Properties

Label 280.2.s.c.237.32
Level $280$
Weight $2$
Character 280.237
Analytic conductor $2.236$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,2,Mod(13,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.s (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(36\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 237.32
Character \(\chi\) \(=\) 280.237
Dual form 280.2.s.c.13.32

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.26563 + 0.631018i) q^{2} +(0.551796 - 0.551796i) q^{3} +(1.20363 + 1.59727i) q^{4} +(-1.17738 + 1.90100i) q^{5} +(1.04656 - 0.350176i) q^{6} +(-1.33994 + 2.28135i) q^{7} +(0.515446 + 2.78106i) q^{8} +2.39104i q^{9} +O(q^{10})\) \(q+(1.26563 + 0.631018i) q^{2} +(0.551796 - 0.551796i) q^{3} +(1.20363 + 1.59727i) q^{4} +(-1.17738 + 1.90100i) q^{5} +(1.04656 - 0.350176i) q^{6} +(-1.33994 + 2.28135i) q^{7} +(0.515446 + 2.78106i) q^{8} +2.39104i q^{9} +(-2.68968 + 1.66301i) q^{10} -4.64871i q^{11} +(1.54553 + 0.217207i) q^{12} +(2.09856 - 2.09856i) q^{13} +(-3.13544 + 2.04182i) q^{14} +(0.399290 + 1.69863i) q^{15} +(-1.10254 + 3.84505i) q^{16} +(3.81531 - 3.81531i) q^{17} +(-1.50879 + 3.02617i) q^{18} -2.48944i q^{19} +(-4.45353 + 0.407511i) q^{20} +(0.519468 + 1.99821i) q^{21} +(2.93342 - 5.88354i) q^{22} +(4.32744 - 4.32744i) q^{23} +(1.81900 + 1.25016i) q^{24} +(-2.22757 - 4.47638i) q^{25} +(3.98023 - 1.33177i) q^{26} +(2.97476 + 2.97476i) q^{27} +(-5.25673 + 0.605667i) q^{28} -2.13116 q^{29} +(-0.566516 + 2.40180i) q^{30} -0.0854741i q^{31} +(-3.82170 + 4.17068i) q^{32} +(-2.56514 - 2.56514i) q^{33} +(7.23629 - 2.42123i) q^{34} +(-2.75923 - 5.23323i) q^{35} +(-3.81914 + 2.87794i) q^{36} +(-5.02706 + 5.02706i) q^{37} +(1.57088 - 3.15071i) q^{38} -2.31596i q^{39} +(-5.89366 - 2.29450i) q^{40} +11.6538i q^{41} +(-0.603455 + 2.85679i) q^{42} +(-5.58987 - 5.58987i) q^{43} +(7.42524 - 5.59534i) q^{44} +(-4.54536 - 2.81516i) q^{45} +(8.20763 - 2.74624i) q^{46} +(2.71446 - 2.71446i) q^{47} +(1.51331 + 2.73006i) q^{48} +(-3.40913 - 6.11374i) q^{49} +(0.00540265 - 7.07107i) q^{50} -4.21054i q^{51} +(5.87787 + 0.826071i) q^{52} +(3.87936 + 3.87936i) q^{53} +(1.88781 + 5.64206i) q^{54} +(8.83718 + 5.47329i) q^{55} +(-7.03525 - 2.55054i) q^{56} +(-1.37366 - 1.37366i) q^{57} +(-2.69725 - 1.34480i) q^{58} +3.84849i q^{59} +(-2.23258 + 2.68230i) q^{60} -6.20980 q^{61} +(0.0539357 - 0.108179i) q^{62} +(-5.45481 - 3.20385i) q^{63} +(-7.46863 + 2.86698i) q^{64} +(1.51856 + 6.46016i) q^{65} +(-1.62787 - 4.86516i) q^{66} +(0.188380 - 0.188380i) q^{67} +(10.6863 + 1.50185i) q^{68} -4.77573i q^{69} +(-0.189896 - 8.36444i) q^{70} +2.92112 q^{71} +(-6.64964 + 1.23245i) q^{72} +(-1.82401 - 1.82401i) q^{73} +(-9.53455 + 3.19022i) q^{74} +(-3.69921 - 1.24088i) q^{75} +(3.97631 - 2.99637i) q^{76} +(10.6053 + 6.22898i) q^{77} +(1.46141 - 2.93114i) q^{78} -1.34986i q^{79} +(-6.01132 - 6.62299i) q^{80} -3.89021 q^{81} +(-7.35377 + 14.7494i) q^{82} +(11.8278 - 11.8278i) q^{83} +(-2.56644 + 3.23485i) q^{84} +(2.76082 + 11.7449i) q^{85} +(-3.54739 - 10.6020i) q^{86} +(-1.17596 + 1.17596i) q^{87} +(12.9284 - 2.39616i) q^{88} -1.37119 q^{89} +(-3.97632 - 6.43115i) q^{90} +(1.97562 + 7.59950i) q^{91} +(12.1207 + 1.70344i) q^{92} +(-0.0471643 - 0.0471643i) q^{93} +(5.14837 - 1.72263i) q^{94} +(4.73242 + 2.93101i) q^{95} +(0.192568 + 4.41017i) q^{96} +(9.83584 - 9.83584i) q^{97} +(-0.456816 - 9.88895i) q^{98} +11.1153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q - 4 q^{2} - 4 q^{7} - 16 q^{8} - 8 q^{15} + 40 q^{16} - 40 q^{18} + 4 q^{22} + 40 q^{23} - 8 q^{25} - 4 q^{28} - 44 q^{30} - 24 q^{32} - 72 q^{36} + 40 q^{42} + 16 q^{46} - 60 q^{50} + 32 q^{56} + 32 q^{57} - 68 q^{58} + 64 q^{60} - 100 q^{63} - 56 q^{65} + 16 q^{70} - 80 q^{71} + 16 q^{72} - 4 q^{78} + 72 q^{81} - 72 q^{86} + 48 q^{88} + 72 q^{92} + 80 q^{95} + 40 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.26563 + 0.631018i 0.894935 + 0.446197i
\(3\) 0.551796 0.551796i 0.318580 0.318580i −0.529642 0.848221i \(-0.677674\pi\)
0.848221 + 0.529642i \(0.177674\pi\)
\(4\) 1.20363 + 1.59727i 0.601816 + 0.798635i
\(5\) −1.17738 + 1.90100i −0.526539 + 0.850151i
\(6\) 1.04656 0.350176i 0.427257 0.142959i
\(7\) −1.33994 + 2.28135i −0.506449 + 0.862270i
\(8\) 0.515446 + 2.78106i 0.182238 + 0.983255i
\(9\) 2.39104i 0.797014i
\(10\) −2.68968 + 1.66301i −0.850553 + 0.525889i
\(11\) 4.64871i 1.40164i −0.713339 0.700819i \(-0.752818\pi\)
0.713339 0.700819i \(-0.247182\pi\)
\(12\) 1.54553 + 0.217207i 0.446155 + 0.0627023i
\(13\) 2.09856 2.09856i 0.582036 0.582036i −0.353426 0.935462i \(-0.614983\pi\)
0.935462 + 0.353426i \(0.114983\pi\)
\(14\) −3.13544 + 2.04182i −0.837981 + 0.545699i
\(15\) 0.399290 + 1.69863i 0.103096 + 0.438585i
\(16\) −1.10254 + 3.84505i −0.275635 + 0.961263i
\(17\) 3.81531 3.81531i 0.925348 0.925348i −0.0720532 0.997401i \(-0.522955\pi\)
0.997401 + 0.0720532i \(0.0229551\pi\)
\(18\) −1.50879 + 3.02617i −0.355625 + 0.713276i
\(19\) 2.48944i 0.571117i −0.958361 0.285559i \(-0.907821\pi\)
0.958361 0.285559i \(-0.0921791\pi\)
\(20\) −4.45353 + 0.407511i −0.995840 + 0.0911223i
\(21\) 0.519468 + 1.99821i 0.113357 + 0.436046i
\(22\) 2.93342 5.88354i 0.625407 1.25438i
\(23\) 4.32744 4.32744i 0.902335 0.902335i −0.0933031 0.995638i \(-0.529743\pi\)
0.995638 + 0.0933031i \(0.0297426\pi\)
\(24\) 1.81900 + 1.25016i 0.371302 + 0.255188i
\(25\) −2.22757 4.47638i −0.445513 0.895275i
\(26\) 3.98023 1.33177i 0.780588 0.261182i
\(27\) 2.97476 + 2.97476i 0.572492 + 0.572492i
\(28\) −5.25673 + 0.605667i −0.993428 + 0.114460i
\(29\) −2.13116 −0.395746 −0.197873 0.980228i \(-0.563403\pi\)
−0.197873 + 0.980228i \(0.563403\pi\)
\(30\) −0.566516 + 2.40180i −0.103431 + 0.438506i
\(31\) 0.0854741i 0.0153516i −0.999971 0.00767580i \(-0.997557\pi\)
0.999971 0.00767580i \(-0.00244331\pi\)
\(32\) −3.82170 + 4.17068i −0.675588 + 0.737280i
\(33\) −2.56514 2.56514i −0.446534 0.446534i
\(34\) 7.23629 2.42123i 1.24101 0.415238i
\(35\) −2.75923 5.23323i −0.466394 0.884577i
\(36\) −3.81914 + 2.87794i −0.636523 + 0.479656i
\(37\) −5.02706 + 5.02706i −0.826443 + 0.826443i −0.987023 0.160580i \(-0.948664\pi\)
0.160580 + 0.987023i \(0.448664\pi\)
\(38\) 1.57088 3.15071i 0.254831 0.511113i
\(39\) 2.31596i 0.370850i
\(40\) −5.89366 2.29450i −0.931870 0.362792i
\(41\) 11.6538i 1.82002i 0.414585 + 0.910011i \(0.363927\pi\)
−0.414585 + 0.910011i \(0.636073\pi\)
\(42\) −0.603455 + 2.85679i −0.0931151 + 0.440812i
\(43\) −5.58987 5.58987i −0.852447 0.852447i 0.137987 0.990434i \(-0.455937\pi\)
−0.990434 + 0.137987i \(0.955937\pi\)
\(44\) 7.42524 5.59534i 1.11940 0.843529i
\(45\) −4.54536 2.81516i −0.677582 0.419659i
\(46\) 8.20763 2.74624i 1.21015 0.404911i
\(47\) 2.71446 2.71446i 0.395945 0.395945i −0.480855 0.876800i \(-0.659674\pi\)
0.876800 + 0.480855i \(0.159674\pi\)
\(48\) 1.51331 + 2.73006i 0.218427 + 0.394050i
\(49\) −3.40913 6.11374i −0.487019 0.873391i
\(50\) 0.00540265 7.07107i 0.000764050 1.00000i
\(51\) 4.21054i 0.589594i
\(52\) 5.87787 + 0.826071i 0.815113 + 0.114556i
\(53\) 3.87936 + 3.87936i 0.532871 + 0.532871i 0.921426 0.388555i \(-0.127026\pi\)
−0.388555 + 0.921426i \(0.627026\pi\)
\(54\) 1.88781 + 5.64206i 0.256899 + 0.767787i
\(55\) 8.83718 + 5.47329i 1.19160 + 0.738018i
\(56\) −7.03525 2.55054i −0.940125 0.340830i
\(57\) −1.37366 1.37366i −0.181946 0.181946i
\(58\) −2.69725 1.34480i −0.354167 0.176581i
\(59\) 3.84849i 0.501031i 0.968113 + 0.250515i \(0.0806000\pi\)
−0.968113 + 0.250515i \(0.919400\pi\)
\(60\) −2.23258 + 2.68230i −0.288224 + 0.346284i
\(61\) −6.20980 −0.795084 −0.397542 0.917584i \(-0.630137\pi\)
−0.397542 + 0.917584i \(0.630137\pi\)
\(62\) 0.0539357 0.108179i 0.00684984 0.0137387i
