Properties

Label 525.2.q.e.374.6
Level $525$
Weight $2$
Character 525.374
Analytic conductor $4.192$
Analytic rank $0$
Dimension $16$
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] = [525,2,Mod(299,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.299");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.q (of order \(6\), degree \(2\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 11x^{14} + 85x^{12} + 332x^{10} + 940x^{8} + 1064x^{6} + 880x^{4} + 128x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 374.6
Root \(-0.539169 - 0.933868i\) of defining polynomial
Character \(\chi\) \(=\) 525.374
Dual form 525.2.q.e.299.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.539169 + 0.933868i) q^{2} +(0.0613278 - 1.73096i) q^{3} +(0.418594 - 0.725026i) q^{4} +(1.64956 - 0.876010i) q^{6} +(0.929227 - 2.47720i) q^{7} +3.05945 q^{8} +(-2.99248 - 0.212312i) q^{9} +O(q^{10})\) \(q+(0.539169 + 0.933868i) q^{2} +(0.0613278 - 1.73096i) q^{3} +(0.418594 - 0.725026i) q^{4} +(1.64956 - 0.876010i) q^{6} +(0.929227 - 2.47720i) q^{7} +3.05945 q^{8} +(-2.99248 - 0.212312i) q^{9} +(-3.84494 - 2.21988i) q^{11} +(-1.22932 - 0.769035i) q^{12} +0.955682 q^{13} +(2.81439 - 0.467856i) q^{14} +(0.812371 + 1.40707i) q^{16} +(0.439527 + 0.253761i) q^{17} +(-1.41518 - 2.90905i) q^{18} +(-4.41107 + 2.54673i) q^{19} +(-4.23096 - 1.76038i) q^{21} -4.78755i q^{22} +(2.14856 + 3.72142i) q^{23} +(0.187629 - 5.29579i) q^{24} +(0.515274 + 0.892481i) q^{26} +(-0.551027 + 5.16685i) q^{27} +(-1.40707 - 1.71066i) q^{28} -6.89526i q^{29} +(5.10397 + 2.94678i) q^{31} +(2.18344 - 3.78182i) q^{32} +(-4.07833 + 6.51931i) q^{33} +0.547280i q^{34} +(-1.40656 + 2.08075i) q^{36} +(6.51863 - 3.76353i) q^{37} +(-4.75663 - 2.74624i) q^{38} +(0.0586099 - 1.65425i) q^{39} +4.65529 q^{41} +(-0.637242 - 4.90030i) q^{42} +0.492478i q^{43} +(-3.21894 + 1.85845i) q^{44} +(-2.31688 + 4.01295i) q^{46} +(5.76715 - 3.32967i) q^{47} +(2.48541 - 1.31989i) q^{48} +(-5.27308 - 4.60377i) q^{49} +(0.466207 - 0.745243i) q^{51} +(0.400043 - 0.692894i) q^{52} +(4.56616 - 7.90881i) q^{53} +(-5.12226 + 2.27122i) q^{54} +(2.84292 - 7.57887i) q^{56} +(4.13778 + 7.79159i) q^{57} +(6.43926 - 3.71771i) q^{58} +(-5.81439 + 10.0708i) q^{59} +(0.399509 - 0.230657i) q^{61} +6.35524i q^{62} +(-3.30663 + 7.21569i) q^{63} +7.95845 q^{64} +(-8.28709 - 0.293610i) q^{66} +(3.20856 + 1.85246i) q^{67} +(0.367967 - 0.212446i) q^{68} +(6.57342 - 3.49086i) q^{69} +7.90386i q^{71} +(-9.15533 - 0.649559i) q^{72} +(-3.15721 + 5.46846i) q^{73} +(7.02929 + 4.05836i) q^{74} +4.26419i q^{76} +(-9.07191 + 7.46193i) q^{77} +(1.57645 - 0.837188i) q^{78} +(7.38052 + 12.7834i) q^{79} +(8.90985 + 1.27068i) q^{81} +(2.50999 + 4.34743i) q^{82} +10.7916i q^{83} +(-3.04738 + 2.33067i) q^{84} +(-0.459909 + 0.265529i) q^{86} +(-11.9355 - 0.422871i) q^{87} +(-11.7634 - 6.79159i) q^{88} +(-3.57713 - 6.19577i) q^{89} +(0.888045 - 2.36742i) q^{91} +3.59750 q^{92} +(5.41378 - 8.65407i) q^{93} +(6.21894 + 3.59050i) q^{94} +(-6.41230 - 4.01138i) q^{96} -6.91148 q^{97} +(1.45623 - 7.40656i) q^{98} +(11.0346 + 7.45926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 6 q^{4} - 10 q^{6} - 8 q^{9} - 24 q^{14} + 2 q^{16} - 18 q^{19} - 44 q^{21} + 14 q^{24} + 12 q^{26} - 42 q^{31} + 18 q^{36} - 30 q^{39} + 60 q^{41} - 14 q^{46} + 8 q^{49} + 24 q^{51} - 14 q^{54} + 42 q^{56} - 24 q^{59} + 30 q^{61} - 76 q^{64} - 32 q^{66} - 26 q^{69} + 108 q^{74} + 58 q^{79} + 56 q^{81} + 102 q^{84} - 18 q^{86} - 6 q^{89} - 6 q^{91} + 48 q^{94} - 84 q^{96} + 68 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.539169 + 0.933868i 0.381250 + 0.660344i 0.991241 0.132064i \(-0.0421604\pi\)
−0.609991 + 0.792408i \(0.708827\pi\)
\(3\) 0.0613278 1.73096i 0.0354076 0.999373i
\(4\) 0.418594 0.725026i 0.209297 0.362513i
\(5\) 0 0
\(6\) 1.64956 0.876010i 0.673429 0.357630i
\(7\) 0.929227 2.47720i 0.351215 0.936295i
\(8\) 3.05945 1.08168
\(9\) −2.99248 0.212312i −0.997493 0.0707708i
\(10\) 0 0
\(11\) −3.84494 2.21988i −1.15929 0.669318i −0.208158 0.978095i \(-0.566747\pi\)
−0.951134 + 0.308777i \(0.900080\pi\)
\(12\) −1.22932 0.769035i −0.354875 0.222001i
\(13\) 0.955682 0.265059 0.132529 0.991179i \(-0.457690\pi\)
0.132529 + 0.991179i \(0.457690\pi\)
\(14\) 2.81439 0.467856i 0.752178 0.125040i
\(15\) 0 0
\(16\) 0.812371 + 1.40707i 0.203093 + 0.351767i
\(17\) 0.439527 + 0.253761i 0.106601 + 0.0615461i 0.552353 0.833611i \(-0.313730\pi\)
−0.445752 + 0.895157i \(0.647064\pi\)
\(18\) −1.41518 2.90905i −0.333561 0.685670i
\(19\) −4.41107 + 2.54673i −1.01197 + 0.584261i −0.911768 0.410706i \(-0.865282\pi\)
−0.100202 + 0.994967i \(0.531949\pi\)
\(20\) 0 0
\(21\) −4.23096 1.76038i −0.923272 0.384146i
\(22\) 4.78755i 1.02071i
\(23\) 2.14856 + 3.72142i 0.448007 + 0.775970i 0.998256 0.0590300i \(-0.0188008\pi\)
−0.550250 + 0.835000i \(0.685467\pi\)
\(24\) 0.187629 5.29579i 0.0382996 1.08100i
\(25\) 0 0
\(26\) 0.515274 + 0.892481i 0.101054 + 0.175030i
\(27\) −0.551027 + 5.16685i −0.106045 + 0.994361i
\(28\) −1.40707 1.71066i −0.265911 0.323283i
\(29\) 6.89526i 1.28042i −0.768201 0.640209i \(-0.778848\pi\)
0.768201 0.640209i \(-0.221152\pi\)
\(30\) 0 0
\(31\) 5.10397 + 2.94678i 0.916699 + 0.529257i 0.882581 0.470161i \(-0.155804\pi\)
0.0341187 + 0.999418i \(0.489138\pi\)
\(32\) 2.18344 3.78182i 0.385981 0.668538i
\(33\) −4.07833 + 6.51931i −0.709946 + 1.13487i
\(34\) 0.547280i 0.0938578i
\(35\) 0 0
\(36\) −1.40656 + 2.08075i −0.234427 + 0.346792i
\(37\) 6.51863 3.76353i 1.07166 0.618721i 0.143023 0.989719i \(-0.454318\pi\)
0.928634 + 0.370998i \(0.120984\pi\)
\(38\) −4.75663 2.74624i −0.771627 0.445499i
\(39\) 0.0586099 1.65425i 0.00938509 0.264892i
\(40\) 0 0
\(41\) 4.65529 0.727034 0.363517 0.931588i \(-0.381576\pi\)
0.363517 + 0.931588i \(0.381576\pi\)
\(42\) −0.637242 4.90030i −0.0983286 0.756133i
\(43\) 0.492478i 0.0751022i 0.999295 + 0.0375511i \(0.0119557\pi\)
−0.999295 + 0.0375511i \(0.988044\pi\)
\(44\) −3.21894 + 1.85845i −0.485273 + 0.280172i
\(45\) 0 0
\(46\) −2.31688 + 4.01295i −0.341605 + 0.591677i
\(47\) 5.76715 3.32967i 0.841225 0.485682i −0.0164553 0.999865i \(-0.505238\pi\)
0.857681 + 0.514183i \(0.171905\pi\)
\(48\) 2.48541 1.31989i 0.358737 0.190510i
\(49\) −5.27308 4.60377i −0.753297 0.657681i
\(50\) 0 0
\(51\) 0.466207 0.745243i 0.0652820 0.104355i
\(52\) 0.400043 0.692894i 0.0554759 0.0960871i
\(53\) 4.56616 7.90881i 0.627210 1.08636i −0.360899 0.932605i \(-0.617530\pi\)
0.988109 0.153754i \(-0.0491365\pi\)
\(54\) −5.12226 + 2.27122i −0.697051 + 0.309074i
\(55\) 0 0
\(56\) 2.84292 7.57887i 0.379901 1.01277i
\(57\) 4.13778 + 7.79159i 0.548063 + 1.03202i
\(58\) 6.43926 3.71771i 0.845517 0.488159i
\(59\) −5.81439 + 10.0708i −0.756969 + 1.31111i 0.187420 + 0.982280i \(0.439987\pi\)
−0.944389 + 0.328829i \(0.893346\pi\)
\(60\) 0 0
\(61\) 0.399509 0.230657i 0.0511519 0.0295326i −0.474206 0.880414i \(-0.657265\pi\)
