Properties

Label 392.2.z.a.53.10
Level $392$
Weight $2$
Character 392.53
Analytic conductor $3.130$
Analytic rank $0$
Dimension $648$
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] = [392,2,Mod(37,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 21, 32]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 392.z (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.13013575923\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 53.10
Character \(\chi\) \(=\) 392.53
Dual form 392.2.z.a.37.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23135 - 0.695533i) q^{2} +(1.73400 - 1.86880i) q^{3} +(1.03247 + 1.71290i) q^{4} +(0.880547 + 2.85466i) q^{5} +(-3.43498 + 1.09511i) q^{6} +(-1.33854 + 2.28217i) q^{7} +(-0.0799587 - 2.82730i) q^{8} +(-0.261493 - 3.48939i) q^{9} +O(q^{10})\) \(q+(-1.23135 - 0.695533i) q^{2} +(1.73400 - 1.86880i) q^{3} +(1.03247 + 1.71290i) q^{4} +(0.880547 + 2.85466i) q^{5} +(-3.43498 + 1.09511i) q^{6} +(-1.33854 + 2.28217i) q^{7} +(-0.0799587 - 2.82730i) q^{8} +(-0.261493 - 3.48939i) q^{9} +(0.901247 - 4.12755i) q^{10} +(1.69662 + 0.127144i) q^{11} +(4.99136 + 1.04067i) q^{12} +(0.482883 + 1.00272i) q^{13} +(3.23554 - 1.87917i) q^{14} +(6.86167 + 3.30441i) q^{15} +(-1.86802 + 3.53702i) q^{16} +(2.79033 - 0.420575i) q^{17} +(-2.10499 + 4.47855i) q^{18} +(0.392754 - 0.226756i) q^{19} +(-3.98060 + 4.45563i) q^{20} +(1.94391 + 6.45875i) q^{21} +(-2.00071 - 1.33661i) q^{22} +(7.01574 + 1.05745i) q^{23} +(-5.42231 - 4.75310i) q^{24} +(-3.24254 + 2.21073i) q^{25} +(0.102823 - 1.57056i) q^{26} +(-0.994929 - 0.793429i) q^{27} +(-5.29112 + 0.0634917i) q^{28} +(-6.88030 + 5.48685i) q^{29} +(-6.15082 - 8.84141i) q^{30} +(4.94919 - 8.57224i) q^{31} +(4.76031 - 3.05605i) q^{32} +(3.17954 - 2.95018i) q^{33} +(-3.72841 - 1.42289i) q^{34} +(-7.69348 - 1.81152i) q^{35} +(5.70697 - 4.05059i) q^{36} +(-9.08232 - 3.56455i) q^{37} +(-0.641335 + 0.00604443i) q^{38} +(2.71120 + 0.836294i) q^{39} +(8.00057 - 2.71782i) q^{40} +(-0.419516 + 1.83802i) q^{41} +(2.09863 - 9.30506i) q^{42} +(3.27731 - 0.748024i) q^{43} +(1.53392 + 3.03740i) q^{44} +(9.73077 - 3.81904i) q^{45} +(-7.90337 - 6.18178i) q^{46} +(-2.83115 - 1.93025i) q^{47} +(3.37085 + 9.62414i) q^{48} +(-3.41662 - 6.10956i) q^{49} +(5.53035 - 0.466894i) q^{50} +(4.05245 - 5.94385i) q^{51} +(-1.21899 + 1.86240i) q^{52} +(7.46464 - 2.92966i) q^{53} +(0.673254 + 1.66900i) q^{54} +(1.13100 + 4.95523i) q^{55} +(6.55941 + 3.60197i) q^{56} +(0.257270 - 1.12717i) q^{57} +(12.2884 - 1.97079i) q^{58} +(-3.14841 + 10.2069i) q^{59} +(1.42435 + 15.1650i) q^{60} +(-6.55445 - 2.57243i) q^{61} +(-12.0565 + 7.11315i) q^{62} +(8.31340 + 4.07391i) q^{63} +(-7.98721 + 0.452134i) q^{64} +(-2.43722 + 2.26141i) q^{65} +(-5.96708 + 1.42124i) q^{66} +(-7.66481 - 4.42528i) q^{67} +(3.60133 + 4.34531i) q^{68} +(14.1414 - 11.2774i) q^{69} +(8.21343 + 7.58169i) q^{70} +(-0.596399 + 0.747861i) q^{71} +(-9.84462 + 1.01833i) q^{72} +(-7.21886 + 4.92174i) q^{73} +(8.70430 + 10.7063i) q^{74} +(-1.49114 + 9.89306i) q^{75} +(0.793915 + 0.438627i) q^{76} +(-2.56116 + 3.70179i) q^{77} +(-2.75678 - 2.91550i) q^{78} +(-4.98291 - 8.63065i) q^{79} +(-11.7419 - 2.21806i) q^{80} +(7.17230 - 1.08105i) q^{81} +(1.79497 - 1.97146i) q^{82} +(1.02290 - 2.12407i) q^{83} +(-9.05613 + 9.99816i) q^{84} +(3.65761 + 7.59512i) q^{85} +(-4.55580 - 1.35839i) q^{86} +(-1.67656 + 22.3721i) q^{87} +(0.223814 - 4.80701i) q^{88} +(-1.13399 - 15.1321i) q^{89} +(-14.6383 - 2.06547i) q^{90} +(-2.93473 - 0.240154i) q^{91} +(5.43222 + 13.1090i) q^{92} +(-7.43797 - 24.1133i) q^{93} +(2.14360 + 4.34598i) q^{94} +(0.993151 + 0.921509i) q^{95} +(2.54319 - 14.1953i) q^{96} -9.10282 q^{97} +(-0.0423227 + 9.89940i) q^{98} -5.95341i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{21}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23135 0.695533i −0.870699 0.491816i
\(3\) 1.73400 1.86880i 1.00112 1.07895i 0.00424585 0.999991i \(-0.498648\pi\)
0.996878 0.0789634i \(-0.0251610\pi\)
\(4\) 1.03247 + 1.71290i 0.516234 + 0.856448i
\(5\) 0.880547 + 2.85466i 0.393792 + 1.27664i 0.907997 + 0.418976i \(0.137611\pi\)
−0.514205 + 0.857667i \(0.671913\pi\)
\(6\) −3.43498 + 1.09511i −1.40232 + 0.447076i
\(7\) −1.33854 + 2.28217i −0.505920 + 0.862580i
\(8\) −0.0799587 2.82730i −0.0282697 0.999600i
\(9\) −0.261493 3.48939i −0.0871645 1.16313i
\(10\) 0.901247 4.12755i 0.284999 1.30525i
\(11\) 1.69662 + 0.127144i 0.511550 + 0.0383353i 0.328005 0.944676i \(-0.393624\pi\)
0.183545 + 0.983011i \(0.441243\pi\)
\(12\) 4.99136 + 1.04067i 1.44088 + 0.300417i
\(13\) 0.482883 + 1.00272i 0.133928 + 0.278104i 0.957138 0.289633i \(-0.0935333\pi\)
−0.823210 + 0.567737i \(0.807819\pi\)
\(14\) 3.23554 1.87917i 0.864735 0.502228i
\(15\) 6.86167 + 3.30441i 1.77168 + 0.853194i
\(16\) −1.86802 + 3.53702i −0.467005 + 0.884255i
\(17\) 2.79033 0.420575i 0.676754 0.102004i 0.198333 0.980135i \(-0.436447\pi\)
0.478421 + 0.878130i \(0.341209\pi\)
\(18\) −2.10499 + 4.47855i −0.496152 + 1.05560i
\(19\) 0.392754 0.226756i 0.0901038 0.0520215i −0.454271 0.890864i \(-0.650100\pi\)
0.544375 + 0.838842i \(0.316767\pi\)
\(20\) −3.98060 + 4.45563i −0.890090 + 0.996309i
\(21\) 1.94391 + 6.45875i 0.424196 + 1.40941i
\(22\) −2.00071 1.33661i −0.426552 0.284967i
\(23\) 7.01574 + 1.05745i 1.46288 + 0.220494i 0.831737 0.555170i \(-0.187347\pi\)
0.631146 + 0.775664i \(0.282585\pi\)
\(24\) −5.42231 4.75310i −1.10682 0.970222i
\(25\) −3.24254 + 2.21073i −0.648508 + 0.442145i
\(26\) 0.102823 1.57056i 0.0201652 0.308012i
\(27\) −0.994929 0.793429i −0.191474 0.152696i
\(28\) −5.29112 + 0.0634917i −0.999928 + 0.0119988i
\(29\) −6.88030 + 5.48685i −1.27764 + 1.01888i −0.279363 + 0.960186i \(0.590123\pi\)
−0.998276 + 0.0586973i \(0.981305\pi\)
\(30\) −6.15082 8.84141i −1.12298 1.61421i
\(31\) 4.94919 8.57224i 0.888900 1.53962i 0.0477228 0.998861i \(-0.484804\pi\)
0.841177 0.540759i \(-0.181863\pi\)
\(32\) 4.76031 3.05605i 0.841512 0.540239i
\(33\) 3.17954 2.95018i 0.553486 0.513560i
\(34\) −3.72841 1.42289i −0.639417 0.244024i
\(35\) −7.69348 1.81152i −1.30044 0.306203i
\(36\) 5.70697 4.05059i 0.951162 0.675098i
\(37\) −9.08232 3.56455i −1.49312 0.586008i −0.528336 0.849035i \(-0.677184\pi\)
−0.964788 + 0.263027i \(0.915279\pi\)
\(38\) −0.641335 + 0.00604443i −0.104038 + 0.000980536i
\(39\) 2.71120 + 0.836294i 0.434139 + 0.133914i
\(40\) 8.00057 2.71782i 1.26500 0.429725i
\(41\) −0.419516 + 1.83802i −0.0655173 + 0.287050i −0.997064 0.0765714i \(-0.975603\pi\)
0.931547 + 0.363621i \(0.118460\pi\)
\(42\) 2.09863 9.30506i 0.323826 1.43580i
\(43\) 3.27731 0.748024i 0.499785 0.114073i 0.0348052 0.999394i \(-0.488919\pi\)
0.464979 + 0.885322i \(0.346062\pi\)
\(44\) 1.53392 + 3.03740i 0.231247 + 0.457906i
\(45\) 9.73077 3.81904i 1.45058 0.569309i
\(46\) −7.90337 6.18178i −1.16529 0.911453i
\(47\) −2.83115 1.93025i −0.412966 0.281556i 0.338963 0.940800i \(-0.389924\pi\)
−0.751929 + 0.659244i \(0.770876\pi\)
\(48\) 3.37085 + 9.62414i 0.486541 + 1.38913i
\(49\) −3.41662 6.10956i −0.488089 0.872794i
\(50\) 5.53035 0.466894i 0.782110 0.0660288i
\(51\) 4.05245 5.94385i 0.567457 0.832306i
\(52\) −1.21899 + 1.86240i −0.169043 + 0.258269i
\(53\) 7.46464 2.92966i 1.02535 0.402419i 0.207733 0.978186i \(-0.433391\pi\)
0.817614 + 0.575766i \(0.195296\pi\)
\(54\) 0.673254 + 1.66900i 0.0916183 + 0.227122i
\(55\) 1.13100 + 4.95523i 0.152504 + 0.668163i
\(56\) 6.55941 + 3.60197i 0.876538 + 0.481333i
\(57\) 0.257270 1.12717i 0.0340763 0.149298i
\(58\) 12.2884 1.97079i 1.61354 0.258777i
\(59\) −3.14841 + 10.2069i −0.409889 + 1.32883i 0.481841 + 0.876258i \(0.339968\pi\)
−0.891730 + 0.452568i \(0.850508\pi\)
\(60\) 1.42435 + 15.1650i 0.183883 + 1.95779i
\(61\) −6.55445 2.57243i −0.839212 0.329366i −0.0934870 0.995620i \(-0.529801\pi\)
−0.745725 + 0.666254i \(0.767897\pi\)
\(62\) −12.0565 + 7.11315i −1.53117 + 0.903370i
\(63\) 8.31340 + 4.07391i 1.04739 + 0.513264i
\(64\) −7.98721 + 0.452134i −0.998402 + 0.0565167i
