Properties

Label 525.2.z.b.64.2
Level $525$
Weight $2$
Character 525.64
Analytic conductor $4.192$
Analytic rank $0$
Dimension $72$
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] = [525,2,Mod(64,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.z (of order \(10\), degree \(4\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 64.2
Character \(\chi\) \(=\) 525.64
Dual form 525.2.z.b.484.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36398 - 1.87736i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.04600 + 3.21926i) q^{4} +(-1.94902 + 1.09605i) q^{5} +(0.717088 + 2.20697i) q^{6} +1.00000i q^{7} +(3.05649 - 0.993115i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\) \(q+(-1.36398 - 1.87736i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-1.04600 + 3.21926i) q^{4} +(-1.94902 + 1.09605i) q^{5} +(0.717088 + 2.20697i) q^{6} +1.00000i q^{7} +(3.05649 - 0.993115i) q^{8} +(0.809017 + 0.587785i) q^{9} +(4.71611 + 2.16402i) q^{10} +(-4.18719 + 3.04217i) q^{11} +(1.98961 - 2.73846i) q^{12} +(2.62561 - 3.61385i) q^{13} +(1.87736 - 1.36398i) q^{14} +(2.19233 - 0.440125i) q^{15} +(-0.556510 - 0.404328i) q^{16} +(2.52913 - 0.821764i) q^{17} -2.32054i q^{18} +(-0.867165 - 2.66886i) q^{19} +(-1.48979 - 7.42086i) q^{20} +(0.309017 - 0.951057i) q^{21} +(11.4225 + 3.71140i) q^{22} +(-0.553499 - 0.761825i) q^{23} -3.21379 q^{24} +(2.59735 - 4.27244i) q^{25} -10.3658 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-3.21926 - 1.04600i) q^{28} +(1.57767 - 4.85556i) q^{29} +(-3.81656 - 3.51546i) q^{30} +(1.74288 + 5.36403i) q^{31} -4.83131i q^{32} +(4.92234 - 1.59937i) q^{33} +(-4.99243 - 3.62721i) q^{34} +(-1.09605 - 1.94902i) q^{35} +(-2.73846 + 1.98961i) q^{36} +(4.39962 - 6.05555i) q^{37} +(-3.82761 + 5.26825i) q^{38} +(-3.61385 + 2.62561i) q^{39} +(-4.86866 + 5.28567i) q^{40} +(-1.27791 - 0.928456i) q^{41} +(-2.20697 + 0.717088i) q^{42} -0.000338608i q^{43} +(-5.41374 - 16.6618i) q^{44} +(-2.22103 - 0.258882i) q^{45} +(-0.675259 + 2.07823i) q^{46} +(8.04788 + 2.61492i) q^{47} +(0.404328 + 0.556510i) q^{48} -1.00000 q^{49} +(-11.5637 + 0.951368i) q^{50} -2.65928 q^{51} +(8.88752 + 12.2326i) q^{52} +(-5.52958 - 1.79667i) q^{53} +(-0.717088 + 2.20697i) q^{54} +(4.82655 - 10.5186i) q^{55} +(0.993115 + 3.05649i) q^{56} +2.80620i q^{57} +(-11.2676 + 3.66105i) q^{58} +(9.94650 + 7.22656i) q^{59} +(-0.876298 + 7.51803i) q^{60} +(-7.69704 + 5.59223i) q^{61} +(7.69296 - 10.5884i) q^{62} +(-0.587785 + 0.809017i) q^{63} +(-10.1831 + 7.39848i) q^{64} +(-1.15642 + 9.92126i) q^{65} +(-9.71657 - 7.05950i) q^{66} +(-1.64256 + 0.533701i) q^{67} +9.00148i q^{68} +(0.290991 + 0.895580i) q^{69} +(-2.16402 + 4.71611i) q^{70} +(4.05432 - 12.4779i) q^{71} +(3.05649 + 0.993115i) q^{72} +(-1.76480 - 2.42904i) q^{73} -17.3695 q^{74} +(-3.79049 + 3.26071i) q^{75} +9.49880 q^{76} +(-3.04217 - 4.18719i) q^{77} +(9.85845 + 3.20320i) q^{78} +(1.83100 - 5.63523i) q^{79} +(1.52781 + 0.178081i) q^{80} +(0.309017 + 0.951057i) q^{81} +3.66549i q^{82} +(8.07227 - 2.62284i) q^{83} +(2.73846 + 1.98961i) q^{84} +(-4.02863 + 4.37368i) q^{85} +(-0.000635689 + 0.000461855i) q^{86} +(-3.00090 + 4.13039i) q^{87} +(-9.77690 + 13.4568i) q^{88} +(14.8266 - 10.7722i) q^{89} +(2.54343 + 4.52279i) q^{90} +(3.61385 + 2.62561i) q^{91} +(3.03147 - 0.984985i) q^{92} -5.64007i q^{93} +(-6.06803 - 18.6755i) q^{94} +(4.61532 + 4.25120i) q^{95} +(-1.49296 + 4.59485i) q^{96} +(8.70890 + 2.82969i) q^{97} +(1.36398 + 1.87736i) q^{98} -5.17565 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 24 q^{4} - 2 q^{5} + 18 q^{9} - 28 q^{10} - 12 q^{11} - 20 q^{13} - 24 q^{16} + 10 q^{19} + 10 q^{20} - 18 q^{21} + 50 q^{22} - 10 q^{23} + 12 q^{25} + 36 q^{26} + 20 q^{28} - 2 q^{29} + 10 q^{30} - 16 q^{31} - 10 q^{33} + 24 q^{34} - 10 q^{35} - 24 q^{36} + 10 q^{37} - 100 q^{38} + 16 q^{39} - 14 q^{40} - 16 q^{41} - 18 q^{44} + 2 q^{45} - 44 q^{46} + 20 q^{47} - 72 q^{49} + 86 q^{50} + 32 q^{51} - 80 q^{52} + 70 q^{53} + 46 q^{55} - 40 q^{58} + 44 q^{59} - 62 q^{60} + 4 q^{61} - 50 q^{62} + 48 q^{64} + 38 q^{65} - 16 q^{66} - 20 q^{67} + 4 q^{69} + 10 q^{70} - 8 q^{71} - 20 q^{73} - 116 q^{74} - 8 q^{75} + 92 q^{76} + 20 q^{77} + 90 q^{78} + 28 q^{79} + 114 q^{80} - 18 q^{81} + 30 q^{83} + 24 q^{84} - 122 q^{85} + 40 q^{86} - 40 q^{87} - 270 q^{88} + 2 q^{89} - 12 q^{90} - 16 q^{91} - 100 q^{92} + 22 q^{94} + 116 q^{95} + 10 q^{96} + 190 q^{97} - 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36398 1.87736i −0.964481 1.32749i −0.944786 0.327688i \(-0.893730\pi\)
−0.0196950 0.999806i \(-0.506270\pi\)
\(3\) −0.951057 0.309017i −0.549093 0.178411i
\(4\) −1.04600 + 3.21926i −0.523000 + 1.60963i
\(5\) −1.94902 + 1.09605i −0.871628 + 0.490168i
\(6\) 0.717088 + 2.20697i 0.292750 + 0.900991i
\(7\) 1.00000i 0.377964i
\(8\) 3.05649 0.993115i 1.08063 0.351119i
\(9\) 0.809017 + 0.587785i 0.269672 + 0.195928i
\(10\) 4.71611 + 2.16402i 1.49136 + 0.684323i
\(11\) −4.18719 + 3.04217i −1.26249 + 0.917250i −0.998877 0.0473799i \(-0.984913\pi\)
−0.263609 + 0.964630i \(0.584913\pi\)
\(12\) 1.98961 2.73846i 0.574351 0.790527i
\(13\) 2.62561 3.61385i 0.728215 1.00230i −0.270996 0.962580i \(-0.587353\pi\)
0.999211 0.0397209i \(-0.0126469\pi\)
\(14\) 1.87736 1.36398i 0.501746 0.364540i
\(15\) 2.19233 0.440125i 0.566056 0.113640i
\(16\) −0.556510 0.404328i −0.139127 0.101082i
\(17\) 2.52913 0.821764i 0.613404 0.199307i 0.0141942 0.999899i \(-0.495482\pi\)
0.599209 + 0.800592i \(0.295482\pi\)
\(18\) 2.32054i 0.546958i
\(19\) −0.867165 2.66886i −0.198941 0.612278i −0.999908 0.0135692i \(-0.995681\pi\)
0.800967 0.598709i \(-0.204319\pi\)
\(20\) −1.48979 7.42086i −0.333127 1.65936i
\(21\) 0.309017 0.951057i 0.0674330 0.207538i
\(22\) 11.4225 + 3.71140i 2.43529 + 0.791273i
\(23\) −0.553499 0.761825i −0.115412 0.158852i 0.747402 0.664372i \(-0.231301\pi\)
−0.862815 + 0.505520i \(0.831301\pi\)
\(24\) −3.21379 −0.656012
\(25\) 2.59735 4.27244i 0.519471 0.854488i
\(26\) −10.3658 −2.03290
\(27\) −0.587785 0.809017i −0.113119 0.155695i
\(28\) −3.21926 1.04600i −0.608383 0.197675i
\(29\) 1.57767 4.85556i 0.292966 0.901655i −0.690932 0.722920i \(-0.742799\pi\)
0.983897 0.178735i \(-0.0572005\pi\)
\(30\) −3.81656 3.51546i −0.696806 0.641833i
\(31\) 1.74288 + 5.36403i 0.313030 + 0.963408i 0.976558 + 0.215256i \(0.0690585\pi\)
−0.663528 + 0.748152i \(0.730941\pi\)
\(32\) 4.83131i 0.854063i
\(33\) 4.92234 1.59937i 0.856869 0.278414i
\(34\) −4.99243 3.62721i −0.856195 0.622062i
\(35\) −1.09605 1.94902i −0.185266 0.329444i
\(36\) −2.73846 + 1.98961i −0.456411 + 0.331602i
\(37\) 4.39962 6.05555i 0.723293 0.995527i −0.276116 0.961124i \(-0.589047\pi\)
0.999408 0.0344023i \(-0.0109528\pi\)
\(38\) −3.82761 + 5.26825i −0.620921 + 0.854624i
\(39\) −3.61385 + 2.62561i −0.578679 + 0.420435i
\(40\) −4.86866 + 5.28567i −0.769803 + 0.835738i
\(41\) −1.27791 0.928456i −0.199576 0.145000i 0.483509 0.875339i \(-0.339362\pi\)
−0.683085 + 0.730339i \(0.739362\pi\)
\(42\) −2.20697 + 0.717088i −0.340543 + 0.110649i
\(43\) 0 0.000338608i 0 5.16372e-5i −1.00000 2.58186e-5i \(-0.999992\pi\)
1.00000 2.58186e-5i \(-8.21831e-6\pi\)
\(44\) −5.41374 16.6618i −0.816151 2.51186i
\(45\) −2.22103 0.258882i −0.331092 0.0385919i
\(46\) −0.675259 + 2.07823i −0.0995615 + 0.306419i
\(47\) 8.04788 + 2.61492i 1.17390 + 0.381425i 0.830099 0.557616i \(-0.188284\pi\)
0.343806 + 0.939041i \(0.388284\pi\)
\(48\) 0.404328 + 0.556510i 0.0583597 + 0.0803253i
\(49\) −1.00000 −0.142857
\(50\) −11.5637 + 0.951368i −1.63535 + 0.134544i
\(51\) −2.65928 −0.372374
\(52\) 8.88752 + 12.2326i 1.23248 + 1.69636i
\(53\) −5.52958 1.79667i −0.759546 0.246791i −0.0964621 0.995337i \(-0.530753\pi\)
