Properties

Label 77.2.n.a.24.3
Level $77$
Weight $2$
Character 77.24
Analytic conductor $0.615$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [77,2,Mod(17,77)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(77, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([5, 27]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("77.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.n (of order \(30\), 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: \(0.614848095564\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(6\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 24.3
Character \(\chi\) \(=\) 77.24
Dual form 77.2.n.a.61.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.311296 - 1.46453i) q^{2} +(0.599886 - 0.0630505i) q^{3} +(-0.220863 + 0.0983344i) q^{4} +(1.75624 + 1.58133i) q^{5} +(-0.279082 - 0.858925i) q^{6} +(-2.26028 - 1.37519i) q^{7} +(-1.54736 - 2.12976i) q^{8} +(-2.57856 + 0.548089i) q^{9} +O(q^{10})\) \(q+(-0.311296 - 1.46453i) q^{2} +(0.599886 - 0.0630505i) q^{3} +(-0.220863 + 0.0983344i) q^{4} +(1.75624 + 1.58133i) q^{5} +(-0.279082 - 0.858925i) q^{6} +(-2.26028 - 1.37519i) q^{7} +(-1.54736 - 2.12976i) q^{8} +(-2.57856 + 0.548089i) q^{9} +(1.76920 - 3.06434i) q^{10} +(0.972028 + 3.17099i) q^{11} +(-0.126292 + 0.0729149i) q^{12} +(-0.304786 + 0.938034i) q^{13} +(-1.31039 + 3.73834i) q^{14} +(1.15325 + 0.837884i) q^{15} +(-2.96096 + 3.28847i) q^{16} +(7.13077 + 1.51569i) q^{17} +(1.60539 + 3.60576i) q^{18} +(-4.47358 - 1.99177i) q^{19} +(-0.543388 - 0.176557i) q^{20} +(-1.44261 - 0.682444i) q^{21} +(4.34143 - 2.41068i) q^{22} +(-0.0581861 - 0.100781i) q^{23} +(-1.06252 - 1.18005i) q^{24} +(0.0611479 + 0.581783i) q^{25} +(1.46866 + 0.154363i) q^{26} +(-3.23328 + 1.05056i) q^{27} +(0.634440 + 0.0814645i) q^{28} +(-4.73419 + 6.51605i) q^{29} +(0.868107 - 1.94980i) q^{30} +(2.70684 - 2.43725i) q^{31} +(1.17815 + 0.680207i) q^{32} +(0.783038 + 1.84094i) q^{33} -10.9151i q^{34} +(-1.79497 - 5.98941i) q^{35} +(0.515611 - 0.374613i) q^{36} +(0.386394 - 3.67629i) q^{37} +(-1.52440 + 7.17174i) q^{38} +(-0.123693 + 0.581930i) q^{39} +(0.650306 - 6.18725i) q^{40} +(3.09269 - 2.24697i) q^{41} +(-0.550381 + 2.32520i) q^{42} -5.00037i q^{43} +(-0.526502 - 0.604769i) q^{44} +(-5.39528 - 3.11497i) q^{45} +(-0.129485 + 0.116588i) q^{46} +(3.27013 - 7.34484i) q^{47} +(-1.56889 + 2.15940i) q^{48} +(3.21772 + 6.21661i) q^{49} +(0.833006 - 0.270660i) q^{50} +(4.37321 + 0.459643i) q^{51} +(-0.0249252 - 0.237148i) q^{52} +(-2.58704 - 2.87320i) q^{53} +(2.54509 + 4.40822i) q^{54} +(-3.30725 + 7.10612i) q^{55} +(0.568646 + 6.94175i) q^{56} +(-2.80922 - 0.912770i) q^{57} +(11.0167 + 4.90495i) q^{58} +(0.577837 + 1.29784i) q^{59} +(-0.337102 - 0.0716533i) q^{60} +(-0.158755 + 0.176315i) q^{61} +(-4.41207 - 3.20555i) q^{62} +(6.58198 + 2.30716i) q^{63} +(-2.10542 + 6.47981i) q^{64} +(-2.01862 + 1.16545i) q^{65} +(2.45237 - 1.71986i) q^{66} +(-2.19586 + 3.80334i) q^{67} +(-1.72396 + 0.366440i) q^{68} +(-0.0412593 - 0.0567886i) q^{69} +(-8.21292 + 4.49328i) q^{70} +(-2.39057 - 7.35741i) q^{71} +(5.15724 + 4.64360i) q^{72} +(-1.47343 + 0.656013i) q^{73} +(-5.50433 + 0.578529i) q^{74} +(0.0733634 + 0.345148i) q^{75} +1.18391 q^{76} +(2.16365 - 8.50404i) q^{77} +0.890761 q^{78} +(-2.53742 - 11.9376i) q^{79} +(-10.4003 + 1.09312i) q^{80} +(5.35140 - 2.38260i) q^{81} +(-4.25350 - 3.82987i) q^{82} +(1.29164 + 3.97526i) q^{83} +(0.385728 + 0.00886766i) q^{84} +(10.1266 + 13.9380i) q^{85} +(-7.32321 + 1.55660i) q^{86} +(-2.42913 + 4.20738i) q^{87} +(5.24935 - 6.97683i) q^{88} +(-11.4287 + 6.59836i) q^{89} +(-2.88244 + 8.87124i) q^{90} +(1.97887 - 1.70108i) q^{91} +(0.0227614 + 0.0165371i) q^{92} +(1.47013 - 1.63274i) q^{93} +(-11.7748 - 2.50280i) q^{94} +(-4.70706 - 10.5722i) q^{95} +(0.749645 + 0.333763i) q^{96} +(16.5965 + 5.39254i) q^{97} +(8.10278 - 6.64766i) q^{98} +(-4.24441 - 7.64381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.311296 1.46453i −0.220120 1.03558i −0.939918 0.341399i \(-0.889099\pi\)
0.719799 0.694183i \(-0.244234\pi\)
\(3\) 0.599886 0.0630505i 0.346344 0.0364022i 0.0702404 0.997530i \(-0.477623\pi\)
0.276104 + 0.961128i \(0.410957\pi\)
\(4\) −0.220863 + 0.0983344i −0.110431 + 0.0491672i
\(5\) 1.75624 + 1.58133i 0.785416 + 0.707191i 0.960780 0.277312i \(-0.0894436\pi\)
−0.175364 + 0.984504i \(0.556110\pi\)
\(6\) −0.279082 0.858925i −0.113935 0.350655i
\(7\) −2.26028 1.37519i −0.854305 0.519772i
\(8\) −1.54736 2.12976i −0.547074 0.752982i
\(9\) −2.57856 + 0.548089i −0.859518 + 0.182696i
\(10\) 1.76920 3.06434i 0.559469 0.969029i
\(11\) 0.972028 + 3.17099i 0.293077 + 0.956089i
\(12\) −0.126292 + 0.0729149i −0.0364575 + 0.0210487i
\(13\) −0.304786 + 0.938034i −0.0845324 + 0.260164i −0.984385 0.176031i \(-0.943674\pi\)
0.899852 + 0.436195i \(0.143674\pi\)
\(14\) −1.31039 + 3.73834i −0.350217 + 0.999115i
\(15\) 1.15325 + 0.837884i 0.297767 + 0.216341i
\(16\) −2.96096 + 3.28847i −0.740239 + 0.822119i
\(17\) 7.13077 + 1.51569i 1.72946 + 0.367609i 0.961908 0.273372i \(-0.0881390\pi\)
0.767557 + 0.640981i \(0.221472\pi\)
\(18\) 1.60539 + 3.60576i 0.378394 + 0.849887i
\(19\) −4.47358 1.99177i −1.02631 0.456943i −0.176650 0.984274i \(-0.556526\pi\)
−0.849660 + 0.527331i \(0.823193\pi\)
\(20\) −0.543388 0.176557i −0.121505 0.0394794i
\(21\) −1.44261 0.682444i −0.314804 0.148921i
\(22\) 4.34143 2.41068i 0.925596 0.513960i
\(23\) −0.0581861 0.100781i −0.0121326 0.0210144i 0.859895 0.510470i \(-0.170529\pi\)
−0.872028 + 0.489456i \(0.837195\pi\)
\(24\) −1.06252 1.18005i −0.216886 0.240876i
\(25\) 0.0611479 + 0.581783i 0.0122296 + 0.116357i
\(26\) 1.46866 + 0.154363i 0.288028 + 0.0302730i
\(27\) −3.23328 + 1.05056i −0.622246 + 0.202180i
\(28\) 0.634440 + 0.0814645i 0.119898 + 0.0153954i
\(29\) −4.73419 + 6.51605i −0.879116 + 1.21000i 0.0975485 + 0.995231i \(0.468900\pi\)
−0.976665 + 0.214769i \(0.931100\pi\)
\(30\) 0.868107 1.94980i 0.158494 0.355983i
\(31\) 2.70684 2.43725i 0.486163 0.437743i −0.389240 0.921136i \(-0.627262\pi\)
0.875403 + 0.483393i \(0.160596\pi\)
\(32\) 1.17815 + 0.680207i 0.208270 + 0.120245i
\(33\) 0.783038 + 1.84094i 0.136309 + 0.320467i
\(34\) 10.9151i 1.87192i
\(35\) −1.79497 5.98941i −0.303406 1.01239i
\(36\) 0.515611 0.374613i 0.0859351 0.0624355i
\(37\) 0.386394 3.67629i 0.0635227 0.604379i −0.915738 0.401775i \(-0.868393\pi\)
0.979261 0.202603i \(-0.0649401\pi\)
\(38\) −1.52440 + 7.17174i −0.247290 + 1.16341i
\(39\) −0.123693 + 0.581930i −0.0198067 + 0.0931834i
\(40\) 0.650306 6.18725i 0.102822 0.978290i
\(41\) 3.09269 2.24697i 0.482996 0.350917i −0.319488 0.947590i \(-0.603511\pi\)
0.802485 + 0.596673i \(0.203511\pi\)
\(42\) −0.550381 + 2.32520i −0.0849256 + 0.358786i
\(43\) 5.00037i 0.762549i −0.924462 0.381275i \(-0.875485\pi\)
0.924462 0.381275i \(-0.124515\pi\)
\(44\) −0.526502 0.604769i −0.0793732 0.0911724i
\(45\) −5.39528 3.11497i −0.804281 0.464352i
\(46\) −0.129485 + 0.116588i −0.0190915 + 0.0171900i
\(47\) 3.27013 7.34484i 0.476998 1.07136i −0.501511 0.865151i \(-0.667222\pi\)
0.978509 0.206204i \(-0.0661111\pi\)
\(48\) −1.56889 + 2.15940i −0.226450 + 0.311682i
\(49\) 3.21772 + 6.21661i 0.459674 + 0.888088i
\(50\) 0.833006 0.270660i 0.117805 0.0382771i
\(51\) 4.37321 + 0.459643i 0.612372 + 0.0643629i
\(52\) −0.0249252 0.237148i −0.00345651 0.0328865i
\(53\) −2.58704 2.87320i −0.355358 0.394665i 0.538787 0.842442i \(-0.318883\pi\)
−0.894145 + 0.447777i \(0.852216\pi\)
\(54\) 2.54509 + 4.40822i 0.346342 + 0.599883i
\(55\) −3.30725 + 7.10612i −0.445950 + 0.958189i
\(56\) 0.568646 + 6.94175i 0.0759885 + 0.927630i
\(57\) −2.80922 0.912770i −0.372090 0.120899i
\(58\) 11.0167 + 4.90495i 1.44656 + 0.644052i
\(59\) 0.577837 + 1.29784i 0.0752279 + 0.168965i 0.947245 0.320511i \(-0.103855\pi\)
−0.872017 + 0.489476i \(0.837188\pi\)
\(60\) −0.337102 0.0716533i −0.0435197 0.00925040i
\(61\) −0.158755 + 0.176315i −0.0203265 + 0.0225748i −0.753222 0.657766i \(-0.771502\pi\)
0.732896 + 0.680341i \(0.238168\pi\)
\(62\) −4.41207 3.20555i −0.560333 0.407106i
\(63\) 6.58198 + 2.30716i 0.829251 + 0.290675i
\(64\) −2.10542 + 6.47981i −0.263177 + 0.809976i
\(65\) −2.01862 + 1.16545i −0.250379 + 0.144556i
\(66\) 2.45237 1.71986i 0.301865 0.211701i
