Properties

Label 3525.2.a.bi.1.2
Level $3525$
Weight $2$
Character 3525.1
Self dual yes
Analytic conductor $28.147$
Analytic rank $0$
Dimension $13$
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] = [3525,2,Mod(1,3525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3525.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.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: \(28.1472667125\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} - 923 x^{4} - 107 x^{3} + 293 x^{2} + 12 x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 705)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.24873\) of defining polynomial
Character \(\chi\) \(=\) 3525.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.24873 q^{2} +1.00000 q^{3} +3.05678 q^{4} -2.24873 q^{6} -1.38491 q^{7} -2.37640 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.24873 q^{2} +1.00000 q^{3} +3.05678 q^{4} -2.24873 q^{6} -1.38491 q^{7} -2.37640 q^{8} +1.00000 q^{9} +5.19292 q^{11} +3.05678 q^{12} +2.59916 q^{13} +3.11429 q^{14} -0.769670 q^{16} -3.45174 q^{17} -2.24873 q^{18} +1.01677 q^{19} -1.38491 q^{21} -11.6775 q^{22} -2.00367 q^{23} -2.37640 q^{24} -5.84480 q^{26} +1.00000 q^{27} -4.23336 q^{28} +7.23539 q^{29} -0.286932 q^{31} +6.48358 q^{32} +5.19292 q^{33} +7.76203 q^{34} +3.05678 q^{36} +4.63981 q^{37} -2.28643 q^{38} +2.59916 q^{39} -0.775913 q^{41} +3.11429 q^{42} +2.06895 q^{43} +15.8736 q^{44} +4.50571 q^{46} +1.00000 q^{47} -0.769670 q^{48} -5.08202 q^{49} -3.45174 q^{51} +7.94504 q^{52} +0.703311 q^{53} -2.24873 q^{54} +3.29111 q^{56} +1.01677 q^{57} -16.2704 q^{58} +10.9167 q^{59} +7.46158 q^{61} +0.645232 q^{62} -1.38491 q^{63} -13.0405 q^{64} -11.6775 q^{66} -3.36130 q^{67} -10.5512 q^{68} -2.00367 q^{69} +3.94927 q^{71} -2.37640 q^{72} -15.0178 q^{73} -10.4337 q^{74} +3.10803 q^{76} -7.19173 q^{77} -5.84480 q^{78} -6.69906 q^{79} +1.00000 q^{81} +1.74482 q^{82} -10.4990 q^{83} -4.23336 q^{84} -4.65249 q^{86} +7.23539 q^{87} -12.3405 q^{88} +15.4868 q^{89} -3.59960 q^{91} -6.12477 q^{92} -0.286932 q^{93} -2.24873 q^{94} +6.48358 q^{96} -10.9476 q^{97} +11.4281 q^{98} +5.19292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 13 q + 3 q^{2} + 13 q^{3} + 17 q^{4} + 3 q^{6} - 4 q^{7} + 15 q^{8} + 13 q^{9} + 16 q^{11} + 17 q^{12} - 8 q^{13} - 4 q^{14} + 29 q^{16} + 12 q^{17} + 3 q^{18} + 28 q^{19} - 4 q^{21} + 6 q^{23} + 15 q^{24} + 4 q^{26} + 13 q^{27} - 20 q^{28} + 12 q^{29} + 26 q^{31} + 53 q^{32} + 16 q^{33} + 8 q^{34} + 17 q^{36} - 4 q^{37} + 2 q^{38} - 8 q^{39} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{44} + 16 q^{46} + 13 q^{47} + 29 q^{48} + 21 q^{49} + 12 q^{51} - 32 q^{52} + 6 q^{53} + 3 q^{54} + 28 q^{57} - 4 q^{58} + 34 q^{59} + 24 q^{61} + 30 q^{62} - 4 q^{63} + 13 q^{64} - 24 q^{67} + 44 q^{68} + 6 q^{69} + 20 q^{71} + 15 q^{72} - 6 q^{73} + 20 q^{74} + 66 q^{76} - 2 q^{77} + 4 q^{78} + 6 q^{79} + 13 q^{81} + 20 q^{82} + 14 q^{83} - 20 q^{84} + 48 q^{86} + 12 q^{87} - 22 q^{88} + 36 q^{89} + 4 q^{91} + 4 q^{92} + 26 q^{93} + 3 q^{94} + 53 q^{96} - 32 q^{97} - 39 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24873 −1.59009 −0.795045 0.606550i \(-0.792553\pi\)
−0.795045 + 0.606550i \(0.792553\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.05678 1.52839
\(5\) 0 0
\(6\) −2.24873 −0.918039
\(7\) −1.38491 −0.523447 −0.261723 0.965143i \(-0.584291\pi\)
−0.261723 + 0.965143i \(0.584291\pi\)
\(8\) −2.37640 −0.840185
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.19292 1.56572 0.782862 0.622196i \(-0.213759\pi\)
0.782862 + 0.622196i \(0.213759\pi\)
\(12\) 3.05678 0.882415
\(13\) 2.59916 0.720876 0.360438 0.932783i \(-0.382627\pi\)
0.360438 + 0.932783i \(0.382627\pi\)
\(14\) 3.11429 0.832328
\(15\) 0 0
\(16\) −0.769670 −0.192417
\(17\) −3.45174 −0.837171 −0.418585 0.908177i \(-0.637474\pi\)
−0.418585 + 0.908177i \(0.637474\pi\)
\(18\) −2.24873 −0.530030
\(19\) 1.01677 0.233262 0.116631 0.993175i \(-0.462790\pi\)
0.116631 + 0.993175i \(0.462790\pi\)
\(20\) 0 0
\(21\) −1.38491 −0.302212
\(22\) −11.6775 −2.48964
\(23\) −2.00367 −0.417794 −0.208897 0.977938i \(-0.566987\pi\)
−0.208897 + 0.977938i \(0.566987\pi\)
\(24\) −2.37640 −0.485081
\(25\) 0 0
\(26\) −5.84480 −1.14626
\(27\) 1.00000 0.192450
\(28\) −4.23336 −0.800030
\(29\) 7.23539 1.34358 0.671789 0.740742i \(-0.265526\pi\)
0.671789 + 0.740742i \(0.265526\pi\)
\(30\) 0 0
\(31\) −0.286932 −0.0515345 −0.0257673 0.999668i \(-0.508203\pi\)
−0.0257673 + 0.999668i \(0.508203\pi\)
\(32\) 6.48358 1.14615
\(33\) 5.19292 0.903971
\(34\) 7.76203 1.33118
\(35\) 0 0
\(36\) 3.05678 0.509463
\(37\) 4.63981 0.762780 0.381390 0.924414i \(-0.375445\pi\)
0.381390 + 0.924414i \(0.375445\pi\)
\(38\) −2.28643 −0.370908
\(39\) 2.59916 0.416198
\(40\) 0 0
\(41\) −0.775913 −0.121177 −0.0605886 0.998163i \(-0.519298\pi\)
−0.0605886 + 0.998163i \(0.519298\pi\)
\(42\) 3.11429 0.480545
