Properties

Label 252.2.n.b.31.3
Level $252$
Weight $2$
Character 252.31
Analytic conductor $2.012$
Analytic rank $0$
Dimension $84$
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] = [252,2,Mod(31,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.31");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.n (of order \(6\), degree \(2\), 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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.3
Character \(\chi\) \(=\) 252.31
Dual form 252.2.n.b.187.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39808 - 0.213015i) q^{2} +(-0.709178 + 1.58021i) q^{3} +(1.90925 + 0.595623i) q^{4} -2.93241i q^{5} +(1.32809 - 2.05819i) q^{6} +(-2.24678 + 1.39713i) q^{7} +(-2.54241 - 1.23943i) q^{8} +(-1.99413 - 2.24130i) q^{9} +O(q^{10})\) \(q+(-1.39808 - 0.213015i) q^{2} +(-0.709178 + 1.58021i) q^{3} +(1.90925 + 0.595623i) q^{4} -2.93241i q^{5} +(1.32809 - 2.05819i) q^{6} +(-2.24678 + 1.39713i) q^{7} +(-2.54241 - 1.23943i) q^{8} +(-1.99413 - 2.24130i) q^{9} +(-0.624647 + 4.09975i) q^{10} -1.83078i q^{11} +(-2.29521 + 2.59461i) q^{12} +(-0.488438 - 0.282000i) q^{13} +(3.43879 - 1.47470i) q^{14} +(4.63383 + 2.07960i) q^{15} +(3.29047 + 2.27438i) q^{16} +(0.330952 + 0.191075i) q^{17} +(2.31053 + 3.55830i) q^{18} +(-4.34210 - 7.52073i) q^{19} +(1.74661 - 5.59871i) q^{20} +(-0.614395 - 4.54120i) q^{21} +(-0.389982 + 2.55957i) q^{22} -4.80432i q^{23} +(3.76157 - 3.13856i) q^{24} -3.59905 q^{25} +(0.622805 + 0.498302i) q^{26} +(4.95592 - 1.56167i) q^{27} +(-5.12183 + 1.32924i) q^{28} +(-1.82266 - 3.15694i) q^{29} +(-6.03548 - 3.89452i) q^{30} +(-0.327099 - 0.566552i) q^{31} +(-4.11586 - 3.88069i) q^{32} +(2.89301 + 1.29835i) q^{33} +(-0.421996 - 0.337636i) q^{34} +(4.09697 + 6.58849i) q^{35} +(-2.47233 - 5.46695i) q^{36} +(3.63968 + 6.30411i) q^{37} +(4.46857 + 11.4395i) q^{38} +(0.792008 - 0.571847i) q^{39} +(-3.63451 + 7.45538i) q^{40} +(-8.94130 - 5.16226i) q^{41} +(-0.108370 + 6.47983i) q^{42} +(5.57437 - 3.21836i) q^{43} +(1.09045 - 3.49541i) q^{44} +(-6.57242 + 5.84763i) q^{45} +(-1.02339 + 6.71682i) q^{46} +(-3.98863 + 6.90851i) q^{47} +(-5.92753 + 3.58669i) q^{48} +(3.09605 - 6.27810i) q^{49} +(5.03175 + 0.766650i) q^{50} +(-0.536643 + 0.387468i) q^{51} +(-0.764584 - 0.829333i) q^{52} +(-3.65087 + 6.32349i) q^{53} +(-7.26143 + 1.12766i) q^{54} -5.36859 q^{55} +(7.44387 - 0.767355i) q^{56} +(14.9637 - 1.52789i) q^{57} +(1.87575 + 4.80190i) q^{58} +(0.0346907 + 0.0600861i) q^{59} +(7.60848 + 6.73050i) q^{60} +(8.51454 + 4.91587i) q^{61} +(0.336626 + 0.861761i) q^{62} +(7.61177 + 2.24965i) q^{63} +(4.92765 + 6.30224i) q^{64} +(-0.826940 + 1.43230i) q^{65} +(-3.76809 - 2.43144i) q^{66} +(-1.57158 + 0.907354i) q^{67} +(0.518062 + 0.561933i) q^{68} +(7.59185 + 3.40712i) q^{69} +(-4.32444 - 10.0839i) q^{70} +9.64068i q^{71} +(2.29197 + 8.16988i) q^{72} +(-13.1397 - 7.58623i) q^{73} +(-3.74569 - 9.58896i) q^{74} +(2.55237 - 5.68726i) q^{75} +(-3.81063 - 16.9452i) q^{76} +(2.55783 + 4.11335i) q^{77} +(-1.22910 + 0.630778i) q^{78} +(5.47218 + 3.15937i) q^{79} +(6.66944 - 9.64901i) q^{80} +(-1.04686 + 8.93891i) q^{81} +(11.4010 + 9.12188i) q^{82} +(-2.90035 - 5.02356i) q^{83} +(1.53181 - 9.03624i) q^{84} +(0.560312 - 0.970489i) q^{85} +(-8.47897 + 3.31210i) q^{86} +(6.28122 - 0.641356i) q^{87} +(-2.26911 + 4.65457i) q^{88} +(-1.91814 + 1.10744i) q^{89} +(10.4344 - 6.77542i) q^{90} +(1.49140 - 0.0488201i) q^{91} +(2.86156 - 9.17265i) q^{92} +(1.12724 - 0.115099i) q^{93} +(7.04804 - 8.80901i) q^{94} +(-22.0539 + 12.7328i) q^{95} +(9.05118 - 3.75182i) q^{96} +(-1.59144 + 0.918820i) q^{97} +(-5.66585 + 8.11777i) q^{98} +(-4.10332 + 3.65081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - q^{2} + q^{4} - 16 q^{8} - 14 q^{9} - 18 q^{10} + 9 q^{12} - 18 q^{13} - 25 q^{14} - 7 q^{16} + 6 q^{17} - 13 q^{18} + 24 q^{20} + 4 q^{21} + 6 q^{22} + 6 q^{24} - 32 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 14 q^{30} + 9 q^{32} - 6 q^{33} + 24 q^{34} - 38 q^{36} + 2 q^{37} - 6 q^{41} + 7 q^{42} - 13 q^{44} - 18 q^{45} + 10 q^{46} - 9 q^{48} + 2 q^{49} - 17 q^{50} - 2 q^{53} - 42 q^{54} - 32 q^{56} + 6 q^{57} + 26 q^{58} + 8 q^{60} - 24 q^{61} - 8 q^{64} + 50 q^{65} + 27 q^{66} + 18 q^{69} - 4 q^{70} - 7 q^{72} + 30 q^{73} + 46 q^{74} + 46 q^{77} + 15 q^{78} + 3 q^{80} - 26 q^{81} - 18 q^{82} + 29 q^{84} - 50 q^{85} + 18 q^{86} - 2 q^{88} - 102 q^{89} + 39 q^{90} + 28 q^{92} - 24 q^{93} + 3 q^{94} - 30 q^{96} - 6 q^{97} + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39808 0.213015i −0.988591 0.150624i
\(3\) −0.709178 + 1.58021i −0.409444 + 0.912335i
\(4\) 1.90925 + 0.595623i 0.954625 + 0.297811i
\(5\) 2.93241i 1.31142i −0.755015 0.655708i \(-0.772370\pi\)
0.755015 0.655708i \(-0.227630\pi\)
\(6\) 1.32809 2.05819i 0.542192 0.840254i
\(7\) −2.24678 + 1.39713i −0.849203 + 0.528066i
\(8\) −2.54241 1.23943i −0.898876 0.438203i
\(9\) −1.99413 2.24130i −0.664711 0.747100i
\(10\) −0.624647 + 4.09975i −0.197531 + 1.29645i
\(11\) 1.83078i 0.552000i −0.961158 0.276000i \(-0.910991\pi\)
0.961158 0.276000i \(-0.0890089\pi\)
\(12\) −2.29521 + 2.59461i −0.662569 + 0.749001i
\(13\) −0.488438 0.282000i −0.135468 0.0782127i 0.430734 0.902479i \(-0.358255\pi\)
−0.566203 + 0.824266i \(0.691588\pi\)
\(14\) 3.43879 1.47470i 0.919054 0.394131i
\(15\) 4.63383 + 2.07960i 1.19645 + 0.536951i
\(16\) 3.29047 + 2.27438i 0.822617 + 0.568596i
\(17\) 0.330952 + 0.191075i 0.0802677 + 0.0463426i 0.539597 0.841924i \(-0.318577\pi\)
−0.459329 + 0.888266i \(0.651910\pi\)
\(18\) 2.31053 + 3.55830i 0.544596 + 0.838698i
\(19\) −4.34210 7.52073i −0.996145 1.72537i −0.574038 0.818829i \(-0.694624\pi\)
−0.422107 0.906546i \(-0.638709\pi\)
\(20\) 1.74661 5.59871i 0.390554 1.25191i
\(21\) −0.614395 4.54120i −0.134072 0.990972i
\(22\) −0.389982 + 2.55957i −0.0831445 + 0.545702i
\(23\) 4.80432i 1.00177i −0.865514 0.500885i \(-0.833008\pi\)
0.865514 0.500885i \(-0.166992\pi\)
\(24\) 3.76157 3.13856i 0.767828 0.640657i
\(25\) −3.59905 −0.719810
\(26\) 0.622805 + 0.498302i 0.122142 + 0.0977251i
\(27\) 4.95592 1.56167i 0.953768 0.300544i
\(28\) −5.12183 + 1.32924i −0.967935 + 0.251202i
\(29\) −1.82266 3.15694i −0.338459 0.586229i 0.645684 0.763605i \(-0.276572\pi\)
−0.984143 + 0.177376i \(0.943239\pi\)
\(30\) −6.03548 3.89452i −1.10192 0.711039i
\(31\) −0.327099 0.566552i −0.0587487 0.101756i 0.835155 0.550014i \(-0.185378\pi\)
−0.893904 + 0.448259i \(0.852044\pi\)
\(32\) −4.11586 3.88069i −0.727587 0.686015i
\(33\) 2.89301 + 1.29835i 0.503609 + 0.226013i
\(34\) −0.421996 0.337636i −0.0723716 0.0579041i
\(35\) 4.09697 + 6.58849i 0.692514 + 1.11366i
\(36\) −2.47233 5.46695i −0.412055 0.911159i
\(37\) 3.63968 + 6.30411i 0.598360 + 1.03639i 0.993063 + 0.117581i \(0.0375141\pi\)
−0.394703 + 0.918809i \(0.629153\pi\)
\(38\) 4.46857 + 11.4395i 0.724897 + 1.85573i
\(39\) 0.792008 0.571847i 0.126823 0.0915688i
\(40\) −3.63451 + 7.45538i −0.574666 + 1.17880i
\(41\) −8.94130 5.16226i −1.39640 0.806210i −0.402384 0.915471i \(-0.631818\pi\)
−0.994013 + 0.109261i \(0.965152\pi\)
\(42\) −0.108370 + 6.47983i −0.0167218 + 0.999860i
\(43\) 5.57437 3.21836i 0.850083 0.490796i −0.0105955 0.999944i \(-0.503373\pi\)
0.860679 + 0.509148i \(0.170039\pi\)
\(44\) 1.09045 3.49541i 0.164392 0.526953i
\(45\) −6.57242 + 5.84763i −0.979759 + 0.871713i
\(46\) −1.02339 + 6.71682i −0.150891 + 0.990342i
\(47\) −3.98863 + 6.90851i −0.581802 + 1.00771i 0.413464 + 0.910520i \(0.364319\pi\)
−0.995266 + 0.0971900i \(0.969015\pi\)
\(48\) −5.92753 + 3.58669i −0.855566 + 0.517694i
\(49\) 3.09605 6.27810i 0.442293 0.896871i
\(50\) 5.03175 + 0.766650i 0.711598 + 0.108421i
\(51\) −0.536643 + 0.387468i −0.0751451 + 0.0542564i
\(52\) −0.764584 0.829333i −0.106029 0.115008i
\(53\) −3.65087 + 6.32349i −0.501485 + 0.868598i 0.498513 + 0.866882i \(0.333880\pi\)
−0.999999 + 0.00171612i \(0.999454\pi\)
\(54\) −7.26143 + 1.12766i −0.988156 + 0.153455i
\(55\) −5.36859 −0.723901
\(56\) 7.44387 0.767355i 0.994729 0.102542i
