Properties

Label 3525.2.a.bh.1.3
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 1.3
Root \(2.57687\) 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)
 
\(f(q)\) \(=\) \(q-2.57687 q^{2} -1.00000 q^{3} +4.64024 q^{4} +2.57687 q^{6} -1.51741 q^{7} -6.80354 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.57687 q^{2} -1.00000 q^{3} +4.64024 q^{4} +2.57687 q^{6} -1.51741 q^{7} -6.80354 q^{8} +1.00000 q^{9} -0.409552 q^{11} -4.64024 q^{12} -1.70509 q^{13} +3.91015 q^{14} +8.25132 q^{16} +3.62967 q^{17} -2.57687 q^{18} -0.485553 q^{19} +1.51741 q^{21} +1.05536 q^{22} -7.71926 q^{23} +6.80354 q^{24} +4.39379 q^{26} -1.00000 q^{27} -7.04112 q^{28} -1.53695 q^{29} +4.32311 q^{31} -7.65548 q^{32} +0.409552 q^{33} -9.35318 q^{34} +4.64024 q^{36} +2.44384 q^{37} +1.25121 q^{38} +1.70509 q^{39} -7.76866 q^{41} -3.91015 q^{42} +7.59452 q^{43} -1.90042 q^{44} +19.8915 q^{46} -1.00000 q^{47} -8.25132 q^{48} -4.69748 q^{49} -3.62967 q^{51} -7.91202 q^{52} -10.2033 q^{53} +2.57687 q^{54} +10.3237 q^{56} +0.485553 q^{57} +3.96052 q^{58} +0.118818 q^{59} +2.25962 q^{61} -11.1401 q^{62} -1.51741 q^{63} +3.22450 q^{64} -1.05536 q^{66} +15.7869 q^{67} +16.8426 q^{68} +7.71926 q^{69} -9.50172 q^{71} -6.80354 q^{72} -8.20986 q^{73} -6.29745 q^{74} -2.25308 q^{76} +0.621456 q^{77} -4.39379 q^{78} +13.2865 q^{79} +1.00000 q^{81} +20.0188 q^{82} -6.59494 q^{83} +7.04112 q^{84} -19.5701 q^{86} +1.53695 q^{87} +2.78640 q^{88} +17.7958 q^{89} +2.58731 q^{91} -35.8192 q^{92} -4.32311 q^{93} +2.57687 q^{94} +7.65548 q^{96} +5.61258 q^{97} +12.1048 q^{98} -0.409552 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13 q - 3 q^{2} - 13 q^{3} + 17 q^{4} + 3 q^{6} + 4 q^{7} - 15 q^{8} + 13 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57687 −1.82212 −0.911060 0.412275i \(-0.864734\pi\)
−0.911060 + 0.412275i \(0.864734\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.64024 2.32012
\(5\) 0 0
\(6\) 2.57687 1.05200
\(7\) −1.51741 −0.573525 −0.286763 0.958002i \(-0.592579\pi\)
−0.286763 + 0.958002i \(0.592579\pi\)
\(8\) −6.80354 −2.40541
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.409552 −0.123485 −0.0617423 0.998092i \(-0.519666\pi\)
−0.0617423 + 0.998092i \(0.519666\pi\)
\(12\) −4.64024 −1.33952
\(13\) −1.70509 −0.472907 −0.236454 0.971643i \(-0.575985\pi\)
−0.236454 + 0.971643i \(0.575985\pi\)
\(14\) 3.91015 1.04503
\(15\) 0 0
\(16\) 8.25132 2.06283
\(17\) 3.62967 0.880325 0.440163 0.897918i \(-0.354921\pi\)
0.440163 + 0.897918i \(0.354921\pi\)
\(18\) −2.57687 −0.607373
\(19\) −0.485553 −0.111394 −0.0556968 0.998448i \(-0.517738\pi\)
−0.0556968 + 0.998448i \(0.517738\pi\)
\(20\) 0 0
\(21\) 1.51741 0.331125
\(22\) 1.05536 0.225004
\(23\) −7.71926 −1.60958 −0.804789 0.593562i \(-0.797721\pi\)
−0.804789 + 0.593562i \(0.797721\pi\)
\(24\) 6.80354 1.38877
\(25\) 0 0
\(26\) 4.39379 0.861693
\(27\) −1.00000 −0.192450
\(28\) −7.04112 −1.33065
\(29\) −1.53695 −0.285405 −0.142702 0.989766i \(-0.545579\pi\)
−0.142702 + 0.989766i \(0.545579\pi\)
\(30\) 0 0
\(31\) 4.32311 0.776453 0.388226 0.921564i \(-0.373088\pi\)
0.388226 + 0.921564i \(0.373088\pi\)
\(32\) −7.65548 −1.35331
\(33\) 0.409552 0.0712939
\(34\) −9.35318 −1.60406
\(35\) 0 0
\(36\) 4.64024 0.773373
\(37\) 2.44384 0.401765 0.200883 0.979615i \(-0.435619\pi\)
0.200883 + 0.979615i \(0.435619\pi\)
\(38\) 1.25121 0.202972
\(39\) 1.70509 0.273033
\(40\) 0 0
\(41\) −7.76866 −1.21326 −0.606630 0.794984i \(-0.707479\pi\)
−0.606630 + 0.794984i \(0.707479\pi\)
\(42\) −3.91015 −0.603349
\(43\) 7.59452 1.15815 0.579077 0.815273i \(-0.303413\pi\)
0.579077 + 0.815273i \(0.303413\pi\)
\(44\) −1.90042 −0.286499
\(45\) 0 0
\(46\) 19.8915 2.93284
\(47\) −1.00000 −0.145865
\(48\) −8.25132 −1.19098
\(49\) −4.69748 −0.671069
\(50\) 0 0
\(51\) −3.62967 −0.508256
\(52\) −7.91202 −1.09720
\(53\) −10.2033 −1.40153 −0.700765 0.713392i \(-0.747158\pi\)
−0.700765 + 0.713392i \(0.747158\pi\)
\(54\) 2.57687 0.350667
\(55\) 0 0
\(56\) 10.3237 1.37957
\(57\) 0.485553 0.0643131
\(58\) 3.96052 0.520042
\(59\) 0.118818 0.0154687 0.00773437 0.999970i \(-0.497538\pi\)
0.00773437 + 0.999970i \(0.497538\pi\)
\(60\) 0 0
\(61\) 2.25962 0.289315 0.144658 0.989482i \(-0.453792\pi\)
0.144658 + 0.989482i \(0.453792\pi\)
\(62\) −11.1401 −1.41479
\(63\) −1.51741 −0.191175
\(64\) 3.22450 0.403063
\(65\) 0 0
\(66\) −1.05536 −0.129906
\(67\) 15.7869 1.92868 0.964338 0.264675i \(-0.0852648\pi\)
0.964338 + 0.264675i \(0.0852648\pi\)
\(68\) 16.8426 2.04246
\(69\) 7.71926 0.929290
\(70\) 0 0
\(71\) −9.50172 −1.12765 −0.563824 0.825895i \(-0.690670\pi\)
−0.563824 + 0.825895i \(0.690670\pi\)
\(72\) −6.80354 −0.801804
\(73\) −8.20986 −0.960891 −0.480446 0.877025i \(-0.659525\pi\)
