Properties

Label 441.2.bh.a.398.48
Level $441$
Weight $2$
Character 441.398
Analytic conductor $3.521$
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] = [441,2,Mod(20,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([7, 39]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.20");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bh (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: \(3.52140272914\)
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 398.48
Character \(\chi\) \(=\) 441.398
Dual form 441.2.bh.a.41.48

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.17816 - 0.854863i) q^{2} +(1.72389 + 0.167981i) q^{3} +(2.54747 - 2.36371i) q^{4} +(0.217005 + 2.89572i) q^{5} +(3.89849 - 1.10780i) q^{6} +(-2.64474 - 0.0731616i) q^{7} +(1.49765 - 3.10990i) q^{8} +(2.94356 + 0.579161i) q^{9} +O(q^{10})\) \(q+(2.17816 - 0.854863i) q^{2} +(1.72389 + 0.167981i) q^{3} +(2.54747 - 2.36371i) q^{4} +(0.217005 + 2.89572i) q^{5} +(3.89849 - 1.10780i) q^{6} +(-2.64474 - 0.0731616i) q^{7} +(1.49765 - 3.10990i) q^{8} +(2.94356 + 0.579161i) q^{9} +(2.94812 + 6.12183i) q^{10} +(-3.18378 + 1.24954i) q^{11} +(4.78860 - 3.64683i) q^{12} +(0.797972 - 5.29420i) q^{13} +(-5.82320 + 2.10153i) q^{14} +(-0.112336 + 5.02835i) q^{15} +(0.0841755 - 1.12324i) q^{16} +(0.598618 - 2.62272i) q^{17} +(6.90665 - 1.25484i) q^{18} -3.20566i q^{19} +(7.39745 + 6.86383i) q^{20} +(-4.54694 - 0.570389i) q^{21} +(-5.86658 + 5.44339i) q^{22} +(-5.71785 - 6.16238i) q^{23} +(3.10418 - 5.10953i) q^{24} +(-3.39398 + 0.511560i) q^{25} +(-2.78771 - 12.2137i) q^{26} +(4.97708 + 1.49287i) q^{27} +(-6.91032 + 6.06501i) q^{28} +(-6.02182 + 6.48998i) q^{29} +(4.05387 + 11.0486i) q^{30} +(4.22906 - 2.44165i) q^{31} +(1.25795 + 4.07819i) q^{32} +(-5.69837 + 1.61925i) q^{33} +(-0.938182 - 6.22443i) q^{34} +(-0.362065 - 7.67431i) q^{35} +(8.86761 - 5.48233i) q^{36} +(-0.00925870 + 0.0405650i) q^{37} +(-2.74040 - 6.98244i) q^{38} +(2.26494 - 8.99255i) q^{39} +(9.33040 + 3.66191i) q^{40} +(0.704310 + 9.39837i) q^{41} +(-10.3915 + 2.64462i) q^{42} +(-0.383109 + 5.11223i) q^{43} +(-5.15703 + 10.7087i) q^{44} +(-1.03832 + 8.64943i) q^{45} +(-17.7224 - 8.53464i) q^{46} +(-1.63657 - 4.16992i) q^{47} +(0.333793 - 1.92220i) q^{48} +(6.98929 + 0.386987i) q^{49} +(-6.95530 + 4.01564i) q^{50} +(1.47252 - 4.42071i) q^{51} +(-10.4811 - 15.3730i) q^{52} +(0.267296 - 0.0610085i) q^{53} +(12.1171 - 1.00302i) q^{54} +(-4.30922 - 8.94820i) q^{55} +(-4.18841 + 8.11529i) q^{56} +(0.538492 - 5.52620i) q^{57} +(-7.56843 + 19.2840i) q^{58} +(9.51729 + 6.48878i) q^{59} +(11.5994 + 13.0751i) q^{60} +(0.682114 - 0.735144i) q^{61} +(7.12428 - 8.93356i) q^{62} +(-7.74259 - 1.74709i) q^{63} +(7.63090 + 9.56885i) q^{64} +(15.5037 + 1.16184i) q^{65} +(-11.0277 + 8.39831i) q^{66} +(-2.84606 - 4.92952i) q^{67} +(-4.67437 - 8.09625i) q^{68} +(-8.82176 - 11.5837i) q^{69} +(-7.34912 - 16.4063i) q^{70} +(10.8006 - 2.46517i) q^{71} +(6.20955 - 8.28680i) q^{72} +(-2.74928 + 2.19247i) q^{73} +(0.0145106 + 0.0962719i) q^{74} +(-5.93676 + 0.311746i) q^{75} +(-7.57725 - 8.16633i) q^{76} +(8.51169 - 3.07178i) q^{77} +(-2.75401 - 21.5234i) q^{78} +(-4.95531 + 8.58285i) q^{79} +3.27087 q^{80} +(8.32914 + 3.40960i) q^{81} +(9.56842 + 19.8690i) q^{82} +(0.483462 - 0.0728702i) q^{83} +(-12.9314 + 9.29458i) q^{84} +(7.72457 + 1.16429i) q^{85} +(3.53579 + 11.4627i) q^{86} +(-11.4711 + 10.1764i) q^{87} +(-0.882234 + 11.7726i) q^{88} +(6.98508 + 8.75902i) q^{89} +(5.13245 + 19.7274i) q^{90} +(-2.49776 + 13.9434i) q^{91} +(-29.1321 - 2.18315i) q^{92} +(7.70057 - 3.49872i) q^{93} +(-7.12942 - 7.68369i) q^{94} +(9.28272 - 0.695644i) q^{95} +(1.48351 + 7.24164i) q^{96} +(-5.28392 - 3.05067i) q^{97} +(15.5546 - 5.13197i) q^{98} +(-10.0954 + 1.83419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 15 q^{2} - 14 q^{3} - 57 q^{4} - 21 q^{5} + 14 q^{6} - 5 q^{7} - 20 q^{9} - 28 q^{10} - 15 q^{11} + 21 q^{12} - 7 q^{13} - 114 q^{14} - 10 q^{15} + 39 q^{16} - 18 q^{18} - 21 q^{20} + 10 q^{21} + 3 q^{22} + 30 q^{23} - 14 q^{24} + 41 q^{25} + 7 q^{27} - 20 q^{28} + 75 q^{29} - 70 q^{30} - 39 q^{32} - 14 q^{33} - 7 q^{34} - 128 q^{36} - 10 q^{37} + 21 q^{38} - 36 q^{39} - 7 q^{40} - 21 q^{41} + 104 q^{42} + 3 q^{43} - 35 q^{45} - 72 q^{46} - 147 q^{47} - 13 q^{49} - 18 q^{50} + 22 q^{51} - 35 q^{52} - 14 q^{54} - 112 q^{55} - 63 q^{56} - 16 q^{57} + 33 q^{58} - 21 q^{59} - 90 q^{60} - 56 q^{61} - 38 q^{63} + 52 q^{64} + 27 q^{65} - 42 q^{66} - 26 q^{67} - 182 q^{69} - 25 q^{70} + 24 q^{72} - 28 q^{73} + 33 q^{74} - 14 q^{75} + 21 q^{76} + 3 q^{77} + 90 q^{78} - 2 q^{79} + 56 q^{81} - 28 q^{82} - 21 q^{83} + 116 q^{84} + 5 q^{85} - 123 q^{86} - 70 q^{87} - 41 q^{88} - 224 q^{90} - 4 q^{91} - 225 q^{92} + 112 q^{93} - 7 q^{94} - 12 q^{95} - 371 q^{96} + 224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.17816 0.854863i 1.54019 0.604480i 0.564850 0.825193i \(-0.308934\pi\)
0.975339 + 0.220714i \(0.0708387\pi\)
\(3\) 1.72389 + 0.167981i 0.995286 + 0.0969840i
\(4\) 2.54747 2.36371i 1.27373 1.18185i
\(5\) 0.217005 + 2.89572i 0.0970474 + 1.29501i 0.806913 + 0.590670i \(0.201137\pi\)
−0.709866 + 0.704337i \(0.751244\pi\)
\(6\) 3.89849 1.10780i 1.59155 0.452256i
\(7\) −2.64474 0.0731616i −0.999618 0.0276525i
\(8\) 1.49765 3.10990i 0.529498 1.09951i
\(9\) 2.94356 + 0.579161i 0.981188 + 0.193054i
\(10\) 2.94812 + 6.12183i 0.932277 + 1.93589i
\(11\) −3.18378 + 1.24954i −0.959946 + 0.376751i −0.793005 0.609216i \(-0.791484\pi\)
−0.166942 + 0.985967i \(0.553389\pi\)
\(12\) 4.78860 3.64683i 1.38235 1.05275i
\(13\) 0.797972 5.29420i 0.221318 1.46835i −0.551743 0.834014i \(-0.686037\pi\)
0.773061 0.634332i \(-0.218725\pi\)
\(14\) −5.82320 + 2.10153i −1.55632 + 0.561658i
\(15\) −0.112336 + 5.02835i −0.0290052 + 1.29831i
\(16\) 0.0841755 1.12324i 0.0210439 0.280811i
\(17\) 0.598618 2.62272i 0.145186 0.636103i −0.848997 0.528398i \(-0.822793\pi\)
0.994183 0.107705i \(-0.0343500\pi\)
\(18\) 6.90665 1.25484i 1.62791 0.295769i
\(19\) 3.20566i 0.735430i −0.929939 0.367715i \(-0.880140\pi\)
0.929939 0.367715i \(-0.119860\pi\)
\(20\) 7.39745 + 6.86383i 1.65412 + 1.53480i
\(21\) −4.54694 0.570389i −0.992223 0.124469i
\(22\) −5.86658 + 5.44339i −1.25076 + 1.16054i
\(23\) −5.71785 6.16238i −1.19225 1.28494i −0.949106 0.314955i \(-0.898010\pi\)
−0.243148 0.969989i \(-0.578180\pi\)
\(24\) 3.10418 5.10953i 0.633637 1.04298i
\(25\) −3.39398 + 0.511560i −0.678795 + 0.102312i
\(26\) −2.78771 12.2137i −0.546714 2.39531i
\(27\) 4.97708 + 1.49287i 0.957840 + 0.287303i
\(28\) −6.91032 + 6.06501i −1.30593 + 1.14618i
\(29\) −6.02182 + 6.48998i −1.11822 + 1.20516i −0.141665 + 0.989915i \(0.545245\pi\)
−0.976560 + 0.215245i \(0.930945\pi\)
\(30\) 4.05387 + 11.0486i 0.740131 + 2.01718i
\(31\) 4.22906 2.44165i 0.759561 0.438533i −0.0695768 0.997577i \(-0.522165\pi\)
0.829138 + 0.559044i \(0.188832\pi\)
\(32\) 1.25795 + 4.07819i 0.222377 + 0.720928i
\(33\) −5.69837 + 1.61925i −0.991960 + 0.281876i
\(34\) −0.938182 6.22443i −0.160897 1.06748i
\(35\) −0.362065 7.67431i −0.0612001 1.29720i
\(36\) 8.86761 5.48233i 1.47793 0.913721i
\(37\) −0.00925870 + 0.0405650i −0.00152212 + 0.00666885i −0.975683 0.219185i \(-0.929660\pi\)
0.974161 + 0.225854i \(0.0725172\pi\)
\(38\) −2.74040 6.98244i −0.444552 1.13270i
\(39\) 2.26494 8.99255i 0.362680 1.43996i
\(40\) 9.33040 + 3.66191i 1.47527 + 0.578999i
\(41\) 0.704310 + 9.39837i 0.109995 + 1.46778i 0.730143 + 0.683294i \(0.239453\pi\)
−0.620149 + 0.784484i \(0.712928\pi\)
\(42\) −10.3915 + 2.64462i −1.60345 + 0.408073i
\(43\) −0.383109 + 5.11223i −0.0584235 + 0.779608i 0.888649 + 0.458588i \(0.151645\pi\)
−0.947072 + 0.321020i \(0.895974\pi\)
\(44\) −5.15703 + 10.7087i −0.777452 + 1.61440i
\(45\) −1.03832 + 8.64943i −0.154784 + 1.28938i
\(46\) −17.7224 8.53464i −2.61302 1.25836i
\(47\) −1.63657 4.16992i −0.238719 0.608245i 0.760433 0.649416i \(-0.224987\pi\)
−0.999152 + 0.0411706i \(0.986891\pi\)
\(48\) 0.333793 1.92220i 0.0481789 0.277446i
\(49\) 6.98929 + 0.386987i 0.998471 + 0.0552838i
\(50\) −6.95530 + 4.01564i −0.983628 + 0.567898i
