Properties

Label 1859.4.a.n.1.3
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $1$
Dimension $39$
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: \(39\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
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)
 
\(f(q)\) \(=\) \(q-4.78473 q^{2} +6.91979 q^{3} +14.8936 q^{4} +9.47124 q^{5} -33.1093 q^{6} +13.6025 q^{7} -32.9841 q^{8} +20.8835 q^{9} +O(q^{10})\) \(q-4.78473 q^{2} +6.91979 q^{3} +14.8936 q^{4} +9.47124 q^{5} -33.1093 q^{6} +13.6025 q^{7} -32.9841 q^{8} +20.8835 q^{9} -45.3173 q^{10} +11.0000 q^{11} +103.061 q^{12} -65.0841 q^{14} +65.5390 q^{15} +38.6711 q^{16} -124.539 q^{17} -99.9219 q^{18} +65.7203 q^{19} +141.061 q^{20} +94.1263 q^{21} -52.6320 q^{22} -58.7387 q^{23} -228.243 q^{24} -35.2956 q^{25} -42.3249 q^{27} +202.590 q^{28} +4.97794 q^{29} -313.586 q^{30} -197.904 q^{31} +78.8422 q^{32} +76.1177 q^{33} +595.883 q^{34} +128.832 q^{35} +311.031 q^{36} -376.446 q^{37} -314.454 q^{38} -312.401 q^{40} -4.21141 q^{41} -450.369 q^{42} -179.398 q^{43} +163.830 q^{44} +197.793 q^{45} +281.049 q^{46} +110.741 q^{47} +267.596 q^{48} -157.973 q^{49} +168.880 q^{50} -861.781 q^{51} -194.292 q^{53} +202.513 q^{54} +104.184 q^{55} -448.666 q^{56} +454.771 q^{57} -23.8181 q^{58} +336.203 q^{59} +976.113 q^{60} +192.023 q^{61} +946.916 q^{62} +284.067 q^{63} -686.608 q^{64} -364.203 q^{66} -438.374 q^{67} -1854.83 q^{68} -406.459 q^{69} -616.427 q^{70} -1116.26 q^{71} -688.824 q^{72} +284.727 q^{73} +1801.19 q^{74} -244.238 q^{75} +978.814 q^{76} +149.627 q^{77} +164.629 q^{79} +366.264 q^{80} -856.734 q^{81} +20.1505 q^{82} +69.9203 q^{83} +1401.88 q^{84} -1179.53 q^{85} +858.370 q^{86} +34.4463 q^{87} -362.826 q^{88} -1121.09 q^{89} -946.384 q^{90} -874.832 q^{92} -1369.45 q^{93} -529.865 q^{94} +622.453 q^{95} +545.572 q^{96} -22.4353 q^{97} +755.857 q^{98} +229.718 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.78473 −1.69166 −0.845829 0.533455i \(-0.820893\pi\)
−0.845829 + 0.533455i \(0.820893\pi\)
\(3\) 6.91979 1.33171 0.665857 0.746079i \(-0.268066\pi\)
0.665857 + 0.746079i \(0.268066\pi\)
\(4\) 14.8936 1.86170
\(5\) 9.47124 0.847133 0.423567 0.905865i \(-0.360778\pi\)
0.423567 + 0.905865i \(0.360778\pi\)
\(6\) −33.1093 −2.25280
\(7\) 13.6025 0.734464 0.367232 0.930129i \(-0.380305\pi\)
0.367232 + 0.930129i \(0.380305\pi\)
\(8\) −32.9841 −1.45771
\(9\) 20.8835 0.773463
\(10\) −45.3173 −1.43306
\(11\) 11.0000 0.301511
\(12\) 103.061 2.47926
\(13\) 0 0
\(14\) −65.0841 −1.24246
\(15\) 65.5390 1.12814
\(16\) 38.6711 0.604237
\(17\) −124.539 −1.77677 −0.888384 0.459101i \(-0.848171\pi\)
−0.888384 + 0.459101i \(0.848171\pi\)
\(18\) −99.9219 −1.30843
\(19\) 65.7203 0.793541 0.396770 0.917918i \(-0.370131\pi\)
0.396770 + 0.917918i \(0.370131\pi\)
\(20\) 141.061 1.57711
\(21\) 94.1263 0.978097
\(22\) −52.6320 −0.510054
\(23\) −58.7387 −0.532516 −0.266258 0.963902i \(-0.585787\pi\)
−0.266258 + 0.963902i \(0.585787\pi\)
\(24\) −228.243 −1.94125
\(25\) −35.2956 −0.282365
\(26\) 0 0
\(27\) −42.3249 −0.301683
\(28\) 202.590 1.36736
\(29\) 4.97794 0.0318752 0.0159376 0.999873i \(-0.494927\pi\)
0.0159376 + 0.999873i \(0.494927\pi\)
\(30\) −313.586 −1.90843
\(31\) −197.904 −1.14660 −0.573300 0.819346i \(-0.694337\pi\)
−0.573300 + 0.819346i \(0.694337\pi\)
\(32\) 78.8422 0.435546
\(33\) 76.1177 0.401527
\(34\) 595.883 3.00568
\(35\) 128.832 0.622189
\(36\) 311.031 1.43996
\(37\) −376.446 −1.67263 −0.836315 0.548249i \(-0.815294\pi\)
−0.836315 + 0.548249i \(0.815294\pi\)
\(38\) −314.454 −1.34240
\(39\) 0 0
\(40\) −312.401 −1.23487
\(41\) −4.21141 −0.0160418 −0.00802088 0.999968i \(-0.502553\pi\)
−0.00802088 + 0.999968i \(0.502553\pi\)
\(42\) −450.369 −1.65460
\(43\) −179.398 −0.636231 −0.318115 0.948052i \(-0.603050\pi\)
−0.318115 + 0.948052i \(0.603050\pi\)
\(44\) 163.830 0.561325
\(45\) 197.793 0.655226
\(46\) 281.049 0.900834
\(47\) 110.741 0.343685 0.171843 0.985124i \(-0.445028\pi\)
0.171843 + 0.985124i \(0.445028\pi\)
\(48\) 267.596 0.804670
\(49\) −157.973 −0.460562
\(50\) 168.880 0.477665
\(51\) −861.781 −2.36615
\(52\) 0 0
\(53\) −194.292 −0.503550 −0.251775 0.967786i \(-0.581014\pi\)
−0.251775 + 0.967786i \(0.581014\pi\)
\(54\) 202.513 0.510344
\(55\) 104.184 0.255420
\(56\) −448.666 −1.07063
\(57\) 454.771 1.05677
\(58\) −23.8181 −0.0539218
\(59\) 336.203 0.741863 0.370931 0.928660i \(-0.379039\pi\)
0.370931 + 0.928660i \(0.379039\pi\)
\(60\) 976.113 2.10026
\(61\) 192.023 0.403050 0.201525 0.979483i \(-0.435410\pi\)
0.201525 + 0.979483i \(0.435410\pi\)
\(62\) 946.916 1.93965
\(63\) 284.067 0.568081
\(64\) −686.608 −1.34103
\(65\) 0 0
\(66\) −364.203 −0.679246
\(67\) −438.374 −0.799341 −0.399671 0.916659i \(-0.630875\pi\)
−0.399671 + 0.916659i \(0.630875\pi\)
\(68\) −1854.83 −3.30781
\(69\) −406.459 −0.709159
\(70\) −616.427 −1.05253
\(71\) −1116.26 −1.86585 −0.932924 0.360072i \(-0.882752\pi\)
