Properties

Label 7105.2.a.p.1.3
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 1.3
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)
 
\(f(q)\) \(=\) \(q+2.67513 q^{2} +0.806063 q^{3} +5.15633 q^{4} +1.00000 q^{5} +2.15633 q^{6} +8.44358 q^{8} -2.35026 q^{9} +O(q^{10})\) \(q+2.67513 q^{2} +0.806063 q^{3} +5.15633 q^{4} +1.00000 q^{5} +2.15633 q^{6} +8.44358 q^{8} -2.35026 q^{9} +2.67513 q^{10} +2.80606 q^{11} +4.15633 q^{12} -1.35026 q^{13} +0.806063 q^{15} +12.2750 q^{16} +7.11871 q^{17} -6.28726 q^{18} -3.76845 q^{19} +5.15633 q^{20} +7.50659 q^{22} +4.80606 q^{23} +6.80606 q^{24} +1.00000 q^{25} -3.61213 q^{26} -4.31265 q^{27} +1.00000 q^{29} +2.15633 q^{30} -0.231548 q^{31} +15.9502 q^{32} +2.26187 q^{33} +19.0435 q^{34} -12.1187 q^{36} -5.50659 q^{37} -10.0811 q^{38} -1.08840 q^{39} +8.44358 q^{40} +6.96239 q^{41} -3.19394 q^{43} +14.4690 q^{44} -2.35026 q^{45} +12.8568 q^{46} -6.41819 q^{47} +9.89446 q^{48} +2.67513 q^{50} +5.73813 q^{51} -6.96239 q^{52} +6.96239 q^{53} -11.5369 q^{54} +2.80606 q^{55} -3.03761 q^{57} +2.67513 q^{58} +2.57452 q^{59} +4.15633 q^{60} -5.35026 q^{61} -0.619421 q^{62} +18.1187 q^{64} -1.35026 q^{65} +6.05079 q^{66} -3.19394 q^{67} +36.7064 q^{68} +3.87399 q^{69} +11.3503 q^{71} -19.8446 q^{72} +11.2447 q^{73} -14.7308 q^{74} +0.806063 q^{75} -19.4314 q^{76} -2.91160 q^{78} -4.73084 q^{79} +12.2750 q^{80} +3.57452 q^{81} +18.6253 q^{82} -2.54420 q^{83} +7.11871 q^{85} -8.54420 q^{86} +0.806063 q^{87} +23.6932 q^{88} -14.3127 q^{89} -6.28726 q^{90} +24.7816 q^{92} -0.186642 q^{93} -17.1695 q^{94} -3.76845 q^{95} +12.8568 q^{96} +1.53102 q^{97} -6.59498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{2} + 2 q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{2} + 2 q^{3} + 5 q^{4} + 3 q^{5} - 4 q^{6} + 9 q^{8} + 3 q^{9} + 3 q^{10} + 8 q^{11} + 2 q^{12} + 6 q^{13} + 2 q^{15} + 5 q^{16} - 13 q^{18} + 5 q^{20} + 2 q^{22} + 14 q^{23} + 20 q^{24} + 3 q^{25} - 10 q^{26} + 8 q^{27} + 3 q^{29} - 4 q^{30} - 12 q^{31} + 11 q^{32} + 16 q^{33} + 14 q^{34} - 15 q^{36} + 4 q^{37} + 2 q^{38} + 16 q^{39} + 9 q^{40} + 10 q^{41} - 10 q^{43} + 12 q^{44} + 3 q^{45} + 8 q^{46} - 18 q^{47} + 10 q^{48} + 3 q^{50} + 8 q^{51} - 10 q^{52} + 10 q^{53} - 12 q^{54} + 8 q^{55} - 20 q^{57} + 3 q^{58} - 4 q^{59} + 2 q^{60} - 6 q^{61} - 14 q^{62} + 33 q^{64} + 6 q^{65} - 12 q^{66} - 10 q^{67} + 36 q^{68} + 20 q^{69} + 24 q^{71} - 3 q^{72} + 4 q^{73} - 22 q^{74} + 2 q^{75} - 16 q^{76} - 28 q^{78} + 8 q^{79} + 5 q^{80} - q^{81} + 14 q^{82} + 2 q^{83} - 16 q^{86} + 2 q^{87} + 38 q^{88} - 22 q^{89} - 13 q^{90} + 22 q^{92} + 12 q^{93} + 8 q^{96} + 36 q^{97} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67513 1.89160 0.945802 0.324745i \(-0.105279\pi\)
0.945802 + 0.324745i \(0.105279\pi\)
\(3\) 0.806063 0.465381 0.232690 0.972551i \(-0.425247\pi\)
0.232690 + 0.972551i \(0.425247\pi\)
\(4\) 5.15633 2.57816
\(5\) 1.00000 0.447214
\(6\) 2.15633 0.880316
\(7\) 0 0
\(8\) 8.44358 2.98526
\(9\) −2.35026 −0.783421
\(10\) 2.67513 0.845951
\(11\) 2.80606 0.846060 0.423030 0.906116i \(-0.360966\pi\)
0.423030 + 0.906116i \(0.360966\pi\)
\(12\) 4.15633 1.19983
\(13\) −1.35026 −0.374495 −0.187248 0.982313i \(-0.559957\pi\)
−0.187248 + 0.982313i \(0.559957\pi\)
\(14\) 0 0
\(15\) 0.806063 0.208125
\(16\) 12.2750 3.06876
\(17\) 7.11871 1.72654 0.863271 0.504741i \(-0.168412\pi\)
0.863271 + 0.504741i \(0.168412\pi\)
\(18\) −6.28726 −1.48192
\(19\) −3.76845 −0.864542 −0.432271 0.901744i \(-0.642288\pi\)
−0.432271 + 0.901744i \(0.642288\pi\)
\(20\) 5.15633 1.15299
\(21\) 0 0
\(22\) 7.50659 1.60041
\(23\) 4.80606 1.00213 0.501067 0.865409i \(-0.332941\pi\)
0.501067 + 0.865409i \(0.332941\pi\)
\(24\) 6.80606 1.38928
\(25\) 1.00000 0.200000
\(26\) −3.61213 −0.708396
\(27\) −4.31265 −0.829970
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 2.15633 0.393689
\(31\) −0.231548 −0.0415872 −0.0207936 0.999784i \(-0.506619\pi\)
−0.0207936 + 0.999784i \(0.506619\pi\)
\(32\) 15.9502 2.81962
\(33\) 2.26187 0.393740
\(34\) 19.0435 3.26593
\(35\) 0 0
\(36\) −12.1187 −2.01979
\(37\) −5.50659 −0.905277 −0.452639 0.891694i \(-0.649517\pi\)
−0.452639 + 0.891694i \(0.649517\pi\)
\(38\) −10.0811 −1.63537
\(39\) −1.08840 −0.174283
\(40\) 8.44358 1.33505
\(41\) 6.96239 1.08734 0.543671 0.839298i \(-0.317034\pi\)
0.543671 + 0.839298i \(0.317034\pi\)
\(42\) 0 0
\(43\) −3.19394 −0.487071 −0.243535 0.969892i \(-0.578307\pi\)
−0.243535 + 0.969892i \(0.578307\pi\)
\(44\) 14.4690 2.18128
\(45\) −2.35026 −0.350356
\(46\) 12.8568 1.89564
\(47\) −6.41819 −0.936189 −0.468095 0.883678i \(-0.655059\pi\)
−0.468095 + 0.883678i \(0.655059\pi\)
\(48\) 9.89446 1.42814
\(49\) 0 0
\(50\) 2.67513 0.378321
\(51\) 5.73813 0.803500
\(52\) −6.96239 −0.965510
\(53\) 6.96239 0.956358 0.478179 0.878263i \(-0.341297\pi\)
0.478179 + 0.878263i \(0.341297\pi\)
\(54\) −11.5369 −1.56997
\(55\) 2.80606 0.378370
\(56\) 0 0
\(57\) −3.03761 −0.402341
\(58\) 2.67513 0.351262