\(57\) 14.9637 1.52789i 1.98199 0.202375i
\(58\) 1.87575 + 4.80190i 0.246298 + 0.630521i
\(59\) 0.0346907 + 0.0600861i 0.00451635 + 0.00782255i 0.868275 0.496084i \(-0.165229\pi\)
−0.863758 + 0.503906i \(0.831896\pi\)
\(60\) 7.60848 + 6.73050i 0.982251 + 0.868903i
\(61\) 8.51454 + 4.91587i 1.09018 + 0.629413i 0.933623 0.358257i \(-0.116629\pi\)
0.156552 + 0.987670i \(0.449962\pi\)
\(62\) 0.336626 + 0.861761i 0.0427516 + 0.109444i
\(63\) 7.61177 + 2.24965i 0.958993 + 0.283429i
\(64\) 4.92765 + 6.30224i 0.615956 + 0.787781i
\(65\) −0.826940 + 1.43230i −0.102569 + 0.177655i
\(66\) −3.76809 2.43144i −0.463820 0.299290i
\(67\) −1.57158 + 0.907354i −0.192000 + 0.110851i −0.592918 0.805263i \(-0.702024\pi\)
0.400919 + 0.916114i \(0.368691\pi\)
\(68\) 0.518062 + 0.561933i 0.0628242 + 0.0681444i
\(69\) 7.59185 + 3.40712i 0.913951 + 0.410169i
\(70\) −4.32444 10.0839i −0.516869 1.20526i
\(71\) 9.64068i 1.14414i 0.820205 + 0.572069i \(0.193859\pi\)
−0.820205 + 0.572069i \(0.806141\pi\)
\(72\) 2.29197 + 8.16988i 0.270111 + 0.962829i
\(73\) −13.1397 7.58623i −1.53789 0.887901i −0.998962 0.0455481i \(-0.985497\pi\)
−0.538927 0.842353i \(-0.681170\pi\)
\(74\) −3.74569 9.58896i −0.435428 1.11469i
\(75\) 2.55237 5.68726i 0.294722 0.656708i
\(76\) −3.81063 16.9452i −0.437109 1.94375i
\(77\) 2.55783 + 4.11335i 0.291492 + 0.468760i
\(78\) −1.22910 + 0.630778i −0.139168 + 0.0714215i
\(79\) 5.47218 + 3.15937i 0.615669 + 0.355456i 0.775181 0.631740i \(-0.217659\pi\)
−0.159512 + 0.987196i \(0.550992\pi\)
\(80\) 6.66944 9.64901i 0.745666 1.07879i
\(81\) −1.04686 + 8.93891i −0.116318 + 0.993212i
\(82\) 11.4010 + 9.12188i 1.25903 + 1.00734i
\(83\) −2.90035 5.02356i −0.318355 0.551407i 0.661790 0.749689i \(-0.269797\pi\)
−0.980145 + 0.198282i \(0.936464\pi\)
\(84\) 1.53181 9.03624i 0.167134 0.985934i
\(85\) 0.560312 0.970489i 0.0607744 0.105264i
\(86\) −8.47897 + 3.31210i −0.914311 + 0.357153i
\(87\) 6.28122 0.641356i 0.673417 0.0687606i
\(88\) −2.26911 + 4.65457i −0.241888 + 0.496179i
\(89\) −1.91814 + 1.10744i −0.203323 + 0.117389i −0.598204 0.801343i \(-0.704119\pi\)
0.394882 + 0.918732i \(0.370786\pi\)
\(90\) 10.4344 6.77542i 1.09988 0.714192i
\(91\) 1.49140 0.0488201i 0.156342 0.00511774i
\(92\) 2.86156 9.17265i 0.298339 0.956315i
\(93\) 1.12724 0.115099i 0.116890 0.0119352i
\(94\) 7.04804 8.80901i 0.726950 0.908580i
\(95\) −22.0539 + 12.7328i −2.26268 + 1.30636i
\(96\) 9.05118 3.75182i 0.923782 0.382919i
\(97\) −1.59144 + 0.918820i −0.161587 + 0.0932921i −0.578613 0.815602i \(-0.696406\pi\)
0.417026 + 0.908895i \(0.363072\pi\)
\(98\) −5.66585 + 8.11777i −0.572337 + 0.820018i
\(99\) −4.10332 + 3.65081i −0.412399 + 0.366920i
\(100\) −6.87148 2.14368i −0.687148 0.214368i
\(101\) 4.52600i 0.450354i −0.974318 0.225177i \(-0.927704\pi\)
0.974318 0.225177i \(-0.0722960\pi\)
\(102\) 0.832806 0.427398i 0.0824601 0.0423187i
\(103\) −14.0545 −1.38483 −0.692416 0.721499i \(-0.743454\pi\)
−0.692416 + 0.721499i \(0.743454\pi\)
\(104\) 0.892289 + 1.32234i 0.0874962 + 0.129666i
\(105\) −13.3167 + 1.80166i −1.29958 + 0.175824i
\(106\) 6.45120 8.06305i 0.626596 0.783153i
\(107\) 7.78206 4.49298i 0.752320 0.434352i −0.0742113 0.997243i \(-0.523644\pi\)
0.826532 + 0.562890i \(0.190311\pi\)
\(108\) 10.3923 0.0297615i 0.999996 0.00286380i
\(109\) 1.49757 2.59388i 0.143442 0.248448i −0.785349 0.619054i \(-0.787516\pi\)
0.928790 + 0.370605i \(0.120850\pi\)
\(110\) 7.50572 + 1.14359i 0.715642 + 0.109037i
\(111\) −12.5430 + 1.28073i −1.19053 + 0.121561i
\(112\) −10.5706 0.512830i −0.998825 0.0484579i
\(113\) −4.05327 + 7.02047i −0.381299 + 0.660430i −0.991248 0.132011i \(-0.957857\pi\)
0.609949 + 0.792441i \(0.291190\pi\)
\(114\) −21.2458 1.05136i −1.98986 0.0984692i
\(115\) −14.0883 −1.31374
\(116\) −1.59957 7.11300i −0.148516 0.660425i
\(117\) 0.341964 + 1.65708i 0.0316146 + 0.153197i
\(118\) −0.0357012 0.0913948i −0.00328656 0.00841357i
\(119\) −1.01053 + 0.0330792i −0.0926356 + 0.00303237i
\(120\) −9.20357 11.0305i −0.840167 1.00694i
\(121\) 7.64826 0.695296
\(122\) −10.8568 8.68650i −0.982933 0.786439i
\(123\) 14.4984 10.4682i 1.30728 0.943884i
\(124\) −0.287062 1.27652i −0.0257789 0.114635i
\(125\) 4.10817i 0.367446i
\(126\) −10.1627 4.76660i −0.905361 0.424643i
\(127\) 5.68040i 0.504054i −0.967720 0.252027i \(-0.918903\pi\)
0.967720 0.252027i \(-0.0810972\pi\)
\(128\) −5.54677 9.86070i −0.490270 0.871571i
\(129\) 1.13248 + 11.0911i 0.0997089 + 0.976515i
\(130\) 1.46123 1.82632i 0.128158 0.160179i
\(131\) 7.76310 0.678265 0.339133 0.940739i \(-0.389866\pi\)
0.339133 + 0.940739i \(0.389866\pi\)
\(132\) 4.75016 + 4.20201i 0.413448 + 0.365738i
\(133\) 20.2632 + 10.8310i 1.75704 + 0.939163i
\(134\) 2.39048 0.933783i 0.206506 0.0806665i
\(135\) −4.57947 14.5328i −0.394138 1.25079i
\(136\) −0.604591 0.895982i −0.0518433 0.0768298i
\(137\) 18.8890 1.61380 0.806900 0.590688i \(-0.201144\pi\)
0.806900 + 0.590688i \(0.201144\pi\)
\(138\) −9.88823 6.38060i −0.841742 0.543152i
\(139\) 3.57292 6.18848i 0.303051 0.524900i −0.673774 0.738937i \(-0.735328\pi\)
0.976826 + 0.214037i \(0.0686613\pi\)
\(140\) 3.89788 + 15.0193i 0.329431 + 1.26936i
\(141\) −8.08826 11.2022i −0.681155 0.943399i
\(142\) 2.05361 13.4784i 0.172335 1.13108i
\(143\) −0.516278 + 0.894220i −0.0431734 + 0.0747785i
\(144\) −1.46405 11.9104i −0.122004 0.992530i
\(145\) −9.25745 + 5.34479i −0.768789 + 0.443861i
\(146\) 16.7544 + 13.4051i 1.38660 + 1.10941i
\(147\) 7.72507 + 9.34470i 0.637153 + 0.770738i
\(148\) 3.19419 + 14.2040i 0.262561 + 1.16756i
\(149\) 9.81557 0.804122 0.402061 0.915613i \(-0.368294\pi\)
0.402061 + 0.915613i \(0.368294\pi\)
\(150\) −4.77988 + 7.40754i −0.390275 + 0.604823i
\(151\) 3.75263i 0.305385i −0.988274 0.152692i \(-0.951206\pi\)
0.988274 0.152692i \(-0.0487944\pi\)
\(152\) 1.71798 + 24.5025i 0.139347 + 1.98741i
\(153\) −0.231706 1.12279i −0.0187323 0.0907725i
\(154\) −2.69985 6.29565i −0.217560 0.507318i
\(155\) −1.66136 + 0.959189i −0.133444 + 0.0770439i
\(156\) 1.85275 0.620061i 0.148338 0.0496446i
\(157\) 5.67206 3.27476i 0.452679 0.261355i −0.256282 0.966602i \(-0.582498\pi\)
0.708961 + 0.705248i \(0.249164\pi\)
\(158\) −6.97755 5.58270i −0.555104 0.444136i
\(159\) −7.40334 10.2536i −0.587123 0.813165i
\(160\) −11.3798 + 12.0694i −0.899651 + 0.954169i
\(161\) 6.71227 + 10.7943i 0.529001 + 0.850707i
\(162\) 3.36771 12.2743i 0.264592 0.964360i
\(163\) 11.1236 6.42221i 0.871268 0.503027i 0.00349827 0.999994i \(-0.498886\pi\)
0.867769 + 0.496967i \(0.165553\pi\)
\(164\) −13.9964 15.1817i −1.09294 1.18549i
\(165\) 3.80729 8.48351i 0.296397 0.660440i
\(166\) 2.98483 + 7.64115i 0.231668 + 0.593068i
\(167\) 1.76904 3.06407i 0.136893 0.237105i −0.789426 0.613846i \(-0.789622\pi\)
0.926319 + 0.376740i \(0.122955\pi\)
\(168\) −4.06644 + 12.3071i −0.313733 + 0.949511i
\(169\) −6.34095 10.9829i −0.487766 0.844835i
\(170\) −0.990089 + 1.23747i −0.0759364 + 0.0949093i
\(171\) −8.19750 + 24.7293i −0.626879 + 1.89110i
\(172\) 12.5598 2.82444i 0.957675 0.215361i
\(173\) 8.62342 + 4.97873i 0.655627 + 0.378526i 0.790609 0.612322i \(-0.209764\pi\)
−0.134982 + 0.990848i \(0.543098\pi\)
\(174\) −8.91826 0.441325i −0.676091 0.0334568i
\(175\) 8.08628 5.02834i 0.611265 0.380107i
\(176\) 4.16389 6.02411i 0.313865 0.454084i
\(177\) −0.119551 + 0.0122070i −0.00898598 + 0.000917531i
\(178\) 2.91762 1.13970i 0.218685 0.0854239i
\(179\) 0.147551 + 0.0851888i 0.0110285 + 0.00636731i 0.505504 0.862824i \(-0.331307\pi\)
−0.494476 + 0.869192i \(0.664640\pi\)
\(180\) −16.0314 + 7.24989i −1.19491 + 0.540375i
\(181\) 15.4196i 1.14613i −0.819511 0.573064i \(-0.805755\pi\)
0.819511 0.573064i \(-0.194245\pi\)
\(182\) −2.09550 0.249437i −0.155329 0.0184895i
\(183\) −13.8064 + 9.96854i −1.02060 + 0.736896i
\(184\) −5.95460 + 12.2145i −0.438979 + 0.900468i
\(185\) 18.4863 10.6731i 1.35914 0.784698i
\(186\) −1.60049 0.0792013i −0.117354 0.00580732i
\(187\) 0.349816 0.605900i 0.0255811 0.0443078i
\(188\) −11.7302 + 10.8144i −0.855510 + 0.788718i