−0.932924 + 0.360072i \(0.882752\pi\)
\(72\) −688.824 −1.12748
\(73\) 284.727 0.456503 0.228252 0.973602i \(-0.426699\pi\)
0.228252 + 0.973602i \(0.426699\pi\)
\(74\) 1801.19 2.82952
\(75\) −244.238 −0.376030
\(76\) 978.814 1.47734
\(77\) 149.627 0.221449
\(78\) 0 0
\(79\) 164.629 0.234459 0.117229 0.993105i \(-0.462599\pi\)
0.117229 + 0.993105i \(0.462599\pi\)
\(80\) 366.264 0.511869
\(81\) −856.734 −1.17522
\(82\) 20.1505 0.0271372
\(83\) 69.9203 0.0924669 0.0462334 0.998931i \(-0.485278\pi\)
0.0462334 + 0.998931i \(0.485278\pi\)
\(84\) 1401.88 1.82093
\(85\) −1179.53 −1.50516
\(86\) 858.370 1.07628
\(87\) 34.4463 0.0424486
\(88\) −362.826 −0.439515
\(89\) −1121.09 −1.33523 −0.667617 0.744505i \(-0.732686\pi\)
−0.667617 + 0.744505i \(0.732686\pi\)
\(90\) −946.384 −1.10842
\(91\) 0 0
\(92\) −874.832 −0.991386
\(93\) −1369.45 −1.52694
\(94\) −529.865 −0.581398
\(95\) 622.453 0.672235
\(96\) 545.572 0.580023
\(97\) −22.4353 −0.0234841 −0.0117421 0.999931i \(-0.503738\pi\)
−0.0117421 + 0.999931i \(0.503738\pi\)
\(98\) 755.857 0.779113
\(99\) 229.718 0.233208
\(100\) −525.680 −0.525680
\(101\) −1417.33 −1.39633 −0.698165 0.715937i \(-0.746000\pi\)
−0.698165 + 0.715937i \(0.746000\pi\)
\(102\) 4123.39 4.00271
\(103\) −1365.22 −1.30601 −0.653007 0.757352i \(-0.726493\pi\)
−0.653007 + 0.757352i \(0.726493\pi\)
\(104\) 0 0
\(105\) 891.492 0.828578
\(106\) 929.637 0.851833
\(107\) 2146.95 1.93975 0.969876 0.243601i \(-0.0783287\pi\)
0.969876 + 0.243601i \(0.0783287\pi\)
\(108\) −630.372 −0.561644
\(109\) −1365.59 −1.20000 −0.599999 0.800001i \(-0.704832\pi\)
−0.599999 + 0.800001i \(0.704832\pi\)
\(110\) −498.490 −0.432084
\(111\) −2604.93 −2.22747
\(112\) 526.023 0.443790
\(113\) 986.088 0.820915 0.410457 0.911880i \(-0.365369\pi\)
0.410457 + 0.911880i \(0.365369\pi\)
\(114\) −2175.95 −1.78769
\(115\) −556.328 −0.451112
\(116\) 74.1395 0.0593421
\(117\) 0 0
\(118\) −1608.64 −1.25498
\(119\) −1694.03 −1.30497
\(120\) −2161.75 −1.64450
\(121\) 121.000 0.0909091
\(122\) −918.778 −0.681822
\(123\) −29.1421 −0.0213630
\(124\) −2947.51 −2.13463
\(125\) −1518.20 −1.08633
\(126\) −1359.18 −0.960998
\(127\) −1528.53 −1.06799 −0.533996 0.845487i \(-0.679310\pi\)
−0.533996 + 0.845487i \(0.679310\pi\)
\(128\) 2654.49 1.83302
\(129\) −1241.40 −0.847278
\(130\) 0 0
\(131\) −2838.18 −1.89292 −0.946462 0.322814i \(-0.895371\pi\)
−0.946462 + 0.322814i \(0.895371\pi\)
\(132\) 1133.67 0.747524
\(133\) 893.959 0.582827
\(134\) 2097.50 1.35221
\(135\) −400.869 −0.255565
\(136\) 4107.80 2.59001
\(137\) 1625.31 1.01357 0.506785 0.862072i \(-0.330834\pi\)
0.506785 + 0.862072i \(0.330834\pi\)
\(138\) 1944.80 1.19965
\(139\) −525.607 −0.320730 −0.160365 0.987058i \(-0.551267\pi\)
−0.160365 + 0.987058i \(0.551267\pi\)
\(140\) 1918.78 1.15833
\(141\) 766.303 0.457691
\(142\) 5340.98 3.15638
\(143\) 0 0
\(144\) 807.589 0.467354
\(145\) 47.1472 0.0270025
\(146\) −1362.34 −0.772247
\(147\) −1093.14 −0.613337
\(148\) −5606.64 −3.11394
\(149\) 2508.85 1.37942 0.689708 0.724088i \(-0.257739\pi\)
0.689708 + 0.724088i \(0.257739\pi\)
\(150\) 1168.61 0.636113
\(151\) 478.191 0.257713 0.128856 0.991663i \(-0.458869\pi\)
0.128856 + 0.991663i \(0.458869\pi\)
\(152\) −2167.73 −1.15675
\(153\) −2600.80 −1.37426
\(154\) −715.925 −0.374616
\(155\) −1874.39 −0.971323
\(156\) 0 0
\(157\) −1677.59 −0.852778 −0.426389 0.904540i \(-0.640215\pi\)
−0.426389 + 0.904540i \(0.640215\pi\)
\(158\) −787.707 −0.396624
\(159\) −1344.46 −0.670584
\(160\) 746.734 0.368965
\(161\) −798.991 −0.391114
\(162\) 4099.24 1.98807
\(163\) 3603.13 1.73141 0.865703 0.500558i \(-0.166872\pi\)
0.865703 + 0.500558i \(0.166872\pi\)
\(164\) −62.7232 −0.0298650
\(165\) 720.929 0.340147
\(166\) −334.550 −0.156422
\(167\) −177.653 −0.0823185 −0.0411593 0.999153i \(-0.513105\pi\)
−0.0411593 + 0.999153i \(0.513105\pi\)
\(168\) −3104.67 −1.42578
\(169\) 0 0
\(170\) 5643.75 2.54621
\(171\) 1372.47 0.613774
\(172\) −2671.89 −1.18447
\(173\) 3704.09 1.62784 0.813921 0.580975i \(-0.197329\pi\)
0.813921 + 0.580975i \(0.197329\pi\)
\(174\) −164.816 −0.0718085
\(175\) −480.108 −0.207387
\(176\) 425.383 0.182184
\(177\) 2326.45 0.987949
\(178\) 5364.13 2.25876
\(179\) 2466.95 1.03011 0.515053 0.857159i \(-0.327772\pi\)
0.515053 + 0.857159i \(0.327772\pi\)
\(180\) 2945.85 1.21984
\(181\) −830.340 −0.340987 −0.170494 0.985359i \(-0.554536\pi\)
−0.170494 + 0.985359i \(0.554536\pi\)
\(182\) 0 0
\(183\) 1328.76 0.536747
\(184\) 1937.44 0.776252
\(185\) −3565.41 −1.41694
\(186\) 6552.46 2.58306
\(187\) −1369.92 −0.535716
\(188\) 1649.33 0.639840
\(189\) −575.723 −0.221575
\(190\) −2978.27 −1.13719
\(191\) 4579.18 1.73475 0.867376 0.497654i \(-0.165805\pi\)
0.867376 + 0.497654i \(0.165805\pi\)
\(192\) −4751.18 −1.78587
\(193\) 4144.05 1.54557 0.772785 0.634668i \(-0.218863\pi\)
0.772785 + 0.634668i \(0.218863\pi\)
\(194\) 107.347 0.0397270
\(195\) 0 0
\(196\) −2352.79 −0.857430
