Properties

Label 675.2.u.b.124.4
Level $675$
Weight $2$
Character 675.124
Analytic conductor $5.390$
Analytic rank $0$
Dimension $24$
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] = [675,2,Mod(49,675)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(675, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([14, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("675.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 675.u (of order \(18\), degree \(6\), not 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: \(5.38990213644\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 124.4
Character \(\chi\) \(=\) 675.124
Dual form 675.2.u.b.49.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36054 - 1.62143i) q^{2} +(-1.42389 + 0.986166i) q^{3} +(-0.430663 - 2.44241i) q^{4} +(-0.338267 + 3.65046i) q^{6} +(0.957561 + 0.168844i) q^{7} +(-0.880031 - 0.508086i) q^{8} +(1.05495 - 2.80839i) q^{9} +O(q^{10})\) \(q+(1.36054 - 1.62143i) q^{2} +(-1.42389 + 0.986166i) q^{3} +(-0.430663 - 2.44241i) q^{4} +(-0.338267 + 3.65046i) q^{6} +(0.957561 + 0.168844i) q^{7} +(-0.880031 - 0.508086i) q^{8} +(1.05495 - 2.80839i) q^{9} +(0.297791 - 0.108387i) q^{11} +(3.02185 + 3.05303i) q^{12} +(0.973200 + 1.15981i) q^{13} +(1.57657 - 1.32290i) q^{14} +(2.63991 - 0.960847i) q^{16} +(1.01731 - 0.587342i) q^{17} +(-3.11830 - 5.53146i) q^{18} +(3.11040 - 5.38737i) q^{19} +(-1.52997 + 0.703898i) q^{21} +(0.229414 - 0.630310i) q^{22} +(2.12988 - 0.375556i) q^{23} +(1.75413 - 0.144396i) q^{24} +3.20463 q^{26} +(1.26740 + 5.03922i) q^{27} -2.41147i q^{28} +(3.37436 + 2.83142i) q^{29} +(-1.50609 - 8.54146i) q^{31} +(2.72885 - 7.49746i) q^{32} +(-0.317135 + 0.448003i) q^{33} +(0.431752 - 2.44859i) q^{34} +(-7.31359 - 1.36716i) q^{36} +(-3.86823 + 2.23332i) q^{37} +(-4.50341 - 12.3730i) q^{38} +(-2.52950 - 0.691717i) q^{39} +(4.47767 - 3.75721i) q^{41} +(-0.940269 + 3.43842i) q^{42} +(1.91223 + 5.25381i) q^{43} +(-0.392973 - 0.680649i) q^{44} +(2.28885 - 3.96441i) q^{46} +(-2.43845 - 0.429965i) q^{47} +(-2.81139 + 3.97153i) q^{48} +(-5.68943 - 2.07078i) q^{49} +(-0.869320 + 1.83955i) q^{51} +(2.41362 - 2.87645i) q^{52} +10.8920i q^{53} +(9.89507 + 4.80105i) q^{54} +(-0.756896 - 0.635111i) q^{56} +(0.883963 + 10.7384i) q^{57} +(9.18189 - 1.61901i) q^{58} +(-1.62023 - 0.589715i) q^{59} +(0.176214 - 0.999361i) q^{61} +(-15.8985 - 9.17898i) q^{62} +(1.48436 - 2.51109i) q^{63} +(-5.63455 - 9.75933i) q^{64} +(0.294929 + 1.12374i) q^{66} +(0.550580 + 0.656156i) q^{67} +(-1.87265 - 2.23174i) q^{68} +(-2.66237 + 2.63517i) q^{69} +(4.79788 + 8.31018i) q^{71} +(-2.35530 + 1.93547i) q^{72} +(-13.1998 - 7.62091i) q^{73} +(-1.64171 + 9.31057i) q^{74} +(-14.4977 - 5.27674i) q^{76} +(0.303453 - 0.0535070i) q^{77} +(-4.56306 + 3.16030i) q^{78} +(8.59024 + 7.20807i) q^{79} +(-6.77415 - 5.92544i) q^{81} -12.3721i q^{82} +(3.01141 - 3.58886i) q^{83} +(2.37811 + 3.43369i) q^{84} +(11.1203 + 4.04747i) q^{86} +(-7.59698 - 0.703969i) q^{87} +(-0.317135 - 0.0559194i) q^{88} +(-7.74976 + 13.4230i) q^{89} +(0.736071 + 1.27491i) q^{91} +(-1.83453 - 5.04032i) q^{92} +(10.5678 + 10.6769i) q^{93} +(-4.01476 + 3.36879i) q^{94} +(3.50815 + 13.3667i) q^{96} +(1.89804 + 5.21481i) q^{97} +(-11.0983 + 6.40762i) q^{98} +(0.00976156 - 0.950656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\)
\(\chi(n)\) \(e\left(\frac{2}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36054 1.62143i 0.962046 1.14652i −0.0271067 0.999633i \(-0.508629\pi\)
0.989153 0.146889i \(-0.0469262\pi\)
\(3\) −1.42389 + 0.986166i −0.822086 + 0.569363i
\(4\) −0.430663 2.44241i −0.215332 1.22121i
\(5\) 0 0
\(6\) −0.338267 + 3.65046i −0.138097 + 1.49029i
\(7\) 0.957561 + 0.168844i 0.361924 + 0.0638170i 0.351653 0.936130i \(-0.385620\pi\)
0.0102706 + 0.999947i \(0.496731\pi\)
\(8\) −0.880031 0.508086i −0.311138 0.179636i
\(9\) 1.05495 2.80839i 0.351651 0.936131i
\(10\) 0 0
\(11\) 0.297791 0.108387i 0.0897872 0.0326799i −0.296736 0.954960i \(-0.595898\pi\)
0.386523 + 0.922280i \(0.373676\pi\)
\(12\) 3.02185 + 3.05303i 0.872332 + 0.881335i
\(13\) 0.973200 + 1.15981i 0.269917 + 0.321675i 0.883928 0.467623i \(-0.154889\pi\)
−0.614011 + 0.789297i \(0.710445\pi\)
\(14\) 1.57657 1.32290i 0.421355 0.353559i
\(15\) 0 0
\(16\) 2.63991 0.960847i 0.659977 0.240212i
\(17\) 1.01731 0.587342i 0.246733 0.142451i −0.371534 0.928419i \(-0.621168\pi\)
0.618267 + 0.785968i \(0.287835\pi\)
\(18\) −3.11830 5.53146i −0.734991 1.30378i
\(19\) 3.11040 5.38737i 0.713575 1.23595i −0.249931 0.968264i \(-0.580408\pi\)
0.963507 0.267685i \(-0.0862586\pi\)
\(20\) 0 0
\(21\) −1.52997 + 0.703898i −0.333868 + 0.153603i
\(22\) 0.229414 0.630310i 0.0489113 0.134383i
\(23\) 2.12988 0.375556i 0.444112 0.0783089i 0.0528796 0.998601i \(-0.483160\pi\)
0.391232 + 0.920292i \(0.372049\pi\)
\(24\) 1.75413 0.144396i 0.358060 0.0294747i
\(25\) 0 0
\(26\) 3.20463 0.628480
\(27\) 1.26740 + 5.03922i 0.243912 + 0.969797i
\(28\) 2.41147i 0.455726i
\(29\) 3.37436 + 2.83142i 0.626602 + 0.525782i 0.899871 0.436156i \(-0.143660\pi\)
−0.273269 + 0.961938i \(0.588105\pi\)
\(30\) 0 0
\(31\) −1.50609 8.54146i −0.270502 1.53409i −0.752897 0.658138i \(-0.771344\pi\)
0.482395 0.875954i \(-0.339767\pi\)
\(32\) 2.72885 7.49746i 0.482398 1.32538i
\(33\) −0.317135 + 0.448003i −0.0552061 + 0.0779872i
\(34\) 0.431752 2.44859i 0.0740449 0.419930i
\(35\) 0 0
\(36\) −7.31359 1.36716i −1.21893 0.227859i
\(37\) −3.86823 + 2.23332i −0.635933 + 0.367156i −0.783046 0.621964i \(-0.786335\pi\)
0.147113 + 0.989120i \(0.453002\pi\)
\(38\) −4.50341 12.3730i −0.730550 2.00717i
\(39\) −2.52950 0.691717i −0.405045 0.110763i
\(40\) 0 0
\(41\) 4.47767 3.75721i 0.699295 0.586778i −0.222278 0.974983i \(-0.571349\pi\)
0.921573 + 0.388205i \(0.126905\pi\)
\(42\) −0.940269 + 3.43842i −0.145087 + 0.530560i
\(43\) 1.91223 + 5.25381i 0.291613 + 0.801199i 0.995831 + 0.0912158i \(0.0290753\pi\)
−0.704219 + 0.709983i \(0.748702\pi\)
\(44\) −0.392973 0.680649i −0.0592429 0.102612i
\(45\) 0 0
\(46\) 2.28885 3.96441i 0.337473 0.584521i
\(47\) −2.43845 0.429965i −0.355685 0.0627168i −0.00704911 0.999975i \(-0.502244\pi\)
−0.348636 + 0.937258i \(0.613355\pi\)
\(48\) −2.81139 + 3.97153i −0.405790 + 0.573241i
\(49\) −5.68943 2.07078i −0.812776 0.295826i
\(50\) 0 0
\(51\) −0.869320 + 1.83955i −0.121729 + 0.257588i
\(52\) 2.41362 2.87645i 0.334710 0.398891i
\(53\) 10.8920i 1.49613i 0.663628 + 0.748063i \(0.269016\pi\)
−0.663628 + 0.748063i \(0.730984\pi\)
\(54\) 9.89507 + 4.80105i 1.34655 + 0.653340i
\(55\) 0 0
\(56\) −0.756896 0.635111i −0.101145 0.0848703i
\(57\) 0.883963 + 10.7384i 0.117084 + 1.42234i
\(58\) 9.18189 1.61901i 1.20564 0.212587i
\(59\) −1.62023 0.589715i −0.210936 0.0767743i 0.234391 0.972142i \(-0.424690\pi\)
−0.445327 + 0.895368i \(0.646913\pi\)
\(60\) 0 0
\(61\) 0.176214 0.999361i 0.0225619 0.127955i −0.971446 0.237259i \(-0.923751\pi\)
0.994008 + 0.109304i \(0.0348621\pi\)
\(62\) −15.8985 9.17898i −2.01911 1.16573i
\(63\) 1.48436 2.51109i 0.187012 0.316367i
\(64\) −5.63455 9.75933i −0.704319 1.21992i
\(65\) 0 0
\(66\) 0.294929 + 1.12374i 0.0363033 + 0.138322i