\(189\) −8.95301 + 10.4328i −0.651236 + 0.758875i
\(190\) 33.5454 13.1037i 2.43364 0.950642i
\(191\) 12.5300 + 7.23418i 0.906637 + 0.523447i 0.879348 0.476180i \(-0.157979\pi\)
0.0272895 + 0.999628i \(0.491312\pi\)
\(192\) −13.4535 + 3.31731i −0.970919 + 0.239406i
\(193\) −9.93613 17.2099i −0.715218 1.23879i −0.962875 0.269946i \(-0.912994\pi\)
0.247657 0.968848i \(-0.420339\pi\)
\(194\) 2.42069 0.945582i 0.173795 0.0678889i
\(195\) −1.67689 2.32250i −0.120085 0.166317i
\(196\) 9.65051 10.1424i 0.689322 0.724455i
\(197\) −18.7081 −1.33289 −0.666447 0.745553i \(-0.732186\pi\)
−0.666447 + 0.745553i \(0.732186\pi\)
\(198\) 6.51444 4.23006i 0.462961 0.300617i
\(199\) −1.44143 + 2.49663i −0.102180 + 0.176981i −0.912583 0.408892i \(-0.865915\pi\)
0.810402 + 0.585874i \(0.199249\pi\)
\(200\) 9.15024 + 4.46075i 0.647020 + 0.315423i
\(201\) −0.319279 3.12691i −0.0225202 0.220555i
\(202\) −0.964104 + 6.32770i −0.0678341 + 0.445216i
\(203\) 8.50577 + 4.54645i 0.596988 + 0.319099i
\(204\) −1.25537 + 0.420136i −0.0878936 + 0.0294154i
\(205\) −15.1379 + 26.2196i −1.05728 + 1.83126i
\(206\) 19.6493 + 2.99382i 1.36903 + 0.208589i
\(207\) −10.7679 + 9.58047i −0.748423 + 0.665889i
\(208\) −0.965813 2.03881i −0.0669671 0.141366i
\(209\) −13.7688 + 7.94941i −0.952406 + 0.549872i
\(210\) 19.0016 + 0.317785i 1.31123 + 0.0219292i
\(211\) 16.7550 + 9.67350i 1.15346 + 0.665951i 0.949728 0.313075i \(-0.101359\pi\)
0.203733 + 0.979026i \(0.434693\pi\)
\(212\) −10.7368 + 9.89858i −0.737409 + 0.679837i
\(213\) −15.2343 6.83695i −1.04384 0.468460i
\(214\) −11.8370 + 4.62384i −0.809161 + 0.316079i
\(215\) −9.43757 16.3464i −0.643637 1.11481i
\(216\) −14.5355 2.17210i −0.989018 0.147792i
\(217\) 1.52647 + 0.815918i 0.103623 + 0.0553881i
\(218\) −2.64626 + 3.30744i −0.179227 + 0.224008i
\(219\) 21.3062 15.3836i 1.43974 1.03952i
\(220\) −10.2500 3.19766i −0.691054 0.215586i
\(221\) −0.107766 0.186657i −0.00724916 0.0125559i
\(222\) 17.8089 + 0.881286i 1.19526 + 0.0591480i
\(223\) 9.86207 + 17.0816i 0.660413 + 1.14387i 0.980507 + 0.196483i \(0.0629520\pi\)
−0.320095 + 0.947386i \(0.603715\pi\)
\(224\) 14.6693 + 2.96866i 0.980131 + 0.198352i
\(225\) 7.17699 + 8.06655i 0.478466 + 0.537770i
\(226\) 7.16225 8.95176i 0.476426 0.595462i
\(227\) 1.29766 0.0861285 0.0430643 0.999072i \(-0.486288\pi\)
0.0430643 + 0.999072i \(0.486288\pi\)
\(228\) 29.4794 + 5.99557i 1.95232 + 0.397066i
\(229\) 13.0374i 0.861538i −0.902462 0.430769i \(-0.858242\pi\)
0.902462 0.430769i \(-0.141758\pi\)
\(230\) 19.6965 + 3.00101i 1.29875 + 0.197881i
\(231\) −8.31392 + 1.12482i −0.547016 + 0.0740077i
\(232\) 0.721147 + 10.2853i 0.0473456 + 0.675261i
\(233\) −8.17297 14.1560i −0.535429 0.927390i −0.999142 0.0414048i \(-0.986817\pi\)
0.463714 0.885985i \(-0.346517\pi\)
\(234\) −0.125111 2.38957i −0.00817873 0.156211i
\(235\) 20.2586 + 11.6963i 1.32153 + 0.762984i
\(236\) 0.0304446 + 0.135382i 0.00198178 + 0.00881262i
\(237\) −8.87321 + 6.40665i −0.576377 + 0.416157i
\(238\) 1.41985 + 0.169011i 0.0920354 + 0.0109554i
\(239\) −7.08294 4.08934i −0.458157 0.264517i 0.253112 0.967437i \(-0.418546\pi\)
−0.711269 + 0.702920i \(0.751879\pi\)
\(240\) 10.5177 + 17.3820i 0.678912 + 1.12200i
\(241\) 8.43974i 0.543652i 0.962346 + 0.271826i \(0.0876275\pi\)
−0.962346 + 0.271826i \(0.912373\pi\)
\(242\) −10.6929 1.62919i −0.687364 0.104728i
\(243\) −13.3830 7.99353i −0.858517 0.512785i
\(244\) 13.3284 + 14.4571i 0.853262 + 0.925520i
\(245\) −18.4100 9.07890i −1.17617 0.580029i
\(246\) −22.4998 + 11.5470i −1.43454 + 0.736208i
\(247\) 4.89788i 0.311645i
\(248\) 0.129419 + 1.84582i 0.00821811 + 0.117210i
\(249\) 9.99515 1.02057i 0.633417 0.0646763i
\(250\) −0.875100 + 5.74354i −0.0553462 + 0.363253i
\(251\) −13.3180 −0.840622 −0.420311 0.907380i \(-0.638079\pi\)
−0.420311 + 0.907380i \(0.638079\pi\)
\(252\) 13.1928 + 8.82888i 0.831070 + 0.556167i
\(253\) −8.79564 −0.552977
\(254\) −1.21001 + 7.94165i −0.0759227 + 0.498303i
\(255\) 1.13622 + 1.57366i 0.0711527 + 0.0985464i
\(256\) 5.65435 + 14.9676i 0.353397 + 0.935474i
\(257\) 2.32005i 0.144721i −0.997379 0.0723604i \(-0.976947\pi\)
0.997379 0.0723604i \(-0.0230532\pi\)
\(258\) 0.779271 15.7474i 0.0485153 0.980392i
\(259\) −16.9852 9.07885i −1.05541 0.564132i
\(260\) −2.43195 + 2.24208i −0.150823 + 0.139048i
\(261\) −3.44102 + 10.3805i −0.212994 + 0.642536i
\(262\) −10.8534 1.65365i −0.670527 0.102163i
\(263\) 28.4330i 1.75325i −0.481173 0.876626i \(-0.659789\pi\)
0.481173 0.876626i \(-0.340211\pi\)
\(264\) −5.74601 6.88659i −0.353642 0.423841i
\(265\) 18.5431 + 10.7059i 1.13909 + 0.657656i
\(266\) −26.0224 19.4589i −1.59553 1.19310i
\(267\) −0.389686 3.81645i −0.0238484 0.233563i
\(268\) −3.54099 + 0.796295i −0.216300 + 0.0486415i
\(269\) 13.5982 + 7.85090i 0.829094 + 0.478678i 0.853542 0.521023i \(-0.174450\pi\)
−0.0244481 + 0.999701i \(0.507783\pi\)
\(270\) 3.30676 + 21.2935i 0.201243 + 1.29588i
\(271\) 0.243398 + 0.421578i 0.0147854 + 0.0256091i 0.873323 0.487141i \(-0.161960\pi\)
−0.858538 + 0.512750i \(0.828627\pi\)
\(272\) 0.654409 + 1.38144i 0.0396794 + 0.0837621i
\(273\) −0.980524 + 2.39135i −0.0593440 + 0.144731i
\(274\) −26.4084 4.02364i −1.59539 0.243077i
\(275\) 6.58905i 0.397335i
\(276\) 12.4654 + 11.0269i 0.750327 + 0.663742i
\(277\) −7.44227 −0.447163 −0.223581 0.974685i \(-0.571775\pi\)
−0.223581 + 0.974685i \(0.571775\pi\)
\(278\) −6.31347 + 7.89090i −0.378657 + 0.473265i
\(279\) −0.617534 + 1.86291i −0.0369708 + 0.111529i
\(280\) −2.25020 21.8285i −0.134475 1.30450i
\(281\) 13.2312 + 22.9172i 0.789310 + 1.36712i 0.926390 + 0.376565i \(0.122895\pi\)
−0.137081 + 0.990560i \(0.543772\pi\)
\(282\) 8.92179 + 17.3845i 0.531285 + 1.03523i
\(283\) 14.7005 + 25.4621i 0.873857 + 1.51356i 0.857976 + 0.513690i \(0.171722\pi\)
0.0158807 + 0.999874i \(0.494945\pi\)
\(284\) −5.74221 + 18.4065i −0.340737 + 1.09222i
\(285\) −4.48042 43.8797i −0.265397 2.59921i
\(286\) 0.912280 1.14022i 0.0539443 0.0674224i
\(287\) 27.3015 0.893697i 1.61156 0.0527533i
\(288\) −0.490220 + 16.9635i −0.0288865 + 0.999583i
\(289\) −8.42698 14.5960i −0.495705 0.858586i
\(290\) 14.0812 5.50047i 0.826874 0.322998i
\(291\) −0.323314 3.16642i −0.0189530 0.185619i
\(292\) −20.5685 22.3103i −1.20368 1.30561i
\(293\) −13.7086 7.91467i −0.800866 0.462380i 0.0429080 0.999079i \(-0.486338\pi\)
−0.843774 + 0.536699i \(0.819671\pi\)
\(294\) −8.80970 14.7102i −0.513792 0.857915i
\(295\) 0.176197 0.101728i 0.0102586 0.00592281i
\(296\) −1.44006 20.5387i −0.0837021 1.19379i
\(297\) −2.85907 9.07319i −0.165900 0.526480i
\(298\) −13.7229 2.09086i −0.794948 0.121120i
\(299\) −1.35482 + 2.34661i −0.0783512 + 0.135708i
\(300\) 8.26056 9.33815i 0.476924 0.539138i
\(301\) −8.02791 + 15.0191i −0.462721 + 0.865686i
\(302\) −0.799365 + 5.24647i −0.0459983 + 0.301901i
\(303\) 7.15203 + 3.20974i 0.410873 + 0.184395i
\(304\) 2.81751 34.6223i 0.161595 1.98573i
\(305\) 14.4154 24.9682i 0.825422 1.42967i
\(306\) 0.0847715 + 1.61911i 0.00484606 + 0.0925584i
\(307\) −2.28683 −0.130517 −0.0652583 0.997868i \(-0.520787\pi\)
−0.0652583 + 0.997868i \(0.520787\pi\)
\(308\) 2.43354 + 9.37692i 0.138664 + 0.534300i
\(309\) 9.96714 22.2091i 0.567011 1.26343i
\(310\) 2.52704 0.987127i 0.143526 0.0560651i
\(311\) −2.80086 4.85124i −0.158822 0.275088i 0.775622 0.631198i \(-0.217436\pi\)
−0.934444 + 0.356109i \(0.884103\pi\)
\(312\) −2.72237 + 0.472231i −0.154124 + 0.0267348i
\(313\) −7.63490 4.40801i −0.431550 0.249155i 0.268457 0.963292i \(-0.413486\pi\)
−0.700007 + 0.714136i \(0.746820\pi\)
\(314\) −8.62755 + 3.37015i −0.486881 + 0.190188i
\(315\) 6.59689 22.3209i 0.371693 1.25764i
\(316\) 8.56597 + 9.29137i 0.481873 + 0.522681i
\(317\) 1.60324 2.77689i 0.0900468 0.155966i −0.817484 0.575952i \(-0.804632\pi\)
0.907531 + 0.419986i \(0.137965\pi\)
\(318\) 8.16628 + 15.9124i 0.457942 + 0.892323i
\(319\) −5.77965 + 3.33688i −0.323598 + 0.186829i
\(320\) 18.4808 14.4499i 1.03311 0.807774i
\(321\) 1.58099 + 15.4836i 0.0882420 + 0.864211i
\(322\) −7.08495 16.5210i −0.394829 0.920682i
