Properties

Label 7105.2.a.o.1.1
Level $7105$
Weight $2$
Character 7105.1
Self dual yes
Analytic conductor $56.734$
Analytic rank $0$
Dimension $3$
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] = [7105,2,Mod(1,7105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7105, 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("7105.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7105 = 5 \cdot 7^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7105.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: \(56.7337106361\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 145)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 7105.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.48119 q^{2} -0.806063 q^{3} +0.193937 q^{4} -1.00000 q^{5} +1.19394 q^{6} +2.67513 q^{8} -2.35026 q^{9} +O(q^{10})\) \(q-1.48119 q^{2} -0.806063 q^{3} +0.193937 q^{4} -1.00000 q^{5} +1.19394 q^{6} +2.67513 q^{8} -2.35026 q^{9} +1.48119 q^{10} +4.15633 q^{11} -0.156325 q^{12} -2.96239 q^{13} +0.806063 q^{15} -4.35026 q^{16} -5.50659 q^{17} +3.48119 q^{18} +3.19394 q^{19} -0.193937 q^{20} -6.15633 q^{22} +1.84367 q^{23} -2.15633 q^{24} +1.00000 q^{25} +4.38787 q^{26} +4.31265 q^{27} -1.00000 q^{29} -1.19394 q^{30} +4.80606 q^{31} +1.09332 q^{32} -3.35026 q^{33} +8.15633 q^{34} -0.455802 q^{36} -9.50659 q^{37} -4.73084 q^{38} +2.38787 q^{39} -2.67513 q^{40} +11.2750 q^{41} -0.0303172 q^{43} +0.806063 q^{44} +2.35026 q^{45} -2.73084 q^{46} -4.80606 q^{47} +3.50659 q^{48} -1.48119 q^{50} +4.43866 q^{51} -0.574515 q^{52} -1.35026 q^{53} -6.38787 q^{54} -4.15633 q^{55} -2.57452 q^{57} +1.48119 q^{58} -13.2750 q^{59} +0.156325 q^{60} -8.88717 q^{61} -7.11871 q^{62} +7.08110 q^{64} +2.96239 q^{65} +4.96239 q^{66} +5.84367 q^{67} -1.06793 q^{68} -1.48612 q^{69} -1.27504 q^{71} -6.28726 q^{72} +15.2447 q^{73} +14.0811 q^{74} -0.806063 q^{75} +0.619421 q^{76} -3.53690 q^{78} -4.93207 q^{79} +4.35026 q^{80} +3.57452 q^{81} -16.7005 q^{82} -4.41819 q^{83} +5.50659 q^{85} +0.0449056 q^{86} +0.806063 q^{87} +11.1187 q^{88} +3.61213 q^{89} -3.48119 q^{90} +0.357556 q^{92} -3.87399 q^{93} +7.11871 q^{94} -3.19394 q^{95} -0.881286 q^{96} +1.38058 q^{97} -9.76845 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} - 2 q^{3} + q^{4} - 3 q^{5} + 4 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} - 2 q^{3} + q^{4} - 3 q^{5} + 4 q^{6} + 3 q^{8} + 3 q^{9} - q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 2 q^{15} - 3 q^{16} + 4 q^{17} + 5 q^{18} + 10 q^{19} - q^{20} - 8 q^{22} + 16 q^{23} + 4 q^{24} + 3 q^{25} + 14 q^{26} - 8 q^{27} - 3 q^{29} - 4 q^{30} + 14 q^{31} - 3 q^{32} + 14 q^{34} - 11 q^{36} - 8 q^{37} + 8 q^{38} + 8 q^{39} - 3 q^{40} + 2 q^{41} + 2 q^{43} + 2 q^{44} - 3 q^{45} + 14 q^{46} - 14 q^{47} - 10 q^{48} + q^{50} - 16 q^{51} + 10 q^{52} + 6 q^{53} - 20 q^{54} - 2 q^{55} + 4 q^{57} - q^{58} - 8 q^{59} - 10 q^{60} + 6 q^{61} - 11 q^{64} - 2 q^{65} + 4 q^{66} + 28 q^{67} - 12 q^{68} - 12 q^{69} + 28 q^{71} - 13 q^{72} + 16 q^{73} + 10 q^{74} - 2 q^{75} + 14 q^{76} + 12 q^{78} - 6 q^{79} + 3 q^{80} - q^{81} - 30 q^{82} - 12 q^{83} - 4 q^{85} + 24 q^{86} + 2 q^{87} + 12 q^{88} + 10 q^{89} - 5 q^{90} + 4 q^{92} - 20 q^{93} - 10 q^{95} - 24 q^{96} - 8 q^{97} - 18 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.48119 −1.04736 −0.523681 0.851914i \(-0.675442\pi\)
−0.523681 + 0.851914i \(0.675442\pi\)
\(3\) −0.806063 −0.465381 −0.232690 0.972551i \(-0.574753\pi\)
−0.232690 + 0.972551i \(0.574753\pi\)
\(4\) 0.193937 0.0969683
\(5\) −1.00000 −0.447214
\(6\) 1.19394 0.487423
\(7\) 0 0
\(8\) 2.67513 0.945802
\(9\) −2.35026 −0.783421
\(10\) 1.48119 0.468395
\(11\) 4.15633 1.25318 0.626590 0.779349i \(-0.284450\pi\)
0.626590 + 0.779349i \(0.284450\pi\)
\(12\) −0.156325 −0.0451272
\(13\) −2.96239 −0.821619 −0.410809 0.911721i \(-0.634754\pi\)
−0.410809 + 0.911721i \(0.634754\pi\)
\(14\) 0 0
\(15\) 0.806063 0.208125
\(16\) −4.35026 −1.08757
\(17\) −5.50659 −1.33554 −0.667772 0.744366i \(-0.732752\pi\)
−0.667772 + 0.744366i \(0.732752\pi\)
\(18\) 3.48119 0.820525
\(19\) 3.19394 0.732739 0.366370 0.930469i \(-0.380601\pi\)
0.366370 + 0.930469i \(0.380601\pi\)
\(20\) −0.193937 −0.0433655
\(21\) 0 0
\(22\) −6.15633 −1.31253
\(23\) 1.84367 0.384433 0.192216 0.981353i \(-0.438432\pi\)
0.192216 + 0.981353i \(0.438432\pi\)
\(24\) −2.15633 −0.440158
\(25\) 1.00000 0.200000
\(26\) 4.38787 0.860533
\(27\) 4.31265 0.829970
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) −1.19394 −0.217982
\(31\) 4.80606 0.863194 0.431597 0.902066i \(-0.357950\pi\)
0.431597 + 0.902066i \(0.357950\pi\)
\(32\) 1.09332 0.193274
\(33\) −3.35026 −0.583206
\(34\) 8.15633 1.39880
\(35\) 0 0
\(36\) −0.455802 −0.0759669
\(37\) −9.50659 −1.56287 −0.781437 0.623985i \(-0.785513\pi\)
−0.781437 + 0.623985i \(0.785513\pi\)
\(38\) −4.73084 −0.767444
\(39\) 2.38787 0.382366
\(40\) −2.67513 −0.422975
\(41\) 11.2750 1.76087 0.880433 0.474171i \(-0.157252\pi\)
0.880433 + 0.474171i \(0.157252\pi\)
\(42\) 0 0
\(43\) −0.0303172 −0.00462332 −0.00231166 0.999997i \(-0.500736\pi\)