\(63\) −5.45481 3.20385i −0.687241 0.403647i
\(64\) −7.46863 + 2.86698i −0.933579 + 0.358372i
\(65\) 1.51856 + 6.46016i 0.188354 + 0.801284i
\(66\) −1.62787 4.86516i −0.200376 0.598860i
\(67\) 0.188380 0.188380i 0.0230143 0.0230143i −0.695506 0.718520i \(-0.744820\pi\)
0.718520 + 0.695506i \(0.244820\pi\)
\(68\) 10.6863 + 1.50185i 1.29590 + 0.182125i
\(69\) 4.77573i 0.574931i
\(70\) −0.189896 8.36444i −0.0226969 0.999742i
\(71\) 2.92112 0.346673 0.173337 0.984863i \(-0.444545\pi\)
0.173337 + 0.984863i \(0.444545\pi\)
\(72\) −6.64964 + 1.23245i −0.783668 + 0.145246i
\(73\) −1.82401 1.82401i −0.213485 0.213485i 0.592261 0.805746i \(-0.298235\pi\)
−0.805746 + 0.592261i \(0.798235\pi\)
\(74\) −9.53455 + 3.19022i −1.10837 + 0.370856i
\(75\) −3.69921 1.24088i −0.427148 0.143285i
\(76\) 3.97631 2.99637i 0.456114 0.343708i
\(77\) 10.6053 + 6.22898i 1.20859 + 0.709859i
\(78\) 1.46141 2.93114i 0.165472 0.331886i
\(79\) 1.34986i 0.151871i −0.997113 0.0759354i \(-0.975806\pi\)
0.997113 0.0759354i \(-0.0241943\pi\)
\(80\) −6.01132 6.62299i −0.672086 0.740473i
\(81\) −3.89021 −0.432246
\(82\) −7.35377 + 14.7494i −0.812088 + 1.62880i
\(83\) 11.8278 11.8278i 1.29826 1.29826i 0.368727 0.929538i \(-0.379794\pi\)
0.929538 0.368727i \(-0.120206\pi\)
\(84\) −2.56644 + 3.23485i −0.280021 + 0.352951i
\(85\) 2.76082 + 11.7449i 0.299453 + 1.27392i
\(86\) −3.54739 10.6020i −0.382525 1.14324i
\(87\) −1.17596 + 1.17596i −0.126076 + 0.126076i
\(88\) 12.9284 2.39616i 1.37817 0.255431i
\(89\) −1.37119 −0.145346 −0.0726732 0.997356i \(-0.523153\pi\)
−0.0726732 + 0.997356i \(0.523153\pi\)
\(90\) −3.97632 6.43115i −0.419141 0.677903i
\(91\) 1.97562 + 7.59950i 0.207101 + 0.796644i
\(92\) 12.1207 + 1.70344i 1.26368 + 0.177596i
\(93\) −0.0471643 0.0471643i −0.00489071 0.00489071i
\(94\) 5.14837 1.72263i 0.531014 0.177675i
\(95\) 4.73242 + 2.93101i 0.485536 + 0.300715i
\(96\) 0.192568 + 4.41017i 0.0196539 + 0.450111i
\(97\) 9.83584 9.83584i 0.998678 0.998678i −0.00132132 0.999999i \(-0.500421\pi\)
0.999999 + 0.00132132i \(0.000420590\pi\)
\(98\) −0.456816 9.88895i −0.0461453 0.998935i
\(99\) 11.1153 1.11713
\(100\) 4.46881 8.94594i 0.446881 0.894594i
\(101\) −14.0923 −1.40223 −0.701116 0.713047i \(-0.747315\pi\)
−0.701116 + 0.713047i \(0.747315\pi\)
\(102\) 2.65693 5.32898i 0.263075 0.527648i
\(103\) −6.89070 6.89070i −0.678961 0.678961i 0.280804 0.959765i \(-0.409399\pi\)
−0.959765 + 0.280804i \(0.909399\pi\)
\(104\) 6.91793 + 4.75454i 0.678359 + 0.466221i
\(105\) −4.41020 1.36514i −0.430392 0.133224i
\(106\) 2.46188 + 7.35777i 0.239119 + 0.714650i
\(107\) 1.00648 1.00648i 0.0973004 0.0973004i −0.656781 0.754081i \(-0.728082\pi\)
0.754081 + 0.656781i \(0.228082\pi\)
\(108\) −1.17097 + 8.33200i −0.112677 + 0.801747i
\(109\) −6.39609 −0.612635 −0.306317 0.951929i \(-0.599097\pi\)
−0.306317 + 0.951929i \(0.599097\pi\)
\(110\) 7.73084 + 12.5036i 0.737107 + 1.19217i
\(111\) 5.54782i 0.526576i
\(112\) −7.29458 7.66741i −0.689273 0.724502i
\(113\) −3.34604 + 3.34604i −0.314769 + 0.314769i −0.846754 0.531985i \(-0.821446\pi\)
0.531985 + 0.846754i \(0.321446\pi\)
\(114\) −0.871742 2.60536i −0.0816461 0.244014i
\(115\) 3.13142 + 13.3215i 0.292006 + 1.24224i
\(116\) −2.56513 3.40403i −0.238166 0.316056i
\(117\) 5.01775 + 5.01775i 0.463891 + 0.463891i
\(118\) −2.42847 + 4.87076i −0.223558 + 0.448390i
\(119\) 3.59178 + 13.8163i 0.329258 + 1.26654i
\(120\) −4.51820 + 1.98600i −0.412453 + 0.181297i
\(121\) −10.6105 −0.964592
\(122\) −7.85931 3.91850i −0.711548 0.354764i
\(123\) 6.43053 + 6.43053i 0.579822 + 0.579822i
\(124\) 0.136525 0.102879i 0.0122603 0.00923884i
\(125\) 11.1323 + 1.03579i 0.995699 + 0.0926439i
\(126\) −4.88208 7.49697i −0.434930 0.667883i
\(127\) −5.21313 5.21313i −0.462590 0.462590i 0.436913 0.899504i \(-0.356072\pi\)
−0.899504 + 0.436913i \(0.856072\pi\)
\(128\) −11.2616 1.08431i −0.995397 0.0958407i
\(129\) −6.16894 −0.543145
\(130\) −2.15454 + 9.13440i −0.188966 + 0.801140i
\(131\) −19.5050 −1.70416 −0.852080 0.523411i \(-0.824659\pi\)
−0.852080 + 0.523411i \(0.824659\pi\)
\(132\) 1.00973 7.18470i 0.0878860 0.625348i
\(133\) 5.67929 + 3.33570i 0.492457 + 0.289242i
\(134\) 0.357290 0.119548i 0.0308652 0.0103274i
\(135\) −9.15741 + 2.15259i −0.788144 + 0.185265i
\(136\) 12.5772 + 8.64402i 1.07849 + 0.741219i
\(137\) 9.08499 + 9.08499i 0.776183 + 0.776183i 0.979179 0.202996i \(-0.0650680\pi\)
−0.202996 + 0.979179i \(0.565068\pi\)
\(138\) 3.01357 6.04431i 0.256532 0.514525i
\(139\) 8.45468i 0.717117i 0.933507 + 0.358559i \(0.116732\pi\)
−0.933507 + 0.358559i \(0.883268\pi\)
\(140\) 5.03778 10.7061i 0.425770 0.904831i
\(141\) 2.99566i 0.252280i
\(142\) 3.69705 + 1.84328i 0.310250 + 0.154685i
\(143\) −9.75561 9.75561i −0.815805 0.815805i
\(144\) −9.19368 2.63622i −0.766140 0.219685i
\(145\) 2.50917 4.05132i 0.208376 0.336444i
\(146\) −1.15754 3.45951i −0.0957985 0.286311i
\(147\) −5.25468 1.49239i −0.433399 0.123090i
\(148\) −14.0803 1.97884i −1.15739 0.162659i
\(149\) 18.5814 1.52224 0.761122 0.648608i \(-0.224649\pi\)
0.761122 + 0.648608i \(0.224649\pi\)
\(150\) −3.89880 3.90477i −0.318336 0.318823i
\(151\) −15.5005 −1.26141 −0.630706 0.776022i \(-0.717235\pi\)
−0.630706 + 0.776022i \(0.717235\pi\)
\(152\) 6.92330 1.28317i 0.561553 0.104079i
\(153\) 9.12256 + 9.12256i 0.737515 + 0.737515i
\(154\) 9.49183 + 14.5757i 0.764873 + 1.17455i
\(155\) 0.162486 + 0.100635i 0.0130512 + 0.00808322i
\(156\) 3.69921 2.78756i 0.296174 0.223183i
\(157\) −7.85107 7.85107i −0.626583 0.626583i 0.320623 0.947207i \(-0.396108\pi\)
−0.947207 + 0.320623i \(0.896108\pi\)
\(158\) 0.851784 1.70842i 0.0677643 0.135914i
\(159\) 4.28123 0.339524
\(160\) −3.42887 12.1755i −0.271076 0.962558i
\(161\) 4.07392 + 15.6709i 0.321070 + 1.23504i
\(162\) −4.92356 2.45479i −0.386832 0.192867i
\(163\) 9.21345 + 9.21345i 0.721653 + 0.721653i 0.968942 0.247289i \(-0.0795396\pi\)
−0.247289 + 0.968942i \(0.579540\pi\)
\(164\) −18.6143 + 14.0269i −1.45353 + 1.09532i
\(165\) 7.89646 1.85618i 0.614738 0.144504i
\(166\) 22.4331 7.50602i 1.74114 0.582580i
\(167\) −13.7944 + 13.7944i −1.06745 + 1.06745i −0.0698911 + 0.997555i \(0.522265\pi\)
−0.997555 + 0.0698911i \(0.977735\pi\)
\(168\) −5.28940 + 2.47465i −0.408086 + 0.190923i
\(169\) 4.19207i 0.322467i
\(170\) −3.91709 + 16.6069i −0.300427 + 1.27369i
\(171\) 5.95236 0.455188
\(172\) 2.20038 15.6567i 0.167777 1.19381i
\(173\) −0.180448 + 0.180448i −0.0137192 + 0.0137192i −0.713933 0.700214i \(-0.753088\pi\)
0.700214 + 0.713933i \(0.253088\pi\)
\(174\) −2.23039 + 0.746279i −0.169085 + 0.0565752i
\(175\) 13.1970 + 0.916205i 0.997599 + 0.0692586i
\(176\) 17.8745 + 5.12538i 1.34734 + 0.386340i
\(177\) 2.12358 + 2.12358i 0.159618 + 0.159618i
\(178\) −1.73542 0.865249i −0.130075 0.0648531i
\(179\) −11.4920 −0.858954 −0.429477 0.903078i \(-0.641302\pi\)
−0.429477 + 0.903078i \(0.641302\pi\)
\(180\) −0.974377 10.6486i −0.0726257 0.793698i
\(181\) 3.62143 0.269179 0.134589 0.990901i \(-0.457028\pi\)
0.134589 + 0.990901i \(0.457028\pi\)
\(182\) −2.29503 + 10.8648i −0.170119 + 0.805352i
\(183\) −3.42655 + 3.42655i −0.253298 + 0.253298i
\(184\) 14.2655 + 9.80434i 1.05166 + 0.722785i
\(185\) −3.63767 15.4752i −0.267447 1.13776i
\(186\) −0.0299310 0.0894540i −0.00219464 0.00655908i
\(187\) −17.7363 17.7363i −1.29700 1.29700i
\(188\) 7.60294 + 1.06851i 0.554501 + 0.0779292i
\(189\) −10.7725 + 2.80048i −0.783581 + 0.203705i
\(190\) 4.13996 + 6.69581i 0.300344 + 0.485765i
\(191\) 8.31007 0.601295 0.300648 0.953735i \(-0.402797\pi\)
0.300648 + 0.953735i \(0.402797\pi\)
\(192\) −2.53917 + 5.70315i −0.183249 + 0.411589i
\(193\) −3.72389 + 3.72389i −0.268052 + 0.268052i −0.828315 0.560263i \(-0.810700\pi\)
0.560263 + 0.828315i \(0.310700\pi\)