\(43\) 2.06895 0.315511 0.157756 0.987478i \(-0.449574\pi\)
0.157756 + 0.987478i \(0.449574\pi\)
\(44\) 15.8736 2.39303
\(45\) 0 0
\(46\) 4.50571 0.664330
\(47\) 1.00000 0.145865
\(48\) −0.769670 −0.111092
\(49\) −5.08202 −0.726003
\(50\) 0 0
\(51\) −3.45174 −0.483341
\(52\) 7.94504 1.10178
\(53\) 0.703311 0.0966072 0.0483036 0.998833i \(-0.484618\pi\)
0.0483036 + 0.998833i \(0.484618\pi\)
\(54\) −2.24873 −0.306013
\(55\) 0 0
\(56\) 3.29111 0.439792
\(57\) 1.01677 0.134674
\(58\) −16.2704 −2.13641
\(59\) 10.9167 1.42123 0.710616 0.703580i \(-0.248416\pi\)
0.710616 + 0.703580i \(0.248416\pi\)
\(60\) 0 0
\(61\) 7.46158 0.955358 0.477679 0.878535i \(-0.341478\pi\)
0.477679 + 0.878535i \(0.341478\pi\)
\(62\) 0.645232 0.0819445
\(63\) −1.38491 −0.174482
\(64\) −13.0405 −1.63006
\(65\) 0 0
\(66\) −11.6775 −1.43740
\(67\) −3.36130 −0.410648 −0.205324 0.978694i \(-0.565825\pi\)
−0.205324 + 0.978694i \(0.565825\pi\)
\(68\) −10.5512 −1.27952
\(69\) −2.00367 −0.241213
\(70\) 0 0
\(71\) 3.94927 0.468692 0.234346 0.972153i \(-0.424705\pi\)
0.234346 + 0.972153i \(0.424705\pi\)
\(72\) −2.37640 −0.280062
\(73\) −15.0178 −1.75770 −0.878852 0.477094i \(-0.841690\pi\)
−0.878852 + 0.477094i \(0.841690\pi\)
\(74\) −10.4337 −1.21289
\(75\) 0 0
\(76\) 3.10803 0.356515
\(77\) −7.19173 −0.819573
\(78\) −5.84480 −0.661793
\(79\) −6.69906 −0.753703 −0.376851 0.926274i \(-0.622993\pi\)
−0.376851 + 0.926274i \(0.622993\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 1.74482 0.192683
\(83\) −10.4990 −1.15241 −0.576207 0.817304i \(-0.695468\pi\)
−0.576207 + 0.817304i \(0.695468\pi\)
\(84\) −4.23336 −0.461898
\(85\) 0 0
\(86\) −4.65249 −0.501691
\(87\) 7.23539 0.775715
\(88\) −12.3405 −1.31550
\(89\) 15.4868 1.64160 0.820798 0.571218i \(-0.193529\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(90\) 0 0
\(91\) −3.59960 −0.377341
\(92\) −6.12477 −0.638551
\(93\) −0.286932 −0.0297535
\(94\) −2.24873 −0.231939
\(95\) 0 0
\(96\) 6.48358 0.661728
\(97\) −10.9476 −1.11156 −0.555781 0.831328i \(-0.687581\pi\)
−0.555781 + 0.831328i \(0.687581\pi\)
\(98\) 11.4281 1.15441
\(99\) 5.19292 0.521908
\(100\) 0 0
\(101\) 16.5503 1.64682 0.823408 0.567451i \(-0.192070\pi\)
0.823408 + 0.567451i \(0.192070\pi\)
\(102\) 7.76203 0.768556
\(103\) 4.90157 0.482966 0.241483 0.970405i \(-0.422366\pi\)
0.241483 + 0.970405i \(0.422366\pi\)
\(104\) −6.17664 −0.605670
\(105\) 0 0
\(106\) −1.58156 −0.153614
\(107\) 10.6478 1.02936 0.514679 0.857383i \(-0.327911\pi\)
0.514679 + 0.857383i \(0.327911\pi\)
\(108\) 3.05678 0.294138
\(109\) −8.60514 −0.824223 −0.412112 0.911133i \(-0.635209\pi\)
−0.412112 + 0.911133i \(0.635209\pi\)
\(110\) 0 0
\(111\) 4.63981 0.440391
\(112\) 1.06592 0.100720
\(113\) 10.5128 0.988965 0.494482 0.869188i \(-0.335358\pi\)
0.494482 + 0.869188i \(0.335358\pi\)
\(114\) −2.28643 −0.214144
\(115\) 0 0
\(116\) 22.1170 2.05351
\(117\) 2.59916 0.240292
\(118\) −24.5487 −2.25989
\(119\) 4.78036 0.438214
\(120\) 0 0
\(121\) 15.9664 1.45149
\(122\) −16.7791 −1.51911
\(123\) −0.775913 −0.0699617
\(124\) −0.877087 −0.0787647
\(125\) 0 0
\(126\) 3.11429 0.277443
\(127\) 12.3634 1.09707 0.548535 0.836127i \(-0.315186\pi\)
0.548535 + 0.836127i \(0.315186\pi\)
\(128\) 16.3573 1.44580
\(129\) 2.06895 0.182160
\(130\) 0 0
\(131\) −7.92428 −0.692347 −0.346174 0.938170i \(-0.612519\pi\)
−0.346174 + 0.938170i \(0.612519\pi\)
\(132\) 15.8736 1.38162
\(133\) −1.40813 −0.122100
\(134\) 7.55865 0.652967
\(135\) 0 0
\(136\) 8.20273 0.703379
\(137\) −7.00433 −0.598420 −0.299210 0.954187i \(-0.596723\pi\)
−0.299210 + 0.954187i \(0.596723\pi\)
\(138\) 4.50571 0.383551
\(139\) −2.33550 −0.198094 −0.0990472 0.995083i \(-0.531579\pi\)
−0.0990472 + 0.995083i \(0.531579\pi\)
\(140\) 0 0
\(141\) 1.00000 0.0842152
\(142\) −8.88084 −0.745263
\(143\) 13.4972 1.12869
\(144\) −0.769670 −0.0641392
\(145\) 0 0
\(146\) 33.7710 2.79491
\(147\) −5.08202 −0.419158
\(148\) 14.1829 1.16582
\(149\) −15.2887 −1.25250 −0.626248 0.779624i \(-0.715410\pi\)
−0.626248 + 0.779624i \(0.715410\pi\)
\(150\) 0 0
\(151\) −15.2657 −1.24231 −0.621154 0.783689i \(-0.713336\pi\)
−0.621154 + 0.783689i \(0.713336\pi\)
\(152\) −2.41625 −0.195983
\(153\) −3.45174 −0.279057
\(154\) 16.1722 1.30320
\(155\) 0 0
\(156\) 7.94504 0.636113
\(157\) −17.7558 −1.41707 −0.708535 0.705676i \(-0.750644\pi\)
−0.708535 + 0.705676i \(0.750644\pi\)
\(158\) 15.0644 1.19846
\(159\) 0.703311 0.0557762
\(160\) 0 0
\(161\) 2.77490 0.218693
\(162\) −2.24873 −0.176677
\(163\) 9.71780 0.761156 0.380578 0.924749i \(-0.375725\pi\)
0.380578 + 0.924749i \(0.375725\pi\)
\(164\) −2.37179 −0.185206
\(165\) 0 0
\(166\) 23.6094 1.83244
\(167\) 13.8924 1.07503 0.537513 0.843256i \(-0.319364\pi\)
0.537513 + 0.843256i \(0.319364\pi\)
\(168\) 3.29111 0.253914
\(169\) −6.24438 −0.480337
\(170\) 0 0
\(171\) 1.01677 0.0777540
\(172\) 6.32430 0.482224