\(51\) 1.47252 4.42071i 0.206194 0.619023i
\(52\) −10.4811 15.3730i −1.45347 2.13185i
\(53\) 0.267296 0.0610085i 0.0367159 0.00838017i −0.204124 0.978945i \(-0.565434\pi\)
0.240839 + 0.970565i \(0.422577\pi\)
\(54\) 12.1171 1.00302i 1.64892 0.136493i
\(55\) −4.30922 8.94820i −0.581056 1.20657i
\(56\) −4.18841 + 8.11529i −0.559700 + 1.08445i
\(57\) 0.538492 5.52620i 0.0713250 0.731963i
\(58\) −7.56843 + 19.2840i −0.993783 + 2.53212i
\(59\) 9.51729 + 6.48878i 1.23905 + 0.844767i 0.992245 0.124299i \(-0.0396683\pi\)
0.246801 + 0.969066i \(0.420621\pi\)
\(60\) 11.5994 + 13.0751i 1.49747 + 1.68799i
\(61\) 0.682114 0.735144i 0.0873358 0.0941256i −0.687872 0.725832i \(-0.741455\pi\)
0.775207 + 0.631707i \(0.217645\pi\)
\(62\) 7.12428 8.93356i 0.904784 1.13456i
\(63\) −7.74259 1.74709i −0.975475 0.220112i
\(64\) 7.63090 + 9.56885i 0.953863 + 1.19611i
\(65\) 15.5037 + 1.16184i 1.92300 + 0.144109i
\(66\) −11.0277 + 8.39831i −1.35742 + 1.03376i
\(67\) −2.84606 4.92952i −0.347701 0.602236i 0.638139 0.769921i \(-0.279704\pi\)
−0.985841 + 0.167684i \(0.946371\pi\)
\(68\) −4.67437 8.09625i −0.566851 0.981815i
\(69\) −8.82176 11.5837i −1.06201 1.39452i
\(70\) −7.34912 16.4063i −0.878388 1.96093i
\(71\) 10.8006 2.46517i 1.28179 0.292561i 0.473215 0.880947i \(-0.343094\pi\)
0.808580 + 0.588386i \(0.200236\pi\)
\(72\) 6.20955 8.28680i 0.731802 0.976609i
\(73\) −2.74928 + 2.19247i −0.321778 + 0.256610i −0.771035 0.636793i \(-0.780260\pi\)
0.449256 + 0.893403i \(0.351689\pi\)
\(74\) 0.0145106 + 0.0962719i 0.00168683 + 0.0111914i
\(75\) −5.93676 + 0.311746i −0.685518 + 0.0359973i
\(76\) −7.57725 8.16633i −0.869170 0.936742i
\(77\) 8.51169 3.07178i 0.969997 0.350062i
\(78\) −2.75401 21.5234i −0.311830 2.43704i
\(79\) −4.95531 + 8.58285i −0.557516 + 0.965646i 0.440187 + 0.897906i \(0.354912\pi\)
−0.997703 + 0.0677396i \(0.978421\pi\)
\(80\) 3.27087 0.365695
\(81\) 8.32914 + 3.40960i 0.925461 + 0.378844i
\(82\) 9.56842 + 19.8690i 1.05665 + 2.19417i
\(83\) 0.483462 0.0728702i 0.0530669 0.00799855i −0.122455 0.992474i \(-0.539077\pi\)
0.175522 + 0.984476i \(0.443839\pi\)
\(84\) −12.9314 + 9.29458i −1.41093 + 1.01412i
\(85\) 7.72457 + 1.16429i 0.837848 + 0.126285i
\(86\) 3.53579 + 11.4627i 0.381274 + 1.23606i
\(87\) −11.4711 + 10.1764i −1.22983 + 1.09103i
\(88\) −0.882234 + 11.7726i −0.0940465 + 1.25496i
\(89\) 6.98508 + 8.75902i 0.740417 + 0.928454i 0.999298 0.0374552i \(-0.0119251\pi\)
−0.258881 + 0.965909i \(0.583354\pi\)
\(90\) 5.13245 + 19.7274i 0.541008 + 2.07945i
\(91\) −2.49776 + 13.9434i −0.261836 + 1.46166i
\(92\) −29.1321 2.18315i −3.03723 0.227609i
\(93\) 7.70057 3.49872i 0.798511 0.362800i
\(94\) −7.12942 7.68369i −0.735344 0.792512i
\(95\) 9.28272 0.695644i 0.952387 0.0713715i
\(96\) 1.48351 + 7.24164i 0.151410 + 0.739097i
\(97\) −5.28392 3.05067i −0.536501 0.309749i 0.207159 0.978307i \(-0.433578\pi\)
−0.743660 + 0.668559i \(0.766912\pi\)
\(98\) 15.5546 5.13197i 1.57125 0.518408i
\(99\) −10.0954 + 1.83419i −1.01462 + 0.184343i
\(100\) −7.43687 + 9.32555i −0.743687 + 0.932555i
\(101\) 5.64323 3.84749i 0.561522 0.382840i −0.249039 0.968494i \(-0.580115\pi\)
0.810561 + 0.585654i \(0.199162\pi\)
\(102\) −0.571730 10.8878i −0.0566097 1.07805i
\(103\) −7.61308 + 0.570521i −0.750139 + 0.0562151i −0.444312 0.895872i \(-0.646552\pi\)
−0.305827 + 0.952087i \(0.598933\pi\)
\(104\) −15.2693 10.4104i −1.49728 1.02083i
\(105\) 0.664983 13.2905i 0.0648957 1.29702i
\(106\) 0.530058 0.361388i 0.0514838 0.0351011i
\(107\) −10.5374 + 8.40326i −1.01868 + 0.812374i −0.982366 0.186966i \(-0.940134\pi\)
−0.0363182 + 0.999340i \(0.511563\pi\)
\(108\) 16.2077 7.96131i 1.55958 0.766078i
\(109\) 3.87839 4.86335i 0.371482 0.465824i −0.560592 0.828092i \(-0.689426\pi\)
0.932074 + 0.362268i \(0.117998\pi\)
\(110\) −17.0356 15.8068i −1.62429 1.50712i
\(111\) −0.0227751 + 0.0683742i −0.00216172 + 0.00648979i
\(112\) −0.304801 + 2.96453i −0.0288010 + 0.280122i
\(113\) −3.39430 1.33217i −0.319309 0.125320i 0.200273 0.979740i \(-0.435817\pi\)
−0.519582 + 0.854421i \(0.673912\pi\)
\(114\) −3.55123 12.4973i −0.332603 1.17048i
\(115\) 16.6038 17.8946i 1.54831 1.66868i
\(116\) 30.7669i 2.85663i
\(117\) 5.41507 15.1217i 0.500624 1.39800i
\(118\) 26.2772 + 5.99759i 2.41901 + 0.552123i
\(119\) −1.77507 + 6.89261i −0.162721 + 0.631845i
\(120\) 15.4694 + 7.88005i 1.41216 + 0.719347i
\(121\) 0.511536 0.474636i 0.0465032 0.0431487i
\(122\) 0.857303 2.18437i 0.0776166 0.197764i
\(123\) −0.364599 + 16.3200i −0.0328748 + 1.47153i
\(124\) 5.00206 16.2163i 0.449198 1.45626i
\(125\) 1.01299 + 4.43818i 0.0906042 + 0.396963i
\(126\) −18.3581 + 2.81343i −1.63547 + 0.250640i
\(127\) 4.10799 17.9983i 0.364525 1.59709i −0.377034 0.926199i \(-0.623056\pi\)
0.741559 0.670888i \(-0.234087\pi\)
\(128\) 17.4093 + 10.0513i 1.53878 + 0.888416i
\(129\) −1.51920 + 8.74855i −0.133758 + 0.770267i
\(130\) 34.7627 10.7229i 3.04889 0.940458i
\(131\) −10.5362 7.18349i −0.920556 0.627625i 0.00753729 0.999972i \(-0.497601\pi\)
−0.928094 + 0.372347i \(0.878553\pi\)
\(132\) −10.6890 + 17.5943i −0.930358 + 1.53139i
\(133\) −0.234532 + 8.47815i −0.0203365 + 0.735149i
\(134\) −10.4132 8.30427i −0.899565 0.717379i
\(135\) −3.24290 + 14.7362i −0.279104 + 1.26829i
\(136\) −7.25986 5.78955i −0.622528 0.496450i
\(137\) 2.07126 + 0.155220i 0.176960 + 0.0132613i 0.162915 0.986640i \(-0.447910\pi\)
0.0140446 + 0.999901i \(0.495529\pi\)
\(138\) −29.1177 17.6898i −2.47866 1.50585i
\(139\) −4.39484 + 0.329348i −0.372766 + 0.0279349i −0.259796 0.965664i \(-0.583655\pi\)
−0.112970 + 0.993598i \(0.536036\pi\)
\(140\) −19.0622 18.6943i −1.61105 1.57995i
\(141\) −2.12080 7.46338i −0.178603 0.628530i
\(142\) 21.4180 14.6025i 1.79736 1.22542i
\(143\) 4.07475 + 17.8527i 0.340748 + 1.49291i
\(144\) 0.898316 3.25759i 0.0748596 0.271466i
\(145\) −20.1000 16.0292i −1.66921 1.33115i
\(146\) −4.11409 + 7.12581i −0.340484 + 0.589736i
\(147\) 11.9837 + 1.84119i 0.988402 + 0.151859i
\(148\) 0.0722975 + 0.125223i 0.00594282 + 0.0102933i
\(149\) −1.00912 + 6.69505i −0.0826700 + 0.548480i 0.908706 + 0.417436i \(0.137071\pi\)
−0.991377 + 0.131044i \(0.958167\pi\)
\(150\) −12.6647 + 5.75415i −1.03407 + 0.469824i
\(151\) 1.87850 + 0.579442i 0.152871 + 0.0471543i 0.370246 0.928934i \(-0.379273\pi\)
−0.217375 + 0.976088i \(0.569750\pi\)
\(152\) −9.96928 4.80095i −0.808615 0.389409i
\(153\) 3.28105 7.37345i 0.265257 0.596108i
\(154\) 15.9138 13.9672i 1.28237 1.12551i
\(155\) 7.98807 + 11.7163i 0.641617 + 0.941079i
\(156\) −15.4859 28.2619i −1.23986 2.26276i
\(157\) 4.08291 5.98853i 0.325852 0.477937i −0.628000 0.778213i \(-0.716126\pi\)
0.953852 + 0.300276i \(0.0970788\pi\)
\(158\) −3.45628 + 22.9309i −0.274967 + 1.82428i
\(159\) 0.471036 0.0602710i 0.0373556 0.00477980i
\(160\) −11.5363 + 4.52767i −0.912026 + 0.357944i
\(161\) 14.6714 + 16.7162i 1.15627 + 1.31742i
\(162\) 21.0569 + 0.306353i 1.65439 + 0.0240694i
\(163\) −15.7968 + 7.60734i −1.23730 + 0.595853i −0.934079 0.357066i \(-0.883777\pi\)
−0.303223 + 0.952920i \(0.598063\pi\)
\(164\) 24.0092 + 22.2773i 1.87480 + 1.73956i
\(165\) −5.92548 16.1495i −0.461298 1.25724i
\(166\) 0.990762 0.572017i 0.0768981 0.0443971i
\(167\) 0.838572 0.258665i 0.0648906 0.0200161i −0.262140 0.965030i \(-0.584428\pi\)
0.327031 + 0.945014i \(0.393952\pi\)
\(168\) −8.58356 + 13.2863i −0.662236 + 1.02506i
\(169\) −14.9693 4.61742i −1.15149 0.355186i
\(170\) 17.8206 4.06744i 1.36678 0.311959i
\(171\) 1.85660 9.43608i 0.141977 0.721595i
\(172\) 11.1079 + 13.9288i 0.846966 + 1.06206i
\(173\) −4.98152 1.53659i −0.378738 0.116825i 0.0995405 0.995034i \(-0.468263\pi\)
−0.478278 + 0.878208i \(0.658739\pi\)
\(174\) −16.2865 + 31.9721i −1.23467 + 2.42380i
\(175\) 9.01361 1.10463i 0.681365 0.0835024i
\(176\) 1.13554 + 3.68134i 0.0855949 + 0.277492i
\(177\) 15.3167 + 12.7846i 1.15128 + 0.960952i
\(178\) 22.7024 + 13.1072i 1.70161 + 0.982428i
\(179\) −8.08373 1.84506i −0.604206 0.137906i −0.0905351 0.995893i \(-0.528858\pi\)
−0.513671 + 0.857987i \(0.671715\pi\)
\(180\) 17.7996 + 24.4885i 1.32671 + 1.82526i
