Properties

Label 2695.2.a.u.1.7
Level $2695$
Weight $2$
Character 2695.1
Self dual yes
Analytic conductor $21.520$
Analytic rank $1$
Dimension $10$
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] = [2695,2,Mod(1,2695)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2695, 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("2695.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2695.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: \(21.5196833447\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 56x^{6} - 92x^{5} - 86x^{4} + 116x^{3} + 31x^{2} - 30x - 7 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.480122\) of defining polynomial
Character \(\chi\) \(=\) 2695.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.480122 q^{2} -0.720208 q^{3} -1.76948 q^{4} +1.00000 q^{5} -0.345788 q^{6} -1.80981 q^{8} -2.48130 q^{9} +O(q^{10})\) \(q+0.480122 q^{2} -0.720208 q^{3} -1.76948 q^{4} +1.00000 q^{5} -0.345788 q^{6} -1.80981 q^{8} -2.48130 q^{9} +0.480122 q^{10} +1.00000 q^{11} +1.27440 q^{12} +2.59533 q^{13} -0.720208 q^{15} +2.67004 q^{16} -2.65161 q^{17} -1.19133 q^{18} +2.83072 q^{19} -1.76948 q^{20} +0.480122 q^{22} +2.01184 q^{23} +1.30344 q^{24} +1.00000 q^{25} +1.24607 q^{26} +3.94768 q^{27} -6.33190 q^{29} -0.345788 q^{30} -4.04011 q^{31} +4.90157 q^{32} -0.720208 q^{33} -1.27310 q^{34} +4.39062 q^{36} +11.6184 q^{37} +1.35909 q^{38} -1.86918 q^{39} -1.80981 q^{40} -3.25462 q^{41} -3.96803 q^{43} -1.76948 q^{44} -2.48130 q^{45} +0.965927 q^{46} -9.41591 q^{47} -1.92298 q^{48} +0.480122 q^{50} +1.90971 q^{51} -4.59239 q^{52} -6.56767 q^{53} +1.89537 q^{54} +1.00000 q^{55} -2.03871 q^{57} -3.04008 q^{58} -12.2383 q^{59} +1.27440 q^{60} +5.18390 q^{61} -1.93974 q^{62} -2.98672 q^{64} +2.59533 q^{65} -0.345788 q^{66} -2.21517 q^{67} +4.69199 q^{68} -1.44894 q^{69} -3.74766 q^{71} +4.49068 q^{72} -7.99291 q^{73} +5.57823 q^{74} -0.720208 q^{75} -5.00891 q^{76} -0.897433 q^{78} +16.3495 q^{79} +2.67004 q^{80} +4.60075 q^{81} -1.56262 q^{82} -1.31388 q^{83} -2.65161 q^{85} -1.90514 q^{86} +4.56029 q^{87} -1.80981 q^{88} -7.47273 q^{89} -1.19133 q^{90} -3.55991 q^{92} +2.90972 q^{93} -4.52078 q^{94} +2.83072 q^{95} -3.53015 q^{96} -6.50946 q^{97} -2.48130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{2} - 8 q^{3} + 10 q^{4} + 10 q^{5} - 4 q^{6} - 6 q^{8} + 10 q^{9} - 2 q^{10} + 10 q^{11} - 20 q^{12} - 8 q^{13} - 8 q^{15} + 6 q^{16} - 28 q^{17} - 14 q^{18} + 10 q^{20} - 2 q^{22} - 16 q^{23} + 8 q^{24} + 10 q^{25} - 20 q^{26} - 32 q^{27} - 4 q^{30} - 20 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} + 42 q^{36} - 36 q^{37} - 24 q^{38} + 24 q^{39} - 6 q^{40} - 36 q^{41} - 4 q^{43} + 10 q^{44} + 10 q^{45} - 4 q^{46} - 12 q^{47} - 40 q^{48} - 2 q^{50} + 20 q^{51} - 4 q^{52} - 16 q^{53} + 48 q^{54} + 10 q^{55} + 4 q^{57} + 16 q^{58} - 32 q^{59} - 20 q^{60} + 16 q^{61} + 4 q^{62} - 34 q^{64} - 8 q^{65} - 4 q^{66} - 20 q^{67} - 32 q^{68} - 28 q^{69} + 12 q^{71} - 2 q^{72} - 20 q^{73} + 32 q^{74} - 8 q^{75} - 12 q^{76} + 20 q^{78} + 12 q^{79} + 6 q^{80} + 42 q^{81} + 40 q^{82} - 8 q^{83} - 28 q^{85} - 4 q^{86} - 28 q^{87} - 6 q^{88} - 68 q^{89} - 14 q^{90} + 32 q^{92} - 32 q^{93} - 16 q^{94} + 80 q^{96} - 36 q^{97} + 10 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.480122 0.339497 0.169749 0.985487i \(-0.445704\pi\)
0.169749 + 0.985487i \(0.445704\pi\)
\(3\) −0.720208 −0.415812 −0.207906 0.978149i \(-0.566665\pi\)
−0.207906 + 0.978149i \(0.566665\pi\)
\(4\) −1.76948 −0.884741
\(5\) 1.00000 0.447214
\(6\) −0.345788 −0.141167
\(7\) 0 0
\(8\) −1.80981 −0.639865
\(9\) −2.48130 −0.827100
\(10\) 0.480122 0.151828
\(11\) 1.00000 0.301511
\(12\) 1.27440 0.367886
\(13\) 2.59533 0.719815 0.359907 0.932988i \(-0.382808\pi\)
0.359907 + 0.932988i \(0.382808\pi\)
\(14\) 0 0
\(15\) −0.720208 −0.185957
\(16\) 2.67004 0.667509
\(17\) −2.65161 −0.643111 −0.321555 0.946891i \(-0.604206\pi\)
−0.321555 + 0.946891i \(0.604206\pi\)
\(18\) −1.19133 −0.280798
\(19\) 2.83072 0.649412 0.324706 0.945815i \(-0.394735\pi\)
0.324706 + 0.945815i \(0.394735\pi\)
\(20\) −1.76948 −0.395668
\(21\) 0 0
\(22\) 0.480122 0.102362
\(23\) 2.01184 0.419497 0.209749 0.977755i \(-0.432735\pi\)
0.209749 + 0.977755i \(0.432735\pi\)
\(24\) 1.30344 0.266064
\(25\) 1.00000 0.200000
\(26\) 1.24607 0.244375
\(27\) 3.94768 0.759731
\(28\) 0 0
\(29\) −6.33190 −1.17580 −0.587902 0.808932i \(-0.700046\pi\)
−0.587902 + 0.808932i \(0.700046\pi\)
\(30\) −0.345788 −0.0631319
\(31\) −4.04011 −0.725625 −0.362812 0.931862i \(-0.618183\pi\)
−0.362812 + 0.931862i \(0.618183\pi\)
\(32\) 4.90157 0.866483
\(33\) −0.720208 −0.125372
\(34\) −1.27310 −0.218334
\(35\) 0 0
\(36\) 4.39062 0.731770
\(37\) 11.6184 1.91005 0.955024 0.296528i \(-0.0958287\pi\)
0.955024 + 0.296528i \(0.0958287\pi\)
\(38\) 1.35909 0.220474
\(39\) −1.86918 −0.299308
\(40\) −1.80981 −0.286156
\(41\) −3.25462 −0.508286 −0.254143 0.967167i \(-0.581793\pi\)
−0.254143 + 0.967167i \(0.581793\pi\)
\(42\) 0 0
