811\pi\)
\(830\) −1254.92 −0.0524807
\(831\) 0 0
\(832\) 42542.5 1.77271
\(833\) −24714.5 −1.02798
\(834\) 0 0
\(835\) 974.216 0.0403762
\(836\) −8242.37 −0.340991
\(837\) 0 0
\(838\) −51571.3 −2.12590
\(839\) −41595.4 −1.71160 −0.855801 0.517306i \(-0.826935\pi\)
−0.855801 + 0.517306i \(0.826935\pi\)
\(840\) 0 0
\(841\) 666.952 0.0273464
\(842\) 46977.0 1.92272
\(843\) 0 0
\(844\) −29718.7 −1.21204
\(845\) 1486.70 0.0605255
\(846\) 0 0
\(847\) −6194.65 −0.251300
\(848\) 20647.7 0.836139
\(849\) 0 0
\(850\) −51950.6 −2.09634
\(851\) 74408.6 2.99729
\(852\) 0 0
\(853\) 5129.86 0.205912 0.102956 0.994686i \(-0.467170\pi\)
0.102956 + 0.994686i \(0.467170\pi\)
\(854\) −2513.40 −0.100710
\(855\) 0 0
\(856\) 6878.80 0.274664
\(857\) −14897.8 −0.593815 −0.296908 0.954906i \(-0.595955\pi\)
−0.296908 + 0.954906i \(0.595955\pi\)
\(858\) 0 0
\(859\) −1214.24 −0.0482298 −0.0241149 0.999709i \(-0.507677\pi\)
−0.0241149 + 0.999709i \(0.507677\pi\)
\(860\) 1511.39 0.0599280
\(861\) 0 0
\(862\) 58303.7 2.30375
\(863\) −34377.1 −1.35598 −0.677990 0.735071i \(-0.737149\pi\)
−0.677990 + 0.735071i \(0.737149\pi\)
\(864\) 0 0
\(865\) −3352.50 −0.131779
\(866\) 14385.3 0.564471
\(867\) 0 0
\(868\) 68934.0 2.69559
\(869\) −8299.59 −0.323987
\(870\) 0 0
\(871\) −13713.9 −0.533498
\(872\) −14739.7 −0.572420
\(873\) 0 0
\(874\) −18728.8 −0.724841
\(875\) 8846.83 0.341803
\(876\) 0 0
\(877\) 13636.4 0.525050 0.262525 0.964925i \(-0.415445\pi\)
0.262525 + 0.964925i \(0.415445\pi\)
\(878\) 21957.9 0.844014
\(879\) 0 0
\(880\) −2364.20 −0.0905651
\(881\) 31632.4 1.20967 0.604837 0.796349i \(-0.293238\pi\)
0.604837 + 0.796349i \(0.293238\pi\)
\(882\) 0 0
\(883\) 8580.37 0.327013 0.163506 0.986542i \(-0.447720\pi\)
0.163506 + 0.986542i \(0.447720\pi\)
\(884\) 57634.9 2.19284
\(885\) 0 0
\(886\) −23287.8 −0.883036
\(887\) −44205.6 −1.67337 −0.836685 0.547685i \(-0.815509\pi\)
−0.836685 + 0.547685i \(0.815509\pi\)
\(888\) 0 0
\(889\) 36549.5 1.37889
\(890\) −4470.91 −0.168388
\(891\) 0 0
\(892\) −33282.6 −1.24931
\(893\) 5120.00 0.191864
\(894\) 0 0
\(895\) 3939.78 0.147142
\(896\) −29204.8 −1.08891
\(897\) 0 0
\(898\) −28316.1 −1.05225
\(899\) −43572.5 −1.61649
\(900\) 0 0
\(901\) 50411.6 1.86399
\(902\) −69648.4 −2.57100
\(903\) 0 0
\(904\) 6965.68 0.256278
\(905\) −652.632 −0.0239715
\(906\) 0 0
\(907\) 8833.45 0.323385 0.161692 0.986841i \(-0.448305\pi\)
0.161692 + 0.986841i \(0.448305\pi\)
\(908\) 8716.22 0.318566
\(909\) 0 0
\(910\) −8649.11 −0.315072
\(911\) −30321.7 −1.10275 −0.551374 0.834258i \(-0.685896\pi\)
−0.551374 + 0.834258i \(0.685896\pi\)
\(912\) 0 0
\(913\) 7971.54 0.288959
\(914\) 33312.6 1.20556
\(915\) 0 0
\(916\) −31116.2 −1.12239
\(917\) −4713.48 −0.169741
\(918\) 0 0
\(919\) −38461.2 −1.38054 −0.690271 0.723551i \(-0.742509\pi\)
