Properties

Label 975.4.a.l.1.2
Level $975$
Weight $4$
Character 975.1
Self dual yes
Analytic conductor $57.527$
Analytic rank $0$
Dimension $3$
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] = [975,4,Mod(1,975)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(975, 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("975.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 975.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: \(57.5268622556\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.3144.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 16x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 39)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.526440\) of defining polynomial
Character \(\chi\) \(=\) 975.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.52644 q^{2} -3.00000 q^{3} -5.66998 q^{4} +4.57932 q^{6} -4.84136 q^{7} +20.8664 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-1.52644 q^{2} -3.00000 q^{3} -5.66998 q^{4} +4.57932 q^{6} -4.84136 q^{7} +20.8664 q^{8} +9.00000 q^{9} -61.0728 q^{11} +17.0099 q^{12} -13.0000 q^{13} +7.39005 q^{14} +13.5085 q^{16} +41.7885 q^{17} -13.7380 q^{18} -107.561 q^{19} +14.5241 q^{21} +93.2239 q^{22} -28.5138 q^{23} -62.5992 q^{24} +19.8437 q^{26} -27.0000 q^{27} +27.4504 q^{28} -89.8886 q^{29} +183.108 q^{31} -187.551 q^{32} +183.218 q^{33} -63.7876 q^{34} -51.0298 q^{36} -418.029 q^{37} +164.185 q^{38} +39.0000 q^{39} -142.674 q^{41} -22.1701 q^{42} +71.0935 q^{43} +346.281 q^{44} +43.5246 q^{46} -323.711 q^{47} -40.5256 q^{48} -319.561 q^{49} -125.365 q^{51} +73.7098 q^{52} +25.1047 q^{53} +41.2139 q^{54} -101.022 q^{56} +322.683 q^{57} +137.210 q^{58} -684.508 q^{59} +308.125 q^{61} -279.503 q^{62} -43.5723 q^{63} +178.217 q^{64} -279.672 q^{66} -672.808 q^{67} -236.940 q^{68} +85.5413 q^{69} -326.837 q^{71} +187.798 q^{72} -24.3058 q^{73} +638.095 q^{74} +609.869 q^{76} +295.675 q^{77} -59.5311 q^{78} +166.810 q^{79} +81.0000 q^{81} +217.783 q^{82} +201.093 q^{83} -82.3513 q^{84} -108.520 q^{86} +269.666 q^{87} -1274.37 q^{88} +108.834 q^{89} +62.9377 q^{91} +161.673 q^{92} -549.323 q^{93} +494.126 q^{94} +562.654 q^{96} -1157.95 q^{97} +487.791 q^{98} -549.655 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{2} - 9 q^{3} + 10 q^{4} + 6 q^{6} - 30 q^{7} + 6 q^{8} + 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{2} - 9 q^{3} + 10 q^{4} + 6 q^{6} - 30 q^{7} + 6 q^{8} + 27 q^{9} - 16 q^{11} - 30 q^{12} - 39 q^{13} - 176 q^{14} - 110 q^{16} + 146 q^{17} - 18 q^{18} + 94 q^{19} + 90 q^{21} + 56 q^{22} + 48 q^{23} - 18 q^{24} + 26 q^{26} - 81 q^{27} - 80 q^{28} - 2 q^{29} + 302 q^{31} - 154 q^{32} + 48 q^{33} + 164 q^{34} + 90 q^{36} - 374 q^{37} - 312 q^{38} + 117 q^{39} + 480 q^{41} + 528 q^{42} + 260 q^{43} + 712 q^{44} - 1104 q^{46} + 24 q^{47} + 330 q^{48} + 447 q^{49} - 438 q^{51} - 130 q^{52} + 678 q^{53} + 54 q^{54} + 96 q^{56} - 282 q^{57} + 628 q^{58} - 1788 q^{59} + 230 q^{61} - 1952 q^{62} - 270 q^{63} - 750 q^{64} - 168 q^{66} - 74 q^{67} + 460 q^{68} - 144 q^{69} - 948 q^{71} + 54 q^{72} + 222 q^{73} + 1724 q^{74} + 2392 q^{76} - 112 q^{77} - 78 q^{78} - 24 q^{79} + 243 q^{81} - 564 q^{82} + 796 q^{83} + 240 q^{84} + 1800 q^{86} + 6 q^{87} - 1608 q^{88} + 1436 q^{89} + 390 q^{91} + 1296 q^{92} - 906 q^{93} - 1920 q^{94} + 462 q^{96} - 3242 q^{97} + 5070 q^{98} - 144 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.52644 −0.539678 −0.269839 0.962905i \(-0.586970\pi\)
−0.269839 + 0.962905i \(0.586970\pi\)
\(3\) −3.00000 −0.577350
\(4\) −5.66998 −0.708748
\(5\) 0 0
\(6\) 4.57932 0.311583
\(7\) −4.84136 −0.261409 −0.130704 0.991421i \(-0.541724\pi\)
−0.130704 + 0.991421i \(0.541724\pi\)
\(8\) 20.8664 0.922173
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −61.0728 −1.67401 −0.837006 0.547194i \(-0.815696\pi\)
−0.837006 + 0.547194i \(0.815696\pi\)
\(12\) 17.0099 0.409196
\(13\) −13.0000 −0.277350
\(14\) 7.39005 0.141077
\(15\) 0 0
\(16\) 13.5085 0.211071
\(17\) 41.7885 0.596188 0.298094 0.954537i \(-0.403649\pi\)
0.298094 + 0.954537i \(0.403649\pi\)
\(18\) −13.7380 −0.179893
\(19\) −107.561 −1.29875 −0.649374 0.760469i \(-0.724969\pi\)
−0.649374 + 0.760469i \(0.724969\pi\)
\(20\) 0 0
\(21\) 14.5241 0.150925
\(22\) 93.2239 0.903427
\(23\) −28.5138 −0.258502 −0.129251 0.991612i \(-0.541257\pi\)
−0.129251 + 0.991612i \(0.541257\pi\)
\(24\) −62.5992 −0.532417
\(25\) 0 0
\(26\) 19.8437 0.149680
\(27\) −27.0000 −0.192450
\(28\) 27.4504 0.185273
\(29\) −89.8886 −0.575583 −0.287791 0.957693i \(-0.592921\pi\)
−0.287791 + 0.957693i \(0.592921\pi\)
\(30\) 0 0
\(31\) 183.108 1.06087 0.530437 0.847724i \(-0.322028\pi\)
0.530437 + 0.847724i \(0.322028\pi\)
\(32\) −187.551 −1.03608
\(33\) 183.218 0.966491
\(34\) −63.7876 −0.321750
\(35\) 0 0
\(36\) −51.0298 −0.236249
\(37\) −418.029 −1.85739 −0.928696 0.370843i \(-0.879069\pi\)
−0.928696 + 0.370843i \(0.879069\pi\)
\(38\) 164.185 0.700905
\(39\) 39.0000 0.160128
\(40\) 0 0
