Properties

Label 116.2.l.b.31.2
Level $116$
Weight $2$
Character 116.31
Analytic conductor $0.926$
Analytic rank $0$
Dimension $144$
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] = [116,2,Mod(3,116)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(116, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([14, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("116.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 116 = 2^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 116.l (of order \(28\), degree \(12\), 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: \(0.926264663447\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(12\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 31.2
Character \(\chi\) \(=\) 116.31
Dual form 116.2.l.b.15.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.16318 - 0.804373i) q^{2} +(0.564706 - 0.898725i) q^{3} +(0.705968 + 1.87126i) q^{4} +(1.84963 - 1.47503i) q^{5} +(-1.37976 + 0.591143i) q^{6} +(-0.762672 + 0.174075i) q^{7} +(0.684023 - 2.74447i) q^{8} +(0.812838 + 1.68788i) q^{9} +O(q^{10})\) \(q+(-1.16318 - 0.804373i) q^{2} +(0.564706 - 0.898725i) q^{3} +(0.705968 + 1.87126i) q^{4} +(1.84963 - 1.47503i) q^{5} +(-1.37976 + 0.591143i) q^{6} +(-0.762672 + 0.174075i) q^{7} +(0.684023 - 2.74447i) q^{8} +(0.812838 + 1.68788i) q^{9} +(-3.33793 + 0.227932i) q^{10} +(-1.41065 - 4.03140i) q^{11} +(2.08041 + 0.422240i) q^{12} +(1.14835 - 2.38457i) q^{13} +(1.02714 + 0.410993i) q^{14} +(-0.281149 - 2.49527i) q^{15} +(-3.00322 + 2.64210i) q^{16} +(-0.864876 + 0.864876i) q^{17} +(0.412206 - 2.61713i) q^{18} +(-3.53894 + 2.22366i) q^{19} +(4.06595 + 2.41981i) q^{20} +(-0.274240 + 0.783733i) q^{21} +(-1.60191 + 5.82392i) q^{22} +(5.08465 + 4.05487i) q^{23} +(-2.08025 - 2.16457i) q^{24} +(0.132814 - 0.581895i) q^{25} +(-3.25382 + 1.84998i) q^{26} +(5.14017 + 0.579158i) q^{27} +(-0.864161 - 1.30427i) q^{28} +(1.27027 + 5.23320i) q^{29} +(-1.68010 + 3.12859i) q^{30} +(-0.840478 + 7.45945i) q^{31} +(5.61851 - 0.657524i) q^{32} +(-4.41972 - 1.00877i) q^{33} +(1.70169 - 0.310322i) q^{34} +(-1.15390 + 1.44694i) q^{35} +(-2.58461 + 2.71262i) q^{36} +(-3.11215 - 1.08899i) q^{37} +(5.90507 + 0.260111i) q^{38} +(-1.49459 - 2.37863i) q^{39} +(-2.78299 - 6.08522i) q^{40} +(-6.22325 - 6.22325i) q^{41} +(0.949404 - 0.691030i) q^{42} +(-2.71002 + 0.305346i) q^{43} +(6.54792 - 5.48573i) q^{44} +(3.99312 + 1.92299i) q^{45} +(-2.65272 - 8.80650i) q^{46} +(5.74030 - 2.00862i) q^{47} +(0.678583 + 4.19108i) q^{48} +(-5.75542 + 2.77166i) q^{49} +(-0.622547 + 0.570016i) q^{50} +(0.288885 + 1.26569i) q^{51} +(5.27285 + 0.465427i) q^{52} +(-1.82511 - 2.28861i) q^{53} +(-5.51308 - 4.80828i) q^{54} +(-8.55563 - 5.37586i) q^{55} +(-0.0439420 + 2.21220i) q^{56} +4.43625i q^{57} +(2.73190 - 7.10892i) q^{58} +3.52748i q^{59} +(4.47081 - 2.28768i) q^{60} +(6.36950 + 4.00222i) q^{61} +(6.97780 - 8.00061i) q^{62} +(-0.913746 - 1.14580i) q^{63} +(-7.06422 - 3.75456i) q^{64} +(-1.39330 - 6.10443i) q^{65} +(4.32949 + 4.72849i) q^{66} +(10.8668 - 5.23315i) q^{67} +(-2.22898 - 1.00783i) q^{68} +(6.51555 - 2.27989i) q^{69} +(2.50607 - 0.754887i) q^{70} +(-7.65922 - 3.68849i) q^{71} +(5.18832 - 1.07626i) q^{72} +(-2.76358 + 0.311381i) q^{73} +(2.74403 + 3.77001i) q^{74} +(-0.447963 - 0.447963i) q^{75} +(-6.65943 - 5.05244i) q^{76} +(1.77763 + 2.82908i) q^{77} +(-0.174828 + 3.96899i) q^{78} +(10.5334 + 3.68581i) q^{79} +(-1.65767 + 9.31675i) q^{80} +(-0.0809487 + 0.101507i) q^{81} +(2.23294 + 12.2446i) q^{82} +(-17.0310 - 3.88722i) q^{83} +(-1.66017 + 0.0401165i) q^{84} +(-0.323982 + 2.87542i) q^{85} +(3.39785 + 1.82469i) q^{86} +(5.42054 + 1.81360i) q^{87} +(-12.0290 + 1.11391i) q^{88} +(-13.9596 - 1.57287i) q^{89} +(-3.09792 - 5.44874i) q^{90} +(-0.460720 + 2.01855i) q^{91} +(-3.99812 + 12.3773i) q^{92} +(6.22937 + 4.96775i) q^{93} +(-8.29268 - 2.28096i) q^{94} +(-3.26576 + 9.33301i) q^{95} +(2.58187 - 5.42080i) q^{96} +(-4.13360 + 2.59731i) q^{97} +(8.92403 + 1.40556i) q^{98} +(5.65787 - 5.65787i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 12 q^{2} - 14 q^{4} - 28 q^{5} - 14 q^{6} - 12 q^{8} - 28 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 12 q^{2} - 14 q^{4} - 28 q^{5} - 14 q^{6} - 12 q^{8} - 28 q^{9} - 8 q^{10} - 12 q^{12} - 28 q^{13} - 14 q^{14} + 2 q^{16} - 4 q^{17} + 14 q^{18} + 14 q^{20} - 28 q^{21} - 14 q^{22} - 22 q^{24} - 12 q^{25} - 30 q^{26} - 36 q^{29} + 16 q^{30} - 12 q^{32} - 28 q^{33} - 56 q^{34} - 50 q^{36} - 36 q^{37} - 14 q^{38} - 60 q^{40} - 12 q^{41} - 14 q^{42} + 30 q^{44} + 36 q^{46} + 136 q^{48} + 12 q^{49} + 56 q^{50} + 66 q^{52} + 48 q^{53} + 56 q^{54} + 52 q^{56} + 184 q^{58} + 108 q^{60} - 28 q^{61} + 84 q^{62} + 112 q^{64} - 68 q^{65} + 92 q^{66} + 68 q^{68} - 44 q^{69} + 46 q^{70} + 4 q^{72} - 148 q^{73} - 32 q^{74} - 14 q^{76} - 60 q^{77} + 2 q^{78} - 14 q^{80} + 36 q^{81} + 6 q^{82} + 28 q^{84} - 92 q^{85} - 48 q^{88} + 28 q^{89} + 28 q^{90} - 14 q^{92} - 28 q^{93} + 62 q^{94} - 56 q^{96} + 184 q^{97} - 110 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/116\mathbb{Z}\right)^\times\).

\(n\) \(59\) \(89\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{28}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16318 0.804373i −0.822491 0.568778i
\(3\) 0.564706 0.898725i 0.326033 0.518879i −0.642982 0.765882i \(-0.722303\pi\)
0.969015 + 0.247003i \(0.0794457\pi\)
\(4\) 0.705968 + 1.87126i 0.352984 + 0.935629i
\(5\) 1.84963 1.47503i 0.827181 0.659655i −0.115516 0.993306i \(-0.536852\pi\)
0.942697 + 0.333651i \(0.108281\pi\)
\(6\) −1.37976 + 0.591143i −0.563286 + 0.241333i
\(7\) −0.762672 + 0.174075i −0.288263 + 0.0657941i −0.364207 0.931318i \(-0.618660\pi\)
0.0759443 + 0.997112i \(0.475803\pi\)
\(8\) 0.684023 2.74447i 0.241839 0.970316i
\(9\) 0.812838 + 1.68788i 0.270946 + 0.562625i
\(10\) −3.33793 + 0.227932i −1.05555 + 0.0720783i
\(11\) −1.41065 4.03140i −0.425326 1.21551i −0.934846 0.355054i \(-0.884463\pi\)
0.509520 0.860459i \(-0.329823\pi\)
\(12\) 2.08041 + 0.422240i 0.600563 + 0.121890i
\(13\) 1.14835 2.38457i 0.318495 0.661361i −0.678843 0.734284i \(-0.737518\pi\)
0.997338 + 0.0729223i \(0.0232325\pi\)
\(14\) 1.02714 + 0.410993i 0.274516 + 0.109842i
\(15\) −0.281149 2.49527i −0.0725925 0.644276i
\(16\) −3.00322 + 2.64210i −0.750804 + 0.660524i
\(17\) −0.864876 + 0.864876i −0.209763 + 0.209763i −0.804167 0.594404i \(-0.797388\pi\)
0.594404 + 0.804167i \(0.297388\pi\)
\(18\) 0.412206 2.61713i 0.0971579 0.616862i
\(19\) −3.53894 + 2.22366i −0.811889 + 0.510143i −0.872845 0.487997i \(-0.837728\pi\)
0.0609567 + 0.998140i \(0.480585\pi\)
\(20\) 4.06595 + 2.41981i 0.909174 + 0.541087i
\(21\) −0.274240 + 0.783733i −0.0598441 + 0.171025i
\(22\) −1.60191 + 5.82392i −0.341529 + 1.24166i
\(23\) 5.08465 + 4.05487i 1.06022 + 0.845499i 0.988393 0.151918i \(-0.0485448\pi\)
0.0718295 + 0.997417i \(0.477116\pi\)
\(24\) −2.08025 2.16457i −0.424629 0.441840i
\(25\) 0.132814 0.581895i 0.0265628 0.116379i
\(26\) −3.25382 + 1.84998i −0.638127 + 0.362811i
\(27\) 5.14017 + 0.579158i 0.989226 + 0.111459i
\(28\) −0.864161 1.30427i −0.163311 0.246483i
\(29\) 1.27027 + 5.23320i 0.235882 + 0.971782i
\(30\) −1.68010 + 3.12859i −0.306743 + 0.571200i
\(31\) −0.840478 + 7.45945i −0.150954 + 1.33976i 0.658503 + 0.752578i \(0.271190\pi\)
−0.809458 + 0.587178i \(0.800239\pi\)
\(32\) 5.61851 0.657524i 0.993222 0.116235i
\(33\) −4.41972 1.00877i −0.769375 0.175605i
\(34\) 1.70169 0.310322i 0.291837 0.0532198i
\(35\) −1.15390 + 1.44694i −0.195044 + 0.244578i
\(36\) −2.58461 + 2.71262i −0.430769 + 0.452103i
\(37\) −3.11215 1.08899i −0.511634 0.179028i 0.0621005 0.998070i \(-0.480220\pi\)
−0.573734 + 0.819042i \(0.694506\pi\)
\(38\) 5.90507 + 0.260111i 0.957930 + 0.0421955i
\(39\) −1.49459 2.37863i −0.239327 0.380886i
\(40\) −2.78299 6.08522i −0.440029 0.962157i
\(41\) −6.22325 6.22325i −0.971908 0.971908i 0.0277078 0.999616i \(-0.491179\pi\)
−0.999616 + 0.0277078i \(0.991179\pi\)
\(42\) 0.949404 0.691030i 0.146496 0.106628i
\(43\) −2.71002 + 0.305346i −0.413274 + 0.0465648i −0.316154 0.948708i \(-0.602392\pi\)
−0.0971199 + 0.995273i \(0.530963\pi\)