\(67\) −2.19586 + 3.80334i −0.268267 + 0.464652i −0.968414 0.249346i \(-0.919784\pi\)
0.700147 + 0.713998i \(0.253118\pi\)
\(68\) −1.72396 + 0.366440i −0.209061 + 0.0444374i
\(69\) −0.0412593 0.0567886i −0.00496704 0.00683654i
\(70\) −8.21292 + 4.49328i −0.981631 + 0.537050i
\(71\) −2.39057 7.35741i −0.283708 0.873164i −0.986783 0.162048i \(-0.948190\pi\)
0.703075 0.711116i \(-0.251810\pi\)
\(72\) 5.15724 + 4.64360i 0.607787 + 0.547254i
\(73\) −1.47343 + 0.656013i −0.172452 + 0.0767805i −0.491147 0.871077i \(-0.663422\pi\)
0.318695 + 0.947857i \(0.396755\pi\)
\(74\) −5.50433 + 0.578529i −0.639866 + 0.0672526i
\(75\) 0.0733634 + 0.345148i 0.00847128 + 0.0398542i
\(76\) 1.18391 0.135803
\(77\) 2.16365 8.50404i 0.246571 0.969125i
\(78\) 0.890761 0.100859
\(79\) −2.53742 11.9376i −0.285482 1.34308i −0.853939 0.520373i \(-0.825793\pi\)
0.568458 0.822712i \(-0.307540\pi\)
\(80\) −10.4003 + 1.09312i −1.16279 + 0.122214i
\(81\) 5.35140 2.38260i 0.594600 0.264733i
\(82\) −4.25350 3.82987i −0.469721 0.422938i
\(83\) 1.29164 + 3.97526i 0.141776 + 0.436341i 0.996582 0.0826058i \(-0.0263242\pi\)
−0.854806 + 0.518947i \(0.826324\pi\)
\(84\) 0.385728 + 0.00886766i 0.0420863 + 0.000967541i
\(85\) 10.1266 + 13.9380i 1.09838 + 1.51179i
\(86\) −7.32321 + 1.55660i −0.789682 + 0.167852i
\(87\) −2.42913 + 4.20738i −0.260430 + 0.451078i
\(88\) 5.24935 6.97683i 0.559583 0.743733i
\(89\) −11.4287 + 6.59836i −1.21144 + 0.699425i −0.963073 0.269241i \(-0.913227\pi\)
−0.248366 + 0.968666i \(0.579894\pi\)
\(90\) −2.88244 + 8.87124i −0.303836 + 0.935111i
\(91\) 1.97887 1.70108i 0.207442 0.178322i
\(92\) 0.0227614 + 0.0165371i 0.00237304 + 0.00172412i
\(93\) 1.47013 1.63274i 0.152445 0.169307i
\(94\) −11.7748 2.50280i −1.21447 0.258144i
\(95\) −4.70706 10.5722i −0.482934 1.08469i
\(96\) 0.749645 + 0.333763i 0.0765103 + 0.0340646i
\(97\) 16.5965 + 5.39254i 1.68512 + 0.547529i 0.985894 0.167370i \(-0.0535275\pi\)
0.699227 + 0.714899i \(0.253527\pi\)
\(98\) 8.10278 6.64766i 0.818504 0.671515i
\(99\) −4.24441 7.64381i −0.426579 0.768232i
\(100\) −0.0707146 0.122481i −0.00707146 0.0122481i
\(101\) 8.86769 + 9.84856i 0.882368 + 0.979969i 0.999914 0.0130986i \(-0.00416953\pi\)
−0.117546 + 0.993067i \(0.537503\pi\)
\(102\) −0.688201 6.54780i −0.0681421 0.648329i
\(103\) 0.326651 + 0.0343324i 0.0321859 + 0.00338287i 0.120608 0.992700i \(-0.461516\pi\)
−0.0884218 + 0.996083i \(0.528182\pi\)
\(104\) 2.46940 0.802355i 0.242144 0.0786774i
\(105\) −1.45441 3.47978i −0.141936 0.339592i
\(106\) −3.40257 + 4.68323i −0.330487 + 0.454876i
\(107\) −0.668376 + 1.50120i −0.0646143 + 0.145126i −0.942966 0.332888i \(-0.891977\pi\)
0.878352 + 0.478015i \(0.158643\pi\)
\(108\) 0.610806 0.549972i 0.0587748 0.0529211i
\(109\) −0.138154 0.0797633i −0.0132328 0.00763994i 0.493369 0.869820i \(-0.335765\pi\)
−0.506602 + 0.862180i \(0.669099\pi\)
\(110\) 11.4367 + 2.63148i 1.09045 + 0.250902i
\(111\) 2.22972i 0.211635i
\(112\) 11.2149 3.36100i 1.05970 0.317584i
\(113\) 6.46936 4.70027i 0.608586 0.442164i −0.240330 0.970691i \(-0.577256\pi\)
0.848916 + 0.528527i \(0.177256\pi\)
\(114\) −0.462284 + 4.39834i −0.0432968 + 0.411942i
\(115\) 0.0571794 0.269008i 0.00533201 0.0250851i
\(116\) 0.404853 1.90469i 0.0375897 0.176846i
\(117\) 0.271781 2.58582i 0.0251262 0.239059i
\(118\) 1.72086 1.25027i 0.158418 0.115097i
\(119\) −14.0332 13.2320i −1.28642 1.21298i
\(120\) 3.75264i 0.342568i
\(121\) −9.11032 + 6.16458i −0.828211 + 0.560416i
\(122\) 0.307639 + 0.177616i 0.0278524 + 0.0160806i
\(123\) 1.71359 1.54292i 0.154509 0.139120i
\(124\) −0.358175 + 0.804474i −0.0321650 + 0.0722439i
\(125\) 6.13284 8.44113i 0.548538 0.754998i
\(126\) 1.32997 10.3577i 0.118484 0.922741i
\(127\) −13.9300 + 4.52612i −1.23608 + 0.401628i −0.852915 0.522050i \(-0.825167\pi\)
−0.383169 + 0.923678i \(0.625167\pi\)
\(128\) 12.8512 + 1.35072i 1.13590 + 0.119388i
\(129\) −0.315276 2.99965i −0.0277585 0.264104i
\(130\) 2.33523 + 2.59353i 0.204813 + 0.227468i
\(131\) 9.33814 + 16.1741i 0.815877 + 1.41314i 0.908696 + 0.417458i \(0.137079\pi\)
−0.0928193 + 0.995683i \(0.529588\pi\)
\(132\) −0.353972 0.329596i −0.0308093 0.0286877i
\(133\) 7.37248 + 10.6540i 0.639275 + 0.923815i
\(134\) 6.25369 + 2.03195i 0.540236 + 0.175533i
\(135\) −7.33971 3.26785i −0.631702 0.281252i
\(136\) −7.80580 17.5321i −0.669341 1.50337i
\(137\) 0.366311 + 0.0778618i 0.0312961 + 0.00665218i 0.223533 0.974696i \(-0.428241\pi\)
−0.192237 + 0.981349i \(0.561574\pi\)
\(138\) −0.0703250 + 0.0781038i −0.00598646 + 0.00664863i
\(139\) 12.7105 + 9.23469i 1.07809 + 0.783276i 0.977348 0.211637i \(-0.0678793\pi\)
0.100739 + 0.994913i \(0.467879\pi\)
\(140\) 0.985408 + 1.14633i 0.0832821 + 0.0968824i
\(141\) 1.49861 4.61225i 0.126206 0.388421i
\(142\) −10.0310 + 5.79140i −0.841782 + 0.486003i
\(143\) −3.27075 0.0546763i −0.273514 0.00457226i
\(144\) 5.83261 10.1024i 0.486051 0.841865i
\(145\) −18.6184 + 3.95746i −1.54617 + 0.328649i
\(146\) 1.41943 + 1.95367i 0.117473 + 0.161687i
\(147\) 2.32222 + 3.52638i 0.191534 + 0.290851i
\(148\) 0.276166 + 0.849951i 0.0227007 + 0.0698656i
\(149\) −7.40652 6.66886i −0.606766 0.546335i 0.307449 0.951565i \(-0.400525\pi\)
−0.914215 + 0.405230i \(0.867191\pi\)
\(150\) 0.482643 0.214886i 0.0394076 0.0175454i
\(151\) −3.90409 + 0.410337i −0.317711 + 0.0333927i −0.262042 0.965057i \(-0.584396\pi\)
−0.0556690 + 0.998449i \(0.517729\pi\)
\(152\) 2.68025 + 12.6096i 0.217397 + 1.02277i
\(153\) −19.2178 −1.55367
\(154\) −13.1280 0.521462i −1.05788 0.0420206i
\(155\) 8.60797 0.691408
\(156\) −0.0299046 0.140690i −0.00239428 0.0112642i
\(157\) −7.57914 + 0.796600i −0.604881 + 0.0635756i −0.402018 0.915632i \(-0.631691\pi\)
−0.202863 + 0.979207i \(0.565025\pi\)
\(158\) −16.6931 + 7.43226i −1.32803 + 0.591279i
\(159\) −1.73309 1.56048i −0.137443 0.123754i
\(160\) 0.993493 + 3.05766i 0.0785425 + 0.241729i
\(161\) −0.00707640 + 0.307811i −0.000557698 + 0.0242589i
\(162\) −5.15526 7.09561i −0.405036 0.557484i
\(163\) 6.82088 1.44982i 0.534252 0.113559i 0.0671177 0.997745i \(-0.478620\pi\)
0.467135 + 0.884186i \(0.345286\pi\)
\(164\) −0.462105 + 0.800389i −0.0360843 + 0.0624999i
\(165\) −1.53593 + 4.47138i −0.119572 + 0.348097i
\(166\) 5.41981 3.12913i 0.420659 0.242868i
\(167\) −3.74083 + 11.5131i −0.289474 + 0.890909i 0.695548 + 0.718479i \(0.255162\pi\)
−0.985022 + 0.172429i \(0.944838\pi\)
\(168\) 0.778803 + 4.12840i 0.0600860 + 0.318513i
\(169\) 9.73021 + 7.06941i 0.748477 + 0.543801i
\(170\) 17.2603 19.1695i 1.32381 1.47024i
\(171\) 12.6270 + 2.68396i 0.965614 + 0.205248i
\(172\) 0.491708 + 1.10440i 0.0374924 + 0.0842093i
\(173\) −2.97050 1.32255i −0.225843 0.100552i 0.290696 0.956816i \(-0.406113\pi\)
−0.516539 + 0.856264i \(0.672780\pi\)
\(174\) 6.91802 + 2.24780i 0.524454 + 0.170405i
\(175\) 0.661850 1.39908i 0.0500311 0.105761i
\(176\) −13.3058 6.19266i −1.00297 0.466790i
\(177\) 0.428466 + 0.742124i 0.0322054 + 0.0557815i
\(178\) 13.2212 + 14.6837i 0.990973 + 1.10059i
\(179\) 1.05817 + 10.0678i 0.0790911 + 0.752502i 0.960148 + 0.279492i \(0.0901659\pi\)
−0.881057 + 0.473010i \(0.843167\pi\)
\(180\) 1.49792 + 0.157438i 0.111649 + 0.0117347i
\(181\) −9.48074 + 3.08048i −0.704698 + 0.228970i −0.639376 0.768894i \(-0.720807\pi\)
−0.0653218 + 0.997864i \(0.520807\pi\)
\(182\) −3.10731 2.36859i −0.230329 0.175571i
\(183\) −0.0841180 + 0.115778i −0.00621818 + 0.00855859i
\(184\) −0.124605 + 0.279867i −0.00918599 + 0.0206321i
\(185\) 6.49202 5.84544i 0.477303 0.429766i
\(186\) −2.84885 1.64478i −0.208888 0.120601i
\(187\) 2.12507 + 24.0849i 0.155400 + 1.76126i
\(188\) 1.94377i 0.141764i
\(189\) 8.75284 + 2.07182i 0.636675 + 0.150703i
\(190\) −14.0181 + 10.1847i −1.01698 + 0.738879i
\(191\) −2.21827 + 21.1054i −0.160508 + 1.52713i 0.556958 + 0.830541i \(0.311969\pi\)
−0.717466 + 0.696593i \(0.754698\pi\)
\(192\) −0.854454 + 4.01989i −0.0616649 + 0.290111i
\(193\) 2.17200 10.2185i 0.156344 0.735541i −0.828204 0.560426i \(-0.810637\pi\)
0.984548 0.175114i \(-0.0560294\pi\)
\(194\) 2.73112 25.9848i 0.196083 1.86560i
\(195\) −1.13746 + 0.826411i −0.0814550 + 0.0591805i
\(196\) −1.32198 1.05661i −0.0944272 0.0754719i
\(197\) 6.57692i 0.468586i −0.972166 0.234293i \(-0.924722\pi\)
0.972166 0.234293i \(-0.0752776\pi\)
\(198\) −9.87335 + 8.59557i −0.701668 + 0.610861i
