Properties

Label 288.2.v.d.37.8
Level $288$
Weight $2$
Character 288.37
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [288,2,Mod(37,288)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(288, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("288.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.v (of order \(8\), degree \(4\), 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: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 37.8
Character \(\chi\) \(=\) 288.37
Dual form 288.2.v.d.109.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.29526 - 0.567706i) q^{2} +(1.35542 - 1.47066i) q^{4} +(-0.825824 - 0.342068i) q^{5} +(1.17750 + 1.17750i) q^{7} +(0.920723 - 2.67437i) q^{8} +O(q^{10})\) \(q+(1.29526 - 0.567706i) q^{2} +(1.35542 - 1.47066i) q^{4} +(-0.825824 - 0.342068i) q^{5} +(1.17750 + 1.17750i) q^{7} +(0.920723 - 2.67437i) q^{8} +(-1.26385 + 0.0257578i) q^{10} +(1.46490 - 3.53657i) q^{11} +(3.01061 - 1.24703i) q^{13} +(2.19365 + 0.856699i) q^{14} +(-0.325679 - 3.98672i) q^{16} +4.58215i q^{17} +(-3.29978 + 1.36681i) q^{19} +(-1.62240 + 0.750861i) q^{20} +(-0.110307 - 5.41243i) q^{22} +(-5.41196 + 5.41196i) q^{23} +(-2.97056 - 2.97056i) q^{25} +(3.19158 - 3.32438i) q^{26} +(3.32770 - 0.135696i) q^{28} +(2.46490 + 5.95078i) q^{29} -5.25495 q^{31} +(-2.68513 - 4.97897i) q^{32} +(2.60132 + 5.93510i) q^{34} +(-0.569623 - 1.37519i) q^{35} +(7.33917 + 3.03998i) q^{37} +(-3.49813 + 3.64369i) q^{38} +(-1.67517 + 1.89361i) q^{40} +(1.35921 - 1.35921i) q^{41} +(-2.95781 + 7.14079i) q^{43} +(-3.21555 - 6.94790i) q^{44} +(-3.93752 + 10.0823i) q^{46} +8.16360i q^{47} -4.22699i q^{49} +(-5.53406 - 2.16125i) q^{50} +(2.24667 - 6.11783i) q^{52} +(3.13863 - 7.57731i) q^{53} +(-2.41949 + 2.41949i) q^{55} +(4.23322 - 2.06492i) q^{56} +(6.57099 + 6.30850i) q^{58} +(-0.221996 - 0.0919539i) q^{59} +(2.66861 + 6.44260i) q^{61} +(-6.80655 + 2.98327i) q^{62} +(-6.30454 - 4.92471i) q^{64} -2.91280 q^{65} +(-5.52539 - 13.3395i) q^{67} +(6.73879 + 6.21074i) q^{68} +(-1.51852 - 1.45786i) q^{70} +(-1.51271 - 1.51271i) q^{71} +(-9.62682 + 9.62682i) q^{73} +(11.2320 - 0.228911i) q^{74} +(-2.46246 + 6.70545i) q^{76} +(5.88923 - 2.43940i) q^{77} -5.34497i q^{79} +(-1.09477 + 3.40373i) q^{80} +(0.988904 - 2.53217i) q^{82} +(-5.64233 + 2.33713i) q^{83} +(1.56741 - 3.78405i) q^{85} +(0.222724 + 10.9284i) q^{86} +(-8.10935 - 7.17388i) q^{88} +(-5.09017 - 5.09017i) q^{89} +(5.01337 + 2.07660i) q^{91} +(0.623678 + 15.2946i) q^{92} +(4.63453 + 10.5740i) q^{94} +3.19258 q^{95} +19.0146 q^{97} +(-2.39969 - 5.47507i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{10} + 32 q^{14} - 8 q^{16} + 32 q^{20} - 8 q^{22} + 16 q^{23} - 40 q^{26} + 40 q^{28} - 48 q^{31} - 40 q^{32} + 40 q^{34} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 16 q^{43} - 8 q^{44} - 32 q^{46} - 24 q^{50} - 8 q^{52} + 32 q^{53} + 32 q^{55} - 56 q^{56} - 32 q^{58} - 64 q^{59} - 32 q^{61} - 48 q^{62} + 24 q^{64} + 16 q^{67} + 8 q^{68} - 24 q^{70} - 64 q^{71} + 32 q^{74} - 56 q^{76} + 32 q^{77} + 56 q^{80} - 40 q^{82} + 64 q^{86} - 48 q^{88} - 48 q^{91} + 80 q^{92} - 32 q^{94} + 80 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29526 0.567706i 0.915890 0.401429i
\(3\) 0 0
\(4\) 1.35542 1.47066i 0.677709 0.735330i
\(5\) −0.825824 0.342068i −0.369320 0.152977i 0.190302 0.981726i \(-0.439053\pi\)
−0.559621 + 0.828748i \(0.689053\pi\)
\(6\) 0 0
\(7\) 1.17750 + 1.17750i 0.445053 + 0.445053i 0.893706 0.448653i \(-0.148096\pi\)
−0.448653 + 0.893706i \(0.648096\pi\)
\(8\) 0.920723 2.67437i 0.325525 0.945534i
\(9\) 0 0
\(10\) −1.26385 + 0.0257578i −0.399666 + 0.00814532i
\(11\) 1.46490 3.53657i 0.441683 1.06632i −0.533675 0.845690i \(-0.679189\pi\)
0.975358 0.220627i \(-0.0708105\pi\)
\(12\) 0 0
\(13\) 3.01061 1.24703i 0.834992 0.345865i 0.0761151 0.997099i \(-0.475748\pi\)
0.758877 + 0.651234i \(0.225748\pi\)
\(14\) 2.19365 + 0.856699i 0.586276 + 0.228962i
\(15\) 0 0
\(16\) −0.325679 3.98672i −0.0814198 0.996680i
\(17\) 4.58215i 1.11134i 0.831404 + 0.555668i \(0.187537\pi\)
−0.831404 + 0.555668i \(0.812463\pi\)
\(18\) 0 0
\(19\) −3.29978 + 1.36681i −0.757021 + 0.313568i −0.727602 0.685999i \(-0.759365\pi\)
−0.0294181 + 0.999567i \(0.509365\pi\)
\(20\) −1.62240 + 0.750861i −0.362780 + 0.167898i
\(21\) 0 0
\(22\) −0.110307 5.41243i −0.0235175 1.15393i
\(23\) −5.41196 + 5.41196i −1.12847 + 1.12847i −0.138046 + 0.990426i \(0.544082\pi\)
−0.990426 + 0.138046i \(0.955918\pi\)
\(24\) 0 0
\(25\) −2.97056 2.97056i −0.594112 0.594112i
\(26\) 3.19158 3.32438i 0.625921 0.651964i
\(27\) 0 0
\(28\) 3.32770 0.135696i 0.628877 0.0256441i
\(29\) 2.46490 + 5.95078i 0.457720 + 1.10503i 0.969318 + 0.245808i \(0.0790534\pi\)
−0.511599 + 0.859224i \(0.670947\pi\)
\(30\) 0 0
\(31\) −5.25495 −0.943816 −0.471908 0.881648i \(-0.656435\pi\)
−0.471908 + 0.881648i \(0.656435\pi\)
\(32\) −2.68513 4.97897i −0.474668 0.880165i
\(33\) 0 0
\(34\) 2.60132 + 5.93510i 0.446122 + 1.01786i
\(35\) −0.569623 1.37519i −0.0962838 0.232450i
\(36\) 0 0
\(37\) 7.33917 + 3.03998i 1.20655 + 0.499770i 0.893111 0.449837i \(-0.148518\pi\)
0.313442 + 0.949607i \(0.398518\pi\)
\(38\) −3.49813 + 3.64369i −0.567472 + 0.591084i
\(39\) 0 0
\(40\) −1.67517 + 1.89361i −0.264868 + 0.299406i
\(41\) 1.35921 1.35921i 0.212273 0.212273i −0.592959 0.805232i \(-0.702041\pi\)
0.805232 + 0.592959i \(0.202041\pi\)
\(42\) 0 0
\(43\) −2.95781 + 7.14079i −0.451062 + 1.08896i 0.520856 + 0.853644i \(0.325613\pi\)
−0.971919 + 0.235317i \(0.924387\pi\)
\(44\) −3.21555 6.94790i −0.484762 1.04744i
\(45\) 0 0
\(46\) −3.93752 + 10.0823i −0.580555 + 1.48656i
\(47\) 8.16360i 1.19078i 0.803436 + 0.595391i \(0.203003\pi\)
−0.803436 + 0.595391i \(0.796997\pi\)
\(48\) 0 0
\(49\) 4.22699i 0.603856i
\(50\) −5.53406 2.16125i −0.782635 0.305647i
\(51\) 0 0
\(52\) 2.24667 6.11783i 0.311557 0.848391i
\(53\) 3.13863 7.57731i 0.431123 1.04082i −0.547802 0.836608i \(-0.684535\pi\)
0.978926 0.204216i \(-0.0654646\pi\)
\(54\) 0 0
\(55\) −2.41949 + 2.41949i −0.326244 + 0.326244i
\(56\) 4.23322 2.06492i 0.565688 0.275937i
\(57\) 0 0
\(58\) 6.57099 + 6.30850i 0.862813 + 0.828347i
\(59\) −0.221996 0.0919539i −0.0289014 0.0119714i 0.368186 0.929752i \(-0.379979\pi\)
−0.397087 + 0.917781i \(0.629979\pi\)
\(60\) 0 0
\(61\) 2.66861 + 6.44260i 0.341681 + 0.824891i 0.997546 + 0.0700128i \(0.0223040\pi\)