−0.00231166 + 0.999997i \(0.500736\pi\)
\(44\) 0.806063 0.121519
\(45\) 2.35026 0.350356
\(46\) −2.73084 −0.402640
\(47\) −4.80606 −0.701036 −0.350518 0.936556i \(-0.613995\pi\)
−0.350518 + 0.936556i \(0.613995\pi\)
\(48\) 3.50659 0.506132
\(49\) 0 0
\(50\) −1.48119 −0.209473
\(51\) 4.43866 0.621536
\(52\) −0.574515 −0.0796710
\(53\) −1.35026 −0.185473 −0.0927364 0.995691i \(-0.529561\pi\)
−0.0927364 + 0.995691i \(0.529561\pi\)
\(54\) −6.38787 −0.869279
\(55\) −4.15633 −0.560439
\(56\) 0 0
\(57\) −2.57452 −0.341003
\(58\) 1.48119 0.194490
\(59\) −13.2750 −1.72826 −0.864131 0.503266i \(-0.832132\pi\)
−0.864131 + 0.503266i \(0.832132\pi\)
\(60\) 0.156325 0.0201815
\(61\) −8.88717 −1.13788 −0.568942 0.822377i \(-0.692647\pi\)
−0.568942 + 0.822377i \(0.692647\pi\)
\(62\) −7.11871 −0.904078
\(63\) 0 0
\(64\) 7.08110 0.885138
\(65\) 2.96239 0.367439
\(66\) 4.96239 0.610828
\(67\) 5.84367 0.713919 0.356959 0.934120i \(-0.383813\pi\)
0.356959 + 0.934120i \(0.383813\pi\)
\(68\) −1.06793 −0.129505
\(69\) −1.48612 −0.178908
\(70\) 0 0
\(71\) −1.27504 −0.151319 −0.0756596 0.997134i \(-0.524106\pi\)
−0.0756596 + 0.997134i \(0.524106\pi\)
\(72\) −6.28726 −0.740960
\(73\) 15.2447 1.78426 0.892130 0.451779i \(-0.149210\pi\)
0.892130 + 0.451779i \(0.149210\pi\)
\(74\) 14.0811 1.63689
\(75\) −0.806063 −0.0930762
\(76\) 0.619421 0.0710525
\(77\) 0 0
\(78\) −3.53690 −0.400476
\(79\) −4.93207 −0.554901 −0.277451 0.960740i \(-0.589490\pi\)
−0.277451 + 0.960740i \(0.589490\pi\)
\(80\) 4.35026 0.486374
\(81\) 3.57452 0.397168
\(82\) −16.7005 −1.84426
\(83\) −4.41819 −0.484959 −0.242480 0.970156i \(-0.577961\pi\)
−0.242480 + 0.970156i \(0.577961\pi\)
\(84\) 0 0
\(85\) 5.50659 0.597273
\(86\) 0.0449056 0.00484230
\(87\) 0.806063 0.0864191
\(88\) 11.1187 1.18526
\(89\) 3.61213 0.382885 0.191442 0.981504i \(-0.438684\pi\)
0.191442 + 0.981504i \(0.438684\pi\)
\(90\) −3.48119 −0.366950
\(91\) 0 0
\(92\) 0.357556 0.0372778
\(93\) −3.87399 −0.401714
\(94\) 7.11871 0.734239
\(95\) −3.19394 −0.327691
\(96\) −0.881286 −0.0899459
\(97\) 1.38058 0.140177 0.0700883 0.997541i \(-0.477672\pi\)
0.0700883 + 0.997541i \(0.477672\pi\)
\(98\) 0 0
\(99\) −9.76845 −0.981766
\(100\) 0.193937 0.0193937
\(101\) 13.0132 1.29486 0.647430 0.762125i \(-0.275844\pi\)
0.647430 + 0.762125i \(0.275844\pi\)
\(102\) −6.57452 −0.650974
\(103\) −5.31994 −0.524190 −0.262095 0.965042i \(-0.584413\pi\)
−0.262095 + 0.965042i \(0.584413\pi\)
\(104\) −7.92478 −0.777088
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) −13.8192 −1.33596 −0.667978 0.744181i \(-0.732840\pi\)
−0.667978 + 0.744181i \(0.732840\pi\)
\(108\) 0.836381 0.0804808
\(109\) −1.87399 −0.179496 −0.0897479 0.995965i \(-0.528606\pi\)
−0.0897479 + 0.995965i \(0.528606\pi\)
\(110\) 6.15633 0.586983
\(111\) 7.66291 0.727331
\(112\) 0 0
\(113\) −11.7685 −1.10708 −0.553541 0.832822i \(-0.686724\pi\)
−0.553541 + 0.832822i \(0.686724\pi\)
\(114\) 3.81336 0.357154
\(115\) −1.84367 −0.171924
\(116\) −0.193937 −0.0180066
\(117\) 6.96239 0.643673
\(118\) 19.6629 1.81012
\(119\) 0 0
\(120\) 2.15633 0.196845
\(121\) 6.27504 0.570458
\(122\) 13.1636 1.19178
\(123\) −9.08840 −0.819473
\(124\) 0.932071 0.0837025
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 14.2677 1.26606 0.633029 0.774128i \(-0.281811\pi\)
0.633029 + 0.774128i \(0.281811\pi\)
\(128\) −12.6751 −1.12033
\(129\) 0.0244376 0.00215161
\(130\) −4.38787 −0.384842
\(131\) −5.89446 −0.515001 −0.257501 0.966278i \(-0.582899\pi\)
−0.257501 + 0.966278i \(0.582899\pi\)
\(132\) −0.649738 −0.0565525
\(133\) 0 0
\(134\) −8.65562 −0.747731
\(135\) −4.31265 −0.371174
\(136\) −14.7308 −1.26316
\(137\) 18.2823 1.56197 0.780983 0.624553i \(-0.214719\pi\)
0.780983 + 0.624553i \(0.214719\pi\)
\(138\) 2.20123 0.187381
\(139\) 11.5369 0.978547 0.489274 0.872130i \(-0.337262\pi\)
0.489274 + 0.872130i \(0.337262\pi\)
\(140\) 0 0
\(141\) 3.87399 0.326249
\(142\) 1.88858 0.158486
\(143\) −12.3127 −1.02964
\(144\) 10.2243 0.852021
\(145\) 1.00000 0.0830455
\(146\) −22.5804 −1.86877
\(147\) 0 0
\(148\) −1.84367 −0.151549
\(149\) 2.77575 0.227398 0.113699 0.993515i \(-0.463730\pi\)
0.113699 + 0.993515i \(0.463730\pi\)
\(150\) 1.19394 0.0974845
\(151\) 1.79877 0.146382 0.0731909 0.997318i \(-0.476682\pi\)
0.0731909 + 0.997318i \(0.476682\pi\)
\(152\) 8.54420 0.693026
\(153\) 12.9419 1.04629
\(154\) 0 0
\(155\) −4.80606 −0.386032
\(156\) 0.463096 0.0370773
\(157\) −3.76845 −0.300755 −0.150378 0.988629i \(-0.548049\pi\)
−0.150378 + 0.988629i \(0.548049\pi\)
\(158\) 7.30536 0.581183
\(159\) 1.08840 0.0863155
\(160\) −1.09332 −0.0864346
\(161\) 0 0
\(162\) −5.29455 −0.415979
\(163\) 1.64244 0.128646 0.0643231 0.997929i \(-0.479511\pi\)
0.0643231 + 0.997929i \(0.479511\pi\)
\(164\) 2.18664 0.170748
\(165\) 3.35026 0.260818
\(166\) 6.54420 0.507928
\(167\) −8.08110 −0.625334 −0.312667 0.949863i \(-0.601222\pi\)
−0.312667 + 0.949863i \(0.601222\pi\)
\(168\) 0 0
\(169\) −4.22425 −0.324943
\(170\) −8.15633 −0.625562
\(171\) −7.50659 −0.574043
\(172\) −0.00587961 −0.000448316 0
\(173\) 7.73813 0.588320 0.294160 0.955756i \(-0.404960\pi\)
