Properties

Label 170.2.r.b.107.5
Level $170$
Weight $2$
Character 170.107
Analytic conductor $1.357$
Analytic rank $0$
Dimension $40$
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] = [170,2,Mod(23,170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(170, base_ring=CyclotomicField(16))
 
chi = DirichletCharacter(H, H._module([12, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("170.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 170 = 2 \cdot 5 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 170.r (of order \(16\), degree \(8\), 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: \(1.35745683436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(5\) over \(\Q(\zeta_{16})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 107.5
Character \(\chi\) \(=\) 170.107
Dual form 170.2.r.b.143.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.382683 + 0.923880i) q^{2} +(3.34096 + 0.664558i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-0.732362 - 2.11273i) q^{5} +(-1.89250 + 2.83233i) q^{6} +(-0.616963 + 0.923351i) q^{7} +(0.923880 - 0.382683i) q^{8} +(7.94873 + 3.29247i) q^{9} +O(q^{10})\) \(q+(-0.382683 + 0.923880i) q^{2} +(3.34096 + 0.664558i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(-0.732362 - 2.11273i) q^{5} +(-1.89250 + 2.83233i) q^{6} +(-0.616963 + 0.923351i) q^{7} +(0.923880 - 0.382683i) q^{8} +(7.94873 + 3.29247i) q^{9} +(2.23217 + 0.131894i) q^{10} +(-0.833476 - 0.556911i) q^{11} +(-1.89250 - 2.83233i) q^{12} -4.43010 q^{13} +(-0.616963 - 0.923351i) q^{14} +(-1.04276 - 7.54525i) q^{15} +1.00000i q^{16} +(-3.76821 + 1.67349i) q^{17} +(-6.08369 + 6.08369i) q^{18} +(0.506906 - 0.209967i) q^{19} +(-0.976070 + 2.01179i) q^{20} +(-2.67487 + 2.67487i) q^{21} +(0.833476 - 0.556911i) q^{22} +(-0.609578 - 3.06456i) q^{23} +(3.34096 - 0.664558i) q^{24} +(-3.92729 + 3.09457i) q^{25} +(1.69533 - 4.09288i) q^{26} +(15.8713 + 10.6049i) q^{27} +(1.08917 - 0.216649i) q^{28} +(0.588900 - 2.96060i) q^{29} +(7.36995 + 1.92406i) q^{30} +(-1.23768 + 0.826988i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(-2.41451 - 2.41451i) q^{33} +(-0.104069 - 4.12179i) q^{34} +(2.40264 + 0.627252i) q^{35} +(-3.29247 - 7.94873i) q^{36} +(-1.12655 + 5.66357i) q^{37} +0.548671i q^{38} +(-14.8008 - 2.94406i) q^{39} +(-1.48512 - 1.67165i) q^{40} +(-1.75620 - 8.82901i) q^{41} +(-1.44763 - 3.49488i) q^{42} +(0.0722156 + 0.174344i) q^{43} +(0.195561 + 0.983152i) q^{44} +(1.13477 - 19.2048i) q^{45} +(3.06456 + 0.609578i) q^{46} -6.10055i q^{47} +(-0.664558 + 3.34096i) q^{48} +(2.20685 + 5.32781i) q^{49} +(-1.35610 - 4.81259i) q^{50} +(-13.7016 + 3.08686i) q^{51} +(3.13255 + 3.13255i) q^{52} +(11.5237 + 4.77327i) q^{53} +(-15.8713 + 10.6049i) q^{54} +(-0.566198 + 2.16877i) q^{55} +(-0.216649 + 1.08917i) q^{56} +(1.83309 - 0.364624i) q^{57} +(2.50988 + 1.67705i) q^{58} +(4.57691 - 11.0496i) q^{59} +(-4.59796 + 6.07264i) q^{60} +(1.88405 - 0.374760i) q^{61} +(-0.290400 - 1.45994i) q^{62} +(-7.94418 + 5.30813i) q^{63} +(0.707107 - 0.707107i) q^{64} +(3.24444 + 9.35962i) q^{65} +(3.15471 - 1.30672i) q^{66} +(0.568902 - 0.568902i) q^{67} +(3.84786 + 1.48119i) q^{68} -10.6437i q^{69} +(-1.49895 + 1.97971i) q^{70} +(-2.52638 - 3.78099i) q^{71} +8.60364 q^{72} +(-1.01360 - 1.51695i) q^{73} +(-4.80134 - 3.20816i) q^{74} +(-15.1774 + 7.72893i) q^{75} +(-0.506906 - 0.209967i) q^{76} +(1.02845 - 0.425997i) q^{77} +(8.38397 - 12.5475i) q^{78} +(-2.90998 + 4.35510i) q^{79} +(2.11273 - 0.732362i) q^{80} +(27.7269 + 27.7269i) q^{81} +(8.82901 + 1.75620i) q^{82} +(-4.60927 + 11.1278i) q^{83} +3.78284 q^{84} +(6.29533 + 6.73563i) q^{85} -0.188708 q^{86} +(3.93498 - 9.49989i) q^{87} +(-0.983152 - 0.195561i) q^{88} +(4.95294 + 4.95294i) q^{89} +(17.3087 + 8.39776i) q^{90} +(2.73321 - 4.09054i) q^{91} +(-1.73593 + 2.59800i) q^{92} +(-4.68460 + 1.94043i) q^{93} +(5.63618 + 2.33458i) q^{94} +(-0.814844 - 0.917186i) q^{95} +(-2.83233 - 1.89250i) q^{96} +(3.75997 + 5.62719i) q^{97} -5.76678 q^{98} +(-4.79146 - 7.17093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 16 q^{10} - 16 q^{18} + 8 q^{25} - 8 q^{26} + 24 q^{27} - 8 q^{28} + 8 q^{29} + 16 q^{30} - 16 q^{31} - 32 q^{33} + 8 q^{34} - 32 q^{35} - 32 q^{39} - 56 q^{41} - 24 q^{42} + 16 q^{43} + 16 q^{44} + 24 q^{45} + 16 q^{49} - 32 q^{51} - 16 q^{52} + 16 q^{53} - 24 q^{54} - 8 q^{55} - 8 q^{56} - 120 q^{57} + 16 q^{58} + 8 q^{60} + 24 q^{61} - 8 q^{62} - 24 q^{63} - 32 q^{65} + 16 q^{67} - 8 q^{70} + 24 q^{71} + 56 q^{72} + 88 q^{73} + 32 q^{74} + 8 q^{75} + 24 q^{77} + 32 q^{78} - 104 q^{79} + 8 q^{80} + 48 q^{81} + 16 q^{82} + 16 q^{83} + 136 q^{85} + 96 q^{86} + 136 q^{87} - 16 q^{89} + 24 q^{90} + 48 q^{91} - 8 q^{92} - 8 q^{93} - 8 q^{94} - 136 q^{95} + 16 q^{97} + 72 q^{98} + 160 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).

\(n\) \(71\) \(137\)
\(\chi(n)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.382683 + 0.923880i −0.270598 + 0.653281i
\(3\) 3.34096 + 0.664558i 1.92890 + 0.383683i 0.999908 + 0.0135921i \(0.00432662\pi\)
0.928996 + 0.370091i \(0.120673\pi\)
\(4\) −0.707107 0.707107i −0.353553 0.353553i
\(5\) −0.732362 2.11273i −0.327522 0.944843i
\(6\) −1.89250 + 2.83233i −0.772610 + 1.15629i
\(7\) −0.616963 + 0.923351i −0.233190 + 0.348994i −0.929548 0.368701i \(-0.879803\pi\)
0.696358 + 0.717695i \(0.254803\pi\)
\(8\) 0.923880 0.382683i 0.326641 0.135299i
\(9\) 7.94873 + 3.29247i 2.64958 + 1.09749i
\(10\) 2.23217 + 0.131894i 0.705876 + 0.0417085i
\(11\) −0.833476 0.556911i −0.251302 0.167915i 0.423539 0.905878i \(-0.360788\pi\)
−0.674841 + 0.737963i \(0.735788\pi\)
\(12\) −1.89250 2.83233i −0.546318 0.817623i
\(13\) −4.43010 −1.22869 −0.614344 0.789038i \(-0.710579\pi\)
−0.614344 + 0.789038i \(0.710579\pi\)
\(14\) −0.616963 0.923351i −0.164890 0.246776i
\(15\) −1.04276 7.54525i −0.269239 1.94818i
\(16\) 1.00000i 0.250000i
\(17\) −3.76821 + 1.67349i −0.913926 + 0.405881i
\(18\) −6.08369 + 6.08369i −1.43394 + 1.43394i
\(19\) 0.506906 0.209967i 0.116292 0.0481698i −0.323779 0.946133i \(-0.604953\pi\)
0.440071 + 0.897963i \(0.354953\pi\)
\(20\) −0.976070 + 2.01179i −0.218256 + 0.449849i
\(21\) −2.67487 + 2.67487i −0.583704 + 0.583704i
\(22\) 0.833476 0.556911i 0.177698 0.118734i
\(23\) −0.609578 3.06456i −0.127106 0.639004i −0.990838 0.135053i \(-0.956879\pi\)
0.863733 0.503950i \(-0.168121\pi\)
\(24\) 3.34096 0.664558i 0.681970 0.135652i
\(25\) −3.92729 + 3.09457i −0.785458 + 0.618915i
\(26\) 1.69533 4.09288i 0.332481 0.802680i
\(27\) 15.8713 + 10.6049i 3.05444 + 2.04091i
\(28\) 1.08917 0.216649i 0.205833 0.0409428i
\(29\) 0.588900 2.96060i 0.109356 0.549770i −0.886799 0.462156i \(-0.847076\pi\)
0.996155 0.0876136i \(-0.0279241\pi\)
\(30\) 7.36995 + 1.92406i 1.34556 + 0.351284i
\(31\) −1.23768 + 0.826988i −0.222293 + 0.148531i −0.661731 0.749742i \(-0.730178\pi\)
0.439438 + 0.898273i \(0.355178\pi\)
\(32\) −0.923880 0.382683i −0.163320 0.0676495i
\(33\) −2.41451 2.41451i −0.420312 0.420312i
\(34\) −0.104069 4.12179i −0.0178477 0.706882i
\(35\) 2.40264 + 0.627252i 0.406119 + 0.106025i
\(36\) −3.29247 7.94873i −0.548745 1.32479i
\(37\) −1.12655 + 5.66357i −0.185204 + 0.931086i 0.770653 + 0.637255i \(0.219930\pi\)
−0.955857 + 0.293831i \(0.905070\pi\)
\(38\) 0.548671i 0.0890063i
\(39\) −14.8008 2.94406i −2.37002 0.471427i
\(40\) −1.48512 1.67165i −0.234819 0.264311i
\(41\) −1.75620 8.82901i −0.274272 1.37886i −0.834722 0.550672i \(-0.814372\pi\)
0.560449 0.828189i \(-0.310628\pi\)
\(42\) −1.44763 3.49488i −0.223374 0.539272i
\(43\) 0.0722156 + 0.174344i 0.0110128 + 0.0265872i 0.929290 0.369350i \(-0.120420\pi\)
−0.918278 + 0.395937i \(0.870420\pi\)
\(44\) 0.195561 + 0.983152i 0.0294819 + 0.148216i
\(45\) 1.13477 19.2048i 0.169161 2.86289i
\(46\) 3.06456 + 0.609578i 0.451844 + 0.0898774i
\(47\) 6.10055i 0.889857i −0.895566 0.444929i \(-0.853229\pi\)
0.895566 0.444929i \(-0.146771\pi\)
\(48\) −0.664558 + 3.34096i −0.0959207 + 0.482226i
\(49\) 2.20685 + 5.32781i 0.315264 + 0.761116i