−0.480446 + 0.877025i \(0.659525\pi\)
\(74\) −6.29745 −0.732064
\(75\) 0 0
\(76\) −2.25308 −0.258446
\(77\) 0.621456 0.0708215
\(78\) −4.39379 −0.497499
\(79\) 13.2865 1.49485 0.747424 0.664348i \(-0.231291\pi\)
0.747424 + 0.664348i \(0.231291\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 20.0188 2.21071
\(83\) −6.59494 −0.723889 −0.361944 0.932200i \(-0.617887\pi\)
−0.361944 + 0.932200i \(0.617887\pi\)
\(84\) 7.04112 0.768249
\(85\) 0 0
\(86\) −19.5701 −2.11029
\(87\) 1.53695 0.164779
\(88\) 2.78640 0.297031
\(89\) 17.7958 1.88635 0.943175 0.332296i \(-0.107823\pi\)
0.943175 + 0.332296i \(0.107823\pi\)
\(90\) 0 0
\(91\) 2.58731 0.271224
\(92\) −35.8192 −3.73441
\(93\) −4.32311 −0.448285
\(94\) 2.57687 0.265783
\(95\) 0 0
\(96\) 7.65548 0.781335
\(97\) 5.61258 0.569872 0.284936 0.958547i \(-0.408028\pi\)
0.284936 + 0.958547i \(0.408028\pi\)
\(98\) 12.1048 1.22277
\(99\) −0.409552 −0.0411615
\(100\) 0 0
\(101\) 1.93695 0.192734 0.0963671 0.995346i \(-0.469278\pi\)
0.0963671 + 0.995346i \(0.469278\pi\)
\(102\) 9.35318 0.926103
\(103\) 6.55151 0.645540 0.322770 0.946477i \(-0.395386\pi\)
0.322770 + 0.946477i \(0.395386\pi\)
\(104\) 11.6006 1.13754
\(105\) 0 0
\(106\) 26.2925 2.55376
\(107\) 0.241779 0.0233737 0.0116868 0.999932i \(-0.496280\pi\)
0.0116868 + 0.999932i \(0.496280\pi\)
\(108\) −4.64024 −0.446507
\(109\) −3.75817 −0.359968 −0.179984 0.983670i \(-0.557605\pi\)
−0.179984 + 0.983670i \(0.557605\pi\)
\(110\) 0 0
\(111\) −2.44384 −0.231959
\(112\) −12.5206 −1.18309
\(113\) 3.00612 0.282792 0.141396 0.989953i \(-0.454841\pi\)
0.141396 + 0.989953i \(0.454841\pi\)
\(114\) −1.25121 −0.117186
\(115\) 0 0
\(116\) −7.13183 −0.662173
\(117\) −1.70509 −0.157636
\(118\) −0.306177 −0.0281859
\(119\) −5.50769 −0.504889
\(120\) 0 0
\(121\) −10.8323 −0.984752
\(122\) −5.82275 −0.527167
\(123\) 7.76866 0.700477
\(124\) 20.0602 1.80146
\(125\) 0 0
\(126\) 3.91015 0.348344
\(127\) 9.77663 0.867536 0.433768 0.901025i \(-0.357184\pi\)
0.433768 + 0.901025i \(0.357184\pi\)
\(128\) 7.00185 0.618882
\(129\) −7.59452 −0.668661
\(130\) 0 0
\(131\) −7.07155 −0.617844 −0.308922 0.951087i \(-0.599968\pi\)
−0.308922 + 0.951087i \(0.599968\pi\)
\(132\) 1.90042 0.165410
\(133\) 0.736781 0.0638870
\(134\) −40.6807 −3.51428
\(135\) 0 0
\(136\) −24.6946 −2.11755
\(137\) −0.552072 −0.0471667 −0.0235833 0.999722i \(-0.507508\pi\)
−0.0235833 + 0.999722i \(0.507508\pi\)
\(138\) −19.8915 −1.69328
\(139\) −3.52217 −0.298746 −0.149373 0.988781i \(-0.547726\pi\)
−0.149373 + 0.988781i \(0.547726\pi\)
\(140\) 0 0
\(141\) 1.00000 0.0842152
\(142\) 24.4847 2.05471
\(143\) 0.698323 0.0583967
\(144\) 8.25132 0.687610
\(145\) 0 0
\(146\) 21.1557 1.75086
\(147\) 4.69748 0.387442
\(148\) 11.3400 0.932143
\(149\) −4.18581 −0.342915 −0.171458 0.985191i \(-0.554848\pi\)
−0.171458 + 0.985191i \(0.554848\pi\)
\(150\) 0 0
\(151\) −15.9025 −1.29413 −0.647064 0.762436i \(-0.724003\pi\)
−0.647064 + 0.762436i \(0.724003\pi\)
\(152\) 3.30348 0.267948
\(153\) 3.62967 0.293442
\(154\) −1.60141 −0.129045
\(155\) 0 0
\(156\) 7.91202 0.633469
\(157\) −13.1534 −1.04976 −0.524880 0.851177i \(-0.675890\pi\)
−0.524880 + 0.851177i \(0.675890\pi\)
\(158\) −34.2375 −2.72379
\(159\) 10.2033 0.809174
\(160\) 0 0
\(161\) 11.7132 0.923133
\(162\) −2.57687 −0.202458
\(163\) 2.82593 0.221344 0.110672 0.993857i \(-0.464700\pi\)
0.110672 + 0.993857i \(0.464700\pi\)
\(164\) −36.0484 −2.81491
\(165\) 0 0
\(166\) 16.9943 1.31901
\(167\) 12.6036 0.975296 0.487648 0.873040i \(-0.337855\pi\)
0.487648 + 0.873040i \(0.337855\pi\)
\(168\) −10.3237 −0.796492
\(169\) −10.0927 −0.776359
\(170\) 0 0
\(171\) −0.485553 −0.0371312
\(172\) 35.2404 2.68705
\(173\) −15.3764 −1.16905 −0.584524 0.811377i \(-0.698719\pi\)
−0.584524 + 0.811377i \(0.698719\pi\)
\(174\) −3.96052 −0.300246
\(175\) 0 0
\(176\) −3.37935 −0.254728
\(177\) −0.118818 −0.00893088
\(178\) −45.8574 −3.43715
\(179\) −24.2359 −1.81147 −0.905737 0.423840i \(-0.860682\pi\)
−0.905737 + 0.423840i \(0.860682\pi\)
\(180\) 0 0
\(181\) −7.51402 −0.558513 −0.279257 0.960217i \(-0.590088\pi\)
−0.279257 + 0.960217i \(0.590088\pi\)
\(182\) −6.66716 −0.494203
\(183\) −2.25962 −0.167036
\(184\) 52.5183 3.87170
\(185\) 0 0
\(186\) 11.1401 0.816829
\(187\) −1.48654 −0.108707
\(188\) −4.64024 −0.338424
\(189\) 1.51741 0.110375
\(190\) 0 0
\(191\) 14.6707 1.06154 0.530768 0.847517i \(-0.321903\pi\)
0.530768 + 0.847517i \(0.321903\pi\)
\(192\) −3.22450 −0.232709
\(193\) 4.00150 0.288034 0.144017 0.989575i \(-0.453998\pi\)
0.144017 + 0.989575i \(0.453998\pi\)
\(194\) −14.4629 −1.03837
\(195\) 0 0
\(196\) −21.7974 −1.55696
\(197\) −17.1433 −1.22141 −0.610704 0.791859i \(-0.709114\pi\)
−0.610704 + 0.791859i \(0.709114\pi\)