−0.655865 + 0.754878i \(0.727696\pi\)
\(62\) −6.80655 + 2.98327i −0.864432 + 0.378875i
\(63\) 0 0
\(64\) −6.30454 4.92471i −0.788067 0.615589i
\(65\) −2.91280 −0.361289
\(66\) 0 0
\(67\) −5.52539 13.3395i −0.675033 1.62968i −0.772940 0.634479i \(-0.781215\pi\)
0.0979063 0.995196i \(-0.468785\pi\)
\(68\) 6.73879 + 6.21074i 0.817198 + 0.753163i
\(69\) 0 0
\(70\) −1.51852 1.45786i −0.181497 0.174247i
\(71\) −1.51271 1.51271i −0.179526 0.179526i 0.611623 0.791149i \(-0.290517\pi\)
−0.791149 + 0.611623i \(0.790517\pi\)
\(72\) 0 0
\(73\) −9.62682 + 9.62682i −1.12673 + 1.12673i −0.136029 + 0.990705i \(0.543434\pi\)
−0.990705 + 0.136029i \(0.956566\pi\)
\(74\) 11.2320 0.228911i 1.30569 0.0266104i
\(75\) 0 0
\(76\) −2.46246 + 6.70545i −0.282464 + 0.769168i
\(77\) 5.88923 2.43940i 0.671140 0.277995i
\(78\) 0 0
\(79\) 5.34497i 0.601356i −0.953726 0.300678i \(-0.902787\pi\)
0.953726 0.300678i \(-0.0972129\pi\)
\(80\) −1.09477 + 3.40373i −0.122399 + 0.380549i
\(81\) 0 0
\(82\) 0.988904 2.53217i 0.109206 0.279631i
\(83\) −5.64233 + 2.33713i −0.619327 + 0.256533i −0.670210 0.742171i \(-0.733796\pi\)
0.0508839 + 0.998705i \(0.483796\pi\)
\(84\) 0 0
\(85\) 1.56741 3.78405i 0.170009 0.410438i
\(86\) 0.222724 + 10.9284i 0.0240169 + 1.17844i
\(87\) 0 0
\(88\) −8.10935 7.17388i −0.864460 0.764739i
\(89\) −5.09017 5.09017i −0.539557 0.539557i 0.383842 0.923399i \(-0.374601\pi\)
−0.923399 + 0.383842i \(0.874601\pi\)
\(90\) 0 0
\(91\) 5.01337 + 2.07660i 0.525544 + 0.217687i
\(92\) 0.623678 + 15.2946i 0.0650229 + 1.59458i
\(93\) 0 0
\(94\) 4.63453 + 10.5740i 0.478015 + 1.09063i
\(95\) 3.19258 0.327551
\(96\) 0 0
\(97\) 19.0146 1.93064 0.965319 0.261072i \(-0.0840761\pi\)
0.965319 + 0.261072i \(0.0840761\pi\)
\(98\) −2.39969 5.47507i −0.242405 0.553066i
\(99\) 0 0
\(100\) −8.39503 + 0.342329i −0.839503 + 0.0342329i
\(101\) 3.55331 + 1.47183i 0.353567 + 0.146452i 0.552396 0.833582i \(-0.313714\pi\)
−0.198828 + 0.980034i \(0.563714\pi\)
\(102\) 0 0
\(103\) 3.30552 + 3.30552i 0.325703 + 0.325703i 0.850950 0.525247i \(-0.176027\pi\)
−0.525247 + 0.850950i \(0.676027\pi\)
\(104\) −0.563100 9.19966i −0.0552165 0.902101i
\(105\) 0 0
\(106\) −0.236339 11.5964i −0.0229553 1.12635i
\(107\) 4.98987 12.0466i 0.482389 1.16459i −0.476082 0.879401i \(-0.657943\pi\)
0.958471 0.285190i \(-0.0920567\pi\)
\(108\) 0 0
\(109\) −4.16532 + 1.72533i −0.398966 + 0.165257i −0.573139 0.819458i \(-0.694275\pi\)
0.174174 + 0.984715i \(0.444275\pi\)
\(110\) −1.76032 + 4.50745i −0.167840 + 0.429768i
\(111\) 0 0
\(112\) 4.31087 5.07784i 0.407339 0.479811i
\(113\) 15.7676i 1.48329i −0.670792 0.741645i \(-0.734046\pi\)
0.670792 0.741645i \(-0.265954\pi\)
\(114\) 0 0
\(115\) 6.32059 2.61807i 0.589398 0.244137i
\(116\) 12.0925 + 4.44078i 1.12276 + 0.412316i
\(117\) 0 0
\(118\) −0.339747 + 0.00692414i −0.0312762 + 0.000637419i
\(119\) −5.39548 + 5.39548i −0.494603 + 0.494603i
\(120\) 0 0
\(121\) −2.58325 2.58325i −0.234841 0.234841i
\(122\) 7.11407 + 6.82989i 0.644077 + 0.618349i
\(123\) 0 0
\(124\) −7.12265 + 7.72824i −0.639633 + 0.694016i
\(125\) 3.14736 + 7.59841i 0.281509 + 0.679623i
\(126\) 0 0
\(127\) 5.62550 0.499182 0.249591 0.968351i \(-0.419704\pi\)
0.249591 + 0.968351i \(0.419704\pi\)
\(128\) −10.9618 2.79968i −0.968898 0.247459i
\(129\) 0 0
\(130\) −3.77285 + 1.65362i −0.330901 + 0.145032i
\(131\) −2.77061 6.68884i −0.242069 0.584407i 0.755419 0.655242i \(-0.227433\pi\)
−0.997488 + 0.0708355i \(0.977433\pi\)
\(132\) 0 0
\(133\) −5.49490 2.27606i −0.476468 0.197360i
\(134\) −14.7297 14.1413i −1.27246 1.22163i
\(135\) 0 0
\(136\) 12.2544 + 4.21889i 1.05081 + 0.361767i
\(137\) −3.13785 + 3.13785i −0.268085 + 0.268085i −0.828328 0.560243i \(-0.810708\pi\)
0.560243 + 0.828328i \(0.310708\pi\)
\(138\) 0 0
\(139\) 3.60636 8.70653i 0.305888 0.738478i −0.693942 0.720031i \(-0.744128\pi\)
0.999830 0.0184473i \(-0.00587229\pi\)
\(140\) −2.79452 1.02624i −0.236180 0.0867330i
\(141\) 0 0
\(142\) −2.81814 1.10059i −0.236493 0.0923591i
\(143\) 12.4740i 1.04313i
\(144\) 0 0
\(145\) 5.75746i 0.478131i
\(146\) −7.00407 + 17.9345i −0.579661 + 1.48427i
\(147\) 0 0
\(148\) 14.4184 6.67297i 1.18519 0.548515i
\(149\) 1.00661 2.43018i 0.0824648 0.199088i −0.877269 0.479999i \(-0.840637\pi\)
0.959734 + 0.280912i \(0.0906368\pi\)
\(150\) 0 0
\(151\) −14.3784 + 14.3784i −1.17010 + 1.17010i −0.187914 + 0.982186i \(0.560173\pi\)
−0.982186 + 0.187914i \(0.939827\pi\)
\(152\) 0.617186 + 10.0833i 0.0500604 + 0.817863i
\(153\) 0 0
\(154\) 6.24324 6.50301i 0.503095 0.524028i
\(155\) 4.33966 + 1.79755i 0.348570 + 0.144382i
\(156\) 0 0
\(157\) −2.10034 5.07067i −0.167625 0.404684i 0.817637 0.575734i \(-0.195284\pi\)
−0.985262 + 0.171051i \(0.945284\pi\)
\(158\) −3.03437 6.92315i −0.241402 0.550776i
\(159\) 0 0
\(160\) 0.514300 + 5.03024i 0.0406590 + 0.397676i
\(161\) −12.7452 −1.00446
\(162\) 0 0
\(163\) −4.14645 10.0104i −0.324775 0.784076i −0.998964 0.0455168i \(-0.985507\pi\)
0.674189 0.738559i \(-0.264493\pi\)
\(164\) −0.156636 3.84124i −0.0122312 0.299950i
\(165\) 0 0
\(166\) −5.98151 + 6.23039i −0.464255 + 0.483572i
\(167\) 5.38194 + 5.38194i 0.416467 + 0.416467i 0.883984 0.467517i \(-0.154851\pi\)
−0.467517 + 0.883984i \(0.654851\pi\)
\(168\) 0 0
\(169\) −1.68373 + 1.68373i −0.129518 + 0.129518i
\(170\) −0.118026 5.79117i −0.00905218 0.444163i
\(171\) 0 0
\(172\) 6.49260 + 14.0287i 0.495056 + 1.06968i
\(173\) 9.62485 3.98675i 0.731764 0.303107i 0.0144874 0.999895i \(-0.495388\pi\)
0.717277 + 0.696788i \(0.245388\pi\)
\(174\) 0 0
\(175\) 6.99566i 0.528822i
\(176\) −14.5764 4.68834i −1.09874 0.353397i
\(177\) 0 0
\(178\) −9.48283 3.70339i −0.710768 0.277581i
\(179\) 12.7809 5.29402i 0.955288 0.395693i 0.150072 0.988675i \(-0.452049\pi\)
0.805216 + 0.592982i \(0.202049\pi\)
\(180\) 0 0
\(181\) 8.21217 19.8259i 0.610406 1.47365i −0.252150 0.967688i \(-0.581138\pi\)
0.862556 0.505962i \(-0.168862\pi\)
\(182\) 7.67254 0.156369i 0.568726 0.0115908i
\(183\) 0 0
\(184\) 9.49069 + 19.4565i 0.699663 + 1.43435i
\(185\) −5.02098 5.02098i −0.369150 0.369150i
\(186\) 0 0
\(187\) 16.2051 + 6.71238i 1.18504 + 0.490858i
\(188\) 12.0059 + 11.0651i 0.875618 + 0.807005i
\(189\) 0 0
\(190\) 4.13523 1.81245i 0.300001 0.131489i
\(191\) 10.3772 0.750866 0.375433 0.926850i \(-0.377494\pi\)