\(41\) −142.674 −0.543460 −0.271730 0.962373i \(-0.587596\pi\)
−0.271730 + 0.962373i \(0.587596\pi\)
\(42\) −22.1701 −0.0814506
\(43\) 71.0935 0.252132 0.126066 0.992022i \(-0.459765\pi\)
0.126066 + 0.992022i \(0.459765\pi\)
\(44\) 346.281 1.18645
\(45\) 0 0
\(46\) 43.5246 0.139508
\(47\) −323.711 −1.00464 −0.502321 0.864681i \(-0.667520\pi\)
−0.502321 + 0.864681i \(0.667520\pi\)
\(48\) −40.5256 −0.121862
\(49\) −319.561 −0.931665
\(50\) 0 0
\(51\) −125.365 −0.344209
\(52\) 73.7098 0.196571
\(53\) 25.1047 0.0650641 0.0325321 0.999471i \(-0.489643\pi\)
0.0325321 + 0.999471i \(0.489643\pi\)
\(54\) 41.2139 0.103861
\(55\) 0 0
\(56\) −101.022 −0.241064
\(57\) 322.683 0.749832
\(58\) 137.210 0.310629
\(59\) −684.508 −1.51043 −0.755215 0.655477i \(-0.772467\pi\)
−0.755215 + 0.655477i \(0.772467\pi\)
\(60\) 0 0
\(61\) 308.125 0.646744 0.323372 0.946272i \(-0.395184\pi\)
0.323372 + 0.946272i \(0.395184\pi\)
\(62\) −279.503 −0.572531
\(63\) −43.5723 −0.0871363
\(64\) 178.217 0.348081
\(65\) 0 0
\(66\) −279.672 −0.521594
\(67\) −672.808 −1.22681 −0.613407 0.789767i \(-0.710202\pi\)
−0.613407 + 0.789767i \(0.710202\pi\)
\(68\) −236.940 −0.422547
\(69\) 85.5413 0.149246
\(70\) 0 0
\(71\) −326.837 −0.546315 −0.273158 0.961969i \(-0.588068\pi\)
−0.273158 + 0.961969i \(0.588068\pi\)
\(72\) 187.798 0.307391
\(73\) −24.3058 −0.0389695 −0.0194847 0.999810i \(-0.506203\pi\)
−0.0194847 + 0.999810i \(0.506203\pi\)
\(74\) 638.095 1.00239
\(75\) 0 0
\(76\) 609.869 0.920484
\(77\) 295.675 0.437602
\(78\) −59.5311 −0.0864176
\(79\) 166.810 0.237565 0.118783 0.992920i \(-0.462101\pi\)
0.118783 + 0.992920i \(0.462101\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 217.783 0.293294
\(83\) 201.093 0.265938 0.132969 0.991120i \(-0.457549\pi\)
0.132969 + 0.991120i \(0.457549\pi\)
\(84\) −82.3513 −0.106967
\(85\) 0 0
\(86\) −108.520 −0.136070
\(87\) 269.666 0.332313
\(88\) −1274.37 −1.54373
\(89\) 108.834 0.129622 0.0648109 0.997898i \(-0.479356\pi\)
0.0648109 + 0.997898i \(0.479356\pi\)
\(90\) 0 0
\(91\) 62.9377 0.0725018
\(92\) 161.673 0.183212
\(93\) −549.323 −0.612496
\(94\) 494.126 0.542183
\(95\) 0 0
\(96\) 562.654 0.598183
\(97\) −1157.95 −1.21208 −0.606041 0.795434i \(-0.707243\pi\)
−0.606041 + 0.795434i \(0.707243\pi\)
\(98\) 487.791 0.502799
\(99\) −549.655 −0.558004
\(100\) 0 0
\(101\) 1702.75 1.67752 0.838761 0.544500i \(-0.183281\pi\)
0.838761 + 0.544500i \(0.183281\pi\)
\(102\) 191.363 0.185762
\(103\) 1455.14 1.39203 0.696015 0.718027i \(-0.254955\pi\)
0.696015 + 0.718027i \(0.254955\pi\)
\(104\) −271.263 −0.255765
\(105\) 0 0
\(106\) −38.3209 −0.0351137
\(107\) 822.762 0.743359 0.371679 0.928361i \(-0.378782\pi\)
0.371679 + 0.928361i \(0.378782\pi\)
\(108\) 153.090 0.136399
\(109\) 457.264 0.401816 0.200908 0.979610i \(-0.435611\pi\)
0.200908 + 0.979610i \(0.435611\pi\)
\(110\) 0 0
\(111\) 1254.09 1.07237
\(112\) −65.3998 −0.0551759
\(113\) 381.693 0.317758 0.158879 0.987298i \(-0.449212\pi\)
0.158879 + 0.987298i \(0.449212\pi\)
\(114\) −492.556 −0.404668
\(115\) 0 0
\(116\) 509.667 0.407943
\(117\) −117.000 −0.0924500
\(118\) 1044.86 0.815146
\(119\) −202.313 −0.155849
\(120\) 0 0
\(121\) 2398.88 1.80232
\(122\) −470.334 −0.349033
\(123\) 428.021 0.313767
\(124\) −1038.22 −0.751892
\(125\) 0 0
\(126\) 66.5104 0.0470255
\(127\) 1129.09 0.788905 0.394452 0.918916i \(-0.370934\pi\)
0.394452 + 0.918916i \(0.370934\pi\)
\(128\) 1228.37 0.848232
\(129\) −213.281 −0.145568
\(130\) 0 0
\(131\) −852.761 −0.568749 −0.284374 0.958713i \(-0.591786\pi\)
−0.284374 + 0.958713i \(0.591786\pi\)
\(132\) −1038.84 −0.684999
\(133\) 520.742 0.339504
\(134\) 1027.00 0.662085
\(135\) 0 0
\(136\) 871.975 0.549789
\(137\) 488.903 0.304889 0.152445 0.988312i \(-0.451285\pi\)
0.152445 + 0.988312i \(0.451285\pi\)
\(138\) −130.574 −0.0805447
\(139\) 407.123 0.248430 0.124215 0.992255i \(-0.460359\pi\)
0.124215 + 0.992255i \(0.460359\pi\)
\(140\) 0 0
\(141\) 971.134 0.580030
\(142\) 498.897 0.294834
\(143\) 793.946 0.464287
\(144\) 121.577 0.0703570
\(145\) 0 0
\(146\) 37.1013 0.0210310
\(147\) 958.684 0.537897
\(148\) 2370.21 1.31642
\(149\) 1717.63 0.944388 0.472194 0.881495i \(-0.343462\pi\)
0.472194 + 0.881495i \(0.343462\pi\)
\(150\) 0 0
\(151\) 1341.79 0.723133 0.361567 0.932346i \(-0.382242\pi\)
0.361567 + 0.932346i \(0.382242\pi\)
\(152\) −2244.41 −1.19767
\(153\) 376.096 0.198729
\(154\) −451.331 −0.236164
\(155\) 0 0
\(156\) −221.129 −0.113490
\(157\) 760.546 0.386612 0.193306 0.981138i \(-0.438079\pi\)
0.193306 + 0.981138i \(0.438079\pi\)
\(158\) −254.626 −0.128209
\(159\) −75.3142 −0.0375648
\(160\) 0 0
\(161\) 138.046 0.0675746
\(162\) −123.642 −0.0599642
\(163\) −2712.09 −1.30323 −0.651616 0.758549i \(-0.725909\pi\)
−0.651616 + 0.758549i \(0.725909\pi\)
\(164\) 808.957 0.385176
\(165\) 0 0
\(166\) −306.957 −0.143521
\(167\) −1551.69 −0.719004 −0.359502 0.933144i \(-0.617053\pi\)
−0.359502 + 0.933144i \(0.617053\pi\)
\(168\) 303.065 0.139179
\(169\) 169.000 0.0769231
\(170\) 0 0
\(171\) −968.050 −0.432916
