Properties

Label 175.2.k.a.74.3
Level $175$
Weight $2$
Character 175.74
Analytic conductor $1.397$
Analytic rank $0$
Dimension $8$
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] = [175,2,Mod(74,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.74");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.k (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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 74.3
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 175.74
Dual form 175.2.k.a.149.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.358719 - 0.207107i) q^{2} +(-2.09077 - 1.20711i) q^{3} +(-0.914214 + 1.58346i) q^{4} -1.00000 q^{6} +(-2.09077 + 1.62132i) q^{7} +1.58579i q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\) \(q+(0.358719 - 0.207107i) q^{2} +(-2.09077 - 1.20711i) q^{3} +(-0.914214 + 1.58346i) q^{4} -1.00000 q^{6} +(-2.09077 + 1.62132i) q^{7} +1.58579i q^{8} +(1.41421 + 2.44949i) q^{9} +(-2.41421 + 4.18154i) q^{11} +(3.82282 - 2.20711i) q^{12} +0.828427i q^{13} +(-0.414214 + 1.01461i) q^{14} +(-1.50000 - 2.59808i) q^{16} +(-0.717439 - 0.414214i) q^{17} +(1.01461 + 0.585786i) q^{18} +(-1.41421 - 2.44949i) q^{19} +(6.32843 - 0.866025i) q^{21} +2.00000i q^{22} +(-2.09077 + 1.20711i) q^{23} +(1.91421 - 3.31552i) q^{24} +(0.171573 + 0.297173i) q^{26} +0.414214i q^{27} +(-0.655892 - 4.79289i) q^{28} +1.00000 q^{29} +(3.00000 - 5.19615i) q^{31} +(-3.82282 - 2.20711i) q^{32} +(10.0951 - 5.82843i) q^{33} -0.343146 q^{34} -5.17157 q^{36} +(-1.01461 - 0.585786i) q^{38} +(1.00000 - 1.73205i) q^{39} -2.17157 q^{41} +(2.09077 - 1.62132i) q^{42} +6.41421i q^{43} +(-4.41421 - 7.64564i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(-1.73205 + 1.00000i) q^{47} +7.24264i q^{48} +(1.74264 - 6.77962i) q^{49} +(1.00000 + 1.73205i) q^{51} +(-1.31178 - 0.757359i) q^{52} +(5.91359 + 3.41421i) q^{53} +(0.0857864 + 0.148586i) q^{54} +(-2.57107 - 3.31552i) q^{56} +6.82843i q^{57} +(0.358719 - 0.207107i) q^{58} +(-6.24264 + 10.8126i) q^{59} +(5.74264 + 9.94655i) q^{61} -2.48528i q^{62} +(-6.92820 - 2.82843i) q^{63} +4.17157 q^{64} +(2.41421 - 4.18154i) q^{66} +(10.7510 + 6.20711i) q^{67} +(1.31178 - 0.757359i) q^{68} +5.82843 q^{69} -12.4853 q^{71} +(-3.88437 + 2.24264i) q^{72} +(-4.18154 - 2.41421i) q^{73} +5.17157 q^{76} +(-1.73205 - 12.6569i) q^{77} -0.828427i q^{78} +(4.58579 + 7.94282i) q^{79} +(4.74264 - 8.21449i) q^{81} +(-0.778985 + 0.449747i) q^{82} -11.7279i q^{83} +(-4.41421 + 10.8126i) q^{84} +(1.32843 + 2.30090i) q^{86} +(-2.09077 - 1.20711i) q^{87} +(-6.63103 - 3.82843i) q^{88} +(1.32843 + 2.30090i) q^{89} +(-1.34315 - 1.73205i) q^{91} -4.41421i q^{92} +(-12.5446 + 7.24264i) q^{93} +(-0.414214 + 0.717439i) q^{94} +(5.32843 + 9.22911i) q^{96} -0.343146i q^{97} +(-0.778985 - 2.79289i) q^{98} -13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 8 q^{6} - 8 q^{11} + 8 q^{14} - 12 q^{16} + 28 q^{21} + 4 q^{24} + 24 q^{26} + 8 q^{29} + 24 q^{31} - 48 q^{34} - 64 q^{36} + 8 q^{39} - 40 q^{41} - 24 q^{44} - 4 q^{46} - 20 q^{49} + 8 q^{51} + 12 q^{54} + 36 q^{56} - 16 q^{59} + 12 q^{61} + 56 q^{64} + 8 q^{66} + 24 q^{69} - 32 q^{71} + 64 q^{76} + 48 q^{79} + 4 q^{81} - 24 q^{84} - 12 q^{86} - 12 q^{89} - 56 q^{91} + 8 q^{94} + 20 q^{96} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.358719 0.207107i 0.253653 0.146447i −0.367783 0.929912i \(-0.619883\pi\)
0.621436 + 0.783465i \(0.286550\pi\)
\(3\) −2.09077 1.20711i −1.20711 0.696923i −0.244981 0.969528i \(-0.578782\pi\)
−0.962126 + 0.272605i \(0.912115\pi\)
\(4\) −0.914214 + 1.58346i −0.457107 + 0.791732i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) −2.09077 + 1.62132i −0.790237 + 0.612801i
\(8\) 1.58579i 0.560660i
\(9\) 1.41421 + 2.44949i 0.471405 + 0.816497i
\(10\) 0 0
\(11\) −2.41421 + 4.18154i −0.727913 + 1.26078i 0.229851 + 0.973226i \(0.426176\pi\)
−0.957764 + 0.287556i \(0.907157\pi\)
\(12\) 3.82282 2.20711i 1.10355 0.637137i
\(13\) 0.828427i 0.229764i 0.993379 + 0.114882i \(0.0366490\pi\)
−0.993379 + 0.114882i \(0.963351\pi\)
\(14\) −0.414214 + 1.01461i −0.110703 + 0.271166i
\(15\) 0 0
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) −0.717439 0.414214i −0.174005 0.100462i 0.410468 0.911875i \(-0.365365\pi\)
−0.584473 + 0.811413i \(0.698699\pi\)
\(18\) 1.01461 + 0.585786i 0.239146 + 0.138071i
\(19\) −1.41421 2.44949i −0.324443 0.561951i 0.656957 0.753928i \(-0.271843\pi\)
−0.981399 + 0.191977i \(0.938510\pi\)
\(20\) 0 0
\(21\) 6.32843 0.866025i 1.38098 0.188982i
\(22\) 2.00000i 0.426401i
\(23\) −2.09077 + 1.20711i −0.435956 + 0.251699i −0.701881 0.712295i \(-0.747656\pi\)
0.265925 + 0.963994i \(0.414323\pi\)
\(24\) 1.91421 3.31552i 0.390737 0.676777i
\(25\) 0 0
\(26\) 0.171573 + 0.297173i 0.0336482 + 0.0582804i
\(27\) 0.414214i 0.0797154i
\(28\) −0.655892 4.79289i −0.123952 0.905772i
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 0 0
\(31\) 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i \(-0.652205\pi\)
0.998968 0.0454165i \(-0.0144615\pi\)
\(32\) −3.82282 2.20711i −0.675786 0.390165i
\(33\) 10.0951 5.82843i 1.75734 1.01460i
\(34\) −0.343146 −0.0588490
\(35\) 0 0
\(36\) −5.17157 −0.861929
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) −1.01461 0.585786i −0.164592 0.0950271i
\(39\) 1.00000 1.73205i 0.160128 0.277350i
\(40\) 0 0
\(41\) −2.17157 −0.339143 −0.169571 0.985518i \(-0.554238\pi\)
−0.169571 + 0.985518i \(0.554238\pi\)
\(42\) 2.09077 1.62132i 0.322613 0.250175i
\(43\) 6.41421i 0.978158i 0.872239 + 0.489079i \(0.162667\pi\)
−0.872239 + 0.489079i \(0.837333\pi\)
\(44\) −4.41421 7.64564i −0.665468 1.15262i
\(45\) 0 0
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) −1.73205 + 1.00000i −0.252646 + 0.145865i −0.620975 0.783830i \(-0.713263\pi\)
0.368329 + 0.929695i \(0.379930\pi\)
\(48\) 7.24264i 1.04539i
\(49\) 1.74264 6.77962i 0.248949 0.968517i
\(50\) 0 0
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) −1.31178 0.757359i −0.181912 0.105027i
\(53\) 5.91359 + 3.41421i 0.812294 + 0.468978i 0.847752 0.530393i \(-0.177956\pi\)
−0.0354577 + 0.999371i \(0.511289\pi\)
\(54\) 0.0857864 + 0.148586i 0.0116741 + 0.0202201i
\(55\) 0 0
\(56\) −2.57107 3.31552i −0.343573 0.443054i
\(57\) 6.82843i 0.904447i
\(58\) 0.358719 0.207107i 0.0471022 0.0271945i
\(59\) −6.24264 + 10.8126i −0.812723 + 1.40768i 0.0982291 + 0.995164i \(0.468682\pi\)
−0.910952 + 0.412513i \(0.864651\pi\)
\(60\) 0 0
\(61\) 5.74264 + 9.94655i 0.735270 + 1.27352i 0.954605 + 0.297875i \(0.0962779\pi\)
−0.219335 + 0.975650i \(0.570389\pi\)
\(62\) 2.48528i 0.315631i
\(63\) −6.92820 2.82843i −0.872872 0.356348i
