Properties

Label 280.2.w.a.43.26
Level $280$
Weight $2$
Character 280.43
Analytic conductor $2.236$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [280,2,Mod(43,280)]
 
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([2, 2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.w (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 43.26
Character \(\chi\) \(=\) 280.43
Dual form 280.2.w.a.267.26

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.888618 - 1.10016i) q^{2} +(-0.558179 - 0.558179i) q^{3} +(-0.420716 - 1.95525i) q^{4} +(2.23601 - 0.0162376i) q^{5} +(-1.11010 + 0.118080i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.52495 - 1.27461i) q^{8} -2.37687i q^{9} +O(q^{10})\) \(q+(0.888618 - 1.10016i) q^{2} +(-0.558179 - 0.558179i) q^{3} +(-0.420716 - 1.95525i) q^{4} +(2.23601 - 0.0162376i) q^{5} +(-1.11010 + 0.118080i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-2.52495 - 1.27461i) q^{8} -2.37687i q^{9} +(1.96909 - 2.47440i) q^{10} -0.332508 q^{11} +(-0.856544 + 1.32621i) q^{12} +(-0.344065 + 0.344065i) q^{13} +(1.40628 - 0.149585i) q^{14} +(-1.25716 - 1.23903i) q^{15} +(-3.64600 + 1.64521i) q^{16} +(2.45246 - 2.45246i) q^{17} +(-2.61495 - 2.11213i) q^{18} +3.31224i q^{19} +(-0.972474 - 4.36512i) q^{20} -0.789384i q^{21} +(-0.295473 + 0.365813i) q^{22} +(-3.67636 + 3.67636i) q^{23} +(0.697911 + 2.12084i) q^{24} +(4.99947 - 0.0726147i) q^{25} +(0.0727851 + 0.684269i) q^{26} +(-3.00126 + 3.00126i) q^{27} +(1.08508 - 1.68006i) q^{28} -4.73736 q^{29} +(-2.48027 + 0.282053i) q^{30} -6.34377i q^{31} +(-1.42990 + 5.47315i) q^{32} +(0.185599 + 0.185599i) q^{33} +(-0.518806 - 4.87741i) q^{34} +(1.59258 + 1.56962i) q^{35} +(-4.64738 + 0.999989i) q^{36} +(3.90552 + 3.90552i) q^{37} +(3.64400 + 2.94331i) q^{38} +0.384099 q^{39} +(-5.66650 - 2.80905i) q^{40} +11.7742 q^{41} +(-0.868451 - 0.701461i) q^{42} +(4.00615 + 4.00615i) q^{43} +(0.139891 + 0.650136i) q^{44} +(-0.0385947 - 5.31471i) q^{45} +(0.777715 + 7.31147i) q^{46} +(8.92790 + 8.92790i) q^{47} +(2.95344 + 1.11680i) q^{48} +1.00000i q^{49} +(4.36273 - 5.56476i) q^{50} -2.73783 q^{51} +(0.817486 + 0.527979i) q^{52} +(-6.32001 + 6.32001i) q^{53} +(0.634900 + 5.96884i) q^{54} +(-0.743491 + 0.00539912i) q^{55} +(-0.884120 - 2.68670i) q^{56} +(1.84882 - 1.84882i) q^{57} +(-4.20971 + 5.21187i) q^{58} -1.33422i q^{59} +(-1.89371 + 2.97933i) q^{60} +4.71238i q^{61} +(-6.97919 - 5.63719i) q^{62} +(1.68070 - 1.68070i) q^{63} +(4.75072 + 6.43666i) q^{64} +(-0.763745 + 0.774919i) q^{65} +(0.369116 - 0.0392625i) q^{66} +(-5.65095 + 5.65095i) q^{67} +(-5.82697 - 3.76338i) q^{68} +4.10413 q^{69} +(3.14203 - 0.357307i) q^{70} -13.9236i q^{71} +(-3.02959 + 6.00148i) q^{72} +(2.81208 + 2.81208i) q^{73} +(7.76723 - 0.826193i) q^{74} +(-2.83113 - 2.75007i) q^{75} +(6.47625 - 1.39351i) q^{76} +(-0.235119 - 0.235119i) q^{77} +(0.341318 - 0.422572i) q^{78} -9.77168 q^{79} +(-8.12577 + 3.73791i) q^{80} -3.78014 q^{81} +(10.4628 - 12.9536i) q^{82} +(-7.54949 - 7.54949i) q^{83} +(-1.54344 + 0.332107i) q^{84} +(5.44391 - 5.52355i) q^{85} +(7.96734 - 0.847479i) q^{86} +(2.64430 + 2.64430i) q^{87} +(0.839565 + 0.423819i) q^{88} -3.25251i q^{89} +(-5.88134 - 4.68028i) q^{90} -0.486581 q^{91} +(8.73490 + 5.64149i) q^{92} +(-3.54096 + 3.54096i) q^{93} +(17.7556 - 1.88865i) q^{94} +(0.0537827 + 7.40619i) q^{95} +(3.85314 - 2.25686i) q^{96} +(-5.14743 + 5.14743i) q^{97} +(1.10016 + 0.888618i) q^{98} +0.790329i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 8 q^{6} + 16 q^{10} - 16 q^{12} - 8 q^{16} + 8 q^{17} - 28 q^{18} - 20 q^{20} - 36 q^{22} - 8 q^{25} - 32 q^{26} - 4 q^{30} + 40 q^{32} + 64 q^{36} - 4 q^{40} + 20 q^{42} - 64 q^{43} + 48 q^{46} - 80 q^{48} - 32 q^{51} + 16 q^{52} - 24 q^{56} + 4 q^{58} - 80 q^{60} - 40 q^{62} - 8 q^{65} + 32 q^{66} - 24 q^{68} + 40 q^{72} - 40 q^{73} + 112 q^{75} - 8 q^{76} + 28 q^{78} - 20 q^{80} - 72 q^{81} + 24 q^{82} + 80 q^{83} + 8 q^{86} - 88 q^{88} + 136 q^{90} - 96 q^{92} - 56 q^{96} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.888618 1.10016i 0.628348 0.777933i
\(3\) −0.558179 0.558179i −0.322265 0.322265i 0.527371 0.849635i \(-0.323178\pi\)
−0.849635 + 0.527371i \(0.823178\pi\)
\(4\) −0.420716 1.95525i −0.210358 0.977624i
\(5\) 2.23601 0.0162376i 0.999974 0.00726167i
\(6\) −1.11010 + 0.118080i −0.453195 + 0.0482059i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) −2.52495 1.27461i −0.892704 0.450644i
\(9\) 2.37687i 0.792291i
\(10\) 1.96909 2.47440i 0.622682 0.782475i
\(11\) −0.332508 −0.100255 −0.0501275 0.998743i \(-0.515963\pi\)
−0.0501275 + 0.998743i \(0.515963\pi\)
\(12\) −0.856544 + 1.32621i −0.247263 + 0.382845i
\(13\) −0.344065 + 0.344065i −0.0954264 + 0.0954264i −0.753208 0.657782i \(-0.771495\pi\)
0.657782 + 0.753208i \(0.271495\pi\)
\(14\) 1.40628 0.149585i 0.375844 0.0399782i
\(15\) −1.25716 1.23903i −0.324596 0.319916i
\(16\) −3.64600 + 1.64521i −0.911499 + 0.411302i
\(17\) 2.45246 2.45246i 0.594810 0.594810i −0.344117 0.938927i \(-0.611822\pi\)
0.938927 + 0.344117i \(0.111822\pi\)
\(18\) −2.61495 2.11213i −0.616349 0.497834i
\(19\) 3.31224i 0.759879i 0.925011 + 0.379940i \(0.124055\pi\)
−0.925011 + 0.379940i \(0.875945\pi\)
\(20\) −0.972474 4.36512i −0.217452 0.976071i
\(21\) 0.789384i 0.172258i
\(22\) −0.295473 + 0.365813i −0.0629950 + 0.0779916i
\(23\) −3.67636 + 3.67636i −0.766574 + 0.766574i −0.977502 0.210928i \(-0.932352\pi\)
0.210928 + 0.977502i \(0.432352\pi\)
\(24\) 0.697911 + 2.12084i 0.142460 + 0.432914i
\(25\) 4.99947 0.0726147i 0.999895 0.0145229i
\(26\) 0.0727851 + 0.684269i 0.0142743 + 0.134196i
\(27\) −3.00126 + 3.00126i −0.577592 + 0.577592i
\(28\) 1.08508 1.68006i 0.205061 0.317502i
\(29\) −4.73736 −0.879706 −0.439853 0.898070i \(-0.644970\pi\)
−0.439853 + 0.898070i \(0.644970\pi\)
\(30\) −2.48027 + 0.282053i −0.452833 + 0.0514956i
\(31\) 6.34377i 1.13938i −0.821861 0.569688i \(-0.807064\pi\)
0.821861 0.569688i \(-0.192936\pi\)
\(32\) −1.42990 + 5.47315i −0.252773 + 0.967526i
\(33\) 0.185599 + 0.185599i 0.0323086 + 0.0323086i
\(34\) −0.518806 4.87741i −0.0889745 0.836469i
\(35\) 1.59258 + 1.56962i 0.269195 + 0.265313i
\(36\) −4.64738 + 0.999989i −0.774563 + 0.166665i
\(37\) 3.90552 + 3.90552i 0.642064 + 0.642064i 0.951062 0.308999i \(-0.0999938\pi\)
−0.308999 + 0.951062i \(0.599994\pi\)
\(38\) 3.64400 + 2.94331i 0.591135 + 0.477468i
\(39\) 0.384099 0.0615051
\(40\) −5.66650 2.80905i −0.895953 0.444149i
\(41\) 11.7742 1.83883 0.919414 0.393291i \(-0.128664\pi\)
0.919414 + 0.393291i \(0.128664\pi\)
\(42\) −0.868451 0.701461i −0.134005 0.108238i
\(43\) 4.00615 + 4.00615i 0.610931 + 0.610931i 0.943189 0.332257i \(-0.107810\pi\)
−0.332257 + 0.943189i \(0.607810\pi\)
\(44\) 0.139891 + 0.650136i 0.0210894 + 0.0980116i
\(45\) −0.0385947 5.31471i −0.00575335 0.792270i
\(46\) 0.777715 + 7.31147i 0.114668 + 1.07802i
\(47\) 8.92790 + 8.92790i 1.30227 + 1.30227i 0.926859 + 0.375409i \(0.122498\pi\)
0.375409 + 0.926859i \(0.377502\pi\)
\(48\) 2.95344 + 1.11680i 0.426292 + 0.161196i
\(49\) 1.00000i 0.142857i
\(50\) 4.36273 5.56476i 0.616984 0.786976i
\(51\) −2.73783 −0.383372
\(52\) 0.817486 + 0.527979i 0.113365 + 0.0732175i
\(53\) −6.32001 + 6.32001i −0.868120 + 0.868120i −0.992264 0.124145i \(-0.960381\pi\)
0.124145 + 0.992264i \(0.460381\pi\)
\(54\) 0.634900 + 5.96884i 0.0863990 + 0.812257i
\(55\) −0.743491 + 0.00539912i −0.100252 + 0.000728018i
\(56\) −0.884120 2.68670i −0.118146 0.359025i
\(57\) 1.84882 1.84882i 0.244882 0.244882i
\(58\) −4.20971 + 5.21187i −0.552761 + 0.684352i
\(59\) 1.33422i 0.173700i −0.996221 0.0868501i \(-0.972320\pi\)