0.294160 + 0.955756i \(0.404960\pi\)
\(174\) −1.19394 −0.0905121
\(175\) 0 0
\(176\) −18.0811 −1.36291
\(177\) 10.7005 0.804301
\(178\) −5.35026 −0.401019
\(179\) −21.4010 −1.59959 −0.799795 0.600274i \(-0.795058\pi\)
−0.799795 + 0.600274i \(0.795058\pi\)
\(180\) 0.455802 0.0339735
\(181\) −15.2750 −1.13538 −0.567692 0.823241i \(-0.692164\pi\)
−0.567692 + 0.823241i \(0.692164\pi\)
\(182\) 0 0
\(183\) 7.16362 0.529550
\(184\) 4.93207 0.363597
\(185\) 9.50659 0.698938
\(186\) 5.73813 0.420740
\(187\) −22.8872 −1.67368
\(188\) −0.932071 −0.0679783
\(189\) 0 0
\(190\) 4.73084 0.343211
\(191\) 3.31994 0.240223 0.120111 0.992760i \(-0.461675\pi\)
0.120111 + 0.992760i \(0.461675\pi\)
\(192\) −5.70782 −0.411926
\(193\) −4.88129 −0.351363 −0.175681 0.984447i \(-0.556213\pi\)
−0.175681 + 0.984447i \(0.556213\pi\)
\(194\) −2.04491 −0.146816
\(195\) −2.38787 −0.170999
\(196\) 0 0
\(197\) −24.2374 −1.72685 −0.863423 0.504481i \(-0.831684\pi\)
−0.863423 + 0.504481i \(0.831684\pi\)
\(198\) 14.4690 1.02827
\(199\) −16.7513 −1.18747 −0.593734 0.804661i \(-0.702347\pi\)
−0.593734 + 0.804661i \(0.702347\pi\)
\(200\) 2.67513 0.189160
\(201\) −4.71037 −0.332244
\(202\) −19.2750 −1.35619
\(203\) 0 0
\(204\) 0.860818 0.0602693
\(205\) −11.2750 −0.787483
\(206\) 7.87987 0.549017
\(207\) −4.33312 −0.301173
\(208\) 12.8872 0.893564
\(209\) 13.2750 0.918254
\(210\) 0 0
\(211\) −25.3054 −1.74209 −0.871046 0.491201i \(-0.836558\pi\)
−0.871046 + 0.491201i \(0.836558\pi\)
\(212\) −0.261865 −0.0179850
\(213\) 1.02776 0.0704211
\(214\) 20.4690 1.39923
\(215\) 0.0303172 0.00206761
\(216\) 11.5369 0.784987
\(217\) 0 0
\(218\) 2.77575 0.187997
\(219\) −12.2882 −0.830360
\(220\) −0.806063 −0.0543448
\(221\) 16.3127 1.09731
\(222\) −11.3503 −0.761780
\(223\) −17.6932 −1.18483 −0.592413 0.805634i \(-0.701825\pi\)
−0.592413 + 0.805634i \(0.701825\pi\)
\(224\) 0 0
\(225\) −2.35026 −0.156684
\(226\) 17.4314 1.15952
\(227\) −26.8423 −1.78158 −0.890792 0.454412i \(-0.849849\pi\)
−0.890792 + 0.454412i \(0.849849\pi\)
\(228\) −0.499293 −0.0330665
\(229\) 17.2243 1.13821 0.569105 0.822265i \(-0.307290\pi\)
0.569105 + 0.822265i \(0.307290\pi\)
\(230\) 2.73084 0.180066
\(231\) 0 0
\(232\) −2.67513 −0.175631
\(233\) −9.07381 −0.594445 −0.297222 0.954808i \(-0.596060\pi\)
−0.297222 + 0.954808i \(0.596060\pi\)
\(234\) −10.3127 −0.674159
\(235\) 4.80606 0.313513
\(236\) −2.57452 −0.167587
\(237\) 3.97556 0.258241
\(238\) 0 0
\(239\) 20.4993 1.32599 0.662995 0.748624i \(-0.269285\pi\)
0.662995 + 0.748624i \(0.269285\pi\)
\(240\) −3.50659 −0.226349
\(241\) −5.47627 −0.352758 −0.176379 0.984322i \(-0.556438\pi\)
−0.176379 + 0.984322i \(0.556438\pi\)
\(242\) −9.29455 −0.597476
\(243\) −15.8192 −1.01480
\(244\) −1.72355 −0.110339
\(245\) 0 0
\(246\) 13.4617 0.858285
\(247\) −9.46168 −0.602032
\(248\) 12.8568 0.816411
\(249\) 3.56134 0.225691
\(250\) 1.48119 0.0936790
\(251\) 29.6180 1.86947 0.934736 0.355343i \(-0.115636\pi\)
0.934736 + 0.355343i \(0.115636\pi\)
\(252\) 0 0
\(253\) 7.66291 0.481763
\(254\) −21.1333 −1.32602
\(255\) −4.43866 −0.277960
\(256\) 4.61213 0.288258
\(257\) −17.6629 −1.10178 −0.550891 0.834577i \(-0.685712\pi\)
−0.550891 + 0.834577i \(0.685712\pi\)
\(258\) −0.0361968 −0.00225351
\(259\) 0 0
\(260\) 0.574515 0.0356299
\(261\) 2.35026 0.145478
\(262\) 8.73084 0.539393
\(263\) 27.3561 1.68685 0.843426 0.537245i \(-0.180535\pi\)
0.843426 + 0.537245i \(0.180535\pi\)
\(264\) −8.96239 −0.551597
\(265\) 1.35026 0.0829459
\(266\) 0 0
\(267\) −2.91160 −0.178187
\(268\) 1.13330 0.0692275
\(269\) −10.4993 −0.640153 −0.320077 0.947392i \(-0.603709\pi\)
−0.320077 + 0.947392i \(0.603709\pi\)
\(270\) 6.38787 0.388754
\(271\) 9.61801 0.584252 0.292126 0.956380i \(-0.405637\pi\)
0.292126 + 0.956380i \(0.405637\pi\)
\(272\) 23.9551 1.45249
\(273\) 0 0
\(274\) −27.0797 −1.63594
\(275\) 4.15633 0.250636
\(276\) −0.288213 −0.0173484
\(277\) 13.3503 0.802139 0.401070 0.916048i \(-0.368638\pi\)
0.401070 + 0.916048i \(0.368638\pi\)
\(278\) −17.0884 −1.02489
\(279\) −11.2955 −0.676244
\(280\) 0 0
\(281\) 20.4241 1.21840 0.609199 0.793017i \(-0.291491\pi\)
0.609199 + 0.793017i \(0.291491\pi\)
\(282\) −5.73813 −0.341701
\(283\) 8.02047 0.476767 0.238384 0.971171i \(-0.423382\pi\)
0.238384 + 0.971171i \(0.423382\pi\)
\(284\) −0.247277 −0.0146732
\(285\) 2.57452 0.152501
\(286\) 18.2374 1.07840
\(287\) 0 0
\(288\) −2.56959 −0.151415
\(289\) 13.3225 0.783676
\(290\) −1.48119 −0.0869787
\(291\) −1.11283 −0.0652355
\(292\) 2.95651 0.173017
\(293\) 23.3054 1.36151 0.680757 0.732510i \(-0.261651\pi\)
0.680757 + 0.732510i \(0.261651\pi\)
\(294\) 0 0
\(295\) 13.2750 0.772903
\(296\) −25.4314 −1.47817
\(297\) 17.9248 1.04010
\(298\) −4.11142 −0.238168
\(299\) −5.46168 −0.315857
\(300\) −0.156325 −0.00902544
\(301\) 0 0
\(302\) −2.66433 −0.153315
\(303\) −10.4894 −0.602603
\(304\) −13.8945 −0.796902
\(305\) 8.88717 0.508878
\(306\) −19.1695 −1.09585
\(307\) 6.73084 0.384149 0.192075 0.981380i \(-0.438478\pi\)
0.192075 + 0.981380i \(0.438478\pi\)
\(308\) 0 0
\(309\) 4.28821 0.243948
\(310\) 7.11871 0.404316