\(65\) −2.43722 + 2.26141i −0.302300 + 0.280493i
\(66\) −5.96708 + 1.42124i −0.734497 + 0.174943i
\(67\) −7.66481 4.42528i −0.936406 0.540634i −0.0475741 0.998868i \(-0.515149\pi\)
−0.888832 + 0.458234i \(0.848482\pi\)
\(68\) 3.60133 + 4.34531i 0.436725 + 0.526947i
\(69\) 14.1414 11.2774i 1.70243 1.35764i
\(70\) 8.21343 + 7.58169i 0.981692 + 0.906185i
\(71\) −0.596399 + 0.747861i −0.0707795 + 0.0887547i −0.815961 0.578107i \(-0.803792\pi\)
0.745181 + 0.666862i \(0.232363\pi\)
\(72\) −9.84462 + 1.01833i −1.16020 + 0.120011i
\(73\) −7.21886 + 4.92174i −0.844904 + 0.576046i −0.906572 0.422051i \(-0.861310\pi\)
0.0616681 + 0.998097i \(0.480358\pi\)
\(74\) 8.70430 + 10.7063i 1.01185 + 1.24458i
\(75\) −1.49114 + 9.89306i −0.172182 + 1.14235i
\(76\) 0.793915 + 0.438627i 0.0910683 + 0.0503140i
\(77\) −2.56116 + 3.70179i −0.291871 + 0.421858i
\(78\) −2.75678 2.91550i −0.312144 0.330116i
\(79\) −4.98291 8.63065i −0.560621 0.971024i −0.997442 0.0714759i \(-0.977229\pi\)
0.436821 0.899548i \(-0.356104\pi\)
\(80\) −11.7419 2.21806i −1.31278 0.247986i
\(81\) 7.17230 1.08105i 0.796922 0.120117i
\(82\) 1.79497 1.97146i 0.198222 0.217712i
\(83\) 1.02290 2.12407i 0.112278 0.233147i −0.837257 0.546810i \(-0.815842\pi\)
0.949534 + 0.313663i \(0.101556\pi\)
\(84\) −9.05613 + 9.99816i −0.988105 + 1.09089i
\(85\) 3.65761 + 7.59512i 0.396724 + 0.823806i
\(86\) −4.55580 1.35839i −0.491265 0.146479i
\(87\) −1.67656 + 22.3721i −0.179746 + 2.39854i
\(88\) 0.223814 4.80701i 0.0238587 0.512429i
\(89\) −1.13399 15.1321i −0.120203 1.60400i −0.652732 0.757589i \(-0.726377\pi\)
0.532529 0.846412i \(-0.321242\pi\)
\(90\) −14.6383 2.06547i −1.54301 0.217720i
\(91\) −2.93473 0.240154i −0.307643 0.0251750i
\(92\) 5.43222 + 13.1090i 0.566348 + 1.36671i
\(93\) −7.43797 24.1133i −0.771281 2.50043i
\(94\) 2.14360 + 4.34598i 0.221096 + 0.448254i
\(95\) 0.993151 + 0.921509i 0.101895 + 0.0945449i
\(96\) 2.54319 14.1953i 0.259564 1.44880i
\(97\) −9.10282 −0.924251 −0.462125 0.886815i \(-0.652913\pi\)
−0.462125 + 0.886815i \(0.652913\pi\)
\(98\) −0.0423227 + 9.89940i −0.00427524 + 0.999991i
\(99\) 5.95341i 0.598340i
\(100\) −7.13456 3.27163i −0.713456 0.327163i
\(101\) 1.77420 1.91214i 0.176540 0.190265i −0.638583 0.769553i \(-0.720479\pi\)
0.815123 + 0.579288i \(0.196669\pi\)
\(102\) −9.12415 + 4.50038i −0.903426 + 0.445604i
\(103\) 6.01711 1.85603i 0.592883 0.182880i 0.0162285 0.999868i \(-0.494834\pi\)
0.576654 + 0.816988i \(0.304358\pi\)
\(104\) 2.79637 1.44543i 0.274206 0.141736i
\(105\) −16.7258 + 11.2364i −1.63227 + 1.09656i
\(106\) −11.2293 1.58446i −1.09069 0.153896i
\(107\) 1.36534 0.102318i 0.131993 0.00989149i −0.00856988 0.999963i \(-0.502728\pi\)
0.140563 + 0.990072i \(0.455109\pi\)
\(108\) 0.331829 2.52340i 0.0319303 0.242814i
\(109\) −11.2330 0.841795i −1.07592 0.0806294i −0.475039 0.879965i \(-0.657566\pi\)
−0.600885 + 0.799335i \(0.705185\pi\)
\(110\) 2.05386 6.88829i 0.195828 0.656773i
\(111\) −22.4102 + 10.7922i −2.12708 + 1.02435i
\(112\) −5.57167 8.99758i −0.526473 0.850192i
\(113\) 5.23073 + 2.51899i 0.492066 + 0.236966i 0.663426 0.748242i \(-0.269102\pi\)
−0.171360 + 0.985208i \(0.554816\pi\)
\(114\) −1.10078 + 1.20901i −0.103097 + 0.113234i
\(115\) 3.15902 + 20.9587i 0.294580 + 1.95441i
\(116\) −16.5021 6.12023i −1.53218 0.568249i
\(117\) 3.37260 1.94717i 0.311797 0.180016i
\(118\) 10.9761 10.3785i 1.01043 0.955418i
\(119\) −2.77514 + 6.93097i −0.254397 + 0.635361i
\(120\) 8.79388 19.6642i 0.802768 1.79509i
\(121\) −8.01479 1.20804i −0.728617 0.109821i
\(122\) 6.28164 + 7.72642i 0.568713 + 0.699517i
\(123\) 2.70746 + 3.97111i 0.244123 + 0.358063i
\(124\) 19.7932 0.373126i 1.77748 0.0335077i
\(125\) 2.51207 + 2.00331i 0.224686 + 0.179181i
\(126\) −7.40321 10.7987i −0.659530 0.962022i
\(127\) 11.3165 + 14.1904i 1.00418 + 1.25920i 0.965625 + 0.259941i \(0.0837030\pi\)
0.0385518 + 0.999257i \(0.487726\pi\)
\(128\) 10.1496 + 4.99863i 0.897103 + 0.441821i
\(129\) 4.28493 7.42171i 0.377267 0.653445i
\(130\) 4.57396 1.08943i 0.401163 0.0955492i
\(131\) 2.22875 + 2.40202i 0.194727 + 0.209866i 0.822866 0.568235i \(-0.192374\pi\)
−0.628139 + 0.778101i \(0.716183\pi\)
\(132\) 8.33612 + 2.40025i 0.725566 + 0.208915i
\(133\) −0.00821897 + 1.19985i −0.000712675 + 0.104041i
\(134\) 6.36017 + 10.7802i 0.549435 + 0.931269i
\(135\) 1.38889 3.53884i 0.119537 0.304575i
\(136\) −1.41220 7.85546i −0.121095 0.673600i
\(137\) 13.5084 + 4.16679i 1.15410 + 0.355993i 0.811993 0.583668i \(-0.198383\pi\)
0.342108 + 0.939661i \(0.388859\pi\)
\(138\) −25.2569 + 4.05067i −2.15001 + 0.344816i
\(139\) −2.07057 0.472595i −0.175624 0.0400850i 0.133805 0.991008i \(-0.457281\pi\)
−0.309428 + 0.950923i \(0.600138\pi\)
\(140\) −4.84033 15.0485i −0.409082 1.27183i
\(141\) −8.51646 + 1.94383i −0.717216 + 0.163700i
\(142\) 1.25454 0.506066i 0.105279 0.0424682i
\(143\) 0.691779 + 1.76262i 0.0578495 + 0.147398i
\(144\) 12.8305 + 5.59334i 1.06921 + 0.466112i
\(145\) −21.7215 14.8095i −1.80387 1.22986i
\(146\) 12.3122 1.03945i 1.01897 0.0860252i
\(147\) −17.3420 4.20895i −1.43034 0.347148i
\(148\) −3.27151 19.2373i −0.268916 1.58130i
\(149\) −5.61414 + 8.23443i −0.459928 + 0.674591i −0.984220 0.176948i \(-0.943378\pi\)
0.524292 + 0.851539i \(0.324330\pi\)
\(150\) 8.71707 11.1447i 0.711746 0.909964i
\(151\) −4.67606 11.9144i −0.380533 0.969581i −0.984939 0.172905i \(-0.944685\pi\)
0.604406 0.796677i \(-0.293411\pi\)
\(152\) −0.672512 1.09230i −0.0545479 0.0885972i
\(153\) −2.19720 9.62657i −0.177633 0.778262i
\(154\) 5.72841 2.77685i 0.461608 0.223765i
\(155\) 28.8288 + 6.58000i 2.31559 + 0.528518i
\(156\) 1.36674 + 5.50745i 0.109427 + 0.440949i
\(157\) −1.78814 + 5.79700i −0.142709 + 0.462651i −0.998505 0.0546627i \(-0.982592\pi\)
0.855796 + 0.517313i \(0.173068\pi\)
\(158\) 0.132825 + 14.0932i 0.0105670 + 1.12119i
\(159\) 7.46871 19.0300i 0.592307 1.50917i
\(160\) 12.9157 + 10.8981i 1.02107 + 0.861568i
\(161\) −11.8041 + 14.5957i −0.930296 + 1.15030i
\(162\) −9.58355 3.65741i −0.752955 0.287354i
\(163\) 16.4824 + 17.7639i 1.29101 + 1.39137i 0.876556 + 0.481300i \(0.159835\pi\)
0.414449 + 0.910072i \(0.363974\pi\)
\(164\) −3.58147 + 1.17911i −0.279666 + 0.0920729i
\(165\) 11.2215 + 6.47873i 0.873592 + 0.504369i
\(166\) −2.73692 + 1.90403i −0.212426 + 0.147781i
\(167\) −14.4422 18.1099i −1.11757 1.40139i −0.905612 0.424107i \(-0.860588\pi\)
−0.211956 0.977279i \(-0.567983\pi\)
\(168\) 18.1054 6.01244i 1.39686 0.463870i
\(169\) 7.33310 9.19542i 0.564085 0.707340i
\(170\) 0.778833 11.8963i 0.0597337 0.912402i
\(171\) −0.893943 1.31117i −0.0683616 0.100268i
\(172\) 4.66500 + 4.84137i 0.355703 + 0.369151i
\(173\) −1.52319 + 10.1057i −0.115806 + 0.768321i 0.853254 + 0.521495i \(0.174626\pi\)
−0.969060 + 0.246826i \(0.920612\pi\)
\(174\) 17.6250 26.3819i 1.33615 2.00001i
\(175\) −0.704991 10.3592i −0.0532923 0.783081i
\(176\) −3.61903 + 5.76346i −0.272795 + 0.434437i
\(177\) 13.6154 + 23.5825i 1.02339 + 1.77257i
\(178\) −9.12853 + 19.4217i −0.684212 + 1.45572i
\(179\) −2.79668 18.5548i −0.209034 1.38685i −0.809463 0.587170i \(-0.800242\pi\)
0.600430 0.799678i \(-0.294996\pi\)
\(180\) 16.5883 + 12.7247i 1.23642 + 0.948446i
\(181\) 8.00330 16.6190i 0.594881 1.23528i −0.358505 0.933528i \(-0.616713\pi\)
0.953386 0.301754i \(-0.0975723\pi\)
\(182\) 3.44666 + 2.33692i 0.255483 + 0.173224i
\(183\) −16.1728 + 7.78840i −1.19553 + 0.575735i
\(184\) 2.42876 19.9201i 0.179051 1.46853i
\(185\) 2.17817 29.0657i 0.160143 2.13695i
\(186\) −7.61282 + 34.8654i −0.558199 + 2.55645i
\(187\) 4.78760 0.358781i 0.350104 0.0262367i
\(188\) 0.383238 6.84239i 0.0279505 0.499032i
\(189\) 3.14249 1.20856i 0.228583 0.0879100i
\(190\) −0.581981 1.82547i −0.0422213 0.132434i
\(191\) 10.4507 3.22361i 0.756185 0.233252i 0.107392 0.994217i \(-0.465750\pi\)
0.648794 + 0.760964i \(0.275274\pi\)
\(192\) −13.0049 + 15.7105i −0.938544 + 1.13381i
\(193\) 4.74268 + 4.40056i 0.341385 + 0.316759i 0.832169 0.554522i \(-0.187099\pi\)
−0.490784 + 0.871282i \(0.663289\pi\)