\(67\) 0.550580 + 0.656156i 0.0672641 + 0.0801622i 0.798627 0.601826i \(-0.205560\pi\)
−0.731363 + 0.681988i \(0.761116\pi\)
\(68\) −1.87265 2.23174i −0.227092 0.270638i
\(69\) −2.66237 + 2.63517i −0.320512 + 0.317238i
\(70\) 0 0
\(71\) 4.79788 + 8.31018i 0.569404 + 0.986237i 0.996625 + 0.0820894i \(0.0261593\pi\)
−0.427221 + 0.904147i \(0.640507\pi\)
\(72\) −2.35530 + 1.93547i −0.277574 + 0.228097i
\(73\) −13.1998 7.62091i −1.54492 0.891960i −0.998517 0.0544385i \(-0.982663\pi\)
−0.546404 0.837522i \(-0.684004\pi\)
\(74\) −1.64171 + 9.31057i −0.190844 + 1.08233i
\(75\) 0 0
\(76\) −14.4977 5.27674i −1.66300 0.605284i
\(77\) 0.303453 0.0535070i 0.0345817 0.00609768i
\(78\) −4.56306 + 3.16030i −0.516664 + 0.357833i
\(79\) 8.59024 + 7.20807i 0.966478 + 0.810971i 0.981995 0.188908i \(-0.0604949\pi\)
−0.0155168 + 0.999880i \(0.504939\pi\)
\(80\) 0 0
\(81\) −6.77415 5.92544i −0.752684 0.658382i
\(82\) 12.3721i 1.36626i
\(83\) 3.01141 3.58886i 0.330546 0.393929i −0.575017 0.818141i \(-0.695005\pi\)
0.905563 + 0.424212i \(0.139449\pi\)
\(84\) 2.37811 + 3.43369i 0.259474 + 0.374646i
\(85\) 0 0
\(86\) 11.1203 + 4.04747i 1.19914 + 0.436450i
\(87\) −7.59698 0.703969i −0.814482 0.0754734i
\(88\) −0.317135 0.0559194i −0.0338067 0.00596103i
\(89\) −7.74976 + 13.4230i −0.821473 + 1.42283i 0.0831130 + 0.996540i \(0.473514\pi\)
−0.904586 + 0.426292i \(0.859820\pi\)
\(90\) 0 0
\(91\) 0.736071 + 1.27491i 0.0771612 + 0.133647i
\(92\) −1.83453 5.04032i −0.191263 0.525490i
\(93\) 10.5678 + 10.6769i 1.09583 + 1.10714i
\(94\) −4.01476 + 3.36879i −0.414091 + 0.347464i
\(95\) 0 0
\(96\) 3.50815 + 13.3667i 0.358049 + 1.36423i
\(97\) 1.89804 + 5.21481i 0.192716 + 0.529484i 0.997987 0.0634241i \(-0.0202021\pi\)
−0.805270 + 0.592908i \(0.797980\pi\)
\(98\) −11.0983 + 6.40762i −1.12110 + 0.647267i
\(99\) 0.00976156 0.950656i 0.000981074 0.0955445i
\(100\) 0 0
\(101\) −1.76063 + 9.98501i −0.175189 + 0.993546i 0.762737 + 0.646709i \(0.223855\pi\)
−0.937926 + 0.346836i \(0.887256\pi\)
\(102\) 1.79995 + 3.91231i 0.178221 + 0.387377i
\(103\) 3.37002 9.25906i 0.332058 0.912323i −0.655518 0.755180i \(-0.727549\pi\)
0.987576 0.157143i \(-0.0502283\pi\)
\(104\) −0.267160 1.51514i −0.0261972 0.148572i
\(105\) 0 0
\(106\) 17.6605 + 14.8189i 1.71534 + 1.43934i
\(107\) 5.17080i 0.499880i 0.968261 + 0.249940i \(0.0804109\pi\)
−0.968261 + 0.249940i \(0.919589\pi\)
\(108\) 11.7620 5.26573i 1.13180 0.506695i
\(109\) 7.31065 0.700234 0.350117 0.936706i \(-0.386142\pi\)
0.350117 + 0.936706i \(0.386142\pi\)
\(110\) 0 0
\(111\) 3.30552 6.99473i 0.313746 0.663911i
\(112\) 2.69010 0.474338i 0.254191 0.0448207i
\(113\) −3.54868 + 9.74991i −0.333832 + 0.917195i 0.653274 + 0.757122i \(0.273395\pi\)
−0.987105 + 0.160073i \(0.948827\pi\)
\(114\) 18.6142 + 13.1768i 1.74338 + 1.23412i
\(115\) 0 0
\(116\) 5.46229 9.46096i 0.507161 0.878428i
\(117\) 4.28390 1.50958i 0.396046 0.139561i
\(118\) −3.16056 + 1.82475i −0.290953 + 0.167982i
\(119\) 1.07330 0.390650i 0.0983894 0.0358108i
\(120\) 0 0
\(121\) −8.34956 + 7.00611i −0.759051 + 0.636919i
\(122\) −1.38064 1.64539i −0.124998 0.148966i
\(123\) −2.67050 + 9.76560i −0.240790 + 0.880535i
\(124\) −20.2132 + 7.35699i −1.81520 + 0.660677i
\(125\) 0 0
\(126\) −2.05201 5.82321i −0.182808 0.518773i
\(127\) −4.52709 2.61372i −0.401714 0.231930i 0.285509 0.958376i \(-0.407837\pi\)
−0.687223 + 0.726446i \(0.741171\pi\)
\(128\) −7.77522 1.37098i −0.687239 0.121179i
\(129\) −7.90395 5.59510i −0.695904 0.492621i
\(130\) 0 0
\(131\) −1.25622 7.12440i −0.109757 0.622461i −0.989213 0.146482i \(-0.953205\pi\)
0.879457 0.475979i \(-0.157906\pi\)
\(132\) 1.23079 + 0.581636i 0.107126 + 0.0506249i
\(133\) 3.88802 4.63357i 0.337134 0.401781i
\(134\) 1.81300 0.156619
\(135\) 0 0
\(136\) −1.19368 −0.102357
\(137\) −7.23092 + 8.61748i −0.617779 + 0.736241i −0.980687 0.195584i \(-0.937340\pi\)
0.362907 + 0.931825i \(0.381784\pi\)
\(138\) 0.650482 + 7.90210i 0.0553727 + 0.672671i
\(139\) −1.62885 9.23766i −0.138157 0.783528i −0.972609 0.232447i \(-0.925327\pi\)
0.834452 0.551081i \(-0.185784\pi\)
\(140\) 0 0
\(141\) 3.89612 1.79249i 0.328112 0.150955i
\(142\) 20.0021 + 3.52690i 1.67854 + 0.295971i
\(143\) 0.415518 + 0.239900i 0.0347474 + 0.0200614i
\(144\) 0.0865360 8.42754i 0.00721133 0.702295i
\(145\) 0 0
\(146\) −30.3156 + 11.0340i −2.50894 + 0.913179i
\(147\) 10.1433 2.66215i 0.836605 0.219570i
\(148\) 7.12060 + 8.48600i 0.585310 + 0.697545i
\(149\) −14.5941 + 12.2459i −1.19560 + 1.00322i −0.195851 + 0.980634i \(0.562747\pi\)
−0.999745 + 0.0225899i \(0.992809\pi\)
\(150\) 0 0
\(151\) −3.77193 + 1.37287i −0.306955 + 0.111723i −0.490905 0.871213i \(-0.663334\pi\)
0.183950 + 0.982936i \(0.441112\pi\)
\(152\) −5.47450 + 3.16070i −0.444041 + 0.256367i
\(153\) −0.576279 3.47661i −0.0465894 0.281068i
\(154\) 0.326102 0.564825i 0.0262780 0.0455149i
\(155\) 0 0
\(156\) −0.600093 + 6.47599i −0.0480459 + 0.518494i
\(157\) 2.48851 6.83713i 0.198605 0.545662i −0.799911 0.600118i \(-0.795120\pi\)
0.998516 + 0.0544560i \(0.0173425\pi\)
\(158\) 23.3747 4.12159i 1.85959 0.327896i
\(159\) −10.7413 15.5090i −0.851839 1.22994i
\(160\) 0 0
\(161\) 2.10290 0.165732
\(162\) −18.8242 + 2.92200i −1.47897 + 0.229574i
\(163\) 12.4492i 0.975094i −0.873097 0.487547i \(-0.837892\pi\)
0.873097 0.487547i \(-0.162108\pi\)
\(164\) −11.1050 9.31823i −0.867157 0.727632i
\(165\) 0 0
\(166\) −1.72194 9.76558i −0.133648 0.757956i
\(167\) −0.797553 + 2.19126i −0.0617165 + 0.169565i −0.966718 0.255843i \(-0.917647\pi\)
0.905002 + 0.425408i \(0.139869\pi\)
\(168\) 1.70407 + 0.157906i 0.131472 + 0.0121827i
\(169\) 1.85937 10.5450i 0.143029 0.811157i
\(170\) 0 0
\(171\) −11.8485 14.4187i −0.906081 1.10262i
\(172\) 12.0085 6.93308i 0.915636 0.528643i
\(173\) −1.22521 3.36623i −0.0931509 0.255930i 0.884363 0.466799i \(-0.154593\pi\)
−0.977514 + 0.210869i \(0.932371\pi\)
\(174\) −11.4774 + 11.3602i −0.870101 + 0.861213i
\(175\) 0 0
\(176\) 0.681996 0.572262i 0.0514074 0.0431359i
\(177\) 2.88859 0.758123i 0.217120 0.0569840i
\(178\) 11.2205 + 30.8281i 0.841014 + 2.31067i
\(179\) −9.99785 17.3168i −0.747275 1.29432i −0.949124 0.314901i \(-0.898029\pi\)
0.201850 0.979416i \(-0.435305\pi\)
\(180\) 0 0
\(181\) −4.86616 + 8.42844i −0.361699 + 0.626481i −0.988241 0.152907i \(-0.951136\pi\)
0.626542 + 0.779388i \(0.284470\pi\)
\(182\) 3.06863 + 0.541082i 0.227462 + 0.0401077i
\(183\) 0.734626 + 1.59676i 0.0543051 + 0.118036i
\(184\) −2.06518 0.751664i −0.152247 0.0554134i
\(185\) 0 0
\(186\) 31.6897 2.60862i 2.32360 0.191274i
\(187\) 0.239284 0.285168i 0.0174982 0.0208535i
\(188\) 6.14088i 0.447869i
\(189\) 0.362776 + 5.03935i 0.0263881 + 0.366559i
\(190\) 0 0
\(191\) −13.6023 11.4137i −0.984227 0.825864i 0.000494763 1.00000i \(-0.499843\pi\)
−0.984722 + 0.174135i \(0.944287\pi\)
\(192\) 17.6473 + 8.33965i 1.27359 + 0.601862i
\(193\) 10.4235 1.83795i 0.750303 0.132299i 0.214596 0.976703i \(-0.431156\pi\)
0.535706 + 0.844404i \(0.320045\pi\)
\(194\) 11.0378 + 4.01743i 0.792467 + 0.288434i
\(195\) 0 0
\(196\) −2.60748 + 14.7878i −0.186249 + 1.05627i
\(197\) −12.2620 7.07945i −0.873628 0.504390i −0.00507615 0.999987i \(-0.501616\pi\)