\(198\) 1.05536 0.0750012
\(199\) −12.0104 −0.851392 −0.425696 0.904866i \(-0.639971\pi\)
−0.425696 + 0.904866i \(0.639971\pi\)
\(200\) 0 0
\(201\) −15.7869 −1.11352
\(202\) −4.99127 −0.351185
\(203\) 2.33218 0.163687
\(204\) −16.8426 −1.17921
\(205\) 0 0
\(206\) −16.8824 −1.17625
\(207\) −7.71926 −0.536526
\(208\) −14.0693 −0.975527
\(209\) 0.198859 0.0137554
\(210\) 0 0
\(211\) 26.1444 1.79986 0.899928 0.436039i \(-0.143619\pi\)
0.899928 + 0.436039i \(0.143619\pi\)
\(212\) −47.3457 −3.25172
\(213\) 9.50172 0.651047
\(214\) −0.623032 −0.0425896
\(215\) 0 0
\(216\) 6.80354 0.462922
\(217\) −6.55990 −0.445315
\(218\) 9.68430 0.655904
\(219\) 8.20986 0.554771
\(220\) 0 0
\(221\) −6.18892 −0.416312
\(222\) 6.29745 0.422657
\(223\) −8.60705 −0.576371 −0.288185 0.957575i \(-0.593052\pi\)
−0.288185 + 0.957575i \(0.593052\pi\)
\(224\) 11.6165 0.776158
\(225\) 0 0
\(226\) −7.74636 −0.515280
\(227\) 29.0547 1.92843 0.964214 0.265124i \(-0.0854129\pi\)
0.964214 + 0.265124i \(0.0854129\pi\)
\(228\) 2.25308 0.149214
\(229\) 5.27755 0.348750 0.174375 0.984679i \(-0.444209\pi\)
0.174375 + 0.984679i \(0.444209\pi\)
\(230\) 0 0
\(231\) −0.621456 −0.0408888
\(232\) 10.4567 0.686517
\(233\) 25.5165 1.67164 0.835821 0.549002i \(-0.184992\pi\)
0.835821 + 0.549002i \(0.184992\pi\)
\(234\) 4.39379 0.287231
\(235\) 0 0
\(236\) 0.551342 0.0358893
\(237\) −13.2865 −0.863051
\(238\) 14.1926 0.919968
\(239\) 23.0647 1.49193 0.745966 0.665984i \(-0.231988\pi\)
0.745966 + 0.665984i \(0.231988\pi\)
\(240\) 0 0
\(241\) −21.2707 −1.37017 −0.685083 0.728465i \(-0.740234\pi\)
−0.685083 + 0.728465i \(0.740234\pi\)
\(242\) 27.9133 1.79433
\(243\) −1.00000 −0.0641500
\(244\) 10.4852 0.671246
\(245\) 0 0
\(246\) −20.0188 −1.27635
\(247\) 0.827913 0.0526788
\(248\) −29.4124 −1.86769
\(249\) 6.59494 0.417937
\(250\) 0 0
\(251\) 18.9282 1.19474 0.597370 0.801966i \(-0.296213\pi\)
0.597370 + 0.801966i \(0.296213\pi\)
\(252\) −7.04112 −0.443549
\(253\) 3.16144 0.198758
\(254\) −25.1931 −1.58075
\(255\) 0 0
\(256\) −24.4918 −1.53074
\(257\) −21.7891 −1.35916 −0.679582 0.733599i \(-0.737839\pi\)
−0.679582 + 0.733599i \(0.737839\pi\)
\(258\) 19.5701 1.21838
\(259\) −3.70830 −0.230423
\(260\) 0 0
\(261\) −1.53695 −0.0951350
\(262\) 18.2224 1.12579
\(263\) 11.1448 0.687219 0.343610 0.939113i \(-0.388350\pi\)
0.343610 + 0.939113i \(0.388350\pi\)
\(264\) −2.78640 −0.171491
\(265\) 0 0
\(266\) −1.89859 −0.116410
\(267\) −17.7958 −1.08908
\(268\) 73.2549 4.47475
\(269\) 25.8889 1.57848 0.789238 0.614088i \(-0.210476\pi\)
0.789238 + 0.614088i \(0.210476\pi\)
\(270\) 0 0
\(271\) 17.7769 1.07987 0.539934 0.841707i \(-0.318449\pi\)
0.539934 + 0.841707i \(0.318449\pi\)
\(272\) 29.9496 1.81596
\(273\) −2.58731 −0.156591
\(274\) 1.42261 0.0859433
\(275\) 0 0
\(276\) 35.8192 2.15606
\(277\) 23.2875 1.39921 0.699604 0.714531i \(-0.253360\pi\)
0.699604 + 0.714531i \(0.253360\pi\)
\(278\) 9.07615 0.544351
\(279\) 4.32311 0.258818
\(280\) 0 0
\(281\) 18.6599 1.11316 0.556578 0.830795i \(-0.312114\pi\)
0.556578 + 0.830795i \(0.312114\pi\)
\(282\) −2.57687 −0.153450
\(283\) 25.1730 1.49638 0.748189 0.663486i \(-0.230924\pi\)
0.748189 + 0.663486i \(0.230924\pi\)
\(284\) −44.0902 −2.61627
\(285\) 0 0
\(286\) −1.79949 −0.106406
\(287\) 11.7882 0.695836
\(288\) −7.65548 −0.451104
\(289\) −3.82546 −0.225027
\(290\) 0 0
\(291\) −5.61258 −0.329016
\(292\) −38.0957 −2.22938
\(293\) −28.6924 −1.67622 −0.838112 0.545497i \(-0.816341\pi\)
−0.838112 + 0.545497i \(0.816341\pi\)
\(294\) −12.1048 −0.705965
\(295\) 0 0
\(296\) −16.6268 −0.966411
\(297\) 0.409552 0.0237646
\(298\) 10.7863 0.624833
\(299\) 13.1620 0.761180
\(300\) 0 0
\(301\) −11.5240 −0.664231
\(302\) 40.9786 2.35806
\(303\) −1.93695 −0.111275
\(304\) −4.00646 −0.229786
\(305\) 0 0
\(306\) −9.35318 −0.534686
\(307\) −8.58383 −0.489905 −0.244953 0.969535i \(-0.578772\pi\)
−0.244953 + 0.969535i \(0.578772\pi\)
\(308\) 2.88371 0.164314
\(309\) −6.55151 −0.372703
\(310\) 0 0
\(311\) 13.5732 0.769664 0.384832 0.922987i \(-0.374259\pi\)
0.384832 + 0.922987i \(0.374259\pi\)
\(312\) −11.6006 −0.656757
\(313\) 7.43322 0.420151 0.210075 0.977685i \(-0.432629\pi\)
0.210075 + 0.977685i \(0.432629\pi\)
\(314\) 33.8947 1.91279
\(315\) 0 0
\(316\) 61.6525 3.46822
\(317\) 16.1762 0.908543 0.454272 0.890863i \(-0.349900\pi\)
0.454272 + 0.890863i \(0.349900\pi\)
\(318\) −26.2925 −1.47441
\(319\) 0.629462 0.0352431
\(320\) 0 0
\(321\) −0.241779 −0.0134948
\(322\) −30.1835 −1.68206
\(323\) −1.76240 −0.0980626
\(324\) 4.64024 0.257791
\(325\) 0 0
\(326\) −7.28203 −0.403315
\(327\) 3.75817 0.207827
\(328\) 52.8544 2.91839
\(329\) 1.51741 0.0836573
\(330\) 0 0
\(331\) 23.9233 1.31494 0.657472 0.753479i \(-0.271626\pi\)
