Properties

Label 1150.3.c.c.1149.7
Level $1150$
Weight $3$
Character 1150.1149
Analytic conductor $31.335$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1150,3,Mod(1149,1150)]
 
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([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1150.1149");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1150.c (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(31.3352304014\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 230)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1149.7
Character \(\chi\) \(=\) 1150.1149
Dual form 1150.3.c.c.1149.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} +0.278523i q^{3} -2.00000 q^{4} +0.393890 q^{6} +8.51262 q^{7} +2.82843i q^{8} +8.92243 q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +0.278523i q^{3} -2.00000 q^{4} +0.393890 q^{6} +8.51262 q^{7} +2.82843i q^{8} +8.92243 q^{9} +7.57553i q^{11} -0.557045i q^{12} +2.64076i q^{13} -12.0387i q^{14} +4.00000 q^{16} +7.56057 q^{17} -12.6182i q^{18} +24.2676i q^{19} +2.37096i q^{21} +10.7134 q^{22} +(-16.7738 + 15.7366i) q^{23} -0.787781 q^{24} +3.73460 q^{26} +4.99180i q^{27} -17.0252 q^{28} +31.8513 q^{29} -56.5071 q^{31} -5.65685i q^{32} -2.10995 q^{33} -10.6923i q^{34} -17.8449 q^{36} +39.9378 q^{37} +34.3195 q^{38} -0.735511 q^{39} -42.5710 q^{41} +3.35304 q^{42} -20.5721 q^{43} -15.1511i q^{44} +(22.2549 + 23.7217i) q^{46} +84.3049i q^{47} +1.11409i q^{48} +23.4647 q^{49} +2.10579i q^{51} -5.28152i q^{52} -11.9189 q^{53} +7.05947 q^{54} +24.0773i q^{56} -6.75907 q^{57} -45.0446i q^{58} -67.6561 q^{59} +35.1621i q^{61} +79.9131i q^{62} +75.9532 q^{63} -8.00000 q^{64} +2.98393i q^{66} +44.0660 q^{67} -15.1211 q^{68} +(-4.38299 - 4.67188i) q^{69} +8.86597 q^{71} +25.2364i q^{72} +87.4150i q^{73} -56.4805i q^{74} -48.5352i q^{76} +64.4876i q^{77} +1.04017i q^{78} -154.217i q^{79} +78.9115 q^{81} +60.2046i q^{82} +141.642 q^{83} -4.74191i q^{84} +29.0933i q^{86} +8.87131i q^{87} -21.4268 q^{88} -63.7252i q^{89} +22.4798i q^{91} +(33.5476 - 31.4732i) q^{92} -15.7385i q^{93} +119.225 q^{94} +1.57556 q^{96} +143.322 q^{97} -33.1841i q^{98} +67.5921i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 64 q^{4} - 16 q^{6} - 128 q^{9} + 128 q^{16} + 32 q^{24} + 192 q^{26} + 216 q^{29} - 232 q^{31} + 256 q^{36} - 496 q^{39} - 312 q^{41} - 248 q^{46} + 56 q^{49} - 448 q^{54} - 408 q^{59} - 256 q^{64} + 536 q^{69} + 472 q^{71} - 272 q^{81} + 432 q^{94} - 64 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(277\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) 0.278523i 0.0928408i 0.998922 + 0.0464204i \(0.0147814\pi\)
−0.998922 + 0.0464204i \(0.985219\pi\)
\(4\) −2.00000 −0.500000
\(5\) 0 0
\(6\) 0.393890 0.0656484
\(7\) 8.51262 1.21609 0.608044 0.793903i \(-0.291954\pi\)
0.608044 + 0.793903i \(0.291954\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 8.92243 0.991381
\(10\) 0 0
\(11\) 7.57553i 0.688684i 0.938844 + 0.344342i \(0.111898\pi\)
−0.938844 + 0.344342i \(0.888102\pi\)
\(12\) 0.557045i 0.0464204i
\(13\) 2.64076i 0.203135i 0.994829 + 0.101568i \(0.0323858\pi\)
−0.994829 + 0.101568i \(0.967614\pi\)
\(14\) 12.0387i 0.859904i
\(15\) 0 0
\(16\) 4.00000 0.250000
\(17\) 7.56057 0.444739 0.222370 0.974962i \(-0.428621\pi\)
0.222370 + 0.974962i \(0.428621\pi\)
\(18\) 12.6182i 0.701012i
\(19\) 24.2676i 1.27724i 0.769522 + 0.638620i \(0.220495\pi\)
−0.769522 + 0.638620i \(0.779505\pi\)
\(20\) 0 0
\(21\) 2.37096i 0.112903i
\(22\) 10.7134 0.486973
\(23\) −16.7738 + 15.7366i −0.729295 + 0.684199i
\(24\) −0.787781 −0.0328242
\(25\) 0 0
\(26\) 3.73460 0.143638
\(27\) 4.99180i 0.184881i
\(28\) −17.0252 −0.608044
\(29\) 31.8513 1.09832 0.549161 0.835717i \(-0.314947\pi\)
0.549161 + 0.835717i \(0.314947\pi\)
\(30\) 0 0
\(31\) −56.5071 −1.82281 −0.911405 0.411511i \(-0.865001\pi\)
−0.911405 + 0.411511i \(0.865001\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −2.10995 −0.0639380
\(34\) 10.6923i 0.314478i
\(35\) 0 0
\(36\) −17.8449 −0.495690
\(37\) 39.9378 1.07940 0.539700 0.841858i \(-0.318538\pi\)
0.539700 + 0.841858i \(0.318538\pi\)
\(38\) 34.3195 0.903146
\(39\) −0.735511 −0.0188593
\(40\) 0 0
\(41\) −42.5710 −1.03832 −0.519159 0.854678i \(-0.673755\pi\)
−0.519159 + 0.854678i \(0.673755\pi\)
\(42\) 3.35304 0.0798342
\(43\) −20.5721 −0.478420 −0.239210 0.970968i \(-0.576888\pi\)
−0.239210 + 0.970968i \(0.576888\pi\)
\(44\) 15.1511i 0.344342i
\(45\) 0 0
\(46\) 22.2549 + 23.7217i 0.483802 + 0.515690i
\(47\) 84.3049i 1.79372i 0.442314 + 0.896860i \(0.354158\pi\)
−0.442314 + 0.896860i \(0.645842\pi\)
\(48\) 1.11409i 0.0232102i
\(49\) 23.4647 0.478871
\(50\) 0 0
\(51\) 2.10579i 0.0412900i
\(52\) 5.28152i 0.101568i
\(53\) −11.9189 −0.224885 −0.112443 0.993658i \(-0.535867\pi\)
−0.112443 + 0.993658i \(0.535867\pi\)
\(54\) 7.05947 0.130731
\(55\) 0 0
\(56\) 24.0773i 0.429952i
\(57\) −6.75907 −0.118580
\(58\) 45.0446i 0.776631i
\(59\) −67.6561 −1.14671 −0.573357 0.819306i \(-0.694359\pi\)
−0.573357 + 0.819306i \(0.694359\pi\)
\(60\) 0 0
