Properties

Label 354.2.e.c.121.3
Level $354$
Weight $2$
Character 354.121
Analytic conductor $2.827$
Analytic rank $0$
Dimension $84$
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] = [354,2,Mod(7,354)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(354, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([0, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("354.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 354.e (of order \(29\), degree \(28\), 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: \(2.82670423155\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(3\) over \(\Q(\zeta_{29})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label 121.3
Character \(\chi\) \(=\) 354.121
Dual form 354.2.e.c.79.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.907575 - 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(1.95481 + 1.17617i) q^{5} +(0.994138 - 0.108119i) q^{6} +(0.00134066 - 0.0247270i) q^{7} +(0.267528 - 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +O(q^{10})\) \(q+(0.907575 - 0.419889i) q^{2} +(0.947653 + 0.319302i) q^{3} +(0.647386 - 0.762162i) q^{4} +(1.95481 + 1.17617i) q^{5} +(0.994138 - 0.108119i) q^{6} +(0.00134066 - 0.0247270i) q^{7} +(0.267528 - 0.963550i) q^{8} +(0.796093 + 0.605174i) q^{9} +(2.26799 + 0.246659i) q^{10} +(-0.227575 + 1.38814i) q^{11} +(0.856857 - 0.515554i) q^{12} +(-4.57419 + 3.47721i) q^{13} +(-0.00916584 - 0.0230045i) q^{14} +(1.47693 + 1.73877i) q^{15} +(-0.161782 - 0.986827i) q^{16} +(-0.409163 - 7.54657i) q^{17} +(0.976621 + 0.214970i) q^{18} +(3.23236 - 3.06186i) q^{19} +(2.16195 - 0.728444i) q^{20} +(0.00916584 - 0.0230045i) q^{21} +(0.376325 + 1.35540i) q^{22} +(-7.40499 + 1.62996i) q^{23} +(0.561187 - 0.827689i) q^{24} +(0.0958550 + 0.180802i) q^{25} +(-2.69138 + 5.07649i) q^{26} +(0.561187 + 0.827689i) q^{27} +(-0.0179780 - 0.0170297i) q^{28} +(4.18650 + 1.93688i) q^{29} +(2.07051 + 0.957922i) q^{30} +(7.48442 + 7.08962i) q^{31} +(-0.561187 - 0.827689i) q^{32} +(-0.658898 + 1.24281i) q^{33} +(-3.54007 - 6.67728i) q^{34} +(0.0317038 - 0.0467596i) q^{35} +(0.976621 - 0.214970i) q^{36} +(-2.90855 - 10.4757i) q^{37} +(1.64797 - 4.13610i) q^{38} +(-5.44503 + 1.83464i) q^{39} +(1.65626 - 1.56890i) q^{40} +(-9.28422 - 2.04361i) q^{41} +(-0.00134066 - 0.0247270i) q^{42} +(-0.628136 - 3.83146i) q^{43} +(0.910662 + 1.07211i) q^{44} +(0.844421 + 2.11934i) q^{45} +(-6.03619 + 4.58859i) q^{46} +(-4.50656 + 2.71151i) q^{47} +(0.161782 - 0.986827i) q^{48} +(6.95836 + 0.756767i) q^{49} +(0.162912 + 0.123843i) q^{50} +(2.02189 - 7.28218i) q^{51} +(-0.311072 + 5.73738i) q^{52} +(0.345271 - 0.0375504i) q^{53} +(0.856857 + 0.515554i) q^{54} +(-2.07755 + 2.44589i) q^{55} +(-0.0234670 - 0.00790696i) q^{56} +(4.04081 - 1.86948i) q^{57} +4.61284 q^{58} +(-6.76228 + 3.64302i) q^{59} +2.28137 q^{60} +(4.08821 - 1.89141i) q^{61} +(9.76953 + 3.29174i) q^{62} +(0.0160314 - 0.0188736i) q^{63} +(-0.856857 - 0.515554i) q^{64} +(-13.0315 + 1.41726i) q^{65} +(-0.0761558 + 1.40461i) q^{66} +(-2.98122 + 10.7374i) q^{67} +(-6.01660 - 4.57370i) q^{68} +(-7.53782 - 0.819787i) q^{69} +(0.00913974 - 0.0557500i) q^{70} +(-7.98287 + 4.80314i) q^{71} +(0.796093 - 0.605174i) q^{72} +(1.26222 + 3.16792i) q^{73} +(-7.03834 - 8.28618i) q^{74} +(0.0331070 + 0.201944i) q^{75} +(-0.241044 - 4.44579i) q^{76} +(0.0340195 + 0.00748826i) q^{77} +(-4.17143 + 3.95139i) q^{78} +(-1.81302 + 0.610877i) q^{79} +(0.844421 - 2.11934i) q^{80} +(0.267528 + 0.963550i) q^{81} +(-9.28422 + 2.04361i) q^{82} +(5.95128 - 8.77749i) q^{83} +(-0.0115993 - 0.0218787i) q^{84} +(8.07620 - 15.2333i) q^{85} +(-2.17887 - 3.21359i) q^{86} +(3.34890 + 3.17225i) q^{87} +(1.27666 + 0.590647i) q^{88} +(-2.80941 - 1.29977i) q^{89} +(1.65626 + 1.56890i) q^{90} +(0.0798485 + 0.117768i) q^{91} +(-3.55160 + 6.69902i) q^{92} +(4.82891 + 9.10829i) q^{93} +(-2.95151 + 4.35315i) q^{94} +(9.91990 - 2.18354i) q^{95} +(-0.267528 - 0.963550i) q^{96} +(-1.58586 + 3.98022i) q^{97} +(6.63299 - 2.23491i) q^{98} +(-1.02124 + 0.967369i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(e\left(\frac{25}{29}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.907575 0.419889i 0.641753 0.296906i
\(3\) 0.947653 + 0.319302i 0.547128 + 0.184349i
\(4\) 0.647386 0.762162i 0.323693 0.381081i
\(5\) 1.95481 + 1.17617i 0.874216 + 0.525998i 0.880535 0.473982i \(-0.157184\pi\)
−0.00631865 + 0.999980i \(0.502011\pi\)
\(6\) 0.994138 0.108119i 0.405855 0.0441394i
\(7\) 0.00134066 0.0247270i 0.000506721 0.00934592i −0.998269 0.0588113i \(-0.981269\pi\)
0.998776 + 0.0494654i \(0.0157517\pi\)
\(8\) 0.267528 0.963550i 0.0945856 0.340666i
\(9\) 0.796093 + 0.605174i 0.265364 + 0.201725i
\(10\) 2.26799 + 0.246659i 0.717203 + 0.0780005i
\(11\) −0.227575 + 1.38814i −0.0686163 + 0.418541i 0.930074 + 0.367373i \(0.119743\pi\)
−0.998690 + 0.0511681i \(0.983706\pi\)
\(12\) 0.856857 0.515554i 0.247353 0.148828i
\(13\) −4.57419 + 3.47721i −1.26865 + 0.964405i −0.268654 + 0.963237i \(0.586579\pi\)
−0.999999 + 0.00116846i \(0.999628\pi\)
\(14\) −0.00916584 0.0230045i −0.00244967 0.00614822i
\(15\) 1.47693 + 1.73877i 0.381341 + 0.448949i
\(16\) −0.161782 0.986827i −0.0404455 0.246707i
\(17\) −0.409163 7.54657i −0.0992367 1.83031i −0.449066 0.893499i \(-0.648243\pi\)
0.349829 0.936814i \(-0.386240\pi\)
\(18\) 0.976621 + 0.214970i 0.230192 + 0.0506690i
\(19\) 3.23236 3.06186i 0.741555 0.702438i −0.220472 0.975393i \(-0.570760\pi\)
0.962027 + 0.272955i \(0.0880011\pi\)
\(20\) 2.16195 0.728444i 0.483426 0.162885i
\(21\) 0.00916584 0.0230045i 0.00200015 0.00502000i
\(22\) 0.376325 + 1.35540i 0.0802328 + 0.288972i
\(23\) −7.40499 + 1.62996i −1.54405 + 0.339871i −0.903684 0.428201i \(-0.859148\pi\)
−0.640364 + 0.768071i \(0.721217\pi\)
\(24\) 0.561187 0.827689i 0.114552 0.168951i
\(25\) 0.0958550 + 0.180802i 0.0191710 + 0.0361603i
\(26\) −2.69138 + 5.07649i −0.527824 + 0.995581i
\(27\) 0.561187 + 0.827689i 0.108001 + 0.159289i
\(28\) −0.0179780 0.0170297i −0.00339753 0.00321831i
\(29\) 4.18650 + 1.93688i 0.777414 + 0.359670i 0.768136 0.640287i \(-0.221184\pi\)
0.00927836 + 0.999957i \(0.497047\pi\)
\(30\) 2.07051 + 0.957922i 0.378022 + 0.174892i
\(31\) 7.48442 + 7.08962i 1.34424 + 1.27333i 0.932094 + 0.362217i \(0.117980\pi\)
0.412148 + 0.911117i \(0.364779\pi\)
\(32\) −0.561187 0.827689i −0.0992048 0.146316i
\(33\) −0.658898 + 1.24281i −0.114699 + 0.216346i
\(34\) −3.54007 6.67728i −0.607117 1.14514i
\(35\) 0.0317038 0.0467596i 0.00535892 0.00790382i
\(36\) 0.976621 0.214970i 0.162770 0.0358284i
\(37\) −2.90855 10.4757i −0.478163 1.72219i −0.671455 0.741045i \(-0.734330\pi\)
0.193292 0.981141i \(-0.438083\pi\)
\(38\) 1.64797 4.13610i 0.267336 0.670964i