\(199\) 0.834354 + 0.481715i 0.0591458 + 0.0341479i 0.529281 0.848446i \(-0.322462\pi\)
−0.470135 + 0.882594i \(0.655795\pi\)
\(200\) 1.14444 1.03046i 0.0809240 0.0728643i
\(201\) −1.07746 + 2.42002i −0.0759984 + 0.170695i
\(202\) 11.6631 16.0528i 0.820611 1.12947i
\(203\) 19.6614 8.21769i 1.37996 0.576769i
\(204\) −1.01108 + 0.328519i −0.0707896 + 0.0230009i
\(205\) 8.98470 + 0.944330i 0.627519 + 0.0659549i
\(206\) −0.0514043 0.489079i −0.00358151 0.0340758i
\(207\) 0.205273 + 0.227979i 0.0142675 + 0.0158456i
\(208\) −2.18224 3.77976i −0.151311 0.262079i
\(209\) 1.96742 16.1217i 0.136089 1.11516i
\(210\) −4.64351 + 3.21328i −0.320432 + 0.221738i
\(211\) 2.38877 + 0.776160i 0.164450 + 0.0534331i 0.390085 0.920779i \(-0.372446\pi\)
−0.225635 + 0.974212i \(0.572446\pi\)
\(212\) 0.853917 + 0.380188i 0.0586472 + 0.0261114i
\(213\) −1.89795 4.26288i −0.130046 0.292087i
\(214\) 2.40662 + 0.511542i 0.164513 + 0.0349683i
\(215\) 7.90722 8.78186i 0.539268 0.598918i
\(216\) 7.24048 + 5.26052i 0.492652 + 0.357933i
\(217\) −9.46989 + 1.78645i −0.642858 + 0.121272i
\(218\) −0.0738092 + 0.227161i −0.00499899 + 0.0153853i
\(219\) −0.842527 + 0.486433i −0.0569327 + 0.0328701i
\(220\) 0.0316731 1.89469i 0.00213540 0.127740i
\(221\) −3.59513 + 6.22694i −0.241834 + 0.418869i
\(222\) −3.26549 + 0.694102i −0.219166 + 0.0465851i
\(223\) −15.0520 20.7173i −1.00796 1.38733i −0.920313 0.391182i \(-0.872066\pi\)
−0.0876440 0.996152i \(-0.527934\pi\)
\(224\) −1.72754 3.15764i −0.115426 0.210979i
\(225\) −0.476542 1.46665i −0.0317695 0.0977764i
\(226\) −8.89759 8.01142i −0.591859 0.532912i
\(227\) −17.7670 + 7.91038i −1.17924 + 0.525030i −0.900296 0.435278i \(-0.856650\pi\)
−0.278941 + 0.960308i \(0.589984\pi\)
\(228\) 0.710208 0.0746459i 0.0470347 0.00494355i
\(229\) −4.35481 20.4878i −0.287774 1.35387i −0.849955 0.526856i \(-0.823371\pi\)
0.562181 0.827014i \(-0.309963\pi\)
\(230\) −0.411771 −0.0271514
\(231\) 0.761758 5.23787i 0.0501200 0.344626i
\(232\) 21.2031 1.39205
\(233\) −3.16366 14.8839i −0.207258 0.975074i −0.951615 0.307292i \(-0.900577\pi\)
0.744357 0.667782i \(-0.232756\pi\)
\(234\) −3.87163 + 0.406925i −0.253096 + 0.0266015i
\(235\) 17.3578 7.72817i 1.13230 0.504130i
\(236\) −0.255245 0.229824i −0.0166150 0.0149603i
\(237\) −2.27483 7.00121i −0.147766 0.454777i
\(238\) −15.0103 + 24.6711i −0.972972 + 1.59919i
\(239\) 5.56179 + 7.65514i 0.359762 + 0.495170i 0.950082 0.311999i \(-0.100999\pi\)
−0.590320 + 0.807169i \(0.700999\pi\)
\(240\) −6.17008 + 1.31149i −0.398277 + 0.0846563i
\(241\) 3.47748 6.02317i 0.224004 0.387987i −0.732016 0.681287i \(-0.761420\pi\)
0.956020 + 0.293301i \(0.0947537\pi\)
\(242\) 11.8642 + 11.4234i 0.762662 + 0.734322i
\(243\) 11.8926 6.86621i 0.762912 0.440467i
\(244\) 0.0177252 0.0545525i 0.00113474 0.00349237i
\(245\) −4.17941 + 16.0062i −0.267013 + 1.02260i
\(246\) −2.79309 2.02930i −0.178081 0.129383i
\(247\) 3.23183 3.58931i 0.205636 0.228382i
\(248\) −9.37920 1.99361i −0.595580 0.126594i
\(249\) 1.02548 + 2.30326i 0.0649870 + 0.145963i
\(250\) −14.2715 6.35406i −0.902606 0.401866i
\(251\) −9.44333 3.06832i −0.596058 0.193671i −0.00457626 0.999990i \(-0.501457\pi\)
−0.591481 + 0.806319i \(0.701457\pi\)
\(252\) −1.68059 + 0.137668i −0.105867 + 0.00867229i
\(253\) 0.263018 0.282470i 0.0165358 0.0177587i
\(254\) 10.9650 + 18.9919i 0.688005 + 1.19166i
\(255\) 6.95357 + 7.72272i 0.435450 + 0.483616i
\(256\) −0.598005 5.68963i −0.0373753 0.355602i
\(257\) −3.88944 0.408797i −0.242617 0.0255001i −0.0175605 0.999846i \(-0.505590\pi\)
−0.225056 + 0.974346i \(0.572257\pi\)
\(258\) −4.29494 + 1.39551i −0.267392 + 0.0868808i
\(259\) −5.92895 + 7.77808i −0.368407 + 0.483306i
\(260\) 0.331234 0.455904i 0.0205422 0.0282740i
\(261\) 8.63599 19.3967i 0.534554 1.20063i
\(262\) 20.7806 18.7110i 1.28383 1.15597i
\(263\) 14.0065 + 8.08668i 0.863680 + 0.498646i 0.865243 0.501353i \(-0.167164\pi\)
−0.00156274 + 0.999999i \(0.500497\pi\)
\(264\) 2.70912 4.51628i 0.166735 0.277958i
\(265\) 9.13701i 0.561282i
\(266\) 13.3081 14.1138i 0.815969 0.865372i
\(267\) −6.43988 + 4.67885i −0.394114 + 0.286341i
\(268\) 0.110984 1.05595i 0.00677945 0.0645021i
\(269\) 1.99749 9.39745i 0.121789 0.572973i −0.874358 0.485281i \(-0.838717\pi\)
0.996148 0.0876923i \(-0.0279492\pi\)
\(270\) −2.50105 + 11.7665i −0.152209 + 0.716088i
\(271\) 0.0129567 0.123274i 0.000787061 0.00748839i −0.994121 0.108272i \(-0.965468\pi\)
0.994908 + 0.100784i \(0.0321350\pi\)
\(272\) −26.0982 + 18.9614i −1.58244 + 1.14971i
\(273\) 1.07984 1.14522i 0.0653551 0.0693120i
\(274\) 0.560713i 0.0338739i
\(275\) −1.78539 + 0.759409i −0.107663 + 0.0457941i
\(276\) 0.0146969 + 0.00848527i 0.000884651 + 0.000510753i
\(277\) −21.9193 + 19.7363i −1.31700 + 1.18584i −0.348367 + 0.937358i \(0.613264\pi\)
−0.968637 + 0.248478i \(0.920070\pi\)
\(278\) 9.56780 21.4896i 0.573838 1.28886i
\(279\) −5.64391 + 7.76818i −0.337892 + 0.465069i
\(280\) −9.97850 + 13.0906i −0.596329 + 0.782314i
\(281\) 12.9022 4.19217i 0.769679 0.250084i 0.102252 0.994759i \(-0.467395\pi\)
0.667428 + 0.744675i \(0.267395\pi\)
\(282\) −7.22131 0.758990i −0.430023 0.0451972i
\(283\) 1.27238 + 12.1059i 0.0756351 + 0.719620i 0.964969 + 0.262362i \(0.0845015\pi\)
−0.889334 + 0.457257i \(0.848832\pi\)
\(284\) 1.25147 + 1.38990i 0.0742613 + 0.0824755i
\(285\) −3.49028 6.04534i −0.206746 0.358095i
\(286\) 0.938098 + 4.80715i 0.0554709 + 0.284253i
\(287\) −10.0803 + 0.825749i −0.595023 + 0.0487424i
\(288\) −3.41075 1.10822i −0.200980 0.0653024i
\(289\) 33.0202 + 14.7016i 1.94237 + 0.864797i
\(290\) 11.5917 + 26.0353i 0.680686 + 1.52885i
\(291\) 10.2960 + 2.18849i 0.603563 + 0.128291i
\(292\) 0.260917 0.289778i 0.0152690 0.0169580i
\(293\) −5.74034 4.17060i −0.335354 0.243649i 0.407345 0.913274i \(-0.366455\pi\)
−0.742699 + 0.669625i \(0.766455\pi\)
\(294\) 4.44160 4.49872i 0.259039 0.262371i
\(295\) −1.03749 + 3.19308i −0.0604052 + 0.185908i
\(296\) −8.42749 + 4.86561i −0.489838 + 0.282808i
\(297\) −6.47415 9.23153i −0.375668 0.535668i
\(298\) −7.46115 + 12.9231i −0.432213 + 0.748615i
\(299\) 0.112271 0.0238639i 0.00649278 0.00138008i
\(300\) −0.0501432 0.0690161i −0.00289502 0.00398465i
\(301\) −6.87645 + 11.3022i −0.396352 + 0.651450i
\(302\) 1.81628 + 5.58994i 0.104515 + 0.321665i
\(303\) 5.94056 + 5.34890i 0.341276 + 0.307286i
\(304\) 19.7959 8.81372i 1.13538 0.505502i
\(305\) −0.557624 + 0.0586087i −0.0319295 + 0.00335592i
\(306\) 5.98243 + 28.1451i 0.341993 + 1.60895i
\(307\) 22.2280 1.26862 0.634309 0.773080i \(-0.281285\pi\)
0.634309 + 0.773080i \(0.281285\pi\)
\(308\) 0.358370 + 2.09099i 0.0204200 + 0.119145i
\(309\) 0.198118 0.0112705
\(310\) −2.67963 12.6067i −0.152193 0.716010i
\(311\) 3.45407 0.363037i 0.195862 0.0205860i −0.00608933 0.999981i \(-0.501938\pi\)
0.201952 + 0.979396i \(0.435272\pi\)
\(312\) 1.43077 0.637018i 0.0810012 0.0360640i
\(313\) −7.42497 6.68548i −0.419684 0.377885i 0.432058 0.901846i \(-0.357787\pi\)
−0.851743 + 0.523960i \(0.824454\pi\)
\(314\) 3.52600 + 10.8519i 0.198984 + 0.612410i
\(315\) 7.91117 + 14.4602i 0.445744 + 0.814740i
\(316\) 1.73430 + 2.38706i 0.0975618 + 0.134282i
\(317\) −20.6388 + 4.38692i −1.15919 + 0.246394i −0.747076 0.664738i \(-0.768543\pi\)
−0.412115 + 0.911132i \(0.635210\pi\)
\(318\) −1.74587 + 3.02394i −0.0979036 + 0.169574i
\(319\) −25.2641 8.67826i −1.41452 0.485890i
\(320\) −13.9443 + 8.05076i −0.779512 + 0.450051i
\(321\) −0.306298 + 0.942687i −0.0170959 + 0.0526157i
\(322\) 0.453002 0.0854567i 0.0252448 0.00476232i
\(323\) −28.8812 20.9834i −1.60699 1.16755i
\(324\) −0.947633 + 1.05245i −0.0526463 + 0.0584696i
\(325\) −0.564369 0.119960i −0.0313056 0.00665421i
\(326\) −4.24663 9.53808i −0.235199 0.528265i
\(327\) −0.0879058 0.0391382i −0.00486120 0.00216435i
\(328\) −9.57099 3.10980i −0.528469 0.171710i
\(329\) −17.4920 + 12.1043i −0.964363 + 0.667334i
\(330\) 7.02662 + 0.857496i 0.386803 + 0.0472036i
\(331\) −10.1074 17.5066i −0.555554 0.962249i −0.997860 0.0653842i \(-0.979173\pi\)
0.442306 0.896864i \(-0.354161\pi\)
\(332\) −0.676179 0.750973i −0.0371102 0.0412150i
\(333\) 1.01860 + 9.69130i 0.0558187 + 0.531080i
\(334\) 18.0258 + 1.89459i 0.986328 + 0.103667i
\(335\) −9.87080 + 3.20722i −0.539299 + 0.175229i
\(336\) 6.51572 2.72332i 0.355461 0.148569i