\(50\) −1.35610 4.81259i −0.191782 0.680602i
\(51\) −13.7016 + 3.08686i −1.91860 + 0.432247i
\(52\) 3.13255 + 3.13255i 0.434407 + 0.434407i
\(53\) 11.5237 + 4.77327i 1.58290 + 0.655658i 0.988870 0.148784i \(-0.0475361\pi\)
0.594030 + 0.804443i \(0.297536\pi\)
\(54\) −15.8713 + 10.6049i −2.15982 + 1.44314i
\(55\) −0.566198 + 2.16877i −0.0763461 + 0.292437i
\(56\) −0.216649 + 1.08917i −0.0289509 + 0.145546i
\(57\) 1.83309 0.364624i 0.242799 0.0482956i
\(58\) 2.50988 + 1.67705i 0.329563 + 0.220207i
\(59\) 4.57691 11.0496i 0.595862 1.43854i −0.281900 0.959444i \(-0.590965\pi\)
0.877763 0.479095i \(-0.159035\pi\)
\(60\) −4.59796 + 6.07264i −0.593594 + 0.783975i
\(61\) 1.88405 0.374760i 0.241227 0.0479831i −0.0729959 0.997332i \(-0.523256\pi\)
0.314223 + 0.949349i \(0.398256\pi\)
\(62\) −0.290400 1.45994i −0.0368808 0.185412i
\(63\) −7.94418 + 5.30813i −1.00087 + 0.668762i
\(64\) 0.707107 0.707107i 0.0883883 0.0883883i
\(65\) 3.24444 + 9.35962i 0.402423 + 1.16092i
\(66\) 3.15471 1.30672i 0.388318 0.160846i
\(67\) 0.568902 0.568902i 0.0695024 0.0695024i −0.671501 0.741004i \(-0.734350\pi\)
0.741004 + 0.671501i \(0.234350\pi\)
\(68\) 3.84786 + 1.48119i 0.466622 + 0.179621i
\(69\) 10.6437i 1.28134i
\(70\) −1.49895 + 1.97971i −0.179159 + 0.236620i
\(71\) −2.52638 3.78099i −0.299826 0.448721i 0.650714 0.759323i \(-0.274470\pi\)
−0.950540 + 0.310601i \(0.899470\pi\)
\(72\) 8.60364 1.01395
\(73\) −1.01360 1.51695i −0.118632 0.177546i 0.767401 0.641168i \(-0.221550\pi\)
−0.886033 + 0.463622i \(0.846550\pi\)
\(74\) −4.80134 3.20816i −0.558145 0.372941i
\(75\) −15.1774 + 7.72893i −1.75254 + 0.892460i
\(76\) −0.506906 0.209967i −0.0581461 0.0240849i
\(77\) 1.02845 0.425997i 0.117203 0.0485469i
\(78\) 8.38397 12.5475i 0.949298 1.42072i
\(79\) −2.90998 + 4.35510i −0.327399 + 0.489987i −0.958256 0.285912i \(-0.907703\pi\)
0.630857 + 0.775899i \(0.282703\pi\)
\(80\) 2.11273 0.732362i 0.236211 0.0818806i
\(81\) 27.7269 + 27.7269i 3.08076 + 3.08076i
\(82\) 8.82901 + 1.75620i 0.975002 + 0.193940i
\(83\) −4.60927 + 11.1278i −0.505933 + 1.22143i 0.440273 + 0.897864i \(0.354882\pi\)
−0.946206 + 0.323566i \(0.895118\pi\)
\(84\) 3.78284 0.412741
\(85\) 6.29533 + 6.73563i 0.682825 + 0.730582i
\(86\) −0.188708 −0.0203490
\(87\) 3.93498 9.49989i 0.421874 1.01849i
\(88\) −0.983152 0.195561i −0.104804 0.0208469i
\(89\) 4.95294 + 4.95294i 0.525011 + 0.525011i 0.919081 0.394070i \(-0.128933\pi\)
−0.394070 + 0.919081i \(0.628933\pi\)
\(90\) 17.3087 + 8.39776i 1.82450 + 0.885202i
\(91\) 2.73321 4.09054i 0.286518 0.428805i
\(92\) −1.73593 + 2.59800i −0.180983 + 0.270861i
\(93\) −4.68460 + 1.94043i −0.485771 + 0.201213i
\(94\) 5.63618 + 2.33458i 0.581327 + 0.240794i
\(95\) −0.814844 0.917186i −0.0836013 0.0941013i
\(96\) −2.83233 1.89250i −0.289073 0.193153i
\(97\) 3.75997 + 5.62719i 0.381767 + 0.571354i 0.971736 0.236072i \(-0.0758600\pi\)
−0.589969 + 0.807426i \(0.700860\pi\)
\(98\) −5.76678 −0.582533
\(99\) −4.79146 7.17093i −0.481560 0.720705i
\(100\) 4.96521 + 0.588821i 0.496521 + 0.0588821i
\(101\) 0.342654i 0.0340954i 0.999855 + 0.0170477i \(0.00542671\pi\)
−0.999855 + 0.0170477i \(0.994573\pi\)
\(102\) 2.39148 13.8399i 0.236792 1.37035i
\(103\) −7.67310 + 7.67310i −0.756053 + 0.756053i −0.975602 0.219548i \(-0.929542\pi\)
0.219548 + 0.975602i \(0.429542\pi\)
\(104\) −4.09288 + 1.69533i −0.401340 + 0.166240i
\(105\) 7.61026 + 3.69231i 0.742685 + 0.360333i
\(106\) −8.81985 + 8.81985i −0.856659 + 0.856659i
\(107\) −9.75732 + 6.51964i −0.943276 + 0.630277i −0.929182 0.369624i \(-0.879487\pi\)
−0.0140946 + 0.999901i \(0.504487\pi\)
\(108\) −3.72394 18.7215i −0.358337 1.80148i
\(109\) 9.42080 1.87391i 0.902349 0.179488i 0.277952 0.960595i \(-0.410344\pi\)
0.624398 + 0.781107i \(0.285344\pi\)
\(110\) −1.78701 1.35305i −0.170385 0.129008i
\(111\) −7.52754 + 18.1731i −0.714483 + 1.72491i
\(112\) −0.923351 0.616963i −0.0872484 0.0582975i
\(113\) 5.55310 1.10458i 0.522392 0.103910i 0.0731509 0.997321i \(-0.476695\pi\)
0.449241 + 0.893411i \(0.351695\pi\)
\(114\) −0.364624 + 1.83309i −0.0341502 + 0.171684i
\(115\) −6.02816 + 3.53224i −0.562129 + 0.329383i
\(116\) −2.50988 + 1.67705i −0.233036 + 0.155710i
\(117\) −35.2137 14.5860i −3.25550 1.34847i
\(118\) 8.45702 + 8.45702i 0.778532 + 0.778532i
\(119\) 0.779632 4.51186i 0.0714688 0.413602i
\(120\) −3.85083 6.57186i −0.351531 0.599926i
\(121\) −3.82499 9.23433i −0.347726 0.839485i
\(122\) −0.374760 + 1.88405i −0.0339292 + 0.170573i
\(123\) 30.6645i 2.76492i
\(124\) 1.45994 + 0.290400i 0.131106 + 0.0260787i
\(125\) 9.41421 + 6.03097i 0.842033 + 0.539427i
\(126\) −1.86397 9.37080i −0.166055 0.834817i
\(127\) 3.86473 + 9.33030i 0.342940 + 0.827930i 0.997416 + 0.0718470i \(0.0228893\pi\)
−0.654476 + 0.756083i \(0.727111\pi\)
\(128\) 0.382683 + 0.923880i 0.0338248 + 0.0816602i
\(129\) 0.125408 + 0.630467i 0.0110415 + 0.0555095i
\(130\) −9.88876 0.584303i −0.867301 0.0512468i
\(131\) −3.08463 0.613572i −0.269506 0.0536080i 0.0584873 0.998288i \(-0.481372\pi\)
−0.327993 + 0.944680i \(0.606372\pi\)
\(132\) 3.41463i 0.297205i
\(133\) −0.118869 + 0.597595i −0.0103072 + 0.0518180i
\(134\) 0.307887 + 0.743306i 0.0265974 + 0.0642118i
\(135\) 10.7818 41.2986i 0.927945 3.55441i
\(136\) −2.84096 + 2.98813i −0.243610 + 0.256230i
\(137\) −2.59083 2.59083i −0.221350 0.221350i 0.587717 0.809067i \(-0.300027\pi\)
−0.809067 + 0.587717i \(0.800027\pi\)
\(138\) 9.83345 + 4.07315i 0.837079 + 0.346729i
\(139\) 9.79226 6.54298i 0.830569 0.554968i −0.0660271 0.997818i \(-0.521032\pi\)
0.896596 + 0.442849i \(0.146032\pi\)
\(140\) −1.25539 2.14245i −0.106099 0.181070i
\(141\) 4.05417 20.3817i 0.341423 1.71645i
\(142\) 4.45998 0.887146i 0.374274 0.0744476i
\(143\) 3.69238 + 2.46717i 0.308772 + 0.206315i
\(144\) −3.29247 + 7.94873i −0.274373 + 0.662394i
\(145\) −6.68625 + 0.924043i −0.555263 + 0.0767376i
\(146\) 1.78937 0.355928i 0.148089 0.0294568i
\(147\) 3.83236 + 19.2666i 0.316088 + 1.58908i
\(148\) 4.80134 3.20816i 0.394668 0.263709i
\(149\) −11.9930 + 11.9930i −0.982508 + 0.982508i −0.999850 0.0173417i \(-0.994480\pi\)
0.0173417 + 0.999850i \(0.494480\pi\)
\(150\) −1.33244 16.9799i −0.108794 1.38640i
\(151\) 10.3652 4.29340i 0.843507 0.349392i 0.0812715 0.996692i \(-0.474102\pi\)
0.762235 + 0.647300i \(0.224102\pi\)
\(152\) 0.387969 0.387969i 0.0314685 0.0314685i
\(153\) −35.4624 + 0.895372i −2.86697 + 0.0723866i
\(154\) 1.11318i 0.0897029i
\(155\) 2.65363 + 2.00922i 0.213145 + 0.161385i
\(156\) 8.38397 + 12.5475i 0.671255 + 1.00460i
\(157\) −7.42419 −0.592515 −0.296257 0.955108i \(-0.595739\pi\)
−0.296257 + 0.955108i \(0.595739\pi\)
\(158\) −2.90998 4.35510i −0.231506 0.346473i
\(159\) 35.3280 + 23.6054i 2.80170 + 1.87203i
\(160\) −0.131894 + 2.23217i −0.0104271 + 0.176469i
\(161\) 3.20575 + 1.32786i 0.252648 + 0.104650i
\(162\) −36.2269 + 15.0057i −2.84625 + 1.17896i
\(163\) 8.75441 13.1019i 0.685698 1.02622i −0.311414 0.950274i \(-0.600802\pi\)
0.997112 0.0759457i \(-0.0241976\pi\)
\(164\) −5.00124 + 7.48488i −0.390531 + 0.584471i
\(165\) −3.33292 + 6.86951i −0.259467 + 0.534791i
\(166\) −8.51681 8.51681i −0.661033 0.661033i
\(167\) −17.7908 3.53881i −1.37669 0.273841i −0.549376 0.835575i \(-0.685134\pi\)
−0.827318 + 0.561734i \(0.810134\pi\)
\(168\) −1.44763 + 3.49488i −0.111687 + 0.269636i
\(169\) 6.62579 0.509676
\(170\) −8.63203 + 3.23851i −0.662047 + 0.248383i
\(171\) 4.72057 0.360991
\(172\) 0.0722156 0.174344i 0.00550639 0.0132936i
\(173\) 20.2455 + 4.02708i 1.53924 + 0.306173i 0.890551 0.454883i \(-0.150319\pi\)
0.648686 + 0.761056i \(0.275319\pi\)
\(174\) 7.27090 + 7.27090i 0.551205 + 0.551205i
\(175\) −0.434382 5.53551i −0.0328362 0.418445i
\(176\) 0.556911 0.833476i 0.0419787 0.0628256i
\(177\) 22.6344 33.8747i 1.70130 2.54618i
\(178\) −6.47133 + 2.68051i −0.485047 + 0.200913i
\(179\) −6.30681 2.61237i −0.471393 0.195257i 0.134324 0.990937i \(-0.457114\pi\)
−0.605717 + 0.795680i \(0.707114\pi\)
\(180\) −14.3823 + 12.7775i −1.07199 + 0.952376i