0.525358 + 0.850881i \(0.323931\pi\)
\(62\) 6.35524i 0.807116i
\(63\) −3.30663 + 7.21569i −0.416596 + 0.909092i
\(64\) 7.95845 0.994806
\(65\) 0 0
\(66\) −8.28709 0.293610i −1.02007 0.0361409i
\(67\) 3.20856 + 1.85246i 0.391988 + 0.226314i 0.683021 0.730399i \(-0.260666\pi\)
−0.291033 + 0.956713i \(0.593999\pi\)
\(68\) 0.367967 0.212446i 0.0446225 0.0257628i
\(69\) 6.57342 3.49086i 0.791346 0.420250i
\(70\) 0 0
\(71\) 7.90386i 0.938015i 0.883194 + 0.469008i \(0.155388\pi\)
−0.883194 + 0.469008i \(0.844612\pi\)
\(72\) −9.15533 0.649559i −1.07897 0.0765512i
\(73\) −3.15721 + 5.46846i −0.369524 + 0.640034i −0.989491 0.144593i \(-0.953813\pi\)
0.619967 + 0.784628i \(0.287146\pi\)
\(74\) 7.02929 + 4.05836i 0.817138 + 0.471775i
\(75\) 0 0
\(76\) 4.26419i 0.489136i
\(77\) −9.07191 + 7.46193i −1.03384 + 0.850366i
\(78\) 1.57645 0.837188i 0.178498 0.0947928i
\(79\) 7.38052 + 12.7834i 0.830374 + 1.43825i 0.897742 + 0.440521i \(0.145206\pi\)
−0.0673684 + 0.997728i \(0.521460\pi\)
\(80\) 0 0
\(81\) 8.90985 + 1.27068i 0.989983 + 0.141187i
\(82\) 2.50999 + 4.34743i 0.277182 + 0.480093i
\(83\) 10.7916i 1.18453i 0.805743 + 0.592266i \(0.201766\pi\)
−0.805743 + 0.592266i \(0.798234\pi\)
\(84\) −3.04738 + 2.33067i −0.332496 + 0.254297i
\(85\) 0 0
\(86\) −0.459909 + 0.265529i −0.0495933 + 0.0286327i
\(87\) −11.9355 0.422871i −1.27962 0.0453365i
\(88\) −11.7634 6.79159i −1.25398 0.723986i
\(89\) −3.57713 6.19577i −0.379175 0.656750i 0.611768 0.791038i \(-0.290459\pi\)
−0.990942 + 0.134287i \(0.957125\pi\)
\(90\) 0 0
\(91\) 0.888045 2.36742i 0.0930925 0.248173i
\(92\) 3.59750 0.375066
\(93\) 5.41378 8.65407i 0.561383 0.897385i
\(94\) 6.21894 + 3.59050i 0.641434 + 0.370332i
\(95\) 0 0
\(96\) −6.41230 4.01138i −0.654452 0.409410i
\(97\) −6.91148 −0.701755 −0.350877 0.936421i \(-0.614117\pi\)
−0.350877 + 0.936421i \(0.614117\pi\)
\(98\) 1.45623 7.40656i 0.147102 0.748176i
\(99\) 11.0346 + 7.45926i 1.10902 + 0.749684i
\(100\) 0 0
\(101\) −1.19538 + 2.07046i −0.118945 + 0.206019i −0.919350 0.393441i \(-0.871285\pi\)
0.800405 + 0.599460i \(0.204618\pi\)
\(102\) 0.947323 + 0.0335635i 0.0937990 + 0.00332328i
\(103\) 7.48110 + 12.9577i 0.737135 + 1.27676i 0.953780 + 0.300505i \(0.0971552\pi\)
−0.216645 + 0.976250i \(0.569511\pi\)
\(104\) 2.92386 0.286708
\(105\) 0 0
\(106\) 9.84772 0.956495
\(107\) −6.78072 11.7445i −0.655517 1.13539i −0.981764 0.190104i \(-0.939118\pi\)
0.326247 0.945284i \(-0.394216\pi\)
\(108\) 3.51544 + 2.56232i 0.338274 + 0.246559i
\(109\) 8.06063 13.9614i 0.772068 1.33726i −0.164359 0.986401i \(-0.552556\pi\)
0.936428 0.350861i \(-0.114111\pi\)
\(110\) 0 0
\(111\) −6.11477 11.5143i −0.580388 1.09289i
\(112\) 4.24047 0.704923i 0.400687 0.0666090i
\(113\) −5.05678 −0.475702 −0.237851 0.971302i \(-0.576443\pi\)
−0.237851 + 0.971302i \(0.576443\pi\)
\(114\) −5.04536 + 8.06513i −0.472541 + 0.755369i
\(115\) 0 0
\(116\) −4.99924 2.88631i −0.464168 0.267987i
\(117\) −2.85986 0.202903i −0.264394 0.0187584i
\(118\) −12.5398 −1.15438
\(119\) 1.03704 0.852997i 0.0950651 0.0781941i
\(120\) 0 0
\(121\) 4.35571 + 7.54431i 0.395973 + 0.685846i
\(122\) 0.430806 + 0.248726i 0.0390033 + 0.0225186i
\(123\) 0.285499 8.05814i 0.0257425 0.726578i
\(124\) 4.27298 2.46700i 0.383725 0.221544i
\(125\) 0 0
\(126\) −8.52133 + 0.802519i −0.759141 + 0.0714941i
\(127\) 8.05009i 0.714330i 0.934041 + 0.357165i \(0.116257\pi\)
−0.934041 + 0.357165i \(0.883743\pi\)
\(128\) −0.0759250 0.131506i −0.00671089 0.0116236i
\(129\) 0.852462 + 0.0302026i 0.0750551 + 0.00265919i
\(130\) 0 0
\(131\) 1.04963 + 1.81802i 0.0917069 + 0.158841i 0.908229 0.418473i \(-0.137434\pi\)
−0.816523 + 0.577314i \(0.804101\pi\)
\(132\) 3.01951 + 5.68584i 0.262814 + 0.494889i
\(133\) 2.20989 + 13.2936i 0.191622 + 1.15270i
\(134\) 3.99516i 0.345129i
\(135\) 0 0
\(136\) 1.34471 + 0.776369i 0.115308 + 0.0665731i
\(137\) −2.47355 + 4.28431i −0.211329 + 0.366033i −0.952131 0.305691i \(-0.901113\pi\)
0.740801 + 0.671724i \(0.234446\pi\)
\(138\) 6.80419 + 4.25654i 0.579211 + 0.362341i
\(139\) 10.7217i 0.909406i 0.890643 + 0.454703i \(0.150255\pi\)
−0.890643 + 0.454703i \(0.849745\pi\)
\(140\) 0 0
\(141\) −5.40985 10.1869i −0.455591 0.857895i
\(142\) −7.38116 + 4.26151i −0.619413 + 0.357618i
\(143\) −3.67454 2.12150i −0.307281 0.177408i
\(144\) −2.13226 4.38310i −0.177689 0.365258i
\(145\) 0 0
\(146\) −6.80909 −0.563524
\(147\) −8.29234 + 8.84517i −0.683941 + 0.729537i
\(148\) 6.30157i 0.517986i
\(149\) −4.55837 + 2.63178i −0.373436 + 0.215604i −0.674959 0.737855i \(-0.735839\pi\)
0.301522 + 0.953459i \(0.402505\pi\)
\(150\) 0 0
\(151\) 3.50451 6.06998i 0.285193 0.493968i −0.687463 0.726219i \(-0.741276\pi\)
0.972656 + 0.232251i \(0.0746091\pi\)
\(152\) −13.4954 + 7.79159i −1.09462 + 0.631982i
\(153\) −1.26140 0.852692i −0.101978 0.0689360i
\(154\) −11.8597 4.44872i −0.955686 0.358488i
\(155\) 0 0
\(156\) −1.17484 0.734953i −0.0940626 0.0588434i
\(157\) −1.45005 + 2.51156i −0.115727 + 0.200445i −0.918070 0.396418i \(-0.870253\pi\)
0.802343 + 0.596863i \(0.203586\pi\)
\(158\) −7.95870 + 13.7849i −0.633160 + 1.09667i
\(159\) −13.4098 8.38889i −1.06347 0.665282i
\(160\) 0 0
\(161\) 11.2152 1.86439i 0.883883 0.146934i
\(162\) 3.61726 + 9.00573i 0.284199 + 0.707557i
\(163\) 11.0493 6.37930i 0.865446 0.499665i −0.000386523 1.00000i \(-0.500123\pi\)
0.865832 + 0.500335i \(0.166790\pi\)
\(164\) 1.94868 3.37521i 0.152166 0.263559i
\(165\) 0 0
\(166\) −10.0779 + 5.81849i −0.782199 + 0.451603i
\(167\) 15.7766i 1.22083i −0.792083 0.610413i \(-0.791003\pi\)
0.792083 0.610413i \(-0.208997\pi\)
\(168\) −12.9444 5.38579i −0.998683 0.415523i
\(169\) −12.0867 −0.929744
\(170\) 0 0
\(171\) 13.7407 6.68452i 1.05078 0.511178i
\(172\) 0.357059 + 0.206148i 0.0272255 + 0.0157186i
\(173\) −8.81037 + 5.08667i −0.669840 + 0.386732i −0.796016 0.605275i \(-0.793063\pi\)
0.126176 + 0.992008i \(0.459730\pi\)
\(174\) −6.04032 11.3741i −0.457916 0.862271i
\(175\) 0 0
\(176\) 7.21345i 0.543735i
\(177\) 17.0757 + 10.6821i 1.28348 + 0.802918i
\(178\) 3.85735 6.68113i 0.289121 0.500772i
\(179\) −4.55716 2.63107i −0.340618 0.196656i 0.319927 0.947442i \(-0.396341\pi\)
−0.660545 + 0.750786i \(0.729675\pi\)
\(180\) 0 0
\(181\) 9.71314i 0.721972i −0.932571 0.360986i \(-0.882440\pi\)
0.932571 0.360986i \(-0.117560\pi\)
\(182\) 2.68966 0.447122i 0.199371 0.0331429i
\(183\) −0.374757 0.705682i −0.0277029 0.0521655i
\(184\) 6.57342 + 11.3855i 0.484599 + 0.839350i
\(185\) 0 0
\(186\) 11.0007 + 0.389753i 0.806610 + 0.0285781i
\(187\) −1.12664 1.95139i −0.0823878 0.142700i
\(188\) 5.57511i 0.406607i
\(189\) 12.2873 + 6.16618i 0.893771 + 0.448524i
\(190\) 0 0
\(191\) −8.30561 + 4.79524i −0.600973 + 0.346972i −0.769424 0.638738i \(-0.779457\pi\)
0.168451 + 0.985710i \(0.446123\pi\)
\(192\) 0.488074 13.7758i 0.0352237 0.994182i
\(193\) 7.23275 + 4.17583i 0.520625 + 0.300583i 0.737190 0.675685i \(-0.236152\pi\)
