Properties

Label 1150.4.a.q.1.5
Level $1150$
Weight $4$
Character 1150.1
Self dual yes
Analytic conductor $67.852$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1150,4,Mod(1,1150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1150, 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("1150.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1150.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: \(67.8521965066\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 107x^{3} - 3x^{2} + 2151x - 2916 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(9.27140\) of defining polynomial
Character \(\chi\) \(=\) 1150.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +8.27140 q^{3} +4.00000 q^{4} -16.5428 q^{6} -22.8621 q^{7} -8.00000 q^{8} +41.4161 q^{9} -0.987996 q^{11} +33.0856 q^{12} +4.22276 q^{13} +45.7241 q^{14} +16.0000 q^{16} -73.8741 q^{17} -82.8322 q^{18} +71.1586 q^{19} -189.101 q^{21} +1.97599 q^{22} -23.0000 q^{23} -66.1712 q^{24} -8.44552 q^{26} +119.241 q^{27} -91.4483 q^{28} +27.8984 q^{29} -136.861 q^{31} -32.0000 q^{32} -8.17211 q^{33} +147.748 q^{34} +165.664 q^{36} +201.718 q^{37} -142.317 q^{38} +34.9281 q^{39} -204.140 q^{41} +378.203 q^{42} +54.1024 q^{43} -3.95198 q^{44} +46.0000 q^{46} +41.4490 q^{47} +132.342 q^{48} +179.674 q^{49} -611.042 q^{51} +16.8910 q^{52} -428.612 q^{53} -238.483 q^{54} +182.897 q^{56} +588.581 q^{57} -55.7969 q^{58} -164.858 q^{59} +188.248 q^{61} +273.722 q^{62} -946.857 q^{63} +64.0000 q^{64} +16.3442 q^{66} -932.167 q^{67} -295.496 q^{68} -190.242 q^{69} -263.336 q^{71} -331.329 q^{72} -900.401 q^{73} -403.437 q^{74} +284.634 q^{76} +22.5876 q^{77} -69.8563 q^{78} -956.182 q^{79} -131.942 q^{81} +408.279 q^{82} -194.877 q^{83} -756.405 q^{84} -108.205 q^{86} +230.759 q^{87} +7.90397 q^{88} -213.751 q^{89} -96.5410 q^{91} -92.0000 q^{92} -1132.03 q^{93} -82.8981 q^{94} -264.685 q^{96} -628.762 q^{97} -359.348 q^{98} -40.9189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} - 5 q^{3} + 20 q^{4} + 10 q^{6} + 3 q^{7} - 40 q^{8} + 84 q^{9} - 26 q^{11} - 20 q^{12} + 61 q^{13} - 6 q^{14} + 80 q^{16} - 231 q^{17} - 168 q^{18} + 74 q^{19} - 88 q^{21} + 52 q^{22} - 115 q^{23}+ \cdots + 2397 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) 8.27140 1.59183 0.795916 0.605407i \(-0.206990\pi\)
0.795916 + 0.605407i \(0.206990\pi\)
\(4\) 4.00000 0.500000
\(5\) 0 0
\(6\) −16.5428 −1.12560
\(7\) −22.8621 −1.23444 −0.617218 0.786792i \(-0.711740\pi\)
−0.617218 + 0.786792i \(0.711740\pi\)
\(8\) −8.00000 −0.353553
\(9\) 41.4161 1.53393
\(10\) 0 0
\(11\) −0.987996 −0.0270811 −0.0135405 0.999908i \(-0.504310\pi\)
−0.0135405 + 0.999908i \(0.504310\pi\)
\(12\) 33.0856 0.795916
\(13\) 4.22276 0.0900910 0.0450455 0.998985i \(-0.485657\pi\)
0.0450455 + 0.998985i \(0.485657\pi\)
\(14\) 45.7241 0.872878
\(15\) 0 0
\(16\) 16.0000 0.250000
\(17\) −73.8741 −1.05395 −0.526973 0.849882i \(-0.676673\pi\)
−0.526973 + 0.849882i \(0.676673\pi\)
\(18\) −82.8322 −1.08465
\(19\) 71.1586 0.859205 0.429602 0.903018i \(-0.358654\pi\)
0.429602 + 0.903018i \(0.358654\pi\)
\(20\) 0 0
\(21\) −189.101 −1.96501
\(22\) 1.97599 0.0191492
\(23\) −23.0000 −0.208514
\(24\) −66.1712 −0.562798
\(25\) 0 0
\(26\) −8.44552 −0.0637039
\(27\) 119.241 0.849926
\(28\) −91.4483 −0.617218
\(29\) 27.8984 0.178642 0.0893209 0.996003i \(-0.471530\pi\)
0.0893209 + 0.996003i \(0.471530\pi\)
\(30\) 0 0
\(31\) −136.861 −0.792935 −0.396468 0.918049i \(-0.629764\pi\)
−0.396468 + 0.918049i \(0.629764\pi\)
\(32\) −32.0000 −0.176777
\(33\) −8.17211 −0.0431085
\(34\) 147.748 0.745253
\(35\) 0 0
\(36\) 165.664 0.766965
\(37\) 201.718 0.896278 0.448139 0.893964i \(-0.352087\pi\)
0.448139 + 0.893964i \(0.352087\pi\)
\(38\) −142.317 −0.607550
\(39\) 34.9281 0.143410
\(40\) 0 0
\(41\) −204.140 −0.777592 −0.388796 0.921324i \(-0.627109\pi\)
−0.388796 + 0.921324i \(0.627109\pi\)
\(42\) 378.203 1.38947
\(43\) 54.1024 0.191873 0.0959365 0.995387i \(-0.469415\pi\)
0.0959365 + 0.995387i \(0.469415\pi\)
\(44\) −3.95198 −0.0135405
\(45\) 0 0
\(46\) 46.0000 0.147442
\(47\) 41.4490 0.128638 0.0643188 0.997929i \(-0.479513\pi\)
0.0643188 + 0.997929i \(0.479513\pi\)
\(48\) 132.342 0.397958
\(49\) 179.674 0.523831
\(50\) 0 0
\(51\) −611.042 −1.67771
\(52\) 16.8910 0.0450455
\(53\) −428.612 −1.11084 −0.555418 0.831571i \(-0.687442\pi\)
−0.555418 + 0.831571i \(0.687442\pi\)
\(54\) −238.483 −0.600988
\(55\) 0 0
\(56\) 182.897 0.436439
\(57\) 588.581 1.36771
\(58\) −55.7969 −0.126319
\(59\) −164.858 −0.363774 −0.181887 0.983319i \(-0.558221\pi\)
−0.181887 + 0.983319i \(0.558221\pi\)
\(60\) 0 0
\(61\) 188.248 0.395125 0.197563 0.980290i \(-0.436697\pi\)
0.197563 + 0.980290i \(0.436697\pi\)
\(62\) 273.722 0.560690
\(63\) −946.857 −1.89354
\(64\) 64.0000 0.125000
\(65\) 0 0
