Properties

Label 1859.4.a.n.1.18
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 1.18
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)
 
\(f(q)\) \(=\) \(q-0.641292 q^{2} -1.91302 q^{3} -7.58874 q^{4} -0.642358 q^{5} +1.22681 q^{6} -23.2338 q^{7} +9.99694 q^{8} -23.3404 q^{9} +O(q^{10})\) \(q-0.641292 q^{2} -1.91302 q^{3} -7.58874 q^{4} -0.642358 q^{5} +1.22681 q^{6} -23.2338 q^{7} +9.99694 q^{8} -23.3404 q^{9} +0.411939 q^{10} +11.0000 q^{11} +14.5174 q^{12} +14.8997 q^{14} +1.22884 q^{15} +54.2990 q^{16} -35.1893 q^{17} +14.9680 q^{18} -37.3835 q^{19} +4.87469 q^{20} +44.4467 q^{21} -7.05421 q^{22} +121.805 q^{23} -19.1244 q^{24} -124.587 q^{25} +96.3021 q^{27} +176.315 q^{28} -19.7597 q^{29} -0.788048 q^{30} -30.1301 q^{31} -114.797 q^{32} -21.0432 q^{33} +22.5666 q^{34} +14.9244 q^{35} +177.124 q^{36} +193.485 q^{37} +23.9738 q^{38} -6.42161 q^{40} +80.8749 q^{41} -28.5033 q^{42} +196.760 q^{43} -83.4762 q^{44} +14.9929 q^{45} -78.1129 q^{46} +182.123 q^{47} -103.875 q^{48} +196.809 q^{49} +79.8969 q^{50} +67.3178 q^{51} +451.627 q^{53} -61.7578 q^{54} -7.06593 q^{55} -232.267 q^{56} +71.5155 q^{57} +12.6718 q^{58} -270.352 q^{59} -9.32538 q^{60} +694.071 q^{61} +19.3222 q^{62} +542.285 q^{63} -360.774 q^{64} +13.4949 q^{66} -364.013 q^{67} +267.042 q^{68} -233.016 q^{69} -9.57091 q^{70} +772.939 q^{71} -233.332 q^{72} -160.608 q^{73} -124.081 q^{74} +238.338 q^{75} +283.694 q^{76} -255.572 q^{77} +46.4472 q^{79} -34.8794 q^{80} +445.961 q^{81} -51.8645 q^{82} +520.415 q^{83} -337.295 q^{84} +22.6041 q^{85} -126.181 q^{86} +37.8008 q^{87} +109.966 q^{88} -394.789 q^{89} -9.61480 q^{90} -924.351 q^{92} +57.6396 q^{93} -116.794 q^{94} +24.0136 q^{95} +219.609 q^{96} +17.2969 q^{97} -126.212 q^{98} -256.744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.641292 −0.226731 −0.113366 0.993553i \(-0.536163\pi\)
−0.113366 + 0.993553i \(0.536163\pi\)
\(3\) −1.91302 −0.368161 −0.184081 0.982911i \(-0.558931\pi\)
−0.184081 + 0.982911i \(0.558931\pi\)
\(4\) −7.58874 −0.948593
\(5\) −0.642358 −0.0574542 −0.0287271 0.999587i \(-0.509145\pi\)
−0.0287271 + 0.999587i \(0.509145\pi\)
\(6\) 1.22681 0.0834735
\(7\) −23.2338 −1.25451 −0.627253 0.778815i \(-0.715821\pi\)
−0.627253 + 0.778815i \(0.715821\pi\)
\(8\) 9.99694 0.441807
\(9\) −23.3404 −0.864457
\(10\) 0.411939 0.0130267
\(11\) 11.0000 0.301511
\(12\) 14.5174 0.349235
\(13\) 0 0
\(14\) 14.8997 0.284436
\(15\) 1.22884 0.0211524
\(16\) 54.2990 0.848422
\(17\) −35.1893 −0.502038 −0.251019 0.967982i \(-0.580766\pi\)
−0.251019 + 0.967982i \(0.580766\pi\)
\(18\) 14.9680 0.195999
\(19\) −37.3835 −0.451388 −0.225694 0.974198i \(-0.572465\pi\)
−0.225694 + 0.974198i \(0.572465\pi\)
\(20\) 4.87469 0.0545007
\(21\) 44.4467 0.461861
\(22\) −7.05421 −0.0683620
\(23\) 121.805 1.10427 0.552135 0.833755i \(-0.313813\pi\)
0.552135 + 0.833755i \(0.313813\pi\)
\(24\) −19.1244 −0.162656
\(25\) −124.587 −0.996699
\(26\) 0 0
\(27\) 96.3021 0.686421
\(28\) 176.315 1.19002
\(29\) −19.7597 −0.126527 −0.0632637 0.997997i \(-0.520151\pi\)
−0.0632637 + 0.997997i \(0.520151\pi\)
\(30\) −0.788048 −0.00479591
\(31\) −30.1301 −0.174566 −0.0872828 0.996184i \(-0.527818\pi\)
−0.0872828 + 0.996184i \(0.527818\pi\)
\(32\) −114.797 −0.634170
\(33\) −21.0432 −0.111005
\(34\) 22.5666 0.113828
\(35\) 14.9244 0.0720767
\(36\) 177.124 0.820018
\(37\) 193.485 0.859697 0.429849 0.902901i \(-0.358567\pi\)
0.429849 + 0.902901i \(0.358567\pi\)
\(38\) 23.9738 0.102344
\(39\) 0 0
\(40\) −6.42161 −0.0253836
\(41\) 80.8749 0.308062 0.154031 0.988066i \(-0.450774\pi\)
0.154031 + 0.988066i \(0.450774\pi\)
\(42\) −28.5033 −0.104718
\(43\) 196.760 0.697805 0.348903 0.937159i \(-0.386554\pi\)
0.348903 + 0.937159i \(0.386554\pi\)
\(44\) −83.4762 −0.286012
\(45\) 14.9929 0.0496667
\(46\) −78.1129 −0.250372
\(47\) 182.123 0.565220 0.282610 0.959235i \(-0.408800\pi\)
0.282610 + 0.959235i \(0.408800\pi\)
\(48\) −103.875 −0.312356
\(49\) 196.809 0.573788
\(50\) 79.8969 0.225983
\(51\) 67.3178 0.184831
\(52\) 0 0
\(53\) 451.627 1.17049 0.585243 0.810858i \(-0.300999\pi\)
0.585243 + 0.810858i \(0.300999\pi\)
\(54\) −61.7578 −0.155633
\(55\) −7.06593 −0.0173231
\(56\) −232.267 −0.554249
\(57\) 71.5155 0.166183
\(58\) 12.6718 0.0286877
\(59\) −270.352 −0.596557 −0.298279 0.954479i \(-0.596412\pi\)
−0.298279 + 0.954479i \(0.596412\pi\)
\(60\) −9.32538 −0.0200650
\(61\) 694.071 1.45683 0.728415 0.685136i \(-0.240257\pi\)
0.728415 + 0.685136i \(0.240257\pi\)
\(62\) 19.3222 0.0395794
\(63\) 542.285 1.08447
\(64\) −360.774 −0.704636
\(65\) 0 0
\(66\) 13.4949 0.0251682
\(67\) −364.013 −0.663749 −0.331875 0.943323i \(-0.607681\pi\)
−0.331875 + 0.943323i \(0.607681\pi\)
\(68\) 267.042 0.476230
\(69\) −233.016 −0.406549
\(70\) −9.57091 −0.0163420
\(71\) 772.939 1.29199 0.645993 0.763344i \(-0.276444\pi\)
0.645993 + 0.763344i \(0.276444\pi\)
\(72\) −233.332 −0.381923
\(73\) −160.608 −0.257504 −0.128752 0.991677i \(-0.541097\pi\)