\(59\) 2.57452 0.335173 0.167587 0.985857i \(-0.446403\pi\)
0.167587 + 0.985857i \(0.446403\pi\)
\(60\) 4.15633 0.536579
\(61\) −5.35026 −0.685031 −0.342515 0.939512i \(-0.611279\pi\)
−0.342515 + 0.939512i \(0.611279\pi\)
\(62\) −0.619421 −0.0786666
\(63\) 0 0
\(64\) 18.1187 2.26484
\(65\) −1.35026 −0.167479
\(66\) 6.05079 0.744800
\(67\) −3.19394 −0.390201 −0.195101 0.980783i \(-0.562503\pi\)
−0.195101 + 0.980783i \(0.562503\pi\)
\(68\) 36.7064 4.45131
\(69\) 3.87399 0.466374
\(70\) 0 0
\(71\) 11.3503 1.34703 0.673514 0.739174i \(-0.264784\pi\)
0.673514 + 0.739174i \(0.264784\pi\)
\(72\) −19.8446 −2.33871
\(73\) 11.2447 1.31610 0.658048 0.752976i \(-0.271383\pi\)
0.658048 + 0.752976i \(0.271383\pi\)
\(74\) −14.7308 −1.71243
\(75\) 0.806063 0.0930762
\(76\) −19.4314 −2.22893
\(77\) 0 0
\(78\) −2.91160 −0.329674
\(79\) −4.73084 −0.532261 −0.266131 0.963937i \(-0.585745\pi\)
−0.266131 + 0.963937i \(0.585745\pi\)
\(80\) 12.2750 1.37239
\(81\) 3.57452 0.397168
\(82\) 18.6253 2.05682
\(83\) −2.54420 −0.279262 −0.139631 0.990204i \(-0.544592\pi\)
−0.139631 + 0.990204i \(0.544592\pi\)
\(84\) 0 0
\(85\) 7.11871 0.772133
\(86\) −8.54420 −0.921345
\(87\) 0.806063 0.0864191
\(88\) 23.6932 2.52571
\(89\) −14.3127 −1.51714 −0.758569 0.651593i \(-0.774101\pi\)
−0.758569 + 0.651593i \(0.774101\pi\)
\(90\) −6.28726 −0.662735
\(91\) 0 0
\(92\) 24.7816 2.58366
\(93\) −0.186642 −0.0193539
\(94\) −17.1695 −1.77090
\(95\) −3.76845 −0.386635
\(96\) 12.8568 1.31220
\(97\) 1.53102 0.155452 0.0777260 0.996975i \(-0.475234\pi\)
0.0777260 + 0.996975i \(0.475234\pi\)
\(98\) 0 0
\(99\) −6.59498 −0.662821
\(100\) 5.15633 0.515633
\(101\) −2.83638 −0.282230 −0.141115 0.989993i \(-0.545069\pi\)
−0.141115 + 0.989993i \(0.545069\pi\)
\(102\) 15.3503 1.51990
\(103\) 9.89446 0.974930 0.487465 0.873142i \(-0.337922\pi\)
0.487465 + 0.873142i \(0.337922\pi\)
\(104\) −11.4010 −1.11796
\(105\) 0 0
\(106\) 18.6253 1.80905
\(107\) −11.6932 −1.13043 −0.565214 0.824945i \(-0.691206\pi\)
−0.565214 + 0.824945i \(0.691206\pi\)
\(108\) −22.2374 −2.13980
\(109\) −14.4993 −1.38878 −0.694390 0.719599i \(-0.744326\pi\)
−0.694390 + 0.719599i \(0.744326\pi\)
\(110\) 7.50659 0.715725
\(111\) −4.43866 −0.421299
\(112\) 0 0
\(113\) −16.3938 −1.54219 −0.771097 0.636717i \(-0.780292\pi\)
−0.771097 + 0.636717i \(0.780292\pi\)
\(114\) −8.12601 −0.761070
\(115\) 4.80606 0.448168
\(116\) 5.15633 0.478753
\(117\) 3.17347 0.293387
\(118\) 6.88717 0.634015
\(119\) 0 0
\(120\) 6.80606 0.621306
\(121\) −3.12601 −0.284183
\(122\) −14.3127 −1.29581
\(123\) 5.61213 0.506028
\(124\) −1.19394 −0.107219
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 15.3561 1.36264 0.681319 0.731987i \(-0.261407\pi\)
0.681319 + 0.731987i \(0.261407\pi\)
\(128\) 16.5696 1.46456
\(129\) −2.57452 −0.226673
\(130\) −3.61213 −0.316804
\(131\) −1.38058 −0.120622 −0.0603109 0.998180i \(-0.519209\pi\)
−0.0603109 + 0.998180i \(0.519209\pi\)
\(132\) 11.6629 1.01513
\(133\) 0 0
\(134\) −8.54420 −0.738106
\(135\) −4.31265 −0.371174
\(136\) 60.1075 5.15417
\(137\) −6.49341 −0.554770 −0.277385 0.960759i \(-0.589468\pi\)
−0.277385 + 0.960759i \(0.589468\pi\)
\(138\) 10.3634 0.882194
\(139\) 19.0132 1.61268 0.806338 0.591455i \(-0.201446\pi\)
0.806338 + 0.591455i \(0.201446\pi\)
\(140\) 0 0
\(141\) −5.17347 −0.435685
\(142\) 30.3634 2.54804
\(143\) −3.78892 −0.316845
\(144\) −28.8496 −2.40413
\(145\) 1.00000 0.0830455
\(146\) 30.0811 2.48953
\(147\) 0 0
\(148\) −28.3938 −2.33395
\(149\) 6.62530 0.542766 0.271383 0.962471i \(-0.412519\pi\)
0.271383 + 0.962471i \(0.412519\pi\)
\(150\) 2.15633 0.176063
\(151\) −9.27504 −0.754792 −0.377396 0.926052i \(-0.623180\pi\)
−0.377396 + 0.926052i \(0.623180\pi\)
\(152\) −31.8192 −2.58088
\(153\) −16.7308 −1.35261
\(154\) 0 0
\(155\) −0.231548 −0.0185984
\(156\) −5.61213 −0.449330
\(157\) 5.00729 0.399626 0.199813 0.979834i \(-0.435967\pi\)
0.199813 + 0.979834i \(0.435967\pi\)
\(158\) −12.6556 −1.00683
\(159\) 5.61213 0.445071
\(160\) 15.9502 1.26097
\(161\) 0 0
\(162\) 9.56230 0.751285
\(163\) 7.50659 0.587961 0.293981 0.955811i \(-0.405020\pi\)
0.293981 + 0.955811i \(0.405020\pi\)
\(164\) 35.9003 2.80335
\(165\) 2.26187 0.176086
\(166\) −6.80606 −0.528253
\(167\) −21.8945 −1.69424 −0.847122 0.531398i \(-0.821667\pi\)
−0.847122 + 0.531398i \(0.821667\pi\)
\(168\) 0 0
\(169\) −11.1768 −0.859753
\(170\) 19.0435 1.46057
\(171\) 8.85685 0.677300
\(172\) −16.4690 −1.25575
\(173\) −7.02302 −0.533951 −0.266975 0.963703i \(-0.586024\pi\)
−0.266975 + 0.963703i \(0.586024\pi\)
\(174\) 2.15633 0.163471
\(175\) 0 0
\(176\) 34.4445 2.59635
\(177\) 2.07522 0.155983
\(178\) −38.2882 −2.86982
\(179\) 4.77575 0.356956 0.178478 0.983944i \(-0.442883\pi\)
0.178478 + 0.983944i \(0.442883\pi\)
\(180\) −12.1187 −0.903276
\(181\) −1.87399 −0.139293 −0.0696464 0.997572i \(-0.522187\pi\)
−0.0696464 + 0.997572i \(0.522187\pi\)
\(182\) 0 0
\(183\) −4.31265 −0.318800
\(184\) 40.5804 2.99163
\(185\) −5.50659 −0.404852