\(311\) 22.0567 1.25072 0.625359 0.780337i \(-0.284952\pi\)
0.625359 + 0.780337i \(0.284952\pi\)
\(312\) 6.38787 0.361642
\(313\) −5.03761 −0.284743 −0.142371 0.989813i \(-0.545473\pi\)
−0.142371 + 0.989813i \(0.545473\pi\)
\(314\) 5.58181 0.315000
\(315\) 0 0
\(316\) −0.956509 −0.0538078
\(317\) 34.2941 1.92615 0.963074 0.269237i \(-0.0867714\pi\)
0.963074 + 0.269237i \(0.0867714\pi\)
\(318\) −1.61213 −0.0904036
\(319\) −4.15633 −0.232710
\(320\) −7.08110 −0.395846
\(321\) 11.1392 0.621729
\(322\) 0 0
\(323\) −17.5877 −0.978605
\(324\) 0.693229 0.0385127
\(325\) −2.96239 −0.164324
\(326\) −2.43278 −0.134739
\(327\) 1.51056 0.0835340
\(328\) 30.1622 1.66543
\(329\) 0 0
\(330\) −4.96239 −0.273171
\(331\) −34.8324 −1.91456 −0.957281 0.289159i \(-0.906625\pi\)
−0.957281 + 0.289159i \(0.906625\pi\)
\(332\) −0.856849 −0.0470257
\(333\) 22.3430 1.22439
\(334\) 11.9697 0.654952
\(335\) −5.84367 −0.319274
\(336\) 0 0
\(337\) −17.6326 −0.960509 −0.480254 0.877129i \(-0.659456\pi\)
−0.480254 + 0.877129i \(0.659456\pi\)
\(338\) 6.25694 0.340333
\(339\) 9.48612 0.515215
\(340\) 1.06793 0.0579166
\(341\) 19.9756 1.08174
\(342\) 11.1187 0.601231
\(343\) 0 0
\(344\) −0.0811024 −0.00437275
\(345\) 1.48612 0.0800099
\(346\) −11.4617 −0.616184
\(347\) −3.11871 −0.167421 −0.0837107 0.996490i \(-0.526677\pi\)
−0.0837107 + 0.996490i \(0.526677\pi\)
\(348\) 0.156325 0.00837991
\(349\) 13.0738 0.699825 0.349912 0.936782i \(-0.386211\pi\)
0.349912 + 0.936782i \(0.386211\pi\)
\(350\) 0 0
\(351\) −12.7757 −0.681919
\(352\) 4.54420 0.242207
\(353\) −5.19982 −0.276758 −0.138379 0.990379i \(-0.544189\pi\)
−0.138379 + 0.990379i \(0.544189\pi\)
\(354\) −15.8496 −0.842394
\(355\) 1.27504 0.0676720
\(356\) 0.700523 0.0371277
\(357\) 0 0
\(358\) 31.6991 1.67535
\(359\) 30.4182 1.60541 0.802705 0.596376i \(-0.203393\pi\)
0.802705 + 0.596376i \(0.203393\pi\)
\(360\) 6.28726 0.331368
\(361\) −8.79877 −0.463093
\(362\) 22.6253 1.18916
\(363\) −5.05808 −0.265480
\(364\) 0 0
\(365\) −15.2447 −0.797945
\(366\) −10.6107 −0.554631
\(367\) −20.6556 −1.07821 −0.539107 0.842237i \(-0.681238\pi\)
−0.539107 + 0.842237i \(0.681238\pi\)
\(368\) −8.02047 −0.418096
\(369\) −26.4993 −1.37950
\(370\) −14.0811 −0.732042
\(371\) 0 0
\(372\) −0.751309 −0.0389535
\(373\) 11.0884 0.574135 0.287068 0.957910i \(-0.407320\pi\)
0.287068 + 0.957910i \(0.407320\pi\)
\(374\) 33.9003 1.75294
\(375\) 0.806063 0.0416249
\(376\) −12.8568 −0.663041
\(377\) 2.96239 0.152571
\(378\) 0 0
\(379\) 10.0811 0.517831 0.258916 0.965900i \(-0.416635\pi\)
0.258916 + 0.965900i \(0.416635\pi\)
\(380\) −0.619421 −0.0317756
\(381\) −11.5007 −0.589199
\(382\) −4.91748 −0.251600
\(383\) −16.3576 −0.835832 −0.417916 0.908486i \(-0.637239\pi\)
−0.417916 + 0.908486i \(0.637239\pi\)
\(384\) 10.2170 0.521382
\(385\) 0 0
\(386\) 7.23013 0.368004
\(387\) 0.0712533 0.00362201
\(388\) 0.267745 0.0135927
\(389\) 31.9003 1.61741 0.808706 0.588213i \(-0.200169\pi\)
0.808706 + 0.588213i \(0.200169\pi\)
\(390\) 3.53690 0.179098
\(391\) −10.1524 −0.513427
\(392\) 0 0
\(393\) 4.75131 0.239672
\(394\) 35.9003 1.80863
\(395\) 4.93207 0.248159
\(396\) −1.89446 −0.0952002
\(397\) −2.98683 −0.149905 −0.0749523 0.997187i \(-0.523880\pi\)
−0.0749523 + 0.997187i \(0.523880\pi\)
\(398\) 24.8119 1.24371
\(399\) 0 0
\(400\) −4.35026 −0.217513
\(401\) −21.9756 −1.09741 −0.548704 0.836017i \(-0.684878\pi\)
−0.548704 + 0.836017i \(0.684878\pi\)
\(402\) 6.97698 0.347980
\(403\) −14.2374 −0.709217
\(404\) 2.52373 0.125560
\(405\) −3.57452 −0.177619
\(406\) 0 0
\(407\) −39.5125 −1.95856
\(408\) 11.8740 0.587850
\(409\) 22.4387 1.10952 0.554760 0.832010i \(-0.312810\pi\)
0.554760 + 0.832010i \(0.312810\pi\)
\(410\) 16.7005 0.824780
\(411\) −14.7367 −0.726909
\(412\) −1.03173 −0.0508298
\(413\) 0 0
\(414\) 6.41819 0.315437
\(415\) 4.41819 0.216880
\(416\) −3.23884 −0.158797
\(417\) −9.29948 −0.455397
\(418\) −19.6629 −0.961744
\(419\) −10.3634 −0.506287 −0.253143 0.967429i \(-0.581464\pi\)
−0.253143 + 0.967429i \(0.581464\pi\)
\(420\) 0 0
\(421\) 34.0362 1.65882 0.829411 0.558638i \(-0.188676\pi\)
0.829411 + 0.558638i \(0.188676\pi\)
\(422\) 37.4821 1.82460
\(423\) 11.2955 0.549206
\(424\) −3.61213 −0.175420
\(425\) −5.50659 −0.267109
\(426\) −1.52232 −0.0737564
\(427\) 0 0
\(428\) −2.68006 −0.129545
\(429\) 9.92478 0.479173
\(430\) −0.0449056 −0.00216554
\(431\) 25.7743 1.24151 0.620753 0.784006i \(-0.286827\pi\)
0.620753 + 0.784006i \(0.286827\pi\)
\(432\) −18.7612 −0.902647
\(433\) −2.18076 −0.104801 −0.0524004 0.998626i \(-0.516687\pi\)
−0.0524004 + 0.998626i \(0.516687\pi\)
\(434\) 0 0
\(435\) −0.806063 −0.0386478
\(436\) −0.363436 −0.0174054
\(437\) 5.88858 0.281689
\(438\) 18.2012 0.869688
\(439\) 35.5125 1.69492 0.847459 0.530861i \(-0.178131\pi\)
0.847459 + 0.530861i \(0.178131\pi\)
\(440\) −11.1187 −0.530064
\(441\) 0 0
\(442\) −24.1622 −1.14928
\(443\) −4.34297 −0.206341 −0.103170 0.994664i \(-0.532899\pi\)
−0.103170 + 0.994664i \(0.532899\pi\)
\(444\) 1.48612 0.0705281
\(445\) −3.61213 −0.171231
\(446\) 26.2071 1.24094
\(447\) −2.23743 −0.105827
\(448\) 0 0