\(323\) 3.31867i 0.184656i
\(324\) −7.32293 + 16.4431i −0.406829 + 0.913504i
\(325\) 1.75791 + 1.01493i 0.0975114 + 0.0562983i
\(326\) −16.9197 + 6.60927i −0.937095 + 0.366054i
\(327\) 3.03682 + 4.20600i 0.167937 + 0.232592i
\(328\) 16.3342 + 24.2066i 0.901904 + 1.33659i
\(329\) −0.690517 21.0946i −0.0380694 1.16298i
\(330\) −7.13000 + 11.0496i −0.392493 + 0.608261i
\(331\) −13.4838 7.78490i −0.741139 0.427897i 0.0813440 0.996686i \(-0.474079\pi\)
−0.822483 + 0.568789i \(0.807412\pi\)
\(332\) −2.54535 11.3187i −0.139694 0.621197i
\(333\) 6.87140 20.7289i 0.376551 1.13594i
\(334\) −3.12596 + 3.90699i −0.171045 + 0.213781i
\(335\) 2.66074 + 4.60853i 0.145372 + 0.251791i
\(336\) 8.30679 16.3400i 0.453173 0.891423i
\(337\) −1.89825 + 3.28787i −0.103404 + 0.179102i −0.913085 0.407769i \(-0.866307\pi\)
0.809681 + 0.586871i \(0.199640\pi\)
\(338\) 6.52564 + 16.7056i 0.354948 + 0.908665i
\(339\) −8.21933 11.3838i −0.446413 0.618282i
\(340\) 1.64782 1.51917i 0.0893656 0.0823886i
\(341\) −1.03723 + 0.598845i −0.0561691 + 0.0324293i
\(342\) 16.7285 32.8273i 0.904571 1.77510i
\(343\) 1.81518 + 18.4311i 0.0980104 + 0.995185i
\(344\) −18.1612 + 1.27337i −0.979188 + 0.0686554i
\(345\) 9.99108 22.2624i 0.537902 1.19857i
\(346\) −10.9957 8.79758i −0.591131 0.472961i
\(347\) 14.3510 8.28557i 0.770404 0.444793i −0.0626149 0.998038i \(-0.519944\pi\)
0.833019 + 0.553245i \(0.186611\pi\)
\(348\) 12.3744 + 2.51673i 0.663338 + 0.134911i
\(349\) 22.4588 12.9666i 1.20219 0.694087i 0.241152 0.970487i \(-0.422475\pi\)
0.961043 + 0.276400i \(0.0891415\pi\)
\(350\) −12.3764 + 5.30753i −0.661544 + 0.283699i
\(351\) −2.86105 0.634789i −0.152712 0.0338825i
\(352\) −7.10467 + 7.53521i −0.378680 + 0.401628i
\(353\) 0.213594i 0.0113685i 0.999984 + 0.00568424i \(0.00180936\pi\)
−0.999984 + 0.00568424i \(0.998191\pi\)
\(354\) 0.169742 + 0.00839976i 0.00902166 + 0.000446442i
\(355\) 28.2705 1.50044
\(356\) −4.32183 + 0.971891i −0.229057 + 0.0515101i
\(357\) 0.664377 1.62032i 0.0351625 0.0857563i
\(358\) −0.188142 0.150531i −0.00994361 0.00795583i
\(359\) −23.6659 + 13.6635i −1.24904 + 0.721133i −0.970918 0.239413i \(-0.923045\pi\)
−0.278121 + 0.960546i \(0.589712\pi\)
\(360\) 23.9575 6.72101i 1.26267 0.354228i
\(361\) −28.2076 + 48.8570i −1.48461 + 2.57142i
\(362\) −3.28460 + 21.5578i −0.172635 + 1.13305i
\(363\) −5.42397 + 12.0859i −0.284685 + 0.634343i
\(364\) 2.87654 + 0.795104i 0.150772 + 0.0416748i
\(365\) −22.2460 + 38.5311i −1.16441 + 2.01681i
\(366\) 21.4259 10.9958i 1.11995 0.574762i
\(367\) −28.1444 −1.46912 −0.734562 0.678542i \(-0.762612\pi\)
−0.734562 + 0.678542i \(0.762612\pi\)
\(368\) 10.9269 15.8085i 0.569603 0.824074i
\(369\) 6.25997 + 30.3344i 0.325881 + 1.57915i
\(370\) −28.1188 + 10.9839i −1.46183 + 0.571027i
\(371\) −0.632043 19.3082i −0.0328140 1.00243i
\(372\) 2.22074 + 0.451658i 0.115140 + 0.0234174i
\(373\) 6.82494 0.353382 0.176691 0.984266i \(-0.443461\pi\)
0.176691 + 0.984266i \(0.443461\pi\)
\(374\) −0.618136 + 0.772579i −0.0319631 + 0.0399491i
\(375\) 6.49177 + 2.91342i 0.335234 + 0.150448i
\(376\) 18.7033 12.6206i 0.964550 0.650859i
\(377\) 2.05596i 0.105887i
\(378\) 14.7394 12.6788i 0.758111 0.652126i
\(379\) 24.6134i 1.26431i −0.774843 0.632153i \(-0.782171\pi\)
0.774843 0.632153i \(-0.217829\pi\)
\(380\) −49.6904 + 11.1743i −2.54906 + 0.573231i
\(381\) 8.97623 + 4.02841i 0.459866 + 0.206382i
\(382\) −15.9769 12.7830i −0.817450 0.654037i
\(383\) 31.1134 1.58982 0.794911 0.606726i \(-0.207518\pi\)
0.794911 + 0.606726i \(0.207518\pi\)
\(384\) 19.5156 1.77208i 0.995903 0.0904311i
\(385\) 12.0621 7.50063i 0.614739 0.382267i
\(386\) 10.2255 + 26.1773i 0.520466 + 1.33239i
\(387\) −18.3294 6.07599i −0.931734 0.308860i
\(388\) −3.58573 + 0.806357i −0.182038 + 0.0409366i
\(389\) −14.3844 −0.729317 −0.364658 0.931141i \(-0.618814\pi\)
−0.364658 + 0.931141i \(0.618814\pi\)
\(390\) 1.84970 + 3.60424i 0.0936633 + 0.182508i
\(391\) 0.917988 1.59000i 0.0464247 0.0804099i
\(392\) −15.6526 + 12.1241i −0.790578 + 0.612361i
\(393\) −5.50542 + 12.2673i −0.277712 + 0.618805i
\(394\) 26.1553 + 3.98509i 1.31769 + 0.200766i
\(395\) 9.26457 16.0467i 0.466151 0.807397i
\(396\) −10.0088 + 4.52628i −0.502959 + 0.227454i
\(397\) 3.00720 1.73621i 0.150927 0.0871377i −0.422635 0.906300i \(-0.638895\pi\)
0.573562 + 0.819162i \(0.305561\pi\)
\(398\) 2.54705 3.18344i 0.127672 0.159571i
\(399\) −31.4854 + 24.3390i −1.57624 + 1.21848i
\(400\) −11.8426 8.18562i −0.592128 0.409281i
\(401\) 33.9836 1.69706 0.848530 0.529147i \(-0.177488\pi\)
0.848530 + 0.529147i \(0.177488\pi\)
\(402\) −0.219700 + 4.43968i −0.0109576 + 0.221431i
\(403\) 0.368967i 0.0183796i
\(404\) 2.69579 8.64126i 0.134120 0.429919i
\(405\) 26.2126 + 3.06982i 1.30251 + 0.152541i
\(406\) −10.9233 8.16816i −0.542113 0.405379i
\(407\) 11.5414 6.66344i 0.572087 0.330295i
\(408\) 1.84460 0.319971i 0.0913215 0.0158409i
\(409\) 12.3756 7.14508i 0.611936 0.353301i −0.161787 0.986826i \(-0.551726\pi\)
0.773723 + 0.633524i \(0.218392\pi\)
\(410\) 26.7491 33.4325i 1.32105 1.65111i
\(411\) −13.3957 + 29.8487i −0.660760 + 1.47233i
\(412\) −26.8336 8.37118i −1.32199 0.412419i
\(413\) −0.161891 0.0865328i −0.00796612 0.00425800i
\(414\) 17.0952 11.1005i 0.840183 0.545561i
\(415\) −14.7311 + 8.50503i −0.723124 + 0.417496i
\(416\) 0.915987 + 3.05615i 0.0449100 + 0.149840i
\(417\) 7.24527 + 10.0347i 0.354803 + 0.491402i
\(418\) 20.9432 8.18095i 1.02436 0.400143i
\(419\) 3.26093 5.64810i 0.159307 0.275928i −0.775312 0.631579i \(-0.782407\pi\)
0.934619 + 0.355651i \(0.115741\pi\)
\(420\) −26.4980 4.49190i −1.29297 0.219182i
\(421\) −3.51243 6.08371i −0.171185 0.296502i 0.767649 0.640870i \(-0.221426\pi\)
−0.938835 + 0.344369i \(0.888093\pi\)
\(422\) −21.3642 17.0934i −1.03999 0.832093i
\(423\) 23.4379 4.83678i 1.13959 0.235172i
\(424\) 17.1195 11.5519i 0.831396 0.561010i
\(425\) −1.19111 0.687690i −0.0577775 0.0333579i
\(426\) 19.8424 + 12.8037i 0.961367 + 0.620343i
\(427\) −25.9984 + 0.851042i −1.25815 + 0.0411848i
\(428\) 17.5340 3.94304i 0.847539 0.190594i
\(429\) −1.04692 1.44999i −0.0505460 0.0700062i
\(430\) 9.71246 + 24.8638i 0.468376 + 1.19904i
\(431\) −16.8002 9.69959i −0.809236 0.467213i 0.0374543 0.999298i \(-0.488075\pi\)
−0.846691 + 0.532086i \(0.821408\pi\)
\(432\) 19.8591 + 6.13305i 0.955474 + 0.295076i
\(433\) 20.5238i 0.986309i −0.869942 0.493154i \(-0.835844\pi\)
0.869942 0.493154i \(-0.164156\pi\)
\(434\) −1.96032 1.46588i −0.0940983 0.0703644i
\(435\) −1.88072 18.4191i −0.0901737 0.883129i
\(436\) 4.40422 4.06037i 0.210924 0.194456i
\(437\) −36.1320 + 20.8608i −1.72843 + 0.997909i
\(438\) −33.0647 + 16.9689i −1.57989 + 0.810805i
\(439\) 3.49698 6.05694i 0.166902 0.289082i −0.770427 0.637528i \(-0.779957\pi\)
0.937329 + 0.348446i \(0.113290\pi\)
\(440\) 13.6491 + 6.65397i 0.650697 + 0.317216i
\(441\) −20.2450 + 5.58019i −0.964049 + 0.265723i
\(442\) 0.110905 + 0.283917i 0.00527523 + 0.0135046i
\(443\) −2.80179 1.61762i −0.133117 0.0768552i 0.431963 0.901892i \(-0.357821\pi\)
−0.565080 + 0.825036i \(0.691155\pi\)
\(444\) −24.7106 5.02567i −1.17271 0.238508i
\(445\) 3.24748 + 5.62479i 0.153945 + 0.266641i
\(446\) −10.1493 25.9822i −0.480584 1.23029i
\(447\) −6.96098 + 15.5107i −0.329243 + 0.733629i
\(448\) −19.8764 7.27519i −0.939072 0.343721i
\(449\) 15.0764 0.711500 0.355750 0.934581i \(-0.384225\pi\)
0.355750 + 0.934581i \(0.384225\pi\)
\(450\) −8.31570 12.8065i −0.392006 0.603703i
\(451\) −9.45095 + 16.3695i −0.445028 + 0.770811i
\(452\) −11.9202 + 10.9896i −0.560681 + 0.516907i
\(453\) 5.92995 + 2.66128i 0.278613 + 0.125038i
\(454\) −1.81423 0.276420i −0.0851459 0.0129730i
\(455\) −0.143161 4.37341i −0.00671148 0.205029i
\(456\) −39.9374 14.6618i −1.87024 0.686603i
\(457\) −13.4530 + 23.3013i −0.629304 + 1.08999i 0.358387 + 0.933573i \(0.383327\pi\)
−0.987692 + 0.156414i \(0.950007\pi\)
\(458\) −2.77717 + 18.2274i −0.129768 + 0.851709i
\(459\) 1.93857 + 0.430116i 0.0904848 + 0.0200761i
\(460\) −26.8980 8.39129i −1.25413 0.391246i