\(181\) 3.95885 + 2.64522i 0.294259 + 0.196618i 0.693933 0.720040i \(-0.255876\pi\)
−0.399674 + 0.916658i \(0.630876\pi\)
\(182\) 2.73321 + 4.09054i 0.202599 + 0.303211i
\(183\) 6.54357 0.483714
\(184\) −1.73593 2.59800i −0.127975 0.191527i
\(185\) 12.7907 1.76768i 0.940389 0.129962i
\(186\) 5.07058i 0.371793i
\(187\) 4.07270 + 0.703746i 0.297825 + 0.0514630i
\(188\) −4.31374 + 4.31374i −0.314612 + 0.314612i
\(189\) −19.5841 + 8.11199i −1.42453 + 0.590060i
\(190\) 1.15920 0.401826i 0.0840970 0.0291515i
\(191\) −7.17897 + 7.17897i −0.519452 + 0.519452i −0.917406 0.397954i \(-0.869720\pi\)
0.397954 + 0.917406i \(0.369720\pi\)
\(192\) 2.83233 1.89250i 0.204406 0.136579i
\(193\) −1.50093 7.54568i −0.108039 0.543150i −0.996456 0.0841126i \(-0.973194\pi\)
0.888417 0.459037i \(-0.151806\pi\)
\(194\) −6.63772 + 1.32032i −0.476561 + 0.0947938i
\(195\) 4.61952 + 33.4262i 0.330811 + 2.39370i
\(196\) 2.20685 5.32781i 0.157632 0.380558i
\(197\) 3.96501 + 2.64933i 0.282495 + 0.188757i 0.688743 0.725006i \(-0.258163\pi\)
−0.406248 + 0.913763i \(0.633163\pi\)
\(198\) 8.45868 1.68254i 0.601132 0.119573i
\(199\) 2.16119 10.8650i 0.153203 0.770201i −0.825417 0.564523i \(-0.809060\pi\)
0.978620 0.205678i \(-0.0659400\pi\)
\(200\) −2.44410 + 4.36192i −0.172824 + 0.308434i
\(201\) 2.27874 1.52261i 0.160730 0.107397i
\(202\) −0.316571 0.131128i −0.0222739 0.00922614i
\(203\) 2.37034 + 2.37034i 0.166365 + 0.166365i
\(204\) 11.8712 + 7.50574i 0.831151 + 0.525507i
\(205\) −17.3672 + 10.1764i −1.21298 + 0.710752i
\(206\) −4.15265 10.0254i −0.289329 0.698502i
\(207\) 5.24459 26.3663i 0.364524 1.83259i
\(208\) 4.43010i 0.307172i
\(209\) −0.539427 0.107299i −0.0373130 0.00742201i
\(210\) −6.32357 + 5.61798i −0.436368 + 0.387677i
\(211\) 1.63864 + 8.23800i 0.112809 + 0.567127i 0.995303 + 0.0968050i \(0.0308623\pi\)
−0.882495 + 0.470322i \(0.844138\pi\)
\(212\) −4.77327 11.5237i −0.327829 0.791450i
\(213\) −5.92784 14.3111i −0.406169 0.980578i
\(214\) −2.28939 11.5095i −0.156500 0.786777i
\(215\) 0.315454 0.280255i 0.0215138 0.0191132i
\(216\) 18.7215 + 3.72394i 1.27384 + 0.253382i
\(217\) 1.65303i 0.112215i
\(218\) −1.87391 + 9.42080i −0.126918 + 0.638057i
\(219\) −2.37828 5.74167i −0.160709 0.387986i
\(220\) 1.93392 1.13319i 0.130385 0.0763998i
\(221\) 16.6936 7.41372i 1.12293 0.498701i
\(222\) −13.9091 13.9091i −0.933517 0.933517i
\(223\) −18.2576 7.56256i −1.22262 0.506426i −0.324379 0.945927i \(-0.605155\pi\)
−0.898242 + 0.439501i \(0.855155\pi\)
\(224\) 0.923351 0.616963i 0.0616940 0.0412226i
\(225\) −41.4058 + 11.6674i −2.76038 + 0.777828i
\(226\) −1.10458 + 5.55310i −0.0734756 + 0.369387i
\(227\) −5.38919 + 1.07198i −0.357693 + 0.0711496i −0.370666 0.928766i \(-0.620871\pi\)
0.0129727 + 0.999916i \(0.495871\pi\)
\(228\) −1.55402 1.03836i −0.102917 0.0687672i
\(229\) −1.33019 + 3.21137i −0.0879016 + 0.212213i −0.961717 0.274045i \(-0.911638\pi\)
0.873815 + 0.486258i \(0.161638\pi\)
\(230\) −0.956488 6.92102i −0.0630690 0.456359i
\(231\) 3.71910 0.739775i 0.244699 0.0486736i
\(232\) −0.588900 2.96060i −0.0386632 0.194373i
\(233\) 10.0669 6.72649i 0.659505 0.440667i −0.180259 0.983619i \(-0.557694\pi\)
0.839764 + 0.542952i \(0.182694\pi\)
\(234\) 26.9514 26.9514i 1.76187 1.76187i
\(235\) −12.8888 + 4.46782i −0.840776 + 0.291448i
\(236\) −11.0496 + 4.57691i −0.719270 + 0.297931i
\(237\) −12.6163 + 12.6163i −0.819519 + 0.819519i
\(238\) 3.87007 + 2.44690i 0.250859 + 0.158609i
\(239\) 14.2194i 0.919776i −0.887977 0.459888i \(-0.847890\pi\)
0.887977 0.459888i \(-0.152110\pi\)
\(240\) 7.54525 1.04276i 0.487044 0.0673097i
\(241\) −2.87172 4.29783i −0.184984 0.276848i 0.727374 0.686241i \(-0.240740\pi\)
−0.912358 + 0.409393i \(0.865740\pi\)
\(242\) 9.99517 0.642514
\(243\) 42.3935 + 63.4464i 2.71955 + 4.07009i
\(244\) −1.59722 1.06723i −0.102251 0.0683221i
\(245\) 9.64003 8.56438i 0.615879 0.547158i
\(246\) 28.3303 + 11.7348i 1.80627 + 0.748183i
\(247\) −2.24565 + 0.930177i −0.142887 + 0.0591857i
\(248\) −0.826988 + 1.23768i −0.0525138 + 0.0785925i
\(249\) −22.7944 + 34.1142i −1.44454 + 2.16190i
\(250\) −9.17456 + 6.38964i −0.580250 + 0.404116i
\(251\) −18.4621 18.4621i −1.16531 1.16531i −0.983295 0.182020i \(-0.941736\pi\)
−0.182020 0.983295i \(-0.558264\pi\)
\(252\) 9.37080 + 1.86397i 0.590305 + 0.117419i
\(253\) −1.19862 + 2.89371i −0.0753563 + 0.181926i
\(254\) −10.0990 −0.633670
\(255\) 16.5562 + 26.6871i 1.03679 + 1.67121i
\(256\) −1.00000 −0.0625000
\(257\) −7.14288 + 17.2444i −0.445561 + 1.07568i 0.528407 + 0.848991i \(0.322790\pi\)
−0.973967 + 0.226688i \(0.927210\pi\)
\(258\) −0.630467 0.125408i −0.0392512 0.00780754i
\(259\) −4.53442 4.53442i −0.281755 0.281755i
\(260\) 4.32409 8.91242i 0.268169 0.552725i
\(261\) 14.4287 21.5941i 0.893114 1.33664i
\(262\) 1.74731 2.61503i 0.107949 0.161557i
\(263\) 21.7344 9.00268i 1.34020 0.555129i 0.406652 0.913583i \(-0.366696\pi\)
0.933547 + 0.358454i \(0.116696\pi\)
\(264\) −3.15471 1.30672i −0.194159 0.0804232i
\(265\) 1.64513 27.8422i 0.101060 1.71034i
\(266\) −0.506616 0.338510i −0.0310626 0.0207554i
\(267\) 13.2561 + 19.8391i 0.811258 + 1.21413i
\(268\) −0.804548 −0.0491456
\(269\) 0.188978 + 0.282826i 0.0115222 + 0.0172442i 0.837186 0.546918i \(-0.184199\pi\)
−0.825664 + 0.564162i \(0.809199\pi\)
\(270\) 34.0289 + 25.7653i 2.07093 + 1.56803i
\(271\) 2.26776i 0.137757i −0.997625 0.0688783i \(-0.978058\pi\)
0.997625 0.0688783i \(-0.0219420\pi\)
\(272\) −1.67349 3.76821i −0.101470 0.228482i
\(273\) 11.8499 11.8499i 0.717191 0.717191i
\(274\) 3.38509 1.40215i 0.204500 0.0847069i
\(275\) 4.99670 0.392101i 0.301313 0.0236446i
\(276\) −7.52620 + 7.52620i −0.453024 + 0.453024i
\(277\) 6.89102 4.60443i 0.414041 0.276654i −0.331054 0.943612i \(-0.607404\pi\)
0.745095 + 0.666958i \(0.232404\pi\)
\(278\) 2.29759 + 11.5508i 0.137800 + 0.692769i
\(279\) −12.5608 + 2.49849i −0.751994 + 0.149581i
\(280\) 2.45978 0.339943i 0.147000 0.0203155i
\(281\) −0.165173 + 0.398764i −0.00985342 + 0.0237883i −0.928730 0.370758i \(-0.879098\pi\)
0.918876 + 0.394546i \(0.129098\pi\)
\(282\) 17.2788 + 11.5453i 1.02894 + 0.687513i
\(283\) 26.1280 5.19719i 1.55315 0.308941i 0.657415 0.753529i \(-0.271650\pi\)
0.895735 + 0.444588i \(0.146650\pi\)
\(284\) −0.887146 + 4.45998i −0.0526424 + 0.264651i
\(285\) −2.11284 3.60579i −0.125154 0.213589i
\(286\) −3.69238 + 2.46717i −0.218335 + 0.145887i
\(287\) 9.23579 + 3.82559i 0.545171 + 0.225817i
\(288\) −6.08369 6.08369i −0.358485 0.358485i
\(289\) 11.3989 12.6121i 0.670522 0.741890i
\(290\) 1.70501 6.53091i 0.100122 0.383508i
\(291\) 8.82230 + 21.2989i 0.517172 + 1.24856i
\(292\) −0.355928 + 1.78937i −0.0208291 + 0.104715i
\(293\) 7.34635i 0.429178i 0.976704 + 0.214589i \(0.0688413\pi\)
−0.976704 + 0.214589i \(0.931159\pi\)
\(294\) −19.2666 3.83236i −1.12365 0.223508i
\(295\) −26.6969 1.57746i −1.55435 0.0918430i
\(296\) 1.12655 + 5.66357i 0.0654797 + 0.329188i
\(297\) −7.32240 17.6778i −0.424889 1.02577i
\(298\) −6.49059 15.6697i −0.375989 0.907719i
\(299\) 2.70049 + 13.5763i 0.156173 + 0.785137i
\(300\) 16.1972 + 5.26689i 0.935149 + 0.304084i
\(301\) −0.205535 0.0408834i −0.0118468 0.00235648i
\(302\) 11.2192i 0.645592i
\(303\) −0.227714 + 1.14479i −0.0130818 + 0.0657667i
\(304\) 0.209967 + 0.506906i 0.0120425 + 0.0290731i
\(305\) −2.17157 3.70603i −0.124344 0.212206i
\(306\) 12.7437 33.1056i 0.728507 1.89252i
\(307\) −10.1701 10.1701i −0.580438 0.580438i 0.354586 0.935024i \(-0.384622\pi\)
−0.935024 + 0.354586i \(0.884622\pi\)
\(308\) −1.02845 0.425997i −0.0586013 0.0242734i
\(309\) −30.7347 + 20.5363i −1.74844 + 1.16827i
\(310\) −2.87178 + 1.68274i −0.163106 + 0.0955732i
\(311\) 5.14414 25.8613i 0.291697 1.46646i −0.505544 0.862801i \(-0.668708\pi\)
0.797242 0.603660i \(-0.206292\pi\)
\(312\) −14.8008 + 2.94406i −0.837929 + 0.166674i
\(313\) −19.1536 12.7980i −1.08262 0.723386i −0.119606 0.992821i \(-0.538163\pi\)
−0.963019 + 0.269435i \(0.913163\pi\)
\(314\) 2.84111 6.85905i 0.160333 0.387079i