\(197\) −2329.13 −0.842353 −0.421177 0.906979i \(-0.638383\pi\)
−0.421177 + 0.906979i \(0.638383\pi\)
\(198\) −1099.14 −0.394508
\(199\) 1558.02 0.555001 0.277500 0.960726i \(-0.410494\pi\)
0.277500 + 0.960726i \(0.410494\pi\)
\(200\) 1164.20 0.411606
\(201\) −3033.45 −1.06449
\(202\) 6781.53 2.36211
\(203\) 67.7122 0.0234112
\(204\) −12835.0 −4.40506
\(205\) −39.8873 −0.0135895
\(206\) 6532.22 2.20933
\(207\) −1226.67 −0.411881
\(208\) 0 0
\(209\) 722.923 0.239262
\(210\) −4265.55 −1.40167
\(211\) −2209.07 −0.720750 −0.360375 0.932807i \(-0.617351\pi\)
−0.360375 + 0.932807i \(0.617351\pi\)
\(212\) −2893.72 −0.937460
\(213\) −7724.26 −2.48478
\(214\) −10272.6 −3.28139
\(215\) −1699.12 −0.538972
\(216\) 1396.05 0.439765
\(217\) −2691.98 −0.842136
\(218\) 6533.97 2.02998
\(219\) 1970.25 0.607932
\(220\) 1551.67 0.475517
\(221\) 0 0
\(222\) 12463.9 3.76811
\(223\) 1157.16 0.347485 0.173742 0.984791i \(-0.444414\pi\)
0.173742 + 0.984791i \(0.444414\pi\)
\(224\) 1072.45 0.319893
\(225\) −737.097 −0.218399
\(226\) −4718.16 −1.38871
\(227\) −597.182 −0.174610 −0.0873048 0.996182i \(-0.527825\pi\)
−0.0873048 + 0.996182i \(0.527825\pi\)
\(228\) 6773.19 1.96739
\(229\) 5158.10 1.48846 0.744229 0.667924i \(-0.232817\pi\)
0.744229 + 0.667924i \(0.232817\pi\)
\(230\) 2661.88 0.763126
\(231\) 1035.39 0.294907
\(232\) −164.193 −0.0464646
\(233\) 1911.49 0.537449 0.268725 0.963217i \(-0.413398\pi\)
0.268725 + 0.963217i \(0.413398\pi\)
\(234\) 0 0
\(235\) 1048.85 0.291147
\(236\) 5007.28 1.38113
\(237\) 1139.20 0.312232
\(238\) 8105.49 2.20757
\(239\) 5178.67 1.40159 0.700796 0.713362i \(-0.252829\pi\)
0.700796 + 0.713362i \(0.252829\pi\)
\(240\) 2534.47 0.681663
\(241\) 4607.16 1.23142 0.615712 0.787971i \(-0.288869\pi\)
0.615712 + 0.787971i \(0.288869\pi\)
\(242\) −578.952 −0.153787
\(243\) −4785.65 −1.26337
\(244\) 2859.92 0.750359
\(245\) −1496.20 −0.390157
\(246\) 139.437 0.0361389
\(247\) 0 0
\(248\) 6527.69 1.67141
\(249\) 483.834 0.123139
\(250\) 7264.17 1.83770
\(251\) −49.9181 −0.0125530 −0.00627650 0.999980i \(-0.501998\pi\)
−0.00627650 + 0.999980i \(0.501998\pi\)
\(252\) 4230.79 1.05760
\(253\) −646.125 −0.160559
\(254\) 7313.59 1.80668
\(255\) −8162.13 −2.00444
\(256\) −7208.17 −1.75981
\(257\) 3151.59 0.764945 0.382473 0.923967i \(-0.375073\pi\)
0.382473 + 0.923967i \(0.375073\pi\)
\(258\) 5939.74 1.43330
\(259\) −5120.59 −1.22849
\(260\) 0 0
\(261\) 103.957 0.0246543
\(262\) 13579.9 3.20218
\(263\) −1309.16 −0.306943 −0.153471 0.988153i \(-0.549045\pi\)
−0.153471 + 0.988153i \(0.549045\pi\)
\(264\) −2510.68 −0.585309
\(265\) −1840.19 −0.426574
\(266\) −4277.35 −0.985944
\(267\) −7757.74 −1.77815
\(268\) −6528.97 −1.48814
\(269\) 5664.18 1.28383 0.641917 0.766774i \(-0.278139\pi\)
0.641917 + 0.766774i \(0.278139\pi\)
\(270\) 1918.05 0.432329
\(271\) −2358.45 −0.528655 −0.264328 0.964433i \(-0.585150\pi\)
−0.264328 + 0.964433i \(0.585150\pi\)
\(272\) −4816.05 −1.07359
\(273\) 0 0
\(274\) −7776.64 −1.71461
\(275\) −388.252 −0.0851363
\(276\) −6053.65 −1.32024
\(277\) −6248.51 −1.35537 −0.677683 0.735354i \(-0.737016\pi\)
−0.677683 + 0.735354i \(0.737016\pi\)
\(278\) 2514.89 0.542564
\(279\) −4132.92 −0.886852
\(280\) −4249.42 −0.906970
\(281\) −3155.15 −0.669823 −0.334912 0.942250i \(-0.608706\pi\)
−0.334912 + 0.942250i \(0.608706\pi\)
\(282\) −3666.55 −0.774256
\(283\) 7581.70 1.59253 0.796264 0.604949i \(-0.206807\pi\)
0.796264 + 0.604949i \(0.206807\pi\)
\(284\) −16625.1 −3.47366
\(285\) 4307.24 0.895225
\(286\) 0 0
\(287\) −57.2856 −0.0117821
\(288\) 1646.50 0.336879
\(289\) 10596.9 2.15690
\(290\) −225.587 −0.0456790
\(291\) −155.247 −0.0312741
\(292\) 4240.62 0.849874
\(293\) 5090.44 1.01497 0.507486 0.861660i \(-0.330575\pi\)
0.507486 + 0.861660i \(0.330575\pi\)
\(294\) 5230.37 1.03756
\(295\) 3184.26 0.628457
\(296\) 12416.7 2.43820
\(297\) −465.574 −0.0909608
\(298\) −12004.2 −2.33350
\(299\) 0 0
\(300\) −3637.60 −0.700056
\(301\) −2440.25 −0.467289
\(302\) −2288.02 −0.435962
\(303\) −9807.61 −1.85951
\(304\) 2541.48 0.479486
\(305\) 1818.70 0.341437
\(306\) 12444.1 2.32478
\(307\) −7020.67 −1.30518 −0.652591 0.757711i \(-0.726318\pi\)
−0.652591 + 0.757711i \(0.726318\pi\)
\(308\) 2228.49 0.412273
\(309\) −9447.05 −1.73924
\(310\) 8968.47 1.64314
\(311\) −10340.8 −1.88544 −0.942721 0.333584i \(-0.891742\pi\)
−0.942721 + 0.333584i \(0.891742\pi\)
\(312\) 0 0
\(313\) −1080.16 −0.195061 −0.0975306 0.995233i \(-0.531094\pi\)
−0.0975306 + 0.995233i \(0.531094\pi\)
\(314\) 8026.81 1.44261
\(315\) 2690.47 0.481240
\(316\) 2451.93 0.436493
\(317\) 9304.71 1.64860 0.824298 0.566157i \(-0.191570\pi\)
0.824298 + 0.566157i \(0.191570\pi\)
\(318\) 6432.89 1.13440
\(319\) 54.7573 0.00961072
\(320\) −6503.03 −1.13603
\(321\) 14856.4 2.58319
\(322\) 3822.95 0.661630
\(323\) −8184.72 −1.40994
\(324\) −12759.9 −2.18791
\(325\) 0 0
\(326\) −17240.0 −2.92894
\(327\) −9449.59 −1.59805
\(328\) 138.910 0.0233842