\(43\) −3.96803 −0.605119 −0.302559 0.953131i \(-0.597841\pi\)
−0.302559 + 0.953131i \(0.597841\pi\)
\(44\) −1.76948 −0.266760
\(45\) −2.48130 −0.369890
\(46\) 0.965927 0.142418
\(47\) −9.41591 −1.37345 −0.686726 0.726917i \(-0.740953\pi\)
−0.686726 + 0.726917i \(0.740953\pi\)
\(48\) −1.92298 −0.277559
\(49\) 0 0
\(50\) 0.480122 0.0678995
\(51\) 1.90971 0.267413
\(52\) −4.59239 −0.636850
\(53\) −6.56767 −0.902139 −0.451069 0.892489i \(-0.648957\pi\)
−0.451069 + 0.892489i \(0.648957\pi\)
\(54\) 1.89537 0.257927
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) −2.03871 −0.270034
\(58\) −3.04008 −0.399183
\(59\) −12.2383 −1.59328 −0.796642 0.604451i \(-0.793393\pi\)
−0.796642 + 0.604451i \(0.793393\pi\)
\(60\) 1.27440 0.164524
\(61\) 5.18390 0.663730 0.331865 0.943327i \(-0.392322\pi\)
0.331865 + 0.943327i \(0.392322\pi\)
\(62\) −1.93974 −0.246348
\(63\) 0 0
\(64\) −2.98672 −0.373340
\(65\) 2.59533 0.321911
\(66\) −0.345788 −0.0425635
\(67\) −2.21517 −0.270626 −0.135313 0.990803i \(-0.543204\pi\)
−0.135313 + 0.990803i \(0.543204\pi\)
\(68\) 4.69199 0.568987
\(69\) −1.44894 −0.174432
\(70\) 0 0
\(71\) −3.74766 −0.444765 −0.222383 0.974959i \(-0.571383\pi\)
−0.222383 + 0.974959i \(0.571383\pi\)
\(72\) 4.49068 0.529232
\(73\) −7.99291 −0.935499 −0.467750 0.883861i \(-0.654935\pi\)
−0.467750 + 0.883861i \(0.654935\pi\)
\(74\) 5.57823 0.648457
\(75\) −0.720208 −0.0831625
\(76\) −5.00891 −0.574562
\(77\) 0 0
\(78\) −0.897433 −0.101614
\(79\) 16.3495 1.83947 0.919733 0.392545i \(-0.128405\pi\)
0.919733 + 0.392545i \(0.128405\pi\)
\(80\) 2.67004 0.298519
\(81\) 4.60075 0.511195
\(82\) −1.56262 −0.172562
\(83\) −1.31388 −0.144217 −0.0721084 0.997397i \(-0.522973\pi\)
−0.0721084 + 0.997397i \(0.522973\pi\)
\(84\) 0 0
\(85\) −2.65161 −0.287608
\(86\) −1.90514 −0.205436
\(87\) 4.56029 0.488914
\(88\) −1.80981 −0.192927
\(89\) −7.47273 −0.792108 −0.396054 0.918227i \(-0.629621\pi\)
−0.396054 + 0.918227i \(0.629621\pi\)
\(90\) −1.19133 −0.125577
\(91\) 0 0
\(92\) −3.55991 −0.371146
\(93\) 2.90972 0.301724
\(94\) −4.52078 −0.466283
\(95\) 2.83072 0.290426
\(96\) −3.53015 −0.360294
\(97\) −6.50946 −0.660936 −0.330468 0.943817i \(-0.607207\pi\)
−0.330468 + 0.943817i \(0.607207\pi\)
\(98\) 0 0
\(99\) −2.48130 −0.249380
\(100\) −1.76948 −0.176948
\(101\) −11.2053 −1.11497 −0.557485 0.830187i \(-0.688234\pi\)
−0.557485 + 0.830187i \(0.688234\pi\)
\(102\) 0.916895 0.0907862
\(103\) −15.0206 −1.48003 −0.740014 0.672591i \(-0.765181\pi\)
−0.740014 + 0.672591i \(0.765181\pi\)
\(104\) −4.69706 −0.460584
\(105\) 0 0
\(106\) −3.15328 −0.306274
\(107\) −5.53990 −0.535563 −0.267781 0.963480i \(-0.586290\pi\)
−0.267781 + 0.963480i \(0.586290\pi\)
\(108\) −6.98535 −0.672165
\(109\) −11.2111 −1.07383 −0.536913 0.843638i \(-0.680410\pi\)
−0.536913 + 0.843638i \(0.680410\pi\)
\(110\) 0.480122 0.0457778
\(111\) −8.36765 −0.794222
\(112\) 0 0
\(113\) −1.89479 −0.178246 −0.0891232 0.996021i \(-0.528406\pi\)
−0.0891232 + 0.996021i \(0.528406\pi\)
\(114\) −0.978829 −0.0916757
\(115\) 2.01184 0.187605
\(116\) 11.2042 1.04028
\(117\) −6.43979 −0.595359
\(118\) −5.87585 −0.540916
\(119\) 0 0
\(120\) 1.30344 0.118987
\(121\) 1.00000 0.0909091
\(122\) 2.48890 0.225335
\(123\) 2.34401 0.211352
\(124\) 7.14890 0.641991
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −0.718996 −0.0638006 −0.0319003 0.999491i \(-0.510156\pi\)
−0.0319003 + 0.999491i \(0.510156\pi\)
\(128\) −11.2371 −0.993231
\(129\) 2.85781 0.251616
\(130\) 1.24607 0.109288
\(131\) 16.5681 1.44756 0.723781 0.690030i \(-0.242403\pi\)
0.723781 + 0.690030i \(0.242403\pi\)
\(132\) 1.27440 0.110922
\(133\) 0 0
\(134\) −1.06355 −0.0918768
\(135\) 3.94768 0.339762
\(136\) 4.79892 0.411504
\(137\) 14.0530 1.20063 0.600315 0.799764i \(-0.295042\pi\)
0.600315 + 0.799764i \(0.295042\pi\)
\(138\) −0.695669 −0.0592192
\(139\) −14.3025 −1.21312 −0.606560 0.795037i \(-0.707451\pi\)
−0.606560 + 0.795037i \(0.707451\pi\)
\(140\) 0 0
\(141\) 6.78141 0.571098
\(142\) −1.79933 −0.150997
\(143\) 2.59533 0.217032
\(144\) −6.62516 −0.552097
\(145\) −6.33190 −0.525836
\(146\) −3.83757 −0.317600
\(147\) 0 0
\(148\) −20.5585 −1.68990
\(149\) −23.7598 −1.94648 −0.973240 0.229790i \(-0.926196\pi\)
−0.973240 + 0.229790i \(0.926196\pi\)
\(150\) −0.345788 −0.0282334
\(151\) 7.18141 0.584415 0.292207 0.956355i \(-0.405610\pi\)
0.292207 + 0.956355i \(0.405610\pi\)
\(152\) −5.12307 −0.415536
\(153\) 6.57945 0.531917
\(154\) 0 0
\(155\) −4.04011 −0.324509
\(156\) 3.30748 0.264810
\(157\) 7.81328 0.623568 0.311784 0.950153i \(-0.399073\pi\)
0.311784 + 0.950153i \(0.399073\pi\)
\(158\) 7.84977 0.624494
\(159\) 4.73009 0.375120
\(160\) 4.90157 0.387503
\(161\) 0 0
\(162\) 2.20892 0.173549
\(163\) −1.78950 −0.140164 −0.0700822 0.997541i \(-0.522326\pi\)
−0.0700822 + 0.997541i \(0.522326\pi\)
\(164\) 5.75900 0.449702
\(165\) −0.720208 −0.0560681
\(166\) −0.630821 −0.0489612
\(167\) −11.9544 −0.925059 −0.462529 0.886604i \(-0.653058\pi\)
−0.462529 + 0.886604i \(0.653058\pi\)
\(168\) 0 0
\(169\) −6.26426 −0.481867