−0.216566 + 0.976268i \(0.569485\pi\)
\(194\) −3.72646 6.45441i −0.267544 0.463400i
\(195\) 0 0
\(196\) −5.54513 + 1.89601i −0.396080 + 0.135429i
\(197\) −1.77574 −0.126516 −0.0632580 0.997997i \(-0.520149\pi\)
−0.0632580 + 0.997997i \(0.520149\pi\)
\(198\) −1.01646 + 14.3267i −0.0722365 + 1.01815i
\(199\) 3.25502 + 1.87929i 0.230742 + 0.133219i 0.610915 0.791697i \(-0.290802\pi\)
−0.380172 + 0.924916i \(0.624135\pi\)
\(200\) 0 0
\(201\) 3.40332 5.44029i 0.240052 0.383729i
\(202\) −2.57805 −0.181391
\(203\) −17.0810 6.40726i −1.19885 0.449702i
\(204\) −0.345169 0.649966i −0.0241667 0.0455067i
\(205\) 0 0
\(206\) −8.06716 + 13.9727i −0.562065 + 0.973526i
\(207\) −5.63943 11.5924i −0.391967 0.805730i
\(208\) 0.776369 + 1.34471i 0.0538315 + 0.0932388i
\(209\) 22.6137 1.56422
\(210\) 0 0
\(211\) −9.12126 −0.627933 −0.313967 0.949434i \(-0.601658\pi\)
−0.313967 + 0.949434i \(0.601658\pi\)
\(212\) −3.82273 6.62116i −0.262546 0.454743i
\(213\) 13.6813 + 0.484726i 0.937427 + 0.0332129i
\(214\) 7.31190 12.6646i 0.499831 0.865734i
\(215\) 0 0
\(216\) −1.68584 + 15.8077i −0.114707 + 1.07558i
\(217\) 12.0425 9.90534i 0.817499 0.672418i
\(218\) 17.3842 1.17740
\(219\) 9.27208 + 5.80040i 0.626549 + 0.391954i
\(220\) 0 0
\(221\) 0.420048 + 0.242515i 0.0282555 + 0.0163133i
\(222\) 7.45597 11.9186i 0.500412 0.799921i
\(223\) −11.7397 −0.786146 −0.393073 0.919507i \(-0.628588\pi\)
−0.393073 + 0.919507i \(0.628588\pi\)
\(224\) −7.33944 8.92299i −0.490387 0.596192i
\(225\) 0 0
\(226\) −2.72646 4.72236i −0.181361 0.314127i
\(227\) 20.9760 + 12.1105i 1.39223 + 0.803802i 0.993561 0.113295i \(-0.0361407\pi\)
0.398664 + 0.917097i \(0.369474\pi\)
\(228\) 7.38116 + 0.261513i 0.488829 + 0.0173191i
\(229\) −18.8003 + 10.8544i −1.24236 + 0.717278i −0.969574 0.244797i \(-0.921279\pi\)
−0.272787 + 0.962075i \(0.587945\pi\)
\(230\) 0 0
\(231\) 12.3600 + 16.1608i 0.813227 + 1.06330i
\(232\) 21.0957i 1.38500i
\(233\) 5.49812 + 9.52303i 0.360194 + 0.623874i 0.987993 0.154502i \(-0.0493772\pi\)
−0.627799 + 0.778376i \(0.716044\pi\)
\(234\) −1.35246 2.78013i −0.0884132 0.181743i
\(235\) 0 0
\(236\) 4.86774 + 8.43117i 0.316863 + 0.548822i
\(237\) 22.5803 11.9914i 1.46675 0.778928i
\(238\) 1.35572 + 0.508547i 0.0878786 + 0.0329642i
\(239\) 9.02649i 0.583875i 0.956437 + 0.291938i \(0.0942999\pi\)
−0.956437 + 0.291938i \(0.905700\pi\)
\(240\) 0 0
\(241\) −4.40027 2.54050i −0.283446 0.163648i 0.351536 0.936174i \(-0.385659\pi\)
−0.634982 + 0.772527i \(0.718993\pi\)
\(242\) −4.69692 + 8.13531i −0.301930 + 0.522958i
\(243\) 2.74592 15.3447i 0.176151 0.984363i
\(244\) 0.386206i 0.0247243i
\(245\) 0 0
\(246\) 7.67917 4.07808i 0.489606 0.260009i
\(247\) −4.21558 + 2.43387i −0.268231 + 0.154863i
\(248\) 15.6153 + 9.01550i 0.991573 + 0.572485i
\(249\) 18.6799 + 0.661824i 1.18379 + 0.0419414i
\(250\) 0 0
\(251\) 18.6748 1.17875 0.589373 0.807861i \(-0.299375\pi\)
0.589373 + 0.807861i \(0.299375\pi\)
\(252\) 3.84743 + 5.41784i 0.242365 + 0.341292i
\(253\) 19.0782i 1.19944i
\(254\) −7.51772 + 4.34036i −0.471704 + 0.272338i
\(255\) 0 0
\(256\) 8.04032 13.9262i 0.502520 0.870390i
\(257\) 10.4639 6.04132i 0.652718 0.376847i −0.136779 0.990602i \(-0.543675\pi\)
0.789497 + 0.613755i \(0.210342\pi\)
\(258\) 0.431416 + 0.812371i 0.0268588 + 0.0505760i
\(259\) −3.26575 19.6452i −0.202924 1.22069i
\(260\) 0 0
\(261\) −1.46395 + 20.6339i −0.0906162 + 1.27721i
\(262\) −1.13186 + 1.96044i −0.0699265 + 0.121116i
\(263\) 6.44388 11.1611i 0.397346 0.688224i −0.596051 0.802946i \(-0.703264\pi\)
0.993398 + 0.114722i \(0.0365978\pi\)
\(264\) −12.4774 + 19.9455i −0.767933 + 1.22756i
\(265\) 0 0
\(266\) −11.2230 + 9.23125i −0.688125 + 0.566004i
\(267\) −10.9440 + 5.81191i −0.669764 + 0.355683i
\(268\) 2.68616 1.55086i 0.164084 0.0947337i
\(269\) 0.233222 0.403952i 0.0142198 0.0246294i −0.858828 0.512264i \(-0.828807\pi\)
0.873048 + 0.487635i \(0.162140\pi\)
\(270\) 0 0
\(271\) −20.1703 + 11.6453i −1.22526 + 0.707404i −0.966035 0.258413i \(-0.916801\pi\)
−0.259225 + 0.965817i \(0.583467\pi\)
\(272\) 0.824593i 0.0499983i
\(273\) −4.04346 1.68236i −0.244721 0.101821i
\(274\) −5.33464 −0.322277
\(275\) 0 0
\(276\) 0.220627 6.22715i 0.0132802 0.374830i
\(277\) 12.0298 + 6.94543i 0.722803 + 0.417310i 0.815783 0.578357i \(-0.196306\pi\)
−0.0929805 + 0.995668i \(0.529639\pi\)
\(278\) −10.0127 + 5.78083i −0.600521 + 0.346711i
\(279\) −14.6479 9.90180i −0.876945 0.592805i
\(280\) 0 0
\(281\) 6.85483i 0.408925i 0.978874 + 0.204462i \(0.0655446\pi\)
−0.978874 + 0.204462i \(0.934455\pi\)
\(282\) 6.59643 10.5446i 0.392812 0.627919i
\(283\) 2.21825 3.84212i 0.131861 0.228391i −0.792533 0.609829i \(-0.791238\pi\)
0.924394 + 0.381439i \(0.124571\pi\)
\(284\) 5.73050 + 3.30850i 0.340043 + 0.196324i
\(285\) 0 0
\(286\) 4.57538i 0.270548i
\(287\) 4.32582 11.5321i 0.255345 0.680718i
\(288\) −7.33681 + 10.8534i −0.432326 + 0.639546i
\(289\) −8.37121 14.4994i −0.492424 0.852904i
\(290\) 0 0
\(291\) −0.423866 + 11.9635i −0.0248475 + 0.701315i
\(292\) 2.64318 + 4.57812i 0.154680 + 0.267914i
\(293\) 30.0822i 1.75742i −0.477357 0.878709i \(-0.658405\pi\)
0.477357 0.878709i \(-0.341595\pi\)
\(294\) −12.7312 2.97491i −0.742498 0.173501i
\(295\) 0 0
\(296\) 19.9434 11.5143i 1.15919 0.669257i
\(297\) 13.5884 18.6430i 0.788481 1.08178i
\(298\) −4.91547 2.83795i −0.284745 0.164398i
\(299\) 2.05334 + 3.55650i 0.118748 + 0.205678i
\(300\) 0 0
\(301\) 1.21997 + 0.457623i 0.0703178 + 0.0263770i
\(302\) 7.55808 0.434919
\(303\) 3.51058 + 2.19614i 0.201678 + 0.126165i
\(304\) −7.16685 4.13778i −0.411047 0.237318i
\(305\) 0 0
\(306\) 0.116194 1.63772i 0.00664239 0.0936225i
\(307\) −32.8300 −1.87371 −0.936853 0.349722i \(-0.886276\pi\)
−0.936853 + 0.349722i \(0.886276\pi\)
\(308\) 1.61265 + 9.70088i 0.0918891 + 0.552759i
\(309\) 22.8880 12.1549i 1.30206 0.691466i
\(310\) 0 0
\(311\) 8.23073 14.2560i 0.466722 0.808386i −0.532556 0.846395i \(-0.678768\pi\)
0.999277 + 0.0380092i \(0.0121016\pi\)
\(312\) 0.179314 5.06110i 0.0101516 0.286528i
\(313\) 2.30422 + 3.99102i 0.130242 + 0.225586i 0.923770 0.382948i \(-0.125091\pi\)
−0.793528 + 0.608534i \(0.791758\pi\)
\(314\) −3.12729 −0.176483
\(315\) 0 0
\(316\) 12.3578 0.695179
\(317\) 14.7151 + 25.4873i 0.826481 + 1.43151i 0.900782 + 0.434272i \(0.142994\pi\)
−0.0743007 + 0.997236i \(0.523672\pi\)
\(318\) 0.603939 17.0461i 0.0338672 0.955895i
\(319\) −15.3066 + 26.5119i −0.857007 + 1.48438i
\(320\) 0 0
\(321\) −20.7452 + 11.0169i −1.15789 + 0.614904i
\(322\) 7.78799 + 9.46832i 0.434008 + 0.527649i
\(323\) −2.58505 −0.143836
\(324\) 4.65088 5.92797i 0.258382 0.329332i
\(325\) 0 0
\(326\) 11.9148 + 6.87904i 0.659902 + 0.380995i
\(327\) −23.6724 14.8089i −1.30909 0.818933i
\(328\) 14.2426 0.786417
\(329\) −2.88927 17.3804i −0.159291 0.958213i
\(330\) 0 0
\(331\) −1.32787 2.29995i −0.0729866 0.126417i 0.827222 0.561875i \(-0.189920\pi\)