\(64\) 4.17157 0.521447
\(65\) 0 0
\(66\) 2.41421 4.18154i 0.297169 0.514712i
\(67\) 10.7510 + 6.20711i 1.31345 + 0.758319i 0.982665 0.185389i \(-0.0593544\pi\)
0.330781 + 0.943707i \(0.392688\pi\)
\(68\) 1.31178 0.757359i 0.159077 0.0918433i
\(69\) 5.82843 0.701660
\(70\) 0 0
\(71\) −12.4853 −1.48173 −0.740865 0.671654i \(-0.765584\pi\)
−0.740865 + 0.671654i \(0.765584\pi\)
\(72\) −3.88437 + 2.24264i −0.457777 + 0.264298i
\(73\) −4.18154 2.41421i −0.489412 0.282562i 0.234918 0.972015i \(-0.424518\pi\)
−0.724331 + 0.689453i \(0.757851\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 5.17157 0.593220
\(77\) −1.73205 12.6569i −0.197386 1.44238i
\(78\) 0.828427i 0.0938009i
\(79\) 4.58579 + 7.94282i 0.515941 + 0.893637i 0.999829 + 0.0185063i \(0.00589107\pi\)
−0.483887 + 0.875130i \(0.660776\pi\)
\(80\) 0 0
\(81\) 4.74264 8.21449i 0.526960 0.912722i
\(82\) −0.778985 + 0.449747i −0.0860246 + 0.0496663i
\(83\) 11.7279i 1.28731i −0.765317 0.643653i \(-0.777418\pi\)
0.765317 0.643653i \(-0.222582\pi\)
\(84\) −4.41421 + 10.8126i −0.481630 + 1.17975i
\(85\) 0 0
\(86\) 1.32843 + 2.30090i 0.143248 + 0.248113i
\(87\) −2.09077 1.20711i −0.224154 0.129415i
\(88\) −6.63103 3.82843i −0.706870 0.408112i
\(89\) 1.32843 + 2.30090i 0.140813 + 0.243895i 0.927803 0.373070i \(-0.121695\pi\)
−0.786990 + 0.616966i \(0.788362\pi\)
\(90\) 0 0
\(91\) −1.34315 1.73205i −0.140800 0.181568i
\(92\) 4.41421i 0.460214i
\(93\) −12.5446 + 7.24264i −1.30082 + 0.751027i
\(94\) −0.414214 + 0.717439i −0.0427229 + 0.0739982i
\(95\) 0 0
\(96\) 5.32843 + 9.22911i 0.543830 + 0.941942i
\(97\) 0.343146i 0.0348412i −0.999848 0.0174206i \(-0.994455\pi\)
0.999848 0.0174206i \(-0.00554543\pi\)
\(98\) −0.778985 2.79289i −0.0786894 0.282125i
\(99\) −13.6569 −1.37257
\(100\) 0 0
\(101\) −6.15685 + 10.6640i −0.612630 + 1.06111i 0.378165 + 0.925738i \(0.376555\pi\)
−0.990795 + 0.135368i \(0.956778\pi\)
\(102\) 0.717439 + 0.414214i 0.0710370 + 0.0410133i
\(103\) 0.358719 0.207107i 0.0353457 0.0204068i −0.482223 0.876048i \(-0.660171\pi\)
0.517569 + 0.855642i \(0.326837\pi\)
\(104\) −1.31371 −0.128820
\(105\) 0 0
\(106\) 2.82843 0.274721
\(107\) −2.38794 + 1.37868i −0.230851 + 0.133282i −0.610965 0.791658i \(-0.709218\pi\)
0.380113 + 0.924940i \(0.375885\pi\)
\(108\) −0.655892 0.378680i −0.0631133 0.0364385i
\(109\) 1.74264 3.01834i 0.166915 0.289105i −0.770419 0.637538i \(-0.779953\pi\)
0.937334 + 0.348433i \(0.113286\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 7.34847 + 3.00000i 0.694365 + 0.283473i
\(113\) 12.4853i 1.17452i 0.809400 + 0.587258i \(0.199793\pi\)
−0.809400 + 0.587258i \(0.800207\pi\)
\(114\) 1.41421 + 2.44949i 0.132453 + 0.229416i
\(115\) 0 0
\(116\) −0.914214 + 1.58346i −0.0848826 + 0.147021i
\(117\) −2.02922 + 1.17157i −0.187602 + 0.108312i
\(118\) 5.17157i 0.476082i
\(119\) 2.17157 0.297173i 0.199068 0.0272418i
\(120\) 0 0
\(121\) −6.15685 10.6640i −0.559714 0.969453i
\(122\) 4.11999 + 2.37868i 0.373007 + 0.215356i
\(123\) 4.54026 + 2.62132i 0.409381 + 0.236356i
\(124\) 5.48528 + 9.50079i 0.492593 + 0.853196i
\(125\) 0 0
\(126\) −3.07107 + 0.420266i −0.273592 + 0.0374403i
\(127\) 13.3137i 1.18140i −0.806891 0.590700i \(-0.798852\pi\)
0.806891 0.590700i \(-0.201148\pi\)
\(128\) 9.14207 5.27817i 0.808052 0.466529i
\(129\) 7.74264 13.4106i 0.681702 1.18074i
\(130\) 0 0
\(131\) −1.65685 2.86976i −0.144760 0.250732i 0.784523 0.620099i \(-0.212908\pi\)
−0.929283 + 0.369368i \(0.879574\pi\)
\(132\) 21.3137i 1.85512i
\(133\) 6.92820 + 2.82843i 0.600751 + 0.245256i
\(134\) 5.14214 0.444213
\(135\) 0 0
\(136\) 0.656854 1.13770i 0.0563248 0.0975574i
\(137\) 1.43488 + 0.828427i 0.122590 + 0.0707773i 0.560041 0.828465i \(-0.310785\pi\)
−0.437451 + 0.899242i \(0.644119\pi\)
\(138\) 2.09077 1.20711i 0.177978 0.102756i
\(139\) −12.1421 −1.02988 −0.514941 0.857225i \(-0.672186\pi\)
−0.514941 + 0.857225i \(0.672186\pi\)
\(140\) 0 0
\(141\) 4.82843 0.406627
\(142\) −4.47871 + 2.58579i −0.375845 + 0.216994i
\(143\) −3.46410 2.00000i −0.289683 0.167248i
\(144\) 4.24264 7.34847i 0.353553 0.612372i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) −11.8272 + 12.0711i −0.975490 + 0.995605i
\(148\) 0 0
\(149\) −3.91421 6.77962i −0.320665 0.555408i 0.659961 0.751300i \(-0.270573\pi\)
−0.980625 + 0.195892i \(0.937240\pi\)
\(150\) 0 0
\(151\) −0.171573 + 0.297173i −0.0139624 + 0.0241836i −0.872922 0.487859i \(-0.837778\pi\)
0.858960 + 0.512043i \(0.171111\pi\)
\(152\) 3.88437 2.24264i 0.315064 0.181902i
\(153\) 2.34315i 0.189432i
\(154\) −3.24264 4.18154i −0.261299 0.336958i
\(155\) 0 0
\(156\) 1.82843 + 3.16693i 0.146391 + 0.253557i
\(157\) −4.60181 2.65685i −0.367264 0.212040i 0.304998 0.952353i \(-0.401344\pi\)
−0.672263 + 0.740313i \(0.734677\pi\)
\(158\) 3.29002 + 1.89949i 0.261740 + 0.151116i
\(159\) −8.24264 14.2767i −0.653684 1.13221i
\(160\) 0 0
\(161\) 2.41421 5.91359i 0.190267 0.466056i
\(162\) 3.92893i 0.308686i
\(163\) 20.4874 11.8284i 1.60470 0.926474i 0.614170 0.789173i \(-0.289491\pi\)
0.990529 0.137301i \(-0.0438426\pi\)
\(164\) 1.98528 3.43861i 0.155024 0.268510i
\(165\) 0 0
\(166\) −2.42893 4.20703i −0.188522 0.326529i
\(167\) 19.5858i 1.51559i −0.652491 0.757797i \(-0.726276\pi\)
0.652491 0.757797i \(-0.273724\pi\)
\(168\) 1.37333 + 10.0355i 0.105955 + 0.774258i
\(169\) 12.3137 0.947208
\(170\) 0 0
\(171\) 4.00000 6.92820i 0.305888 0.529813i
\(172\) −10.1567 5.86396i −0.774439 0.447123i
\(173\) −16.7262 + 9.65685i −1.27167 + 0.734197i −0.975302 0.220878i \(-0.929108\pi\)
−0.296365 + 0.955075i \(0.595774\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 0 0
\(176\) 14.4853 1.09187
\(177\) 26.1039 15.0711i 1.96209 1.13281i
\(178\) 0.953065 + 0.550253i 0.0714353 + 0.0412432i
\(179\) −5.00000 + 8.66025i −0.373718 + 0.647298i −0.990134 0.140122i \(-0.955250\pi\)
0.616417 + 0.787420i \(0.288584\pi\)
\(180\) 0 0
\(181\) −8.65685 −0.643459 −0.321729 0.946832i \(-0.604264\pi\)
−0.321729 + 0.946832i \(0.604264\pi\)
\(182\) −0.840532 0.343146i −0.0623044 0.0254357i
\(183\) 27.7279i 2.04971i
\(184\) −1.91421 3.31552i −0.141118 0.244423i
\(185\) 0 0
\(186\) −3.00000 + 5.19615i −0.219971 + 0.381000i
\(187\) 3.46410 2.00000i 0.253320 0.146254i
\(188\) 3.65685i 0.266704i
\(189\) −0.671573 0.866025i −0.0488497 0.0629941i
\(190\) 0 0
\(191\) 3.58579 + 6.21076i 0.259458 + 0.449395i 0.966097 0.258180i \(-0.0831226\pi\)
−0.706639 + 0.707575i \(0.749789\pi\)
\(192\) −8.72180 5.03553i −0.629442 0.363408i
\(193\) 1.73205 + 1.00000i 0.124676 + 0.0719816i 0.561041 0.827788i \(-0.310401\pi\)
−0.436365 + 0.899770i \(0.643734\pi\)