\(315\) 17.0327 + 12.8965i 0.959683 + 0.726633i
\(316\) 5.13719 1.02185i 0.288989 0.0574835i
\(317\) 3.81173 + 19.1629i 0.214088 + 1.07629i 0.927006 + 0.375046i \(0.122373\pi\)
−0.712918 + 0.701247i \(0.752627\pi\)
\(318\) −35.3280 + 23.6054i −1.98110 + 1.32373i
\(319\) −2.13962 + 2.13962i −0.119796 + 0.119796i
\(320\) −2.01179 0.976070i −0.112462 0.0545640i
\(321\) −36.9315 + 15.2975i −2.06131 + 0.853824i
\(322\) −2.45357 + 2.45357i −0.136732 + 0.136732i
\(323\) −1.55875 + 1.63950i −0.0867313 + 0.0912245i
\(324\) 39.2117i 2.17843i
\(325\) 17.3983 13.7093i 0.965084 0.760453i
\(326\) 8.75441 + 13.1019i 0.484862 + 0.725647i
\(327\) 32.7198 1.80941
\(328\) −5.00124 7.48488i −0.276147 0.413283i
\(329\) 5.63295 + 3.76382i 0.310555 + 0.207506i
\(330\) −5.07115 5.70806i −0.279157 0.314219i
\(331\) 14.3226 + 5.93263i 0.787243 + 0.326087i 0.739835 0.672789i \(-0.234904\pi\)
0.0474085 + 0.998876i \(0.484904\pi\)
\(332\) 11.1278 4.60927i 0.610715 0.252966i
\(333\) −27.6018 + 41.3090i −1.51257 + 2.26372i
\(334\) 10.0777 15.0823i 0.551426 0.825268i
\(335\) −1.61858 0.785296i −0.0884325 0.0429053i
\(336\) −2.67487 2.67487i −0.145926 0.145926i
\(337\) −7.52942 1.49770i −0.410154 0.0815847i −0.0142990 0.999898i \(-0.504552\pi\)
−0.395855 + 0.918313i \(0.629552\pi\)
\(338\) −2.53558 + 6.12143i −0.137917 + 0.332962i
\(339\) 19.2867 1.04751
\(340\) 0.311339 9.21429i 0.0168847 0.499715i
\(341\) 1.49213 0.0808034
\(342\) −1.80648 + 4.36124i −0.0976835 + 0.235829i
\(343\) −13.9051 2.76591i −0.750807 0.149345i
\(344\) 0.133437 + 0.133437i 0.00719444 + 0.00719444i
\(345\) −22.4872 + 7.79501i −1.21067 + 0.419669i
\(346\) −11.4682 + 17.1633i −0.616532 + 0.922705i
\(347\) 9.07091 13.5756i 0.486952 0.728775i −0.503895 0.863765i \(-0.668100\pi\)
0.990847 + 0.134990i \(0.0431002\pi\)
\(348\) −9.49989 + 3.93498i −0.509247 + 0.210937i
\(349\) −1.69599 0.702502i −0.0907842 0.0376041i 0.336829 0.941566i \(-0.390646\pi\)
−0.427613 + 0.903962i \(0.640646\pi\)
\(350\) 5.28037 + 1.71703i 0.282248 + 0.0917791i
\(351\) −70.3117 46.9808i −3.75296 2.50765i
\(352\) 0.556911 + 0.833476i 0.0296834 + 0.0444244i
\(353\) −19.2067 −1.02227 −0.511134 0.859501i \(-0.670775\pi\)
−0.511134 + 0.859501i \(0.670775\pi\)
\(354\) 22.6344 + 33.8747i 1.20300 + 1.80042i
\(355\) −6.13801 + 8.10662i −0.325772 + 0.430255i
\(356\) 7.00452i 0.371239i
\(357\) 5.60311 14.5558i 0.296548 0.770377i
\(358\) 4.82702 4.82702i 0.255116 0.255116i
\(359\) −14.0392 + 5.81524i −0.740962 + 0.306916i −0.721048 0.692885i \(-0.756339\pi\)
−0.0199139 + 0.999802i \(0.506339\pi\)
\(360\) −6.30098 18.1772i −0.332091 0.958023i
\(361\) −13.2222 + 13.2222i −0.695903 + 0.695903i
\(362\) −3.95885 + 2.64522i −0.208073 + 0.139030i
\(363\) −6.64237 33.3934i −0.348634 1.75270i
\(364\) −4.82512 + 0.959775i −0.252905 + 0.0503059i
\(365\) −2.46260 + 3.25242i −0.128898 + 0.170239i
\(366\) −2.50411 + 6.04547i −0.130892 + 0.316002i
\(367\) −12.2318 8.17305i −0.638496 0.426630i 0.193738 0.981053i \(-0.437939\pi\)
−0.832235 + 0.554424i \(0.812939\pi\)
\(368\) 3.06456 0.609578i 0.159751 0.0317764i
\(369\) 15.1097 75.9617i 0.786580 3.95441i
\(370\) −3.26166 + 12.4935i −0.169566 + 0.649506i
\(371\) −11.5171 + 7.69547i −0.597937 + 0.399529i
\(372\) 4.68460 + 1.94043i 0.242885 + 0.100606i
\(373\) 1.82717 + 1.82717i 0.0946071 + 0.0946071i 0.752826 0.658219i \(-0.228690\pi\)
−0.658219 + 0.752826i \(0.728690\pi\)
\(374\) −2.20873 + 3.49337i −0.114211 + 0.180638i
\(375\) 27.4446 + 26.4055i 1.41723 + 1.36358i
\(376\) −2.33458 5.63618i −0.120397 0.290664i
\(377\) −2.60889 + 13.1158i −0.134364 + 0.675496i
\(378\) 21.1977i 1.09029i
\(379\) 1.77933 + 0.353931i 0.0913981 + 0.0181802i 0.240577 0.970630i \(-0.422663\pi\)
−0.149179 + 0.988810i \(0.547663\pi\)
\(380\) −0.0723664 + 1.22473i −0.00371232 + 0.0628274i
\(381\) 6.71140 + 33.7405i 0.343835 + 1.72858i
\(382\) −3.88523 9.37977i −0.198786 0.479911i
\(383\) −7.90246 19.0782i −0.403797 0.974852i −0.986736 0.162336i \(-0.948097\pi\)
0.582939 0.812516i \(-0.301903\pi\)
\(384\) 0.664558 + 3.34096i 0.0339131 + 0.170493i
\(385\) −1.65321 1.86085i −0.0842556 0.0948378i
\(386\) 7.54568 + 1.50093i 0.384065 + 0.0763953i
\(387\) 1.62358i 0.0825312i
\(388\) 1.32032 6.63772i 0.0670293 0.336979i
\(389\) 0.669963 + 1.61743i 0.0339685 + 0.0820071i 0.939953 0.341303i \(-0.110868\pi\)
−0.905985 + 0.423310i \(0.860868\pi\)
\(390\) −32.6496 8.52379i −1.65328 0.431619i
\(391\) 7.42552 + 10.5278i 0.375525 + 0.532413i
\(392\) 4.07773 + 4.07773i 0.205956 + 0.205956i
\(393\) −9.89788 4.09984i −0.499282 0.206809i
\(394\) −3.96501 + 2.64933i −0.199754 + 0.133472i
\(395\) 11.3323 + 2.95851i 0.570191 + 0.148859i
\(396\) −1.68254 + 8.45868i −0.0845507 + 0.425065i
\(397\) −1.64219 + 0.326653i −0.0824193 + 0.0163942i −0.236128 0.971722i \(-0.575878\pi\)
0.153708 + 0.988116i \(0.450878\pi\)
\(398\) 9.21092 + 6.15454i 0.461702 + 0.308499i
\(399\) −0.794272 + 1.91754i −0.0397634 + 0.0959972i
\(400\) −3.09457 3.92729i −0.154729 0.196365i
\(401\) 20.5762 4.09286i 1.02753 0.204388i 0.347581 0.937650i \(-0.387003\pi\)
0.679946 + 0.733262i \(0.262003\pi\)
\(402\) 0.534669 + 2.68796i 0.0266669 + 0.134063i
\(403\) 5.48303 3.66364i 0.273129 0.182499i
\(404\) 0.242293 0.242293i 0.0120545 0.0120545i
\(405\) 38.2734 78.8856i 1.90182 3.91986i
\(406\) −3.09700 + 1.28282i −0.153702 + 0.0636653i
\(407\) 4.09306 4.09306i 0.202885 0.202885i
\(408\) −11.4773 + 8.09525i −0.568212 + 0.400775i
\(409\) 38.0662i 1.88225i 0.338057 + 0.941126i \(0.390230\pi\)
−0.338057 + 0.941126i \(0.609770\pi\)
\(410\) −2.75565 19.9395i −0.136092 0.984743i
\(411\) −6.93410 10.3776i −0.342034 0.511890i
\(412\) 10.8514 0.534611
\(413\) 7.37890 + 11.0433i 0.363092 + 0.543406i
\(414\) 22.3523 + 14.9353i 1.09856 + 0.734031i
\(415\) 26.8856 + 1.58861i 1.31976 + 0.0779817i
\(416\) 4.09288 + 1.69533i 0.200670 + 0.0831202i
\(417\) 37.0637 15.3523i 1.81502 0.751805i
\(418\) 0.305561 0.457304i 0.0149455 0.0223675i
\(419\) −7.41531 + 11.0978i −0.362262 + 0.542163i −0.967169 0.254133i \(-0.918210\pi\)
0.604908 + 0.796296i \(0.293210\pi\)
\(420\) −2.77041 7.99213i −0.135182 0.389976i
\(421\) 14.3935 + 14.3935i 0.701496 + 0.701496i 0.964732 0.263236i \(-0.0847897\pi\)
−0.263236 + 0.964732i \(0.584790\pi\)
\(422\) −8.23800 1.63864i −0.401019 0.0797677i
\(423\) 20.0859 48.4916i 0.976610 2.35774i
\(424\) 12.4731 0.605749
\(425\) 9.62014 18.2333i 0.466645 0.884445i
\(426\) 15.4902 0.750502
\(427\) −0.816352 + 1.97085i −0.0395060 + 0.0953760i
\(428\) 11.5095 + 2.28939i 0.556335 + 0.110662i
\(429\) 10.6965 + 10.6965i 0.516433 + 0.516433i
\(430\) 0.138203 + 0.398691i 0.00666474 + 0.0192266i
\(431\) −11.5624 + 17.3044i −0.556943 + 0.833524i −0.997951 0.0639791i \(-0.979621\pi\)
0.441008 + 0.897503i \(0.354621\pi\)
\(432\) −10.6049 + 15.8713i −0.510228 + 0.763611i
\(433\) −6.00076 + 2.48560i −0.288378 + 0.119450i −0.522183 0.852833i \(-0.674882\pi\)
0.233805 + 0.972284i \(0.424882\pi\)
\(434\) 1.52720 + 0.632587i 0.0733080 + 0.0303652i
\(435\) −22.9526 1.35621i −1.10049 0.0650254i
\(436\) −7.98657 5.33646i −0.382487 0.255570i
\(437\) −0.952456 1.42545i −0.0455621 0.0681886i
\(438\) 6.21474 0.296952
\(439\) 10.0507 + 15.0419i 0.479692 + 0.717910i 0.989841 0.142176i \(-0.0454099\pi\)
−0.510149 + 0.860086i \(0.670410\pi\)
\(440\) 0.306855 + 2.22036i 0.0146287 + 0.105851i
\(441\) 49.6153i 2.36263i
\(442\) 0.461036 + 18.2600i 0.0219293 + 0.868537i
\(443\) −26.2032 + 26.2032i −1.24495 + 1.24495i −0.287029 + 0.957922i \(0.592668\pi\)
−0.957922 + 0.287029i \(0.907332\pi\)
\(444\) 18.1731 7.52754i 0.862457 0.357241i
\(445\) 6.83691 14.0916i 0.324100 0.668006i
\(446\) 13.9738 13.9738i 0.661678 0.661678i
\(447\) −48.0383 + 32.0982i −2.27213 + 1.51819i
\(448\) 0.216649 + 1.08917i 0.0102357 + 0.0514583i
\(449\) −31.4989 + 6.26553i −1.48653 + 0.295689i −0.870552 0.492077i \(-0.836238\pi\)
−0.615975 + 0.787765i \(0.711238\pi\)
\(450\) 5.06600 42.7189i 0.238814 2.01379i
\(451\) −3.45322 + 8.33682i −0.162606 + 0.392565i