\(194\) 18.6551 6.24193i 1.33936 0.448144i
\(195\) 4.40262 + 2.72675i 0.315278 + 0.195267i
\(196\) 5.66195 12.8040i 0.404425 0.914571i
\(197\) 12.7667 12.7667i 0.909592 0.909592i −0.0866472 0.996239i \(-0.527615\pi\)
0.996239 + 0.0866472i \(0.0276153\pi\)
\(198\) 14.0678 + 7.01393i 0.999755 + 0.498458i
\(199\) −7.29921 −0.517427 −0.258714 0.965954i \(-0.583299\pi\)
−0.258714 + 0.965954i \(0.583299\pi\)
\(200\) 11.3009 8.50233i 0.799094 0.601206i
\(201\) 0.207894i 0.0146637i
\(202\) −17.8356 8.89247i −1.25491 0.625672i
\(203\) 2.85562 4.86192i 0.200425 0.341240i
\(204\) 6.72537 5.06794i 0.470870 0.354827i
\(205\) −22.1539 13.7209i −1.54729 0.958312i
\(206\) −4.37291 13.0692i −0.304675 0.910576i
\(207\) 10.3471 + 10.3471i 0.719173 + 0.719173i
\(208\) 5.75533 + 10.3828i 0.399060 + 0.719919i
\(209\) −11.5727 −0.800500
\(210\) −4.72025 4.51068i −0.325728 0.311267i
\(211\) 20.4675i 1.40904i 0.709683 + 0.704521i \(0.248838\pi\)
−0.709683 + 0.704521i \(0.751162\pi\)
\(212\) −1.52706 + 10.8657i −0.104879 + 0.746260i
\(213\) 1.61186 1.61186i 0.110443 0.110443i
\(214\) 1.90894 0.638725i 0.130493 0.0436623i
\(215\) 17.2077 4.04493i 1.17356 0.275862i
\(216\) −6.73966 + 9.80631i −0.458576 + 0.667235i
\(217\) 0.194997 + 0.114530i 0.0132372 + 0.00777480i
\(218\) −8.09508 4.03605i −0.548268 0.273356i
\(219\) −2.01297 −0.136024
\(220\) 1.89440 + 20.7032i 0.127721 + 1.39581i
\(221\) 16.0133i 1.07717i
\(222\) −3.50077 + 7.02148i −0.234957 + 0.471251i
\(223\) −0.739912 0.739912i −0.0495482 0.0495482i 0.681899 0.731447i \(-0.261155\pi\)
−0.731447 + 0.681899i \(0.761155\pi\)
\(224\) −4.39396 14.3071i −0.293584 0.955933i
\(225\) 10.7032 5.32621i 0.713547 0.355080i
\(226\) −6.34625 + 2.12343i −0.422146 + 0.141248i
\(227\) 13.9536 + 13.9536i 0.926134 + 0.926134i 0.997454 0.0713191i \(-0.0227209\pi\)
−0.0713191 + 0.997454i \(0.522721\pi\)
\(228\) 0.540725 3.84750i 0.0358104 0.254807i
\(229\) 9.35690i 0.618321i 0.951010 + 0.309161i \(0.100048\pi\)
−0.951010 + 0.309161i \(0.899952\pi\)
\(230\) −4.44289 + 18.8360i −0.292955 + 1.24201i
\(231\) 9.28912 2.41486i 0.611179 0.158886i
\(232\) −1.09850 5.92688i −0.0721198 0.389119i
\(233\) 13.4285 13.4285i 0.879732 0.879732i −0.113775 0.993507i \(-0.536294\pi\)
0.993507 + 0.113775i \(0.0362942\pi\)
\(234\) 3.18432 + 9.51690i 0.208165 + 0.622139i
\(235\) 1.96423 + 8.35612i 0.128132 + 0.545093i
\(236\) −6.14707 + 4.63217i −0.400140 + 0.301528i
\(237\) −0.744846 0.744846i −0.0483829 0.0483829i
\(238\) −4.17249 + 19.7528i −0.270462 + 1.28039i
\(239\) 16.5047i 1.06760i −0.845610 0.533801i \(-0.820763\pi\)
0.845610 0.533801i \(-0.179237\pi\)
\(240\) −6.97156 0.337520i −0.450012 0.0217868i
\(241\) 13.1354i 0.846126i 0.906100 + 0.423063i \(0.139045\pi\)
−0.906100 + 0.423063i \(0.860955\pi\)
\(242\) −13.4290 6.69542i −0.863247 0.430398i
\(243\) −11.0709 + 11.0709i −0.710197 + 0.710197i
\(244\) −7.47432 9.91873i −0.478494 0.634982i
\(245\) 15.6360 + 0.717433i 0.998949 + 0.0458351i
\(246\) 4.08089 + 12.1965i 0.260188 + 0.777617i
\(247\) −5.22425 5.22425i −0.332411 0.332411i
\(248\) 0.237709 0.0440573i 0.0150945 0.00279764i
\(249\) 13.0530i 0.827201i
\(250\) 13.4357 + 8.33558i 0.849748 + 0.527188i
\(251\) 11.2469 0.709898 0.354949 0.934886i \(-0.384498\pi\)
0.354949 + 0.934886i \(0.384498\pi\)
\(252\) −1.44818 12.5691i −0.0912265 0.791776i
\(253\) −20.1170 20.1170i −1.26475 1.26475i
\(254\) −3.30831 9.88746i −0.207582 0.620395i
\(255\) 8.00422 + 4.95739i 0.501244 + 0.310444i
\(256\) −13.5688 8.47863i −0.848051 0.529914i
\(257\) 11.2007 11.2007i 0.698682 0.698682i −0.265444 0.964126i \(-0.585519\pi\)
0.964126 + 0.265444i \(0.0855185\pi\)
\(258\) −7.80758 3.89271i −0.486079 0.242350i
\(259\) −4.73254 18.2044i −0.294066 1.13117i
\(260\) −8.49082 + 10.2012i −0.526579 + 0.632652i
\(261\) 5.09568i 0.315415i
\(262\) −24.6861 12.3080i −1.52511 0.760392i
\(263\) 6.04243 6.04243i 0.372592 0.372592i −0.495828 0.868421i \(-0.665135\pi\)
0.868421 + 0.495828i \(0.165135\pi\)
\(264\) 5.81163 8.45601i 0.357681 0.520431i
\(265\) −11.9421 + 2.80717i −0.733598 + 0.172443i
\(266\) 5.08299 + 7.80549i 0.311658 + 0.478585i
\(267\) −0.756620 + 0.756620i −0.0463044 + 0.0463044i
\(268\) 0.527633 + 0.0741532i 0.0322303 + 0.00452963i
\(269\) 26.8043i 1.63429i −0.576432 0.817145i \(-0.695556\pi\)
0.576432 0.817145i \(-0.304444\pi\)
\(270\) −12.9482 3.05411i −0.788002 0.185867i
\(271\) 26.1223i 1.58682i −0.608689 0.793409i \(-0.708304\pi\)
0.608689 0.793409i \(-0.291696\pi\)
\(272\) 10.4635 + 18.8766i 0.634444 + 1.14456i
\(273\) 5.28351 + 3.10324i 0.319773 + 0.187817i
\(274\) 5.76543 + 17.2310i 0.348302 + 1.04096i
\(275\) −20.8094 + 10.3553i −1.25485 + 0.624449i
\(276\) 7.62813 5.74823i 0.459160 0.346003i
\(277\) −15.1106 + 15.1106i −0.907906 + 0.907906i −0.996103 0.0881970i \(-0.971889\pi\)
0.0881970 + 0.996103i \(0.471889\pi\)
\(278\) −5.33506 + 10.7005i −0.319976 + 0.641773i
\(279\) 0.204372 0.0122354
\(280\) 13.1317 10.3710i 0.784770 0.619788i
\(281\) −2.04869 −0.122215 −0.0611073 0.998131i \(-0.519463\pi\)
−0.0611073 + 0.998131i \(0.519463\pi\)
\(282\) 1.89031 3.79139i 0.112567 0.225774i
\(283\) −6.90261 + 6.90261i −0.410317 + 0.410317i −0.881849 0.471532i \(-0.843701\pi\)
0.471532 + 0.881849i \(0.343701\pi\)
\(284\) 3.51595 + 4.66582i 0.208634 + 0.276865i
\(285\) 4.22865 0.994008i 0.250484 0.0588800i
\(286\) −6.19101 18.5029i −0.366082 1.09410i
\(287\) −26.5865 15.6154i −1.56935 0.921748i
\(288\) −9.97228 9.13785i −0.587622 0.538453i
\(289\) 12.1131i 0.712536i
\(290\) 5.73214 3.54413i 0.336603 0.208118i
\(291\) 10.8547i 0.636317i
\(292\) 0.717999 5.10888i 0.0420177 0.298975i
\(293\) −10.6207 + 10.6207i −0.620470 + 0.620470i −0.945652 0.325182i \(-0.894575\pi\)
0.325182 + 0.945652i \(0.394575\pi\)
\(294\) −5.70875 5.20461i −0.332941 0.303539i
\(295\) −7.31596 4.53112i −0.425952 0.263812i
\(296\) −16.5717 11.3894i −0.963213 0.661995i
\(297\) 13.8288 13.8288i 0.802427 0.802427i
\(298\) 23.5171 + 11.7252i 1.36231 + 0.679221i
\(299\) 18.1628i 1.05038i
\(300\) −2.47046 7.40220i −0.142632 0.427366i
\(301\) 20.2425 5.26238i 1.16676 0.303319i
\(302\) −19.6179 9.78109i −1.12888 0.562838i
\(303\) −7.77606 + 7.77606i −0.446723 + 0.446723i
\(304\) 9.57203 + 2.74470i 0.548993 + 0.157420i
\(305\) 7.31128 11.8048i 0.418643 0.675941i
\(306\) 5.78927 + 17.3023i 0.330951 + 0.989105i
\(307\) 0.0625648 + 0.0625648i 0.00357076 + 0.00357076i 0.708890 0.705319i \(-0.249196\pi\)
−0.705319 + 0.708890i \(0.749196\pi\)
\(308\) 2.81557 + 24.4370i 0.160432 + 1.39243i
\(309\) −7.60452 −0.432606
\(310\) 0.142144 + 0.229898i 0.00807325 + 0.0130574i
\(311\) 6.06288i 0.343795i 0.985115 + 0.171897i \(0.0549897\pi\)
−0.985115 + 0.171897i \(0.945010\pi\)
\(312\) 6.44082 1.19375i 0.364640 0.0675828i
\(313\) 7.81668 + 7.81668i 0.441825 + 0.441825i 0.892625 0.450800i \(-0.148861\pi\)
−0.450800 + 0.892625i \(0.648861\pi\)
\(314\) −4.98237 14.8907i −0.281172 0.840331i
\(315\) 12.5129 6.59743i 0.705020 0.371723i
\(316\) 2.15608 1.62473i 0.121289 0.0913983i
\(317\) 9.46406 9.46406i 0.531555 0.531555i −0.389480 0.921035i \(-0.627345\pi\)
0.921035 + 0.389480i \(0.127345\pi\)
\(318\) 5.41845 + 2.70153i 0.303851 + 0.151494i
\(319\) 9.90713i 0.554693i
\(320\) 3.34329 17.5733i 0.186895 0.982380i
\(321\) 1.11075i 0.0619958i
\(322\) −4.73258 + 22.4043i −0.263736 + 1.24854i
\(323\) −9.49798 9.49798i −0.528482 0.528482i
\(324\) −4.68238 6.21371i −0.260132 0.345206i
\(325\) −14.0686 4.71927i −0.780388 0.261778i
\(326\) 5.84695 + 17.4747i 0.323833 + 0.967832i
\(327\) −3.52934 + 3.52934i −0.195173 + 0.195173i
\(328\) −32.4100 + 6.00692i −1.78954 + 0.331677i
\(329\) 2.55543 + 9.82985i 0.140885 + 0.541937i
\(330\) 11.1653 + 2.63357i 0.614628 + 0.144973i