0.996221 0.0868501i \(-0.0276801\pi\)
\(60\) −1.89371 + 2.97933i −0.244476 + 0.384630i
\(61\) 4.71238i 0.603358i 0.953410 + 0.301679i \(0.0975471\pi\)
−0.953410 + 0.301679i \(0.902453\pi\)
\(62\) −6.97919 5.63719i −0.886357 0.715924i
\(63\) 1.68070 1.68070i 0.211749 0.211749i
\(64\) 4.75072 + 6.43666i 0.593841 + 0.804583i
\(65\) −0.763745 + 0.774919i −0.0947309 + 0.0961168i
\(66\) 0.369116 0.0392625i 0.0454350 0.00483288i
\(67\) −5.65095 + 5.65095i −0.690374 + 0.690374i −0.962314 0.271940i \(-0.912335\pi\)
0.271940 + 0.962314i \(0.412335\pi\)
\(68\) −5.82697 3.76338i −0.706623 0.456377i
\(69\) 4.10413 0.494080
\(70\) 3.14203 0.357307i 0.375544 0.0427064i
\(71\) 13.9236i 1.65243i −0.563354 0.826216i \(-0.690489\pi\)
0.563354 0.826216i \(-0.309511\pi\)
\(72\) −3.02959 + 6.00148i −0.357041 + 0.707281i
\(73\) 2.81208 + 2.81208i 0.329129 + 0.329129i 0.852255 0.523126i \(-0.175234\pi\)
−0.523126 + 0.852255i \(0.675234\pi\)
\(74\) 7.76723 0.826193i 0.902922 0.0960430i
\(75\) −2.83113 2.75007i −0.326911 0.317551i
\(76\) 6.47625 1.39351i 0.742876 0.159847i
\(77\) −0.235119 0.235119i −0.0267943 0.0267943i
\(78\) 0.341318 0.422572i 0.0386466 0.0478468i
\(79\) −9.77168 −1.09940 −0.549700 0.835362i \(-0.685258\pi\)
−0.549700 + 0.835362i \(0.685258\pi\)
\(80\) −8.12577 + 3.73791i −0.908488 + 0.417911i
\(81\) −3.78014 −0.420016
\(82\) 10.4628 12.9536i 1.15542 1.43048i
\(83\) −7.54949 7.54949i −0.828664 0.828664i 0.158668 0.987332i \(-0.449280\pi\)
−0.987332 + 0.158668i \(0.949280\pi\)
\(84\) −1.54344 + 0.332107i −0.168403 + 0.0362358i
\(85\) 5.44391 5.52355i 0.590475 0.599113i
\(86\) 7.96734 0.847479i 0.859141 0.0913860i
\(87\) 2.64430 + 2.64430i 0.283498 + 0.283498i
\(88\) 0.839565 + 0.423819i 0.0894979 + 0.0451792i
\(89\) 3.25251i 0.344765i −0.985030 0.172383i \(-0.944853\pi\)
0.985030 0.172383i \(-0.0551465\pi\)
\(90\) −5.88134 4.68028i −0.619948 0.493345i
\(91\) −0.486581 −0.0510076
\(92\) 8.73490 + 5.64149i 0.910676 + 0.588166i
\(93\) −3.54096 + 3.54096i −0.367181 + 0.367181i
\(94\) 17.7556 1.88865i 1.83135 0.194799i
\(95\) 0.0537827 + 7.40619i 0.00551799 + 0.759859i
\(96\) 3.85314 2.25686i 0.393259 0.230340i
\(97\) −5.14743 + 5.14743i −0.522642 + 0.522642i −0.918368 0.395726i \(-0.870493\pi\)
0.395726 + 0.918368i \(0.370493\pi\)
\(98\) 1.10016 + 0.888618i 0.111133 + 0.0897640i
\(99\) 0.790329i 0.0794310i
\(100\) −2.24534 9.74466i −0.224534 0.974466i
\(101\) 9.75111i 0.970272i −0.874439 0.485136i \(-0.838770\pi\)
0.874439 0.485136i \(-0.161230\pi\)
\(102\) −2.43288 + 3.01206i −0.240891 + 0.298238i
\(103\) −3.23389 + 3.23389i −0.318645 + 0.318645i −0.848246 0.529602i \(-0.822341\pi\)
0.529602 + 0.848246i \(0.322341\pi\)
\(104\) 1.30729 0.430196i 0.128191 0.0421842i
\(105\) −0.0128177 1.76507i −0.00125088 0.172253i
\(106\) 1.33696 + 12.5691i 0.129857 + 1.22082i
\(107\) 2.83452 2.83452i 0.274024 0.274024i −0.556694 0.830718i \(-0.687930\pi\)
0.830718 + 0.556694i \(0.187930\pi\)
\(108\) 7.13088 + 4.60553i 0.686169 + 0.443167i
\(109\) −7.34261 −0.703294 −0.351647 0.936133i \(-0.614378\pi\)
−0.351647 + 0.936133i \(0.614378\pi\)
\(110\) −0.654739 + 0.822759i −0.0624269 + 0.0784470i
\(111\) 4.35996i 0.413829i
\(112\) −3.74145 1.41477i −0.353534 0.133683i
\(113\) −5.54684 5.54684i −0.521803 0.521803i 0.396313 0.918115i \(-0.370290\pi\)
−0.918115 + 0.396313i \(0.870290\pi\)
\(114\) −0.391108 3.67690i −0.0366307 0.344373i
\(115\) −8.16068 + 8.28007i −0.760987 + 0.772120i
\(116\) 1.99309 + 9.26272i 0.185053 + 0.860022i
\(117\) 0.817798 + 0.817798i 0.0756055 + 0.0756055i
\(118\) −1.46785 1.18561i −0.135127 0.109144i
\(119\) 3.46831 0.317939
\(120\) 1.59497 + 4.73087i 0.145600 + 0.431868i
\(121\) −10.8894 −0.989949
\(122\) 5.18438 + 4.18750i 0.469372 + 0.379119i
\(123\) −6.57214 6.57214i −0.592590 0.592590i
\(124\) −12.4037 + 2.66893i −1.11388 + 0.239677i
\(125\) 11.1777 0.243547i 0.999763 0.0217835i
\(126\) −0.355544 3.34255i −0.0316744 0.297778i
\(127\) −5.14901 5.14901i −0.456901 0.456901i 0.440736 0.897637i \(-0.354718\pi\)
−0.897637 + 0.440736i \(0.854718\pi\)
\(128\) 11.3030 + 0.493164i 0.999050 + 0.0435899i
\(129\) 4.47229i 0.393763i
\(130\) 0.173859 + 1.52885i 0.0152484 + 0.134089i
\(131\) −2.41071 −0.210625 −0.105312 0.994439i \(-0.533584\pi\)
−0.105312 + 0.994439i \(0.533584\pi\)
\(132\) 0.284808 0.440977i 0.0247893 0.0383821i
\(133\) −2.34210 + 2.34210i −0.203086 + 0.203086i
\(134\) 1.19543 + 11.2385i 0.103269 + 0.970859i
\(135\) −6.66211 + 6.75957i −0.573383 + 0.581771i
\(136\) −9.31828 + 3.06640i −0.799036 + 0.262942i
\(137\) 1.67262 1.67262i 0.142902 0.142902i −0.632037 0.774938i \(-0.717781\pi\)
0.774938 + 0.632037i \(0.217781\pi\)
\(138\) 3.64701 4.51521i 0.310454 0.384361i
\(139\) 3.97137i 0.336847i 0.985715 + 0.168424i \(0.0538677\pi\)
−0.985715 + 0.168424i \(0.946132\pi\)
\(140\) 2.39896 3.77425i 0.202750 0.318982i
\(141\) 9.96673i 0.839350i
\(142\) −15.3183 12.3728i −1.28548 1.03830i
\(143\) 0.114404 0.114404i 0.00956696 0.00956696i
\(144\) 3.91045 + 8.66607i 0.325871 + 0.722172i
\(145\) −10.5928 + 0.0769233i −0.879683 + 0.00638813i
\(146\) 5.59261 0.594881i 0.462848 0.0492327i
\(147\) 0.558179 0.558179i 0.0460378 0.0460378i
\(148\) 5.99315 9.27938i 0.492634 0.762761i
\(149\) 23.6830 1.94019 0.970093 0.242734i \(-0.0780443\pi\)
0.970093 + 0.242734i \(0.0780443\pi\)
\(150\) −5.54132 + 0.670946i −0.452447 + 0.0547825i
\(151\) 4.67325i 0.380304i −0.981755 0.190152i \(-0.939102\pi\)
0.981755 0.190152i \(-0.0608981\pi\)
\(152\) 4.22182 8.36322i 0.342435 0.678347i
\(153\) −5.82919 5.82919i −0.471262 0.471262i
\(154\) −0.467599 + 0.0497381i −0.0376802 + 0.00400801i
\(155\) −0.103008 14.1847i −0.00827377 1.13935i
\(156\) −0.161597 0.751010i −0.0129381 0.0601289i
\(157\) −10.9134 10.9134i −0.870986 0.870986i 0.121594 0.992580i \(-0.461199\pi\)
−0.992580 + 0.121594i \(0.961199\pi\)
\(158\) −8.68329 + 10.7504i −0.690805 + 0.855259i
\(159\) 7.05539 0.559529
\(160\) −3.10840 + 12.2612i −0.245740 + 0.969336i
\(161\) −5.19916 −0.409751
\(162\) −3.35910 + 4.15877i −0.263916 + 0.326744i
\(163\) 5.80117 + 5.80117i 0.454383 + 0.454383i 0.896806 0.442423i \(-0.145881\pi\)
−0.442423 + 0.896806i \(0.645881\pi\)
\(164\) −4.95362 23.0216i −0.386812 1.79768i
\(165\) 0.418015 + 0.411987i 0.0325424 + 0.0320732i
\(166\) −15.0143 + 1.59705i −1.16533 + 0.123955i
\(167\) 4.69952 + 4.69952i 0.363660 + 0.363660i 0.865158 0.501499i \(-0.167218\pi\)
−0.501499 + 0.865158i \(0.667218\pi\)
\(168\) −1.00616 + 1.99315i −0.0776269 + 0.153775i
\(169\) 12.7632i 0.981788i
\(170\) −1.23925 10.8975i −0.0950463 0.835801i
\(171\) 7.87276 0.602045
\(172\) 6.14756 9.51846i 0.468747 0.725776i
\(173\) −11.7008 + 11.7008i −0.889592 + 0.889592i −0.994484 0.104891i \(-0.966551\pi\)
0.104891 + 0.994484i \(0.466551\pi\)
\(174\) 5.25893 0.559387i 0.398678 0.0424070i
\(175\) 3.58651 + 3.48381i 0.271114 + 0.263352i
\(176\) 1.21232 0.547045i 0.0913822 0.0412351i
\(177\) −0.744731 + 0.744731i −0.0559774 + 0.0559774i
\(178\) −3.57829 2.89024i −0.268204 0.216632i
\(179\) 15.7077i 1.17405i −0.809569 0.587024i \(-0.800299\pi\)
0.809569 0.587024i \(-0.199701\pi\)
\(180\) −10.3753 + 2.31145i −0.773332 + 0.172285i
\(181\) 16.4949i 1.22605i 0.790062 + 0.613027i \(0.210048\pi\)
−0.790062 + 0.613027i \(0.789952\pi\)
\(182\) −0.432385 + 0.535318i −0.0320505 + 0.0396804i
\(183\) 2.63035 2.63035i 0.194441 0.194441i
\(184\) 13.9686 4.59668i 1.02978 0.338872i
\(185\) 8.79620 + 8.66937i 0.646709 + 0.637384i
\(186\) 0.749072 + 7.04220i 0.0549246 + 0.516359i
\(187\) −0.815463 + 0.815463i −0.0596326 + 0.0596326i
\(188\) 13.7002 21.2124i 0.999186 1.54707i
\(189\) −4.24442 −0.308736
