Properties

Label 115.2.l.a.17.10
Level $115$
Weight $2$
Character 115.17
Analytic conductor $0.918$
Analytic rank $0$
Dimension $200$
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] = [115,2,Mod(7,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(44))
 
chi = DirichletCharacter(H, H._module([11, 38]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("115.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 115.l (of order \(44\), degree \(20\), 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: \(0.918279623245\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(10\) over \(\Q(\zeta_{44})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label 17.10
Character \(\chi\) \(=\) 115.17
Dual form 115.2.l.a.88.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.04194 - 0.761604i) q^{2} +(-1.49195 + 0.814667i) q^{3} +(2.07797 - 1.80057i) q^{4} +(1.48286 - 1.67366i) q^{5} +(-2.42602 + 2.79977i) q^{6} +(0.435377 + 0.581596i) q^{7} +(0.782870 - 1.43372i) q^{8} +(-0.0596878 + 0.0928760i) q^{9} +O(q^{10})\) \(q+(2.04194 - 0.761604i) q^{2} +(-1.49195 + 0.814667i) q^{3} +(2.07797 - 1.80057i) q^{4} +(1.48286 - 1.67366i) q^{5} +(-2.42602 + 2.79977i) q^{6} +(0.435377 + 0.581596i) q^{7} +(0.782870 - 1.43372i) q^{8} +(-0.0596878 + 0.0928760i) q^{9} +(1.75324 - 4.54686i) q^{10} +(-2.27747 + 1.04009i) q^{11} +(-1.63337 + 4.37922i) q^{12} +(-3.71639 - 2.78205i) q^{13} +(1.33196 + 0.855999i) q^{14} +(-0.848876 + 3.70505i) q^{15} +(-0.275958 + 1.91933i) q^{16} +(-0.0675456 - 0.944411i) q^{17} +(-0.0511441 + 0.235105i) q^{18} +(3.28986 + 3.79670i) q^{19} +(0.0677916 - 6.14781i) q^{20} +(-1.12337 - 0.513025i) q^{21} +(-3.85832 + 3.85832i) q^{22} +(-4.39351 + 1.92278i) q^{23} +2.77682i q^{24} +(-0.602267 - 4.96359i) q^{25} +(-9.70746 - 2.85037i) q^{26} +(0.377193 - 5.27384i) q^{27} +(1.95191 + 0.424612i) q^{28} +(-1.25041 - 1.08349i) q^{29} +(1.08843 + 8.21199i) q^{30} +(8.01545 - 2.35355i) q^{31} +(1.59274 + 7.32173i) q^{32} +(2.55055 - 3.40713i) q^{33} +(-0.857191 - 1.87699i) q^{34} +(1.61900 + 0.133751i) q^{35} +(0.0432005 + 0.300466i) q^{36} +(-1.27054 + 0.276390i) q^{37} +(9.60927 + 5.24706i) q^{38} +(7.81112 + 1.12307i) q^{39} +(-1.23867 - 3.43626i) q^{40} +(10.1659 - 6.53324i) q^{41} +(-2.68457 - 0.192004i) q^{42} +(1.40279 + 2.56902i) q^{43} +(-2.85977 + 6.26202i) q^{44} +(0.0669343 + 0.237619i) q^{45} +(-7.50687 + 7.27231i) q^{46} +(-1.07853 - 1.07853i) q^{47} +(-1.15190 - 3.08836i) q^{48} +(1.82343 - 6.21002i) q^{49} +(-5.01008 - 9.67667i) q^{50} +(0.870155 + 1.35399i) q^{51} +(-12.7319 + 0.910600i) q^{52} +(0.463040 - 0.346627i) q^{53} +(-3.24637 - 11.0561i) q^{54} +(-1.63641 + 5.35401i) q^{55} +(1.17469 - 0.168895i) q^{56} +(-8.00135 - 2.98435i) q^{57} +(-3.37845 - 1.26010i) q^{58} +(-10.0883 + 1.45049i) q^{59} +(4.90728 + 9.22746i) q^{60} +(2.68042 + 9.12869i) q^{61} +(14.5746 - 10.9104i) q^{62} +(-0.0800030 + 0.00572193i) q^{63} +(6.73187 + 10.4750i) q^{64} +(-10.1671 + 2.09458i) q^{65} +(2.61318 - 8.89967i) q^{66} +(-2.66448 - 7.14375i) q^{67} +(-1.84084 - 1.84084i) q^{68} +(4.98847 - 6.44794i) q^{69} +(3.40776 - 0.959922i) q^{70} +(-1.10186 + 2.41274i) q^{71} +(0.0864303 + 0.158285i) q^{72} +(-0.636162 - 0.0454992i) q^{73} +(-2.38387 + 1.53202i) q^{74} +(4.94223 + 6.91479i) q^{75} +(13.6725 + 1.96580i) q^{76} +(-1.59647 - 0.871738i) q^{77} +(16.8051 - 3.65574i) q^{78} +(1.94550 + 13.5312i) q^{79} +(2.80310 + 3.30795i) q^{80} +(3.59608 + 7.87433i) q^{81} +(15.7824 - 21.0829i) q^{82} +(-2.91048 - 13.3793i) q^{83} +(-3.25807 + 0.956656i) q^{84} +(-1.68078 - 1.28738i) q^{85} +(4.82098 + 4.17741i) q^{86} +(2.74823 + 0.597841i) q^{87} +(-0.291772 + 4.07950i) q^{88} +(1.11643 + 0.327814i) q^{89} +(0.317647 + 0.434226i) q^{90} -3.37268i q^{91} +(-5.66748 + 11.9063i) q^{92} +(-10.0413 + 10.0413i) q^{93} +(-3.02369 - 1.38087i) q^{94} +(11.2328 + 0.123863i) q^{95} +(-8.34107 - 9.62610i) q^{96} +(-3.49831 + 16.0815i) q^{97} +(-1.00625 - 14.0692i) q^{98} +(0.0393381 - 0.273603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{7}{22}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.04194 0.761604i 1.44387 0.538535i 0.499178 0.866499i \(-0.333635\pi\)
0.944690 + 0.327964i \(0.106363\pi\)
\(3\) −1.49195 + 0.814667i −0.861378 + 0.470348i −0.848269 0.529566i \(-0.822355\pi\)
−0.0131093 + 0.999914i \(0.504173\pi\)
\(4\) 2.07797 1.80057i 1.03899 0.900287i
\(5\) 1.48286 1.67366i 0.663154 0.748483i
\(6\) −2.42602 + 2.79977i −0.990418 + 1.14300i
\(7\) 0.435377 + 0.581596i 0.164557 + 0.219823i 0.875239 0.483691i \(-0.160704\pi\)
−0.710682 + 0.703514i \(0.751613\pi\)
\(8\) 0.782870 1.43372i 0.276786 0.506896i
\(9\) −0.0596878 + 0.0928760i −0.0198959 + 0.0309587i
\(10\) 1.75324 4.54686i 0.554423 1.43784i
\(11\) −2.27747 + 1.04009i −0.686683 + 0.313598i −0.728028 0.685547i \(-0.759563\pi\)
0.0413451 + 0.999145i \(0.486836\pi\)
\(12\) −1.63337 + 4.37922i −0.471512 + 1.26417i
\(13\) −3.71639 2.78205i −1.03074 0.771603i −0.0567956 0.998386i \(-0.518088\pi\)
−0.973945 + 0.226783i \(0.927179\pi\)
\(14\) 1.33196 + 0.855999i 0.355981 + 0.228775i
\(15\) −0.848876 + 3.70505i −0.219179 + 0.956640i
\(16\) −0.275958 + 1.91933i −0.0689895 + 0.479832i
\(17\) −0.0675456 0.944411i −0.0163822 0.229053i −0.999046 0.0436593i \(-0.986098\pi\)
0.982664 0.185394i \(-0.0593561\pi\)
\(18\) −0.0511441 + 0.235105i −0.0120548 + 0.0554149i
\(19\) 3.28986 + 3.79670i 0.754745 + 0.871022i 0.995019 0.0996828i \(-0.0317828\pi\)
−0.240274 + 0.970705i \(0.577237\pi\)
\(20\) 0.0677916 6.14781i 0.0151587 1.37469i
\(21\) −1.12337 0.513025i −0.245139 0.111951i
\(22\) −3.85832 + 3.85832i −0.822597 + 0.822597i
\(23\) −4.39351 + 1.92278i −0.916110 + 0.400928i
\(24\) 2.77682i 0.566815i
\(25\) −0.602267 4.96359i −0.120453 0.992719i
\(26\) −9.70746 2.85037i −1.90379 0.559003i
\(27\) 0.377193 5.27384i 0.0725908 1.01495i
\(28\) 1.95191 + 0.424612i 0.368876 + 0.0802441i
\(29\) −1.25041 1.08349i −0.232195 0.201198i 0.530990 0.847378i \(-0.321820\pi\)
−0.763185 + 0.646180i \(0.776366\pi\)
\(30\) 1.08843 + 8.21199i 0.198719 + 1.49930i
\(31\) 8.01545 2.35355i 1.43962 0.422710i 0.533523 0.845785i \(-0.320868\pi\)
0.906094 + 0.423076i \(0.139050\pi\)
\(32\) 1.59274 + 7.32173i 0.281560 + 1.29431i
\(33\) 2.55055 3.40713i 0.443994 0.593106i
\(34\) −0.857191 1.87699i −0.147007 0.321900i
\(35\) 1.61900 + 0.133751i 0.273660 + 0.0226080i
\(36\) 0.0432005 + 0.300466i 0.00720008 + 0.0500777i
\(37\) −1.27054 + 0.276390i −0.208876 + 0.0454382i −0.315786 0.948831i \(-0.602268\pi\)
0.106910 + 0.994269i \(0.465904\pi\)
\(38\) 9.60927 + 5.24706i 1.55883 + 0.851185i
\(39\) 7.81112 + 1.12307i 1.25078 + 0.179835i
\(40\) −1.23867 3.43626i −0.195851 0.543320i
\(41\) 10.1659 6.53324i 1.58765 1.02032i 0.614859 0.788637i \(-0.289213\pi\)
0.972791 0.231684i \(-0.0744236\pi\)
\(42\) −2.68457 0.192004i −0.414238 0.0296269i
\(43\) 1.40279 + 2.56902i 0.213923 + 0.391772i 0.962502 0.271275i \(-0.0874451\pi\)
−0.748579 + 0.663046i \(0.769263\pi\)
\(44\) −2.85977 + 6.26202i −0.431126 + 0.944035i
\(45\) 0.0669343 + 0.237619i 0.00997797 + 0.0354221i
\(46\) −7.50687 + 7.27231i −1.10683 + 1.07224i
\(47\) −1.07853 1.07853i −0.157319 0.157319i 0.624058 0.781378i \(-0.285483\pi\)
−0.781378 + 0.624058i \(0.785483\pi\)
\(48\) −1.15190 3.08836i −0.166262 0.445766i
\(49\) 1.82343 6.21002i 0.260490 0.887146i
\(50\) −5.01008 9.67667i −0.708533 1.36849i
\(51\) 0.870155 + 1.35399i 0.121846 + 0.189596i
\(52\) −12.7319 + 0.910600i −1.76559 + 0.126277i
\(53\) 0.463040 0.346627i 0.0636034 0.0476129i −0.567003 0.823716i \(-0.691897\pi\)
0.630606 + 0.776103i \(0.282806\pi\)
\(54\) −3.24637 11.0561i −0.441776 1.50455i
\(55\) −1.63641 + 5.35401i −0.220654 + 0.721934i
\(56\) 1.17469 0.168895i 0.156974 0.0225695i
\(57\) −8.00135 2.98435i −1.05980 0.395287i
\(58\) −3.37845 1.26010i −0.443612 0.165459i
\(59\) −10.0883 + 1.45049i −1.31339 + 0.188837i −0.763179 0.646188i \(-0.776362\pi\)
−0.550212 + 0.835025i \(0.685453\pi\)
\(60\) 4.90728 + 9.22746i 0.633527 + 1.19126i
\(61\) 2.68042 + 9.12869i 0.343193 + 1.16881i 0.932582 + 0.360959i \(0.117551\pi\)
