Properties

Label 525.2.q.g.299.7
Level $525$
Weight $2$
Character 525.299
Analytic conductor $4.192$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

Related objects

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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: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 299.7
Character \(\chi\) \(=\) 525.299
Dual form 525.2.q.g.374.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.450666 + 0.780577i) q^{2} +(0.248842 - 1.71408i) q^{3} +(0.593800 + 1.02849i) q^{4} +(1.22583 + 0.966719i) q^{6} +(-2.64365 - 0.105498i) q^{7} -2.87309 q^{8} +(-2.87616 - 0.853070i) q^{9} +O(q^{10})\) \(q+(-0.450666 + 0.780577i) q^{2} +(0.248842 - 1.71408i) q^{3} +(0.593800 + 1.02849i) q^{4} +(1.22583 + 0.966719i) q^{6} +(-2.64365 - 0.105498i) q^{7} -2.87309 q^{8} +(-2.87616 - 0.853070i) q^{9} +(5.46176 - 3.15335i) q^{11} +(1.91068 - 0.761890i) q^{12} +3.77183 q^{13} +(1.27375 - 2.01603i) q^{14} +(0.107205 - 0.185685i) q^{16} +(3.27294 - 1.88963i) q^{17} +(1.96207 - 1.86061i) q^{18} +(4.57893 + 2.64365i) q^{19} +(-0.838682 + 4.50518i) q^{21} +5.68443i q^{22} +(3.38933 - 5.87050i) q^{23} +(-0.714944 + 4.92471i) q^{24} +(-1.69984 + 2.94420i) q^{26} +(-2.17794 + 4.71769i) q^{27} +(-1.46129 - 2.78161i) q^{28} -3.06327i q^{29} +(0.349819 - 0.201968i) q^{31} +(-2.77646 - 4.80897i) q^{32} +(-4.04598 - 10.1466i) q^{33} +3.40637i q^{34} +(-0.830485 - 3.46465i) q^{36} +(1.15705 + 0.668021i) q^{37} +(-4.12714 + 2.38281i) q^{38} +(0.938588 - 6.46523i) q^{39} -6.53749 q^{41} +(-3.13867 - 2.68499i) q^{42} +4.84564i q^{43} +(6.48638 + 3.74491i) q^{44} +(3.05492 + 5.29127i) q^{46} +(1.68073 + 0.970371i) q^{47} +(-0.291602 - 0.229964i) q^{48} +(6.97774 + 0.557800i) q^{49} +(-2.42454 - 6.08030i) q^{51} +(2.23971 + 3.87929i) q^{52} +(0.720381 + 1.24774i) q^{53} +(-2.70100 - 3.82615i) q^{54} +(7.59543 + 0.303106i) q^{56} +(5.67086 - 7.19082i) q^{57} +(2.39112 + 1.38051i) q^{58} +(1.60223 + 2.77514i) q^{59} +(-11.3644 - 6.56124i) q^{61} +0.364081i q^{62} +(7.51354 + 2.55864i) q^{63} +5.43385 q^{64} +(9.74358 + 1.41452i) q^{66} +(-2.68611 + 1.55082i) q^{67} +(3.88694 + 2.24412i) q^{68} +(-9.21911 - 7.27042i) q^{69} -2.21562i q^{71} +(8.26345 + 2.45094i) q^{72} +(1.25932 + 2.18121i) q^{73} +(-1.04288 + 0.602109i) q^{74} +6.27919i q^{76} +(-14.7716 + 7.76013i) q^{77} +(4.62362 + 3.64630i) q^{78} +(3.05960 - 5.29938i) q^{79} +(7.54454 + 4.90712i) q^{81} +(2.94623 - 5.10301i) q^{82} +8.53654i q^{83} +(-5.13154 + 1.81259i) q^{84} +(-3.78240 - 2.18377i) q^{86} +(-5.25069 - 0.762268i) q^{87} +(-15.6921 + 9.05984i) q^{88} +(0.590783 - 1.02327i) q^{89} +(-9.97138 - 0.397921i) q^{91} +8.05034 q^{92} +(-0.259141 - 0.649878i) q^{93} +(-1.51490 + 0.874627i) q^{94} +(-8.93387 + 3.56241i) q^{96} -9.10556 q^{97} +(-3.58004 + 5.19528i) q^{98} +(-18.3989 + 4.41026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.450666 + 0.780577i −0.318669 + 0.551951i −0.980211 0.197957i \(-0.936569\pi\)
0.661541 + 0.749909i \(0.269903\pi\)
\(3\) 0.248842 1.71408i 0.143669 0.989626i
\(4\) 0.593800 + 1.02849i 0.296900 + 0.514245i
\(5\) 0 0
\(6\) 1.22583 + 0.966719i 0.500443 + 0.394662i
\(7\) −2.64365 0.105498i −0.999205 0.0398746i
\(8\) −2.87309 −1.01579
\(9\) −2.87616 0.853070i −0.958719 0.284357i
\(10\) 0 0
\(11\) 5.46176 3.15335i 1.64678 0.950770i 0.668442 0.743765i \(-0.266962\pi\)
0.978340 0.207005i \(-0.0663717\pi\)
\(12\) 1.91068 0.761890i 0.551566 0.219939i
\(13\) 3.77183 1.04612 0.523059 0.852297i \(-0.324791\pi\)
0.523059 + 0.852297i \(0.324791\pi\)
\(14\) 1.27375 2.01603i 0.340425 0.538806i
\(15\) 0 0
\(16\) 0.107205 0.185685i 0.0268013 0.0464212i
\(17\) 3.27294 1.88963i 0.793804 0.458303i −0.0474963 0.998871i \(-0.515124\pi\)
0.841300 + 0.540569i \(0.181791\pi\)
\(18\) 1.96207 1.86061i 0.462465 0.438550i
\(19\) 4.57893 + 2.64365i 1.05048 + 0.606494i 0.922783 0.385319i \(-0.125909\pi\)
0.127695 + 0.991813i \(0.459242\pi\)
\(20\) 0 0
\(21\) −0.838682 + 4.50518i −0.183015 + 0.983110i
\(22\) 5.68443i 1.21192i
\(23\) 3.38933 5.87050i 0.706725 1.22408i −0.259340 0.965786i \(-0.583505\pi\)
0.966065 0.258298i \(-0.0831615\pi\)
\(24\) −0.714944 + 4.92471i −0.145937 + 1.00525i
\(25\) 0 0
\(26\) −1.69984 + 2.94420i −0.333365 + 0.577406i
\(27\) −2.17794 + 4.71769i −0.419144 + 0.907920i
\(28\) −1.46129 2.78161i −0.276158 0.525675i
\(29\) 3.06327i 0.568834i −0.958701 0.284417i \(-0.908200\pi\)
0.958701 0.284417i \(-0.0918000\pi\)
\(30\) 0 0
\(31\) 0.349819 0.201968i 0.0628294 0.0362746i −0.468256 0.883593i \(-0.655118\pi\)
0.531086 + 0.847318i \(0.321784\pi\)
\(32\) −2.77646 4.80897i −0.490813 0.850114i
\(33\) −4.04598 10.1466i −0.704315 1.76629i
\(34\) 3.40637i 0.584188i
\(35\) 0 0
\(36\) −0.830485 3.46465i −0.138414 0.577442i
\(37\) 1.15705 + 0.668021i 0.190217 + 0.109822i 0.592084 0.805876i \(-0.298305\pi\)
−0.401867 + 0.915698i \(0.631639\pi\)
\(38\) −4.12714 + 2.38281i −0.669511 + 0.386542i
\(39\) 0.938588 6.46523i 0.150294 1.03526i
\(40\) 0 0
\(41\) −6.53749 −1.02098 −0.510492 0.859882i \(-0.670537\pi\)
−0.510492 + 0.859882i \(0.670537\pi\)
\(42\) −3.13867 2.68499i −0.484308 0.414303i
\(43\) 4.84564i 0.738954i 0.929240 + 0.369477i \(0.120463\pi\)
−0.929240 + 0.369477i \(0.879537\pi\)
\(44\) 6.48638 + 3.74491i 0.977858 + 0.564567i
\(45\) 0 0
\(46\) 3.05492 + 5.29127i 0.450423 + 0.780156i
\(47\) 1.68073 + 0.970371i 0.245160 + 0.141543i 0.617546 0.786535i \(-0.288127\pi\)
−0.372386 + 0.928078i \(0.621460\pi\)
\(48\) −0.291602 0.229964i −0.0420891 0.0331925i
\(49\) 6.97774 + 0.557800i 0.996820 + 0.0796858i
\(50\) 0 0
\(51\) −2.42454 6.08030i −0.339503 0.851412i
\(52\) 2.23971 + 3.87929i 0.310592 + 0.537961i
\(53\) 0.720381 + 1.24774i 0.0989519 + 0.171390i 0.911251 0.411851i \(-0.135118\pi\)
−0.812299 + 0.583241i \(0.801784\pi\)
\(54\) −2.70100 3.82615i −0.367559 0.520673i
\(55\) 0 0
\(56\) 7.59543 + 0.303106i 1.01498 + 0.0405042i
\(57\) 5.67086 7.19082i 0.751123 0.952447i
\(58\) 2.39112 + 1.38051i 0.313969 + 0.181270i
\(59\) 1.60223 + 2.77514i 0.208592 + 0.361293i 0.951271 0.308355i \(-0.0997785\pi\)
−0.742679 + 0.669648i \(0.766445\pi\)
\(60\) 0 0
\(61\) −11.3644 6.56124i −1.45506 0.840080i −0.456300 0.889826i \(-0.650825\pi\)
−0.998762 + 0.0497461i \(0.984159\pi\)
\(62\) 0.364081i 0.0462384i
\(63\) 7.51354 + 2.55864i 0.946618 + 0.322359i
\(64\) 5.43385 0.679231
\(65\) 0 0
\(66\) 9.74358 + 1.41452i 1.19935 + 0.174116i
\(67\) −2.68611 + 1.55082i −0.328160 + 0.189463i −0.655024 0.755608i \(-0.727341\pi\)
0.326864 + 0.945071i \(0.394008\pi\)
\(68\) 3.88694 + 2.24412i 0.471360 + 0.272140i
\(69\) −9.21911 7.27042i −1.10985 0.875256i
\(70\) 0 0
\(71\) 2.21562i 0.262946i −0.991320 0.131473i \(-0.958029\pi\)
0.991320 0.131473i \(-0.0419707\pi\)
