Properties

Label 441.2.z.a.142.12
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(4,441)]
 
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([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), 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 \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.12
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.700413 + 1.78462i) q^{2} +(-1.50834 + 0.851417i) q^{3} +(-1.22820 - 1.13960i) q^{4} +(2.53828 - 1.22237i) q^{5} +(-0.462997 - 3.28816i) q^{6} +(-2.05984 - 1.66044i) q^{7} +(-0.560571 + 0.269957i) q^{8} +(1.55018 - 2.56845i) q^{9} +O(q^{10})\) \(q+(-0.700413 + 1.78462i) q^{2} +(-1.50834 + 0.851417i) q^{3} +(-1.22820 - 1.13960i) q^{4} +(2.53828 - 1.22237i) q^{5} +(-0.462997 - 3.28816i) q^{6} +(-2.05984 - 1.66044i) q^{7} +(-0.560571 + 0.269957i) q^{8} +(1.55018 - 2.56845i) q^{9} +(0.403627 + 5.38603i) q^{10} +(0.0782134 + 0.0980766i) q^{11} +(2.82282 + 0.673199i) q^{12} +(1.84195 - 4.69320i) q^{13} +(4.40600 - 2.51305i) q^{14} +(-2.78784 + 4.00488i) q^{15} +(-0.339555 - 4.53105i) q^{16} +(3.92669 - 3.64343i) q^{17} +(3.49795 + 4.56547i) q^{18} +(-0.421303 + 0.729718i) q^{19} +(-4.51053 - 1.39131i) q^{20} +(4.52067 + 0.750722i) q^{21} +(-0.229812 + 0.0708875i) q^{22} +(1.52618 - 6.68661i) q^{23} +(0.615686 - 0.884466i) q^{24} +(1.83121 - 2.29626i) q^{25} +(7.08548 + 6.57436i) q^{26} +(-0.151375 + 5.19395i) q^{27} +(0.637657 + 4.38675i) q^{28} +(0.484894 + 0.149570i) q^{29} +(-5.19457 - 7.78031i) q^{30} +(-5.01663 + 8.68906i) q^{31} +(7.13495 + 2.20084i) q^{32} +(-0.201476 - 0.0813406i) q^{33} +(3.75186 + 9.55957i) q^{34} +(-7.25811 - 1.69676i) q^{35} +(-4.83095 + 1.38798i) q^{36} +(-4.98367 - 1.53726i) q^{37} +(-1.00719 - 1.26297i) q^{38} +(1.21759 + 8.64721i) q^{39} +(-1.09290 + 1.37045i) q^{40} +(3.97627 + 2.71098i) q^{41} +(-4.50609 + 7.54187i) q^{42} +(-1.27446 + 0.868914i) q^{43} +(0.0157066 - 0.209590i) q^{44} +(0.795187 - 8.41433i) q^{45} +(10.8641 + 7.40704i) q^{46} +(3.10005 - 7.89879i) q^{47} +(4.36997 + 6.54525i) q^{48} +(1.48589 + 6.84048i) q^{49} +(2.81537 + 4.87636i) q^{50} +(-2.82070 + 8.83879i) q^{51} +(-7.61067 + 3.66510i) q^{52} +(0.276852 - 0.0853976i) q^{53} +(-9.16322 - 3.90806i) q^{54} +(0.318413 + 0.153340i) q^{55} +(1.60293 + 0.374725i) q^{56} +(0.0141740 - 1.45937i) q^{57} +(-0.606553 + 0.760593i) q^{58} +(4.55198 - 3.10349i) q^{59} +(7.98800 - 1.74177i) q^{60} +(2.24351 - 2.08167i) q^{61} +(-11.9930 - 15.0387i) q^{62} +(-7.45788 + 2.71663i) q^{63} +(-3.25913 + 4.08681i) q^{64} +(-1.06146 - 14.1642i) q^{65} +(0.286279 - 0.302588i) q^{66} +(6.95882 - 12.0530i) q^{67} -8.97483 q^{68} +(3.39110 + 11.3851i) q^{69} +(8.11177 - 11.7646i) q^{70} +(-0.117503 + 0.514814i) q^{71} +(-0.175615 + 1.85828i) q^{72} +(-7.59302 - 1.14446i) q^{73} +(6.23406 - 7.81727i) q^{74} +(-0.807009 + 5.02267i) q^{75} +(1.34903 - 0.416122i) q^{76} +(0.00174278 - 0.331891i) q^{77} +(-16.2848 - 3.88368i) q^{78} +(0.119801 + 0.207501i) q^{79} +(-6.40049 - 11.0860i) q^{80} +(-4.19389 - 7.96312i) q^{81} +(-7.62311 + 5.19735i) q^{82} +(0.530135 + 1.35076i) q^{83} +(-4.69676 - 6.07381i) q^{84} +(5.51340 - 14.0479i) q^{85} +(-0.658034 - 2.88304i) q^{86} +(-0.858732 + 0.187245i) q^{87} +(-0.0703206 - 0.0338646i) q^{88} +(-0.315115 - 0.802899i) q^{89} +(14.4595 + 7.31262i) q^{90} +(-11.5869 + 6.60881i) q^{91} +(-9.49454 + 6.47327i) q^{92} +(0.168775 - 17.3773i) q^{93} +(11.9251 + 11.0648i) q^{94} +(-0.177398 + 2.36721i) q^{95} +(-12.6358 + 2.75520i) q^{96} +(-8.79556 + 15.2344i) q^{97} +(-13.2484 - 2.13940i) q^{98} +(0.373150 - 0.0488512i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.700413 + 1.78462i −0.495267 + 1.26192i 0.436775 + 0.899571i \(0.356120\pi\)
−0.932042 + 0.362349i \(0.881975\pi\)
\(3\) −1.50834 + 0.851417i −0.870841 + 0.491566i
\(4\) −1.22820 1.13960i −0.614100 0.569802i
\(5\) 2.53828 1.22237i 1.13515 0.546660i 0.230610 0.973046i \(-0.425928\pi\)
0.904541 + 0.426386i \(0.140213\pi\)
\(6\) −0.462997 3.28816i −0.189018 1.34239i
\(7\) −2.05984 1.66044i −0.778547 0.627587i
\(8\) −0.560571 + 0.269957i −0.198192 + 0.0954442i
\(9\) 1.55018 2.56845i 0.516726 0.856151i
\(10\) 0.403627 + 5.38603i 0.127638 + 1.70321i
\(11\) 0.0782134 + 0.0980766i 0.0235822 + 0.0295712i 0.793483 0.608593i \(-0.208266\pi\)
−0.769901 + 0.638164i \(0.779694\pi\)
\(12\) 2.82282 + 0.673199i 0.814879 + 0.194336i
\(13\) 1.84195 4.69320i 0.510864 1.30166i −0.410110 0.912036i \(-0.634510\pi\)
0.920974 0.389624i \(-0.127395\pi\)
\(14\) 4.40600 2.51305i 1.17755 0.671641i
\(15\) −2.78784 + 4.00488i −0.719817 + 1.03406i
\(16\) −0.339555 4.53105i −0.0848887 1.13276i
\(17\) 3.92669 3.64343i 0.952362 0.883663i −0.0409457 0.999161i \(-0.513037\pi\)
0.993308 + 0.115499i \(0.0368466\pi\)
\(18\) 3.49795 + 4.56547i 0.824476 + 1.07609i
\(19\) −0.421303 + 0.729718i −0.0966536 + 0.167409i −0.910298 0.413955i \(-0.864147\pi\)
0.813644 + 0.581363i \(0.197481\pi\)
\(20\) −4.51053 1.39131i −1.00859 0.311107i
\(21\) 4.52067 + 0.750722i 0.986490 + 0.163821i
\(22\) −0.229812 + 0.0708875i −0.0489960 + 0.0151133i
\(23\) 1.52618 6.68661i 0.318230 1.39426i −0.522426 0.852685i \(-0.674973\pi\)
0.840655 0.541570i \(-0.182170\pi\)
\(24\) 0.615686 0.884466i 0.125676 0.180541i
\(25\) 1.83121 2.29626i 0.366242 0.459253i
\(26\) 7.08548 + 6.57436i 1.38958 + 1.28934i
\(27\) −0.151375 + 5.19395i −0.0291322 + 0.999576i
\(28\) 0.637657 + 4.38675i 0.120506 + 0.829019i
\(29\) 0.484894 + 0.149570i 0.0900426 + 0.0277745i 0.339449 0.940624i \(-0.389759\pi\)
−0.249407 + 0.968399i \(0.580236\pi\)
\(30\) −5.19457 7.78031i −0.948394 1.42048i
\(31\) −5.01663 + 8.68906i −0.901013 + 1.56060i −0.0748317 + 0.997196i \(0.523842\pi\)
−0.826181 + 0.563404i \(0.809491\pi\)
\(32\) 7.13495 + 2.20084i 1.26129 + 0.389057i
\(33\) −0.201476 0.0813406i −0.0350726 0.0141596i
\(34\) 3.75186 + 9.55957i 0.643438 + 1.63945i
\(35\) −7.25811 1.69676i −1.22685 0.286805i
\(36\) −4.83095 + 1.38798i −0.805158 + 0.231331i
\(37\) −4.98367 1.53726i −0.819311 0.252724i −0.143360 0.989671i \(-0.545791\pi\)
−0.675951 + 0.736947i \(0.736267\pi\)
\(38\) −1.00719 1.26297i −0.163387 0.204881i
\(39\) 1.21759 + 8.64721i 0.194970 + 1.38466i
\(40\) −1.09290 + 1.37045i −0.172802 + 0.216687i
\(41\) 3.97627 + 2.71098i 0.620989 + 0.423383i 0.832525 0.553987i \(-0.186894\pi\)
−0.211536 + 0.977370i \(0.567847\pi\)
\(42\) −4.50609 + 7.54187i −0.695305 + 1.16374i
\(43\) −1.27446 + 0.868914i −0.194354 + 0.132508i −0.656587 0.754250i \(-0.728001\pi\)
0.462233 + 0.886758i \(0.347048\pi\)
\(44\) 0.0157066 0.209590i 0.00236786 0.0315969i
\(45\) 0.795187 8.41433i 0.118539 1.25433i
\(46\) 10.8641 + 7.40704i 1.60183 + 1.09211i
\(47\) 3.10005 7.89879i 0.452188 1.15216i −0.505110 0.863055i \(-0.668548\pi\)
0.957298 0.289102i \(-0.0933566\pi\)
\(48\) 4.36997 + 6.54525i 0.630751 + 0.944726i
\(49\) 1.48589 + 6.84048i 0.212270 + 0.977211i
\(50\) 2.81537 + 4.87636i 0.398153 + 0.689621i
\(51\) −2.82070 + 8.83879i −0.394977 + 1.23768i
\(52\) −7.61067 + 3.66510i −1.05541 + 0.508259i
\(53\) 0.276852 0.0853976i 0.0380286 0.0117303i −0.275683 0.961249i \(-0.588904\pi\)
0.313711 + 0.949518i \(0.398428\pi\)
\(54\) −9.16322 3.90806i −1.24696 0.531819i
\(55\) 0.318413 + 0.153340i 0.0429348 + 0.0206763i
\(56\) 1.60293 + 0.374725i 0.214201 + 0.0500748i
\(57\) 0.0141740 1.45937i 0.00187739 0.193298i
\(58\) −0.606553 + 0.760593i −0.0796443 + 0.0998708i
\(59\) 4.55198 3.10349i 0.592617 0.404039i −0.229541 0.973299i \(-0.573722\pi\)
0.822158 + 0.569260i \(0.192770\pi\)
\(60\) 7.98800 1.74177i 1.03125 0.224861i
\(61\) 2.24351 2.08167i 0.287252 0.266531i −0.523364 0.852109i \(-0.675323\pi\)
0.810616 + 0.585579i \(0.199133\pi\)
\(62\) −11.9930 15.0387i −1.52311 1.90992i
\(63\) −7.45788 + 2.71663i −0.939604 + 0.342263i
\(64\) −3.25913 + 4.08681i −0.407391 + 0.510852i
\(65\) −1.06146 14.1642i −0.131658 1.75685i
\(66\) 0.286279 0.302588i 0.0352385 0.0372460i
\(67\) 6.95882 12.0530i 0.850156 1.47251i −0.0309121 0.999522i \(-0.509841\pi\)