\(194\) −0.0710678 0.123093i −0.00510237 0.00883757i
\(195\) 0 0
\(196\) 9.14214 + 8.95743i 0.653010 + 0.639816i
\(197\) 23.6569i 1.68548i 0.538320 + 0.842741i \(0.319059\pi\)
−0.538320 + 0.842741i \(0.680941\pi\)
\(198\) −4.89898 + 2.82843i −0.348155 + 0.201008i
\(199\) 0.828427 1.43488i 0.0587256 0.101716i −0.835168 0.549995i \(-0.814630\pi\)
0.893894 + 0.448279i \(0.147963\pi\)
\(200\) 0 0
\(201\) −14.9853 25.9553i −1.05698 1.83074i
\(202\) 5.10051i 0.358870i
\(203\) −2.09077 + 1.62132i −0.146743 + 0.113794i
\(204\) −3.65685 −0.256031
\(205\) 0 0
\(206\) 0.0857864 0.148586i 0.00597702 0.0103525i
\(207\) −5.91359 3.41421i −0.411023 0.237304i
\(208\) 2.15232 1.24264i 0.149236 0.0861616i
\(209\) 13.6569 0.944664
\(210\) 0 0
\(211\) 3.51472 0.241963 0.120982 0.992655i \(-0.461396\pi\)
0.120982 + 0.992655i \(0.461396\pi\)
\(212\) −10.8126 + 6.24264i −0.742610 + 0.428746i
\(213\) 26.1039 + 15.0711i 1.78861 + 1.03265i
\(214\) −0.571068 + 0.989118i −0.0390374 + 0.0676147i
\(215\) 0 0
\(216\) −0.656854 −0.0446933
\(217\) 2.15232 + 15.7279i 0.146109 + 1.06768i
\(218\) 1.44365i 0.0977764i
\(219\) 5.82843 + 10.0951i 0.393849 + 0.682166i
\(220\) 0 0
\(221\) 0.343146 0.594346i 0.0230825 0.0399800i
\(222\) 0 0
\(223\) 11.6569i 0.780601i 0.920688 + 0.390300i \(0.127629\pi\)
−0.920688 + 0.390300i \(0.872371\pi\)
\(224\) 11.5711 1.58346i 0.773124 0.105800i
\(225\) 0 0
\(226\) 2.58579 + 4.47871i 0.172004 + 0.297920i
\(227\) 23.3572 + 13.4853i 1.55027 + 0.895050i 0.998119 + 0.0613063i \(0.0195266\pi\)
0.552152 + 0.833743i \(0.313807\pi\)
\(228\) −10.8126 6.24264i −0.716080 0.413429i
\(229\) −0.171573 0.297173i −0.0113379 0.0196377i 0.860301 0.509787i \(-0.170276\pi\)
−0.871639 + 0.490149i \(0.836942\pi\)
\(230\) 0 0
\(231\) −11.6569 + 28.5533i −0.766965 + 1.87867i
\(232\) 1.58579i 0.104112i
\(233\) −9.67487 + 5.58579i −0.633822 + 0.365937i −0.782231 0.622989i \(-0.785918\pi\)
0.148409 + 0.988926i \(0.452585\pi\)
\(234\) −0.485281 + 0.840532i −0.0317238 + 0.0549473i
\(235\) 0 0
\(236\) −11.4142 19.7700i −0.743002 1.28692i
\(237\) 22.1421i 1.43829i
\(238\) 0.717439 0.556349i 0.0465047 0.0360628i
\(239\) −1.31371 −0.0849767 −0.0424884 0.999097i \(-0.513529\pi\)
−0.0424884 + 0.999097i \(0.513529\pi\)
\(240\) 0 0
\(241\) −8.17157 + 14.1536i −0.526377 + 0.911712i 0.473150 + 0.880982i \(0.343117\pi\)
−0.999528 + 0.0307305i \(0.990217\pi\)
\(242\) −4.41717 2.55025i −0.283946 0.163936i
\(243\) −18.7554 + 10.8284i −1.20316 + 0.694644i
\(244\) −21.0000 −1.34439
\(245\) 0 0
\(246\) 2.17157 0.138454
\(247\) 2.02922 1.17157i 0.129116 0.0745454i
\(248\) 8.23999 + 4.75736i 0.523240 + 0.302093i
\(249\) −14.1569 + 24.5204i −0.897154 + 1.55392i
\(250\) 0 0
\(251\) 13.3137 0.840354 0.420177 0.907442i \(-0.361968\pi\)
0.420177 + 0.907442i \(0.361968\pi\)
\(252\) 10.8126 8.38478i 0.681128 0.528191i
\(253\) 11.6569i 0.732860i
\(254\) −2.75736 4.77589i −0.173012 0.299666i
\(255\) 0 0
\(256\) −1.98528 + 3.43861i −0.124080 + 0.214913i
\(257\) −15.2913 + 8.82843i −0.953844 + 0.550702i −0.894273 0.447522i \(-0.852307\pi\)
−0.0595711 + 0.998224i \(0.518973\pi\)
\(258\) 6.41421i 0.399331i
\(259\) 0 0
\(260\) 0 0
\(261\) 1.41421 + 2.44949i 0.0875376 + 0.151620i
\(262\) −1.18869 0.686292i −0.0734376 0.0423992i
\(263\) −16.4905 9.52082i −1.01685 0.587079i −0.103660 0.994613i \(-0.533055\pi\)
−0.913190 + 0.407534i \(0.866389\pi\)
\(264\) 9.24264 + 16.0087i 0.568845 + 0.985269i
\(265\) 0 0
\(266\) 3.07107 0.420266i 0.188299 0.0257682i
\(267\) 6.41421i 0.392543i
\(268\) −19.6575 + 11.3492i −1.20077 + 0.693265i
\(269\) −15.2279 + 26.3755i −0.928463 + 1.60814i −0.142568 + 0.989785i \(0.545536\pi\)
−0.785895 + 0.618360i \(0.787798\pi\)
\(270\) 0 0
\(271\) 0.242641 + 0.420266i 0.0147394 + 0.0255293i 0.873301 0.487181i \(-0.161975\pi\)
−0.858562 + 0.512710i \(0.828641\pi\)
\(272\) 2.48528i 0.150692i
\(273\) 0.717439 + 5.24264i 0.0434214 + 0.317299i
\(274\) 0.686292 0.0414604
\(275\) 0 0
\(276\) −5.32843 + 9.22911i −0.320734 + 0.555527i
\(277\) −10.5154 6.07107i −0.631809 0.364775i 0.149643 0.988740i \(-0.452187\pi\)
−0.781452 + 0.623965i \(0.785521\pi\)
\(278\) −4.35562 + 2.51472i −0.261233 + 0.150823i
\(279\) 16.9706 1.01600
\(280\) 0 0
\(281\) 26.2843 1.56799 0.783994 0.620768i \(-0.213179\pi\)
0.783994 + 0.620768i \(0.213179\pi\)
\(282\) 1.73205 1.00000i 0.103142 0.0595491i
\(283\) −12.1244 7.00000i −0.720718 0.416107i 0.0942988 0.995544i \(-0.469939\pi\)
−0.815017 + 0.579437i \(0.803272\pi\)
\(284\) 11.4142 19.7700i 0.677309 1.17313i
\(285\) 0 0
\(286\) −1.65685 −0.0979718
\(287\) 4.54026 3.52082i 0.268003 0.207827i
\(288\) 12.4853i 0.735702i
\(289\) −8.15685 14.1281i −0.479815 0.831064i
\(290\) 0 0
\(291\) −0.414214 + 0.717439i −0.0242816 + 0.0420570i
\(292\) 7.64564 4.41421i 0.447427 0.258322i
\(293\) 16.0000i 0.934730i −0.884064 0.467365i \(-0.845203\pi\)
0.884064 0.467365i \(-0.154797\pi\)
\(294\) −1.74264 + 6.77962i −0.101633 + 0.395395i
\(295\) 0 0
\(296\) 0 0
\(297\) −1.73205 1.00000i −0.100504 0.0580259i
\(298\) −2.80821 1.62132i −0.162675 0.0939206i
\(299\) −1.00000 1.73205i −0.0578315 0.100167i
\(300\) 0 0
\(301\) −10.3995 13.4106i −0.599417 0.772977i
\(302\) 0.142136i 0.00817899i
\(303\) 25.7451 14.8640i 1.47902 0.853912i
\(304\) −4.24264 + 7.34847i −0.243332 + 0.421464i
\(305\) 0 0
\(306\) −0.485281 0.840532i −0.0277417 0.0480500i
\(307\) 13.2426i 0.755797i 0.925847 + 0.377899i \(0.123353\pi\)
−0.925847 + 0.377899i \(0.876647\pi\)
\(308\) 21.6251 + 8.82843i 1.23221 + 0.503046i
\(309\) −1.00000 −0.0568880
\(310\) 0 0
\(311\) 9.41421 16.3059i 0.533831 0.924623i −0.465388 0.885107i \(-0.654085\pi\)
0.999219 0.0395157i \(-0.0125815\pi\)
\(312\) 2.74666 + 1.58579i 0.155499 + 0.0897775i
\(313\) −15.2913 + 8.82843i −0.864314 + 0.499012i −0.865455 0.500987i \(-0.832970\pi\)
0.00114023 + 0.999999i \(0.499637\pi\)
\(314\) −2.20101 −0.124210
\(315\) 0 0
\(316\) −16.7696 −0.943361
\(317\) −22.3426 + 12.8995i −1.25488 + 0.724508i −0.972075 0.234668i \(-0.924600\pi\)
−0.282809 + 0.959176i \(0.591266\pi\)
\(318\) −5.91359 3.41421i −0.331618 0.191460i
\(319\) −2.41421 + 4.18154i −0.135170 + 0.234121i
\(320\) 0 0
\(321\) 6.65685 0.371549
\(322\) −0.358719 2.62132i −0.0199907 0.146080i
\(323\) 2.34315i 0.130376i
\(324\) 8.67157 + 15.0196i 0.481754 + 0.834422i
\(325\) 0 0
\(326\) 4.89949 8.48617i 0.271358 0.470006i
\(327\) −7.28692 + 4.20711i −0.402968 + 0.232654i
\(328\) 3.44365i 0.190144i
\(329\) 2.00000 4.89898i 0.110264 0.270089i
\(330\) 0 0
\(331\) 5.48528 + 9.50079i 0.301498 + 0.522210i 0.976476 0.215628i \(-0.0691799\pi\)
−0.674977 + 0.737839i \(0.735847\pi\)
