Properties

Label 169.2.g.a.14.1
Level $169$
Weight $2$
Character 169.14
Analytic conductor $1.349$
Analytic rank $0$
Dimension $156$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,2,Mod(14,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(26))
 
chi = DirichletCharacter(H, H._module([18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.14");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.g (of order \(13\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.34947179416\)
Analytic rank: \(0\)
Dimension: \(156\)
Relative dimension: \(13\) over \(\Q(\zeta_{13})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label 14.1
Character \(\chi\) \(=\) 169.14
Dual form 169.2.g.a.157.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.55724 + 2.25606i) q^{2} +(-1.88671 + 0.990222i) q^{3} +(-1.95558 - 5.15643i) q^{4} +(-0.621291 - 0.550416i) q^{5} +(0.704070 - 5.79854i) q^{6} +(-0.145399 - 0.0358377i) q^{7} +(9.35521 + 2.30585i) q^{8} +(0.874940 - 1.26757i) q^{9} +O(q^{10})\) \(q+(-1.55724 + 2.25606i) q^{2} +(-1.88671 + 0.990222i) q^{3} +(-1.95558 - 5.15643i) q^{4} +(-0.621291 - 0.550416i) q^{5} +(0.704070 - 5.79854i) q^{6} +(-0.145399 - 0.0358377i) q^{7} +(9.35521 + 2.30585i) q^{8} +(0.874940 - 1.26757i) q^{9} +(2.20927 - 0.544537i) q^{10} +(-1.32031 - 1.91280i) q^{11} +(8.79562 + 7.79224i) q^{12} +(-1.38245 - 3.32999i) q^{13} +(0.307274 - 0.272221i) q^{14} +(1.71723 + 0.423259i) q^{15} +(-11.5147 + 10.2011i) q^{16} +(7.27623 + 1.79343i) q^{17} +(1.49721 + 3.94783i) q^{18} -4.83578 q^{19} +(-1.62320 + 4.28003i) q^{20} +(0.309814 - 0.0763622i) q^{21} +6.37142 q^{22} -0.397056 q^{23} +(-19.9339 + 4.91326i) q^{24} +(-0.519638 - 4.27961i) q^{25} +(9.66546 + 2.06672i) q^{26} +(0.374927 - 3.08781i) q^{27} +(0.0995449 + 0.819826i) q^{28} +(2.35738 - 3.41526i) q^{29} +(-3.62904 + 3.21505i) q^{30} +(1.08938 - 8.97185i) q^{31} +(-2.76036 - 22.7336i) q^{32} +(4.38513 + 2.30149i) q^{33} +(-15.3769 + 13.6228i) q^{34} +(0.0706097 + 0.102296i) q^{35} +(-8.24715 - 2.03274i) q^{36} +(0.160405 - 1.32105i) q^{37} +(7.53049 - 10.9098i) q^{38} +(5.90571 + 4.91379i) q^{39} +(-4.54313 - 6.58186i) q^{40} +(-1.62386 + 0.852270i) q^{41} +(-0.310178 + 0.817872i) q^{42} +(-0.0303490 - 0.249947i) q^{43} +(-7.28124 + 10.5487i) q^{44} +(-1.24128 + 0.305949i) q^{45} +(0.618313 - 0.895782i) q^{46} +(-2.15607 + 5.68510i) q^{47} +(11.6235 - 30.6487i) q^{48} +(-6.17834 - 3.24264i) q^{49} +(10.4642 + 5.49206i) q^{50} +(-15.5040 + 3.82140i) q^{51} +(-14.4674 + 13.6406i) q^{52} +(-9.96375 - 2.45584i) q^{53} +(6.38241 + 5.65432i) q^{54} +(-0.232538 + 1.91512i) q^{55} +(-1.27761 - 0.670539i) q^{56} +(9.12371 - 4.78849i) q^{57} +(4.03400 + 10.6368i) q^{58} +(-5.40729 - 4.79044i) q^{59} +(-1.17567 - 9.68249i) q^{60} +(10.9926 - 2.70942i) q^{61} +(18.5446 + 16.4291i) q^{62} +(-0.172643 + 0.152948i) q^{63} +(28.3441 + 14.8761i) q^{64} +(-0.973976 + 2.82982i) q^{65} +(-12.0210 + 6.30912i) q^{66} +(-2.87179 + 7.57230i) q^{67} +(-4.98153 - 41.0266i) q^{68} +(0.749130 - 0.393174i) q^{69} -0.340742 q^{70} +(-12.3077 + 6.45959i) q^{71} +(11.1081 - 9.84089i) q^{72} +(-1.16000 - 1.68056i) q^{73} +(2.73058 + 2.41908i) q^{74} +(5.21817 + 7.55982i) q^{75} +(9.45674 + 24.9354i) q^{76} +(0.123422 + 0.325436i) q^{77} +(-20.2824 + 5.67165i) q^{78} +(0.376038 - 0.991530i) q^{79} +12.7688 q^{80} +(3.98873 + 10.5174i) q^{81} +(0.605983 - 4.99072i) q^{82} +(-3.07692 - 1.61489i) q^{83} +(-0.999621 - 1.44820i) q^{84} +(-3.53352 - 5.11919i) q^{85} +(0.611155 + 0.320759i) q^{86} +(-1.06583 + 8.77794i) q^{87} +(-7.94113 - 20.9390i) q^{88} +5.53769 q^{89} +(1.24274 - 3.27684i) q^{90} +(0.0816681 + 0.533722i) q^{91} +(0.776474 + 2.04739i) q^{92} +(6.82877 + 18.0060i) q^{93} +(-9.46838 - 13.7173i) q^{94} +(3.00443 + 2.66169i) q^{95} +(27.7193 + 40.1583i) q^{96} +(1.99744 - 1.76958i) q^{97} +(16.9368 - 8.88910i) q^{98} -3.57979 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 156 q - 10 q^{2} - 9 q^{3} - 20 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - 14 q^{9} + q^{10} - q^{11} + 11 q^{12} - 65 q^{13} + 9 q^{14} - 41 q^{15} + 3 q^{17} - 13 q^{18} - 6 q^{19} + 29 q^{20} + 19 q^{21} - 22 q^{22} - 82 q^{23} - 31 q^{24} + 2 q^{25} + 26 q^{26} + 21 q^{27} + 43 q^{28} + 13 q^{29} - 81 q^{30} - 33 q^{31} - 93 q^{32} + 35 q^{33} - 24 q^{34} + 27 q^{35} + 54 q^{36} + 25 q^{37} - 56 q^{38} - 13 q^{39} - 52 q^{40} + 29 q^{41} - 63 q^{42} + 21 q^{43} + 45 q^{44} + 33 q^{46} - 69 q^{47} + 54 q^{48} - 54 q^{49} + 80 q^{50} - 16 q^{51} + 13 q^{52} - 45 q^{53} + 29 q^{54} - 83 q^{55} + 91 q^{56} - 11 q^{57} + 25 q^{58} - 57 q^{59} + 51 q^{60} + 39 q^{61} + 4 q^{62} + 26 q^{63} + 86 q^{64} + 65 q^{65} - 138 q^{66} - 101 q^{67} + 36 q^{68} + 32 q^{69} - 90 q^{70} + 20 q^{71} + 13 q^{72} + 61 q^{73} - 4 q^{74} - 67 q^{75} - 107 q^{76} + 67 q^{77} + 13 q^{78} + 57 q^{79} + 160 q^{80} + 78 q^{81} - 31 q^{82} - 59 q^{83} - 36 q^{84} - 61 q^{85} + 41 q^{86} - 9 q^{87} - 45 q^{88} - 66 q^{89} + 191 q^{90} + 39 q^{91} + 79 q^{92} - 80 q^{93} - 21 q^{94} - 28 q^{95} + 70 q^{96} + 7 q^{97} + 158 q^{98} + 130 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{9}{13}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.55724 + 2.25606i −1.10114 + 1.59527i −0.347892 + 0.937535i \(0.613102\pi\)
−0.753246 + 0.657739i \(0.771513\pi\)
\(3\) −1.88671 + 0.990222i −1.08929 + 0.571705i −0.911056 0.412283i \(-0.864731\pi\)
−0.178236 + 0.983988i \(0.557039\pi\)
\(4\) −1.95558 5.15643i −0.977789 2.57822i
\(5\) −0.621291 0.550416i −0.277850 0.246153i 0.512676 0.858582i \(-0.328654\pi\)
−0.790526 + 0.612429i \(0.790193\pi\)
\(6\) 0.704070 5.79854i 0.287436 2.36724i
\(7\) −0.145399 0.0358377i −0.0549558 0.0135454i 0.211742 0.977326i \(-0.432086\pi\)
−0.266698 + 0.963780i \(0.585933\pi\)
\(8\) 9.35521 + 2.30585i 3.30757 + 0.815242i
\(9\) 0.874940 1.26757i 0.291647 0.422523i
\(10\) 2.20927 0.544537i 0.698633 0.172198i
\(11\) −1.32031 1.91280i −0.398088 0.576730i 0.571766 0.820417i \(-0.306259\pi\)
−0.969854 + 0.243687i \(0.921643\pi\)
\(12\) 8.79562 + 7.79224i 2.53908 + 2.24942i
\(13\) −1.38245 3.32999i −0.383423 0.923573i
\(14\) 0.307274 0.272221i 0.0821225 0.0727542i
\(15\) 1.71723 + 0.423259i 0.443387 + 0.109285i
\(16\) −11.5147 + 10.2011i −2.87867 + 2.55028i
\(17\) 7.27623 + 1.79343i 1.76474 + 0.434970i 0.982233 0.187666i \(-0.0600921\pi\)
0.782512 + 0.622636i \(0.213938\pi\)
\(18\) 1.49721 + 3.94783i 0.352897 + 0.930512i
\(19\) −4.83578 −1.10940 −0.554702 0.832049i \(-0.687168\pi\)
−0.554702 + 0.832049i \(0.687168\pi\)
\(20\) −1.62320 + 4.28003i −0.362959 + 0.957043i
\(21\) 0.309814 0.0763622i 0.0676069 0.0166636i
\(22\) 6.37142 1.35839
\(23\) −0.397056 −0.0827919 −0.0413960 0.999143i \(-0.513181\pi\)
−0.0413960 + 0.999143i \(0.513181\pi\)
\(24\) −19.9339 + 4.91326i −4.06898 + 1.00291i
\(25\) −0.519638 4.27961i −0.103928 0.855921i
\(26\) 9.66546 + 2.06672i 1.89555 + 0.405317i
\(27\) 0.374927 3.08781i 0.0721548 0.594248i
\(28\) 0.0995449 + 0.819826i 0.0188122 + 0.154933i
\(29\) 2.35738 3.41526i 0.437755 0.634198i −0.540563 0.841303i \(-0.681789\pi\)
0.978319 + 0.207105i \(0.0664043\pi\)
\(30\) −3.62904 + 3.21505i −0.662569 + 0.586985i
\(31\) 1.08938 8.97185i 0.195658 1.61139i −0.482106 0.876113i \(-0.660128\pi\)
0.677765 0.735279i \(-0.262949\pi\)
\(32\) −2.76036 22.7336i −0.487967 4.01877i
\(33\) 4.38513 + 2.30149i 0.763353 + 0.400639i
\(34\) −15.3769 + 13.6228i −2.63712 + 2.33629i
\(35\) 0.0706097 + 0.102296i 0.0119352 + 0.0172911i
\(36\) −8.24715 2.03274i −1.37452 0.338790i
\(37\) 0.160405 1.32105i 0.0263704 0.217179i −0.973567 0.228403i \(-0.926650\pi\)
0.999937 + 0.0112236i \(0.00357266\pi\)
\(38\) 7.53049 10.9098i 1.22161 1.76980i
\(39\) 5.90571 + 4.91379i 0.945670 + 0.786836i
\(40\) −4.54313 6.58186i −0.718332 1.04068i
\(41\) −1.62386 + 0.852270i −0.253605 + 0.133102i −0.586736 0.809778i \(-0.699587\pi\)
0.333131 + 0.942881i \(0.391895\pi\)
\(42\) −0.310178 + 0.817872i −0.0478615 + 0.126200i
\(43\) −0.0303490 0.249947i −0.00462818 0.0381165i 0.990212 0.139573i \(-0.0445729\pi\)