\(449\) 31.3357 1.47882 0.739411 0.673254i \(-0.235104\pi\)
0.739411 + 0.673254i \(0.235104\pi\)
\(450\) 3.48119 0.164105
\(451\) 46.8627 2.20668
\(452\) −2.28233 −0.107352
\(453\) −1.44992 −0.0681233
\(454\) 39.7586 1.86596
\(455\) 0 0
\(456\) −6.88717 −0.322521
\(457\) 34.3488 1.60677 0.803386 0.595459i \(-0.203030\pi\)
0.803386 + 0.595459i \(0.203030\pi\)
\(458\) −25.5125 −1.19212
\(459\) −23.7480 −1.10846
\(460\) −0.357556 −0.0166711
\(461\) −11.8641 −0.552568 −0.276284 0.961076i \(-0.589103\pi\)
−0.276284 + 0.961076i \(0.589103\pi\)
\(462\) 0 0
\(463\) 40.4953 1.88198 0.940989 0.338438i \(-0.109899\pi\)
0.940989 + 0.338438i \(0.109899\pi\)
\(464\) 4.35026 0.201956
\(465\) 3.87399 0.179652
\(466\) 13.4401 0.622599
\(467\) 30.2071 1.39782 0.698909 0.715210i \(-0.253669\pi\)
0.698909 + 0.715210i \(0.253669\pi\)
\(468\) 1.35026 0.0624159
\(469\) 0 0
\(470\) −7.11871 −0.328362
\(471\) 3.03761 0.139966
\(472\) −35.5125 −1.63459
\(473\) −0.126008 −0.00579385
\(474\) −5.88858 −0.270471
\(475\) 3.19394 0.146548
\(476\) 0 0
\(477\) 3.17347 0.145303
\(478\) −30.3634 −1.38879
\(479\) −0.0547547 −0.00250181 −0.00125090 0.999999i \(-0.500398\pi\)
−0.00125090 + 0.999999i \(0.500398\pi\)
\(480\) 0.881286 0.0402250
\(481\) 28.1622 1.28409
\(482\) 8.11142 0.369465
\(483\) 0 0
\(484\) 1.21696 0.0553163
\(485\) −1.38058 −0.0626889
\(486\) 23.4314 1.06287
\(487\) −0.881286 −0.0399349 −0.0199674 0.999801i \(-0.506356\pi\)
−0.0199674 + 0.999801i \(0.506356\pi\)
\(488\) −23.7743 −1.07621
\(489\) −1.32391 −0.0598695
\(490\) 0 0
\(491\) 41.0698 1.85346 0.926728 0.375733i \(-0.122609\pi\)
0.926728 + 0.375733i \(0.122609\pi\)
\(492\) −1.76257 −0.0794629
\(493\) 5.50659 0.248004
\(494\) 14.0146 0.630546
\(495\) 9.76845 0.439059
\(496\) −20.9076 −0.938780
\(497\) 0 0
\(498\) −5.27504 −0.236380
\(499\) 12.3733 0.553904 0.276952 0.960884i \(-0.410676\pi\)
0.276952 + 0.960884i \(0.410676\pi\)
\(500\) −0.193937 −0.00867311
\(501\) 6.51388 0.291019
\(502\) −43.8700 −1.95801
\(503\) 2.26774 0.101114 0.0505569 0.998721i \(-0.483900\pi\)
0.0505569 + 0.998721i \(0.483900\pi\)
\(504\) 0 0
\(505\) −13.0132 −0.579079
\(506\) −11.3503 −0.504581
\(507\) 3.40502 0.151222
\(508\) 2.76704 0.122767
\(509\) 10.9018 0.483212 0.241606 0.970374i \(-0.422326\pi\)
0.241606 + 0.970374i \(0.422326\pi\)
\(510\) 6.57452 0.291124
\(511\) 0 0
\(512\) 18.5188 0.818423
\(513\) 13.7743 0.608152
\(514\) 26.1622 1.15397
\(515\) 5.31994 0.234425
\(516\) 0.00473934 0.000208638 0
\(517\) −19.9756 −0.878524
\(518\) 0 0
\(519\) −6.23743 −0.273793
\(520\) 7.92478 0.347524
\(521\) 4.72496 0.207004 0.103502 0.994629i \(-0.466995\pi\)
0.103502 + 0.994629i \(0.466995\pi\)
\(522\) −3.48119 −0.152368
\(523\) 1.06793 0.0466973 0.0233486 0.999727i \(-0.492567\pi\)
0.0233486 + 0.999727i \(0.492567\pi\)
\(524\) −1.14315 −0.0499388
\(525\) 0 0
\(526\) −40.5198 −1.76675
\(527\) −26.4650 −1.15283
\(528\) 14.5745 0.634274
\(529\) −19.6009 −0.852211
\(530\) −2.00000 −0.0868744
\(531\) 31.1998 1.35396
\(532\) 0 0
\(533\) −33.4010 −1.44676
\(534\) 4.31265 0.186627
\(535\) 13.8192 0.597458
\(536\) 15.6326 0.675225
\(537\) 17.2506 0.744418
\(538\) 15.5515 0.670472
\(539\) 0 0
\(540\) −0.836381 −0.0359921
\(541\) −7.46168 −0.320803 −0.160401 0.987052i \(-0.551279\pi\)
−0.160401 + 0.987052i \(0.551279\pi\)
\(542\) −14.2461 −0.611924
\(543\) 12.3127 0.528386
\(544\) −6.02047 −0.258125
\(545\) 1.87399 0.0802730
\(546\) 0 0
\(547\) −38.9683 −1.66616 −0.833081 0.553150i \(-0.813425\pi\)
−0.833081 + 0.553150i \(0.813425\pi\)
\(548\) 3.54561 0.151461
\(549\) 20.8872 0.891443
\(550\) −6.15633 −0.262507
\(551\) −3.19394 −0.136066
\(552\) −3.97556 −0.169211
\(553\) 0 0
\(554\) −19.7743 −0.840131
\(555\) −7.66291 −0.325273
\(556\) 2.23743 0.0948881
\(557\) −22.9986 −0.974481 −0.487241 0.873268i \(-0.661997\pi\)
−0.487241 + 0.873268i \(0.661997\pi\)
\(558\) 16.7308 0.708273
\(559\) 0.0898112 0.00379861
\(560\) 0 0
\(561\) 18.4485 0.778897
\(562\) −30.2520 −1.27610
\(563\) −11.6688 −0.491781 −0.245890 0.969298i \(-0.579080\pi\)
−0.245890 + 0.969298i \(0.579080\pi\)
\(564\) 0.751309 0.0316358
\(565\) 11.7685 0.495102
\(566\) −11.8799 −0.499348
\(567\) 0 0
\(568\) −3.41090 −0.143118
\(569\) 11.3357 0.475216 0.237608 0.971361i \(-0.423637\pi\)
0.237608 + 0.971361i \(0.423637\pi\)
\(570\) −3.81336 −0.159724
\(571\) 27.1754 1.13725 0.568627 0.822595i \(-0.307475\pi\)
0.568627 + 0.822595i \(0.307475\pi\)
\(572\) −2.38787 −0.0998420
\(573\) −2.67609 −0.111795
\(574\) 0 0
\(575\) 1.84367 0.0768866
\(576\) −16.6424 −0.693435
\(577\) −22.5950 −0.940641 −0.470321 0.882496i \(-0.655862\pi\)
−0.470321 + 0.882496i \(0.655862\pi\)
\(578\) −19.7332 −0.820793
\(579\) 3.93463 0.163517
\(580\) 0.193937 0.00805278
\(581\) 0 0
\(582\) 1.64832 0.0683252
\(583\) −5.61213 −0.232431
\(584\) 40.7816 1.68756
\(585\) −6.96239 −0.287859
\(586\) −34.5198 −1.42600
\(587\) −9.31994 −0.384675 −0.192338 0.981329i \(-0.561607\pi\)
−0.192338 + 0.981329i \(0.561607\pi\)
\(588\) 0 0
\(589\) 15.3503 0.632497
\(590\) −19.6629 −0.809509
\(591\) 19.5369 0.803641
\(592\) 41.3561 1.69973