\(332\) 18.5707 + 10.7218i 1.01920 + 0.588437i
\(333\) 0 0
\(334\) −4.05635 7.02580i −0.221954 0.384435i
\(335\) 0 0
\(336\) −11.7426 15.1427i −0.640614 0.826102i
\(337\) 14.8284i 0.807756i −0.914813 0.403878i \(-0.867662\pi\)
0.914813 0.403878i \(-0.132338\pi\)
\(338\) 4.41717 2.55025i 0.240262 0.138715i
\(339\) 15.0711 26.1039i 0.818548 1.41777i
\(340\) 0 0
\(341\) 14.4853 + 25.0892i 0.784422 + 1.35866i
\(342\) 3.31371i 0.179185i
\(343\) 7.34847 + 17.0000i 0.396780 + 0.917914i
\(344\) −10.1716 −0.548414
\(345\) 0 0
\(346\) −4.00000 + 6.92820i −0.215041 + 0.372463i
\(347\) 19.1141 + 11.0355i 1.02610 + 0.592418i 0.915865 0.401487i \(-0.131507\pi\)
0.110234 + 0.993906i \(0.464840\pi\)
\(348\) 3.82282 2.20711i 0.204925 0.118313i
\(349\) 26.6569 1.42691 0.713454 0.700702i \(-0.247130\pi\)
0.713454 + 0.700702i \(0.247130\pi\)
\(350\) 0 0
\(351\) −0.343146 −0.0183158
\(352\) 18.4582 10.6569i 0.983826 0.568012i
\(353\) 18.3351 + 10.5858i 0.975880 + 0.563425i 0.901024 0.433770i \(-0.142817\pi\)
0.0748562 + 0.997194i \(0.476150\pi\)
\(354\) 6.24264 10.8126i 0.331793 0.574682i
\(355\) 0 0
\(356\) −4.85786 −0.257466
\(357\) −4.89898 2.00000i −0.259281 0.105851i
\(358\) 4.14214i 0.218919i
\(359\) −5.00000 8.66025i −0.263890 0.457071i 0.703382 0.710812i \(-0.251672\pi\)
−0.967272 + 0.253741i \(0.918339\pi\)
\(360\) 0 0
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) −3.10538 + 1.79289i −0.163215 + 0.0942324i
\(363\) 29.7279i 1.56031i
\(364\) 3.97056 0.543359i 0.208114 0.0284798i
\(365\) 0 0
\(366\) −5.74264 9.94655i −0.300173 0.519914i
\(367\) −9.73641 5.62132i −0.508237 0.293431i 0.223872 0.974619i \(-0.428130\pi\)
−0.732108 + 0.681188i \(0.761464\pi\)
\(368\) 6.27231 + 3.62132i 0.326967 + 0.188774i
\(369\) −3.07107 5.31925i −0.159873 0.276909i
\(370\) 0 0
\(371\) −17.8995 + 2.44949i −0.929295 + 0.127171i
\(372\) 26.4853i 1.37320i
\(373\) 11.2328 6.48528i 0.581614 0.335795i −0.180160 0.983637i \(-0.557662\pi\)
0.761775 + 0.647842i \(0.224328\pi\)
\(374\) 0.828427 1.43488i 0.0428369 0.0741958i
\(375\) 0 0
\(376\) −1.58579 2.74666i −0.0817807 0.141648i
\(377\) 0.828427i 0.0426662i
\(378\) −0.420266 0.171573i −0.0216162 0.00882476i
\(379\) −21.1716 −1.08751 −0.543755 0.839244i \(-0.682998\pi\)
−0.543755 + 0.839244i \(0.682998\pi\)
\(380\) 0 0
\(381\) −16.0711 + 27.8359i −0.823346 + 1.42608i
\(382\) 2.57258 + 1.48528i 0.131625 + 0.0759936i
\(383\) 14.6354 8.44975i 0.747834 0.431762i −0.0770770 0.997025i \(-0.524559\pi\)
0.824911 + 0.565263i \(0.191225\pi\)
\(384\) −25.4853 −1.30054
\(385\) 0 0
\(386\) 0.828427 0.0421658
\(387\) −15.7116 + 9.07107i −0.798663 + 0.461108i
\(388\) 0.543359 + 0.313708i 0.0275849 + 0.0159261i
\(389\) 6.17157 10.6895i 0.312911 0.541978i −0.666080 0.745880i \(-0.732029\pi\)
0.978991 + 0.203902i \(0.0653625\pi\)
\(390\) 0 0
\(391\) 2.00000 0.101144
\(392\) 10.7510 + 2.76346i 0.543009 + 0.139576i
\(393\) 8.00000i 0.403547i
\(394\) 4.89949 + 8.48617i 0.246833 + 0.427527i
\(395\) 0 0
\(396\) 12.4853 21.6251i 0.627409 1.08670i
\(397\) −24.7921 + 14.3137i −1.24428 + 0.718384i −0.969962 0.243255i \(-0.921785\pi\)
−0.274316 + 0.961640i \(0.588451\pi\)
\(398\) 0.686292i 0.0344007i
\(399\) −11.0711 14.2767i −0.554247 0.714728i
\(400\) 0 0
\(401\) −3.84315 6.65652i −0.191918 0.332411i 0.753968 0.656911i \(-0.228137\pi\)
−0.945886 + 0.324500i \(0.894804\pi\)
\(402\) −10.7510 6.20711i −0.536212 0.309582i
\(403\) 4.30463 + 2.48528i 0.214429 + 0.123801i
\(404\) −11.2574 19.4983i −0.560075 0.970078i
\(405\) 0 0
\(406\) −0.414214 + 1.01461i −0.0205571 + 0.0503543i
\(407\) 0 0
\(408\) −2.74666 + 1.58579i −0.135980 + 0.0785081i
\(409\) 12.3995 21.4766i 0.613116 1.06195i −0.377596 0.925970i \(-0.623249\pi\)
0.990712 0.135977i \(-0.0434173\pi\)
\(410\) 0 0
\(411\) −2.00000 3.46410i −0.0986527 0.170872i
\(412\) 0.757359i 0.0373124i
\(413\) −4.47871 32.7279i −0.220383 1.61044i
\(414\) −2.82843 −0.139010
\(415\) 0 0
\(416\) 1.82843 3.16693i 0.0896460 0.155271i
\(417\) 25.3864 + 14.6569i 1.24318 + 0.717749i
\(418\) 4.89898 2.82843i 0.239617 0.138343i
\(419\) 23.3137 1.13895 0.569475 0.822009i \(-0.307147\pi\)
0.569475 + 0.822009i \(0.307147\pi\)
\(420\) 0 0
\(421\) −3.48528 −0.169862 −0.0849311 0.996387i \(-0.527067\pi\)
−0.0849311 + 0.996387i \(0.527067\pi\)
\(422\) 1.26080 0.727922i 0.0613747 0.0354347i
\(423\) −4.89898 2.82843i −0.238197 0.137523i
\(424\) −5.41421 + 9.37769i −0.262937 + 0.455421i
\(425\) 0 0
\(426\) 12.4853 0.604914
\(427\) −28.1331 11.4853i −1.36146 0.555812i
\(428\) 5.04163i 0.243696i
\(429\) 4.82843 + 8.36308i 0.233119 + 0.403773i
\(430\) 0 0
\(431\) 10.8995 18.8785i 0.525010 0.909344i −0.474566 0.880220i \(-0.657395\pi\)
0.999576 0.0291242i \(-0.00927183\pi\)
\(432\) 1.07616 0.621320i 0.0517767 0.0298933i
\(433\) 31.7990i 1.52816i −0.645120 0.764081i \(-0.723193\pi\)
0.645120 0.764081i \(-0.276807\pi\)
\(434\) 4.02944 + 5.19615i 0.193419 + 0.249423i
\(435\) 0 0
\(436\) 3.18629 + 5.51882i 0.152596 + 0.264303i
\(437\) 5.91359 + 3.41421i 0.282885 + 0.163324i
\(438\) 4.18154 + 2.41421i 0.199802 + 0.115356i
\(439\) 16.9706 + 29.3939i 0.809961 + 1.40289i 0.912890 + 0.408205i \(0.133845\pi\)
−0.102930 + 0.994689i \(0.532822\pi\)
\(440\) 0 0
\(441\) 19.0711 5.31925i 0.908146 0.253297i
\(442\) 0.284271i 0.0135214i
\(443\) −10.5769 + 6.10660i −0.502526 + 0.290133i −0.729756 0.683708i \(-0.760366\pi\)
0.227230 + 0.973841i \(0.427033\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2.41421 + 4.18154i 0.114316 + 0.198002i
\(447\) 18.8995i 0.893915i
\(448\) −8.72180 + 6.76346i −0.412066 + 0.319543i
\(449\) 1.82843 0.0862888 0.0431444 0.999069i \(-0.486262\pi\)
0.0431444 + 0.999069i \(0.486262\pi\)
\(450\) 0 0
\(451\) 5.24264 9.08052i 0.246866 0.427585i
\(452\) −19.7700 11.4142i −0.929902 0.536879i
\(453\) 0.717439 0.414214i 0.0337082 0.0194615i
\(454\) 11.1716 0.524308
\(455\) 0 0
\(456\) −10.8284 −0.507088
\(457\) 27.9590 16.1421i 1.30787 0.755097i 0.326127 0.945326i \(-0.394256\pi\)
0.981740 + 0.190229i \(0.0609230\pi\)
\(458\) −0.123093 0.0710678i −0.00575176 0.00332078i
\(459\) 0.171573 0.297173i 0.00800834 0.0138708i
\(460\) 0 0
\(461\) 18.6863 0.870307 0.435154 0.900356i \(-0.356694\pi\)
0.435154 + 0.900356i \(0.356694\pi\)
\(462\) 1.73205 + 12.6569i 0.0805823 + 0.588850i
\(463\) 11.0416i 0.513148i 0.966525 + 0.256574i \(0.0825937\pi\)
−0.966525 + 0.256574i \(0.917406\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 0 0
\(466\) −2.31371 + 4.00746i −0.107180 + 0.185642i
\(467\) 19.8315 11.4497i 0.917694 0.529831i 0.0347956 0.999394i \(-0.488922\pi\)
0.882899 + 0.469563i \(0.155589\pi\)