−0.128752 + 0.991677i \(0.541097\pi\)
\(74\) −124.081 −0.194920
\(75\) 238.338 0.366946
\(76\) 283.694 0.428184
\(77\) −255.572 −0.378248
\(78\) 0 0
\(79\) 46.4472 0.0661483 0.0330741 0.999453i \(-0.489470\pi\)
0.0330741 + 0.999453i \(0.489470\pi\)
\(80\) −34.8794 −0.0487454
\(81\) 445.961 0.611744
\(82\) −51.8645 −0.0698472
\(83\) 520.415 0.688228 0.344114 0.938928i \(-0.388179\pi\)
0.344114 + 0.938928i \(0.388179\pi\)
\(84\) −337.295 −0.438118
\(85\) 22.6041 0.0288442
\(86\) −126.181 −0.158214
\(87\) 37.8008 0.0465824
\(88\) 109.966 0.133210
\(89\) −394.789 −0.470197 −0.235099 0.971971i \(-0.575541\pi\)
−0.235099 + 0.971971i \(0.575541\pi\)
\(90\) −9.61480 −0.0112610
\(91\) 0 0
\(92\) −924.351 −1.04750
\(93\) 57.6396 0.0642683
\(94\) −116.794 −0.128153
\(95\) 24.0136 0.0259341
\(96\) 219.609 0.233477
\(97\) 17.2969 0.0181055 0.00905276 0.999959i \(-0.497118\pi\)
0.00905276 + 0.999959i \(0.497118\pi\)
\(98\) −126.212 −0.130095
\(99\) −256.744 −0.260644
\(100\) 945.462 0.945462
\(101\) −310.625 −0.306023 −0.153012 0.988224i \(-0.548897\pi\)
−0.153012 + 0.988224i \(0.548897\pi\)
\(102\) −43.1704 −0.0419069
\(103\) −1176.13 −1.12512 −0.562561 0.826756i \(-0.690184\pi\)
−0.562561 + 0.826756i \(0.690184\pi\)
\(104\) 0 0
\(105\) −28.5507 −0.0265358
\(106\) −289.625 −0.265385
\(107\) −312.926 −0.282727 −0.141363 0.989958i \(-0.545149\pi\)
−0.141363 + 0.989958i \(0.545149\pi\)
\(108\) −730.812 −0.651134
\(109\) 1339.09 1.17671 0.588355 0.808603i \(-0.299776\pi\)
0.588355 + 0.808603i \(0.299776\pi\)
\(110\) 4.53133 0.00392768
\(111\) −370.142 −0.316507
\(112\) −1261.57 −1.06435
\(113\) 1217.74 1.01377 0.506883 0.862015i \(-0.330798\pi\)
0.506883 + 0.862015i \(0.330798\pi\)
\(114\) −45.8623 −0.0376790
\(115\) −78.2427 −0.0634449
\(116\) 149.952 0.120023
\(117\) 0 0
\(118\) 173.375 0.135258
\(119\) 817.580 0.629811
\(120\) 12.2847 0.00934527
\(121\) 121.000 0.0909091
\(122\) −445.102 −0.330309
\(123\) −154.715 −0.113416
\(124\) 228.650 0.165592
\(125\) 160.324 0.114719
\(126\) −347.763 −0.245883
\(127\) −1594.23 −1.11390 −0.556950 0.830546i \(-0.688028\pi\)
−0.556950 + 0.830546i \(0.688028\pi\)
\(128\) 1149.74 0.793933
\(129\) −376.406 −0.256905
\(130\) 0 0
\(131\) −2627.82 −1.75262 −0.876311 0.481745i \(-0.840003\pi\)
−0.876311 + 0.481745i \(0.840003\pi\)
\(132\) 159.692 0.105298
\(133\) 868.562 0.566269
\(134\) 233.438 0.150493
\(135\) −61.8604 −0.0394378
\(136\) −351.785 −0.221804
\(137\) −3032.80 −1.89131 −0.945655 0.325173i \(-0.894577\pi\)
−0.945655 + 0.325173i \(0.894577\pi\)
\(138\) 149.432 0.0921773
\(139\) 1685.94 1.02878 0.514388 0.857558i \(-0.328019\pi\)
0.514388 + 0.857558i \(0.328019\pi\)
\(140\) −113.258 −0.0683715
\(141\) −348.404 −0.208092
\(142\) −495.680 −0.292933
\(143\) 0 0
\(144\) −1267.36 −0.733425
\(145\) 12.6928 0.00726953
\(146\) 102.997 0.0583841
\(147\) −376.500 −0.211246
\(148\) −1468.31 −0.815503
\(149\) 1612.83 0.886764 0.443382 0.896333i \(-0.353778\pi\)
0.443382 + 0.896333i \(0.353778\pi\)
\(150\) −152.844 −0.0831980
\(151\) 2699.78 1.45500 0.727501 0.686106i \(-0.240682\pi\)
0.727501 + 0.686106i \(0.240682\pi\)
\(152\) −373.721 −0.199426
\(153\) 821.330 0.433991
\(154\) 163.896 0.0857606
\(155\) 19.3543 0.0100295
\(156\) 0 0
\(157\) −761.773 −0.387236 −0.193618 0.981077i \(-0.562022\pi\)
−0.193618 + 0.981077i \(0.562022\pi\)
\(158\) −29.7862 −0.0149979
\(159\) −863.972 −0.430927
\(160\) 73.7408 0.0364357
\(161\) −2830.00 −1.38531
\(162\) −285.992 −0.138701
\(163\) −565.770 −0.271868 −0.135934 0.990718i \(-0.543404\pi\)
−0.135934 + 0.990718i \(0.543404\pi\)
\(164\) −613.739 −0.292226
\(165\) 13.5173 0.00637769
\(166\) −333.738 −0.156043
\(167\) −1746.16 −0.809114 −0.404557 0.914513i \(-0.632574\pi\)
−0.404557 + 0.914513i \(0.632574\pi\)
\(168\) 444.331 0.204053
\(169\) 0 0
\(170\) −14.4958 −0.00653988
\(171\) 872.545 0.390206
\(172\) −1493.16 −0.661933
\(173\) −58.9246 −0.0258957 −0.0129478 0.999916i \(-0.504122\pi\)
−0.0129478 + 0.999916i \(0.504122\pi\)
\(174\) −24.2414 −0.0105617
\(175\) 2894.64 1.25037
\(176\) 597.289 0.255809
\(177\) 517.190 0.219629
\(178\) 253.175 0.106608
\(179\) 436.558 0.182290 0.0911448 0.995838i \(-0.470947\pi\)
0.0911448 + 0.995838i \(0.470947\pi\)
\(180\) −113.777 −0.0471135
\(181\) 453.369 0.186181 0.0930903 0.995658i \(-0.470325\pi\)
0.0930903 + 0.995658i \(0.470325\pi\)
\(182\) 0 0
\(183\) −1327.77 −0.536348
\(184\) 1217.68 0.487873
\(185\) −124.287 −0.0493932
\(186\) −36.9638 −0.0145716
\(187\) −387.082 −0.151370
\(188\) −1382.08 −0.536163
\(189\) −2237.46 −0.861119
\(190\) −15.3997 −0.00588008
\(191\) −1937.48 −0.733986 −0.366993 0.930224i \(-0.619613\pi\)
−0.366993 + 0.930224i \(0.619613\pi\)
\(192\) 690.167 0.259419
\(193\) 1622.95 0.605300 0.302650 0.953102i \(-0.402129\pi\)
0.302650 + 0.953102i \(0.402129\pi\)
\(194\) −11.0924 −0.00410508
\(195\) 0 0
\(196\) −1493.53 −0.544291
\(197\) 2742.17 0.991732 0.495866 0.868399i \(-0.334851\pi\)
0.495866 + 0.868399i \(0.334851\pi\)
\(198\) 164.648 0.0590960
