Properties

Label 1155.2.k.b.769.20
Level $1155$
Weight $2$
Character 1155.769
Analytic conductor $9.223$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(769,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.769");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.k (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 769.20
Character \(\chi\) \(=\) 1155.769
Dual form 1155.2.k.b.769.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.567201 q^{2} +1.00000 q^{3} -1.67828 q^{4} +(-2.10264 + 0.760858i) q^{5} -0.567201 q^{6} +(-2.63586 - 0.228555i) q^{7} +2.08633 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.567201 q^{2} +1.00000 q^{3} -1.67828 q^{4} +(-2.10264 + 0.760858i) q^{5} -0.567201 q^{6} +(-2.63586 - 0.228555i) q^{7} +2.08633 q^{8} +1.00000 q^{9} +(1.19262 - 0.431559i) q^{10} +(-0.727850 + 3.23577i) q^{11} -1.67828 q^{12} +4.44869i q^{13} +(1.49506 + 0.129637i) q^{14} +(-2.10264 + 0.760858i) q^{15} +2.17320 q^{16} -3.87358i q^{17} -0.567201 q^{18} +0.293716 q^{19} +(3.52882 - 1.27693i) q^{20} +(-2.63586 - 0.228555i) q^{21} +(0.412837 - 1.83534i) q^{22} -1.67062i q^{23} +2.08633 q^{24} +(3.84219 - 3.19962i) q^{25} -2.52330i q^{26} +1.00000 q^{27} +(4.42372 + 0.383579i) q^{28} +0.242329i q^{29} +(1.19262 - 0.431559i) q^{30} -6.28613i q^{31} -5.40529 q^{32} +(-0.727850 + 3.23577i) q^{33} +2.19710i q^{34} +(5.71616 - 1.52495i) q^{35} -1.67828 q^{36} -11.3596i q^{37} -0.166596 q^{38} +4.44869i q^{39} +(-4.38679 + 1.58740i) q^{40} -5.68888 q^{41} +(1.49506 + 0.129637i) q^{42} -7.05842 q^{43} +(1.22154 - 5.43054i) q^{44} +(-2.10264 + 0.760858i) q^{45} +0.947579i q^{46} -2.92937 q^{47} +2.17320 q^{48} +(6.89553 + 1.20488i) q^{49} +(-2.17930 + 1.81483i) q^{50} -3.87358i q^{51} -7.46615i q^{52} -10.1514i q^{53} -0.567201 q^{54} +(-0.931557 - 7.35746i) q^{55} +(-5.49927 - 0.476840i) q^{56} +0.293716 q^{57} -0.137449i q^{58} +5.48413i q^{59} +(3.52882 - 1.27693i) q^{60} +5.57566 q^{61} +3.56550i q^{62} +(-2.63586 - 0.228555i) q^{63} -1.28051 q^{64} +(-3.38482 - 9.35398i) q^{65} +(0.412837 - 1.83534i) q^{66} -12.1655i q^{67} +6.50096i q^{68} -1.67062i q^{69} +(-3.24222 + 0.864952i) q^{70} +10.3614 q^{71} +2.08633 q^{72} -4.76758i q^{73} +6.44320i q^{74} +(3.84219 - 3.19962i) q^{75} -0.492938 q^{76} +(2.65806 - 8.36270i) q^{77} -2.52330i q^{78} -7.37915i q^{79} +(-4.56945 + 1.65349i) q^{80} +1.00000 q^{81} +3.22674 q^{82} +12.9770i q^{83} +(4.42372 + 0.383579i) q^{84} +(2.94724 + 8.14475i) q^{85} +4.00355 q^{86} +0.242329i q^{87} +(-1.51853 + 6.75088i) q^{88} +13.0001i q^{89} +(1.19262 - 0.431559i) q^{90} +(1.01677 - 11.7261i) q^{91} +2.80378i q^{92} -6.28613i q^{93} +1.66154 q^{94} +(-0.617578 + 0.223476i) q^{95} -5.40529 q^{96} -14.1192 q^{97} +(-3.91115 - 0.683408i) q^{98} +(-0.727850 + 3.23577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 48 q^{3} + 48 q^{4} - 4 q^{5} + 48 q^{9} + 48 q^{12} - 4 q^{15} + 40 q^{16} - 18 q^{20} + 20 q^{25} + 48 q^{27} + 48 q^{36} - 20 q^{38} - 16 q^{44} - 4 q^{45} + 8 q^{47} + 40 q^{48} + 24 q^{49} - 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} + 20 q^{75} - 32 q^{77} - 46 q^{80} + 48 q^{81} - 32 q^{82} - 16 q^{86} + 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.567201 −0.401072 −0.200536 0.979686i \(-0.564268\pi\)
−0.200536 + 0.979686i \(0.564268\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.67828 −0.839141
\(5\) −2.10264 + 0.760858i −0.940329 + 0.340266i
\(6\) −0.567201 −0.231559
\(7\) −2.63586 0.228555i −0.996262 0.0863855i
\(8\) 2.08633 0.737628
\(9\) 1.00000 0.333333
\(10\) 1.19262 0.431559i 0.377140 0.136471i
\(11\) −0.727850 + 3.23577i −0.219455 + 0.975623i
\(12\) −1.67828 −0.484478
\(13\) 4.44869i 1.23384i 0.787025 + 0.616922i \(0.211620\pi\)
−0.787025 + 0.616922i \(0.788380\pi\)
\(14\) 1.49506 + 0.129637i 0.399573 + 0.0346468i
\(15\) −2.10264 + 0.760858i −0.542899 + 0.196453i
\(16\) 2.17320 0.543299
\(17\) 3.87358i 0.939481i −0.882804 0.469741i \(-0.844347\pi\)
0.882804 0.469741i \(-0.155653\pi\)
\(18\) −0.567201 −0.133691
\(19\) 0.293716 0.0673830 0.0336915 0.999432i \(-0.489274\pi\)
0.0336915 + 0.999432i \(0.489274\pi\)
\(20\) 3.52882 1.27693i 0.789069 0.285531i
\(21\) −2.63586 0.228555i −0.575192 0.0498747i
\(22\) 0.412837 1.83534i 0.0880172 0.391295i
\(23\) 1.67062i 0.348349i −0.984715 0.174174i \(-0.944274\pi\)
0.984715 0.174174i \(-0.0557256\pi\)
\(24\) 2.08633 0.425870
\(25\) 3.84219 3.19962i 0.768438 0.639924i
\(26\) 2.52330i 0.494860i
\(27\) 1.00000 0.192450
\(28\) 4.42372 + 0.383579i 0.836004 + 0.0724897i
\(29\) 0.242329i 0.0449993i 0.999747 + 0.0224997i \(0.00716247\pi\)
−0.999747 + 0.0224997i \(0.992838\pi\)
\(30\) 1.19262 0.431559i 0.217742 0.0787916i
\(31\) 6.28613i 1.12902i −0.825426 0.564511i \(-0.809065\pi\)
0.825426 0.564511i \(-0.190935\pi\)
\(32\) −5.40529 −0.955530
\(33\) −0.727850 + 3.23577i −0.126702 + 0.563276i
\(34\) 2.19710i 0.376800i
\(35\) 5.71616 1.52495i 0.966208 0.257763i
\(36\) −1.67828 −0.279714
\(37\) 11.3596i 1.86751i −0.357911 0.933756i \(-0.616511\pi\)
0.357911 0.933756i \(-0.383489\pi\)
\(38\) −0.166596 −0.0270254
\(39\) 4.44869i 0.712360i
\(40\) −4.38679 + 1.58740i −0.693613 + 0.250990i
\(41\) −5.68888 −0.888455 −0.444227 0.895914i \(-0.646522\pi\)
−0.444227 + 0.895914i \(0.646522\pi\)
\(42\) 1.49506 + 0.129637i 0.230693 + 0.0200033i
\(43\) −7.05842 −1.07640 −0.538200 0.842817i \(-0.680895\pi\)
−0.538200 + 0.842817i \(0.680895\pi\)
\(44\) 1.22154 5.43054i 0.184154 0.818685i
\(45\) −2.10264 + 0.760858i −0.313443 + 0.113422i
\(46\) 0.947579i 0.139713i
\(47\) −2.92937 −0.427293 −0.213646 0.976911i \(-0.568534\pi\)
−0.213646 + 0.976911i \(0.568534\pi\)
\(48\) 2.17320 0.313674
\(49\) 6.89553 + 1.20488i 0.985075 + 0.172125i
\(50\) −2.17930 + 1.81483i −0.308199 + 0.256656i
\(51\) 3.87358i 0.542410i
\(52\) 7.46615i 1.03537i
\(53\) 10.1514i 1.39441i −0.716873 0.697203i \(-0.754427\pi\)
0.716873 0.697203i \(-0.245573\pi\)
\(54\) −0.567201 −0.0771863
\(55\) −0.931557 7.35746i −0.125611 0.992080i
\(56\) −5.49927 0.476840i −0.734871 0.0637204i
\(57\) 0.293716 0.0389036
\(58\) 0.137449i 0.0180480i
\(59\) 5.48413i 0.713972i 0.934110 + 0.356986i \(0.116196\pi\)
−0.934110 + 0.356986i \(0.883804\pi\)
\(60\) 3.52882 1.27693i 0.455569 0.164851i
\(61\) 5.57566 0.713889 0.356945 0.934125i \(-0.383818\pi\)
0.356945 + 0.934125i \(0.383818\pi\)
\(62\) 3.56550i 0.452819i
\(63\) −2.63586 0.228555i −0.332087 0.0287952i