\(173\) 21.5086 1.63526 0.817632 0.575741i \(-0.195286\pi\)
0.817632 + 0.575741i \(0.195286\pi\)
\(174\) −16.2704 −1.23346
\(175\) 0 0
\(176\) −3.99683 −0.301273
\(177\) 10.9167 0.820548
\(178\) −34.8256 −2.61029
\(179\) −3.20665 −0.239676 −0.119838 0.992793i \(-0.538238\pi\)
−0.119838 + 0.992793i \(0.538238\pi\)
\(180\) 0 0
\(181\) 2.05576 0.152803 0.0764017 0.997077i \(-0.475657\pi\)
0.0764017 + 0.997077i \(0.475657\pi\)
\(182\) 8.09452 0.600006
\(183\) 7.46158 0.551576
\(184\) 4.76153 0.351024
\(185\) 0 0
\(186\) 0.645232 0.0473107
\(187\) −17.9246 −1.31078
\(188\) 3.05678 0.222938
\(189\) −1.38491 −0.100737
\(190\) 0 0
\(191\) −4.25008 −0.307525 −0.153762 0.988108i \(-0.549139\pi\)
−0.153762 + 0.988108i \(0.549139\pi\)
\(192\) −13.0405 −0.941115
\(193\) 18.3835 1.32327 0.661635 0.749826i \(-0.269863\pi\)
0.661635 + 0.749826i \(0.269863\pi\)
\(194\) 24.6182 1.76749
\(195\) 0 0
\(196\) −15.5346 −1.10961
\(197\) 9.01182 0.642065 0.321033 0.947068i \(-0.395970\pi\)
0.321033 + 0.947068i \(0.395970\pi\)
\(198\) −11.6775 −0.829881
\(199\) 24.9219 1.76666 0.883332 0.468749i \(-0.155295\pi\)
0.883332 + 0.468749i \(0.155295\pi\)
\(200\) 0 0
\(201\) −3.36130 −0.237088
\(202\) −37.2171 −2.61859
\(203\) −10.0204 −0.703292
\(204\) −10.5512 −0.738732
\(205\) 0 0
\(206\) −11.0223 −0.767960
\(207\) −2.00367 −0.139265
\(208\) −2.00049 −0.138709
\(209\) 5.27998 0.365224
\(210\) 0 0
\(211\) 12.2396 0.842610 0.421305 0.906919i \(-0.361572\pi\)
0.421305 + 0.906919i \(0.361572\pi\)
\(212\) 2.14987 0.147653
\(213\) 3.94927 0.270600
\(214\) −23.9439 −1.63677
\(215\) 0 0
\(216\) −2.37640 −0.161694
\(217\) 0.397375 0.0269756
\(218\) 19.3506 1.31059
\(219\) −15.0178 −1.01481
\(220\) 0 0
\(221\) −8.97162 −0.603497
\(222\) −10.4337 −0.700262
\(223\) −21.4122 −1.43387 −0.716934 0.697141i \(-0.754455\pi\)
−0.716934 + 0.697141i \(0.754455\pi\)
\(224\) −8.97918 −0.599947
\(225\) 0 0
\(226\) −23.6405 −1.57254
\(227\) 7.59972 0.504411 0.252206 0.967674i \(-0.418844\pi\)
0.252206 + 0.967674i \(0.418844\pi\)
\(228\) 3.10803 0.205834
\(229\) −24.0119 −1.58675 −0.793374 0.608735i \(-0.791677\pi\)
−0.793374 + 0.608735i \(0.791677\pi\)
\(230\) 0 0
\(231\) −7.19173 −0.473181
\(232\) −17.1942 −1.12886
\(233\) −13.8785 −0.909211 −0.454605 0.890693i \(-0.650220\pi\)
−0.454605 + 0.890693i \(0.650220\pi\)
\(234\) −5.84480 −0.382086
\(235\) 0 0
\(236\) 33.3699 2.17219
\(237\) −6.69906 −0.435150
\(238\) −10.7497 −0.696801
\(239\) 4.91814 0.318128 0.159064 0.987268i \(-0.449152\pi\)
0.159064 + 0.987268i \(0.449152\pi\)
\(240\) 0 0
\(241\) 22.0191 1.41838 0.709188 0.705019i \(-0.249062\pi\)
0.709188 + 0.705019i \(0.249062\pi\)
\(242\) −35.9041 −2.30800
\(243\) 1.00000 0.0641500
\(244\) 22.8084 1.46016
\(245\) 0 0
\(246\) 1.74482 0.111245
\(247\) 2.64273 0.168153
\(248\) 0.681866 0.0432985
\(249\) −10.4990 −0.665346
\(250\) 0 0
\(251\) −19.7608 −1.24729 −0.623644 0.781709i \(-0.714348\pi\)
−0.623644 + 0.781709i \(0.714348\pi\)
\(252\) −4.23336 −0.266677
\(253\) −10.4049 −0.654150
\(254\) −27.8018 −1.74444
\(255\) 0 0
\(256\) −10.7022 −0.668887
\(257\) 25.9677 1.61982 0.809911 0.586552i \(-0.199515\pi\)
0.809911 + 0.586552i \(0.199515\pi\)
\(258\) −4.65249 −0.289652
\(259\) −6.42572 −0.399275
\(260\) 0 0
\(261\) 7.23539 0.447860
\(262\) 17.8195 1.10090
\(263\) −23.5775 −1.45385 −0.726926 0.686716i \(-0.759052\pi\)
−0.726926 + 0.686716i \(0.759052\pi\)
\(264\) −12.3405 −0.759503
\(265\) 0 0
\(266\) 3.16650 0.194151
\(267\) 15.4868 0.947776
\(268\) −10.2747 −0.627630
\(269\) −12.3825 −0.754977 −0.377489 0.926014i \(-0.623212\pi\)
−0.377489 + 0.926014i \(0.623212\pi\)
\(270\) 0 0
\(271\) 18.7346 1.13804 0.569022 0.822322i \(-0.307322\pi\)
0.569022 + 0.822322i \(0.307322\pi\)
\(272\) 2.65670 0.161086
\(273\) −3.59960 −0.217858
\(274\) 15.7508 0.951543
\(275\) 0 0
\(276\) −6.12477 −0.368668
\(277\) 8.15990 0.490281 0.245140 0.969488i \(-0.421166\pi\)
0.245140 + 0.969488i \(0.421166\pi\)
\(278\) 5.25190 0.314988
\(279\) −0.286932 −0.0171782
\(280\) 0 0
\(281\) 19.3677 1.15538 0.577689 0.816257i \(-0.303954\pi\)
0.577689 + 0.816257i \(0.303954\pi\)
\(282\) −2.24873 −0.133910
\(283\) −11.1945 −0.665446 −0.332723 0.943025i \(-0.607967\pi\)
−0.332723 + 0.943025i \(0.607967\pi\)
\(284\) 12.0720 0.716344
\(285\) 0 0
\(286\) −30.3515 −1.79472
\(287\) 1.07457 0.0634298
\(288\) 6.48358 0.382049
\(289\) −5.08547 −0.299145
\(290\) 0 0
\(291\) −10.9476 −0.641761
\(292\) −45.9062 −2.68645
\(293\) −13.7883 −0.805522 −0.402761 0.915305i \(-0.631949\pi\)
−0.402761 + 0.915305i \(0.631949\pi\)
\(294\) 11.4281 0.666500
\(295\) 0 0
\(296\) −11.0261 −0.640877
\(297\) 5.19292 0.301324
\(298\) 34.3800 1.99158
\(299\) −5.20785 −0.301178
\(300\) 0 0
\(301\) −2.86530 −0.165153
\(302\) 34.3285 1.97538
\(303\) 16.5503 0.950789
\(304\) −0.782574 −0.0448837
\(305\) 0 0
\(306\) 7.76203 0.443726
\(307\) 14.4636 0.825483 0.412742 0.910848i \(-0.364571\pi\)