\(61\) 35.1621i 0.576428i 0.957566 + 0.288214i \(0.0930614\pi\)
−0.957566 + 0.288214i \(0.906939\pi\)
\(62\) 79.9131i 1.28892i
\(63\) 75.9532 1.20561
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) 2.98393i 0.0452110i
\(67\) 44.0660 0.657701 0.328850 0.944382i \(-0.393339\pi\)
0.328850 + 0.944382i \(0.393339\pi\)
\(68\) −15.1211 −0.222370
\(69\) −4.38299 4.67188i −0.0635216 0.0677084i
\(70\) 0 0
\(71\) 8.86597 0.124873 0.0624364 0.998049i \(-0.480113\pi\)
0.0624364 + 0.998049i \(0.480113\pi\)
\(72\) 25.2364i 0.350506i
\(73\) 87.4150i 1.19747i 0.800949 + 0.598733i \(0.204329\pi\)
−0.800949 + 0.598733i \(0.795671\pi\)
\(74\) 56.4805i 0.763250i
\(75\) 0 0
\(76\) 48.5352i 0.638620i
\(77\) 64.4876i 0.837501i
\(78\) 1.04017i 0.0133355i
\(79\) 154.217i 1.95211i −0.217517 0.976057i \(-0.569796\pi\)
0.217517 0.976057i \(-0.430204\pi\)
\(80\) 0 0
\(81\) 78.9115 0.974216
\(82\) 60.2046i 0.734202i
\(83\) 141.642 1.70653 0.853266 0.521476i \(-0.174618\pi\)
0.853266 + 0.521476i \(0.174618\pi\)
\(84\) 4.74191i 0.0564513i
\(85\) 0 0
\(86\) 29.0933i 0.338294i
\(87\) 8.87131i 0.101969i
\(88\) −21.4268 −0.243487
\(89\) 63.7252i 0.716013i −0.933719 0.358007i \(-0.883457\pi\)
0.933719 0.358007i \(-0.116543\pi\)
\(90\) 0 0
\(91\) 22.4798i 0.247030i
\(92\) 33.5476 31.4732i 0.364648 0.342100i
\(93\) 15.7385i 0.169231i
\(94\) 119.225 1.26835
\(95\) 0 0
\(96\) 1.57556 0.0164121
\(97\) 143.322 1.47755 0.738775 0.673952i \(-0.235404\pi\)
0.738775 + 0.673952i \(0.235404\pi\)
\(98\) 33.1841i 0.338613i
\(99\) 67.5921i 0.682748i
\(100\) 0 0
\(101\) 27.7102 0.274359 0.137179 0.990546i \(-0.456196\pi\)
0.137179 + 0.990546i \(0.456196\pi\)
\(102\) 2.97803 0.0291964
\(103\) 133.542 1.29652 0.648261 0.761418i \(-0.275497\pi\)
0.648261 + 0.761418i \(0.275497\pi\)
\(104\) −7.46919 −0.0718192
\(105\) 0 0
\(106\) 16.8559i 0.159018i
\(107\) 50.3091 0.470179 0.235089 0.971974i \(-0.424462\pi\)
0.235089 + 0.971974i \(0.424462\pi\)
\(108\) 9.98360i 0.0924407i
\(109\) 128.819i 1.18182i 0.806737 + 0.590911i \(0.201232\pi\)
−0.806737 + 0.590911i \(0.798768\pi\)
\(110\) 0 0
\(111\) 11.1236i 0.100212i
\(112\) 34.0505 0.304022
\(113\) −86.3028 −0.763742 −0.381871 0.924216i \(-0.624720\pi\)
−0.381871 + 0.924216i \(0.624720\pi\)
\(114\) 9.55876i 0.0838488i
\(115\) 0 0
\(116\) −63.7027 −0.549161
\(117\) 23.5620i 0.201384i
\(118\) 95.6802i 0.810849i
\(119\) 64.3602 0.540842
\(120\) 0 0
\(121\) 63.6114 0.525714
\(122\) 49.7267 0.407596
\(123\) 11.8570i 0.0963983i
\(124\) 113.014 0.911405
\(125\) 0 0
\(126\) 107.414i 0.852492i
\(127\) 11.0135i 0.0867206i −0.999059 0.0433603i \(-0.986194\pi\)
0.999059 0.0433603i \(-0.0138063\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) 5.72978i 0.0444169i
\(130\) 0 0
\(131\) 3.63941 0.0277818 0.0138909 0.999904i \(-0.495578\pi\)
0.0138909 + 0.999904i \(0.495578\pi\)
\(132\) 4.21991 0.0319690
\(133\) 206.581i 1.55324i
\(134\) 62.3187i 0.465065i
\(135\) 0 0
\(136\) 21.3845i 0.157239i
\(137\) −9.69785 −0.0707873 −0.0353936 0.999373i \(-0.511268\pi\)
−0.0353936 + 0.999373i \(0.511268\pi\)
\(138\) −6.60703 + 6.19849i −0.0478771 + 0.0449166i
\(139\) −8.05485 −0.0579486 −0.0289743 0.999580i \(-0.509224\pi\)
−0.0289743 + 0.999580i \(0.509224\pi\)
\(140\) 0 0
\(141\) −23.4808 −0.166531
\(142\) 12.5384i 0.0882984i
\(143\) −20.0051 −0.139896
\(144\) 35.6897 0.247845
\(145\) 0 0
\(146\) 123.624 0.846737
\(147\) 6.53544i 0.0444588i
\(148\) −79.8755 −0.539700
\(149\) 144.062i 0.966859i −0.875383 0.483430i \(-0.839391\pi\)
0.875383 0.483430i \(-0.160609\pi\)
\(150\) 0 0
\(151\) −109.956 −0.728188 −0.364094 0.931362i \(-0.618621\pi\)
−0.364094 + 0.931362i \(0.618621\pi\)
\(152\) −68.6391 −0.451573
\(153\) 67.4586 0.440906
\(154\) 91.1992 0.592202
\(155\) 0 0
\(156\) 1.47102 0.00942963
\(157\) 24.8208 0.158094 0.0790471 0.996871i \(-0.474812\pi\)
0.0790471 + 0.996871i \(0.474812\pi\)
\(158\) −218.096 −1.38035
\(159\) 3.31969i 0.0208785i
\(160\) 0 0
\(161\) −142.789 + 133.960i −0.886887 + 0.832047i
\(162\) 111.598i 0.688875i
\(163\) 108.964i 0.668489i −0.942486 0.334244i \(-0.891519\pi\)
0.942486 0.334244i \(-0.108481\pi\)
\(164\) 85.1421 0.519159
\(165\) 0 0
\(166\) 200.312i 1.20670i
\(167\) 72.1383i 0.431966i 0.976397 + 0.215983i \(0.0692955\pi\)
−0.976397 + 0.215983i \(0.930704\pi\)
\(168\) −6.70608 −0.0399171
\(169\) 162.026 0.958736
\(170\) 0 0
\(171\) 216.526i 1.26623i
\(172\) 41.1441 0.239210
\(173\) 150.077i 0.867497i 0.901034 + 0.433748i \(0.142809\pi\)
−0.901034 + 0.433748i \(0.857191\pi\)
\(174\) 12.5459 0.0721031
\(175\) 0 0
\(176\) 30.3021i 0.172171i
\(177\) 18.8437i 0.106462i
\(178\) −90.1210 −0.506298
\(179\) −207.058 −1.15675 −0.578375 0.815771i \(-0.696313\pi\)
−0.578375 + 0.815771i \(0.696313\pi\)
\(180\) 0 0
\(181\) 331.138i 1.82949i −0.404031 0.914746i \(-0.632391\pi\)
0.404031 0.914746i \(-0.367609\pi\)
\(182\) 31.7912 0.174677
\(183\) −9.79343 −0.0535160
\(184\) −44.5098 47.4434i −0.241901 0.257845i
\(185\) 0 0
\(186\) −22.2576 −0.119665
\(187\) 57.2753i 0.306285i
\(188\) 168.610i 0.896860i
\(189\) 42.4933i 0.224832i
\(190\) 0 0