\(64\) −1.28051 −0.160063
\(65\) −3.38482 9.35398i −0.419835 1.16022i
\(66\) 0.412837 1.83534i 0.0508168 0.225914i
\(67\) 12.1655i 1.48625i −0.669153 0.743125i \(-0.733343\pi\)
0.669153 0.743125i \(-0.266657\pi\)
\(68\) 6.50096i 0.788358i
\(69\) 1.67062i 0.201119i
\(70\) −3.24222 + 0.864952i −0.387519 + 0.103382i
\(71\) 10.3614 1.22967 0.614836 0.788655i \(-0.289222\pi\)
0.614836 + 0.788655i \(0.289222\pi\)
\(72\) 2.08633 0.245876
\(73\) 4.76758i 0.558003i −0.960291 0.279001i \(-0.909997\pi\)
0.960291 0.279001i \(-0.0900034\pi\)
\(74\) 6.44320i 0.749006i
\(75\) 3.84219 3.19962i 0.443658 0.369460i
\(76\) −0.492938 −0.0565438
\(77\) 2.65806 8.36270i 0.302914 0.953018i
\(78\) 2.52330i 0.285708i
\(79\) 7.37915i 0.830219i −0.909771 0.415110i \(-0.863743\pi\)
0.909771 0.415110i \(-0.136257\pi\)
\(80\) −4.56945 + 1.65349i −0.510880 + 0.184866i
\(81\) 1.00000 0.111111
\(82\) 3.22674 0.356334
\(83\) 12.9770i 1.42441i 0.701971 + 0.712206i \(0.252304\pi\)
−0.701971 + 0.712206i \(0.747696\pi\)
\(84\) 4.42372 + 0.383579i 0.482667 + 0.0418519i
\(85\) 2.94724 + 8.14475i 0.319673 + 0.883422i
\(86\) 4.00355 0.431713
\(87\) 0.242329i 0.0259804i
\(88\) −1.51853 + 6.75088i −0.161876 + 0.719646i
\(89\) 13.0001i 1.37801i 0.724757 + 0.689004i \(0.241952\pi\)
−0.724757 + 0.689004i \(0.758048\pi\)
\(90\) 1.19262 0.431559i 0.125713 0.0454904i
\(91\) 1.01677 11.7261i 0.106586 1.22923i
\(92\) 2.80378i 0.292314i
\(93\) 6.28613i 0.651841i
\(94\) 1.66154 0.171375
\(95\) −0.617578 + 0.223476i −0.0633622 + 0.0229281i
\(96\) −5.40529 −0.551676
\(97\) −14.1192 −1.43359 −0.716794 0.697285i \(-0.754391\pi\)
−0.716794 + 0.697285i \(0.754391\pi\)
\(98\) −3.91115 0.683408i −0.395086 0.0690346i
\(99\) −0.727850 + 3.23577i −0.0731517 + 0.325208i
\(100\) −6.44828 + 5.36987i −0.644828 + 0.536987i
\(101\) 12.2453 1.21845 0.609226 0.792997i \(-0.291480\pi\)
0.609226 + 0.792997i \(0.291480\pi\)
\(102\) 2.19710i 0.217545i
\(103\) 6.50035 0.640498 0.320249 0.947333i \(-0.396233\pi\)
0.320249 + 0.947333i \(0.396233\pi\)
\(104\) 9.28141i 0.910117i
\(105\) 5.71616 1.52495i 0.557841 0.148820i
\(106\) 5.75791i 0.559257i
\(107\) 12.8529 1.24254 0.621269 0.783598i \(-0.286617\pi\)
0.621269 + 0.783598i \(0.286617\pi\)
\(108\) −1.67828 −0.161493
\(109\) 7.31694i 0.700836i −0.936593 0.350418i \(-0.886040\pi\)
0.936593 0.350418i \(-0.113960\pi\)
\(110\) 0.528380 + 4.17316i 0.0503791 + 0.397895i
\(111\) 11.3596i 1.07821i
\(112\) −5.72825 0.496694i −0.541268 0.0469332i
\(113\) 5.30123i 0.498698i −0.968414 0.249349i \(-0.919783\pi\)
0.968414 0.249349i \(-0.0802166\pi\)
\(114\) −0.166596 −0.0156031
\(115\) 1.27111 + 3.51272i 0.118531 + 0.327562i
\(116\) 0.406696i 0.0377608i
\(117\) 4.44869i 0.411281i
\(118\) 3.11060i 0.286354i
\(119\) −0.885325 + 10.2102i −0.0811576 + 0.935969i
\(120\) −4.38679 + 1.58740i −0.400458 + 0.144909i
\(121\) −9.94047 4.71032i −0.903679 0.428211i
\(122\) −3.16252 −0.286321
\(123\) −5.68888 −0.512949
\(124\) 10.5499i 0.947409i
\(125\) −5.64429 + 9.65101i −0.504841 + 0.863212i
\(126\) 1.49506 + 0.129637i 0.133191 + 0.0115489i
\(127\) 4.15420 0.368626 0.184313 0.982868i \(-0.440994\pi\)
0.184313 + 0.982868i \(0.440994\pi\)
\(128\) 11.5369 1.01973
\(129\) −7.05842 −0.621459
\(130\) 1.91987 + 5.30559i 0.168384 + 0.465331i
\(131\) −8.17994 −0.714685 −0.357343 0.933973i \(-0.616317\pi\)
−0.357343 + 0.933973i \(0.616317\pi\)
\(132\) 1.22154 5.43054i 0.106321 0.472668i
\(133\) −0.774193 0.0671301i −0.0671311 0.00582091i
\(134\) 6.90027i 0.596093i
\(135\) −2.10264 + 0.760858i −0.180966 + 0.0654842i
\(136\) 8.08156i 0.692988i
\(137\) 7.72402i 0.659908i 0.943997 + 0.329954i \(0.107033\pi\)
−0.943997 + 0.329954i \(0.892967\pi\)
\(138\) 0.947579i 0.0806633i
\(139\) −3.34279 −0.283532 −0.141766 0.989900i \(-0.545278\pi\)
−0.141766 + 0.989900i \(0.545278\pi\)
\(140\) −9.59334 + 2.55929i −0.810785 + 0.216300i
\(141\) −2.92937 −0.246697
\(142\) −5.87700 −0.493187
\(143\) −14.3949 3.23798i −1.20377 0.270773i
\(144\) 2.17320 0.181100
\(145\) −0.184378 0.509530i −0.0153117 0.0423142i
\(146\) 2.70418i 0.223799i
\(147\) 6.89553 + 1.20488i 0.568733 + 0.0993765i
\(148\) 19.0647i 1.56711i
\(149\) 15.9689i 1.30822i −0.756399 0.654110i \(-0.773043\pi\)
0.756399 0.654110i \(-0.226957\pi\)
\(150\) −2.17930 + 1.81483i −0.177939 + 0.148180i
\(151\) 11.4976i 0.935662i −0.883818 0.467831i \(-0.845036\pi\)
0.883818 0.467831i \(-0.154964\pi\)
\(152\) 0.612787 0.0497036
\(153\) 3.87358i 0.313160i
\(154\) −1.50766 + 4.74333i −0.121490 + 0.382229i
\(155\) 4.78285 + 13.2175i 0.384168 + 1.06165i
\(156\) 7.46615i 0.597771i
\(157\) 11.5302 0.920207 0.460103 0.887865i \(-0.347812\pi\)
0.460103 + 0.887865i \(0.347812\pi\)
\(158\) 4.18546i 0.332978i
\(159\) 10.1514i 0.805061i
\(160\) 11.3654 4.11266i 0.898513 0.325134i
\(161\) −0.381828 + 4.40353i −0.0300923 + 0.347046i
\(162\) −0.567201 −0.0445635
\(163\) 11.0609i 0.866357i 0.901308 + 0.433178i \(0.142608\pi\)
−0.901308 + 0.433178i \(0.857392\pi\)
\(164\) 9.54756 0.745539
\(165\) −0.931557 7.35746i −0.0725216 0.572777i
\(166\) 7.36058i 0.571292i
\(167\) 14.7919i 1.14463i 0.820033 + 0.572316i \(0.193955\pi\)
−0.820033 + 0.572316i \(0.806045\pi\)
\(168\) −5.49927 0.476840i −0.424278 0.0367890i
\(169\) −6.79080 −0.522369
\(170\) −1.67168 4.61971i −0.128212 0.354316i
\(171\) 0.293716 0.0224610
\(172\) 11.8460 0.903251
\(173\) 18.2598i 1.38827i −0.719847 0.694133i \(-0.755788\pi\)
0.719847 0.694133i \(-0.244212\pi\)
\(174\) 0.137449i 0.0104200i
\(175\) −10.8588 + 7.55560i −0.820846 + 0.571150i
\(176\) −1.58176 + 7.03198i −0.119230 + 0.530055i
\(177\) 5.48413i 0.412212i
\(178\) 7.37368i 0.552681i
\(179\) −3.28199 −0.245307 −0.122654 0.992450i \(-0.539140\pi\)
−0.122654 + 0.992450i \(0.539140\pi\)
\(180\) 3.52882 1.27693i 0.263023 0.0951770i
\(181\) 23.4137i 1.74032i −0.492766 0.870162i \(-0.664014\pi\)
0.492766 0.870162i \(-0.335986\pi\)
\(182\) −0.576712 + 6.65107i −0.0427487 + 0.493010i
\(183\) 5.57566 0.412164
\(184\) 3.48546i 0.256952i
\(185\) 8.64306 + 23.8852i 0.635450 + 1.75608i
\(186\) 3.56550i 0.261435i
\(187\) 12.5340 + 2.81939i 0.916579 + 0.206174i
\(188\) 4.91631 0.358559
\(189\) −2.63586 0.228555i −0.191731 0.0166249i
\(190\) 0.350291 0.126756i 0.0254128 0.00919583i
\(191\) −20.9902 −1.51880 −0.759400 0.650624i \(-0.774508\pi\)
−0.759400 + 0.650624i \(0.774508\pi\)
\(192\) −1.28051 −0.0924125