\(199\) −4261.14 −1.51791 −0.758956 0.651142i \(-0.774290\pi\)
−0.758956 + 0.651142i \(0.774290\pi\)
\(200\) −1245.49 −0.440348
\(201\) 696.364 0.244367
\(202\) 199.201 0.0693850
\(203\) 459.094 0.158729
\(204\) −510.858 −0.175329
\(205\) −51.9506 −0.0176995
\(206\) 754.244 0.255100
\(207\) −2842.98 −0.954594
\(208\) 0 0
\(209\) −411.219 −0.136099
\(210\) 18.3093 0.00601650
\(211\) −13.6015 −0.00443776 −0.00221888 0.999998i \(-0.500706\pi\)
−0.00221888 + 0.999998i \(0.500706\pi\)
\(212\) −3427.28 −1.11031
\(213\) −1478.65 −0.475659
\(214\) 200.677 0.0641029
\(215\) −126.390 −0.0400918
\(216\) 962.727 0.303265
\(217\) 700.038 0.218994
\(218\) −858.746 −0.266797
\(219\) 307.247 0.0948029
\(220\) 53.6216 0.0164326
\(221\) 0 0
\(222\) 237.369 0.0717620
\(223\) 4944.64 1.48483 0.742417 0.669938i \(-0.233679\pi\)
0.742417 + 0.669938i \(0.233679\pi\)
\(224\) 2667.17 0.795571
\(225\) 2907.91 0.861604
\(226\) −780.928 −0.229852
\(227\) −978.487 −0.286099 −0.143049 0.989716i \(-0.545691\pi\)
−0.143049 + 0.989716i \(0.545691\pi\)
\(228\) −542.713 −0.157641
\(229\) 4614.01 1.33145 0.665725 0.746197i \(-0.268122\pi\)
0.665725 + 0.746197i \(0.268122\pi\)
\(230\) 50.1764 0.0143849
\(231\) 488.914 0.139256
\(232\) −197.537 −0.0559006
\(233\) −3289.10 −0.924789 −0.462395 0.886674i \(-0.653010\pi\)
−0.462395 + 0.886674i \(0.653010\pi\)
\(234\) 0 0
\(235\) −116.988 −0.0324742
\(236\) 2051.64 0.565890
\(237\) −88.8544 −0.0243532
\(238\) −524.308 −0.142798
\(239\) −1517.69 −0.410757 −0.205379 0.978683i \(-0.565843\pi\)
−0.205379 + 0.978683i \(0.565843\pi\)
\(240\) 66.7250 0.0179462
\(241\) −2219.80 −0.593320 −0.296660 0.954983i \(-0.595873\pi\)
−0.296660 + 0.954983i \(0.595873\pi\)
\(242\) −77.5964 −0.0206119
\(243\) −3453.29 −0.911641
\(244\) −5267.12 −1.38194
\(245\) −126.422 −0.0329665
\(246\) 99.2178 0.0257150
\(247\) 0 0
\(248\) −301.209 −0.0771242
\(249\) −995.564 −0.253379
\(250\) −102.815 −0.0260103
\(251\) −3805.91 −0.957080 −0.478540 0.878066i \(-0.658834\pi\)
−0.478540 + 0.878066i \(0.658834\pi\)
\(252\) −4115.26 −1.02872
\(253\) 1339.86 0.332950
\(254\) 1022.37 0.252556
\(255\) −43.2421 −0.0106193
\(256\) 2148.87 0.524627
\(257\) −4987.53 −1.21056 −0.605279 0.796013i \(-0.706939\pi\)
−0.605279 + 0.796013i \(0.706939\pi\)
\(258\) 241.386 0.0582483
\(259\) −4495.40 −1.07850
\(260\) 0 0
\(261\) 461.199 0.109377
\(262\) 1685.20 0.397374
\(263\) −1099.76 −0.257847 −0.128924 0.991655i \(-0.541152\pi\)
−0.128924 + 0.991655i \(0.541152\pi\)
\(264\) −210.368 −0.0490426
\(265\) −290.106 −0.0672494
\(266\) −557.002 −0.128391
\(267\) 755.240 0.173108
\(268\) 2762.40 0.629628
\(269\) 4740.51 1.07448 0.537238 0.843431i \(-0.319468\pi\)
0.537238 + 0.843431i \(0.319468\pi\)
\(270\) 39.6706 0.00894176
\(271\) 7507.72 1.68288 0.841441 0.540348i \(-0.181708\pi\)
0.841441 + 0.540348i \(0.181708\pi\)
\(272\) −1910.74 −0.425940
\(273\) 0 0
\(274\) 1944.91 0.428818
\(275\) −1370.46 −0.300516
\(276\) 1768.30 0.385650
\(277\) −8224.58 −1.78400 −0.891999 0.452038i \(-0.850697\pi\)
−0.891999 + 0.452038i \(0.850697\pi\)
\(278\) −1081.18 −0.233255
\(279\) 703.248 0.150905
\(280\) 149.198 0.0318440
\(281\) 374.647 0.0795358 0.0397679 0.999209i \(-0.487338\pi\)
0.0397679 + 0.999209i \(0.487338\pi\)
\(282\) 223.429 0.0471809
\(283\) −6545.41 −1.37486 −0.687428 0.726253i \(-0.741260\pi\)
−0.687428 + 0.726253i \(0.741260\pi\)
\(284\) −5865.63 −1.22557
\(285\) −45.9385 −0.00954794
\(286\) 0 0
\(287\) −1879.03 −0.386466
\(288\) 2679.40 0.548213
\(289\) −3674.72 −0.747957
\(290\) −8.13981 −0.00164823
\(291\) −33.0894 −0.00666575
\(292\) 1218.82 0.244266
\(293\) −9231.30 −1.84061 −0.920304 0.391203i \(-0.872059\pi\)
−0.920304 + 0.391203i \(0.872059\pi\)
\(294\) 241.447 0.0478961
\(295\) 173.663 0.0342747
\(296\) 1934.26 0.379820
\(297\) 1059.32 0.206964
\(298\) −1034.29 −0.201057
\(299\) 0 0
\(300\) −1808.69 −0.348082
\(301\) −4571.48 −0.875401
\(302\) −1731.35 −0.329894
\(303\) 594.232 0.112666
\(304\) −2029.89 −0.382967
\(305\) −445.842 −0.0837010
\(306\) −526.712 −0.0983992
\(307\) 3679.11 0.683968 0.341984 0.939706i \(-0.388901\pi\)
0.341984 + 0.939706i \(0.388901\pi\)
\(308\) 1939.47 0.358803
\(309\) 2249.96 0.414226
\(310\) −12.4118 −0.00227401
\(311\) −8590.95 −1.56639 −0.783196 0.621775i \(-0.786412\pi\)
−0.783196 + 0.621775i \(0.786412\pi\)
\(312\) 0 0
\(313\) −8092.74 −1.46143 −0.730717 0.682681i \(-0.760814\pi\)
−0.730717 + 0.682681i \(0.760814\pi\)
\(314\) 488.519 0.0877985
\(315\) −348.341 −0.0623073
\(316\) −352.476 −0.0627478
\(317\) 6112.44 1.08299 0.541496 0.840703i \(-0.317858\pi\)
0.541496 + 0.840703i \(0.317858\pi\)
\(318\) 554.059 0.0977046
\(319\) −217.357 −0.0381494
\(320\) 231.746 0.0404843
\(321\) 598.635 0.104089
\(322\) 1814.86 0.314094
\(323\) 1315.50 0.226614
\(324\) −3384.29 −0.580296
\(325\) 0 0
\(326\) 362.824 0.0616409
\(327\) −2561.70 −0.433219
\(328\) 808.502 0.136104
\(329\) −4231.40 −0.709072
\(330\) −8.66853 −0.00144602
