Properties

Label 324.3.j.a.19.19
Level $324$
Weight $3$
Character 324.19
Analytic conductor $8.828$
Analytic rank $0$
Dimension $204$
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] = [324,3,Mod(19,324)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(324, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("324.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.j (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: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 19.19
Character \(\chi\) \(=\) 324.19
Dual form 324.3.j.a.307.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.443343 - 1.95024i) q^{2} +(-3.60689 - 1.72925i) q^{4} +(0.890579 + 5.05073i) q^{5} +(-0.0265129 + 0.0315969i) q^{7} +(-4.97155 + 6.26767i) q^{8} +O(q^{10})\) \(q+(0.443343 - 1.95024i) q^{2} +(-3.60689 - 1.72925i) q^{4} +(0.890579 + 5.05073i) q^{5} +(-0.0265129 + 0.0315969i) q^{7} +(-4.97155 + 6.26767i) q^{8} +(10.2450 + 0.502357i) q^{10} +(4.18050 + 0.737135i) q^{11} +(-1.91152 - 0.695736i) q^{13} +(0.0498672 + 0.0657149i) q^{14} +(10.0194 + 12.4745i) q^{16} +(15.1353 + 26.2152i) q^{17} +(5.91027 + 3.41230i) q^{19} +(5.52176 - 19.7575i) q^{20} +(3.29099 - 7.82619i) q^{22} +(25.3540 + 30.2157i) q^{23} +(-1.22440 + 0.445645i) q^{25} +(-2.20431 + 3.41948i) q^{26} +(0.150268 - 0.0681190i) q^{28} +(20.7044 - 7.53578i) q^{29} +(-25.1859 - 30.0153i) q^{31} +(28.7702 - 14.0097i) q^{32} +(57.8360 - 17.8953i) q^{34} +(-0.183199 - 0.105770i) q^{35} +(15.9508 + 27.6276i) q^{37} +(9.27508 - 10.0136i) q^{38} +(-36.0838 - 19.5281i) q^{40} +(-53.8833 - 19.6119i) q^{41} +(-40.8395 - 7.20111i) q^{43} +(-13.8039 - 9.88791i) q^{44} +(70.1685 - 36.0505i) q^{46} +(9.40005 - 11.2025i) q^{47} +(8.50847 + 48.2539i) q^{49} +(0.326287 + 2.58545i) q^{50} +(5.69155 + 5.81495i) q^{52} +43.0946 q^{53} +21.7710i q^{55} +(-0.0662283 - 0.323260i) q^{56} +(-5.51746 - 43.7195i) q^{58} +(-40.5818 + 7.15567i) q^{59} +(14.2464 + 11.9542i) q^{61} +(-69.7032 + 35.8115i) q^{62} +(-14.5673 - 62.3201i) q^{64} +(1.81161 - 10.2742i) q^{65} +(-16.7275 + 45.9585i) q^{67} +(-9.25890 - 120.728i) q^{68} +(-0.287497 + 0.310390i) q^{70} +(-111.053 + 64.1166i) q^{71} +(63.7153 - 110.358i) q^{73} +(60.9523 - 18.8595i) q^{74} +(-15.4170 - 22.5281i) q^{76} +(-0.134128 + 0.112547i) q^{77} +(-1.11267 - 3.05705i) q^{79} +(-54.0821 + 61.7146i) q^{80} +(-62.1368 + 96.3907i) q^{82} +(40.0201 + 109.954i) q^{83} +(-118.926 + 99.7911i) q^{85} +(-32.1498 + 76.4544i) q^{86} +(-25.4037 + 22.5373i) q^{88} +(26.9272 - 46.6393i) q^{89} +(0.0726630 - 0.0419520i) q^{91} +(-39.1986 - 152.828i) q^{92} +(-17.6802 - 23.2989i) q^{94} +(-11.9710 + 32.8901i) q^{95} +(-5.60171 + 31.7689i) q^{97} +(97.8790 + 4.79945i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.443343 1.95024i 0.221671 0.975121i
\(3\) 0 0
\(4\) −3.60689 1.72925i −0.901724 0.432313i
\(5\) 0.890579 + 5.05073i 0.178116 + 1.01015i 0.934486 + 0.356001i \(0.115860\pi\)
−0.756370 + 0.654144i \(0.773029\pi\)
\(6\) 0 0
\(7\) −0.0265129 + 0.0315969i −0.00378756 + 0.00451384i −0.767935 0.640528i \(-0.778716\pi\)
0.764147 + 0.645042i \(0.223160\pi\)
\(8\) −4.97155 + 6.26767i −0.621444 + 0.783459i
\(9\) 0 0
\(10\) 10.2450 + 0.502357i 1.02450 + 0.0502357i
\(11\) 4.18050 + 0.737135i 0.380045 + 0.0670123i 0.360408 0.932795i \(-0.382638\pi\)
0.0196378 + 0.999807i \(0.493749\pi\)
\(12\) 0 0
\(13\) −1.91152 0.695736i −0.147040 0.0535182i 0.267452 0.963571i \(-0.413818\pi\)
−0.414492 + 0.910053i \(0.636041\pi\)
\(14\) 0.0498672 + 0.0657149i 0.00356195 + 0.00469392i
\(15\) 0 0
\(16\) 10.0194 + 12.4745i 0.626211 + 0.779654i
\(17\) 15.1353 + 26.2152i 0.890313 + 1.54207i 0.839500 + 0.543359i \(0.182848\pi\)
0.0508130 + 0.998708i \(0.483819\pi\)
\(18\) 0 0
\(19\) 5.91027 + 3.41230i 0.311067 + 0.179595i 0.647404 0.762147i \(-0.275855\pi\)
−0.336337 + 0.941742i \(0.609188\pi\)
\(20\) 5.52176 19.7575i 0.276088 0.987874i
\(21\) 0 0
\(22\) 3.29099 7.82619i 0.149590 0.355736i
\(23\) 25.3540 + 30.2157i 1.10235 + 1.31373i 0.945324 + 0.326133i \(0.105746\pi\)
0.157024 + 0.987595i \(0.449810\pi\)
\(24\) 0 0
\(25\) −1.22440 + 0.445645i −0.0489760 + 0.0178258i
\(26\) −2.20431 + 3.41948i −0.0847813 + 0.131518i
\(27\) 0 0
\(28\) 0.150268 0.0681190i 0.00536672 0.00243282i
\(29\) 20.7044 7.53578i 0.713944 0.259854i 0.0405915 0.999176i \(-0.487076\pi\)
0.673353 + 0.739321i \(0.264854\pi\)
\(30\) 0 0
\(31\) −25.1859 30.0153i −0.812447 0.968237i 0.187454 0.982273i \(-0.439976\pi\)
−0.999901 + 0.0140364i \(0.995532\pi\)
\(32\) 28.7702 14.0097i 0.899070 0.437805i
\(33\) 0 0
\(34\) 57.8360 17.8953i 1.70106 0.526331i
\(35\) −0.183199 0.105770i −0.00523426 0.00302200i
\(36\) 0 0
\(37\) 15.9508 + 27.6276i 0.431103 + 0.746693i 0.996969 0.0778047i \(-0.0247911\pi\)
−0.565865 + 0.824498i \(0.691458\pi\)
\(38\) 9.27508 10.0136i 0.244081 0.263517i
\(39\) 0 0
\(40\) −36.0838 19.5281i −0.902096 0.488203i
\(41\) −53.8833 19.6119i −1.31423 0.478340i −0.412623 0.910902i \(-0.635387\pi\)
−0.901604 + 0.432562i \(0.857610\pi\)
\(42\) 0 0
\(43\) −40.8395 7.20111i −0.949756 0.167468i −0.322752 0.946484i \(-0.604608\pi\)
−0.627004 + 0.779016i \(0.715719\pi\)
\(44\) −13.8039 9.88791i −0.313726 0.224725i
\(45\) 0 0
\(46\) 70.1685 36.0505i 1.52540 0.783708i
\(47\) 9.40005 11.2025i 0.200001 0.238352i −0.656717 0.754137i \(-0.728055\pi\)
0.856718 + 0.515785i \(0.172500\pi\)
\(48\) 0 0
\(49\) 8.50847 + 48.2539i 0.173642 + 0.984774i
\(50\) 0.326287 + 2.58545i 0.00652574 + 0.0517090i
\(51\) 0 0
\(52\) 5.69155 + 5.81495i 0.109453 + 0.111826i
\(53\) 43.0946 0.813105 0.406553 0.913627i \(-0.366731\pi\)
0.406553 + 0.913627i \(0.366731\pi\)
\(54\) 0 0
\(55\) 21.7710i 0.395837i
\(56\) −0.0662283 0.323260i −0.00118265 0.00577249i
\(57\) 0 0
\(58\) −5.51746 43.7195i −0.0951286 0.753785i
\(59\) −40.5818 + 7.15567i −0.687828 + 0.121283i −0.506629 0.862164i \(-0.669109\pi\)
−0.181199 + 0.983447i \(0.557998\pi\)
\(60\) 0 0
\(61\) 14.2464 + 11.9542i 0.233548 + 0.195970i 0.752050 0.659107i \(-0.229065\pi\)
−0.518501 + 0.855077i \(0.673510\pi\)
\(62\) −69.7032 + 35.8115i −1.12424 + 0.577604i
\(63\) 0 0
\(64\) −14.5673 62.3201i −0.227614 0.973751i
\(65\) 1.81161 10.2742i 0.0278710 0.158064i
\(66\) 0 0
\(67\) −16.7275 + 45.9585i −0.249664 + 0.685948i 0.750034 + 0.661399i \(0.230037\pi\)
−0.999699 + 0.0245484i \(0.992185\pi\)
\(68\) −9.25890 120.728i −0.136160 1.77541i
\(69\) 0 0
\(70\) −0.287497 + 0.310390i −0.00410710 + 0.00443414i