\(66\) 16.3442 0.0304823
\(67\) −932.167 −1.69974 −0.849868 0.526995i \(-0.823318\pi\)
−0.849868 + 0.526995i \(0.823318\pi\)
\(68\) −295.496 −0.526973
\(69\) −190.242 −0.331920
\(70\) 0 0
\(71\) −263.336 −0.440173 −0.220086 0.975480i \(-0.570634\pi\)
−0.220086 + 0.975480i \(0.570634\pi\)
\(72\) −331.329 −0.542326
\(73\) −900.401 −1.44362 −0.721808 0.692094i \(-0.756689\pi\)
−0.721808 + 0.692094i \(0.756689\pi\)
\(74\) −403.437 −0.633764
\(75\) 0 0
\(76\) 284.634 0.429602
\(77\) 22.5876 0.0334299
\(78\) −69.8563 −0.101406
\(79\) −956.182 −1.36176 −0.680879 0.732396i \(-0.738402\pi\)
−0.680879 + 0.732396i \(0.738402\pi\)
\(80\) 0 0
\(81\) −131.942 −0.180990
\(82\) 408.279 0.549841
\(83\) −194.877 −0.257717 −0.128858 0.991663i \(-0.541131\pi\)
−0.128858 + 0.991663i \(0.541131\pi\)
\(84\) −756.405 −0.982507
\(85\) 0 0
\(86\) −108.205 −0.135675
\(87\) 230.759 0.284368
\(88\) 7.90397 0.00957461
\(89\) −213.751 −0.254580 −0.127290 0.991866i \(-0.540628\pi\)
−0.127290 + 0.991866i \(0.540628\pi\)
\(90\) 0 0
\(91\) −96.5410 −0.111211
\(92\) −92.0000 −0.104257
\(93\) −1132.03 −1.26222
\(94\) −82.8981 −0.0909605
\(95\) 0 0
\(96\) −264.685 −0.281399
\(97\) −628.762 −0.658156 −0.329078 0.944303i \(-0.606738\pi\)
−0.329078 + 0.944303i \(0.606738\pi\)
\(98\) −359.348 −0.370404
\(99\) −40.9189 −0.0415405
\(100\) 0 0
\(101\) −51.1371 −0.0503796 −0.0251898 0.999683i \(-0.508019\pi\)
−0.0251898 + 0.999683i \(0.508019\pi\)
\(102\) 1222.08 1.18632
\(103\) −363.089 −0.347342 −0.173671 0.984804i \(-0.555563\pi\)
−0.173671 + 0.984804i \(0.555563\pi\)
\(104\) −33.7821 −0.0318520
\(105\) 0 0
\(106\) 857.223 0.785480
\(107\) −1514.53 −1.36837 −0.684184 0.729310i \(-0.739841\pi\)
−0.684184 + 0.729310i \(0.739841\pi\)
\(108\) 476.965 0.424963
\(109\) 811.356 0.712971 0.356485 0.934301i \(-0.383975\pi\)
0.356485 + 0.934301i \(0.383975\pi\)
\(110\) 0 0
\(111\) 1668.49 1.42672
\(112\) −365.793 −0.308609
\(113\) −12.4496 −0.0103642 −0.00518211 0.999987i \(-0.501650\pi\)
−0.00518211 + 0.999987i \(0.501650\pi\)
\(114\) −1177.16 −0.967117
\(115\) 0 0
\(116\) 111.594 0.0893209
\(117\) 174.890 0.138193
\(118\) 329.716 0.257227
\(119\) 1688.91 1.30103
\(120\) 0 0
\(121\) −1330.02 −0.999267
\(122\) −376.495 −0.279396
\(123\) −1688.52 −1.23780
\(124\) −547.445 −0.396468
\(125\) 0 0
\(126\) 1893.71 1.33893
\(127\) 632.599 0.442000 0.221000 0.975274i \(-0.429068\pi\)
0.221000 + 0.975274i \(0.429068\pi\)
\(128\) −128.000 −0.0883883
\(129\) 447.503 0.305430
\(130\) 0 0
\(131\) 2243.16 1.49607 0.748036 0.663658i \(-0.230997\pi\)
0.748036 + 0.663658i \(0.230997\pi\)
\(132\) −32.6884 −0.0215543
\(133\) −1626.83 −1.06063
\(134\) 1864.33 1.20190
\(135\) 0 0
\(136\) 590.993 0.372626
\(137\) −1252.77 −0.781252 −0.390626 0.920550i \(-0.627741\pi\)
−0.390626 + 0.920550i \(0.627741\pi\)
\(138\) 380.484 0.234703
\(139\) 2815.19 1.71785 0.858925 0.512101i \(-0.171133\pi\)
0.858925 + 0.512101i \(0.171133\pi\)
\(140\) 0 0
\(141\) 342.842 0.204769
\(142\) 526.673 0.311249
\(143\) −4.17207 −0.00243976
\(144\) 662.657 0.383482
\(145\) 0 0
\(146\) 1800.80 1.02079
\(147\) 1486.16 0.833851
\(148\) 806.873 0.448139
\(149\) 2406.46 1.32312 0.661560 0.749892i \(-0.269895\pi\)
0.661560 + 0.749892i \(0.269895\pi\)
\(150\) 0 0
\(151\) 2185.59 1.17788 0.588942 0.808175i \(-0.299545\pi\)
0.588942 + 0.808175i \(0.299545\pi\)
\(152\) −569.268 −0.303775
\(153\) −3059.58 −1.61668
\(154\) −45.1753 −0.0236385
\(155\) 0 0
\(156\) 139.713 0.0717048
\(157\) −1074.18 −0.546044 −0.273022 0.962008i \(-0.588023\pi\)
−0.273022 + 0.962008i \(0.588023\pi\)
\(158\) 1912.36 0.962908
\(159\) −3545.22 −1.76827
\(160\) 0 0
\(161\) 525.828 0.257398
\(162\) 263.884 0.127979
\(163\) −2706.30 −1.30045 −0.650226 0.759741i \(-0.725326\pi\)
−0.650226 + 0.759741i \(0.725326\pi\)
\(164\) −816.559 −0.388796
\(165\) 0 0
\(166\) 389.754 0.182233
\(167\) −455.547 −0.211086 −0.105543 0.994415i \(-0.533658\pi\)
−0.105543 + 0.994415i \(0.533658\pi\)
\(168\) 1512.81 0.694737
\(169\) −2179.17 −0.991884
\(170\) 0 0
\(171\) 2947.11 1.31796
\(172\) 216.410 0.0959365
\(173\) 1342.64 0.590051 0.295026 0.955489i \(-0.404672\pi\)
0.295026 + 0.955489i \(0.404672\pi\)
\(174\) −461.518 −0.201078
\(175\) 0 0
\(176\) −15.8079 −0.00677027
\(177\) −1363.61 −0.579068
\(178\) 427.503 0.180015
\(179\) −4655.64 −1.94401 −0.972007 0.234951i \(-0.924507\pi\)
−0.972007 + 0.234951i \(0.924507\pi\)
\(180\) 0 0
\(181\) −176.320 −0.0724074 −0.0362037 0.999344i \(-0.511527\pi\)
−0.0362037 + 0.999344i \(0.511527\pi\)
\(182\) 193.082 0.0786384
\(183\) 1557.07 0.628973
\(184\) 184.000 0.0737210
\(185\) 0 0
\(186\) 2264.07 0.892524
\(187\) 72.9873 0.0285420
\(188\) 165.796 0.0643188
\(189\) −2726.10 −1.04918
\(190\) 0 0
\(191\) 1672.03 0.633422 0.316711 0.948522i \(-0.397421\pi\)