\(181\) −1.19410 + 0.952260i −0.0887565 + 0.0707809i −0.666863 0.745181i \(-0.732363\pi\)
0.578106 + 0.815961i \(0.303792\pi\)
\(182\) 6.47918 + 32.5061i 0.480269 + 2.40951i
\(183\) 1.29938 1.15272i 0.0960527 0.0852117i
\(184\) −27.7277 + 8.55285i −2.04411 + 0.630525i
\(185\) −0.119474 0.0180079i −0.00878393 0.00132396i
\(186\) 13.7821 14.2037i 1.01055 1.04147i
\(187\) 1.37133 + 9.09816i 0.100281 + 0.665323i
\(188\) −14.0256 6.75436i −1.02292 0.492613i
\(189\) −13.0539 4.31239i −0.949529 0.313680i
\(190\) 19.6245 9.45068i 1.42371 0.685624i
\(191\) −12.1397 17.8057i −0.878401 1.28838i −0.956590 0.291438i \(-0.905866\pi\)
0.0781890 0.996939i \(-0.475086\pi\)
\(192\) 11.5474 + 17.7774i 0.833363 + 1.28298i
\(193\) 0.637484 + 8.50663i 0.0458871 + 0.612321i 0.971986 + 0.235039i \(0.0755219\pi\)
−0.926099 + 0.377281i \(0.876859\pi\)
\(194\) −14.1171 2.12781i −1.01355 0.152768i
\(195\) 26.5314 + 4.60721i 1.89996 + 0.329929i
\(196\) 18.7197 15.5348i 1.33712 1.10963i
\(197\) 17.7088i 1.26170i −0.775905 0.630850i \(-0.782706\pi\)
0.775905 0.630850i \(-0.217294\pi\)
\(198\) −20.4213 + 12.6253i −1.45128 + 0.897240i
\(199\) 6.45938 13.4130i 0.457893 0.950826i −0.536382 0.843976i \(-0.680209\pi\)
0.994275 0.106850i \(-0.0340765\pi\)
\(200\) −3.49208 + 11.3210i −0.246927 + 0.800519i
\(201\) −4.07821 8.97601i −0.287655 0.633119i
\(202\) 9.00276 13.2046i 0.633432 0.929074i
\(203\) 16.4010 16.7237i 1.15112 1.17378i
\(204\) −6.69807 14.7422i −0.468959 1.03216i
\(205\) −27.0622 + 4.07898i −1.89011 + 0.284888i
\(206\) −16.0948 + 7.75083i −1.12137 + 0.540026i
\(207\) −13.2619 21.4509i −0.921763 1.49094i
\(208\) −5.87951 1.34196i −0.407670 0.0930481i
\(209\) 4.00561 + 10.2061i 0.277074 + 0.705973i
\(210\) −9.91309 29.5172i −0.684068 2.03688i
\(211\) 5.61843 14.3155i 0.386788 0.985521i −0.596361 0.802716i \(-0.703387\pi\)
0.983149 0.182804i \(-0.0585175\pi\)
\(212\) 0.536722 0.787226i 0.0368622 0.0540669i
\(213\) 19.0331 2.43537i 1.30413 0.166869i
\(214\) −15.7684 + 27.3116i −1.07790 + 1.86698i
\(215\) −14.8868 −1.01527
\(216\) 12.0966 13.2424i 0.823068 0.901032i
\(217\) −11.3634 + 6.14812i −0.771397 + 0.417362i
\(218\) 4.29024 13.9086i 0.290572 0.942011i
\(219\) −5.10773 + 3.31775i −0.345149 + 0.224193i
\(220\) −32.1285 12.6095i −2.16610 0.850133i
\(221\) −13.4075 5.26206i −0.901887 0.353964i
\(222\) 0.00884283 + 0.168399i 0.000593492 + 0.0113022i
\(223\) 2.94878 9.55970i 0.197465 0.640165i −0.801638 0.597810i \(-0.796038\pi\)
0.999103 0.0423549i \(-0.0134860\pi\)
\(224\) −3.02859 10.8778i −0.202356 0.726802i
\(225\) −10.2867 0.459850i −0.685778 0.0306567i
\(226\) −8.53214 −0.567550
\(227\) 4.47327 7.74793i 0.296901 0.514248i −0.678524 0.734578i \(-0.737380\pi\)
0.975425 + 0.220330i \(0.0707134\pi\)
\(228\) −11.6905 15.3507i −0.774223 1.01662i
\(229\) −7.42790 + 10.8947i −0.490849 + 0.719944i −0.989125 0.147075i \(-0.953014\pi\)
0.498276 + 0.867018i \(0.333967\pi\)
\(230\) 20.8681 53.1711i 1.37600 3.50600i
\(231\) 15.1892 3.86560i 0.999375 0.254338i
\(232\) 11.1646 + 28.4469i 0.732992 + 1.86763i
\(233\) 17.5788 + 4.01225i 1.15163 + 0.262851i 0.755376 0.655291i \(-0.227454\pi\)
0.396250 + 0.918143i \(0.370311\pi\)
\(234\) −1.13207 37.5665i −0.0740058 2.45580i
\(235\) 11.7198 5.64396i 0.764515 0.368171i
\(236\) 39.5826 5.96611i 2.57661 0.388361i
\(237\) −9.98414 + 13.9634i −0.648540 + 0.907023i
\(238\) 2.02586 + 16.5306i 0.131317 + 1.07152i
\(239\) −8.01523 + 11.7562i −0.518462 + 0.760444i −0.992785 0.119907i \(-0.961740\pi\)
0.474323 + 0.880351i \(0.342693\pi\)
\(240\) 5.63861 + 0.549445i 0.363971 + 0.0354666i
\(241\) 6.10576 19.7944i 0.393307 1.27507i −0.515154 0.857098i \(-0.672265\pi\)
0.908460 0.417971i \(-0.137259\pi\)
\(242\) 0.708456 1.47112i 0.0455413 0.0945674i
\(243\) 13.7857 + 7.27690i 0.884356 + 0.466813i
\(244\) 3.48507i 0.223109i
\(245\) 0.396102 + 20.3231i 0.0253060 + 1.29839i
\(246\) 13.1572 + 35.8592i 0.838875 + 2.28630i
\(247\) −16.9714 2.55803i −1.07987 0.162764i
\(248\) −1.25963 16.8087i −0.0799869 1.06735i
\(249\) 0.845675 0.0444073i 0.0535925 0.00281420i
\(250\) 6.00048 + 8.80109i 0.379504 + 0.556630i
\(251\) 9.67035 4.65700i 0.610387 0.293947i −0.103039 0.994677i \(-0.532857\pi\)
0.713426 + 0.700730i \(0.247142\pi\)
\(252\) −23.8536 + 13.8506i −1.50264 + 0.872503i
\(253\) 25.9045 + 12.4750i 1.62860 + 0.784294i
\(254\) −6.43822 42.7148i −0.403970 2.68016i
\(255\) 13.1207 + 3.30469i 0.821650 + 0.206948i
\(256\) 22.3080 + 3.36240i 1.39425 + 0.210150i
\(257\) 8.84057 2.72695i 0.551459 0.170103i −0.00648814 0.999979i \(-0.502065\pi\)
0.557947 + 0.829876i \(0.311589\pi\)
\(258\) 4.16977 + 20.3544i 0.259598 + 1.26721i
\(259\) 0.0274547 0.106607i 0.00170595 0.00662421i
\(260\) 42.2414 33.6864i 2.61970 2.08914i
\(261\) −21.4844 + 15.6161i −1.32985 + 0.966611i
\(262\) −29.0905 6.63972i −1.79722 0.410203i
\(263\) −8.90218 5.13968i −0.548932 0.316926i 0.199759 0.979845i \(-0.435984\pi\)
−0.748691 + 0.662919i \(0.769317\pi\)
\(264\) −3.49845 + 20.1464i −0.215315 + 1.23993i
\(265\) 0.234668 + 0.760776i 0.0144156 + 0.0467341i
\(266\) 6.73681 + 18.6672i 0.413060 + 1.14456i
\(267\) 10.5701 + 16.2729i 0.646882 + 0.995886i
\(268\) −18.9022 5.83055i −1.15463 0.356157i
\(269\) 8.24859 + 10.3434i 0.502925 + 0.630648i 0.966886 0.255207i \(-0.0821437\pi\)
−0.463961 + 0.885856i \(0.653572\pi\)
\(270\) 5.53392 + 34.8700i 0.336784 + 2.12212i
\(271\) 13.2632 3.02724i 0.805683 0.183892i 0.200205 0.979754i \(-0.435839\pi\)
0.605478 + 0.795862i \(0.292982\pi\)
\(272\) −2.89556 0.893163i −0.175569 0.0541560i
\(273\) −6.64808 + 23.6172i −0.402360 + 1.42938i
\(274\) 4.64422 1.43255i 0.280568 0.0865437i
\(275\) 10.1665 5.86961i 0.613061 0.353951i
\(276\) −49.8537 8.65715i −3.00084 0.521099i
\(277\) −9.73805 9.03559i −0.585103 0.542896i 0.331108 0.943593i \(-0.392578\pi\)
−0.916211 + 0.400697i \(0.868768\pi\)
\(278\) −9.29111 + 4.47436i −0.557244 + 0.268354i
\(279\) 13.8626 4.73784i 0.829933 0.283647i
\(280\) −24.4086 10.3674i −1.45869 0.619572i
\(281\) 13.7391 5.39218i 0.819603 0.321671i 0.0817679 0.996651i \(-0.473943\pi\)
0.737835 + 0.674981i \(0.235848\pi\)
\(282\) −10.9996 14.4434i −0.655016 0.860093i
\(283\) −0.154160 + 1.02279i −0.00916388 + 0.0607984i −0.992945 0.118573i \(-0.962168\pi\)
0.983782 + 0.179371i \(0.0574063\pi\)
\(284\) 21.6873 31.8094i 1.28690 1.88754i
\(285\) 16.1192 + 0.360113i 0.954819 + 0.0213313i
\(286\) 24.1370 + 35.4025i 1.42725 + 2.09340i
\(287\) −1.17512 24.9078i −0.0693650 1.47026i
\(288\) 1.34094 + 12.7330i 0.0790157 + 0.750297i
\(289\) 8.79616 + 4.23601i 0.517421 + 0.249177i
\(290\) −57.4836 17.7314i −3.37556 1.04122i
\(291\) −8.59642 6.14661i −0.503931 0.360321i
\(292\) −1.82133 + 12.0837i −0.106585 + 0.707148i
\(293\) −8.49703 14.7173i −0.496402 0.859793i 0.503590 0.863943i \(-0.332012\pi\)
−0.999991 + 0.00415008i \(0.998679\pi\)
\(294\) 27.6764 6.23406i 1.61412 0.363578i
\(295\) −16.7244 + 28.9675i −0.973733 + 1.68656i
\(296\) 0.112287 + 0.0895457i 0.00652653 + 0.00520474i
\(297\) −17.7113 + 1.46610i −1.02772 + 0.0850715i
\(298\) 3.52534 + 15.4455i 0.204217 + 0.894735i
\(299\) −37.1875 + 25.3540i −2.15061 + 1.46626i
\(300\) −14.3868 + 14.8269i −0.830625 + 0.856033i
\(301\) 1.38724 13.4925i 0.0799593 0.777694i
\(302\) 4.58702 0.343750i 0.263953 0.0197806i
\(303\) 10.3746 5.68468i 0.596005 0.326576i
\(304\) −3.60074 0.269838i −0.206517 0.0154763i
\(305\) 2.27680 + 1.81568i 0.130369 + 0.103966i
\(306\) 0.843349 18.8654i 0.0482110 1.07846i
\(307\) 3.33551 + 2.65998i 0.190368 + 0.151813i 0.714036 0.700109i \(-0.246865\pi\)
−0.523668 + 0.851922i \(0.675437\pi\)
\(308\) 14.4225 27.9444i 0.821797 1.59228i
\(309\) −13.2199 0.295341i −0.752055 0.0168014i
\(310\) 27.4151 + 18.6913i 1.55707 + 1.06160i
\(311\) 32.4090 9.99686i 1.83775 0.566870i 0.837970 0.545716i \(-0.183742\pi\)
0.999776 0.0211542i \(-0.00673410\pi\)
\(312\) −24.5738 20.5114i −1.39122 1.16123i
\(313\) 1.99744 + 1.15322i 0.112902 + 0.0651839i 0.555388 0.831592i \(-0.312570\pi\)
−0.442486 + 0.896776i \(0.645903\pi\)
\(314\) 3.77384 16.5343i 0.212970 0.933084i