−0.690271 + 0.723551i \(0.742509\pi\)
\(920\) 3116.02 0.111665
\(921\) 0 0
\(922\) 5682.02 0.202958
\(923\) −275.941 −0.00984044
\(924\) 0 0
\(925\) 42008.2 1.49321
\(926\) −58652.8 −2.08148
\(927\) 0 0
\(928\) 39786.4 1.40739
\(929\) 6433.61 0.227212 0.113606 0.993526i \(-0.463760\pi\)
0.113606 + 0.993526i \(0.463760\pi\)
\(930\) 0 0
\(931\) −5030.17 −0.177075
\(932\) −51554.6 −1.81194
\(933\) 0 0
\(934\) −39820.8 −1.39505
\(935\) −5772.22 −0.201895
\(936\) 0 0
\(937\) 533.942 0.0186159 0.00930796 0.999957i \(-0.497037\pi\)
0.00930796 + 0.999957i \(0.497037\pi\)
\(938\) 25197.8 0.877118
\(939\) 0 0
\(940\) −3834.91 −0.133065
\(941\) −4862.87 −0.168464 −0.0842322 0.996446i \(-0.526844\pi\)
−0.0842322 + 0.996446i \(0.526844\pi\)
\(942\) 0 0
\(943\) −89016.2 −3.07398
\(944\) 32728.6 1.12842
\(945\) 0 0
\(946\) −17068.8 −0.586634
\(947\) −21694.9 −0.744444 −0.372222 0.928144i \(-0.621404\pi\)
−0.372222 + 0.928144i \(0.621404\pi\)
\(948\) 0 0
\(949\) −2605.17 −0.0891120
\(950\) −10573.5 −0.361106
\(951\) 0 0
\(952\) −23523.0 −0.800824
\(953\) 25594.3 0.869971 0.434985 0.900438i \(-0.356754\pi\)
0.434985 + 0.900438i \(0.356754\pi\)
\(954\) 0 0
\(955\) 214.149 0.00725623
\(956\) 2457.99 0.0831560
\(957\) 0 0
\(958\) 56441.1 1.90347
\(959\) −1259.05 −0.0423951
\(960\) 0 0
\(961\) 45982.0 1.54349
\(962\) −82857.0 −2.77694
\(963\) 0 0
\(964\) −48162.9 −1.60915
\(965\) 1694.35 0.0565211
\(966\) 0 0
\(967\) 46972.0 1.56206 0.781032 0.624490i \(-0.214693\pi\)
0.781032 + 0.624490i \(0.214693\pi\)
\(968\) −2485.14 −0.0825160
\(969\) 0 0
\(970\) 10020.4 0.331685
\(971\) −46294.7 −1.53004 −0.765019 0.644007i \(-0.777271\pi\)
−0.765019 + 0.644007i \(0.777271\pi\)
\(972\) 0 0
\(973\) 74612.7 2.45835
\(974\) 28334.4 0.932127
\(975\) 0 0
\(976\) 977.773 0.0320674
\(977\) 12342.1 0.404154 0.202077 0.979370i \(-0.435231\pi\)
0.202077 + 0.979370i \(0.435231\pi\)
\(978\) 0 0
\(979\) 28400.2 0.927144
\(980\) 3767.62 0.122808
\(981\) 0 0
\(982\) 2721.51 0.0884386
\(983\) −30527.1 −0.990502 −0.495251 0.868750i \(-0.664924\pi\)
−0.495251 + 0.868750i \(0.664924\pi\)
\(984\) 0 0
\(985\) −4368.62 −0.141316
\(986\) 66937.1 2.16198
\(987\) 0 0
\(988\) 11730.5 0.377729
\(989\) −21815.3 −0.701401
\(990\) 0 0
\(991\) −28138.6 −0.901970 −0.450985 0.892532i \(-0.648927\pi\)
−0.450985 + 0.892532i \(0.648927\pi\)
\(992\) −69188.9 −2.21447
\(993\) 0 0
\(994\) 507.013 0.0161785
\(995\) −3147.47 −0.100283
\(996\) 0 0
\(997\) 29322.3 0.931442 0.465721 0.884932i \(-0.345795\pi\)
0.465721 + 0.884932i \(0.345795\pi\)
\(998\) 58886.2 1.86774
\(999\) 0 0
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 2151.4.a.c.1.2 28
3.2 odd 2 717.4.a.a.1.27 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
717.4.a.a.1.27 28 3.2 odd 2
2151.4.a.c.1.2 28 1.1 even 1 trivial