\(190\) 8.19581 + 6.52210i 0.594586 + 0.473163i
\(191\) 14.9385i 1.08091i −0.841371 0.540457i \(-0.818251\pi\)
0.841371 0.540457i \(-0.181749\pi\)
\(192\) 0.941055 6.24456i 0.0679148 0.450663i
\(193\) −11.2868 11.2868i −0.812444 0.812444i 0.172556 0.985000i \(-0.444797\pi\)
−0.985000 + 0.172556i \(0.944797\pi\)
\(194\) 1.08891 + 10.2371i 0.0781793 + 0.734981i
\(195\) 0.858850 0.00623685i 0.0615035 0.000446630i
\(196\) 1.95525 0.420716i 0.139661 0.0300512i
\(197\) −15.9354 15.9354i −1.13535 1.13535i −0.989273 0.146075i \(-0.953336\pi\)
−0.146075 0.989273i \(-0.546664\pi\)
\(198\) 0.869490 + 0.702300i 0.0617920 + 0.0499103i
\(199\) 1.10949 0.0786500 0.0393250 0.999226i \(-0.487479\pi\)
0.0393250 + 0.999226i \(0.487479\pi\)
\(200\) −12.7160 6.18904i −0.899154 0.437631i
\(201\) 6.30849 0.444966
\(202\) −10.7278 8.66501i −0.754806 0.609668i
\(203\) −3.34982 3.34982i −0.235111 0.235111i
\(204\) 1.15185 + 5.35313i 0.0806455 + 0.374794i
\(205\) 26.3273 0.191185i 1.83878 0.0133530i
\(206\) 0.684113 + 6.43150i 0.0476644 + 0.448104i
\(207\) 8.73824 + 8.73824i 0.607349 + 0.607349i
\(208\) 0.688400 1.82052i 0.0477319 0.126230i
\(209\) 1.10134i 0.0761816i
\(210\) −1.95325 1.55437i −0.134787 0.107262i
\(211\) 3.66270 0.252150 0.126075 0.992021i \(-0.459762\pi\)
0.126075 + 0.992021i \(0.459762\pi\)
\(212\) 15.0161 + 9.69825i 1.03131 + 0.666079i
\(213\) −7.77188 + 7.77188i −0.532520 + 0.532520i
\(214\) −0.599629 5.63725i −0.0409898 0.385354i
\(215\) 9.02283 + 8.89273i 0.615352 + 0.606479i
\(216\) 11.4035 3.75258i 0.775907 0.255331i
\(217\) 4.48573 4.48573i 0.304511 0.304511i
\(218\) −6.52477 + 8.07806i −0.441913 + 0.547115i
\(219\) 3.13929i 0.212134i
\(220\) 0.323355 + 1.45144i 0.0218006 + 0.0978559i
\(221\) 1.68761i 0.113521i
\(222\) −4.79667 3.87434i −0.321931 0.260029i
\(223\) 3.58964 3.58964i 0.240380 0.240380i −0.576627 0.817007i \(-0.695632\pi\)
0.817007 + 0.576627i \(0.195632\pi\)
\(224\) −4.88119 + 2.85901i −0.326138 + 0.191026i
\(225\) −0.172596 11.8831i −0.0115064 0.792207i
\(226\) −11.0314 + 1.17340i −0.733801 + 0.0780537i
\(227\) 15.5690 15.5690i 1.03335 1.03335i 0.0339274 0.999424i \(-0.489198\pi\)
0.999424 0.0339274i \(-0.0108015\pi\)
\(228\) −4.39273 2.83708i −0.290916 0.187890i
\(229\) −10.1663 −0.671810 −0.335905 0.941896i \(-0.609042\pi\)
−0.335905 + 0.941896i \(0.609042\pi\)
\(230\) 1.85770 + 16.3359i 0.122493 + 1.07716i
\(231\) 0.262477i 0.0172697i
\(232\) 11.9616 + 6.03830i 0.785317 + 0.396434i
\(233\) 16.6989 + 16.6989i 1.09398 + 1.09398i 0.995099 + 0.0988787i \(0.0315256\pi\)
0.0988787 + 0.995099i \(0.468474\pi\)
\(234\) 1.62642 0.173001i 0.106322 0.0113094i
\(235\) 20.1078 + 19.8179i 1.31169 + 1.29278i
\(236\) −2.60872 + 0.561326i −0.169813 + 0.0365392i
\(237\) 5.45434 + 5.45434i 0.354298 + 0.354298i
\(238\) 3.08200 3.81570i 0.199776 0.247335i
\(239\) −27.2384 −1.76190 −0.880952 0.473206i \(-0.843097\pi\)
−0.880952 + 0.473206i \(0.843097\pi\)
\(240\) 6.62205 + 2.44921i 0.427452 + 0.158096i
\(241\) −19.1327 −1.23244 −0.616222 0.787573i \(-0.711338\pi\)
−0.616222 + 0.787573i \(0.711338\pi\)
\(242\) −9.67655 + 11.9802i −0.622032 + 0.770114i
\(243\) 11.1138 + 11.1138i 0.712948 + 0.712948i
\(244\) 9.21387 1.98257i 0.589857 0.126921i
\(245\) 0.0162376 + 2.23601i 0.00103738 + 0.142853i
\(246\) −13.0705 + 1.39030i −0.833347 + 0.0886424i
\(247\) −1.13962 1.13962i −0.0725125 0.0725125i
\(248\) −8.08586 + 16.0177i −0.513452 + 1.01713i
\(249\) 8.42793i 0.534098i
\(250\) 9.66475 12.5137i 0.611253 0.791436i
\(251\) 26.9766 1.70275 0.851374 0.524559i \(-0.175770\pi\)
0.851374 + 0.524559i \(0.175770\pi\)
\(252\) −3.99329 2.57909i −0.251554 0.162468i
\(253\) 1.22242 1.22242i 0.0768528 0.0768528i
\(254\) −10.2403 + 1.08925i −0.642531 + 0.0683454i
\(255\) −6.12181 + 0.0444557i −0.383362 + 0.00278392i
\(256\) 10.5866 11.9969i 0.661661 0.749804i
\(257\) −11.3237 + 11.3237i −0.706353 + 0.706353i −0.965766 0.259413i \(-0.916471\pi\)
0.259413 + 0.965766i \(0.416471\pi\)
\(258\) −4.92025 3.97416i −0.306321 0.247420i
\(259\) 5.52324i 0.343198i
\(260\) 1.83648 + 1.16729i 0.113894 + 0.0723923i
\(261\) 11.2601i 0.696983i
\(262\) −2.14220 + 2.65217i −0.132345 + 0.163852i
\(263\) 12.4550 12.4550i 0.768010 0.768010i −0.209746 0.977756i \(-0.567264\pi\)
0.977756 + 0.209746i \(0.0672636\pi\)
\(264\) −0.232061 0.705194i −0.0142824 0.0434017i
\(265\) −14.0290 + 14.2342i −0.861793 + 0.874401i
\(266\) 0.495460 + 4.65793i 0.0303786 + 0.285596i
\(267\) −1.81548 + 1.81548i −0.111106 + 0.111106i
\(268\) 13.4265 + 8.67157i 0.820152 + 0.529701i
\(269\) −15.7030 −0.957432 −0.478716 0.877970i \(-0.658898\pi\)
−0.478716 + 0.877970i \(0.658898\pi\)
\(270\) 1.51656 + 13.3361i 0.0922951 + 0.811608i
\(271\) 5.72812i 0.347958i 0.984749 + 0.173979i \(0.0556625\pi\)
−0.984749 + 0.173979i \(0.944337\pi\)
\(272\) −4.90685 + 12.9765i −0.297522 + 0.786815i
\(273\) 0.271599 + 0.271599i 0.0164379 + 0.0164379i
\(274\) −0.353835 3.32648i −0.0213759 0.200960i
\(275\) −1.66236 + 0.0241450i −0.100244 + 0.00145600i
\(276\) −1.72668 8.02460i −0.103934 0.483024i
\(277\) −20.6198 20.6198i −1.23892 1.23892i −0.960442 0.278480i \(-0.910170\pi\)
−0.278480 0.960442i \(-0.589830\pi\)
\(278\) 4.36915 + 3.52903i 0.262044 + 0.211657i
\(279\) −15.0783 −0.902717
\(280\) −2.02053 5.99312i −0.120750 0.358157i
\(281\) 18.7401 1.11794 0.558970 0.829188i \(-0.311197\pi\)
0.558970 + 0.829188i \(0.311197\pi\)
\(282\) −10.9650 8.85662i −0.652958 0.527404i
\(283\) 4.19190 + 4.19190i 0.249183 + 0.249183i 0.820635 0.571452i \(-0.193620\pi\)
−0.571452 + 0.820635i \(0.693620\pi\)
\(284\) −27.2242 + 5.85790i −1.61546 + 0.347602i
\(285\) 4.10396 4.16400i 0.243098 0.246654i
\(286\) −0.0242016 0.227525i −0.00143107 0.0134538i
\(287\) 8.32565 + 8.32565i 0.491447 + 0.491447i
\(288\) 13.0090 + 3.39869i 0.766562 + 0.200270i
\(289\) 4.97085i 0.292403i
\(290\) −9.32831 + 11.7221i −0.547777 + 0.688348i
\(291\) 5.74637 0.336858
\(292\) 4.31523 6.68141i 0.252530 0.391000i
\(293\) 5.68735 5.68735i 0.332258 0.332258i −0.521185 0.853444i \(-0.674510\pi\)
0.853444 + 0.521185i \(0.174510\pi\)
\(294\) −0.118080 1.11010i −0.00688656 0.0647421i
\(295\) −0.0216644 2.98332i −0.00126135 0.173696i
\(296\) −4.88321 14.8393i −0.283831 0.862515i
\(297\) 0.997942 0.997942i 0.0579065 0.0579065i
\(298\) 21.0451 26.0551i 1.21911 1.50933i
\(299\) 2.52981i 0.146303i
\(300\) −4.18596 + 6.69257i −0.241677 + 0.386396i
\(301\) 5.66554i 0.326557i
\(302\) −5.14134 4.15274i −0.295851 0.238963i
\(303\) −5.44287 + 5.44287i −0.312684 + 0.312684i
\(304\) −5.44932 12.0764i −0.312540 0.692629i
\(305\) 0.0765176 + 10.5369i 0.00438138 + 0.603342i
\(306\) −11.5930 + 1.23314i −0.662727 + 0.0704937i
\(307\) −3.12720 + 3.12720i −0.178479 + 0.178479i −0.790692 0.612214i \(-0.790279\pi\)
0.612214 + 0.790692i \(0.290279\pi\)
\(308\) −0.360797 + 0.558634i −0.0205583 + 0.0318311i
\(309\) 3.61018 0.205376
\(310\) −15.6971 12.4915i −0.891533 0.709469i
\(311\) 1.94456i 0.110266i 0.998479 + 0.0551331i \(0.0175583\pi\)
−0.998479 + 0.0551331i \(0.982442\pi\)
\(312\) −0.969831 0.489578i −0.0549059 0.0277169i
\(313\) 14.9476 + 14.9476i 0.844891 + 0.844891i 0.989490 0.144599i \(-0.0461893\pi\)
−0.144599 + 0.989490i \(0.546189\pi\)
\(314\) −21.7044 + 2.30868i −1.22485 + 0.130286i
\(315\) 3.73078 3.78536i 0.210205 0.213281i
\(316\) 4.11110 + 19.1061i 0.231268 + 1.07480i
\(317\) 14.3334 + 14.3334i 0.805044 + 0.805044i 0.983879 0.178835i \(-0.0572329\pi\)
−0.178835 + 0.983879i \(0.557233\pi\)
\(318\) 6.26955 7.76208i 0.351579 0.435276i
\(319\) 1.57521 0.0881949
\(320\) 10.7272 + 14.3153i 0.599667 + 0.800249i
\(321\) −3.16434 −0.176616