\(44\) 6.54792 5.48573i 0.987136 0.827004i
\(45\) 3.99312 + 1.92299i 0.595260 + 0.286662i
\(46\) −2.65272 8.80650i −0.391123 1.29845i
\(47\) 5.74030 2.00862i 0.837309 0.292987i 0.122641 0.992451i \(-0.460863\pi\)
0.714668 + 0.699464i \(0.246578\pi\)
\(48\) 0.678583 + 4.19108i 0.0979450 + 0.604930i
\(49\) −5.75542 + 2.77166i −0.822202 + 0.395952i
\(50\) −0.622547 + 0.570016i −0.0880415 + 0.0806125i
\(51\) 0.288885 + 1.26569i 0.0404519 + 0.177232i
\(52\) 5.27285 + 0.465427i 0.731213 + 0.0645431i
\(53\) −1.82511 2.28861i −0.250698 0.314365i 0.640519 0.767942i \(-0.278719\pi\)
−0.891217 + 0.453577i \(0.850148\pi\)
\(54\) −5.51308 4.80828i −0.750235 0.654324i
\(55\) −8.55563 5.37586i −1.15364 0.724880i
\(56\) −0.0439420 + 2.21220i −0.00587199 + 0.295618i
\(57\) 4.43625i 0.587596i
\(58\) 2.73190 7.10892i 0.358716 0.933447i
\(59\) 3.52748i 0.459239i 0.973280 + 0.229620i \(0.0737482\pi\)
−0.973280 + 0.229620i \(0.926252\pi\)
\(60\) 4.47081 2.28768i 0.577180 0.295339i
\(61\) 6.36950 + 4.00222i 0.815530 + 0.512432i 0.874039 0.485855i \(-0.161492\pi\)
−0.0585089 + 0.998287i \(0.518635\pi\)
\(62\) 6.97780 8.00061i 0.886182 1.01608i
\(63\) −0.913746 1.14580i −0.115121 0.144357i
\(64\) −7.06422 3.75456i −0.883028 0.469320i
\(65\) −1.39330 6.10443i −0.172817 0.757162i
\(66\) 4.32949 + 4.72849i 0.532924 + 0.582036i
\(67\) 10.8668 5.23315i 1.32759 0.639332i 0.370418 0.928865i \(-0.379214\pi\)
0.957168 + 0.289534i \(0.0935002\pi\)
\(68\) −2.22898 1.00783i −0.270304 0.122218i
\(69\) 6.51555 2.27989i 0.784380 0.274466i
\(70\) 2.50607 0.754887i 0.299532 0.0902262i
\(71\) −7.65922 3.68849i −0.908983 0.437743i −0.0798577 0.996806i \(-0.525447\pi\)
−0.829125 + 0.559063i \(0.811161\pi\)
\(72\) 5.18832 1.07626i 0.611450 0.126839i
\(73\) −2.76358 + 0.311381i −0.323452 + 0.0364443i −0.272198 0.962241i \(-0.587751\pi\)
−0.0512545 + 0.998686i \(0.516322\pi\)
\(74\) 2.74403 + 3.77001i 0.318987 + 0.438255i
\(75\) −0.447963 0.447963i −0.0517263 0.0517263i
\(76\) −6.65943 5.05244i −0.763889 0.579554i
\(77\) 1.77763 + 2.82908i 0.202579 + 0.322403i
\(78\) −0.174828 + 3.96899i −0.0197954 + 0.449399i
\(79\) 10.5334 + 3.68581i 1.18510 + 0.414686i 0.849638 0.527366i \(-0.176820\pi\)
0.335466 + 0.942052i \(0.391106\pi\)
\(80\) −1.65767 + 9.31675i −0.185333 + 1.04164i
\(81\) −0.0809487 + 0.101507i −0.00899430 + 0.0112785i
\(82\) 2.23294 + 12.2446i 0.246586 + 1.35219i
\(83\) −17.0310 3.88722i −1.86940 0.426678i −0.871438 0.490505i \(-0.836812\pi\)
−0.997961 + 0.0638270i \(0.979669\pi\)
\(84\) −1.66017 + 0.0401165i −0.181140 + 0.00437707i
\(85\) −0.323982 + 2.87542i −0.0351408 + 0.311883i
\(86\) 3.39785 + 1.82469i 0.366399 + 0.196762i
\(87\) 5.42054 + 1.81360i 0.581143 + 0.194439i
\(88\) −12.0290 + 1.11391i −1.28229 + 0.118743i
\(89\) −13.9596 1.57287i −1.47971 0.166723i −0.665111 0.746745i \(-0.731616\pi\)
−0.814601 + 0.580021i \(0.803044\pi\)
\(90\) −3.09792 5.44874i −0.326549 0.574347i
\(91\) −0.460720 + 2.01855i −0.0482966 + 0.211601i
\(92\) −3.99812 + 12.3773i −0.416832 + 1.29042i
\(93\) 6.22937 + 4.96775i 0.645955 + 0.515132i
\(94\) −8.29268 2.28096i −0.855324 0.235263i
\(95\) −3.26576 + 9.33301i −0.335060 + 0.957547i
\(96\) 2.58187 5.42080i 0.263512 0.553258i
\(97\) −4.13360 + 2.59731i −0.419704 + 0.263717i −0.725285 0.688449i \(-0.758292\pi\)
0.305581 + 0.952166i \(0.401149\pi\)
\(98\) 8.92403 + 1.40556i 0.901463 + 0.141983i
\(99\) 5.65787 5.65787i 0.568638 0.568638i
\(100\) 1.18264 0.162271i 0.118264 0.0162271i
\(101\) −0.829336 7.36056i −0.0825221 0.732403i −0.965036 0.262117i \(-0.915579\pi\)
0.882514 0.470286i \(-0.155849\pi\)
\(102\) 0.682059 1.70459i 0.0675339 0.168780i
\(103\) −1.90204 + 3.94962i −0.187413 + 0.389168i −0.973412 0.229060i \(-0.926435\pi\)
0.785999 + 0.618228i \(0.212149\pi\)
\(104\) −5.75889 4.78271i −0.564705 0.468984i
\(105\) 0.648789 + 1.85413i 0.0633153 + 0.180945i
\(106\) 0.282028 + 4.13013i 0.0273929 + 0.401154i
\(107\) 5.51421 + 11.4504i 0.533079 + 1.10695i 0.977462 + 0.211113i \(0.0677087\pi\)
−0.444383 + 0.895837i \(0.646577\pi\)
\(108\) 2.54504 + 10.0275i 0.244897 + 0.964892i
\(109\) 14.0554 3.20806i 1.34626 0.307276i 0.512164 0.858888i \(-0.328844\pi\)
0.834101 + 0.551612i \(0.185987\pi\)
\(110\) 5.62753 + 13.1350i 0.536564 + 1.25237i
\(111\) −2.73615 + 2.18201i −0.259704 + 0.207107i
\(112\) 1.83055 2.53784i 0.172970 0.239803i
\(113\) 10.5606 16.8071i 0.993457 1.58108i 0.193431 0.981114i \(-0.438038\pi\)
0.800027 0.599965i \(-0.204819\pi\)
\(114\) 3.56840 5.16015i 0.334211 0.483292i
\(115\) 15.3858 1.43473
\(116\) −8.89591 + 6.07147i −0.825965 + 0.563722i
\(117\) 4.95828 0.458394
\(118\) 2.83741 4.10309i 0.261205 0.377720i
\(119\) 0.509063 0.810170i 0.0466658 0.0742681i
\(120\) −7.04051 0.935216i −0.642707 0.0853732i
\(121\) −5.66211 + 4.51538i −0.514738 + 0.410489i
\(122\) −4.18958 9.77875i −0.379307 0.885326i
\(123\) −9.10730 + 2.07868i −0.821177 + 0.187428i
\(124\) −14.5519 + 3.69338i −1.30680 + 0.331675i
\(125\) 4.51968 + 9.38522i 0.404253 + 0.839440i
\(126\) 0.141198 + 2.06776i 0.0125789 + 0.184211i
\(127\) −6.44697 18.4244i −0.572076 1.63490i −0.757941 0.652323i \(-0.773795\pi\)
0.185865 0.982575i \(-0.440491\pi\)
\(128\) 5.19689 + 10.0495i 0.459344 + 0.888258i
\(129\) −1.25594 + 2.60799i −0.110580 + 0.229621i
\(130\) −3.28959 + 8.22128i −0.288516 + 0.721054i
\(131\) −1.29608 11.5030i −0.113239 1.00503i −0.913909 0.405920i \(-0.866951\pi\)
0.800670 0.599106i \(-0.204477\pi\)
\(132\) −1.23251 8.98260i −0.107276 0.781835i
\(133\) 2.31197 2.31197i 0.200473 0.200473i
\(134\) −16.8494 2.65383i −1.45557 0.229256i
\(135\) 10.3617 6.51069i 0.891793 0.560351i
\(136\) 1.78203 + 2.96522i 0.152808 + 0.254266i
\(137\) 1.14587 3.27470i 0.0978980 0.279777i −0.884511 0.466520i \(-0.845508\pi\)
0.982409 + 0.186743i \(0.0597933\pi\)
\(138\) −9.41263 2.58901i −0.801256 0.220391i
\(139\) −5.03820 4.01783i −0.427334 0.340788i 0.386087 0.922462i \(-0.373826\pi\)
−0.813422 + 0.581674i \(0.802398\pi\)
\(140\) −3.52221 1.13774i −0.297681 0.0961570i
\(141\) 1.43639 6.29323i 0.120966 0.529986i
\(142\) 5.94212 + 10.4512i 0.498652 + 0.877049i
\(143\) −11.2331 1.26566i −0.939358 0.105840i
\(144\) −6.90066 2.92146i −0.575055 0.243455i
\(145\) 10.0687 + 7.80582i 0.836158 + 0.648238i
\(146\) 3.46500 + 1.86076i 0.286766 + 0.153997i
\(147\) −0.759158 + 6.73771i −0.0626143 + 0.555717i
\(148\) −0.159300 6.59242i −0.0130943 0.541894i
\(149\) −6.02225 1.37454i −0.493362 0.112607i −0.0314010 0.999507i \(-0.509997\pi\)
−0.461961 + 0.886900i \(0.652854\pi\)
\(150\) 0.160732 + 0.881390i 0.0131237 + 0.0719652i
\(151\) 4.92919 6.18101i 0.401132 0.503003i −0.539709 0.841851i \(-0.681466\pi\)
0.940841 + 0.338848i \(0.110037\pi\)
\(152\) 3.68206 + 11.2336i 0.298655 + 0.911161i
\(153\) −2.16281 0.756799i −0.174853 0.0611836i
\(154\) 0.207936 4.72060i 0.0167560 0.380397i
\(155\) 9.44835 + 15.0370i 0.758910 + 1.20780i
\(156\) 3.39590 4.47601i 0.271890 0.358368i
\(157\) 10.1649 + 10.1649i 0.811243 + 0.811243i 0.984820 0.173577i \(-0.0555325\pi\)
−0.173577 + 0.984820i \(0.555533\pi\)
\(158\) −9.28750 12.7601i −0.738874 1.01514i
\(159\) −3.08748 + 0.347876i −0.244853 + 0.0275883i
\(160\) 9.42231 9.50366i 0.744899 0.751331i
\(161\) −4.58377 2.20743i −0.361252 0.173970i
\(162\) 0.175807 0.0529572i 0.0138127 0.00416071i
\(163\) −9.48396 + 3.31858i −0.742841 + 0.259931i −0.675054 0.737769i \(-0.735880\pi\)
−0.0677872 + 0.997700i \(0.521594\pi\)
\(164\) 7.25189 16.0387i 0.566278 1.25241i
\(165\) −9.66283 + 4.65337i −0.752250 + 0.362265i
\(166\) 16.6834 + 18.2208i 1.29488 + 1.41421i
\(167\) −2.37234 10.3939i −0.183577 0.804305i −0.979909 0.199445i \(-0.936086\pi\)
0.796332 0.604860i \(-0.206771\pi\)
\(168\) 1.96335 + 1.28874i 0.151475 + 0.0994281i
\(169\) 3.73789 + 4.68716i 0.287530 + 0.360551i
\(170\) 2.68976 3.08403i 0.206295 0.236534i
\(171\) −6.62985 4.16581i −0.506998 0.318568i
\(172\) −2.48457 4.85558i −0.189446 0.370234i
\(173\) 8.38639i 0.637605i −0.947821 0.318803i \(-0.896719\pi\)
0.947821 0.318803i \(-0.103281\pi\)
\(174\) −4.84624 6.46968i −0.367392 0.490465i
\(175\) 0.466915i 0.0352954i
\(176\) 14.8878 + 8.38010i 1.12221 + 0.631674i
\(177\) 3.17024 + 1.99199i 0.238290 + 0.149727i