−0.900209 + 0.435458i \(0.856586\pi\)
\(332\) 7.82418 + 4.51729i 0.429408 + 0.247919i
\(333\) −20.3059 + 9.87830i −1.11276 + 0.541328i
\(334\) 14.7332 8.50623i 0.806166 0.465440i
\(335\) 0 0
\(336\) −0.960139 7.38334i −0.0523799 0.402794i
\(337\) 21.4599i 1.16900i −0.811395 0.584499i \(-0.801291\pi\)
0.811395 0.584499i \(-0.198709\pi\)
\(338\) −6.51676 11.2874i −0.354465 0.613951i
\(339\) −0.310121 + 8.75311i −0.0168435 + 0.475403i
\(340\) 0 0
\(341\) −13.0830 22.6604i −0.708482 1.22713i
\(342\) 13.6510 + 9.22795i 0.738163 + 0.498990i
\(343\) −16.3044 + 8.78454i −0.880352 + 0.474321i
\(344\) 1.50671i 0.0812363i
\(345\) 0 0
\(346\) −9.50056 5.48515i −0.510753 0.294883i
\(347\) −9.08183 + 15.7302i −0.487538 + 0.844441i −0.999897 0.0143301i \(-0.995438\pi\)
0.512359 + 0.858771i \(0.328772\pi\)
\(348\) −5.30270 + 8.47650i −0.284255 + 0.454388i
\(349\) 13.1543i 0.704135i −0.935975 0.352067i \(-0.885479\pi\)
0.935975 0.352067i \(-0.114521\pi\)
\(350\) 0 0
\(351\) −0.526607 + 4.93787i −0.0281082 + 0.263564i
\(352\) −16.7904 + 9.69392i −0.894929 + 0.516688i
\(353\) 8.91499 + 5.14707i 0.474497 + 0.273951i 0.718120 0.695919i \(-0.245003\pi\)
−0.243623 + 0.969870i \(0.578336\pi\)
\(354\) −0.769035 + 21.7059i −0.0408738 + 1.15365i
\(355\) 0 0
\(356\) −5.98946 −0.317441
\(357\) −1.41291 1.84739i −0.0747790 0.0977742i
\(358\) 5.67438i 0.299900i
\(359\) 10.2193 5.90010i 0.539352 0.311395i −0.205464 0.978665i \(-0.565870\pi\)
0.744816 + 0.667270i \(0.232537\pi\)
\(360\) 0 0
\(361\) 3.47170 6.01316i 0.182721 0.316482i
\(362\) 9.07079 5.23703i 0.476750 0.275252i
\(363\) 13.3261 7.07690i 0.699436 0.371441i
\(364\) −1.34471 1.63484i −0.0704819 0.0856890i
\(365\) 0 0
\(366\) 0.456956 0.730456i 0.0238855 0.0381815i
\(367\) −7.98697 + 13.8338i −0.416916 + 0.722120i −0.995628 0.0934122i \(-0.970223\pi\)
0.578711 + 0.815533i \(0.303556\pi\)
\(368\) −3.49086 + 6.04635i −0.181974 + 0.315188i
\(369\) −13.9309 0.988376i −0.725211 0.0514528i
\(370\) 0 0
\(371\) −15.3488 18.6604i −0.796867 0.968799i
\(372\) −4.00825 7.54767i −0.207818 0.391328i
\(373\) −4.60438 + 2.65834i −0.238406 + 0.137644i −0.614444 0.788961i \(-0.710620\pi\)
0.376038 + 0.926604i \(0.377286\pi\)
\(374\) 1.21490 2.10426i 0.0628207 0.108809i
\(375\) 0 0
\(376\) 17.6443 10.1869i 0.909935 0.525351i
\(377\) 6.58968i 0.339386i
\(378\) 0.866538 + 14.7993i 0.0445699 + 0.761196i
\(379\) −24.0427 −1.23499 −0.617494 0.786575i \(-0.711852\pi\)
−0.617494 + 0.786575i \(0.711852\pi\)
\(380\) 0 0
\(381\) 13.9344 + 0.493694i 0.713882 + 0.0252927i
\(382\) −8.95625 5.17089i −0.458242 0.264566i
\(383\) 16.2822 9.40053i 0.831982 0.480345i −0.0225490 0.999746i \(-0.507178\pi\)
0.854531 + 0.519401i \(0.173845\pi\)
\(384\) −0.232289 + 0.123359i −0.0118539 + 0.00629512i
\(385\) 0 0
\(386\) 9.00591i 0.458389i
\(387\) 0.104559 1.47373i 0.00531504 0.0749139i
\(388\) −2.89310 + 5.01100i −0.146875 + 0.254395i
\(389\) −10.5804 6.10860i −0.536448 0.309718i 0.207190 0.978301i \(-0.433568\pi\)
−0.743638 + 0.668582i \(0.766901\pi\)
\(390\) 0 0
\(391\) 2.18089i 0.110292i
\(392\) −16.1327 14.0850i −0.814824 0.711399i
\(393\) 3.21130 1.70538i 0.161988 0.0860252i
\(394\) −0.957422 1.65830i −0.0482342 0.0835442i
\(395\) 0 0
\(396\) 10.0272 4.87796i 0.503884 0.245127i
\(397\) 9.38254 + 16.2510i 0.470896 + 0.815616i 0.999446 0.0332862i \(-0.0105973\pi\)
−0.528550 + 0.848902i \(0.677264\pi\)
\(398\) 4.05302i 0.203159i
\(399\) 23.1463 3.00998i 1.15876 0.150687i
\(400\) 0 0
\(401\) −20.7823 + 11.9987i −1.03782 + 0.599184i −0.919214 0.393757i \(-0.871175\pi\)
−0.118603 + 0.992942i \(0.537842\pi\)
\(402\) 6.91548 + 0.245014i 0.344913 + 0.0122202i
\(403\) 4.87777 + 2.81618i 0.242979 + 0.140284i
\(404\) 1.00076 + 1.73336i 0.0497896 + 0.0862381i
\(405\) 0 0
\(406\) −3.22599 19.4060i −0.160103 0.963102i
\(407\) −33.4183 −1.65648
\(408\) 1.42633 2.28003i 0.0706141 0.112878i
\(409\) 14.7941 + 8.54140i 0.731523 + 0.422345i 0.818979 0.573823i \(-0.194540\pi\)
−0.0874559 + 0.996168i \(0.527874\pi\)
\(410\) 0 0
\(411\) 7.26429 + 4.54437i 0.358321 + 0.224157i
\(412\) 12.5262 0.617120
\(413\) 19.5446 + 23.7615i 0.961726 + 1.16923i
\(414\) 7.78521 11.5168i 0.382622 0.566018i
\(415\) 0 0
\(416\) 2.08667 3.61422i 0.102307 0.177202i
\(417\) 18.5590 + 0.657540i 0.908836 + 0.0321999i
\(418\) 12.1926 + 21.1182i 0.596361 + 1.03293i
\(419\) −39.6524 −1.93714 −0.968572 0.248732i \(-0.919986\pi\)
−0.968572 + 0.248732i \(0.919986\pi\)
\(420\) 0 0
\(421\) −34.1423 −1.66399 −0.831997 0.554779i \(-0.812803\pi\)
−0.831997 + 0.554779i \(0.812803\pi\)
\(422\) −4.91790 8.51805i −0.239400 0.414652i
\(423\) −17.9650 + 8.73951i −0.873488 + 0.424930i
\(424\) 13.9699 24.1966i 0.678439 1.17509i
\(425\) 0 0
\(426\) 6.92386 + 13.0379i 0.335462 + 0.631687i
\(427\) −0.200149 1.20400i −0.00968589 0.0582655i
\(428\) −11.3535 −0.548790
\(429\) −3.89759 + 6.23039i −0.188177 + 0.300806i
\(430\) 0 0
\(431\) −22.3182 12.8854i −1.07503 0.620668i −0.145478 0.989361i \(-0.546472\pi\)
−0.929551 + 0.368693i \(0.879805\pi\)
\(432\) −7.71775 + 3.42207i −0.371320 + 0.164644i
\(433\) −11.9120 −0.572454 −0.286227 0.958162i \(-0.592401\pi\)
−0.286227 + 0.958162i \(0.592401\pi\)
\(434\) 15.7432 + 5.90546i 0.755699 + 0.283471i
\(435\) 0 0
\(436\) −6.74826 11.6883i −0.323183 0.559769i
\(437\) −18.9549 10.9436i −0.906738 0.523505i
\(438\) −0.417586 + 11.7863i −0.0199530 + 0.563171i
\(439\) 14.5260 8.38661i 0.693290 0.400271i −0.111553 0.993758i \(-0.535583\pi\)
0.804843 + 0.593487i \(0.202249\pi\)
\(440\) 0 0
\(441\) 14.8021 + 14.8962i 0.704863 + 0.709343i
\(442\) 0.523026i 0.0248778i
\(443\) 1.19795 + 2.07491i 0.0569163 + 0.0985819i 0.893080 0.449899i \(-0.148540\pi\)
−0.836163 + 0.548480i \(0.815207\pi\)
\(444\) −10.9078 0.386461i −0.517661 0.0183406i
\(445\) 0 0
\(446\) −6.32967 10.9633i −0.299718 0.519127i
\(447\) 4.27596 + 8.05178i 0.202246 + 0.380836i
\(448\) 7.39520 19.7147i 0.349390 0.931432i
\(449\) 25.4692i 1.20196i 0.799262 + 0.600982i \(0.205224\pi\)
−0.799262 + 0.600982i \(0.794776\pi\)
\(450\) 0 0
\(451\) −17.8993 10.3342i −0.842846 0.486617i
\(452\) −2.11674 + 3.66629i −0.0995629 + 0.172448i
\(453\) −10.2920 6.43844i −0.483561 0.302504i
\(454\) 26.1184i 1.22580i
\(455\) 0 0
\(456\) 12.6593 + 23.8380i 0.592827 + 1.11632i
\(457\) −2.98078 + 1.72096i −0.139435 + 0.0805029i −0.568095 0.822963i \(-0.692319\pi\)
0.428660 + 0.903466i \(0.358986\pi\)
\(458\) −20.2731 11.7047i −0.947300 0.546924i
\(459\) −1.55334 + 2.13114i −0.0725036 + 0.0994732i
\(460\) 0 0
\(461\) 13.5376 0.630509 0.315254 0.949007i \(-0.397910\pi\)
0.315254 + 0.949007i \(0.397910\pi\)
\(462\) −8.42791 + 20.2560i −0.392102 + 0.942393i
\(463\) 5.13770i 0.238769i 0.992848 + 0.119385i \(0.0380921\pi\)
−0.992848 + 0.119385i \(0.961908\pi\)
\(464\) 9.70210 5.60151i 0.450409 0.260044i
\(465\) 0 0
\(466\) −5.92883 + 10.2690i −0.274648 + 0.475704i