\(331\) 2.31382i 0.127179i −0.997976 0.0635896i \(-0.979745\pi\)
0.997976 0.0635896i \(-0.0202549\pi\)
\(332\) 33.1284 + 4.65584i 1.81816 + 0.255522i
\(333\) −12.0199 12.0199i −0.658687 0.658687i
\(334\) −26.1632 + 8.75410i −1.43159 + 0.479003i
\(335\) 0.136315 + 0.579903i 0.00744769 + 0.0316835i
\(336\) −8.25596 0.205724i −0.450400 0.0112232i
\(337\) 2.84780 + 2.84780i 0.155130 + 0.155130i 0.780405 0.625275i \(-0.215013\pi\)
−0.625275 + 0.780405i \(0.715013\pi\)
\(338\) −2.64527 + 5.30561i −0.143884 + 0.288587i
\(339\) 3.69266i 0.200558i
\(340\) −15.4368 + 18.5464i −0.837178 + 1.00582i
\(341\) −0.397344 −0.0215174
\(342\) 7.53348 + 3.75605i 0.407364 + 0.203104i
\(343\) 18.5156 + 0.414602i 0.999749 + 0.0223864i
\(344\) 12.6645 18.4271i 0.682825 0.993521i
\(345\) 9.07865 + 5.62284i 0.488778 + 0.302723i
\(346\) −0.342246 + 0.114514i −0.0183993 + 0.00615632i
\(347\) −16.5111 + 16.5111i −0.886362 + 0.886362i −0.994172 0.107810i \(-0.965616\pi\)
0.107810 + 0.994172i \(0.465616\pi\)
\(348\) −3.29376 0.462902i −0.176564 0.0248142i
\(349\) 10.0277i 0.536770i −0.963312 0.268385i \(-0.913510\pi\)
0.963312 0.268385i \(-0.0864899\pi\)
\(350\) 16.1243 + 9.48712i 0.861883 + 0.507108i
\(351\) 12.4854 0.666422
\(352\) 19.3883 + 17.7660i 1.03340 + 0.946930i
\(353\) 12.7496 + 12.7496i 0.678591 + 0.678591i 0.959681 0.281091i \(-0.0906962\pi\)
−0.281091 + 0.959681i \(0.590696\pi\)
\(354\) 1.34765 + 4.02768i 0.0716266 + 0.214069i
\(355\) −3.43926 + 5.55304i −0.182537 + 0.294725i
\(356\) −1.65041 2.19017i −0.0874718 0.116079i
\(357\) 9.60573 + 5.64186i 0.508389 + 0.298599i
\(358\) −14.5446 7.25167i −0.768708 0.383263i
\(359\) 5.65203i 0.298303i −0.988814 0.149151i \(-0.952346\pi\)
0.988814 0.149151i \(-0.0476542\pi\)
\(360\) 5.48625 14.0920i 0.289151 0.742714i
\(361\) 12.8027 0.673825
\(362\) 4.58338 + 2.28519i 0.240897 + 0.120107i
\(363\) −5.85484 + 5.85484i −0.307299 + 0.307299i
\(364\) −9.76054 + 12.3026i −0.511591 + 0.644831i
\(365\) 5.61499 1.31989i 0.293902 0.0690861i
\(366\) −6.49895 + 2.17452i −0.339705 + 0.113664i
\(367\) −24.6260 + 24.6260i −1.28547 + 1.28547i −0.347958 + 0.937510i \(0.613125\pi\)
−0.937510 + 0.347958i \(0.886875\pi\)
\(368\) 11.8681 + 21.4104i 0.618666 + 1.11609i
\(369\) −27.8648 −1.45058
\(370\) 5.16116 21.8812i 0.268316 1.13755i
\(371\) −14.0483 + 3.65208i −0.729351 + 0.189607i
\(372\) 0.0185656 0.132103i 0.000962581 0.00684920i
\(373\) 13.0678 + 13.0678i 0.676627 + 0.676627i 0.959235 0.282608i \(-0.0911997\pi\)
−0.282608 + 0.959235i \(0.591200\pi\)
\(374\) −11.2556 33.6394i −0.582014 1.73945i
\(375\) 6.71428 5.57119i 0.346724 0.287695i
\(376\) 8.94825 + 6.14993i 0.461471 + 0.317158i
\(377\) −4.47236 + 4.47236i −0.230338 + 0.230338i
\(378\) −15.4011 3.25325i −0.792146 0.167329i
\(379\) 1.25274 0.0643491 0.0321746 0.999482i \(-0.489757\pi\)
0.0321746 + 0.999482i \(0.489757\pi\)
\(380\) 1.01448 + 11.0868i 0.0520415 + 0.568741i
\(381\) −5.75317 −0.294744
\(382\) 10.5175 + 5.24380i 0.538120 + 0.268296i
\(383\) −3.82945 3.82945i −0.195676 0.195676i 0.602468 0.798143i \(-0.294184\pi\)
−0.798143 + 0.602468i \(0.794184\pi\)
\(384\) −6.81244 + 5.61580i −0.347646 + 0.286580i
\(385\) −24.3278 + 12.8268i −1.23986 + 0.653717i
\(386\) −7.06291 + 2.36322i −0.359492 + 0.120285i
\(387\) 13.3656 13.3656i 0.679412 0.679412i
\(388\) 27.5492 + 3.87175i 1.39860 + 0.196558i
\(389\) 34.3824 1.74326 0.871629 0.490167i \(-0.163064\pi\)
0.871629 + 0.490167i \(0.163064\pi\)
\(390\) 3.85145 + 6.22919i 0.195026 + 0.315427i
\(391\) 33.0211i 1.66995i
\(392\) 15.2455 12.6323i 0.770013 0.638028i
\(393\) −10.7628 + 10.7628i −0.542911 + 0.542911i
\(394\) 24.2140 8.10190i 1.21988 0.408168i
\(395\) 2.56607 + 1.58929i 0.129113 + 0.0799659i
\(396\) 13.3787 + 17.7541i 0.672305 + 0.892176i
\(397\) 14.4139 + 14.4139i 0.723411 + 0.723411i 0.969298 0.245888i \(-0.0790794\pi\)
−0.245888 + 0.969298i \(0.579079\pi\)
\(398\) −9.23809 4.60593i −0.463064 0.230875i
\(399\) 4.97444 1.29319i 0.249033 0.0647403i
\(400\) 19.6679 3.62973i 0.983393 0.181486i
\(401\) −4.95208 −0.247295 −0.123647 0.992326i \(-0.539459\pi\)
−0.123647 + 0.992326i \(0.539459\pi\)
\(402\) 0.131185 0.263117i 0.00654292 0.0131231i
\(403\) −0.179373 0.179373i −0.00893519 0.00893519i
\(404\) −16.9619 22.5091i −0.843886 1.11987i
\(405\) 4.58024 7.39527i 0.227594 0.367474i
\(406\) 6.68211 4.35143i 0.331627 0.215958i
\(407\) 23.3693 + 23.3693i 1.15837 + 1.15837i
\(408\) 11.7098 2.17031i 0.579721 0.107446i
\(409\) 16.1141 0.796792 0.398396 0.917213i \(-0.369567\pi\)
0.398396 + 0.917213i \(0.369567\pi\)
\(410\) −19.3804 31.3451i −0.957130 1.54802i
\(411\) 10.0261 0.494552
\(412\) 2.71243 19.3002i 0.133632 0.950851i
\(413\) −8.77976 5.15674i −0.432024 0.253746i
\(414\) 6.56638 + 19.6248i 0.322720 + 0.964506i
\(415\) 8.55878 + 36.4102i 0.420134 + 1.78731i
\(416\) 0.732365 + 16.7725i 0.0359072 + 0.822340i
\(417\) 4.66526 + 4.66526i 0.228459 + 0.228459i
\(418\) −14.6467 7.30258i −0.716395 0.357181i
\(419\) 18.6093i 0.909125i 0.890715 + 0.454562i \(0.150204\pi\)
−0.890715 + 0.454562i \(0.849796\pi\)
\(420\) −3.12776 8.68741i −0.152619 0.423902i
\(421\) 28.1609i 1.37248i 0.727375 + 0.686240i \(0.240740\pi\)
−0.727375 + 0.686240i \(0.759260\pi\)
\(422\) −12.9154 + 25.9043i −0.628711 + 1.26100i
\(423\) 6.49039 + 6.49039i 0.315574 + 0.315574i
\(424\) −8.78914 + 12.7883i −0.426839 + 0.621057i
\(425\) −25.5776 8.57990i −1.24070 0.416186i
\(426\) 3.05713 1.02291i 0.148119 0.0495599i
\(427\) 8.32075 14.1667i 0.402669 0.685577i
\(428\) 2.81906 + 0.396189i 0.136264 + 0.0191505i
\(429\) −10.7662 −0.519798
\(430\) 24.3310 + 5.73899i 1.17334 + 0.276759i
\(431\) −18.4841 −0.890346 −0.445173 0.895445i \(-0.646858\pi\)
−0.445173 + 0.895445i \(0.646858\pi\)
\(432\) −14.7179 + 8.15830i −0.708114 + 0.392517i
\(433\) −10.5528 10.5528i −0.507134 0.507134i 0.406512 0.913646i \(-0.366745\pi\)
−0.913646 + 0.406512i \(0.866745\pi\)
\(434\) 0.174523 + 0.267999i 0.00837736 + 0.0128644i
\(435\) −0.850948 3.62005i −0.0407998 0.173568i
\(436\) −7.69854 10.2163i −0.368693 0.489271i
\(437\) −10.7729 10.7729i −0.515339 0.515339i
\(438\) −2.54767 1.27022i −0.121732 0.0606933i
\(439\) 5.78596 0.276149 0.138074 0.990422i \(-0.455909\pi\)
0.138074 + 0.990422i \(0.455909\pi\)
\(440\) −10.6665 + 27.3979i −0.508504 + 1.30615i
\(441\) 14.6182 8.15138i 0.696105 0.388161i
\(442\) 10.1047 20.2669i 0.480631 0.963999i
\(443\) −0.444980 0.444980i −0.0211416 0.0211416i 0.696457 0.717599i \(-0.254759\pi\)
−0.717599 + 0.696457i \(0.754759\pi\)
\(444\) −8.86136 + 6.67754i −0.420542 + 0.316902i
\(445\) 1.61441 2.60663i 0.0765305 0.123566i
\(446\) −0.469556 1.40335i −0.0222341 0.0664506i
\(447\) 10.2531 10.2531i 0.484956 0.484956i
\(448\) 3.46692 20.8801i 0.163797 0.986494i
\(449\) 29.6129i 1.39752i 0.715356 + 0.698761i \(0.246265\pi\)
−0.715356 + 0.698761i \(0.753735\pi\)
\(450\) 16.9072 + 0.0129180i 0.797014 + 0.000608959i
\(451\) 54.1753 2.55101
\(452\) −9.37192 1.31712i −0.440818 0.0619522i
\(453\) −8.55311 + 8.55311i −0.401860 + 0.401860i
\(454\) 8.85512 + 26.4651i 0.415591 + 1.24207i
\(455\) −16.7727 5.19184i −0.786315 0.243397i
\(456\) 3.11220 4.52830i 0.145742 0.212057i
\(457\) −18.0346 18.0346i −0.843623 0.843623i 0.145705 0.989328i \(-0.453455\pi\)
−0.989328 + 0.145705i \(0.953455\pi\)
\(458\) −5.90437 + 11.8424i −0.275893 + 0.553357i
\(459\) 22.6992 1.05951
\(460\) −17.5089 + 21.0359i −0.816358 + 0.980803i
\(461\) −17.8301 −0.830430 −0.415215 0.909723i \(-0.636294\pi\)
−0.415215 + 0.909723i \(0.636294\pi\)
\(462\) 13.2804 + 2.80529i 0.617860 + 0.130514i
\(463\) −9.68008 + 9.68008i −0.449872 + 0.449872i −0.895312 0.445440i \(-0.853047\pi\)
0.445440 + 0.895312i \(0.353047\pi\)
\(464\) 2.34968 8.19440i 0.109081 0.380415i