\(452\) −4.70769 3.14558i −0.221431 0.147956i
\(453\) 37.4829 7.45581i 1.76110 0.350304i
\(454\) 1.07198 5.38919i 0.0503104 0.252927i
\(455\) −10.6439 2.77879i −0.498994 0.130272i
\(456\) 1.55402 1.03836i 0.0727735 0.0486257i
\(457\) −22.9675 9.51343i −1.07437 0.445020i −0.225841 0.974164i \(-0.572513\pi\)
−0.848532 + 0.529145i \(0.822513\pi\)
\(458\) −2.45788 2.45788i −0.114849 0.114849i
\(459\) −77.5538 13.4010i −3.61990 0.625505i
\(460\) 6.76022 + 1.76488i 0.315197 + 0.0822880i
\(461\) 4.92471 + 11.8893i 0.229367 + 0.553740i 0.996101 0.0882249i \(-0.0281194\pi\)
−0.766734 + 0.641965i \(0.778119\pi\)
\(462\) −0.739775 + 3.71910i −0.0344175 + 0.173028i
\(463\) 26.9358i 1.25181i 0.779898 + 0.625907i \(0.215271\pi\)
−0.779898 + 0.625907i \(0.784729\pi\)
\(464\) 2.96060 + 0.588900i 0.137442 + 0.0273390i
\(465\) 7.53043 + 8.47623i 0.349215 + 0.393076i
\(466\) 2.36203 + 11.8747i 0.109419 + 0.550086i
\(467\) −4.57740 11.0508i −0.211817 0.511371i 0.781886 0.623422i \(-0.214258\pi\)
−0.993702 + 0.112051i \(0.964258\pi\)
\(468\) 14.5860 + 35.2137i 0.674237 + 1.62775i
\(469\) 0.174304 + 0.876287i 0.00804863 + 0.0404632i
\(470\) 0.804626 13.6175i 0.0371146 0.628129i
\(471\) −24.8039 4.93380i −1.14290 0.227338i
\(472\) 11.9600i 0.550505i
\(473\) 0.0369040 0.185529i 0.00169685 0.00853063i
\(474\) −6.82791 16.4840i −0.313617 0.757137i
\(475\) −1.34101 + 2.39326i −0.0615297 + 0.109810i
\(476\) −3.74165 + 2.63909i −0.171498 + 0.120962i
\(477\) 75.8828 + 75.8828i 3.47443 + 3.47443i
\(478\) 13.1370 + 5.44152i 0.600872 + 0.248890i
\(479\) 23.8498 15.9359i 1.08972 0.728131i 0.125202 0.992131i \(-0.460042\pi\)
0.964523 + 0.264000i \(0.0850420\pi\)
\(480\) −1.92406 + 7.36995i −0.0878210 + 0.336391i
\(481\) 4.99075 25.0902i 0.227559 1.14401i
\(482\) 5.06964 1.00841i 0.230916 0.0459320i
\(483\) 9.82782 + 6.56674i 0.447181 + 0.298797i
\(484\) −3.82499 + 9.23433i −0.173863 + 0.419742i
\(485\) 9.13510 12.0650i 0.414803 0.547841i
\(486\) −74.8401 + 14.8866i −3.39482 + 0.675271i
\(487\) −6.56730 33.0161i −0.297593 1.49610i −0.783116 0.621876i \(-0.786371\pi\)
0.485523 0.874224i \(-0.338629\pi\)
\(488\) 1.59722 1.06723i 0.0723026 0.0483110i
\(489\) 37.9551 37.9551i 1.71639 1.71639i
\(490\) 4.22337 + 12.1837i 0.190792 + 0.550402i
\(491\) 11.5798 4.79652i 0.522590 0.216464i −0.105764 0.994391i \(-0.533729\pi\)
0.628354 + 0.777927i \(0.283729\pi\)
\(492\) −21.6831 + 21.6831i −0.977548 + 0.977548i
\(493\) 2.73543 + 12.1417i 0.123198 + 0.546834i
\(494\) 2.43067i 0.109361i
\(495\) −11.6412 + 15.3748i −0.523232 + 0.691046i
\(496\) −0.826988 1.23768i −0.0371329 0.0555733i
\(497\) 5.04986 0.226517
\(498\) −22.7944 34.1142i −1.02144 1.52870i
\(499\) −5.43966 3.63466i −0.243512 0.162710i 0.427825 0.903862i \(-0.359280\pi\)
−0.671338 + 0.741152i \(0.734280\pi\)
\(500\) −2.39231 10.9214i −0.106987 0.488420i
\(501\) −57.0866 23.6460i −2.55044 1.05643i
\(502\) 24.1218 9.99159i 1.07661 0.445947i
\(503\) −5.47341 + 8.19153i −0.244047 + 0.365242i −0.933190 0.359383i \(-0.882987\pi\)
0.689143 + 0.724625i \(0.257987\pi\)
\(504\) −5.30813 + 7.94418i −0.236443 + 0.353862i
\(505\) 0.723938 0.250947i 0.0322148 0.0111670i
\(506\) −2.21475 2.21475i −0.0984577 0.0984577i
\(507\) 22.1365 + 4.40322i 0.983116 + 0.195554i
\(508\) 3.86473 9.33030i 0.171470 0.413965i
\(509\) −32.3534 −1.43404 −0.717020 0.697052i \(-0.754494\pi\)
−0.717020 + 0.697052i \(0.754494\pi\)
\(510\) −30.9915 + 5.08326i −1.37232 + 0.225090i
\(511\) 2.02603 0.0896264
\(512\) 0.382683 0.923880i 0.0169124 0.0408301i
\(513\) 10.2720 + 2.04322i 0.453519 + 0.0902104i
\(514\) −13.1983 13.1983i −0.582153 0.582153i
\(515\) 21.8307 + 10.5917i 0.961976 + 0.466728i
\(516\) 0.357131 0.534484i 0.0157218 0.0235294i
\(517\) −3.39746 + 5.08466i −0.149420 + 0.223623i
\(518\) 5.92451 2.45401i 0.260308 0.107823i
\(519\) 64.9632 + 26.9086i 2.85157 + 1.18116i
\(520\) 6.57924 + 7.40557i 0.288519 + 0.324756i
\(521\) 6.37903 + 4.26233i 0.279471 + 0.186736i 0.687404 0.726276i \(-0.258750\pi\)
−0.407933 + 0.913012i \(0.633750\pi\)
\(522\) 14.4287 + 21.5941i 0.631527 + 0.945147i
\(523\) −21.2279 −0.928230 −0.464115 0.885775i \(-0.653628\pi\)
−0.464115 + 0.885775i \(0.653628\pi\)
\(524\) 1.74731 + 2.61503i 0.0763314 + 0.114238i
\(525\) 2.22741 18.7826i 0.0972122 0.819738i
\(526\) 23.5251i 1.02574i
\(527\) 3.27987 5.18750i 0.142873 0.225971i
\(528\) 2.41451 2.41451i 0.105078 0.105078i
\(529\) 12.2293 5.06555i 0.531709 0.220241i
\(530\) 25.0933 + 12.1747i 1.08998 + 0.528834i
\(531\) 72.7612 72.7612i 3.15757 3.15757i
\(532\) 0.506616 0.338510i 0.0219646 0.0146763i
\(533\) 7.78014 + 39.1134i 0.336995 + 1.69419i
\(534\) −23.4018 + 4.65491i −1.01270 + 0.201438i
\(535\) 20.9202 + 15.8399i 0.904457 + 0.684818i
\(536\) 0.307887 0.743306i 0.0132987 0.0321059i
\(537\) −19.3347 12.9190i −0.834355 0.557498i
\(538\) −0.333616 + 0.0663603i −0.0143832 + 0.00286099i
\(539\) 1.12776 5.66962i 0.0485759 0.244208i
\(540\) −36.8263 + 21.5786i −1.58475 + 0.928597i
\(541\) −22.8895 + 15.2943i −0.984095 + 0.657551i −0.939892 0.341471i \(-0.889075\pi\)
−0.0442028 + 0.999023i \(0.514075\pi\)
\(542\) 2.09514 + 0.867834i 0.0899938 + 0.0372766i
\(543\) 11.4685 + 11.4685i 0.492159 + 0.492159i
\(544\) 4.12179 0.104069i 0.176720 0.00446192i
\(545\) −10.8585 18.5313i −0.465128 0.793792i
\(546\) 6.41314 + 15.4827i 0.274457 + 0.662598i
\(547\) 1.09867 5.52336i 0.0469755 0.236162i −0.950163 0.311752i \(-0.899084\pi\)
0.997139 + 0.0755903i \(0.0240841\pi\)
\(548\) 3.66399i 0.156518i
\(549\) 16.2096 + 3.22430i 0.691811 + 0.137610i
\(550\) −1.54990 + 4.76640i −0.0660880 + 0.203240i
\(551\) −0.323113 1.62440i −0.0137651 0.0692016i
\(552\) −4.07315 9.83345i −0.173365 0.418539i
\(553\) −2.22593 5.37387i −0.0946561 0.228520i
\(554\) 1.61686 + 8.12851i 0.0686939 + 0.345347i
\(555\) 43.9078 + 2.59441i 1.86378 + 0.110127i
\(556\) −11.5508 2.29759i −0.489861 0.0974395i
\(557\) 27.2007i 1.15253i 0.817262 + 0.576266i \(0.195491\pi\)
−0.817262 + 0.576266i \(0.804509\pi\)
\(558\) 2.49849 12.5608i 0.105770 0.531740i
\(559\) −0.319922 0.772361i −0.0135313 0.0326674i
\(560\) −0.627252 + 2.40264i −0.0265062 + 0.101530i
\(561\) 13.1390 + 5.05773i 0.554731 + 0.213538i
\(562\) −0.305201 0.305201i −0.0128741 0.0128741i
\(563\) −36.8345 15.2574i −1.55239 0.643021i −0.568644 0.822583i \(-0.692532\pi\)
−0.983747 + 0.179562i \(0.942532\pi\)
\(564\) −17.2788 + 11.5453i −0.727567 + 0.486145i
\(565\) −6.40056 10.9233i −0.269274 0.459545i
\(566\) −5.19719 + 26.1280i −0.218454 + 1.09824i
\(567\) −42.7081 + 8.49517i −1.79357 + 0.356763i
\(568\) −3.78099 2.52638i −0.158647 0.106004i
\(569\) 4.40995 10.6465i 0.184875 0.446327i −0.804085 0.594515i \(-0.797344\pi\)
0.988959 + 0.148188i \(0.0473442\pi\)
\(570\) 4.13987 0.572131i 0.173400 0.0239639i
\(571\) 21.2192 4.22076i 0.887996 0.176633i 0.270043 0.962848i \(-0.412962\pi\)
0.617953 + 0.786215i \(0.287962\pi\)
\(572\) −0.866355 4.35546i −0.0362241 0.182111i
\(573\) −28.7555 + 19.2138i −1.20128 + 0.802668i
\(574\) −7.06877 + 7.06877i −0.295045 + 0.295045i
\(575\) 11.8775 + 10.1490i 0.495325 + 0.423243i
\(576\) 7.94873 3.29247i 0.331197 0.137186i
\(577\) 30.0318 30.0318i 1.25024 1.25024i 0.294630 0.955612i \(-0.404804\pi\)
0.955612 0.294630i \(-0.0951962\pi\)
\(578\) 7.28993 + 15.3576i 0.303221 + 0.638793i
\(579\) 26.2073i 1.08914i
\(580\) 5.38129 + 4.07450i 0.223446 + 0.169184i
\(581\) −7.43107 11.1214i −0.308293 0.461393i
\(582\) −23.0538 −0.955610
\(583\) −6.94643 10.3961i −0.287692 0.430561i
\(584\) −1.51695 1.01360i −0.0627720 0.0419429i
\(585\) −5.02714 + 85.0793i −0.207847 + 3.51760i
\(586\) −6.78714 2.81133i −0.280374 0.116135i
\(587\) −0.926898 + 0.383934i −0.0382572 + 0.0158466i −0.401730 0.915758i \(-0.631591\pi\)
0.363473 + 0.931605i \(0.381591\pi\)
\(588\) 10.9136 16.3334i 0.450071 0.673578i
\(589\) −0.453745 + 0.679077i −0.0186962 + 0.0279809i
\(590\) 11.6738 24.0610i 0.480604 0.990577i
\(591\) 11.4863 + 11.4863i 0.472483 + 0.472483i