\(331\) −200.492 −0.0332931 −0.0166466 0.999861i \(-0.505299\pi\)
−0.0166466 + 0.999861i \(0.505299\pi\)
\(332\) −3949.30 −0.652849
\(333\) −4516.02 −0.743172
\(334\) 1119.80 0.183451
\(335\) 233.826 0.0381352
\(336\) 2413.41 0.391853
\(337\) 7750.18 1.25276 0.626379 0.779519i \(-0.284536\pi\)
0.626379 + 0.779519i \(0.284536\pi\)
\(338\) 0 0
\(339\) −2329.57 −0.373229
\(340\) −171.537 −0.0273614
\(341\) −331.432 −0.0526335
\(342\) −559.556 −0.0884718
\(343\) 3396.57 0.534686
\(344\) 1967.00 0.308295
\(345\) 149.680 0.0233580
\(346\) 37.7879 0.00587135
\(347\) −2636.26 −0.407844 −0.203922 0.978987i \(-0.565369\pi\)
−0.203922 + 0.978987i \(0.565369\pi\)
\(348\) −286.861 −0.0441878
\(349\) −1218.52 −0.186893 −0.0934466 0.995624i \(-0.529788\pi\)
−0.0934466 + 0.995624i \(0.529788\pi\)
\(350\) −1856.31 −0.283497
\(351\) 0 0
\(352\) −1262.77 −0.191209
\(353\) 7942.50 1.19755 0.598777 0.800916i \(-0.295654\pi\)
0.598777 + 0.800916i \(0.295654\pi\)
\(354\) −331.670 −0.0497968
\(355\) −496.503 −0.0742300
\(356\) 2995.95 0.446026
\(357\) −1564.05 −0.231872
\(358\) −279.961 −0.0413307
\(359\) −8507.63 −1.25074 −0.625370 0.780328i \(-0.715052\pi\)
−0.625370 + 0.780328i \(0.715052\pi\)
\(360\) 149.883 0.0219431
\(361\) −5461.47 −0.796249
\(362\) −290.742 −0.0422129
\(363\) −231.476 −0.0334692
\(364\) 0 0
\(365\) 103.168 0.0147947
\(366\) 851.490 0.121607
\(367\) 9323.72 1.32614 0.663071 0.748557i \(-0.269253\pi\)
0.663071 + 0.748557i \(0.269253\pi\)
\(368\) 6613.91 0.936886
\(369\) −1887.65 −0.266307
\(370\) 79.7042 0.0111990
\(371\) −10493.0 −1.46838
\(372\) −437.412 −0.0609644
\(373\) 10712.5 1.48705 0.743526 0.668707i \(-0.233152\pi\)
0.743526 + 0.668707i \(0.233152\pi\)
\(374\) 248.233 0.0343203
\(375\) −306.704 −0.0422350
\(376\) 1820.67 0.249718
\(377\) 0 0
\(378\) 1434.87 0.195242
\(379\) −7598.29 −1.02981 −0.514905 0.857247i \(-0.672173\pi\)
−0.514905 + 0.857247i \(0.672173\pi\)
\(380\) −182.233 −0.0246010
\(381\) 3049.80 0.410094
\(382\) 1242.49 0.166417
\(383\) −6189.02 −0.825703 −0.412851 0.910798i \(-0.635467\pi\)
−0.412851 + 0.910798i \(0.635467\pi\)
\(384\) −2199.47 −0.292295
\(385\) 164.168 0.0217319
\(386\) −1040.79 −0.137240
\(387\) −4592.45 −0.603223
\(388\) −131.262 −0.0171748
\(389\) −6579.48 −0.857566 −0.428783 0.903408i \(-0.641057\pi\)
−0.428783 + 0.903408i \(0.641057\pi\)
\(390\) 0 0
\(391\) −4286.25 −0.554386
\(392\) 1967.49 0.253503
\(393\) 5027.07 0.645247
\(394\) −1758.53 −0.224857
\(395\) −29.8357 −0.00380050
\(396\) 1948.36 0.247245
\(397\) −1423.19 −0.179920 −0.0899598 0.995945i \(-0.528674\pi\)
−0.0899598 + 0.995945i \(0.528674\pi\)
\(398\) 2732.64 0.344158
\(399\) −1661.58 −0.208478
\(400\) −6764.97 −0.845621
\(401\) 12569.6 1.56532 0.782661 0.622448i \(-0.213862\pi\)
0.782661 + 0.622448i \(0.213862\pi\)
\(402\) −446.573 −0.0554055
\(403\) 0 0
\(404\) 2357.25 0.290292
\(405\) −286.467 −0.0351473
\(406\) −294.413 −0.0359889
\(407\) 2128.34 0.259209
\(408\) 672.972 0.0816595
\(409\) −13436.8 −1.62447 −0.812236 0.583329i \(-0.801750\pi\)
−0.812236 + 0.583329i \(0.801750\pi\)
\(410\) 33.3155 0.00401302
\(411\) 5801.80 0.696306
\(412\) 8925.36 1.06728
\(413\) 6281.31 0.748385
\(414\) 1823.18 0.216436
\(415\) −334.292 −0.0395416
\(416\) 0 0
\(417\) −3225.24 −0.378755
\(418\) 263.712 0.0308578
\(419\) 13701.6 1.59754 0.798769 0.601638i \(-0.205485\pi\)
0.798769 + 0.601638i \(0.205485\pi\)
\(420\) 216.664 0.0251717
\(421\) 6376.59 0.738186 0.369093 0.929393i \(-0.379668\pi\)
0.369093 + 0.929393i \(0.379668\pi\)
\(422\) 8.72255 0.00100618
\(423\) −4250.81 −0.488608
\(424\) 4514.89 0.517128
\(425\) 4384.14 0.500381
\(426\) 948.245 0.107847
\(427\) −16125.9 −1.82760
\(428\) 2374.72 0.268192
\(429\) 0 0
\(430\) 81.0531 0.00909007
\(431\) −7396.12 −0.826586 −0.413293 0.910598i \(-0.635621\pi\)
−0.413293 + 0.910598i \(0.635621\pi\)
\(432\) 5229.11 0.582374
\(433\) −8609.35 −0.955518 −0.477759 0.878491i \(-0.658551\pi\)
−0.477759 + 0.878491i \(0.658551\pi\)
\(434\) −448.929 −0.0496527
\(435\) −24.2816 −0.00267636
\(436\) −10162.0 −1.11622
\(437\) −4553.52 −0.498454
\(438\) −197.035 −0.0214948
\(439\) 13835.1 1.50413 0.752067 0.659086i \(-0.229057\pi\)
0.752067 + 0.659086i \(0.229057\pi\)
\(440\) −70.6377 −0.00765346
\(441\) −4593.60 −0.496015
\(442\) 0 0
\(443\) −1210.42 −0.129816 −0.0649082 0.997891i \(-0.520675\pi\)
−0.0649082 + 0.997891i \(0.520675\pi\)
\(444\) 2808.91 0.300236
\(445\) 253.596 0.0270148
\(446\) −3170.96 −0.336658
\(447\) −3085.37 −0.326472
\(448\) 8382.14 0.883970
\(449\) −8956.87 −0.941427 −0.470713 0.882286i \(-0.656003\pi\)
−0.470713 + 0.882286i \(0.656003\pi\)
\(450\) −1864.82 −0.195352
\(451\) 889.624 0.0928842
\(452\) −9241.13 −0.961651
\(453\) −5164.74 −0.535675
\(454\) 627.496 0.0648675
\(455\) 0 0
\(456\) 714.936 0.0734209
\(457\) −5215.31 −0.533834 −0.266917 0.963720i \(-0.586005\pi\)
−0.266917 + 0.963720i \(0.586005\pi\)
\(458\) −2958.93 −0.301881
\(459\) −3388.80 −0.344609
\(460\) 593.764 0.0601834
