Properties

Label 2695.2.a.y.1.6
Level $2695$
Weight $2$
Character 2695.1
Self dual yes
Analytic conductor $21.520$
Analytic rank $0$
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: \(0\)
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: \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 51x^{6} - 184x^{5} - 45x^{4} + 297x^{3} - 59x^{2} - 109x + 21 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 385)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.06607\) 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)
 
\(f(q)\) \(=\) \(q+1.06607 q^{2} +3.07491 q^{3} -0.863486 q^{4} -1.00000 q^{5} +3.27808 q^{6} -3.05269 q^{8} +6.45507 q^{9} +O(q^{10})\) \(q+1.06607 q^{2} +3.07491 q^{3} -0.863486 q^{4} -1.00000 q^{5} +3.27808 q^{6} -3.05269 q^{8} +6.45507 q^{9} -1.06607 q^{10} +1.00000 q^{11} -2.65514 q^{12} +2.06228 q^{13} -3.07491 q^{15} -1.52742 q^{16} -1.12330 q^{17} +6.88158 q^{18} +8.47065 q^{19} +0.863486 q^{20} +1.06607 q^{22} +3.99926 q^{23} -9.38674 q^{24} +1.00000 q^{25} +2.19854 q^{26} +10.6240 q^{27} -4.01868 q^{29} -3.27808 q^{30} -0.325585 q^{31} +4.47703 q^{32} +3.07491 q^{33} -1.19753 q^{34} -5.57386 q^{36} +5.40922 q^{37} +9.03034 q^{38} +6.34131 q^{39} +3.05269 q^{40} +1.23247 q^{41} -12.0838 q^{43} -0.863486 q^{44} -6.45507 q^{45} +4.26350 q^{46} -1.05368 q^{47} -4.69668 q^{48} +1.06607 q^{50} -3.45406 q^{51} -1.78075 q^{52} -0.884442 q^{53} +11.3260 q^{54} -1.00000 q^{55} +26.0465 q^{57} -4.28421 q^{58} +13.8692 q^{59} +2.65514 q^{60} +1.63867 q^{61} -0.347098 q^{62} +7.82769 q^{64} -2.06228 q^{65} +3.27808 q^{66} +10.7570 q^{67} +0.969957 q^{68} +12.2974 q^{69} +8.18682 q^{71} -19.7053 q^{72} -12.9612 q^{73} +5.76663 q^{74} +3.07491 q^{75} -7.31428 q^{76} +6.76031 q^{78} +7.43983 q^{79} +1.52742 q^{80} +13.3027 q^{81} +1.31391 q^{82} +4.20154 q^{83} +1.12330 q^{85} -12.8822 q^{86} -12.3571 q^{87} -3.05269 q^{88} -14.0917 q^{89} -6.88158 q^{90} -3.45330 q^{92} -1.00115 q^{93} -1.12330 q^{94} -8.47065 q^{95} +13.7665 q^{96} -16.8254 q^{97} +6.45507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9} - 3 q^{10} + 10 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{15} + 21 q^{16} - 5 q^{17} + q^{18} + q^{19} - 15 q^{20} + 3 q^{22} + 18 q^{23} + 10 q^{24} + 10 q^{25} + 13 q^{26} - 15 q^{27} + 14 q^{29} - 5 q^{30} + 10 q^{31} + 46 q^{32} - 3 q^{33} - 2 q^{34} + 26 q^{36} + 13 q^{37} + 9 q^{38} + 3 q^{39} - 9 q^{40} - 7 q^{41} + 6 q^{43} + 15 q^{44} - 19 q^{45} + 10 q^{46} + q^{47} - 35 q^{48} + 3 q^{50} + 9 q^{51} - 17 q^{52} + 16 q^{53} + 73 q^{54} - 10 q^{55} + 12 q^{57} - 9 q^{58} + 13 q^{59} + 3 q^{60} + 18 q^{61} + 14 q^{62} + 43 q^{64} + 6 q^{65} + 5 q^{66} + 29 q^{67} + 13 q^{68} + 19 q^{71} - 48 q^{72} - 31 q^{73} - 8 q^{74} - 3 q^{75} - 8 q^{76} + 3 q^{78} - 21 q^{80} + 42 q^{81} + q^{82} - 2 q^{83} + 5 q^{85} + 10 q^{86} - 50 q^{87} + 9 q^{88} + 23 q^{89} - q^{90} + 14 q^{92} + 4 q^{93} - 5 q^{94} - q^{95} + 39 q^{96} - 43 q^{97} + 19 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06607 0.753828 0.376914 0.926248i \(-0.376985\pi\)
0.376914 + 0.926248i \(0.376985\pi\)
\(3\) 3.07491 1.77530 0.887650 0.460519i \(-0.152337\pi\)
0.887650 + 0.460519i \(0.152337\pi\)
\(4\) −0.863486 −0.431743
\(5\) −1.00000 −0.447214
\(6\) 3.27808 1.33827
\(7\) 0 0
\(8\) −3.05269 −1.07929
\(9\) 6.45507 2.15169
\(10\) −1.06607 −0.337122
\(11\) 1.00000 0.301511
\(12\) −2.65514 −0.766473
\(13\) 2.06228 0.571973 0.285986 0.958234i \(-0.407679\pi\)
0.285986 + 0.958234i \(0.407679\pi\)
\(14\) 0 0
\(15\) −3.07491 −0.793938
\(16\) −1.52742 −0.381855
\(17\) −1.12330 −0.272441 −0.136221 0.990679i \(-0.543496\pi\)
−0.136221 + 0.990679i \(0.543496\pi\)
\(18\) 6.88158 1.62200
\(19\) 8.47065 1.94330 0.971650 0.236424i \(-0.0759753\pi\)
0.971650 + 0.236424i \(0.0759753\pi\)
\(20\) 0.863486 0.193081
\(21\) 0 0
\(22\) 1.06607 0.227288
\(23\) 3.99926 0.833903 0.416951 0.908929i \(-0.363099\pi\)
0.416951 + 0.908929i \(0.363099\pi\)
\(24\) −9.38674 −1.91606
\(25\) 1.00000 0.200000
\(26\) 2.19854 0.431169
\(27\) 10.6240 2.04459
\(28\) 0 0
\(29\) −4.01868 −0.746250 −0.373125 0.927781i \(-0.621714\pi\)
−0.373125 + 0.927781i \(0.621714\pi\)
\(30\) −3.27808 −0.598493
\(31\) −0.325585 −0.0584768 −0.0292384 0.999572i \(-0.509308\pi\)
−0.0292384 + 0.999572i \(0.509308\pi\)
\(32\) 4.47703 0.791435
\(33\) 3.07491 0.535273
\(34\) −1.19753 −0.205374
\(35\) 0 0
\(36\) −5.57386 −0.928977
\(37\) 5.40922 0.889270 0.444635 0.895712i \(-0.353333\pi\)
0.444635 + 0.895712i \(0.353333\pi\)
\(38\) 9.03034 1.46491
\(39\) 6.34131 1.01542
\(40\) 3.05269 0.482672
\(41\) 1.23247 0.192480 0.0962399 0.995358i \(-0.469318\pi\)
0.0962399 + 0.995358i \(0.469318\pi\)
\(42\) 0 0
\(43\) −12.0838 −1.84276 −0.921381 0.388660i \(-0.872938\pi\)
−0.921381 + 0.388660i \(0.872938\pi\)
\(44\) −0.863486 −0.130175
\(45\) −6.45507 −0.962265
\(46\) 4.26350 0.628619
\(47\) −1.05368 −0.153695 −0.0768477 0.997043i \(-0.524486\pi\)
−0.0768477 + 0.997043i \(0.524486\pi\)
