Properties

Label 201.2.d.a.200.15
Level $201$
Weight $2$
Character 201.200
Analytic conductor $1.605$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,2,Mod(200,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.200");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.d (of order \(2\), degree \(1\), 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: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 7 x^{18} + 32 x^{16} + 128 x^{14} + 423 x^{12} + 1186 x^{10} + 3807 x^{8} + 10368 x^{6} + 23328 x^{4} + 45927 x^{2} + 59049 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 200.15
Root \(1.24906 + 1.19993i\) of defining polynomial
Character \(\chi\) \(=\) 201.200
Dual form 201.2.d.a.200.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.18817 q^{2} +(1.24906 - 1.19993i) q^{3} -0.588256 q^{4} +2.08509 q^{5} +(1.48410 - 1.42572i) q^{6} -0.284155i q^{7} -3.07528 q^{8} +(0.120318 - 2.99759i) q^{9} +O(q^{10})\) \(q+1.18817 q^{2} +(1.24906 - 1.19993i) q^{3} -0.588256 q^{4} +2.08509 q^{5} +(1.48410 - 1.42572i) q^{6} -0.284155i q^{7} -3.07528 q^{8} +(0.120318 - 2.99759i) q^{9} +2.47744 q^{10} -1.80373 q^{11} +(-0.734769 + 0.705868i) q^{12} +5.82854i q^{13} -0.337624i q^{14} +(2.60442 - 2.50198i) q^{15} -2.47744 q^{16} +2.11827i q^{17} +(0.142958 - 3.56164i) q^{18} +3.37994 q^{19} -1.22657 q^{20} +(-0.340967 - 0.354927i) q^{21} -2.14313 q^{22} -5.85449i q^{23} +(-3.84122 + 3.69014i) q^{24} -0.652380 q^{25} +6.92529i q^{26} +(-3.44662 - 3.88855i) q^{27} +0.167156i q^{28} -1.18816i q^{29} +(3.09448 - 2.97277i) q^{30} +9.35599i q^{31} +3.20695 q^{32} +(-2.25297 + 2.16435i) q^{33} +2.51687i q^{34} -0.592489i q^{35} +(-0.0707775 + 1.76335i) q^{36} -9.06621 q^{37} +4.01594 q^{38} +(6.99386 + 7.28021i) q^{39} -6.41226 q^{40} -6.14602 q^{41} +(-0.405126 - 0.421713i) q^{42} -1.57889i q^{43} +1.06105 q^{44} +(0.250874 - 6.25025i) q^{45} -6.95612i q^{46} +3.59553i q^{47} +(-3.09448 + 2.97277i) q^{48} +6.91926 q^{49} -0.775137 q^{50} +(2.54179 + 2.64586i) q^{51} -3.42867i q^{52} +5.90760 q^{53} +(-4.09517 - 4.62025i) q^{54} -3.76094 q^{55} +0.873856i q^{56} +(4.22176 - 4.05570i) q^{57} -1.41174i q^{58} -8.92620i q^{59} +(-1.53206 + 1.47180i) q^{60} +3.69460i q^{61} +11.1165i q^{62} +(-0.851778 - 0.0341888i) q^{63} +8.76528 q^{64} +12.1531i q^{65} +(-2.67691 + 2.57162i) q^{66} +(-1.97202 - 7.94425i) q^{67} -1.24609i q^{68} +(-7.02500 - 7.31263i) q^{69} -0.703977i q^{70} -12.9205i q^{71} +(-0.370011 + 9.21843i) q^{72} +2.98669 q^{73} -10.7722 q^{74} +(-0.814863 + 0.782812i) q^{75} -1.98827 q^{76} +0.512537i q^{77} +(8.30988 + 8.65012i) q^{78} +2.32354i q^{79} -5.16571 q^{80} +(-8.97105 - 0.721325i) q^{81} -7.30251 q^{82} -10.4066i q^{83} +(0.200576 + 0.208788i) q^{84} +4.41680i q^{85} -1.87599i q^{86} +(-1.42571 - 1.48409i) q^{87} +5.54697 q^{88} -4.96972i q^{89} +(0.298080 - 7.42635i) q^{90} +1.65621 q^{91} +3.44394i q^{92} +(11.2266 + 11.6862i) q^{93} +4.27210i q^{94} +7.04749 q^{95} +(4.00568 - 3.84812i) q^{96} +8.79672i q^{97} +8.22124 q^{98} +(-0.217020 + 5.40683i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 12 q^{4} - 4 q^{6} - 14 q^{9} - 12 q^{10} + 2 q^{15} + 12 q^{16} + 24 q^{19} + 12 q^{21} - 28 q^{22} + 2 q^{24} - 4 q^{25} + 10 q^{33} - 44 q^{36} + 24 q^{37} - 8 q^{39} - 32 q^{40} - 48 q^{49} - 26 q^{54} - 8 q^{55} - 38 q^{60} - 16 q^{64} + 32 q^{67} + 4 q^{73} + 116 q^{76} - 30 q^{81} - 32 q^{82} + 90 q^{84} - 40 q^{88} + 74 q^{90} + 20 q^{91} - 2 q^{93} + 30 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.18817 0.840162 0.420081 0.907487i \(-0.362002\pi\)
0.420081 + 0.907487i \(0.362002\pi\)
\(3\) 1.24906 1.19993i 0.721147 0.692782i
\(4\) −0.588256 −0.294128
\(5\) 2.08509 0.932483 0.466241 0.884658i \(-0.345608\pi\)
0.466241 + 0.884658i \(0.345608\pi\)
\(6\) 1.48410 1.42572i 0.605880 0.582049i
\(7\) 0.284155i 0.107400i −0.998557 0.0537002i \(-0.982898\pi\)
0.998557 0.0537002i \(-0.0171015\pi\)
\(8\) −3.07528 −1.08728
\(9\) 0.120318 2.99759i 0.0401059 0.999195i
\(10\) 2.47744 0.783437
\(11\) −1.80373 −0.543844 −0.271922 0.962319i \(-0.587659\pi\)
−0.271922 + 0.962319i \(0.587659\pi\)
\(12\) −0.734769 + 0.705868i −0.212109 + 0.203767i
\(13\) 5.82854i 1.61655i 0.588808 + 0.808273i \(0.299597\pi\)
−0.588808 + 0.808273i \(0.700403\pi\)
\(14\) 0.337624i 0.0902337i
\(15\) 2.60442 2.50198i 0.672457 0.646007i
\(16\) −2.47744 −0.619361
\(17\) 2.11827i 0.513757i 0.966444 + 0.256878i \(0.0826940\pi\)
−0.966444 + 0.256878i \(0.917306\pi\)
\(18\) 0.142958 3.56164i 0.0336954 0.839486i
\(19\) 3.37994 0.775411 0.387706 0.921783i \(-0.373268\pi\)
0.387706 + 0.921783i \(0.373268\pi\)
\(20\) −1.22657 −0.274269
\(21\) −0.340967 0.354927i −0.0744051 0.0774514i
\(22\) −2.14313 −0.456917
\(23\) 5.85449i 1.22075i −0.792114 0.610373i \(-0.791020\pi\)
0.792114 0.610373i \(-0.208980\pi\)
\(24\) −3.84122 + 3.69014i −0.784087 + 0.753246i
\(25\) −0.652380 −0.130476
\(26\) 6.92529i 1.35816i
\(27\) −3.44662 3.88855i −0.663302 0.748351i
\(28\) 0.167156i 0.0315894i
\(29\) 1.18816i 0.220636i −0.993896 0.110318i \(-0.964813\pi\)
0.993896 0.110318i \(-0.0351869\pi\)
\(30\) 3.09448 2.97277i 0.564973 0.542751i
\(31\) 9.35599i 1.68038i 0.542288 + 0.840192i \(0.317558\pi\)
−0.542288 + 0.840192i \(0.682442\pi\)
\(32\) 3.20695 0.566913
\(33\) −2.25297 + 2.16435i −0.392191 + 0.376765i
\(34\) 2.51687i 0.431639i
\(35\) 0.592489i 0.100149i
\(36\) −0.0707775 + 1.76335i −0.0117963 + 0.293891i
\(37\) −9.06621 −1.49048 −0.745238 0.666798i \(-0.767664\pi\)
−0.745238 + 0.666798i \(0.767664\pi\)
\(38\) 4.01594 0.651471
\(39\) 6.99386 + 7.28021i 1.11991 + 1.16577i
\(40\) −6.41226 −1.01387
\(41\) −6.14602 −0.959847 −0.479924 0.877310i \(-0.659336\pi\)
−0.479924 + 0.877310i \(0.659336\pi\)
\(42\) −0.405126 0.421713i −0.0625123 0.0650718i
\(43\) 1.57889i 0.240779i −0.992727 0.120389i \(-0.961586\pi\)
0.992727 0.120389i \(-0.0384143\pi\)
\(44\) 1.06105 0.159960
\(45\) 0.250874 6.25025i 0.0373980 0.931733i
\(46\) 6.95612i 1.02562i
\(47\) 3.59553i 0.524462i 0.965005 + 0.262231i \(0.0844583\pi\)
−0.965005 + 0.262231i \(0.915542\pi\)
\(48\) −3.09448 + 2.97277i −0.446650 + 0.429082i
\(49\) 6.91926 0.988465
\(50\) −0.775137 −0.109621
\(51\) 2.54179 + 2.64586i 0.355922 + 0.370494i
\(52\) 3.42867i 0.475471i
\(53\) 5.90760 0.811471 0.405736 0.913990i \(-0.367015\pi\)
