Properties

Label 845.2.bg.a.621.35
Level $845$
Weight $2$
Character 845.621
Analytic conductor $6.747$
Analytic rank $0$
Dimension $1440$
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] = [845,2,Mod(36,845)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(845, base_ring=CyclotomicField(78))
 
chi = DirichletCharacter(H, H._module([0, 47]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("845.36");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.bg (of order \(78\), degree \(24\), 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: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(1440\)
Relative dimension: \(60\) over \(\Q(\zeta_{78})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label 621.35
Character \(\chi\) \(=\) 845.621
Dual form 845.2.bg.a.381.35

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.370506 + 0.302509i) q^{2} +(0.900783 + 0.0727188i) q^{3} +(-0.354288 - 1.73542i) q^{4} +(-0.992709 + 0.120537i) q^{5} +(0.311748 + 0.299438i) q^{6} +(-1.50574 - 2.38113i) q^{7} +(0.838283 - 1.59721i) q^{8} +(-2.15503 - 0.350226i) q^{9} +O(q^{10})\) \(q+(0.370506 + 0.302509i) q^{2} +(0.900783 + 0.0727188i) q^{3} +(-0.354288 - 1.73542i) q^{4} +(-0.992709 + 0.120537i) q^{5} +(0.311748 + 0.299438i) q^{6} +(-1.50574 - 2.38113i) q^{7} +(0.838283 - 1.59721i) q^{8} +(-2.15503 - 0.350226i) q^{9} +(-0.404268 - 0.255644i) q^{10} +(-0.0262280 - 0.161388i) q^{11} +(-0.192939 - 1.58900i) q^{12} +(3.19984 + 1.66164i) q^{13} +(0.162429 - 1.33772i) q^{14} +(-0.902981 + 0.0363889i) q^{15} +(-2.46520 + 1.05032i) q^{16} +(-4.54303 + 2.87284i) q^{17} +(-0.692505 - 0.781676i) q^{18} +(-0.812143 - 0.468891i) q^{19} +(0.560887 + 1.68006i) q^{20} +(-1.18319 - 2.25438i) q^{21} +(0.0391035 - 0.0677293i) q^{22} +(-2.99675 - 5.19053i) q^{23} +(0.871259 - 1.37779i) q^{24} +(0.970942 - 0.239316i) q^{25} +(0.682898 + 1.58363i) q^{26} +(-4.54811 - 1.12101i) q^{27} +(-3.59880 + 3.45669i) q^{28} +(-1.78218 + 2.18278i) q^{29} +(-0.345568 - 0.259677i) q^{30} +(1.11082 - 4.50679i) q^{31} +(-4.69633 - 1.36031i) q^{32} +(-0.0118899 - 0.147283i) q^{33} +(-2.55228 - 0.309903i) q^{34} +(1.78177 + 2.18228i) q^{35} +(0.155712 + 3.86396i) q^{36} +(-10.0083 + 2.89893i) q^{37} +(-0.159060 - 0.419407i) q^{38} +(2.76153 + 1.72947i) q^{39} +(-0.639648 + 1.68661i) q^{40} +(0.110836 - 1.37295i) q^{41} +(0.243591 - 1.19319i) q^{42} +(3.32764 - 11.4884i) q^{43} +(-0.270783 + 0.102694i) q^{44} +(2.18153 + 0.0879127i) q^{45} +(0.459866 - 2.82967i) q^{46} +(1.17660 - 1.32811i) q^{47} +(-2.29699 + 0.766848i) q^{48} +(-0.401703 + 0.846571i) q^{49} +(0.432135 + 0.205051i) q^{50} +(-4.30120 + 2.25744i) q^{51} +(1.74998 - 6.14175i) q^{52} +(9.12504 + 4.78919i) q^{53} +(-1.34599 - 1.79118i) q^{54} +(0.0454899 + 0.157049i) q^{55} +(-5.06542 + 0.408923i) q^{56} +(-0.697468 - 0.481427i) q^{57} +(-1.32062 + 0.269607i) q^{58} +(2.97010 - 6.97109i) q^{59} +(0.383065 + 1.55416i) q^{60} +(0.291738 - 7.23940i) q^{61} +(1.77491 - 1.33376i) q^{62} +(2.41097 + 5.65876i) q^{63} +(1.71589 + 2.48589i) q^{64} +(-3.37679 - 1.26383i) q^{65} +(0.0401490 - 0.0581659i) q^{66} +(10.8939 + 2.22400i) q^{67} +(6.59512 + 6.86625i) q^{68} +(-2.32198 - 4.89346i) q^{69} +1.34755i q^{70} +(-9.23869 + 4.38381i) q^{71} +(-2.36591 + 3.14845i) q^{72} +(7.33364 + 2.78128i) q^{73} +(-4.58508 - 1.95352i) q^{74} +(0.892011 - 0.144966i) q^{75} +(-0.525989 + 1.57553i) q^{76} +(-0.344793 + 0.305460i) q^{77} +(0.499983 + 1.47616i) q^{78} +(6.82714 + 6.04832i) q^{79} +(2.32062 - 1.33981i) q^{80} +(2.19748 + 0.733627i) q^{81} +(0.456397 - 0.475159i) q^{82} +(-11.6953 + 8.07270i) q^{83} +(-3.49310 + 2.85203i) q^{84} +(4.16363 - 3.39949i) q^{85} +(4.70824 - 3.24986i) q^{86} +(-1.76409 + 1.83661i) q^{87} +(-0.279757 - 0.0933967i) q^{88} +(10.3938 - 6.00085i) q^{89} +(0.781676 + 0.692505i) q^{90} +(-0.861524 - 10.1212i) q^{91} +(-7.94602 + 7.03956i) q^{92} +(1.32834 - 3.97886i) q^{93} +(0.837705 - 0.136140i) q^{94} +(0.862740 + 0.367579i) q^{95} +(-4.13146 - 1.56686i) q^{96} +(-4.49160 + 5.97723i) q^{97} +(-0.404929 + 0.192141i) q^{98} +0.356981i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1440 q - 2 q^{3} - 58 q^{4} + 18 q^{6} + 6 q^{7} + 60 q^{9} + 2 q^{10} - 20 q^{12} + 26 q^{13} + 4 q^{14} + 6 q^{15} + 58 q^{16} + 6 q^{17} - 156 q^{18} - 12 q^{19} - 12 q^{20} + 60 q^{22} - 146 q^{23} - 144 q^{24} + 120 q^{25} - 10 q^{26} + 4 q^{27} + 18 q^{28} + 4 q^{29} - 4 q^{30} + 52 q^{31} + 20 q^{32} - 42 q^{33} + 130 q^{34} - 10 q^{35} - 56 q^{36} - 6 q^{37} - 162 q^{38} + 12 q^{40} - 12 q^{41} - 24 q^{42} + 2 q^{43} + 42 q^{46} - 156 q^{47} + 30 q^{48} + 18 q^{49} - 124 q^{52} + 48 q^{53} - 330 q^{54} - 4 q^{55} + 20 q^{56} + 78 q^{57} + 68 q^{58} - 196 q^{59} + 12 q^{61} - 118 q^{62} + 24 q^{63} + 96 q^{64} + 8 q^{65} + 44 q^{66} + 98 q^{67} + 120 q^{68} + 28 q^{69} - 156 q^{71} + 386 q^{72} - 30 q^{74} + 2 q^{75} - 392 q^{76} + 4 q^{77} - 204 q^{78} + 40 q^{79} + 40 q^{81} - 244 q^{82} + 30 q^{84} - 18 q^{85} - 30 q^{87} + 30 q^{88} - 24 q^{89} - 56 q^{90} + 76 q^{91} + 20 q^{92} - 130 q^{93} - 148 q^{94} + 16 q^{95} - 338 q^{96} + 30 q^{97} - 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{17}{78}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.370506 + 0.302509i 0.261987 + 0.213906i 0.754330 0.656495i \(-0.227962\pi\)
−0.492343 + 0.870401i \(0.663859\pi\)
\(3\) 0.900783 + 0.0727188i 0.520068 + 0.0419842i 0.337714 0.941249i \(-0.390346\pi\)
0.182354 + 0.983233i \(0.441628\pi\)
\(4\) −0.354288 1.73542i −0.177144 0.867709i
\(5\) −0.992709 + 0.120537i −0.443953 + 0.0539056i
\(6\) 0.311748 + 0.299438i 0.127270 + 0.122245i
\(7\) −1.50574 2.38113i −0.569115 0.899984i 0.430882 0.902408i \(-0.358203\pi\)
−0.999997 + 0.00242454i \(0.999228\pi\)
\(8\) 0.838283 1.59721i 0.296378 0.564701i
\(9\) −2.15503 0.350226i −0.718343 0.116742i
\(10\) −0.404268 0.255644i −0.127841 0.0808416i
\(11\) −0.0262280 0.161388i −0.00790805 0.0486602i 0.982796 0.184693i \(-0.0591290\pi\)
−0.990704 + 0.136032i \(0.956565\pi\)
\(12\) −0.192939 1.58900i −0.0556968 0.458705i
\(13\) 3.19984 + 1.66164i 0.887475 + 0.460856i
\(14\) 0.162429 1.33772i 0.0434110 0.357522i
\(15\) −0.902981 + 0.0363889i −0.233149 + 0.00939557i
\(16\) −2.46520 + 1.05032i −0.616300 + 0.262581i
\(17\) −4.54303 + 2.87284i −1.10185 + 0.696766i −0.956242 0.292577i \(-0.905487\pi\)
−0.145605 + 0.989343i \(0.546513\pi\)
\(18\) −0.692505 0.781676i −0.163225 0.184243i
\(19\) −0.812143 0.468891i −0.186318 0.107571i 0.403940 0.914786i \(-0.367641\pi\)
−0.590258 + 0.807215i \(0.700974\pi\)
\(20\) 0.560887 + 1.68006i 0.125418 + 0.375673i
\(21\) −1.18319 2.25438i −0.258193 0.491946i
\(22\) 0.0391035 0.0677293i 0.00833690 0.0144399i
\(23\) −2.99675 5.19053i −0.624866 1.08230i −0.988567 0.150784i \(-0.951820\pi\)
0.363701 0.931516i \(-0.381513\pi\)
\(24\) 0.871259 1.37779i 0.177845 0.281239i
\(25\) 0.970942 0.239316i 0.194188 0.0478631i
\(26\) 0.682898 + 1.58363i 0.133927 + 0.310575i
\(27\) −4.54811 1.12101i −0.875283 0.215738i
\(28\) −3.59880 + 3.45669i −0.680109 + 0.653253i
\(29\) −1.78218 + 2.18278i −0.330943 + 0.405332i −0.913094 0.407749i \(-0.866314\pi\)
0.582151 + 0.813081i \(0.302211\pi\)
\(30\) −0.345568 0.259677i −0.0630918 0.0474104i
\(31\) 1.11082 4.50679i 0.199510 0.809443i −0.782814 0.622255i \(-0.786217\pi\)
0.982324 0.187188i \(-0.0599373\pi\)
\(32\) −4.69633 1.36031i −0.830202 0.240471i
\(33\) −0.0118899 0.147283i −0.00206976 0.0256386i
\(34\) −2.55228 0.309903i −0.437712 0.0531479i
\(35\) 1.78177 + 2.18228i 0.301175 + 0.368872i
\(36\) 0.155712 + 3.86396i 0.0259520 + 0.643993i
\(37\) −10.0083 + 2.89893i −1.64535 + 0.476581i −0.966280 0.257493i \(-0.917103\pi\)
−0.679069 + 0.734075i \(0.737616\pi\)
\(38\) −0.159060 0.419407i −0.0258030 0.0680369i
\(39\) 2.76153 + 1.72947i 0.442198 + 0.276936i
\(40\) −0.639648 + 1.68661i −0.101137 + 0.266677i
\(41\) 0.110836 1.37295i 0.0173097 0.214420i −0.982320 0.187210i \(-0.940056\pi\)
0.999630 0.0272100i \(-0.00866228\pi\)
\(42\) 0.243591 1.19319i 0.0375869 0.184113i
\(43\) 3.32764 11.4884i 0.507461 1.75196i −0.140296 0.990110i \(-0.544805\pi\)
0.647756 0.761848i \(-0.275708\pi\)
\(44\) −0.270783 + 0.102694i −0.0408220 + 0.0154818i
\(45\) 2.18153 + 0.0879127i 0.325203 + 0.0131052i