−0.868552 + 0.495597i \(0.834949\pi\)
\(198\) −1.52814 1.30923i −0.108600 0.0930431i
\(199\) 3.77010 + 6.53000i 0.267255 + 0.462899i 0.968152 0.250363i \(-0.0805501\pi\)
−0.700897 + 0.713263i \(0.747217\pi\)
\(200\) 0 0
\(201\) −1.43105 0.391333i −0.100938 0.0276025i
\(202\) 13.7946 + 16.4397i 0.970582 + 1.15669i
\(203\) 2.75308 + 3.28100i 0.193229 + 0.230281i
\(204\) 4.86732 + 1.33101i 0.340780 + 0.0931896i
\(205\) 0 0
\(206\) −10.4278 18.0616i −0.726543 1.25841i
\(207\) 1.19222 6.37775i 0.0828648 0.443284i
\(208\) 3.68356 + 2.12670i 0.255409 + 0.147460i
\(209\) 0.342328 1.94144i 0.0236793 0.134292i
\(210\) 0 0
\(211\) −4.89922 1.78317i −0.337276 0.122758i 0.167829 0.985816i \(-0.446324\pi\)
−0.505106 + 0.863058i \(0.668546\pi\)
\(212\) 26.6027 4.69077i 1.82708 0.322163i
\(213\) −15.0269 7.10131i −1.02963 0.486573i
\(214\) 8.38408 + 7.03508i 0.573124 + 0.480908i
\(215\) 0 0
\(216\) 1.44500 5.07862i 0.0983199 0.345556i
\(217\) 8.43326i 0.572487i
\(218\) 9.94643 11.8537i 0.673657 0.802833i
\(219\) 26.3106 2.16583i 1.77791 0.146353i
\(220\) 0 0
\(221\) 1.67125 + 0.608285i 0.112420 + 0.0409177i
\(222\) −6.84416 14.8763i −0.459350 0.998430i
\(223\) −17.4250 3.07250i −1.16686 0.205750i −0.443537 0.896256i \(-0.646277\pi\)
−0.723326 + 0.690506i \(0.757388\pi\)
\(224\) 3.87894 6.71853i 0.259173 0.448901i
\(225\) 0 0
\(226\) 10.9807 + 19.0191i 0.730423 + 1.26513i
\(227\) 5.39434 + 14.8208i 0.358035 + 0.983692i 0.979711 + 0.200418i \(0.0642299\pi\)
−0.621676 + 0.783275i \(0.713548\pi\)
\(228\) 25.8470 6.78365i 1.71176 0.449258i
\(229\) 1.35350 1.13572i 0.0894415 0.0750504i −0.596971 0.802263i \(-0.703629\pi\)
0.686412 + 0.727213i \(0.259185\pi\)
\(230\) 0 0
\(231\) −0.379318 + 0.375443i −0.0249573 + 0.0247024i
\(232\) −1.53093 4.20620i −0.100511 0.276151i
\(233\) 12.0364 6.94920i 0.788529 0.455257i −0.0509157 0.998703i \(-0.516214\pi\)
0.839444 + 0.543446i \(0.182881\pi\)
\(234\) 3.38073 8.99987i 0.221005 0.588340i
\(235\) 0 0
\(236\) −0.742554 + 4.21123i −0.0483362 + 0.274128i
\(237\) −19.3400 1.79212i −1.25627 0.116411i
\(238\) 0.826858 2.27177i 0.0535973 0.147257i
\(239\) 3.44391 + 19.5314i 0.222768 + 1.26338i 0.866906 + 0.498471i \(0.166105\pi\)
−0.644138 + 0.764909i \(0.722784\pi\)
\(240\) 0 0
\(241\) 14.8419 + 12.4538i 0.956050 + 0.802221i 0.980306 0.197485i \(-0.0632773\pi\)
−0.0242563 + 0.999706i \(0.507722\pi\)
\(242\) 23.0703i 1.48301i
\(243\) 15.4892 + 1.75676i 0.993629 + 0.112696i
\(244\) −2.51674 −0.161118
\(245\) 0 0
\(246\) 12.2009 + 17.6165i 0.777901 + 1.12319i
\(247\) 9.27540 1.63550i 0.590179 0.104065i
\(248\) −3.01439 + 8.28198i −0.191414 + 0.525906i
\(249\) −0.748720 + 8.07992i −0.0474482 + 0.512044i
\(250\) 0 0
\(251\) 2.73786 4.74212i 0.172812 0.299320i −0.766590 0.642137i \(-0.778048\pi\)
0.939402 + 0.342818i \(0.111381\pi\)
\(252\) −6.77237 2.54399i −0.426619 0.160256i
\(253\) 0.593554 0.342689i 0.0373164 0.0215447i
\(254\) −10.3972 + 3.78428i −0.652380 + 0.237447i
\(255\) 0 0
\(256\) 4.46383 3.74560i 0.278989 0.234100i
\(257\) −7.43395 8.85943i −0.463717 0.552636i 0.482615 0.875833i \(-0.339687\pi\)
−0.946332 + 0.323196i \(0.895243\pi\)
\(258\) −19.8257 + 5.20333i −1.23429 + 0.323945i
\(259\) −4.08115 + 1.48542i −0.253590 + 0.0922993i
\(260\) 0 0
\(261\) 11.5115 6.48951i 0.712546 0.401691i
\(262\) −13.2608 7.65614i −0.819257 0.472998i
\(263\) −6.37952 1.12488i −0.393378 0.0693632i −0.0265395 0.999648i \(-0.508449\pi\)
−0.366839 + 0.930285i \(0.619560\pi\)
\(264\) 0.506712 0.233124i 0.0311860 0.0143478i
\(265\) 0 0
\(266\) −2.22318 12.6083i −0.136312 0.773064i
\(267\) −2.20245 26.7554i −0.134788 1.63741i
\(268\) 1.36549 1.62733i 0.0834106 0.0994048i
\(269\) 13.8387 0.843758 0.421879 0.906652i \(-0.361371\pi\)
0.421879 + 0.906652i \(0.361371\pi\)
\(270\) 0 0
\(271\) 1.94536 0.118172 0.0590860 0.998253i \(-0.481181\pi\)
0.0590860 + 0.998253i \(0.481181\pi\)
\(272\) 2.12125 2.52800i 0.128619 0.153283i
\(273\) −2.30536 1.08945i −0.139527 0.0659366i
\(274\) 4.13466 + 23.4488i 0.249784 + 1.41660i
\(275\) 0 0
\(276\) 7.58277 + 5.36774i 0.456429 + 0.323100i
\(277\) 12.2832 + 2.16586i 0.738026 + 0.130134i 0.530010 0.847991i \(-0.322188\pi\)
0.208016 + 0.978125i \(0.433299\pi\)
\(278\) −17.1943 9.92713i −1.03125 0.595390i
\(279\) −25.5766 4.78114i −1.53123 0.286239i
\(280\) 0 0
\(281\) −9.16752 + 3.33670i −0.546888 + 0.199051i −0.600663 0.799502i \(-0.705097\pi\)
0.0537751 + 0.998553i \(0.482875\pi\)
\(282\) 2.39442 8.75602i 0.142585 0.521414i
\(283\) −17.0797 20.3547i −1.01528 1.20996i −0.977556 0.210676i \(-0.932433\pi\)
−0.0377246 0.999288i \(-0.512011\pi\)
\(284\) 18.2306 15.2973i 1.08179 0.907728i
\(285\) 0 0
\(286\) 0.954309 0.347340i 0.0564295 0.0205386i
\(287\) 4.92202 2.84173i 0.290538 0.167742i
\(288\) −18.1770 15.5732i −1.07109 0.917657i
\(289\) −7.81006 + 13.5274i −0.459415 + 0.795730i
\(290\) 0 0
\(291\) −7.84527 5.55356i −0.459898 0.325556i
\(292\) −12.9287 + 35.5214i −0.756598 + 2.07873i
\(293\) 12.0712 2.12849i 0.705210 0.124347i 0.190469 0.981693i \(-0.438999\pi\)
0.514741 + 0.857346i \(0.327888\pi\)
\(294\) 9.48386 20.0686i 0.553110 1.17042i
\(295\) 0 0
\(296\) 4.53888 0.263817
\(297\) 0.923606 + 1.36326i 0.0535930 + 0.0791044i
\(298\) 40.3243i 2.33592i
\(299\) 2.50838 + 2.10478i 0.145063 + 0.121723i
\(300\) 0 0
\(301\) 0.944004 + 5.35371i 0.0544115 + 0.308583i
\(302\) −2.90585 + 7.98375i −0.167213 + 0.459413i
\(303\) −7.33993 15.9539i −0.421668 0.916526i
\(304\) 3.03473 17.2108i 0.174053 0.987106i
\(305\) 0 0
\(306\) −6.42113 3.79567i −0.367071 0.216984i
\(307\) −22.9271 + 13.2370i −1.30852 + 0.755475i −0.981849 0.189663i \(-0.939260\pi\)
−0.326671 + 0.945138i \(0.605927\pi\)
\(308\) −0.261372 0.718114i −0.0148931 0.0409184i
\(309\) 4.33242 + 16.5073i 0.246463 + 0.939070i
\(310\) 0 0
\(311\) −13.5280 + 11.3513i −0.767100 + 0.643673i −0.939964 0.341272i \(-0.889142\pi\)
0.172865 + 0.984946i \(0.444698\pi\)
\(312\) 1.87459 + 1.89394i 0.106128 + 0.107223i
\(313\) 3.29954 + 9.06541i 0.186501 + 0.512407i 0.997342 0.0728589i \(-0.0232123\pi\)
−0.810841 + 0.585266i \(0.800990\pi\)
\(314\) −7.70019 13.3371i −0.434547 0.752657i
\(315\) 0 0
\(316\) 13.9056 24.0852i 0.782250 1.35490i
\(317\) −3.65412 0.644320i −0.205236 0.0361886i 0.0700850 0.997541i \(-0.477673\pi\)
−0.275321 + 0.961352i \(0.588784\pi\)
\(318\) −39.7606 3.68439i −2.22967 0.206610i
\(319\) 1.31174 + 0.477435i 0.0734434 + 0.0267312i
\(320\) 0 0
\(321\) −5.09927 7.36268i −0.284614 0.410945i
\(322\) 2.86108 3.40971i 0.159442 0.190016i
\(323\) 7.30748i 0.406599i
\(324\) −11.5550 + 19.0972i −0.641944 + 1.06095i
\(325\) 0 0
\(326\) −20.1854 16.9376i −1.11797 0.938085i
\(327\) −10.4096 + 7.20952i −0.575652 + 0.398687i
\(328\) −5.84948 + 1.03142i −0.322983 + 0.0569507i
\(329\) −2.26237 0.823435i −0.124728 0.0453974i
\(330\) 0 0
\(331\) −0.245329 + 1.39133i −0.0134845 + 0.0764745i −0.990807 0.135280i \(-0.956807\pi\)
0.977323 + 0.211755i \(0.0679177\pi\)
\(332\) −10.0624 5.80953i −0.552246 0.318839i
\(333\) 2.19126 + 13.2196i 0.120080 + 0.724427i
\(334\) 2.46786 + 4.27446i 0.135035 + 0.233888i
\(335\) 0 0