\(48\) −4.69668 −0.677908
\(49\) 0 0
\(50\) 1.06607 0.150766
\(51\) −3.45406 −0.483665
\(52\) −1.78075 −0.246945
\(53\) −0.884442 −0.121487 −0.0607437 0.998153i \(-0.519347\pi\)
−0.0607437 + 0.998153i \(0.519347\pi\)
\(54\) 11.3260 1.54127
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 26.0465 3.44994
\(58\) −4.28421 −0.562545
\(59\) 13.8692 1.80562 0.902809 0.430041i \(-0.141501\pi\)
0.902809 + 0.430041i \(0.141501\pi\)
\(60\) 2.65514 0.342777
\(61\) 1.63867 0.209810 0.104905 0.994482i \(-0.466546\pi\)
0.104905 + 0.994482i \(0.466546\pi\)
\(62\) −0.347098 −0.0440815
\(63\) 0 0
\(64\) 7.82769 0.978461
\(65\) −2.06228 −0.255794
\(66\) 3.27808 0.403504
\(67\) 10.7570 1.31418 0.657091 0.753811i \(-0.271787\pi\)
0.657091 + 0.753811i \(0.271787\pi\)
\(68\) 0.969957 0.117625
\(69\) 12.2974 1.48043
\(70\) 0 0
\(71\) 8.18682 0.971597 0.485799 0.874071i \(-0.338529\pi\)
0.485799 + 0.874071i \(0.338529\pi\)
\(72\) −19.7053 −2.32229
\(73\) −12.9612 −1.51700 −0.758499 0.651674i \(-0.774067\pi\)
−0.758499 + 0.651674i \(0.774067\pi\)
\(74\) 5.76663 0.670357
\(75\) 3.07491 0.355060
\(76\) −7.31428 −0.839006
\(77\) 0 0
\(78\) 6.76031 0.765454
\(79\) 7.43983 0.837047 0.418523 0.908206i \(-0.362548\pi\)
0.418523 + 0.908206i \(0.362548\pi\)
\(80\) 1.52742 0.170771
\(81\) 13.3027 1.47808
\(82\) 1.31391 0.145097
\(83\) 4.20154 0.461179 0.230590 0.973051i \(-0.425935\pi\)
0.230590 + 0.973051i \(0.425935\pi\)
\(84\) 0 0
\(85\) 1.12330 0.121839
\(86\) −12.8822 −1.38913
\(87\) −12.3571 −1.32482
\(88\) −3.05269 −0.325418
\(89\) −14.0917 −1.49371 −0.746856 0.664986i \(-0.768438\pi\)
−0.746856 + 0.664986i \(0.768438\pi\)
\(90\) −6.88158 −0.725383
\(91\) 0 0
\(92\) −3.45330 −0.360031
\(93\) −1.00115 −0.103814
\(94\) −1.12330 −0.115860
\(95\) −8.47065 −0.869070
\(96\) 13.7665 1.40503
\(97\) −16.8254 −1.70836 −0.854180 0.519977i \(-0.825940\pi\)
−0.854180 + 0.519977i \(0.825940\pi\)
\(98\) 0 0
\(99\) 6.45507 0.648759
\(100\) −0.863486 −0.0863486
\(101\) 14.2529 1.41822 0.709109 0.705099i \(-0.249098\pi\)
0.709109 + 0.705099i \(0.249098\pi\)
\(102\) −3.68228 −0.364600
\(103\) −16.2582 −1.60197 −0.800985 0.598684i \(-0.795691\pi\)
−0.800985 + 0.598684i \(0.795691\pi\)
\(104\) −6.29549 −0.617323
\(105\) 0 0
\(106\) −0.942881 −0.0915807
\(107\) 8.58032 0.829491 0.414745 0.909937i \(-0.363871\pi\)
0.414745 + 0.909937i \(0.363871\pi\)
\(108\) −9.17369 −0.882739
\(109\) 4.14170 0.396703 0.198351 0.980131i \(-0.436441\pi\)
0.198351 + 0.980131i \(0.436441\pi\)
\(110\) −1.06607 −0.101646
\(111\) 16.6329 1.57872
\(112\) 0 0
\(113\) 2.95520 0.278002 0.139001 0.990292i \(-0.455611\pi\)
0.139001 + 0.990292i \(0.455611\pi\)
\(114\) 27.7675 2.60066
\(115\) −3.99926 −0.372933
\(116\) 3.47007 0.322188
\(117\) 13.3121 1.23071
\(118\) 14.7856 1.36113
\(119\) 0 0
\(120\) 9.38674 0.856888
\(121\) 1.00000 0.0909091
\(122\) 1.74694 0.158161
\(123\) 3.78974 0.341709
\(124\) 0.281138 0.0252470
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −6.78852 −0.602383 −0.301192 0.953564i \(-0.597384\pi\)
−0.301192 + 0.953564i \(0.597384\pi\)
\(128\) −0.609164 −0.0538430
\(129\) −37.1566 −3.27146
\(130\) −2.19854 −0.192825
\(131\) −4.12189 −0.360131 −0.180065 0.983655i \(-0.557631\pi\)
−0.180065 + 0.983655i \(0.557631\pi\)
\(132\) −2.65514 −0.231100
\(133\) 0 0
\(134\) 11.4678 0.990668
\(135\) −10.6240 −0.914370
\(136\) 3.42910 0.294043
\(137\) 11.5079 0.983188 0.491594 0.870825i \(-0.336414\pi\)
0.491594 + 0.870825i \(0.336414\pi\)
\(138\) 13.1099 1.11599
\(139\) −0.783249 −0.0664343 −0.0332172 0.999448i \(-0.510575\pi\)
−0.0332172 + 0.999448i \(0.510575\pi\)
\(140\) 0 0
\(141\) −3.23998 −0.272855
\(142\) 8.72776 0.732417
\(143\) 2.06228 0.172456
\(144\) −9.85961 −0.821634
\(145\) 4.01868 0.333733
\(146\) −13.8176 −1.14356
\(147\) 0 0
\(148\) −4.67078 −0.383936
\(149\) 10.9739 0.899017 0.449509 0.893276i \(-0.351599\pi\)
0.449509 + 0.893276i \(0.351599\pi\)
\(150\) 3.27808 0.267654
\(151\) −9.62635 −0.783381 −0.391691 0.920097i \(-0.628110\pi\)
−0.391691 + 0.920097i \(0.628110\pi\)
\(152\) −25.8583 −2.09738
\(153\) −7.25101 −0.586209
\(154\) 0 0
\(155\) 0.325585 0.0261516
\(156\) −5.47563 −0.438401
\(157\) −19.3521 −1.54446 −0.772231 0.635341i \(-0.780859\pi\)
−0.772231 + 0.635341i \(0.780859\pi\)
\(158\) 7.93142 0.630990
\(159\) −2.71958 −0.215677
\(160\) −4.47703 −0.353940
\(161\) 0 0
\(162\) 14.1817 1.11422
\(163\) 16.1186 1.26251 0.631254 0.775576i \(-0.282541\pi\)
0.631254 + 0.775576i \(0.282541\pi\)
\(164\) −1.06422 −0.0831018
\(165\) −3.07491 −0.239381
\(166\) 4.47916 0.347650
\(167\) −9.27253 −0.717530 −0.358765 0.933428i \(-0.616802\pi\)
−0.358765 + 0.933428i \(0.616802\pi\)
\(168\) 0 0
\(169\) −8.74702 −0.672847
\(170\) 1.19753 0.0918460
\(171\) 54.6786 4.18138
\(172\) 10.4342 0.795599
\(173\) −19.2414 −1.46290 −0.731448 0.681897i \(-0.761155\pi\)
−0.731448 + 0.681897i \(0.761155\pi\)
\(174\) −13.1736 −0.998685
\(175\) 0 0
\(176\) −1.52742 −0.115134
\(177\) 42.6466 3.20552