\(191\) 172.749i 0.904447i −0.891905 0.452223i \(-0.850631\pi\)
0.891905 0.452223i \(-0.149369\pi\)
\(192\) 2.22818i 0.0116051i
\(193\) 136.450i 0.706996i −0.935435 0.353498i \(-0.884992\pi\)
0.935435 0.353498i \(-0.115008\pi\)
\(194\) 202.689i 1.04479i
\(195\) 0 0
\(196\) −46.9293 −0.239435
\(197\) 271.090i 1.37609i −0.725667 0.688046i \(-0.758469\pi\)
0.725667 0.688046i \(-0.241531\pi\)
\(198\) 95.5896 0.482776
\(199\) 257.292i 1.29292i 0.762946 + 0.646462i \(0.223752\pi\)
−0.762946 + 0.646462i \(0.776248\pi\)
\(200\) 0 0
\(201\) 12.2734i 0.0610615i
\(202\) 39.1882i 0.194001i
\(203\) 271.138 1.33566
\(204\) 4.21158i 0.0206450i
\(205\) 0 0
\(206\) 188.857i 0.916780i
\(207\) −149.663 + 140.408i −0.723009 + 0.678302i
\(208\) 10.5630i 0.0507838i
\(209\) −183.840 −0.879615
\(210\) 0 0
\(211\) 54.1944 0.256846 0.128423 0.991720i \(-0.459009\pi\)
0.128423 + 0.991720i \(0.459009\pi\)
\(212\) 23.8378 0.112443
\(213\) 2.46937i 0.0115933i
\(214\) 71.1478i 0.332467i
\(215\) 0 0
\(216\) −14.1189 −0.0653655
\(217\) −481.023 −2.21670
\(218\) 182.177 0.835674
\(219\) −24.3471 −0.111174
\(220\) 0 0
\(221\) 19.9656i 0.0903423i
\(222\) 15.7311 0.0708608
\(223\) 104.611i 0.469105i −0.972103 0.234553i \(-0.924637\pi\)
0.972103 0.234553i \(-0.0753625\pi\)
\(224\) 48.1546i 0.214976i
\(225\) 0 0
\(226\) 122.051i 0.540047i
\(227\) 200.484 0.883190 0.441595 0.897215i \(-0.354413\pi\)
0.441595 + 0.897215i \(0.354413\pi\)
\(228\) 13.5181 0.0592901
\(229\) 22.0718i 0.0963834i 0.998838 + 0.0481917i \(0.0153458\pi\)
−0.998838 + 0.0481917i \(0.984654\pi\)
\(230\) 0 0
\(231\) −17.9612 −0.0777543
\(232\) 90.0892i 0.388315i
\(233\) 338.632i 1.45335i 0.686979 + 0.726677i \(0.258936\pi\)
−0.686979 + 0.726677i \(0.741064\pi\)
\(234\) 33.3217 0.142400
\(235\) 0 0
\(236\) 135.312 0.573357
\(237\) 42.9529 0.181236
\(238\) 91.0191i 0.382433i
\(239\) −149.374 −0.624997 −0.312499 0.949918i \(-0.601166\pi\)
−0.312499 + 0.949918i \(0.601166\pi\)
\(240\) 0 0
\(241\) 133.030i 0.551991i −0.961159 0.275995i \(-0.910993\pi\)
0.961159 0.275995i \(-0.0890074\pi\)
\(242\) 89.9601i 0.371736i
\(243\) 66.9048i 0.275328i
\(244\) 70.3242i 0.288214i
\(245\) 0 0
\(246\) −16.7683 −0.0681639
\(247\) −64.0848 −0.259453
\(248\) 159.826i 0.644461i
\(249\) 39.4505i 0.158436i
\(250\) 0 0
\(251\) 376.920i 1.50167i 0.660489 + 0.750836i \(0.270349\pi\)
−0.660489 + 0.750836i \(0.729651\pi\)
\(252\) −151.906 −0.602803
\(253\) −119.213 127.070i −0.471197 0.502254i
\(254\) −15.5755 −0.0613208
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 226.085i 0.879708i 0.898069 + 0.439854i \(0.144970\pi\)
−0.898069 + 0.439854i \(0.855030\pi\)
\(258\) −8.10314 −0.0314075
\(259\) 339.975 1.31264
\(260\) 0 0
\(261\) 284.191 1.08885
\(262\) 5.14690i 0.0196447i
\(263\) 2.43654 0.00926441 0.00463221 0.999989i \(-0.498526\pi\)
0.00463221 + 0.999989i \(0.498526\pi\)
\(264\) 5.96785i 0.0226055i
\(265\) 0 0
\(266\) 292.149 1.09830
\(267\) 17.7489 0.0664753
\(268\) −88.1319 −0.328850
\(269\) 311.337 1.15739 0.578694 0.815545i \(-0.303563\pi\)
0.578694 + 0.815545i \(0.303563\pi\)
\(270\) 0 0
\(271\) 260.751 0.962182 0.481091 0.876671i \(-0.340241\pi\)
0.481091 + 0.876671i \(0.340241\pi\)
\(272\) 30.2423 0.111185
\(273\) −6.26112 −0.0229345
\(274\) 13.7148i 0.0500541i
\(275\) 0 0
\(276\) 8.76599 + 9.34376i 0.0317608 + 0.0338542i
\(277\) 182.267i 0.658004i −0.944329 0.329002i \(-0.893288\pi\)
0.944329 0.329002i \(-0.106712\pi\)
\(278\) 11.3913i 0.0409758i
\(279\) −504.180 −1.80710
\(280\) 0 0
\(281\) 4.60502i 0.0163880i −0.999966 0.00819398i \(-0.997392\pi\)
0.999966 0.00819398i \(-0.00260825\pi\)
\(282\) 33.2069i 0.117755i
\(283\) −332.897 −1.17631 −0.588157 0.808747i \(-0.700146\pi\)
−0.588157 + 0.808747i \(0.700146\pi\)
\(284\) −17.7319 −0.0624364
\(285\) 0 0
\(286\) 28.2915i 0.0989215i
\(287\) −362.391 −1.26269
\(288\) 50.4729i 0.175253i
\(289\) −231.838 −0.802207
\(290\) 0 0
\(291\) 39.9185i 0.137177i
\(292\) 174.830i 0.598733i
\(293\) −336.114 −1.14715 −0.573574 0.819154i \(-0.694443\pi\)
−0.573574 + 0.819154i \(0.694443\pi\)
\(294\) 9.24251 0.0314371
\(295\) 0 0
\(296\) 112.961i 0.381625i
\(297\) −37.8155 −0.127325
\(298\) −203.734 −0.683673
\(299\) −41.5565 44.2955i −0.138985 0.148146i
\(300\) 0 0
\(301\) −175.122 −0.581801
\(302\) 155.502i 0.514907i
\(303\) 7.71792i 0.0254717i
\(304\) 97.0703i 0.319310i
\(305\) 0 0
\(306\) 95.4009i 0.311768i
\(307\) 457.934i 1.49164i −0.666147 0.745821i \(-0.732057\pi\)
0.666147 0.745821i \(-0.267943\pi\)
\(308\) 128.975i 0.418750i
\(309\) 37.1944i 0.120370i
\(310\) 0 0
\(311\) −455.620 −1.46502 −0.732508 0.680758i \(-0.761650\pi\)
−0.732508 + 0.680758i \(0.761650\pi\)
\(312\) 2.08034i 0.00666775i
\(313\) 589.353 1.88292 0.941458 0.337130i \(-0.109456\pi\)
0.941458 + 0.337130i \(0.109456\pi\)
\(314\) 35.1019i 0.111789i
\(315\) 0 0
\(316\) 308.434i 0.976057i
\(317\) 386.251i 1.21846i −0.792994 0.609229i \(-0.791479\pi\)
0.792994 0.609229i \(-0.208521\pi\)
\(318\) −4.69475 −0.0147634
\(319\) 241.291i 0.756397i
\(320\) 0 0
\(321\) 14.0122i 0.0436518i
\(322\) 189.447 + 201.934i 0.588346 + 0.627124i