\(461\) 307.230 0.0310393 0.0155197 0.999880i \(-0.495060\pi\)
0.0155197 + 0.999880i \(0.495060\pi\)
\(462\) −313.537 −0.0315737
\(463\) 12781.2 1.28292 0.641461 0.767156i \(-0.278329\pi\)
0.641461 + 0.767156i \(0.278329\pi\)
\(464\) −1072.93 −0.107349
\(465\) −37.0252 −0.00369248
\(466\) 2109.27 0.209678
\(467\) 3416.13 0.338500 0.169250 0.985573i \(-0.445865\pi\)
0.169250 + 0.985573i \(0.445865\pi\)
\(468\) 0 0
\(469\) 8457.39 0.832678
\(470\) 75.0234 0.00736292
\(471\) 1457.29 0.142565
\(472\) −2702.70 −0.263563
\(473\) 2164.36 0.210396
\(474\) 56.9816 0.00552163
\(475\) 4657.52 0.449898
\(476\) −6204.41 −0.597434
\(477\) −10541.1 −1.01184
\(478\) 973.280 0.0931314
\(479\) 10912.7 1.04094 0.520472 0.853879i \(-0.325756\pi\)
0.520472 + 0.853879i \(0.325756\pi\)
\(480\) −141.068 −0.0134142
\(481\) 0 0
\(482\) 1423.54 0.134524
\(483\) 5413.86 0.510019
\(484\) −918.238 −0.0862357
\(485\) −11.1108 −0.00104024
\(486\) 2214.57 0.206697
\(487\) 11010.1 1.02447 0.512234 0.858846i \(-0.328818\pi\)
0.512234 + 0.858846i \(0.328818\pi\)
\(488\) 6938.58 0.643637
\(489\) 1082.33 0.100091
\(490\) 81.0734 0.00747453
\(491\) 11064.5 1.01698 0.508488 0.861069i \(-0.330205\pi\)
0.508488 + 0.861069i \(0.330205\pi\)
\(492\) 1174.10 0.107586
\(493\) 695.331 0.0635216
\(494\) 0 0
\(495\) 164.921 0.0149751
\(496\) −1636.04 −0.148105
\(497\) −17958.3 −1.62080
\(498\) 638.448 0.0574488
\(499\) −3107.21 −0.278754 −0.139377 0.990239i \(-0.544510\pi\)
−0.139377 + 0.990239i \(0.544510\pi\)
\(500\) −1216.66 −0.108821
\(501\) 3340.45 0.297884
\(502\) 2440.70 0.217000
\(503\) −10479.9 −0.928973 −0.464487 0.885580i \(-0.653761\pi\)
−0.464487 + 0.885580i \(0.653761\pi\)
\(504\) 5421.19 0.479125
\(505\) 199.532 0.0175823
\(506\) −859.242 −0.0754900
\(507\) 0 0
\(508\) 12098.2 1.05664
\(509\) −3034.10 −0.264213 −0.132106 0.991236i \(-0.542174\pi\)
−0.132106 + 0.991236i \(0.542174\pi\)
\(510\) 27.7308 0.00240773
\(511\) 3731.54 0.323040
\(512\) −10576.0 −0.912882
\(513\) −3600.12 −0.309842
\(514\) 3198.46 0.274471
\(515\) 755.497 0.0646431
\(516\) 2856.45 0.243698
\(517\) 2003.35 0.170420
\(518\) 2882.87 0.244529
\(519\) 112.724 0.00953378
\(520\) 0 0
\(521\) −11635.9 −0.978462 −0.489231 0.872154i \(-0.662723\pi\)
−0.489231 + 0.872154i \(0.662723\pi\)
\(522\) −295.764 −0.0247993
\(523\) 23580.2 1.97149 0.985744 0.168253i \(-0.0538125\pi\)
0.985744 + 0.168253i \(0.0538125\pi\)
\(524\) 19941.8 1.66253
\(525\) −5537.50 −0.460336
\(526\) 705.265 0.0584620
\(527\) 1060.26 0.0876386
\(528\) −1142.63 −0.0941788
\(529\) 2669.57 0.219411
\(530\) 186.043 0.0152475
\(531\) 6310.12 0.515699
\(532\) −6591.29 −0.537159
\(533\) 0 0
\(534\) −484.330 −0.0392490
\(535\) 201.011 0.0162438
\(536\) −3639.01 −0.293249
\(537\) −835.144 −0.0671120
\(538\) −3040.05 −0.243617
\(539\) 2164.90 0.173003
\(540\) 469.443 0.0374104
\(541\) −3474.82 −0.276145 −0.138072 0.990422i \(-0.544091\pi\)
−0.138072 + 0.990422i \(0.544091\pi\)
\(542\) −4814.64 −0.381562
\(543\) −867.305 −0.0685444
\(544\) 4039.62 0.318378
\(545\) −860.173 −0.0676069
\(546\) 0 0
\(547\) 614.529 0.0480354 0.0240177 0.999712i \(-0.492354\pi\)
0.0240177 + 0.999712i \(0.492354\pi\)
\(548\) 23015.1 1.79408
\(549\) −16199.9 −1.25937
\(550\) 878.866 0.0681363
\(551\) 738.689 0.0571129
\(552\) −2329.45 −0.179616
\(553\) −1079.14 −0.0829835
\(554\) 5274.36 0.404488
\(555\) 237.763 0.0181847
\(556\) −12794.2 −0.975889
\(557\) 14685.3 1.11712 0.558561 0.829463i \(-0.311354\pi\)
0.558561 + 0.829463i \(0.311354\pi\)
\(558\) −450.988 −0.0342147
\(559\) 0 0
\(560\) 810.380 0.0611515
\(561\) 740.496 0.0557286
\(562\) −240.258 −0.0180332
\(563\) −13189.3 −0.987326 −0.493663 0.869653i \(-0.664342\pi\)
−0.493663 + 0.869653i \(0.664342\pi\)
\(564\) 2643.95 0.197394
\(565\) −782.226 −0.0582451
\(566\) 4197.52 0.311722
\(567\) −10361.4 −0.767437
\(568\) 7727.02 0.570807
\(569\) −2606.91 −0.192069 −0.0960346 0.995378i \(-0.530616\pi\)
−0.0960346 + 0.995378i \(0.530616\pi\)
\(570\) 29.4600 0.00216481
\(571\) 12777.9 0.936496 0.468248 0.883597i \(-0.344885\pi\)
0.468248 + 0.883597i \(0.344885\pi\)
\(572\) 0 0
\(573\) 3706.44 0.270225
\(574\) 1205.01 0.0876238
\(575\) −15175.4 −1.10062
\(576\) 8420.58 0.609128
\(577\) −19155.7 −1.38208 −0.691040 0.722816i \(-0.742847\pi\)
−0.691040 + 0.722816i \(0.742847\pi\)
\(578\) 2356.57 0.169585
\(579\) −3104.75 −0.222848
\(580\) −96.3226 −0.00689582
\(581\) −12091.2 −0.863387
\(582\) 21.2199 0.00151133
\(583\) 4967.90 0.352915
\(584\) −1605.59 −0.113767
\(585\) 0 0
\(586\) 5919.96 0.417323
\(587\) −15737.9 −1.10660 −0.553300 0.832982i \(-0.686632\pi\)
−0.553300 + 0.832982i \(0.686632\pi\)
\(588\) 2857.16 0.200387
\(589\) 1126.37 0.0787968
\(590\) −111.369 −0.00777115
\(591\) −5245.82 −0.365117
\(592\) 10506.1 0.729386
\(593\) −20361.6 −1.41004 −0.705018 0.709189i \(-0.749061\pi\)
−0.705018 + 0.709189i \(0.749061\pi\)
\(594\) −679.336 −0.0469251
\(595\) −525.179 −0.0361853
\(596\) −12239.3 −0.841178
\(597\) 8151.66 0.558836