0.316711 + 0.948522i \(0.397421\pi\)
\(192\) 529.370 0.198979
\(193\) 2954.45 1.10189 0.550947 0.834540i \(-0.314267\pi\)
0.550947 + 0.834540i \(0.314267\pi\)
\(194\) 1257.52 0.465386
\(195\) 0 0
\(196\) 718.696 0.261915
\(197\) −1817.35 −0.657264 −0.328632 0.944458i \(-0.606588\pi\)
−0.328632 + 0.944458i \(0.606588\pi\)
\(198\) 81.8379 0.0293735
\(199\) 4780.99 1.70309 0.851546 0.524280i \(-0.175666\pi\)
0.851546 + 0.524280i \(0.175666\pi\)
\(200\) 0 0
\(201\) −7710.33 −2.70569
\(202\) 102.274 0.0356237
\(203\) −637.816 −0.220522
\(204\) −2444.17 −0.838853
\(205\) 0 0
\(206\) 726.179 0.245608
\(207\) −952.570 −0.319846
\(208\) 67.5641 0.0225227
\(209\) −70.3044 −0.0232682
\(210\) 0 0
\(211\) 3201.72 1.04462 0.522312 0.852755i \(-0.325070\pi\)
0.522312 + 0.852755i \(0.325070\pi\)
\(212\) −1714.45 −0.555418
\(213\) −2178.16 −0.700681
\(214\) 3029.06 0.967582
\(215\) 0 0
\(216\) −953.930 −0.300494
\(217\) 3128.93 0.978828
\(218\) −1622.71 −0.504147
\(219\) −7447.58 −2.29799
\(220\) 0 0
\(221\) −311.952 −0.0949511
\(222\) −3336.99 −1.00885
\(223\) 1897.23 0.569721 0.284860 0.958569i \(-0.408053\pi\)
0.284860 + 0.958569i \(0.408053\pi\)
\(224\) 731.586 0.218219
\(225\) 0 0
\(226\) 24.8991 0.00732861
\(227\) −4468.42 −1.30652 −0.653258 0.757135i \(-0.726598\pi\)
−0.653258 + 0.757135i \(0.726598\pi\)
\(228\) 2354.32 0.683855
\(229\) −5345.88 −1.54264 −0.771322 0.636445i \(-0.780404\pi\)
−0.771322 + 0.636445i \(0.780404\pi\)
\(230\) 0 0
\(231\) 186.831 0.0532147
\(232\) −223.187 −0.0631594
\(233\) 4480.46 1.25976 0.629882 0.776691i \(-0.283103\pi\)
0.629882 + 0.776691i \(0.283103\pi\)
\(234\) −349.780 −0.0977173
\(235\) 0 0
\(236\) −659.432 −0.181887
\(237\) −7908.97 −2.16769
\(238\) −3377.83 −0.919967
\(239\) 779.836 0.211060 0.105530 0.994416i \(-0.466346\pi\)
0.105530 + 0.994416i \(0.466346\pi\)
\(240\) 0 0
\(241\) −4204.89 −1.12390 −0.561952 0.827170i \(-0.689950\pi\)
−0.561952 + 0.827170i \(0.689950\pi\)
\(242\) 2660.05 0.706588
\(243\) −4310.86 −1.13803
\(244\) 752.991 0.197563
\(245\) 0 0
\(246\) 3377.04 0.875254
\(247\) 300.485 0.0774066
\(248\) 1094.89 0.280345
\(249\) −1611.90 −0.410242
\(250\) 0 0
\(251\) 2761.48 0.694433 0.347217 0.937785i \(-0.387127\pi\)
0.347217 + 0.937785i \(0.387127\pi\)
\(252\) −3787.43 −0.946768
\(253\) 22.7239 0.00564680
\(254\) −1265.20 −0.312542
\(255\) 0 0
\(256\) 256.000 0.0625000
\(257\) 586.469 0.142346 0.0711730 0.997464i \(-0.477326\pi\)
0.0711730 + 0.997464i \(0.477326\pi\)
\(258\) −895.006 −0.215971
\(259\) −4611.70 −1.10640
\(260\) 0 0
\(261\) 1155.44 0.274024
\(262\) −4486.31 −1.05788
\(263\) −5970.38 −1.39981 −0.699903 0.714238i \(-0.746774\pi\)
−0.699903 + 0.714238i \(0.746774\pi\)
\(264\) 65.3769 0.0152412
\(265\) 0 0
\(266\) 3253.66 0.749981
\(267\) −1768.02 −0.405248
\(268\) −3728.67 −0.849868
\(269\) 3914.34 0.887217 0.443608 0.896221i \(-0.353698\pi\)
0.443608 + 0.896221i \(0.353698\pi\)
\(270\) 0 0
\(271\) 78.0865 0.0175034 0.00875170 0.999962i \(-0.497214\pi\)
0.00875170 + 0.999962i \(0.497214\pi\)
\(272\) −1181.99 −0.263487
\(273\) −798.529 −0.177030
\(274\) 2505.54 0.552428
\(275\) 0 0
\(276\) −760.969 −0.165960
\(277\) 76.0512 0.0164963 0.00824815 0.999966i \(-0.497375\pi\)
0.00824815 + 0.999966i \(0.497375\pi\)
\(278\) −5630.38 −1.21470
\(279\) −5668.26 −1.21631
\(280\) 0 0
\(281\) −3852.67 −0.817905 −0.408952 0.912556i \(-0.634106\pi\)
−0.408952 + 0.912556i \(0.634106\pi\)
\(282\) −685.683 −0.144794
\(283\) 1550.13 0.325603 0.162802 0.986659i \(-0.447947\pi\)
0.162802 + 0.986659i \(0.447947\pi\)
\(284\) −1053.35 −0.220086
\(285\) 0 0
\(286\) 8.34414 0.00172517
\(287\) 4667.06 0.959887
\(288\) −1325.31 −0.271163
\(289\) 544.378 0.110804
\(290\) 0 0
\(291\) −5200.74 −1.04767
\(292\) −3601.60 −0.721808
\(293\) −4236.01 −0.844608 −0.422304 0.906454i \(-0.638779\pi\)
−0.422304 + 0.906454i \(0.638779\pi\)
\(294\) −2972.31 −0.589622
\(295\) 0 0
\(296\) −1613.75 −0.316882
\(297\) −117.810 −0.0230169
\(298\) −4812.92 −0.935587
\(299\) −97.1234 −0.0187853
\(300\) 0 0
\(301\) −1236.89 −0.236855
\(302\) −4371.17 −0.832890
\(303\) −422.976 −0.0801958
\(304\) 1138.54 0.214801
\(305\) 0 0
\(306\) 6119.15 1.14317
\(307\) 10078.1 1.87357 0.936786 0.349903i \(-0.113785\pi\)
0.936786 + 0.349903i \(0.113785\pi\)
\(308\) 90.3505 0.0167149
\(309\) −3003.26 −0.552911
\(310\) 0 0
\(311\) −2652.97 −0.483717 −0.241859 0.970312i \(-0.577757\pi\)
−0.241859 + 0.970312i \(0.577757\pi\)
\(312\) −279.425 −0.0507030
\(313\) −6710.68 −1.21185 −0.605926 0.795521i \(-0.707197\pi\)
−0.605926 + 0.795521i \(0.707197\pi\)
\(314\) 2148.36 0.386111
\(315\) 0 0
\(316\) −3824.73 −0.680879
\(317\) 3677.89 0.651642 0.325821 0.945431i \(-0.394359\pi\)
0.325821 + 0.945431i \(0.394359\pi\)
\(318\) 7090.44 1.25035
\(319\) −27.5635 −0.00483781
\(320\) 0 0