\(323\) 183.477i 0.568039i
\(324\) −157.823 −0.487108
\(325\) 0 0
\(326\) −154.098 −0.472693
\(327\) −35.8789 −0.109721
\(328\) 120.409i 0.367101i
\(329\) 717.655i 2.18132i
\(330\) 0 0
\(331\) 220.712 0.666803 0.333402 0.942785i \(-0.391804\pi\)
0.333402 + 0.942785i \(0.391804\pi\)
\(332\) −283.284 −0.853266
\(333\) 356.342 1.07010
\(334\) 102.019 0.305446
\(335\) 0 0
\(336\) 9.48382i 0.0282257i
\(337\) 193.563 0.574371 0.287185 0.957875i \(-0.407280\pi\)
0.287185 + 0.957875i \(0.407280\pi\)
\(338\) 229.140i 0.677929i
\(339\) 24.0373i 0.0709064i
\(340\) 0 0
\(341\) 428.071i 1.25534i
\(342\) 306.213 0.895361
\(343\) −217.373 −0.633739
\(344\) 58.1866i 0.169147i
\(345\) 0 0
\(346\) 212.241 0.613413
\(347\) 262.429i 0.756278i −0.925749 0.378139i \(-0.876564\pi\)
0.925749 0.378139i \(-0.123436\pi\)
\(348\) 17.7426i 0.0509846i
\(349\) −229.831 −0.658543 −0.329271 0.944235i \(-0.606803\pi\)
−0.329271 + 0.944235i \(0.606803\pi\)
\(350\) 0 0
\(351\) −13.1821 −0.0375560
\(352\) 42.8536 0.121743
\(353\) 367.482i 1.04103i −0.853854 0.520513i \(-0.825741\pi\)
0.853854 0.520513i \(-0.174259\pi\)
\(354\) −26.6491 −0.0752799
\(355\) 0 0
\(356\) 127.450i 0.358007i
\(357\) 17.9258i 0.0502123i
\(358\) 292.824i 0.817945i
\(359\) 239.971i 0.668442i 0.942495 + 0.334221i \(0.108473\pi\)
−0.942495 + 0.334221i \(0.891527\pi\)
\(360\) 0 0
\(361\) −227.915 −0.631344
\(362\) −468.300 −1.29365
\(363\) 17.7172i 0.0488077i
\(364\) 44.9595i 0.123515i
\(365\) 0 0
\(366\) 13.8500i 0.0378416i
\(367\) 389.113 1.06025 0.530127 0.847918i \(-0.322144\pi\)
0.530127 + 0.847918i \(0.322144\pi\)
\(368\) −67.0952 + 62.9463i −0.182324 + 0.171050i
\(369\) −379.837 −1.02937
\(370\) 0 0
\(371\) −101.461 −0.273480
\(372\) 31.4770i 0.0846156i
\(373\) 546.309 1.46463 0.732317 0.680964i \(-0.238439\pi\)
0.732317 + 0.680964i \(0.238439\pi\)
\(374\) 80.9995 0.216576
\(375\) 0 0
\(376\) −238.450 −0.634176
\(377\) 84.1117i 0.223108i
\(378\) 60.0946 0.158980
\(379\) 295.837i 0.780573i −0.920693 0.390287i \(-0.872376\pi\)
0.920693 0.390287i \(-0.127624\pi\)
\(380\) 0 0
\(381\) 3.06751 0.00805122
\(382\) −244.304 −0.639541
\(383\) −566.033 −1.47789 −0.738946 0.673765i \(-0.764676\pi\)
−0.738946 + 0.673765i \(0.764676\pi\)
\(384\) −3.15112 −0.00820605
\(385\) 0 0
\(386\) −192.970 −0.499921
\(387\) −183.553 −0.474296
\(388\) −286.645 −0.738775
\(389\) 196.043i 0.503966i 0.967732 + 0.251983i \(0.0810826\pi\)
−0.967732 + 0.251983i \(0.918917\pi\)
\(390\) 0 0
\(391\) −126.819 + 118.978i −0.324346 + 0.304290i
\(392\) 66.3681i 0.169306i
\(393\) 1.01366i 0.00257928i
\(394\) −383.380 −0.973045
\(395\) 0 0
\(396\) 135.184i 0.341374i
\(397\) 298.788i 0.752616i −0.926495 0.376308i \(-0.877194\pi\)
0.926495 0.376308i \(-0.122806\pi\)
\(398\) 363.866 0.914236
\(399\) −57.5374 −0.144204
\(400\) 0 0
\(401\) 785.114i 1.95789i 0.204121 + 0.978946i \(0.434567\pi\)
−0.204121 + 0.978946i \(0.565433\pi\)
\(402\) 17.3572 0.0431770
\(403\) 149.222i 0.370277i
\(404\) −55.4204 −0.137179
\(405\) 0 0
\(406\) 383.447i 0.944452i
\(407\) 302.550i 0.743365i
\(408\) −5.95607 −0.0145982
\(409\) −358.186 −0.875761 −0.437881 0.899033i \(-0.644271\pi\)
−0.437881 + 0.899033i \(0.644271\pi\)
\(410\) 0 0
\(411\) 2.70107i 0.00657195i
\(412\) −267.084 −0.648261
\(413\) −575.930 −1.39450
\(414\) 198.568 + 211.655i 0.479632 + 0.511245i
\(415\) 0 0
\(416\) 14.9384 0.0359096
\(417\) 2.24346i 0.00537999i
\(418\) 259.988i 0.621982i
\(419\) 195.271i 0.466042i 0.972472 + 0.233021i \(0.0748610\pi\)
−0.972472 + 0.233021i \(0.925139\pi\)
\(420\) 0 0
\(421\) 768.042i 1.82433i −0.409826 0.912164i \(-0.634410\pi\)
0.409826 0.912164i \(-0.365590\pi\)
\(422\) 76.6425i 0.181617i
\(423\) 752.204i 1.77826i
\(424\) 33.7118i 0.0795089i
\(425\) 0 0
\(426\) 3.49222 0.00819770
\(427\) 299.321i 0.700987i
\(428\) −100.618 −0.235089
\(429\) 5.57188i 0.0129881i
\(430\) 0 0
\(431\) 333.122i 0.772905i 0.922309 + 0.386453i \(0.126300\pi\)
−0.922309 + 0.386453i \(0.873700\pi\)
\(432\) 19.9672i 0.0462204i
\(433\) −7.49741 −0.0173150 −0.00865752 0.999963i \(-0.502756\pi\)
−0.00865752 + 0.999963i \(0.502756\pi\)
\(434\) 680.270i 1.56744i
\(435\) 0 0
\(436\) 257.637i 0.590911i
\(437\) −381.889 407.059i −0.873887 0.931485i
\(438\) 34.4319i 0.0786117i
\(439\) 303.939 0.692344 0.346172 0.938171i \(-0.387481\pi\)
0.346172 + 0.938171i \(0.387481\pi\)
\(440\) 0 0
\(441\) 209.362 0.474743
\(442\) 28.2357 0.0638816
\(443\) 637.145i 1.43825i −0.694881 0.719125i \(-0.744543\pi\)
0.694881 0.719125i \(-0.255457\pi\)
\(444\) 22.2471i 0.0501062i
\(445\) 0 0
\(446\) −147.942 −0.331708
\(447\) 40.1245 0.0897640
\(448\) −68.1009 −0.152011
\(449\) −88.9331 −0.198069 −0.0990346 0.995084i \(-0.531575\pi\)
−0.0990346 + 0.995084i \(0.531575\pi\)
\(450\) 0 0
\(451\) 322.498i 0.715073i
\(452\) 172.606 0.381871
\(453\) 30.6253i 0.0676056i
\(454\) 283.527i 0.624509i
\(455\) 0 0
\(456\) 19.1175i 0.0419244i
\(457\) −377.669 −0.826410 −0.413205 0.910638i \(-0.635591\pi\)
−0.413205 + 0.910638i \(0.635591\pi\)
\(458\) 31.2142 0.0681534
\(459\) 37.7408i 0.0822240i