\(170\) −1.27310 −0.0976421
\(171\) −7.02387 −0.537129
\(172\) 7.02136 0.535374
\(173\) −20.4569 −1.55531 −0.777653 0.628694i \(-0.783590\pi\)
−0.777653 + 0.628694i \(0.783590\pi\)
\(174\) 2.18949 0.165985
\(175\) 0 0
\(176\) 2.67004 0.201262
\(177\) 8.81409 0.662508
\(178\) −3.58782 −0.268919
\(179\) −2.14591 −0.160393 −0.0801965 0.996779i \(-0.525555\pi\)
−0.0801965 + 0.996779i \(0.525555\pi\)
\(180\) 4.39062 0.327257
\(181\) 8.76578 0.651556 0.325778 0.945446i \(-0.394374\pi\)
0.325778 + 0.945446i \(0.394374\pi\)
\(182\) 0 0
\(183\) −3.73349 −0.275987
\(184\) −3.64105 −0.268421
\(185\) 11.6184 0.854200
\(186\) 1.39702 0.102434
\(187\) −2.65161 −0.193905
\(188\) 16.6613 1.21515
\(189\) 0 0
\(190\) 1.35909 0.0985989
\(191\) 1.48453 0.107417 0.0537085 0.998557i \(-0.482896\pi\)
0.0537085 + 0.998557i \(0.482896\pi\)
\(192\) 2.15106 0.155240
\(193\) 22.5446 1.62279 0.811397 0.584495i \(-0.198707\pi\)
0.811397 + 0.584495i \(0.198707\pi\)
\(194\) −3.12534 −0.224386
\(195\) −1.86918 −0.133855
\(196\) 0 0
\(197\) 6.11322 0.435549 0.217774 0.975999i \(-0.430120\pi\)
0.217774 + 0.975999i \(0.430120\pi\)
\(198\) −1.19133 −0.0846639
\(199\) −24.7090 −1.75158 −0.875788 0.482695i \(-0.839658\pi\)
−0.875788 + 0.482695i \(0.839658\pi\)
\(200\) −1.80981 −0.127973
\(201\) 1.59538 0.112530
\(202\) −5.37992 −0.378530
\(203\) 0 0
\(204\) −3.37921 −0.236592
\(205\) −3.25462 −0.227313
\(206\) −7.21174 −0.502466
\(207\) −4.99197 −0.346966
\(208\) 6.92962 0.480483
\(209\) 2.83072 0.195805
\(210\) 0 0
\(211\) −8.69492 −0.598583 −0.299292 0.954162i \(-0.596750\pi\)
−0.299292 + 0.954162i \(0.596750\pi\)
\(212\) 11.6214 0.798160
\(213\) 2.69909 0.184939
\(214\) −2.65983 −0.181822
\(215\) −3.96803 −0.270617
\(216\) −7.14455 −0.486125
\(217\) 0 0
\(218\) −5.38268 −0.364561
\(219\) 5.75656 0.388992
\(220\) −1.76948 −0.119299
\(221\) −6.88181 −0.462921
\(222\) −4.01749 −0.269636
\(223\) 23.8971 1.60027 0.800134 0.599822i \(-0.204762\pi\)
0.800134 + 0.599822i \(0.204762\pi\)
\(224\) 0 0
\(225\) −2.48130 −0.165420
\(226\) −0.909728 −0.0605142
\(227\) −19.8750 −1.31915 −0.659574 0.751640i \(-0.729263\pi\)
−0.659574 + 0.751640i \(0.729263\pi\)
\(228\) 3.60746 0.238910
\(229\) −7.34417 −0.485316 −0.242658 0.970112i \(-0.578019\pi\)
−0.242658 + 0.970112i \(0.578019\pi\)
\(230\) 0.965927 0.0636913
\(231\) 0 0
\(232\) 11.4595 0.752356
\(233\) −9.33992 −0.611879 −0.305939 0.952051i \(-0.598970\pi\)
−0.305939 + 0.952051i \(0.598970\pi\)
\(234\) −3.09188 −0.202123
\(235\) −9.41591 −0.614226
\(236\) 21.6554 1.40965
\(237\) −11.7751 −0.764873
\(238\) 0 0
\(239\) −4.14840 −0.268338 −0.134169 0.990958i \(-0.542836\pi\)
−0.134169 + 0.990958i \(0.542836\pi\)
\(240\) −1.92298 −0.124128
\(241\) −2.45358 −0.158049 −0.0790246 0.996873i \(-0.525181\pi\)
−0.0790246 + 0.996873i \(0.525181\pi\)
\(242\) 0.480122 0.0308634
\(243\) −15.1565 −0.972292
\(244\) −9.17282 −0.587230
\(245\) 0 0
\(246\) 1.12541 0.0717534
\(247\) 7.34666 0.467457
\(248\) 7.31183 0.464302
\(249\) 0.946265 0.0599671
\(250\) 0.480122 0.0303656
\(251\) 6.73338 0.425007 0.212504 0.977160i \(-0.431838\pi\)
0.212504 + 0.977160i \(0.431838\pi\)
\(252\) 0 0
\(253\) 2.01184 0.126483
\(254\) −0.345206 −0.0216601
\(255\) 1.90971 0.119591
\(256\) 0.578258 0.0361411
\(257\) 17.3927 1.08493 0.542464 0.840079i \(-0.317492\pi\)
0.542464 + 0.840079i \(0.317492\pi\)
\(258\) 1.37210 0.0854229
\(259\) 0 0
\(260\) −4.59239 −0.284808
\(261\) 15.7114 0.972508
\(262\) 7.95471 0.491443
\(263\) 6.31203 0.389217 0.194608 0.980881i \(-0.437656\pi\)
0.194608 + 0.980881i \(0.437656\pi\)
\(264\) 1.30344 0.0802212
\(265\) −6.56767 −0.403449
\(266\) 0 0
\(267\) 5.38192 0.329368
\(268\) 3.91970 0.239434
\(269\) 0.304989 0.0185955 0.00929776 0.999957i \(-0.497040\pi\)
0.00929776 + 0.999957i \(0.497040\pi\)
\(270\) 1.89537 0.115348
\(271\) 5.76238 0.350039 0.175020 0.984565i \(-0.444001\pi\)
0.175020 + 0.984565i \(0.444001\pi\)
\(272\) −7.07990 −0.429282
\(273\) 0 0
\(274\) 6.74715 0.407611
\(275\) 1.00000 0.0603023
\(276\) 2.56388 0.154327
\(277\) −29.6336 −1.78051 −0.890254 0.455464i \(-0.849473\pi\)
−0.890254 + 0.455464i \(0.849473\pi\)
\(278\) −6.86693 −0.411851
\(279\) 10.0247 0.600164
\(280\) 0 0
\(281\) 12.7559 0.760951 0.380475 0.924791i \(-0.375760\pi\)
0.380475 + 0.924791i \(0.375760\pi\)
\(282\) 3.25590 0.193886
\(283\) 3.54406 0.210672 0.105336 0.994437i \(-0.466408\pi\)
0.105336 + 0.994437i \(0.466408\pi\)
\(284\) 6.63141 0.393502
\(285\) −2.03871 −0.120763
\(286\) 1.24607 0.0736819
\(287\) 0 0
\(288\) −12.1623 −0.716668
\(289\) −9.96894 −0.586408
\(290\) −3.04008 −0.178520
\(291\) 4.68817 0.274825
\(292\) 14.1433 0.827675
\(293\) −4.92175 −0.287532 −0.143766 0.989612i \(-0.545921\pi\)
−0.143766 + 0.989612i \(0.545921\pi\)
\(294\) 0 0
\(295\) −12.2383 −0.712539
\(296\) −21.0271 −1.22217
\(297\) 3.94768 0.229067
\(298\) −11.4076 −0.660825
\(299\) 5.22138 0.301960
\(300\) 1.27440 0.0735773
\(301\) 0 0
\(302\) 3.44795 0.198407
\(303\) 8.07016 0.463619
\(304\) 7.55813 0.433488