0.375433 + 0.926850i \(0.377494\pi\)
\(192\) 0 0
\(193\) −8.76090 −0.630623 −0.315312 0.948988i \(-0.602109\pi\)
−0.315312 + 0.948988i \(0.602109\pi\)
\(194\) 24.6289 10.7947i 1.76825 0.775014i
\(195\) 0 0
\(196\) −6.21647 5.72935i −0.444033 0.409239i
\(197\) 4.35045 + 1.80201i 0.309956 + 0.128388i 0.532239 0.846594i \(-0.321351\pi\)
−0.222283 + 0.974982i \(0.571351\pi\)
\(198\) 0 0
\(199\) 3.47990 + 3.47990i 0.246684 + 0.246684i 0.819608 0.572925i \(-0.194191\pi\)
−0.572925 + 0.819608i \(0.694191\pi\)
\(200\) −10.6794 + 5.20932i −0.755151 + 0.368355i
\(201\) 0 0
\(202\) 5.43804 0.110829i 0.382619 0.00779790i
\(203\) −4.10463 + 9.90945i −0.288088 + 0.695507i
\(204\) 0 0
\(205\) −1.58741 + 0.657527i −0.110870 + 0.0459237i
\(206\) 6.15809 + 2.40496i 0.429054 + 0.167561i
\(207\) 0 0
\(208\) −5.95207 11.5963i −0.412702 0.804060i
\(209\) 13.6721i 0.945722i
\(210\) 0 0
\(211\) −4.76129 + 1.97219i −0.327781 + 0.135771i −0.540505 0.841341i \(-0.681767\pi\)
0.212724 + 0.977112i \(0.431767\pi\)
\(212\) −6.88950 14.8863i −0.473173 1.02239i
\(213\) 0 0
\(214\) −0.375739 18.4363i −0.0256850 1.26028i
\(215\) 4.88527 4.88527i 0.333173 0.333173i
\(216\) 0 0
\(217\) −6.18769 6.18769i −0.420048 0.420048i
\(218\) −4.41571 + 4.59944i −0.299070 + 0.311514i
\(219\) 0 0
\(220\) 0.278824 + 6.83768i 0.0187983 + 0.460996i
\(221\) 5.71410 + 13.7951i 0.384372 + 0.927956i
\(222\) 0 0
\(223\) 12.6045 0.844059 0.422029 0.906582i \(-0.361318\pi\)
0.422029 + 0.906582i \(0.361318\pi\)
\(224\) 2.70099 9.02446i 0.180468 0.602972i
\(225\) 0 0
\(226\) −8.95136 20.4232i −0.595436 1.35853i
\(227\) −1.84453 4.45310i −0.122426 0.295563i 0.850771 0.525537i \(-0.176136\pi\)
−0.973197 + 0.229975i \(0.926136\pi\)
\(228\) 0 0
\(229\) −19.3957 8.03395i −1.28170 0.530898i −0.365200 0.930929i \(-0.618999\pi\)
−0.916502 + 0.400031i \(0.868999\pi\)
\(230\) 6.70053 6.97933i 0.441820 0.460204i
\(231\) 0 0
\(232\) 18.1841 1.11303i 1.19384 0.0730737i
\(233\) −13.4162 + 13.4162i −0.878921 + 0.878921i −0.993423 0.114502i \(-0.963473\pi\)
0.114502 + 0.993423i \(0.463473\pi\)
\(234\) 0 0
\(235\) 2.79250 6.74169i 0.182163 0.439780i
\(236\) −0.436131 + 0.201845i −0.0283897 + 0.0131390i
\(237\) 0 0
\(238\) −3.92552 + 10.0516i −0.254454 + 0.651550i
\(239\) 4.57889i 0.296184i −0.988974 0.148092i \(-0.952687\pi\)
0.988974 0.148092i \(-0.0473131\pi\)
\(240\) 0 0
\(241\) 14.5911i 0.939895i 0.882694 + 0.469948i \(0.155727\pi\)
−0.882694 + 0.469948i \(0.844273\pi\)
\(242\) −4.81253 1.87947i −0.309361 0.120817i
\(243\) 0 0
\(244\) 13.0920 + 4.80780i 0.838127 + 0.307788i
\(245\) −1.44592 + 3.49075i −0.0923763 + 0.223016i
\(246\) 0 0
\(247\) −8.22987 + 8.22987i −0.523654 + 0.523654i
\(248\) −4.83835 + 14.0537i −0.307236 + 0.892410i
\(249\) 0 0
\(250\) 8.39034 + 8.05517i 0.530651 + 0.509454i
\(251\) 1.91315 + 0.792453i 0.120757 + 0.0500192i 0.442244 0.896895i \(-0.354183\pi\)
−0.321487 + 0.946914i \(0.604183\pi\)
\(252\) 0 0
\(253\) 11.2118 + 27.0678i 0.704882 + 1.70174i
\(254\) 7.28650 3.19363i 0.457196 0.200386i
\(255\) 0 0
\(256\) −15.7879 + 2.59678i −0.986742 + 0.162299i
\(257\) 21.4012 1.33497 0.667485 0.744624i \(-0.267371\pi\)
0.667485 + 0.744624i \(0.267371\pi\)
\(258\) 0 0
\(259\) 5.06229 + 12.2214i 0.314555 + 0.759403i
\(260\) −3.94807 + 4.28374i −0.244849 + 0.265666i
\(261\) 0 0
\(262\) −7.38597 7.09093i −0.456307 0.438079i
\(263\) −4.14877 4.14877i −0.255824 0.255824i 0.567529 0.823353i \(-0.307899\pi\)
−0.823353 + 0.567529i \(0.807899\pi\)
\(264\) 0 0
\(265\) −5.18391 + 5.18391i −0.318445 + 0.318445i
\(266\) −8.40949 + 0.171388i −0.515619 + 0.0105085i
\(267\) 0 0
\(268\) −27.1070 9.95460i −1.65583 0.608074i
\(269\) −28.0039 + 11.5996i −1.70743 + 0.707241i −0.707430 + 0.706783i \(0.750146\pi\)
−1.00000 0.000457143i \(0.999854\pi\)
\(270\) 0 0
\(271\) 10.3370i 0.627930i 0.949435 + 0.313965i \(0.101657\pi\)
−0.949435 + 0.313965i \(0.898343\pi\)
\(272\) 18.2678 1.49231i 1.10765 0.0904847i
\(273\) 0 0
\(274\) −2.28297 + 5.84572i −0.137919 + 0.353153i
\(275\) −14.8572 + 6.15404i −0.895920 + 0.371102i
\(276\) 0 0
\(277\) −6.39508 + 15.4391i −0.384243 + 0.927645i 0.606892 + 0.794785i \(0.292416\pi\)
−0.991135 + 0.132860i \(0.957584\pi\)
\(278\) −0.271560 13.3246i −0.0162871 0.799157i
\(279\) 0 0
\(280\) −4.20224 + 0.257214i −0.251132 + 0.0153715i
\(281\) −7.85631 7.85631i −0.468668 0.468668i 0.432815 0.901483i \(-0.357520\pi\)
−0.901483 + 0.432815i \(0.857520\pi\)
\(282\) 0 0
\(283\) 6.76840 + 2.80356i 0.402340 + 0.166655i 0.574671 0.818385i \(-0.305130\pi\)
−0.172331 + 0.985039i \(0.555130\pi\)
\(284\) −4.27504 + 0.174326i −0.253677 + 0.0103443i
\(285\) 0 0
\(286\) −7.08157 16.1571i −0.418742 0.955392i
\(287\) 3.20094 0.188945
\(288\) 0 0
\(289\) −3.99613 −0.235067
\(290\) −3.26855 7.45743i −0.191936 0.437916i
\(291\) 0 0
\(292\) 1.10940 + 27.2061i 0.0649228 + 1.59212i
\(293\) −12.3397 5.11128i −0.720895 0.298604i −0.00809031 0.999967i \(-0.502575\pi\)
−0.712804 + 0.701363i \(0.752575\pi\)
\(294\) 0 0
\(295\) 0.151875 + 0.151875i 0.00884253 + 0.00884253i
\(296\) 14.8874 16.8287i 0.865312 0.978148i
\(297\) 0 0
\(298\) −0.0757981 3.71918i −0.00439086 0.215446i
\(299\) −9.54439 + 23.0422i −0.551966 + 1.33256i
\(300\) 0 0
\(301\) −11.8911 + 4.92545i −0.685392 + 0.283898i
\(302\) −10.4611 + 26.7866i −0.601971 + 1.54139i
\(303\) 0 0
\(304\) 6.52376 + 12.7101i 0.374164 + 0.728977i
\(305\) 6.23330i 0.356918i
\(306\) 0 0
\(307\) −7.47343 + 3.09560i −0.426531 + 0.176675i −0.585614 0.810590i \(-0.699146\pi\)
0.159082 + 0.987265i \(0.449146\pi\)
\(308\) 4.39484 11.9675i 0.250420 0.681909i
\(309\) 0 0
\(310\) 6.64149 0.135356i 0.377211 0.00768768i
\(311\) −12.5179 + 12.5179i −0.709823 + 0.709823i −0.966498 0.256675i \(-0.917373\pi\)
0.256675 + 0.966498i \(0.417373\pi\)
\(312\) 0 0
\(313\) 2.11020 + 2.11020i 0.119276 + 0.119276i 0.764225 0.644950i \(-0.223122\pi\)
−0.644950 + 0.764225i \(0.723122\pi\)
\(314\) −5.59915 5.37548i −0.315978 0.303356i
\(315\) 0 0
\(316\) −7.86063 7.24467i −0.442195 0.407545i
\(317\) −13.3122 32.1384i −0.747686 1.80507i −0.571278 0.820756i \(-0.693552\pi\)
−0.176408 0.984317i \(-0.556448\pi\)
\(318\) 0 0
\(319\) 24.6562 1.38048
\(320\) 3.52186 + 6.22352i 0.196878 + 0.347906i
\(321\) 0 0
\(322\) −16.5083 + 7.23551i −0.919974 + 0.403219i
\(323\) −6.26294 15.1201i −0.348479 0.841304i