−0.663084 + 0.748545i \(0.730753\pi\)
\(54\) −0.717088 + 2.20697i −0.0975833 + 0.300330i
\(55\) 4.82655 10.5186i 0.650811 1.41833i
\(56\) 0.993115 + 3.05649i 0.132711 + 0.408441i
\(57\) 2.80620i 0.371691i
\(58\) −11.2676 + 3.66105i −1.47950 + 0.480719i
\(59\) 9.94650 + 7.22656i 1.29492 + 0.940817i 0.999892 0.0146702i \(-0.00466982\pi\)
0.295032 + 0.955487i \(0.404670\pi\)
\(60\) −0.876298 + 7.51803i −0.113130 + 0.970574i
\(61\) −7.69704 + 5.59223i −0.985505 + 0.716012i −0.958932 0.283635i \(-0.908459\pi\)
−0.0265731 + 0.999647i \(0.508459\pi\)
\(62\) 7.69296 10.5884i 0.977006 1.34473i
\(63\) −0.587785 + 0.809017i −0.0740540 + 0.101927i
\(64\) −10.1831 + 7.39848i −1.27289 + 0.924810i
\(65\) −1.15642 + 9.92126i −0.143436 + 1.23058i
\(66\) −9.71657 7.05950i −1.19603 0.868964i
\(67\) −1.64256 + 0.533701i −0.200671 + 0.0652019i −0.407628 0.913148i \(-0.633644\pi\)
0.206957 + 0.978350i \(0.433644\pi\)
\(68\) 9.00148i 1.09159i
\(69\) 0.290991 + 0.895580i 0.0350313 + 0.107815i
\(70\) −2.16402 + 4.71611i −0.258650 + 0.563683i
\(71\) 4.05432 12.4779i 0.481160 1.48086i −0.356307 0.934369i \(-0.615964\pi\)
0.837467 0.546488i \(-0.184036\pi\)
\(72\) 3.05649 + 0.993115i 0.360211 + 0.117040i
\(73\) −1.76480 2.42904i −0.206554 0.284298i 0.693154 0.720790i \(-0.256221\pi\)
−0.899708 + 0.436492i \(0.856221\pi\)
\(74\) −17.3695 −2.01916
\(75\) −3.79049 + 3.26071i −0.437688 + 0.376514i
\(76\) 9.49880 1.08959
\(77\) −3.04217 4.18719i −0.346688 0.477175i
\(78\) 9.85845 + 3.20320i 1.11625 + 0.362691i
\(79\) 1.83100 5.63523i 0.206003 0.634013i −0.793667 0.608352i \(-0.791831\pi\)
0.999671 0.0256611i \(-0.00816908\pi\)
\(80\) 1.52781 + 0.178081i 0.170815 + 0.0199101i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 3.66549i 0.404786i
\(83\) 8.07227 2.62284i 0.886047 0.287894i 0.169581 0.985516i \(-0.445759\pi\)
0.716466 + 0.697622i \(0.245759\pi\)
\(84\) 2.73846 + 1.98961i 0.298791 + 0.217084i
\(85\) −4.02863 + 4.37368i −0.436966 + 0.474392i
\(86\) −0.000635689 0 0.000461855i −6.85481e−5 0 4.98031e-5i
\(87\) −3.00090 + 4.13039i −0.321731 + 0.442824i
\(88\) −9.77690 + 13.4568i −1.04222 + 1.43449i
\(89\) 14.8266 10.7722i 1.57162 1.14185i 0.646031 0.763311i \(-0.276428\pi\)
0.925587 0.378536i \(-0.123572\pi\)
\(90\) 2.54343 + 4.52279i 0.268101 + 0.476744i
\(91\) 3.61385 + 2.62561i 0.378834 + 0.275239i
\(92\) 3.03147 0.984985i 0.316053 0.102692i
\(93\) 5.64007i 0.584848i
\(94\) −6.06803 18.6755i −0.625869 1.92623i
\(95\) 4.61532 + 4.25120i 0.473522 + 0.436164i
\(96\) −1.49296 + 4.59485i −0.152374 + 0.468960i
\(97\) 8.70890 + 2.82969i 0.884255 + 0.287312i 0.715723 0.698384i \(-0.246097\pi\)
0.168532 + 0.985696i \(0.446097\pi\)
\(98\) 1.36398 + 1.87736i 0.137783 + 0.189642i
\(99\) −5.17565 −0.520173
\(100\) 11.0373 + 12.8305i 1.10373 + 1.28305i
\(101\) −5.44108 −0.541407 −0.270704 0.962663i \(-0.587256\pi\)
−0.270704 + 0.962663i \(0.587256\pi\)
\(102\) 3.62721 + 4.99243i 0.359148 + 0.494324i
\(103\) 10.6207 + 3.45087i 1.04649 + 0.340024i 0.781288 0.624170i \(-0.214563\pi\)
0.265197 + 0.964194i \(0.414563\pi\)
\(104\) 4.43621 13.6532i 0.435006 1.33881i
\(105\) 0.440125 + 2.19233i 0.0429518 + 0.213949i
\(106\) 4.16925 + 12.8316i 0.404953 + 1.24632i
\(107\) 19.0588i 1.84249i −0.388985 0.921244i \(-0.627174\pi\)
0.388985 0.921244i \(-0.372826\pi\)
\(108\) 3.21926 1.04600i 0.309773 0.100651i
\(109\) 4.76672 + 3.46323i 0.456569 + 0.331717i 0.792184 0.610282i \(-0.208944\pi\)
−0.335615 + 0.941999i \(0.608944\pi\)
\(110\) −26.3306 + 5.28604i −2.51052 + 0.504005i
\(111\) −6.05555 + 4.39962i −0.574768 + 0.417593i
\(112\) 0.404328 0.556510i 0.0382054 0.0525852i
\(113\) 7.84198 10.7936i 0.737711 1.01537i −0.261036 0.965329i \(-0.584064\pi\)
0.998747 0.0500432i \(-0.0159359\pi\)
\(114\) 5.26825 3.82761i 0.493417 0.358489i
\(115\) 1.91378 + 0.878151i 0.178461 + 0.0818880i
\(116\) 13.9811 + 10.1578i 1.29811 + 0.943132i
\(117\) 4.24833 1.38037i 0.392759 0.127615i
\(118\) 28.5301i 2.62640i
\(119\) 0.821764 + 2.52913i 0.0753309 + 0.231845i
\(120\) 6.26374 3.52247i 0.571798 0.321556i
\(121\) 4.87857 15.0147i 0.443507 1.36497i
\(122\) 20.9973 + 6.82242i 1.90100 + 0.617673i
\(123\) 0.928456 + 1.27791i 0.0837160 + 0.115225i
\(124\) −19.0912 −1.71444
\(125\) −0.379484 + 11.1739i −0.0339421 + 0.999424i
\(126\) 2.32054 0.206731
\(127\) −4.91633 6.76675i −0.436254 0.600452i 0.533121 0.846039i \(-0.321019\pi\)
−0.969374 + 0.245587i \(0.921019\pi\)
\(128\) 18.5895 + 6.04010i 1.64310 + 0.533875i
\(129\) −0.000104636 0 0.000322035i −9.21265e−6 0 2.83536e-5i
\(130\) 20.2031 11.3614i 1.77193 0.996462i
\(131\) 6.17484 + 19.0042i 0.539498 + 1.66040i 0.733724 + 0.679447i \(0.237780\pi\)
−0.194226 + 0.980957i \(0.562220\pi\)
\(132\) 17.5192i 1.52485i
\(133\) 2.66886 0.867165i 0.231419 0.0751927i
\(134\) 3.24237 + 2.35572i 0.280098 + 0.203503i
\(135\) 2.03233 + 0.932548i 0.174915 + 0.0802610i
\(136\) 6.91416 5.02343i 0.592884 0.430756i
\(137\) −7.85983 + 10.8181i −0.671511 + 0.924255i −0.999793 0.0203245i \(-0.993530\pi\)
0.328283 + 0.944579i \(0.393530\pi\)
\(138\) 1.28442 1.76785i 0.109337 0.150489i
\(139\) −1.76113 + 1.27953i −0.149377 + 0.108529i −0.659963 0.751298i \(-0.729428\pi\)
0.510587 + 0.859826i \(0.329428\pi\)
\(140\) 7.42086 1.48979i 0.627178 0.125910i
\(141\) −6.84594 4.97387i −0.576532 0.418875i
\(142\) −28.9556 + 9.40824i −2.42990 + 0.789522i
\(143\) 23.1195i 1.93335i
\(144\) −0.212568 0.654216i −0.0177140 0.0545180i
\(145\) 2.24703 + 11.1928i 0.186606 + 0.929510i
\(146\) −2.15303 + 6.62633i −0.178186 + 0.548399i
\(147\) 0.951057 + 0.309017i 0.0784418 + 0.0254873i
\(148\) 14.8924 + 20.4976i 1.22415 + 1.68489i
\(149\) 14.1901 1.16250 0.581249 0.813726i \(-0.302564\pi\)
0.581249 + 0.813726i \(0.302564\pi\)
\(150\) 11.2917 + 2.66856i 0.921962 + 0.217887i
\(151\) 1.90118 0.154716 0.0773580 0.997003i \(-0.475352\pi\)
0.0773580 + 0.997003i \(0.475352\pi\)
\(152\) −5.30097 7.29616i −0.429965 0.591796i
\(153\) 2.52913 + 0.821764i 0.204468 + 0.0664356i
\(154\) −3.71140 + 11.4225i −0.299073 + 0.920452i
\(155\) −9.27614 8.54431i −0.745077 0.686296i
\(156\) −4.67244 14.3803i −0.374095 1.15135i
\(157\) 18.5547i 1.48082i −0.672153 0.740412i \(-0.734630\pi\)
0.672153 0.740412i \(-0.265370\pi\)
\(158\) −13.0768 + 4.24891i −1.04033 + 0.338025i
\(159\) 4.70374 + 3.41747i 0.373031 + 0.271023i
\(160\) 5.29536 + 9.41632i 0.418635 + 0.744425i
\(161\) 0.761825 0.553499i 0.0600403 0.0436218i
\(162\) 1.36398 1.87736i 0.107165 0.147499i
\(163\) −5.45357 + 7.50620i −0.427157 + 0.587931i −0.967298 0.253644i \(-0.918371\pi\)
0.540141 + 0.841575i \(0.318371\pi\)
\(164\) 4.32563 3.14276i 0.337775 0.245408i
\(165\) −7.84075 + 8.51232i −0.610402 + 0.662683i
\(166\) −15.9345 11.5771i −1.23675 0.898554i
\(167\) −15.8223 + 5.14098i −1.22437 + 0.397821i −0.848670 0.528922i \(-0.822596\pi\)
−0.375696 + 0.926743i \(0.622596\pi\)
\(168\) 3.21379i 0.247949i
\(169\) −2.14883 6.61341i −0.165294 0.508724i
\(170\) 13.7059 + 1.59756i 1.05120 + 0.122527i
\(171\) 0.867165 2.66886i 0.0663137 0.204093i
\(172\) 0.00109007 0.000354184i 8.31167e−5 2.70063e-5i
\(173\) −1.07522 1.47992i −0.0817477 0.112516i 0.766185 0.642620i \(-0.222153\pi\)
−0.847932 + 0.530104i \(0.822153\pi\)
\(174\) 11.8474 0.898149
\(175\) 4.27244 + 2.59735i 0.322966 + 0.196341i
\(176\) 3.56025 0.268364
\(177\) −7.22656 9.94650i −0.543181 0.747625i
\(178\) −40.4465 13.1419i −3.03159 0.985024i
\(179\) 4.96964 15.2950i 0.371449 1.14320i −0.574395 0.818578i \(-0.694763\pi\)
0.945844 0.324623i \(-0.105237\pi\)
\(180\) 3.15661 6.87928i 0.235280 0.512751i
\(181\) −1.57723 4.85421i −0.117235 0.360811i 0.875172 0.483812i \(-0.160748\pi\)
−0.992407 + 0.123001i \(0.960748\pi\)
\(182\) 10.3658i 0.768363i