\(465\) 0.145189 0.0341289i 0.00673299 0.00158269i
\(466\) 25.4692 8.52189i 1.17984 0.394769i
\(467\) −21.3193 21.3193i −0.986541 0.986541i 0.0133696 0.999911i \(-0.495744\pi\)
−0.999911 + 0.0133696i \(0.995744\pi\)
\(468\) −1.97517 + 14.0542i −0.0913024 + 0.649657i
\(469\) 0.177343 + 0.682178i 0.00818895 + 0.0315000i
\(470\) −2.78687 + 11.8152i −0.128549 + 0.544995i
\(471\) −8.66438 −0.399233
\(472\) −10.7029 + 1.98369i −0.492641 + 0.0913066i
\(473\) −25.9857 + 25.9857i −1.19482 + 1.19482i
\(474\) −0.472687 1.41271i −0.0217112 0.0648879i
\(475\) −11.1437 + 5.54540i −0.511307 + 0.254440i
\(476\) −17.7452 + 22.3668i −0.813350 + 1.02518i
\(477\) −9.27571 + 9.27571i −0.424706 + 0.424706i
\(478\) 10.4148 20.8889i 0.476361 0.955434i
\(479\) 33.4261 1.52728 0.763639 0.645644i \(-0.223411\pi\)
0.763639 + 0.645644i \(0.223411\pi\)
\(480\) −8.61043 4.82636i −0.393011 0.220292i
\(481\) 21.0992i 0.962040i
\(482\) −8.28868 + 16.6246i −0.377539 + 0.757228i
\(483\) 10.8951 + 6.39919i 0.495745 + 0.291173i
\(484\) −12.7712 16.9478i −0.580507 0.770356i
\(485\) 7.11739 + 30.2784i 0.323184 + 1.37487i
\(486\) −20.9975 + 7.02569i −0.952467 + 0.318692i
\(487\) −8.32102 8.32102i −0.377062 0.377062i 0.492979 0.870041i \(-0.335908\pi\)
−0.870041 + 0.492979i \(0.835908\pi\)
\(488\) −3.20082 17.2699i −0.144894 0.781770i
\(489\) 10.1679 0.459808
\(490\) 19.3367 + 10.7746i 0.873543 + 0.486748i
\(491\) 1.35905i 0.0613331i 0.999530 + 0.0306665i \(0.00976299\pi\)
−0.999530 + 0.0306665i \(0.990237\pi\)
\(492\) −2.53130 + 18.0113i −0.114120 + 0.812012i
\(493\) −8.13101 + 8.13101i −0.366202 + 0.366202i
\(494\) −3.31536 9.90855i −0.149165 0.445807i
\(495\) −13.0869 + 21.1301i −0.588210 + 0.949726i
\(496\) 0.328652 + 0.0942385i 0.0147569 + 0.00423143i
\(497\) −3.91412 + 6.66410i −0.175572 + 0.298926i
\(498\) 8.23669 16.5203i 0.369095 0.740291i
\(499\) 3.36535 0.150654 0.0753269 0.997159i \(-0.476000\pi\)
0.0753269 + 0.997159i \(0.476000\pi\)
\(500\) 11.7447 + 19.0279i 0.525239 + 0.850955i
\(501\) 15.2234i 0.680133i
\(502\) 14.2344 + 7.09700i 0.635313 + 0.316755i
\(503\) 0.00647766 + 0.00647766i 0.000288825 + 0.000288825i 0.707251 0.706962i \(-0.249935\pi\)
−0.706962 + 0.707251i \(0.749935\pi\)
\(504\) 6.09845 16.8216i 0.271646 0.749293i
\(505\) 16.5919 26.7893i 0.738330 1.19211i
\(506\) −12.7665 38.1549i −0.567540 1.69619i
\(507\) 2.31317 + 2.31317i 0.102731 + 0.102731i
\(508\) 2.05208 14.6015i 0.0910463 0.647835i
\(509\) 32.6060i 1.44524i 0.691247 + 0.722618i \(0.257062\pi\)
−0.691247 + 0.722618i \(0.742938\pi\)
\(510\) 7.00216 + 11.3250i 0.310061 + 0.501481i
\(511\) 6.60528 1.71715i 0.292200 0.0759623i
\(512\) −11.8229 19.2930i −0.522504 0.852637i
\(513\) 7.40548 7.40548i 0.326960 0.326960i
\(514\) 21.2438 7.10810i 0.937025 0.313525i
\(515\) 21.2121 4.98624i 0.934719 0.219720i
\(516\) −7.42513 9.85345i −0.326873 0.433774i
\(517\) −12.6187 12.6187i −0.554972 0.554972i
\(518\) 5.49768 26.0264i 0.241554 1.14353i
\(519\) 0.199141i 0.00874131i
\(520\) −17.1834 + 7.55307i −0.753541 + 0.331224i
\(521\) 21.6501i 0.948508i −0.880388 0.474254i \(-0.842718\pi\)
0.880388 0.474254i \(-0.157282\pi\)
\(522\) 3.21547 6.44924i 0.140737 0.282276i
\(523\) 8.03977 8.03977i 0.351554 0.351554i −0.509133 0.860688i \(-0.670034\pi\)
0.860688 + 0.509133i \(0.170034\pi\)
\(524\) −23.4769 31.1547i −1.02559 1.36100i
\(525\) 7.78761 6.77649i 0.339879 0.295750i
\(526\) 11.4604 3.83459i 0.499696 0.167196i
\(527\) −0.326110 0.326110i −0.0142056 0.0142056i
\(528\) 12.6913 7.03493i 0.552316 0.306156i
\(529\) 14.4536i 0.628415i
\(530\) −16.8857 3.98285i −0.733466 0.173004i
\(531\) −9.20190 −0.399328
\(532\) 1.50777 + 13.0863i 0.0653703 + 0.567364i
\(533\) 24.4563 + 24.4563i 1.05932 + 1.05932i
\(534\) −1.43504 + 0.480159i −0.0621003 + 0.0207785i
\(535\) 0.728309 + 3.09833i 0.0314876 + 0.133952i
\(536\) 0.620996 + 0.426797i 0.0268229 + 0.0184348i
\(537\) −6.34125 + 6.34125i −0.273645 + 0.273645i
\(538\) 16.9140 33.9244i 0.729216 1.46258i
\(539\) −28.4210 + 15.8481i −1.22418 + 0.682625i
\(540\) −14.4604 12.0359i −0.622277 0.517943i
\(541\) 6.87080i 0.295399i −0.989032 0.147699i \(-0.952813\pi\)
0.989032 0.147699i \(-0.0471868\pi\)
\(542\) 16.4837 33.0612i 0.708034 1.42010i
\(543\) 1.99829 1.99829i 0.0857548 0.0857548i
\(544\) 1.33148 + 30.4934i 0.0570868 + 1.30739i
\(545\) 7.53061 12.1589i 0.322576 0.520832i
\(546\) 4.72877 + 7.26154i 0.202372 + 0.310765i
\(547\) 13.7972 13.7972i 0.589925 0.589925i −0.347686 0.937611i \(-0.613032\pi\)
0.937611 + 0.347686i \(0.113032\pi\)
\(548\) −3.57619 + 25.4462i −0.152767 + 1.08701i
\(549\) 14.8479i 0.633693i
\(550\) −32.8713 0.0251154i −1.40164 0.00107092i
\(551\) 5.30539i 0.226017i
\(552\) 13.2816 2.46163i 0.565303 0.104774i
\(553\) 3.07950 + 1.80872i 0.130954 + 0.0769148i
\(554\) −28.6594 + 9.58933i −1.21762 + 0.407412i
\(555\) −10.5464 6.53188i −0.447669 0.277263i
\(556\) −13.5044 + 10.1763i −0.572714 + 0.431573i
\(557\) −18.5084 + 18.5084i −0.784225 + 0.784225i −0.980541 0.196316i \(-0.937102\pi\)
0.196316 + 0.980541i \(0.437102\pi\)
\(558\) 0.258659 + 0.128963i 0.0109499 + 0.00545942i
\(559\) −23.4614 −0.992311
\(560\) 23.1642 4.83953i 0.978865 0.204508i
\(561\) −19.5736 −0.826398
\(562\) −2.59288 1.29276i −0.109374 0.0545318i
\(563\) 9.06869 9.06869i 0.382200 0.382200i −0.489694 0.871894i \(-0.662892\pi\)
0.871894 + 0.489694i \(0.162892\pi\)
\(564\) 4.78487 3.60567i 0.201479 0.151826i
\(565\) −2.42125 10.3003i −0.101863 0.433339i
\(566\) −13.0918 + 4.38047i −0.550290 + 0.184125i
\(567\) 5.21264 8.87494i 0.218910 0.372712i
\(568\) 1.50568 + 8.12382i 0.0631769 + 0.340868i
\(569\) 17.4892i 0.733186i 0.930381 + 0.366593i \(0.119476\pi\)
−0.930381 + 0.366593i \(0.880524\pi\)
\(570\) 5.97914 + 1.41031i 0.250439 + 0.0590713i
\(571\) 33.1973i 1.38926i −0.719365 0.694632i \(-0.755567\pi\)
0.719365 0.694632i \(-0.244433\pi\)
\(572\) 3.84017 27.3245i 0.160565 1.14249i
\(573\) 4.58546 4.58546i 0.191560 0.191560i
\(574\) −23.7950 36.5398i −0.993184 1.52514i
\(575\) −29.0109 9.73160i −1.20984 0.405836i
\(576\) −6.85506 17.8578i −0.285628 0.744076i
\(577\) 1.72186 1.72186i 0.0716819 0.0716819i −0.670357 0.742039i \(-0.733859\pi\)
0.742039 + 0.670357i \(0.233859\pi\)
\(578\) 7.64360 15.3307i 0.317932 0.637674i
\(579\) 4.10966i 0.170791i
\(580\) 9.49117 0.868470i 0.394099 0.0360612i
\(581\) 11.1348 + 42.8317i 0.461950 + 1.77696i
\(582\) 6.84954 13.7381i 0.283923 0.569462i
\(583\) 18.0340 18.0340i 0.746893 0.746893i
\(584\) 4.13251 6.01287i 0.171005 0.248815i
\(585\) −15.4465 + 3.63094i −0.638634 + 0.150121i
\(586\) −20.1438 + 6.74003i −0.832132 + 0.278428i
\(587\) 3.21075 + 3.21075i 0.132522 + 0.132522i 0.770256 0.637734i \(-0.220128\pi\)
−0.637734 + 0.770256i \(0.720128\pi\)
\(588\) −3.94096 10.1894i −0.162522 0.420205i
\(589\) −0.212783 −0.00876756
\(590\) −6.40007 10.3512i −0.263487 0.426153i
\(591\) 14.0893i 0.579555i
\(592\) −13.7868 24.8718i −0.566633 1.02223i
\(593\) 6.17288 + 6.17288i 0.253490 + 0.253490i 0.822400 0.568910i \(-0.192635\pi\)
−0.568910 + 0.822400i \(0.692635\pi\)
\(594\) 26.2283 8.77589i 1.07616 0.360079i
\(595\) −30.4937 9.43907i −1.25012 0.386964i
\(596\) 22.3651 + 29.6794i 0.916111 + 1.21572i
\(597\) −4.02767 + 4.02767i −0.164842 + 0.164842i
\(598\) 11.4611 22.9874i 0.468678 0.940024i
\(599\) 3.66118i 0.149592i −0.997199 0.0747960i \(-0.976169\pi\)
0.997199 0.0747960i \(-0.0238306\pi\)
\(600\) 1.54424 10.9273i 0.0630432 0.446107i
\(601\) 37.3577i 1.52385i −0.647663 0.761927i \(-0.724254\pi\)
0.647663 0.761927i \(-0.275746\pi\)
\(602\) 28.9402 + 6.11319i 1.17951 + 0.249155i
\(603\) 0.450424 + 0.450424i 0.0183427 + 0.0183427i
\(604\) −18.6569 24.7585i −0.759138 1.00741i