\(178\) −15.0227 −1.12600
\(179\) −8.34322 −0.623601 −0.311801 0.950148i \(-0.600932\pi\)
−0.311801 + 0.950148i \(0.600932\pi\)
\(180\) 5.57386 0.415451
\(181\) −18.9132 −1.40580 −0.702902 0.711287i \(-0.748113\pi\)
−0.702902 + 0.711287i \(0.748113\pi\)
\(182\) 0 0
\(183\) 5.03876 0.372476
\(184\) −12.2085 −0.900021
\(185\) −5.40922 −0.397694
\(186\) −1.06730 −0.0782579
\(187\) −1.12330 −0.0821441
\(188\) 0.909840 0.0663569
\(189\) 0 0
\(190\) −9.03034 −0.655130
\(191\) 1.19403 0.0863972 0.0431986 0.999067i \(-0.486245\pi\)
0.0431986 + 0.999067i \(0.486245\pi\)
\(192\) 24.0694 1.73706
\(193\) −22.2090 −1.59864 −0.799319 0.600907i \(-0.794806\pi\)
−0.799319 + 0.600907i \(0.794806\pi\)
\(194\) −17.9371 −1.28781
\(195\) −6.34131 −0.454111
\(196\) 0 0
\(197\) −5.35087 −0.381234 −0.190617 0.981664i \(-0.561049\pi\)
−0.190617 + 0.981664i \(0.561049\pi\)
\(198\) 6.88158 0.489053
\(199\) −11.0229 −0.781394 −0.390697 0.920519i \(-0.627766\pi\)
−0.390697 + 0.920519i \(0.627766\pi\)
\(200\) −3.05269 −0.215858
\(201\) 33.0769 2.33307
\(202\) 15.1947 1.06909
\(203\) 0 0
\(204\) 2.98253 0.208819
\(205\) −1.23247 −0.0860796
\(206\) −17.3325 −1.20761
\(207\) 25.8155 1.79430
\(208\) −3.14996 −0.218411
\(209\) 8.47065 0.585927
\(210\) 0 0
\(211\) 4.84291 0.333400 0.166700 0.986008i \(-0.446689\pi\)
0.166700 + 0.986008i \(0.446689\pi\)
\(212\) 0.763703 0.0524513
\(213\) 25.1737 1.72488
\(214\) 9.14726 0.625294
\(215\) 12.0838 0.824108
\(216\) −32.4318 −2.20671
\(217\) 0 0
\(218\) 4.41536 0.299046
\(219\) −39.8546 −2.69313
\(220\) 0.863486 0.0582162
\(221\) −2.31656 −0.155829
\(222\) 17.7319 1.19008
\(223\) −10.7581 −0.720412 −0.360206 0.932873i \(-0.617294\pi\)
−0.360206 + 0.932873i \(0.617294\pi\)
\(224\) 0 0
\(225\) 6.45507 0.430338
\(226\) 3.15046 0.209566
\(227\) 4.62447 0.306937 0.153469 0.988154i \(-0.450956\pi\)
0.153469 + 0.988154i \(0.450956\pi\)
\(228\) −22.4908 −1.48949
\(229\) −1.65401 −0.109300 −0.0546500 0.998506i \(-0.517404\pi\)
−0.0546500 + 0.998506i \(0.517404\pi\)
\(230\) −4.26350 −0.281127
\(231\) 0 0
\(232\) 12.2678 0.805419
\(233\) 2.09030 0.136940 0.0684700 0.997653i \(-0.478188\pi\)
0.0684700 + 0.997653i \(0.478188\pi\)
\(234\) 14.1917 0.927742
\(235\) 1.05368 0.0687347
\(236\) −11.9759 −0.779563
\(237\) 22.8768 1.48601
\(238\) 0 0
\(239\) −13.1060 −0.847754 −0.423877 0.905720i \(-0.639331\pi\)
−0.423877 + 0.905720i \(0.639331\pi\)
\(240\) 4.69668 0.303170
\(241\) 5.92643 0.381755 0.190877 0.981614i \(-0.438867\pi\)
0.190877 + 0.981614i \(0.438867\pi\)
\(242\) 1.06607 0.0685298
\(243\) 9.03255 0.579438
\(244\) −1.41497 −0.0905840
\(245\) 0 0
\(246\) 4.04014 0.257590
\(247\) 17.4688 1.11151
\(248\) 0.993910 0.0631134
\(249\) 12.9194 0.818731
\(250\) −1.06607 −0.0674245
\(251\) 8.12067 0.512572 0.256286 0.966601i \(-0.417501\pi\)
0.256286 + 0.966601i \(0.417501\pi\)
\(252\) 0 0
\(253\) 3.99926 0.251431
\(254\) −7.23706 −0.454094
\(255\) 3.45406 0.216302
\(256\) −16.3048 −1.01905
\(257\) 26.3816 1.64564 0.822818 0.568304i \(-0.192400\pi\)
0.822818 + 0.568304i \(0.192400\pi\)
\(258\) −39.6117 −2.46612
\(259\) 0 0
\(260\) 1.78075 0.110437
\(261\) −25.9409 −1.60570
\(262\) −4.39424 −0.271477
\(263\) −20.7690 −1.28067 −0.640337 0.768094i \(-0.721205\pi\)
−0.640337 + 0.768094i \(0.721205\pi\)
\(264\) −9.38674 −0.577714
\(265\) 0.884442 0.0543308
\(266\) 0 0
\(267\) −43.3306 −2.65179
\(268\) −9.28855 −0.567389
\(269\) −10.6726 −0.650717 −0.325359 0.945591i \(-0.605485\pi\)
−0.325359 + 0.945591i \(0.605485\pi\)
\(270\) −11.3260 −0.689278
\(271\) −5.24361 −0.318527 −0.159263 0.987236i \(-0.550912\pi\)
−0.159263 + 0.987236i \(0.550912\pi\)
\(272\) 1.71576 0.104033
\(273\) 0 0
\(274\) 12.2683 0.741155
\(275\) 1.00000 0.0603023
\(276\) −10.6186 −0.639164
\(277\) −18.3766 −1.10414 −0.552072 0.833797i \(-0.686163\pi\)
−0.552072 + 0.833797i \(0.686163\pi\)
\(278\) −0.835002 −0.0500801
\(279\) −2.10168 −0.125824
\(280\) 0 0
\(281\) −2.89615 −0.172770 −0.0863849 0.996262i \(-0.527531\pi\)
−0.0863849 + 0.996262i \(0.527531\pi\)
\(282\) −3.45406 −0.205686
\(283\) 4.39212 0.261084 0.130542 0.991443i \(-0.458328\pi\)
0.130542 + 0.991443i \(0.458328\pi\)
\(284\) −7.06920 −0.419480
\(285\) −26.0465 −1.54286
\(286\) 2.19854 0.130002
\(287\) 0 0
\(288\) 28.8996 1.70292
\(289\) −15.7382 −0.925776
\(290\) 4.28421 0.251578
\(291\) −51.7366 −3.03285
\(292\) 11.1918 0.654953
\(293\) −21.0343 −1.22884 −0.614418 0.788981i \(-0.710609\pi\)
−0.614418 + 0.788981i \(0.710609\pi\)
\(294\) 0 0
\(295\) −13.8692 −0.807497
\(296\) −16.5127 −0.959779
\(297\) 10.6240 0.616468
\(298\) 11.6990 0.677705
\(299\) 8.24757 0.476969
\(300\) −2.65514 −0.153295
\(301\) 0 0
\(302\) −10.2624 −0.590535
\(303\) 43.8264 2.51776
\(304\) −12.9382 −0.742059
\(305\) −1.63867 −0.0938299
\(306\) −7.73011 −0.441901
\(307\) 24.8681 1.41930 0.709648 0.704556i \(-0.248854\pi\)
0.709648 + 0.704556i \(0.248854\pi\)
\(308\) 0 0
\(309\) −49.9926 −2.84398
\(310\) 0.347098 0.0197138