\(71\) −111.053 + 64.1166i −1.56413 + 0.903051i −0.567298 + 0.823512i \(0.692011\pi\)
−0.996832 + 0.0795386i \(0.974655\pi\)
\(72\) 0 0
\(73\) 63.7153 110.358i 0.872813 1.51176i 0.0137383 0.999906i \(-0.495627\pi\)
0.859075 0.511851i \(-0.171040\pi\)
\(74\) 60.9523 18.8595i 0.823680 0.254858i
\(75\) 0 0
\(76\) −15.4170 22.5281i −0.202855 0.296423i
\(77\) −0.134128 + 0.112547i −0.00174193 + 0.00146165i
\(78\) 0 0
\(79\) −1.11267 3.05705i −0.0140845 0.0386968i 0.932451 0.361296i \(-0.117666\pi\)
−0.946536 + 0.322599i \(0.895443\pi\)
\(80\) −54.0821 + 61.7146i −0.676026 + 0.771433i
\(81\) 0 0
\(82\) −62.1368 + 96.3907i −0.757766 + 1.17550i
\(83\) 40.0201 + 109.954i 0.482169 + 1.32475i 0.907629 + 0.419772i \(0.137890\pi\)
−0.425460 + 0.904977i \(0.639888\pi\)
\(84\) 0 0
\(85\) −118.926 + 99.7911i −1.39913 + 1.17401i
\(86\) −32.1498 + 76.4544i −0.373835 + 0.889004i
\(87\) 0 0
\(88\) −25.4037 + 22.5373i −0.288678 + 0.256105i
\(89\) 26.9272 46.6393i 0.302553 0.524037i −0.674160 0.738585i \(-0.735494\pi\)
0.976714 + 0.214548i \(0.0688277\pi\)
\(90\) 0 0
\(91\) 0.0726630 0.0419520i 0.000798495 0.000461011i
\(92\) −39.1986 152.828i −0.426072 1.66118i
\(93\) 0 0
\(94\) −17.6802 23.2989i −0.188088 0.247861i
\(95\) −11.9710 + 32.8901i −0.126011 + 0.346211i
\(96\) 0 0
\(97\) −5.60171 + 31.7689i −0.0577496 + 0.327514i −0.999972 0.00747351i \(-0.997621\pi\)
0.942222 + 0.334988i \(0.108732\pi\)
\(98\) 97.8790 + 4.79945i 0.998765 + 0.0489740i
\(99\) 0 0
\(100\) 5.18691 + 0.509901i 0.0518691 + 0.00509901i
\(101\) 105.877 + 88.8411i 1.04828 + 0.879615i 0.992912 0.118851i \(-0.0379210\pi\)
0.0553723 + 0.998466i \(0.482365\pi\)
\(102\) 0 0
\(103\) 70.1342 12.3665i 0.680914 0.120064i 0.177516 0.984118i \(-0.443194\pi\)
0.503398 + 0.864054i \(0.332083\pi\)
\(104\) 13.8639 8.52188i 0.133306 0.0819412i
\(105\) 0 0
\(106\) 19.1057 84.0449i 0.180242 0.792876i
\(107\) 106.755i 0.997712i −0.866685 0.498856i \(-0.833754\pi\)
0.866685 0.498856i \(-0.166246\pi\)
\(108\) 0 0
\(109\) 53.1106 0.487253 0.243627 0.969869i \(-0.421663\pi\)
0.243627 + 0.969869i \(0.421663\pi\)
\(110\) 42.4588 + 9.65203i 0.385989 + 0.0877458i
\(111\) 0 0
\(112\) −0.659797 0.0141536i −0.00589104 0.000126371i
\(113\) −22.6559 128.488i −0.200494 1.13706i −0.904374 0.426740i \(-0.859662\pi\)
0.703880 0.710319i \(-0.251449\pi\)
\(114\) 0 0
\(115\) −130.032 + 154.966i −1.13071 + 1.34753i
\(116\) −87.7098 8.62234i −0.756119 0.0743305i
\(117\) 0 0
\(118\) −4.03637 + 82.3169i −0.0342065 + 0.697601i
\(119\) −1.22960 0.216811i −0.0103328 0.00182194i
\(120\) 0 0
\(121\) −96.7696 35.2213i −0.799749 0.291085i
\(122\) 29.6296 22.4842i 0.242866 0.184297i
\(123\) 0 0
\(124\) 38.9386 + 151.815i 0.314021 + 1.22431i
\(125\) 60.7668 + 105.251i 0.486134 + 0.842009i
\(126\) 0 0
\(127\) −90.4208 52.2045i −0.711975 0.411059i 0.0998168 0.995006i \(-0.468174\pi\)
−0.811792 + 0.583947i \(0.801508\pi\)
\(128\) −127.998 + 0.780665i −0.999981 + 0.00609894i
\(129\) 0 0
\(130\) −19.2340 8.08807i −0.147954 0.0622159i
\(131\) −87.8938 104.748i −0.670945 0.799601i 0.317968 0.948102i \(-0.397000\pi\)
−0.988912 + 0.148501i \(0.952555\pi\)
\(132\) 0 0
\(133\) −0.264516 + 0.0962761i −0.00198884 + 0.000723880i
\(134\) 82.2142 + 52.9981i 0.613539 + 0.395508i
\(135\) 0 0
\(136\) −239.554 35.4668i −1.76143 0.260785i
\(137\) −100.206 + 36.4722i −0.731434 + 0.266220i −0.680772 0.732496i \(-0.738355\pi\)
−0.0506624 + 0.998716i \(0.516133\pi\)
\(138\) 0 0
\(139\) 55.0613 + 65.6195i 0.396124 + 0.472083i 0.926834 0.375471i \(-0.122519\pi\)
−0.530710 + 0.847554i \(0.678075\pi\)
\(140\) 0.477876 + 0.698298i 0.00341340 + 0.00498785i
\(141\) 0 0
\(142\) 75.8083 + 245.006i 0.533861 + 1.72540i
\(143\) −7.47826 4.31757i −0.0522955 0.0301928i
\(144\) 0 0
\(145\) 56.5001 + 97.8610i 0.389656 + 0.674903i
\(146\) −186.978 173.187i −1.28067 1.18621i
\(147\) 0 0
\(148\) −9.75778 127.233i −0.0659310 0.859682i
\(149\) −147.356 53.6331i −0.988965 0.359954i −0.203646 0.979045i \(-0.565279\pi\)
−0.785319 + 0.619091i \(0.787501\pi\)
\(150\) 0 0
\(151\) −24.6643 4.34897i −0.163339 0.0288011i 0.0913803 0.995816i \(-0.470872\pi\)
−0.254720 + 0.967015i \(0.581983\pi\)
\(152\) −50.7704 + 20.0792i −0.334015 + 0.132100i
\(153\) 0 0
\(154\) 0.160029 + 0.311480i 0.00103915 + 0.00202260i
\(155\) 129.169 153.938i 0.833350 0.993148i
\(156\) 0 0
\(157\) −19.7195 111.835i −0.125602 0.712324i −0.980949 0.194268i \(-0.937767\pi\)
0.855347 0.518056i \(-0.173344\pi\)
\(158\) −6.45528 + 0.814665i −0.0408562 + 0.00515611i
\(159\) 0 0
\(160\) 96.3816 + 132.834i 0.602385 + 0.830212i
\(161\) −1.62693 −0.0101052
\(162\) 0 0
\(163\) 228.549i 1.40214i −0.713091 0.701072i \(-0.752705\pi\)
0.713091 0.701072i \(-0.247295\pi\)
\(164\) 160.437 + 163.916i 0.978277 + 0.999488i
\(165\) 0 0
\(166\) 232.180 29.3014i 1.39867 0.176515i
\(167\) −15.9992 + 2.82109i −0.0958035 + 0.0168927i −0.221344 0.975196i \(-0.571044\pi\)
0.125541 + 0.992088i \(0.459933\pi\)
\(168\) 0 0
\(169\) −126.292 105.971i −0.747288 0.627049i
\(170\) 141.892 + 276.177i 0.834657 + 1.62457i
\(171\) 0 0
\(172\) 134.851 + 96.5954i 0.784019 + 0.561601i
\(173\) −16.7323 + 94.8933i −0.0967182 + 0.548516i 0.897489 + 0.441037i \(0.145389\pi\)
−0.994207 + 0.107480i \(0.965722\pi\)
\(174\) 0 0
\(175\) 0.0183814 0.0505025i 0.000105037 0.000288586i
\(176\) 32.6906 + 59.5351i 0.185742 + 0.338268i
\(177\) 0 0
\(178\) −79.0200 73.1918i −0.443933 0.411190i
\(179\) 198.630 114.679i 1.10967 0.640666i 0.170923 0.985284i \(-0.445325\pi\)
0.938743 + 0.344619i \(0.111992\pi\)
\(180\) 0 0
\(181\) 154.487 267.580i 0.853522 1.47834i −0.0244878 0.999700i \(-0.507795\pi\)
0.878010 0.478643i \(-0.158871\pi\)
\(182\) −0.0496020 0.160310i −0.000272538 0.000880823i
\(183\) 0 0
\(184\) −315.431 + 8.69141i −1.71430 + 0.0472359i
\(185\) −125.334 + 105.168i −0.677482 + 0.568475i
\(186\) 0 0
\(187\) 43.9491 + 120.749i 0.235022 + 0.645718i
\(188\) −53.2770 + 24.1513i −0.283388 + 0.128465i
\(189\) 0 0
\(190\) 58.8364 + 37.9280i 0.309665 + 0.199621i
\(191\) 76.7399 + 210.841i 0.401779 + 1.10388i 0.961406 + 0.275135i \(0.0887224\pi\)
−0.559626 + 0.828745i \(0.689055\pi\)
\(192\) 0 0
\(193\) −130.384 + 109.405i −0.675564 + 0.566865i −0.914706 0.404119i \(-0.867578\pi\)
0.239142 + 0.970984i \(0.423134\pi\)
\(194\) 59.4736 + 25.0092i 0.306565 + 0.128913i
\(195\) 0 0
\(196\) 52.7540 188.760i 0.269153 0.963061i