\(324\) 0 0
\(325\) −12.6476 5.23880i −0.701561 0.290596i
\(326\) −11.0537 10.6122i −0.612209 0.587753i
\(327\) 0 0
\(328\) −2.38358 4.88649i −0.131611 0.269811i
\(329\) −9.61262 + 9.61262i −0.529961 + 0.529961i
\(330\) 0 0
\(331\) −1.26744 + 3.05988i −0.0696650 + 0.168186i −0.954877 0.297002i \(-0.904013\pi\)
0.885212 + 0.465188i \(0.154013\pi\)
\(332\) −4.21060 + 11.4657i −0.231087 + 0.629264i
\(333\) 0 0
\(334\) 10.0264 + 3.91567i 0.548620 + 0.214256i
\(335\) 12.9061i 0.705136i
\(336\) 0 0
\(337\) 10.1534i 0.553088i −0.961001 0.276544i \(-0.910811\pi\)
0.961001 0.276544i \(-0.0891892\pi\)
\(338\) −1.22501 + 3.13674i −0.0666317 + 0.170616i
\(339\) 0 0
\(340\) −3.44056 7.43410i −0.186591 0.403171i
\(341\) −7.69795 + 18.5845i −0.416868 + 1.00641i
\(342\) 0 0
\(343\) 13.2198 13.2198i 0.713801 0.713801i
\(344\) 16.3738 + 14.4850i 0.882817 + 0.780978i
\(345\) 0 0
\(346\) 10.2034 10.6280i 0.548540 0.571364i
\(347\) 25.9794 + 10.7610i 1.39465 + 0.577681i 0.948356 0.317208i \(-0.102745\pi\)
0.446289 + 0.894889i \(0.352745\pi\)
\(348\) 0 0
\(349\) 5.71239 + 13.7909i 0.305777 + 0.738212i 0.999833 + 0.0182903i \(0.00582231\pi\)
−0.694055 + 0.719922i \(0.744178\pi\)
\(350\) −3.97148 9.06123i −0.212285 0.484343i
\(351\) 0 0
\(352\) −21.5419 + 2.20248i −1.14819 + 0.117392i
\(353\) 18.8434 1.00293 0.501467 0.865177i \(-0.332794\pi\)
0.501467 + 0.865177i \(0.332794\pi\)
\(354\) 0 0
\(355\) 0.731784 + 1.76668i 0.0388391 + 0.0937658i
\(356\) −14.3852 + 0.586594i −0.762415 + 0.0310894i
\(357\) 0 0
\(358\) 13.5492 14.1129i 0.716096 0.745892i
\(359\) 18.8776 + 18.8776i 0.996324 + 0.996324i 0.999993 0.00366976i \(-0.00116812\pi\)
−0.00366976 + 0.999993i \(0.501168\pi\)
\(360\) 0 0
\(361\) −4.41468 + 4.41468i −0.232352 + 0.232352i
\(362\) −0.618378 30.3419i −0.0325012 1.59474i
\(363\) 0 0
\(364\) 9.84919 4.55829i 0.516238 0.238919i
\(365\) 11.2431 4.65704i 0.588490 0.243760i
\(366\) 0 0
\(367\) 25.6668i 1.33980i −0.742453 0.669898i \(-0.766338\pi\)
0.742453 0.669898i \(-0.233662\pi\)
\(368\) 23.3385 + 19.8134i 1.21661 + 1.03285i
\(369\) 0 0
\(370\) −9.35395 3.65306i −0.486288 0.189913i
\(371\) 12.6180 5.22655i 0.655094 0.271349i
\(372\) 0 0
\(373\) 3.11418 7.51829i 0.161246 0.389282i −0.822521 0.568735i \(-0.807433\pi\)
0.983767 + 0.179453i \(0.0574328\pi\)
\(374\) 24.8006 0.505444i 1.28241 0.0261359i
\(375\) 0 0
\(376\) 21.8325 + 7.51641i 1.12593 + 0.387629i
\(377\) 14.8417 + 14.8417i 0.764384 + 0.764384i
\(378\) 0 0
\(379\) −5.17051 2.14170i −0.265591 0.110012i 0.245914 0.969292i \(-0.420912\pi\)
−0.511505 + 0.859280i \(0.670912\pi\)
\(380\) 4.32728 4.69519i 0.221985 0.240858i
\(381\) 0 0
\(382\) 13.4412 5.89119i 0.687711 0.301419i
\(383\) −33.8865 −1.73152 −0.865758 0.500462i \(-0.833163\pi\)
−0.865758 + 0.500462i \(0.833163\pi\)
\(384\) 0 0
\(385\) −5.69790 −0.290392
\(386\) −11.3477 + 4.97362i −0.577582 + 0.253150i
\(387\) 0 0
\(388\) 25.7727 27.9640i 1.30841 1.41966i
\(389\) 3.06573 + 1.26987i 0.155439 + 0.0643847i 0.459046 0.888412i \(-0.348191\pi\)
−0.303608 + 0.952797i \(0.598191\pi\)
\(390\) 0 0
\(391\) −24.7984 24.7984i −1.25411 1.25411i
\(392\) −11.3046 3.89189i −0.570966 0.196570i
\(393\) 0 0
\(394\) 6.65799 0.135692i 0.335425 0.00683606i
\(395\) −1.82834 + 4.41400i −0.0919938 + 0.222093i
\(396\) 0 0
\(397\) 21.9201 9.07961i 1.10014 0.455693i 0.242608 0.970124i \(-0.421997\pi\)
0.857531 + 0.514432i \(0.171997\pi\)
\(398\) 6.48295 + 2.53183i 0.324961 + 0.126909i
\(399\) 0 0
\(400\) −10.8753 + 12.8102i −0.543767 + 0.640512i
\(401\) 7.03254i 0.351188i −0.984463 0.175594i \(-0.943815\pi\)
0.984463 0.175594i \(-0.0561846\pi\)
\(402\) 0 0
\(403\) −15.8206 + 6.55310i −0.788079 + 0.326433i
\(404\) 6.98078 3.23076i 0.347307 0.160736i
\(405\) 0 0
\(406\) 0.309079 + 15.1656i 0.0153394 + 0.752655i
\(407\) 21.5023 21.5023i 1.06583 1.06583i
\(408\) 0 0
\(409\) −5.52966 5.52966i −0.273424 0.273424i 0.557053 0.830477i \(-0.311932\pi\)
−0.830477 + 0.557053i \(0.811932\pi\)
\(410\) −1.68283 + 1.75285i −0.0831093 + 0.0865673i
\(411\) 0 0
\(412\) 9.34166 0.380930i 0.460231 0.0187671i
\(413\) −0.153125 0.369676i −0.00753478 0.0181906i
\(414\) 0 0
\(415\) 5.45903 0.267973
\(416\) −14.2928 11.6413i −0.700762 0.570760i
\(417\) 0 0
\(418\) 7.76176 + 17.7090i 0.379640 + 0.866177i
\(419\) 7.37792 + 17.8119i 0.360435 + 0.870167i 0.995236 + 0.0974917i \(0.0310819\pi\)
−0.634801 + 0.772675i \(0.718918\pi\)
\(420\) 0 0
\(421\) −5.73622 2.37602i −0.279566 0.115800i 0.238495 0.971144i \(-0.423346\pi\)
−0.518061 + 0.855344i \(0.673346\pi\)
\(422\) −5.04751 + 5.25753i −0.245709 + 0.255932i
\(423\) 0 0
\(424\) −17.3748 15.3705i −0.843793 0.746456i
\(425\) 13.6116 13.6116i 0.660257 0.660257i
\(426\) 0 0
\(427\) −4.44387 + 10.7284i −0.215054 + 0.519186i
\(428\) −10.9531 23.6666i −0.529439 1.14397i
\(429\) 0 0
\(430\) 3.55432 9.10111i 0.171404 0.438895i
\(431\) 16.9436i 0.816146i −0.912949 0.408073i \(-0.866201\pi\)
0.912949 0.408073i \(-0.133799\pi\)
\(432\) 0 0
\(433\) 26.4587i 1.27152i 0.771886 + 0.635761i \(0.219314\pi\)
−0.771886 + 0.635761i \(0.780686\pi\)
\(434\) −11.5275 4.50191i −0.553337 0.216098i
\(435\) 0 0
\(436\) −3.10838 + 8.46432i −0.148864 + 0.405367i
\(437\) 10.4611 25.2554i 0.500424 1.20813i
\(438\) 0 0
\(439\) 9.68299 9.68299i 0.462144 0.462144i −0.437214 0.899358i \(-0.644035\pi\)
0.899358 + 0.437214i \(0.144035\pi\)
\(440\) 4.24295 + 8.69831i 0.202274 + 0.414676i
\(441\) 0 0
\(442\) 15.2328 + 14.6243i 0.724551 + 0.695608i
\(443\) −10.4314 4.32084i −0.495612 0.205289i 0.120855 0.992670i \(-0.461437\pi\)
−0.616467 + 0.787381i \(0.711437\pi\)
\(444\) 0 0
\(445\) 2.46240 + 5.94476i 0.116729 + 0.281809i
\(446\) 16.3261 7.15565i 0.773065 0.338830i
\(447\) 0 0
\(448\) −1.62474 13.2224i −0.0767620 0.624701i
\(449\) 23.6353 1.11542 0.557708 0.830037i \(-0.311681\pi\)
0.557708 + 0.830037i \(0.311681\pi\)
\(450\) 0 0
\(451\) −2.81585 6.79805i −0.132593 0.320108i
\(452\) −23.1888 21.3717i −1.09071 1.00524i
\(453\) 0 0
\(454\) −4.91721 4.72079i −0.230776 0.221557i
\(455\) −3.42982 3.42982i −0.160792 0.160792i
\(456\) 0 0
\(457\) 23.4812 23.4812i 1.09840 1.09840i 0.103807 0.994597i \(-0.466898\pi\)
0.994597 0.103807i \(-0.0331025\pi\)
\(458\) −29.6834 + 0.604958i −1.38702 + 0.0282678i
\(459\) 0 0
\(460\) 4.71675 12.8440i 0.219920 0.598855i