\(329\) 1506.35 0.252425
\(330\) −3449.45 −0.575412
\(331\) −141.932 −0.0235689 −0.0117845 0.999931i \(-0.503751\pi\)
−0.0117845 + 0.999931i \(0.503751\pi\)
\(332\) 1041.37 0.172146
\(333\) −7861.50 −1.29372
\(334\) 850.021 0.139255
\(335\) −4151.94 −0.677149
\(336\) 3639.97 0.591002
\(337\) 2278.75 0.368343 0.184171 0.982894i \(-0.441040\pi\)
0.184171 + 0.982894i \(0.441040\pi\)
\(338\) 0 0
\(339\) 6823.52 1.09322
\(340\) −17567.6 −2.80216
\(341\) −2176.94 −0.345713
\(342\) −6566.90 −1.03830
\(343\) −6814.47 −1.07273
\(344\) 5917.29 0.927438
\(345\) −3849.67 −0.600752
\(346\) −17723.1 −2.75375
\(347\) −8293.00 −1.28297 −0.641487 0.767134i \(-0.721682\pi\)
−0.641487 + 0.767134i \(0.721682\pi\)
\(348\) 513.030 0.0790267
\(349\) −249.059 −0.0382000 −0.0191000 0.999818i \(-0.506080\pi\)
−0.0191000 + 0.999818i \(0.506080\pi\)
\(350\) 2297.19 0.350828
\(351\) 0 0
\(352\) 867.265 0.131322
\(353\) −6399.58 −0.964916 −0.482458 0.875919i \(-0.660256\pi\)
−0.482458 + 0.875919i \(0.660256\pi\)
\(354\) −11131.5 −1.67127
\(355\) −10572.3 −1.58062
\(356\) −16697.2 −2.48581
\(357\) −11722.4 −1.73785
\(358\) −11803.7 −1.74258
\(359\) 7763.63 1.14136 0.570680 0.821172i \(-0.306680\pi\)
0.570680 + 0.821172i \(0.306680\pi\)
\(360\) −6524.02 −0.955128
\(361\) −2539.84 −0.370293
\(362\) 3972.95 0.576833
\(363\) 837.295 0.121065
\(364\) 0 0
\(365\) 2696.72 0.386719
\(366\) −6357.75 −0.907992
\(367\) 7599.42 1.08089 0.540445 0.841379i \(-0.318256\pi\)
0.540445 + 0.841379i \(0.318256\pi\)
\(368\) −2271.49 −0.321765
\(369\) −87.9490 −0.0124077
\(370\) 17059.5 2.39698
\(371\) −2642.86 −0.369839
\(372\) −20396.1 −2.84271
\(373\) 1585.63 0.220109 0.110055 0.993926i \(-0.464897\pi\)
0.110055 + 0.993926i \(0.464897\pi\)
\(374\) 6554.72 0.906247
\(375\) −10505.6 −1.44669
\(376\) −3652.69 −0.500993
\(377\) 0 0
\(378\) 2754.68 0.374829
\(379\) −2849.50 −0.386198 −0.193099 0.981179i \(-0.561854\pi\)
−0.193099 + 0.981179i \(0.561854\pi\)
\(380\) 9270.58 1.25150
\(381\) −10577.1 −1.42226
\(382\) −21910.1 −2.93460
\(383\) −4613.59 −0.615518 −0.307759 0.951464i \(-0.599579\pi\)
−0.307759 + 0.951464i \(0.599579\pi\)
\(384\) 18368.5 2.44106
\(385\) 1417.15 0.187597
\(386\) −19828.1 −2.61457
\(387\) −3746.46 −0.492101
\(388\) −334.143 −0.0437204
\(389\) 11704.3 1.52553 0.762763 0.646679i \(-0.223843\pi\)
0.762763 + 0.646679i \(0.223843\pi\)
\(390\) 0 0
\(391\) 7315.23 0.946156
\(392\) 5210.60 0.671364
\(393\) −19639.6 −2.52084
\(394\) 11144.3 1.42497
\(395\) 1559.24 0.198618
\(396\) 3421.34 0.434164
\(397\) −7918.29 −1.00103 −0.500513 0.865729i \(-0.666855\pi\)
−0.500513 + 0.865729i \(0.666855\pi\)
\(398\) −7454.71 −0.938871
\(399\) 6186.01 0.776160
\(400\) −1364.92 −0.170615
\(401\) −11600.6 −1.44466 −0.722328 0.691550i \(-0.756928\pi\)
−0.722328 + 0.691550i \(0.756928\pi\)
\(402\) 14514.3 1.80076
\(403\) 0 0
\(404\) −21109.2 −2.59955
\(405\) −8114.33 −0.995566
\(406\) −323.985 −0.0396037
\(407\) −4140.90 −0.504317
\(408\) 28425.1 3.44915
\(409\) 1603.65 0.193876 0.0969378 0.995290i \(-0.469095\pi\)
0.0969378 + 0.995290i \(0.469095\pi\)
\(410\) 190.850 0.0229888
\(411\) 11246.8 1.34979
\(412\) −20333.1 −2.43141
\(413\) 4573.19 0.544872
\(414\) 5869.28 0.696761
\(415\) 662.232 0.0783318
\(416\) 0 0
\(417\) −3637.09 −0.427120
\(418\) −3458.99 −0.404748
\(419\) −13735.6 −1.60150 −0.800748 0.599001i \(-0.795565\pi\)
−0.800748 + 0.599001i \(0.795565\pi\)
\(420\) 13277.6 1.54257
\(421\) 14940.0 1.72953 0.864763 0.502180i \(-0.167469\pi\)
0.864763 + 0.502180i \(0.167469\pi\)
\(422\) 10569.8 1.21926
\(423\) 2312.66 0.265828
\(424\) 6408.57 0.734028
\(425\) 4395.67 0.501697
\(426\) 36958.5 4.20339
\(427\) 2611.99 0.296026
\(428\) 31975.9 3.61124
\(429\) 0 0
\(430\) 8129.83 0.911756
\(431\) 9734.67 1.08794 0.543971 0.839104i \(-0.316920\pi\)
0.543971 + 0.839104i \(0.316920\pi\)
\(432\) −1636.75 −0.182288
\(433\) −12297.0 −1.36480 −0.682398 0.730981i \(-0.739063\pi\)
−0.682398 + 0.730981i \(0.739063\pi\)
\(434\) 12880.4 1.42461
\(435\) 326.249 0.0359596
\(436\) −20338.6 −2.23404
\(437\) −3860.32 −0.422573
\(438\) −9427.11 −1.02841
\(439\) −3741.54 −0.406775 −0.203387 0.979098i \(-0.565195\pi\)
−0.203387 + 0.979098i \(0.565195\pi\)
\(440\) −3436.41 −0.372328
\(441\) −3299.02 −0.356228
\(442\) 0 0
\(443\) 16586.0 1.77884 0.889421 0.457090i \(-0.151108\pi\)
0.889421 + 0.457090i \(0.151108\pi\)
\(444\) −38796.8 −4.14688
\(445\) −10618.2 −1.13112
\(446\) −5536.69 −0.587825
\(447\) 17360.7 1.83699
\(448\) −9339.56 −0.984939
\(449\) −4518.98 −0.474975 −0.237487 0.971391i \(-0.576324\pi\)
−0.237487 + 0.971391i \(0.576324\pi\)
\(450\) 3526.81 0.369456
\(451\) −46.3255 −0.00483677
\(452\) 14686.4 1.52830
\(453\) 3308.98 0.343200
\(454\) 2857.36 0.295380
\(455\) 0 0
\(456\) −15000.2 −1.54046
\(457\) 11676.9 1.19523 0.597615 0.801783i \(-0.296115\pi\)
0.597615 + 0.801783i \(0.296115\pi\)
\(458\) −24680.1 −2.51796
\(459\) 5271.09 0.536020
\(460\) −8285.74 −0.839836