\(193\) 19.3802 1.39502 0.697510 0.716575i \(-0.254291\pi\)
0.697510 + 0.716575i \(0.254291\pi\)
\(194\) 8.00843 0.574972
\(195\) −3.38482 9.35398i −0.242392 0.669853i
\(196\) −11.5726 2.02212i −0.826617 0.144437i
\(197\) −21.2474 −1.51382 −0.756908 0.653521i \(-0.773291\pi\)
−0.756908 + 0.653521i \(0.773291\pi\)
\(198\) 0.412837 1.83534i 0.0293391 0.130432i
\(199\) 24.9705i 1.77011i −0.465486 0.885055i \(-0.654120\pi\)
0.465486 0.885055i \(-0.345880\pi\)
\(200\) 8.01607 6.67545i 0.566822 0.472026i
\(201\) 12.1655i 0.858086i
\(202\) −6.94554 −0.488687
\(203\) 0.0553853 0.638745i 0.00388729 0.0448311i
\(204\) 6.50096i 0.455159i
\(205\) 11.9617 4.32843i 0.835440 0.302311i
\(206\) −3.68700 −0.256886
\(207\) 1.67062i 0.116116i
\(208\) 9.66787i 0.670346i
\(209\) −0.213781 + 0.950397i −0.0147875 + 0.0657404i
\(210\) −3.24222 + 0.864952i −0.223734 + 0.0596873i
\(211\) 2.78208i 0.191526i 0.995404 + 0.0957631i \(0.0305291\pi\)
−0.995404 + 0.0957631i \(0.969471\pi\)
\(212\) 17.0370i 1.17010i
\(213\) 10.3614 0.709951
\(214\) −7.29019 −0.498347
\(215\) 14.8413 5.37045i 1.01217 0.366262i
\(216\) 2.08633 0.141957
\(217\) −1.43672 + 16.5694i −0.0975311 + 1.12480i
\(218\) 4.15018i 0.281086i
\(219\) 4.76758i 0.322163i
\(220\) 1.56342 + 12.3479i 0.105405 + 0.832495i
\(221\) 17.2323 1.15917
\(222\) 6.44320i 0.432439i
\(223\) 16.3794 1.09684 0.548422 0.836202i \(-0.315229\pi\)
0.548422 + 0.836202i \(0.315229\pi\)
\(224\) 14.2476 + 1.23541i 0.951958 + 0.0825440i
\(225\) 3.84219 3.19962i 0.256146 0.213308i
\(226\) 3.00687i 0.200014i
\(227\) 16.7625i 1.11257i −0.830993 0.556283i \(-0.812227\pi\)
0.830993 0.556283i \(-0.187773\pi\)
\(228\) −0.492938 −0.0326456
\(229\) 0.130024i 0.00859224i −0.999991 0.00429612i \(-0.998632\pi\)
0.999991 0.00429612i \(-0.00136750\pi\)
\(230\) −0.720972 1.99242i −0.0475395 0.131376i
\(231\) 2.65806 8.36270i 0.174888 0.550225i
\(232\) 0.505577i 0.0331927i
\(233\) −5.89232 −0.386019 −0.193009 0.981197i \(-0.561825\pi\)
−0.193009 + 0.981197i \(0.561825\pi\)
\(234\) 2.52330i 0.164953i
\(235\) 6.15941 2.22883i 0.401796 0.145393i
\(236\) 9.20391i 0.599124i
\(237\) 7.37915i 0.479327i
\(238\) 0.502158 5.79125i 0.0325500 0.375391i
\(239\) 2.70370i 0.174888i −0.996169 0.0874438i \(-0.972130\pi\)
0.996169 0.0874438i \(-0.0278698\pi\)
\(240\) −4.56945 + 1.65349i −0.294957 + 0.106733i
\(241\) −26.4906 −1.70641 −0.853205 0.521575i \(-0.825345\pi\)
−0.853205 + 0.521575i \(0.825345\pi\)
\(242\) 5.63825 + 2.67170i 0.362440 + 0.171743i
\(243\) 1.00000 0.0641500
\(244\) −9.35753 −0.599054
\(245\) −15.4155 + 2.71309i −0.984863 + 0.173333i
\(246\) 3.22674 0.205730
\(247\) 1.30665i 0.0831400i
\(248\) 13.1149i 0.832798i
\(249\) 12.9770i 0.822385i
\(250\) 3.20145 5.47407i 0.202477 0.346210i
\(251\) 0.841941i 0.0531428i −0.999647 0.0265714i \(-0.991541\pi\)
0.999647 0.0265714i \(-0.00845894\pi\)
\(252\) 4.42372 + 0.383579i 0.278668 + 0.0241632i
\(253\) 5.40575 + 1.21596i 0.339857 + 0.0764469i
\(254\) −2.35627 −0.147845
\(255\) 2.94724 + 8.14475i 0.184564 + 0.510044i
\(256\) −3.98273 −0.248921
\(257\) −22.7075 −1.41646 −0.708228 0.705984i \(-0.750505\pi\)
−0.708228 + 0.705984i \(0.750505\pi\)
\(258\) 4.00355 0.249250
\(259\) −2.59630 + 29.9424i −0.161326 + 1.86053i
\(260\) 5.68068 + 15.6986i 0.352301 + 0.973588i
\(261\) 0.242329i 0.0149998i
\(262\) 4.63968 0.286640
\(263\) −17.2218 −1.06194 −0.530972 0.847389i \(-0.678173\pi\)
−0.530972 + 0.847389i \(0.678173\pi\)
\(264\) −1.51853 + 6.75088i −0.0934592 + 0.415488i
\(265\) 7.72380 + 21.3448i 0.474469 + 1.31120i
\(266\) 0.439124 + 0.0380763i 0.0269244 + 0.00233461i
\(267\) 13.0001i 0.795594i
\(268\) 20.4171i 1.24717i
\(269\) 1.77799i 0.108406i 0.998530 + 0.0542029i \(0.0172618\pi\)
−0.998530 + 0.0542029i \(0.982738\pi\)
\(270\) 1.19262 0.431559i 0.0725806 0.0262639i
\(271\) −24.0555 −1.46126 −0.730632 0.682771i \(-0.760775\pi\)
−0.730632 + 0.682771i \(0.760775\pi\)
\(272\) 8.41806i 0.510420i
\(273\) 1.01677 11.7261i 0.0615376 0.709697i
\(274\) 4.38107i 0.264670i
\(275\) 7.55671 + 14.7613i 0.455687 + 0.890140i
\(276\) 2.80378i 0.168767i
\(277\) −21.5534 −1.29502 −0.647509 0.762058i \(-0.724189\pi\)
−0.647509 + 0.762058i \(0.724189\pi\)
\(278\) 1.89604 0.113717
\(279\) 6.28613i 0.376341i
\(280\) 11.9258 3.18154i 0.712702 0.190133i
\(281\) 7.14637i 0.426317i 0.977018 + 0.213158i \(0.0683750\pi\)
−0.977018 + 0.213158i \(0.931625\pi\)
\(282\) 1.66154 0.0989434
\(283\) 24.3695i 1.44862i 0.689475 + 0.724309i \(0.257841\pi\)
−0.689475 + 0.724309i \(0.742159\pi\)
\(284\) −17.3893 −1.03187
\(285\) −0.617578 + 0.223476i −0.0365822 + 0.0132376i
\(286\) 8.16483 + 1.83658i 0.482797 + 0.108599i
\(287\) 14.9951 + 1.30022i 0.885133 + 0.0767496i
\(288\) −5.40529 −0.318510
\(289\) 1.99537 0.117375
\(290\) 0.104579 + 0.289006i 0.00614110 + 0.0169710i
\(291\) −14.1192 −0.827683
\(292\) 8.00134i 0.468243i
\(293\) 25.4567i 1.48720i 0.668625 + 0.743599i \(0.266883\pi\)
−0.668625 + 0.743599i \(0.733117\pi\)
\(294\) −3.91115 0.683408i −0.228103 0.0398571i
\(295\) −4.17264 11.5311i −0.242940 0.671369i
\(296\) 23.6999i 1.37753i
\(297\) −0.727850 + 3.23577i −0.0422341 + 0.187759i
\(298\) 9.05756i 0.524690i
\(299\) 7.43207 0.429808
\(300\) −6.44828 + 5.36987i −0.372292 + 0.310029i
\(301\) 18.6050 + 1.61323i 1.07238 + 0.0929853i
\(302\) 6.52146i 0.375268i
\(303\) 12.2453 0.703473
\(304\) 0.638302 0.0366091
\(305\) −11.7236 + 4.24228i −0.671291 + 0.242912i
\(306\) 2.19710i 0.125600i
\(307\) 26.5078i 1.51288i −0.654062 0.756441i \(-0.726936\pi\)
0.654062 0.756441i \(-0.273064\pi\)
\(308\) −4.46098 + 14.0350i −0.254188 + 0.799717i
\(309\) 6.50035 0.369792
\(310\) −2.71284 7.49696i −0.154079 0.425799i
\(311\) 14.0105i 0.794464i 0.917718 + 0.397232i \(0.130029\pi\)
−0.917718 + 0.397232i \(0.869971\pi\)
\(312\) 9.28141i 0.525456i
\(313\) −26.0111 −1.47023 −0.735116 0.677941i \(-0.762873\pi\)
−0.735116 + 0.677941i \(0.762873\pi\)
\(314\) −6.53992 −0.369069
\(315\) 5.71616 1.52495i 0.322069 0.0859210i
\(316\) 12.3843i 0.696671i
\(317\) 8.25895i 0.463869i 0.972731 + 0.231934i \(0.0745055\pi\)
−0.972731 + 0.231934i \(0.925495\pi\)
\(318\) 5.75791i 0.322887i
\(319\) −0.784121 0.176379i −0.0439023 0.00987532i
\(320\) 2.69244 0.974282i 0.150512 0.0544640i
\(321\) 12.8529 0.717379
\(322\) 0.216574 2.49769i 0.0120692 0.139191i
\(323\) 1.13773i 0.0633051i
\(324\) −1.67828 −0.0932379
\(325\) 14.2341 + 17.0927i 0.789566 + 0.948132i