\(336\) −3.36265 + 3.32830i −0.183447 + 0.181573i
\(337\) −8.34986 9.95097i −0.454846 0.542064i 0.489073 0.872243i \(-0.337335\pi\)
−0.943918 + 0.330179i \(0.892891\pi\)
\(338\) −14.5683 17.3618i −0.792409 0.944356i
\(339\) −4.56209 17.3824i −0.247779 0.944084i
\(340\) 0 0
\(341\) −1.37428 2.38033i −0.0744215 0.128902i
\(342\) −39.4992 0.405587i −2.13587 0.0219316i
\(343\) −10.9928 6.34669i −0.593555 0.342689i
\(344\) 0.986567 5.59510i 0.0531921 0.301667i
\(345\) 0 0
\(346\) −7.12504 2.59330i −0.383045 0.139417i
\(347\) 4.72753 0.833591i 0.253787 0.0447495i −0.0453070 0.998973i \(-0.514427\pi\)
0.299094 + 0.954224i \(0.403316\pi\)
\(348\) 1.55236 + 18.8581i 0.0832152 + 1.01090i
\(349\) 17.2954 + 14.5126i 0.925803 + 0.776841i 0.975059 0.221946i \(-0.0712407\pi\)
−0.0492565 + 0.998786i \(0.515685\pi\)
\(350\) 0 0
\(351\) −4.61112 + 6.37412i −0.246123 + 0.340225i
\(352\) 2.52845i 0.134767i
\(353\) −19.0950 + 22.7565i −1.01632 + 1.21121i −0.0390490 + 0.999237i \(0.512433\pi\)
−0.977276 + 0.211972i \(0.932012\pi\)
\(354\) 2.70080 5.71509i 0.143546 0.303754i
\(355\) 0 0
\(356\) 36.1220 + 13.1473i 1.91446 + 0.696807i
\(357\) −1.14302 + 1.61470i −0.0604952 + 0.0854589i
\(358\) −41.6804 7.34937i −2.20288 0.388427i
\(359\) 6.70991 11.6219i 0.354136 0.613381i −0.632834 0.774288i \(-0.718108\pi\)
0.986970 + 0.160906i \(0.0514418\pi\)
\(360\) 0 0
\(361\) −9.84920 17.0593i −0.518379 0.897858i
\(362\) 7.04550 + 19.3573i 0.370303 + 1.01740i
\(363\) 4.97970 18.2100i 0.261366 0.955778i
\(364\) 2.79686 2.34685i 0.146595 0.123008i
\(365\) 0 0
\(366\) 3.58852 + 0.981314i 0.187575 + 0.0512941i
\(367\) 2.71905 + 7.47054i 0.141933 + 0.389959i 0.990208 0.139597i \(-0.0445808\pi\)
−0.848275 + 0.529556i \(0.822359\pi\)
\(368\) 5.26184 3.03793i 0.274293 0.158363i
\(369\) −5.82801 16.5387i −0.303394 0.860973i
\(370\) 0 0
\(371\) −1.83904 + 10.4297i −0.0954782 + 0.541484i
\(372\) 21.5262 30.4091i 1.11608 1.57664i
\(373\) 3.90604 10.7318i 0.202247 0.555670i −0.796557 0.604564i \(-0.793347\pi\)
0.998804 + 0.0488939i \(0.0155696\pi\)
\(374\) −0.136823 0.775963i −0.00707496 0.0401241i
\(375\) 0 0
\(376\) 1.92745 + 1.61733i 0.0994009 + 0.0834072i
\(377\) 6.66917i 0.343480i
\(378\) 8.66451 + 6.26801i 0.445654 + 0.322392i
\(379\) 24.1705 1.24155 0.620777 0.783987i \(-0.286817\pi\)
0.620777 + 0.783987i \(0.286817\pi\)
\(380\) 0 0
\(381\) 9.02366 0.742807i 0.462296 0.0380551i
\(382\) −37.0129 + 6.52637i −1.89374 + 0.333918i
\(383\) −3.22979 + 8.87378i −0.165035 + 0.453429i −0.994451 0.105202i \(-0.966451\pi\)
0.829416 + 0.558631i \(0.188673\pi\)
\(384\) 12.4231 5.71553i 0.633964 0.291669i
\(385\) 0 0
\(386\) 11.2015 19.4016i 0.570143 0.987516i
\(387\) 16.7721 + 0.172220i 0.852573 + 0.00875442i
\(388\) 11.9193 6.88162i 0.605111 0.349361i
\(389\) −2.39406 + 0.871367i −0.121384 + 0.0441801i −0.401998 0.915641i \(-0.631684\pi\)
0.280614 + 0.959821i \(0.409462\pi\)
\(390\) 0 0
\(391\) 1.94617 1.63303i 0.0984218 0.0825857i
\(392\) 3.95474 + 4.71308i 0.199745 + 0.238046i
\(393\) 8.81457 + 8.90554i 0.444636 + 0.449225i
\(394\) −28.1617 + 10.2500i −1.41876 + 0.516388i
\(395\) 0 0
\(396\) −2.32610 + 0.385571i −0.116891 + 0.0193757i
\(397\) −3.18279 1.83759i −0.159740 0.0922258i 0.417999 0.908447i \(-0.362731\pi\)
−0.577739 + 0.816222i \(0.696065\pi\)
\(398\) 15.7173 + 2.77138i 0.787836 + 0.138917i
\(399\) −0.966669 + 10.4319i −0.0483940 + 0.522251i
\(400\) 0 0
\(401\) 2.80420 + 15.9034i 0.140035 + 0.794177i 0.971220 + 0.238182i \(0.0765516\pi\)
−0.831186 + 0.555995i \(0.812337\pi\)
\(402\) −2.58151 + 1.78791i −0.128754 + 0.0891731i
\(403\) 8.44078 10.0593i 0.420465 0.501091i
\(404\) 25.1458 1.25105
\(405\) 0 0
\(406\) 9.06558 0.449917
\(407\) −0.909859 + 1.08433i −0.0451000 + 0.0537481i
\(408\) 1.69968 1.17717i 0.0841465 0.0582785i
\(409\) −1.59443 9.04248i −0.0788396 0.447122i −0.998517 0.0544462i \(-0.982661\pi\)
0.919677 0.392676i \(-0.128450\pi\)
\(410\) 0 0
\(411\) 1.79780 19.4013i 0.0886792 0.956994i
\(412\) −24.0658 4.24345i −1.18564 0.209060i
\(413\) −1.45190 0.838253i −0.0714432 0.0412477i
\(414\) −8.71900 10.6103i −0.428515 0.521466i
\(415\) 0 0
\(416\) 11.3514 4.13157i 0.556548 0.202567i
\(417\) 11.4292 + 11.5471i 0.559689 + 0.565466i
\(418\) −2.68215 3.19646i −0.131188 0.156344i
\(419\) 5.34613 4.48594i 0.261176 0.219152i −0.502791 0.864408i \(-0.667694\pi\)
0.763967 + 0.645256i \(0.223249\pi\)
\(420\) 0 0
\(421\) −28.9525 + 10.5379i −1.41106 + 0.513584i −0.931441 0.363894i \(-0.881447\pi\)
−0.479619 + 0.877477i \(0.659225\pi\)
\(422\) −9.55686 + 5.51765i −0.465221 + 0.268595i
\(423\) −3.77996 + 6.39454i −0.183788 + 0.310913i
\(424\) 5.53405 9.58526i 0.268757 0.465502i
\(425\) 0 0
\(426\) −31.9589 + 14.7034i −1.54842 + 0.712383i
\(427\) 0.337472 0.927196i 0.0163314 0.0448702i
\(428\) 12.6292 2.22687i 0.610457 0.107640i
\(429\) −0.828236 + 0.0681784i −0.0399876 + 0.00329169i
\(430\) 0 0
\(431\) 27.8971 1.34376 0.671879 0.740661i \(-0.265487\pi\)
0.671879 + 0.740661i \(0.265487\pi\)
\(432\) 8.18774 + 12.0853i 0.393933 + 0.581453i
\(433\) 19.1706i 0.921278i −0.887588 0.460639i \(-0.847620\pi\)
0.887588 0.460639i \(-0.152380\pi\)
\(434\) −13.6739 11.4738i −0.656369 0.550759i
\(435\) 0 0
\(436\) −3.14843 17.8556i −0.150782 0.855130i
\(437\) 4.60154 12.6426i 0.220121 0.604778i
\(438\) 32.2849 45.6075i 1.54263 2.17921i
\(439\) 4.12397 23.3882i 0.196826 1.11626i −0.712968 0.701197i \(-0.752649\pi\)
0.909794 0.415060i \(-0.136239\pi\)
\(440\) 0 0
\(441\) −11.8177 + 13.7936i −0.562746 + 0.656838i
\(442\) 3.26009 1.88221i 0.155067 0.0895278i
\(443\) 7.98900 + 21.9496i 0.379569 + 1.04286i 0.971536 + 0.236894i \(0.0761294\pi\)
−0.591967 + 0.805962i \(0.701648\pi\)
\(444\) −18.5076 5.06108i −0.878332 0.240188i
\(445\) 0 0
\(446\) −28.6892 + 24.0731i −1.35847 + 1.13989i
\(447\) 8.70396 31.8291i 0.411683 1.50546i
\(448\) −3.74762 10.2965i −0.177059 0.486464i
\(449\) 2.40953 + 4.17343i 0.113713 + 0.196956i 0.917264 0.398279i \(-0.130392\pi\)
−0.803552 + 0.595235i \(0.797059\pi\)
\(450\) 0 0
\(451\) 0.926176 1.60418i 0.0436119 0.0755380i
\(452\) 25.3416 + 4.46841i 1.19197 + 0.210176i
\(453\) 4.01695 5.67457i 0.188733 0.266615i
\(454\) 31.3701 + 11.4178i 1.47227 + 0.535863i
\(455\) 0 0
\(456\) 4.67813 9.89928i 0.219074 0.463576i
\(457\) 3.14555 3.74872i 0.147142 0.175358i −0.687439 0.726242i \(-0.741265\pi\)
0.834581 + 0.550885i \(0.185710\pi\)
\(458\) 3.73978i 0.174749i
\(459\) 4.24908 + 4.38203i 0.198330 + 0.204535i
\(460\) 0 0
\(461\) 21.4419 + 17.9919i 0.998650 + 0.837967i 0.986797 0.161963i \(-0.0517824\pi\)
0.0118535 + 0.999930i \(0.496227\pi\)
\(462\) 0.0926768 + 1.12584i 0.00431171 + 0.0523789i
\(463\) −27.0579 + 4.77104i −1.25749 + 0.221729i −0.762396 0.647111i \(-0.775977\pi\)
−0.495093 + 0.868840i \(0.664866\pi\)
\(464\) 11.6285 + 4.23245i 0.539842 + 0.196486i
\(465\) 0 0
\(466\) 5.10832 28.9707i 0.236639 1.34204i
\(467\) 18.4000 + 10.6232i 0.851450 + 0.491585i 0.861140 0.508368i \(-0.169751\pi\)
−0.00968963 + 0.999953i \(0.503084\pi\)
\(468\) −5.53194 9.81292i −0.255714 0.453602i
\(469\) 0.416426 + 0.721272i 0.0192288 + 0.0333052i
\(470\) 0 0
\(471\) 3.19917 + 12.1894i 0.147410 + 0.561659i
