Properties

Label 1045.4.a.h.1.14
Level $1045$
Weight $4$
Character 1045.1
Self dual yes
Analytic conductor $61.657$
Analytic rank $0$
Dimension $24$
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] = [1045,4,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.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: \(61.6569959560\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.998459 q^{2} +4.82825 q^{3} -7.00308 q^{4} +5.00000 q^{5} +4.82081 q^{6} -5.45452 q^{7} -14.9800 q^{8} -3.68800 q^{9} +O(q^{10})\) \(q+0.998459 q^{2} +4.82825 q^{3} -7.00308 q^{4} +5.00000 q^{5} +4.82081 q^{6} -5.45452 q^{7} -14.9800 q^{8} -3.68800 q^{9} +4.99229 q^{10} -11.0000 q^{11} -33.8126 q^{12} -28.9587 q^{13} -5.44611 q^{14} +24.1413 q^{15} +41.0678 q^{16} -44.4214 q^{17} -3.68231 q^{18} +19.0000 q^{19} -35.0154 q^{20} -26.3358 q^{21} -10.9830 q^{22} +152.854 q^{23} -72.3270 q^{24} +25.0000 q^{25} -28.9141 q^{26} -148.169 q^{27} +38.1984 q^{28} +182.157 q^{29} +24.1040 q^{30} +182.989 q^{31} +160.844 q^{32} -53.1108 q^{33} -44.3529 q^{34} -27.2726 q^{35} +25.8273 q^{36} +279.209 q^{37} +18.9707 q^{38} -139.820 q^{39} -74.8998 q^{40} -41.6226 q^{41} -26.2952 q^{42} +290.563 q^{43} +77.0339 q^{44} -18.4400 q^{45} +152.618 q^{46} +38.6536 q^{47} +198.285 q^{48} -313.248 q^{49} +24.9615 q^{50} -214.478 q^{51} +202.800 q^{52} +521.847 q^{53} -147.941 q^{54} -55.0000 q^{55} +81.7085 q^{56} +91.7368 q^{57} +181.876 q^{58} +126.032 q^{59} -169.063 q^{60} +295.884 q^{61} +182.707 q^{62} +20.1162 q^{63} -167.946 q^{64} -144.793 q^{65} -53.0289 q^{66} +165.988 q^{67} +311.086 q^{68} +738.017 q^{69} -27.2306 q^{70} +223.721 q^{71} +55.2461 q^{72} -274.718 q^{73} +278.778 q^{74} +120.706 q^{75} -133.059 q^{76} +59.9997 q^{77} -139.604 q^{78} -16.3617 q^{79} +205.339 q^{80} -615.823 q^{81} -41.5585 q^{82} -372.736 q^{83} +184.432 q^{84} -222.107 q^{85} +290.115 q^{86} +879.500 q^{87} +164.780 q^{88} +489.012 q^{89} -18.4116 q^{90} +157.956 q^{91} -1070.45 q^{92} +883.518 q^{93} +38.5940 q^{94} +95.0000 q^{95} +776.596 q^{96} -880.289 q^{97} -312.765 q^{98} +40.5680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 4 q^{2} + 21 q^{3} + 98 q^{4} + 120 q^{5} + 15 q^{6} + 71 q^{7} + 84 q^{8} + 339 q^{9} + 20 q^{10} - 264 q^{11} + 164 q^{12} - 15 q^{13} + 77 q^{14} + 105 q^{15} + 230 q^{16} + 187 q^{17} - 109 q^{18} + 456 q^{19} + 490 q^{20} + 295 q^{21} - 44 q^{22} + 451 q^{23} + 416 q^{24} + 600 q^{25} + 375 q^{26} + 1335 q^{27} + 815 q^{28} + 271 q^{29} + 75 q^{30} + 302 q^{31} + 1181 q^{32} - 231 q^{33} + 285 q^{34} + 355 q^{35} + 2445 q^{36} + 974 q^{37} + 76 q^{38} + 601 q^{39} + 420 q^{40} + 316 q^{41} + 2158 q^{42} + 686 q^{43} - 1078 q^{44} + 1695 q^{45} - 217 q^{46} + 1798 q^{47} + 353 q^{48} + 1845 q^{49} + 100 q^{50} + 383 q^{51} - 134 q^{52} + 815 q^{53} - 974 q^{54} - 1320 q^{55} + 2001 q^{56} + 399 q^{57} - 888 q^{58} + 1793 q^{59} + 820 q^{60} + 62 q^{61} + 3994 q^{62} + 366 q^{63} - 588 q^{64} - 75 q^{65} - 165 q^{66} + 2363 q^{67} - 1720 q^{68} - 287 q^{69} + 385 q^{70} + 1266 q^{71} + 3838 q^{72} + 127 q^{73} - 2861 q^{74} + 525 q^{75} + 1862 q^{76} - 781 q^{77} - 3916 q^{78} - 1922 q^{79} + 1150 q^{80} + 3688 q^{81} + 2666 q^{82} + 3666 q^{83} + 438 q^{84} + 935 q^{85} + 78 q^{86} + 2685 q^{87} - 924 q^{88} + 2344 q^{89} - 545 q^{90} + 127 q^{91} + 4800 q^{92} + 1344 q^{93} + 1756 q^{94} + 2280 q^{95} + 2874 q^{96} + 1182 q^{97} - 4328 q^{98} - 3729 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.998459 0.353009 0.176504 0.984300i \(-0.443521\pi\)
0.176504 + 0.984300i \(0.443521\pi\)
\(3\) 4.82825 0.929197 0.464599 0.885521i \(-0.346199\pi\)
0.464599 + 0.885521i \(0.346199\pi\)
\(4\) −7.00308 −0.875385
\(5\) 5.00000 0.447214
\(6\) 4.82081 0.328015
\(7\) −5.45452 −0.294516 −0.147258 0.989098i \(-0.547045\pi\)
−0.147258 + 0.989098i \(0.547045\pi\)
\(8\) −14.9800 −0.662027
\(9\) −3.68800 −0.136593
\(10\) 4.99229 0.157870
\(11\) −11.0000 −0.301511
\(12\) −33.8126 −0.813405
\(13\) −28.9587 −0.617823 −0.308911 0.951091i \(-0.599965\pi\)
−0.308911 + 0.951091i \(0.599965\pi\)
\(14\) −5.44611 −0.103967
\(15\) 24.1413 0.415550
\(16\) 41.0678 0.641684
\(17\) −44.4214 −0.633751 −0.316875 0.948467i \(-0.602634\pi\)
−0.316875 + 0.948467i \(0.602634\pi\)
\(18\) −3.68231 −0.0482183
\(19\) 19.0000 0.229416
\(20\) −35.0154 −0.391484
\(21\) −26.3358 −0.273664
\(22\) −10.9830 −0.106436
\(23\) 152.854 1.38575 0.692875 0.721058i \(-0.256344\pi\)
0.692875 + 0.721058i \(0.256344\pi\)
\(24\) −72.3270 −0.615154
\(25\) 25.0000 0.200000
\(26\) −28.9141 −0.218097
\(27\) −148.169 −1.05612
\(28\) 38.1984 0.257815
\(29\) 182.157 1.16640 0.583202 0.812327i \(-0.301800\pi\)
0.583202 + 0.812327i \(0.301800\pi\)
\(30\) 24.1040 0.146693
\(31\) 182.989 1.06019 0.530094 0.847939i \(-0.322157\pi\)
0.530094 + 0.847939i \(0.322157\pi\)
\(32\) 160.844 0.888547
\(33\) −53.1108 −0.280164
\(34\) −44.3529 −0.223719
\(35\) −27.2726 −0.131712
\(36\) 25.8273 0.119571
\(37\) 279.209 1.24058 0.620292 0.784371i \(-0.287014\pi\)
0.620292 + 0.784371i \(0.287014\pi\)
\(38\) 18.9707 0.0809857
\(39\) −139.820 −0.574079
\(40\) −74.8998 −0.296067
\(41\) −41.6226 −0.158545 −0.0792727 0.996853i \(-0.525260\pi\)
−0.0792727 + 0.996853i \(0.525260\pi\)
\(42\) −26.2952 −0.0966056