\(326\) 6.27376i 0.347471i
\(327\) 7.31694i 0.404628i
\(328\) −11.8689 −0.655349
\(329\) 7.72141 + 0.669521i 0.425695 + 0.0369119i
\(330\) 0.528380 + 4.17316i 0.0290864 + 0.229725i
\(331\) 21.0761 1.15845 0.579223 0.815169i \(-0.303356\pi\)
0.579223 + 0.815169i \(0.303356\pi\)
\(332\) 21.7791i 1.19528i
\(333\) 11.3596i 0.622504i
\(334\) 8.38999i 0.459080i
\(335\) 9.25619 + 25.5796i 0.505720 + 1.39756i
\(336\) −5.72825 0.496694i −0.312502 0.0270969i
\(337\) −2.95010 −0.160702 −0.0803512 0.996767i \(-0.525604\pi\)
−0.0803512 + 0.996767i \(0.525604\pi\)
\(338\) 3.85175 0.209508
\(339\) 5.30123i 0.287923i
\(340\) −4.94631 13.6692i −0.268251 0.741316i
\(341\) 20.3405 + 4.57536i 1.10150 + 0.247769i
\(342\) −0.166596 −0.00900847
\(343\) −17.9003 4.75189i −0.966524 0.256578i
\(344\) −14.7262 −0.793982
\(345\) 1.27111 + 3.51272i 0.0684340 + 0.189118i
\(346\) 10.3570i 0.556795i
\(347\) 15.9201 0.854637 0.427318 0.904101i \(-0.359458\pi\)
0.427318 + 0.904101i \(0.359458\pi\)
\(348\) 0.406696i 0.0218012i
\(349\) 35.0032 1.87368 0.936840 0.349758i \(-0.113736\pi\)
0.936840 + 0.349758i \(0.113736\pi\)
\(350\) 6.15911 4.28555i 0.329218 0.229072i
\(351\) 4.44869i 0.237453i
\(352\) 3.93424 17.4903i 0.209696 0.932237i
\(353\) −15.8285 −0.842469 −0.421234 0.906952i \(-0.638403\pi\)
−0.421234 + 0.906952i \(0.638403\pi\)
\(354\) 3.11060i 0.165327i
\(355\) −21.7863 + 7.88354i −1.15630 + 0.418415i
\(356\) 21.8179i 1.15634i
\(357\) −0.885325 + 10.2102i −0.0468564 + 0.540382i
\(358\) 1.86155 0.0983858
\(359\) 20.5387i 1.08399i −0.840382 0.541995i \(-0.817669\pi\)
0.840382 0.541995i \(-0.182331\pi\)
\(360\) −4.38679 + 1.58740i −0.231204 + 0.0836632i
\(361\) −18.9137 −0.995460
\(362\) 13.2803i 0.697995i
\(363\) −9.94047 4.71032i −0.521739 0.247227i
\(364\) −1.70642 + 19.6797i −0.0894409 + 1.03150i
\(365\) 3.62745 + 10.0245i 0.189869 + 0.524706i
\(366\) −3.16252 −0.165308
\(367\) −10.8338 −0.565519 −0.282759 0.959191i \(-0.591250\pi\)
−0.282759 + 0.959191i \(0.591250\pi\)
\(368\) 3.63059i 0.189258i
\(369\) −5.68888 −0.296152
\(370\) −4.90236 13.5477i −0.254861 0.704313i
\(371\) −2.32016 + 26.7578i −0.120457 + 1.38919i
\(372\) 10.5499i 0.546987i
\(373\) −4.55950 −0.236082 −0.118041 0.993009i \(-0.537661\pi\)
−0.118041 + 0.993009i \(0.537661\pi\)
\(374\) −7.10932 1.59916i −0.367614 0.0826906i
\(375\) −5.64429 + 9.65101i −0.291470 + 0.498376i
\(376\) −6.11162 −0.315183
\(377\) −1.07804 −0.0555221
\(378\) 1.49506 + 0.129637i 0.0768978 + 0.00666778i
\(379\) 8.64377 0.444001 0.222000 0.975047i \(-0.428741\pi\)
0.222000 + 0.975047i \(0.428741\pi\)
\(380\) 1.03647 0.375055i 0.0531698 0.0192399i
\(381\) 4.15420 0.212826
\(382\) 11.9057 0.609148
\(383\) 14.1718 0.724143 0.362071 0.932150i \(-0.382070\pi\)
0.362071 + 0.932150i \(0.382070\pi\)
\(384\) 11.5369 0.588740
\(385\) 0.773873 + 19.6062i 0.0394402 + 0.999222i
\(386\) −10.9925 −0.559504
\(387\) −7.05842 −0.358800
\(388\) 23.6960 1.20298
\(389\) 18.9857 0.962612 0.481306 0.876553i \(-0.340163\pi\)
0.481306 + 0.876553i \(0.340163\pi\)
\(390\) 1.91987 + 5.30559i 0.0972165 + 0.268659i
\(391\) −6.47129 −0.327267
\(392\) 14.3863 + 2.51377i 0.726619 + 0.126964i
\(393\) −8.17994 −0.412624
\(394\) 12.0516 0.607149
\(395\) 5.61448 + 15.5157i 0.282495 + 0.780680i
\(396\) 1.22154 5.43054i 0.0613846 0.272895i
\(397\) 12.3940 0.622035 0.311018 0.950404i \(-0.399330\pi\)
0.311018 + 0.950404i \(0.399330\pi\)
\(398\) 14.1633i 0.709942i
\(399\) −0.774193 0.0671301i −0.0387581 0.00336071i
\(400\) 8.34984 6.95341i 0.417492 0.347670i
\(401\) −10.3186 −0.515287 −0.257643 0.966240i \(-0.582946\pi\)
−0.257643 + 0.966240i \(0.582946\pi\)
\(402\) 6.90027i 0.344154i
\(403\) 27.9650 1.39304
\(404\) −20.5511 −1.02245
\(405\) −2.10264 + 0.760858i −0.104481 + 0.0378073i
\(406\) −0.0314146 + 0.362297i −0.00155908 + 0.0179805i
\(407\) 36.7572 + 8.26810i 1.82199 + 0.409835i
\(408\) 8.08156i 0.400097i
\(409\) −21.9324 −1.08449 −0.542243 0.840222i \(-0.682425\pi\)
−0.542243 + 0.840222i \(0.682425\pi\)
\(410\) −6.78468 + 2.45509i −0.335071 + 0.121248i
\(411\) 7.72402i 0.380998i
\(412\) −10.9094 −0.537468
\(413\) 1.25342 14.4554i 0.0616769 0.711303i
\(414\) 0.947579i 0.0465710i
\(415\) −9.87366 27.2860i −0.484679 1.33942i
\(416\) 24.0465i 1.17897i
\(417\) −3.34279 −0.163697
\(418\) 0.121257 0.539067i 0.00593086 0.0263666i
\(419\) 1.82773i 0.0892904i −0.999003 0.0446452i \(-0.985784\pi\)
0.999003 0.0446452i \(-0.0142157\pi\)
\(420\) −9.59334 + 2.55929i −0.468107 + 0.124881i
\(421\) −7.93395 −0.386677 −0.193339 0.981132i \(-0.561932\pi\)
−0.193339 + 0.981132i \(0.561932\pi\)
\(422\) 1.57800i 0.0768158i
\(423\) −2.92937 −0.142431
\(424\) 21.1792i 1.02855i
\(425\) −12.3940 14.8830i −0.601197 0.721934i
\(426\) −5.87700 −0.284741
\(427\) −14.6967 1.27434i −0.711221 0.0616697i
\(428\) −21.5708 −1.04266
\(429\) −14.3949 3.23798i −0.694994 0.156331i
\(430\) −8.41802 + 3.04613i −0.405953 + 0.146897i
\(431\) 15.5772i 0.750327i −0.926959 0.375164i \(-0.877587\pi\)
0.926959 0.375164i \(-0.122413\pi\)
\(432\) 2.17320 0.104558
\(433\) 18.2940 0.879153 0.439576 0.898205i \(-0.355129\pi\)
0.439576 + 0.898205i \(0.355129\pi\)
\(434\) 0.814911 9.39816i 0.0391170 0.451126i
\(435\) −0.184378 0.509530i −0.00884023 0.0244301i
\(436\) 12.2799i 0.588100i
\(437\) 0.490688i 0.0234728i
\(438\) 2.70418i 0.129211i
\(439\) 5.99399 0.286078 0.143039 0.989717i \(-0.454313\pi\)
0.143039 + 0.989717i \(0.454313\pi\)
\(440\) −1.94353 15.3501i −0.0926543 0.731786i
\(441\) 6.89553 + 1.20488i 0.328358 + 0.0573751i
\(442\) −9.77421 −0.464912
\(443\) 15.4074i 0.732027i −0.930610 0.366013i \(-0.880722\pi\)
0.930610 0.366013i \(-0.119278\pi\)
\(444\) 19.0647i 0.904769i
\(445\) −9.89123 27.3345i −0.468889 1.29578i
\(446\) −9.29040 −0.439913
\(447\) 15.9689i 0.755301i
\(448\) 3.37523 + 0.292665i 0.159465 + 0.0138271i
\(449\) −9.10949 −0.429904 −0.214952 0.976625i \(-0.568959\pi\)
−0.214952 + 0.976625i \(0.568959\pi\)
\(450\) −2.17930 + 1.81483i −0.102733 + 0.0855518i
\(451\) 4.14065 18.4079i 0.194976 0.866796i
\(452\) 8.89697i 0.418478i
\(453\) 11.4976i 0.540204i
\(454\) 9.50771i 0.446219i
\(455\) 6.78401 + 25.4294i 0.318039 + 1.19215i
\(456\) 0.612787 0.0286964
\(457\) 15.6456 0.731869 0.365934 0.930641i \(-0.380749\pi\)
0.365934 + 0.930641i \(0.380749\pi\)
\(458\) 0.0737499i 0.00344611i
\(459\) 3.87358i 0.180803i
\(460\) −2.13327 5.89533i −0.0994644 0.274871i