\(311\) −24.3484 −1.38067 −0.690336 0.723489i \(-0.742537\pi\)
−0.690336 + 0.723489i \(0.742537\pi\)
\(312\) −19.3581 −1.09593
\(313\) 1.14902 0.0649464 0.0324732 0.999473i \(-0.489662\pi\)
0.0324732 + 0.999473i \(0.489662\pi\)
\(314\) −20.6307 −1.16426
\(315\) 0 0
\(316\) −6.42419 −0.361389
\(317\) 19.3547 1.08707 0.543533 0.839387i \(-0.317086\pi\)
0.543533 + 0.839387i \(0.317086\pi\)
\(318\) −2.89927 −0.162583
\(319\) −4.01868 −0.225003
\(320\) −7.82769 −0.437581
\(321\) 26.3837 1.47260
\(322\) 0 0
\(323\) −9.51511 −0.529435
\(324\) −11.4867 −0.638150
\(325\) 2.06228 0.114395
\(326\) 17.1836 0.951714
\(327\) 12.7353 0.704266
\(328\) −3.76235 −0.207741
\(329\) 0 0
\(330\) −3.27808 −0.180452
\(331\) −3.25973 −0.179171 −0.0895856 0.995979i \(-0.528554\pi\)
−0.0895856 + 0.995979i \(0.528554\pi\)
\(332\) −3.62797 −0.199111
\(333\) 34.9169 1.91343
\(334\) −9.88521 −0.540894
\(335\) −10.7570 −0.587720
\(336\) 0 0
\(337\) −0.431489 −0.0235047 −0.0117523 0.999931i \(-0.503741\pi\)
−0.0117523 + 0.999931i \(0.503741\pi\)
\(338\) −9.32497 −0.507211
\(339\) 9.08697 0.493536
\(340\) −0.969957 −0.0526033
\(341\) −0.325585 −0.0176314
\(342\) 58.2915 3.15204
\(343\) 0 0
\(344\) 36.8881 1.98887
\(345\) −12.2974 −0.662067
\(346\) −20.5128 −1.10277
\(347\) −2.59500 −0.139307 −0.0696535 0.997571i \(-0.522189\pi\)
−0.0696535 + 0.997571i \(0.522189\pi\)
\(348\) 10.6702 0.571981
\(349\) −11.7944 −0.631340 −0.315670 0.948869i \(-0.602229\pi\)
−0.315670 + 0.948869i \(0.602229\pi\)
\(350\) 0 0
\(351\) 21.9097 1.16945
\(352\) 4.47703 0.238627
\(353\) −2.07304 −0.110337 −0.0551685 0.998477i \(-0.517570\pi\)
−0.0551685 + 0.998477i \(0.517570\pi\)
\(354\) 45.4644 2.41641
\(355\) −8.18682 −0.434511
\(356\) 12.1679 0.644899
\(357\) 0 0
\(358\) −8.89449 −0.470088
\(359\) −30.2756 −1.59789 −0.798943 0.601407i \(-0.794607\pi\)
−0.798943 + 0.601407i \(0.794607\pi\)
\(360\) 19.7053 1.03856
\(361\) 52.7519 2.77642
\(362\) −20.1628 −1.05974
\(363\) 3.07491 0.161391
\(364\) 0 0
\(365\) 12.9612 0.678422
\(366\) 5.37169 0.280783
\(367\) 8.03951 0.419659 0.209830 0.977738i \(-0.432709\pi\)
0.209830 + 0.977738i \(0.432709\pi\)
\(368\) −6.10855 −0.318430
\(369\) 7.95569 0.414157
\(370\) −5.76663 −0.299793
\(371\) 0 0
\(372\) 0.864474 0.0448209
\(373\) −29.9656 −1.55156 −0.775780 0.631003i \(-0.782644\pi\)
−0.775780 + 0.631003i \(0.782644\pi\)
\(374\) −1.19753 −0.0619226
\(375\) −3.07491 −0.158788
\(376\) 3.21657 0.165882
\(377\) −8.28763 −0.426835
\(378\) 0 0
\(379\) 19.3330 0.993068 0.496534 0.868017i \(-0.334606\pi\)
0.496534 + 0.868017i \(0.334606\pi\)
\(380\) 7.31428 0.375215
\(381\) −20.8741 −1.06941
\(382\) 1.27293 0.0651287
\(383\) −10.0923 −0.515693 −0.257846 0.966186i \(-0.583013\pi\)
−0.257846 + 0.966186i \(0.583013\pi\)
\(384\) −1.87312 −0.0955875
\(385\) 0 0
\(386\) −23.6764 −1.20510
\(387\) −78.0018 −3.96505
\(388\) 14.5285 0.737572
\(389\) 27.2856 1.38343 0.691717 0.722169i \(-0.256855\pi\)
0.691717 + 0.722169i \(0.256855\pi\)
\(390\) −6.76031 −0.342322
\(391\) −4.49238 −0.227189
\(392\) 0 0
\(393\) −12.6744 −0.639340
\(394\) −5.70443 −0.287385
\(395\) −7.43983 −0.374339
\(396\) −5.57386 −0.280097
\(397\) −25.2595 −1.26774 −0.633870 0.773440i \(-0.718535\pi\)
−0.633870 + 0.773440i \(0.718535\pi\)
\(398\) −11.7512 −0.589037
\(399\) 0 0
\(400\) −1.52742 −0.0763711
\(401\) 5.31132 0.265235 0.132617 0.991167i \(-0.457662\pi\)
0.132617 + 0.991167i \(0.457662\pi\)
\(402\) 35.2625 1.75873
\(403\) −0.671447 −0.0334471
\(404\) −12.3072 −0.612305
\(405\) −13.3027 −0.661017
\(406\) 0 0
\(407\) 5.40922 0.268125
\(408\) 10.5442 0.522014
\(409\) −30.0680 −1.48677 −0.743384 0.668865i \(-0.766780\pi\)
−0.743384 + 0.668865i \(0.766780\pi\)
\(410\) −1.31391 −0.0648892
\(411\) 35.3858 1.74545
\(412\) 14.0387 0.691639
\(413\) 0 0
\(414\) 27.5212 1.35259
\(415\) −4.20154 −0.206246
\(416\) 9.23288 0.452679
\(417\) −2.40842 −0.117941
\(418\) 9.03034 0.441688
\(419\) 12.9969 0.634938 0.317469 0.948269i \(-0.397167\pi\)
0.317469 + 0.948269i \(0.397167\pi\)
\(420\) 0 0
\(421\) −2.56078 −0.124805 −0.0624024 0.998051i \(-0.519876\pi\)
−0.0624024 + 0.998051i \(0.519876\pi\)
\(422\) 5.16291 0.251326
\(423\) −6.80159 −0.330705
\(424\) 2.69993 0.131120
\(425\) −1.12330 −0.0544883
\(426\) 26.8371 1.30026
\(427\) 0 0
\(428\) −7.40898 −0.358127
\(429\) 6.34131 0.306161
\(430\) 12.8822 0.621236
\(431\) 0.989866 0.0476802 0.0238401 0.999716i \(-0.492411\pi\)
0.0238401 + 0.999716i \(0.492411\pi\)
\(432\) −16.2274 −0.780739
\(433\) 32.4815 1.56096 0.780482 0.625179i \(-0.214974\pi\)
0.780482 + 0.625179i \(0.214974\pi\)
\(434\) 0 0
\(435\) 12.3571 0.592477
\(436\) −3.57630 −0.171274
\(437\) 33.8763 1.62052
\(438\) −42.4880 −2.03016
\(439\) 2.44093 0.116499 0.0582495 0.998302i \(-0.481448\pi\)
0.0582495 + 0.998302i \(0.481448\pi\)
\(440\) 3.05269 0.145531
\(441\) 0 0
\(442\) −2.46963 −0.117468
\(443\) 29.7927 1.41549 0.707746 0.706467i \(-0.249712\pi\)
0.707746 + 0.706467i \(0.249712\pi\)
\(444\) −14.3622 −0.681602