\(194\) 11.2088 + 6.33131i 0.804744 + 0.454561i
\(195\) 8.47595i 0.606976i
\(196\) 6.93748 12.1602i 0.495534 0.868589i
\(197\) 16.9909i 1.21055i 0.796016 + 0.605276i \(0.206937\pi\)
−0.796016 + 0.605276i \(0.793063\pi\)
\(198\) −4.14079 + 7.33075i −0.294273 + 0.520974i
\(199\) −3.11351 2.88891i −0.220711 0.204790i 0.562066 0.827093i \(-0.310007\pi\)
−0.782777 + 0.622303i \(0.786197\pi\)
\(200\) 6.50965 + 8.99086i 0.460302 + 0.635750i
\(201\) −21.5607 + 6.65061i −1.52078 + 0.469098i
\(202\) −3.51463 + 1.12050i −0.247288 + 0.0788382i
\(203\) −3.31240 23.0464i −0.232485 1.61754i
\(204\) 14.3652 + 0.804587i 1.00577 + 0.0563323i
\(205\) −5.61632 + 0.420885i −0.392261 + 0.0293959i
\(206\) −8.70012 1.89966i −0.606166 0.132356i
\(207\) 1.85529 24.7571i 0.128952 1.72074i
\(208\) −4.44866 0.165130i −0.308459 0.0114497i
\(209\) 0.695184 0.334783i 0.0480869 0.0231574i
\(210\) 28.4107 2.20266i 1.96053 0.151998i
\(211\) 8.43679 17.5192i 0.580812 1.20607i −0.378992 0.925400i \(-0.623729\pi\)
0.959805 0.280669i \(-0.0905564\pi\)
\(212\) 12.7252 + 9.76137i 0.873970 + 0.670414i
\(213\) 0.363451 + 2.41134i 0.0249033 + 0.165222i
\(214\) −1.75239 0.823651i −0.119791 0.0563036i
\(215\) 5.02118 + 8.69693i 0.342441 + 0.593126i
\(216\) −2.16371 + 2.87640i −0.147222 + 0.195714i
\(217\) 12.9387 + 22.7692i 0.878333 + 1.54567i
\(218\) 13.2463 + 8.84945i 0.897151 + 0.599361i
\(219\) −3.31972 + 22.0249i −0.224326 + 1.48831i
\(220\) −7.32007 + 7.05340i −0.493519 + 0.475540i
\(221\) 1.76912 + 2.59482i 0.119004 + 0.174547i
\(222\) 35.1012 + 2.29803i 2.35584 + 0.154233i
\(223\) −2.63725 + 3.30701i −0.176603 + 0.221453i −0.862253 0.506479i \(-0.830947\pi\)
0.685649 + 0.727932i \(0.259518\pi\)
\(224\) 0.602581 + 14.9545i 0.0402616 + 0.999189i
\(225\) 8.56198 + 10.7364i 0.570799 + 0.715759i
\(226\) −4.68884 6.73991i −0.311897 0.448332i
\(227\) −24.1910 13.9667i −1.60561 0.927002i −0.990336 0.138692i \(-0.955710\pi\)
−0.615279 0.788310i \(-0.710956\pi\)
\(228\) 2.19635 0.723094i 0.145457 0.0478881i
\(229\) −10.4279 11.2386i −0.689097 0.742670i 0.287492 0.957783i \(-0.407179\pi\)
−0.976589 + 0.215113i \(0.930988\pi\)
\(230\) 10.6876 28.0048i 0.704719 1.84658i
\(231\) 2.47688 + 11.2052i 0.162967 + 0.737247i
\(232\) 16.0631 + 19.0139i 1.05459 + 1.24832i
\(233\) 6.14665 15.6614i 0.402680 1.02601i −0.575416 0.817861i \(-0.695160\pi\)
0.978096 0.208152i \(-0.0667449\pi\)
\(234\) −5.50718 + 0.0519039i −0.360016 + 0.00339306i
\(235\) 3.01724 9.78166i 0.196823 0.638085i
\(236\) −20.7340 + 5.14540i −1.34967 + 0.334937i
\(237\) −24.7693 5.65344i −1.60894 0.367230i
\(238\) 8.23790 6.60428i 0.533984 0.428092i
\(239\) 3.05782 + 13.3972i 0.197794 + 0.866593i 0.972246 + 0.233960i \(0.0751685\pi\)
−0.774452 + 0.632633i \(0.781974\pi\)
\(240\) −24.5055 + 18.0972i −1.58182 + 1.16817i
\(241\) 2.24015 + 5.70780i 0.144301 + 0.367672i 0.984691 0.174310i \(-0.0557695\pi\)
−0.840390 + 0.541982i \(0.817674\pi\)
\(242\) 9.02882 + 7.06207i 0.580395 + 0.453967i
\(243\) 12.5671 18.4325i 0.806177 1.18244i
\(244\) −2.36095 13.8830i −0.151145 0.888771i
\(245\) 14.4322 15.1331i 0.922041 0.966816i
\(246\) −0.571801 6.77297i −0.0364567 0.431829i
\(247\) 0.417027 + 0.284324i 0.0265348 + 0.0180911i
\(248\) −24.6320 13.3074i −1.56413 0.845020i
\(249\) −2.19577 5.59474i −0.139151 0.354552i
\(250\) −1.69988 4.21400i −0.107510 0.266517i
\(251\) −10.2618 + 2.34219i −0.647720 + 0.147838i −0.533744 0.845646i \(-0.679216\pi\)
−0.113975 + 0.993484i \(0.536358\pi\)
\(252\) 1.60514 + 18.4462i 0.101114 + 1.16200i
\(253\) 11.7686 + 2.68610i 0.739884 + 0.168874i
\(254\) −4.06470 25.3444i −0.255042 1.59025i
\(255\) 20.5361 + 6.33454i 1.28602 + 0.396684i
\(256\) −9.02100 13.2144i −0.563812 0.825903i
\(257\) 3.09244 7.87940i 0.192901 0.491503i −0.801398 0.598131i \(-0.795910\pi\)
0.994299 + 0.106628i \(0.0340054\pi\)
\(258\) −10.4383 + 6.15845i −0.649861 + 0.383408i
\(259\) 20.2920 15.9561i 1.26088 0.991466i
\(260\) −6.38990 1.83987i −0.396285 0.114104i
\(261\) 20.9449 + 22.5732i 1.29646 + 1.39725i
\(262\) −1.07370 4.50791i −0.0663333 0.278500i
\(263\) 4.90521 8.49608i 0.302468 0.523890i −0.674226 0.738525i \(-0.735523\pi\)
0.976694 + 0.214635i \(0.0688560\pi\)
\(264\) −8.59526 8.75360i −0.529002 0.538747i
\(265\) 14.9361 + 18.7293i 0.917520 + 1.15053i
\(266\) 0.844658 1.47173i 0.0517893 0.0902375i
\(267\) −30.2453 24.1198i −1.85098 1.47611i
\(268\) −0.333628 17.6980i −0.0203796 1.08108i
\(269\) −14.8724 21.8139i −0.906789 1.33001i −0.943737 0.330698i \(-0.892716\pi\)
0.0369480 0.999317i \(-0.488236\pi\)
\(270\) −4.17160 + 3.39154i −0.253875 + 0.206403i
\(271\) 5.07541 + 0.764994i 0.308309 + 0.0464701i 0.301374 0.953506i \(-0.402555\pi\)
0.00693446 + 0.999976i \(0.497793\pi\)
\(272\) −3.72481 + 10.6551i −0.225850 + 0.646060i
\(273\) −5.53762 + 5.06801i −0.335152 + 0.306730i
\(274\) −13.7355 14.5263i −0.829792 0.877568i
\(275\) −5.78243 + 3.33849i −0.348694 + 0.201319i
\(276\) 33.9176 + 12.5792i 2.04160 + 0.757181i
\(277\) 0.658585 + 4.36943i 0.0395706 + 0.262533i 0.999865 0.0164565i \(-0.00523849\pi\)
−0.960294 + 0.278990i \(0.910000\pi\)
\(278\) 2.22090 + 2.02208i 0.133201 + 0.121276i
\(279\) −31.2061 15.0280i −1.86826 0.899705i
\(280\) −4.50654 + 21.8966i −0.269317 + 1.30857i
\(281\) 10.3704 4.99412i 0.618646 0.297924i −0.0981882 0.995168i \(-0.531305\pi\)
0.716834 + 0.697244i \(0.245590\pi\)
\(282\) 11.8388 + 3.52994i 0.704989 + 0.210205i
\(283\) −24.3030 1.82126i −1.44466 0.108262i −0.670810 0.741629i \(-0.734053\pi\)
−0.773852 + 0.633367i \(0.781673\pi\)
\(284\) −1.89677 0.249427i −0.112553 0.0148008i
\(285\) 3.44424 0.258110i 0.204019 0.0152891i
\(286\) 0.374138 2.65157i 0.0221232 0.156791i
\(287\) −3.63314 3.41767i −0.214457 0.201738i
\(288\) −11.9085 15.8114i −0.701718 0.931697i
\(289\) −8.63568 + 2.66375i −0.507981 + 0.156691i
\(290\) 16.4464 + 33.3438i 0.965767 + 1.95801i
\(291\) −15.7843 + 17.0114i −0.925289 + 0.997225i
\(292\) −15.8837 7.28362i −0.929521 0.426242i
\(293\) 8.72727i 0.509852i 0.966961 + 0.254926i \(0.0820512\pi\)
−0.966961 + 0.254926i \(0.917949\pi\)
\(294\) 18.4267 + 17.2446i 1.07466 + 1.00573i
\(295\) −31.9096 −1.85785
\(296\) −9.35183 + 25.9634i −0.543564 + 1.50909i
\(297\) −1.58713 1.47265i −0.0920949 0.0854516i
\(298\) 12.6403 6.23469i 0.732234 0.361166i
\(299\) 2.32746 + 7.54543i 0.134600 + 0.436363i
\(300\) −18.4853 + 7.66010i −1.06725 + 0.442256i
\(301\) −2.67968 + 8.48064i −0.154454 + 0.488816i
\(302\) −2.52898 + 17.9232i −0.145526 + 1.03137i
\(303\) −0.496946 6.63128i −0.0285488 0.380957i
\(304\) 0.0683697 + 1.81276i 0.00392127 + 0.103969i
\(305\) 1.57193 20.9759i 0.0900082 1.20108i
\(306\) −3.99006 + 13.3819i −0.228097 + 0.764995i
\(307\) −1.62702 3.37854i −0.0928588 0.192823i 0.849366 0.527804i \(-0.176984\pi\)
−0.942225 + 0.334981i \(0.891270\pi\)
\(308\) −8.98509 0.565013i −0.511973 0.0321946i
\(309\) 6.96508 14.4631i 0.396230 0.822779i
\(310\) −30.9219 28.1537i −1.75625 1.59902i
\(311\) −23.9073 + 3.60345i −1.35566 + 0.204333i −0.786346 0.617786i \(-0.788030\pi\)
−0.569315 + 0.822119i \(0.692792\pi\)
\(312\) 2.14767 7.73223i 0.121588 0.437752i
\(313\) 9.23228 + 15.9908i 0.521839 + 0.903852i 0.999677 + 0.0254041i \(0.00808725\pi\)
−0.477838 + 0.878448i \(0.658579\pi\)
\(314\) 6.23383 5.89445i 0.351796 0.332643i
\(315\) −4.30930 + 27.3192i −0.242801 + 1.53926i
\(316\) 9.63871 17.4461i 0.542220 0.981418i
\(317\) −2.29639 + 15.2356i −0.128978 + 0.855715i 0.826984 + 0.562225i \(0.190055\pi\)
−0.955962 + 0.293489i \(0.905183\pi\)
\(318\) −22.4326 + 18.2379i −1.25796 + 1.02273i
\(319\) −12.3709 + 8.43431i −0.692635 + 0.472230i
\(320\) −8.32380 22.4027i −0.465315 1.25235i
\(321\) 2.17629 2.72898i 0.121469 0.152317i
\(322\) 24.6869 9.76230i 1.37574 0.544032i
\(323\) 1.00054 0.797907i 0.0556718 0.0443968i
\(324\) 9.25689 + 11.1692i 0.514272 + 0.620514i
\(325\) −3.78250 2.18383i −0.209815 0.121137i
\(326\) −7.94039 33.3377i −0.439778 1.84640i
\(327\) −21.0511 + 19.5326i −1.16413 + 1.08015i