\(46\) 0.459866 2.82967i 0.0678035 0.417212i
\(47\) 1.17660 1.32811i 0.171625 0.193725i −0.656404 0.754409i \(-0.727923\pi\)
0.828030 + 0.560684i \(0.189462\pi\)
\(48\) −2.29699 + 0.766848i −0.331542 + 0.110685i
\(49\) −0.401703 + 0.846571i −0.0573862 + 0.120939i
\(50\) 0.432135 + 0.205051i 0.0611131 + 0.0289985i
\(51\) −4.30120 + 2.25744i −0.602288 + 0.316105i
\(52\) 1.74998 6.14175i 0.242678 0.851708i
\(53\) 9.12504 + 4.78919i 1.25342 + 0.657846i 0.955005 0.296590i \(-0.0958496\pi\)
0.298416 + 0.954436i \(0.403542\pi\)
\(54\) −1.34599 1.79118i −0.183166 0.243749i
\(55\) 0.0454899 + 0.157049i 0.00613386 + 0.0211765i
\(56\) −5.06542 + 0.408923i −0.676895 + 0.0546446i
\(57\) −0.697468 0.481427i −0.0923819 0.0637666i
\(58\) −1.32062 + 0.269607i −0.173406 + 0.0354011i
\(59\) 2.97010 6.97109i 0.386674 0.907558i −0.606942 0.794746i \(-0.707604\pi\)
0.993616 0.112812i \(-0.0359858\pi\)
\(60\) 0.383065 + 1.55416i 0.0494535 + 0.200641i
\(61\) 0.291738 7.23940i 0.0373532 0.926910i −0.866528 0.499128i \(-0.833654\pi\)
0.903882 0.427783i \(-0.140705\pi\)
\(62\) 1.77491 1.33376i 0.225414 0.169388i
\(63\) 2.41097 + 5.65876i 0.303754 + 0.712937i
\(64\) 1.71589 + 2.48589i 0.214486 + 0.310736i
\(65\) −3.37679 1.26383i −0.418840 0.156759i
\(66\) 0.0401490 0.0581659i 0.00494200 0.00715972i
\(67\) 10.8939 + 2.22400i 1.33090 + 0.271705i 0.812264 0.583289i \(-0.198235\pi\)
0.518636 + 0.854995i \(0.326440\pi\)
\(68\) 6.59512 + 6.86625i 0.799776 + 0.832655i
\(69\) −2.32198 4.89346i −0.279533 0.589103i
\(70\) 1.34755i 0.161063i
\(71\) −9.23869 + 4.38381i −1.09643 + 0.520263i −0.888963 0.457979i \(-0.848574\pi\)
−0.207468 + 0.978242i \(0.566522\pi\)
\(72\) −2.36591 + 3.14845i −0.278825 + 0.371049i
\(73\) 7.33364 + 2.78128i 0.858337 + 0.325524i 0.744213 0.667942i \(-0.232825\pi\)
0.114124 + 0.993467i \(0.463594\pi\)
\(74\) −4.58508 1.95352i −0.533004 0.227092i
\(75\) 0.892011 0.144966i 0.103001 0.0167392i
\(76\) −0.525989 + 1.57553i −0.0603351 + 0.180726i
\(77\) −0.344793 + 0.305460i −0.0392928 + 0.0348104i
\(78\) 0.499983 + 1.47616i 0.0566120 + 0.167143i
\(79\) 6.82714 + 6.04832i 0.768114 + 0.680489i 0.953236 0.302226i \(-0.0977298\pi\)
−0.185123 + 0.982715i \(0.559268\pi\)
\(80\) 2.32062 1.33981i 0.259454 0.149796i
\(81\) 2.19748 + 0.733627i 0.244165 + 0.0815142i
\(82\) 0.456397 0.475159i 0.0504006 0.0524726i
\(83\) −11.6953 + 8.07270i −1.28373 + 0.886094i −0.997402 0.0720381i \(-0.977050\pi\)
−0.286327 + 0.958132i \(0.592434\pi\)
\(84\) −3.49310 + 2.85203i −0.381129 + 0.311182i
\(85\) 4.16363 3.39949i 0.451609 0.368727i
\(86\) 4.70824 3.24986i 0.507703 0.350442i
\(87\) −1.76409 + 1.83661i −0.189130 + 0.196906i
\(88\) −0.279757 0.0933967i −0.0298222 0.00995612i
\(89\) 10.3938 6.00085i 1.10174 0.636089i 0.165061 0.986283i \(-0.447218\pi\)
0.936677 + 0.350194i \(0.113884\pi\)
\(90\) 0.781676 + 0.692505i 0.0823959 + 0.0729964i
\(91\) −0.861524 10.1212i −0.0903122 1.06099i
\(92\) −7.94602 + 7.03956i −0.828430 + 0.733925i
\(93\) 1.32834 3.97886i 0.137742 0.412589i
\(94\) 0.837705 0.136140i 0.0864026 0.0140418i
\(95\) 0.862740 + 0.367579i 0.0885153 + 0.0377128i
\(96\) −4.13146 1.56686i −0.421665 0.159916i
\(97\) −4.49160 + 5.97723i −0.456053 + 0.606896i −0.967640 0.252335i \(-0.918801\pi\)
0.511587 + 0.859231i \(0.329058\pi\)
\(98\) −0.404929 + 0.192141i −0.0409040 + 0.0194092i
\(99\) 0.356981i 0.0358779i
\(100\) −0.759306 1.60020i −0.0759306 0.160020i
\(101\) −8.43039 8.77696i −0.838855 0.873340i 0.154552 0.987985i \(-0.450607\pi\)
−0.993407 + 0.114644i \(0.963427\pi\)
\(102\) −2.27652 0.464754i −0.225409 0.0460175i
\(103\) 10.2669 14.8742i 1.01163 1.46560i 0.131242 0.991350i \(-0.458104\pi\)
0.880390 0.474251i \(-0.157281\pi\)
\(104\) 5.33636 3.71790i 0.523274 0.364570i
\(105\) 1.44630 + 2.09533i 0.141144 + 0.204483i
\(106\) 1.93211 + 4.53483i 0.187663 + 0.440462i
\(107\) 9.42087 7.07932i 0.910750 0.684384i −0.0383819 0.999263i \(-0.512220\pi\)
0.949132 + 0.314879i \(0.101964\pi\)
\(108\) −0.334077 + 8.29003i −0.0321465 + 0.797708i
\(109\) −0.622366 2.52504i −0.0596119 0.241855i 0.933576 0.358380i \(-0.116671\pi\)
−0.993188 + 0.116525i \(0.962825\pi\)
\(110\) −0.0306546 + 0.0719489i −0.00292280 + 0.00686006i
\(111\) −9.22609 + 1.88352i −0.875701 + 0.178776i
\(112\) 6.21290 + 4.28846i 0.587064 + 0.405221i
\(113\) −19.9383 + 1.60959i −1.87564 + 0.151417i −0.965079 0.261959i \(-0.915631\pi\)
−0.910560 + 0.413377i \(0.864349\pi\)
\(114\) −0.112780 0.389362i −0.0105628 0.0364671i
\(115\) 3.60055 + 4.79146i 0.335753 + 0.446806i
\(116\) 4.41944 + 2.31950i 0.410335 + 0.215360i
\(117\) −6.31379 4.70155i −0.583710 0.434658i
\(118\) 3.20926 1.68435i 0.295436 0.155057i
\(119\) 13.6812 + 6.49182i 1.25416 + 0.595104i
\(120\) −0.698833 + 1.47276i −0.0637944 + 0.134444i
\(121\) 10.4085 3.47488i 0.946231 0.315898i
\(122\) 2.29807 2.59399i 0.208058 0.234849i
\(123\) 0.199679 1.22867i 0.0180045 0.110786i
\(124\) −8.21472 0.331042i −0.737703 0.0297284i
\(125\) −0.935016 + 0.354605i −0.0836304 + 0.0317168i
\(126\) −0.818545 + 2.82595i −0.0729218 + 0.251755i
\(127\) 0.186210 0.912116i 0.0165235 0.0809372i −0.970693 0.240324i \(-0.922746\pi\)
0.987216 + 0.159386i \(0.0509516\pi\)
\(128\) −0.903120 + 11.1871i −0.0798253 + 0.988813i
\(129\) 3.83290 10.1065i 0.337468 0.889831i
\(130\) −0.868804 1.48977i −0.0761991 0.130661i
\(131\) 1.11614 + 2.94301i 0.0975173 + 0.257132i 0.974894 0.222671i \(-0.0714775\pi\)
−0.877376 + 0.479803i \(0.840708\pi\)
\(132\) −0.251384 + 0.0728144i −0.0218802 + 0.00633768i
\(133\) 0.106382 + 2.63985i 0.00922451 + 0.228904i
\(134\) 3.36347 + 4.11951i 0.290560 + 0.355871i
\(135\) 4.65007 + 0.564620i 0.400214 + 0.0485948i
\(136\) 0.780195 + 9.66445i 0.0669012 + 0.828720i
\(137\) 15.0951 + 4.37235i 1.28966 + 0.373555i 0.851033 0.525113i \(-0.175977\pi\)
0.438630 + 0.898668i \(0.355464\pi\)
\(138\) 0.620009 2.51548i 0.0527787 0.214132i
\(139\) −15.9242 11.9663i −1.35068 1.01497i −0.996822 0.0796668i \(-0.974614\pi\)
−0.353855 0.935300i \(-0.615129\pi\)
\(140\) 3.15590 3.86528i 0.266722 0.326675i
\(141\) 1.15644 1.11078i 0.0973901 0.0935445i
\(142\) −4.74913 1.17056i −0.398538 0.0982309i
\(143\) 0.184243 0.559995i 0.0154072 0.0468292i
\(144\) 5.68043 1.40010i 0.473369 0.116675i
\(145\) 1.50609 2.38168i 0.125074 0.197788i
\(146\) 1.87580 + 3.24897i 0.155242 + 0.268887i
\(147\) −0.423409 + 0.733366i −0.0349222 + 0.0604870i
\(148\) 8.57667 + 16.3415i 0.704998 + 1.34326i
\(149\) 1.24266 + 3.72222i 0.101803 + 0.304936i 0.987104 0.160082i \(-0.0511759\pi\)
−0.885301 + 0.465018i \(0.846048\pi\)
\(150\) 0.374349 + 0.216131i 0.0305655 + 0.0176470i
\(151\) −5.76680 6.50937i −0.469295 0.529725i 0.465435 0.885082i \(-0.345898\pi\)
−0.934731 + 0.355357i \(0.884359\pi\)
\(152\) −1.42973 + 0.904103i −0.115966 + 0.0733325i
\(153\) 10.7965 4.59996i 0.872846 0.371885i
\(154\) −0.220152 + 0.00887183i −0.0177404 + 0.000714912i
\(155\) −0.559491 + 4.60783i −0.0449394 + 0.370109i
\(156\) 2.02297 5.40513i 0.161967 0.432757i
\(157\) −0.293497 2.41717i −0.0234236 0.192911i 0.976300 0.216422i \(-0.0694386\pi\)
−0.999724 + 0.0235109i \(0.992516\pi\)
\(158\) 0.699828 + 4.30621i 0.0556753 + 0.342584i
\(159\) 7.87142 + 4.97758i 0.624244 + 0.394748i
\(160\) 4.82606 + 0.784311i 0.381533 + 0.0620052i
\(161\) −7.84702 + 14.9512i −0.618431 + 1.17832i
\(162\) 0.592252 + 0.936571i 0.0465317 + 0.0735840i
\(163\) 4.18352 + 4.01833i 0.327679 + 0.314740i 0.838452 0.544976i \(-0.183461\pi\)
−0.510773 + 0.859716i \(0.670641\pi\)
\(164\) −2.42192 + 0.294074i −0.189120 + 0.0229633i
\(165\) 0.0295561 + 0.144776i 0.00230094 + 0.0112708i
\(166\) −6.77525 0.546955i −0.525862 0.0424519i
\(167\) −2.05507 1.67792i −0.159026 0.129841i 0.549591 0.835434i \(-0.314783\pi\)
−0.708618 + 0.705593i \(0.750681\pi\)
\(168\) −4.59258 −0.354325
\(169\) 7.47790 + 10.6340i 0.575223 + 0.817997i
\(170\) 2.57103 0.197189
\(171\) 1.58597 + 1.29491i 0.121282 + 0.0990240i
\(172\) −21.1160 1.70466i −1.61008 0.129979i
\(173\) 2.47623 + 12.1294i 0.188264 + 0.922180i 0.958647 + 0.284598i \(0.0918601\pi\)
−0.770383 + 0.637582i \(0.779935\pi\)
\(174\) −1.20920 + 0.146823i −0.0916691 + 0.0111306i
\(175\) −2.03183 1.95160i −0.153592 0.147527i
\(176\) 0.234167 + 0.370305i 0.0176510 + 0.0279128i
\(177\) 3.18235 6.06346i 0.239200 0.455757i