\(592\) −5.66357 1.12655i −0.232771 0.0463011i
\(593\) −3.40175 + 8.21255i −0.139693 + 0.337249i −0.978207 0.207631i \(-0.933425\pi\)
0.838514 + 0.544880i \(0.183425\pi\)
\(594\) 19.1344 0.785092
\(595\) −10.1033 + 1.65716i −0.414197 + 0.0679371i
\(596\) 16.9607 0.694738
\(597\) 14.4409 34.8634i 0.591026 1.42686i
\(598\) −13.5763 2.70049i −0.555176 0.110431i
\(599\) 6.14617 + 6.14617i 0.251126 + 0.251126i 0.821432 0.570306i \(-0.193176\pi\)
−0.570306 + 0.821432i \(0.693176\pi\)
\(600\) −11.0644 + 12.9488i −0.451702 + 0.528631i
\(601\) 10.2301 15.3104i 0.417294 0.624525i −0.561959 0.827165i \(-0.689952\pi\)
0.979253 + 0.202640i \(0.0649522\pi\)
\(602\) 0.116426 0.174244i 0.00474518 0.00710166i
\(603\) 6.39514 2.64895i 0.260430 0.107874i
\(604\) −10.3652 4.29340i −0.421753 0.174696i
\(605\) −16.7084 + 14.8441i −0.679294 + 0.603497i
\(606\) −0.970509 0.648474i −0.0394243 0.0263424i
\(607\) 23.2009 + 34.7226i 0.941696 + 1.40935i 0.912183 + 0.409783i \(0.134396\pi\)
0.0295133 + 0.999564i \(0.490604\pi\)
\(608\) −0.548671 −0.0222516
\(609\) 6.34399 + 9.49445i 0.257071 + 0.384734i
\(610\) 4.25495 0.588035i 0.172278 0.0238089i
\(611\) 27.0261i 1.09336i
\(612\) 25.7088 + 24.4426i 1.03922 + 0.988033i
\(613\) −14.8737 + 14.8737i −0.600741 + 0.600741i −0.940509 0.339768i \(-0.889651\pi\)
0.339768 + 0.940509i \(0.389651\pi\)
\(614\) 13.2879 5.50402i 0.536255 0.222124i
\(615\) −64.7859 + 22.4575i −2.61242 + 0.905574i
\(616\) 0.787140 0.787140i 0.0317148 0.0317148i
\(617\) 23.6669 15.8137i 0.952792 0.636635i 0.0210586 0.999778i \(-0.493296\pi\)
0.931733 + 0.363143i \(0.118296\pi\)
\(618\) −7.21139 36.2541i −0.290085 1.45835i
\(619\) −15.5083 + 3.08480i −0.623332 + 0.123988i −0.496644 0.867954i \(-0.665435\pi\)
−0.126688 + 0.991943i \(0.540435\pi\)
\(620\) −0.455666 3.29714i −0.0183000 0.132416i
\(621\) 22.8245 55.1031i 0.915914 2.21121i
\(622\) 21.9242 + 14.6493i 0.879079 + 0.587382i
\(623\) −7.62909 + 1.51752i −0.305653 + 0.0607982i
\(624\) 2.94406 14.8008i 0.117857 0.592505i
\(625\) 5.84723 24.3066i 0.233889 0.972263i
\(626\) 19.1536 12.7980i 0.765531 0.511511i
\(627\) −1.73090 0.716961i −0.0691254 0.0286327i
\(628\) 5.24969 + 5.24969i 0.209486 + 0.209486i
\(629\) −5.23283 23.2268i −0.208646 0.926114i
\(630\) −18.4329 + 10.8009i −0.734384 + 0.430318i
\(631\) −12.6072 30.4365i −0.501885 1.21166i −0.948456 0.316910i \(-0.897355\pi\)
0.446570 0.894749i \(-0.352645\pi\)
\(632\) −1.02185 + 5.13719i −0.0406470 + 0.204346i
\(633\) 28.6118i 1.13722i
\(634\) −19.1629 3.81173i −0.761054 0.151383i
\(635\) 16.8820 14.9983i 0.669944 0.595190i
\(636\) −8.28913 41.6723i −0.328685 1.65241i
\(637\) −9.77657 23.6027i −0.387362 0.935174i
\(638\) −1.15796 2.79555i −0.0458439 0.110677i
\(639\) −7.63269 38.3721i −0.301944 1.51798i
\(640\) 1.67165 1.48512i 0.0660777 0.0587046i
\(641\) 13.3488 + 2.65524i 0.527246 + 0.104876i 0.451534 0.892254i \(-0.350877\pi\)
0.0757122 + 0.997130i \(0.475877\pi\)
\(642\) 39.9744i 1.57766i
\(643\) 0.480598 2.41613i 0.0189529 0.0952828i −0.970151 0.242501i \(-0.922032\pi\)
0.989104 + 0.147219i \(0.0470321\pi\)
\(644\) −1.32786 3.20575i −0.0523252 0.126324i
\(645\) 1.24017 0.726683i 0.0488315 0.0286131i
\(646\) −0.918195 2.06751i −0.0361259 0.0813451i
\(647\) −21.2530 21.2530i −0.835542 0.835542i 0.152727 0.988268i \(-0.451195\pi\)
−0.988268 + 0.152727i \(0.951195\pi\)
\(648\) 36.2269 + 15.0057i 1.42313 + 0.589478i
\(649\) −9.96840 + 6.66067i −0.391294 + 0.261454i
\(650\) 6.00767 + 21.3202i 0.235640 + 0.836249i
\(651\) 1.09853 5.52270i 0.0430549 0.216452i
\(652\) −15.4547 + 3.07414i −0.605255 + 0.120393i
\(653\) −4.35193 2.90787i −0.170304 0.113794i 0.467497 0.883995i \(-0.345156\pi\)
−0.637801 + 0.770201i \(0.720156\pi\)
\(654\) −12.5213 + 30.2292i −0.489623 + 1.18205i
\(655\) 0.962755 + 6.96637i 0.0376180 + 0.272199i
\(656\) 8.82901 1.75620i 0.344715 0.0685681i
\(657\) −3.06227 15.3951i −0.119471 0.600620i
\(658\) −5.63295 + 3.76382i −0.219595 + 0.146729i
\(659\) −5.87271 + 5.87271i −0.228768 + 0.228768i −0.812178 0.583410i \(-0.801718\pi\)
0.583410 + 0.812178i \(0.301718\pi\)
\(660\) 7.21421 2.50075i 0.280813 0.0973414i
\(661\) 29.9673 12.4128i 1.16559 0.482804i 0.285858 0.958272i \(-0.407721\pi\)
0.879733 + 0.475468i \(0.157721\pi\)
\(662\) −10.9621 + 10.9621i −0.426053 + 0.426053i
\(663\) 60.6994 13.6751i 2.35737 0.531097i
\(664\) 12.0446i 0.467421i
\(665\) 1.34961 0.186517i 0.0523358 0.00723283i
\(666\) −27.6018 41.3090i −1.06955 1.60069i
\(667\) −9.43190 −0.365205
\(668\) 10.0777 + 15.0823i 0.389917 + 0.583552i
\(669\) −55.9722 37.3994i −2.16401 1.44595i
\(670\) 1.34492 1.19485i 0.0519589 0.0461612i
\(671\) −1.77901 0.736892i −0.0686781 0.0284474i
\(672\) 3.49488 1.44763i 0.134818 0.0558435i
\(673\) −1.33538 + 1.99854i −0.0514751 + 0.0770379i −0.856314 0.516455i \(-0.827251\pi\)
0.804839 + 0.593493i \(0.202251\pi\)
\(674\) 4.26508 6.38314i 0.164285 0.245869i
\(675\) −95.1490 + 7.46653i −3.66229 + 0.287387i
\(676\) −4.68514 4.68514i −0.180198 0.180198i
\(677\) −41.0135 8.15809i −1.57628 0.313541i −0.672021 0.740532i \(-0.734573\pi\)
−0.904256 + 0.426992i \(0.859573\pi\)
\(678\) −7.38071 + 17.8186i −0.283455 + 0.684320i
\(679\) −7.51563 −0.288423
\(680\) 8.39375 + 3.81379i 0.321885 + 0.146252i
\(681\) −18.7175 −0.717255
\(682\) −0.571014 + 1.37855i −0.0218652 + 0.0527874i
\(683\) −23.5331 4.68103i −0.900470 0.179115i −0.276916 0.960894i \(-0.589312\pi\)
−0.623555 + 0.781780i \(0.714312\pi\)
\(684\) −3.33795 3.33795i −0.127630 0.127630i
\(685\) −3.57631 + 7.37117i −0.136644 + 0.281638i
\(686\) 7.87663 11.7882i 0.300731 0.450076i
\(687\) −6.57826 + 9.84506i −0.250976 + 0.375612i
\(688\) −0.174344 + 0.0722156i −0.00664680 + 0.00275319i
\(689\) −51.0511 21.1460i −1.94489 0.805600i
\(690\) 1.40383 23.7585i 0.0534430 0.904470i
\(691\) 37.4684 + 25.0356i 1.42536 + 0.952398i 0.998851 + 0.0479168i \(0.0152582\pi\)
0.426513 + 0.904481i \(0.359742\pi\)
\(692\) −11.4682 17.1633i −0.435954 0.652451i
\(693\) 9.57743 0.363817
\(694\) 9.07091 + 13.5756i 0.344327 + 0.515322i
\(695\) −20.9951 15.8966i −0.796388 0.602993i
\(696\) 10.2826i 0.389761i
\(697\) 21.3930 + 30.3306i 0.810317 + 1.14885i
\(698\) 1.29805 1.29805i 0.0491321 0.0491321i
\(699\) 38.1032 15.7829i 1.44120 0.596963i
\(700\) −3.60704 + 4.22135i −0.136333 + 0.159552i
\(701\) −28.9028 + 28.9028i −1.09164 + 1.09164i −0.0962904 + 0.995353i \(0.530698\pi\)
−0.995353 + 0.0962904i \(0.969302\pi\)
\(702\) 70.3117 46.9808i 2.65374 1.77317i
\(703\) 0.618108 + 3.10744i 0.0233124 + 0.117199i
\(704\) −0.983152 + 0.195561i −0.0370539 + 0.00737048i
\(705\) −46.0302 + 6.36140i −1.73360 + 0.239584i
\(706\) 7.35008 17.7447i 0.276624 0.667829i
\(707\) −0.316390 0.211405i −0.0118991 0.00795071i
\(708\) −39.9580 + 7.94813i −1.50171 + 0.298709i
\(709\) −8.57537 + 43.1113i −0.322055 + 1.61908i 0.392675 + 0.919677i \(0.371550\pi\)
−0.714729 + 0.699401i \(0.753450\pi\)
\(710\) −5.14063 8.77305i −0.192924 0.329247i
\(711\) −37.4697 + 25.0364i −1.40522 + 0.938940i
\(712\) 6.47133 + 2.68051i 0.242523 + 0.100457i
\(713\) 3.28881 + 3.28881i 0.123167 + 0.123167i
\(714\) 11.3036 + 10.7469i 0.423027 + 0.402192i
\(715\) 2.50831 9.60788i 0.0938056 0.359314i
\(716\) 2.61237 + 6.30681i 0.0976287 + 0.235697i
\(717\) 9.44961 47.5064i 0.352902 1.77416i
\(718\) 15.1959i 0.567108i
\(719\) −2.24438 0.446435i −0.0837012 0.0166492i 0.153062 0.988217i \(-0.451087\pi\)
−0.236763 + 0.971567i \(0.576087\pi\)
\(720\) 19.2048 + 1.13477i 0.715722 + 0.0422903i
\(721\) −2.35094 11.8190i −0.0875537 0.440162i
\(722\) −7.15578 17.2756i −0.266311 0.642931i
\(723\) −6.73814 16.2673i −0.250594 0.604988i
\(724\) −0.928878 4.66979i −0.0345215 0.173551i
\(725\) 6.84901 + 13.4495i 0.254366 + 0.499503i
\(726\) 33.3934 + 6.64237i 1.23935 + 0.246521i
\(727\) 3.30429i 0.122549i −0.998121 0.0612747i \(-0.980483\pi\)
0.998121 0.0612747i \(-0.0195166\pi\)
\(728\) 0.959775 4.82512i 0.0355716 0.178831i
\(729\) 54.4542 + 131.464i 2.01682 + 4.86904i
\(730\) −2.06245 3.51979i −0.0763346 0.130273i
