Properties

Label 1155.2.k.a.769.19
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 769.19
Character \(\chi\) \(=\) 1155.769
Dual form 1155.2.k.a.769.20

$q$-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} +(-5.36837 + 2.48608i) 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} +(3.04495 - 1.41011i) 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} +(1.17896 - 8.69540i) 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 \(-0.788380\pi\)
0.787025 0.616922i \(-0.211620\pi\)
\(14\) 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 \(0.155653\pi\)
−0.882804 + 0.469741i \(0.844347\pi\)
\(18\) −0.567201 −0.133691
\(19\) −0.293716 −0.0673830 −0.0336915 0.999432i \(-0.510726\pi\)
−0.0336915 + 0.999432i \(0.510726\pi\)
\(20\) −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 \(0.190935\pi\)
−0.825426 + 0.564511i \(0.809065\pi\)
\(32\) −5.40529 −0.955530
\(33\) 0.727850 3.23577i 0.126702 0.563276i
\(34\) 2.19710i 0.376800i
\(35\) −5.36837 + 2.48608i −0.907420 + 0.420225i
\(36\) −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 \(-0.353478\pi\)
0.444227 + 0.895914i \(0.353478\pi\)
\(42\) −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 \(-0.431466\pi\)
0.213646 + 0.976911i \(0.431466\pi\)
\(48\) −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 \(-0.883804\pi\)
0.934110 0.356986i \(-0.116196\pi\)
\(60\) 3.52882 1.27693i 0.455569 0.164851i
\(61\) −5.57566 −0.713889 −0.356945 0.934125i \(-0.616182\pi\)
−0.356945 + 0.934125i \(0.616182\pi\)
\(62\) 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
\(70\) 3.04495 1.41011i 0.363941 0.168540i
\(71\) 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 \(0.0900034\pi\)
−0.960291 + 0.279001i \(0.909997\pi\)
\(74\) 6.44320i 0.749006i
\(75\) −3.84219 + 3.19962i −0.443658 + 0.369460i
\(76\) 0.492938 0.0565438
\(77\) 1.17896 8.69540i 0.134355 0.990933i
\(78\) 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 \(-0.747696\pi\)
0.701971 0.712206i \(-0.252304\pi\)
\(84\) −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 \(-0.758048\pi\)
0.724757 0.689004i \(-0.241952\pi\)
\(90\) −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 \(-0.245609\pi\)
0.716794 + 0.697285i \(0.245609\pi\)
\(98\) −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 \(-0.708520\pi\)
−0.609226 + 0.792997i \(0.708520\pi\)
\(102\) 2.19710i 0.217545i
\(103\) −6.50035 −0.640498 −0.320249 0.947333i \(-0.603767\pi\)
−0.320249 + 0.947333i \(0.603767\pi\)
\(104\) 9.28141i 0.910117i
\(105\) 5.36837 2.48608i 0.523899 0.242617i
\(106\) 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 \(-0.383683\pi\)
0.357343 + 0.933973i \(0.383683\pi\)
\(132\) −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 \(-0.454722\pi\)
0.141766 + 0.989900i \(0.454722\pi\)
\(140\) 9.00964 4.17235i 0.761454 0.352628i
\(141\) −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
\(154\) −0.668708 + 4.93204i −0.0538860 + 0.397436i
\(155\) 4.78285 + 13.2175i 0.384168 + 1.06165i
\(156\) 7.46615i 0.597771i
\(157\) −11.5302 −0.920207 −0.460103 0.887865i \(-0.652188\pi\)
−0.460103 + 0.887865i \(0.652188\pi\)
\(158\) 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 \(-0.806045\pi\)
0.820033 0.572316i \(-0.193955\pi\)
\(168\) 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 \(0.244212\pi\)
−0.719847 + 0.694133i \(0.755788\pi\)
\(174\) 0.137449i 0.0104200i
\(175\) −9.39619 + 9.31190i −0.710286 + 0.703914i
\(176\) −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 \(0.335986\pi\)
−0.492766 + 0.870162i \(0.664014\pi\)
\(182\) −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 \(0.345880\pi\)
−0.465486 + 0.885055i \(0.654120\pi\)
\(200\) 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
\(210\) −3.04495 + 1.41011i −0.210121 + 0.0973068i