\(178\) 14.9723 + 13.0582i 1.12222 + 0.978756i
\(179\) 0.514989 + 0.645776i 0.0384921 + 0.0482676i 0.800705 0.599059i \(-0.204458\pi\)
−0.762213 + 0.647326i \(0.775887\pi\)
\(180\) −0.779388 + 8.82973i −0.0580921 + 0.658129i
\(181\) −4.91769 21.5458i −0.365529 1.60149i −0.738907 0.673808i \(-0.764658\pi\)
0.373378 0.927679i \(-0.378199\pi\)
\(182\) 2.15956 1.97734i 0.160077 0.146570i
\(183\) 7.19379 3.46435i 0.531780 0.256092i
\(184\) 14.6065 11.1810i 1.07680 0.824277i
\(185\) −7.36262 + 2.57629i −0.541310 + 0.189413i
\(186\) −3.24994 10.7891i −0.238297 0.791097i
\(187\) 4.70670 + 2.26663i 0.344188 + 0.165752i
\(188\) 7.81112 + 9.32357i 0.569684 + 0.679991i
\(189\) −4.02108 + 0.453067i −0.292491 + 0.0329558i
\(190\) 11.3059 8.22907i 0.820215 0.596999i
\(191\) 10.4717 + 10.4717i 0.757709 + 0.757709i 0.975905 0.218196i \(-0.0700172\pi\)
−0.218196 + 0.975905i \(0.570017\pi\)
\(192\) −7.36353 + 4.22857i −0.531417 + 0.305171i
\(193\) 2.21317 + 3.52224i 0.159307 + 0.253536i 0.916835 0.399267i \(-0.130735\pi\)
−0.757527 + 0.652804i \(0.773593\pi\)
\(194\) 6.89733 + 0.303818i 0.495199 + 0.0218129i
\(195\) −6.27301 2.19502i −0.449220 0.157189i
\(196\) −9.24964 8.81317i −0.660688 0.629512i
\(197\) −7.23081 + 9.06714i −0.515174 + 0.646007i −0.969576 0.244789i \(-0.921281\pi\)
0.454403 + 0.890796i \(0.349853\pi\)
\(198\) −11.1322 + 2.03008i −0.791128 + 0.144271i
\(199\) 1.75033 + 0.399501i 0.124078 + 0.0283199i 0.284109 0.958792i \(-0.408302\pi\)
−0.160031 + 0.987112i \(0.551159\pi\)
\(200\) −1.50615 0.762533i −0.106501 0.0539192i
\(201\) 1.43336 12.7214i 0.101101 0.897300i
\(202\) −4.95597 + 9.22875i −0.348701 + 0.649332i
\(203\) −1.87977 3.77010i −0.131934 0.264609i
\(204\) −2.16448 + 1.43411i −0.151544 + 0.100408i
\(205\) −20.6902 2.33123i −1.44507 0.162820i
\(206\) 5.38938 3.06417i 0.375496 0.213491i
\(207\) −2.71112 + 11.8782i −0.188436 + 0.825593i
\(208\) 2.85153 + 10.1954i 0.197718 + 0.706927i
\(209\) 13.9567 + 11.1301i 0.965404 + 0.769884i
\(210\) 0.736756 2.67855i 0.0508410 0.184838i
\(211\) −3.01995 + 8.63052i −0.207902 + 0.594150i −0.999865 0.0164191i \(-0.994773\pi\)
0.791963 + 0.610569i \(0.209059\pi\)
\(212\) 2.99412 5.03093i 0.205637 0.345526i
\(213\) −7.64015 + 4.80062i −0.523494 + 0.328933i
\(214\) 2.79636 17.7543i 0.191155 1.21366i
\(215\) −4.56214 + 4.56214i −0.311135 + 0.311135i
\(216\) 5.10548 13.7109i 0.347384 0.932907i
\(217\) −0.657494 5.83542i −0.0446336 0.396134i
\(218\) −18.9294 7.57425i −1.28206 0.512993i
\(219\) −1.28076 + 2.65954i −0.0865461 + 0.179715i
\(220\) 4.01962 19.8050i 0.271003 1.33525i
\(221\) 1.06918 + 3.05554i 0.0719208 + 0.205538i
\(222\) 4.93777 0.337178i 0.331402 0.0226299i
\(223\) −2.59602 5.39069i −0.173842 0.360987i 0.795783 0.605582i \(-0.207060\pi\)
−0.969626 + 0.244594i \(0.921345\pi\)
\(224\) −4.17062 + 1.47952i −0.278661 + 0.0988544i
\(225\) 1.09012 0.248813i 0.0726749 0.0165876i
\(226\) −25.8030 + 11.0550i −1.71639 + 0.735367i
\(227\) 10.5305 8.39779i 0.698933 0.557381i −0.208271 0.978071i \(-0.566784\pi\)
0.907204 + 0.420690i \(0.138212\pi\)
\(228\) −8.30137 + 3.13185i −0.549772 + 0.207412i
\(229\) −4.22508 + 6.72418i −0.279201 + 0.444346i −0.956657 0.291217i \(-0.905940\pi\)
0.677456 + 0.735564i \(0.263083\pi\)
\(230\) −17.8964 12.3759i −1.18006 0.816044i
\(231\) 3.54640 0.233336
\(232\) 15.2313 + 0.0934259i 0.999981 + 0.00613371i
\(233\) −19.6364 −1.28642 −0.643212 0.765688i \(-0.722399\pi\)
−0.643212 + 0.765688i \(0.722399\pi\)
\(234\) −5.76737 3.98831i −0.377025 0.260724i
\(235\) 7.65467 12.1823i 0.499336 0.794688i
\(236\) −6.60083 + 2.49029i −0.429678 + 0.162104i
\(237\) 9.26083 7.38526i 0.601555 0.479724i
\(238\) −1.24381 + 0.532895i −0.0806242 + 0.0345425i
\(239\) −10.6771 + 2.43699i −0.690647 + 0.157636i −0.553418 0.832904i \(-0.686677\pi\)
−0.137229 + 0.990539i \(0.543820\pi\)
\(240\) 7.43710 + 6.75102i 0.480063 + 0.435776i
\(241\) 10.5630 + 21.9343i 0.680424 + 1.41291i 0.899375 + 0.437179i \(0.144022\pi\)
−0.218951 + 0.975736i \(0.570263\pi\)
\(242\) 10.2181 0.697747i 0.656844 0.0448529i
\(243\) 5.17081 + 14.7773i 0.331708 + 0.947966i
\(244\) −2.99253 + 14.7444i −0.191577 + 0.943914i
\(245\) −6.55711 + 13.6160i −0.418918 + 0.869893i
\(246\) 12.2654 + 4.90779i 0.782016 + 0.312909i
\(247\) 1.23855 + 10.9924i 0.0788068 + 0.699430i
\(248\) 19.8973 + 7.40910i 1.26348 + 0.470478i
\(249\) −13.1111 + 13.1111i −0.830881 + 0.830881i
\(250\) 2.29202 14.5522i 0.144960 0.920362i
\(251\) 12.0771 7.58855i 0.762301 0.478985i −0.0939302 0.995579i \(-0.529943\pi\)
0.856231 + 0.516594i \(0.172800\pi\)
\(252\) 1.49901 2.51875i 0.0944290 0.158667i
\(253\) 9.17416 26.2183i 0.576775 1.64833i
\(254\) −7.32109 + 26.6166i −0.459366 + 1.67007i
\(255\) 2.40126 + 1.91494i 0.150373 + 0.119918i
\(256\) 2.03864 15.8696i 0.127415 0.991850i
\(257\) 4.02815 17.6485i 0.251269 1.10088i −0.679039 0.734103i \(-0.737603\pi\)
0.930308 0.366780i \(-0.119540\pi\)
\(258\) 3.55868 2.02331i 0.221554 0.125966i
\(259\) 2.56311 + 0.288793i 0.159264 + 0.0179447i
\(260\) 10.4394 6.91676i 0.647421 0.428959i
\(261\) −7.80048 + 6.39780i −0.482837 + 0.396014i
\(262\) −7.74517 + 14.4226i −0.478498 + 0.891033i
\(263\) −1.71506 + 15.2215i −0.105755 + 0.938600i 0.823034 + 0.567992i \(0.192279\pi\)
−0.928789 + 0.370609i \(0.879149\pi\)
\(264\) −5.79174 + 11.4398i −0.356457 + 0.704069i
\(265\) −6.75155 1.54100i −0.414745 0.0946627i
\(266\) −4.54891 + 0.829546i −0.278912 + 0.0508627i
\(267\) −9.29663 + 11.6576i −0.568945 + 0.713434i
\(268\) 17.4642 + 16.6401i 1.06679 + 1.01645i
\(269\) −6.80604 2.38153i −0.414971 0.145205i 0.114715 0.993398i \(-0.463405\pi\)
−0.529686 + 0.848194i \(0.677690\pi\)
\(270\) −17.2895 0.761580i −1.05221 0.0463483i
\(271\) 6.93414 + 11.0356i 0.421219 + 0.670366i 0.988166 0.153388i \(-0.0490184\pi\)
−0.566947 + 0.823754i \(0.691876\pi\)
\(272\) 0.312324 4.88250i 0.0189374 0.296045i
\(273\) 1.55395 + 1.55395i 0.0940491 + 0.0940491i
\(274\) −3.96693 + 2.88736i −0.239651 + 0.174432i
\(275\) −2.53321 + 0.285424i −0.152758 + 0.0172117i
\(276\) 8.86603 + 10.5827i 0.533672 + 0.637006i
\(277\) −23.8181 11.4702i −1.43109 0.689176i −0.451890 0.892074i \(-0.649250\pi\)
−0.979200 + 0.202897i \(0.934964\pi\)
\(278\) 2.62849 + 8.72604i 0.157646 + 0.523353i
\(279\) −13.2738 + 4.64470i −0.794681 + 0.278071i
\(280\) 3.18179 + 4.15657i 0.190148 + 0.248403i
\(281\) 9.82233 4.73019i 0.585951 0.282179i −0.117328 0.993093i \(-0.537433\pi\)
0.703279 + 0.710914i \(0.251718\pi\)
\(282\) −6.73288 + 6.16476i −0.400937 + 0.367106i
\(283\) −2.51402 11.0146i −0.149443 0.654753i −0.993040 0.117776i \(-0.962423\pi\)
0.843597 0.536977i \(-0.180434\pi\)
\(284\) 1.49495 16.9363i 0.0887088 1.00499i
\(285\) 6.54361 + 8.20543i 0.387610 + 0.486048i
\(286\) 12.0480 + 10.5078i 0.712414 + 0.621338i
\(287\) 5.82961 + 3.66299i 0.344111 + 0.216219i
\(288\) 5.67676 + 8.94889i 0.334506 + 0.527318i
\(289\) 15.5040i 0.911999i
\(290\) −5.43287 17.1785i −0.319029 1.00876i
\(291\) 5.18169i 0.303756i
\(292\) −2.53367 4.95155i −0.148272 0.289767i
\(293\) 5.88840 + 3.69993i 0.344004 + 0.216152i 0.692941 0.720994i \(-0.256314\pi\)
−0.348937 + 0.937146i \(0.613457\pi\)
\(294\) 6.30267 7.22651i 0.367579 0.421459i
\(295\) 5.20315 + 6.52455i 0.302939 + 0.379874i
\(296\) −5.11747 + 7.79630i −0.297447 + 0.453151i
\(297\) −4.91615 21.5391i −0.285264 1.24982i
\(298\) 5.89931 + 6.44297i 0.341738 + 0.373231i
\(299\) 15.5081 7.46830i 0.896856 0.431903i
\(300\) 0.522007 1.15450i 0.0301381 0.0666552i
\(301\) 2.01370 0.704624i 0.116068 0.0406139i
\(302\) −10.7054 + 3.22471i −0.616024 + 0.185561i
\(303\) −7.08345 3.41121i −0.406934 0.195969i
\(304\) 4.75307 16.0284i 0.272607 0.919290i
\(305\) 17.6846 1.99258i 1.01262 0.114095i
\(306\) 1.90698 + 2.62000i 0.109015 + 0.149775i
\(307\) −11.5602 11.5602i −0.659776 0.659776i 0.295551 0.955327i \(-0.404497\pi\)
−0.955327 + 0.295551i \(0.904497\pi\)
\(308\) −4.03899 + 5.32364i −0.230143 + 0.303342i
\(309\) 2.47553 + 3.93979i 0.140828 + 0.224127i
\(310\) 1.10521 25.0907i 0.0627717 1.42505i
\(311\) −29.0609 10.1689i −1.64789 0.576623i −0.662823 0.748776i \(-0.730642\pi\)
−0.985070 + 0.172153i \(0.944928\pi\)