\(321\) −12527.3 −2.17821
\(322\) −1051.66 −0.182008
\(323\) −5256.77 −0.905556
\(324\) −527.768 −0.0904952
\(325\) 0 0
\(326\) 5412.60 0.919558
\(327\) 6711.05 1.13493
\(328\) 1633.12 0.274920
\(329\) −947.611 −0.158795
\(330\) 0 0
\(331\) −9806.39 −1.62842 −0.814212 0.580568i \(-0.802831\pi\)
−0.814212 + 0.580568i \(0.802831\pi\)
\(332\) −779.507 −0.128858
\(333\) 8354.38 1.37483
\(334\) 911.094 0.149260
\(335\) 0 0
\(336\) −3025.62 −0.491253
\(337\) 7143.41 1.15468 0.577339 0.816505i \(-0.304091\pi\)
0.577339 + 0.816505i \(0.304091\pi\)
\(338\) 4358.34 0.701368
\(339\) −102.975 −0.0164981
\(340\) 0 0
\(341\) 135.218 0.0214736
\(342\) −5894.22 −0.931938
\(343\) 3733.97 0.587800
\(344\) −432.819 −0.0678374
\(345\) 0 0
\(346\) −2685.28 −0.417229
\(347\) 5160.20 0.798312 0.399156 0.916883i \(-0.369303\pi\)
0.399156 + 0.916883i \(0.369303\pi\)
\(348\) 923.037 0.142184
\(349\) 8712.04 1.33623 0.668115 0.744058i \(-0.267101\pi\)
0.668115 + 0.744058i \(0.267101\pi\)
\(350\) 0 0
\(351\) 503.527 0.0765706
\(352\) 31.6159 0.00478731
\(353\) 7117.30 1.07313 0.536566 0.843858i \(-0.319721\pi\)
0.536566 + 0.843858i \(0.319721\pi\)
\(354\) 2727.21 0.409463
\(355\) 0 0
\(356\) −855.005 −0.127290
\(357\) 13969.7 2.07102
\(358\) 9311.27 1.37463
\(359\) 3548.73 0.521712 0.260856 0.965378i \(-0.415995\pi\)
0.260856 + 0.965378i \(0.415995\pi\)
\(360\) 0 0
\(361\) −1795.46 −0.261767
\(362\) 352.639 0.0511998
\(363\) −11001.2 −1.59066
\(364\) −386.164 −0.0556057
\(365\) 0 0
\(366\) −3114.15 −0.444751
\(367\) −80.0110 −0.0113802 −0.00569011 0.999984i \(-0.501811\pi\)
−0.00569011 + 0.999984i \(0.501811\pi\)
\(368\) −368.000 −0.0521286
\(369\) −8454.67 −1.19277
\(370\) 0 0
\(371\) 9798.95 1.37126
\(372\) −4528.14 −0.631110
\(373\) −3211.09 −0.445747 −0.222874 0.974847i \(-0.571544\pi\)
−0.222874 + 0.974847i \(0.571544\pi\)
\(374\) −145.975 −0.0201823
\(375\) 0 0
\(376\) −331.592 −0.0454802
\(377\) 117.808 0.0160940
\(378\) 5452.20 0.741881
\(379\) −8177.57 −1.10832 −0.554160 0.832410i \(-0.686961\pi\)
−0.554160 + 0.832410i \(0.686961\pi\)
\(380\) 0 0
\(381\) 5232.48 0.703591
\(382\) −3344.05 −0.447897
\(383\) −12926.5 −1.72458 −0.862291 0.506413i \(-0.830971\pi\)
−0.862291 + 0.506413i \(0.830971\pi\)
\(384\) −1058.74 −0.140699
\(385\) 0 0
\(386\) −5908.89 −0.779157
\(387\) 2240.71 0.294320
\(388\) −2515.05 −0.329078
\(389\) 4734.66 0.617113 0.308556 0.951206i \(-0.400154\pi\)
0.308556 + 0.951206i \(0.400154\pi\)
\(390\) 0 0
\(391\) 1699.10 0.219763
\(392\) −1437.39 −0.185202
\(393\) 18554.0 2.38150
\(394\) 3634.71 0.464756
\(395\) 0 0
\(396\) −163.676 −0.0207702
\(397\) 9938.80 1.25646 0.628229 0.778028i \(-0.283780\pi\)
0.628229 + 0.778028i \(0.283780\pi\)
\(398\) −9561.98 −1.20427
\(399\) −13456.2 −1.68835
\(400\) 0 0
\(401\) −335.296 −0.0417553 −0.0208777 0.999782i \(-0.506646\pi\)
−0.0208777 + 0.999782i \(0.506646\pi\)
\(402\) 15420.7 1.91322
\(403\) −577.932 −0.0714363
\(404\) −204.549 −0.0251898
\(405\) 0 0
\(406\) 1275.63 0.155932
\(407\) −199.297 −0.0242722
\(408\) 4888.34 0.593159
\(409\) 6560.85 0.793186 0.396593 0.917995i \(-0.370192\pi\)
0.396593 + 0.917995i \(0.370192\pi\)
\(410\) 0 0
\(411\) −10362.2 −1.24362
\(412\) −1452.36 −0.173671
\(413\) 3769.00 0.449056
\(414\) 1905.14 0.226166
\(415\) 0 0
\(416\) −135.128 −0.0159260
\(417\) 23285.6 2.73453
\(418\) 140.609 0.0164531
\(419\) 7116.69 0.829768 0.414884 0.909874i \(-0.363822\pi\)
0.414884 + 0.909874i \(0.363822\pi\)
\(420\) 0 0
\(421\) 9799.43 1.13443 0.567215 0.823570i \(-0.308021\pi\)
0.567215 + 0.823570i \(0.308021\pi\)
\(422\) −6403.44 −0.738660
\(423\) 1716.66 0.197321
\(424\) 3428.89 0.392740
\(425\) 0 0
\(426\) 4356.32 0.495456
\(427\) −4303.73 −0.487757
\(428\) −6058.13 −0.684184
\(429\) −34.5089 −0.00388369
\(430\) 0 0
\(431\) −10523.3 −1.17608 −0.588039 0.808832i \(-0.700100\pi\)
−0.588039 + 0.808832i \(0.700100\pi\)
\(432\) 1907.86 0.212481
\(433\) 4770.97 0.529511 0.264755 0.964316i \(-0.414709\pi\)
0.264755 + 0.964316i \(0.414709\pi\)
\(434\) −6257.86 −0.692136
\(435\) 0 0
\(436\) 3245.42 0.356485
\(437\) −1636.65 −0.179157
\(438\) 14895.2 1.62493
\(439\) 10231.2 1.11232 0.556159 0.831076i \(-0.312274\pi\)
0.556159 + 0.831076i \(0.312274\pi\)
\(440\) 0 0
\(441\) 7441.40 0.803520
\(442\) 623.905 0.0671405
\(443\) −10508.1 −1.12699 −0.563493 0.826121i \(-0.690543\pi\)
−0.563493 + 0.826121i \(0.690543\pi\)
\(444\) 6673.97 0.713362
\(445\) 0 0
\(446\) −3794.46 −0.402854
\(447\) 19904.8 2.10618
\(448\) −1463.17 −0.154304
\(449\) 7230.71 0.759996 0.379998 0.924987i \(-0.375925\pi\)
0.379998 + 0.924987i \(0.375925\pi\)
\(450\) 0 0
\(451\) 201.689 0.0210580
\(452\) −49.7983 −0.00518211
\(453\) 18077.9 1.87499
\(454\) 8936.83 0.923847
\(455\) 0 0
\(456\) −4708.65 −0.483558