\(315\) 3.37890 22.7995i 0.190380 1.28461i
\(316\) 7.66383 + 33.5774i 0.431124 + 1.88888i
\(317\) −0.660319 + 2.14070i −0.0370872 + 0.120234i −0.972224 0.234054i \(-0.924801\pi\)
0.935136 + 0.354288i \(0.115277\pi\)
\(318\) 0.974466 0.533951i 0.0546453 0.0299425i
\(319\) 11.0627 28.1872i 0.619390 1.57818i
\(320\) −26.0528 + 24.1735i −1.45640 + 1.35134i
\(321\) −19.5768 + 12.7162i −1.09267 + 0.709748i
\(322\) 46.2466 + 23.8685i 2.57722 + 1.33014i
\(323\) −8.40755 1.91897i −0.467809 0.106774i
\(324\) 29.2775 11.0018i 1.62653 0.611212i
\(325\) 18.3766i 1.01935i
\(326\) −27.9047 + 30.0741i −1.54550 + 1.66565i
\(327\) 7.50285 7.73236i 0.414909 0.427600i
\(328\) 30.2827 + 11.8851i 1.67208 + 0.656245i
\(329\) 4.02323 + 11.1481i 0.221808 + 0.614614i
\(330\) −26.7123 30.1107i −1.47046 1.65754i
\(331\) 16.8723 + 15.6552i 0.927384 + 0.860487i 0.990499 0.137520i \(-0.0439130\pi\)
−0.0631150 + 0.998006i \(0.520103\pi\)
\(332\) 1.05936 1.32840i 0.0581400 0.0729053i
\(333\) −0.0507473 + 0.114043i −0.00278093 + 0.00624954i
\(334\) 1.60542 1.28028i 0.0878445 0.0700537i
\(335\) 13.6569 9.31113i 0.746157 0.508721i
\(336\) −1.02343 + 5.05931i −0.0558325 + 0.276008i
\(337\) −16.2373 11.0704i −0.884499 0.603041i 0.0335809 0.999436i \(-0.489309\pi\)
−0.918080 + 0.396395i \(0.870261\pi\)
\(338\) −36.5528 + 2.73925i −1.98821 + 0.148996i
\(339\) −5.62761 2.86668i −0.305650 0.155697i
\(340\) 22.4302 15.2926i 1.21645 0.829359i
\(341\) −10.4135 + 13.0581i −0.563920 + 0.707134i
\(342\) −4.02260 22.1404i −0.217517 1.19722i
\(343\) −18.4566 1.53483i −0.996560 0.0828729i
\(344\) 15.3247 + 8.84775i 0.826255 + 0.477038i
\(345\) 31.6289 28.0591i 1.70284 1.51065i
\(346\) −12.1641 + 0.911573i −0.653946 + 0.0490065i
\(347\) −0.223439 0.240810i −0.0119948 0.0129273i 0.727026 0.686610i \(-0.240902\pi\)
−0.739021 + 0.673683i \(0.764711\pi\)
\(348\) −5.16826 + 53.0385i −0.277048 + 2.84316i
\(349\) −28.1933 2.11279i −1.50915 0.113095i −0.705719 0.708492i \(-0.749376\pi\)
−0.803432 + 0.595396i \(0.796995\pi\)
\(350\) 18.6887 10.1115i 0.998955 0.540481i
\(351\) 11.8751 25.1584i 0.633847 1.34285i
\(352\) −9.10091 11.4122i −0.485080 0.608271i
\(353\) 0.488442 6.51780i 0.0259971 0.346908i −0.969004 0.247045i \(-0.920541\pi\)
0.995001 0.0998629i \(-0.0318404\pi\)
\(354\) 44.2913 + 14.7532i 2.35406 + 0.784125i
\(355\) 9.48222 + 30.7406i 0.503264 + 1.63154i
\(356\) 38.4980 + 5.80264i 2.04039 + 0.307540i
\(357\) −4.21785 + 11.5839i −0.223232 + 0.613085i
\(358\) −19.1849 + 2.89166i −1.01395 + 0.152829i
\(359\) −6.65289 13.8149i −0.351126 0.729121i 0.648355 0.761338i \(-0.275457\pi\)
−0.999481 + 0.0322175i \(0.989743\pi\)
\(360\) 25.3438 + 16.1829i 1.33573 + 0.852912i
\(361\) 8.72372 0.459143
\(362\) −1.78688 + 3.09496i −0.0939161 + 0.162667i
\(363\) 0.961559 0.732289i 0.0504688 0.0384352i
\(364\) 26.5951 + 41.4243i 1.39396 + 2.17122i
\(365\) −6.94541 7.48537i −0.363539 0.391802i
\(366\) 1.84483 3.62160i 0.0964306 0.189304i
\(367\) 4.31508 + 28.6287i 0.225245 + 1.49441i 0.760291 + 0.649582i \(0.225056\pi\)
−0.535046 + 0.844823i \(0.679706\pi\)
\(368\) −7.40316 + 5.90382i −0.385916 + 0.307758i
\(369\) −3.36999 + 28.0726i −0.175434 + 1.46140i
\(370\) −0.275628 + 0.0629103i −0.0143292 + 0.00327055i
\(371\) −0.711391 + 0.141796i −0.0369336 + 0.00736168i
\(372\) 11.3470 27.1148i 0.588315 1.40583i
\(373\) 6.21304 + 10.7613i 0.321699 + 0.557199i 0.980839 0.194821i \(-0.0624127\pi\)
−0.659140 + 0.752021i \(0.729079\pi\)
\(374\) 10.7646 + 18.6449i 0.556627 + 0.964106i
\(375\) 1.00074 + 7.82108i 0.0516780 + 0.403879i
\(376\) −15.4190 1.15550i −0.795175 0.0595901i
\(377\) 29.5540 + 37.0595i 1.52211 + 1.90866i
\(378\) −32.1199 + 1.76621i −1.65207 + 0.0908443i
\(379\) 6.49202 8.14073i 0.333472 0.418161i −0.586620 0.809862i \(-0.699542\pi\)
0.920093 + 0.391701i \(0.128113\pi\)
\(380\) 22.0031 23.7138i 1.12874 1.21649i
\(381\) 10.1051 30.3369i 0.517698 1.55421i
\(382\) −41.6637 28.4058i −2.13170 1.45337i
\(383\) 11.0484 28.1508i 0.564545 1.43844i −0.308702 0.951159i \(-0.599895\pi\)
0.873247 0.487278i \(-0.162010\pi\)
\(384\) 28.3233 + 20.2517i 1.44536 + 1.03346i
\(385\) 10.7421 + 23.9809i 0.547469 + 1.22218i
\(386\) 8.66054 + 17.9838i 0.440810 + 0.915351i
\(387\) −4.08851 + 14.8263i −0.207831 + 0.753663i
\(388\) −20.6715 + 4.71814i −1.04944 + 0.239527i
\(389\) 11.9758 + 17.5653i 0.607199 + 0.890597i 0.999573 0.0292086i \(-0.00929871\pi\)
−0.392375 + 0.919805i \(0.628346\pi\)
\(390\) 61.7282 12.6455i 3.12573 0.640331i
\(391\) −19.5850 + 11.3074i −0.990456 + 0.571840i
\(392\) 11.6710 21.1564i 0.589474 1.06856i
\(393\) −16.9566 14.1534i −0.855347 0.713945i
\(394\) −15.1386 38.5725i −0.762672 1.94326i
\(395\) −25.9289 12.4867i −1.30462 0.628274i
\(396\) −21.3821 + 28.5350i −1.07449 + 1.43394i
\(397\) −6.39242 + 13.2740i −0.320826 + 0.666202i −0.997544 0.0700399i \(-0.977687\pi\)
0.676718 + 0.736242i \(0.263402\pi\)
\(398\) 2.60322 34.7376i 0.130488 1.74124i
\(399\) −1.82848 + 14.5760i −0.0915383 + 0.729711i
\(400\) 0.288917 + 3.85533i 0.0144458 + 0.192766i
\(401\) 23.6911 + 9.29809i 1.18308 + 0.464324i 0.873630 0.486592i \(-0.161760\pi\)
0.309450 + 0.950916i \(0.399855\pi\)
\(402\) −16.5562 16.0648i −0.825750 0.801241i
\(403\) −9.55190 24.3378i −0.475814 1.21235i
\(404\) 5.28162 23.1403i 0.262771 1.15127i
\(405\) −8.06579 + 24.8588i −0.400792 + 1.23524i
\(406\) 21.4274 50.4475i 1.06342 2.50367i
\(407\) −0.0212100 0.140719i −0.00105134 0.00697520i
\(408\) −11.5426 11.2000i −0.571446 0.554484i
\(409\) −7.12826 23.1092i −0.352470 1.14268i −0.942192 0.335073i \(-0.891239\pi\)
0.589723 0.807606i \(-0.299237\pi\)
\(410\) −55.4588 + 32.0192i −2.73892 + 1.58131i
\(411\) 3.54455 + 0.615514i 0.174840 + 0.0303611i
\(412\) −18.0455 + 19.4485i −0.889040 + 0.958157i
\(413\) −24.6960 17.8574i −1.21521 0.878707i
\(414\) −47.2240 35.3864i −2.32093 1.73915i
\(415\) 0.315926 + 1.38416i 0.0155082 + 0.0679458i
\(416\) 22.5945 3.40558i 1.10779 0.166972i
\(417\) −7.63153 0.170493i −0.373718 0.00834908i
\(418\) 17.4497 + 18.8063i 0.853492 + 0.919846i
\(419\) −24.4130 + 22.6520i −1.19265 + 1.10662i −0.200747 + 0.979643i \(0.564337\pi\)
−0.991906 + 0.126977i \(0.959472\pi\)
\(420\) −29.7207 35.4289i −1.45022 1.72875i
\(421\) 25.1243 + 23.3120i 1.22448 + 1.13616i 0.986305 + 0.164934i \(0.0527412\pi\)
0.238180 + 0.971221i \(0.423449\pi\)
\(422\) 35.9844i 1.75169i
\(423\) −2.40230 13.2223i −0.116804 0.642889i
\(424\) 0.210585 0.922631i 0.0102269 0.0448069i
\(425\) −0.690020 + 9.20768i −0.0334709 + 0.446638i
\(426\) 39.3751 21.5753i 1.90773 1.04533i
\(427\) −1.85780 + 1.89436i −0.0899052 + 0.0916745i
\(428\) −6.98075 + 46.3143i −0.337427 + 2.23868i
\(429\) 4.02550 + 31.4604i 0.194353 + 1.51892i
\(430\) −32.4257 + 12.7261i −1.56370 + 0.613709i
\(431\) −4.35771 9.04887i −0.209903 0.435869i 0.769262 0.638934i \(-0.220624\pi\)
−0.979165 + 0.203065i \(0.934910\pi\)
\(432\) 2.09581 5.46481i 0.100835 0.262926i
\(433\) −6.13626 + 12.7421i −0.294890 + 0.612345i −0.994796 0.101890i \(-0.967511\pi\)
0.699906 + 0.714235i \(0.253225\pi\)
\(434\) −19.4954 + 23.1057i −0.935811 + 1.10911i
\(435\) −31.9574 31.0089i −1.53224 1.48676i
\(436\) −1.61544 21.5566i −0.0773657 1.03237i
\(437\) −19.7545 + 18.3295i −0.944986 + 0.876819i
\(438\) −8.28922 + 11.5930i −0.396074 + 0.553934i
\(439\) −20.3223 + 7.97590i −0.969929 + 0.380669i −0.796809 0.604232i \(-0.793480\pi\)
−0.173120 + 0.984901i \(0.555385\pi\)
\(440\) −34.2817 −1.63431
\(441\) 20.3493 + 5.18705i 0.969015 + 0.247002i
\(442\) −33.7020 −1.60304
\(443\) −33.6794 + 13.2182i −1.60016 + 0.628016i −0.986823 0.161806i \(-0.948268\pi\)
−0.613336 + 0.789822i \(0.710173\pi\)
\(444\) 0.103598 + 0.228015i 0.00491652 + 0.0108211i
\(445\) −23.8479 + 22.1276i −1.13050 + 1.04895i
\(446\) −1.74934 23.3433i −0.0828336 1.10534i
\(447\) −2.86424 + 11.3720i −0.135474 + 0.537877i
\(448\) −19.4817 25.8654i −0.920423 1.22203i
\(449\) −2.24904 + 4.67019i −0.106139 + 0.220400i −0.947273 0.320426i \(-0.896174\pi\)
0.841135 + 0.540826i \(0.181888\pi\)
\(450\) −22.7991 + 7.79207i −1.07476 + 0.367322i
\(451\) −13.9860 29.0423i −0.658576 1.36755i