\(322\) −4.62006 + 5.71992i −0.257466 + 0.318759i
\(323\) 8.12314 + 8.12314i 0.451983 + 0.451983i
\(324\) 1.59037 + 7.39111i 0.0883537 + 0.410617i
\(325\) −1.69516 + 1.74513i −0.0940305 + 0.0968022i
\(326\) 11.5373 1.22721i 0.638990 0.0679688i
\(327\) 4.09849 + 4.09849i 0.226647 + 0.226647i
\(328\) −29.7294 15.0076i −1.64153 0.828656i
\(329\) 12.6260i 0.696092i
\(330\) 0.824708 0.0937848i 0.0453987 0.00516268i
\(331\) −6.19729 −0.340634 −0.170317 0.985389i \(-0.554479\pi\)
−0.170317 + 0.985389i \(0.554479\pi\)
\(332\) −11.5849 + 17.9373i −0.635806 + 0.984438i
\(333\) 9.28293 9.28293i 0.508701 0.508701i
\(334\) 9.34631 0.994159i 0.511407 0.0543980i
\(335\) −12.5438 + 12.7273i −0.685342 + 0.695369i
\(336\) 1.29870 + 2.87809i 0.0708500 + 0.157013i
\(337\) −8.25360 + 8.25360i −0.449602 + 0.449602i −0.895222 0.445620i \(-0.852983\pi\)
0.445620 + 0.895222i \(0.352983\pi\)
\(338\) 14.0416 + 11.3416i 0.763765 + 0.616904i
\(339\) 6.19226i 0.336317i
\(340\) −13.0903 8.32035i −0.709919 0.451234i
\(341\) 2.10936i 0.114228i
\(342\) 6.99588 8.66132i 0.378294 0.468351i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) −5.00902 15.2216i −0.270068 0.820693i
\(345\) 9.17688 0.0666412i 0.494067 0.00358784i
\(346\) 2.47524 + 23.2702i 0.133069 + 1.25102i
\(347\) 8.25513 8.25513i 0.443158 0.443158i −0.449914 0.893072i \(-0.648545\pi\)
0.893072 + 0.449914i \(0.148545\pi\)
\(348\) 4.05776 6.28276i 0.217519 0.336791i
\(349\) 16.8787 0.903495 0.451747 0.892146i \(-0.350801\pi\)
0.451747 + 0.892146i \(0.350801\pi\)
\(350\) 7.01980 0.849962i 0.375224 0.0454324i
\(351\) 2.06525i 0.110235i
\(352\) 0.475453 1.81987i 0.0253417 0.0969992i
\(353\) −3.09866 3.09866i −0.164925 0.164925i 0.619820 0.784744i \(-0.287206\pi\)
−0.784744 + 0.619820i \(0.787206\pi\)
\(354\) 0.157544 + 1.48111i 0.00837337 + 0.0787200i
\(355\) −0.226086 31.1334i −0.0119994 1.65239i
\(356\) −6.35946 + 1.36838i −0.337051 + 0.0725242i
\(357\) −1.93594 1.93594i −0.102461 0.102461i
\(358\) −17.2810 13.9581i −0.913330 0.737711i
\(359\) −21.0490 −1.11092 −0.555461 0.831542i \(-0.687458\pi\)
−0.555461 + 0.831542i \(0.687458\pi\)
\(360\) −6.67675 + 13.4686i −0.351895 + 0.709855i
\(361\) 8.02909 0.422584
\(362\) 18.1470 + 14.6576i 0.953787 + 0.770388i
\(363\) 6.07826 + 6.07826i 0.319026 + 0.319026i
\(364\) 0.204713 + 0.951387i 0.0107299 + 0.0498662i
\(365\) 6.33350 + 6.24218i 0.331511 + 0.326731i
\(366\) −0.556437 5.23119i −0.0290854 0.273439i
\(367\) 25.8405 + 25.8405i 1.34886 + 1.34886i 0.886901 + 0.461960i \(0.152854\pi\)
0.461960 + 0.886901i \(0.347146\pi\)
\(368\) 7.35561 19.4524i 0.383438 1.01403i
\(369\) 27.9859i 1.45689i
\(370\) 17.3542 1.97350i 0.902201 0.102597i
\(371\) −8.93784 −0.464029
\(372\) 8.41320 + 5.43372i 0.436204 + 0.281725i
\(373\) 15.8658 15.8658i 0.821498 0.821498i −0.164825 0.986323i \(-0.552706\pi\)
0.986323 + 0.164825i \(0.0527058\pi\)
\(374\) 0.172507 + 1.62178i 0.00892013 + 0.0838601i
\(375\) −6.37509 6.10321i −0.329208 0.315168i
\(376\) −11.1629 33.9221i −0.575681 1.74940i
\(377\) 1.62996 1.62996i 0.0839472 0.0839472i
\(378\) −3.77167 + 4.66955i −0.193994 + 0.240176i
\(379\) 16.0207i 0.822930i −0.911425 0.411465i \(-0.865017\pi\)
0.911425 0.411465i \(-0.134983\pi\)
\(380\) 14.4583 3.22106i 0.741696 0.165237i
\(381\) 5.74814i 0.294486i
\(382\) −16.4348 13.2747i −0.840879 0.679190i
\(383\) 18.6863 18.6863i 0.954827 0.954827i −0.0441960 0.999023i \(-0.514073\pi\)
0.999023 + 0.0441960i \(0.0140726\pi\)
\(384\) −6.03380 6.58435i −0.307911 0.336006i
\(385\) −0.529545 0.521910i −0.0269881 0.0265990i
\(386\) −22.4470 + 2.38767i −1.14252 + 0.121529i
\(387\) 9.52210 9.52210i 0.484035 0.484035i
\(388\) 12.2301 + 7.89890i 0.620890 + 0.401006i
\(389\) 3.87501 0.196471 0.0982355 0.995163i \(-0.468680\pi\)
0.0982355 + 0.995163i \(0.468680\pi\)
\(390\) 0.756328 0.950417i 0.0382981 0.0481262i
\(391\) 18.0323i 0.911931i
\(392\) 1.27461 2.52495i 0.0643777 0.127529i
\(393\) 1.34561 + 1.34561i 0.0678769 + 0.0678769i
\(394\) −31.6920 + 3.37105i −1.59662 + 0.169831i
\(395\) −21.8496 + 0.158668i −1.09937 + 0.00798347i
\(396\) 1.54529 0.332504i 0.0776537 0.0167090i
\(397\) −25.0494 25.0494i −1.25720 1.25720i −0.952426 0.304769i \(-0.901421\pi\)
−0.304769 0.952426i \(-0.598579\pi\)
\(398\) 0.985917 1.22063i 0.0494196 0.0611844i
\(399\) 2.61463 0.130895
\(400\) −18.1086 + 8.48993i −0.905429 + 0.424497i
\(401\) −27.4614 −1.37136 −0.685679 0.727904i \(-0.740494\pi\)
−0.685679 + 0.727904i \(0.740494\pi\)
\(402\) 5.60583 6.94036i 0.279594 0.346154i
\(403\) 2.18267 + 2.18267i 0.108727 + 0.108727i
\(404\) −19.0658 + 4.10245i −0.948561 + 0.204105i
\(405\) −8.45243 + 0.0613803i −0.420004 + 0.00305001i
\(406\) −6.66206 + 0.708637i −0.330633 + 0.0351691i
\(407\) −1.29862 1.29862i −0.0643701 0.0643701i
\(408\) 6.91287 + 3.48967i 0.342238 + 0.172764i
\(409\) 23.7218i 1.17297i −0.809960 0.586485i \(-0.800511\pi\)
0.809960 0.586485i \(-0.199489\pi\)
\(410\) 23.1846 29.1342i 1.14501 1.43884i
\(411\) −1.86725 −0.0921045
\(412\) 7.68361 + 4.96251i 0.378544 + 0.244485i
\(413\) 0.943433 0.943433i 0.0464233 0.0464233i
\(414\) 17.3784 1.84853i 0.854104 0.0908502i
\(415\) −17.0033 16.7581i −0.834659 0.822624i
\(416\) −1.39114 2.37510i −0.0682063 0.116449i
\(417\) 2.21674 2.21674i 0.108554 0.108554i
\(418\) −1.21166 0.978675i −0.0592642 0.0478685i
\(419\) 27.5451i 1.34567i −0.739794 0.672833i \(-0.765077\pi\)
0.739794 0.672833i \(-0.234923\pi\)
\(420\) −3.44576 + 0.767656i −0.168136 + 0.0374578i
\(421\) 27.7410i 1.35201i 0.736896 + 0.676007i \(0.236291\pi\)
−0.736896 + 0.676007i \(0.763709\pi\)
\(422\) 3.25474 4.02956i 0.158438 0.196156i
\(423\) 21.2205 21.2205i 1.03177 1.03177i
\(424\) 24.0132 7.90213i 1.16619 0.383761i
\(425\) 12.0829 12.4391i 0.586109 0.603385i
\(426\) 1.64410 + 15.4566i 0.0796569 + 0.748873i
\(427\) −3.33215 + 3.33215i −0.161254 + 0.161254i
\(428\) −6.73473 4.34967i −0.325535 0.210249i
\(429\) −0.127716 −0.00616619
\(430\) 17.8013 2.02434i 0.858455 0.0976224i
\(431\) 10.8523i 0.522737i −0.965239 0.261369i \(-0.915826\pi\)
0.965239 0.261369i \(-0.0841738\pi\)
\(432\) 6.00487 15.8803i 0.288910 0.764040i
\(433\) −12.1968 12.1968i −0.586141 0.586141i 0.350443 0.936584i \(-0.386031\pi\)
−0.936584 + 0.350443i \(0.886031\pi\)
\(434\) −0.948932 8.92113i −0.0455502 0.428228i
\(435\) 5.95561 + 5.86973i 0.285550 + 0.281432i
\(436\) 3.08915 + 14.3566i 0.147944 + 0.687557i
\(437\) −12.1770 12.1770i −0.582504 0.582504i
\(438\) −3.45373 2.78963i −0.165026 0.133294i
\(439\) 1.54041 0.0735198 0.0367599 0.999324i \(-0.488296\pi\)
0.0367599 + 0.999324i \(0.488296\pi\)
\(440\) 1.88416 + 0.934030i 0.0898237 + 0.0445281i
\(441\) 2.37687 0.113184
\(442\) 1.85665 + 1.49964i 0.0883117 + 0.0713307i
\(443\) −25.8026 25.8026i −1.22592 1.22592i −0.965494 0.260425i \(-0.916137\pi\)
−0.260425 0.965494i \(-0.583863\pi\)
\(444\) −8.52481 + 1.83431i −0.404569 + 0.0870523i
\(445\) −0.0528129 7.27264i −0.00250357 0.344756i
\(446\) −0.759370 7.13901i −0.0359572 0.338042i
\(447\) −13.2193 13.2193i −0.625254 0.625254i
\(448\) −1.19214 + 7.91068i −0.0563232 + 0.373744i
\(449\) 20.0509i 0.946259i 0.880993 + 0.473129i \(0.156876\pi\)
−0.880993 + 0.473129i \(0.843124\pi\)
\(450\) −13.2267 10.3697i −0.623514 0.488830i
\(451\) −3.91503 −0.184352
\(452\) −8.51180 + 13.1791i −0.400362 + 0.619892i
\(453\) −2.60851 + 2.60851i −0.122559 + 0.122559i
\(454\) −3.29354 30.9634i −0.154574 1.45318i
\(455\) −1.08800 + 0.00790090i −0.0510062 + 0.000370400i
\(456\) −7.02471 + 2.31165i −0.328962 + 0.108253i
\(457\) 20.8010 20.8010i 0.973030 0.973030i −0.0266161 0.999646i \(-0.508473\pi\)
0.999646 + 0.0266161i \(0.00847317\pi\)