\(197\) 100.143 173.453i 0.508341 0.880473i −0.491612 0.870814i \(-0.663592\pi\)
0.999953 0.00965858i \(-0.00307447\pi\)
\(198\) 0 0
\(199\) 230.445 133.047i 1.15801 0.668579i 0.207186 0.978301i \(-0.433569\pi\)
0.950827 + 0.309722i \(0.100236\pi\)
\(200\) 3.29401 9.88967i 0.0164701 0.0494484i
\(201\) 0 0
\(202\) 220.201 167.098i 1.09011 0.827219i
\(203\) −0.310826 + 0.853989i −0.00153117 + 0.00420684i
\(204\) 0 0
\(205\) 51.0671 289.616i 0.249108 1.41276i
\(206\) 6.97571 142.261i 0.0338627 0.690589i
\(207\) 0 0
\(208\) −10.4733 30.8160i −0.0503524 0.148154i
\(209\) 22.1926 + 18.6218i 0.106184 + 0.0890994i
\(210\) 0 0
\(211\) 393.246 69.3398i 1.86372 0.328625i 0.875691 0.482872i \(-0.160406\pi\)
0.988032 + 0.154247i \(0.0492953\pi\)
\(212\) −155.438 74.5214i −0.733196 0.351516i
\(213\) 0 0
\(214\) −208.199 47.3292i −0.972891 0.221164i
\(215\) 212.682i 0.989220i
\(216\) 0 0
\(217\) 1.61614 0.00744765
\(218\) 23.5462 103.579i 0.108010 0.475131i
\(219\) 0 0
\(220\) 37.6476 78.5258i 0.171126 0.356936i
\(221\) −10.6926 60.6410i −0.0483830 0.274394i
\(222\) 0 0
\(223\) 178.190 212.358i 0.799056 0.952278i −0.200568 0.979680i \(-0.564279\pi\)
0.999625 + 0.0274016i \(0.00872331\pi\)
\(224\) −0.320119 + 1.28049i −0.00142910 + 0.00571647i
\(225\) 0 0
\(226\) −260.627 12.7797i −1.15321 0.0565473i
\(227\) −157.783 27.8214i −0.695079 0.122561i −0.185064 0.982727i \(-0.559249\pi\)
−0.510015 + 0.860165i \(0.670360\pi\)
\(228\) 0 0
\(229\) 391.957 + 142.661i 1.71160 + 0.622972i 0.997060 0.0766226i \(-0.0244136\pi\)
0.714540 + 0.699594i \(0.246636\pi\)
\(230\) 244.572 + 322.296i 1.06336 + 1.40129i
\(231\) 0 0
\(232\) −55.7012 + 167.233i −0.240091 + 0.720831i
\(233\) −113.470 196.537i −0.486998 0.843505i 0.512890 0.858454i \(-0.328575\pi\)
−0.999888 + 0.0149492i \(0.995241\pi\)
\(234\) 0 0
\(235\) 64.9525 + 37.5003i 0.276394 + 0.159576i
\(236\) 158.748 + 44.3665i 0.672663 + 0.187994i
\(237\) 0 0
\(238\) −0.967968 + 2.30189i −0.00406709 + 0.00967182i
\(239\) 100.927 + 120.281i 0.422290 + 0.503266i 0.934682 0.355486i \(-0.115685\pi\)
−0.512391 + 0.858752i \(0.671240\pi\)
\(240\) 0 0
\(241\) −113.715 + 41.3887i −0.471845 + 0.171737i −0.566988 0.823726i \(-0.691891\pi\)
0.0951430 + 0.995464i \(0.469669\pi\)
\(242\) −111.592 + 173.109i −0.461124 + 0.715327i
\(243\) 0 0
\(244\) −30.7136 67.7532i −0.125875 0.277677i
\(245\) −236.140 + 85.9479i −0.963836 + 0.350808i
\(246\) 0 0
\(247\) −8.92354 10.6347i −0.0361277 0.0430553i
\(248\) 313.339 8.63377i 1.26346 0.0348136i
\(249\) 0 0
\(250\) 232.206 71.8476i 0.928823 0.287391i
\(251\) 3.42052 + 1.97484i 0.0136276 + 0.00786788i 0.506798 0.862065i \(-0.330829\pi\)
−0.493171 + 0.869933i \(0.664162\pi\)
\(252\) 0 0
\(253\) 83.7194 + 145.006i 0.330907 + 0.573147i
\(254\) −141.899 + 153.198i −0.558657 + 0.603142i
\(255\) 0 0
\(256\) −55.2243 + 249.973i −0.215720 + 0.976455i
\(257\) −70.1778 25.5426i −0.273065 0.0993876i 0.201858 0.979415i \(-0.435302\pi\)
−0.474923 + 0.880027i \(0.657524\pi\)
\(258\) 0 0
\(259\) −1.29585 0.228493i −0.00500328 0.000882213i
\(260\) −24.3009 + 33.9251i −0.0934652 + 0.130481i
\(261\) 0 0
\(262\) −243.251 + 124.975i −0.928437 + 0.477004i
\(263\) 258.741 308.356i 0.983807 1.17246i −0.00121067 0.999999i \(-0.500385\pi\)
0.985017 0.172456i \(-0.0551702\pi\)
\(264\) 0 0
\(265\) 38.3791 + 217.659i 0.144827 + 0.821354i
\(266\) 0.0704903 + 0.558554i 0.000265001 + 0.00209983i
\(267\) 0 0
\(268\) 139.808 136.841i 0.521672 0.510602i
\(269\) 256.494 0.953508 0.476754 0.879037i \(-0.341813\pi\)
0.476754 + 0.879037i \(0.341813\pi\)
\(270\) 0 0
\(271\) 98.1325i 0.362112i 0.983473 + 0.181056i \(0.0579516\pi\)
−0.983473 + 0.181056i \(0.942048\pi\)
\(272\) −175.373 + 451.464i −0.644755 + 1.65980i
\(273\) 0 0
\(274\) 26.7038 + 211.597i 0.0974591 + 0.772251i
\(275\) −5.44710 + 0.960471i −0.0198076 + 0.00349262i
\(276\) 0 0
\(277\) −240.716 201.985i −0.869011 0.729187i 0.0948788 0.995489i \(-0.469754\pi\)
−0.963890 + 0.266302i \(0.914198\pi\)
\(278\) 152.385 78.2910i 0.548147 0.281622i
\(279\) 0 0
\(280\) 1.57371 0.622389i 0.00562041 0.00222282i
\(281\) −13.7932 + 78.2252i −0.0490862 + 0.278381i −0.999465 0.0327143i \(-0.989585\pi\)
0.950379 + 0.311096i \(0.100696\pi\)
\(282\) 0 0
\(283\) −49.7122 + 136.583i −0.175661 + 0.482626i −0.996010 0.0892374i \(-0.971557\pi\)
0.820349 + 0.571863i \(0.193779\pi\)
\(284\) 511.431 39.2228i 1.80081 0.138108i
\(285\) 0 0
\(286\) −11.7357 + 12.6703i −0.0410341 + 0.0443016i
\(287\) 2.04828 1.18257i 0.00713686 0.00412047i
\(288\) 0 0
\(289\) −313.656 + 543.268i −1.08532 + 1.87982i
\(290\) 215.902 66.8029i 0.744488 0.230355i
\(291\) 0 0
\(292\) −420.652 + 287.870i −1.44059 + 0.985858i
\(293\) 91.9061 77.1184i 0.313673 0.263203i −0.472335 0.881419i \(-0.656589\pi\)
0.786008 + 0.618216i \(0.212144\pi\)
\(294\) 0 0
\(295\) −72.2827 198.595i −0.245026 0.673204i
\(296\) −252.461 37.3778i −0.852910 0.126276i
\(297\) 0 0
\(298\) −169.927 + 263.602i −0.570224 + 0.884570i
\(299\) −27.4425 75.3977i −0.0917810 0.252166i
\(300\) 0 0
\(301\) 1.31031 1.09948i 0.00435318 0.00365275i
\(302\) −19.4163 + 46.1732i −0.0642923 + 0.152891i
\(303\) 0 0
\(304\) 16.6506 + 107.916i 0.0547719 + 0.354988i
\(305\) −47.6897 + 82.6010i −0.156360 + 0.270823i
\(306\) 0 0
\(307\) −177.597 + 102.536i −0.578491 + 0.333992i −0.760534 0.649299i \(-0.775063\pi\)
0.182042 + 0.983291i \(0.441729\pi\)
\(308\) 0.678409 0.174004i 0.00220263 0.000564947i
\(309\) 0 0
\(310\) −242.950 320.159i −0.783710 1.03277i
\(311\) −83.6144 + 229.729i −0.268857 + 0.738677i 0.729638 + 0.683833i \(0.239688\pi\)
−0.998495 + 0.0548442i \(0.982534\pi\)
\(312\) 0 0
\(313\) 23.7303 134.581i 0.0758156 0.429971i −0.923148 0.384446i \(-0.874393\pi\)
0.998963 0.0455257i \(-0.0144963\pi\)
\(314\) −226.848 11.1234i −0.722445 0.0354247i
\(315\) 0 0
\(316\) −1.27311 + 12.9505i −0.00402882 + 0.0409827i
\(317\) 108.274 + 90.8524i 0.341557 + 0.286601i 0.797389 0.603465i \(-0.206214\pi\)
−0.455832 + 0.890066i \(0.650658\pi\)
\(318\) 0 0
\(319\) 92.1095 16.2414i 0.288745 0.0509135i
\(320\) 301.788 129.077i 0.943089 0.403364i
\(321\) 0 0
\(322\) −0.721288 + 3.17291i −0.00224003 + 0.00985376i
\(323\) 206.585i 0.639581i
\(324\) 0 0
\(325\) 2.65051 0.00815543
\(326\) −445.727 101.326i −1.36726 0.310815i
\(327\) 0 0
\(328\) 390.805 240.221i 1.19148 0.732381i
\(329\) 0.104742 + 0.594024i 0.000318366 + 0.00180554i
\(330\) 0 0
\(331\) −97.6833 + 116.414i −0.295116 + 0.351705i −0.893145 0.449769i \(-0.851506\pi\)
