Properties

Label 140.2.w.b.23.15
Level $140$
Weight $2$
Character 140.23
Analytic conductor $1.118$
Analytic rank $0$
Dimension $72$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [140,2,Mod(23,140)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(140, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("140.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.w (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 23.15
Character \(\chi\) \(=\) 140.23
Dual form 140.2.w.b.67.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.18977 - 0.764487i) q^{2} +(-2.38471 - 0.638980i) q^{3} +(0.831118 - 1.81913i) q^{4} +(-0.525600 - 2.17342i) q^{5} +(-3.32575 + 1.06284i) q^{6} +(-2.10106 + 1.60796i) q^{7} +(-0.401862 - 2.79973i) q^{8} +(2.68045 + 1.54756i) q^{9} +O(q^{10})\) \(q+(1.18977 - 0.764487i) q^{2} +(-2.38471 - 0.638980i) q^{3} +(0.831118 - 1.81913i) q^{4} +(-0.525600 - 2.17342i) q^{5} +(-3.32575 + 1.06284i) q^{6} +(-2.10106 + 1.60796i) q^{7} +(-0.401862 - 2.79973i) q^{8} +(2.68045 + 1.54756i) q^{9} +(-2.28689 - 2.18406i) q^{10} +(4.09588 - 2.36476i) q^{11} +(-3.14436 + 3.80703i) q^{12} +(0.0592655 + 0.0592655i) q^{13} +(-1.27053 + 3.51934i) q^{14} +(-0.135370 + 5.51881i) q^{15} +(-2.61849 - 3.02383i) q^{16} +(4.77484 + 1.27942i) q^{17} +(4.37222 - 0.207927i) q^{18} +(1.31544 - 2.27842i) q^{19} +(-4.39057 - 0.850232i) q^{20} +(6.03788 - 2.49197i) q^{21} +(3.06534 - 5.94478i) q^{22} +(0.292774 + 1.09265i) q^{23} +(-0.830651 + 6.93332i) q^{24} +(-4.44749 + 2.28469i) q^{25} +(0.115820 + 0.0252047i) q^{26} +(-0.166053 - 0.166053i) q^{27} +(1.17885 + 5.15852i) q^{28} +7.27332i q^{29} +(4.05800 + 6.66962i) q^{30} +(4.01558 - 2.31840i) q^{31} +(-5.42708 - 1.59587i) q^{32} +(-11.2785 + 3.02207i) q^{33} +(6.65908 - 2.12809i) q^{34} +(4.59908 + 3.72135i) q^{35} +(5.04299 - 3.58989i) q^{36} +(-0.596933 - 2.22779i) q^{37} +(-0.176741 - 3.71644i) q^{38} +(-0.103461 - 0.179200i) q^{39} +(-5.87377 + 2.34495i) q^{40} -5.71767 q^{41} +(5.27862 - 7.58075i) q^{42} +(1.57302 - 1.57302i) q^{43} +(-0.897647 - 9.41635i) q^{44} +(1.95465 - 6.63914i) q^{45} +(1.18365 + 1.07618i) q^{46} +(-2.67468 + 0.716679i) q^{47} +(4.31215 + 8.88410i) q^{48} +(1.82895 - 6.75684i) q^{49} +(-3.54488 + 6.11832i) q^{50} +(-10.5691 - 6.10206i) q^{51} +(0.157068 - 0.0585551i) q^{52} +(2.44441 - 9.12265i) q^{53} +(-0.324510 - 0.0706197i) q^{54} +(-7.29241 - 7.65915i) q^{55} +(5.34619 + 5.23624i) q^{56} +(-4.59281 + 4.59281i) q^{57} +(5.56036 + 8.65360i) q^{58} +(1.67748 + 2.90547i) q^{59} +(9.92694 + 4.83304i) q^{60} +(-0.978771 + 1.69528i) q^{61} +(3.00524 - 5.82822i) q^{62} +(-8.12021 + 1.05853i) q^{63} +(-7.67701 + 2.25021i) q^{64} +(0.0976587 - 0.159959i) q^{65} +(-11.1085 + 12.2179i) q^{66} +(0.131802 - 0.491893i) q^{67} +(6.29589 - 7.62273i) q^{68} -2.79272i q^{69} +(8.31679 + 0.911622i) q^{70} +14.4625i q^{71} +(3.25558 - 8.12646i) q^{72} +(-2.48257 + 9.26507i) q^{73} +(-2.41333 - 2.19421i) q^{74} +(12.0658 - 2.60647i) q^{75} +(-3.05145 - 4.28660i) q^{76} +(-4.80329 + 11.5545i) q^{77} +(-0.260092 - 0.134113i) q^{78} +(-3.05204 + 5.28630i) q^{79} +(-5.19577 + 7.28039i) q^{80} +(-4.35280 - 7.53927i) q^{81} +(-6.80273 + 4.37109i) q^{82} +(5.62620 - 5.62620i) q^{83} +(0.484971 - 13.0548i) q^{84} +(0.271049 - 11.0502i) q^{85} +(0.668982 - 3.07409i) q^{86} +(4.64751 - 17.3447i) q^{87} +(-8.26668 - 10.5171i) q^{88} +(14.4482 + 8.34169i) q^{89} +(-2.74995 - 9.39337i) q^{90} +(-0.219817 - 0.0292243i) q^{91} +(2.23100 + 0.375524i) q^{92} +(-11.0574 + 2.96282i) q^{93} +(-2.63437 + 2.89745i) q^{94} +(-5.64335 - 1.66148i) q^{95} +(11.9223 + 7.27348i) q^{96} +(5.81505 - 5.81505i) q^{97} +(-2.98949 - 9.43732i) q^{98} +14.6384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 2 q^{2} - 8 q^{5} - 16 q^{6} - 4 q^{8} + 2 q^{10} + 10 q^{12} - 28 q^{16} + 4 q^{17} - 20 q^{18} - 56 q^{20} + 4 q^{21} - 16 q^{22} - 16 q^{25} - 4 q^{26} + 42 q^{28} - 32 q^{30} - 38 q^{32} - 64 q^{33} + 16 q^{36} - 4 q^{37} + 12 q^{38} + 2 q^{40} - 40 q^{41} + 78 q^{42} - 12 q^{45} - 28 q^{46} + 12 q^{48} - 28 q^{50} + 48 q^{52} - 24 q^{53} + 36 q^{56} - 16 q^{57} + 30 q^{58} - 10 q^{60} - 20 q^{61} + 56 q^{62} + 4 q^{65} + 44 q^{66} - 12 q^{68} + 84 q^{70} + 44 q^{72} - 12 q^{73} + 112 q^{76} + 16 q^{77} + 64 q^{78} + 52 q^{80} - 52 q^{81} - 34 q^{82} + 16 q^{85} + 64 q^{86} + 16 q^{88} - 32 q^{90} + 44 q^{92} + 12 q^{93} - 48 q^{96} - 24 q^{97} - 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.18977 0.764487i 0.841296 0.540574i
\(3\) −2.38471 0.638980i −1.37681 0.368915i −0.506849 0.862035i \(-0.669190\pi\)
−0.869962 + 0.493119i \(0.835857\pi\)
\(4\) 0.831118 1.81913i 0.415559 0.909566i
\(5\) −0.525600 2.17342i −0.235055 0.971982i
\(6\) −3.32575 + 1.06284i −1.35773 + 0.433901i
\(7\) −2.10106 + 1.60796i −0.794128 + 0.607751i
\(8\) −0.401862 2.79973i −0.142080 0.989855i
\(9\) 2.68045 + 1.54756i 0.893484 + 0.515853i
\(10\) −2.28689 2.18406i −0.723180 0.690660i
\(11\) 4.09588 2.36476i 1.23496 0.713002i 0.266897 0.963725i \(-0.414002\pi\)
0.968059 + 0.250723i \(0.0806684\pi\)
\(12\) −3.14436 + 3.80703i −0.907699 + 1.09899i
\(13\) 0.0592655 + 0.0592655i 0.0164373 + 0.0164373i 0.715278 0.698840i \(-0.246300\pi\)
−0.698840 + 0.715278i \(0.746300\pi\)
\(14\) −1.27053 + 3.51934i −0.339563 + 0.940583i
\(15\) −0.135370 + 5.51881i −0.0349524 + 1.42495i
\(16\) −2.61849 3.02383i −0.654621 0.755957i
\(17\) 4.77484 + 1.27942i 1.15807 + 0.310304i 0.786195 0.617979i \(-0.212048\pi\)
0.371875 + 0.928283i \(0.378715\pi\)
\(18\) 4.37222 0.207927i 1.03054 0.0490090i
\(19\) 1.31544 2.27842i 0.301784 0.522705i −0.674756 0.738041i \(-0.735751\pi\)
0.976540 + 0.215336i \(0.0690846\pi\)
\(20\) −4.39057 0.850232i −0.981761 0.190118i
\(21\) 6.03788 2.49197i 1.31757 0.543792i
\(22\) 3.06534 5.94478i 0.653533 1.26743i
\(23\) 0.292774 + 1.09265i 0.0610475 + 0.227832i 0.989709 0.143097i \(-0.0457060\pi\)
−0.928661 + 0.370929i \(0.879039\pi\)
\(24\) −0.830651 + 6.93332i −0.169556 + 1.41526i
\(25\) −4.44749 + 2.28469i −0.889498 + 0.456939i
\(26\) 0.115820 + 0.0252047i 0.0227142 + 0.00494306i
\(27\) −0.166053 0.166053i −0.0319568 0.0319568i
\(28\) 1.17885 + 5.15852i 0.222782 + 0.974868i
\(29\) 7.27332i 1.35062i 0.737533 + 0.675311i \(0.235991\pi\)
−0.737533 + 0.675311i \(0.764009\pi\)
\(30\) 4.05800 + 6.66962i 0.740886 + 1.21770i
\(31\) 4.01558 2.31840i 0.721219 0.416396i −0.0939821 0.995574i \(-0.529960\pi\)
0.815201 + 0.579178i \(0.196626\pi\)
\(32\) −5.42708 1.59587i −0.959381 0.282112i
\(33\) −11.2785 + 3.02207i −1.96334 + 0.526075i
\(34\) 6.65908 2.12809i 1.14202 0.364965i
\(35\) 4.59908 + 3.72135i 0.777387 + 0.629023i
\(36\) 5.04299 3.58989i 0.840498 0.598315i
\(37\) −0.596933 2.22779i −0.0981352 0.366246i 0.899341 0.437248i \(-0.144047\pi\)
−0.997476 + 0.0710024i \(0.977380\pi\)
\(38\) −0.176741 3.71644i −0.0286712 0.602886i
\(39\) −0.103461 0.179200i −0.0165671 0.0286950i
\(40\) −5.87377 + 2.34495i −0.928725 + 0.370770i
\(41\) −5.71767 −0.892950 −0.446475 0.894796i \(-0.647321\pi\)
−0.446475 + 0.894796i \(0.647321\pi\)
\(42\) 5.27862 7.58075i 0.814509 1.16974i
\(43\) 1.57302 1.57302i 0.239883 0.239883i −0.576918 0.816802i \(-0.695745\pi\)
0.816802 + 0.576918i \(0.195745\pi\)
\(44\) −0.897647 9.41635i −0.135325 1.41957i
\(45\) 1.95465 6.63914i 0.291382 0.989704i
\(46\) 1.18365 + 1.07618i 0.174519 + 0.158674i
\(47\) −2.67468 + 0.716679i −0.390143 + 0.104538i −0.448558 0.893754i \(-0.648062\pi\)
0.0584148 + 0.998292i \(0.481395\pi\)
\(48\) 4.31215 + 8.88410i 0.622406 + 1.28231i
\(49\) 1.82895 6.75684i 0.261278 0.965264i
\(50\) −3.54488 + 6.11832i −0.501322 + 0.865261i
\(51\) −10.5691 6.10206i −1.47997 0.854459i
\(52\) 0.157068 0.0585551i 0.0217815 0.00812014i
\(53\) 2.44441 9.12265i 0.335765 1.25309i −0.567272 0.823530i \(-0.692001\pi\)
0.903037 0.429562i \(-0.141332\pi\)
\(54\) −0.324510 0.0706197i −0.0441602 0.00961013i
\(55\) −7.29241 7.65915i −0.983308 1.03276i
\(56\) 5.34619 + 5.23624i 0.714415 + 0.699723i
\(57\) −4.59281 + 4.59281i −0.608333 + 0.608333i
\(58\) 5.56036 + 8.65360i 0.730112 + 1.13627i
\(59\) 1.67748 + 2.90547i 0.218389 + 0.378260i 0.954315 0.298801i \(-0.0965866\pi\)
−0.735927 + 0.677061i \(0.763253\pi\)
\(60\) 9.92694 + 4.83304i 1.28156 + 0.623943i