\(457\) −2418.74 −0.247580 −0.123790 0.992308i \(-0.539505\pi\)
−0.123790 + 0.992308i \(0.539505\pi\)
\(458\) 10691.8 1.09081
\(459\) −8808.84 −0.895776
\(460\) 0 0
\(461\) −11342.8 −1.14596 −0.572979 0.819570i \(-0.694212\pi\)
−0.572979 + 0.819570i \(0.694212\pi\)
\(462\) −373.663 −0.0376285
\(463\) 11785.9 1.18302 0.591508 0.806299i \(-0.298533\pi\)
0.591508 + 0.806299i \(0.298533\pi\)
\(464\) 446.375 0.0446604
\(465\) 0 0
\(466\) −8960.93 −0.890787
\(467\) −16294.5 −1.61461 −0.807303 0.590137i \(-0.799074\pi\)
−0.807303 + 0.590137i \(0.799074\pi\)
\(468\) 699.561 0.0690966
\(469\) 21311.3 2.09821
\(470\) 0 0
\(471\) −8884.97 −0.869210
\(472\) 1318.86 0.128614
\(473\) −53.4530 −0.00519613
\(474\) 15817.9 1.53279
\(475\) 0 0
\(476\) 6755.66 0.650515
\(477\) −17751.4 −1.70394
\(478\) −1559.67 −0.149242
\(479\) −785.274 −0.0749062 −0.0374531 0.999298i \(-0.511924\pi\)
−0.0374531 + 0.999298i \(0.511924\pi\)
\(480\) 0 0
\(481\) 851.808 0.0807466
\(482\) 8409.79 0.794721
\(483\) 4349.33 0.409734
\(484\) −5320.10 −0.499633
\(485\) 0 0
\(486\) 8621.72 0.804710
\(487\) −8714.29 −0.810846 −0.405423 0.914129i \(-0.632876\pi\)
−0.405423 + 0.914129i \(0.632876\pi\)
\(488\) −1505.98 −0.139698
\(489\) −22384.9 −2.07010
\(490\) 0 0
\(491\) −10943.1 −1.00582 −0.502909 0.864339i \(-0.667737\pi\)
−0.502909 + 0.864339i \(0.667737\pi\)
\(492\) −6754.09 −0.618898
\(493\) −2060.97 −0.188279
\(494\) −600.971 −0.0547347
\(495\) 0 0
\(496\) −2189.78 −0.198234
\(497\) 6020.41 0.543365
\(498\) 3223.81 0.290085
\(499\) −5601.85 −0.502552 −0.251276 0.967916i \(-0.580850\pi\)
−0.251276 + 0.967916i \(0.580850\pi\)
\(500\) 0 0
\(501\) −3768.01 −0.336013
\(502\) −5522.95 −0.491039
\(503\) −21689.8 −1.92266 −0.961331 0.275395i \(-0.911191\pi\)
−0.961331 + 0.275395i \(0.911191\pi\)
\(504\) 7574.86 0.669466
\(505\) 0 0
\(506\) −45.4478 −0.00399289
\(507\) −18024.8 −1.57891
\(508\) 2530.39 0.221000
\(509\) 13826.0 1.20399 0.601993 0.798501i \(-0.294373\pi\)
0.601993 + 0.798501i \(0.294373\pi\)
\(510\) 0 0
\(511\) 20585.0 1.78205
\(512\) −512.000 −0.0441942
\(513\) 8485.04 0.730260
\(514\) −1172.94 −0.100654
\(515\) 0 0
\(516\) 1790.01 0.152715
\(517\) −40.9515 −0.00348364
\(518\) 9223.40 0.782341
\(519\) 11105.5 0.939263
\(520\) 0 0
\(521\) −11971.1 −1.00664 −0.503322 0.864099i \(-0.667889\pi\)
−0.503322 + 0.864099i \(0.667889\pi\)
\(522\) −2310.89 −0.193764
\(523\) 9668.82 0.808390 0.404195 0.914673i \(-0.367552\pi\)
0.404195 + 0.914673i \(0.367552\pi\)
\(524\) 8972.62 0.748036
\(525\) 0 0
\(526\) 11940.8 0.989813
\(527\) 10110.5 0.835712
\(528\) −130.754 −0.0107771
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) −6827.78 −0.558004
\(532\) −6507.33 −0.530317
\(533\) −862.033 −0.0700540
\(534\) 3536.05 0.286554
\(535\) 0 0
\(536\) 7457.34 0.600948
\(537\) −38508.6 −3.09454
\(538\) −7828.67 −0.627357
\(539\) −177.517 −0.0141859
\(540\) 0 0
\(541\) 6793.28 0.539863 0.269932 0.962880i \(-0.412999\pi\)
0.269932 + 0.962880i \(0.412999\pi\)
\(542\) −156.173 −0.0123768
\(543\) −1458.41 −0.115260
\(544\) 2363.97 0.186313
\(545\) 0 0
\(546\) 1597.06 0.125179
\(547\) 5584.91 0.436551 0.218276 0.975887i \(-0.429957\pi\)
0.218276 + 0.975887i \(0.429957\pi\)
\(548\) −5011.08 −0.390626
\(549\) 7796.49 0.606095
\(550\) 0 0
\(551\) 1985.21 0.153490
\(552\) 1521.94 0.117351
\(553\) 21860.3 1.68100
\(554\) −152.102 −0.0116646
\(555\) 0 0
\(556\) 11260.8 0.858925
\(557\) −4172.24 −0.317385 −0.158693 0.987328i \(-0.550728\pi\)
−0.158693 + 0.987328i \(0.550728\pi\)
\(558\) 11336.5 0.860059
\(559\) 228.461 0.0172860
\(560\) 0 0
\(561\) 603.707 0.0454341
\(562\) 7705.34 0.578346
\(563\) −7734.17 −0.578963 −0.289482 0.957184i \(-0.593483\pi\)
−0.289482 + 0.957184i \(0.593483\pi\)
\(564\) 1371.37 0.102385
\(565\) 0 0
\(566\) −3100.26 −0.230236
\(567\) 3016.47 0.223421
\(568\) 2106.69 0.155625
\(569\) 1392.55 0.102599 0.0512995 0.998683i \(-0.483664\pi\)
0.0512995 + 0.998683i \(0.483664\pi\)
\(570\) 0 0
\(571\) 16996.1 1.24565 0.622823 0.782363i \(-0.285986\pi\)
0.622823 + 0.782363i \(0.285986\pi\)
\(572\) −16.6883 −0.00121988
\(573\) 13830.0 1.00830
\(574\) −9334.11 −0.678743
\(575\) 0 0
\(576\) 2650.63 0.191741
\(577\) 6849.23 0.494172 0.247086 0.968994i \(-0.420527\pi\)
0.247086 + 0.968994i \(0.420527\pi\)
\(578\) −1088.76 −0.0783500
\(579\) 24437.4 1.75403
\(580\) 0 0
\(581\) 4455.29 0.318135
\(582\) 10401.5 0.740817
\(583\) 423.467 0.0300827
\(584\) 7203.21 0.510395
\(585\) 0 0
\(586\) 8472.01 0.597228
\(587\) −6701.08 −0.471181 −0.235590 0.971852i \(-0.575702\pi\)
−0.235590 + 0.971852i \(0.575702\pi\)
\(588\) 5944.62 0.416925
\(589\) −9738.85 −0.681294
\(590\) 0 0
\(591\) −15032.1 −1.04625
\(592\) 3227.49 0.224070
\(593\) −9898.21 −0.685448 −0.342724 0.939436i \(-0.611350\pi\)
−0.342724 + 0.939436i \(0.611350\pi\)