\(183\) 9.04842 2.94001i 0.668878 0.217332i
\(184\) −2.44835 1.77883i −0.180494 0.131137i
\(185\) −1.93775 + 16.6246i −0.142467 + 1.22226i
\(186\) −10.5884 + 7.69296i −0.776383 + 0.564075i
\(187\) −8.09000 + 11.1349i −0.591599 + 0.814266i
\(188\) −16.8362 + 23.1730i −1.22790 + 1.69007i
\(189\) 0.809017 0.587785i 0.0588473 0.0427551i
\(190\) 1.68582 14.4632i 0.122302 1.04927i
\(191\) 21.4682 + 15.5976i 1.55339 + 1.12860i 0.941181 + 0.337904i \(0.109718\pi\)
0.612206 + 0.790698i \(0.290282\pi\)
\(192\) 11.9710 3.88961i 0.863932 0.280708i
\(193\) 5.11772i 0.368382i 0.982891 + 0.184191i \(0.0589664\pi\)
−0.982891 + 0.184191i \(0.941034\pi\)
\(194\) −6.56643 20.2094i −0.471442 1.45095i
\(195\) 4.16566 9.07833i 0.298309 0.650113i
\(196\) 1.04600 3.21926i 0.0747143 0.229947i
\(197\) −20.4420 6.64200i −1.45643 0.473223i −0.529453 0.848339i \(-0.677603\pi\)
−0.926978 + 0.375116i \(0.877603\pi\)
\(198\) 7.05950 + 9.71657i 0.501697 + 0.690526i
\(199\) 13.5664 0.961693 0.480847 0.876805i \(-0.340329\pi\)
0.480847 + 0.876805i \(0.340329\pi\)
\(200\) 3.69577 15.6382i 0.261330 1.10579i
\(201\) 1.72709 0.121820
\(202\) 7.42153 + 10.2149i 0.522177 + 0.718715i
\(203\) 4.85556 + 1.57767i 0.340794 + 0.110731i
\(204\) 2.78161 8.56092i 0.194752 0.599384i
\(205\) 3.50830 + 0.408926i 0.245031 + 0.0285607i
\(206\) −8.00789 24.6457i −0.557936 1.71715i
\(207\) 0.941668i 0.0654505i
\(208\) −2.92236 + 0.949532i −0.202629 + 0.0658382i
\(209\) 11.7501 + 8.53696i 0.812772 + 0.590514i
\(210\) 3.51546 3.81656i 0.242590 0.263368i
\(211\) 2.48123 1.80272i 0.170815 0.124104i −0.499093 0.866548i \(-0.666333\pi\)
0.669908 + 0.742444i \(0.266333\pi\)
\(212\) 11.5679 15.9218i 0.794485 1.09352i
\(213\) −7.71178 + 10.6144i −0.528403 + 0.727284i
\(214\) −35.7803 + 25.9959i −2.44589 + 1.77705i
\(215\) 0.000371131 0 0.000659953i 2.53109e−5 0 4.50084e-5i
\(216\) −2.60001 1.88902i −0.176908 0.128531i
\(217\) −5.36403 + 1.74288i −0.364134 + 0.118314i
\(218\) 13.6726i 0.926028i
\(219\) 0.927811 + 2.85551i 0.0626956 + 0.192957i
\(220\) 28.8136 + 26.5404i 1.94261 + 1.78935i
\(221\) 3.67079 11.2975i 0.246924 0.759953i
\(222\) 16.5193 + 5.36746i 1.10870 + 0.360240i
\(223\) 3.40625 + 4.68830i 0.228100 + 0.313952i 0.907691 0.419638i \(-0.137843\pi\)
−0.679592 + 0.733590i \(0.737843\pi\)
\(224\) 4.83131 0.322806
\(225\) 4.61258 1.92979i 0.307505 0.128653i
\(226\) −30.9597 −2.05941
\(227\) −6.77250 9.32154i −0.449506 0.618692i 0.522785 0.852465i \(-0.324893\pi\)
−0.972291 + 0.233772i \(0.924893\pi\)
\(228\) −9.03389 2.93529i −0.598284 0.194394i
\(229\) 2.56148 7.88344i 0.169268 0.520952i −0.830058 0.557677i \(-0.811693\pi\)
0.999325 + 0.0367252i \(0.0116926\pi\)
\(230\) −0.961753 4.79063i −0.0634161 0.315885i
\(231\) 1.59937 + 4.92234i 0.105230 + 0.323866i
\(232\) 16.4078i 1.07723i
\(233\) −26.3766 + 8.57027i −1.72799 + 0.561457i −0.993156 0.116792i \(-0.962739\pi\)
−0.734832 + 0.678249i \(0.762739\pi\)
\(234\) −8.38610 6.09286i −0.548216 0.398303i
\(235\) −18.5516 + 3.72435i −1.21017 + 0.242950i
\(236\) −33.6682 + 24.4614i −2.19161 + 1.59230i
\(237\) −3.48276 + 4.79361i −0.226230 + 0.311379i
\(238\) 3.62721 4.99243i 0.235117 0.323611i
\(239\) −12.4374 + 9.03629i −0.804507 + 0.584509i −0.912233 0.409672i \(-0.865643\pi\)
0.107726 + 0.994181i \(0.465643\pi\)
\(240\) −1.39800 0.641485i −0.0902408 0.0414077i
\(241\) −16.2048 11.7735i −1.04384 0.758395i −0.0728098 0.997346i \(-0.523197\pi\)
−0.971032 + 0.238951i \(0.923197\pi\)
\(242\) −34.8423 + 11.3209i −2.23975 + 0.727738i
\(243\) 1.00000i 0.0641500i
\(244\) −9.95172 30.6282i −0.637094 1.96077i
\(245\) 1.94902 1.09605i 0.124518 0.0700240i
\(246\) 1.13270 3.48609i 0.0722183 0.222265i
\(247\) −11.9217 3.87359i −0.758559 0.246471i
\(248\) 10.6542 + 14.6642i 0.676542 + 0.931180i
\(249\) −8.48769 −0.537886
\(250\) 21.4950 14.5286i 1.35947 0.918867i
\(251\) 0.298988 0.0188719 0.00943597 0.999955i \(-0.496996\pi\)
0.00943597 + 0.999955i \(0.496996\pi\)
\(252\) −1.98961 2.73846i −0.125334 0.172507i
\(253\) 4.63521 + 1.50607i 0.291413 + 0.0946859i
\(254\) −5.99784 + 18.4594i −0.376338 + 1.15825i
\(255\) 5.18299 2.91470i 0.324572 0.182526i
\(256\) −6.23710 19.1958i −0.389819 1.19974i
\(257\) 13.8078i 0.861310i 0.902517 + 0.430655i \(0.141717\pi\)
−0.902517 + 0.430655i \(0.858283\pi\)
\(258\) 0.000747297 0 0.000242811i 4.65247e−5 0 1.51168e-5i
\(259\) 6.05555 + 4.39962i 0.376274 + 0.273379i
\(260\) −30.7295 14.1005i −1.90576 0.874473i
\(261\) 4.13039 3.00090i 0.255665 0.185751i
\(262\) 27.2554 37.5138i 1.68384 2.31761i
\(263\) 1.82712 2.51481i 0.112665 0.155070i −0.748961 0.662614i \(-0.769447\pi\)
0.861625 + 0.507545i \(0.169447\pi\)
\(264\) 13.4568 9.77690i 0.828206 0.601727i
\(265\) 12.7465 2.55895i 0.783011 0.157195i
\(266\) −5.26825 3.82761i −0.323017 0.234686i
\(267\) −17.4297 + 5.66326i −1.06668 + 0.346586i
\(268\) 5.84608i 0.357106i
\(269\) −4.80841 14.7988i −0.293174 0.902297i −0.983829 0.179112i \(-0.942677\pi\)
0.690655 0.723185i \(-0.257323\pi\)
\(270\) −1.02133 5.08739i −0.0621561 0.309609i
\(271\) −4.79752 + 14.7652i −0.291429 + 0.896925i 0.692969 + 0.720967i \(0.256302\pi\)
−0.984398 + 0.175958i \(0.943698\pi\)
\(272\) −1.73975 0.565278i −0.105488 0.0342750i
\(273\) −2.62561 3.61385i −0.158909 0.218720i
\(274\) 31.0302 1.87460
\(275\) 2.12189 + 25.7911i 0.127955 + 1.55526i
\(276\) −3.18748 −0.191864
\(277\) −14.5003 19.9579i −0.871237 1.19915i −0.978772 0.204954i \(-0.934296\pi\)
0.107535 0.994201i \(-0.465704\pi\)
\(278\) 4.80429 + 1.56101i 0.288142 + 0.0936230i
\(279\) −1.74288 + 5.36403i −0.104343 + 0.321136i
\(280\) −5.28567 4.86866i −0.315879 0.290958i
\(281\) 5.61246 + 17.2734i 0.334812 + 1.03044i 0.966815 + 0.255478i \(0.0822329\pi\)
−0.632003 + 0.774966i \(0.717767\pi\)
\(282\) 19.6366i 1.16934i
\(283\) −25.2398 + 8.20092i −1.50035 + 0.487494i −0.940120 0.340842i \(-0.889288\pi\)
−0.560231 + 0.828336i \(0.689288\pi\)
\(284\) 35.9288 + 26.1038i 2.13198 + 1.54898i
\(285\) −3.07574 5.46934i −0.182191 0.323976i
\(286\) 43.4035 31.5345i 2.56651 1.86468i
\(287\) 0.928456 1.27791i 0.0548050 0.0754326i
\(288\) 2.83977 3.90861i 0.167335 0.230317i
\(289\) −8.03210 + 5.83566i −0.472476 + 0.343274i
\(290\) 17.9480 19.4852i 1.05394 1.14421i
\(291\) −7.40823 5.38240i −0.434278 0.315522i
\(292\) 9.66569 3.14057i 0.565642 0.183788i
\(293\) 17.1749i 1.00337i 0.865051 + 0.501684i \(0.167286\pi\)
−0.865051 + 0.501684i \(0.832714\pi\)
\(294\) −0.717088 2.20697i −0.0418214 0.128713i
\(295\) −27.3066 3.18284i −1.58985 0.185312i
\(296\) 7.43354 22.8781i 0.432066 1.32976i
\(297\) 4.92234 + 1.59937i 0.285623 + 0.0928046i
\(298\) −19.3550 26.6399i −1.12121 1.54321i
\(299\) −4.20640 −0.243262
\(300\) −6.53221 15.6133i −0.377137 0.901432i
\(301\) 0.000338608 0 1.95170e−5 0
\(302\) −2.59318 3.56920i −0.149221 0.205385i
\(303\) 5.17477 + 1.68138i 0.297283 + 0.0965930i
\(304\) −0.596508 + 1.83586i −0.0342121 + 0.105294i
\(305\) 8.87233 19.3357i 0.508028 1.10716i
\(306\) −1.90694 5.86895i −0.109012 0.335506i
\(307\) 1.04893i 0.0598658i −0.999552 0.0299329i \(-0.990471\pi\)
0.999552 0.0299329i \(-0.00952936\pi\)
\(308\) 16.6618 5.41374i 0.949392 0.308476i
\(309\) −9.03448 6.56394i −0.513954 0.373409i
\(310\) −3.38826 + 29.0689i −0.192440 + 1.65101i
\(311\) 4.12322 2.99570i 0.233806 0.169870i −0.464713 0.885461i \(-0.653843\pi\)
0.698520 + 0.715591i \(0.253843\pi\)
\(312\) −8.43817 + 11.6141i −0.477717 + 0.657522i
\(313\) 14.7072 20.2427i 0.831299 1.14418i −0.156381 0.987697i \(-0.549983\pi\)
0.987680 0.156488i \(-0.0500173\pi\)
\(314\) −34.8338 + 25.3082i −1.96579 + 1.42823i
\(315\) 0.258882 2.22103i 0.0145864 0.125141i
\(316\) 16.2260 + 11.7889i 0.912786 + 0.663178i
\(317\) 30.1417 9.79362i 1.69292 0.550064i 0.705576 0.708634i \(-0.250688\pi\)