\(461\) 13.3994 7.73613i 0.624071 0.360307i −0.154381 0.988011i \(-0.549338\pi\)
0.778452 + 0.627704i \(0.216005\pi\)
\(462\) 11.8631 + 0.198401i 0.551923 + 0.00923044i
\(463\) −5.18126 2.99140i −0.240793 0.139022i 0.374748 0.927127i \(-0.377729\pi\)
−0.615541 + 0.788105i \(0.711063\pi\)
\(464\) 1.18269 14.5332i 0.0549051 0.674688i
\(465\) −0.337519 3.30554i −0.0156521 0.153291i
\(466\) 8.41102 + 21.5322i 0.389633 + 0.997458i
\(467\) −16.0086 27.7278i −0.740791 1.28309i −0.952136 0.305676i \(-0.901118\pi\)
0.211345 0.977412i \(-0.432216\pi\)
\(468\) −0.334100 + 3.36746i −0.0154438 + 0.155661i
\(469\) 2.26331 4.23434i 0.104510 0.195523i
\(470\) −25.8317 20.6678i −1.19153 0.953333i
\(471\) 1.15232 + 11.2854i 0.0530962 + 0.520005i
\(472\) −0.0137256 0.195760i −0.000631773 0.00901058i
\(473\) −5.89210 10.2054i −0.270919 0.469246i
\(474\) 13.7702 7.06688i 0.632485 0.324592i
\(475\) 15.6274 + 27.0675i 0.717035 + 1.24194i
\(476\) −1.94907 0.538741i −0.0893353 0.0246932i
\(477\) 21.4532 4.42719i 0.982273 0.202707i
\(478\) 9.03142 + 7.22599i 0.413088 + 0.330509i
\(479\) 23.8764 1.09094 0.545470 0.838130i \(-0.316351\pi\)
0.545470 + 0.838130i \(0.316351\pi\)
\(480\) −11.0019 26.5418i −0.502166 1.21146i
\(481\) 4.10556i 0.187197i
\(482\) 1.79779 11.7994i 0.0818871 0.537449i
\(483\) −21.8174 + 2.95175i −0.992727 + 0.134309i
\(484\) 14.6024 + 4.55548i 0.663747 + 0.207067i
\(485\) 2.69436 + 4.66677i 0.122345 + 0.211907i
\(486\) 17.0077 + 14.0264i 0.771484 + 0.636248i
\(487\) −3.70986 2.14189i −0.168110 0.0970582i 0.413585 0.910466i \(-0.364277\pi\)
−0.581694 + 0.813408i \(0.697610\pi\)
\(488\) −15.5546 23.0513i −0.704122 1.04348i
\(489\) 2.25984 + 22.1321i 0.102194 + 1.00085i
\(490\) 23.8047 + 16.6146i 1.07538 + 0.750572i
\(491\) −6.60375 3.81268i −0.298023 0.172064i 0.343531 0.939141i \(-0.388377\pi\)
−0.641555 + 0.767077i \(0.721710\pi\)
\(492\) 33.9162 11.3508i 1.52906 0.511732i
\(493\) 1.39306i 0.0627403i
\(494\) 1.04332 6.84763i 0.0469412 0.308089i
\(495\) 10.7057 + 12.0326i 0.481185 + 0.540826i
\(496\) 0.212249 2.60817i 0.00953025 0.117110i
\(497\) −13.4693 21.6605i −0.604180 0.971606i
\(498\) −14.1914 0.702270i −0.635932 0.0314695i
\(499\) 20.8317i 0.932556i −0.884638 0.466278i \(-0.845595\pi\)
0.884638 0.466278i \(-0.154405\pi\)
\(500\) 2.44692 7.84352i 0.109429 0.350773i
\(501\) 3.58732 + 4.96844i 0.160270 + 0.221973i
\(502\) 18.6195 + 2.83692i 0.831031 + 0.126618i
\(503\) 13.9678 0.622792 0.311396 0.950280i \(-0.399204\pi\)
0.311396 + 0.950280i \(0.399204\pi\)
\(504\) −16.5639 15.1537i −0.737817 0.675001i
\(505\) −13.2721 −0.590600
\(506\) 12.2970 + 1.87360i 0.546668 + 0.0832917i
\(507\) 21.8521 2.23125i 0.970485 0.0990933i
\(508\) 3.38338 10.8453i 0.150113 0.481182i
\(509\) 27.5762i 1.22229i 0.791518 + 0.611146i \(0.209291\pi\)
−0.791518 + 0.611146i \(0.790709\pi\)
\(510\) −1.25331 2.44213i −0.0554974 0.108139i
\(511\) 40.1210 1.31334i 1.77485 0.0580986i
\(512\) −4.71691 22.1303i −0.208460 0.978031i
\(513\) −33.2640 30.4912i −1.46864 1.34622i
\(514\) −0.494205 + 3.24361i −0.0217984 + 0.143070i
\(515\) 41.2136i 1.81609i
\(516\) −4.44392 + 21.8502i −0.195633 + 0.961899i
\(517\) 12.6479 + 7.30229i 0.556256 + 0.321154i
\(518\) 21.8128 + 16.3111i 0.958399 + 0.716667i
\(519\) −13.9830 + 10.0960i −0.613785 + 0.443166i
\(520\) 3.87765 2.61656i 0.170046 0.114744i
\(521\) 25.2177 + 14.5594i 1.10481 + 0.637860i 0.937479 0.348041i \(-0.113153\pi\)
0.167327 + 0.985901i \(0.446486\pi\)
\(522\) 7.02201 13.7797i 0.307345 0.603123i
\(523\) 2.77500 + 4.80644i 0.121342 + 0.210171i 0.920297 0.391220i \(-0.127947\pi\)
−0.798955 + 0.601391i \(0.794613\pi\)
\(524\) 14.8217 + 4.62388i 0.647489 + 0.201995i
\(525\) 2.21124 + 16.3440i 0.0965064 + 0.713311i
\(526\) −6.05664 + 39.7515i −0.264082 + 1.73325i
\(527\) 0.250002i 0.0108903i
\(528\) 6.56643 + 10.8520i 0.285767 + 0.472272i
\(529\) −0.0815338 −0.00354495
\(530\) −23.6442 18.9176i −1.02704 0.821727i
\(531\) 0.0654931 0.197572i 0.00284216 0.00857390i
\(532\) 32.2363 + 32.7482i 1.39762 + 1.41982i
\(533\) 2.91151 + 5.04289i 0.126112 + 0.218432i
\(534\) −0.268148 + 5.41870i −0.0116039 + 0.234490i
\(535\) −13.1753 22.8202i −0.569616 0.986604i
\(536\) 5.12020 0.359001i 0.221159 0.0155065i
\(537\) −0.239256 + 0.172748i −0.0103247 + 0.00745464i
\(538\) −17.3389 13.8728i −0.747535 0.598098i
\(539\) −11.4938 5.66817i −0.495072 0.244145i
\(540\) −0.0872729 30.4744i −0.00375563 1.31141i
\(541\) 15.4643 + 26.7849i 0.664862 + 1.15157i 0.979323 + 0.202304i \(0.0648430\pi\)
−0.314461 + 0.949270i \(0.601824\pi\)
\(542\) −0.250488 0.641247i −0.0107594 0.0275439i
\(543\) 24.3662 + 10.9352i 1.04565 + 0.469275i
\(544\) −0.620648 2.07076i −0.0266101 0.0887832i
\(545\) −7.60632 4.39151i −0.325819 0.188112i
\(546\) 1.88024 3.13444i 0.0804670 0.134142i
\(547\) −8.81420 + 5.08888i −0.376868 + 0.217585i −0.676455 0.736484i \(-0.736485\pi\)
0.299587 + 0.954069i \(0.403151\pi\)
\(548\) 36.0639 + 11.2507i 1.54057 + 0.480608i
\(549\) −5.96119 28.8866i −0.254417 1.23285i
\(550\) 1.40357 9.21202i 0.0598482 0.392802i
\(551\) −15.8283 + 27.4155i −0.674309 + 1.16794i
\(552\) −15.0787 18.0718i −0.641791 0.769187i
\(553\) −16.7088 + 0.546953i −0.710532 + 0.0232588i
\(554\) 10.4049 + 1.58531i 0.442061 + 0.0673535i
\(555\) 3.75563 + 36.7813i 0.159417 + 1.56128i
\(556\) 10.5076 9.68725i 0.445622 0.410831i
\(557\) −8.10369 + 14.0360i −0.343364 + 0.594724i −0.985055 0.172239i \(-0.944900\pi\)
0.641691 + 0.766963i \(0.278233\pi\)
\(558\) 1.26019 2.47295i 0.0533480 0.104688i
\(559\) −3.63031 −0.153546
\(560\) −1.50383 + 30.9973i −0.0635484 + 1.30987i
\(561\) 0.709367 + 0.982474i 0.0299495 + 0.0414801i
\(562\) −13.6166 34.8585i −0.574383 1.47042i
\(563\) −3.59953 6.23456i −0.151702 0.262756i 0.780151 0.625591i \(-0.215142\pi\)
−0.931853 + 0.362835i \(0.881809\pi\)
\(564\) −8.77020 26.2054i −0.369292 1.10345i
\(565\) 20.5869 + 11.8859i 0.866098 + 0.500042i
\(566\) −15.1287 38.7294i −0.635908 1.62792i
\(567\) −10.1368 21.5464i −0.425704 0.904862i
\(568\) 11.9489 24.5105i 0.501365 1.02844i
\(569\) 3.83664 6.64525i 0.160840 0.278583i −0.774330 0.632782i \(-0.781913\pi\)
0.935170 + 0.354199i \(0.115246\pi\)
\(570\) −3.08303 + 62.3016i −0.129134 + 2.60953i
\(571\) −31.4736 + 18.1713i −1.31713 + 0.760446i −0.983266 0.182175i \(-0.941686\pi\)
−0.333865 + 0.942621i \(0.608353\pi\)
\(572\) −1.51832 + 1.39978i −0.0634842 + 0.0585279i
\(573\) −20.3175 + 14.6697i −0.848776 + 0.612835i
\(574\) −38.3600 4.56616i −1.60112 0.190588i
\(575\) 17.2910i 0.721085i
\(576\) 4.29884 23.6119i 0.179118 0.983828i
\(577\) 33.2642 + 19.2051i 1.38481 + 0.799520i 0.992724 0.120410i \(-0.0384208\pi\)
0.392084 + 0.919929i \(0.371754\pi\)
\(578\) 8.67243 + 22.2014i 0.360726 + 0.923455i
\(579\) 34.2417 3.49632i 1.42304 0.145302i
\(580\) −20.8583 + 4.69059i −0.866092 + 0.194766i
\(581\) 13.5350 + 7.23466i 0.561527 + 0.300144i
\(582\) −0.222476 + 4.49578i −0.00922194 + 0.186356i
\(583\) 11.5769 + 6.68392i 0.479466 + 0.276820i
\(584\) 24.0040 + 35.5730i 0.993291 + 1.47202i
\(585\) 4.85925 1.00278i 0.200905 0.0414599i
\(586\) 17.4798 + 13.9855i 0.722083 + 0.577735i
\(587\) −1.74472 3.02195i −0.0720124 0.124729i 0.827771 0.561066i \(-0.189609\pi\)
−0.899783 + 0.436337i \(0.856275\pi\)
\(588\) 9.18317 + 22.4426i 0.378707 + 0.925516i
\(589\) −2.84059 + 4.92005i −0.117044 + 0.202727i
\(590\) −0.268007 + 0.104691i −0.0110337 + 0.00431004i
\(591\) 13.2673 29.5627i 0.545745 1.21605i
\(592\) −2.36173 + 29.0215i −0.0970664 + 1.19278i
\(593\) −8.09945 + 4.67622i −0.332604 + 0.192029i −0.656997 0.753893i \(-0.728174\pi\)
0.324392 + 0.945923i \(0.394840\pi\)
\(594\) 2.06449 + 13.2941i 0.0847069 + 0.545462i
\(595\) 0.0970019 + 2.96331i 0.00397669 + 0.121484i
\(596\) 18.7404 + 5.84637i 0.767635 + 0.239477i
\(597\) −2.92297 4.04832i −0.119629 0.165687i
\(598\) 2.39401 2.99216i 0.0978982 0.122358i
\(599\) −6.05522 + 3.49598i −0.247410 + 0.142842i −0.618578 0.785724i \(-0.712291\pi\)
0.371168 + 0.928566i \(0.378957\pi\)