\(467\) 7.98292 4.60894i 0.369405 0.213276i −0.303793 0.952738i \(-0.598253\pi\)
0.673199 + 0.739462i \(0.264920\pi\)
\(468\) −1.34423 + 1.98854i −0.0621370 + 0.0919201i
\(469\) 7.57040 6.22689i 0.349569 0.287531i
\(470\) 0 0
\(471\) 4.25850 + 2.66402i 0.196221 + 0.122751i
\(472\) −17.7888 + 30.8111i −0.818797 + 1.41820i
\(473\) 1.09324 1.89355i 0.0502672 0.0870654i
\(474\) 23.3730 + 14.6216i 1.07356 + 0.671593i
\(475\) 0 0
\(476\) −0.184347 1.10894i −0.00844952 0.0508281i
\(477\) −15.3433 + 22.6975i −0.702520 + 1.03925i
\(478\) −8.42955 + 4.86680i −0.385559 + 0.222602i
\(479\) 10.3187 17.8724i 0.471472 0.816613i −0.527996 0.849247i \(-0.677056\pi\)
0.999467 + 0.0326342i \(0.0103896\pi\)
\(480\) 0 0
\(481\) 6.22974 3.59674i 0.284052 0.163997i
\(482\) 5.47902i 0.249563i
\(483\) −2.53938 19.5275i −0.115546 0.888532i
\(484\) 7.29309 0.331504
\(485\) 0 0
\(486\) 15.8104 5.70906i 0.717176 0.258968i
\(487\) −2.14340 1.23749i −0.0971267 0.0560761i 0.450650 0.892701i \(-0.351192\pi\)
−0.547777 + 0.836625i \(0.684526\pi\)
\(488\) 1.22228 0.705682i 0.0553298 0.0319447i
\(489\) −10.3647 19.5171i −0.468709 0.882595i
\(490\) 0 0
\(491\) 21.2827i 0.960476i −0.877138 0.480238i \(-0.840550\pi\)
0.877138 0.480238i \(-0.159450\pi\)
\(492\) −5.72285 3.58008i −0.258006 0.161403i
\(493\) 1.74975 3.03065i 0.0788047 0.136494i
\(494\) −4.54582 2.62453i −0.204526 0.118083i
\(495\) 0 0
\(496\) 9.57550i 0.429953i
\(497\) 19.5795 + 7.34447i 0.878259 + 0.329445i
\(498\) 9.45355 + 17.8014i 0.423624 + 0.797698i
\(499\) 16.3690 + 28.3519i 0.732775 + 1.26920i 0.955693 + 0.294366i \(0.0951086\pi\)
−0.222918 + 0.974837i \(0.571558\pi\)
\(500\) 0 0
\(501\) −27.3087 0.967541i −1.22006 0.0432265i
\(502\) 10.0689 + 17.4398i 0.449397 + 0.778378i
\(503\) 0.675693i 0.0301277i 0.999887 + 0.0150638i \(0.00479515\pi\)
−0.999887 + 0.0150638i \(0.995205\pi\)
\(504\) −10.1165 + 22.0760i −0.450623 + 0.983344i
\(505\) 0 0
\(506\) 17.8165 10.2864i 0.792041 0.457285i
\(507\) −0.741249 + 20.9216i −0.0329200 + 0.929161i
\(508\) 5.83652 + 3.36972i 0.258954 + 0.149507i
\(509\) 16.5519 + 28.6687i 0.733649 + 1.27072i 0.955313 + 0.295595i \(0.0955178\pi\)
−0.221664 + 0.975123i \(0.571149\pi\)
\(510\) 0 0
\(511\) 10.6127 + 12.9025i 0.469479 + 0.570773i
\(512\) 17.0367 0.752921
\(513\) −10.7280 24.1947i −0.473652 1.06822i
\(514\) 11.2836 + 6.51458i 0.497697 + 0.287346i
\(515\) 0 0
\(516\) 0.378733 0.605414i 0.0166728 0.0266519i
\(517\) −29.5658 −1.30030
\(518\) 16.5852 13.6418i 0.728711 0.599388i
\(519\) 8.26453 + 15.5624i 0.362773 + 0.683114i
\(520\) 0 0
\(521\) −21.4725 + 37.1914i −0.940726 + 1.62938i −0.176634 + 0.984277i \(0.556521\pi\)
−0.764092 + 0.645108i \(0.776812\pi\)
\(522\) −20.0587 + 9.75803i −0.877944 + 0.427097i
\(523\) −19.0959 33.0751i −0.835007 1.44627i −0.894025 0.448018i \(-0.852130\pi\)
0.0590174 0.998257i \(-0.481203\pi\)
\(524\) 1.75748 0.0767759
\(525\) 0 0
\(526\) 13.8974 0.605953
\(527\) 1.49555 + 2.59038i 0.0651474 + 0.112839i
\(528\) −12.4862 0.442385i −0.543394 0.0192523i
\(529\) 2.26734 3.92715i 0.0985802 0.170746i
\(530\) 0 0
\(531\) 19.5376 28.9022i 0.847859 1.25425i
\(532\) 10.5633 + 3.96240i 0.457975 + 0.171792i
\(533\) 4.44898 0.192707
\(534\) −11.3282 7.08668i −0.490221 0.306671i
\(535\) 0 0
\(536\) 9.81641 + 5.66751i 0.424004 + 0.244799i
\(537\) −4.83378 + 7.72692i −0.208593 + 0.333441i
\(538\) 0.502984 0.0216852
\(539\) 10.0549 + 29.4068i 0.433094 + 1.26664i
\(540\) 0 0
\(541\) 0.204923 + 0.354938i 0.00881035 + 0.0152600i 0.870397 0.492351i \(-0.163862\pi\)
−0.861587 + 0.507611i \(0.830529\pi\)
\(542\) −21.7504 12.5576i −0.934261 0.539396i
\(543\) −16.8131 0.595685i −0.721520 0.0255633i
\(544\) 1.91936 1.10814i 0.0822918 0.0475112i
\(545\) 0 0
\(546\) −0.609001 4.68313i −0.0260628 0.200420i
\(547\) 10.9605i 0.468638i −0.972160 0.234319i \(-0.924714\pi\)
0.972160 0.234319i \(-0.0752860\pi\)
\(548\) 2.07082 + 3.58677i 0.0884612 + 0.153219i
\(549\) −1.24449 + 0.605414i −0.0531137 + 0.0258384i
\(550\) 0 0
\(551\) 17.5604 + 30.4155i 0.748098 + 1.29574i
\(552\) 20.1110 10.6801i 0.855982 0.454576i
\(553\) 38.5254 6.40434i 1.63827 0.272340i
\(554\) 14.9790i 0.636398i
\(555\) 0 0
\(556\) 7.77354 + 4.48805i 0.329671 + 0.190336i
\(557\) 3.00967 5.21291i 0.127524 0.220878i −0.795193 0.606357i \(-0.792630\pi\)
0.922717 + 0.385479i \(0.125964\pi\)
\(558\) 1.34930 19.0179i 0.0571203 0.805093i
\(559\) 0.470652i 0.0199065i
\(560\) 0 0
\(561\) −3.44689 + 1.83049i −0.145528 + 0.0772835i
\(562\) −6.40150 + 3.69591i −0.270031 + 0.155903i
\(563\) 12.8772 + 7.43466i 0.542710 + 0.313334i 0.746176 0.665748i \(-0.231887\pi\)
−0.203467 + 0.979082i \(0.565221\pi\)
\(564\) −9.65032 0.341909i −0.406352 0.0143970i
\(565\) 0 0
\(566\) 4.78405 0.201089
\(567\) 11.4270 20.8908i 0.479889 0.877329i
\(568\) 24.1814i 1.01463i
\(569\) 4.55880 2.63203i 0.191115 0.110340i −0.401389 0.915907i \(-0.631473\pi\)
0.592504 + 0.805567i \(0.298139\pi\)
\(570\) 0 0
\(571\) −22.8775 + 39.6250i −0.957394 + 1.65825i −0.228601 + 0.973520i \(0.573415\pi\)
−0.728793 + 0.684734i \(0.759918\pi\)
\(572\) −3.07628 + 1.77609i −0.128626 + 0.0742621i
\(573\) 7.79103 + 14.6708i 0.325475 + 0.612881i
\(574\) 13.1018 2.17801i 0.546859 0.0909082i
\(575\) 0 0
\(576\) −23.8155 1.68968i −0.992312 0.0704032i
\(577\) 2.51561 4.35716i 0.104726 0.181391i −0.808900 0.587946i \(-0.799937\pi\)
0.913626 + 0.406555i \(0.133270\pi\)
\(578\) 9.02699 15.6352i 0.375473 0.650339i
\(579\) 7.67178 12.2635i 0.318828 0.509655i
\(580\) 0 0
\(581\) 26.7330 + 10.0278i 1.10907 + 0.416025i
\(582\) −11.4009 + 6.05453i −0.472582 + 0.250968i
\(583\) −35.1132 + 20.2726i −1.45424 + 0.839606i
\(584\) −9.65933 + 16.7305i −0.399706 + 0.692311i
\(585\) 0 0
\(586\) 28.0928 16.2194i 1.16050 0.670016i
\(587\) 18.5075i 0.763887i −0.924186 0.381944i \(-0.875255\pi\)
0.924186 0.381944i \(-0.124745\pi\)
\(588\) 2.94185 + 9.71470i 0.121320 + 0.400627i
\(589\) −30.0186 −1.23690
\(590\) 0 0
\(591\) −0.108902 + 3.07374i −0.00447963 + 0.126437i
\(592\) 10.5911 + 6.11477i 0.435291 + 0.251316i
\(593\) −16.0548 + 9.26927i −0.659293 + 0.380643i −0.792008 0.610511i \(-0.790964\pi\)
0.132714 + 0.991154i \(0.457631\pi\)
\(594\) 24.7366 + 2.63807i 1.01495 + 0.108241i
\(595\) 0 0
\(596\) 4.40658i 0.180501i
\(597\) 3.45261 5.51908i 0.141306 0.225881i
\(598\) −2.21420 + 3.83511i −0.0905453 + 0.156829i
\(599\) −0.501417 0.289493i −0.0204873 0.0118284i 0.489721 0.871879i \(-0.337099\pi\)
−0.510209 + 0.860051i \(0.670432\pi\)
\(600\) 0 0
\(601\) 29.8618i 1.21809i −0.793137 0.609044i \(-0.791553\pi\)
0.793137 0.609044i \(-0.208447\pi\)
\(602\) 0.230409 + 1.38603i 0.00939076 + 0.0564902i
\(603\) −9.20824 6.22467i −0.374988 0.253488i
\(604\) −2.93393 5.08172i −0.119380 0.206772i
\(605\) 0 0
\(606\) −0.158106 + 4.46251i −0.00642262 + 0.181277i
\(607\) 12.5550 + 21.7458i 0.509591 + 0.882637i 0.999938 + 0.0111098i \(0.00353644\pi\)
