Properties

Label 175.4.a.d.1.1
Level $175$
Weight $4$
Character 175.1
Self dual yes
Analytic conductor $10.325$
Analytic rank $1$
Dimension $2$
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] = [175,4,Mod(1,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.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: \(10.3253342510\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.70156\) of defining polynomial
Character \(\chi\) \(=\) 175.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.70156 q^{2} +5.70156 q^{3} +5.70156 q^{4} -21.1047 q^{6} -7.00000 q^{7} +8.50781 q^{8} +5.50781 q^{9} +O(q^{10})\) \(q-3.70156 q^{2} +5.70156 q^{3} +5.70156 q^{4} -21.1047 q^{6} -7.00000 q^{7} +8.50781 q^{8} +5.50781 q^{9} -60.0156 q^{11} +32.5078 q^{12} -0.387503 q^{13} +25.9109 q^{14} -77.1047 q^{16} +35.4922 q^{17} -20.3875 q^{18} -6.08907 q^{19} -39.9109 q^{21} +222.152 q^{22} +31.5078 q^{23} +48.5078 q^{24} +1.43437 q^{26} -122.539 q^{27} -39.9109 q^{28} -292.942 q^{29} +130.303 q^{31} +217.345 q^{32} -342.183 q^{33} -131.377 q^{34} +31.4031 q^{36} -219.989 q^{37} +22.5391 q^{38} -2.20937 q^{39} -447.795 q^{41} +147.733 q^{42} -210.020 q^{43} -342.183 q^{44} -116.628 q^{46} -457.769 q^{47} -439.617 q^{48} +49.0000 q^{49} +202.361 q^{51} -2.20937 q^{52} -144.334 q^{53} +453.586 q^{54} -59.5547 q^{56} -34.7172 q^{57} +1084.34 q^{58} +767.328 q^{59} +667.884 q^{61} -482.325 q^{62} -38.5547 q^{63} -187.680 q^{64} +1266.61 q^{66} +77.4593 q^{67} +202.361 q^{68} +179.644 q^{69} -906.573 q^{71} +46.8594 q^{72} +1029.72 q^{73} +814.303 q^{74} -34.7172 q^{76} +420.109 q^{77} +8.17813 q^{78} -690.764 q^{79} -847.375 q^{81} +1657.54 q^{82} +979.408 q^{83} -227.555 q^{84} +777.403 q^{86} -1670.23 q^{87} -510.602 q^{88} -910.927 q^{89} +2.71252 q^{91} +179.644 q^{92} +742.931 q^{93} +1694.46 q^{94} +1239.21 q^{96} -11.1751 q^{97} -181.377 q^{98} -330.555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 5 q^{3} + 5 q^{4} - 23 q^{6} - 14 q^{7} - 15 q^{8} - 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + 5 q^{3} + 5 q^{4} - 23 q^{6} - 14 q^{7} - 15 q^{8} - 21 q^{9} - 56 q^{11} + 33 q^{12} - 52 q^{13} + 7 q^{14} - 135 q^{16} + 103 q^{17} - 92 q^{18} - 57 q^{19} - 35 q^{21} + 233 q^{22} + 31 q^{23} + 65 q^{24} - 138 q^{26} - 85 q^{27} - 35 q^{28} - 413 q^{29} - 162 q^{31} + 249 q^{32} - 345 q^{33} + 51 q^{34} + 50 q^{36} - 75 q^{37} - 115 q^{38} + 34 q^{39} - 505 q^{41} + 161 q^{42} + 73 q^{43} - 345 q^{44} - 118 q^{46} - 224 q^{47} - 399 q^{48} + 98 q^{49} + 155 q^{51} + 34 q^{52} + 262 q^{53} + 555 q^{54} + 105 q^{56} + q^{57} + 760 q^{58} + 190 q^{59} + 990 q^{61} - 1272 q^{62} + 147 q^{63} + 361 q^{64} + 1259 q^{66} - 908 q^{67} + 155 q^{68} + 180 q^{69} + 127 q^{71} + 670 q^{72} + 337 q^{73} + 1206 q^{74} + q^{76} + 392 q^{77} + 106 q^{78} - 1119 q^{79} - 158 q^{81} + 1503 q^{82} + 1517 q^{83} - 231 q^{84} + 1542 q^{86} - 1586 q^{87} - 605 q^{88} - 1713 q^{89} + 364 q^{91} + 180 q^{92} + 948 q^{93} + 2326 q^{94} + 1217 q^{96} - 1764 q^{97} - 49 q^{98} - 437 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.70156 −1.30870 −0.654350 0.756192i \(-0.727058\pi\)
−0.654350 + 0.756192i \(0.727058\pi\)
\(3\) 5.70156 1.09727 0.548633 0.836063i \(-0.315148\pi\)
0.548633 + 0.836063i \(0.315148\pi\)
\(4\) 5.70156 0.712695
\(5\) 0 0
\(6\) −21.1047 −1.43599
\(7\) −7.00000 −0.377964
\(8\) 8.50781 0.375996
\(9\) 5.50781 0.203993
\(10\) 0 0
\(11\) −60.0156 −1.64504 −0.822518 0.568739i \(-0.807431\pi\)
−0.822518 + 0.568739i \(0.807431\pi\)
\(12\) 32.5078 0.782016
\(13\) −0.387503 −0.00826723 −0.00413362 0.999991i \(-0.501316\pi\)
−0.00413362 + 0.999991i \(0.501316\pi\)
\(14\) 25.9109 0.494642
\(15\) 0 0
\(16\) −77.1047 −1.20476
\(17\) 35.4922 0.506360 0.253180 0.967419i \(-0.418524\pi\)
0.253180 + 0.967419i \(0.418524\pi\)
\(18\) −20.3875 −0.266966
\(19\) −6.08907 −0.0735225 −0.0367612 0.999324i \(-0.511704\pi\)
−0.0367612 + 0.999324i \(0.511704\pi\)
\(20\) 0 0
\(21\) −39.9109 −0.414728
\(22\) 222.152 2.15286
\(23\) 31.5078 0.285645 0.142822 0.989748i \(-0.454382\pi\)
0.142822 + 0.989748i \(0.454382\pi\)
\(24\) 48.5078 0.412567
\(25\) 0 0
\(26\) 1.43437 0.0108193
\(27\) −122.539 −0.873432
\(28\) −39.9109 −0.269373
\(29\) −292.942 −1.87579 −0.937896 0.346915i \(-0.887229\pi\)
−0.937896 + 0.346915i \(0.887229\pi\)
\(30\) 0 0
\(31\) 130.303 0.754940 0.377470 0.926022i \(-0.376794\pi\)
0.377470 + 0.926022i \(0.376794\pi\)
\(32\) 217.345 1.20067
\(33\) −342.183 −1.80504
\(34\) −131.377 −0.662673
\(35\) 0 0
\(36\) 31.4031 0.145385
\(37\) −219.989 −0.977459 −0.488729 0.872435i \(-0.662539\pi\)
−0.488729 + 0.872435i \(0.662539\pi\)
\(38\) 22.5391 0.0962189
\(39\) −2.20937 −0.00907135
\(40\) 0 0
\(41\) −447.795 −1.70570 −0.852852 0.522153i \(-0.825129\pi\)
−0.852852 + 0.522153i \(0.825129\pi\)
\(42\) 147.733 0.542754
\(43\) −210.020 −0.744832 −0.372416 0.928066i \(-0.621471\pi\)
−0.372416 + 0.928066i \(0.621471\pi\)