\(594\) 235.620 0.0162754
\(595\) 0 0
\(596\) 9625.84 0.661560
\(597\) 39545.5 2.71104
\(598\) 194.247 0.0132832
\(599\) 13149.2 0.896934 0.448467 0.893799i \(-0.351970\pi\)
0.448467 + 0.893799i \(0.351970\pi\)
\(600\) 0 0
\(601\) 27142.4 1.84220 0.921100 0.389326i \(-0.127292\pi\)
0.921100 + 0.389326i \(0.127292\pi\)
\(602\) 2473.79 0.167482
\(603\) −38606.7 −2.60728
\(604\) 8742.34 0.588942
\(605\) 0 0
\(606\) 845.952 0.0567070
\(607\) 6708.40 0.448576 0.224288 0.974523i \(-0.427994\pi\)
0.224288 + 0.974523i \(0.427994\pi\)
\(608\) −2277.07 −0.151887
\(609\) −5275.63 −0.351033
\(610\) 0 0
\(611\) 175.029 0.0115891
\(612\) −12238.3 −0.808340
\(613\) 17755.6 1.16989 0.584943 0.811074i \(-0.301117\pi\)
0.584943 + 0.811074i \(0.301117\pi\)
\(614\) −20156.2 −1.32482
\(615\) 0 0
\(616\) −180.701 −0.0118192
\(617\) −14555.4 −0.949722 −0.474861 0.880061i \(-0.657502\pi\)
−0.474861 + 0.880061i \(0.657502\pi\)
\(618\) 6006.52 0.390967
\(619\) 29452.5 1.91243 0.956215 0.292665i \(-0.0945422\pi\)
0.956215 + 0.292665i \(0.0945422\pi\)
\(620\) 0 0
\(621\) −2742.55 −0.177222
\(622\) 5305.94 0.342040
\(623\) 4886.80 0.314262
\(624\) 558.850 0.0358524
\(625\) 0 0
\(626\) 13421.4 0.856909
\(627\) −581.516 −0.0370391
\(628\) −4296.72 −0.273022
\(629\) −14901.8 −0.944629
\(630\) 0 0
\(631\) 9911.19 0.625290 0.312645 0.949870i \(-0.398785\pi\)
0.312645 + 0.949870i \(0.398785\pi\)
\(632\) 7649.46 0.481454
\(633\) 26482.7 1.66286
\(634\) −7355.77 −0.460781
\(635\) 0 0
\(636\) −14180.9 −0.884133
\(637\) 758.720 0.0471924
\(638\) 55.1271 0.00342085
\(639\) −10906.4 −0.675194
\(640\) 0 0
\(641\) −13548.5 −0.834844 −0.417422 0.908713i \(-0.637066\pi\)
−0.417422 + 0.908713i \(0.637066\pi\)
\(642\) 25054.6 1.54023
\(643\) −2254.31 −0.138260 −0.0691302 0.997608i \(-0.522022\pi\)
−0.0691302 + 0.997608i \(0.522022\pi\)
\(644\) 2103.31 0.128699
\(645\) 0 0
\(646\) 10513.5 0.640325
\(647\) 17967.1 1.09175 0.545874 0.837868i \(-0.316198\pi\)
0.545874 + 0.837868i \(0.316198\pi\)
\(648\) 1055.54 0.0639897
\(649\) 162.879 0.00985141
\(650\) 0 0
\(651\) 25880.6 1.55813
\(652\) −10825.2 −0.650226
\(653\) −365.239 −0.0218881 −0.0109440 0.999940i \(-0.503484\pi\)
−0.0109440 + 0.999940i \(0.503484\pi\)
\(654\) −13422.1 −0.802517
\(655\) 0 0
\(656\) −3266.24 −0.194398
\(657\) −37291.1 −2.21440
\(658\) 1895.22 0.112285
\(659\) 29229.1 1.72778 0.863889 0.503683i \(-0.168022\pi\)
0.863889 + 0.503683i \(0.168022\pi\)
\(660\) 0 0
\(661\) −23681.1 −1.39348 −0.696740 0.717324i \(-0.745367\pi\)
−0.696740 + 0.717324i \(0.745367\pi\)
\(662\) 19612.8 1.15147
\(663\) −2580.28 −0.151146
\(664\) 1559.01 0.0911167
\(665\) 0 0
\(666\) −16708.8 −0.972150
\(667\) −641.664 −0.0372494
\(668\) −1822.19 −0.105543
\(669\) 15692.7 0.906900
\(670\) 0 0
\(671\) −185.988 −0.0107004
\(672\) 6051.24 0.347369
\(673\) 16016.2 0.917351 0.458676 0.888604i \(-0.348324\pi\)
0.458676 + 0.888604i \(0.348324\pi\)
\(674\) −14286.8 −0.816480
\(675\) 0 0
\(676\) −8716.67 −0.495942
\(677\) 24082.5 1.36715 0.683577 0.729878i \(-0.260423\pi\)
0.683577 + 0.729878i \(0.260423\pi\)
\(678\) 205.951 0.0116659
\(679\) 14374.8 0.812451
\(680\) 0 0
\(681\) −36960.1 −2.07975
\(682\) −270.437 −0.0151841
\(683\) 24224.1 1.35711 0.678556 0.734549i \(-0.262606\pi\)
0.678556 + 0.734549i \(0.262606\pi\)
\(684\) 11788.4 0.658980
\(685\) 0 0
\(686\) −7467.94 −0.415637
\(687\) −44217.9 −2.45563
\(688\) 865.639 0.0479683
\(689\) −1809.92 −0.100076
\(690\) 0 0
\(691\) 13948.7 0.767919 0.383960 0.923350i \(-0.374560\pi\)
0.383960 + 0.923350i \(0.374560\pi\)
\(692\) 5370.55 0.295026
\(693\) 935.491 0.0512790
\(694\) −10320.4 −0.564492
\(695\) 0 0
\(696\) −1846.07 −0.100539
\(697\) 15080.6 0.819540
\(698\) −17424.1 −0.944858
\(699\) 37059.7 2.00533
\(700\) 0 0
\(701\) −33334.1 −1.79602 −0.898011 0.439973i \(-0.854988\pi\)
−0.898011 + 0.439973i \(0.854988\pi\)
\(702\) −1007.05 −0.0541436
\(703\) 14354.0 0.770087
\(704\) −63.2317 −0.00338514
\(705\) 0 0
\(706\) −14234.6 −0.758819
\(707\) 1169.10 0.0621903
\(708\) −5454.43 −0.289534
\(709\) −7107.92 −0.376507 −0.188253 0.982120i \(-0.560283\pi\)
−0.188253 + 0.982120i \(0.560283\pi\)
\(710\) 0 0
\(711\) −39601.3 −2.08884
\(712\) 1710.01 0.0900075
\(713\) 3147.81 0.165338
\(714\) −27939.4 −1.46443
\(715\) 0 0
\(716\) −18622.5 −0.972007
\(717\) 6450.34 0.335972
\(718\) −7097.45 −0.368906
\(719\) −13003.1 −0.674456 −0.337228 0.941423i \(-0.609489\pi\)
−0.337228 + 0.941423i \(0.609489\pi\)
\(720\) 0 0
\(721\) 8300.98 0.428772
\(722\) 3590.92 0.185097
\(723\) −34780.4 −1.78907
\(724\) −705.279 −0.0362037
\(725\) 0 0
\(726\) 22002.3 1.12477
\(727\) −5524.86 −0.281851 −0.140926 0.990020i \(-0.545008\pi\)
−0.140926 + 0.990020i \(0.545008\pi\)
\(728\) 772.328 0.0393192
\(729\) −32094.4 −1.63057
\(730\) 0 0
\(731\) −3996.77 −0.202224