\(468\) 4.28427i 0.198041i
\(469\) −32.5416 + 4.45322i −1.50263 + 0.205631i
\(470\) 0 0
\(471\) 6.41421 + 11.1097i 0.295551 + 0.511910i
\(472\) −17.1464 9.89949i −0.789228 0.455661i
\(473\) −26.8213 15.4853i −1.23324 0.712014i
\(474\) −4.58579 7.94282i −0.210632 0.364826i
\(475\) 0 0
\(476\) −1.51472 + 3.71029i −0.0694270 + 0.170061i
\(477\) 19.3137i 0.884314i
\(478\) −0.471253 + 0.272078i −0.0215546 + 0.0124446i
\(479\) −12.1716 + 21.0818i −0.556133 + 0.963251i 0.441681 + 0.897172i \(0.354382\pi\)
−0.997814 + 0.0660791i \(0.978951\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 6.76955i 0.308345i
\(483\) −12.1859 + 9.44975i −0.554478 + 0.429978i
\(484\) 22.5147 1.02340
\(485\) 0 0
\(486\) −4.48528 + 7.76874i −0.203456 + 0.352397i
\(487\) 13.5592 + 7.82843i 0.614428 + 0.354740i 0.774696 0.632334i \(-0.217903\pi\)
−0.160269 + 0.987073i \(0.551236\pi\)
\(488\) −15.7731 + 9.10660i −0.714015 + 0.412236i
\(489\) −57.1127 −2.58273
\(490\) 0 0
\(491\) −13.3137 −0.600839 −0.300420 0.953807i \(-0.597127\pi\)
−0.300420 + 0.953807i \(0.597127\pi\)
\(492\) −8.30153 + 4.79289i −0.374262 + 0.216080i
\(493\) −0.717439 0.414214i −0.0323118 0.0186552i
\(494\) 0.485281 0.840532i 0.0218338 0.0378173i
\(495\) 0 0
\(496\) −18.0000 −0.808224
\(497\) 26.1039 20.2426i 1.17092 0.908007i
\(498\) 11.7279i 0.525541i
\(499\) 2.41421 + 4.18154i 0.108075 + 0.187191i 0.914990 0.403476i \(-0.132198\pi\)
−0.806915 + 0.590667i \(0.798865\pi\)
\(500\) 0 0
\(501\) −23.6421 + 40.9494i −1.05625 + 1.82948i
\(502\) 4.77589 2.75736i 0.213158 0.123067i
\(503\) 37.8701i 1.68854i 0.535916 + 0.844271i \(0.319966\pi\)
−0.535916 + 0.844271i \(0.680034\pi\)
\(504\) 4.48528 10.9867i 0.199790 0.489384i
\(505\) 0 0
\(506\) −2.41421 4.18154i −0.107325 0.185892i
\(507\) −25.7451 14.8640i −1.14338 0.660132i
\(508\) 21.0818 + 12.1716i 0.935353 + 0.540026i
\(509\) 12.3284 + 21.3535i 0.546448 + 0.946476i 0.998514 + 0.0544912i \(0.0173537\pi\)
−0.452066 + 0.891984i \(0.649313\pi\)
\(510\) 0 0
\(511\) 12.6569 1.73205i 0.559906 0.0766214i
\(512\) 22.7574i 1.00574i
\(513\) 1.01461 0.585786i 0.0447962 0.0258631i
\(514\) −3.65685 + 6.33386i −0.161297 + 0.279374i
\(515\) 0 0
\(516\) 14.1569 + 24.5204i 0.623221 + 1.07945i
\(517\) 9.65685i 0.424708i
\(518\) 0 0
\(519\) 46.6274 2.04672
\(520\) 0 0
\(521\) 9.48528 16.4290i 0.415558 0.719767i −0.579929 0.814667i \(-0.696920\pi\)
0.995487 + 0.0948999i \(0.0302531\pi\)
\(522\) 1.01461 + 0.585786i 0.0444084 + 0.0256392i
\(523\) 21.0818 12.1716i 0.921842 0.532226i 0.0376197 0.999292i \(-0.488022\pi\)
0.884222 + 0.467066i \(0.154689\pi\)
\(524\) 6.05887 0.264683
\(525\) 0 0
\(526\) −7.88730 −0.343903
\(527\) −4.30463 + 2.48528i −0.187513 + 0.108261i
\(528\) −30.2854 17.4853i −1.31800 0.760949i
\(529\) −8.58579 + 14.8710i −0.373295 + 0.646566i
\(530\) 0 0
\(531\) −35.3137 −1.53248
\(532\) −10.8126 + 8.38478i −0.468784 + 0.363526i
\(533\) 1.79899i 0.0779229i
\(534\) −1.32843 2.30090i −0.0574867 0.0995698i
\(535\) 0 0
\(536\) −9.84315 + 17.0488i −0.425159 + 0.736397i
\(537\) 20.9077 12.0711i 0.902234 0.520905i
\(538\) 12.6152i 0.543881i
\(539\) 24.1421 + 23.6544i 1.03988 + 1.01887i
\(540\) 0 0
\(541\) −9.32843 16.1573i −0.401060 0.694657i 0.592794 0.805354i \(-0.298025\pi\)
−0.993854 + 0.110697i \(0.964692\pi\)
\(542\) 0.174080 + 0.100505i 0.00747737 + 0.00431706i
\(543\) 18.0995 + 10.4497i 0.776724 + 0.448442i
\(544\) 1.82843 + 3.16693i 0.0783932 + 0.135781i
\(545\) 0 0
\(546\) 1.34315 + 1.73205i 0.0574813 + 0.0741249i
\(547\) 5.10051i 0.218082i −0.994037 0.109041i \(-0.965222\pi\)
0.994037 0.109041i \(-0.0347780\pi\)
\(548\) −2.62357 + 1.51472i −0.112073 + 0.0647056i
\(549\) −16.2426 + 28.1331i −0.693219 + 1.20069i
\(550\) 0 0
\(551\) −1.41421 2.44949i −0.0602475 0.104352i
\(552\) 9.24264i 0.393393i
\(553\) −22.4657 9.17157i −0.955338 0.390015i
\(554\) −5.02944 −0.213680
\(555\) 0 0
\(556\) 11.1005 19.2266i 0.470766 0.815391i
\(557\) −29.6910 17.1421i −1.25805 0.726336i −0.285355 0.958422i \(-0.592111\pi\)
−0.972695 + 0.232086i \(0.925445\pi\)
\(558\) 6.08767 3.51472i 0.257712 0.148790i
\(559\) −5.31371 −0.224746
\(560\) 0 0
\(561\) −9.65685 −0.407713
\(562\) 9.42868 5.44365i 0.397725 0.229627i
\(563\) −14.0920 8.13604i −0.593908 0.342893i 0.172733 0.984969i \(-0.444740\pi\)
−0.766641 + 0.642076i \(0.778074\pi\)
\(564\) −4.41421 + 7.64564i −0.185872 + 0.321940i
\(565\) 0 0
\(566\) −5.79899 −0.243750
\(567\) 3.40256 + 24.8640i 0.142894 + 1.04419i
\(568\) 19.7990i 0.830747i
\(569\) −1.82843 3.16693i −0.0766517 0.132765i 0.825152 0.564911i \(-0.191090\pi\)
−0.901803 + 0.432147i \(0.857756\pi\)
\(570\) 0 0
\(571\) −7.41421 + 12.8418i −0.310275 + 0.537412i −0.978422 0.206617i \(-0.933755\pi\)
0.668147 + 0.744030i \(0.267088\pi\)
\(572\) 6.33386 3.65685i 0.264832 0.152901i
\(573\) 17.3137i 0.723291i
\(574\) 0.899495 2.20330i 0.0375442 0.0919641i
\(575\) 0 0
\(576\) 5.89949 + 10.2182i 0.245812 + 0.425759i
\(577\) 20.7336 + 11.9706i 0.863152 + 0.498341i 0.865067 0.501657i \(-0.167276\pi\)
−0.00191453 + 0.999998i \(0.500609\pi\)
\(578\) −5.85204 3.37868i −0.243413 0.140535i
\(579\) −2.41421 4.18154i −0.100331 0.173779i
\(580\) 0 0
\(581\) 19.0147 + 24.5204i 0.788863 + 1.01728i
\(582\) 0.343146i 0.0142238i
\(583\) −28.5533 + 16.4853i −1.18256 + 0.682751i
\(584\) 3.82843 6.63103i 0.158421 0.274394i
\(585\) 0 0
\(586\) −3.31371 5.73951i −0.136888 0.237097i
\(587\) 22.2843i 0.919770i −0.887978 0.459885i \(-0.847891\pi\)
0.887978 0.459885i \(-0.152109\pi\)
\(588\) −8.30153 29.7635i −0.342350 1.22742i
\(589\) −16.9706 −0.699260
\(590\) 0 0
\(591\) 28.5563 49.4610i 1.17465 2.03456i
\(592\) 0 0
\(593\) 37.9310 21.8995i 1.55764 0.899304i 0.560159 0.828385i \(-0.310740\pi\)
0.997482 0.0709193i \(-0.0225933\pi\)
\(594\) −0.828427 −0.0339908
\(595\) 0 0
\(596\) 14.3137 0.586312
\(597\) −3.46410 + 2.00000i −0.141776 + 0.0818546i
\(598\) −0.717439 0.414214i −0.0293383 0.0169385i
\(599\) 8.82843 15.2913i 0.360720 0.624785i −0.627360 0.778730i \(-0.715864\pi\)
0.988079 + 0.153945i \(0.0491977\pi\)
\(600\) 0 0
\(601\) 8.34315 0.340324 0.170162 0.985416i \(-0.445571\pi\)
0.170162 + 0.985416i \(0.445571\pi\)
\(602\) −6.50794 2.65685i −0.265244 0.108285i
\(603\) 35.1127i 1.42990i
\(604\) −0.313708 0.543359i −0.0127646 0.0221090i
\(605\) 0 0
\(606\) 6.15685 10.6640i 0.250105 0.433195i
\(607\) 3.64874 2.10660i 0.148098 0.0855043i −0.424120 0.905606i \(-0.639417\pi\)
0.572218 + 0.820102i \(0.306083\pi\)
\(608\) 12.4853i 0.506345i
\(609\) 6.32843 0.866025i 0.256441 0.0350931i
\(610\) 0 0
\(611\) −0.828427 1.43488i −0.0335146 0.0580489i