\(460\) 0 0
\(461\) −585.070 −1.26913 −0.634566 0.772869i \(-0.718821\pi\)
−0.634566 + 0.772869i \(0.718821\pi\)
\(462\) 25.4010i 0.0549806i
\(463\) 225.877i 0.487854i 0.969794 + 0.243927i \(0.0784358\pi\)
−0.969794 + 0.243927i \(0.921564\pi\)
\(464\) 127.405 0.274580
\(465\) 0 0
\(466\) 478.897 1.02768
\(467\) 702.984 1.50532 0.752659 0.658410i \(-0.228771\pi\)
0.752659 + 0.658410i \(0.228771\pi\)
\(468\) 47.1240i 0.100692i
\(469\) 375.117 0.799822
\(470\) 0 0
\(471\) 6.91315i 0.0146776i
\(472\) 191.360i 0.405424i
\(473\) 155.844i 0.329480i
\(474\) 60.7446i 0.128153i
\(475\) 0 0
\(476\) −128.720 −0.270421
\(477\) −106.346 −0.222947
\(478\) 211.247i 0.441940i
\(479\) 291.706i 0.608989i 0.952514 + 0.304494i \(0.0984875\pi\)
−0.952514 + 0.304494i \(0.901512\pi\)
\(480\) 0 0
\(481\) 105.466i 0.219264i
\(482\) −188.132 −0.390316
\(483\) −37.3107 39.7699i −0.0772479 0.0823394i
\(484\) −127.223 −0.262857
\(485\) 0 0
\(486\) 94.6177 0.194687
\(487\) 205.957i 0.422909i 0.977388 + 0.211454i \(0.0678200\pi\)
−0.977388 + 0.211454i \(0.932180\pi\)
\(488\) −99.4534 −0.203798
\(489\) 30.3488 0.0620630
\(490\) 0 0
\(491\) −192.478 −0.392012 −0.196006 0.980603i \(-0.562797\pi\)
−0.196006 + 0.980603i \(0.562797\pi\)
\(492\) 23.7140i 0.0481992i
\(493\) 240.814 0.488467
\(494\) 90.6296i 0.183461i
\(495\) 0 0
\(496\) −226.028 −0.455703
\(497\) 75.4726 0.151856
\(498\) 55.7915 0.112031
\(499\) −887.386 −1.77833 −0.889164 0.457589i \(-0.848713\pi\)
−0.889164 + 0.457589i \(0.848713\pi\)
\(500\) 0 0
\(501\) −20.0921 −0.0401041
\(502\) 533.045 1.06184
\(503\) −330.810 −0.657673 −0.328837 0.944387i \(-0.606657\pi\)
−0.328837 + 0.944387i \(0.606657\pi\)
\(504\) 214.828i 0.426246i
\(505\) 0 0
\(506\) −179.704 + 168.592i −0.355147 + 0.333187i
\(507\) 45.1280i 0.0890099i
\(508\) 22.0270i 0.0433603i
\(509\) 407.928 0.801430 0.400715 0.916203i \(-0.368762\pi\)
0.400715 + 0.916203i \(0.368762\pi\)
\(510\) 0 0
\(511\) 744.131i 1.45622i
\(512\) 22.6274i 0.0441942i
\(513\) −121.139 −0.236138
\(514\) 319.733 0.622048
\(515\) 0 0
\(516\) 11.4596i 0.0222085i
\(517\) −638.654 −1.23531
\(518\) 480.797i 0.928180i
\(519\) −41.7998 −0.0805391
\(520\) 0 0
\(521\) 458.780i 0.880576i −0.897857 0.440288i \(-0.854876\pi\)
0.897857 0.440288i \(-0.145124\pi\)
\(522\) 401.907i 0.769937i
\(523\) −404.987 −0.774354 −0.387177 0.922005i \(-0.626550\pi\)
−0.387177 + 0.922005i \(0.626550\pi\)
\(524\) −7.27882 −0.0138909
\(525\) 0 0
\(526\) 3.44579i 0.00655093i
\(527\) −427.226 −0.810675
\(528\) −8.43982 −0.0159845
\(529\) 33.7199 527.924i 0.0637427 0.997966i
\(530\) 0 0
\(531\) −603.656 −1.13683
\(532\) 413.161i 0.776619i
\(533\) 112.420i 0.210919i
\(534\) 25.1007i 0.0470051i
\(535\) 0 0
\(536\) 124.637i 0.232532i
\(537\) 57.6703i 0.107394i
\(538\) 440.298i 0.818397i
\(539\) 177.757i 0.329791i
\(540\) 0 0
\(541\) 1047.51 1.93625 0.968123 0.250477i \(-0.0805875\pi\)
0.968123 + 0.250477i \(0.0805875\pi\)
\(542\) 368.758i 0.680366i
\(543\) 92.2294 0.169851
\(544\) 42.7690i 0.0786195i
\(545\) 0 0
\(546\) 8.85457i 0.0162172i
\(547\) 123.784i 0.226296i 0.993578 + 0.113148i \(0.0360934\pi\)
−0.993578 + 0.113148i \(0.963907\pi\)
\(548\) 19.3957 0.0353936
\(549\) 313.731i 0.571459i
\(550\) 0 0
\(551\) 772.955i 1.40282i
\(552\) 13.2141 12.3970i 0.0239385 0.0224583i
\(553\) 1312.79i 2.37394i
\(554\) −257.765 −0.465279
\(555\) 0 0
\(556\) 16.1097 0.0289743
\(557\) −246.292 −0.442176 −0.221088 0.975254i \(-0.570961\pi\)
−0.221088 + 0.975254i \(0.570961\pi\)
\(558\) 713.019i 1.27781i
\(559\) 54.3259i 0.0971840i
\(560\) 0 0
\(561\) −15.9525 −0.0284357
\(562\) −6.51248 −0.0115880
\(563\) 574.776 1.02092 0.510458 0.859902i \(-0.329476\pi\)
0.510458 + 0.859902i \(0.329476\pi\)
\(564\) 46.9616 0.0832653
\(565\) 0 0
\(566\) 470.787i 0.831780i
\(567\) 671.743 1.18473
\(568\) 25.0768i 0.0441492i
\(569\) 794.332i 1.39601i −0.716091 0.698007i \(-0.754070\pi\)
0.716091 0.698007i \(-0.245930\pi\)
\(570\) 0 0
\(571\) 416.688i 0.729751i −0.931056 0.364876i \(-0.881111\pi\)
0.931056 0.364876i \(-0.118889\pi\)
\(572\) 40.0103 0.0699480
\(573\) 48.1146 0.0839696
\(574\) 512.498i 0.892854i
\(575\) 0 0
\(576\) −71.3794 −0.123923
\(577\) 282.647i 0.489856i −0.969541 0.244928i \(-0.921236\pi\)
0.969541 0.244928i \(-0.0787643\pi\)
\(578\) 327.868i 0.567246i
\(579\) 38.0044 0.0656381
\(580\) 0 0
\(581\) 1205.75 2.07529
\(582\) 56.4533 0.0969988
\(583\) 90.2920i 0.154875i
\(584\) −247.247 −0.423368
\(585\) 0 0
\(586\) 475.337i 0.811156i
\(587\) 168.123i 0.286410i −0.989693 0.143205i \(-0.954259\pi\)
0.989693 0.143205i \(-0.0457408\pi\)
\(588\) 13.0709i 0.0222294i
\(589\) 1371.29i 2.32817i
\(590\) 0 0
\(591\) 75.5048 0.127758
\(592\) 159.751 0.269850
\(593\) 419.364i 0.707191i 0.935398 + 0.353595i \(0.115041\pi\)
−0.935398 + 0.353595i \(0.884959\pi\)
\(594\) 53.4792i 0.0900323i
\(595\) 0 0
\(596\) 288.124i 0.483430i
\(597\) −71.6616 −0.120036
\(598\) −62.6433 + 58.7698i −0.104755 + 0.0982773i
\(599\) 519.774 0.867736 0.433868 0.900977i \(-0.357148\pi\)
0.433868 + 0.900977i \(0.357148\pi\)
\(600\) 0 0