\(472\) 1.12623 + 1.34218i 0.0518387 + 0.0617790i
\(473\) 1.13889 + 1.35728i 0.0523662 + 0.0624076i
\(474\) −29.2186 + 28.9201i −1.34205 + 1.32834i
\(475\) 0 0
\(476\) −1.41636 2.45321i −0.0649188 0.112443i
\(477\) 30.5889 + 11.4905i 1.40057 + 0.526113i
\(478\) 36.3543 + 20.9892i 1.66281 + 0.960022i
\(479\) 7.23745 41.0456i 0.330688 1.87542i −0.135560 0.990769i \(-0.543283\pi\)
0.466248 0.884654i \(-0.345606\pi\)
\(480\) 0 0
\(481\) −6.35480 2.31296i −0.289754 0.105462i
\(482\) 40.3859 7.12113i 1.83953 0.324358i
\(483\) −2.99431 + 2.07381i −0.136246 + 0.0943618i
\(484\) 20.7077 + 17.3758i 0.941258 + 0.789809i
\(485\) 0 0
\(486\) 23.9220 22.7244i 1.08513 1.03080i
\(487\) 4.02801i 0.182527i 0.995827 + 0.0912634i \(0.0290905\pi\)
−0.995827 + 0.0912634i \(0.970909\pi\)
\(488\) −0.662836 + 0.789937i −0.0300052 + 0.0357588i
\(489\) 12.2769 + 17.7263i 0.555183 + 0.801611i
\(490\) 0 0
\(491\) 36.2922 + 13.2093i 1.63784 + 0.596126i 0.986660 0.162793i \(-0.0520504\pi\)
0.651184 + 0.758920i \(0.274273\pi\)
\(492\) 25.0017 + 2.31677i 1.12716 + 0.104448i
\(493\) 5.09577 + 0.898521i 0.229502 + 0.0404674i
\(494\) 9.96769 17.2645i 0.448468 0.776769i
\(495\) 0 0
\(496\) −12.1830 21.1015i −0.547032 0.947487i
\(497\) 3.19114 + 8.76759i 0.143142 + 0.393280i
\(498\) 12.0823 + 12.2070i 0.541423 + 0.547011i
\(499\) 3.11922 2.61734i 0.139636 0.117168i −0.570295 0.821440i \(-0.693171\pi\)
0.709930 + 0.704272i \(0.248726\pi\)
\(500\) 0 0
\(501\) −1.02531 3.90664i −0.0458076 0.174536i
\(502\) −3.96403 10.8911i −0.176923 0.486093i
\(503\) 2.96695 1.71297i 0.132290 0.0763775i −0.432395 0.901684i \(-0.642331\pi\)
0.564684 + 0.825307i \(0.308998\pi\)
\(504\) −2.58213 + 1.45565i −0.115017 + 0.0648398i
\(505\) 0 0
\(506\) 0.251909 1.42865i 0.0111987 0.0635111i
\(507\) 7.75161 + 16.8487i 0.344261 + 0.748276i
\(508\) −4.43412 + 12.1827i −0.196732 + 0.540518i
\(509\) 2.12952 + 12.0771i 0.0943893 + 0.535308i 0.994933 + 0.100542i \(0.0320578\pi\)
−0.900543 + 0.434766i \(0.856831\pi\)
\(510\) 0 0
\(511\) −11.3529 9.52619i −0.502222 0.421414i
\(512\) 28.1241i 1.24292i
\(513\) 31.0903 + 8.84601i 1.37267 + 0.390561i
\(514\) −24.4791 −1.07973
\(515\) 0 0
\(516\) −10.2616 + 21.7143i −0.451742 + 0.955920i
\(517\) −0.772750 + 0.136257i −0.0339855 + 0.00599257i
\(518\) −3.14407 + 8.63825i −0.138142 + 0.379543i
\(519\) 5.06423 + 3.58490i 0.222295 + 0.157360i
\(520\) 0 0
\(521\) −7.04117 + 12.1957i −0.308479 + 0.534302i −0.978030 0.208465i \(-0.933153\pi\)
0.669551 + 0.742766i \(0.266487\pi\)
\(522\) 5.13962 27.4943i 0.224955 1.20339i
\(523\) −8.46897 + 4.88956i −0.370322 + 0.213806i −0.673599 0.739097i \(-0.735253\pi\)
0.303277 + 0.952902i \(0.401919\pi\)
\(524\) −16.8597 + 6.13643i −0.736520 + 0.268071i
\(525\) 0 0
\(526\) −10.5035 + 8.81348i −0.457974 + 0.384286i
\(527\) −6.54892 7.80469i −0.285275 0.339978i
\(528\) −0.406744 + 1.48740i −0.0177013 + 0.0647309i
\(529\) −17.2176 + 6.26668i −0.748590 + 0.272464i
\(530\) 0 0
\(531\) −3.36541 + 3.92812i −0.146047 + 0.170466i
\(532\) −12.9915 7.50065i −0.563254 0.325195i
\(533\) 8.71534 + 1.53675i 0.377503 + 0.0665640i
\(534\) −46.3785 32.8307i −2.00699 1.42072i
\(535\) 0 0
\(536\) −0.151144 0.857180i −0.00652843 0.0370245i
\(537\) 31.3131 + 14.7977i 1.35126 + 0.638569i
\(538\) 18.8280 22.4384i 0.811734 0.967387i
\(539\) −1.91871 −0.0826445
\(540\) 0 0
\(541\) 40.9454 1.76038 0.880189 0.474623i \(-0.157416\pi\)
0.880189 + 0.474623i \(0.157416\pi\)
\(542\) 2.64674 3.15426i 0.113687 0.135487i
\(543\) −1.38294 16.8001i −0.0593477 0.720959i
\(544\) −1.62750 9.22999i −0.0697783 0.395732i
\(545\) 0 0
\(546\) −4.90300 + 2.25573i −0.209829 + 0.0965365i
\(547\) 1.09341 + 0.192798i 0.0467508 + 0.00824343i 0.196975 0.980409i \(-0.436888\pi\)
−0.150224 + 0.988652i \(0.547999\pi\)
\(548\) 24.1615 + 13.9497i 1.03213 + 0.595900i
\(549\) −2.62070 1.54916i −0.111849 0.0661164i
\(550\) 0 0
\(551\) 25.7495 9.37206i 1.09697 0.399263i
\(552\) 3.68186 0.966321i 0.156711 0.0411293i
\(553\) 7.00864 + 8.35257i 0.298038 + 0.355188i
\(554\) 20.2236 16.9696i 0.859216 0.720968i
\(555\) 0 0
\(556\) −21.8607 + 7.95664i −0.927100 + 0.337437i
\(557\) 30.3458 17.5201i 1.28579 0.742352i 0.307890 0.951422i \(-0.400377\pi\)
0.977901 + 0.209070i \(0.0670437\pi\)
\(558\) −42.5503 + 34.9657i −1.80130 + 1.48022i
\(559\) −4.23247 + 7.33084i −0.179014 + 0.310062i
\(560\) 0 0
\(561\) −0.0594925 + 0.642022i −0.00251178 + 0.0271062i
\(562\) −7.06254 + 19.4042i −0.297915 + 0.818516i
\(563\) −38.1822 + 6.73255i −1.60919 + 0.283743i −0.904724 0.425998i \(-0.859923\pi\)
−0.704463 + 0.709741i \(0.748812\pi\)
\(564\) −6.05593 8.74396i −0.255001 0.368187i
\(565\) 0 0
\(566\) −56.2413 −2.36400
\(567\) −5.48619 6.81774i −0.230398 0.286318i
\(568\) 9.75095i 0.409141i
\(569\) 26.0213 + 21.8344i 1.09087 + 0.915347i 0.996777 0.0802169i \(-0.0255613\pi\)
0.0940904 + 0.995564i \(0.470006\pi\)
\(570\) 0 0
\(571\) 1.75191 + 9.93559i 0.0733153 + 0.415792i 0.999272 + 0.0381610i \(0.0121500\pi\)
−0.925956 + 0.377631i \(0.876739\pi\)
\(572\) 0.406986 1.11818i 0.0170169 0.0467536i
\(573\) 30.6240 + 2.83775i 1.27934 + 0.118549i
\(574\) 2.08894 11.8470i 0.0871908 0.494484i
\(575\) 0 0
\(576\) −33.3522 + 5.52842i −1.38968 + 0.230351i
\(577\) −10.5069 + 6.06615i −0.437407 + 0.252537i −0.702497 0.711687i \(-0.747932\pi\)
0.265090 + 0.964224i \(0.414598\pi\)
\(578\) 11.3078 + 31.0680i 0.470344 + 1.29226i
\(579\) −13.0295 + 12.8964i −0.541487 + 0.535956i
\(580\) 0 0
\(581\) 3.48957 2.92810i 0.144772 0.121478i
\(582\) −19.6785 + 5.16470i −0.815700 + 0.214084i
\(583\) 1.18055 + 3.24352i 0.0488932 + 0.134333i
\(584\) 7.74416 + 13.4133i 0.320456 + 0.555046i
\(585\) 0 0
\(586\) 12.9722 22.4685i 0.535877 0.928167i
\(587\) 31.2669 + 5.51319i 1.29052 + 0.227554i 0.776442 0.630189i \(-0.217023\pi\)
0.514079 + 0.857743i \(0.328134\pi\)
\(588\) −10.8704 23.6276i −0.448288 0.974387i
\(589\) −50.7006 18.4535i −2.08908 0.760363i
\(590\) 0 0
\(591\) 24.4412 2.01195i 1.00538 0.0827605i
\(592\) −8.06588 + 9.61254i −0.331506 + 0.395073i
\(593\) 13.4906i 0.553993i −0.960871 0.276996i \(-0.910661\pi\)
0.960871 0.276996i \(-0.0893390\pi\)
\(594\) 3.46703 + 0.357210i 0.142254 + 0.0146565i
\(595\) 0 0
\(596\) 36.1947 + 30.3710i 1.48259 + 1.24404i
\(597\) −11.8079 5.58009i −0.483265 0.228378i
\(598\) 6.82550 1.20352i 0.279115 0.0492156i
\(599\) −39.8715 14.5120i −1.62911 0.592946i −0.644020 0.765009i \(-0.722735\pi\)
−0.985086 + 0.172063i \(0.944957\pi\)
\(600\) 0 0
\(601\) −3.43906 + 19.5039i −0.140282 + 0.795579i 0.830753 + 0.556641i \(0.187910\pi\)
−0.971035 + 0.238938i \(0.923201\pi\)
\(602\) 9.96501 + 5.75330i 0.406144 + 0.234487i
\(603\) 2.42358 0.854034i 0.0986958 0.0347789i
\(604\) 4.97755 + 8.62136i 0.202533 + 0.350798i
\(605\) 0 0
\(606\) −35.8543 9.80470i −1.45648 0.398289i
\(607\) −23.1397 27.5769i −0.939213 1.11931i −0.992684 0.120741i \(-0.961473\pi\)
0.0534715 0.998569i \(-0.482971\pi\)
\(608\) −31.9038 38.0215i −1.29387 1.54197i
\(609\) −7.15571 1.95680i −0.289964 0.0792934i
\(610\) 0 0
\(611\) −1.87442 3.24659i −0.0758310 0.131343i
\(612\) −8.24315 + 2.90476i −0.333209 + 0.117418i