\(172\) −403.099 −0.178698
\(173\) 3970.26 1.74482 0.872409 0.488777i \(-0.162557\pi\)
0.872409 + 0.488777i \(0.162557\pi\)
\(174\) −411.629 −0.179342
\(175\) 0 0
\(176\) −825.004 −0.353335
\(177\) 2053.52 0.872047
\(178\) −166.128 −0.0699540
\(179\) −2690.95 −1.12364 −0.561818 0.827261i \(-0.689898\pi\)
−0.561818 + 0.827261i \(0.689898\pi\)
\(180\) 0 0
\(181\) −4371.10 −1.79503 −0.897517 0.440980i \(-0.854631\pi\)
−0.897517 + 0.440980i \(0.854631\pi\)
\(182\) −96.0706 −0.0391276
\(183\) −924.375 −0.373398
\(184\) −594.980 −0.238383
\(185\) 0 0
\(186\) 838.508 0.330551
\(187\) −2552.14 −0.998026
\(188\) 1835.44 0.712038
\(189\) 130.717 0.0503082
\(190\) 0 0
\(191\) 1408.47 0.533578 0.266789 0.963755i \(-0.414037\pi\)
0.266789 + 0.963755i \(0.414037\pi\)
\(192\) −534.652 −0.200964
\(193\) 4131.69 1.54096 0.770481 0.637463i \(-0.220016\pi\)
0.770481 + 0.637463i \(0.220016\pi\)
\(194\) 1767.54 0.654134
\(195\) 0 0
\(196\) 1811.91 0.660316
\(197\) 3401.23 1.23009 0.615045 0.788492i \(-0.289138\pi\)
0.615045 + 0.788492i \(0.289138\pi\)
\(198\) 839.015 0.301142
\(199\) −3520.74 −1.25416 −0.627081 0.778954i \(-0.715751\pi\)
−0.627081 + 0.778954i \(0.715751\pi\)
\(200\) 0 0
\(201\) 2018.42 0.708302
\(202\) −2599.14 −0.905321
\(203\) 435.183 0.150463
\(204\) 710.820 0.243958
\(205\) 0 0
\(206\) −2221.18 −0.751248
\(207\) −256.624 −0.0861672
\(208\) −175.611 −0.0585406
\(209\) 6569.05 2.17412
\(210\) 0 0
\(211\) −2245.22 −0.732545 −0.366272 0.930508i \(-0.619366\pi\)
−0.366272 + 0.930508i \(0.619366\pi\)
\(212\) −142.343 −0.0461141
\(213\) 980.510 0.315415
\(214\) −1255.90 −0.401174
\(215\) 0 0
\(216\) −563.393 −0.177472
\(217\) −886.490 −0.277322
\(218\) −697.986 −0.216851
\(219\) 72.9173 0.0224990
\(220\) 0 0
\(221\) −543.250 −0.165353
\(222\) −1914.29 −0.578732
\(223\) −3431.26 −1.03038 −0.515188 0.857077i \(-0.672278\pi\)
−0.515188 + 0.857077i \(0.672278\pi\)
\(224\) 908.003 0.270842
\(225\) 0 0
\(226\) −582.631 −0.171487
\(227\) 4757.91 1.39116 0.695581 0.718448i \(-0.255147\pi\)
0.695581 + 0.718448i \(0.255147\pi\)
\(228\) −1829.61 −0.531442
\(229\) −4368.93 −1.26073 −0.630364 0.776300i \(-0.717094\pi\)
−0.630364 + 0.776300i \(0.717094\pi\)
\(230\) 0 0
\(231\) −887.026 −0.252649
\(232\) −1875.65 −0.530787
\(233\) 3642.00 1.02401 0.512007 0.858981i \(-0.328902\pi\)
0.512007 + 0.858981i \(0.328902\pi\)
\(234\) 178.593 0.0498932
\(235\) 0 0
\(236\) 3881.15 1.07051
\(237\) −500.431 −0.137158
\(238\) 308.819 0.0841082
\(239\) 2236.17 0.605213 0.302606 0.953116i \(-0.402143\pi\)
0.302606 + 0.953116i \(0.402143\pi\)
\(240\) 0 0
\(241\) 6538.78 1.74772 0.873858 0.486181i \(-0.161610\pi\)
0.873858 + 0.486181i \(0.161610\pi\)
\(242\) −3661.75 −0.972670
\(243\) −243.000 −0.0641500
\(244\) −1747.06 −0.458378
\(245\) 0 0
\(246\) −653.348 −0.169333
\(247\) 1398.29 0.360208
\(248\) 3820.80 0.978310
\(249\) −603.280 −0.153539
\(250\) 0 0
\(251\) 2507.12 0.630470 0.315235 0.949014i \(-0.397917\pi\)
0.315235 + 0.949014i \(0.397917\pi\)
\(252\) 247.054 0.0617577
\(253\) 1741.42 0.432735
\(254\) −1723.49 −0.425755
\(255\) 0 0
\(256\) −3300.77 −0.805853
\(257\) 808.131 0.196147 0.0980735 0.995179i \(-0.468732\pi\)
0.0980735 + 0.995179i \(0.468732\pi\)
\(258\) 325.560 0.0785600
\(259\) 2023.83 0.485539
\(260\) 0 0
\(261\) −808.998 −0.191861
\(262\) 1301.69 0.306941
\(263\) −2940.70 −0.689472 −0.344736 0.938700i \(-0.612032\pi\)
−0.344736 + 0.938700i \(0.612032\pi\)
\(264\) 3823.11 0.891273
\(265\) 0 0
\(266\) −794.881 −0.183223
\(267\) −326.501 −0.0748371
\(268\) 3814.81 0.869502
\(269\) 7111.50 1.61188 0.805940 0.591997i \(-0.201660\pi\)
0.805940 + 0.591997i \(0.201660\pi\)
\(270\) 0 0
\(271\) 2034.96 0.456145 0.228072 0.973644i \(-0.426758\pi\)
0.228072 + 0.973644i \(0.426758\pi\)
\(272\) 564.502 0.125838
\(273\) −188.813 −0.0418589
\(274\) −746.281 −0.164542
\(275\) 0 0
\(276\) −485.018 −0.105778
\(277\) −2723.20 −0.590689 −0.295345 0.955391i \(-0.595434\pi\)
−0.295345 + 0.955391i \(0.595434\pi\)
\(278\) −621.449 −0.134072
\(279\) 1647.97 0.353625
\(280\) 0 0
\(281\) 3265.56 0.693263 0.346632 0.938001i \(-0.387325\pi\)
0.346632 + 0.938001i \(0.387325\pi\)
\(282\) −1482.38 −0.313030
\(283\) −1144.02 −0.240299 −0.120150 0.992756i \(-0.538337\pi\)
−0.120150 + 0.992756i \(0.538337\pi\)
\(284\) 1853.16 0.387200
\(285\) 0 0
\(286\) −1211.91 −0.250566
\(287\) 690.735 0.142065
\(288\) −1687.96 −0.345361
\(289\) −3166.72 −0.644560
\(290\) 0 0
\(291\) 3473.85 0.699796
\(292\) 137.813 0.0276195
\(293\) 1677.35 0.334444 0.167222 0.985919i \(-0.446520\pi\)
0.167222 + 0.985919i \(0.446520\pi\)
\(294\) −1463.37 −0.290291
\(295\) 0 0
\(296\) −8722.75 −1.71284
\(297\) 1648.96 0.322164
\(298\) −2621.86 −0.509666
\(299\) 370.679 0.0716954
\(300\) 0 0
\(301\) −344.190 −0.0659095
\(302\) −2048.16 −0.390259
\(303\) −5108.24 −0.968518
\(304\) −1452.99 −0.274128
\(305\) 0 0
\(306\) −574.088 −0.107250
\(307\) −7207.70 −1.33995 −0.669975 0.742383i \(-0.733695\pi\)
−0.669975 + 0.742383i \(0.733695\pi\)