\(337\) 7.87101 10.8335i 0.428761 0.590139i −0.538907 0.842365i \(-0.681163\pi\)
0.967668 + 0.252226i \(0.0811626\pi\)
\(338\) 7.32441 16.4509i 0.398395 0.894811i
\(339\) 3.58452 3.22752i 0.194685 0.175295i
\(340\) −3.60716 2.08260i −0.195626 0.112945i
\(341\) 10.3596 + 6.21428i 0.561005 + 0.336522i
\(342\) 19.3282i 1.04515i
\(343\) 1.27607 18.4762i 0.0689016 0.997623i
\(344\) −10.6496 + 7.73736i −0.574186 + 0.417170i
\(345\) 0.0173400 0.164979i 0.000933555 0.00888218i
\(346\) −1.01222 + 4.76211i −0.0544171 + 0.256012i
\(347\) −0.0733255 + 0.344969i −0.00393632 + 0.0185189i −0.980072 0.198643i \(-0.936347\pi\)
0.976136 + 0.217162i \(0.0696799\pi\)
\(348\) 0.122774 1.16812i 0.00658140 0.0626178i
\(349\) 28.5886 20.7709i 1.53032 1.11184i 0.574252 0.818679i \(-0.305293\pi\)
0.956063 0.293160i \(-0.0947070\pi\)
\(350\) −2.25503 0.533772i −0.120537 0.0285313i
\(351\) 3.35313i 0.178977i
\(352\) −1.01173 + 4.39709i −0.0539254 + 0.234366i
\(353\) −17.0258 9.82986i −0.906193 0.523191i −0.0269887 0.999636i \(-0.508592\pi\)
−0.879204 + 0.476445i \(0.841925\pi\)
\(354\) 0.953486 0.858523i 0.0506772 0.0456300i
\(355\) 7.43606 16.7017i 0.394665 0.886432i
\(356\) 1.87533 2.58117i 0.0993921 0.136802i
\(357\) −9.25258 7.05290i −0.489698 0.373279i
\(358\) 14.4152 4.68379i 0.761868 0.247546i
\(359\) −6.02528 0.633283i −0.318002 0.0334234i −0.0558172 0.998441i \(-0.517776\pi\)
−0.262185 + 0.965018i \(0.584443\pi\)
\(360\) 1.71431 + 16.3106i 0.0903522 + 0.859643i
\(361\) 3.33231 + 3.70090i 0.175385 + 0.194784i
\(362\) 7.46279 + 12.9259i 0.392235 + 0.679372i
\(363\) −5.07647 + 4.27245i −0.266446 + 0.224246i
\(364\) −0.269785 + 0.570297i −0.0141406 + 0.0298917i
\(365\) −3.62507 1.17786i −0.189745 0.0616519i
\(366\) 0.195747 + 0.0871522i 0.0102319 + 0.00455552i
\(367\) −6.23005 13.9929i −0.325206 0.730425i 0.674765 0.738033i \(-0.264245\pi\)
−0.999971 + 0.00760800i \(0.997578\pi\)
\(368\) 0.503703 + 0.107065i 0.0262574 + 0.00558117i
\(369\) −6.74313 + 7.48900i −0.351033 + 0.389862i
\(370\) −10.5818 7.68812i −0.550121 0.399686i
\(371\) 1.89625 + 10.0519i 0.0984482 + 0.521869i
\(372\) −0.164141 + 0.505175i −0.00851033 + 0.0261921i
\(373\) −4.60679 + 2.65973i −0.238530 + 0.137716i −0.614501 0.788916i \(-0.710643\pi\)
0.375971 + 0.926632i \(0.377309\pi\)
\(374\) 34.6116 10.6098i 1.78972 0.548618i
\(375\) 3.14679 5.45039i 0.162499 0.281457i
\(376\) −20.7028 + 4.40051i −1.06766 + 0.226939i
\(377\) −4.66936 6.42683i −0.240484 0.330998i
\(378\) 0.309525 13.4638i 0.0159202 0.692502i
\(379\) 5.21419 + 16.0476i 0.267835 + 0.824312i 0.991027 + 0.133664i \(0.0426744\pi\)
−0.723191 + 0.690648i \(0.757326\pi\)
\(380\) 2.07923 + 1.87214i 0.106662 + 0.0960390i
\(381\) −8.07100 + 3.59344i −0.413490 + 0.184098i
\(382\) 31.6001 3.32131i 1.61680 0.169933i
\(383\) 4.53768 + 21.3481i 0.231865 + 1.09084i 0.927900 + 0.372830i \(0.121612\pi\)
−0.696035 + 0.718008i \(0.745054\pi\)
\(384\) 7.79443 0.397758
\(385\) 17.2476 11.5137i 0.879017 0.586793i
\(386\) −15.6414 −0.796127
\(387\) 2.74065 + 12.8937i 0.139315 + 0.655425i
\(388\) −4.19582 + 0.440999i −0.213011 + 0.0223883i
\(389\) 6.62431 2.94933i 0.335866 0.149537i −0.231873 0.972746i \(-0.574485\pi\)
0.567738 + 0.823209i \(0.307819\pi\)
\(390\) 1.56439 + 1.40859i 0.0792161 + 0.0713265i
\(391\) −0.262158 0.806840i −0.0132579 0.0408037i
\(392\) 8.26091 16.4723i 0.417239 0.831976i
\(393\) 6.62160 + 9.11386i 0.334016 + 0.459733i
\(394\) −9.63213 + 2.04737i −0.485260 + 0.103145i
\(395\) 14.4209 24.9778i 0.725597 1.25677i
\(396\) 1.68908 + 1.27086i 0.0848795 + 0.0638632i
\(397\) 19.0789 11.0152i 0.957545 0.552839i 0.0621284 0.998068i \(-0.480211\pi\)
0.895417 + 0.445229i \(0.146878\pi\)
\(398\) 0.445756 1.37190i 0.0223437 0.0687669i
\(399\) 5.09439 + 5.92632i 0.255038 + 0.296687i
\(400\) −2.09423 1.52155i −0.104712 0.0760775i
\(401\) −19.2191 + 21.3450i −0.959756 + 1.06592i 0.0380205 + 0.999277i \(0.487895\pi\)
−0.997777 + 0.0666406i \(0.978772\pi\)
\(402\) 3.87961 + 0.824637i 0.193497 + 0.0411292i
\(403\) 1.46122 + 3.28195i 0.0727885 + 0.163486i
\(404\) −2.92699 1.30318i −0.145623 0.0648357i
\(405\) 13.1660 + 4.27790i 0.654225 + 0.212571i
\(406\) −18.1556 26.2366i −0.901047 1.30210i
\(407\) 12.0331 2.34821i 0.596457 0.116396i
\(408\) −5.78799 10.0251i −0.286548 0.496316i
\(409\) −0.959728 1.06589i −0.0474555 0.0527047i 0.718950 0.695062i \(-0.244623\pi\)
−0.766405 + 0.642357i \(0.777956\pi\)
\(410\) −1.41390 13.4524i −0.0698276 0.664365i
\(411\) 0.224654 + 0.0236121i 0.0110814 + 0.00116470i
\(412\) −0.0755211 + 0.0245383i −0.00372066 + 0.00120892i
\(413\) 0.478705 3.72812i 0.0235555 0.183449i
\(414\) 0.269982 0.371599i 0.0132689 0.0182631i
\(415\) −4.01775 + 9.02402i −0.197224 + 0.442972i
\(416\) −0.997142 + 0.897831i −0.0488889 + 0.0440198i
\(417\) 8.20708 + 4.73836i 0.401902 + 0.232038i
\(418\) −24.2233 + 2.13728i −1.18480 + 0.104538i
\(419\) 27.7505i 1.35570i 0.735199 + 0.677851i \(0.237089\pi\)
−0.735199 + 0.677851i \(0.762911\pi\)
\(420\) 0.663408 + 0.625536i 0.0323710 + 0.0305230i
\(421\) 16.9889 12.3432i 0.827989 0.601569i −0.0910006 0.995851i \(-0.529007\pi\)
0.918990 + 0.394282i \(0.129007\pi\)
\(422\) 0.393096 3.74006i 0.0191356 0.182063i
\(423\) −4.40660 + 20.7314i −0.214256 + 1.00800i
\(424\) −2.11614 + 9.95565i −0.102769 + 0.483489i
\(425\) −0.445772 + 4.24124i −0.0216231 + 0.205730i
\(426\) −5.65230 + 4.10664i −0.273855 + 0.198967i
\(427\) 0.601297 0.180204i 0.0290988 0.00872066i
\(428\) 0.397283i 0.0192034i
\(429\) −1.96553 + 0.173423i −0.0948965 + 0.00837295i
\(430\) −15.3228 8.84664i −0.738932 0.426623i
\(431\) 20.1234 18.1192i 0.969311 0.872771i −0.0225952 0.999745i \(-0.507193\pi\)
0.991906 + 0.126973i \(0.0405262\pi\)
\(432\) 6.11888 13.7432i 0.294395 0.661221i
\(433\) −13.1270 + 18.0677i −0.630843 + 0.868280i −0.998086 0.0618445i \(-0.980302\pi\)
0.367243 + 0.930125i \(0.380302\pi\)
\(434\) 5.56426 + 13.3129i 0.267093 + 0.639038i
\(435\) −10.9194 + 3.54792i −0.523544 + 0.170110i
\(436\) 0.0383566 + 0.00403144i 0.00183695 + 0.000193071i
\(437\) 0.0595675 + 0.566747i 0.00284950 + 0.0271112i
\(438\) 0.974674 + 1.08248i 0.0465717 + 0.0517231i
\(439\) 3.78492 + 6.55567i 0.180644 + 0.312885i 0.942100 0.335332i \(-0.108848\pi\)
−0.761456 + 0.648217i \(0.775515\pi\)
\(440\) 20.2518 3.95207i 0.965467 0.188407i
\(441\) −11.7043 14.2663i −0.557349 0.679347i
\(442\) 10.2387 + 3.32676i 0.487006 + 0.158238i
\(443\) 7.08585 + 3.15482i 0.336659 + 0.149890i 0.568102 0.822958i \(-0.307678\pi\)
−0.231443 + 0.972848i \(0.574345\pi\)
\(444\) 0.219258 + 0.492461i 0.0104055 + 0.0233712i
\(445\) −30.5057 6.48419i −1.44611 0.307380i
\(446\) −25.6556 + 28.4934i −1.21483 + 1.34920i
\(447\) −4.86354 3.53357i −0.230038 0.167132i
\(448\) 13.6698 11.7508i 0.645837 0.555174i
\(449\) 0.951113 2.92722i 0.0448858 0.138144i −0.926102 0.377273i \(-0.876862\pi\)
0.970988 + 0.239129i \(0.0768618\pi\)
\(450\) −1.99961 + 1.15447i −0.0942623 + 0.0544224i
\(451\) 10.1313 + 7.62275i 0.477064 + 0.358941i
\(452\) −0.966643 + 1.67427i −0.0454670 + 0.0787512i
\(453\) −2.31614 + 0.492310i −0.108822 + 0.0231308i
\(454\) 17.1158 + 23.5579i 0.803285 + 1.10563i
\(455\) 6.16535 + 0.141738i 0.289036 + 0.00664478i
\(456\) 2.40289 + 7.39533i 0.112526 + 0.346318i
\(457\) 2.87258 + 2.58648i 0.134374 + 0.120990i 0.733577 0.679606i \(-0.237849\pi\)
−0.599204 + 0.800597i \(0.704516\pi\)
\(458\) −28.6494 + 12.7555i −1.33870 + 0.596027i
\(459\) −24.6481 + 2.59062i −1.15048 + 0.120920i
\(460\) 0.0138239 + 0.0650365i 0.000644544 + 0.00303234i
\(461\) 21.6189 1.00689 0.503446 0.864027i \(-0.332065\pi\)
0.503446 + 0.864027i \(0.332065\pi\)
\(462\) −7.90817 + 0.514908i −0.367921 + 0.0239557i
\(463\) −38.1528 −1.77311 −0.886555 0.462623i \(-0.846908\pi\)
−0.886555 + 0.462623i \(0.846908\pi\)
\(464\) −7.41014 34.8620i −0.344007 1.61843i
\(465\) 5.16379 0.542737i 0.239465 0.0251688i
\(466\) −20.8131 + 9.26658i −0.964148 + 0.429266i
\(467\) −0.0206099 0.0185572i −0.000953711 0.000858726i 0.668654 0.743574i \(-0.266871\pi\)
−0.669607 + 0.742715i \(0.733538\pi\)
\(468\) 0.194249 + 0.597837i 0.00897917 + 0.0276350i
\(469\) 10.1936 5.57689i 0.470695 0.257517i
\(470\) −16.7216 23.0153i −0.771309 1.06162i
\(471\) −4.49639 + 0.955737i −0.207183 + 0.0440381i
\(472\) 1.86997 3.23888i 0.0860722 0.149081i