\(305\) 5.18390 0.296829
\(306\) 3.15894 0.180584
\(307\) 1.29737 0.0740451 0.0370225 0.999314i \(-0.488213\pi\)
0.0370225 + 0.999314i \(0.488213\pi\)
\(308\) 0 0
\(309\) 10.8180 0.615414
\(310\) −1.93974 −0.110170
\(311\) 12.4456 0.705725 0.352862 0.935675i \(-0.385208\pi\)
0.352862 + 0.935675i \(0.385208\pi\)
\(312\) 3.38286 0.191517
\(313\) −1.63401 −0.0923598 −0.0461799 0.998933i \(-0.514705\pi\)
−0.0461799 + 0.998933i \(0.514705\pi\)
\(314\) 3.75133 0.211700
\(315\) 0 0
\(316\) −28.9302 −1.62745
\(317\) −8.92497 −0.501277 −0.250638 0.968081i \(-0.580640\pi\)
−0.250638 + 0.968081i \(0.580640\pi\)
\(318\) 2.27102 0.127352
\(319\) −6.33190 −0.354518
\(320\) −2.98672 −0.166963
\(321\) 3.98988 0.222694
\(322\) 0 0
\(323\) −7.50598 −0.417644
\(324\) −8.14095 −0.452275
\(325\) 2.59533 0.143963
\(326\) −0.859178 −0.0475855
\(327\) 8.07430 0.446510
\(328\) 5.89025 0.325235
\(329\) 0 0
\(330\) −0.345788 −0.0190350
\(331\) 19.5320 1.07357 0.536787 0.843718i \(-0.319638\pi\)
0.536787 + 0.843718i \(0.319638\pi\)
\(332\) 2.32488 0.127595
\(333\) −28.8287 −1.57980
\(334\) −5.73957 −0.314055
\(335\) −2.21517 −0.121028
\(336\) 0 0
\(337\) −13.4497 −0.732654 −0.366327 0.930486i \(-0.619385\pi\)
−0.366327 + 0.930486i \(0.619385\pi\)
\(338\) −3.00761 −0.163592
\(339\) 1.36464 0.0741171
\(340\) 4.69199 0.254459
\(341\) −4.04011 −0.218784
\(342\) −3.37231 −0.182354
\(343\) 0 0
\(344\) 7.18138 0.387194
\(345\) −1.44894 −0.0780084
\(346\) −9.82178 −0.528022
\(347\) 10.5737 0.567628 0.283814 0.958879i \(-0.408400\pi\)
0.283814 + 0.958879i \(0.408400\pi\)
\(348\) −8.06935 −0.432563
\(349\) 11.5704 0.619349 0.309675 0.950843i \(-0.399780\pi\)
0.309675 + 0.950843i \(0.399780\pi\)
\(350\) 0 0
\(351\) 10.2455 0.546866
\(352\) 4.90157 0.261254
\(353\) −15.6700 −0.834030 −0.417015 0.908900i \(-0.636924\pi\)
−0.417015 + 0.908900i \(0.636924\pi\)
\(354\) 4.23184 0.224920
\(355\) −3.74766 −0.198905
\(356\) 13.2229 0.700811
\(357\) 0 0
\(358\) −1.03030 −0.0544530
\(359\) 29.4977 1.55683 0.778413 0.627752i \(-0.216025\pi\)
0.778413 + 0.627752i \(0.216025\pi\)
\(360\) 4.49068 0.236680
\(361\) −10.9870 −0.578264
\(362\) 4.20864 0.221201
\(363\) −0.720208 −0.0378011
\(364\) 0 0
\(365\) −7.99291 −0.418368
\(366\) −1.79253 −0.0936970
\(367\) −30.8844 −1.61215 −0.806076 0.591812i \(-0.798413\pi\)
−0.806076 + 0.591812i \(0.798413\pi\)
\(368\) 5.37168 0.280018
\(369\) 8.07569 0.420404
\(370\) 5.57823 0.289999
\(371\) 0 0
\(372\) −5.14870 −0.266948
\(373\) −21.3841 −1.10723 −0.553613 0.832774i \(-0.686751\pi\)
−0.553613 + 0.832774i \(0.686751\pi\)
\(374\) −1.27310 −0.0658303
\(375\) −0.720208 −0.0371914
\(376\) 17.0410 0.878823
\(377\) −16.4334 −0.846362
\(378\) 0 0
\(379\) 4.60024 0.236299 0.118149 0.992996i \(-0.462304\pi\)
0.118149 + 0.992996i \(0.462304\pi\)
\(380\) −5.00891 −0.256952
\(381\) 0.517827 0.0265291
\(382\) 0.712756 0.0364678
\(383\) −7.77268 −0.397165 −0.198583 0.980084i \(-0.563634\pi\)
−0.198583 + 0.980084i \(0.563634\pi\)
\(384\) 8.09307 0.412998
\(385\) 0 0
\(386\) 10.8241 0.550934
\(387\) 9.84587 0.500494
\(388\) 11.5184 0.584757
\(389\) 7.98574 0.404893 0.202447 0.979293i \(-0.435111\pi\)
0.202447 + 0.979293i \(0.435111\pi\)
\(390\) −0.897433 −0.0454433
\(391\) −5.33461 −0.269783
\(392\) 0 0
\(393\) −11.9325 −0.601914
\(394\) 2.93509 0.147868
\(395\) 16.3495 0.822634
\(396\) 4.39062 0.220637
\(397\) −1.32722 −0.0666112 −0.0333056 0.999445i \(-0.510603\pi\)
−0.0333056 + 0.999445i \(0.510603\pi\)
\(398\) −11.8633 −0.594656
\(399\) 0 0
\(400\) 2.67004 0.133502
\(401\) −4.94204 −0.246793 −0.123397 0.992357i \(-0.539379\pi\)
−0.123397 + 0.992357i \(0.539379\pi\)
\(402\) 0.765978 0.0382035
\(403\) −10.4854 −0.522316
\(404\) 19.8276 0.986461
\(405\) 4.60075 0.228613
\(406\) 0 0
\(407\) 11.6184 0.575901
\(408\) −3.45622 −0.171108
\(409\) 5.52113 0.273002 0.136501 0.990640i \(-0.456414\pi\)
0.136501 + 0.990640i \(0.456414\pi\)
\(410\) −1.56262 −0.0771721
\(411\) −10.1211 −0.499236
\(412\) 26.5788 1.30944
\(413\) 0 0
\(414\) −2.39675 −0.117794
\(415\) −1.31388 −0.0644957
\(416\) 12.7212 0.623707
\(417\) 10.3008 0.504431
\(418\) 1.35909 0.0664753
\(419\) 10.7144 0.523432 0.261716 0.965145i \(-0.415712\pi\)
0.261716 + 0.965145i \(0.415712\pi\)
\(420\) 0 0
\(421\) 28.9844 1.41261 0.706307 0.707905i \(-0.250360\pi\)
0.706307 + 0.707905i \(0.250360\pi\)
\(422\) −4.17462 −0.203217
\(423\) 23.3637 1.13598
\(424\) 11.8862 0.577247
\(425\) −2.65161 −0.128622
\(426\) 1.29589 0.0627863
\(427\) 0 0
\(428\) 9.80276 0.473834
\(429\) −1.86918 −0.0902447
\(430\) −1.90514 −0.0918739
\(431\) 26.4566 1.27437 0.637185 0.770711i \(-0.280099\pi\)
0.637185 + 0.770711i \(0.280099\pi\)
\(432\) 10.5404 0.507127
\(433\) 13.6978 0.658275 0.329137 0.944282i \(-0.393242\pi\)
0.329137 + 0.944282i \(0.393242\pi\)
\(434\) 0 0
\(435\) 4.56029 0.218649
\(436\) 19.8378 0.950058
\(437\) 5.69495 0.272426
\(438\) 2.76385 0.132062
\(439\) 30.8989 1.47472 0.737362 0.675498i \(-0.236071\pi\)
0.737362 + 0.675498i \(0.236071\pi\)