\(61\) −0.978771 + 1.69528i −0.125319 + 0.217058i −0.921857 0.387529i \(-0.873329\pi\)
0.796539 + 0.604587i \(0.206662\pi\)
\(62\) 3.00524 5.82822i 0.381666 0.740185i
\(63\) −8.12021 + 1.05853i −1.02305 + 0.133362i
\(64\) −7.67701 + 2.25021i −0.959627 + 0.281277i
\(65\) 0.0976587 0.159959i 0.0121131 0.0198404i
\(66\) −11.1085 + 12.2179i −1.36737 + 1.50391i
\(67\) 0.131802 0.491893i 0.0161022 0.0600943i −0.957407 0.288741i \(-0.906763\pi\)
0.973509 + 0.228647i \(0.0734300\pi\)
\(68\) 6.29589 7.62273i 0.763488 0.924392i
\(69\) 2.79272i 0.336204i
\(70\) 8.31679 + 0.911622i 0.994046 + 0.108960i
\(71\) 14.4625i 1.71638i 0.513329 + 0.858192i \(0.328412\pi\)
−0.513329 + 0.858192i \(0.671588\pi\)
\(72\) 3.25558 8.12646i 0.383674 0.957712i
\(73\) −2.48257 + 9.26507i −0.290563 + 1.08439i 0.654115 + 0.756395i \(0.273041\pi\)
−0.944678 + 0.327999i \(0.893626\pi\)
\(74\) −2.41333 2.19421i −0.280544 0.255072i
\(75\) 12.0658 2.60647i 1.39324 0.300969i
\(76\) −3.05145 4.28660i −0.350026 0.491707i
\(77\) −4.80329 + 11.5545i −0.547385 + 1.31676i
\(78\) −0.260092 0.134113i −0.0294496 0.0151853i
\(79\) −3.05204 + 5.28630i −0.343382 + 0.594755i −0.985058 0.172221i \(-0.944906\pi\)
0.641677 + 0.766975i \(0.278239\pi\)
\(80\) −5.19577 + 7.28039i −0.580904 + 0.813972i
\(81\) −4.35280 7.53927i −0.483644 0.837696i
\(82\) −6.80273 + 4.37109i −0.751235 + 0.482706i
\(83\) 5.62620 5.62620i 0.617555 0.617555i −0.327348 0.944904i \(-0.606155\pi\)
0.944904 + 0.327348i \(0.106155\pi\)
\(84\) 0.484971 13.0548i 0.0529146 1.42440i
\(85\) 0.271049 11.0502i 0.0293994 1.19856i
\(86\) 0.668982 3.07409i 0.0721382 0.331488i
\(87\) 4.64751 17.3447i 0.498265 1.85955i
\(88\) −8.26668 10.5171i −0.881231 1.12112i
\(89\) 14.4482 + 8.34169i 1.53151 + 0.884218i 0.999292 + 0.0376100i \(0.0119745\pi\)
0.532217 + 0.846608i \(0.321359\pi\)
\(90\) −2.74995 9.39337i −0.289870 0.990148i
\(91\) −0.219817 0.0292243i −0.0230431 0.00306354i
\(92\) 2.23100 + 0.375524i 0.232598 + 0.0391511i
\(93\) −11.0574 + 2.96282i −1.14660 + 0.307230i
\(94\) −2.63437 + 2.89745i −0.271715 + 0.298849i
\(95\) −5.64335 1.66148i −0.578996 0.170464i
\(96\) 11.9223 + 7.27348i 1.21681 + 0.742346i
\(97\) 5.81505 5.81505i 0.590429 0.590429i −0.347318 0.937747i \(-0.612908\pi\)
0.937747 + 0.347318i \(0.112908\pi\)
\(98\) −2.98949 9.43732i −0.301984 0.953313i
\(99\) 14.6384 1.47122
\(100\) 0.459773 + 9.98942i 0.0459773 + 0.998942i
\(101\) 4.28723 + 7.42571i 0.426596 + 0.738885i 0.996568 0.0827785i \(-0.0263794\pi\)
−0.569972 + 0.821664i \(0.693046\pi\)
\(102\) −17.2398 + 0.819862i −1.70699 + 0.0811785i
\(103\) −0.845330 3.15482i −0.0832929 0.310853i 0.911693 0.410873i \(-0.134776\pi\)
−0.994985 + 0.100020i \(0.968109\pi\)
\(104\) 0.142111 0.189744i 0.0139351 0.0186059i
\(105\) −8.58959 11.8130i −0.838258 1.15284i
\(106\) −4.06586 12.7226i −0.394911 1.23573i
\(107\) −6.56081 + 1.75796i −0.634257 + 0.169949i −0.561601 0.827408i \(-0.689814\pi\)
−0.0726563 + 0.997357i \(0.523148\pi\)
\(108\) −0.440081 + 0.164062i −0.0423468 + 0.0157869i
\(109\) −3.39423 + 1.95966i −0.325108 + 0.187701i −0.653667 0.756782i \(-0.726770\pi\)
0.328559 + 0.944483i \(0.393437\pi\)
\(110\) −14.5316 3.53770i −1.38554 0.337306i
\(111\) 5.69404i 0.540455i
\(112\) 10.3638 + 2.14285i 0.979286 + 0.202480i
\(113\) −0.0280186 0.0280186i −0.00263577 0.00263577i 0.705788 0.708423i \(-0.250593\pi\)
−0.708423 + 0.705788i \(0.750593\pi\)
\(114\) −1.95326 + 8.97555i −0.182939 + 0.840637i
\(115\) 2.22089 1.21061i 0.207100 0.112890i
\(116\) 13.2311 + 6.04499i 1.22848 + 0.561263i
\(117\) 0.0671414 + 0.250575i 0.00620723 + 0.0231657i
\(118\) 4.21701 + 2.17444i 0.388207 + 0.200174i
\(119\) −12.0895 + 4.98961i −1.10824 + 0.457397i
\(120\) 15.5056 1.83880i 1.41546 0.167859i
\(121\) 5.68418 9.84529i 0.516744 0.895026i
\(122\) 0.131506 + 2.76526i 0.0119060 + 0.250355i
\(123\) 13.6350 + 3.65348i 1.22942 + 0.329423i
\(124\) −0.880048 9.23173i −0.0790306 0.829034i
\(125\) 7.30320 + 8.46542i 0.653218 + 0.757170i
\(126\) −8.85198 + 7.46721i −0.788597 + 0.665232i
\(127\) 6.53450 + 6.53450i 0.579843 + 0.579843i 0.934860 0.355017i \(-0.115525\pi\)
−0.355017 + 0.934860i \(0.615525\pi\)
\(128\) −7.41364 + 8.54622i −0.655280 + 0.755386i
\(129\) −4.75632 + 2.74606i −0.418770 + 0.241777i
\(130\) −0.00609459 0.264973i −0.000534531 0.0232397i
\(131\) −3.19588 1.84514i −0.279225 0.161211i 0.353847 0.935303i \(-0.384873\pi\)
−0.633073 + 0.774092i \(0.718207\pi\)
\(132\) −3.87624 + 23.0288i −0.337383 + 2.00440i
\(133\) 0.899762 + 6.90228i 0.0780193 + 0.598504i
\(134\) −0.219231 0.686002i −0.0189387 0.0592616i
\(135\) −0.273625 + 0.448179i −0.0235499 + 0.0385731i
\(136\) 1.66319 13.8824i 0.142618 1.19041i
\(137\) 19.1819 + 5.13977i 1.63882 + 0.439120i 0.956452 0.291890i \(-0.0942843\pi\)
0.682366 + 0.731010i \(0.260951\pi\)
\(138\) −2.13500 3.32270i −0.181743 0.282847i
\(139\) −1.15593 −0.0980447 −0.0490223 0.998798i \(-0.515611\pi\)
−0.0490223 + 0.998798i \(0.515611\pi\)
\(140\) 10.5920 5.27346i 0.895188 0.445688i
\(141\) 6.83628 0.575719
\(142\) 11.0564 + 17.2071i 0.927833 + 1.44399i
\(143\) 0.382893 + 0.102596i 0.0320191 + 0.00857950i
\(144\) −2.33917 12.1575i −0.194931 1.01312i
\(145\) 15.8080 3.82286i 1.31278 0.317471i
\(146\) 4.12934 + 12.9212i 0.341746 + 1.06937i
\(147\) −8.67899 + 14.9444i −0.715831 + 1.23260i
\(148\) −4.54876 0.765652i −0.373906 0.0629362i
\(149\) −5.37045 3.10063i −0.439965 0.254014i 0.263618 0.964627i \(-0.415084\pi\)
−0.703583 + 0.710613i \(0.748418\pi\)
\(150\) 12.3630 12.3253i 1.00943 1.00636i
\(151\) −8.72300 + 5.03623i −0.709868 + 0.409842i −0.811012 0.585029i \(-0.801083\pi\)
0.101144 + 0.994872i \(0.467750\pi\)
\(152\) −6.90759 2.76729i −0.560279 0.224457i
\(153\) 10.8188 + 10.8188i 0.874646 + 0.874646i
\(154\) 3.11847 + 17.4193i 0.251293 + 1.40369i
\(155\) −7.14943 7.50898i −0.574256 0.603136i
\(156\) −0.411977 + 0.0392732i −0.0329846 + 0.00314438i
\(157\) −14.0732 3.77089i −1.12316 0.300950i −0.350999 0.936376i \(-0.614158\pi\)
−0.772162 + 0.635426i \(0.780825\pi\)
\(158\) 0.410067 + 8.62274i 0.0326232 + 0.685988i
\(159\) −11.6584 + 20.1929i −0.924570 + 1.60140i
\(160\) −0.616019 + 12.6341i −0.0487006 + 0.998813i
\(161\) −2.37206 1.82495i −0.186945 0.143826i
\(162\) −10.9425 5.64235i −0.859725 0.443305i
\(163\) 0.763938 + 2.85106i 0.0598363 + 0.223312i 0.989369 0.145428i \(-0.0464559\pi\)
−0.929533 + 0.368740i \(0.879789\pi\)
\(164\) −4.75206 + 10.4012i −0.371073 + 0.812197i
\(165\) 12.4962 + 22.9245i 0.972828 + 1.78467i
\(166\) 2.39274 10.9950i 0.185713 0.853381i
\(167\) 6.13096 + 6.13096i 0.474428 + 0.474428i 0.903344 0.428916i \(-0.141105\pi\)
−0.428916 + 0.903344i \(0.641105\pi\)
\(168\) −9.40323 15.9030i −0.725475 1.22694i
\(169\) 12.9930i 0.999460i
\(170\) −8.12525 13.3544i −0.623178 1.02424i
\(171\) 7.05197 4.07146i 0.539278 0.311352i
\(172\) −1.55417 4.16890i −0.118504 0.317875i
\(173\) 1.73431 0.464708i 0.131857 0.0353311i −0.192287 0.981339i \(-0.561590\pi\)
0.324144 + 0.946008i \(0.394924\pi\)
\(174\) −7.73035 24.1893i −0.586037 1.83378i
\(175\) 5.67077 11.9517i 0.428670 0.903461i
\(176\) −17.8756 6.19316i −1.34743 0.466827i
\(177\) −2.14375 8.00057i −0.161134 0.601360i
\(178\) 23.5672 1.12078i 1.76644 0.0840057i
\(179\) −10.7713 18.6564i −0.805084 1.39445i −0.916234 0.400643i \(-0.868787\pi\)
0.111150 0.993804i \(-0.464547\pi\)
\(180\) −10.4529 9.07368i −0.779115 0.676312i
\(181\) −16.2122 −1.20504 −0.602520 0.798104i \(-0.705837\pi\)
−0.602520 + 0.798104i \(0.705837\pi\)
\(182\) −0.283874 + 0.133277i −0.0210421 + 0.00987915i
\(183\) 3.41733 3.41733i 0.252616 0.252616i
\(184\) 2.94146 1.25878i 0.216848 0.0927986i
\(185\) −4.52816 + 2.46831i −0.332917 + 0.181474i
\(186\) −10.8907 + 11.9783i −0.798548 + 0.878292i
\(187\) 22.5827 6.05102i 1.65141 0.442495i
\(188\) −0.919244 + 5.46125i −0.0670427 + 0.398303i
\(189\) 0.615893 + 0.0818818i 0.0447996 + 0.00595603i
\(190\) −7.98448 + 2.33749i −0.579255 + 0.169579i
\(191\) 14.2331 + 8.21746i 1.02987 + 0.594595i 0.916947 0.399009i \(-0.130646\pi\)
0.112921 + 0.993604i \(0.463979\pi\)
\(192\) 19.7453 0.460637i 1.42499 0.0332436i
\(193\) 1.28369 4.79080i 0.0924021 0.344849i −0.904211 0.427087i \(-0.859540\pi\)
0.996613 + 0.0822374i \(0.0262066\pi\)