\(601\) 1089.19 1.81230 0.906151 0.422955i \(-0.139007\pi\)
0.906151 + 0.422955i \(0.139007\pi\)
\(602\) 247.660i 0.411395i
\(603\) 393.175 0.652032
\(604\) 219.913 0.364094
\(605\) 0 0
\(606\) 10.9148 0.0180112
\(607\) 890.673i 1.46734i 0.679508 + 0.733668i \(0.262193\pi\)
−0.679508 + 0.733668i \(0.737807\pi\)
\(608\) 137.278 0.225786
\(609\) 75.5181i 0.124003i
\(610\) 0 0
\(611\) −222.629 −0.364368
\(612\) −134.917 −0.220453
\(613\) −629.354 −1.02668 −0.513339 0.858186i \(-0.671592\pi\)
−0.513339 + 0.858186i \(0.671592\pi\)
\(614\) −647.616 −1.05475
\(615\) 0 0
\(616\) −182.398 −0.296101
\(617\) −157.187 −0.254760 −0.127380 0.991854i \(-0.540657\pi\)
−0.127380 + 0.991854i \(0.540657\pi\)
\(618\) 52.6008 0.0851146
\(619\) 462.293i 0.746838i −0.927663 0.373419i \(-0.878185\pi\)
0.927663 0.373419i \(-0.121815\pi\)
\(620\) 0 0
\(621\) −78.5539 83.7314i −0.126496 0.134833i
\(622\) 644.344i 1.03592i
\(623\) 542.468i 0.870735i
\(624\) −2.94204 −0.00471481
\(625\) 0 0
\(626\) 833.471i 1.33142i
\(627\) 51.2035i 0.0816642i
\(628\) −49.6416 −0.0790471
\(629\) 301.952 0.480051
\(630\) 0 0
\(631\) 411.630i 0.652345i 0.945310 + 0.326173i \(0.105759\pi\)
−0.945310 + 0.326173i \(0.894241\pi\)
\(632\) 436.191 0.690176
\(633\) 15.0944i 0.0238458i
\(634\) −546.242 −0.861581
\(635\) 0 0
\(636\) 6.63937i 0.0104393i
\(637\) 61.9645i 0.0972756i
\(638\) 341.236 0.534853
\(639\) 79.1060 0.123797
\(640\) 0 0
\(641\) 251.089i 0.391715i −0.980632 0.195857i \(-0.937251\pi\)
0.980632 0.195857i \(-0.0627490\pi\)
\(642\) 19.8163 0.0308665
\(643\) 102.907 0.160042 0.0800211 0.996793i \(-0.474501\pi\)
0.0800211 + 0.996793i \(0.474501\pi\)
\(644\) 285.578 267.919i 0.443444 0.416023i
\(645\) 0 0
\(646\) 259.475 0.401664
\(647\) 437.368i 0.675993i −0.941147 0.337997i \(-0.890251\pi\)
0.941147 0.337997i \(-0.109749\pi\)
\(648\) 223.195i 0.344437i
\(649\) 512.530i 0.789723i
\(650\) 0 0
\(651\) 133.976i 0.205800i
\(652\) 217.927i 0.334244i
\(653\) 94.4001i 0.144564i 0.997384 + 0.0722819i \(0.0230281\pi\)
−0.997384 + 0.0722819i \(0.976972\pi\)
\(654\) 50.7404i 0.0775847i
\(655\) 0 0
\(656\) −170.284 −0.259580
\(657\) 779.954i 1.18714i
\(658\) 1014.92 1.54243
\(659\) 759.727i 1.15285i 0.817151 + 0.576424i \(0.195552\pi\)
−0.817151 + 0.576424i \(0.804448\pi\)
\(660\) 0 0
\(661\) 581.754i 0.880112i −0.897970 0.440056i \(-0.854959\pi\)
0.897970 0.440056i \(-0.145041\pi\)
\(662\) 312.134i 0.471501i
\(663\) −5.56088 −0.00838745
\(664\) 400.625i 0.603350i
\(665\) 0 0
\(666\) 503.943i 0.756672i
\(667\) −534.267 + 501.231i −0.801001 + 0.751471i
\(668\) 144.277i 0.215983i
\(669\) 29.1364 0.0435521
\(670\) 0 0
\(671\) −266.371 −0.396977
\(672\) 13.4122 0.0199586
\(673\) 831.173i 1.23503i 0.786560 + 0.617513i \(0.211860\pi\)
−0.786560 + 0.617513i \(0.788140\pi\)
\(674\) 273.739i 0.406142i
\(675\) 0 0
\(676\) −324.053 −0.479368
\(677\) 106.706 0.157616 0.0788079 0.996890i \(-0.474889\pi\)
0.0788079 + 0.996890i \(0.474889\pi\)
\(678\) −33.9938 −0.0501384
\(679\) 1220.05 1.79683
\(680\) 0 0
\(681\) 55.8393i 0.0819961i
\(682\) −605.384 −0.887660
\(683\) 380.675i 0.557357i −0.960385 0.278678i \(-0.910104\pi\)
0.960385 0.278678i \(-0.0898963\pi\)
\(684\) 433.051i 0.633116i
\(685\) 0 0
\(686\) 307.411i 0.448121i
\(687\) −6.14749 −0.00894832
\(688\) −82.2883 −0.119605
\(689\) 31.4750i 0.0456821i
\(690\) 0 0
\(691\) −318.845 −0.461425 −0.230713 0.973022i \(-0.574106\pi\)
−0.230713 + 0.973022i \(0.574106\pi\)
\(692\) 300.154i 0.433748i
\(693\) 575.385i 0.830282i
\(694\) −371.130 −0.534769
\(695\) 0 0
\(696\) −25.0919 −0.0360515
\(697\) −321.861 −0.461781
\(698\) 325.031i 0.465660i
\(699\) −94.3165 −0.134931
\(700\) 0 0
\(701\) 112.754i 0.160848i −0.996761 0.0804239i \(-0.974373\pi\)
0.996761 0.0804239i \(-0.0256274\pi\)
\(702\) 18.6424i 0.0265561i
\(703\) 969.193i 1.37865i
\(704\) 60.6042i 0.0860855i
\(705\) 0 0
\(706\) −519.698 −0.736116
\(707\) 235.887 0.333644
\(708\) 37.6875i 0.0532309i
\(709\) 465.481i 0.656531i −0.944585 0.328266i \(-0.893536\pi\)
0.944585 0.328266i \(-0.106464\pi\)
\(710\) 0 0
\(711\) 1375.99i 1.93529i
\(712\) 180.242 0.253149
\(713\) 947.838 889.229i 1.32937 1.24717i
\(714\) 25.3509 0.0355054
\(715\) 0 0
\(716\) 414.116 0.578375
\(717\) 41.6041i 0.0580253i
\(718\) 339.370 0.472660
\(719\) 347.913 0.483885 0.241943 0.970291i \(-0.422215\pi\)
0.241943 + 0.970291i \(0.422215\pi\)
\(720\) 0 0
\(721\) 1136.79 1.57669
\(722\) 322.321i 0.446428i
\(723\) 37.0518 0.0512473
\(724\) 662.276i 0.914746i
\(725\) 0 0
\(726\) 25.0559 0.0345123
\(727\) 88.3077 0.121469 0.0607343 0.998154i \(-0.480656\pi\)
0.0607343 + 0.998154i \(0.480656\pi\)
\(728\) −63.5824 −0.0873385
\(729\) 691.569 0.948654
\(730\) 0 0
\(731\) −155.536 −0.212772
\(732\) 19.5869 0.0267580
\(733\) 510.848 0.696928 0.348464 0.937322i \(-0.386703\pi\)
0.348464 + 0.937322i \(0.386703\pi\)
\(734\) 550.289i 0.749712i
\(735\) 0 0
\(736\) 89.0196 + 94.8869i 0.120950 + 0.128922i
\(737\) 333.823i 0.452948i
\(738\) 537.171i 0.727873i
\(739\) 416.763 0.563955 0.281978 0.959421i \(-0.409010\pi\)