\(44\) −342.183 −1.17241
\(45\) 0 0
\(46\) −116.628 −0.373823
\(47\) −457.769 −1.42069 −0.710345 0.703854i \(-0.751461\pi\)
−0.710345 + 0.703854i \(0.751461\pi\)
\(48\) −439.617 −1.32194
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 202.361 0.555612
\(52\) −2.20937 −0.00589202
\(53\) −144.334 −0.374073 −0.187036 0.982353i \(-0.559888\pi\)
−0.187036 + 0.982353i \(0.559888\pi\)
\(54\) 453.586 1.14306
\(55\) 0 0
\(56\) −59.5547 −0.142113
\(57\) −34.7172 −0.0806737
\(58\) 1084.34 2.45485
\(59\) 767.328 1.69318 0.846590 0.532246i \(-0.178652\pi\)
0.846590 + 0.532246i \(0.178652\pi\)
\(60\) 0 0
\(61\) 667.884 1.40187 0.700933 0.713227i \(-0.252767\pi\)
0.700933 + 0.713227i \(0.252767\pi\)
\(62\) −482.325 −0.987989
\(63\) −38.5547 −0.0771021
\(64\) −187.680 −0.366562
\(65\) 0 0
\(66\) 1266.61 2.36226
\(67\) 77.4593 0.141241 0.0706206 0.997503i \(-0.477502\pi\)
0.0706206 + 0.997503i \(0.477502\pi\)
\(68\) 202.361 0.360880
\(69\) 179.644 0.313428
\(70\) 0 0
\(71\) −906.573 −1.51536 −0.757679 0.652627i \(-0.773667\pi\)
−0.757679 + 0.652627i \(0.773667\pi\)
\(72\) 46.8594 0.0767005
\(73\) 1029.72 1.65095 0.825477 0.564436i \(-0.190906\pi\)
0.825477 + 0.564436i \(0.190906\pi\)
\(74\) 814.303 1.27920
\(75\) 0 0
\(76\) −34.7172 −0.0523991
\(77\) 420.109 0.621765
\(78\) 8.17813 0.0118717
\(79\) −690.764 −0.983760 −0.491880 0.870663i \(-0.663690\pi\)
−0.491880 + 0.870663i \(0.663690\pi\)
\(80\) 0 0
\(81\) −847.375 −1.16238
\(82\) 1657.54 2.23225
\(83\) 979.408 1.29523 0.647614 0.761968i \(-0.275767\pi\)
0.647614 + 0.761968i \(0.275767\pi\)
\(84\) −227.555 −0.295574
\(85\) 0 0
\(86\) 777.403 0.974762
\(87\) −1670.23 −2.05824
\(88\) −510.602 −0.618526
\(89\) −910.927 −1.08492 −0.542461 0.840081i \(-0.682507\pi\)
−0.542461 + 0.840081i \(0.682507\pi\)
\(90\) 0 0
\(91\) 2.71252 0.00312472
\(92\) 179.644 0.203578
\(93\) 742.931 0.828370
\(94\) 1694.46 1.85926
\(95\) 0 0
\(96\) 1239.21 1.31746
\(97\) −11.1751 −0.0116975 −0.00584876 0.999983i \(-0.501862\pi\)
−0.00584876 + 0.999983i \(0.501862\pi\)
\(98\) −181.377 −0.186957
\(99\) −330.555 −0.335576
\(100\) 0 0
\(101\) 675.850 0.665837 0.332919 0.942956i \(-0.391967\pi\)
0.332919 + 0.942956i \(0.391967\pi\)
\(102\) −749.052 −0.727129
\(103\) 1528.88 1.46257 0.731286 0.682071i \(-0.238921\pi\)
0.731286 + 0.682071i \(0.238921\pi\)
\(104\) −3.29680 −0.00310844
\(105\) 0 0
\(106\) 534.263 0.489549
\(107\) −701.595 −0.633886 −0.316943 0.948445i \(-0.602656\pi\)
−0.316943 + 0.948445i \(0.602656\pi\)
\(108\) −698.664 −0.622491
\(109\) −597.130 −0.524722 −0.262361 0.964970i \(-0.584501\pi\)
−0.262361 + 0.964970i \(0.584501\pi\)
\(110\) 0 0
\(111\) −1254.28 −1.07253
\(112\) 539.733 0.455357
\(113\) −88.1187 −0.0733585 −0.0366792 0.999327i \(-0.511678\pi\)
−0.0366792 + 0.999327i \(0.511678\pi\)
\(114\) 128.508 0.105578
\(115\) 0 0
\(116\) −1670.23 −1.33687
\(117\) −2.13429 −0.00168646
\(118\) −2840.31 −2.21586
\(119\) −248.445 −0.191386
\(120\) 0 0
\(121\) 2270.87 1.70614
\(122\) −2472.22 −1.83462
\(123\) −2553.13 −1.87161
\(124\) 742.931 0.538042
\(125\) 0 0
\(126\) 142.713 0.100904
\(127\) 2119.35 1.48080 0.740401 0.672166i \(-0.234636\pi\)
0.740401 + 0.672166i \(0.234636\pi\)
\(128\) −1044.05 −0.720955
\(129\) −1197.44 −0.817279
\(130\) 0 0
\(131\) −264.294 −0.176271 −0.0881353 0.996109i \(-0.528091\pi\)
−0.0881353 + 0.996109i \(0.528091\pi\)
\(132\) −1950.98 −1.28644
\(133\) 42.6235 0.0277889
\(134\) −286.720 −0.184842
\(135\) 0 0
\(136\) 301.961 0.190389
\(137\) −468.227 −0.291995 −0.145997 0.989285i \(-0.546639\pi\)
−0.145997 + 0.989285i \(0.546639\pi\)
\(138\) −664.962 −0.410184
\(139\) 956.908 0.583913 0.291956 0.956432i \(-0.405694\pi\)
0.291956 + 0.956432i \(0.405694\pi\)
\(140\) 0 0
\(141\) −2610.00 −1.55888
\(142\) 3355.74 1.98315
\(143\) 23.2562 0.0135999
\(144\) −424.678 −0.245763
\(145\) 0 0
\(146\) −3811.57 −2.16060
\(147\) 279.377 0.156752
\(148\) −1254.28 −0.696630
\(149\) −382.967 −0.210563 −0.105282 0.994442i \(-0.533574\pi\)
−0.105282 + 0.994442i \(0.533574\pi\)
\(150\) 0 0
\(151\) 1302.98 0.702218 0.351109 0.936335i \(-0.385805\pi\)
0.351109 + 0.936335i \(0.385805\pi\)
\(152\) −51.8046 −0.0276441
\(153\) 195.484 0.103294
\(154\) −1555.06 −0.813704
\(155\) 0 0
\(156\) −12.5969 −0.00646511
\(157\) 3203.32 1.62836 0.814182 0.580610i \(-0.197186\pi\)
0.814182 + 0.580610i \(0.197186\pi\)
\(158\) 2556.91 1.28745
\(159\) −822.931 −0.410457
\(160\) 0 0
\(161\) −220.555 −0.107964
\(162\) 3136.61 1.52121
\(163\) −1368.81 −0.657752 −0.328876 0.944373i \(-0.606670\pi\)
−0.328876 + 0.944373i \(0.606670\pi\)
\(164\) −2553.13 −1.21565
\(165\) 0 0
\(166\) −3625.34 −1.69507
\(167\) −3073.34 −1.42409 −0.712043 0.702136i \(-0.752230\pi\)
−0.712043 + 0.702136i \(0.752230\pi\)
\(168\) −339.555 −0.155936
\(169\) −2196.85 −0.999932
\(170\) 0 0
\(171\) −33.5374 −0.0149981
\(172\) −1197.44 −0.530839
\(173\) 2402.16 1.05568 0.527841 0.849343i \(-0.323002\pi\)