\(186\) −0.499293 −0.0366099
\(187\) 19.9756 1.46076
\(188\) −33.0943 −2.41365
\(189\) 0 0
\(190\) −10.0811 −0.731360
\(191\) 19.1187 1.38338 0.691691 0.722194i \(-0.256866\pi\)
0.691691 + 0.722194i \(0.256866\pi\)
\(192\) 14.6048 1.05401
\(193\) 19.8945 1.43203 0.716017 0.698083i \(-0.245963\pi\)
0.716017 + 0.698083i \(0.245963\pi\)
\(194\) 4.09569 0.294053
\(195\) −1.08840 −0.0779417
\(196\) 0 0
\(197\) −13.5369 −0.964464 −0.482232 0.876043i \(-0.660174\pi\)
−0.482232 + 0.876043i \(0.660174\pi\)
\(198\) −17.6424 −1.25379
\(199\) −2.57452 −0.182503 −0.0912513 0.995828i \(-0.529087\pi\)
−0.0912513 + 0.995828i \(0.529087\pi\)
\(200\) 8.44358 0.597051
\(201\) −2.57452 −0.181592
\(202\) −7.58769 −0.533868
\(203\) 0 0
\(204\) 29.5877 2.07155
\(205\) 6.96239 0.486274
\(206\) 26.4690 1.84418
\(207\) −11.2955 −0.785092
\(208\) −16.5745 −1.14924
\(209\) −10.5745 −0.731455
\(210\) 0 0
\(211\) 11.8945 0.818848 0.409424 0.912344i \(-0.365730\pi\)
0.409424 + 0.912344i \(0.365730\pi\)
\(212\) 35.9003 2.46565
\(213\) 9.14903 0.626881
\(214\) −31.2809 −2.13832
\(215\) −3.19394 −0.217825
\(216\) −36.4142 −2.47767
\(217\) 0 0
\(218\) −38.7875 −2.62702
\(219\) 9.06396 0.612486
\(220\) 14.4690 0.975498
\(221\) −9.61213 −0.646582
\(222\) −11.8740 −0.796930
\(223\) 1.11871 0.0749146 0.0374573 0.999298i \(-0.488074\pi\)
0.0374573 + 0.999298i \(0.488074\pi\)
\(224\) 0 0
\(225\) −2.35026 −0.156684
\(226\) −43.8554 −2.91722
\(227\) −0.0303172 −0.00201222 −0.00100611 0.999999i \(-0.500320\pi\)
−0.00100611 + 0.999999i \(0.500320\pi\)
\(228\) −15.6629 −1.03730
\(229\) 5.84955 0.386549 0.193275 0.981145i \(-0.438089\pi\)
0.193275 + 0.981145i \(0.438089\pi\)
\(230\) 12.8568 0.847755
\(231\) 0 0
\(232\) 8.44358 0.554348
\(233\) 26.1016 1.70997 0.854985 0.518652i \(-0.173566\pi\)
0.854985 + 0.518652i \(0.173566\pi\)
\(234\) 8.48944 0.554972
\(235\) −6.41819 −0.418677
\(236\) 13.2750 0.864131
\(237\) −3.81336 −0.247704
\(238\) 0 0
\(239\) 1.42548 0.0922069 0.0461035 0.998937i \(-0.485320\pi\)
0.0461035 + 0.998937i \(0.485320\pi\)
\(240\) 9.89446 0.638685
\(241\) 0.0752228 0.00484553 0.00242276 0.999997i \(-0.499229\pi\)
0.00242276 + 0.999997i \(0.499229\pi\)
\(242\) −8.36248 −0.537561
\(243\) 15.8192 1.01480
\(244\) −27.5877 −1.76612
\(245\) 0 0
\(246\) 15.0132 0.957205
\(247\) 5.08840 0.323767
\(248\) −1.95509 −0.124149
\(249\) −2.05079 −0.129963
\(250\) 2.67513 0.169190
\(251\) −16.9829 −1.07195 −0.535974 0.844234i \(-0.680056\pi\)
−0.535974 + 0.844234i \(0.680056\pi\)
\(252\) 0 0
\(253\) 13.4861 0.847865
\(254\) 41.0797 2.57757
\(255\) 5.73813 0.359336
\(256\) 8.08840 0.505525
\(257\) −25.1998 −1.57192 −0.785961 0.618276i \(-0.787831\pi\)
−0.785961 + 0.618276i \(0.787831\pi\)
\(258\) −6.88717 −0.428776
\(259\) 0 0
\(260\) −6.96239 −0.431789
\(261\) −2.35026 −0.145478
\(262\) −3.69323 −0.228168
\(263\) −16.1319 −0.994735 −0.497367 0.867540i \(-0.665700\pi\)
−0.497367 + 0.867540i \(0.665700\pi\)
\(264\) 19.0982 1.17542
\(265\) 6.96239 0.427696
\(266\) 0 0
\(267\) −11.5369 −0.706047
\(268\) −16.4690 −1.00600
\(269\) −5.28963 −0.322514 −0.161257 0.986912i \(-0.551555\pi\)
−0.161257 + 0.986912i \(0.551555\pi\)
\(270\) −11.5369 −0.702114
\(271\) −1.13330 −0.0688432 −0.0344216 0.999407i \(-0.510959\pi\)
−0.0344216 + 0.999407i \(0.510959\pi\)
\(272\) 87.3825 5.29834
\(273\) 0 0
\(274\) −17.3707 −1.04940
\(275\) 2.80606 0.169212
\(276\) 19.9756 1.20239
\(277\) −16.3634 −0.983184 −0.491592 0.870826i \(-0.663585\pi\)
−0.491592 + 0.870826i \(0.663585\pi\)
\(278\) 50.8627 3.05054
\(279\) 0.544198 0.0325803
\(280\) 0 0
\(281\) −24.8265 −1.48103 −0.740513 0.672042i \(-0.765418\pi\)
−0.740513 + 0.672042i \(0.765418\pi\)
\(282\) −13.8397 −0.824142
\(283\) 4.18076 0.248521 0.124260 0.992250i \(-0.460344\pi\)
0.124260 + 0.992250i \(0.460344\pi\)
\(284\) 58.5256 3.47286
\(285\) −3.03761 −0.179933
\(286\) −10.1359 −0.599346
\(287\) 0 0
\(288\) −37.4871 −2.20895
\(289\) 33.6761 1.98095
\(290\) 2.67513 0.157089
\(291\) 1.23410 0.0723444
\(292\) 57.9814 3.39311
\(293\) −23.6180 −1.37978 −0.689889 0.723915i \(-0.742341\pi\)
−0.689889 + 0.723915i \(0.742341\pi\)
\(294\) 0 0
\(295\) 2.57452 0.149894
\(296\) −46.4953 −2.70249
\(297\) −12.1016 −0.702204
\(298\) 17.7235 1.02670
\(299\) −6.48944 −0.375294
\(300\) 4.15633 0.239966
\(301\) 0 0
\(302\) −24.8119 −1.42777
\(303\) −2.28630 −0.131345
\(304\) −46.2579 −2.65307
\(305\) −5.35026 −0.306355
\(306\) −44.7572 −2.55860
\(307\) −32.5052 −1.85517 −0.927584 0.373614i \(-0.878118\pi\)
−0.927584 + 0.373614i \(0.878118\pi\)
\(308\) 0 0
\(309\) 7.97556 0.453714
\(310\) −0.619421 −0.0351808
\(311\) 9.31994 0.528486 0.264243 0.964456i \(-0.414878\pi\)
0.264243 + 0.964456i \(0.414878\pi\)
\(312\) −9.18997 −0.520279
\(313\) −9.60228 −0.542753 −0.271376 0.962473i \(-0.587479\pi\)
−0.271376 + 0.962473i \(0.587479\pi\)
\(314\) 13.3952 0.755933
\(315\) 0 0
\(316\) −24.3938 −1.37226
\(317\) 19.3707 1.08797 0.543984 0.839095i \(-0.316915\pi\)
0.543984 + 0.839095i \(0.316915\pi\)