\(612\) 3.71029 + 2.14214i 0.149979 + 0.0865907i
\(613\) 13.3852 + 7.72792i 0.540621 + 0.312128i 0.745331 0.666695i \(-0.232292\pi\)
−0.204709 + 0.978823i \(0.565625\pi\)
\(614\) 2.74264 + 4.75039i 0.110684 + 0.191710i
\(615\) 0 0
\(616\) 20.0711 2.74666i 0.808686 0.110666i
\(617\) 11.3137i 0.455473i 0.973723 + 0.227736i \(0.0731324\pi\)
−0.973723 + 0.227736i \(0.926868\pi\)
\(618\) −0.358719 + 0.207107i −0.0144298 + 0.00833106i
\(619\) 21.2426 36.7933i 0.853814 1.47885i −0.0239273 0.999714i \(-0.507617\pi\)
0.877741 0.479135i \(-0.159050\pi\)
\(620\) 0 0
\(621\) −0.500000 0.866025i −0.0200643 0.0347524i
\(622\) 7.79899i 0.312711i
\(623\) −6.50794 2.65685i −0.260735 0.106445i
\(624\) −6.00000 −0.240192
\(625\) 0 0
\(626\) −3.65685 + 6.33386i −0.146157 + 0.253152i
\(627\) −28.5533 16.4853i −1.14031 0.658359i
\(628\) 8.41407 4.85786i 0.335758 0.193850i
\(629\) 0 0
\(630\) 0 0
\(631\) 8.14214 0.324133 0.162067 0.986780i \(-0.448184\pi\)
0.162067 + 0.986780i \(0.448184\pi\)
\(632\) −12.5956 + 7.27208i −0.501026 + 0.289268i
\(633\) −7.34847 4.24264i −0.292075 0.168630i
\(634\) −5.34315 + 9.25460i −0.212203 + 0.367547i
\(635\) 0 0
\(636\) 30.1421 1.19521
\(637\) 5.61642 + 1.44365i 0.222531 + 0.0571995i
\(638\) 2.00000i 0.0791808i
\(639\) −17.6569 30.5826i −0.698494 1.20983i
\(640\) 0 0
\(641\) −7.25736 + 12.5701i −0.286648 + 0.496490i −0.973008 0.230773i \(-0.925875\pi\)
0.686359 + 0.727263i \(0.259208\pi\)
\(642\) 2.38794 1.37868i 0.0942446 0.0544121i
\(643\) 30.2843i 1.19430i −0.802131 0.597148i \(-0.796301\pi\)
0.802131 0.597148i \(-0.203699\pi\)
\(644\) 7.15685 + 9.22911i 0.282020 + 0.363678i
\(645\) 0 0
\(646\) 0.485281 + 0.840532i 0.0190931 + 0.0330703i
\(647\) 14.7585 + 8.52082i 0.580216 + 0.334988i 0.761219 0.648495i \(-0.224601\pi\)
−0.181003 + 0.983482i \(0.557934\pi\)
\(648\) 13.0264 + 7.52082i 0.511727 + 0.295446i
\(649\) −30.1421 52.2077i −1.18318 2.04933i
\(650\) 0 0
\(651\) 14.4853 35.4815i 0.567723 1.39063i
\(652\) 43.2548i 1.69399i
\(653\) −21.5020 + 12.4142i −0.841440 + 0.485806i −0.857754 0.514061i \(-0.828140\pi\)
0.0163133 + 0.999867i \(0.494807\pi\)
\(654\) −1.74264 + 3.01834i −0.0681426 + 0.118027i
\(655\) 0 0
\(656\) 3.25736 + 5.64191i 0.127179 + 0.220280i
\(657\) 13.6569i 0.532805i
\(658\) −0.297173 2.17157i −0.0115850 0.0846567i
\(659\) −26.8284 −1.04509 −0.522544 0.852613i \(-0.675017\pi\)
−0.522544 + 0.852613i \(0.675017\pi\)
\(660\) 0 0
\(661\) −13.0858 + 22.6652i −0.508978 + 0.881576i 0.490968 + 0.871178i \(0.336643\pi\)
−0.999946 + 0.0103982i \(0.996690\pi\)
\(662\) 3.93535 + 2.27208i 0.152952 + 0.0883068i
\(663\) −1.43488 + 0.828427i −0.0557260 + 0.0321734i
\(664\) 18.5980 0.721742
\(665\) 0 0
\(666\) 0 0
\(667\) −2.09077 + 1.20711i −0.0809549 + 0.0467394i
\(668\) 31.0134 + 17.9056i 1.19994 + 0.692788i
\(669\) 14.0711 24.3718i 0.544019 0.942268i
\(670\) 0 0
\(671\) −55.4558 −2.14085
\(672\) −26.1039 10.6569i −1.00698 0.411097i
\(673\) 18.3431i 0.707076i 0.935420 + 0.353538i \(0.115022\pi\)
−0.935420 + 0.353538i \(0.884978\pi\)
\(674\) −3.07107 5.31925i −0.118293 0.204890i
\(675\) 0 0
\(676\) −11.2574 + 19.4983i −0.432975 + 0.749935i
\(677\) −0.123093 + 0.0710678i −0.00473085 + 0.00273136i −0.502364 0.864656i \(-0.667536\pi\)
0.497633 + 0.867388i \(0.334203\pi\)
\(678\) 12.4853i 0.479494i
\(679\) 0.556349 + 0.717439i 0.0213507 + 0.0275328i
\(680\) 0 0
\(681\) −32.5563 56.3893i −1.24756 2.16084i
\(682\) 10.3923 + 6.00000i 0.397942 + 0.229752i
\(683\) 37.4492 + 21.6213i 1.43295 + 0.827317i 0.997345 0.0728189i \(-0.0231995\pi\)
0.435610 + 0.900136i \(0.356533\pi\)
\(684\) 7.31371 + 12.6677i 0.279647 + 0.484362i
\(685\) 0 0
\(686\) 6.15685 + 4.57631i 0.235070 + 0.174724i
\(687\) 0.828427i 0.0316065i
\(688\) 16.6646 9.62132i 0.635333 0.366809i
\(689\) −2.82843 + 4.89898i −0.107754 + 0.186636i
\(690\) 0 0
\(691\) 2.41421 + 4.18154i 0.0918410 + 0.159073i 0.908286 0.418350i \(-0.137392\pi\)
−0.816445 + 0.577423i \(0.804058\pi\)
\(692\) 35.3137i 1.34243i
\(693\) 28.5533 22.1421i 1.08465 0.841110i
\(694\) 9.14214 0.347031
\(695\) 0 0
\(696\) 1.91421 3.31552i 0.0725581 0.125674i
\(697\) 1.55797 + 0.899495i 0.0590124 + 0.0340708i
\(698\) 9.56233 5.52082i 0.361940 0.208966i
\(699\) 26.9706 1.02012
\(700\) 0 0
\(701\) −42.7990 −1.61650 −0.808248 0.588843i \(-0.799584\pi\)
−0.808248 + 0.588843i \(0.799584\pi\)
\(702\) −0.123093 + 0.0710678i −0.00464585 + 0.00268228i
\(703\) 0 0
\(704\) −10.0711 + 17.4436i −0.379568 + 0.657430i
\(705\) 0 0
\(706\) 8.76955 0.330046
\(707\) −4.41717 32.2782i −0.166125 1.21395i
\(708\) 55.1127i 2.07126i
\(709\) 19.1569 + 33.1806i 0.719451 + 1.24613i 0.961218 + 0.275791i \(0.0889397\pi\)
−0.241767 + 0.970334i \(0.577727\pi\)
\(710\) 0 0
\(711\) −12.9706 + 22.4657i −0.486434 + 0.842529i
\(712\) −3.64874 + 2.10660i −0.136742 + 0.0789482i
\(713\) 14.4853i 0.542478i
\(714\) −2.17157 + 0.297173i −0.0812691 + 0.0111214i
\(715\) 0 0
\(716\) −9.14214 15.8346i −0.341658 0.591768i
\(717\) 2.74666 + 1.58579i 0.102576 + 0.0592223i
\(718\) −3.58719 2.07107i −0.133873 0.0772916i
\(719\) −20.5563 35.6046i −0.766622 1.32783i −0.939385 0.342865i \(-0.888602\pi\)
0.172762 0.984964i \(-0.444731\pi\)
\(720\) 0 0
\(721\) −0.414214 + 1.01461i −0.0154261 + 0.0377861i
\(722\) 4.55635i 0.169570i
\(723\) 34.1698 19.7279i 1.27079 0.733689i
\(724\) 7.91421 13.7078i 0.294129 0.509447i
\(725\) 0 0
\(726\) 6.15685 + 10.6640i 0.228502 + 0.395778i
\(727\) 40.4142i 1.49888i 0.662072 + 0.749440i \(0.269677\pi\)
−0.662072 + 0.749440i \(0.730323\pi\)
\(728\) 2.74666 2.12994i 0.101798 0.0789409i
\(729\) 23.8284 0.882534
\(730\) 0 0
\(731\) 2.65685 4.60181i 0.0982673 0.170204i
\(732\) 43.9062 + 25.3492i 1.62282 + 0.936935i
\(733\) −19.0526 + 11.0000i −0.703722 + 0.406294i −0.808732 0.588177i \(-0.799846\pi\)
0.105010 + 0.994471i \(0.466513\pi\)
\(734\) −4.65685 −0.171888
\(735\) 0 0
\(736\) 10.6569 0.392817
\(737\) −51.9105 + 29.9706i −1.91215 + 1.10398i
\(738\) −2.20330 1.27208i −0.0811047 0.0468258i
\(739\) 20.5563 35.6046i 0.756178 1.30974i −0.188609 0.982052i \(-0.560398\pi\)
0.944787 0.327686i \(-0.106269\pi\)
\(740\) 0 0
\(741\) −5.65685 −0.207810
\(742\) −5.91359 + 4.58579i −0.217095 + 0.168350i
\(743\) 1.92893i 0.0707657i −0.999374 0.0353828i \(-0.988735\pi\)
0.999374 0.0353828i \(-0.0112651\pi\)
\(744\) −11.4853 19.8931i −0.421071 0.729316i
\(745\) 0 0
\(746\) 2.68629 4.65279i 0.0983521 0.170351i
\(747\) 28.7274 16.5858i 1.05108 0.606842i
\(748\) 7.31371i 0.267416i
\(749\) 2.75736 6.75412i 0.100752 0.246790i
\(750\) 0 0
\(751\) 20.8284 + 36.0759i 0.760040 + 1.31643i 0.942829 + 0.333276i \(0.108154\pi\)