\(72\) 8.26345 + 2.45094i 0.973857 + 0.288847i
\(73\) 1.25932 + 2.18121i 0.147393 + 0.255292i 0.930263 0.366893i \(-0.119579\pi\)
−0.782870 + 0.622185i \(0.786245\pi\)
\(74\) −1.04288 + 0.602109i −0.121233 + 0.0699938i
\(75\) 0 0
\(76\) 6.27919i 0.720272i
\(77\) −14.7716 + 7.76013i −1.68338 + 0.884349i
\(78\) 4.62362 + 3.64630i 0.523522 + 0.412862i
\(79\) 3.05960 5.29938i 0.344232 0.596227i −0.640982 0.767556i \(-0.721473\pi\)
0.985214 + 0.171329i \(0.0548061\pi\)
\(80\) 0 0
\(81\) 7.54454 + 4.90712i 0.838283 + 0.545236i
\(82\) 2.94623 5.10301i 0.325356 0.563534i
\(83\) 8.53654i 0.937007i 0.883462 + 0.468503i \(0.155207\pi\)
−0.883462 + 0.468503i \(0.844793\pi\)
\(84\) −5.13154 + 1.81259i −0.559897 + 0.197770i
\(85\) 0 0
\(86\) −3.78240 2.18377i −0.407867 0.235482i
\(87\) −5.25069 0.762268i −0.562933 0.0817237i
\(88\) −15.6921 + 9.05984i −1.67278 + 0.965782i
\(89\) 0.590783 1.02327i 0.0626229 0.108466i −0.833014 0.553252i \(-0.813387\pi\)
0.895637 + 0.444786i \(0.146720\pi\)
\(90\) 0 0
\(91\) −9.97138 0.397921i −1.04529 0.0417135i
\(92\) 8.05034 0.839306
\(93\) −0.259141 0.649878i −0.0268716 0.0673892i
\(94\) −1.51490 + 0.874627i −0.156250 + 0.0902109i
\(95\) 0 0
\(96\) −8.93387 + 3.56241i −0.911809 + 0.363587i
\(97\) −9.10556 −0.924530 −0.462265 0.886742i \(-0.652963\pi\)
−0.462265 + 0.886742i \(0.652963\pi\)
\(98\) −3.58004 + 5.19528i −0.361639 + 0.524803i
\(99\) −18.3989 + 4.41026i −1.84916 + 0.443247i
\(100\) 0 0
\(101\) 1.15241 + 1.99604i 0.114669 + 0.198613i 0.917647 0.397395i \(-0.130086\pi\)
−0.802978 + 0.596008i \(0.796753\pi\)
\(102\) 5.83880 + 0.847647i 0.578128 + 0.0839296i
\(103\) −3.89335 + 6.74347i −0.383623 + 0.664454i −0.991577 0.129518i \(-0.958657\pi\)
0.607954 + 0.793972i \(0.291990\pi\)
\(104\) −10.8368 −1.06264
\(105\) 0 0
\(106\) −1.29861 −0.126132
\(107\) 2.72952 4.72768i 0.263873 0.457042i −0.703395 0.710800i \(-0.748333\pi\)
0.967268 + 0.253758i \(0.0816666\pi\)
\(108\) −6.14536 + 0.561371i −0.591337 + 0.0540179i
\(109\) −3.29331 5.70418i −0.315442 0.546362i 0.664089 0.747653i \(-0.268819\pi\)
−0.979531 + 0.201292i \(0.935486\pi\)
\(110\) 0 0
\(111\) 1.43296 1.81704i 0.136011 0.172466i
\(112\) −0.303002 + 0.479575i −0.0286310 + 0.0453156i
\(113\) −0.214344 −0.0201638 −0.0100819 0.999949i \(-0.503209\pi\)
−0.0100819 + 0.999949i \(0.503209\pi\)
\(114\) 3.05732 + 7.66720i 0.286344 + 0.718099i
\(115\) 0 0
\(116\) 3.15054 1.81897i 0.292520 0.168887i
\(117\) −10.8484 3.21763i −1.00293 0.297470i
\(118\) −2.88828 −0.265888
\(119\) −8.85184 + 4.65023i −0.811447 + 0.426286i
\(120\) 0 0
\(121\) 14.3872 24.9193i 1.30793 2.26539i
\(122\) 10.2431 5.91386i 0.927367 0.535415i
\(123\) −1.62680 + 11.2058i −0.146683 + 1.01039i
\(124\) 0.415445 + 0.239857i 0.0373081 + 0.0215398i
\(125\) 0 0
\(126\) −5.38332 + 4.71181i −0.479584 + 0.419761i
\(127\) 1.05320i 0.0934560i 0.998908 + 0.0467280i \(0.0148794\pi\)
−0.998908 + 0.0467280i \(0.985121\pi\)
\(128\) 3.10407 5.37640i 0.274363 0.475211i
\(129\) 8.30583 + 1.20580i 0.731288 + 0.106165i
\(130\) 0 0
\(131\) −5.22860 + 9.05621i −0.456825 + 0.791245i −0.998791 0.0491560i \(-0.984347\pi\)
0.541966 + 0.840401i \(0.317680\pi\)
\(132\) 8.03317 10.1863i 0.699197 0.886603i
\(133\) −11.8262 7.47194i −1.02546 0.647899i
\(134\) 2.79562i 0.241505i
\(135\) 0 0
\(136\) −9.40343 + 5.42907i −0.806338 + 0.465539i
\(137\) 3.64697 + 6.31673i 0.311581 + 0.539675i 0.978705 0.205272i \(-0.0658080\pi\)
−0.667124 + 0.744947i \(0.732475\pi\)
\(138\) 9.82987 3.91969i 0.836774 0.333666i
\(139\) 10.8548i 0.920693i 0.887739 + 0.460347i \(0.152275\pi\)
−0.887739 + 0.460347i \(0.847725\pi\)
\(140\) 0 0
\(141\) 2.08153 2.63944i 0.175297 0.222281i
\(142\) 1.72946 + 0.998507i 0.145133 + 0.0837928i
\(143\) 20.6008 11.8939i 1.72273 0.994617i
\(144\) −0.466740 + 0.442605i −0.0388950 + 0.0368837i
\(145\) 0 0
\(146\) −2.27014 −0.187878
\(147\) 2.69247 11.8216i 0.222071 0.975031i
\(148\) 1.58668i 0.130425i
\(149\) −2.54658 1.47027i −0.208624 0.120449i 0.392048 0.919945i \(-0.371767\pi\)
−0.600672 + 0.799496i \(0.705100\pi\)
\(150\) 0 0
\(151\) −2.49298 4.31797i −0.202876 0.351391i 0.746578 0.665298i \(-0.231695\pi\)
−0.949454 + 0.313907i \(0.898362\pi\)
\(152\) −13.1557 7.59543i −1.06707 0.616071i
\(153\) −11.0255 + 2.64283i −0.891356 + 0.213660i
\(154\) 0.599698 15.0276i 0.0483250 1.21096i
\(155\) 0 0
\(156\) 7.20676 2.87372i 0.577002 0.230082i
\(157\) 3.54960 + 6.14808i 0.283289 + 0.490671i 0.972193 0.234182i \(-0.0752412\pi\)
−0.688904 + 0.724853i \(0.741908\pi\)
\(158\) 2.75772 + 4.77650i 0.219392 + 0.379998i
\(159\) 2.31798 0.924303i 0.183828 0.0733020i
\(160\) 0 0
\(161\) −9.57953 + 15.1620i −0.754973 + 1.19493i
\(162\) −7.23046 + 3.67762i −0.568079 + 0.288941i
\(163\) 15.3156 + 8.84246i 1.19961 + 0.692595i 0.960468 0.278390i \(-0.0898008\pi\)
0.239141 + 0.970985i \(0.423134\pi\)
\(164\) −3.88196 6.72375i −0.303130 0.525036i
\(165\) 0 0
\(166\) −6.66343 3.84713i −0.517182 0.298595i
\(167\) 10.9235i 0.845287i 0.906296 + 0.422643i \(0.138898\pi\)
−0.906296 + 0.422643i \(0.861102\pi\)
\(168\) 2.40961 12.9438i 0.185905 0.998633i
\(169\) 1.22669 0.0943611
\(170\) 0 0
\(171\) −10.9145 11.5097i −0.834653 0.880168i
\(172\) −4.98370 + 2.87734i −0.380004 + 0.219395i
\(173\) −20.0145 11.5554i −1.52167 0.878539i −0.999672 0.0255936i \(-0.991852\pi\)
−0.522001 0.852945i \(-0.674814\pi\)
\(174\) 2.96132 3.75504i 0.224497 0.284669i
\(175\) 0 0
\(176\) 1.35222i 0.101927i
\(177\) 5.15552 2.05578i 0.387513 0.154522i
\(178\) 0.532492 + 0.922304i 0.0399120 + 0.0691296i
\(179\) −15.2776 + 8.82051i −1.14190 + 0.659276i −0.946900 0.321527i \(-0.895804\pi\)
−0.194999 + 0.980803i \(0.562470\pi\)
\(180\) 0 0
\(181\) 14.8545i 1.10413i 0.833802 + 0.552064i \(0.186160\pi\)
−0.833802 + 0.552064i \(0.813840\pi\)
\(182\) 4.80438 7.60411i 0.356124 0.563654i
\(183\) −14.0744 + 17.8468i −1.04041 + 1.31927i
\(184\) −9.73785 + 16.8665i −0.717884 + 1.24341i
\(185\) 0 0
\(186\) 0.624066 + 0.0905986i 0.0457587 + 0.00664301i
\(187\) 11.9173 20.6414i 0.871481 1.50945i
\(188\) 2.30482i 0.168097i
\(189\) 6.25541 12.2421i 0.455014 0.890484i
\(190\) 0 0
\(191\) −16.1877 9.34599i −1.17130 0.676252i −0.217316 0.976101i \(-0.569730\pi\)
−0.953987 + 0.299850i \(0.903064\pi\)
\(192\) 1.35217 9.31407i 0.0975843 0.672185i
\(193\) 2.24781 1.29778i 0.161801 0.0934160i −0.416913 0.908946i \(-0.636888\pi\)
0.578714 + 0.815530i \(0.303555\pi\)
\(194\) 4.10357 7.10759i 0.294619 0.510295i
\(195\) 0 0
\(196\) 3.56969 + 7.50776i 0.254978 + 0.536269i
\(197\) −7.83600 −0.558292 −0.279146 0.960249i \(-0.590051\pi\)
−0.279146 + 0.960249i \(0.590051\pi\)
\(198\) 4.84921 16.3493i 0.344619 1.16189i
\(199\) −3.06915 + 1.77198i −0.217566 + 0.125612i −0.604823 0.796360i \(-0.706756\pi\)
0.387256 + 0.921972i \(0.373423\pi\)