−0.589389 + 0.807850i \(0.700631\pi\)
\(62\) 14.5746 10.9104i 1.85097 1.38562i
\(63\) −0.0800030 + 0.00572193i −0.0100794 + 0.000720896i
\(64\) 6.73187 + 10.4750i 0.841483 + 1.30937i
\(65\) −10.1671 + 2.09458i −1.26107 + 0.259800i
\(66\) 2.61318 8.89967i 0.321660 1.09547i
\(67\) −2.66448 7.14375i −0.325518 0.872747i −0.991887 0.127125i \(-0.959425\pi\)
0.666369 0.745622i \(-0.267848\pi\)
\(68\) −1.84084 1.84084i −0.223235 0.223235i
\(69\) 4.98847 6.44794i 0.600541 0.776241i
\(70\) 3.40776 0.959922i 0.407305 0.114733i
\(71\) −1.10186 + 2.41274i −0.130767 + 0.286340i −0.963678 0.267067i \(-0.913945\pi\)
0.832911 + 0.553407i \(0.186673\pi\)
\(72\) 0.0864303 + 0.158285i 0.0101859 + 0.0186541i
\(73\) −0.636162 0.0454992i −0.0744571 0.00532528i 0.0340609 0.999420i \(-0.489156\pi\)
−0.108518 + 0.994094i \(0.534611\pi\)
\(74\) −2.38387 + 1.53202i −0.277119 + 0.178094i
\(75\) 4.94223 + 6.91479i 0.570679 + 0.798451i
\(76\) 13.6725 + 1.96580i 1.56834 + 0.225493i
\(77\) −1.59647 0.871738i −0.181935 0.0993438i
\(78\) 16.8051 3.65574i 1.90281 0.413931i
\(79\) 1.94550 + 13.5312i 0.218886 + 1.52238i 0.742163 + 0.670220i \(0.233800\pi\)
−0.523277 + 0.852162i \(0.675291\pi\)
\(80\) 2.80310 + 3.30795i 0.313396 + 0.369840i
\(81\) 3.59608 + 7.87433i 0.399565 + 0.874925i
\(82\) 15.7824 21.0829i 1.74288 2.32821i
\(83\) −2.91048 13.3793i −0.319467 1.46857i −0.804438 0.594037i \(-0.797533\pi\)
0.484971 0.874530i \(-0.338830\pi\)
\(84\) −3.25807 + 0.956656i −0.355485 + 0.104380i
\(85\) −1.68078 1.28738i −0.182306 0.139636i
\(86\) 4.82098 + 4.17741i 0.519860 + 0.450461i
\(87\) 2.74823 + 0.597841i 0.294641 + 0.0640953i
\(88\) −0.291772 + 4.07950i −0.0311030 + 0.434876i
\(89\) 1.11643 + 0.327814i 0.118342 + 0.0347483i 0.340367 0.940293i \(-0.389449\pi\)
−0.222025 + 0.975041i \(0.571267\pi\)
\(90\) 0.317647 + 0.434226i 0.0334829 + 0.0457714i
\(91\) 3.37268i 0.353553i
\(92\) −5.66748 + 11.9063i −0.590875 + 1.24132i
\(93\) −10.0413 + 10.0413i −1.04123 + 1.04123i
\(94\) −3.02369 1.38087i −0.311870 0.142426i
\(95\) 11.2328 + 0.123863i 1.15246 + 0.0127081i
\(96\) −8.34107 9.62610i −0.851306 0.982460i
\(97\) −3.49831 + 16.0815i −0.355200 + 1.63283i 0.359321 + 0.933214i \(0.383008\pi\)
−0.714521 + 0.699614i \(0.753355\pi\)
\(98\) −1.00625 14.0692i −0.101647 1.42121i
\(99\) 0.0393381 0.273603i 0.00395363 0.0274981i
\(100\) −10.1888 9.22979i −1.01888 0.922979i
\(101\) −15.1886 9.76110i −1.51132 0.971266i −0.993258 0.115922i \(-0.963018\pi\)
−0.518061 0.855344i \(-0.673346\pi\)
\(102\) 2.80800 + 2.10205i 0.278034 + 0.208133i
\(103\) −5.69713 + 15.2746i −0.561355 + 1.50505i 0.277516 + 0.960721i \(0.410489\pi\)
−0.838871 + 0.544330i \(0.816784\pi\)
\(104\) −6.89813 + 3.15027i −0.676418 + 0.308910i
\(105\) −2.52442 + 1.11939i −0.246359 + 0.109242i
\(106\) 0.681506 1.06044i 0.0661937 0.102999i
\(107\) 2.29704 4.20671i 0.222063 0.406678i −0.742768 0.669549i \(-0.766487\pi\)
0.964831 + 0.262871i \(0.0846693\pi\)
\(108\) −8.71215 11.6381i −0.838327 1.11987i
\(109\) −0.858685 + 0.990975i −0.0822471 + 0.0949182i −0.795381 0.606109i \(-0.792729\pi\)
0.713134 + 0.701027i \(0.247275\pi\)
\(110\) 0.736172 + 12.1788i 0.0701913 + 1.16121i
\(111\) 1.67042 1.44743i 0.158549 0.137384i
\(112\) −1.23642 + 0.675137i −0.116831 + 0.0637944i
\(113\) 16.3266 6.08950i 1.53587 0.572852i 0.567724 0.823219i \(-0.307824\pi\)
0.968151 + 0.250368i \(0.0805515\pi\)
\(114\) −18.6112 −1.74309
\(115\) −3.29686 + 10.2044i −0.307434 + 0.951569i
\(116\) −4.54922 −0.422384
\(117\) 0.480209 0.179109i 0.0443953 0.0165586i
\(118\) −19.4951 + 10.6451i −1.79467 + 0.979963i
\(119\) 0.519858 0.450459i 0.0476553 0.0412936i
\(120\) 4.64744 + 4.11762i 0.424251 + 0.375886i
\(121\) −3.09838 + 3.57572i −0.281671 + 0.325065i
\(122\) 12.4257 + 16.5988i 1.12497 + 1.50278i
\(123\) −9.84464 + 18.0291i −0.887661 + 1.62563i
\(124\) 12.4182 19.3230i 1.11518 1.73526i
\(125\) −9.20044 6.35231i −0.822912 0.568168i
\(126\) −0.159003 + 0.0726144i −0.0141652 + 0.00646901i
\(127\) 1.67083 4.47967i 0.148262 0.397506i −0.841495 0.540264i \(-0.818324\pi\)
0.989758 + 0.142758i \(0.0455970\pi\)
\(128\) 9.72698 + 7.28153i 0.859752 + 0.643602i
\(129\) −4.18579 2.69004i −0.368538 0.236845i
\(130\) −19.1653 + 12.0203i −1.68091 + 1.05425i
\(131\) 0.626779 4.35935i 0.0547620 0.380878i −0.943948 0.330095i \(-0.892919\pi\)
0.998710 0.0507829i \(-0.0161717\pi\)
\(132\) −0.834825 11.6724i −0.0726622 1.01595i
\(133\) −0.775815 + 3.56637i −0.0672717 + 0.309243i
\(134\) −10.8814 12.5578i −0.940010 1.08483i
\(135\) −8.26729 8.45165i −0.711535 0.727402i
\(136\) −1.40690 0.642509i −0.120641 0.0550947i
\(137\) −1.02181 + 1.02181i −0.0872994 + 0.0872994i −0.749408 0.662109i \(-0.769662\pi\)
0.662109 + 0.749408i \(0.269662\pi\)
\(138\) 5.27537 16.9655i 0.449070 1.44420i
\(139\) 11.5566i 0.980219i −0.871661 0.490109i \(-0.836957\pi\)
0.871661 0.490109i \(-0.163043\pi\)
\(140\) 3.60506 2.63719i 0.304683 0.222883i
\(141\) 2.48775 + 0.730468i 0.209506 + 0.0615165i
\(142\) −0.412382 + 5.76585i −0.0346063 + 0.483860i
\(143\) 11.3575 + 2.47068i 0.949765 + 0.206609i
\(144\) −0.161788 0.140190i −0.0134824 0.0116825i
\(145\) −3.66757 + 0.486104i −0.304575 + 0.0403687i
\(146\) −1.33366 + 0.391596i −0.110374 + 0.0324088i
\(147\) 2.33864 + 10.7505i 0.192887 + 0.886689i
\(148\) −2.14249 + 2.86204i −0.176112 + 0.235258i
\(149\) 4.36658 + 9.56148i 0.357724 + 0.783307i 0.999860 + 0.0167161i \(0.00532114\pi\)
−0.642136 + 0.766591i \(0.721952\pi\)
\(150\) 15.3581 + 10.3556i 1.25398 + 0.845528i
\(151\) 0.210384 + 1.46326i 0.0171208 + 0.119078i 0.996590 0.0825181i \(-0.0262962\pi\)
−0.979469 + 0.201596i \(0.935387\pi\)
\(152\) 8.01893 1.74441i 0.650421 0.141490i
\(153\) 0.0917447 + 0.0500964i 0.00741712 + 0.00405006i
\(154\) −3.92381 0.564159i −0.316190 0.0454612i
\(155\) 7.94673 16.9051i 0.638297 1.35785i
\(156\) 18.2535 11.7308i 1.46145 0.939214i
\(157\) 20.5233 + 1.46785i 1.63793 + 0.117147i 0.859691 0.510815i \(-0.170656\pi\)
0.778244 + 0.627962i \(0.216111\pi\)
\(158\) 14.2780 + 26.1482i 1.13590 + 2.08024i
\(159\) −0.408447 + 0.894374i −0.0323919 + 0.0709285i
\(160\) 14.6159 + 8.19137i 1.15549 + 0.647585i
\(161\) −3.03112 1.71811i −0.238885 0.135406i
\(162\) 13.3401 + 13.3401i 1.04810 + 1.04810i
\(163\) 3.28668 + 8.81193i 0.257433 + 0.690204i 0.999796 + 0.0202061i \(0.00643224\pi\)
−0.742363 + 0.669998i \(0.766295\pi\)
\(164\) 9.36093 31.8804i 0.730966 2.48944i
\(165\) −1.92028 9.32104i −0.149494 0.725642i
\(166\) −16.1327 25.1030i −1.25214 1.94837i
\(167\) −7.42048 + 0.530724i −0.574214 + 0.0410686i −0.355427 0.934704i \(-0.615665\pi\)
−0.218787 + 0.975773i \(0.570210\pi\)
\(168\) −1.61499 + 1.20896i −0.124599 + 0.0932735i
\(169\) 2.40920 + 8.20498i 0.185323 + 0.631153i
\(170\) −4.41253 1.34866i −0.338425 0.103437i
\(171\) −0.548986 + 0.0789323i −0.0419820 + 0.00603611i
\(172\) 7.54067 + 2.81252i 0.574970 + 0.214453i
\(173\) −1.88314 0.702375i −0.143173 0.0534006i 0.276856 0.960911i \(-0.410707\pi\)
−0.420029 + 0.907511i \(0.637980\pi\)
\(174\) 6.06704 0.872308i 0.459941 0.0661295i
\(175\) 2.62459 2.51131i 0.198401 0.189837i
\(176\) −1.36778 4.65824i −0.103100 0.351128i
\(177\) 13.8697 10.3827i 1.04251 0.780411i
\(178\) 2.52935 0.180903i 0.189583 0.0135592i
\(179\) −2.87839 4.47887i −0.215141 0.334766i 0.716863 0.697214i \(-0.245577\pi\)
−0.932004 + 0.362448i \(0.881941\pi\)
\(180\) 0.566938 + 0.373245i 0.0422571 + 0.0278201i
\(181\) 1.99350 6.78925i 0.148176 0.504641i −0.851634 0.524137i \(-0.824388\pi\)
0.999810 + 0.0194959i \(0.00620613\pi\)
\(182\) −2.56865 6.88681i −0.190401 0.510484i
\(183\) −11.4359 11.4359i −0.845366 0.845366i
\(184\) −0.682815 + 7.80434i −0.0503378 + 0.575344i
\(185\) −1.42145 + 2.53630i −0.104507 + 0.186473i
\(186\) −12.8562 + 28.1512i −0.942664 + 2.06415i
\(187\) 1.13610 + 2.08061i 0.0830799 + 0.152150i
\(188\) −4.18311 0.299182i −0.305085 0.0218201i
\(189\) 3.23147 2.07674i 0.235055 0.151061i
\(190\) 23.0310 8.30200i 1.67084 0.602290i
\(191\) −0.890408 0.128021i −0.0644276 0.00926330i 0.110026 0.993929i \(-0.464907\pi\)