0.598029 + 0.801474i \(0.295951\pi\)
\(332\) 45.7905 465.798i 0.137923 1.40301i
\(333\) 0 0
\(334\) −1.59132 + 32.4530i −0.00476442 + 0.0971647i
\(335\) −247.021 43.5565i −0.737376 0.130019i
\(336\) 0 0
\(337\) 119.675 + 43.5582i 0.355119 + 0.129253i 0.513418 0.858138i \(-0.328379\pi\)
−0.158299 + 0.987391i \(0.550601\pi\)
\(338\) −262.660 + 199.318i −0.777101 + 0.589698i
\(339\) 0 0
\(340\) 601.519 154.282i 1.76917 0.453771i
\(341\) −83.1641 144.045i −0.243883 0.422418i
\(342\) 0 0
\(343\) −3.50057 2.02106i −0.0102058 0.00589229i
\(344\) 248.170 220.168i 0.721424 0.640023i
\(345\) 0 0
\(346\) 177.647 + 74.7022i 0.513430 + 0.215902i
\(347\) 19.4708 + 23.2044i 0.0561119 + 0.0668715i 0.793370 0.608739i \(-0.208324\pi\)
−0.737258 + 0.675611i \(0.763880\pi\)
\(348\) 0 0
\(349\) 162.407 59.1115i 0.465351 0.169374i −0.0986944 0.995118i \(-0.531467\pi\)
0.564045 + 0.825744i \(0.309244\pi\)
\(350\) −0.0903429 0.0582381i −0.000258123 0.000166395i
\(351\) 0 0
\(352\) 130.601 37.3602i 0.371026 0.106137i
\(353\) −364.507 + 132.670i −1.03260 + 0.375835i −0.802069 0.597231i \(-0.796267\pi\)
−0.230528 + 0.973066i \(0.574045\pi\)
\(354\) 0 0
\(355\) −422.737 503.799i −1.19081 1.41915i
\(356\) −177.775 + 121.659i −0.499367 + 0.341739i
\(357\) 0 0
\(358\) −135.591 438.219i −0.378746 1.22408i
\(359\) −494.326 285.399i −1.37695 0.794983i −0.385160 0.922850i \(-0.625854\pi\)
−0.991791 + 0.127866i \(0.959187\pi\)
\(360\) 0 0
\(361\) −157.212 272.300i −0.435492 0.754294i
\(362\) −453.355 419.918i −1.25236 1.15999i
\(363\) 0 0
\(364\) −0.334634 + 0.0256638i −0.000919323 + 7.05049e-5i
\(365\) 614.133 + 223.526i 1.68256 + 0.612400i
\(366\) 0 0
\(367\) 77.7710 + 13.7131i 0.211910 + 0.0373655i 0.278595 0.960409i \(-0.410131\pi\)
−0.0666852 + 0.997774i \(0.521242\pi\)
\(368\) −122.894 + 619.020i −0.333950 + 1.68212i
\(369\) 0 0
\(370\) 149.537 + 291.058i 0.404154 + 0.786642i
\(371\) −1.14256 + 1.36165i −0.00307968 + 0.00367022i
\(372\) 0 0
\(373\) −102.883 583.480i −0.275827 1.56429i −0.736324 0.676629i \(-0.763440\pi\)
0.460498 0.887661i \(-0.347671\pi\)
\(374\) 254.975 32.1782i 0.681751 0.0860378i
\(375\) 0 0
\(376\) 23.4810 + 114.610i 0.0624494 + 0.304815i
\(377\) −44.8198 −0.118885
\(378\) 0 0
\(379\) 93.1184i 0.245695i 0.992426 + 0.122847i \(0.0392026\pi\)
−0.992426 + 0.122847i \(0.960797\pi\)
\(380\) 100.053 97.9301i 0.263298 0.257711i
\(381\) 0 0
\(382\) 445.213 56.1865i 1.16548 0.147085i
\(383\) 185.774 32.7570i 0.485051 0.0855275i 0.0742251 0.997242i \(-0.476352\pi\)
0.410825 + 0.911714i \(0.365241\pi\)
\(384\) 0 0
\(385\) −0.687896 0.577214i −0.00178674 0.00149926i
\(386\) 155.562 + 302.784i 0.403009 + 0.784415i
\(387\) 0 0
\(388\) 75.1412 104.900i 0.193663 0.270361i
\(389\) 27.7003 157.096i 0.0712091 0.403847i −0.928280 0.371882i \(-0.878712\pi\)
0.999489 0.0319646i \(-0.0101764\pi\)
\(390\) 0 0
\(391\) −408.369 + 1121.98i −1.04442 + 2.86952i
\(392\) −344.740 186.569i −0.879438 0.475940i
\(393\) 0 0
\(394\) −293.878 272.203i −0.745883 0.690870i
\(395\) 14.4494 8.34236i 0.0365807 0.0211199i
\(396\) 0 0
\(397\) 58.9618 102.125i 0.148518 0.257241i −0.782162 0.623075i \(-0.785883\pi\)
0.930680 + 0.365834i \(0.119216\pi\)
\(398\) −157.309 508.409i −0.395248 1.27741i
\(399\) 0 0
\(400\) −17.8269 10.8086i −0.0445672 0.0270216i
\(401\) 104.236 87.4644i 0.259940 0.218116i −0.503498 0.863996i \(-0.667954\pi\)
0.763439 + 0.645881i \(0.223510\pi\)
\(402\) 0 0
\(403\) 27.2605 + 74.8977i 0.0676440 + 0.185850i
\(404\) −228.257 503.528i −0.564994 1.24636i
\(405\) 0 0
\(406\) 1.52768 + 0.984797i 0.00376277 + 0.00242561i
\(407\) 46.3171 + 127.255i 0.113801 + 0.312667i
\(408\) 0 0
\(409\) −98.1152 + 82.3284i −0.239890 + 0.201292i −0.754804 0.655950i \(-0.772268\pi\)
0.514914 + 0.857242i \(0.327824\pi\)
\(410\) −542.181 227.992i −1.32239 0.556079i
\(411\) 0 0
\(412\) −274.351 76.6748i −0.665901 0.186104i
\(413\) 0.849846 1.47198i 0.00205774 0.00356411i
\(414\) 0 0
\(415\) −519.708 + 300.053i −1.25231 + 0.723020i
\(416\) −64.7420 + 6.76341i −0.155630 + 0.0162582i
\(417\) 0 0
\(418\) 46.1559 35.0251i 0.110421 0.0837920i
\(419\) −139.827 + 384.171i −0.333716 + 0.916876i 0.653421 + 0.756995i \(0.273333\pi\)
−0.987136 + 0.159881i \(0.948889\pi\)
\(420\) 0 0
\(421\) −26.5187 + 150.395i −0.0629897 + 0.357233i 0.936979 + 0.349384i \(0.113609\pi\)
−0.999969 + 0.00784813i \(0.997502\pi\)
\(422\) 39.1131 797.666i 0.0926852 1.89020i
\(423\) 0 0
\(424\) −214.247 + 270.102i −0.505299 + 0.637034i
\(425\) −30.2143 25.3528i −0.0710925 0.0596537i
\(426\) 0 0
\(427\) −0.755429 + 0.133203i −0.00176916 + 0.000311950i
\(428\) −184.607 + 385.055i −0.431324 + 0.899661i
\(429\) 0 0
\(430\) −414.782 94.2912i −0.964610 0.219282i
\(431\) 640.109i 1.48517i 0.669751 + 0.742585i \(0.266401\pi\)
−0.669751 + 0.742585i \(0.733599\pi\)
\(432\) 0 0
\(433\) 343.700 0.793765 0.396883 0.917869i \(-0.370092\pi\)
0.396883 + 0.917869i \(0.370092\pi\)
\(434\) 0.716505 3.15187i 0.00165093 0.00726237i
\(435\) 0 0
\(436\) −191.564 91.8416i −0.439368 0.210646i
\(437\) 46.7440 + 265.099i 0.106966 + 0.606633i
\(438\) 0 0
\(439\) 58.0596 69.1928i 0.132254 0.157615i −0.695853 0.718184i \(-0.744973\pi\)
0.828107 + 0.560570i \(0.189418\pi\)
\(440\) −136.454 108.236i −0.310122 0.245991i
\(441\) 0 0
\(442\) −123.005 6.03150i −0.278292 0.0136459i
\(443\) −288.931 50.9464i −0.652215 0.115003i −0.162256 0.986749i \(-0.551877\pi\)
−0.489959 + 0.871746i \(0.662988\pi\)
\(444\) 0 0
\(445\) 259.543 + 94.4660i 0.583243 + 0.212283i
\(446\) −335.151 441.660i −0.751459 0.990270i
\(447\) 0 0
\(448\) 2.35534 + 1.19201i 0.00525746 + 0.00266073i
\(449\) −63.8556 110.601i −0.142217 0.246328i 0.786114 0.618082i \(-0.212090\pi\)
−0.928331 + 0.371754i \(0.878757\pi\)
\(450\) 0 0
\(451\) −210.803 121.707i −0.467411 0.269860i
\(452\) −140.470 + 502.619i −0.310775 + 1.11199i
\(453\) 0 0
\(454\) −124.210 + 295.381i −0.273591 + 0.650618i
\(455\) 0.276600 + 0.329640i 0.000607913 + 0.000724483i
\(456\) 0 0
\(457\) −394.951 + 143.750i −0.864225 + 0.314552i −0.735826 0.677170i \(-0.763206\pi\)
−0.128399 + 0.991723i \(0.540984\pi\)
\(458\) 451.994 701.163i 0.986886 1.53092i
\(459\) 0 0
\(460\) 736.985 334.087i 1.60214 0.726277i
\(461\) 648.376 235.990i 1.40646 0.511908i 0.476368 0.879246i \(-0.341953\pi\)
0.930088 + 0.367338i \(0.119731\pi\)
\(462\) 0 0
\(463\) −354.216 422.138i −0.765045 0.911745i 0.233111 0.972450i \(-0.425109\pi\)