\(598\) 0 0
\(599\) 10727.2 0.731723 0.365862 0.930669i \(-0.380774\pi\)
0.365862 + 0.930669i \(0.380774\pi\)
\(600\) 2382.65 0.162119
\(601\) −24952.4 −1.69356 −0.846780 0.531943i \(-0.821462\pi\)
−0.846780 + 0.531943i \(0.821462\pi\)
\(602\) 2931.66 0.198481
\(603\) 8496.18 0.573783
\(604\) −20488.0 −1.38021
\(605\) −77.7253 −0.00522311
\(606\) −381.076 −0.0255448
\(607\) 6389.25 0.427235 0.213617 0.976917i \(-0.431475\pi\)
0.213617 + 0.976917i \(0.431475\pi\)
\(608\) 4291.52 0.286257
\(609\) −878.256 −0.0584380
\(610\) 285.915 0.0189776
\(611\) 0 0
\(612\) −6232.86 −0.411681
\(613\) 2053.42 0.135297 0.0676483 0.997709i \(-0.478450\pi\)
0.0676483 + 0.997709i \(0.478450\pi\)
\(614\) −2359.39 −0.155077
\(615\) 99.3827 0.00651625
\(616\) −2554.94 −0.167112
\(617\) 10442.3 0.681350 0.340675 0.940181i \(-0.389344\pi\)
0.340675 + 0.940181i \(0.389344\pi\)
\(618\) −1442.88 −0.0939180
\(619\) 9436.66 0.612749 0.306374 0.951911i \(-0.400884\pi\)
0.306374 + 0.951911i \(0.400884\pi\)
\(620\) −146.875 −0.00951394
\(621\) 11730.1 0.757993
\(622\) 5509.31 0.355150
\(623\) 9172.45 0.589866
\(624\) 0 0
\(625\) 15470.4 0.990108
\(626\) 5189.81 0.331352
\(627\) 786.670 0.0501062
\(628\) 5780.90 0.367330
\(629\) −6808.61 −0.431601
\(630\) 223.388 0.0141270
\(631\) 14355.2 0.905663 0.452831 0.891596i \(-0.350414\pi\)
0.452831 + 0.891596i \(0.350414\pi\)
\(632\) 464.330 0.0292247
\(633\) 26.0200 0.00163381
\(634\) −3919.86 −0.245548
\(635\) 1024.07 0.0639982
\(636\) 6556.46 0.408775
\(637\) 0 0
\(638\) 139.389 0.00864966
\(639\) −18040.7 −1.11687
\(640\) −738.543 −0.0456148
\(641\) −4003.79 −0.246709 −0.123354 0.992363i \(-0.539365\pi\)
−0.123354 + 0.992363i \(0.539365\pi\)
\(642\) −383.900 −0.0236002
\(643\) 21342.9 1.30899 0.654497 0.756064i \(-0.272880\pi\)
0.654497 + 0.756064i \(0.272880\pi\)
\(644\) 21476.2 1.31410
\(645\) 241.787 0.0147603
\(646\) −843.620 −0.0513805
\(647\) −11010.9 −0.669063 −0.334531 0.942385i \(-0.608578\pi\)
−0.334531 + 0.942385i \(0.608578\pi\)
\(648\) 4458.25 0.270273
\(649\) −2973.88 −0.179869
\(650\) 0 0
\(651\) −1339.19 −0.0806250
\(652\) 4293.48 0.257892
\(653\) −3056.38 −0.183163 −0.0915815 0.995798i \(-0.529192\pi\)
−0.0915815 + 0.995798i \(0.529192\pi\)
\(654\) 1642.80 0.0982241
\(655\) 1688.00 0.100696
\(656\) 4391.43 0.261367
\(657\) 3748.65 0.222601
\(658\) 2713.56 0.160769
\(659\) −3838.61 −0.226906 −0.113453 0.993543i \(-0.536191\pi\)
−0.113453 + 0.993543i \(0.536191\pi\)
\(660\) −102.579 −0.00604983
\(661\) −18941.5 −1.11458 −0.557290 0.830318i \(-0.688159\pi\)
−0.557290 + 0.830318i \(0.688159\pi\)
\(662\) 128.574 0.00754858
\(663\) 0 0
\(664\) 5202.56 0.304064
\(665\) −557.927 −0.0325346
\(666\) 2896.09 0.168500
\(667\) −2406.84 −0.139720
\(668\) 13251.2 0.767520
\(669\) −9459.21 −0.546658
\(670\) −149.951 −0.00864643
\(671\) 7634.78 0.439251
\(672\) −5102.35 −0.292898
\(673\) 5208.05 0.298300 0.149150 0.988815i \(-0.452346\pi\)
0.149150 + 0.988815i \(0.452346\pi\)
\(674\) −4970.13 −0.284039
\(675\) −11998.0 −0.684155
\(676\) 0 0
\(677\) −15939.9 −0.904905 −0.452453 0.891788i \(-0.649451\pi\)
−0.452453 + 0.891788i \(0.649451\pi\)
\(678\) 1493.93 0.0846226
\(679\) −401.873 −0.0227135
\(680\) 225.972 0.0127436
\(681\) 1871.87 0.105330
\(682\) 212.545 0.0119337
\(683\) 28757.2 1.61107 0.805537 0.592546i \(-0.201877\pi\)
0.805537 + 0.592546i \(0.201877\pi\)
\(684\) −6621.52 −0.370146
\(685\) 1948.14 0.108664
\(686\) −2178.19 −0.121230
\(687\) −8826.69 −0.490188
\(688\) 10683.9 0.592033
\(689\) 0 0
\(690\) −95.9885 −0.00529597
\(691\) −4884.96 −0.268933 −0.134466 0.990918i \(-0.542932\pi\)
−0.134466 + 0.990918i \(0.542932\pi\)
\(692\) 447.163 0.0245645
\(693\) 5965.13 0.326979
\(694\) 1690.61 0.0924709
\(695\) −1082.98 −0.0591075
\(696\) 377.892 0.0205804
\(697\) −2845.93 −0.154659
\(698\) 781.425 0.0423745
\(699\) 6292.11 0.340471
\(700\) −21966.7 −1.18609
\(701\) 35673.0 1.92204 0.961019 0.276481i \(-0.0891682\pi\)
0.961019 + 0.276481i \(0.0891682\pi\)
\(702\) 0 0
\(703\) −7233.17 −0.388057
\(704\) −3968.51 −0.212456
\(705\) 223.800 0.0119558
\(706\) −5093.46 −0.271523
\(707\) 7217.00 0.383908
\(708\) −3924.82 −0.208339
\(709\) 7058.41 0.373885 0.186942 0.982371i \(-0.440142\pi\)
0.186942 + 0.982371i \(0.440142\pi\)
\(710\) 318.404 0.0168302
\(711\) −1084.09 −0.0571824
\(712\) −3946.68 −0.207736
\(713\) −3670.02 −0.192767
\(714\) 1003.01 0.0525725
\(715\) 0 0
\(716\) −3312.92 −0.172919
\(717\) 2903.37 0.151225
\(718\) 5455.88 0.283582
\(719\) 20783.4 1.07801 0.539005 0.842302i \(-0.318800\pi\)
0.539005 + 0.842302i \(0.318800\pi\)
\(720\) 814.097 0.0421383
\(721\) 27326.0 1.41147
\(722\) 3502.40 0.180534
\(723\) 4246.53 0.218437
\(724\) −3440.50 −0.176610
\(725\) 2461.81 0.126110
\(726\) 148.443 0.00758850
\(727\) 7296.24 0.372218 0.186109 0.982529i \(-0.440412\pi\)
0.186109 + 0.982529i \(0.440412\pi\)
\(728\) 0 0
\(729\) −5434.74 −0.276113
\(730\) −66.1608 −0.00335441
\(731\) −6923.84 −0.350325