0.527841 + 0.849343i \(0.323002\pi\)
\(174\) 6182.45 2.69362
\(175\) 0 0
\(176\) 4627.49 1.98187
\(177\) 4374.97 1.85787
\(178\) 3371.85 1.41984
\(179\) −1146.25 −0.478628 −0.239314 0.970942i \(-0.576923\pi\)
−0.239314 + 0.970942i \(0.576923\pi\)
\(180\) 0 0
\(181\) −475.847 −0.195411 −0.0977056 0.995215i \(-0.531150\pi\)
−0.0977056 + 0.995215i \(0.531150\pi\)
\(182\) −10.0406 −0.00408932
\(183\) 3807.98 1.53822
\(184\) 268.062 0.107401
\(185\) 0 0
\(186\) −2750.01 −1.08409
\(187\) −2130.09 −0.832980
\(188\) −2610.00 −1.01252
\(189\) 857.773 0.330126
\(190\) 0 0
\(191\) 990.003 0.375048 0.187524 0.982260i \(-0.439954\pi\)
0.187524 + 0.982260i \(0.439954\pi\)
\(192\) −1070.07 −0.402216
\(193\) −1392.88 −0.519492 −0.259746 0.965677i \(-0.583639\pi\)
−0.259746 + 0.965677i \(0.583639\pi\)
\(194\) 41.3653 0.0153085
\(195\) 0 0
\(196\) 279.377 0.101814
\(197\) 3583.39 1.29597 0.647985 0.761653i \(-0.275612\pi\)
0.647985 + 0.761653i \(0.275612\pi\)
\(198\) 1223.57 0.439168
\(199\) 623.947 0.222263 0.111132 0.993806i \(-0.464552\pi\)
0.111132 + 0.993806i \(0.464552\pi\)
\(200\) 0 0
\(201\) 441.639 0.154979
\(202\) −2501.70 −0.871381
\(203\) 2050.60 0.708983
\(204\) 1153.77 0.395982
\(205\) 0 0
\(206\) −5659.24 −1.91407
\(207\) 173.539 0.0582696
\(208\) 29.8783 0.00996004
\(209\) 365.439 0.120947
\(210\) 0 0
\(211\) 2266.48 0.739482 0.369741 0.929135i \(-0.379446\pi\)
0.369741 + 0.929135i \(0.379446\pi\)
\(212\) −822.931 −0.266600
\(213\) −5168.88 −1.66275
\(214\) 2597.00 0.829566
\(215\) 0 0
\(216\) −1042.54 −0.328406
\(217\) −912.122 −0.285340
\(218\) 2210.31 0.686703
\(219\) 5871.01 1.81154
\(220\) 0 0
\(221\) −13.7533 −0.00418620
\(222\) 4642.80 1.40362
\(223\) −2118.67 −0.636217 −0.318108 0.948054i \(-0.603048\pi\)
−0.318108 + 0.948054i \(0.603048\pi\)
\(224\) −1521.42 −0.453812
\(225\) 0 0
\(226\) 326.177 0.0960042
\(227\) −2790.62 −0.815948 −0.407974 0.912994i \(-0.633765\pi\)
−0.407974 + 0.912994i \(0.633765\pi\)
\(228\) −197.942 −0.0574958
\(229\) −5813.77 −1.67766 −0.838832 0.544390i \(-0.816761\pi\)
−0.838832 + 0.544390i \(0.816761\pi\)
\(230\) 0 0
\(231\) 2395.28 0.682242
\(232\) −2492.30 −0.705290
\(233\) −1936.18 −0.544392 −0.272196 0.962242i \(-0.587750\pi\)
−0.272196 + 0.962242i \(0.587750\pi\)
\(234\) 7.90022 0.00220707
\(235\) 0 0
\(236\) 4374.97 1.20672
\(237\) −3938.43 −1.07945
\(238\) 919.636 0.250467
\(239\) −2755.79 −0.745845 −0.372923 0.927862i \(-0.621644\pi\)
−0.372923 + 0.927862i \(0.621644\pi\)
\(240\) 0 0
\(241\) −4025.23 −1.07588 −0.537942 0.842982i \(-0.680798\pi\)
−0.537942 + 0.842982i \(0.680798\pi\)
\(242\) −8405.78 −2.23283
\(243\) −1522.81 −0.402009
\(244\) 3807.98 0.999103
\(245\) 0 0
\(246\) 9450.58 2.44938
\(247\) 2.35953 0.000607827 0
\(248\) 1108.59 0.283854
\(249\) 5584.15 1.42121
\(250\) 0 0
\(251\) 7166.64 1.80221 0.901104 0.433602i \(-0.142758\pi\)
0.901104 + 0.433602i \(0.142758\pi\)
\(252\) −219.822 −0.0549503
\(253\) −1890.96 −0.469896
\(254\) −7844.90 −1.93792
\(255\) 0 0
\(256\) 5366.07 1.31008
\(257\) −647.756 −0.157221 −0.0786107 0.996905i \(-0.525048\pi\)
−0.0786107 + 0.996905i \(0.525048\pi\)
\(258\) 4432.41 1.06957
\(259\) 1539.92 0.369445
\(260\) 0 0
\(261\) −1613.47 −0.382649
\(262\) 978.300 0.230685
\(263\) 6131.33 1.43754 0.718771 0.695246i \(-0.244705\pi\)
0.718771 + 0.695246i \(0.244705\pi\)
\(264\) −2911.23 −0.678688
\(265\) 0 0
\(266\) −157.773 −0.0363673
\(267\) −5193.70 −1.19045
\(268\) 441.639 0.100662
\(269\) −975.631 −0.221135 −0.110567 0.993869i \(-0.535267\pi\)
−0.110567 + 0.993869i \(0.535267\pi\)
\(270\) 0 0
\(271\) 4672.83 1.04743 0.523716 0.851893i \(-0.324545\pi\)
0.523716 + 0.851893i \(0.324545\pi\)
\(272\) −2736.61 −0.610043
\(273\) 15.4656 0.00342865
\(274\) 1733.17 0.382134
\(275\) 0 0
\(276\) 1024.25 0.223379
\(277\) −2390.16 −0.518451 −0.259226 0.965817i \(-0.583467\pi\)
−0.259226 + 0.965817i \(0.583467\pi\)
\(278\) −3542.05 −0.764166
\(279\) 717.685 0.154002
\(280\) 0 0
\(281\) −3321.28 −0.705092 −0.352546 0.935794i \(-0.614684\pi\)
−0.352546 + 0.935794i \(0.614684\pi\)
\(282\) 9661.07 2.04010
\(283\) −8260.15 −1.73504 −0.867518 0.497406i \(-0.834286\pi\)
−0.867518 + 0.497406i \(0.834286\pi\)
\(284\) −5168.88 −1.07999
\(285\) 0 0
\(286\) −86.0844 −0.0177982
\(287\) 3134.57 0.644696
\(288\) 1197.10 0.244929
\(289\) −3653.30 −0.743600
\(290\) 0 0
\(291\) −63.7155 −0.0128353
\(292\) 5871.01 1.17663
\(293\) 628.249 0.125265 0.0626326 0.998037i \(-0.480050\pi\)
0.0626326 + 0.998037i \(0.480050\pi\)
\(294\) −1034.13 −0.205142
\(295\) 0 0
\(296\) −1871.63 −0.367520
\(297\) 7354.26 1.43683
\(298\) 1417.58 0.275564
\(299\) −12.2094 −0.00236149
\(300\) 0 0
\(301\) 1470.14 0.281520
\(302\) −4823.06 −0.918993
\(303\) 3853.40 0.730601
\(304\) 469.495 0.0885770
\(305\) 0 0
\(306\) −723.597 −0.135181
\(307\) −25.2045 −0.00468565 −0.00234283 0.999997i \(-0.500746\pi\)
−0.00234283 + 0.999997i \(0.500746\pi\)
\(308\) 2395.28 0.443129