0.405736 + 0.913990i \(0.367015\pi\)
\(54\) −4.09517 4.62025i −0.557282 0.628736i
\(55\) −3.76094 −0.507125
\(56\) 0.873856i 0.116774i
\(57\) 4.22176 4.05570i 0.559185 0.537191i
\(58\) 1.41174i 0.185370i
\(59\) 8.92620i 1.16209i −0.813871 0.581046i \(-0.802644\pi\)
0.813871 0.581046i \(-0.197356\pi\)
\(60\) −1.53206 + 1.47180i −0.197788 + 0.190009i
\(61\) 3.69460i 0.473046i 0.971626 + 0.236523i \(0.0760078\pi\)
−0.971626 + 0.236523i \(0.923992\pi\)
\(62\) 11.1165i 1.41180i
\(63\) −0.851778 0.0341888i −0.107314 0.00430739i
\(64\) 8.76528 1.09566
\(65\) 12.1531i 1.50740i
\(66\) −2.67691 + 2.57162i −0.329504 + 0.316544i
\(67\) −1.97202 7.94425i −0.240921 0.970545i
\(68\) 1.24609i 0.151110i
\(69\) −7.02500 7.31263i −0.845711 0.880337i
\(70\) 0.703977i 0.0841414i
\(71\) 12.9205i 1.53338i −0.642020 0.766688i \(-0.721903\pi\)
0.642020 0.766688i \(-0.278097\pi\)
\(72\) −0.370011 + 9.21843i −0.0436062 + 1.08640i
\(73\) 2.98669 0.349566 0.174783 0.984607i \(-0.444078\pi\)
0.174783 + 0.984607i \(0.444078\pi\)
\(74\) −10.7722 −1.25224
\(75\) −0.814863 + 0.782812i −0.0940923 + 0.0903914i
\(76\) −1.98827 −0.228070
\(77\) 0.512537i 0.0584090i
\(78\) 8.30988 + 8.65012i 0.940909 + 0.979433i
\(79\) 2.32354i 0.261419i 0.991421 + 0.130709i \(0.0417255\pi\)
−0.991421 + 0.130709i \(0.958275\pi\)
\(80\) −5.16571 −0.577543
\(81\) −8.97105 0.721325i −0.996783 0.0801472i
\(82\) −7.30251 −0.806427
\(83\) 10.4066i 1.14228i −0.820854 0.571138i \(-0.806502\pi\)
0.820854 0.571138i \(-0.193498\pi\)
\(84\) 0.200576 + 0.208788i 0.0218846 + 0.0227806i
\(85\) 4.41680i 0.479070i
\(86\) 1.87599i 0.202293i
\(87\) −1.42571 1.48409i −0.152853 0.159111i
\(88\) 5.54697 0.591309
\(89\) 4.96972i 0.526789i −0.964688 0.263395i \(-0.915158\pi\)
0.964688 0.263395i \(-0.0848422\pi\)
\(90\) 0.298080 7.42635i 0.0314204 0.782806i
\(91\) 1.65621 0.173618
\(92\) 3.44394i 0.359055i
\(93\) 11.2266 + 11.6862i 1.16414 + 1.21180i
\(94\) 4.27210i 0.440633i
\(95\) 7.04749 0.723058
\(96\) 4.00568 3.84812i 0.408828 0.392748i
\(97\) 8.79672i 0.893171i 0.894741 + 0.446586i \(0.147360\pi\)
−0.894741 + 0.446586i \(0.852640\pi\)
\(98\) 8.22124 0.830471
\(99\) −0.217020 + 5.40683i −0.0218113 + 0.543406i
\(100\) 0.383766 0.0383766
\(101\) 8.83225 0.878842 0.439421 0.898281i \(-0.355184\pi\)
0.439421 + 0.898281i \(0.355184\pi\)
\(102\) 3.02007 + 3.14373i 0.299032 + 0.311275i
\(103\) 14.5531 1.43396 0.716982 0.697092i \(-0.245523\pi\)
0.716982 + 0.697092i \(0.245523\pi\)
\(104\) 17.9244i 1.75763i
\(105\) −0.710948 0.740057i −0.0693814 0.0722221i
\(106\) 7.01922 0.681767
\(107\) 2.82813i 0.273406i −0.990612 0.136703i \(-0.956349\pi\)
0.990612 0.136703i \(-0.0436505\pi\)
\(108\) 2.02749 + 2.28746i 0.195096 + 0.220111i
\(109\) 14.9319i 1.43021i −0.699016 0.715106i \(-0.746378\pi\)
0.699016 0.715106i \(-0.253622\pi\)
\(110\) −4.46863 −0.426067
\(111\) −11.3243 + 10.8789i −1.07485 + 1.03258i
\(112\) 0.703977i 0.0665196i
\(113\) 6.11810 0.575543 0.287771 0.957699i \(-0.407086\pi\)
0.287771 + 0.957699i \(0.407086\pi\)
\(114\) 5.01616 4.81886i 0.469806 0.451328i
\(115\) 12.2072i 1.13832i
\(116\) 0.698943i 0.0648952i
\(117\) 17.4715 + 0.701276i 1.61525 + 0.0648330i
\(118\) 10.6058i 0.976345i
\(119\) 0.601918 0.0551777
\(120\) −8.00932 + 7.69429i −0.731147 + 0.702389i
\(121\) −7.74657 −0.704234
\(122\) 4.38981i 0.397435i
\(123\) −7.67677 + 7.37482i −0.692191 + 0.664965i
\(124\) 5.50371i 0.494248i
\(125\) −11.7857 −1.05415
\(126\) −1.01206 0.0406221i −0.0901611 0.00361890i
\(127\) 2.89301 0.256714 0.128357 0.991728i \(-0.459030\pi\)
0.128357 + 0.991728i \(0.459030\pi\)
\(128\) 4.00074 0.353619
\(129\) −1.89457 1.97214i −0.166807 0.173637i
\(130\) 14.4399i 1.26646i
\(131\) 11.7543i 1.02698i 0.858096 + 0.513490i \(0.171648\pi\)
−0.858096 + 0.513490i \(0.828352\pi\)
\(132\) 1.32532 1.27319i 0.115354 0.110817i
\(133\) 0.960426i 0.0832795i
\(134\) −2.34309 9.43911i −0.202412 0.815415i
\(135\) −7.18653 8.10799i −0.618518 0.697825i
\(136\) 6.51429i 0.558596i
\(137\) −5.72373 −0.489011 −0.244505 0.969648i \(-0.578626\pi\)
−0.244505 + 0.969648i \(0.578626\pi\)
\(138\) −8.34688 8.68863i −0.710534 0.739626i
\(139\) 9.17061i 0.777841i 0.921271 + 0.388921i \(0.127152\pi\)
−0.921271 + 0.388921i \(0.872848\pi\)
\(140\) 0.348535i 0.0294566i
\(141\) 4.31440 + 4.49105i 0.363338 + 0.378214i
\(142\) 15.3517i 1.28828i
\(143\) 10.5131i 0.879149i
\(144\) −0.298080 + 7.42635i −0.0248400 + 0.618863i
\(145\) 2.47743i 0.205739i
\(146\) 3.54869 0.293692
\(147\) 8.64259 8.30265i 0.712829 0.684791i
\(148\) 5.33325 0.438391
\(149\) 12.8862i 1.05568i 0.849344 + 0.527840i \(0.176998\pi\)
−0.849344 + 0.527840i \(0.823002\pi\)
\(150\) −0.968195 + 0.930113i −0.0790528 + 0.0759434i
\(151\) 13.2071 1.07478 0.537389 0.843334i \(-0.319411\pi\)
0.537389 + 0.843334i \(0.319411\pi\)
\(152\) −10.3943 −0.843087
\(153\) 6.34971 + 0.254866i 0.513344 + 0.0206047i
\(154\) 0.608981i 0.0490731i
\(155\) 19.5081i 1.56693i
\(156\) −4.11418 4.28263i −0.329398 0.342885i
\(157\) −11.7999 −0.941731 −0.470865 0.882205i \(-0.656058\pi\)
−0.470865 + 0.882205i \(0.656058\pi\)
\(158\) 2.76076i 0.219634i
\(159\) 7.37896 7.08873i 0.585190 0.562173i
\(160\) 6.68679 0.528637
\(161\) −1.66358 −0.131109
\(162\) −10.6591 0.857056i −0.837459 0.0673367i
\(163\) −4.07931 −0.319516 −0.159758 0.987156i \(-0.551071\pi\)
−0.159758 + 0.987156i \(0.551071\pi\)
\(164\) 3.61543 0.282318
\(165\) −4.69765 + 4.51288i −0.365712 + 0.351327i
\(166\) 12.3648i 0.959697i
\(167\) 5.34158i 0.413343i 0.978410 + 0.206672i \(0.0662632\pi\)
−0.978410 + 0.206672i \(0.933737\pi\)
\(168\) 1.04857 + 1.09150i 0.0808989 + 0.0842112i
\(169\) −20.9719 −1.61322
\(170\) 5.24791i 0.402496i
\(171\) 0.406666 10.1317i 0.0310986 0.774787i
\(172\) 0.928792i 0.0708197i
\(173\) 24.8155i 1.88668i 0.331821 + 0.943342i \(0.392337\pi\)
−0.331821 + 0.943342i \(0.607663\pi\)
\(174\) −1.69399 1.76335i −0.128421 0.133679i
\(175\) 0.185377i 0.0140132i
\(176\) 4.46863 0.336836
\(177\) −10.7108 11.1494i −0.805076 0.838039i
\(178\) 5.90487i 0.442588i
\(179\) 15.4421 1.15420 0.577098 0.816675i \(-0.304185\pi\)
0.577098 + 0.816675i \(0.304185\pi\)
\(180\) −0.147578 + 3.67675i −0.0109998 + 0.274048i
\(181\) −6.79326 −0.504939 −0.252469 0.967605i \(-0.581243\pi\)
−0.252469 + 0.967605i \(0.581243\pi\)