\(461\) −25.8692 + 10.7154i −1.20485 + 0.499064i −0.892562 0.450924i \(-0.851095\pi\)
−0.312286 + 0.949988i \(0.601095\pi\)
\(462\) 0 0
\(463\) 19.5222i 0.907272i −0.891187 0.453636i \(-0.850127\pi\)
0.891187 0.453636i \(-0.149873\pi\)
\(464\) 22.9213 11.7649i 1.06410 0.546171i
\(465\) 0 0
\(466\) −9.76103 + 24.9939i −0.452171 + 1.15782i
\(467\) 5.42932 2.24890i 0.251239 0.104067i −0.253510 0.967333i \(-0.581585\pi\)
0.504749 + 0.863266i \(0.331585\pi\)
\(468\) 0 0
\(469\) 9.20107 22.2133i 0.424866 1.02572i
\(470\) −0.210276 10.3176i −0.00969930 0.475915i
\(471\) 0 0
\(472\) −0.450316 + 0.509037i −0.0207275 + 0.0234303i
\(473\) 20.9211 + 20.9211i 0.961951 + 0.961951i
\(474\) 0 0
\(475\) 13.8624 + 5.74198i 0.636049 + 0.263460i
\(476\) 0.621779 + 15.2481i 0.0284992 + 0.698893i
\(477\) 0 0
\(478\) −2.59946 5.93087i −0.118897 0.271272i
\(479\) −14.2300 −0.650187 −0.325094 0.945682i \(-0.605396\pi\)
−0.325094 + 0.945682i \(0.605396\pi\)
\(480\) 0 0
\(481\) 25.8863 1.18031
\(482\) 8.28346 + 18.8993i 0.377301 + 0.860841i
\(483\) 0 0
\(484\) −7.30048 + 0.297696i −0.331840 + 0.0135316i
\(485\) −15.7027 6.50427i −0.713023 0.295344i
\(486\) 0 0
\(487\) 17.2727 + 17.2727i 0.782700 + 0.782700i 0.980286 0.197586i \(-0.0633102\pi\)
−0.197586 + 0.980286i \(0.563310\pi\)
\(488\) 19.6870 1.20502i 0.891188 0.0545485i
\(489\) 0 0
\(490\) 0.108878 + 5.34230i 0.00491860 + 0.241341i
\(491\) 2.16195 5.21940i 0.0975673 0.235548i −0.867558 0.497335i \(-0.834312\pi\)
0.965126 + 0.261787i \(0.0843118\pi\)
\(492\) 0 0
\(493\) −27.2674 + 11.2945i −1.22806 + 0.508680i
\(494\) −5.98771 + 15.3320i −0.269400 + 0.689819i
\(495\) 0 0
\(496\) 1.71143 + 20.9500i 0.0768453 + 0.940683i
\(497\) 3.56243i 0.159797i
\(498\) 0 0
\(499\) −14.2581 + 5.90591i −0.638281 + 0.264385i −0.678267 0.734816i \(-0.737269\pi\)
0.0399860 + 0.999200i \(0.487269\pi\)
\(500\) 15.4407 + 5.67033i 0.690528 + 0.253585i
\(501\) 0 0
\(502\) 2.92792 0.0596719i 0.130679 0.00266329i
\(503\) 9.06568 9.06568i 0.404219 0.404219i −0.475498 0.879717i \(-0.657732\pi\)
0.879717 + 0.475498i \(0.157732\pi\)
\(504\) 0 0
\(505\) −2.43094 2.43094i −0.108176 0.108176i
\(506\) 29.8888 + 28.6949i 1.32872 + 1.27564i
\(507\) 0 0
\(508\) 7.62490 8.27319i 0.338300 0.367063i
\(509\) −8.46300 20.4315i −0.375116 0.905610i −0.992866 0.119236i \(-0.961956\pi\)
0.617750 0.786375i \(-0.288044\pi\)
\(510\) 0 0
\(511\) −22.6711 −1.00291
\(512\) −18.9752 + 12.3264i −0.838595 + 0.544755i
\(513\) 0 0
\(514\) 27.7202 12.1496i 1.22269 0.535895i
\(515\) −1.59907 3.86049i −0.0704633 0.170114i
\(516\) 0 0
\(517\) 28.8712 + 11.9588i 1.26975 + 0.525949i
\(518\) 13.4952 + 12.9561i 0.592945 + 0.569259i
\(519\) 0 0
\(520\) −2.68188 + 7.78992i −0.117608 + 0.341610i
\(521\) 6.25345 6.25345i 0.273969 0.273969i −0.556727 0.830696i \(-0.687943\pi\)
0.830696 + 0.556727i \(0.187943\pi\)
\(522\) 0 0
\(523\) 0.570636 1.37764i 0.0249522 0.0602399i −0.910912 0.412600i \(-0.864621\pi\)
0.935865 + 0.352360i \(0.114621\pi\)
\(524\) −13.5923 4.99156i −0.593784 0.218057i
\(525\) 0 0
\(526\) −7.72904 3.01847i −0.337002 0.131612i
\(527\) 24.0790i 1.04890i
\(528\) 0 0
\(529\) 35.5787i 1.54690i
\(530\) −3.77159 + 9.65747i −0.163827 + 0.419493i
\(531\) 0 0
\(532\) −10.7952 + 4.99611i −0.468032 + 0.216609i
\(533\) 2.39707 5.78703i 0.103829 0.250664i
\(534\) 0 0
\(535\) −8.24152 + 8.24152i −0.356312 + 0.356312i
\(536\) −40.7621 + 2.49499i −1.76065 + 0.107767i
\(537\) 0 0
\(538\) −29.6873 + 30.9226i −1.27991 + 1.33317i
\(539\) −14.9491 6.19211i −0.643902 0.266713i
\(540\) 0 0
\(541\) −12.3150 29.7310i −0.529463 1.27824i −0.931876 0.362778i \(-0.881828\pi\)
0.402413 0.915458i \(-0.368172\pi\)
\(542\) 5.86840 + 13.3892i 0.252069 + 0.575115i
\(543\) 0 0
\(544\) 22.8144 12.3037i 0.978159 0.527515i
\(545\) 4.03000 0.172626
\(546\) 0 0
\(547\) 12.9326 + 31.2221i 0.552959 + 1.33496i 0.915246 + 0.402895i \(0.131996\pi\)
−0.362287 + 0.932067i \(0.618004\pi\)
\(548\) 0.361608 + 8.86781i 0.0154471 + 0.378814i
\(549\) 0 0
\(550\) −15.7503 + 16.4056i −0.671593 + 0.699538i
\(551\) −16.2672 16.2672i −0.693006 0.693006i
\(552\) 0 0
\(553\) 6.29369 6.29369i 0.267635 0.267635i
\(554\) 0.481551 + 23.6282i 0.0204591 + 1.00387i
\(555\) 0 0
\(556\) −7.91621 17.1047i −0.335722 0.725402i
\(557\) 2.78310 1.15280i 0.117924 0.0488456i −0.322941 0.946419i \(-0.604672\pi\)
0.440865 + 0.897573i \(0.354672\pi\)
\(558\) 0 0
\(559\) 25.1866i 1.06528i
\(560\) −5.29699 + 2.71880i −0.223839 + 0.114890i
\(561\) 0 0
\(562\) −14.6361 5.71592i −0.617386 0.241112i
\(563\) −35.0055 + 14.4998i −1.47531 + 0.611092i −0.968062 0.250709i \(-0.919336\pi\)
−0.507245 + 0.861802i \(0.669336\pi\)
\(564\) 0 0
\(565\) −5.39358 + 13.0213i −0.226910 + 0.547808i
\(566\) 10.3585 0.211109i 0.435399 0.00887357i
\(567\) 0 0
\(568\) −5.43834 + 2.65277i −0.228188 + 0.111308i
\(569\) −11.2443 11.2443i −0.471387 0.471387i 0.430976 0.902363i \(-0.358169\pi\)
−0.902363 + 0.430976i \(0.858169\pi\)
\(570\) 0 0
\(571\) −17.4655 7.23445i −0.730909 0.302752i −0.0139834 0.999902i \(-0.504451\pi\)
−0.716925 + 0.697150i \(0.754451\pi\)
\(572\) −18.3450 16.9075i −0.767044 0.706938i
\(573\) 0 0
\(574\) 4.14606 1.81719i 0.173053 0.0758482i
\(575\) 32.1531 1.34088
\(576\) 0 0
\(577\) −1.06924 −0.0445129 −0.0222564 0.999752i \(-0.507085\pi\)
−0.0222564 + 0.999752i \(0.507085\pi\)
\(578\) −5.17605 + 2.26863i −0.215295 + 0.0943626i
\(579\) 0 0
\(580\) −8.46726 7.80377i −0.351584 0.324034i
\(581\) −9.39581 3.89187i −0.389804 0.161462i
\(582\) 0 0
\(583\) −22.2000 22.2000i −0.919429 0.919429i
\(584\) 16.8821 + 34.6093i 0.698585 + 1.43214i
\(585\) 0 0
\(586\) −18.8849 + 0.384881i −0.780129 + 0.0158993i
\(587\) 5.82611 14.0655i 0.240469 0.580544i −0.756860 0.653577i \(-0.773268\pi\)
0.997330 + 0.0730327i \(0.0232677\pi\)
\(588\) 0 0
\(589\) 17.3402 7.18253i 0.714488 0.295951i
\(590\) 0.282939 + 0.110498i 0.0116484 + 0.00454914i
\(591\) 0 0
\(592\) 9.72935 30.2493i 0.399874 1.24324i
\(593\) 41.5874i 1.70779i 0.520447 + 0.853894i \(0.325765\pi\)
−0.520447 + 0.853894i \(0.674235\pi\)
\(594\) 0 0
\(595\) 6.30134 2.61010i 0.258330 0.107004i
\(596\) −2.20958 4.77429i −0.0905079 0.195562i
\(597\) 0 0
\(598\) 0.718695 + 35.2641i 0.0293896 + 1.44206i
\(599\) −2.97009 + 2.97009i −0.121354 + 0.121354i −0.765176 0.643821i \(-0.777348\pi\)
0.643821 + 0.765176i \(0.277348\pi\)