0.881068 0.472990i \(-0.156825\pi\)
\(68\) −8.97483 −1.08836
\(69\) 3.39110 + 11.3851i 0.408241 + 1.37060i
\(70\) 8.11177 11.7646i 0.969541 1.40614i
\(71\) −0.117503 + 0.514814i −0.0139450 + 0.0610971i −0.981422 0.191863i \(-0.938547\pi\)
0.967477 + 0.252960i \(0.0814042\pi\)
\(72\) −0.175615 + 1.85828i −0.0206964 + 0.219001i
\(73\) −7.59302 1.14446i −0.888696 0.133949i −0.311201 0.950344i \(-0.600731\pi\)
−0.577494 + 0.816395i \(0.695969\pi\)
\(74\) 6.23406 7.81727i 0.724695 0.908739i
\(75\) −0.807009 + 5.02267i −0.0931854 + 0.579968i
\(76\) 1.34903 0.416122i 0.154745 0.0477325i
\(77\) 0.00174278 0.331891i 0.000198608 0.0378225i
\(78\) −16.2848 3.88368i −1.84389 0.439740i
\(79\) 0.119801 + 0.207501i 0.0134786 + 0.0233456i 0.872686 0.488282i \(-0.162376\pi\)
−0.859207 + 0.511627i \(0.829043\pi\)
\(80\) −6.40049 11.0860i −0.715597 1.23945i
\(81\) −4.19389 7.96312i −0.465988 0.884791i
\(82\) −7.62311 + 5.19735i −0.841831 + 0.573951i
\(83\) 0.530135 + 1.35076i 0.0581899 + 0.148265i 0.957012 0.290048i \(-0.0936712\pi\)
−0.898822 + 0.438313i \(0.855576\pi\)
\(84\) −4.69676 6.07381i −0.512458 0.662707i
\(85\) 5.51340 14.0479i 0.598012 1.52371i
\(86\) −0.658034 2.88304i −0.0709577 0.310886i
\(87\) −0.858732 + 0.187245i −0.0920657 + 0.0200747i
\(88\) −0.0703206 0.0338646i −0.00749621 0.00360998i
\(89\) −0.315115 0.802899i −0.0334021 0.0851071i 0.913200 0.407513i \(-0.133604\pi\)
−0.946602 + 0.322406i \(0.895509\pi\)
\(90\) 14.4595 + 7.31262i 1.52416 + 0.770818i
\(91\) −11.5869 + 6.60881i −1.21464 + 0.692792i
\(92\) −9.49454 + 6.47327i −0.989874 + 0.674885i
\(93\) 0.168775 17.3773i 0.0175012 1.80194i
\(94\) 11.9251 + 11.0648i 1.22998 + 1.14125i
\(95\) −0.177398 + 2.36721i −0.0182007 + 0.242871i
\(96\) −12.6358 + 2.75520i −1.28963 + 0.281201i
\(97\) −8.79556 + 15.2344i −0.893054 + 1.54682i −0.0568598 + 0.998382i \(0.518109\pi\)
−0.836194 + 0.548433i \(0.815225\pi\)
\(98\) −13.2484 2.13940i −1.33829 0.216113i
\(99\) 0.373150 0.0488512i 0.0375030 0.00490973i
\(100\) −4.86592 + 0.733420i −0.486592 + 0.0733420i
\(101\) −4.04117 + 1.94612i −0.402111 + 0.193647i −0.623998 0.781426i \(-0.714493\pi\)
0.221887 + 0.975072i \(0.428778\pi\)
\(102\) −13.7983 11.2247i −1.36623 1.11141i
\(103\) 11.7897 5.67762i 1.16167 0.559432i 0.249153 0.968464i \(-0.419848\pi\)
0.912520 + 0.409032i \(0.134134\pi\)
\(104\) 0.234420 + 3.12812i 0.0229868 + 0.306737i
\(105\) 12.3924 3.62038i 1.20937 0.353313i
\(106\) −0.0415084 + 0.553891i −0.00403165 + 0.0537986i
\(107\) 2.09431 + 5.33622i 0.202465 + 0.515872i 0.995657 0.0930999i \(-0.0296776\pi\)
−0.793192 + 0.608972i \(0.791582\pi\)
\(108\) 6.10496 6.20670i 0.587450 0.597240i
\(109\) 3.26980 8.33131i 0.313190 0.797994i −0.684433 0.729076i \(-0.739950\pi\)
0.997622 0.0689182i \(-0.0219548\pi\)
\(110\) −0.496674 + 0.460847i −0.0473561 + 0.0439400i
\(111\) 8.82592 1.92447i 0.837719 0.182663i
\(112\) −6.82409 + 9.89704i −0.644816 + 0.935183i
\(113\) 13.6623 + 2.05926i 1.28524 + 0.193718i 0.755897 0.654691i \(-0.227201\pi\)
0.529341 + 0.848409i \(0.322439\pi\)
\(114\) 2.59450 + 1.04746i 0.242997 + 0.0981032i
\(115\) −4.29966 18.8380i −0.400945 1.75665i
\(116\) −0.425097 0.736290i −0.0394693 0.0683628i
\(117\) −9.19891 12.0063i −0.850440 1.10998i
\(118\) 2.35029 + 10.2973i 0.216362 + 0.947942i
\(119\) −14.1381 + 0.984873i −1.29603 + 0.0902832i
\(120\) 0.481637 2.99762i 0.0439672 0.273644i
\(121\) 2.44423 10.7089i 0.222203 0.973533i
\(122\) 2.14362 + 5.46185i 0.194074 + 0.494492i
\(123\) −8.30574 0.703610i −0.748903 0.0634424i
\(124\) 16.0635 4.95494i 1.44255 0.444966i
\(125\) −1.29328 + 5.66623i −0.115674 + 0.506803i
\(126\) 0.375442 15.2123i 0.0334470 1.35522i
\(127\) −4.48853 19.6655i −0.398293 1.74503i −0.634116 0.773238i \(-0.718636\pi\)
0.235823 0.971796i \(-0.424221\pi\)
\(128\) 2.45598 + 4.25389i 0.217080 + 0.375994i
\(129\) 1.18252 2.39572i 0.104115 0.210931i
\(130\) 26.0212 + 8.02647i 2.28221 + 0.703968i
\(131\) 15.1805 + 7.31054i 1.32633 + 0.638725i 0.956868 0.290523i \(-0.0938292\pi\)
0.369457 + 0.929248i \(0.379544\pi\)
\(132\) 0.154758 + 0.329506i 0.0134699 + 0.0286798i
\(133\) 2.07947 0.803556i 0.180313 0.0696772i
\(134\) 16.6361 + 20.8610i 1.43714 + 1.80212i
\(135\) 5.96469 + 13.3687i 0.513359 + 1.15060i
\(136\) −1.21762 + 3.10244i −0.104410 + 0.266032i
\(137\) 4.21693 + 2.03077i 0.360277 + 0.173500i 0.605261 0.796027i \(-0.293069\pi\)
−0.244985 + 0.969527i \(0.578783\pi\)
\(138\) −22.6933 1.92243i −1.93178 0.163648i
\(139\) −6.83857 4.66246i −0.580040 0.395464i 0.237457 0.971398i \(-0.423686\pi\)
−0.817496 + 0.575934i \(0.804639\pi\)
\(140\) 6.98078 + 10.3553i 0.589984 + 0.875186i
\(141\) 2.04924 + 14.5535i 0.172577 + 1.22562i
\(142\) −0.836448 0.570281i −0.0701932 0.0478569i
\(143\) 0.604358 0.186420i 0.0505389 0.0155892i
\(144\) −12.1641 6.15180i −1.01368 0.512650i
\(145\) 1.41363 0.213070i 0.117395 0.0176945i
\(146\) 7.36069 12.7491i 0.609175 1.05512i
\(147\) −8.06532 9.05265i −0.665217 0.746650i
\(148\) 4.36908 + 7.56748i 0.359137 + 0.622043i
\(149\) −10.7102 13.4302i −0.877417 1.10025i −0.994249 0.107094i \(-0.965845\pi\)
0.116832 0.993152i \(-0.462726\pi\)
\(150\) −8.39834 4.95815i −0.685721 0.404832i
\(151\) −3.07331 + 13.4651i −0.250102 + 1.09577i 0.681365 + 0.731944i \(0.261387\pi\)
−0.931467 + 0.363826i \(0.881470\pi\)
\(152\) 0.0391779 0.522793i 0.00317775 0.0424041i
\(153\) −3.27091 15.7335i −0.264438 1.27198i
\(154\) 0.591080 + 0.235571i 0.0476305 + 0.0189828i
\(155\) −2.11235 + 28.1874i −0.169668 + 2.26407i
\(156\) 8.35894 12.0081i 0.669251 0.961415i
\(157\) −17.3208 + 11.8091i −1.38235 + 0.942468i −0.382518 + 0.923948i \(0.624943\pi\)
−0.999828 + 0.0185197i \(0.994105\pi\)
\(158\) −0.454221 + 0.0684627i −0.0361358 + 0.00544660i
\(159\) −0.344878 + 0.364525i −0.0273506 + 0.0289087i
\(160\) 20.8007 3.13520i 1.64444 0.247860i
\(161\) −14.2464 + 11.2392i −1.12277 + 0.885776i
\(162\) 17.1486 1.90704i 1.34732 0.149831i
\(163\) 13.0766 8.91544i 1.02423 0.698311i 0.0700543 0.997543i \(-0.477683\pi\)
0.954180 + 0.299232i \(0.0967304\pi\)
\(164\) −1.79422 7.86100i −0.140105 0.613841i
\(165\) −0.610831 + 0.0398139i −0.0475531 + 0.00309950i
\(166\) −2.78192 −0.215919
\(167\) −15.8701 + 14.7253i −1.22807 + 1.13948i −0.242507 + 0.970150i \(0.577970\pi\)
−0.985560 + 0.169329i \(0.945840\pi\)
\(168\) −2.73682 + 0.799551i −0.211150 + 0.0616867i
\(169\) −9.10369 8.44699i −0.700284 0.649769i
\(170\) 21.2086 + 19.6787i 1.62662 + 1.50929i
\(171\) 1.22115 + 2.21329i 0.0933837 + 0.169255i
\(172\) 2.55551 + 0.385182i 0.194856 + 0.0293698i
\(173\) 14.9263 4.60415i 1.13483 0.350047i 0.330248 0.943894i \(-0.392868\pi\)
0.804578 + 0.593847i \(0.202392\pi\)
\(174\) 0.267306 1.66366i 0.0202644 0.126122i
\(175\) −7.58481 + 1.68933i −0.573357 + 0.127701i
\(176\) 0.417832 0.387691i 0.0314952 0.0292233i
\(177\) −4.22357 + 8.55674i −0.317463 + 0.643164i
\(178\) 1.65358 0.123941
\(179\) −2.34915 + 2.17969i −0.175583 + 0.162918i −0.763069 0.646317i \(-0.776308\pi\)
0.587486 + 0.809235i \(0.300118\pi\)
\(180\) −10.5657 + 9.42829i −0.787517 + 0.702743i
\(181\) −1.37004 + 1.71797i −0.101834 + 0.127696i −0.830137 0.557559i \(-0.811738\pi\)
0.728303 + 0.685255i \(0.240309\pi\)
\(182\) −3.67864 25.3071i −0.272679 1.87589i
\(183\) −1.61160 + 5.05003i −0.119133 + 0.373309i
\(184\) 0.949567 + 4.16032i 0.0700030 + 0.306703i
\(185\) −14.5290 + 2.18990i −1.06820 + 0.161005i
\(186\) 30.8937 + 12.4725i 2.26524 + 0.914527i
\(187\) 0.664455 + 0.100151i 0.0485898 + 0.00732373i
\(188\) −12.8090 + 6.16847i −0.934190 + 0.449882i
\(189\) 8.93604 10.4474i 0.650001 0.759933i
\(190\) −4.10034 1.97462i −0.297470 0.143254i
\(191\) −8.20371 5.59319i −0.593599 0.404709i 0.228921 0.973445i \(-0.426480\pi\)
−0.822520 + 0.568736i \(0.807433\pi\)
\(192\) 1.43629 8.93918i 0.103655 0.645130i
\(193\) −0.652715 + 8.70988i −0.0469835 + 0.626951i 0.923160 + 0.384417i \(0.125598\pi\)
−0.970143 + 0.242534i \(0.922022\pi\)
\(194\) −21.0271 26.3671i −1.50966 1.89305i
\(195\) 13.6607 + 20.4607i 0.978260 + 1.46522i