\(308\) −1676.47 −0.310149
\(309\) −4365.42 −0.803689
\(310\) 0 0
\(311\) 412.963 0.0752958 0.0376479 0.999291i \(-0.488013\pi\)
0.0376479 + 0.999291i \(0.488013\pi\)
\(312\) 813.790 0.147666
\(313\) −2936.39 −0.530270 −0.265135 0.964211i \(-0.585417\pi\)
−0.265135 + 0.964211i \(0.585417\pi\)
\(314\) −1160.93 −0.208646
\(315\) 0 0
\(316\) −945.812 −0.168374
\(317\) −377.956 −0.0669657 −0.0334828 0.999439i \(-0.510660\pi\)
−0.0334828 + 0.999439i \(0.510660\pi\)
\(318\) 114.963 0.0202729
\(319\) 5489.75 0.963533
\(320\) 0 0
\(321\) −2468.28 −0.429178
\(322\) −210.718 −0.0364685
\(323\) −4494.81 −0.774298
\(324\) −459.269 −0.0787497
\(325\) 0 0
\(326\) 4139.83 0.703326
\(327\) −1371.79 −0.231989
\(328\) −2977.09 −0.501165
\(329\) 1567.20 0.262622
\(330\) 0 0
\(331\) −4428.17 −0.735330 −0.367665 0.929958i \(-0.619843\pi\)
−0.367665 + 0.929958i \(0.619843\pi\)
\(332\) −1140.20 −0.188483
\(333\) −3762.26 −0.619130
\(334\) 2368.57 0.388031
\(335\) 0 0
\(336\) 196.199 0.0318558
\(337\) 1768.76 0.285907 0.142953 0.989729i \(-0.454340\pi\)
0.142953 + 0.989729i \(0.454340\pi\)
\(338\) −257.968 −0.0415137
\(339\) −1145.08 −0.183458
\(340\) 0 0
\(341\) −11182.9 −1.77592
\(342\) 1477.67 0.233635
\(343\) 3207.70 0.504955
\(344\) 1483.47 0.232509
\(345\) 0 0
\(346\) −6060.36 −0.941639
\(347\) −2412.97 −0.373300 −0.186650 0.982426i \(-0.559763\pi\)
−0.186650 + 0.982426i \(0.559763\pi\)
\(348\) −1529.00 −0.235526
\(349\) −9967.45 −1.52878 −0.764392 0.644752i \(-0.776961\pi\)
−0.764392 + 0.644752i \(0.776961\pi\)
\(350\) 0 0
\(351\) 351.000 0.0533761
\(352\) 11454.3 1.73442
\(353\) −4516.30 −0.680959 −0.340479 0.940252i \(-0.610589\pi\)
−0.340479 + 0.940252i \(0.610589\pi\)
\(354\) −3134.58 −0.470625
\(355\) 0 0
\(356\) −617.084 −0.0918691
\(357\) 606.939 0.0899794
\(358\) 4107.57 0.606401
\(359\) 12159.8 1.78767 0.893833 0.448400i \(-0.148006\pi\)
0.893833 + 0.448400i \(0.148006\pi\)
\(360\) 0 0
\(361\) 4710.38 0.686745
\(362\) 6672.22 0.968740
\(363\) −7196.65 −1.04057
\(364\) −356.856 −0.0513855
\(365\) 0 0
\(366\) 1411.00 0.201514
\(367\) 2674.25 0.380367 0.190183 0.981749i \(-0.439092\pi\)
0.190183 + 0.981749i \(0.439092\pi\)
\(368\) −385.180 −0.0545622
\(369\) −1284.06 −0.181153
\(370\) 0 0
\(371\) −121.541 −0.0170083
\(372\) 3114.65 0.434105
\(373\) −9601.74 −1.33287 −0.666433 0.745564i \(-0.732180\pi\)
−0.666433 + 0.745564i \(0.732180\pi\)
\(374\) 3895.69 0.538613
\(375\) 0 0
\(376\) −6754.69 −0.926454
\(377\) 1168.55 0.159638
\(378\) −199.531 −0.0271502
\(379\) 9019.65 1.22245 0.611225 0.791457i \(-0.290677\pi\)
0.611225 + 0.791457i \(0.290677\pi\)
\(380\) 0 0
\(381\) −3387.28 −0.455474
\(382\) −2149.95 −0.287960
\(383\) 4015.34 0.535703 0.267852 0.963460i \(-0.413686\pi\)
0.267852 + 0.963460i \(0.413686\pi\)
\(384\) −3685.12 −0.489727
\(385\) 0 0
\(386\) −6306.78 −0.831623
\(387\) 639.842 0.0840439
\(388\) 6565.55 0.859060
\(389\) −2725.35 −0.355221 −0.177610 0.984101i \(-0.556837\pi\)
−0.177610 + 0.984101i \(0.556837\pi\)
\(390\) 0 0
\(391\) −1191.55 −0.154115
\(392\) −6668.09 −0.859157
\(393\) 2558.28 0.328367
\(394\) −5191.78 −0.663853
\(395\) 0 0
\(396\) 3116.53 0.395484
\(397\) 4391.59 0.555182 0.277591 0.960699i \(-0.410464\pi\)
0.277591 + 0.960699i \(0.410464\pi\)
\(398\) 5374.19 0.676844
\(399\) −1562.23 −0.196013
\(400\) 0 0
\(401\) 3762.48 0.468552 0.234276 0.972170i \(-0.424728\pi\)
0.234276 + 0.972170i \(0.424728\pi\)
\(402\) −3081.00 −0.382255
\(403\) −2380.40 −0.294234
\(404\) −9654.55 −1.18894
\(405\) 0 0
\(406\) −664.281 −0.0812013
\(407\) 25530.2 3.10930
\(408\) −2615.93 −0.317421
\(409\) −6797.81 −0.821833 −0.410917 0.911673i \(-0.634791\pi\)
−0.410917 + 0.911673i \(0.634791\pi\)
\(410\) 0 0
\(411\) −1466.71 −0.176028
\(412\) −8250.61 −0.986599
\(413\) 3313.95 0.394840
\(414\) 391.721 0.0465025
\(415\) 0 0
\(416\) 2438.17 0.287358
\(417\) −1221.37 −0.143431
\(418\) −10027.3 −1.17332
\(419\) −12594.2 −1.46841 −0.734207 0.678925i \(-0.762446\pi\)
−0.734207 + 0.678925i \(0.762446\pi\)
\(420\) 0 0
\(421\) 6888.04 0.797393 0.398697 0.917083i \(-0.369463\pi\)
0.398697 + 0.917083i \(0.369463\pi\)
\(422\) 3427.19 0.395338
\(423\) −2913.40 −0.334881
\(424\) 523.845 0.0600004
\(425\) 0 0
\(426\) −1496.69 −0.170223
\(427\) −1491.74 −0.169065
\(428\) −4665.04 −0.526854
\(429\) −2381.84 −0.268056
\(430\) 0 0
\(431\) −7384.53 −0.825291 −0.412645 0.910892i \(-0.635395\pi\)
−0.412645 + 0.910892i \(0.635395\pi\)
\(432\) −364.731 −0.0406206
\(433\) −9068.33 −1.00646 −0.503229 0.864153i \(-0.667855\pi\)
−0.503229 + 0.864153i \(0.667855\pi\)
\(434\) 1353.17 0.149665
\(435\) 0 0
\(436\) −2592.68 −0.284786
\(437\) 3066.97 0.335728
\(438\) −111.304 −0.0121422
\(439\) 16875.4 1.83466 0.917331 0.398125i \(-0.130339\pi\)
0.917331 + 0.398125i \(0.130339\pi\)
\(440\) 0 0
\(441\) −2876.05 −0.310555
\(442\) 829.239 0.0892373
\(443\) 6766.18 0.725668 0.362834 0.931854i \(-0.381809\pi\)
0.362834 + 0.931854i \(0.381809\pi\)
\(444\) −7110.64 −0.760037
\(445\) 0 0