\(461\) −16.4860 −0.767831 −0.383916 0.923368i \(-0.625425\pi\)
−0.383916 + 0.923368i \(0.625425\pi\)
\(462\) −1.50766 + 4.74333i −0.0701425 + 0.220680i
\(463\) 19.9642i 0.927816i 0.885883 + 0.463908i \(0.153553\pi\)
−0.885883 + 0.463908i \(0.846447\pi\)
\(464\) 0.526628i 0.0244481i
\(465\) 4.78285 + 13.2175i 0.221799 + 0.612945i
\(466\) 3.34213 0.154821
\(467\) 3.73472 0.172822 0.0864112 0.996260i \(-0.472460\pi\)
0.0864112 + 0.996260i \(0.472460\pi\)
\(468\) 7.46615i 0.345123i
\(469\) −2.78048 + 32.0665i −0.128390 + 1.48069i
\(470\) −3.49363 + 1.26420i −0.161149 + 0.0583131i
\(471\) 11.5302 0.531282
\(472\) 11.4417i 0.526646i
\(473\) 5.13747 22.8395i 0.236221 1.05016i
\(474\) 4.18546i 0.192245i
\(475\) 1.12851 0.939778i 0.0517797 0.0431200i
\(476\) 1.48583 17.1356i 0.0681027 0.785411i
\(477\) 10.1514i 0.464802i
\(478\) 1.53354i 0.0701425i
\(479\) −18.9654 −0.866550 −0.433275 0.901262i \(-0.642642\pi\)
−0.433275 + 0.901262i \(0.642642\pi\)
\(480\) 11.3654 4.11266i 0.518757 0.187716i
\(481\) 50.5354 2.30422
\(482\) 15.0255 0.684393
\(483\) −0.381828 + 4.40353i −0.0173738 + 0.200367i
\(484\) 16.6829 + 7.90524i 0.758314 + 0.359329i
\(485\) 29.6876 10.7427i 1.34805 0.487801i
\(486\) −0.567201 −0.0257288
\(487\) 6.48529i 0.293877i 0.989146 + 0.146938i \(0.0469419\pi\)
−0.989146 + 0.146938i \(0.953058\pi\)
\(488\) 11.6326 0.526585
\(489\) 11.0609i 0.500191i
\(490\) 8.74372 1.53887i 0.395001 0.0695190i
\(491\) 10.6943i 0.482627i 0.970447 + 0.241314i \(0.0775782\pi\)
−0.970447 + 0.241314i \(0.922422\pi\)
\(492\) 9.54756 0.430437
\(493\) 0.938680 0.0422760
\(494\) 0.741133i 0.0333451i
\(495\) −0.931557 7.35746i −0.0418704 0.330693i
\(496\) 13.6610i 0.613397i
\(497\) −27.3112 2.36814i −1.22507 0.106226i
\(498\) 7.36058i 0.329835i
\(499\) −23.0123 −1.03017 −0.515087 0.857138i \(-0.672240\pi\)
−0.515087 + 0.857138i \(0.672240\pi\)
\(500\) 9.47272 16.1971i 0.423633 0.724357i
\(501\) 14.7919i 0.660854i
\(502\) 0.477550i 0.0213141i
\(503\) 34.8954i 1.55591i 0.628320 + 0.777955i \(0.283743\pi\)
−0.628320 + 0.777955i \(0.716257\pi\)
\(504\) −5.49927 0.476840i −0.244957 0.0212401i
\(505\) −25.7474 + 9.31692i −1.14575 + 0.414598i
\(506\) −3.06615 0.689695i −0.136307 0.0306607i
\(507\) −6.79080 −0.301590
\(508\) −6.97193 −0.309329
\(509\) 28.7970i 1.27641i −0.769868 0.638203i \(-0.779678\pi\)
0.769868 0.638203i \(-0.220322\pi\)
\(510\) −1.67168 4.61971i −0.0740233 0.204564i
\(511\) −1.08965 + 12.5667i −0.0482034 + 0.555917i
\(512\) −20.8148 −0.919892
\(513\) 0.293716 0.0129679
\(514\) 12.8797 0.568101
\(515\) −13.6679 + 4.94584i −0.602279 + 0.217940i
\(516\) 11.8460 0.521492
\(517\) 2.13214 9.47878i 0.0937715 0.416876i
\(518\) 1.47262 16.9834i 0.0647033 0.746206i
\(519\) 18.2598i 0.801516i
\(520\) −7.06183 19.5155i −0.309682 0.855810i
\(521\) 14.7346i 0.645534i −0.946478 0.322767i \(-0.895387\pi\)
0.946478 0.322767i \(-0.104613\pi\)
\(522\) 0.137449i 0.00601599i
\(523\) 6.03297i 0.263803i −0.991263 0.131902i \(-0.957892\pi\)
0.991263 0.131902i \(-0.0421083\pi\)
\(524\) 13.7283 0.599722
\(525\) −10.8588 + 7.55560i −0.473916 + 0.329753i
\(526\) 9.76825 0.425916
\(527\) −24.3498 −1.06069
\(528\) −1.58176 + 7.03198i −0.0688373 + 0.306028i
\(529\) 20.2090 0.878653
\(530\) −4.38095 12.1068i −0.190296 0.525886i
\(531\) 5.48413i 0.237991i
\(532\) 1.29932 + 0.112663i 0.0563325 + 0.00488457i
\(533\) 25.3081i 1.09621i
\(534\) 7.37368i 0.319090i
\(535\) −27.0250 + 9.77923i −1.16839 + 0.422793i
\(536\) 25.3812i 1.09630i
\(537\) −3.28199 −0.141628
\(538\) 1.00848i 0.0434785i
\(539\) −8.91762 + 21.4354i −0.384109 + 0.923288i
\(540\) 3.52882 1.27693i 0.151856 0.0549505i
\(541\) 31.3633i 1.34841i −0.738543 0.674206i \(-0.764486\pi\)
0.738543 0.674206i \(-0.235514\pi\)
\(542\) 13.6443 0.586072
\(543\) 23.4137i 1.00478i
\(544\) 20.9378i 0.897703i
\(545\) 5.56715 + 15.3849i 0.238470 + 0.659016i
\(546\) −0.576712 + 6.65107i −0.0246810 + 0.284639i
\(547\) −9.01256 −0.385349 −0.192675 0.981263i \(-0.561716\pi\)
−0.192675 + 0.981263i \(0.561716\pi\)
\(548\) 12.9631i 0.553756i
\(549\) 5.57566 0.237963
\(550\) −4.28617 8.37263i −0.182763 0.357010i
\(551\) 0.0711757i 0.00303219i
\(552\) 3.48546i 0.148351i
\(553\) −1.68654 + 19.4504i −0.0717189 + 0.827116i
\(554\) 12.2251 0.519395
\(555\) 8.64306 + 23.8852i 0.366877 + 1.01387i
\(556\) 5.61015 0.237923
\(557\) 15.2949 0.648066 0.324033 0.946046i \(-0.394961\pi\)
0.324033 + 0.946046i \(0.394961\pi\)
\(558\) 3.56550i 0.150940i
\(559\) 31.4007i 1.32811i
\(560\) 12.4224 3.31401i 0.524940 0.140043i
\(561\) 12.5340 + 2.81939i 0.529187 + 0.119035i
\(562\) 4.05343i 0.170984i
\(563\) 6.61395i 0.278745i −0.990240 0.139372i \(-0.955491\pi\)
0.990240 0.139372i \(-0.0445085\pi\)
\(564\) 4.91631 0.207014
\(565\) 4.03348 + 11.1466i 0.169690 + 0.468940i
\(566\) 13.8224i 0.581000i
\(567\) −2.63586 0.228555i −0.110696 0.00959839i
\(568\) 21.6173 0.907040
\(569\) 19.8797i 0.833400i −0.909044 0.416700i \(-0.863187\pi\)
0.909044 0.416700i \(-0.136813\pi\)
\(570\) 0.350291 0.126756i 0.0146721 0.00530921i
\(571\) 14.4599i 0.605127i −0.953129 0.302563i \(-0.902158\pi\)
0.953129 0.302563i \(-0.0978424\pi\)
\(572\) 24.1588 + 5.43424i 1.01013 + 0.227217i
\(573\) −20.9902 −0.876880
\(574\) −8.50525 0.737487i −0.355002 0.0307821i
\(575\) −5.34535 6.41885i −0.222917 0.267684i
\(576\) −1.28051 −0.0533544
\(577\) 2.85370 0.118801 0.0594005 0.998234i \(-0.481081\pi\)
0.0594005 + 0.998234i \(0.481081\pi\)
\(578\) −1.13178 −0.0470756
\(579\) 19.3802 0.805415
\(580\) 0.309438 + 0.855135i 0.0128487 + 0.0355076i
\(581\) 2.96596 34.2056i 0.123049 1.41909i
\(582\) 8.00843 0.331960
\(583\) 32.8477 + 7.38872i 1.36041 + 0.306010i
\(584\) 9.94672i 0.411598i
\(585\) −3.38482 9.35398i −0.139945 0.386740i
\(586\) 14.4391i 0.596474i
\(587\) −8.41194 −0.347198 −0.173599 0.984816i \(-0.555540\pi\)
−0.173599 + 0.984816i \(0.555540\pi\)
\(588\) −11.5726 2.02212i −0.477248 0.0833910i
\(589\) 1.84633i 0.0760768i
\(590\) 2.36673 + 6.54048i 0.0974366 + 0.269267i
\(591\) −21.2474 −0.874002
\(592\) 24.6867i 1.01462i
\(593\) 18.3022i 0.751583i −0.926704 0.375791i \(-0.877371\pi\)
0.926704 0.375791i \(-0.122629\pi\)
\(594\) 0.412837 1.83534i 0.0169389 0.0753047i
\(595\) −5.90700 22.1420i −0.242164 0.907735i
\(596\) 26.8003i 1.09778i
\(597\) 24.9705i 1.02197i
\(598\) −4.21548 −0.172384
\(599\) 4.67527 0.191027 0.0955133 0.995428i \(-0.469551\pi\)