\(194\) 2.47306 11.3641i 0.177555 0.815897i
\(195\) −0.335098 + 0.319052i −0.0239968 + 0.0228478i
\(196\) −10.7715 8.94283i −0.769395 0.638774i
\(197\) −3.89922 + 3.89922i −0.277808 + 0.277808i −0.832233 0.554425i \(-0.812938\pi\)
0.554425 + 0.832233i \(0.312938\pi\)
\(198\) 17.4164 11.1909i 1.23773 0.795302i
\(199\) −9.44788 16.3642i −0.669743 1.16003i −0.977976 0.208717i \(-0.933071\pi\)
0.308233 0.951311i \(-0.400262\pi\)
\(200\) 8.18381 + 11.5337i 0.578683 + 0.815553i
\(201\) −0.628620 + 1.08880i −0.0443394 + 0.0767981i
\(202\) 10.7777 + 5.55737i 0.758316 + 0.391015i
\(203\) −11.6952 15.2817i −0.820842 1.07257i
\(204\) −19.8846 + 14.1550i −1.39220 + 0.991050i
\(205\) 3.00520 + 12.4269i 0.209893 + 0.867931i
\(206\) −3.41757 3.10727i −0.238113 0.216494i
\(207\) −0.906169 + 3.38187i −0.0629831 + 0.235056i
\(208\) 0.0240228 0.334394i 0.00166568 0.0231861i
\(209\) 12.4428i 0.860690i
\(210\) −19.2506 7.48821i −1.32842 0.516736i
\(211\) 10.9795i 0.755859i 0.925834 + 0.377929i \(0.123364\pi\)
−0.925834 + 0.377929i \(0.876636\pi\)
\(212\) −14.5637 12.0287i −1.00024 0.826135i
\(213\) 9.24126 34.4888i 0.633201 2.36314i
\(214\) −6.46193 + 7.10723i −0.441728 + 0.485840i
\(215\) −4.24561 2.59205i −0.289548 0.176776i
\(216\) −0.398173 + 0.531633i −0.0270922 + 0.0361731i
\(217\) −4.70911 + 11.3280i −0.319675 + 0.768993i
\(218\) −2.54022 + 4.92639i −0.172046 + 0.333657i
\(219\) 11.8404 20.5082i 0.800099 1.38581i
\(220\) −19.9939 + 6.90019i −1.34799 + 0.465211i
\(221\) 0.207158 + 0.358809i 0.0139350 + 0.0241361i
\(222\) 4.35302 + 6.77462i 0.292156 + 0.454683i
\(223\) −13.6990 + 13.6990i −0.917356 + 0.917356i −0.996836 0.0794806i \(-0.974674\pi\)
0.0794806 + 0.996836i \(0.474674\pi\)
\(224\) 13.9687 5.37349i 0.933326 0.359031i
\(225\) −15.4570 0.758741i −1.03047 0.0505828i
\(226\) −0.0547556 0.0119159i −0.00364229 0.000792634i
\(227\) −5.94107 + 22.1724i −0.394322 + 1.47163i 0.428609 + 0.903490i \(0.359004\pi\)
−0.822931 + 0.568141i \(0.807663\pi\)
\(228\) 4.53776 + 12.1721i 0.300521 + 0.806117i
\(229\) −10.3396 5.96955i −0.683258 0.394479i 0.117824 0.993035i \(-0.462408\pi\)
−0.801081 + 0.598556i \(0.795742\pi\)
\(230\) 1.71686 3.13820i 0.113206 0.206927i
\(231\) 18.8375 24.4849i 1.23942 1.61099i
\(232\) 20.3634 2.92287i 1.33692 0.191896i
\(233\) 22.9805 6.15761i 1.50550 0.403399i 0.590565 0.806990i \(-0.298905\pi\)
0.914939 + 0.403592i \(0.132238\pi\)
\(234\) 0.271445 + 0.246799i 0.0177449 + 0.0161337i
\(235\) 2.96346 + 5.43652i 0.193315 + 0.354639i
\(236\) 6.67962 0.636759i 0.434806 0.0414495i
\(237\) 10.6561 10.6561i 0.692186 0.692186i
\(238\) −10.5693 + 15.1788i −0.685104 + 0.983894i
\(239\) −1.50749 −0.0975113 −0.0487556 0.998811i \(-0.515526\pi\)
−0.0487556 + 0.998811i \(0.515526\pi\)
\(240\) 17.0424 14.0416i 1.10008 0.906381i
\(241\) 9.26556 + 16.0484i 0.596847 + 1.03377i 0.993283 + 0.115708i \(0.0369136\pi\)
−0.396436 + 0.918062i \(0.629753\pi\)
\(242\) −0.763716 16.0591i −0.0490935 1.03232i
\(243\) 5.74504 + 21.4408i 0.368544 + 1.37543i
\(244\) 2.27047 + 3.18949i 0.145352 + 0.204186i
\(245\) −15.6467 0.423673i −0.999634 0.0270675i
\(246\) 19.0155 6.07695i 1.21239 0.387452i
\(247\) 0.212992 0.0570710i 0.0135524 0.00363134i
\(248\) −8.10460 10.3109i −0.514642 0.654741i
\(249\) −17.0119 + 9.82180i −1.07808 + 0.622431i
\(250\) 15.1608 + 4.48872i 0.958856 + 0.283892i
\(251\) 18.0219i 1.13753i −0.822500 0.568765i \(-0.807421\pi\)
0.822500 0.568765i \(-0.192579\pi\)
\(252\) −4.82325 + 15.6515i −0.303836 + 0.985952i
\(253\) 3.78301 + 3.78301i 0.237836 + 0.237836i
\(254\) 12.7701 + 2.77903i 0.801268 + 0.174372i
\(255\) −7.70722 + 26.1783i −0.482645 + 1.63935i
\(256\) −2.28707 + 15.8357i −0.142942 + 0.989731i
\(257\) −3.85933 14.4032i −0.240738 0.898448i −0.975478 0.220098i \(-0.929362\pi\)
0.734739 0.678350i \(-0.237304\pi\)
\(258\) −3.55961 + 6.90333i −0.221611 + 0.429783i
\(259\) 4.83638 + 3.72088i 0.300518 + 0.231204i
\(260\) −0.209820 0.310599i −0.0130125 0.0192625i
\(261\) −11.2559 + 19.4958i −0.696723 + 1.20676i
\(262\) −5.21295 + 0.247910i −0.322057 + 0.0153159i
\(263\) 6.84826 + 1.83499i 0.422282 + 0.113150i 0.463701 0.885992i \(-0.346521\pi\)
−0.0414191 + 0.999142i \(0.513188\pi\)
\(264\) 12.9934 + 30.3624i 0.799688 + 1.86868i
\(265\) −21.1121 0.517856i −1.29691 0.0318117i
\(266\) 6.34722 + 7.52429i 0.389173 + 0.461344i
\(267\) −29.1246 29.1246i −1.78240 1.78240i
\(268\) −0.785275 0.648587i −0.0479683 0.0396188i
\(269\) 5.23463 3.02221i 0.319161 0.184268i −0.331858 0.943329i \(-0.607675\pi\)
0.651019 + 0.759062i \(0.274342\pi\)
\(270\) 0.0170761 + 0.742414i 0.00103922 + 0.0451819i
\(271\) −20.3476 11.7477i −1.23603 0.713622i −0.267750 0.963488i \(-0.586280\pi\)
−0.968280 + 0.249866i \(0.919613\pi\)
\(272\) −8.63413 17.7884i −0.523521 1.07858i
\(273\) 0.505525 + 0.210150i 0.0305958 + 0.0127189i
\(274\) 26.7514 8.54914i 1.61611 0.516473i
\(275\) −12.8137 + 19.8751i −0.772692 + 1.19851i
\(276\) −5.08032 2.32108i −0.305799 0.139712i
\(277\) −22.5298 6.03684i −1.35369 0.362719i −0.492191 0.870487i \(-0.663804\pi\)
−0.861494 + 0.507768i \(0.830471\pi\)
\(278\) −1.37529 + 0.883694i −0.0824846 + 0.0530004i
\(279\) 14.3514 0.859197
\(280\) 8.57059 14.3717i 0.512191 0.858872i
\(281\) −19.3011 −1.15141 −0.575703 0.817659i \(-0.695272\pi\)
−0.575703 + 0.817659i \(0.695272\pi\)
\(282\) 8.13362 5.22625i 0.484350 0.311219i
\(283\) −6.88593 1.84508i −0.409326 0.109679i 0.0482794 0.998834i \(-0.484626\pi\)
−0.457606 + 0.889155i \(0.651293\pi\)
\(284\) 26.3092 + 12.0201i 1.56117 + 0.713259i
\(285\) 12.3961 + 7.56812i 0.734281 + 0.448297i
\(286\) 0.533989 0.170651i 0.0315754 0.0100908i
\(287\) 12.0132 9.19377i 0.709116 0.542691i
\(288\) −12.0773 12.6764i −0.711663 0.746963i
\(289\) 6.43980 + 3.71802i 0.378812 + 0.218707i
\(290\) 15.8854 16.6333i 0.932821 0.976742i
\(291\) −17.5829 + 10.1515i −1.03073 + 0.595091i
\(292\) 14.7911 + 12.2165i 0.865583 + 0.714916i
\(293\) 1.29442 + 1.29442i 0.0756208 + 0.0756208i 0.743906 0.668285i \(-0.232971\pi\)
−0.668285 + 0.743906i \(0.732971\pi\)
\(294\) 1.09880 + 24.4155i 0.0640832 + 1.42394i
\(295\) 5.43312 5.17297i 0.316329 0.301182i
\(296\) −5.99732 + 2.56652i −0.348587 + 0.149176i
\(297\) −1.07281 0.287458i −0.0622506 0.0166800i
\(298\) −8.76001 + 0.416596i −0.507454 + 0.0241327i
\(299\) −0.0474048 + 0.0821076i −0.00274149 + 0.00474840i
\(300\) 5.28662 24.1156i 0.305223 1.39232i
\(301\) −0.775668 + 5.83436i −0.0447088 + 0.336287i
\(302\) −6.52826 + 12.6606i −0.375659 + 0.728535i
\(303\) −5.47891 20.4476i −0.314755 1.17468i
\(304\) −10.3340 + 1.98832i −0.592696 + 0.114038i
\(305\) 4.19899 + 1.23624i 0.240434 + 0.0707868i
\(306\) 21.1427 + 4.60106i 1.20865 + 0.263025i
\(307\) −3.86175 3.86175i −0.220402 0.220402i 0.588266 0.808667i \(-0.299811\pi\)
−0.808667 + 0.588266i \(0.799811\pi\)
\(308\) 17.0271 + 18.3410i 0.970209 + 1.04507i
\(309\) 8.06346i 0.458714i
\(310\) −14.2467 3.46833i −0.809159 0.196988i
\(311\) 17.7808 10.2657i 1.00826 0.582116i 0.0975749 0.995228i \(-0.468891\pi\)
0.910680 + 0.413112i \(0.135558\pi\)
\(312\) −0.460136 + 0.361678i −0.0260501 + 0.0204760i
\(313\) −26.9598 + 7.22385i −1.52386 + 0.408316i −0.921009 0.389540i \(-0.872634\pi\)
−0.602847 + 0.797856i \(0.705967\pi\)
\(314\) −19.6267 + 6.27225i −1.10760 + 0.353964i
\(315\) 6.56861 + 17.0923i 0.370099 + 0.963039i
\(316\) 7.07986 + 9.94561i 0.398273 + 0.559484i
\(317\) −3.35388 12.5169i −0.188373 0.703016i −0.993883 0.110435i \(-0.964776\pi\)
0.805511 0.592581i \(-0.201891\pi\)
\(318\) 1.56640 + 32.9377i 0.0878394 + 1.84705i
\(319\) 17.1997 + 29.7907i 0.962996 + 1.66796i
\(320\) 8.92569 + 15.5026i 0.498961 + 0.866624i
\(321\) 16.7689 0.935949
\(322\) −4.21737 0.357866i −0.235025 0.0199431i
\(323\) 9.19609 9.19609i 0.511684 0.511684i
\(324\) −17.3326 + 1.65229i −0.962923 + 0.0917941i
\(325\) −0.398986 0.128179i −0.0221318 0.00711010i
\(326\) 3.08851 + 2.80809i 0.171057 + 0.155526i
\(327\) 9.34642 2.50436i 0.516858 0.138492i
\(328\) 2.29771 + 16.0079i 0.126870 + 0.883891i
\(329\) 4.46729 5.80657i 0.246290 0.320126i
\(330\) 32.3932 + 17.7218i 1.78318 + 0.975552i
\(331\) 6.41324 + 3.70269i 0.352504 + 0.203518i 0.665787 0.746142i \(-0.268096\pi\)
−0.313284 + 0.949660i \(0.601429\pi\)