−0.998156 + 0.0607054i \(0.980665\pi\)
\(464\) 301.450 + 182.772i 0.649676 + 0.393906i
\(465\) 0 0
\(466\) −433.600 + 134.162i −0.930473 + 0.287901i
\(467\) 535.942 + 309.426i 1.14763 + 0.662583i 0.948308 0.317351i \(-0.102793\pi\)
0.199320 + 0.979934i \(0.436127\pi\)
\(468\) 0 0
\(469\) −1.00865 1.74703i −0.00215064 0.00372501i
\(470\) 101.931 110.048i 0.216874 0.234144i
\(471\) 0 0
\(472\) 156.905 289.928i 0.332427 0.614255i
\(473\) −165.421 60.2084i −0.349728 0.127291i
\(474\) 0 0
\(475\) −8.75720 1.54413i −0.0184362 0.00325080i
\(476\) 4.06011 + 2.90830i 0.00852964 + 0.00610987i
\(477\) 0 0
\(478\) 279.322 143.507i 0.584355 0.300225i
\(479\) −205.959 + 245.453i −0.429977 + 0.512427i −0.936916 0.349555i \(-0.886333\pi\)
0.506938 + 0.861982i \(0.330777\pi\)
\(480\) 0 0
\(481\) −11.2688 63.9084i −0.0234278 0.132866i
\(482\) 30.3035 + 240.120i 0.0628704 + 0.498175i
\(483\) 0 0
\(484\) 288.131 + 294.378i 0.595313 + 0.608220i
\(485\) −165.445 −0.341123
\(486\) 0 0
\(487\) 5.24750i 0.0107752i −0.999985 0.00538758i \(-0.998285\pi\)
0.999985 0.00538758i \(-0.00171493\pi\)
\(488\) −145.752 + 29.8611i −0.298672 + 0.0611908i
\(489\) 0 0
\(490\) 62.9283 + 498.634i 0.128425 + 1.01762i
\(491\) −593.831 + 104.708i −1.20943 + 0.213255i −0.741771 0.670653i \(-0.766014\pi\)
−0.467660 + 0.883908i \(0.654903\pi\)
\(492\) 0 0
\(493\) 510.919 + 428.712i 1.03635 + 0.869598i
\(494\) −24.6964 + 12.6883i −0.0499926 + 0.0256848i
\(495\) 0 0
\(496\) 122.079 614.915i 0.246126 1.23975i
\(497\) 0.918461 5.20885i 0.00184801 0.0104806i
\(498\) 0 0
\(499\) 1.99347 5.47702i 0.00399494 0.0109760i −0.937679 0.347502i \(-0.887030\pi\)
0.941674 + 0.336526i \(0.109252\pi\)
\(500\) −37.1736 484.711i −0.0743471 0.969422i
\(501\) 0 0
\(502\) 5.36788 5.79532i 0.0106930 0.0115445i
\(503\) 103.706 59.8746i 0.206175 0.119035i −0.393358 0.919386i \(-0.628687\pi\)
0.599532 + 0.800350i \(0.295353\pi\)
\(504\) 0 0
\(505\) −354.421 + 613.875i −0.701823 + 1.21559i
\(506\) 319.914 98.9856i 0.632240 0.195624i
\(507\) 0 0
\(508\) 235.864 + 344.657i 0.464299 + 0.678458i
\(509\) 280.047 234.987i 0.550190 0.461664i −0.324816 0.945777i \(-0.605302\pi\)
0.875005 + 0.484113i \(0.160858\pi\)
\(510\) 0 0
\(511\) 1.79769 + 4.93912i 0.00351799 + 0.00966560i
\(512\) 463.024 + 218.524i 0.904343 + 0.426805i
\(513\) 0 0
\(514\) −80.9271 + 125.540i −0.157446 + 0.244240i
\(515\) 124.920 + 343.215i 0.242563 + 0.666437i
\(516\) 0 0
\(517\) 47.5547 39.9031i 0.0919820 0.0771821i
\(518\) −1.02012 + 2.42592i −0.00196935 + 0.00468324i
\(519\) 0 0
\(520\) 55.3886 + 62.4332i 0.106517 + 0.120064i
\(521\) −109.267 + 189.256i −0.209726 + 0.363255i −0.951628 0.307253i \(-0.900590\pi\)
0.741903 + 0.670508i \(0.233924\pi\)
\(522\) 0 0
\(523\) 696.524 402.138i 1.33179 0.768907i 0.346212 0.938156i \(-0.387468\pi\)
0.985573 + 0.169250i \(0.0541344\pi\)
\(524\) 135.888 + 529.804i 0.259329 + 1.01108i
\(525\) 0 0
\(526\) −486.657 641.315i −0.925204 1.21923i
\(527\) 405.661 1114.54i 0.769754 2.11488i
\(528\) 0 0
\(529\) −178.305 + 1011.22i −0.337060 + 1.91156i
\(530\) 441.503 + 21.6489i 0.833024 + 0.0408469i
\(531\) 0 0
\(532\) 1.12057 + 0.110158i 0.00210633 + 0.000207064i
\(533\) 89.3543 + 74.9772i 0.167644 + 0.140670i
\(534\) 0 0
\(535\) 539.192 95.0740i 1.00783 0.177708i
\(536\) −204.891 333.328i −0.382259 0.621880i
\(537\) 0 0
\(538\) 113.715 500.225i 0.211366 0.929787i
\(539\) 207.997i 0.385895i
\(540\) 0 0
\(541\) −172.884 −0.319563 −0.159782 0.987152i \(-0.551079\pi\)
−0.159782 + 0.987152i \(0.551079\pi\)
\(542\) 191.382 + 43.5063i 0.353104 + 0.0802700i
\(543\) 0 0
\(544\) 802.715 + 542.174i 1.47558 + 0.996644i
\(545\) 47.2992 + 268.247i 0.0867875 + 0.492197i
\(546\) 0 0
\(547\) −164.443 + 195.975i −0.300627 + 0.358273i −0.895118 0.445829i \(-0.852909\pi\)
0.594491 + 0.804102i \(0.297353\pi\)
\(548\) 424.504 + 41.7310i 0.774642 + 0.0761515i
\(549\) 0 0
\(550\) −0.541782 + 11.0490i −0.000985058 + 0.0200891i
\(551\) 148.083 + 26.1110i 0.268753 + 0.0473884i
\(552\) 0 0
\(553\) 0.126093 + 0.0458942i 0.000228017 + 8.29913e-5i
\(554\) −500.639 + 379.906i −0.903680 + 0.685751i
\(555\) 0 0
\(556\) −85.1276 331.897i −0.153107 0.596938i
\(557\) 177.380 + 307.231i 0.318456 + 0.551582i 0.980166 0.198178i \(-0.0635023\pi\)
−0.661710 + 0.749760i \(0.730169\pi\)
\(558\) 0 0
\(559\) 73.0554 + 42.1786i 0.130690 + 0.0754536i
\(560\) −0.516115 3.34506i −0.000921635 0.00597332i
\(561\) 0 0
\(562\) 146.443 + 61.5807i 0.260575 + 0.109574i
\(563\) −7.92579 9.44559i −0.0140778 0.0167773i 0.758960 0.651138i \(-0.225708\pi\)
−0.773037 + 0.634360i \(0.781264\pi\)
\(564\) 0 0
\(565\) 628.780 228.857i 1.11288 0.405057i
\(566\) 244.331 + 157.504i 0.431680 + 0.278276i
\(567\) 0 0
\(568\) 150.245 1014.80i 0.264516 1.78663i
\(569\) 168.484 61.3233i 0.296106 0.107774i −0.189695 0.981843i \(-0.560750\pi\)
0.485801 + 0.874069i \(0.338528\pi\)
\(570\) 0 0
\(571\) −254.026 302.737i −0.444880 0.530187i 0.496274 0.868166i \(-0.334701\pi\)
−0.941154 + 0.337979i \(0.890257\pi\)
\(572\) 19.5071 + 28.5048i 0.0341033 + 0.0498336i
\(573\) 0 0
\(574\) −1.39822 4.51893i −0.00243592 0.00787269i
\(575\) −44.5089 25.6972i −0.0774068 0.0446908i
\(576\) 0 0
\(577\) −344.513 596.713i −0.597075 1.03417i −0.993250 0.115990i \(-0.962996\pi\)
0.396175 0.918175i \(-0.370337\pi\)
\(578\) 920.448 + 852.560i 1.59247 + 1.47502i
\(579\) 0 0
\(580\) −34.5634 450.677i −0.0595921 0.777029i
\(581\) −4.53526 1.65070i −0.00780595 0.00284113i
\(582\) 0 0
\(583\) 180.157 + 31.7665i 0.309017 + 0.0544880i
\(584\) 374.924 + 947.998i 0.641994 + 1.62328i
\(585\) 0 0
\(586\) −109.654 213.429i −0.187122 0.364213i
\(587\) −207.235 + 246.973i −0.353040 + 0.420737i −0.913113 0.407706i \(-0.866329\pi\)
0.560073 + 0.828443i \(0.310773\pi\)
\(588\) 0 0
\(589\) −46.4340 263.340i −0.0788353 0.447097i
\(590\) −419.355 + 52.9231i −0.710771 + 0.0897002i
\(591\) 0 0
\(592\) −184.823 + 475.790i −0.312200 + 0.803699i
\(593\) −469.564 −0.791846 −0.395923 0.918284i \(-0.629575\pi\)
−0.395923 + 0.918284i \(0.629575\pi\)
\(594\) 0 0
\(595\) 6.40345i 0.0107621i
\(596\) 438.752 + 448.264i 0.736160 + 0.752121i
\(597\) 0 0
\(598\) −159.210 + 20.0925i −0.266238 + 0.0335996i
\(599\) 527.632 93.0357i 0.880854 0.155318i 0.285112 0.958494i \(-0.407969\pi\)
0.595742 + 0.803176i \(0.296858\pi\)
\(600\) 0 0
\(601\) 647.757 + 543.533i 1.07780 + 0.904381i 0.995736 0.0922465i \(-0.0294048\pi\)