\(732\) 6228.29 0.314487
\(733\) −22106.6 −1.11395 −0.556976 0.830529i \(-0.688038\pi\)
−0.556976 + 0.830529i \(0.688038\pi\)
\(734\) 160.022 0.00804703
\(735\) 0 0
\(736\) 736.000 0.0368605
\(737\) 920.977 0.0460307
\(738\) 16909.3 0.843416
\(739\) −6619.82 −0.329518 −0.164759 0.986334i \(-0.552685\pi\)
−0.164759 + 0.986334i \(0.552685\pi\)
\(740\) 0 0
\(741\) 2485.44 0.123218
\(742\) −19597.9 −0.969625
\(743\) −18894.1 −0.932919 −0.466460 0.884543i \(-0.654471\pi\)
−0.466460 + 0.884543i \(0.654471\pi\)
\(744\) 9056.27 0.446262
\(745\) 0 0
\(746\) 6422.17 0.315191
\(747\) −8071.03 −0.395320
\(748\) 291.949 0.0142710
\(749\) 34625.3 1.68916
\(750\) 0 0
\(751\) 4931.32 0.239609 0.119805 0.992797i \(-0.461773\pi\)
0.119805 + 0.992797i \(0.461773\pi\)
\(752\) 663.185 0.0321594
\(753\) 22841.3 1.10542
\(754\) −235.617 −0.0113802
\(755\) 0 0
\(756\) −10904.4 −0.524589
\(757\) −6248.31 −0.299998 −0.149999 0.988686i \(-0.547927\pi\)
−0.149999 + 0.988686i \(0.547927\pi\)
\(758\) 16355.1 0.783701
\(759\) 187.959 0.00898875
\(760\) 0 0
\(761\) −18867.0 −0.898723 −0.449361 0.893350i \(-0.648348\pi\)
−0.449361 + 0.893350i \(0.648348\pi\)
\(762\) −10465.0 −0.497514
\(763\) −18549.3 −0.880117
\(764\) 6688.11 0.316711
\(765\) 0 0
\(766\) 25853.1 1.21946
\(767\) −696.156 −0.0327728
\(768\) 2117.48 0.0994895
\(769\) −4752.05 −0.222839 −0.111420 0.993773i \(-0.535540\pi\)
−0.111420 + 0.993773i \(0.535540\pi\)
\(770\) 0 0
\(771\) 4850.92 0.226591
\(772\) 11817.8 0.550947
\(773\) −7050.12 −0.328040 −0.164020 0.986457i \(-0.552446\pi\)
−0.164020 + 0.986457i \(0.552446\pi\)
\(774\) −4481.42 −0.208115
\(775\) 0 0
\(776\) 5030.10 0.232693
\(777\) −38145.2 −1.76120
\(778\) −9469.32 −0.436364
\(779\) −14526.3 −0.668111
\(780\) 0 0
\(781\) 260.175 0.0119204
\(782\) −3398.21 −0.155396
\(783\) 3326.64 0.151832
\(784\) 2874.78 0.130958
\(785\) 0 0
\(786\) −37108.1 −1.68397
\(787\) −19524.7 −0.884345 −0.442173 0.896930i \(-0.645792\pi\)
−0.442173 + 0.896930i \(0.645792\pi\)
\(788\) −7269.41 −0.328632
\(789\) −49383.4 −2.22826
\(790\) 0 0
\(791\) 284.623 0.0127940
\(792\) 327.351 0.0146868
\(793\) 794.925 0.0355972
\(794\) −19877.6 −0.888450
\(795\) 0 0
\(796\) 19124.0 0.851546
\(797\) 25078.7 1.11459 0.557297 0.830313i \(-0.311838\pi\)
0.557297 + 0.830313i \(0.311838\pi\)
\(798\) 26912.4 1.19384
\(799\) −3062.01 −0.135577
\(800\) 0 0
\(801\) −8852.74 −0.390507
\(802\) 670.592 0.0295255
\(803\) 889.592 0.0390947
\(804\) −30841.3 −1.35285
\(805\) 0 0
\(806\) 1155.86 0.0505131
\(807\) 32377.0 1.41230
\(808\) 409.097 0.0178119
\(809\) 11722.0 0.509425 0.254712 0.967017i \(-0.418019\pi\)
0.254712 + 0.967017i \(0.418019\pi\)
\(810\) 0 0
\(811\) −3540.61 −0.153302 −0.0766509 0.997058i \(-0.524423\pi\)
−0.0766509 + 0.997058i \(0.524423\pi\)
\(812\) −2551.26 −0.110261
\(813\) 645.885 0.0278625
\(814\) 398.594 0.0171630
\(815\) 0 0
\(816\) −9776.67 −0.419427
\(817\) 3849.85 0.164858
\(818\) −13121.7 −0.560867
\(819\) −3998.35 −0.170591
\(820\) 0 0
\(821\) −43675.7 −1.85663 −0.928315 0.371794i \(-0.878743\pi\)
−0.928315 + 0.371794i \(0.878743\pi\)
\(822\) 20724.3 0.879373
\(823\) 28732.5 1.21695 0.608476 0.793572i \(-0.291781\pi\)
0.608476 + 0.793572i \(0.291781\pi\)
\(824\) 2904.72 0.122804
\(825\) 0 0
\(826\) −7537.99 −0.317531
\(827\) −33810.2 −1.42164 −0.710821 0.703373i \(-0.751676\pi\)
−0.710821 + 0.703373i \(0.751676\pi\)
\(828\) −3810.28 −0.159923
\(829\) −34664.8 −1.45230 −0.726150 0.687536i \(-0.758692\pi\)
−0.726150 + 0.687536i \(0.758692\pi\)
\(830\) 0 0
\(831\) 629.050 0.0262593
\(832\) 270.257 0.0112614
\(833\) −13273.3 −0.552090
\(834\) −46571.1 −1.93360
\(835\) 0 0
\(836\) −281.217 −0.0116341
\(837\) −16319.5 −0.673936
\(838\) −14233.4 −0.586735
\(839\) 11115.4 0.457384 0.228692 0.973499i \(-0.426555\pi\)
0.228692 + 0.973499i \(0.426555\pi\)
\(840\) 0 0
\(841\) −23610.7 −0.968087
\(842\) −19598.9 −0.802163
\(843\) −31867.0 −1.30197
\(844\) 12806.9 0.522312
\(845\) 0 0
\(846\) −3433.31 −0.139527
\(847\) 30407.1 1.23353
\(848\) −6857.79 −0.277709
\(849\) 12821.8 0.518306
\(850\) 0 0
\(851\) −4639.52 −0.186887
\(852\) −8712.64 −0.350341
\(853\) −23695.9 −0.951153 −0.475577 0.879674i \(-0.657761\pi\)
−0.475577 + 0.879674i \(0.657761\pi\)
\(854\) 8607.46 0.344896
\(855\) 0 0
\(856\) 12116.3 0.483791
\(857\) 20605.9 0.821336 0.410668 0.911785i \(-0.365295\pi\)
0.410668 + 0.911785i \(0.365295\pi\)
\(858\) 69.0177 0.00274618
\(859\) −43187.1 −1.71540 −0.857698 0.514154i \(-0.828106\pi\)
−0.857698 + 0.514154i \(0.828106\pi\)
\(860\) 0 0
\(861\) 38603.1 1.52798
\(862\) 21046.6 0.831613
\(863\) 47551.7 1.87564 0.937822 0.347117i \(-0.112839\pi\)
0.937822 + 0.347117i \(0.112839\pi\)
\(864\) −3815.72 −0.150247
\(865\) 0 0
\(866\) −9541.94 −0.374421
\(867\) 4502.77 0.176381
\(868\) 12515.7 0.489414