\(461\) 1426.40 0.144108 0.0720541 0.997401i \(-0.477045\pi\)
0.0720541 + 0.997401i \(0.477045\pi\)
\(462\) −4954.05 −0.498882
\(463\) −3128.59 −0.314035 −0.157017 0.987596i \(-0.550188\pi\)
−0.157017 + 0.987596i \(0.550188\pi\)
\(464\) 192.502 0.0192601
\(465\) −12970.4 −1.29352
\(466\) −9145.94 −0.909180
\(467\) −15810.7 −1.56666 −0.783330 0.621606i \(-0.786481\pi\)
−0.783330 + 0.621606i \(0.786481\pi\)
\(468\) 0 0
\(469\) −5962.96 −0.587088
\(470\) −5018.48 −0.492521
\(471\) −11608.6 −1.13566
\(472\) −11089.4 −1.08142
\(473\) −1973.38 −0.191831
\(474\) −5450.77 −0.528190
\(475\) −2319.64 −0.224068
\(476\) −25230.3 −2.42947
\(477\) −4057.51 −0.389477
\(478\) −24778.5 −2.37101
\(479\) −9792.42 −0.934086 −0.467043 0.884235i \(-0.654681\pi\)
−0.467043 + 0.884235i \(0.654681\pi\)
\(480\) 5167.24 0.491357
\(481\) 0 0
\(482\) −22044.0 −2.08315
\(483\) −5528.85 −0.520852
\(484\) 1802.13 0.169246
\(485\) −212.490 −0.0198942
\(486\) 22898.0 2.13719
\(487\) 135.188 0.0125790 0.00628949 0.999980i \(-0.497998\pi\)
0.00628949 + 0.999980i \(0.497998\pi\)
\(488\) −6333.71 −0.587528
\(489\) 24932.9 2.30574
\(490\) 7158.90 0.660013
\(491\) 650.322 0.0597732 0.0298866 0.999553i \(-0.490485\pi\)
0.0298866 + 0.999553i \(0.490485\pi\)
\(492\) −434.032 −0.0397716
\(493\) −619.945 −0.0566348
\(494\) 0 0
\(495\) 2175.72 0.197558
\(496\) −7653.17 −0.692817
\(497\) −15183.8 −1.37040
\(498\) −2315.01 −0.208310
\(499\) −17313.7 −1.55324 −0.776620 0.629970i \(-0.783067\pi\)
−0.776620 + 0.629970i \(0.783067\pi\)
\(500\) −22611.5 −2.02243
\(501\) −1229.32 −0.109625
\(502\) 238.845 0.0212354
\(503\) 14852.8 1.31661 0.658304 0.752752i \(-0.271274\pi\)
0.658304 + 0.752752i \(0.271274\pi\)
\(504\) −9369.71 −0.828096
\(505\) −13423.9 −1.18288
\(506\) 3091.53 0.271612
\(507\) 0 0
\(508\) −22765.3 −1.98828
\(509\) 13500.5 1.17564 0.587818 0.808993i \(-0.299987\pi\)
0.587818 + 0.808993i \(0.299987\pi\)
\(510\) 39053.6 3.39083
\(511\) 3872.99 0.335286
\(512\) 13253.2 1.14397
\(513\) −2781.61 −0.239398
\(514\) −15079.5 −1.29403
\(515\) −12930.3 −1.10637
\(516\) −18488.9 −1.57738
\(517\) 1218.15 0.103625
\(518\) 24500.6 2.07818
\(519\) 25631.5 2.16782
\(520\) 0 0
\(521\) 1162.37 0.0977433 0.0488717 0.998805i \(-0.484437\pi\)
0.0488717 + 0.998805i \(0.484437\pi\)
\(522\) −497.405 −0.0417065
\(523\) −20125.6 −1.68266 −0.841329 0.540523i \(-0.818226\pi\)
−0.841329 + 0.540523i \(0.818226\pi\)
\(524\) −42270.8 −3.52406
\(525\) −3322.25 −0.276180
\(526\) 6263.96 0.519242
\(527\) 24646.7 2.03724
\(528\) 2943.56 0.242617
\(529\) −8716.77 −0.716427
\(530\) 8804.81 0.721616
\(531\) 7021.09 0.573803
\(532\) 13314.3 1.08505
\(533\) 0 0
\(534\) 37118.7 3.00802
\(535\) 20334.3 1.64323
\(536\) 14459.4 1.16521
\(537\) 17070.8 1.37181
\(538\) −27101.6 −2.17181
\(539\) −1737.70 −0.138865
\(540\) −5970.40 −0.475787
\(541\) −20346.9 −1.61698 −0.808488 0.588513i \(-0.799714\pi\)
−0.808488 + 0.588513i \(0.799714\pi\)
\(542\) 11284.5 0.894304
\(543\) −5745.78 −0.454097
\(544\) −9818.90 −0.773864
\(545\) −12933.8 −1.01656
\(546\) 0 0
\(547\) 17583.2 1.37441 0.687205 0.726464i \(-0.258837\pi\)
0.687205 + 0.726464i \(0.258837\pi\)
\(548\) 24206.7 1.88697
\(549\) 4010.11 0.311744
\(550\) 1857.68 0.144021
\(551\) 327.152 0.0252942
\(552\) 13406.7 1.03375
\(553\) 2239.37 0.172202
\(554\) 29897.4 2.29282
\(555\) −24671.9 −1.88696
\(556\) −7828.20 −0.597103
\(557\) −5140.53 −0.391044 −0.195522 0.980699i \(-0.562640\pi\)
−0.195522 + 0.980699i \(0.562640\pi\)
\(558\) 19774.9 1.50025
\(559\) 0 0
\(560\) 4982.09 0.375949
\(561\) −9479.59 −0.713420
\(562\) 15096.5 1.13311
\(563\) −6559.64 −0.491040 −0.245520 0.969391i \(-0.578959\pi\)
−0.245520 + 0.969391i \(0.578959\pi\)
\(564\) 11413.0 0.852084
\(565\) 9339.47 0.695424
\(566\) −36276.4 −2.69401
\(567\) −11653.7 −0.863156
\(568\) 36818.8 2.71986
\(569\) −18111.7 −1.33441 −0.667206 0.744874i \(-0.732510\pi\)
−0.667206 + 0.744874i \(0.732510\pi\)
\(570\) −20609.0 −1.51441
\(571\) −1142.62 −0.0837428 −0.0418714 0.999123i \(-0.513332\pi\)
−0.0418714 + 0.999123i \(0.513332\pi\)
\(572\) 0 0
\(573\) 31686.9 2.31019
\(574\) 274.096 0.0199313
\(575\) 2073.22 0.150364
\(576\) −14338.8 −1.03724
\(577\) 15361.9 1.10836 0.554181 0.832396i \(-0.313032\pi\)
0.554181 + 0.832396i \(0.313032\pi\)
\(578\) −50703.1 −3.64874
\(579\) 28675.9 2.05826
\(580\) 702.193 0.0502707
\(581\) 951.089 0.0679136
\(582\) 742.817 0.0529051
\(583\) −2137.22 −0.151826
\(584\) −9391.47 −0.665448
\(585\) 0 0
\(586\) −24356.4 −1.71698
\(587\) 13019.8 0.915476 0.457738 0.889087i \(-0.348660\pi\)
0.457738 + 0.889087i \(0.348660\pi\)
\(588\) −16280.8 −1.14185
\(589\) −13006.3 −0.909873
\(590\) −15235.8 −1.06313
\(591\) −16117.1 −1.12177
\(592\) −14557.6 −1.01066
\(593\) 14132.0 0.978634 0.489317 0.872106i \(-0.337246\pi\)
0.489317 + 0.872106i \(0.337246\pi\)
\(594\) 2227.65 0.153874
\(595\) −16044.6 −1.10549
\(596\) 37365.9 2.56806