0.987348 + 0.158569i \(0.0506881\pi\)
\(318\) 13.4920i 0.756592i
\(319\) 8.16546 + 25.1307i 0.457178 + 1.40705i
\(320\) 11.7380 25.5810i 0.656176 1.43002i
\(321\) −5.88951 + 18.1260i −0.328720 + 1.01170i
\(322\) −2.07823 0.675259i −0.115815 0.0376307i
\(323\) −4.38634 6.03728i −0.244063 0.335923i
\(324\) −3.38493 −0.188052
\(325\) −8.62031 20.6042i −0.478169 1.14292i
\(326\) 21.5304 1.19246
\(327\) −3.46323 4.76672i −0.191517 0.263600i
\(328\) −4.82799 1.56871i −0.266581 0.0866174i
\(329\) −2.61492 + 8.04788i −0.144165 + 0.443694i
\(330\) 26.6753 + 3.10927i 1.46843 + 0.171159i
\(331\) −8.04458 24.7587i −0.442170 1.36086i −0.885557 0.464530i \(-0.846223\pi\)
0.443387 0.896330i \(-0.353777\pi\)
\(332\) 28.7302i 1.57678i
\(333\) 7.11873 2.31302i 0.390104 0.126752i
\(334\) 31.2328 + 22.6920i 1.70898 + 1.24165i
\(335\) 2.61642 2.84052i 0.142950 0.155194i
\(336\) −0.556510 + 0.404328i −0.0303601 + 0.0220579i
\(337\) 13.0626 17.9791i 0.711566 0.979387i −0.288196 0.957571i \(-0.593055\pi\)
0.999762 0.0218151i \(-0.00694451\pi\)
\(338\) −9.48480 + 13.0547i −0.515905 + 0.710082i
\(339\) −10.7936 + 7.84198i −0.586225 + 0.425918i
\(340\) −9.86607 17.5441i −0.535063 0.951460i
\(341\) −23.6161 17.1581i −1.27888 0.929162i
\(342\) −6.19321 + 2.01229i −0.334890 + 0.108812i
\(343\) 1.00000i 0.0539949i
\(344\) −0.000336276 0.00103495i −1.81308e−5 5.58009e-5i
\(345\) −1.54875 1.42656i −0.0833817 0.0768035i
\(346\) −1.31175 + 4.03716i −0.0705203 + 0.217039i
\(347\) −6.85580 2.22758i −0.368039 0.119583i 0.119158 0.992875i \(-0.461980\pi\)
−0.487197 + 0.873292i \(0.661980\pi\)
\(348\) −10.1578 13.9811i −0.544517 0.749464i
\(349\) 14.7927 0.791835 0.395917 0.918286i \(-0.370427\pi\)
0.395917 + 0.918286i \(0.370427\pi\)
\(350\) −0.951368 11.5637i −0.0508527 0.618103i
\(351\) −4.46696 −0.238429
\(352\) 14.6977 + 20.2296i 0.783389 + 1.07824i
\(353\) 0.953456 + 0.309797i 0.0507473 + 0.0164888i 0.334281 0.942474i \(-0.391507\pi\)
−0.283533 + 0.958962i \(0.591507\pi\)
\(354\) −8.81627 + 27.1337i −0.468580 + 1.44214i
\(355\) 5.77446 + 28.7635i 0.306477 + 1.52661i
\(356\) 19.1697 + 58.9984i 1.01599 + 3.12691i
\(357\) 2.65928i 0.140744i
\(358\) −35.4927 + 11.5323i −1.87585 + 0.609500i
\(359\) 15.6940 + 11.4023i 0.828297 + 0.601793i 0.919077 0.394078i \(-0.128936\pi\)
−0.0907803 + 0.995871i \(0.528936\pi\)
\(360\) −7.04567 + 1.41447i −0.371339 + 0.0745490i
\(361\) 9.00049 6.53924i 0.473710 0.344171i
\(362\) −6.96180 + 9.58209i −0.365904 + 0.503623i
\(363\) −9.27960 + 12.7723i −0.487053 + 0.670370i
\(364\) −12.2326 + 8.88752i −0.641163 + 0.465833i
\(365\) 6.10198 + 2.79994i 0.319392 + 0.146555i
\(366\) −17.8613 12.9770i −0.933627 0.678320i
\(367\) −7.43395 + 2.41544i −0.388049 + 0.126085i −0.496543 0.868012i \(-0.665397\pi\)
0.108493 + 0.994097i \(0.465397\pi\)
\(368\) 0.647758i 0.0337667i
\(369\) −0.488118 1.50227i −0.0254104 0.0782052i
\(370\) 33.8534 19.0378i 1.75995 0.989727i
\(371\) 1.79667 5.52958i 0.0932784 0.287081i
\(372\) 18.1568 + 5.89952i 0.941389 + 0.305876i
\(373\) 7.31748 + 10.0716i 0.378885 + 0.521490i 0.955289 0.295675i \(-0.0955445\pi\)
−0.576404 + 0.817165i \(0.695544\pi\)
\(374\) 31.9389 1.65152
\(375\) 3.81384 10.5097i 0.196946 0.542721i
\(376\) 27.1952 1.40249
\(377\) −13.4049 18.4503i −0.690388 0.950238i
\(378\) −2.20697 0.717088i −0.113514 0.0368830i
\(379\) −10.7804 + 33.1785i −0.553750 + 1.70427i 0.145473 + 0.989362i \(0.453530\pi\)
−0.699223 + 0.714904i \(0.746470\pi\)
\(380\) −18.5133 + 10.4111i −0.949714 + 0.534081i
\(381\) 2.58467 + 7.95479i 0.132417 + 0.407536i
\(382\) 61.5784i 3.15063i
\(383\) −10.0040 + 3.25051i −0.511183 + 0.166093i −0.553240 0.833022i \(-0.686609\pi\)
0.0420573 + 0.999115i \(0.486609\pi\)
\(384\) −15.8132 11.4890i −0.806963 0.586293i
\(385\) 10.5186 + 4.82655i 0.536079 + 0.245984i
\(386\) 9.60781 6.98048i 0.489024 0.355297i
\(387\) 0.000199029 0 0.000273939i 1.01172e−5 0 1.39251e-5i
\(388\) −18.2190 + 25.0763i −0.924931 + 1.27306i
\(389\) 20.9037 15.1875i 1.05986 0.770035i 0.0857993 0.996312i \(-0.472656\pi\)
0.974063 + 0.226278i \(0.0726556\pi\)
\(390\) −22.7252 + 4.56224i −1.15073 + 0.231018i
\(391\) −2.02591 1.47191i −0.102455 0.0744376i
\(392\) −3.05649 + 0.993115i −0.154376 + 0.0501599i
\(393\) 19.9822i 1.00797i
\(394\) 15.4131 + 47.4365i 0.776499 + 2.38982i
\(395\) 2.60784 + 12.9900i 0.131215 + 0.653600i
\(396\) 5.41374 16.6618i 0.272050 0.837285i
\(397\) 30.8636 + 10.0282i 1.54900 + 0.503301i 0.953842 0.300308i \(-0.0970894\pi\)
0.595158 + 0.803609i \(0.297089\pi\)
\(398\) −18.5043 25.4689i −0.927535 1.27664i
\(399\) −2.80620 −0.140486
\(400\) −3.17292 + 1.32747i −0.158646 + 0.0663737i
\(401\) −20.1859 −1.00804 −0.504018 0.863693i \(-0.668145\pi\)
−0.504018 + 0.863693i \(0.668145\pi\)
\(402\) −2.35572 3.24237i −0.117493 0.161715i
\(403\) 23.9609 + 7.78537i 1.19358 + 0.387817i
\(404\) 5.69137 17.5162i 0.283156 0.871465i
\(405\) −1.64468 1.51493i −0.0817250 0.0752775i
\(406\) −3.66105 11.2676i −0.181695 0.559199i
\(407\) 38.7402i 1.92028i
\(408\) −8.12808 + 2.64097i −0.402400 + 0.130748i
\(409\) 2.97174 + 2.15910i 0.146943 + 0.106760i 0.658828 0.752294i \(-0.271053\pi\)
−0.511885 + 0.859054i \(0.671053\pi\)
\(410\) −4.01756 7.14412i −0.198413 0.352823i
\(411\) 10.8181 7.85983i 0.533619 0.387697i
\(412\) −22.2185 + 30.5811i −1.09462 + 1.50662i
\(413\) −7.22656 + 9.94650i −0.355596 + 0.489435i
\(414\) −1.76785 + 1.28442i −0.0868851 + 0.0631257i
\(415\) −12.8583 + 13.9596i −0.631187 + 0.685249i
\(416\) −17.4596 12.6852i −0.856029 0.621941i
\(417\) 2.07033 0.672690i 0.101384 0.0329418i
\(418\) 33.7035i 1.64849i
\(419\) −8.44992 26.0062i −0.412805 1.27048i −0.914199 0.405265i \(-0.867179\pi\)
0.501394 0.865219i \(-0.332821\pi\)
\(420\) −7.51803 0.876298i −0.366842 0.0427590i
\(421\) −8.21384 + 25.2796i −0.400318 + 1.23205i 0.524424 + 0.851457i \(0.324281\pi\)
−0.924742 + 0.380595i \(0.875719\pi\)
\(422\) −6.76871 2.19929i −0.329496 0.107060i
\(423\) 4.97387 + 6.84594i 0.241838 + 0.332861i
\(424\) −18.6854 −0.907444
\(425\) 3.05810 12.9400i 0.148340 0.627680i
\(426\) 30.4457 1.47510
\(427\) −5.59223 7.69704i −0.270627 0.372486i
\(428\) 61.3554 + 19.9356i 2.96572 + 0.963622i
\(429\) 7.14430 21.9879i 0.344930 1.06159i
\(430\) 0.000732754 0.00159691i 3.53365e−5 7.70098e-5i
\(431\) 3.04293 + 9.36517i 0.146573 + 0.451104i 0.997210 0.0746487i \(-0.0237836\pi\)
−0.850637 + 0.525753i \(0.823784\pi\)
\(432\) 0.687884i 0.0330958i
\(433\) 33.9462 11.0298i 1.63135 0.530057i 0.656767 0.754093i \(-0.271923\pi\)
0.974581 + 0.224036i \(0.0719233\pi\)
\(434\) 10.5884 + 7.69296i 0.508262 + 0.369274i
\(435\) 1.32171 11.3393i 0.0633711 0.543680i
\(436\) −16.1350 + 11.7228i −0.772727 + 0.561419i
\(437\) −1.55323 + 2.13784i −0.0743011 + 0.102267i
\(438\) 4.09530 5.63670i 0.195681 0.269332i
\(439\) −16.8325 + 12.2296i −0.803374 + 0.583685i −0.911902 0.410408i \(-0.865386\pi\)
0.108528 + 0.994093i \(0.465386\pi\)
\(440\) 4.30611 36.9434i 0.205286 1.76121i
\(441\) −0.809017 0.587785i −0.0385246 0.0279898i
\(442\) −26.2164 + 8.51823i −1.24699 + 0.405171i
\(443\) 20.6984i 0.983409i −0.870762 0.491705i \(-0.836374\pi\)
0.870762 0.491705i \(-0.163626\pi\)
\(444\) −7.82939 24.0964i −0.371566 1.14356i
\(445\) −17.0905 + 37.2459i −0.810169 + 1.76562i
\(446\) 4.15557 12.7895i 0.196772 0.605602i
\(447\) −13.4956 4.38498i −0.638319 0.207402i
\(448\) −7.39848 10.1831i −0.349545 0.481108i
\(449\) 20.1811 0.952403 0.476202 0.879336i \(-0.342013\pi\)
0.476202 + 0.879336i \(0.342013\pi\)
\(450\) −9.91439 6.02727i −0.467369 0.284128i
\(451\) 8.17538 0.384963
\(452\) 26.5445 + 36.5354i 1.24855 + 1.71848i
\(453\) −1.80813 0.587497i −0.0849534 0.0276030i