−0.994840 + 0.101456i \(0.967650\pi\)
\(44\) −7.28124 + 10.5487i −1.09769 + 1.59028i
\(45\) −1.24128 + 0.305949i −0.185039 + 0.0456081i
\(46\) 0.618313 0.895782i 0.0911653 0.132076i
\(47\) −2.15607 + 5.68510i −0.314496 + 0.829257i 0.680808 + 0.732462i \(0.261629\pi\)
−0.995304 + 0.0967958i \(0.969141\pi\)
\(48\) 11.6235 30.6487i 1.67771 4.42375i
\(49\) −6.17834 3.24264i −0.882619 0.463234i
\(50\) 10.4642 + 5.49206i 1.47987 + 0.776695i
\(51\) −15.5040 + 3.82140i −2.17100 + 0.535103i
\(52\) −14.4674 + 13.6406i −2.00627 + 1.89161i
\(53\) −9.96375 2.45584i −1.36863 0.337336i −0.514540 0.857467i \(-0.672037\pi\)
−0.854087 + 0.520130i \(0.825883\pi\)
\(54\) 6.38241 + 5.65432i 0.868536 + 0.769456i
\(55\) −0.232538 + 1.91512i −0.0313554 + 0.258235i
\(56\) −1.27761 0.670539i −0.170727 0.0896045i
\(57\) 9.12371 4.78849i 1.20847 0.634251i
\(58\) 4.03400 + 10.6368i 0.529690 + 1.39668i
\(59\) −5.40729 4.79044i −0.703969 0.623662i 0.233245 0.972418i \(-0.425066\pi\)
−0.937214 + 0.348756i \(0.886604\pi\)
\(60\) −1.17567 9.68249i −0.151778 1.25000i
\(61\) 10.9926 2.70942i 1.40745 0.346906i 0.538845 0.842405i \(-0.318861\pi\)
0.868609 + 0.495499i \(0.165015\pi\)
\(62\) 18.5446 + 16.4291i 2.35516 + 2.08649i
\(63\) −0.172643 + 0.152948i −0.0217509 + 0.0192696i
\(64\) 28.3441 + 14.8761i 3.54301 + 1.85951i
\(65\) −0.973976 + 2.82982i −0.120807 + 0.350995i
\(66\) −12.0210 + 6.30912i −1.47969 + 0.776599i
\(67\) −2.87179 + 7.57230i −0.350846 + 0.925104i 0.637166 + 0.770726i \(0.280106\pi\)
−0.988012 + 0.154377i \(0.950663\pi\)
\(68\) −4.98153 41.0266i −0.604099 4.97520i
\(69\) 0.749130 0.393174i 0.0901846 0.0473325i
\(70\) −0.340742 −0.0407264
\(71\) −12.3077 + 6.45959i −1.46066 + 0.766612i −0.993091 0.117346i \(-0.962561\pi\)
−0.467566 + 0.883958i \(0.654869\pi\)
\(72\) 11.1081 9.84089i 1.30910 1.15976i
\(73\) −1.16000 1.68056i −0.135768 0.196694i 0.749202 0.662341i \(-0.230437\pi\)
−0.884971 + 0.465647i \(0.845822\pi\)
\(74\) 2.73058 + 2.41908i 0.317423 + 0.281213i
\(75\) 5.21817 + 7.55982i 0.602542 + 0.872933i
\(76\) 9.45674 + 24.9354i 1.08476 + 2.86028i
\(77\) 0.123422 + 0.325436i 0.0140652 + 0.0370869i
\(78\) −20.2824 + 5.67165i −2.29653 + 0.642187i
\(79\) 0.376038 0.991530i 0.0423076 0.111556i −0.912197 0.409751i \(-0.865615\pi\)
0.954505 + 0.298195i \(0.0963847\pi\)
\(80\) 12.7688 1.42760
\(81\) 3.98873 + 10.5174i 0.443192 + 1.16860i
\(82\) 0.605983 4.99072i 0.0669197 0.551133i
\(83\) −3.07692 1.61489i −0.337736 0.177257i 0.287326 0.957833i \(-0.407234\pi\)
−0.625061 + 0.780576i \(0.714926\pi\)
\(84\) −0.999621 1.44820i −0.109068 0.158012i
\(85\) −3.53352 5.11919i −0.383264 0.555254i
\(86\) 0.611155 + 0.320759i 0.0659026 + 0.0345883i
\(87\) −1.06583 + 8.77794i −0.114269 + 0.941094i
\(88\) −7.94113 20.9390i −0.846528 2.23211i
\(89\) 5.53769 0.586994 0.293497 0.955960i \(-0.405181\pi\)
0.293497 + 0.955960i \(0.405181\pi\)
\(90\) 1.24274 3.27684i 0.130997 0.345409i
\(91\) 0.0816681 + 0.533722i 0.00856114 + 0.0559493i
\(92\) 0.776474 + 2.04739i 0.0809530 + 0.213456i
\(93\) 6.82877 + 18.0060i 0.708111 + 1.86714i
\(94\) −9.46838 13.7173i −0.976589 1.41483i
\(95\) 3.00443 + 2.66169i 0.308248 + 0.273084i
\(96\) 27.7193 + 40.1583i 2.82909 + 4.09864i
\(97\) 1.99744 1.76958i 0.202810 0.179674i −0.555604 0.831447i \(-0.687513\pi\)
0.758414 + 0.651773i \(0.225975\pi\)
\(98\) 16.9368 8.88910i 1.71087 0.897935i
\(99\) −3.57979 −0.359783
\(100\) −21.0513 + 11.0486i −2.10513 + 1.10486i
\(101\) −1.75956 14.4913i −0.175083 1.44194i −0.769946 0.638109i \(-0.779717\pi\)
0.594863 0.803827i \(-0.297206\pi\)
\(102\) 15.5223 40.9288i 1.53693 4.05256i
\(103\) 10.1145 5.30849i 0.996610 0.523061i 0.114158 0.993463i \(-0.463583\pi\)
0.882453 + 0.470401i \(0.155891\pi\)
\(104\) −5.25464 34.3405i −0.515260 3.36736i
\(105\) −0.234516 0.123083i −0.0228864 0.0120117i
\(106\) 21.0565 18.6544i 2.04519 1.81188i
\(107\) 2.15561 + 1.90970i 0.208390 + 0.184618i 0.760862 0.648914i \(-0.224777\pi\)
−0.552471 + 0.833532i \(0.686315\pi\)
\(108\) −16.6553 + 4.10515i −1.60265 + 0.395019i
\(109\) −0.214892 1.76979i −0.0205829 0.169515i 0.978792 0.204854i \(-0.0656720\pi\)
−0.999375 + 0.0353389i \(0.988749\pi\)
\(110\) −3.95851 3.50693i −0.377429 0.334373i
\(111\) 1.00550 + 2.65128i 0.0954375 + 0.251648i
\(112\) 2.03982 1.07058i 0.192744 0.101160i
\(113\) 0.324550 + 0.170337i 0.0305311 + 0.0160239i 0.479920 0.877312i \(-0.340666\pi\)
−0.449389 + 0.893336i \(0.648358\pi\)
\(114\) −3.40473 + 28.0405i −0.318882 + 2.62623i
\(115\) 0.246687 + 0.218546i 0.0230037 + 0.0203795i
\(116\) −22.2206 5.47689i −2.06313 0.508516i
\(117\) −5.43055 1.16119i −0.502055 0.107352i
\(118\) 19.2280 4.73927i 1.77008 0.436285i
\(119\) −0.993687 0.521527i −0.0910911 0.0478083i
\(120\) 15.0891 + 7.91935i 1.37744 + 0.722935i
\(121\) 1.98508 5.23422i 0.180461 0.475838i
\(122\) −11.0055 + 29.0191i −0.996390 + 2.62727i
\(123\) 2.21982 3.21597i 0.200155 0.289974i
\(124\) −48.3931 + 11.9278i −4.34583 + 1.07115i
\(125\) −4.39029 + 6.36043i −0.392679 + 0.568894i
\(126\) −0.0762128 0.627669i −0.00678958 0.0559172i
\(127\) −3.19704 + 8.42990i −0.283691 + 0.748032i 0.715107 + 0.699015i \(0.246378\pi\)
−0.998798 + 0.0490171i \(0.984391\pi\)
\(128\) −37.1451 + 19.4953i −3.28319 + 1.72315i
\(129\) 0.304763 + 0.441525i 0.0268328 + 0.0388741i
\(130\) −4.86751 6.60406i −0.426909 0.579214i
\(131\) −5.21032 + 7.54845i −0.455227 + 0.659511i −0.981645 0.190715i \(-0.938919\pi\)
0.526418 + 0.850226i \(0.323535\pi\)
\(132\) 3.29204 27.1124i 0.286535 2.35983i
\(133\) 0.703119 + 0.173303i 0.0609682 + 0.0150273i
\(134\) −12.6115 18.2709i −1.08946 1.57836i
\(135\) −1.93252 + 1.71206i −0.166325 + 0.147351i
\(136\) 63.9352 + 33.5558i 5.48240 + 2.87739i
\(137\) 2.04284 + 16.8243i 0.174531 + 1.43740i 0.772061 + 0.635548i \(0.219226\pi\)
−0.597530 + 0.801847i \(0.703851\pi\)
\(138\) −0.279556 + 2.30235i −0.0237973 + 0.195989i
\(139\) 1.69393 1.50070i 0.143678 0.127287i −0.588223 0.808699i \(-0.700172\pi\)
0.731900 + 0.681412i \(0.238634\pi\)
\(140\) 0.389399 0.564142i 0.0329102 0.0476787i
\(141\) −1.56162 12.8611i −0.131512 1.08310i
\(142\) 4.59292 37.8261i 0.385429 3.17429i
\(143\) −4.54433 + 7.04096i −0.380016 + 0.588795i
\(144\) 2.85597 + 23.5210i 0.237998 + 1.96009i
\(145\) −3.34444 + 0.824329i −0.277740 + 0.0684568i
\(146\) 5.59784 0.463281
\(147\) 14.8677 1.22626
\(148\) −7.12560 + 1.75630i −0.585720 + 0.144367i
\(149\) 5.11549 13.4884i 0.419077 1.10502i −0.544776 0.838582i \(-0.683385\pi\)
0.963853 0.266435i \(-0.0858456\pi\)
\(150\) −25.1813 −2.05605
\(151\) −2.24776 5.92687i −0.182920 0.482321i 0.811921 0.583768i \(-0.198422\pi\)
−0.994841 + 0.101446i \(0.967653\pi\)
\(152\) −45.2397 11.1506i −3.66943 0.904432i
\(153\) 8.63956 7.65398i 0.698467 0.618788i
\(154\) −0.926401 0.228337i −0.0746515 0.0183999i
\(155\) −5.61507 + 4.97452i −0.451013 + 0.399563i
\(156\) 13.7886 40.0617i 1.10397 3.20750i
\(157\) 1.82181 + 1.61398i 0.145396 + 0.128810i 0.732686 0.680567i \(-0.238267\pi\)
−0.587290 + 0.809377i \(0.699805\pi\)
\(158\) 1.65137 + 2.39242i 0.131376 + 0.190331i
\(159\) 21.2305 5.23286i 1.68369 0.414993i
\(160\) −10.7979 + 15.6435i −0.853652 + 1.23673i
\(161\) 0.0577317 + 0.0142296i 0.00454990 + 0.00112145i
\(162\) −29.9393 7.37938i −2.35226 0.579779i
\(163\) 1.27512 10.5016i 0.0998754 0.822548i −0.853569 0.520980i \(-0.825567\pi\)
0.953444 0.301569i \(-0.0975102\pi\)
\(164\) 7.57026 + 6.70667i 0.591138 + 0.523703i
\(165\) −1.45766 3.84354i −0.113479 0.299219i
\(166\) 8.43480 4.42692i 0.654667 0.343596i
\(167\) 1.98794 2.88003i 0.153831 0.222863i −0.738489 0.674265i \(-0.764460\pi\)
0.892321 + 0.451402i \(0.149076\pi\)
\(168\) 3.07445 0.237199
\(169\) −9.17767 + 9.20709i −0.705974 + 0.708237i
\(170\) 17.0518 1.30781
\(171\) −4.23102 + 6.12968i −0.323554 + 0.468749i
\(172\) −1.22948 + 0.645283i −0.0937473 + 0.0492024i
\(173\) 5.40207 + 14.2441i 0.410712 + 1.08296i 0.967626 + 0.252388i \(0.0812159\pi\)
−0.556915 + 0.830570i \(0.688015\pi\)
\(174\) −18.1438 16.0740i −1.37548 1.21857i