0.281978 + 0.959421i \(0.409010\pi\)
\(740\) 0 0
\(741\) 17.8491i 0.0240878i
\(742\) 143.488i 0.193380i
\(743\) −633.469 −0.852583 −0.426291 0.904586i \(-0.640180\pi\)
−0.426291 + 0.904586i \(0.640180\pi\)
\(744\) 44.5152 0.0598323
\(745\) 0 0
\(746\) 772.597i 1.03565i
\(747\) 1263.79 1.69182
\(748\) 114.551i 0.153142i
\(749\) 428.262 0.571779
\(750\) 0 0
\(751\) 1282.52i 1.70775i −0.520475 0.853877i \(-0.674245\pi\)
0.520475 0.853877i \(-0.325755\pi\)
\(752\) 337.219i 0.448430i
\(753\) −104.981 −0.139416
\(754\) 118.952 0.157761
\(755\) 0 0
\(756\) 84.9866i 0.112416i
\(757\) 1233.64 1.62964 0.814819 0.579716i \(-0.196836\pi\)
0.814819 + 0.579716i \(0.196836\pi\)
\(758\) −418.377 −0.551949
\(759\) 35.3919 33.2035i 0.0466297 0.0437463i
\(760\) 0 0
\(761\) −262.559 −0.345018 −0.172509 0.985008i \(-0.555187\pi\)
−0.172509 + 0.985008i \(0.555187\pi\)
\(762\) 4.33812i 0.00569307i
\(763\) 1096.58i 1.43720i
\(764\) 345.499i 0.452223i
\(765\) 0 0
\(766\) 800.491i 1.04503i
\(767\) 178.663i 0.232938i
\(768\) 4.45636i 0.00580255i
\(769\) 801.510i 1.04228i −0.853473 0.521138i \(-0.825508\pi\)
0.853473 0.521138i \(-0.174492\pi\)
\(770\) 0 0
\(771\) −62.9698 −0.0816729
\(772\) 272.900i 0.353498i
\(773\) −1143.79 −1.47967 −0.739837 0.672786i \(-0.765097\pi\)
−0.739837 + 0.672786i \(0.765097\pi\)
\(774\) 259.583i 0.335378i
\(775\) 0 0
\(776\) 405.377i 0.522393i
\(777\) 94.6907i 0.121867i
\(778\) 277.246 0.356357
\(779\) 1033.10i 1.32618i
\(780\) 0 0
\(781\) 67.1644i 0.0859979i
\(782\) 168.260 + 179.350i 0.215166 + 0.229347i
\(783\) 158.995i 0.203059i
\(784\) 93.8587 0.119718
\(785\) 0 0
\(786\) 1.43353 0.00182383
\(787\) 111.467 0.141635 0.0708175 0.997489i \(-0.477439\pi\)
0.0708175 + 0.997489i \(0.477439\pi\)
\(788\) 542.181i 0.688046i
\(789\) 0.678632i 0.000860116i
\(790\) 0 0
\(791\) −734.663 −0.928777
\(792\) −191.179 −0.241388
\(793\) −92.8546 −0.117093
\(794\) −422.551 −0.532180
\(795\) 0 0
\(796\) 514.584i 0.646462i
\(797\) 231.014 0.289855 0.144927 0.989442i \(-0.453705\pi\)
0.144927 + 0.989442i \(0.453705\pi\)
\(798\) 81.3701i 0.101968i
\(799\) 637.393i 0.797738i
\(800\) 0 0
\(801\) 568.583i 0.709842i
\(802\) 1110.32 1.38444
\(803\) −662.215 −0.824676
\(804\) 24.5467i 0.0305307i
\(805\) 0 0
\(806\) −211.031 −0.261825
\(807\) 86.7145i 0.107453i
\(808\) 78.3763i 0.0970004i
\(809\) 165.201 0.204204 0.102102 0.994774i \(-0.467443\pi\)
0.102102 + 0.994774i \(0.467443\pi\)
\(810\) 0 0
\(811\) 317.322 0.391273 0.195636 0.980677i \(-0.437323\pi\)
0.195636 + 0.980677i \(0.437323\pi\)
\(812\) −542.276 −0.667828
\(813\) 72.6251i 0.0893298i
\(814\) 427.870 0.525638
\(815\) 0 0
\(816\) 8.42315i 0.0103225i
\(817\) 499.234i 0.611058i
\(818\) 506.552i 0.619257i
\(819\) 200.574i 0.244901i
\(820\) 0 0
\(821\) −1389.82 −1.69284 −0.846421 0.532514i \(-0.821247\pi\)
−0.846421 + 0.532514i \(0.821247\pi\)
\(822\) −3.81989 −0.00464707
\(823\) 948.001i 1.15188i −0.817490 0.575942i \(-0.804635\pi\)
0.817490 0.575942i \(-0.195365\pi\)
\(824\) 377.713i 0.458390i
\(825\) 0 0
\(826\) 814.489i 0.986064i
\(827\) 1177.54 1.42387 0.711935 0.702245i \(-0.247819\pi\)
0.711935 + 0.702245i \(0.247819\pi\)
\(828\) 299.326 280.817i 0.361505 0.339151i
\(829\) 1278.78 1.54256 0.771279 0.636497i \(-0.219617\pi\)
0.771279 + 0.636497i \(0.219617\pi\)
\(830\) 0 0
\(831\) 50.7655 0.0610897
\(832\) 21.1261i 0.0253919i
\(833\) 177.406 0.212973
\(834\) −3.17273 −0.00380423
\(835\) 0 0
\(836\) 367.679 0.439808
\(837\) 282.072i 0.337004i
\(838\) 276.156 0.329541
\(839\) 1435.77i 1.71128i −0.517570 0.855641i \(-0.673163\pi\)
0.517570 0.855641i \(-0.326837\pi\)
\(840\) 0 0
\(841\) 173.507 0.206311
\(842\) −1086.18 −1.28999
\(843\) 1.28260 0.00152147
\(844\) −108.389 −0.128423
\(845\) 0 0
\(846\) 1063.78 1.25742
\(847\) 541.500 0.639315
\(848\) −47.6757 −0.0562213
\(849\) 92.7193i 0.109210i
\(850\) 0 0
\(851\) −669.908 + 628.484i −0.787201 + 0.738524i
\(852\) 4.93875i 0.00579665i
\(853\) 812.996i 0.953102i −0.879147 0.476551i \(-0.841887\pi\)
0.879147 0.476551i \(-0.158113\pi\)
\(854\) 423.304 0.495673
\(855\) 0 0
\(856\) 142.296i 0.166233i
\(857\) 958.841i 1.11883i −0.828886 0.559417i \(-0.811025\pi\)
0.828886 0.559417i \(-0.188975\pi\)
\(858\) −7.87983 −0.00918395
\(859\) 383.654 0.446628 0.223314 0.974747i \(-0.428312\pi\)
0.223314 + 0.974747i \(0.428312\pi\)
\(860\) 0 0
\(861\) 100.934i 0.117229i
\(862\) 471.106 0.546526
\(863\) 1017.48i 1.17900i −0.807767 0.589502i \(-0.799324\pi\)
0.807767 0.589502i \(-0.200676\pi\)
\(864\) 28.2379 0.0326827
\(865\) 0 0
\(866\) 10.6029i 0.0122436i
\(867\) 64.5721i 0.0744776i
\(868\) 962.047 1.10835
\(869\) 1168.27 1.34439
\(870\) 0 0
\(871\) 116.368i 0.133602i
\(872\) −364.354 −0.417837
\(873\) 1278.78 1.46482
\(874\) −575.669 + 540.072i −0.658660 + 0.617932i
\(875\) 0 0
\(876\) 48.6941 0.0555869
\(877\) 1443.83i 1.64633i 0.567806 + 0.823163i \(0.307793\pi\)
−0.567806 + 0.823163i \(0.692207\pi\)
\(878\) 429.835i 0.489561i
\(879\) 93.6154i 0.106502i
\(880\) 0 0
\(881\) 894.988i 1.01588i 0.861393 + 0.507939i \(0.169592\pi\)
−0.861393 + 0.507939i \(0.830408\pi\)