\(196\) 5.97046 10.0948i 0.426462 0.721058i
\(197\) −19.1338 −1.36323 −0.681614 0.731712i \(-0.738722\pi\)
−0.681614 + 0.731712i \(0.738722\pi\)
\(198\) −0.174178 + 0.700148i −0.0123783 + 0.0497574i
\(199\) 18.4859 + 12.6035i 1.31043 + 0.893439i 0.998395 0.0566304i \(-0.0180357\pi\)
0.312039 + 0.950069i \(0.398988\pi\)
\(200\) −0.406631 + 1.78157i −0.0287532 + 0.125976i
\(201\) −0.234117 + 24.1049i −0.0165133 + 1.70023i
\(202\) −0.642612 8.57506i −0.0452140 0.603339i
\(203\) −0.750453 1.11323i −0.0526715 0.0781333i
\(204\) 13.5371 7.64132i 0.947787 0.535000i
\(205\) 13.4067 + 2.02073i 0.936364 + 0.141134i
\(206\) 1.87475 + 25.0168i 0.130620 + 1.74301i
\(207\) −14.8084 14.2854i −1.02925 0.992901i
\(208\) −21.8905 6.75234i −1.51784 0.468190i
\(209\) −0.104520 + 0.0157538i −0.00722979 + 0.00108972i
\(210\) −2.21875 + 24.6515i −0.153108 + 1.70111i
\(211\) −9.52226 1.43525i −0.655539 0.0988066i −0.187153 0.982331i \(-0.559926\pi\)
−0.468386 + 0.883524i \(0.655164\pi\)
\(212\) −0.437349 0.210616i −0.0300373 0.0144652i
\(213\) −0.261087 0.876558i −0.0178894 0.0600608i
\(214\) −10.9900 −0.751263
\(215\) −2.17281 + 3.76341i −0.148184 + 0.256662i
\(216\) −1.31729 2.95244i −0.0896299 0.200888i
\(217\) 24.7611 9.56827i 1.68089 0.649537i
\(218\) 12.5780 + 11.6707i 0.851892 + 0.790441i
\(219\) 12.4273 4.73858i 0.839757 0.320204i
\(220\) −0.216329 0.551197i −0.0145849 0.0371617i
\(221\) −9.86662 25.1397i −0.663701 1.69108i
\(222\) −2.74733 + 17.0989i −0.184389 + 1.14760i
\(223\) −9.68406 8.98549i −0.648493 0.601713i 0.285770 0.958298i \(-0.407751\pi\)
−0.934263 + 0.356585i \(0.883941\pi\)
\(224\) −11.0425 16.3805i −0.737809 1.09447i
\(225\) −3.05914 8.26299i −0.203943 0.550866i
\(226\) −13.2442 + 22.9397i −0.880993 + 1.52592i
\(227\) −24.9145 −1.65364 −0.826818 0.562469i \(-0.809852\pi\)
−0.826818 + 0.562469i \(0.809852\pi\)
\(228\) −1.68051 + 1.77624i −0.111294 + 0.117635i
\(229\) 17.4960 + 8.42562i 1.15617 + 0.556781i 0.910881 0.412670i \(-0.135404\pi\)
0.245286 + 0.969451i \(0.421118\pi\)
\(230\) 36.6303 + 5.52113i 2.41533 + 0.364053i
\(231\) 0.279949 + 0.502088i 0.0184193 + 0.0330350i
\(232\) −0.312195 + 0.0470559i −0.0204966 + 0.00308937i
\(233\) 14.6695 + 4.52495i 0.961032 + 0.296439i 0.735294 0.677749i \(-0.237044\pi\)
0.225739 + 0.974188i \(0.427520\pi\)
\(234\) 27.8697 8.00726i 1.82190 0.523451i
\(235\) −1.78646 23.8387i −0.116536 1.55507i
\(236\) −9.12749 1.37575i −0.594149 0.0895535i
\(237\) −0.357369 0.210981i −0.0232136 0.0137047i
\(238\) 8.14485 25.9209i 0.527952 1.68020i
\(239\) 0.174779 + 2.33226i 0.0113055 + 0.150862i 1.00000 0.000914828i \(0.000291199\pi\)
−0.988694 + 0.149947i \(0.952090\pi\)
\(240\) 19.0929 + 11.2719i 1.23244 + 0.727601i
\(241\) −2.60855 + 11.4288i −0.168031 + 0.736194i 0.818752 + 0.574148i \(0.194667\pi\)
−0.986783 + 0.162046i \(0.948191\pi\)
\(242\) 17.3993 + 11.8627i 1.11847 + 0.762561i
\(243\) 13.1057 + 8.44035i 0.840734 + 0.541449i
\(244\) −5.12776 −0.328271
\(245\) 12.1332 + 15.5467i 0.775161 + 0.993243i
\(246\) 7.07313 14.3298i 0.450966 0.913635i
\(247\) 2.64870 + 3.32136i 0.168533 + 0.211333i
\(248\) 0.466507 6.22511i 0.0296232 0.395295i
\(249\) −1.94969 1.58604i −0.123556 0.100511i
\(250\) −9.20626 6.27672i −0.582255 0.396975i
\(251\) 17.9137 + 8.62676i 1.13070 + 0.544516i 0.903182 0.429258i \(-0.141225\pi\)
0.227518 + 0.973774i \(0.426939\pi\)
\(252\) 12.2556 + 5.16246i 0.772033 + 0.325205i
\(253\) 0.775167 0.373301i 0.0487344 0.0234692i
\(254\) 38.2394 + 5.76367i 2.39935 + 0.361645i
\(255\) 3.64454 + 25.8832i 0.228230 + 1.62087i
\(256\) −19.6495 + 2.96168i −1.22809 + 0.185105i
\(257\) 5.52123 + 24.1901i 0.344405 + 1.50894i 0.789667 + 0.613536i \(0.210254\pi\)
−0.445262 + 0.895401i \(0.646889\pi\)
\(258\) 3.44721 + 3.78834i 0.214614 + 0.235852i
\(259\) 7.71305 + 11.4416i 0.479266 + 0.710946i
\(260\) −14.8379 + 18.6061i −0.920205 + 1.15390i
\(261\) 1.13584 1.01357i 0.0703065 0.0627382i
\(262\) −23.6792 + 21.9711i −1.46290 + 1.35738i
\(263\) −7.63981 −0.471091 −0.235545 0.971863i \(-0.575688\pi\)
−0.235545 + 0.971863i \(0.575688\pi\)
\(264\) 0.134900 0.00879278i 0.00830254 0.000541158i
\(265\) 0.598340 0.555178i 0.0367557 0.0341043i
\(266\) −0.0224425 + 4.27389i −0.00137604 + 0.262049i
\(267\) 1.15890 + 0.942751i 0.0709236 + 0.0576954i
\(268\) −22.2825 + 6.87325i −1.36112 + 0.419850i
\(269\) 17.1716 + 2.58820i 1.04697 + 0.157805i 0.649928 0.759996i \(-0.274799\pi\)
0.397041 + 0.917801i \(0.370037\pi\)
\(270\) −28.0359 + 1.28111i −1.70621 + 0.0779657i
\(271\) −11.7712 10.9221i −0.715049 0.663468i 0.236267 0.971688i \(-0.424076\pi\)
−0.951315 + 0.308220i \(0.900267\pi\)
\(272\) −17.8419 16.5549i −1.08182 1.00379i
\(273\) 11.8501 19.8336i 0.717201 1.20038i
\(274\) −6.57775 + 6.10326i −0.397376 + 0.368711i
\(275\) 0.368435 0.0222175
\(276\) 8.80955 17.8477i 0.530272 1.07431i
\(277\) 2.75504 + 12.0706i 0.165535 + 0.725254i 0.987746 + 0.156072i \(0.0498831\pi\)
−0.822211 + 0.569183i \(0.807260\pi\)
\(278\) 13.1106 8.93863i 0.786319 0.536103i
\(279\) 14.5407 + 26.3546i 0.870532 + 1.57781i
\(280\) 4.52674 1.00822i 0.270525 0.0602527i
\(281\) 12.9525 1.95228i 0.772683 0.116463i 0.249146 0.968466i \(-0.419850\pi\)
0.523537 + 0.852003i \(0.324612\pi\)
\(282\) −27.4078 6.53634i −1.63211 0.389233i
\(283\) −2.51935 + 0.379732i −0.149760 + 0.0225727i −0.223494 0.974705i \(-0.571746\pi\)
0.0737343 + 0.997278i \(0.476508\pi\)
\(284\) 0.731001 0.498388i 0.0433769 0.0295739i
\(285\) −1.74791 3.72160i −0.103537 0.220449i
\(286\) −0.0906112 + 1.20912i −0.00535795 + 0.0714969i
\(287\) −3.68908 12.1865i −0.217759 0.719348i
\(288\) 16.7132 14.9141i 0.984835 0.878821i
\(289\) 0.873856 11.6608i 0.0514033 0.685930i
\(290\) −0.609873 + 2.67203i −0.0358130 + 0.156907i
\(291\) 0.295911 30.4673i 0.0173466 1.78602i
\(292\) 8.02152 + 10.0587i 0.469424 + 0.588639i
\(293\) −0.203357 0.352225i −0.0118803 0.0205772i 0.860024 0.510253i \(-0.170448\pi\)
−0.871904 + 0.489676i \(0.837115\pi\)
\(294\) 21.8046 8.05297i 1.27167 0.469659i
\(295\) 7.76057 13.4417i 0.451838 0.782606i
\(296\) 3.20870 0.483633i 0.186502 0.0281106i
\(297\) −0.521244 + 0.391390i −0.0302456 + 0.0227108i
\(298\) 31.4695 9.70705i 1.82298 0.562314i
\(299\) −28.5705 19.4790i −1.65227 1.12650i
\(300\) 6.71502 5.24918i 0.387692 0.303061i
\(301\) 4.06797 + 0.326342i 0.234474 + 0.0188100i
\(302\) −21.8775 14.9158i −1.25891 0.858308i
\(303\) 4.43849 6.37614i 0.254985 0.366299i
\(304\) 3.44944 + 1.66116i 0.197839 + 0.0952743i
\(305\) 3.15007 8.02625i 0.180372 0.459582i
\(306\) 30.3694 + 5.18259i 1.73610 + 0.296269i
\(307\) 8.00003 + 10.0317i 0.456586 + 0.572541i 0.955830 0.293921i \(-0.0949602\pi\)
−0.499244 + 0.866462i \(0.666389\pi\)
\(308\) −0.380364 + 0.405642i −0.0216733 + 0.0231136i
\(309\) −12.9488 + 18.6017i −0.736634 + 1.05821i
\(310\) −48.8244 23.5126i −2.77304 1.33543i
\(311\) 16.2161 + 5.00200i 0.919529 + 0.283637i 0.718160 0.695878i \(-0.244985\pi\)
0.201369 + 0.979515i \(0.435461\pi\)
\(312\) −3.01692 4.51868i −0.170799 0.255820i
\(313\) −2.28367 3.95543i −0.129081 0.223574i 0.794240 0.607604i \(-0.207869\pi\)
−0.923321 + 0.384030i \(0.874536\pi\)
\(314\) −8.94310 39.1823i −0.504688 2.21118i
\(315\) −15.6094 + 16.0118i −0.879492 + 0.902164i
\(316\) 0.0893294 0.391378i 0.00502517 0.0220167i
\(317\) −5.39801 + 1.66507i −0.303183 + 0.0935194i −0.442614 0.896712i \(-0.645949\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(318\) −0.408983 0.870796i −0.0229346 0.0488318i
\(319\) 0.0232559 + 0.0592552i 0.00130208 + 0.00331765i
\(320\) −3.27696 + 14.3573i −0.183188 + 0.802599i
\(321\) −7.70228 6.26570i −0.429899 0.349717i
\(322\) −10.0795 33.2966i −0.561706 1.85554i
\(323\) 1.00436 + 4.40037i 0.0558838 + 0.244843i
\(324\) −3.92387 + 14.5597i −0.217993 + 0.808871i
\(325\) −7.40384 12.8238i −0.410691 0.711338i
\(326\) 6.75172 + 29.5812i 0.373943 + 1.63835i
\(327\) 2.16145 + 15.3504i 0.119528 + 0.848879i
\(328\) −2.96083 0.446273i −0.163484 0.0246413i
\(329\) −19.5010 + 11.1228i −1.07513 + 0.613220i