−0.174453 + 0.984665i \(0.555816\pi\)
\(192\) −18.5772 10.1439i −1.34070 0.732076i
\(193\) −0.352722 + 0.0767299i −0.0253895 + 0.00552314i −0.225242 0.974303i \(-0.572317\pi\)
0.199853 + 0.979826i \(0.435954\pi\)
\(194\) 5.10438 + 35.5017i 0.366473 + 2.54888i
\(195\) 13.4624 11.4078i 0.964063 0.816929i
\(196\) −7.39257 16.1875i −0.528041 1.15625i
\(197\) −8.02392 + 10.7187i −0.571681 + 0.763676i −0.989450 0.144877i \(-0.953721\pi\)
0.417769 + 0.908553i \(0.362812\pi\)
\(198\) −0.128051 0.588640i −0.00910017 0.0418328i
\(199\) −13.0556 + 3.83348i −0.925490 + 0.271748i −0.709548 0.704658i \(-0.751101\pi\)
−0.215943 + 0.976406i \(0.569282\pi\)
\(200\) −7.58790 3.02237i −0.536545 0.213714i
\(201\) 9.79504 + 8.48745i 0.690889 + 0.598659i
\(202\) −38.4482 8.36390i −2.70521 0.588482i
\(203\) 0.0857513 1.19896i 0.00601856 0.0841505i
\(204\) 4.24611 + 1.24677i 0.297287 + 0.0872914i
\(205\) 4.14020 26.7022i 0.289164 1.86496i
\(206\) 35.5287i 2.47540i
\(207\) 0.0836584 0.522818i 0.00581466 0.0363384i
\(208\) 6.36525 6.36525i 0.441350 0.441350i
\(209\) −11.4414 5.22513i −0.791421 0.361430i
\(210\) −4.30219 + 4.20834i −0.296879 + 0.290403i
\(211\) 8.26332 + 9.53638i 0.568870 + 0.656511i 0.965174 0.261608i \(-0.0842528\pi\)
−0.396304 + 0.918119i \(0.629707\pi\)
\(212\) 0.338056 1.55402i 0.0232178 0.106730i
\(213\) −0.321656 4.49734i −0.0220395 0.308153i
\(214\) 1.48656 10.3393i 0.101619 0.706778i
\(215\) 6.37980 + 1.46170i 0.435099 + 0.0996868i
\(216\) −7.26592 4.66952i −0.494383 0.317721i
\(217\) 4.85856 + 3.63707i 0.329821 + 0.246901i
\(218\) −0.998651 + 2.67749i −0.0676372 + 0.181342i
\(219\) 0.986188 0.450377i 0.0666404 0.0304337i
\(220\) 6.23986 + 14.0720i 0.420691 + 0.948732i
\(221\) −2.37638 + 3.69771i −0.159852 + 0.248735i
\(222\) 2.30853 4.22776i 0.154938 0.283749i
\(223\) −1.16302 1.55361i −0.0778814 0.104037i 0.759909 0.650030i \(-0.225244\pi\)
−0.837790 + 0.545992i \(0.816153\pi\)
\(224\) −3.56485 + 4.11405i −0.238186 + 0.274882i
\(225\) 0.496947 + 0.240330i 0.0331298 + 0.0160220i
\(226\) 28.7001 24.8688i 1.90910 1.65424i
\(227\) −7.02237 + 3.83451i −0.466091 + 0.254505i −0.695091 0.718921i \(-0.744636\pi\)
0.229000 + 0.973426i \(0.426454\pi\)
\(228\) −22.0001 + 8.20562i −1.45699 + 0.543431i
\(229\) −23.6255 −1.56122 −0.780608 0.625022i \(-0.785090\pi\)
−0.780608 + 0.625022i \(0.785090\pi\)
\(230\) 1.03975 + 23.3478i 0.0685590 + 1.53951i
\(231\) 3.09203 0.203441
\(232\) −2.53232 + 0.944508i −0.166255 + 0.0620100i
\(233\) 14.6259 7.98634i 0.958174 0.523202i 0.0775344 0.996990i \(-0.475295\pi\)
0.880639 + 0.473787i \(0.157113\pi\)
\(234\) 0.844147 0.731458i 0.0551836 0.0478169i
\(235\) −3.40438 + 0.205784i −0.222078 + 0.0134239i
\(236\) −18.3516 + 21.1789i −1.19459 + 1.37863i
\(237\) −13.9260 18.6030i −0.904593 1.20839i
\(238\) 0.718446 1.31574i 0.0465700 0.0852865i
\(239\) −8.84299 + 13.7600i −0.572005 + 0.890058i −0.999905 0.0137684i \(-0.995617\pi\)
0.427900 + 0.903826i \(0.359254\pi\)
\(240\) −6.87696 2.65171i −0.443906 0.171167i
\(241\) 23.1736 10.5830i 1.49274 0.681713i 0.508914 0.860817i \(-0.330047\pi\)
0.983830 + 0.179104i \(0.0573198\pi\)
\(242\) −3.60342 + 9.66113i −0.231636 + 0.621041i
\(243\) 0.918013 + 0.687216i 0.0588906 + 0.0440849i
\(244\) 22.0067 + 14.1429i 1.40884 + 0.905404i
\(245\) −7.68958 12.2604i −0.491269 0.783287i
\(246\) −6.37111 + 44.3121i −0.406207 + 2.82523i
\(247\) −1.66377 23.2626i −0.105863 1.48016i
\(248\) 2.90073 13.3344i 0.184196 0.846737i
\(249\) 15.2420 + 17.5901i 0.965919 + 1.11473i
\(250\) −23.6247 5.96394i −1.49416 0.377193i
\(251\) −7.47548 3.41394i −0.471848 0.215486i 0.165276 0.986247i \(-0.447149\pi\)
−0.637124 + 0.770762i \(0.719876\pi\)
\(252\) −0.155941 + 0.155941i −0.00982339 + 0.00982339i
\(253\) 8.00622 8.94870i 0.503347 0.562600i
\(254\) 10.4197i 0.653791i
\(255\) 3.55643 + 0.551428i 0.222712 + 0.0345318i
\(256\) 1.51301 + 0.444261i 0.0945634 + 0.0277663i
\(257\) −1.37279 + 19.1941i −0.0856323 + 1.19730i 0.755013 + 0.655710i \(0.227631\pi\)
−0.840645 + 0.541586i \(0.817824\pi\)
\(258\) −10.5959 2.30499i −0.659670 0.143502i
\(259\) −0.713913 0.618609i −0.0443604 0.0384385i
\(260\) −17.3555 + 22.6591i −1.07634 + 1.40526i
\(261\) 0.175264 0.0514622i 0.0108486 0.00318543i
\(262\) −2.04025 9.37887i −0.126047 0.579429i
\(263\) 4.05460 5.41631i 0.250017 0.333984i −0.657922 0.753086i \(-0.728564\pi\)
0.907939 + 0.419102i \(0.137655\pi\)
\(264\) −2.88813 6.32411i −0.177752 0.389222i
\(265\) 0.106486 1.28897i 0.00654140 0.0791808i
\(266\) 1.13199 + 7.87316i 0.0694068 + 0.482735i
\(267\) −1.93272 + 0.420438i −0.118281 + 0.0257304i
\(268\) −18.3996 10.0469i −1.12393 0.613713i
\(269\) 7.07727 + 1.01756i 0.431509 + 0.0620416i 0.354647 0.935000i \(-0.384601\pi\)
0.0768615 + 0.997042i \(0.475510\pi\)
\(270\) −23.3181 10.9614i −1.41909 0.667087i
\(271\) 1.49386 0.960049i 0.0907458 0.0583188i −0.494481 0.869188i \(-0.664642\pi\)
0.585227 + 0.810870i \(0.301005\pi\)
\(272\) 1.83128 + 0.130975i 0.111037 + 0.00794155i
\(273\) 2.74761 + 5.03187i 0.166293 + 0.304543i
\(274\) −1.30826 + 2.86470i −0.0790351 + 0.173063i
\(275\) 6.53421 + 10.6780i 0.394028 + 0.643909i
\(276\) −1.24409 22.3808i −0.0748853 1.34716i
\(277\) 6.54540 + 6.54540i 0.393275 + 0.393275i 0.875853 0.482578i \(-0.160300\pi\)
−0.482578 + 0.875853i \(0.660300\pi\)
\(278\) −8.80155 23.5979i −0.527882 1.41531i
\(279\) −0.259836 + 0.884921i −0.0155560 + 0.0529788i
\(280\) 1.45922 2.21648i 0.0872053 0.132460i
\(281\) −5.53890 8.61869i −0.330423 0.514148i 0.635801 0.771853i \(-0.280670\pi\)
−0.966224 + 0.257705i \(0.917034\pi\)
\(282\) 5.63615 0.403106i 0.335628 0.0240046i
\(283\) 13.1785 9.86530i 0.783380 0.586431i −0.130955 0.991388i \(-0.541804\pi\)
0.914336 + 0.404957i \(0.132714\pi\)
\(284\) 2.05468 + 6.99760i 0.121923 + 0.415231i
\(285\) −16.8596 + 8.96616i −0.998679 + 0.531110i
\(286\) 25.0731 3.60496i 1.48260 0.213166i
\(287\) 8.22572 + 3.06804i 0.485549 + 0.181100i
\(288\) −0.775080 0.289090i −0.0456720 0.0170348i
\(289\) 15.9396 2.29177i 0.937624 0.134810i
\(290\) −7.11873 + 3.78583i −0.418026 + 0.222311i
\(291\) −7.88174 26.8428i −0.462036 1.57355i
\(292\) −1.40385 + 1.05091i −0.0821542 + 0.0614999i
\(293\) −26.9530 + 1.92771i −1.57461 + 0.112618i −0.831106 0.556114i \(-0.812292\pi\)
−0.743503 + 0.668733i \(0.766837\pi\)
\(294\) 12.9630 + 20.1708i 0.756017 + 1.17639i
\(295\) −12.5320 + 19.0353i −0.729639 + 1.10828i
\(296\) −0.598404 + 2.03798i −0.0347816 + 0.118455i
\(297\) 4.62620 + 12.4033i 0.268440 + 0.719714i
\(298\) 16.1983 + 16.1983i 0.938345 + 0.938345i
\(299\) 21.6773 + 5.07717i 1.25363 + 0.293620i
\(300\) 22.7204 + 5.46990i 1.31176 + 0.315805i
\(301\) −0.883388 + 1.93435i −0.0509176 + 0.111494i
\(302\) 1.54401 + 2.82765i 0.0888479 + 0.162713i
\(303\) 30.6126 + 2.18946i 1.75865 + 0.125781i
\(304\) −8.19498 + 5.26659i −0.470014 + 0.302060i
\(305\) 19.2530 + 9.05043i 1.10242 + 0.518226i
\(306\) 0.225491 + 0.0324207i 0.0128904 + 0.00185337i
\(307\) −12.9523 7.07248i −0.739225 0.403647i 0.0650675 0.997881i \(-0.479274\pi\)
−0.804293 + 0.594233i \(0.797456\pi\)
\(308\) −4.88705 + 1.06311i −0.278465 + 0.0605764i
\(309\) −3.94387 27.4302i −0.224359 1.56045i
\(310\) 3.35175 40.5715i 0.190367 2.30430i
\(311\) −3.97284 8.69931i −0.225279 0.493293i 0.762915 0.646499i \(-0.223767\pi\)
−0.988194 + 0.153206i \(0.951040\pi\)
\(312\) 7.72525 10.3197i 0.437356 0.584239i
\(313\) 0.284908 + 1.30970i 0.0161039 + 0.0740286i 0.984498 0.175398i \(-0.0561214\pi\)
−0.968394 + 0.249427i \(0.919758\pi\)
\(314\) 43.0251 12.6333i 2.42805 0.712940i
\(315\) −0.109057 + 0.142383i −0.00614464 + 0.00802235i
\(316\) 28.4067 + 24.6145i 1.59800 + 1.38467i
\(317\) −5.22065 1.13568i −0.293221 0.0637863i 0.0635486 0.997979i \(-0.479758\pi\)
−0.356770 + 0.934192i \(0.616122\pi\)
\(318\) −0.152865 + 2.13733i −0.00857224 + 0.119856i
\(319\) 3.97469 + 1.16707i 0.222540 + 0.0653436i
\(320\) 27.5140 + 4.26607i 1.53808 + 0.238480i
\(321\) 8.14752i 0.454750i
\(322\) −7.49787 1.19977i −0.417840 0.0668604i
\(323\) 3.36343 3.36343i 0.187146 0.187146i
\(324\) 21.6509 + 9.88762i 1.20283 + 0.549312i