\(200\) 0 0
\(201\) 1.98983 + 4.99012i 0.140351 + 0.351976i
\(202\) −2.07741 −0.146166
\(203\) −0.323169 + 8.09819i −0.0226820 + 0.568382i
\(204\) 4.81384 6.10410i 0.337036 0.427372i
\(205\) 0 0
\(206\) −3.50920 6.07811i −0.244498 0.423482i
\(207\) −14.7562 + 13.9931i −1.02563 + 0.972590i
\(208\) 0.404359 0.700371i 0.0280373 0.0485620i
\(209\) 33.3453 2.30655
\(210\) 0 0
\(211\) 23.9742 1.65045 0.825225 0.564804i \(-0.191048\pi\)
0.825225 + 0.564804i \(0.191048\pi\)
\(212\) −0.855523 + 1.48181i −0.0587576 + 0.101771i
\(213\) −3.79776 0.551339i −0.260218 0.0377771i
\(214\) 2.46021 + 4.26121i 0.168177 + 0.291290i
\(215\) 0 0
\(216\) 6.25741 13.5543i 0.425763 0.922256i
\(217\) −0.946107 + 0.497028i −0.0642259 + 0.0337404i
\(218\) 5.93674 0.402087
\(219\) 4.05215 1.61581i 0.273819 0.109186i
\(220\) 0 0
\(221\) 12.3450 7.12736i 0.830412 0.479438i
\(222\) 0.772552 + 1.93742i 0.0518503 + 0.130031i
\(223\) 16.9380 1.13425 0.567125 0.823632i \(-0.308056\pi\)
0.567125 + 0.823632i \(0.308056\pi\)
\(224\) 6.83264 + 13.0061i 0.456525 + 0.869009i
\(225\) 0 0
\(226\) 0.0965976 0.167312i 0.00642557 0.0111294i
\(227\) −18.9635 + 10.9486i −1.25865 + 0.726685i −0.972813 0.231592i \(-0.925606\pi\)
−0.285842 + 0.958277i \(0.592273\pi\)
\(228\) 10.7630 + 1.56252i 0.712800 + 0.103481i
\(229\) 0.218276 + 0.126022i 0.0144241 + 0.00832775i 0.507195 0.861831i \(-0.330682\pi\)
−0.492771 + 0.870159i \(0.664016\pi\)
\(230\) 0 0
\(231\) 9.62570 + 27.2508i 0.633325 + 1.79297i
\(232\) 8.80103i 0.577816i
\(233\) −7.47118 + 12.9405i −0.489453 + 0.847758i −0.999926 0.0121359i \(-0.996137\pi\)
0.510473 + 0.859894i \(0.329470\pi\)
\(234\) 7.40061 7.01791i 0.483793 0.458775i
\(235\) 0 0
\(236\) −1.90281 + 3.29576i −0.123862 + 0.214535i
\(237\) −8.32221 6.56311i −0.540586 0.426320i
\(238\) 0.359366 9.00525i 0.0232943 0.583723i
\(239\) 19.5021i 1.26149i 0.775991 + 0.630744i \(0.217250\pi\)
−0.775991 + 0.630744i \(0.782750\pi\)
\(240\) 0 0
\(241\) 8.54154 4.93146i 0.550209 0.317663i −0.198997 0.980000i \(-0.563768\pi\)
0.749206 + 0.662337i \(0.230435\pi\)
\(242\) 12.9676 + 22.4606i 0.833592 + 1.44382i
\(243\) 10.2886 11.7109i 0.660015 0.751253i
\(244\) 15.5842i 0.997678i
\(245\) 0 0
\(246\) −8.01384 6.31992i −0.510944 0.402943i
\(247\) 17.2709 + 9.97138i 1.09892 + 0.634464i
\(248\) −1.00506 + 0.580273i −0.0638215 + 0.0368474i
\(249\) 14.6323 + 2.12425i 0.927286 + 0.134619i
\(250\) 0 0
\(251\) 26.5460 1.67557 0.837784 0.546002i \(-0.183851\pi\)
0.837784 + 0.546002i \(0.183851\pi\)
\(252\) 1.83000 + 9.24693i 0.115279 + 0.582502i
\(253\) 42.7510i 2.68773i
\(254\) −0.822100 0.474640i −0.0515832 0.0297815i
\(255\) 0 0
\(256\) 8.23165 + 14.2576i 0.514478 + 0.891102i
\(257\) 13.2758 + 7.66481i 0.828124 + 0.478117i 0.853210 0.521568i \(-0.174653\pi\)
−0.0250861 + 0.999685i \(0.507986\pi\)
\(258\) −4.68438 + 5.93993i −0.291637 + 0.369804i
\(259\) −2.98835 1.88808i −0.185687 0.117319i
\(260\) 0 0
\(261\) −2.61318 + 8.81043i −0.161752 + 0.545352i
\(262\) −4.71271 8.16266i −0.291152 0.504291i
\(263\) −10.9949 19.0437i −0.677972 1.17428i −0.975591 0.219598i \(-0.929526\pi\)
0.297618 0.954685i \(-0.403808\pi\)
\(264\) 11.6245 + 29.1520i 0.715436 + 1.79418i
\(265\) 0 0
\(266\) 11.1621 5.86389i 0.684391 0.359538i
\(267\) −1.60695 1.26728i −0.0983438 0.0775564i
\(268\) −3.19002 1.84176i −0.194861 0.112503i
\(269\) −14.9395 25.8760i −0.910878 1.57769i −0.812826 0.582506i \(-0.802072\pi\)
−0.0980517 0.995181i \(-0.531261\pi\)
\(270\) 0 0
\(271\) −10.7412 6.20142i −0.652480 0.376710i 0.136926 0.990581i \(-0.456278\pi\)
−0.789406 + 0.613872i \(0.789611\pi\)
\(272\) 0.810312i 0.0491324i
\(273\) −3.16336 + 16.9928i −0.191456 + 1.02845i
\(274\) −6.57426 −0.397166
\(275\) 0 0
\(276\) 2.00326 13.7989i 0.120582 0.830599i
\(277\) −6.98725 + 4.03409i −0.419823 + 0.242385i −0.695002 0.719008i \(-0.744596\pi\)
0.275178 + 0.961393i \(0.411263\pi\)
\(278\) −8.47302 4.89190i −0.508178 0.293397i
\(279\) −1.17843 + 0.282472i −0.0705507 + 0.0169112i
\(280\) 0 0
\(281\) 17.6732i 1.05430i −0.849773 0.527149i \(-0.823261\pi\)
0.849773 0.527149i \(-0.176739\pi\)
\(282\) 1.12221 + 2.81430i 0.0668268 + 0.167589i
\(283\) 11.8369 + 20.5021i 0.703629 + 1.21872i 0.967184 + 0.254077i \(0.0817715\pi\)
−0.263555 + 0.964644i \(0.584895\pi\)
\(284\) 2.27875 1.31564i 0.135219 0.0780686i
\(285\) 0 0
\(286\) 21.4407i 1.26781i
\(287\) 17.2828 + 0.689694i 1.02017 + 0.0407113i
\(288\) 3.88315 + 16.1999i 0.228817 + 0.954586i
\(289\) −1.35859 + 2.35315i −0.0799172 + 0.138421i
\(290\) 0 0
\(291\) −2.26584 + 15.6077i −0.132826 + 0.914938i
\(292\) −1.49557 + 2.59041i −0.0875217 + 0.151592i
\(293\) 2.70804i 0.158205i −0.996866 0.0791026i \(-0.974795\pi\)
0.996866 0.0791026i \(-0.0252055\pi\)
\(294\) 8.01428 + 7.42928i 0.467402 + 0.433285i
\(295\) 0 0
\(296\) −3.32430 1.91928i −0.193221 0.111556i
\(297\) 2.98114 + 32.6347i 0.172983 + 1.89365i
\(298\) 2.29532 1.32520i 0.132964 0.0767670i
\(299\) 12.7840 22.1425i 0.739317 1.28053i
\(300\) 0 0
\(301\) 0.511207 12.8102i 0.0294655 0.738366i
\(302\) 4.49401 0.258601
\(303\) 3.70814 1.47863i 0.213027 0.0849452i
\(304\) 0.981769 0.566825i 0.0563083 0.0325096i
\(305\) 0 0
\(306\) 2.90587 9.79726i 0.166118 0.560072i
\(307\) 5.49592 0.313669 0.156834 0.987625i \(-0.449871\pi\)
0.156834 + 0.987625i \(0.449871\pi\)
\(308\) −16.7526 10.5845i −0.954569 0.603109i
\(309\) 10.5900 + 8.35157i 0.602446 + 0.475104i
\(310\) 0 0
\(311\) 10.9235 + 18.9201i 0.619416 + 1.07286i 0.989593 + 0.143898i \(0.0459637\pi\)
−0.370177 + 0.928961i \(0.620703\pi\)
\(312\) −2.69664 + 18.5752i −0.152667 + 1.05161i
\(313\) 12.2955 21.2964i 0.694983 1.20375i −0.275203 0.961386i \(-0.588745\pi\)
0.970186 0.242360i \(-0.0779214\pi\)
\(314\) −6.39874 −0.361102
\(315\) 0 0
\(316\) 7.26715 0.408809
\(317\) 11.9775 20.7457i 0.672726 1.16520i −0.304402 0.952544i \(-0.598457\pi\)
0.977128 0.212652i \(-0.0682101\pi\)
\(318\) −0.323147 + 2.22592i −0.0181212 + 0.124823i
\(319\) −9.65954 16.7308i −0.540830 0.936746i
\(320\) 0 0
\(321\) −7.42441 5.85507i −0.414390 0.326798i
\(322\) −7.51791 14.3105i −0.418956 0.797496i
\(323\) 19.9821 1.11183
\(324\) −0.566985 + 10.6733i −0.0314992 + 0.592963i
\(325\) 0 0
\(326\) −13.8044 + 7.97000i −0.764557 + 0.441417i
\(327\) −10.5969 + 4.22557i −0.586013 + 0.233674i
\(328\) 18.7828 1.03711
\(329\) −4.34089 2.74263i −0.239321 0.151206i
\(330\) 0 0
\(331\) −13.5511 + 23.4712i −0.744837 + 1.29009i 0.205434 + 0.978671i \(0.434139\pi\)
−0.950271 + 0.311424i \(0.899194\pi\)
\(332\) −8.77975 + 5.06899i −0.481852 + 0.278197i
\(333\) −2.75798 2.90837i −0.151136 0.159378i
\(334\) −8.52664 4.92286i −0.466557 0.269367i
\(335\) 0 0
\(336\) 0.746631 + 0.638708i 0.0407321 + 0.0348444i
\(337\) 3.19846i 0.174231i −0.996198 0.0871155i \(-0.972235\pi\)