\(458\) −9.03399 + 11.1846i −0.422130 + 0.522623i
\(459\) 14.7209i 0.687115i
\(460\) 19.6229 + 12.4726i 0.914923 + 0.581538i
\(461\) 7.28498i 0.339295i 0.985505 + 0.169648i \(0.0542630\pi\)
−0.985505 + 0.169648i \(0.945737\pi\)
\(462\) 0.288767 + 0.233241i 0.0134347 + 0.0108514i
\(463\) 1.15056 1.15056i 0.0534708 0.0534708i −0.679866 0.733337i \(-0.737962\pi\)
0.733337 + 0.679866i \(0.237962\pi\)
\(464\) 17.2724 7.79396i 0.801851 0.361825i
\(465\) −7.86013 + 7.97512i −0.364505 + 0.369837i
\(466\) 33.2104 3.53256i 1.53844 0.163642i
\(467\) −26.4814 + 26.4814i −1.22541 + 1.22541i −0.259731 + 0.965681i \(0.583634\pi\)
−0.965681 + 0.259731i \(0.916366\pi\)
\(468\) 1.25494 1.94306i 0.0580095 0.0898180i
\(469\) −7.99165 −0.369020
\(470\) 39.6711 4.51135i 1.82989 0.208093i
\(471\) 12.1833i 0.561376i
\(472\) −1.70061 + 3.36883i −0.0782769 + 0.155063i
\(473\) −1.33208 1.33208i −0.0612489 0.0612489i
\(474\) 10.8475 1.15384i 0.498242 0.0529975i
\(475\) 0.240517 + 16.5594i 0.0110357 + 0.759799i
\(476\) −1.45917 6.78140i −0.0668811 0.310825i
\(477\) 15.0218 + 15.0218i 0.687803 + 0.687803i
\(478\) −24.2045 + 29.9666i −1.10709 + 1.37064i
\(479\) 24.2775 1.10927 0.554633 0.832095i \(-0.312859\pi\)
0.554633 + 0.832095i \(0.312859\pi\)
\(480\) 8.57900 5.10892i 0.391576 0.233189i
\(481\) −2.68750 −0.122540
\(482\) −17.0016 + 21.0491i −0.774403 + 0.958758i
\(483\) 2.90206 + 2.90206i 0.132048 + 0.132048i
\(484\) 4.58136 + 21.2916i 0.208244 + 0.967798i
\(485\) −11.4261 + 11.5933i −0.518833 + 0.526424i
\(486\) 22.1028 2.35106i 1.00261 0.106646i
\(487\) 0.755598 + 0.755598i 0.0342394 + 0.0342394i 0.724019 0.689780i \(-0.242293\pi\)
−0.689780 + 0.724019i \(0.742293\pi\)
\(488\) 6.00645 11.8985i 0.271899 0.538620i
\(489\) 6.47618i 0.292863i
\(490\) 2.47440 + 1.96909i 0.111782 + 0.0889546i
\(491\) −41.6441 −1.87937 −0.939685 0.342040i \(-0.888882\pi\)
−0.939685 + 0.342040i \(0.888882\pi\)
\(492\) −10.0852 + 15.6152i −0.454674 + 0.703986i
\(493\) −11.6182 + 11.6182i −0.523258 + 0.523258i
\(494\) −2.26646 + 0.241081i −0.101973 + 0.0108468i
\(495\) 0.0128330 + 1.76718i 0.000576802 + 0.0794289i
\(496\) 10.4368 + 23.1294i 0.468628 + 1.03854i
\(497\) 9.84550 9.84550i 0.441631 0.441631i
\(498\) 9.27209 + 7.48921i 0.415492 + 0.335599i
\(499\) 32.9178i 1.47360i 0.676109 + 0.736802i \(0.263665\pi\)
−0.676109 + 0.736802i \(0.736335\pi\)
\(500\) −5.17883 21.7527i −0.231604 0.972810i
\(501\) 5.24635i 0.234389i
\(502\) 23.9719 29.6786i 1.06992 1.32462i
\(503\) −10.7907 + 10.7907i −0.481134 + 0.481134i −0.905494 0.424360i \(-0.860499\pi\)
0.424360 + 0.905494i \(0.360499\pi\)
\(504\) −6.38593 + 2.10144i −0.284452 + 0.0936056i
\(505\) −0.158334 21.8036i −0.00704579 0.970246i
\(506\) −0.258596 2.43112i −0.0114960 0.108077i
\(507\) 7.12417 7.12417i 0.316396 0.316396i
\(508\) −7.90133 + 12.2339i −0.350565 + 0.542790i
\(509\) 20.6456 0.915102 0.457551 0.889183i \(-0.348727\pi\)
0.457551 + 0.889183i \(0.348727\pi\)
\(510\) −5.39104 + 6.77449i −0.238719 + 0.299979i
\(511\) 3.97688i 0.175927i
\(512\) −3.79108 22.3076i −0.167544 0.985865i
\(513\) −9.94087 9.94087i −0.438900 0.438900i
\(514\) 2.39547 + 22.5204i 0.105660 + 0.993330i
\(515\) −7.17850 + 7.28352i −0.316323 + 0.320950i
\(516\) −8.74444 + 1.88157i −0.384953 + 0.0828313i
\(517\) −2.96860 2.96860i −0.130559 0.130559i
\(518\) 6.07647 + 4.90805i 0.266985 + 0.215647i
\(519\) 13.0622 0.573369
\(520\) 2.91614 0.983150i 0.127881 0.0431140i
\(521\) 14.4180 0.631666 0.315833 0.948815i \(-0.397716\pi\)
0.315833 + 0.948815i \(0.397716\pi\)
\(522\) 12.3880 + 10.0059i 0.542206 + 0.437948i
\(523\) 8.28643 + 8.28643i 0.362340 + 0.362340i 0.864674 0.502334i \(-0.167525\pi\)
−0.502334 + 0.864674i \(0.667525\pi\)
\(524\) 1.01422 + 4.71353i 0.0443066 + 0.205912i
\(525\) −0.0573209 3.94651i −0.00250169 0.172240i
\(526\) −2.63480 24.7703i −0.114883 1.08004i
\(527\) −15.5579 15.5579i −0.677712 0.677712i
\(528\) −0.982042 0.371344i −0.0427379 0.0161607i
\(529\) 4.03124i 0.175271i
\(530\) 3.19356 + 28.0829i 0.138719 + 1.21984i
\(531\) −3.17126 −0.137621
\(532\) 5.56476 + 3.59404i 0.241263 + 0.155821i
\(533\) −4.05110 + 4.05110i −0.175473 + 0.175473i
\(534\) 0.384056 + 3.61060i 0.0166197 + 0.156246i
\(535\) 6.29199 6.38405i 0.272027 0.276006i
\(536\) 21.4711 7.06558i 0.927412 0.305187i
\(537\) −8.76771 + 8.76771i −0.378354 + 0.378354i
\(538\) −13.9540 + 17.2759i −0.601600 + 0.744817i
\(539\) 0.332508i 0.0143221i
\(540\) 16.0195 + 10.1822i 0.689370 + 0.438173i
\(541\) 9.33609i 0.401390i −0.979654 0.200695i \(-0.935680\pi\)
0.979654 0.200695i \(-0.0643200\pi\)
\(542\) 6.30186 + 5.09011i 0.270688 + 0.218639i
\(543\) 9.20708 9.20708i 0.395114 0.395114i
\(544\) 9.91593 + 16.9295i 0.425142 + 0.725845i
\(545\) −16.4181 + 0.119226i −0.703276 + 0.00510709i
\(546\) 0.540151 0.0574554i 0.0231163 0.00245887i
\(547\) −13.4893 + 13.4893i −0.576759 + 0.576759i −0.934009 0.357250i \(-0.883714\pi\)
0.357250 + 0.934009i \(0.383714\pi\)
\(548\) −3.97409 2.56669i −0.169765 0.109644i
\(549\) 11.2007 0.478035
\(550\) −1.45064 + 1.85033i −0.0618556 + 0.0788982i
\(551\) 15.6913i 0.668470i
\(552\) −10.3627 5.23118i −0.441067 0.222654i
\(553\) −6.90962 6.90962i −0.293827 0.293827i
\(554\) −41.0082 + 4.36200i −1.74227 + 0.185324i
\(555\) −0.0707952 9.74891i −0.00300509 0.413818i
\(556\) 7.76502 1.67082i 0.329310 0.0708586i
\(557\) 7.32124 + 7.32124i 0.310211 + 0.310211i 0.844991 0.534780i \(-0.179606\pi\)
−0.534780 + 0.844991i \(0.679606\pi\)
\(558\) −13.3989 + 16.5886i −0.567220 + 0.702253i
\(559\) −2.75675 −0.116598
\(560\) −8.38888 3.10268i −0.354495 0.131112i
\(561\) 0.910349 0.0384350
\(562\) 16.6528 20.6172i 0.702455 0.869682i
\(563\) −18.1641 18.1641i −0.765528 0.765528i 0.211788 0.977316i \(-0.432071\pi\)
−0.977316 + 0.211788i \(0.932071\pi\)
\(564\) −19.4874 + 4.19317i −0.820569 + 0.176564i
\(565\) −12.4928 12.3127i −0.525578 0.518000i
\(566\) 8.33677 0.886775i 0.350421 0.0372739i
\(567\) −2.67296 2.67296i −0.112254 0.112254i
\(568\) −17.7472 + 35.1565i −0.744658 + 1.47513i
\(569\) 9.51195i 0.398762i 0.979922 + 0.199381i \(0.0638931\pi\)
−0.979922 + 0.199381i \(0.936107\pi\)
\(570\) −0.934226 8.21523i −0.0391304 0.344098i
\(571\) −28.4290 −1.18972 −0.594859 0.803830i \(-0.702792\pi\)
−0.594859 + 0.803830i \(0.702792\pi\)
\(572\) −0.271821 0.175557i −0.0113654 0.00734041i
\(573\) −8.33838 + 8.33838i −0.348341 + 0.348341i
\(574\) 16.5579 1.76125i 0.691113 0.0735131i
\(575\) −18.1129 + 18.6468i −0.755360 + 0.777626i
\(576\) 15.2991 11.2919i 0.637464 0.470494i
\(577\) −5.69208 + 5.69208i −0.236965 + 0.236965i −0.815592 0.578627i \(-0.803589\pi\)
0.578627 + 0.815592i \(0.303589\pi\)
\(578\) 5.46874 + 4.41719i 0.227470 + 0.183731i
\(579\) 12.6001i 0.523644i
\(580\) 4.60696 + 20.6792i 0.191294 + 0.858656i
\(581\) 10.6766i 0.442939i
\(582\) 5.10633 6.32194i 0.211664 0.262053i
\(583\) 2.10145 2.10145i 0.0870332 0.0870332i
\(584\) −3.51604 10.6847i −0.145495 0.442135i
\(585\) 1.84188 + 1.81532i 0.0761525 + 0.0750544i
\(586\) −1.20313 11.3109i −0.0497008 0.467248i
\(587\) −30.2089 + 30.2089i −1.24685 + 1.24685i −0.289751 + 0.957102i \(0.593572\pi\)
−0.957102 + 0.289751i \(0.906428\pi\)
\(588\) −1.32621 0.856544i −0.0546921 0.0353233i
\(589\) 21.0121 0.865788
\(590\) −3.30139 2.62720i −0.135916 0.108160i
\(591\) 17.7896i 0.731766i
\(592\) −20.6649 7.81411i −0.849323 0.321158i
\(593\) 17.0546 + 17.0546i 0.700348 + 0.700348i 0.964485 0.264137i \(-0.0850871\pi\)
−0.264137 + 0.964485i \(0.585087\pi\)
\(594\) −0.211109 1.98469i −0.00866192 0.0814327i
\(595\) 7.75516 0.0563169i 0.317931 0.00230877i
\(596\) −9.96382 46.3061i −0.408134 1.89677i