\(325\) −11.5707 + 20.1222i −0.641829 + 1.11618i
\(326\) 13.4224 + 15.4903i 0.743398 + 0.857927i
\(327\) 0.473801 2.17803i 0.0262013 0.120445i
\(328\) −1.40824 19.6898i −0.0777570 1.08718i
\(329\) 0.157701 1.09683i 0.00869432 0.0604703i
\(330\) −11.0200 17.5705i −0.606633 0.967224i
\(331\) −28.9268 18.5901i −1.58996 1.02180i −0.971817 0.235738i \(-0.924249\pi\)
−0.618142 0.786066i \(-0.712115\pi\)
\(332\) −30.1383 22.5612i −1.65405 1.23821i
\(333\) 0.0501659 0.134500i 0.00274908 0.00737056i
\(334\) −14.7480 + 6.73517i −0.806973 + 0.368532i
\(335\) −15.9072 6.13373i −0.869105 0.335121i
\(336\) 1.29467 2.01454i 0.0706299 0.109902i
\(337\) −7.17200 + 13.1345i −0.390684 + 0.715484i −0.996804 0.0798893i \(-0.974543\pi\)
0.606120 + 0.795373i \(0.292725\pi\)
\(338\) 11.1684 + 14.9192i 0.607480 + 0.811498i
\(339\) −19.3975 + 22.3859i −1.05353 + 1.21584i
\(340\) −5.81064 + 0.351234i −0.315126 + 0.0190484i
\(341\) −15.8071 + 13.6969i −0.856000 + 0.741728i
\(342\) −1.06088 + 0.579285i −0.0573659 + 0.0313241i
\(343\) 9.17049 3.42042i 0.495160 0.184685i
\(344\) 4.78145 0.257799
\(345\) −3.39446 17.9104i −0.182752 0.964262i
\(346\) −4.38019 −0.235480
\(347\) −20.8785 + 7.78729i −1.12082 + 0.418043i −0.840472 0.541856i \(-0.817722\pi\)
−0.280346 + 0.959899i \(0.590449\pi\)
\(348\) 6.78721 3.70609i 0.363832 0.198668i
\(349\) 16.4091 14.2186i 0.878360 0.761103i −0.0937582 0.995595i \(-0.529888\pi\)
0.972118 + 0.234492i \(0.0753426\pi\)
\(350\) 3.44663 7.12685i 0.184230 0.380946i
\(351\) −16.0739 + 18.5503i −0.857962 + 0.990141i
\(352\) −11.2427 15.0184i −0.599235 0.800485i
\(353\) −9.88539 + 18.1037i −0.526146 + 0.963565i 0.470552 + 0.882372i \(0.344055\pi\)
−0.996698 + 0.0811930i \(0.974127\pi\)
\(354\) 20.4135 31.7640i 1.08496 1.68824i
\(355\) 2.40420 + 5.42189i 0.127602 + 0.287764i
\(356\) 2.91017 1.32903i 0.154239 0.0704385i
\(357\) −0.408628 + 1.09557i −0.0216269 + 0.0579839i
\(358\) −9.28862 6.95338i −0.490919 0.367497i
\(359\) −19.6185 12.6080i −1.03543 0.665427i −0.0915741 0.995798i \(-0.529190\pi\)
−0.943851 + 0.330371i \(0.892826\pi\)
\(360\) 0.393079 + 0.0900597i 0.0207171 + 0.00474656i
\(361\) −0.887772 + 6.17459i −0.0467248 + 0.324978i
\(362\) −1.10011 15.3815i −0.0578203 0.808434i
\(363\) 1.70961 7.85894i 0.0897312 0.412487i
\(364\) −6.07276 7.00834i −0.318299 0.367337i
\(365\) −1.01949 + 0.997249i −0.0533624 + 0.0521984i
\(366\) −32.0610 14.6418i −1.67586 0.765338i
\(367\) 18.8545 18.8545i 0.984199 0.984199i −0.0156784 0.999877i \(-0.504991\pi\)
0.999877 + 0.0156784i \(0.00499078\pi\)
\(368\) −2.47803 8.96320i −0.129176 0.467239i
\(369\) 1.33412i 0.0694518i
\(370\) −0.970861 + 6.26155i −0.0504726 + 0.325523i
\(371\) 0.403194 + 0.118389i 0.0209328 + 0.00614642i
\(372\) −2.78545 + 38.9456i −0.144419 + 2.01924i
\(373\) 9.84942 + 2.14261i 0.509983 + 0.110940i 0.460192 0.887820i \(-0.347781\pi\)
0.0497916 + 0.998760i \(0.484144\pi\)
\(374\) 3.90445 + 3.38323i 0.201894 + 0.174942i
\(375\) 18.9016 + 1.98205i 0.976075 + 0.102352i
\(376\) −2.39065 + 0.701958i −0.123288 + 0.0362007i
\(377\) 1.63269 + 7.50537i 0.0840880 + 0.386546i
\(378\) 5.01681 6.70167i 0.258037 0.344697i
\(379\) 5.78157 + 12.6599i 0.296979 + 0.650294i 0.998025 0.0628229i \(-0.0200103\pi\)
−0.701046 + 0.713116i \(0.747283\pi\)
\(380\) 23.5644 19.9680i 1.20883 1.02434i
\(381\) 1.15664 + 8.04461i 0.0592565 + 0.412138i
\(382\) −1.91566 + 0.416726i −0.0980137 + 0.0213216i
\(383\) 13.9973 + 7.64310i 0.715228 + 0.390544i 0.795277 0.606247i \(-0.207326\pi\)
−0.0800484 + 0.996791i \(0.525507\pi\)
\(384\) −20.4442 2.93943i −1.04329 0.150002i
\(385\) −3.82633 + 1.37928i −0.195008 + 0.0702947i
\(386\) −0.661798 + 0.425312i −0.0336846 + 0.0216478i
\(387\) −0.322329 0.0230535i −0.0163849 0.00117187i
\(388\) 21.6865 + 39.7159i 1.10097 + 2.01627i
\(389\) −3.67446 + 8.04595i −0.186303 + 0.407946i −0.979619 0.200863i \(-0.935625\pi\)
0.793317 + 0.608809i \(0.208353\pi\)
\(390\) 18.8012 33.5470i 0.952035 1.69872i
\(391\) 2.11266 + 4.01940i 0.106842 + 0.203270i
\(392\) −7.47592 7.47592i −0.377591 0.377591i
\(393\) 2.61629 + 7.01454i 0.131974 + 0.353837i
\(394\) −8.22095 + 27.9980i −0.414165 + 1.41052i
\(395\) 25.5316 + 16.8088i 1.28463 + 0.845742i
\(396\) −0.410898 0.639370i −0.0206484 0.0321296i
\(397\) 25.3278 1.81148i 1.27116 0.0909155i 0.580602 0.814188i \(-0.302817\pi\)
0.690563 + 0.723272i \(0.257363\pi\)
\(398\) −23.7392 + 17.7710i −1.18994 + 0.890778i
\(399\) −1.74792 5.95287i −0.0875055 0.298016i
\(400\) 9.69298 + 0.213794i 0.484649 + 0.0106897i
\(401\) 20.7700 2.98628i 1.03721 0.149128i 0.397385 0.917652i \(-0.369918\pi\)
0.639820 + 0.768524i \(0.279009\pi\)
\(402\) 26.4649 + 9.87091i 1.31995 + 0.492316i
\(403\) −36.3362 13.5527i −1.81004 0.675109i
\(404\) −49.1370 + 7.06484i −2.44466 + 0.351489i
\(405\) 18.5114 + 5.65789i 0.919840 + 0.281143i
\(406\) −0.738033 2.51351i −0.0366280 0.124743i
\(407\) 2.60615 1.95094i 0.129182 0.0967046i
\(408\) 2.62245 0.187562i 0.129831 0.00928569i
\(409\) 1.45533 + 2.26455i 0.0719617 + 0.111975i 0.875369 0.483455i \(-0.160618\pi\)
−0.803408 + 0.595429i \(0.796982\pi\)
\(410\) −11.8824 57.6773i −0.586831 2.84848i
\(411\) 0.692058 2.35693i 0.0341367 0.116259i
\(412\) 15.6646 + 41.9983i 0.771737 + 2.06911i
\(413\) −5.23584 5.23584i −0.257639 0.257639i
\(414\) −0.227355 1.13128i −0.0111739 0.0555992i
\(415\) −26.7082 14.9684i −1.31105 0.734770i
\(416\) 14.4502 31.6415i 0.708479 1.55135i
\(417\) 9.41478 + 17.2419i 0.461044 + 0.844339i
\(418\) −27.3422 1.95555i −1.33735 0.0956492i
\(419\) 14.0754 9.04568i 0.687626 0.441911i −0.149615 0.988744i \(-0.547803\pi\)
0.837241 + 0.546834i \(0.184167\pi\)
\(420\) −3.23014 + 6.87148i −0.157615 + 0.335294i
\(421\) −17.9570 2.58182i −0.875168 0.125830i −0.309931 0.950759i \(-0.600306\pi\)
−0.565237 + 0.824929i \(0.691215\pi\)
\(422\) 24.1361 + 13.1793i 1.17493 + 0.641559i
\(423\) 0.164544 0.0357944i 0.00800040 0.00174038i
\(424\) −0.134466 0.935233i −0.00653026 0.0454189i
\(425\) −4.64699 + 0.904057i −0.225412 + 0.0438532i
\(426\) −4.08200 8.93832i −0.197773 0.433063i
\(427\) −4.14221 + 5.53335i −0.200456 + 0.267778i
\(428\) −2.80131 12.8774i −0.135406 0.622453i
\(429\) −18.9577 + 5.56647i −0.915285 + 0.268752i
\(430\) 14.1404 1.87418i 0.681910 0.0903812i
\(431\) 10.1506 + 8.79555i 0.488937 + 0.423667i 0.864121 0.503284i \(-0.167875\pi\)
−0.375184 + 0.926950i \(0.622420\pi\)
\(432\) 10.0182 + 2.17932i 0.481999 + 0.104852i
\(433\) −2.23600 + 31.2634i −0.107455 + 1.50242i 0.602467 + 0.798144i \(0.294185\pi\)
−0.709922 + 0.704280i \(0.751270\pi\)
\(434\) 12.6909 + 3.72638i 0.609182 + 0.178872i
\(435\) 5.07582 3.71309i 0.243367 0.178029i
\(436\) 3.60535i 0.172665i
\(437\) −21.7542 10.3551i −1.04065 0.495354i
\(438\) 1.67073 1.67073i 0.0798304 0.0798304i
\(439\) −16.6287 7.59407i −0.793644 0.362445i −0.0230202 0.999735i \(-0.507328\pi\)
−0.770624 + 0.637290i \(0.780055\pi\)
\(440\) 6.39504 + 6.53765i 0.304872 + 0.311670i
\(441\) 0.467926 + 0.540015i 0.0222822 + 0.0257150i
\(442\) −2.03622 + 9.36036i −0.0968532 + 0.445227i
\(443\) −1.65917 23.1983i −0.0788297 1.10218i −0.870804 0.491630i \(-0.836401\pi\)
0.791975 0.610554i \(-0.209053\pi\)
\(444\) 0.864889 6.01544i 0.0410458 0.285480i
\(445\) 2.20416 1.38243i 0.104487 0.0655333i
\(446\) −3.55804 2.28662i −0.168478 0.108274i
\(447\) −14.3041 10.7079i −0.676563 0.506468i
\(448\) −3.16131 + 8.47580i −0.149358 + 0.400444i
\(449\) 36.9540 16.8763i 1.74397 0.796443i 0.753708 0.657209i \(-0.228263\pi\)
0.990259 0.139234i \(-0.0444641\pi\)
\(450\) 1.19777 + 0.112262i 0.0564635 + 0.00529209i
\(451\) −16.3575 + 25.4527i −0.770242 + 1.19852i
\(452\) 22.9616 42.0510i 1.08002 1.97791i
\(453\) −1.50595 2.01171i −0.0707556 0.0945185i
\(454\) −11.4189 + 13.1781i −0.535915 + 0.618478i
\(455\) −5.64472 5.00121i −0.264628 0.234460i
\(456\) −10.5427 + 9.13533i −0.493709 + 0.427801i
\(457\) −17.0738 + 9.32302i −0.798681 + 0.436113i −0.826108 0.563511i \(-0.809450\pi\)
0.0274279 + 0.999624i \(0.491268\pi\)
\(458\) −48.2418 + 17.9932i −2.25419 + 0.840769i
\(459\) −5.00615 −0.233667