\(445\) 14.0917 0.668008
\(446\) −11.4689 −0.543067
\(447\) 33.7438 1.59603
\(448\) 0 0
\(449\) 32.6965 1.54304 0.771521 0.636203i \(-0.219496\pi\)
0.771521 + 0.636203i \(0.219496\pi\)
\(450\) 6.88158 0.324401
\(451\) 1.23247 0.0580348
\(452\) −2.55177 −0.120025
\(453\) −29.6002 −1.39074
\(454\) 4.93003 0.231378
\(455\) 0 0
\(456\) −79.5118 −3.72348
\(457\) 12.3905 0.579603 0.289801 0.957087i \(-0.406411\pi\)
0.289801 + 0.957087i \(0.406411\pi\)
\(458\) −1.76330 −0.0823935
\(459\) −11.9340 −0.557032
\(460\) 3.45330 0.161011
\(461\) −36.7587 −1.71202 −0.856011 0.516957i \(-0.827065\pi\)
−0.856011 + 0.516957i \(0.827065\pi\)
\(462\) 0 0
\(463\) 18.1518 0.843585 0.421793 0.906692i \(-0.361401\pi\)
0.421793 + 0.906692i \(0.361401\pi\)
\(464\) 6.13822 0.284960
\(465\) 1.00115 0.0464270
\(466\) 2.22841 0.103229
\(467\) 33.6677 1.55795 0.778977 0.627052i \(-0.215739\pi\)
0.778977 + 0.627052i \(0.215739\pi\)
\(468\) −11.4948 −0.531349
\(469\) 0 0
\(470\) 1.12330 0.0518142
\(471\) −59.5059 −2.74188
\(472\) −42.3384 −1.94878
\(473\) −12.0838 −0.555614
\(474\) 24.3884 1.12020
\(475\) 8.47065 0.388660
\(476\) 0 0
\(477\) −5.70913 −0.261403
\(478\) −13.9719 −0.639061
\(479\) 21.9471 1.00279 0.501393 0.865219i \(-0.332821\pi\)
0.501393 + 0.865219i \(0.332821\pi\)
\(480\) −13.7665 −0.628350
\(481\) 11.1553 0.508638
\(482\) 6.31801 0.287778
\(483\) 0 0
\(484\) −0.863486 −0.0392493
\(485\) 16.8254 0.764002
\(486\) 9.62937 0.436797
\(487\) 19.4520 0.881454 0.440727 0.897641i \(-0.354721\pi\)
0.440727 + 0.897641i \(0.354721\pi\)
\(488\) −5.00235 −0.226446
\(489\) 49.5633 2.24133
\(490\) 0 0
\(491\) 6.22618 0.280984 0.140492 0.990082i \(-0.455132\pi\)
0.140492 + 0.990082i \(0.455132\pi\)
\(492\) −3.27239 −0.147531
\(493\) 4.51420 0.203309
\(494\) 18.6231 0.837891
\(495\) −6.45507 −0.290134
\(496\) 0.497306 0.0223297
\(497\) 0 0
\(498\) 13.7730 0.617183
\(499\) 10.3643 0.463968 0.231984 0.972720i \(-0.425478\pi\)
0.231984 + 0.972720i \(0.425478\pi\)
\(500\) 0.863486 0.0386163
\(501\) −28.5122 −1.27383
\(502\) 8.65723 0.386391
\(503\) −4.68935 −0.209088 −0.104544 0.994520i \(-0.533338\pi\)
−0.104544 + 0.994520i \(0.533338\pi\)
\(504\) 0 0
\(505\) −14.2529 −0.634246
\(506\) 4.26350 0.189536
\(507\) −26.8963 −1.19451
\(508\) 5.86179 0.260075
\(509\) 30.3913 1.34707 0.673535 0.739155i \(-0.264775\pi\)
0.673535 + 0.739155i \(0.264775\pi\)
\(510\) 3.68228 0.163054
\(511\) 0 0
\(512\) −16.1638 −0.714346
\(513\) 89.9924 3.97326
\(514\) 28.1247 1.24053
\(515\) 16.2582 0.716423
\(516\) 32.0842 1.41243
\(517\) −1.05368 −0.0463409
\(518\) 0 0
\(519\) −59.1656 −2.59708
\(520\) 6.29549 0.276075
\(521\) 20.3815 0.892932 0.446466 0.894801i \(-0.352682\pi\)
0.446466 + 0.894801i \(0.352682\pi\)
\(522\) −27.6549 −1.21042
\(523\) 2.05927 0.0900458 0.0450229 0.998986i \(-0.485664\pi\)
0.0450229 + 0.998986i \(0.485664\pi\)
\(524\) 3.55919 0.155484
\(525\) 0 0
\(526\) −22.1413 −0.965408
\(527\) 0.365731 0.0159315
\(528\) −4.69668 −0.204397
\(529\) −7.00595 −0.304606
\(530\) 0.942881 0.0409561
\(531\) 89.5268 3.88513
\(532\) 0 0
\(533\) 2.54170 0.110093
\(534\) −46.1936 −1.99899
\(535\) −8.58032 −0.370960
\(536\) −32.8379 −1.41838
\(537\) −25.6546 −1.10708
\(538\) −11.3777 −0.490529
\(539\) 0 0
\(540\) 9.17369 0.394773
\(541\) 2.61676 0.112503 0.0562516 0.998417i \(-0.482085\pi\)
0.0562516 + 0.998417i \(0.482085\pi\)
\(542\) −5.59008 −0.240114
\(543\) −58.1563 −2.49572
\(544\) −5.02907 −0.215620
\(545\) −4.14170 −0.177411
\(546\) 0 0
\(547\) 44.6670 1.90982 0.954910 0.296894i \(-0.0959507\pi\)
0.954910 + 0.296894i \(0.0959507\pi\)
\(548\) −9.93692 −0.424484
\(549\) 10.5777 0.451446
\(550\) 1.06607 0.0454576
\(551\) −34.0408 −1.45019
\(552\) −37.5400 −1.59781
\(553\) 0 0
\(554\) −19.5908 −0.832335
\(555\) −16.6329 −0.706026
\(556\) 0.676324 0.0286825
\(557\) 27.6836 1.17299 0.586497 0.809952i \(-0.300507\pi\)
0.586497 + 0.809952i \(0.300507\pi\)
\(558\) −2.24054 −0.0948497
\(559\) −24.9201 −1.05401
\(560\) 0 0
\(561\) −3.45406 −0.145830
\(562\) −3.08751 −0.130239
\(563\) −17.8633 −0.752849 −0.376425 0.926447i \(-0.622847\pi\)
−0.376425 + 0.926447i \(0.622847\pi\)
\(564\) 2.79768 0.117803
\(565\) −2.95520 −0.124326
\(566\) 4.68232 0.196813
\(567\) 0 0
\(568\) −24.9918 −1.04863
\(569\) 27.0943 1.13585 0.567925 0.823080i \(-0.307746\pi\)
0.567925 + 0.823080i \(0.307746\pi\)
\(570\) −27.7675 −1.16305
\(571\) 33.6184 1.40689 0.703443 0.710752i \(-0.251645\pi\)
0.703443 + 0.710752i \(0.251645\pi\)
\(572\) −1.78075 −0.0744567
\(573\) 3.67154 0.153381
\(574\) 0 0
\(575\) 3.99926 0.166781
\(576\) 50.5283 2.10535
\(577\) 0.511024 0.0212742 0.0106371 0.999943i \(-0.496614\pi\)
0.0106371 + 0.999943i \(0.496614\pi\)
\(578\) −16.7781 −0.697876
\(579\) −68.2906 −2.83806
\(580\) −3.47007 −0.144087
\(581\) 0 0
\(582\) −55.1550 −2.28625
\(583\) −0.884442 −0.0366298
\(584\) 39.5666 1.63728
\(585\) −13.3121 −0.550389
\(586\) −22.4241 −0.926331
\(587\) 24.8042 1.02378 0.511889 0.859052i \(-0.328946\pi\)