\(473\) 15.8561 4.86050i 0.729065 0.223486i
\(474\) −9.54536 + 5.51102i −0.438433 + 0.253129i
\(475\) 0.885226 2.72445i 0.0406170 0.125006i
\(476\) 4.40056 + 1.54252i 0.201700 + 0.0707012i
\(477\) 8.24561 + 5.99079i 0.377541 + 0.274299i
\(478\) 9.47985 10.5284i 0.433598 0.481560i
\(479\) 6.24723 + 1.32789i 0.285443 + 0.0606728i 0.348408 0.937343i \(-0.386722\pi\)
−0.0629650 + 0.998016i \(0.520056\pi\)
\(480\) 0.788769 + 1.77160i 0.0360022 + 0.0808623i
\(481\) 3.33072 + 1.48293i 0.151868 + 0.0676159i
\(482\) −9.90367 3.21790i −0.451100 0.146571i
\(483\) 0.0151626 + 0.185097i 0.000689922 + 0.00842222i
\(484\) 1.40594 2.25738i 0.0639064 0.102608i
\(485\) 20.6202 + 35.7152i 0.936313 + 1.62174i
\(486\) −13.7579 15.2797i −0.624072 0.693102i
\(487\) −3.69357 35.1419i −0.167371 1.59243i −0.679599 0.733584i \(-0.737846\pi\)
0.512228 0.858850i \(-0.328820\pi\)
\(488\) 0.621159 + 0.0652864i 0.0281185 + 0.00295538i
\(489\) 4.00033 1.29979i 0.180901 0.0587784i
\(490\) 24.7426 + 1.13824i 1.11776 + 0.0514204i
\(491\) −6.84289 + 9.41843i −0.308815 + 0.425048i −0.935011 0.354618i \(-0.884611\pi\)
0.626196 + 0.779666i \(0.284611\pi\)
\(492\) −0.226745 + 0.509278i −0.0102225 + 0.0229600i
\(493\) −43.6347 + 39.2889i −1.96521 + 1.76948i
\(494\) −6.26272 3.61578i −0.281773 0.162682i
\(495\) 4.63315 20.1362i 0.208245 0.905055i
\(496\) 16.1180i 0.723718i
\(497\) −4.71447 + 19.9173i −0.211473 + 0.893411i
\(498\) 3.05398 2.21884i 0.136852 0.0994287i
\(499\) −2.11697 + 20.1416i −0.0947686 + 0.901663i 0.839083 + 0.544003i \(0.183092\pi\)
−0.933852 + 0.357660i \(0.883575\pi\)
\(500\) −0.524462 + 2.46740i −0.0234547 + 0.110346i
\(501\) −1.51816 + 7.14239i −0.0678265 + 0.319098i
\(502\) −1.55399 + 14.7852i −0.0693580 + 0.659897i
\(503\) −12.1336 + 8.81555i −0.541009 + 0.393066i −0.824460 0.565921i \(-0.808521\pi\)
0.283451 + 0.958987i \(0.408521\pi\)
\(504\) −5.27098 17.5880i −0.234788 0.783432i
\(505\) 31.3192i 1.39369i
\(506\) −0.495563 0.297267i −0.0220305 0.0132151i
\(507\) 6.28274 + 3.62734i 0.279026 + 0.161096i
\(508\) 2.63153 2.36944i 0.116755 0.105127i
\(509\) −9.98332 + 22.4229i −0.442503 + 0.993878i 0.545310 + 0.838234i \(0.316412\pi\)
−0.987813 + 0.155644i \(0.950255\pi\)
\(510\) 9.14557 12.5878i 0.404973 0.557397i
\(511\) 4.23250 + 0.543470i 0.187235 + 0.0240417i
\(512\) 16.4326 5.33929i 0.726227 0.235965i
\(513\) 16.5568 + 1.74019i 0.731002 + 0.0768314i
\(514\) 0.612072 + 5.82348i 0.0269973 + 0.256863i
\(515\) 0.519388 + 0.576839i 0.0228870 + 0.0254186i
\(516\) 0.364601 + 0.631508i 0.0160507 + 0.0278006i
\(517\) 26.4691 + 3.23016i 1.16411 + 0.142062i
\(518\) 13.2369 + 6.26186i 0.581597 + 0.275130i
\(519\) −1.86535 0.606089i −0.0818797 0.0266043i
\(520\) 5.60565 + 2.49579i 0.245824 + 0.109448i
\(521\) −11.6722 26.2162i −0.511368 1.14855i −0.966157 0.257953i \(-0.916952\pi\)
0.454789 0.890599i \(-0.349715\pi\)
\(522\) −31.0955 6.60956i −1.36101 0.289293i
\(523\) 24.1216 26.7897i 1.05476 1.17143i 0.0699971 0.997547i \(-0.477701\pi\)
0.984766 0.173886i \(-0.0556323\pi\)
\(524\) −3.65292 2.65400i −0.159579 0.115941i
\(525\) 0.308821 0.881019i 0.0134781 0.0384508i
\(526\) 7.48303 23.0304i 0.326276 1.00417i
\(527\) 22.9960 13.2767i 1.00172 0.578344i
\(528\) −8.37243 2.87595i −0.364363 0.125160i
\(529\) 11.4932 19.9069i 0.499706 0.865515i
\(530\) −13.3815 + 2.84432i −0.581254 + 0.123549i
\(531\) −2.20132 3.02985i −0.0955290 0.131484i
\(532\) −2.67596 1.62809i −0.116017 0.0705868i
\(533\) 1.16513 + 3.58589i 0.0504672 + 0.155322i
\(534\) 8.85704 + 7.97491i 0.383282 + 0.345108i
\(535\) −3.54771 + 1.57954i −0.153381 + 0.0682896i
\(536\) 11.4980 1.20849i 0.496637 0.0521986i
\(537\) 1.26956 + 5.97280i 0.0547855 + 0.257745i
\(538\) −14.3847 −0.620168
\(539\) −16.5851 + 16.2461i −0.714371 + 0.699768i
\(540\) 1.94241 0.0835880
\(541\) −4.00668 18.8500i −0.172261 0.810423i −0.976398 0.215979i \(-0.930706\pi\)
0.804137 0.594444i \(-0.202628\pi\)
\(542\) −0.184573 + 0.0193994i −0.00792808 + 0.000833275i
\(543\) −5.49314 + 2.44570i −0.235733 + 0.104955i
\(544\) 7.37015 + 6.63612i 0.315993 + 0.284521i
\(545\) −0.116500 0.358551i −0.00499032 0.0153586i
\(546\) −2.01337 1.22496i −0.0861642 0.0524236i
\(547\) −15.2932 21.0493i −0.653891 0.900003i 0.345369 0.938467i \(-0.387754\pi\)
−0.999260 + 0.0384635i \(0.987754\pi\)
\(548\) −0.0885609 + 0.0188242i −0.00378314 + 0.000804130i
\(549\) 0.312722 0.541650i 0.0133466 0.0231171i
\(550\) 1.66796 + 2.37836i 0.0711222 + 0.101414i
\(551\) 34.1572 19.7207i 1.45515 0.840129i
\(552\) −0.0571029 + 0.175745i −0.00243046 + 0.00748019i
\(553\) −10.6812 + 30.4717i −0.454210 + 1.29579i
\(554\) 35.7278 + 25.9578i 1.51793 + 1.10284i
\(555\) 3.52591 3.91592i 0.149667 0.166222i
\(556\) −3.71536 0.789723i −0.157566 0.0334917i
\(557\) −9.95918 22.3687i −0.421984 0.947791i −0.992009 0.126164i \(-0.959733\pi\)
0.570025 0.821627i \(-0.306933\pi\)
\(558\) 13.1337 + 5.84749i 0.555993 + 0.247544i
\(559\) 4.69052 + 1.52404i 0.198388 + 0.0644601i
\(560\) 25.0108 + 11.8316i 1.05690 + 0.499978i
\(561\) 2.79336 + 14.3142i 0.117936 + 0.604345i
\(562\) −10.1560 17.5907i −0.428404 0.742017i
\(563\) −2.72138 3.02240i −0.114693 0.127379i 0.683064 0.730358i \(-0.260647\pi\)
−0.797757 + 0.602979i \(0.793980\pi\)
\(564\) 0.122556 + 1.16604i 0.00516052 + 0.0490991i
\(565\) 18.7944 + 1.97537i 0.790688 + 0.0831046i
\(566\) 17.3334 5.63196i 0.728576 0.236729i
\(567\) −15.3722 1.97385i −0.645570 0.0828938i
\(568\) −11.9704 + 16.4759i −0.502267 + 0.691312i
\(569\) 5.90866 13.2711i 0.247704 0.556352i −0.746311 0.665597i \(-0.768177\pi\)
0.994015 + 0.109245i \(0.0348434\pi\)
\(570\) −7.76710 + 6.99353i −0.325328 + 0.292927i
\(571\) −15.6855 9.05601i −0.656416 0.378982i 0.134494 0.990914i \(-0.457059\pi\)
−0.790910 + 0.611932i \(0.790392\pi\)
\(572\) 0.727764 0.309552i 0.0304294 0.0129430i
\(573\) 12.8007i 0.534757i
\(574\) 4.34731 + 14.5059i 0.181453 + 0.605466i
\(575\) 0.0550749 0.0400143i 0.00229678 0.00166871i
\(576\) 1.87742 17.8625i 0.0782260 0.744271i
\(577\) −0.988551 + 4.65077i −0.0411539 + 0.193614i −0.993922 0.110084i \(-0.964888\pi\)
0.952768 + 0.303698i \(0.0982214\pi\)
\(578\) 11.2518 52.9358i 0.468015 2.20184i
\(579\) 0.658672 6.26685i 0.0273735 0.260441i
\(580\) 3.72295 2.70488i 0.154587 0.112314i
\(581\) 2.54726 10.7614i 0.105678 0.446459i
\(582\) 15.7601i 0.653278i
\(583\) 6.59621 10.9963i 0.273187 0.455421i
\(584\) 3.67707 + 2.12296i 0.152158 + 0.0878486i
\(585\) 4.56635 4.11156i 0.188795 0.169992i
\(586\) −4.32104 + 9.70522i −0.178501 + 0.400919i
\(587\) −21.3316 + 29.3605i −0.880451 + 1.21184i 0.0958445 + 0.995396i \(0.469445\pi\)
−0.976296 + 0.216441i \(0.930555\pi\)
\(588\) −0.859657 0.550491i −0.0354517 0.0227019i
\(589\) −16.9637 + 5.51184i −0.698977 + 0.227112i
\(590\) 4.99934 + 0.525451i 0.205819 + 0.0216325i
\(591\) −0.414678 3.94540i −0.0170576 0.162292i
\(592\) 10.9453 + 12.1560i 0.449849 + 0.499608i
\(593\) −22.1014 38.2808i −0.907596 1.57200i −0.817394 0.576079i \(-0.804582\pi\)
−0.0902024 0.995923i \(-0.528751\pi\)
\(594\) −11.5045 + 12.3553i −0.472036 + 0.506946i
\(595\) −3.72146 45.4297i −0.152565 1.86244i
\(596\) 2.29160 + 0.744587i 0.0938678 + 0.0304995i
\(597\) 0.530890 + 0.236367i 0.0217279 + 0.00967387i
\(598\) −0.0698989 0.156995i −0.00285838 0.00642002i
\(599\) 40.4703 + 8.60223i 1.65357 + 0.351478i 0.937886 0.346944i \(-0.112781\pi\)
0.715687 + 0.698422i \(0.246114\pi\)
\(600\) 0.621561 0.690313i 0.0253751 0.0281819i
\(601\) −29.8418 21.6813i −1.21727 0.884400i −0.221401 0.975183i \(-0.571063\pi\)
−0.995871 + 0.0907828i \(0.971063\pi\)
\(602\) 18.6931 + 6.55245i 0.761874 + 0.267058i
\(603\) 3.57758 11.0107i 0.145690 0.448389i
\(604\) 0.821919 0.474535i 0.0334434 0.0193086i
\(605\) −25.7482 3.57991i −1.04681 0.145544i
\(606\) 5.98437 10.3652i 0.243098 0.421059i
\(607\) −27.0361 + 5.74669i −1.09736 + 0.233251i −0.720801 0.693142i \(-0.756226\pi\)
−0.376558 + 0.926393i \(0.622893\pi\)
\(608\) −3.91575 5.38957i −0.158805 0.218576i
\(609\) 11.2764 6.16933i 0.456945 0.249994i
\(610\) 0.259421 + 0.798415i 0.0105036 + 0.0323269i
\(611\) 5.89302 + 5.30610i 0.238406 + 0.214662i
\(612\) 4.24450 1.88977i 0.171574 0.0763895i
\(613\) −13.6163 + 1.43113i −0.549956 + 0.0578027i −0.375432 0.926850i \(-0.622506\pi\)