0.412742 + 0.910848i \(0.364571\pi\)
\(308\) −21.9835 −1.25263
\(309\) 4.90157 0.278841
\(310\) 0 0
\(311\) −1.67137 −0.0947747 −0.0473873 0.998877i \(-0.515090\pi\)
−0.0473873 + 0.998877i \(0.515090\pi\)
\(312\) −6.17664 −0.349684
\(313\) 11.6450 0.658212 0.329106 0.944293i \(-0.393253\pi\)
0.329106 + 0.944293i \(0.393253\pi\)
\(314\) 39.9280 2.25327
\(315\) 0 0
\(316\) −20.4775 −1.15195
\(317\) 17.8715 1.00376 0.501882 0.864936i \(-0.332641\pi\)
0.501882 + 0.864936i \(0.332641\pi\)
\(318\) −1.58156 −0.0886892
\(319\) 37.5728 2.10367
\(320\) 0 0
\(321\) 10.6478 0.594300
\(322\) −6.24000 −0.347742
\(323\) −3.50962 −0.195280
\(324\) 3.05678 0.169821
\(325\) 0 0
\(326\) −21.8527 −1.21031
\(327\) −8.60514 −0.475865
\(328\) 1.84388 0.101811
\(329\) −1.38491 −0.0763526
\(330\) 0 0
\(331\) 15.3796 0.845339 0.422669 0.906284i \(-0.361093\pi\)
0.422669 + 0.906284i \(0.361093\pi\)
\(332\) −32.0931 −1.76134
\(333\) 4.63981 0.254260
\(334\) −31.2402 −1.70939
\(335\) 0 0
\(336\) 1.06592 0.0581509
\(337\) 23.7793 1.29534 0.647669 0.761922i \(-0.275744\pi\)
0.647669 + 0.761922i \(0.275744\pi\)
\(338\) 14.0419 0.763780
\(339\) 10.5128 0.570979
\(340\) 0 0
\(341\) −1.49001 −0.0806888
\(342\) −2.28643 −0.123636
\(343\) 16.7325 0.903471
\(344\) −4.91665 −0.265088
\(345\) 0 0
\(346\) −48.3669 −2.60022
\(347\) 0.909029 0.0487992 0.0243996 0.999702i \(-0.492233\pi\)
0.0243996 + 0.999702i \(0.492233\pi\)
\(348\) 22.1170 1.18559
\(349\) −6.80159 −0.364081 −0.182041 0.983291i \(-0.558270\pi\)
−0.182041 + 0.983291i \(0.558270\pi\)
\(350\) 0 0
\(351\) 2.59916 0.138733
\(352\) 33.6687 1.79455
\(353\) 36.2525 1.92952 0.964762 0.263123i \(-0.0847524\pi\)
0.964762 + 0.263123i \(0.0847524\pi\)
\(354\) −24.5487 −1.30475
\(355\) 0 0
\(356\) 47.3397 2.50900
\(357\) 4.78036 0.253003
\(358\) 7.21088 0.381107
\(359\) 16.1026 0.849863 0.424931 0.905226i \(-0.360298\pi\)
0.424931 + 0.905226i \(0.360298\pi\)
\(360\) 0 0
\(361\) −17.9662 −0.945589
\(362\) −4.62285 −0.242971
\(363\) 15.9664 0.838018
\(364\) −11.0032 −0.576723
\(365\) 0 0
\(366\) −16.7791 −0.877056
\(367\) 16.3763 0.854835 0.427417 0.904054i \(-0.359423\pi\)
0.427417 + 0.904054i \(0.359423\pi\)
\(368\) 1.54216 0.0803909
\(369\) −0.775913 −0.0403924
\(370\) 0 0
\(371\) −0.974023 −0.0505688
\(372\) −0.877087 −0.0454748
\(373\) 15.9249 0.824561 0.412281 0.911057i \(-0.364732\pi\)
0.412281 + 0.911057i \(0.364732\pi\)
\(374\) 40.3076 2.08426
\(375\) 0 0
\(376\) −2.37640 −0.122554
\(377\) 18.8059 0.968554
\(378\) 3.11429 0.160182
\(379\) −6.41058 −0.329289 −0.164645 0.986353i \(-0.552648\pi\)
−0.164645 + 0.986353i \(0.552648\pi\)
\(380\) 0 0
\(381\) 12.3634 0.633394
\(382\) 9.55727 0.488992
\(383\) 37.6109 1.92183 0.960913 0.276851i \(-0.0892909\pi\)
0.960913 + 0.276851i \(0.0892909\pi\)
\(384\) 16.3573 0.834731
\(385\) 0 0
\(386\) −41.3394 −2.10412
\(387\) 2.06895 0.105170
\(388\) −33.4644 −1.69890
\(389\) 16.4422 0.833650 0.416825 0.908987i \(-0.363143\pi\)
0.416825 + 0.908987i \(0.363143\pi\)
\(390\) 0 0
\(391\) 6.91615 0.349765
\(392\) 12.0769 0.609977
\(393\) −7.92428 −0.399727
\(394\) −20.2651 −1.02094
\(395\) 0 0
\(396\) 15.8736 0.797678
\(397\) 2.48769 0.124854 0.0624269 0.998050i \(-0.480116\pi\)
0.0624269 + 0.998050i \(0.480116\pi\)
\(398\) −56.0425 −2.80915
\(399\) −1.40813 −0.0704947
\(400\) 0 0
\(401\) −21.0039 −1.04889 −0.524443 0.851445i \(-0.675726\pi\)
−0.524443 + 0.851445i \(0.675726\pi\)
\(402\) 7.55865 0.376991
\(403\) −0.745781 −0.0371500
\(404\) 50.5905 2.51697
\(405\) 0 0
\(406\) 22.5331 1.11830
\(407\) 24.0942 1.19430
\(408\) 8.20273 0.406096
\(409\) 33.9322 1.67784 0.838920 0.544254i \(-0.183187\pi\)
0.838920 + 0.544254i \(0.183187\pi\)
\(410\) 0 0
\(411\) −7.00433 −0.345498
\(412\) 14.9830 0.738160
\(413\) −15.1186 −0.743939
\(414\) 4.50571 0.221443
\(415\) 0 0
\(416\) 16.8519 0.826230
\(417\) −2.33550 −0.114370
\(418\) −11.8732 −0.580739
\(419\) 28.4851 1.39159 0.695794 0.718241i \(-0.255052\pi\)
0.695794 + 0.718241i \(0.255052\pi\)
\(420\) 0 0
\(421\) −15.1675 −0.739219 −0.369610 0.929187i \(-0.620509\pi\)
−0.369610 + 0.929187i \(0.620509\pi\)
\(422\) −27.5236 −1.33983
\(423\) 1.00000 0.0486217
\(424\) −1.67135 −0.0811680
\(425\) 0 0
\(426\) −8.88084 −0.430278
\(427\) −10.3336 −0.500079
\(428\) 32.5478 1.57326
\(429\) 13.4972 0.651651
\(430\) 0 0
\(431\) −26.7117 −1.28666 −0.643328 0.765591i \(-0.722447\pi\)
−0.643328 + 0.765591i \(0.722447\pi\)
\(432\) −0.769670 −0.0370308
\(433\) 6.84811 0.329099 0.164550 0.986369i \(-0.447383\pi\)
0.164550 + 0.986369i \(0.447383\pi\)
\(434\) −0.893589 −0.0428936
\(435\) 0 0
\(436\) −26.3040 −1.25973
\(437\) −2.03726 −0.0974555
\(438\) 33.7710 1.61364
\(439\) −29.4001 −1.40319 −0.701594 0.712577i \(-0.747528\pi\)
−0.701594 + 0.712577i \(0.747528\pi\)
\(440\) 0 0
\(441\) −5.08202 −0.242001
\(442\) 20.1747 0.959615
\(443\) −13.5666 −0.644569 −0.322285 0.946643i \(-0.604451\pi\)