\(460\) 11.5231 + 27.1408i 0.537265 + 1.26545i
\(461\) 5.05572 0.235468 0.117734 0.993045i \(-0.462437\pi\)
0.117734 + 0.993045i \(0.462437\pi\)
\(462\) 6.31373 2.35490i 0.293741 0.109560i
\(463\) 8.93312 4.87785i 0.415157 0.226693i −0.258074 0.966125i \(-0.583088\pi\)
0.673231 + 0.739432i \(0.264906\pi\)
\(464\) 2.42463 2.10095i 0.112561 0.0975343i
\(465\) 1.91589 + 31.6955i 0.0888474 + 1.46984i
\(466\) 23.7827 27.4467i 1.10171 1.27145i
\(467\) 23.1349 + 30.9046i 1.07056 + 1.43009i 0.895241 + 0.445582i \(0.147003\pi\)
0.175314 + 0.984513i \(0.443906\pi\)
\(468\) 0.675363 1.23684i 0.0312187 0.0571727i
\(469\) 2.99472 4.65988i 0.138283 0.215173i
\(470\) −6.79482 + 3.01299i −0.313422 + 0.138979i
\(471\) −31.8155 + 14.5296i −1.46598 + 0.669491i
\(472\) −5.81827 + 15.5994i −0.267808 + 0.718020i
\(473\) −5.86681 4.39184i −0.269756 0.201937i
\(474\) −42.6042 27.3801i −1.95688 1.25761i
\(475\) 16.8639 18.6161i 0.773769 0.854167i
\(476\) 0.269165 1.87209i 0.0123372 0.0858069i
\(477\) 0.00455553 + 0.0636947i 0.000208584 + 0.00291638i
\(478\) −7.57720 + 34.8318i −0.346573 + 1.59317i
\(479\) −9.94926 11.4821i −0.454593 0.524628i 0.481469 0.876463i \(-0.340103\pi\)
−0.936062 + 0.351835i \(0.885558\pi\)
\(480\) −28.4794 0.314041i −1.29990 0.0143340i
\(481\) 5.49076 + 2.50755i 0.250357 + 0.114334i
\(482\) 39.2590 39.2590i 1.78820 1.78820i
\(483\) 5.92196 + 0.0939872i 0.269459 + 0.00427656i
\(484\) 13.0091i 0.591323i
\(485\) 21.7274 + 29.7015i 0.986592 + 1.34868i
\(486\) 2.39791 + 0.704090i 0.108771 + 0.0319382i
\(487\) 1.13423 15.8586i 0.0513969 0.718622i −0.904789 0.425861i \(-0.859971\pi\)
0.956186 0.292761i \(-0.0945741\pi\)
\(488\) 15.1864 + 3.30360i 0.687456 + 0.149547i
\(489\) −12.0824 10.4694i −0.546383 0.473444i
\(490\) −25.0392 19.1785i −1.13116 0.866397i
\(491\) 23.8524 7.00368i 1.07644 0.316072i 0.304987 0.952356i \(-0.401348\pi\)
0.771454 + 0.636285i \(0.219530\pi\)
\(492\) 12.0059 + 55.1900i 0.541266 + 2.48816i
\(493\) −0.938797 + 1.25409i −0.0422813 + 0.0564812i
\(494\) −21.1142 46.2336i −0.949972 2.08015i
\(495\) −0.399585 0.471552i −0.0179600 0.0211947i
\(496\) 2.30531 + 16.0338i 0.103511 + 0.719938i
\(497\) −1.88297 + 0.409615i −0.0844627 + 0.0183737i
\(498\) 44.5198 + 24.3097i 1.99498 + 1.08934i
\(499\) −24.4167 3.51059i −1.09304 0.157156i −0.427865 0.903842i \(-0.640734\pi\)
−0.665176 + 0.746687i \(0.731643\pi\)
\(500\) −30.5561 + 3.36614i −1.36651 + 0.150538i
\(501\) 10.6386 6.83703i 0.475299 0.305456i
\(502\) −17.8645 1.27770i −0.797333 0.0570264i
\(503\) −10.0012 18.3159i −0.445932 0.816664i 0.553942 0.832556i \(-0.313123\pi\)
−0.999874 + 0.0158918i \(0.994941\pi\)
\(504\) −0.0544283 + 0.119181i −0.00242443 + 0.00530876i
\(505\) −38.8592 + 10.9462i −1.72921 + 0.487098i
\(506\) 9.53285 24.3703i 0.423787 1.08339i
\(507\) −10.2787 10.2787i −0.456495 0.456495i
\(508\) −4.59404 12.3171i −0.203827 0.546482i
\(509\) −0.0147013 + 0.0500681i −0.000651624 + 0.00221923i −0.959818 0.280623i \(-0.909459\pi\)
0.959167 + 0.282842i \(0.0912772\pi\)
\(510\) 7.68198 1.58261i 0.340164 0.0700790i
\(511\) −0.250508 0.389799i −0.0110818 0.0172437i
\(512\) −20.8113 + 1.48845i −0.919737 + 0.0657809i
\(513\) 21.2641 15.9181i 0.938833 0.702802i
\(514\) 11.8152 + 40.2387i 0.521144 + 1.77485i
\(515\) 17.1164 + 32.1851i 0.754240 + 1.41825i
\(516\) −13.5416 + 1.94698i −0.596134 + 0.0857112i
\(517\) 3.57807 + 1.33455i 0.157363 + 0.0586935i
\(518\) −1.92890 0.719443i −0.0847511 0.0316105i
\(519\) 3.38176 0.486223i 0.148443 0.0213428i
\(520\) −4.95647 + 16.2165i −0.217355 + 0.711142i
\(521\) −0.606315 2.06492i −0.0265632 0.0904658i 0.945145 0.326652i \(-0.105921\pi\)
−0.971708 + 0.236186i \(0.924102\pi\)
\(522\) 0.318685 0.238564i 0.0139485 0.0104417i
\(523\) 34.5049 2.46784i 1.50879 0.107911i 0.707728 0.706485i \(-0.249720\pi\)
0.801067 + 0.598574i \(0.204266\pi\)
\(524\) −6.54689 10.1872i −0.286002 0.445028i
\(525\) −1.86988 + 5.88493i −0.0816083 + 0.256839i
\(526\) 4.15416 14.1478i 0.181130 0.616872i
\(527\) −2.76413 7.41091i −0.120407 0.322824i
\(528\) 5.83557 + 5.83557i 0.253961 + 0.253961i
\(529\) 15.6058 16.8955i 0.678514 0.734588i
\(530\) −0.764245 2.71310i −0.0331967 0.117849i
\(531\) 0.467436 1.02354i 0.0202850 0.0444179i
\(532\) 4.80938 + 8.80772i 0.208513 + 0.381863i
\(533\) −55.9564 4.00208i −2.42374 0.173349i
\(534\) −3.62629 + 2.33048i −0.156925 + 0.100850i
\(535\) −3.63442 10.0824i −0.157130 0.435901i
\(536\) −12.3281 1.77251i −0.532491 0.0765607i
\(537\) 7.94320 + 4.33732i 0.342775 + 0.187169i
\(538\) 15.2263 3.31228i 0.656453 0.142803i
\(539\) 2.30615 + 16.0397i 0.0993331 + 0.690877i
\(540\) −32.3970 2.67643i −1.39415 0.115175i
\(541\) 3.27868 + 7.17931i 0.140962 + 0.308663i 0.966925 0.255061i \(-0.0820956\pi\)
−0.825963 + 0.563724i \(0.809368\pi\)
\(542\) 2.31920 3.09809i 0.0996183 0.133074i
\(543\) 2.55677 + 11.7533i 0.109721 + 0.504381i
\(544\) 6.80714 1.99876i 0.291854 0.0856960i
\(545\) 0.385247 + 2.90662i 0.0165022 + 0.124506i
\(546\) 9.44275 + 8.18219i 0.404112 + 0.350165i
\(547\) −2.63697 0.573637i −0.112748 0.0245269i 0.155837 0.987783i \(-0.450193\pi\)
−0.268585 + 0.963256i \(0.586556\pi\)
\(548\) −0.283450 + 3.96315i −0.0121084 + 0.169297i
\(549\) −1.00782 0.295924i −0.0430129 0.0126297i
\(550\) 21.4749 + 16.8274i 0.915692 + 0.717523i
\(551\) 8.31195i 0.354101i
\(552\) −5.33921 12.2000i −0.227252 0.519265i
\(553\) −7.02269 + 7.02269i −0.298635 + 0.298635i
\(554\) 18.3503 + 8.38030i 0.779629 + 0.356045i
\(555\) 0.0544957 4.94205i 0.00231321 0.209778i
\(556\) −20.8085 24.0143i −0.882478 1.01843i
\(557\) 5.77671 26.5551i 0.244767 1.12518i −0.676560 0.736388i \(-0.736530\pi\)
0.921327 0.388789i \(-0.127106\pi\)
\(558\) 0.143389 + 2.00485i 0.00607016 + 0.0848719i
\(559\) 1.93383 13.4501i 0.0817924 0.568879i
\(560\) −0.703487 + 3.07048i −0.0297278 + 0.129751i
\(561\) −3.39001 2.17863i −0.143126 0.0919818i
\(562\) −17.8741 13.3804i −0.753974 0.564418i
\(563\) 2.75729 7.39259i 0.116206 0.311560i −0.865806 0.500380i \(-0.833194\pi\)
0.982012 + 0.188820i \(0.0604662\pi\)
\(564\) 6.48473 2.96148i 0.273056 0.124701i
\(565\) 14.0182 36.3550i 0.589752 1.52946i
\(566\) 19.3962 30.1811i 0.815284 1.26861i
\(567\) −3.01402 + 5.51977i −0.126577 + 0.231809i
\(568\) 2.59658 + 3.46862i 0.108950 + 0.145540i
\(569\) 6.22934 7.18904i 0.261148 0.301380i −0.610000 0.792401i \(-0.708831\pi\)
0.871148 + 0.491021i \(0.163376\pi\)
\(570\) −27.5977 + 31.1487i −1.15594 + 1.30468i
\(571\) 4.67314 4.04930i 0.195565 0.169458i −0.551574 0.834126i \(-0.685973\pi\)
0.747139 + 0.664668i \(0.231427\pi\)
\(572\) 28.0493 15.3161i 1.17280 0.640397i
\(573\) 1.43274 0.534384i 0.0598535 0.0223242i
\(574\) 19.1330 0.798598
\(575\) 12.1900 + 20.6496i 0.508357 + 0.861146i
\(576\) −1.37468 −0.0572785
\(577\) 29.2746 10.9189i 1.21872 0.454558i 0.343898 0.939007i \(-0.388253\pi\)
0.874820 + 0.484449i \(0.160980\pi\)
\(578\) 30.8023 16.8193i 1.28121 0.699592i
\(579\) 0.463734 0.401828i 0.0192721 0.0166994i
\(580\) −6.74584 + 7.61384i −0.280106 + 0.316147i
\(581\) 6.51418 7.51776i 0.270254 0.311889i
\(582\) −36.5376 48.8085i −1.51453 2.02318i
\(583\) −0.694037 + 1.27103i −0.0287441 + 0.0526409i
\(584\) −0.563265 + 0.876457i −0.0233081 + 0.0362680i
\(585\) 0.412315 1.06930i 0.0170471 0.0442101i
\(586\) −53.5681 + 24.4637i −2.21288 + 1.01059i
\(587\) −2.43684 + 6.53342i −0.100579 + 0.269663i −0.977487 0.210995i \(-0.932330\pi\)
0.876908 + 0.480658i \(0.159602\pi\)
\(588\) 24.2167 + 18.1284i 0.998682 + 0.747604i
\(589\) 35.3054 + 22.6894i 1.45473 + 0.934901i
\(590\) −11.0921 + 48.4133i −0.456656 + 1.99315i
\(591\) 3.23912 22.5286i 0.133240 0.926703i
\(592\) −0.179867 2.51486i −0.00739247 0.103360i
\(593\) 2.21822 10.1970i 0.0910914 0.418741i −0.908907 0.416999i \(-0.863082\pi\)
0.999998 0.00174180i \(-0.000554432\pi\)
\(594\) 18.8928 + 21.8035i 0.775183 + 0.894609i
\(595\) 0.0169598 1.53803i 0.000695284 0.0630532i
\(596\) 26.2898 + 12.0061i 1.07687 + 0.491791i
\(597\) 16.3554 16.3554i 0.669381 0.669381i
\(598\) 48.1304 6.14222i 1.96820 0.251174i
\(599\) 13.0622i 0.533708i 0.963737 + 0.266854i \(0.0859841\pi\)