\(175\) −0.0778163 + 0.640875i −0.00588236 + 0.0484456i
\(176\) 34.7156 + 8.55663i 2.61679 + 0.644981i
\(177\) 14.9456 + 3.68375i 1.12338 + 0.276888i
\(178\) −8.62354 + 12.4934i −0.646361 + 0.936416i
\(179\) 12.9084 3.18163i 0.964817 0.237806i 0.274721 0.961524i \(-0.411415\pi\)
0.690096 + 0.723718i \(0.257568\pi\)
\(180\) 4.00503 + 5.80228i 0.298517 + 0.432477i
\(181\) −0.434900 0.385288i −0.0323258 0.0286382i 0.646805 0.762655i \(-0.276105\pi\)
−0.679131 + 0.734017i \(0.737643\pi\)
\(182\) −1.33129 0.646888i −0.0986815 0.0479506i
\(183\) −18.0568 + 15.9970i −1.33480 + 1.18253i
\(184\) −3.71454 0.915553i −0.273840 0.0674954i
\(185\) −0.826786 + 0.732468i −0.0607865 + 0.0538521i
\(186\) −51.2566 12.6336i −3.75832 0.926343i
\(187\) −6.17640 16.2858i −0.451663 1.19094i
\(188\) 33.5312 2.44552
\(189\) −0.165174 + 0.435529i −0.0120147 + 0.0316800i
\(190\) −10.6836 + 2.63326i −0.775066 + 0.191037i
\(191\) 7.62088 0.551428 0.275714 0.961240i \(-0.411086\pi\)
0.275714 + 0.961240i \(0.411086\pi\)
\(192\) −68.2076 −4.92246
\(193\) −14.4892 + 3.57126i −1.04295 + 0.257065i −0.723346 0.690485i \(-0.757397\pi\)
−0.319607 + 0.947550i \(0.603551\pi\)
\(194\) 0.881769 + 7.26202i 0.0633073 + 0.521382i
\(195\) −0.964535 6.30349i −0.0690718 0.451402i
\(196\) −4.63825 + 38.1994i −0.331303 + 2.72853i
\(197\) −0.203270 1.67408i −0.0144824 0.119273i 0.983675 0.179956i \(-0.0575954\pi\)
−0.998157 + 0.0606824i \(0.980672\pi\)
\(198\) 5.57461 8.07622i 0.396170 0.573952i
\(199\) 15.3803 13.6258i 1.09028 0.965905i 0.0907311 0.995875i \(-0.471080\pi\)
0.999551 + 0.0299699i \(0.00954115\pi\)
\(200\) 5.00681 41.2348i 0.354035 2.91574i
\(201\) −2.08001 17.1304i −0.146713 1.20829i
\(202\) 35.4332 + 18.5968i 2.49307 + 1.30847i
\(203\) −0.465158 + 0.412094i −0.0326477 + 0.0289233i
\(204\) 50.0241 + 72.4724i 3.50239 + 5.07408i
\(205\) 1.47800 + 0.364293i 0.103228 + 0.0254433i
\(206\) −3.77446 + 31.0855i −0.262979 + 2.16583i
\(207\) −0.347400 + 0.503296i −0.0241460 + 0.0349815i
\(208\) 49.8881 + 24.2413i 3.45912 + 1.68083i
\(209\) 6.38472 + 9.24986i 0.441640 + 0.639826i
\(210\) 0.642881 0.337410i 0.0443630 0.0232835i
\(211\) −8.44004 + 22.2546i −0.581036 + 1.53207i 0.245624 + 0.969365i \(0.421007\pi\)
−0.826660 + 0.562702i \(0.809762\pi\)
\(212\) 6.82149 + 56.1800i 0.468502 + 3.85846i
\(213\) 16.8247 24.3747i 1.15281 1.67013i
\(214\) −7.66521 + 1.88930i −0.523983 + 0.129150i
\(215\) −0.118719 + 0.171994i −0.00809658 + 0.0117299i
\(216\) 10.6275 28.0225i 0.723113 1.90669i
\(217\) −0.479926 + 1.26546i −0.0325795 + 0.0859051i
\(218\) 4.32739 + 2.27119i 0.293088 + 0.153824i
\(219\) 3.85271 + 2.02206i 0.260342 + 0.136638i
\(220\) 10.3299 2.54610i 0.696445 0.171658i
\(221\) −4.08692 26.7091i −0.274916 1.79665i
\(222\) −7.54724 1.86023i −0.506537 0.124850i
\(223\) −10.1018 8.94942i −0.676467 0.599298i 0.253326 0.967381i \(-0.418476\pi\)
−0.929793 + 0.368083i \(0.880014\pi\)
\(224\) −0.413366 + 3.40438i −0.0276192 + 0.227464i
\(225\) −5.87935 3.08572i −0.391957 0.205715i
\(226\) −0.889693 + 0.466947i −0.0591815 + 0.0310608i
\(227\) 3.29021 + 8.67556i 0.218379 + 0.575817i 0.998776 0.0494669i \(-0.0157522\pi\)
−0.780397 + 0.625284i \(0.784983\pi\)
\(228\) −42.5337 37.6815i −2.81686 2.49552i
\(229\) 0.689428 + 5.67795i 0.0455587 + 0.375210i 0.997600 + 0.0692401i \(0.0220575\pi\)
−0.952041 + 0.305969i \(0.901019\pi\)
\(230\) −0.877205 + 0.216212i −0.0578412 + 0.0142566i
\(231\) −0.555115 0.491789i −0.0365239 0.0323573i
\(232\) 29.9289 26.5147i 1.96493 1.74077i
\(233\) −14.7828 7.75863i −0.968455 0.508285i −0.0951528 0.995463i \(-0.530334\pi\)
−0.873303 + 0.487178i \(0.838026\pi\)
\(234\) 11.0764 10.4434i 0.724087 0.682705i
\(235\) 4.46872 2.34537i 0.291507 0.152995i
\(236\) −14.1272 + 37.2504i −0.919603 + 2.42479i
\(237\) 0.272361 + 2.24309i 0.0176917 + 0.145704i
\(238\) 2.72401 1.42967i 0.176571 0.0926717i
\(239\) 7.69811 0.497949 0.248975 0.968510i \(-0.419906\pi\)
0.248975 + 0.968510i \(0.419906\pi\)
\(240\) −24.0911 + 12.6440i −1.55507 + 0.816165i
\(241\) −3.37147 + 2.98686i −0.217175 + 0.192401i −0.764695 0.644392i \(-0.777110\pi\)
0.547520 + 0.836793i \(0.315572\pi\)
\(242\) 8.71744 + 12.6294i 0.560379 + 0.811848i
\(243\) −10.9555 9.70569i −0.702793 0.622620i
\(244\) −35.4678 51.3839i −2.27059 3.28952i
\(245\) 2.05374 + 5.41528i 0.131209 + 0.345969i
\(246\) 3.79861 + 10.0161i 0.242190 + 0.638603i
\(247\) 6.68522 + 16.1031i 0.425370 + 1.02462i
\(248\) 30.8791 81.4216i 1.96083 5.17027i
\(249\) 7.40435 0.469232
\(250\) −7.51275 19.8095i −0.475148 1.25286i
\(251\) 2.18687 18.0105i 0.138034 1.13681i −0.744854 0.667227i \(-0.767481\pi\)
0.882888 0.469584i \(-0.155596\pi\)
\(252\) 1.12628 + 0.591118i 0.0709491 + 0.0372369i
\(253\) 0.524237 + 0.759488i 0.0329585 + 0.0477486i
\(254\) −14.0398 20.3401i −0.880933 1.27625i
\(255\) 11.7359 + 6.15946i 0.734929 + 0.385720i
\(256\) 6.14465 50.6058i 0.384041 3.16286i
\(257\) −1.36561 3.60082i −0.0851845 0.224613i 0.885655 0.464344i \(-0.153710\pi\)
−0.970839 + 0.239731i \(0.922941\pi\)
\(258\) −1.47069 −0.0915615
\(259\) −0.0706662 + 0.186332i −0.00439099 + 0.0115781i
\(260\) 16.4964 0.511682i 1.02307 0.0317332i
\(261\) −2.26651 5.97630i −0.140293 0.369923i
\(262\) −8.91599 23.5095i −0.550832 1.45242i
\(263\) 3.27118 + 4.73913i 0.201710 + 0.292227i 0.910764 0.412927i \(-0.135493\pi\)
−0.709055 + 0.705154i \(0.750878\pi\)
\(264\) 35.7169 + 31.6424i 2.19822 + 1.94746i
\(265\) 4.83865 + 7.01000i 0.297236 + 0.430621i
\(266\) −1.48591 + 1.31640i −0.0911071 + 0.0807138i
\(267\) −10.4480 + 5.48354i −0.639408 + 0.335587i
\(268\) 44.6621 2.72817
\(269\) −7.92266 + 4.15813i −0.483053 + 0.253526i −0.688627 0.725116i \(-0.741786\pi\)
0.205574 + 0.978642i \(0.434094\pi\)
\(270\) −0.853106 7.02596i −0.0519184 0.427587i
\(271\) 6.69340 17.6490i 0.406595 1.07210i −0.562799 0.826593i \(-0.690276\pi\)
0.969394 0.245509i \(-0.0789551\pi\)
\(272\) −102.079 + 53.5749i −6.18942 + 3.24846i
\(273\) −0.682587 0.926110i −0.0413121 0.0560507i
\(274\) −41.1377 21.5908i −2.48522 1.30434i
\(275\) −7.49994 + 6.64436i −0.452263 + 0.400670i
\(276\) −3.49235 3.09396i −0.210215 0.186234i
\(277\) −4.37358 + 1.07799i −0.262783 + 0.0647703i −0.368506 0.929625i \(-0.620131\pi\)
0.105723 + 0.994396i \(0.466284\pi\)
\(278\) 0.747785 + 6.15856i 0.0448492 + 0.369366i
\(279\) −10.4193 9.23069i −0.623787 0.552627i
\(280\) 0.424689 + 1.11981i 0.0253800 + 0.0669217i
\(281\) −7.69793 + 4.04018i −0.459220 + 0.241017i −0.678437 0.734659i \(-0.737342\pi\)
0.219217 + 0.975676i \(0.429650\pi\)
\(282\) 31.4473 + 16.5048i 1.87266 + 0.982847i
\(283\) 3.21640 26.4894i 0.191195 1.57463i −0.509055 0.860734i \(-0.670005\pi\)
0.700250 0.713898i \(-0.253072\pi\)
\(284\) 57.3771 + 50.8317i 3.40471 + 3.01631i
\(285\) −8.30414 2.04679i −0.491895 0.121241i
\(286\) −8.80817 21.2168i −0.520838 1.25457i
\(287\) 0.266652 0.0657239i 0.0157400 0.00387956i
\(288\) −31.2315 16.3916i −1.84034 0.965883i
\(289\) 34.6744 + 18.1985i 2.03967 + 1.07050i
\(290\) 3.34837 8.82892i 0.196623 0.518452i
\(291\) −2.01632 + 5.31660i −0.118199 + 0.311664i
\(292\) −6.39720 + 9.26794i −0.374368 + 0.542365i
\(293\) −16.7820 + 4.13639i −0.980415 + 0.241651i −0.696782 0.717283i \(-0.745386\pi\)
−0.283632 + 0.958933i \(0.591540\pi\)
\(294\) −23.1526 + 33.5423i −1.35029 + 1.95623i
\(295\) 0.722766 + 5.95251i 0.0420811 + 0.346569i
\(296\) 4.54677 11.9888i 0.264275 0.696837i
\(297\) −6.40136 + 3.35970i −0.371445 + 0.194949i
\(298\) 22.4646 + 32.5456i 1.30134 + 1.88532i
\(299\) 0.548910 + 1.32219i 0.0317443 + 0.0764644i
\(300\) 28.7772 41.6909i 1.66145 2.40703i
\(301\) −0.00454480 + 0.0374298i −0.000261958 + 0.00215742i
\(302\) 16.8717 + 4.15849i 0.970855 + 0.239294i
\(303\) 17.6694 + 25.5985i 1.01508 + 1.47059i
\(304\) 55.6825 49.3304i 3.19361 2.82929i
\(305\) −8.32089 4.36714i −0.476453 0.250062i
\(306\) 3.81392 + 31.4105i 0.218027 + 1.79562i
\(307\) 1.18177 9.73272i 0.0674469 0.555476i −0.919341 0.393461i \(-0.871278\pi\)
0.986788 0.162015i \(-0.0517992\pi\)
\(308\) 1.43673 1.27283i 0.0818653 0.0725263i