\(312\) −7.55042 + 2.47483i −0.427459 + 0.140110i
\(313\) 12.6209 15.8262i 0.713378 0.894548i −0.284565 0.958657i \(-0.591849\pi\)
0.997943 + 0.0641089i \(0.0204205\pi\)
\(314\) −3.64720 19.9999i −0.205824 1.12866i
\(315\) −3.38019 0.771506i −0.190452 0.0434694i
\(316\) 0.539169 + 22.3129i 0.0303306 + 1.25520i
\(317\) −2.56917 + 22.8021i −0.144299 + 1.28069i 0.687733 + 0.725964i \(0.258606\pi\)
−0.832032 + 0.554727i \(0.812823\pi\)
\(318\) 3.87111 + 2.07885i 0.217081 + 0.116576i
\(319\) 19.3052 12.5032i 1.08089 0.700042i
\(320\) −18.6043 + 3.47540i −1.04001 + 0.194281i
\(321\) 13.4046 + 1.51034i 0.748174 + 0.0842990i
\(322\) 3.55615 + 6.25469i 0.198176 + 0.348560i
\(323\) 1.13755 4.98394i 0.0632950 0.277314i
\(324\) −0.247092 0.0798157i −0.0137273 0.00443420i
\(325\) −1.23505 0.984923i −0.0685085 0.0546337i
\(326\) 13.7009 + 3.76854i 0.758823 + 0.208720i
\(327\) 5.05402 14.4436i 0.279488 0.798731i
\(328\) −21.3364 + 12.8227i −1.17810 + 0.708014i
\(329\) −4.02832 + 2.53116i −0.222088 + 0.139547i
\(330\) 14.9826 + 2.35982i 0.824767 + 0.129904i
\(331\) 6.07845 6.07845i 0.334102 0.334102i −0.520040 0.854142i \(-0.674083\pi\)
0.854142 + 0.520040i \(0.174083\pi\)
\(332\) −4.74937 34.6137i −0.260656 1.89968i
\(333\) −0.691596 6.13809i −0.0378992 0.336365i
\(334\) −5.60113 + 13.9982i −0.306480 + 0.765949i
\(335\) 12.3804 25.7082i 0.676415 1.40459i
\(336\) −1.24710 3.07829i −0.0680347 0.167935i
\(337\) 8.30069 + 23.7220i 0.452167 + 1.29222i 0.914166 + 0.405340i \(0.132847\pi\)
−0.461999 + 0.886881i \(0.652868\pi\)
\(338\) −0.577603 8.45866i −0.0314175 0.460091i
\(339\) −9.14132 18.9821i −0.496488 1.03097i
\(340\) −5.60938 + 1.42370i −0.304211 + 0.0772111i
\(341\) 31.2576 7.13435i 1.69270 0.386347i
\(342\) 4.36083 + 10.1785i 0.235807 + 0.550388i
\(343\) 8.18833 6.52997i 0.442128 0.352585i
\(344\) −1.01570 + 7.64642i −0.0547630 + 0.412267i
\(345\) 8.68846 13.8276i 0.467771 0.744453i
\(346\) −6.74578 + 9.75486i −0.362656 + 0.524425i
\(347\) −36.2951 −1.94842 −0.974212 0.225633i \(-0.927555\pi\)
−0.974212 + 0.225633i \(0.927555\pi\)
\(348\) 0.433006 + 11.4236i 0.0232115 + 0.612368i
\(349\) 15.9525 0.853918 0.426959 0.904271i \(-0.359585\pi\)
0.426959 + 0.904271i \(0.359585\pi\)
\(350\) 0.375574 0.543105i 0.0200753 0.0290302i
\(351\) 7.28376 11.5920i 0.388778 0.618737i
\(352\) −10.5765 21.7229i −0.563728 1.15784i
\(353\) 5.72501 4.56555i 0.304712 0.242999i −0.459181 0.888343i \(-0.651857\pi\)
0.763893 + 0.645343i \(0.223286\pi\)
\(354\) −2.08525 4.86709i −0.110830 0.258683i
\(355\) −19.6074 + 4.47526i −1.04065 + 0.237522i
\(356\) −6.91177 27.2324i −0.366323 1.44331i
\(357\) −0.440648 0.915016i −0.0233216 0.0484278i
\(358\) −0.0795795 1.16540i −0.00420591 0.0615931i
\(359\) 4.85484 + 13.8743i 0.256229 + 0.732260i 0.998094 + 0.0617111i \(0.0196557\pi\)
−0.741865 + 0.670549i \(0.766059\pi\)
\(360\) 8.00897 9.64364i 0.422110 0.508264i
\(361\) −0.664371 + 1.37958i −0.0349669 + 0.0726095i
\(362\) −11.6107 + 29.0173i −0.610245 + 1.52511i
\(363\) 0.860657 + 7.63855i 0.0451728 + 0.400920i
\(364\) −4.10247 + 0.562903i −0.215028 + 0.0295041i
\(365\) −4.65231 + 4.65231i −0.243513 + 0.243513i
\(366\) −11.1543 1.75684i −0.583044 0.0918313i
\(367\) −13.5733 + 8.52869i −0.708522 + 0.445194i −0.837488 0.546455i \(-0.815977\pi\)
0.128966 + 0.991649i \(0.458834\pi\)
\(368\) −25.9837 + 1.25648i −1.35449 + 0.0654983i
\(369\) 5.44558 15.5626i 0.283485 0.810155i
\(370\) 10.6363 + 2.92560i 0.552957 + 0.152095i
\(371\) 1.79035 + 1.42775i 0.0929502 + 0.0741253i
\(372\) −4.89822 + 15.1638i −0.253961 + 0.786208i
\(373\) 2.01554 8.83065i 0.104361 0.457234i −0.895564 0.444933i \(-0.853227\pi\)
0.999924 0.0123004i \(-0.00391545\pi\)
\(374\) −3.65151 6.42243i −0.188815 0.332096i
\(375\) 10.9870 + 1.23794i 0.567368 + 0.0639270i
\(376\) −1.58609 17.1280i −0.0817966 0.883311i
\(377\) 13.9377 + 2.98051i 0.717826 + 0.153504i
\(378\) 5.04167 + 2.70745i 0.259315 + 0.139256i
\(379\) −1.09499 + 9.71832i −0.0562460 + 0.499197i 0.933732 + 0.357973i \(0.116532\pi\)
−0.989978 + 0.141223i \(0.954896\pi\)
\(380\) −19.7700 + 0.477723i −1.01418 + 0.0245067i
\(381\) −20.1991 4.61031i −1.03483 0.236193i
\(382\) −3.75732 20.6037i −0.192241 1.05418i
\(383\) 15.4010 19.3122i 0.786955 0.986810i −0.212998 0.977053i \(-0.568323\pi\)
0.999952 0.00975709i \(-0.00310583\pi\)
\(384\) 11.9664 + 1.00444i 0.610660 + 0.0512577i
\(385\) 7.46094 + 2.61069i 0.380245 + 0.133053i
\(386\) 0.258883 5.87721i 0.0131768 0.299142i
\(387\) −2.71819 4.32598i −0.138173 0.219902i
\(388\) −7.77844 5.90142i −0.394890 0.299599i
\(389\) −2.88848 2.88848i −0.146452 0.146452i 0.630079 0.776531i \(-0.283022\pi\)
−0.776531 + 0.630079i \(0.783022\pi\)
\(390\) 5.53101 + 7.59904i 0.280074 + 0.384792i
\(391\) −7.90455 + 0.890629i −0.399750 + 0.0450410i
\(392\) 3.66990 + 17.6914i 0.185358 + 0.893553i
\(393\) −11.0700 5.33102i −0.558407 0.268914i
\(394\) 15.7041 4.73044i 0.791160 0.238316i
\(395\) 24.9197 8.71977i 1.25385 0.438739i
\(396\) 14.5816 + 6.59307i 0.732754 + 0.331314i
\(397\) 12.6248 6.07977i 0.633619 0.305135i −0.0893658 0.995999i \(-0.528484\pi\)
0.722985 + 0.690864i \(0.242770\pi\)
\(398\) −1.71460 1.87261i −0.0859450 0.0938654i
\(399\) −0.772240 3.38340i −0.0386603 0.169382i
\(400\) 1.13856 + 2.09847i 0.0569278 + 0.104923i
\(401\) 12.7554 + 15.9947i 0.636973 + 0.798739i 0.990621 0.136640i \(-0.0436302\pi\)
−0.353648 + 0.935379i \(0.615059\pi\)
\(402\) −11.9000 + 13.6443i −0.593519 + 0.680517i
\(403\) 16.8224 + 10.5702i 0.837985 + 0.526541i
\(404\) 13.1880 6.74823i 0.656129 0.335737i
\(405\) 0.307152i 0.0152625i
\(406\) −0.846061 + 5.89733i −0.0419893 + 0.292679i
\(407\) 14.0825i 0.698043i
\(408\) 3.67124 + 0.0729235i 0.181753 + 0.00361025i
\(409\) 0.895309 + 0.562560i 0.0442702 + 0.0278168i 0.553985 0.832526i \(-0.313106\pi\)
−0.509715 + 0.860343i \(0.670249\pi\)
\(410\) 22.1912 + 19.3543i 1.09595 + 0.955840i
\(411\) −2.29598 2.87906i −0.113252 0.142014i
\(412\) −8.73355 0.770898i −0.430271 0.0379794i
\(413\) −0.614046 2.69031i −0.0302152 0.132382i
\(414\) 12.7080 11.6357i 0.624566 0.571865i
\(415\) −37.2349 + 17.9314i −1.82779 + 0.880218i
\(416\) 4.88410 14.1528i 0.239463 0.693899i
\(417\) −6.45602 + 2.25906i −0.316153 + 0.110627i
\(418\) −7.28137 24.1726i −0.356143 1.18232i
\(419\) 15.7883 + 7.60324i 0.771308 + 0.371442i 0.777780 0.628537i \(-0.216346\pi\)
−0.00647185 + 0.999979i \(0.502060\pi\)
\(420\) −3.01154 + 2.52301i −0.146948 + 0.123110i
\(421\) −27.8538 + 3.13837i −1.35751 + 0.152955i −0.760530 0.649302i \(-0.775061\pi\)
−0.596979 + 0.802257i \(0.703632\pi\)
\(422\) 10.4549 7.60967i 0.508937 0.370433i
\(423\) 8.05624 + 8.05624i 0.391708 + 0.391708i
\(424\) −7.52944 + 3.44349i −0.365662 + 0.167231i
\(425\) 0.388400 + 0.618135i 0.0188402 + 0.0299839i
\(426\) 12.7483 + 0.561547i 0.617659 + 0.0272071i
\(427\) −5.55452 1.94361i −0.268802 0.0940580i
\(428\) −17.5338 + 18.4021i −0.847526 + 0.889500i
\(429\) −7.48088 + 9.38072i −0.361180 + 0.452905i
\(430\) 8.97625 1.63692i 0.432873 0.0789393i
\(431\) 11.4853 + 2.62145i 0.553228 + 0.126271i 0.489990 0.871728i \(-0.337000\pi\)
0.0632374 + 0.997999i \(0.479857\pi\)
\(432\) −16.9672 + 11.8415i −0.816337 + 0.569724i
\(433\) 1.51457 13.4422i 0.0727855 0.645989i −0.903362 0.428879i \(-0.858909\pi\)
0.976147 0.217110i \(-0.0696629\pi\)
\(434\) −3.92907 + 7.31650i −0.188601 + 0.351203i
\(435\) 12.7011 4.64097i 0.608972 0.222517i
\(436\) 15.9258 + 24.0365i 0.762706 + 1.15114i
\(437\) −27.0109 3.04340i −1.29211 0.145586i
\(438\) 3.62902 2.06330i 0.173401 0.0985884i
\(439\) −4.48987 + 19.6714i −0.214290 + 0.938864i 0.747324 + 0.664459i \(0.231338\pi\)
−0.961614 + 0.274405i \(0.911519\pi\)
\(440\) −20.6061 + 19.8034i −0.982358 + 0.944092i
\(441\) −9.35644 7.46151i −0.445545 0.355310i
\(442\) 1.21415 4.41416i 0.0577511 0.209960i
\(443\) 5.24946 15.0021i 0.249409 0.712771i −0.749312 0.662217i \(-0.769616\pi\)
0.998721 0.0505539i \(-0.0160987\pi\)
\(444\) −6.01473 3.57961i −0.285446 0.169881i
\(445\) −28.1401 + 17.6816i −1.33397 + 0.838188i
\(446\) −1.31649 + 8.35851i −0.0623377 + 0.395787i
\(447\) −4.63614 + 4.63614i −0.219282 + 0.219282i