\(600\) −13.5381 + 11.2958i −0.552690 + 0.461151i
\(601\) −5.17769 + 2.98934i −0.211202 + 0.121938i −0.601870 0.798594i \(-0.705577\pi\)
0.390668 + 0.920532i \(0.372244\pi\)
\(602\) 14.4229 19.2878i 0.587835 0.786112i
\(603\) 5.16760 + 1.71301i 0.210441 + 0.0697590i
\(604\) 2.23515 7.16471i 0.0909470 0.291528i
\(605\) 22.4279i 0.911822i
\(606\) −9.31538 6.01095i −0.378412 0.244178i
\(607\) 26.2317 1.06471 0.532356 0.846521i \(-0.321307\pi\)
0.532356 + 0.846521i \(0.321307\pi\)
\(608\) −11.3142 + 47.8046i −0.458850 + 1.93873i
\(609\) −13.2165 + 10.2167i −0.535558 + 0.414000i
\(610\) −25.4724 + 31.8368i −1.03135 + 1.28903i
\(611\) 3.89640 2.24959i 0.157631 0.0910086i
\(612\) 0.226377 2.28170i 0.00915075 0.0922324i
\(613\) −0.414372 + 0.717713i −0.0167363 + 0.0289882i −0.874272 0.485436i \(-0.838661\pi\)
0.857536 + 0.514424i \(0.171994\pi\)
\(614\) 3.19717 + 0.487129i 0.129027 + 0.0196589i
\(615\) −30.6970 42.5154i −1.23782 1.71439i
\(616\) −1.40486 13.6281i −0.0566032 0.549090i
\(617\) 3.69129 6.39349i 0.148606 0.257392i −0.782107 0.623144i \(-0.785855\pi\)
0.930712 + 0.365752i \(0.119188\pi\)
\(618\) −18.6657 + 28.9269i −0.750845 + 1.16361i
\(619\) 20.1621 0.810384 0.405192 0.914232i \(-0.367205\pi\)
0.405192 + 0.914232i \(0.367205\pi\)
\(620\) −3.74327 + 0.841785i −0.150334 + 0.0338069i
\(621\) −7.50278 23.8099i −0.301076 0.955457i
\(622\) 2.88244 + 7.37904i 0.115575 + 0.295872i
\(623\) 2.76241 5.16808i 0.110674 0.207055i
\(624\) 3.90668 0.0803122i 0.156392 0.00321506i
\(625\) −30.0421 −1.20168
\(626\) 9.73522 + 7.78909i 0.389098 + 0.311315i
\(627\) −2.79723 27.3951i −0.111711 1.09406i
\(628\) 12.7799 2.87393i 0.509973 0.114682i
\(629\) 2.78181i 0.110918i
\(630\) −13.9776 + 29.8011i −0.556883 + 1.18730i
\(631\) 8.38135i 0.333656i 0.985986 + 0.166828i \(0.0533525\pi\)
−0.985986 + 0.166828i \(0.946647\pi\)
\(632\) −9.99670 14.8147i −0.397648 0.589299i
\(633\) −27.1684 + 19.6162i −1.07985 + 0.779674i
\(634\) −2.83297 + 3.54080i −0.112512 + 0.140623i
\(635\) −16.6573 −0.661024
\(636\) −8.02752 23.9863i −0.318312 0.951119i
\(637\) −3.28265 + 2.19337i −0.130063 + 0.0869047i
\(638\) 8.79120 3.43407i 0.348047 0.135956i
\(639\) 21.6077 19.2248i 0.854786 0.760522i
\(640\) −28.9156 + 16.2654i −1.14299 + 0.642947i
\(641\) −13.4028 −0.529378 −0.264689 0.964334i \(-0.585269\pi\)
−0.264689 + 0.964334i \(0.585269\pi\)
\(642\) 1.08790 21.9841i 0.0429358 0.867643i
\(643\) 7.76497 13.4493i 0.306220 0.530389i −0.671312 0.741175i \(-0.734269\pi\)
0.977532 + 0.210786i \(0.0676022\pi\)
\(644\) 6.38609 + 24.6069i 0.251647 + 0.969649i
\(645\) 32.5236 3.32089i 1.28062 0.130760i
\(646\) −0.706926 + 4.63977i −0.0278136 + 0.182549i
\(647\) −21.2347 + 36.7795i −0.834821 + 1.44595i 0.0593553 + 0.998237i \(0.481096\pi\)
−0.894176 + 0.447715i \(0.852238\pi\)
\(648\) 13.7407 21.4288i 0.539784 0.841804i
\(649\) 0.110004 0.0635110i 0.00431804 0.00249302i
\(650\) −2.24150 1.79342i −0.0879191 0.0703435i
\(651\) −2.37186 + 1.83351i −0.0929605 + 0.0718609i
\(652\) 25.0629 5.63614i 0.981541 0.220728i
\(653\) 45.7962 1.79214 0.896072 0.443910i \(-0.146409\pi\)
0.896072 + 0.443910i \(0.146409\pi\)
\(654\) −3.34978 6.52721i −0.130987 0.255234i
\(655\) 22.7646i 0.889487i
\(656\) −17.6801 37.3222i −0.690291 1.45719i
\(657\) 9.19937 + 44.5780i 0.358902 + 1.73915i
\(658\) −3.52805 + 29.6390i −0.137538 + 1.15545i
\(659\) −37.8619 + 21.8596i −1.47489 + 0.851527i −0.999599 0.0283024i \(-0.990990\pi\)
−0.475289 + 0.879830i \(0.657657\pi\)
\(660\) 12.3220 13.9294i 0.479634 0.542202i
\(661\) −30.4522 + 17.5816i −1.18445 + 0.683845i −0.957041 0.289954i \(-0.906360\pi\)
−0.227413 + 0.973798i \(0.573027\pi\)
\(662\) 17.1932 + 13.7562i 0.668232 + 0.534649i
\(663\) 0.371383 0.0379208i 0.0144233 0.00147272i
\(664\) 1.14754 + 16.3667i 0.0445333 + 0.635151i
\(665\) 31.7609 59.4201i 1.23163 2.30421i
\(666\) −14.0223 + 27.5169i −0.543354 + 1.06626i
\(667\) −15.1670 + 8.75664i −0.587267 + 0.339059i
\(668\) 5.20258 4.79640i 0.201294 0.185578i
\(669\) −33.9865 + 3.47026i −1.31399 + 0.134168i
\(670\) −2.73824 7.00987i −0.105787 0.270815i
\(671\) 8.99986 15.5882i 0.347436 0.601776i
\(672\) −15.0942 + 21.0752i −0.582272 + 0.812994i
\(673\) −14.6335 25.3459i −0.564078 0.977012i −0.997135 0.0756454i \(-0.975898\pi\)
0.433057 0.901367i \(-0.357435\pi\)
\(674\) 3.35427 4.19235i 0.129202 0.161483i
\(675\) −17.8366 + 5.62054i −0.686532 + 0.216335i
\(676\) −5.56482 24.7458i −0.214032 0.951762i
\(677\) −6.23026 3.59704i −0.239448 0.138246i 0.375475 0.926833i \(-0.377480\pi\)
−0.614923 + 0.788587i \(0.710813\pi\)
\(678\) 9.06636 + 17.6663i 0.348191 + 0.678468i
\(679\) 2.29191 4.28784i 0.0879555 0.164552i
\(680\) −2.62739 + 1.77291i −0.100756 + 0.0679880i
\(681\) −0.920269 + 2.05057i −0.0352648 + 0.0785781i
\(682\) 1.57769 0.616287i 0.0604129 0.0235989i
\(683\) 34.3959 + 19.8585i 1.31612 + 0.759863i 0.983102 0.183056i \(-0.0585991\pi\)
0.333020 + 0.942920i \(0.391932\pi\)
\(684\) −30.3804 + 42.3318i −1.16162 + 1.61860i
\(685\) 55.3905i 2.11636i
\(686\) 1.38833 26.1548i 0.0530067 0.998594i
\(687\) 20.6019 + 9.24586i 0.786012 + 0.352752i
\(688\) 25.6621 + 2.08834i 0.978358 + 0.0796173i
\(689\) 3.56645 2.05909i 0.135871 0.0784450i
\(690\) −18.7105 + 28.9964i −0.712298 + 1.10387i
\(691\) 3.88972 6.73719i 0.147972 0.256295i −0.782506 0.622643i \(-0.786059\pi\)
0.930478 + 0.366348i \(0.119392\pi\)
\(692\) 13.4988 + 14.6420i 0.513148 + 0.556604i
\(693\) 4.11860 13.9355i 0.156453 0.529364i
\(694\) −21.8288 + 8.52690i −0.828611 + 0.323677i
\(695\) −18.1472 10.4773i −0.688362 0.397426i
\(696\) −16.7643 6.15452i −0.635450 0.233286i
\(697\) −1.97276 3.41693i −0.0747237 0.129425i
\(698\) −34.1613 + 13.3443i −1.29303 + 0.505089i
\(699\) 28.1655 2.87590i 1.06532 0.108776i
\(700\) 18.4337 4.78399i 0.696729 0.180818i
\(701\) −17.1899 −0.649253 −0.324626 0.945842i \(-0.605239\pi\)
−0.324626 + 0.945842i \(0.605239\pi\)
\(702\) 3.86476 + 1.49693i 0.145866 + 0.0564981i
\(703\) 31.6077 54.7462i 1.19211 2.06479i
\(704\) 11.5380 9.02142i 0.434855 0.340007i
\(705\) −32.8496 + 23.7181i −1.23719 + 0.893276i
\(706\) 0.0454987 0.298622i 0.00171237 0.0112388i
\(707\) 6.32341 + 10.1689i 0.237816 + 0.382442i
\(708\) −0.235523 0.0479010i −0.00885149 0.00180023i
\(709\) 12.4954 21.6427i 0.469276 0.812810i −0.530107 0.847931i \(-0.677848\pi\)
0.999383 + 0.0351206i \(0.0111815\pi\)
\(710\) −39.5243 6.02202i −1.48332 0.226002i
\(711\) −3.83118 18.5650i −0.143680 0.696242i
\(712\) 6.24929 0.438167i 0.234202 0.0164210i
\(713\) −2.72190 + 1.57149i −0.101936 + 0.0588527i
\(714\) −1.27400 + 2.12381i −0.0476783 + 0.0794816i
\(715\) 2.62222 + 1.51394i 0.0980656 + 0.0566182i
\(716\) 0.230972 + 0.250532i 0.00863183 + 0.00936281i
\(717\) 11.4851 8.29248i 0.428918 0.309688i
\(718\) 35.9973 14.0615i 1.34341 0.524770i
\(719\) 14.2772 + 24.7289i 0.532451 + 0.922233i 0.999282 + 0.0378861i \(0.0120624\pi\)
−0.466831 + 0.884347i \(0.654604\pi\)
\(720\) −34.9261 + 4.29321i −1.30162 + 0.159998i
\(721\) 31.5774 19.6360i 1.17600 0.731282i
\(722\) 49.8437 62.2973i 1.85499 2.31847i
\(723\) −13.3366 5.98528i −0.495993 0.222595i
\(724\) 9.18425 29.4398i 0.341330 1.09412i
\(725\) 6.55984 + 11.3620i 0.243626 + 0.421973i
\(726\) 10.1576 15.7416i 0.376984 0.584226i
\(727\) −5.98570 10.3675i −0.221997 0.384511i 0.733417 0.679779i \(-0.237924\pi\)
−0.955414 + 0.295268i \(0.904591\pi\)
\(728\) −3.85226 1.72436i −0.142774 0.0639092i
\(729\) 22.1224 15.4791i 0.819347 0.573298i
\(730\) 39.3093 49.1308i 1.45490 1.81841i
\(731\) 2.45980 0.0909790
\(732\) −32.2974 + 10.8090i −1.19375 + 0.399513i
\(733\) 15.6160i 0.576791i −0.957511 0.288395i \(-0.906878\pi\)
0.957511 0.288395i \(-0.0931217\pi\)
\(734\) 39.3480 + 5.99516i 1.45236 + 0.221285i
\(735\) 27.4025 22.6531i 1.01076 0.835572i
\(736\) −18.6441 + 19.7739i −0.687230 + 0.728876i
\(737\) 1.66116 + 2.87722i 0.0611897 + 0.105984i
\(738\) −2.29026 43.7433i −0.0843057 1.61021i
\(739\) −14.6499 8.45814i −0.538906 0.311138i 0.205729 0.978609i \(-0.434043\pi\)
−0.744635 + 0.667471i \(0.767377\pi\)