\(454\) −8.26233 + 25.4288i −0.387770 + 1.19343i
\(455\) −9.92126 1.15642i −0.465116 0.0542137i
\(456\) 2.78688 + 8.57715i 0.130508 + 0.401662i
\(457\) 2.77398i 0.129761i 0.997893 + 0.0648806i \(0.0206666\pi\)
−0.997893 + 0.0648806i \(0.979333\pi\)
\(458\) −18.2939 + 5.94404i −0.854816 + 0.277747i
\(459\) −2.15140 1.56309i −0.100419 0.0729587i
\(460\) −4.82881 + 5.24240i −0.225144 + 0.244428i
\(461\) 5.87667 4.26965i 0.273704 0.198858i −0.442463 0.896787i \(-0.645895\pi\)
0.716167 + 0.697929i \(0.245895\pi\)
\(462\) 7.05950 9.71657i 0.328438 0.452056i
\(463\) 11.0040 15.1457i 0.511398 0.703879i −0.472756 0.881193i \(-0.656741\pi\)
0.984154 + 0.177314i \(0.0567409\pi\)
\(464\) −2.84123 + 2.06427i −0.131901 + 0.0958314i
\(465\) 6.18180 + 10.9926i 0.286674 + 0.509770i
\(466\) 52.0667 + 37.8287i 2.41194 + 1.75238i
\(467\) 22.5250 7.31883i 1.04233 0.338675i 0.262679 0.964883i \(-0.415394\pi\)
0.779656 + 0.626208i \(0.215394\pi\)
\(468\) 15.1203i 0.698938i
\(469\) −0.533701 1.64256i −0.0246440 0.0758464i
\(470\) 32.2959 + 29.7480i 1.48970 + 1.37217i
\(471\) −5.73371 + 17.6465i −0.264195 + 0.813110i
\(472\) 37.5782 + 12.2099i 1.72968 + 0.562006i
\(473\) 0.00103010 + 0.00141782i 4.73642e−5 + 6.51912e-5i
\(474\) 13.7498 0.631548
\(475\) −13.6549 3.22706i −0.626529 0.148067i
\(476\) −9.00148 −0.412582
\(477\) −3.41747 4.70374i −0.156475 0.215369i
\(478\) 33.9287 + 11.0241i 1.55186 + 0.504231i
\(479\) 10.8092 33.2674i 0.493887 1.52003i −0.324798 0.945783i \(-0.605296\pi\)
0.818685 0.574243i \(-0.194704\pi\)
\(480\) −2.12638 10.5918i −0.0970555 0.483448i
\(481\) −10.3322 31.7991i −0.471106 1.44991i
\(482\) 46.4810i 2.11715i
\(483\) −0.895580 + 0.290991i −0.0407503 + 0.0132406i
\(484\) 43.2332 + 31.4108i 1.96515 + 1.42776i
\(485\) −20.0753 + 4.03026i −0.911572 + 0.183004i
\(486\) −1.87736 + 1.36398i −0.0851588 + 0.0618715i
\(487\) 1.09813 1.51144i 0.0497609 0.0684899i −0.783411 0.621503i \(-0.786522\pi\)
0.833172 + 0.553013i \(0.186522\pi\)
\(488\) −17.9722 + 24.7367i −0.813565 + 1.11978i
\(489\) 7.50620 5.45357i 0.339442 0.246619i
\(490\) −4.71611 2.16402i −0.213052 0.0977605i
\(491\) −21.5149 15.6315i −0.970952 0.705438i −0.0152839 0.999883i \(-0.504865\pi\)
−0.955668 + 0.294445i \(0.904865\pi\)
\(492\) −5.08509 + 1.65224i −0.229253 + 0.0744890i
\(493\) 13.5768i 0.611469i
\(494\) 8.98884 + 27.6648i 0.404427 + 1.24470i
\(495\) 10.0874 5.67277i 0.453397 0.254972i
\(496\) 1.19890 3.68983i 0.0538321 0.165678i
\(497\) 12.4779 + 4.05432i 0.559711 + 0.181861i
\(498\) 11.5771 + 15.9345i 0.518780 + 0.714040i
\(499\) −29.5129 −1.32118 −0.660590 0.750747i \(-0.729694\pi\)
−0.660590 + 0.750747i \(0.729694\pi\)
\(500\) −35.5747 12.9096i −1.59095 0.577333i
\(501\) 16.6366 0.743267
\(502\) −0.407814 0.561308i −0.0182016 0.0250524i
\(503\) 24.6477 + 8.00852i 1.09899 + 0.357082i 0.801713 0.597710i \(-0.203923\pi\)
0.297274 + 0.954792i \(0.403923\pi\)
\(504\) −0.993115 + 3.05649i −0.0442369 + 0.136147i
\(505\) 10.6048 5.96369i 0.471906 0.265381i
\(506\) −3.49491 10.7562i −0.155367 0.478172i
\(507\) 6.95375i 0.308827i
\(508\) 26.9264 8.74892i 1.19467 0.388170i
\(509\) 2.74657 + 1.99550i 0.121740 + 0.0884491i 0.646989 0.762499i \(-0.276028\pi\)
−0.525249 + 0.850948i \(0.676028\pi\)
\(510\) −12.5415 5.75474i −0.555345 0.254824i
\(511\) 2.42904 1.76480i 0.107454 0.0780702i
\(512\) −4.55228 + 6.26568i −0.201184 + 0.276907i
\(513\) −1.64945 + 2.27027i −0.0728248 + 0.100235i
\(514\) 25.9223 18.8336i 1.14338 0.830717i
\(515\) −24.4822 + 4.91497i −1.07882 + 0.216580i
\(516\) −0.000927265 0 0.000673698i −4.08206e−5 0 2.96579e-5i
\(517\) −41.6531 + 13.5339i −1.83190 + 0.595220i
\(518\) 17.3695i 0.763170i
\(519\) 0.565278 + 1.73975i 0.0248129 + 0.0763664i
\(520\) 6.31837 + 31.4727i 0.277079 + 1.38017i
\(521\) 8.24271 25.3684i 0.361119 1.11141i −0.591256 0.806484i \(-0.701368\pi\)
0.952376 0.304928i \(-0.0986323\pi\)
\(522\) −11.2676 3.66105i −0.493167 0.160240i
\(523\) −21.2217 29.2092i −0.927961 1.27723i −0.960650 0.277763i \(-0.910407\pi\)
0.0326887 0.999466i \(-0.489593\pi\)
\(524\) −67.6383 −2.95479
\(525\) −3.26071 3.79049i −0.142309 0.165430i
\(526\) −7.21335 −0.314517
\(527\) 8.81592 + 12.1341i 0.384028 + 0.528569i
\(528\) −3.38600 1.10018i −0.147357 0.0478791i
\(529\) 6.83337 21.0310i 0.297103 0.914390i
\(530\) −22.1900 20.4394i −0.963874 0.887831i
\(531\) 3.79922 + 11.6928i 0.164872 + 0.507425i
\(532\) 9.49880i 0.411825i
\(533\) −6.71060 + 2.18041i −0.290668 + 0.0944438i
\(534\) 34.4058 + 24.9973i 1.48889 + 1.08174i
\(535\) 20.8894 + 37.1461i 0.903129 + 1.60596i
\(536\) −4.49045 + 3.26251i −0.193958 + 0.140919i
\(537\) −9.45282 + 13.0107i −0.407919 + 0.561453i
\(538\) −21.2240 + 29.2124i −0.915033 + 1.25944i
\(539\) 4.18719 3.04217i 0.180355 0.131036i
\(540\) −5.12793 + 5.56714i −0.220671 + 0.239572i
\(541\) 6.30383 + 4.58000i 0.271023 + 0.196910i 0.714992 0.699132i \(-0.246430\pi\)
−0.443969 + 0.896042i \(0.646430\pi\)
\(542\) 34.2634 11.1329i 1.47174 0.478197i
\(543\) 5.10402i 0.219035i
\(544\) −3.97020 12.2190i −0.170221 0.523886i
\(545\) −13.0863 1.52533i −0.560556 0.0653381i
\(546\) −3.20320 + 9.85845i −0.137084 + 0.421903i
\(547\) −24.1224 7.83784i −1.03140 0.335122i −0.256055 0.966662i \(-0.582423\pi\)
−0.775343 + 0.631540i \(0.782423\pi\)
\(548\) −26.6050 36.6186i −1.13651 1.56427i
\(549\) −9.51407 −0.406051
\(550\) 45.5250 39.1622i 1.94119 1.66988i
\(551\) −14.3269 −0.610347
\(552\) 1.77883 + 2.44835i 0.0757119 + 0.104209i
\(553\) 5.63523 + 1.83100i 0.239634 + 0.0778619i
\(554\) −17.6901 + 54.4445i −0.751580 + 2.31312i
\(555\) 6.98019 15.2121i 0.296293 0.645719i
\(556\) −2.27701 7.00791i −0.0965666 0.297202i
\(557\) 23.7938i 1.00818i 0.863652 + 0.504088i \(0.168171\pi\)
−0.863652 + 0.504088i \(0.831829\pi\)
\(558\) 12.4475 4.04443i 0.526943 0.171214i
\(559\) −0.00122368 0.000889053i −5.17560e−5 3.76030e-5i
\(560\) −0.178081 + 1.52781i −0.00752530 + 0.0645618i
\(561\) 11.1349 8.09000i 0.470117 0.341560i
\(562\) 24.7731 34.0972i 1.04499 1.43830i
\(563\) 6.13365 8.44224i 0.258502 0.355798i −0.659964 0.751297i \(-0.729428\pi\)
0.918466 + 0.395499i \(0.129428\pi\)
\(564\) 23.1730 16.8362i 0.975760 0.708931i
\(565\) −3.45390 + 29.6320i −0.145307 + 1.24663i
\(566\) 49.8227 + 36.1983i 2.09421 + 1.52153i
\(567\) −0.951057 + 0.309017i −0.0399406 + 0.0129775i
\(568\) 42.1651i 1.76921i
\(569\) −11.3054 34.7944i −0.473947 1.45866i −0.847373 0.530998i \(-0.821817\pi\)
0.373426 0.927660i \(-0.378183\pi\)
\(570\) −6.07268 + 13.2344i −0.254357 + 0.554326i
\(571\) −8.14400 + 25.0647i −0.340816 + 1.04892i 0.622970 + 0.782246i \(0.285926\pi\)
−0.963786 + 0.266678i \(0.914074\pi\)
\(572\) −74.4275 24.1830i −3.11197 1.01114i
\(573\) −15.5976 21.4682i −0.651599 0.896848i
\(574\) −3.66549 −0.152995
\(575\) −4.69249 + 0.386061i −0.195690 + 0.0160999i
\(576\) −12.5870 −0.524460
\(577\) −23.1382 31.8470i −0.963254 1.32581i −0.945382 0.325966i \(-0.894311\pi\)
−0.0178728 0.999840i \(-0.505689\pi\)
\(578\) 21.9113 + 7.11940i 0.911389 + 0.296128i
\(579\) 1.58146 4.86724i 0.0657233 0.202276i
\(580\) −38.3829 4.47389i −1.59376 0.185768i
\(581\) 2.62284 + 8.07227i 0.108814 + 0.334894i
\(582\) 21.2494i 0.880816i
\(583\) 28.6192 9.29893i 1.18529 0.385122i
\(584\) −7.80642 5.67170i −0.323032 0.234696i
\(585\) −6.76713 + 7.34675i −0.279787 + 0.303751i
\(586\) 32.2435 23.4262i 1.33196 0.967729i
\(587\) 11.9192 16.4053i 0.491956 0.677120i −0.488791 0.872401i \(-0.662562\pi\)
0.980747 + 0.195281i \(0.0625619\pi\)
\(588\) −1.98961 + 2.73846i −0.0820502 + 0.112932i
\(589\) 12.8045 9.30299i 0.527599 0.383323i
\(590\) 31.2703 + 55.6056i 1.28738 + 2.28925i
\(591\) 17.3890 + 12.6338i 0.715287 + 0.519687i
\(592\) −4.89686 + 1.59109i −0.201260 + 0.0653932i