0.657472 + 0.753479i \(0.271626\pi\)
\(332\) −30.6021 −1.67951
\(333\) 2.44384 0.133922
\(334\) −32.4778 −1.77710
\(335\) 0 0
\(336\) 12.5206 0.683055
\(337\) 0.151324 0.00824317 0.00412158 0.999992i \(-0.498688\pi\)
0.00412158 + 0.999992i \(0.498688\pi\)
\(338\) 26.0074 1.41462
\(339\) −3.00612 −0.163270
\(340\) 0 0
\(341\) −1.77054 −0.0958799
\(342\) 1.25121 0.0676575
\(343\) 17.7498 0.958400
\(344\) −51.6696 −2.78584
\(345\) 0 0
\(346\) 39.6230 2.13014
\(347\) 6.17087 0.331270 0.165635 0.986187i \(-0.447033\pi\)
0.165635 + 0.986187i \(0.447033\pi\)
\(348\) 7.13183 0.382306
\(349\) 27.4329 1.46845 0.734226 0.678905i \(-0.237545\pi\)
0.734226 + 0.678905i \(0.237545\pi\)
\(350\) 0 0
\(351\) 1.70509 0.0910110
\(352\) 3.13532 0.167113
\(353\) 30.5374 1.62534 0.812671 0.582723i \(-0.198013\pi\)
0.812671 + 0.582723i \(0.198013\pi\)
\(354\) 0.306177 0.0162731
\(355\) 0 0
\(356\) 82.5767 4.37656
\(357\) 5.50769 0.291498
\(358\) 62.4526 3.30072
\(359\) −2.99142 −0.157881 −0.0789406 0.996879i \(-0.525154\pi\)
−0.0789406 + 0.996879i \(0.525154\pi\)
\(360\) 0 0
\(361\) −18.7642 −0.987591
\(362\) 19.3626 1.01768
\(363\) 10.8323 0.568547
\(364\) 12.0057 0.629272
\(365\) 0 0
\(366\) 5.82275 0.304360
\(367\) 5.64402 0.294615 0.147308 0.989091i \(-0.452939\pi\)
0.147308 + 0.989091i \(0.452939\pi\)
\(368\) −63.6941 −3.32029
\(369\) −7.76866 −0.404420
\(370\) 0 0
\(371\) 15.4825 0.803813
\(372\) −20.0602 −1.04007
\(373\) −32.7211 −1.69423 −0.847116 0.531408i \(-0.821663\pi\)
−0.847116 + 0.531408i \(0.821663\pi\)
\(374\) 3.83062 0.198076
\(375\) 0 0
\(376\) 6.80354 0.350866
\(377\) 2.62064 0.134970
\(378\) −3.91015 −0.201116
\(379\) −16.4931 −0.847194 −0.423597 0.905851i \(-0.639233\pi\)
−0.423597 + 0.905851i \(0.639233\pi\)
\(380\) 0 0
\(381\) −9.77663 −0.500872
\(382\) −37.8045 −1.93425
\(383\) −11.3694 −0.580950 −0.290475 0.956883i \(-0.593813\pi\)
−0.290475 + 0.956883i \(0.593813\pi\)
\(384\) −7.00185 −0.357312
\(385\) 0 0
\(386\) −10.3113 −0.524833
\(387\) 7.59452 0.386051
\(388\) 26.0437 1.32217
\(389\) −4.34727 −0.220415 −0.110208 0.993909i \(-0.535152\pi\)
−0.110208 + 0.993909i \(0.535152\pi\)
\(390\) 0 0
\(391\) −28.0184 −1.41695
\(392\) 31.9595 1.61420
\(393\) 7.07155 0.356713
\(394\) 44.1759 2.22555
\(395\) 0 0
\(396\) −1.90042 −0.0954996
\(397\) 23.3610 1.17245 0.586227 0.810147i \(-0.300613\pi\)
0.586227 + 0.810147i \(0.300613\pi\)
\(398\) 30.9491 1.55134
\(399\) −0.736781 −0.0368852
\(400\) 0 0
\(401\) −1.43302 −0.0715614 −0.0357807 0.999360i \(-0.511392\pi\)
−0.0357807 + 0.999360i \(0.511392\pi\)
\(402\) 40.6807 2.02897
\(403\) −7.37129 −0.367190
\(404\) 8.98793 0.447166
\(405\) 0 0
\(406\) −6.00972 −0.298257
\(407\) −1.00088 −0.0496118
\(408\) 24.6946 1.22257
\(409\) 10.2611 0.507378 0.253689 0.967286i \(-0.418356\pi\)
0.253689 + 0.967286i \(0.418356\pi\)
\(410\) 0 0
\(411\) 0.552072 0.0272317
\(412\) 30.4006 1.49773
\(413\) −0.180295 −0.00887171
\(414\) 19.8915 0.977614
\(415\) 0 0
\(416\) 13.0533 0.639990
\(417\) 3.52217 0.172481
\(418\) −0.512434 −0.0250640
\(419\) 4.69348 0.229291 0.114646 0.993406i \(-0.463427\pi\)
0.114646 + 0.993406i \(0.463427\pi\)
\(420\) 0 0
\(421\) 15.7878 0.769448 0.384724 0.923032i \(-0.374297\pi\)
0.384724 + 0.923032i \(0.374297\pi\)
\(422\) −67.3706 −3.27955
\(423\) −1.00000 −0.0486217
\(424\) 69.4185 3.37126
\(425\) 0 0
\(426\) −24.4847 −1.18629
\(427\) −3.42877 −0.165930
\(428\) 1.12191 0.0542297
\(429\) −0.698323 −0.0337154
\(430\) 0 0
\(431\) 15.5978 0.751319 0.375659 0.926758i \(-0.377416\pi\)
0.375659 + 0.926758i \(0.377416\pi\)
\(432\) −8.25132 −0.396992
\(433\) 31.9312 1.53452 0.767259 0.641338i \(-0.221620\pi\)
0.767259 + 0.641338i \(0.221620\pi\)
\(434\) 16.9040 0.811418
\(435\) 0 0
\(436\) −17.4388 −0.835167
\(437\) 3.74811 0.179297
\(438\) −21.1557 −1.01086
\(439\) 37.0698 1.76925 0.884623 0.466307i \(-0.154416\pi\)
0.884623 + 0.466307i \(0.154416\pi\)
\(440\) 0 0
\(441\) −4.69748 −0.223690
\(442\) 15.9480 0.758570
\(443\) 29.5069 1.40192 0.700958 0.713202i \(-0.252756\pi\)
0.700958 + 0.713202i \(0.252756\pi\)
\(444\) −11.3400 −0.538173
\(445\) 0 0
\(446\) 22.1792 1.05022
\(447\) 4.18581 0.197982
\(448\) −4.89288 −0.231167
\(449\) 7.79984 0.368097 0.184049 0.982917i \(-0.441080\pi\)
0.184049 + 0.982917i \(0.441080\pi\)
\(450\) 0 0
\(451\) 3.18167 0.149819
\(452\) 13.9491 0.656110
\(453\) 15.9025 0.747165
\(454\) −74.8701 −3.51383
\(455\) 0 0
\(456\) −3.30348 −0.154700
\(457\) 21.6451 1.01252 0.506258 0.862382i \(-0.331028\pi\)
0.506258 + 0.862382i \(0.331028\pi\)
\(458\) −13.5995 −0.635465
\(459\) −3.62967 −0.169419
\(460\) 0 0
\(461\) −35.0177 −1.63094 −0.815469 0.578801i \(-0.803521\pi\)
−0.815469 + 0.578801i \(0.803521\pi\)
\(462\) 1.60141 0.0745043