\(182\) 1.96785 0.145867
\(183\) 4.43328 + 4.61479i 0.327718 + 0.341135i
\(184\) 18.0042i 1.32729i
\(185\) −18.9039 −1.38984
\(186\) 13.3391 + 13.8852i 0.978067 + 1.01811i
\(187\) 3.82079i 0.279404i
\(188\) 2.11509i 0.154259i
\(189\) −1.10495 + 0.979373i −0.0803732 + 0.0712389i
\(190\) 8.37361 0.607486
\(191\) −22.3294 −1.61570 −0.807849 0.589390i \(-0.799368\pi\)
−0.807849 + 0.589390i \(0.799368\pi\)
\(192\) 10.9484 10.5178i 0.790132 0.759054i
\(193\) −23.6517 −1.70248 −0.851242 0.524773i \(-0.824150\pi\)
−0.851242 + 0.524773i \(0.824150\pi\)
\(194\) 10.4520i 0.750408i
\(195\) 14.5829 + 15.1799i 1.04430 + 1.08706i
\(196\) −4.07029 −0.290735
\(197\) 19.5884 1.39562 0.697809 0.716284i \(-0.254158\pi\)
0.697809 + 0.716284i \(0.254158\pi\)
\(198\) −0.257856 + 6.42422i −0.0183251 + 0.456549i
\(199\) 12.8766 0.912798 0.456399 0.889775i \(-0.349139\pi\)
0.456399 + 0.889775i \(0.349139\pi\)
\(200\) 2.00625 0.141863
\(201\) −11.9958 7.55658i −0.846115 0.533000i
\(202\) 10.4942 0.738370
\(203\) −0.337622 −0.0236964
\(204\) −1.49522 1.55644i −0.104686 0.108973i
\(205\) −12.8150 −0.895041
\(206\) 17.2916 1.20476
\(207\) −17.5493 0.704398i −1.21976 0.0489591i
\(208\) 14.4399i 1.00123i
\(209\) −6.09649 −0.421703
\(210\) −0.844726 0.879312i −0.0582916 0.0606783i
\(211\) −9.41052 −0.647847 −0.323923 0.946083i \(-0.605002\pi\)
−0.323923 + 0.946083i \(0.605002\pi\)
\(212\) −3.47518 −0.238676
\(213\) −15.5037 16.1385i −1.06230 1.10579i
\(214\) 3.36029i 0.229705i
\(215\) 3.29214i 0.224522i
\(216\) 10.5993 + 11.9584i 0.721194 + 0.813665i
\(217\) 2.65855 0.180474
\(218\) 17.7416i 1.20161i
\(219\) 3.73057 3.58383i 0.252088 0.242173i
\(220\) 2.21239 0.149160
\(221\) −12.3464 −0.830512
\(222\) −13.4551 + 12.9259i −0.903050 + 0.867531i
\(223\) −4.29838 −0.287841 −0.143920 0.989589i \(-0.545971\pi\)
−0.143920 + 0.989589i \(0.545971\pi\)
\(224\) 0.911269i 0.0608867i
\(225\) −0.0784928 + 1.95556i −0.00523285 + 0.130371i
\(226\) 7.26934 0.483549
\(227\) 18.7640i 1.24541i 0.782456 + 0.622706i \(0.213967\pi\)
−0.782456 + 0.622706i \(0.786033\pi\)
\(228\) −2.48347 + 2.38579i −0.164472 + 0.158003i
\(229\) 18.5224i 1.22399i 0.790861 + 0.611996i \(0.209633\pi\)
−0.790861 + 0.611996i \(0.790367\pi\)
\(230\) 14.5042i 0.956377i
\(231\) 0.615011 + 0.640191i 0.0404647 + 0.0421215i
\(232\) 3.65393i 0.239892i
\(233\) −5.72185 −0.374851 −0.187426 0.982279i \(-0.560014\pi\)
−0.187426 + 0.982279i \(0.560014\pi\)
\(234\) 20.7591 + 0.833234i 1.35707 + 0.0544702i
\(235\) 7.49702i 0.489052i
\(236\) 5.25088i 0.341803i
\(237\) 2.78809 + 2.90225i 0.181106 + 0.188521i
\(238\) 0.715179 0.0463582
\(239\) 10.2059 0.660163 0.330082 0.943952i \(-0.392924\pi\)
0.330082 + 0.943952i \(0.392924\pi\)
\(240\) −6.45229 + 6.19850i −0.416494 + 0.400112i
\(241\) 24.4388 1.57424 0.787120 0.616800i \(-0.211571\pi\)
0.787120 + 0.616800i \(0.211571\pi\)
\(242\) −9.20423 −0.591670
\(243\) −12.0709 + 9.86368i −0.774352 + 0.632756i
\(244\) 2.17337i 0.139136i
\(245\) 14.4273 0.921727
\(246\) −9.12129 + 8.76253i −0.581552 + 0.558678i
\(247\) 19.7001i 1.25349i
\(248\) 28.7723i 1.82704i
\(249\) −12.4873 12.9985i −0.791349 0.823749i
\(250\) −14.0035 −0.885656
\(251\) −19.6684 −1.24146 −0.620730 0.784025i \(-0.713164\pi\)
−0.620730 + 0.784025i \(0.713164\pi\)
\(252\) 0.501063 + 0.0201118i 0.0315640 + 0.00126692i
\(253\) 10.5599i 0.663895i
\(254\) 3.43739 0.215681
\(255\) 5.29987 + 5.51687i 0.331891 + 0.345480i
\(256\) −12.7770 −0.798563
\(257\) 16.0646i 1.00208i 0.865424 + 0.501040i \(0.167049\pi\)
−0.865424 + 0.501040i \(0.832951\pi\)
\(258\) −2.25106 2.34323i −0.140145 0.145883i
\(259\) 2.57621i 0.160078i
\(260\) 7.14910i 0.443369i
\(261\) −3.56162 0.142957i −0.220458 0.00884880i
\(262\) 13.9661i 0.862830i
\(263\) 25.0924i 1.54726i −0.633637 0.773631i \(-0.718439\pi\)
0.633637 0.773631i \(-0.281561\pi\)
\(264\) 6.92852 6.65600i 0.426421 0.409648i
\(265\) 12.3179 0.756683
\(266\) 1.14115i 0.0699682i
\(267\) −5.96334 6.20750i −0.364950 0.379893i
\(268\) 1.16005 + 4.67325i 0.0708615 + 0.285464i
\(269\) 32.6631i 1.99151i −0.0920625 0.995753i \(-0.529346\pi\)
0.0920625 0.995753i \(-0.470654\pi\)
\(270\) −8.53881 9.63366i −0.519655 0.586286i
\(271\) 29.8679i 1.81434i −0.420759 0.907172i \(-0.638236\pi\)
0.420759 0.907172i \(-0.361764\pi\)
\(272\) 5.24791i 0.318201i
\(273\) 2.06871 1.98734i 0.125204 0.120279i
\(274\) −6.80075 −0.410848
\(275\) 1.17671 0.0709585
\(276\) 4.13250 + 4.30169i 0.248747 + 0.258932i
\(277\) 4.29277 0.257927 0.128964 0.991649i \(-0.458835\pi\)
0.128964 + 0.991649i \(0.458835\pi\)
\(278\) 10.8962i 0.653512i
\(279\) 28.0454 + 1.12569i 1.67903 + 0.0673933i
\(280\) 1.82207i 0.108890i
\(281\) −27.5062 −1.64088 −0.820442 0.571730i \(-0.806273\pi\)
−0.820442 + 0.571730i \(0.806273\pi\)
\(282\) 5.12623 + 5.33612i 0.305263 + 0.317761i
\(283\) 1.67756 0.0997205 0.0498603 0.998756i \(-0.484122\pi\)
0.0498603 + 0.998756i \(0.484122\pi\)
\(284\) 7.60053i 0.451009i
\(285\) 8.80277 8.45653i 0.521431 0.500921i
\(286\) 12.4913i 0.738627i
\(287\) 1.74642i 0.103088i
\(288\) 0.385852 9.61310i 0.0227366 0.566457i
\(289\) 12.5129 0.736054
\(290\) 2.94360i 0.172854i
\(291\) 10.5555 + 10.9877i 0.618773 + 0.644108i
\(292\) −1.75694 −0.102817
\(293\) 18.4716i 1.07912i −0.841947 0.539560i \(-0.818591\pi\)
0.841947 0.539560i \(-0.181409\pi\)
\(294\) 10.2689 9.86495i 0.598892 0.575335i
\(295\) 18.6120i 1.08363i
\(296\) 27.8812 1.62056
\(297\) 6.21676 + 7.01388i 0.360733 + 0.406986i
\(298\) 15.3110i 0.886943i
\(299\) 34.1231 1.97339
\(300\) 0.479348 0.460494i 0.0276752 0.0265866i
\(301\) −0.448649 −0.0258597
\(302\) 15.6923 0.902988
\(303\) 11.0320 10.5981i 0.633774 0.608846i
\(304\) −8.37361 −0.480259
\(305\) 7.70360i 0.441107i
\(306\) 7.54453 + 0.302824i 0.431292 + 0.0173113i
\(307\) 7.26092 0.414403 0.207201 0.978298i \(-0.433564\pi\)
0.207201 + 0.978298i \(0.433564\pi\)
\(308\) 0.301503i 0.0171797i
\(309\) 18.1778 17.4628i 1.03410 0.993424i
\(310\) 23.1789i 1.31647i
\(311\) 21.0740 1.19500 0.597499 0.801870i \(-0.296161\pi\)
0.597499 + 0.801870i \(0.296161\pi\)
\(312\) −21.5081 22.3887i −1.21766 1.26751i
\(313\) 15.0937i 0.853146i 0.904453 + 0.426573i \(0.140279\pi\)
−0.904453 + 0.426573i \(0.859721\pi\)
\(314\) −14.0202 −0.791206
\(315\) −1.77604 0.0712869i −0.100068 0.00401656i