−0.174525 + 0.984653i \(0.555839\pi\)
\(614\) −6.91949 32.5536i −0.279248 1.31376i
\(615\) 5.44933 0.219738
\(616\) −21.4595 + 8.55074i −0.864626 + 0.344519i
\(617\) −34.9288 −1.40618 −0.703090 0.711100i \(-0.748197\pi\)
−0.703090 + 0.711100i \(0.748197\pi\)
\(618\) −0.0616734 0.290151i −0.00248087 0.0116716i
\(619\) −39.3970 + 4.14079i −1.58350 + 0.166432i −0.855005 0.518620i \(-0.826446\pi\)
−0.728494 + 0.685053i \(0.759779\pi\)
\(620\) −1.90118 + 0.846459i −0.0763532 + 0.0339946i
\(621\) 0.294009 + 0.264727i 0.0117982 + 0.0106231i
\(622\) −1.60692 4.94559i −0.0644316 0.198300i
\(623\) 34.9060 + 0.802470i 1.39848 + 0.0321503i
\(624\) −1.54741 2.12983i −0.0619461 0.0852615i
\(625\) 26.9800 5.73477i 1.07920 0.229391i
\(626\) −7.47974 + 12.9553i −0.298950 + 0.517797i
\(627\) 0.163744 9.79523i 0.00653932 0.391184i
\(628\) 1.59562 0.921229i 0.0636720 0.0367611i
\(629\) 8.32741 25.6291i 0.332035 1.02190i
\(630\) 18.7147 16.0876i 0.745613 0.640945i
\(631\) −13.4804 9.79409i −0.536647 0.389897i 0.286191 0.958172i \(-0.407611\pi\)
−0.822838 + 0.568276i \(0.807611\pi\)
\(632\) −21.4979 + 23.8758i −0.855140 + 0.949729i
\(633\) 1.48193 + 0.314994i 0.0589014 + 0.0125199i
\(634\) 12.8496 + 28.8606i 0.510322 + 1.14620i
\(635\) −31.6217 14.0789i −1.25487 0.558703i
\(636\) 0.536223 + 0.174230i 0.0212626 + 0.00690865i
\(637\) −6.81211 + 1.12359i −0.269906 + 0.0445184i
\(638\) −4.84500 + 39.7016i −0.191815 + 1.57180i
\(639\) 10.1967 + 17.6612i 0.403376 + 0.698668i
\(640\) 20.4340 + 22.6942i 0.807723 + 0.897067i
\(641\) 4.07566 + 38.7773i 0.160979 + 1.53161i 0.715010 + 0.699115i \(0.246422\pi\)
−0.554031 + 0.832496i \(0.686911\pi\)
\(642\) 1.47595 + 0.155128i 0.0582510 + 0.00612242i
\(643\) 13.6671 4.44072i 0.538979 0.175125i −0.0268622 0.999639i \(-0.508552\pi\)
0.565841 + 0.824514i \(0.308552\pi\)
\(644\) −0.0287055 0.0686798i −0.00113115 0.00270636i
\(645\) 4.18973 5.76667i 0.164970 0.227062i
\(646\) −21.7403 + 48.8295i −0.855360 + 1.92117i
\(647\) 19.5675 17.6187i 0.769278 0.692661i −0.187891 0.982190i \(-0.560165\pi\)
0.957169 + 0.289529i \(0.0934985\pi\)
\(648\) −13.3549 7.71044i −0.524629 0.302895i
\(649\) −3.55377 + 3.09385i −0.139498 + 0.121444i
\(650\) 0.863881i 0.0338842i
\(651\) −5.56822 + 1.66875i −0.218236 + 0.0654034i
\(652\) −1.36391 + 0.990938i −0.0534148 + 0.0388081i
\(653\) 1.54058 14.6577i 0.0602877 0.573599i −0.922127 0.386887i \(-0.873550\pi\)
0.982415 0.186712i \(-0.0597831\pi\)
\(654\) −0.0299544 + 0.140925i −0.00117131 + 0.00551059i
\(655\) −9.17657 + 43.1724i −0.358558 + 1.68688i
\(656\) −1.76821 + 16.8234i −0.0690370 + 0.656843i
\(657\) 3.43977 2.49914i 0.134198 0.0975006i
\(658\) 23.1724 + 21.8495i 0.903354 + 0.851783i
\(659\) 8.67875i 0.338076i 0.985610 + 0.169038i \(0.0540661\pi\)
−0.985610 + 0.169038i \(0.945934\pi\)
\(660\) −0.100461 1.13860i −0.00391045 0.0443198i
\(661\) 42.8215 + 24.7230i 1.66556 + 0.961613i 0.969986 + 0.243160i \(0.0781841\pi\)
0.695576 + 0.718452i \(0.255149\pi\)
\(662\) −22.4926 + 20.2524i −0.874198 + 0.787132i
\(663\) −1.76405 + 3.96213i −0.0685101 + 0.153876i
\(664\) 6.46770 8.90202i 0.250995 0.345465i
\(665\) −3.89953 + 30.3693i −0.151217 + 1.17767i
\(666\) 13.8761 4.50863i 0.537690 0.174706i
\(667\) 0.932160 + 0.0979740i 0.0360934 + 0.00379357i
\(668\) −0.305923 2.91066i −0.0118365 0.112617i
\(669\) −10.3357 11.4790i −0.399602 0.443803i
\(670\) 7.76982 + 13.4577i 0.300174 + 0.519917i
\(671\) −0.713407 0.332026i −0.0275408 0.0128177i
\(672\) −1.23542 1.78530i −0.0476573 0.0688695i
\(673\) 43.1998 + 14.0365i 1.66523 + 0.541066i 0.981958 0.189097i \(-0.0605560\pi\)
0.683273 + 0.730163i \(0.260556\pi\)
\(674\) −18.3163 8.15493i −0.705516 0.314116i
\(675\) −0.808905 1.81683i −0.0311348 0.0699298i
\(676\) −2.84421 0.604555i −0.109393 0.0232521i
\(677\) 4.55078 5.05415i 0.174901 0.194247i −0.649321 0.760515i \(-0.724947\pi\)
0.824221 + 0.566268i \(0.191613\pi\)
\(678\) −5.84266 4.24494i −0.224386 0.163026i
\(679\) −30.0970 35.0120i −1.15502 1.34364i
\(680\) 14.0151 43.1342i 0.537456 1.65412i
\(681\) −10.1594 + 5.86554i −0.389310 + 0.224768i
\(682\) 5.87612 17.1065i 0.225008 0.655042i
\(683\) 4.76061 8.24562i 0.182160 0.315510i −0.760456 0.649389i \(-0.775025\pi\)
0.942616 + 0.333880i \(0.108358\pi\)
\(684\) −3.05277 + 0.648886i −0.116725 + 0.0248108i
\(685\) 0.520206 + 0.716002i 0.0198760 + 0.0273570i
\(686\) −27.4563 + 3.88273i −1.04829 + 0.148243i
\(687\) −3.90415 12.0157i −0.148953 0.458429i
\(688\) 16.4436 + 14.8059i 0.626906 + 0.564469i
\(689\) 3.48366 1.55102i 0.132717 0.0590893i
\(690\) −0.247015 + 0.0259624i −0.00940372 + 0.000988370i
\(691\) 2.93988 + 13.8311i 0.111838 + 0.526158i 0.998024 + 0.0628284i \(0.0200121\pi\)
−0.886186 + 0.463330i \(0.846655\pi\)
\(692\) 0.786126 0.0298840
\(693\) −0.918121 + 23.1140i −0.0348766 + 0.878028i
\(694\) 0.528045 0.0200443
\(695\) 7.71958 + 36.3178i 0.292820 + 1.37761i
\(696\) 12.7194 1.33686i 0.482128 0.0506737i
\(697\) 25.4589 11.3350i 0.964326 0.429346i
\(698\) −39.3192 35.4031i −1.48825 1.34003i
\(699\) −2.83627 8.72915i −0.107278 0.330167i
\(700\) −0.00860007 + 0.374088i −0.000325052 + 0.0141392i
\(701\) −0.0985827 0.135687i −0.00372342 0.00512485i 0.807151 0.590345i \(-0.201008\pi\)
−0.810875 + 0.585220i \(0.801008\pi\)
\(702\) −4.91077 + 1.04382i −0.185345 + 0.0393963i
\(703\) −9.05088 + 15.6766i −0.341360 + 0.591253i
\(704\) −22.5939 0.377696i −0.851540 0.0142350i
\(705\) 9.92540 5.73043i 0.373812 0.215821i
\(706\) −9.09609 + 27.9949i −0.342336 + 1.05360i
\(707\) −6.49982 34.4552i −0.244451 1.29582i
\(708\) −0.167608 0.121775i −0.00629911 0.00457657i
\(709\) 18.1324 20.1381i 0.680978 0.756303i −0.299250 0.954175i \(-0.596736\pi\)
0.980228 + 0.197872i \(0.0634030\pi\)
\(710\) −26.7750 5.69119i −1.00485 0.213587i
\(711\) 13.0857 + 29.3910i 0.490753 + 1.10225i
\(712\) 31.7372 + 14.1303i 1.18940 + 0.529555i
\(713\) −0.403130 0.130985i −0.0150973 0.00490542i
\(714\) −7.44892 + 15.7463i −0.278769 + 0.589289i
\(715\) −5.65778 5.26816i −0.211589 0.197018i
\(716\) −1.22372 2.11954i −0.0457326 0.0792111i
\(717\) 3.81910 + 4.24154i 0.142627 + 0.158403i
\(718\) 0.948184 + 9.02137i 0.0353859 + 0.336674i
\(719\) 9.14335 + 0.961005i 0.340989 + 0.0358394i 0.273476 0.961879i \(-0.411827\pi\)
0.0675137 + 0.997718i \(0.478493\pi\)
\(720\) 26.2187 8.51896i 0.977112 0.317483i
\(721\) −0.691109 0.526808i −0.0257382 0.0196193i
\(722\) 4.38276 6.03235i 0.163109 0.224501i
\(723\) 1.70633 3.83247i 0.0634590 0.142531i
\(724\) 1.79103 1.61265i 0.0665629 0.0599335i
\(725\) −4.08041 2.35583i −0.151543 0.0874932i
\(726\) 7.83744 + 6.10467i 0.290875 + 0.226565i
\(727\) 12.8249i 0.475647i 0.971308 + 0.237824i \(0.0764341\pi\)
−0.971308 + 0.237824i \(0.923566\pi\)
\(728\) −6.68491 1.58234i −0.247759 0.0586453i
\(729\) −7.51597 + 5.46067i −0.278369 + 0.202247i
\(730\) −0.596541 + 5.67570i −0.0220790 + 0.210067i
\(731\) 7.57902 35.6565i 0.280320 1.31880i
\(732\) 0.00719352 0.0338428i 0.000265880 0.00125087i
\(733\) −3.35004 + 31.8735i −0.123737 + 1.17728i 0.739742 + 0.672890i \(0.234947\pi\)
−0.863479 + 0.504385i \(0.831719\pi\)
\(734\) −18.5537 + 13.4801i −0.684830 + 0.497558i
\(735\) −1.49797 + 9.86537i −0.0552536 + 0.363890i
\(736\) 0.158315i 0.00583555i
\(737\) −14.1948 3.26609i −0.522872 0.120308i
\(738\) 13.0670 + 7.54424i 0.481003 + 0.277707i
\(739\) 8.27030 7.44661i 0.304228 0.273928i −0.502849 0.864374i \(-0.667715\pi\)
0.807077 + 0.590446i \(0.201048\pi\)
\(740\) −0.859038 + 1.92943i −0.0315789 + 0.0709273i
\(741\) 1.71242 2.35694i 0.0629073 0.0865845i
\(742\) 14.1311 5.90624i 0.518768 0.216825i
\(743\) −3.50271 + 1.13810i −0.128502 + 0.0417528i −0.372562 0.928007i \(-0.621521\pi\)
0.244060 + 0.969760i \(0.421521\pi\)
\(744\) −5.75215 0.604575i −0.210884 0.0221648i
\(745\) −2.46199 23.4243i −0.0902004 0.858200i
\(746\) 5.32934 + 5.91883i 0.195121 + 0.216704i
\(747\) −5.50936 9.54249i −0.201577 0.349141i
\(748\) −2.83772 5.11048i −0.103757 0.186858i
\(749\) 3.57514 2.47398i 0.130633 0.0903972i
\(750\) −8.96187 2.91189i −0.327241 0.106327i
\(751\) −44.1412 19.6529i −1.61074 0.717146i −0.613377 0.789790i \(-0.710189\pi\)
−0.997358 + 0.0726445i \(0.976856\pi\)
\(752\) 14.4706 + 32.5015i 0.527689 + 1.18521i
\(753\) −5.85838 1.24524i −0.213491 0.0453789i