\(605\) 12.4926 20.1705i 0.507895 0.820049i
\(606\) −14.7484 + 4.93477i −0.599114 + 0.200461i
\(607\) −11.7160 + 11.7160i −0.475537 + 0.475537i −0.903701 0.428164i \(-0.859161\pi\)
0.428164 + 0.903701i \(0.359161\pi\)
\(608\) 10.3827 + 9.51390i 0.421073 + 0.385840i
\(609\) −1.10707 4.25850i −0.0448607 0.172563i
\(610\) 16.7024 10.3270i 0.676261 0.418126i
\(611\) 11.3929i 0.460909i
\(612\) −3.59098 + 25.5514i −0.145157 + 1.03285i
\(613\) −1.94839 1.94839i −0.0786947 0.0786947i 0.666664 0.745359i \(-0.267722\pi\)
−0.745359 + 0.666664i \(0.767722\pi\)
\(614\) 0.0397043 + 0.118663i 0.00160234 + 0.00478887i
\(615\) −19.7956 + 4.65325i −0.798235 + 0.187637i
\(616\) −11.8567 + 32.7048i −0.477721 + 1.31772i
\(617\) −27.8887 27.8887i −1.12276 1.12276i −0.991325 0.131431i \(-0.958043\pi\)
−0.131431 0.991325i \(-0.541957\pi\)
\(618\) −9.62450 4.79859i −0.387154 0.193028i
\(619\) 29.6526i 1.19184i 0.803045 + 0.595919i \(0.203212\pi\)
−0.803045 + 0.595919i \(0.796788\pi\)
\(620\) 0.0348317 + 0.380662i 0.00139887 + 0.0152877i
\(621\) 25.7462 1.03316
\(622\) −3.82579 + 7.67336i −0.153400 + 0.307674i
\(623\) 1.83732 3.12818i 0.0736105 0.125328i
\(624\) 8.90497 + 2.55343i 0.356484 + 0.102219i
\(625\) −15.0759 + 19.9429i −0.603036 + 0.797714i
\(626\) 4.96055 + 14.8255i 0.198263 + 0.592545i
\(627\) −6.38577 + 6.38577i −0.255023 + 0.255023i
\(628\) 3.09047 21.9901i 0.123323 0.877499i
\(629\) 38.3595i 1.52949i
\(630\) 19.9997 0.454049i 0.796809 0.0180897i
\(631\) 23.5926 0.939205 0.469603 0.882878i \(-0.344397\pi\)
0.469603 + 0.882878i \(0.344397\pi\)
\(632\) 3.75404 0.695778i 0.149328 0.0276766i
\(633\) 11.2939 + 11.2939i 0.448892 + 0.448892i
\(634\) 17.9500 6.00599i 0.712885 0.238529i
\(635\) 16.0480 3.77231i 0.636844 0.149700i
\(636\) 5.15303 + 6.83828i 0.204331 + 0.271155i
\(637\) −19.9843 5.67579i −0.791808 0.224883i
\(638\) −6.25157 + 12.5387i −0.247502 + 0.496414i
\(639\) 6.98452i 0.276303i
\(640\) 15.3205 20.1317i 0.605594 0.795774i
\(641\) −35.1428 −1.38806 −0.694028 0.719948i \(-0.744166\pi\)
−0.694028 + 0.719948i \(0.744166\pi\)
\(642\) 0.700901 1.40579i 0.0276624 0.0554822i
\(643\) −10.1811 + 10.1811i −0.401505 + 0.401505i −0.878763 0.477258i \(-0.841631\pi\)
0.477258 + 0.878763i \(0.341631\pi\)
\(644\) −20.1272 + 25.3692i −0.793123 + 0.999686i
\(645\) 7.26316 11.7271i 0.285987 0.461755i
\(646\) −6.02752 18.0143i −0.237150 0.708764i
\(647\) 5.73728 5.73728i 0.225556 0.225556i −0.585277 0.810833i \(-0.699014\pi\)
0.810833 + 0.585277i \(0.199014\pi\)
\(648\) −2.00519 10.8189i −0.0787714 0.425007i
\(649\) 17.8905 0.702264
\(650\) −14.8277 14.8504i −0.581592 0.582481i
\(651\) 0.170796 0.0444011i 0.00669400 0.00174022i
\(652\) −3.62675 + 25.8060i −0.142035 + 1.01064i
\(653\) 11.4985 + 11.4985i 0.449970 + 0.449970i 0.895345 0.445374i \(-0.146929\pi\)
−0.445374 + 0.895345i \(0.646929\pi\)
\(654\) −6.69391 + 2.23976i −0.261753 + 0.0875814i
\(655\) 22.9647 37.0789i 0.897307 1.44879i
\(656\) −44.8095 12.8488i −1.74952 0.501661i
\(657\) 4.36129 4.36129i 0.170150 0.170150i
\(658\) −2.96859 + 14.0535i −0.115728 + 0.547861i
\(659\) −30.8901 −1.20331 −0.601653 0.798758i \(-0.705491\pi\)
−0.601653 + 0.798758i \(0.705491\pi\)
\(660\) 12.4693 + 10.3786i 0.485365 + 0.403987i
\(661\) −11.2071 −0.435905 −0.217953 0.975959i \(-0.569938\pi\)
−0.217953 + 0.975959i \(0.569938\pi\)
\(662\) 1.46006 2.92844i 0.0567470 0.113817i
\(663\) −8.83608 8.83608i −0.343165 0.343165i
\(664\) 38.9903 + 26.7972i 1.51312 + 1.03993i
\(665\) −13.0278 + 6.86893i −0.505197 + 0.266366i
\(666\) −7.62796 22.7975i −0.295577 0.883386i
\(667\) −9.22246 + 9.22246i −0.357095 + 0.357095i
\(668\) −38.6369 5.43000i −1.49491 0.210093i
\(669\) −0.816561 −0.0315701
\(670\) −0.193405 + 0.819959i −0.00747189 + 0.0316778i
\(671\) 28.8676i 1.11442i
\(672\) −10.3192 5.47003i −0.398071 0.211011i
\(673\) 26.8667 26.8667i 1.03563 1.03563i 0.0362934 0.999341i \(-0.488445\pi\)
0.999341 0.0362934i \(-0.0115551\pi\)
\(674\) 1.80724 + 5.40127i 0.0696124 + 0.208049i
\(675\) 6.68966 19.9426i 0.257485 0.767591i
\(676\) −6.69587 + 5.04571i −0.257533 + 0.194066i
\(677\) 11.5202 + 11.5202i 0.442758 + 0.442758i 0.892938 0.450180i \(-0.148640\pi\)
−0.450180 + 0.892938i \(0.648640\pi\)
\(678\) −2.33013 + 4.67353i −0.0894882 + 0.179486i
\(679\) 9.25959 + 35.6184i 0.355351 + 1.36691i
\(680\) −31.2404 + 13.7319i −1.19801 + 0.526595i
\(681\) 15.3991 0.590095
\(682\) −0.502891 0.250732i −0.0192567 0.00960101i
\(683\) −28.3949 28.3949i −1.08650 1.08650i −0.995886 0.0906141i \(-0.971117\pi\)
−0.0906141 0.995886i \(-0.528883\pi\)
\(684\) 7.16445 + 9.50752i 0.273940 + 0.363529i
\(685\) −27.9670 + 6.57406i −1.06856 + 0.251182i
\(686\) 23.1723 + 12.2084i 0.884722 + 0.466120i
\(687\) 5.16310 + 5.16310i 0.196985 + 0.196985i
\(688\) 27.6564 15.3303i 1.05439 0.584462i
\(689\) 16.2822 0.620301
\(690\) 7.94208 + 12.8452i 0.302350 + 0.489009i
\(691\) 14.0813 0.535679 0.267839 0.963464i \(-0.413690\pi\)
0.267839 + 0.963464i \(0.413690\pi\)
\(692\) −0.505417 0.0710309i −0.0192131 0.00270019i
\(693\) −14.8938 + 25.3578i −0.565767 + 0.963264i
\(694\) −31.3157 + 10.4781i −1.18873 + 0.397744i
\(695\) −16.0723 9.95435i −0.609658 0.377590i
\(696\) −3.87657 2.66428i −0.146941 0.100989i
\(697\) 44.4629 + 44.4629i 1.68415 + 1.68415i
\(698\) 6.32765 12.6913i 0.239505 0.480374i
\(699\) 14.8196i 0.560529i
\(700\) 14.4209 + 22.1819i 0.545059 + 0.838398i
\(701\) 17.8758i 0.675159i −0.941297 0.337580i \(-0.890392\pi\)
0.941297 0.337580i \(-0.109608\pi\)
\(702\) 15.8019 + 7.87853i 0.596405 + 0.297356i
\(703\) 12.5146 + 12.5146i 0.471996 + 0.471996i
\(704\) 13.3277 + 34.7195i 0.502308 + 1.30854i
\(705\) 5.69473 + 3.52702i 0.214476 + 0.132835i
\(706\) 8.09101 + 24.1814i 0.304509 + 0.910079i
\(707\) 18.8828 32.1494i 0.710159 1.20910i
\(708\) −0.835920 + 5.94794i −0.0314158 + 0.223537i
\(709\) −15.4871 −0.581629 −0.290815 0.956779i \(-0.593926\pi\)
−0.290815 + 0.956779i \(0.593926\pi\)
\(710\) −7.85689 + 4.85785i −0.294864 + 0.182312i
\(711\) 3.22756 0.121043
\(712\) −0.706777 3.81338i −0.0264876 0.142912i
\(713\) −0.369885 0.369885i −0.0138523 0.0138523i
\(714\) 8.59717 + 13.2019i 0.321741 + 0.494068i
\(715\) 30.0314 7.05934i 1.12311 0.264004i
\(716\) −13.8322 18.3559i −0.516933 0.685991i
\(717\) −9.10724 9.10724i −0.340116 0.340116i
\(718\) 3.56654 7.15338i 0.133102 0.266962i
\(719\) 26.6840 0.995145 0.497573 0.867422i \(-0.334225\pi\)
0.497573 + 0.867422i \(0.334225\pi\)
\(720\) 15.8359 14.3733i 0.590168 0.535662i
\(721\) 24.9532 6.48700i 0.929307 0.241589i
\(722\) 16.2034 + 8.07872i 0.603030 + 0.300659i
\(723\) 7.24807 + 7.24807i 0.269559 + 0.269559i
\(724\) 4.35887 + 5.78439i 0.161996 + 0.214975i
\(725\) 4.74729 + 9.53985i 0.176310 + 0.354301i
\(726\) −11.1046 + 3.71554i −0.412129 + 0.137897i
\(727\) −0.469475 + 0.469475i −0.0174119 + 0.0174119i −0.715759 0.698347i \(-0.753919\pi\)
0.698347 + 0.715759i \(0.253919\pi\)
\(728\) −20.1164 + 9.41145i −0.745563 + 0.348811i
\(729\) 0.547092i 0.0202627i
\(730\) 7.93937 + 1.87267i 0.293849 + 0.0693107i
\(731\) −42.6541 −1.57762
\(732\) −9.59742 1.34881i −0.354731 0.0498536i
\(733\) 36.1499 36.1499i 1.33523 1.33523i 0.434604 0.900622i \(-0.356888\pi\)
0.900622 0.434604i \(-0.143112\pi\)
\(734\) −46.7069 + 15.6279i −1.72398 + 0.576838i
\(735\) 9.02377 8.23202i 0.332847 0.303643i
\(736\) 1.51021 + 34.5866i 0.0556671 + 1.27488i
\(737\) −0.875723 0.875723i −0.0322577 0.0322577i
\(738\) −35.2665 17.5832i −1.29818 0.647246i
\(739\) 15.8043 0.581371 0.290686 0.956819i \(-0.406117\pi\)
0.290686 + 0.956819i \(0.406117\pi\)
\(740\) 20.3396 24.4367i 0.747697 0.898312i
\(741\) −5.76544 −0.211799
\(742\) −20.0844 4.24254i −0.737323 0.155749i
\(743\) −24.2752 + 24.2752i −0.890570 + 0.890570i −0.994577 0.104006i \(-0.966834\pi\)