−0.322285 + 0.946643i \(0.604451\pi\)
\(444\) 14.1829 0.673089
\(445\) 0 0
\(446\) 48.1502 2.27998
\(447\) −15.2887 −0.723129
\(448\) 18.0599 0.853250
\(449\) −0.690194 −0.0325723 −0.0162861 0.999867i \(-0.505184\pi\)
−0.0162861 + 0.999867i \(0.505184\pi\)
\(450\) 0 0
\(451\) −4.02925 −0.189730
\(452\) 32.1354 1.51152
\(453\) −15.2657 −0.717246
\(454\) −17.0897 −0.802059
\(455\) 0 0
\(456\) −2.41625 −0.113151
\(457\) 20.0644 0.938574 0.469287 0.883046i \(-0.344511\pi\)
0.469287 + 0.883046i \(0.344511\pi\)
\(458\) 53.9961 2.52307
\(459\) −3.45174 −0.161114
\(460\) 0 0
\(461\) −0.0748678 −0.00348694 −0.00174347 0.999998i \(-0.500555\pi\)
−0.00174347 + 0.999998i \(0.500555\pi\)
\(462\) 16.1722 0.752400
\(463\) 13.1562 0.611423 0.305711 0.952124i \(-0.401106\pi\)
0.305711 + 0.952124i \(0.401106\pi\)
\(464\) −5.56886 −0.258528
\(465\) 0 0
\(466\) 31.2090 1.44573
\(467\) 24.1841 1.11911 0.559553 0.828795i \(-0.310973\pi\)
0.559553 + 0.828795i \(0.310973\pi\)
\(468\) 7.94504 0.367260
\(469\) 4.65510 0.214952
\(470\) 0 0
\(471\) −17.7558 −0.818146
\(472\) −25.9424 −1.19410
\(473\) 10.7439 0.494003
\(474\) 15.0644 0.691929
\(475\) 0 0
\(476\) 14.6125 0.669762
\(477\) 0.703311 0.0322024
\(478\) −11.0596 −0.505852
\(479\) −37.3687 −1.70742 −0.853709 0.520751i \(-0.825652\pi\)
−0.853709 + 0.520751i \(0.825652\pi\)
\(480\) 0 0
\(481\) 12.0596 0.549870
\(482\) −49.5150 −2.25535
\(483\) 2.77490 0.126262
\(484\) 48.8057 2.21844
\(485\) 0 0
\(486\) −2.24873 −0.102004
\(487\) −2.66731 −0.120867 −0.0604337 0.998172i \(-0.519248\pi\)
−0.0604337 + 0.998172i \(0.519248\pi\)
\(488\) −17.7317 −0.802678
\(489\) 9.71780 0.439454
\(490\) 0 0
\(491\) −22.9997 −1.03796 −0.518981 0.854786i \(-0.673689\pi\)
−0.518981 + 0.854786i \(0.673689\pi\)
\(492\) −2.37179 −0.106929
\(493\) −24.9747 −1.12480
\(494\) −5.94279 −0.267379
\(495\) 0 0
\(496\) 0.220843 0.00991614
\(497\) −5.46939 −0.245336
\(498\) 23.6094 1.05796
\(499\) 32.9237 1.47387 0.736933 0.675965i \(-0.236273\pi\)
0.736933 + 0.675965i \(0.236273\pi\)
\(500\) 0 0
\(501\) 13.8924 0.620666
\(502\) 44.4366 1.98330
\(503\) −27.2034 −1.21294 −0.606469 0.795107i \(-0.707415\pi\)
−0.606469 + 0.795107i \(0.707415\pi\)
\(504\) 3.29111 0.146597
\(505\) 0 0
\(506\) 23.3978 1.04016
\(507\) −6.24438 −0.277323
\(508\) 37.7920 1.67675
\(509\) 18.2534 0.809068 0.404534 0.914523i \(-0.367434\pi\)
0.404534 + 0.914523i \(0.367434\pi\)
\(510\) 0 0
\(511\) 20.7984 0.920065
\(512\) −8.64831 −0.382205
\(513\) 1.01677 0.0448913
\(514\) −58.3944 −2.57566
\(515\) 0 0
\(516\) 6.32430 0.278412
\(517\) 5.19292 0.228384
\(518\) 14.4497 0.634884
\(519\) 21.5086 0.944121
\(520\) 0 0
\(521\) −28.6237 −1.25403 −0.627013 0.779009i \(-0.715723\pi\)
−0.627013 + 0.779009i \(0.715723\pi\)
\(522\) −16.2704 −0.712137
\(523\) 40.7455 1.78168 0.890838 0.454320i \(-0.150118\pi\)
0.890838 + 0.454320i \(0.150118\pi\)
\(524\) −24.2227 −1.05818
\(525\) 0 0
\(526\) 53.0194 2.31176
\(527\) 0.990416 0.0431432
\(528\) −3.99683 −0.173940
\(529\) −18.9853 −0.825448
\(530\) 0 0
\(531\) 10.9167 0.473744
\(532\) −4.30434 −0.186617
\(533\) −2.01672 −0.0873538
\(534\) −34.8256 −1.50705
\(535\) 0 0
\(536\) 7.98780 0.345020
\(537\) −3.20665 −0.138377
\(538\) 27.8450 1.20048
\(539\) −26.3905 −1.13672
\(540\) 0 0
\(541\) −16.5428 −0.711231 −0.355615 0.934632i \(-0.615729\pi\)
−0.355615 + 0.934632i \(0.615729\pi\)
\(542\) −42.1289 −1.80959
\(543\) 2.05576 0.0882211
\(544\) −22.3797 −0.959520
\(545\) 0 0
\(546\) 8.09452 0.346414
\(547\) −27.4024 −1.17164 −0.585820 0.810441i \(-0.699228\pi\)
−0.585820 + 0.810441i \(0.699228\pi\)
\(548\) −21.4107 −0.914619
\(549\) 7.46158 0.318453
\(550\) 0 0
\(551\) 7.35670 0.313406
\(552\) 4.76153 0.202664
\(553\) 9.27759 0.394523
\(554\) −18.3494 −0.779591
\(555\) 0 0
\(556\) −7.13910 −0.302765
\(557\) 0.716768 0.0303704 0.0151852 0.999885i \(-0.495166\pi\)
0.0151852 + 0.999885i \(0.495166\pi\)
\(558\) 0.645232 0.0273148
\(559\) 5.37751 0.227445
\(560\) 0 0
\(561\) −17.9246 −0.756778
\(562\) −43.5526 −1.83716
\(563\) 25.7954 1.08715 0.543573 0.839362i \(-0.317071\pi\)
0.543573 + 0.839362i \(0.317071\pi\)
\(564\) 3.05678 0.128714
\(565\) 0 0
\(566\) 25.1735 1.05812
\(567\) −1.38491 −0.0581608
\(568\) −9.38506 −0.393788
\(569\) 45.3234 1.90005 0.950027 0.312167i \(-0.101055\pi\)
0.950027 + 0.312167i \(0.101055\pi\)
\(570\) 0 0
\(571\) 31.7434 1.32842 0.664209 0.747547i \(-0.268768\pi\)
0.664209 + 0.747547i \(0.268768\pi\)
\(572\) 41.2580 1.72508
\(573\) −4.25008 −0.177550
\(574\) −2.41641 −0.100859
\(575\) 0 0
\(576\) −13.0405 −0.543353
\(577\) −2.06921 −0.0861425 −0.0430713 0.999072i \(-0.513714\pi\)
−0.0430713 + 0.999072i \(0.513714\pi\)
\(578\) 11.4358 0.475668
\(579\) 18.3835 0.763991
\(580\) 0 0
\(581\) 14.5402 0.603227
\(582\) 24.6182 1.02046
\(583\) 3.65224 0.151260
\(584\) 35.6884 1.47680
\(585\) 0 0
\(586\) 31.0062 1.28085