\(316\) 1.36684i 0.0768905i
\(317\) 8.49323i 0.477028i 0.971139 + 0.238514i \(0.0766602\pi\)
−0.971139 + 0.238514i \(0.923340\pi\)
\(318\) 8.76745 8.42260i 0.491654 0.472316i
\(319\) 2.14312i 0.119992i
\(320\) 18.2764 1.02168
\(321\) −3.39357 3.53251i −0.189410 0.197166i
\(322\) −1.97661 −0.110152
\(323\) 7.15964i 0.398373i
\(324\) 5.27727 + 0.424324i 0.293182 + 0.0235735i
\(325\) 3.80242i 0.210920i
\(326\) −4.84691 −0.268445
\(327\) −17.9172 18.6508i −0.990826 1.03139i
\(328\) 18.9008 1.04362
\(329\) 1.02169 0.0563274
\(330\) −5.58160 + 5.36206i −0.307257 + 0.295172i
\(331\) 14.3805i 0.790426i 0.918590 + 0.395213i \(0.129329\pi\)
−0.918590 + 0.395213i \(0.870671\pi\)
\(332\) 6.12176i 0.335975i
\(333\) −1.09083 + 27.1768i −0.0597769 + 1.48928i
\(334\) 6.34669i 0.347275i
\(335\) −4.11185 16.5645i −0.224654 0.905016i
\(336\) 0.844726 + 0.879312i 0.0460836 + 0.0479704i
\(337\) 12.0321i 0.655428i 0.944777 + 0.327714i \(0.106278\pi\)
−0.944777 + 0.327714i \(0.893722\pi\)
\(338\) −24.9181 −1.35537
\(339\) 7.64190 7.34132i 0.415051 0.398726i
\(340\) 2.59821i 0.140908i
\(341\) 16.8756i 0.913867i
\(342\) 0.483188 12.0381i 0.0261278 0.650947i
\(343\) 3.95522i 0.213562i
\(344\) 4.85554i 0.261793i
\(345\) −14.6478 15.2475i −0.788611 0.820899i
\(346\) 29.4850i 1.58512i
\(347\) −10.7604 −0.577650 −0.288825 0.957382i \(-0.593265\pi\)
−0.288825 + 0.957382i \(0.593265\pi\)
\(348\) 0.838685 + 0.873023i 0.0449582 + 0.0467990i
\(349\) 18.9659 1.01522 0.507612 0.861586i \(-0.330528\pi\)
0.507612 + 0.861586i \(0.330528\pi\)
\(350\) 0.220259i 0.0117733i
\(351\) 22.6646 20.0888i 1.20974 1.07226i
\(352\) −5.78445 −0.308312
\(353\) 3.90528 0.207857 0.103929 0.994585i \(-0.466859\pi\)
0.103929 + 0.994585i \(0.466859\pi\)
\(354\) −12.7263 13.2473i −0.676394 0.704088i
\(355\) 26.9404i 1.42985i
\(356\) 2.92347i 0.154943i
\(357\) 0.751833 0.722261i 0.0397912 0.0382261i
\(358\) 18.3478 0.969711
\(359\) 5.81988i 0.307162i 0.988136 + 0.153581i \(0.0490805\pi\)
−0.988136 + 0.153581i \(0.950919\pi\)
\(360\) −0.771508 + 19.2213i −0.0406620 + 1.01305i
\(361\) −7.57601 −0.398737
\(362\) −8.07154 −0.424231
\(363\) −9.67596 + 9.29537i −0.507856 + 0.487881i
\(364\) −0.974273 −0.0510658
\(365\) 6.22754 0.325964
\(366\) 5.26748 + 5.48315i 0.275336 + 0.286609i
\(367\) 18.1437i 0.947092i 0.880769 + 0.473546i \(0.157026\pi\)
−0.880769 + 0.473546i \(0.842974\pi\)
\(368\) 14.5042i 0.756082i
\(369\) −0.739475 + 18.4232i −0.0384955 + 0.959075i
\(370\) −22.4610 −1.16769
\(371\) 1.67867i 0.0871523i
\(372\) −6.60409 6.87448i −0.342406 0.356425i
\(373\) 32.9179i 1.70442i 0.523198 + 0.852211i \(0.324739\pi\)
−0.523198 + 0.852211i \(0.675261\pi\)
\(374\) 4.53974i 0.234744i
\(375\) −14.7211 + 14.1421i −0.760197 + 0.730296i
\(376\) 11.0573i 0.570236i
\(377\) 6.92524 0.356668
\(378\) −1.31287 + 1.16366i −0.0675265 + 0.0598522i
\(379\) 27.1075i 1.39242i −0.717838 0.696210i \(-0.754868\pi\)
0.717838 0.696210i \(-0.245132\pi\)
\(380\) −4.14573 −0.212671
\(381\) 3.61356 3.47143i 0.185128 0.177847i
\(382\) −26.5311 −1.35745
\(383\) −16.2915 −0.832458 −0.416229 0.909260i \(-0.636648\pi\)
−0.416229 + 0.909260i \(0.636648\pi\)
\(384\) 4.99717 4.80062i 0.255011 0.244981i
\(385\) 1.06869i 0.0544654i
\(386\) −28.1022 −1.43036
\(387\) −4.73286 0.189969i −0.240585 0.00965664i
\(388\) 5.17472i 0.262706i
\(389\) 11.6479i 0.590570i 0.955409 + 0.295285i \(0.0954147\pi\)
−0.955409 + 0.295285i \(0.904585\pi\)
\(390\) 17.3269 + 18.0363i 0.877382 + 0.913305i
\(391\) 12.4014 0.627166
\(392\) −21.2787 −1.07474
\(393\) 14.1044 + 14.6819i 0.711473 + 0.740604i
\(394\) 23.2744 1.17255
\(395\) 4.84480i 0.243768i
\(396\) 0.127663 3.18060i 0.00641532 0.159831i
\(397\) −22.5704 −1.13278 −0.566388 0.824139i \(-0.691660\pi\)
−0.566388 + 0.824139i \(0.691660\pi\)
\(398\) 15.2996 0.766899
\(399\) −1.15245 1.19963i −0.0576945 0.0600567i
\(400\) 1.61623 0.0808117
\(401\) 22.4255 1.11987 0.559937 0.828535i \(-0.310825\pi\)
0.559937 + 0.828535i \(0.310825\pi\)
\(402\) −14.2530 8.97849i −0.710874 0.447806i
\(403\) −54.5317 −2.71642
\(404\) −5.19562 −0.258492
\(405\) −18.7055 1.50403i −0.929483 0.0747359i
\(406\) −0.401151 −0.0199088
\(407\) 16.3530 0.810587
\(408\) −7.81672 8.13677i −0.386985 0.402830i
\(409\) 5.36804i 0.265433i −0.991154 0.132716i \(-0.957630\pi\)
0.991154 0.132716i \(-0.0423699\pi\)
\(410\) −15.2264 −0.751979
\(411\) −7.14930 + 6.86809i −0.352649 + 0.338778i
\(412\) −8.56097 −0.421769
\(413\) −2.53642 −0.124809
\(414\) −20.8516 0.836944i −1.02480 0.0411336i
\(415\) 21.6988i 1.06515i
\(416\) 18.6918i 0.916442i
\(417\) 11.0041 + 11.4547i 0.538874 + 0.560938i
\(418\) −7.24365 −0.354299
\(419\) 25.3733i 1.23957i 0.784772 + 0.619785i \(0.212780\pi\)
−0.784772 + 0.619785i \(0.787220\pi\)
\(420\) 0.418219 + 0.435343i 0.0204070 + 0.0212425i
\(421\) 23.4937 1.14501 0.572505 0.819901i \(-0.305972\pi\)
0.572505 + 0.819901i \(0.305972\pi\)
\(422\) −11.1813 −0.544296
\(423\) 10.7779 + 0.432606i 0.524040 + 0.0210340i
\(424\) −18.1675 −0.882294
\(425\) 1.38192i 0.0670329i
\(426\) −18.4210 19.1752i −0.892500 0.929042i
\(427\) 1.04984 0.0508053
\(428\) 1.66366i 0.0804162i
\(429\) −12.6150 13.1315i −0.609058 0.633995i
\(430\) 3.91161i 0.188635i
\(431\) 13.7134i 0.660554i 0.943884 + 0.330277i \(0.107142\pi\)
−0.943884 + 0.330277i \(0.892858\pi\)
\(432\) 8.53881 + 9.63366i 0.410824 + 0.463500i
\(433\) 5.71949i 0.274861i 0.990511 + 0.137431i \(0.0438844\pi\)
−0.990511 + 0.137431i \(0.956116\pi\)
\(434\) 3.15880 0.151627
\(435\) −2.97275 3.09447i −0.142532 0.148368i
\(436\) 8.78375i 0.420665i
\(437\) 19.7878i 0.946580i
\(438\) 4.43254 4.25820i 0.211795 0.203465i
\(439\) 20.4267 0.974912 0.487456 0.873148i \(-0.337925\pi\)
0.487456 + 0.873148i \(0.337925\pi\)
\(440\) 11.5660 0.551385
\(441\) 0.832509 20.7411i 0.0396433 0.987670i
\(442\) −14.6697 −0.697764
\(443\) −32.1851 −1.52916 −0.764580 0.644529i \(-0.777053\pi\)
−0.764580 + 0.644529i \(0.777053\pi\)
\(444\) 6.66157 6.39955i 0.316144 0.303709i
\(445\) 10.3623i 0.491222i
\(446\) −5.10720 −0.241833
\(447\) 15.4626 + 16.0957i 0.731357 + 0.761301i
\(448\) 2.49070i 0.117674i
\(449\) 2.60431i 0.122905i −0.998110 0.0614525i \(-0.980427\pi\)
0.998110 0.0614525i \(-0.0195733\pi\)
\(450\) −0.0932627 + 2.32354i −0.00439644 + 0.109533i
\(451\) 11.0857 0.522007
\(452\) −3.59901 −0.169283