\(597\) −0.619297 0.619297i −0.0253461 0.0253461i
\(598\) −2.78320 2.24804i −0.113814 0.0919290i
\(599\) 22.5470 0.921244 0.460622 0.887596i \(-0.347626\pi\)
0.460622 + 0.887596i \(0.347626\pi\)
\(600\) 3.64319 + 10.5524i 0.148733 + 0.430799i
\(601\) 35.0872 1.43124 0.715619 0.698491i \(-0.246145\pi\)
0.715619 + 0.698491i \(0.246145\pi\)
\(602\) 6.23302 + 5.03450i 0.254039 + 0.205191i
\(603\) 13.4316 + 13.4316i 0.546977 + 0.546977i
\(604\) −9.13737 + 1.96611i −0.371794 + 0.0800000i
\(605\) −24.3489 + 0.176818i −0.989923 + 0.00718868i
\(606\) 1.15141 + 10.8247i 0.0467728 + 0.439722i
\(607\) 2.26137 + 2.26137i 0.0917862 + 0.0917862i 0.751509 0.659723i \(-0.229326\pi\)
−0.659723 + 0.751509i \(0.729326\pi\)
\(608\) −18.1284 4.73616i −0.735203 0.192077i
\(609\) 3.73960i 0.151536i
\(610\) 11.6603 + 9.27911i 0.472112 + 0.375700i
\(611\) −6.14355 −0.248541
\(612\) −8.94508 + 13.8500i −0.361584 + 0.559851i
\(613\) 11.9680 11.9680i 0.483382 0.483382i −0.422828 0.906210i \(-0.638962\pi\)
0.906210 + 0.422828i \(0.138962\pi\)
\(614\) 0.661543 + 6.21932i 0.0266977 + 0.250991i
\(615\) −14.8021 14.5886i −0.596877 0.588271i
\(616\) 0.293977 + 0.893347i 0.0118447 + 0.0359940i
\(617\) −0.714640 + 0.714640i −0.0287703 + 0.0287703i −0.721346 0.692575i \(-0.756476\pi\)
0.692575 + 0.721346i \(0.256476\pi\)
\(618\) 3.20807 3.97179i 0.129048 0.159769i
\(619\) 47.8163i 1.92190i 0.276720 + 0.960951i \(0.410752\pi\)
−0.276720 + 0.960951i \(0.589248\pi\)
\(620\) −27.6914 + 6.16916i −1.11211 + 0.247759i
\(621\) 22.0674i 0.885534i
\(622\) 2.13934 + 1.72797i 0.0857796 + 0.0692855i
\(623\) 2.29987 2.29987i 0.0921424 0.0921424i
\(624\) −1.40042 + 0.631924i −0.0560619 + 0.0252972i
\(625\) 24.9895 0.726071i 0.999578 0.0290428i
\(626\) 29.7276 3.16210i 1.18815 0.126383i
\(627\) −0.614748 + 0.614748i −0.0245507 + 0.0245507i
\(628\) −16.7470 + 25.9299i −0.668278 + 1.03472i
\(629\) 19.1563 0.763812
\(630\) −0.849274 7.46820i −0.0338359 0.297540i
\(631\) 23.5322i 0.936803i 0.883516 + 0.468402i \(0.155170\pi\)
−0.883516 + 0.468402i \(0.844830\pi\)
\(632\) 24.6730 + 12.4551i 0.981438 + 0.495437i
\(633\) −2.04444 2.04444i −0.0812592 0.0812592i
\(634\) 28.5060 3.03216i 1.13212 0.120422i
\(635\) −11.5968 11.4296i −0.460207 0.453571i
\(636\) −2.96832 13.7950i −0.117701 0.547009i
\(637\) −0.344065 0.344065i −0.0136323 0.0136323i
\(638\) 1.39976 1.73299i 0.0554171 0.0686097i
\(639\) −33.0947 −1.30921
\(640\) 25.2815 + 0.919186i 0.999340 + 0.0363340i
\(641\) 8.07010 0.318750 0.159375 0.987218i \(-0.449052\pi\)
0.159375 + 0.987218i \(0.449052\pi\)
\(642\) −2.81189 + 3.48129i −0.110977 + 0.137396i
\(643\) −17.8241 17.8241i −0.702913 0.702913i 0.262122 0.965035i \(-0.415578\pi\)
−0.965035 + 0.262122i \(0.915578\pi\)
\(644\) 2.18737 + 10.1656i 0.0861945 + 0.400583i
\(645\) −0.0726192 10.0001i −0.00285938 0.393753i
\(646\) 16.1551 1.71841i 0.635615 0.0676098i
\(647\) −12.2092 12.2092i −0.479992 0.479992i 0.425137 0.905129i \(-0.360226\pi\)
−0.905129 + 0.425137i \(0.860226\pi\)
\(648\) 9.54466 + 4.81821i 0.374949 + 0.189277i
\(649\) 0.443637i 0.0174143i
\(650\) 0.413575 + 3.41570i 0.0162218 + 0.133975i
\(651\) −5.00768 −0.196266
\(652\) 8.90209 13.7834i 0.348633 0.539799i
\(653\) −6.12420 + 6.12420i −0.239659 + 0.239659i −0.816709 0.577050i \(-0.804204\pi\)
0.577050 + 0.816709i \(0.304204\pi\)
\(654\) 8.15099 0.867014i 0.318729 0.0339029i
\(655\) −5.39037 + 0.0391441i −0.210619 + 0.00152949i
\(656\) −42.9288 + 19.3711i −1.67609 + 0.756315i
\(657\) 6.68396 6.68396i 0.260766 0.260766i
\(658\) 13.8906 + 11.2197i 0.541512 + 0.437388i
\(659\) 17.1578i 0.668373i −0.942507 0.334187i \(-0.891538\pi\)
0.942507 0.334187i \(-0.108462\pi\)
\(660\) 0.629672 0.990652i 0.0245099 0.0385611i
\(661\) 40.9486i 1.59272i 0.604825 + 0.796358i \(0.293243\pi\)
−0.604825 + 0.796358i \(0.706757\pi\)
\(662\) −5.50702 + 6.81802i −0.214036 + 0.264990i
\(663\) 0.941990 0.941990i 0.0365838 0.0365838i
\(664\) 9.43939 + 28.6847i 0.366319 + 1.11318i
\(665\) −5.19894 + 5.27500i −0.201606 + 0.204556i
\(666\) −1.96376 18.4617i −0.0760940 0.715377i
\(667\) 17.4163 17.4163i 0.674360 0.674360i
\(668\) 7.21156 11.1659i 0.279024 0.432021i
\(669\) −4.00732 −0.154932
\(670\) 2.85548 + 25.1100i 0.110317 + 0.970084i
\(671\) 1.56690i 0.0604896i
\(672\) 4.32042 + 1.12874i 0.166664 + 0.0435421i
\(673\) −1.45903 1.45903i −0.0562415 0.0562415i 0.678427 0.734668i \(-0.262662\pi\)
−0.734668 + 0.678427i \(0.762662\pi\)
\(674\) 1.74601 + 16.4146i 0.0672537 + 0.632267i
\(675\) −14.7868 + 15.2226i −0.569143 + 0.585920i
\(676\) 24.9553 5.36970i 0.959820 0.206527i
\(677\) −2.30325 2.30325i −0.0885211 0.0885211i 0.661460 0.749981i \(-0.269937\pi\)
−0.749981 + 0.661460i \(0.769937\pi\)
\(678\) 6.81249 + 5.50255i 0.261632 + 0.211324i
\(679\) −7.27956 −0.279364
\(680\) −20.7860 + 7.00781i −0.797106 + 0.268737i
\(681\) −17.3806 −0.666026
\(682\) 2.32063 + 1.87441i 0.0888617 + 0.0717749i
\(683\) 4.63398 + 4.63398i 0.177314 + 0.177314i 0.790184 0.612870i \(-0.209985\pi\)
−0.612870 + 0.790184i \(0.709985\pi\)
\(684\) −3.31220 15.3932i −0.126645 0.588574i
\(685\) 3.71284 3.76716i 0.141860 0.143936i
\(686\) 0.149585 + 1.40628i 0.00571117 + 0.0536920i
\(687\) 5.67463 + 5.67463i 0.216501 + 0.216501i
\(688\) −21.1973 8.01544i −0.808141 0.305586i
\(689\) 4.34898i 0.165683i
\(690\) 8.08142 10.1553i 0.307655 0.386605i
\(691\) 43.6704 1.66130 0.830650 0.556794i \(-0.187969\pi\)
0.830650 + 0.556794i \(0.187969\pi\)
\(692\) 27.8006 + 17.9552i 1.05682 + 0.682554i
\(693\) −0.558847 + 0.558847i −0.0212288 + 0.0212288i
\(694\) −1.74633 16.4176i −0.0662898 0.623205i
\(695\) 0.0644855 + 8.88002i 0.00244607 + 0.336838i
\(696\) −3.30626 10.0472i −0.125323 0.380837i
\(697\) 28.8759 28.8759i 1.09375 1.09375i
\(698\) 14.9987 18.5693i 0.567709 0.702858i
\(699\) 18.6419i 0.705101i
\(700\) 5.30282 8.47821i 0.200428 0.320446i
\(701\) 9.46429i 0.357461i −0.983898 0.178731i \(-0.942801\pi\)
0.983898 0.178731i \(-0.0571991\pi\)
\(702\) −2.27212 1.83522i −0.0857555 0.0692660i
\(703\) −12.9360 + 12.9360i −0.487891 + 0.487891i
\(704\) −1.57965 2.14024i −0.0595354 0.0806634i
\(705\) −0.161836 22.2857i −0.00609508 0.839328i
\(706\) −6.16255 + 0.655505i −0.231931 + 0.0246703i
\(707\) 6.89508 6.89508i 0.259316 0.259316i
\(708\) 1.76946 + 1.14281i 0.0665002 + 0.0429496i
\(709\) 21.0235 0.789554 0.394777 0.918777i \(-0.370822\pi\)
0.394777 + 0.918777i \(0.370822\pi\)
\(710\) −34.4527 27.4169i −1.29299 1.02894i
\(711\) 23.2260i 0.871044i
\(712\) −4.14569 + 8.21242i −0.155366 + 0.307773i
\(713\) 23.3220 + 23.3220i 0.873416 + 0.873416i
\(714\) −3.85015 + 0.409537i −0.144088 + 0.0153265i
\(715\) 0.253951 0.257667i 0.00949724 0.00963618i
\(716\) −30.7125 + 6.60848i −1.14778 + 0.246971i
\(717\) 15.2039 + 15.2039i 0.567799 + 0.567799i
\(718\) −18.7045 + 23.1573i −0.698046 + 0.864223i
\(719\) 32.4326 1.20953 0.604766 0.796403i \(-0.293267\pi\)
0.604766 + 0.796403i \(0.293267\pi\)
\(720\) 8.88453 + 19.3139i 0.331107 + 0.719787i
\(721\) −4.57341 −0.170323
\(722\) 7.13479 8.83331i 0.265530 0.328742i
\(723\) 10.6795 + 10.6795i 0.397173 + 0.397173i
\(724\) 32.2516 6.93965i 1.19862 0.257910i
\(725\) −23.6843 + 0.344002i −0.879613 + 0.0127759i
\(726\) 12.0883 1.28582i 0.448640 0.0477214i
\(727\) −6.58358 6.58358i −0.244171 0.244171i 0.574402 0.818573i \(-0.305235\pi\)
−0.818573 + 0.574402i \(0.805235\pi\)
\(728\) 1.22859 + 0.620202i 0.0455346 + 0.0229862i
\(729\) 1.06652i 0.0395008i
\(730\) 12.4955 1.42097i 0.462478 0.0525925i
\(731\) 19.6498 0.726776
\(732\) −6.24962 4.03636i −0.230993 0.149188i
\(733\) −3.76794 + 3.76794i −0.139172 + 0.139172i −0.773261 0.634088i \(-0.781376\pi\)