\(463\) 13.1365 0.610503 0.305252 0.952272i \(-0.401259\pi\)
0.305252 + 0.952272i \(0.401259\pi\)
\(464\) −12.6819 −0.588742
\(465\) 0 0
\(466\) −65.7526 −3.04593
\(467\) 15.5109 0.717757 0.358878 0.933384i \(-0.383159\pi\)
0.358878 + 0.933384i \(0.383159\pi\)
\(468\) −7.91202 −0.365733
\(469\) −23.9551 −1.10614
\(470\) 0 0
\(471\) 13.1534 0.606079
\(472\) −0.808380 −0.0372087
\(473\) −3.11035 −0.143014
\(474\) 34.2375 1.57258
\(475\) 0 0
\(476\) −25.5570 −1.17140
\(477\) −10.2033 −0.467177
\(478\) −59.4347 −2.71848
\(479\) 18.6295 0.851204 0.425602 0.904910i \(-0.360062\pi\)
0.425602 + 0.904910i \(0.360062\pi\)
\(480\) 0 0
\(481\) −4.16697 −0.189998
\(482\) 54.8117 2.49661
\(483\) −11.7132 −0.532971
\(484\) −50.2643 −2.28474
\(485\) 0 0
\(486\) 2.57687 0.116889
\(487\) −36.0131 −1.63191 −0.815955 0.578115i \(-0.803788\pi\)
−0.815955 + 0.578115i \(0.803788\pi\)
\(488\) −15.3734 −0.695923
\(489\) −2.82593 −0.127793
\(490\) 0 0
\(491\) 17.0040 0.767379 0.383690 0.923462i \(-0.374653\pi\)
0.383690 + 0.923462i \(0.374653\pi\)
\(492\) 36.0484 1.62519
\(493\) −5.57864 −0.251249
\(494\) −2.13342 −0.0959871
\(495\) 0 0
\(496\) 35.6714 1.60169
\(497\) 14.4180 0.646734
\(498\) −16.9943 −0.761531
\(499\) −20.0215 −0.896283 −0.448142 0.893963i \(-0.647914\pi\)
−0.448142 + 0.893963i \(0.647914\pi\)
\(500\) 0 0
\(501\) −12.6036 −0.563087
\(502\) −48.7755 −2.17696
\(503\) −1.34377 −0.0599159 −0.0299579 0.999551i \(-0.509537\pi\)
−0.0299579 + 0.999551i \(0.509537\pi\)
\(504\) 10.3237 0.459855
\(505\) 0 0
\(506\) −8.14660 −0.362161
\(507\) 10.0927 0.448231
\(508\) 45.3659 2.01279
\(509\) 37.6244 1.66767 0.833837 0.552011i \(-0.186139\pi\)
0.833837 + 0.552011i \(0.186139\pi\)
\(510\) 0 0
\(511\) 12.4577 0.551095
\(512\) 49.1085 2.17031
\(513\) 0.485553 0.0214377
\(514\) 56.1475 2.47656
\(515\) 0 0
\(516\) −35.2404 −1.55137
\(517\) 0.409552 0.0180121
\(518\) 9.55579 0.419857
\(519\) 15.3764 0.674950
\(520\) 0 0
\(521\) −23.1702 −1.01510 −0.507551 0.861621i \(-0.669449\pi\)
−0.507551 + 0.861621i \(0.669449\pi\)
\(522\) 3.96052 0.173347
\(523\) −41.1342 −1.79867 −0.899335 0.437259i \(-0.855949\pi\)
−0.899335 + 0.437259i \(0.855949\pi\)
\(524\) −32.8137 −1.43347
\(525\) 0 0
\(526\) −28.7187 −1.25220
\(527\) 15.6915 0.683531
\(528\) 3.37935 0.147067
\(529\) 36.5870 1.59074
\(530\) 0 0
\(531\) 0.118818 0.00515625
\(532\) 3.41884 0.148226
\(533\) 13.2463 0.573760
\(534\) 45.8574 1.98444
\(535\) 0 0
\(536\) −107.407 −4.63926
\(537\) 24.2359 1.04586
\(538\) −66.7123 −2.87617
\(539\) 1.92386 0.0828666
\(540\) 0 0
\(541\) 7.92870 0.340882 0.170441 0.985368i \(-0.445481\pi\)
0.170441 + 0.985368i \(0.445481\pi\)
\(542\) −45.8086 −1.96765
\(543\) 7.51402 0.322458
\(544\) −27.7869 −1.19135
\(545\) 0 0
\(546\) 6.66716 0.285328
\(547\) −18.6294 −0.796537 −0.398268 0.917269i \(-0.630389\pi\)
−0.398268 + 0.917269i \(0.630389\pi\)
\(548\) −2.56174 −0.109432
\(549\) 2.25962 0.0964384
\(550\) 0 0
\(551\) 0.746273 0.0317923
\(552\) −52.5183 −2.23533
\(553\) −20.1610 −0.857333
\(554\) −60.0087 −2.54952
\(555\) 0 0
\(556\) −16.3437 −0.693127
\(557\) 13.1979 0.559214 0.279607 0.960115i \(-0.409796\pi\)
0.279607 + 0.960115i \(0.409796\pi\)
\(558\) −11.1401 −0.471597
\(559\) −12.9494 −0.547699
\(560\) 0 0
\(561\) 1.48654 0.0627618
\(562\) −48.0840 −2.02830
\(563\) −6.28490 −0.264877 −0.132438 0.991191i \(-0.542281\pi\)
−0.132438 + 0.991191i \(0.542281\pi\)
\(564\) 4.64024 0.195389
\(565\) 0 0
\(566\) −64.8674 −2.72658
\(567\) −1.51741 −0.0637250
\(568\) 64.6453 2.71246
\(569\) −0.393539 −0.0164980 −0.00824900 0.999966i \(-0.502626\pi\)
−0.00824900 + 0.999966i \(0.502626\pi\)
\(570\) 0 0
\(571\) 26.3529 1.10284 0.551418 0.834229i \(-0.314087\pi\)
0.551418 + 0.834229i \(0.314087\pi\)
\(572\) 3.24039 0.135487
\(573\) −14.6707 −0.612879
\(574\) −30.3766 −1.26790
\(575\) 0 0
\(576\) 3.22450 0.134354
\(577\) 29.8939 1.24450 0.622249 0.782819i \(-0.286219\pi\)
0.622249 + 0.782819i \(0.286219\pi\)
\(578\) 9.85770 0.410026
\(579\) −4.00150 −0.166297
\(580\) 0 0
\(581\) 10.0072 0.415168
\(582\) 14.4629 0.599506
\(583\) 4.17878 0.173067
\(584\) 55.8561 2.31134
\(585\) 0 0
\(586\) 73.9363 3.05428
\(587\) 33.5669 1.38545 0.692727 0.721200i \(-0.256409\pi\)
0.692727 + 0.721200i \(0.256409\pi\)
\(588\) 21.7974 0.898911
\(589\) −2.09910 −0.0864919
\(590\) 0 0
\(591\) 17.1433 0.705181
\(592\) 20.1649 0.828774
\(593\) 16.7068 0.686067 0.343033 0.939323i \(-0.388546\pi\)
0.343033 + 0.939323i \(0.388546\pi\)
\(594\) −1.05536 −0.0433020
\(595\) 0 0
\(596\) −19.4232 −0.795604
\(597\) 12.0104 0.491551
\(598\) −33.9168 −1.38696
\(599\) −31.9754 −1.30648 −0.653241 0.757150i \(-0.726591\pi\)
−0.653241 + 0.757150i \(0.726591\pi\)
\(600\) 0 0