0.0955133 + 0.995428i \(0.469551\pi\)
\(600\) 8.01607 6.67545i 0.327255 0.272524i
\(601\) −27.1569 −1.10775 −0.553876 0.832599i \(-0.686852\pi\)
−0.553876 + 0.832599i \(0.686852\pi\)
\(602\) −10.5528 0.915029i −0.430100 0.0372938i
\(603\) 12.1655i 0.495416i
\(604\) 19.2962i 0.785152i
\(605\) 24.4851 + 2.34082i 0.995461 + 0.0951678i
\(606\) −6.94554 −0.282143
\(607\) 6.98908i 0.283678i 0.989890 + 0.141839i \(0.0453015\pi\)
−0.989890 + 0.141839i \(0.954698\pi\)
\(608\) −1.58762 −0.0643865
\(609\) 0.0553853 0.638745i 0.00224433 0.0258832i
\(610\) 6.64964 2.40623i 0.269236 0.0974253i
\(611\) 13.0318i 0.527212i
\(612\) 6.50096i 0.262786i
\(613\) −43.5667 −1.75964 −0.879822 0.475304i \(-0.842338\pi\)
−0.879822 + 0.475304i \(0.842338\pi\)
\(614\) 15.0353i 0.606774i
\(615\) 11.9617 4.32843i 0.482341 0.174539i
\(616\) 5.54559 17.4473i 0.223438 0.702973i
\(617\) 29.3838i 1.18295i −0.806325 0.591473i \(-0.798546\pi\)
0.806325 0.591473i \(-0.201454\pi\)
\(618\) −3.68700 −0.148313
\(619\) 23.0883i 0.927997i 0.885836 + 0.463999i \(0.153586\pi\)
−0.885836 + 0.463999i \(0.846414\pi\)
\(620\) −8.02697 22.1826i −0.322371 0.890876i
\(621\) 1.67062i 0.0670397i
\(622\) 7.94678i 0.318637i
\(623\) 2.97124 34.2665i 0.119040 1.37286i
\(624\) 9.66787i 0.387025i
\(625\) 4.52487 24.5871i 0.180995 0.983484i
\(626\) 14.7535 0.589669
\(627\) −0.213781 + 0.950397i −0.00853758 + 0.0379552i
\(628\) −19.3509 −0.772184
\(629\) −44.0024 −1.75449
\(630\) −3.24222 + 0.864952i −0.129173 + 0.0344605i
\(631\) −18.8289 −0.749566 −0.374783 0.927113i \(-0.622283\pi\)
−0.374783 + 0.927113i \(0.622283\pi\)
\(632\) 15.3953i 0.612393i
\(633\) 2.78208i 0.110578i
\(634\) 4.68449i 0.186045i
\(635\) −8.73479 + 3.16076i −0.346630 + 0.125431i
\(636\) 17.0370i 0.675560i
\(637\) −5.36012 + 30.6760i −0.212376 + 1.21543i
\(638\) 0.444754 + 0.100042i 0.0176080 + 0.00396071i
\(639\) 10.3614 0.409890
\(640\) −24.2579 + 8.77793i −0.958879 + 0.346978i
\(641\) 32.9736 1.30238 0.651190 0.758915i \(-0.274270\pi\)
0.651190 + 0.758915i \(0.274270\pi\)
\(642\) −7.29019 −0.287721
\(643\) 5.85837 0.231032 0.115516 0.993306i \(-0.463148\pi\)
0.115516 + 0.993306i \(0.463148\pi\)
\(644\) 0.640816 7.39036i 0.0252517 0.291221i
\(645\) 14.8413 5.37045i 0.584376 0.211461i
\(646\) 0.645323i 0.0253899i
\(647\) −21.6502 −0.851156 −0.425578 0.904922i \(-0.639929\pi\)
−0.425578 + 0.904922i \(0.639929\pi\)
\(648\) 2.08633 0.0819587
\(649\) −17.7454 3.99162i −0.696568 0.156685i
\(650\) −8.07360 9.69500i −0.316673 0.380269i
\(651\) −1.43672 + 16.5694i −0.0563096 + 0.649404i
\(652\) 18.5633i 0.726996i
\(653\) 49.1478i 1.92330i −0.274276 0.961651i \(-0.588438\pi\)
0.274276 0.961651i \(-0.411562\pi\)
\(654\) 4.15018i 0.162285i
\(655\) 17.1995 6.22377i 0.672039 0.243183i
\(656\) −12.3631 −0.482697
\(657\) 4.76758i 0.186001i
\(658\) −4.37960 0.379753i −0.170734 0.0148043i
\(659\) 44.7970i 1.74504i −0.488576 0.872521i \(-0.662484\pi\)
0.488576 0.872521i \(-0.337516\pi\)
\(660\) 1.56342 + 12.3479i 0.0608559 + 0.480641i
\(661\) 8.39566i 0.326553i 0.986580 + 0.163277i \(0.0522063\pi\)
−0.986580 + 0.163277i \(0.947794\pi\)
\(662\) −11.9544 −0.464620
\(663\) 17.2323 0.669249
\(664\) 27.0743i 1.05069i
\(665\) 1.67893 0.447901i 0.0651060 0.0173688i
\(666\) 6.44320i 0.249669i
\(667\) 0.404839 0.0156754
\(668\) 24.8250i 0.960508i
\(669\) 16.3794 0.633263
\(670\) −5.25013 14.5088i −0.202830 0.560524i
\(671\) −4.05824 + 18.0416i −0.156667 + 0.696487i
\(672\) 14.2476 + 1.23541i 0.549613 + 0.0476568i
\(673\) 7.01933 0.270575 0.135288 0.990806i \(-0.456804\pi\)
0.135288 + 0.990806i \(0.456804\pi\)
\(674\) 1.67330 0.0644532
\(675\) 3.84219 3.19962i 0.147886 0.123153i
\(676\) 11.3969 0.438342
\(677\) 2.31998i 0.0891642i 0.999006 + 0.0445821i \(0.0141956\pi\)
−0.999006 + 0.0445821i \(0.985804\pi\)
\(678\) 3.00687i 0.115478i
\(679\) 37.2163 + 3.22701i 1.42823 + 0.123841i
\(680\) 6.14891 + 16.9926i 0.235800 + 0.651637i
\(681\) 16.7625i 0.642340i
\(682\) −11.5372 2.59515i −0.441780 0.0993734i
\(683\) 20.1258i 0.770091i 0.922898 + 0.385045i \(0.125814\pi\)
−0.922898 + 0.385045i \(0.874186\pi\)
\(684\) −0.492938 −0.0188479
\(685\) −5.87688 16.2408i −0.224544 0.620530i
\(686\) 10.1531 + 2.69528i 0.387645 + 0.102906i
\(687\) 0.130024i 0.00496073i
\(688\) −15.3393 −0.584807
\(689\) 45.1605 1.72048
\(690\) −0.720972 1.99242i −0.0274470 0.0758500i
\(691\) 33.8892i 1.28920i 0.764518 + 0.644602i \(0.222977\pi\)
−0.764518 + 0.644602i \(0.777023\pi\)
\(692\) 30.6451i 1.16495i
\(693\) 2.65806 8.36270i 0.100971 0.317673i
\(694\) −9.02992 −0.342771
\(695\) 7.02869 2.54339i 0.266613 0.0964762i
\(696\) 0.505577i 0.0191638i
\(697\) 22.0364i 0.834687i
\(698\) −19.8539 −0.751480
\(699\) −5.89232 −0.222868
\(700\) 18.2241 12.6804i 0.688806 0.479275i
\(701\) 10.4432i 0.394434i −0.980360 0.197217i \(-0.936810\pi\)
0.980360 0.197217i \(-0.0631903\pi\)
\(702\) 2.52330i 0.0952358i
\(703\) 3.33650i 0.125838i
\(704\) 0.932016 4.14343i 0.0351267 0.156161i
\(705\) 6.15941 2.22883i 0.231977 0.0839427i
\(706\) 8.97797 0.337890
\(707\) −32.2769 2.79872i −1.21390 0.105257i
\(708\) 9.20391i 0.345904i
\(709\) −6.53089 −0.245273 −0.122636 0.992452i \(-0.539135\pi\)
−0.122636 + 0.992452i \(0.539135\pi\)
\(710\) 12.3572 4.47156i 0.463758 0.167815i
\(711\) 7.37915i 0.276740i
\(712\) 27.1225i 1.01646i
\(713\) −10.5017 −0.393293
\(714\) 0.502158 5.79125i 0.0187928 0.216732i
\(715\) 32.7310 4.14420i 1.22407 0.154984i
\(716\) 5.50810 0.205847
\(717\) 2.70370i 0.100971i
\(718\) 11.6496i 0.434758i
\(719\) 5.95963i 0.222257i −0.993806 0.111128i \(-0.964554\pi\)
0.993806 0.111128i \(-0.0354465\pi\)
\(720\) −4.56945 + 1.65349i −0.170293 + 0.0616221i
\(721\) −17.1340 1.48568i −0.638104 0.0553298i
\(722\) 10.7279 0.399251
\(723\) −26.4906 −0.985197
\(724\) 39.2947i 1.46038i
\(725\) 0.775360 + 0.931073i 0.0287961 + 0.0345792i
\(726\) 5.63825 + 2.67170i 0.209255 + 0.0991560i
\(727\) 19.8405 0.735845 0.367922 0.929856i \(-0.380069\pi\)
0.367922 + 0.929856i \(0.380069\pi\)
\(728\) 2.12131 24.4645i 0.0786210 0.906715i
\(729\) 1.00000 0.0370370
\(730\) −2.05749 5.68591i −0.0761512 0.210445i
\(731\) 27.3414i 1.01126i
\(732\) −9.35753 −0.345864
\(733\) 36.0282i 1.33073i −0.746517 0.665366i \(-0.768275\pi\)
0.746517 0.665366i \(-0.231725\pi\)
\(734\) 6.14493 0.226814
\(735\) −15.4155 + 2.71309i −0.568611 + 0.100074i
\(736\) 9.03020i 0.332858i