0.0820627 + 0.996627i \(0.473849\pi\)
\(602\) −1.56333 3.04286i −0.00259690 0.00505459i
\(603\) 0 0
\(604\) 81.4409 + 58.3370i 0.134836 + 0.0965844i
\(605\) 91.7119 520.124i 0.151590 0.859709i
\(606\) 0 0
\(607\) 138.471 380.445i 0.228123 0.626763i −0.771836 0.635822i \(-0.780661\pi\)
0.999959 + 0.00905875i \(0.00288353\pi\)
\(608\) 217.845 + 15.3712i 0.358298 + 0.0252816i
\(609\) 0 0
\(610\) 139.949 + 129.627i 0.229425 + 0.212504i
\(611\) −25.7624 + 14.8739i −0.0421643 + 0.0243436i
\(612\) 0 0
\(613\) 62.6459 108.506i 0.102196 0.177008i −0.810393 0.585886i \(-0.800747\pi\)
0.912589 + 0.408878i \(0.134080\pi\)
\(614\) 121.233 + 391.815i 0.197448 + 0.638136i
\(615\) 0 0
\(616\) −0.0385814 1.40021i −6.26321e−5 0.00227306i
\(617\) −221.013 + 185.452i −0.358205 + 0.300570i −0.804075 0.594528i \(-0.797339\pi\)
0.445870 + 0.895098i \(0.352895\pi\)
\(618\) 0 0
\(619\) −122.807 337.411i −0.198397 0.545090i 0.800102 0.599864i \(-0.204779\pi\)
−0.998499 + 0.0547735i \(0.982556\pi\)
\(620\) −732.098 + 331.872i −1.18080 + 0.535277i
\(621\) 0 0
\(622\) 410.957 + 264.917i 0.660702 + 0.425911i
\(623\) 0.759737 + 2.08736i 0.00121948 + 0.00335050i
\(624\) 0 0
\(625\) −502.431 + 421.589i −0.803889 + 0.674543i
\(626\) −251.945 105.945i −0.402468 0.169242i
\(627\) 0 0
\(628\) −122.265 + 437.476i −0.194689 + 0.696619i
\(629\) −482.842 + 836.307i −0.767634 + 1.32958i
\(630\) 0 0
\(631\) −874.059 + 504.638i −1.38520 + 0.799743i −0.992769 0.120040i \(-0.961698\pi\)
−0.392427 + 0.919783i \(0.628364\pi\)
\(632\) 24.6923 + 8.22440i 0.0390700 + 0.0130133i
\(633\) 0 0
\(634\) 225.187 170.881i 0.355184 0.269529i
\(635\) 183.144 503.183i 0.288415 0.792415i
\(636\) 0 0
\(637\) 17.3079 98.1580i 0.0271710 0.154094i
\(638\) 9.16144 186.836i 0.0143596 0.292847i
\(639\) 0 0
\(640\) −117.935 645.786i −0.184273 1.00904i
\(641\) −610.695 512.434i −0.952722 0.799429i 0.0270317 0.999635i \(-0.491394\pi\)
−0.979754 + 0.200206i \(0.935839\pi\)
\(642\) 0 0
\(643\) 696.625 122.834i 1.08340 0.191032i 0.396680 0.917957i \(-0.370162\pi\)
0.686717 + 0.726925i \(0.259051\pi\)
\(644\) 5.86817 + 2.81337i 0.00911206 + 0.00436859i
\(645\) 0 0
\(646\) 402.891 + 91.5879i 0.623670 + 0.141777i
\(647\) 595.093i 0.919774i −0.887978 0.459887i \(-0.847890\pi\)
0.887978 0.459887i \(-0.152110\pi\)
\(648\) 0 0
\(649\) −174.927 −0.269533
\(650\) 1.17509 5.16915i 0.00180783 0.00795253i
\(651\) 0 0
\(652\) −395.220 + 824.354i −0.606165 + 1.26435i
\(653\) 128.322 + 727.750i 0.196511 + 1.11447i 0.910250 + 0.414060i \(0.135889\pi\)
−0.713738 + 0.700412i \(0.752999\pi\)
\(654\) 0 0
\(655\) 450.776 537.214i 0.688207 0.820173i
\(656\) −295.229 868.664i −0.450044 1.32418i
\(657\) 0 0
\(658\) 1.20493 + 0.0590831i 0.00183120 + 8.97919e-5i
\(659\) 225.185 + 39.7062i 0.341707 + 0.0602522i 0.341869 0.939748i \(-0.388940\pi\)
−0.000161354 1.00000i \(0.500051\pi\)
\(660\) 0 0
\(661\) 247.564 + 90.1059i 0.374529 + 0.136318i 0.522425 0.852686i \(-0.325028\pi\)
−0.147895 + 0.989003i \(0.547250\pi\)
\(662\) 183.729 + 242.118i 0.277537 + 0.365737i
\(663\) 0 0
\(664\) −888.118 295.811i −1.33753 0.445498i
\(665\) −0.721837 1.25026i −0.00108547 0.00188009i
\(666\) 0 0
\(667\) 752.638 + 434.536i 1.12839 + 0.651478i
\(668\) 62.5858 + 17.4913i 0.0936913 + 0.0261845i
\(669\) 0 0
\(670\) −194.461 + 462.440i −0.290240 + 0.690210i
\(671\) 50.7454 + 60.4760i 0.0756265 + 0.0901282i
\(672\) 0 0
\(673\) 262.025 95.3693i 0.389339 0.141708i −0.139931 0.990161i \(-0.544688\pi\)
0.529270 + 0.848453i \(0.322466\pi\)
\(674\) 138.006 214.084i 0.204757 0.317632i
\(675\) 0 0
\(676\) 272.270 + 600.617i 0.402766 + 0.888487i
\(677\) 213.983 77.8835i 0.316076 0.115042i −0.179111 0.983829i \(-0.557322\pi\)
0.495186 + 0.868787i \(0.335100\pi\)
\(678\) 0 0
\(679\) −0.855279 1.01928i −0.00125962 0.00150115i
\(680\) −34.2086 1241.51i −0.0503068 1.82575i
\(681\) 0 0
\(682\) −317.792 + 98.3292i −0.465971 + 0.144178i
\(683\) 662.983 + 382.773i 0.970692 + 0.560429i 0.899447 0.437030i \(-0.143969\pi\)
0.0712449 + 0.997459i \(0.477303\pi\)
\(684\) 0 0
\(685\) −273.453 473.634i −0.399201 0.691437i
\(686\) −5.49350 + 5.93095i −0.00800802 + 0.00864569i
\(687\) 0 0
\(688\) −319.356 581.601i −0.464181 0.845351i
\(689\) −82.3761 29.9825i −0.119559 0.0435159i
\(690\) 0 0
\(691\) −460.568 81.2105i −0.666523 0.117526i −0.169858 0.985468i \(-0.554331\pi\)
−0.496665 + 0.867942i \(0.665442\pi\)
\(692\) 224.446 313.336i 0.324344 0.452798i
\(693\) 0 0
\(694\) 53.8865 27.6853i 0.0776462 0.0398924i
\(695\) −282.390 + 336.539i −0.406316 + 0.484229i
\(696\) 0 0
\(697\) −301.412 1709.39i −0.432442 2.45250i
\(698\) −43.2795 342.941i −0.0620051 0.491319i
\(699\) 0 0
\(700\) −0.153631 + 0.150371i −0.000219473 + 0.000214816i
\(701\) 88.4726 0.126209 0.0631046 0.998007i \(-0.479900\pi\)
0.0631046 + 0.998007i \(0.479900\pi\)
\(702\) 0 0
\(703\) 217.716i 0.309695i
\(704\) −14.9604 271.267i −0.0212506 0.385323i
\(705\) 0 0
\(706\) 97.1365 + 769.695i 0.137587 + 1.09022i
\(707\) −5.61420 + 0.989935i −0.00794088 + 0.00140019i
\(708\) 0 0
\(709\) −0.313958 0.263442i −0.000442819 0.000371569i 0.642566 0.766230i \(-0.277870\pi\)
−0.643009 + 0.765859i \(0.722314\pi\)
\(710\) −1169.95 + 601.085i −1.64781 + 0.846598i
\(711\) 0 0
\(712\) 158.450 + 400.641i 0.222542 + 0.562698i
\(713\) 268.373 1522.02i 0.376400 2.13467i
\(714\) 0 0
\(715\) 15.1469 41.6158i 0.0211845 0.0582039i
\(716\) −914.747 + 70.1540i −1.27758 + 0.0979804i
\(717\) 0 0
\(718\) −775.753 + 837.525i −1.08044 + 1.16647i
\(719\) −437.936 + 252.842i −0.609090 + 0.351658i −0.772609 0.634882i \(-0.781049\pi\)
0.163519 + 0.986540i \(0.447715\pi\)
\(720\) 0 0
\(721\) −1.46872 + 2.54389i −0.00203706 + 0.00352828i
\(722\) −600.750 + 185.880i −0.832064 + 0.257452i
\(723\) 0 0
\(724\) −1019.93 + 697.985i −1.40875 + 0.964068i
\(725\) −21.9921 + 18.4536i −0.0303340 + 0.0254532i
\(726\) 0 0
\(727\) 317.879 + 873.365i 0.437247 + 1.20133i 0.941275 + 0.337640i \(0.109629\pi\)
−0.504028 + 0.863687i \(0.668149\pi\)
\(728\) −0.0983068 + 0.663995i −0.000135037 + 0.000912080i
\(729\) 0 0
\(730\) 708.201 1098.61i 0.970139 1.50494i
\(731\) −429.341 1179.60i −0.587334 1.61369i
\(732\) 0 0
\(733\) 465.367 390.489i 0.634880 0.532728i −0.267561 0.963541i \(-0.586218\pi\)
0.902441 + 0.430813i \(0.141773\pi\)
\(734\) 61.2231 145.593i 0.0834103 0.198355i
\(735\) 0 0
\(736\) 1152.76 + 514.111i 1.56624 + 0.698520i