\(43\) 290.563 1.03048 0.515238 0.857047i \(-0.327704\pi\)
0.515238 + 0.857047i \(0.327704\pi\)
\(44\) 77.0339 0.263939
\(45\) −18.4400 −0.0610860
\(46\) 152.618 0.489182
\(47\) 38.6536 0.119962 0.0599809 0.998200i \(-0.480896\pi\)
0.0599809 + 0.998200i \(0.480896\pi\)
\(48\) 198.285 0.596251
\(49\) −313.248 −0.913260
\(50\) 24.9615 0.0706017
\(51\) −214.478 −0.588880
\(52\) 202.800 0.540833
\(53\) 521.847 1.35248 0.676238 0.736684i \(-0.263609\pi\)
0.676238 + 0.736684i \(0.263609\pi\)
\(54\) −147.941 −0.372819
\(55\) −55.0000 −0.134840
\(56\) 81.7085 0.194978
\(57\) 91.7368 0.213172
\(58\) 181.876 0.411751
\(59\) 126.032 0.278101 0.139050 0.990285i \(-0.455595\pi\)
0.139050 + 0.990285i \(0.455595\pi\)
\(60\) −169.063 −0.363766
\(61\) 295.884 0.621049 0.310525 0.950565i \(-0.399495\pi\)
0.310525 + 0.950565i \(0.399495\pi\)
\(62\) 182.707 0.374255
\(63\) 20.1162 0.0402287
\(64\) −167.946 −0.328019
\(65\) −144.793 −0.276299
\(66\) −53.0289 −0.0989001
\(67\) 165.988 0.302666 0.151333 0.988483i \(-0.451643\pi\)
0.151333 + 0.988483i \(0.451643\pi\)
\(68\) 311.086 0.554776
\(69\) 738.017 1.28764
\(70\) −27.2306 −0.0464953
\(71\) 223.721 0.373955 0.186977 0.982364i \(-0.440131\pi\)
0.186977 + 0.982364i \(0.440131\pi\)
\(72\) 55.2461 0.0904279
\(73\) −274.718 −0.440457 −0.220228 0.975448i \(-0.570680\pi\)
−0.220228 + 0.975448i \(0.570680\pi\)
\(74\) 278.778 0.437937
\(75\) 120.706 0.185839
\(76\) −133.059 −0.200827
\(77\) 59.9997 0.0888000
\(78\) −139.604 −0.202655
\(79\) −16.3617 −0.0233018 −0.0116509 0.999932i \(-0.503709\pi\)
−0.0116509 + 0.999932i \(0.503709\pi\)
\(80\) 205.339 0.286970
\(81\) −615.823 −0.844750
\(82\) −41.5585 −0.0559679
\(83\) −372.736 −0.492929 −0.246464 0.969152i \(-0.579269\pi\)
−0.246464 + 0.969152i \(0.579269\pi\)
\(84\) 184.432 0.239561
\(85\) −222.107 −0.283422
\(86\) 290.115 0.363767
\(87\) 879.500 1.08382
\(88\) 164.780 0.199609
\(89\) 489.012 0.582418 0.291209 0.956659i \(-0.405942\pi\)
0.291209 + 0.956659i \(0.405942\pi\)
\(90\) −18.4116 −0.0215639
\(91\) 157.956 0.181959
\(92\) −1070.45 −1.21306
\(93\) 883.518 0.985124
\(94\) 38.5940 0.0423475
\(95\) 95.0000 0.102598
\(96\) 776.596 0.825635
\(97\) −880.289 −0.921441 −0.460721 0.887545i \(-0.652409\pi\)
−0.460721 + 0.887545i \(0.652409\pi\)
\(98\) −312.765 −0.322389
\(99\) 40.5680 0.0411842
\(100\) −175.077 −0.175077
\(101\) −605.680 −0.596707 −0.298353 0.954455i \(-0.596437\pi\)
−0.298353 + 0.954455i \(0.596437\pi\)
\(102\) −214.147 −0.207880
\(103\) −224.049 −0.214332 −0.107166 0.994241i \(-0.534178\pi\)
−0.107166 + 0.994241i \(0.534178\pi\)
\(104\) 433.800 0.409015
\(105\) −131.679 −0.122386
\(106\) 521.043 0.477435
\(107\) −1586.56 −1.43344 −0.716721 0.697360i \(-0.754358\pi\)
−0.716721 + 0.697360i \(0.754358\pi\)
\(108\) 1037.64 0.924510
\(109\) 666.119 0.585345 0.292672 0.956213i \(-0.405455\pi\)
0.292672 + 0.956213i \(0.405455\pi\)
\(110\) −54.9152 −0.0475997
\(111\) 1348.09 1.15275
\(112\) −224.005 −0.188986
\(113\) 2347.13 1.95398 0.976989 0.213290i \(-0.0684178\pi\)
0.976989 + 0.213290i \(0.0684178\pi\)
\(114\) 91.5954 0.0752517
\(115\) 764.270 0.619726
\(116\) −1275.66 −1.02105
\(117\) 106.800 0.0843900
\(118\) 125.838 0.0981719
\(119\) 242.297 0.186650
\(120\) −361.635 −0.275105
\(121\) 121.000 0.0909091
\(122\) 295.428 0.219236
\(123\) −200.965 −0.147320
\(124\) −1281.49 −0.928073
\(125\) 125.000 0.0894427
\(126\) 20.0852 0.0142011
\(127\) 2361.88 1.65026 0.825129 0.564944i \(-0.191102\pi\)
0.825129 + 0.564944i \(0.191102\pi\)
\(128\) −1454.44 −1.00434
\(129\) 1402.91 0.957515
\(130\) −144.570 −0.0975358
\(131\) −986.974 −0.658262 −0.329131 0.944284i \(-0.606756\pi\)
−0.329131 + 0.944284i \(0.606756\pi\)
\(132\) 371.939 0.245251
\(133\) −103.636 −0.0675667
\(134\) 165.732 0.106844
\(135\) −740.847 −0.472311
\(136\) 665.430 0.419560
\(137\) 2651.56 1.65356 0.826781 0.562524i \(-0.190170\pi\)
0.826781 + 0.562524i \(0.190170\pi\)
\(138\) 736.880 0.454546
\(139\) 2360.21 1.44022 0.720110 0.693860i \(-0.244092\pi\)
0.720110 + 0.693860i \(0.244092\pi\)
\(140\) 190.992 0.115298
\(141\) 186.629 0.111468
\(142\) 223.376 0.132009
\(143\) 318.546 0.186281
\(144\) −151.458 −0.0876492
\(145\) 910.786 0.521632
\(146\) −274.295 −0.155485
\(147\) −1512.44 −0.848599
\(148\) −1955.32 −1.08599
\(149\) 655.848 0.360598 0.180299 0.983612i \(-0.442293\pi\)
0.180299 + 0.983612i \(0.442293\pi\)
\(150\) 120.520 0.0656029
\(151\) −1222.79 −0.659001 −0.329501 0.944155i \(-0.606880\pi\)
−0.329501 + 0.944155i \(0.606880\pi\)
\(152\) −284.619 −0.151879
\(153\) 163.826 0.0865656
\(154\) 59.9072 0.0313472
\(155\) 914.946 0.474131
\(156\) 979.169 0.502540
\(157\) −860.979 −0.437666 −0.218833 0.975762i \(-0.570225\pi\)
−0.218833 + 0.975762i \(0.570225\pi\)
\(158\) −16.3365 −0.00822573
\(159\) 2519.61 1.25672
\(160\) 804.221 0.397370
\(161\) −833.745 −0.408126
\(162\) −614.874 −0.298204
\(163\) −1707.69 −0.820592 −0.410296 0.911952i \(-0.634575\pi\)
−0.410296 + 0.911952i \(0.634575\pi\)
\(164\) 291.487 0.138788
\(165\) −265.554 −0.125293
\(166\) −372.162 −0.174008
\(167\) −2733.85 −1.26678 −0.633389 0.773834i \(-0.718336\pi\)
−0.633389 + 0.773834i \(0.718336\pi\)
\(168\) 394.509 0.181173
\(169\) −1358.39 −0.618295
\(170\) −221.765 −0.100050
\(171\) −70.0720 −0.0313365
\(172\) −2034.84 −0.902063