\(309\) 8716.99 1.60483
\(310\) 0 0
\(311\) −9436.18 −1.72050 −0.860252 0.509870i \(-0.829694\pi\)
−0.860252 + 0.509870i \(0.829694\pi\)
\(312\) −18.7969 −0.00341079
\(313\) 2778.60 0.501776 0.250888 0.968016i \(-0.419277\pi\)
0.250888 + 0.968016i \(0.419277\pi\)
\(314\) −11857.3 −2.13104
\(315\) 0 0
\(316\) −3938.43 −0.701121
\(317\) 2980.21 0.528030 0.264015 0.964519i \(-0.414953\pi\)
0.264015 + 0.964519i \(0.414953\pi\)
\(318\) 3046.13 0.537165
\(319\) 17581.1 3.08575
\(320\) 0 0
\(321\) −4000.19 −0.695541
\(322\) 816.397 0.141292
\(323\) −216.114 −0.0372289
\(324\) −4831.36 −0.828423
\(325\) 0 0
\(326\) 5066.74 0.860800
\(327\) −3404.57 −0.575759
\(328\) −3809.76 −0.641337
\(329\) 3204.38 0.536970
\(330\) 0 0
\(331\) 2588.16 0.429782 0.214891 0.976638i \(-0.431060\pi\)
0.214891 + 0.976638i \(0.431060\pi\)
\(332\) 5584.15 0.923103
\(333\) −1211.66 −0.199395
\(334\) 11376.2 1.86370
\(335\) 0 0
\(336\) 3077.32 0.499648
\(337\) −5284.64 −0.854221 −0.427110 0.904199i \(-0.640468\pi\)
−0.427110 + 0.904199i \(0.640468\pi\)
\(338\) 8131.78 1.30861
\(339\) −502.414 −0.0804938
\(340\) 0 0
\(341\) −7820.22 −1.24190
\(342\) 124.141 0.0196280
\(343\) −343.000 −0.0539949
\(344\) −1786.81 −0.280054
\(345\) 0 0
\(346\) −8891.75 −1.38157
\(347\) 11787.7 1.82363 0.911813 0.410606i \(-0.134683\pi\)
0.911813 + 0.410606i \(0.134683\pi\)
\(348\) −9522.91 −1.46690
\(349\) 8765.61 1.34445 0.672224 0.740347i \(-0.265339\pi\)
0.672224 + 0.740347i \(0.265339\pi\)
\(350\) 0 0
\(351\) 47.4843 0.00722086
\(352\) −13044.1 −1.97515
\(353\) −8578.29 −1.29342 −0.646709 0.762737i \(-0.723855\pi\)
−0.646709 + 0.762737i \(0.723855\pi\)
\(354\) −16194.2 −2.43139
\(355\) 0 0
\(356\) −5193.70 −0.773218
\(357\) −1416.53 −0.210001
\(358\) 4242.90 0.626380
\(359\) 3730.38 0.548417 0.274209 0.961670i \(-0.411584\pi\)
0.274209 + 0.961670i \(0.411584\pi\)
\(360\) 0 0
\(361\) −6821.92 −0.994594
\(362\) 1761.38 0.255735
\(363\) 12947.5 1.87209
\(364\) 15.4656 0.00222697
\(365\) 0 0
\(366\) −14095.5 −2.01307
\(367\) 515.769 0.0733594 0.0366797 0.999327i \(-0.488322\pi\)
0.0366797 + 0.999327i \(0.488322\pi\)
\(368\) −2429.40 −0.344134
\(369\) −2466.37 −0.347952
\(370\) 0 0
\(371\) 1010.34 0.141386
\(372\) 4235.87 0.590375
\(373\) −10922.0 −1.51614 −0.758071 0.652173i \(-0.773858\pi\)
−0.758071 + 0.652173i \(0.773858\pi\)
\(374\) 7884.64 1.09012
\(375\) 0 0
\(376\) −3894.61 −0.534173
\(377\) 113.516 0.0155076
\(378\) −3175.10 −0.432036
\(379\) −8403.14 −1.13889 −0.569446 0.822029i \(-0.692842\pi\)
−0.569446 + 0.822029i \(0.692842\pi\)
\(380\) 0 0
\(381\) 12083.6 1.62483
\(382\) −3664.56 −0.490825
\(383\) 3030.68 0.404336 0.202168 0.979351i \(-0.435201\pi\)
0.202168 + 0.979351i \(0.435201\pi\)
\(384\) −5952.74 −0.791080
\(385\) 0 0
\(386\) 5155.85 0.679859
\(387\) −1156.75 −0.151941
\(388\) −63.7155 −0.00833677
\(389\) 1403.25 0.182899 0.0914497 0.995810i \(-0.470850\pi\)
0.0914497 + 0.995810i \(0.470850\pi\)
\(390\) 0 0
\(391\) 1118.28 0.144639
\(392\) 416.883 0.0537137
\(393\) −1506.89 −0.193416
\(394\) −13264.1 −1.69604
\(395\) 0 0
\(396\) −1884.68 −0.239163
\(397\) −55.9118 −0.00706835 −0.00353417 0.999994i \(-0.501125\pi\)
−0.00353417 + 0.999994i \(0.501125\pi\)
\(398\) −2309.58 −0.290876
\(399\) 243.020 0.0304918
\(400\) 0 0
\(401\) −3730.18 −0.464529 −0.232264 0.972653i \(-0.574613\pi\)
−0.232264 + 0.972653i \(0.574613\pi\)
\(402\) −1634.75 −0.202821
\(403\) −50.4928 −0.00624126
\(404\) 3853.40 0.474539
\(405\) 0 0
\(406\) −7590.41 −0.927846
\(407\) 13202.8 1.60795
\(408\) 1721.65 0.208908
\(409\) −1968.50 −0.237985 −0.118993 0.992895i \(-0.537967\pi\)
−0.118993 + 0.992895i \(0.537967\pi\)
\(410\) 0 0
\(411\) −2669.62 −0.320396
\(412\) 8716.99 1.04237
\(413\) −5371.30 −0.639962
\(414\) −642.366 −0.0762574
\(415\) 0 0
\(416\) −84.2220 −0.00992625
\(417\) 5455.87 0.640708
\(418\) −1352.70 −0.158283
\(419\) −13208.4 −1.54003 −0.770015 0.638026i \(-0.779751\pi\)
−0.770015 + 0.638026i \(0.779751\pi\)
\(420\) 0 0
\(421\) −7485.74 −0.866586 −0.433293 0.901253i \(-0.642648\pi\)
−0.433293 + 0.901253i \(0.642648\pi\)
\(422\) −8389.50 −0.967760
\(423\) −2521.30 −0.289811
\(424\) −1227.97 −0.140650
\(425\) 0 0
\(426\) 19132.9 2.17604
\(427\) −4675.19 −0.529856
\(428\) −4000.19 −0.451767
\(429\) 132.597 0.0149227
\(430\) 0 0
\(431\) 10623.4 1.18726 0.593631 0.804737i \(-0.297694\pi\)
0.593631 + 0.804737i \(0.297694\pi\)
\(432\) 9448.34 1.05228
\(433\) −7268.73 −0.806727 −0.403364 0.915040i \(-0.632159\pi\)
−0.403364 + 0.915040i \(0.632159\pi\)
\(434\) 3376.28 0.373425
\(435\) 0 0
\(436\) −3404.57 −0.373967
\(437\) −191.853 −0.0210013
\(438\) −21731.9 −2.37076
\(439\) −743.352 −0.0808161 −0.0404080 0.999183i \(-0.512866\pi\)
−0.0404080 + 0.999183i \(0.512866\pi\)
\(440\) 0 0
\(441\) 269.883 0.0291419
\(442\) 50.9088 0.00547847
\(443\) −10857.8 −1.16449 −0.582246 0.813013i \(-0.697826\pi\)
−0.582246 + 0.813013i \(0.697826\pi\)
\(444\) −7151.36 −0.764389