\(754\) −7.95875 + 8.83909i −0.289841 + 0.321901i
\(755\) −7.50542 5.45300i −0.273150 0.198455i
\(756\) −2.13691 + 0.403117i −0.0777185 + 0.0146612i
\(757\) −16.6580 + 51.2680i −0.605444 + 1.86337i −0.111736 + 0.993738i \(0.535641\pi\)
−0.493708 + 0.869628i \(0.664359\pi\)
\(758\) 21.8792 12.6319i 0.794687 0.458813i
\(759\) 0.139971 0.186033i 0.00508062 0.00675257i
\(760\) −15.2327 + 26.3839i −0.552550 + 0.957044i
\(761\) 45.6961 9.71300i 1.65648 0.352096i 0.717632 0.696423i \(-0.245226\pi\)
0.938850 + 0.344327i \(0.111893\pi\)
\(762\) 7.77519 + 10.7016i 0.281665 + 0.387679i
\(763\) 0.202577 + 0.370275i 0.00733379 + 0.0134049i
\(764\) −1.58546 4.87953i −0.0573598 0.176535i
\(765\) −33.7511 30.3897i −1.22028 1.09874i
\(766\) 29.8525 13.2912i 1.07861 0.480229i
\(767\) −1.39354 + 0.146467i −0.0503177 + 0.00528860i
\(768\) −0.717469 3.37542i −0.0258894 0.121800i
\(769\) −23.0259 −0.830334 −0.415167 0.909745i \(-0.636277\pi\)
−0.415167 + 0.909745i \(0.636277\pi\)
\(770\) −22.2313 21.6755i −0.801161 0.781129i
\(771\) −2.35900 −0.0849572
\(772\) 0.525112 + 2.47046i 0.0188992 + 0.0889137i
\(773\) 46.1058 4.84592i 1.65831 0.174296i 0.771437 0.636305i \(-0.219538\pi\)
0.886875 + 0.462010i \(0.152872\pi\)
\(774\) 18.0301 8.02754i 0.648080 0.288544i
\(775\) 1.58347 + 1.42576i 0.0568799 + 0.0512149i
\(776\) −14.1960 43.6907i −0.509606 1.56841i
\(777\) −3.06628 + 5.03978i −0.110002 + 0.180801i
\(778\) −6.38152 8.78341i −0.228788 0.314900i
\(779\) −18.3108 + 3.89208i −0.656053 + 0.139448i
\(780\) 0.169957 0.294375i 0.00608545 0.0105403i
\(781\) 21.0065 14.7321i 0.751673 0.527155i
\(782\) −1.10004 + 0.635106i −0.0393372 + 0.0227113i
\(783\) 8.46149 26.0418i 0.302389 0.930657i
\(784\) −29.9707 7.82574i −1.07038 0.279491i
\(785\) −14.5705 10.5861i −0.520043 0.377834i
\(786\) 11.2863 12.5347i 0.402568 0.447097i
\(787\) 8.10628 + 1.72304i 0.288958 + 0.0614198i 0.350110 0.936709i \(-0.386144\pi\)
−0.0611524 + 0.998128i \(0.519478\pi\)
\(788\) 0.646738 + 1.45260i 0.0230391 + 0.0517466i
\(789\) 8.91219 + 3.96796i 0.317282 + 0.141263i
\(790\) −41.0700 13.3445i −1.46121 0.474775i
\(791\) −21.0863 + 1.72732i −0.749743 + 0.0614166i
\(792\) −9.71182 + 20.8673i −0.345095 + 0.741486i
\(793\) −0.117003 0.202656i −0.00415491 0.00719652i
\(794\) −22.0714 24.5128i −0.783284 0.869925i
\(795\) −0.576093 5.48116i −0.0204319 0.194397i
\(796\) −0.231647 0.0243471i −0.00821051 0.000862959i
\(797\) 3.02147 0.981734i 0.107026 0.0347748i −0.255014 0.966937i \(-0.582080\pi\)
0.362040 + 0.932162i \(0.382080\pi\)
\(798\) 7.09343 9.30574i 0.251105 0.329420i
\(799\) 34.4511 47.4178i 1.21879 1.67752i
\(800\) −0.323691 + 0.727023i −0.0114442 + 0.0257041i
\(801\) 25.8530 23.2782i 0.913472 0.822494i
\(802\) 37.2433 + 21.5024i 1.31511 + 0.759277i
\(803\) −3.51243 4.03456i −0.123951 0.142377i
\(804\) 0.640444i 0.0225867i
\(805\) −0.499178 + 0.529400i −0.0175937 + 0.0186589i
\(806\) 4.35165 3.16166i 0.153280 0.111365i
\(807\) 0.605751 5.76334i 0.0213235 0.202879i
\(808\) 7.25355 34.1253i 0.255179 1.20052i
\(809\) −5.58845 + 26.2916i −0.196480 + 0.924364i 0.763828 + 0.645420i \(0.223318\pi\)
−0.960307 + 0.278944i \(0.910016\pi\)
\(810\) 2.16660 20.6138i 0.0761264 0.724294i
\(811\) 14.9220 10.8414i 0.523981 0.380695i −0.294120 0.955768i \(-0.595027\pi\)
0.818102 + 0.575074i \(0.195027\pi\)
\(812\) −3.53438 + 3.74837i −0.124032 + 0.131542i
\(813\) 0.0747675i 0.00262221i
\(814\) −7.18488 16.8918i −0.251830 0.592058i
\(815\) 14.2718 + 8.23980i 0.499918 + 0.288628i
\(816\) −14.4604 + 13.0202i −0.506215 + 0.455798i
\(817\) −9.95957 + 22.3696i −0.348441 + 0.782612i
\(818\) −1.26227 + 1.73736i −0.0441341 + 0.0607454i
\(819\) −4.17029 + 5.47093i −0.145722 + 0.191170i
\(820\) −2.07725 + 0.674938i −0.0725406 + 0.0235699i
\(821\) −11.6861 1.22826i −0.407849 0.0428666i −0.101617 0.994824i \(-0.532402\pi\)
−0.306232 + 0.951957i \(0.599068\pi\)
\(822\) −0.0353532 0.336364i −0.00123309 0.0117320i
\(823\) −6.20559 6.89200i −0.216313 0.240240i 0.625216 0.780452i \(-0.285011\pi\)
−0.841529 + 0.540212i \(0.818344\pi\)
\(824\) −0.432327 0.748812i −0.0150608 0.0260861i
\(825\) −1.02315 + 0.568128i −0.0356215 + 0.0197797i
\(826\) −5.60898 + 0.459470i −0.195161 + 0.0159870i
\(827\) 20.9538 + 6.80830i 0.728635 + 0.236748i 0.649763 0.760137i \(-0.274868\pi\)
0.0788720 + 0.996885i \(0.474868\pi\)
\(828\) −0.0677554 0.0301667i −0.00235466 0.00104836i
\(829\) 10.8323 + 24.3297i 0.376220 + 0.845005i 0.998084 + 0.0618790i \(0.0197093\pi\)
−0.621863 + 0.783126i \(0.713624\pi\)
\(830\) 14.4667 + 3.07499i 0.502146 + 0.106734i
\(831\) −11.9047 + 13.2215i −0.412970 + 0.458649i
\(832\) −5.43658 3.94991i −0.188479 0.136938i
\(833\) 13.5223 + 49.2063i 0.468521 + 1.70490i
\(834\) 4.38465 13.4946i 0.151828 0.467279i
\(835\) −24.7758 + 14.3043i −0.857400 + 0.495020i
\(836\) 1.15079 + 3.75415i 0.0398009 + 0.129840i
\(837\) −6.19152 + 10.7240i −0.214010 + 0.370676i
\(838\) 40.6416 8.63864i 1.40394 0.298417i
\(839\) −1.29965 1.78881i −0.0448689 0.0617567i 0.785993 0.618235i \(-0.212152\pi\)
−0.830862 + 0.556479i \(0.812152\pi\)
\(840\) −5.16059 + 8.48202i −0.178057 + 0.292657i
\(841\) −11.0849 34.1157i −0.382237 1.17640i
\(842\) −23.3656 21.0385i −0.805231 0.725033i
\(843\) 7.47551 3.32831i 0.257470 0.114633i
\(844\) −0.603914 + 0.0634740i −0.0207876 + 0.00218486i
\(845\) 5.90955 + 27.8023i 0.203295 + 0.956426i
\(846\) 31.7336 1.09102
\(847\) 29.0693 1.40526i 0.998834 0.0482852i
\(848\) 17.1086 0.587511
\(849\) 1.52656 + 7.18192i 0.0523915 + 0.246483i
\(850\) 6.35021 0.667434i 0.217810 0.0228928i
\(851\) −0.392984 + 0.174968i −0.0134713 + 0.00599782i
\(852\) 0.838375 + 0.754876i 0.0287222 + 0.0258616i
\(853\) 2.49530 + 7.67974i 0.0854374 + 0.262949i 0.984644 0.174575i \(-0.0558552\pi\)
−0.899206 + 0.437525i \(0.855855\pi\)
\(854\) −0.451096 0.824523i −0.0154362 0.0282146i
\(855\) 17.9319 + 24.6812i 0.613259 + 0.844079i
\(856\) 4.23140 0.899411i 0.144626 0.0307412i
\(857\) 6.55177 11.3480i 0.223804 0.387640i −0.732156 0.681137i \(-0.761486\pi\)
0.955960 + 0.293497i \(0.0948190\pi\)
\(858\) 0.865845 + 2.82459i 0.0295595 + 0.0964300i
\(859\) −5.96487 + 3.44382i −0.203519 + 0.117502i −0.598296 0.801275i \(-0.704155\pi\)
0.394777 + 0.918777i \(0.370822\pi\)
\(860\) −0.882852 + 2.71714i −0.0301050 + 0.0926536i
\(861\) −5.99498 + 1.13093i −0.204309 + 0.0385418i
\(862\) −32.8005 23.8310i −1.11719 0.811686i
\(863\) 14.2935 15.8746i 0.486557 0.540376i −0.449010 0.893527i \(-0.648223\pi\)
0.935566 + 0.353151i \(0.114890\pi\)
\(864\) −4.52390 0.961585i −0.153906 0.0327138i
\(865\) −3.12553 7.02006i −0.106271 0.238689i
\(866\) 30.5472 + 13.6005i 1.03804 + 0.462164i
\(867\) 20.7353 + 6.73731i 0.704208 + 0.228811i
\(868\) 1.91588 1.32578i 0.0650291 0.0449998i
\(869\) 35.3875 19.6498i 1.20044 0.666574i
\(870\) 8.59522 + 14.8874i 0.291405 + 0.504729i
\(871\) −2.89840 3.21900i −0.0982085 0.109072i
\(872\) 0.0438975 + 0.417657i 0.00148656 + 0.0141436i
\(873\) −45.7506 4.80859i −1.54842 0.162746i
\(874\) 0.811476 0.263665i 0.0274486 0.00891859i
\(875\) −25.4701 + 10.6455i −0.861046 + 0.359884i
\(876\) 0.138250 0.190284i 0.00467103 0.00642912i
\(877\) −9.53687 + 21.4202i −0.322037 + 0.723307i −0.999930 0.0118537i \(-0.996227\pi\)
0.677893 + 0.735161i \(0.262893\pi\)
\(878\) 8.42277 7.58390i 0.284255 0.255944i
\(879\) −3.70651 2.13995i −0.125017 0.0721788i
\(880\) −13.5757 31.9167i −0.457635 1.07591i
\(881\) 39.3172i 1.32463i 0.749225 + 0.662315i \(0.230426\pi\)
−0.749225 + 0.662315i \(0.769574\pi\)
\(882\) −17.2500 + 21.5824i −0.580836 + 0.726718i
\(883\) 21.9250 15.9295i 0.737836 0.536069i −0.154196 0.988040i \(-0.549279\pi\)
0.892033 + 0.451971i \(0.149279\pi\)
\(884\) 0.181707 1.72882i 0.00611146 0.0581466i
\(885\) −0.421052 + 1.98089i −0.0141535 + 0.0665870i
\(886\) 2.41455 11.3595i 0.0811182 0.381631i
\(887\) −1.66387 + 15.8306i −0.0558671 + 0.531540i 0.930419 + 0.366497i \(0.119443\pi\)
−0.986286 + 0.165043i \(0.947224\pi\)
\(888\) −4.74875 + 3.45017i −0.159358 + 0.115780i
\(889\) 37.7098 + 8.92602i 1.26475 + 0.299369i
\(890\) 46.6952i 1.56523i
\(891\) 12.7569 + 14.6533i 0.427372 + 0.490903i
\(892\) 5.36165 + 3.09555i 0.179521 + 0.103647i
\(893\) −29.2584 + 26.3444i −0.979096 + 0.881582i
\(894\) −3.66103 + 8.22281i −0.122443 + 0.275012i