\(601\) 11.4369 0.466520 0.233260 0.972414i \(-0.425061\pi\)
0.233260 + 0.972414i \(0.425061\pi\)
\(602\) 29.6957 1.21031
\(603\) 15.7869 0.642892
\(604\) −73.7914 −3.00253
\(605\) 0 0
\(606\) 4.99127 0.202756
\(607\) 0.310562 0.0126053 0.00630266 0.999980i \(-0.497994\pi\)
0.00630266 + 0.999980i \(0.497994\pi\)
\(608\) 3.71715 0.150750
\(609\) −2.33218 −0.0945047
\(610\) 0 0
\(611\) 1.70509 0.0689806
\(612\) 16.8426 0.680820
\(613\) 11.6310 0.469770 0.234885 0.972023i \(-0.424529\pi\)
0.234885 + 0.972023i \(0.424529\pi\)
\(614\) 22.1194 0.892665
\(615\) 0 0
\(616\) −4.22810 −0.170355
\(617\) −13.0457 −0.525199 −0.262599 0.964905i \(-0.584580\pi\)
−0.262599 + 0.964905i \(0.584580\pi\)
\(618\) 16.8824 0.679108
\(619\) 23.8892 0.960190 0.480095 0.877217i \(-0.340602\pi\)
0.480095 + 0.877217i \(0.340602\pi\)
\(620\) 0 0
\(621\) 7.71926 0.309763
\(622\) −34.9763 −1.40242
\(623\) −27.0034 −1.08187
\(624\) 14.0693 0.563221
\(625\) 0 0
\(626\) −19.1544 −0.765565
\(627\) −0.198859 −0.00794168
\(628\) −61.0351 −2.43557
\(629\) 8.87035 0.353684
\(630\) 0 0
\(631\) −3.97907 −0.158404 −0.0792022 0.996859i \(-0.525237\pi\)
−0.0792022 + 0.996859i \(0.525237\pi\)
\(632\) −90.3952 −3.59573
\(633\) −26.1444 −1.03915
\(634\) −41.6838 −1.65547
\(635\) 0 0
\(636\) 47.3457 1.87738
\(637\) 8.00963 0.317353
\(638\) −1.62204 −0.0642172
\(639\) −9.50172 −0.375882
\(640\) 0 0
\(641\) 16.7620 0.662060 0.331030 0.943620i \(-0.392604\pi\)
0.331030 + 0.943620i \(0.392604\pi\)
\(642\) 0.623032 0.0245891
\(643\) −1.13421 −0.0447289 −0.0223644 0.999750i \(-0.507119\pi\)
−0.0223644 + 0.999750i \(0.507119\pi\)
\(644\) 54.3522 2.14178
\(645\) 0 0
\(646\) 4.54147 0.178682
\(647\) −24.1301 −0.948652 −0.474326 0.880349i \(-0.657308\pi\)
−0.474326 + 0.880349i \(0.657308\pi\)
\(648\) −6.80354 −0.267268
\(649\) −0.0486620 −0.00191015
\(650\) 0 0
\(651\) 6.55990 0.257103
\(652\) 13.1130 0.513543
\(653\) 3.75913 0.147106 0.0735531 0.997291i \(-0.476566\pi\)
0.0735531 + 0.997291i \(0.476566\pi\)
\(654\) −9.68430 −0.378686
\(655\) 0 0
\(656\) −64.1017 −2.50275
\(657\) −8.20986 −0.320297
\(658\) −3.91015 −0.152434
\(659\) −10.4017 −0.405193 −0.202597 0.979262i \(-0.564938\pi\)
−0.202597 + 0.979262i \(0.564938\pi\)
\(660\) 0 0
\(661\) −7.27614 −0.283009 −0.141505 0.989938i \(-0.545194\pi\)
−0.141505 + 0.989938i \(0.545194\pi\)
\(662\) −61.6472 −2.39598
\(663\) 6.18892 0.240358
\(664\) 44.8689 1.74125
\(665\) 0 0
\(666\) −6.29745 −0.244021
\(667\) 11.8641 0.459381
\(668\) 58.4837 2.26280
\(669\) 8.60705 0.332768
\(670\) 0 0
\(671\) −0.925434 −0.0357260
\(672\) −11.6165 −0.448115
\(673\) 31.4216 1.21121 0.605607 0.795764i \(-0.292930\pi\)
0.605607 + 0.795764i \(0.292930\pi\)
\(674\) −0.389943 −0.0150200
\(675\) 0 0
\(676\) −46.8324 −1.80124
\(677\) 19.6313 0.754493 0.377247 0.926113i \(-0.376871\pi\)
0.377247 + 0.926113i \(0.376871\pi\)
\(678\) 7.74636 0.297497
\(679\) −8.51657 −0.326836
\(680\) 0 0
\(681\) −29.0547 −1.11338
\(682\) 4.56244 0.174705
\(683\) −3.80221 −0.145487 −0.0727437 0.997351i \(-0.523176\pi\)
−0.0727437 + 0.997351i \(0.523176\pi\)
\(684\) −2.25308 −0.0861488
\(685\) 0 0
\(686\) −45.7389 −1.74632
\(687\) −5.27755 −0.201351
\(688\) 62.6649 2.38908
\(689\) 17.3975 0.662794
\(690\) 0 0
\(691\) 47.0061 1.78819 0.894097 0.447873i \(-0.147818\pi\)
0.894097 + 0.447873i \(0.147818\pi\)
\(692\) −71.3502 −2.71233
\(693\) 0.621456 0.0236072
\(694\) −15.9015 −0.603613
\(695\) 0 0
\(696\) −10.4567 −0.396361
\(697\) −28.1977 −1.06806
\(698\) −70.6910 −2.67569
\(699\) −25.5165 −0.965123
\(700\) 0 0
\(701\) 37.4539 1.41461 0.707307 0.706906i \(-0.249910\pi\)
0.707307 + 0.706906i \(0.249910\pi\)
\(702\) −4.39379 −0.165833
\(703\) −1.18662 −0.0447541
\(704\) −1.32060 −0.0497721
\(705\) 0 0
\(706\) −78.6907 −2.96157
\(707\) −2.93914 −0.110538
\(708\) −0.551342 −0.0207207
\(709\) 34.7204 1.30395 0.651976 0.758240i \(-0.273940\pi\)
0.651976 + 0.758240i \(0.273940\pi\)
\(710\) 0 0
\(711\) 13.2865 0.498283
\(712\) −121.074 −4.53745
\(713\) −33.3712 −1.24976
\(714\) −14.1926 −0.531144
\(715\) 0 0
\(716\) −112.460 −4.20284
\(717\) −23.0647 −0.861368
\(718\) 7.70850 0.287679
\(719\) −15.7765 −0.588363 −0.294181 0.955750i \(-0.595047\pi\)
−0.294181 + 0.955750i \(0.595047\pi\)
\(720\) 0 0
\(721\) −9.94130 −0.370233
\(722\) 48.3529 1.79951
\(723\) 21.2707 0.791066
\(724\) −34.8669 −1.29582
\(725\) 0 0
\(726\) −27.9133 −1.03596
\(727\) 9.80778 0.363750 0.181875 0.983322i \(-0.441783\pi\)
0.181875 + 0.983322i \(0.441783\pi\)
\(728\) −17.6029 −0.652406
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 27.5657 1.01955
\(732\) −10.4852 −0.387544
\(733\) −29.9733 −1.10709 −0.553544 0.832820i \(-0.686725\pi\)
−0.553544 + 0.832820i \(0.686725\pi\)