\(178\) 5.66627 + 0.920858i 0.424705 + 0.0690213i
\(179\) −8.70938 5.50748i −0.650970 0.411648i 0.167760 0.985828i \(-0.446347\pi\)
−0.818729 + 0.574180i \(0.805321\pi\)
\(180\) −0.620325 3.81702i −0.0462363 0.284504i
\(181\) −2.02013 16.6373i −0.150155 1.23664i −0.851707 0.524019i \(-0.824432\pi\)
0.701552 0.712618i \(-0.252491\pi\)
\(182\) 2.74256 4.01060i 0.203292 0.297285i
\(183\) 0.789233 6.49992i 0.0583418 0.480488i
\(184\) −10.8025 + 0.435326i −0.796372 + 0.0320927i
\(185\) 9.58587 4.08416i 0.704767 0.300273i
\(186\) 1.69580 1.07236i 0.124342 0.0786292i
\(187\) 0.582795 + 0.657840i 0.0426182 + 0.0481060i
\(188\) −2.72169 1.57137i −0.198499 0.114604i
\(189\) 4.17899 + 12.5176i 0.303976 + 0.910521i
\(190\) 0.208455 + 0.397177i 0.0151229 + 0.0288142i
\(191\) 5.43317 9.41053i 0.393131 0.680922i −0.599730 0.800202i \(-0.704725\pi\)
0.992861 + 0.119280i \(0.0380587\pi\)
\(192\) 1.36487 + 2.36403i 0.0985011 + 0.170609i
\(193\) 4.48520 7.09277i 0.322852 0.510549i −0.644292 0.764780i \(-0.722848\pi\)
0.967144 + 0.254231i \(0.0818222\pi\)
\(194\) −3.47233 + 0.855853i −0.249299 + 0.0614467i
\(195\) −2.94986 1.38399i −0.211244 0.0991097i
\(196\) 1.61147 + 0.397193i 0.115105 + 0.0283709i
\(197\) −4.42351 + 4.24884i −0.315162 + 0.302717i −0.833567 0.552418i \(-0.813705\pi\)
0.518405 + 0.855135i \(0.326526\pi\)
\(198\) −0.107990 + 0.132263i −0.00767450 + 0.00939956i
\(199\) −18.0120 13.5351i −1.27684 0.959481i −0.276839 0.960916i \(-0.589287\pi\)
−0.999999 + 0.00143533i \(0.999543\pi\)
\(200\) 0.431685 1.75142i 0.0305248 0.123844i
\(201\) 9.65131 + 2.79554i 0.680751 + 0.197182i
\(202\) −0.468401 5.80219i −0.0329566 0.408240i
\(203\) 7.88099 + 0.956926i 0.553137 + 0.0671630i
\(204\) 5.44147 + 6.66459i 0.380979 + 0.466615i
\(205\) 0.0554632 + 1.37630i 0.00387372 + 0.0961253i
\(206\) 8.30355 2.40515i 0.578536 0.167575i
\(207\) 4.64023 + 12.2353i 0.322518 + 0.850410i
\(208\) −9.63349 0.735415i −0.667963 0.0509918i
\(209\) −0.0543723 + 0.143368i −0.00376101 + 0.00991696i
\(210\) −0.0979921 + 1.21385i −0.00676209 + 0.0837636i
\(211\) 1.08836 5.33114i 0.0749257 0.367010i −0.924990 0.379991i \(-0.875927\pi\)
0.999916 + 0.0129809i \(0.00413207\pi\)
\(212\) 5.07835 17.5325i 0.348783 1.20414i
\(213\) −8.64084 + 3.27704i −0.592061 + 0.224539i
\(214\) 5.63205 + 0.226964i 0.384999 + 0.0155149i
\(215\) −1.91861 + 11.8057i −0.130848 + 0.805142i
\(216\) −5.60309 + 6.32458i −0.381242 + 0.430333i
\(217\) −12.4039 + 4.14102i −0.842030 + 0.281111i
\(218\) 0.533257 1.12381i 0.0361167 0.0761143i
\(219\) 6.40377 + 3.03863i 0.432726 + 0.205331i
\(220\) 0.256430 0.134585i 0.0172885 0.00907371i
\(221\) −19.3106 + 1.64373i −1.29897 + 0.110569i
\(222\) −3.98810 2.09312i −0.267664 0.140481i
\(223\) 12.4565 + 16.5766i 0.834149 + 1.11005i 0.992449 + 0.122660i \(0.0391423\pi\)
−0.158300 + 0.987391i \(0.550601\pi\)
\(224\) 3.83237 + 13.2309i 0.256061 + 0.884024i
\(225\) −2.17622 + 0.175683i −0.145081 + 0.0117122i
\(226\) −7.87418 5.43516i −0.523783 0.361541i
\(227\) −9.98051 + 2.03754i −0.662430 + 0.135236i −0.519465 0.854492i \(-0.673869\pi\)
−0.142965 + 0.989728i \(0.545664\pi\)
\(228\) −0.588373 + 1.38096i −0.0389660 + 0.0914565i
\(229\) 1.85181 + 7.51308i 0.122371 + 0.496478i 0.999858 + 0.0168771i \(0.00537241\pi\)
−0.877487 + 0.479601i \(0.840781\pi\)
\(230\) −0.115434 + 2.86447i −0.00761149 + 0.188877i
\(231\) −0.332796 + 0.250080i −0.0218964 + 0.0164541i
\(232\) 1.99239 + 4.67632i 0.130807 + 0.307015i
\(233\) 15.9882 + 23.1629i 1.04742 + 1.51745i 0.842515 + 0.538672i \(0.181074\pi\)
0.204907 + 0.978781i \(0.434311\pi\)
\(234\) −0.917036 3.65193i −0.0599485 0.238734i
\(235\) −1.00794 + 1.46025i −0.0657507 + 0.0952563i
\(236\) −13.1500 2.68460i −0.855994 0.174752i
\(237\) 5.70995 + 5.94469i 0.370901 + 0.386149i
\(238\) 3.10514 + 6.54395i 0.201277 + 0.424181i
\(239\) 28.4820i 1.84235i 0.389148 + 0.921175i \(0.372770\pi\)
−0.389148 + 0.921175i \(0.627230\pi\)
\(240\) 2.18781 1.03813i 0.141222 0.0670109i
\(241\) −0.933102 + 1.24173i −0.0601064 + 0.0799870i −0.828495 0.559997i \(-0.810802\pi\)
0.768389 + 0.639984i \(0.221059\pi\)
\(242\) 4.90761 + 1.86121i 0.315473 + 0.119643i
\(243\) 14.8543 + 6.32881i 0.952902 + 0.405994i
\(244\) −12.6668 + 2.05855i −0.810906 + 0.131785i
\(245\) 0.296731 0.888819i 0.0189575 0.0567846i
\(246\) 0.445667 0.394827i 0.0284147 0.0251732i
\(247\) −1.81960 2.84986i −0.115778 0.181333i
\(248\) −6.26713 5.55219i −0.397963 0.352564i
\(249\) −11.1220 + 6.42128i −0.704828 + 0.406932i
\(250\) −0.453700 0.151467i −0.0286945 0.00957964i
\(251\) −0.943341 + 0.982122i −0.0595431 + 0.0619910i −0.750308 0.661089i \(-0.770095\pi\)
0.690765 + 0.723080i \(0.257274\pi\)
\(252\) 8.96613 6.18888i 0.564813 0.389863i
\(253\) −0.759088 + 0.619776i −0.0477234 + 0.0389650i
\(254\) 0.344915 0.281615i 0.0216419 0.0176701i
\(255\) 3.99773 2.75943i 0.250348 0.172803i
\(256\) 0.466039 0.485198i 0.0291274 0.0303249i
\(257\) 23.6570 + 7.89788i 1.47569 + 0.492656i 0.936843 0.349750i \(-0.113734\pi\)
0.538843 + 0.842406i \(0.318862\pi\)
\(258\) 4.47743 2.58505i 0.278753 0.160938i
\(259\) 21.9726 + 19.4660i 1.36531 + 1.20956i
\(260\) −0.996913 + 6.30791i −0.0618259 + 0.391200i
\(261\) 4.60513 4.07978i 0.285050 0.252532i
\(262\) −0.476751 + 1.42804i −0.0294538 + 0.0882249i
\(263\) 12.6432 2.05471i 0.779611 0.126699i 0.242433 0.970168i \(-0.422055\pi\)
0.537178 + 0.843469i \(0.319490\pi\)
\(264\) −0.245209 0.104474i −0.0150916 0.00642991i
\(265\) −9.63578 3.65437i −0.591921 0.224486i
\(266\) −0.759162 + 1.01026i −0.0465472 + 0.0619431i
\(267\) 9.79892 4.64964i 0.599684 0.284554i
\(268\) 19.6934i 1.20297i
\(269\) −11.3194 23.8551i −0.690155 1.45447i −0.881129 0.472876i \(-0.843216\pi\)
0.190973 0.981595i \(-0.438836\pi\)
\(270\) 1.55208 + 1.61588i 0.0944563 + 0.0983395i
\(271\) −5.10037 1.04125i −0.309825 0.0632513i 0.0425971 0.999092i \(-0.486437\pi\)
−0.352422 + 0.935841i \(0.614642\pi\)
\(272\) 8.18207 11.8538i 0.496111 0.718741i
\(273\) −0.0400428 9.17969i −0.00242350 0.555580i
\(274\) 4.27016 + 6.18639i 0.257970 + 0.373733i
\(275\) −0.0640885 0.150421i −0.00386468 0.00907074i
\(276\) −7.66955 + 5.76330i −0.461653 + 0.346910i
\(277\) 0.611439 15.1727i 0.0367378 0.911639i −0.870792 0.491652i \(-0.836393\pi\)
0.907530 0.419988i \(-0.137966\pi\)
\(278\) −2.28012 9.25081i −0.136752 0.554827i
\(279\) −3.97225 + 9.32322i −0.237813 + 0.558167i
\(280\) 4.97919 1.01651i 0.297564 0.0607481i
\(281\) −12.7807 8.82187i −0.762432 0.526269i 0.122230 0.992502i \(-0.460995\pi\)
−0.884662 + 0.466233i \(0.845611\pi\)
\(282\) 0.764490 0.0617160i 0.0455247 0.00367514i
\(283\) 3.19979 + 11.0469i 0.190208 + 0.656673i 0.997761 + 0.0668785i \(0.0213040\pi\)
−0.807554 + 0.589794i \(0.799209\pi\)
\(284\) 10.8809 + 14.4799i 0.645663 + 0.859222i
\(285\) 0.750412 + 0.393847i 0.0444506 + 0.0233295i
\(286\) 0.237667 0.151747i 0.0140535 0.00897297i
\(287\) −3.43608 + 1.80339i −0.202825 + 0.106451i
\(288\) 9.64431 + 4.57628i 0.568296 + 0.269660i
\(289\) 5.09816 10.7441i 0.299892 0.632008i
\(290\) 1.27849 0.426824i 0.0750758 0.0250640i
\(291\) −4.48062 + 5.05757i −0.262658 + 0.296480i
\(292\) 2.22847 13.7123i 0.130411 0.802452i
\(293\) 12.6152 + 0.508374i 0.736986 + 0.0296995i 0.405921 0.913908i \(-0.366951\pi\)
0.331065 + 0.943608i \(0.392592\pi\)
\(294\) −0.378725 + 0.143632i −0.0220877 + 0.00837677i
\(295\) −2.10818 + 7.27827i −0.122743 + 0.423757i
\(296\) −3.75955 + 18.4155i −0.218519 + 1.07038i
\(297\) −0.0616288 + 0.763410i −0.00357607 + 0.0442975i
\(298\) −0.665592 + 1.75502i −0.0385567 + 0.101666i
\(299\) −0.964322 21.5884i −0.0557682 1.24849i
\(300\) −0.567605 1.49665i −0.0327707 0.0864093i
\(301\) −32.3659 + 9.37488i −1.86554 + 0.540359i
\(302\) −0.167492 4.15627i −0.00963808 0.239166i
\(303\) −6.95570 8.51919i −0.399595 0.489415i
\(304\) 2.49458 + 0.302897i 0.143074 + 0.0173723i
\(305\) 0.583003 + 7.22178i 0.0333826 + 0.413518i
\(306\) 5.39170 + 1.56172i 0.308223 + 0.0892779i
\(307\) 2.30411 9.34814i 0.131503 0.533527i −0.867825 0.496869i \(-0.834483\pi\)
0.999328 0.0366574i \(-0.0116710\pi\)
\(308\) 0.652257 + 0.490139i 0.0371658 + 0.0279283i
\(309\) 10.3299 12.6519i 0.587649 0.719739i
\(310\) −1.60120 + 1.53798i −0.0909422 + 0.0873512i