0.996198 0.0871155i \(-0.0277649\pi\)
\(338\) −0.552830 + 0.957529i −0.0300700 + 0.0520827i
\(339\) −0.0533377 + 0.367403i −0.00289690 + 0.0199546i
\(340\) 0 0
\(341\) 1.27375 2.20620i 0.0689776 0.119473i
\(342\) 13.9030 3.33258i 0.751788 0.180205i
\(343\) −18.3878 2.21077i −0.992850 0.119370i
\(344\) 13.9220i 0.750622i
\(345\) 0 0
\(346\) 18.0397 10.4152i 0.969821 0.559926i
\(347\) −16.3140 28.2567i −0.875783 1.51690i −0.855927 0.517097i \(-0.827012\pi\)
−0.0198563 0.999803i \(-0.506321\pi\)
\(348\) −2.33387 5.85292i −0.125109 0.313750i
\(349\) 32.4849i 1.73888i 0.494041 + 0.869439i \(0.335519\pi\)
−0.494041 + 0.869439i \(0.664481\pi\)
\(350\) 0 0
\(351\) −8.21481 + 17.7943i −0.438474 + 0.949790i
\(352\) −30.3287 17.5103i −1.61653 0.933301i
\(353\) −5.77784 + 3.33584i −0.307523 + 0.177549i −0.645818 0.763492i \(-0.723483\pi\)
0.338294 + 0.941040i \(0.390150\pi\)
\(354\) −0.718725 + 4.95075i −0.0381998 + 0.263130i
\(355\) 0 0
\(356\) 1.40323 0.0743709
\(357\) 5.76817 + 16.3300i 0.305284 + 0.864273i
\(358\) 15.9004i 0.840364i
\(359\) 14.0322 + 8.10148i 0.740590 + 0.427580i 0.822284 0.569078i \(-0.192700\pi\)
−0.0816940 + 0.996657i \(0.526033\pi\)
\(360\) 0 0
\(361\) 4.47774 + 7.75567i 0.235671 + 0.408193i
\(362\) −11.5951 6.69443i −0.609425 0.351852i
\(363\) −39.1337 30.8618i −2.05398 1.61982i
\(364\) −5.51175 10.4918i −0.288894 0.549918i
\(365\) 0 0
\(366\) −7.58793 19.0291i −0.396627 0.994669i
\(367\) −8.60716 14.9080i −0.449290 0.778193i 0.549050 0.835789i \(-0.314990\pi\)
−0.998340 + 0.0575965i \(0.981656\pi\)
\(368\) −0.726708 1.25869i −0.0378823 0.0656140i
\(369\) 18.8028 + 5.57693i 0.978836 + 0.290324i
\(370\) 0 0
\(371\) −1.77280 3.37457i −0.0920391 0.175199i
\(372\) 0.514515 0.652421i 0.0266764 0.0338264i
\(373\) 10.6793 + 6.16568i 0.552952 + 0.319247i 0.750312 0.661084i \(-0.229903\pi\)
−0.197360 + 0.980331i \(0.563237\pi\)
\(374\) 10.7415 + 18.6048i 0.555428 + 0.962030i
\(375\) 0 0
\(376\) −4.82889 2.78796i −0.249031 0.143778i
\(377\) 11.5541i 0.595067i
\(378\) 6.73683 + 10.3999i 0.346505 + 0.534916i
\(379\) 3.57576 0.183675 0.0918373 0.995774i \(-0.470726\pi\)
0.0918373 + 0.995774i \(0.470726\pi\)
\(380\) 0 0
\(381\) 1.80526 + 0.262079i 0.0924864 + 0.0134267i
\(382\) 14.5905 8.42384i 0.746516 0.431001i
\(383\) 20.0319 + 11.5654i 1.02358 + 0.590965i 0.915139 0.403138i \(-0.132081\pi\)
0.108442 + 0.994103i \(0.465414\pi\)
\(384\) −8.44317 6.65850i −0.430864 0.339790i
\(385\) 0 0
\(386\) 2.33946i 0.119075i
\(387\) 4.13367 13.9368i 0.210126 0.708449i
\(388\) −5.40688 9.36499i −0.274493 0.475435i
\(389\) −14.7169 + 8.49679i −0.746175 + 0.430804i −0.824310 0.566138i \(-0.808437\pi\)
0.0781352 + 0.996943i \(0.475103\pi\)
\(390\) 0 0
\(391\) 25.6184i 1.29558i
\(392\) −20.0477 1.60261i −1.01256 0.0809440i
\(393\) 14.2220 + 11.2158i 0.717405 + 0.565763i
\(394\) 3.53142 6.11660i 0.177910 0.308150i
\(395\) 0 0
\(396\) −15.4612 16.3043i −0.776952 0.819321i
\(397\) 10.8448 18.7837i 0.544283 0.942726i −0.454368 0.890814i \(-0.650135\pi\)
0.998652 0.0519125i \(-0.0165317\pi\)
\(398\) 3.19428i 0.160115i
\(399\) −15.7504 + 18.4117i −0.788504 + 0.921739i
\(400\) 0 0
\(401\) −0.425230 0.245507i −0.0212350 0.0122600i 0.489345 0.872090i \(-0.337236\pi\)
−0.510580 + 0.859830i \(0.670569\pi\)
\(402\) −4.79192 0.695666i −0.238999 0.0346967i
\(403\) 1.31946 0.761790i 0.0657270 0.0379475i
\(404\) −1.36860 + 2.37049i −0.0680906 + 0.117936i
\(405\) 0 0
\(406\) −6.17562 3.90184i −0.306491 0.193645i
\(407\) 8.42601 0.417662
\(408\) 6.96592 + 17.4692i 0.344864 + 0.864856i
\(409\) −24.2867 + 14.0219i −1.20090 + 0.693339i −0.960755 0.277399i \(-0.910528\pi\)
−0.240143 + 0.970738i \(0.577194\pi\)
\(410\) 0 0
\(411\) 11.7349 4.67933i 0.578840 0.230815i
\(412\) −9.24747 −0.455590
\(413\) −3.94295 7.50553i −0.194020 0.369323i
\(414\) −4.27260 17.8246i −0.209987 0.876031i
\(415\) 0 0
\(416\) −10.4723 18.1386i −0.513448 0.889319i
\(417\) 18.6060 + 2.70113i 0.911142 + 0.132275i
\(418\) −15.0276 + 26.0286i −0.735025 + 1.27310i
\(419\) 3.44153 0.168130 0.0840649 0.996460i \(-0.473210\pi\)
0.0840649 + 0.996460i \(0.473210\pi\)
\(420\) 0 0
\(421\) 18.7964 0.916078 0.458039 0.888932i \(-0.348552\pi\)
0.458039 + 0.888932i \(0.348552\pi\)
\(422\) −10.8044 + 18.7137i −0.525948 + 0.910968i
\(423\) −4.00625 4.22472i −0.194791 0.205413i
\(424\) −2.06972 3.58485i −0.100514 0.174096i
\(425\) 0 0
\(426\) 2.14188 2.71597i 0.103775 0.131589i
\(427\) 29.3512 + 18.5445i 1.42041 + 0.897432i
\(428\) 6.48316 0.313375
\(429\) −15.2608 38.2712i −0.736796 1.84775i
\(430\) 0 0
\(431\) −5.95390 + 3.43749i −0.286789 + 0.165578i −0.636493 0.771282i \(-0.719616\pi\)
0.349704 + 0.936860i \(0.386282\pi\)
\(432\) 0.642516 + 0.910170i 0.0309131 + 0.0437906i
\(433\) −15.2776 −0.734193 −0.367096 0.930183i \(-0.619648\pi\)
−0.367096 + 0.930183i \(0.619648\pi\)
\(434\) 0.0384100 0.962503i 0.00184374 0.0462016i
\(435\) 0 0
\(436\) 3.91113 6.77428i 0.187309 0.324429i
\(437\) 31.0391 17.9204i 1.48480 0.857249i
\(438\) −0.564905 + 3.89121i −0.0269922 + 0.185929i
\(439\) −33.3367 19.2469i −1.59107 0.918606i −0.993124 0.117071i \(-0.962650\pi\)
−0.597948 0.801535i \(-0.704017\pi\)
\(440\) 0 0
\(441\) −19.5932 7.55682i −0.933011 0.359849i
\(442\) 12.8483i 0.611129i
\(443\) −1.92829 + 3.33990i −0.0916158 + 0.158683i −0.908191 0.418556i \(-0.862536\pi\)
0.816575 + 0.577239i \(0.195870\pi\)
\(444\) 2.71970 + 0.394833i 0.129071 + 0.0187379i
\(445\) 0 0
\(446\) −7.63337 + 13.2214i −0.361450 + 0.626050i
\(447\) −3.15386 + 3.99919i −0.149172 + 0.189155i
\(448\) −14.3652 0.573262i −0.678691 0.0270841i
\(449\) 2.52159i 0.119001i 0.998228 + 0.0595005i \(0.0189508\pi\)
−0.998228 + 0.0595005i \(0.981049\pi\)
\(450\) 0 0
\(451\) −35.7062 + 20.6150i −1.68134 + 0.970721i
\(452\) −0.127277 0.220451i −0.00598662 0.0103691i
\(453\) −8.02171 + 3.19868i −0.376893 + 0.150287i
\(454\) 19.7367i 0.926288i
\(455\) 0 0
\(456\) −16.2929 + 20.6598i −0.762984 + 0.967486i
\(457\) 8.05795 + 4.65226i 0.376935 + 0.217623i 0.676484 0.736457i \(-0.263503\pi\)
−0.299549 + 0.954081i \(0.596836\pi\)
\(458\) −0.196739 + 0.113588i −0.00919303 + 0.00530760i
\(459\) 1.78643 + 19.5562i 0.0833836 + 0.912805i
\(460\) 0 0
\(461\) 11.3898 0.530477 0.265238 0.964183i \(-0.414549\pi\)
0.265238 + 0.964183i \(0.414549\pi\)
\(462\) −25.6094 4.76743i −1.19146 0.221801i
\(463\) 0.322319i 0.0149795i 0.999972 + 0.00748973i \(0.00238408\pi\)
−0.999972 + 0.00748973i \(0.997616\pi\)
\(464\) −0.568801 0.328398i −0.0264059 0.0152455i
\(465\) 0 0
\(466\) −6.73402 11.6637i −0.311947 0.540309i
\(467\) −20.1915 11.6576i −0.934353 0.539449i −0.0461675 0.998934i \(-0.514701\pi\)
−0.888186 + 0.459485i \(0.848034\pi\)
\(468\) −3.13245 13.0681i −0.144798 0.604072i