\(895\) −14.0621 + 19.3548i −0.470043 + 0.646959i
\(896\) −27.1899 20.7259i −0.908350 0.692402i
\(897\) 0.0658449 0.0213943i 0.00219850 0.000714335i
\(898\) −4.58310 0.481703i −0.152940 0.0160746i
\(899\) 3.06655 + 29.1763i 0.102275 + 0.973085i
\(900\) 0.249472 + 0.277067i 0.00831574 + 0.00923556i
\(901\) −14.0927 24.4093i −0.469497 0.813192i
\(902\) 8.00995 17.2105i 0.266702 0.573048i
\(903\) −3.41247 + 7.21361i −0.113560 + 0.240054i
\(904\) −20.0208 6.50516i −0.665883 0.216358i
\(905\) −21.5217 9.58210i −0.715407 0.318520i
\(906\) 1.44201 + 3.23881i 0.0479076 + 0.107602i
\(907\) 12.6206 + 2.68259i 0.419060 + 0.0890739i 0.412615 0.910905i \(-0.364615\pi\)
0.00644423 + 0.999979i \(0.497949\pi\)
\(908\) 3.14621 3.49422i 0.104411 0.115960i
\(909\) −28.2637 20.5348i −0.937448 0.681096i
\(910\) −1.71167 9.07348i −0.0567413 0.300783i
\(911\) −6.23228 + 19.1810i −0.206485 + 0.635494i 0.793165 + 0.609007i \(0.208432\pi\)
−0.999649 + 0.0264869i \(0.991568\pi\)
\(912\) 11.3196 6.53537i 0.374829 0.216408i
\(913\) −11.3500 + 7.95983i −0.375629 + 0.263432i
\(914\) 2.89377 5.01215i 0.0957172 0.165787i
\(915\) −0.330815 + 0.0703170i −0.0109364 + 0.00232461i
\(916\) 2.97647 + 4.09676i 0.0983453 + 0.135361i
\(917\) 1.13567 49.3997i 0.0375032 1.63132i
\(918\) 11.4669 + 35.2915i 0.378465 + 1.16479i
\(919\) −0.827337 0.744938i −0.0272913 0.0245732i 0.655372 0.755306i \(-0.272512\pi\)
−0.682663 + 0.730733i \(0.739178\pi\)
\(920\) −0.661398 + 0.294473i −0.0218056 + 0.00970850i
\(921\) 13.3342 1.40149i 0.439378 0.0461805i
\(922\) −6.72988 31.6616i −0.221637 1.04272i
\(923\) 7.63011 0.251148
\(924\) 0.346819 + 1.23176i 0.0114095 + 0.0405218i
\(925\) 2.16243 0.0711003
\(926\) 11.8768 + 55.8760i 0.390297 + 1.83620i
\(927\) −0.861105 + 0.0905058i −0.0282824 + 0.00297260i
\(928\) −10.0099 + 4.45668i −0.328590 + 0.146298i
\(929\) 6.87169 + 6.18730i 0.225453 + 0.202999i 0.774114 0.633046i \(-0.218196\pi\)
−0.548661 + 0.836045i \(0.684862\pi\)
\(930\) −2.40233 7.39360i −0.0787754 0.242446i
\(931\) −2.01267 34.2195i −0.0659627 1.12150i
\(932\) 2.16233 + 2.97619i 0.0708295 + 0.0974885i
\(933\) 2.04916 0.435562i 0.0670864 0.0142596i
\(934\) −0.0207619 + 0.0359606i −0.000679350 + 0.00117667i
\(935\) −34.3539 + 45.6593i −1.12349 + 1.49322i
\(936\) −5.92771 + 3.42237i −0.193753 + 0.111864i
\(937\) −7.01380 + 21.5862i −0.229131 + 0.705192i 0.768715 + 0.639591i \(0.220896\pi\)
−0.997846 + 0.0656008i \(0.979104\pi\)
\(938\) −11.3408 13.1928i −0.370289 0.430759i
\(939\) −4.87566 3.54237i −0.159111 0.115601i
\(940\) −3.07374 + 3.41373i −0.100254 + 0.111344i
\(941\) −6.75829 1.43652i −0.220314 0.0468292i 0.0964321 0.995340i \(-0.469257\pi\)
−0.316746 + 0.948510i \(0.602590\pi\)
\(942\) 2.79942 + 6.28760i 0.0912100 + 0.204861i
\(943\) −0.406404 0.180943i −0.0132343 0.00589230i
\(944\) −5.97887 1.94265i −0.194596 0.0632280i
\(945\) 12.0959 + 17.4797i 0.393479 + 0.568616i
\(946\) −12.0543 21.7087i −0.391919 0.705812i
\(947\) −12.4130 21.4999i −0.403368 0.698654i 0.590762 0.806846i \(-0.298827\pi\)
−0.994130 + 0.108192i \(0.965494\pi\)
\(948\) 1.19089 + 1.32261i 0.0386781 + 0.0429564i
\(949\) −0.166282 1.58207i −0.00539775 0.0513562i
\(950\) −4.26561 0.448334i −0.138395 0.0145459i
\(951\) −12.1043 + 3.93294i −0.392510 + 0.127534i
\(952\) −6.46666 + 50.3619i −0.209586 + 1.63224i
\(953\) 12.1732 16.7550i 0.394328 0.542747i −0.564981 0.825104i \(-0.691116\pi\)
0.959309 + 0.282357i \(0.0911164\pi\)
\(954\) 6.20688 13.9409i 0.200955 0.451353i
\(955\) −37.2704 + 33.5584i −1.20604 + 1.08593i
\(956\) −1.98116 1.14382i −0.0640751 0.0369938i
\(957\) −15.7027 3.61305i −0.507597 0.116793i
\(958\) 9.56265i 0.308955i
\(959\) −0.720890 0.679736i −0.0232788 0.0219498i
\(960\) −7.85740 + 5.70873i −0.253596 + 0.184249i
\(961\) −1.85358 + 17.6357i −0.0597930 + 0.568893i
\(962\) 1.13496 5.33958i 0.0365927 0.172155i
\(963\) 0.900655 4.23725i 0.0290232 0.136543i
\(964\) −0.175761 + 1.67225i −0.00566087 + 0.0538596i
\(965\) 19.9733 14.5114i 0.642963 0.467140i
\(966\) 0.266361 0.0798263i 0.00857004 0.00256837i
\(967\) 19.7404i 0.634809i 0.948290 + 0.317404i \(0.102811\pi\)
−0.948290 + 0.317404i \(0.897189\pi\)
\(968\) 27.2260 + 9.86395i 0.875076 + 0.317039i
\(969\) −18.6484 10.7667i −0.599073 0.345875i
\(970\) 45.8871 41.3169i 1.47335 1.32661i
\(971\) 7.50765 16.8625i 0.240932 0.541142i −0.752091 0.659059i \(-0.770955\pi\)
0.993024 + 0.117916i \(0.0376215\pi\)
\(972\) −1.95145 + 2.68594i −0.0625929 + 0.0861517i
\(973\) −16.0297 38.3522i −0.513890 1.22952i
\(974\) −50.3168 + 16.3489i −1.61225 + 0.523853i
\(975\) −0.346121 0.0363787i −0.0110847 0.00116505i
\(976\) −0.109742 1.04412i −0.00351275 0.0334216i
\(977\) 6.68269 + 7.42188i 0.213798 + 0.237447i 0.840499 0.541813i \(-0.182262\pi\)
−0.626701 + 0.779260i \(0.715595\pi\)
\(978\) −3.14887 5.45400i −0.100690 0.174400i
\(979\) −32.0323 29.8265i −1.02376 0.953258i
\(980\) −0.650879 3.94614i −0.0207916 0.126055i
\(981\) 0.399956 + 0.129953i 0.0127696 + 0.00414909i
\(982\) 15.9238 + 7.08972i 0.508148 + 0.226242i
\(983\) −7.51250 16.8734i −0.239612 0.538177i 0.753210 0.657780i \(-0.228504\pi\)
−0.992822 + 0.119603i \(0.961838\pi\)
\(984\) −5.93757 1.26207i −0.189283 0.0402333i
\(985\) 10.4003 11.5507i 0.331380 0.368035i
\(986\) 71.1232 + 51.6740i 2.26502 + 1.64564i
\(987\) −9.72999 + 8.36410i −0.309709 + 0.266232i
\(988\) −0.360838 + 1.11054i −0.0114798 + 0.0353311i
\(989\) −0.503944 + 0.290952i −0.0160245 + 0.00925174i
\(990\) −30.9324 0.517089i −0.983097 0.0164342i
\(991\) −3.23393 + 5.60134i −0.102729 + 0.177932i −0.912808 0.408388i \(-0.866091\pi\)
0.810079 + 0.586321i \(0.199424\pi\)
\(992\) 4.84691 1.03024i 0.153890 0.0327102i
\(993\) −7.16710 9.86467i −0.227441 0.313046i
\(994\) 30.6371 + 0.704330i 0.971750 + 0.0223400i
\(995\) 0.703580 + 2.16540i 0.0223050 + 0.0686477i
\(996\) −0.452980 0.407865i −0.0143532 0.0129237i
\(997\) −5.07757 + 2.26068i −0.160808 + 0.0715965i −0.485562 0.874202i \(-0.661385\pi\)
0.324754 + 0.945798i \(0.394718\pi\)
\(998\) 30.1571 3.16964i 0.954606 0.100333i
\(999\) 2.61284 + 12.2924i 0.0826664 + 0.388915i
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 77.2.n.a.24.3 yes 48
3.2 odd 2 693.2.cg.a.640.4 48
7.2 even 3 539.2.s.d.68.3 48
7.3 odd 6 539.2.m.a.244.8 48
7.4 even 3 539.2.m.a.244.7 48
7.5 odd 6 inner 77.2.n.a.68.3 yes 48
7.6 odd 2 539.2.s.d.178.3 48
11.2 odd 10 847.2.r.a.360.4 48
11.3 even 5 847.2.r.a.766.3 48
11.4 even 5 847.2.i.b.241.19 48
11.5 even 5 847.2.r.c.94.4 48
11.6 odd 10 inner 77.2.n.a.17.3 48
11.7 odd 10 847.2.i.b.241.6 48
11.8 odd 10 847.2.r.d.766.4 48
11.9 even 5 847.2.r.d.360.3 48
11.10 odd 2 847.2.r.c.717.4 48
21.5 even 6 693.2.cg.a.145.4 48
33.17 even 10 693.2.cg.a.325.4 48
77.5 odd 30 847.2.r.c.215.4 48
77.6 even 10 539.2.s.d.325.3 48
77.17 even 30 539.2.m.a.391.7 48
77.19 even 30 847.2.r.d.40.3 48
77.26 odd 30 847.2.i.b.362.6 48
77.39 odd 30 539.2.m.a.391.8 48
77.40 even 30 847.2.i.b.362.19 48
77.47 odd 30 847.2.r.a.40.4 48
77.54 even 6 847.2.r.c.838.4 48
77.61 even 30 inner 77.2.n.a.61.3 yes 48
77.68 even 30 847.2.r.a.481.3 48
77.72 odd 30 539.2.s.d.215.3 48
77.75 odd 30 847.2.r.d.481.4 48
231.215 odd 30 693.2.cg.a.523.4 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.n.a.17.3 48 11.6 odd 10 inner
77.2.n.a.24.3 yes 48 1.1 even 1 trivial
77.2.n.a.61.3 yes 48 77.61 even 30 inner
77.2.n.a.68.3 yes 48 7.5 odd 6 inner
539.2.m.a.244.7 48 7.4 even 3
539.2.m.a.244.8 48 7.3 odd 6
539.2.m.a.391.7 48 77.17 even 30
539.2.m.a.391.8 48 77.39 odd 30
539.2.s.d.68.3 48 7.2 even 3
539.2.s.d.178.3 48 7.6 odd 2
539.2.s.d.215.3 48 77.72 odd 30
539.2.s.d.325.3 48 77.6 even 10
693.2.cg.a.145.4 48 21.5 even 6
693.2.cg.a.325.4 48 33.17 even 10
693.2.cg.a.523.4 48 231.215 odd 30
693.2.cg.a.640.4 48 3.2 odd 2
847.2.i.b.241.6 48 11.7 odd 10
847.2.i.b.241.19 48 11.4 even 5
847.2.i.b.362.6 48 77.26 odd 30
847.2.i.b.362.19 48 77.40 even 30
847.2.r.a.40.4 48 77.47 odd 30
847.2.r.a.360.4 48 11.2 odd 10
847.2.r.a.481.3 48 77.68 even 30
847.2.r.a.766.3 48 11.3 even 5
847.2.r.c.94.4 48 11.5 even 5
847.2.r.c.215.4 48 77.5 odd 30
847.2.r.c.717.4 48 11.10 odd 2
847.2.r.c.838.4 48 77.54 even 6
847.2.r.d.40.3 48 77.19 even 30
847.2.r.d.360.3 48 11.9 even 5
847.2.r.d.481.4 48 77.75 odd 30
847.2.r.d.766.4 48 11.8 odd 10