\(613\) 22.9175 + 13.2314i 0.925627 + 0.534411i 0.885426 0.464780i \(-0.153867\pi\)
0.0402013 + 0.999192i \(0.487200\pi\)
\(614\) −9.73045 + 55.1841i −0.392689 + 2.22705i
\(615\) 0 0
\(616\) −0.294234 0.107093i −0.0118550 0.00431488i
\(617\) −48.3705 + 8.52903i −1.94732 + 0.343366i −0.947611 + 0.319425i \(0.896510\pi\)
−0.999713 + 0.0239406i \(0.992379\pi\)
\(618\) 32.6599 + 15.4342i 1.31377 + 0.620853i
\(619\) 18.5430 + 15.5595i 0.745307 + 0.625387i 0.934257 0.356600i \(-0.116064\pi\)
−0.188950 + 0.981987i \(0.560508\pi\)
\(620\) 0 0
\(621\) 4.59193 + 10.2570i 0.184268 + 0.411598i
\(622\) 37.3785i 1.49874i
\(623\) −9.68725 + 11.5448i −0.388111 + 0.462533i
\(624\) −7.34229 + 0.604400i −0.293927 + 0.0241954i
\(625\) 0 0
\(626\) 19.1881 + 6.98388i 0.766909 + 0.279132i
\(627\) 1.42714 + 3.10199i 0.0569945 + 0.123882i
\(628\) −17.7708 3.13347i −0.709132 0.125039i
\(629\) −2.62345 + 4.54395i −0.104604 + 0.181179i
\(630\) 0 0
\(631\) −8.84842 15.3259i −0.352250 0.610115i 0.634393 0.773010i \(-0.281250\pi\)
−0.986643 + 0.162895i \(0.947917\pi\)
\(632\) −3.89736 10.7079i −0.155029 0.425938i
\(633\) 8.73447 2.29240i 0.347164 0.0911147i
\(634\) −6.01629 + 5.04827i −0.238937 + 0.200492i
\(635\) 0 0
\(636\) −33.2535 + 32.9138i −1.31859 + 1.30512i
\(637\) −3.13523 8.61398i −0.124222 0.341298i
\(638\) 2.55880 1.47732i 0.101304 0.0584878i
\(639\) 28.3998 4.70751i 1.12348 0.186226i
\(640\) 0 0
\(641\) 6.60738 37.4723i 0.260976 1.48007i −0.519278 0.854605i \(-0.673799\pi\)
0.780254 0.625463i \(-0.215090\pi\)
\(642\) −18.8758 1.74911i −0.744968 0.0690319i
\(643\) −16.0553 + 44.1115i −0.633158 + 1.73959i 0.0390615 + 0.999237i \(0.487563\pi\)
−0.672220 + 0.740352i \(0.734659\pi\)
\(644\) −0.905644 5.13616i −0.0356874 0.202393i
\(645\) 0 0
\(646\) −11.8485 9.94211i −0.466175 0.391167i
\(647\) 28.2333i 1.10997i −0.831862 0.554983i \(-0.812725\pi\)
0.831862 0.554983i \(-0.187275\pi\)
\(648\) 2.95083 + 8.65643i 0.115920 + 0.340057i
\(649\) −0.546406 −0.0214483
\(650\) 0 0
\(651\) 8.31660 + 12.0081i 0.325953 + 0.470634i
\(652\) −30.4060 + 5.36140i −1.19079 + 0.209969i
\(653\) −12.0758 + 33.1779i −0.472562 + 1.29835i 0.443125 + 0.896460i \(0.353870\pi\)
−0.915687 + 0.401893i \(0.868353\pi\)
\(654\) −2.47295 + 26.6872i −0.0967001 + 1.04355i
\(655\) 0 0
\(656\) 8.21052 14.2210i 0.320567 0.555239i
\(657\) −35.3277 + 29.0306i −1.37826 + 1.13259i
\(658\) −4.41318 + 2.54795i −0.172044 + 0.0993295i
\(659\) 39.1793 14.2601i 1.52621 0.555494i 0.563519 0.826103i \(-0.309447\pi\)
0.962689 + 0.270609i \(0.0872250\pi\)
\(660\) 0 0
\(661\) 0.975874 0.818856i 0.0379571 0.0318498i −0.623612 0.781734i \(-0.714335\pi\)
0.661569 + 0.749884i \(0.269891\pi\)
\(662\) 1.92216 + 2.29075i 0.0747070 + 0.0890324i
\(663\) −2.97956 + 0.781997i −0.115716 + 0.0303702i
\(664\) −4.47359 + 1.62825i −0.173609 + 0.0631885i
\(665\) 0 0
\(666\) 24.4158 + 14.4328i 0.946095 + 0.559258i
\(667\) 8.25035 + 4.76334i 0.319455 + 0.184437i
\(668\) 5.69543 + 1.00426i 0.220363 + 0.0388559i
\(669\) 27.8413 12.8090i 1.07641 0.495226i
\(670\) 0 0
\(671\) −0.0558427 0.316700i −0.00215578 0.0122261i
\(672\) 1.10238 + 13.3918i 0.0425252 + 0.516598i
\(673\) 22.9043 27.2963i 0.882896 1.05219i −0.115370 0.993323i \(-0.536805\pi\)
0.998266 0.0588715i \(-0.0187502\pi\)
\(674\) −27.4951 −1.05907
\(675\) 0 0
\(676\) −26.5561 −1.02139
\(677\) −11.5714 + 13.7902i −0.444725 + 0.530002i −0.941110 0.338100i \(-0.890216\pi\)
0.496386 + 0.868102i \(0.334660\pi\)
\(678\) −34.3913 16.2524i −1.32079 0.624169i
\(679\) 0.936996 + 5.31397i 0.0359586 + 0.203931i
\(680\) 0 0
\(681\) −22.2968 15.7836i −0.854414 0.604828i
\(682\) −5.72929 1.01023i −0.219386 0.0386836i
\(683\) 34.4344 + 19.8807i 1.31760 + 0.760715i 0.983341 0.181768i \(-0.0581820\pi\)
0.334255 + 0.942483i \(0.391515\pi\)
\(684\) −30.1136 + 35.1486i −1.15142 + 1.34394i
\(685\) 0 0
\(686\) −25.2468 + 9.18909i −0.963928 + 0.350841i
\(687\) −0.807229 + 2.95192i −0.0307977 + 0.112623i
\(688\) 10.0962 + 12.0322i 0.384915 + 0.458724i
\(689\) −12.6327 + 10.6001i −0.481266 + 0.403830i
\(690\) 0 0
\(691\) 15.8251 5.75986i 0.602015 0.219115i −0.0229909 0.999736i \(-0.507319\pi\)
0.625006 + 0.780620i \(0.285097\pi\)
\(692\) −7.69408 + 4.44218i −0.292485 + 0.168866i
\(693\) 0.169860 0.908663i 0.00645244 0.0345173i
\(694\) 5.08038 8.79948i 0.192849 0.334024i
\(695\) 0 0
\(696\) 6.32790 + 4.47944i 0.239859 + 0.169793i
\(697\) 2.34839 6.45216i 0.0889518 0.244393i
\(698\) 47.0622 8.29833i 1.78133 0.314097i
\(699\) −10.2854 + 21.7648i −0.389031 + 0.823220i
\(700\) 0 0
\(701\) −8.96921 −0.338762 −0.169381 0.985551i \(-0.554177\pi\)
−0.169381 + 0.985551i \(0.554177\pi\)
\(702\) 4.06156 + 16.1488i 0.153294 + 0.609498i
\(703\) 27.7861i 1.04797i
\(704\) −2.73570 2.29552i −0.103106 0.0865158i
\(705\) 0 0
\(706\) 10.9186 + 61.9223i 0.410926 + 2.33048i
\(707\) −3.37181 + 9.26398i −0.126810 + 0.348408i
\(708\) −3.09566 6.72864i −0.116342 0.252878i
\(709\) −3.15026 + 17.8660i −0.118311 + 0.670973i 0.866747 + 0.498748i \(0.166207\pi\)
−0.985058 + 0.172225i \(0.944904\pi\)
\(710\) 0 0
\(711\) 29.3054 16.5206i 1.09904 0.619572i
\(712\) 13.6401 7.87509i 0.511183 0.295131i
\(713\) −6.41560 17.6267i −0.240266 0.660125i
\(714\) 1.06299 + 4.05019i 0.0397814 + 0.151574i
\(715\) 0 0
\(716\) −37.9890 + 31.8766i −1.41972 + 1.19128i
\(717\) −24.1650 24.4144i −0.902457 0.911771i
\(718\) −9.71498 26.6917i −0.362560 0.996125i
\(719\) 15.7860 + 27.3421i 0.588718 + 1.01969i 0.994401 + 0.105675i \(0.0337004\pi\)
−0.405683 + 0.914014i \(0.632966\pi\)
\(720\) 0 0
\(721\) 4.79034 8.29711i 0.178402 0.309001i
\(722\) −41.0606 7.24010i −1.52812 0.269449i
\(723\) −33.4148 3.09636i −1.24271 0.115155i
\(724\) 22.6814 + 8.25536i 0.842948 + 0.306808i
\(725\) 0 0
\(726\) −22.7511 32.8497i −0.844374 1.21916i
\(727\) −24.6890 + 29.4232i −0.915664 + 1.09125i 0.0798662 + 0.996806i \(0.474551\pi\)
−0.995530 + 0.0944407i \(0.969894\pi\)
\(728\) 1.49595i 0.0554436i
\(729\) −23.7874 + 12.7734i −0.881014 + 0.473090i
\(730\) 0 0
\(731\) 5.03111 + 4.22160i 0.186082 + 0.156142i
\(732\) 3.58358 2.48193i 0.132453 0.0917346i
\(733\) −29.8695 + 5.26680i −1.10326 + 0.194534i −0.695478 0.718547i \(-0.744807\pi\)
−0.407778 + 0.913081i \(0.633696\pi\)
\(734\) 15.8123 + 5.75521i 0.583643 + 0.212429i
\(735\) 0 0
\(736\) 2.99643 16.9936i 0.110450 0.626391i
\(737\) 0.235076 + 0.135721i 0.00865915 + 0.00499936i
\(738\) −34.7456 13.0519i −1.27900 0.480448i
\(739\) 5.00127 + 8.66245i 0.183975 + 0.318653i 0.943230 0.332139i \(-0.107770\pi\)
−0.759256 + 0.650792i \(0.774437\pi\)
\(740\) 0 0
\(741\) −11.5943 + 11.4759i −0.425928 + 0.421577i
\(742\) 14.4089 + 17.1719i 0.528969 + 0.630400i
\(743\) −23.3163 27.7873i −0.855394 1.01942i −0.999554 0.0298642i \(-0.990493\pi\)
0.144160 0.989554i \(-0.453952\pi\)
\(744\) −3.87523 14.7654i −0.142073 0.541324i
\(745\) 0 0
\(746\) −12.0865 20.9344i −0.442517 0.766461i
\(747\) −6.90205 12.2433i −0.252533 0.447960i
\(748\) −0.799548 0.461619i −0.0292344 0.0168785i
\(749\) −0.873058 + 4.95136i −0.0319008 + 0.180919i
\(750\) 0 0
\(751\) 13.6766 + 4.97788i 0.499067 + 0.181646i 0.579274 0.815133i \(-0.303336\pi\)