\(453\) 16.4965 15.8476i 0.775073 0.744587i
\(454\) 22.2948i 1.04635i
\(455\) 3.45335 0.161895
\(456\) −12.9831 + 12.4724i −0.607990 + 0.584075i
\(457\) −2.03308 −0.0951034 −0.0475517 0.998869i \(-0.515142\pi\)
−0.0475517 + 0.998869i \(0.515142\pi\)
\(458\) 22.0077i 1.02835i
\(459\) 8.23701 7.30089i 0.384471 0.340776i
\(460\) 7.18093i 0.334813i
\(461\) 7.30863i 0.340397i −0.985410 0.170198i \(-0.945559\pi\)
0.985410 0.170198i \(-0.0544409\pi\)
\(462\) 0.730736 + 0.760655i 0.0339969 + 0.0353889i
\(463\) 18.7222i 0.870097i −0.900407 0.435048i \(-0.856731\pi\)
0.900407 0.435048i \(-0.143269\pi\)
\(464\) 2.94360i 0.136653i
\(465\) 23.4085 + 24.3669i 1.08554 + 1.12999i
\(466\) −6.79853 −0.314936
\(467\) 12.4044i 0.574005i 0.957930 + 0.287003i \(0.0926589\pi\)
−0.957930 + 0.287003i \(0.907341\pi\)
\(468\) −10.2777 0.412530i −0.475089 0.0190692i
\(469\) −2.25740 + 0.560359i −0.104237 + 0.0258750i
\(470\) 8.90773i 0.410883i
\(471\) −14.7388 + 14.1590i −0.679126 + 0.652414i
\(472\) 27.4506i 1.26352i
\(473\) 2.84789i 0.130946i
\(474\) 3.31273 + 3.44836i 0.152159 + 0.158388i
\(475\) −2.20500 −0.101173
\(476\) −0.354081 −0.0162293
\(477\) 0.710789 17.7085i 0.0325448 0.810818i
\(478\) 12.1263 0.554644
\(479\) 26.6194i 1.21627i −0.793832 0.608137i \(-0.791917\pi\)
0.793832 0.608137i \(-0.208083\pi\)
\(480\) 8.35222 8.02370i 0.381225 0.366230i
\(481\) 52.8428i 2.40942i
\(482\) 29.0374 1.32262
\(483\) −2.07792 + 1.99619i −0.0945485 + 0.0908296i
\(484\) 4.55696 0.207135
\(485\) 18.3420i 0.832867i
\(486\) −14.3423 + 11.7197i −0.650581 + 0.531617i
\(487\) 1.99331i 0.0903256i 0.998980 + 0.0451628i \(0.0143807\pi\)
−0.998980 + 0.0451628i \(0.985619\pi\)
\(488\) 11.3620i 0.514332i
\(489\) −5.09531 + 4.89490i −0.230418 + 0.221355i
\(490\) 17.1421 0.774400
\(491\) 5.02744i 0.226885i 0.993545 + 0.113443i \(0.0361878\pi\)
−0.993545 + 0.113443i \(0.963812\pi\)
\(492\) 4.51590 4.33828i 0.203593 0.195585i
\(493\) 2.51685 0.113353
\(494\) 23.4070i 1.05313i
\(495\) −0.452508 + 11.2737i −0.0203387 + 0.506717i
\(496\) 23.1789i 1.04076i
\(497\) −3.67141 −0.164685
\(498\) −14.8370 15.4445i −0.664861 0.692083i
\(499\) 16.1557i 0.723227i −0.932328 0.361614i \(-0.882226\pi\)
0.932328 0.361614i \(-0.117774\pi\)
\(500\) 6.93303 0.310055
\(501\) 6.40954 + 6.67196i 0.286357 + 0.298081i
\(502\) −23.3694 −1.04303
\(503\) 30.1953 1.34634 0.673170 0.739488i \(-0.264932\pi\)
0.673170 + 0.739488i \(0.264932\pi\)
\(504\) 2.61946 + 0.105140i 0.116680 + 0.00468332i
\(505\) 18.4161 0.819505
\(506\) 12.5469i 0.557779i
\(507\) −26.1952 + 25.1648i −1.16337 + 1.11761i
\(508\) −1.70183 −0.0755066
\(509\) 26.3273i 1.16694i 0.812135 + 0.583469i \(0.198305\pi\)
−0.812135 + 0.583469i \(0.801695\pi\)
\(510\) 6.29714 + 6.55497i 0.278842 + 0.290259i
\(511\) 0.848683i 0.0375435i
\(512\) −23.1827 −1.02454
\(513\) −11.6494 13.1431i −0.514332 0.580280i
\(514\) 19.0874i 0.841909i
\(515\) 30.3447 1.33715
\(516\) 1.11449 + 1.16012i 0.0490626 + 0.0510714i
\(517\) 6.48535i 0.285226i
\(518\) 3.06097i 0.134491i
\(519\) 29.7769 + 30.9961i 1.30706 + 1.36058i
\(520\) 37.3741i 1.63896i
\(521\) 29.4500 1.29023 0.645113 0.764087i \(-0.276810\pi\)
0.645113 + 0.764087i \(0.276810\pi\)
\(522\) −4.23180 0.169857i −0.185221 0.00743443i
\(523\) 30.4914 1.33329 0.666647 0.745373i \(-0.267729\pi\)
0.666647 + 0.745373i \(0.267729\pi\)
\(524\) 6.91455i 0.302063i
\(525\) 0.222440 + 0.231547i 0.00970807 + 0.0101055i
\(526\) 29.8139i 1.29995i
\(527\) −19.8185 −0.863309
\(528\) 5.58160 5.36206i 0.242908 0.233354i
\(529\) −11.2750 −0.490219
\(530\) 14.6357 0.635736
\(531\) −26.7570 1.07398i −1.16116 0.0466067i
\(532\) 0.564976i 0.0244948i
\(533\) 35.8223i 1.55164i
\(534\) −7.08545 7.37555i −0.306617 0.319171i
\(535\) 5.89692i 0.254946i
\(536\) 6.06453 + 24.4308i 0.261948 + 1.05525i
\(537\) 19.2881 18.5295i 0.832345 0.799606i
\(538\) 38.8093i 1.67319i
\(539\) −12.4804 −0.537571
\(540\) 4.22752 + 4.76957i 0.181923 + 0.205250i
\(541\) 28.7585i 1.23643i 0.786011 + 0.618213i \(0.212143\pi\)
−0.786011 + 0.618213i \(0.787857\pi\)
\(542\) 35.4881i 1.52434i
\(543\) −8.48521 + 8.15146i −0.364135 + 0.349813i
\(544\) 6.79319i 0.291256i
\(545\) 31.1343i 1.33365i
\(546\) 2.45797 2.36129i 0.105191 0.101054i
\(547\) 11.4401i 0.489142i 0.969631 + 0.244571i \(0.0786471\pi\)
−0.969631 + 0.244571i \(0.921353\pi\)
\(548\) 3.36701 0.143832
\(549\) 11.0749 + 0.444526i 0.472665 + 0.0189719i
\(550\) 1.39813 0.0596167
\(551\) 4.01591i 0.171084i
\(552\) 21.6039 + 22.4884i 0.919522 + 0.957170i
\(553\) 0.660245 0.0280765
\(554\) 5.10053 0.216701
\(555\) −23.6122 + 22.6834i −1.00228 + 0.962859i
\(556\) 5.39466i 0.228785i
\(557\) 23.2899i 0.986823i −0.869796 0.493411i \(-0.835750\pi\)
0.869796 0.493411i \(-0.164250\pi\)
\(558\) 33.3226 + 1.33751i 1.41066 + 0.0566213i
\(559\) 9.20263 0.389230
\(560\) 1.46786i 0.0620284i
\(561\) −4.58469 4.77240i −0.193566 0.201491i
\(562\) −32.6820 −1.37861
\(563\) −32.6882 −1.37764 −0.688822 0.724930i \(-0.741872\pi\)
−0.688822 + 0.724930i \(0.741872\pi\)
\(564\) −2.53797 2.64188i −0.106868 0.111243i
\(565\) 12.7568 0.536684
\(566\) 1.99322 0.0837814
\(567\) −0.204968 + 2.54916i −0.00860784 + 0.107055i
\(568\) 39.7341i 1.66720i
\(569\) 27.4431i 1.15047i −0.817987 0.575237i \(-0.804910\pi\)
0.817987 0.575237i \(-0.195090\pi\)
\(570\) 10.4592 10.0478i 0.438086 0.420855i
\(571\) −6.20555 −0.259694 −0.129847 0.991534i \(-0.541449\pi\)
−0.129847 + 0.991534i \(0.541449\pi\)
\(572\) 6.18438i 0.258582i
\(573\) −27.8908 + 26.7938i −1.16516 + 1.11933i
\(574\) 2.07504i 0.0866106i
\(575\) 3.81935i 0.159278i
\(576\) 1.05462 26.2747i 0.0439424 1.09478i
\(577\) 21.8157i 0.908198i −0.890951 0.454099i \(-0.849961\pi\)
0.890951 0.454099i \(-0.150039\pi\)
\(578\) 14.8675 0.618404
\(579\) −29.5424 + 28.3804i −1.22774 + 1.17945i
\(580\) 1.45736i 0.0605136i
\(581\) −2.95709 −0.122681
\(582\) 12.5417 + 13.0552i 0.519870 + 0.541155i
\(583\) −10.6557 −0.441314
\(584\) −9.18493 −0.380075
\(585\) 36.4298 + 1.46223i 1.50619 + 0.0604557i
\(586\) 21.9473i 0.906635i
\(587\) −22.8171 −0.941761 −0.470881 0.882197i \(-0.656064\pi\)
−0.470881 + 0.882197i \(0.656064\pi\)
\(588\) −5.08405 + 4.88408i −0.209663 + 0.201416i
\(589\) 31.6227i 1.30299i
\(590\) 22.1141i 0.910425i
\(591\) 24.4672 23.5048i 1.00645 0.966860i