\(330\) 0.356782 1.11799i 0.0196402 0.0615433i
\(331\) −26.1610 + 24.2738i −1.43794 + 1.33421i −0.586280 + 0.810109i \(0.699408\pi\)
−0.851656 + 0.524101i \(0.824401\pi\)
\(332\) 0.888222 2.26315i 0.0487475 0.124207i
\(333\) −11.6740 + 10.4173i −0.639729 + 0.570864i
\(334\) −15.1635 38.6360i −0.829710 2.11407i
\(335\) 2.93015 39.1002i 0.160091 2.13627i
\(336\) 1.86654 20.7383i 0.101828 1.13136i
\(337\) −0.103588 1.38229i −0.00564280 0.0752979i 0.993671 0.112326i \(-0.0358300\pi\)
−0.999314 + 0.0370279i \(0.988211\pi\)
\(338\) 21.4511 10.3303i 1.16678 0.561893i
\(339\) −22.3606 + 8.52622i −1.21446 + 0.463081i
\(340\) −22.7806 + 10.9706i −1.23545 + 0.594962i
\(341\) −1.24456 + 0.187587i −0.0673967 + 0.0101584i
\(342\) −4.80520 + 0.629077i −0.259836 + 0.0340166i
\(343\) 8.29749 16.5575i 0.448022 0.894022i
\(344\) 0.479858 0.831138i 0.0258722 0.0448120i
\(345\) 22.5243 + 24.7533i 1.21267 + 1.33268i
\(346\) −2.23790 + 29.8627i −0.120310 + 1.60543i
\(347\) 12.2445 + 11.3613i 0.657322 + 0.609905i 0.936640 0.350293i \(-0.113918\pi\)
−0.279319 + 0.960199i \(0.590109\pi\)
\(348\) 1.26808 + 0.748640i 0.0679762 + 0.0401313i
\(349\) 2.54306 1.73383i 0.136127 0.0928099i −0.493342 0.869835i \(-0.664225\pi\)
0.629469 + 0.777026i \(0.283272\pi\)
\(350\) 2.29768 14.7193i 0.122816 0.786777i
\(351\) 24.0974 + 10.2774i 1.28622 + 0.548567i
\(352\) 0.342198 + 0.871907i 0.0182392 + 0.0464728i
\(353\) 19.8394 + 9.55415i 1.05594 + 0.508516i 0.879551 0.475804i \(-0.157843\pi\)
0.176393 + 0.984320i \(0.443557\pi\)
\(354\) −12.3123 13.5307i −0.654392 0.719151i
\(355\) 0.331038 + 1.45037i 0.0175697 + 0.0769777i
\(356\) −0.527963 + 1.34523i −0.0279820 + 0.0712969i
\(357\) 20.4865 13.5229i 1.08426 0.715708i
\(358\) −2.24455 5.71903i −0.118628 0.302260i
\(359\) −14.4616 + 9.85974i −0.763253 + 0.520377i −0.881258 0.472636i \(-0.843303\pi\)
0.118005 + 0.993013i \(0.462350\pi\)
\(360\) 1.82575 + 4.93150i 0.0962253 + 0.259913i
\(361\) 9.14501 + 15.8396i 0.481316 + 0.833664i
\(362\) −2.10634 3.64829i −0.110707 0.191750i
\(363\) 5.43098 + 18.2337i 0.285052 + 0.957019i
\(364\) 21.7624 + 5.08751i 1.14066 + 0.266658i
\(365\) −20.6721 + 6.37651i −1.08203 + 0.333762i
\(366\) −7.88361 6.41321i −0.412083 0.335224i
\(367\) −4.16945 + 5.22833i −0.217644 + 0.272916i −0.878653 0.477461i \(-0.841557\pi\)
0.661009 + 0.750378i \(0.270128\pi\)
\(368\) −30.8156 4.64470i −1.60637 0.242122i
\(369\) 13.1269 6.01036i 0.683361 0.312887i
\(370\) 6.26818 27.4627i 0.325867 1.42772i
\(371\) −0.712069 0.283790i −0.0369688 0.0147337i
\(372\) −20.0105 + 21.1505i −1.03750 + 1.09660i
\(373\) −32.6579 −1.69096 −0.845480 0.534007i \(-0.820686\pi\)
−0.845480 + 0.534007i \(0.820686\pi\)
\(374\) −0.644124 + 1.11566i −0.0333069 + 0.0576892i
\(375\) −2.87362 9.64772i −0.148393 0.498206i
\(376\) 0.394536 + 5.26471i 0.0203466 + 0.271507i
\(377\) 1.59511 2.00021i 0.0821524 0.103016i
\(378\) 12.3857 + 23.2649i 0.637051 + 1.19662i
\(379\) 8.64261 + 10.8375i 0.443941 + 0.556685i 0.952577 0.304297i \(-0.0984215\pi\)
−0.508636 + 0.860982i \(0.669850\pi\)
\(380\) 2.91557 2.70525i 0.149565 0.138776i
\(381\) 23.5138 + 25.8407i 1.20465 + 1.32386i
\(382\) 15.7277 10.7230i 0.804701 0.548636i
\(383\) 14.2488 17.8674i 0.728079 0.912982i −0.270686 0.962668i \(-0.587251\pi\)
0.998765 + 0.0496857i \(0.0158220\pi\)
\(384\) −7.32629 4.32524i −0.373868 0.220722i
\(385\) −0.401269 0.844561i −0.0204506 0.0430428i
\(386\) −15.0867 7.26537i −0.767892 0.369797i
\(387\) 0.256118 + 4.62037i 0.0130192 + 0.234867i
\(388\) 28.1639 8.68740i 1.42980 0.441036i
\(389\) −8.27647 + 3.98574i −0.419634 + 0.202085i −0.631771 0.775155i \(-0.717672\pi\)
0.212138 + 0.977240i \(0.431957\pi\)
\(390\) −46.0827 + 10.0482i −2.33349 + 0.508812i
\(391\) −18.3694 31.8168i −0.928982 1.60904i
\(392\) −2.67958 3.43345i −0.135339 0.173415i
\(393\) −29.1217 + 1.89814i −1.46899 + 0.0957487i
\(394\) 13.4016 34.1467i 0.675162 1.72029i
\(395\) 0.557729 + 0.380253i 0.0280624 + 0.0191326i
\(396\) −0.513974 0.365244i −0.0258282 0.0183542i
\(397\) −0.0445092 + 0.593934i −0.00223385 + 0.0298087i −0.998209 0.0598174i \(-0.980948\pi\)
0.995975 + 0.0896261i \(0.0285672\pi\)
\(398\) −35.4403 + 24.1628i −1.77646 + 1.21117i
\(399\) −2.45239 + 2.98253i −0.122773 + 0.149313i
\(400\) −11.0263 7.51759i −0.551314 0.375879i
\(401\) 9.63564 12.0827i 0.481181 0.603382i −0.480688 0.876892i \(-0.659613\pi\)
0.961869 + 0.273510i \(0.0881845\pi\)
\(402\) −42.8543 17.3012i −2.13738 0.862907i
\(403\) 31.5391 + 39.5488i 1.57108 + 1.97007i
\(404\) 7.18118 + 2.21510i 0.357277 + 0.110205i
\(405\) −20.3791 15.0861i −1.01265 0.749635i
\(406\) 2.51232 0.559558i 0.124684 0.0277704i
\(407\) −0.239021 0.609016i −0.0118478 0.0301878i
\(408\) −0.804887 5.71624i −0.0398479 0.282996i
\(409\) 1.36428 + 0.420825i 0.0674594 + 0.0208085i 0.328301 0.944573i \(-0.393524\pi\)
−0.260842 + 0.965382i \(0.584000\pi\)
\(410\) −12.9965 + 22.5106i −0.641850 + 1.11172i
\(411\) −8.08959 + 0.527278i −0.399030 + 0.0260087i
\(412\) −20.9503 6.46232i −1.03215 0.318376i
\(413\) −14.5295 1.16559i −0.714950 0.0573549i
\(414\) 35.8660 16.4218i 1.76272 0.807086i
\(415\) 2.99676 + 2.78059i 0.147105 + 0.136494i
\(416\) 23.4712 29.4319i 1.15077 1.44302i
\(417\) 14.2846 + 1.21010i 0.699519 + 0.0592588i
\(418\) 0.0450924 0.197563i 0.00220554 0.00966311i
\(419\) 29.5138 9.10379i 1.44184 0.444749i 0.527452 0.849585i \(-0.323148\pi\)
0.914389 + 0.404836i \(0.132671\pi\)
\(420\) −19.3461 9.67582i −0.943993 0.472132i
\(421\) −21.0336 6.48800i −1.02511 0.316206i −0.263791 0.964580i \(-0.584973\pi\)
−0.761322 + 0.648374i \(0.775449\pi\)
\(422\) 9.23090 15.9884i 0.449353 0.778302i
\(423\) −15.4820 20.2069i −0.752762 0.982491i
\(424\) −0.132142 + 0.122610i −0.00641737 + 0.00595444i
\(425\) −1.17570 15.6886i −0.0570298 0.761009i
\(426\) 1.74720 + 0.148011i 0.0846519 + 0.00717117i
\(427\) −8.07775 + 0.562706i −0.390910 + 0.0272312i
\(428\) 3.50894 8.94063i 0.169611 0.432162i
\(429\) −0.752856 + 0.795745i −0.0363482 + 0.0384189i
\(430\) −5.19441 6.51358i −0.250497 0.314113i
\(431\) 0.523492 + 6.98551i 0.0252157 + 0.336480i 0.995517 + 0.0945812i \(0.0301512\pi\)
−0.970301 + 0.241899i \(0.922230\pi\)
\(432\) 23.5854 1.07774i 1.13475 0.0518529i
\(433\) 7.06177 3.40077i 0.339367 0.163431i −0.256436 0.966561i \(-0.582548\pi\)
0.595803 + 0.803131i \(0.296834\pi\)
\(434\) −0.267232 + 50.8910i −0.0128275 + 2.44285i
\(435\) −1.95082 + 1.52497i −0.0935345 + 0.0731165i
\(436\) −13.5104 + 6.50624i −0.647029 + 0.311593i
\(437\) 4.23636 + 3.93077i 0.202653 + 0.188034i
\(438\) −0.247637 + 25.4970i −0.0118325 + 1.21829i
\(439\) 6.85038 17.4545i 0.326951 0.833057i −0.669009 0.743255i \(-0.733281\pi\)
0.995960 0.0898026i \(-0.0286236\pi\)
\(440\) −0.219888 −0.0104828
\(441\) 19.8728 + 6.78753i 0.946325 + 0.323216i
\(442\) 51.7757 2.46272
\(443\) −9.09024 + 23.1616i −0.431890 + 1.10044i 0.534911 + 0.844909i \(0.320345\pi\)
−0.966801 + 0.255530i \(0.917750\pi\)
\(444\) −13.0331 7.69442i −0.618525 0.365161i
\(445\) −1.78129 1.65279i −0.0844411 0.0783499i
\(446\) 22.8186 10.9888i 1.08049 0.520337i
\(447\) 27.5894 + 11.1385i 1.30493 + 0.526831i
\(448\) 13.4992 3.00661i 0.637776 0.142049i
\(449\) 31.2892 15.0681i 1.47663 0.711108i 0.489646 0.871921i \(-0.337126\pi\)
0.986985 + 0.160813i \(0.0514117\pi\)
\(450\) 16.8890 + 0.328096i 0.796155 + 0.0154666i
\(451\) 0.0451147 + 0.602014i 0.00212437 + 0.0283477i
\(452\) −14.4333 18.0987i −0.678884 0.851294i
\(453\) −6.82877 22.9265i −0.320844 1.07718i
\(454\) 17.4505 44.4631i 0.818992 2.08676i
\(455\) −21.3323 + 30.9384i −1.00007 + 1.45042i
\(456\) 0.386021 + 0.821906i 0.0180771 + 0.0384893i
\(457\) −0.240922 3.21487i −0.0112698 0.150386i −1.00000 0.000675406i \(-0.999785\pi\)
0.988730 0.149710i \(-0.0478340\pi\)
\(458\) −27.2910 + 25.3223i −1.27522 + 1.18323i
\(459\) 18.3294 + 20.9465i 0.855543 + 0.977701i
\(460\) −16.1870 + 28.0368i −0.754725 + 1.30722i
\(461\) −37.2862 11.5013i −1.73659 0.535668i −0.745229 0.666808i \(-0.767660\pi\)