−0.182789 + 0.983152i \(0.558513\pi\)
\(752\) 5.19615 + 3.00000i 0.189484 + 0.109399i
\(753\) −27.8359 16.0711i −1.01440 0.585662i
\(754\) 0.171573 + 0.297173i 0.00624832 + 0.0108224i
\(755\) 0 0
\(756\) 1.98528 0.271680i 0.0722040 0.00988089i
\(757\) 19.4558i 0.707135i −0.935409 0.353567i \(-0.884969\pi\)
0.935409 0.353567i \(-0.115031\pi\)
\(758\) −7.59466 + 4.38478i −0.275850 + 0.159262i
\(759\) −14.0711 + 24.3718i −0.510747 + 0.884640i
\(760\) 0 0
\(761\) 6.65685 + 11.5300i 0.241311 + 0.417963i 0.961088 0.276243i \(-0.0890894\pi\)
−0.719777 + 0.694205i \(0.755756\pi\)
\(762\) 13.3137i 0.482305i
\(763\) 1.25024 + 9.13604i 0.0452617 + 0.330747i
\(764\) −13.1127 −0.474401
\(765\) 0 0
\(766\) 3.50000 6.06218i 0.126460 0.219035i
\(767\) −8.95743 5.17157i −0.323434 0.186735i
\(768\) 8.30153 4.79289i 0.299556 0.172949i
\(769\) −44.6274 −1.60931 −0.804653 0.593745i \(-0.797649\pi\)
−0.804653 + 0.593745i \(0.797649\pi\)
\(770\) 0 0
\(771\) 42.6274 1.53519
\(772\) −3.16693 + 1.82843i −0.113980 + 0.0658065i
\(773\) −21.7482 12.5563i −0.782230 0.451620i 0.0549903 0.998487i \(-0.482487\pi\)
−0.837220 + 0.546866i \(0.815821\pi\)
\(774\) −3.75736 + 6.50794i −0.135055 + 0.233923i
\(775\) 0 0
\(776\) 0.544156 0.0195341
\(777\) 0 0
\(778\) 5.11270i 0.183299i
\(779\) 3.07107 + 5.31925i 0.110032 + 0.190582i
\(780\) 0 0
\(781\) 30.1421 52.2077i 1.07857 1.86814i
\(782\) 0.717439 0.414214i 0.0256556 0.0148122i
\(783\) 0.414214i 0.0148028i
\(784\) −20.2279 + 5.64191i −0.722426 + 0.201497i
\(785\) 0 0
\(786\) 1.65685 + 2.86976i 0.0590980 + 0.102361i
\(787\) −24.7305 14.2782i −0.881548 0.508962i −0.0103795 0.999946i \(-0.503304\pi\)
−0.871168 + 0.490984i \(0.836637\pi\)
\(788\) −37.4598 21.6274i −1.33445 0.770445i
\(789\) 22.9853 + 39.8117i 0.818298 + 1.41733i
\(790\) 0 0
\(791\) −20.2426 26.1039i −0.719745 0.928146i
\(792\) 21.6569i 0.769543i
\(793\) −8.23999 + 4.75736i −0.292611 + 0.168939i
\(794\) −5.92893 + 10.2692i −0.210410 + 0.364441i
\(795\) 0 0
\(796\) 1.51472 + 2.62357i 0.0536878 + 0.0929900i
\(797\) 8.00000i 0.283375i 0.989911 + 0.141687i \(0.0452527\pi\)
−0.989911 + 0.141687i \(0.954747\pi\)
\(798\) −6.92820 2.82843i −0.245256 0.100125i
\(799\) 1.65685 0.0586153
\(800\) 0 0
\(801\) −3.75736 + 6.50794i −0.132760 + 0.229947i
\(802\) −2.75722 1.59188i −0.0973609 0.0562113i
\(803\) 20.1903 11.6569i 0.712499 0.411361i
\(804\) 54.7990 1.93261
\(805\) 0 0
\(806\) 2.05887 0.0725208
\(807\) 63.6762 36.7635i 2.24151 1.29413i
\(808\) −16.9108 9.76346i −0.594920 0.343477i
\(809\) −4.81371 + 8.33759i −0.169241 + 0.293134i −0.938153 0.346220i \(-0.887465\pi\)
0.768912 + 0.639354i \(0.220798\pi\)
\(810\) 0 0
\(811\) 24.6274 0.864786 0.432393 0.901685i \(-0.357669\pi\)
0.432393 + 0.901685i \(0.357669\pi\)
\(812\) −0.655892 4.79289i −0.0230173 0.168198i
\(813\) 1.17157i 0.0410889i
\(814\) 0 0
\(815\) 0 0
\(816\) 3.00000 5.19615i 0.105021 0.181902i
\(817\) 15.7116 9.07107i 0.549678 0.317356i
\(818\) 10.2721i 0.359155i
\(819\) 2.34315 5.73951i 0.0818761 0.200555i
\(820\) 0 0
\(821\) 9.97056 + 17.2695i 0.347975 + 0.602710i 0.985890 0.167397i \(-0.0535361\pi\)
−0.637915 + 0.770107i \(0.720203\pi\)
\(822\) −1.43488 0.828427i −0.0500471 0.0288947i
\(823\) 10.4539 + 6.03553i 0.364398 + 0.210385i 0.671008 0.741450i \(-0.265861\pi\)
−0.306610 + 0.951835i \(0.599195\pi\)
\(824\) 0.328427 + 0.568852i 0.0114413 + 0.0198169i
\(825\) 0 0
\(826\) −8.38478 10.8126i −0.291744 0.376217i
\(827\) 16.2132i 0.563788i −0.959446 0.281894i \(-0.909037\pi\)
0.959446 0.281894i \(-0.0909627\pi\)
\(828\) 10.8126 6.24264i 0.375763 0.216947i
\(829\) 3.34315 5.79050i 0.116112 0.201112i −0.802112 0.597174i \(-0.796290\pi\)
0.918224 + 0.396062i \(0.129623\pi\)
\(830\) 0 0
\(831\) 14.6569 + 25.3864i 0.508441 + 0.880645i
\(832\) 3.45584i 0.119810i
\(833\) −4.05845 + 4.14214i −0.140617 + 0.143516i
\(834\) 12.1421 0.420448
\(835\) 0 0
\(836\) −12.4853 + 21.6251i −0.431812 + 0.747921i
\(837\) 2.15232 + 1.24264i 0.0743950 + 0.0429519i
\(838\) 8.36308 4.82843i 0.288898 0.166795i
\(839\) −20.8284 −0.719077 −0.359539 0.933130i \(-0.617066\pi\)
−0.359539 + 0.933130i \(0.617066\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) −1.25024 + 0.721825i −0.0430861 + 0.0248757i
\(843\) −54.9544 31.7279i −1.89273 1.09277i
\(844\) −3.21320 + 5.56543i −0.110603 + 0.191570i
\(845\) 0 0
\(846\) −2.34315 −0.0805590
\(847\) 30.1623 + 12.3137i 1.03639 + 0.423104i
\(848\) 20.4853i 0.703467i
\(849\) 16.8995 + 29.2708i 0.579989 + 1.00457i
\(850\) 0 0
\(851\) 0 0
\(852\) −47.7290 + 27.5563i −1.63517 + 0.944065i
\(853\) 53.4558i 1.83029i 0.403121 + 0.915147i \(0.367925\pi\)
−0.403121 + 0.915147i \(0.632075\pi\)
\(854\) −12.4706 + 1.70656i −0.426734 + 0.0583972i
\(855\) 0 0
\(856\) −2.18629 3.78677i −0.0747259 0.129429i
\(857\) −19.2987 11.1421i −0.659233 0.380608i 0.132752 0.991149i \(-0.457619\pi\)
−0.791985 + 0.610541i \(0.790952\pi\)
\(858\) 3.46410 + 2.00000i 0.118262 + 0.0682789i
\(859\) 23.3137 + 40.3805i 0.795453 + 1.37777i 0.922551 + 0.385876i \(0.126101\pi\)
−0.127097 + 0.991890i \(0.540566\pi\)
\(860\) 0 0
\(861\) −13.7426 + 1.88064i −0.468348 + 0.0640919i
\(862\) 9.02944i 0.307544i
\(863\) −14.3382 + 8.27817i −0.488079 + 0.281792i −0.723777 0.690034i \(-0.757596\pi\)
0.235698 + 0.971826i \(0.424262\pi\)
\(864\) 0.914214 1.58346i 0.0311022 0.0538706i
\(865\) 0 0
\(866\) −6.58579 11.4069i −0.223794 0.387623i
\(867\) 39.3848i 1.33758i
\(868\) −26.8723 10.9706i −0.912105 0.372365i
\(869\) −44.2843 −1.50224
\(870\) 0 0
\(871\) −5.14214 + 8.90644i −0.174235 + 0.301783i
\(872\) 4.78645 + 2.76346i 0.162090 + 0.0935824i
\(873\) 0.840532 0.485281i 0.0284477 0.0164243i
\(874\) 2.82843 0.0956730
\(875\) 0 0
\(876\) −21.3137 −0.720123
\(877\) −26.6982 + 15.4142i −0.901534 + 0.520501i −0.877698 0.479215i \(-0.840921\pi\)
−0.0238366 + 0.999716i \(0.507588\pi\)
\(878\) 12.1753 + 7.02944i 0.410898 + 0.237232i
\(879\) −19.3137 + 33.4523i −0.651435 + 1.12832i
\(880\) 0 0
\(881\) −3.82843 −0.128983 −0.0644915 0.997918i \(-0.520543\pi\)
−0.0644915 + 0.997918i \(0.520543\pi\)
\(882\) 5.73951 5.85786i 0.193259 0.197245i
\(883\) 38.2843i 1.28837i −0.764870 0.644184i \(-0.777197\pi\)
0.764870 0.644184i \(-0.222803\pi\)
\(884\) 0.627417 + 1.08672i 0.0211023 + 0.0365503i
\(885\) 0 0
\(886\) −2.52944 + 4.38111i −0.0849781 + 0.147186i
\(887\) −38.1667 + 22.0355i −1.28151 + 0.739881i −0.977125 0.212668i \(-0.931785\pi\)
−0.304387 + 0.952549i \(0.598451\pi\)
\(888\) 0 0
\(889\) 21.5858 + 27.8359i 0.723964 + 0.933586i
\(890\) 0 0
\(891\) 22.8995 + 39.6631i 0.767162 + 1.32876i