\(587\) −46.6127 −1.92391 −0.961957 0.273202i \(-0.911917\pi\)
−0.961957 + 0.273202i \(0.911917\pi\)
\(588\) −15.5346 −0.640636
\(589\) −0.291743 −0.0120210
\(590\) 0 0
\(591\) 9.01182 0.370697
\(592\) −3.57112 −0.146772
\(593\) 37.7442 1.54997 0.774985 0.631980i \(-0.217757\pi\)
0.774985 + 0.631980i \(0.217757\pi\)
\(594\) −11.6775 −0.479132
\(595\) 0 0
\(596\) −46.7340 −1.91430
\(597\) 24.9219 1.01998
\(598\) 11.7110 0.478900
\(599\) −16.6614 −0.680765 −0.340382 0.940287i \(-0.610556\pi\)
−0.340382 + 0.940287i \(0.610556\pi\)
\(600\) 0 0
\(601\) 20.6432 0.842052 0.421026 0.907049i \(-0.361670\pi\)
0.421026 + 0.907049i \(0.361670\pi\)
\(602\) 6.44329 0.262609
\(603\) −3.36130 −0.136883
\(604\) −46.6639 −1.89873
\(605\) 0 0
\(606\) −37.2171 −1.51184
\(607\) 11.5930 0.470545 0.235273 0.971929i \(-0.424402\pi\)
0.235273 + 0.971929i \(0.424402\pi\)
\(608\) 6.59229 0.267353
\(609\) −10.0204 −0.406046
\(610\) 0 0
\(611\) 2.59916 0.105151
\(612\) −10.5512 −0.426507
\(613\) −14.6236 −0.590642 −0.295321 0.955398i \(-0.595427\pi\)
−0.295321 + 0.955398i \(0.595427\pi\)
\(614\) −32.5248 −1.31259
\(615\) 0 0
\(616\) 17.0904 0.688593
\(617\) 18.7899 0.756452 0.378226 0.925713i \(-0.376534\pi\)
0.378226 + 0.925713i \(0.376534\pi\)
\(618\) −11.0223 −0.443382
\(619\) 18.5086 0.743923 0.371961 0.928248i \(-0.378685\pi\)
0.371961 + 0.928248i \(0.378685\pi\)
\(620\) 0 0
\(621\) −2.00367 −0.0804045
\(622\) 3.75845 0.150700
\(623\) −21.4478 −0.859289
\(624\) −2.00049 −0.0800838
\(625\) 0 0
\(626\) −26.1863 −1.04662
\(627\) 5.27998 0.210862
\(628\) −54.2756 −2.16583
\(629\) −16.0154 −0.638577
\(630\) 0 0
\(631\) 5.28725 0.210482 0.105241 0.994447i \(-0.466439\pi\)
0.105241 + 0.994447i \(0.466439\pi\)
\(632\) 15.9197 0.633250
\(633\) 12.2396 0.486481
\(634\) −40.1881 −1.59607
\(635\) 0 0
\(636\) 2.14987 0.0852477
\(637\) −13.2090 −0.523359
\(638\) −84.4910 −3.34503
\(639\) 3.94927 0.156231
\(640\) 0 0
\(641\) −24.4627 −0.966217 −0.483108 0.875561i \(-0.660492\pi\)
−0.483108 + 0.875561i \(0.660492\pi\)
\(642\) −23.9439 −0.944990
\(643\) 11.0093 0.434166 0.217083 0.976153i \(-0.430346\pi\)
0.217083 + 0.976153i \(0.430346\pi\)
\(644\) 8.48226 0.334248
\(645\) 0 0
\(646\) 7.89217 0.310513
\(647\) −6.22989 −0.244922 −0.122461 0.992473i \(-0.539079\pi\)
−0.122461 + 0.992473i \(0.539079\pi\)
\(648\) −2.37640 −0.0933539
\(649\) 56.6895 2.22526
\(650\) 0 0
\(651\) 0.397375 0.0155744
\(652\) 29.7051 1.16334
\(653\) −31.9087 −1.24868 −0.624342 0.781151i \(-0.714633\pi\)
−0.624342 + 0.781151i \(0.714633\pi\)
\(654\) 19.3506 0.756669
\(655\) 0 0
\(656\) 0.597197 0.0233166
\(657\) −15.0178 −0.585901
\(658\) 3.11429 0.121408
\(659\) 40.4861 1.57712 0.788558 0.614961i \(-0.210828\pi\)
0.788558 + 0.614961i \(0.210828\pi\)
\(660\) 0 0
\(661\) −48.1092 −1.87123 −0.935616 0.353019i \(-0.885155\pi\)
−0.935616 + 0.353019i \(0.885155\pi\)
\(662\) −34.5845 −1.34417
\(663\) −8.97162 −0.348429
\(664\) 24.9498 0.968241
\(665\) 0 0
\(666\) −10.4337 −0.404297
\(667\) −14.4973 −0.561339
\(668\) 42.4659 1.64306
\(669\) −21.4122 −0.827844
\(670\) 0 0
\(671\) 38.7474 1.49583
\(672\) −8.97918 −0.346380
\(673\) −41.7722 −1.61020 −0.805100 0.593140i \(-0.797888\pi\)
−0.805100 + 0.593140i \(0.797888\pi\)
\(674\) −53.4731 −2.05971
\(675\) 0 0
\(676\) −19.0877 −0.734142
\(677\) −4.47192 −0.171870 −0.0859350 0.996301i \(-0.527388\pi\)
−0.0859350 + 0.996301i \(0.527388\pi\)
\(678\) −23.6405 −0.907909
\(679\) 15.1615 0.581844
\(680\) 0 0
\(681\) 7.59972 0.291222
\(682\) 3.35064 0.128303
\(683\) −39.7016 −1.51914 −0.759570 0.650425i \(-0.774591\pi\)
−0.759570 + 0.650425i \(0.774591\pi\)
\(684\) 3.10803 0.118838
\(685\) 0 0
\(686\) −37.6269 −1.43660
\(687\) −24.0119 −0.916109
\(688\) −1.59240 −0.0607099
\(689\) 1.82802 0.0696419
\(690\) 0 0
\(691\) −33.1679 −1.26177 −0.630883 0.775878i \(-0.717307\pi\)
−0.630883 + 0.775878i \(0.717307\pi\)
\(692\) 65.7468 2.49932
\(693\) −7.19173 −0.273191
\(694\) −2.04416 −0.0775952
\(695\) 0 0
\(696\) −17.1942 −0.651745
\(697\) 2.67825 0.101446
\(698\) 15.2949 0.578922
\(699\) −13.8785 −0.524933
\(700\) 0 0
\(701\) −14.4394 −0.545367 −0.272683 0.962104i \(-0.587911\pi\)
−0.272683 + 0.962104i \(0.587911\pi\)
\(702\) −5.84480 −0.220598
\(703\) 4.71760 0.177928
\(704\) −67.7181 −2.55222
\(705\) 0 0
\(706\) −81.5220 −3.06812
\(707\) −22.9207 −0.862020
\(708\) 33.3699 1.25412
\(709\) −20.0737 −0.753885 −0.376943 0.926237i \(-0.623025\pi\)
−0.376943 + 0.926237i \(0.623025\pi\)
\(710\) 0 0
\(711\) −6.69906 −0.251234
\(712\) −36.8029 −1.37925
\(713\) 0.574917 0.0215308
\(714\) −10.7497 −0.402298
\(715\) 0 0
\(716\) −9.80201 −0.366318
\(717\) 4.91814 0.183671
\(718\) −36.2104 −1.35136
\(719\) −13.6562 −0.509288 −0.254644 0.967035i \(-0.581958\pi\)
−0.254644 + 0.967035i \(0.581958\pi\)
\(720\) 0 0
\(721\) −6.78824 −0.252807
\(722\) 40.4011 1.50357
\(723\) 22.0191 0.818900
\(724\) 6.28400 0.233543
\(725\) 0 0