\(446\) 5237.61 0.556072
\(447\) −5152.90 −0.545243
\(448\) −862.814 −0.0909914
\(449\) 140.944 0.0148141 0.00740706 0.999973i \(-0.497642\pi\)
0.00740706 + 0.999973i \(0.497642\pi\)
\(450\) 0 0
\(451\) 8713.47 0.909759
\(452\) −2164.19 −0.225210
\(453\) −4025.36 −0.417501
\(454\) −7262.67 −0.750779
\(455\) 0 0
\(456\) 6733.24 0.691475
\(457\) 17733.1 1.81514 0.907571 0.419898i \(-0.137934\pi\)
0.907571 + 0.419898i \(0.137934\pi\)
\(458\) 6668.90 0.680387
\(459\) −1128.29 −0.114736
\(460\) 0 0
\(461\) 2293.37 0.231699 0.115849 0.993267i \(-0.463041\pi\)
0.115849 + 0.993267i \(0.463041\pi\)
\(462\) 1353.99 0.136349
\(463\) −13770.9 −1.38226 −0.691129 0.722731i \(-0.742887\pi\)
−0.691129 + 0.722731i \(0.742887\pi\)
\(464\) −1214.27 −0.121489
\(465\) 0 0
\(466\) −5559.29 −0.552638
\(467\) 3477.37 0.344568 0.172284 0.985047i \(-0.444885\pi\)
0.172284 + 0.985047i \(0.444885\pi\)
\(468\) 663.388 0.0655237
\(469\) 3257.31 0.320700
\(470\) 0 0
\(471\) −2281.64 −0.223211
\(472\) −14283.2 −1.39288
\(473\) −4341.88 −0.422072
\(474\) 763.878 0.0740213
\(475\) 0 0
\(476\) 1147.11 0.110458
\(477\) 225.943 0.0216880
\(478\) −3413.38 −0.326620
\(479\) −3137.39 −0.299271 −0.149636 0.988741i \(-0.547810\pi\)
−0.149636 + 0.988741i \(0.547810\pi\)
\(480\) 0 0
\(481\) 5434.37 0.515148
\(482\) −9981.05 −0.943204
\(483\) −414.137 −0.0390142
\(484\) −13601.6 −1.27739
\(485\) 0 0
\(486\) 370.925 0.0346204
\(487\) −5996.52 −0.557964 −0.278982 0.960296i \(-0.589997\pi\)
−0.278982 + 0.960296i \(0.589997\pi\)
\(488\) 6429.46 0.596410
\(489\) 8136.26 0.752422
\(490\) 0 0
\(491\) −9401.49 −0.864121 −0.432060 0.901845i \(-0.642213\pi\)
−0.432060 + 0.901845i \(0.642213\pi\)
\(492\) −2426.87 −0.222382
\(493\) −3756.31 −0.343156
\(494\) −2134.41 −0.194396
\(495\) 0 0
\(496\) 2473.52 0.223920
\(497\) 1582.34 0.142812
\(498\) 920.871 0.0828619
\(499\) −5052.33 −0.453253 −0.226626 0.973982i \(-0.572770\pi\)
−0.226626 + 0.973982i \(0.572770\pi\)
\(500\) 0 0
\(501\) 4655.08 0.415117
\(502\) −3826.96 −0.340251
\(503\) −8184.02 −0.725462 −0.362731 0.931894i \(-0.618156\pi\)
−0.362731 + 0.931894i \(0.618156\pi\)
\(504\) −909.196 −0.0803548
\(505\) 0 0
\(506\) −2658.17 −0.233537
\(507\) −507.000 −0.0444116
\(508\) −6401.94 −0.559134
\(509\) 6039.12 0.525892 0.262946 0.964811i \(-0.415306\pi\)
0.262946 + 0.964811i \(0.415306\pi\)
\(510\) 0 0
\(511\) 117.673 0.0101870
\(512\) −4788.54 −0.413331
\(513\) 2904.15 0.249944
\(514\) −1233.56 −0.105856
\(515\) 0 0
\(516\) 1209.30 0.103171
\(517\) 19770.0 1.68178
\(518\) −3089.25 −0.262035
\(519\) −11910.8 −1.00737
\(520\) 0 0
\(521\) −14602.5 −1.22792 −0.613960 0.789337i \(-0.710424\pi\)
−0.613960 + 0.789337i \(0.710424\pi\)
\(522\) 1234.89 0.103543
\(523\) −8910.70 −0.745005 −0.372502 0.928031i \(-0.621500\pi\)
−0.372502 + 0.928031i \(0.621500\pi\)
\(524\) 4835.14 0.403099
\(525\) 0 0
\(526\) 4488.80 0.372093
\(527\) 7651.79 0.632481
\(528\) 2475.01 0.203998
\(529\) −11354.0 −0.933177
\(530\) 0 0
\(531\) −6160.57 −0.503477
\(532\) −2952.60 −0.240623
\(533\) 1854.76 0.150729
\(534\) 498.384 0.0403879
\(535\) 0 0
\(536\) −14039.1 −1.13134
\(537\) 8072.84 0.648731
\(538\) −10855.3 −0.869897
\(539\) 19516.5 1.55962
\(540\) 0 0
\(541\) −13313.6 −1.05803 −0.529017 0.848611i \(-0.677439\pi\)
−0.529017 + 0.848611i \(0.677439\pi\)
\(542\) −3106.25 −0.246171
\(543\) 13113.3 1.03636
\(544\) −7837.48 −0.617701
\(545\) 0 0
\(546\) 288.212 0.0225903
\(547\) 4116.94 0.321806 0.160903 0.986970i \(-0.448559\pi\)
0.160903 + 0.986970i \(0.448559\pi\)
\(548\) −2772.07 −0.216090
\(549\) 2773.12 0.215581
\(550\) 0 0
\(551\) 9668.52 0.747537
\(552\) 1784.94 0.137631
\(553\) −807.590 −0.0621016
\(554\) 4156.79 0.318782
\(555\) 0 0
\(556\) −2308.38 −0.176074
\(557\) 6888.37 0.524003 0.262002 0.965067i \(-0.415617\pi\)
0.262002 + 0.965067i \(0.415617\pi\)
\(558\) −2515.53 −0.190844
\(559\) −924.216 −0.0699288
\(560\) 0 0
\(561\) 7656.42 0.576211
\(562\) −4984.68 −0.374139
\(563\) −10537.1 −0.788782 −0.394391 0.918943i \(-0.629045\pi\)
−0.394391 + 0.918943i \(0.629045\pi\)
\(564\) −5506.31 −0.411095
\(565\) 0 0
\(566\) 1746.27 0.129684
\(567\) −392.150 −0.0290454
\(568\) −6819.91 −0.503798
\(569\) 26930.1 1.98413 0.992065 0.125722i \(-0.0401248\pi\)
0.992065 + 0.125722i \(0.0401248\pi\)
\(570\) 0 0
\(571\) −3125.60 −0.229076 −0.114538 0.993419i \(-0.536539\pi\)
−0.114538 + 0.993419i \(0.536539\pi\)
\(572\) −4501.66 −0.329063
\(573\) −4225.42 −0.308062
\(574\) −1054.36 −0.0766696
\(575\) 0 0
\(576\) 1603.96 0.116027
\(577\) −4787.13 −0.345391 −0.172696 0.984975i \(-0.555248\pi\)
−0.172696 + 0.984975i \(0.555248\pi\)
\(578\) 4833.81 0.347855
\(579\) −12395.1 −0.889675
\(580\) 0 0
\(581\) −973.566 −0.0695186
\(582\) −5302.62 −0.377664
\(583\) −1533.22 −0.108918
\(584\) −507.174 −0.0359366
\(585\) 0 0
\(586\) −2560.38 −0.180492
\(587\) −18380.8 −1.29243 −0.646214 0.763156i \(-0.723649\pi\)
−0.646214 + 0.763156i \(0.723649\pi\)
\(588\) −5435.72 −0.381233
\(589\) −19695.3 −1.37781