\(318\) 15.0132 0.841897
\(319\) 2.80606 0.157109
\(320\) 18.1187 1.01287
\(321\) −9.42548 −0.526079
\(322\) 0 0
\(323\) −26.8265 −1.49267
\(324\) 18.4314 1.02396
\(325\) −1.35026 −0.0748990
\(326\) 20.0811 1.11219
\(327\) −11.6873 −0.646312
\(328\) 58.7875 3.24600
\(329\) 0 0
\(330\) 6.05079 0.333085
\(331\) −29.5428 −1.62382 −0.811909 0.583784i \(-0.801572\pi\)
−0.811909 + 0.583784i \(0.801572\pi\)
\(332\) −13.1187 −0.719983
\(333\) 12.9419 0.709213
\(334\) −58.5705 −3.20484
\(335\) −3.19394 −0.174503
\(336\) 0 0
\(337\) 12.5442 0.683326 0.341663 0.939823i \(-0.389010\pi\)
0.341663 + 0.939823i \(0.389010\pi\)
\(338\) −29.8994 −1.62631
\(339\) −13.2144 −0.717708
\(340\) 36.7064 1.99068
\(341\) −0.649738 −0.0351853
\(342\) 23.6932 1.28118
\(343\) 0 0
\(344\) −26.9683 −1.45403
\(345\) 3.87399 0.208569
\(346\) −18.7875 −1.01002
\(347\) −25.0943 −1.34713 −0.673566 0.739127i \(-0.735238\pi\)
−0.673566 + 0.739127i \(0.735238\pi\)
\(348\) 4.15633 0.222802
\(349\) 17.0738 0.913940 0.456970 0.889482i \(-0.348935\pi\)
0.456970 + 0.889482i \(0.348935\pi\)
\(350\) 0 0
\(351\) 5.82321 0.310820
\(352\) 44.7572 2.38557
\(353\) −5.66291 −0.301406 −0.150703 0.988579i \(-0.548154\pi\)
−0.150703 + 0.988579i \(0.548154\pi\)
\(354\) 5.55149 0.295058
\(355\) 11.3503 0.602409
\(356\) −73.8007 −3.91143
\(357\) 0 0
\(358\) 12.7757 0.675219
\(359\) 0.755278 0.0398621 0.0199310 0.999801i \(-0.493655\pi\)
0.0199310 + 0.999801i \(0.493655\pi\)
\(360\) −19.8446 −1.04590
\(361\) −4.79877 −0.252567
\(362\) −5.01317 −0.263487
\(363\) −2.51976 −0.132253
\(364\) 0 0
\(365\) 11.2447 0.588576
\(366\) −11.5369 −0.603044
\(367\) −11.4460 −0.597474 −0.298737 0.954335i \(-0.596565\pi\)
−0.298737 + 0.954335i \(0.596565\pi\)
\(368\) 58.9946 3.07531
\(369\) −16.3634 −0.851846
\(370\) −14.7308 −0.765820
\(371\) 0 0
\(372\) −0.962389 −0.0498975
\(373\) 3.86414 0.200078 0.100039 0.994984i \(-0.468103\pi\)
0.100039 + 0.994984i \(0.468103\pi\)
\(374\) 53.4372 2.76317
\(375\) 0.806063 0.0416249
\(376\) −54.1925 −2.79477
\(377\) −1.35026 −0.0695420
\(378\) 0 0
\(379\) 12.1055 0.621820 0.310910 0.950439i \(-0.399366\pi\)
0.310910 + 0.950439i \(0.399366\pi\)
\(380\) −19.4314 −0.996808
\(381\) 12.3780 0.634145
\(382\) 51.1451 2.61681
\(383\) 10.0205 0.512022 0.256011 0.966674i \(-0.417592\pi\)
0.256011 + 0.966674i \(0.417592\pi\)
\(384\) 13.3561 0.681578
\(385\) 0 0
\(386\) 53.2203 2.70884
\(387\) 7.50659 0.381581
\(388\) 7.89446 0.400780
\(389\) −25.6629 −1.30116 −0.650581 0.759437i \(-0.725474\pi\)
−0.650581 + 0.759437i \(0.725474\pi\)
\(390\) −2.91160 −0.147435
\(391\) 34.2130 1.73023
\(392\) 0 0
\(393\) −1.11283 −0.0561351
\(394\) −36.2130 −1.82438
\(395\) −4.73084 −0.238034
\(396\) −34.0059 −1.70886
\(397\) −27.7137 −1.39091 −0.695455 0.718569i \(-0.744797\pi\)
−0.695455 + 0.718569i \(0.744797\pi\)
\(398\) −6.88717 −0.345222
\(399\) 0 0
\(400\) 12.2750 0.613752
\(401\) 7.42548 0.370811 0.185406 0.982662i \(-0.440640\pi\)
0.185406 + 0.982662i \(0.440640\pi\)
\(402\) −6.88717 −0.343501
\(403\) 0.312650 0.0155742
\(404\) −14.6253 −0.727636
\(405\) 3.57452 0.177619
\(406\) 0 0
\(407\) −15.4518 −0.765919
\(408\) 48.4504 2.39865
\(409\) 33.1998 1.64163 0.820813 0.571198i \(-0.193521\pi\)
0.820813 + 0.571198i \(0.193521\pi\)
\(410\) 18.6253 0.919838
\(411\) −5.23410 −0.258179
\(412\) 51.0191 2.51353
\(413\) 0 0
\(414\) −30.2170 −1.48508
\(415\) −2.54420 −0.124890
\(416\) −21.5369 −1.05593
\(417\) 15.3258 0.750509
\(418\) −28.2882 −1.38362
\(419\) −16.5599 −0.809005 −0.404503 0.914537i \(-0.632555\pi\)
−0.404503 + 0.914537i \(0.632555\pi\)
\(420\) 0 0
\(421\) −8.82653 −0.430179 −0.215089 0.976594i \(-0.569004\pi\)
−0.215089 + 0.976594i \(0.569004\pi\)
\(422\) 31.8192 1.54894
\(423\) 15.0844 0.733430
\(424\) 58.7875 2.85497
\(425\) 7.11871 0.345308
\(426\) 24.4749 1.18581
\(427\) 0 0
\(428\) −60.2941 −2.91442
\(429\) −3.05411 −0.147454
\(430\) −8.54420 −0.412038
\(431\) 4.25202 0.204812 0.102406 0.994743i \(-0.467346\pi\)
0.102406 + 0.994743i \(0.467346\pi\)
\(432\) −52.9380 −2.54698
\(433\) 1.81924 0.0874270 0.0437135 0.999044i \(-0.486081\pi\)
0.0437135 + 0.999044i \(0.486081\pi\)
\(434\) 0 0
\(435\) 0.806063 0.0386478
\(436\) −74.7631 −3.58050
\(437\) −18.1114 −0.866387
\(438\) 24.2473 1.15858
\(439\) −14.1114 −0.673501 −0.336751 0.941594i \(-0.609328\pi\)
−0.336751 + 0.941594i \(0.609328\pi\)
\(440\) 23.6932 1.12953
\(441\) 0 0
\(442\) −25.7137 −1.22308
\(443\) −17.2809 −0.821041 −0.410521 0.911851i \(-0.634653\pi\)
−0.410521 + 0.911851i \(0.634653\pi\)
\(444\) −22.8872 −1.08618
\(445\) −14.3127 −0.678485
\(446\) 2.99271 0.141709
\(447\) 5.34041 0.252593
\(448\) 0 0
\(449\) 9.35026 0.441266 0.220633 0.975357i \(-0.429188\pi\)
0.220633 + 0.975357i \(0.429188\pi\)
\(450\) −6.28726 −0.296384
\(451\) 19.5369 0.919957
\(452\) −84.5315 −3.97603
\(453\) −7.47627 −0.351266
\(454\) −0.0811024 −0.00380632
\(455\) 0 0
\(456\) −25.6483 −1.20109
\(457\) −17.6629 −0.826236 −0.413118 0.910677i \(-0.635560\pi\)