\(737\) −103.807 + 179.799i −0.140851 + 0.243961i
\(738\) 0 0
\(739\) 1027.02 592.950i 1.38974 0.802368i 0.396457 0.918053i \(-0.370240\pi\)
0.993286 + 0.115685i \(0.0369063\pi\)
\(740\) 633.929 162.595i 0.856661 0.219723i
\(741\) 0 0
\(742\) 2.14901 + 2.83195i 0.00289624 + 0.00381665i
\(743\) 66.6908 183.232i 0.0897589 0.246610i −0.886688 0.462368i \(-0.847000\pi\)
0.976447 + 0.215758i \(0.0692221\pi\)
\(744\) 0 0
\(745\) 139.654 792.018i 0.187455 1.06311i
\(746\) −1183.54 58.0343i −1.58652 0.0777940i
\(747\) 0 0
\(748\) 50.2860 511.529i 0.0672273 0.683862i
\(749\) 3.37313 + 2.83039i 0.00450351 + 0.00377889i
\(750\) 0 0
\(751\) −352.727 + 62.1954i −0.469677 + 0.0828167i −0.403477 0.914990i \(-0.632199\pi\)
−0.0661997 + 0.997806i \(0.521087\pi\)
\(752\) 233.928 + 5.01810i 0.311075 + 0.00667300i
\(753\) 0 0
\(754\) −19.8705 + 87.4094i −0.0263535 + 0.115928i
\(755\) 128.446i 0.170127i
\(756\) 0 0
\(757\) −692.369 −0.914622 −0.457311 0.889307i \(-0.651187\pi\)
−0.457311 + 0.889307i \(0.651187\pi\)
\(758\) 181.603 + 41.2834i 0.239582 + 0.0544636i
\(759\) 0 0
\(760\) −146.630 238.545i −0.192934 0.313875i
\(761\) −202.751 1149.86i −0.266427 1.51098i −0.764941 0.644100i \(-0.777232\pi\)
0.498514 0.866882i \(-0.333879\pi\)
\(762\) 0 0
\(763\) −1.40812 + 1.67813i −0.00184550 + 0.00219938i
\(764\) 87.8048 893.184i 0.114928 1.16909i
\(765\) 0 0
\(766\) 18.4776 376.828i 0.0241221 0.491942i
\(767\) 82.5515 + 14.5561i 0.107629 + 0.0189779i
\(768\) 0 0
\(769\) 332.286 + 120.942i 0.432102 + 0.157272i 0.548908 0.835882i \(-0.315044\pi\)
−0.116807 + 0.993155i \(0.537266\pi\)
\(770\) −1.43068 + 1.08566i −0.00185803 + 0.00140995i
\(771\) 0 0
\(772\) 659.470 169.146i 0.854235 0.219101i
\(773\) 530.607 + 919.038i 0.686425 + 1.18892i 0.972987 + 0.230862i \(0.0741545\pi\)
−0.286561 + 0.958062i \(0.592512\pi\)
\(774\) 0 0
\(775\) 44.2137 + 25.5268i 0.0570500 + 0.0329378i
\(776\) −171.268 193.050i −0.220706 0.248776i
\(777\) 0 0
\(778\) −294.095 123.670i −0.378015 0.158959i
\(779\) −251.543 299.778i −0.322905 0.384824i
\(780\) 0 0
\(781\) −511.521 + 186.178i −0.654956 + 0.238384i
\(782\) 2007.09 + 1293.84i 2.56662 + 1.65453i
\(783\) 0 0
\(784\) −516.692 + 589.612i −0.659046 + 0.752057i
\(785\) 547.286 199.196i 0.697179 0.253752i
\(786\) 0 0
\(787\) −936.718 1116.34i −1.19024 1.41847i −0.884617 0.466318i \(-0.845580\pi\)
−0.305621 0.952153i \(-0.598864\pi\)
\(788\) −661.150 + 452.454i −0.839023 + 0.574181i
\(789\) 0 0
\(790\) −9.86359 31.8783i −0.0124856 0.0403523i
\(791\) 4.66048 + 2.69073i 0.00589188 + 0.00340168i
\(792\) 0 0
\(793\) −18.9154 32.7624i −0.0238530 0.0413145i
\(794\) −173.028 160.266i −0.217919 0.201846i
\(795\) 0 0
\(796\) −1061.26 + 81.3906i −1.33324 + 0.102249i
\(797\) −508.103 184.934i −0.637519 0.232038i 0.00298155 0.999996i \(-0.499051\pi\)
−0.640501 + 0.767958i \(0.721273\pi\)
\(798\) 0 0
\(799\) 435.949 + 76.8696i 0.545618 + 0.0962073i
\(800\) −28.9829 + 29.9748i −0.0362286 + 0.0374685i
\(801\) 0 0
\(802\) −124.364 242.062i −0.155068 0.301823i
\(803\) 347.711 414.386i 0.433015 0.516047i
\(804\) 0 0
\(805\) −1.44891 8.21718i −0.00179989 0.0102077i
\(806\) 158.154 19.9593i 0.196221 0.0247634i
\(807\) 0 0
\(808\) −1083.20 + 221.922i −1.34059 + 0.274656i
\(809\) −1070.62 −1.32338 −0.661692 0.749776i \(-0.730161\pi\)
−0.661692 + 0.749776i \(0.730161\pi\)
\(810\) 0 0
\(811\) 1307.05i 1.61165i 0.592153 + 0.805826i \(0.298278\pi\)
−0.592153 + 0.805826i \(0.701722\pi\)
\(812\) 2.59788 2.54275i 0.00319936 0.00313147i
\(813\) 0 0
\(814\) 268.713 33.9119i 0.330114 0.0416609i
\(815\) 1154.34 203.541i 1.41637 0.249744i
\(816\) 0 0
\(817\) −216.800 181.917i −0.265361 0.222665i
\(818\) 117.062 + 227.848i 0.143107 + 0.278543i
\(819\) 0 0
\(820\) −685.013 + 956.306i −0.835381 + 1.16623i
\(821\) −113.123 + 641.554i −0.137787 + 0.781430i 0.835091 + 0.550112i \(0.185415\pi\)
−0.972878 + 0.231318i \(0.925696\pi\)
\(822\) 0 0
\(823\) −175.770 + 482.923i −0.213572 + 0.586784i −0.999503 0.0315306i \(-0.989962\pi\)
0.785931 + 0.618314i \(0.212184\pi\)
\(824\) −271.166 + 501.059i −0.329085 + 0.608081i
\(825\) 0 0
\(826\) −2.49394 2.31000i −0.00301930 0.00279661i
\(827\) −144.231 + 83.2717i −0.174402 + 0.100691i −0.584660 0.811278i \(-0.698772\pi\)
0.410258 + 0.911970i \(0.365439\pi\)
\(828\) 0 0
\(829\) 569.032 985.592i 0.686407 1.18889i −0.286585 0.958055i \(-0.592520\pi\)
0.972992 0.230838i \(-0.0741466\pi\)
\(830\) 354.768 + 1146.58i 0.427432 + 1.38142i
\(831\) 0 0
\(832\) −15.5126 + 129.261i −0.0186450 + 0.155362i
\(833\) −1136.20 + 953.389i −1.36399 + 1.14452i
\(834\) 0 0
\(835\) −28.4971 78.2951i −0.0341283 0.0937666i
\(836\) −47.8445 105.543i −0.0572302 0.126248i
\(837\) 0 0
\(838\) 687.236 + 443.016i 0.820091 + 0.528659i
\(839\) −254.878 700.272i −0.303788 0.834650i −0.993833 0.110884i \(-0.964632\pi\)
0.690045 0.723766i \(-0.257591\pi\)
\(840\) 0 0
\(841\) −272.360 + 228.537i −0.323853 + 0.271745i
\(842\) 281.550 + 118.394i 0.334382 + 0.140611i
\(843\) 0 0
\(844\) −1538.30 429.919i −1.82263 0.509383i
\(845\) 422.759 732.241i 0.500307 0.866557i
\(846\) 0 0
\(847\) 3.67852 2.12380i 0.00434300 0.00250743i
\(848\) 431.781 + 537.582i 0.509175 + 0.633941i
\(849\) 0 0
\(850\) −62.8395 + 47.6853i −0.0739288 + 0.0561003i
\(851\) −430.372 + 1182.44i −0.505725 + 1.38947i
\(852\) 0 0
\(853\) −202.360 + 1147.64i −0.237233 + 1.34542i 0.600626 + 0.799530i \(0.294918\pi\)
−0.837859 + 0.545886i \(0.816193\pi\)
\(854\) −0.0751368 + 1.53233i −8.79822e−5 + 0.00179429i
\(855\) 0 0
\(856\) 669.106 + 530.739i 0.781666 + 0.620022i
\(857\) −350.934 294.468i −0.409491 0.343604i 0.414658 0.909978i \(-0.363901\pi\)
−0.824148 + 0.566374i \(0.808346\pi\)
\(858\) 0 0
\(859\) −1043.94 + 184.076i −1.21530 + 0.214291i −0.744302 0.667843i \(-0.767218\pi\)
−0.471000 + 0.882133i \(0.656107\pi\)
\(860\) −367.781 + 767.123i −0.427653 + 0.892003i
\(861\) 0 0
\(862\) 1248.37 + 283.788i 1.44822 + 0.329220i
\(863\) 842.741i 0.976525i −0.872697 0.488262i \(-0.837631\pi\)
0.872697 0.488262i \(-0.162369\pi\)
\(864\) 0 0
\(865\) −494.182 −0.571308
\(866\) 152.377 670.299i 0.175955 0.774017i
\(867\) 0 0
\(868\) −5.82925 2.79472i −0.00671573 0.00321972i
\(869\) −2.39808 13.6002i −0.00275958 0.0156504i
\(870\) 0 0
\(871\) 63.9500 76.2126i 0.0734213 0.0875001i
\(872\) −264.042 + 332.880i −0.302801 + 0.381743i
\(873\) 0 0
\(874\) 537.730 + 26.3673i 0.615252 + 0.0301686i
\(875\) −4.93671 0.870475i −0.00564195 0.000994829i