\(892\) −18.4582 10.6569i −0.618027 0.356818i
\(893\) 4.89898 + 2.82843i 0.163938 + 0.0946497i
\(894\) 3.91421 + 6.77962i 0.130911 + 0.226744i
\(895\) 0 0
\(896\) −10.5563 + 25.8577i −0.352663 + 0.863844i
\(897\) 4.82843i 0.161216i
\(898\) 0.655892 0.378680i 0.0218874 0.0126367i
\(899\) 3.00000 5.19615i 0.100056 0.173301i
\(900\) 0 0
\(901\) −2.82843 4.89898i −0.0942286 0.163209i
\(902\) 4.34315i 0.144611i
\(903\) 5.55487 + 40.5919i 0.184855 + 1.35081i
\(904\) −19.7990 −0.658505
\(905\) 0 0
\(906\) 0.171573 0.297173i 0.00570013 0.00987291i
\(907\) 24.4334 + 14.1066i 0.811296 + 0.468402i 0.847406 0.530946i \(-0.178163\pi\)
−0.0361097 + 0.999348i \(0.511497\pi\)
\(908\) −42.7069 + 24.6569i −1.41728 + 0.818266i
\(909\) −34.8284 −1.15519
\(910\) 0 0
\(911\) −49.7990 −1.64991 −0.824957 0.565195i \(-0.808801\pi\)
−0.824957 + 0.565195i \(0.808801\pi\)
\(912\) 17.7408 10.2426i 0.587456 0.339168i
\(913\) 49.0408 + 28.3137i 1.62301 + 0.937047i
\(914\) 6.68629 11.5810i 0.221163 0.383065i
\(915\) 0 0
\(916\) 0.627417 0.0207304
\(917\) 8.11689 + 3.31371i 0.268043 + 0.109428i
\(918\) 0.142136i 0.00469117i
\(919\) 9.55635 + 16.5521i 0.315235 + 0.546003i 0.979487 0.201505i \(-0.0645834\pi\)
−0.664253 + 0.747508i \(0.731250\pi\)
\(920\) 0 0
\(921\) 15.9853 27.6873i 0.526733 0.912328i
\(922\) 6.70314 3.87006i 0.220756 0.127454i
\(923\) 10.3431i 0.340449i
\(924\) −34.5563 44.5621i −1.13682 1.46598i
\(925\) 0 0
\(926\) 2.28680 + 3.96085i 0.0751488 + 0.130162i
\(927\) 1.01461 + 0.585786i 0.0333242 + 0.0192398i
\(928\) −3.82282 2.20711i −0.125490 0.0724518i
\(929\) −5.74264 9.94655i −0.188410 0.326336i 0.756310 0.654213i \(-0.227000\pi\)
−0.944720 + 0.327877i \(0.893667\pi\)
\(930\) 0 0
\(931\) −19.0711 + 5.31925i −0.625029 + 0.174331i
\(932\) 20.4264i 0.669089i
\(933\) −39.3659 + 22.7279i −1.28878 + 0.744079i
\(934\) 4.74264 8.21449i 0.155184 0.268786i
\(935\) 0 0
\(936\) −1.85786 3.21792i −0.0607262 0.105181i
\(937\) 10.6274i 0.347183i 0.984818 + 0.173591i \(0.0555372\pi\)
−0.984818 + 0.173591i \(0.944463\pi\)
\(938\) −10.7510 + 8.33705i −0.351033 + 0.272214i
\(939\) 42.6274 1.39109
\(940\) 0 0
\(941\) −5.14214 + 8.90644i −0.167629 + 0.290342i −0.937586 0.347754i \(-0.886944\pi\)
0.769957 + 0.638096i \(0.220278\pi\)
\(942\) 4.60181 + 2.65685i 0.149935 + 0.0865650i
\(943\) 4.54026 2.62132i 0.147851 0.0853619i
\(944\) 37.4558 1.21908
\(945\) 0 0
\(946\) −12.8284 −0.417088
\(947\) 37.3982 21.5919i 1.21528 0.701642i 0.251375 0.967890i \(-0.419117\pi\)
0.963905 + 0.266248i \(0.0857840\pi\)
\(948\) 35.0613 + 20.2426i 1.13874 + 0.657450i
\(949\) 2.00000 3.46410i 0.0649227 0.112449i
\(950\) 0 0
\(951\) 62.2843 2.01971
\(952\) 0.471253 + 3.44365i 0.0152734 + 0.111609i
\(953\) 2.34315i 0.0759019i −0.999280 0.0379510i \(-0.987917\pi\)
0.999280 0.0379510i \(-0.0120831\pi\)
\(954\) 4.00000 + 6.92820i 0.129505 + 0.224309i
\(955\) 0 0
\(956\) 1.20101 2.08021i 0.0388434 0.0672788i
\(957\) 10.0951 5.82843i 0.326329 0.188406i
\(958\) 10.0833i 0.325775i
\(959\) −4.34315 + 0.594346i −0.140247 + 0.0191924i
\(960\) 0 0
\(961\) −2.50000 4.33013i −0.0806452 0.139682i
\(962\) 0 0
\(963\) −6.75412 3.89949i −0.217649 0.125659i
\(964\) −14.9411 25.8788i −0.481221 0.833500i
\(965\) 0 0
\(966\) −2.41421 + 5.91359i −0.0776760 + 0.190267i
\(967\) 27.5269i 0.885206i 0.896718 + 0.442603i \(0.145945\pi\)
−0.896718 + 0.442603i \(0.854055\pi\)
\(968\) 16.9108 9.76346i 0.543534 0.313809i
\(969\) 2.82843 4.89898i 0.0908622 0.157378i
\(970\) 0 0
\(971\) 12.0000 + 20.7846i 0.385098 + 0.667010i 0.991783 0.127933i \(-0.0408342\pi\)
−0.606685 + 0.794943i \(0.707501\pi\)
\(972\) 39.5980i 1.27011i
\(973\) 25.3864 19.6863i 0.813851 0.631114i
\(974\) 6.48528 0.207802
\(975\) 0 0
\(976\) 17.2279 29.8396i 0.551452 0.955143i
\(977\) 18.4582 + 10.6569i 0.590531 + 0.340943i 0.765307 0.643665i \(-0.222587\pi\)
−0.174777 + 0.984608i \(0.555920\pi\)
\(978\) −20.4874 + 11.8284i −0.655116 + 0.378231i
\(979\) −12.8284 −0.409998
\(980\) 0 0
\(981\) 9.85786 0.314737
\(982\) −4.77589 + 2.75736i −0.152405 + 0.0879909i
\(983\) 12.3090 + 7.10660i 0.392596 + 0.226665i 0.683284 0.730152i \(-0.260551\pi\)
−0.290688 + 0.956818i \(0.593884\pi\)
\(984\) −4.15685 + 7.19988i −0.132516 + 0.229524i
\(985\) 0 0
\(986\) −0.343146 −0.0109280
\(987\) −10.0951 + 7.82843i −0.321332 + 0.249182i
\(988\) 4.28427i 0.136301i
\(989\) −7.74264 13.4106i −0.246202 0.426434i
\(990\) 0 0
\(991\) 7.82843 13.5592i 0.248678 0.430723i −0.714481 0.699655i \(-0.753337\pi\)
0.963159 + 0.268931i \(0.0866705\pi\)
\(992\) −22.9369 + 13.2426i −0.728248 + 0.420454i
\(993\) 26.4853i 0.840485i
\(994\) 5.17157 12.6677i 0.164032 0.401796i
\(995\) 0 0
\(996\) −25.8848 44.8337i −0.820191 1.42061i
\(997\) −15.1172 8.72792i −0.478767 0.276416i 0.241136 0.970491i \(-0.422480\pi\)
−0.719902 + 0.694075i \(0.755813\pi\)
\(998\) 1.73205 + 1.00000i 0.0548271 + 0.0316544i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 175.2.k.a.74.3 8
5.2 odd 4 35.2.e.a.11.2 4
5.3 odd 4 175.2.e.c.151.1 4
5.4 even 2 inner 175.2.k.a.74.2 8
7.2 even 3 inner 175.2.k.a.149.2 8
7.3 odd 6 1225.2.b.h.99.3 4
7.4 even 3 1225.2.b.g.99.3 4
15.2 even 4 315.2.j.e.46.1 4
20.7 even 4 560.2.q.k.81.2 4
35.2 odd 12 35.2.e.a.16.2 yes 4
35.3 even 12 1225.2.a.m.1.2 2
35.4 even 6 1225.2.b.g.99.2 4
35.9 even 6 inner 175.2.k.a.149.3 8
35.12 even 12 245.2.e.e.226.2 4
35.17 even 12 245.2.a.g.1.1 2
35.18 odd 12 1225.2.a.k.1.2 2
35.23 odd 12 175.2.e.c.51.1 4
35.24 odd 6 1225.2.b.h.99.2 4
35.27 even 4 245.2.e.e.116.2 4
35.32 odd 12 245.2.a.h.1.1 2
105.2 even 12 315.2.j.e.226.1 4
105.17 odd 12 2205.2.a.q.1.2 2
105.32 even 12 2205.2.a.n.1.2 2
140.67 even 12 3920.2.a.bq.1.1 2
140.87 odd 12 3920.2.a.bv.1.2 2
140.107 even 12 560.2.q.k.401.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.2.e.a.11.2 4 5.2 odd 4
35.2.e.a.16.2 yes 4 35.2 odd 12
175.2.e.c.51.1 4 35.23 odd 12
175.2.e.c.151.1 4 5.3 odd 4
175.2.k.a.74.2 8 5.4 even 2 inner
175.2.k.a.74.3 8 1.1 even 1 trivial
175.2.k.a.149.2 8 7.2 even 3 inner
175.2.k.a.149.3 8 35.9 even 6 inner
245.2.a.g.1.1 2 35.17 even 12
245.2.a.h.1.1 2 35.32 odd 12
245.2.e.e.116.2 4 35.27 even 4
245.2.e.e.226.2 4 35.12 even 12
315.2.j.e.46.1 4 15.2 even 4
315.2.j.e.226.1 4 105.2 even 12
560.2.q.k.81.2 4 20.7 even 4
560.2.q.k.401.2 4 140.107 even 12
1225.2.a.k.1.2 2 35.18 odd 12
1225.2.a.m.1.2 2 35.3 even 12
1225.2.b.g.99.2 4 35.4 even 6
1225.2.b.g.99.3 4 7.4 even 3
1225.2.b.h.99.2 4 35.24 odd 6
1225.2.b.h.99.3 4 7.3 odd 6
2205.2.a.n.1.2 2 105.32 even 12
2205.2.a.q.1.2 2 105.17 odd 12
3920.2.a.bq.1.1 2 140.67 even 12
3920.2.a.bv.1.2 2 140.87 odd 12