\(440\) −1.80981 −0.0862794
\(441\) 0 0
\(442\) −3.30411 −0.157160
\(443\) −5.96262 −0.283292 −0.141646 0.989917i \(-0.545240\pi\)
−0.141646 + 0.989917i \(0.545240\pi\)
\(444\) 14.8064 0.702681
\(445\) −7.47273 −0.354241
\(446\) 11.4735 0.543287
\(447\) 17.1120 0.809371
\(448\) 0 0
\(449\) 26.8561 1.26742 0.633710 0.773571i \(-0.281531\pi\)
0.633710 + 0.773571i \(0.281531\pi\)
\(450\) −1.19133 −0.0561597
\(451\) −3.25462 −0.153254
\(452\) 3.35279 0.157702
\(453\) −5.17211 −0.243007
\(454\) −9.54241 −0.447847
\(455\) 0 0
\(456\) 3.68968 0.172785
\(457\) −15.9877 −0.747874 −0.373937 0.927454i \(-0.621992\pi\)
−0.373937 + 0.927454i \(0.621992\pi\)
\(458\) −3.52610 −0.164764
\(459\) −10.4677 −0.488591
\(460\) −3.55991 −0.165982
\(461\) −23.7501 −1.10615 −0.553077 0.833130i \(-0.686547\pi\)
−0.553077 + 0.833130i \(0.686547\pi\)
\(462\) 0 0
\(463\) 15.5550 0.722903 0.361451 0.932391i \(-0.382281\pi\)
0.361451 + 0.932391i \(0.382281\pi\)
\(464\) −16.9064 −0.784860
\(465\) 2.90972 0.134935
\(466\) −4.48430 −0.207731
\(467\) 16.2132 0.750258 0.375129 0.926973i \(-0.377598\pi\)
0.375129 + 0.926973i \(0.377598\pi\)
\(468\) 11.3951 0.526739
\(469\) 0 0
\(470\) −4.52078 −0.208528
\(471\) −5.62719 −0.259287
\(472\) 22.1489 1.01949
\(473\) −3.96803 −0.182450
\(474\) −5.65347 −0.259672
\(475\) 2.83072 0.129882
\(476\) 0 0
\(477\) 16.2964 0.746159
\(478\) −1.99174 −0.0910999
\(479\) 31.7472 1.45057 0.725283 0.688451i \(-0.241709\pi\)
0.725283 + 0.688451i \(0.241709\pi\)
\(480\) −3.53015 −0.161128
\(481\) 30.1535 1.37488
\(482\) −1.17802 −0.0536573
\(483\) 0 0
\(484\) −1.76948 −0.0804310
\(485\) −6.50946 −0.295579
\(486\) −7.27698 −0.330091
\(487\) −37.8990 −1.71737 −0.858684 0.512506i \(-0.828717\pi\)
−0.858684 + 0.512506i \(0.828717\pi\)
\(488\) −9.38188 −0.424698
\(489\) 1.28881 0.0582821
\(490\) 0 0
\(491\) 41.6097 1.87782 0.938910 0.344164i \(-0.111838\pi\)
0.938910 + 0.344164i \(0.111838\pi\)
\(492\) −4.14768 −0.186992
\(493\) 16.7898 0.756173
\(494\) 3.52729 0.158700
\(495\) −2.48130 −0.111526
\(496\) −10.7872 −0.484361
\(497\) 0 0
\(498\) 0.454323 0.0203587
\(499\) 33.9699 1.52070 0.760351 0.649513i \(-0.225027\pi\)
0.760351 + 0.649513i \(0.225027\pi\)
\(500\) −1.76948 −0.0791337
\(501\) 8.60965 0.384651
\(502\) 3.23284 0.144289
\(503\) 32.2366 1.43736 0.718679 0.695342i \(-0.244747\pi\)
0.718679 + 0.695342i \(0.244747\pi\)
\(504\) 0 0
\(505\) −11.2053 −0.498630
\(506\) 0.965927 0.0429407
\(507\) 4.51158 0.200366
\(508\) 1.27225 0.0564470
\(509\) 8.29547 0.367690 0.183845 0.982955i \(-0.441146\pi\)
0.183845 + 0.982955i \(0.441146\pi\)
\(510\) 0.916895 0.0406008
\(511\) 0 0
\(512\) 22.7519 1.00550
\(513\) 11.1748 0.493379
\(514\) 8.35062 0.368330
\(515\) −15.0206 −0.661889
\(516\) −5.05684 −0.222615
\(517\) −9.41591 −0.414111
\(518\) 0 0
\(519\) 14.7332 0.646715
\(520\) −4.69706 −0.205980
\(521\) −19.1556 −0.839224 −0.419612 0.907704i \(-0.637834\pi\)
−0.419612 + 0.907704i \(0.637834\pi\)
\(522\) 7.54336 0.330164
\(523\) −36.4567 −1.59414 −0.797069 0.603888i \(-0.793617\pi\)
−0.797069 + 0.603888i \(0.793617\pi\)
\(524\) −29.3170 −1.28072
\(525\) 0 0
\(526\) 3.03055 0.132138
\(527\) 10.7128 0.466657
\(528\) −1.92298 −0.0836870
\(529\) −18.9525 −0.824022
\(530\) −3.15328 −0.136970
\(531\) 30.3668 1.31781
\(532\) 0 0
\(533\) −8.44682 −0.365872
\(534\) 2.58398 0.111820
\(535\) −5.53990 −0.239511
\(536\) 4.00904 0.173164
\(537\) 1.54550 0.0666934
\(538\) 0.146432 0.00631313
\(539\) 0 0
\(540\) −6.98535 −0.300602
\(541\) 5.09481 0.219043 0.109522 0.993984i \(-0.465068\pi\)
0.109522 + 0.993984i \(0.465068\pi\)
\(542\) 2.76664 0.118837
\(543\) −6.31319 −0.270925
\(544\) −12.9971 −0.557244
\(545\) −11.2111 −0.480229
\(546\) 0 0
\(547\) −5.47799 −0.234222 −0.117111 0.993119i \(-0.537363\pi\)
−0.117111 + 0.993119i \(0.537363\pi\)
\(548\) −24.8665 −1.06225
\(549\) −12.8628 −0.548972
\(550\) 0.480122 0.0204725
\(551\) −17.9239 −0.763582
\(552\) 2.62231 0.111613
\(553\) 0 0
\(554\) −14.2277 −0.604478
\(555\) −8.36765 −0.355187
\(556\) 25.3080 1.07330
\(557\) −40.7436 −1.72636 −0.863180 0.504896i \(-0.831531\pi\)
−0.863180 + 0.504896i \(0.831531\pi\)
\(558\) 4.81309 0.203754
\(559\) −10.2983 −0.435573
\(560\) 0 0
\(561\) 1.90971 0.0806282
\(562\) 6.12437 0.258341
\(563\) 29.0662 1.22499 0.612497 0.790473i \(-0.290165\pi\)
0.612497 + 0.790473i \(0.290165\pi\)
\(564\) −11.9996 −0.505274
\(565\) −1.89479 −0.0797142
\(566\) 1.70158 0.0715227
\(567\) 0 0
\(568\) 6.78255 0.284590
\(569\) 1.03493 0.0433864 0.0216932 0.999765i \(-0.493094\pi\)
0.0216932 + 0.999765i \(0.493094\pi\)
\(570\) −0.978829 −0.0409986
\(571\) −2.66578 −0.111559 −0.0557796 0.998443i \(-0.517764\pi\)
−0.0557796 + 0.998443i \(0.517764\pi\)
\(572\) −4.59239 −0.192018
\(573\) −1.06917 −0.0446653
\(574\) 0 0
\(575\) 2.01184 0.0838994
\(576\) 7.41096 0.308790
\(577\) −14.0006 −0.582854 −0.291427 0.956593i \(-0.594130\pi\)
−0.291427 + 0.956593i \(0.594130\pi\)
\(578\) −4.78631 −0.199084
\(579\) −16.2368 −0.674778
\(580\) 11.2042 0.465229
\(581\) 0 0