\(311\) 12.8202 + 3.15990i 0.726969 + 0.179182i 0.585398 0.810746i \(-0.300938\pi\)
0.141571 + 0.989928i \(0.454785\pi\)
\(312\) 5.07727 2.96097i 0.287444 0.167632i
\(313\) −24.7010 + 6.08825i −1.39618 + 0.344128i −0.864423 0.502766i \(-0.832316\pi\)
−0.531761 + 0.846894i \(0.678470\pi\)
\(314\) 0.622472 0.984361i 0.0351281 0.0555507i
\(315\) −3.07548 5.32689i −0.173284 0.300136i
\(316\) 8.07759 13.9908i 0.454400 0.787044i
\(317\) −7.40872 14.1161i −0.416115 0.792842i 0.583702 0.811968i \(-0.301604\pi\)
−0.999817 + 0.0191265i \(0.993911\pi\)
\(318\) 1.41065 + 4.22540i 0.0791051 + 0.236949i
\(319\) 0.399017 + 0.230372i 0.0223407 + 0.0128984i
\(320\) −2.00302 2.26094i −0.111972 0.126390i
\(321\) 9.00096 5.69186i 0.502385 0.317689i
\(322\) −7.43025 + 3.16573i −0.414072 + 0.176419i
\(323\) 5.03664 0.202970i 0.280246 0.0112935i
\(324\) 0.494608 4.07347i 0.0274782 0.226304i
\(325\) 3.50451 + 0.847586i 0.194395 + 0.0470156i
\(326\) 0.334441 + 2.75437i 0.0185230 + 0.152550i
\(327\) −0.377000 2.31977i −0.0208481 0.128284i
\(328\) −2.09999 1.32795i −0.115953 0.0733240i
\(329\) −4.93407 0.801864i −0.272024 0.0442082i
\(330\) −0.0328452 + 0.0625812i −0.00180807 + 0.00344498i
\(331\) 3.16502 + 5.00508i 0.173965 + 0.275104i 0.920905 0.389788i \(-0.127452\pi\)
−0.746939 + 0.664892i \(0.768477\pi\)
\(332\) 18.1530 + 17.4362i 0.996277 + 0.956937i
\(333\) 22.5834 2.74212i 1.23756 0.150267i
\(334\) −0.253833 1.24336i −0.0138891 0.0680334i
\(335\) −11.0825 0.894675i −0.605504 0.0488813i
\(336\) 5.28463 + 4.31477i 0.288300 + 0.235390i
\(337\) −27.8831 −1.51889 −0.759444 0.650572i \(-0.774529\pi\)
−0.759444 + 0.650572i \(0.774529\pi\)
\(338\) −0.446260 + 6.20208i −0.0242733 + 0.337349i
\(339\) −18.0772 −0.981816
\(340\) −7.37467 6.02123i −0.399948 0.326547i
\(341\) −0.756475 0.0610690i −0.0409654 0.00330707i
\(342\) 0.195892 + 0.959542i 0.0105926 + 0.0518861i
\(343\) −16.9565 + 2.05889i −0.915564 + 0.111170i
\(344\) −15.5599 14.9454i −0.838931 0.805804i
\(345\) 2.89489 + 4.57790i 0.155856 + 0.246466i
\(346\) −2.75179 + 5.24309i −0.147937 + 0.281870i
\(347\) 21.0592 + 3.42245i 1.13051 + 0.183726i 0.696760 0.717305i \(-0.254624\pi\)
0.433755 + 0.901031i \(0.357188\pi\)
\(348\) 3.81229 + 2.41075i 0.204360 + 0.129230i
\(349\) −4.98647 30.6830i −0.266919 1.64242i −0.681074 0.732214i \(-0.738487\pi\)
0.414155 0.910206i \(-0.364077\pi\)
\(350\) −0.162429 1.33772i −0.00868220 0.0715043i
\(351\) −12.6905 11.1444i −0.677368 0.594842i
\(352\) −0.0963614 + 0.793608i −0.00513608 + 0.0422994i
\(353\) 26.9670 1.08673i 1.43531 0.0578409i 0.689636 0.724156i \(-0.257770\pi\)
0.745670 + 0.666315i \(0.232129\pi\)
\(354\) 3.01333 1.28386i 0.160157 0.0682364i
\(355\) 8.64292 5.46545i 0.458719 0.290076i
\(356\) −14.0964 15.9115i −0.747107 0.843309i
\(357\) 11.8517 + 6.84261i 0.627261 + 0.362149i
\(358\) −1.56082 4.67522i −0.0824918 0.247093i
\(359\) −9.88539 18.8350i −0.521731 0.994075i −0.993659 0.112438i \(-0.964134\pi\)
0.471928 0.881637i \(-0.343558\pi\)
\(360\) 1.96916 3.41068i 0.103784 0.179758i
\(361\) −9.06028 15.6929i −0.476857 0.825941i
\(362\) 4.28445 6.77531i 0.225186 0.356102i
\(363\) 9.62853 2.37322i 0.505367 0.124562i
\(364\) −17.2593 + 5.08094i −0.904635 + 0.266313i
\(365\) −7.61541 1.87703i −0.398609 0.0982483i
\(366\) 2.25870 2.16951i 0.118064 0.113402i
\(367\) 15.4871 18.9683i 0.808421 0.990136i −0.191541 0.981485i \(-0.561349\pi\)
0.999963 0.00865182i \(-0.00275399\pi\)
\(368\) 12.8393 + 9.64813i 0.669296 + 0.502943i
\(369\) −0.719700 + 2.91994i −0.0374661 + 0.152006i
\(370\) 4.78712 + 1.38661i 0.248870 + 0.0720862i
\(371\) −2.33621 28.9392i −0.121290 1.50245i
\(372\) −7.37561 0.895561i −0.382407 0.0464327i
\(373\) −13.7993 16.9011i −0.714501 0.875105i 0.281937 0.959433i \(-0.409023\pi\)
−0.996438 + 0.0843283i \(0.973126\pi\)
\(374\) 0.0169268 + 0.420035i 0.000875265 + 0.0217195i
\(375\) −0.868034 + 0.251429i −0.0448251 + 0.0129837i
\(376\) −1.13495 2.99262i −0.0585307 0.154333i
\(377\) −9.32970 + 4.02319i −0.480504 + 0.207205i
\(378\) −2.23834 + 5.90202i −0.115128 + 0.303567i
\(379\) −2.26042 + 28.0003i −0.116110 + 1.43828i 0.632136 + 0.774857i \(0.282178\pi\)
−0.748246 + 0.663421i \(0.769104\pi\)
\(380\) 0.332245 1.62744i 0.0170438 0.0834861i
\(381\) 0.234063 0.808078i 0.0119914 0.0413991i
\(382\) 4.85979 1.84308i 0.248649 0.0943000i
\(383\) 0.0528512 + 0.00212983i 0.00270057 + 0.000108829i 0.0416162 0.999134i \(-0.486749\pi\)
−0.0389156 + 0.999243i \(0.512390\pi\)
\(384\) −1.62703 + 10.0115i −0.0830291 + 0.510898i
\(385\) 0.305460 0.344793i 0.0155677 0.0175723i
\(386\) 3.80742 1.27110i 0.193793 0.0646975i
\(387\) −11.1947 + 23.5923i −0.569058 + 1.19926i
\(388\) 11.9643 + 5.67714i 0.607396 + 0.288213i
\(389\) 27.3653 14.3624i 1.38748 0.728205i 0.404953 0.914337i \(-0.367288\pi\)
0.982525 + 0.186133i \(0.0595955\pi\)
\(390\) −0.674270 1.40514i −0.0341430 0.0711518i
\(391\) 28.5259 + 14.9715i 1.44262 + 0.757143i
\(392\) 1.01542 + 1.35127i 0.0512862 + 0.0682496i
\(393\) 0.791385 + 2.73218i 0.0399201 + 0.137820i
\(394\) −2.92425 + 0.236070i −0.147322 + 0.0118930i
\(395\) −7.50641 5.18130i −0.377689 0.260700i
\(396\) 0.619511 0.126474i 0.0311316 0.00635556i
\(397\) −12.1722 + 28.5693i −0.610907 + 1.43385i 0.271069 + 0.962560i \(0.412623\pi\)
−0.881977 + 0.471293i \(0.843788\pi\)
\(398\) −2.57906 10.4636i −0.129276 0.524495i
\(399\) −0.0961391 + 2.38567i −0.00481297 + 0.119433i
\(400\) −2.14221 + 1.60976i −0.107110 + 0.0804882i
\(401\) 5.99857 + 14.0792i 0.299554 + 0.703080i 0.999943 0.0106817i \(-0.00340017\pi\)
−0.700389 + 0.713762i \(0.746990\pi\)
\(402\) 2.73020 + 3.95537i 0.136170 + 0.197276i
\(403\) 11.0431 12.5752i 0.550097 0.626415i
\(404\) −12.2449 + 17.7398i −0.609207 + 0.882589i
\(405\) −2.26989 0.463401i −0.112792 0.0230266i
\(406\) 2.63048 + 2.73862i 0.130548 + 0.135915i
\(407\) 0.730348 + 1.53918i 0.0362020 + 0.0762942i
\(408\) 8.76231i 0.433799i
\(409\) −14.8713 + 7.05653i −0.735339 + 0.348923i −0.759257 0.650791i \(-0.774437\pi\)
0.0239175 + 0.999714i \(0.492386\pi\)
\(410\) −0.395795 + 0.526707i −0.0195469 + 0.0260122i
\(411\) 13.2795 + 5.03624i 0.655028 + 0.248419i
\(412\) −29.4505 12.5477i −1.45092 0.618179i
\(413\) −21.0713 + 3.42442i −1.03685 + 0.168505i
\(414\) −1.98205 + 5.93695i −0.0974123 + 0.291785i
\(415\) 10.6370 9.42356i 0.522150 0.462584i
\(416\) −12.7671 12.1564i −0.625961 0.596016i
\(417\) −13.4741 11.9370i −0.659830 0.584559i
\(418\) −0.0635153 + 0.0366706i −0.00310664 + 0.00179362i
\(419\) −25.5959 8.54518i −1.25044 0.417459i −0.387082 0.922045i \(-0.626517\pi\)
−0.863362 + 0.504586i \(0.831645\pi\)
\(420\) 3.12386 3.25228i 0.152429 0.158695i
\(421\) −7.03139 + 4.85342i −0.342689 + 0.236541i −0.726961 0.686679i \(-0.759068\pi\)
0.384272 + 0.923220i \(0.374453\pi\)
\(422\) 2.01596 1.64598i 0.0981354 0.0801251i
\(423\) −3.00075 + 2.45004i −0.145902 + 0.119125i
\(424\) 15.2987 10.5599i 0.742972 0.512836i
\(425\) −3.72350 + 3.87658i −0.180616 + 0.188042i
\(426\) −4.19282 1.39977i −0.203143 0.0678190i
\(427\) −17.6773 + 10.2060i −0.855463 + 0.493902i
\(428\) −15.6233 13.8410i −0.755180 0.669031i
\(429\) 0.206685 0.491037i 0.00997885 0.0237075i
\(430\) −4.28218 + 3.79368i −0.206505 + 0.182948i
\(431\) 3.76680 11.2829i 0.181440 0.543480i −0.818058 0.575135i \(-0.804949\pi\)
0.999499 + 0.0316547i \(0.0100777\pi\)
\(432\) 12.3894 2.01348i 0.596086 0.0968734i
\(433\) 0.591568 + 0.252043i 0.0284289 + 0.0121124i 0.406134 0.913813i \(-0.366877\pi\)
−0.377705 + 0.925926i \(0.623287\pi\)
\(434\) −5.84841 2.21801i −0.280733 0.106468i
\(435\) 1.52985 2.03586i 0.0733507 0.0976120i
\(436\) −4.16150 + 1.97466i −0.199300 + 0.0945690i
\(437\) 5.62060i 0.268870i
\(438\) 1.45342 + 3.06303i 0.0694473 + 0.146357i
\(439\) −0.357722 0.372428i −0.0170731 0.0177750i 0.712611 0.701559i \(-0.247512\pi\)
−0.729684 + 0.683784i \(0.760333\pi\)
\(440\) 0.288975 + 0.0589947i 0.0137763 + 0.00281246i
\(441\) 1.16217 1.68370i 0.0553416 0.0801761i
\(442\) −7.65193 5.23261i −0.363965 0.248890i
\(443\) −19.7180 28.5664i −0.936828 1.35723i −0.934015 0.357234i \(-0.883720\pi\)
−0.00281345 0.999996i \(-0.500896\pi\)
\(444\) 6.53739 + 15.3438i 0.310251 + 0.728185i
\(445\) −9.59467 + 7.20993i −0.454831 + 0.341783i
\(446\) −0.399357 + 9.90993i −0.0189101 + 0.469249i
\(447\) 0.848693 + 3.44328i 0.0401418 + 0.162862i