\(600\) 0 0
\(601\) 24.7211 + 24.7211i 1.00840 + 1.00840i 0.999964 + 0.00843176i \(0.00268394\pi\)
0.00843176 + 0.999964i \(0.497316\pi\)
\(602\) −12.6059 + 13.1304i −0.513778 + 0.535156i
\(603\) 0 0
\(604\) 1.65698 + 40.6345i 0.0674215 + 1.65340i
\(605\) 1.24967 + 3.01696i 0.0508062 + 0.122657i
\(606\) 0 0
\(607\) −6.96020 −0.282506 −0.141253 0.989974i \(-0.545113\pi\)
−0.141253 + 0.989974i \(0.545113\pi\)
\(608\) 15.6656 + 12.7594i 0.635325 + 0.517462i
\(609\) 0 0
\(610\) −3.53869 8.07378i −0.143277 0.326898i
\(611\) 10.1803 + 24.5774i 0.411850 + 0.994294i
\(612\) 0 0
\(613\) 7.35571 + 3.04684i 0.297094 + 0.123061i 0.526252 0.850329i \(-0.323597\pi\)
−0.229157 + 0.973389i \(0.573597\pi\)
\(614\) −7.92268 + 8.25233i −0.319733 + 0.333037i
\(615\) 0 0
\(616\) −1.10151 17.9960i −0.0443812 0.725079i
\(617\) 9.81719 9.81719i 0.395225 0.395225i −0.481320 0.876545i \(-0.659842\pi\)
0.876545 + 0.481320i \(0.159842\pi\)
\(618\) 0 0
\(619\) −4.68397 + 11.3081i −0.188265 + 0.454511i −0.989626 0.143670i \(-0.954110\pi\)
0.801361 + 0.598181i \(0.204110\pi\)
\(620\) 8.52564 3.94574i 0.342398 0.158465i
\(621\) 0 0
\(622\) −9.10747 + 23.3204i −0.365176 + 0.935063i
\(623\) 11.9873i 0.480262i
\(624\) 0 0
\(625\) 13.6535i 0.546138i
\(626\) 3.93124 + 1.53529i 0.157124 + 0.0613626i
\(627\) 0 0
\(628\) −10.3041 3.78400i −0.411177 0.150998i
\(629\) −13.9297 + 33.6292i −0.555412 + 1.34088i
\(630\) 0 0
\(631\) −29.7384 + 29.7384i −1.18387 + 1.18387i −0.205130 + 0.978735i \(0.565762\pi\)
−0.978735 + 0.205130i \(0.934238\pi\)
\(632\) −14.2944 4.92123i −0.568602 0.195756i
\(633\) 0 0
\(634\) −35.4880 34.0703i −1.40941 1.35311i
\(635\) −4.64567 1.92430i −0.184358 0.0763635i
\(636\) 0 0
\(637\) −5.27121 12.7258i −0.208853 0.504215i
\(638\) 31.9363 13.9975i 1.26437 0.554166i
\(639\) 0 0
\(640\) 8.09487 + 6.06173i 0.319978 + 0.239611i
\(641\) −10.7253 −0.423623 −0.211811 0.977311i \(-0.567936\pi\)
−0.211811 + 0.977311i \(0.567936\pi\)
\(642\) 0 0
\(643\) −6.96903 16.8247i −0.274832 0.663502i 0.724846 0.688911i \(-0.241911\pi\)
−0.999677 + 0.0254092i \(0.991911\pi\)
\(644\) −17.2750 + 18.7438i −0.680732 + 0.738609i
\(645\) 0 0
\(646\) −16.6959 16.0290i −0.656893 0.630652i
\(647\) −33.4123 33.4123i −1.31357 1.31357i −0.918764 0.394808i \(-0.870811\pi\)
−0.394808 0.918764i \(-0.629189\pi\)
\(648\) 0 0
\(649\) −0.650403 + 0.650403i −0.0255306 + 0.0255306i
\(650\) −19.3560 + 0.394482i −0.759207 + 0.0154729i
\(651\) 0 0
\(652\) −20.3421 7.47029i −0.796657 0.292559i
\(653\) 10.9408 4.53181i 0.428145 0.177343i −0.158196 0.987408i \(-0.550568\pi\)
0.586341 + 0.810064i \(0.300568\pi\)
\(654\) 0 0
\(655\) 6.47154i 0.252864i
\(656\) −5.86146 4.97613i −0.228852 0.194285i
\(657\) 0 0
\(658\) −6.99374 + 17.9080i −0.272644 + 0.698128i
\(659\) 0.739338 0.306244i 0.0288005 0.0119296i −0.368237 0.929732i \(-0.620038\pi\)
0.397037 + 0.917803i \(0.370038\pi\)
\(660\) 0 0
\(661\) 3.14127 7.58370i 0.122181 0.294972i −0.850941 0.525262i \(-0.823967\pi\)
0.973122 + 0.230290i \(0.0739674\pi\)
\(662\) 0.0954387 + 4.68289i 0.00370933 + 0.182006i
\(663\) 0 0
\(664\) 1.05533 + 17.2416i 0.0409549 + 0.669102i
\(665\) 3.75926 + 3.75926i 0.145778 + 0.145778i
\(666\) 0 0
\(667\) −45.5453 18.8655i −1.76352 0.730475i
\(668\) 15.2098 0.620218i 0.588484 0.0239969i
\(669\) 0 0
\(670\) 7.32688 + 16.7168i 0.283062 + 0.645827i
\(671\) 26.6940 1.03051
\(672\) 0 0
\(673\) 32.0221 1.23436 0.617180 0.786822i \(-0.288275\pi\)
0.617180 + 0.786822i \(0.288275\pi\)
\(674\) −5.76412 13.1513i −0.222026 0.506568i
\(675\) 0 0
\(676\) 0.194034 + 4.75835i 0.00746284 + 0.183013i
\(677\) 22.8528 + 9.46594i 0.878304 + 0.363805i 0.775839 0.630931i \(-0.217327\pi\)
0.102465 + 0.994737i \(0.467327\pi\)
\(678\) 0 0
\(679\) 22.3897 + 22.3897i 0.859236 + 0.859236i
\(680\) −8.67682 7.67589i −0.332741 0.294357i
\(681\) 0 0
\(682\) 0.579658 + 28.4420i 0.0221962 + 1.08910i
\(683\) −6.46834 + 15.6160i −0.247504 + 0.597528i −0.997991 0.0633577i \(-0.979819\pi\)
0.750487 + 0.660885i \(0.229819\pi\)
\(684\) 0 0
\(685\) 3.66467 1.51796i 0.140020 0.0579981i
\(686\) 9.61815 24.6280i 0.367223 0.940303i
\(687\) 0 0
\(688\) 29.4316 + 9.46637i 1.12207 + 0.360902i
\(689\) 26.7263i 1.01819i
\(690\) 0 0
\(691\) 23.6307 9.78817i 0.898955 0.372359i 0.115137 0.993350i \(-0.463269\pi\)
0.783818 + 0.620990i \(0.213269\pi\)
\(692\) 7.18256 19.5586i 0.273040 0.743506i
\(693\) 0 0
\(694\) 39.7592 0.810306i 1.50924 0.0307588i
\(695\) −5.95644 + 5.95644i −0.225941 + 0.225941i
\(696\) 0 0
\(697\) 6.22811 + 6.22811i 0.235907 + 0.235907i
\(698\) 15.2283 + 14.6199i 0.576398 + 0.553373i
\(699\) 0 0
\(700\) −10.2882 9.48205i −0.388859 0.358388i
\(701\) 9.69117 + 23.3965i 0.366030 + 0.883675i 0.994392 + 0.105754i \(0.0337257\pi\)
−0.628362 + 0.777921i \(0.716274\pi\)
\(702\) 0 0
\(703\) −28.3727 −1.07010
\(704\) −26.6521 + 15.0823i −1.00449 + 0.568434i
\(705\) 0 0
\(706\) 24.4072 10.6975i 0.918577 0.402606i
\(707\) 2.45094 + 5.91709i 0.0921771 + 0.222535i
\(708\) 0 0
\(709\) −11.9720 4.95898i −0.449619 0.186238i 0.146372 0.989230i \(-0.453240\pi\)
−0.595991 + 0.802991i \(0.703240\pi\)
\(710\) 1.95081 + 1.87288i 0.0732126 + 0.0702881i
\(711\) 0 0
\(712\) −18.2996 + 8.92637i −0.685808 + 0.334530i
\(713\) 28.4396 28.4396i 1.06507 1.06507i
\(714\) 0 0
\(715\) −4.26695 + 10.3013i −0.159575 + 0.385248i
\(716\) 9.53776 25.9719i 0.356443 0.970617i
\(717\) 0 0
\(718\) 35.1685 + 13.7346i 1.31248 + 0.512570i
\(719\) 18.7152i 0.697960i 0.937130 + 0.348980i \(0.113472\pi\)
−0.937130 + 0.348980i \(0.886528\pi\)
\(720\) 0 0
\(721\) 7.78449i 0.289910i
\(722\) −3.21194 + 8.22442i −0.119536 + 0.306081i
\(723\) 0 0
\(724\) −18.0263 38.9497i −0.669941 1.44756i
\(725\) 10.3550 24.9993i 0.384576 0.928449i
\(726\) 0 0
\(727\) 37.4952 37.4952i 1.39062 1.39062i 0.566690 0.823931i \(-0.308224\pi\)
0.823931 0.566690i \(-0.191776\pi\)
\(728\) 10.1695 11.4956i 0.376908 0.426057i
\(729\) 0 0
\(730\) 11.9189 12.4149i 0.441139 0.459495i
\(731\) −32.7202 13.5532i −1.21020 0.501282i
\(732\) 0 0
\(733\) −11.1057 26.8115i −0.410198 0.990305i −0.985084 0.172072i \(-0.944954\pi\)
0.574887 0.818233i \(-0.305046\pi\)
\(734\) −14.5712 33.2453i −0.537833 1.22711i
\(735\) 0 0
\(736\) 41.4778 + 12.4142i 1.52889 + 0.457592i
\(737\) −55.2701 −2.03590
\(738\) 0 0