\(469\) 7.26473 3.81645i 0.335454 0.176227i
\(470\) 0 0
\(471\) 11.4216 4.55440i 0.526280 0.209856i
\(472\) −4.60334 7.97323i −0.211886 0.366997i
\(473\) 15.2800 + 26.4657i 0.702575 + 1.21690i
\(474\) 8.87355 3.53836i 0.407576 0.162522i
\(475\) 0 0
\(476\) −10.0389 6.34274i −0.460134 0.290719i
\(477\) −1.00752 4.20322i −0.0461312 0.192452i
\(478\) −15.2229 8.78895i −0.696280 0.401997i
\(479\) −0.316556 0.548292i −0.0144638 0.0250521i 0.858703 0.512474i \(-0.171271\pi\)
−0.873167 + 0.487422i \(0.837937\pi\)
\(480\) 0 0
\(481\) 4.36418 + 2.51966i 0.198990 + 0.114887i
\(482\) 8.88978i 0.404918i
\(483\) 23.6051 + 20.1930i 1.07407 + 0.918815i
\(484\) 34.1724 1.55329
\(485\) 0 0
\(486\) 4.50451 + 13.3087i 0.204329 + 0.603697i
\(487\) 18.7500 10.8253i 0.849642 0.490541i −0.0108880 0.999941i \(-0.503466\pi\)
0.860530 + 0.509400i \(0.170132\pi\)
\(488\) 32.6509 + 18.8510i 1.47804 + 0.853345i
\(489\) 18.9679 24.0518i 0.857756 1.08766i
\(490\) 0 0
\(491\) 36.1608i 1.63191i 0.578112 + 0.815957i \(0.303789\pi\)
−0.578112 + 0.815957i \(0.696211\pi\)
\(492\) −12.4910 + 4.98085i −0.563140 + 0.224554i
\(493\) −5.78844 10.0259i −0.260698 0.451543i
\(494\) −15.5669 + 8.98754i −0.700387 + 0.404368i
\(495\) 0 0
\(496\) 0.0866082i 0.00388882i
\(497\) −0.233744 + 5.85732i −0.0104849 + 0.262737i
\(498\) −8.25244 + 10.4643i −0.369801 + 0.468918i
\(499\) −4.50676 + 7.80593i −0.201750 + 0.349442i −0.949092 0.314998i \(-0.897996\pi\)
0.747342 + 0.664439i \(0.231330\pi\)
\(500\) 0 0
\(501\) 18.7238 + 2.71822i 0.836518 + 0.121441i
\(502\) −11.9634 + 20.7212i −0.533952 + 0.924832i
\(503\) 18.9044i 0.842907i 0.906850 + 0.421453i \(0.138480\pi\)
−0.906850 + 0.421453i \(0.861520\pi\)
\(504\) −21.5871 7.35121i −0.961565 0.327449i
\(505\) 0 0
\(506\) 33.3704 + 19.2664i 1.48350 + 0.856497i
\(507\) 0.305252 2.10265i 0.0135567 0.0933822i
\(508\) −1.08320 + 0.625387i −0.0480593 + 0.0277471i
\(509\) −19.6636 + 34.0584i −0.871574 + 1.50961i −0.0112055 + 0.999937i \(0.503567\pi\)
−0.860368 + 0.509673i \(0.829766\pi\)
\(510\) 0 0
\(511\) −3.09909 5.89921i −0.137096 0.260966i
\(512\) −2.42264 −0.107067
\(513\) −22.4445 + 15.8443i −0.990950 + 0.699542i
\(514\) −11.9659 + 6.90854i −0.527795 + 0.304723i
\(515\) 0 0
\(516\) 3.69185 + 9.25848i 0.162525 + 0.407582i
\(517\) 12.2397 0.538300
\(518\) 2.82054 1.48174i 0.123927 0.0651040i
\(519\) −24.7873 + 31.4310i −1.08804 + 1.37967i
\(520\) 0 0
\(521\) −8.61869 14.9280i −0.377592 0.654008i 0.613120 0.789990i \(-0.289914\pi\)
−0.990711 + 0.135982i \(0.956581\pi\)
\(522\) −5.69955 6.01035i −0.249462 0.263066i
\(523\) −18.8880 + 32.7149i −0.825914 + 1.43052i 0.0753051 + 0.997161i \(0.476007\pi\)
−0.901219 + 0.433364i \(0.857326\pi\)
\(524\) −12.4190 −0.542525
\(525\) 0 0
\(526\) 19.8201 0.864196
\(527\) 0.763291 1.32206i 0.0332495 0.0575898i
\(528\) −2.31781 0.336488i −0.100870 0.0146438i
\(529\) −11.4752 19.8756i −0.498920 0.864156i
\(530\) 0 0
\(531\) −2.24087 9.34855i −0.0972455 0.405693i
\(532\) 0.662443 16.6000i 0.0287206 0.719699i
\(533\) −24.6583 −1.06807
\(534\) 1.71341 0.683228i 0.0741465 0.0295662i
\(535\) 0 0
\(536\) 7.71742 4.45565i 0.333342 0.192455i
\(537\) 11.3174 + 28.3819i 0.488381 + 1.22477i
\(538\) 26.9309 1.16108
\(539\) 39.8697 18.9567i 1.71731 0.816521i
\(540\) 0 0
\(541\) −9.89533 + 17.1392i −0.425433 + 0.736872i −0.996461 0.0840587i \(-0.973212\pi\)
0.571027 + 0.820931i \(0.306545\pi\)
\(542\) 9.68138 5.58955i 0.415851 0.240092i
\(543\) 25.4619 + 3.69642i 1.09267 + 0.158629i
\(544\) −18.1744 10.4930i −0.779219 0.449882i
\(545\) 0 0
\(546\) −11.8385 10.1273i −0.506642 0.433409i
\(547\) 8.91454i 0.381158i −0.981672 0.190579i \(-0.938963\pi\)
0.981672 0.190579i \(-0.0610365\pi\)
\(548\) −4.33113 + 7.50174i −0.185017 + 0.320459i
\(549\) 27.0886 + 28.5658i 1.15611 + 1.21916i
\(550\) 0 0
\(551\) 8.09819 14.0265i 0.344995 0.597548i
\(552\) 26.4873 + 20.8886i 1.12737 + 0.889076i
\(553\) −8.64757 + 13.6869i −0.367732 + 0.582026i
\(554\) 7.27212i 0.308963i
\(555\) 0 0
\(556\) −11.1641 + 6.44558i −0.473462 + 0.273354i
\(557\) −10.4847 18.1599i −0.444249 0.769462i 0.553751 0.832683i \(-0.313196\pi\)
−0.998000 + 0.0632208i \(0.979863\pi\)
\(558\) 0.310587 1.04716i 0.0131482 0.0443296i
\(559\) 18.2769i 0.773032i
\(560\) 0 0
\(561\) −32.4155 25.5637i −1.36859 1.07930i
\(562\) 13.7953 + 7.96474i 0.581921 + 0.335972i
\(563\) −15.6638 + 9.04347i −0.660148 + 0.381137i −0.792333 0.610088i \(-0.791134\pi\)
0.132185 + 0.991225i \(0.457801\pi\)
\(564\) 3.95066 + 0.573536i 0.166353 + 0.0241502i
\(565\) 0 0
\(566\) −21.3379 −0.896900
\(567\) −19.4274 13.7686i −0.815875 0.578228i
\(568\) 6.36568i 0.267098i
\(569\) −22.0888 12.7530i −0.926010 0.534632i −0.0404626 0.999181i \(-0.512883\pi\)
−0.885547 + 0.464549i \(0.846216\pi\)
\(570\) 0 0
\(571\) −19.8853 34.4424i −0.832175 1.44137i −0.896310 0.443428i \(-0.853762\pi\)
0.0641352 0.997941i \(-0.479571\pi\)
\(572\) 24.4655 + 14.1252i 1.02295 + 0.590603i
\(573\) −20.0480 + 25.4214i −0.837516 + 1.06199i
\(574\) −8.32714 + 13.1797i −0.347568 + 0.550112i
\(575\) 0 0
\(576\) −15.6286 4.63545i −0.651192 0.193144i
\(577\) −0.997811 1.72826i −0.0415394 0.0719484i 0.844508 0.535543i \(-0.179893\pi\)
−0.886048 + 0.463594i \(0.846560\pi\)
\(578\) −1.22454 2.12097i −0.0509343 0.0882208i
\(579\) −1.66515 4.17588i −0.0692011 0.173544i
\(580\) 0 0
\(581\) 0.900590 22.5676i 0.0373628 0.936262i
\(582\) −11.1619 8.80252i −0.462674 0.364876i
\(583\) 7.86909 + 4.54322i 0.325904 + 0.188161i
\(584\) −3.61815 6.26682i −0.149720 0.259323i
\(585\) 0 0
\(586\) 2.11383 + 1.22042i 0.0873216 + 0.0504152i
\(587\) 27.4257i 1.13198i 0.824413 + 0.565989i \(0.191506\pi\)
−0.824413 + 0.565989i \(0.808494\pi\)
\(588\) 13.7572 4.25049i 0.567338 0.175287i
\(589\) 2.13573 0.0880013
\(590\) 0 0
\(591\) −1.94992 + 13.4315i −0.0802090 + 0.552500i
\(592\) 0.248083 0.143231i 0.0101961 0.00588674i
\(593\) 1.05094 + 0.606763i 0.0431571 + 0.0249168i 0.521423 0.853298i \(-0.325401\pi\)
−0.478266 + 0.878215i \(0.658735\pi\)
\(594\) −26.8174 12.3803i −1.10033 0.507971i
\(595\) 0 0
\(596\) 3.49218i 0.143045i
\(597\) 2.27358 + 5.70172i 0.0930514 + 0.233356i
\(598\) 11.5226 + 19.9578i 0.471195 + 0.816134i
\(599\) 32.9617 19.0304i 1.34678 0.777563i 0.358986 0.933343i \(-0.383122\pi\)
0.987792 + 0.155780i \(0.0497891\pi\)
\(600\) 0 0
\(601\) 8.32414i 0.339549i 0.985483 + 0.169774i \(0.0543039\pi\)
−0.985483 + 0.169774i \(0.945696\pi\)
\(602\) 9.76894 + 6.17215i 0.398152 + 0.251558i
\(603\) 9.04862 2.16898i 0.368488 0.0883275i
\(604\) 2.96066 5.12802i 0.120468 0.208656i
\(605\) 0 0
\(606\) −0.516947 + 3.56086i −0.0209995 + 0.144650i
\(607\) −15.1263 + 26.1996i −0.613959 + 1.06341i 0.376607 + 0.926373i \(0.377091\pi\)
−0.990566 + 0.137036i \(0.956242\pi\)
\(608\) 29.3599i 1.19070i