\(448\) 3.33556 7.82885i 0.157591 0.369879i
\(449\) −15.5276 + 3.16999i −0.732795 + 0.149601i −0.551911 0.833903i \(-0.686101\pi\)
−0.180884 + 0.983504i \(0.557896\pi\)
\(450\) −0.859449 0.593235i −0.0405148 0.0279654i
\(451\) −0.224485 + 0.0181223i −0.0105706 + 0.000853345i
\(452\) 9.85722 + 34.0311i 0.463645 + 1.60069i
\(453\) −4.72128 6.28289i −0.221825 0.295196i
\(454\) −4.31421 2.26427i −0.202476 0.106268i
\(455\) 2.07522 + 9.94359i 0.0972879 + 0.466163i
\(456\) −1.35362 + 0.710433i −0.0633890 + 0.0332691i
\(457\) −21.8207 10.3541i −1.02073 0.484342i −0.156627 0.987658i \(-0.550062\pi\)
−0.864103 + 0.503316i \(0.832113\pi\)
\(458\) −1.58667 + 3.34383i −0.0741401 + 0.156247i
\(459\) 23.8827 7.97320i 1.11475 0.372157i
\(460\) 7.03956 7.94602i 0.328221 0.370485i
\(461\) 1.10675 6.81008i 0.0515463 0.317177i −0.948454 0.316916i \(-0.897353\pi\)
1.00000 0.000261175i \(-8.31347e-5\pi\)
\(462\) −0.198955 0.00801760i −0.00925620 0.000373012i
\(463\) 9.79464 3.71462i 0.455195 0.172633i −0.116341 0.993209i \(-0.537117\pi\)
0.571537 + 0.820576i \(0.306347\pi\)
\(464\) 2.10082 7.25286i 0.0975279 0.336706i
\(465\) −0.839056 + 4.10997i −0.0389103 + 0.190595i
\(466\) −1.08326 + 13.4186i −0.0501810 + 0.621604i
\(467\) −1.75691 + 4.63259i −0.0813000 + 0.214371i −0.969502 0.245082i \(-0.921185\pi\)
0.888202 + 0.459452i \(0.151954\pi\)
\(468\) −5.92226 + 12.6228i −0.273756 + 0.583487i
\(469\) −11.1077 29.2886i −0.512906 1.35242i
\(470\) −0.815187 + 0.236122i −0.0376018 + 0.0108915i
\(471\) −0.0886040 2.19869i −0.00408266 0.101310i
\(472\) −8.64454 10.5876i −0.397897 0.487335i
\(473\) −1.94136 0.235723i −0.0892636 0.0108386i
\(474\) 0.317251 + 3.92985i 0.0145718 + 0.180504i
\(475\) −0.900757 0.260907i −0.0413295 0.0119712i
\(476\) 6.41893 26.0426i 0.294211 1.19366i
\(477\) −17.9874 13.5167i −0.823587 0.618886i
\(478\) −8.61607 + 10.5528i −0.394090 + 0.482673i
\(479\) −16.7857 + 16.1229i −0.766958 + 0.736674i −0.970161 0.242463i \(-0.922045\pi\)
0.203202 + 0.979137i \(0.434865\pi\)
\(480\) 4.29020 + 1.05744i 0.195820 + 0.0482653i
\(481\) −36.8418 7.35405i −1.67984 0.335316i
\(482\) −0.721355 + 0.177798i −0.0328568 + 0.00809848i
\(483\) −8.15570 + 12.8972i −0.371097 + 0.586843i
\(484\) −9.71800 16.8321i −0.441727 0.765094i
\(485\) 3.73838 6.47506i 0.169751 0.294017i
\(486\) 3.58908 + 6.83841i 0.162804 + 0.310197i
\(487\) −2.70562 8.10431i −0.122603 0.367241i 0.869292 0.494299i \(-0.164575\pi\)
−0.991895 + 0.127057i \(0.959447\pi\)
\(488\) −11.3183 6.53464i −0.512356 0.295809i
\(489\) 3.47624 + 3.92387i 0.157201 + 0.177443i
\(490\) 0.378816 0.239549i 0.0171132 0.0108217i
\(491\) 14.1370 6.02320i 0.637993 0.271823i −0.0486526 0.998816i \(-0.515493\pi\)
0.686646 + 0.726992i \(0.259082\pi\)
\(492\) −2.20301 + 0.0887782i −0.0993193 + 0.00400243i
\(493\) 1.82575 15.0364i 0.0822275 0.677204i
\(494\) 0.187938 1.60634i 0.00845573 0.0722725i
\(495\) −0.0430292 0.354378i −0.00193402 0.0159281i
\(496\) 1.99518 + 12.2769i 0.0895864 + 0.551247i
\(497\) 24.3495 + 15.3977i 1.09222 + 0.690680i
\(498\) −6.06326 0.985376i −0.271701 0.0441557i
\(499\) 4.66288 8.88438i 0.208739 0.397719i −0.758467 0.651711i \(-0.774051\pi\)
0.967206 + 0.253992i \(0.0817437\pi\)
\(500\) 0.946653 + 1.49701i 0.0423356 + 0.0669484i
\(501\) −1.72916 1.66088i −0.0772532 0.0742027i
\(502\) −0.646614 + 0.0785132i −0.0288598 + 0.00350421i
\(503\) 2.10101 + 10.2914i 0.0936792 + 0.458871i 0.999388 + 0.0349714i \(0.0111340\pi\)
−0.905709 + 0.423900i \(0.860661\pi\)
\(504\) 11.0593 + 0.892801i 0.492622 + 0.0397685i
\(505\) 9.42687 + 7.69680i 0.419490 + 0.342503i
\(506\) −0.468734 −0.0208378
\(507\) 5.96268 + 10.1227i 0.264812 + 0.449564i
\(508\) −1.64888 −0.0731570
\(509\) −11.2230 9.16326i −0.497449 0.406154i 0.350230 0.936664i \(-0.386103\pi\)
−0.847679 + 0.530509i \(0.822001\pi\)
\(510\) 2.31594 + 0.186962i 0.102551 + 0.00827881i
\(511\) −4.41993 21.6502i −0.195526 0.957751i
\(512\) 22.6029 2.74448i 0.998915 0.121290i
\(513\) 3.16808 + 3.04298i 0.139874 + 0.134351i
\(514\) 6.37590 + 10.0827i 0.281229 + 0.444728i
\(515\) −8.39919 + 16.0033i −0.370113 + 0.705191i
\(516\) −18.8970 3.07106i −0.831895 0.135196i
\(517\) −0.245201 0.155056i −0.0107839 0.00681933i
\(518\) 2.25233 + 13.8592i 0.0989619 + 0.608937i
\(519\) 1.34851 + 11.1060i 0.0591932 + 0.487500i
\(520\) −4.84931 + 4.33402i −0.212656 + 0.190059i
\(521\) 1.11465 9.17994i 0.0488335 0.402180i −0.947712 0.319128i \(-0.896610\pi\)
0.996545 0.0830525i \(-0.0264669\pi\)
\(522\) 2.94040 0.118494i 0.128698 0.00518634i
\(523\) −4.40896 + 1.87848i −0.192790 + 0.0821403i −0.486204 0.873845i \(-0.661619\pi\)
0.293414 + 0.955986i \(0.405209\pi\)
\(524\) 4.71192 2.97964i 0.205841 0.130166i
\(525\) −1.68832 1.90572i −0.0736842 0.0831723i
\(526\) 5.30594 + 3.06339i 0.231350 + 0.133570i
\(527\) 7.90077 + 23.6657i 0.344163 + 1.03089i
\(528\) 0.184005 + 0.350593i 0.00800780 + 0.0152576i
\(529\) −6.46105 + 11.1909i −0.280915 + 0.486559i
\(530\) −2.46464 4.26888i −0.107057 0.185428i
\(531\) −8.84211 + 13.9827i −0.383715 + 0.606797i
\(532\) 4.54355 1.11988i 0.196988 0.0485532i
\(533\) 2.63602 4.20906i 0.114179 0.182315i
\(534\) 5.03712 + 1.24154i 0.217977 + 0.0537266i
\(535\) −8.49886 + 8.16327i −0.367438 + 0.352929i
\(536\) 12.6844 15.5355i 0.547882 0.671033i
\(537\) −7.44477 5.59438i −0.321266 0.241415i
\(538\) 3.02248 12.2627i 0.130308 0.528682i
\(539\) 0.147162 + 0.0426260i 0.00633872 + 0.00183603i
\(540\) −0.667611 8.26985i −0.0287294 0.355878i
\(541\) 7.39696 + 0.898153i 0.318020 + 0.0386146i 0.277990 0.960584i \(-0.410332\pi\)
0.0400297 + 0.999198i \(0.487255\pi\)
\(542\) −1.57473 1.92870i −0.0676405 0.0828446i
\(543\) −0.609858 15.1335i −0.0261715 0.649439i
\(544\) 25.2435 7.31188i 1.08231 0.313494i
\(545\) 0.922189 + 2.43161i 0.0395022 + 0.104159i
\(546\) 2.76210 3.41324i 0.118207 0.146073i
\(547\) −14.1764 + 37.3801i −0.606139 + 1.59826i 0.182366 + 0.983231i \(0.441624\pi\)
−0.788506 + 0.615027i \(0.789145\pi\)
\(548\) 2.23984 27.7454i 0.0956813 1.18523i
\(549\) −3.16413 + 15.4989i −0.135042 + 0.661479i
\(550\) 0.0217586 0.0751193i 0.000927789 0.00320310i
\(551\) 2.47087 0.937079i 0.105263 0.0399209i
\(552\) −9.76238 0.393410i −0.415514 0.0167447i
\(553\) 4.12197 25.3635i 0.175284 1.07857i
\(554\) 4.81642 5.43661i 0.204630 0.230980i
\(555\) 8.93179 2.98187i 0.379133 0.126573i
\(556\) −15.1247 + 31.8747i −0.641432 + 1.35179i
\(557\) 6.93218 + 3.28936i 0.293726 + 0.139375i 0.569854 0.821746i \(-0.307000\pi\)
−0.276128 + 0.961121i \(0.589051\pi\)
\(558\) −4.29210 + 2.25267i −0.181699 + 0.0953631i
\(559\) 29.7374 31.2315i 1.25776 1.32095i
\(560\) −6.68452 3.50831i −0.282473 0.148253i
\(561\) 0.477135 + 0.634951i 0.0201447 + 0.0268077i
\(562\) −2.06663 7.13483i −0.0871755 0.300965i
\(563\) 0.386199 0.0311772i 0.0162763 0.00131396i −0.0723257 0.997381i \(-0.523042\pi\)
0.0886021 + 0.996067i \(0.471760\pi\)
\(564\) −2.33738 1.61338i −0.0984215 0.0679355i
\(565\) 19.5989 4.00115i 0.824533 0.168330i
\(566\) −2.15626 + 5.06093i −0.0906343 + 0.212727i
\(567\) −1.56197 6.33715i −0.0655964 0.266135i
\(568\) −0.742746 + 18.4310i −0.0311649 + 0.773350i
\(569\) −12.0309 + 9.04060i −0.504360 + 0.379002i −0.822251 0.569125i \(-0.807282\pi\)
0.317891 + 0.948127i \(0.397025\pi\)
\(570\) 0.158890 + 0.372929i 0.00665518 + 0.0156203i
\(571\) 12.5280 + 18.1500i 0.524282 + 0.759554i 0.992259 0.124187i \(-0.0396322\pi\)
−0.467977 + 0.883741i \(0.655017\pi\)
\(572\) −1.03710 0.121339i −0.0433634 0.00507343i
\(573\) 5.57843 8.08176i 0.233042 0.337620i
\(574\) −1.81863 0.371276i −0.0759082 0.0154968i
\(575\) −4.15185 4.32253i −0.173144 0.180262i
\(576\) −2.82716 5.95811i −0.117798 0.248255i
\(577\) 4.84556i 0.201723i −0.994900 0.100862i \(-0.967840\pi\)
0.994900 0.100862i \(-0.0321599\pi\)
\(578\) 5.13910 2.43853i 0.213758 0.101430i
\(579\) 4.55597 6.06289i 0.189340 0.251965i
\(580\) −4.66681 1.76989i −0.193779 0.0734905i
\(581\) 36.8323 + 15.6928i 1.52806 + 0.651045i
\(582\) −3.19006 + 0.518434i −0.132232 + 0.0214898i
\(583\) 0.533584 1.59828i 0.0220988 0.0661940i
\(584\) 10.5900 9.38189i 0.438216 0.388225i
\(585\) 6.83446 + 3.90623i 0.282570 + 0.161503i
\(586\) 4.52021 + 4.00456i 0.186728 + 0.165427i