\(173\) 3871.83 1.70156 0.850779 0.525523i \(-0.176130\pi\)
0.850779 + 0.525523i \(0.176130\pi\)
\(174\) 878.145 0.382598
\(175\) −136.363 −0.0589033
\(176\) −451.745 −0.193475
\(177\) 608.513 0.258410
\(178\) 488.259 0.205599
\(179\) −3334.16 −1.39222 −0.696109 0.717936i \(-0.745087\pi\)
−0.696109 + 0.717936i \(0.745087\pi\)
\(180\) 129.137 0.0534738
\(181\) 3124.85 1.28325 0.641625 0.767019i \(-0.278261\pi\)
0.641625 + 0.767019i \(0.278261\pi\)
\(182\) 157.712 0.0642330
\(183\) 1428.60 0.577077
\(184\) −2289.75 −0.917404
\(185\) 1396.04 0.554806
\(186\) 882.156 0.347757
\(187\) 488.635 0.191083
\(188\) −270.694 −0.105013
\(189\) 808.192 0.311044
\(190\) 94.8536 0.0362179
\(191\) 4957.27 1.87799 0.938994 0.343933i \(-0.111759\pi\)
0.938994 + 0.343933i \(0.111759\pi\)
\(192\) −810.885 −0.304795
\(193\) 336.139 0.125367 0.0626834 0.998033i \(-0.480034\pi\)
0.0626834 + 0.998033i \(0.480034\pi\)
\(194\) −878.932 −0.325277
\(195\) −699.099 −0.256736
\(196\) 2193.70 0.799454
\(197\) −3812.32 −1.37877 −0.689383 0.724397i \(-0.742118\pi\)
−0.689383 + 0.724397i \(0.742118\pi\)
\(198\) 40.5055 0.0145384
\(199\) −332.540 −0.118458 −0.0592290 0.998244i \(-0.518864\pi\)
−0.0592290 + 0.998244i \(0.518864\pi\)
\(200\) −374.499 −0.132405
\(201\) 801.431 0.281237
\(202\) −604.746 −0.210643
\(203\) −993.579 −0.343525
\(204\) 1502.00 0.515496
\(205\) −208.113 −0.0709037
\(206\) −223.704 −0.0756612
\(207\) −563.725 −0.189283
\(208\) −1189.27 −0.396447
\(209\) −209.000 −0.0691714
\(210\) −131.476 −0.0432033
\(211\) −2997.24 −0.977909 −0.488954 0.872309i \(-0.662622\pi\)
−0.488954 + 0.872309i \(0.662622\pi\)
\(212\) −3654.54 −1.18394
\(213\) 1080.18 0.347478
\(214\) −1584.11 −0.506017
\(215\) 1452.82 0.460843
\(216\) 2219.57 0.699179
\(217\) −998.118 −0.312243
\(218\) 665.092 0.206632
\(219\) −1326.41 −0.409271
\(220\) 385.169 0.118037
\(221\) 1286.39 0.391546
\(222\) 1346.01 0.406930
\(223\) 4352.79 1.30710 0.653552 0.756882i \(-0.273278\pi\)
0.653552 + 0.756882i \(0.273278\pi\)
\(224\) −877.327 −0.261691
\(225\) −92.1999 −0.0273185
\(226\) 2343.51 0.689771
\(227\) −886.376 −0.259167 −0.129583 0.991569i \(-0.541364\pi\)
−0.129583 + 0.991569i \(0.541364\pi\)
\(228\) −642.440 −0.186608
\(229\) 4343.89 1.25350 0.626752 0.779218i \(-0.284384\pi\)
0.626752 + 0.779218i \(0.284384\pi\)
\(230\) 763.092 0.218769
\(231\) 289.694 0.0825127
\(232\) −2728.71 −0.772191
\(233\) −3296.68 −0.926921 −0.463461 0.886117i \(-0.653392\pi\)
−0.463461 + 0.886117i \(0.653392\pi\)
\(234\) 106.635 0.0297904
\(235\) 193.268 0.0536485
\(236\) −882.611 −0.243445
\(237\) −78.9986 −0.0216519
\(238\) 241.924 0.0658890
\(239\) 6076.91 1.64470 0.822348 0.568985i \(-0.192664\pi\)
0.822348 + 0.568985i \(0.192664\pi\)
\(240\) 991.427 0.266651
\(241\) 285.570 0.0763287 0.0381643 0.999271i \(-0.487849\pi\)
0.0381643 + 0.999271i \(0.487849\pi\)
\(242\) 120.814 0.0320917
\(243\) 1027.23 0.271179
\(244\) −2072.10 −0.543657
\(245\) −1566.24 −0.408422
\(246\) −200.655 −0.0520052
\(247\) −550.215 −0.141738
\(248\) −2741.17 −0.701873
\(249\) −1799.66 −0.458028
\(250\) 124.807 0.0315740
\(251\) −4454.58 −1.12020 −0.560101 0.828424i \(-0.689238\pi\)
−0.560101 + 0.828424i \(0.689238\pi\)
\(252\) −140.876 −0.0352156
\(253\) −1681.39 −0.417819
\(254\) 2358.24 0.582555
\(255\) −1072.39 −0.263355
\(256\) −108.632 −0.0265215
\(257\) −7030.62 −1.70645 −0.853225 0.521542i \(-0.825357\pi\)
−0.853225 + 0.521542i \(0.825357\pi\)
\(258\) 1400.75 0.338011
\(259\) −1522.95 −0.365372
\(260\) 1014.00 0.241868
\(261\) −671.795 −0.159322
\(262\) −985.452 −0.232372
\(263\) −4769.61 −1.11828 −0.559138 0.829074i \(-0.688868\pi\)
−0.559138 + 0.829074i \(0.688868\pi\)
\(264\) 795.597 0.185476
\(265\) 2609.23 0.604845
\(266\) −103.476 −0.0238516
\(267\) 2361.07 0.541181
\(268\) −1162.43 −0.264950
\(269\) 5513.04 1.24958 0.624788 0.780794i \(-0.285185\pi\)
0.624788 + 0.780794i \(0.285185\pi\)
\(270\) −739.705 −0.166730
\(271\) 8440.43 1.89196 0.945978 0.324232i \(-0.105106\pi\)
0.945978 + 0.324232i \(0.105106\pi\)
\(272\) −1824.29 −0.406668
\(273\) 762.650 0.169076
\(274\) 2647.47 0.583721
\(275\) −275.000 −0.0603023
\(276\) −5168.39 −1.12718
\(277\) −1579.33 −0.342572 −0.171286 0.985221i \(-0.554792\pi\)
−0.171286 + 0.985221i \(0.554792\pi\)
\(278\) 2356.57 0.508410
\(279\) −674.864 −0.144814
\(280\) 408.542 0.0871967
\(281\) 8944.42 1.89886 0.949429 0.313980i \(-0.101663\pi\)
0.949429 + 0.313980i \(0.101663\pi\)
\(282\) 186.341 0.0393492
\(283\) 4606.18 0.967523 0.483762 0.875200i \(-0.339270\pi\)
0.483762 + 0.875200i \(0.339270\pi\)
\(284\) −1566.74 −0.327354
\(285\) 458.684 0.0953336
\(286\) 318.055 0.0657586
\(287\) 227.031 0.0466942
\(288\) −593.193 −0.121369
\(289\) −2939.74 −0.598360
\(290\) 909.382 0.184141
\(291\) −4250.25 −0.856200
\(292\) 1923.87 0.385569
\(293\) 6623.14 1.32057 0.660287 0.751014i \(-0.270435\pi\)
0.660287 + 0.751014i \(0.270435\pi\)
\(294\) −1510.11 −0.299563
\(295\) 630.159 0.124370
\(296\) −4182.53 −0.821300
\(297\) 1629.86 0.318432
\(298\) 654.837 0.127294
\(299\) −4426.45 −0.856148
\(300\) −845.316 −0.162681
\(301\) −1584.88 −0.303492
\(302\) −1220.91 −0.232633
\(303\) −2924.37 −0.554458
\(304\) 780.288 0.147212
\(305\) 1479.42 0.277742
\(306\) 163.573 0.0305584