\(445\) 0 0
\(446\) 7842.37 0.832617
\(447\) −2183.51 −0.231044
\(448\) 1313.76 0.138547
\(449\) −11162.9 −1.17329 −0.586645 0.809844i \(-0.699552\pi\)
−0.586645 + 0.809844i \(0.699552\pi\)
\(450\) 0 0
\(451\) 26874.7 2.80594
\(452\) −502.414 −0.0522822
\(453\) 7429.02 0.770520
\(454\) 10329.7 1.06783
\(455\) 0 0
\(456\) −295.367 −0.0303330
\(457\) −13451.0 −1.37683 −0.688414 0.725318i \(-0.741693\pi\)
−0.688414 + 0.725318i \(0.741693\pi\)
\(458\) 21520.0 2.19556
\(459\) −4349.18 −0.442271
\(460\) 0 0
\(461\) −9139.46 −0.923356 −0.461678 0.887048i \(-0.652752\pi\)
−0.461678 + 0.887048i \(0.652752\pi\)
\(462\) −8866.28 −0.892850
\(463\) 13122.5 1.31718 0.658588 0.752504i \(-0.271154\pi\)
0.658588 + 0.752504i \(0.271154\pi\)
\(464\) 22587.2 2.25988
\(465\) 0 0
\(466\) 7166.89 0.712446
\(467\) −11921.2 −1.18126 −0.590629 0.806943i \(-0.701120\pi\)
−0.590629 + 0.806943i \(0.701120\pi\)
\(468\) −12.1688 −0.00120193
\(469\) −542.215 −0.0533842
\(470\) 0 0
\(471\) 18264.0 1.78675
\(472\) 6528.28 0.636628
\(473\) 12604.5 1.22528
\(474\) 14578.4 1.41267
\(475\) 0 0
\(476\) −1416.53 −0.136400
\(477\) −794.966 −0.0763082
\(478\) 10200.7 0.976088
\(479\) 825.281 0.0787224 0.0393612 0.999225i \(-0.487468\pi\)
0.0393612 + 0.999225i \(0.487468\pi\)
\(480\) 0 0
\(481\) 85.2464 0.00808088
\(482\) 14899.6 1.40801
\(483\) −1257.51 −0.118465
\(484\) 12947.5 1.21596
\(485\) 0 0
\(486\) 5636.76 0.526108
\(487\) 6678.32 0.621404 0.310702 0.950507i \(-0.399436\pi\)
0.310702 + 0.950507i \(0.399436\pi\)
\(488\) 5682.23 0.527096
\(489\) −7804.36 −0.721729
\(490\) 0 0
\(491\) −3098.65 −0.284807 −0.142403 0.989809i \(-0.545483\pi\)
−0.142403 + 0.989809i \(0.545483\pi\)
\(492\) −14556.8 −1.33389
\(493\) −10397.2 −0.949827
\(494\) −8.73395 −0.000795464 0
\(495\) 0 0
\(496\) −10047.0 −0.909522
\(497\) 6346.01 0.572752
\(498\) −20670.1 −1.85994
\(499\) −2265.10 −0.203206 −0.101603 0.994825i \(-0.532397\pi\)
−0.101603 + 0.994825i \(0.532397\pi\)
\(500\) 0 0
\(501\) −17522.8 −1.56260
\(502\) −26527.8 −2.35855
\(503\) 9980.43 0.884703 0.442351 0.896842i \(-0.354144\pi\)
0.442351 + 0.896842i \(0.354144\pi\)
\(504\) −328.016 −0.0289901
\(505\) 0 0
\(506\) 6999.51 0.614953
\(507\) −12525.5 −1.09719
\(508\) 12083.6 1.05536
\(509\) −4956.16 −0.431588 −0.215794 0.976439i \(-0.569234\pi\)
−0.215794 + 0.976439i \(0.569234\pi\)
\(510\) 0 0
\(511\) −7208.04 −0.624002
\(512\) −11510.4 −0.993541
\(513\) 746.148 0.0642169
\(514\) 2397.71 0.205756
\(515\) 0 0
\(516\) −6827.30 −0.582471
\(517\) 27473.3 2.33709
\(518\) −5700.12 −0.483492
\(519\) 13696.1 1.15836
\(520\) 0 0
\(521\) 3442.97 0.289519 0.144759 0.989467i \(-0.453759\pi\)
0.144759 + 0.989467i \(0.453759\pi\)
\(522\) 5972.36 0.500772
\(523\) 11109.9 0.928878 0.464439 0.885605i \(-0.346256\pi\)
0.464439 + 0.885605i \(0.346256\pi\)
\(524\) −1506.89 −0.125627
\(525\) 0 0
\(526\) −22695.5 −1.88131
\(527\) 4624.74 0.382271
\(528\) 26383.9 2.17464
\(529\) −11174.3 −0.918407
\(530\) 0 0
\(531\) 4226.30 0.345397
\(532\) 243.020 0.0198050
\(533\) 173.522 0.0141015
\(534\) 19224.8 1.55794
\(535\) 0 0
\(536\) 659.009 0.0531061
\(537\) −6535.39 −0.525182
\(538\) 3611.36 0.289399
\(539\) −2940.77 −0.235005
\(540\) 0 0
\(541\) 3680.65 0.292502 0.146251 0.989248i \(-0.453279\pi\)
0.146251 + 0.989248i \(0.453279\pi\)
\(542\) −17296.8 −1.37078
\(543\) −2713.07 −0.214418
\(544\) 7714.06 0.607974
\(545\) 0 0
\(546\) −57.2469 −0.00448707
\(547\) −14657.4 −1.14572 −0.572858 0.819655i \(-0.694165\pi\)
−0.572858 + 0.819655i \(0.694165\pi\)
\(548\) −2669.62 −0.208103
\(549\) 3678.58 0.285971
\(550\) 0 0
\(551\) 1783.74 0.137913
\(552\) 1528.37 0.117848
\(553\) 4835.35 0.371826
\(554\) 8847.33 0.678497
\(555\) 0 0
\(556\) 5455.87 0.416152
\(557\) 6547.61 0.498081 0.249040 0.968493i \(-0.419885\pi\)
0.249040 + 0.968493i \(0.419885\pi\)
\(558\) −2656.55 −0.201543
\(559\) 81.3835 0.00615770
\(560\) 0 0
\(561\) −12144.8 −0.914001
\(562\) 12293.9 0.922754
\(563\) 11983.3 0.897047 0.448523 0.893771i \(-0.351950\pi\)
0.448523 + 0.893771i \(0.351950\pi\)
\(564\) −14881.1 −1.11100
\(565\) 0 0
\(566\) 30575.5 2.27064
\(567\) 5931.62 0.439338
\(568\) −7712.95 −0.569768
\(569\) 19164.8 1.41200 0.706002 0.708210i \(-0.250497\pi\)
0.706002 + 0.708210i \(0.250497\pi\)
\(570\) 0 0
\(571\) 14618.8 1.07142 0.535708 0.844403i \(-0.320045\pi\)
0.535708 + 0.844403i \(0.320045\pi\)
\(572\) 132.597 0.00969258
\(573\) 5644.57 0.411527
\(574\) −11602.8 −0.843713
\(575\) 0 0
\(576\) −1033.70 −0.0747760
\(577\) −12446.8 −0.898033 −0.449017 0.893523i \(-0.648226\pi\)
−0.449017 + 0.893523i \(0.648226\pi\)
\(578\) 13522.9 0.973149
\(579\) −7941.62 −0.570021
\(580\) 0 0
\(581\) −6855.85 −0.489550
\(582\) 235.847 0.0167976
\(583\) 8662.32 0.615363
\(584\) 8760.66 0.620752
\(585\) 0 0
\(586\) −2325.50 −0.163935
\(587\) 7467.53 0.525073 0.262537 0.964922i \(-0.415441\pi\)
0.262537 + 0.964922i \(0.415441\pi\)
\(588\) 1592.88 0.111717