0.511889 + 0.859052i \(0.328946\pi\)
\(588\) 0 0
\(589\) −2.75792 −0.113638
\(590\) −14.7856 −0.608714
\(591\) −16.4535 −0.676805
\(592\) −8.26216 −0.339573
\(593\) −29.2813 −1.20244 −0.601219 0.799084i \(-0.705318\pi\)
−0.601219 + 0.799084i \(0.705318\pi\)
\(594\) 11.3260 0.464711
\(595\) 0 0
\(596\) −9.47581 −0.388144
\(597\) −33.8945 −1.38721
\(598\) 8.79252 0.359553
\(599\) −15.8331 −0.646922 −0.323461 0.946241i \(-0.604846\pi\)
−0.323461 + 0.946241i \(0.604846\pi\)
\(600\) −9.38674 −0.383212
\(601\) 16.8302 0.686516 0.343258 0.939241i \(-0.388469\pi\)
0.343258 + 0.939241i \(0.388469\pi\)
\(602\) 0 0
\(603\) 69.4374 2.82771
\(604\) 8.31221 0.338219
\(605\) −1.00000 −0.0406558
\(606\) 46.7222 1.89796
\(607\) 9.72751 0.394828 0.197414 0.980320i \(-0.436746\pi\)
0.197414 + 0.980320i \(0.436746\pi\)
\(608\) 37.9234 1.53800
\(609\) 0 0
\(610\) −1.74694 −0.0707317
\(611\) −2.17298 −0.0879096
\(612\) 6.26114 0.253092
\(613\) 10.7530 0.434311 0.217156 0.976137i \(-0.430322\pi\)
0.217156 + 0.976137i \(0.430322\pi\)
\(614\) 26.5112 1.06991
\(615\) −3.78974 −0.152817
\(616\) 0 0
\(617\) −18.5288 −0.745942 −0.372971 0.927843i \(-0.621661\pi\)
−0.372971 + 0.927843i \(0.621661\pi\)
\(618\) −53.2958 −2.14387
\(619\) −24.4585 −0.983070 −0.491535 0.870858i \(-0.663564\pi\)
−0.491535 + 0.870858i \(0.663564\pi\)
\(620\) −0.281138 −0.0112908
\(621\) 42.4882 1.70499
\(622\) −25.9572 −1.04079
\(623\) 0 0
\(624\) −9.68586 −0.387745
\(625\) 1.00000 0.0400000
\(626\) 1.22494 0.0489584
\(627\) 26.0465 1.04020
\(628\) 16.7102 0.666811
\(629\) −6.07620 −0.242274
\(630\) 0 0
\(631\) −38.3589 −1.52704 −0.763522 0.645782i \(-0.776532\pi\)
−0.763522 + 0.645782i \(0.776532\pi\)
\(632\) −22.7115 −0.903415
\(633\) 14.8915 0.591885
\(634\) 20.6335 0.819462
\(635\) 6.78852 0.269394
\(636\) 2.34832 0.0931168
\(637\) 0 0
\(638\) −4.28421 −0.169614
\(639\) 52.8465 2.09058
\(640\) 0.609164 0.0240793
\(641\) −32.1823 −1.27113 −0.635563 0.772049i \(-0.719232\pi\)
−0.635563 + 0.772049i \(0.719232\pi\)
\(642\) 28.1270 1.11008
\(643\) −12.1417 −0.478821 −0.239410 0.970918i \(-0.576954\pi\)
−0.239410 + 0.970918i \(0.576954\pi\)
\(644\) 0 0
\(645\) 37.1566 1.46304
\(646\) −10.1438 −0.399103
\(647\) 22.2116 0.873229 0.436615 0.899649i \(-0.356177\pi\)
0.436615 + 0.899649i \(0.356177\pi\)
\(648\) −40.6090 −1.59527
\(649\) 13.8692 0.544415
\(650\) 2.19854 0.0862338
\(651\) 0 0
\(652\) −13.9182 −0.545079
\(653\) 41.7877 1.63528 0.817640 0.575730i \(-0.195282\pi\)
0.817640 + 0.575730i \(0.195282\pi\)
\(654\) 13.5768 0.530896
\(655\) 4.12189 0.161055
\(656\) −1.88250 −0.0734994
\(657\) −83.6657 −3.26411
\(658\) 0 0
\(659\) −11.0308 −0.429700 −0.214850 0.976647i \(-0.568926\pi\)
−0.214850 + 0.976647i \(0.568926\pi\)
\(660\) 2.65514 0.103351
\(661\) 40.6832 1.58239 0.791196 0.611562i \(-0.209459\pi\)
0.791196 + 0.611562i \(0.209459\pi\)
\(662\) −3.47512 −0.135064
\(663\) −7.12322 −0.276643
\(664\) −12.8260 −0.497745
\(665\) 0 0
\(666\) 37.2240 1.44240
\(667\) −16.0717 −0.622300
\(668\) 8.00670 0.309788
\(669\) −33.0800 −1.27895
\(670\) −11.4678 −0.443040
\(671\) 1.63867 0.0632601
\(672\) 0 0
\(673\) −9.01027 −0.347320 −0.173660 0.984806i \(-0.555559\pi\)
−0.173660 + 0.984806i \(0.555559\pi\)
\(674\) −0.459999 −0.0177185
\(675\) 10.6240 0.408919
\(676\) 7.55292 0.290497
\(677\) −48.6358 −1.86922 −0.934612 0.355669i \(-0.884253\pi\)
−0.934612 + 0.355669i \(0.884253\pi\)
\(678\) 9.68738 0.372042
\(679\) 0 0
\(680\) −3.42910 −0.131500
\(681\) 14.2198 0.544905
\(682\) −0.347098 −0.0132911
\(683\) −10.4881 −0.401316 −0.200658 0.979661i \(-0.564308\pi\)
−0.200658 + 0.979661i \(0.564308\pi\)
\(684\) −47.2142 −1.80528
\(685\) −11.5079 −0.439695
\(686\) 0 0
\(687\) −5.08593 −0.194040
\(688\) 18.4571 0.703669
\(689\) −1.82396 −0.0694875
\(690\) −13.1099 −0.499085
\(691\) 22.5536 0.857978 0.428989 0.903310i \(-0.358870\pi\)
0.428989 + 0.903310i \(0.358870\pi\)
\(692\) 16.6147 0.631595
\(693\) 0 0
\(694\) −2.76647 −0.105014
\(695\) 0.783249 0.0297103
\(696\) 37.7223 1.42986
\(697\) −1.38444 −0.0524394
\(698\) −12.5737 −0.475922
\(699\) 6.42748 0.243110
\(700\) 0 0
\(701\) −25.9143 −0.978769 −0.489385 0.872068i \(-0.662779\pi\)
−0.489385 + 0.872068i \(0.662779\pi\)
\(702\) 23.3573 0.881566
\(703\) 45.8196 1.72812
\(704\) 7.82769 0.295017
\(705\) 3.23998 0.122025
\(706\) −2.21002 −0.0831751
\(707\) 0 0
\(708\) −36.8247 −1.38396
\(709\) −52.0656 −1.95536 −0.977682 0.210089i \(-0.932625\pi\)
−0.977682 + 0.210089i \(0.932625\pi\)
\(710\) −8.72776 −0.327547
\(711\) 48.0246 1.80106
\(712\) 43.0174 1.61215
\(713\) −1.30210 −0.0487640
\(714\) 0 0
\(715\) −2.06228 −0.0771248
\(716\) 7.20425 0.269235
\(717\) −40.2996 −1.50502
\(718\) −32.2761 −1.20453
\(719\) 33.1393 1.23589 0.617944 0.786222i \(-0.287966\pi\)
0.617944 + 0.786222i \(0.287966\pi\)
\(720\) 9.85961 0.367446
\(721\) 0 0
\(722\) 56.2374 2.09294
\(723\) 18.2232 0.677729
\(724\) 16.3312 0.606946
\(725\) −4.01868 −0.149250
\(726\) 3.27808 0.121661