\(587\) −11.8839 + 6.86118i −0.490501 + 0.283191i −0.724782 0.688978i \(-0.758060\pi\)
0.234281 + 0.972169i \(0.424726\pi\)
\(588\) 1.42271 + 0.474969i 0.0586714 + 0.0195874i
\(589\) −3.01534 + 3.13930i −0.124245 + 0.129353i
\(590\) −2.98283 + 2.05890i −0.122801 + 0.0847636i
\(591\) −4.29360 + 3.50561i −0.176615 + 0.144202i
\(592\) 21.6276 17.6584i 0.888887 0.725754i
\(593\) −21.3212 + 14.7169i −0.875555 + 0.604352i −0.918805 0.394712i \(-0.870844\pi\)
0.0432498 + 0.999064i \(0.486229\pi\)
\(594\) −0.253772 + 0.264205i −0.0104124 + 0.0108405i
\(595\) −14.3640 4.79540i −0.588866 0.196592i
\(596\) 6.01935 3.47528i 0.246562 0.142353i
\(597\) −15.2407 13.5020i −0.623759 0.552602i
\(598\) 6.17338 8.29034i 0.252448 0.339017i
\(599\) −4.00919 + 3.55184i −0.163811 + 0.145124i −0.741046 0.671454i \(-0.765670\pi\)
0.577235 + 0.816578i \(0.304132\pi\)
\(600\) 0.516216 1.54626i 0.0210744 0.0631256i
\(601\) 41.0843 6.67686i 1.67587 0.272355i 0.753153 0.657845i \(-0.228532\pi\)
0.922712 + 0.385490i \(0.125968\pi\)
\(602\) −14.8277 6.31751i −0.604333 0.257482i
\(603\) −22.6977 8.60812i −0.924323 0.350550i
\(604\) −9.25337 + 12.3140i −0.376514 + 0.501050i
\(605\) −9.91380 + 4.70416i −0.403053 + 0.191251i
\(606\) 5.26057i 0.213696i
\(607\) 2.06385 + 4.34946i 0.0837689 + 0.176539i 0.941012 0.338372i \(-0.109876\pi\)
−0.857244 + 0.514911i \(0.827825\pi\)
\(608\) 3.17626 + 3.30683i 0.128814 + 0.134110i
\(609\) 7.02948 + 1.43508i 0.284849 + 0.0581523i
\(610\) −1.96865 + 2.85208i −0.0797082 + 0.115477i
\(611\) 5.97178 2.29464i 0.241593 0.0928314i
\(612\) −11.8079 17.1067i −0.477307 0.691499i
\(613\) 3.64805 + 8.56230i 0.147344 + 0.345828i 0.977255 0.212067i \(-0.0680195\pi\)
−0.829912 + 0.557895i \(0.811609\pi\)
\(614\) 3.68158 2.76653i 0.148577 0.111648i
\(615\) −0.0501228 + 1.24379i −0.00202115 + 0.0501543i
\(616\) 0.198851 + 0.806770i 0.00801193 + 0.0325057i
\(617\) −2.82137 + 6.62200i −0.113584 + 0.266592i −0.967064 0.254535i \(-0.918078\pi\)
0.853480 + 0.521126i \(0.174488\pi\)
\(618\) 7.65460 1.56270i 0.307913 0.0628609i
\(619\) −9.40251 6.49009i −0.377919 0.260859i 0.363929 0.931427i \(-0.381435\pi\)
−0.741848 + 0.670568i \(0.766050\pi\)
\(620\) 8.19473 0.661547i 0.329108 0.0265684i
\(621\) 7.81093 + 26.9665i 0.313442 + 1.08213i
\(622\) 3.79408 + 5.04900i 0.152129 + 0.202446i
\(623\) −29.9391 15.7133i −1.19949 0.629539i
\(624\) −8.62421 1.36299i −0.345245 0.0545631i
\(625\) 0.885456 0.464723i 0.0354182 0.0185889i
\(626\) −10.9936 5.21654i −0.439394 0.208495i
\(627\) −0.0594032 + 0.125190i −0.00237233 + 0.00499959i
\(628\) −4.09081 + 1.36571i −0.163241 + 0.0544979i
\(629\) 37.1397 41.9221i 1.48086 1.67154i
\(630\) 0.471947 2.90401i 0.0188028 0.115698i
\(631\) 46.3788 + 1.86900i 1.84631 + 0.0744037i 0.938562 0.345112i \(-0.112159\pi\)
0.907748 + 0.419516i \(0.137800\pi\)
\(632\) 15.3835 5.83421i 0.611925 0.232072i
\(633\) 1.36805 4.72305i 0.0543751 0.187725i
\(634\) 1.52528 7.47132i 0.0605767 0.296724i
\(635\) −0.0749087 + 0.927911i −0.00297266 + 0.0368230i
\(636\) 5.84944 15.4237i 0.231945 0.611590i
\(637\) −2.69208 + 2.04140i −0.106664 + 0.0808833i
\(638\) 0.0781485 + 0.206061i 0.00309393 + 0.00815802i
\(639\) 21.4450 6.21161i 0.848350 0.245727i
\(640\) −0.451926 11.2144i −0.0178640 0.443290i
\(641\) −9.21742 11.2893i −0.364066 0.445900i 0.559793 0.828632i \(-0.310881\pi\)
−0.923859 + 0.382732i \(0.874983\pi\)
\(642\) 5.05675 + 0.614001i 0.199574 + 0.0242327i
\(643\) 0.265656 + 3.29074i 0.0104764 + 0.129774i 0.999881 0.0154089i \(-0.00490500\pi\)
−0.989405 + 0.145183i \(0.953623\pi\)
\(644\) 28.7268 + 8.32081i 1.13199 + 0.327886i
\(645\) −2.58675 + 10.4949i −0.101853 + 0.413234i
\(646\) 1.92751 + 1.44843i 0.0758367 + 0.0569876i
\(647\) −9.61246 + 11.7731i −0.377905 + 0.462849i −0.928179 0.372135i \(-0.878626\pi\)
0.550274 + 0.834984i \(0.314523\pi\)
\(648\) 3.01387 2.89486i 0.118396 0.113721i
\(649\) −1.20295 0.296500i −0.0472198 0.0116386i
\(650\) 1.04204 + 1.37418i 0.0408722 + 0.0538998i
\(651\) −11.4743 + 2.82817i −0.449715 + 0.110845i
\(652\) 5.49131 8.68381i 0.215056 0.340084i
\(653\) 19.7128 + 34.1436i 0.771422 + 1.33614i 0.936783 + 0.349910i \(0.113788\pi\)
−0.165361 + 0.986233i \(0.552879\pi\)
\(654\) 0.562071 0.973535i 0.0219787 0.0380682i
\(655\) −1.46274 2.78702i −0.0571539 0.108898i
\(656\) 1.16881 + 3.50102i 0.0456345 + 0.136692i
\(657\) −14.8301 8.56217i −0.578578 0.334042i
\(658\) −1.58553 1.78969i −0.0618104 0.0697696i
\(659\) −35.4635 + 22.4258i −1.38146 + 0.873584i −0.998735 0.0502767i \(-0.983990\pi\)
−0.382728 + 0.923861i \(0.625015\pi\)
\(660\) 0.240775 0.102585i 0.00937214 0.00399310i
\(661\) −42.7847 + 1.72416i −1.66413 + 0.0670622i −0.854360 0.519682i \(-0.826050\pi\)
−0.809772 + 0.586744i \(0.800409\pi\)
\(662\) −0.341422 + 2.81186i −0.0132697 + 0.109286i
\(663\) −17.5142 + 0.0763987i −0.680194 + 0.00296708i
\(664\) 3.08984 + 25.4471i 0.119909 + 0.987541i
\(665\) −0.423805 2.60778i −0.0164345 0.101125i
\(666\) 9.19680 + 5.81570i 0.356369 + 0.225354i
\(667\) 16.6705 + 2.70923i 0.645486 + 0.104902i
\(668\) −2.18380 + 4.16088i −0.0844937 + 0.160989i
\(669\) 10.0152 + 15.8377i 0.387209 + 0.612322i
\(670\) −3.83550 3.68405i −0.148178 0.142327i
\(671\) −1.17600 + 0.142792i −0.0453990 + 0.00551244i
\(672\) 2.49000 + 12.1968i 0.0960538 + 0.470503i
\(673\) −13.8348 1.11686i −0.533293 0.0430519i −0.189113 0.981955i \(-0.560561\pi\)
−0.344180 + 0.938904i \(0.611843\pi\)
\(674\) −10.3309 8.43488i −0.397930 0.324899i
\(675\) −4.68422 −0.180296
\(676\) 15.8050 16.7448i 0.607886 0.644030i
\(677\) −9.94663 −0.382280 −0.191140 0.981563i \(-0.561218\pi\)
−0.191140 + 0.981563i \(0.561218\pi\)
\(678\) −6.69770 5.46850i −0.257223 0.210016i
\(679\) 20.9958 + 1.69495i 0.805743 + 0.0650463i
\(680\) −1.93943 9.49994i −0.0743736 0.364306i
\(681\) −9.13844 + 1.10961i −0.350186 + 0.0425203i
\(682\) −0.261805 0.251467i −0.0100250 0.00962916i
\(683\) 14.6019 + 23.0911i 0.558726 + 0.883555i 0.999904 0.0138647i \(-0.00441340\pi\)
−0.441177 + 0.897420i \(0.645439\pi\)
\(684\) 1.68531 3.21110i 0.0644396 0.122779i
\(685\) −15.5121 2.52096i −0.592686 0.0963209i
\(686\) −6.90531 4.36666i −0.263646 0.166720i
\(687\) 1.12174 + 6.90232i 0.0427969 + 0.263340i
\(688\) 3.86318 + 31.8162i 0.147282 + 1.21298i
\(689\) 21.2407 + 30.4872i 0.809207 + 1.16147i
\(690\) −0.312281 + 2.57187i −0.0118884 + 0.0979094i
\(691\) 45.4696 1.83236i 1.72975 0.0697063i 0.844708 0.535227i \(-0.179774\pi\)
0.885037 + 0.465521i \(0.154133\pi\)
\(692\) 20.1723 8.59459i 0.766834 0.326717i
\(693\) 0.850018 0.537519i 0.0322895 0.0204187i
\(694\) 6.76722 + 7.63862i 0.256880 + 0.289958i
\(695\) 17.2505 + 9.95959i 0.654349 + 0.377789i
\(696\) 1.45466 + 4.35723i 0.0551387 + 0.165161i
\(697\) 3.44074 + 6.55579i 0.130328 + 0.248318i
\(698\) 7.43435 12.8767i 0.281394 0.487389i
\(699\) 12.7175 + 22.0274i 0.481021 + 0.833154i
\(700\) −2.66698 + 4.21750i −0.100802 + 0.159406i
\(701\) −8.02623 + 1.97829i −0.303147 + 0.0747189i −0.387955 0.921678i \(-0.626818\pi\)
0.0848083 + 0.996397i \(0.472972\pi\)
\(702\) −1.33063 7.96804i −0.0502215 0.300734i
\(703\) 9.48743 + 2.33844i 0.357825 + 0.0881960i
\(704\) 0.356188 0.342123i 0.0134243 0.0128942i
\(705\) −1.01412 + 1.24207i −0.0381941 + 0.0467792i
\(706\) 10.3202 + 7.75510i 0.388405 + 0.291867i
\(707\) −8.20517 + 33.2897i −0.308587 + 1.25199i
\(708\) −11.6501 3.37449i −0.437838 0.126821i
\(709\) −0.772636 9.57081i −0.0290169 0.359439i −0.994930 0.100572i \(-0.967933\pi\)
0.965913 0.258867i \(-0.0833493\pi\)
\(710\) 4.85560 + 0.589577i 0.182228 + 0.0221264i
\(711\) −12.5944 15.4253i −0.472327 0.578496i
\(712\) −0.871720 21.6315i −0.0326691 0.810675i
\(713\) −26.7215 + 7.73997i −1.00073 + 0.289864i
\(714\) 2.32119 + 6.12049i 0.0868685 + 0.229053i
\(715\) −0.115400 + 0.578120i −0.00431570 + 0.0216205i
\(716\) −6.47215 + 17.0657i −0.241876 + 0.637774i
\(717\) −2.07118 + 25.6562i −0.0773496 + 0.958147i
\(718\) 2.03517 9.96891i 0.0759518 0.372037i
\(719\) 11.9149 41.1350i 0.444351 1.53408i −0.355966 0.934499i \(-0.615848\pi\)
0.800317 0.599578i \(-0.204665\pi\)
\(720\) −5.47025 + 2.07459i −0.203864 + 0.0773154i
\(721\) −50.8768 2.05027i −1.89475 0.0763559i
\(722\) 1.39034 8.55512i 0.0517432 0.318389i
\(723\) −0.930820 + 1.05068i −0.0346176 + 0.0390751i
\(724\) −28.1569 + 9.40015i −1.04644 + 0.349354i