\(731\) −0.563886 0.536113i −0.0208561 0.0198289i
\(732\) −4.62700 4.62700i −0.171019 0.171019i
\(733\) 31.5964 + 13.0877i 1.16704 + 0.483404i 0.880213 0.474579i \(-0.157400\pi\)
0.286827 + 0.957982i \(0.407400\pi\)
\(734\) 12.2318 8.17305i 0.451485 0.301673i
\(735\) 37.8985 22.2069i 1.39791 0.819113i
\(736\) −0.609578 + 3.06456i −0.0224693 + 0.112961i
\(737\) −0.790993 + 0.157338i −0.0291366 + 0.00579563i
\(738\) 64.3972 + 43.0288i 2.37049 + 1.58391i
\(739\) −15.4004 + 37.1799i −0.566514 + 1.36769i 0.337961 + 0.941160i \(0.390263\pi\)
−0.904475 + 0.426526i \(0.859737\pi\)
\(740\) −10.2943 7.79443i −0.378426 0.286529i
\(741\) −8.12077 + 1.61532i −0.298324 + 0.0593403i
\(742\) −2.70229 13.5853i −0.0992042 0.498733i
\(743\) 31.3758 20.9647i 1.15107 0.769119i 0.174569 0.984645i \(-0.444147\pi\)
0.976498 + 0.215526i \(0.0691467\pi\)
\(744\) −3.58544 + 3.58544i −0.131449 + 0.131449i
\(745\) 34.1213 + 16.5549i 1.25011 + 0.606523i
\(746\) −2.38731 + 0.988856i −0.0874056 + 0.0362046i
\(747\) −73.2756 + 73.2756i −2.68101 + 2.68101i
\(748\) −2.38221 3.37746i −0.0871022 0.123492i
\(749\) 13.0318i 0.476172i
\(750\) −34.8981 + 15.2505i −1.27430 + 0.556870i
\(751\) 11.8751 + 17.7723i 0.433328 + 0.648521i 0.982299 0.187321i \(-0.0599803\pi\)
−0.548971 + 0.835841i \(0.684980\pi\)
\(752\) 6.10055 0.222464
\(753\) −49.4119 73.9501i −1.80067 2.69489i
\(754\) −11.1190 7.42948i −0.404930 0.270566i
\(755\) −16.6619 18.7546i −0.606388 0.682548i
\(756\) 19.5841 + 8.11199i 0.712266 + 0.295030i
\(757\) −31.2607 + 12.9486i −1.13619 + 0.470625i −0.869880 0.493263i \(-0.835804\pi\)
−0.266309 + 0.963888i \(0.585804\pi\)
\(758\) −1.00791 + 1.50844i −0.0366089 + 0.0547891i
\(759\) −5.92756 + 8.87122i −0.215157 + 0.322005i
\(760\) −1.10381 0.535542i −0.0400394 0.0194261i
\(761\) −24.4932 24.4932i −0.887877 0.887877i 0.106442 0.994319i \(-0.466054\pi\)
−0.994319 + 0.106442i \(0.966054\pi\)
\(762\) −33.7405 6.71140i −1.22229 0.243128i
\(763\) −4.08201 + 9.85484i −0.147779 + 0.356769i
\(764\) 10.1526 0.367308
\(765\) 27.8630 + 74.2669i 1.00739 + 2.68513i
\(766\) 20.6501 0.746119
\(767\) −20.2762 + 48.9510i −0.732129 + 1.76752i
\(768\) −3.34096 0.664558i −0.120556 0.0239802i
\(769\) −27.9366 27.9366i −1.00742 1.00742i −0.999972 0.00744621i \(-0.997630\pi\)
−0.00744621 0.999972i \(-0.502370\pi\)
\(770\) 2.35186 0.815254i 0.0847552 0.0293797i
\(771\) −35.3240 + 52.8661i −1.27216 + 1.90393i
\(772\) −4.27428 + 6.39692i −0.153835 + 0.230230i
\(773\) 43.6329 18.0733i 1.56937 0.650053i 0.582683 0.812700i \(-0.302003\pi\)
0.986684 + 0.162647i \(0.0520031\pi\)
\(774\) −1.49999 0.621317i −0.0539161 0.0223328i
\(775\) 2.30154 7.07790i 0.0826736 0.254246i
\(776\) 5.62719 + 3.75997i 0.202004 + 0.134975i
\(777\) −12.1359 18.1627i −0.435374 0.651583i
\(778\) −1.75070 −0.0627656
\(779\) −2.74403 4.10674i −0.0983153 0.147139i
\(780\) 20.3694 26.9024i 0.729342 0.963261i
\(781\) 4.55833i 0.163110i
\(782\) −12.5680 + 2.83148i −0.449431 + 0.101253i
\(783\) 40.7435 40.7435i 1.45605 1.45605i
\(784\) −5.32781 + 2.20685i −0.190279 + 0.0788161i
\(785\) 5.43719 + 15.6853i 0.194062 + 0.559834i
\(786\) 7.57551 7.57551i 0.270210 0.270210i
\(787\) 25.9285 17.3249i 0.924252 0.617565i 0.000269208 1.00000i \(-0.499914\pi\)
0.923983 + 0.382435i \(0.124914\pi\)
\(788\) −0.930323 4.67705i −0.0331414 0.166613i
\(789\) 78.5965 15.6338i 2.79811 0.556578i
\(790\) −7.07000 + 9.33753i −0.251539 + 0.332214i
\(791\) −2.40614 + 5.80894i −0.0855526 + 0.206542i
\(792\) −7.17093 4.79146i −0.254808 0.170257i
\(793\) −8.34651 + 1.66022i −0.296393 + 0.0589563i
\(794\) 0.326653 1.64219i 0.0115925 0.0582793i
\(795\) 23.9991 91.9265i 0.851160 3.26030i
\(796\) −9.21092 + 6.15454i −0.326473 + 0.218142i
\(797\) 21.5715 + 8.93522i 0.764103 + 0.316502i 0.730481 0.682933i \(-0.239296\pi\)
0.0336218 + 0.999435i \(0.489296\pi\)
\(798\) −1.46762 1.46762i −0.0519533 0.0519533i
\(799\) 10.2092 + 22.9882i 0.361176 + 0.813264i
\(800\) 4.81259 1.35610i 0.170151 0.0479455i
\(801\) 23.0622 + 55.6770i 0.814862 + 1.96725i
\(802\) −4.09286 + 20.5762i −0.144524 + 0.726571i
\(803\) 1.82883i 0.0645379i
\(804\) −2.68796 0.534669i −0.0947971 0.0188563i
\(805\) 0.457655 7.74537i 0.0161302 0.272988i
\(806\) 1.28650 + 6.46767i 0.0453150 + 0.227814i
\(807\) 0.443414 + 1.07050i 0.0156089 + 0.0376832i
\(808\) 0.131128 + 0.316571i 0.00461307 + 0.0111369i
\(809\) −0.811177 4.07806i −0.0285194 0.143377i 0.963902 0.266257i \(-0.0857870\pi\)
−0.992422 + 0.122880i \(0.960787\pi\)
\(810\) 58.2342 + 65.5482i 2.04614 + 2.30313i
\(811\) 17.7718 + 3.53503i 0.624053 + 0.124132i 0.496981 0.867762i \(-0.334442\pi\)
0.127072 + 0.991893i \(0.459442\pi\)
\(812\) 3.35217i 0.117638i
\(813\) 1.50706 7.57649i 0.0528548 0.265719i
\(814\) 2.21515 + 5.34784i 0.0776409 + 0.187442i
\(815\) −34.0922 8.90041i −1.19420 0.311768i
\(816\) −3.08686 13.7016i −0.108062 0.479651i
\(817\) 0.0732131 + 0.0732131i 0.00256140 + 0.00256140i
\(818\) −35.1686 14.5673i −1.22964 0.509333i
\(819\) 35.1935 23.5156i 1.22976 0.821700i
\(820\) 19.4763 + 5.08464i 0.680141 + 0.177563i
\(821\) −4.40020 + 22.1213i −0.153568 + 0.772038i 0.824842 + 0.565364i \(0.191264\pi\)
−0.978410 + 0.206675i \(0.933736\pi\)
\(822\) 12.2412 2.43493i 0.426962 0.0849281i
\(823\) −37.0162 24.7335i −1.29031 0.862154i −0.294680 0.955596i \(-0.595213\pi\)
−0.995625 + 0.0934416i \(0.970213\pi\)
\(824\) −4.15265 + 10.0254i −0.144665 + 0.349251i
\(825\) 16.9544 + 2.01060i 0.590275 + 0.0700003i
\(826\) −13.0265 + 2.59113i −0.453249 + 0.0901568i
\(827\) −3.82787 19.2440i −0.133108 0.669180i −0.988503 0.151203i \(-0.951685\pi\)
0.855395 0.517977i \(-0.173315\pi\)
\(828\) −22.3523 + 14.9353i −0.776796 + 0.519038i
\(829\) 8.97190 8.97190i 0.311607 0.311607i −0.533925 0.845532i \(-0.679284\pi\)
0.845532 + 0.533925i \(0.179284\pi\)
\(830\) −11.7564 + 24.2312i −0.408070 + 0.841076i
\(831\) 26.0825 10.8037i 0.904793 0.374777i
\(832\) −3.13255 + 3.13255i −0.108602 + 0.108602i
\(833\) −17.2319 16.3832i −0.597051 0.567644i
\(834\) 40.1175i 1.38916i
\(835\) 5.55275 + 40.1789i 0.192161 + 1.39045i
\(836\) 0.305561 + 0.457304i 0.0105680 + 0.0158162i
\(837\) −28.4137 −0.982121
\(838\) −7.41531 11.0978i −0.256158 0.383367i
\(839\) 14.2297 + 9.50797i 0.491263 + 0.328252i 0.776406 0.630234i \(-0.217041\pi\)
−0.285142 + 0.958485i \(0.592041\pi\)
\(840\) 8.44395 + 0.498933i 0.291344 + 0.0172148i
\(841\) 18.3742 + 7.61082i 0.633591 + 0.262442i
\(842\) −18.8060 + 7.78970i −0.648098 + 0.268451i
\(843\) −0.816840 + 1.22249i −0.0281335 + 0.0421047i
\(844\) 4.66645 6.98384i 0.160626 0.240394i
\(845\) −4.85248 13.9985i −0.166930 0.481564i
\(846\) 37.1139 + 37.1139i 1.27600 + 1.27600i
\(847\) 10.8864 + 2.16544i 0.374061 + 0.0744054i
\(848\) −4.77327 + 11.5237i −0.163915 + 0.395725i
\(849\) 90.7465 3.11441
\(850\) 13.1639 + 15.8654i 0.451518 + 0.544180i
\(851\) 18.0431 0.618508
\(852\) −5.92784 + 14.3111i −0.203084 + 0.490289i
\(853\) 42.3926 + 8.43242i 1.45150 + 0.288721i 0.856974 0.515359i \(-0.172341\pi\)
0.594522 + 0.804079i \(0.297341\pi\)
\(854\) −1.50842 1.50842i −0.0516171 0.0516171i
\(855\) −3.45717 9.97331i −0.118233 0.341080i
\(856\) −6.51964 + 9.75732i −0.222837 + 0.333498i
\(857\) −12.8748 + 19.2685i −0.439796 + 0.658201i −0.983465 0.181099i \(-0.942035\pi\)
0.543669 + 0.839300i \(0.317035\pi\)
\(858\) −13.9757 + 5.78891i −0.477122 + 0.197630i
\(859\) 38.0926 + 15.7785i 1.29970 + 0.538354i 0.921862 0.387517i \(-0.126667\pi\)
0.377839 + 0.925871i \(0.376667\pi\)
\(860\) −0.421230 0.0248895i −0.0143638 0.000848725i
\(861\) 28.3141 + 18.9189i 0.964941 + 0.644753i
\(862\) −11.5624 17.3044i −0.393818 0.589390i
\(863\) −13.6290 −0.463935 −0.231968 0.972724i \(-0.574516\pi\)
−0.231968 + 0.972724i \(0.574516\pi\)
\(864\) −10.6049 15.8713i −0.360786 0.539954i
\(865\) −6.31889 45.7227i −0.214849 1.55462i
\(866\) 6.49518i 0.220715i
\(867\) 46.4646 34.5614i 1.57802 1.17377i
\(868\) −1.16887 + 1.16887i −0.0396740 + 0.0396740i
\(869\) 4.85080 2.00927i 0.164552 0.0681597i