\(740\) 41.6520 9.36668i 1.53116 0.344326i
\(741\) −7.73969 3.47347i −0.284325 0.127601i
\(742\) −3.22929 + 27.1291i −0.118551 + 0.995940i
\(743\) −11.3689 6.56386i −0.417086 0.240805i 0.276744 0.960944i \(-0.410745\pi\)
−0.693830 + 0.720139i \(0.744078\pi\)
\(744\) −3.00857 1.10450i −0.110299 0.0404931i
\(745\) 28.7833i 1.05454i
\(746\) −9.54181 1.45381i −0.349350 0.0532279i
\(747\) −5.47561 + 16.5182i −0.200342 + 0.604370i
\(748\) 1.02877 0.948455i 0.0376157 0.0346789i
\(749\) −11.2073 + 20.9673i −0.409506 + 0.766128i
\(750\) −8.45541 5.45603i −0.308748 0.199226i
\(751\) 18.9699i 0.692221i −0.938194 0.346111i \(-0.887502\pi\)
0.938194 0.346111i \(-0.112498\pi\)
\(752\) −28.8371 + 13.6606i −1.05158 + 0.498149i
\(753\) 9.44479 21.0452i 0.344187 0.766929i
\(754\) 0.437949 2.87439i 0.0159492 0.104679i
\(755\) −11.0043 −0.400486
\(756\) −23.3076 + 14.5862i −0.847688 + 0.530496i
\(757\) 30.3460 1.10294 0.551471 0.834194i \(-0.314067\pi\)
0.551471 + 0.834194i \(0.314067\pi\)
\(758\) −5.24302 + 34.4115i −0.190435 + 1.24988i
\(759\) 6.23767 13.8990i 0.226413 0.504501i
\(760\) 71.8513 5.03783i 2.60632 0.182741i
\(761\) 24.5770i 0.890916i −0.895303 0.445458i \(-0.853041\pi\)
0.895303 0.445458i \(-0.146959\pi\)
\(762\) −11.6914 7.54411i −0.423534 0.273294i
\(763\) 0.259262 + 7.92018i 0.00938591 + 0.286730i
\(764\) 19.6140 + 21.2750i 0.709610 + 0.769702i
\(765\) −3.29250 + 0.679457i −0.119040 + 0.0245658i
\(766\) −43.4990 6.62762i −1.57168 0.239466i
\(767\) 0.0391311i 0.00141294i
\(768\) −27.6619 1.67961i −0.998162 0.0606076i
\(769\) −11.7047 6.75773i −0.422083 0.243690i 0.273885 0.961762i \(-0.411691\pi\)
−0.695968 + 0.718073i \(0.745025\pi\)
\(770\) −18.4614 + 7.91707i −0.665304 + 0.285312i
\(771\) 3.66617 + 1.64533i 0.132034 + 0.0592551i
\(772\) −8.71995 38.7761i −0.313838 1.39558i
\(773\) −41.3688 23.8843i −1.48793 0.859059i −0.488028 0.872828i \(-0.662284\pi\)
−0.999905 + 0.0137693i \(0.995617\pi\)
\(774\) 24.3316 + 12.3991i 0.874582 + 0.445678i
\(775\) 1.17725 + 2.03905i 0.0422879 + 0.0732448i
\(776\) 5.18490 0.363537i 0.186127 0.0130502i
\(777\) 26.3921 20.4018i 0.946810 0.731909i
\(778\) 20.1105 + 3.06408i 0.720996 + 0.109853i
\(779\) 89.6602i 3.21241i
\(780\) −1.81827 5.43302i −0.0651047 0.194533i
\(781\) 17.6499 0.631564
\(782\) −1.62211 + 2.02740i −0.0580067 + 0.0724998i
\(783\) −13.9631 12.7991i −0.498999 0.457404i
\(784\) 24.4663 13.6163i 0.873795 0.486295i
\(785\) −9.60296 16.6328i −0.342744 0.593651i
\(786\) 10.3101 15.9780i 0.367750 0.569915i
\(787\) −3.97010 6.87641i −0.141519 0.245118i 0.786550 0.617527i \(-0.211865\pi\)
−0.928069 + 0.372409i \(0.878532\pi\)
\(788\) −35.7183 11.1429i −1.27241 0.396951i
\(789\) 44.9301 + 20.1640i 1.59955 + 0.717858i
\(790\) −16.3708 + 20.4611i −0.582446 + 0.727972i
\(791\) −0.701706 21.4364i −0.0249498 0.762190i
\(792\) 14.9572 4.19608i 0.531481 0.149101i
\(793\) −2.77255 4.80220i −0.0984561 0.170531i
\(794\) −4.57414 + 1.78678i −0.162330 + 0.0634103i
\(795\) −30.0679 + 21.7096i −1.06640 + 0.769962i
\(796\) −4.23910 + 3.90814i −0.150251 + 0.138520i
\(797\) −22.6742 13.0910i −0.803162 0.463706i 0.0414133 0.999142i \(-0.486814\pi\)
−0.844576 + 0.535436i \(0.820147\pi\)
\(798\) 49.2037 27.3211i 1.74179 0.967155i
\(799\) −2.64009 + 1.52426i −0.0933998 + 0.0539244i
\(800\) 14.8132 + 13.9668i 0.523725 + 0.493800i
\(801\) 6.30715 + 2.09075i 0.222852 + 0.0738731i
\(802\) −47.5118 7.23901i −1.67770 0.255618i
\(803\) −13.8887 + 24.0559i −0.490121 + 0.848914i
\(804\) 1.25287 6.16022i 0.0441855 0.217254i
\(805\) 31.6532 19.6832i 1.11563 0.693740i
\(806\) 0.0785955 0.515845i 0.00276841 0.0181699i
\(807\) −22.0496 + 15.9203i −0.776182 + 0.560420i
\(808\) −5.60964 + 11.5069i −0.197346 + 0.404812i
\(809\) −20.3769 + 35.2939i −0.716414 + 1.24087i 0.245997 + 0.969271i \(0.420885\pi\)
−0.962412 + 0.271595i \(0.912449\pi\)
\(810\) −35.9933 9.87552i −1.26468 0.346990i
\(811\) 3.31693 0.116473 0.0582367 0.998303i \(-0.481452\pi\)
0.0582367 + 0.998303i \(0.481452\pi\)
\(812\) 13.5317 + 13.7465i 0.474868 + 0.482409i
\(813\) −0.838795 + 0.0856468i −0.0294178 + 0.00300377i
\(814\) −17.5552 + 6.85753i −0.615310 + 0.240356i
\(815\) −18.8326 32.6190i −0.659677 1.14259i
\(816\) −2.64706 + 0.0544174i −0.0926656 + 0.00190499i
\(817\) −48.4089 27.9489i −1.69361 0.977808i
\(818\) −18.8241 + 7.35319i −0.658170 + 0.257098i
\(819\) −3.08348 3.24533i −0.107746 0.113401i
\(820\) −44.5190 + 41.0433i −1.55467 + 1.43329i
\(821\) −20.0038 + 34.6476i −0.698137 + 1.20921i 0.270974 + 0.962587i \(0.412654\pi\)
−0.969112 + 0.246623i \(0.920679\pi\)
\(822\) 25.0864 38.8773i 0.874990 1.35600i
\(823\) 6.06307 3.50051i 0.211345 0.122020i −0.390591 0.920564i \(-0.627729\pi\)
0.601936 + 0.798544i \(0.294396\pi\)
\(824\) 35.7322 + 17.4195i 1.24479 + 0.606838i
\(825\) −10.4121 4.67281i −0.362503 0.162686i
\(826\) 0.207903 + 0.155465i 0.00723388 + 0.00540931i
\(827\) 25.4507i 0.885008i −0.896766 0.442504i \(-0.854090\pi\)
0.896766 0.442504i \(-0.145910\pi\)
\(828\) −26.2650 + 11.8779i −0.912773 + 0.412785i
\(829\) 5.05603 + 2.91910i 0.175603 + 0.101385i 0.585225 0.810871i \(-0.301006\pi\)
−0.409622 + 0.912255i \(0.634339\pi\)
\(830\) 22.4070 8.75276i 0.777758 0.303813i
\(831\) 5.27789 11.7604i 0.183088 0.407963i
\(832\) −0.629618 4.46785i −0.0218281 0.154895i
\(833\) 2.22423 1.48617i 0.0770651 0.0514928i
\(834\) −7.99193 15.5727i −0.276738 0.539237i
\(835\) −8.98513 5.18757i −0.310943 0.179523i
\(836\) −31.0229 + 6.97640i −1.07295 + 0.241284i
\(837\) −2.50585 2.29697i −0.0866147 0.0793948i
\(838\) −5.76217 + 7.20187i −0.199051 + 0.248784i
\(839\) 11.3989 + 19.7435i 0.393534 + 0.681621i 0.992913 0.118845i \(-0.0379190\pi\)
−0.599379 + 0.800465i \(0.704586\pi\)
\(840\) 36.0894 + 11.9245i 1.24520 + 0.411434i
\(841\) 7.85583 13.6067i 0.270891 0.469196i
\(842\) 3.61474 + 9.25370i 0.124572 + 0.318904i
\(843\) −45.5973 + 4.65580i −1.57045 + 0.160354i
\(844\) 26.2277 + 28.4488i 0.902795 + 0.979248i
\(845\) −32.2063 + 18.5943i −1.10793 + 0.639663i
\(846\) −33.7984 + 1.76958i −1.16201 + 0.0608393i
\(847\) −17.1840 + 10.6856i −0.590448 + 0.367162i
\(848\) −26.3951 + 12.5038i −0.906412 + 0.429381i
\(849\) −50.6608 + 5.17282i −1.73867 + 0.177531i
\(850\) 1.51878 + 1.21517i 0.0520938 + 0.0416800i
\(851\) 30.2870 17.4862i 1.03823 0.599420i
\(852\) −25.0138 22.1274i −0.856960 0.758071i
\(853\) −14.0823 + 8.13042i −0.482169 + 0.278380i −0.721320 0.692602i \(-0.756464\pi\)
0.239151 + 0.970982i \(0.423131\pi\)
\(854\) 36.5291 + 4.34822i 1.25000 + 0.148793i
\(855\) 72.5165 + 24.0385i 2.48001 + 0.822098i
\(856\) −25.3539 + 1.77768i −0.866577 + 0.0607597i
\(857\) 7.51937i 0.256857i 0.991719 + 0.128428i \(0.0409932\pi\)
−0.991719 + 0.128428i \(0.959007\pi\)
\(858\) 1.15481 + 2.25021i 0.0394247 + 0.0768209i
\(859\) −28.3717 −0.968031 −0.484016 0.875059i \(-0.660822\pi\)
−0.484016 + 0.875059i \(0.660822\pi\)
\(860\) −8.28242 36.8305i −0.282428 1.25591i
\(861\) −17.9494 + 43.7759i −0.611713 + 1.49188i
\(862\) 21.4218 + 17.1395i 0.729630 + 0.583773i
\(863\) −3.94874 + 2.27980i −0.134417 + 0.0776054i −0.565700 0.824611i \(-0.691394\pi\)
0.431284 + 0.902216i \(0.358061\pi\)
\(864\) −26.4582 12.8048i −0.900127 0.435627i
\(865\) 14.5997 25.2874i 0.496405 0.859799i
\(866\) −4.37186 + 28.6938i −0.148562 + 0.975056i
\(867\) 29.0409 2.96528i 0.986281 0.100706i
\(868\) 2.42843 + 2.46699i 0.0824262 + 0.0837351i
\(869\) 5.78409 10.0183i 0.196212 0.339849i
\(870\) −1.29415 + 26.1520i −0.0438757 + 0.886636i
\(871\) 1.02350 0.0346798
\(872\) −7.02236 + 4.73855i −0.237807 + 0.160468i
\(873\) 5.23290 + 1.73465i 0.177107 + 0.0587091i
\(874\) 54.9591 21.4685i 1.85902 0.726181i
\(875\) 5.73965 + 9.23015i 0.194036 + 0.312036i
\(876\) 49.8417 16.6806i 1.68400 0.563585i
\(877\) −27.6128 −0.932419 −0.466210 0.884674i \(-0.654381\pi\)
−0.466210 + 0.884674i \(0.654381\pi\)
\(878\) −6.17927 + 7.72318i −0.208540 + 0.260645i
\(879\) 22.2287 16.0496i 0.749755 0.541339i
\(880\) −17.6652 12.2102i −0.595493 0.411607i