\(448\) 6.04126 + 1.63379i 0.285423 + 0.0771895i
\(449\) 1.28065 + 11.3661i 0.0604378 + 0.536400i 0.987054 + 0.160391i \(0.0512754\pi\)
−0.926616 + 0.376009i \(0.877296\pi\)
\(450\) −1.46815 0.587451i −0.0692091 0.0276927i
\(451\) −16.3096 + 33.8672i −0.767989 + 1.59475i
\(452\) 38.9059 + 7.89634i 1.82998 + 0.371412i
\(453\) −2.77148 7.92044i −0.130215 0.372135i
\(454\) −19.0038 + 1.29768i −0.891892 + 0.0609032i
\(455\) 2.12526 + 4.41314i 0.0996336 + 0.206891i
\(456\) 12.1752 + 3.03450i 0.570154 + 0.142103i
\(457\) 2.98497 0.681299i 0.139631 0.0318698i −0.152134 0.988360i \(-0.548615\pi\)
0.291765 + 0.956490i \(0.405757\pi\)
\(458\) 10.3233 4.42288i 0.482375 0.206667i
\(459\) −4.94651 + 3.94471i −0.230883 + 0.184123i
\(460\) 10.8619 + 28.7908i 0.506438 + 1.34238i
\(461\) −2.17426 + 3.46031i −0.101265 + 0.161163i −0.893514 0.449036i \(-0.851768\pi\)
0.792248 + 0.610199i \(0.208910\pi\)
\(462\) −4.12510 2.85263i −0.191917 0.132716i
\(463\) 7.23025 0.336018 0.168009 0.985785i \(-0.446266\pi\)
0.168009 + 0.985785i \(0.446266\pi\)
\(464\) −17.6415 12.3603i −0.818987 0.573812i
\(465\) 18.8496 0.874131
\(466\) 22.8407 + 15.7950i 1.05807 + 0.731689i
\(467\) −7.34971 + 11.6970i −0.340104 + 0.541272i −0.972360 0.233487i \(-0.924986\pi\)
0.632256 + 0.774760i \(0.282129\pi\)
\(468\) 3.50039 + 9.27823i 0.161806 + 0.428886i
\(469\) −7.37681 + 5.88281i −0.340629 + 0.271643i
\(470\) −18.7029 + 8.01303i −0.862700 + 0.369613i
\(471\) 14.8756 3.39525i 0.685430 0.156445i
\(472\) 9.68107 + 2.41288i 0.445607 + 0.111062i
\(473\) 5.05385 + 10.4944i 0.232376 + 0.482534i
\(474\) −16.7125 + 1.14122i −0.767631 + 0.0524180i
\(475\) 0.823919 + 2.35463i 0.0378040 + 0.108038i
\(476\) 1.87542 + 0.380635i 0.0859597 + 0.0174464i
\(477\) 2.37938 4.94082i 0.108944 0.226225i
\(478\) 14.3797 + 5.75376i 0.657711 + 0.263171i
\(479\) 3.00221 + 26.6453i 0.137174 + 1.21746i 0.854026 + 0.520230i \(0.174154\pi\)
−0.716852 + 0.697225i \(0.754418\pi\)
\(480\) −3.22034 13.8348i −0.146988 0.631471i
\(481\) −6.17060 + 6.17060i −0.281355 + 0.281355i
\(482\) 5.35671 34.0102i 0.243992 1.54912i
\(483\) −4.57235 + 2.87300i −0.208049 + 0.130726i
\(484\) −12.4467 7.40756i −0.565760 0.336707i
\(485\) −3.81452 + 10.9013i −0.173208 + 0.495001i
\(486\) 5.87191 21.3479i 0.266355 0.968362i
\(487\) −16.3336 13.0256i −0.740144 0.590245i 0.179147 0.983822i \(-0.442666\pi\)
−0.919292 + 0.393577i \(0.871238\pi\)
\(488\) 15.3409 14.7433i 0.694448 0.667397i
\(489\) −2.37316 + 10.3975i −0.107318 + 0.470191i
\(490\) 18.5794 10.5635i 0.839332 0.477208i
\(491\) −17.7336 1.99810i −0.800306 0.0901728i −0.297667 0.954670i \(-0.596209\pi\)
−0.502638 + 0.864497i \(0.667637\pi\)
\(492\) −10.3192 15.5746i −0.465226 0.702158i
\(493\) −5.62469 3.42745i −0.253323 0.154365i
\(494\) 7.40134 13.7824i 0.333002 0.620099i
\(495\) 2.11944 18.8105i 0.0952617 0.845471i
\(496\) −17.1845 24.6230i −0.771605 1.10560i
\(497\) 6.48355 + 1.47983i 0.290827 + 0.0663793i
\(498\) 25.7967 4.70433i 1.15598 0.210806i
\(499\) 22.8214 28.6171i 1.02163 1.28108i 0.0625170 0.998044i \(-0.480087\pi\)
0.959110 0.283035i \(-0.0913413\pi\)
\(500\) −14.3714 + 15.0832i −0.642710 + 0.674540i
\(501\) −10.6809 3.73742i −0.477189 0.166976i
\(502\) −20.1519 0.887662i −0.899422 0.0396183i
\(503\) −7.21504 11.4827i −0.321703 0.511987i 0.646248 0.763128i \(-0.276337\pi\)
−0.967951 + 0.251141i \(0.919194\pi\)
\(504\) −3.76964 + 1.72399i −0.167913 + 0.0767927i
\(505\) −12.3910 12.3910i −0.551394 0.551394i
\(506\) −31.7604 + 23.1171i −1.41192 + 1.02768i
\(507\) 6.32328 0.712462i 0.280827 0.0316416i
\(508\) 29.9254 25.0710i 1.32773 1.11234i
\(509\) 18.3428 + 8.83344i 0.813031 + 0.391535i 0.793724 0.608278i \(-0.208140\pi\)
0.0193074 + 0.999814i \(0.493854\pi\)
\(510\) −1.25277 4.15892i −0.0554734 0.184160i
\(511\) 2.05350 0.718551i 0.0908415 0.0317868i
\(512\) −15.1364 + 16.8193i −0.668939 + 0.743317i
\(513\) −19.4786 + 9.38040i −0.860002 + 0.414155i
\(514\) −18.8814 + 17.2882i −0.832824 + 0.762550i
\(515\) 2.30775 + 10.1109i 0.101692 + 0.445540i
\(516\) −5.76688 0.509034i −0.253873 0.0224090i
\(517\) −16.1951 20.3080i −0.712260 0.893145i
\(518\) −2.74906 2.39762i −0.120787 0.105345i
\(519\) −7.53705 4.73584i −0.330840 0.207880i
\(520\) −17.7065 0.351712i −0.776481 0.0154236i
\(521\) 2.57001i 0.112594i 0.998414 + 0.0562971i \(0.0179294\pi\)
−0.998414 + 0.0562971i \(0.982071\pi\)
\(522\) 14.2196 1.16729i 0.622373 0.0510908i
\(523\) 33.3214i 1.45704i −0.685023 0.728521i \(-0.740208\pi\)
0.685023 0.728521i \(-0.259792\pi\)
\(524\) 20.6102 10.5461i 0.900360 0.460708i
\(525\) 0.419628 + 0.263670i 0.0183141 + 0.0115075i
\(526\) 14.2387 16.3258i 0.620837 0.711840i
\(527\) −5.72459 7.17840i −0.249367 0.312696i
\(528\) 15.9387 8.64777i 0.693641 0.376346i
\(529\) 4.29369 + 18.8119i 0.186682 + 0.817907i
\(530\) 6.61372 + 7.22322i 0.287282 + 0.313757i
\(531\) −5.95395 + 2.86727i −0.258379 + 0.124429i
\(532\) 5.95846 + 2.69411i 0.258332 + 0.116805i
\(533\) −21.9863 + 7.69332i −0.952330 + 0.333235i
\(534\) 20.1907 6.08192i 0.873737 0.263190i
\(535\) 27.0889 + 13.0453i 1.17116 + 0.563999i
\(536\) −6.92912 33.4031i −0.299292 1.44279i
\(537\) 0.871192 0.0981598i 0.0375947 0.00423591i
\(538\) 6.00099 + 8.24474i 0.258721 + 0.355456i
\(539\) 19.2925 + 19.2925i 0.830989 + 0.830989i
\(540\) 19.4982 + 14.7931i 0.839069 + 0.636593i
\(541\) −11.2033 17.8300i −0.481668 0.766570i 0.514172 0.857687i \(-0.328099\pi\)
−0.995840 + 0.0911169i \(0.970956\pi\)
\(542\) 0.811113 18.4140i 0.0348403 0.790950i
\(543\) −22.1408 7.74740i −0.950153 0.332473i
\(544\) −4.29064 + 5.42799i −0.183960 + 0.232723i
\(545\) 21.2654 26.6659i 0.910908 1.14224i
\(546\) −0.557564 3.05747i −0.0238615 0.130848i
\(547\) 6.37690 + 1.45549i 0.272656 + 0.0622320i 0.356663 0.934233i \(-0.383914\pi\)
−0.0840064 + 0.996465i \(0.526772\pi\)
\(548\) 6.93676 0.167620i 0.296324 0.00716038i
\(549\) −1.57788 + 14.0041i −0.0673423 + 0.597679i
\(550\) 3.17616 + 1.70564i 0.135432 + 0.0727289i
\(551\) −16.1323 15.6954i −0.687258 0.668645i
\(552\) −1.80030 19.4412i −0.0766259 0.827473i
\(553\) −8.67517 0.977457i −0.368906 0.0415657i
\(554\) 18.4784 + 32.5005i 0.785071 + 1.38081i
\(555\) −1.84234 + 8.07181i −0.0782029 + 0.342629i
\(556\) 3.96159 12.2642i 0.168009 0.520119i
\(557\) 7.49091 + 5.97380i 0.317400 + 0.253118i 0.769210 0.638996i \(-0.220650\pi\)
−0.451810 + 0.892114i \(0.649221\pi\)
\(558\) 19.1759 + 5.27446i 0.811779 + 0.223286i
\(559\) −2.38393 + 6.81288i −0.100829 + 0.288154i
\(560\) −0.357556 7.39419i −0.0151095 0.312461i
\(561\) 4.69497 2.95005i 0.198222 0.124551i
\(562\) −15.2300 2.39877i −0.642437 0.101186i
\(563\) −20.3426 + 20.3426i −0.857339 + 0.857339i −0.991024 0.133685i \(-0.957319\pi\)
0.133685 + 0.991024i \(0.457319\pi\)
\(564\) 12.7903 1.75497i 0.538569 0.0738974i
\(565\) −5.25779 46.6642i −0.221197 1.96318i
\(566\) −5.93563 + 14.8342i −0.249493 + 0.623529i
\(567\) 0.0440676 0.0915073i 0.00185067 0.00384295i
\(568\) −15.3620 + 18.4975i −0.644576 + 0.776138i
\(569\) 11.7965 + 33.7126i 0.494536 + 1.41330i 0.873015 + 0.487694i \(0.162162\pi\)
−0.378479 + 0.925610i \(0.623553\pi\)
\(570\) −1.01116 14.8079i −0.0423529 0.620234i
\(571\) 11.5707 + 24.0268i 0.484218 + 1.00549i 0.989767 + 0.142691i \(0.0455756\pi\)
−0.505549 + 0.862798i \(0.668710\pi\)
\(572\) −5.56181 21.9135i −0.232551 0.916250i
\(573\) 15.3247 3.49776i 0.640198 0.146121i
\(574\) −3.83447 8.94989i −0.160048 0.373561i
\(575\) 3.03482 2.42019i 0.126561 0.100929i
\(576\) 0.595160 14.9754i 0.0247984 0.623974i
\(577\) 11.0405 17.5709i 0.459624 0.731487i −0.533846 0.845582i \(-0.679254\pi\)
0.993470 + 0.114095i \(0.0363967\pi\)
\(578\) 12.4710 18.0339i 0.518724 0.750111i
\(579\) 4.41531 0.183494
\(580\) −7.49855 + 24.3517i −0.311360 + 1.01115i
\(581\) 13.6658 0.566951
\(582\) 4.16801 6.02723i 0.172770 0.249837i
\(583\) −6.65173 + 10.5862i −0.275486 + 0.438434i
\(584\) −1.03578 + 7.79755i −0.0428608 + 0.322665i
\(585\) 9.17100 7.31363i 0.379174 0.302381i
\(586\) −3.87314 9.04015i −0.159998 0.373445i
\(587\) 4.82554 1.10140i 0.199171 0.0454596i −0.121771 0.992558i \(-0.538857\pi\)
0.320943 + 0.947099i \(0.396000\pi\)