−0.963737 + 0.266854i \(0.914016\pi\)
\(600\) 13.7830 1.67239i 0.562688 0.0682748i
\(601\) −17.2325 5.05991i −0.702928 0.206398i −0.0893127 0.996004i \(-0.528467\pi\)
−0.613615 + 0.789605i \(0.710285\pi\)
\(602\) −0.330616 + 4.62261i −0.0134749 + 0.188404i
\(603\) 0.822519 + 0.178928i 0.0334956 + 0.00728652i
\(604\) 3.07187 + 2.66179i 0.124993 + 0.108307i
\(605\) 1.39008 + 10.4879i 0.0565148 + 0.426394i
\(606\) 64.1766 18.8440i 2.60700 0.765483i
\(607\) −0.429041 1.97227i −0.0174142 0.0800519i 0.967620 0.252413i \(-0.0812241\pi\)
−0.985034 + 0.172361i \(0.944860\pi\)
\(608\) −22.5585 + 30.1346i −0.914868 + 1.22212i
\(609\) 0.848816 + 1.85865i 0.0343957 + 0.0753162i
\(610\) 46.2063 + 3.81726i 1.87084 + 0.154556i
\(611\) 1.00770 + 7.00874i 0.0407674 + 0.283543i
\(612\) 0.280845 0.0610942i 0.0113525 0.00246959i
\(613\) −6.14769 3.35689i −0.248303 0.135584i 0.350279 0.936646i \(-0.386087\pi\)
−0.598581 + 0.801062i \(0.704269\pi\)
\(614\) −31.8342 4.57706i −1.28472 0.184715i
\(615\) 15.5764 + 43.2112i 0.628100 + 1.74244i
\(616\) −2.49965 + 1.60643i −0.100714 + 0.0647249i
\(617\) 6.89303 + 0.492999i 0.277503 + 0.0198474i 0.209397 0.977831i \(-0.432850\pi\)
0.0681059 + 0.997678i \(0.478304\pi\)
\(618\) −28.9441 53.0071i −1.16430 2.13226i
\(619\) 8.87920 19.4427i 0.356885 0.781469i −0.642993 0.765872i \(-0.722308\pi\)
0.999878 0.0155976i \(-0.00496506\pi\)
\(620\) −13.9258 49.4370i −0.559273 1.98544i
\(621\) 8.48325 + 23.8959i 0.340421 + 0.958911i
\(622\) −14.7377 14.7377i −0.590929 0.590929i
\(623\) 0.295414 + 0.792036i 0.0118355 + 0.0317323i
\(624\) −4.31108 + 14.6822i −0.172581 + 0.587758i
\(625\) −24.2745 + 5.97882i −0.970982 + 0.239153i
\(626\) 1.57924 + 2.45734i 0.0631190 + 0.0982151i
\(627\) 21.3268 1.52532i 0.851711 0.0609155i
\(628\) 45.2897 33.9035i 1.80726 1.35290i
\(629\) 0.346845 + 1.18125i 0.0138296 + 0.0470993i
\(630\) −0.114248 + 0.373794i −0.00455174 + 0.0148923i
\(631\) 13.1874 1.89606i 0.524981 0.0754809i 0.125271 0.992123i \(-0.460020\pi\)
0.399710 + 0.916642i \(0.369111\pi\)
\(632\) 20.9230 + 7.80389i 0.832274 + 0.310422i
\(633\) −20.0974 7.49595i −0.798801 0.297937i
\(634\) −11.5252 + 1.65707i −0.457724 + 0.0658107i
\(635\) −5.01983 9.43911i −0.199206 0.374580i
\(636\) 0.761645 + 2.59392i 0.0302012 + 0.102856i
\(637\) −24.0532 + 18.0060i −0.953022 + 0.713423i
\(638\) 9.00492 0.644045i 0.356508 0.0254980i
\(639\) −0.158318 0.246348i −0.00626297 0.00974537i
\(640\) 26.6105 5.48218i 1.05187 0.216702i
\(641\) −4.71759 + 16.0666i −0.186333 + 0.634594i 0.812344 + 0.583179i \(0.198191\pi\)
−0.998677 + 0.0514149i \(0.983627\pi\)
\(642\) 6.20518 + 16.6367i 0.244899 + 0.656600i
\(643\) −18.4910 18.4910i −0.729215 0.729215i 0.241248 0.970463i \(-0.422443\pi\)
−0.970463 + 0.241248i \(0.922443\pi\)
\(644\) −9.39217 + 1.88756i −0.370103 + 0.0743803i
\(645\) −10.7091 + 3.01663i −0.421672 + 0.118780i
\(646\) 4.30631 9.42951i 0.169430 0.370999i
\(647\) −20.3010 37.1786i −0.798116 1.46164i −0.885085 0.465430i \(-0.845900\pi\)
0.0869688 0.996211i \(-0.472282\pi\)
\(648\) 14.1048 + 1.00880i 0.554090 + 0.0396293i
\(649\) 21.4673 13.7962i 0.842664 0.541547i
\(650\) −8.30158 + 49.9006i −0.325615 + 1.95726i
\(651\) −10.2117 1.46823i −0.400230 0.0575443i
\(652\) 22.6962 + 12.3930i 0.888851 + 0.485349i
\(653\) −11.4552 + 2.49193i −0.448277 + 0.0975166i −0.431036 0.902335i \(-0.641852\pi\)
−0.0172406 + 0.999851i \(0.505488\pi\)
\(654\) −0.691322 4.80825i −0.0270328 0.188017i
\(655\) −6.36663 7.51330i −0.248765 0.293569i
\(656\) 9.73408 + 21.3147i 0.380052 + 0.832198i
\(657\) 0.0421969 0.0563684i 0.00164626 0.00219914i
\(658\) −0.513337 2.35977i −0.0200119 0.0919934i
\(659\) −16.0097 + 4.70088i −0.623651 + 0.183120i −0.578265 0.815849i \(-0.696270\pi\)
−0.0453861 + 0.998970i \(0.514452\pi\)
\(660\) −20.7735 15.9113i −0.808608 0.619345i
\(661\) 25.5413 + 22.1316i 0.993441 + 0.860821i 0.990268 0.139174i \(-0.0444446\pi\)
0.00317269 + 0.999995i \(0.498990\pi\)
\(662\) −73.2250 15.9291i −2.84597 0.619103i
\(663\) 0.533032 7.45276i 0.0207012 0.289441i
\(664\) −21.4607 6.30142i −0.832835 0.244542i
\(665\) 4.81846 + 6.58686i 0.186852 + 0.255428i
\(666\) 0.312847i 0.0121226i
\(667\) 7.57700 + 2.35604i 0.293382 + 0.0912262i
\(668\) −14.4640 + 14.4640i −0.559627 + 0.559627i
\(669\) 3.00084 + 1.37044i 0.116019 + 0.0529841i
\(670\) −37.1531 0.409685i −1.43535 0.0158275i
\(671\) −15.5992 18.0024i −0.602200 0.694976i
\(672\) 1.96699 9.04212i 0.0758784 0.348807i
\(673\) 0.503651 + 7.04195i 0.0194143 + 0.271447i 0.997882 + 0.0650480i \(0.0207201\pi\)
−0.978468 + 0.206399i \(0.933825\pi\)
\(674\) −4.64147 + 32.2821i −0.178783 + 1.24346i
\(675\) −26.4044 + 1.30403i −1.01631 + 0.0501922i
\(676\) 19.7799 + 12.7118i 0.760767 + 0.488915i
\(677\) −4.81352 3.60336i −0.184999 0.138488i 0.502764 0.864423i \(-0.332316\pi\)
−0.687763 + 0.725935i \(0.741407\pi\)
\(678\) −22.5593 + 60.4839i −0.866386 + 2.32287i
\(679\) −10.8760 + 4.96691i −0.417383 + 0.190613i
\(680\) −3.16157 + 1.40192i −0.121241 + 0.0537611i
\(681\) 7.35319 11.4418i 0.281775 0.438450i
\(682\) −21.8454 + 40.0069i −0.836505 + 1.53194i
\(683\) 18.9555 + 25.3215i 0.725310 + 0.968901i 0.999973 + 0.00736044i \(0.00234292\pi\)
−0.274663 + 0.961541i \(0.588566\pi\)
\(684\) −0.998656 + 1.15251i −0.0381845 + 0.0440673i
\(685\) 0.194963 + 3.22537i 0.00744917 + 0.123235i
\(686\) 16.1206 13.9686i 0.615486 0.533322i
\(687\) 35.2480 19.2469i 1.34480 0.734314i
\(688\) −5.31790 + 1.98348i −0.202743 + 0.0756193i
\(689\) −2.68517 −0.102297
\(690\) −20.5719 33.9866i −0.783158 1.29385i
\(691\) 3.74985 0.142651 0.0713254 0.997453i \(-0.477277\pi\)
0.0713254 + 0.997453i \(0.477277\pi\)
\(692\) −5.17780 + 1.93122i −0.196830 + 0.0734139i
\(693\) 0.176253 0.0962415i 0.00669531 0.00365591i
\(694\) −36.7018 + 31.8023i −1.39318 + 1.20720i
\(695\) −19.3418 17.1368i −0.733677 0.650036i
\(696\) 3.00864 3.47216i 0.114042 0.131612i
\(697\) −6.85673 9.15952i −0.259717 0.346941i
\(698\) 22.6775 41.5307i 0.858355 1.57196i
\(699\) −15.3149 + 23.8304i −0.579263 + 0.901350i
\(700\) 0.932030 9.94422i 0.0352274 0.375856i
\(701\) −44.6501 + 20.3910i −1.68641 + 0.770158i −0.687373 + 0.726304i \(0.741236\pi\)
−0.999038 + 0.0438537i \(0.986036\pi\)
\(702\) −18.6940 + 50.1205i −0.705559 + 1.89168i
\(703\) −5.22927 3.91459i −0.197226 0.147641i
\(704\) −26.2265 16.8547i −0.988448 0.635237i
\(705\) 4.91153 3.08046i 0.184979 0.116017i
\(706\) −6.39749 + 44.4955i −0.240773 + 1.67461i
\(707\) −0.935742 13.0834i −0.0351922 0.492051i
\(708\) 10.1260 46.5483i 0.380557 1.74939i
\(709\) −22.7950 26.3069i −0.856085 0.987975i 0.143914 0.989590i \(-0.454031\pi\)
−0.999999 + 0.00161551i \(0.999486\pi\)
\(710\) 9.03857 + 9.24013i 0.339211 + 0.346776i
\(711\) −1.37285 0.626959i −0.0514859 0.0235128i
\(712\) 1.34402 1.34402i 0.0503691 0.0503691i
\(713\) −30.6906 + 25.7523i −1.14937 + 0.964431i
\(714\) 2.54831i 0.0953680i
\(715\) 20.9767 15.3450i 0.784484 0.573870i
\(716\) −14.0458 4.12421i −0.524914 0.154129i
\(717\) 1.98352 27.7333i 0.0740760 1.03572i
\(718\) −49.6621 10.8033i −1.85337 0.403177i
\(719\) −10.9488 9.48719i −0.408321 0.353812i 0.426352 0.904557i \(-0.359798\pi\)
−0.834674 + 0.550745i \(0.814344\pi\)
\(720\) −0.474540 + 0.0628961i −0.0176851 + 0.00234400i
\(721\) −11.3641 + 3.33679i −0.423219 + 0.124268i
\(722\) 2.88981 + 13.2843i 0.107548 + 0.494389i
\(723\) −25.9522 + 34.6681i −0.965175 + 1.28932i
\(724\) −8.08210 17.6973i −0.300369 0.657716i
\(725\) −4.62491 + 6.85908i −0.171765 + 0.254740i
\(726\) −2.49448 17.3495i −0.0925790 0.643901i
\(727\) −27.7101 + 6.02797i −1.02771 + 0.223565i −0.694656 0.719342i \(-0.744443\pi\)
−0.333056 + 0.942907i \(0.608080\pi\)
\(728\) −4.83548 2.64037i −0.179215 0.0978586i
\(729\) −27.6350 3.97331i −1.02352 0.147160i
\(730\) −1.32222 + 2.81277i −0.0489376 + 0.104105i
\(731\) 2.33146 1.49834i 0.0862320 0.0554179i
\(732\) −44.3547 3.17231i −1.63940 0.117252i
\(733\) −3.73075 6.83235i −0.137798 0.252359i 0.799662 0.600450i \(-0.205012\pi\)
−0.937461 + 0.348091i \(0.886830\pi\)
\(734\) 24.1401 52.8595i 0.891028 1.95108i