\(609\) 13.8006 + 2.56911i 0.559227 + 0.104105i
\(610\) 0 0
\(611\) 6.33943 + 3.66007i 0.256466 + 0.148071i
\(612\) −9.26504 9.77028i −0.374517 0.394940i
\(613\) 2.45694 1.41851i 0.0992349 0.0572933i −0.449561 0.893249i \(-0.648420\pi\)
0.548796 + 0.835956i \(0.315086\pi\)
\(614\) −2.47683 + 4.28999i −0.0999566 + 0.173130i
\(615\) 0 0
\(616\) 42.4402 22.2955i 1.70996 0.898313i
\(617\) −23.3983 −0.941979 −0.470990 0.882139i \(-0.656103\pi\)
−0.470990 + 0.882139i \(0.656103\pi\)
\(618\) −11.2916 + 4.50257i −0.454216 + 0.181120i
\(619\) 34.7980 20.0907i 1.39865 0.807511i 0.404400 0.914582i \(-0.367481\pi\)
0.994251 + 0.107071i \(0.0341472\pi\)
\(620\) 0 0
\(621\) 20.3134 + 28.7754i 0.815150 + 1.15472i
\(622\) −19.6914 −0.789555
\(623\) −1.66978 + 2.64283i −0.0668981 + 0.105883i
\(624\) −1.09987 0.867386i −0.0440301 0.0347232i
\(625\) 0 0
\(626\) 11.0823 + 19.1952i 0.442939 + 0.767194i
\(627\) 8.29771 57.1567i 0.331378 2.28262i
\(628\) −4.21550 + 7.30146i −0.168217 + 0.291360i
\(629\) 5.04925 0.201327
\(630\) 0 0
\(631\) −22.9329 −0.912945 −0.456473 0.889737i \(-0.650887\pi\)
−0.456473 + 0.889737i \(0.650887\pi\)
\(632\) −8.79049 + 15.2256i −0.349667 + 0.605641i
\(633\) 5.96577 41.0937i 0.237118 1.63333i
\(634\) 10.7958 + 18.6988i 0.428754 + 0.742624i
\(635\) 0 0
\(636\) 2.32705 + 1.83517i 0.0922737 + 0.0727694i
\(637\) 26.3188 + 2.10393i 1.04279 + 0.0833607i
\(638\) 17.4129 0.689384
\(639\) −1.89008 + 6.37248i −0.0747704 + 0.252091i
\(640\) 0 0
\(641\) −1.70493 + 0.984339i −0.0673405 + 0.0388791i −0.533292 0.845931i \(-0.679045\pi\)
0.465952 + 0.884810i \(0.345712\pi\)
\(642\) 7.91627 3.15664i 0.312430 0.124583i
\(643\) 18.9036 0.745483 0.372742 0.927935i \(-0.378418\pi\)
0.372742 + 0.927935i \(0.378418\pi\)
\(644\) −21.2823 0.849297i −0.838638 0.0334670i
\(645\) 0 0
\(646\) −9.00525 + 15.5975i −0.354307 + 0.613677i
\(647\) −5.77380 + 3.33350i −0.226991 + 0.131054i −0.609183 0.793029i \(-0.708503\pi\)
0.382192 + 0.924083i \(0.375169\pi\)
\(648\) −21.6761 14.0986i −0.851519 0.553845i
\(649\) 17.5020 + 10.1048i 0.687012 + 0.396647i
\(650\) 0 0
\(651\) 0.616516 + 1.74539i 0.0241632 + 0.0684071i
\(652\) 21.0026i 0.822525i
\(653\) 16.9206 29.3074i 0.662156 1.14689i −0.317892 0.948127i \(-0.602975\pi\)
0.980048 0.198761i \(-0.0636917\pi\)
\(654\) 1.47731 10.1761i 0.0577673 0.397915i
\(655\) 0 0
\(656\) −0.700852 + 1.21391i −0.0273637 + 0.0473953i
\(657\) −1.76129 7.34780i −0.0687143 0.286665i
\(658\) 4.09713 2.15239i 0.159723 0.0839088i
\(659\) 22.0797i 0.860101i 0.902805 + 0.430051i \(0.141504\pi\)
−0.902805 + 0.430051i \(0.858496\pi\)
\(660\) 0 0
\(661\) 27.1770 15.6907i 1.05706 0.610296i 0.132445 0.991190i \(-0.457717\pi\)
0.924619 + 0.380894i \(0.124384\pi\)
\(662\) −12.2141 21.1554i −0.474713 0.822227i
\(663\) −9.14495 22.9339i −0.355160 0.890677i
\(664\) 24.5262i 0.951802i
\(665\) 0 0
\(666\) 3.51314 0.842108i 0.136131 0.0326310i
\(667\) −17.9829 10.3824i −0.696301 0.402009i
\(668\) −11.2347 + 6.48638i −0.434685 + 0.250965i
\(669\) 4.21487 29.0330i 0.162956 1.12248i
\(670\) 0 0
\(671\) −82.7594 −3.19489
\(672\) 23.9938 8.47525i 0.925582 0.326940i
\(673\) 40.5686i 1.56380i −0.623401 0.781902i \(-0.714249\pi\)
0.623401 0.781902i \(-0.285751\pi\)
\(674\) 2.49664 + 1.44144i 0.0961671 + 0.0555221i
\(675\) 0 0
\(676\) 0.728410 + 1.26164i 0.0280158 + 0.0485248i
\(677\) 34.4733 + 19.9031i 1.32491 + 0.764940i 0.984508 0.175338i \(-0.0561019\pi\)
0.340407 + 0.940278i \(0.389435\pi\)
\(678\) −0.262749 0.207210i −0.0100908 0.00795786i
\(679\) 24.0719 + 0.960621i 0.923794 + 0.0368653i
\(680\) 0 0
\(681\) 14.0479 + 35.2295i 0.538317 + 1.35000i
\(682\) 1.14808 + 1.98852i 0.0439621 + 0.0761445i
\(683\) −11.4962 19.9121i −0.439892 0.761915i 0.557789 0.829983i \(-0.311650\pi\)
−0.997681 + 0.0680680i \(0.978317\pi\)
\(684\) 5.35658 18.0599i 0.204814 0.690538i
\(685\) 0 0
\(686\) 10.0125 13.3568i 0.382277 0.509965i
\(687\) 0.270328 0.342784i 0.0103137 0.0130780i
\(688\) 0.899762 + 0.519478i 0.0343031 + 0.0198049i
\(689\) 2.71715 + 4.70625i 0.103515 + 0.179294i
\(690\) 0 0
\(691\) 20.7325 + 11.9699i 0.788702 + 0.455358i 0.839506 0.543351i \(-0.182845\pi\)
−0.0508031 + 0.998709i \(0.516178\pi\)
\(692\) 27.4463i 1.04335i
\(693\) 49.1054 9.71811i 1.86536 0.369161i
\(694\) 29.4087 1.11634
\(695\) 0 0
\(696\) 15.0857 + 2.19006i 0.571822 + 0.0830141i
\(697\) −21.3968 + 12.3534i −0.810461 + 0.467920i
\(698\) −25.3570 14.6399i −0.959776 0.554127i
\(699\) 20.3219 + 16.0263i 0.768644 + 0.606172i
\(700\) 0 0
\(701\) 7.70996i 0.291201i 0.989343 + 0.145601i \(0.0465115\pi\)
−0.989343 + 0.145601i \(0.953489\pi\)
\(702\) −10.1877 14.4316i −0.384510 0.544685i
\(703\) 3.53202 + 6.11765i 0.133213 + 0.230731i
\(704\) 29.6784 17.1348i 1.11855 0.645793i
\(705\) 0 0
\(706\) 6.01340i 0.226317i
\(707\) −2.83599 5.39839i −0.106658 0.203027i
\(708\) 5.17570 + 4.08169i 0.194515 + 0.153399i
\(709\) −1.62353 + 2.81203i −0.0609729 + 0.105608i −0.894901 0.446266i \(-0.852754\pi\)
0.833928 + 0.551874i \(0.186087\pi\)
\(710\) 0 0
\(711\) −13.3206 + 12.6318i −0.499562 + 0.473729i
\(712\) −1.69737 + 2.93993i −0.0636117 + 0.110179i
\(713\) 2.73815i 0.102545i
\(714\) −15.3463 2.85686i −0.574321 0.106915i
\(715\) 0 0
\(716\) −18.1436 10.4752i −0.678060 0.391478i
\(717\) 33.4282 + 4.85294i 1.24840 + 0.181236i
\(718\) −12.6477 + 7.30213i −0.472006 + 0.272513i
\(719\) −17.8697 + 30.9513i −0.666429 + 1.15429i 0.312467 + 0.949929i \(0.398845\pi\)
−0.978896 + 0.204360i \(0.934489\pi\)
\(720\) 0 0
\(721\) 11.0041 17.4166i 0.409813 0.648629i
\(722\) −8.07187 −0.300404
\(723\) −6.32744 15.8681i −0.235320 0.590139i
\(724\) −15.2777 + 8.82061i −0.567793 + 0.327815i
\(725\) 0 0
\(726\) 41.7262 16.6385i 1.54861 0.617512i
\(727\) −33.2693 −1.23389 −0.616945 0.787006i \(-0.711630\pi\)
−0.616945 + 0.787006i \(0.711630\pi\)
\(728\) 28.6487 + 1.14326i 1.06179 + 0.0423722i
\(729\) −17.5132 20.5497i −0.648636 0.761099i
\(730\) 0 0
\(731\) 9.15648 + 15.8595i 0.338665 + 0.586584i
\(732\) −26.7127 3.87800i −0.987328 0.143335i
\(733\) −8.40163 + 14.5521i −0.310321 + 0.537492i −0.978432 0.206570i \(-0.933770\pi\)
0.668111 + 0.744062i \(0.267103\pi\)
\(734\) 15.5158 0.572700
\(735\) 0 0
\(736\) −37.6414 −1.38748
\(737\) −9.78057 + 16.9404i −0.360272 + 0.624009i
\(738\) −12.8270 + 12.1637i −0.472170 + 0.447753i
\(739\) 18.4120 + 31.8906i 0.677297 + 1.17311i 0.975792 + 0.218702i \(0.0701823\pi\)
−0.298494 + 0.954411i \(0.596484\pi\)
\(740\) 0 0
\(741\) 21.3895 27.1225i 0.785763 0.996371i
\(742\) 3.43305 + 0.137001i 0.126031 + 0.00502945i
\(743\) −45.3970 −1.66545 −0.832727 0.553684i \(-0.813221\pi\)
−0.832727 + 0.553684i \(0.813221\pi\)
\(744\) 0.744534 + 1.86716i 0.0272959 + 0.0684532i
\(745\) 0 0
\(746\) −9.62558 + 5.55733i −0.352417 + 0.203468i