\(588\) −13.1439 + 3.33603i −0.542047 + 0.137575i
\(589\) −13.6129 28.2675i −0.560910 1.16474i
\(590\) −0.804025 11.7745i −0.0331012 0.484748i
\(591\) 4.06559 + 11.6188i 0.167236 + 0.477933i
\(592\) 12.2237 4.95213i 0.502390 0.203531i
\(593\) −8.03058 + 16.6757i −0.329777 + 0.684788i −0.998262 0.0589374i \(-0.981229\pi\)
0.668485 + 0.743726i \(0.266943\pi\)
\(594\) −11.6071 + 29.0082i −0.476244 + 1.19022i
\(595\) −0.253447 2.24940i −0.0103903 0.0922164i
\(596\) −1.67940 12.2396i −0.0687908 0.501352i
\(597\) 1.34746 1.34746i 0.0551480 0.0551480i
\(598\) −24.0460 3.78732i −0.983313 0.154875i
\(599\) 22.4419 14.1012i 0.916953 0.576160i 0.0111869 0.999937i \(-0.496439\pi\)
0.905766 + 0.423778i \(0.139296\pi\)
\(600\) −1.53584 + 0.923004i −0.0627003 + 0.0376815i
\(601\) −1.28953 + 3.68525i −0.0526009 + 0.150325i −0.967186 0.254068i \(-0.918231\pi\)
0.914586 + 0.404393i \(0.132517\pi\)
\(602\) −2.90907 0.800163i −0.118565 0.0326122i
\(603\) 17.6658 + 14.0880i 0.719408 + 0.573709i
\(604\) 15.0461 + 4.86019i 0.612218 + 0.197758i
\(605\) −3.81249 + 16.7036i −0.155000 + 0.679098i
\(606\) 5.49543 + 9.66559i 0.223237 + 0.392638i
\(607\) −14.0893 1.58748i −0.571867 0.0644339i −0.178704 0.983903i \(-0.557191\pi\)
−0.393163 + 0.919469i \(0.628619\pi\)
\(608\) −18.4215 + 14.8206i −0.747089 + 0.601055i
\(609\) −4.44979 0.439605i −0.180315 0.0178137i
\(610\) −22.1732 11.9073i −0.897765 0.482113i
\(611\) 1.80218 15.9948i 0.0729083 0.647079i
\(612\) −0.110706 4.58145i −0.00447504 0.185194i
\(613\) 1.45423 + 0.331918i 0.0587357 + 0.0134060i 0.251788 0.967782i \(-0.418981\pi\)
−0.193052 + 0.981189i \(0.561839\pi\)
\(614\) 4.14786 + 22.7453i 0.167394 + 0.917925i
\(615\) −13.7790 + 17.2784i −0.555624 + 0.696730i
\(616\) 8.98025 2.94349i 0.361825 0.118597i
\(617\) −4.49657 1.57342i −0.181025 0.0633434i 0.238245 0.971205i \(-0.423428\pi\)
−0.419269 + 0.907862i \(0.637714\pi\)
\(618\) 0.289573 6.57393i 0.0116483 0.264442i
\(619\) −15.9013 25.3068i −0.639127 1.01716i −0.996532 0.0832147i \(-0.973481\pi\)
0.357405 0.933949i \(-0.383662\pi\)
\(620\) −21.4678 + 28.2959i −0.862168 + 1.13639i
\(621\) 23.7876 + 23.7876i 0.954562 + 0.954562i
\(622\) 25.6235 + 35.2040i 1.02741 + 1.41155i
\(623\) 10.9204 1.23043i 0.437515 0.0492962i
\(624\) 10.7732 + 3.19469i 0.431272 + 0.127890i
\(625\) 24.8920 + 11.9874i 0.995681 + 0.479495i
\(626\) −27.4106 + 8.25671i −1.09555 + 0.330004i
\(627\) 17.8843 6.25799i 0.714230 0.249920i
\(628\) −11.8450 + 26.1971i −0.472667 + 1.04538i
\(629\) 3.63346 1.74978i 0.144875 0.0697684i
\(630\) 3.31118 + 3.61633i 0.131921 + 0.144078i
\(631\) −4.17410 18.2879i −0.166168 0.728030i −0.987505 0.157587i \(-0.949629\pi\)
0.821337 0.570443i \(-0.193229\pi\)
\(632\) 17.3207 26.3875i 0.688981 1.04964i
\(633\) 6.05108 + 7.58781i 0.240509 + 0.301589i
\(634\) 21.3298 24.4563i 0.847113 0.971283i
\(635\) −39.1011 24.5688i −1.55168 0.974984i
\(636\) −2.83063 5.53189i −0.112242 0.219354i
\(637\) 16.9070i 0.669881i
\(638\) −32.5126 0.985210i −1.28719 0.0390048i
\(639\) 15.9260i 0.630021i
\(640\) 24.4357 + 10.9223i 0.965904 + 0.431742i
\(641\) −25.1959 15.8316i −0.995177 0.625311i −0.0671184 0.997745i \(-0.521381\pi\)
−0.928059 + 0.372434i \(0.878523\pi\)
\(642\) −14.3771 12.5391i −0.567420 0.494880i
\(643\) −0.718474 0.900938i −0.0283339 0.0355295i 0.767463 0.641094i \(-0.221519\pi\)
−0.795797 + 0.605564i \(0.792948\pi\)
\(644\) 0.894672 10.1358i 0.0352550 0.399406i
\(645\) 1.52384 + 6.67638i 0.0600011 + 0.262882i
\(646\) −5.33212 + 4.88219i −0.209789 + 0.192087i
\(647\) 20.6835 9.96065i 0.813152 0.391594i 0.0193828 0.999812i \(-0.493830\pi\)
0.793770 + 0.608219i \(0.208116\pi\)
\(648\) 0.223211 + 0.291594i 0.00876854 + 0.0114549i
\(649\) 14.2207 4.97604i 0.558211 0.195326i
\(650\) 0.644343 + 2.13909i 0.0252732 + 0.0839019i
\(651\) −5.61573 2.70439i −0.220098 0.105993i
\(652\) −12.9053 15.4041i −0.505410 0.603272i
\(653\) 19.4039 2.18629i 0.759332 0.0855562i 0.276196 0.961101i \(-0.410926\pi\)
0.483136 + 0.875545i \(0.339498\pi\)
\(654\) −17.4967 + 12.7351i −0.684176 + 0.497983i
\(655\) −19.3646 19.3646i −0.756639 0.756639i
\(656\) 35.1322 + 2.24734i 1.37168 + 0.0877439i
\(657\) −2.77191 4.41148i −0.108143 0.172108i
\(658\) 6.72165 + 0.296080i 0.262037 + 0.0115424i
\(659\) 37.0851 + 12.9766i 1.44463 + 0.505498i 0.934923 0.354851i \(-0.115468\pi\)
0.509707 + 0.860348i \(0.329754\pi\)
\(660\) −15.5293 14.7965i −0.604478 0.575954i
\(661\) −2.07371 + 2.60035i −0.0806580 + 0.101142i −0.820523 0.571613i \(-0.806318\pi\)
0.739865 + 0.672755i \(0.234889\pi\)
\(662\) −11.9597 + 2.18098i −0.464826 + 0.0847663i
\(663\) 3.34986 + 0.764584i 0.130098 + 0.0296940i
\(664\) −22.3180 + 44.0822i −0.866106 + 1.71072i
\(665\) 0.866062 7.68651i 0.0335844 0.298070i
\(666\) −4.13286 + 7.69599i −0.160145 + 0.298214i
\(667\) −14.7611 + 31.7598i −0.571553 + 1.22974i
\(668\) 17.7749 11.7770i 0.687732 0.455667i
\(669\) −6.31074 0.711049i −0.243987 0.0274908i
\(670\) −35.0797 + 19.9448i −1.35525 + 0.770534i
\(671\) 7.14943 31.3237i 0.276001 1.20924i
\(672\) −1.02550 + 4.58373i −0.0395594 + 0.176821i
\(673\) 17.3801 + 13.8601i 0.669952 + 0.534269i 0.898340 0.439302i \(-0.144774\pi\)
−0.228388 + 0.973570i \(0.573345\pi\)
\(674\) 9.42616 34.2698i 0.363082 1.32002i
\(675\) 1.01970 2.91412i 0.0392481 0.112165i
\(676\) −6.13207 + 10.3035i −0.235849 + 0.396290i
\(677\) 27.3957 17.2139i 1.05290 0.661583i 0.109756 0.993959i \(-0.464993\pi\)
0.943147 + 0.332376i \(0.107850\pi\)
\(678\) −4.63574 + 29.4326i −0.178034 + 1.13035i
\(679\) 2.70046 2.70046i 0.103634 0.103634i
\(680\) 7.66990 + 2.85601i 0.294127 + 0.109523i
\(681\) −1.60067 14.2063i −0.0613376 0.544387i
\(682\) −42.0969 16.8443i −1.61197 0.645001i
\(683\) 2.53543 5.26488i 0.0970156 0.201455i −0.846813 0.531891i \(-0.821482\pi\)
0.943828 + 0.330436i \(0.107196\pi\)
\(684\) 3.11485 15.3471i 0.119099 0.586811i
\(685\) −2.71086 7.74718i −0.103576 0.296005i
\(686\) −14.7770 + 1.00905i −0.564189 + 0.0385259i
\(687\) 3.65725 + 7.59437i 0.139533 + 0.289743i
\(688\) 7.33202 8.07715i 0.279531 0.307938i
\(689\) −7.55322 + 1.72397i −0.287755 + 0.0656782i
\(690\) −21.2288 + 9.09521i −0.808166 + 0.346249i
\(691\) −21.3760 + 17.0468i −0.813183 + 0.648492i −0.939136 0.343544i \(-0.888372\pi\)
0.125954 + 0.992036i \(0.459801\pi\)
\(692\) 15.6931 5.92052i 0.596562 0.225064i
\(693\) −3.33021 + 5.30000i −0.126504 + 0.201330i
\(694\) 42.2177 + 29.1948i 1.60256 + 1.10822i
\(695\) −15.2452 −0.578285
\(696\) 8.68515 13.6360i 0.329210 0.516869i
\(697\) 10.7647 0.407741
\(698\) −18.5556 12.8318i −0.702340 0.485689i
\(699\) −11.0888 + 17.6477i −0.419417 + 0.667499i
\(700\) −0.873718 + 0.329627i −0.0330235 + 0.0124587i
\(701\) 20.3212 16.2056i 0.767521 0.612078i −0.159452 0.987206i \(-0.550973\pi\)
0.926973 + 0.375128i \(0.122401\pi\)
\(702\) −17.7966 + 7.62474i −0.671690 + 0.287777i
\(703\) 13.4352 3.06651i 0.506720 0.115655i
\(704\) −5.17100 + 33.7751i −0.194889 + 1.27295i
\(705\) −6.62593 13.7589i −0.249547 0.518190i
\(706\) −10.3316 + 0.705498i −0.388835 + 0.0265518i
\(707\) 1.91380 + 5.46933i 0.0719759 + 0.205695i
\(708\) −1.48945 + 7.33861i −0.0559768 + 0.275802i
\(709\) 4.27540 8.87796i 0.160566 0.333419i −0.805128 0.593101i \(-0.797903\pi\)
0.965694 + 0.259682i \(0.0836178\pi\)
\(710\) 26.4067 + 10.5661i 0.991025 + 0.396540i
\(711\) 2.34079 + 20.7751i 0.0877866 + 0.779127i
\(712\) −13.8654 + 37.2357i −0.519626 + 1.39547i
\(713\) −34.5206 + 34.5206i −1.29281 + 1.29281i
\(714\) −0.223461 + 1.41877i −0.00836283 + 0.0530962i
\(715\) −22.6440 + 14.2281i −0.846836 + 0.532103i
\(716\) −0.844848 + 1.41958i −0.0315734 + 0.0530520i
\(717\) −3.83927 + 10.9720i −0.143380 + 0.409757i
\(718\) 5.51310 20.0435i 0.205747 0.748015i
\(719\) −19.3314 15.4162i −0.720938 0.574929i 0.192797 0.981239i \(-0.438244\pi\)
−0.913735 + 0.406310i \(0.866815\pi\)
\(720\) −17.0729 + 4.77507i −0.636271 + 0.177956i
\(721\) 0.763101 3.34337i 0.0284194 0.124513i
\(722\) 1.88248 1.07030i 0.0700587 0.0398323i
\(723\) 25.6779 + 2.89321i 0.954973 + 0.107600i
\(724\) 36.8460 24.4129i 1.36937 0.907299i
\(725\) 3.21389 0.0441201i 0.119361 0.00163858i
\(726\) 5.14314 9.57728i 0.190880 0.355446i