\(307\) 6926.55 1.28768 0.643842 0.765158i \(-0.277339\pi\)
0.643842 + 0.765158i \(0.277339\pi\)
\(308\) −420.183 −0.0777342
\(309\) −1081.77 −0.199157
\(310\) 913.536 0.167372
\(311\) −3859.97 −0.703790 −0.351895 0.936039i \(-0.614463\pi\)
−0.351895 + 0.936039i \(0.614463\pi\)
\(312\) 2094.50 0.380056
\(313\) 2522.62 0.455550 0.227775 0.973714i \(-0.426855\pi\)
0.227775 + 0.973714i \(0.426855\pi\)
\(314\) −859.652 −0.154500
\(315\) 100.581 0.0179908
\(316\) 114.583 0.0203980
\(317\) −8532.28 −1.51174 −0.755869 0.654723i \(-0.772785\pi\)
−0.755869 + 0.654723i \(0.772785\pi\)
\(318\) 2515.72 0.443632
\(319\) −2003.73 −0.351684
\(320\) −839.729 −0.146695
\(321\) −7660.29 −1.33195
\(322\) −832.460 −0.144072
\(323\) −844.006 −0.145392
\(324\) 4312.66 0.739481
\(325\) −723.967 −0.123565
\(326\) −1705.06 −0.289676
\(327\) 3216.19 0.543901
\(328\) 623.505 0.104961
\(329\) −210.837 −0.0353307
\(330\) −265.145 −0.0442295
\(331\) −7224.77 −1.19973 −0.599863 0.800103i \(-0.704778\pi\)
−0.599863 + 0.800103i \(0.704778\pi\)
\(332\) 2610.30 0.431502
\(333\) −1029.72 −0.169454
\(334\) −2729.64 −0.447183
\(335\) 829.939 0.135356
\(336\) −1081.55 −0.175606
\(337\) −7562.26 −1.22238 −0.611190 0.791484i \(-0.709309\pi\)
−0.611190 + 0.791484i \(0.709309\pi\)
\(338\) −1356.30 −0.218263
\(339\) 11332.5 1.81563
\(340\) 1555.43 0.248103
\(341\) −2012.88 −0.319659
\(342\) −69.9640 −0.0110620
\(343\) 3579.52 0.563486
\(344\) −4352.62 −0.682203
\(345\) 3690.09 0.575848
\(346\) 3865.86 0.600665
\(347\) −7611.70 −1.17757 −0.588786 0.808289i \(-0.700394\pi\)
−0.588786 + 0.808289i \(0.700394\pi\)
\(348\) −6159.21 −0.948760
\(349\) 72.3720 0.0111002 0.00555012 0.999985i \(-0.498233\pi\)
0.00555012 + 0.999985i \(0.498233\pi\)
\(350\) −136.153 −0.0207934
\(351\) 4290.79 0.652494
\(352\) −1769.29 −0.267907
\(353\) −4364.92 −0.658134 −0.329067 0.944307i \(-0.606734\pi\)
−0.329067 + 0.944307i \(0.606734\pi\)
\(354\) 607.575 0.0912211
\(355\) 1118.60 0.167238
\(356\) −3424.59 −0.509840
\(357\) 1169.87 0.173435
\(358\) −3329.03 −0.491465
\(359\) 6094.21 0.895933 0.447966 0.894050i \(-0.352148\pi\)
0.447966 + 0.894050i \(0.352148\pi\)
\(360\) 276.230 0.0404406
\(361\) 361.000 0.0526316
\(362\) 3120.03 0.452998
\(363\) 584.218 0.0844725
\(364\) −1106.18 −0.159284
\(365\) −1373.59 −0.196978
\(366\) 1426.40 0.203713
\(367\) 7299.18 1.03819 0.519093 0.854718i \(-0.326270\pi\)
0.519093 + 0.854718i \(0.326270\pi\)
\(368\) 6277.37 0.889213
\(369\) 153.504 0.0216561
\(370\) 1393.89 0.195851
\(371\) −2846.42 −0.398326
\(372\) −6187.35 −0.862363
\(373\) 6056.32 0.840709 0.420355 0.907360i \(-0.361906\pi\)
0.420355 + 0.907360i \(0.361906\pi\)
\(374\) 487.882 0.0674540
\(375\) 603.531 0.0831099
\(376\) −579.029 −0.0794179
\(377\) −5275.03 −0.720631
\(378\) 806.947 0.109801
\(379\) 10524.2 1.42637 0.713185 0.700976i \(-0.247252\pi\)
0.713185 + 0.700976i \(0.247252\pi\)
\(380\) −665.293 −0.0898126
\(381\) 11403.7 1.53342
\(382\) 4949.63 0.662946
\(383\) 2558.18 0.341297 0.170649 0.985332i \(-0.445414\pi\)
0.170649 + 0.985332i \(0.445414\pi\)
\(384\) −7022.40 −0.933230
\(385\) 299.998 0.0397126
\(386\) 335.621 0.0442555
\(387\) −1071.60 −0.140755
\(388\) 6164.73 0.806616
\(389\) −4038.68 −0.526399 −0.263200 0.964741i \(-0.584778\pi\)
−0.263200 + 0.964741i \(0.584778\pi\)
\(390\) −698.022 −0.0906300
\(391\) −6789.98 −0.878220
\(392\) 4692.45 0.604603
\(393\) −4765.36 −0.611655
\(394\) −3806.45 −0.486716
\(395\) −81.8087 −0.0104209
\(396\) −284.101 −0.0360520
\(397\) 6406.47 0.809903 0.404951 0.914338i \(-0.367288\pi\)
0.404951 + 0.914338i \(0.367288\pi\)
\(398\) −332.028 −0.0418167
\(399\) −500.380 −0.0627828
\(400\) 1026.69 0.128337
\(401\) 12365.1 1.53986 0.769928 0.638130i \(-0.220292\pi\)
0.769928 + 0.638130i \(0.220292\pi\)
\(402\) 800.196 0.0992789
\(403\) −5299.13 −0.655008
\(404\) 4241.62 0.522348
\(405\) −3079.11 −0.377784
\(406\) −992.048 −0.121267
\(407\) −3071.29 −0.374050
\(408\) 3212.86 0.389854
\(409\) −8543.97 −1.03294 −0.516469 0.856306i \(-0.672754\pi\)
−0.516469 + 0.856306i \(0.672754\pi\)
\(410\) −207.792 −0.0250296
\(411\) 12802.4 1.53648
\(412\) 1569.04 0.187623
\(413\) −687.443 −0.0819052
\(414\) −562.856 −0.0668185
\(415\) −1863.68 −0.220444
\(416\) −4657.84 −0.548964
\(417\) 11395.7 1.33825
\(418\) −208.678 −0.0244181
\(419\) 5168.26 0.602593 0.301296 0.953531i \(-0.402581\pi\)
0.301296 + 0.953531i \(0.402581\pi\)
\(420\) 922.158 0.107135
\(421\) 10451.1 1.20987 0.604934 0.796276i \(-0.293199\pi\)
0.604934 + 0.796276i \(0.293199\pi\)
\(422\) −2992.62 −0.345210
\(423\) −142.554 −0.0163859
\(424\) −7817.24 −0.895375
\(425\) −1110.53 −0.126750
\(426\) 1078.52 0.122663
\(427\) −1613.90 −0.182909
\(428\) 11110.8 1.25481
\(429\) 1538.02 0.173091
\(430\) 1450.58 0.162681
\(431\) −13009.8 −1.45397 −0.726984 0.686655i \(-0.759079\pi\)
−0.726984 + 0.686655i \(0.759079\pi\)
\(432\) −6084.98 −0.677694
\(433\) 4228.27 0.469279 0.234640 0.972082i \(-0.424609\pi\)
0.234640 + 0.972082i \(0.424609\pi\)
\(434\) −996.580 −0.110224
\(435\) 4397.50 0.484699
\(436\) −4664.88 −0.512402
\(437\) 2904.22 0.317913
\(438\) −1324.36 −0.144476
\(439\) 3566.23 0.387715 0.193857 0.981030i \(-0.437900\pi\)
0.193857 + 0.981030i \(0.437900\pi\)
\(440\) 823.898 0.0892677
\(441\) 1155.26 0.124744