\(211\) 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 \(-0.684771\pi\)
−0.548422 + 0.836202i \(0.684771\pi\)
\(224\) 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 \(0.187773\pi\)
−0.830993 + 0.556283i \(0.812227\pi\)
\(228\) −0.492938 −0.0326456
\(229\) 0.130024i 0.00859224i 0.999991 + 0.00429612i \(0.00136750\pi\)
−0.999991 + 0.00429612i \(0.998632\pi\)
\(230\) 0.720972 + 1.99242i 0.0475395 + 0.131376i
\(231\) −1.17896 + 8.69540i −0.0775699 + 0.572116i
\(232\) 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 \(-0.174655\pi\)
0.853205 + 0.521575i \(0.174655\pi\)
\(242\) 5.63825 + 2.67170i 0.362440 + 0.171743i
\(243\) −1.00000 −0.0641500
\(244\) 9.35753 0.599054
\(245\) 13.5821 7.77993i 0.867727 0.497042i
\(246\) 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 \(0.00845894\pi\)
−0.999647 + 0.0265714i \(0.991541\pi\)
\(252\) 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 \(-0.249495\pi\)
0.708228 + 0.705984i \(0.249495\pi\)
\(258\) −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 \(-0.982738\pi\)
0.998530 0.0542029i \(-0.0172618\pi\)
\(270\) 1.19262 0.431559i 0.0725806 0.0262639i
\(271\) 24.0555 1.46126 0.730632 0.682771i \(-0.239225\pi\)
0.730632 + 0.682771i \(0.239225\pi\)
\(272\) 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
\(280\) −11.2002 + 5.18678i −0.669338 + 0.309969i
\(281\) 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 \(-0.742159\pi\)
0.689475 0.724309i \(-0.257841\pi\)
\(284\) −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 \(-0.733117\pi\)
0.668625 0.743599i \(-0.266883\pi\)
\(294\) 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 \(0.273064\pi\)
−0.654062 + 0.756441i \(0.726936\pi\)
\(308\) −1.97863 + 14.5933i −0.112743 + 0.831533i
\(309\) 6.50035 0.369792
\(310\) −2.71284 7.49696i −0.154079 0.425799i
\(311\) 14.0105i 0.794464i −0.917718 0.397232i \(-0.869971\pi\)
0.917718 0.397232i \(-0.130029\pi\)
\(312\) 9.28141i 0.525456i
\(313\) 26.0111 1.47023 0.735116 0.677941i \(-0.237127\pi\)
0.735116 + 0.677941i \(0.237127\pi\)
\(314\) 6.53992 0.369069
\(315\) −5.36837 + 2.48608i −0.302473 + 0.140075i
\(316\) 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 \(-0.886264\pi\)
−0.936840 + 0.349758i \(0.886264\pi\)
\(350\) 5.32953 5.28172i 0.284876 0.282320i
\(351\) 4.44869i 0.237453i
\(352\) 3.93424 17.4903i 0.209696 0.932237i
\(353\) 15.8285 0.842469 0.421234 0.906952i \(-0.361597\pi\)
0.421234 + 0.906952i \(0.361597\pi\)
\(354\) 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 \(-0.408750\pi\)
0.282759 + 0.959191i \(0.408750\pi\)
\(368\) 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 \(-0.617930\pi\)
−0.362071 + 0.932150i \(0.617930\pi\)
\(384\) −11.5369 −0.588740
\(385\) −4.13704 19.1803i −0.210843 0.977520i
\(386\) −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 \(-0.600670\pi\)
−0.311018 + 0.950404i \(0.600670\pi\)
\(398\) 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 \(-0.317575\pi\)
0.542243 + 0.840222i \(0.317575\pi\)
\(410\) −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 \(0.0142157\pi\)
−0.999003 + 0.0446452i \(0.985784\pi\)
\(420\) −9.00964 + 4.17235i −0.439625 + 0.203590i
\(421\) −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 \(-0.644871\pi\)
−0.439576 + 0.898205i \(0.644871\pi\)
\(434\) 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 \(-0.545687\pi\)
−0.143039 + 0.989717i \(0.545687\pi\)
\(440\) 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
\(455\) 11.0598 + 23.8822i 0.518491 + 1.11961i
\(456\) 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 \(-0.374575\pi\)
0.383916 + 0.923368i \(0.374575\pi\)
\(462\) 0.668708 4.93204i 0.0311111 0.229459i
\(463\) 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 \(-0.527540\pi\)