\(727\) 0.991505 8.79985i 0.0367729 0.326368i −0.961835 0.273629i \(-0.911776\pi\)
0.998608 0.0527397i \(-0.0167953\pi\)
\(728\) 5.22469 + 2.64516i 0.193640 + 0.0980363i
\(729\) 15.8210 + 3.61104i 0.585964 + 0.133742i
\(730\) 9.15365 1.66927i 0.338792 0.0617826i
\(731\) 2.07974 2.60791i 0.0769220 0.0964572i
\(732\) 11.5613 + 11.0157i 0.427317 + 0.407153i
\(733\) 19.0805 + 6.67656i 0.704755 + 0.246604i 0.658777 0.752338i \(-0.271074\pi\)
0.0459776 + 0.998942i \(0.485360\pi\)
\(734\) 22.6484 + 0.997634i 0.835969 + 0.0368233i
\(735\) 8.53418 + 13.5821i 0.314788 + 0.500982i
\(736\) 31.2343 + 19.4391i 1.15131 + 0.716533i
\(737\) −36.4261 36.4261i −1.34177 1.34177i
\(738\) −18.8523 + 13.7218i −0.693962 + 0.505105i
\(739\) −4.54368 + 0.511950i −0.167142 + 0.0188324i −0.195139 0.980776i \(-0.562516\pi\)
0.0279968 + 0.999608i \(0.491087\pi\)
\(740\) −10.0187 11.9586i −0.368294 0.439606i
\(741\) 10.5786 + 5.09437i 0.388613 + 0.187146i
\(742\) −0.934047 3.10084i −0.0342899 0.113835i
\(743\) 2.18529 0.764666i 0.0801705 0.0280529i −0.289896 0.957058i \(-0.593621\pi\)
0.370066 + 0.929005i \(0.379335\pi\)
\(744\) 17.8949 13.6982i 0.656058 0.502202i
\(745\) −13.1664 + 6.34062i −0.482381 + 0.232302i
\(746\) −9.44757 + 8.65038i −0.345900 + 0.316713i
\(747\) −7.28233 31.9060i −0.266446 1.16738i
\(748\) −0.918665 + 10.4076i −0.0335897 + 0.380540i
\(749\) −6.19876 7.77300i −0.226498 0.284019i
\(750\) −11.7841 10.2776i −0.430295 0.375285i
\(751\) 24.4734 + 15.3777i 0.893047 + 0.561138i 0.898562 0.438846i \(-0.144613\pi\)
−0.00551534 + 0.999985i \(0.501756\pi\)
\(752\) −11.9324 + 21.1988i −0.435130 + 0.773040i
\(753\) 15.1393i 0.551707i
\(754\) −13.8146 14.6779i −0.503096 0.534539i
\(755\) 18.7033i 0.680683i
\(756\) −3.68656 7.20463i −0.134079 0.262030i
\(757\) 6.28429 + 3.94868i 0.228406 + 0.143517i 0.641374 0.767229i \(-0.278365\pi\)
−0.412967 + 0.910746i \(0.635508\pi\)
\(758\) 9.09083 10.4234i 0.330194 0.378594i
\(759\) −18.3823 23.0507i −0.667235 0.836686i
\(760\) 23.3803 + 15.3468i 0.848093 + 0.556686i
\(761\) 3.71038 + 16.2562i 0.134501 + 0.589288i 0.996589 + 0.0825289i \(0.0262997\pi\)
−0.862087 + 0.506760i \(0.830843\pi\)
\(762\) 19.7867 + 21.6102i 0.716797 + 0.782855i
\(763\) −10.1612 + 4.89339i −0.367861 + 0.177153i
\(764\) −12.2026 + 26.9881i −0.441476 + 0.976394i
\(765\) −5.11670 + 1.79041i −0.184995 + 0.0647324i
\(766\) −33.4484 + 10.0754i −1.20854 + 0.364040i
\(767\) 8.41154 + 4.05078i 0.303723 + 0.146265i
\(768\) −13.1112 10.7938i −0.473108 0.389489i
\(769\) −48.8719 + 5.50654i −1.76236 + 0.198571i −0.932936 0.360043i \(-0.882762\pi\)
−0.829428 + 0.558613i \(0.811334\pi\)
\(770\) −6.57843 9.03808i −0.237070 0.325710i
\(771\) −13.5864 13.5864i −0.489303 0.489303i
\(772\) −5.02859 + 6.62800i −0.180983 + 0.238547i
\(773\) −1.73239 2.75708i −0.0623097 0.0991653i 0.814116 0.580702i \(-0.197222\pi\)
−0.876426 + 0.481536i \(0.840079\pi\)
\(774\) −0.317957 + 7.21832i −0.0114287 + 0.259457i
\(775\) 4.22899 + 1.47979i 0.151910 + 0.0531555i
\(776\) 4.30077 + 13.1212i 0.154389 + 0.471023i
\(777\) 1.70695 2.14045i 0.0612365 0.0767882i
\(778\) 1.03640 + 5.68324i 0.0371569 + 0.203754i
\(779\) 35.8621 + 8.18530i 1.28489 + 0.293269i
\(780\) −0.321093 13.2880i −0.0114970 0.475788i
\(781\) −4.06530 + 36.0806i −0.145468 + 1.29106i
\(782\) 9.91080 + 5.32225i 0.354410 + 0.190323i
\(783\) 3.49853 + 27.6352i 0.125027 + 0.987603i
\(784\) 9.96176 23.5303i 0.355777 0.840367i
\(785\) 33.7947 + 3.80775i 1.20619 + 0.135904i
\(786\) 8.58823 + 15.1053i 0.306332 + 0.538789i
\(787\) 2.69493 11.8073i 0.0960640 0.420884i −0.903913 0.427717i \(-0.859318\pi\)
0.999977 + 0.00683316i \(0.00217508\pi\)
\(788\) −22.0717 7.12959i −0.786271 0.253981i
\(789\) 12.7115 + 10.1371i 0.452540 + 0.360889i
\(790\) −36.0000 9.90207i −1.28082 0.352300i
\(791\) −5.12858 + 14.6566i −0.182351 + 0.521130i
\(792\) −11.6577 19.3980i −0.414240 0.689277i
\(793\) 16.8580 10.5926i 0.598645 0.376153i
\(794\) −19.5753 3.08317i −0.694700 0.109418i
\(795\) −5.19758 + 5.19758i −0.184339 + 0.184339i
\(796\) 0.488106 + 3.55735i 0.0173005 + 0.126087i
\(797\) 0.948701 + 8.41995i 0.0336047 + 0.298250i 0.999261 + 0.0384284i \(0.0122352\pi\)
−0.965657 + 0.259822i \(0.916336\pi\)
\(798\) −1.82327 + 4.55667i −0.0645429 + 0.161304i
\(799\) −3.22744 + 6.70186i −0.114179 + 0.237095i
\(800\) 0.363606 3.35671i 0.0128554 0.118678i
\(801\) −8.69207 24.8405i −0.307119 0.877696i
\(802\) −1.97105 28.8648i −0.0696000 1.01925i
\(803\) 5.15374 + 10.7018i 0.181871 + 0.377660i
\(804\) 24.8170 6.29873i 0.875227 0.222139i
\(805\) −11.7343 + 2.67828i −0.413580 + 0.0943970i
\(806\) −11.0651 25.8266i −0.389751 0.909702i
\(807\) −5.98376 + 4.77189i −0.210638 + 0.167978i
\(808\) −20.7681 2.75871i −0.730620 0.0970510i
\(809\) 3.38908 5.39369i 0.119154 0.189632i −0.781822 0.623502i \(-0.785709\pi\)
0.900976 + 0.433870i \(0.142852\pi\)
\(810\) 0.247065 0.357272i 0.00868096 0.0125533i
\(811\) 43.9722 1.54407 0.772037 0.635578i \(-0.219238\pi\)
0.772037 + 0.635578i \(0.219238\pi\)
\(812\) 5.72777 6.17910i 0.201005 0.216844i
\(813\) 13.8337 0.485170
\(814\) 11.3276 16.3804i 0.397031 0.574134i
\(815\) −12.6468 + 20.1273i −0.442999 + 0.705029i
\(816\) −4.21165 3.03787i −0.147437 0.106347i
\(817\) 8.91160 7.10677i 0.311778 0.248634i
\(818\) −0.588896 1.37452i −0.0205903 0.0480590i
\(819\) −3.78154 + 0.863113i −0.132138 + 0.0301596i
\(820\) −10.2443 40.3625i −0.357747 1.40952i
\(821\) 2.94986 + 6.12546i 0.102951 + 0.213780i 0.946081 0.323929i \(-0.105004\pi\)
−0.843130 + 0.537709i \(0.819290\pi\)
\(822\) 0.354789 + 5.19568i 0.0123747 + 0.181220i
\(823\) 10.8142 + 30.9052i 0.376960 + 1.07729i 0.963578 + 0.267426i \(0.0861730\pi\)
−0.586619 + 0.809863i \(0.699541\pi\)
\(824\) 9.53859 + 7.92172i 0.332292 + 0.275966i
\(825\) −1.17400 + 2.43784i −0.0408734 + 0.0848746i
\(826\) −1.44977 + 3.62324i −0.0504439 + 0.126068i
\(827\) −2.87378 25.5055i −0.0999312 0.886914i −0.939241 0.343260i \(-0.888469\pi\)
0.839309 0.543654i \(-0.182960\pi\)
\(828\) −24.1412 + 3.31242i −0.838964 + 0.115115i
\(829\) 34.0060 34.0060i 1.18108 1.18108i 0.201614 0.979465i \(-0.435381\pi\)
0.979465 0.201614i \(-0.0646186\pi\)
\(830\) 57.7344 + 9.09336i 2.00399 + 0.315635i
\(831\) −23.7588 + 14.9286i −0.824182 + 0.517868i
\(832\) −17.0652 + 12.5336i −0.591630 + 0.434525i
\(833\) 2.58058 7.37486i 0.0894117 0.255524i
\(834\) 9.32663 + 2.56536i 0.322955 + 0.0888312i
\(835\) −19.7193 15.7256i −0.682415 0.544208i
\(836\) −10.9743 + 33.9740i −0.379554 + 1.17502i
\(837\) −8.64040 + 37.8561i −0.298656 + 1.30850i
\(838\) −12.2488 21.5436i −0.423126 0.744211i
\(839\) 22.6363 + 2.55050i 0.781491 + 0.0880529i 0.493691 0.869637i \(-0.335647\pi\)
0.287800 + 0.957690i \(0.407076\pi\)
\(840\) 5.53239 0.512312i 0.190886 0.0176764i
\(841\) −25.7728 + 13.2951i −0.888719 + 0.458452i
\(842\) 34.9233 + 18.7543i 1.20354 + 0.646317i
\(843\) 1.29560 11.4987i 0.0446227 0.396038i
\(844\) −18.2819 + 0.441766i −0.629290 + 0.0152062i
\(845\) 13.8274 + 3.15602i 0.475678 + 0.108570i
\(846\) −2.89062 15.8511i −0.0993816 0.544971i
\(847\) 3.53232 4.42939i 0.121372 0.152196i
\(848\) 11.5279 + 2.05109i 0.395871 + 0.0704347i
\(849\) −11.3188 3.96063i −0.388461 0.135928i
\(850\) 0.0454326 1.03142i 0.00155833 0.0353774i
\(851\) −11.4085 18.1565i −0.391077 0.622396i
\(852\) −14.3769 10.9076i −0.492545 0.373688i
\(853\) 7.59466 + 7.59466i 0.260036 + 0.260036i 0.825069 0.565033i \(-0.191136\pi\)
−0.565033 + 0.825069i \(0.691136\pi\)
\(854\) 4.89751 + 6.72867i 0.167589 + 0.230251i
\(855\) −18.4075 + 2.07403i −0.629523 + 0.0709302i
\(856\) 35.1971 7.30126i 1.20301 0.249552i
\(857\) −42.4667 20.4509i −1.45064 0.698590i −0.467931 0.883765i \(-0.655000\pi\)
−0.982705 + 0.185176i \(0.940715\pi\)
\(858\) 16.2472 4.89404i 0.554670 0.167080i
\(859\) 28.7871 10.0731i 0.982205 0.343688i 0.209050 0.977905i \(-0.432963\pi\)
0.773155 + 0.634217i \(0.218677\pi\)
\(860\) −11.7577 5.31622i −0.400933 0.181282i
\(861\) 6.58403 3.17070i 0.224383 0.108057i
\(862\) −11.2508 12.2877i −0.383205 0.418520i
\(863\) 3.59011 + 15.7293i 0.122209 + 0.535431i 0.998554 + 0.0537488i \(0.0171170\pi\)
−0.876346 + 0.481683i \(0.840026\pi\)