\(452\) −11.7957 + 4.62948i −0.554824 + 0.217753i
\(453\) 3.14099 + 1.31445i 0.147577 + 0.0617580i
\(454\) 3.12006 20.7002i 0.146432 0.971510i
\(455\) −40.9182 4.20704i −1.91828 0.197229i
\(456\) −16.3794 9.95095i −0.767037 0.465996i
\(457\) 0.853200 11.3852i 0.0399110 0.532575i −0.941037 0.338304i \(-0.890147\pi\)
0.980948 0.194271i \(-0.0622342\pi\)
\(458\) −6.86562 + 30.0803i −0.320809 + 1.40556i
\(459\) 6.89475 12.1598i 0.321820 0.567572i
\(460\) 84.8323i 3.95533i
\(461\) −13.4608 12.4898i −0.626931 0.581707i 0.301384 0.953503i \(-0.402552\pi\)
−0.928314 + 0.371796i \(0.878742\pi\)
\(462\) 29.7799 21.4046i 1.38548 0.995830i
\(463\) −22.4659 + 20.8453i −1.04408 + 0.968762i −0.999543 0.0302454i \(-0.990371\pi\)
−0.0445351 + 0.999008i \(0.514181\pi\)
\(464\) 6.78295 + 7.31028i 0.314890 + 0.339371i
\(465\) 11.8024 + 21.5395i 0.547323 + 0.998870i
\(466\) 41.7193 6.28818i 1.93261 0.291294i
\(467\) 3.99779 + 17.5155i 0.184996 + 0.810520i 0.979205 + 0.202875i \(0.0650285\pi\)
−0.794209 + 0.607645i \(0.792114\pi\)
\(468\) −21.9484 51.3216i −1.01457 2.37234i
\(469\) 7.16643 + 13.2455i 0.330915 + 0.611621i
\(470\) 20.7027 22.3122i 0.954946 1.02919i
\(471\) 8.04444 9.63769i 0.370668 0.444081i
\(472\) 34.4330 19.8799i 1.58491 0.915045i
\(473\) −5.16821 16.7549i −0.237635 0.770393i
\(474\) −9.81018 + 38.9496i −0.450597 + 1.78902i
\(475\) 1.63989 + 10.8800i 0.0752432 + 0.499206i
\(476\) 11.7702 + 21.7545i 0.539485 + 0.997114i
\(477\) 0.822136 0.0247752i 0.0376430 0.00113438i
\(478\) −7.40849 + 32.4587i −0.338856 + 1.48463i
\(479\) 12.4204 + 31.6467i 0.567503 + 1.44597i 0.870109 + 0.492859i \(0.164048\pi\)
−0.302606 + 0.953116i \(0.597857\pi\)
\(480\) −20.6479 + 5.86730i −0.942442 + 0.267805i
\(481\) 0.207371 + 0.0813871i 0.00945530 + 0.00371093i
\(482\) −3.62220 48.3349i −0.164987 2.20159i
\(483\) 22.4838 + 31.2814i 1.02305 + 1.42335i
\(484\) 0.181222 2.41824i 0.00823736 0.109920i
\(485\) 7.68727 15.9628i 0.349061 0.724833i
\(486\) 36.2483 + 4.06529i 1.64425 + 0.184405i
\(487\) −30.7063 14.7874i −1.39144 0.670081i −0.420032 0.907509i \(-0.637981\pi\)
−0.971405 + 0.237428i \(0.923695\pi\)
\(488\) −1.26466 3.22229i −0.0572483 0.145866i
\(489\) −28.5098 + 10.4606i −1.28926 + 0.473046i
\(490\) 18.2362 + 43.9282i 0.823828 + 1.98447i
\(491\) −12.0650 + 6.96572i −0.544485 + 0.314358i −0.746895 0.664942i \(-0.768456\pi\)
0.202410 + 0.979301i \(0.435123\pi\)
\(492\) 37.6469 + 42.4366i 1.69725 + 1.91319i
\(493\) 13.4166 + 19.6786i 0.604254 + 0.886278i
\(494\) −39.1532 + 8.93645i −1.76158 + 0.402070i
\(495\) −7.50203 28.8353i −0.337191 1.29605i
\(496\) −2.38658 4.95579i −0.107161 0.222522i
\(497\) −28.7451 + 5.72953i −1.28939 + 0.257005i
\(498\) 1.80405 0.819662i 0.0808414 0.0367300i
\(499\) 2.38567 6.07859i 0.106797 0.272115i −0.867478 0.497475i \(-0.834261\pi\)
0.974276 + 0.225360i \(0.0723558\pi\)
\(500\) 13.0711 + 8.91173i 0.584558 + 0.398545i
\(501\) 1.48905 0.305045i 0.0665260 0.0136284i
\(502\) 17.0824 18.4105i 0.762427 0.821700i
\(503\) −7.70979 + 9.66777i −0.343763 + 0.431065i −0.923417 0.383798i \(-0.874616\pi\)
0.579655 + 0.814862i \(0.303187\pi\)
\(504\) −17.0289 + 21.4621i −0.758528 + 0.955999i
\(505\) 12.3659 + 15.5063i 0.550274 + 0.690022i
\(506\) 67.0885 + 5.02759i 2.98245 + 0.223504i
\(507\) −25.0297 10.4745i −1.11161 0.465188i
\(508\) −32.0776 55.5601i −1.42321 2.46508i
\(509\) −19.5237 33.8160i −0.865371 1.49887i −0.866679 0.498867i \(-0.833750\pi\)
0.00130794 0.999999i \(-0.499584\pi\)
\(510\) 31.4040 4.01828i 1.39059 0.177932i
\(511\) 7.43152 5.59738i 0.328751 0.247614i
\(512\) 12.2677 2.80003i 0.542162 0.123745i
\(513\) 4.78564 15.9548i 0.211291 0.704424i
\(514\) 16.9250 13.4972i 0.746528 0.595336i
\(515\) −3.30415 21.9216i −0.145598 0.965980i
\(516\) 16.8089 + 25.8776i 0.739970 + 1.13920i
\(517\) 10.4210 + 11.2311i 0.458314 + 0.493945i
\(518\) −0.0313335 0.255676i −0.00137671 0.0112337i
\(519\) −8.32945 3.48571i −0.365622 0.153006i
\(520\) 26.8323 46.4749i 1.17667 2.03806i
\(521\) −7.03655 −0.308277 −0.154139 0.988049i \(-0.549260\pi\)
−0.154139 + 0.988049i \(0.549260\pi\)
\(522\) −33.4467 + 52.3805i −1.46392 + 2.29263i
\(523\) −5.43752 11.2911i −0.237766 0.493727i 0.747606 0.664143i \(-0.231203\pi\)
−0.985372 + 0.170416i \(0.945489\pi\)
\(524\) −43.8204 + 6.60487i −1.91430 + 0.288535i
\(525\) 15.7240 0.390144i 0.686251 0.0170273i
\(526\) −23.7841 3.58487i −1.03703 0.156308i
\(527\) −3.87216 12.5532i −0.168674 0.546828i
\(528\) 1.33915 + 6.53697i 0.0582791 + 0.284485i
\(529\) −3.56229 + 47.5354i −0.154882 + 2.06676i
\(530\) 1.16150 + 1.45648i 0.0504525 + 0.0632654i
\(531\) 24.2567 + 24.6122i 1.05265 + 1.06808i
\(532\) 19.4424 + 22.1522i 0.842934 + 0.960419i
\(533\) 50.3188 + 3.77087i 2.17955 + 0.163335i
\(534\) 36.9345 + 26.4089i 1.59831 + 1.14283i
\(535\) −26.6202 28.6897i −1.15089 1.24037i
\(536\) −19.5927 + 1.46827i −0.846274 + 0.0634195i
\(537\) −13.6255 4.53859i −0.587983 0.195854i
\(538\) 26.8089 + 15.4781i 1.15581 + 0.667310i
\(539\) −22.7359 + 7.50134i −0.979306 + 0.323105i
\(540\) 26.5709 + 45.2053i 1.14343 + 1.94533i
\(541\) −18.4912 + 23.1872i −0.794997 + 0.996895i 0.204839 + 0.978796i \(0.434333\pi\)
−0.999836 + 0.0180996i \(0.994238\pi\)
\(542\) 26.3015 17.9321i 1.12975 0.770248i
\(543\) −2.21845 + 1.44100i −0.0952027 + 0.0618393i
\(544\) 11.4490 0.857982i 0.490870 0.0367857i
\(545\) 14.9245 + 10.1754i 0.639297 + 0.435865i
\(546\) 5.70895 + 57.1252i 0.244321 + 2.44473i
\(547\) 5.68996 3.87935i 0.243285 0.165869i −0.435539 0.900170i \(-0.643442\pi\)
0.678824 + 0.734301i \(0.262490\pi\)
\(548\) 5.64337 4.50044i 0.241073 0.192249i
\(549\) 2.43361 1.76889i 0.103864 0.0754944i
\(550\) 17.1264 21.4759i 0.730273 0.915734i
\(551\) 20.8047 + 19.3039i 0.886310 + 0.822376i
\(552\) −49.2361 + 10.0864i −2.09563 + 0.429306i
\(553\) 13.7334 22.3369i 0.584005 0.949860i
\(554\) −28.9352 11.3562i −1.22934 0.482480i
\(555\) −0.202935 0.0511129i −0.00861411 0.00216962i
\(556\) −10.4172 + 11.2271i −0.441790 + 0.476136i
\(557\) 18.4015i 0.779698i 0.920879 + 0.389849i \(0.127473\pi\)
−0.920879 + 0.389849i \(0.872527\pi\)
\(558\) 26.1447 22.1704i 1.10679 0.938548i
\(559\) 26.7595 + 6.10767i 1.13180 + 0.258327i
\(560\) −8.65061 0.239302i −0.365555 0.0101124i
\(561\) 0.835691 + 15.9145i 0.0352829 + 0.671913i
\(562\) 25.3162 23.4900i 1.06790 0.990867i
\(563\) −7.08656 + 18.0563i −0.298663 + 0.760981i 0.700229 + 0.713918i \(0.253081\pi\)
−0.998892 + 0.0470624i \(0.985014\pi\)
\(564\) −23.0439 13.9998i −0.970323 0.589497i
\(565\) 3.12101 10.1181i 0.131302 0.425670i
\(566\) 0.538558 + 2.35958i 0.0226373 + 0.0991804i
\(567\) −21.7790 9.62687i −0.914631 0.404290i
\(568\) 8.50907 37.2807i 0.357033 1.56426i
\(569\) −23.4946 13.5646i −0.984946 0.568659i −0.0811860 0.996699i \(-0.525871\pi\)
−0.903760 + 0.428040i \(0.859204\pi\)
\(570\) 35.4180 12.9953i 1.48350 0.544315i
\(571\) 7.34814 2.26660i 0.307510 0.0948543i −0.137160 0.990549i \(-0.543797\pi\)
0.444670 + 0.895695i \(0.353321\pi\)
\(572\) 52.5788 + 35.8476i 2.19843 + 1.49886i
\(573\) −17.9365 32.7343i −0.749308 1.36749i
\(574\) −23.8523 53.2484i −0.995577 2.22255i
\(575\) 22.5587 + 17.9899i 0.940762 + 0.750233i
\(576\) 16.9201 + 32.5860i 0.705006 + 1.35775i
\(577\) 36.3951 + 29.0241i 1.51515 + 1.20829i 0.911681 + 0.410899i \(0.134785\pi\)
0.603465 + 0.797389i \(0.293786\pi\)
\(578\) 22.7806 + 1.70717i 0.947549 + 0.0710090i
\(579\) −0.330005 + 14.7715i −0.0137146 + 0.613884i
\(580\) −89.0923 + 6.67655i −3.69936 + 0.277229i
\(581\) −1.28396 + 0.157352i −0.0532678 + 0.00652806i
\(582\) −23.9788 6.03951i −0.993955 0.250346i
\(583\) −0.774779 + 0.528235i −0.0320881 + 0.0218773i
\(584\) 2.70092 + 11.8335i 0.111765 + 0.489674i
\(585\) 44.9632 + 12.3991i 1.85900 + 0.512640i
\(586\) −31.0891 24.7927i −1.28428 1.02418i
\(587\) 5.47233 9.47835i 0.225867 0.391213i −0.730712 0.682686i \(-0.760812\pi\)
0.956579 + 0.291472i \(0.0941451\pi\)
\(588\) 34.8802 23.6357i 1.43844 0.974718i
\(589\) −7.82710 13.5569i −0.322510 0.558604i
\(590\) −11.6651 + 77.3929i −0.480245 + 3.18622i