\(732\) 10076.1 0.508776
\(733\) 24021.0 1.21041 0.605207 0.796068i \(-0.293090\pi\)
0.605207 + 0.796068i \(0.293090\pi\)
\(734\) −5979.23 −0.300677
\(735\) 241.848 0.0121370
\(736\) −13982.9 −0.700295
\(737\) −4004.14 −0.200128
\(738\) 1210.53 0.0603800
\(739\) −34721.3 −1.72834 −0.864171 0.503198i \(-0.832157\pi\)
−0.864171 + 0.503198i \(0.832157\pi\)
\(740\) 943.181 0.0468541
\(741\) 0 0
\(742\) 6729.09 0.332928
\(743\) −25702.4 −1.26909 −0.634543 0.772887i \(-0.718812\pi\)
−0.634543 + 0.772887i \(0.718812\pi\)
\(744\) 576.220 0.0283941
\(745\) −1036.01 −0.0509483
\(746\) −6869.82 −0.337161
\(747\) −12146.7 −0.594944
\(748\) 2937.47 0.143589
\(749\) 7270.47 0.354682
\(750\) 196.687 0.00957598
\(751\) −14220.7 −0.690973 −0.345486 0.938424i \(-0.612286\pi\)
−0.345486 + 0.938424i \(0.612286\pi\)
\(752\) 9889.08 0.479545
\(753\) 7280.79 0.352360
\(754\) 0 0
\(755\) −1734.23 −0.0835960
\(756\) 16979.5 0.816852
\(757\) −21078.6 −1.01204 −0.506020 0.862522i \(-0.668884\pi\)
−0.506020 + 0.862522i \(0.668884\pi\)
\(758\) 4872.72 0.233490
\(759\) −2563.18 −0.122579
\(760\) 240.063 0.0114579
\(761\) −16736.1 −0.797217 −0.398608 0.917121i \(-0.630507\pi\)
−0.398608 + 0.917121i \(0.630507\pi\)
\(762\) −1955.81 −0.0929811
\(763\) −31112.1 −1.47619
\(764\) 14703.1 0.696254
\(765\) −527.588 −0.0249346
\(766\) 3968.97 0.187212
\(767\) 0 0
\(768\) −4110.83 −0.193147
\(769\) −33100.3 −1.55218 −0.776092 0.630620i \(-0.782801\pi\)
−0.776092 + 0.630620i \(0.782801\pi\)
\(770\) −105.280 −0.00492731
\(771\) 9541.25 0.445681
\(772\) −12316.2 −0.574183
\(773\) −11960.8 −0.556532 −0.278266 0.960504i \(-0.589760\pi\)
−0.278266 + 0.960504i \(0.589760\pi\)
\(774\) 2945.10 0.136769
\(775\) 3753.84 0.173989
\(776\) 172.916 0.00799914
\(777\) 8599.79 0.397060
\(778\) 4219.37 0.194437
\(779\) −3023.39 −0.139056
\(780\) 0 0
\(781\) 8502.33 0.389548
\(782\) 2748.74 0.125696
\(783\) −1902.91 −0.0868510
\(784\) 10686.5 0.486814
\(785\) 489.331 0.0222484
\(786\) −3223.82 −0.146298
\(787\) 23486.2 1.06378 0.531888 0.846815i \(-0.321483\pi\)
0.531888 + 0.846815i \(0.321483\pi\)
\(788\) −20809.6 −0.940750
\(789\) 2103.86 0.0949293
\(790\) 19.1334 0.000861691 0
\(791\) −28292.8 −1.27178
\(792\) −2566.65 −0.115154
\(793\) 0 0
\(794\) 912.683 0.0407934
\(795\) 554.979 0.0247586
\(796\) 32336.7 1.43988
\(797\) 15997.4 0.710987 0.355493 0.934679i \(-0.384313\pi\)
0.355493 + 0.934679i \(0.384313\pi\)
\(798\) 1065.56 0.0472685
\(799\) −6408.76 −0.283762
\(800\) 14302.3 0.632077
\(801\) 9214.52 0.406466
\(802\) −8060.76 −0.354907
\(803\) −1766.69 −0.0776403
\(804\) −5284.53 −0.231805
\(805\) 1817.87 0.0795921
\(806\) 0 0
\(807\) −9068.70 −0.395580
\(808\) −3105.30 −0.135203
\(809\) 10407.2 0.452282 0.226141 0.974095i \(-0.427389\pi\)
0.226141 + 0.974095i \(0.427389\pi\)
\(810\) 183.709 0.00796898
\(811\) 34198.0 1.48071 0.740355 0.672216i \(-0.234657\pi\)
0.740355 + 0.672216i \(0.234657\pi\)
\(812\) −3483.95 −0.150570
\(813\) −14362.4 −0.619572
\(814\) −1364.89 −0.0587706
\(815\) 363.427 0.0156200
\(816\) 3655.29 0.156815
\(817\) −7355.59 −0.314981
\(818\) 8616.94 0.368318
\(819\) 0 0
\(820\) 394.240 0.0167896
\(821\) 13645.8 0.580075 0.290038 0.957015i \(-0.406332\pi\)
0.290038 + 0.957015i \(0.406332\pi\)
\(822\) −3720.65 −0.157874
\(823\) 3660.62 0.155044 0.0775220 0.996991i \(-0.475299\pi\)
0.0775220 + 0.996991i \(0.475299\pi\)
\(824\) −11757.7 −0.497087
\(825\) 2621.72 0.110638
\(826\) −4028.16 −0.169682
\(827\) −13815.9 −0.580927 −0.290463 0.956886i \(-0.593809\pi\)
−0.290463 + 0.956886i \(0.593809\pi\)
\(828\) 21574.7 0.905521
\(829\) 21839.6 0.914985 0.457492 0.889214i \(-0.348748\pi\)
0.457492 + 0.889214i \(0.348748\pi\)
\(830\) 214.379 0.00896531
\(831\) 15733.8 0.656798
\(832\) 0 0
\(833\) −6925.57 −0.288063
\(834\) 2068.32 0.0858755
\(835\) 1121.66 0.0464870
\(836\) 3120.64 0.129102
\(837\) −2901.60 −0.119825
\(838\) −8786.75 −0.362211
\(839\) 3940.06 0.162129 0.0810643 0.996709i \(-0.474168\pi\)
0.0810643 + 0.996709i \(0.474168\pi\)
\(840\) −285.420 −0.0117237
\(841\) −23998.6 −0.983991
\(842\) −4089.26 −0.167370
\(843\) −716.707 −0.0292820
\(844\) 103.218 0.00420963
\(845\) 0 0
\(846\) 2726.01 0.110783
\(847\) −2811.29 −0.114046
\(848\) 24522.9 0.993066
\(849\) 12521.5 0.506168
\(850\) −2811.51 −0.113452
\(851\) 23567.6 0.949338
\(852\) 11221.1 0.451206
\(853\) −8929.29 −0.358421 −0.179211 0.983811i \(-0.557354\pi\)
−0.179211 + 0.983811i \(0.557354\pi\)
\(854\) 10341.4 0.414374
\(855\) −560.486 −0.0224190
\(856\) −3128.31 −0.124910
\(857\) 6873.94 0.273990 0.136995 0.990572i \(-0.456256\pi\)
0.136995 + 0.990572i \(0.456256\pi\)
\(858\) 0 0
\(859\) 11987.7 0.476153 0.238077 0.971246i \(-0.423483\pi\)
0.238077 + 0.971246i \(0.423483\pi\)
\(860\) 959.144 0.0380308
\(861\) 3594.63 0.142282
\(862\) 4743.08 0.187413
\(863\) −440.273 −0.0173662 −0.00868312 0.999962i \(-0.502764\pi\)
−0.00868312 + 0.999962i \(0.502764\pi\)
\(864\) −11055.2 −0.435307
\(865\) 37.8506 0.00148782