\(593\) 19.2384i 0.790026i 0.918676 + 0.395013i \(0.129260\pi\)
−0.918676 + 0.395013i \(0.870740\pi\)
\(594\) −3.71140 11.4225i −0.152281 0.468671i
\(595\) −4.37368 4.02863i −0.179303 0.165158i
\(596\) −14.8428 + 45.6816i −0.607986 + 1.87119i
\(597\) −12.9024 4.19223i −0.528059 0.171577i
\(598\) 5.73745 + 7.89692i 0.234622 + 0.322929i
\(599\) −19.3811 −0.791891 −0.395945 0.918274i \(-0.629583\pi\)
−0.395945 + 0.918274i \(0.629583\pi\)
\(600\) −8.34734 + 13.7307i −0.340779 + 0.560555i
\(601\) −7.35381 −0.299968 −0.149984 0.988688i \(-0.547922\pi\)
−0.149984 + 0.988688i \(0.547922\pi\)
\(602\) −0.000461855 0 0.000635689i −1.88238e−5 0 2.59087e-5i
\(603\) −1.64256 0.533701i −0.0668903 0.0217340i
\(604\) −1.98864 + 6.12040i −0.0809165 + 0.249035i
\(605\) 6.94842 + 34.6111i 0.282493 + 1.40714i
\(606\) −3.90173 12.0083i −0.158497 0.487803i
\(607\) 16.9661i 0.688633i −0.938854 0.344317i \(-0.888111\pi\)
0.938854 0.344317i \(-0.111889\pi\)
\(608\) −12.8941 + 4.18954i −0.522924 + 0.169908i
\(609\) −4.13039 3.00090i −0.167372 0.121603i
\(610\) −48.4018 + 9.71699i −1.95973 + 0.393430i
\(611\) 30.5806 22.2181i 1.23716 0.898847i
\(612\) −5.29094 + 7.28235i −0.213873 + 0.294372i
\(613\) −4.93803 + 6.79661i −0.199445 + 0.274513i −0.897011 0.442008i \(-0.854266\pi\)
0.697566 + 0.716520i \(0.254266\pi\)
\(614\) −1.96923 + 1.43073i −0.0794715 + 0.0577394i
\(615\) −3.21023 1.47304i −0.129449 0.0593986i
\(616\) −13.4568 9.77690i −0.542188 0.393923i
\(617\) −7.23935 + 2.35221i −0.291445 + 0.0946963i −0.451091 0.892478i \(-0.648965\pi\)
0.159645 + 0.987174i \(0.448965\pi\)
\(618\) 25.9141i 1.04242i
\(619\) 2.02277 + 6.22546i 0.0813022 + 0.250222i 0.983443 0.181220i \(-0.0580047\pi\)
−0.902140 + 0.431443i \(0.858005\pi\)
\(620\) 37.2092 20.9249i 1.49436 0.840366i
\(621\) −0.290991 + 0.895580i −0.0116771 + 0.0359384i
\(622\) −11.2480 3.65470i −0.451004 0.146540i
\(623\) 10.7722 + 14.8266i 0.431578 + 0.594016i
\(624\) 3.07275 0.123008
\(625\) −11.5075 22.1941i −0.460301 0.887763i
\(626\) −58.0632 −2.32067
\(627\) −8.53696 11.7501i −0.340933 0.469254i
\(628\) 59.7323 + 19.4082i 2.38358 + 0.774472i
\(629\) 6.15096 18.9307i 0.245255 0.754817i
\(630\) −4.52279 + 2.54343i −0.180192 + 0.101333i
\(631\) 3.76901 + 11.5998i 0.150042 + 0.461782i 0.997625 0.0688813i \(-0.0219430\pi\)
−0.847583 + 0.530663i \(0.821943\pi\)
\(632\) 19.0424i 0.757468i
\(633\) −2.91686 + 0.947746i −0.115935 + 0.0376695i
\(634\) −59.4988 43.2284i −2.36300 1.71682i
\(635\) 16.9987 + 7.79998i 0.674573 + 0.309533i
\(636\) −15.9218 + 11.5679i −0.631341 + 0.458696i
\(637\) −2.62561 + 3.61385i −0.104031 + 0.143186i
\(638\) 36.0419 49.6074i 1.42691 1.96397i
\(639\) 10.6144 7.71178i 0.419898 0.305073i
\(640\) −42.8516 + 8.60275i −1.69386 + 0.340054i
\(641\) 28.1749 + 20.4703i 1.11284 + 0.808528i 0.983109 0.183021i \(-0.0585876\pi\)
0.129734 + 0.991549i \(0.458588\pi\)
\(642\) 42.0623 13.6669i 1.66007 0.539388i
\(643\) 35.4073i 1.39633i 0.715937 + 0.698165i \(0.246000\pi\)
−0.715937 + 0.698165i \(0.754000\pi\)
\(644\) 0.984985 + 3.03147i 0.0388139 + 0.119457i
\(645\) −0.000149030 0 0.000742338i −5.86803e−6 0 2.92295e-5i
\(646\) −5.35126 + 16.4695i −0.210542 + 0.647983i
\(647\) 7.56790 + 2.45896i 0.297525 + 0.0966717i 0.453976 0.891014i \(-0.350005\pi\)
−0.156451 + 0.987686i \(0.550005\pi\)
\(648\) 1.88902 + 2.60001i 0.0742076 + 0.102138i
\(649\) −63.6323 −2.49779
\(650\) −26.9236 + 44.2872i −1.05603 + 1.73709i
\(651\) 5.64007 0.221052
\(652\) −18.4599 25.4079i −0.722947 0.995052i
\(653\) −22.3450 7.26033i −0.874427 0.284119i −0.162786 0.986661i \(-0.552048\pi\)
−0.711642 + 0.702543i \(0.752048\pi\)
\(654\) −4.22508 + 13.0034i −0.165214 + 0.508475i
\(655\) −32.8644 30.2716i −1.28412 1.18281i
\(656\) 0.335769 + 1.03339i 0.0131096 + 0.0403471i
\(657\) 3.00246i 0.117137i
\(658\) 18.6755 6.06803i 0.728046 0.236556i
\(659\) −31.7548 23.0712i −1.23699 0.898726i −0.239597 0.970873i \(-0.577015\pi\)
−0.997394 + 0.0721462i \(0.977015\pi\)
\(660\) −19.2019 34.1453i −0.747434 1.32910i
\(661\) 7.41041 5.38398i 0.288231 0.209412i −0.434268 0.900784i \(-0.642993\pi\)
0.722500 + 0.691371i \(0.242993\pi\)
\(662\) −35.5083 + 48.8730i −1.38007 + 1.89950i
\(663\) −6.98225 + 9.61024i −0.271168 + 0.373231i
\(664\) 22.0681 16.0334i 0.856407 0.622216i
\(665\) −4.25120 + 4.61532i −0.164855 + 0.178974i
\(666\) −14.0522 10.2095i −0.544511 0.395610i
\(667\) −4.57233 + 1.48564i −0.177041 + 0.0575242i
\(668\) 56.3136i 2.17884i
\(669\) −1.79077 5.51143i −0.0692353 0.213084i
\(670\) −8.90143 1.03755i −0.343892 0.0400839i
\(671\) 15.2165 46.8315i 0.587425 1.80791i
\(672\) −4.59485 1.49296i −0.177250 0.0575921i
\(673\) 12.0813 + 16.6284i 0.465698 + 0.640979i 0.975678 0.219207i \(-0.0703471\pi\)
−0.509980 + 0.860186i \(0.670347\pi\)
\(674\) −51.5705 −1.98642
\(675\) −4.98316 + 0.409976i −0.191802 + 0.0157800i
\(676\) 23.5380 0.905306
\(677\) 13.0856 + 18.0108i 0.502921 + 0.692212i 0.982706 0.185175i \(-0.0592851\pi\)
−0.479784 + 0.877386i \(0.659285\pi\)
\(678\) 29.4444 + 9.56708i 1.13081 + 0.367421i
\(679\) −2.82969 + 8.70890i −0.108594 + 0.334217i
\(680\) −7.96990 + 17.3690i −0.305632 + 0.666072i
\(681\) 3.56051 + 10.9581i 0.136439 + 0.419916i
\(682\) 67.7392i 2.59387i
\(683\) −17.0845 + 5.55108i −0.653718 + 0.212406i −0.617053 0.786922i \(-0.711674\pi\)
−0.0366655 + 0.999328i \(0.511674\pi\)
\(684\) 7.68469 + 5.58325i 0.293831 + 0.213481i
\(685\) 3.46176 29.6995i 0.132267 1.13476i
\(686\) −1.87736 + 1.36398i −0.0716779 + 0.0520771i
\(687\) −4.87223 + 6.70605i −0.185887 + 0.255852i
\(688\) −0.000136909 0 0.000188438i −5.21959e−6 0 7.18415e-6i
\(689\) −21.0114 + 15.2657i −0.800472 + 0.581577i
\(690\) −0.565705 + 4.85336i −0.0215360 + 0.184764i
\(691\) 13.5245 + 9.82614i 0.514497 + 0.373804i 0.814527 0.580126i \(-0.196997\pi\)
−0.300030 + 0.953930i \(0.596997\pi\)
\(692\) 5.88892 1.91343i 0.223863 0.0727375i
\(693\) 5.17565i 0.196607i
\(694\) 5.16921 + 15.9092i 0.196220 + 0.603904i
\(695\) 2.03004 4.42411i 0.0770037 0.167816i
\(696\) −5.07029 + 15.6048i −0.192189 + 0.591497i
\(697\) −3.99497 1.29804i −0.151320 0.0491669i
\(698\) −20.1770 27.7712i −0.763710 1.05116i
\(699\) 27.7340 1.04900
\(700\) −12.8305 + 11.0373i −0.484948 + 0.417169i
\(701\) 6.05281 0.228611 0.114306 0.993446i \(-0.463536\pi\)
0.114306 + 0.993446i \(0.463536\pi\)
\(702\) 6.09286 + 8.38610i 0.229960 + 0.316513i
\(703\) −19.9766 6.49079i −0.753432 0.244805i
\(704\) 20.1313 61.9577i 0.758726 2.33512i
\(705\) 18.7945 + 2.19067i 0.707841 + 0.0825056i
\(706\) −0.718897 2.21254i −0.0270560 0.0832699i
\(707\) 5.44108i 0.204633i
\(708\) 39.5793 12.8601i 1.48748 0.483312i
\(709\) −1.82096 1.32300i −0.0683875 0.0496864i 0.553066 0.833137i \(-0.313458\pi\)
−0.621454 + 0.783451i \(0.713458\pi\)
\(710\) 46.1231 50.0736i 1.73097 1.87923i
\(711\) 4.79361 3.48276i 0.179775 0.130614i
\(712\) 34.6195 47.6496i 1.29742 1.78574i
\(713\) 3.12177 4.29675i 0.116911 0.160915i
\(714\) −4.99243 + 3.62721i −0.186837 + 0.135745i
\(715\) −25.3401 45.0603i −0.947664 1.68516i
\(716\) 44.0403 + 31.9971i 1.64586 + 1.19579i
\(717\) 14.6210 4.75066i 0.546032 0.177417i
\(718\) 45.0158i 1.67998i
\(719\) 12.4551 + 38.3330i 0.464499 + 1.42958i 0.859612 + 0.510947i \(0.170705\pi\)
−0.395114 + 0.918632i \(0.629295\pi\)
\(720\) 1.13135 + 1.04210i 0.0421630 + 0.0388366i
\(721\) −3.45087 + 10.6207i −0.128517 + 0.395534i
\(722\) −24.5530 7.97776i −0.913769 0.296902i
\(723\) 11.7735 + 16.2048i 0.437860 + 0.602662i
\(724\) 17.2768 0.642085
\(725\) −16.6473 19.3521i −0.618267 0.718719i
\(726\) 36.6354 1.35967
\(727\) 15.6801 + 21.5818i 0.581544 + 0.800426i 0.993864 0.110613i \(-0.0352813\pi\)
−0.412320 + 0.911039i \(0.635281\pi\)