\(442\) 1284.40 0.138219
\(443\) −1680.04 −0.180183 −0.0900916 0.995933i \(-0.528716\pi\)
−0.0900916 + 0.995933i \(0.528716\pi\)
\(444\) −9440.77 −1.00910
\(445\) 2445.06 0.260465
\(446\) 4346.08 0.461419
\(447\) 3166.60 0.335067
\(448\) 916.064 0.0966070
\(449\) −13705.2 −1.44051 −0.720257 0.693708i \(-0.755976\pi\)
−0.720257 + 0.693708i \(0.755976\pi\)
\(450\) −92.0579 −0.00964366
\(451\) 457.849 0.0478033
\(452\) −16437.1 −1.71048
\(453\) −5903.94 −0.612342
\(454\) −885.010 −0.0914881
\(455\) 789.779 0.0813745
\(456\) −1374.21 −0.141126
\(457\) −16073.4 −1.64526 −0.822630 0.568576i \(-0.807494\pi\)
−0.822630 + 0.568576i \(0.807494\pi\)
\(458\) 4337.20 0.442498
\(459\) 6581.89 0.669316
\(460\) −5352.24 −0.542499
\(461\) −1555.96 −0.157198 −0.0785992 0.996906i \(-0.525045\pi\)
−0.0785992 + 0.996906i \(0.525045\pi\)
\(462\) 289.247 0.0291277
\(463\) −9649.31 −0.968556 −0.484278 0.874914i \(-0.660918\pi\)
−0.484278 + 0.874914i \(0.660918\pi\)
\(464\) 7480.79 0.748463
\(465\) 4417.59 0.440561
\(466\) −3291.60 −0.327211
\(467\) 13894.1 1.37675 0.688373 0.725357i \(-0.258325\pi\)
0.688373 + 0.725357i \(0.258325\pi\)
\(468\) −747.926 −0.0738737
\(469\) −905.384 −0.0891402
\(470\) 192.970 0.0189384
\(471\) −4157.02 −0.406678
\(472\) −1887.95 −0.184110
\(473\) −3196.19 −0.310700
\(474\) −78.8769 −0.00764332
\(475\) 475.000 0.0458831
\(476\) −1696.83 −0.163391
\(477\) −1924.57 −0.184738
\(478\) 6067.54 0.580592
\(479\) −17265.3 −1.64691 −0.823457 0.567379i \(-0.807957\pi\)
−0.823457 + 0.567379i \(0.807957\pi\)
\(480\) 3882.98 0.369235
\(481\) −8085.52 −0.766461
\(482\) 285.130 0.0269447
\(483\) −4025.53 −0.379229
\(484\) −847.373 −0.0795805
\(485\) −4401.44 −0.412081
\(486\) 1025.64 0.0957286
\(487\) −17531.9 −1.63130 −0.815652 0.578542i \(-0.803622\pi\)
−0.815652 + 0.578542i \(0.803622\pi\)
\(488\) −4432.32 −0.411151
\(489\) −8245.15 −0.762492
\(490\) −1563.83 −0.144177
\(491\) −5697.92 −0.523714 −0.261857 0.965107i \(-0.584335\pi\)
−0.261857 + 0.965107i \(0.584335\pi\)
\(492\) 1407.37 0.128962
\(493\) −8091.67 −0.739210
\(494\) −549.367 −0.0500348
\(495\) 202.840 0.0184181
\(496\) 7514.96 0.680306
\(497\) −1220.29 −0.110136
\(498\) −1796.89 −0.161688
\(499\) −1513.35 −0.135765 −0.0678827 0.997693i \(-0.521624\pi\)
−0.0678827 + 0.997693i \(0.521624\pi\)
\(500\) −875.385 −0.0782968
\(501\) −13199.7 −1.17709
\(502\) −4447.72 −0.395441
\(503\) −9687.94 −0.858775 −0.429388 0.903120i \(-0.641271\pi\)
−0.429388 + 0.903120i \(0.641271\pi\)
\(504\) −301.341 −0.0266325
\(505\) −3028.40 −0.266855
\(506\) −1678.80 −0.147494
\(507\) −6558.67 −0.574518
\(508\) −16540.4 −1.44461
\(509\) −10573.5 −0.920750 −0.460375 0.887725i \(-0.652285\pi\)
−0.460375 + 0.887725i \(0.652285\pi\)
\(510\) −1070.73 −0.0929665
\(511\) 1498.46 0.129722
\(512\) 11527.1 0.994978
\(513\) −2815.22 −0.242290
\(514\) −7019.78 −0.602392
\(515\) −1120.25 −0.0958524
\(516\) −9824.70 −0.838194
\(517\) −425.189 −0.0361698
\(518\) −1520.60 −0.128979
\(519\) 18694.2 1.58108
\(520\) 2169.00 0.182917
\(521\) −6922.30 −0.582095 −0.291047 0.956709i \(-0.594004\pi\)
−0.291047 + 0.956709i \(0.594004\pi\)
\(522\) −670.760 −0.0562421
\(523\) 9395.11 0.785506 0.392753 0.919644i \(-0.371523\pi\)
0.392753 + 0.919644i \(0.371523\pi\)
\(524\) 6911.85 0.576232
\(525\) −658.394 −0.0547327
\(526\) −4762.26 −0.394761
\(527\) −8128.63 −0.671895
\(528\) −2181.14 −0.179776
\(529\) 11197.3 0.920303
\(530\) 2605.21 0.213516
\(531\) −464.805 −0.0379865
\(532\) 725.770 0.0591468
\(533\) 1205.34 0.0979530
\(534\) 2357.44 0.191042
\(535\) −7932.78 −0.641054
\(536\) −2486.49 −0.200373
\(537\) −16098.2 −1.29365
\(538\) 5504.54 0.441111
\(539\) 3445.73 0.275358
\(540\) 5188.21 0.413454
\(541\) −16286.8 −1.29431 −0.647156 0.762357i \(-0.724042\pi\)
−0.647156 + 0.762357i \(0.724042\pi\)
\(542\) 8427.43 0.667876
\(543\) 15087.5 1.19239
\(544\) −7144.92 −0.563117
\(545\) 3330.59 0.261774
\(546\) 761.474 0.0596852
\(547\) 11621.3 0.908389 0.454195 0.890902i \(-0.349927\pi\)
0.454195 + 0.890902i \(0.349927\pi\)
\(548\) −18569.1 −1.44750
\(549\) −1091.22 −0.0848307
\(550\) −274.576 −0.0212872
\(551\) 3460.99 0.267592
\(552\) −11055.5 −0.852449
\(553\) 89.2454 0.00686275
\(554\) −1576.89 −0.120931
\(555\) 6740.44 0.515524
\(556\) −16528.7 −1.26075
\(557\) 1281.49 0.0974836 0.0487418 0.998811i \(-0.484479\pi\)
0.0487418 + 0.998811i \(0.484479\pi\)
\(558\) −673.824 −0.0511205
\(559\) −8414.33 −0.636651
\(560\) −1120.02 −0.0845173
\(561\) 2359.25 0.177554
\(562\) 8930.64 0.670313
\(563\) −2831.57 −0.211965 −0.105983 0.994368i \(-0.533799\pi\)
−0.105983 + 0.994368i \(0.533799\pi\)
\(564\) −1306.98 −0.0975775
\(565\) 11735.7 0.873846
\(566\) 4599.08 0.341544
\(567\) 3359.02 0.248793
\(568\) −3351.33 −0.247568
\(569\) −2659.84 −0.195969 −0.0979845 0.995188i \(-0.531240\pi\)
−0.0979845 + 0.995188i \(0.531240\pi\)
\(570\) 457.977 0.0336536
\(571\) −14305.1 −1.04843 −0.524213 0.851587i \(-0.675640\pi\)
−0.524213 + 0.851587i \(0.675640\pi\)
\(572\) −2230.80 −0.163067
\(573\) 23935.0 1.74502
\(574\) 226.682 0.0164835
\(575\) 3821.35 0.277150
\(576\) 619.384 0.0448050
\(577\) −17711.9 −1.27791 −0.638956 0.769243i \(-0.720633\pi\)
−0.638956 + 0.769243i \(0.720633\pi\)
\(578\) −2935.21 −0.211226
\(579\) 1622.96 0.116490
\(580\) −6378.30 −0.456629