\(591\) 2.97475 30.5280i 0.122365 1.25575i
\(592\) 0.0447851 + 0.0138144i 0.00184065 + 0.000567767i
\(593\) 34.3719 + 16.5526i 1.41148 + 0.679735i 0.975455 0.220198i \(-0.0706703\pi\)
0.436029 + 0.899933i \(0.356385\pi\)
\(594\) −37.3248 + 18.3342i −1.53145 + 0.752260i
\(595\) −20.3443 3.64439i −0.834035 0.149406i
\(596\) 13.2544 + 19.4407i 0.542923 + 0.796322i
\(597\) 13.3884 22.0375i 0.547950 0.901935i
\(598\) −59.3260 + 87.0153i −2.42602 + 3.55832i
\(599\) 3.18419 21.1257i 0.130102 0.863173i −0.824623 0.565683i \(-0.808612\pi\)
0.954725 0.297490i \(-0.0961494\pi\)
\(600\) −7.92167 + 18.9296i −0.323401 + 0.772797i
\(601\) 18.1218 7.11228i 0.739204 0.290116i 0.0342926 0.999412i \(-0.489082\pi\)
0.704911 + 0.709296i \(0.250987\pi\)
\(602\) −8.51261 30.5747i −0.346948 1.24613i
\(603\) −5.52257 16.1587i −0.224896 0.658032i
\(604\) 6.15506 2.96412i 0.250446 0.120608i
\(605\) 1.48542 + 1.37827i 0.0603909 + 0.0560346i
\(606\) 17.7379 21.2510i 0.720551 0.863262i
\(607\) 16.9452 9.78331i 0.687784 0.397092i −0.114997 0.993366i \(-0.536686\pi\)
0.802781 + 0.596273i \(0.203353\pi\)
\(608\) 13.0733 4.03258i 0.530192 0.163543i
\(609\) 31.0827 26.0748i 1.25953 1.05660i
\(610\) 6.51138 + 2.00850i 0.263638 + 0.0813216i
\(611\) −23.3823 + 5.33686i −0.945947 + 0.215906i
\(612\) −9.07029 26.5391i −0.366645 1.07278i
\(613\) 15.8933 + 19.9296i 0.641926 + 0.804950i 0.991242 0.132055i \(-0.0421576\pi\)
−0.349317 + 0.937005i \(0.613586\pi\)
\(614\) 9.53919 + 2.94245i 0.384970 + 0.118748i
\(615\) −47.3374 + 2.48574i −1.90883 + 0.100235i
\(616\) 3.19458 31.0709i 0.128713 1.25188i
\(617\) 11.7833 + 38.2004i 0.474376 + 1.53789i 0.804501 + 0.593952i \(0.202433\pi\)
−0.330125 + 0.943937i \(0.607091\pi\)
\(618\) −29.0475 + 10.6579i −1.16846 + 0.428724i
\(619\) 31.2465 + 18.0402i 1.25590 + 0.725096i 0.972275 0.233839i \(-0.0751289\pi\)
0.283627 + 0.958935i \(0.408462\pi\)
\(620\) 48.0433 + 10.9656i 1.92947 + 0.440388i
\(621\) −19.2586 39.2067i −0.772820 1.57331i
\(622\) 62.0460 49.4800i 2.48782 1.98397i
\(623\) −17.8329 23.6764i −0.714460 0.948573i
\(624\) −9.91017 3.30103i −0.396724 0.132147i
\(625\) −29.0311 + 8.95490i −1.16124 + 0.358196i
\(626\) 5.33657 + 0.804359i 0.213292 + 0.0321487i
\(627\) 5.19078 + 18.2671i 0.207300 + 0.729517i
\(628\) −3.75404 24.9064i −0.149802 0.993874i
\(629\) 0.100848 + 0.0485659i 0.00402108 + 0.00193645i
\(630\) −12.1307 52.5494i −0.483299 2.09362i
\(631\) 25.5472 12.3029i 1.01702 0.489769i 0.150337 0.988635i \(-0.451964\pi\)
0.866679 + 0.498865i \(0.166250\pi\)
\(632\) 19.2705 + 28.2646i 0.766537 + 1.12430i
\(633\) 12.0903 23.7345i 0.480545 0.943363i
\(634\) 0.391729 + 5.22727i 0.0155576 + 0.207601i
\(635\) 53.0095 + 7.98989i 2.10362 + 0.317069i
\(636\) 1.05749 1.26693i 0.0419321 0.0502370i
\(637\) 7.62604 36.6939i 0.302155 1.45387i
\(638\) 70.8532i 2.80511i
\(639\) 33.2200 1.00109i 1.31416 0.0396025i
\(640\) −25.3278 + 52.5938i −1.00117 + 2.07895i
\(641\) 3.76317 12.1999i 0.148636 0.481867i −0.850382 0.526166i \(-0.823629\pi\)
0.999018 + 0.0442985i \(0.0141053\pi\)
\(642\) −31.7707 + 44.4333i −1.25389 + 1.75364i
\(643\) 18.2620 26.7855i 0.720184 1.05632i −0.275298 0.961359i \(-0.588776\pi\)
0.995481 0.0949566i \(-0.0302712\pi\)
\(644\) 76.8871 + 7.90521i 3.02978 + 0.311509i
\(645\) −25.6631 2.50070i −1.01048 0.0984648i
\(646\) −19.9534 + 3.00749i −0.785057 + 0.118328i
\(647\) −11.1003 + 5.34560i −0.436396 + 0.210157i −0.639165 0.769069i \(-0.720720\pi\)
0.202769 + 0.979227i \(0.435006\pi\)
\(648\) 23.0776 20.7964i 0.906574 0.816960i
\(649\) −38.4090 8.76659i −1.50768 0.344119i
\(650\) 15.7095 + 40.0271i 0.616176 + 1.56999i
\(651\) −20.6220 + 8.68982i −0.808238 + 0.340581i
\(652\) −22.2604 + 56.7185i −0.871783 + 2.22127i
\(653\) −9.22461 + 13.5300i −0.360987 + 0.529470i −0.963172 0.268886i \(-0.913344\pi\)
0.602185 + 0.798356i \(0.294297\pi\)
\(654\) 9.73227 23.2562i 0.380562 0.909389i
\(655\) 18.5150 32.0689i 0.723441 1.25304i
\(656\) 10.6159 0.414483
\(657\) −9.36247 + 4.86142i −0.365265 + 0.189662i
\(658\) 18.2933 + 20.8430i 0.713148 + 0.812543i
\(659\) −7.98008 + 25.8708i −0.310860 + 1.00778i 0.656490 + 0.754335i \(0.272041\pi\)
−0.967349 + 0.253447i \(0.918436\pi\)
\(660\) −53.2677 27.1344i −2.07344 1.05620i
\(661\) −11.4809 4.50591i −0.446554 0.175260i 0.131399 0.991330i \(-0.458053\pi\)
−0.577953 + 0.816070i \(0.696148\pi\)
\(662\) 50.1335 + 19.6759i 1.94849 + 0.764727i
\(663\) −22.2291 11.3234i −0.863306 0.439764i
\(664\) 0.497437 1.61265i 0.0193043 0.0625830i
\(665\) −24.6013 + 1.16066i −0.953996 + 0.0450084i
\(666\) −0.0130439 + 0.291786i −0.000505440 + 0.0113065i
\(667\) 74.4256 2.88177
\(668\) 1.52483 2.64108i 0.0589973 0.102186i
\(669\) 6.68920 15.9845i 0.258620 0.617996i
\(670\) 21.7872 31.9559i 0.841711 1.23456i
\(671\) −1.25311 + 3.19287i −0.0483757 + 0.123259i
\(672\) −3.39369 19.2608i −0.130914 0.743001i
\(673\) −11.3869 29.0134i −0.438934 1.11838i −0.963664 0.267116i \(-0.913929\pi\)
0.524731 0.851268i \(-0.324166\pi\)
\(674\) −44.8309 10.2324i −1.72682 0.394136i
\(675\) −17.6558 2.52070i −0.679572 0.0970217i
\(676\) −49.0481 + 23.6203i −1.88646 + 0.908474i
\(677\) −18.2411 + 2.74940i −0.701063 + 0.105668i −0.489895 0.871782i \(-0.662965\pi\)
−0.211168 + 0.977450i \(0.567727\pi\)
\(678\) −14.7084 1.43324i −0.564874 0.0550433i
\(679\) 13.7514 + 8.45481i 0.527730 + 0.324466i
\(680\) 15.1895 22.2789i 0.582491 0.854358i
\(681\) 9.01291 12.6051i 0.345376 0.483029i
\(682\) −11.5193 + 37.3446i −0.441096 + 1.43000i
\(683\) 18.1451 37.6787i 0.694303 1.44173i −0.193307 0.981138i \(-0.561921\pi\)
0.887610 0.460596i \(-0.152364\pi\)
\(684\) −17.5745 28.4266i −0.671978 1.08692i
\(685\) 6.03149i 0.230451i
\(686\) −41.5133 + 12.4347i −1.58499 + 0.474760i
\(687\) −14.6350 + 17.5335i −0.558359 + 0.668945i
\(688\) 5.71004 + 0.860650i 0.217693 + 0.0328120i
\(689\) −0.109697 1.46380i −0.00417911 0.0557663i
\(690\) 44.9060 88.1555i 1.70954 3.35602i
\(691\) −2.00315 2.93807i −0.0762032 0.111770i 0.786245 0.617915i \(-0.212022\pi\)
−0.862448 + 0.506145i \(0.831070\pi\)
\(692\) −16.3223 + 7.86041i −0.620481 + 0.298808i
\(693\) 26.8338 4.11235i 1.01933 0.156215i
\(694\) −0.692544 0.333512i −0.0262886 0.0126599i
\(695\) −1.90740 12.6548i −0.0723519 0.480023i
\(696\) 14.4679 + 50.9147i 0.548406 + 1.92992i
\(697\) 25.0709 + 3.77883i 0.949628 + 0.143133i
\(698\) −63.2155 + 19.4994i −2.39274 + 0.738063i
\(699\) 29.6299 + 9.86957i 1.12071 + 0.373302i
\(700\) 20.3509 24.1195i 0.769191 0.911633i
\(701\) 0.0785064 0.0626068i 0.00296515 0.00236462i −0.622006 0.783012i \(-0.713682\pi\)
0.624971 + 0.780648i \(0.285111\pi\)
\(702\) 4.35890 64.9505i 0.164516 2.45140i
\(703\) 0.130038 + 0.0296803i 0.00490447 + 0.00111941i
\(704\) −36.2518 20.9300i −1.36629 0.788828i
\(705\) 21.1517 7.76083i 0.796618 0.292290i
\(706\) −4.50793 14.6143i −0.169658 0.550018i
\(707\) −15.2064 + 9.76274i −0.571894 + 0.367166i
\(708\) 69.2380 3.63576i 2.60212 0.136640i
\(709\) −21.8314 6.73410i −0.819896 0.252904i −0.143695 0.989622i \(-0.545899\pi\)
−0.676201 + 0.736718i \(0.736375\pi\)
\(710\) 46.9328 + 58.8518i 1.76136 + 2.20867i
\(711\) −19.5571 + 22.3942i −0.733449 + 0.839850i
\(712\) 37.7008 8.60497i 1.41290 0.322485i
\(713\) −39.2275 12.1001i −1.46908 0.453151i
\(714\) 0.715509 + 28.8372i 0.0267773 + 1.07921i
\(715\) −50.8122 + 15.6735i −1.90027 + 0.586155i
\(716\) −24.9542 + 14.4073i −0.932583 + 0.538427i
\(717\) −15.7922 + 18.9199i −0.589769 + 0.706577i
\(718\) −26.3009 24.4036i −0.981539 0.910735i
\(719\) −13.1001 + 6.30869i −0.488552 + 0.235274i −0.661908 0.749585i \(-0.730253\pi\)
0.173356 + 0.984859i \(0.444539\pi\)
\(720\) 9.62803 + 1.89436i 0.358815 + 0.0705987i
\(721\) 20.1764 0.951895i 0.751407 0.0354504i
\(722\) 19.0016 7.45759i 0.707167 0.277543i
\(723\) 13.8507 33.0976i 0.515114 1.23091i
\(724\) −0.791061 + 5.24834i −0.0293995 + 0.195053i
\(725\) 17.1179 25.1074i 0.635744 0.932465i
\(726\) 1.46842 2.41704i 0.0544981 0.0897048i
\(727\) −9.04568 13.2676i −0.335486 0.492067i 0.621014 0.783799i \(-0.286721\pi\)
−0.956500 + 0.291732i \(0.905768\pi\)