−0.991364 + 0.131140i \(0.958136\pi\)
\(462\) −1.09212 + 0.147934i −0.0508099 + 0.00688251i
\(463\) 20.9117 6.45041i 0.971850 0.299776i 0.232125 0.972686i \(-0.425432\pi\)
0.739724 + 0.672910i \(0.234956\pi\)
\(464\) 0.513061 2.24787i 0.0238182 0.104355i
\(465\) −20.8131 44.3147i −0.965183 2.05504i
\(466\) −18.3501 + 23.0102i −0.850050 + 1.06593i
\(467\) −17.5712 16.3037i −0.813097 0.754444i 0.159436 0.987208i \(-0.449032\pi\)
−0.972533 + 0.232764i \(0.925223\pi\)
\(468\) −2.38426 + 25.2292i −0.110212 + 1.16622i
\(469\) −34.3474 + 13.2726i −1.58601 + 0.612874i
\(470\) 43.7944 + 13.5088i 2.02008 + 0.623113i
\(471\) 16.0711 32.5593i 0.740518 1.50025i
\(472\) −1.71390 + 2.96856i −0.0788886 + 0.136639i
\(473\) −0.184900 0.0570342i −0.00850172 0.00262243i
\(474\) 0.626829 0.489996i 0.0287912 0.0225063i
\(475\) 0.904132 + 2.30369i 0.0414844 + 0.105701i
\(476\) 18.4867 + 14.9022i 0.847338 + 0.683039i
\(477\) 0.209831 0.843463i 0.00960750 0.0386195i
\(478\) −4.28463 1.32163i −0.195975 0.0604501i
\(479\) −10.4343 13.0842i −0.476756 0.597834i 0.484055 0.875038i \(-0.339164\pi\)
−0.960811 + 0.277204i \(0.910592\pi\)
\(480\) −28.7052 + 22.4390i −1.31021 + 1.02420i
\(481\) −16.3943 + 20.5578i −0.747517 + 0.937356i
\(482\) −18.5691 12.6602i −0.845797 0.576655i
\(483\) 11.9191 29.0822i 0.542339 1.32329i
\(484\) −15.2059 + 10.3672i −0.691176 + 0.471236i
\(485\) −3.70355 + 49.4204i −0.168170 + 2.24407i
\(486\) −24.2423 + 17.4771i −1.09965 + 0.792777i
\(487\) 0.427223 + 0.291276i 0.0193593 + 0.0131990i 0.572961 0.819583i \(-0.305795\pi\)
−0.553602 + 0.832782i \(0.686747\pi\)
\(488\) −0.695684 + 1.77257i −0.0314921 + 0.0802407i
\(489\) −12.1331 + 24.5811i −0.548679 + 1.11160i
\(490\) −36.2433 + 10.7641i −1.63730 + 0.486271i
\(491\) −3.42033 5.92418i −0.154357 0.267355i 0.778468 0.627685i \(-0.215997\pi\)
−0.932825 + 0.360330i \(0.882664\pi\)
\(492\) 9.39928 + 10.3294i 0.423752 + 0.465687i
\(493\) 2.44898 1.17937i 0.110296 0.0531160i
\(494\) −7.78256 + 2.40060i −0.350154 + 0.108008i
\(495\) 0.887443 0.580125i 0.0398876 0.0260747i
\(496\) 41.0739 + 19.7802i 1.84427 + 0.888155i
\(497\) 1.09685 0.865328i 0.0492006 0.0388153i
\(498\) 4.19608 2.36857i 0.188031 0.106138i
\(499\) 2.42039 3.03508i 0.108352 0.135869i −0.724699 0.689066i \(-0.758021\pi\)
0.833050 + 0.553197i \(0.186592\pi\)
\(500\) 8.04566 5.48544i 0.359813 0.245316i
\(501\) 11.4002 35.7229i 0.509321 1.59598i
\(502\) −27.9425 + 25.9268i −1.24713 + 1.15717i
\(503\) 17.5710 + 22.0333i 0.783452 + 0.982417i 0.999981 + 0.00614110i \(0.00195479\pi\)
−0.216530 + 0.976276i \(0.569474\pi\)
\(504\) 3.44730 3.53617i 0.153555 0.157513i
\(505\) −7.87872 + 9.87960i −0.350598 + 0.439637i
\(506\) 0.123264 + 1.64485i 0.00547977 + 0.0731224i
\(507\) 20.9234 + 4.98990i 0.929240 + 0.221609i
\(508\) −16.8981 + 29.2684i −0.749732 + 1.29857i
\(509\) 11.3718 0.504045 0.252022 0.967721i \(-0.418904\pi\)
0.252022 + 0.967721i \(0.418904\pi\)
\(510\) −48.7445 11.6248i −2.15844 0.514755i
\(511\) 13.7401 + 14.9652i 0.607826 + 0.662019i
\(512\) 6.29124 27.5637i 0.278036 1.21816i
\(513\) −3.72634 2.29869i −0.164522 0.101490i
\(514\) −47.0374 7.08974i −2.07473 0.312715i
\(515\) 22.9853 28.8227i 1.01286 1.27008i
\(516\) −4.18254 + 1.59482i −0.184126 + 0.0702081i
\(517\) 1.01715 0.313750i 0.0447342 0.0137987i
\(518\) −25.8213 + 5.75105i −1.13452 + 0.252687i
\(519\) −18.5939 + 19.6531i −0.816181 + 0.862677i
\(520\) 4.41874 + 7.65348i 0.193775 + 0.335627i
\(521\) 1.89588 + 3.28377i 0.0830602 + 0.143864i 0.904563 0.426340i \(-0.140197\pi\)
−0.821503 + 0.570204i \(0.806864\pi\)
\(522\) 1.01328 + 2.73696i 0.0443501 + 0.119793i
\(523\) 22.9408 15.6408i 1.00313 0.683924i 0.0539151 0.998546i \(-0.482830\pi\)
0.949217 + 0.314621i \(0.101878\pi\)
\(524\) −10.3136 26.2786i −0.450551 1.14798i
\(525\) 10.0021 9.00591i 0.436529 0.393050i
\(526\) 5.35103 13.6342i 0.233316 0.594479i
\(527\) 11.9593 + 52.3970i 0.520954 + 2.28245i
\(528\) −0.300145 + 0.940519i −0.0130622 + 0.0409308i
\(529\) −21.6593 10.4306i −0.941709 0.453503i
\(530\) 0.571699 + 1.45667i 0.0248330 + 0.0632735i
\(531\) −0.914771 16.5025i −0.0396977 0.716147i
\(532\) −3.46974 1.38284i −0.150432 0.0599539i
\(533\) 20.0472 13.6680i 0.868342 0.592025i
\(534\) −2.49417 + 1.40789i −0.107933 + 0.0609253i
\(535\) 11.8388 + 10.9848i 0.511835 + 0.474913i
\(536\) −0.647116 + 8.63517i −0.0279512 + 0.372982i
\(537\) 1.68749 5.28781i 0.0728205 0.228186i
\(538\) −16.6461 + 28.8320i −0.717666 + 1.24303i
\(539\) −0.554674 + 0.680748i −0.0238915 + 0.0293219i
\(540\) 7.90919 23.2168i 0.340358 0.999094i
\(541\) −10.1532 + 1.53035i −0.436520 + 0.0657947i −0.363626 0.931545i \(-0.618461\pi\)
−0.0728935 + 0.997340i \(0.523223\pi\)
\(542\) 27.7365 13.3572i 1.19138 0.573740i
\(543\) 0.603771 3.75776i 0.0259103 0.161261i
\(544\) 36.0354 17.3537i 1.54500 0.744034i
\(545\) −1.88429 25.1441i −0.0807140 1.07705i
\(546\) 27.0955 + 35.0397i 1.15958 + 1.49956i
\(547\) −1.03593 + 13.8235i −0.0442931 + 0.591050i 0.930261 + 0.366898i \(0.119580\pi\)
−0.974554 + 0.224152i \(0.928039\pi\)
\(548\) −2.86497 7.29982i −0.122385 0.311833i
\(549\) −1.86883 8.98930i −0.0797598 0.383654i
\(550\) −0.258057 + 0.657518i −0.0110036 + 0.0280367i
\(551\) −0.313432 + 0.290822i −0.0133526 + 0.0123894i
\(552\) −4.97444 5.46671i −0.211726 0.232679i
\(553\) 0.0977719 0.626340i 0.00415768 0.0266347i
\(554\) −23.4712 3.53772i −0.997197 0.150303i
\(555\) 20.0502 15.6734i 0.851084 0.665298i
\(556\) 3.08578 + 13.5197i 0.130866 + 0.573363i
\(557\) 6.84289 + 11.8522i 0.289942 + 0.502195i 0.973796 0.227425i \(-0.0730305\pi\)
−0.683853 + 0.729620i \(0.739697\pi\)
\(558\) −57.2175 + 7.49068i −2.42221 + 0.317106i
\(559\) 1.73050 + 7.58180i 0.0731922 + 0.320676i
\(560\) −5.22358 + 33.4630i −0.220737 + 1.41407i
\(561\) −1.08749 + 0.414667i −0.0459141 + 0.0175073i
\(562\) −5.58804 + 24.4828i −0.235717 + 1.03274i
\(563\) 7.79770 + 19.8682i 0.328634 + 0.837346i 0.995725 + 0.0923692i \(0.0294440\pi\)
−0.667091 + 0.744976i \(0.732461\pi\)
\(564\) 14.0683 20.2099i 0.592384 0.850991i
\(565\) 37.1958 11.4734i 1.56484 0.482689i
\(566\) 1.08691 4.76207i 0.0456863 0.200165i
\(567\) −4.58353 + 23.3665i −0.192490 + 0.981299i
\(568\) −0.0731088 0.320310i −0.00306758 0.0134399i
\(569\) 1.84900 + 3.20257i 0.0775142 + 0.134259i 0.902177 0.431366i \(-0.141968\pi\)
−0.824663 + 0.565625i \(0.808635\pi\)
\(570\) 7.86592 0.512699i 0.329467 0.0214746i
\(571\) −33.7337 10.4055i −1.41171 0.435455i −0.507170 0.861846i \(-0.669309\pi\)
−0.904539 + 0.426391i \(0.859785\pi\)
\(572\) −0.954717 0.459768i −0.0399187 0.0192239i
\(573\) 17.1361 + 1.45166i 0.715872 + 0.0606441i
\(574\) 24.3323 + 1.95199i 1.01561 + 0.0814745i
\(575\) −12.5595 15.7491i −0.523767 0.656783i
\(576\) 5.44456 + 14.7062i 0.226856 + 0.612758i
\(577\) 10.9219 27.8286i 0.454685 1.15852i −0.501344 0.865248i \(-0.667161\pi\)
0.956029 0.293271i \(-0.0947439\pi\)
\(578\) 20.1981 + 9.72689i 0.840130 + 0.404585i
\(579\) −6.43122 13.6932i −0.267272 0.569070i
\(580\) −1.97903 1.34928i −0.0821748 0.0560258i
\(581\) 1.15086 3.66261i 0.0477459 0.151951i
\(582\) 54.1654 + 21.8678i 2.24523 + 0.906449i
\(583\) 0.0300291 + 0.0204735i 0.00124368 + 0.000847924i
\(584\) 4.56538 1.40823i 0.188917 0.0582731i
\(585\) −38.0255 19.2307i −1.57216 0.795092i
\(586\) 0.771023 0.116213i 0.0318507 0.00480072i
\(587\) −13.6172 + 23.5857i −0.562042 + 0.973486i 0.435276 + 0.900297i \(0.356651\pi\)
−0.997318 + 0.0731888i \(0.976682\pi\)
\(588\) −0.410600 + 20.3098i −0.0169328 + 0.837560i
\(589\) −4.22704 7.32145i −0.174172 0.301675i
\(590\) 18.5528 + 23.2644i 0.763806 + 0.957782i
\(591\) 28.8603 16.2909i 1.18715 0.670116i
\(592\) −5.27316 + 23.1032i −0.216726 + 0.949537i
\(593\) −2.03323 + 27.1315i −0.0834947 + 1.11416i 0.785343 + 0.619061i \(0.212487\pi\)
−0.868837 + 0.495098i \(0.835132\pi\)
\(594\) −0.333398 1.20436i −0.0136795 0.0494155i
\(595\) −34.6824 + 19.7818i −1.42184 + 0.810975i
\(596\) −2.15080 + 28.7004i −0.0881002 + 1.17562i