\(328\) 5.23017 + 1.03913i 0.288788 + 0.0573763i
\(329\) 8.19477 3.87747i 0.451792 0.213772i
\(330\) −9.31147 15.7825i −0.512579 0.868800i
\(331\) 9.43962 + 3.70478i 0.518848 + 0.203633i 0.610291 0.792177i \(-0.291053\pi\)
−0.0914426 + 0.995810i \(0.529148\pi\)
\(332\) 4.69443 0.440917i 0.257640 0.0241985i
\(333\) −10.0631 + 32.6238i −0.551456 + 1.78778i
\(334\) 5.18739 + 32.3447i 0.283841 + 1.76982i
\(335\) 5.88346 25.7771i 0.321448 1.40835i
\(336\) −26.4760 5.18943i −1.44438 0.283106i
\(337\) 1.14520 + 5.01745i 0.0623830 + 0.273318i 0.996494 0.0836650i \(-0.0266626\pi\)
−0.934111 + 0.356983i \(0.883805\pi\)
\(338\) −15.4254 + 6.22241i −0.839029 + 0.338454i
\(339\) 13.7776 5.40729i 0.748294 0.293684i
\(340\) −9.23327 + 14.1068i −0.500744 + 0.765050i
\(341\) 9.48679 13.9146i 0.513738 0.753516i
\(342\) 0.188796 + 2.23629i 0.0102089 + 0.120925i
\(343\) 18.5163 + 0.380557i 0.999789 + 0.0205481i
\(344\) −2.37693 9.20611i −0.128156 0.496360i
\(345\) 44.6454 + 30.4387i 2.40363 + 1.63877i
\(346\) 8.90442 11.3843i 0.478705 0.612021i
\(347\) 22.1765 8.70364i 1.19050 0.467236i 0.314363 0.949303i \(-0.398209\pi\)
0.876134 + 0.482067i \(0.160114\pi\)
\(348\) −40.0521 + 20.2267i −2.14702 + 1.08427i
\(349\) −17.2581 + 3.93905i −0.923804 + 0.210852i −0.657864 0.753137i \(-0.728540\pi\)
−0.265941 + 0.963989i \(0.585683\pi\)
\(350\) −6.33706 + 13.2462i −0.338730 + 0.708038i
\(351\) 0.315151 1.38077i 0.0168215 0.0736998i
\(352\) 8.46499 4.57971i 0.451185 0.244099i
\(353\) −7.59305 2.34215i −0.404137 0.124660i 0.0860210 0.996293i \(-0.472585\pi\)
−0.490158 + 0.871634i \(0.663061\pi\)
\(354\) −0.362932 38.5084i −0.0192896 2.04670i
\(355\) −2.66005 1.04399i −0.141181 0.0554093i
\(356\) 24.7489 17.5658i 1.31169 0.930987i
\(357\) 8.14054 + 17.2045i 0.430843 + 0.910558i
\(358\) −9.46174 + 24.7927i −0.500069 + 1.31033i
\(359\) 5.26458 4.88482i 0.277854 0.257811i −0.528919 0.848672i \(-0.677402\pi\)
0.806773 + 0.590861i \(0.201212\pi\)
\(360\) −11.5756 27.2064i −0.610089 1.43390i
\(361\) −9.39716 + 16.2764i −0.494588 + 0.856651i
\(362\) −21.4140 + 14.8973i −1.12549 + 0.782987i
\(363\) −16.1552 + 12.8833i −0.847928 + 0.676200i
\(364\) −2.61866 5.27484i −0.137255 0.276477i
\(365\) −20.4064 16.2736i −1.06812 0.851799i
\(366\) 25.3315 + 1.65842i 1.32410 + 0.0866870i
\(367\) 17.4575 11.9023i 0.911274 0.621296i −0.0142855 0.999898i \(-0.504547\pi\)
0.925560 + 0.378602i \(0.123595\pi\)
\(368\) −16.8458 + 22.8395i −0.878147 + 1.19059i
\(369\) 6.52326 + 0.983223i 0.339587 + 0.0511845i
\(370\) −22.8983 + 34.2752i −1.19042 + 1.78188i
\(371\) −3.30574 + 20.9571i −0.171625 + 1.08804i
\(372\) 33.6241 37.6367i 1.74333 1.95137i
\(373\) 12.7062 7.33594i 0.657903 0.379840i −0.133574 0.991039i \(-0.542646\pi\)
0.791478 + 0.611198i \(0.209312\pi\)
\(374\) −6.14478 2.88815i −0.317739 0.149342i
\(375\) 8.09970 1.22083i 0.418267 0.0630435i
\(376\) −5.23101 + 8.15885i −0.269769 + 0.420761i
\(377\) −8.82414 4.24948i −0.454466 0.218859i
\(378\) −4.71012 0.697539i −0.242262 0.0358775i
\(379\) 11.3912 + 23.6542i 0.585129 + 1.21503i 0.957898 + 0.287108i \(0.0926939\pi\)
−0.372770 + 0.927924i \(0.621592\pi\)
\(380\) −0.553053 + 2.65259i −0.0283710 + 0.136075i
\(381\) 46.1419 + 3.45786i 2.36392 + 0.177151i
\(382\) −15.1106 3.29939i −0.773127 0.168812i
\(383\) 0.703275 + 9.38455i 0.0359357 + 0.479528i 0.985919 + 0.167226i \(0.0534811\pi\)
−0.949983 + 0.312302i \(0.898900\pi\)
\(384\) 26.9408 10.2999i 1.37482 0.525616i
\(385\) −12.8226 4.05164i −0.653499 0.206490i
\(386\) −2.77918 8.71734i −0.141457 0.443701i
\(387\) −3.46714 11.2402i −0.176245 0.571371i
\(388\) −9.39836 15.5922i −0.477130 0.791572i
\(389\) −8.30312 + 8.94863i −0.420985 + 0.453714i −0.907558 0.419926i \(-0.862056\pi\)
0.486574 + 0.873640i \(0.338247\pi\)
\(390\) 5.89531 10.4369i 0.298520 0.528493i
\(391\) 20.0210 1.01250
\(392\) −17.0003 + 10.1483i −0.858647 + 0.512568i
\(393\) 8.35356 0.421381
\(394\) 11.8177 20.9218i 0.595369 1.05403i
\(395\) 20.2499 21.8242i 1.01888 1.09810i
\(396\) 10.1976 6.14670i 0.512447 0.308883i
\(397\) 3.51013 + 11.3796i 0.176168 + 0.571124i 0.999991 + 0.00427579i \(0.00136103\pi\)
−0.823823 + 0.566848i \(0.808163\pi\)
\(398\) 1.82450 + 5.72283i 0.0914539 + 0.286859i
\(399\) 2.22804 + 2.09590i 0.111542 + 0.104926i
\(400\) −1.76225 15.5986i −0.0881124 0.779930i
\(401\) 0.498112 + 6.64684i 0.0248745 + 0.331927i 0.995733 + 0.0922757i \(0.0294141\pi\)
−0.970859 + 0.239651i \(0.922967\pi\)
\(402\) 31.1746 + 6.80695i 1.55485 + 0.339500i
\(403\) 10.9854 + 0.823243i 0.547222 + 0.0410086i
\(404\) 5.10710 + 1.06481i 0.254088 + 0.0529761i
\(405\) 9.40158 + 19.5226i 0.467168 + 0.970085i
\(406\) −11.9508 + 30.6822i −0.593108 + 1.52273i
\(407\) −14.9560 7.20244i −0.741343 0.357012i
\(408\) −17.1291 10.9822i −0.848015 0.543701i
\(409\) 8.46298 1.27559i 0.418467 0.0630738i 0.0635662 0.997978i \(-0.479753\pi\)
0.354901 + 0.934904i \(0.384514\pi\)
\(410\) 7.20842 + 3.38808i 0.355999 + 0.167325i
\(411\) 31.2104 18.0194i 1.53950 0.888829i
\(412\) 9.39165 + 8.39038i 0.462694 + 0.413364i
\(413\) −19.0797 20.8476i −0.938848 1.02584i
\(414\) −19.5039 + 29.1944i −0.958566 + 1.43483i
\(415\) 6.96422 + 1.04969i 0.341860 + 0.0515272i
\(416\) 5.36303 + 3.29753i 0.262944 + 0.161675i
\(417\) −4.47355 + 3.05002i −0.219071 + 0.149360i
\(418\) −1.08887 0.0712868i −0.0532584 0.00348675i
\(419\) 22.6721 + 18.0804i 1.10761 + 0.883286i 0.993906 0.110229i \(-0.0351584\pi\)
0.113700 + 0.993515i \(0.463730\pi\)
\(420\) −36.5157 17.0484i −1.78179 0.831874i
\(421\) −8.07775 + 6.44179i −0.393685 + 0.313954i −0.800248 0.599669i \(-0.795299\pi\)
0.406563 + 0.913623i \(0.366727\pi\)
\(422\) −22.5738 + 15.7042i −1.09888 + 0.764470i
\(423\) −5.99505 + 10.3837i −0.291489 + 0.504875i
\(424\) −8.87987 20.8705i −0.431245 1.01356i
\(425\) −8.11798 + 7.53239i −0.393780 + 0.365374i
\(426\) 1.22963 3.22201i 0.0595758 0.156107i
\(427\) 14.6441 11.5151i 0.708679 0.557254i
\(428\) 1.58493 + 2.23305i 0.0766107 + 0.107939i
\(429\) 4.49354 + 1.76358i 0.216950 + 0.0851467i
\(430\) −0.133845 14.2014i −0.00645457 0.684852i
\(431\) 0.429098 + 0.132359i 0.0206689 + 0.00637552i 0.305072 0.952329i \(-0.401319\pi\)
−0.284403 + 0.958705i \(0.591796\pi\)
\(432\) 4.66492 2.03694i 0.224441 0.0980023i
\(433\) −4.20956 + 18.4433i −0.202299 + 0.886328i 0.767234 + 0.641367i \(0.221632\pi\)
−0.969533 + 0.244961i \(0.921225\pi\)
\(434\) −0.0953540 37.0362i −0.00457714 1.77779i
\(435\) −65.3411 + 14.9137i −3.13287 + 0.715056i
\(436\) −10.1558 20.1100i −0.486374 0.963096i
\(437\) 2.99524 1.17555i 0.143282 0.0562340i
\(438\) 19.4068 24.8115i 0.927293 1.18554i
\(439\) 1.26880 + 0.865056i 0.0605567 + 0.0412869i 0.593220 0.805040i \(-0.297856\pi\)
−0.532663 + 0.846327i \(0.678809\pi\)
\(440\) 13.9195 3.59388i 0.663585 0.171332i
\(441\) −20.4252 + 13.5195i −0.972628 + 0.643787i
\(442\) −0.373629 4.42563i −0.0177717 0.210506i
\(443\) 2.44680 3.58880i 0.116251 0.170509i −0.763703 0.645568i \(-0.776621\pi\)
0.879954 + 0.475059i \(0.157573\pi\)
\(444\) −41.6236 27.2437i −1.97537 1.29293i
\(445\) 42.1985 16.5617i 2.00040 0.785100i
\(446\) 5.54752 2.23780i 0.262683 0.105963i
\(447\) 5.65364 + 24.7702i 0.267408 + 1.17159i
\(448\) 9.65935 18.8334i 0.456362 0.889794i
\(449\) −0.698543 + 3.06052i −0.0329663 + 0.144435i −0.988733 0.149692i \(-0.952172\pi\)
0.955766 + 0.294127i \(0.0950289\pi\)
\(450\) −3.07533 19.1754i −0.144972 0.903939i
\(451\) −0.945451 + 3.06508i −0.0445195 + 0.144329i
\(452\) 1.08580 + 11.5605i 0.0510717 + 0.543758i
\(453\) −30.3740 11.9209i −1.42709 0.560093i
\(454\) 20.0734 + 34.0236i 0.942092 + 1.59681i
\(455\) −1.89861 8.58913i −0.0890082 0.402665i
\(456\) −3.20743 0.637252i −0.150202 0.0298420i
\(457\) −10.7665 + 9.98988i −0.503637 + 0.467307i −0.890599 0.454789i \(-0.849715\pi\)
0.386962 + 0.922096i \(0.373524\pi\)
\(458\) 5.02364 + 21.0917i 0.234739 + 0.985551i
\(459\) −3.10988 1.79549i −0.145157 0.0838062i
\(460\) −32.6385 + 27.0502i −1.52178 + 1.26122i