\(728\) 39.6217 + 28.6500i 1.46848 + 1.06184i
\(729\) 22.5427 + 14.8603i 0.834914 + 0.550381i
\(730\) −21.5272 10.3669i −0.796756 0.383697i
\(731\) 13.1786 + 4.06506i 0.487429 + 0.150352i
\(732\) 0.585427 6.00787i 0.0216380 0.222057i
\(733\) 0.401651 2.66478i 0.0148353 0.0984260i −0.980188 0.198071i \(-0.936532\pi\)
0.995023 + 0.0996446i \(0.0317706\pi\)
\(734\) 33.8725 + 58.6689i 1.25026 + 2.16551i
\(735\) −2.73106 + 35.1012i −0.100737 + 1.29473i
\(736\) 17.9385 31.0704i 0.661223 1.14527i
\(737\) 15.2209 + 12.1382i 0.560668 + 0.447118i
\(738\) 16.6579 + 64.0274i 0.613185 + 2.35688i
\(739\) 2.46825 + 10.8141i 0.0907961 + 0.397804i 0.999821 0.0189388i \(-0.00602876\pi\)
−0.909025 + 0.416743i \(0.863172\pi\)
\(740\) −0.346922 + 0.236528i −0.0127531 + 0.00869493i
\(741\) −28.8271 7.26063i −1.05899 0.266726i
\(742\) −1.42831 + 0.916996i −0.0524347 + 0.0336640i
\(743\) −8.23145 + 0.616862i −0.301983 + 0.0226305i −0.224860 0.974391i \(-0.572192\pi\)
−0.0771229 + 0.997022i \(0.524573\pi\)
\(744\) 0.652073 29.1878i 0.0239062 1.07008i
\(745\) −19.6060 1.46927i −0.718308 0.0538298i
\(746\) 22.7324 + 18.1285i 0.832293 + 0.663732i
\(747\) 1.46531 + 0.0655044i 0.0536128 + 0.00239668i
\(748\) 24.9988 + 19.9359i 0.914046 + 0.728928i
\(749\) 28.4834 21.4535i 1.04076 0.783894i
\(750\) 8.86573 + 16.1800i 0.323731 + 0.590812i
\(751\) 5.73950 + 3.91313i 0.209437 + 0.142792i 0.663496 0.748180i \(-0.269072\pi\)
−0.454059 + 0.890972i \(0.650024\pi\)
\(752\) −4.82160 + 1.48727i −0.175826 + 0.0542350i
\(753\) 17.4529 6.40369i 0.636018 0.233363i
\(754\) 96.0541 + 55.4568i 3.49808 + 2.01962i
\(755\) −1.27026 + 5.56537i −0.0462295 + 0.202545i
\(756\) −43.4475 + 19.8698i −1.58017 + 0.722658i
\(757\) 0.290071 + 1.27088i 0.0105428 + 0.0461910i 0.979926 0.199363i \(-0.0638873\pi\)
−0.969383 + 0.245554i \(0.921030\pi\)
\(758\) 7.18141 23.2816i 0.260841 0.845625i
\(759\) 42.5609 + 25.8569i 1.54486 + 0.938546i
\(760\) 11.7389 29.9101i 0.425813 1.08495i
\(761\) −10.2665 + 9.52594i −0.372161 + 0.345315i −0.843974 0.536384i \(-0.819790\pi\)
0.471813 + 0.881698i \(0.343600\pi\)
\(762\) −3.92347 74.7169i −0.142132 2.70671i
\(763\) −10.6131 + 12.5785i −0.384221 + 0.455374i
\(764\) −73.0131 16.6648i −2.64152 0.602910i
\(765\) 22.0635 + 7.90094i 0.797706 + 0.285659i
\(766\) 70.7616i 2.55672i
\(767\) 41.9474 45.2085i 1.51463 1.63239i
\(768\) 37.8917 + 9.54372i 1.36730 + 0.344379i
\(769\) −0.907476 0.356158i −0.0327244 0.0128434i 0.348922 0.937152i \(-0.386548\pi\)
−0.381647 + 0.924308i \(0.624643\pi\)
\(770\) 43.8984 + 43.0512i 1.58199 + 1.55146i
\(771\) 15.6982 3.21591i 0.565357 0.115818i
\(772\) 21.7311 + 20.1635i 0.782121 + 0.725702i
\(773\) −3.14865 + 3.94828i −0.113249 + 0.142010i −0.835225 0.549908i \(-0.814663\pi\)
0.721976 + 0.691918i \(0.243234\pi\)
\(774\) 3.76905 + 35.7891i 0.135476 + 1.28641i
\(775\) −13.1043 + 10.4503i −0.470720 + 0.375386i
\(776\) −17.4007 + 11.8636i −0.624649 + 0.425879i
\(777\) 0.0652366 0.179166i 0.00234035 0.00642753i
\(778\) 41.1012 + 28.0223i 1.47355 + 1.00465i
\(779\) 30.1280 2.25778i 1.07945 0.0808934i
\(780\) 78.4781 50.9758i 2.80997 1.82523i
\(781\) −31.3064 + 21.3443i −1.12023 + 0.763761i
\(782\) −32.9929 + 41.3718i −1.17982 + 1.47945i
\(783\) −39.6598 + 23.3114i −1.41733 + 0.833080i
\(784\) 1.02301 7.81811i 0.0365360 0.279218i
\(785\) 18.2272 + 10.5235i 0.650555 + 0.375598i
\(786\) −49.0334 16.3328i −1.74896 0.582571i
\(787\) 29.5739 2.21626i 1.05420 0.0790011i 0.463661 0.886013i \(-0.346536\pi\)
0.590535 + 0.807012i \(0.298917\pi\)
\(788\) −41.8584 45.1126i −1.49114 1.60707i
\(789\) −14.4830 10.3556i −0.515607 0.368670i
\(790\) −67.1516 5.03231i −2.38915 0.179042i
\(791\) 8.87958 + 3.77156i 0.315722 + 0.134101i
\(792\) −9.41514 + 34.1424i −0.334553 + 1.21320i
\(793\) −3.34769 4.19787i −0.118880 0.149071i
\(794\) −2.57623 + 34.3775i −0.0914271 + 1.22001i
\(795\) 0.276745 + 1.35091i 0.00981514 + 0.0479119i
\(796\) −15.2494 49.4374i −0.540501 1.75226i
\(797\) 10.3769 + 1.56406i 0.367568 + 0.0554020i 0.330230 0.943901i \(-0.392874\pi\)
0.0373387 + 0.999303i \(0.488112\pi\)
\(798\) 8.47775 + 33.3118i 0.300109 + 1.17923i
\(799\) −11.9162 + 1.79608i −0.421565 + 0.0635407i
\(800\) −6.35570 13.1978i −0.224708 0.466611i
\(801\) 15.4882 + 29.8282i 0.547247 + 1.05393i
\(802\) 59.5516 2.10284
\(803\) 6.01350 10.4157i 0.212212 0.367562i
\(804\) −31.6058 13.2264i −1.11465 0.466460i
\(805\) −45.2218 + 46.1118i −1.59386 + 1.62523i
\(806\) −41.6110 44.8460i −1.46569 1.57963i
\(807\) 12.4821 + 19.2165i 0.439392 + 0.676451i
\(808\) −3.51372 23.3120i −0.123612 0.820115i
\(809\) 25.9799 20.7183i 0.913404 0.728415i −0.0493538 0.998781i \(-0.515716\pi\)
0.962758 + 0.270366i \(0.0871448\pi\)
\(810\) 3.68233 + 61.0415i 0.129384 + 2.14478i
\(811\) 35.7440 8.15833i 1.25514 0.286478i 0.457282 0.889322i \(-0.348823\pi\)
0.797859 + 0.602844i \(0.205966\pi\)
\(812\) 2.25095 81.3703i 0.0789929 2.85554i
\(813\) 23.3728 2.99065i 0.819720 0.104887i
\(814\) −0.166494 0.288377i −0.00583563 0.0101076i
\(815\) −25.4568 44.0924i −0.891711 1.54449i
\(816\) −4.84159 2.02611i −0.169489 0.0709281i
\(817\) 16.3881 + 1.22812i 0.573347 + 0.0429664i
\(818\) −35.2817 44.2419i −1.23360 1.54688i
\(819\) −15.4278 + 39.5967i −0.539090 + 1.38362i
\(820\) −59.2987 + 74.3583i −2.07080 + 2.59670i
\(821\) −25.5336 + 27.5187i −0.891129 + 0.960409i −0.999432 0.0337089i \(-0.989268\pi\)
0.108302 + 0.994118i \(0.465459\pi\)
\(822\) 8.24675 1.68942i 0.287639 0.0589251i
\(823\) 33.5417 + 22.8684i 1.16919 + 0.797141i 0.982680 0.185312i \(-0.0593296\pi\)
0.186511 + 0.982453i \(0.440282\pi\)
\(824\) −9.62744 + 24.5303i −0.335388 + 0.854554i
\(825\) 18.5118 8.41076i 0.644498 0.292825i
\(826\) −69.0574 17.7845i −2.40282 0.618803i
\(827\) 17.4564 + 36.2485i 0.607017 + 1.26048i 0.947356 + 0.320182i \(0.103744\pi\)
−0.340339 + 0.940303i \(0.610542\pi\)
\(828\) −84.4878 23.2984i −2.93615 0.809676i
\(829\) 39.9229 9.11214i 1.38658 0.316478i 0.536842 0.843683i \(-0.319617\pi\)
0.849738 + 0.527205i \(0.176760\pi\)
\(830\) 1.87140 + 2.74485i 0.0649574 + 0.0952750i
\(831\) −15.2695 17.2121i −0.529692 0.597082i
\(832\) 56.7486 32.7638i 1.96740 1.13588i
\(833\) 5.19888 18.0993i 0.180130 0.627103i
\(834\) −16.7684 + 6.15256i −0.580643 + 0.213046i
\(835\) 0.930997 + 2.37214i 0.0322185 + 0.0820914i
\(836\) 34.3285 + 16.5317i 1.18727 + 0.571761i
\(837\) 24.6934 5.83884i 0.853530 0.201820i
\(838\) −33.8110 + 70.2093i −1.16798 + 2.42534i
\(839\) 2.41381 32.2100i 0.0833338 1.11201i −0.786145 0.618042i \(-0.787926\pi\)
0.869479 0.493970i \(-0.164455\pi\)
\(840\) −40.3360 21.9724i −1.39173 0.758121i
\(841\) −3.69034 49.2442i −0.127253 1.69807i
\(842\) 74.6532 + 29.2992i 2.57272 + 1.00972i
\(843\) 24.5903 6.98760i 0.846936 0.240666i
\(844\) −19.5249 49.7486i −0.672075 1.71242i
\(845\) 10.1224 44.3490i 0.348220 1.52565i
\(846\) −16.5358 26.7465i −0.568513 0.919564i
\(847\) −1.38760 + 1.21786i −0.0476786 + 0.0418463i
\(848\) −0.0460277 0.305374i −0.00158060 0.0104866i
\(849\) −0.437564 + 1.73727i −0.0150172 + 0.0596230i
\(850\) 6.36833 + 20.6456i 0.218432 + 0.708139i
\(851\) 0.302917 0.174889i 0.0103839 0.00599512i
\(852\) 42.7297 51.1927i 1.46390 1.75383i
\(853\) −2.23966 + 2.41377i −0.0766843 + 0.0826461i −0.770228 0.637768i \(-0.779858\pi\)
0.693544 + 0.720414i \(0.256048\pi\)
\(854\) −2.42716 + 5.71438i −0.0830556 + 0.195542i
\(855\) 27.7272 + 3.32852i 0.948249 + 0.113833i
\(856\) 10.3520 + 45.3552i 0.353825 + 1.55021i
\(857\) −30.4416 + 4.58833i −1.03987 + 0.156734i −0.646709 0.762737i \(-0.723855\pi\)
−0.393157 + 0.919472i \(0.628617\pi\)
\(858\) 35.6625 + 65.0845i 1.21750 + 2.22195i
\(859\) −25.0685 27.0174i −0.855326 0.921822i 0.142360 0.989815i \(-0.454531\pi\)
−0.997686 + 0.0679930i \(0.978340\pi\)
\(860\) −37.9235 + 35.1879i −1.29318 + 1.19990i
\(861\) 2.15827 43.1355i 0.0735536 1.47006i
\(862\) −17.2273 15.9846i −0.586765 0.544438i
\(863\) 16.6862i 0.568005i 0.958824 + 0.284002i \(0.0916623\pi\)
−0.958824 + 0.284002i \(0.908338\pi\)
\(864\) 0.172731 + 22.1754i 0.00587641 + 0.754423i
\(865\) 3.36854 14.7585i 0.114534 0.501806i