−0.413118 + 0.910677i \(0.635560\pi\)
\(458\) 15.6483 0.731198
\(459\) −30.7005 −1.43298
\(460\) 24.7816 1.15545
\(461\) −15.5633 −0.724853 −0.362426 0.932012i \(-0.618052\pi\)
−0.362426 + 0.932012i \(0.618052\pi\)
\(462\) 0 0
\(463\) 2.98286 0.138625 0.0693126 0.997595i \(-0.477919\pi\)
0.0693126 + 0.997595i \(0.477919\pi\)
\(464\) 12.2750 0.569854
\(465\) −0.186642 −0.00865533
\(466\) 69.8251 3.23459
\(467\) −34.5804 −1.60019 −0.800095 0.599873i \(-0.795218\pi\)
−0.800095 + 0.599873i \(0.795218\pi\)
\(468\) 16.3634 0.756400
\(469\) 0 0
\(470\) −17.1695 −0.791970
\(471\) 4.03620 0.185978
\(472\) 21.7381 1.00058
\(473\) −8.96239 −0.412091
\(474\) −10.2012 −0.468558
\(475\) −3.76845 −0.172908
\(476\) 0 0
\(477\) −16.3634 −0.749230
\(478\) 3.81336 0.174419
\(479\) 34.1925 1.56230 0.781148 0.624346i \(-0.214634\pi\)
0.781148 + 0.624346i \(0.214634\pi\)
\(480\) 12.8568 0.586832
\(481\) 7.43533 0.339022
\(482\) 0.201231 0.00916581
\(483\) 0 0
\(484\) −16.1187 −0.732669
\(485\) 1.53102 0.0695202
\(486\) 42.3185 1.91961
\(487\) 38.4953 1.74439 0.872195 0.489159i \(-0.162696\pi\)
0.872195 + 0.489159i \(0.162696\pi\)
\(488\) −45.1754 −2.04499
\(489\) 6.05079 0.273626
\(490\) 0 0
\(491\) −27.4676 −1.23959 −0.619797 0.784762i \(-0.712785\pi\)
−0.619797 + 0.784762i \(0.712785\pi\)
\(492\) 28.9380 1.30462
\(493\) 7.11871 0.320611
\(494\) 13.6121 0.612439
\(495\) −6.59498 −0.296422
\(496\) −2.84226 −0.127621
\(497\) 0 0
\(498\) −5.48612 −0.245839
\(499\) −32.1016 −1.43706 −0.718532 0.695494i \(-0.755186\pi\)
−0.718532 + 0.695494i \(0.755186\pi\)
\(500\) 5.15633 0.230598
\(501\) −17.6483 −0.788469
\(502\) −45.4314 −2.02770
\(503\) −9.74401 −0.434464 −0.217232 0.976120i \(-0.569703\pi\)
−0.217232 + 0.976120i \(0.569703\pi\)
\(504\) 0 0
\(505\) −2.83638 −0.126217
\(506\) 36.0771 1.60382
\(507\) −9.00920 −0.400113
\(508\) 79.1813 3.51310
\(509\) 8.57452 0.380059 0.190029 0.981778i \(-0.439142\pi\)
0.190029 + 0.981778i \(0.439142\pi\)
\(510\) 15.3503 0.679721
\(511\) 0 0
\(512\) −11.5017 −0.508306
\(513\) 16.2520 0.717544
\(514\) −67.4128 −2.97345
\(515\) 9.89446 0.436002
\(516\) −13.2750 −0.584401
\(517\) −18.0098 −0.792072
\(518\) 0 0
\(519\) −5.66100 −0.248490
\(520\) −11.4010 −0.499969
\(521\) 37.8251 1.65715 0.828574 0.559879i \(-0.189152\pi\)
0.828574 + 0.559879i \(0.189152\pi\)
\(522\) −6.28726 −0.275186
\(523\) 13.5818 0.593891 0.296946 0.954894i \(-0.404032\pi\)
0.296946 + 0.954894i \(0.404032\pi\)
\(524\) −7.11871 −0.310982
\(525\) 0 0
\(526\) −43.1549 −1.88164
\(527\) −1.64832 −0.0718021
\(528\) 27.7645 1.20829
\(529\) 0.0982457 0.00427155
\(530\) 18.6253 0.809031
\(531\) −6.05079 −0.262582
\(532\) 0 0
\(533\) −9.40105 −0.407205
\(534\) −30.8627 −1.33556
\(535\) −11.6932 −0.505542
\(536\) −26.9683 −1.16485
\(537\) 3.84955 0.166121
\(538\) −14.1504 −0.610069
\(539\) 0 0
\(540\) −22.2374 −0.956947
\(541\) 42.3127 1.81916 0.909581 0.415526i \(-0.136402\pi\)
0.909581 + 0.415526i \(0.136402\pi\)
\(542\) −3.03173 −0.130224
\(543\) −1.51056 −0.0648242
\(544\) 113.545 4.86819
\(545\) −14.4993 −0.621081
\(546\) 0 0
\(547\) −36.4690 −1.55930 −0.779650 0.626215i \(-0.784603\pi\)
−0.779650 + 0.626215i \(0.784603\pi\)
\(548\) −33.4821 −1.43029
\(549\) 12.5745 0.536667
\(550\) 7.50659 0.320082
\(551\) −3.76845 −0.160541
\(552\) 32.7104 1.39225
\(553\) 0 0
\(554\) −43.7743 −1.85979
\(555\) −4.43866 −0.188411
\(556\) 98.0381 4.15774
\(557\) 19.5223 0.827187 0.413594 0.910462i \(-0.364273\pi\)
0.413594 + 0.910462i \(0.364273\pi\)
\(558\) 1.45580 0.0616290
\(559\) 4.31265 0.182406
\(560\) 0 0
\(561\) 16.1016 0.679809
\(562\) −66.4142 −2.80151
\(563\) 2.94192 0.123987 0.0619936 0.998077i \(-0.480254\pi\)
0.0619936 + 0.998077i \(0.480254\pi\)
\(564\) −26.6761 −1.12327
\(565\) −16.3938 −0.689690
\(566\) 11.1841 0.470102
\(567\) 0 0
\(568\) 95.8369 4.02123
\(569\) 2.49929 0.104776 0.0523879 0.998627i \(-0.483317\pi\)
0.0523879 + 0.998627i \(0.483317\pi\)
\(570\) −8.12601 −0.340361
\(571\) 43.8007 1.83300 0.916501 0.400033i \(-0.131001\pi\)
0.916501 + 0.400033i \(0.131001\pi\)
\(572\) −19.5369 −0.816879
\(573\) 15.4109 0.643799
\(574\) 0 0
\(575\) 4.80606 0.200427
\(576\) −42.5837 −1.77432
\(577\) 23.9062 0.995229 0.497614 0.867398i \(-0.334209\pi\)
0.497614 + 0.867398i \(0.334209\pi\)
\(578\) 90.0879 3.74716
\(579\) 16.0362 0.666442
\(580\) 5.15633 0.214105
\(581\) 0 0
\(582\) 3.30139 0.136847
\(583\) 19.5369 0.809136
\(584\) 94.9457 3.92888
\(585\) 3.17347 0.131207
\(586\) −63.1813 −2.60999
\(587\) 3.71767 0.153445 0.0767223 0.997053i \(-0.475555\pi\)
0.0767223 + 0.997053i \(0.475555\pi\)
\(588\) 0 0
\(589\) 0.872577 0.0359539
\(590\) 6.88717 0.283540
\(591\) −10.9116 −0.448843
\(592\) −67.5936 −2.77808
\(593\) 25.5125 1.04767 0.523836 0.851819i \(-0.324501\pi\)
0.523836 + 0.851819i \(0.324501\pi\)
\(594\) −32.3733 −1.32829
\(595\) 0 0
\(596\) 34.1622 1.39934
\(597\) −2.07522 −0.0849332
\(598\) −17.3601 −0.709908