\(589\) −793.424 −0.0555050
\(590\) 0 0
\(591\) 20430.9 1.42202
\(592\) 16962.2 1.17760
\(593\) −26703.9 −1.84924 −0.924619 0.380892i \(-0.875617\pi\)
−0.924619 + 0.380892i \(0.875617\pi\)
\(594\) −27222.2 −1.88037
\(595\) 0 0
\(596\) −2183.51 −0.150067
\(597\) 3557.47 0.243882
\(598\) 45.1938 0.00309048
\(599\) 6896.60 0.470430 0.235215 0.971943i \(-0.424421\pi\)
0.235215 + 0.971943i \(0.424421\pi\)
\(600\) 0 0
\(601\) 18156.5 1.23231 0.616154 0.787626i \(-0.288690\pi\)
0.616154 + 0.787626i \(0.288690\pi\)
\(602\) −5441.82 −0.368425
\(603\) 426.631 0.0288122
\(604\) 7429.02 0.500468
\(605\) 0 0
\(606\) −14263.6 −0.956137
\(607\) 2074.50 0.138717 0.0693587 0.997592i \(-0.477905\pi\)
0.0693587 + 0.997592i \(0.477905\pi\)
\(608\) −1323.43 −0.0882766
\(609\) 11691.6 0.777943
\(610\) 0 0
\(611\) 177.387 0.0117452
\(612\) 1114.57 0.0736171
\(613\) −12159.4 −0.801162 −0.400581 0.916261i \(-0.631192\pi\)
−0.400581 + 0.916261i \(0.631192\pi\)
\(614\) 93.2959 0.00613211
\(615\) 0 0
\(616\) 3574.21 0.233781
\(617\) 4359.84 0.284474 0.142237 0.989833i \(-0.454570\pi\)
0.142237 + 0.989833i \(0.454570\pi\)
\(618\) −32266.5 −2.10024
\(619\) −29046.6 −1.88608 −0.943038 0.332684i \(-0.892046\pi\)
−0.943038 + 0.332684i \(0.892046\pi\)
\(620\) 0 0
\(621\) −3860.94 −0.249491
\(622\) 34928.6 2.25162
\(623\) 6376.49 0.410062
\(624\) 170.353 0.0109288
\(625\) 0 0
\(626\) −10285.2 −0.656674
\(627\) 2083.57 0.132711
\(628\) 18264.0 1.16053
\(629\) −7807.89 −0.494946
\(630\) 0 0
\(631\) −14708.4 −0.927946 −0.463973 0.885849i \(-0.653577\pi\)
−0.463973 + 0.885849i \(0.653577\pi\)
\(632\) −5876.89 −0.369889
\(633\) 12922.5 0.811408
\(634\) −11031.4 −0.691033
\(635\) 0 0
\(636\) −4691.99 −0.292531
\(637\) −18.9876 −0.00118103
\(638\) −65077.6 −4.03832
\(639\) −4993.23 −0.309123
\(640\) 0 0
\(641\) −24048.7 −1.48185 −0.740925 0.671588i \(-0.765612\pi\)
−0.740925 + 0.671588i \(0.765612\pi\)
\(642\) 14806.9 0.910255
\(643\) −19196.1 −1.17732 −0.588661 0.808380i \(-0.700345\pi\)
−0.588661 + 0.808380i \(0.700345\pi\)
\(644\) −1257.51 −0.0769452
\(645\) 0 0
\(646\) 799.960 0.0487214
\(647\) −7185.82 −0.436636 −0.218318 0.975878i \(-0.570057\pi\)
−0.218318 + 0.975878i \(0.570057\pi\)
\(648\) −7209.31 −0.437050
\(649\) −46051.7 −2.78534
\(650\) 0 0
\(651\) −5200.52 −0.313094
\(652\) −7804.36 −0.468777
\(653\) −403.329 −0.0241707 −0.0120854 0.999927i \(-0.503847\pi\)
−0.0120854 + 0.999927i \(0.503847\pi\)
\(654\) 12602.2 0.753496
\(655\) 0 0
\(656\) 34527.1 2.05497
\(657\) 5671.50 0.336783
\(658\) −11861.2 −0.702733
\(659\) 20527.9 1.21343 0.606716 0.794919i \(-0.292487\pi\)
0.606716 + 0.794919i \(0.292487\pi\)
\(660\) 0 0
\(661\) −4372.75 −0.257307 −0.128654 0.991690i \(-0.541066\pi\)
−0.128654 + 0.991690i \(0.541066\pi\)
\(662\) −9580.22 −0.562456
\(663\) −78.4155 −0.00459337
\(664\) 8332.62 0.487000
\(665\) 0 0
\(666\) 4485.03 0.260948
\(667\) −9229.97 −0.535811
\(668\) −17522.8 −1.01494
\(669\) −12079.7 −0.698099
\(670\) 0 0
\(671\) −40083.5 −2.30612
\(672\) −8674.45 −0.497953
\(673\) 19902.7 1.13996 0.569980 0.821659i \(-0.306951\pi\)
0.569980 + 0.821659i \(0.306951\pi\)
\(674\) 19561.4 1.11792
\(675\) 0 0
\(676\) −12525.5 −0.712647
\(677\) −9714.40 −0.551484 −0.275742 0.961232i \(-0.588924\pi\)
−0.275742 + 0.961232i \(0.588924\pi\)
\(678\) 1859.72 0.105342
\(679\) 78.2257 0.00442125
\(680\) 0 0
\(681\) −15910.9 −0.895312
\(682\) 28947.0 1.62528
\(683\) 88.0227 0.00493132 0.00246566 0.999997i \(-0.499215\pi\)
0.00246566 + 0.999997i \(0.499215\pi\)
\(684\) −191.216 −0.0106891
\(685\) 0 0
\(686\) 1269.64 0.0706631
\(687\) −33147.6 −1.84084
\(688\) 16193.5 0.897345
\(689\) 55.9300 0.00309254
\(690\) 0 0
\(691\) 3722.48 0.204934 0.102467 0.994736i \(-0.467326\pi\)
0.102467 + 0.994736i \(0.467326\pi\)
\(692\) 13696.1 0.752380
\(693\) 2313.88 0.126836
\(694\) −43633.0 −2.38658
\(695\) 0 0
\(696\) −14210.0 −0.773891
\(697\) −15893.2 −0.863700
\(698\) −32446.5 −1.75948
\(699\) −11039.2 −0.597343
\(700\) 0 0
\(701\) 13167.2 0.709443 0.354722 0.934972i \(-0.384576\pi\)
0.354722 + 0.934972i \(0.384576\pi\)
\(702\) −175.766 −0.00944994
\(703\) 1339.53 0.0718652
\(704\) 11263.7 0.603007
\(705\) 0 0
\(706\) 31753.1 1.69270
\(707\) −4730.95 −0.251663
\(708\) 24944.2 1.32409
\(709\) −14539.6 −0.770166 −0.385083 0.922882i \(-0.625827\pi\)
−0.385083 + 0.922882i \(0.625827\pi\)
\(710\) 0 0
\(711\) −3804.60 −0.200680
\(712\) −7749.99 −0.407926
\(713\) 4105.57 0.215645
\(714\) 5243.36 0.274829
\(715\) 0 0
\(716\) −6535.39 −0.341116
\(717\) −15712.3 −0.818391
\(718\) −13808.2 −0.717713
\(719\) 26509.9 1.37504 0.687519 0.726166i \(-0.258700\pi\)
0.687519 + 0.726166i \(0.258700\pi\)
\(720\) 0 0
\(721\) −10702.1 −0.552800
\(722\) 25251.8 1.30163
\(723\) −22950.1 −1.18053
\(724\) −2713.07 −0.139269
\(725\) 0 0
\(726\) −47926.1 −2.45001
\(727\) −11761.8 −0.600030 −0.300015 0.953934i \(-0.596992\pi\)
−0.300015 + 0.953934i \(0.596992\pi\)