\(309\) −13.8265 + 20.0312i −0.786563 + 1.13953i
\(310\) −2.47876 20.4145i −0.140784 1.15946i
\(311\) −0.541815 + 4.46225i −0.0307235 + 0.253031i 0.969252 + 0.246069i \(0.0791391\pi\)
−0.999976 + 0.00696175i \(0.997784\pi\)
\(312\) 43.9187 + 59.5872i 2.48640 + 3.37346i
\(313\) 3.31513 + 27.3026i 0.187382 + 1.54323i 0.718255 + 0.695780i \(0.244941\pi\)
−0.530873 + 0.847452i \(0.678136\pi\)
\(314\) −6.47824 + 1.59674i −0.365588 + 0.0901094i
\(315\) 0.191446 0.0107868
\(316\) −5.84813 −0.328983
\(317\) −18.4364 + 4.54416i −1.03549 + 0.255225i −0.720198 0.693769i \(-0.755949\pi\)
−0.315293 + 0.948994i \(0.602103\pi\)
\(318\) −21.2555 + 56.0461i −1.19195 + 3.14291i
\(319\) −9.64517 −0.540026
\(320\) −9.42186 24.8434i −0.526698 1.38879i
\(321\) −5.95803 1.46852i −0.332545 0.0819650i
\(322\) −0.122005 + 0.108087i −0.00679908 + 0.00602346i
\(323\) −35.1862 8.67263i −1.95781 0.482558i
\(324\) 46.4321 41.1353i 2.57956 2.28529i
\(325\) −13.5327 + 7.64673i −0.750658 + 0.424164i
\(326\) 21.7065 + 19.2303i 1.20221 + 1.06507i
\(327\) 2.15792 + 3.12629i 0.119334 + 0.172884i
\(328\) −17.1568 + 4.22877i −0.947325 + 0.233495i
\(329\) 0.517233 0.749342i 0.0285160 0.0413125i
\(330\) 10.9412 + 2.69676i 0.602293 + 0.148452i
\(331\) −20.6936 5.10051i −1.13742 0.280349i −0.374744 0.927128i \(-0.622269\pi\)
−0.762677 + 0.646779i \(0.776116\pi\)
\(332\) −2.30993 + 19.0240i −0.126774 + 1.04408i
\(333\) −1.53418 1.35916i −0.0840725 0.0744817i
\(334\) 3.40180 + 8.96982i 0.186138 + 0.490807i
\(335\) 5.95213 3.12392i 0.325200 0.170678i
\(336\) −2.78843 + 4.03974i −0.152121 + 0.220386i
\(337\) 3.53075 0.192332 0.0961660 0.995365i \(-0.469342\pi\)
0.0961660 + 0.995365i \(0.469342\pi\)
\(338\) −6.47985 35.0430i −0.352458 1.90609i
\(339\) −0.781002 −0.0424182
\(340\) −19.4867 + 28.2314i −1.05681 + 1.53106i
\(341\) −18.5996 + 9.76184i −1.00723 + 0.528634i
\(342\) −7.24020 19.0908i −0.391505 1.03231i
\(343\) 1.56675 + 1.38802i 0.0845965 + 0.0749459i
\(344\) 0.292419 2.40828i 0.0157662 0.129846i
\(345\) −0.681837 0.168058i −0.0367088 0.00904792i
\(346\) −40.5478 9.99414i −2.17986 0.537288i
\(347\) 2.39386 3.46810i 0.128509 0.186178i −0.753448 0.657508i \(-0.771611\pi\)
0.881957 + 0.471330i \(0.156226\pi\)
\(348\) 47.3472 11.6700i 2.53807 0.625579i
\(349\) 4.71206 + 6.82659i 0.252231 + 0.365419i 0.928561 0.371179i \(-0.121046\pi\)
−0.676331 + 0.736598i \(0.736431\pi\)
\(350\) −1.32467 1.17356i −0.0708067 0.0627293i
\(351\) −10.8007 + 3.02023i −0.576498 + 0.161208i
\(352\) −39.8402 + 35.2953i −2.12349 + 1.88125i
\(353\) 22.0862 + 5.44375i 1.17553 + 0.289741i 0.778249 0.627956i \(-0.216108\pi\)
0.397279 + 0.917698i \(0.369955\pi\)
\(354\) −31.5847 + 27.9816i −1.67871 + 1.48720i
\(355\) 11.2021 + 2.76108i 0.594548 + 0.146543i
\(356\) −10.8294 28.5547i −0.573956 1.51340i
\(357\) 2.39123 0.126557
\(358\) −12.9235 + 34.0766i −0.683031 + 1.80100i
\(359\) 16.0009 3.94388i 0.844498 0.208150i 0.206749 0.978394i \(-0.433712\pi\)
0.637749 + 0.770244i \(0.279866\pi\)
\(360\) −12.3179 −0.649212
\(361\) 4.38476 0.230777
\(362\) 1.54648 0.381172i 0.0812810 0.0200340i
\(363\) 1.43777 + 11.8411i 0.0754634 + 0.621497i
\(364\) 2.59240 1.46485i 0.135878 0.0767791i
\(365\) −0.204304 + 1.68260i −0.0106938 + 0.0880713i
\(366\) −7.97117 65.6485i −0.416660 3.43150i
\(367\) 4.26193 6.17448i 0.222471 0.322305i −0.695816 0.718220i \(-0.744957\pi\)
0.918287 + 0.395915i \(0.129573\pi\)
\(368\) 4.57198 4.05042i 0.238331 0.211143i
\(369\) −0.340473 + 2.80404i −0.0177243 + 0.145973i
\(370\) −0.364983 3.00591i −0.0189746 0.156270i
\(371\) 1.36071 + 0.714157i 0.0706446 + 0.0370772i
\(372\) 79.4925 70.4242i 4.12150 3.65133i
\(373\) 6.26347 + 9.07421i 0.324310 + 0.469845i 0.950897 0.309507i \(-0.100164\pi\)
−0.626587 + 0.779352i \(0.715549\pi\)
\(374\) 46.3599 + 11.4267i 2.39721 + 0.590860i
\(375\) 1.98496 16.3476i 0.102503 0.844189i
\(376\) −33.2795 + 48.2137i −1.71626 + 2.48643i
\(377\) −14.6317 3.12864i −0.753573 0.161133i
\(378\) −0.725361 1.05087i −0.0373085 0.0540508i
\(379\) −19.6954 + 10.3369i −1.01168 + 0.530973i −0.887266 0.461257i \(-0.847399\pi\)
−0.124418 + 0.992230i \(0.539706\pi\)
\(380\) 7.84944 20.6973i 0.402668 1.06175i
\(381\) −2.31558 19.0705i −0.118631 0.977014i
\(382\) −11.8676 + 17.1932i −0.607198 + 0.879678i
\(383\) 34.1920 8.42758i 1.74713 0.430629i 0.769107 0.639119i \(-0.220701\pi\)
0.978024 + 0.208490i \(0.0668549\pi\)
\(384\) 50.7774 73.5638i 2.59122 3.75404i
\(385\) 0.102445 0.270124i 0.00522106 0.0137668i
\(386\) 14.5062 38.2497i 0.738347 1.94686i
\(387\) −0.343378 0.180219i −0.0174549 0.00916104i
\(388\) −13.0309 6.83913i −0.661543 0.347204i
\(389\) 26.8627 6.62106i 1.36199 0.335701i 0.510415 0.859929i \(-0.329492\pi\)
0.851578 + 0.524227i \(0.175646\pi\)
\(390\) 15.7231 + 7.64003i 0.796168 + 0.386868i
\(391\) −2.88907 0.712092i −0.146107 0.0360120i
\(392\) −50.3226 44.5819i −2.54167 2.25173i
\(393\) 2.35572 19.4011i 0.118830 0.978656i
\(394\) 4.09336 + 2.14836i 0.206220 + 0.108233i
\(395\) −0.779383 + 0.409052i −0.0392150 + 0.0205816i
\(396\) 7.00056 + 18.4590i 0.351791 + 0.927598i
\(397\) −2.99744 2.65550i −0.150437 0.133276i 0.584547 0.811360i \(-0.301272\pi\)
−0.734985 + 0.678084i \(0.762811\pi\)
\(398\) 6.78962 + 55.9175i 0.340333 + 2.80289i
\(399\) −1.49819 + 0.369271i −0.0750034 + 0.0184867i
\(400\) 49.6403 + 43.9775i 2.48202 + 2.19887i
\(401\) −13.9406 + 12.3503i −0.696162 + 0.616746i −0.935140 0.354279i \(-0.884726\pi\)
0.238978 + 0.971025i \(0.423188\pi\)
\(402\) 41.8864 + 21.9837i 2.08910 + 1.09644i
\(403\) −31.3822 + 8.77551i −1.56326 + 0.437139i
\(404\) −71.2824 + 37.4119i −3.54643 + 1.86131i
\(405\) 3.31079 8.72984i 0.164515 0.433789i
\(406\) −0.205343 1.69115i −0.0101910 0.0839305i
\(407\) −2.73869 + 1.43737i −0.135752 + 0.0712480i
\(408\) −153.855 −7.61695
\(409\) 34.0539 17.8729i 1.68386 0.883757i 0.698016 0.716082i \(-0.254066\pi\)
0.985842 0.167675i \(-0.0536258\pi\)
\(410\) −3.12347 + 2.76715i −0.154257 + 0.136660i
\(411\) −20.5140 29.7197i −1.01188 1.46596i
\(412\) −47.1526 41.7735i −2.32304 2.05803i
\(413\) 0.614538 + 0.890312i 0.0302394 + 0.0438094i
\(414\) −0.594478 1.56751i −0.0292170 0.0770389i
\(415\) 1.02280 + 2.69690i 0.0502073 + 0.132386i
\(416\) −71.8866 + 40.6200i −3.52453 + 1.99156i
\(417\) −1.70994 + 4.50875i −0.0837362 + 0.220794i
\(418\) −30.8108 −1.50701
\(419\) 7.77502 + 20.5010i 0.379835 + 1.00154i 0.979527 + 0.201311i \(0.0645203\pi\)
−0.599693 + 0.800230i \(0.704710\pi\)
\(420\) −0.176057 + 1.44996i −0.00859072 + 0.0707509i
\(421\) 20.9508 + 10.9958i 1.02108 + 0.535903i 0.890236 0.455500i \(-0.150540\pi\)
0.130842 + 0.991403i \(0.458232\pi\)
\(422\) −37.0644 53.6970i −1.80426 2.61393i
\(423\) 5.31982 + 7.70710i 0.258659 + 0.374732i
\(424\) −87.5501 45.9499i −4.25181 2.23152i
\(425\) 3.89417 32.0713i 0.188895 1.55569i
\(426\) 28.7907 + 75.9148i 1.39491 + 3.67809i
\(427\) −1.69541 −0.0820467
\(428\) 5.63179 14.8498i 0.272223 0.717793i
\(429\) 1.60173 17.7841i 0.0773322 0.858626i
\(430\) −0.203154 0.535674i −0.00979698 0.0258325i
\(431\) −0.347675 0.916743i −0.0167469 0.0441579i 0.926382 0.376585i \(-0.122902\pi\)
−0.943129 + 0.332427i \(0.892132\pi\)
\(432\) 27.1819 + 39.3798i 1.30779 + 1.89466i
\(433\) −23.6258 20.9306i −1.13538 1.00586i −0.999886 0.0150823i \(-0.995199\pi\)
−0.135495 0.990778i \(-0.543263\pi\)
\(434\) −2.10759 3.05337i −0.101168 0.146567i
\(435\) 5.49371 4.86700i 0.263403 0.233355i
\(436\) −8.70558 + 4.56904i −0.416922 + 0.218817i
\(437\) 1.92008 0.0918497
\(438\) −10.5615 + 5.54310i −0.504648 + 0.264860i
\(439\) 0.196796 + 1.62076i 0.00939255 + 0.0773546i 0.996651 0.0817678i \(-0.0260566\pi\)
−0.987259 + 0.159122i \(0.949134\pi\)
\(440\) −6.59143 + 17.3802i −0.314234 + 0.828567i
\(441\) −9.51594 + 4.99435i −0.453140 + 0.237826i
\(442\) 66.6216 + 32.3723i 3.16887 + 1.53979i
\(443\) 20.2970 + 10.6527i 0.964340 + 0.506125i 0.871948 0.489598i \(-0.162856\pi\)
0.0923918 + 0.995723i \(0.470549\pi\)
\(444\) 11.7048 10.3695i 0.555485 0.492117i
\(445\) −3.44052 3.04803i −0.163096 0.144491i