\(727\) 2.62195 0.0972428 0.0486214 0.998817i \(-0.484517\pi\)
0.0486214 + 0.998817i \(0.484517\pi\)
\(728\) 0 0
\(729\) −12.1339 −0.449402
\(730\) 13.8176 0.511414
\(731\) 13.5738 0.502044
\(732\) −4.35090 −0.160814
\(733\) −13.7308 −0.507158 −0.253579 0.967315i \(-0.581608\pi\)
−0.253579 + 0.967315i \(0.581608\pi\)
\(734\) 8.57072 0.316351
\(735\) 0 0
\(736\) 17.9048 0.659980
\(737\) 10.7570 0.396241
\(738\) 8.48136 0.312203
\(739\) 4.54057 0.167028 0.0835138 0.996507i \(-0.473386\pi\)
0.0835138 + 0.996507i \(0.473386\pi\)
\(740\) 4.67078 0.171701
\(741\) 53.7150 1.97327
\(742\) 0 0
\(743\) 23.7757 0.872245 0.436123 0.899887i \(-0.356351\pi\)
0.436123 + 0.899887i \(0.356351\pi\)
\(744\) 3.05618 0.112045
\(745\) −10.9739 −0.402053
\(746\) −31.9456 −1.16961
\(747\) 27.1213 0.992315
\(748\) 0.969957 0.0354651
\(749\) 0 0
\(750\) −3.27808 −0.119699
\(751\) 35.2109 1.28486 0.642432 0.766343i \(-0.277925\pi\)
0.642432 + 0.766343i \(0.277925\pi\)
\(752\) 1.60942 0.0586894
\(753\) 24.9703 0.909969
\(754\) −8.83523 −0.321760
\(755\) 9.62635 0.350339
\(756\) 0 0
\(757\) 5.66097 0.205752 0.102876 0.994694i \(-0.467196\pi\)
0.102876 + 0.994694i \(0.467196\pi\)
\(758\) 20.6104 0.748603
\(759\) 12.2974 0.446366
\(760\) 25.8583 0.937977
\(761\) −15.5703 −0.564422 −0.282211 0.959352i \(-0.591068\pi\)
−0.282211 + 0.959352i \(0.591068\pi\)
\(762\) −22.2533 −0.806152
\(763\) 0 0
\(764\) −1.03103 −0.0373014
\(765\) 7.25101 0.262161
\(766\) −10.7591 −0.388744
\(767\) 28.6022 1.03276
\(768\) −50.1358 −1.80912
\(769\) −11.4329 −0.412281 −0.206140 0.978522i \(-0.566090\pi\)
−0.206140 + 0.978522i \(0.566090\pi\)
\(770\) 0 0
\(771\) 81.1209 2.92150
\(772\) 19.1771 0.690200
\(773\) 8.33168 0.299670 0.149835 0.988711i \(-0.452126\pi\)
0.149835 + 0.988711i \(0.452126\pi\)
\(774\) −83.1557 −2.98897
\(775\) −0.325585 −0.0116954
\(776\) 51.3627 1.84381
\(777\) 0 0
\(778\) 29.0884 1.04287
\(779\) 10.4398 0.374046
\(780\) 5.47563 0.196059
\(781\) 8.18682 0.292948
\(782\) −4.78921 −0.171262
\(783\) −42.6946 −1.52578
\(784\) 0 0
\(785\) 19.3521 0.690705
\(786\) −13.5119 −0.481953
\(787\) −20.3518 −0.725463 −0.362731 0.931894i \(-0.618156\pi\)
−0.362731 + 0.931894i \(0.618156\pi\)
\(788\) 4.62040 0.164595
\(789\) −63.8629 −2.27358
\(790\) −7.93142 −0.282187
\(791\) 0 0
\(792\) −19.7053 −0.700198
\(793\) 3.37939 0.120006
\(794\) −26.9285 −0.955658
\(795\) 2.71958 0.0964535
\(796\) 9.51813 0.337361
\(797\) −11.4434 −0.405345 −0.202672 0.979247i \(-0.564963\pi\)
−0.202672 + 0.979247i \(0.564963\pi\)
\(798\) 0 0
\(799\) 1.18361 0.0418730
\(800\) 4.47703 0.158287
\(801\) −90.9626 −3.21400
\(802\) 5.66227 0.199942
\(803\) −12.9612 −0.457392
\(804\) −28.5615 −1.00728
\(805\) 0 0
\(806\) −0.715812 −0.0252134
\(807\) −32.8172 −1.15522
\(808\) −43.5097 −1.53067
\(809\) −41.2939 −1.45182 −0.725908 0.687792i \(-0.758580\pi\)
−0.725908 + 0.687792i \(0.758580\pi\)
\(810\) −14.1817 −0.498293
\(811\) −7.63142 −0.267976 −0.133988 0.990983i \(-0.542778\pi\)
−0.133988 + 0.990983i \(0.542778\pi\)
\(812\) 0 0
\(813\) −16.1236 −0.565480
\(814\) 5.76663 0.202120
\(815\) −16.1186 −0.564610
\(816\) 5.27580 0.184690
\(817\) −102.358 −3.58104
\(818\) −32.0547 −1.12077
\(819\) 0 0
\(820\) 1.06422 0.0371642
\(821\) 55.5421 1.93843 0.969216 0.246214i \(-0.0791864\pi\)
0.969216 + 0.246214i \(0.0791864\pi\)
\(822\) 37.7239 1.31577
\(823\) −4.45307 −0.155224 −0.0776122 0.996984i \(-0.524730\pi\)
−0.0776122 + 0.996984i \(0.524730\pi\)
\(824\) 49.6313 1.72899
\(825\) 3.07491 0.107055
\(826\) 0 0
\(827\) −3.60111 −0.125223 −0.0626114 0.998038i \(-0.519943\pi\)
−0.0626114 + 0.998038i \(0.519943\pi\)
\(828\) −22.2913 −0.774676
\(829\) −16.0872 −0.558732 −0.279366 0.960185i \(-0.590124\pi\)
−0.279366 + 0.960185i \(0.590124\pi\)
\(830\) −4.47916 −0.155474
\(831\) −56.5064 −1.96019
\(832\) 16.1429 0.559653
\(833\) 0 0
\(834\) −2.56755 −0.0889071
\(835\) 9.27253 0.320889
\(836\) −7.31428 −0.252970
\(837\) −3.45903 −0.119561
\(838\) 13.8556 0.478634
\(839\) −14.6263 −0.504956 −0.252478 0.967603i \(-0.581246\pi\)
−0.252478 + 0.967603i \(0.581246\pi\)
\(840\) 0 0
\(841\) −12.8502 −0.443110
\(842\) −2.72998 −0.0940814
\(843\) −8.90540 −0.306718
\(844\) −4.18179 −0.143943
\(845\) 8.74702 0.300907
\(846\) −7.25101 −0.249295
\(847\) 0 0
\(848\) 1.35092 0.0463906
\(849\) 13.5054 0.463503
\(850\) −1.19753 −0.0410748
\(851\) 21.6329 0.741565
\(852\) −21.7372 −0.744703
\(853\) −44.9908 −1.54046 −0.770228 0.637769i \(-0.779857\pi\)
−0.770228 + 0.637769i \(0.779857\pi\)
\(854\) 0 0
\(855\) −54.6786 −1.86997
\(856\) −26.1930 −0.895260
\(857\) −38.9813 −1.33158 −0.665789 0.746140i \(-0.731905\pi\)
−0.665789 + 0.746140i \(0.731905\pi\)
\(858\) 6.76031 0.230793
\(859\) 27.5179 0.938898 0.469449 0.882960i \(-0.344453\pi\)
0.469449 + 0.882960i \(0.344453\pi\)
\(860\) −10.4342 −0.355803
\(861\) 0 0
\(862\) 1.05527 0.0359427
\(863\) −21.6767 −0.737882 −0.368941 0.929453i \(-0.620280\pi\)
−0.368941 + 0.929453i \(0.620280\pi\)