\(739\) 0.383327 + 0.925433i 0.0141009 + 0.0340426i 0.930773 0.365597i \(-0.119135\pi\)
−0.916672 + 0.399640i \(0.869135\pi\)
\(740\) −14.1897 + 0.578621i −0.521624 + 0.0212705i
\(741\) 0 0
\(742\) 13.3765 13.9331i 0.491067 0.511500i
\(743\) 34.4148 + 34.4148i 1.26256 + 1.26256i 0.949849 + 0.312708i \(0.101236\pi\)
0.312708 + 0.949849i \(0.398764\pi\)
\(744\) 0 0
\(745\) −1.66257 + 1.66257i −0.0609118 + 0.0609118i
\(746\) −0.234498 11.5061i −0.00858559 0.421269i
\(747\) 0 0
\(748\) 31.8364 14.7341i 1.16405 0.538733i
\(749\) 20.0605 8.30931i 0.732993 0.303616i
\(750\) 0 0
\(751\) 20.2742i 0.739816i 0.929068 + 0.369908i \(0.120611\pi\)
−0.929068 + 0.369908i \(0.879389\pi\)
\(752\) 32.5460 2.65871i 1.18683 0.0969533i
\(753\) 0 0
\(754\) 27.6496 + 10.7982i 1.00694 + 0.393246i
\(755\) 16.7924 6.95566i 0.611139 0.253142i
\(756\) 0 0
\(757\) −18.5068 + 44.6794i −0.672641 + 1.62390i 0.104465 + 0.994529i \(0.466687\pi\)
−0.777106 + 0.629370i \(0.783313\pi\)
\(758\) −7.91303 + 0.161270i −0.287414 + 0.00585760i
\(759\) 0 0
\(760\) 2.93948 8.53814i 0.106626 0.309711i
\(761\) −13.1682 13.1682i −0.477345 0.477345i 0.426936 0.904282i \(-0.359593\pi\)
−0.904282 + 0.426936i \(0.859593\pi\)
\(762\) 0 0
\(763\) −6.93624 2.87308i −0.251109 0.104013i
\(764\) 14.0654 15.2613i 0.508869 0.552134i
\(765\) 0 0
\(766\) −43.8919 + 19.2376i −1.58588 + 0.695081i
\(767\) −0.783013 −0.0282730
\(768\) 0 0
\(769\) −40.4343 −1.45810 −0.729049 0.684461i \(-0.760037\pi\)
−0.729049 + 0.684461i \(0.760037\pi\)
\(770\) −7.38029 + 3.23474i −0.265967 + 0.116572i
\(771\) 0 0
\(772\) −11.8747 + 12.8843i −0.427379 + 0.463716i
\(773\) −2.36151 0.978168i −0.0849375 0.0351823i 0.339810 0.940494i \(-0.389637\pi\)
−0.424748 + 0.905312i \(0.639637\pi\)
\(774\) 0 0
\(775\) 15.6101 + 15.6101i 0.560732 + 0.560732i
\(776\) 17.5072 50.8521i 0.628470 1.82548i
\(777\) 0 0
\(778\) 4.69184 0.0956211i 0.168211 0.00342818i
\(779\) −2.62731 + 6.34288i −0.0941330 + 0.227257i
\(780\) 0 0
\(781\) −7.56578 + 3.13385i −0.270725 + 0.112138i
\(782\) −46.1988 18.0423i −1.65206 0.645191i
\(783\) 0 0
\(784\) −16.8518 + 1.37664i −0.601851 + 0.0491658i
\(785\) 4.90594i 0.175101i
\(786\) 0 0
\(787\) 27.5997 11.4322i 0.983825 0.407514i 0.167984 0.985790i \(-0.446274\pi\)
0.815841 + 0.578276i \(0.196274\pi\)
\(788\) 8.54682 3.95554i 0.304468 0.140910i
\(789\) 0 0
\(790\) 0.137674 + 6.75526i 0.00489824 + 0.240341i
\(791\) 18.5663 18.5663i 0.660142 0.660142i
\(792\) 0 0
\(793\) 16.0683 + 16.0683i 0.570602 + 0.570602i
\(794\) 23.2378 24.2047i 0.824679 0.858993i
\(795\) 0 0
\(796\) 9.83447 0.401026i 0.348574 0.0142140i
\(797\) 21.0345 + 50.7818i 0.745080 + 1.79878i 0.583842 + 0.811867i \(0.301549\pi\)
0.161238 + 0.986916i \(0.448451\pi\)
\(798\) 0 0
\(799\) −37.4069 −1.32336
\(800\) −6.81398 + 22.7666i −0.240911 + 0.804922i
\(801\) 0 0
\(802\) −3.99242 9.10900i −0.140977 0.321650i
\(803\) 19.9437 + 48.1483i 0.703796 + 1.69911i
\(804\) 0 0
\(805\) 10.5253 + 4.35971i 0.370967 + 0.153659i
\(806\) −16.7716 + 17.4694i −0.590754 + 0.615335i
\(807\) 0 0
\(808\) 7.20783 8.14773i 0.253571 0.286636i
\(809\) −10.8210 + 10.8210i −0.380446 + 0.380446i −0.871263 0.490817i \(-0.836698\pi\)
0.490817 + 0.871263i \(0.336698\pi\)
\(810\) 0 0
\(811\) 9.28572 22.4177i 0.326066 0.787192i −0.672811 0.739814i \(-0.734913\pi\)
0.998877 0.0473779i \(-0.0150865\pi\)
\(812\) 9.00994 + 19.4680i 0.316187 + 0.683192i
\(813\) 0 0
\(814\) 15.6441 40.0581i 0.548327 1.40403i
\(815\) 9.68520i 0.339258i
\(816\) 0 0
\(817\) 27.6058i 0.965805i
\(818\) −10.3016 4.02315i −0.360187 0.140666i
\(819\) 0 0
\(820\) −1.18461 + 3.22577i −0.0413683 + 0.112649i
\(821\) −2.83930 + 6.85468i −0.0990924 + 0.239230i −0.965650 0.259847i \(-0.916328\pi\)
0.866557 + 0.499078i \(0.166328\pi\)
\(822\) 0 0
\(823\) 25.2545 25.2545i 0.880317 0.880317i −0.113250 0.993567i \(-0.536126\pi\)
0.993567 + 0.113250i \(0.0361260\pi\)
\(824\) 11.8837 5.79673i 0.413987 0.201939i
\(825\) 0 0
\(826\) −0.408204 0.391898i −0.0142032 0.0136359i
\(827\) 30.9624 + 12.8251i 1.07667 + 0.445971i 0.849339 0.527847i \(-0.177001\pi\)
0.227330 + 0.973818i \(0.427001\pi\)
\(828\) 0 0
\(829\) −9.26963 22.3789i −0.321948 0.777251i −0.999141 0.0414451i \(-0.986804\pi\)
0.677193 0.735805i \(-0.263196\pi\)
\(830\) 7.07089 3.09913i 0.245434 0.107572i
\(831\) 0 0
\(832\) −25.1218 6.96440i −0.870941 0.241447i
\(833\) 19.3687 0.671087
\(834\) 0 0
\(835\) −2.60355 6.28552i −0.0900994 0.217519i
\(836\) 20.1071 + 18.5315i 0.695417 + 0.640925i
\(837\) 0 0
\(838\) 19.6683 + 18.8826i 0.679429 + 0.652288i
\(839\) −23.7415 23.7415i −0.819648 0.819648i 0.166409 0.986057i \(-0.446783\pi\)
−0.986057 + 0.166409i \(0.946783\pi\)
\(840\) 0 0
\(841\) −8.83001 + 8.83001i −0.304483 + 0.304483i
\(842\) −8.77880 + 0.178915i −0.302538 + 0.00616581i
\(843\) 0 0
\(844\) −3.55312 + 9.67539i −0.122304 + 0.333041i
\(845\) 1.96641 0.814514i 0.0676466 0.0280201i
\(846\) 0 0
\(847\) 6.08356i 0.209034i
\(848\) −31.2308 10.0451i −1.07247 0.344948i
\(849\) 0 0
\(850\) 9.90320 25.3579i 0.339677 0.869770i
\(851\) −56.1716 + 23.2670i −1.92554 + 0.797584i
\(852\) 0 0
\(853\) −7.82863 + 18.9000i −0.268047 + 0.647123i −0.999391 0.0348853i \(-0.988893\pi\)
0.731344 + 0.682009i \(0.238893\pi\)
\(854\) 0.334624 + 16.4190i 0.0114506 + 0.561846i
\(855\) 0 0
\(856\) −27.6229 24.4364i −0.944130 0.835218i
\(857\) 19.1000 + 19.1000i 0.652445 + 0.652445i 0.953581 0.301136i \(-0.0973659\pi\)
−0.301136 + 0.953581i \(0.597366\pi\)
\(858\) 0 0
\(859\) 23.7460 + 9.83590i 0.810202 + 0.335597i 0.749035 0.662531i \(-0.230518\pi\)
0.0611672 + 0.998128i \(0.480518\pi\)
\(860\) −0.562981 13.8062i −0.0191975 0.470786i
\(861\) 0 0
\(862\) −9.61901 21.9465i −0.327625 0.747500i
\(863\) −7.14216 −0.243122 −0.121561 0.992584i \(-0.538790\pi\)
−0.121561 + 0.992584i \(0.538790\pi\)
\(864\) 0 0
\(865\) −9.31217 −0.316623
\(866\) 15.0207 + 34.2709i 0.510426 + 1.16457i
\(867\) 0 0
\(868\) −17.4869 + 0.713074i −0.593544 + 0.0242033i
\(869\) −18.9029 7.82983i −0.641236 0.265609i
\(870\) 0 0
\(871\) −33.2695 33.2695i −1.12730 1.12730i
\(872\) 0.779076 + 12.7282i 0.0263828 + 0.431031i
\(873\) 0 0
\(874\) −0.787725 38.6513i −0.0266452 1.30740i
\(875\) −5.24110 + 12.6531i −0.177182 + 0.427754i
\(876\) 0 0
\(877\) 13.2121 5.47264i 0.446141 0.184798i −0.148290 0.988944i \(-0.547377\pi\)