\(593\) 15.1246 0.621093 0.310546 0.950558i \(-0.399488\pi\)
0.310546 + 0.950558i \(0.399488\pi\)
\(594\) −26.5501 −1.08936
\(595\) 0 0
\(596\) 0.538319 0.0220504
\(597\) 13.5026 0.552625
\(598\) 8.08981 0.330817
\(599\) 4.09569 0.167345 0.0836727 0.996493i \(-0.473335\pi\)
0.0836727 + 0.996493i \(0.473335\pi\)
\(600\) −2.15633 −0.0880316
\(601\) −22.2276 −0.906682 −0.453341 0.891337i \(-0.649768\pi\)
−0.453341 + 0.891337i \(0.649768\pi\)
\(602\) 0 0
\(603\) −13.7342 −0.559298
\(604\) 0.348847 0.0141944
\(605\) −6.27504 −0.255117
\(606\) 15.5369 0.631144
\(607\) 48.2941 1.96020 0.980098 0.198512i \(-0.0636110\pi\)
0.980098 + 0.198512i \(0.0636110\pi\)
\(608\) 3.49200 0.141619
\(609\) 0 0
\(610\) −13.1636 −0.532979
\(611\) 14.2374 0.575985
\(612\) 2.50991 0.101457
\(613\) −9.74798 −0.393717 −0.196859 0.980432i \(-0.563074\pi\)
−0.196859 + 0.980432i \(0.563074\pi\)
\(614\) −9.96968 −0.402344
\(615\) 9.08840 0.366480
\(616\) 0 0
\(617\) 18.2170 0.733387 0.366694 0.930342i \(-0.380490\pi\)
0.366694 + 0.930342i \(0.380490\pi\)
\(618\) −6.35168 −0.255502
\(619\) −25.0943 −1.00862 −0.504312 0.863521i \(-0.668254\pi\)
−0.504312 + 0.863521i \(0.668254\pi\)
\(620\) −0.932071 −0.0374329
\(621\) 7.95112 0.319068
\(622\) −32.6702 −1.30996
\(623\) 0 0
\(624\) −10.3879 −0.415848
\(625\) 1.00000 0.0400000
\(626\) 7.46168 0.298229
\(627\) −10.7005 −0.427338
\(628\) −0.730841 −0.0291637
\(629\) 52.3488 2.08729
\(630\) 0 0
\(631\) 21.4617 0.854376 0.427188 0.904163i \(-0.359504\pi\)
0.427188 + 0.904163i \(0.359504\pi\)
\(632\) −13.1939 −0.524827
\(633\) 20.3977 0.810737
\(634\) −50.7962 −2.01738
\(635\) −14.2677 −0.566198
\(636\) 0.211080 0.00836986
\(637\) 0 0
\(638\) 6.15633 0.243731
\(639\) 2.99668 0.118547
\(640\) 12.6751 0.501029
\(641\) 3.17347 0.125344 0.0626722 0.998034i \(-0.480038\pi\)
0.0626722 + 0.998034i \(0.480038\pi\)
\(642\) −16.4993 −0.651175
\(643\) 2.74069 0.108082 0.0540411 0.998539i \(-0.482790\pi\)
0.0540411 + 0.998539i \(0.482790\pi\)
\(644\) 0 0
\(645\) −0.0244376 −0.000962228 0
\(646\) 26.0508 1.02495
\(647\) −6.34297 −0.249368 −0.124684 0.992197i \(-0.539792\pi\)
−0.124684 + 0.992197i \(0.539792\pi\)
\(648\) 9.56230 0.375642
\(649\) −55.1754 −2.16582
\(650\) 4.38787 0.172107
\(651\) 0 0
\(652\) 0.318530 0.0124746
\(653\) 4.08110 0.159706 0.0798529 0.996807i \(-0.474555\pi\)
0.0798529 + 0.996807i \(0.474555\pi\)
\(654\) −2.23743 −0.0874903
\(655\) 5.89446 0.230316
\(656\) −49.0494 −1.91506
\(657\) −35.8291 −1.39783
\(658\) 0 0
\(659\) 9.58181 0.373254 0.186627 0.982431i \(-0.440244\pi\)
0.186627 + 0.982431i \(0.440244\pi\)
\(660\) 0.649738 0.0252910
\(661\) 27.5271 1.07068 0.535339 0.844637i \(-0.320184\pi\)
0.535339 + 0.844637i \(0.320184\pi\)
\(662\) 51.5936 2.00524
\(663\) −13.1490 −0.510666
\(664\) −11.8192 −0.458675
\(665\) 0 0
\(666\) −33.0943 −1.28238
\(667\) −1.84367 −0.0713874
\(668\) −1.56722 −0.0606376
\(669\) 14.2619 0.551396
\(670\) 8.65562 0.334396
\(671\) −36.9380 −1.42597
\(672\) 0 0
\(673\) 3.13727 0.120933 0.0604665 0.998170i \(-0.480741\pi\)
0.0604665 + 0.998170i \(0.480741\pi\)
\(674\) 26.1173 1.00600
\(675\) 4.31265 0.165994
\(676\) −0.819237 −0.0315091
\(677\) 46.2579 1.77784 0.888918 0.458067i \(-0.151458\pi\)
0.888918 + 0.458067i \(0.151458\pi\)
\(678\) −14.0508 −0.539617
\(679\) 0 0
\(680\) 14.7308 0.564902
\(681\) 21.6366 0.829115
\(682\) −29.5877 −1.13297
\(683\) −9.01905 −0.345104 −0.172552 0.985000i \(-0.555201\pi\)
−0.172552 + 0.985000i \(0.555201\pi\)
\(684\) −1.45580 −0.0556640
\(685\) −18.2823 −0.698532
\(686\) 0 0
\(687\) −13.8838 −0.529702
\(688\) 0.131888 0.00502817
\(689\) 4.00000 0.152388
\(690\) −2.20123 −0.0837994
\(691\) 50.0625 1.90447 0.952234 0.305368i \(-0.0987794\pi\)
0.952234 + 0.305368i \(0.0987794\pi\)
\(692\) 1.50071 0.0570483
\(693\) 0 0
\(694\) 4.61942 0.175351
\(695\) −11.5369 −0.437620
\(696\) 2.15633 0.0817353
\(697\) −62.0870 −2.35171
\(698\) −19.3649 −0.732970
\(699\) 7.31406 0.276643
\(700\) 0 0
\(701\) 45.3014 1.71101 0.855505 0.517795i \(-0.173247\pi\)
0.855505 + 0.517795i \(0.173247\pi\)
\(702\) 18.9234 0.714216
\(703\) −30.3634 −1.14518
\(704\) 29.4314 1.10924
\(705\) −3.87399 −0.145903
\(706\) 7.70194 0.289866
\(707\) 0 0
\(708\) 2.07522 0.0779916
\(709\) −3.27504 −0.122997 −0.0614983 0.998107i \(-0.519588\pi\)
−0.0614983 + 0.998107i \(0.519588\pi\)
\(710\) −1.88858 −0.0708772
\(711\) 11.5917 0.434721
\(712\) 9.66291 0.362133
\(713\) 8.86082 0.331840
\(714\) 0 0
\(715\) 12.3127 0.460467
\(716\) −4.15045 −0.155109
\(717\) −16.5237 −0.617090
\(718\) −45.0553 −1.68145
\(719\) −27.7235 −1.03391 −0.516957 0.856011i \(-0.672935\pi\)
−0.516957 + 0.856011i \(0.672935\pi\)
\(720\) −10.2243 −0.381035
\(721\) 0 0
\(722\) 13.0327 0.485026
\(723\) 4.41422 0.164167
\(724\) −2.96239 −0.110096
\(725\) −1.00000 −0.0371391
\(726\) 7.49200 0.278054
\(727\) 26.8930 0.997408 0.498704 0.866772i \(-0.333810\pi\)
0.498704 + 0.866772i \(0.333810\pi\)
\(728\) 0 0
\(729\) 2.02776 0.0751023
\(730\) 22.5804 0.835738
\(731\) 0.166944 0.00617465
\(732\) 1.38929 0.0513496
\(733\) −3.17935 −0.117432 −0.0587160 0.998275i \(-0.518701\pi\)