\(582\) 2.25089 0.0933025
\(583\) −6.56767 −0.272005
\(584\) 14.4657 0.598593
\(585\) −6.43979 −0.266253
\(586\) −2.36304 −0.0976162
\(587\) −13.6037 −0.561486 −0.280743 0.959783i \(-0.590581\pi\)
−0.280743 + 0.959783i \(0.590581\pi\)
\(588\) 0 0
\(589\) −11.4364 −0.471230
\(590\) −5.87585 −0.241905
\(591\) −4.40279 −0.181106
\(592\) 31.0215 1.27497
\(593\) −19.7326 −0.810322 −0.405161 0.914245i \(-0.632784\pi\)
−0.405161 + 0.914245i \(0.632784\pi\)
\(594\) 1.89537 0.0777678
\(595\) 0 0
\(596\) 42.0426 1.72213
\(597\) 17.7956 0.728327
\(598\) 2.50690 0.102515
\(599\) 5.93747 0.242598 0.121299 0.992616i \(-0.461294\pi\)
0.121299 + 0.992616i \(0.461294\pi\)
\(600\) 1.30344 0.0532128
\(601\) −37.1451 −1.51518 −0.757590 0.652731i \(-0.773623\pi\)
−0.757590 + 0.652731i \(0.773623\pi\)
\(602\) 0 0
\(603\) 5.49650 0.223835
\(604\) −12.7074 −0.517056
\(605\) 1.00000 0.0406558
\(606\) 3.87466 0.157397
\(607\) 7.07506 0.287168 0.143584 0.989638i \(-0.454137\pi\)
0.143584 + 0.989638i \(0.454137\pi\)
\(608\) 13.8750 0.562704
\(609\) 0 0
\(610\) 2.48890 0.100773
\(611\) −24.4374 −0.988630
\(612\) −11.6422 −0.470609
\(613\) 33.2245 1.34193 0.670963 0.741491i \(-0.265881\pi\)
0.670963 + 0.741491i \(0.265881\pi\)
\(614\) 0.622898 0.0251381
\(615\) 2.34401 0.0945194
\(616\) 0 0
\(617\) 46.6813 1.87932 0.939660 0.342109i \(-0.111141\pi\)
0.939660 + 0.342109i \(0.111141\pi\)
\(618\) 5.19396 0.208932
\(619\) 1.35992 0.0546597 0.0273298 0.999626i \(-0.491300\pi\)
0.0273298 + 0.999626i \(0.491300\pi\)
\(620\) 7.14890 0.287107
\(621\) 7.94208 0.318705
\(622\) 5.97540 0.239592
\(623\) 0 0
\(624\) −4.99077 −0.199791
\(625\) 1.00000 0.0400000
\(626\) −0.784525 −0.0313559
\(627\) −2.03871 −0.0814182
\(628\) −13.8255 −0.551696
\(629\) −30.8074 −1.22837
\(630\) 0 0
\(631\) 33.7939 1.34531 0.672657 0.739954i \(-0.265153\pi\)
0.672657 + 0.739954i \(0.265153\pi\)
\(632\) −29.5896 −1.17701
\(633\) 6.26215 0.248898
\(634\) −4.28508 −0.170182
\(635\) −0.718996 −0.0285325
\(636\) −8.36981 −0.331885
\(637\) 0 0
\(638\) −3.04008 −0.120358
\(639\) 9.29906 0.367865
\(640\) −11.2371 −0.444186
\(641\) −32.7946 −1.29531 −0.647655 0.761934i \(-0.724250\pi\)
−0.647655 + 0.761934i \(0.724250\pi\)
\(642\) 1.91563 0.0756039
\(643\) 5.31001 0.209406 0.104703 0.994504i \(-0.466611\pi\)
0.104703 + 0.994504i \(0.466611\pi\)
\(644\) 0 0
\(645\) 2.85781 0.112526
\(646\) −3.60379 −0.141789
\(647\) 4.66136 0.183257 0.0916286 0.995793i \(-0.470793\pi\)
0.0916286 + 0.995793i \(0.470793\pi\)
\(648\) −8.32649 −0.327095
\(649\) −12.2383 −0.480393
\(650\) 1.24607 0.0488751
\(651\) 0 0
\(652\) 3.16649 0.124009
\(653\) −45.1554 −1.76707 −0.883533 0.468369i \(-0.844842\pi\)
−0.883533 + 0.468369i \(0.844842\pi\)
\(654\) 3.87665 0.151589
\(655\) 16.5681 0.647369
\(656\) −8.68996 −0.339286
\(657\) 19.8328 0.773751
\(658\) 0 0
\(659\) 3.31420 0.129103 0.0645514 0.997914i \(-0.479438\pi\)
0.0645514 + 0.997914i \(0.479438\pi\)
\(660\) 1.27440 0.0496058
\(661\) −9.71398 −0.377830 −0.188915 0.981993i \(-0.560497\pi\)
−0.188915 + 0.981993i \(0.560497\pi\)
\(662\) 9.37773 0.364476
\(663\) 4.95634 0.192488
\(664\) 2.37787 0.0922793
\(665\) 0 0
\(666\) −13.8413 −0.536338
\(667\) −12.7388 −0.493247
\(668\) 21.1531 0.818438
\(669\) −17.2109 −0.665411
\(670\) −1.06355 −0.0410885
\(671\) 5.18390 0.200122
\(672\) 0 0
\(673\) −8.16771 −0.314842 −0.157421 0.987532i \(-0.550318\pi\)
−0.157421 + 0.987532i \(0.550318\pi\)
\(674\) −6.45752 −0.248734
\(675\) 3.94768 0.151946
\(676\) 11.0845 0.426327
\(677\) 39.9698 1.53616 0.768082 0.640352i \(-0.221211\pi\)
0.768082 + 0.640352i \(0.221211\pi\)
\(678\) 0.655194 0.0251626
\(679\) 0 0
\(680\) 4.79892 0.184030
\(681\) 14.3141 0.548518
\(682\) −1.93974 −0.0742767
\(683\) −37.6069 −1.43899 −0.719495 0.694498i \(-0.755627\pi\)
−0.719495 + 0.694498i \(0.755627\pi\)
\(684\) 12.4286 0.475220
\(685\) 14.0530 0.536938
\(686\) 0 0
\(687\) 5.28933 0.201800
\(688\) −10.5948 −0.403922
\(689\) −17.0453 −0.649373
\(690\) −0.695669 −0.0264836
\(691\) 35.2203 1.33984 0.669921 0.742432i \(-0.266328\pi\)
0.669921 + 0.742432i \(0.266328\pi\)
\(692\) 36.1981 1.37604
\(693\) 0 0
\(694\) 5.07668 0.192708
\(695\) −14.3025 −0.542524
\(696\) −8.25326 −0.312839
\(697\) 8.63000 0.326885
\(698\) 5.55520 0.210267
\(699\) 6.72669 0.254427
\(700\) 0 0
\(701\) 13.4463 0.507861 0.253930 0.967222i \(-0.418277\pi\)
0.253930 + 0.967222i \(0.418277\pi\)
\(702\) 4.91910 0.185659
\(703\) 32.8884 1.24041
\(704\) −2.98672 −0.112566
\(705\) 6.78141 0.255403
\(706\) −7.52351 −0.283151
\(707\) 0 0
\(708\) −15.5964 −0.586148
\(709\) 7.19749 0.270308 0.135154 0.990825i \(-0.456847\pi\)
0.135154 + 0.990825i \(0.456847\pi\)
\(710\) −1.79933 −0.0675277
\(711\) −40.5681 −1.52142
\(712\) 13.5242 0.506842
\(713\) −8.12804 −0.304398
\(714\) 0 0
\(715\) 2.59533 0.0970598
\(716\) 3.79716 0.141906
\(717\) 2.98771 0.111578
\(718\) 14.1625 0.528539
\(719\) −43.7755 −1.63255 −0.816275 0.577663i \(-0.803965\pi\)
−0.816275 + 0.577663i \(0.803965\pi\)
\(720\) −6.62516 −0.246905