0.104006 + 0.994577i \(0.466834\pi\)
\(744\) 0.106856 0.155478i 0.00391754 0.00570008i
\(745\) −21.8773 + 35.3231i −0.801521 + 1.29414i
\(746\) 8.29299 + 24.7851i 0.303628 + 0.907446i
\(747\) 28.2807 + 28.2807i 1.03474 + 1.03474i
\(748\) 6.98164 49.6775i 0.255274 1.81639i
\(749\) 0.947517 + 3.64477i 0.0346215 + 0.133177i
\(750\) 12.0133 2.81423i 0.438664 0.102761i
\(751\) 29.5770 1.07928 0.539640 0.841896i \(-0.318561\pi\)
0.539640 + 0.841896i \(0.318561\pi\)
\(752\) 7.44444 + 13.4300i 0.271471 + 0.489743i
\(753\) 6.20600 6.20600i 0.226159 0.226159i
\(754\) −8.48249 + 2.83821i −0.308914 + 0.103361i
\(755\) 18.2499 29.4664i 0.664183 1.07239i
\(756\) −17.4392 13.8358i −0.634257 0.503202i
\(757\) 6.37366 6.37366i 0.231655 0.231655i −0.581728 0.813383i \(-0.697623\pi\)
0.813383 + 0.581728i \(0.197623\pi\)
\(758\) 1.58551 + 0.790504i 0.0575883 + 0.0287124i
\(759\) −22.2010 −0.805845
\(760\) −5.71202 + 14.6719i −0.207197 + 0.532207i
\(761\) 19.2317i 0.697147i −0.937281 0.348574i \(-0.886666\pi\)
0.937281 0.348574i \(-0.113334\pi\)
\(762\) −7.28137 3.63035i −0.263776 0.131514i
\(763\) 8.57037 14.5917i 0.310268 0.528256i
\(764\) 10.0023 + 13.2734i 0.361869 + 0.480215i
\(765\) −28.0826 + 6.60125i −1.01533 + 0.238669i
\(766\) −2.43021 7.26311i −0.0878071 0.262427i
\(767\) 8.07629 + 8.07629i 0.291618 + 0.291618i
\(768\) −12.1657 + 2.80875i −0.438992 + 0.101352i
\(769\) 6.50297 0.234503 0.117251 0.993102i \(-0.462592\pi\)
0.117251 + 0.993102i \(0.462592\pi\)
\(770\) −38.8839 + 0.882771i −1.40128 + 0.0318128i
\(771\) 12.3610i 0.445172i
\(772\) −10.4303 1.46586i −0.375393 0.0527575i
\(773\) 10.2963 10.2963i 0.370331 0.370331i −0.497267 0.867598i \(-0.665663\pi\)
0.867598 + 0.497267i \(0.165663\pi\)
\(774\) 25.3499 8.48196i 0.911182 0.304878i
\(775\) −0.382614 + 0.190399i −0.0137439 + 0.00683934i
\(776\) 32.4239 + 22.2842i 1.16395 + 0.799958i
\(777\) −12.6565 7.43374i −0.454050 0.266684i
\(778\) 43.5154 + 21.6959i 1.56010 + 0.777836i
\(779\) 29.0115 1.03945
\(780\) 0.943778 + 10.3142i 0.0337927 + 0.369307i
\(781\) 13.5794i 0.485911i
\(782\) 20.8369 41.7924i 0.745125 1.49449i
\(783\) −6.33967 6.33967i −0.226561 0.226561i
\(784\) 27.2663 6.36765i 0.973798 0.227416i
\(785\) 24.1685 5.68118i 0.862611 0.202770i
\(786\) −20.4132 + 6.83018i −0.728115 + 0.243624i
\(787\) 25.3866 + 25.3866i 0.904934 + 0.904934i 0.995858 0.0909241i \(-0.0289821\pi\)
−0.0909241 + 0.995858i \(0.528982\pi\)
\(788\) 35.7584 + 5.02546i 1.27384 + 0.179024i
\(789\) 6.66838i 0.237401i
\(790\) 2.24482 + 3.63069i 0.0798672 + 0.129174i
\(791\) −3.15000 12.1170i −0.112001 0.430830i
\(792\) 5.72932 + 30.9123i 0.203582 + 1.09842i
\(793\) −13.0317 + 13.0317i −0.462768 + 0.462768i
\(794\) 9.14719 + 27.3380i 0.324622 + 0.970189i
\(795\) −5.04062 + 8.13860i −0.178772 + 0.288646i
\(796\) −8.78556 11.6588i −0.311396 0.413235i
\(797\) −4.02491 4.02491i −0.142569 0.142569i 0.632220 0.774789i \(-0.282144\pi\)
−0.774789 + 0.632220i \(0.782144\pi\)
\(798\) 7.11181 + 1.50226i 0.251755 + 0.0531796i
\(799\) 20.7130i 0.732773i
\(800\) 27.1826 + 7.81689i 0.961052 + 0.276369i
\(801\) 3.27858i 0.115843i
\(802\) −6.26749 3.12485i −0.221313 0.110342i
\(803\) −8.47931 + 8.47931i −0.299228 + 0.299228i
\(804\) 0.332063 0.250228i 0.0117110 0.00882488i
\(805\) −34.5869 10.7061i −1.21903 0.377340i
\(806\) −0.113832 0.340207i −0.00400956 0.0119833i
\(807\) −14.7905 14.7905i −0.520651 0.520651i
\(808\) −7.26380 39.1915i −0.255540 1.37875i
\(809\) 42.5226i 1.49501i −0.664254 0.747507i \(-0.731250\pi\)
0.664254 0.747507i \(-0.268750\pi\)
\(810\) 10.4634 6.46945i 0.367648 0.227313i
\(811\) −20.6990 −0.726840 −0.363420 0.931625i \(-0.618391\pi\)
−0.363420 + 0.931625i \(0.618391\pi\)
\(812\) 11.2029 1.29077i 0.393145 0.0452972i
\(813\) −14.4142 14.4142i −0.505528 0.505528i
\(814\) 14.8304 + 44.3234i 0.519806 + 1.55353i
\(815\) −28.3624 + 6.66702i −0.993493 + 0.233536i
\(816\) 16.1897 + 4.64228i 0.566754 + 0.162512i
\(817\) −13.9157 + 13.9157i −0.486847 + 0.486847i
\(818\) 20.3945 + 10.1683i 0.713077 + 0.355526i
\(819\) −18.1707 + 4.72378i −0.634937 + 0.165062i
\(820\) −4.74906 51.9007i −0.165845 1.81245i
\(821\) 26.1394i 0.912271i −0.889910 0.456136i \(-0.849233\pi\)
0.889910 0.456136i \(-0.150767\pi\)
\(822\) 12.6893 + 6.32666i 0.442592 + 0.220668i
\(823\) −29.5764 + 29.5764i −1.03097 + 1.03097i −0.0314647 + 0.999505i \(0.510017\pi\)
−0.999505 + 0.0314647i \(0.989983\pi\)
\(824\) 15.6117 22.7153i 0.543859 0.791324i
\(825\) −5.76851 + 17.1966i −0.200834 + 0.598707i
\(826\) −7.85792 12.0667i −0.273412 0.419854i
\(827\) −23.5260 + 23.5260i −0.818079 + 0.818079i −0.985829 0.167751i \(-0.946350\pi\)
0.167751 + 0.985829i \(0.446350\pi\)
\(828\) −4.07300 + 28.9812i −0.141547 + 1.00717i
\(829\) 42.3287i 1.47014i 0.677993 + 0.735068i \(0.262850\pi\)
−0.677993 + 0.735068i \(0.737150\pi\)
\(830\) −12.1433 + 51.4826i −0.421499 + 1.78699i
\(831\) 16.6759i 0.578481i
\(832\) −9.65686 + 21.6899i −0.334791 + 0.751963i
\(833\) −36.3327 10.3189i −1.25885 0.357529i
\(834\) 2.96062 + 8.84835i 0.102518 + 0.306393i
\(835\) −9.98191 42.4644i −0.345438 1.46954i
\(836\) −13.9293 18.4847i −0.481754 0.639307i
\(837\) 0.254265 0.254265i 0.00878867 0.00878867i
\(838\) −11.7428 + 23.5525i −0.405649 + 0.813607i
\(839\) 37.7176 1.30216 0.651078 0.759011i \(-0.274317\pi\)
0.651078 + 0.759011i \(0.274317\pi\)
\(840\) 1.52333 12.9687i 0.0525599 0.447463i
\(841\) −24.4582 −0.843385
\(842\) −17.7701 + 35.6413i −0.612397 + 1.22828i
\(843\) −1.13046 + 1.13046i −0.0389351 + 0.0389351i
\(844\) −32.6921 + 24.6354i −1.12531 + 0.847984i
\(845\) −7.96911 4.93565i −0.274146 0.169792i
\(846\) 4.11887 + 12.3100i 0.141610 + 0.423226i
\(847\) 14.2174 24.2063i 0.488516 0.831738i
\(848\) −19.1935 + 10.6392i −0.659106 + 0.365351i
\(849\) 7.61766i 0.261438i
\(850\) −26.9577 26.9989i −0.924640 0.926054i
\(851\) 43.5086i 1.49146i
\(852\) 4.51467 + 0.634488i 0.154670 + 0.0217372i
\(853\) 4.87957 4.87957i 0.167073 0.167073i −0.618618 0.785692i \(-0.712307\pi\)
0.785692 + 0.618618i \(0.212307\pi\)
\(854\) 19.4705 12.6793i 0.666265 0.433877i
\(855\) −7.00817 + 11.3154i −0.239674 + 0.386979i
\(856\) 3.31788 + 2.28031i 0.113403 + 0.0779392i
\(857\) −35.5786 + 35.5786i −1.21534 + 1.21534i −0.246097 + 0.969245i \(0.579148\pi\)
−0.969245 + 0.246097i \(0.920852\pi\)
\(858\) −13.6260 6.79367i −0.465185 0.231932i
\(859\) 10.7279i 0.366030i −0.983110 0.183015i \(-0.941414\pi\)
0.983110 0.183015i \(-0.0585857\pi\)
\(860\) 27.1726 + 22.6167i 0.926578 + 0.771224i
\(861\) −23.2868 + 6.05379i −0.793613 + 0.206313i
\(862\) −23.3940 11.6638i −0.796802 0.397270i
\(863\) 18.6740 18.6740i 0.635672 0.635672i −0.313813 0.949485i \(-0.601607\pi\)
0.949485 + 0.313813i \(0.101607\pi\)
\(864\) −23.7754 + 1.03814i −0.808855 + 0.0353183i
\(865\) −0.130575 0.555486i −0.00443970 0.0188871i
\(866\) −6.69690 20.0149i −0.227570 0.680133i
\(867\) −6.68397 6.68397i −0.227000 0.227000i
\(868\) 0.0517689 + 0.449314i 0.00175715 + 0.0152507i
\(869\) −6.27509 −0.212868
\(870\) 1.20733 5.11861i 0.0409325 0.173537i
\(871\) 0.790653i 0.0267903i
\(872\) −3.29684 17.7879i −0.111645 0.602376i
\(873\) 23.5179 + 23.5179i 0.795960 + 0.795960i
\(874\) −6.83661 20.4324i −0.231252 0.691137i
\(875\) −17.2795 + 24.0087i −0.584155 + 0.811642i
\(876\) −2.42287 3.21525i −0.0818612 0.108633i
\(877\) 33.2618 33.2618i 1.12317 1.12317i 0.131908 0.991262i \(-0.457890\pi\)
0.991262 0.131908i \(-0.0421104\pi\)
\(878\) 7.32288 + 3.65105i 0.247135 + 0.123217i
\(879\) 11.7210i 0.395338i
\(880\) −30.7884 + 27.9449i −1.03788 + 0.942022i
\(881\) 20.6136i 0.694489i 0.937775 + 0.347245i \(0.112883\pi\)
−0.937775 + 0.347245i \(0.887117\pi\)