\(726\) −35.9041 −1.33253
\(727\) 12.6002 0.467315 0.233658 0.972319i \(-0.424931\pi\)
0.233658 + 0.972319i \(0.424931\pi\)
\(728\) 8.55410 0.317036
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.14147 −0.264137
\(732\) 22.8084 0.843022
\(733\) 41.9299 1.54872 0.774359 0.632747i \(-0.218073\pi\)
0.774359 + 0.632747i \(0.218073\pi\)
\(734\) −36.8258 −1.35926
\(735\) 0 0
\(736\) −12.9910 −0.478853
\(737\) −17.4549 −0.642961
\(738\) 1.74482 0.0642276
\(739\) 28.3150 1.04158 0.520792 0.853683i \(-0.325637\pi\)
0.520792 + 0.853683i \(0.325637\pi\)
\(740\) 0 0
\(741\) 2.64273 0.0970833
\(742\) 2.19031 0.0804089
\(743\) 19.5904 0.718702 0.359351 0.933202i \(-0.382998\pi\)
0.359351 + 0.933202i \(0.382998\pi\)
\(744\) 0.681866 0.0249984
\(745\) 0 0
\(746\) −35.8108 −1.31113
\(747\) −10.4990 −0.384138
\(748\) −54.7916 −2.00338
\(749\) −14.7462 −0.538814
\(750\) 0 0
\(751\) 19.1807 0.699914 0.349957 0.936766i \(-0.386196\pi\)
0.349957 + 0.936766i \(0.386196\pi\)
\(752\) −0.769670 −0.0280670
\(753\) −19.7608 −0.720122
\(754\) −42.2894 −1.54009
\(755\) 0 0
\(756\) −4.23336 −0.153966
\(757\) −37.1406 −1.34990 −0.674948 0.737865i \(-0.735834\pi\)
−0.674948 + 0.737865i \(0.735834\pi\)
\(758\) 14.4157 0.523600
\(759\) −10.4049 −0.377674
\(760\) 0 0
\(761\) 9.66892 0.350498 0.175249 0.984524i \(-0.443927\pi\)
0.175249 + 0.984524i \(0.443927\pi\)
\(762\) −27.8018 −1.00715
\(763\) 11.9174 0.431437
\(764\) −12.9915 −0.470017
\(765\) 0 0
\(766\) −84.5766 −3.05588
\(767\) 28.3742 1.02453
\(768\) −10.7022 −0.386182
\(769\) 28.3930 1.02388 0.511938 0.859022i \(-0.328928\pi\)
0.511938 + 0.859022i \(0.328928\pi\)
\(770\) 0 0
\(771\) 25.9677 0.935205
\(772\) 56.1941 2.02247
\(773\) −22.3138 −0.802573 −0.401286 0.915953i \(-0.631437\pi\)
−0.401286 + 0.915953i \(0.631437\pi\)
\(774\) −4.65249 −0.167230
\(775\) 0 0
\(776\) 26.0160 0.933919
\(777\) −6.42572 −0.230522
\(778\) −36.9739 −1.32558
\(779\) −0.788921 −0.0282660
\(780\) 0 0
\(781\) 20.5082 0.733843
\(782\) −15.5525 −0.556158
\(783\) 7.23539 0.258572
\(784\) 3.91148 0.139696
\(785\) 0 0
\(786\) 17.8195 0.635602
\(787\) 31.9455 1.13874 0.569368 0.822083i \(-0.307188\pi\)
0.569368 + 0.822083i \(0.307188\pi\)
\(788\) 27.5471 0.981325
\(789\) −23.5775 −0.839382
\(790\) 0 0
\(791\) −14.5593 −0.517671
\(792\) −12.3405 −0.438499
\(793\) 19.3938 0.688695
\(794\) −5.59414 −0.198529
\(795\) 0 0
\(796\) 76.1805 2.70015
\(797\) 10.6664 0.377822 0.188911 0.981994i \(-0.439504\pi\)
0.188911 + 0.981994i \(0.439504\pi\)
\(798\) 3.16650 0.112093
\(799\) −3.45174 −0.122114
\(800\) 0 0
\(801\) 15.4868 0.547199
\(802\) 47.2321 1.66782
\(803\) −77.9864 −2.75208
\(804\) −10.2747 −0.362362
\(805\) 0 0
\(806\) 1.67706 0.0590719
\(807\) −12.3825 −0.435886
\(808\) −39.3301 −1.38363
\(809\) −38.8845 −1.36711 −0.683554 0.729900i \(-0.739566\pi\)
−0.683554 + 0.729900i \(0.739566\pi\)
\(810\) 0 0
\(811\) −10.3259 −0.362591 −0.181296 0.983429i \(-0.558029\pi\)
−0.181296 + 0.983429i \(0.558029\pi\)
\(812\) −30.6300 −1.07490
\(813\) 18.7346 0.657050
\(814\) −54.1812 −1.89905
\(815\) 0 0
\(816\) 2.65670 0.0930032
\(817\) 2.10363 0.0735968
\(818\) −76.3043 −2.66792
\(819\) −3.59960 −0.125780
\(820\) 0 0
\(821\) 11.3767 0.397050 0.198525 0.980096i \(-0.436385\pi\)
0.198525 + 0.980096i \(0.436385\pi\)
\(822\) 15.7508 0.549373
\(823\) −12.9241 −0.450506 −0.225253 0.974300i \(-0.572321\pi\)
−0.225253 + 0.974300i \(0.572321\pi\)
\(824\) −11.6481 −0.405781
\(825\) 0 0
\(826\) 33.9977 1.18293
\(827\) 45.8003 1.59263 0.796316 0.604880i \(-0.206779\pi\)
0.796316 + 0.604880i \(0.206779\pi\)
\(828\) −6.12477 −0.212850
\(829\) 0.234799 0.00815491 0.00407746 0.999992i \(-0.498702\pi\)
0.00407746 + 0.999992i \(0.498702\pi\)
\(830\) 0 0
\(831\) 8.15990 0.283064
\(832\) −33.8942 −1.17507
\(833\) 17.5418 0.607789
\(834\) 5.25190 0.181858
\(835\) 0 0
\(836\) 16.1397 0.558204
\(837\) −0.286932 −0.00991782
\(838\) −64.0553 −2.21275
\(839\) 30.7648 1.06212 0.531060 0.847334i \(-0.321794\pi\)
0.531060 + 0.847334i \(0.321794\pi\)
\(840\) 0 0
\(841\) 23.3509 0.805204
\(842\) 34.1076 1.17543
\(843\) 19.3677 0.667058
\(844\) 37.4138 1.28784
\(845\) 0 0
\(846\) −2.24873 −0.0773129
\(847\) −22.1120 −0.759778
\(848\) −0.541318 −0.0185889
\(849\) −11.1945 −0.384196
\(850\) 0 0
\(851\) −9.29665 −0.318685
\(852\) 12.0720 0.413581
\(853\) −24.8759 −0.851736 −0.425868 0.904785i \(-0.640031\pi\)
−0.425868 + 0.904785i \(0.640031\pi\)
\(854\) 23.2375 0.795171
\(855\) 0 0
\(856\) −25.3034 −0.864851
\(857\) −49.5602 −1.69294 −0.846472 0.532433i \(-0.821278\pi\)
−0.846472 + 0.532433i \(0.821278\pi\)
\(858\) −30.3515 −1.03618
\(859\) 44.0603 1.50332 0.751658 0.659553i \(-0.229254\pi\)
0.751658 + 0.659553i \(0.229254\pi\)
\(860\) 0 0
\(861\) 1.07457 0.0366212
\(862\) 60.0673 2.04590
\(863\) 30.8561 1.05035 0.525177 0.850993i \(-0.323999\pi\)
0.525177 + 0.850993i \(0.323999\pi\)