\(461\) −8.84185 + 7.05114i −0.411806 + 0.328404i −0.807382 0.590029i \(-0.799116\pi\)
0.395576 + 0.918433i \(0.370545\pi\)
\(462\) 4.74366 15.5203i 0.220695 0.722070i
\(463\) 16.6478 20.8756i 0.773687 0.970173i −0.226305 0.974056i \(-0.572665\pi\)
0.999992 + 0.00388357i \(0.00123618\pi\)
\(464\) −6.55456 34.5853i −0.304288 1.60558i
\(465\) 62.2858 42.4658i 2.88844 1.96930i
\(466\) −18.4617 + 15.0096i −0.855223 + 0.695304i
\(467\) −1.68665 + 11.1902i −0.0780490 + 0.517821i 0.915309 + 0.402753i \(0.131947\pi\)
−0.993358 + 0.115068i \(0.963291\pi\)
\(468\) 6.81740 + 3.76652i 0.315134 + 0.174107i
\(469\) 20.3589 11.5690i 0.940087 0.534207i
\(470\) −10.5188 + 9.94610i −0.485194 + 0.458779i
\(471\) 7.73283 + 13.3937i 0.356310 + 0.617147i
\(472\) 29.1097 + 8.08537i 1.33988 + 0.372159i
\(473\) 5.65544 0.852421i 0.260038 0.0391944i
\(474\) 26.5677 + 24.1893i 1.22029 + 1.11105i
\(475\) −0.772223 + 1.60354i −0.0354320 + 0.0735753i
\(476\) −14.7373 + 2.40247i −0.675482 + 0.110117i
\(477\) −12.1747 25.2809i −0.557439 1.15753i
\(478\) 5.55293 18.6235i 0.253985 0.851820i
\(479\) 1.11592 14.8909i 0.0509876 0.680382i −0.911888 0.410438i \(-0.865376\pi\)
0.962876 0.269944i \(-0.0870052\pi\)
\(480\) 42.7621 5.23964i 1.95181 0.239156i
\(481\) −0.811466 10.8283i −0.0369997 0.493726i
\(482\) 1.21155 8.58642i 0.0551845 0.391101i
\(483\) 6.80815 + 47.3685i 0.309781 + 2.15534i
\(484\) −6.20578 14.9758i −0.282081 0.680716i
\(485\) −8.01545 25.9855i −0.363963 1.17994i
\(486\) −28.2949 + 13.9561i −1.28348 + 0.633062i
\(487\) −27.1938 25.2322i −1.23227 1.14338i −0.984654 0.174520i \(-0.944163\pi\)
−0.247616 0.968858i \(-0.579647\pi\)
\(488\) −6.74895 + 18.7371i −0.305510 + 0.848187i
\(489\) 61.7777 2.79368
\(490\) −28.2967 + 8.59607i −1.27832 + 0.388331i
\(491\) 7.51968i 0.339359i 0.985499 + 0.169679i \(0.0542732\pi\)
−0.985499 + 0.169679i \(0.945727\pi\)
\(492\) −4.00673 + 8.73763i −0.180637 + 0.393923i
\(493\) −16.8907 + 18.2038i −0.760717 + 0.819858i
\(494\) −0.315751 0.640159i −0.0142063 0.0288021i
\(495\) 16.9950 5.24225i 0.763867 0.235622i
\(496\) 21.0750 + 33.5185i 0.946295 + 1.50502i
\(497\) −0.908444 2.36213i −0.0407493 0.105956i
\(498\) −1.18755 + 8.41634i −0.0532154 + 0.377145i
\(499\) 14.2907 1.07094i 0.639740 0.0479419i 0.249089 0.968481i \(-0.419869\pi\)
0.390651 + 0.920539i \(0.372250\pi\)
\(500\) −0.837826 + 6.37125i −0.0374687 + 0.284931i
\(501\) −58.8865 4.41293i −2.63086 0.197155i
\(502\) 14.2650 + 4.25336i 0.636678 + 0.189837i
\(503\) −38.5332 + 18.5566i −1.71811 + 0.827399i −0.728258 + 0.685303i \(0.759670\pi\)
−0.989853 + 0.142096i \(0.954616\pi\)
\(504\) 10.8534 23.8302i 0.483450 1.06148i
\(505\) 7.02077 + 3.38103i 0.312420 + 0.150454i
\(506\) −12.6230 11.4930i −0.561162 0.510925i
\(507\) −4.46886 29.6490i −0.198469 1.31676i
\(508\) −12.6228 + 34.0351i −0.560047 + 1.51006i
\(509\) 11.8759 6.85655i 0.526390 0.303911i −0.213155 0.977018i \(-0.568374\pi\)
0.739545 + 0.673107i \(0.235041\pi\)
\(510\) −20.8813 22.0836i −0.924640 0.977877i
\(511\) −1.56952 23.0626i −0.0694315 1.02023i
\(512\) 1.91696 + 22.5461i 0.0847186 + 0.996405i
\(513\) −0.570677 0.0860157i −0.0251960 0.00379769i
\(514\) −9.28827 + 7.55144i −0.409688 + 0.333080i
\(515\) 10.5967 + 15.5425i 0.466946 + 0.684884i
\(516\) 17.1367 0.323046i 0.754400 0.0142213i
\(517\) −4.55797 3.63486i −0.200459 0.159861i
\(518\) −36.0846 + 5.53393i −1.58547 + 0.243147i
\(519\) 16.2443 + 20.3698i 0.713048 + 0.894133i
\(520\) 6.58855 + 6.70992i 0.288927 + 0.294249i
\(521\) −16.0337 + 27.7712i −0.702449 + 1.21668i 0.265156 + 0.964206i \(0.414577\pi\)
−0.967604 + 0.252471i \(0.918757\pi\)
\(522\) −10.0902 42.3635i −0.441635 1.85420i
\(523\) −25.1238 27.0770i −1.09859 1.18400i −0.981617 0.190861i \(-0.938872\pi\)
−0.116971 0.993135i \(-0.537318\pi\)
\(524\) −1.81330 + 6.29763i −0.0792144 + 0.275113i
\(525\) −20.5817 16.6453i −0.898260 0.726460i
\(526\) −11.9494 + 7.04994i −0.521017 + 0.307392i
\(527\) 10.2046 26.0009i 0.444519 1.13262i
\(528\) 4.49540 + 16.7571i 0.195637 + 0.729258i
\(529\) 26.1242 + 8.05825i 1.13584 + 0.350359i
\(530\) −5.36482 33.4510i −0.233033 1.45302i
\(531\) 36.4391 + 8.31700i 1.58132 + 0.360927i
\(532\) −2.06371 + 1.22473i −0.0894732 + 0.0530989i
\(533\) −2.04559 + 0.466892i −0.0886043 + 0.0202234i
\(534\) 20.4665 + 50.7366i 0.885674 + 2.19559i
\(535\) 1.49433 + 3.80750i 0.0646057 + 0.164613i
\(536\) −11.8987 + 22.0245i −0.513946 + 0.951315i
\(537\) −39.5246 26.9474i −1.70561 1.16287i
\(538\) 3.14099 + 37.2049i 0.135417 + 1.60402i
\(539\) −5.01991 10.8000i −0.216223 0.465188i
\(540\) 7.49564 1.27471i 0.322561 0.0548548i
\(541\) 8.35485 12.2543i 0.359203 0.526854i −0.603518 0.797349i \(-0.706235\pi\)
0.962721 + 0.270495i \(0.0871873\pi\)
\(542\) −5.71754 4.47209i −0.245590 0.192093i
\(543\) −17.1800 43.7739i −0.737264 1.87852i
\(544\) 11.9975 10.5295i 0.514390 0.451447i
\(545\) −7.48812 32.8076i −0.320756 1.40532i
\(546\) 10.3437 2.38893i 0.442671 0.102237i
\(547\) 3.08921 + 0.705092i 0.132085 + 0.0301475i 0.288052 0.957615i \(-0.406992\pi\)
−0.155967 + 0.987762i \(0.549849\pi\)
\(548\) 6.80972 + 27.4406i 0.290897 + 1.17220i
\(549\) −7.26227 + 23.5437i −0.309946 + 1.00482i
\(550\) 9.44226 0.0889909i 0.402619 0.00379459i
\(551\) −1.45808 + 3.71513i −0.0621164 + 0.158270i
\(552\) −33.0153 39.0803i −1.40523 1.66337i
\(553\) 26.3665 + 0.180610i 1.12122 + 0.00768030i
\(554\) 2.22813 5.83838i 0.0946641 0.248049i
\(555\) −50.5412 54.4704i −2.14535 2.31214i
\(556\) −1.32829 4.03461i −0.0563322 0.171106i
\(557\) 39.2613 + 22.6675i 1.66356 + 0.960454i 0.970997 + 0.239092i \(0.0768498\pi\)
0.692558 + 0.721362i \(0.256484\pi\)
\(558\) 27.9732 + 40.2097i 1.18420 + 1.70221i
\(559\) 2.33261 + 2.92500i 0.0986590 + 0.123714i
\(560\) 20.7790 23.8280i 0.878071 1.00692i
\(561\) 7.63119 9.56921i 0.322189 0.404012i
\(562\) −16.2432 1.06342i −0.685178 0.0448577i
\(563\) 17.0286 + 24.9764i 0.717670 + 1.05263i 0.995752 + 0.0920717i \(0.0293489\pi\)
−0.278082 + 0.960557i \(0.589699\pi\)
\(564\) −12.1225 12.5809i −0.510451 0.529750i
\(565\) −2.58495 + 17.1501i −0.108750 + 0.721508i
\(566\) 28.6588 + 19.1461i 1.20462 + 0.804772i
\(567\) −7.13326 + 17.8155i −0.299569 + 0.748179i
\(568\) 2.16211 + 1.62640i 0.0907202 + 0.0682422i
\(569\) 4.19555 + 7.26691i 0.175887 + 0.304645i 0.940468 0.339883i \(-0.110387\pi\)
−0.764581 + 0.644528i \(0.777054\pi\)
\(570\) −4.42060 2.07776i −0.185159 0.0870277i
\(571\) 3.65829 + 24.2712i 0.153095 + 1.01572i 0.924996 + 0.379976i \(0.124068\pi\)
−0.771902 + 0.635742i \(0.780694\pi\)
\(572\) −2.30495 + 3.00480i −0.0963748 + 0.125637i
\(573\) 12.0972 25.1200i 0.505366 1.04940i
\(574\) 2.09658 + 6.73532i 0.0875095 + 0.281127i
\(575\) −25.0866 + 12.0810i −1.04618 + 0.503815i
\(576\) 3.66627 + 27.7523i 0.152761 + 1.15634i
\(577\) −0.375051 + 5.00470i −0.0156136 + 0.208349i 0.983941 + 0.178495i \(0.0571230\pi\)
−0.999554 + 0.0298531i \(0.990496\pi\)
\(578\) 12.4863 + 2.72637i 0.519362 + 0.113402i
\(579\) 16.4476 1.23258i 0.683538 0.0512241i
\(580\) 2.94032 52.4970i 0.122090 2.17982i
\(581\) 3.47831 + 5.17759i 0.144305 + 0.214803i
\(582\) 31.2680 9.96857i 1.29610 0.413210i
\(583\) 13.0371 4.02142i 0.539943 0.166550i
\(584\) 14.4924 + 20.0163i 0.599701 + 0.828282i
\(585\) 8.52824 + 7.91305i 0.352599 + 0.327164i
\(586\) 6.07010 10.7464i 0.250754 0.443928i
\(587\) 28.9817i 1.19620i −0.801420 0.598102i \(-0.795922\pi\)
0.801420 0.598102i \(-0.204078\pi\)
\(588\) −10.6955 34.0506i −0.441077 1.40422i
\(589\) 4.48904i 0.184968i
\(590\) 39.2920 + 22.1942i 1.61763 + 0.913720i
\(591\) 31.7527 + 29.4622i 1.30613 + 1.21191i
\(592\) 29.5738 25.4657i 1.21548 1.04663i
\(593\) 2.49494 0.769586i 0.102455 0.0316031i −0.243104 0.970000i \(-0.578166\pi\)
0.345559 + 0.938397i \(0.387689\pi\)
\(594\) 0.930052 + 2.91725i 0.0381605 + 0.119696i
\(595\) −22.2292 1.81905i −0.911309 0.0745739i
\(596\) −19.9011 1.11465i −0.815183 0.0456578i
\(597\) −10.7976 + 0.809170i −0.441918 + 0.0331171i
\(598\) 2.38217 10.9099i 0.0974142 0.446140i