\(581\) 2033.09 0.145176
\(582\) −4243.70 −0.302246
\(583\) −5740.32 −0.407787
\(584\) 4115.27 0.291594
\(585\) 533.998 0.0377403
\(586\) 6612.93 0.466174
\(587\) −1709.75 −0.120220 −0.0601098 0.998192i \(-0.519145\pi\)
−0.0601098 + 0.998192i \(0.519145\pi\)
\(588\) 10591.7 0.742851
\(589\) 3476.80 0.243224
\(590\) 629.188 0.0439038
\(591\) −18406.9 −1.28115
\(592\) 11466.5 0.796063
\(593\) −11865.0 −0.821647 −0.410823 0.911715i \(-0.634759\pi\)
−0.410823 + 0.911715i \(0.634759\pi\)
\(594\) 1627.35 0.112409
\(595\) 1211.49 0.0834724
\(596\) −4592.95 −0.315662
\(597\) −1605.59 −0.110071
\(598\) −4419.63 −0.302228
\(599\) 18384.2 1.25402 0.627009 0.779012i \(-0.284279\pi\)
0.627009 + 0.779012i \(0.284279\pi\)
\(600\) −1808.17 −0.123031
\(601\) 2605.59 0.176845 0.0884227 0.996083i \(-0.471817\pi\)
0.0884227 + 0.996083i \(0.471817\pi\)
\(602\) −1582.44 −0.107135
\(603\) −612.163 −0.0413419
\(604\) 8563.29 0.576880
\(605\) 605.000 0.0406558
\(606\) −2919.87 −0.195729
\(607\) 8719.58 0.583059 0.291530 0.956562i \(-0.405836\pi\)
0.291530 + 0.956562i \(0.405836\pi\)
\(608\) 3056.04 0.203847
\(609\) −4797.25 −0.319203
\(610\) 1477.14 0.0980452
\(611\) −1119.36 −0.0741151
\(612\) −1147.29 −0.0757782
\(613\) 11894.1 0.783682 0.391841 0.920033i \(-0.371838\pi\)
0.391841 + 0.920033i \(0.371838\pi\)
\(614\) 6915.88 0.454564
\(615\) −1004.82 −0.0658835
\(616\) −898.793 −0.0587880
\(617\) 24484.4 1.59757 0.798787 0.601614i \(-0.205475\pi\)
0.798787 + 0.601614i \(0.205475\pi\)
\(618\) −1080.10 −0.0703042
\(619\) −23343.4 −1.51575 −0.757876 0.652399i \(-0.773763\pi\)
−0.757876 + 0.652399i \(0.773763\pi\)
\(620\) −6407.44 −0.415047
\(621\) −22648.3 −1.46352
\(622\) −3854.02 −0.248444
\(623\) −2667.33 −0.171532
\(624\) −5742.09 −0.368377
\(625\) 625.000 0.0400000
\(626\) 2518.73 0.160813
\(627\) −1009.10 −0.0642739
\(628\) 6029.51 0.383127
\(629\) −12402.8 −0.786221
\(630\) 100.426 0.00635092
\(631\) −19335.8 −1.21989 −0.609943 0.792445i \(-0.708808\pi\)
−0.609943 + 0.792445i \(0.708808\pi\)
\(632\) 245.098 0.0154264
\(633\) −14471.4 −0.908670
\(634\) −8519.13 −0.533656
\(635\) 11809.4 0.738018
\(636\) −17645.0 −1.10011
\(637\) 9071.26 0.564233
\(638\) −2000.64 −0.124148
\(639\) −825.082 −0.0510794
\(640\) −7272.20 −0.449155
\(641\) −16829.4 −1.03701 −0.518504 0.855075i \(-0.673511\pi\)
−0.518504 + 0.855075i \(0.673511\pi\)
\(642\) −7648.49 −0.470190
\(643\) 3545.10 0.217426 0.108713 0.994073i \(-0.465327\pi\)
0.108713 + 0.994073i \(0.465327\pi\)
\(644\) 5838.78 0.357267
\(645\) 7014.56 0.428214
\(646\) −842.705 −0.0513248
\(647\) 22433.7 1.36315 0.681577 0.731747i \(-0.261295\pi\)
0.681577 + 0.731747i \(0.261295\pi\)
\(648\) 9225.00 0.559247
\(649\) −1386.35 −0.0838505
\(650\) −722.852 −0.0436193
\(651\) −4819.16 −0.290135
\(652\) 11959.1 0.718334
\(653\) 21081.8 1.26339 0.631696 0.775216i \(-0.282359\pi\)
0.631696 + 0.775216i \(0.282359\pi\)
\(654\) 3211.23 0.192002
\(655\) −4934.87 −0.294384
\(656\) −1709.35 −0.101736
\(657\) 1013.16 0.0601631
\(658\) −210.512 −0.0124720
\(659\) −9423.03 −0.557009 −0.278505 0.960435i \(-0.589839\pi\)
−0.278505 + 0.960435i \(0.589839\pi\)
\(660\) 1859.69 0.109680
\(661\) 1328.37 0.0781659 0.0390829 0.999236i \(-0.487556\pi\)
0.0390829 + 0.999236i \(0.487556\pi\)
\(662\) −7213.64 −0.423514
\(663\) 6210.99 0.363823
\(664\) 5583.57 0.326332
\(665\) −518.179 −0.0302167
\(666\) −1028.13 −0.0598189
\(667\) 27843.4 1.61634
\(668\) 19145.4 1.10892
\(669\) 21016.3 1.21456
\(670\) 828.660 0.0477820
\(671\) −3254.72 −0.187253
\(672\) −4235.96 −0.243163
\(673\) 14340.8 0.821390 0.410695 0.911773i \(-0.365286\pi\)
0.410695 + 0.911773i \(0.365286\pi\)
\(674\) −7550.60 −0.431511
\(675\) −3704.23 −0.211224
\(676\) 9512.94 0.541246
\(677\) 5522.39 0.313505 0.156752 0.987638i \(-0.449898\pi\)
0.156752 + 0.987638i \(0.449898\pi\)
\(678\) 11315.1 0.640933
\(679\) 4801.55 0.271379
\(680\) 3327.15 0.187633
\(681\) −4279.65 −0.240817
\(682\) −2009.78 −0.112842
\(683\) 15232.8 0.853395 0.426698 0.904394i \(-0.359677\pi\)
0.426698 + 0.904394i \(0.359677\pi\)
\(684\) 490.719 0.0274315
\(685\) 13257.8 0.739495
\(686\) 3574.00 0.198915
\(687\) 20973.4 1.16475
\(688\) 11932.8 0.661240
\(689\) −15112.0 −0.835590
\(690\) 3684.40 0.203279
\(691\) 2107.11 0.116003 0.0580015 0.998316i \(-0.481527\pi\)
0.0580015 + 0.998316i \(0.481527\pi\)
\(692\) −27114.7 −1.48952
\(693\) −221.279 −0.0121294
\(694\) −7599.97 −0.415693
\(695\) 11801.1 0.644086
\(696\) −13174.9 −0.717518
\(697\) 1848.93 0.100478
\(698\) 72.2605 0.00391848
\(699\) −15917.2 −0.861293
\(700\) 954.961 0.0515630
\(701\) −26102.8 −1.40641 −0.703203 0.710989i \(-0.748248\pi\)
−0.703203 + 0.710989i \(0.748248\pi\)
\(702\) 4284.18 0.230336
\(703\) 5304.96 0.284609
\(704\) 1847.40 0.0989015
\(705\) 933.145 0.0498500
\(706\) −4358.19 −0.232327
\(707\) 3303.69 0.175740
\(708\) −4261.46 −0.226209
\(709\) 19669.9 1.04192 0.520958 0.853582i \(-0.325575\pi\)
0.520958 + 0.853582i \(0.325575\pi\)
\(710\) 1116.88 0.0590363
\(711\) 60.3421 0.00318285
\(712\) −7325.38 −0.385576
\(713\) 27970.6 1.46916
\(714\) 1168.07 0.0612239
\(715\) 1592.73 0.0833072
\(716\) 23349.4 1.21873
\(717\) 29340.8 1.52825
\(718\) 6084.81 0.316272
\(719\) −7374.35 −0.382499 −0.191250 0.981541i \(-0.561254\pi\)