\(881\) 10.3088i 0.347313i −0.984806 0.173657i \(-0.944442\pi\)
0.984806 0.173657i \(-0.0555583\pi\)
\(882\) 29.4928 3.48905i 0.993075 0.117482i
\(883\) 33.0806i 1.11325i −0.830764 0.556625i \(-0.812096\pi\)
0.830764 0.556625i \(-0.187904\pi\)
\(884\) −0.0945759 0.420563i −0.00318093 0.0141451i
\(885\) 0.0357958 + 0.350572i 0.00120326 + 0.0117843i
\(886\) 3.57255 + 2.85838i 0.120022 + 0.0960290i
\(887\) −7.17805 −0.241015 −0.120508 0.992712i \(-0.538452\pi\)
−0.120508 + 0.992712i \(0.538452\pi\)
\(888\) 33.4768 + 12.2900i 1.12341 + 0.412425i
\(889\) 7.93626 + 12.7626i 0.266174 + 0.428044i
\(890\) −3.34206 8.55566i −0.112026 0.286787i
\(891\) 16.3651 + 1.91656i 0.548253 + 0.0642073i
\(892\) 8.65496 + 38.4871i 0.289789 + 1.28864i
\(893\) 69.2761 2.31824
\(894\) 13.0360 20.2023i 0.435989 0.675667i
\(895\) 0.249809 0.432682i 0.00835019 0.0144630i
\(896\) 26.2391 + 14.4053i 0.876586 + 0.481246i
\(897\) −2.74734 3.80507i −0.0917310 0.127047i
\(898\) −21.0780 3.21150i −0.703383 0.107169i
\(899\) −1.19238 + 2.06526i −0.0397681 + 0.0688803i
\(900\) 8.89804 + 19.6758i 0.296601 + 0.655861i
\(901\) −2.41653 + 1.39518i −0.0805062 + 0.0464803i
\(902\) 16.7001 20.8727i 0.556053 0.694985i
\(903\) −18.0401 23.3370i −0.600337 0.776607i
\(904\) 19.0064 12.8251i 0.632143 0.426558i
\(905\) −45.2166 −1.50305
\(906\) −7.72364 4.98385i −0.256601 0.165577i
\(907\) 17.7340i 0.588847i −0.955675 0.294423i \(-0.904872\pi\)
0.955675 0.294423i \(-0.0951276\pi\)
\(908\) 2.47755 + 0.772914i 0.0822204 + 0.0256501i
\(909\) −10.1441 + 9.02545i −0.336459 + 0.299355i
\(910\) −0.731451 + 6.14487i −0.0242474 + 0.203701i
\(911\) 29.3352 16.9367i 0.971918 0.561137i 0.0720973 0.997398i \(-0.477031\pi\)
0.899820 + 0.436261i \(0.143697\pi\)
\(912\) 52.7125 + 29.0056i 1.74548 + 0.960473i
\(913\) −9.19701 + 5.30989i −0.304377 + 0.175732i
\(914\) 23.7718 29.7113i 0.786303 0.982763i
\(915\) 29.2319 + 40.4862i 0.966377 + 1.33843i
\(916\) 7.76540 24.8917i 0.256576 0.822446i
\(917\) −17.4420 + 10.8461i −0.575985 + 0.358169i
\(918\) −2.61866 1.01428i −0.0864285 0.0334762i
\(919\) −45.7550 + 26.4167i −1.50932 + 0.871406i −0.509378 + 0.860543i \(0.670124\pi\)
−0.999941 + 0.0108626i \(0.996542\pi\)
\(920\) 35.8181 + 17.4614i 1.18089 + 0.575684i
\(921\) 1.62177 3.61368i 0.0534392 0.119075i
\(922\) −20.3813 + 7.96146i −0.671222 + 0.262197i
\(923\) 2.71867 4.70887i 0.0894861 0.154994i
\(924\) −16.5433 2.80440i −0.544235 0.0922580i
\(925\) −13.0994 22.6888i −0.430705 0.746004i
\(926\) 6.60659 + 5.28590i 0.217106 + 0.173705i
\(927\) 28.0266 + 31.5004i 0.920513 + 1.03461i
\(928\) −4.74929 + 20.0667i −0.155903 + 0.658721i
\(929\) 35.8534 + 20.7000i 1.17631 + 0.679144i 0.955159 0.296095i \(-0.0956844\pi\)
0.221154 + 0.975239i \(0.429018\pi\)
\(930\) −0.232251 + 4.69331i −0.00761581 + 0.153900i
\(931\) −60.6592 + 3.97554i −1.98803 + 0.130293i
\(932\) −7.17260 31.8953i −0.234946 1.04477i
\(933\) 9.65229 0.985566i 0.316002 0.0322660i
\(934\) 16.4749 + 42.1757i 0.539075 + 1.38003i
\(935\) −1.77675 1.02581i −0.0581059 0.0335474i
\(936\) 1.18442 4.63681i 0.0387139 0.151559i
\(937\) 34.0441i 1.11217i 0.831125 + 0.556086i \(0.187697\pi\)
−0.831125 + 0.556086i \(0.812303\pi\)
\(938\) −4.06626 + 5.43782i −0.132768 + 0.177551i
\(939\) 12.3801 8.93869i 0.404009 0.291703i
\(940\) 31.7122 + 34.3977i 1.03434 + 1.12193i
\(941\) 39.3815 22.7369i 1.28380 0.741203i 0.306260 0.951948i \(-0.400922\pi\)
0.977541 + 0.210745i \(0.0675889\pi\)
\(942\) 0.792927 16.0234i 0.0258350 0.522070i
\(943\) −24.8012 + 42.9569i −0.807638 + 1.39887i
\(944\) −0.0225102 + 0.276612i −0.000732645 + 0.00900294i
\(945\) 30.5933 + 26.2539i 0.995201 + 0.854041i
\(946\) 6.06372 + 15.5231i 0.197149 + 0.504699i
\(947\) −32.1310 18.5508i −1.04412 0.602822i −0.123121 0.992392i \(-0.539290\pi\)
−0.920997 + 0.389570i \(0.872624\pi\)
\(948\) −20.7571 + 6.94681i −0.674160 + 0.225622i
\(949\) 4.27863 + 7.41080i 0.138890 + 0.240565i
\(950\) −16.0826 41.1714i −0.521788 1.33578i
\(951\) 3.25109 + 4.50276i 0.105424 + 0.146012i
\(952\) 2.61019 + 1.16838i 0.0845967 + 0.0378675i
\(953\) 28.7039 0.929812 0.464906 0.885360i \(-0.346088\pi\)
0.464906 + 0.885360i \(0.346088\pi\)
\(954\) −30.9363 + 1.61973i −1.00160 + 0.0524405i
\(955\) 21.2136 36.7431i 0.686457 1.18898i
\(956\) −11.0874 12.0263i −0.358592 0.388959i
\(957\) −1.17418 11.4995i −0.0379558 0.371726i
\(958\) −33.3811 5.08603i −1.07849 0.164322i
\(959\) −42.4395 + 26.3905i −1.37044 + 0.852193i
\(960\) 9.72773 + 39.4511i 0.313961 + 1.27328i
\(961\) 15.2860 26.4762i 0.493097 0.854069i
\(962\) −0.874544 + 5.73989i −0.0281964 + 0.185062i
\(963\) −25.5886 8.48235i −0.824581 0.273340i
\(964\) −5.02690 + 16.1136i −0.161906 + 0.518983i
\(965\) −50.4665 + 29.1368i −1.62457 + 0.937948i
\(966\) 31.1312 + 0.520643i 1.00163 + 0.0167514i
\(967\) −15.4417 8.91526i −0.496571 0.286695i 0.230725 0.973019i \(-0.425890\pi\)
−0.727296 + 0.686324i \(0.759223\pi\)
\(968\) −19.4450 9.47945i −0.624985 0.304681i
\(969\) 5.24420 + 2.35353i 0.168468 + 0.0756062i
\(970\) −2.77284 7.09845i −0.0890305 0.227918i
\(971\) 11.4504 + 19.8326i 0.367460 + 0.636459i 0.989168 0.146790i \(-0.0468942\pi\)
−0.621708 + 0.783249i \(0.713561\pi\)
\(972\) −20.7903 23.2328i −0.666848 0.745194i
\(973\) 0.618549 + 18.8960i 0.0198298 + 0.605778i
\(974\) 4.73042 + 3.78478i 0.151572 + 0.121272i
\(975\) −2.85048 + 2.05811i −0.0912883 + 0.0659121i
\(976\) 16.8362 + 35.5409i 0.538915 + 1.13764i
\(977\) 19.0964 + 33.0759i 0.610947 + 1.05819i 0.991081 + 0.133260i \(0.0425445\pi\)
−0.380134 + 0.924931i \(0.624122\pi\)
\(978\) 1.55503 31.4238i 0.0497243 1.00482i
\(979\) 2.02748 + 3.51169i 0.0647984 + 0.112234i
\(980\) −29.7416 28.2993i −0.950062 0.903987i
\(981\) −8.80002 + 1.81602i −0.280963 + 0.0579811i
\(982\) 8.42041 + 6.73712i 0.268706 + 0.214990i
\(983\) 4.41019 0.140663 0.0703316 0.997524i \(-0.477594\pi\)
0.0703316 + 0.997524i \(0.477594\pi\)
\(984\) −49.8354 + 8.64462i −1.58870 + 0.275581i
\(985\) 54.8598i 1.74798i
\(986\) −0.296742 + 1.94761i −0.00945021 + 0.0620245i
\(987\) 33.8236 + 13.8686i 1.07662 + 0.441443i
\(988\) −2.91729 + 9.35128i −0.0928114 + 0.297504i
\(989\) −15.4621 26.7811i −0.491665 0.851589i
\(990\) −12.4043 19.1030i −0.394234 0.607134i
\(991\) 46.5115 + 26.8534i 1.47749 + 0.853027i 0.999676 0.0254358i \(-0.00809734\pi\)
0.477810 + 0.878463i \(0.341431\pi\)
\(992\) −0.852319 + 3.60121i −0.0270612 + 0.114339i
\(993\) 21.8642 15.7864i 0.693841 0.500968i
\(994\) 14.2171 + 33.1522i 0.450940 + 1.05153i
\(995\) 7.32115 + 4.22687i 0.232096 + 0.134001i
\(996\) 19.6911 + 4.00481i 0.623937 + 0.126897i
\(997\) 41.2717i 1.30709i 0.756888 + 0.653544i \(0.226719\pi\)
−0.756888 + 0.653544i \(0.773281\pi\)
\(998\) −4.43746 + 29.1244i −0.140465 + 0.921917i
\(999\) 27.8829 + 25.5587i 0.882177 + 0.808642i
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 252.2.n.b.31.3 84
3.2 odd 2 756.2.n.b.199.40 84
4.3 odd 2 inner 252.2.n.b.31.32 yes 84
7.5 odd 6 252.2.bj.b.103.26 yes 84
9.2 odd 6 756.2.bj.b.451.17 84
9.7 even 3 252.2.bj.b.115.26 yes 84
12.11 even 2 756.2.n.b.199.11 84
21.5 even 6 756.2.bj.b.523.17 84
28.19 even 6 252.2.bj.b.103.25 yes 84
36.7 odd 6 252.2.bj.b.115.25 yes 84
36.11 even 6 756.2.bj.b.451.18 84
63.47 even 6 756.2.n.b.19.11 84
63.61 odd 6 inner 252.2.n.b.187.32 yes 84
84.47 odd 6 756.2.bj.b.523.18 84
252.47 odd 6 756.2.n.b.19.40 84
252.187 even 6 inner 252.2.n.b.187.3 yes 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.n.b.31.3 84 1.1 even 1 trivial
252.2.n.b.31.32 yes 84 4.3 odd 2 inner
252.2.n.b.187.3 yes 84 252.187 even 6 inner
252.2.n.b.187.32 yes 84 63.61 odd 6 inner
252.2.bj.b.103.25 yes 84 28.19 even 6
252.2.bj.b.103.26 yes 84 7.5 odd 6
252.2.bj.b.115.25 yes 84 36.7 odd 6
252.2.bj.b.115.26 yes 84 9.7 even 3
756.2.n.b.19.11 84 63.47 even 6
756.2.n.b.19.40 84 252.47 odd 6
756.2.n.b.199.11 84 12.11 even 2
756.2.n.b.199.40 84 3.2 odd 2
756.2.bj.b.451.17 84 9.2 odd 6
756.2.bj.b.451.18 84 36.11 even 6
756.2.bj.b.523.17 84 21.5 even 6
756.2.bj.b.523.18 84 84.47 odd 6