\(737\) 39.3647 + 8.85464i 1.45002 + 0.326165i
\(738\) 3.22674 0.118778
\(739\) 15.1483i 0.557239i 0.960402 + 0.278619i \(0.0898768\pi\)
−0.960402 + 0.278619i \(0.910123\pi\)
\(740\) −14.5055 40.0861i −0.533233 1.47360i
\(741\) 1.30665i 0.0480009i
\(742\) 1.31600 15.1770i 0.0483117 0.557167i
\(743\) −17.7211 −0.650126 −0.325063 0.945692i \(-0.605385\pi\)
−0.325063 + 0.945692i \(0.605385\pi\)
\(744\) 13.1149i 0.480816i
\(745\) 12.1500 + 33.5768i 0.445143 + 1.23016i
\(746\) 2.58616 0.0946859
\(747\) 12.9770i 0.474804i
\(748\) −21.0357 4.73173i −0.769140 0.173009i
\(749\) −33.8785 2.93759i −1.23789 0.107337i
\(750\) 3.20145 5.47407i 0.116900 0.199885i
\(751\) −28.1754 −1.02813 −0.514067 0.857750i \(-0.671862\pi\)
−0.514067 + 0.857750i \(0.671862\pi\)
\(752\) −6.36610 −0.232148
\(753\) 0.841941i 0.0306820i
\(754\) 0.611468 0.0222684
\(755\) 8.74804 + 24.1753i 0.318374 + 0.879830i
\(756\) 4.42372 + 0.383579i 0.160889 + 0.0139506i
\(757\) 3.33748i 0.121303i −0.998159 0.0606514i \(-0.980682\pi\)
0.998159 0.0606514i \(-0.0193178\pi\)
\(758\) −4.90276 −0.178076
\(759\) 5.40575 + 1.21596i 0.196216 + 0.0441366i
\(760\) −1.28847 + 0.466243i −0.0467377 + 0.0169124i
\(761\) 20.3177 0.736517 0.368259 0.929723i \(-0.379954\pi\)
0.368259 + 0.929723i \(0.379954\pi\)
\(762\) −2.35627 −0.0853586
\(763\) −1.67232 + 19.2864i −0.0605421 + 0.698216i
\(764\) 35.2276 1.27449
\(765\) 2.94724 + 8.14475i 0.106558 + 0.294474i
\(766\) −8.03824 −0.290433
\(767\) −24.3972 −0.880930
\(768\) −3.98273 −0.143714
\(769\) −15.4946 −0.558748 −0.279374 0.960182i \(-0.590127\pi\)
−0.279374 + 0.960182i \(0.590127\pi\)
\(770\) −0.438942 11.1206i −0.0158184 0.400760i
\(771\) −22.7075 −0.817791
\(772\) −32.5255 −1.17062
\(773\) 20.9096 0.752066 0.376033 0.926606i \(-0.377288\pi\)
0.376033 + 0.926606i \(0.377288\pi\)
\(774\) 4.00355 0.143904
\(775\) −20.1132 24.1525i −0.722488 0.867583i
\(776\) −29.4573 −1.05745
\(777\) −2.59630 + 29.9424i −0.0931416 + 1.07418i
\(778\) −10.7687 −0.386077
\(779\) −1.67091 −0.0598667
\(780\) 5.68068 + 15.6986i 0.203401 + 0.562101i
\(781\) −7.54154 + 33.5271i −0.269857 + 1.19970i
\(782\) 3.67052 0.131258
\(783\) 0.242329i 0.00866012i
\(784\) 14.9853 + 2.61844i 0.535191 + 0.0935155i
\(785\) −24.2438 + 8.77281i −0.865298 + 0.313115i
\(786\) 4.63968 0.165492
\(787\) 16.8501i 0.600640i −0.953838 0.300320i \(-0.902906\pi\)
0.953838 0.300320i \(-0.0970935\pi\)
\(788\) 35.6592 1.27031
\(789\) −17.2218 −0.613114
\(790\) −3.18454 8.80053i −0.113301 0.313109i
\(791\) −1.21162 + 13.9733i −0.0430803 + 0.496834i
\(792\) −1.51853 + 6.75088i −0.0539587 + 0.239882i
\(793\) 24.8043i 0.880828i
\(794\) −7.02987 −0.249481
\(795\) 7.72380 + 21.3448i 0.273935 + 0.757023i
\(796\) 41.9075i 1.48537i
\(797\) 53.7507 1.90395 0.951974 0.306180i \(-0.0990510\pi\)
0.951974 + 0.306180i \(0.0990510\pi\)
\(798\) 0.439124 + 0.0380763i 0.0155448 + 0.00134789i
\(799\) 11.3472i 0.401433i
\(800\) −20.7682 + 17.2949i −0.734266 + 0.611467i
\(801\) 13.0001i 0.459336i
\(802\) 5.85273 0.206667
\(803\) 15.4268 + 3.47008i 0.544400 + 0.122456i
\(804\) 20.4171i 0.720056i
\(805\) −2.54761 9.54955i −0.0897914 0.336577i
\(806\) −15.8618 −0.558708
\(807\) 1.77799i 0.0625882i
\(808\) 25.5477 0.898764
\(809\) 35.6740i 1.25423i 0.778927 + 0.627115i \(0.215764\pi\)
−0.778927 + 0.627115i \(0.784236\pi\)
\(810\) 1.19262 0.431559i 0.0419044 0.0151635i
\(811\) 49.5430 1.73969 0.869845 0.493324i \(-0.164218\pi\)
0.869845 + 0.493324i \(0.164218\pi\)
\(812\) −0.0929523 + 1.07199i −0.00326199 + 0.0376196i
\(813\) −24.0555 −0.843662
\(814\) −20.8487 4.68968i −0.730748 0.164373i
\(815\) −8.41577 23.2571i −0.294792 0.814661i
\(816\) 8.41806i 0.294691i
\(817\) −2.07317 −0.0725310
\(818\) 12.4401 0.434957
\(819\) 1.01677 11.7261i 0.0355287 0.409744i
\(820\) −20.0751 + 7.26433i −0.701052 + 0.253681i
\(821\) 22.5260i 0.786164i 0.919503 + 0.393082i \(0.128591\pi\)
−0.919503 + 0.393082i \(0.871409\pi\)
\(822\) 4.38107i 0.152808i
\(823\) 43.3588i 1.51139i 0.654922 + 0.755696i \(0.272701\pi\)
−0.654922 + 0.755696i \(0.727299\pi\)
\(824\) 13.5618 0.472449
\(825\) 7.55671 + 14.7613i 0.263091 + 0.513923i
\(826\) −0.710943 + 8.19912i −0.0247369 + 0.285284i
\(827\) −19.3870 −0.674152 −0.337076 0.941477i \(-0.609438\pi\)
−0.337076 + 0.941477i \(0.609438\pi\)
\(828\) 2.80378i 0.0974379i
\(829\) 35.3424i 1.22749i −0.789504 0.613746i \(-0.789662\pi\)
0.789504 0.613746i \(-0.210338\pi\)
\(830\) 5.60035 + 15.4766i 0.194391 + 0.537202i
\(831\) −21.5534 −0.747679
\(832\) 5.69657i 0.197493i
\(833\) 4.66719 26.7104i 0.161708 0.925460i
\(834\) 1.89604 0.0656543
\(835\) −11.2545 31.1021i −0.389479 1.07633i
\(836\) 0.358785 1.59504i 0.0124088 0.0551654i
\(837\) 6.28613i 0.217280i
\(838\) 1.03669i 0.0358119i
\(839\) 6.53422i 0.225586i 0.993618 + 0.112793i \(0.0359797\pi\)
−0.993618 + 0.112793i \(0.964020\pi\)
\(840\) 11.9258 3.18154i 0.411479 0.109773i
\(841\) 28.9413 0.997975
\(842\) 4.50015 0.155085
\(843\) 7.14637i 0.246134i
\(844\) 4.66911i 0.160718i
\(845\) 14.2786 5.16683i 0.491199 0.177744i
\(846\) 1.66154 0.0571250
\(847\) 25.1251 + 14.6877i 0.863310 + 0.504675i
\(848\) 22.0611i 0.757580i
\(849\) 24.3695i 0.836360i
\(850\) 7.02989 + 8.44168i 0.241123 + 0.289547i
\(851\) −18.9776 −0.650545
\(852\) −17.3893 −0.595749
\(853\) 9.26467i 0.317216i 0.987342 + 0.158608i \(0.0507006\pi\)
−0.987342 + 0.158608i \(0.949299\pi\)
\(854\) 8.33596 + 0.722808i 0.285251 + 0.0247340i
\(855\) −0.617578 + 0.223476i −0.0211207 + 0.00764271i
\(856\) 26.8154 0.916530
\(857\) 52.4191i 1.79060i −0.445460 0.895302i \(-0.646960\pi\)
0.445460 0.895302i \(-0.353040\pi\)
\(858\) 8.16483 + 1.83658i 0.278743 + 0.0626999i
\(859\) 4.69044i 0.160036i −0.996793 0.0800178i \(-0.974502\pi\)
0.996793 0.0800178i \(-0.0254977\pi\)
\(860\) −24.9079 + 9.01314i −0.849353 + 0.307345i
\(861\) 14.9951 + 1.30022i 0.511032 + 0.0443114i
\(862\) 8.83541i 0.300935i
\(863\) 34.5431i 1.17586i 0.808911 + 0.587931i \(0.200057\pi\)
−0.808911 + 0.587931i \(0.799943\pi\)
\(864\) −5.40529 −0.183892
\(865\) 13.8931 + 38.3938i 0.472380 + 1.30543i
\(866\) −10.3764 −0.352603
\(867\) 1.99537 0.0677662
\(868\) 2.41123 27.8081i 0.0818424 0.943867i
\(869\) 23.8773 + 5.37091i 0.809981 + 0.182196i
\(870\) 0.104579 + 0.289006i 0.00354557 + 0.00979822i
\(871\) 54.1204 1.83380
\(872\) 15.2655i 0.516956i
\(873\) −14.1192 −0.477863
\(874\) 0.278319i 0.00941427i
\(875\) 17.0833 24.1487i 0.577523 0.816375i