\(747\) 7.28226 24.5524i 0.266444 0.898326i
\(748\) 28.3060 1.03497
\(749\) −7.71466 + 12.2103i −0.281888 + 0.446156i
\(750\) 0 0
\(751\) −9.49215 + 16.4409i −0.346374 + 0.599937i −0.985602 0.169080i \(-0.945920\pi\)
0.639229 + 0.769017i \(0.279254\pi\)
\(752\) 0.360366 0.208057i 0.0131412 0.00758707i
\(753\) 6.60575 45.5020i 0.240727 1.65819i
\(754\) 9.01888 + 5.20705i 0.328448 + 0.189630i
\(755\) 0 0
\(756\) 16.3054 0.835742i 0.593021 0.0303956i
\(757\) 24.7352i 0.899017i −0.893276 0.449508i \(-0.851599\pi\)
0.893276 0.449508i \(-0.148401\pi\)
\(758\) −1.61148 + 2.79116i −0.0585315 + 0.101379i
\(759\) −73.2787 10.6382i −2.65985 0.386143i
\(760\) 0 0
\(761\) 23.8401 41.2923i 0.864204 1.49685i −0.00363106 0.999993i \(-0.501156\pi\)
0.867835 0.496852i \(-0.165511\pi\)
\(762\) −1.01814 + 1.29104i −0.0368835 + 0.0467693i
\(763\) 8.10457 + 15.4273i 0.293405 + 0.558505i
\(764\) 22.1986i 0.803116i
\(765\) 0 0
\(766\) −18.0554 + 10.4243i −0.652368 + 0.376645i
\(767\) 6.04333 + 10.4674i 0.218212 + 0.377954i
\(768\) 26.4871 10.5618i 0.955772 0.381117i
\(769\) 48.8811i 1.76270i 0.472467 + 0.881349i \(0.343364\pi\)
−0.472467 + 0.881349i \(0.656636\pi\)
\(770\) 0 0
\(771\) 16.4417 20.8485i 0.592133 0.750842i
\(772\) 2.66950 + 1.54124i 0.0960775 + 0.0554704i
\(773\) −9.55974 + 5.51932i −0.343840 + 0.198516i −0.661969 0.749531i \(-0.730279\pi\)
0.318129 + 0.948047i \(0.396946\pi\)
\(774\) 9.01586 + 9.50751i 0.324068 + 0.341740i
\(775\) 0 0
\(776\) 26.1611 0.939128
\(777\) −3.97995 + 4.65244i −0.142780 + 0.166905i
\(778\) 15.3169i 0.549136i
\(779\) −29.9347 17.2828i −1.07252 0.619221i
\(780\) 0 0
\(781\) −6.98662 12.1012i −0.250001 0.433015i
\(782\) 19.9971 + 11.5453i 0.715095 + 0.412860i
\(783\) 14.4515 + 6.67161i 0.516456 + 0.238424i
\(784\) 0.851624 1.23586i 0.0304152 0.0441379i
\(785\) 0 0
\(786\) −15.1642 + 6.04677i −0.540889 + 0.215681i
\(787\) 8.48325 + 14.6934i 0.302395 + 0.523764i 0.976678 0.214709i \(-0.0688804\pi\)
−0.674283 + 0.738473i \(0.735547\pi\)
\(788\) −4.65301 8.05925i −0.165757 0.287099i
\(789\) −35.3784 + 14.1072i −1.25950 + 0.502231i
\(790\) 0 0
\(791\) 0.566649 + 0.0226129i 0.0201477 + 0.000804022i
\(792\) 52.8616 12.6711i 1.87836 0.450246i
\(793\) −42.8645 24.7479i −1.52216 0.878822i
\(794\) 9.77475 + 16.9304i 0.346893 + 0.600836i
\(795\) 0 0
\(796\) −3.64492 2.10440i −0.129191 0.0745884i
\(797\) 11.9116i 0.421930i 0.977494 + 0.210965i \(0.0676605\pi\)
−0.977494 + 0.210965i \(0.932339\pi\)
\(798\) −7.27360 20.5919i −0.257483 0.728946i
\(799\) 7.33457 0.259478
\(800\) 0 0
\(801\) −2.57210 + 2.43909i −0.0908808 + 0.0861812i
\(802\) 0.383274 0.221283i 0.0135339 0.00781378i
\(803\) 13.7562 + 7.94217i 0.485447 + 0.280273i
\(804\) −3.95073 + 5.00965i −0.139332 + 0.176677i
\(805\) 0 0
\(806\) 1.37325i 0.0483708i
\(807\) −48.0712 + 19.1685i −1.69218 + 0.674764i
\(808\) −3.31098 5.73479i −0.116480 0.201749i
\(809\) 8.58544 4.95680i 0.301848 0.174272i −0.341425 0.939909i \(-0.610909\pi\)
0.643273 + 0.765637i \(0.277576\pi\)
\(810\) 0 0
\(811\) 40.3504i 1.41689i 0.705765 + 0.708446i \(0.250604\pi\)
−0.705765 + 0.708446i \(0.749396\pi\)
\(812\) −8.52082 + 4.47633i −0.299022 + 0.157088i
\(813\) −13.3026 + 16.8681i −0.466543 + 0.591590i
\(814\) −3.79732 + 6.57715i −0.133096 + 0.230529i
\(815\) 0 0
\(816\) −1.38894 0.201639i −0.0486227 0.00705879i
\(817\) −12.8102 + 22.1879i −0.448171 + 0.776255i
\(818\) 25.2768i 0.883783i
\(819\) 28.3398 + 9.65077i 0.990273 + 0.337225i
\(820\) 0 0
\(821\) 21.2757 + 12.2835i 0.742527 + 0.428698i 0.822987 0.568060i \(-0.192306\pi\)
−0.0804605 + 0.996758i \(0.525639\pi\)
\(822\) −1.63595 + 11.2688i −0.0570603 + 0.393045i
\(823\) 28.9152 16.6942i 1.00792 0.581924i 0.0973396 0.995251i \(-0.468967\pi\)
0.910583 + 0.413327i \(0.135633\pi\)
\(824\) 11.1859 19.3746i 0.389680 0.674946i
\(825\) 0 0
\(826\) 7.63560 + 0.304709i 0.265677 + 0.0106022i
\(827\) 35.0677 1.21942 0.609712 0.792623i \(-0.291285\pi\)
0.609712 + 0.792623i \(0.291285\pi\)
\(828\) −23.1540 6.86750i −0.804658 0.238662i
\(829\) 20.7299 11.9684i 0.719979 0.415680i −0.0947660 0.995500i \(-0.530210\pi\)
0.814745 + 0.579820i \(0.196877\pi\)
\(830\) 0 0
\(831\) 5.17605 + 12.9806i 0.179555 + 0.450291i
\(832\) 20.4956 0.710555
\(833\) 23.8917 11.3597i 0.827800 0.393590i
\(834\) −10.4936 + 13.3061i −0.363362 + 0.460754i
\(835\) 0 0
\(836\) 19.8004 + 34.2954i 0.684813 + 1.18613i
\(837\) 0.190938 + 2.09021i 0.00659980 + 0.0722484i
\(838\) −1.55098 + 2.68638i −0.0535778 + 0.0927994i
\(839\) −44.6267 −1.54068 −0.770342 0.637631i \(-0.779914\pi\)
−0.770342 + 0.637631i \(0.779914\pi\)
\(840\) 0 0
\(841\) 19.6164 0.676428
\(842\) −8.47088 + 14.6720i −0.291926 + 0.505631i
\(843\) −30.2934 4.39784i −1.04336 0.151470i
\(844\) 14.2358 + 24.6572i 0.490018 + 0.848736i
\(845\) 0 0
\(846\) 5.10320 1.22325i 0.175452 0.0420562i
\(847\) −40.6636 + 64.3601i −1.39722 + 2.21144i
\(848\) 0.308914 0.0106081
\(849\) 38.0877 15.1876i 1.30717 0.521237i
\(850\) 0 0
\(851\) 7.84323 4.52829i 0.268863 0.155228i
\(852\) −1.68806 4.23335i −0.0578320 0.145032i
\(853\) 1.24909 0.0427680 0.0213840 0.999771i \(-0.493193\pi\)
0.0213840 + 0.999771i \(0.493193\pi\)
\(854\) −27.7030 + 14.5535i −0.947979 + 0.498011i
\(855\) 0 0
\(856\) −7.84216 + 13.5830i −0.268040 + 0.464258i
\(857\) −7.97918 + 4.60678i −0.272564 + 0.157365i −0.630052 0.776553i \(-0.716966\pi\)
0.357488 + 0.933918i \(0.383633\pi\)
\(858\) 36.7511 + 5.33534i 1.25466 + 0.182145i
\(859\) −0.860775 0.496969i −0.0293693 0.0169564i 0.485243 0.874379i \(-0.338731\pi\)
−0.514613 + 0.857423i \(0.672064\pi\)
\(860\) 0 0
\(861\) 5.48287 29.4525i 0.186856 1.00374i
\(862\) 6.19664i 0.211058i
\(863\) −2.04843 + 3.54799i −0.0697295 + 0.120775i −0.898782 0.438395i \(-0.855547\pi\)
0.829053 + 0.559170i \(0.188880\pi\)
\(864\) 28.7342 2.62483i 0.977557 0.0892986i
\(865\) 0 0
\(866\) 6.88508 11.9253i 0.233965 0.405239i
\(867\) 3.69542 + 2.91430i 0.125503 + 0.0989749i
\(868\) −1.07299 0.677927i −0.0364195 0.0230104i
\(869\) 38.5919i 1.30914i
\(870\) 0 0
\(871\) −10.1315 + 5.84944i −0.343294 + 0.198201i
\(872\) 9.46197 + 16.3886i 0.320423 + 0.554989i
\(873\) 26.1890 + 7.76768i 0.886364 + 0.262896i
\(874\) 32.3045i 1.09272i
\(875\) 0 0
\(876\) 4.06801 + 3.20813i 0.137445 + 0.108393i
\(877\) −8.72731 5.03871i −0.294700 0.170145i 0.345359 0.938471i \(-0.387757\pi\)
−0.640060 + 0.768325i \(0.721090\pi\)
\(878\) 30.0474 17.3479i 1.01405 0.585463i
\(879\) −4.64180 0.673872i −0.156564 0.0227291i
\(880\) 0 0
\(881\) 30.3645 1.02301 0.511503 0.859281i \(-0.329089\pi\)
0.511503 + 0.859281i \(0.329089\pi\)
\(882\) 14.7287 11.8884i 0.495941 0.400304i
\(883\) 16.1748i 0.544326i −0.962251 0.272163i \(-0.912261\pi\)
0.962251 0.272163i \(-0.0877390\pi\)