\(597\) −38.6139 3.27113i −1.58036 0.133878i
\(598\) 54.7739 37.3442i 2.23987 1.52712i
\(599\) −10.9161 + 1.64534i −0.446021 + 0.0672268i −0.368213 0.929742i \(-0.620030\pi\)
−0.0778079 + 0.996968i \(0.524792\pi\)
\(600\) −0.903518 3.03342i −0.0368860 0.123839i
\(601\) 45.4436 6.84952i 1.85368 0.279398i 0.874900 0.484303i \(-0.160927\pi\)
0.978782 + 0.204906i \(0.0656888\pi\)
\(602\) −3.43166 + 7.03122i −0.139864 + 0.286571i
\(603\) −20.1702 36.5578i −0.821395 1.48875i
\(604\) 19.1195 13.0354i 0.777960 0.530404i
\(605\) −6.88606 30.1698i −0.279958 1.22658i
\(606\) 8.27023 + 12.3870i 0.335955 + 0.503186i
\(607\) −20.1274 −0.816945 −0.408473 0.912771i \(-0.633938\pi\)
−0.408473 + 0.912771i \(0.633938\pi\)
\(608\) −4.61197 + 4.27928i −0.187040 + 0.173548i
\(609\) 2.07976 + 1.04018i 0.0842761 + 0.0421501i
\(610\) 12.1175 + 11.2434i 0.490623 + 0.455231i
\(611\) −31.3605 29.0983i −1.26871 1.17719i
\(612\) −13.9126 + 23.0514i −0.562384 + 0.931799i
\(613\) −9.43167 1.42159i −0.380941 0.0574177i −0.0442196 0.999022i \(-0.514080\pi\)
−0.336722 + 0.941604i \(0.609318\pi\)
\(614\) −23.5062 + 7.25070i −0.948633 + 0.292614i
\(615\) −21.9423 + 8.36672i −0.884800 + 0.337379i
\(616\) 0.0886192 + 0.186519i 0.00357057 + 0.00751506i
\(617\) 23.8277 22.1089i 0.959267 0.890070i −0.0347388 0.999396i \(-0.511060\pi\)
0.994006 + 0.109327i \(0.0348694\pi\)
\(618\) −24.1275 36.1377i −0.970551 1.45367i
\(619\) 25.6329 1.03027 0.515136 0.857108i \(-0.327741\pi\)
0.515136 + 0.857108i \(0.327741\pi\)
\(620\) 34.7169 32.2125i 1.39426 1.29369i
\(621\) 34.4989 + 8.93906i 1.38439 + 0.358712i
\(622\) −20.2846 + 25.4361i −0.813340 + 1.01990i
\(623\) −0.684078 + 2.17707i −0.0274070 + 0.0872226i
\(624\) 38.7674 8.45315i 1.55194 0.338397i
\(625\) 6.91128 + 30.2803i 0.276451 + 1.21121i
\(626\) 8.65846 1.30505i 0.346062 0.0521604i
\(627\) 0.144238 0.112752i 0.00576033 0.00450288i
\(628\) 34.7310 + 5.23486i 1.38592 + 0.208894i
\(629\) −25.1702 + 12.1213i −1.00360 + 0.483310i
\(630\) −17.6420 39.0719i −0.702876 1.55666i
\(631\) 20.6906 + 9.96404i 0.823678 + 0.396662i 0.797740 0.603001i \(-0.206029\pi\)
0.0259376 + 0.999664i \(0.491743\pi\)
\(632\) −0.123173 0.0839779i −0.00489956 0.00334046i
\(633\) 15.5848 5.94256i 0.619440 0.236196i
\(634\) 0.809323 10.7997i 0.0321423 0.428909i
\(635\) −35.4317 44.4299i −1.40606 1.76315i
\(636\) 0.838994 0.0546854i 0.0332683 0.00216842i
\(637\) 34.8407 + 5.62620i 1.38044 + 0.222918i
\(638\) −0.122037 −0.00483149
\(639\) 1.14012 + 1.09985i 0.0451026 + 0.0435096i
\(640\) 11.4338 + 7.79542i 0.451960 + 0.308141i
\(641\) 3.61855 15.8539i 0.142924 0.626192i −0.851823 0.523830i \(-0.824503\pi\)
0.994747 0.102362i \(-0.0326401\pi\)
\(642\) 16.5767 9.35709i 0.654230 0.369295i
\(643\) −1.51379 20.2001i −0.0596980 0.796615i −0.944052 0.329797i \(-0.893020\pi\)
0.884354 0.466817i \(-0.154600\pi\)
\(644\) 30.3057 + 2.43119i 1.19421 + 0.0958024i
\(645\) 0.0731000 7.52646i 0.00287831 0.296354i
\(646\) −8.55647 1.28968i −0.336650 0.0507418i
\(647\) 0.924961 + 12.3427i 0.0363640 + 0.485244i 0.985420 + 0.170137i \(0.0544211\pi\)
−0.949056 + 0.315106i \(0.897960\pi\)
\(648\) 4.50067 + 3.33173i 0.176803 + 0.130883i
\(649\) 0.660405 + 0.203708i 0.0259232 + 0.00799624i
\(650\) 28.0715 4.23109i 1.10105 0.165957i
\(651\) −29.2016 + 35.5142i −1.14450 + 1.39191i
\(652\) −26.2207 3.95214i −1.02688 0.154778i
\(653\) −29.8284 14.3646i −1.16727 0.562129i −0.253095 0.967441i \(-0.581449\pi\)
−0.914178 + 0.405312i \(0.867163\pi\)
\(654\) −28.9086 6.89426i −1.13042 0.269587i
\(655\) 47.4685 1.85475
\(656\) 10.9334 18.9372i 0.426877 0.739373i
\(657\) −14.7100 + 17.7282i −0.573893 + 0.691642i
\(658\) −6.19125 42.5926i −0.241360 1.66043i
\(659\) −13.7075 12.7187i −0.533970 0.495452i 0.366471 0.930429i \(-0.380566\pi\)
−0.900441 + 0.434977i \(0.856756\pi\)
\(660\) 0.795595 + 0.647206i 0.0309685 + 0.0251925i
\(661\) −1.69336 4.31462i −0.0658642 0.167819i 0.894152 0.447763i \(-0.147779\pi\)
−0.960016 + 0.279944i \(0.909684\pi\)
\(662\) −24.9962 63.6892i −0.971503 2.47535i
\(663\) 36.2866 + 29.5187i 1.40926 + 1.14641i
\(664\) −0.661826 0.614085i −0.0256838 0.0238311i
\(665\) 4.29603 4.58153i 0.166593 0.177664i
\(666\) −10.4144 28.1300i −0.403548 1.09002i
\(667\) 1.74015 3.01403i 0.0673789 0.116704i
\(668\) 36.2727 1.40343
\(669\) 22.2573 + 5.30801i 0.860515 + 0.205220i
\(670\) 67.7268 + 32.6155i 2.61651 + 1.26005i
\(671\) 0.379635 + 0.0572208i 0.0146557 + 0.00220899i
\(672\) 30.6025 + 15.3056i 1.18052 + 0.590428i
\(673\) −3.47658 + 0.524009i −0.134012 + 0.0201991i −0.215706 0.976458i \(-0.569205\pi\)
0.0816936 + 0.996657i \(0.473967\pi\)
\(674\) 2.53942 + 0.783306i 0.0978146 + 0.0301718i
\(675\) 11.6495 + 9.85880i 0.448389 + 0.379466i
\(676\) 1.55494 + 20.7492i 0.0598053 + 0.798046i
\(677\) −11.5319 1.73815i −0.443206 0.0668025i −0.0763514 0.997081i \(-0.524327\pi\)
−0.366854 + 0.930278i \(0.619565\pi\)
\(678\) 0.445578 45.8772i 0.0171123 1.76190i
\(679\) 43.4132 16.7759i 1.66605 0.643799i
\(680\) 0.701677 + 9.36323i 0.0269081 + 0.359064i
\(681\) 37.5796 21.2127i 1.44005 0.812871i
\(682\) 0.536934 2.35246i 0.0205603 0.0900804i
\(683\) 0.277375 + 0.189111i 0.0106135 + 0.00723613i 0.568615 0.822604i \(-0.307479\pi\)
−0.558002 + 0.829840i \(0.688432\pi\)
\(684\) 1.02246 4.10999i 0.0390946 0.157150i
\(685\) 13.1861 0.503814
\(686\) 23.7373 + 26.4050i 0.906294 + 1.00815i
\(687\) −33.5636 + 2.18767i −1.28053 + 0.0834648i
\(688\) 4.36984 + 5.47961i 0.166599 + 0.208908i
\(689\) 0.109159 1.45662i 0.00415861 0.0554928i
\(690\) −59.9518 + 22.8599i −2.28232 + 0.870262i
\(691\) 30.3936 + 20.7220i 1.15623 + 0.788302i 0.980574 0.196151i \(-0.0628442\pi\)
0.175652 + 0.984452i \(0.443797\pi\)
\(692\) −23.5794 11.3552i −0.896355 0.431662i
\(693\) −0.849744 0.518966i −0.0322791 0.0197139i
\(694\) −28.8519 + 13.8943i −1.09520 + 0.527421i
\(695\) −23.0574 3.47535i −0.874618 0.131827i
\(696\) 0.430833 0.336785i 0.0163307 0.0127658i
\(697\) 25.4908 3.84213i 0.965535 0.145531i
\(698\) 1.31304 + 5.75281i 0.0496994 + 0.217747i
\(699\) −25.9792 + 5.66471i −0.982625 + 0.214259i
\(700\) 11.2408 + 6.56884i 0.424863 + 0.248279i
\(701\) 15.8421 19.8654i 0.598350 0.750307i −0.386770 0.922176i \(-0.626409\pi\)
0.985120 + 0.171869i \(0.0549807\pi\)
\(702\) −35.2194 + 35.8064i −1.32927 + 1.35143i
\(703\) 3.22140 2.98903i 0.121498 0.112733i
\(704\) −0.655728 −0.0247137
\(705\) 22.9913 + 34.4358i 0.865901 + 1.29693i
\(706\) −30.9463 + 28.7140i −1.16468 + 1.08067i
\(707\) 11.5556 + 2.70140i 0.434593 + 0.101597i
\(708\) 14.9387 5.69620i 0.561430 0.214076i
\(709\) 19.5442 6.02860i 0.733999 0.226409i 0.0948499 0.995492i \(-0.469763\pi\)
0.639149 + 0.769083i \(0.279287\pi\)
\(710\) −2.82023 0.425081i −0.105841 0.0159530i
\(711\) 0.718668 + 0.0139613i 0.0269521 + 0.000523589i
\(712\) 0.393392 + 0.365015i 0.0147430 + 0.0136795i
\(713\) 50.4441 + 46.8053i 1.88915 + 1.75287i
\(714\) 9.78430 + 46.0322i 0.366168 + 1.72271i
\(715\) 1.30615 1.21193i 0.0488474 0.0453237i
\(716\) 5.36920 0.200657
\(717\) −2.24935 3.36904i −0.0840037 0.125819i
\(718\) −7.46684 32.7144i −0.278660 1.22089i
\(719\) 17.9830 12.2606i 0.670654 0.457244i −0.179514 0.983755i \(-0.557453\pi\)
0.850168 + 0.526511i \(0.176500\pi\)
\(720\) −38.3957 0.745900i −1.43092 0.0277980i
\(721\) −33.7122 7.88106i −1.25551 0.293506i
\(722\) −34.6731 + 5.22612i −1.29040 + 0.194496i
\(723\) −5.79609 19.4595i −0.215559 0.723706i
\(724\) 3.64049 0.548715i 0.135298 0.0203928i
\(725\) 1.23140 0.839551i 0.0457329 0.0311802i
\(726\) −36.3442 3.07885i −1.34886 0.114267i
\(727\) −1.66209 + 22.1790i −0.0616434 + 0.822574i 0.877616 + 0.479365i \(0.159133\pi\)
−0.939259 + 0.343209i \(0.888486\pi\)
\(728\) 4.71118 6.83267i 0.174608 0.253236i
\(729\) −26.9542 1.57247i −0.998303 0.0582396i
\(730\) 3.09937 41.3582i 0.114713 1.53074i
\(731\) −1.83859 + 8.05538i −0.0680026 + 0.297939i
\(732\) 7.73440 4.36586i 0.285872 0.161367i
\(733\) 11.5636 + 14.5004i 0.427113 + 0.535583i 0.948096 0.317984i \(-0.103006\pi\)