0.594432 + 0.804146i \(0.297377\pi\)
\(878\) 7.04493 18.0391i 0.237755 0.608791i
\(879\) 0 0
\(880\) 10.4338 + 8.85787i 0.351724 + 0.298599i
\(881\) 8.29862i 0.279588i −0.990181 0.139794i \(-0.955356\pi\)
0.990181 0.139794i \(-0.0446440\pi\)
\(882\) 0 0
\(883\) 23.1211 9.57707i 0.778087 0.322294i 0.0419435 0.999120i \(-0.486645\pi\)
0.736143 + 0.676826i \(0.236645\pi\)
\(884\) 28.0328 + 10.2946i 0.942847 + 0.346245i
\(885\) 0 0
\(886\) −15.9644 + 0.325360i −0.536336 + 0.0109307i
\(887\) −27.8541 + 27.8541i −0.935249 + 0.935249i −0.998027 0.0627784i \(-0.980004\pi\)
0.0627784 + 0.998027i \(0.480004\pi\)
\(888\) 0 0
\(889\) 6.62401 + 6.62401i 0.222162 + 0.222162i
\(890\) 6.56434 + 6.30212i 0.220037 + 0.211247i
\(891\) 0 0
\(892\) 17.0844 18.5369i 0.572026 0.620661i
\(893\) −11.1581 26.9380i −0.373392 0.901447i
\(894\) 0 0
\(895\) −12.3657 −0.413339
\(896\) −9.61093 16.2042i −0.321079 0.541343i
\(897\) 0 0
\(898\) 30.6139 13.4179i 1.02160 0.447761i
\(899\) −12.9529 31.2711i −0.432003 1.04295i
\(900\) 0 0
\(901\) 34.7204 + 14.3817i 1.15670 + 0.479123i
\(902\) −7.50656 7.20670i −0.249941 0.239957i
\(903\) 0 0
\(904\) −42.1684 14.5176i −1.40250 0.482848i
\(905\) −13.5636 + 13.5636i −0.450870 + 0.450870i
\(906\) 0 0
\(907\) −5.14391 + 12.4185i −0.170801 + 0.412349i −0.985981 0.166858i \(-0.946638\pi\)
0.815180 + 0.579207i \(0.196638\pi\)
\(908\) −9.04911 3.32313i −0.300305 0.110282i
\(909\) 0 0
\(910\) −6.38966 2.49539i −0.211815 0.0827215i
\(911\) 43.4302i 1.43891i 0.694541 + 0.719454i \(0.255608\pi\)
−0.694541 + 0.719454i \(0.744392\pi\)
\(912\) 0 0
\(913\) 23.3782i 0.773705i
\(914\) 17.0839 43.7448i 0.565086 1.44695i
\(915\) 0 0
\(916\) −38.1044 + 17.6351i −1.25901 + 0.582679i
\(917\) 4.61371 11.1385i 0.152358 0.367825i
\(918\) 0 0
\(919\) 13.6438 13.6438i 0.450068 0.450068i −0.445309 0.895377i \(-0.646906\pi\)
0.895377 + 0.445309i \(0.146906\pi\)
\(920\) −1.18219 19.3141i −0.0389758 0.636768i
\(921\) 0 0
\(922\) −27.4242 + 28.5653i −0.903170 + 0.940749i
\(923\) −6.44058 2.66778i −0.211994 0.0878110i
\(924\) 0 0
\(925\) −12.7710 30.8319i −0.419907 1.01375i
\(926\) −11.0829 25.2864i −0.364205 0.830961i
\(927\) 0 0
\(928\) 23.0102 28.2512i 0.755346 0.927392i
\(929\) −52.3939 −1.71899 −0.859494 0.511146i \(-0.829221\pi\)
−0.859494 + 0.511146i \(0.829221\pi\)
\(930\) 0 0
\(931\) 5.77751 + 13.9481i 0.189350 + 0.457132i
\(932\) 1.54609 + 37.9151i 0.0506437 + 1.24195i
\(933\) 0 0
\(934\) 5.75569 5.99518i 0.188332 0.196168i
\(935\) −11.0865 11.0865i −0.362567 0.362567i
\(936\) 0 0
\(937\) −18.9484 + 18.9484i −0.619017 + 0.619017i −0.945279 0.326262i \(-0.894211\pi\)
0.326262 + 0.945279i \(0.394211\pi\)
\(938\) −0.692842 33.9957i −0.0226221 1.11000i
\(939\) 0 0
\(940\) −6.12973 13.2446i −0.199930 0.431992i
\(941\) 3.46272 1.43430i 0.112881 0.0467570i −0.325528 0.945532i \(-0.605542\pi\)
0.438409 + 0.898775i \(0.355542\pi\)
\(942\) 0 0
\(943\) 14.7120i 0.479088i
\(944\) −0.294295 + 0.914984i −0.00957848 + 0.0297802i
\(945\) 0 0
\(946\) 38.9753 + 15.2213i 1.26720 + 0.494886i
\(947\) 52.3991 21.7044i 1.70274 0.705298i 0.702760 0.711427i \(-0.251951\pi\)
0.999981 + 0.00612896i \(0.00195092\pi\)
\(948\) 0 0
\(949\) −16.9776 + 40.9875i −0.551116 + 1.33051i
\(950\) 21.2152 0.432373i 0.688312 0.0140280i
\(951\) 0 0
\(952\) 9.46178 + 19.3973i 0.306658 + 0.628669i
\(953\) 10.0461 + 10.0461i 0.325424 + 0.325424i 0.850843 0.525419i \(-0.176092\pi\)
−0.525419 + 0.850843i \(0.676092\pi\)
\(954\) 0 0
\(955\) −8.56972 3.54970i −0.277310 0.114865i
\(956\) −6.73398 6.20631i −0.217793 0.200726i
\(957\) 0 0
\(958\) −18.4317 + 8.07848i −0.595500 + 0.261004i
\(959\) −7.38963 −0.238624
\(960\) 0 0
\(961\) −3.38553 −0.109211
\(962\) 33.5296 14.6958i 1.08104 0.473813i
\(963\) 0 0
\(964\) 21.4585 + 19.7771i 0.691133 + 0.636976i
\(965\) 7.23496 + 2.99682i 0.232902 + 0.0964710i
\(966\) 0 0
\(967\) 34.5937 + 34.5937i 1.11246 + 1.11246i 0.992817 + 0.119640i \(0.0381741\pi\)
0.119640 + 0.992817i \(0.461826\pi\)
\(968\) −9.28705 + 4.53012i −0.298497 + 0.145604i
\(969\) 0 0
\(970\) −24.0317 + 0.489773i −0.771610 + 0.0157257i
\(971\) 11.4425 27.6245i 0.367206 0.886513i −0.627000 0.779019i \(-0.715717\pi\)
0.994206 0.107494i \(-0.0342827\pi\)
\(972\) 0 0
\(973\) 14.4984 6.00544i 0.464798 0.192526i
\(974\) 32.1785 + 12.5669i 1.03107 + 0.402668i
\(975\) 0 0
\(976\) 24.8157 12.7372i 0.794333 0.407709i
\(977\) 7.83370i 0.250622i −0.992117 0.125311i \(-0.960007\pi\)
0.992117 0.125311i \(-0.0399929\pi\)
\(978\) 0 0
\(979\) −25.4583 + 10.5452i −0.813651 + 0.337025i
\(980\) 3.17389 + 6.85788i 0.101386 + 0.219067i
\(981\) 0 0
\(982\) −0.162795 7.98785i −0.00519500 0.254903i
\(983\) 13.3719 13.3719i 0.426497 0.426497i −0.460937 0.887433i \(-0.652486\pi\)
0.887433 + 0.460937i \(0.152486\pi\)
\(984\) 0 0
\(985\) −2.97629 2.97629i −0.0948326 0.0948326i
\(986\) −28.9065 + 30.1093i −0.920571 + 0.958875i
\(987\) 0 0
\(988\) 0.948415 + 23.2583i 0.0301731 + 0.739944i
\(989\) −22.6381 54.6533i −0.719851 1.73787i
\(990\) 0 0
\(991\) 42.1375 1.33854 0.669270 0.743019i \(-0.266607\pi\)
0.669270 + 0.743019i \(0.266607\pi\)
\(992\) 14.1102 + 26.1642i 0.447999 + 0.830714i
\(993\) 0 0
\(994\) −2.02242 4.61429i −0.0641471 0.146356i
\(995\) −1.68342 4.06415i −0.0533681 0.128842i
\(996\) 0 0
\(997\) 6.17091 + 2.55607i 0.195435 + 0.0809517i 0.478254 0.878221i \(-0.341270\pi\)
−0.282820 + 0.959173i \(0.591270\pi\)
\(998\) −15.1152 + 15.7441i −0.478464 + 0.498372i
\(999\) 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 288.2.v.d.37.8 32
3.2 odd 2 96.2.n.a.37.1 yes 32
4.3 odd 2 1152.2.v.c.1009.4 32
12.11 even 2 384.2.n.a.241.3 32
24.5 odd 2 768.2.n.a.481.2 32
24.11 even 2 768.2.n.b.481.6 32
32.13 even 8 inner 288.2.v.d.109.8 32
32.19 odd 8 1152.2.v.c.145.4 32
96.29 odd 8 768.2.n.a.289.2 32
96.35 even 8 768.2.n.b.289.6 32
96.77 odd 8 96.2.n.a.13.1 32
96.83 even 8 384.2.n.a.145.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
96.2.n.a.13.1 32 96.77 odd 8
96.2.n.a.37.1 yes 32 3.2 odd 2
288.2.v.d.37.8 32 1.1 even 1 trivial
288.2.v.d.109.8 32 32.13 even 8 inner
384.2.n.a.145.3 32 96.83 even 8
384.2.n.a.241.3 32 12.11 even 2
768.2.n.a.289.2 32 96.29 odd 8
768.2.n.a.481.2 32 24.5 odd 2
768.2.n.b.289.6 32 96.35 even 8
768.2.n.b.481.6 32 24.11 even 2
1152.2.v.c.145.4 32 32.19 odd 8
1152.2.v.c.1009.4 32 4.3 odd 2