−0.191250 + 0.981541i \(0.561254\pi\)
\(720\) −757.289 −0.0391979
\(721\) 1222.08 0.0631244
\(722\) 360.444 0.0185794
\(723\) 1378.81 0.0709244
\(724\) −21883.6 −1.12334
\(725\) 4553.93 0.233281
\(726\) 583.318 0.0298195
\(727\) −1129.37 −0.0576148 −0.0288074 0.999585i \(-0.509171\pi\)
−0.0288074 + 0.999585i \(0.509171\pi\)
\(728\) −2366.17 −0.120462
\(729\) 21586.9 1.09673
\(730\) −1371.47 −0.0695350
\(731\) −12907.2 −0.653065
\(732\) −10004.6 −0.505165
\(733\) 30429.8 1.53336 0.766678 0.642032i \(-0.221908\pi\)
0.766678 + 0.642032i \(0.221908\pi\)
\(734\) 7287.93 0.366488
\(735\) −7562.20 −0.379505
\(736\) 24585.7 1.23130
\(737\) −1825.87 −0.0912573
\(738\) 153.268 0.00764480
\(739\) 16230.8 0.807928 0.403964 0.914775i \(-0.367632\pi\)
0.403964 + 0.914775i \(0.367632\pi\)
\(740\) −9776.60 −0.485669
\(741\) −2656.58 −0.131703
\(742\) −2842.04 −0.140612
\(743\) 21007.2 1.03726 0.518628 0.855000i \(-0.326443\pi\)
0.518628 + 0.855000i \(0.326443\pi\)
\(744\) −13235.1 −0.652179
\(745\) 3279.24 0.161264
\(746\) 6046.99 0.296777
\(747\) 1374.65 0.0673304
\(748\) −3421.95 −0.167271
\(749\) 8653.90 0.422172
\(750\) 602.601 0.0293385
\(751\) −14406.5 −0.699999 −0.350000 0.936750i \(-0.613818\pi\)
−0.350000 + 0.936750i \(0.613818\pi\)
\(752\) 1587.42 0.0769775
\(753\) −21507.8 −1.04089
\(754\) −5266.90 −0.254389
\(755\) −6113.95 −0.294714
\(756\) −5659.84 −0.272283
\(757\) −12943.9 −0.621474 −0.310737 0.950496i \(-0.600576\pi\)
−0.310737 + 0.950496i \(0.600576\pi\)
\(758\) 10508.0 0.503521
\(759\) −8118.19 −0.388237
\(760\) −1423.10 −0.0679225
\(761\) 24426.1 1.16353 0.581765 0.813357i \(-0.302362\pi\)
0.581765 + 0.813357i \(0.302362\pi\)
\(762\) 11386.2 0.541309
\(763\) −3633.36 −0.172394
\(764\) −34716.2 −1.64396
\(765\) 819.130 0.0387133
\(766\) 2554.24 0.120481
\(767\) −3649.72 −0.171817
\(768\) −524.502 −0.0246437
\(769\) 10766.1 0.504860 0.252430 0.967615i \(-0.418770\pi\)
0.252430 + 0.967615i \(0.418770\pi\)
\(770\) 299.536 0.0140189
\(771\) −33945.6 −1.58563
\(772\) −2354.01 −0.109744
\(773\) 4089.46 0.190282 0.0951409 0.995464i \(-0.469670\pi\)
0.0951409 + 0.995464i \(0.469670\pi\)
\(774\) −1069.94 −0.0496878
\(775\) 4574.73 0.212038
\(776\) 13186.7 0.610019
\(777\) −7353.18 −0.339503
\(778\) −4032.46 −0.185823
\(779\) −790.830 −0.0363728
\(780\) 4895.85 0.224743
\(781\) −2460.93 −0.112752
\(782\) −6779.52 −0.310019
\(783\) −26990.1 −1.23186
\(784\) −12864.4 −0.586024
\(785\) −4304.90 −0.195730
\(786\) −4758.01 −0.215919
\(787\) 8132.48 0.368350 0.184175 0.982893i \(-0.441039\pi\)
0.184175 + 0.982893i \(0.441039\pi\)
\(788\) 26698.0 1.20695
\(789\) −23028.9 −1.03910
\(790\) −81.6827 −0.00367866
\(791\) −12802.5 −0.575478
\(792\) −607.707 −0.0272650
\(793\) −8568.40 −0.383699
\(794\) 6396.59 0.285903
\(795\) 12598.0 0.562021
\(796\) 2328.81 0.103696
\(797\) 18215.1 0.809553 0.404776 0.914416i \(-0.367349\pi\)
0.404776 + 0.914416i \(0.367349\pi\)
\(798\) −499.609 −0.0221629
\(799\) −1717.04 −0.0760258
\(800\) 4021.10 0.177709
\(801\) −1803.48 −0.0795539
\(802\) 12346.0 0.543583
\(803\) 3021.90 0.132803
\(804\) −5612.48 −0.246190
\(805\) −4168.72 −0.182519
\(806\) −5290.96 −0.231224
\(807\) 26618.3 1.16110
\(808\) 9073.06 0.395036
\(809\) 26419.1 1.14814 0.574071 0.818805i \(-0.305363\pi\)
0.574071 + 0.818805i \(0.305363\pi\)
\(810\) −3074.37 −0.133361
\(811\) −23759.4 −1.02874 −0.514368 0.857569i \(-0.671974\pi\)
−0.514368 + 0.857569i \(0.671974\pi\)
\(812\) 6958.11 0.300717
\(813\) 40752.5 1.75800
\(814\) −3066.56 −0.132043
\(815\) −8538.45 −0.366980
\(816\) −8808.11 −0.377875
\(817\) 5520.70 0.236407
\(818\) −8530.80 −0.364636
\(819\) −582.540 −0.0248542
\(820\) 1457.43 0.0620680
\(821\) −17542.7 −0.745731 −0.372865 0.927885i \(-0.621625\pi\)
−0.372865 + 0.927885i \(0.621625\pi\)
\(822\) 12782.7 0.542392
\(823\) 8113.49 0.343643 0.171822 0.985128i \(-0.445035\pi\)
0.171822 + 0.985128i \(0.445035\pi\)
\(824\) 3356.25 0.141894
\(825\) −1327.77 −0.0560327
\(826\) −686.383 −0.0289132
\(827\) −29229.7 −1.22904 −0.614520 0.788901i \(-0.710650\pi\)
−0.614520 + 0.788901i \(0.710650\pi\)
\(828\) 3947.81 0.165696
\(829\) 45007.9 1.88563 0.942816 0.333312i \(-0.108166\pi\)
0.942816 + 0.333312i \(0.108166\pi\)
\(830\) −1860.81 −0.0778188
\(831\) −7625.38 −0.318317
\(832\) 4863.49 0.202658
\(833\) 13914.9 0.578779
\(834\) 11378.1 0.472413
\(835\) −13669.3 −0.566520
\(836\) 1463.64 0.0605516
\(837\) −27113.4 −1.11968
\(838\) 5160.30 0.212720
\(839\) 28183.2 1.15970 0.579852 0.814722i \(-0.303110\pi\)
0.579852 + 0.814722i \(0.303110\pi\)
\(840\) 1972.54 0.0810229
\(841\) 8792.22 0.360499
\(842\) 10435.0 0.427094
\(843\) 43185.9 1.76441
\(844\) 20989.9 0.856046
\(845\) −6791.97 −0.276510
\(846\) −142.335 −0.00578435
\(847\) −659.997 −0.0267742
\(848\) 21431.1 0.867861
\(849\) 22239.8 0.899020
\(850\) −1108.82 −0.0447439
\(851\) 42678.1 1.71914
\(852\) −7564.59 −0.304177
\(853\) −37984.9 −1.52471 −0.762356 0.647158i \(-0.775957\pi\)
−0.762356 + 0.647158i \(0.775957\pi\)
\(854\) −1611.42 −0.0645685
\(855\) −350.360 −0.0140141
\(856\) 23766.5 0.948977
\(857\) 26097.6 1.04023 0.520115 0.854096i \(-0.325889\pi\)
0.520115 + 0.854096i \(0.325889\pi\)
\(858\) 1535.65 0.0611027
\(859\) 13130.6 0.521548 0.260774 0.965400i \(-0.416022\pi\)
0.260774 + 0.965400i \(0.416022\pi\)