\(597\) 10781.2 0.739102
\(598\) 0 0
\(599\) −3010.01 −0.205318 −0.102659 0.994717i \(-0.532735\pi\)
−0.102659 + 0.994717i \(0.532735\pi\)
\(600\) 8056.00 0.548141
\(601\) −14701.2 −0.997795 −0.498898 0.866661i \(-0.666262\pi\)
−0.498898 + 0.866661i \(0.666262\pi\)
\(602\) 11676.0 0.790493
\(603\) −9154.77 −0.618261
\(604\) 7122.00 0.479785
\(605\) 1146.02 0.0770121
\(606\) 46926.8 3.14566
\(607\) −10025.8 −0.670403 −0.335201 0.942147i \(-0.608804\pi\)
−0.335201 + 0.942147i \(0.608804\pi\)
\(608\) 5181.54 0.345623
\(609\) 468.555 0.0311770
\(610\) −8701.96 −0.577594
\(611\) 0 0
\(612\) −38735.4 −2.55847
\(613\) 5228.64 0.344507 0.172254 0.985053i \(-0.444895\pi\)
0.172254 + 0.985053i \(0.444895\pi\)
\(614\) 33592.0 2.20792
\(615\) −276.012 −0.0180973
\(616\) −4935.32 −0.322808
\(617\) −18312.7 −1.19488 −0.597440 0.801914i \(-0.703815\pi\)
−0.597440 + 0.801914i \(0.703815\pi\)
\(618\) 45201.6 2.94219
\(619\) −16796.5 −1.09064 −0.545322 0.838227i \(-0.683593\pi\)
−0.545322 + 0.838227i \(0.683593\pi\)
\(620\) −27916.5 −1.80831
\(621\) 2486.11 0.160651
\(622\) 49477.9 3.18952
\(623\) −15249.7 −0.980682
\(624\) 0 0
\(625\) −9967.26 −0.637905
\(626\) 5168.27 0.329977
\(627\) 5002.48 0.318628
\(628\) −24985.4 −1.58762
\(629\) 46882.0 2.97187
\(630\) −12873.2 −0.814094
\(631\) −3215.37 −0.202856 −0.101428 0.994843i \(-0.532341\pi\)
−0.101428 + 0.994843i \(0.532341\pi\)
\(632\) −5430.16 −0.341772
\(633\) −15286.3 −0.959833
\(634\) −44520.5 −2.78886
\(635\) −14477.1 −0.904731
\(636\) −20023.9 −1.24843
\(637\) 0 0
\(638\) −261.999 −0.0162580
\(639\) −23311.3 −1.44316
\(640\) 25141.3 1.55281
\(641\) 8865.27 0.546267 0.273134 0.961976i \(-0.411940\pi\)
0.273134 + 0.961976i \(0.411940\pi\)
\(642\) −71084.0 −4.36988
\(643\) −4311.38 −0.264424 −0.132212 0.991221i \(-0.542208\pi\)
−0.132212 + 0.991221i \(0.542208\pi\)
\(644\) −11899.9 −0.728138
\(645\) −11757.6 −0.717757
\(646\) 39161.6 2.38513
\(647\) 14425.5 0.876544 0.438272 0.898842i \(-0.355591\pi\)
0.438272 + 0.898842i \(0.355591\pi\)
\(648\) 28258.6 1.71312
\(649\) 3698.23 0.223680
\(650\) 0 0
\(651\) −18627.9 −1.12149
\(652\) 53663.7 3.22336
\(653\) 1884.04 0.112907 0.0564535 0.998405i \(-0.482021\pi\)
0.0564535 + 0.998405i \(0.482021\pi\)
\(654\) 45213.7 2.70336
\(655\) −26881.1 −1.60356
\(656\) −162.860 −0.00969302
\(657\) 5946.09 0.353088
\(658\) −7207.47 −0.427016
\(659\) 23210.1 1.37198 0.685991 0.727610i \(-0.259369\pi\)
0.685991 + 0.727610i \(0.259369\pi\)
\(660\) 10737.2 0.633253
\(661\) −115.397 −0.00679037 −0.00339518 0.999994i \(-0.501081\pi\)
−0.00339518 + 0.999994i \(0.501081\pi\)
\(662\) 679.108 0.0398705
\(663\) 0 0
\(664\) −2306.26 −0.134790
\(665\) 8466.90 0.493733
\(666\) 37615.2 2.18853
\(667\) −292.397 −0.0169740
\(668\) −2645.90 −0.153253
\(669\) 8007.30 0.462750
\(670\) 19865.9 1.14550
\(671\) 2112.25 0.121524
\(672\) 7421.12 0.426006
\(673\) −8293.86 −0.475044 −0.237522 0.971382i \(-0.576335\pi\)
−0.237522 + 0.971382i \(0.576335\pi\)
\(674\) −10903.2 −0.623110
\(675\) 1493.89 0.0851847
\(676\) 0 0
\(677\) 7252.49 0.411722 0.205861 0.978581i \(-0.434001\pi\)
0.205861 + 0.978581i \(0.434001\pi\)
\(678\) −32648.7 −1.84936
\(679\) −305.175 −0.0172482
\(680\) 38905.9 2.19408
\(681\) −4132.38 −0.232530
\(682\) 10416.1 0.584827
\(683\) 22073.0 1.23661 0.618303 0.785940i \(-0.287821\pi\)
0.618303 + 0.785940i \(0.287821\pi\)
\(684\) 20441.1 1.14267
\(685\) 15393.7 0.858630
\(686\) 32605.4 1.81469
\(687\) 35693.0 1.98220
\(688\) −6937.52 −0.384434
\(689\) 0 0
\(690\) 18419.6 1.01627
\(691\) 28633.0 1.57634 0.788170 0.615458i \(-0.211029\pi\)
0.788170 + 0.615458i \(0.211029\pi\)
\(692\) 55167.3 3.03056
\(693\) 3124.74 0.171283
\(694\) 39679.8 2.17035
\(695\) −4978.15 −0.271701
\(696\) −1136.18 −0.0618776
\(697\) 524.484 0.0285025
\(698\) 1191.68 0.0646213
\(699\) 13227.1 0.715729
\(700\) −7150.55 −0.386093
\(701\) 15832.0 0.853018 0.426509 0.904483i \(-0.359743\pi\)
0.426509 + 0.904483i \(0.359743\pi\)
\(702\) 0 0
\(703\) −24740.1 −1.32730
\(704\) −7552.69 −0.404336
\(705\) 7257.84 0.387725
\(706\) 30620.3 1.63231
\(707\) −19279.2 −1.02556
\(708\) 34649.3 1.83927
\(709\) −12423.3 −0.658064 −0.329032 0.944319i \(-0.606722\pi\)
−0.329032 + 0.944319i \(0.606722\pi\)
\(710\) 50585.7 2.67387
\(711\) 3438.04 0.181345
\(712\) 36978.3 1.94638
\(713\) 11624.6 0.610582
\(714\) 56088.3 2.93985
\(715\) 0 0
\(716\) 36741.9 1.91775
\(717\) 35835.3 1.86652
\(718\) −37146.8 −1.93079
\(719\) −19323.3 −1.00227 −0.501137 0.865368i \(-0.667085\pi\)
−0.501137 + 0.865368i \(0.667085\pi\)
\(720\) 7648.86 0.395912
\(721\) −18570.4 −0.959220
\(722\) 12152.4 0.626409
\(723\) 31880.6 1.63990
\(724\) −12366.8 −0.634817
\(725\) −175.700 −0.00900044
\(726\) −4006.23 −0.204800
\(727\) −9754.61 −0.497632 −0.248816 0.968551i \(-0.580041\pi\)
−0.248816 + 0.968551i \(0.580041\pi\)
\(728\) 0 0
\(729\) −9983.85 −0.507232
\(730\) −12903.1 −0.654196
\(731\) 22342.0 1.13043