\(728\) 23.0776 0.00117488
\(729\) 14196.7 0.721270
\(730\) 0 0
\(731\) −7454.08 −0.377153
\(732\) 21711.5 1.09628
\(733\) 6458.47 0.325442 0.162721 0.986672i \(-0.447973\pi\)
0.162721 + 0.986672i \(0.447973\pi\)
\(734\) −1909.15 −0.0960055
\(735\) 0 0
\(736\) 6848.07 0.342967
\(737\) −4648.77 −0.232347
\(738\) 9129.43 0.455364
\(739\) 33663.0 1.67566 0.837830 0.545932i \(-0.183824\pi\)
0.837830 + 0.545932i \(0.183824\pi\)
\(740\) 0 0
\(741\) 13.4530 0.000666948 0
\(742\) −3739.84 −0.185032
\(743\) 19979.4 0.986506 0.493253 0.869886i \(-0.335808\pi\)
0.493253 + 0.869886i \(0.335808\pi\)
\(744\) 6320.72 0.311463
\(745\) 0 0
\(746\) 40428.5 1.98417
\(747\) 5394.39 0.264218
\(748\) −12144.8 −0.593661
\(749\) 4911.17 0.239586
\(750\) 0 0
\(751\) −31850.0 −1.54757 −0.773785 0.633449i \(-0.781639\pi\)
−0.773785 + 0.633449i \(0.781639\pi\)
\(752\) 35296.1 1.71159
\(753\) 40861.1 1.97750
\(754\) −420.186 −0.0202948
\(755\) 0 0
\(756\) 4890.65 0.235279
\(757\) 39396.6 1.89154 0.945769 0.324840i \(-0.105310\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(758\) 31104.7 1.49047
\(759\) −10781.4 −0.515601
\(760\) 0 0
\(761\) −7170.87 −0.341582 −0.170791 0.985307i \(-0.554632\pi\)
−0.170791 + 0.985307i \(0.554632\pi\)
\(762\) −44728.2 −2.12642
\(763\) 4179.91 0.198326
\(764\) 5644.57 0.267295
\(765\) 0 0
\(766\) −11218.3 −0.529154
\(767\) −297.342 −0.0139979
\(768\) 30595.0 1.43750
\(769\) 27056.7 1.26878 0.634388 0.773015i \(-0.281252\pi\)
0.634388 + 0.773015i \(0.281252\pi\)
\(770\) 0 0
\(771\) −3693.22 −0.172514
\(772\) −7941.62 −0.370240
\(773\) −40087.8 −1.86527 −0.932637 0.360815i \(-0.882499\pi\)
−0.932637 + 0.360815i \(0.882499\pi\)
\(774\) 4281.79 0.198845
\(775\) 0 0
\(776\) −95.0757 −0.00439822
\(777\) 8779.97 0.405379
\(778\) −5194.23 −0.239360
\(779\) 2726.65 0.125408
\(780\) 0 0
\(781\) 54408.6 2.49282
\(782\) −4139.39 −0.189289
\(783\) 35896.9 1.63838
\(784\) −3778.13 −0.172109
\(785\) 0 0
\(786\) 5577.84 0.253123
\(787\) 23501.4 1.06447 0.532233 0.846598i \(-0.321353\pi\)
0.532233 + 0.846598i \(0.321353\pi\)
\(788\) 20430.9 0.923632
\(789\) 34958.1 1.57737
\(790\) 0 0
\(791\) 616.831 0.0277269
\(792\) −2812.30 −0.126175
\(793\) −258.807 −0.0115896
\(794\) 206.961 0.00925035
\(795\) 0 0
\(796\) 3557.47 0.158406
\(797\) 1635.92 0.0727066 0.0363533 0.999339i \(-0.488426\pi\)
0.0363533 + 0.999339i \(0.488426\pi\)
\(798\) −899.555 −0.0399046
\(799\) −16247.2 −0.719381
\(800\) 0 0
\(801\) −5017.21 −0.221316
\(802\) 13807.5 0.607929
\(803\) −61799.3 −2.71588
\(804\) 2518.03 0.110453
\(805\) 0 0
\(806\) 186.902 0.00816794
\(807\) −5562.62 −0.242644
\(808\) 5750.00 0.250352
\(809\) −33824.6 −1.46998 −0.734988 0.678080i \(-0.762812\pi\)
−0.734988 + 0.678080i \(0.762812\pi\)
\(810\) 0 0
\(811\) −3636.30 −0.157445 −0.0787224 0.996897i \(-0.525084\pi\)
−0.0787224 + 0.996897i \(0.525084\pi\)
\(812\) 11691.6 0.505289
\(813\) 26642.4 1.14931
\(814\) −48870.9 −2.10433
\(815\) 0 0
\(816\) −15603.0 −0.669379
\(817\) 1278.83 0.0547619
\(818\) 7286.52 0.311451
\(819\) 14.9401 0.000637421 0
\(820\) 0 0
\(821\) 2417.39 0.102762 0.0513808 0.998679i \(-0.483638\pi\)
0.0513808 + 0.998679i \(0.483638\pi\)
\(822\) 9881.78 0.419302
\(823\) −15752.2 −0.667178 −0.333589 0.942719i \(-0.608260\pi\)
−0.333589 + 0.942719i \(0.608260\pi\)
\(824\) 13007.4 0.549920
\(825\) 0 0
\(826\) 19882.2 0.837518
\(827\) −4850.49 −0.203952 −0.101976 0.994787i \(-0.532516\pi\)
−0.101976 + 0.994787i \(0.532516\pi\)
\(828\) 989.444 0.0415284
\(829\) 33160.3 1.38927 0.694636 0.719362i \(-0.255566\pi\)
0.694636 + 0.719362i \(0.255566\pi\)
\(830\) 0 0
\(831\) −13627.7 −0.568879
\(832\) 72.7264 0.00303045
\(833\) 1739.12 0.0723371
\(834\) −20195.2 −0.838494
\(835\) 0 0
\(836\) 2083.57 0.0861984
\(837\) −15967.2 −0.659388
\(838\) 48891.7 2.01544
\(839\) 14966.6 0.615857 0.307929 0.951409i \(-0.400364\pi\)
0.307929 + 0.951409i \(0.400364\pi\)
\(840\) 0 0
\(841\) 61426.1 2.51860
\(842\) 27708.9 1.13410
\(843\) −18936.5 −0.773674
\(844\) 12922.5 0.527025
\(845\) 0 0
\(846\) 9332.76 0.379275
\(847\) −15896.1 −0.644861
\(848\) 11128.9 0.450668
\(849\) −47095.8 −1.90380
\(850\) 0 0
\(851\) −6931.37 −0.279206
\(852\) −29470.7 −1.18504
\(853\) 5806.35 0.233066 0.116533 0.993187i \(-0.462822\pi\)
0.116533 + 0.993187i \(0.462822\pi\)
\(854\) 17305.5 0.693422
\(855\) 0 0
\(856\) −5969.04 −0.238338
\(857\) 9191.52 0.366367 0.183183 0.983079i \(-0.441360\pi\)
0.183183 + 0.983079i \(0.441360\pi\)
\(858\) −490.816 −0.0195293
\(859\) 15029.2 0.596962 0.298481 0.954416i \(-0.403520\pi\)
0.298481 + 0.954416i \(0.403520\pi\)
\(860\) 0 0
\(861\) 17871.9 0.707403
\(862\) −39323.1 −1.55377
\(863\) −17147.5 −0.676369 −0.338185 0.941080i \(-0.609813\pi\)
−0.338185 + 0.941080i \(0.609813\pi\)
\(864\) −26633.3 −1.04871
\(865\) 0 0
\(866\) 26905.7 1.05576
\(867\) −20829.5 −0.815927
\(868\) −5200.52 −0.203361
\(869\) 41456.6 1.61832
\(870\) 0 0
\(871\) −30.0157 −0.00116767