−0.0587160 + 0.998275i \(0.518701\pi\)
\(734\) 30.5950 1.12928
\(735\) 0 0
\(736\) 2.01573 0.0743007
\(737\) 24.2882 0.894668
\(738\) 39.2506 1.44483
\(739\) −29.7440 −1.09415 −0.547076 0.837083i \(-0.684259\pi\)
−0.547076 + 0.837083i \(0.684259\pi\)
\(740\) 1.84367 0.0677748
\(741\) 7.62672 0.280174
\(742\) 0 0
\(743\) −4.34297 −0.159328 −0.0796640 0.996822i \(-0.525385\pi\)
−0.0796640 + 0.996822i \(0.525385\pi\)
\(744\) −10.3634 −0.379942
\(745\) −2.77575 −0.101695
\(746\) −16.4241 −0.601328
\(747\) 10.3839 0.379927
\(748\) −4.43866 −0.162293
\(749\) 0 0
\(750\) −1.19394 −0.0435964
\(751\) 22.5804 0.823970 0.411985 0.911191i \(-0.364836\pi\)
0.411985 + 0.911191i \(0.364836\pi\)
\(752\) 20.9076 0.762423
\(753\) −23.8740 −0.870017
\(754\) −4.38787 −0.159797
\(755\) −1.79877 −0.0654639
\(756\) 0 0
\(757\) 9.88461 0.359262 0.179631 0.983734i \(-0.442510\pi\)
0.179631 + 0.983734i \(0.442510\pi\)
\(758\) −14.9321 −0.542357
\(759\) −6.17679 −0.224203
\(760\) −8.54420 −0.309931
\(761\) −13.6991 −0.496592 −0.248296 0.968684i \(-0.579871\pi\)
−0.248296 + 0.968684i \(0.579871\pi\)
\(762\) 17.0348 0.617105
\(763\) 0 0
\(764\) 0.643859 0.0232940
\(765\) −12.9419 −0.467916
\(766\) 24.2287 0.875419
\(767\) 39.3258 1.41997
\(768\) −3.71767 −0.134150
\(769\) −25.0132 −0.901998 −0.450999 0.892524i \(-0.648932\pi\)
−0.450999 + 0.892524i \(0.648932\pi\)
\(770\) 0 0
\(771\) 14.2374 0.512748
\(772\) −0.946660 −0.0340710
\(773\) 35.9062 1.29146 0.645728 0.763567i \(-0.276554\pi\)
0.645728 + 0.763567i \(0.276554\pi\)
\(774\) −0.105540 −0.00379356
\(775\) 4.80606 0.172639
\(776\) 3.69323 0.132579
\(777\) 0 0
\(778\) −47.2506 −1.69402
\(779\) 36.0118 1.29026
\(780\) −0.463096 −0.0165815
\(781\) −5.29948 −0.189630
\(782\) 15.0376 0.537744
\(783\) −4.31265 −0.154122
\(784\) 0 0
\(785\) 3.76845 0.134502
\(786\) −7.03761 −0.251023
\(787\) −50.3839 −1.79599 −0.897996 0.440003i \(-0.854977\pi\)
−0.897996 + 0.440003i \(0.854977\pi\)
\(788\) −4.70052 −0.167449
\(789\) −22.0508 −0.785029
\(790\) −7.30536 −0.259913
\(791\) 0 0
\(792\) −26.1319 −0.928556
\(793\) 26.3272 0.934908
\(794\) 4.42407 0.157004
\(795\) −1.08840 −0.0386014
\(796\) −3.24869 −0.115147
\(797\) 5.69323 0.201665 0.100832 0.994903i \(-0.467849\pi\)
0.100832 + 0.994903i \(0.467849\pi\)
\(798\) 0 0
\(799\) 26.4650 0.936265
\(800\) 1.09332 0.0386547
\(801\) −8.48944 −0.299960
\(802\) 32.5501 1.14938
\(803\) 63.3620 2.23600
\(804\) −0.913513 −0.0322171
\(805\) 0 0
\(806\) 21.0884 0.742807
\(807\) 8.46310 0.297915
\(808\) 34.8119 1.22468
\(809\) −7.76257 −0.272918 −0.136459 0.990646i \(-0.543572\pi\)
−0.136459 + 0.990646i \(0.543572\pi\)
\(810\) 5.29455 0.186032
\(811\) 26.4894 0.930170 0.465085 0.885266i \(-0.346024\pi\)
0.465085 + 0.885266i \(0.346024\pi\)
\(812\) 0 0
\(813\) −7.75272 −0.271900
\(814\) 58.5256 2.05132
\(815\) −1.64244 −0.0575323
\(816\) −19.3093 −0.675962
\(817\) −0.0968311 −0.00338769
\(818\) −33.2360 −1.16207
\(819\) 0 0
\(820\) −2.18664 −0.0763609
\(821\) 25.4763 0.889128 0.444564 0.895747i \(-0.353359\pi\)
0.444564 + 0.895747i \(0.353359\pi\)
\(822\) 21.8279 0.761337
\(823\) −9.22028 −0.321399 −0.160699 0.987003i \(-0.551375\pi\)
−0.160699 + 0.987003i \(0.551375\pi\)
\(824\) −14.2315 −0.495779
\(825\) −3.35026 −0.116641
\(826\) 0 0
\(827\) 24.5343 0.853143 0.426571 0.904454i \(-0.359721\pi\)
0.426571 + 0.904454i \(0.359721\pi\)
\(828\) −0.840350 −0.0292042
\(829\) −0.201231 −0.00698903 −0.00349452 0.999994i \(-0.501112\pi\)
−0.00349452 + 0.999994i \(0.501112\pi\)
\(830\) −6.54420 −0.227152
\(831\) −10.7612 −0.373300
\(832\) −20.9770 −0.727246
\(833\) 0 0
\(834\) 13.7743 0.476966
\(835\) 8.08110 0.279658
\(836\) 2.57452 0.0890415
\(837\) 20.7269 0.716425
\(838\) 15.3503 0.530266
\(839\) −1.45580 −0.0502599 −0.0251299 0.999684i \(-0.508000\pi\)
−0.0251299 + 0.999684i \(0.508000\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −50.4142 −1.73739
\(843\) −16.4631 −0.567019
\(844\) −4.90763 −0.168928
\(845\) 4.22425 0.145319
\(846\) −16.7308 −0.575218
\(847\) 0 0
\(848\) 5.87399 0.201714
\(849\) −6.46501 −0.221878
\(850\) 8.15633 0.279760
\(851\) −17.5271 −0.600820
\(852\) 0.199321 0.00682861
\(853\) −43.1793 −1.47843 −0.739216 0.673468i \(-0.764804\pi\)
−0.739216 + 0.673468i \(0.764804\pi\)
\(854\) 0 0
\(855\) 7.50659 0.256720
\(856\) −36.9683 −1.26355
\(857\) 20.9887 0.716962 0.358481 0.933537i \(-0.383295\pi\)
0.358481 + 0.933537i \(0.383295\pi\)
\(858\) −14.7005 −0.501868
\(859\) 49.4069 1.68574 0.842871 0.538115i \(-0.180863\pi\)
0.842871 + 0.538115i \(0.180863\pi\)
\(860\) 0.00587961 0.000200493 0
\(861\) 0 0
\(862\) −38.1768 −1.30031
\(863\) 56.6820 1.92948 0.964738 0.263211i \(-0.0847816\pi\)
0.964738 + 0.263211i \(0.0847816\pi\)
\(864\) 4.71511 0.160411
\(865\) −7.73813 −0.263104
\(866\) 3.23013 0.109764
\(867\) −10.7388 −0.364708
\(868\) 0 0
\(869\) −20.4993 −0.695391
\(870\) 1.19394 0.0404782
\(871\) −17.3112 −0.586569
\(872\) −5.01317 −0.169767
\(873\) −3.24472 −0.109817
\(874\) −8.72213 −0.295031
\(875\) 0 0
\(876\) −2.38313 −0.0805186