\(599\) −15.6834 −0.640806 −0.320403 0.947281i \(-0.603818\pi\)
−0.320403 + 0.947281i \(0.603818\pi\)
\(600\) 6.80606 0.277856
\(601\) −13.1392 −0.535958 −0.267979 0.963425i \(-0.586356\pi\)
−0.267979 + 0.963425i \(0.586356\pi\)
\(602\) 0 0
\(603\) 7.50659 0.305692
\(604\) −47.8251 −1.94598
\(605\) −3.12601 −0.127090
\(606\) −6.11616 −0.248452
\(607\) −18.1465 −0.736543 −0.368271 0.929718i \(-0.620050\pi\)
−0.368271 + 0.929718i \(0.620050\pi\)
\(608\) −60.1075 −2.43768
\(609\) 0 0
\(610\) −14.3127 −0.579502
\(611\) 8.66624 0.350598
\(612\) −86.2697 −3.48724
\(613\) −32.5501 −1.31469 −0.657343 0.753592i \(-0.728320\pi\)
−0.657343 + 0.753592i \(0.728320\pi\)
\(614\) −86.9556 −3.50924
\(615\) 5.61213 0.226303
\(616\) 0 0
\(617\) 20.2433 0.814965 0.407482 0.913213i \(-0.366407\pi\)
0.407482 + 0.913213i \(0.366407\pi\)
\(618\) 21.3357 0.858247
\(619\) 16.2071 0.651419 0.325709 0.945470i \(-0.394397\pi\)
0.325709 + 0.945470i \(0.394397\pi\)
\(620\) −1.19394 −0.0479496
\(621\) −20.7269 −0.831741
\(622\) 24.9321 0.999685
\(623\) 0 0
\(624\) −13.3601 −0.534832
\(625\) 1.00000 0.0400000
\(626\) −25.6873 −1.02667
\(627\) −8.52373 −0.340405
\(628\) 25.8192 1.03030
\(629\) −39.1998 −1.56300
\(630\) 0 0
\(631\) 2.13586 0.0850271 0.0425136 0.999096i \(-0.486463\pi\)
0.0425136 + 0.999096i \(0.486463\pi\)
\(632\) −39.9452 −1.58894
\(633\) 9.58769 0.381076
\(634\) 51.8192 2.05800
\(635\) 15.3561 0.609390
\(636\) 28.9380 1.14746
\(637\) 0 0
\(638\) 7.50659 0.297189
\(639\) −26.6761 −1.05529
\(640\) 16.5696 0.654971
\(641\) −14.0362 −0.554396 −0.277198 0.960813i \(-0.589406\pi\)
−0.277198 + 0.960813i \(0.589406\pi\)
\(642\) −25.2144 −0.995133
\(643\) 43.8799 1.73045 0.865227 0.501381i \(-0.167174\pi\)
0.865227 + 0.501381i \(0.167174\pi\)
\(644\) 0 0
\(645\) −2.57452 −0.101371
\(646\) −71.7645 −2.82354
\(647\) 22.5560 0.886766 0.443383 0.896332i \(-0.353778\pi\)
0.443383 + 0.896332i \(0.353778\pi\)
\(648\) 30.1817 1.18565
\(649\) 7.22425 0.283577
\(650\) −3.61213 −0.141679
\(651\) 0 0
\(652\) 38.7064 1.51586
\(653\) 27.3054 1.06854 0.534271 0.845314i \(-0.320586\pi\)
0.534271 + 0.845314i \(0.320586\pi\)
\(654\) −31.2652 −1.22257
\(655\) −1.38058 −0.0539437
\(656\) 85.4636 3.33679
\(657\) −26.4280 −1.03106
\(658\) 0 0
\(659\) 14.0665 0.547954 0.273977 0.961736i \(-0.411661\pi\)
0.273977 + 0.961736i \(0.411661\pi\)
\(660\) 11.6629 0.453978
\(661\) −38.9741 −1.51592 −0.757959 0.652302i \(-0.773803\pi\)
−0.757959 + 0.652302i \(0.773803\pi\)
\(662\) −79.0308 −3.07162
\(663\) −7.74798 −0.300907
\(664\) −21.4821 −0.833669
\(665\) 0 0
\(666\) 34.6213 1.34155
\(667\) 4.80606 0.186092
\(668\) −112.895 −4.36804
\(669\) 0.901754 0.0348638
\(670\) −8.54420 −0.330091
\(671\) −15.0132 −0.579577
\(672\) 0 0
\(673\) 20.3390 0.784011 0.392005 0.919963i \(-0.371781\pi\)
0.392005 + 0.919963i \(0.371781\pi\)
\(674\) 33.5574 1.29258
\(675\) −4.31265 −0.165994
\(676\) −57.6312 −2.21658
\(677\) 19.1841 0.737304 0.368652 0.929567i \(-0.379819\pi\)
0.368652 + 0.929567i \(0.379819\pi\)
\(678\) −35.3503 −1.35762
\(679\) 0 0
\(680\) 60.1075 2.30502
\(681\) −0.0244376 −0.000936449 0
\(682\) −1.73813 −0.0665566
\(683\) −24.1319 −0.923381 −0.461691 0.887041i \(-0.652757\pi\)
−0.461691 + 0.887041i \(0.652757\pi\)
\(684\) 45.6688 1.74619
\(685\) −6.49341 −0.248101
\(686\) 0 0
\(687\) 4.71511 0.179893
\(688\) −39.2057 −1.49470
\(689\) −9.40105 −0.358151
\(690\) 10.3634 0.394529
\(691\) 4.28821 0.163131 0.0815657 0.996668i \(-0.474008\pi\)
0.0815657 + 0.996668i \(0.474008\pi\)
\(692\) −36.2130 −1.37661
\(693\) 0 0
\(694\) −67.1305 −2.54824
\(695\) 19.0132 0.721211
\(696\) 6.80606 0.257983
\(697\) 49.5633 1.87734
\(698\) 45.6747 1.72881
\(699\) 21.0395 0.795788
\(700\) 0 0
\(701\) −14.1260 −0.533532 −0.266766 0.963761i \(-0.585955\pi\)
−0.266766 + 0.963761i \(0.585955\pi\)
\(702\) 15.5778 0.587948
\(703\) 20.7513 0.782650
\(704\) 50.8423 1.91619
\(705\) −5.17347 −0.194844
\(706\) −15.1490 −0.570141
\(707\) 0 0
\(708\) 10.7005 0.402150
\(709\) 6.75131 0.253551 0.126775 0.991931i \(-0.459537\pi\)
0.126775 + 0.991931i \(0.459537\pi\)
\(710\) 30.3634 1.13952
\(711\) 11.1187 0.416984
\(712\) −120.850 −4.52905
\(713\) −1.11283 −0.0416760
\(714\) 0 0
\(715\) −3.78892 −0.141698
\(716\) 24.6253 0.920291
\(717\) 1.14903 0.0429113
\(718\) 2.02047 0.0754032
\(719\) 43.8251 1.63440 0.817201 0.576353i \(-0.195525\pi\)
0.817201 + 0.576353i \(0.195525\pi\)
\(720\) −28.8496 −1.07516
\(721\) 0 0
\(722\) −12.8373 −0.477756
\(723\) 0.0606343 0.00225502
\(724\) −9.66291 −0.359119
\(725\) 1.00000 0.0371391
\(726\) −6.74069 −0.250170
\(727\) 14.8813 0.551916 0.275958 0.961170i \(-0.411005\pi\)
0.275958 + 0.961170i \(0.411005\pi\)
\(728\) 0 0
\(729\) 2.02776 0.0751023
\(730\) 30.0811 1.11335
\(731\) −22.7367 −0.840948
\(732\) −22.2374 −0.821919
\(733\) −7.17935 −0.265175 −0.132588 0.991171i \(-0.542329\pi\)
−0.132588 + 0.991171i \(0.542329\pi\)
\(734\) −30.6194 −1.13018
\(735\) 0 0
\(736\) 76.6575 2.82563
\(737\) −8.96239 −0.330134