\(446\) 35.9214 8.85383i 1.70093 0.419241i
\(447\) 3.70510 + 30.5142i 0.175245 + 1.44327i
\(448\) −3.58808 3.17876i −0.169521 0.150183i
\(449\) −13.2843 35.0277i −0.626924 1.65306i −0.750614 0.660741i \(-0.770242\pi\)
0.123691 0.992321i \(-0.460527\pi\)
\(450\) 16.1171 8.45893i 0.759770 0.398758i
\(451\) 3.77422 + 1.98086i 0.177721 + 0.0932752i
\(452\) 0.243649 2.00663i 0.0114603 0.0943837i
\(453\) 10.1098 + 8.95649i 0.474999 + 0.420813i
\(454\) −24.6962 6.08707i −1.15905 0.285681i
\(455\) 0.243030 0.376548i 0.0113934 0.0176529i
\(456\) 96.3958 23.7594i 4.51414 1.11264i
\(457\) 20.6764 + 10.8518i 0.967199 + 0.507625i 0.872890 0.487918i \(-0.162243\pi\)
0.0943094 + 0.995543i \(0.469936\pi\)
\(458\) −13.8834 7.28657i −0.648728 0.340479i
\(459\) 8.26582 21.7952i 0.385815 1.01731i
\(460\) 0.644502 1.69941i 0.0300500 0.0792354i
\(461\) 6.81226 9.86926i 0.317278 0.459657i −0.631602 0.775293i \(-0.717602\pi\)
0.948880 + 0.315636i \(0.102218\pi\)
\(462\) 1.97395 0.486536i 0.0918367 0.0226357i
\(463\) 16.3870 23.7407i 0.761570 1.10333i −0.229928 0.973208i \(-0.573849\pi\)
0.991499 0.130118i \(-0.0415355\pi\)
\(464\) 7.69496 + 63.3737i 0.357229 + 2.94205i
\(465\) 5.66813 14.9456i 0.262853 0.693087i
\(466\) 40.5244 21.2688i 1.87726 0.985260i
\(467\) −16.6690 24.1492i −0.771348 1.11749i −0.989914 0.141668i \(-0.954753\pi\)
0.218566 0.975822i \(-0.429862\pi\)
\(468\) 4.63226 + 30.2731i 0.214127 + 1.39937i
\(469\) 0.688931 0.998089i 0.0318119 0.0460875i
\(470\) −1.66761 + 13.7340i −0.0769211 + 0.633502i
\(471\) −5.03543 1.24112i −0.232020 0.0571878i
\(472\) −39.5403 57.2840i −1.81999 2.63671i
\(473\) −0.438027 + 0.388058i −0.0201405 + 0.0178429i
\(474\) −5.48467 2.87858i −0.251919 0.132218i
\(475\) 2.51286 + 20.6952i 0.115298 + 0.949563i
\(476\) −0.745988 + 6.14377i −0.0341923 + 0.281599i
\(477\) −11.8306 + 10.4810i −0.541688 + 0.479893i
\(478\) −11.9878 + 17.3674i −0.548311 + 0.794365i
\(479\) −3.50884 28.8979i −0.160323 1.32038i −0.821526 0.570171i \(-0.806877\pi\)
0.661203 0.750207i \(-0.270046\pi\)
\(480\) 4.88203 40.2071i 0.222833 1.83520i
\(481\) −4.62084 + 1.29214i −0.210692 + 0.0589166i
\(482\) −1.48833 12.2575i −0.0677916 0.558314i
\(483\) −0.123013 + 0.0303201i −0.00559731 + 0.00137961i
\(484\) −30.8718 −1.40327
\(485\) −2.21500 −0.100578
\(486\) 38.9569 9.60202i 1.76712 0.435557i
\(487\) −4.11457 + 10.8492i −0.186449 + 0.491625i −0.995351 0.0963187i \(-0.969293\pi\)
0.808902 + 0.587944i \(0.200062\pi\)
\(488\) 109.085 4.93806
\(489\) 7.99311 + 21.0761i 0.361461 + 0.953095i
\(490\) −15.4154 3.79954i −0.696395 0.171646i
\(491\) −29.3736 + 26.0227i −1.32561 + 1.17439i −0.354692 + 0.934983i \(0.615414\pi\)
−0.970919 + 0.239406i \(0.923047\pi\)
\(492\) −20.9240 5.15730i −0.943326 0.232509i
\(493\) 23.2779 20.6224i 1.04838 0.928787i
\(494\) −46.7400 9.99421i −2.10293 0.449661i
\(495\) 2.22409 + 1.97037i 0.0999656 + 0.0885618i
\(496\) 78.9791 + 114.421i 3.54627 + 5.13765i
\(497\) 2.02103 0.498140i 0.0906557 0.0223446i
\(498\) −11.5304 + 16.7046i −0.516689 + 0.748553i
\(499\) 9.46133 + 2.33201i 0.423547 + 0.104395i 0.445328 0.895368i \(-0.353087\pi\)
−0.0217802 + 0.999763i \(0.506933\pi\)
\(500\) 41.3827 + 10.1999i 1.85069 + 0.456154i
\(501\) −0.898800 + 7.40228i −0.0401554 + 0.330710i
\(502\) 37.2272 + 32.9804i 1.66153 + 1.47199i
\(503\) 9.23093 + 24.3400i 0.411587 + 1.08527i 0.967243 + 0.253853i \(0.0816980\pi\)
−0.555656 + 0.831412i \(0.687533\pi\)
\(504\) −1.96778 + 1.03277i −0.0876520 + 0.0460033i
\(505\) −6.88303 + 9.97179i −0.306291 + 0.443739i
\(506\) −2.52981 −0.112464
\(507\) 8.19853 26.4590i 0.364110 1.17509i
\(508\) 49.7203 2.20598
\(509\) 8.24859 11.9501i 0.365612 0.529681i −0.596400 0.802688i \(-0.703403\pi\)
0.962012 + 0.273006i \(0.0880181\pi\)
\(510\) −32.1717 + 16.8850i −1.42459 + 0.747681i
\(511\) 0.108437 + 0.285924i 0.00479695 + 0.0126485i
\(512\) 41.8004 + 37.0319i 1.84733 + 1.63660i
\(513\) −1.81307 + 14.9319i −0.0800488 + 0.659261i
\(514\) 10.2502 + 2.52646i 0.452119 + 0.111437i
\(515\) −9.20592 2.26906i −0.405661 0.0999866i
\(516\) 1.68071 2.43492i 0.0739890 0.107192i
\(517\) 13.7211 3.38195i 0.603455 0.148738i
\(518\) −0.310330 0.449591i −0.0136351 0.0197539i
\(519\) −24.2969 21.5252i −1.06652 0.944852i
\(520\) −15.6369 + 24.2277i −0.685722 + 1.06245i
\(521\) −0.134622 + 0.119265i −0.00589791 + 0.00522509i −0.666066 0.745892i \(-0.732023\pi\)
0.660169 + 0.751117i \(0.270485\pi\)
\(522\) 17.0124 + 4.19317i 0.744611 + 0.183530i
\(523\) 27.2051 24.1016i 1.18960 1.05389i 0.192231 0.981350i \(-0.438428\pi\)
0.997365 0.0725411i \(-0.0231109\pi\)
\(524\) 49.1122 + 12.1051i 2.14548 + 0.528813i
\(525\) −0.487792 1.28620i −0.0212890 0.0561344i
\(526\) −15.7858 −0.688293
\(527\) 24.0169 63.3275i 1.04619 2.75859i
\(528\) −73.9713 + 18.2323i −3.21919 + 0.793458i
\(529\) −22.8423 −0.993145
\(530\) −23.3499 −1.01426
\(531\) −10.8033 + 2.66277i −0.468822 + 0.115554i
\(532\) −0.481377 3.96450i −0.0208703 0.171883i
\(533\) 5.08296 + 4.22923i 0.220167 + 0.183188i
\(534\) 3.89892 32.1105i 0.168723 1.38956i
\(535\) −0.288130 2.37296i −0.0124569 0.102592i
\(536\) −44.3268 + 64.2185i −1.91463 + 2.77382i
\(537\) −21.2038 + 18.7849i −0.915012 + 0.810630i
\(538\) 2.95653 24.3492i 0.127465 1.04977i
\(539\) 1.95480 + 16.0992i 0.0841990 + 0.693441i
\(540\) 12.6073 + 6.61682i 0.542532 + 0.284743i
\(541\) −31.3245 + 27.7511i −1.34675 + 1.19311i −0.383802 + 0.923415i \(0.625386\pi\)
−0.962945 + 0.269698i \(0.913076\pi\)
\(542\) 29.3940 + 42.5845i 1.26258 + 1.82916i
\(543\) 1.20205 + 0.296279i 0.0515849 + 0.0127145i
\(544\) 20.6861 170.365i 0.886909 7.30435i
\(545\) −0.840611 + 1.21784i −0.0360078 + 0.0521664i
\(546\) 3.15231 0.0977775i 0.134907 0.00418449i
\(547\) −17.2970 25.0590i −0.739565 1.07145i −0.994526 0.104494i \(-0.966678\pi\)
0.254960 0.966952i \(-0.417938\pi\)
\(548\) 82.7583 43.4349i 3.53526 1.85545i
\(549\) 6.18345 16.3044i 0.263903 0.695856i
\(550\) −3.31084 27.2672i −0.141175 1.16268i
\(551\) −11.3998 + 16.5154i −0.485647 + 0.703582i
\(552\) 7.91486 1.95084i 0.336879 0.0830332i
\(553\) −0.0902099 + 0.130692i −0.00383612 + 0.00555757i
\(554\) 4.37873 11.5458i 0.186034 0.490532i
\(555\) 0.834599 2.20066i 0.0354267 0.0934126i
\(556\) −11.0509 5.79994i −0.468661 0.245972i
\(557\) 19.7792 + 10.3809i 0.838071 + 0.439854i 0.828425 0.560100i \(-0.189237\pi\)
0.00964615 + 0.999953i \(0.496929\pi\)
\(558\) 37.0504 9.13209i 1.56847 0.386592i
\(559\) −0.790364 + 0.446601i −0.0334288 + 0.0188892i
\(560\) −1.85658 0.457606i −0.0784549 0.0193374i
\(561\) 27.7796 + 24.6106i 1.17286 + 1.03906i
\(562\) 2.87266 23.6585i 0.121176 0.997975i
\(563\) −2.45956 1.29088i −0.103658 0.0544039i 0.412097 0.911140i \(-0.364796\pi\)
−0.515755 + 0.856736i \(0.672489\pi\)
\(564\) −63.2637 + 33.2033i −2.66388 + 1.39811i
\(565\) −0.107884 0.284466i −0.00453870 0.0119676i
\(566\) 54.7529 + 48.5069i 2.30144 + 2.03890i
\(567\) −0.203039 1.67217i −0.00852682 0.0702247i
\(568\) −130.036 + 32.0510i −5.45619 + 1.34483i
\(569\) −20.6238 18.2711i −0.864596 0.765965i 0.109048 0.994036i \(-0.465220\pi\)
−0.973645 + 0.228071i \(0.926758\pi\)
\(570\) 17.5492 15.5473i 0.735057 0.651204i
\(571\) −14.4914 7.60566i −0.606445 0.318287i 0.133402 0.991062i \(-0.457410\pi\)
−0.739847 + 0.672775i \(0.765102\pi\)
\(572\) 45.1930 + 9.66342i 1.88962 + 0.404048i
\(573\) −14.3784 + 7.54636i −0.600666 + 0.315254i
\(574\) −0.266966 + 0.703931i −0.0111429 + 0.0293815i
\(575\) 0.206326 + 1.69924i 0.00860437 + 0.0708634i
\(576\) 43.6558 22.9124i 1.81899 0.954681i
\(577\) 25.9049 1.07843 0.539217 0.842167i \(-0.318720\pi\)
0.539217 + 0.842167i \(0.318720\pi\)
\(578\) −95.0533 + 49.8878i −3.95370 + 2.07506i
\(579\) 23.8005 21.0854i 0.989116 0.876280i
\(580\) 10.7909 + 15.6333i 0.448068 + 0.649138i
\(581\) 0.389508 + 0.345074i 0.0161595 + 0.0143161i
\(582\) −8.85465 12.8282i −0.367037 0.531745i
\(583\) 8.45769 + 22.3011i 0.350282 + 0.923617i
\(584\) −6.97697 18.3967i −0.288709 0.761263i
\(585\) 2.73482 + 3.71050i 0.113071 + 0.153410i