\(728\) 13.6532 + 4.43621i 0.506023 + 0.164417i
\(729\) −0.309017 + 0.951057i −0.0114451 + 0.0352243i
\(730\) −3.06650 15.2747i −0.113496 0.565341i
\(731\) −0.000278255 0 0.000856382i −1.02916e−5 0 3.16744e-5i
\(732\) 32.2044i 1.19031i
\(733\) 4.83856 1.57214i 0.178716 0.0580684i −0.218292 0.975884i \(-0.570048\pi\)
0.397008 + 0.917815i \(0.370048\pi\)
\(734\) 14.6744 + 10.6616i 0.541643 + 0.393527i
\(735\) −2.19233 + 0.440125i −0.0808651 + 0.0162342i
\(736\) −3.68062 + 2.67412i −0.135669 + 0.0985695i
\(737\) 5.25411 7.23166i 0.193538 0.266382i
\(738\) −2.15452 + 2.96545i −0.0793091 + 0.109160i
\(739\) 13.5298 9.82996i 0.497701 0.361601i −0.310437 0.950594i \(-0.600475\pi\)
0.808138 + 0.588993i \(0.200475\pi\)
\(740\) −51.4919 23.6275i −1.89288 0.868563i
\(741\) 10.1412 + 7.36801i 0.372546 + 0.270671i
\(742\) −12.8316 + 4.16925i −0.471064 + 0.153058i
\(743\) 40.3290i 1.47953i −0.672867 0.739764i \(-0.734937\pi\)
0.672867 0.739764i \(-0.265063\pi\)
\(744\) −5.60124 17.2388i −0.205351 0.632007i
\(745\) −27.6568 + 15.5530i −1.01327 + 0.569819i
\(746\) 8.92720 27.4751i 0.326848 1.00593i
\(747\) 8.07227 + 2.62284i 0.295349 + 0.0959647i
\(748\) −27.3841 37.6909i −1.00126 1.37812i
\(749\) 19.0588 0.696395
\(750\) −24.9326 + 7.17516i −0.910409 + 0.262000i
\(751\) −18.9864 −0.692822 −0.346411 0.938083i \(-0.612600\pi\)
−0.346411 + 0.938083i \(0.612600\pi\)
\(752\) −3.42144 4.70921i −0.124767 0.171727i
\(753\) −0.284354 0.0923923i −0.0103624 0.00336696i
\(754\) −16.3538 + 50.3317i −0.595569 + 1.83297i
\(755\) −3.70544 + 2.08379i −0.134855 + 0.0758368i
\(756\) 1.04600 + 3.21926i 0.0380427 + 0.117083i
\(757\) 25.6342i 0.931690i −0.884866 0.465845i \(-0.845750\pi\)
0.884866 0.465845i \(-0.154250\pi\)
\(758\) 76.9923 25.0163i 2.79648 0.908633i
\(759\) −3.94295 2.86472i −0.143120 0.103983i
\(760\) 18.3286 + 8.41023i 0.664849 + 0.305071i
\(761\) 2.57348 1.86974i 0.0932886 0.0677782i −0.540163 0.841560i \(-0.681637\pi\)
0.633452 + 0.773782i \(0.281637\pi\)
\(762\) 11.4086 15.7025i 0.413289 0.568843i
\(763\) −3.46323 + 4.76672i −0.125377 + 0.172567i
\(764\) −72.6684 + 52.7967i −2.62905 + 1.91012i
\(765\) −5.83001 + 1.17042i −0.210785 + 0.0423165i
\(766\) 19.7477 + 14.3476i 0.713514 + 0.518398i
\(767\) 52.2314 16.9710i 1.88596 0.612787i
\(768\) 20.1837i 0.728316i
\(769\) −13.3440 41.0687i −0.481198 1.48098i −0.837413 0.546571i \(-0.815933\pi\)
0.356215 0.934404i \(-0.384067\pi\)
\(770\) −5.28604 26.3306i −0.190496 0.948888i
\(771\) 4.26686 13.1320i 0.153667 0.472939i
\(772\) −16.4753 5.35314i −0.592958 0.192664i
\(773\) 5.40026 + 7.43283i 0.194234 + 0.267340i 0.895015 0.446037i \(-0.147165\pi\)
−0.700781 + 0.713377i \(0.747165\pi\)
\(774\) −0.000785754 0 −2.82434e−5 0
\(775\) 27.4444 + 6.48592i 0.985831 + 0.232981i
\(776\) 29.4289 1.05644
\(777\) −4.39962 6.05555i −0.157835 0.217242i
\(778\) −57.0247 18.5284i −2.04443 0.664277i
\(779\) −1.36976 + 4.21568i −0.0490767 + 0.151043i
\(780\) 24.8682 + 22.9063i 0.890425 + 0.820176i
\(781\) 20.9838 + 64.5814i 0.750859 + 2.31091i
\(782\) 5.81102i 0.207802i
\(783\) −4.85556 + 1.57767i −0.173524 + 0.0563813i
\(784\) 0.556510 + 0.404328i 0.0198753 + 0.0144403i
\(785\) 20.3368 + 36.1634i 0.725853 + 1.29073i
\(786\) −37.5138 + 27.2554i −1.33807 + 0.972166i
\(787\) 4.70018 6.46925i 0.167543 0.230604i −0.716987 0.697087i \(-0.754479\pi\)
0.884530 + 0.466483i \(0.154479\pi\)
\(788\) 42.7646 58.8605i 1.52343 2.09682i
\(789\) −2.51481 + 1.82712i −0.0895295 + 0.0650470i
\(790\) 20.8299 22.6140i 0.741096 0.804571i
\(791\) 10.7936 + 7.84198i 0.383775 + 0.278829i
\(792\) −15.8194 + 5.14002i −0.562116 + 0.182643i
\(793\) 42.4990i 1.50918i
\(794\) −23.2709 71.6204i −0.825853 2.54171i
\(795\) −12.9134 1.50518i −0.457991 0.0533832i
\(796\) −14.1904 + 43.6736i −0.502966 + 1.54797i
\(797\) 40.1674 + 13.0512i 1.42280 + 0.462297i 0.916491 0.400054i \(-0.131009\pi\)
0.506311 + 0.862351i \(0.331009\pi\)
\(798\) 3.82761 + 5.26825i 0.135496 + 0.186494i
\(799\) 22.5030 0.796098
\(800\) −20.6415 12.5486i −0.729787 0.443661i
\(801\) 18.3267 0.647542
\(802\) 27.5332 + 37.8962i 0.972232 + 1.33816i
\(803\) 14.7791 + 4.80203i 0.521544 + 0.169460i
\(804\) −1.80654 + 5.55995i −0.0637117 + 0.196084i
\(805\) −0.878151 + 1.91378i −0.0309508 + 0.0674518i
\(806\) −18.0663 55.6024i −0.636358 1.95851i
\(807\) 15.5604i 0.547750i
\(808\) −16.6306 + 5.40362i −0.585063 + 0.190099i
\(809\) 2.89419 + 2.10275i 0.101754 + 0.0739287i 0.637499 0.770451i \(-0.279969\pi\)
−0.535745 + 0.844380i \(0.679969\pi\)
\(810\) −0.600748 + 5.15400i −0.0211081 + 0.181093i
\(811\) 45.7545 33.2426i 1.60666 1.16731i 0.733750 0.679420i \(-0.237769\pi\)
0.872908 0.487885i \(-0.162231\pi\)
\(812\) −10.1578 + 13.9811i −0.356470 + 0.490639i
\(813\) 9.12542 12.5601i 0.320043 0.440501i
\(814\) 72.7292 52.8409i 2.54916 1.85207i
\(815\) 2.40195 20.6071i 0.0841368 0.721835i
\(816\) 1.47992 + 1.07522i 0.0518074 + 0.0376403i
\(817\) −0.000903696 0 0.000293629i −3.16163e−5 0 1.02728e-5i
\(818\) 8.52400i 0.298035i
\(819\) 1.38037 + 4.24833i 0.0482339 + 0.148449i
\(820\) −4.98613 + 10.8664i −0.174123 + 0.379471i
\(821\) −3.72071 + 11.4512i −0.129854 + 0.399649i −0.994754 0.102295i \(-0.967381\pi\)
0.864900 + 0.501944i \(0.167381\pi\)
\(822\) −29.5115 9.58886i −1.02933 0.334450i
\(823\) 13.1583 + 18.1108i 0.458668 + 0.631302i 0.974232 0.225549i \(-0.0724175\pi\)
−0.515564 + 0.856851i \(0.672417\pi\)
\(824\) 35.8891 1.25026
\(825\) 5.95186 25.1845i 0.207217 0.876813i
\(826\) 28.5301 0.992688
\(827\) −9.39440 12.9303i −0.326675 0.449630i 0.613815 0.789450i \(-0.289634\pi\)
−0.940491 + 0.339820i \(0.889634\pi\)
\(828\) 3.03147 + 0.984985i 0.105351 + 0.0342306i
\(829\) 0.0162211 0.0499233i 0.000563381 0.00173391i −0.950774 0.309884i \(-0.899710\pi\)
0.951338 + 0.308150i \(0.0997098\pi\)
\(830\) 43.7456 + 5.09897i 1.51843 + 0.176988i
\(831\) 7.62325 + 23.4619i 0.264447 + 0.813886i
\(832\) 56.2259i 1.94928i
\(833\) −2.52913 + 0.821764i −0.0876291 + 0.0284724i
\(834\) −4.08677 2.96921i −0.141513 0.102815i
\(835\) 25.2032 27.3619i 0.872193 0.946897i
\(836\) −39.7733 + 28.8970i −1.37559 + 0.999423i
\(837\) 3.31515 4.56291i 0.114588 0.157717i
\(838\) −37.2974 + 51.3355i −1.28842 + 1.77335i
\(839\) −1.41909 + 1.03103i −0.0489925 + 0.0355951i −0.612012 0.790848i \(-0.709640\pi\)
0.563019 + 0.826444i \(0.309640\pi\)
\(840\) 3.52247 + 6.26374i 0.121537 + 0.216119i
\(841\) 2.37404 + 1.72484i 0.0818635 + 0.0594773i
\(842\) 58.6624 19.0606i 2.02164 0.656871i
\(843\) 18.1623i 0.625543i
\(844\) 3.20805 + 9.87337i 0.110426 + 0.339855i
\(845\) 11.4367 + 10.5344i 0.393436 + 0.362396i
\(846\) 6.06803 18.6755i 0.208623 0.642076i
\(847\) 15.0147 + 4.87857i 0.515911 + 0.167630i
\(848\) 2.35082 + 3.23563i 0.0807275 + 0.111112i
\(849\) 26.5387 0.910807
\(850\) −28.4642 + 11.9087i −0.976313 + 0.408466i
\(851\) −7.04846 −0.241618
\(852\) −26.1038 35.9288i −0.894303 1.23090i
\(853\) −34.0995 11.0796i −1.16754 0.379358i −0.339819 0.940491i \(-0.610366\pi\)
−0.827726 + 0.561133i \(0.810366\pi\)
\(854\) −6.82242 + 20.9973i −0.233458 + 0.718511i
\(855\) 1.23508 + 6.15211i 0.0422388 + 0.210398i
\(856\) −18.9276 58.2533i −0.646933 1.99106i
\(857\) 38.5172i 1.31572i 0.753140 + 0.657861i \(0.228538\pi\)
−0.753140 + 0.657861i \(0.771462\pi\)
\(858\) −51.0239 + 16.5787i −1.74193 + 0.565987i
\(859\) −16.3219 11.8585i −0.556895 0.404608i 0.273426 0.961893i \(-0.411843\pi\)
−0.830321 + 0.557285i \(0.811843\pi\)
\(860\) −0.00251276 0.000504454i −8.56845e−5 1.72018e-5i
\(861\) −1.27791 + 0.928456i −0.0435510 + 0.0316417i
\(862\) 13.4313 18.4866i 0.457472 0.629656i
\(863\) 14.2071 19.5544i 0.483614 0.665638i −0.495580 0.868562i \(-0.665045\pi\)
0.979194 + 0.202924i \(0.0650445\pi\)