\(870\) 10.0365 20.6864i 0.340271 0.701335i
\(871\) −2.52029 + 2.52029i −0.0853968 + 0.0853968i
\(872\) 7.98657 5.33646i 0.270459 0.180715i
\(873\) 11.3596 + 57.1086i 0.384464 + 1.93283i
\(874\) 1.68143 0.334458i 0.0568753 0.0113132i
\(875\) −11.3769 + 4.97173i −0.384610 + 0.168075i
\(876\) −2.37828 + 5.74167i −0.0803546 + 0.193993i
\(877\) −38.6429 25.8203i −1.30488 0.871891i −0.308041 0.951373i \(-0.599673\pi\)
−0.996836 + 0.0794822i \(0.974673\pi\)
\(878\) −17.7431 + 3.52932i −0.598801 + 0.119109i
\(879\) −4.88208 + 24.5439i −0.164668 + 0.827844i
\(880\) −2.16877 0.566198i −0.0731093 0.0190865i
\(881\) 4.84417 3.23677i 0.163204 0.109050i −0.471286 0.881980i \(-0.656210\pi\)
0.634490 + 0.772931i \(0.281210\pi\)
\(882\) −45.8386 18.9870i −1.54346 0.639324i
\(883\) −0.724623 0.724623i −0.0243855 0.0243855i 0.694809 0.719194i \(-0.255489\pi\)
−0.719194 + 0.694809i \(0.755489\pi\)
\(884\) −17.0464 6.56184i −0.573333 0.220699i
\(885\) −88.1449 23.0118i −2.96296 0.773534i
\(886\) −14.1811 34.2361i −0.476422 1.15018i
\(887\) 8.72243 43.8506i 0.292871 1.47236i −0.501622 0.865087i \(-0.667263\pi\)
0.794493 0.607273i \(-0.207737\pi\)
\(888\) 19.6704i 0.660096i
\(889\) −10.9995 2.18794i −0.368913 0.0733813i
\(890\) 10.4026 + 11.7091i 0.348695 + 0.392490i
\(891\) −7.66828 38.5511i −0.256897 1.29151i
\(892\) 7.56256 + 18.2576i 0.253213 + 0.611311i
\(893\) −1.28092 3.09241i −0.0428643 0.103484i
\(894\) −11.2714 56.6650i −0.376971 1.89516i
\(895\) −0.900366 + 15.2378i −0.0300959 + 0.509344i
\(896\) −1.08917 0.216649i −0.0363865 0.00723772i
\(897\) 47.1524i 1.57437i
\(898\) 6.26553 31.4989i 0.209083 1.05113i
\(899\) 1.71951 + 4.15128i 0.0573490 + 0.138453i
\(900\) 37.5284 + 21.0282i 1.25095 + 0.700939i
\(901\) −51.4117 + 1.29807i −1.71277 + 0.0432449i
\(902\) −6.38072 6.38072i −0.212455 0.212455i
\(903\) −0.659514 0.273180i −0.0219473 0.00909085i
\(904\) 4.70769 3.14558i 0.156575 0.104620i
\(905\) 2.68933 10.3013i 0.0893965 0.342426i
\(906\) −7.45581 + 37.4829i −0.247703 + 1.24528i
\(907\) 33.2496 6.61375i 1.10403 0.219606i 0.390761 0.920492i \(-0.372212\pi\)
0.713273 + 0.700886i \(0.247212\pi\)
\(908\) 4.56874 + 3.05273i 0.151619 + 0.101309i
\(909\) −1.12818 + 2.72367i −0.0374194 + 0.0903383i
\(910\) 6.64052 8.77030i 0.220131 0.290733i
\(911\) −20.1173 + 4.00159i −0.666517 + 0.132578i −0.516741 0.856142i \(-0.672855\pi\)
−0.149776 + 0.988720i \(0.547855\pi\)
\(912\) 0.364624 + 1.83309i 0.0120739 + 0.0606996i
\(913\) 10.0389 6.70776i 0.332238 0.221995i
\(914\) 17.5785 17.5785i 0.581446 0.581446i
\(915\) −4.79226 13.8248i −0.158427 0.457034i
\(916\) 3.21137 1.33019i 0.106107 0.0439508i
\(917\) 2.46965 2.46965i 0.0815550 0.0815550i
\(918\) 42.0595 66.5220i 1.38817 2.19555i
\(919\) 12.2300i 0.403430i −0.979444 0.201715i \(-0.935348\pi\)
0.979444 0.201715i \(-0.0646515\pi\)
\(920\) −4.21756 + 5.57024i −0.139049 + 0.183645i
\(921\) −27.2192 40.7365i −0.896905 1.34231i
\(922\) −12.8689 −0.423814
\(923\) 11.1921 + 16.7502i 0.368393 + 0.551339i
\(924\) −3.15290 2.10670i −0.103723 0.0693054i
\(925\) −13.1020 25.7287i −0.430792 0.845955i
\(926\) −24.8855 10.3079i −0.817787 0.338738i
\(927\) −86.2549 + 35.7279i −2.83298 + 1.17346i
\(928\) −1.67705 + 2.50988i −0.0550517 + 0.0823907i
\(929\) −13.7243 + 20.5398i −0.450279 + 0.673890i −0.985277 0.170963i \(-0.945312\pi\)
0.534999 + 0.844853i \(0.320312\pi\)
\(930\) −10.7128 + 3.71350i −0.351286 + 0.121770i
\(931\) 2.23733 + 2.23733i 0.0733256 + 0.0733256i
\(932\) −11.8747 2.36203i −0.388969 0.0773708i
\(933\) 34.3727 82.9830i 1.12531 2.71674i
\(934\) 11.9613 0.391386
\(935\) −1.49586 9.11993i −0.0489199 0.298253i
\(936\) −38.1150 −1.24583
\(937\) −16.8852 + 40.7645i −0.551615 + 1.33172i 0.364650 + 0.931145i \(0.381189\pi\)
−0.916265 + 0.400573i \(0.868811\pi\)
\(938\) −0.876287 0.174304i −0.0286118 0.00569124i
\(939\) −55.4863 55.4863i −1.81073 1.81073i
\(940\) 12.2730 + 5.95457i 0.400302 + 0.194217i
\(941\) 21.3969 32.0227i 0.697518 1.04391i −0.298469 0.954419i \(-0.596476\pi\)
0.995988 0.0894907i \(-0.0285239\pi\)
\(942\) 14.0503 21.0277i 0.457783 0.685120i
\(943\) −25.9865 + 10.7639i −0.846236 + 0.350522i
\(944\) 11.0496 + 4.57691i 0.359635 + 0.148966i
\(945\) 31.4811 + 35.4350i 1.02408 + 1.15270i
\(946\) 0.157284 + 0.105094i 0.00511374 + 0.00341689i
\(947\) 3.46639 + 5.18781i 0.112642 + 0.168581i 0.883507 0.468417i \(-0.155176\pi\)
−0.770865 + 0.636999i \(0.780176\pi\)
\(948\) 17.8422 0.579488
\(949\) 4.49033 + 6.72026i 0.145762 + 0.218149i
\(950\) −1.69790 2.15479i −0.0550873 0.0699107i
\(951\) 66.5554i 2.15821i
\(952\) −1.00633 4.46677i −0.0326153 0.144769i
\(953\) 36.0165 36.0165i 1.16669 1.16669i 0.183710 0.982981i \(-0.441189\pi\)
0.982981 0.183710i \(-0.0588106\pi\)
\(954\) −99.1456 + 41.0675i −3.20996 + 1.32961i
\(955\) 20.4249 + 9.90965i 0.660933 + 0.320669i
\(956\) −10.0546 + 10.0546i −0.325190 + 0.325190i
\(957\) −8.57030 + 5.72649i −0.277038 + 0.185111i
\(958\) 5.59595 + 28.1328i 0.180797 + 0.908928i
\(959\) 3.99070 0.793799i 0.128866 0.0256331i
\(960\) −6.07264 4.59796i −0.195994 0.148399i
\(961\) −11.0153 + 26.5932i −0.355331 + 0.857845i
\(962\) 21.2704 + 14.2125i 0.685787 + 0.458228i
\(963\) −99.0240 + 19.6971i −3.19100 + 0.634730i
\(964\) −1.00841 + 5.06964i −0.0324788 + 0.163282i
\(965\) −14.8428 + 8.69723i −0.477806 + 0.279974i
\(966\) −9.82782 + 6.56674i −0.316205 + 0.211281i
\(967\) 45.3258 + 18.7746i 1.45758 + 0.603749i 0.963988 0.265945i \(-0.0856840\pi\)
0.493591 + 0.869694i \(0.335684\pi\)
\(968\) −7.06765 7.06765i −0.227163 0.227163i
\(969\) −6.29728 + 4.44163i −0.202298 + 0.142686i
\(970\) 7.65071 + 13.0568i 0.245650 + 0.419228i
\(971\) −14.8579 35.8702i −0.476813 1.15113i −0.961095 0.276217i \(-0.910919\pi\)
0.484282 0.874912i \(-0.339081\pi\)
\(972\) 14.8866 74.8401i 0.477489 2.40050i
\(973\) 13.0785i 0.419277i
\(974\) 33.0161 + 6.56730i 1.05790 + 0.210430i
\(975\) 67.2376 34.2399i 2.15333 1.09656i
\(976\) 0.374760 + 1.88405i 0.0119958 + 0.0603068i
\(977\) 19.1568 + 46.2485i 0.612879 + 1.47962i 0.859824 + 0.510591i \(0.170573\pi\)
−0.246944 + 0.969030i \(0.579427\pi\)
\(978\) 20.5412 + 49.5907i 0.656834 + 1.58574i
\(979\) −1.36981 6.88651i −0.0437794 0.220094i
\(980\) −12.8725 0.760603i −0.411196 0.0242966i
\(981\) 81.0532 + 16.1225i 2.58783 + 0.514751i
\(982\) 12.5339i 0.399973i
\(983\) 4.26520 21.4426i 0.136039 0.683913i −0.851222 0.524805i \(-0.824138\pi\)
0.987261 0.159108i \(-0.0508618\pi\)
\(984\) −11.7348 28.3303i −0.374091 0.903136i
\(985\) 2.69352 10.3173i 0.0858226 0.328736i
\(986\) −12.2643 2.11922i −0.390574 0.0674896i
\(987\) 16.3182 + 16.3182i 0.519413 + 0.519413i
\(988\) 2.24565 + 0.930177i 0.0714435 + 0.0295929i
\(989\) 0.490265 0.327585i 0.0155895 0.0104166i
\(990\) −9.74957 16.6387i −0.309862 0.528813i
\(991\) 6.75639 33.9667i 0.214624 1.07899i −0.711765 0.702418i \(-0.752104\pi\)
0.926389 0.376569i \(-0.122896\pi\)
\(992\) 1.45994 0.290400i 0.0463531 0.00922020i
\(993\) 43.9087 + 29.3389i 1.39340 + 0.931041i
\(994\) −1.93250 + 4.66547i −0.0612952 + 0.147980i
\(995\) −24.5377 + 3.39112i −0.777897 + 0.107506i
\(996\) 40.2405 8.00433i 1.27507 0.253627i
\(997\) −7.18595 36.1262i −0.227581 1.14413i −0.910460 0.413597i \(-0.864272\pi\)
0.682879 0.730532i \(-0.260728\pi\)
\(998\) 5.43966 3.63466i 0.172189 0.115053i
\(999\) −77.9415 + 77.9415i −2.46596 + 2.46596i
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 170.2.r.b.107.5 yes 40
5.2 odd 4 850.2.s.d.243.5 40
5.3 odd 4 170.2.o.b.73.1 yes 40
5.4 even 2 850.2.v.d.107.1 40
17.7 odd 16 170.2.o.b.7.1 40
85.7 even 16 850.2.v.d.143.1 40
85.24 odd 16 850.2.s.d.7.5 40
85.58 even 16 inner 170.2.r.b.143.5 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.o.b.7.1 40 17.7 odd 16
170.2.o.b.73.1 yes 40 5.3 odd 4
170.2.r.b.107.5 yes 40 1.1 even 1 trivial
170.2.r.b.143.5 yes 40 85.58 even 16 inner
850.2.s.d.7.5 40 85.24 odd 16
850.2.s.d.243.5 40 5.2 odd 4
850.2.v.d.107.1 40 5.4 even 2
850.2.v.d.143.1 40 85.7 even 16