\(590\) 0 0
\(591\) −10203.7 −0.710193
\(592\) −5646.96 −0.392042
\(593\) 13831.7 0.957843 0.478922 0.877858i \(-0.341028\pi\)
0.478922 + 0.877858i \(0.341028\pi\)
\(594\) −2517.05 −0.173865
\(595\) 0 0
\(596\) −9738.94 −0.669333
\(597\) 10562.2 0.724091
\(598\) −565.819 −0.0386924
\(599\) 12248.6 0.835502 0.417751 0.908562i \(-0.362818\pi\)
0.417751 + 0.908562i \(0.362818\pi\)
\(600\) 0 0
\(601\) 9719.56 0.659682 0.329841 0.944036i \(-0.393005\pi\)
0.329841 + 0.944036i \(0.393005\pi\)
\(602\) 525.385 0.0355699
\(603\) −6055.27 −0.408938
\(604\) −7607.91 −0.512519
\(605\) 0 0
\(606\) 7797.42 0.522688
\(607\) −1607.83 −0.107512 −0.0537560 0.998554i \(-0.517119\pi\)
−0.0537560 + 0.998554i \(0.517119\pi\)
\(608\) 20173.2 1.34561
\(609\) −1305.55 −0.0868696
\(610\) 0 0
\(611\) 4208.25 0.278638
\(612\) −2132.46 −0.140849
\(613\) −14731.1 −0.970610 −0.485305 0.874345i \(-0.661291\pi\)
−0.485305 + 0.874345i \(0.661291\pi\)
\(614\) 11002.1 0.723142
\(615\) 0 0
\(616\) 6169.68 0.403545
\(617\) −27951.8 −1.82382 −0.911909 0.410392i \(-0.865392\pi\)
−0.911909 + 0.410392i \(0.865392\pi\)
\(618\) 6663.55 0.433733
\(619\) 16200.2 1.05192 0.525961 0.850509i \(-0.323706\pi\)
0.525961 + 0.850509i \(0.323706\pi\)
\(620\) 0 0
\(621\) 769.872 0.0497486
\(622\) −630.364 −0.0406355
\(623\) −526.903 −0.0338843
\(624\) 526.833 0.0337984
\(625\) 0 0
\(626\) 4482.22 0.286175
\(627\) −19707.2 −1.25523
\(628\) −4312.28 −0.274011
\(629\) −17468.8 −1.10735
\(630\) 0 0
\(631\) 12731.8 0.803239 0.401619 0.915807i \(-0.368447\pi\)
0.401619 + 0.915807i \(0.368447\pi\)
\(632\) 3480.73 0.219076
\(633\) 6735.65 0.422935
\(634\) 576.927 0.0361399
\(635\) 0 0
\(636\) 427.030 0.0266240
\(637\) 4154.30 0.258397
\(638\) −8379.77 −0.519997
\(639\) −2941.53 −0.182105
\(640\) 0 0
\(641\) −11556.9 −0.712119 −0.356059 0.934463i \(-0.615880\pi\)
−0.356059 + 0.934463i \(0.615880\pi\)
\(642\) 3767.69 0.231618
\(643\) 9181.25 0.563100 0.281550 0.959547i \(-0.409152\pi\)
0.281550 + 0.959547i \(0.409152\pi\)
\(644\) −782.716 −0.0478934
\(645\) 0 0
\(646\) 6861.06 0.417871
\(647\) −5244.11 −0.318651 −0.159326 0.987226i \(-0.550932\pi\)
−0.159326 + 0.987226i \(0.550932\pi\)
\(648\) 1690.18 0.102464
\(649\) 41804.8 2.52848
\(650\) 0 0
\(651\) 2659.47 0.160112
\(652\) 15377.5 0.923663
\(653\) 16421.4 0.984106 0.492053 0.870565i \(-0.336247\pi\)
0.492053 + 0.870565i \(0.336247\pi\)
\(654\) 2093.96 0.125199
\(655\) 0 0
\(656\) −1927.31 −0.114709
\(657\) −218.752 −0.0129898
\(658\) −2392.24 −0.141732
\(659\) 1838.11 0.108653 0.0543266 0.998523i \(-0.482699\pi\)
0.0543266 + 0.998523i \(0.482699\pi\)
\(660\) 0 0
\(661\) −5500.93 −0.323694 −0.161847 0.986816i \(-0.551745\pi\)
−0.161847 + 0.986816i \(0.551745\pi\)
\(662\) 6759.34 0.396841
\(663\) 1629.75 0.0954665
\(664\) 4196.10 0.245241
\(665\) 0 0
\(666\) 5742.86 0.334131
\(667\) 2563.07 0.148789
\(668\) 8798.08 0.509593
\(669\) 10293.8 0.594888
\(670\) 0 0
\(671\) −18818.0 −1.08266
\(672\) −2724.01 −0.156370
\(673\) 25986.7 1.48843 0.744216 0.667939i \(-0.232823\pi\)
0.744216 + 0.667939i \(0.232823\pi\)
\(674\) −2699.91 −0.154298
\(675\) 0 0
\(676\) −958.227 −0.0545191
\(677\) 11691.3 0.663714 0.331857 0.943330i \(-0.392325\pi\)
0.331857 + 0.943330i \(0.392325\pi\)
\(678\) 1747.89 0.0990080
\(679\) 5606.05 0.316849
\(680\) 0 0
\(681\) −14273.7 −0.803188
\(682\) 17070.0 0.958423
\(683\) 11111.5 0.622501 0.311251 0.950328i \(-0.399252\pi\)
0.311251 + 0.950328i \(0.399252\pi\)
\(684\) 5488.82 0.306828
\(685\) 0 0
\(686\) −4896.36 −0.272513
\(687\) 13106.8 0.727882
\(688\) 960.370 0.0532177
\(689\) −326.361 −0.0180455
\(690\) 0 0
\(691\) −7542.55 −0.415242 −0.207621 0.978209i \(-0.566572\pi\)
−0.207621 + 0.978209i \(0.566572\pi\)
\(692\) −22511.3 −1.23664
\(693\) 2661.08 0.145867
\(694\) 3683.26 0.201462
\(695\) 0 0
\(696\) 5626.96 0.306450
\(697\) −5962.11 −0.324005
\(698\) 15214.7 0.825051
\(699\) −10926.0 −0.591215
\(700\) 0 0
\(701\) −8231.17 −0.443491 −0.221745 0.975105i \(-0.571175\pi\)
−0.221745 + 0.975105i \(0.571175\pi\)
\(702\) −535.780 −0.0288059
\(703\) 44963.6 2.41228
\(704\) −10884.2 −0.582691
\(705\) 0 0
\(706\) 6893.86 0.367498
\(707\) −8243.61 −0.438519
\(708\) −11643.4 −0.618061
\(709\) 28044.6 1.48553 0.742764 0.669554i \(-0.233515\pi\)
0.742764 + 0.669554i \(0.233515\pi\)
\(710\) 0 0
\(711\) 1501.29 0.0791884
\(712\) 2270.96 0.119534
\(713\) −5221.09 −0.274238
\(714\) −926.457 −0.0485599
\(715\) 0 0
\(716\) 15257.6 0.796374
\(717\) −6708.51 −0.349420
\(718\) −18561.3 −0.964764
\(719\) 29686.4 1.53980 0.769901 0.638163i \(-0.220306\pi\)
0.769901 + 0.638163i \(0.220306\pi\)
\(720\) 0 0
\(721\) −7044.86 −0.363889
\(722\) −7190.12 −0.370621
\(723\) −19616.3 −1.00904
\(724\) 24784.0 1.27223
\(725\) 0 0
\(726\) 10985.3 0.561572
\(727\) 27654.5 1.41080 0.705398 0.708812i \(-0.250768\pi\)
0.705398 + 0.708812i \(0.250768\pi\)
\(728\) 1313.28 0.0668592
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 2970.89 0.150318
\(732\) 5241.19 0.264645