\(725\) −1.20802 + 2.54586i −0.0448649 + 0.0945508i
\(726\) 4.28535 + 2.03342i 0.159044 + 0.0754674i
\(727\) 25.4667 13.3660i 0.944509 0.495717i 0.0791468 0.996863i \(-0.474780\pi\)
0.865363 + 0.501146i \(0.167088\pi\)
\(728\) −16.8880 7.10842i −0.625910 0.263455i
\(729\) 6.76622 + 3.55119i 0.250601 + 0.131526i
\(730\) −2.25374 2.99918i −0.0834146 0.111005i
\(731\) 17.8866 + 61.7517i 0.661560 + 2.28397i
\(732\) −11.5597 + 0.933195i −0.427259 + 0.0344919i
\(733\) −31.6470 21.8444i −1.16891 0.806840i −0.184517 0.982829i \(-0.559072\pi\)
−0.984392 + 0.175989i \(0.943688\pi\)
\(734\) 11.4761 2.34287i 0.423592 0.0864770i
\(735\) 0.331924 0.779055i 0.0122432 0.0287359i
\(736\) 7.01302 + 28.4529i 0.258503 + 1.04879i
\(737\) 0.0732013 1.81647i 0.00269640 0.0669105i
\(738\) −1.14996 + 0.864139i −0.0423306 + 0.0318094i
\(739\) −3.96596 9.30844i −0.145890 0.342417i 0.830963 0.556328i \(-0.187790\pi\)
−0.976853 + 0.213911i \(0.931380\pi\)
\(740\) −10.4839 15.1885i −0.385395 0.558341i
\(741\) −1.43182 2.69943i −0.0525993 0.0991660i
\(742\) 7.88878 11.4289i 0.289606 0.419567i
\(743\) 36.6006 + 7.47207i 1.34275 + 0.274124i 0.817059 0.576554i \(-0.195603\pi\)
0.525687 + 0.850678i \(0.323808\pi\)
\(744\) −5.24157 5.45706i −0.192165 0.200065i
\(745\) −1.68226 3.54530i −0.0616334 0.129890i
\(746\) 10.4364i 0.382102i
\(747\) 28.0310 13.3009i 1.02560 0.486654i
\(748\) 0.935150 1.24446i 0.0341925 0.0455019i
\(749\) −31.0422 11.7727i −1.13426 0.430167i
\(750\) −0.397671 0.169432i −0.0145209 0.00618678i
\(751\) 18.0190 2.92838i 0.657524 0.106858i 0.177510 0.984119i \(-0.443196\pi\)
0.480014 + 0.877261i \(0.340632\pi\)
\(752\) −1.50562 + 4.50987i −0.0549042 + 0.164458i
\(753\) −0.921164 + 0.816080i −0.0335691 + 0.0297396i
\(754\) −4.67376 1.33170i −0.170208 0.0484977i
\(755\) 6.50937 + 5.76680i 0.236900 + 0.209875i
\(756\) 20.2427 11.6871i 0.736220 0.425057i
\(757\) −26.2995 8.78006i −0.955871 0.319117i −0.204404 0.978887i \(-0.565526\pi\)
−0.751468 + 0.659770i \(0.770654\pi\)
\(758\) −9.30784 + 9.69049i −0.338076 + 0.351974i
\(759\) −0.728843 + 0.503084i −0.0264553 + 0.0182608i
\(760\) 1.31032 1.06985i 0.0475304 0.0388074i
\(761\) 18.4783 15.0870i 0.669836 0.546904i −0.235355 0.971910i \(-0.575625\pi\)
0.905191 + 0.425005i \(0.139728\pi\)
\(762\) 0.331173 0.228592i 0.0119971 0.00828101i
\(763\) −5.07534 + 5.28399i −0.183740 + 0.191293i
\(764\) −18.2561 6.09479i −0.660483 0.220502i
\(765\) −10.1633 + 5.86780i −0.367456 + 0.212151i
\(766\) 0.0189374 + 0.0167771i 0.000684236 + 0.000606180i
\(767\) 21.0873 17.3711i 0.761418 0.627234i
\(768\) 0.455083 0.403169i 0.0164214 0.0145481i
\(769\) −5.79965 + 17.3721i −0.209141 + 0.626453i 0.790757 + 0.612131i \(0.209687\pi\)
−0.999897 + 0.0143225i \(0.995441\pi\)
\(770\) 0.217478 0.0353436i 0.00783735 0.00127369i
\(771\) 20.7355 + 8.83459i 0.746772 + 0.318170i
\(772\) −13.8980 5.27081i −0.500199 0.189701i
\(773\) −13.3755 + 17.7996i −0.481084 + 0.640207i −0.973101 0.230379i \(-0.926003\pi\)
0.492017 + 0.870586i \(0.336260\pi\)
\(774\) −11.2846 + 5.35460i −0.405616 + 0.192467i
\(775\) 4.64167i 0.166734i
\(776\) 5.78169 + 12.1847i 0.207551 + 0.437404i
\(777\) 18.3770 + 19.1325i 0.659270 + 0.686373i
\(778\) 14.4838 + 2.95689i 0.519269 + 0.106010i
\(779\) −0.733781 + 1.06307i −0.0262904 + 0.0380883i
\(780\) −1.35671 + 5.60957i −0.0485779 + 0.200855i
\(781\) 0.949806 + 1.37603i 0.0339867 + 0.0492383i
\(782\) 6.03999 + 14.1764i 0.215990 + 0.506946i
\(783\) 10.5525 7.92967i 0.377115 0.283383i
\(784\) 0.101105 2.50889i 0.00361088 0.0896030i
\(785\) 0.582714 + 2.36417i 0.0207980 + 0.0843807i
\(786\) −0.533295 + 1.25169i −0.0190220 + 0.0446463i
\(787\) −4.55246 + 0.929392i −0.162278 + 0.0331293i −0.280478 0.959861i \(-0.590493\pi\)
0.118200 + 0.992990i \(0.462288\pi\)
\(788\) 8.94071 + 6.17133i 0.318500 + 0.219844i
\(789\) 11.5382 0.931457i 0.410770 0.0331608i
\(790\) −1.21378 4.19046i −0.0431844 0.149090i
\(791\) 33.8545 + 45.0522i 1.20373 + 1.60187i
\(792\) 0.570175 + 0.299251i 0.0202603 + 0.0106334i
\(793\) 12.9628 22.6801i 0.460323 0.805395i
\(794\) −13.1524 + 6.90289i −0.466760 + 0.244974i
\(795\) −8.41401 3.99250i −0.298414 0.141599i
\(796\) −17.1077 + 36.0537i −0.606366 + 1.27789i
\(797\) −10.6062 + 3.54088i −0.375692 + 0.125424i −0.498242 0.867038i \(-0.666021\pi\)
0.122550 + 0.992462i \(0.460893\pi\)
\(798\) −0.757306 + 0.854821i −0.0268083 + 0.0302603i
\(799\) −1.52990 + 9.41385i −0.0541239 + 0.333038i
\(800\) −4.88541 0.196875i −0.172725 0.00696059i
\(801\) −24.5005 + 9.29183i −0.865684 + 0.328311i
\(802\) −2.03657 + 7.03104i −0.0719136 + 0.248275i
\(803\) 0.256517 1.25651i 0.00905230 0.0443411i
\(804\) 1.43208 17.7395i 0.0505056 0.625624i
\(805\) 5.98763 15.7881i 0.211036 0.556457i
\(806\) 7.89565 1.31854i 0.278113 0.0464438i
\(807\) −8.46160 22.3114i −0.297863 0.785399i
\(808\) −21.0857 + 6.10756i −0.741794 + 0.214863i
\(809\) −1.54930 38.4455i −0.0544705 1.35167i −0.763187 0.646178i \(-0.776366\pi\)
0.708716 0.705494i \(-0.249275\pi\)
\(810\) −0.700825 0.858355i −0.0246245 0.0301595i
\(811\) 27.2443 + 3.30806i 0.956678 + 0.116162i 0.583960 0.811783i \(-0.301503\pi\)
0.372718 + 0.927944i \(0.378426\pi\)
\(812\) −1.13148 14.0158i −0.0397070 0.491860i
\(813\) −4.51861 1.30883i −0.158475 0.0459027i
\(814\) −0.195016 + 0.791211i −0.00683531 + 0.0277319i
\(815\) −4.63738 3.48476i −0.162440 0.122066i
\(816\) 8.23226 10.0827i 0.288187 0.352965i
\(817\) −8.08931 + 7.76988i −0.283009 + 0.271834i
\(818\) −7.64458 1.88422i −0.267286 0.0658802i
\(819\) −1.68811 + 22.1133i −0.0589874 + 0.772700i
\(820\) 2.36881 0.583860i 0.0827226 0.0203893i
\(821\) −12.8483 + 20.3180i −0.448410 + 0.709104i −0.991433 0.130614i \(-0.958305\pi\)
0.543023 + 0.839718i \(0.317280\pi\)
\(822\) 3.39662 + 5.88312i 0.118471 + 0.205197i
\(823\) 12.9337 22.4018i 0.450841 0.780879i −0.547598 0.836742i \(-0.684458\pi\)
0.998438 + 0.0558627i \(0.0177909\pi\)
\(824\) −15.1507 28.8673i −0.527801 1.00564i
\(825\) −0.0467914 0.140157i −0.00162907 0.00487965i
\(826\) −8.84296 5.10548i −0.307686 0.177643i
\(827\) 31.4943 + 35.5498i 1.09517 + 1.23619i 0.969755 + 0.244081i \(0.0784864\pi\)
0.125411 + 0.992105i \(0.459975\pi\)
\(828\) 19.5893 12.3875i 0.680777 0.430497i
\(829\) 21.3100 9.07934i 0.740126 0.315338i 0.0112063 0.999937i \(-0.496433\pi\)
0.728920 + 0.684599i \(0.240023\pi\)
\(830\) 6.79178 0.273699i 0.235746 0.00950025i
\(831\) 1.65411 13.6229i 0.0573806 0.472572i
\(832\) 1.35990 + 10.8056i 0.0471459 + 0.374618i
\(833\) −0.607113 5.00003i −0.0210352 0.173241i
\(834\) −1.38119 8.49878i −0.0478266 0.294289i
\(835\) 2.24234 + 1.41797i 0.0775994 + 0.0490709i
\(836\) 0.268067 + 0.0435651i 0.00927128 + 0.00150673i
\(837\) −10.1043 + 19.2521i −0.349255 + 0.665450i
\(838\) −6.89846 10.9090i −0.238303 0.376847i
\(839\) 8.92314 + 8.57079i 0.308061 + 0.295897i 0.830771 0.556614i \(-0.187900\pi\)
−0.522710 + 0.852510i \(0.675079\pi\)
\(840\) 4.55909 0.553574i 0.157304 0.0191001i
\(841\) 4.21240 + 20.6337i 0.145255 + 0.711507i
\(842\) −4.07338 0.328837i −0.140378 0.0113325i
\(843\) −10.8711 8.87599i −0.374421 0.305705i
\(844\) −9.63734 −0.331731
\(845\) −8.70516 9.65506i −0.299467 0.332144i
\(846\) −1.85296 −0.0637060
\(847\) −23.9467 19.5519i −0.822818 0.671810i
\(848\) −27.5252 2.22207i −0.945221 0.0763061i
\(849\) 2.07899 + 10.1836i 0.0713509 + 0.349500i
\(850\) −2.55228 + 0.309903i −0.0875425 + 0.0106296i
\(851\) 45.0393 + 43.2608i 1.54393 + 1.48296i
\(852\) 8.74838 + 13.8345i 0.299715 + 0.473961i
\(853\) 19.6609 37.4607i 0.673176 1.28263i −0.273943 0.961746i \(-0.588328\pi\)
0.947119 0.320884i \(-0.103980\pi\)
\(854\) −9.63693 1.56615i −0.329769 0.0535927i
\(855\) −1.73049 1.09430i −0.0591816 0.0374242i
\(856\) −3.40985 20.9816i −0.116546 0.717137i
\(857\) 4.20181 + 34.6051i 0.143531 + 1.18209i 0.869349 + 0.494199i \(0.164539\pi\)
−0.725818 + 0.687887i \(0.758538\pi\)
\(858\) 0.225121 0.119408i 0.00768551 0.00407652i
\(859\) −3.65434 + 30.0962i −0.124684 + 1.02687i 0.787279 + 0.616597i \(0.211489\pi\)
−0.911964 + 0.410271i \(0.865434\pi\)
\(860\) 21.1676 0.853023i 0.721808 0.0290879i
\(861\) −3.22630 + 1.37460i −0.109952 + 0.0468462i
\(862\) 4.80881 3.04091i 0.163789 0.103574i
\(863\) −12.5435 14.1586i −0.426984 0.481965i 0.495166 0.868799i \(-0.335107\pi\)