\(869\) 944.704 0.0368779
\(870\) 0 0
\(871\) −3936.32 −0.153131
\(872\) −6490.85 −0.252073
\(873\) −26040.9 −1.00956
\(874\) 3273.29 0.126683
\(875\) 0 0
\(876\) −29790.3 −1.14900
\(877\) −8116.63 −0.312519 −0.156260 0.987716i \(-0.549944\pi\)
−0.156260 + 0.987716i \(0.549944\pi\)
\(878\) −20462.4 −0.786528
\(879\) −35037.7 −1.34447
\(880\) 0 0
\(881\) 24256.1 0.927594 0.463797 0.885942i \(-0.346487\pi\)
0.463797 + 0.885942i \(0.346487\pi\)
\(882\) −14882.8 −0.568174
\(883\) 46859.3 1.78589 0.892945 0.450167i \(-0.148635\pi\)
0.892945 + 0.450167i \(0.148635\pi\)
\(884\) −1247.81 −0.0474755
\(885\) 0 0
\(886\) 21016.2 0.796899
\(887\) 14372.4 0.544057 0.272028 0.962289i \(-0.412306\pi\)
0.272028 + 0.962289i \(0.412306\pi\)
\(888\) −13347.9 −0.504423
\(889\) −14462.5 −0.545621
\(890\) 0 0
\(891\) 130.358 0.00490142
\(892\) 7588.91 0.284860
\(893\) 2949.45 0.110526
\(894\) −39809.6 −1.48930
\(895\) 0 0
\(896\) 2926.34 0.109110
\(897\) −803.347 −0.0299030
\(898\) −14461.4 −0.537398
\(899\) −3818.21 −0.141651
\(900\) 0 0
\(901\) 31663.3 1.17076
\(902\) −403.378 −0.0148903
\(903\) −10230.8 −0.377033
\(904\) 99.5965 0.00366431
\(905\) 0 0
\(906\) −36155.7 −1.32582
\(907\) 17332.1 0.634512 0.317256 0.948340i \(-0.397239\pi\)
0.317256 + 0.948340i \(0.397239\pi\)
\(908\) −17873.7 −0.653258
\(909\) −2117.90 −0.0772787
\(910\) 0 0
\(911\) 44304.9 1.61129 0.805646 0.592397i \(-0.201818\pi\)
0.805646 + 0.592397i \(0.201818\pi\)
\(912\) 9417.30 0.341927
\(913\) 192.537 0.00697926
\(914\) 4837.49 0.175066
\(915\) 0 0
\(916\) −21383.5 −0.771322
\(917\) −51283.2 −1.84680
\(918\) 17617.7 0.633410
\(919\) −4764.32 −0.171013 −0.0855063 0.996338i \(-0.527251\pi\)
−0.0855063 + 0.996338i \(0.527251\pi\)
\(920\) 0 0
\(921\) 83359.9 2.98241
\(922\) 22685.6 0.810315
\(923\) −1112.01 −0.0396556
\(924\) 747.325 0.0266074
\(925\) 0 0
\(926\) −23571.8 −0.836519
\(927\) −15037.7 −0.532799
\(928\) −892.750 −0.0315797
\(929\) −23226.2 −0.820267 −0.410134 0.912025i \(-0.634518\pi\)
−0.410134 + 0.912025i \(0.634518\pi\)
\(930\) 0 0
\(931\) 12785.3 0.450078
\(932\) 17921.9 0.629882
\(933\) −21943.8 −0.769996
\(934\) 32589.1 1.14170
\(935\) 0 0
\(936\) −1399.12 −0.0488587
\(937\) 23752.5 0.828133 0.414066 0.910247i \(-0.364108\pi\)
0.414066 + 0.910247i \(0.364108\pi\)
\(938\) −42622.5 −1.48366
\(939\) −55506.7 −1.92907
\(940\) 0 0
\(941\) −23210.4 −0.804079 −0.402040 0.915622i \(-0.631699\pi\)
−0.402040 + 0.915622i \(0.631699\pi\)
\(942\) 17769.9 0.614624
\(943\) 4695.21 0.162139
\(944\) −2637.73 −0.0909436
\(945\) 0 0
\(946\) 106.906 0.00367422
\(947\) 7778.59 0.266917 0.133458 0.991054i \(-0.457392\pi\)
0.133458 + 0.991054i \(0.457392\pi\)
\(948\) −31635.9 −1.08385
\(949\) −3802.18 −0.130057
\(950\) 0 0
\(951\) 30421.3 1.03731
\(952\) −13511.3 −0.459983
\(953\) −3979.52 −0.135267 −0.0676334 0.997710i \(-0.521545\pi\)
−0.0676334 + 0.997710i \(0.521545\pi\)
\(954\) 35502.8 1.20487
\(955\) 0 0
\(956\) 3119.34 0.105530
\(957\) −227.989 −0.00770098
\(958\) 1570.55 0.0529667
\(959\) 28640.9 0.964405
\(960\) 0 0
\(961\) −11060.0 −0.371254
\(962\) −1703.62 −0.0570964
\(963\) −62726.0 −2.09898
\(964\) −16819.6 −0.561952
\(965\) 0 0
\(966\) −8698.66 −0.289726
\(967\) −17325.9 −0.576178 −0.288089 0.957604i \(-0.593020\pi\)
−0.288089 + 0.957604i \(0.593020\pi\)
\(968\) 10640.2 0.353294
\(969\) −43480.9 −1.44149
\(970\) 0 0
\(971\) 20183.0 0.667048 0.333524 0.942742i \(-0.391762\pi\)
0.333524 + 0.942742i \(0.391762\pi\)
\(972\) −17243.4 −0.569016
\(973\) −64361.0 −2.12058
\(974\) 17428.6 0.573355
\(975\) 0 0
\(976\) 3011.96 0.0987814
\(977\) −47185.7 −1.54514 −0.772571 0.634928i \(-0.781030\pi\)
−0.772571 + 0.634928i \(0.781030\pi\)
\(978\) 44769.8 1.46378
\(979\) 211.185 0.00689430
\(980\) 0 0
\(981\) 33603.2 1.09365
\(982\) 21886.3 0.711221
\(983\) 7347.90 0.238415 0.119207 0.992869i \(-0.461965\pi\)
0.119207 + 0.992869i \(0.461965\pi\)
\(984\) 13508.2 0.437627
\(985\) 0 0
\(986\) 4121.94 0.133133
\(987\) −7838.07 −0.252775
\(988\) 1201.94 0.0387033
\(989\) −1244.36 −0.0400083
\(990\) 0 0
\(991\) 34327.0 1.10034 0.550168 0.835054i \(-0.314564\pi\)
0.550168 + 0.835054i \(0.314564\pi\)
\(992\) 4379.56 0.140172
\(993\) −81112.6 −2.59218
\(994\) −12040.8 −0.384217
\(995\) 0 0
\(996\) −6447.62 −0.205121
\(997\) −37611.0 −1.19474 −0.597368 0.801967i \(-0.703787\pi\)
−0.597368 + 0.801967i \(0.703787\pi\)
\(998\) 11203.7 0.355358
\(999\) 24053.1 0.761770
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 1150.4.a.q.1.5 5
5.2 odd 4 1150.4.b.r.599.1 10
5.3 odd 4 1150.4.b.r.599.10 10
5.4 even 2 1150.4.a.v.1.1 yes 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1150.4.a.q.1.5 5 1.1 even 1 trivial
1150.4.a.v.1.1 yes 5 5.4 even 2
1150.4.b.r.599.1 10 5.2 odd 4
1150.4.b.r.599.10 10 5.3 odd 4