\(864\) 6.48358 0.220576
\(865\) 0 0
\(866\) −15.3995 −0.523298
\(867\) −5.08547 −0.172712
\(868\) 1.21469 0.0412292
\(869\) −34.7876 −1.18009
\(870\) 0 0
\(871\) −8.73654 −0.296026
\(872\) 20.4493 0.692500
\(873\) −10.9476 −0.370521
\(874\) 4.58125 0.154963
\(875\) 0 0
\(876\) −45.9062 −1.55103
\(877\) 7.78595 0.262913 0.131456 0.991322i \(-0.458035\pi\)
0.131456 + 0.991322i \(0.458035\pi\)
\(878\) 66.1128 2.23120
\(879\) −13.7883 −0.465068
\(880\) 0 0
\(881\) −10.5411 −0.355139 −0.177569 0.984108i \(-0.556823\pi\)
−0.177569 + 0.984108i \(0.556823\pi\)
\(882\) 11.4281 0.384804
\(883\) −12.9527 −0.435893 −0.217946 0.975961i \(-0.569936\pi\)
−0.217946 + 0.975961i \(0.569936\pi\)
\(884\) −27.4243 −0.922377
\(885\) 0 0
\(886\) 30.5076 1.02492
\(887\) 4.04891 0.135949 0.0679745 0.997687i \(-0.478346\pi\)
0.0679745 + 0.997687i \(0.478346\pi\)
\(888\) −11.0261 −0.370010
\(889\) −17.1221 −0.574258
\(890\) 0 0
\(891\) 5.19292 0.173969
\(892\) −65.4523 −2.19151
\(893\) 1.01677 0.0340248
\(894\) 34.3800 1.14984
\(895\) 0 0
\(896\) −22.6534 −0.756797
\(897\) −5.20785 −0.173885
\(898\) 1.55206 0.0517929
\(899\) −2.07607 −0.0692407
\(900\) 0 0
\(901\) −2.42765 −0.0808768
\(902\) 9.06069 0.301688
\(903\) −2.86530 −0.0953513
\(904\) −24.9827 −0.830914
\(905\) 0 0
\(906\) 34.3285 1.14049
\(907\) −20.8645 −0.692794 −0.346397 0.938088i \(-0.612595\pi\)
−0.346397 + 0.938088i \(0.612595\pi\)
\(908\) 23.2306 0.770936
\(909\) 16.5503 0.548938
\(910\) 0 0
\(911\) 15.0423 0.498372 0.249186 0.968456i \(-0.419837\pi\)
0.249186 + 0.968456i \(0.419837\pi\)
\(912\) −0.782574 −0.0259136
\(913\) −54.5204 −1.80436
\(914\) −45.1194 −1.49242
\(915\) 0 0
\(916\) −73.3989 −2.42517
\(917\) 10.9744 0.362407
\(918\) 7.76203 0.256185
\(919\) −18.6661 −0.615737 −0.307869 0.951429i \(-0.599616\pi\)
−0.307869 + 0.951429i \(0.599616\pi\)
\(920\) 0 0
\(921\) 14.4636 0.476593
\(922\) 0.168357 0.00554455
\(923\) 10.2648 0.337869
\(924\) −21.9835 −0.723204
\(925\) 0 0
\(926\) −29.5848 −0.972217
\(927\) 4.90157 0.160989
\(928\) 46.9113 1.53994
\(929\) −37.1223 −1.21794 −0.608971 0.793192i \(-0.708418\pi\)
−0.608971 + 0.793192i \(0.708418\pi\)
\(930\) 0 0
\(931\) −5.16723 −0.169349
\(932\) −42.4235 −1.38963
\(933\) −1.67137 −0.0547182
\(934\) −54.3834 −1.77948
\(935\) 0 0
\(936\) −6.17664 −0.201890
\(937\) −39.0704 −1.27638 −0.638188 0.769881i \(-0.720316\pi\)
−0.638188 + 0.769881i \(0.720316\pi\)
\(938\) −10.4680 −0.341794
\(939\) 11.6450 0.380019
\(940\) 0 0
\(941\) −50.8417 −1.65739 −0.828697 0.559698i \(-0.810917\pi\)
−0.828697 + 0.559698i \(0.810917\pi\)
\(942\) 39.9280 1.30093
\(943\) 1.55467 0.0506271
\(944\) −8.40225 −0.273470
\(945\) 0 0
\(946\) −24.1600 −0.785510
\(947\) −2.25640 −0.0733231 −0.0366615 0.999328i \(-0.511672\pi\)
−0.0366615 + 0.999328i \(0.511672\pi\)
\(948\) −20.4775 −0.665079
\(949\) −39.0337 −1.26709
\(950\) 0 0
\(951\) 17.8715 0.579523
\(952\) −11.3601 −0.368181
\(953\) 22.2597 0.721064 0.360532 0.932747i \(-0.382595\pi\)
0.360532 + 0.932747i \(0.382595\pi\)
\(954\) −1.58156 −0.0512048
\(955\) 0 0
\(956\) 15.0336 0.486223
\(957\) 37.5728 1.21456
\(958\) 84.0319 2.71495
\(959\) 9.70037 0.313241
\(960\) 0 0
\(961\) −30.9177 −0.997344
\(962\) −27.1188 −0.874344
\(963\) 10.6478 0.343119
\(964\) 67.3075 2.16783
\(965\) 0 0
\(966\) −6.24000 −0.200769
\(967\) −54.3893 −1.74904 −0.874521 0.484988i \(-0.838824\pi\)
−0.874521 + 0.484988i \(0.838824\pi\)
\(968\) −37.9426 −1.21952
\(969\) −3.50962 −0.112745
\(970\) 0 0
\(971\) 21.5812 0.692573 0.346286 0.938129i \(-0.387443\pi\)
0.346286 + 0.938129i \(0.387443\pi\)
\(972\) 3.05678 0.0980462
\(973\) 3.23446 0.103692
\(974\) 5.99805 0.192190
\(975\) 0 0
\(976\) −5.74296 −0.183828
\(977\) 23.6500 0.756631 0.378315 0.925677i \(-0.376503\pi\)
0.378315 + 0.925677i \(0.376503\pi\)
\(978\) −21.8527 −0.698772
\(979\) 80.4216 2.57029
\(980\) 0 0
\(981\) −8.60514 −0.274741
\(982\) 51.7201 1.65045
\(983\) 5.74522 0.183244 0.0916220 0.995794i \(-0.470795\pi\)
0.0916220 + 0.995794i \(0.470795\pi\)
\(984\) 1.84388 0.0587808
\(985\) 0 0
\(986\) 56.1613 1.78854
\(987\) −1.38491 −0.0440822
\(988\) 8.07825 0.257003
\(989\) −4.14548 −0.131819
\(990\) 0 0
\(991\) −43.4775 −1.38111 −0.690555 0.723280i \(-0.742634\pi\)
−0.690555 + 0.723280i \(0.742634\pi\)
\(992\) −1.86035 −0.0590661
\(993\) 15.3796 0.488057
\(994\) 12.2992 0.390106
\(995\) 0 0
\(996\) −32.0931 −1.01691
\(997\) −34.3858 −1.08901 −0.544505 0.838758i \(-0.683283\pi\)
−0.544505 + 0.838758i \(0.683283\pi\)
\(998\) −74.0364 −2.34358
\(999\) 4.63981 0.146797
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 3525.2.a.bi.1.2 13
5.2 odd 4 705.2.c.c.424.5 26
5.3 odd 4 705.2.c.c.424.22 yes 26
5.4 even 2 3525.2.a.bh.1.12 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
705.2.c.c.424.5 26 5.2 odd 4
705.2.c.c.424.22 yes 26 5.3 odd 4
3525.2.a.bh.1.12 13 5.4 even 2
3525.2.a.bi.1.2 13 1.1 even 1 trivial