\(876\) 0 0
\(877\) −919.491 334.667i −1.04845 0.381605i −0.240373 0.970681i \(-0.577270\pi\)
−0.808078 + 0.589076i \(0.799492\pi\)
\(878\) −109.202 143.906i −0.124376 0.163903i
\(879\) 0 0
\(880\) −271.582 + 218.132i −0.308616 + 0.247877i
\(881\) −22.0835 38.2497i −0.0250664 0.0434163i 0.853220 0.521551i \(-0.174646\pi\)
−0.878286 + 0.478135i \(0.841313\pi\)
\(882\) 0 0
\(883\) 445.575 + 257.253i 0.504615 + 0.291339i 0.730617 0.682787i \(-0.239232\pi\)
−0.226002 + 0.974127i \(0.572566\pi\)
\(884\) −66.2963 + 237.216i −0.0749959 + 0.268344i
\(885\) 0 0
\(886\) −227.453 + 540.900i −0.256719 + 0.610496i
\(887\) −918.503 1094.63i −1.03552 1.23408i −0.971725 0.236117i \(-0.924125\pi\)
−0.0637919 0.997963i \(-0.520319\pi\)
\(888\) 0 0
\(889\) 4.04682 1.47292i 0.00455210 0.00165683i
\(890\) 299.298 464.292i 0.336290 0.521676i
\(891\) 0 0
\(892\) −1009.93 + 457.818i −1.13221 + 0.513249i
\(893\) 93.7832 34.1343i 0.105020 0.0382243i
\(894\) 0 0
\(895\) 756.109 + 901.096i 0.844814 + 1.00681i
\(896\) 3.36892 4.06502i 0.00375996 0.00453685i
\(897\) 0 0
\(898\) −244.009 + 75.4998i −0.271725 + 0.0840755i
\(899\) −747.647 431.654i −0.831643 0.480149i
\(900\) 0 0
\(901\) 652.250 + 1129.73i 0.723918 + 1.25386i
\(902\) −330.816 + 357.158i −0.366758 + 0.395963i
\(903\) 0 0
\(904\) 917.953 + 496.784i 1.01543 + 0.549540i
\(905\) 1489.06 + 541.973i 1.64537 + 0.598865i
\(906\) 0 0
\(907\) 1252.53 + 220.855i 1.38096 + 0.243501i 0.814297 0.580449i \(-0.197123\pi\)
0.566663 + 0.823949i \(0.308234\pi\)
\(908\) 520.996 + 373.195i 0.573784 + 0.411008i
\(909\) 0 0
\(910\) 0.765506 0.393295i 0.000841216 0.000432192i
\(911\) −985.284 + 1174.22i −1.08154 + 1.28893i −0.126659 + 0.991946i \(0.540425\pi\)
−0.954882 + 0.296985i \(0.904019\pi\)
\(912\) 0 0
\(913\) 86.2528 + 489.164i 0.0944718 + 0.535776i
\(914\) 105.249 + 833.981i 0.115153 + 0.912452i
\(915\) 0 0
\(916\) −1167.05 1192.35i −1.27407 1.30170i
\(917\) 5.64002 0.00615051
\(918\) 0 0
\(919\) 958.663i 1.04316i −0.853203 0.521580i \(-0.825343\pi\)
0.853203 0.521580i \(-0.174657\pi\)
\(920\) −324.814 1585.42i −0.353059 1.72328i
\(921\) 0 0
\(922\) −172.784 1369.12i −0.187401 1.48494i
\(923\) 256.889 45.2964i 0.278319 0.0490752i
\(924\) 0 0
\(925\) −31.8423 26.7189i −0.0344241 0.0288853i
\(926\) −980.310 + 503.655i −1.05865 + 0.543904i
\(927\) 0 0
\(928\) 490.096 506.869i 0.528120 0.546195i
\(929\) −249.626 + 1415.70i −0.268704 + 1.52389i 0.489573 + 0.871962i \(0.337153\pi\)
−0.758277 + 0.651933i \(0.773958\pi\)
\(930\) 0 0
\(931\) −114.369 + 314.227i −0.122846 + 0.337516i
\(932\) 69.4146 + 905.106i 0.0744792 + 0.971144i
\(933\) 0 0
\(934\) 841.063 908.036i 0.900495 0.972201i
\(935\) −570.731 + 329.512i −0.610408 + 0.352419i
\(936\) 0 0
\(937\) 151.138 261.779i 0.161300 0.279380i −0.774035 0.633143i \(-0.781765\pi\)
0.935335 + 0.353763i \(0.115098\pi\)
\(938\) −3.85431 + 1.19258i −0.00410907 + 0.00127140i
\(939\) 0 0
\(940\) −169.429 247.579i −0.180244 0.263382i
\(941\) 629.923 528.568i 0.669419 0.561709i −0.243475 0.969907i \(-0.578287\pi\)
0.912893 + 0.408198i \(0.133843\pi\)
\(942\) 0 0
\(943\) −773.569 2125.36i −0.820328 2.25383i
\(944\) −495.868 434.541i −0.525284 0.460319i
\(945\) 0 0
\(946\) −190.759 + 295.919i −0.201648 + 0.312811i
\(947\) −456.809 1255.07i −0.482375 1.32531i −0.907451 0.420157i \(-0.861975\pi\)
0.425076 0.905158i \(-0.360247\pi\)
\(948\) 0 0
\(949\) −198.573 + 166.623i −0.209245 + 0.175577i
\(950\) −6.89387 + 16.3941i −0.00725671 + 0.0172569i
\(951\) 0 0
\(952\) 7.47191 6.62882i 0.00784865 0.00696305i
\(953\) 156.667 271.356i 0.164394 0.284739i −0.772046 0.635567i \(-0.780767\pi\)
0.936440 + 0.350828i \(0.114100\pi\)
\(954\) 0 0
\(955\) −996.558 + 575.363i −1.04352 + 0.602474i
\(956\) −156.039 608.368i −0.163221 0.636369i
\(957\) 0 0
\(958\) 387.382 + 510.490i 0.404365 + 0.532871i
\(959\) 1.50436 4.13319i 0.00156868 0.00430990i
\(960\) 0 0
\(961\) −99.7172 + 565.524i −0.103764 + 0.588475i
\(962\) −129.633 6.35648i −0.134753 0.00660757i
\(963\) 0 0
\(964\) 481.728 + 47.3565i 0.499718 + 0.0491250i
\(965\) −668.692 561.099i −0.692945 0.581450i
\(966\) 0 0
\(967\) 1793.17 316.184i 1.85437 0.326975i 0.868654 0.495419i \(-0.164986\pi\)
0.985711 + 0.168444i \(0.0538744\pi\)
\(968\) 701.850 431.415i 0.725052 0.445677i
\(969\) 0 0
\(970\) −73.3487 + 322.657i −0.0756173 + 0.332637i
\(971\) 1200.07i 1.23592i 0.786211 + 0.617958i \(0.212040\pi\)
−0.786211 + 0.617958i \(0.787960\pi\)
\(972\) 0 0
\(973\) −3.53321 −0.00363125
\(974\) −10.2339 2.32644i −0.0105071 0.00238854i
\(975\) 0 0
\(976\) −6.38159 + 297.490i −0.00653851 + 0.304805i
\(977\) −35.8447 203.285i −0.0366885 0.208071i 0.960953 0.276712i \(-0.0892448\pi\)
−0.997641 + 0.0686410i \(0.978134\pi\)
\(978\) 0 0
\(979\) 146.949 175.127i 0.150101 0.178883i
\(980\) 1000.36 + 98.3405i 1.02077 + 0.100347i
\(981\) 0 0
\(982\) −59.0638 + 1204.54i −0.0601464 + 1.22661i
\(983\) 1420.62 + 250.494i 1.44519 + 0.254826i 0.840575 0.541695i \(-0.182217\pi\)
0.604612 + 0.796520i \(0.293328\pi\)
\(984\) 0 0
\(985\) 965.250 + 351.322i 0.979949 + 0.356672i
\(986\) 1062.60 806.350i 1.07769 0.817799i
\(987\) 0 0
\(988\) 13.7963 + 53.7892i 0.0139638 + 0.0544425i
\(989\) −817.858 1416.57i −0.826955 1.43233i
\(990\) 0 0
\(991\) −814.600 470.309i −0.821998 0.474581i 0.0291073 0.999576i \(-0.490734\pi\)
−0.851105 + 0.524996i \(0.824067\pi\)
\(992\) −1145.11 510.701i −1.15435 0.514820i
\(993\) 0 0
\(994\) −9.75133 4.10053i −0.00981019 0.00412528i
\(995\) 877.215 + 1045.42i 0.881623 + 1.05068i
\(996\) 0 0
\(997\) 173.772 63.2477i 0.174294 0.0634380i −0.253399 0.967362i \(-0.581549\pi\)
0.427693 + 0.903924i \(0.359326\pi\)
\(998\) −9.79773 6.31596i −0.00981737 0.00632861i
\(999\) 0 0
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 324.3.j.a.19.19 204
3.2 odd 2 108.3.j.a.7.16 yes 204
4.3 odd 2 inner 324.3.j.a.19.27 204
12.11 even 2 108.3.j.a.7.8 204
27.4 even 9 inner 324.3.j.a.307.27 204
27.23 odd 18 108.3.j.a.31.8 yes 204
108.23 even 18 108.3.j.a.31.16 yes 204
108.31 odd 18 inner 324.3.j.a.307.19 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.7.8 204 12.11 even 2
108.3.j.a.7.16 yes 204 3.2 odd 2
108.3.j.a.31.8 yes 204 27.23 odd 18
108.3.j.a.31.16 yes 204 108.23 even 18
324.3.j.a.19.19 204 1.1 even 1 trivial
324.3.j.a.19.27 204 4.3 odd 2 inner
324.3.j.a.307.19 204 108.31 odd 18 inner
324.3.j.a.307.27 204 27.4 even 9 inner