\(332\) −5.55876 14.9108i −0.305077 0.818338i
\(333\) 1.84758 6.89526i 0.101247 0.377858i
\(334\) 11.9815 + 2.60741i 0.655598 + 0.142671i
\(335\) −1.13836 0.0279228i −0.0621955 0.00152559i
\(336\) −23.3454 11.7323i −1.27359 0.640050i
\(337\) −5.81990 + 5.81990i −0.317030 + 0.317030i −0.847625 0.530595i \(-0.821968\pi\)
0.530595 + 0.847625i \(0.321968\pi\)
\(338\) −9.93297 15.4587i −0.540282 0.840842i
\(339\) 0.0489128 + 0.0847195i 0.00265658 + 0.00460133i
\(340\) −19.8765 9.67709i −1.07795 0.524814i
\(341\) 10.9649 18.9918i 0.593782 1.02846i
\(342\) 5.27767 10.2353i 0.285384 0.553459i
\(343\) 7.02198 + 17.1374i 0.379151 + 0.925335i
\(344\) −5.03617 3.77190i −0.271532 0.203367i
\(345\) −6.06974 + 1.46785i −0.326784 + 0.0790264i
\(346\) 1.70817 1.87876i 0.0918320 0.101003i
\(347\) 2.85823 10.6671i 0.153438 0.572638i −0.845796 0.533506i \(-0.820874\pi\)
0.999234 0.0391317i \(-0.0124592\pi\)
\(348\) −27.6897 22.8700i −1.48433 1.22596i
\(349\) 10.3995i 0.556672i 0.960484 + 0.278336i \(0.0897829\pi\)
−0.960484 + 0.278336i \(0.910217\pi\)
\(350\) −2.38997 18.5550i −0.127749 0.991807i
\(351\) 0.0196824i 0.00105057i
\(352\) −26.0025 + 6.29725i −1.38594 + 0.335644i
\(353\) −1.95306 + 7.28892i −0.103951 + 0.387950i −0.998224 0.0595714i \(-0.981027\pi\)
0.894273 + 0.447522i \(0.147693\pi\)
\(354\) −8.66691 7.87999i −0.460641 0.418817i
\(355\) 31.4331 7.60149i 1.66829 0.403445i
\(356\) 27.1828 19.3503i 1.44069 1.02556i
\(357\) 32.0182 4.17380i 1.69458 0.220901i
\(358\) −27.0780 13.9624i −1.43112 0.737935i
\(359\) 5.74179 9.94507i 0.303040 0.524881i −0.673783 0.738929i \(-0.735332\pi\)
0.976823 + 0.214049i \(0.0686651\pi\)
\(360\) −19.3733 2.80448i −1.02106 0.147809i
\(361\) 6.03921 + 10.4602i 0.317853 + 0.550538i
\(362\) −19.2888 + 12.3940i −1.01380 + 0.651413i
\(363\) −19.8460 + 19.8460i −1.04165 + 1.04165i
\(364\) −0.235857 + 0.375587i −0.0123622 + 0.0196861i
\(365\) 21.4417 + 0.525941i 1.12231 + 0.0275290i
\(366\) 1.45334 6.67835i 0.0759673 0.349083i
\(367\) −3.27735 + 12.2312i −0.171076 + 0.638465i 0.826111 + 0.563508i \(0.190549\pi\)
−0.997187 + 0.0749570i \(0.976118\pi\)
\(368\) 2.53735 3.74637i 0.132269 0.195293i
\(369\) −15.3259 8.84843i −0.797836 0.460631i
\(370\) −3.50049 + 6.39845i −0.181982 + 0.332639i
\(371\) 9.53297 + 23.0978i 0.494927 + 1.19918i
\(372\) −3.80024 + 22.5773i −0.197033 + 1.17058i
\(373\) 24.0550 6.44552i 1.24552 0.333737i 0.424917 0.905232i \(-0.360303\pi\)
0.820605 + 0.571496i \(0.193637\pi\)
\(374\) 22.2424 24.4635i 1.15013 1.26498i
\(375\) −12.0067 24.8541i −0.620025 1.28346i
\(376\) 3.08137 + 7.20040i 0.158909 + 0.371332i
\(377\) −0.431057 + 0.431057i −0.0222006 + 0.0222006i
\(378\) 0.795370 0.373422i 0.0409094 0.0192067i
\(379\) −4.18354 −0.214894 −0.107447 0.994211i \(-0.534268\pi\)
−0.107447 + 0.994211i \(0.534268\pi\)
\(380\) −7.71274 + 8.88512i −0.395655 + 0.455797i
\(381\) −11.4074 19.7583i −0.584421 1.01225i
\(382\) 23.2163 1.10408i 1.18785 0.0564898i
\(383\) −3.47535 12.9702i −0.177582 0.662745i −0.996097 0.0882604i \(-0.971869\pi\)
0.818515 0.574484i \(-0.194797\pi\)
\(384\) 23.1402 15.6431i 1.18087 0.798282i
\(385\) 27.6374 + 4.36650i 1.40853 + 0.222537i
\(386\) −2.13521 6.68133i −0.108679 0.340071i
\(387\) 6.65075 1.78206i 0.338076 0.0905873i
\(388\) −5.74535 15.4113i −0.291676 0.782393i
\(389\) −15.5106 + 8.95506i −0.786419 + 0.454039i −0.838700 0.544593i \(-0.816684\pi\)
0.0522811 + 0.998632i \(0.483351\pi\)
\(390\) −0.154779 + 0.635778i −0.00783753 + 0.0321938i
\(391\) 5.59179i 0.282789i
\(392\) −19.6523 2.40525i −0.992593 0.121483i
\(393\) 6.44222 + 6.44222i 0.324967 + 0.324967i
\(394\) −1.65828 + 7.62009i −0.0835430 + 0.383895i
\(395\) 13.0935 + 3.85489i 0.658805 + 0.193961i
\(396\) 12.1663 26.6292i 0.611378 1.33817i
\(397\) −1.58258 5.90626i −0.0794273 0.296427i 0.914773 0.403967i \(-0.132369\pi\)
−0.994201 + 0.107541i \(0.965702\pi\)
\(398\) −23.7511 12.2469i −1.19053 0.613882i
\(399\) 2.26475 17.0348i 0.113379 0.852809i
\(400\) 18.5542 + 7.46601i 0.927711 + 0.373300i
\(401\) −9.81777 + 17.0049i −0.490276 + 0.849183i −0.999937 0.0111923i \(-0.996437\pi\)
0.509662 + 0.860375i \(0.329771\pi\)
\(402\) 0.0844603 + 1.77600i 0.00421250 + 0.0885788i
\(403\) 0.375386 + 0.100584i 0.0186993 + 0.00501046i
\(404\) 17.0715 1.62741i 0.849341 0.0809665i
\(405\) −14.0981 + 13.4231i −0.700542 + 0.666998i
\(406\) −25.5973 9.24095i −1.27037 0.458621i
\(407\) −7.71315 7.71315i −0.382327 0.382327i
\(408\) −12.8368 + 32.0428i −0.635518 + 1.58635i
\(409\) 8.70611 5.02647i 0.430489 0.248543i −0.269066 0.963122i \(-0.586715\pi\)
0.699555 + 0.714579i \(0.253382\pi\)
\(410\) 13.0757 + 12.4877i 0.645763 + 0.616725i
\(411\) −42.4589 24.5137i −2.09434 1.20917i
\(412\) −6.44160 1.08426i −0.317355 0.0534175i
\(413\) −8.19636 3.40728i −0.403316 0.167661i
\(414\) 1.50726 + 4.71641i 0.0740779 + 0.231799i
\(415\) −15.1852 9.27095i −0.745412 0.455093i
\(416\) −0.227059 0.416218i −0.0111325 0.0204068i
\(417\) 2.75655 + 0.738616i 0.134989 + 0.0361702i
\(418\) −9.51240 14.8042i −0.465267 0.724095i
\(419\) 17.7853 0.868870 0.434435 0.900703i \(-0.356948\pi\)
0.434435 + 0.900703i \(0.356948\pi\)
\(420\) −28.6285 + 5.80756i −1.39693 + 0.283380i
\(421\) 39.6482 1.93234 0.966168 0.257913i \(-0.0830348\pi\)
0.966168 + 0.257913i \(0.0830348\pi\)
\(422\) 8.39368 + 13.0631i 0.408598 + 0.635901i
\(423\) −8.27847 2.21821i −0.402513 0.107853i
\(424\) −26.5233 3.17764i −1.28809 0.154320i
\(425\) −24.1591 + 5.21887i −1.17189 + 0.253153i
\(426\) −15.3713 48.0987i −0.744741 2.33039i
\(427\) −0.669478 5.13572i −0.0323983 0.248535i
\(428\) −2.25484 + 13.3960i −0.108992 + 0.647522i
\(429\) −0.847531 0.489322i −0.0409192 0.0236247i
\(430\) −7.03290 + 0.161762i −0.339156 + 0.00780087i
\(431\) −21.7939 + 12.5827i −1.04977 + 0.606087i −0.922586 0.385792i \(-0.873928\pi\)
−0.127187 + 0.991879i \(0.540595\pi\)
\(432\) −0.0673082 + 0.936921i −0.00323837 + 0.0450776i
\(433\) 9.19231 + 9.19231i 0.441754 + 0.441754i 0.892601 0.450847i \(-0.148878\pi\)
−0.450847 + 0.892601i \(0.648878\pi\)
\(434\) 3.05732 + 17.0778i 0.146756 + 0.819759i
\(435\) −40.1401 0.984591i −1.92457 0.0472075i
\(436\) 0.743873 + 7.80325i 0.0356251 + 0.373708i
\(437\) 2.87463 + 0.770255i 0.137512 + 0.0368463i
\(438\) −1.59085 33.4519i −0.0760139 1.59839i
\(439\) −14.8997 + 25.8071i −0.711125 + 1.23170i 0.253310 + 0.967385i \(0.418481\pi\)
−0.964435 + 0.264320i \(0.914853\pi\)
\(440\) −18.5130 + 23.4947i −0.882575 + 1.12007i
\(441\) 15.3590 15.2810i 0.731382 0.727666i
\(442\) 0.520776 + 0.268531i 0.0247708 + 0.0127727i
\(443\) 10.5682 + 39.4412i 0.502112 + 1.87391i 0.485856 + 0.874039i \(0.338508\pi\)
0.0162556 + 0.999868i \(0.494825\pi\)
\(444\) 10.3582 + 4.73242i 0.491579 + 0.224591i
\(445\) 10.5360 35.7864i 0.499454 1.69644i
\(446\) −5.82600 + 26.7715i −0.275869 + 1.26767i
\(447\) 10.8257 + 10.8257i 0.512039 + 0.512039i
\(448\) 12.5117 17.0722i 0.591120 0.806583i
\(449\) 20.7052i 0.977139i 0.872525 + 0.488570i \(0.162481\pi\)
−0.872525 + 0.488570i \(0.837519\pi\)
\(450\) −18.9703 + 10.9139i −0.894271 + 0.514488i
\(451\) −23.4189 + 13.5209i −1.10275 + 0.636675i
\(452\) −0.0742563 + 0.0276828i −0.00349272 + 0.00130209i
\(453\) 24.0199 6.43610i 1.12855 0.302394i
\(454\) 9.88197 + 30.9219i 0.463784 + 1.45124i
\(455\) 0.0520192 + 0.493114i 0.00243870 + 0.0231176i
\(456\) 14.7043 + 11.0130i 0.688593 + 0.515730i
\(457\) 0.969683 + 3.61891i 0.0453599 + 0.169285i 0.984890 0.173181i \(-0.0554045\pi\)
−0.939530 + 0.342466i \(0.888738\pi\)
\(458\) −16.8654 + 0.802058i −0.788067 + 0.0374777i
\(459\) −0.580425 1.00533i −0.0270919 0.0469246i
\(460\) −0.356441 5.04626i −0.0166191 0.235283i
\(461\) −6.66823 −0.310570 −0.155285 0.987870i \(-0.549630\pi\)
−0.155285 + 0.987870i \(0.549630\pi\)
\(462\) 3.69396 43.5326i 0.171859 2.02532i
\(463\) 14.7884 14.7884i 0.687277 0.687277i −0.274353 0.961629i \(-0.588464\pi\)
0.961629 + 0.274353i \(0.0884635\pi\)
\(464\) 21.9933 19.0451i 1.02101 0.884146i
\(465\) 12.2512 + 22.4751i 0.568136 + 1.04226i
\(466\) 22.6342 24.8945i 1.04851 1.15321i
\(467\) −27.1281 + 7.26895i −1.25534 + 0.336367i −0.824396 0.566013i \(-0.808485\pi\)
−0.430941 + 0.902380i \(0.641818\pi\)
\(468\) 0.511632 + 0.0861184i 0.0236502 + 0.00398083i