\(882\) 296.082i 0.335694i
\(883\) 870.115i 0.985407i 0.870197 + 0.492704i \(0.163991\pi\)
−0.870197 + 0.492704i \(0.836009\pi\)
\(884\) 39.9313i 0.0451711i
\(885\) 0 0
\(886\) −901.058 −1.01700
\(887\) 529.330i 0.596764i −0.954446 0.298382i \(-0.903553\pi\)
0.954446 0.298382i \(-0.0964470\pi\)
\(888\) −31.4622 −0.0354304
\(889\) 93.7539i 0.105460i
\(890\) 0 0
\(891\) 597.796i 0.670927i
\(892\) 209.221i 0.234553i
\(893\) −2045.87 −2.29101
\(894\) 56.7446i 0.0634728i
\(895\) 0 0
\(896\) 96.3093i 0.107488i
\(897\) 12.3373 11.5744i 0.0137540 0.0129035i
\(898\) 125.770i 0.140056i
\(899\) −1799.83 −2.00203
\(900\) 0 0
\(901\) −90.1138 −0.100015
\(902\) −456.081 −0.505633
\(903\) 48.7755i 0.0540149i
\(904\) 244.101i 0.270023i
\(905\) 0 0
\(906\) −43.3107 −0.0478044
\(907\) 691.482 0.762384 0.381192 0.924496i \(-0.375514\pi\)
0.381192 + 0.924496i \(0.375514\pi\)
\(908\) −400.968 −0.441595
\(909\) 247.242 0.271994
\(910\) 0 0
\(911\) 1794.49i 1.96980i 0.173115 + 0.984902i \(0.444617\pi\)
−0.173115 + 0.984902i \(0.555383\pi\)
\(912\) −27.0363 −0.0296450
\(913\) 1073.01i 1.17526i
\(914\) 534.105i 0.584360i
\(915\) 0 0
\(916\) 44.1436i 0.0481917i
\(917\) 30.9809 0.0337851
\(918\) 53.3736 0.0581412
\(919\) 428.705i 0.466491i 0.972418 + 0.233245i \(0.0749345\pi\)
−0.972418 + 0.233245i \(0.925065\pi\)
\(920\) 0 0
\(921\) 127.545 0.138485
\(922\) 827.413i 0.897411i
\(923\) 23.4129i 0.0253661i
\(924\) 35.9225 0.0388771
\(925\) 0 0
\(926\) 319.438 0.344965
\(927\) 1191.52 1.28535
\(928\) 180.178i 0.194158i
\(929\) −1577.01 −1.69754 −0.848768 0.528766i \(-0.822655\pi\)
−0.848768 + 0.528766i \(0.822655\pi\)
\(930\) 0 0
\(931\) 569.431i 0.611633i
\(932\) 677.263i 0.726677i
\(933\) 126.900i 0.136013i
\(934\) 994.169i 1.06442i
\(935\) 0 0
\(936\) −66.6433 −0.0712001
\(937\) 141.317 0.150818 0.0754091 0.997153i \(-0.475974\pi\)
0.0754091 + 0.997153i \(0.475974\pi\)
\(938\) 530.495i 0.565560i
\(939\) 164.148i 0.174812i
\(940\) 0 0
\(941\) 1506.21i 1.60065i −0.599566 0.800325i \(-0.704660\pi\)
0.599566 0.800325i \(-0.295340\pi\)
\(942\) 9.77667 0.0103786
\(943\) 714.078 669.923i 0.757240 0.710417i
\(944\) −270.624 −0.286678
\(945\) 0 0
\(946\) −220.397 −0.232978
\(947\) 1689.84i 1.78441i 0.451632 + 0.892205i \(0.350842\pi\)
−0.451632 + 0.892205i \(0.649158\pi\)
\(948\) −85.9058 −0.0906179
\(949\) −230.842 −0.243248
\(950\) 0 0
\(951\) 107.580 0.113123
\(952\) 182.038i 0.191217i
\(953\) −990.482 −1.03933 −0.519665 0.854370i \(-0.673943\pi\)
−0.519665 + 0.854370i \(0.673943\pi\)
\(954\) 150.395i 0.157647i
\(955\) 0 0
\(956\) 298.749 0.312499
\(957\) −67.2049 −0.0702245
\(958\) 412.534 0.430620
\(959\) −82.5541 −0.0860836
\(960\) 0 0
\(961\) 2232.05 2.32264
\(962\) 149.151 0.155043
\(963\) 448.879 0.466126
\(964\) 266.059i 0.275995i
\(965\) 0 0
\(966\) −56.2432 + 52.7654i −0.0582227 + 0.0546225i
\(967\) 1528.09i 1.58024i 0.612954 + 0.790118i \(0.289981\pi\)
−0.612954 + 0.790118i \(0.710019\pi\)
\(968\) 179.920i 0.185868i
\(969\) −51.1024 −0.0527372
\(970\) 0 0
\(971\) 616.239i 0.634643i 0.948318 + 0.317322i \(0.102783\pi\)
−0.948318 + 0.317322i \(0.897217\pi\)
\(972\) 133.810i 0.137664i
\(973\) −68.5679 −0.0704706
\(974\) 291.267 0.299042
\(975\) 0 0
\(976\) 140.648i 0.144107i
\(977\) −1393.79 −1.42660 −0.713299 0.700859i \(-0.752800\pi\)
−0.713299 + 0.700859i \(0.752800\pi\)
\(978\) 42.9197i 0.0438852i
\(979\) 482.752 0.493107
\(980\) 0 0
\(981\) 1149.37i 1.17164i
\(982\) 272.205i 0.277195i
\(983\) 1033.22 1.05109 0.525543 0.850767i \(-0.323862\pi\)
0.525543 + 0.850767i \(0.323862\pi\)
\(984\) 33.5367 0.0340820
\(985\) 0 0
\(986\) 340.563i 0.345398i
\(987\) −199.883 −0.202516
\(988\) 128.170 0.129726
\(989\) 345.071 323.734i 0.348909 0.327335i
\(990\) 0 0
\(991\) −1122.80 −1.13300 −0.566501 0.824061i \(-0.691703\pi\)
−0.566501 + 0.824061i \(0.691703\pi\)
\(992\) 319.652i 0.322230i
\(993\) 61.4732i 0.0619066i
\(994\) 106.734i 0.107379i
\(995\) 0 0
\(996\) 78.9011i 0.0792179i
\(997\) 718.650i 0.720812i −0.932795 0.360406i \(-0.882638\pi\)
0.932795 0.360406i \(-0.117362\pi\)
\(998\) 1254.95i 1.25747i
\(999\) 199.361i 0.199561i
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 1150.3.c.c.1149.7 32
5.2 odd 4 1150.3.d.b.551.14 16
5.3 odd 4 230.3.d.a.91.4 yes 16
5.4 even 2 inner 1150.3.c.c.1149.26 32
15.8 even 4 2070.3.c.a.91.9 16
20.3 even 4 1840.3.k.d.321.10 16
23.22 odd 2 inner 1150.3.c.c.1149.25 32
115.22 even 4 1150.3.d.b.551.13 16
115.68 even 4 230.3.d.a.91.3 16
115.114 odd 2 inner 1150.3.c.c.1149.8 32
345.68 odd 4 2070.3.c.a.91.16 16
460.183 odd 4 1840.3.k.d.321.9 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.3.d.a.91.3 16 115.68 even 4
230.3.d.a.91.4 yes 16 5.3 odd 4
1150.3.c.c.1149.7 32 1.1 even 1 trivial
1150.3.c.c.1149.8 32 115.114 odd 2 inner
1150.3.c.c.1149.25 32 23.22 odd 2 inner
1150.3.c.c.1149.26 32 5.4 even 2 inner
1150.3.d.b.551.13 16 115.22 even 4
1150.3.d.b.551.14 16 5.2 odd 4
1840.3.k.d.321.9 16 460.183 odd 4
1840.3.k.d.321.10 16 20.3 even 4
2070.3.c.a.91.9 16 15.8 even 4
2070.3.c.a.91.16 16 345.68 odd 4