−0.0802073 + 0.996778i \(0.525558\pi\)
\(752\) −6.85041 + 1.20791i −0.249809 + 0.0440480i
\(753\) 0.778089 + 9.45226i 0.0283551 + 0.344460i
\(754\) 10.8136 + 9.07366i 0.393807 + 0.330443i
\(755\) 0 0
\(756\) 12.1519 3.05631i 0.441962 0.111157i
\(757\) 45.5754i 1.65646i −0.560385 0.828232i \(-0.689347\pi\)
0.560385 0.828232i \(-0.310653\pi\)
\(758\) 32.8849 39.1907i 1.19443 1.42347i
\(759\) −0.507211 + 1.07330i −0.0184106 + 0.0389582i
\(760\) 0 0
\(761\) −20.9040 7.60843i −0.757769 0.275805i −0.0658978 0.997826i \(-0.520991\pi\)
−0.691871 + 0.722021i \(0.743213\pi\)
\(762\) 11.0726 15.6418i 0.401119 0.566643i
\(763\) 7.00040 + 1.23436i 0.253431 + 0.0446868i
\(764\) −22.0189 + 38.1379i −0.796616 + 1.37978i
\(765\) 0 0
\(766\) 9.99393 + 17.3100i 0.361096 + 0.625436i
\(767\) −0.892846 2.45307i −0.0322388 0.0885754i
\(768\) −2.66224 + 9.73542i −0.0960654 + 0.351297i
\(769\) −10.4679 + 8.78365i −0.377484 + 0.316747i −0.811714 0.584056i \(-0.801465\pi\)
0.434230 + 0.900802i \(0.357021\pi\)
\(770\) 0 0
\(771\) 19.3220 + 5.28379i 0.695866 + 0.190291i
\(772\) −8.97807 24.6670i −0.323128 0.887786i
\(773\) 17.8869 10.3270i 0.643345 0.371436i −0.142557 0.989787i \(-0.545532\pi\)
0.785902 + 0.618351i \(0.212199\pi\)
\(774\) 23.0983 26.9604i 0.830252 0.969072i
\(775\) 0 0
\(776\) 0.979243 5.55356i 0.0351528 0.199361i
\(777\) 4.34626 6.13977i 0.155921 0.220263i
\(778\) −1.84436 + 5.06732i −0.0661233 + 0.181672i
\(779\) −6.31415 35.8093i −0.226228 1.28300i
\(780\) 0 0
\(781\) 2.32948 + 1.95466i 0.0833553 + 0.0699434i
\(782\) 5.37736i 0.192294i
\(783\) −9.99147 + 20.5927i −0.357066 + 0.735922i
\(784\) −17.0093 −0.607474
\(785\) 0 0
\(786\) 26.4323 2.17584i 0.942807 0.0776097i
\(787\) 24.3281 4.28970i 0.867202 0.152911i 0.277690 0.960671i \(-0.410431\pi\)
0.589512 + 0.807759i \(0.299320\pi\)
\(788\) −12.0102 + 32.9976i −0.427844 + 1.17549i
\(789\) 10.1931 4.68956i 0.362884 0.166953i
\(790\) 0 0
\(791\) −5.04429 + 8.73696i −0.179354 + 0.310651i
\(792\) −0.491606 + 0.831647i −0.0174685 + 0.0295513i
\(793\) 1.33057 0.768202i 0.0472498 0.0272797i
\(794\) −7.30983 + 2.66056i −0.259416 + 0.0944197i
\(795\) 0 0
\(796\) 14.3253 12.0204i 0.507747 0.426051i
\(797\) −19.6473 23.4148i −0.695943 0.829393i 0.296117 0.955152i \(-0.404308\pi\)
−0.992061 + 0.125758i \(0.959864\pi\)
\(798\) 15.5995 + 15.7605i 0.552215 + 0.557914i
\(799\) −2.73319 + 0.994799i −0.0966933 + 0.0351935i
\(800\) 0 0
\(801\) 29.5214 + 35.9250i 1.04309 + 1.26935i
\(802\) 29.6014 + 17.0904i 1.04526 + 0.603482i
\(803\) −4.75679 0.838750i −0.167863 0.0295988i
\(804\) −0.339498 + 3.66374i −0.0119732 + 0.129210i
\(805\) 0 0
\(806\) −4.82646 27.3722i −0.170005 0.964146i
\(807\) −19.7048 + 13.6472i −0.693642 + 0.480405i
\(808\) 6.62265 7.89257i 0.232984 0.277660i
\(809\) −46.8599 −1.64751 −0.823753 0.566949i \(-0.808124\pi\)
−0.823753 + 0.566949i \(0.808124\pi\)
\(810\) 0 0
\(811\) 10.9984 0.386206 0.193103 0.981178i \(-0.438145\pi\)
0.193103 + 0.981178i \(0.438145\pi\)
\(812\) 6.82790 8.13717i 0.239612 0.285559i
\(813\) −2.76999 + 1.91845i −0.0971476 + 0.0672829i
\(814\) 0.520260 + 2.95054i 0.0182351 + 0.103416i
\(815\) 0 0
\(816\) −0.527400 + 5.69151i −0.0184627 + 0.199243i
\(817\) 34.2521 + 6.03956i 1.19833 + 0.211298i
\(818\) −16.8310 9.71738i −0.588482 0.339760i
\(819\) 4.35697 0.722206i 0.152245 0.0252359i
\(820\) 0 0
\(821\) 33.8133 12.3070i 1.18009 0.429518i 0.323857 0.946106i \(-0.395020\pi\)
0.856234 + 0.516588i \(0.172798\pi\)
\(822\) −29.0118 29.3112i −1.01190 1.02235i
\(823\) 31.4880 + 37.5259i 1.09760 + 1.30807i 0.947626 + 0.319383i \(0.103476\pi\)
0.149977 + 0.988689i \(0.452080\pi\)
\(824\) −7.67013 + 6.43600i −0.267202 + 0.224209i
\(825\) 0 0
\(826\) −3.33453 + 1.21367i −0.116023 + 0.0422290i
\(827\) −13.5192 + 7.80533i −0.470109 + 0.271418i −0.716286 0.697807i \(-0.754159\pi\)
0.246176 + 0.969225i \(0.420826\pi\)
\(828\) −16.0905 0.165222i −0.559185 0.00574184i
\(829\) 5.73541 9.93401i 0.199199 0.345023i −0.749070 0.662491i \(-0.769499\pi\)
0.948269 + 0.317468i \(0.102833\pi\)
\(830\) 0 0
\(831\) −19.6259 + 9.02932i −0.680814 + 0.313224i
\(832\) 5.83547 16.0328i 0.202308 0.555838i
\(833\) −7.00416 + 1.23502i −0.242680 + 0.0427910i
\(834\) 34.2727 2.82125i 1.18677 0.0976918i
\(835\) 0 0
\(836\) −4.88922 −0.169097
\(837\) 41.1334 18.4150i 1.42178 0.636515i
\(838\) 14.7716i 0.510278i
\(839\) 0.517329 + 0.434090i 0.0178602 + 0.0149865i 0.651674 0.758499i \(-0.274067\pi\)
−0.633814 + 0.773486i \(0.718511\pi\)
\(840\) 0 0
\(841\) −1.66646 9.45097i −0.0574642 0.325895i
\(842\) −22.3047 + 61.2815i −0.768669 + 2.11190i
\(843\) 9.76304 13.7918i 0.336257 0.475015i
\(844\) −2.24532 + 12.7339i −0.0772872 + 0.438318i
\(845\) 0 0
\(846\) 5.22550 + 14.8290i 0.179656 + 0.509830i
\(847\) −9.17815 + 5.29901i −0.315365 + 0.182076i
\(848\) 10.4655 + 28.7537i 0.359387 + 0.987408i
\(849\) 44.3928 + 12.1396i 1.52356 + 0.416631i
\(850\) 0 0
\(851\) −7.40014 + 6.20946i −0.253674 + 0.212857i
\(852\) −10.8728 + 39.7602i −0.372496 + 1.36216i
\(853\) 13.4605 + 36.9823i 0.460877 + 1.26625i 0.924827 + 0.380388i \(0.124210\pi\)
−0.463949 + 0.885862i \(0.653568\pi\)
\(854\) −1.04424 1.80867i −0.0357331 0.0618915i
\(855\) 0 0
\(856\) 2.62721 4.55047i 0.0897963 0.155532i
\(857\) 32.1659 + 5.67172i 1.09877 + 0.193742i 0.693500 0.720457i \(-0.256068\pi\)
0.405266 + 0.914199i \(0.367179\pi\)
\(858\) −1.01630 + 1.43568i −0.0346959 + 0.0490134i
\(859\) −31.1946 11.3539i −1.06435 0.387391i −0.250287 0.968172i \(-0.580525\pi\)
−0.814060 + 0.580781i \(0.802747\pi\)
\(860\) 0 0
\(861\) −4.20602 + 8.90026i −0.143341 + 0.303320i
\(862\) 37.9551 45.2332i 1.29276 1.54065i
\(863\) 22.6796i 0.772024i −0.922494 0.386012i \(-0.873852\pi\)
0.922494 0.386012i \(-0.126148\pi\)
\(864\) 41.2399 + 4.24897i 1.40301 + 0.144553i
\(865\) 0 0
\(866\) −31.0837 26.0823i −1.05627 0.886312i
\(867\) −2.21958 26.9636i −0.0753810 0.915733i
\(868\) −20.5975 + 3.63190i −0.699125 + 0.123275i
\(869\) 3.33935 + 1.21543i 0.113280 + 0.0412305i
\(870\) 0 0
\(871\) −0.225195 + 1.27714i −0.00763043 + 0.0432743i
\(872\) −6.43360 3.71444i −0.217869 0.125787i
\(873\) 16.6476 + 0.170941i 0.563435 + 0.00578549i
\(874\) −14.2385 24.6618i −0.481625 0.834199i
\(875\) 0 0
\(876\) −16.6209 63.3287i −0.561567 2.13968i
\(877\) 5.94178 + 7.08113i 0.200640 + 0.239113i 0.856977 0.515354i \(-0.172340\pi\)
−0.656338 + 0.754467i \(0.727895\pi\)
\(878\) −32.3114 38.5072i −1.09046 1.29956i
\(879\) −15.0891 + 14.9350i −0.508944 + 0.503745i
\(880\) 0 0
\(881\) −3.89378 6.74422i −0.131185 0.227219i 0.792949 0.609288i \(-0.208545\pi\)
−0.924134 + 0.382070i \(0.875211\pi\)
\(882\) 6.28692 + 37.9282i 0.211692 + 1.27711i
\(883\) −28.1127 16.2309i −0.946068 0.546213i −0.0542106 0.998530i \(-0.517264\pi\)
−0.891857 + 0.452317i \(0.850598\pi\)
\(884\) 0.765938 4.34385i 0.0257613 0.146099i
\(885\) 0 0
\(886\) 46.4590 + 16.9097i 1.56082 + 0.568092i
\(887\) 33.3334 5.87759i 1.11923 0.197350i 0.416726 0.909032i \(-0.363177\pi\)
0.702502 + 0.711682i \(0.252066\pi\)
\(888\) −6.46289 + 4.47609i −0.216880 + 0.150208i
\(889\) −3.89365 3.26716i −0.130589 0.109577i
\(890\) 0 0