\(866\) −2.47300 + 32.9999i −0.0840359 + 1.12138i
\(867\) 14.4520 + 8.77998i 0.490816 + 0.298184i
\(868\) −14.4156 + 42.5219i −0.489296 + 1.44329i
\(869\) 5.05199 33.5178i 0.171377 1.13701i
\(870\) −96.1167 40.2230i −3.25866 1.36369i
\(871\) −28.3689 + 11.1340i −0.961244 + 0.377260i
\(872\) −9.31604 19.3450i −0.315481 0.655103i
\(873\) −13.7867 12.0401i −0.466610 0.407495i
\(874\) −27.3592 + 56.8119i −0.925438 + 1.92169i
\(875\) −2.35438 11.8119i −0.0795926 0.399317i
\(876\) −5.16961 + 20.5250i −0.174665 + 0.693477i
\(877\) −0.750003 10.0081i −0.0253258 0.337949i −0.995446 0.0953252i \(-0.969611\pi\)
0.970120 0.242624i \(-0.0780081\pi\)
\(878\) −37.4468 + 34.7455i −1.26377 + 1.17260i
\(879\) −12.1757 26.7983i −0.410675 0.903883i
\(880\) −10.4137 + 4.08709i −0.351047 + 0.137776i
\(881\) −34.4967 −1.16222 −0.581111 0.813824i \(-0.697382\pi\)
−0.581111 + 0.813824i \(0.697382\pi\)
\(882\) 48.7582 6.09768i 1.64177 0.205320i
\(883\) −9.79133 −0.329504 −0.164752 0.986335i \(-0.552682\pi\)
−0.164752 + 0.986335i \(0.552682\pi\)
\(884\) −46.5932 + 18.2865i −1.56710 + 0.615041i
\(885\) −33.6970 + 47.1273i −1.13271 + 1.58417i
\(886\) −62.0593 + 57.5826i −2.08492 + 1.93453i
\(887\) −1.33953 17.8748i −0.0449770 0.600176i −0.973468 0.228822i \(-0.926513\pi\)
0.928491 0.371354i \(-0.121106\pi\)
\(888\) 0.178527 + 0.173229i 0.00599099 + 0.00581317i
\(889\) −12.1813 + 47.3002i −0.408549 + 1.58640i
\(890\) −33.0284 + 68.5841i −1.10711 + 2.29895i
\(891\) −30.7786 0.447792i −1.03112 0.0150016i
\(892\) −15.0844 31.3231i −0.505063 1.04877i
\(893\) −13.3674 + 5.24630i −0.447322 + 0.175561i
\(894\) 3.48272 + 27.2185i 0.116480 + 0.910323i
\(895\) 3.58858 23.8086i 0.119953 0.795835i
\(896\) −45.3077 27.8567i −1.51363 0.930627i
\(897\) −68.3660 + 37.4606i −2.28268 + 1.25077i
\(898\) −0.906396 + 12.0950i −0.0302468 + 0.403616i
\(899\) −9.62039 + 42.1497i −0.320858 + 1.40577i
\(900\) −27.2919 + 23.1432i −0.909731 + 0.771440i
\(901\) 0.737563i 0.0245718i
\(902\) −55.2909 51.3025i −1.84099 1.70819i
\(903\) 4.65793 23.0265i 0.155006 0.766273i
\(904\) −9.22636 + 8.56081i −0.306864 + 0.284728i
\(905\) −3.01661 3.25113i −0.100275 0.108071i
\(906\) 7.96524 + 0.177948i 0.264627 + 0.00591194i
\(907\) −33.6477 + 5.07158i −1.11725 + 0.168399i −0.681607 0.731719i \(-0.738719\pi\)
−0.435647 + 0.900117i \(0.643480\pi\)
\(908\) −6.91831 30.3111i −0.229592 1.00591i
\(909\) 18.8395 8.05699i 0.624868 0.267234i
\(910\) −92.7228 + 25.8159i −3.07373 + 0.855789i
\(911\) −22.5945 + 24.3511i −0.748589 + 0.806787i −0.986372 0.164531i \(-0.947389\pi\)
0.237783 + 0.971318i \(0.423579\pi\)
\(912\) −6.16194 1.07003i −0.204042 0.0354322i
\(913\) −1.44818 + 0.836109i −0.0479279 + 0.0276712i
\(914\) −7.87435 25.5280i −0.260460 0.844392i
\(915\) 3.61994 + 3.51249i 0.119671 + 0.116119i
\(916\) 6.82959 + 45.3114i 0.225656 + 1.49713i
\(917\) 27.3401 + 19.7693i 0.902849 + 0.652840i
\(918\) 4.62286 32.3801i 0.152577 1.06870i
\(919\) 0.663033 2.90494i 0.0218715 0.0958251i −0.962814 0.270165i \(-0.912922\pi\)
0.984686 + 0.174340i \(0.0557790\pi\)
\(920\) −30.7837 78.4357i −1.01491 2.58595i
\(921\) 5.30322 + 5.14581i 0.174747 + 0.169560i
\(922\) −39.9967 15.6976i −1.31722 0.516971i
\(923\) −4.43250 59.1476i −0.145898 1.94687i
\(924\) 29.5568 45.7503i 0.972349 1.50507i
\(925\) 0.0106724 0.142413i 0.000350906 0.00468251i
\(926\) −31.1143 + 64.6095i −1.02248 + 2.12320i
\(927\) −22.7400 2.72983i −0.746880 0.0896595i
\(928\) −34.0425 16.3940i −1.11750 0.538160i
\(929\) −12.0158 30.6157i −0.394224 1.00447i −0.980877 0.194629i \(-0.937650\pi\)
0.586653 0.809839i \(-0.300445\pi\)
\(930\) 44.1208 + 36.8269i 1.44678 + 1.20760i
\(931\) 1.24055 22.4053i 0.0406574 0.734305i
\(932\) 54.2653 31.3301i 1.77752 1.02625i
\(933\) 57.5487 11.7893i 1.88406 0.385965i
\(934\) 23.6812 + 34.7339i 0.774871 + 1.13653i
\(935\) −26.0482 + 5.94533i −0.851867 + 0.194433i
\(936\) −38.9169 39.4872i −1.27204 1.29068i
\(937\) −19.3759 40.2344i −0.632982 1.31440i −0.932796 0.360404i \(-0.882639\pi\)
0.299814 0.953998i \(-0.403075\pi\)
\(938\) 26.9327 + 22.7245i 0.879384 + 0.741980i
\(939\) 3.24963 + 2.32355i 0.106048 + 0.0758263i
\(940\) 16.5152 42.0799i 0.538665 1.37250i
\(941\) −6.02389 4.10702i −0.196373 0.133885i 0.461142 0.887327i \(-0.347440\pi\)
−0.657515 + 0.753441i \(0.728392\pi\)
\(942\) 9.28313 27.8693i 0.302461 0.908031i
\(943\) 53.8891 58.0787i 1.75487 1.89130i
\(944\) 8.08960 10.1440i 0.263294 0.330160i
\(945\) 9.65474 38.7362i 0.314069 1.26009i
\(946\) −25.5804 32.0768i −0.831689 1.04291i
\(947\) 14.8811 + 1.11518i 0.483571 + 0.0362386i 0.314286 0.949328i \(-0.398235\pi\)
0.169285 + 0.985567i \(0.445854\pi\)
\(948\) 7.57119 + 59.1710i 0.245901 + 1.92179i
\(949\) 9.41355 + 16.3047i 0.305577 + 0.529274i
\(950\) 12.8728 + 22.2963i 0.417649 + 0.723389i
\(951\) −1.49791 + 3.57940i −0.0485731 + 0.116070i
\(952\) 18.7769 + 15.8430i 0.608562 + 0.513474i
\(953\) 0.0868031 0.0198122i 0.00281183 0.000641781i −0.221115 0.975248i \(-0.570970\pi\)
0.223927 + 0.974606i \(0.428112\pi\)
\(954\) 1.76956 0.756778i 0.0572917 0.0245016i
\(955\) 48.9261 39.0173i 1.58321 1.26257i
\(956\) 7.36961 + 48.8941i 0.238350 + 1.58135i
\(957\) 23.8057 46.7332i 0.769529 1.51067i
\(958\) 54.1072 + 58.3137i 1.74812 + 1.88403i
\(959\) −5.46659 0.562052i −0.176526 0.0181496i
\(960\) −48.9728 + 37.2959i −1.58059 + 1.20372i
\(961\) −3.57671 + 6.19504i −0.115378 + 0.199840i
\(962\) 0.521261 0.0168061
\(963\) −35.8842 + 18.6327i −1.15635 + 0.600431i
\(964\) −31.2339 64.8578i −1.00598 2.08893i
\(965\) −24.4945 + 3.69195i −0.788506 + 0.118848i
\(966\) 75.7144 + 48.9151i 2.43607 + 1.57382i
\(967\) 42.1963 + 6.36007i 1.35694 + 0.204526i 0.786895 0.617087i \(-0.211687\pi\)
0.570046 + 0.821613i \(0.306925\pi\)
\(968\) −0.709968 2.30166i −0.0228192 0.0739781i
\(969\) −14.1713 4.72040i −0.455248 0.151641i
\(970\) 3.09808 41.3410i 0.0994733 1.32738i
\(971\) −36.2881 45.5039i −1.16454 1.46029i −0.861823 0.507209i \(-0.830677\pi\)
−0.302719 0.953080i \(-0.597894\pi\)
\(972\) 52.3192 14.0478i 1.67814 0.450583i
\(973\) 11.6473 0.549506i 0.373396 0.0176163i
\(974\) −79.5244 5.95953i −2.54813 0.190956i
\(975\) −3.08692 + 31.6791i −0.0988607 + 1.01454i
\(976\) −0.768329 0.828062i −0.0245936 0.0265056i
\(977\) 15.4107 1.15487i 0.493032 0.0369476i 0.174105 0.984727i \(-0.444297\pi\)
0.318927 + 0.947779i \(0.396678\pi\)
\(978\) −53.1564 + 47.1568i −1.69975 + 1.50791i
\(979\) −33.1837 19.1586i −1.06056 0.612313i
\(980\) 49.0468 + 50.8361i 1.56674 + 1.62390i
\(981\) 14.2329 12.0694i 0.454423 0.385345i
\(982\) −20.3247 + 25.4863i −0.648586 + 0.813301i
\(983\) −20.7900 + 14.1744i −0.663098 + 0.452093i −0.847526 0.530753i \(-0.821909\pi\)
0.184428 + 0.982846i \(0.440957\pi\)
\(984\) 50.2075 + 25.5755i 1.60056 + 0.815317i
\(985\) 51.2798 3.84289i 1.63391 0.122445i
\(986\) 46.0460 + 31.3936i 1.46640 + 0.999777i
\(987\) 5.06292 + 19.8939i 0.161155 + 0.633228i
\(988\) −49.2806 + 33.5989i −1.56782 + 1.06892i
\(989\) 33.6941 26.8701i 1.07141 0.854420i
\(990\) −40.9909 56.3946i −1.30278 1.79234i
\(991\) −29.4056 + 36.8735i −0.934100 + 1.17132i 0.0508883 + 0.998704i \(0.483795\pi\)
−0.984988 + 0.172620i \(0.944777\pi\)
\(992\) 15.2775 + 14.1754i 0.485060 + 0.450070i
\(993\) 26.4561 + 29.8220i 0.839559 + 0.946372i
\(994\) −57.7134 + 37.0530i −1.83056 + 1.17525i
\(995\) 40.2422 + 15.7939i 1.27576 + 0.500700i
\(996\) 2.04936 2.11205i 0.0649366 0.0669230i
\(997\) 21.4090 23.0734i 0.678029 0.730741i −0.296493 0.955035i \(-0.595817\pi\)
0.974522 + 0.224294i \(0.0720075\pi\)
\(998\) 15.2795i 0.483666i
\(999\) −0.106640 + 0.188073i −0.00337393 + 0.00595038i
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 441.2.bh.a.398.48 yes 648
9.5 odd 6 inner 441.2.bh.a.104.48 yes 648
49.41 odd 14 inner 441.2.bh.a.335.48 yes 648
441.41 even 42 inner 441.2.bh.a.41.48 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.bh.a.41.48 648 441.41 even 42 inner
441.2.bh.a.104.48 yes 648 9.5 odd 6 inner
441.2.bh.a.335.48 yes 648 49.41 odd 14 inner
441.2.bh.a.398.48 yes 648 1.1 even 1 trivial