\(738\) −43.7743 −1.61136
\(739\) 16.1709 0.594857 0.297428 0.954744i \(-0.403871\pi\)
0.297428 + 0.954744i \(0.403871\pi\)
\(740\) −28.3938 −1.04378
\(741\) 4.10157 0.150675
\(742\) 0 0
\(743\) 27.8192 1.02059 0.510294 0.860000i \(-0.329536\pi\)
0.510294 + 0.860000i \(0.329536\pi\)
\(744\) −1.57593 −0.0577764
\(745\) 6.62530 0.242732
\(746\) 10.3371 0.378468
\(747\) 5.97953 0.218780
\(748\) 103.000 3.76607
\(749\) 0 0
\(750\) 2.15633 0.0787379
\(751\) −17.6326 −0.643423 −0.321711 0.946838i \(-0.604258\pi\)
−0.321711 + 0.946838i \(0.604258\pi\)
\(752\) −78.7835 −2.87294
\(753\) −13.6893 −0.498864
\(754\) −3.61213 −0.131546
\(755\) −9.27504 −0.337553
\(756\) 0 0
\(757\) 1.53102 0.0556460 0.0278230 0.999613i \(-0.491143\pi\)
0.0278230 + 0.999613i \(0.491143\pi\)
\(758\) 32.3839 1.17624
\(759\) 10.8707 0.394580
\(760\) −31.8192 −1.15421
\(761\) 34.4749 1.24971 0.624856 0.780740i \(-0.285158\pi\)
0.624856 + 0.780740i \(0.285158\pi\)
\(762\) 33.1128 1.19955
\(763\) 0 0
\(764\) 98.5823 3.56658
\(765\) −16.7308 −0.604905
\(766\) 26.8061 0.968542
\(767\) −3.47627 −0.125521
\(768\) 6.51976 0.235262
\(769\) 19.3404 0.697433 0.348717 0.937228i \(-0.386618\pi\)
0.348717 + 0.937228i \(0.386618\pi\)
\(770\) 0 0
\(771\) −20.3127 −0.731542
\(772\) 102.582 3.69202
\(773\) −36.2677 −1.30446 −0.652230 0.758021i \(-0.726166\pi\)
−0.652230 + 0.758021i \(0.726166\pi\)
\(774\) 20.0811 0.721800
\(775\) −0.231548 −0.00831745
\(776\) 12.9273 0.464064
\(777\) 0 0
\(778\) −68.6516 −2.46128
\(779\) −26.2374 −0.940053
\(780\) −5.61213 −0.200946
\(781\) 31.8496 1.13967
\(782\) 91.5242 3.27290
\(783\) −4.31265 −0.154122
\(784\) 0 0
\(785\) 5.00729 0.178718
\(786\) −2.97698 −0.106185
\(787\) −32.0059 −1.14089 −0.570443 0.821337i \(-0.693229\pi\)
−0.570443 + 0.821337i \(0.693229\pi\)
\(788\) −69.8007 −2.48655
\(789\) −13.0033 −0.462931
\(790\) −12.6556 −0.450267
\(791\) 0 0
\(792\) −55.6853 −1.97869
\(793\) 7.22425 0.256541
\(794\) −74.1378 −2.63105
\(795\) 5.61213 0.199042
\(796\) −13.2750 −0.470521
\(797\) 41.6932 1.47685 0.738425 0.674336i \(-0.235570\pi\)
0.738425 + 0.674336i \(0.235570\pi\)
\(798\) 0 0
\(799\) −45.6893 −1.61637
\(800\) 15.9502 0.563924
\(801\) 33.6385 1.18856
\(802\) 19.8641 0.701427
\(803\) 31.5534 1.11350
\(804\) −13.2750 −0.468175
\(805\) 0 0
\(806\) 0.836381 0.0294603
\(807\) −4.26378 −0.150092
\(808\) −23.9492 −0.842530
\(809\) 30.6371 1.07714 0.538571 0.842580i \(-0.318964\pi\)
0.538571 + 0.842580i \(0.318964\pi\)
\(810\) 9.56230 0.335985
\(811\) −25.4617 −0.894081 −0.447040 0.894514i \(-0.647522\pi\)
−0.447040 + 0.894514i \(0.647522\pi\)
\(812\) 0 0
\(813\) −0.913513 −0.0320383
\(814\) −41.3357 −1.44881
\(815\) 7.50659 0.262944
\(816\) 70.4358 2.46575
\(817\) 12.0362 0.421093
\(818\) 88.8139 3.10530
\(819\) 0 0
\(820\) 35.9003 1.25369
\(821\) −32.7005 −1.14126 −0.570628 0.821209i \(-0.693300\pi\)
−0.570628 + 0.821209i \(0.693300\pi\)
\(822\) −14.0019 −0.488373
\(823\) −31.1041 −1.08422 −0.542111 0.840307i \(-0.682375\pi\)
−0.542111 + 0.840307i \(0.682375\pi\)
\(824\) 83.5447 2.91042
\(825\) 2.26187 0.0787480
\(826\) 0 0
\(827\) −1.58181 −0.0550049 −0.0275025 0.999622i \(-0.508755\pi\)
−0.0275025 + 0.999622i \(0.508755\pi\)
\(828\) −58.2433 −2.02409
\(829\) 0.111420 0.00386976 0.00193488 0.999998i \(-0.499384\pi\)
0.00193488 + 0.999998i \(0.499384\pi\)
\(830\) −6.80606 −0.236242
\(831\) −13.1900 −0.457555
\(832\) −24.4650 −0.848171
\(833\) 0 0
\(834\) 40.9986 1.41966
\(835\) −21.8945 −0.757689
\(836\) −54.5256 −1.88581
\(837\) 0.998585 0.0345162
\(838\) −44.3000 −1.53032
\(839\) −28.9829 −1.00060 −0.500300 0.865852i \(-0.666777\pi\)
−0.500300 + 0.865852i \(0.666777\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −23.6121 −0.813728
\(843\) −20.0118 −0.689242
\(844\) 61.3317 2.11112
\(845\) −11.1768 −0.384493
\(846\) 40.3528 1.38736
\(847\) 0 0
\(848\) 85.4636 2.93483
\(849\) 3.36996 0.115657
\(850\) 19.0435 0.653186
\(851\) −26.4650 −0.907209
\(852\) 47.1754 1.61620
\(853\) 7.77319 0.266149 0.133075 0.991106i \(-0.457515\pi\)
0.133075 + 0.991106i \(0.457515\pi\)
\(854\) 0 0
\(855\) 8.85685 0.302898
\(856\) −98.7328 −3.37462
\(857\) 13.8740 0.473927 0.236963 0.971519i \(-0.423848\pi\)
0.236963 + 0.971519i \(0.423848\pi\)
\(858\) −8.17014 −0.278924
\(859\) 15.2809 0.521378 0.260689 0.965423i \(-0.416050\pi\)
0.260689 + 0.965423i \(0.416050\pi\)
\(860\) −16.4690 −0.561587
\(861\) 0 0
\(862\) 11.3747 0.387424
\(863\) 31.2301 1.06309 0.531543 0.847031i \(-0.321612\pi\)
0.531543 + 0.847031i \(0.321612\pi\)
\(864\) −68.7875 −2.34020
\(865\) −7.02302 −0.238790
\(866\) 4.86670 0.165377
\(867\) 27.1451 0.921895
\(868\) 0 0
\(869\) −13.2750 −0.450325
\(870\) 2.15633 0.0731063
\(871\) 4.31265 0.146129
\(872\) −122.426 −4.14587
\(873\) −3.59831 −0.121784
\(874\) −48.4504 −1.63886
\(875\) 0 0
\(876\) 46.7367 1.57909
\(877\) −4.26187 −0.143913 −0.0719565 0.997408i \(-0.522924\pi\)
−0.0719565 + 0.997408i \(0.522924\pi\)
\(878\) −37.7499 −1.27400