−0.490348 + 0.871527i \(0.663130\pi\)
\(608\) 22.2425i 0.902053i
\(609\) −12.1383 + 29.1736i −0.491868 + 1.18217i
\(610\) 0 0
\(611\) 5.51156 3.18210i 0.222974 0.128734i
\(612\) −1.14624 + 0.557615i −0.0463339 + 0.0225402i
\(613\) −1.26428 0.729932i −0.0510638 0.0294817i 0.474251 0.880390i \(-0.342719\pi\)
−0.525315 + 0.850908i \(0.676052\pi\)
\(614\) −17.7009 30.6589i −0.714351 1.23729i
\(615\) 0 0
\(616\) −27.7550 + 22.8294i −1.11828 + 0.919822i
\(617\) 6.56208 0.264179 0.132090 0.991238i \(-0.457831\pi\)
0.132090 + 0.991238i \(0.457831\pi\)
\(618\) 23.6916 + 14.8209i 0.953014 + 0.596183i
\(619\) −18.2419 10.5319i −0.733202 0.423315i 0.0863902 0.996261i \(-0.472467\pi\)
−0.819593 + 0.572947i \(0.805800\pi\)
\(620\) 0 0
\(621\) −20.4120 + 9.05071i −0.819104 + 0.363192i
\(622\) 17.7510 0.711751
\(623\) −18.6721 + 3.10400i −0.748084 + 0.124359i
\(624\) 2.37526 1.26140i 0.0950864 0.0504964i
\(625\) 0 0
\(626\) −2.48473 + 4.30367i −0.0993096 + 0.172009i
\(627\) 1.38685 39.1436i 0.0553855 1.56324i
\(628\) 1.21396 + 2.10265i 0.0484425 + 0.0839048i
\(629\) 3.82015 0.152319
\(630\) 0 0
\(631\) 17.5069 0.696937 0.348468 0.937321i \(-0.386702\pi\)
0.348468 + 0.937321i \(0.386702\pi\)
\(632\) 22.5803 + 39.1103i 0.898197 + 1.55572i
\(633\) −0.559387 + 15.7886i −0.0222336 + 0.627540i
\(634\) −15.8678 + 27.4839i −0.630192 + 1.09152i
\(635\) 0 0
\(636\) −11.6954 + 6.21095i −0.463754 + 0.246280i
\(637\) −5.03939 4.39974i −0.199668 0.174324i
\(638\) −33.0114 −1.30694
\(639\) 1.67809 23.6521i 0.0663841 0.935663i
\(640\) 0 0
\(641\) −9.98943 5.76740i −0.394559 0.227798i 0.289575 0.957155i \(-0.406486\pi\)
−0.684133 + 0.729357i \(0.739819\pi\)
\(642\) −21.4735 13.4333i −0.847493 0.530172i
\(643\) 17.3489 0.684173 0.342087 0.939668i \(-0.388866\pi\)
0.342087 + 0.939668i \(0.388866\pi\)
\(644\) 3.34290 8.91175i 0.131729 0.351172i
\(645\) 0 0
\(646\) −1.39378 2.41409i −0.0548374 0.0949812i
\(647\) −6.81366 3.93387i −0.267873 0.154656i 0.360048 0.932934i \(-0.382760\pi\)
−0.627920 + 0.778278i \(0.716094\pi\)
\(648\) 27.2592 + 3.88758i 1.07084 + 0.152719i
\(649\) 44.7120 25.8145i 1.75510 1.01331i
\(650\) 0 0
\(651\) −16.4073 21.4526i −0.643051 0.840795i
\(652\) 10.6813i 0.418314i
\(653\) −1.00180 1.73516i −0.0392033 0.0679021i 0.845758 0.533567i \(-0.179149\pi\)
−0.884961 + 0.465665i \(0.845815\pi\)
\(654\) 1.06613 30.0914i 0.0416891 1.17667i
\(655\) 0 0
\(656\) 3.78182 + 6.55031i 0.147655 + 0.255747i
\(657\) 10.6089 15.6939i 0.413893 0.612278i
\(658\) 14.6732 12.0692i 0.572021 0.470506i
\(659\) 44.8494i 1.74709i −0.486747 0.873543i \(-0.661817\pi\)
0.486747 0.873543i \(-0.338183\pi\)
\(660\) 0 0
\(661\) 10.4404 + 6.02776i 0.406084 + 0.234453i 0.689106 0.724661i \(-0.258004\pi\)
−0.283022 + 0.959113i \(0.591337\pi\)
\(662\) 1.43190 2.48012i 0.0556523 0.0963926i
\(663\) 0.445546 0.712216i 0.0173036 0.0276602i
\(664\) 33.0163i 1.28128i
\(665\) 0 0
\(666\) −20.1733 13.6370i −0.781701 0.528421i
\(667\) 25.6602 14.8149i 0.993566 0.573636i
\(668\) −11.4384 6.60397i −0.442565 0.255515i
\(669\) −0.719968 + 20.3210i −0.0278356 + 0.785654i
\(670\) 0 0
\(671\) −2.04812 −0.0790667
\(672\) −15.8955 + 12.1571i −0.613182 + 0.468970i
\(673\) 11.5641i 0.445763i −0.974845 0.222882i \(-0.928454\pi\)
0.974845 0.222882i \(-0.0715464\pi\)
\(674\) 20.0407 11.5705i 0.771941 0.445680i
\(675\) 0 0
\(676\) −5.05941 + 8.76315i −0.194593 + 0.337044i
\(677\) −18.6138 + 10.7467i −0.715388 + 0.413029i −0.813053 0.582190i \(-0.802196\pi\)
0.0976651 + 0.995219i \(0.468863\pi\)
\(678\) −8.34145 + 4.42979i −0.320352 + 0.170125i
\(679\) −6.42234 + 17.1212i −0.246467 + 0.657050i
\(680\) 0 0
\(681\) 22.2492 35.5660i 0.852593 1.36289i
\(682\) 14.1079 24.4355i 0.540218 0.935684i
\(683\) 8.66837 15.0140i 0.331686 0.574497i −0.651157 0.758943i \(-0.725716\pi\)
0.982843 + 0.184447i \(0.0590493\pi\)
\(684\) 0.905340 12.7605i 0.0346165 0.487909i
\(685\) 0 0
\(686\) −16.9944 10.4898i −0.648849 0.400501i
\(687\) 17.6356 + 33.2084i 0.672839 + 1.26698i
\(688\) −0.692950 + 0.400075i −0.0264185 + 0.0152527i
\(689\) 4.36379 7.55831i 0.166247 0.287949i
\(690\) 0 0
\(691\) −11.7251 + 6.76951i −0.446045 + 0.257524i −0.706158 0.708054i \(-0.749573\pi\)
0.260114 + 0.965578i \(0.416240\pi\)
\(692\) 8.51700i 0.323768i
\(693\) 28.7317 20.4036i 1.09143 0.775068i
\(694\) −19.5866 −0.743496
\(695\) 0 0
\(696\) −36.5159 1.29375i −1.38413 0.0490395i
\(697\) 2.04613 + 1.18133i 0.0775026 + 0.0447461i
\(698\) 12.2844 7.09240i 0.464971 0.268451i
\(699\) 16.8212 8.93303i 0.636237 0.337878i
\(700\) 0 0
\(701\) 41.8503i 1.58066i −0.612679 0.790332i \(-0.709908\pi\)
0.612679 0.790332i \(-0.290092\pi\)
\(702\) −4.89525 + 2.17056i −0.184759 + 0.0819227i
\(703\) −19.1694 + 33.2024i −0.722989 + 1.25225i
\(704\) −30.5998 17.6668i −1.15327 0.665842i
\(705\) 0 0
\(706\) 11.1006i 0.417775i
\(707\) 4.01817 + 4.88513i 0.151119 + 0.183724i
\(708\) 14.8926 7.90881i 0.559697 0.297231i
\(709\) −22.7397 39.3863i −0.854008 1.47918i −0.877563 0.479462i \(-0.840832\pi\)
0.0235552 0.999723i \(-0.492501\pi\)
\(710\) 0 0
\(711\) −19.3720 39.8211i −0.726506 1.49341i
\(712\) −10.9440 18.9556i −0.410145 0.710392i
\(713\) 25.3253i 0.948442i
\(714\) 0.963421 2.31552i 0.0360551 0.0866563i
\(715\) 0 0
\(716\) −3.81519 + 2.20270i −0.142580 + 0.0823189i
\(717\) 15.6245 + 0.553574i 0.583509 + 0.0206736i
\(718\) 11.0198 + 6.36230i 0.411256 + 0.237439i
\(719\) −0.114311 0.197992i −0.00426307 0.00738386i 0.863886 0.503687i \(-0.168024\pi\)
−0.868149 + 0.496304i \(0.834690\pi\)
\(720\) 0 0
\(721\) 39.0504 6.49162i 1.45431 0.241761i
\(722\) 7.48733 0.278650
\(723\) −4.66737 + 7.46090i −0.173581 + 0.277474i
\(724\) −7.04228 4.06586i −0.261724 0.151107i
\(725\) 0 0
\(726\) 13.7939 + 8.62913i 0.511939 + 0.320257i
\(727\) −19.2284 −0.713140 −0.356570 0.934269i \(-0.616054\pi\)
−0.356570 + 0.934269i \(0.616054\pi\)
\(728\) 2.71693 7.24299i 0.100696 0.268443i
\(729\) −26.3927 5.69415i −0.977509 0.210895i
\(730\) 0 0
\(731\) −0.124972 + 0.216457i −0.00462225 + 0.00800596i
\(732\) −0.668508 0.0236851i −0.0247088 0.000875428i
\(733\) 4.12825 + 7.15035i 0.152481 + 0.264104i 0.932139 0.362101i \(-0.117941\pi\)
−0.779658 + 0.626205i \(0.784607\pi\)
\(734\) −17.2253 −0.635797
\(735\) 0 0
\(736\) 18.7650 0.691688
\(737\) −8.22447 14.2452i −0.302952 0.524729i
\(738\) −6.58807 13.5425i −0.242510 0.498506i
\(739\) −5.17166 + 8.95758i −0.190243 + 0.329510i −0.945331 0.326114i \(-0.894261\pi\)
0.755088 + 0.655623i \(0.227594\pi\)
\(740\) 0 0
\(741\) 3.95441 + 7.44629i 0.145269 + 0.273546i
\(742\) 9.15076 24.3948i 0.335935 0.895561i
\(743\) −37.7580 −1.38521 −0.692604 0.721318i \(-0.743537\pi\)
−0.692604 + 0.721318i \(0.743537\pi\)
\(744\) 16.5632 26.4767i 0.607235 0.970681i
\(745\) 0 0
\(746\) −4.96508 2.86659i −0.181785 0.104953i
\(747\) 2.29119 32.2936i 0.0838302 1.18156i
\(748\) −1.88641 −0.0689741
\(749\) −35.3945 + 5.88387i −1.29329 + 0.214992i