\(732\) 19790.0 0.999264
\(733\) 1179.05 0.0594123 0.0297061 0.999559i \(-0.490543\pi\)
0.0297061 + 0.999559i \(0.490543\pi\)
\(734\) −36361.2 −1.82849
\(735\) −10353.4 −0.519578
\(736\) −4631.09 −0.231935
\(737\) −4822.11 −0.241010
\(738\) 420.812 0.0209896
\(739\) −3361.06 −0.167305 −0.0836527 0.996495i \(-0.526659\pi\)
−0.0836527 + 0.996495i \(0.526659\pi\)
\(740\) −53101.9 −2.63792
\(741\) 0 0
\(742\) 12645.4 0.625641
\(743\) −27407.8 −1.35329 −0.676645 0.736309i \(-0.736567\pi\)
−0.676645 + 0.736309i \(0.736567\pi\)
\(744\) 45170.2 2.22583
\(745\) 23761.9 1.16855
\(746\) −7586.81 −0.372350
\(747\) 1460.18 0.0715197
\(748\) −20403.1 −0.997344
\(749\) 29203.8 1.42468
\(750\) 50266.5 2.44730
\(751\) −24340.3 −1.18268 −0.591338 0.806424i \(-0.701400\pi\)
−0.591338 + 0.806424i \(0.701400\pi\)
\(752\) 4282.47 0.207667
\(753\) −345.423 −0.0167170
\(754\) 0 0
\(755\) 4529.06 0.218317
\(756\) −8574.61 −0.412507
\(757\) −29842.3 −1.43281 −0.716405 0.697684i \(-0.754214\pi\)
−0.716405 + 0.697684i \(0.754214\pi\)
\(758\) 13634.1 0.653314
\(759\) −4471.05 −0.213819
\(760\) −20531.1 −0.979921
\(761\) −21399.3 −1.01935 −0.509674 0.860368i \(-0.670234\pi\)
−0.509674 + 0.860368i \(0.670234\pi\)
\(762\) 50608.5 2.40598
\(763\) −18575.4 −0.881355
\(764\) 68200.5 3.22959
\(765\) −24632.8 −1.16418
\(766\) 22074.8 1.04125
\(767\) 0 0
\(768\) −49879.0 −2.34356
\(769\) 414.640 0.0194438 0.00972190 0.999953i \(-0.496905\pi\)
0.00972190 + 0.999953i \(0.496905\pi\)
\(770\) −6780.70 −0.317350
\(771\) 21808.4 1.01869
\(772\) 61719.9 2.87739
\(773\) −28186.7 −1.31152 −0.655760 0.754970i \(-0.727652\pi\)
−0.655760 + 0.754970i \(0.727652\pi\)
\(774\) 17925.8 0.832466
\(775\) 6985.14 0.323760
\(776\) 740.009 0.0342329
\(777\) −35433.4 −1.63599
\(778\) −56001.7 −2.58067
\(779\) −276.775 −0.0127298
\(780\) 0 0
\(781\) −12278.8 −0.562575
\(782\) −35001.4 −1.60057
\(783\) −210.691 −0.00961619
\(784\) −6108.99 −0.278288
\(785\) −15888.8 −0.722417
\(786\) 93970.3 4.26439
\(787\) −1613.93 −0.0731007 −0.0365504 0.999332i \(-0.511637\pi\)
−0.0365504 + 0.999332i \(0.511637\pi\)
\(788\) −34689.2 −1.56821
\(789\) −9059.08 −0.408760
\(790\) −7460.56 −0.335993
\(791\) 13413.2 0.602933
\(792\) −7577.07 −0.339949
\(793\) 0 0
\(794\) 37886.9 1.69339
\(795\) −12733.7 −0.568074
\(796\) 23204.6 1.03325
\(797\) 2819.19 0.125296 0.0626479 0.998036i \(-0.480045\pi\)
0.0626479 + 0.998036i \(0.480045\pi\)
\(798\) −29598.4 −1.31300
\(799\) −13791.5 −0.610649
\(800\) −2782.79 −0.122983
\(801\) −23412.4 −1.03275
\(802\) 55505.8 2.44386
\(803\) 3131.99 0.137641
\(804\) −45179.1 −1.98177
\(805\) −7567.43 −0.331325
\(806\) 0 0
\(807\) 39195.0 1.70970
\(808\) 46749.3 2.03544
\(809\) 29670.9 1.28946 0.644730 0.764410i \(-0.276970\pi\)
0.644730 + 0.764410i \(0.276970\pi\)
\(810\) 38824.9 1.68416
\(811\) −10375.4 −0.449234 −0.224617 0.974447i \(-0.572113\pi\)
−0.224617 + 0.974447i \(0.572113\pi\)
\(812\) 1008.48 0.0435847
\(813\) −16320.0 −0.704018
\(814\) 19813.1 0.853131
\(815\) 34126.1 1.46673
\(816\) −33326.1 −1.42971
\(817\) −11790.1 −0.504875
\(818\) −7673.01 −0.327971
\(819\) 0 0
\(820\) −594.067 −0.0252996
\(821\) 19432.4 0.826058 0.413029 0.910718i \(-0.364471\pi\)
0.413029 + 0.910718i \(0.364471\pi\)
\(822\) −53812.7 −2.28338
\(823\) −4256.77 −0.180294 −0.0901469 0.995928i \(-0.528734\pi\)
−0.0901469 + 0.995928i \(0.528734\pi\)
\(824\) 45030.7 1.90378
\(825\) −2686.62 −0.113377
\(826\) −21881.5 −0.921736
\(827\) 4083.89 0.171718 0.0858590 0.996307i \(-0.472637\pi\)
0.0858590 + 0.996307i \(0.472637\pi\)
\(828\) −18269.5 −0.766800
\(829\) −18779.9 −0.786795 −0.393398 0.919368i \(-0.628700\pi\)
−0.393398 + 0.919368i \(0.628700\pi\)
\(830\) −3168.60 −0.132510
\(831\) −43238.4 −1.80496
\(832\) 0 0
\(833\) 19673.7 0.818312
\(834\) 17402.5 0.722541
\(835\) −1682.59 −0.0697348
\(836\) 10767.0 0.445434
\(837\) 8376.26 0.345909
\(838\) 65721.0 2.70918
\(839\) 26837.5 1.10433 0.552165 0.833735i \(-0.313802\pi\)
0.552165 + 0.833735i \(0.313802\pi\)
\(840\) −29405.1 −1.20782
\(841\) −24364.2 −0.998984
\(842\) −71483.8 −2.92576
\(843\) −21833.0 −0.892013
\(844\) −32901.0 −1.34182
\(845\) 0 0
\(846\) −11065.4 −0.449690
\(847\) 1645.90 0.0667695
\(848\) −7513.51 −0.304263
\(849\) 52463.8 2.12079
\(850\) −21032.1 −0.848700
\(851\) 22111.9 0.890701
\(852\) −115042. −4.62592
\(853\) −18694.5 −0.750396 −0.375198 0.926945i \(-0.622425\pi\)
−0.375198 + 0.926945i \(0.622425\pi\)
\(854\) −12497.7 −0.500774
\(855\) 12999.0 0.519949
\(856\) −70815.3 −2.82759
\(857\) −10730.7 −0.427718 −0.213859 0.976864i \(-0.568603\pi\)
−0.213859 + 0.976864i \(0.568603\pi\)
\(858\) 0 0
\(859\) 20797.6 0.826083 0.413042 0.910712i \(-0.364466\pi\)
0.413042 + 0.910712i \(0.364466\pi\)
\(860\) −25306.1 −1.00341
\(861\) −396.405 −0.0156904
\(862\) −46577.8 −1.84042
\(863\) 9812.01 0.387027 0.193514 0.981098i \(-0.438012\pi\)
0.193514 + 0.981098i \(0.438012\pi\)
\(864\) −3336.99 −0.131397