\(876\) 8.00134i 0.270340i
\(877\) 20.6612 0.697679 0.348840 0.937182i \(-0.386576\pi\)
0.348840 + 0.937182i \(0.386576\pi\)
\(878\) −3.39980 −0.114738
\(879\) 25.4567i 0.858635i
\(880\) −2.02446 15.9892i −0.0682445 0.538996i
\(881\) 11.5976i 0.390732i −0.980730 0.195366i \(-0.937410\pi\)
0.980730 0.195366i \(-0.0625895\pi\)
\(882\) −3.91115 0.683408i −0.131695 0.0230115i
\(883\) 21.6925i 0.730011i 0.931005 + 0.365006i \(0.118933\pi\)
−0.931005 + 0.365006i \(0.881067\pi\)
\(884\) −28.9207 −0.972710
\(885\) −4.17264 11.5311i −0.140262 0.387615i
\(886\) 8.73909i 0.293595i
\(887\) 30.7127i 1.03123i 0.856820 + 0.515616i \(0.172437\pi\)
−0.856820 + 0.515616i \(0.827563\pi\)
\(888\) 23.6999i 0.795317i
\(889\) −10.9499 0.949462i −0.367248 0.0318439i
\(890\) 5.61032 + 15.5042i 0.188058 + 0.519702i
\(891\) −0.727850 + 3.23577i −0.0243839 + 0.108403i
\(892\) −27.4892 −0.920407
\(893\) −0.860402 −0.0287922
\(894\) 9.05756i 0.302930i
\(895\) 6.90084 2.49712i 0.230670 0.0834697i
\(896\) −30.4096 2.63681i −1.01591 0.0880897i
\(897\) 7.43207 0.248150
\(898\) 5.16692 0.172422
\(899\) 1.52331 0.0508052
\(900\) −6.44828 + 5.36987i −0.214943 + 0.178996i
\(901\) −39.3224 −1.31002
\(902\) −2.34858 + 10.4410i −0.0781993 + 0.347648i
\(903\) 18.6050 + 1.61323i 0.619136 + 0.0536851i
\(904\) 11.0601i 0.367854i
\(905\) 17.8145 + 49.2305i 0.592173 + 1.63648i
\(906\) 6.52146i 0.216661i
\(907\) 3.30534i 0.109752i 0.998493 + 0.0548761i \(0.0174764\pi\)
−0.998493 + 0.0548761i \(0.982524\pi\)
\(908\) 28.1322i 0.933600i
\(909\) 12.2453 0.406151
\(910\) −3.84790 14.4236i −0.127557 0.478138i
\(911\) 34.8475 1.15455 0.577275 0.816550i \(-0.304116\pi\)
0.577275 + 0.816550i \(0.304116\pi\)
\(912\) 0.638302 0.0211363
\(913\) −41.9907 9.44531i −1.38969 0.312594i
\(914\) −8.87419 −0.293532
\(915\) −11.7236 + 4.24228i −0.387570 + 0.140245i
\(916\) 0.218217i 0.00721011i
\(917\) 21.5612 + 1.86956i 0.712013 + 0.0617385i
\(918\) 2.19710i 0.0725151i
\(919\) 7.59218i 0.250443i 0.992129 + 0.125222i \(0.0399642\pi\)
−0.992129 + 0.125222i \(0.960036\pi\)
\(920\) 2.65194 + 7.32867i 0.0874319 + 0.241619i
\(921\) 26.5078i 0.873463i
\(922\) 9.35090 0.307956
\(923\) 46.0946i 1.51722i
\(924\) −4.46098 + 14.0350i −0.146755 + 0.461717i
\(925\) −36.3465 43.6459i −1.19507 1.43507i
\(926\) 11.3237i 0.372121i
\(927\) 6.50035 0.213499
\(928\) 1.30986i 0.0429982i
\(929\) 48.9705i 1.60667i −0.595528 0.803334i \(-0.703057\pi\)
0.595528 0.803334i \(-0.296943\pi\)
\(930\) −2.71284 7.49696i −0.0889574 0.245835i
\(931\) 2.02532 + 0.353891i 0.0663773 + 0.0115983i
\(932\) 9.88898 0.323924
\(933\) 14.0105i 0.458684i
\(934\) −2.11834 −0.0693142
\(935\) −28.4997 + 3.60846i −0.932040 + 0.118009i
\(936\) 9.28141i 0.303372i
\(937\) 35.3138i 1.15365i −0.816868 0.576825i \(-0.804291\pi\)
0.816868 0.576825i \(-0.195709\pi\)
\(938\) 1.57709 18.1882i 0.0514938 0.593865i
\(939\) −26.0111 −0.848839
\(940\) −10.3372 + 3.74061i −0.337163 + 0.122005i
\(941\) −58.8989 −1.92005 −0.960024 0.279918i \(-0.909693\pi\)
−0.960024 + 0.279918i \(0.909693\pi\)
\(942\) −6.53992 −0.213082
\(943\) 9.50397i 0.309492i
\(944\) 11.9181i 0.387901i
\(945\) 5.71616 1.52495i 0.185947 0.0496065i
\(946\) −2.91398 + 12.9546i −0.0947417 + 0.421189i
\(947\) 45.3395i 1.47334i 0.676254 + 0.736668i \(0.263602\pi\)
−0.676254 + 0.736668i \(0.736398\pi\)
\(948\) 12.3843i 0.402223i
\(949\) 21.2094 0.688488
\(950\) −0.640093 + 0.533043i −0.0207674 + 0.0172942i
\(951\) 8.25895i 0.267815i
\(952\) −1.84708 + 21.3019i −0.0598641 + 0.690397i
\(953\) 23.0721 0.747380 0.373690 0.927554i \(-0.378092\pi\)
0.373690 + 0.927554i \(0.378092\pi\)
\(954\) 5.75791i 0.186419i
\(955\) 44.1349 15.9706i 1.42817 0.516796i
\(956\) 4.53757i 0.146755i
\(957\) −0.784121 0.176379i −0.0253470 0.00570152i
\(958\) 10.7572 0.347549
\(959\) 1.76536 20.3594i 0.0570065 0.657441i
\(960\) 2.69244 0.974282i 0.0868982 0.0314448i
\(961\) −8.51538 −0.274690
\(962\) −28.6638 −0.924157
\(963\) 12.8529 0.414179
\(964\) 44.4587 1.43192
\(965\) −40.7497 + 14.7456i −1.31178 + 0.474678i
\(966\) 0.216574 2.49769i 0.00696814 0.0803617i
\(967\) 6.94580 0.223362 0.111681 0.993744i \(-0.464377\pi\)
0.111681 + 0.993744i \(0.464377\pi\)
\(968\) −20.7391 9.82726i −0.666579 0.315860i
\(969\) 1.13773i 0.0365492i
\(970\) −16.8389 + 6.09328i −0.540663 + 0.195643i
\(971\) 58.1686i 1.86672i 0.358942 + 0.933360i \(0.383138\pi\)
−0.358942 + 0.933360i \(0.616862\pi\)
\(972\) −1.67828 −0.0538309
\(973\) 8.81113 + 0.764010i 0.282472 + 0.0244930i
\(974\) 3.67847i 0.117866i
\(975\) 14.2341 + 17.0927i 0.455856 + 0.547405i
\(976\) 12.1170 0.387856
\(977\) 21.2862i 0.681005i −0.940244 0.340503i \(-0.889403\pi\)
0.940244 0.340503i \(-0.110597\pi\)
\(978\) 6.27376i 0.200613i
\(979\) −42.0654 9.46213i −1.34442 0.302411i
\(980\) 25.8716 4.55333i 0.826439 0.145451i
\(981\) 7.31694i 0.233612i
\(982\) 6.06582i 0.193568i
\(983\) −29.6052 −0.944259 −0.472130 0.881529i \(-0.656515\pi\)
−0.472130 + 0.881529i \(0.656515\pi\)
\(984\) −11.8689 −0.378366
\(985\) 44.6757 16.1663i 1.42349 0.515100i
\(986\) −0.532420 −0.0169557
\(987\) 7.72141 + 0.669521i 0.245775 + 0.0213111i
\(988\) 2.19293i 0.0697662i
\(989\) 11.7919i 0.374962i
\(990\) 0.528380 + 4.17316i 0.0167930 + 0.132632i
\(991\) −14.2985 −0.454208 −0.227104 0.973870i \(-0.572926\pi\)
−0.227104 + 0.973870i \(0.572926\pi\)
\(992\) 33.9784i 1.07881i
\(993\) 21.0761 0.668829
\(994\) 15.4909 + 1.34321i 0.491343 + 0.0426042i
\(995\) 18.9990 + 52.5039i 0.602308 + 1.66449i
\(996\) 21.7791i 0.690097i
\(997\) 42.2847i 1.33917i −0.742736 0.669585i \(-0.766472\pi\)
0.742736 0.669585i \(-0.233528\pi\)
\(998\) 13.0526 0.413174
\(999\) 11.3596i 0.359403i
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 1155.2.k.b.769.20 yes 48
5.4 even 2 1155.2.k.a.769.29 yes 48
7.6 odd 2 1155.2.k.a.769.19 48
11.10 odd 2 inner 1155.2.k.b.769.29 yes 48
35.34 odd 2 inner 1155.2.k.b.769.30 yes 48
55.54 odd 2 1155.2.k.a.769.20 yes 48
77.76 even 2 1155.2.k.a.769.30 yes 48
385.384 even 2 inner 1155.2.k.b.769.19 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.k.a.769.19 48 7.6 odd 2
1155.2.k.a.769.20 yes 48 55.54 odd 2
1155.2.k.a.769.29 yes 48 5.4 even 2
1155.2.k.a.769.30 yes 48 77.76 even 2
1155.2.k.b.769.19 yes 48 385.384 even 2 inner
1155.2.k.b.769.20 yes 48 1.1 even 1 trivial
1155.2.k.b.769.29 yes 48 11.10 odd 2 inner
1155.2.k.b.769.30 yes 48 35.34 odd 2 inner