\(735\) 21.4606 + 12.0274i 0.791586 + 0.443638i
\(736\) −21.0758 29.1056i −0.776865 1.07285i
\(737\) 13.4984 + 13.4984i 0.497219 + 0.497219i
\(738\) 1.01607 + 2.72420i 0.0374022 + 0.100279i
\(739\) −1.97149 + 6.71426i −0.0725223 + 0.246988i −0.987774 0.155895i \(-0.950174\pi\)
0.915251 + 0.402883i \(0.131992\pi\)
\(740\) 1.61306 + 7.82980i 0.0592973 + 0.287829i
\(741\) 21.4335 + 33.3512i 0.787379 + 1.22519i
\(742\) 0.913463 0.0653322i 0.0335343 0.00239842i
\(743\) 13.5563 10.1481i 0.497334 0.372299i −0.320966 0.947091i \(-0.604008\pi\)
0.818300 + 0.574791i \(0.194917\pi\)
\(744\) 6.53537 + 22.2574i 0.239598 + 0.815997i
\(745\) 22.4777 + 6.87014i 0.823518 + 0.251703i
\(746\) 21.7437 3.12627i 0.796094 0.114461i
\(747\) 1.41633 + 0.528265i 0.0518210 + 0.0193282i
\(748\) 6.10709 + 2.27783i 0.223297 + 0.0832855i
\(749\) 3.44669 0.495558i 0.125939 0.0181073i
\(750\) 40.1055 10.3483i 1.46444 0.377867i
\(751\) 2.63840 + 8.98556i 0.0962766 + 0.327888i 0.993521 0.113646i \(-0.0362528\pi\)
−0.897245 + 0.441533i \(0.854435\pi\)
\(752\) 2.36767 1.77242i 0.0863402 0.0646335i
\(753\) 13.9343 0.996598i 0.507793 0.0363181i
\(754\) 9.04997 + 14.0820i 0.329581 + 0.512837i
\(755\) 2.76096 + 1.81769i 0.100482 + 0.0661524i
\(756\) 2.97558 10.1339i 0.108221 0.368567i
\(757\) 14.4659 + 38.7846i 0.525773 + 1.40965i 0.880216 + 0.474574i \(0.157398\pi\)
−0.354443 + 0.935078i \(0.615329\pi\)
\(758\) 21.4474 + 21.4474i 0.779005 + 0.779005i
\(759\) −4.65468 + 19.8734i −0.168954 + 0.721360i
\(760\) 8.97138 16.0077i 0.325426 0.580659i
\(761\) 9.23382 20.2192i 0.334726 0.732947i −0.665180 0.746683i \(-0.731645\pi\)
0.999906 + 0.0137362i \(0.00437251\pi\)
\(762\) 8.48860 + 15.5457i 0.307509 + 0.563162i
\(763\) −0.950200 0.0679596i −0.0343995 0.00246030i
\(764\) −2.08076 + 1.33722i −0.0752791 + 0.0483789i
\(765\) 0.219889 0.0792635i 0.00795009 0.00286578i
\(766\) 34.4026 + 4.94635i 1.24302 + 0.178719i
\(767\) 41.5276 + 22.6758i 1.49947 + 0.818774i
\(768\) −2.61927 + 0.569787i −0.0945147 + 0.0205604i
\(769\) −6.77748 47.1384i −0.244402 1.69985i −0.629518 0.776986i \(-0.716748\pi\)
0.385116 0.922868i \(-0.374162\pi\)
\(770\) −6.76266 + 5.73055i −0.243709 + 0.206515i
\(771\) −13.5887 29.7550i −0.489384 1.07160i
\(772\) −0.594788 + 0.794544i −0.0214069 + 0.0285963i
\(773\) 1.03421 + 4.75417i 0.0371978 + 0.170996i 0.991998 0.126252i \(-0.0402949\pi\)
−0.954800 + 0.297248i \(0.903931\pi\)
\(774\) −0.675735 + 0.198414i −0.0242888 + 0.00713183i
\(775\) −16.5095 38.3680i −0.593039 1.37822i
\(776\) 20.3176 + 17.6053i 0.729360 + 0.631994i
\(777\) 1.56908 + 0.341333i 0.0562905 + 0.0122453i
\(778\) −1.37520 + 19.2278i −0.0493033 + 0.689350i
\(779\) 58.2492 + 17.1035i 2.08699 + 0.612797i
\(780\) 7.43394 47.9451i 0.266178 1.71671i
\(781\) 6.64098i 0.237633i
\(782\) 7.37511 + 6.59836i 0.263733 + 0.235957i
\(783\) −6.18579 + 6.18579i −0.221062 + 0.221062i
\(784\) 11.4159 + 5.21346i 0.407710 + 0.186195i
\(785\) 32.8897 32.1723i 1.17389 1.14828i
\(786\) 10.6846 + 12.3307i 0.381107 + 0.439821i
\(787\) −7.17337 + 32.9754i −0.255703 + 1.17545i 0.652787 + 0.757541i \(0.273599\pi\)
−0.908490 + 0.417906i \(0.862764\pi\)
\(788\) 2.62633 + 36.7208i 0.0935590 + 1.30813i
\(789\) −1.63678 + 11.3840i −0.0582707 + 0.405282i
\(790\) 64.9355 + 14.8776i 2.31030 + 0.529321i
\(791\) 10.6498 + 6.84424i 0.378665 + 0.243353i
\(792\) −0.361473 0.270595i −0.0128444 0.00961518i
\(793\) 15.4350 41.3828i 0.548113 1.46955i
\(794\) 50.3381 22.9887i 1.78643 0.815837i
\(795\) 0.891208 + 2.00983i 0.0316079 + 0.0712813i
\(796\) −20.2268 + 31.4735i −0.716920 + 1.11555i
\(797\) −4.18172 + 7.65825i −0.148124 + 0.271269i −0.941197 0.337857i \(-0.890298\pi\)
0.793073 + 0.609126i \(0.208480\pi\)
\(798\) −8.10288 10.8242i −0.286839 0.383172i
\(799\) −0.945722 + 1.09142i −0.0334572 + 0.0386117i
\(800\) 35.3828 12.3154i 1.25097 0.435414i
\(801\) −0.0970835 + 0.0841233i −0.00343028 + 0.00297235i
\(802\) 40.1367 21.9163i 1.41728 0.773892i
\(803\) 1.49616 0.558039i 0.0527984 0.0196928i
\(804\) 35.6361 1.25679
\(805\) −7.37025 + 2.52534i −0.259767 + 0.0890066i
\(806\) −84.5182 −2.97703
\(807\) −11.3879 + 4.24747i −0.400873 + 0.149518i
\(808\) −25.8853 + 14.1345i −0.910643 + 0.497249i
\(809\) 6.86057 5.94472i 0.241205 0.209005i −0.525866 0.850567i \(-0.676259\pi\)
0.767071 + 0.641562i \(0.221713\pi\)
\(810\) 42.1082 2.54531i 1.47953 0.0894330i
\(811\) −12.5909 + 14.5307i −0.442128 + 0.510243i −0.932450 0.361298i \(-0.882334\pi\)
0.490322 + 0.871541i \(0.336879\pi\)
\(812\) −1.98063 2.64581i −0.0695064 0.0928496i
\(813\) −1.44665 + 2.64935i −0.0507363 + 0.0929166i
\(814\) 3.83576 5.96856i 0.134443 0.209198i
\(815\) 19.6218 + 7.56606i 0.687323 + 0.265027i
\(816\) −2.83887 + 1.29647i −0.0993805 + 0.0453855i
\(817\) −5.13881 + 13.7777i −0.179784 + 0.482020i
\(818\) 4.69639 + 3.51567i 0.164205 + 0.122923i
\(819\) 0.313241 + 0.201308i 0.0109455 + 0.00703427i
\(820\) −39.4760 62.9411i −1.37856 2.19800i
\(821\) 5.13943 35.7455i 0.179367 1.24753i −0.678864 0.734264i \(-0.737528\pi\)
0.858232 0.513263i \(-0.171563\pi\)
\(822\) −0.381909 5.33978i −0.0133206 0.186246i
\(823\) 2.59695 11.9380i 0.0905241 0.416133i −0.909476 0.415757i \(-0.863517\pi\)
1.00000 0.000375820i \(-0.000119627\pi\)
\(824\) 17.4394 + 20.1261i 0.607529 + 0.701126i
\(825\) −18.4477 10.6079i −0.642268 0.369319i
\(826\) −14.6789 6.70362i −0.510744 0.233249i
\(827\) 5.51644 5.51644i 0.191825 0.191825i −0.604659 0.796484i \(-0.706691\pi\)
0.796484 + 0.604659i \(0.206691\pi\)
\(828\) −0.767533 1.23703i −0.0266736 0.0429899i
\(829\) 10.9025i 0.378659i −0.981914 0.189329i \(-0.939369\pi\)
0.981914 0.189329i \(-0.0606314\pi\)
\(830\) −65.9365 10.2235i −2.28869 0.354863i
\(831\) −15.0977 4.43309i −0.523734 0.153782i
\(832\) 4.12375 57.6575i 0.142965 1.99892i
\(833\) −5.98798 1.30260i −0.207471 0.0451326i
\(834\) 32.3559 + 28.0365i 1.12039 + 0.970826i
\(835\) −10.1153 + 13.2063i −0.350053 + 0.457024i
\(836\) −33.1832 + 9.74348i −1.14767 + 0.336985i
\(837\) −9.38888 43.1600i −0.324527 1.49183i
\(838\) 21.8518 29.1906i 0.754858 1.00837i
\(839\) 18.4551 + 40.4110i 0.637141 + 1.39514i 0.902372 + 0.430958i \(0.141824\pi\)
−0.265231 + 0.964185i \(0.585448\pi\)
\(840\) −0.371402 + 4.49565i −0.0128146 + 0.155115i
\(841\) −3.73755 25.9952i −0.128881 0.896387i
\(842\) −38.6333 + 8.40416i −1.33139 + 0.289627i
\(843\) 15.2851 + 8.34631i 0.526448 + 0.287462i
\(844\) 34.3419 + 4.93762i 1.18210 + 0.169960i
\(845\) 17.3048 + 8.13464i 0.595305 + 0.279840i
\(846\) 0.308728 0.198407i 0.0106143 0.00682138i
\(847\) −3.42859 0.245218i −0.117808 0.00842577i
\(848\) 0.537512 + 0.984381i 0.0184583 + 0.0338038i
\(849\) −11.6247 + 25.4546i −0.398960 + 0.873600i
\(850\) −8.80034 + 5.38519i −0.301849 + 0.184711i
\(851\) 5.05070 3.65730i 0.173136 0.125371i
\(852\) −8.76619 8.76619i −0.300325 0.300325i
\(853\) −3.80956 10.2138i −0.130437 0.349714i 0.855271 0.518182i \(-0.173391\pi\)
−0.985707 + 0.168467i \(0.946118\pi\)
\(854\) −4.24393 + 14.4535i −0.145224 + 0.494588i
\(855\) −0.681963 + 1.03586i −0.0233226 + 0.0354257i
\(856\) −4.23296 6.58661i −0.144680 0.225126i
\(857\) 4.23745 0.303069i 0.144749 0.0103526i 0.00122315 0.999999i \(-0.499611\pi\)
0.143525 + 0.989647i \(0.454156\pi\)
\(858\) −34.4709 + 25.8046i −1.17682 + 0.880955i
\(859\) −4.08771 13.9215i −0.139471 0.474994i 0.859900 0.510463i \(-0.170526\pi\)
−0.999371 + 0.0354684i \(0.988708\pi\)
\(860\) 15.8889 8.44993i 0.541808 0.288140i
\(861\) −14.7718 + 2.12386i −0.503422 + 0.0723811i
\(862\) 27.4256 + 10.2292i 0.934121 + 0.348409i
\(863\) 33.1146 + 12.3511i 1.12723 + 0.420436i 0.842782 0.538255i \(-0.180916\pi\)
0.284450 + 0.958691i \(0.408189\pi\)
\(864\) 39.2144 5.63818i 1.33410 0.191815i
\(865\) −3.96797 + 2.11021i −0.134915 + 0.0717494i
\(866\) 19.2445 + 65.5409i 0.653956 + 2.22717i
\(867\) −21.9141 + 16.4047i −0.744241 + 0.557132i
\(868\) 16.6448 1.19046i 0.564961 0.0404068i
\(869\) −18.5044 28.7935i −0.627720 0.976752i
\(870\) 7.53660 11.4477i 0.255515 0.388112i
\(871\) −9.97204 + 33.9617i −0.337890 + 1.15075i