\(865\) 35082.3 1.37900
\(866\) 58837.9 2.30877
\(867\) 73328.1 2.87238
\(868\) −40093.4 −1.56781
\(869\) 1810.92 0.0706920
\(870\) −1561.01 −0.0608314
\(871\) 0 0
\(872\) 45042.8 1.74924
\(873\) −468.527 −0.0181641
\(874\) 18470.6 0.714848
\(875\) −20651.2 −0.797874
\(876\) 29344.2 1.13179
\(877\) 22194.0 0.854548 0.427274 0.904122i \(-0.359474\pi\)
0.427274 + 0.904122i \(0.359474\pi\)
\(878\) 17902.3 0.688123
\(879\) 35224.8 1.35165
\(880\) 4028.90 0.154334
\(881\) 30618.1 1.17089 0.585443 0.810713i \(-0.300921\pi\)
0.585443 + 0.810713i \(0.300921\pi\)
\(882\) 15784.9 0.602615
\(883\) 4940.15 0.188278 0.0941389 0.995559i \(-0.469990\pi\)
0.0941389 + 0.995559i \(0.469990\pi\)
\(884\) 0 0
\(885\) 22034.4 0.836925
\(886\) −79359.7 −3.00919
\(887\) −31193.7 −1.18081 −0.590407 0.807105i \(-0.701033\pi\)
−0.590407 + 0.807105i \(0.701033\pi\)
\(888\) 85921.2 3.24699
\(889\) −20791.8 −0.784402
\(890\) 50805.0 1.91347
\(891\) −9424.07 −0.354342
\(892\) 17234.3 0.646914
\(893\) 7277.92 0.272728
\(894\) −83066.3 −3.10755
\(895\) 23365.1 0.872636
\(896\) 36107.7 1.34629
\(897\) 0 0
\(898\) 21622.1 0.803495
\(899\) −985.153 −0.0365480
\(900\) −10978.0 −0.406594
\(901\) 24196.9 0.894691
\(902\) 221.655 0.00818216
\(903\) −16886.1 −0.622295
\(904\) −32525.3 −1.19665
\(905\) −7864.34 −0.288861
\(906\) −15832.6 −0.580577
\(907\) −26746.4 −0.979160 −0.489580 0.871958i \(-0.662850\pi\)
−0.489580 + 0.871958i \(0.662850\pi\)
\(908\) −8894.21 −0.325071
\(909\) −29598.8 −1.08001
\(910\) 0 0
\(911\) −25483.0 −0.926773 −0.463386 0.886156i \(-0.653366\pi\)
−0.463386 + 0.886156i \(0.653366\pi\)
\(912\) 17586.5 0.638539
\(913\) 769.123 0.0278798
\(914\) −55870.6 −2.02192
\(915\) 12585.0 0.454696
\(916\) 76822.8 2.77107
\(917\) −38606.3 −1.39029
\(918\) −25220.7 −0.906762
\(919\) −41862.9 −1.50264 −0.751322 0.659936i \(-0.770583\pi\)
−0.751322 + 0.659936i \(0.770583\pi\)
\(920\) 18350.0 0.657589
\(921\) −48581.5 −1.73813
\(922\) −6824.92 −0.243782
\(923\) 0 0
\(924\) 15420.7 0.549030
\(925\) 13286.9 0.472292
\(926\) 14969.5 0.531239
\(927\) −28510.6 −1.01015
\(928\) 392.472 0.0138831
\(929\) 8178.69 0.288842 0.144421 0.989516i \(-0.453868\pi\)
0.144421 + 0.989516i \(0.453868\pi\)
\(930\) 62059.9 2.18820
\(931\) −10382.0 −0.365475
\(932\) 28469.0 1.00057
\(933\) −71556.1 −2.51087
\(934\) 75649.8 2.65025
\(935\) −12974.9 −0.453823
\(936\) 0 0
\(937\) −25429.5 −0.886600 −0.443300 0.896373i \(-0.646192\pi\)
−0.443300 + 0.896373i \(0.646192\pi\)
\(938\) 28531.2 0.993151
\(939\) −7474.47 −0.259766
\(940\) 15621.2 0.542030
\(941\) −18030.3 −0.624625 −0.312312 0.949979i \(-0.601104\pi\)
−0.312312 + 0.949979i \(0.601104\pi\)
\(942\) 55543.8 1.92114
\(943\) 247.373 0.00854249
\(944\) 13001.3 0.448260
\(945\) −5452.81 −0.187704
\(946\) 9442.07 0.324512
\(947\) 51078.4 1.75272 0.876360 0.481657i \(-0.159965\pi\)
0.876360 + 0.481657i \(0.159965\pi\)
\(948\) 16966.8 0.581284
\(949\) 0 0
\(950\) 11098.9 0.379047
\(951\) 64386.7 2.19546
\(952\) 55876.2 1.90227
\(953\) 37024.2 1.25848 0.629239 0.777212i \(-0.283367\pi\)
0.629239 + 0.777212i \(0.283367\pi\)
\(954\) 19414.1 0.658861
\(955\) 43370.5 1.46957
\(956\) 77129.2 2.60935
\(957\) 378.909 0.0127987
\(958\) 46854.1 1.58015
\(959\) 22108.2 0.744432
\(960\) −44999.6 −1.51287
\(961\) 9374.93 0.314690
\(962\) 0 0
\(963\) 44835.8 1.50033
\(964\) 68617.3 2.29255
\(965\) 39249.2 1.30930
\(966\) 26454.0 0.881102
\(967\) 45358.6 1.50841 0.754207 0.656637i \(-0.228022\pi\)
0.754207 + 0.656637i \(0.228022\pi\)
\(968\) −3991.08 −0.132519
\(969\) −56636.5 −1.87763
\(970\) 1016.71 0.0336541
\(971\) −20674.7 −0.683299 −0.341650 0.939827i \(-0.610986\pi\)
−0.341650 + 0.939827i \(0.610986\pi\)
\(972\) −71275.6 −2.35202
\(973\) −7149.56 −0.235564
\(974\) −646.839 −0.0212793
\(975\) 0 0
\(976\) 7425.75 0.243537
\(977\) −7864.58 −0.257533 −0.128767 0.991675i \(-0.541102\pi\)
−0.128767 + 0.991675i \(0.541102\pi\)
\(978\) −119297. −3.90052
\(979\) −12332.0 −0.402588
\(980\) −22283.8 −0.726357
\(981\) −28518.3 −0.928153
\(982\) −3111.62 −0.101116
\(983\) −40089.5 −1.30077 −0.650384 0.759606i \(-0.725392\pi\)
−0.650384 + 0.759606i \(0.725392\pi\)
\(984\) 961.227 0.0311411
\(985\) −22059.7 −0.713586
\(986\) 2966.27 0.0958066
\(987\) 10423.6 0.336158
\(988\) 0 0
\(989\) 10537.6 0.338803
\(990\) −10410.2 −0.334201
\(991\) −53389.6 −1.71138 −0.855690 0.517489i \(-0.826867\pi\)
−0.855690 + 0.517489i \(0.826867\pi\)
\(992\) −15603.2 −0.499397
\(993\) −982.142 −0.0313870
\(994\) 72650.6 2.31825
\(995\) 14756.4 0.470160
\(996\) 7206.04 0.229249
\(997\) 27207.0 0.864246 0.432123 0.901815i \(-0.357765\pi\)
0.432123 + 0.901815i \(0.357765\pi\)
\(998\) 82841.2 2.62755
\(999\) 15933.0 0.504604
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.n.1.3 39
13.12 even 2 1859.4.a.o.1.37 yes 39
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.4.a.n.1.3 39 1.1 even 1 trivial
1859.4.a.o.1.37 yes 39 13.12 even 2