\(733\) 13077.5 0.658975 0.329488 0.944160i \(-0.393124\pi\)
0.329488 + 0.944160i \(0.393124\pi\)
\(734\) −4082.08 −0.205276
\(735\) 0 0
\(736\) 5347.79 0.267829
\(737\) 41090.3 2.05370
\(738\) 1960.04 0.0977645
\(739\) −4218.33 −0.209978 −0.104989 0.994473i \(-0.533481\pi\)
−0.104989 + 0.994473i \(0.533481\pi\)
\(740\) 0 0
\(741\) −4194.88 −0.207966
\(742\) 185.525 0.00917903
\(743\) −7725.54 −0.381457 −0.190728 0.981643i \(-0.561085\pi\)
−0.190728 + 0.981643i \(0.561085\pi\)
\(744\) −11462.4 −0.564828
\(745\) 0 0
\(746\) 14656.5 0.719319
\(747\) 1809.84 0.0886460
\(748\) 14470.6 0.707349
\(749\) −3983.29 −0.194321
\(750\) 0 0
\(751\) 7506.12 0.364717 0.182358 0.983232i \(-0.441627\pi\)
0.182358 + 0.983232i \(0.441627\pi\)
\(752\) −4372.87 −0.212051
\(753\) −7521.35 −0.364002
\(754\) −1783.72 −0.0861531
\(755\) 0 0
\(756\) −741.162 −0.0356558
\(757\) 2741.62 0.131632 0.0658162 0.997832i \(-0.479035\pi\)
0.0658162 + 0.997832i \(0.479035\pi\)
\(758\) −13768.0 −0.659729
\(759\) −5224.25 −0.249839
\(760\) 0 0
\(761\) 29740.0 1.41666 0.708328 0.705883i \(-0.249450\pi\)
0.708328 + 0.705883i \(0.249450\pi\)
\(762\) 5170.48 0.245809
\(763\) −2213.78 −0.105038
\(764\) −7986.01 −0.378172
\(765\) 0 0
\(766\) −6129.18 −0.289107
\(767\) 8898.60 0.418918
\(768\) 9902.32 0.465259
\(769\) −19896.3 −0.933004 −0.466502 0.884520i \(-0.654486\pi\)
−0.466502 + 0.884520i \(0.654486\pi\)
\(770\) 0 0
\(771\) −2424.39 −0.113246
\(772\) −23426.6 −1.09215
\(773\) 13601.3 0.632866 0.316433 0.948615i \(-0.397515\pi\)
0.316433 + 0.948615i \(0.397515\pi\)
\(774\) −976.680 −0.0453566
\(775\) 0 0
\(776\) −24162.2 −1.11775
\(777\) −6071.48 −0.280326
\(778\) 4160.09 0.191705
\(779\) 15346.1 0.705818
\(780\) 0 0
\(781\) 19960.8 0.914539
\(782\) 1818.83 0.0831727
\(783\) 2426.99 0.110771
\(784\) −4316.81 −0.196648
\(785\) 0 0
\(786\) −3905.06 −0.177212
\(787\) 1498.29 0.0678631 0.0339315 0.999424i \(-0.489197\pi\)
0.0339315 + 0.999424i \(0.489197\pi\)
\(788\) −19284.9 −0.871824
\(789\) 8822.09 0.398067
\(790\) 0 0
\(791\) −1847.91 −0.0830647
\(792\) −11469.3 −0.514577
\(793\) −4005.62 −0.179374
\(794\) −6703.49 −0.299620
\(795\) 0 0
\(796\) 19962.5 0.888885
\(797\) 3713.30 0.165034 0.0825168 0.996590i \(-0.473704\pi\)
0.0825168 + 0.996590i \(0.473704\pi\)
\(798\) 2384.64 0.105784
\(799\) −13527.4 −0.598955
\(800\) 0 0
\(801\) 979.502 0.0432072
\(802\) −5743.20 −0.252867
\(803\) 1484.42 0.0652354
\(804\) −11444.4 −0.502007
\(805\) 0 0
\(806\) 3633.54 0.158791
\(807\) −21334.5 −0.930620
\(808\) 35530.2 1.54697
\(809\) −34527.6 −1.50053 −0.750263 0.661139i \(-0.770073\pi\)
−0.750263 + 0.661139i \(0.770073\pi\)
\(810\) 0 0
\(811\) −37279.2 −1.61412 −0.807059 0.590471i \(-0.798942\pi\)
−0.807059 + 0.590471i \(0.798942\pi\)
\(812\) −2467.48 −0.106640
\(813\) −6104.89 −0.263355
\(814\) −38970.3 −1.67802
\(815\) 0 0
\(816\) −1693.51 −0.0726526
\(817\) −7646.90 −0.327455
\(818\) 10376.4 0.443525
\(819\) 566.439 0.0241673
\(820\) 0 0
\(821\) 13877.9 0.589943 0.294972 0.955506i \(-0.404690\pi\)
0.294972 + 0.955506i \(0.404690\pi\)
\(822\) 2238.84 0.0949983
\(823\) −18945.1 −0.802410 −0.401205 0.915988i \(-0.631408\pi\)
−0.401205 + 0.915988i \(0.631408\pi\)
\(824\) 30363.5 1.28369
\(825\) 0 0
\(826\) −5058.55 −0.213086
\(827\) 7804.75 0.328171 0.164086 0.986446i \(-0.447533\pi\)
0.164086 + 0.986446i \(0.447533\pi\)
\(828\) 1455.05 0.0610708
\(829\) 5784.85 0.242360 0.121180 0.992631i \(-0.461332\pi\)
0.121180 + 0.992631i \(0.461332\pi\)
\(830\) 0 0
\(831\) 8169.59 0.341035
\(832\) −2316.82 −0.0965402
\(833\) −13354.0 −0.555448
\(834\) 1864.35 0.0774065
\(835\) 0 0
\(836\) −37246.4 −1.54090
\(837\) −4943.91 −0.204165
\(838\) 19224.3 0.792471
\(839\) −5011.42 −0.206214 −0.103107 0.994670i \(-0.532878\pi\)
−0.103107 + 0.994670i \(0.532878\pi\)
\(840\) 0 0
\(841\) −16309.0 −0.668704
\(842\) −10514.2 −0.430336
\(843\) −9796.68 −0.400256
\(844\) 12730.3 0.519190
\(845\) 0 0
\(846\) 4447.13 0.180728
\(847\) −11613.9 −0.471142
\(848\) 339.128 0.0137332
\(849\) 3432.05 0.138737
\(850\) 0 0
\(851\) 11919.6 0.480138
\(852\) −5559.48 −0.223550
\(853\) 22059.0 0.885446 0.442723 0.896659i \(-0.354013\pi\)
0.442723 + 0.896659i \(0.354013\pi\)
\(854\) 2277.06 0.0912404
\(855\) 0 0
\(856\) 17168.1 0.685506
\(857\) −13956.2 −0.556283 −0.278141 0.960540i \(-0.589718\pi\)
−0.278141 + 0.960540i \(0.589718\pi\)
\(858\) 3635.73 0.144664
\(859\) 12498.5 0.496442 0.248221 0.968703i \(-0.420154\pi\)
0.248221 + 0.968703i \(0.420154\pi\)
\(860\) 0 0
\(861\) −2072.20 −0.0820215
\(862\) 11272.0 0.445391
\(863\) 38631.2 1.52378 0.761890 0.647707i \(-0.224272\pi\)
0.761890 + 0.647707i \(0.224272\pi\)
\(864\) 5063.88 0.199394
\(865\) 0 0
\(866\) 13842.3 0.543163
\(867\) 9500.17 0.372137
\(868\) 5026.38 0.196551
\(869\) −10187.6 −0.397687
\(870\) 0 0
\(871\) 8746.51 0.340257
\(872\) 9541.46 0.370544
\(873\) −10421.5 −0.404027
\(874\) −4681.55 −0.181185
\(875\) 0 0
\(876\) −413.440 −0.0159462
\(877\) 856.756 0.0329881 0.0164941 0.999864i \(-0.494750\pi\)