−0.520983 + 0.853567i \(0.674435\pi\)
\(734\) −6.41026 11.1029i −0.236607 0.409815i
\(735\) −31.5377 13.1193i −1.16329 0.483914i
\(736\) 25.6054 44.3498i 0.943826 1.63476i
\(737\) 1.72639 0.260212i 0.0635925 0.00958503i
\(738\) 1.53195 + 27.6364i 0.0563918 + 1.01731i
\(739\) −3.97194 + 1.22518i −0.146110 + 0.0450690i −0.366948 0.930242i \(-0.619597\pi\)
0.220837 + 0.975311i \(0.429121\pi\)
\(740\) 20.3402 + 13.8677i 0.747720 + 0.509787i
\(741\) −6.82300 2.75460i −0.250649 0.101193i
\(742\) 1.00520 1.07200i 0.0369021 0.0393545i
\(743\) −8.13412 5.54575i −0.298412 0.203454i 0.404853 0.914382i \(-0.367323\pi\)
−0.703265 + 0.710928i \(0.748275\pi\)
\(744\) 4.59651 + 9.78677i 0.168516 + 0.358800i
\(745\) −43.6022 20.9977i −1.59746 0.769297i
\(746\) 22.8740 58.2820i 0.837477 2.13386i
\(747\) 4.29117 + 0.732298i 0.157006 + 0.0267934i
\(748\) −0.701953 0.880221i −0.0256659 0.0321841i
\(749\) 4.54651 14.4692i 0.166126 0.528694i
\(750\) 19.2303 + 1.62907i 0.702190 + 0.0594851i
\(751\) 32.0321 + 15.4258i 1.16887 + 0.562897i 0.914648 0.404250i \(-0.132468\pi\)
0.254218 + 0.967147i \(0.418182\pi\)
\(752\) −36.8424 11.3644i −1.34350 0.414416i
\(753\) −34.3648 + 2.23989i −1.25232 + 0.0816263i
\(754\) 2.45238 + 4.24765i 0.0893104 + 0.154690i
\(755\) 8.65836 + 37.9347i 0.315110 + 1.38059i
\(756\) −22.8811 + 2.64791i −0.832177 + 0.0963036i
\(757\) −11.9373 + 52.3009i −0.433870 + 1.90091i 0.000139990 1.00000i \(0.499955\pi\)
−0.434010 + 0.900908i \(0.642902\pi\)
\(758\) −25.3943 + 7.83309i −0.922361 + 0.284511i
\(759\) −0.851382 + 1.22306i −0.0309032 + 0.0443941i
\(760\) −0.539601 1.37488i −0.0195734 0.0498722i
\(761\) −2.91765 + 12.7831i −0.105765 + 0.463386i 0.894114 + 0.447839i \(0.147806\pi\)
−0.999879 + 0.0155474i \(0.995051\pi\)
\(762\) −62.5853 + 23.8641i −2.26723 + 0.864506i
\(763\) −20.5689 + 11.7319i −0.744643 + 0.424722i
\(764\) 3.70178 + 16.2185i 0.133926 + 0.586766i
\(765\) −27.5346 35.9377i −0.995516 1.29933i
\(766\) 21.9066 + 37.9433i 0.791517 + 1.37095i
\(767\) −6.18079 27.0798i −0.223175 0.977795i
\(768\) 27.1165 21.1971i 0.978482 0.764885i
\(769\) 17.6255 + 2.65662i 0.635593 + 0.0958002i 0.458932 0.888471i \(-0.348232\pi\)
0.176661 + 0.984272i \(0.443470\pi\)
\(770\) 1.78828 0.124574i 0.0644451 0.00448932i
\(771\) −28.9237 31.7860i −1.04166 1.14475i
\(772\) 10.7275 9.95364i 0.386090 0.358239i
\(773\) 4.85154 12.3615i 0.174498 0.444613i −0.816690 0.577076i \(-0.804194\pi\)
0.991188 + 0.132464i \(0.0422888\pi\)
\(774\) −8.42501 2.77909i −0.302831 0.0998925i
\(775\) 10.7659 + 27.4310i 0.386721 + 0.985350i
\(776\) 0.817919 10.9144i 0.0293616 0.391803i
\(777\) −21.3755 10.6908i −0.766840 0.383530i
\(778\) −1.31609 17.5620i −0.0471842 0.629630i
\(779\) −3.65346 + 1.75942i −0.130899 + 0.0630376i
\(780\) 6.53901 40.6975i 0.234134 1.45721i
\(781\) −0.0596815 + 0.0287411i −0.00213557 + 0.00102844i
\(782\) 69.6472 10.4976i 2.49058 0.375394i
\(783\) −0.850260 + 2.49587i −0.0303858 + 0.0891953i
\(784\) 30.4900 9.05536i 1.08893 0.323406i
\(785\) −29.5298 + 51.1471i −1.05396 + 1.82552i
\(786\) 17.0097 53.3007i 0.606717 1.90117i
\(787\) −0.219783 + 2.93279i −0.00783440 + 0.104543i −0.999750 0.0223559i \(-0.992883\pi\)
0.991916 + 0.126899i \(0.0405023\pi\)
\(788\) 23.5002 + 21.8050i 0.837159 + 0.776770i
\(789\) 11.5234 6.50466i 0.410245 0.231572i
\(790\) −1.06925 + 0.729003i −0.0380422 + 0.0259367i
\(791\) −24.7228 26.9271i −0.879043 0.957417i
\(792\) −0.195989 + 0.128119i −0.00696418 + 0.00455251i
\(793\) −5.63728 14.3635i −0.200186 0.510065i
\(794\) −1.02877 0.495432i −0.0365098 0.0175822i
\(795\) −0.429812 + 1.34683i −0.0152439 + 0.0477673i
\(796\) −8.34145 36.5463i −0.295655 1.29535i
\(797\) −12.2282 + 31.1569i −0.433145 + 1.10363i 0.533110 + 0.846046i \(0.321023\pi\)
−0.966255 + 0.257589i \(0.917072\pi\)
\(798\) −3.60501 6.46559i −0.127616 0.228879i
\(799\) −16.6058 42.3109i −0.587471 1.49685i
\(800\) 18.1193 12.3535i 0.640614 0.436763i
\(801\) −2.55069 0.435281i −0.0901242 0.0153799i
\(802\) 14.8142 + 25.6589i 0.523107 + 0.906047i
\(803\) −0.481631 0.834210i −0.0169964 0.0294386i
\(804\) 27.7576 29.3389i 0.978936 1.03470i
\(805\) −22.4228 + 45.9426i −0.790298 + 1.61927i
\(806\) −92.6702 + 28.5850i −3.26417 + 1.00686i
\(807\) −28.1042 + 10.7163i −0.989314 + 0.377231i
\(808\) 1.73999 2.18188i 0.0612127 0.0767584i
\(809\) 41.7025 + 6.28563i 1.46618 + 0.220991i 0.833112 0.553105i \(-0.186557\pi\)
0.633068 + 0.774096i \(0.281795\pi\)
\(810\) 41.1969 25.8026i 1.44751 0.906609i
\(811\) 4.21781 18.4794i 0.148107 0.648901i −0.845303 0.534288i \(-0.820580\pi\)
0.993410 0.114613i \(-0.0365629\pi\)
\(812\) −0.346931 + 2.22249i −0.0121749 + 0.0779940i
\(813\) 27.0542 + 6.45200i 0.948831 + 0.226282i
\(814\) 1.25428 0.0439624
\(815\) 22.2939 38.6142i 0.780923 1.35260i
\(816\) 41.0067 + 9.77947i 1.43552 + 0.342350i
\(817\) −0.0971274 1.29608i −0.00339806 0.0453439i
\(818\) −1.70658 + 2.13998i −0.0596690 + 0.0748226i
\(819\) −0.987337 + 40.0052i −0.0345003 + 1.39789i
\(820\) −14.1633 17.7602i −0.494603 0.620212i
\(821\) 9.30745 8.63605i 0.324832 0.301400i −0.500852 0.865533i \(-0.666980\pi\)
0.825684 + 0.564133i \(0.190789\pi\)
\(822\) 4.72506 14.8062i 0.164806 0.516425i
\(823\) −13.3086 + 9.07364i −0.463908 + 0.316287i −0.772620 0.634868i \(-0.781054\pi\)
0.308712 + 0.951155i \(0.400102\pi\)
\(824\) −5.07625 + 6.36542i −0.176840 + 0.221750i
\(825\) −0.555725 + 0.313692i −0.0193479 + 0.0109213i
\(826\) 12.2568 25.1133i 0.426468 0.873803i
\(827\) −15.4610 7.44563i −0.537632 0.258910i 0.145305 0.989387i \(-0.453584\pi\)
−0.682937 + 0.730477i \(0.739298\pi\)
\(828\) 1.90804 + 34.4210i 0.0663088 + 1.19621i
\(829\) −27.5230 + 8.48972i −0.955913 + 0.294860i −0.733192 0.680022i \(-0.761970\pi\)
−0.222721 + 0.974882i \(0.571494\pi\)
\(830\) −7.06128 + 3.40053i −0.245100 + 0.118034i
\(831\) −14.4327 15.8609i −0.500664 0.550210i
\(832\) 13.1771 + 22.8234i 0.456834 + 0.791260i
\(833\) 30.7575 + 21.4467i 1.06568 + 0.743083i
\(834\) −12.1647 + 24.6450i −0.421229 + 0.853388i
\(835\) −22.2830 + 56.7761i −0.771134 + 1.96482i
\(836\) 0.146324 + 0.0997623i 0.00506074 + 0.00345035i
\(837\) −44.3711 27.3714i −1.53369 0.946094i
\(838\) −4.42499 + 59.0474i −0.152859 + 2.03976i
\(839\) −5.30253 + 3.61520i −0.183064 + 0.124811i −0.651385 0.758748i \(-0.725812\pi\)
0.468321 + 0.883558i \(0.344859\pi\)
\(840\) −5.96945 + 5.37488i −0.205966 + 0.185451i
\(841\) −23.7482 16.1912i −0.818903 0.558318i
\(842\) 26.3108 32.9927i 0.906731 1.13700i
\(843\) −17.8746 + 13.9727i −0.615634 + 0.481245i
\(844\) 10.0596 + 12.6144i 0.346267 + 0.434205i
\(845\) −33.4330 10.3127i −1.15013 0.354769i
\(846\) 46.9055 13.4764i 1.61264 0.463330i
\(847\) −22.8161 + 18.0001i −0.783972 + 0.618490i
\(848\) −0.480947 1.22543i −0.0165158 0.0420815i
\(849\) 3.47673 2.71778i 0.119321 0.0932741i
\(850\) 28.8217 + 8.89033i 0.988578 + 0.304936i
\(851\) −17.8850 + 30.9778i −0.613091 + 1.06190i
\(852\) −0.678262 + 1.37412i −0.0232369 + 0.0470767i
\(853\) 10.2712 + 3.16825i 0.351680 + 0.108479i 0.465562 0.885015i \(-0.345852\pi\)
−0.113882 + 0.993494i \(0.536329\pi\)
\(854\) 4.65355 14.8099i 0.159241 0.506784i
\(855\) 5.80508 + 4.12525i 0.198529 + 0.141080i
\(856\) −2.61456 2.42596i −0.0893638 0.0829175i
\(857\) 8.49965 10.6582i 0.290342 0.364078i −0.615172 0.788393i \(-0.710914\pi\)
0.905515 + 0.424315i \(0.139485\pi\)
\(858\) −0.892794 1.90092i −0.0304795 0.0648962i
\(859\) −8.40331 + 36.8173i −0.286717 + 1.25619i 0.602282 + 0.798283i \(0.294258\pi\)
−0.889000 + 0.457908i \(0.848599\pi\)
\(860\) 6.95744 2.14608i 0.237247 0.0731809i
\(861\) 15.9402 + 15.2405i 0.543241 + 0.519395i
\(862\) −12.8332 3.95851i −0.437099 0.134827i
\(863\) −5.55345 + 9.61886i −0.189042 + 0.327430i −0.944931 0.327270i \(-0.893871\pi\)
0.755889 + 0.654700i \(0.227205\pi\)
\(864\) −12.5111 + 36.7254i −0.425636 + 1.24942i
\(865\) 32.2591 29.9321i 1.09684 1.01772i
\(866\) 1.12294 + 14.9846i 0.0381590 + 0.509196i
\(867\) 8.61013 + 18.3325i 0.292415 + 0.622603i
\(868\) −41.3156 16.4661i −1.40234 0.558895i