−0.0864112 + 0.996260i \(0.527540\pi\)
\(468\) 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 \(-0.357358\pi\)
0.433275 + 0.901262i \(0.357358\pi\)
\(480\) 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
\(490\) −7.70377 + 4.41279i −0.348021 + 0.199350i
\(491\) 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 \(-0.716257\pi\)
0.628320 0.777955i \(-0.283743\pi\)
\(504\) −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 \(0.220322\pi\)
−0.769868 + 0.638203i \(0.779678\pi\)
\(510\) 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 \(0.104613\pi\)
−0.946478 + 0.322767i \(0.895387\pi\)
\(522\) 0.137449i 0.00601599i
\(523\) 6.03297i 0.263803i 0.991263 + 0.131902i \(0.0421083\pi\)
−0.991263 + 0.131902i \(0.957892\pi\)
\(524\) −13.7283 −0.599722
\(525\) 9.39619 9.31190i 0.410084 0.406405i
\(526\) 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
\(539\) −1.12020 + 23.1893i −0.0482504 + 0.998835i
\(540\) 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
\(560\) −11.6665 + 5.40275i −0.493001 + 0.228308i
\(561\) 12.5340 + 2.81939i 0.529187 + 0.119035i
\(562\) 4.05343i 0.170984i
\(563\) 6.61395i 0.278745i 0.990240 + 0.139372i \(0.0445085\pi\)
−0.990240 + 0.139372i \(0.955491\pi\)
\(564\) 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 \(-0.518919\pi\)
−0.0594005 + 0.998234i \(0.518919\pi\)
\(578\) −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 \(-0.444460\pi\)
0.173599 + 0.984816i \(0.444460\pi\)
\(588\) 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 \(0.122629\pi\)
−0.926704 + 0.375791i \(0.877371\pi\)
\(594\) −0.412837 + 1.83534i −0.0169389 + 0.0753047i
\(595\) −9.63004 20.7948i −0.394793 0.852504i
\(596\) 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 \(-0.313148\pi\)
0.553876 + 0.832599i \(0.313148\pi\)
\(602\) −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 \(-0.954698\pi\)
0.989890 0.141839i \(-0.0453015\pi\)
\(608\) 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
\(616\) 2.45970 18.1415i 0.0991040 0.730940i
\(617\) 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 \(-0.846414\pi\)
0.885836 0.463999i \(-0.153586\pi\)
\(620\) −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
\(630\) 3.04495 1.41011i 0.121314 0.0561801i
\(631\) −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 \(-0.536852\pi\)
−0.115516 + 0.993306i \(0.536852\pi\)
\(644\) −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 \(-0.360071\pi\)
0.425578 + 0.904922i \(0.360071\pi\)
\(648\) 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 \(-0.947794\pi\)
0.986580 0.163277i \(-0.0522063\pi\)
\(662\) −11.9544 −0.464620
\(663\) −17.2323 −0.669249
\(664\) 27.0743i 1.05069i
\(665\) 1.57677 0.730201i 0.0611447 0.0283160i
\(666\) 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 \(-0.985804\pi\)
0.999006 0.0445821i \(-0.0141956\pi\)
\(678\) 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 \(-0.777023\pi\)
0.764518 0.644602i \(-0.222977\pi\)
\(692\) 30.6451i 1.16495i
\(693\) 1.17896 8.69540i 0.0447850 0.330311i
\(694\) −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
\(700\) 15.7695 15.6280i 0.596030 0.590683i
\(701\) 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 \(0.0354465\pi\)
−0.993806 + 0.111128i \(0.964554\pi\)
\(720\) 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 \(-0.619931\pi\)
−0.367922 + 0.929856i \(0.619931\pi\)
\(728\) 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 \(0.231725\pi\)
−0.746517 + 0.665366i \(0.768275\pi\)
\(734\) −6.14493 −0.226814
\(735\) −13.5821 + 7.77993i −0.500982 + 0.286967i
\(736\) 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 \(-0.620046\pi\)
−0.368259 + 0.929723i \(0.620046\pi\)
\(762\) 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 \(-0.409873\pi\)