\(586\) 16.8017 44.3025i 0.694073 1.83012i
\(587\) −3.55521 −0.146739 −0.0733695 0.997305i \(-0.523375\pi\)
−0.0733695 + 0.997305i \(0.523375\pi\)
\(588\) −29.0748 76.6641i −1.19903 3.16157i
\(589\) −5.26800 + 43.3859i −0.217064 + 1.78768i
\(590\) −14.5547 7.63892i −0.599209 0.314489i
\(591\) 2.04122 + 2.95722i 0.0839645 + 0.121644i
\(592\) 11.6292 + 16.8478i 0.477957 + 0.692441i
\(593\) −4.86838 2.55512i −0.199920 0.104926i 0.361792 0.932259i \(-0.382165\pi\)
−0.561713 + 0.827332i \(0.689857\pi\)
\(594\) 2.38882 19.6737i 0.0980145 0.807222i
\(595\) 0.330312 + 0.870961i 0.0135415 + 0.0357059i
\(596\) −79.5560 −3.25874
\(597\) −15.5257 + 40.9378i −0.635423 + 1.67547i
\(598\) −3.83773 0.820604i −0.156936 0.0335570i
\(599\) 9.39088 + 24.7617i 0.383701 + 1.01174i 0.978205 + 0.207643i \(0.0665794\pi\)
−0.594504 + 0.804093i \(0.702651\pi\)
\(600\) 31.3852 + 82.7560i 1.28130 + 3.37850i
\(601\) −6.56145 9.50591i −0.267647 0.387754i 0.665998 0.745954i \(-0.268006\pi\)
−0.933645 + 0.358200i \(0.883391\pi\)
\(602\) −0.0773663 0.0685406i −0.00315322 0.00279351i
\(603\) 7.08577 + 10.2655i 0.288555 + 0.418044i
\(604\) −26.1658 + 23.1809i −1.06467 + 0.943217i
\(605\) −4.11431 + 2.15935i −0.167270 + 0.0877902i
\(606\) −85.2671 −3.46374
\(607\) −3.46802 + 1.82016i −0.140763 + 0.0738779i −0.533634 0.845715i \(-0.679174\pi\)
0.392871 + 0.919593i \(0.371482\pi\)
\(608\) 13.3485 + 109.935i 0.541352 + 4.45844i
\(609\) 0.469553 1.23811i 0.0190273 0.0501707i
\(610\) 22.8102 11.9717i 0.923557 0.484720i
\(611\) 21.9120 0.679660i 0.886464 0.0274961i
\(612\) −56.3626 29.5813i −2.27832 1.19576i
\(613\) −7.53170 + 6.67251i −0.304203 + 0.269500i −0.801389 0.598144i \(-0.795905\pi\)
0.497186 + 0.867644i \(0.334367\pi\)
\(614\) 20.1173 + 17.8224i 0.811867 + 0.719252i
\(615\) −3.14928 + 0.776227i −0.126991 + 0.0313005i
\(616\) 0.404228 + 3.32912i 0.0162868 + 0.134134i
\(617\) 0.857525 + 0.759701i 0.0345226 + 0.0305844i 0.680208 0.733019i \(-0.261890\pi\)
−0.645685 + 0.763604i \(0.723428\pi\)
\(618\) −23.6602 62.3869i −0.951753 2.50957i
\(619\) 26.6766 14.0010i 1.07222 0.562747i 0.166252 0.986083i \(-0.446834\pi\)
0.905972 + 0.423337i \(0.139141\pi\)
\(620\) 36.6315 + 19.2257i 1.47116 + 0.772122i
\(621\) −0.148867 + 1.22603i −0.00597384 + 0.0491990i
\(622\) −9.22336 8.17118i −0.369823 0.327635i
\(623\) −0.805177 0.198458i −0.0322587 0.00795106i
\(624\) −118.129 + 3.66408i −4.72893 + 0.146681i
\(625\) −14.7003 + 3.62330i −0.588013 + 0.144932i
\(626\) −66.7586 35.0376i −2.66821 1.40038i
\(627\) −21.2055 11.1295i −0.846867 0.444470i
\(628\) 4.75970 12.5503i 0.189933 0.500812i
\(629\) 3.53635 9.32460i 0.141004 0.371796i
\(630\) −0.298129 + 0.431914i −0.0118777 + 0.0172079i
\(631\) 37.3678 9.21033i 1.48759 0.366657i 0.589967 0.807427i \(-0.299141\pi\)
0.897620 + 0.440770i \(0.145295\pi\)
\(632\) 5.80423 8.40889i 0.230880 0.334488i
\(633\) −6.11304 50.3454i −0.242971 2.00105i
\(634\) 18.4581 48.6699i 0.733063 1.93293i
\(635\) 6.62624 3.47772i 0.262954 0.138009i
\(636\) −68.5008 99.2406i −2.71623 3.93514i
\(637\) −2.25672 + 25.0566i −0.0894146 + 0.992778i
\(638\) 15.0199 21.7601i 0.594643 0.861489i
\(639\) −2.58054 + 21.2526i −0.102084 + 0.840741i
\(640\) 33.8084 + 8.33303i 1.33640 + 0.329392i
\(641\) −3.77228 5.46509i −0.148996 0.215858i 0.741378 0.671088i \(-0.234173\pi\)
−0.890374 + 0.455230i \(0.849557\pi\)
\(642\) 12.5912 11.1548i 0.496935 0.440246i
\(643\) 12.4590 + 6.53900i 0.491336 + 0.257873i 0.692146 0.721757i \(-0.256665\pi\)
−0.200810 + 0.979630i \(0.564358\pi\)
\(644\) −0.0395249 0.325517i −0.00155750 0.0128272i
\(645\) 0.0536760 0.442062i 0.00211349 0.0174062i
\(646\) 74.3595 65.8768i 2.92564 2.59189i
\(647\) −17.4544 + 25.2871i −0.686205 + 0.994139i 0.312812 + 0.949815i \(0.398729\pi\)
−0.999017 + 0.0443243i \(0.985887\pi\)
\(648\) 13.0638 + 107.590i 0.513195 + 4.22654i
\(649\) −2.02385 + 16.6679i −0.0794431 + 0.654272i
\(650\) 3.82221 42.4383i 0.149919 1.66457i
\(651\) −0.347606 2.86279i −0.0136237 0.112202i
\(652\) −56.6444 + 13.9616i −2.21836 + 0.546778i
\(653\) −34.4778 −1.34922 −0.674610 0.738174i \(-0.735688\pi\)
−0.674610 + 0.738174i \(0.735688\pi\)
\(654\) −10.4135 −0.407201
\(655\) 7.39191 1.82194i 0.288826 0.0711891i
\(656\) 10.0042 26.3789i 0.390598 1.02992i
\(657\) −3.14515 −0.122704
\(658\) 0.885100 + 2.33382i 0.0345048 + 0.0909816i
\(659\) 10.8350 + 2.67060i 0.422073 + 0.104032i 0.444631 0.895714i \(-0.353335\pi\)
−0.0225578 + 0.999746i \(0.507181\pi\)
\(660\) −16.9684 + 15.0327i −0.660494 + 0.585147i
\(661\) 37.0081 + 9.12167i 1.43945 + 0.354792i 0.880356 0.474314i \(-0.157304\pi\)
0.559092 + 0.829106i \(0.311150\pi\)
\(662\) 43.7320 38.7431i 1.69969 1.50580i
\(663\) 34.1587 + 46.3453i 1.32662 + 1.79990i
\(664\) −25.0615 22.2026i −0.972575 0.861626i
\(665\) −0.341453 0.494680i −0.0132410 0.0191829i
\(666\) 5.45545 1.34465i 0.211394 0.0521040i
\(667\) −0.936014 + 1.35605i −0.0362426 + 0.0525065i
\(668\) −18.7383 4.61856i −0.725005 0.178698i
\(669\) 27.9211 + 6.88193i 1.07949 + 0.266071i
\(670\) −2.22118 + 18.2931i −0.0858117 + 0.706723i
\(671\) −19.6962 17.4493i −0.760362 0.673622i
\(672\) −2.59118 6.83239i −0.0999571 0.263565i
\(673\) −23.2137 + 12.1835i −0.894822 + 0.469639i −0.848444 0.529285i \(-0.822460\pi\)
−0.0463782 + 0.998924i \(0.514768\pi\)
\(674\) −5.49824 + 7.96557i −0.211784 + 0.306822i
\(675\) −13.4094 −0.516129
\(676\) 65.4234 + 29.3189i 2.51628 + 1.12765i
\(677\) 14.1413 0.543493 0.271747 0.962369i \(-0.412399\pi\)
0.271747 + 0.962369i \(0.412399\pi\)
\(678\) 1.21621 1.76199i 0.0467083 0.0676687i
\(679\) −0.353845 + 0.185712i −0.0135793 + 0.00712698i
\(680\) −21.2527 56.0389i −0.815006 2.14899i
\(681\) −14.7984 13.1102i −0.567076 0.502385i
\(682\) 6.94090 57.1634i 0.265781 2.18890i
\(683\) −9.76963 2.40800i −0.373825 0.0921395i 0.0479272 0.998851i \(-0.484738\pi\)
−0.421752 + 0.906711i \(0.638585\pi\)
\(684\) 39.8814 + 9.82988i 1.52490 + 0.375855i
\(685\) 7.99115 11.5772i 0.305326 0.442341i
\(686\) −5.57126 + 1.37319i −0.212712 + 0.0524287i
\(687\) −6.92318 10.0300i −0.264136 0.382667i
\(688\) 2.89920 + 2.56847i 0.110531 + 0.0979219i
\(689\) 5.59645 + 36.5743i 0.213208 + 1.39337i
\(690\) 1.44093 1.27656i 0.0548554 0.0485976i
\(691\) 10.0675 + 2.48141i 0.382984 + 0.0943971i 0.426107 0.904673i \(-0.359885\pi\)
−0.0431231 + 0.999070i \(0.513731\pi\)
\(692\) 62.8845 55.7108i 2.39051 2.11781i
\(693\) 0.520500 + 0.128292i 0.0197722 + 0.00487340i
\(694\) 4.09642 + 10.8014i 0.155498 + 0.410014i
\(695\) −1.87843 −0.0712530
\(696\) −30.2117 + 79.6618i −1.14517 + 3.01957i
\(697\) −13.3441 + 3.28902i −0.505444 + 0.124581i
\(698\) −22.7390 −0.860684
\(699\) 35.5737 1.34552
\(700\) 3.45681 0.852026i 0.130655 0.0322036i
\(701\) 2.84762 + 23.4523i 0.107553 + 0.885780i 0.942213 + 0.335014i \(0.108741\pi\)
−0.834660 + 0.550766i \(0.814336\pi\)
\(702\) 10.0055 29.0702i 0.377632 1.09718i
\(703\) −0.775682 + 6.38831i −0.0292554 + 0.240940i
\(704\) −8.96792 73.8575i −0.337991 2.78361i
\(705\) −6.10875 + 8.85005i −0.230069 + 0.333312i
\(706\) −46.6749 + 41.3504i −1.75663 + 1.55624i
\(707\) −0.263496 + 2.17008i −0.00990977 + 0.0816143i
\(708\) −10.2322 84.2697i −0.384550 3.16705i
\(709\) 44.0347 + 23.1112i 1.65376 + 0.867959i 0.993100 + 0.117271i \(0.0374146\pi\)
0.660657 + 0.750688i \(0.270278\pi\)
\(710\) −23.6736 + 20.9730i −0.888455 + 0.787102i
\(711\) −0.927823 1.34418i −0.0347961 0.0504108i
\(712\) 51.8062 + 12.7691i 1.94152 + 0.478542i
\(713\) −0.432545 + 3.56233i −0.0161989 + 0.133410i
\(714\) −3.72372 + 5.39474i −0.139357 + 0.201893i
\(715\) 6.69881 1.87321i 0.250521 0.0700541i
\(716\) −41.6491 60.3392i −1.55650 2.25498i
\(717\) −14.5241 + 7.62283i −0.542412 + 0.284680i
\(718\) −16.0198 + 42.2406i −0.597852 + 1.57641i
\(719\) 3.36354 + 27.7012i 0.125439 + 1.03308i 0.910456 + 0.413607i \(0.135731\pi\)
−0.785017 + 0.619474i \(0.787346\pi\)
\(720\) 11.1720 16.1854i 0.416355 0.603194i
\(721\) −1.66089 + 0.409372i −0.0618546 + 0.0152458i
\(722\) −6.82814 + 9.89228i −0.254117 + 0.368152i