\(872\) −5080.27 −0.197293
\(873\) −61.5504 −0.00238621
\(874\) 710.156 0.0274844
\(875\) 0 0
\(876\) 33473.9 1.29107
\(877\) −33483.6 −1.28924 −0.644618 0.764505i \(-0.722984\pi\)
−0.644618 + 0.764505i \(0.722984\pi\)
\(878\) 2751.56 0.105764
\(879\) 3582.00 0.137449
\(880\) 0 0
\(881\) −10695.6 −0.409019 −0.204509 0.978865i \(-0.565560\pi\)
−0.204509 + 0.978865i \(0.565560\pi\)
\(882\) −998.988 −0.0381379
\(883\) 31934.0 1.21706 0.608531 0.793530i \(-0.291759\pi\)
0.608531 + 0.793530i \(0.291759\pi\)
\(884\) −78.4155 −0.00298348
\(885\) 0 0
\(886\) 40190.9 1.52397
\(887\) 10655.2 0.403345 0.201672 0.979453i \(-0.435362\pi\)
0.201672 + 0.979453i \(0.435362\pi\)
\(888\) −10671.2 −0.403268
\(889\) −14835.4 −0.559690
\(890\) 0 0
\(891\) 50855.7 1.91216
\(892\) −12079.7 −0.453429
\(893\) 2787.38 0.104453
\(894\) 8082.41 0.302367
\(895\) 0 0
\(896\) 7308.38 0.272495
\(897\) −69.6125 −0.00259119
\(898\) 41320.0 1.53549
\(899\) −38171.3 −1.41611
\(900\) 0 0
\(901\) −5122.74 −0.189415
\(902\) −99478.4 −3.67214
\(903\) 8382.11 0.308903
\(904\) −749.697 −0.0275825
\(905\) 0 0
\(906\) −27499.0 −1.00838
\(907\) −20737.2 −0.759171 −0.379585 0.925157i \(-0.623933\pi\)
−0.379585 + 0.925157i \(0.623933\pi\)
\(908\) −15910.9 −0.581522
\(909\) 3722.45 0.135826
\(910\) 0 0
\(911\) 11734.8 0.426774 0.213387 0.976968i \(-0.431550\pi\)
0.213387 + 0.976968i \(0.431550\pi\)
\(912\) 2676.86 0.0971926
\(913\) −58779.8 −2.13070
\(914\) 49789.7 1.80185
\(915\) 0 0
\(916\) −33147.6 −1.19566
\(917\) 1850.06 0.0666240
\(918\) 16098.8 0.578800
\(919\) −21922.8 −0.786906 −0.393453 0.919345i \(-0.628720\pi\)
−0.393453 + 0.919345i \(0.628720\pi\)
\(920\) 0 0
\(921\) −143.705 −0.00514141
\(922\) 33830.3 1.20840
\(923\) 351.300 0.0125278
\(924\) 13656.8 0.486230
\(925\) 0 0
\(926\) −48573.6 −1.72379
\(927\) 8420.77 0.298354
\(928\) −63669.6 −2.25222
\(929\) −36647.7 −1.29427 −0.647133 0.762377i \(-0.724032\pi\)
−0.647133 + 0.762377i \(0.724032\pi\)
\(930\) 0 0
\(931\) −298.364 −0.0105032
\(932\) −11039.2 −0.387986
\(933\) −53801.0 −1.88785
\(934\) 44127.1 1.54591
\(935\) 0 0
\(936\) −18.1582 −0.000634101 0
\(937\) 24959.7 0.870222 0.435111 0.900377i \(-0.356709\pi\)
0.435111 + 0.900377i \(0.356709\pi\)
\(938\) 2007.04 0.0698638
\(939\) 15842.4 0.550581
\(940\) 0 0
\(941\) 17086.7 0.591935 0.295968 0.955198i \(-0.404358\pi\)
0.295968 + 0.955198i \(0.404358\pi\)
\(942\) −67605.2 −2.33832
\(943\) −14109.0 −0.487226
\(944\) −59164.6 −2.03988
\(945\) 0 0
\(946\) −46656.3 −1.60352
\(947\) 54034.9 1.85417 0.927085 0.374852i \(-0.122307\pi\)
0.927085 + 0.374852i \(0.122307\pi\)
\(948\) −22455.2 −0.769316
\(949\) −399.020 −0.0136488
\(950\) 0 0
\(951\) 16991.9 0.579389
\(952\) −2113.73 −0.0719603
\(953\) −24377.9 −0.828622 −0.414311 0.910135i \(-0.635977\pi\)
−0.414311 + 0.910135i \(0.635977\pi\)
\(954\) 2942.62 0.0998645
\(955\) 0 0
\(956\) −15712.3 −0.531561
\(957\) 100240. 3.38588
\(958\) −3054.83 −0.103024
\(959\) 3277.59 0.110364
\(960\) 0 0
\(961\) −12812.1 −0.430066
\(962\) −315.545 −0.0105754
\(963\) −3864.25 −0.129308
\(964\) −22950.1 −0.766777
\(965\) 0 0
\(966\) 4654.74 0.155035
\(967\) −32668.1 −1.08639 −0.543194 0.839607i \(-0.682785\pi\)
−0.543194 + 0.839607i \(0.682785\pi\)
\(968\) 19320.2 0.641502
\(969\) −1232.19 −0.0408500
\(970\) 0 0
\(971\) 24623.2 0.813795 0.406898 0.913474i \(-0.366611\pi\)
0.406898 + 0.913474i \(0.366611\pi\)
\(972\) −8682.37 −0.286510
\(973\) −6698.36 −0.220698
\(974\) −24720.2 −0.813231
\(975\) 0 0
\(976\) −51497.0 −1.68891
\(977\) −18320.6 −0.599926 −0.299963 0.953951i \(-0.596974\pi\)
−0.299963 + 0.953951i \(0.596974\pi\)
\(978\) 28888.3 0.944526
\(979\) 54669.8 1.78473
\(980\) 0 0
\(981\) −3288.88 −0.107040
\(982\) 11469.8 0.372727
\(983\) 2176.33 0.0706145 0.0353072 0.999377i \(-0.488759\pi\)
0.0353072 + 0.999377i \(0.488759\pi\)
\(984\) −21721.6 −0.703718
\(985\) 0 0
\(986\) 38485.7 1.24304
\(987\) 18270.0 0.589199
\(988\) 13.4530 0.000433196 0
\(989\) −6617.28 −0.212758
\(990\) 0 0
\(991\) −21487.2 −0.688761 −0.344381 0.938830i \(-0.611911\pi\)
−0.344381 + 0.938830i \(0.611911\pi\)
\(992\) 28320.8 0.906437
\(993\) 14756.5 0.471586
\(994\) −23490.2 −0.749560
\(995\) 0 0
\(996\) 31838.4 1.01289
\(997\) −19083.0 −0.606182 −0.303091 0.952962i \(-0.598019\pi\)
−0.303091 + 0.952962i \(0.598019\pi\)
\(998\) 8384.41 0.265936
\(999\) 26957.2 0.853743
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 175.4.a.d.1.1 2
3.2 odd 2 1575.4.a.v.1.2 2
5.2 odd 4 175.4.b.d.99.1 4
5.3 odd 4 175.4.b.d.99.4 4
5.4 even 2 175.4.a.e.1.2 yes 2
7.6 odd 2 1225.4.a.r.1.1 2
15.14 odd 2 1575.4.a.s.1.1 2
35.34 odd 2 1225.4.a.t.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.4.a.d.1.1 2 1.1 even 1 trivial
175.4.a.e.1.2 yes 2 5.4 even 2
175.4.b.d.99.1 4 5.2 odd 4
175.4.b.d.99.4 4 5.3 odd 4
1225.4.a.r.1.1 2 7.6 odd 2
1225.4.a.t.1.2 2 35.34 odd 2
1575.4.a.s.1.1 2 15.14 odd 2
1575.4.a.v.1.2 2 3.2 odd 2