\(750\) 0 0
\(751\) 21.4442 + 37.1424i 0.782509 + 1.35534i 0.930476 + 0.366352i \(0.119394\pi\)
−0.147968 + 0.988992i \(0.547273\pi\)
\(752\) 9.37013 + 5.40985i 0.341693 + 0.197277i
\(753\) 1.14529 32.3255i 0.0417365 1.17801i
\(754\) 6.15389 3.55295i 0.224111 0.129391i
\(755\) 0 0
\(756\) 9.61404 6.32749i 0.349659 0.230129i
\(757\) 30.1051i 1.09419i −0.837071 0.547094i \(-0.815734\pi\)
0.837071 0.547094i \(-0.184266\pi\)
\(758\) −12.9631 22.4527i −0.470840 0.815518i
\(759\) −33.0237 1.17002i −1.19868 0.0424691i
\(760\) 0 0
\(761\) 18.8860 + 32.7115i 0.684618 + 1.18579i 0.973557 + 0.228445i \(0.0733641\pi\)
−0.288939 + 0.957347i \(0.593303\pi\)
\(762\) 7.05196 + 13.2791i 0.255466 + 0.481051i
\(763\) −27.0951 32.9411i −0.980910 1.19255i
\(764\) 8.02904i 0.290480i
\(765\) 0 0
\(766\) 17.5577 + 10.1370i 0.634386 + 0.366263i
\(767\) −5.55671 + 9.62451i −0.200641 + 0.347521i
\(768\) −23.6127 14.7716i −0.852051 0.533023i
\(769\) 33.3656i 1.20319i 0.798800 + 0.601597i \(0.205469\pi\)
−0.798800 + 0.601597i \(0.794531\pi\)
\(770\) 0 0
\(771\) −9.81558 18.4831i −0.353499 0.665652i
\(772\) 6.05517 3.49595i 0.217930 0.125822i
\(773\) −0.993081 0.573356i −0.0357186 0.0206222i 0.482034 0.876152i \(-0.339898\pi\)
−0.517753 + 0.855530i \(0.673231\pi\)
\(774\) 1.43264 0.696944i 0.0514953 0.0250511i
\(775\) 0 0
\(776\) −21.1453 −0.759073
\(777\) −34.2053 + 4.44811i −1.22711 + 0.159575i
\(778\) 13.1743i 0.472321i
\(779\) −20.5348 + 11.8558i −0.735736 + 0.424778i
\(780\) 0 0
\(781\) 17.5456 30.3898i 0.627830 1.08743i
\(782\) −2.03666 + 1.17587i −0.0728309 + 0.0420489i
\(783\) 35.6268 + 3.79948i 1.27320 + 0.135782i
\(784\) 2.19412 11.1595i 0.0783614 0.398555i
\(785\) 0 0
\(786\) 3.32403 + 2.07944i 0.118564 + 0.0741711i
\(787\) 20.7393 35.9215i 0.739276 1.28046i −0.213546 0.976933i \(-0.568501\pi\)
0.952822 0.303530i \(-0.0981653\pi\)
\(788\) −0.743313 + 1.28746i −0.0264794 + 0.0458637i
\(789\) −18.9243 11.8386i −0.673724 0.421466i
\(790\) 0 0
\(791\) −4.69889 + 12.5267i −0.167073 + 0.445397i
\(792\) 33.7597 + 22.8212i 1.19960 + 0.810916i
\(793\) 0.381804 0.220434i 0.0135582 0.00782786i
\(794\) −10.1175 + 17.5241i −0.359058 + 0.621907i
\(795\) 0 0
\(796\) 2.72506 1.57332i 0.0965874 0.0557647i
\(797\) 49.5086i 1.75369i 0.480777 + 0.876843i \(0.340355\pi\)
−0.480777 + 0.876843i \(0.659645\pi\)
\(798\) 15.2907 + 19.9927i 0.541285 + 0.707734i
\(799\) 3.37976 0.119567
\(800\) 0 0
\(801\) 9.38904 + 19.3002i 0.331745 + 0.681938i
\(802\) −22.4103 12.9386i −0.791336 0.456878i
\(803\) 24.2786 14.0173i 0.856773 0.494658i
\(804\) −2.51974 4.74477i −0.0888645 0.167335i
\(805\) 0 0
\(806\) 6.07359i 0.213933i
\(807\) −0.684924 0.428472i −0.0241105 0.0150829i
\(808\) −3.65720 + 6.33446i −0.128660 + 0.222846i
\(809\) 21.7594 + 12.5628i 0.765018 + 0.441683i 0.831095 0.556131i \(-0.187715\pi\)
−0.0660764 + 0.997815i \(0.521048\pi\)
\(810\) 0 0
\(811\) 4.97517i 0.174702i 0.996178 + 0.0873509i \(0.0278401\pi\)
−0.996178 + 0.0873509i \(0.972160\pi\)
\(812\) −11.7954 + 9.70210i −0.413938 + 0.340477i
\(813\) 18.9207 + 35.6283i 0.663577 + 1.24954i
\(814\) −18.0181 31.2083i −0.631535 1.09385i
\(815\) 0 0
\(816\) 1.42734 + 0.0505704i 0.0499669 + 0.00177032i
\(817\) −1.25421 2.17235i −0.0438792 0.0760011i
\(818\) 18.4210i 0.644076i
\(819\) −3.16009 + 6.89591i −0.110422 + 0.240963i
\(820\) 0 0
\(821\) 12.0008 6.92866i 0.418830 0.241812i −0.275746 0.961230i \(-0.588925\pi\)
0.694577 + 0.719419i \(0.255592\pi\)
\(822\) −0.327162 + 9.23407i −0.0114111 + 0.322075i
\(823\) 39.9721 + 23.0779i 1.39334 + 0.804446i 0.993684 0.112219i \(-0.0357957\pi\)
0.399658 + 0.916665i \(0.369129\pi\)
\(824\) 22.8880 + 39.6432i 0.797343 + 1.38104i
\(825\) 0 0
\(826\) −11.6523 + 31.0635i −0.405435 + 1.08084i
\(827\) 18.6880 0.649844 0.324922 0.945741i \(-0.394662\pi\)
0.324922 + 0.945741i \(0.394662\pi\)
\(828\) −10.7654 0.763794i −0.374125 0.0265437i
\(829\) 14.9458 + 8.62894i 0.519088 + 0.299695i 0.736561 0.676371i \(-0.236448\pi\)
−0.217474 + 0.976066i \(0.569782\pi\)
\(830\) 0 0
\(831\) 12.7601 20.3973i 0.442642 0.707574i
\(832\) 7.60575 0.263682
\(833\) −1.14940 3.36158i −0.0398244 0.116472i
\(834\) 9.39235 + 17.6861i 0.325231 + 0.612421i
\(835\) 0 0
\(836\) 9.46597 16.3955i 0.327387 0.567052i
\(837\) −18.0380 + 24.7477i −0.623484 + 0.855405i
\(838\) −21.3793 37.0301i −0.738536 1.27918i
\(839\) 49.1689 1.69750 0.848750 0.528795i \(-0.177356\pi\)
0.848750 + 0.528795i \(0.177356\pi\)
\(840\) 0 0
\(841\) −18.5446 −0.639470
\(842\) −18.4085 31.8844i −0.634398 1.09881i
\(843\) 11.8655 + 0.420391i 0.408668 + 0.0144790i
\(844\) −3.81810 + 6.61315i −0.131425 + 0.227634i
\(845\) 0 0
\(846\) −17.8477 12.0649i −0.613617 0.414798i
\(847\) 22.7362 3.77960i 0.781226 0.129869i
\(848\) 14.8377 0.509527
\(849\) −6.51454 4.07534i −0.223578 0.139865i
\(850\) 0 0
\(851\) 28.0114 + 16.1724i 0.960218 + 0.554382i
\(852\) 6.07834 9.71639i 0.208241 0.332878i
\(853\) −8.86218 −0.303435 −0.151718 0.988424i \(-0.548480\pi\)
−0.151718 + 0.988424i \(0.548480\pi\)
\(854\) 1.01646 0.836071i 0.0347826 0.0286097i
\(855\) 0 0
\(856\) −20.7452 35.9318i −0.709058 1.22812i
\(857\) −0.851790 0.491781i −0.0290966 0.0167989i 0.485381 0.874303i \(-0.338681\pi\)
−0.514478 + 0.857504i \(0.672014\pi\)
\(858\) −7.91982 0.280598i −0.270378 0.00957945i
\(859\) 23.6244 13.6395i 0.806053 0.465375i −0.0395302 0.999218i \(-0.512586\pi\)
0.845583 + 0.533843i \(0.179253\pi\)
\(860\) 0 0
\(861\) −19.6964 8.19508i −0.671250 0.279288i
\(862\) 27.7897i 0.946519i
\(863\) −2.27629 3.94265i −0.0774857 0.134209i 0.824679 0.565601i \(-0.191356\pi\)
−0.902165 + 0.431392i \(0.858023\pi\)
\(864\) 18.3370 + 13.3654i 0.623837 + 0.454700i
\(865\) 0 0
\(866\) −6.42257 11.1242i −0.218248 0.378016i
\(867\) −25.6113 + 13.6011i −0.869804 + 0.461916i
\(868\) −2.14071 12.8774i −0.0726604 0.437089i
\(869\) 65.5354i 2.22314i
\(870\) 0 0
\(871\) 3.06636 + 1.77036i 0.103900 + 0.0599865i
\(872\) 24.6611 42.7142i 0.835129 1.44649i
\(873\) 20.6825 + 1.46739i 0.699995 + 0.0496638i
\(874\) 23.6019i 0.798346i
\(875\) 0 0
\(876\) 8.08667 4.29449i 0.273223 0.145097i
\(877\) 18.4956 10.6784i 0.624551 0.360584i −0.154088 0.988057i \(-0.549244\pi\)
0.778639 + 0.627473i \(0.215911\pi\)
\(878\) 15.6640 + 9.04360i 0.528634 + 0.305207i
\(879\) −52.0712 1.84487i −1.75632 0.0622260i
\(880\) 0 0
\(881\) −33.2551 −1.12039 −0.560196 0.828360i \(-0.689274\pi\)
−0.560196 + 0.828360i \(0.689274\pi\)
\(882\) −5.93025 + 21.8548i −0.199682 + 0.735890i
\(883\) 12.0561i 0.405721i −0.979208 0.202860i \(-0.934976\pi\)
0.979208 0.202860i \(-0.0650238\pi\)
\(884\) 0.351659 0.203031i 0.0118276 0.00682866i
\(885\) 0 0
\(886\) −1.29179 + 2.23745i −0.0433987 + 0.0751687i
\(887\) −20.2760 + 11.7064i −0.680803 + 0.393062i −0.800157 0.599790i \(-0.795251\pi\)
0.119355 + 0.992852i \(0.461917\pi\)
\(888\) −18.7078 35.2275i −0.627793 1.18216i