\(877\) −13.1998 −0.445726 −0.222863 0.974850i \(-0.571540\pi\)
−0.222863 + 0.974850i \(0.571540\pi\)
\(878\) −52.6009 −1.77519
\(879\) −18.7856 −0.633622
\(880\) 18.0811 0.609514
\(881\) −6.37802 −0.214881 −0.107441 0.994212i \(-0.534266\pi\)
−0.107441 + 0.994212i \(0.534266\pi\)
\(882\) 0 0
\(883\) 48.6213 1.63624 0.818119 0.575049i \(-0.195017\pi\)
0.818119 + 0.575049i \(0.195017\pi\)
\(884\) 3.16362 0.106404
\(885\) −10.7005 −0.359694
\(886\) 6.43278 0.216113
\(887\) 15.0317 0.504716 0.252358 0.967634i \(-0.418794\pi\)
0.252358 + 0.967634i \(0.418794\pi\)
\(888\) 20.4993 0.687911
\(889\) 0 0
\(890\) 5.35026 0.179341
\(891\) 14.8568 0.497723
\(892\) −3.43136 −0.114891
\(893\) −15.3503 −0.513677
\(894\) 3.31406 0.110839
\(895\) 21.4010 0.715358
\(896\) 0 0
\(897\) 4.40246 0.146994
\(898\) −46.4142 −1.54886
\(899\) −4.80606 −0.160291
\(900\) −0.455802 −0.0151934
\(901\) 7.43533 0.247707
\(902\) −69.4128 −2.31119
\(903\) 0 0
\(904\) −31.4821 −1.04708
\(905\) 15.2750 0.507759
\(906\) 2.14762 0.0713498
\(907\) −0.342968 −0.0113880 −0.00569402 0.999984i \(-0.501812\pi\)
−0.00569402 + 0.999984i \(0.501812\pi\)
\(908\) −5.20570 −0.172757
\(909\) −30.5844 −1.01442
\(910\) 0 0
\(911\) 20.9076 0.692701 0.346350 0.938105i \(-0.387421\pi\)
0.346350 + 0.938105i \(0.387421\pi\)
\(912\) 11.1998 0.370863
\(913\) −18.3634 −0.607741
\(914\) −50.8773 −1.68287
\(915\) −7.16362 −0.236822
\(916\) 3.34041 0.110370
\(917\) 0 0
\(918\) 35.1754 1.16096
\(919\) −1.90034 −0.0626864 −0.0313432 0.999509i \(-0.509978\pi\)
−0.0313432 + 0.999509i \(0.509978\pi\)
\(920\) −4.93207 −0.162606
\(921\) −5.42548 −0.178776
\(922\) 17.5731 0.578739
\(923\) 3.77716 0.124327
\(924\) 0 0
\(925\) −9.50659 −0.312575
\(926\) −59.9814 −1.97111
\(927\) 12.5033 0.410661
\(928\) −1.09332 −0.0358900
\(929\) −39.3522 −1.29110 −0.645551 0.763717i \(-0.723372\pi\)
−0.645551 + 0.763717i \(0.723372\pi\)
\(930\) −5.73813 −0.188161
\(931\) 0 0
\(932\) −1.75974 −0.0576423
\(933\) −17.7791 −0.582061
\(934\) −44.7426 −1.46402
\(935\) 22.8872 0.748490
\(936\) 18.6253 0.608787
\(937\) 6.37802 0.208361 0.104180 0.994558i \(-0.466778\pi\)
0.104180 + 0.994558i \(0.466778\pi\)
\(938\) 0 0
\(939\) 4.06063 0.132514
\(940\) 0.932071 0.0304008
\(941\) 26.6253 0.867960 0.433980 0.900923i \(-0.357109\pi\)
0.433980 + 0.900923i \(0.357109\pi\)
\(942\) −4.49929 −0.146595
\(943\) 20.7875 0.676934
\(944\) 57.7499 1.87960
\(945\) 0 0
\(946\) 0.186642 0.00606827
\(947\) −12.2823 −0.399122 −0.199561 0.979885i \(-0.563952\pi\)
−0.199561 + 0.979885i \(0.563952\pi\)
\(948\) 0.771007 0.0250411
\(949\) −45.1608 −1.46598
\(950\) −4.73084 −0.153489
\(951\) −27.6432 −0.896393
\(952\) 0 0
\(953\) 0.821792 0.0266205 0.0133102 0.999911i \(-0.495763\pi\)
0.0133102 + 0.999911i \(0.495763\pi\)
\(954\) −4.70052 −0.152185
\(955\) −3.31994 −0.107431
\(956\) 3.97556 0.128579
\(957\) 3.35026 0.108299
\(958\) 0.0811024 0.00262030
\(959\) 0 0
\(960\) 5.70782 0.184219
\(961\) −7.90175 −0.254895
\(962\) −41.7137 −1.34490
\(963\) 32.4788 1.04662
\(964\) −1.06205 −0.0342063
\(965\) 4.88129 0.157134
\(966\) 0 0
\(967\) −37.4314 −1.20371 −0.601856 0.798605i \(-0.705572\pi\)
−0.601856 + 0.798605i \(0.705572\pi\)
\(968\) 16.7866 0.539540
\(969\) 14.1768 0.455424
\(970\) 2.04491 0.0656580
\(971\) 8.71625 0.279718 0.139859 0.990171i \(-0.455335\pi\)
0.139859 + 0.990171i \(0.455335\pi\)
\(972\) −3.06793 −0.0984039
\(973\) 0 0
\(974\) 1.30536 0.0418263
\(975\) 2.38787 0.0764731
\(976\) 38.6615 1.23752
\(977\) −33.7645 −1.08022 −0.540111 0.841594i \(-0.681618\pi\)
−0.540111 + 0.841594i \(0.681618\pi\)
\(978\) 1.96097 0.0627050
\(979\) 15.0132 0.479823
\(980\) 0 0
\(981\) 4.40437 0.140621
\(982\) −60.8324 −1.94124
\(983\) −43.6082 −1.39088 −0.695442 0.718582i \(-0.744791\pi\)
−0.695442 + 0.718582i \(0.744791\pi\)
\(984\) −24.3127 −0.775059
\(985\) 24.2374 0.772269
\(986\) −8.15633 −0.259750
\(987\) 0 0
\(988\) −1.83497 −0.0583780
\(989\) −0.0558950 −0.00177736
\(990\) −14.4690 −0.459854
\(991\) −52.9741 −1.68278 −0.841390 0.540429i \(-0.818262\pi\)
−0.841390 + 0.540429i \(0.818262\pi\)
\(992\) 5.25457 0.166833
\(993\) 28.0771 0.891001
\(994\) 0 0
\(995\) 16.7513 0.531052
\(996\) 0.690674 0.0218849
\(997\) −13.6326 −0.431749 −0.215874 0.976421i \(-0.569260\pi\)
−0.215874 + 0.976421i \(0.569260\pi\)
\(998\) −18.3272 −0.580139
\(999\) −40.9986 −1.29714
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 7105.2.a.o.1.1 3
7.6 odd 2 145.2.a.c.1.1 3
21.20 even 2 1305.2.a.p.1.3 3
28.27 even 2 2320.2.a.n.1.2 3
35.13 even 4 725.2.b.e.349.5 6
35.27 even 4 725.2.b.e.349.2 6
35.34 odd 2 725.2.a.e.1.3 3
56.13 odd 2 9280.2.a.bj.1.2 3
56.27 even 2 9280.2.a.br.1.2 3
105.104 even 2 6525.2.a.be.1.1 3
203.202 odd 2 4205.2.a.f.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
145.2.a.c.1.1 3 7.6 odd 2
725.2.a.e.1.3 3 35.34 odd 2
725.2.b.e.349.2 6 35.27 even 4
725.2.b.e.349.5 6 35.13 even 4
1305.2.a.p.1.3 3 21.20 even 2
2320.2.a.n.1.2 3 28.27 even 2
4205.2.a.f.1.3 3 203.202 odd 2
6525.2.a.be.1.1 3 105.104 even 2
7105.2.a.o.1.1 3 1.1 even 1 trivial
9280.2.a.bj.1.2 3 56.13 odd 2
9280.2.a.br.1.2 3 56.27 even 2