\(734\) −14.5439 −0.536824
\(735\) 0 0
\(736\) 59.0947 2.17826
\(737\) −6.46555 −0.238162
\(738\) 20.0188 0.736902
\(739\) 20.7720 0.764109 0.382055 0.924140i \(-0.375217\pi\)
0.382055 + 0.924140i \(0.375217\pi\)
\(740\) 0 0
\(741\) −0.827913 −0.0304141
\(742\) −39.8964 −1.46464
\(743\) −30.5350 −1.12022 −0.560110 0.828418i \(-0.689241\pi\)
−0.560110 + 0.828418i \(0.689241\pi\)
\(744\) 29.4124 1.07831
\(745\) 0 0
\(746\) 84.3178 3.08709
\(747\) −6.59494 −0.241296
\(748\) −6.89790 −0.252212
\(749\) −0.366877 −0.0134054
\(750\) 0 0
\(751\) −30.9000 −1.12756 −0.563779 0.825926i \(-0.690653\pi\)
−0.563779 + 0.825926i \(0.690653\pi\)
\(752\) −8.25132 −0.300895
\(753\) −18.9282 −0.689783
\(754\) −6.75305 −0.245931
\(755\) 0 0
\(756\) 7.04112 0.256083
\(757\) −9.99773 −0.363374 −0.181687 0.983356i \(-0.558156\pi\)
−0.181687 + 0.983356i \(0.558156\pi\)
\(758\) 42.5005 1.54369
\(759\) −3.16144 −0.114753
\(760\) 0 0
\(761\) 18.0677 0.654953 0.327476 0.944859i \(-0.393802\pi\)
0.327476 + 0.944859i \(0.393802\pi\)
\(762\) 25.1931 0.912648
\(763\) 5.70267 0.206451
\(764\) 68.0757 2.46289
\(765\) 0 0
\(766\) 29.2975 1.05856
\(767\) −0.202595 −0.00731528
\(768\) 24.4918 0.883773
\(769\) 5.15329 0.185832 0.0929162 0.995674i \(-0.470381\pi\)
0.0929162 + 0.995674i \(0.470381\pi\)
\(770\) 0 0
\(771\) 21.7891 0.784714
\(772\) 18.5679 0.668273
\(773\) 16.5239 0.594322 0.297161 0.954827i \(-0.403960\pi\)
0.297161 + 0.954827i \(0.403960\pi\)
\(774\) −19.5701 −0.703432
\(775\) 0 0
\(776\) −38.1854 −1.37078
\(777\) 3.70830 0.133035
\(778\) 11.2023 0.401623
\(779\) 3.77210 0.135149
\(780\) 0 0
\(781\) 3.89145 0.139247
\(782\) 72.1997 2.58186
\(783\) 1.53695 0.0549262
\(784\) −38.7604 −1.38430
\(785\) 0 0
\(786\) −18.2224 −0.649973
\(787\) 2.05263 0.0731684 0.0365842 0.999331i \(-0.488352\pi\)
0.0365842 + 0.999331i \(0.488352\pi\)
\(788\) −79.5489 −2.83381
\(789\) −11.1448 −0.396766
\(790\) 0 0
\(791\) −4.56150 −0.162188
\(792\) 2.78640 0.0990105
\(793\) −3.85286 −0.136819
\(794\) −60.1981 −2.13635
\(795\) 0 0
\(796\) −55.7309 −1.97533
\(797\) −37.3883 −1.32436 −0.662180 0.749345i \(-0.730369\pi\)
−0.662180 + 0.749345i \(0.730369\pi\)
\(798\) 1.89859 0.0672092
\(799\) −3.62967 −0.128409
\(800\) 0 0
\(801\) 17.7958 0.628783
\(802\) 3.69269 0.130393
\(803\) 3.36236 0.118655
\(804\) −73.2549 −2.58350
\(805\) 0 0
\(806\) 18.9948 0.669064
\(807\) −25.8889 −0.911333
\(808\) −13.1781 −0.463605
\(809\) −23.1030 −0.812257 −0.406128 0.913816i \(-0.633121\pi\)
−0.406128 + 0.913816i \(0.633121\pi\)
\(810\) 0 0
\(811\) −23.6977 −0.832140 −0.416070 0.909333i \(-0.636593\pi\)
−0.416070 + 0.909333i \(0.636593\pi\)
\(812\) 10.8219 0.379773
\(813\) −17.7769 −0.623462
\(814\) 2.57914 0.0903986
\(815\) 0 0
\(816\) −29.9496 −1.04845
\(817\) −3.68755 −0.129011
\(818\) −26.4414 −0.924503
\(819\) 2.58731 0.0904081
\(820\) 0 0
\(821\) 42.8599 1.49582 0.747911 0.663799i \(-0.231057\pi\)
0.747911 + 0.663799i \(0.231057\pi\)
\(822\) −1.42261 −0.0496194
\(823\) −22.2558 −0.775788 −0.387894 0.921704i \(-0.626797\pi\)
−0.387894 + 0.921704i \(0.626797\pi\)
\(824\) −44.5735 −1.55279
\(825\) 0 0
\(826\) 0.464595 0.0161653
\(827\) 25.8507 0.898917 0.449459 0.893301i \(-0.351617\pi\)
0.449459 + 0.893301i \(0.351617\pi\)
\(828\) −35.8192 −1.24480
\(829\) −8.19269 −0.284544 −0.142272 0.989828i \(-0.545441\pi\)
−0.142272 + 0.989828i \(0.545441\pi\)
\(830\) 0 0
\(831\) −23.2875 −0.807833
\(832\) −5.49807 −0.190611
\(833\) −17.0503 −0.590759
\(834\) −9.07615 −0.314281
\(835\) 0 0
\(836\) 0.922755 0.0319141
\(837\) −4.32311 −0.149428
\(838\) −12.0945 −0.417796
\(839\) −13.6146 −0.470027 −0.235013 0.971992i \(-0.575513\pi\)
−0.235013 + 0.971992i \(0.575513\pi\)
\(840\) 0 0
\(841\) −26.6378 −0.918544
\(842\) −40.6829 −1.40203
\(843\) −18.6599 −0.642681
\(844\) 121.316 4.17588
\(845\) 0 0
\(846\) 2.57687 0.0885945
\(847\) 16.4369 0.564780
\(848\) −84.1907 −2.89112
\(849\) −25.1730 −0.863934
\(850\) 0 0
\(851\) −18.8647 −0.646672
\(852\) 44.0902 1.51051
\(853\) −19.4589 −0.666261 −0.333130 0.942881i \(-0.608105\pi\)
−0.333130 + 0.942881i \(0.608105\pi\)
\(854\) 8.83547 0.302344
\(855\) 0 0
\(856\) −1.64495 −0.0562233
\(857\) −18.3188 −0.625758 −0.312879 0.949793i \(-0.601293\pi\)
−0.312879 + 0.949793i \(0.601293\pi\)
\(858\) 1.79949 0.0614334
\(859\) −57.3781 −1.95772 −0.978858 0.204540i \(-0.934430\pi\)
−0.978858 + 0.204540i \(0.934430\pi\)
\(860\) 0 0
\(861\) −11.7882 −0.401741
\(862\) −40.1934 −1.36899
\(863\) −18.0524 −0.614510 −0.307255 0.951627i \(-0.599410\pi\)
−0.307255 + 0.951627i \(0.599410\pi\)
\(864\) 7.65548 0.260445
\(865\) 0 0
\(866\) −82.2825 −2.79607
\(867\) 3.82546 0.129919
\(868\) −30.4395 −1.03318
\(869\) −5.44151 −0.184591