\(599\) 0.504370 6.73036i 0.0206080 0.274995i −0.977375 0.211514i \(-0.932161\pi\)
0.997983 0.0634811i \(-0.0202203\pi\)
\(600\) 28.0899 + 3.42486i 1.14676 + 0.139819i
\(601\) −25.9707 + 12.5068i −1.05937 + 0.510164i −0.880665 0.473739i \(-0.842904\pi\)
−0.178701 + 0.983903i \(0.557190\pi\)
\(602\) 9.19821 8.57886i 0.374891 0.349648i
\(603\) −13.4372 + 27.9027i −0.547206 + 1.13629i
\(604\) 15.5803 20.3109i 0.633952 0.826437i
\(605\) −3.60886 23.9433i −0.146721 0.973432i
\(606\) −4.00036 + 8.51110i −0.162503 + 0.345740i
\(607\) 3.63926 + 6.30338i 0.147713 + 0.255846i 0.930382 0.366592i \(-0.119475\pi\)
−0.782669 + 0.622438i \(0.786142\pi\)
\(608\) 1.17665 2.27971i 0.0477194 0.0924543i
\(609\) −48.8129 33.7721i −1.97800 1.36852i
\(610\) −16.5250 + 24.7354i −0.669079 + 1.00151i
\(611\) 0.568376 3.77093i 0.0229940 0.152555i
\(612\) 14.2208 13.7027i 0.574840 0.553899i
\(613\) −26.2621 38.5194i −1.06072 1.55578i −0.808844 0.588024i \(-0.799906\pi\)
−0.251872 0.967761i \(-0.581046\pi\)
\(614\) −0.346448 + 5.29182i −0.0139815 + 0.213561i
\(615\) −8.95213 + 11.2256i −0.360985 + 0.452661i
\(616\) 10.6708 + 6.94516i 0.429940 + 0.279828i
\(617\) −20.2298 25.3674i −0.814422 1.02125i −0.999259 0.0384840i \(-0.987747\pi\)
0.184837 0.982769i \(-0.440824\pi\)
\(618\) −18.6361 + 12.9648i −0.749653 + 0.521521i
\(619\) −10.0066 5.77731i −0.402199 0.232210i 0.285233 0.958458i \(-0.407929\pi\)
−0.687432 + 0.726248i \(0.741262\pi\)
\(620\) 18.4940 + 56.1744i 0.742737 + 2.25602i
\(621\) −6.14115 6.61858i −0.246436 0.265595i
\(622\) 31.9447 + 12.1912i 1.28087 + 0.488823i
\(623\) 36.0520 + 17.6670i 1.44439 + 0.707811i
\(624\) −8.02256 + 8.02735i −0.321160 + 0.321351i
\(625\) −10.6756 + 27.2010i −0.427024 + 1.08804i
\(626\) −0.246096 26.1117i −0.00983598 1.04363i
\(627\) 0.579803 1.87967i 0.0231551 0.0750669i
\(628\) −11.7758 + 2.92232i −0.469907 + 0.116613i
\(629\) −26.8418 6.12647i −1.07025 0.244279i
\(630\) 24.3077 30.6424i 0.968442 1.22082i
\(631\) 8.94465 + 39.1891i 0.356081 + 1.56009i 0.762859 + 0.646565i \(0.223795\pi\)
−0.406778 + 0.913527i \(0.633348\pi\)
\(632\) −24.0030 + 14.7783i −0.954788 + 0.587848i
\(633\) −18.1105 46.1449i −0.719829 1.83409i
\(634\) 13.4245 17.1632i 0.533155 0.681636i
\(635\) −30.5442 + 44.8001i −1.21211 + 1.77784i
\(636\) 40.3075 6.85471i 1.59830 0.271807i
\(637\) 4.47633 6.37611i 0.177359 0.252631i
\(638\) 21.0992 1.78128i 0.835327 0.0705217i
\(639\) 2.76553 + 1.88551i 0.109403 + 0.0745895i
\(640\) −5.33224 + 33.3751i −0.210775 + 1.31927i
\(641\) 4.91803 + 12.5309i 0.194251 + 0.494942i 0.994501 0.104723i \(-0.0333956\pi\)
−0.800251 + 0.599665i \(0.795300\pi\)
\(642\) −4.57788 + 1.84666i −0.180674 + 0.0728819i
\(643\) −6.09394 + 1.39090i −0.240322 + 0.0548518i −0.340985 0.940069i \(-0.610761\pi\)
0.100664 + 0.994921i \(0.467903\pi\)
\(644\) −37.1883 5.14967i −1.46542 0.202925i
\(645\) 24.9596 + 5.69686i 0.982782 + 0.224314i
\(646\) −1.78700 + 0.286595i −0.0703084 + 0.0112759i
\(647\) 28.9299 + 8.92369i 1.13735 + 0.350827i 0.805553 0.592524i \(-0.201868\pi\)
0.331799 + 0.943350i \(0.392345\pi\)
\(648\) −3.62994 20.1918i −0.142597 0.793208i
\(649\) −6.63940 + 16.9169i −0.260619 + 0.664047i
\(650\) 3.13868 + 5.31992i 0.123109 + 0.208664i
\(651\) 64.9867 + 15.3019i 2.54703 + 0.599728i
\(652\) −13.4100 + 46.5733i −0.525177 + 1.82395i
\(653\) 28.0391 + 30.2190i 1.09726 + 1.18256i 0.981932 + 0.189232i \(0.0605999\pi\)
0.115323 + 0.993328i \(0.463210\pi\)
\(654\) 39.5069 9.40978i 1.54484 0.367951i
\(655\) −4.89445 + 8.47743i −0.191242 + 0.331241i
\(656\) −5.71744 4.91729i −0.223228 0.191988i
\(657\) 19.0615 + 23.9024i 0.743661 + 0.932522i
\(658\) −12.7876 0.925194i −0.498511 0.0360678i
\(659\) 2.67152 + 2.13046i 0.104067 + 0.0829910i 0.674141 0.738603i \(-0.264514\pi\)
−0.570074 + 0.821594i \(0.693085\pi\)
\(660\) 0.488440 + 25.9103i 0.0190125 + 1.00856i
\(661\) 3.70330 + 5.43175i 0.144042 + 0.211271i 0.891479 0.453062i \(-0.149668\pi\)
−0.747437 + 0.664332i \(0.768716\pi\)
\(662\) −9.04672 11.1275i −0.351611 0.432481i
\(663\) 7.91687 + 1.19328i 0.307466 + 0.0463430i
\(664\) −6.08718 2.72220i −0.236228 0.105642i
\(665\) −3.43241 + 1.03306i −0.133103 + 0.0400605i
\(666\) 35.0822 33.1723i 1.35941 1.28540i
\(667\) −54.0724 + 31.2187i −2.09369 + 1.20879i
\(668\) 16.1093 43.4358i 0.623287 1.68058i
\(669\) 1.60716 + 10.6628i 0.0621365 + 0.412249i
\(670\) −25.1735 + 27.6486i −0.972536 + 1.06816i
\(671\) −10.7933 5.19780i −0.416672 0.200659i
\(672\) 28.9919 + 24.8049i 1.11839 + 0.956871i
\(673\) −11.4440 + 5.51114i −0.441134 + 0.212439i −0.641248 0.767334i \(-0.721583\pi\)
0.200114 + 0.979773i \(0.435869\pi\)
\(674\) 2.07965 6.97478i 0.0801053 0.268659i
\(675\) 4.98015 + 0.373211i 0.191686 + 0.0143649i
\(676\) 23.3220 + 3.06686i 0.896999 + 0.117956i
\(677\) 42.1104 3.15574i 1.61843 0.121285i 0.765546 0.643381i \(-0.222469\pi\)
0.852887 + 0.522096i \(0.174850\pi\)
\(678\) −20.7260 2.92445i −0.795978 0.112313i
\(679\) 12.1845 20.7742i 0.467597 0.797240i
\(680\) 21.1812 10.9485i 0.812261 0.419854i
\(681\) −68.0481 + 20.9901i −2.60761 + 0.804341i
\(682\) −21.3596 + 10.5354i −0.817903 + 0.403421i
\(683\) 6.68451 7.20419i 0.255776 0.275661i −0.592090 0.805872i \(-0.701697\pi\)
0.847866 + 0.530211i \(0.177887\pi\)
\(684\) 1.32294 2.88498i 0.0505837 0.110310i
\(685\) 42.2310i 1.61356i
\(686\) −22.5355 13.3473i −0.860409 0.509603i
\(687\) −39.0848 −1.49118
\(688\) −3.47630 + 12.9892i −0.132533 + 0.495209i
\(689\) 6.54217 + 6.07024i 0.249237 + 0.231258i
\(690\) −33.8032 68.5332i −1.28687 2.60902i
\(691\) −7.87113 25.5176i −0.299432 0.970734i −0.972843 0.231466i \(-0.925648\pi\)
0.673411 0.739268i \(-0.264828\pi\)
\(692\) −18.8826 + 7.82474i −0.717810 + 0.297452i
\(693\) 13.5867 + 7.96887i 0.516116 + 0.302712i
\(694\) −33.3608 4.70723i −1.26636 0.178684i
\(695\) −0.474138 6.32693i −0.0179851 0.239994i
\(696\) 63.3866 + 2.95128i 2.40266 + 0.111868i
\(697\) −0.397563 + 5.30511i −0.0150588 + 0.200946i
\(698\) 23.9906 + 7.15321i 0.908056 + 0.270753i
\(699\) −18.6098 38.6437i −0.703889 1.46164i
\(700\) 17.0163 11.9031i 0.643156 0.449895i
\(701\) 14.4361 29.9769i 0.545244 1.13221i −0.428284 0.903644i \(-0.640882\pi\)
0.973528 0.228567i \(-0.0734039\pi\)
\(702\) −1.34843 + 1.48101i −0.0508932 + 0.0558973i
\(703\) −4.37540 + 0.659485i −0.165021 + 0.0248730i
\(704\) −13.6087 0.248428i −0.512899 0.00936297i
\(705\) −13.0481 22.6000i −0.491420 0.851165i
\(706\) 7.72069 + 8.16523i 0.290572 + 0.307302i
\(707\) 1.98898 + 6.60851i 0.0748035 + 0.248539i
\(708\) −26.3369 + 47.6699i −0.989803 + 1.79154i
\(709\) −5.79027 + 38.4159i −0.217458 + 1.44274i 0.567593 + 0.823309i \(0.307875\pi\)
−0.785051 + 0.619431i \(0.787364\pi\)
\(710\) 2.54933 + 3.13567i 0.0956747 + 0.117680i
\(711\) −28.8127 + 19.6442i −1.08056 + 0.736714i
\(712\) −42.6923 + 4.41608i −1.59996 + 0.165500i
\(713\) 43.7869 54.9071i 1.63983 2.05629i
\(714\) 1.94240 26.8468i 0.0726924 1.00472i
\(715\) −4.42255 + 3.52687i −0.165394 + 0.131897i
\(716\) 28.8949 23.9476i 1.07985 0.894964i
\(717\) 30.3390 + 17.5162i 1.13303 + 0.654155i
\(718\) −9.88012 + 2.35325i −0.368723 + 0.0878226i
\(719\) 27.5368 25.5504i 1.02695 0.952869i 0.0280416 0.999607i \(-0.491073\pi\)
0.998907 + 0.0467375i \(0.0148824\pi\)
\(720\) −4.66924 + 41.5519i −0.174012 + 1.54855i
\(721\) −3.81835 + 16.2164i −0.142203 + 0.603932i
\(722\) 22.8920 13.5059i 0.851952 0.502639i
\(723\) 14.5512 + 5.71091i 0.541164 + 0.212391i
\(724\) 36.7298 3.44979i 1.36505 0.128210i
\(725\) 10.1797 33.0018i 0.378065 1.22566i
\(726\) 28.8536 4.62749i 1.07086 0.171742i
\(727\) −3.67808 + 16.1147i −0.136412 + 0.597662i 0.859794 + 0.510641i \(0.170592\pi\)
−0.996206 + 0.0870208i \(0.972265\pi\)
\(728\) −0.444329 + 8.31656i −0.0164679 + 0.308232i
\(729\) −7.81342 34.2328i −0.289386 1.26788i
\(730\) 13.8087 + 34.2319i 0.511085 + 1.26698i
\(731\) 8.83017 3.46559i 0.326596 0.128179i
\(732\) −30.0386 19.6610i −1.11026 0.726691i