\(723\) 3.40333 8.97384i 0.126571 0.333741i
\(724\) −1.13623 + 2.99599i −0.0422276 + 0.111345i
\(725\) −15.8410 8.31398i −0.588319 0.308773i
\(726\) −28.9532 15.1958i −1.07455 0.563969i
\(727\) 30.9503 7.62855i 1.14788 0.282927i 0.380912 0.924611i \(-0.375610\pi\)
0.766969 + 0.641684i \(0.221764\pi\)
\(728\) −0.466663 + 5.18140i −0.0172957 + 0.192035i
\(729\) −2.48402 0.612255i −0.0920007 0.0226761i
\(730\) −3.47789 3.08114i −0.128722 0.114038i
\(731\) 0.227435 1.87310i 0.00841200 0.0692791i
\(732\) 117.799 + 61.8256i 4.35397 + 2.28514i
\(733\) −21.2364 + 11.1457i −0.784383 + 0.411676i −0.808843 0.588025i \(-0.799906\pi\)
0.0244599 + 0.999701i \(0.492213\pi\)
\(734\) 7.29310 + 19.2303i 0.269193 + 0.709805i
\(735\) −9.23714 8.18339i −0.340717 0.301849i
\(736\) 1.09602 + 9.02651i 0.0403997 + 0.332722i
\(737\) 18.2759 4.50461i 0.673202 0.165929i
\(738\) −5.79589 5.13471i −0.213350 0.189011i
\(739\) −12.8967 + 11.4254i −0.474411 + 0.420292i −0.866149 0.499785i \(-0.833412\pi\)
0.391738 + 0.920077i \(0.371874\pi\)
\(740\) 5.39377 + 2.83087i 0.198279 + 0.104065i
\(741\) −28.5587 23.7620i −1.04913 0.872919i
\(742\) −3.73014 + 1.95773i −0.136938 + 0.0718705i
\(743\) 8.38052 22.0976i 0.307452 0.810683i −0.688862 0.724893i \(-0.741889\pi\)
0.996313 0.0857904i \(-0.0273415\pi\)
\(744\) 22.3654 + 184.196i 0.819957 + 6.75295i
\(745\) −10.6025 + 5.56460i −0.388444 + 0.203871i
\(746\) −30.2257 −1.10664
\(747\) −4.73910 + 2.48727i −0.173395 + 0.0910046i
\(748\) −71.8983 + 63.6964i −2.62886 + 2.32897i
\(749\) −0.244985 0.354922i −0.00895155 0.0129686i
\(750\) 33.7902 + 29.9355i 1.23384 + 1.09309i
\(751\) 5.25016 + 7.60616i 0.191581 + 0.277553i 0.906989 0.421154i \(-0.138375\pi\)
−0.715408 + 0.698707i \(0.753759\pi\)
\(752\) −33.1679 87.4566i −1.20951 3.18921i
\(753\) 13.7084 + 36.1460i 0.499561 + 1.31723i
\(754\) 29.8436 28.1380i 1.08684 1.02473i
\(755\) −1.86573 + 4.91951i −0.0679007 + 0.179039i
\(756\) 2.56878 0.0934258
\(757\) 1.08290 + 2.85536i 0.0393586 + 0.103780i 0.953255 0.302168i \(-0.0977105\pi\)
−0.913896 + 0.405948i \(0.866941\pi\)
\(758\) 7.34980 60.5311i 0.266957 2.19859i
\(759\) −1.74114 0.913822i −0.0631995 0.0331697i
\(760\) 21.9696 + 31.8284i 0.796920 + 1.15454i
\(761\) −17.9798 26.0482i −0.651766 0.944246i −0.999977 0.00683006i \(-0.997826\pi\)
0.348210 0.937416i \(-0.386789\pi\)
\(762\) 46.6302 + 24.4734i 1.68923 + 0.886578i
\(763\) −0.0321802 + 0.265028i −0.00116500 + 0.00959466i
\(764\) −14.9032 39.2966i −0.539180 1.42170i
\(765\) −9.58055 −0.346386
\(766\) −34.2323 + 90.2630i −1.23686 + 3.26134i
\(767\) −8.47681 + 24.6288i −0.306080 + 0.889293i
\(768\) 38.5178 + 101.563i 1.38989 + 3.66484i
\(769\) −5.85305 15.4332i −0.211066 0.556536i 0.787116 0.616805i \(-0.211573\pi\)
−0.998182 + 0.0602690i \(0.980804\pi\)
\(770\) 0.449884 + 0.651770i 0.0162127 + 0.0234882i
\(771\) 6.14212 + 5.44144i 0.221203 + 0.195969i
\(772\) 46.7497 + 67.7286i 1.68256 + 2.43760i
\(773\) −8.72645 + 7.73096i −0.313868 + 0.278063i −0.805318 0.592843i \(-0.798006\pi\)
0.491450 + 0.870906i \(0.336467\pi\)
\(774\) 0.941308 0.494037i 0.0338346 0.0177578i
\(775\) −38.9621 −1.39956
\(776\) 22.7669 11.9490i 0.817284 0.428944i
\(777\) −0.0511829 0.421529i −0.00183617 0.0151223i
\(778\) −26.8943 + 70.9144i −0.964207 + 2.54240i
\(779\) 7.85265 4.12139i 0.281350 0.147664i
\(780\) −30.6173 + 17.3005i −1.09628 + 0.619458i
\(781\) 28.6059 + 15.0135i 1.02360 + 0.537226i
\(782\) 6.10551 5.40901i 0.218333 0.193426i
\(783\) −9.66181 8.55962i −0.345285 0.305896i
\(784\) 104.220 25.6880i 3.72215 0.917428i
\(785\) −0.243512 2.00551i −0.00869133 0.0715796i
\(786\) 40.1016 + 35.5269i 1.43037 + 1.26720i
\(787\) 9.86163 + 26.0030i 0.351529 + 0.926906i 0.987840 + 0.155474i \(0.0496903\pi\)
−0.636311 + 0.771433i \(0.719540\pi\)
\(788\) −8.23476 + 4.32193i −0.293351 + 0.153963i
\(789\) −10.8646 5.70216i −0.386789 0.203002i
\(790\) 0.290845 2.39533i 0.0103478 0.0852219i
\(791\) −0.0410849 0.0363980i −0.00146081 0.00129416i
\(792\) −33.4897 8.25447i −1.19000 0.293310i
\(793\) −24.2190 32.8595i −0.860043 1.16687i
\(794\) 10.6587 2.62714i 0.378264 0.0932336i
\(795\) −16.0706 8.43450i −0.569965 0.299141i
\(796\) −100.338 52.6613i −3.55638 1.86653i
\(797\) −7.52214 + 19.8342i −0.266448 + 0.702565i 0.733296 + 0.679910i \(0.237981\pi\)
−0.999743 + 0.0226550i \(0.992788\pi\)
\(798\) 1.49995 3.95505i 0.0530977 0.140007i
\(799\) −25.8839 + 37.4993i −0.915707 + 1.32663i
\(800\) −95.8564 + 23.6265i −3.38904 + 0.835323i
\(801\) 4.84515 7.01941i 0.171195 0.248019i
\(802\) −6.15407 50.6834i −0.217308 1.78969i
\(803\) −1.68300 + 4.43770i −0.0593917 + 0.156603i
\(804\) −84.2643 + 44.2253i −2.97177 + 1.55971i
\(805\) −0.0280360 0.0406172i −0.000988140 0.00143157i
\(806\) 29.0717 84.4656i 1.02401 2.97517i
\(807\) 10.8303 15.6904i 0.381244 0.552327i
\(808\) 16.9537 139.626i 0.596429 4.91203i
\(809\) −33.4714 8.24995i −1.17679 0.290053i −0.398029 0.917373i \(-0.630306\pi\)
−0.778762 + 0.627320i \(0.784152\pi\)
\(810\) 14.5393 + 21.0638i 0.510859 + 0.740108i
\(811\) 4.61895 4.09203i 0.162193 0.143691i −0.578123 0.815950i \(-0.696214\pi\)
0.740316 + 0.672259i \(0.234676\pi\)
\(812\) 3.03458 + 1.59267i 0.106493 + 0.0558919i
\(813\) 4.84796 + 39.9265i 0.170025 + 1.40028i
\(814\) 1.02201 8.41698i 0.0358213 0.295015i
\(815\) −6.57247 + 5.82270i −0.230223 + 0.203960i
\(816\) 139.541 202.161i 4.88493 7.07704i
\(817\) 0.146761 + 1.20869i 0.00513453 + 0.0422866i
\(818\) −12.7080 + 104.660i −0.444326 + 3.65935i
\(819\) 0.747985 + 0.363455i 0.0261367 + 0.0127001i
\(820\) −1.01188 8.33359i −0.0353364 0.291021i
\(821\) 47.7161 11.7610i 1.66530 0.410460i 0.709555 0.704650i \(-0.248896\pi\)
0.955747 + 0.294189i \(0.0950496\pi\)
\(822\) 98.9946 3.45283
\(823\) 29.9277 1.04321 0.521607 0.853186i \(-0.325333\pi\)
0.521607 + 0.853186i \(0.325333\pi\)
\(824\) 106.864 26.3396i 3.72278 0.917582i
\(825\) 7.57081 19.9626i 0.263582 0.695008i
\(826\) −2.96558 −0.103186
\(827\) −3.48581 9.19133i −0.121214 0.319614i 0.860652 0.509194i \(-0.170057\pi\)
−0.981865 + 0.189580i \(0.939287\pi\)
\(828\) 3.27458 + 0.807112i 0.113800 + 0.0280491i
\(829\) −14.1383 + 12.5254i −0.491043 + 0.435026i −0.871956 0.489585i \(-0.837148\pi\)
0.380913 + 0.924611i \(0.375610\pi\)
\(830\) −7.67711 1.89224i −0.266477 0.0656806i
\(831\) 7.18423 6.36468i 0.249218 0.220788i
\(832\) 10.3531 114.951i 0.358928 3.98521i
\(833\) −39.1395 34.6746i −1.35610 1.20140i
\(834\) −7.50919 10.8789i −0.260022 0.376707i
\(835\) −2.82030 + 0.695143i −0.0976006 + 0.0240564i
\(836\) 35.2105 51.0112i 1.21778 1.76426i
\(837\) −27.2949 6.72758i −0.943449 0.232539i
\(838\) −58.3592 14.3842i −2.01598 0.496895i
\(839\) 1.60527 13.2206i 0.0554200 0.456425i −0.938411 0.345521i \(-0.887702\pi\)
0.993831 0.110904i \(-0.0353747\pi\)
\(840\) −1.91013 1.69223i −0.0659057 0.0583874i
\(841\) 4.17680 + 11.0133i 0.144027 + 0.379769i
\(842\) −57.4326 + 30.1430i −1.97926 + 1.03880i
\(843\) 10.5231 15.2453i 0.362434 0.525076i
\(844\) 131.259 4.51813
\(845\) 10.7697 0.668748i 0.370490 0.0230056i
\(846\) −25.6719 −0.882619
\(847\) −0.476211 + 0.689911i −0.0163628 + 0.0237056i
\(848\) 139.782 73.3632i 4.80013 2.51930i
\(849\) 20.1620 + 53.1628i 0.691957 + 1.82454i
\(850\) 66.2906 + 58.7284i 2.27375 + 2.01437i
\(851\) −0.0636897 + 0.524532i −0.00218325 + 0.0179807i
\(852\) −158.589 39.0886i −5.43316 1.33915i
\(853\) −7.60088 1.87345i −0.260249 0.0641457i 0.107032 0.994256i \(-0.465865\pi\)
−0.367281 + 0.930110i \(0.619711\pi\)
\(854\) 2.64017 3.82495i 0.0903448 0.130887i
\(855\) 6.00257 1.47950i 0.205283 0.0505978i
\(856\) 15.7627 + 22.8362i 0.538757 + 0.780524i
\(857\) −3.71728 3.29322i −0.126980 0.112494i 0.597243 0.802060i \(-0.296263\pi\)
−0.724223 + 0.689566i \(0.757801\pi\)
\(858\) 37.6278 + 31.3078i 1.28459 + 1.06883i
\(859\) 12.0920 10.7125i 0.412572 0.365507i −0.431156 0.902277i \(-0.641894\pi\)
0.843728 + 0.536770i \(0.180356\pi\)
\(860\) 1.11904 + 0.275819i 0.0381590 + 0.00940535i
\(861\) −0.438014 + 0.388047i −0.0149275 + 0.0132246i