\(889\) 19.9417 + 7.48036i 0.668824 + 0.250883i
\(890\) 0 0
\(891\) −31.4371 24.6645i −1.05318 0.826290i
\(892\) −4.91415 + 8.51156i −0.164538 + 0.284988i
\(893\) −16.9595 + 29.3748i −0.567529 + 0.982990i
\(894\) −5.21384 + 8.33445i −0.174377 + 0.278746i
\(895\) 0 0
\(896\) −0.396319 + 0.0658829i −0.0132401 + 0.00220099i
\(897\) 6.28210 3.33616i 0.209753 0.111391i
\(898\) −23.7848 + 13.7322i −0.793711 + 0.458249i
\(899\) 20.3188 35.1932i 0.677670 1.17376i
\(900\) 0 0
\(901\) 4.01390 2.31743i 0.133722 0.0772046i
\(902\) 22.2875i 0.742091i
\(903\) 0.866948 2.08366i 0.0288502 0.0693397i
\(904\) −15.4709 −0.514556
\(905\) 0 0
\(906\) 0.463521 13.0828i 0.0153994 0.434646i
\(907\) 35.9415 + 20.7508i 1.19342 + 0.689020i 0.959080 0.283135i \(-0.0913744\pi\)
0.234338 + 0.972155i \(0.424708\pi\)
\(908\) 17.5608 10.1388i 0.582777 0.336466i
\(909\) 4.01674 5.94201i 0.133227 0.197084i
\(910\) 0 0
\(911\) 57.6428i 1.90979i 0.296941 + 0.954896i \(0.404034\pi\)
−0.296941 + 0.954896i \(0.595966\pi\)
\(912\) −7.60189 + 12.1518i −0.251724 + 0.402387i
\(913\) 23.9560 41.4930i 0.792828 1.37322i
\(914\) −3.21429 1.85577i −0.106319 0.0613835i
\(915\) 0 0
\(916\) 18.1743i 0.600496i
\(917\) 5.47895 0.910804i 0.180931 0.0300774i
\(918\) −2.82772 0.301566i −0.0933286 0.00995318i
\(919\) −5.45769 9.45300i −0.180033 0.311826i 0.761859 0.647743i \(-0.224287\pi\)
−0.941891 + 0.335918i \(0.890954\pi\)
\(920\) 0 0
\(921\) −2.01339 + 56.8276i −0.0663435 + 1.87253i
\(922\) 7.29905 + 12.6423i 0.240381 + 0.416353i
\(923\) 7.55357i 0.248629i
\(924\) 16.8908 2.19650i 0.555666 0.0722596i
\(925\) 0 0
\(926\) −4.79793 + 2.77009i −0.157670 + 0.0910307i
\(927\) −19.6360 40.3638i −0.644930 1.32572i
\(928\) −26.0767 15.0554i −0.856008 0.494217i
\(929\) 20.2064 + 34.9985i 0.662950 + 1.14826i 0.979837 + 0.199799i \(0.0640289\pi\)
−0.316887 + 0.948463i \(0.602638\pi\)
\(930\) 0 0
\(931\) 34.9845 + 6.87843i 1.14657 + 0.225431i
\(932\) 9.20592 0.301550
\(933\) −24.1719 15.1214i −0.791353 0.495052i
\(934\) 8.60828 + 4.96999i 0.281672 + 0.162623i
\(935\) 0 0
\(936\) −8.74958 0.620772i −0.285989 0.0202906i
\(937\) −5.67805 −0.185494 −0.0927468 0.995690i \(-0.529565\pi\)
−0.0927468 + 0.995690i \(0.529565\pi\)
\(938\) 9.89682 + 3.71241i 0.323143 + 0.121214i
\(939\) 7.04963 3.74376i 0.230056 0.122173i
\(940\) 0 0
\(941\) 6.29634 10.9056i 0.205255 0.355512i −0.744959 0.667110i \(-0.767531\pi\)
0.950214 + 0.311598i \(0.100864\pi\)
\(942\) −0.191790 + 5.41323i −0.00624885 + 0.176373i
\(943\) 10.0022 + 17.3243i 0.325716 + 0.564157i
\(944\) −18.8938 −0.614940
\(945\) 0 0
\(946\) 2.35776 0.0766575
\(947\) −15.6709 27.1427i −0.509234 0.882020i −0.999943 0.0106960i \(-0.996595\pi\)
0.490708 0.871324i \(-0.336738\pi\)
\(948\) 0.757874 21.3909i 0.0246146 0.694743i
\(949\) −3.01729 + 5.22611i −0.0979455 + 0.169647i
\(950\) 0 0
\(951\) 45.0200 23.9082i 1.45987 0.775277i
\(952\) 3.17276 2.60970i 0.102830 0.0845808i
\(953\) 43.7751 1.41802 0.709008 0.705200i \(-0.249143\pi\)
0.709008 + 0.705200i \(0.249143\pi\)
\(954\) −29.4691 2.09079i −0.954097 0.0676919i
\(955\) 0 0
\(956\) 6.54444 + 3.77843i 0.211662 + 0.122203i
\(957\) 44.9524 + 28.1212i 1.45310 + 0.909028i
\(958\) 22.2540 0.718994
\(959\) 8.31462 + 10.1086i 0.268493 + 0.326423i
\(960\) 0 0
\(961\) 1.86698 + 3.23370i 0.0602251 + 0.104313i
\(962\) 6.71776 + 3.87850i 0.216589 + 0.125048i
\(963\) 17.7976 + 36.5849i 0.573521 + 1.17893i
\(964\) −3.68385 + 2.12687i −0.118649 + 0.0685019i
\(965\) 0 0
\(966\) 16.8669 12.9001i 0.542685 0.415053i
\(967\) 36.3052i 1.16750i 0.811935 + 0.583748i \(0.198415\pi\)
−0.811935 + 0.583748i \(0.801585\pi\)
\(968\) 13.3261 + 23.0814i 0.428316 + 0.741864i
\(969\) −0.158535 + 4.47463i −0.00509288 + 0.143746i
\(970\) 0 0
\(971\) −24.9129 43.1503i −0.799492 1.38476i −0.919948 0.392041i \(-0.871769\pi\)
0.120456 0.992719i \(-0.461564\pi\)
\(972\) −9.97588 8.41406i −0.319976 0.269881i
\(973\) 26.5599 + 9.96292i 0.851472 + 0.319397i
\(974\) 2.66887i 0.0855161i
\(975\) 0 0
\(976\) 0.649099 + 0.374757i 0.0207772 + 0.0119957i
\(977\) 13.8777 24.0369i 0.443987 0.769008i −0.553994 0.832521i \(-0.686897\pi\)
0.997981 + 0.0635127i \(0.0202304\pi\)
\(978\) 12.6381 20.2023i 0.404121 0.645998i
\(979\) 31.7631i 1.01515i
\(980\) 0 0
\(981\) −27.0854 + 40.0679i −0.864772 + 1.27927i
\(982\) 19.8753 11.4750i 0.634245 0.366181i
\(983\) −36.4417 21.0396i −1.16231 0.671060i −0.210453 0.977604i \(-0.567494\pi\)
−0.951856 + 0.306544i \(0.900827\pi\)
\(984\) 0.873468 24.6535i 0.0278451 0.785924i
\(985\) 0 0
\(986\) 3.77364 0.120177
\(987\) −30.2621 + 3.93532i −0.963253 + 0.125263i
\(988\) 4.07521i 0.129650i
\(989\) −1.83272 + 1.05812i −0.0582770 + 0.0336463i
\(990\) 0 0
\(991\) −2.86154 + 4.95633i −0.0908997 + 0.157443i −0.907890 0.419209i \(-0.862308\pi\)
0.816990 + 0.576652i \(0.195641\pi\)
\(992\) 22.2884 12.8682i 0.707656 0.408566i
\(993\) −4.06256 + 2.15745i −0.128922 + 0.0684647i
\(994\) 3.69787 + 22.2445i 0.117289 + 0.705554i
\(995\) 0 0
\(996\) 8.29912 13.2663i 0.262968 0.420360i
\(997\) −5.56719 + 9.64266i −0.176315 + 0.305386i −0.940615 0.339474i \(-0.889751\pi\)
0.764301 + 0.644860i \(0.223084\pi\)
\(998\) −17.6513 + 30.5729i −0.558741 + 0.967768i
\(999\) 15.8537 + 35.7546i 0.501588 + 1.13123i
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 525.2.q.e.374.6 16
3.2 odd 2 525.2.q.f.374.3 16
5.2 odd 4 525.2.t.f.101.2 8
5.3 odd 4 105.2.s.d.101.3 yes 8
5.4 even 2 inner 525.2.q.e.374.3 16
7.5 odd 6 525.2.q.f.299.6 16
15.2 even 4 525.2.t.g.101.3 8
15.8 even 4 105.2.s.c.101.2 yes 8
15.14 odd 2 525.2.q.f.374.6 16
21.5 even 6 inner 525.2.q.e.299.3 16
35.3 even 12 735.2.b.d.146.6 8
35.12 even 12 525.2.t.g.26.3 8
35.13 even 4 735.2.s.l.521.3 8
35.18 odd 12 735.2.b.c.146.6 8
35.19 odd 6 525.2.q.f.299.3 16
35.23 odd 12 735.2.s.k.656.2 8
35.33 even 12 105.2.s.c.26.2 8
105.23 even 12 735.2.s.l.656.3 8
105.38 odd 12 735.2.b.c.146.3 8
105.47 odd 12 525.2.t.f.26.2 8
105.53 even 12 735.2.b.d.146.3 8
105.68 odd 12 105.2.s.d.26.3 yes 8
105.83 odd 4 735.2.s.k.521.2 8
105.89 even 6 inner 525.2.q.e.299.6 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.s.c.26.2 8 35.33 even 12
105.2.s.c.101.2 yes 8 15.8 even 4
105.2.s.d.26.3 yes 8 105.68 odd 12
105.2.s.d.101.3 yes 8 5.3 odd 4
525.2.q.e.299.3 16 21.5 even 6 inner
525.2.q.e.299.6 16 105.89 even 6 inner
525.2.q.e.374.3 16 5.4 even 2 inner
525.2.q.e.374.6 16 1.1 even 1 trivial
525.2.q.f.299.3 16 35.19 odd 6
525.2.q.f.299.6 16 7.5 odd 6
525.2.q.f.374.3 16 3.2 odd 2
525.2.q.f.374.6 16 15.14 odd 2
525.2.t.f.26.2 8 105.47 odd 12
525.2.t.f.101.2 8 5.2 odd 4
525.2.t.g.26.3 8 35.12 even 12
525.2.t.g.101.3 8 15.2 even 4
735.2.b.c.146.3 8 105.38 odd 12
735.2.b.c.146.6 8 35.18 odd 12
735.2.b.d.146.3 8 105.53 even 12
735.2.b.d.146.6 8 35.3 even 12
735.2.s.k.521.2 8 105.83 odd 4
735.2.s.k.656.2 8 35.23 odd 12
735.2.s.l.521.3 8 35.13 even 4
735.2.s.l.656.3 8 105.23 even 12