0.279374 + 0.960182i \(0.409873\pi\)
\(770\) 2.34653 + 10.8791i 0.0845632 + 0.392056i
\(771\) −22.7075 −0.817791
\(772\) −32.5255 −1.17062
\(773\) −20.9096 −0.752066 −0.376033 0.926606i \(-0.622712\pi\)
−0.376033 + 0.926606i \(0.622712\pi\)
\(774\) 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 \(0.0970935\pi\)
−0.953838 + 0.300320i \(0.902906\pi\)
\(788\) 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 \(-0.900949\pi\)
−0.951974 + 0.306180i \(0.900949\pi\)
\(798\) 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
\(805\) 4.15330 + 8.96851i 0.146385 + 0.316099i
\(806\) −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 \(-0.835782\pi\)
−0.869845 + 0.493324i \(0.835782\pi\)
\(812\) 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 \(0.210338\pi\)
−0.789504 + 0.613746i \(0.789662\pi\)
\(830\) 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 \(-0.964020\pi\)
0.993618 0.112793i \(-0.0359797\pi\)
\(840\) 11.2002 5.18678i 0.386443 0.178961i
\(841\) 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
\(847\) 27.2783 + 10.1438i 0.937292 + 0.348545i
\(848\) 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 \(-0.949299\pi\)
0.987342 0.158608i \(-0.0507006\pi\)
\(854\) −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 \(0.353040\pi\)
−0.445460 + 0.895302i \(0.646960\pi\)
\(858\) 8.16483 + 1.83658i 0.278743 + 0.0626999i
\(859\) 4.69044i 0.160036i 0.996793 + 0.0800178i \(0.0254977\pi\)
−0.996793 + 0.0800178i \(0.974502\pi\)
\(860\) 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
\(875\) −12.6718 + 26.7287i −0.428384 + 0.903597i
\(876\) 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 \(0.0625895\pi\)
−0.980730 + 0.195366i \(0.937410\pi\)
\(882\) −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 \(-0.827563\pi\)
0.856820 0.515616i \(-0.172437\pi\)
\(888\) 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
\(910\) −6.27313 13.5460i −0.207952 0.449046i
\(911\) 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
\(924\) 1.97863 14.5933i 0.0650921 0.480086i
\(925\) −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 \(0.296943\pi\)
−0.595528 + 0.803334i \(0.703057\pi\)
\(930\) 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 \(0.195709\pi\)
−0.816868 + 0.576825i \(0.804291\pi\)
\(938\) −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 \(-0.0903073\pi\)
0.960024 + 0.279918i \(0.0903073\pi\)
\(942\) −6.53992 −0.213082
\(943\) 9.50397i 0.309492i
\(944\) 11.9181i 0.387901i
\(945\) 5.36837 2.48608i 0.174633 0.0808723i
\(946\) −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 \(-0.616862\pi\)
0.358942 0.933360i \(-0.383138\pi\)
\(972\) 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
\(980\) −22.7946 + 13.0569i −0.728145 + 0.417088i
\(981\) 7.31694i 0.233612i
\(982\) 6.06582i 0.193568i
\(983\) 29.6052 0.944259 0.472130 0.881529i \(-0.343485\pi\)
0.472130 + 0.881529i \(0.343485\pi\)
\(984\) −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 \(0.233528\pi\)
−0.742736 + 0.669585i \(0.766472\pi\)
\(998\) 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.a.769.19 48
5.4 even 2 1155.2.k.b.769.30 yes 48
7.6 odd 2 1155.2.k.b.769.20 yes 48
11.10 odd 2 inner 1155.2.k.a.769.30 yes 48
35.34 odd 2 inner 1155.2.k.a.769.29 yes 48
55.54 odd 2 1155.2.k.b.769.19 yes 48
77.76 even 2 1155.2.k.b.769.29 yes 48
385.384 even 2 inner 1155.2.k.a.769.20 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.k.a.769.19 48 1.1 even 1 trivial
1155.2.k.a.769.20 yes 48 385.384 even 2 inner
1155.2.k.a.769.29 yes 48 35.34 odd 2 inner
1155.2.k.a.769.30 yes 48 11.10 odd 2 inner
1155.2.k.b.769.19 yes 48 55.54 odd 2
1155.2.k.b.769.20 yes 48 7.6 odd 2
1155.2.k.b.769.29 yes 48 77.76 even 2
1155.2.k.b.769.30 yes 48 5.4 even 2