\(592\) 22.4610 0.923143
\(593\) −23.2240 −0.953695 −0.476847 0.878986i \(-0.658221\pi\)
−0.476847 + 0.878986i \(0.658221\pi\)
\(594\) 7.38656 + 8.33367i 0.303074 + 0.341934i
\(595\) 1.25506 0.0514522
\(596\) 7.58040i 0.310505i
\(597\) 16.0837 15.4511i 0.658262 0.632370i
\(598\) 40.5440 1.65797
\(599\) −18.3890 −0.751355 −0.375678 0.926750i \(-0.622590\pi\)
−0.375678 + 0.926750i \(0.622590\pi\)
\(600\) 2.50594 2.40737i 0.102304 0.0982805i
\(601\) 16.5923 0.676814 0.338407 0.941000i \(-0.390112\pi\)
0.338407 + 0.941000i \(0.390112\pi\)
\(602\) −0.533071 −0.0217264
\(603\) −24.0508 + 4.95547i −0.979426 + 0.201802i
\(604\) −7.76915 −0.316122
\(605\) −16.1523 −0.656686
\(606\) 13.1079 12.5924i 0.532473 0.511529i
\(607\) 21.3350 0.865961 0.432981 0.901403i \(-0.357462\pi\)
0.432981 + 0.901403i \(0.357462\pi\)
\(608\) 10.8393 0.439591
\(609\) −0.421711 + 0.405124i −0.0170886 + 0.0164164i
\(610\) 9.15318i 0.370601i
\(611\) −20.9567 −0.847817
\(612\) −3.73525 0.149926i −0.150989 0.00606041i
\(613\) 23.0971 0.932884 0.466442 0.884552i \(-0.345536\pi\)
0.466442 + 0.884552i \(0.345536\pi\)
\(614\) 8.62720 0.348165
\(615\) −16.0068 + 15.3772i −0.645456 + 0.620068i
\(616\) 1.57620i 0.0635068i
\(617\) 15.1138i 0.608460i 0.952599 + 0.304230i \(0.0983991\pi\)
−0.952599 + 0.304230i \(0.901601\pi\)
\(618\) 21.5983 20.7488i 0.868810 0.834637i
\(619\) −29.4064 −1.18194 −0.590972 0.806692i \(-0.701256\pi\)
−0.590972 + 0.806692i \(0.701256\pi\)
\(620\) 11.4758i 0.460878i
\(621\) −22.7655 + 20.1782i −0.913547 + 0.809723i
\(622\) 25.0395 1.00399
\(623\) −1.41217 −0.0565774
\(624\) −17.3269 18.0363i −0.693631 0.722031i
\(625\) −21.3125 −0.852500
\(626\) 17.9339i 0.716781i
\(627\) −7.61490 + 7.31538i −0.304110 + 0.292148i
\(628\) 6.94133 0.276989
\(629\) 19.2047i 0.765743i
\(630\) −2.11023 0.0847009i −0.0840737 0.00337456i
\(631\) 38.5932i 1.53637i −0.640227 0.768186i \(-0.721160\pi\)
0.640227 0.768186i \(-0.278840\pi\)
\(632\) 7.14554i 0.284234i
\(633\) −11.7543 + 11.2920i −0.467193 + 0.448817i
\(634\) 10.0914i 0.400780i
\(635\) 6.03221 0.239381
\(636\) −4.34072 + 4.16998i −0.172121 + 0.165351i
\(637\) 40.3292i 1.59790i
\(638\) 2.54638i 0.100812i
\(639\) −38.7302 1.55456i −1.53214 0.0614974i
\(640\) 8.34192 0.329743
\(641\) 44.8759 1.77249 0.886245 0.463216i \(-0.153305\pi\)
0.886245 + 0.463216i \(0.153305\pi\)
\(642\) −4.03213 4.19722i −0.159135 0.165651i
\(643\) −0.785522 −0.0309780 −0.0154890 0.999880i \(-0.504930\pi\)
−0.0154890 + 0.999880i \(0.504930\pi\)
\(644\) 0.978611 0.0385627
\(645\) −3.95035 4.11209i −0.155545 0.161913i
\(646\) 8.50686i 0.334698i
\(647\) −7.38168 −0.290204 −0.145102 0.989417i \(-0.546351\pi\)
−0.145102 + 0.989417i \(0.546351\pi\)
\(648\) 27.5885 + 2.21828i 1.08378 + 0.0871422i
\(649\) 16.1004i 0.631996i
\(650\) 4.51792i 0.177207i
\(651\) 3.32069 3.19008i 0.130148 0.125029i
\(652\) 2.39968 0.0939786
\(653\) 32.4608 1.27029 0.635144 0.772394i \(-0.280941\pi\)
0.635144 + 0.772394i \(0.280941\pi\)
\(654\) −21.2887 22.1603i −0.832454 0.866538i
\(655\) 24.5089i 0.957641i
\(656\) 15.2264 0.594492
\(657\) 0.359352 8.95287i 0.0140197 0.349285i
\(658\) 1.21394 0.0473242
\(659\) 25.2488i 0.983554i −0.870721 0.491777i \(-0.836348\pi\)
0.870721 0.491777i \(-0.163652\pi\)
\(660\) 2.76342 2.65473i 0.107566 0.103335i
\(661\) 34.1358i 1.32773i −0.747854 0.663863i \(-0.768916\pi\)
0.747854 0.663863i \(-0.231084\pi\)
\(662\) 17.0865i 0.664086i
\(663\) −15.4215 + 14.8149i −0.598921 + 0.575364i
\(664\) 32.0034i 1.24197i
\(665\) 2.00258i 0.0776567i
\(666\) −1.29608 + 32.2906i −0.0502223 + 1.25123i
\(667\) −6.95608 −0.269340
\(668\) 3.14221i 0.121576i
\(669\) −5.36895 + 5.15777i −0.207575 + 0.199411i
\(670\) −4.88557 19.6814i −0.188746 0.760360i
\(671\) 6.66405i 0.257263i
\(672\) −1.09346 1.13823i −0.0421812 0.0439083i
\(673\) 36.3860i 1.40258i −0.712878 0.701288i \(-0.752609\pi\)
0.712878 0.701288i \(-0.247391\pi\)
\(674\) 14.2961i 0.550666i
\(675\) 2.24851 + 2.53681i 0.0865450 + 0.0976418i
\(676\) 12.3368 0.474493
\(677\) −28.0827 −1.07931 −0.539654 0.841887i \(-0.681445\pi\)
−0.539654 + 0.841887i \(0.681445\pi\)
\(678\) 9.07986 8.72273i 0.348710 0.334994i
\(679\) 2.49963 0.0959269
\(680\) 13.5829i 0.520881i
\(681\) 22.5156 + 23.4375i 0.862800 + 0.898126i
\(682\) 20.0511i 0.767796i
\(683\) −33.9446 −1.29885 −0.649427 0.760424i \(-0.724991\pi\)
−0.649427 + 0.760424i \(0.724991\pi\)
\(684\) −0.239224 + 5.96001i −0.00914695 + 0.227887i
\(685\) −11.9345 −0.455994
\(686\) 4.69947i 0.179427i
\(687\) 22.2256 + 23.1356i 0.847960 + 0.882679i
\(688\) 3.91161i 0.149129i
\(689\) 34.4327i 1.31178i
\(690\) −17.4040 18.1166i −0.662561 0.689688i
\(691\) −46.2852 −1.76077 −0.880387 0.474257i \(-0.842717\pi\)
−0.880387 + 0.474257i \(0.842717\pi\)
\(692\) 14.5978i 0.554927i
\(693\) 1.53637 + 0.0616673i 0.0583620 + 0.00234255i
\(694\) −12.7852 −0.485319
\(695\) 19.1216i 0.725323i
\(696\) 4.38448 + 4.56399i 0.166193 + 0.172998i
\(697\) 13.0190i 0.493128i
\(698\) 22.5347 0.852952
\(699\) −7.14696 + 6.86585i −0.270323 + 0.259690i
\(700\) 0.109049i 0.00412166i
\(701\) 12.1107 0.457415 0.228707 0.973495i \(-0.426550\pi\)
0.228707 + 0.973495i \(0.426550\pi\)
\(702\) 26.9293 23.8688i 1.01638 0.900871i
\(703\) −30.6433 −1.15573
\(704\) −15.8102 −0.595868
\(705\) 8.99593 + 9.36426i 0.338806 + 0.352678i
\(706\) 4.64013 0.174634
\(707\) 2.50973i 0.0943880i
\(708\) 6.30071 + 6.55869i 0.236795 + 0.246491i
\(709\) 24.5566 0.922242 0.461121 0.887337i \(-0.347447\pi\)
0.461121 + 0.887337i \(0.347447\pi\)
\(710\) 32.0097i 1.20130i
\(711\) 6.96501 + 0.279563i 0.261208 + 0.0104844i
\(712\) 15.2833i 0.572766i
\(713\) 54.7745 2.05132
\(714\) 0.893304 0.858168i 0.0334311 0.0321161i
\(715\) 21.9208i 0.819791i
\(716\) −9.08389 −0.339481
\(717\) 12.7478 12.2464i 0.476075 0.457349i
\(718\) 6.91500i 0.258066i
\(719\) 0.813125i 0.0303244i −0.999885 0.0151622i \(-0.995174\pi\)
0.999885 0.0151622i \(-0.00482647\pi\)
\(720\) −0.621526 + 15.4846i −0.0231629 + 0.577079i
\(721\) 4.13534i 0.154008i
\(722\) −9.00158 −0.335004
\(723\) 30.5256 29.3249i 1.13526 1.09060i
\(724\) 3.99617 0.148517
\(725\) 0.775132i 0.0287877i
\(726\) −11.4967 + 11.0445i −0.426681 + 0.409899i
\(727\) 3.76568i 0.139661i −0.997559 0.0698306i \(-0.977754\pi\)
0.997559 0.0698306i \(-0.0222459\pi\)
\(728\) −5.09330 −0.188770