\(879\) −19.0376 −0.642123
\(880\) 34.4445 1.16113
\(881\) −15.2144 −0.512586 −0.256293 0.966599i \(-0.582501\pi\)
−0.256293 + 0.966599i \(0.582501\pi\)
\(882\) 0 0
\(883\) −13.7078 −0.461305 −0.230652 0.973036i \(-0.574086\pi\)
−0.230652 + 0.973036i \(0.574086\pi\)
\(884\) −49.5633 −1.66699
\(885\) 2.07522 0.0697579
\(886\) −46.2287 −1.55308
\(887\) −12.6556 −0.424934 −0.212467 0.977168i \(-0.568150\pi\)
−0.212467 + 0.977168i \(0.568150\pi\)
\(888\) −37.4782 −1.25769
\(889\) 0 0
\(890\) −38.2882 −1.28342
\(891\) 10.0303 0.336028
\(892\) 5.76845 0.193142
\(893\) 24.1866 0.809375
\(894\) 14.2863 0.477805
\(895\) 4.77575 0.159636
\(896\) 0 0
\(897\) −5.23090 −0.174655
\(898\) 25.0132 0.834700
\(899\) −0.231548 −0.00772256
\(900\) −12.1187 −0.403957
\(901\) 49.5633 1.65119
\(902\) 52.2638 1.74019
\(903\) 0 0
\(904\) −138.422 −4.60385
\(905\) −1.87399 −0.0622936
\(906\) −20.0000 −0.664455
\(907\) −12.5540 −0.416850 −0.208425 0.978038i \(-0.566834\pi\)
−0.208425 + 0.978038i \(0.566834\pi\)
\(908\) −0.156325 −0.00518783
\(909\) 6.66624 0.221105
\(910\) 0 0
\(911\) 22.8714 0.757765 0.378882 0.925445i \(-0.376309\pi\)
0.378882 + 0.925445i \(0.376309\pi\)
\(912\) −37.2868 −1.23469
\(913\) −7.13918 −0.236272
\(914\) −47.2506 −1.56291
\(915\) −4.31265 −0.142572
\(916\) 30.1622 0.996587
\(917\) 0 0
\(918\) −82.1279 −2.71063
\(919\) 9.67750 0.319231 0.159616 0.987179i \(-0.448975\pi\)
0.159616 + 0.987179i \(0.448975\pi\)
\(920\) 40.5804 1.33790
\(921\) −26.2012 −0.863360
\(922\) −41.6337 −1.37113
\(923\) −15.3258 −0.504456
\(924\) 0 0
\(925\) −5.50659 −0.181055
\(926\) 7.97953 0.262224
\(927\) −23.2546 −0.763780
\(928\) 15.9502 0.523590
\(929\) −51.9248 −1.70360 −0.851798 0.523870i \(-0.824488\pi\)
−0.851798 + 0.523870i \(0.824488\pi\)
\(930\) −0.499293 −0.0163725
\(931\) 0 0
\(932\) 134.588 4.40858
\(933\) 7.51247 0.245947
\(934\) −92.5071 −3.02692
\(935\) 19.9756 0.653271
\(936\) 26.7954 0.875837
\(937\) −3.58769 −0.117205 −0.0586024 0.998281i \(-0.518664\pi\)
−0.0586024 + 0.998281i \(0.518664\pi\)
\(938\) 0 0
\(939\) −7.74004 −0.252587
\(940\) −33.0943 −1.07942
\(941\) 18.6253 0.607167 0.303584 0.952805i \(-0.401817\pi\)
0.303584 + 0.952805i \(0.401817\pi\)
\(942\) 10.7974 0.351797
\(943\) 33.4617 1.08966
\(944\) 31.6023 1.02857
\(945\) 0 0
\(946\) −23.9756 −0.779513
\(947\) −16.5950 −0.539265 −0.269632 0.962963i \(-0.586902\pi\)
−0.269632 + 0.962963i \(0.586902\pi\)
\(948\) −19.6629 −0.638622
\(949\) −15.1833 −0.492871
\(950\) −10.0811 −0.327074
\(951\) 15.6140 0.506320
\(952\) 0 0
\(953\) −12.7005 −0.411410 −0.205705 0.978614i \(-0.565949\pi\)
−0.205705 + 0.978614i \(0.565949\pi\)
\(954\) −43.7743 −1.41725
\(955\) 19.1187 0.618667
\(956\) 7.35026 0.237724
\(957\) 2.26187 0.0731157
\(958\) 91.4695 2.95524
\(959\) 0 0
\(960\) 14.6048 0.471369
\(961\) −30.9464 −0.998271
\(962\) 19.8905 0.641295
\(963\) 27.4821 0.885600
\(964\) 0.387873 0.0124926
\(965\) 19.8945 0.640425
\(966\) 0 0
\(967\) 37.4314 1.20371 0.601856 0.798605i \(-0.294428\pi\)
0.601856 + 0.798605i \(0.294428\pi\)
\(968\) −26.3947 −0.848358
\(969\) −21.6239 −0.694659
\(970\) 4.09569 0.131505
\(971\) −7.51644 −0.241214 −0.120607 0.992700i \(-0.538484\pi\)
−0.120607 + 0.992700i \(0.538484\pi\)
\(972\) 81.5691 2.61633
\(973\) 0 0
\(974\) 102.980 3.29969
\(975\) −1.08840 −0.0348566
\(976\) −65.6747 −2.10220
\(977\) −2.52847 −0.0808929 −0.0404465 0.999182i \(-0.512878\pi\)
−0.0404465 + 0.999182i \(0.512878\pi\)
\(978\) 16.1866 0.517592
\(979\) −40.1622 −1.28359
\(980\) 0 0
\(981\) 34.0771 1.08800
\(982\) −73.4793 −2.34482
\(983\) 9.32979 0.297574 0.148787 0.988869i \(-0.452463\pi\)
0.148787 + 0.988869i \(0.452463\pi\)
\(984\) 47.3865 1.51063
\(985\) −13.5369 −0.431322
\(986\) 19.0435 0.606468
\(987\) 0 0
\(988\) 26.2374 0.834724
\(989\) −15.3503 −0.488110
\(990\) −17.6424 −0.560714
\(991\) 38.4241 1.22058 0.610290 0.792178i \(-0.291053\pi\)
0.610290 + 0.792178i \(0.291053\pi\)
\(992\) −3.69323 −0.117260
\(993\) −23.8134 −0.755694
\(994\) 0 0
\(995\) −2.57452 −0.0816176
\(996\) −10.5745 −0.335066
\(997\) 18.8423 0.596740 0.298370 0.954450i \(-0.403557\pi\)
0.298370 + 0.954450i \(0.403557\pi\)
\(998\) −85.8759 −2.71835
\(999\) 23.7480 0.751353
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.p.1.3 3
7.6 odd 2 145.2.a.d.1.3 3
21.20 even 2 1305.2.a.o.1.1 3
28.27 even 2 2320.2.a.s.1.2 3
35.13 even 4 725.2.b.d.349.1 6
35.27 even 4 725.2.b.d.349.6 6
35.34 odd 2 725.2.a.d.1.1 3
56.13 odd 2 9280.2.a.bu.1.2 3
56.27 even 2 9280.2.a.bm.1.2 3
105.104 even 2 6525.2.a.bh.1.3 3
203.202 odd 2 4205.2.a.e.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
145.2.a.d.1.3 3 7.6 odd 2
725.2.a.d.1.1 3 35.34 odd 2
725.2.b.d.349.1 6 35.13 even 4
725.2.b.d.349.6 6 35.27 even 4
1305.2.a.o.1.1 3 21.20 even 2
2320.2.a.s.1.2 3 28.27 even 2
4205.2.a.e.1.1 3 203.202 odd 2
6525.2.a.bh.1.3 3 105.104 even 2
7105.2.a.p.1.3 3 1.1 even 1 trivial
9280.2.a.bm.1.2 3 56.27 even 2
9280.2.a.bu.1.2 3 56.13 odd 2