\(864\) −3.90861 + 2.83977i −0.132974 + 0.0966111i
\(865\) 3.71769 + 1.70589i 0.126405 + 0.0580020i
\(866\) −67.0088 48.6848i −2.27705 1.65438i
\(867\) 9.44229 3.06799i 0.320677 0.104194i
\(868\) 19.0912i 0.647999i
\(869\) 9.47661 + 29.1660i 0.321472 + 0.989389i
\(870\) −23.0908 + 12.9853i −0.782852 + 0.440244i
\(871\) −2.38402 + 7.33726i −0.0807795 + 0.248614i
\(872\) 18.0088 + 5.85143i 0.609856 + 0.198154i
\(873\) 5.38240 + 7.40823i 0.182167 + 0.250731i
\(874\) 6.13207 0.207420
\(875\) −11.1739 0.379484i −0.377747 0.0128289i
\(876\) −10.1631 −0.343380
\(877\) −5.42670 7.46921i −0.183247 0.252217i 0.707504 0.706709i \(-0.249821\pi\)
−0.890751 + 0.454492i \(0.849821\pi\)
\(878\) 45.9186 + 14.9199i 1.54968 + 0.503521i
\(879\) 5.30733 16.3343i 0.179012 0.550942i
\(880\) −6.93899 + 3.90221i −0.233913 + 0.131543i
\(881\) −8.22581 25.3164i −0.277134 0.852932i −0.988647 0.150258i \(-0.951989\pi\)
0.711512 0.702674i \(-0.248011\pi\)
\(882\) 2.32054i 0.0781368i
\(883\) −30.8191 + 10.0137i −1.03714 + 0.336988i −0.777611 0.628746i \(-0.783569\pi\)
−0.259533 + 0.965734i \(0.583569\pi\)
\(884\) 32.5300 + 23.6344i 1.09410 + 0.794912i
\(885\) 24.9865 + 11.4653i 0.839914 + 0.385401i
\(886\) −38.8583 + 28.2322i −1.30547 + 0.948480i
\(887\) −15.5231 + 21.3658i −0.521216 + 0.717392i −0.985760 0.168158i \(-0.946218\pi\)
0.464544 + 0.885550i \(0.346218\pi\)
\(888\) −14.1394 + 19.4613i −0.474489 + 0.653077i
\(889\) 6.76675 4.91633i 0.226949 0.164888i
\(890\) 93.2351 18.7176i 3.12525 0.627415i
\(891\) −4.18719 3.04217i −0.140276 0.101917i
\(892\) −18.6558 + 6.06164i −0.624643 + 0.202959i
\(893\) 23.7462i 0.794637i
\(894\) 10.1755 + 31.3171i 0.340321 + 1.04740i
\(895\) 7.07813 + 35.2572i 0.236596 + 1.17852i
\(896\) −6.04010 + 18.5895i −0.201786 + 0.621032i
\(897\) 4.00052 + 1.29985i 0.133573 + 0.0434007i
\(898\) −27.5266 37.8871i −0.918575 1.26431i
\(899\) 28.7950 0.960369
\(900\) 1.38774 + 16.8677i 0.0462580 + 0.562255i
\(901\) −15.4614 −0.515095
\(902\) −11.1511 15.3481i −0.371290 0.511037i
\(903\) −0.000322035 0 0.000104636i −1.07167e−5 0 3.48205e-6i
\(904\) 13.2497 40.7784i 0.440679 1.35627i
\(905\) 8.39451 + 7.73224i 0.279043 + 0.257028i
\(906\) 1.36331 + 4.19585i 0.0452931 + 0.139398i
\(907\) 0.471242i 0.0156473i 0.999969 + 0.00782367i \(0.00249038\pi\)
−0.999969 + 0.00782367i \(0.997510\pi\)
\(908\) 37.0925 12.0521i 1.23096 0.399962i
\(909\) −4.40192 3.19818i −0.146003 0.106077i
\(910\) 11.3614 + 20.2031i 0.376627 + 0.669727i
\(911\) −23.1612 + 16.8276i −0.767365 + 0.557523i −0.901160 0.433486i \(-0.857283\pi\)
0.133796 + 0.991009i \(0.457283\pi\)
\(912\) 1.13463 1.56168i 0.0375712 0.0517124i
\(913\) −25.8210 + 35.5396i −0.854551 + 1.17619i
\(914\) 5.20775 3.78365i 0.172257 0.125152i
\(915\) −14.4131 + 15.6476i −0.476484 + 0.517295i
\(916\) 22.6995 + 16.4922i 0.750013 + 0.544916i
\(917\) −19.0042 + 6.17484i −0.627574 + 0.203911i
\(918\) 6.17098i 0.203673i
\(919\) −15.4330 47.4979i −0.509088 1.56681i −0.793788 0.608195i \(-0.791894\pi\)
0.284700 0.958617i \(-0.408106\pi\)
\(920\) 6.72156 + 0.783462i 0.221603 + 0.0258300i
\(921\) −0.324138 + 0.997595i −0.0106807 + 0.0328719i
\(922\) −16.0314 5.20890i −0.527965 0.171546i
\(923\) −34.4482 47.4139i −1.13388 1.56065i
\(924\) −17.5192 −0.576340
\(925\) −14.4446 34.5255i −0.474937 1.13519i
\(926\) −43.4431 −1.42763
\(927\) 6.56394 + 9.03448i 0.215588 + 0.296731i
\(928\) −23.4587 7.62221i −0.770071 0.250211i
\(929\) −10.7065 + 32.9512i −0.351268 + 1.08109i 0.606874 + 0.794798i \(0.292423\pi\)
−0.958142 + 0.286294i \(0.907577\pi\)
\(930\) 12.2052 26.5992i 0.400225 0.872221i
\(931\) 0.867165 + 2.66886i 0.0284202 + 0.0874683i
\(932\) 93.8776i 3.07506i
\(933\) −4.84714 + 1.57493i −0.158688 + 0.0515609i
\(934\) −44.4638 32.3049i −1.45490 1.05705i
\(935\) 3.56314 30.5692i 0.116527 0.999720i
\(936\) 11.6141 8.43817i 0.379620 0.275810i
\(937\) −1.24560 + 1.71442i −0.0406919 + 0.0560076i −0.828878 0.559429i \(-0.811020\pi\)
0.788186 + 0.615437i \(0.211020\pi\)
\(938\) −2.35572 + 3.24237i −0.0769170 + 0.105867i
\(939\) −20.2427 + 14.7072i −0.660595 + 0.479951i
\(940\) 7.41528 63.6179i 0.241860 2.07499i
\(941\) −5.94898 4.32219i −0.193931 0.140899i 0.486582 0.873635i \(-0.338243\pi\)
−0.680514 + 0.732735i \(0.738243\pi\)
\(942\) 40.9496 13.3053i 1.33421 0.433511i
\(943\) 1.48744i 0.0484378i
\(944\) −2.61343 8.04330i −0.0850597 0.261787i
\(945\) −0.932548 + 2.03233i −0.0303358 + 0.0661116i
\(946\) 0.00125671 0.00386775i 4.08591e−5 0.000125751i
\(947\) 12.8267 + 4.16766i 0.416813 + 0.135431i 0.509913 0.860226i \(-0.329678\pi\)
−0.0931000 + 0.995657i \(0.529678\pi\)
\(948\) −11.7889 16.2260i −0.382886 0.526997i
\(949\) −13.4119 −0.435368
\(950\) 12.5667 + 30.0368i 0.407716 + 0.974521i
\(951\) −31.6928 −1.02771
\(952\) 5.02343 + 6.91416i 0.162810 + 0.224089i
\(953\) −32.3471 10.5102i −1.04783 0.340459i −0.266011 0.963970i \(-0.585706\pi\)
−0.781815 + 0.623511i \(0.785706\pi\)
\(954\) −4.16925 + 12.8316i −0.134984 + 0.415439i
\(955\) −58.9377 6.86976i −1.90718 0.222300i
\(956\) −16.0806 49.4911i −0.520085 1.60066i
\(957\) 26.4240i 0.854166i
\(958\) −77.1985 + 25.0833i −2.49417 + 0.810405i
\(959\) −10.8181 7.85983i −0.349336 0.253807i
\(960\) −19.0685 + 20.7017i −0.615433 + 0.668145i
\(961\) −0.655631 + 0.476344i −0.0211494 + 0.0153659i
\(962\) −45.6055 + 62.7706i −1.47038 + 2.02380i
\(963\) 11.2025 15.4189i 0.360996 0.496868i
\(964\) 54.8520 39.8523i 1.76666 1.28356i
\(965\) −5.60927 9.97454i −0.180569 0.321092i
\(966\) 1.76785 + 1.28442i 0.0568796 + 0.0413255i
\(967\) 11.9868 3.89474i 0.385468 0.125246i −0.109871 0.993946i \(-0.535044\pi\)
0.495339 + 0.868700i \(0.335044\pi\)
\(968\) 50.7373i 1.63076i
\(969\) 2.30604 + 7.09725i 0.0740805 + 0.227996i
\(970\) 34.9486 + 32.1914i 1.12213 + 1.03360i
\(971\) 10.9966 33.8439i 0.352896 1.08610i −0.604323 0.796739i \(-0.706556\pi\)
0.957219 0.289364i \(-0.0934437\pi\)
\(972\) 3.21926 + 1.04600i 0.103258 + 0.0335505i
\(973\) −1.27953 1.76113i −0.0410199 0.0564591i
\(974\) −4.33534 −0.138913
\(975\) 1.83135 + 22.2596i 0.0586501 + 0.712878i
\(976\) 6.54457 0.209487
\(977\) −1.64254 2.26076i −0.0525495 0.0723282i 0.781934 0.623362i \(-0.214234\pi\)
−0.834483 + 0.551034i \(0.814234\pi\)
\(978\) −20.4766 6.65326i −0.654771 0.212748i
\(979\) −29.3111 + 90.2102i −0.936786 + 2.88313i
\(980\) 1.48979 + 7.42086i 0.0475896 + 0.237051i
\(981\) 1.82073 + 5.60362i 0.0581313 + 0.178910i
\(982\) 61.7122i 1.96932i
\(983\) −30.0303 + 9.75743i −0.957818 + 0.311214i −0.745888 0.666071i \(-0.767975\pi\)
−0.211929 + 0.977285i \(0.567975\pi\)
\(984\) 4.10693 + 2.98386i 0.130924 + 0.0951220i
\(985\) 47.1218 9.46002i 1.50142 0.301421i
\(986\) −25.4886 + 18.5185i −0.811721 + 0.589750i
\(987\) 4.97387 6.84594i 0.158320 0.217909i
\(988\) 24.9402 34.3272i 0.793453 1.09209i
\(989\) −0.000257960 0 0.000187419i −8.20265e−6 0 5.95957e-6i
\(990\) −24.4089 11.2002i −0.775767 0.355966i
\(991\) −1.33266 0.968235i −0.0423334 0.0307570i 0.566417 0.824119i \(-0.308329\pi\)
−0.608751 + 0.793362i \(0.708329\pi\)
\(992\) 25.9153 8.42039i 0.822811 0.267348i
\(993\) 26.0328i 0.826127i
\(994\) −9.40824 28.9556i −0.298411 0.918415i
\(995\) −26.4411 + 14.8694i −0.838239 + 0.471391i
\(996\) 8.87813 27.3241i 0.281314 0.865796i
\(997\) 43.0771 + 13.9966i 1.36427 + 0.443277i 0.897465 0.441086i \(-0.145406\pi\)
0.466801 + 0.884362i \(0.345406\pi\)
\(998\) 40.2551 + 55.4064i 1.27425 + 1.75386i
\(999\) −7.48508 −0.236817
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 525.2.z.b.64.2 72
25.9 even 10 inner 525.2.z.b.484.2 yes 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.z.b.64.2 72 1.1 even 1 trivial
525.2.z.b.484.2 yes 72 25.9 even 10 inner