0.634088 + 0.773261i \(0.281376\pi\)
\(734\) 51.3910 5.46641i 1.89688 0.201769i
\(735\) 1.23903 1.25716i 0.0457023 0.0463709i
\(736\) −14.8645 25.3781i −0.547911 0.935449i
\(737\) 1.87899 1.87899i 0.0692134 0.0692134i
\(738\) −30.7890 24.8688i −1.13336 0.915431i
\(739\) 35.2066i 1.29510i −0.762025 0.647548i \(-0.775795\pi\)
0.762025 0.647548i \(-0.224205\pi\)
\(740\) 13.2501 20.8461i 0.487082 0.766318i
\(741\) 1.27223i 0.0467365i
\(742\) −7.94232 + 9.83308i −0.291572 + 0.360984i
\(743\) −25.6824 + 25.6824i −0.942197 + 0.942197i −0.998418 0.0562215i \(-0.982095\pi\)
0.0562215 + 0.998418i \(0.482095\pi\)
\(744\) 13.4541 4.42739i 0.493251 0.162316i
\(745\) 52.9554 0.384554i 1.94013 0.0140890i
\(746\) −3.35632 31.5535i −0.122884 1.15526i
\(747\) −17.9442 + 17.9442i −0.656543 + 0.656543i
\(748\) 1.93751 + 1.25136i 0.0708425 + 0.0457541i
\(749\) 4.00862 0.146472
\(750\) −12.3795 + 1.59022i −0.452037 + 0.0580666i
\(751\) 40.4685i 1.47672i −0.674409 0.738358i \(-0.735602\pi\)
0.674409 0.738358i \(-0.264398\pi\)
\(752\) −47.2394 17.8628i −1.72264 0.651390i
\(753\) −15.0578 15.0578i −0.548736 0.548736i
\(754\) −0.344810 3.24163i −0.0125572 0.118053i
\(755\) −0.0758823 10.4494i −0.00276164 0.380294i
\(756\) 1.78570 + 8.29889i 0.0649451 + 0.301828i
\(757\) 17.7325 + 17.7325i 0.644498 + 0.644498i 0.951658 0.307160i \(-0.0993787\pi\)
−0.307160 + 0.951658i \(0.599379\pi\)
\(758\) −17.6254 14.2363i −0.640184 0.517086i
\(759\) −1.36466 −0.0495339
\(760\) 9.30423 18.7688i 0.337500 0.680816i
\(761\) 0.648081 0.0234929 0.0117465 0.999931i \(-0.496261\pi\)
0.0117465 + 0.999931i \(0.496261\pi\)
\(762\) 6.32389 + 5.10790i 0.229090 + 0.185040i
\(763\) −5.19201 5.19201i −0.187963 0.187963i
\(764\) −29.2086 + 6.28488i −1.05673 + 0.227379i
\(765\) −13.1288 12.9395i −0.474672 0.467828i
\(766\) −3.95300 37.1630i −0.142828 1.34275i
\(767\) 0.459057 + 0.459057i 0.0165756 + 0.0165756i
\(768\) −12.6056 + 0.787193i −0.454865 + 0.0284054i
\(769\) 4.54580i 0.163926i −0.996635 0.0819628i \(-0.973881\pi\)
0.996635 0.0819628i \(-0.0261189\pi\)
\(770\) −1.04475 + 0.118808i −0.0376501 + 0.00428153i
\(771\) 12.6413 0.455265
\(772\) −17.3200 + 26.8171i −0.623361 + 0.965169i
\(773\) 18.3484 18.3484i 0.659948 0.659948i −0.295420 0.955368i \(-0.595460\pi\)
0.955368 + 0.295420i \(0.0954595\pi\)
\(774\) −2.01435 18.9374i −0.0724043 0.680689i
\(775\) −0.460652 31.7155i −0.0165471 1.13926i
\(776\) 19.5580 6.43601i 0.702090 0.231039i
\(777\) 3.08296 3.08296i 0.110600 0.110600i
\(778\) 3.44341 4.26314i 0.123452 0.152841i
\(779\) 38.9991i 1.39729i
\(780\) −0.373527 1.67664i −0.0133744 0.0600334i
\(781\) 4.62972i 0.165664i
\(782\) 19.8384 + 16.0238i 0.709421 + 0.573010i
\(783\) 14.2180 14.2180i 0.508112 0.508112i
\(784\) −1.64521 3.64600i −0.0587575 0.130214i
\(785\) −24.5797 24.2253i −0.877287 0.864638i
\(786\) 2.67612 0.284656i 0.0954539 0.0101533i
\(787\) 23.4025 23.4025i 0.834209 0.834209i −0.153880 0.988089i \(-0.549177\pi\)
0.988089 + 0.153880i \(0.0491770\pi\)
\(788\) −24.4534 + 37.8619i −0.871115 + 1.34877i
\(789\) −13.9043 −0.495005
\(790\) −19.2413 + 24.1791i −0.684576 + 0.860252i
\(791\) 7.84441i 0.278915i
\(792\) 1.00736 1.99554i 0.0357951 0.0709084i
\(793\) −1.62136 1.62136i −0.0575763 0.0575763i
\(794\) −49.8178 + 5.29908i −1.76797 + 0.188057i
\(795\) 15.7759 0.114562i 0.559514 0.00406311i
\(796\) −0.466783 2.16934i −0.0165447 0.0768902i
\(797\) −11.6332 11.6332i −0.412069 0.412069i 0.470390 0.882459i \(-0.344113\pi\)
−0.882459 + 0.470390i \(0.844113\pi\)
\(798\) 2.32340 2.87652i 0.0822476 0.101828i
\(799\) 43.7907 1.54920
\(800\) −6.75131 + 27.4667i −0.238695 + 0.971095i
\(801\) −7.73080 −0.273154
\(802\) −24.4027 + 30.2120i −0.861689 + 1.06682i
\(803\) −0.935039 0.935039i −0.0329968 0.0329968i
\(804\) −2.65408 12.3347i −0.0936023 0.435010i
\(805\) −11.6254 + 0.0844217i −0.409740 + 0.00297548i
\(806\) 4.34085 0.461732i 0.152900 0.0162638i
\(807\) 8.76511 + 8.76511i 0.308547 + 0.308547i
\(808\) −12.4289 + 24.6210i −0.437247 + 0.866166i
\(809\) 37.4253i 1.31580i 0.753104 + 0.657902i \(0.228556\pi\)
−0.753104 + 0.657902i \(0.771444\pi\)
\(810\) −7.44345 + 9.35359i −0.261536 + 0.328652i
\(811\) 7.52281 0.264161 0.132081 0.991239i \(-0.457834\pi\)
0.132081 + 0.991239i \(0.457834\pi\)
\(812\) −5.14041 + 7.95906i −0.180393 + 0.279308i
\(813\) 3.19731 3.19731i 0.112135 0.112135i
\(814\) −2.58266 + 0.274716i −0.0905223 + 0.00962878i
\(815\) 13.0657 + 12.8773i 0.457670 + 0.451071i
\(816\) 9.98210 4.50430i 0.349444 0.157682i
\(817\) −13.2693 + 13.2693i −0.464234 + 0.464234i
\(818\) −26.0979 21.0796i −0.912491 0.737033i
\(819\) 1.15654i 0.0404128i
\(820\) −11.4501 51.3960i −0.399856 1.79483i
\(821\) 2.07312i 0.0723523i 0.999345 + 0.0361762i \(0.0115177\pi\)
−0.999345 + 0.0361762i \(0.988482\pi\)
\(822\) −1.65927 + 2.05427i −0.0578736 + 0.0716511i
\(823\) −31.1423 + 31.1423i −1.08555 + 1.08555i −0.0895705 + 0.995980i \(0.528549\pi\)
−0.995980 + 0.0895705i \(0.971451\pi\)
\(824\) 12.2874 4.04345i 0.428051 0.140860i
\(825\) 0.941374 + 0.914420i 0.0327744 + 0.0318360i
\(826\) −0.199578 1.87628i −0.00694422 0.0652842i
\(827\) 9.18398 9.18398i 0.319358 0.319358i −0.529162 0.848521i \(-0.677494\pi\)
0.848521 + 0.529162i \(0.177494\pi\)
\(828\) 13.4091 20.7617i 0.465999 0.721521i
\(829\) −28.5039 −0.989981 −0.494991 0.868898i \(-0.664829\pi\)
−0.494991 + 0.868898i \(0.664829\pi\)
\(830\) −33.5461 + 3.81482i −1.16440 + 0.132414i
\(831\) 23.0190i 0.798522i
\(832\) −3.84919 0.580072i −0.133446 0.0201104i
\(833\) 2.45246 + 2.45246i 0.0849728 + 0.0849728i
\(834\) −0.468939 4.40860i −0.0162380 0.152657i
\(835\) 10.5845 + 10.4319i 0.366291 + 0.361009i
\(836\) −2.15340 + 0.463354i −0.0744770 + 0.0160254i
\(837\) 19.0393 + 19.0393i 0.658095 + 0.658095i
\(838\) −30.3041 24.4771i −1.04684 0.845546i
\(839\) 28.3334 0.978176 0.489088 0.872234i \(-0.337330\pi\)
0.489088 + 0.872234i \(0.337330\pi\)
\(840\) −2.21742 + 4.47305i −0.0765082 + 0.154335i
\(841\) −6.55739 −0.226117
\(842\) 30.5196 + 24.6511i 1.05178 + 0.849535i
\(843\) −10.4603 10.4603i −0.360273 0.360273i
\(844\) −1.54096 7.16148i −0.0530419 0.246508i
\(845\) 0.207244 + 28.5387i 0.00712941 + 0.981762i
\(846\) −4.48908 42.2029i −0.154338 1.45096i
\(847\) −7.70000 7.70000i −0.264575 0.264575i
\(848\) 12.6450 33.4404i 0.434230 1.14835i
\(849\) 4.67966i 0.160606i
\(850\) −2.94793 24.3468i −0.101113 0.835089i
\(851\) −28.7162 −0.984379
\(852\) 18.4657 + 11.9262i 0.632625 + 0.408585i
\(853\) 25.5098 25.5098i 0.873440 0.873440i −0.119406 0.992846i \(-0.538099\pi\)
0.992846 + 0.119406i \(0.0380989\pi\)
\(854\) 0.704900 + 6.62692i 0.0241212 + 0.226769i
\(855\) 17.6036 0.127835i 0.602029 0.00437185i
\(856\) −10.7699 + 3.54410i −0.368109 + 0.121135i
\(857\) −38.1674 + 38.1674i −1.30377 + 1.30377i −0.377946 + 0.925828i \(0.623370\pi\)
−0.925828 + 0.377946i \(0.876630\pi\)
\(858\) −0.113491 + 0.140509i −0.00387451 + 0.00479688i
\(859\) 38.8201i 1.32453i −0.749272 0.662263i \(-0.769596\pi\)
0.749272 0.662263i \(-0.230404\pi\)
\(860\) 13.5914 21.3832i 0.463464 0.729161i
\(861\) 9.29440i 0.316752i
\(862\) −11.9393 9.64356i −0.406654 0.328461i
\(863\) 11.5955 11.5955i 0.394716 0.394716i −0.481649 0.876364i \(-0.659962\pi\)
0.876364 + 0.481649i \(0.159962\pi\)
\(864\) −12.1348 20.7178i −0.412836 0.704835i
\(865\) −25.9730 + 26.3530i −0.883109 + 0.896029i
\(866\) −24.2568 + 2.58017i −0.824278 + 0.0876778i
\(867\) 2.77462 2.77462i 0.0942312 0.0942312i
\(868\) −10.6579 6.88349i −0.361754 0.233641i
\(869\) 3.24916 0.110220
\(870\) 11.7499 1.33619i 0.398360 0.0453010i
\(871\) 3.88859i 0.131760i
\(872\) 18.5397 + 9.35898i 0.627833 + 0.316935i