\(469\) 0.514018 + 1.24543i 0.0237351 + 0.0575087i
\(470\) 7.68199 + 4.20270i 0.354344 + 0.193856i
\(471\) 31.1509 + 17.9850i 1.43536 + 0.828703i
\(472\) 7.46043 5.86408i 0.343394 0.269916i
\(473\) 2.72309 10.1627i 0.125208 0.467282i
\(474\) 4.53187 20.8247i 0.208156 0.956511i
\(475\) −0.644940 + 13.1386i −0.0295919 + 0.602842i
\(476\) −0.971046 + 26.1394i −0.0445078 + 1.19810i
\(477\) 20.6700 20.6700i 0.946413 0.946413i
\(478\) −1.79357 + 1.15246i −0.0820359 + 0.0527121i
\(479\) 5.27141 + 9.13034i 0.240857 + 0.417176i 0.960959 0.276692i \(-0.0892383\pi\)
−0.720102 + 0.693868i \(0.755905\pi\)
\(480\) 9.54196 29.7350i 0.435529 1.35721i
\(481\) 0.0966532 0.167408i 0.00440701 0.00763316i
\(482\) 23.2927 + 12.0106i 1.06096 + 0.547067i
\(483\) 4.49057 + 5.86768i 0.204328 + 0.266989i
\(484\) −13.1857 18.5229i −0.599348 0.841949i
\(485\) −15.6949 9.58215i −0.712670 0.435103i
\(486\) 23.2265 + 21.1176i 1.05358 + 0.957916i
\(487\) 9.85078 36.7636i 0.446381 1.66592i −0.265882 0.964006i \(-0.585663\pi\)
0.712263 0.701913i \(-0.247670\pi\)
\(488\) 5.13966 + 2.05903i 0.232662 + 0.0932078i
\(489\) 7.28707i 0.329533i
\(490\) −18.9400 + 11.4577i −0.855620 + 0.517604i
\(491\) 3.59770i 0.162362i −0.996699 0.0811809i \(-0.974131\pi\)
0.996699 0.0811809i \(-0.0258691\pi\)
\(492\) 17.9784 21.7673i 0.810530 0.981347i
\(493\) −9.30560 + 34.7290i −0.419103 + 1.56411i
\(494\) 0.209782 0.230731i 0.00943854 0.0103811i
\(495\) −7.69395 31.8154i −0.345817 1.43000i
\(496\) −17.5252 6.07173i −0.786903 0.272629i
\(497\) −23.2551 30.3867i −1.04313 1.36303i
\(498\) −12.7316 + 24.6910i −0.570516 + 1.10643i
\(499\) 5.11616 8.86145i 0.229031 0.396693i −0.728490 0.685056i \(-0.759778\pi\)
0.957521 + 0.288363i \(0.0931110\pi\)
\(500\) 21.4695 6.24972i 0.960147 0.279496i
\(501\) −10.7030 18.5381i −0.478174 0.828221i
\(502\) −13.7775 21.4419i −0.614920 0.957000i
\(503\) 30.0943 30.0943i 1.34184 1.34184i 0.447605 0.894231i \(-0.352277\pi\)
0.894231 0.447605i \(-0.147723\pi\)
\(504\) 6.22680 + 22.3091i 0.277364 + 0.993724i
\(505\) 13.8858 13.2209i 0.617910 0.588322i
\(506\) 7.39299 + 1.60886i 0.328659 + 0.0715225i
\(507\) −8.30225 + 30.9844i −0.368716 + 1.37607i
\(508\) 17.3181 6.45618i 0.768365 0.286447i
\(509\) 0.0145211 + 0.00838376i 0.000643637 + 0.000371604i 0.500322 0.865840i \(-0.333215\pi\)
−0.499678 + 0.866211i \(0.666548\pi\)
\(510\) 10.8431 + 37.0383i 0.480141 + 1.64008i
\(511\) −9.68180 23.4584i −0.428298 1.03774i
\(512\) 9.38510 + 20.5893i 0.414767 + 0.909928i
\(513\) −0.596770 + 0.159904i −0.0263481 + 0.00705994i
\(514\) −15.6028 14.1861i −0.688210 0.625724i
\(515\) −6.41243 + 3.49543i −0.282565 + 0.154027i
\(516\) 1.04239 + 10.9347i 0.0458885 + 0.481372i
\(517\) −9.26042 + 9.26042i −0.407273 + 0.407273i
\(518\) 8.59876 + 0.729649i 0.377808 + 0.0320589i
\(519\) −4.43276 −0.194577
\(520\) −0.487087 0.209137i −0.0213602 0.00917127i
\(521\) 0.00830997 + 0.0143933i 0.000364066 + 0.000630582i 0.866207 0.499685i \(-0.166551\pi\)
−0.865843 + 0.500315i \(0.833217\pi\)
\(522\) 1.51232 + 31.8006i 0.0661926 + 1.39187i
\(523\) 8.00409 + 29.8717i 0.349994 + 1.30620i 0.886668 + 0.462407i \(0.153014\pi\)
−0.536674 + 0.843790i \(0.680319\pi\)
\(524\) −6.01271 + 4.28019i −0.262666 + 0.186981i
\(525\) −21.1600 + 24.8777i −0.923498 + 1.08575i
\(526\) 9.55070 3.05219i 0.416430 0.133082i
\(527\) 22.1400 5.93238i 0.964432 0.258419i
\(528\) 38.6708 + 26.1910i 1.68293 + 1.13982i
\(529\) 18.8104 10.8602i 0.817845 0.472183i
\(530\) −25.5145 + 15.5238i −1.10828 + 0.674311i
\(531\) 10.3840i 0.450626i
\(532\) 13.3040 + 4.09983i 0.576800 + 0.177750i
\(533\) −0.338860 0.338860i −0.0146777 0.0146777i
\(534\) −56.9171 12.3863i −2.46304 0.536007i
\(535\) 7.26914 + 13.3354i 0.314272 + 0.576539i
\(536\) −1.43014 0.171338i −0.0617725 0.00740069i
\(537\) 13.7653 + 51.3727i 0.594016 + 2.21690i
\(538\) 3.91757 7.59756i 0.168899 0.327554i
\(539\) −8.48716 32.0003i −0.365568 1.37835i
\(540\) 0.587882 + 0.870249i 0.0252984 + 0.0374496i
\(541\) −14.5885 + 25.2681i −0.627211 + 1.08636i 0.360898 + 0.932605i \(0.382470\pi\)
−0.988109 + 0.153756i \(0.950863\pi\)
\(542\) −33.1900 + 1.57840i −1.42563 + 0.0677981i
\(543\) 38.6612 + 10.3592i 1.65911 + 0.444558i
\(544\) −23.8717 14.5635i −1.02349 0.624406i
\(545\) 6.04316 + 6.34708i 0.258860 + 0.271879i
\(546\) 0.762117 0.136437i 0.0326156 0.00583896i
\(547\) −0.913792 0.913792i −0.0390709 0.0390709i 0.687301 0.726372i \(-0.258795\pi\)
−0.726372 + 0.687301i \(0.758795\pi\)
\(548\) 25.2923 30.6226i 1.08043 1.30813i
\(549\) −5.24710 + 3.02941i −0.223941 + 0.129292i
\(550\) −0.0510742 + 33.4427i −0.00217781 + 1.42600i
\(551\) 16.5717 + 9.56766i 0.705977 + 0.407596i
\(552\) −7.81886 + 1.12229i −0.332793 + 0.0477677i
\(553\) −2.08759 16.0144i −0.0887735 0.681002i
\(554\) −31.4204 + 10.0413i −1.33493 + 0.426613i
\(555\) 12.3755 2.99279i 0.525312 0.127037i
\(556\) −0.960714 + 2.10279i −0.0407434 + 0.0891781i
\(557\) −2.78027 0.744970i −0.117804 0.0315654i 0.199436 0.979911i \(-0.436089\pi\)
−0.317239 + 0.948346i \(0.602756\pi\)
\(558\) 17.0749 10.9715i 0.722839 0.464460i
\(559\) 0.186452 0.00788606
\(560\) −0.789903 23.6511i −0.0333795 0.999443i
\(561\) −57.7196 −2.43693
\(562\) −22.9639 + 14.7554i −0.968674 + 0.622421i
\(563\) −26.9945 7.23315i −1.13768 0.304841i −0.359663 0.933082i \(-0.617108\pi\)
−0.778018 + 0.628241i \(0.783775\pi\)
\(564\) 5.68176 12.4361i 0.239245 0.523654i
\(565\) −0.0461696 + 0.0756227i −0.00194237 + 0.00318147i
\(566\) −9.60324 + 3.06898i −0.403654 + 0.128999i
\(567\) 21.2683 + 8.84138i 0.893186 + 0.371303i
\(568\) 40.4912 5.81193i 1.69897 0.243863i
\(569\) −31.8950 18.4146i −1.33711 0.771981i −0.350732 0.936476i \(-0.614067\pi\)
−0.986378 + 0.164495i \(0.947400\pi\)
\(570\) 20.5343 0.472304i 0.860085 0.0197826i
\(571\) 35.5147 20.5044i 1.48624 0.858084i 0.486367 0.873754i \(-0.338322\pi\)
0.999877 + 0.0156706i \(0.00498830\pi\)
\(572\) 0.504865 0.611264i 0.0211095 0.0255582i
\(573\) −28.6909 28.6909i −1.19858 1.19858i
\(574\) 7.26445 20.1224i 0.303212 0.839894i
\(575\) −3.79847 4.19063i −0.158407 0.174762i
\(576\) −24.0602 5.84905i −1.00251 0.243710i
\(577\) −20.6267 5.52692i −0.858703 0.230089i −0.197506 0.980302i \(-0.563284\pi\)
−0.661196 + 0.750213i \(0.729951\pi\)
\(578\) 10.5043 0.499547i 0.436921 0.0207784i
\(579\) −6.12245 + 10.6044i −0.254440 + 0.440704i
\(580\) 6.18401 31.9340i 0.256777 1.32599i
\(581\) −2.77432 + 20.8677i −0.115098 + 0.865737i
\(582\) −13.1590 + 25.5199i −0.545457 + 1.05783i
\(583\) −11.5609 43.1458i −0.478802 1.78691i
\(584\) 26.9374 + 3.22725i 1.11468 + 0.133545i
\(585\) 0.509315 0.277629i 0.0210576 0.0114785i
\(586\) 2.52963 + 0.550498i 0.104498 + 0.0227408i
\(587\) 0.870374 + 0.870374i 0.0359242 + 0.0359242i 0.724841 0.688917i \(-0.241913\pi\)
−0.688917 + 0.724841i \(0.741913\pi\)
\(588\) 19.9726 + 28.2088i 0.823657 + 1.16331i
\(589\) 12.1989i 0.502646i
\(590\) 2.50951 10.3082i 0.103315 0.424382i
\(591\) 11.7900 6.80697i 0.484977 0.280001i
\(592\) −5.17338 + 7.63845i −0.212625 + 0.313938i
\(593\) −2.04214 + 0.547190i −0.0838607 + 0.0224704i −0.300505 0.953780i \(-0.597155\pi\)
0.216645 + 0.976251i \(0.430489\pi\)
\(594\) −1.49615 + 0.478138i −0.0613880 + 0.0196182i
\(595\) 17.1987 + 23.6530i 0.705080 + 0.969679i
\(596\) −10.1039 + 7.19257i −0.413874 + 0.294619i
\(597\) 12.0740 + 45.0608i 0.494157 + 1.84422i
\(598\) 0.00636923 + 0.133930i 0.000260457 + 0.00547679i
\(599\) 12.9248 + 22.3864i 0.528092 + 0.914683i 0.999464 + 0.0327479i \(0.0104258\pi\)
−0.471371 + 0.881935i \(0.656241\pi\)
\(600\) −12.1462 32.7337i −0.495867 1.33635i
\(601\) 20.5570 0.838537 0.419269 0.907862i \(-0.362287\pi\)
0.419269 + 0.907862i \(0.362287\pi\)
\(602\) 3.53743 + 7.53456i 0.144175 + 0.307086i
\(603\) 1.11452 1.11452i 0.0453869 0.0453869i
\(604\) 1.91172 + 20.0540i 0.0777868 + 0.815986i
\(605\) −24.3855 7.17942i −0.991412 0.291885i
\(606\) −22.1506 20.1394i −0.899806 0.818108i
\(607\) −21.6414 + 5.79881i −0.878399 + 0.235366i −0.669716 0.742617i \(-0.733584\pi\)
−0.208683 + 0.977983i \(0.566918\pi\)
\(608\) −10.7751 + 10.2659i −0.436987 + 0.416336i
\(609\) 18.1249 + 43.9154i 0.734457 + 1.77954i
\(610\) 5.94094 1.73923i 0.240542 0.0704196i
\(611\) −0.200991 0.116042i −0.00813122 0.00469456i