\(872\) 0.748541 + 2.00692i 0.0253488 + 0.0679628i
\(873\) −1.28478 1.28478i −0.0434832 0.0434832i
\(874\) −52.3073 4.57646i −1.76932 0.154801i
\(875\) −0.311183 8.11660i −0.0105199 0.274391i
\(876\) 1.23834 2.71158i 0.0418395 0.0916157i
\(877\) 11.9020 + 21.7968i 0.401901 + 0.736026i 0.997748 0.0670715i \(-0.0213656\pi\)
−0.595848 + 0.803098i \(0.703184\pi\)
\(878\) −39.7385 2.84215i −1.34111 0.0959179i
\(879\) 38.6420 24.8337i 1.30336 0.837621i
\(880\) −9.82452 4.61830i −0.331185 0.155683i
\(881\) −53.9713 7.75990i −1.81834 0.261438i −0.852902 0.522071i \(-0.825160\pi\)
−0.965438 + 0.260633i \(0.916069\pi\)
\(882\) 1.36675 + 0.746304i 0.0460210 + 0.0251293i
\(883\) 5.01684 1.09135i 0.168830 0.0367267i −0.127356 0.991857i \(-0.540649\pi\)
0.296186 + 0.955130i \(0.404285\pi\)
\(884\) 1.71996 + 11.9626i 0.0578485 + 0.402345i
\(885\) 3.18964 38.6091i 0.107218 1.29783i
\(886\) −21.0558 46.1058i −0.707384 1.54896i
\(887\) 4.79490 6.40524i 0.160997 0.215067i −0.712788 0.701380i \(-0.752568\pi\)
0.873785 + 0.486313i \(0.161659\pi\)
\(888\) −0.767483 3.52806i −0.0257550 0.118394i
\(889\) 3.33280 0.978599i 0.111779 0.0328211i
\(890\) 3.44790 4.50153i 0.115574 0.150892i
\(891\) −16.3799 14.1933i −0.548749 0.475494i
\(892\) −5.21411 1.13426i −0.174581 0.0379778i
\(893\) 0.546641 7.64303i 0.0182926 0.255764i
\(894\) −37.3634 10.9709i −1.24962 0.366921i
\(895\) −11.7643 1.82407i −0.393239 0.0609721i
\(896\) 8.82739i 0.294902i
\(897\) −36.4776 + 10.0849i −1.21795 + 0.336724i
\(898\) 62.6047 62.6047i 2.08915 2.08915i
\(899\) −12.5726 5.74173i −0.419321 0.191498i
\(900\) 1.46537 0.395391i 0.0488458 0.0131797i
\(901\) −0.358635 0.413887i −0.0119479 0.0137886i
\(902\) −14.0160 + 64.4307i −0.466683 + 2.14531i
\(903\) −0.257879 3.60562i −0.00858168 0.119988i
\(904\) 4.05095 28.1750i 0.134733 0.937086i
\(905\) −8.40681 13.4039i −0.279452 0.445562i
\(906\) −4.60718 2.96086i −0.153063 0.0983678i
\(907\) 33.9238 + 25.3951i 1.12642 + 0.843229i 0.989092 0.147296i \(-0.0470570\pi\)
0.137330 + 0.990525i \(0.456148\pi\)
\(908\) −7.68799 + 20.6123i −0.255135 + 0.684043i
\(909\) 1.81314 0.828035i 0.0601382 0.0274642i
\(910\) −15.3351 5.91312i −0.508354 0.196018i
\(911\) −7.22469 + 11.2418i −0.239365 + 0.372459i −0.940064 0.340998i \(-0.889235\pi\)
0.700699 + 0.713457i \(0.252871\pi\)
\(912\) 7.93598 14.5337i 0.262787 0.481258i
\(913\) 20.5441 + 27.4438i 0.679912 + 0.908256i
\(914\) −27.7633 + 32.0405i −0.918328 + 1.05981i
\(915\) −36.0976 + 2.18198i −1.19335 + 0.0721341i
\(916\) −49.0931 + 42.5394i −1.62208 + 1.40554i
\(917\) 2.80826 1.53343i 0.0927371 0.0506383i
\(918\) −10.2223 + 3.81270i −0.337385 + 0.125838i
\(919\) 41.1414 1.35713 0.678565 0.734540i \(-0.262602\pi\)
0.678565 + 0.734540i \(0.262602\pi\)
\(920\) 12.0493 + 12.7155i 0.397253 + 0.419219i
\(921\) 25.0859 0.826607
\(922\) 10.3235 3.85045i 0.339985 0.126808i
\(923\) 10.8073 5.90125i 0.355728 0.194242i
\(924\) 6.42515 5.56743i 0.211372 0.183155i
\(925\) 2.13709 + 6.14000i 0.0702672 + 0.201882i
\(926\) 14.5259 16.7638i 0.477350 0.550892i
\(927\) −1.07859 1.44083i −0.0354257 0.0473232i
\(928\) 5.94141 10.8809i 0.195036 0.357183i
\(929\) 13.7602 21.4114i 0.451459 0.702484i −0.538690 0.842504i \(-0.681080\pi\)
0.990149 + 0.140020i \(0.0447168\pi\)
\(930\) 28.0516 + 63.2612i 0.919847 + 2.07442i
\(931\) 29.5764 13.5071i 0.969327 0.442677i
\(932\) 16.0122 42.9304i 0.524497 1.40623i
\(933\) 13.0143 + 9.74240i 0.426070 + 0.318952i
\(934\) 70.7771 + 45.4857i 2.31590 + 1.48834i
\(935\) 5.16691 + 1.18381i 0.168976 + 0.0387147i
\(936\) 0.119150 0.828704i 0.00389453 0.0270870i
\(937\) −1.35058 18.8836i −0.0441216 0.616900i −0.970622 0.240608i \(-0.922653\pi\)
0.926501 0.376292i \(-0.122801\pi\)
\(938\) 2.56606 11.7960i 0.0837847 0.385152i
\(939\) −1.49204 1.72190i −0.0486908 0.0561922i
\(940\) −6.70369 + 6.55746i −0.218650 + 0.213881i
\(941\) 19.8866 + 9.08189i 0.648283 + 0.296061i 0.712287 0.701889i \(-0.247660\pi\)
−0.0640035 + 0.997950i \(0.520387\pi\)
\(942\) −53.8994 + 53.8994i −1.75614 + 1.75614i
\(943\) −32.1021 + 48.2507i −1.04539 + 1.57126i
\(944\) 19.7631i 0.643235i
\(945\) 1.31606 8.48788i 0.0428113 0.276111i
\(946\) −15.3245 4.49968i −0.498243 0.146297i
\(947\) −3.09378 + 43.2567i −0.100534 + 1.40565i 0.657507 + 0.753448i \(0.271611\pi\)
−0.758042 + 0.652206i \(0.773844\pi\)
\(948\) −62.4340 13.5817i −2.02776 0.441112i
\(949\) 2.23764 + 1.93893i 0.0726370 + 0.0629403i
\(950\) 20.2569 50.8566i 0.657221 1.65001i
\(951\) 8.71416 2.55871i 0.282576 0.0829718i
\(952\) −0.238851 1.09798i −0.00774121 0.0355858i
\(953\) 15.5028 20.7093i 0.502185 0.670841i −0.475791 0.879559i \(-0.657838\pi\)
0.977976 + 0.208717i \(0.0669289\pi\)
\(954\) 0.0578122 + 0.126591i 0.00187174 + 0.00409854i
\(955\) −1.53461 + 1.30040i −0.0496589 + 0.0420800i
\(956\) 6.40033 + 44.5153i 0.207001 + 1.43973i
\(957\) −6.88082 + 1.49683i −0.222425 + 0.0483856i
\(958\) −29.0605 15.8683i −0.938904 0.512680i
\(959\) −1.03916 0.149408i −0.0335561 0.00482465i
\(960\) −44.5249 + 16.0499i −1.43703 + 0.518009i
\(961\) 32.6294 20.9696i 1.05256 0.676440i
\(962\) 13.1216 + 0.938472i 0.423056 + 0.0302576i
\(963\) 0.253597 + 0.464429i 0.00817206 + 0.0149660i
\(964\) 29.0986 63.7171i 0.937203 2.05219i
\(965\) −0.394616 + 0.704115i −0.0127031 + 0.0226663i
\(966\) 12.1639 4.31827i 0.391366 0.138938i
\(967\) 31.0212 + 31.0212i 0.997574 + 0.997574i 0.999997 0.00242292i \(-0.000771239\pi\)
−0.00242292 + 0.999997i \(0.500771\pi\)
\(968\) 2.70095 + 7.24153i 0.0868118 + 0.232751i
\(969\) −2.27800 + 7.75814i −0.0731798 + 0.249227i
\(970\) 66.9869 + 44.1010i 2.15082 + 1.41600i
\(971\) 2.47177 + 3.84616i 0.0793230 + 0.123429i 0.878648 0.477470i \(-0.158446\pi\)
−0.799325 + 0.600899i \(0.794810\pi\)
\(972\) 3.14499 0.224934i 0.100876 0.00721476i
\(973\) 6.72128 5.03149i 0.215474 0.161302i
\(974\) −9.76195 33.2461i −0.312793 1.06527i
\(975\) 0.870079 39.4476i 0.0278648 1.26333i
\(976\) −18.2606 + 2.62548i −0.584509 + 0.0840397i
\(977\) −44.0110 16.4152i −1.40804 0.525170i −0.473423 0.880835i \(-0.656982\pi\)
−0.934613 + 0.355665i \(0.884254\pi\)
\(978\) −32.6450 12.1759i −1.04387 0.389344i
\(979\) −2.88360 + 0.414599i −0.0921602 + 0.0132506i
\(980\) −38.0544 11.6311i −1.21560 0.371541i
\(981\) −0.0407848 0.138900i −0.00130216 0.00443475i
\(982\) 43.3710 32.4671i 1.38402 1.03607i
\(983\) −28.7241 + 2.05439i −0.916157 + 0.0655249i −0.521450 0.853282i \(-0.674609\pi\)
−0.394708 + 0.918807i \(0.629154\pi\)
\(984\) 18.1416 + 28.2289i 0.578333 + 0.899904i
\(985\) 6.04112 + 29.3236i 0.192486 + 0.934328i
\(986\) −0.961849 + 3.27576i −0.0306315 + 0.104321i
\(987\) 0.658271 + 1.76489i 0.0209530 + 0.0561772i
\(988\) −45.3432 45.3432i −1.44256 1.44256i
\(989\) −11.1028 8.58974i −0.353049 0.273138i
\(990\) −1.17506 0.658556i −0.0373460 0.0209303i
\(991\) −8.31802 + 18.2139i −0.264231 + 0.578584i −0.994519 0.104554i \(-0.966658\pi\)
0.730289 + 0.683139i \(0.239386\pi\)
\(992\) 29.9986 + 54.9384i 0.952457 + 1.74429i
\(993\) 58.3020 + 4.16984i 1.85016 + 0.132326i
\(994\) −3.53294 + 2.27048i −0.112058 + 0.0720153i
\(995\) −12.9437 + 27.5352i −0.410344 + 0.872925i
\(996\) 63.3447 + 9.10760i 2.00715 + 0.288585i
\(997\) −45.8495 25.0357i −1.45207 0.792889i −0.456754 0.889593i \(-0.650988\pi\)
−0.995313 + 0.0967040i \(0.969170\pi\)
\(998\) −52.5310 + 11.4274i −1.66284 + 0.361729i
\(999\) 0.978397 + 6.80490i 0.0309551 + 0.215297i
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 115.2.l.a.17.10 200
5.2 odd 4 575.2.r.b.293.10 200
5.3 odd 4 inner 115.2.l.a.63.1 yes 200
5.4 even 2 575.2.r.b.132.1 200
23.19 odd 22 inner 115.2.l.a.42.1 yes 200
115.19 odd 22 575.2.r.b.157.10 200
115.42 even 44 575.2.r.b.318.1 200
115.88 even 44 inner 115.2.l.a.88.10 yes 200
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.2.l.a.17.10 200 1.1 even 1 trivial
115.2.l.a.42.1 yes 200 23.19 odd 22 inner
115.2.l.a.63.1 yes 200 5.3 odd 4 inner
115.2.l.a.88.10 yes 200 115.88 even 44 inner
575.2.r.b.132.1 200 5.4 even 2
575.2.r.b.157.10 200 115.19 odd 22
575.2.r.b.293.10 200 5.2 odd 4
575.2.r.b.318.1 200 115.42 even 44