\(721\) 0 0
\(722\) −5.27510 −0.196319
\(723\) 1.76709 0.0657188
\(724\) −15.5109 −0.576458
\(725\) −6.33190 −0.235161
\(726\) −0.345788 −0.0128334
\(727\) 11.5718 0.429173 0.214587 0.976705i \(-0.431160\pi\)
0.214587 + 0.976705i \(0.431160\pi\)
\(728\) 0 0
\(729\) −2.88639 −0.106903
\(730\) −3.83757 −0.142035
\(731\) 10.5217 0.389158
\(732\) 6.60634 0.244177
\(733\) −52.9098 −1.95427 −0.977133 0.212627i \(-0.931798\pi\)
−0.977133 + 0.212627i \(0.931798\pi\)
\(734\) −14.8283 −0.547322
\(735\) 0 0
\(736\) 9.86115 0.363487
\(737\) −2.21517 −0.0815968
\(738\) 3.87732 0.142726
\(739\) −1.60903 −0.0591891 −0.0295945 0.999562i \(-0.509422\pi\)
−0.0295945 + 0.999562i \(0.509422\pi\)
\(740\) −20.5585 −0.755746
\(741\) −5.29112 −0.194374
\(742\) 0 0
\(743\) −35.4436 −1.30030 −0.650150 0.759806i \(-0.725294\pi\)
−0.650150 + 0.759806i \(0.725294\pi\)
\(744\) −5.26604 −0.193063
\(745\) −23.7598 −0.870493
\(746\) −10.2670 −0.375900
\(747\) 3.26012 0.119282
\(748\) 4.69199 0.171556
\(749\) 0 0
\(750\) −0.345788 −0.0126264
\(751\) 37.8138 1.37984 0.689922 0.723884i \(-0.257645\pi\)
0.689922 + 0.723884i \(0.257645\pi\)
\(752\) −25.1408 −0.916791
\(753\) −4.84944 −0.176723
\(754\) −7.89002 −0.287338
\(755\) 7.18141 0.261358
\(756\) 0 0
\(757\) 9.03504 0.328384 0.164192 0.986428i \(-0.447498\pi\)
0.164192 + 0.986428i \(0.447498\pi\)
\(758\) 2.20868 0.0802228
\(759\) −1.44894 −0.0525932
\(760\) −5.12307 −0.185833
\(761\) −41.5744 −1.50707 −0.753535 0.657407i \(-0.771653\pi\)
−0.753535 + 0.657407i \(0.771653\pi\)
\(762\) 0.248620 0.00900655
\(763\) 0 0
\(764\) −2.62685 −0.0950362
\(765\) 6.57945 0.237881
\(766\) −3.73183 −0.134837
\(767\) −31.7623 −1.14687
\(768\) −0.416466 −0.0150279
\(769\) 20.8863 0.753180 0.376590 0.926380i \(-0.377097\pi\)
0.376590 + 0.926380i \(0.377097\pi\)
\(770\) 0 0
\(771\) −12.5264 −0.451126
\(772\) −39.8922 −1.43575
\(773\) −50.1351 −1.80324 −0.901618 0.432533i \(-0.857620\pi\)
−0.901618 + 0.432533i \(0.857620\pi\)
\(774\) 4.72722 0.169916
\(775\) −4.04011 −0.145125
\(776\) 11.7809 0.422910
\(777\) 0 0
\(778\) 3.83413 0.137460
\(779\) −9.21293 −0.330087
\(780\) 3.30748 0.118427
\(781\) −3.74766 −0.134102
\(782\) −2.56127 −0.0915907
\(783\) −24.9963 −0.893295
\(784\) 0 0
\(785\) 7.81328 0.278868
\(786\) −5.72904 −0.204348
\(787\) −9.39061 −0.334739 −0.167370 0.985894i \(-0.553527\pi\)
−0.167370 + 0.985894i \(0.553527\pi\)
\(788\) −10.8172 −0.385348
\(789\) −4.54598 −0.161841
\(790\) 7.84977 0.279282
\(791\) 0 0
\(792\) 4.49068 0.159570
\(793\) 13.4539 0.477763
\(794\) −0.637227 −0.0226143
\(795\) 4.73009 0.167759
\(796\) 43.7222 1.54969
\(797\) −32.0295 −1.13454 −0.567272 0.823531i \(-0.692001\pi\)
−0.567272 + 0.823531i \(0.692001\pi\)
\(798\) 0 0
\(799\) 24.9673 0.883281
\(800\) 4.90157 0.173297
\(801\) 18.5421 0.655153
\(802\) −2.37278 −0.0837858
\(803\) −7.99291 −0.282064
\(804\) −2.82300 −0.0995596
\(805\) 0 0
\(806\) −5.03428 −0.177325
\(807\) −0.219656 −0.00773225
\(808\) 20.2795 0.713431
\(809\) 44.6204 1.56877 0.784384 0.620275i \(-0.212979\pi\)
0.784384 + 0.620275i \(0.212979\pi\)
\(810\) 2.20892 0.0776136
\(811\) −22.7734 −0.799683 −0.399842 0.916584i \(-0.630935\pi\)
−0.399842 + 0.916584i \(0.630935\pi\)
\(812\) 0 0
\(813\) −4.15011 −0.145551
\(814\) 5.57823 0.195517
\(815\) −1.78950 −0.0626834
\(816\) 5.09901 0.178501
\(817\) −11.2324 −0.392971
\(818\) 2.65081 0.0926835
\(819\) 0 0
\(820\) 5.75900 0.201113
\(821\) 11.9500 0.417059 0.208529 0.978016i \(-0.433132\pi\)
0.208529 + 0.978016i \(0.433132\pi\)
\(822\) −4.85936 −0.169490
\(823\) 29.4262 1.02573 0.512867 0.858468i \(-0.328584\pi\)
0.512867 + 0.858468i \(0.328584\pi\)
\(824\) 27.1845 0.947018
\(825\) −0.720208 −0.0250744
\(826\) 0 0
\(827\) −27.1635 −0.944569 −0.472285 0.881446i \(-0.656571\pi\)
−0.472285 + 0.881446i \(0.656571\pi\)
\(828\) 8.83321 0.306975
\(829\) 51.6294 1.79316 0.896582 0.442879i \(-0.146043\pi\)
0.896582 + 0.442879i \(0.146043\pi\)
\(830\) −0.630821 −0.0218961
\(831\) 21.3423 0.740357
\(832\) −7.75153 −0.268736
\(833\) 0 0
\(834\) 4.94562 0.171253
\(835\) −11.9544 −0.413699
\(836\) −5.00891 −0.173237
\(837\) −15.9490 −0.551280
\(838\) 5.14421 0.177704
\(839\) 21.4801 0.741576 0.370788 0.928718i \(-0.379088\pi\)
0.370788 + 0.928718i \(0.379088\pi\)
\(840\) 0 0
\(841\) 11.0930 0.382517
\(842\) 13.9161 0.479579
\(843\) −9.18687 −0.316413
\(844\) 15.3855 0.529591
\(845\) −6.26426 −0.215497
\(846\) 11.2174 0.385663
\(847\) 0 0
\(848\) −17.5359 −0.602186
\(849\) −2.55246 −0.0876002
\(850\) −1.27310 −0.0436669
\(851\) 23.3743 0.801260
\(852\) −4.77600 −0.163623
\(853\) 44.6910 1.53019 0.765095 0.643917i \(-0.222692\pi\)
0.765095 + 0.643917i \(0.222692\pi\)
\(854\) 0 0
\(855\) −7.02387 −0.240211
\(856\) 10.0262 0.342688
\(857\) 4.48284 0.153131 0.0765654 0.997065i \(-0.475605\pi\)
0.0765654 + 0.997065i \(0.475605\pi\)
\(858\) −0.897433 −0.0306379
\(859\) −24.6914 −0.842461 −0.421230 0.906954i \(-0.638402\pi\)
−0.421230 + 0.906954i \(0.638402\pi\)
\(860\) 7.02136 0.239426