\(612\) 28.6725 10.6891i 1.15902 0.432081i
\(613\) −8.56832 + 31.9774i −0.346071 + 1.29156i 0.545285 + 0.838251i \(0.316422\pi\)
−0.891356 + 0.453304i \(0.850245\pi\)
\(614\) −7.54686 1.64234i −0.304566 0.0662796i
\(615\) 0.774002 31.5547i 0.0312108 1.27241i
\(616\) 34.2798 + 8.80460i 1.38117 + 0.354747i
\(617\) 27.2948 27.2948i 1.09885 1.09885i 0.104300 0.994546i \(-0.466740\pi\)
0.994546 0.104300i \(-0.0332603\pi\)
\(618\) 6.16441 + 9.59368i 0.247969 + 0.385914i
\(619\) −18.1903 31.5065i −0.731130 1.26635i −0.956400 0.292059i \(-0.905660\pi\)
0.225270 0.974296i \(-0.427674\pi\)
\(620\) −19.6019 + 6.76490i −0.787229 + 0.271685i
\(621\) 0.132821 0.230053i 0.00532992 0.00923169i
\(622\) 13.3071 25.8071i 0.533564 1.03477i
\(623\) −43.7698 + 5.70571i −1.75360 + 0.228594i
\(624\) −0.270959 + 0.782082i −0.0108470 + 0.0313083i
\(625\) 14.5603 20.3223i 0.582414 0.812893i
\(626\) −26.5535 + 29.2052i −1.06129 + 1.16727i
\(627\) −7.95073 + 29.6725i −0.317522 + 1.18501i
\(628\) −18.5562 + 22.4669i −0.740474 + 0.896527i
\(629\) 11.4011i 0.454590i
\(630\) 20.8820 + 15.3143i 0.831957 + 0.610136i
\(631\) 10.6984i 0.425897i 0.977063 + 0.212949i \(0.0683067\pi\)
−0.977063 + 0.212949i \(0.931693\pi\)
\(632\) 16.0267 + 6.42055i 0.637509 + 0.255396i
\(633\) 7.01567 26.1828i 0.278848 1.04067i
\(634\) −13.5593 12.3282i −0.538510 0.489616i
\(635\) 10.7677 17.6367i 0.427302 0.699892i
\(636\) 27.0441 + 37.9908i 1.07237 + 1.50643i
\(637\) 0.508841 0.292054i 0.0201610 0.0115716i
\(638\) 43.2383 + 22.2952i 1.71182 + 0.882676i
\(639\) −22.3816 + 38.7661i −0.885402 + 1.53356i
\(640\) 22.4711 + 11.6211i 0.888249 + 0.459362i
\(641\) −2.64450 4.58042i −0.104452 0.180916i 0.809062 0.587723i \(-0.199975\pi\)
−0.913514 + 0.406807i \(0.866642\pi\)
\(642\) 19.9512 12.8196i 0.787410 0.505950i
\(643\) 6.36844 6.36844i 0.251147 0.251147i −0.570294 0.821441i \(-0.693171\pi\)
0.821441 + 0.570294i \(0.193171\pi\)
\(644\) −5.29130 + 2.79835i −0.208506 + 0.110270i
\(645\) 8.46826 + 8.89414i 0.333437 + 0.350206i
\(646\) 3.91096 17.9715i 0.153875 0.707081i
\(647\) −1.58576 + 5.91812i −0.0623425 + 0.232665i −0.990066 0.140602i \(-0.955096\pi\)
0.927724 + 0.373268i \(0.121763\pi\)
\(648\) −19.3587 + 15.2164i −0.760482 + 0.597757i
\(649\) 13.7415 + 7.93365i 0.539401 + 0.311423i
\(650\) −0.572694 + 0.152516i −0.0224629 + 0.00598217i
\(651\) 18.4682 24.0049i 0.723826 0.940825i
\(652\) 5.82137 + 0.979860i 0.227983 + 0.0383743i
\(653\) −37.7871 + 10.1250i −1.47872 + 0.396223i −0.905913 0.423464i \(-0.860814\pi\)
−0.572812 + 0.819687i \(0.694147\pi\)
\(654\) 9.20555 10.1248i 0.359966 0.395913i
\(655\) −2.33051 + 7.91578i −0.0910606 + 0.309295i
\(656\) 14.9716 + 17.2892i 0.584544 + 0.675032i
\(657\) −20.9927 + 20.9927i −0.819001 + 0.819001i
\(658\) 0.876018 10.3237i 0.0341508 0.402459i
\(659\) 7.96382 0.310226 0.155113 0.987897i \(-0.450426\pi\)
0.155113 + 0.987897i \(0.450426\pi\)
\(660\) 52.0886 3.67925i 2.02754 0.143215i
\(661\) −17.8362 30.8932i −0.693748 1.20161i −0.970601 0.240694i \(-0.922625\pi\)
0.276854 0.960912i \(-0.410708\pi\)
\(662\) 10.4610 0.497486i 0.406577 0.0193354i
\(663\) −0.264740 0.988023i −0.0102817 0.0383716i
\(664\) −18.0128 13.4909i −0.699032 0.523548i
\(665\) 14.5286 5.58340i 0.563396 0.216515i
\(666\) −3.07314 9.61625i −0.119082 0.372622i
\(667\) −7.94717 + 2.12944i −0.307716 + 0.0824521i
\(668\) 16.2486 6.05747i 0.628676 0.234371i
\(669\) 41.4216 23.9148i 1.60145 0.924599i
\(670\) −1.37574 + 0.837044i −0.0531495 + 0.0323378i
\(671\) 9.25823i 0.357410i
\(672\) −36.7449 + 3.88844i −1.41746 + 0.150000i
\(673\) −29.4853 29.4853i −1.13657 1.13657i −0.989060 0.147515i \(-0.952873\pi\)
−0.147515 0.989060i \(-0.547127\pi\)
\(674\) −2.47512 + 11.3736i −0.0953380 + 0.438094i
\(675\) 1.11790 + 0.359138i 0.0430279 + 0.0138232i
\(676\) −23.6359 10.7987i −0.909075 0.415335i
\(677\) 11.9320 + 44.5308i 0.458584 + 1.71146i 0.677333 + 0.735676i \(0.263136\pi\)
−0.218750 + 0.975781i \(0.570198\pi\)
\(678\) 0.122962 + 0.0634037i 0.00472233 + 0.00243500i
\(679\) −2.86745 + 21.5682i −0.110043 + 0.827710i
\(680\) −31.0465 + 3.68179i −1.19058 + 0.141190i
\(681\) 28.3354 49.0783i 1.08581 1.88069i
\(682\) −1.47322 30.9784i −0.0564127 1.18622i
\(683\) −40.1276 10.7522i −1.53544 0.411420i −0.610652 0.791899i \(-0.709093\pi\)
−0.924790 + 0.380479i \(0.875759\pi\)
\(684\) −1.54550 16.2123i −0.0590936 0.619894i
\(685\) 1.08888 44.3917i 0.0416039 1.69612i
\(686\) 21.4559 + 15.0214i 0.819191 + 0.573521i
\(687\) 20.8424 + 20.8424i 0.795187 + 0.795187i
\(688\) −8.87547 0.637612i −0.338374 0.0243087i
\(689\) 0.685527 0.395789i 0.0261165 0.0150784i
\(690\) −6.09946 + 6.38665i −0.232202 + 0.243136i
\(691\) −15.8798 9.16821i −0.604096 0.348775i 0.166555 0.986032i \(-0.446736\pi\)
−0.770651 + 0.637257i \(0.780069\pi\)
\(692\) 0.596054 3.54117i 0.0226586 0.134615i
\(693\) −30.7563 + 23.5380i −1.16833 + 0.894133i
\(694\) −4.75419 14.8765i −0.180466 0.564703i
\(695\) 0.607556 + 2.51232i 0.0230459 + 0.0952977i
\(696\) −50.4283 6.04159i −1.91148 0.229006i
\(697\) −27.3010 7.31528i −1.03410 0.277086i
\(698\) 7.95028 + 12.3730i 0.300922 + 0.468326i
\(699\) −58.7364 −2.22161
\(700\) −17.0286 20.2491i −0.643620 0.765345i
\(701\) 3.42628 0.129409 0.0647045 0.997904i \(-0.479390\pi\)
0.0647045 + 0.997904i \(0.479390\pi\)
\(702\) −0.0150469 0.0234176i −0.000567910 0.000883839i
\(703\) −5.86106 1.57047i −0.221054 0.0592312i
\(704\) −26.1229 + 27.3709i −0.984546 + 1.03158i
\(705\) −3.59315 14.8581i −0.135326 0.559588i
\(706\) 3.24859 + 10.1653i 0.122262 + 0.382574i
\(707\) −20.9480 8.70820i −0.787830 0.327506i
\(708\) −16.3358 2.74966i −0.613937 0.103339i
\(709\) 26.8261 + 15.4881i 1.00748 + 0.581667i 0.910452 0.413615i \(-0.135734\pi\)
0.0970248 + 0.995282i \(0.469067\pi\)
\(710\) 31.5870 33.0742i 1.18544 1.24125i
\(711\) −16.3617 + 9.44644i −0.613612 + 0.354269i
\(712\) 17.5483 43.8034i 0.657651 1.64160i
\(713\) 3.70884 + 3.70884i 0.138897 + 0.138897i
\(714\) 34.9035 29.4434i 1.30623 1.10189i
\(715\) 0.0217353 0.886111i 0.000812854 0.0331387i
\(716\) −42.8907 + 4.08871i −1.60290 + 0.152802i
\(717\) 3.59492 + 0.963255i 0.134255 + 0.0359734i
\(718\) −0.771456 16.2219i −0.0287905 0.605396i
\(719\) 21.3674 37.0094i 0.796869 1.38022i −0.124777 0.992185i \(-0.539821\pi\)
0.921646 0.388033i \(-0.126845\pi\)
\(720\) −25.1938 + 11.4740i −0.938919 + 0.427609i
\(721\) 6.84890 + 5.26922i 0.255066 + 0.196236i
\(722\) 15.1820 + 7.82838i 0.565015 + 0.291342i
\(723\) −11.8410 44.1913i −0.440372 1.64349i
\(724\) −13.4742 + 29.4920i −0.500765 + 1.09606i
\(725\) −16.6173 32.3480i −0.617152 1.20138i
\(726\) −8.44023 + 38.7843i −0.313246 + 1.43942i
\(727\) −21.7303 21.7303i −0.805931 0.805931i 0.178084 0.984015i \(-0.443010\pi\)
−0.984015 + 0.178084i \(0.943010\pi\)
\(728\) 0.00651592 + 0.627173i 0.000241496 + 0.0232446i
\(729\) 28.6841i 1.06238i
\(730\) 25.9128 15.7662i 0.959077 0.583532i
\(731\) 9.52347 5.49838i 0.352238 0.203365i
\(732\) −3.37637 9.05678i −0.124794 0.334748i
\(733\) −3.68215 + 0.986629i −0.136003 + 0.0364420i −0.326179 0.945308i \(-0.605761\pi\)
0.190175 + 0.981750i \(0.439094\pi\)
\(734\) 5.45132 + 17.0579i 0.201212 + 0.629618i
\(735\) 37.0422 + 11.0083i 1.36632 + 0.406047i
\(736\) 0.154814 6.39711i 0.00570652 0.235800i
\(737\) −0.623362 2.32642i −0.0229618 0.0856947i
\(738\) −24.9989 + 1.18886i −0.920222 + 0.0437625i
\(739\) −6.00177 10.3954i −0.220779 0.382400i 0.734266 0.678862i \(-0.237526\pi\)
−0.955045 + 0.296462i \(0.904193\pi\)
\(740\) 0.726743 + 10.2888i 0.0267156 + 0.378223i
\(741\) −0.544391 −0.0199987
\(742\) 29.0000 + 20.1933i 1.06462 + 0.741318i
\(743\) 7.86007 7.86007i 0.288358 0.288358i −0.548073 0.836431i \(-0.684638\pi\)
0.836431 + 0.548073i \(0.184638\pi\)
\(744\) 12.7386 + 29.7671i 0.467021 + 1.09131i
\(745\) −3.91626 + 13.3019i −0.143481 + 0.487345i
\(746\) 23.6925 26.0585i 0.867443 0.954068i
\(747\) 23.7876 6.37387i 0.870344 0.233208i
\(748\) 7.76130 46.1101i 0.283781 1.68595i
\(749\) 10.9580 14.2431i 0.400395 0.520431i
\(750\) −33.2860 20.3918i −1.21543 0.744602i
\(751\) −1.00430 0.579834i −0.0366475 0.0211584i 0.481564 0.876411i \(-0.340069\pi\)
−0.518212 + 0.855252i \(0.673402\pi\)
\(752\) 9.17074 + 6.21117i 0.334422 + 0.226498i