\(891\) −2.65952 1.03031i −0.0890972 0.0345167i
\(892\) 43.8822i 1.46929i
\(893\) −9.90095 + 11.7995i −0.331323 + 0.394855i
\(894\) −39.7665 57.4176i −1.32999 1.92033i
\(895\) 0 0
\(896\) −7.21376 2.62560i −0.240995 0.0877150i
\(897\) −5.64733 0.523306i −0.188559 0.0174727i
\(898\) 10.0452 + 1.77124i 0.335212 + 0.0591069i
\(899\) 19.1024 33.0863i 0.637101 1.10349i
\(900\) 0 0
\(901\) 6.39731 + 11.0805i 0.213125 + 0.369144i
\(902\) −1.34097 3.68428i −0.0446494 0.122673i
\(903\) −6.62382 6.69218i −0.220427 0.222702i
\(904\) 8.07674 6.77719i 0.268629 0.225406i
\(905\) 0 0
\(906\) −3.73568 14.2337i −0.124110 0.472882i
\(907\) 3.78269 + 10.3929i 0.125602 + 0.345089i 0.986517 0.163660i \(-0.0523301\pi\)
−0.860915 + 0.508750i \(0.830108\pi\)
\(908\) 33.8754 19.5580i 1.12420 0.649054i
\(909\) 26.1845 + 15.4782i 0.868484 + 0.513381i
\(910\) 0 0
\(911\) 2.17845 12.3546i 0.0721751 0.409325i −0.927219 0.374520i \(-0.877808\pi\)
0.999394 0.0348058i \(-0.0110813\pi\)
\(912\) 12.6516 + 27.4991i 0.418935 + 0.910586i
\(913\) 0.507785 1.39513i 0.0168052 0.0461720i
\(914\) −1.79863 10.2005i −0.0594934 0.337404i
\(915\) 0 0
\(916\) −3.35679 2.81668i −0.110912 0.0930659i
\(917\) 7.03415i 0.232288i
\(918\) 12.8862 0.927658i 0.425307 0.0306173i
\(919\) 5.92909 0.195583 0.0977913 0.995207i \(-0.468822\pi\)
0.0977913 + 0.995207i \(0.468822\pi\)
\(920\) 0 0
\(921\) 19.5920 41.4580i 0.645577 1.36609i
\(922\) 58.3452 10.2878i 1.92150 0.338812i
\(923\) −4.96897 + 13.6521i −0.163555 + 0.449365i
\(924\) 1.08035 + 0.764763i 0.0355408 + 0.0251588i
\(925\) 0 0
\(926\) −29.0775 + 50.3636i −0.955545 + 1.65505i
\(927\) −22.4479 19.2322i −0.737285 0.631669i
\(928\) 30.4366 17.5726i 0.999131 0.576848i
\(929\) −9.42772 + 3.43141i −0.309314 + 0.112581i −0.492013 0.870588i \(-0.663739\pi\)
0.182699 + 0.983169i \(0.441517\pi\)
\(930\) 0 0
\(931\) −28.8525 + 24.2101i −0.945603 + 0.793455i
\(932\) −22.1564 26.4050i −0.725758 0.864925i
\(933\) 8.06811 29.5039i 0.264138 0.965913i
\(934\) 42.2587 15.3809i 1.38275 0.503279i
\(935\) 0 0
\(936\) −4.53696 0.848110i −0.148295 0.0277214i
\(937\) 20.3811 + 11.7671i 0.665823 + 0.384413i 0.794492 0.607274i \(-0.207737\pi\)
−0.128669 + 0.991688i \(0.541070\pi\)
\(938\) 1.73605 + 0.306113i 0.0566841 + 0.00999494i
\(939\) −13.6382 9.65429i −0.445066 0.315056i
\(940\) 0 0
\(941\) −5.08781 28.8544i −0.165858 0.940627i −0.948175 0.317747i \(-0.897074\pi\)
0.782317 0.622880i \(-0.214038\pi\)
\(942\) 24.1169 + 11.3970i 0.785770 + 0.371334i
\(943\) 8.12588 9.68405i 0.264615 0.315356i
\(944\) −4.84388 −0.157655
\(945\) 0 0
\(946\) 3.75023 0.121930
\(947\) −34.4932 + 41.1074i −1.12088 + 1.33581i −0.185304 + 0.982681i \(0.559327\pi\)
−0.935574 + 0.353130i \(0.885117\pi\)
\(948\) 3.95191 + 48.0080i 0.128352 + 1.55923i
\(949\) −4.00721 22.7260i −0.130079 0.737717i
\(950\) 0 0
\(951\) 5.83849 2.68613i 0.189326 0.0871036i
\(952\) −1.14302 0.201546i −0.0370456 0.00653214i
\(953\) −4.24055 2.44828i −0.137365 0.0793076i 0.429743 0.902951i \(-0.358604\pi\)
−0.567108 + 0.823644i \(0.691938\pi\)
\(954\) 60.2484 33.9644i 1.95061 1.09964i
\(955\) 0 0
\(956\) 46.2205 16.8229i 1.49488 0.544092i
\(957\) −2.33861 + 0.613778i −0.0755965 + 0.0198406i
\(958\) −56.7057 67.5792i −1.83208 2.18338i
\(959\) −8.37906 + 7.03086i −0.270574 + 0.227038i
\(960\) 0 0
\(961\) −41.5578 + 15.1258i −1.34057 + 0.487929i
\(962\) −12.3962 + 7.15698i −0.399671 + 0.230750i
\(963\) 14.5216 + 5.45495i 0.467954 + 0.175783i
\(964\) 24.0255 41.6134i 0.773810 1.34028i
\(965\) 0 0
\(966\) −0.711343 + 7.67657i −0.0228871 + 0.246990i
\(967\) 5.81200 15.9683i 0.186901 0.513507i −0.810485 0.585759i \(-0.800796\pi\)
0.997386 + 0.0722523i \(0.0230187\pi\)
\(968\) 10.9076 1.92330i 0.350583 0.0618172i
\(969\) 7.20639 + 10.4051i 0.231503 + 0.334259i
\(970\) 0 0
\(971\) −2.68374 −0.0861253 −0.0430627 0.999072i \(-0.513712\pi\)
−0.0430627 + 0.999072i \(0.513712\pi\)
\(972\) −2.37987 38.5875i −0.0763345 1.23769i
\(973\) 9.12064i 0.292394i
\(974\) 6.53113 + 5.48027i 0.209271 + 0.175599i
\(975\) 0 0
\(976\) −0.495044 2.80753i −0.0158460 0.0898670i
\(977\) 3.75984 10.3301i 0.120288 0.330488i −0.864906 0.501935i \(-0.832622\pi\)
0.985193 + 0.171446i \(0.0548440\pi\)
\(978\) 45.4452 + 4.21114i 1.45318 + 0.134657i
\(979\) −0.852930 + 4.83721i −0.0272598 + 0.154598i
\(980\) 0 0
\(981\) 7.71239 20.5312i 0.246238 0.655511i
\(982\) 70.7948 40.8734i 2.25915 1.30432i
\(983\) −16.3402 44.8944i −0.521172 1.43191i −0.869217 0.494431i \(-0.835376\pi\)
0.348044 0.937478i \(-0.386846\pi\)
\(984\) 7.31189 7.23719i 0.233094 0.230713i
\(985\) 0 0
\(986\) 8.38988 7.03994i 0.267188 0.224197i
\(987\) 4.03342 1.05859i 0.128385 0.0336952i
\(988\) −7.98915 21.9500i −0.254169 0.698323i
\(989\) 6.04594 + 10.4719i 0.192250 + 0.332986i
\(990\) 0 0
\(991\) −27.7503 + 48.0649i −0.881517 + 1.52683i −0.0318627 + 0.999492i \(0.510144\pi\)
−0.849654 + 0.527340i \(0.823189\pi\)
\(992\) −68.1492 12.0165i −2.16374 0.381526i
\(993\) −1.02276 2.22305i −0.0324564 0.0705462i
\(994\) 18.5577 + 6.75445i 0.588614 + 0.214238i
\(995\) 0 0
\(996\) 20.0570 1.65104i 0.635529 0.0523153i
\(997\) 28.9555 34.5078i 0.917029 1.09287i −0.0783575 0.996925i \(-0.524968\pi\)
0.995386 0.0959472i \(-0.0305880\pi\)
\(998\) 8.61859i 0.272817i
\(999\) −16.1568 16.6623i −0.511179 0.527172i
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 675.2.u.b.124.4 24
5.2 odd 4 675.2.l.c.151.2 12
5.3 odd 4 27.2.e.a.16.1 12
5.4 even 2 inner 675.2.u.b.124.1 24
15.8 even 4 81.2.e.a.46.2 12
20.3 even 4 432.2.u.c.97.2 12
27.22 even 9 inner 675.2.u.b.49.1 24
45.13 odd 12 243.2.e.c.55.2 12
45.23 even 12 243.2.e.b.55.1 12
45.38 even 12 243.2.e.a.217.2 12
45.43 odd 12 243.2.e.d.217.1 12
135.13 odd 36 243.2.e.c.190.2 12
135.22 odd 36 675.2.l.c.76.2 12
135.23 even 36 243.2.e.a.28.2 12
135.38 even 36 729.2.c.b.487.2 12
135.43 odd 36 729.2.c.e.487.5 12
135.49 even 18 inner 675.2.u.b.49.4 24
135.58 odd 36 243.2.e.d.28.1 12
135.68 even 36 243.2.e.b.190.1 12
135.83 even 36 729.2.c.b.244.2 12
135.88 odd 36 729.2.a.a.1.2 6
135.103 odd 36 27.2.e.a.22.1 yes 12
135.113 even 36 81.2.e.a.37.2 12
135.128 even 36 729.2.a.d.1.5 6
135.133 odd 36 729.2.c.e.244.5 12
540.103 even 36 432.2.u.c.49.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.2.e.a.16.1 12 5.3 odd 4
27.2.e.a.22.1 yes 12 135.103 odd 36
81.2.e.a.37.2 12 135.113 even 36
81.2.e.a.46.2 12 15.8 even 4
243.2.e.a.28.2 12 135.23 even 36
243.2.e.a.217.2 12 45.38 even 12
243.2.e.b.55.1 12 45.23 even 12
243.2.e.b.190.1 12 135.68 even 36
243.2.e.c.55.2 12 45.13 odd 12
243.2.e.c.190.2 12 135.13 odd 36
243.2.e.d.28.1 12 135.58 odd 36
243.2.e.d.217.1 12 45.43 odd 12
432.2.u.c.49.2 12 540.103 even 36
432.2.u.c.97.2 12 20.3 even 4
675.2.l.c.76.2 12 135.22 odd 36
675.2.l.c.151.2 12 5.2 odd 4
675.2.u.b.49.1 24 27.22 even 9 inner
675.2.u.b.49.4 24 135.49 even 18 inner
675.2.u.b.124.1 24 5.4 even 2 inner
675.2.u.b.124.4 24 1.1 even 1 trivial
729.2.a.a.1.2 6 135.88 odd 36
729.2.a.d.1.5 6 135.128 even 36
729.2.c.b.244.2 12 135.83 even 36
729.2.c.b.487.2 12 135.38 even 36
729.2.c.e.244.5 12 135.133 odd 36
729.2.c.e.487.5 12 135.43 odd 36