\(862\) 2.60964 + 0.643218i 0.0888847 + 0.0219081i
\(863\) −4.33422 11.4284i −0.147539 0.389027i 0.840791 0.541361i \(-0.182091\pi\)
−0.988329 + 0.152333i \(0.951321\pi\)
\(864\) −71.2318 −2.42336
\(865\) 4.48391 11.8231i 0.152458 0.401998i
\(866\) 84.0117 20.7070i 2.85483 0.703653i
\(867\) −83.4410 −2.83380
\(868\) 7.46379 0.253338
\(869\) −2.39308 + 0.589842i −0.0811798 + 0.0200090i
\(870\) 2.42519 + 19.9732i 0.0822216 + 0.677156i
\(871\) 29.1858 0.905276i 0.988923 0.0306741i
\(872\) 2.07052 17.0523i 0.0701167 0.577463i
\(873\) −0.495423 4.08017i −0.0167675 0.138093i
\(874\) −2.99003 + 4.33180i −0.101139 + 0.146525i
\(875\) 0.866289 0.767465i 0.0292859 0.0259451i
\(876\) 2.89234 23.8205i 0.0977231 0.804822i
\(877\) −0.422733 3.48152i −0.0142747 0.117563i 0.983830 0.179106i \(-0.0573207\pi\)
−0.998104 + 0.0615439i \(0.980398\pi\)
\(878\) −3.96299 2.07994i −0.133744 0.0701944i
\(879\) 27.5668 24.4221i 0.929806 0.823736i
\(880\) −16.8588 24.4242i −0.568310 0.823339i
\(881\) −40.3547 9.94655i −1.35959 0.335108i −0.508920 0.860814i \(-0.669955\pi\)
−0.850666 + 0.525706i \(0.823801\pi\)
\(882\) 3.55110 29.2459i 0.119572 0.984762i
\(883\) 5.64050 8.17167i 0.189818 0.274999i −0.716507 0.697580i \(-0.754260\pi\)
0.906325 + 0.422581i \(0.138876\pi\)
\(884\) −129.731 + 73.3056i −4.36334 + 2.46553i
\(885\) −7.25796 10.5150i −0.243974 0.353457i
\(886\) −55.6405 + 29.2024i −1.86928 + 0.981073i
\(887\) 0.870097 2.29426i 0.0292150 0.0770336i −0.919615 0.392821i \(-0.871499\pi\)
0.948830 + 0.315787i \(0.102269\pi\)
\(888\) 3.29318 + 27.1218i 0.110512 + 0.910147i
\(889\) 0.766956 1.11113i 0.0257229 0.0372660i
\(890\) 12.2343 3.01548i 0.410094 0.101079i
\(891\) 14.8513 21.5159i 0.497538 0.720809i
\(892\) −26.3922 + 69.5906i −0.883677 + 2.33007i
\(893\) 10.4263 27.4919i 0.348903 0.919981i
\(894\) −74.6117 39.1592i −2.49539 1.30968i
\(895\) −9.77107 5.12825i −0.326611 0.171419i
\(896\) 6.09954 1.50340i 0.203771 0.0502251i
\(897\) −2.34490 1.95105i −0.0782939 0.0651437i
\(898\) 99.7115 + 24.5767i 3.32741 + 0.820134i
\(899\) −28.0731 24.8706i −0.936291 0.829481i
\(900\) −4.41379 + 36.3508i −0.147126 + 1.21169i
\(901\) −68.0941 35.7386i −2.26854 1.19062i
\(902\) −10.3463 + 5.43017i −0.344495 + 0.180805i
\(903\) −0.0284890 0.0751194i −0.000948056 0.00249982i
\(904\) 2.64346 + 2.34190i 0.0879201 + 0.0778904i
\(905\) 0.0581309 + 0.478751i 0.00193234 + 0.0159142i
\(906\) −35.9498 + 8.86082i −1.19435 + 0.294381i
\(907\) −37.8891 33.5668i −1.25809 1.11457i −0.988441 0.151608i \(-0.951555\pi\)
−0.269646 0.962959i \(-0.586907\pi\)
\(908\) 38.3007 33.9315i 1.27105 1.12606i
\(909\) −19.9082 10.4486i −0.660313 0.346559i
\(910\) 0.471058 + 1.13467i 0.0156154 + 0.0376138i
\(911\) 23.2811 12.2188i 0.771336 0.404829i −0.0326572 0.999467i \(-0.510397\pi\)
0.803994 + 0.594638i \(0.202705\pi\)
\(912\) −56.2087 + 148.210i −1.86126 + 4.90773i
\(913\) 0.973522 + 8.01767i 0.0322189 + 0.265346i
\(914\) −56.6804 + 29.7482i −1.87482 + 0.983982i
\(915\) 20.0235 0.661958
\(916\) 27.9297 14.6587i 0.922825 0.484336i
\(917\) 1.02810 0.910814i 0.0339507 0.0300777i
\(918\) 36.2993 + 52.5886i 1.19805 + 1.73568i
\(919\) 23.9444 + 21.2129i 0.789852 + 0.699748i 0.958238 0.285973i \(-0.0923168\pi\)
−0.168385 + 0.985721i \(0.553855\pi\)
\(920\) 1.80388 + 2.61337i 0.0594721 + 0.0861602i
\(921\) 7.40790 + 19.5330i 0.244099 + 0.643635i
\(922\) 11.6573 + 30.7377i 0.383912 + 1.01229i
\(923\) 38.5252 + 32.0545i 1.26807 + 1.05509i
\(924\) −1.45031 + 3.82415i −0.0477116 + 0.125805i
\(925\) −5.73693 −0.188629
\(926\) 28.0418 + 73.9402i 0.921512 + 2.42983i
\(927\) 2.12069 17.4654i 0.0696525 0.573640i
\(928\) −84.1483 44.1645i −2.76230 1.44977i
\(929\) 21.9504 + 31.8006i 0.720168 + 1.04334i 0.996607 + 0.0823117i \(0.0262303\pi\)
−0.276439 + 0.961032i \(0.589154\pi\)
\(930\) 24.8915 + 36.0616i 0.816226 + 1.18251i
\(931\) 29.8771 + 15.6807i 0.979181 + 0.513914i
\(932\) −11.0979 + 91.3993i −0.363523 + 2.99388i
\(933\) −3.39637 8.95549i −0.111192 0.293190i
\(934\) 80.4396 2.63206
\(935\) −5.12664 + 13.5178i −0.167659 + 0.442080i
\(936\) −48.1264 23.3852i −1.57306 0.764370i
\(937\) −2.86638 7.55802i −0.0936405 0.246910i 0.880010 0.474955i \(-0.157536\pi\)
−0.973650 + 0.228046i \(0.926766\pi\)
\(938\) 1.17891 + 3.10854i 0.0384929 + 0.101497i
\(939\) −33.2903 48.2293i −1.08639 1.57390i
\(940\) −20.8326 18.4561i −0.679486 0.601972i
\(941\) 16.1057 + 23.3331i 0.525030 + 0.760638i 0.992351 0.123450i \(-0.0393960\pi\)
−0.467321 + 0.884088i \(0.654781\pi\)
\(942\) 10.6414 9.42748i 0.346716 0.307164i
\(943\) 0.644765 0.338399i 0.0209964 0.0110198i
\(944\) 111.131 3.61701
\(945\) 0.342343 0.179676i 0.0111364 0.00584484i
\(946\) −0.193367 1.59252i −0.00628689 0.0517772i
\(947\) 0.0221416 0.0583825i 0.000719505 0.00189718i −0.934656 0.355553i \(-0.884292\pi\)
0.935376 + 0.353656i \(0.115062\pi\)
\(948\) 11.0337 5.79095i 0.358359 0.188081i
\(949\) −3.99259 + 6.18609i −0.129605 + 0.200809i
\(950\) −50.6028 26.5584i −1.64177 0.861668i
\(951\) 30.2844 26.8296i 0.982038 0.870010i
\(952\) −8.09358 7.17029i −0.262315 0.232390i
\(953\) 8.95559 2.20735i 0.290100 0.0715032i −0.0915802 0.995798i \(-0.529192\pi\)
0.381680 + 0.924294i \(0.375346\pi\)
\(954\) −5.22262 43.0121i −0.169088 1.39257i
\(955\) −4.73479 4.19465i −0.153214 0.135736i
\(956\) −15.0542 39.6948i −0.486889 1.28382i
\(957\) 18.1976 9.55086i 0.588246 0.308735i
\(958\) 70.6594 + 37.0849i 2.28290 + 1.19816i
\(959\) 0.305917 2.51945i 0.00987857 0.0813573i
\(960\) 42.3768 + 37.5426i 1.36771 + 1.21168i
\(961\) −49.2081 12.1287i −1.58736 0.391249i
\(962\) 4.28063 12.4371i 0.138013 0.400987i
\(963\) 4.30671 1.06151i 0.138782 0.0342066i
\(964\) 21.9947 + 11.5437i 0.708402 + 0.371798i
\(965\) 10.9677 + 5.75628i 0.353062 + 0.185301i
\(966\) 0.123158 0.324741i 0.00396255 0.0104484i
\(967\) 2.06604 5.44770i 0.0664394 0.175186i −0.897685 0.440639i \(-0.854752\pi\)
0.964124 + 0.265452i \(0.0855213\pi\)
\(968\) 30.6401 44.3899i 0.984811 1.42674i
\(969\) 74.9740 18.4794i 2.40851 0.593645i
\(970\) 3.44929 4.99717i 0.110750 0.160449i
\(971\) 1.70098 + 14.0088i 0.0545871 + 0.449565i 0.994218 + 0.107377i \(0.0342451\pi\)
−0.939631 + 0.342188i \(0.888832\pi\)
\(972\) −28.6225 + 75.4713i −0.918067 + 2.42074i
\(973\) −0.300079 + 0.157493i −0.00962008 + 0.00504901i
\(974\) −18.0691 26.1776i −0.578971 0.838784i
\(975\) 17.9603 27.8275i 0.575189 0.891194i
\(976\) −98.9368 + 143.335i −3.16689 + 4.58803i
\(977\) −4.07758 + 33.5819i −0.130453 + 1.07438i 0.769577 + 0.638554i \(0.220467\pi\)
−0.900031 + 0.435827i \(0.856456\pi\)
\(978\) −59.9962 14.7877i −1.91847 0.472859i
\(979\) −7.31146 10.5925i −0.233675 0.338537i
\(980\) 23.9073 21.1800i 0.763689 0.676570i
\(981\) −2.43135 1.27607i −0.0776271 0.0407418i
\(982\) −12.9669 106.792i −0.413791 3.40788i
\(983\) −1.42989 + 11.7762i −0.0456065 + 0.375603i 0.951980 + 0.306162i \(0.0990448\pi\)
−0.997586 + 0.0694417i \(0.977878\pi\)
\(984\) 28.1825 24.9675i 0.898424 0.795934i
\(985\) −0.795149 + 1.15197i −0.0253356 + 0.0367049i
\(986\) 10.2760 + 84.6304i 0.327254 + 2.69518i
\(987\) −0.233855 + 1.92597i −0.00744367 + 0.0613042i
\(988\) 69.9611 65.9627i 2.22576 2.09855i
\(989\) 0.0120503 + 0.0992429i 0.000383176 + 0.00315574i
\(990\) −7.90873 + 1.94933i −0.251356 + 0.0619537i
\(991\) 45.3306 1.43997 0.719987 0.693988i \(-0.244148\pi\)
0.719987 + 0.693988i \(0.244148\pi\)
\(992\) −206.969 −6.57128
\(993\) 44.0934 10.8680i 1.39926 0.344887i
\(994\) −2.02341 + 5.33529i −0.0641786 + 0.169225i
\(995\) −17.0555 −0.540696
\(996\) −14.4798 38.1800i −0.458809 1.20978i
\(997\) 18.8546 + 4.64724i 0.597131 + 0.147180i 0.526286 0.850308i \(-0.323584\pi\)
0.0708451 + 0.997487i \(0.477430\pi\)
\(998\) −19.9947 + 17.7138i −0.632923 + 0.560721i
\(999\) −4.01901 0.990597i −0.127156 0.0313411i
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 169.2.g.a.14.1 156
169.157 even 13 inner 169.2.g.a.157.1 yes 156
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
169.2.g.a.14.1 156 1.1 even 1 trivial
169.2.g.a.157.1 yes 156 169.157 even 13 inner