\(753\) −11.5156 + 42.9769i −0.419653 + 1.56616i
\(754\) −0.183322 + 0.842397i −0.00667620 + 0.0306783i
\(755\) 15.5306 + 16.3117i 0.565218 + 0.593643i
\(756\) 0.660834 1.05234i 0.0240343 0.0382731i
\(757\) −15.7431 + 15.7431i −0.572192 + 0.572192i −0.932740 0.360549i \(-0.882590\pi\)
0.360549 + 0.932740i \(0.382590\pi\)
\(758\) −4.97747 + 3.19827i −0.180790 + 0.116166i
\(759\) −6.60410 11.4386i −0.239714 0.415196i
\(760\) −2.38384 + 16.4676i −0.0864711 + 0.597341i
\(761\) 9.62047 16.6631i 0.348742 0.604039i −0.637284 0.770629i \(-0.719942\pi\)
0.986026 + 0.166590i \(0.0532757\pi\)
\(762\) −28.6772 14.7870i −1.03887 0.535677i
\(763\) 3.98044 9.57514i 0.144102 0.346643i
\(764\) 26.7780 19.0621i 0.968794 0.689644i
\(765\) 17.8274 29.2000i 0.644550 1.05573i
\(766\) −14.0504 12.7747i −0.507662 0.461569i
\(767\) −0.0727778 + 0.271611i −0.00262786 + 0.00980729i
\(768\) 15.5727 36.3021i 0.561931 1.30994i
\(769\) 30.8833i 1.11368i 0.830620 + 0.556840i \(0.187986\pi\)
−0.830620 + 0.556840i \(0.812014\pi\)
\(770\) 36.2204 15.9333i 1.30529 0.574197i
\(771\) 36.8135i 1.32580i
\(772\) −7.64820 6.31693i −0.275265 0.227351i
\(773\) −4.19873 + 15.6699i −0.151018 + 0.563607i 0.848396 + 0.529363i \(0.177569\pi\)
−0.999414 + 0.0342438i \(0.989098\pi\)
\(774\) 6.55051 7.20466i 0.235453 0.258966i
\(775\) −12.5624 + 19.4854i −0.451255 + 0.699937i
\(776\) −18.6174 13.9437i −0.668327 0.500551i
\(777\) −9.15578 11.9636i −0.328462 0.429190i
\(778\) −11.6081 + 22.5122i −0.416170 + 0.807100i
\(779\) −7.52128 + 13.0272i −0.269478 + 0.466749i
\(780\) 0.301892 + 0.874757i 0.0108095 + 0.0313213i
\(781\) 34.2004 + 59.2368i 1.22379 + 2.11966i
\(782\) 4.27486 + 6.65296i 0.152869 + 0.237910i
\(783\) 1.20775 1.20775i 0.0431616 0.0431616i
\(784\) −25.2206 + 12.1623i −0.900736 + 0.434367i
\(785\) −0.798877 + 32.5689i −0.0285132 + 1.16243i
\(786\) 12.5898 + 2.73978i 0.449062 + 0.0977248i
\(787\) 10.8721 40.5750i 0.387547 1.44634i −0.446566 0.894751i \(-0.647353\pi\)
0.834113 0.551594i \(-0.185980\pi\)
\(788\) 3.85249 + 10.3339i 0.137239 + 0.368130i
\(789\) −15.1586 8.75180i −0.539659 0.311572i
\(790\) 18.5253 5.42336i 0.659100 0.192954i
\(791\) 0.103922 + 0.0138162i 0.00369503 + 0.000491247i
\(792\) −5.88263 40.9837i −0.209030 1.45629i
\(793\) −0.158479 + 0.0424643i −0.00562775 + 0.00150795i
\(794\) −6.39817 5.81724i −0.227062 0.206446i
\(795\) 50.0153 + 14.7252i 1.77386 + 0.522247i
\(796\) −37.6210 + 3.58635i −1.33344 + 0.127115i
\(797\) 5.01705 5.01705i 0.177713 0.177713i −0.612645 0.790358i \(-0.709894\pi\)
0.790358 + 0.612645i \(0.209894\pi\)
\(798\) −10.3284 21.9990i −0.365621 0.778755i
\(799\) −13.6881 −0.484251
\(800\) 27.7830 5.30161i 0.982276 0.187440i
\(801\) 25.8185 + 44.7190i 0.912253 + 1.58007i
\(802\) 1.31910 + 27.7375i 0.0465790 + 0.979445i
\(803\) 11.7414 + 43.8193i 0.414343 + 1.54635i
\(804\) 1.45822 + 2.04847i 0.0514273 + 0.0722438i
\(805\) −2.71963 + 6.11468i −0.0958543 + 0.215514i
\(806\) 0.523519 0.167305i 0.0184402 0.00589308i
\(807\) −14.4142 + 3.86227i −0.507403 + 0.135958i
\(808\) 19.0671 14.9872i 0.670779 0.527249i
\(809\) −16.3576 + 9.44409i −0.575104 + 0.332036i −0.759185 0.650875i \(-0.774402\pi\)
0.184081 + 0.982911i \(0.441069\pi\)
\(810\) −6.51181 + 26.7483i −0.228802 + 0.939838i
\(811\) 21.4189i 0.752118i 0.926596 + 0.376059i \(0.122721\pi\)
−0.926596 + 0.376059i \(0.877279\pi\)
\(812\) −37.5196 + 8.57418i −1.31668 + 0.300895i
\(813\) 41.0166 + 41.0166i 1.43851 + 1.43851i
\(814\) −15.0735 3.28029i −0.528326 0.114974i
\(815\) 5.79501 3.15887i 0.202990 0.110650i
\(816\) 9.22340 + 47.9372i 0.322883 + 1.67814i
\(817\) −1.51477 5.65322i −0.0529953 0.197781i
\(818\) 6.51561 12.6361i 0.227813 0.441810i
\(819\) −0.543983 0.418514i −0.0190083 0.0146241i
\(820\) 25.1038 + 4.86134i 0.876664 + 0.169765i
\(821\) 20.8528 36.1180i 0.727766 1.26053i −0.230059 0.973177i \(-0.573892\pi\)
0.957825 0.287351i \(-0.0927747\pi\)
\(822\) −69.2569 + 3.29361i −2.41561 + 0.114878i
\(823\) −39.0933 10.4750i −1.36271 0.365136i −0.497897 0.867236i \(-0.665894\pi\)
−0.864809 + 0.502100i \(0.832561\pi\)
\(824\) −8.49294 + 3.63450i −0.295865 + 0.126614i
\(825\) 43.2566 39.2086i 1.50600 1.36507i
\(826\) −12.3566 + 2.21213i −0.429942 + 0.0769697i
\(827\) 30.7849 + 30.7849i 1.07050 + 1.07050i 0.997319 + 0.0731766i \(0.0233137\pi\)
0.0731766 + 0.997319i \(0.476686\pi\)
\(828\) 5.39894 + 4.45918i 0.187626 + 0.154967i
\(829\) 36.1486 20.8704i 1.25549 0.724859i 0.283298 0.959032i \(-0.408571\pi\)
0.972195 + 0.234172i \(0.0752380\pi\)
\(830\) −25.1545 + 0.578573i −0.873124 + 0.0200825i
\(831\) 49.8696 + 28.7922i 1.72996 + 0.998790i
\(832\) −0.588342 0.321622i −0.0203971 0.0111502i
\(833\) 17.3778 29.9229i 0.602104 1.03677i
\(834\) 3.84433 1.22856i 0.133118 0.0425417i
\(835\) 10.1027 16.5476i 0.349619 0.572652i
\(836\) −22.6352 10.3415i −0.782854 0.357667i
\(837\) −1.05177 0.281822i −0.0363546 0.00974118i
\(838\) 21.1605 13.5967i 0.730977 0.469689i
\(839\) 20.9842 0.724456 0.362228 0.932090i \(-0.382016\pi\)
0.362228 + 0.932090i \(0.382016\pi\)
\(840\) −29.6216 + 28.7958i −1.02204 + 0.993549i
\(841\) −23.9012 −0.824180
\(842\) 47.1724 30.3106i 1.62567 1.04457i
\(843\) 46.0274 + 12.3330i 1.58527 + 0.424772i
\(844\) 19.9731 + 9.12525i 0.687504 + 0.314104i
\(845\) −28.2392 + 6.82910i −0.971457 + 0.234928i
\(846\) −11.5453 + 3.68962i −0.396935 + 0.126852i
\(847\) 3.88797 + 29.8255i 0.133592 + 1.02482i
\(848\) −33.9860 + 16.4961i −1.16708 + 0.566477i
\(849\) 15.2420 + 8.79995i 0.523103 + 0.302014i
\(850\) −24.7541 + 24.6786i −0.849060 + 0.846470i
\(851\) 2.25941 1.30447i 0.0774517 0.0447168i
\(852\) −55.0592 45.4754i −1.88630 1.55796i
\(853\) 19.9509 + 19.9509i 0.683106 + 0.683106i 0.960699 0.277593i \(-0.0895367\pi\)
−0.277593 + 0.960699i \(0.589537\pi\)
\(854\) −4.72272 5.59853i −0.161608 0.191578i
\(855\) −12.5555 13.1869i −0.429389 0.450983i
\(856\) 7.55837 + 17.6620i 0.258340 + 0.603676i
\(857\) 37.0531 + 9.92835i 1.26571 + 0.339146i 0.828386 0.560158i \(-0.189260\pi\)
0.437324 + 0.899304i \(0.355926\pi\)
\(858\) −1.38245 + 0.0657445i −0.0471961 + 0.00224448i
\(859\) −3.51740 + 6.09232i −0.120012 + 0.207867i −0.919772 0.392453i \(-0.871627\pi\)
0.799760 + 0.600320i \(0.204960\pi\)
\(860\) −8.24388 + 5.56902i −0.281114 + 0.189902i
\(861\) −34.5226 + 14.2482i −1.17653 + 0.485579i
\(862\) −16.3104 + 31.6317i −0.555536 + 1.07738i
\(863\) 11.5958 + 43.2762i 0.394726 + 1.47314i 0.822246 + 0.569132i \(0.192721\pi\)
−0.427520 + 0.904006i \(0.640613\pi\)
\(864\) 0.636183 + 1.16618i 0.0216434 + 0.0396742i
\(865\) −1.92156 3.52514i −0.0653349 0.119858i
\(866\) 17.9642 + 3.90936i 0.610447 + 0.132845i
\(867\) −12.9813 12.9813i −0.440868 0.440868i
\(868\) 16.6933 + 17.9814i 0.566606 + 0.610328i
\(869\) 28.8694i 0.979328i
\(870\) −48.5103 + 29.5152i −1.64465 + 1.00066i
\(871\) 0.0369636 0.0213410i 0.00125246 0.000723111i
\(872\) 6.85053 + 8.71542i 0.231988 + 0.295141i
\(873\) 24.5861 6.58783i 0.832114 0.222964i
\(874\) 4.00901 1.28119i 0.135607 0.0433369i
\(875\) −28.9565 6.04317i −0.978909 0.204296i
\(876\) −27.4663 38.5839i −0.928000 1.30363i
\(877\) 1.48622 + 5.54663i 0.0501860 + 0.187297i 0.986468 0.163951i \(-0.0524241\pi\)
−0.936282 + 0.351248i \(0.885757\pi\)
\(878\) 2.00190 + 42.0952i 0.0675609 + 1.42064i
\(879\) −2.25970 3.91392i −0.0762179 0.132013i
\(880\) −4.06490 + 42.1064i −0.137028 + 1.41940i
\(881\) 3.68416 0.124122 0.0620612 0.998072i \(-0.480233\pi\)
0.0620612 + 0.998072i \(0.480233\pi\)
\(882\) 6.59163 29.9227i 0.221952 1.00755i
\(883\) 10.4605 10.4605i 0.352023 0.352023i −0.508839 0.860862i \(-0.669925\pi\)
0.860862 + 0.508839i \(0.169925\pi\)
\(884\) 0.824893 0.0786359i 0.0277442 0.00264481i
\(885\) −16.2618 + 8.86435i −0.546635 + 0.297972i
\(886\) 42.7261 + 38.8468i 1.43541 + 1.30508i
\(887\) 30.8995 8.27950i 1.03750 0.277998i 0.300426 0.953805i \(-0.402871\pi\)
0.737079 + 0.675807i \(0.236205\pi\)
\(888\) 15.9418 2.28822i 0.534972 0.0767876i
\(889\) −24.2366 3.22221i −0.812869 0.108070i
\(890\) −14.8228 50.6324i −0.496863 1.69720i
\(891\) −35.6571 20.5866i −1.19456 0.689678i
\(892\) 13.5348 + 36.3059i 0.453180 + 1.21561i
\(893\) −1.88550 + 7.03680i −0.0630960 + 0.235477i
\(894\) 21.1563 + 4.60402i 0.707571 + 0.153981i
\(895\) −34.8868 + 33.2163i −1.16614 + 1.11030i