0.0164941 + 0.999864i \(0.494750\pi\)
\(878\) −25759.2 −0.990127
\(879\) −5032.06 −0.193091
\(880\) 0 0
\(881\) 33638.6 1.28640 0.643198 0.765700i \(-0.277607\pi\)
0.643198 + 0.765700i \(0.277607\pi\)
\(882\) 4390.12 0.167600
\(883\) 31109.1 1.18562 0.592811 0.805342i \(-0.298018\pi\)
0.592811 + 0.805342i \(0.298018\pi\)
\(884\) 3080.22 0.117193
\(885\) 0 0
\(886\) −10328.2 −0.391627
\(887\) −26080.3 −0.987248 −0.493624 0.869675i \(-0.664328\pi\)
−0.493624 + 0.869675i \(0.664328\pi\)
\(888\) 26168.3 0.988907
\(889\) −5466.35 −0.206227
\(890\) 0 0
\(891\) −4946.89 −0.186001
\(892\) 19455.2 0.730277
\(893\) 34818.8 1.30478
\(894\) 7865.58 0.294256
\(895\) 0 0
\(896\) −5946.99 −0.221736
\(897\) −1112.04 −0.0413934
\(898\) −215.142 −0.00799486
\(899\) −16459.3 −0.610621
\(900\) 0 0
\(901\) 1049.09 0.0387905
\(902\) −13300.6 −0.490977
\(903\) 1032.57 0.0380529
\(904\) 7964.56 0.293028
\(905\) 0 0
\(906\) 6144.47 0.225316
\(907\) −20169.0 −0.738369 −0.369184 0.929356i \(-0.620363\pi\)
−0.369184 + 0.929356i \(0.620363\pi\)
\(908\) −26977.3 −0.985983
\(909\) 15324.7 0.559174
\(910\) 0 0
\(911\) 19982.2 0.726716 0.363358 0.931650i \(-0.381630\pi\)
0.363358 + 0.931650i \(0.381630\pi\)
\(912\) 4358.98 0.158268
\(913\) −12281.3 −0.445184
\(914\) −27068.5 −0.979593
\(915\) 0 0
\(916\) 24771.7 0.893538
\(917\) 4128.52 0.148676
\(918\) 1722.27 0.0619207
\(919\) 38513.1 1.38241 0.691203 0.722661i \(-0.257081\pi\)
0.691203 + 0.722661i \(0.257081\pi\)
\(920\) 0 0
\(921\) 21623.1 0.773621
\(922\) −3500.70 −0.125043
\(923\) 4248.88 0.151521
\(924\) 5029.42 0.179065
\(925\) 0 0
\(926\) 21020.4 0.745975
\(927\) 13096.3 0.464010
\(928\) 16858.7 0.596352
\(929\) 23218.9 0.820009 0.410005 0.912083i \(-0.365527\pi\)
0.410005 + 0.912083i \(0.365527\pi\)
\(930\) 0 0
\(931\) 34372.3 1.21000
\(932\) −20650.1 −0.725768
\(933\) −1238.89 −0.0434721
\(934\) −5307.99 −0.185956
\(935\) 0 0
\(936\) −2441.37 −0.0852550
\(937\) 11112.9 0.387452 0.193726 0.981056i \(-0.437943\pi\)
0.193726 + 0.981056i \(0.437943\pi\)
\(938\) −4972.08 −0.173075
\(939\) 8809.17 0.306152
\(940\) 0 0
\(941\) 45570.4 1.57869 0.789347 0.613947i \(-0.210419\pi\)
0.789347 + 0.613947i \(0.210419\pi\)
\(942\) 3482.78 0.120462
\(943\) 4068.16 0.140485
\(944\) −9246.71 −0.318808
\(945\) 0 0
\(946\) 6627.62 0.227783
\(947\) −34903.9 −1.19770 −0.598852 0.800860i \(-0.704376\pi\)
−0.598852 + 0.800860i \(0.704376\pi\)
\(948\) 2837.44 0.0972106
\(949\) 315.975 0.0108082
\(950\) 0 0
\(951\) 1133.87 0.0386626
\(952\) −4221.55 −0.143720
\(953\) 2886.52 0.0981151 0.0490575 0.998796i \(-0.484378\pi\)
0.0490575 + 0.998796i \(0.484378\pi\)
\(954\) −344.888 −0.0117046
\(955\) 0 0
\(956\) −12679.0 −0.428943
\(957\) −16469.2 −0.556296
\(958\) 4789.03 0.161510
\(959\) −2366.96 −0.0797008
\(960\) 0 0
\(961\) 3737.42 0.125455
\(962\) −8295.24 −0.278014
\(963\) 7404.85 0.247786
\(964\) −37074.8 −1.23869
\(965\) 0 0
\(966\) 632.155 0.0210551
\(967\) −11593.8 −0.385556 −0.192778 0.981242i \(-0.561750\pi\)
−0.192778 + 0.981242i \(0.561750\pi\)
\(968\) 50056.1 1.66205
\(969\) 13484.4 0.447041
\(970\) 0 0
\(971\) −4952.12 −0.163667 −0.0818337 0.996646i \(-0.526078\pi\)
−0.0818337 + 0.996646i \(0.526078\pi\)
\(972\) 1377.81 0.0454662
\(973\) −1971.03 −0.0649418
\(974\) 9153.33 0.301121
\(975\) 0 0
\(976\) 4162.32 0.136509
\(977\) 19650.1 0.643462 0.321731 0.946831i \(-0.395735\pi\)
0.321731 + 0.946831i \(0.395735\pi\)
\(978\) −12419.5 −0.406065
\(979\) −6646.77 −0.216988
\(980\) 0 0
\(981\) 4115.38 0.133939
\(982\) 14350.8 0.466347
\(983\) −56818.4 −1.84357 −0.921783 0.387707i \(-0.873267\pi\)
−0.921783 + 0.387707i \(0.873267\pi\)
\(984\) 8931.26 0.289348
\(985\) 0 0
\(986\) 5733.78 0.185193
\(987\) −4701.61 −0.151625
\(988\) −7928.30 −0.255296
\(989\) −2027.15 −0.0651764
\(990\) 0 0
\(991\) −19120.4 −0.612897 −0.306448 0.951887i \(-0.599141\pi\)
−0.306448 + 0.951887i \(0.599141\pi\)
\(992\) −34342.1 −1.09915
\(993\) 13284.5 0.424543
\(994\) −2415.34 −0.0770723
\(995\) 0 0
\(996\) 3420.59 0.108821
\(997\) −38887.9 −1.23530 −0.617650 0.786453i \(-0.711915\pi\)
−0.617650 + 0.786453i \(0.711915\pi\)
\(998\) 7712.07 0.244611
\(999\) 11286.8 0.357455
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 975.4.a.l.1.2 3
5.4 even 2 39.4.a.c.1.2 3
15.14 odd 2 117.4.a.f.1.2 3
20.19 odd 2 624.4.a.t.1.3 3
35.34 odd 2 1911.4.a.k.1.2 3
40.19 odd 2 2496.4.a.bp.1.1 3
40.29 even 2 2496.4.a.bl.1.1 3
60.59 even 2 1872.4.a.bk.1.1 3
65.34 odd 4 507.4.b.g.337.4 6
65.44 odd 4 507.4.b.g.337.3 6
65.64 even 2 507.4.a.h.1.2 3
195.194 odd 2 1521.4.a.u.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.a.c.1.2 3 5.4 even 2
117.4.a.f.1.2 3 15.14 odd 2
507.4.a.h.1.2 3 65.64 even 2
507.4.b.g.337.3 6 65.44 odd 4
507.4.b.g.337.4 6 65.34 odd 4
624.4.a.t.1.3 3 20.19 odd 2
975.4.a.l.1.2 3 1.1 even 1 trivial
1521.4.a.u.1.2 3 195.194 odd 2
1872.4.a.bk.1.1 3 60.59 even 2
1911.4.a.k.1.2 3 35.34 odd 2
2496.4.a.bl.1.1 3 40.29 even 2
2496.4.a.bp.1.1 3 40.19 odd 2