\(860\) −10174.2 −0.403415
\(861\) 1096.16 0.0433881
\(862\) −12989.8 −0.513263
\(863\) 6736.45 0.265714 0.132857 0.991135i \(-0.457585\pi\)
0.132857 + 0.991135i \(0.457585\pi\)
\(864\) −23832.2 −0.938411
\(865\) 19359.1 0.760960
\(866\) 4221.76 0.165660
\(867\) −14193.8 −0.555994
\(868\) 6989.90 0.273333
\(869\) 179.979 0.00702575
\(870\) 4390.72 0.171103
\(871\) −4806.79 −0.186994
\(872\) −9978.43 −0.387514
\(873\) 3246.50 0.125862
\(874\) 2899.75 0.112226
\(875\) −681.815 −0.0263423
\(876\) 9288.94 0.358270
\(877\) −10543.4 −0.405959 −0.202979 0.979183i \(-0.565062\pi\)
−0.202979 + 0.979183i \(0.565062\pi\)
\(878\) 3560.73 0.136867
\(879\) 31978.2 1.22707
\(880\) −2258.73 −0.0865246
\(881\) 44371.6 1.69684 0.848420 0.529323i \(-0.177554\pi\)
0.848420 + 0.529323i \(0.177554\pi\)
\(882\) 1153.48 0.0440359
\(883\) −6983.35 −0.266148 −0.133074 0.991106i \(-0.542485\pi\)
−0.133074 + 0.991106i \(0.542485\pi\)
\(884\) −9008.66 −0.342753
\(885\) 3042.56 0.115565
\(886\) −1677.45 −0.0636062
\(887\) 58.6566 0.00222040 0.00111020 0.999999i \(-0.499647\pi\)
0.00111020 + 0.999999i \(0.499647\pi\)
\(888\) −20194.3 −0.763150
\(889\) −12882.9 −0.486028
\(890\) 2441.29 0.0919465
\(891\) 6774.05 0.254702
\(892\) −30482.9 −1.14422
\(893\) 734.418 0.0275211
\(894\) 3161.72 0.118281
\(895\) −16670.8 −0.622619
\(896\) 7933.27 0.295795
\(897\) −21372.0 −0.795530
\(898\) −13684.1 −0.508514
\(899\) 33332.8 1.23661
\(900\) 645.684 0.0239142
\(901\) −23181.2 −0.857132
\(902\) 457.143 0.0168750
\(903\) −7652.20 −0.282004
\(904\) −35159.9 −1.29359
\(905\) 15624.2 0.573886
\(906\) −5894.84 −0.216162
\(907\) −8790.86 −0.321825 −0.160913 0.986969i \(-0.551444\pi\)
−0.160913 + 0.986969i \(0.551444\pi\)
\(908\) 6207.36 0.226871
\(909\) 2233.75 0.0815057
\(910\) 788.561 0.0287259
\(911\) 11883.6 0.432188 0.216094 0.976373i \(-0.430668\pi\)
0.216094 + 0.976373i \(0.430668\pi\)
\(912\) 3767.42 0.136789
\(913\) 4100.10 0.148624
\(914\) −16048.7 −0.580791
\(915\) 7143.00 0.258077
\(916\) −30420.6 −1.09730
\(917\) 5383.46 0.193869
\(918\) 6571.74 0.236274
\(919\) −45359.0 −1.62813 −0.814067 0.580770i \(-0.802751\pi\)
−0.814067 + 0.580770i \(0.802751\pi\)
\(920\) −11448.7 −0.410275
\(921\) 33443.1 1.19651
\(922\) −1553.57 −0.0554924
\(923\) −6478.67 −0.231038
\(924\) −2028.75 −0.0722304
\(925\) 6980.21 0.248117
\(926\) −9634.44 −0.341909
\(927\) 826.294 0.0292762
\(928\) 29298.9 1.03640
\(929\) 11907.7 0.420536 0.210268 0.977644i \(-0.432566\pi\)
0.210268 + 0.977644i \(0.432566\pi\)
\(930\) 4410.78 0.155522
\(931\) −5951.72 −0.209516
\(932\) 23086.9 0.811413
\(933\) −18636.9 −0.653960
\(934\) 13872.7 0.486003
\(935\) 2443.18 0.0854550
\(936\) −1599.85 −0.0558684
\(937\) 10362.9 0.361303 0.180651 0.983547i \(-0.442179\pi\)
0.180651 + 0.983547i \(0.442179\pi\)
\(938\) −903.988 −0.0314672
\(939\) 12179.9 0.423295
\(940\) −1353.47 −0.0469631
\(941\) −39616.2 −1.37243 −0.686213 0.727401i \(-0.740728\pi\)
−0.686213 + 0.727401i \(0.740728\pi\)
\(942\) −4150.62 −0.143561
\(943\) −6362.18 −0.219704
\(944\) 5175.84 0.178453
\(945\) 4040.96 0.139103
\(946\) −3191.27 −0.109680
\(947\) −40101.9 −1.37607 −0.688034 0.725678i \(-0.741526\pi\)
−0.688034 + 0.725678i \(0.741526\pi\)
\(948\) 553.234 0.0189538
\(949\) 7955.48 0.272124
\(950\) 474.268 0.0161971
\(951\) −41196.0 −1.40470
\(952\) −3629.60 −0.123567
\(953\) 43628.0 1.48295 0.741475 0.670981i \(-0.234127\pi\)
0.741475 + 0.670981i \(0.234127\pi\)
\(954\) −1921.60 −0.0652141
\(955\) 24786.4 0.839862
\(956\) −42557.1 −1.43974
\(957\) −9674.50 −0.326784
\(958\) −17238.7 −0.581375
\(959\) −14463.0 −0.487001
\(960\) −4054.42 −0.136308
\(961\) 3694.06 0.123999
\(962\) −8073.06 −0.270567
\(963\) 5851.22 0.195797
\(964\) −1999.87 −0.0668170
\(965\) 1680.69 0.0560657
\(966\) −4019.32 −0.133871
\(967\) 38617.4 1.28423 0.642116 0.766607i \(-0.278057\pi\)
0.642116 + 0.766607i \(0.278057\pi\)
\(968\) −1812.57 −0.0601843
\(969\) −4075.07 −0.135098
\(970\) −4394.66 −0.145468
\(971\) 18200.4 0.601521 0.300761 0.953700i \(-0.402759\pi\)
0.300761 + 0.953700i \(0.402759\pi\)
\(972\) −7193.74 −0.237386
\(973\) −12873.8 −0.424168
\(974\) −17504.9 −0.575864
\(975\) −3495.50 −0.114816
\(976\) 12151.3 0.398517
\(977\) 30881.1 1.01123 0.505617 0.862758i \(-0.331265\pi\)
0.505617 + 0.862758i \(0.331265\pi\)
\(978\) −8232.44 −0.269166
\(979\) −5379.14 −0.175606
\(980\) 10968.5 0.357527
\(981\) −2456.64 −0.0799537
\(982\) −5689.14 −0.184876
\(983\) 54916.6 1.78186 0.890929 0.454143i \(-0.150054\pi\)
0.890929 + 0.454143i \(0.150054\pi\)
\(984\) 3010.44 0.0975298
\(985\) −19061.6 −0.616603
\(986\) −8079.20 −0.260947
\(987\) −1017.97 −0.0328292
\(988\) 3853.20 0.124076
\(989\) 44413.7 1.42798
\(990\) 202.527 0.00650176
\(991\) 52780.6 1.69186 0.845929 0.533296i \(-0.179047\pi\)
0.845929 + 0.533296i \(0.179047\pi\)
\(992\) 29432.7 0.942027
\(993\) −34883.0 −1.11478
\(994\) −1218.41 −0.0388789
\(995\) −1662.70 −0.0529760
\(996\) 12603.2 0.400951
\(997\) −54096.9 −1.71842 −0.859211 0.511622i \(-0.829045\pi\)
−0.859211 + 0.511622i \(0.829045\pi\)
\(998\) −1511.02 −0.0479263
\(999\) −41370.2 −1.31020
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 1045.4.a.h.1.14 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.4.a.h.1.14 24 1.1 even 1 trivial