\(882\) 23.6449 1.09227i 0.796165 0.0367785i
\(883\) −6.41892 6.41892i −0.216014 0.216014i 0.590802 0.806816i \(-0.298811\pi\)
−0.806816 + 0.590802i \(0.798811\pi\)
\(884\) 25.5776 19.2741i 0.860267 0.648260i
\(885\) −6.53717 + 1.53666i −0.219745 + 0.0516543i
\(886\) −0.282389 0.843969i −0.00948704 0.0283537i
\(887\) 15.0032 15.0032i 0.503757 0.503757i −0.408846 0.912603i \(-0.634069\pi\)
0.912603 + 0.408846i \(0.134069\pi\)
\(888\) −15.4288 + 2.85960i −0.517758 + 0.0959620i
\(889\) 18.8783 4.90771i 0.633156 0.164599i
\(890\) 3.68808 2.28031i 0.123625 0.0764361i
\(891\) 18.0845i 0.605852i
\(892\) 0.291257 2.07242i 0.00975200 0.0693898i
\(893\) −6.75749 6.75749i −0.226131 0.226131i
\(894\) 19.4466 6.50674i 0.650390 0.217618i
\(895\) 13.5304 21.8463i 0.452273 0.730241i
\(896\) 17.5636 24.2388i 0.586758 0.809762i
\(897\) −10.0222 10.0222i −0.334631 0.334631i
\(898\) −18.6863 + 37.4790i −0.623570 + 1.25069i
\(899\) 0.182159i 0.00607533i
\(900\) 21.3901 + 10.6851i 0.713004 + 0.356170i
\(901\) 29.6019 0.986182
\(902\) 68.5658 + 34.1856i 2.28299 + 1.13825i
\(903\) 8.26599 14.0735i 0.275075 0.468337i
\(904\) −11.0302 7.58084i −0.366860 0.252135i
\(905\) −4.26379 + 6.88432i −0.141733 + 0.228842i
\(906\) −16.2222 + 5.42789i −0.538947 + 0.180330i
\(907\) 7.67879 7.67879i 0.254970 0.254970i −0.568035 0.823005i \(-0.692296\pi\)
0.823005 + 0.568035i \(0.192296\pi\)
\(908\) −5.49266 + 39.0827i −0.182280 + 1.29701i
\(909\) 33.6952i 1.11760i
\(910\) −17.9518 17.1548i −0.595097 0.568676i
\(911\) 5.54831 0.183824 0.0919119 0.995767i \(-0.470702\pi\)
0.0919119 + 0.995767i \(0.470702\pi\)
\(912\) 6.79632 3.76729i 0.225049 0.124747i
\(913\) −54.9838 54.9838i −1.81970 1.81970i
\(914\) −11.4450 34.2053i −0.378565 1.13141i
\(915\) −2.47951 10.5482i −0.0819701 0.348712i
\(916\) −14.9455 + 11.2623i −0.493813 + 0.372116i
\(917\) 26.1355 44.4978i 0.863070 1.46945i
\(918\) 28.7288 + 14.3236i 0.948191 + 0.472750i
\(919\) 27.0724i 0.893038i −0.894774 0.446519i \(-0.852664\pi\)
0.894774 0.446519i \(-0.147336\pi\)
\(920\) −35.4338 + 15.5752i −1.16822 + 0.513498i
\(921\) 0.0690461 0.00227515
\(922\) −22.5663 11.2511i −0.743180 0.370535i
\(923\) 6.13015 6.13015i 0.201776 0.201776i
\(924\) 15.0379 + 11.9306i 0.494709 + 0.392488i
\(925\) 33.7011 + 11.3049i 1.10809 + 0.371703i
\(926\) −18.3597 + 6.14308i −0.603337 + 0.201874i
\(927\) 16.4760 16.4760i 0.541141 0.541141i
\(928\) 8.14464 8.88838i 0.267361 0.291775i
\(929\) 24.3594 0.799205 0.399603 0.916688i \(-0.369148\pi\)
0.399603 + 0.916688i \(0.369148\pi\)
\(930\) 0.205292 + 0.0484225i 0.00673178 + 0.00158784i
\(931\) −15.2198 + 8.48684i −0.498809 + 0.278145i
\(932\) 37.6120 + 5.28596i 1.23202 + 0.173147i
\(933\) 3.34547 + 3.34547i 0.109526 + 0.109526i
\(934\) −13.5295 40.4352i −0.442698 1.32308i
\(935\) 54.5988 12.8343i 1.78557 0.419726i
\(936\) −11.3683 + 16.5411i −0.371585 + 0.540662i
\(937\) −0.272375 + 0.272375i −0.00889812 + 0.00889812i −0.711542 0.702644i \(-0.752003\pi\)
0.702644 + 0.711542i \(0.252003\pi\)
\(938\) −0.206016 + 0.975291i −0.00672665 + 0.0318444i
\(939\) 8.62643 0.281513
\(940\) −10.9828 + 13.1951i −0.358218 + 0.430377i
\(941\) 25.5665 0.833443 0.416721 0.909034i \(-0.363179\pi\)
0.416721 + 0.909034i \(0.363179\pi\)
\(942\) −10.9659 5.46738i −0.357288 0.178137i
\(943\) 50.4313 + 50.4313i 1.64227 + 1.64227i
\(944\) −14.7976 4.24311i −0.481622 0.138101i
\(945\) 7.35955 23.7756i 0.239406 0.773420i
\(946\) −49.2857 + 16.4908i −1.60242 + 0.536162i
\(947\) −27.0080 + 27.0080i −0.877643 + 0.877643i −0.993290 0.115647i \(-0.963106\pi\)
0.115647 + 0.993290i \(0.463106\pi\)
\(948\) 0.293199 2.08624i 0.00952265 0.0677579i
\(949\) −7.65561 −0.248512
\(950\) −17.6030 0.0134496i −0.571117 0.000436362i
\(951\) 10.4445i 0.338685i
\(952\) −36.5727 + 17.1105i −1.18533 + 0.554556i
\(953\) 25.7052 25.7052i 0.832673 0.832673i −0.155209 0.987882i \(-0.549605\pi\)
0.987882 + 0.155209i \(0.0496050\pi\)
\(954\) −17.5927 + 5.88647i −0.569586 + 0.190581i
\(955\) −9.78408 + 15.7974i −0.316605 + 0.511192i
\(956\) 26.3625 19.8656i 0.852624 0.642500i
\(957\) 5.46671 + 5.46671i 0.176714 + 0.176714i
\(958\) 42.3050 + 21.0925i 1.36681 + 0.681467i
\(959\) −32.8994 + 8.55273i −1.06238 + 0.276182i
\(960\) −7.85209 11.5417i −0.253425 0.372507i
\(961\) 30.9927 0.999764
\(962\) −13.3140 + 26.7037i −0.429260 + 0.860963i
\(963\) 2.40654 + 2.40654i 0.0775498 + 0.0775498i
\(964\) −20.9808 + 15.8102i −0.675746 + 0.509213i
\(965\) −2.69467 11.4635i −0.0867447 0.369024i
\(966\) 9.75119 + 14.9740i 0.313739 + 0.481781i
\(967\) 24.8907 + 24.8907i 0.800429 + 0.800429i 0.983163 0.182733i \(-0.0584944\pi\)
−0.182733 + 0.983163i \(0.558494\pi\)
\(968\) −5.46914 29.5085i −0.175785 0.948439i
\(969\) −10.4819 −0.336727
\(970\) −10.0982 + 42.8124i −0.324234 + 1.37462i
\(971\) 37.0215 1.18807 0.594037 0.804437i \(-0.297533\pi\)
0.594037 + 0.804437i \(0.297533\pi\)
\(972\) −31.0084 4.35790i −0.994595 0.139780i
\(973\) −19.2881 11.3288i −0.618348 0.363183i
\(974\) −5.28061 15.7820i −0.169202 0.505689i
\(975\) −10.3671 + 5.15895i −0.332013 + 0.165219i
\(976\) 6.84655 23.8770i 0.219153 0.764284i
\(977\) 20.7322 + 20.7322i 0.663280 + 0.663280i 0.956152 0.292872i \(-0.0946108\pi\)
−0.292872 + 0.956152i \(0.594611\pi\)
\(978\) 12.8688 + 6.41612i 0.411498 + 0.205165i
\(979\) 6.37429i 0.203723i
\(980\) 17.6741 + 25.8385i 0.564578 + 0.825380i
\(981\) 15.2933i 0.488278i
\(982\) −0.857585 + 1.72005i −0.0273666 + 0.0548891i
\(983\) −18.5754 18.5754i −0.592463 0.592463i 0.345833 0.938296i \(-0.387596\pi\)
−0.938296 + 0.345833i \(0.887596\pi\)
\(984\) −14.5691 + 21.1983i −0.464447 + 0.675778i
\(985\) 9.23824 + 39.3007i 0.294355 + 1.25223i
\(986\) −15.4217 + 5.16003i −0.491126 + 0.164329i
\(987\) 6.83415 + 4.01400i 0.217533 + 0.127767i
\(988\) 2.05646 14.6326i 0.0654246 0.465525i
\(989\) −48.3797 −1.53839
\(990\) −29.8966 + 18.4848i −0.950175 + 0.587485i
\(991\) −53.0136 −1.68403 −0.842016 0.539453i \(-0.818631\pi\)
−0.842016 + 0.539453i \(0.818631\pi\)
\(992\) 0.356486 + 0.326656i 0.0113184 + 0.0103714i
\(993\) −1.27676 1.27676i −0.0405167 0.0405167i
\(994\) −9.15899 + 5.96440i −0.290506 + 0.189179i
\(995\) 8.59392 13.8758i 0.272446 0.439891i
\(996\) 20.8492 15.7110i 0.660631 0.497823i
\(997\) 31.6721 + 31.6721i 1.00306 + 1.00306i 0.999995 + 0.00306877i \(0.000976823\pi\)
0.00306877 + 0.999995i \(0.499023\pi\)
\(998\) 4.25928 + 2.12360i 0.134825 + 0.0672213i
\(999\) −29.9085 −0.946264
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 280.2.s.c.237.32 yes 72
4.3 odd 2 1120.2.w.c.657.16 72
5.3 odd 4 inner 280.2.s.c.13.24 yes 72
7.6 odd 2 inner 280.2.s.c.237.31 yes 72
8.3 odd 2 1120.2.w.c.657.21 72
8.5 even 2 inner 280.2.s.c.237.23 yes 72
20.3 even 4 1120.2.w.c.433.15 72
28.27 even 2 1120.2.w.c.657.22 72
35.13 even 4 inner 280.2.s.c.13.23 72
40.3 even 4 1120.2.w.c.433.22 72
40.13 odd 4 inner 280.2.s.c.13.31 yes 72
56.13 odd 2 inner 280.2.s.c.237.24 yes 72
56.27 even 2 1120.2.w.c.657.15 72
140.83 odd 4 1120.2.w.c.433.21 72
280.13 even 4 inner 280.2.s.c.13.32 yes 72
280.83 odd 4 1120.2.w.c.433.16 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.s.c.13.23 72 35.13 even 4 inner
280.2.s.c.13.24 yes 72 5.3 odd 4 inner
280.2.s.c.13.31 yes 72 40.13 odd 4 inner
280.2.s.c.13.32 yes 72 280.13 even 4 inner
280.2.s.c.237.23 yes 72 8.5 even 2 inner
280.2.s.c.237.24 yes 72 56.13 odd 2 inner
280.2.s.c.237.31 yes 72 7.6 odd 2 inner
280.2.s.c.237.32 yes 72 1.1 even 1 trivial
1120.2.w.c.433.15 72 20.3 even 4
1120.2.w.c.433.16 72 280.83 odd 4
1120.2.w.c.433.21 72 140.83 odd 4
1120.2.w.c.433.22 72 40.3 even 4
1120.2.w.c.657.15 72 56.27 even 2
1120.2.w.c.657.16 72 4.3 odd 2
1120.2.w.c.657.21 72 8.3 odd 2
1120.2.w.c.657.22 72 28.27 even 2