\(729\) −3.24161 + 26.8047i −0.120060 + 0.992767i
\(730\) 7.39936 0.273863
\(731\) 3.34452 0.123702
\(732\) −2.60790 2.71468i −0.0963909 0.100337i
\(733\) 13.3040i 0.491396i −0.969346 0.245698i \(-0.920983\pi\)
0.969346 0.245698i \(-0.0790172\pi\)
\(734\) 21.5577i 0.795710i
\(735\) 18.0206 17.3118i 0.664700 0.638556i
\(736\) 18.7750i 0.692057i
\(737\) 3.55699 + 14.3293i 0.131023 + 0.527825i
\(738\) −0.878621 + 21.8899i −0.0323425 + 0.805778i
\(739\) 31.3888i 1.15466i −0.816512 0.577328i \(-0.804095\pi\)
0.816512 0.577328i \(-0.195905\pi\)
\(740\) 11.1203 0.408792
\(741\) 23.6388 + 24.6067i 0.868394 + 0.903949i
\(742\) 1.99455i 0.0732221i
\(743\) 44.9992i 1.65086i 0.564504 + 0.825430i \(0.309068\pi\)
−0.564504 + 0.825430i \(0.690932\pi\)
\(744\) −34.5249 35.9384i −1.26574 1.31757i
\(745\) 26.8690i 0.984404i
\(746\) 39.1120i 1.43199i
\(747\) −31.1948 1.25210i −1.14136 0.0458120i
\(748\) 2.24760i 0.0821804i
\(749\) −0.803626 −0.0293639
\(750\) −17.4912 + 16.8032i −0.638688 + 0.613567i
\(751\) 13.1434 0.479611 0.239805 0.970821i \(-0.422916\pi\)
0.239805 + 0.970821i \(0.422916\pi\)
\(752\) 8.90773i 0.324831i
\(753\) −24.5671 + 23.6008i −0.895275 + 0.860061i
\(754\) 8.22836 0.299659
\(755\) 27.5380 1.00221
\(756\) 0.649993 0.576122i 0.0236400 0.0209534i
\(757\) 10.0377i 0.364825i 0.983222 + 0.182412i \(0.0583906\pi\)
−0.983222 + 0.182412i \(0.941609\pi\)
\(758\) 32.2083i 1.16986i
\(759\) 12.6712 + 13.1900i 0.459935 + 0.478766i
\(760\) −21.6730 −0.786164
\(761\) 27.5790i 0.999739i −0.866101 0.499869i \(-0.833381\pi\)
0.866101 0.499869i \(-0.166619\pi\)
\(762\) 4.29352 4.12464i 0.155538 0.149420i
\(763\) −4.24296 −0.153605
\(764\) 13.1354 0.475222
\(765\) 13.2397 + 0.531419i 0.478684 + 0.0192135i
\(766\) −19.3571 −0.699399
\(767\) 52.0267 1.87857
\(768\) −15.9593 + 15.3316i −0.575881 + 0.553230i
\(769\) 46.2944i 1.66942i −0.550690 0.834710i \(-0.685635\pi\)
0.550690 0.834710i \(-0.314365\pi\)
\(770\) 1.26978i 0.0457598i
\(771\) 19.2764 + 20.0657i 0.694223 + 0.722647i
\(772\) 13.9132 0.500748
\(773\) 5.77454i 0.207696i 0.994593 + 0.103848i \(0.0331155\pi\)
−0.994593 + 0.103848i \(0.966885\pi\)
\(774\) −5.62344 0.225715i −0.202130 0.00811314i
\(775\) 6.10366i 0.219250i
\(776\) 27.0524i 0.971124i
\(777\) 3.09128 + 3.21785i 0.110899 + 0.115440i
\(778\) 13.8396i 0.496175i
\(779\) −20.7732 −0.744276
\(780\) −8.57845 8.92968i −0.307158 0.319734i
\(781\) 23.3050i 0.833917i
\(782\) 14.7350 0.526921
\(783\) −4.62022 + 4.09514i −0.165113 + 0.146348i
\(784\) −17.1421 −0.612217
\(785\) −24.6038 −0.878148
\(786\) 16.7584 + 17.4446i 0.597753 + 0.622227i
\(787\) 36.7066i 1.30845i 0.756301 + 0.654224i \(0.227005\pi\)
−0.756301 + 0.654224i \(0.772995\pi\)
\(788\) −11.5230 −0.410490
\(789\) −30.1092 31.3419i −1.07191 1.11580i
\(790\) 5.75644i 0.204805i
\(791\) 1.73849i 0.0618135i
\(792\) 0.667398 16.6275i 0.0237150 0.590833i
\(793\) −21.5341 −0.764700
\(794\) −26.8175 −0.951716
\(795\) 15.3858 14.7807i 0.545680 0.524216i
\(796\) −7.57474 −0.268479
\(797\) 28.5045i 1.00968i −0.863213 0.504840i \(-0.831551\pi\)
0.863213 0.504840i \(-0.168449\pi\)
\(798\) −1.36930 1.42537i −0.0484727 0.0504574i
\(799\) −7.61632 −0.269446
\(800\) −2.09215 −0.0739686
\(801\) −14.8972 0.597945i −0.526366 0.0211274i
\(802\) 26.6452 0.940876
\(803\) −5.38718 −0.190109
\(804\) 7.05657 + 4.44520i 0.248866 + 0.156770i
\(805\) −3.46872 −0.122256
\(806\) −64.7929 −2.28223
\(807\) −39.1936 40.7983i −1.37968 1.43617i
\(808\) −27.1617 −0.955545
\(809\) 10.3307 0.363209 0.181605 0.983372i \(-0.441871\pi\)
0.181605 + 0.983372i \(0.441871\pi\)
\(810\) −22.2253 1.78704i −0.780916 0.0627903i
\(811\) 5.53520i 0.194367i 0.995266 + 0.0971836i \(0.0309834\pi\)
−0.995266 + 0.0971836i \(0.969017\pi\)
\(812\) 0.198608 0.00696977
\(813\) −35.8395 37.3069i −1.25695 1.30841i
\(814\) 19.4301 0.681024
\(815\) −8.50575 −0.297943
\(816\) −6.29714 6.55497i −0.220444 0.229470i
\(817\) 5.33656i 0.186702i
\(818\) 6.37814i 0.223006i
\(819\) 0.199271 4.96462i 0.00696309 0.173478i
\(820\) 7.53852 0.263256
\(821\) 49.4968i 1.72745i 0.503964 + 0.863725i \(0.331875\pi\)
−0.503964 + 0.863725i \(0.668125\pi\)
\(822\) −8.49457 + 8.16045i −0.296282 + 0.284628i
\(823\) −20.7084 −0.721851 −0.360925 0.932595i \(-0.617539\pi\)
−0.360925 + 0.932595i \(0.617539\pi\)
\(824\) −44.7550 −1.55912
\(825\) 1.46979 1.41198i 0.0511715 0.0491588i
\(826\) −3.01369 −0.104860
\(827\) 21.2556i 0.739131i 0.929205 + 0.369565i \(0.120493\pi\)
−0.929205 + 0.369565i \(0.879507\pi\)
\(828\) 10.3235 + 0.414366i 0.358766 + 0.0144002i
\(829\) −20.3605 −0.707150 −0.353575 0.935406i \(-0.615034\pi\)
−0.353575 + 0.935406i \(0.615034\pi\)
\(830\) 25.7819i 0.894901i
\(831\) 5.36193 5.15103i 0.186003 0.178687i
\(832\) 51.0888i 1.77118i
\(833\) 14.6569i 0.507831i
\(834\) 13.0748 + 13.6101i 0.452742 + 0.471279i
\(835\) 11.1377i 0.385436i
\(836\) 3.58629 0.124035
\(837\) 36.3812 32.2465i 1.25752 1.11460i
\(838\) 30.1478i 1.04144i
\(839\) 14.1993i 0.490215i 0.969496 + 0.245107i \(0.0788232\pi\)
−0.969496 + 0.245107i \(0.921177\pi\)
\(840\) 2.18637 + 2.27588i 0.0754368 + 0.0785255i
\(841\) 27.5883 0.951320
\(842\) 27.9144 0.961995
\(843\) −34.3570 + 33.0057i −1.18332 + 1.13678i
\(844\) 5.53579 0.190550
\(845\) −43.7283 −1.50430
\(846\) 12.8060 + 0.514009i 0.440279 + 0.0176720i
\(847\) 2.20122i 0.0756350i
\(848\) −14.6357 −0.502594
\(849\) 2.09538 2.01296i 0.0719132 0.0690846i
\(850\) 1.64195i 0.0563185i
\(851\) 53.0780i 1.81949i
\(852\) 9.12014 + 9.49355i 0.312451 + 0.325244i
\(853\) −42.0998 −1.44147 −0.720735 0.693210i \(-0.756196\pi\)
−0.720735 + 0.693210i \(0.756196\pi\)
\(854\) 1.24739 0.0426847
\(855\) 0.847938 21.1255i 0.0289989 0.722476i
\(856\) 8.69730i 0.297268i
\(857\) −4.49937 −0.153695 −0.0768477 0.997043i \(-0.524486\pi\)
−0.0768477 + 0.997043i \(0.524486\pi\)
\(858\) −14.9888 15.6024i −0.511708 0.532659i
\(859\) −54.3034 −1.85281 −0.926404 0.376530i \(-0.877117\pi\)
−0.926404 + 0.376530i \(0.877117\pi\)
\(860\) 1.93662i 0.0660382i
\(861\) 2.09559 + 2.18139i 0.0714175 + 0.0743416i
\(862\) 16.2939i 0.554972i
\(863\) 19.2335i 0.654716i 0.944900 + 0.327358i \(0.106158\pi\)
−0.944900 + 0.327358i \(0.893842\pi\)
\(864\) −11.0531 12.4704i −0.376035 0.424250i
\(865\) 51.7426i 1.75930i
\(866\) 6.79572i 0.230928i