\(864\) 29.2609 0.125779i 0.995476 0.00427909i
\(865\) −12.3702 15.5117i −0.420599 0.527415i
\(866\) −12.5742 + 14.4174i −0.427290 + 0.489922i
\(867\) 13.9338 + 8.75519i 0.473217 + 0.297342i
\(868\) 10.4554 5.34996i 0.354880 0.181589i
\(869\) 47.6639i 1.61689i
\(870\) −18.5067 4.81817i −0.627437 0.163351i
\(871\) 31.9221i 1.08164i
\(872\) 0.809814 40.7690i 0.0274238 1.38061i
\(873\) −7.74389 4.86581i −0.262091 0.164683i
\(874\) 28.9705 + 25.2669i 0.979942 + 0.854665i
\(875\) −5.08077 6.37108i −0.171761 0.215382i
\(876\) −5.88086 0.519095i −0.198696 0.0175386i
\(877\) 9.47310 + 41.5044i 0.319884 + 1.40150i 0.837756 + 0.546045i \(0.183867\pi\)
−0.517872 + 0.855458i \(0.673276\pi\)
\(878\) 21.0457 19.2698i 0.710257 0.650325i
\(879\) 6.65044 3.20268i 0.224314 0.108024i
\(880\) 39.8979 6.45993i 1.34496 0.217764i
\(881\) 6.55566 2.29393i 0.220866 0.0772843i −0.217578 0.976043i \(-0.569816\pi\)
0.438444 + 0.898759i \(0.355530\pi\)
\(882\) 4.88137 + 16.2051i 0.164364 + 0.545655i
\(883\) −11.5407 5.55769i −0.388374 0.187031i 0.229499 0.973309i \(-0.426291\pi\)
−0.617873 + 0.786278i \(0.712006\pi\)
\(884\) −4.96290 + 4.15782i −0.166920 + 0.139843i
\(885\) 8.80202 0.991750i 0.295877 0.0333373i
\(886\) −18.1733 + 13.2276i −0.610545 + 0.444390i
\(887\) 16.6278 + 16.6278i 0.558308 + 0.558308i 0.928825 0.370518i \(-0.120820\pi\)
−0.370518 + 0.928825i \(0.620820\pi\)
\(888\) 4.11686 + 9.00182i 0.138153 + 0.302081i
\(889\) 8.12414 + 12.9295i 0.272475 + 0.433641i
\(890\) 46.9546 + 2.06829i 1.57392 + 0.0693291i
\(891\) 0.523403 + 0.183147i 0.0175347 + 0.00613565i
\(892\) 8.25467 8.66348i 0.276387 0.290075i
\(893\) −15.8481 + 19.8729i −0.530337 + 0.665021i
\(894\) 9.12183 1.66347i 0.305080 0.0556348i
\(895\) 1.90508 + 0.434822i 0.0636798 + 0.0145345i
\(896\) −5.71289 6.75982i −0.190854 0.225830i
\(897\) 2.04557 18.1549i 0.0682995 0.606175i
\(898\) 7.65296 14.2509i 0.255383 0.475560i
\(899\) −40.1044 + 5.07709i −1.33756 + 0.169330i
\(900\) 1.23519 + 1.86425i 0.0411729 + 0.0621416i
\(901\) 3.55786 + 0.400874i 0.118529 + 0.0133551i
\(902\) 46.2128 26.2746i 1.53872 0.874849i
\(903\) 0.503886 2.20767i 0.0167683 0.0734666i
\(904\) −38.9029 40.4797i −1.29389 1.34633i
\(905\) −40.8767 32.5981i −1.35879 1.08360i
\(906\) −3.14726 + 11.4422i −0.104561 + 0.380141i
\(907\) −3.98534 + 11.3894i −0.132331 + 0.378180i −0.990914 0.134493i \(-0.957059\pi\)
0.858583 + 0.512674i \(0.171345\pi\)
\(908\) 23.1486 + 13.7767i 0.768214 + 0.457196i
\(909\) 11.7496 7.38276i 0.389710 0.244871i
\(910\) 1.07776 6.84277i 0.0357274 0.226836i
\(911\) −9.78510 + 9.78510i −0.324195 + 0.324195i −0.850374 0.526179i \(-0.823624\pi\)
0.526179 + 0.850374i \(0.323624\pi\)
\(912\) −11.7210 13.3230i −0.388121 0.441170i
\(913\) 8.35385 + 74.1424i 0.276472 + 2.45376i
\(914\) −4.02007 1.60855i −0.132972 0.0532062i
\(915\) 8.19584 17.0188i 0.270946 0.562625i
\(916\) −15.5654 3.15916i −0.514297 0.104382i
\(917\) 2.99088 + 8.54744i 0.0987675 + 0.282261i
\(918\) 8.92669 0.609562i 0.294625 0.0201186i
\(919\) −17.2711 35.8638i −0.569721 1.18304i −0.964456 0.264242i \(-0.914878\pi\)
0.394736 0.918795i \(-0.370836\pi\)
\(920\) 10.5242 42.2259i 0.346974 1.39215i
\(921\) −16.9176 + 3.86132i −0.557453 + 0.127235i
\(922\) 5.31243 2.27605i 0.174956 0.0749576i
\(923\) −17.5909 + 14.0283i −0.579013 + 0.461747i
\(924\) 2.50364 + 6.63623i 0.0823639 + 0.218316i
\(925\) −1.04701 + 1.66631i −0.0344256 + 0.0547880i
\(926\) −8.41007 5.81582i −0.276372 0.191120i
\(927\) −8.21253 −0.269735
\(928\) 10.5780 + 28.5676i 0.347239 + 0.937777i
\(929\) −57.0980 −1.87333 −0.936663 0.350233i \(-0.886102\pi\)
−0.936663 + 0.350233i \(0.886102\pi\)
\(930\) −21.9255 15.1621i −0.718965 0.497186i
\(931\) 14.2048 22.6069i 0.465544 0.740910i
\(932\) −13.8627 36.7448i −0.454087 1.20362i
\(933\) −25.5499 + 20.3754i −0.836466 + 0.667059i
\(934\) 17.9578 7.69378i 0.587596 0.251748i
\(935\) 12.0490 2.75011i 0.394044 0.0899381i
\(936\) 3.39158 13.6079i 0.110857 0.444787i
\(937\) −9.75579 20.2581i −0.318708 0.661804i 0.678649 0.734463i \(-0.262566\pi\)
−0.997357 + 0.0726591i \(0.976852\pi\)
\(938\) 13.3125 0.909051i 0.434669 0.0296816i
\(939\) −7.09624 20.2799i −0.231577 0.661809i
\(940\) 28.2003 + 5.72353i 0.919791 + 0.186681i
\(941\) 3.94342 8.18859i 0.128552 0.266940i −0.826752 0.562567i \(-0.809814\pi\)
0.955304 + 0.295626i \(0.0955283\pi\)
\(942\) −20.0340 8.01622i −0.652742 0.261182i
\(943\) −6.40856 56.8775i −0.208691 1.85219i
\(944\) −9.31995 10.5938i −0.303339 0.344799i
\(945\) −6.76923 + 6.76923i −0.220203 + 0.220203i
\(946\) 2.56290 16.2721i 0.0833272 0.529051i
\(947\) −50.3140 + 31.6144i −1.63498 + 1.02733i −0.678902 + 0.734229i \(0.737544\pi\)
−0.956082 + 0.293100i \(0.905313\pi\)
\(948\) 20.3576 + 12.1156i 0.661184 + 0.393498i
\(949\) −2.43105 + 6.94753i −0.0789151 + 0.225526i
\(950\) 0.935633 3.40159i 0.0303559 0.110362i
\(951\) 19.0419 + 15.1854i 0.617477 + 0.492422i
\(952\) −1.87527 1.95128i −0.0607780 0.0632415i
\(953\) 1.09074 4.77886i 0.0353327 0.154803i −0.954184 0.299220i \(-0.903274\pi\)
0.989517 + 0.144417i \(0.0461308\pi\)
\(954\) −6.74190 + 3.83315i −0.218277 + 0.124103i
\(955\) 34.8150 + 3.92271i 1.12659 + 0.126936i
\(956\) −12.0980 18.2593i −0.391276 0.590547i
\(957\) −0.335109 24.4107i −0.0108325 0.789086i
\(958\) 17.9407 33.4081i 0.579637 1.07937i
\(959\) −0.303878 + 2.69699i −0.00981272 + 0.0870903i
\(960\) −7.38254 + 18.6827i −0.238270 + 0.602983i
\(961\) −24.7142 5.64085i −0.797232 0.181963i
\(962\) 12.1410 2.21405i 0.391441 0.0713837i
\(963\) −14.8447 + 18.6146i −0.478362 + 0.599847i
\(964\) −33.5877 + 35.2511i −1.08179 + 1.13536i
\(965\) 9.28897 + 3.25035i 0.299022 + 0.104632i
\(966\) 7.62943 + 0.336066i 0.245473 + 0.0108127i
\(967\) 23.7769 + 37.8407i 0.764612 + 1.21687i 0.971158 + 0.238437i \(0.0766349\pi\)
−0.206546 + 0.978437i \(0.566222\pi\)
\(968\) 8.51932 + 18.6281i 0.273821 + 0.598731i
\(969\) −3.83681 3.83681i −0.123256 0.123256i
\(970\) 13.2057 9.61183i 0.424008 0.308617i
\(971\) −32.3192 + 3.64150i −1.03717 + 0.116861i −0.614095 0.789232i \(-0.710479\pi\)
−0.423078 + 0.906093i \(0.639050\pi\)
\(972\) −24.0018 + 20.1083i −0.769858 + 0.644973i
\(973\) 4.54190 + 2.18726i 0.145606 + 0.0701204i
\(974\) 8.52142 + 28.2893i 0.273044 + 0.906449i
\(975\) −1.58262 + 0.553782i −0.0506844 + 0.0177352i
\(976\) −29.7032 + 4.80929i −0.950778 + 0.153942i
\(977\) −8.97436 + 4.32182i −0.287115 + 0.138267i −0.571898 0.820325i \(-0.693793\pi\)
0.284783 + 0.958592i \(0.408078\pi\)
\(978\) 11.1239 10.1852i 0.355702 0.325688i
\(979\) 13.3512 + 58.4954i 0.426706 + 1.86952i
\(980\) −30.1081 2.65760i −0.961769 0.0848940i
\(981\) 16.8396 + 21.1162i 0.537646 + 0.674187i
\(982\) 19.0201 + 16.5886i 0.606956 + 0.529362i
\(983\) −7.01502 4.40783i −0.223744 0.140588i 0.415496 0.909595i \(-0.363608\pi\)
−0.639240 + 0.769007i \(0.720751\pi\)
\(984\) −0.524724 + 26.4166i −0.0167276 + 0.842129i
\(985\) 27.4366i 0.874201i
\(986\) 3.78557 + 8.51109i 0.120557 + 0.271048i
\(987\) 5.04971i 0.160734i
\(988\) −19.6953 + 10.0779i −0.626590 + 0.320622i
\(989\) −15.0176 9.43620i −0.477533 0.300054i
\(990\) −17.5960 + 20.1752i −0.559237 + 0.641210i
\(991\) 19.9500 + 25.0164i 0.633731 + 0.794674i 0.990203 0.139632i \(-0.0445920\pi\)
−0.356472 + 0.934306i \(0.616021\pi\)
\(992\) 0.182531 + 42.4636i 0.00579538 + 1.34822i
\(993\) −2.03032 8.89540i −0.0644301 0.282287i
\(994\) −6.35119 6.93650i −0.201448 0.220012i
\(995\) 3.82674 1.84286i 0.121316 0.0584226i
\(996\) −33.7902 15.2782i −1.07068 0.484109i
\(997\) −5.61224 + 1.96381i −0.177741 + 0.0621944i −0.417683 0.908593i \(-0.637158\pi\)
0.239941 + 0.970787i \(0.422872\pi\)
\(998\) −49.5642 + 14.9299i −1.56893 + 0.472598i
\(999\) −15.3663 7.40000i −0.486167 0.234126i
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 116.2.l.b.31.2 yes 144
4.3 odd 2 inner 116.2.l.b.31.1 yes 144
29.15 odd 28 inner 116.2.l.b.15.1 144
116.15 even 28 inner 116.2.l.b.15.2 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
116.2.l.b.15.1 144 29.15 odd 28 inner
116.2.l.b.15.2 yes 144 116.15 even 28 inner
116.2.l.b.31.1 yes 144 4.3 odd 2 inner
116.2.l.b.31.2 yes 144 1.1 even 1 trivial