\(870\) 0 0
\(871\) −26.9181 −0.912084
\(872\) 25.5689 0.865871
\(873\) 5.61258 0.189957
\(874\) −9.65838 −0.326700
\(875\) 0 0
\(876\) 38.0957 1.28713
\(877\) 14.4579 0.488209 0.244105 0.969749i \(-0.421506\pi\)
0.244105 + 0.969749i \(0.421506\pi\)
\(878\) −95.5240 −3.22378
\(879\) 28.6924 0.967769
\(880\) 0 0
\(881\) 56.1913 1.89313 0.946567 0.322509i \(-0.104526\pi\)
0.946567 + 0.322509i \(0.104526\pi\)
\(882\) 12.1048 0.407589
\(883\) 41.7329 1.40443 0.702213 0.711967i \(-0.252196\pi\)
0.702213 + 0.711967i \(0.252196\pi\)
\(884\) −28.7181 −0.965893
\(885\) 0 0
\(886\) −76.0354 −2.55446
\(887\) −32.3399 −1.08587 −0.542933 0.839776i \(-0.682686\pi\)
−0.542933 + 0.839776i \(0.682686\pi\)
\(888\) 16.6268 0.557958
\(889\) −14.8351 −0.497554
\(890\) 0 0
\(891\) −0.409552 −0.0137205
\(892\) −39.9388 −1.33725
\(893\) 0.485553 0.0162484
\(894\) −10.7863 −0.360747
\(895\) 0 0
\(896\) −10.6246 −0.354945
\(897\) −13.1620 −0.439468
\(898\) −20.0991 −0.670717
\(899\) −6.64441 −0.221603
\(900\) 0 0
\(901\) −37.0347 −1.23380
\(902\) −8.19874 −0.272988
\(903\) 11.5240 0.383494
\(904\) −20.4522 −0.680231
\(905\) 0 0
\(906\) −40.9786 −1.36142
\(907\) −8.06590 −0.267824 −0.133912 0.990993i \(-0.542754\pi\)
−0.133912 + 0.990993i \(0.542754\pi\)
\(908\) 134.821 4.47418
\(909\) 1.93695 0.0642447
\(910\) 0 0
\(911\) −10.8121 −0.358222 −0.179111 0.983829i \(-0.557322\pi\)
−0.179111 + 0.983829i \(0.557322\pi\)
\(912\) 4.00646 0.132667
\(913\) 2.70097 0.0893891
\(914\) −55.7766 −1.84493
\(915\) 0 0
\(916\) 24.4891 0.809142
\(917\) 10.7304 0.354349
\(918\) 9.35318 0.308701
\(919\) 46.7910 1.54349 0.771747 0.635930i \(-0.219383\pi\)
0.771747 + 0.635930i \(0.219383\pi\)
\(920\) 0 0
\(921\) 8.58383 0.282847
\(922\) 90.2360 2.97176
\(923\) 16.2013 0.533272
\(924\) −2.88371 −0.0948669
\(925\) 0 0
\(926\) −33.8509 −1.11241
\(927\) 6.55151 0.215180
\(928\) 11.7661 0.386242
\(929\) −6.27773 −0.205966 −0.102983 0.994683i \(-0.532839\pi\)
−0.102983 + 0.994683i \(0.532839\pi\)
\(930\) 0 0
\(931\) 2.28088 0.0747527
\(932\) 118.403 3.87841
\(933\) −13.5732 −0.444366
\(934\) −39.9694 −1.30784
\(935\) 0 0
\(936\) 11.6006 0.379179
\(937\) −23.1765 −0.757145 −0.378572 0.925572i \(-0.623585\pi\)
−0.378572 + 0.925572i \(0.623585\pi\)
\(938\) 61.7291 2.01553
\(939\) −7.43322 −0.242574
\(940\) 0 0
\(941\) −46.6445 −1.52057 −0.760283 0.649592i \(-0.774940\pi\)
−0.760283 + 0.649592i \(0.774940\pi\)
\(942\) −33.8947 −1.10435
\(943\) 59.9683 1.95284
\(944\) 0.980403 0.0319094
\(945\) 0 0
\(946\) 8.01496 0.260589
\(947\) −26.5370 −0.862336 −0.431168 0.902272i \(-0.641898\pi\)
−0.431168 + 0.902272i \(0.641898\pi\)
\(948\) −61.6525 −2.00238
\(949\) 13.9986 0.454412
\(950\) 0 0
\(951\) −16.1762 −0.524548
\(952\) 37.4718 1.21447
\(953\) 3.25613 0.105476 0.0527381 0.998608i \(-0.483205\pi\)
0.0527381 + 0.998608i \(0.483205\pi\)
\(954\) 26.2925 0.851252
\(955\) 0 0
\(956\) 107.026 3.46146
\(957\) −0.629462 −0.0203476
\(958\) −48.0058 −1.55100
\(959\) 0.837716 0.0270513
\(960\) 0 0
\(961\) −12.3108 −0.397121
\(962\) 10.7377 0.346198
\(963\) 0.241779 0.00779122
\(964\) −98.7010 −3.17895
\(965\) 0 0
\(966\) 30.1835 0.971137
\(967\) 57.0081 1.83326 0.916629 0.399739i \(-0.130899\pi\)
0.916629 + 0.399739i \(0.130899\pi\)
\(968\) 73.6977 2.36873
\(969\) 1.76240 0.0566165
\(970\) 0 0
\(971\) 48.7556 1.56464 0.782321 0.622876i \(-0.214036\pi\)
0.782321 + 0.622876i \(0.214036\pi\)
\(972\) −4.64024 −0.148836
\(973\) 5.34456 0.171339
\(974\) 92.8010 2.97354
\(975\) 0 0
\(976\) 18.6449 0.596809
\(977\) −39.3330 −1.25838 −0.629188 0.777253i \(-0.716612\pi\)
−0.629188 + 0.777253i \(0.716612\pi\)
\(978\) 7.28203 0.232854
\(979\) −7.28830 −0.232935
\(980\) 0 0
\(981\) −3.75817 −0.119989
\(982\) −43.8170 −1.39826
\(983\) −46.2193 −1.47417 −0.737083 0.675802i \(-0.763797\pi\)
−0.737083 + 0.675802i \(0.763797\pi\)
\(984\) −52.8544 −1.68494
\(985\) 0 0
\(986\) 14.3754 0.457806
\(987\) −1.51741 −0.0482995
\(988\) 3.84171 0.122221
\(989\) −58.6241 −1.86414
\(990\) 0 0
\(991\) −25.4629 −0.808856 −0.404428 0.914570i \(-0.632529\pi\)
−0.404428 + 0.914570i \(0.632529\pi\)
\(992\) −33.0955 −1.05078
\(993\) −23.9233 −0.759183
\(994\) −37.1532 −1.17843
\(995\) 0 0
\(996\) 30.6021 0.969664
\(997\) 39.1066 1.23852 0.619260 0.785186i \(-0.287433\pi\)
0.619260 + 0.785186i \(0.287433\pi\)
\(998\) 51.5926 1.63314
\(999\) −2.44384 −0.0773198
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.bh.1.3 13
5.2 odd 4 705.2.c.c.424.3 26
5.3 odd 4 705.2.c.c.424.24 yes 26
5.4 even 2 3525.2.a.bi.1.11 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
705.2.c.c.424.3 26 5.2 odd 4
705.2.c.c.424.24 yes 26 5.3 odd 4
3525.2.a.bh.1.3 13 1.1 even 1 trivial
3525.2.a.bi.1.11 13 5.4 even 2