\(733\) −17.3068 + 25.3845i −0.639242 + 0.937596i 0.360745 + 0.932664i \(0.382522\pi\)
−0.999988 + 0.00493206i \(0.998430\pi\)
\(734\) −29.7748 + 2.51371i −1.09901 + 0.0927828i
\(735\) −3.25529 53.2117i −0.120073 1.96274i
\(736\) 36.6287 16.4067i 1.35015 0.604758i
\(737\) −12.4416 8.48255i −0.458293 0.312459i
\(738\) −7.34858 5.74784i −0.270505 0.211581i
\(739\) −34.6686 + 13.6064i −1.27531 + 0.500521i −0.903818 0.427917i \(-0.859248\pi\)
−0.371488 + 0.928438i \(0.621152\pi\)
\(740\) 52.0354 26.2784i 1.91286 0.966014i
\(741\) 1.25447 0.286324i 0.0460840 0.0105184i
\(742\) 18.6469 23.5063i 0.684548 0.862944i
\(743\) −4.48591 + 19.6541i −0.164572 + 0.721038i 0.823534 + 0.567266i \(0.191999\pi\)
−0.988106 + 0.153771i \(0.950858\pi\)
\(744\) −67.5807 + 22.9574i −2.47763 + 0.841659i
\(745\) −28.4500 8.77567i −1.04233 0.321516i
\(746\) −20.7482 + 0.195547i −0.759647 + 0.00715949i
\(747\) −7.67920 3.01386i −0.280967 0.110271i
\(748\) 5.55760 + 7.83023i 0.203206 + 0.286301i
\(749\) −1.59406 + 3.25291i −0.0582456 + 0.118859i
\(750\) −10.8227 4.13033i −0.395190 0.150818i
\(751\) 21.9514 20.3679i 0.801018 0.743236i −0.169171 0.985587i \(-0.554109\pi\)
0.970189 + 0.242351i \(0.0779186\pi\)
\(752\) 12.1160 6.40810i 0.441824 0.233679i
\(753\) −13.4168 + 23.2387i −0.488937 + 0.846864i
\(754\) 7.90999 + 11.3701i 0.288065 + 0.414075i
\(755\) 29.8941 23.8398i 1.08796 0.867618i
\(756\) 5.31467 + 4.13496i 0.193293 + 0.150387i
\(757\) 33.0262 + 26.3375i 1.20036 + 0.957253i 0.999749 0.0224180i \(-0.00713647\pi\)
0.200609 + 0.979671i \(0.435708\pi\)
\(758\) 2.42559 37.0496i 0.0881014 1.34570i
\(759\) 25.4265 17.3355i 0.922923 0.629238i
\(760\) 2.52597 2.88161i 0.0916265 0.104527i
\(761\) 10.5215 + 1.58586i 0.381403 + 0.0574873i 0.336946 0.941524i \(-0.390606\pi\)
0.0444573 + 0.999011i \(0.485844\pi\)
\(762\) −54.4120 36.3511i −1.97114 1.31686i
\(763\) 16.9569 24.5088i 0.613881 0.887279i
\(764\) 16.3117 + 14.5727i 0.590137 + 0.527220i
\(765\) 25.5459 14.7489i 0.923612 0.533248i
\(766\) 5.66129 12.0449i 0.204551 0.435199i
\(767\) −11.7550 + 1.77177i −0.424447 + 0.0639751i
\(768\) −40.3376 6.05533i −1.45556 0.218503i
\(769\) 31.8710 + 15.3483i 1.14930 + 0.553473i 0.908823 0.417183i \(-0.136983\pi\)
0.240475 + 0.970655i \(0.422697\pi\)
\(770\) 12.9711 + 13.9075i 0.467446 + 0.501192i
\(771\) −9.36278 19.4420i −0.337192 0.700187i
\(772\) −2.64104 + 12.6671i −0.0950531 + 0.455901i
\(773\) −26.5411 1.98898i −0.954617 0.0715386i −0.411695 0.911322i \(-0.635063\pi\)
−0.542922 + 0.839783i \(0.682682\pi\)
\(774\) −3.54864 + 16.2522i −0.127553 + 0.584172i
\(775\) 2.90295 + 38.7371i 0.104277 + 1.39148i
\(776\) 0.727849 + 25.7364i 0.0261283 + 0.923881i
\(777\) 5.36730 65.5896i 0.192551 2.35301i
\(778\) 16.4482 5.24385i 0.589695 0.188001i
\(779\) 0.252016 + 0.817016i 0.00902941 + 0.0292726i
\(780\) −14.5184 + 8.75115i −0.519843 + 0.313341i
\(781\) −1.10695 + 1.19301i −0.0396097 + 0.0426891i
\(782\) −24.6529 13.9252i −0.881586 0.497966i
\(783\) 11.1988 0.400214
\(784\) 27.9919 0.671884i 0.999712 0.0239959i
\(785\) −18.1230 −0.646838
\(786\) −10.2862 5.81018i −0.366896 0.207242i
\(787\) 18.0461 19.4491i 0.643274 0.693285i −0.324276 0.945962i \(-0.605121\pi\)
0.967550 + 0.252678i \(0.0813113\pi\)
\(788\) −29.1036 + 17.5426i −1.03677 + 0.624928i
\(789\) −7.37188 23.8990i −0.262446 0.850828i
\(790\) −40.1143 + 12.7889i −1.42720 + 0.455007i
\(791\) −12.7503 + 8.56566i −0.453348 + 0.304560i
\(792\) −16.8320 + 0.476026i −0.598101 + 0.0169149i
\(793\) −0.585612 7.81445i −0.0207957 0.277499i
\(794\) 3.59264 16.4537i 0.127498 0.583919i
\(795\) 60.9007 + 4.56387i 2.15992 + 0.161864i
\(796\) 1.73381 8.31583i 0.0614533 0.294747i
\(797\) 19.4781 + 40.4467i 0.689950 + 1.43270i 0.891409 + 0.453199i \(0.149717\pi\)
−0.201459 + 0.979497i \(0.564568\pi\)
\(798\) −1.28574 4.13047i −0.0455146 0.146217i
\(799\) −8.71166 4.19532i −0.308197 0.148420i
\(800\) −8.67939 + 20.4331i −0.306863 + 0.722420i
\(801\) −52.5053 + 7.91389i −1.85518 + 0.279624i
\(802\) 4.00974 8.53107i 0.141589 0.301242i
\(803\) −12.8734 + 7.43248i −0.454293 + 0.262286i
\(804\) −33.6526 30.0648i −1.18683 1.06030i
\(805\) −52.0598 20.8446i −1.83487 0.734677i
\(806\) −12.9543 8.65442i −0.456297 0.304839i
\(807\) −66.5546 10.0315i −2.34283 0.353125i
\(808\) −5.54804 4.86331i −0.195179 0.171091i
\(809\) −7.22359 + 4.92496i −0.253968 + 0.173152i −0.683611 0.729846i \(-0.739592\pi\)
0.429643 + 0.902999i \(0.358639\pi\)
\(810\) 2.00192 30.5783i 0.0703403 1.07441i
\(811\) −31.1595 24.8488i −1.09416 0.872561i −0.101658 0.994819i \(-0.532415\pi\)
−0.992498 + 0.122259i \(0.960986\pi\)
\(812\) 36.0561 29.4684i 1.26532 1.03414i
\(813\) 10.2304 8.15844i 0.358794 0.286129i
\(814\) 13.4066 + 19.2712i 0.469902 + 0.675454i
\(815\) −36.1962 + 62.6937i −1.26790 + 2.19607i
\(816\) 13.4535 + 25.4368i 0.470965 + 0.890467i
\(817\) 1.11755 1.03694i 0.0390983 0.0362779i
\(818\) −11.3081 4.31558i −0.395380 0.150891i
\(819\) −0.0705767 + 10.3032i −0.00246615 + 0.360023i
\(820\) −6.51960 9.18562i −0.227674 0.320776i
\(821\) −22.2867 8.74688i −0.777811 0.305268i −0.0569762 0.998376i \(-0.518146\pi\)
−0.720834 + 0.693107i \(0.756241\pi\)
\(822\) −50.9642 + 0.480325i −1.77758 + 0.0167533i
\(823\) −0.467640 0.144248i −0.0163009 0.00502817i 0.286594 0.958052i \(-0.407477\pi\)
−0.302895 + 0.953024i \(0.597953\pi\)
\(824\) −5.72867 16.8637i −0.199568 0.587476i
\(825\) −3.78774 + 16.5952i −0.131872 + 0.577769i
\(826\) 8.99364 + 38.9413i 0.312929 + 1.35494i
\(827\) 18.5054 4.22373i 0.643494 0.146873i 0.111693 0.993743i \(-0.464373\pi\)
0.531801 + 0.846869i \(0.321515\pi\)
\(828\) 44.3219 22.3830i 1.54029 0.777864i
\(829\) −20.8028 + 8.16451i −0.722512 + 0.283565i −0.697963 0.716134i \(-0.745910\pi\)
−0.0245488 + 0.999699i \(0.507815\pi\)
\(830\) −7.84534 6.13639i −0.272316 0.212997i
\(831\) 9.30759 + 6.34581i 0.322877 + 0.220134i
\(832\) −4.31025 7.79059i −0.149431 0.270090i
\(833\) −12.1030 15.6107i −0.419345 0.540880i
\(834\) 7.62992 0.644148i 0.264202 0.0223050i
\(835\) 38.9807 57.1741i 1.34898 1.97859i
\(836\) 1.29120 + 0.845124i 0.0446572 + 0.0292292i
\(837\) −11.7256 + 4.60194i −0.405295 + 0.159066i
\(838\) −15.3419 38.0326i −0.529977 1.31381i
\(839\) −0.776633 3.40265i −0.0268123 0.117473i 0.959751 0.280853i \(-0.0906173\pi\)
−0.986563 + 0.163380i \(0.947760\pi\)
\(840\) 33.1061 + 46.3905i 1.14227 + 1.60062i
\(841\) 10.7798 47.2294i 0.371717 1.62860i
\(842\) 14.4270 2.31379i 0.497189 0.0797383i
\(843\) 8.64920 28.0400i 0.297894 0.965750i
\(844\) 38.7192 3.63664i 1.33277 0.125178i
\(845\) 32.7070 + 12.8365i 1.12515 + 0.441590i
\(846\) 14.6043 8.61630i 0.502105 0.296235i
\(847\) 13.4851 16.6741i 0.463352 0.572930i
\(848\) −3.58186 + 31.8752i −0.123001 + 1.09460i
\(849\) −45.5448 + 42.2594i −1.56310 + 1.45034i
\(850\) 15.2351 3.62871i 0.522561 0.124464i
\(851\) −59.9499 34.6121i −2.05505 1.18649i
\(852\) −3.75512 + 3.11219i −0.128648 + 0.106622i
\(853\) 16.1767 12.9005i 0.553881 0.441706i −0.306123 0.951992i \(-0.599032\pi\)
0.860005 + 0.510286i \(0.170461\pi\)
\(854\) −26.0412 + 3.99368i −0.891113 + 0.136661i
\(855\) 2.95580 3.70646i 0.101086 0.126758i
\(856\) −0.398455 3.85205i −0.0136189 0.131660i
\(857\) 17.7054 12.0713i 0.604804 0.412348i −0.221833 0.975085i \(-0.571204\pi\)
0.826636 + 0.562737i \(0.190251\pi\)
\(858\) −4.30651 5.29700i −0.147022 0.180837i
\(859\) −7.36698 + 48.8767i −0.251358 + 1.66765i 0.405847 + 0.913941i \(0.366976\pi\)
−0.657205 + 0.753711i \(0.728262\pi\)
\(860\) −9.71273 + 17.5801i −0.331201 + 0.599475i
\(861\) −12.6868 + 0.863396i −0.432365 + 0.0294245i
\(862\) −0.436312 0.461433i −0.0148608 0.0157165i
\(863\) 6.01086 + 10.4111i 0.204612 + 0.354398i 0.950009 0.312222i \(-0.101073\pi\)
−0.745397 + 0.666621i \(0.767740\pi\)
\(864\) −7.16093 0.736412i −0.243620 0.0250533i
\(865\) −30.1896 + 4.55034i −1.02648 + 0.154716i
\(866\) 18.0114 19.7823i 0.612051 0.672231i
\(867\) −9.99620 + 20.7573i −0.339489 + 0.704956i
\(868\) −25.6425 + 45.6710i −0.870362 + 1.55017i