\(869\) −0.0109809 + 0.0279790i −0.000372503 + 0.000949121i
\(870\) −1.35511 4.54958i −0.0459426 0.154245i
\(871\) −43.7495 54.8602i −1.48240 1.85887i
\(872\) 0.416139 + 5.55299i 0.0140923 + 0.188048i
\(873\) 25.4940 + 46.2070i 0.862842 + 1.56387i
\(874\) −9.98215 + 4.80715i −0.337651 + 0.162604i
\(875\) 12.0724 9.52412i 0.408121 0.321974i
\(876\) −20.6633 8.34223i −0.698148 0.281858i
\(877\) −22.2099 + 10.6957i −0.749975 + 0.361169i −0.769505 0.638640i \(-0.779497\pi\)
0.0195303 + 0.999809i \(0.493783\pi\)
\(878\) 26.3516 + 24.4507i 0.889323 + 0.825171i
\(879\) 0.606622 + 0.358133i 0.0204609 + 0.0120795i
\(880\) 0.586670 1.49481i 0.0197766 0.0503901i
\(881\) −10.7830 −0.363287 −0.181643 0.983364i \(-0.558142\pi\)
−0.181643 + 0.983364i \(0.558142\pi\)
\(882\) −26.0324 + 30.7115i −0.876556 + 1.03411i
\(883\) −18.1439 −0.610590 −0.305295 0.952258i \(-0.598755\pi\)
−0.305295 + 0.952258i \(0.598755\pi\)
\(884\) −16.5312 + 42.1207i −0.556003 + 1.41667i
\(885\) −0.261090 + 26.8821i −0.00877645 + 0.903633i
\(886\) −34.9677 32.4453i −1.17476 1.09002i
\(887\) 34.0549 16.4000i 1.14345 0.550657i 0.236390 0.971658i \(-0.424036\pi\)
0.907060 + 0.421002i \(0.138321\pi\)
\(888\) −4.42803 + 3.46142i −0.148595 + 0.116158i
\(889\) −23.4077 + 47.9608i −0.785071 + 1.60855i
\(890\) 4.19725 2.02129i 0.140692 0.0677538i
\(891\) 0.452977 1.03415i 0.0151753 0.0346452i
\(892\) 1.65407 + 22.0720i 0.0553822 + 0.739025i
\(893\) 4.45783 + 5.58994i 0.149176 + 0.187060i
\(894\) −39.2019 + 41.4352i −1.31111 + 1.38580i
\(895\) −3.29840 + 8.40418i −0.110253 + 0.280921i
\(896\) 2.00438 12.8403i 0.0669617 0.428966i
\(897\) 59.6788 + 5.05561i 1.99262 + 0.168802i
\(898\) 4.97550 + 66.3935i 0.166035 + 2.21558i
\(899\) −3.73216 + 3.46294i −0.124474 + 0.115495i
\(900\) −5.65930 + 13.6348i −0.188643 + 0.454494i
\(901\) 0.775972 1.34402i 0.0258514 0.0447759i
\(902\) −1.10597 0.341146i −0.0368247 0.0113589i
\(903\) −6.41373 + 2.97130i −0.213436 + 0.0988788i
\(904\) −8.21458 + 2.53386i −0.273213 + 0.0842750i
\(905\) −1.37753 + 6.03538i −0.0457908 + 0.200623i
\(906\) 45.6982 + 3.87127i 1.51822 + 0.128614i
\(907\) −5.36688 + 6.72985i −0.178204 + 0.223461i −0.862909 0.505360i \(-0.831360\pi\)
0.684705 + 0.728821i \(0.259931\pi\)
\(908\) 30.6001 + 28.3927i 1.01550 + 0.942245i
\(909\) −1.26601 + 13.3964i −0.0419909 + 0.444330i
\(910\) −40.2721 59.7398i −1.33501 1.98036i
\(911\) 18.0338 + 5.56269i 0.597486 + 0.184300i 0.578723 0.815524i \(-0.303551\pi\)
0.0187628 + 0.999824i \(0.494027\pi\)
\(912\) −6.61727 + 0.431313i −0.219120 + 0.0142822i
\(913\) −0.0910145 + 0.157642i −0.00301214 + 0.00521718i
\(914\) 5.90609 + 1.82179i 0.195356 + 0.0602594i
\(915\) 2.08230 + 14.7883i 0.0688388 + 0.488887i
\(916\) −11.8867 30.2868i −0.392748 1.00071i
\(917\) −19.1307 40.2648i −0.631751 1.32966i
\(918\) −50.2199 + 18.0399i −1.65750 + 0.595404i
\(919\) 38.4684 + 11.8659i 1.26896 + 0.391421i 0.854883 0.518822i \(-0.173629\pi\)
0.414074 + 0.910243i \(0.364105\pi\)
\(920\) 7.49572 + 9.39933i 0.247126 + 0.309887i
\(921\) −20.6079 8.31989i −0.679055 0.274150i
\(922\) 46.6412 58.4863i 1.53605 1.92614i
\(923\) 2.19969 + 1.49972i 0.0724037 + 0.0493640i
\(924\) 0.228348 0.935695i 0.00751210 0.0307821i
\(925\) −12.6561 + 8.62878i −0.416130 + 0.283713i
\(926\) −3.13529 + 41.8375i −0.103032 + 1.37487i
\(927\) 3.69345 39.0826i 0.121309 1.28364i
\(928\) 3.13052 + 2.13435i 0.102764 + 0.0700635i
\(929\) −19.1743 + 48.8554i −0.629090 + 1.60289i 0.158962 + 0.987285i \(0.449185\pi\)
−0.788052 + 0.615609i \(0.788910\pi\)
\(930\) 93.6628 6.10492i 3.07132 0.200188i
\(931\) −5.61763 1.79763i −0.184110 0.0589150i
\(932\) −12.8605 22.2750i −0.421259 0.729642i
\(933\) −28.7181 + 6.26192i −0.940190 + 0.205006i
\(934\) 41.4030 19.9386i 1.35475 0.652412i
\(935\) 1.80899 0.558000i 0.0591604 0.0182486i
\(936\) 8.39781 + 4.24705i 0.274491 + 0.138819i
\(937\) −4.48104 2.15795i −0.146389 0.0704972i 0.359255 0.933239i \(-0.383031\pi\)
−0.505644 + 0.862742i \(0.668745\pi\)
\(938\) 0.370691 70.5935i 0.0121035 2.30496i
\(939\) 6.81226 + 4.02178i 0.222310 + 0.131246i
\(940\) −24.9725 + 31.3146i −0.814514 + 1.02137i
\(941\) −7.92322 + 5.40196i −0.258290 + 0.176099i −0.685541 0.728034i \(-0.740434\pi\)
0.427251 + 0.904133i \(0.359482\pi\)
\(942\) 46.8497 + 51.4859i 1.52644 + 1.67750i
\(943\) 24.1957 22.4504i 0.787922 0.731084i
\(944\) −15.6077 19.5714i −0.507987 0.636995i
\(945\) 9.91160 37.4414i 0.322424 1.21797i
\(946\) 0.231291 0.290030i 0.00751993 0.00942969i
\(947\) 0.850999 + 11.3558i 0.0276538 + 0.369014i 0.993813 + 0.111067i \(0.0354268\pi\)
−0.966159 + 0.257947i \(0.916954\pi\)
\(948\) 0.198486 + 0.666387i 0.00644654 + 0.0216432i
\(949\) −19.3571 + 33.5275i −0.628359 + 1.08835i
\(950\) −4.74449 −0.153932
\(951\) 6.72437 7.10744i 0.218053 0.230475i
\(952\) 7.65951 4.36876i 0.248246 0.141592i
\(953\) 10.8533 47.5516i 0.351574 1.54035i −0.421973 0.906608i \(-0.638662\pi\)
0.773547 0.633739i \(-0.218481\pi\)
\(954\) 1.35830 + 0.965242i 0.0439764 + 0.0312509i
\(955\) −27.6602 4.16911i −0.895064 0.134909i
\(956\) 2.44319 3.06367i 0.0790185 0.0990861i
\(957\) −0.0855287 0.0695764i −0.00276475 0.00224909i
\(958\) 30.6588 9.45698i 0.990540 0.305541i
\(959\) −5.31424 11.1850i −0.171606 0.361183i
\(960\) −7.28128 24.4458i −0.235002 0.788984i
\(961\) −34.8331 60.3327i −1.12365 1.94622i
\(962\) −25.2052 43.6567i −0.812648 1.40755i
\(963\) 16.9524 + 2.89296i 0.546283 + 0.0932243i
\(964\) 16.2281 11.0642i 0.522673 0.356352i
\(965\) 8.98992 + 22.9059i 0.289396 + 0.737368i
\(966\) 43.5525 + 41.6407i 1.40128 + 1.33977i
\(967\) 16.5821 42.2506i 0.533246 1.35869i −0.369787 0.929117i \(-0.620569\pi\)
0.903033 0.429571i \(-0.141335\pi\)
\(968\) 1.52077 + 6.66292i 0.0488793 + 0.214154i
\(969\) −5.26146 5.78213i −0.169022 0.185749i
\(970\) −85.6029 41.2242i −2.74854 1.32363i
\(971\) −12.3424 31.4480i −0.396087 1.00921i −0.980283 0.197601i \(-0.936685\pi\)
0.584195 0.811613i \(-0.301410\pi\)
\(972\) −6.47783 25.3018i −0.207777 0.811556i
\(973\) 6.34464 + 20.9589i 0.203400 + 0.671913i
\(974\) −0.819051 + 0.558419i −0.0262441 + 0.0178929i
\(975\) 22.0859 + 13.0389i 0.707316 + 0.417580i
\(976\) −10.1939 9.45859i −0.326300 0.302762i
\(977\) −1.56972 + 20.9465i −0.0502200 + 0.670139i 0.914115 + 0.405455i \(0.132887\pi\)
−0.964335 + 0.264684i \(0.914732\pi\)
\(978\) −35.3698 38.8700i −1.13100 1.24293i
\(979\) 0.0540994 0.0937028i 0.00172902 0.00299476i
\(980\) 2.81510 32.9215i 0.0899250 1.05164i
\(981\) −16.3298 21.3133i −0.521370 0.680482i
\(982\) 12.9681 1.95462i 0.413828 0.0623746i
\(983\) 26.0665 12.5529i 0.831391 0.400377i 0.0307545 0.999527i \(-0.490209\pi\)
0.800637 + 0.599150i \(0.204495\pi\)
\(984\) 4.84590 1.84777i 0.154482 0.0589047i
\(985\) −48.5669 + 23.3886i −1.54747 + 0.745223i
\(986\) 0.389428 + 5.19655i 0.0124019 + 0.165492i
\(987\) 19.9441 33.3805i 0.634826 1.06251i
\(988\) 0.531904 7.09776i 0.0169221 0.225810i
\(989\) 3.86504 + 9.84796i 0.122901 + 0.313147i
\(990\) 0.413728 + 1.99008i 0.0131491 + 0.0632489i
\(991\) −2.22647 + 5.67296i −0.0707263 + 0.180208i −0.961866 0.273522i \(-0.911811\pi\)
0.891140 + 0.453729i \(0.149907\pi\)
\(992\) −54.9166 + 50.9552i −1.74360 + 1.61783i
\(993\) 18.7925 58.8870i 0.596361 1.86872i
\(994\) 0.776035 + 2.56356i 0.0246143 + 0.0813111i
\(995\) 62.3286 + 9.39452i 1.97595 + 0.297826i
\(996\) 0.587145 + 4.16985i 0.0186044 + 0.132127i
\(997\) −10.0311 43.9493i −0.317689 1.39189i −0.841594 0.540111i \(-0.818382\pi\)
0.523905 0.851777i \(-0.324475\pi\)
\(998\) 3.72120 + 6.44530i 0.117792 + 0.204022i
\(999\) 8.73885 25.6522i 0.276485 0.811601i
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.z.a.142.12 yes 648
9.4 even 3 441.2.y.a.436.12 yes 648
49.39 even 21 441.2.y.a.88.12 648
441.382 even 21 inner 441.2.z.a.382.12 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.12 648 49.39 even 21
441.2.y.a.436.12 yes 648 9.4 even 3
441.2.z.a.142.12 yes 648 1.1 even 1 trivial
441.2.z.a.382.12 yes 648 441.382 even 21 inner