\(896\) 1.83459 29.8770i 0.0612892 0.998120i
\(897\) 0.165512 0.165512i 0.00552627 0.00552627i
\(898\) 15.8289 + 24.6345i 0.528216 + 0.822064i
\(899\) 16.8624 + 29.2066i 0.562394 + 0.974095i
\(900\) −14.2268 + 27.4877i −0.474228 + 0.916257i
\(901\) 23.3433 40.4318i 0.777679 1.34698i
\(902\) −17.5266 + 33.9903i −0.583572 + 1.13175i
\(903\) 5.57778 13.4176i 0.185617 0.446510i
\(904\) −0.0671850 + 0.0897042i −0.00223454 + 0.00298352i
\(905\) 8.52110 + 35.2358i 0.283251 + 1.17128i
\(906\) 23.6578 26.0204i 0.785979 0.864469i
\(907\) −3.58771 + 13.3895i −0.119128 + 0.444592i −0.999563 0.0295760i \(-0.990584\pi\)
0.880435 + 0.474168i \(0.157251\pi\)
\(908\) 35.3967 + 29.2354i 1.17468 + 0.970212i
\(909\) 26.5390i 0.880243i
\(910\) 0.438871 + 0.546926i 0.0145484 + 0.0181304i
\(911\) 47.8573i 1.58558i −0.609494 0.792791i \(-0.708627\pi\)
0.609494 0.792791i \(-0.291373\pi\)
\(912\) 25.9141 + 1.86166i 0.858101 + 0.0616458i
\(913\) 9.73964 36.3488i 0.322335 1.20297i
\(914\) 3.92031 + 3.56437i 0.129672 + 0.117899i
\(915\) −9.22344 5.63114i −0.304917 0.186160i
\(916\) −19.4528 + 13.8476i −0.642739 + 0.457539i
\(917\) 9.68165 1.26207i 0.319716 0.0416773i
\(918\) −1.45913 0.752382i −0.0481586 0.0248323i
\(919\) 3.56719 6.17855i 0.117671 0.203812i −0.801173 0.598432i \(-0.795791\pi\)
0.918844 + 0.394620i \(0.129124\pi\)
\(920\) −4.28189 5.73141i −0.141170 0.188959i
\(921\) 6.74155 + 11.6767i 0.222142 + 0.384761i
\(922\) −7.93367 + 5.09778i −0.261282 + 0.167886i
\(923\) −0.857128 + 0.857128i −0.0282127 + 0.0282127i
\(924\) −28.8851 54.6178i −0.950251 1.79680i
\(925\) 7.74467 + 8.54424i 0.254643 + 0.280933i
\(926\) 6.28930 28.9004i 0.206679 0.949727i
\(927\) 2.61640 9.76453i 0.0859338 0.320709i
\(928\) 11.6073 39.4729i 0.381027 1.29576i
\(929\) −22.9712 13.2625i −0.753662 0.435127i 0.0733534 0.997306i \(-0.476630\pi\)
−0.827016 + 0.562179i \(0.809963\pi\)
\(930\) 31.7580 + 17.3743i 1.04139 + 0.569727i
\(931\) −12.9890 13.0554i −0.425698 0.427872i
\(932\) 7.89802 46.9223i 0.258708 1.53699i
\(933\) −48.9615 + 13.1192i −1.60293 + 0.429503i
\(934\) −26.7192 + 29.3875i −0.874280 + 0.961587i
\(935\) −25.0209 45.9013i −0.818270 1.50113i
\(936\) 0.674562 0.288675i 0.0220487 0.00943563i
\(937\) 4.34151 4.34151i 0.141831 0.141831i −0.632626 0.774457i \(-0.718023\pi\)
0.774457 + 0.632626i \(0.218023\pi\)
\(938\) 1.56368 + 1.08882i 0.0510560 + 0.0355513i
\(939\) 68.9071 2.24870
\(940\) 12.3527 0.872530i 0.402902 0.0284588i
\(941\) −12.9331 22.4008i −0.421607 0.730245i 0.574490 0.818512i \(-0.305200\pi\)
−0.996097 + 0.0882670i \(0.971867\pi\)
\(942\) 50.8117 2.41643i 1.65553 0.0787314i
\(943\) −1.67398 6.24739i −0.0545124 0.203443i
\(944\) 4.39320 12.6803i 0.142987 0.412710i
\(945\) −0.145750 1.38163i −0.00474123 0.0449444i
\(946\) −4.52941 14.1731i −0.147264 0.460807i
\(947\) −28.6706 + 7.68227i −0.931670 + 0.249640i −0.692567 0.721354i \(-0.743520\pi\)
−0.239103 + 0.970994i \(0.576853\pi\)
\(948\) −10.5283 28.2413i −0.341945 0.917233i
\(949\) −0.696229 + 0.401968i −0.0226006 + 0.0130484i
\(950\) 9.27698 + 16.1250i 0.300985 + 0.523165i
\(951\) 31.9921i 1.03741i
\(952\) 18.8279 + 31.8423i 0.610215 + 1.03201i
\(953\) −33.9836 33.9836i −1.10084 1.10084i −0.994310 0.106528i \(-0.966027\pi\)
−0.106528 0.994310i \(-0.533973\pi\)
\(954\) 8.79063 40.3945i 0.284607 1.30782i
\(955\) 10.3791 35.2535i 0.335859 1.14078i
\(956\) −1.25290 + 2.74232i −0.0405217 + 0.0886930i
\(957\) −21.9805 82.0323i −0.710528 2.65173i
\(958\) 13.2518 + 6.83311i 0.428146 + 0.220768i
\(959\) −48.5669 + 20.0446i −1.56831 + 0.647275i
\(960\) −11.3793 42.6726i −0.367264 1.37725i
\(961\) −4.75009 + 8.22739i −0.153229 + 0.265400i
\(962\) −0.0129862 0.273068i −0.000418691 0.00880407i
\(963\) −20.3065 5.44110i −0.654367 0.175337i
\(964\) 36.8950 3.51715i 1.18831 0.113280i
\(965\) −11.0871 0.271955i −0.356907 0.00875453i
\(966\) 9.82852 + 3.54822i 0.316228 + 0.114162i
\(967\) −26.2766 26.2766i −0.844999 0.844999i 0.144505 0.989504i \(-0.453841\pi\)
−0.989504 + 0.144505i \(0.953841\pi\)
\(968\) −29.8484 11.9577i −0.959365 0.384336i
\(969\) −27.8061 + 16.0539i −0.893260 + 0.515724i
\(970\) −25.9988 + 0.597994i −0.834772 + 0.0192004i
\(971\) −40.7412 23.5219i −1.30745 0.754855i −0.325778 0.945446i \(-0.605626\pi\)
−0.981670 + 0.190591i \(0.938960\pi\)
\(972\) 43.7784 + 7.36883i 1.40419 + 0.236355i
\(973\) 2.42868 1.85869i 0.0778600 0.0595867i
\(974\) −16.3851 51.2711i −0.525013 1.64283i
\(975\) 0.869561 + 0.560614i 0.0278482 + 0.0179540i
\(976\) 7.68913 1.47943i 0.246123 0.0473555i
\(977\) 21.3849 + 5.73007i 0.684163 + 0.183321i 0.584126 0.811663i \(-0.301437\pi\)
0.100037 + 0.994984i \(0.468104\pi\)
\(978\) −5.57087 8.66996i −0.178137 0.277235i
\(979\) 78.9044 2.52180
\(980\) −13.7750 + 28.1114i −0.440026 + 0.897985i
\(981\) −12.1307 −0.387305
\(982\) −2.75039 4.28044i −0.0877686 0.136594i
\(983\) 17.0668 + 4.57305i 0.544348 + 0.145858i 0.520506 0.853858i \(-0.325743\pi\)
0.0238421 + 0.999716i \(0.492410\pi\)
\(984\) 4.74939 39.6424i 0.151405 1.26376i
\(985\) 10.5241 + 6.42521i 0.335325 + 0.204724i
\(986\) 15.4783 + 48.4336i 0.492930 + 1.54244i
\(987\) −14.3635 + 10.9924i −0.457194 + 0.349893i
\(988\) 0.0732017 0.434893i 0.00232886 0.0138358i
\(989\) 2.17929 + 1.25821i 0.0692975 + 0.0400089i
\(990\) −33.4765 31.9712i −1.06395 1.01611i
\(991\) 3.59673 2.07657i 0.114254 0.0659645i −0.441784 0.897121i \(-0.645654\pi\)
0.556038 + 0.831157i \(0.312321\pi\)
\(992\) −25.4927 + 6.17378i −0.809395 + 0.196018i
\(993\) −12.9278 12.9278i −0.410250 0.410250i
\(994\) −50.8985 18.3750i −1.61440 0.582820i
\(995\) −30.6005 + 29.1352i −0.970100 + 0.923649i
\(996\) 3.72829 + 39.1099i 0.118135 + 1.23924i
\(997\) 23.3879 + 6.26677i 0.740702 + 0.198471i 0.609390 0.792870i \(-0.291414\pi\)
0.131312 + 0.991341i \(0.458081\pi\)
\(998\) −0.687398 14.4544i −0.0217592 0.457545i
\(999\) −0.270807 + 0.469052i −0.00856796 + 0.0148401i
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 140.2.w.b.23.15 yes 72
4.3 odd 2 inner 140.2.w.b.23.1 72
5.2 odd 4 inner 140.2.w.b.107.12 yes 72
5.3 odd 4 700.2.be.e.107.7 72
5.4 even 2 700.2.be.e.443.4 72
7.2 even 3 980.2.k.k.883.4 36
7.3 odd 6 980.2.x.m.263.9 72
7.4 even 3 inner 140.2.w.b.123.9 yes 72
7.5 odd 6 980.2.k.j.883.4 36
7.6 odd 2 980.2.x.m.863.15 72
20.3 even 4 700.2.be.e.107.10 72
20.7 even 4 inner 140.2.w.b.107.9 yes 72
20.19 odd 2 700.2.be.e.443.18 72
28.3 even 6 980.2.x.m.263.12 72
28.11 odd 6 inner 140.2.w.b.123.12 yes 72
28.19 even 6 980.2.k.j.883.14 36
28.23 odd 6 980.2.k.k.883.14 36
28.27 even 2 980.2.x.m.863.1 72
35.2 odd 12 980.2.k.k.687.14 36
35.4 even 6 700.2.be.e.543.10 72
35.12 even 12 980.2.k.j.687.14 36
35.17 even 12 980.2.x.m.67.1 72
35.18 odd 12 700.2.be.e.207.18 72
35.27 even 4 980.2.x.m.667.12 72
35.32 odd 12 inner 140.2.w.b.67.1 yes 72
140.27 odd 4 980.2.x.m.667.9 72
140.39 odd 6 700.2.be.e.543.7 72
140.47 odd 12 980.2.k.j.687.4 36
140.67 even 12 inner 140.2.w.b.67.15 yes 72
140.87 odd 12 980.2.x.m.67.15 72
140.107 even 12 980.2.k.k.687.4 36
140.123 even 12 700.2.be.e.207.4 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.w.b.23.1 72 4.3 odd 2 inner
140.2.w.b.23.15 yes 72 1.1 even 1 trivial
140.2.w.b.67.1 yes 72 35.32 odd 12 inner
140.2.w.b.67.15 yes 72 140.67 even 12 inner
140.2.w.b.107.9 yes 72 20.7 even 4 inner
140.2.w.b.107.12 yes 72 5.2 odd 4 inner
140.2.w.b.123.9 yes 72 7.4 even 3 inner
140.2.w.b.123.12 yes 72 28.11 odd 6 inner
700.2.be.e.107.7 72 5.3 odd 4
700.2.be.e.107.10 72 20.3 even 4
700.2.be.e.207.4 72 140.123 even 12
700.2.be.e.207.18 72 35.18 odd 12
700.2.be.e.443.4 72 5.4 even 2
700.2.be.e.443.18 72 20.19 odd 2
700.2.be.e.543.7 72 140.39 odd 6
700.2.be.e.543.10 72 35.4 even 6
980.2.k.j.687.4 36 140.47 odd 12
980.2.k.j.687.14 36 35.12 even 12
980.2.k.j.883.4 36 7.5 odd 6
980.2.k.j.883.14 36 28.19 even 6
980.2.k.k.687.4 36 140.107 even 12
980.2.k.k.687.14 36 35.2 odd 12
980.2.k.k.883.4 36 7.2 even 3
980.2.k.k.883.14 36 28.23 odd 6
980.2.x.m.67.1 72 35.17 even 12
980.2.x.m.67.15 72 140.87 odd 12
980.2.x.m.263.9 72 7.3 odd 6
980.2.x.m.263.12 72 28.3 even 6
980.2.x.m.667.9 72 140.27 odd 4
980.2.x.m.667.12 72 35.27 even 4
980.2.x.m.863.1 72 28.27 even 2
980.2.x.m.863.15 72 7.6 odd 2