\(867\) 15.6294 15.0147i 0.530803 0.509925i
\(868\) −1.56391 −0.0530824
\(869\) 4.19103i 0.142171i
\(870\) −3.53213 3.67675i −0.119750 0.124653i
\(871\) 46.3034 11.4940i 1.56893 0.389459i
\(872\) 45.9197i 1.55504i
\(873\) 26.3689 + 1.05840i 0.892453 + 0.0358214i
\(874\) 23.5113i 0.795280i
\(875\) 3.34898i 0.113216i
\(876\) −2.19453 + 2.10821i −0.0741462 + 0.0712298i
\(877\) 24.1312 0.814854 0.407427 0.913238i \(-0.366426\pi\)
0.407427 + 0.913238i \(0.366426\pi\)
\(878\) 24.2703 0.819084
\(879\) −22.1646 23.0721i −0.747595 0.778204i
\(880\) 9.31752 0.314093
\(881\) 5.93369i 0.199911i 0.994992 + 0.0999555i \(0.0318700\pi\)
−0.994992 + 0.0999555i \(0.968130\pi\)
\(882\) 0.989161 24.6439i 0.0333068 0.829803i
\(883\) 10.8852i 0.366315i −0.983084 0.183158i \(-0.941368\pi\)
0.983084 0.183158i \(-0.0586319\pi\)
\(884\) 7.26287 0.244277
\(885\) −22.3331 23.2475i −0.750720 0.781457i
\(886\) −38.2413 −1.28474
\(887\) 26.3504i 0.884761i −0.896827 0.442381i \(-0.854134\pi\)
0.896827 0.442381i \(-0.145866\pi\)
\(888\) 34.8254 33.4556i 1.16866 1.12270i
\(889\) 0.822064i 0.0275711i
\(890\) 12.3122i 0.412706i
\(891\) 16.1813 + 1.30107i 0.542094 + 0.0435876i
\(892\) 2.52855 0.0846620
\(893\) 12.1527i 0.406674i
\(894\) 18.3722 + 19.1244i 0.614458 + 0.639616i
\(895\) 32.1982 1.07627
\(896\) 1.13683i 0.0379788i
\(897\) 42.6219 40.9455i 1.42310 1.36713i
\(898\) 3.09436i 0.103260i
\(899\) 11.1164 0.370753
\(900\) 0.0461738 1.15037i 0.00153913 0.0383457i
\(901\) 12.5139i 0.416899i
\(902\) 13.1717 0.438571
\(903\) −0.560391 + 0.538350i −0.0186487 + 0.0179151i
\(904\) −18.8149 −0.625775
\(905\) −14.1646 −0.470847
\(906\) 19.6006 18.8297i 0.651187 0.625574i
\(907\) 37.8798 1.25778 0.628889 0.777495i \(-0.283510\pi\)
0.628889 + 0.777495i \(0.283510\pi\)
\(908\) 11.0381i 0.366311i
\(909\) 1.06268 26.4754i 0.0352467 0.878135i
\(910\) 4.10316 0.136018
\(911\) 8.16988i 0.270680i −0.990799 0.135340i \(-0.956787\pi\)
0.990799 0.135340i \(-0.0432127\pi\)
\(912\) −10.4592 + 10.0478i −0.346338 + 0.332715i
\(913\) 18.7707i 0.621220i
\(914\) −2.41564 −0.0799023
\(915\) 9.24381 + 9.62228i 0.305591 + 0.318103i
\(916\) 10.8959i 0.360010i
\(917\) 3.34005 0.110298
\(918\) 9.78696 8.67469i 0.323018 0.286307i
\(919\) 16.7633i 0.552969i −0.961018 0.276485i \(-0.910831\pi\)
0.961018 0.276485i \(-0.0891695\pi\)
\(920\) 37.5405i 1.23767i
\(921\) 9.06935 8.71262i 0.298845 0.287091i
\(922\) 8.68389i 0.285989i
\(923\) 75.3074 2.47877
\(924\) −0.361784 0.376596i −0.0119018 0.0123891i
\(925\) 5.91461 0.194471
\(926\) 22.2452i 0.731022i
\(927\) 1.75100 43.6243i 0.0575104 1.43281i
\(928\) 3.81037i 0.125082i
\(929\) −28.7510 −0.943289 −0.471644 0.881789i \(-0.656339\pi\)
−0.471644 + 0.881789i \(0.656339\pi\)
\(930\) 27.8132 + 28.9520i 0.912030 + 0.949372i
\(931\) 23.3867 0.766467
\(932\) 3.36591 0.110254
\(933\) 26.3228 25.2874i 0.861768 0.827873i
\(934\) 14.7385i 0.482258i
\(935\) 7.96670i 0.260539i
\(936\) −53.7300 2.15662i −1.75622 0.0704914i
\(937\) 32.1691i 1.05092i 0.850818 + 0.525460i \(0.176107\pi\)
−0.850818 + 0.525460i \(0.823893\pi\)
\(938\) −2.68217 + 0.665801i −0.0875759 + 0.0217392i
\(939\) 18.1114 + 18.8530i 0.591044 + 0.615244i
\(940\) 4.41017i 0.143844i
\(941\) 14.8956 0.485581 0.242791 0.970079i \(-0.421937\pi\)
0.242791 + 0.970079i \(0.421937\pi\)
\(942\) −17.5121 + 16.8233i −0.570576 + 0.548134i
\(943\) 35.9818i 1.17173i
\(944\) 22.1141i 0.719754i
\(945\) −2.30392 + 2.04209i −0.0749466 + 0.0664291i
\(946\) 3.38377i 0.110016i
\(947\) 49.1528i 1.59725i 0.601828 + 0.798626i \(0.294439\pi\)
−0.601828 + 0.798626i \(0.705561\pi\)
\(948\) −1.64011 1.70726i −0.0532684 0.0554494i
\(949\) 17.4081i 0.565089i
\(950\) −2.61992 −0.0850013
\(951\) 10.1913 + 10.6086i 0.330476 + 0.344007i
\(952\) −1.85107 −0.0599934
\(953\) 26.4663i 0.857329i 0.903464 + 0.428664i \(0.141016\pi\)
−0.903464 + 0.428664i \(0.858984\pi\)
\(954\) 0.844537 21.0407i 0.0273429 0.681219i
\(955\) −46.5589 −1.50661
\(956\) −6.00366 −0.194172
\(957\) 2.57160 + 2.67689i 0.0831280 + 0.0865315i
\(958\) 31.6284i 1.02187i
\(959\) 1.62642i 0.0525200i
\(960\) 22.8284 21.9305i 0.736784 0.707805i
\(961\) −56.5345 −1.82369
\(962\) 62.7861i 2.02431i
\(963\) −8.47756 0.340274i −0.273186 0.0109652i
\(964\) −14.3762 −0.463028
\(965\) −49.3160 −1.58754
\(966\) −2.46892 + 2.37181i −0.0794361 + 0.0763116i
\(967\) −10.0427 −0.322951 −0.161476 0.986877i \(-0.551625\pi\)
−0.161476 + 0.986877i \(0.551625\pi\)
\(968\) 23.8229 0.765697
\(969\) 8.59109 + 8.94284i 0.275986 + 0.287285i
\(970\) 21.7934i 0.699743i
\(971\) 46.2031i 1.48273i −0.671103 0.741365i \(-0.734179\pi\)
0.671103 0.741365i \(-0.265821\pi\)
\(972\) 7.10080 5.80237i 0.227758 0.186111i
\(973\) 2.60587 0.0835404
\(974\) 2.36839i 0.0758881i
\(975\) −4.56265 4.74946i −0.146122 0.152105i
\(976\) 9.15318i 0.292986i
\(977\) 53.6359i 1.71597i −0.513679 0.857983i \(-0.671718\pi\)
0.513679 0.857983i \(-0.328282\pi\)
\(978\) −6.05409 + 5.81597i −0.193589 + 0.185974i
\(979\) 8.96402i 0.286491i
\(980\) −8.48694 −0.271105
\(981\) −44.7595 1.79657i −1.42906 0.0573599i
\(982\) 5.97345i 0.190620i
\(983\) −10.0426 −0.320308 −0.160154 0.987092i \(-0.551199\pi\)
−0.160154 + 0.987092i \(0.551199\pi\)
\(984\) 23.6082 22.6797i 0.752603 0.723001i
\(985\) 40.8438 1.30139
\(986\) 2.99044 0.0952351
\(987\) 1.27615 1.22596i 0.0406204 0.0390226i
\(988\) 11.5887i 0.368686i
\(989\) −9.24360 −0.293929
\(990\) −0.537655 + 13.3951i −0.0170878 + 0.425724i
\(991\) 21.7474i 0.690830i 0.938450 + 0.345415i \(0.112262\pi\)
−0.938450 + 0.345415i \(0.887738\pi\)
\(992\) 30.0042i 0.952633i
\(993\) 17.2557 + 17.9622i 0.547593 + 0.570013i
\(994\) −4.36225 −0.138362
\(995\) 26.8489 0.851169
\(996\) 7.34571 + 7.64647i 0.232758 + 0.242288i
\(997\) 30.6083 0.969374 0.484687 0.874688i \(-0.338933\pi\)
0.484687 + 0.874688i \(0.338933\pi\)
\(998\) 19.1957i 0.607628i
\(999\) 31.2478 + 35.2544i 0.988637 + 1.11540i
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 201.2.d.a.200.15 yes 20
3.2 odd 2 inner 201.2.d.a.200.5 20
67.66 odd 2 inner 201.2.d.a.200.6 yes 20
201.200 even 2 inner 201.2.d.a.200.16 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.2.d.a.200.5 20 3.2 odd 2 inner
201.2.d.a.200.6 yes 20 67.66 odd 2 inner
201.2.d.a.200.15 yes 20 1.1 even 1 trivial
201.2.d.a.200.16 yes 20 201.200 even 2 inner