\(884\) 14.6609 + 8.46445i 0.493098 + 0.284690i
\(885\) 0 0
\(886\) −1.73803 3.01036i −0.0583903 0.101135i
\(887\) −3.97469 2.29479i −0.133457 0.0770514i 0.431785 0.901977i \(-0.357884\pi\)
−0.565242 + 0.824925i \(0.691217\pi\)
\(888\) −4.11703 + 5.22052i −0.138159 + 0.175189i
\(889\) 0.111110 2.78428i 0.00372652 0.0933816i
\(890\) 0 0
\(891\) 56.6803 + 3.01095i 1.89886 + 0.100871i
\(892\) 10.0577 + 17.4205i 0.336758 + 0.583283i
\(893\) 5.13064 + 8.88652i 0.171690 + 0.297376i
\(894\) −1.70034 4.26413i −0.0568678 0.142614i
\(895\) 0 0
\(896\) −8.77326 + 13.8858i −0.293094 + 0.463893i
\(897\) −34.7729 27.4228i −1.16103 0.915620i
\(898\) −1.96829 1.13639i −0.0656827 0.0379220i
\(899\) −0.618683 1.07159i −0.0206342 0.0357395i
\(900\) 0 0
\(901\) 4.71552 + 2.72251i 0.157097 + 0.0906998i
\(902\) 37.1619i 1.23736i
\(903\) −21.8305 4.06395i −0.726473 0.135240i
\(904\) 0.615829 0.0204822
\(905\) 0 0
\(906\) 1.11830 7.70310i 0.0371529 0.255918i
\(907\) 27.1205 15.6580i 0.900521 0.519916i 0.0231520 0.999732i \(-0.492630\pi\)
0.877369 + 0.479816i \(0.159297\pi\)
\(908\) −22.5211 13.0026i −0.747389 0.431505i
\(909\) −1.61176 6.72400i −0.0534586 0.223021i
\(910\) 0 0
\(911\) 2.78118i 0.0921447i −0.998938 0.0460724i \(-0.985330\pi\)
0.998938 0.0460724i \(-0.0146705\pi\)
\(912\) −0.727279 1.82388i −0.0240826 0.0603948i
\(913\) 26.9187 + 46.6245i 0.890878 + 1.54305i
\(914\) −7.26289 + 4.19323i −0.240235 + 0.138700i
\(915\) 0 0
\(916\) 0.299327i 0.00989003i
\(917\) 14.7780 23.3898i 0.488012 0.772400i
\(918\) −16.0702 7.41887i −0.530396 0.244859i
\(919\) 29.0225 50.2685i 0.957365 1.65821i 0.228506 0.973543i \(-0.426616\pi\)
0.728860 0.684663i \(-0.240051\pi\)
\(920\) 0 0
\(921\) 1.36761 9.42046i 0.0450644 0.310415i
\(922\) −5.13301 + 8.89063i −0.169047 + 0.292797i
\(923\) 8.35695i 0.275072i
\(924\) −22.3115 + 26.0815i −0.733994 + 0.858018i
\(925\) 0 0
\(926\) −0.251595 0.145259i −0.00826793 0.00477349i
\(927\) 16.9505 16.0740i 0.556728 0.527939i
\(928\) −14.7312 + 8.50504i −0.483574 + 0.279191i
\(929\) 20.7329 35.9104i 0.680224 1.17818i −0.294689 0.955593i \(-0.595216\pi\)
0.974912 0.222589i \(-0.0714508\pi\)
\(930\) 0 0
\(931\) 30.4760 + 21.0008i 0.998809 + 0.688274i
\(932\) −17.7455 −0.581274
\(933\) 35.1488 14.0157i 1.15072 0.458853i
\(934\) 18.1993 10.5074i 0.595499 0.343812i
\(935\) 0 0
\(936\) 31.1683 + 9.24454i 1.01877 + 0.302167i
\(937\) −15.3201 −0.500486 −0.250243 0.968183i \(-0.580511\pi\)
−0.250243 + 0.968183i \(0.580511\pi\)
\(938\) −0.294933 + 7.39063i −0.00962990 + 0.241312i
\(939\) −33.4442 26.3749i −1.09141 0.860714i
\(940\) 0 0
\(941\) −25.5592 44.2698i −0.833206 1.44316i −0.895483 0.445096i \(-0.853170\pi\)
0.0622769 0.998059i \(-0.480164\pi\)
\(942\) −1.59227 + 10.9680i −0.0518790 + 0.357356i
\(943\) −22.1577 + 38.3783i −0.721555 + 1.24977i
\(944\) 0.687068 0.0223622
\(945\) 0 0
\(946\) −27.5447 −0.895556
\(947\) 4.01829 6.95988i 0.130577 0.226166i −0.793322 0.608802i \(-0.791650\pi\)
0.923899 + 0.382636i \(0.124984\pi\)
\(948\) 1.80837 12.4565i 0.0587331 0.404568i
\(949\) 4.74996 + 8.22716i 0.154190 + 0.267065i
\(950\) 0 0
\(951\) −32.5794 25.6929i −1.05646 0.833149i
\(952\) 25.4321 13.3605i 0.824260 0.433017i
\(953\) −43.7448 −1.41703 −0.708516 0.705695i \(-0.750635\pi\)
−0.708516 + 0.705695i \(0.750635\pi\)
\(954\) 3.73499 + 1.10780i 0.120925 + 0.0358664i
\(955\) 0 0
\(956\) −20.0578 + 11.5804i −0.648714 + 0.374535i
\(957\) −31.0817 + 12.3939i −1.00473 + 0.400639i
\(958\) 0.570645 0.0184367
\(959\) −8.97489 17.0840i −0.289814 0.551670i
\(960\) 0 0
\(961\) −15.4184 + 26.7055i −0.497368 + 0.861467i
\(962\) −3.93358 + 2.27105i −0.126824 + 0.0732217i
\(963\) −11.8836 + 11.2691i −0.382943 + 0.363140i
\(964\) 10.1439 + 5.85660i 0.326714 + 0.188628i
\(965\) 0 0
\(966\) −26.4002 + 9.32525i −0.849413 + 0.300035i
\(967\) 28.3067i 0.910281i 0.890420 + 0.455140i \(0.150411\pi\)
−0.890420 + 0.455140i \(0.849589\pi\)
\(968\) −41.3357 + 71.5954i −1.32858 + 2.30116i
\(969\) 4.97237 34.2509i 0.159735 1.10030i
\(970\) 0 0
\(971\) 16.4304 28.4583i 0.527277 0.913270i −0.472218 0.881482i \(-0.656546\pi\)
0.999495 0.0317882i \(-0.0101202\pi\)
\(972\) 18.1539 + 3.62783i 0.582287 + 0.116363i
\(973\) 1.14516 28.6963i 0.0367123 0.919961i
\(974\) 19.5144i 0.625282i
\(975\) 0 0
\(976\) −2.43664 + 1.40680i −0.0779950 + 0.0450304i
\(977\) 25.5291 + 44.2178i 0.816750 + 1.41465i 0.908065 + 0.418830i \(0.137560\pi\)
−0.0913150 + 0.995822i \(0.529107\pi\)
\(978\) 10.2261 + 25.6452i 0.326995 + 0.820044i
\(979\) 7.45178i 0.238160i
\(980\) 0 0
\(981\) 4.60601 + 19.2155i 0.147059 + 0.613505i
\(982\) −28.2263 16.2965i −0.900737 0.520041i
\(983\) 26.1076 15.0732i 0.832704 0.480762i −0.0220736 0.999756i \(-0.507027\pi\)
0.854778 + 0.518994i \(0.173693\pi\)
\(984\) 4.67394 32.1952i 0.149000 1.02635i
\(985\) 0 0
\(986\) 10.4346 0.332306
\(987\) −5.78129 + 6.75816i −0.184021 + 0.215115i
\(988\) 23.6840i 0.753489i
\(989\) 28.4463 + 16.4235i 0.904541 + 0.522237i
\(990\) 0 0
\(991\) −25.9382 44.9263i −0.823955 1.42713i −0.902715 0.430238i \(-0.858430\pi\)
0.0787606 0.996894i \(-0.474904\pi\)
\(992\) −1.94252 1.12151i −0.0616751 0.0356081i
\(993\) 36.8595 + 29.0683i 1.16970 + 0.922456i
\(994\) −4.46675 2.82215i −0.141677 0.0895133i
\(995\) 0 0
\(996\) 6.50390 + 16.3106i 0.206084 + 0.516821i
\(997\) −25.3390 43.8884i −0.802494 1.38996i −0.917970 0.396649i \(-0.870173\pi\)
0.115477 0.993310i \(-0.463160\pi\)
\(998\) −4.06209 7.03574i −0.128583 0.222713i
\(999\) −5.67149 + 4.00368i −0.179438 + 0.126671i
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.g.299.7 40
3.2 odd 2 inner 525.2.q.g.299.13 40
5.2 odd 4 525.2.t.h.26.4 20
5.3 odd 4 525.2.t.i.26.7 yes 20
5.4 even 2 inner 525.2.q.g.299.14 40
7.3 odd 6 inner 525.2.q.g.374.8 40
15.2 even 4 525.2.t.h.26.7 yes 20
15.8 even 4 525.2.t.i.26.4 yes 20
15.14 odd 2 inner 525.2.q.g.299.8 40
21.17 even 6 inner 525.2.q.g.374.14 40
35.3 even 12 525.2.t.i.101.4 yes 20
35.17 even 12 525.2.t.h.101.7 yes 20
35.24 odd 6 inner 525.2.q.g.374.13 40
105.17 odd 12 525.2.t.h.101.4 yes 20
105.38 odd 12 525.2.t.i.101.7 yes 20
105.59 even 6 inner 525.2.q.g.374.7 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.q.g.299.7 40 1.1 even 1 trivial
525.2.q.g.299.8 40 15.14 odd 2 inner
525.2.q.g.299.13 40 3.2 odd 2 inner
525.2.q.g.299.14 40 5.4 even 2 inner
525.2.q.g.374.7 40 105.59 even 6 inner
525.2.q.g.374.8 40 7.3 odd 6 inner
525.2.q.g.374.13 40 35.24 odd 6 inner
525.2.q.g.374.14 40 21.17 even 6 inner
525.2.t.h.26.4 20 5.2 odd 4
525.2.t.h.26.7 yes 20 15.2 even 4
525.2.t.h.101.4 yes 20 105.17 odd 12
525.2.t.h.101.7 yes 20 35.17 even 12
525.2.t.i.26.4 yes 20 15.8 even 4
525.2.t.i.26.7 yes 20 5.3 odd 4
525.2.t.i.101.4 yes 20 35.3 even 12
525.2.t.i.101.7 yes 20 105.38 odd 12