\(864\) 47.5641 1.61816
\(865\) 19.2414 0.654227
\(866\) 34.6277 1.17670
\(867\) −48.3935 −1.64353
\(868\) 0 0
\(869\) 7.43983 0.252379
\(870\) 13.1736 0.446626
\(871\) 22.1840 0.751676
\(872\) −12.6433 −0.428156
\(873\) −108.609 −3.67586
\(874\) 36.1146 1.22160
\(875\) 0 0
\(876\) 34.4139 1.16274
\(877\) −21.1178 −0.713097 −0.356549 0.934277i \(-0.616047\pi\)
−0.356549 + 0.934277i \(0.616047\pi\)
\(878\) 2.60221 0.0878202
\(879\) −64.6785 −2.18155
\(880\) 1.52742 0.0514894
\(881\) 12.4701 0.420128 0.210064 0.977688i \(-0.432633\pi\)
0.210064 + 0.977688i \(0.432633\pi\)
\(882\) 0 0
\(883\) 29.8363 1.00407 0.502035 0.864847i \(-0.332585\pi\)
0.502035 + 0.864847i \(0.332585\pi\)
\(884\) 2.00032 0.0672780
\(885\) −42.6466 −1.43355
\(886\) 31.7612 1.06704
\(887\) 28.4571 0.955495 0.477748 0.878497i \(-0.341453\pi\)
0.477748 + 0.878497i \(0.341453\pi\)
\(888\) −50.7749 −1.70390
\(889\) 0 0
\(890\) 15.0227 0.503564
\(891\) 13.3027 0.445657
\(892\) 9.28942 0.311033
\(893\) −8.92538 −0.298676
\(894\) 35.9734 1.20313
\(895\) 8.34322 0.278883
\(896\) 0 0
\(897\) 25.3605 0.846764
\(898\) 34.8569 1.16319
\(899\) 1.30842 0.0436384
\(900\) −5.57386 −0.185795
\(901\) 0.993497 0.0330982
\(902\) 1.31391 0.0437483
\(903\) 0 0
\(904\) −9.02130 −0.300044
\(905\) 18.9132 0.628695
\(906\) −31.5560 −1.04838
\(907\) −10.9305 −0.362941 −0.181471 0.983396i \(-0.558086\pi\)
−0.181471 + 0.983396i \(0.558086\pi\)
\(908\) −3.99317 −0.132518
\(909\) 92.0035 3.05156
\(910\) 0 0
\(911\) 4.19124 0.138862 0.0694310 0.997587i \(-0.477882\pi\)
0.0694310 + 0.997587i \(0.477882\pi\)
\(912\) −39.7839 −1.31738
\(913\) 4.20154 0.139051
\(914\) 13.2092 0.436921
\(915\) −5.03876 −0.166576
\(916\) 1.42821 0.0471895
\(917\) 0 0
\(918\) −12.7225 −0.419906
\(919\) 29.8465 0.984545 0.492272 0.870441i \(-0.336166\pi\)
0.492272 + 0.870441i \(0.336166\pi\)
\(920\) 12.2085 0.402502
\(921\) 76.4671 2.51968
\(922\) −39.1875 −1.29057
\(923\) 16.8835 0.555727
\(924\) 0 0
\(925\) 5.40922 0.177854
\(926\) 19.3512 0.635918
\(927\) −104.948 −3.44694
\(928\) −17.9918 −0.590609
\(929\) −16.6544 −0.546414 −0.273207 0.961955i \(-0.588084\pi\)
−0.273207 + 0.961955i \(0.588084\pi\)
\(930\) 1.06730 0.0349980
\(931\) 0 0
\(932\) −1.80494 −0.0591229
\(933\) −74.8692 −2.45111
\(934\) 35.8923 1.17443
\(935\) 1.12330 0.0367360
\(936\) −40.6378 −1.32829
\(937\) 8.35998 0.273109 0.136554 0.990633i \(-0.456397\pi\)
0.136554 + 0.990633i \(0.456397\pi\)
\(938\) 0 0
\(939\) 3.53313 0.115299
\(940\) −0.909840 −0.0296757
\(941\) 21.3159 0.694880 0.347440 0.937702i \(-0.387051\pi\)
0.347440 + 0.937702i \(0.387051\pi\)
\(942\) −63.4377 −2.06691
\(943\) 4.92897 0.160509
\(944\) −21.1841 −0.689485
\(945\) 0 0
\(946\) −12.8822 −0.418837
\(947\) −12.6887 −0.412327 −0.206164 0.978518i \(-0.566098\pi\)
−0.206164 + 0.978518i \(0.566098\pi\)
\(948\) −19.7538 −0.641574
\(949\) −26.7297 −0.867681
\(950\) 9.03034 0.292983
\(951\) 59.5139 1.92987
\(952\) 0 0
\(953\) −38.6944 −1.25343 −0.626717 0.779247i \(-0.715602\pi\)
−0.626717 + 0.779247i \(0.715602\pi\)
\(954\) −6.08636 −0.197053
\(955\) −1.19403 −0.0386380
\(956\) 11.3168 0.366012
\(957\) −12.3571 −0.399448
\(958\) 23.3972 0.755929
\(959\) 0 0
\(960\) −24.0694 −0.776838
\(961\) −30.8940 −0.996580
\(962\) 11.8924 0.383426
\(963\) 55.3866 1.78481
\(964\) −5.11739 −0.164820
\(965\) 22.2090 0.714933
\(966\) 0 0
\(967\) −13.1619 −0.423259 −0.211630 0.977350i \(-0.567877\pi\)
−0.211630 + 0.977350i \(0.567877\pi\)
\(968\) −3.05269 −0.0981171
\(969\) −29.2581 −0.939906
\(970\) 17.9371 0.575926
\(971\) −35.5953 −1.14231 −0.571153 0.820844i \(-0.693504\pi\)
−0.571153 + 0.820844i \(0.693504\pi\)
\(972\) −7.79948 −0.250168
\(973\) 0 0
\(974\) 20.7373 0.664465
\(975\) 6.34131 0.203085
\(976\) −2.50294 −0.0801171
\(977\) −19.2003 −0.614273 −0.307136 0.951666i \(-0.599371\pi\)
−0.307136 + 0.951666i \(0.599371\pi\)
\(978\) 52.8381 1.68958
\(979\) −14.0917 −0.450371
\(980\) 0 0
\(981\) 26.7349 0.853581
\(982\) 6.63757 0.211813
\(983\) −32.8956 −1.04921 −0.524603 0.851347i \(-0.675786\pi\)
−0.524603 + 0.851347i \(0.675786\pi\)
\(984\) −11.5689 −0.368803
\(985\) 5.35087 0.170493
\(986\) 4.81247 0.153260
\(987\) 0 0
\(988\) −15.0841 −0.479888
\(989\) −48.3262 −1.53668
\(990\) −6.88158 −0.218711
\(991\) −19.9760 −0.634560 −0.317280 0.948332i \(-0.602770\pi\)
−0.317280 + 0.948332i \(0.602770\pi\)
\(992\) −1.45766 −0.0462806
\(993\) −10.0234 −0.318083
\(994\) 0 0
\(995\) 11.0229 0.349450
\(996\) −11.1557 −0.353481
\(997\) −4.04129 −0.127989 −0.0639945 0.997950i \(-0.520384\pi\)
−0.0639945 + 0.997950i \(0.520384\pi\)
\(998\) 11.0491 0.349752
\(999\) 57.4677 1.81820
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.y.1.6 10
7.2 even 3 385.2.i.d.221.5 20
7.4 even 3 385.2.i.d.331.5 yes 20
7.6 odd 2 2695.2.a.z.1.6 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
385.2.i.d.221.5 20 7.2 even 3
385.2.i.d.331.5 yes 20 7.4 even 3
2695.2.a.y.1.6 10 1.1 even 1 trivial
2695.2.a.z.1.6 10 7.6 odd 2