\(861\) 0 0
\(862\) 12.7024 0.432645
\(863\) −22.1998 −0.755689 −0.377844 0.925869i \(-0.623335\pi\)
−0.377844 + 0.925869i \(0.623335\pi\)
\(864\) 19.3498 0.658294
\(865\) −20.4569 −0.695554
\(866\) 6.57662 0.223483
\(867\) 7.17972 0.243836
\(868\) 0 0
\(869\) 16.3495 0.554620
\(870\) 2.18949 0.0742308
\(871\) −5.74909 −0.194800
\(872\) 20.2899 0.687103
\(873\) 16.1519 0.546660
\(874\) 2.73427 0.0924881
\(875\) 0 0
\(876\) −10.1861 −0.344157
\(877\) −48.2069 −1.62783 −0.813916 0.580982i \(-0.802669\pi\)
−0.813916 + 0.580982i \(0.802669\pi\)
\(878\) 14.8352 0.500665
\(879\) 3.54468 0.119559
\(880\) 2.67004 0.0900069
\(881\) −46.8659 −1.57895 −0.789477 0.613780i \(-0.789648\pi\)
−0.789477 + 0.613780i \(0.789648\pi\)
\(882\) 0 0
\(883\) −14.6461 −0.492879 −0.246440 0.969158i \(-0.579261\pi\)
−0.246440 + 0.969158i \(0.579261\pi\)
\(884\) 12.1772 0.409565
\(885\) 8.81409 0.296282
\(886\) −2.86278 −0.0961771
\(887\) −41.7705 −1.40252 −0.701258 0.712907i \(-0.747378\pi\)
−0.701258 + 0.712907i \(0.747378\pi\)
\(888\) 15.1439 0.508195
\(889\) 0 0
\(890\) −3.58782 −0.120264
\(891\) 4.60075 0.154131
\(892\) −42.2855 −1.41582
\(893\) −26.6538 −0.891936
\(894\) 8.21586 0.274779
\(895\) −2.14591 −0.0717299
\(896\) 0 0
\(897\) −3.76048 −0.125559
\(898\) 12.8942 0.430286
\(899\) 25.5816 0.853193
\(900\) 4.39062 0.146354
\(901\) 17.4149 0.580175
\(902\) −1.56262 −0.0520294
\(903\) 0 0
\(904\) 3.42920 0.114054
\(905\) 8.76578 0.291385
\(906\) −2.48324 −0.0825002
\(907\) 12.4729 0.414155 0.207077 0.978325i \(-0.433605\pi\)
0.207077 + 0.978325i \(0.433605\pi\)
\(908\) 35.1684 1.16711
\(909\) 27.8038 0.922192
\(910\) 0 0
\(911\) −19.1114 −0.633191 −0.316595 0.948561i \(-0.602540\pi\)
−0.316595 + 0.948561i \(0.602540\pi\)
\(912\) −5.44343 −0.180250
\(913\) −1.31388 −0.0434830
\(914\) −7.67605 −0.253901
\(915\) −3.73349 −0.123425
\(916\) 12.9954 0.429379
\(917\) 0 0
\(918\) −5.02578 −0.165875
\(919\) −8.14450 −0.268662 −0.134331 0.990936i \(-0.542889\pi\)
−0.134331 + 0.990936i \(0.542889\pi\)
\(920\) −3.64105 −0.120042
\(921\) −0.934380 −0.0307889
\(922\) −11.4030 −0.375537
\(923\) −9.72640 −0.320148
\(924\) 0 0
\(925\) 11.6184 0.382010
\(926\) 7.46830 0.245424
\(927\) 37.2707 1.22413
\(928\) −31.0362 −1.01881
\(929\) −23.2542 −0.762946 −0.381473 0.924380i \(-0.624583\pi\)
−0.381473 + 0.924380i \(0.624583\pi\)
\(930\) 1.39702 0.0458101
\(931\) 0 0
\(932\) 16.5268 0.541354
\(933\) −8.96342 −0.293449
\(934\) 7.78432 0.254711
\(935\) −2.65161 −0.0867170
\(936\) 11.6548 0.380949
\(937\) 53.7860 1.75711 0.878556 0.477640i \(-0.158508\pi\)
0.878556 + 0.477640i \(0.158508\pi\)
\(938\) 0 0
\(939\) 1.17683 0.0384044
\(940\) 16.6613 0.543431
\(941\) −33.2193 −1.08292 −0.541458 0.840728i \(-0.682128\pi\)
−0.541458 + 0.840728i \(0.682128\pi\)
\(942\) −2.70174 −0.0880274
\(943\) −6.54777 −0.213225
\(944\) −32.6766 −1.06353
\(945\) 0 0
\(946\) −1.90514 −0.0619414
\(947\) 20.6050 0.669573 0.334786 0.942294i \(-0.391336\pi\)
0.334786 + 0.942294i \(0.391336\pi\)
\(948\) 20.8358 0.676715
\(949\) −20.7442 −0.673386
\(950\) 1.35909 0.0440948
\(951\) 6.42784 0.208437
\(952\) 0 0
\(953\) 10.4071 0.337118 0.168559 0.985692i \(-0.446089\pi\)
0.168559 + 0.985692i \(0.446089\pi\)
\(954\) 7.82424 0.253319
\(955\) 1.48453 0.0480383
\(956\) 7.34052 0.237409
\(957\) 4.56029 0.147413
\(958\) 15.2425 0.492463
\(959\) 0 0
\(960\) 2.15106 0.0694252
\(961\) −14.6775 −0.473468
\(962\) 14.4774 0.466769
\(963\) 13.7462 0.442964
\(964\) 4.34157 0.139833
\(965\) 22.5446 0.725736
\(966\) 0 0
\(967\) −55.4271 −1.78241 −0.891207 0.453596i \(-0.850141\pi\)
−0.891207 + 0.453596i \(0.850141\pi\)
\(968\) −1.80981 −0.0581695
\(969\) 5.40587 0.173662
\(970\) −3.12534 −0.100348
\(971\) 26.7900 0.859732 0.429866 0.902893i \(-0.358561\pi\)
0.429866 + 0.902893i \(0.358561\pi\)
\(972\) 26.8192 0.860227
\(973\) 0 0
\(974\) −18.1961 −0.583042
\(975\) −1.86918 −0.0598616
\(976\) 13.8412 0.443046
\(977\) 31.0373 0.992970 0.496485 0.868045i \(-0.334624\pi\)
0.496485 + 0.868045i \(0.334624\pi\)
\(978\) 0.618787 0.0197866
\(979\) −7.47273 −0.238830
\(980\) 0 0
\(981\) 27.8180 0.888161
\(982\) 19.9777 0.637515
\(983\) −5.26620 −0.167966 −0.0839828 0.996467i \(-0.526764\pi\)
−0.0839828 + 0.996467i \(0.526764\pi\)
\(984\) −4.24221 −0.135237
\(985\) 6.11322 0.194783
\(986\) 8.06113 0.256719
\(987\) 0 0
\(988\) −12.9998 −0.413578
\(989\) −7.98303 −0.253845
\(990\) −1.19133 −0.0378628
\(991\) −60.3436 −1.91688 −0.958439 0.285298i \(-0.907908\pi\)
−0.958439 + 0.285298i \(0.907908\pi\)
\(992\) −19.8029 −0.628741
\(993\) −14.0671 −0.446406
\(994\) 0 0
\(995\) −24.7090 −0.783329
\(996\) −1.67440 −0.0530554
\(997\) −8.84168 −0.280019 −0.140009 0.990150i \(-0.544713\pi\)
−0.140009 + 0.990150i \(0.544713\pi\)
\(998\) 16.3097 0.516274
\(999\) 45.8656 1.45112
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 2695.2.a.u.1.7 10
7.6 odd 2 2695.2.a.v.1.7 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2695.2.a.u.1.7 10 1.1 even 1 trivial
2695.2.a.v.1.7 yes 10 7.6 odd 2