\(873\) 12.2348 + 12.2348i 0.414085 + 0.414085i
\(874\) −24.2173 + 2.57598i −0.819163 + 0.0871337i
\(875\) 8.07603 + 7.73160i 0.273020 + 0.261376i
\(876\) −6.13809 + 1.32075i −0.207387 + 0.0446240i
\(877\) −3.28961 3.28961i −0.111082 0.111082i 0.649381 0.760463i \(-0.275028\pi\)
−0.760463 + 0.649381i \(0.775028\pi\)
\(878\) 1.36884 1.69470i 0.0461960 0.0571935i
\(879\) −6.34912 −0.214150
\(880\) 2.70188 1.24288i 0.0910804 0.0418976i
\(881\) 21.8695 0.736803 0.368402 0.929667i \(-0.379905\pi\)
0.368402 + 0.929667i \(0.379905\pi\)
\(882\) 2.11213 2.61495i 0.0711192 0.0880498i
\(883\) 17.3219 + 17.3219i 0.582930 + 0.582930i 0.935707 0.352778i \(-0.114763\pi\)
−0.352778 + 0.935707i \(0.614763\pi\)
\(884\) 3.29970 0.710006i 0.110981 0.0238801i
\(885\) −1.65313 + 1.67732i −0.0555695 + 0.0563825i
\(886\) −51.3157 + 5.45841i −1.72399 + 0.183379i
\(887\) −39.8192 39.8192i −1.33700 1.33700i −0.898955 0.438042i \(-0.855672\pi\)
−0.438042 0.898955i \(-0.644328\pi\)
\(888\) −5.55726 + 11.0087i −0.186490 + 0.369427i
\(889\) 7.28180i 0.244224i
\(890\) −8.04802 6.40450i −0.269770 0.214679i
\(891\) 1.25693 0.0421086
\(892\) −8.52886 5.50842i −0.285567 0.184436i
\(893\) −29.5713 + 29.5713i −0.989566 + 0.989566i
\(894\) −26.2904 + 2.79648i −0.879282 + 0.0935284i
\(895\) −0.255055 35.1226i −0.00852555 1.17402i
\(896\) 7.64368 + 8.34112i 0.255357 + 0.278657i
\(897\) −1.41209 + 1.41209i −0.0471482 + 0.0471482i
\(898\) 22.0592 + 17.8176i 0.736126 + 0.594580i
\(899\) 30.0528i 1.00232i
\(900\) −23.1618 + 5.33688i −0.772061 + 0.177896i
\(901\) 30.9992i 1.03273i
\(902\) −3.47897 + 4.30717i −0.115837 + 0.143413i
\(903\) 3.16239 3.16239i 0.105238 0.105238i
\(904\) 6.93541 + 21.0755i 0.230668 + 0.700962i
\(905\) 0.267837 + 36.8827i 0.00890319 + 1.22602i
\(906\) 0.551817 + 5.18776i 0.0183329 + 0.172352i
\(907\) −8.71673 + 8.71673i −0.289434 + 0.289434i −0.836857 0.547422i \(-0.815609\pi\)
0.547422 + 0.836857i \(0.315609\pi\)
\(908\) −36.9914 23.8912i −1.22760 0.792856i
\(909\) −23.1771 −0.768738
\(910\) −0.958124 + 1.20400i −0.0317615 + 0.0399121i
\(911\) 8.98671i 0.297743i 0.988857 + 0.148871i \(0.0475641\pi\)
−0.988857 + 0.148871i \(0.952436\pi\)
\(912\) −3.69909 + 9.78249i −0.122489 + 0.323931i
\(913\) 2.51026 + 2.51026i 0.0830776 + 0.0830776i
\(914\) −4.40034 41.3686i −0.145550 1.36835i
\(915\) 5.83877 5.92419i 0.193024 0.195848i
\(916\) 4.27714 + 19.8777i 0.141321 + 0.656778i
\(917\) −1.70463 1.70463i −0.0562918 0.0562918i
\(918\) 16.1954 + 13.0813i 0.534529 + 0.431747i
\(919\) 51.6484 1.70372 0.851862 0.523766i \(-0.175473\pi\)
0.851862 + 0.523766i \(0.175473\pi\)
\(920\) 31.1592 10.5050i 1.02729 0.346341i
\(921\) 3.49108 0.115035
\(922\) 8.01467 + 6.47357i 0.263949 + 0.213196i
\(923\) 4.79063 + 4.79063i 0.157686 + 0.157686i
\(924\) 0.513207 0.110428i 0.0168833 0.00363282i
\(925\) 19.8091 + 19.2420i 0.651321 + 0.632671i
\(926\) −0.243394 2.28820i −0.00799842 0.0751950i
\(927\) 7.68655 + 7.68655i 0.252459 + 0.252459i
\(928\) 6.77395 25.9283i 0.222366 0.851138i
\(929\) 16.9549i 0.556271i −0.960542 0.278135i \(-0.910284\pi\)
0.960542 0.278135i \(-0.0897164\pi\)
\(930\) 1.78928 + 15.7343i 0.0586728 + 0.515946i
\(931\) −3.31224 −0.108554
\(932\) 25.6249 39.6759i 0.839373 1.29963i
\(933\) 1.08541 1.08541i 0.0355349 0.0355349i
\(934\) 5.60200 + 52.6656i 0.183303 + 1.72327i
\(935\) −1.81014 + 1.83662i −0.0591980 + 0.0600640i
\(936\) −1.02252 3.10727i −0.0334222 0.101564i
\(937\) 3.02935 3.02935i 0.0989645 0.0989645i −0.655891 0.754856i \(-0.727707\pi\)
0.754856 + 0.655891i \(0.227707\pi\)
\(938\) −7.10153 + 8.79212i −0.231873 + 0.287073i
\(939\) 16.6869i 0.544557i
\(940\) 30.2892 47.6535i 0.987926 1.55429i
\(941\) 51.3487i 1.67392i −0.547265 0.836959i \(-0.684331\pi\)
0.547265 0.836959i \(-0.315669\pi\)
\(942\) 13.4036 + 10.8263i 0.436713 + 0.352739i
\(943\) −43.2864 + 43.2864i −1.40960 + 1.40960i
\(944\) 2.19507 + 4.86455i 0.0714433 + 0.158327i
\(945\) −9.49056 + 0.0689191i −0.308728 + 0.00224194i
\(946\) −2.64921 + 0.281794i −0.0861331 + 0.00916190i
\(947\) 35.7158 35.7158i 1.16061 1.16061i 0.176264 0.984343i \(-0.443599\pi\)
0.984343 0.176264i \(-0.0564013\pi\)
\(948\) 8.36987 12.9593i 0.271841 0.420899i
\(949\) −1.93508 −0.0628152
\(950\) 18.4318 + 14.4504i 0.598007 + 0.468833i
\(951\) 16.0012i 0.518875i
\(952\) −8.75729 4.42075i −0.283826 0.143277i
\(953\) 8.40969 + 8.40969i 0.272416 + 0.272416i 0.830072 0.557656i \(-0.188299\pi\)
−0.557656 + 0.830072i \(0.688299\pi\)
\(954\) 29.8752 3.17779i 0.967244 0.102885i
\(955\) −0.242566 33.4027i −0.00784924 1.08089i
\(956\) 11.4596 + 53.2578i 0.370631 + 1.72248i
\(957\) −0.879250 0.879250i −0.0284221 0.0284221i
\(958\) 21.5734 26.7092i 0.697005 0.862934i
\(959\) 2.36545 0.0763843
\(960\) 2.00281 13.9782i 0.0646405 0.451144i
\(961\) −9.24348 −0.298177
\(962\) −2.38817 + 2.95669i −0.0769975 + 0.0953276i
\(963\) −6.73730 6.73730i −0.217106 0.217106i
\(964\) 8.04943 + 37.4091i 0.259255 + 1.20487i
\(965\) −25.4207 25.0542i −0.818322 0.806523i
\(966\) 5.77156 0.613916i 0.185697 0.0197524i
\(967\) 18.5734 + 18.5734i 0.597279 + 0.597279i 0.939588 0.342308i \(-0.111209\pi\)
−0.342308 + 0.939588i \(0.611209\pi\)
\(968\) 27.4953 + 13.8798i 0.883731 + 0.446114i
\(969\) 9.06833i 0.291317i
\(970\) 2.60104 + 22.8726i 0.0835144 + 0.734394i
\(971\) 45.5918 1.46311 0.731556 0.681782i \(-0.238795\pi\)
0.731556 + 0.681782i \(0.238795\pi\)
\(972\) 17.0544 26.4059i 0.547021 0.846970i
\(973\) −2.80818 + 2.80818i −0.0900262 + 0.0900262i
\(974\) 1.50272 0.159843i 0.0481502 0.00512170i
\(975\) 1.92029 0.0278913i 0.0614986 0.000893236i
\(976\) −7.75285 17.1813i −0.248163 0.549960i
\(977\) 16.4665 16.4665i 0.526809 0.526809i −0.392810 0.919619i \(-0.628497\pi\)
0.919619 + 0.392810i \(0.128497\pi\)
\(978\) −7.12486 5.75485i −0.227828 0.184020i
\(979\) 1.08148i 0.0345644i
\(980\) 4.36512 0.972474i 0.139439 0.0310645i
\(981\) 17.4524i 0.557213i
\(982\) −37.0057 + 45.8153i −1.18090 + 1.46202i
\(983\) 1.08961 1.08961i 0.0347532 0.0347532i −0.689517 0.724270i \(-0.742177\pi\)
0.724270 + 0.689517i \(0.242177\pi\)
\(984\) 8.21737 + 24.9712i 0.261960 + 0.796054i
\(985\) −35.8904 35.3729i −1.14356 1.12707i
\(986\) 2.45777 + 23.1061i 0.0782714 + 0.735847i
\(987\) 7.04754 7.04754i 0.224326 0.224326i
\(988\) −1.74879 + 2.70771i −0.0556364 + 0.0861436i
\(989\) −29.4561 −0.936648
\(990\) 1.95559 + 1.55623i 0.0621528 + 0.0494603i
\(991\) 45.8069i 1.45510i 0.686052 + 0.727552i \(0.259342\pi\)
−0.686052 + 0.727552i \(0.740658\pi\)
\(992\) 34.7204 + 9.07096i 1.10238 + 0.288003i
\(993\) 3.45920 + 3.45920i 0.109774 + 0.109774i
\(994\) −2.08276 19.5805i −0.0660612 0.621057i
\(995\) 2.48084 0.0180155i 0.0786479 0.000571130i
\(996\) 16.4787 3.54577i 0.522147 0.112352i
\(997\) 6.62710 + 6.62710i 0.209882 + 0.209882i 0.804217 0.594335i \(-0.202585\pi\)
−0.594335 + 0.804217i \(0.702585\pi\)
\(998\) 36.2149 + 29.2514i 1.14636 + 0.925935i
\(999\) −23.4430 −0.741702
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.w.a.43.26 72
4.3 odd 2 1120.2.bi.a.463.21 72
5.2 odd 4 inner 280.2.w.a.267.30 yes 72
8.3 odd 2 inner 280.2.w.a.43.30 yes 72
8.5 even 2 1120.2.bi.a.463.22 72
20.7 even 4 1120.2.bi.a.687.22 72
40.27 even 4 inner 280.2.w.a.267.26 yes 72
40.37 odd 4 1120.2.bi.a.687.21 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.w.a.43.26 72 1.1 even 1 trivial
280.2.w.a.43.30 yes 72 8.3 odd 2 inner
280.2.w.a.267.26 yes 72 40.27 even 4 inner
280.2.w.a.267.30 yes 72 5.2 odd 4 inner
1120.2.bi.a.463.21 72 4.3 odd 2
1120.2.bi.a.463.22 72 8.5 even 2
1120.2.bi.a.687.21 72 40.37 odd 4
1120.2.bi.a.687.22 72 20.7 even 4