−0.922150 + 0.386833i \(0.873569\pi\)
\(864\) 19.8345 + 11.4515i 0.674783 + 0.389586i
\(865\) −3.92021 11.7425i −0.133291 0.399256i
\(866\) 0.142934 + 0.272338i 0.00485710 + 0.00925443i
\(867\) 5.37364 9.30741i 0.182498 0.316096i
\(868\) 11.5810 + 20.0588i 0.393083 + 0.680840i
\(869\) 0.797061 1.26045i 0.0270385 0.0427579i
\(870\) 1.18268 0.291506i 0.0400968 0.00988297i
\(871\) 31.1632 + 25.2182i 1.05592 + 0.854486i
\(872\) −4.55475 1.12265i −0.154243 0.0380176i
\(873\) 11.7729 11.3080i 0.398453 0.382719i
\(874\) −1.70028 + 2.08247i −0.0575129 + 0.0704405i
\(875\) 2.25225 + 1.69246i 0.0761400 + 0.0572155i
\(876\) 3.00451 12.1898i 0.101513 0.411854i
\(877\) 48.2736 + 13.9826i 1.63009 + 0.472160i 0.962254 0.272153i \(-0.0877357\pi\)
0.667831 + 0.744313i \(0.267223\pi\)
\(878\) −0.0198754 0.246201i −0.000670762 0.00830887i
\(879\) 11.3266 + 1.37529i 0.382036 + 0.0463875i
\(880\) −0.277094 0.339379i −0.00934085 0.0114405i
\(881\) 0.833132 + 20.6740i 0.0280689 + 0.696524i 0.950567 + 0.310521i \(0.100503\pi\)
−0.922498 + 0.386003i \(0.873855\pi\)
\(882\) 0.939926 0.272253i 0.0316489 0.00916723i
\(883\) −9.20875 24.2815i −0.309899 0.817137i −0.995977 0.0896087i \(-0.971438\pi\)
0.686078 0.727528i \(-0.259331\pi\)
\(884\) 9.69406 + 32.9296i 0.326047 + 1.10754i
\(885\) −2.42828 + 6.40284i −0.0816256 + 0.215229i
\(886\) 1.33596 16.5489i 0.0448826 0.555970i
\(887\) 2.52498 12.3682i 0.0847806 0.415283i −0.915145 0.403124i \(-0.867924\pi\)
0.999926 0.0121592i \(-0.00387049\pi\)
\(888\) −4.72569 + 16.3150i −0.158584 + 0.547494i
\(889\) −2.45225 + 0.930017i −0.0822460 + 0.0311918i
\(890\) −5.73595 0.231151i −0.192270 0.00774820i
\(891\) 0.0607627 0.373888i 0.00203563 0.0125257i
\(892\) 24.3541 27.4901i 0.815437 0.920438i
\(893\) −1.57831 + 0.526917i −0.0528161 + 0.0176326i
\(894\) −0.727177 + 1.53249i −0.0243205 + 0.0512543i
\(895\) 9.30973 + 4.41752i 0.311190 + 0.147662i
\(896\) 27.9979 14.6945i 0.935346 0.490907i
\(897\) 0.701234 19.5166i 0.0234135 0.651639i
\(898\) −6.71204 3.52275i −0.223984 0.117556i
\(899\) 7.85764 + 10.4566i 0.262067 + 0.348748i
\(900\) 1.07589 + 3.71441i 0.0358631 + 0.123814i
\(901\) −55.2139 + 4.45733i −1.83944 + 0.148495i
\(902\) −0.0886552 0.0611943i −0.00295189 0.00203755i
\(903\) −29.8364 + 6.09114i −0.992892 + 0.202700i
\(904\) −14.1431 + 33.1951i −0.470392 + 1.10405i
\(905\) 4.01080 + 16.2724i 0.133323 + 0.540914i
\(906\) 0.151365 3.75608i 0.00502876 0.124787i
\(907\) −35.2176 + 26.4643i −1.16938 + 0.878732i −0.994384 0.105837i \(-0.966248\pi\)
−0.174997 + 0.984569i \(0.555992\pi\)
\(908\) 7.07195 + 16.5985i 0.234691 + 0.550840i
\(909\) 15.0938 + 21.8671i 0.500630 + 0.725287i
\(910\) −2.23914 + 4.31193i −0.0742269 + 0.142939i
\(911\) 10.6917 15.4896i 0.354233 0.513195i −0.604843 0.796345i \(-0.706764\pi\)
0.959076 + 0.283150i \(0.0913795\pi\)
\(912\) 2.22505 + 0.454248i 0.0736788 + 0.0150416i
\(913\) 1.60958 + 1.67575i 0.0532693 + 0.0554592i
\(914\) −4.95251 10.4372i −0.163815 0.345232i
\(915\) 6.54766i 0.216459i
\(916\) 12.3823 5.87545i 0.409121 0.194130i
\(917\) 5.32709 7.08907i 0.175916 0.234102i
\(918\) 11.2606 + 4.27060i 0.371656 + 0.140951i
\(919\) −28.5095 12.1468i −0.940443 0.400685i −0.133323 0.991073i \(-0.542565\pi\)
−0.807120 + 0.590387i \(0.798975\pi\)
\(920\) 10.6713 1.73425i 0.351822 0.0571766i
\(921\) 2.75529 8.25310i 0.0907899 0.271949i
\(922\) 2.47016 2.18837i 0.0813505 0.0720703i
\(923\) −36.8466 1.32391i −1.21282 0.0435769i
\(924\) 0.551900 + 0.488940i 0.0181562 + 0.0160850i
\(925\) −9.02369 + 5.20983i −0.296697 + 0.171298i
\(926\) 4.75268 + 1.58668i 0.156183 + 0.0521414i
\(927\) −27.3349 + 28.4586i −0.897795 + 0.934704i
\(928\) 11.3390 7.82674i 0.372220 0.256925i
\(929\) 1.77135 1.44626i 0.0581162 0.0474504i −0.602942 0.797785i \(-0.706005\pi\)
0.661058 + 0.750335i \(0.270108\pi\)
\(930\) −1.55418 + 1.26895i −0.0509635 + 0.0416104i
\(931\) 0.723190 0.499182i 0.0237016 0.0163600i
\(932\) 34.5329 35.9526i 1.13116 1.17767i
\(933\) 11.3185 + 3.77866i 0.370550 + 0.123708i
\(934\) −2.05234 + 1.18492i −0.0671547 + 0.0387718i
\(935\) −0.657840 0.582795i −0.0215137 0.0190594i
\(936\) −12.8021 + 6.14324i −0.418450 + 0.200798i
\(937\) −23.7681 + 21.0567i −0.776470 + 0.687893i −0.955185 0.296008i \(-0.904344\pi\)
0.178715 + 0.983901i \(0.442806\pi\)
\(938\) 4.74459 14.2118i 0.154916 0.464031i
\(939\) −22.6930 + 3.68797i −0.740558 + 0.120352i
\(940\) 2.89125 + 1.23185i 0.0943021 + 0.0401784i
\(941\) −11.9933 4.54846i −0.390971 0.148276i 0.151283 0.988491i \(-0.451660\pi\)
−0.542254 + 0.840215i \(0.682429\pi\)
\(942\) 0.632294 0.841430i 0.0206012 0.0274153i
\(943\) −7.45851 + 3.53911i −0.242882 + 0.115249i
\(944\) 20.3047i 0.660861i
\(945\) −5.65735 11.9226i −0.184033 0.387842i
\(946\) −0.647976 0.674614i −0.0210675 0.0219336i
\(947\) 13.9580 + 2.84954i 0.453573 + 0.0925975i 0.421380 0.906884i \(-0.361546\pi\)
0.0321927 + 0.999482i \(0.489751\pi\)
\(948\) 8.29355 12.0153i 0.269362 0.390238i
\(949\) 18.8449 + 21.0855i 0.611733 + 0.684465i
\(950\) −0.254809 0.369155i −0.00826710 0.0119770i
\(951\) −5.64715 13.2543i −0.183121 0.429802i
\(952\) 21.8376 16.4099i 0.707760 0.531847i
\(953\) −0.222649 + 5.52498i −0.00721232 + 0.178972i 0.991568 + 0.129590i \(0.0413661\pi\)
−0.998780 + 0.0493818i \(0.984275\pi\)
\(954\) −2.57554 10.4494i −0.0833861 0.338311i
\(955\) −4.25924 + 9.99681i −0.137826 + 0.323489i
\(956\) 49.4283 10.0909i 1.59862 0.326362i
\(957\) 0.342675 + 0.236532i 0.0110771 + 0.00764598i
\(958\) −11.0965 + 0.895804i −0.358512 + 0.0289421i
\(959\) −12.3181 42.5271i −0.397773 1.37327i
\(960\) −1.63987 2.18227i −0.0529266 0.0704325i
\(961\) 8.37191 + 4.39392i 0.270062 + 0.141739i
\(962\) −11.4254 13.8697i −0.368371 0.447177i
\(963\) −22.7816 + 11.9567i −0.734127 + 0.385300i
\(964\) 2.48551 + 1.17939i 0.0800530 + 0.0379856i
\(965\) −3.59756 + 7.58169i −0.115809 + 0.244063i
\(966\) −6.92325 + 2.31132i −0.222752 + 0.0743656i
\(967\) 18.9330 21.3709i 0.608843 0.687242i −0.360554 0.932738i \(-0.617412\pi\)
0.969398 + 0.245496i \(0.0789509\pi\)
\(968\) 3.17517 19.5376i 0.102054 0.627963i
\(969\) 4.55168 + 0.183426i 0.146221 + 0.00589251i
\(970\) 3.34385 1.26816i 0.107365 0.0407180i
\(971\) −3.27222 + 11.2970i −0.105011 + 0.362538i −0.995764 0.0919489i \(-0.970690\pi\)
0.890753 + 0.454487i \(0.150178\pi\)
\(972\) 5.72045 28.0206i 0.183483 0.898761i
\(973\) −4.51561 + 55.9358i −0.144764 + 1.79322i
\(974\) 1.44918 3.82117i 0.0464347 0.122438i
\(975\) 3.09517 + 1.01834i 0.0991248 + 0.0326128i
\(976\) 6.88452 + 18.1530i 0.220368 + 0.581063i
\(977\) 33.6109 9.73552i 1.07531 0.311467i 0.307107 0.951675i \(-0.400639\pi\)
0.768202 + 0.640208i \(0.221152\pi\)
\(978\) 0.100965 + 2.50541i 0.00322849 + 0.0801142i
\(979\) −1.24107 1.52004i −0.0396648 0.0485806i
\(980\) −1.64760 0.200055i −0.0526307 0.00639052i
\(981\) 0.456882 + 5.65950i 0.0145871 + 0.180694i
\(982\) 7.05991 + 2.04493i 0.225291 + 0.0652563i
\(983\) 8.96850 36.3866i 0.286051 1.16055i −0.635439 0.772151i \(-0.719181\pi\)
0.921490 0.388402i \(-0.126973\pi\)
\(984\) −1.79507 1.34891i −0.0572247 0.0430016i
\(985\) 3.87912 4.75106i 0.123599 0.151381i
\(986\) 5.22509 5.01876i 0.166401 0.159830i
\(987\) −4.38622 1.08110i −0.139615 0.0344120i
\(988\) −4.30105 + 4.16743i −0.136835 + 0.132584i
\(989\) −69.6027 + 17.1555i −2.21324 + 0.545514i
\(990\) 0.0912598 0.144316i 0.00290043 0.00458666i
\(991\) −9.09294 15.7494i −0.288847 0.500297i 0.684688 0.728836i \(-0.259939\pi\)
−0.973535 + 0.228539i \(0.926605\pi\)
\(992\) −11.3474 + 19.6543i −0.360281 + 0.624025i
\(993\) 2.48704 + 4.73865i 0.0789237 + 0.150377i
\(994\) 4.36370 + 13.0709i 0.138408 + 0.414583i
\(995\) 19.5122 + 11.2654i 0.618577 + 0.357136i
\(996\) 15.0840 + 17.0263i 0.477955 + 0.539500i
\(997\) 35.0048 22.1357i 1.10861 0.701045i 0.150837 0.988559i \(-0.451803\pi\)
0.957776 + 0.287514i \(0.0928288\pi\)
\(998\) 4.41523 1.88115i 0.139762 0.0595469i
\(999\) 48.7684 1.96530i 1.54296 0.0621793i
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 845.2.bg.a.621.35 yes 1440
169.43 even 78 inner 845.2.bg.a.381.35 1440
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
845.2.bg.a.381.35 1440 169.43 even 78 inner
845.2.bg.a.621.35 yes 1440 1.1 even 1 trivial