\(866\) 5521.11 0.216645
\(867\) 7029.81 0.275369
\(868\) −5312.41 −0.207736
\(869\) 510.919 0.0199445
\(870\) 15.5716 0.000606813 0
\(871\) 0 0
\(872\) 13386.8 0.519878
\(873\) −403.716 −0.0156515
\(874\) 2920.14 0.113015
\(875\) −3724.94 −0.143916
\(876\) −2331.62 −0.0899293
\(877\) 46606.1 1.79450 0.897251 0.441521i \(-0.145561\pi\)
0.897251 + 0.441521i \(0.145561\pi\)
\(878\) −8872.37 −0.341034
\(879\) 17659.7 0.677640
\(880\) −383.673 −0.0146973
\(881\) 16735.5 0.639991 0.319996 0.947419i \(-0.396319\pi\)
0.319996 + 0.947419i \(0.396319\pi\)
\(882\) 2945.84 0.112462
\(883\) 31789.3 1.21155 0.605773 0.795637i \(-0.292864\pi\)
0.605773 + 0.795637i \(0.292864\pi\)
\(884\) 0 0
\(885\) −332.221 −0.0126186
\(886\) 776.231 0.0294334
\(887\) −757.412 −0.0286713 −0.0143356 0.999897i \(-0.504563\pi\)
−0.0143356 + 0.999897i \(0.504563\pi\)
\(888\) −3700.28 −0.139835
\(889\) 37040.1 1.39739
\(890\) −162.629 −0.00612510
\(891\) 4905.58 0.184448
\(892\) −37523.6 −1.40850
\(893\) −6808.39 −0.255133
\(894\) 1978.62 0.0740213
\(895\) −280.426 −0.0104733
\(896\) −26712.8 −0.995994
\(897\) 0 0
\(898\) 5743.97 0.213451
\(899\) 595.364 0.0220873
\(900\) −22067.4 −0.817311
\(901\) −15892.4 −0.587629
\(902\) −570.509 −0.0210597
\(903\) 8745.34 0.322289
\(904\) 12173.7 0.447888
\(905\) −291.225 −0.0106969
\(906\) 3312.11 0.121454
\(907\) −8676.53 −0.317640 −0.158820 0.987308i \(-0.550769\pi\)
−0.158820 + 0.987308i \(0.550769\pi\)
\(908\) 7425.49 0.271391
\(909\) 7250.10 0.264544
\(910\) 0 0
\(911\) 34427.4 1.25206 0.626032 0.779797i \(-0.284678\pi\)
0.626032 + 0.779797i \(0.284678\pi\)
\(912\) 3883.22 0.140994
\(913\) 5724.56 0.207509
\(914\) 3344.54 0.121037
\(915\) 852.904 0.0308155
\(916\) −35014.5 −1.26300
\(917\) 61054.2 2.19868
\(918\) 2173.21 0.0781337
\(919\) −28622.6 −1.02739 −0.513696 0.857972i \(-0.671724\pi\)
−0.513696 + 0.857972i \(0.671724\pi\)
\(920\) −782.187 −0.0280304
\(921\) −7038.22 −0.251810
\(922\) −197.024 −0.00703757
\(923\) 0 0
\(924\) −3710.24 −0.132097
\(925\) −24105.8 −0.856860
\(926\) −8196.48 −0.290878
\(927\) 27451.3 0.972621
\(928\) 2268.36 0.0802398
\(929\) −24018.3 −0.848240 −0.424120 0.905606i \(-0.639416\pi\)
−0.424120 + 0.905606i \(0.639416\pi\)
\(930\) 23.7440 0.000837200 0
\(931\) −7357.42 −0.259001
\(932\) 24960.1 0.877249
\(933\) 16434.7 0.576684
\(934\) −2190.74 −0.0767485
\(935\) 248.645 0.00869686
\(936\) 0 0
\(937\) 38501.7 1.34236 0.671182 0.741292i \(-0.265787\pi\)
0.671182 + 0.741292i \(0.265787\pi\)
\(938\) −5423.66 −0.188794
\(939\) 15481.6 0.538043
\(940\) 887.791 0.0308048
\(941\) 54231.7 1.87875 0.939375 0.342890i \(-0.111406\pi\)
0.939375 + 0.342890i \(0.111406\pi\)
\(942\) −934.547 −0.0323240
\(943\) 9851.01 0.340184
\(944\) −14679.9 −0.506132
\(945\) 1437.25 0.0494749
\(946\) −1387.99 −0.0477033
\(947\) 42375.7 1.45409 0.727046 0.686589i \(-0.240893\pi\)
0.727046 + 0.686589i \(0.240893\pi\)
\(948\) 674.293 0.0231013
\(949\) 0 0
\(950\) −2986.83 −0.102006
\(951\) −11693.2 −0.398716
\(952\) 8173.30 0.278254
\(953\) −41712.9 −1.41785 −0.708927 0.705282i \(-0.750820\pi\)
−0.708927 + 0.705282i \(0.750820\pi\)
\(954\) 6759.95 0.229414
\(955\) 1244.56 0.0421706
\(956\) 11517.3 0.389641
\(957\) 415.809 0.0140451
\(958\) −6998.21 −0.236014
\(959\) 70463.4 2.37266
\(960\) −443.334 −0.0149047
\(961\) −28883.2 −0.969527
\(962\) 0 0
\(963\) 7303.81 0.244405
\(964\) 16845.5 0.562819
\(965\) −1042.52 −0.0347770
\(966\) −3471.86 −0.115637
\(967\) 865.994 0.0287988 0.0143994 0.999896i \(-0.495416\pi\)
0.0143994 + 0.999896i \(0.495416\pi\)
\(968\) 1209.63 0.0401642
\(969\) −2516.58 −0.0834305
\(970\) 7.12527 0.000235854 0
\(971\) −55107.5 −1.82130 −0.910651 0.413175i \(-0.864420\pi\)
−0.910651 + 0.413175i \(0.864420\pi\)
\(972\) 26206.1 0.864776
\(973\) −39170.8 −1.29061
\(974\) −7060.71 −0.232279
\(975\) 0 0
\(976\) 37687.3 1.23601
\(977\) −22585.3 −0.739579 −0.369789 0.929116i \(-0.620570\pi\)
−0.369789 + 0.929116i \(0.620570\pi\)
\(978\) −694.089 −0.0226938
\(979\) −4342.68 −0.141770
\(980\) 959.383 0.0312718
\(981\) −31254.8 −1.01722
\(982\) −7095.60 −0.230580
\(983\) 10571.6 0.343013 0.171506 0.985183i \(-0.445137\pi\)
0.171506 + 0.985183i \(0.445137\pi\)
\(984\) −1546.68 −0.0501081
\(985\) −1761.45 −0.0569792
\(986\) −445.910 −0.0144023
\(987\) 8094.76 0.261053
\(988\) 0 0
\(989\) 23966.4 0.770565
\(990\) −105.763 −0.00339532
\(991\) −13212.6 −0.423523 −0.211762 0.977321i \(-0.567920\pi\)
−0.211762 + 0.977321i \(0.567920\pi\)
\(992\) 3458.85 0.110704
\(993\) 383.545 0.0122572
\(994\) 11516.5 0.367487
\(995\) 2737.18 0.0872104
\(996\) 7555.08 0.240353
\(997\) −33543.8 −1.06554 −0.532770 0.846260i \(-0.678849\pi\)
−0.532770 + 0.846260i \(0.678849\pi\)
\(998\) 1992.63 0.0632021
\(999\) 18633.1 0.590114
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.1.18 39
13.12 even 2 1859.4.a.o.1.22 yes 39
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.4.a.n.1.18 39 1.1 even 1 trivial
1859.4.a.o.1.22 yes 39 13.12 even 2