\(869\) −7.35676 15.2765i −0.249561 0.518219i
\(870\) 90.8310 + 27.0829i 3.07946 + 0.918195i
\(871\) 0.736097 9.82253i 0.0249417 0.332824i
\(872\) −1.48183 + 31.8263i −0.0501811 + 1.07777i
\(873\) 2.38033 + 31.7632i 0.0805618 + 1.07502i
\(874\) −4.50583 0.635776i −0.152412 0.0215054i
\(875\) −7.93439 + 3.05146i −0.268231 + 0.103158i
\(876\) −41.1539 + 17.0537i −1.39046 + 0.576190i
\(877\) −3.38610 10.9775i −0.114340 0.370683i 0.880256 0.474499i \(-0.157371\pi\)
−0.994596 + 0.103816i \(0.966895\pi\)
\(878\) −0.960672 1.94768i −0.0324211 0.0657312i
\(879\) 16.3095 + 15.1330i 0.550107 + 0.510425i
\(880\) −19.6395 5.25611i −0.662046 0.177183i
\(881\) −24.7737 −0.834646 −0.417323 0.908758i \(-0.637032\pi\)
−0.417323 + 0.908758i \(0.637032\pi\)
\(882\) 34.5539 2.44095i 1.16349 0.0821910i
\(883\) 0.128370i 0.00432000i 0.999998 + 0.00216000i \(0.000687549\pi\)
−0.999998 + 0.00216000i \(0.999312\pi\)
\(884\) −2.61810 + 5.70939i −0.0880563 + 0.192028i
\(885\) −55.3311 + 59.6328i −1.85994 + 2.00453i
\(886\) −5.50901 + 2.71725i −0.185079 + 0.0912879i
\(887\) −20.8644 + 6.43583i −0.700560 + 0.216094i −0.624518 0.781011i \(-0.714704\pi\)
−0.0760419 + 0.997105i \(0.524228\pi\)
\(888\) 32.3045 + 62.4972i 1.08407 + 2.09727i
\(889\) −47.5326 + 6.83173i −1.59419 + 0.229129i
\(890\) −63.4805 8.95714i −2.12787 0.300244i
\(891\) 12.3061 0.922215i 0.412270 0.0308954i
\(892\) −8.38743 1.10295i −0.280832 0.0369296i
\(893\) −1.54964 0.116130i −0.0518568 0.00388613i
\(894\) 10.2669 34.4332i 0.343375 1.15162i
\(895\) 50.5050 24.3219i 1.68820 0.812992i
\(896\) −24.9933 + 16.4722i −0.834969 + 0.550297i
\(897\) 18.1367 + 8.73419i 0.605568 + 0.291626i
\(898\) 2.98885 3.28272i 0.0997391 0.109546i
\(899\) 12.9828 + 86.1350i 0.432999 + 2.87276i
\(900\) −9.55034 + 25.7508i −0.318345 + 0.858359i
\(901\) 19.5967 11.3141i 0.652860 0.376929i
\(902\) 3.29605 3.11660i 0.109746 0.103772i
\(903\) 11.2021 + 19.7132i 0.372782 + 0.656014i
\(904\) 6.70368 14.9902i 0.222961 0.498568i
\(905\) 54.4890 + 8.21289i 1.81127 + 0.273006i
\(906\) 29.1098 + 35.8050i 0.967107 + 1.18954i
\(907\) 1.33488 + 1.95790i 0.0443238 + 0.0650111i 0.847761 0.530378i \(-0.177950\pi\)
−0.803437 + 0.595389i \(0.796998\pi\)
\(908\) −1.05297 55.8568i −0.0349439 1.85367i
\(909\) −7.13613 5.69087i −0.236690 0.188754i
\(910\) −3.63616 + 11.8968i −0.120538 + 0.394376i
\(911\) 10.7552 + 13.4866i 0.356336 + 0.446832i 0.927398 0.374075i \(-0.122040\pi\)
−0.571062 + 0.820907i \(0.693468\pi\)
\(912\) 3.50625 + 3.01555i 0.116104 + 0.0998550i
\(913\) 2.00553 3.47369i 0.0663735 0.114962i
\(914\) 20.2057 4.81261i 0.668346 0.159187i
\(915\) −36.4741 39.3098i −1.20580 1.29954i
\(916\) 8.48411 29.4655i 0.280323 0.973567i
\(917\) −8.46511 + 1.87119i −0.279542 + 0.0617923i
\(918\) 2.58054 + 4.37390i 0.0851705 + 0.144360i
\(919\) −5.36391 + 13.6670i −0.176939 + 0.450833i −0.991638 0.129051i \(-0.958807\pi\)
0.814699 + 0.579884i \(0.196902\pi\)
\(920\) 59.0039 10.6073i 1.94530 0.349712i
\(921\) −9.13507 2.81779i −0.301011 0.0928495i
\(922\) 15.7917 2.53265i 0.520073 0.0834085i
\(923\) −1.03788 0.236890i −0.0341624 0.00779734i
\(924\) −16.6360 + 15.8116i −0.547284 + 0.520165i
\(925\) 37.3300 8.52034i 1.22740 0.280147i
\(926\) −35.0190 + 14.1262i −1.15080 + 0.464217i
\(927\) −8.04984 20.5107i −0.264392 0.673659i
\(928\) −15.9842 + 47.1457i −0.524707 + 1.54763i
\(929\) 8.17387 + 5.57285i 0.268176 + 0.182839i 0.689940 0.723866i \(-0.257637\pi\)
−0.421764 + 0.906705i \(0.638589\pi\)
\(930\) −106.232 + 8.96856i −3.48349 + 0.294091i
\(931\) −2.72727 1.62481i −0.0893827 0.0532510i
\(932\) 33.1726 5.64133i 1.08660 0.184788i
\(933\) −34.7211 + 50.9265i −1.13672 + 1.66726i
\(934\) 9.86003 12.6060i 0.322630 0.412481i
\(935\) 5.23990 + 13.3511i 0.171363 + 0.436626i
\(936\) −5.77490 9.37964i −0.188758 0.306583i
\(937\) 7.53217 + 33.0006i 0.246065 + 1.07808i 0.935387 + 0.353626i \(0.115052\pi\)
−0.689322 + 0.724456i \(0.742091\pi\)
\(938\) −33.1157 + 0.0852601i −1.08126 + 0.00278384i
\(939\) 45.8924 + 10.4746i 1.49764 + 0.341827i
\(940\) 19.8702 4.93103i 0.648093 0.160832i
\(941\) 1.43471 4.65122i 0.0467703 0.151625i −0.929176 0.369639i \(-0.879481\pi\)
0.975946 + 0.218013i \(0.0699576\pi\)
\(942\) −0.206127 21.8708i −0.00671597 0.712588i
\(943\) −4.88683 + 12.4514i −0.159137 + 0.405474i
\(944\) −30.2207 30.2027i −0.983601 0.983015i
\(945\) 6.21715 + 7.90656i 0.202244 + 0.257201i
\(946\) −7.55674 2.88392i −0.245691 0.0937642i
\(947\) −11.8807 12.8044i −0.386072 0.416087i 0.509874 0.860249i \(-0.329692\pi\)
−0.895946 + 0.444162i \(0.853501\pi\)
\(948\) −15.8898 48.2643i −0.516077 1.56755i
\(949\) −8.42098 4.86185i −0.273357 0.157822i
\(950\) 2.06619 1.43742i 0.0670362 0.0466360i
\(951\) 24.4903 + 30.7099i 0.794154 + 0.995837i
\(952\) 19.8178 + 7.29196i 0.642299 + 0.236334i
\(953\) −20.0429 + 25.1330i −0.649254 + 0.814139i −0.992126 0.125243i \(-0.960029\pi\)
0.342872 + 0.939382i \(0.388600\pi\)
\(954\) −2.59241 + 39.5977i −0.0839323 + 1.28202i
\(955\) 18.4046 + 26.9947i 0.595560 + 0.873526i
\(956\) −19.7909 + 19.0699i −0.640083 + 0.616765i
\(957\) −5.68896 + 37.7438i −0.183898 + 1.22008i
\(958\) −11.7312 + 17.5598i −0.379018 + 0.567331i
\(959\) −27.5909 + 25.2511i −0.890956 + 0.815401i
\(960\) −56.2996 23.2906i −1.81706 0.751701i
\(961\) −33.4889 58.0044i −1.08029 1.87111i
\(962\) −6.53221 + 13.8978i −0.210607 + 0.448084i
\(963\) −0.714057 4.73746i −0.0230102 0.152662i
\(964\) −7.46398 + 9.73025i −0.240399 + 0.313390i
\(965\) −8.38597 + 17.4136i −0.269954 + 0.560565i
\(966\) 24.5631 63.0627i 0.790305 2.02901i
\(967\) 18.7057 9.00818i 0.601534 0.289683i −0.108227 0.994126i \(-0.534517\pi\)
0.709761 + 0.704443i \(0.248803\pi\)
\(968\) −2.77462 + 22.7568i −0.0891797 + 0.731431i
\(969\) 0.243808 3.25339i 0.00783224 0.104514i
\(970\) −8.20388 + 37.5723i −0.263411 + 1.20637i
\(971\) −32.3348 + 2.42316i −1.03767 + 0.0777629i −0.582656 0.812719i \(-0.697986\pi\)
−0.455018 + 0.890482i \(0.650367\pi\)
\(972\) 44.5480 + 2.49510i 1.42888 + 0.0800305i
\(973\) 3.85009 4.09282i 0.123428 0.131210i
\(974\) 15.9354 + 49.9839i 0.510604 + 1.60159i
\(975\) −10.6400 + 3.28200i −0.340752 + 0.105108i
\(976\) 21.3426 18.3779i 0.683160 0.588261i
\(977\) −3.67636 3.41117i −0.117617 0.109133i 0.619172 0.785256i \(-0.287468\pi\)
−0.736789 + 0.676123i \(0.763659\pi\)
\(978\) −76.0702 42.9684i −2.43246 1.37398i
\(979\) 25.8176i 0.825134i
\(980\) 40.8221 + 9.09649i 1.30402 + 0.290577i
\(981\) 39.4163i 1.25847i
\(982\) 5.23019 9.25940i 0.166902 0.295479i
\(983\) 0.218784 + 0.203002i 0.00697812 + 0.00647475i 0.683654 0.729806i \(-0.260390\pi\)
−0.676676 + 0.736281i \(0.736580\pi\)
\(984\) 11.0110 7.97231i 0.351018 0.254148i
\(985\) −48.5033 + 14.9613i −1.54544 + 0.476706i
\(986\) 33.4597 10.6673i 1.06558 0.339717i
\(987\) 6.96347 22.0379i 0.221650 0.701475i
\(988\) −0.0564506 + 1.00788i −0.00179593 + 0.0320649i
\(989\) 23.7837 1.78234i 0.756278 0.0566752i
\(990\) −24.5730 5.36549i −0.780981 0.170526i
\(991\) −0.730632 + 9.74961i −0.0232093 + 0.309706i 0.973502 + 0.228677i \(0.0734399\pi\)
−0.996712 + 0.0810297i \(0.974179\pi\)
\(992\) −2.63758 55.9315i −0.0837432 1.77583i
\(993\) 23.2918 11.2167i 0.739142 0.355952i
\(994\) −0.524321 + 3.54047i −0.0166304 + 0.112297i
\(995\) 5.50529 11.4318i 0.174529 0.362414i
\(996\) 7.31613 9.53751i 0.231821 0.302208i
\(997\) −8.32188 55.2121i −0.263557 1.74858i −0.593731 0.804664i \(-0.702345\pi\)
0.330174 0.943920i \(-0.392893\pi\)
\(998\) −18.3418 8.62095i −0.580599 0.272891i
\(999\) 6.20805 + 10.7527i 0.196414 + 0.340199i
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 392.2.z.a.53.10 yes 648
8.5 even 2 inner 392.2.z.a.53.12 yes 648
49.37 even 21 inner 392.2.z.a.37.12 yes 648
392.37 even 42 inner 392.2.z.a.37.10 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
392.2.z.a.37.10 648 392.37 even 42 inner
392.2.z.a.37.12 yes 648 49.37 even 21 inner
392.2.z.a.53.10 yes 648 1.1 even 1 trivial
392.2.z.a.53.12 yes 648 8.5 even 2 inner