\(39\) −5.44503 + 1.83464i −0.871902 + 0.293778i
\(40\) 1.65626 1.56890i 0.261878 0.248064i
\(41\) −9.28422 2.04361i −1.44995 0.319158i −0.580938 0.813948i \(-0.697314\pi\)
−0.869013 + 0.494789i \(0.835245\pi\)
\(42\) −0.00134066 0.0247270i −0.000206868 0.00381546i
\(43\) −0.628136 3.83146i −0.0957898 0.584292i −0.990486 0.137616i \(-0.956056\pi\)
0.894696 0.446676i \(-0.147392\pi\)
\(44\) 0.910662 + 1.07211i 0.137287 + 0.161627i
\(45\) 0.844421 + 2.11934i 0.125879 + 0.315932i
\(46\) −6.03619 + 4.58859i −0.889987 + 0.676551i
\(47\) −4.50656 + 2.71151i −0.657349 + 0.395514i −0.804792 0.593557i \(-0.797723\pi\)
0.147443 + 0.989071i \(0.452896\pi\)
\(48\) 0.161782 0.986827i 0.0233512 0.142436i
\(49\) 6.95836 + 0.756767i 0.994051 + 0.108110i
\(50\) 0.162912 + 0.123843i 0.0230393 + 0.0175140i
\(51\) 2.02189 7.28218i 0.283121 1.01971i
\(52\) −0.311072 + 5.73738i −0.0431379 + 0.795631i
\(53\) 0.345271 0.0375504i 0.0474266 0.00515795i −0.0843750 0.996434i \(-0.526889\pi\)
0.131802 + 0.991276i \(0.457924\pi\)
\(54\) 0.856857 + 0.515554i 0.116603 + 0.0701580i
\(55\) −2.07755 + 2.44589i −0.280137 + 0.329803i
\(56\) −0.0234670 0.00790696i −0.00313591 0.00105661i
\(57\) 4.04081 1.86948i 0.535219 0.247619i
\(58\) 4.61284 0.605696
\(59\) −6.76228 + 3.64302i −0.880374 + 0.474280i
\(60\) 2.28137 0.294523
\(61\) 4.08821 1.89141i 0.523442 0.242170i −0.140330 0.990105i \(-0.544816\pi\)
0.663772 + 0.747935i \(0.268954\pi\)
\(62\) 9.76953 + 3.29174i 1.24073 + 0.418051i
\(63\) 0.0160314 0.0188736i 0.00201977 0.00237786i
\(64\) −0.856857 0.515554i −0.107107 0.0644442i
\(65\) −13.0315 + 1.41726i −1.61635 + 0.175789i
\(66\) −0.0761558 + 1.40461i −0.00937413 + 0.172896i
\(67\) −2.98122 + 10.7374i −0.364214 + 1.31178i 0.523752 + 0.851871i \(0.324532\pi\)
−0.887966 + 0.459910i \(0.847882\pi\)
\(68\) −6.01660 4.57370i −0.729620 0.554642i
\(69\) −7.53782 0.819787i −0.907446 0.0986907i
\(70\) 0.00913974 0.0557500i 0.00109241 0.00666339i
\(71\) −7.98287 + 4.80314i −0.947393 + 0.570027i −0.903304 0.429000i \(-0.858866\pi\)
−0.0440886 + 0.999028i \(0.514038\pi\)
\(72\) 0.796093 0.605174i 0.0938205 0.0713205i
\(73\) 1.26222 + 3.16792i 0.147731 + 0.370778i 0.984156 0.177304i \(-0.0567376\pi\)
−0.836425 + 0.548082i \(0.815358\pi\)
\(74\) −7.03834 8.28618i −0.818191 0.963248i
\(75\) 0.0331070 + 0.201944i 0.00382287 + 0.0233185i
\(76\) −0.241044 4.44579i −0.0276496 0.509967i
\(77\) 0.0340195 + 0.00748826i 0.00387688 + 0.000853366i
\(78\) −4.17143 + 3.95139i −0.472321 + 0.447406i
\(79\) −1.81302 + 0.610877i −0.203980 + 0.0687290i −0.419437 0.907784i \(-0.637773\pi\)
0.215457 + 0.976513i \(0.430876\pi\)
\(80\) 0.844421 2.11934i 0.0944092 0.236949i
\(81\) 0.267528 + 0.963550i 0.0297254 + 0.107061i
\(82\) −9.28422 + 2.04361i −1.02527 + 0.225679i
\(83\) 5.95128 8.77749i 0.653238 0.963454i −0.346440 0.938072i \(-0.612609\pi\)
0.999678 0.0253821i \(-0.00808024\pi\)
\(84\) −0.0115993 0.0218787i −0.00126559 0.00238716i
\(85\) 8.07620 15.2333i 0.875987 1.65229i
\(86\) −2.17887 3.21359i −0.234953 0.346530i
\(87\) 3.34890 + 3.17225i 0.359040 + 0.340101i
\(88\) 1.27666 + 0.590647i 0.136093 + 0.0629632i
\(89\) −2.80941 1.29977i −0.297797 0.137775i 0.265301 0.964166i \(-0.414529\pi\)
−0.563098 + 0.826390i \(0.690391\pi\)
\(90\) 1.65626 + 1.56890i 0.174585 + 0.165376i
\(91\) 0.0798485 + 0.117768i 0.00837040 + 0.0123454i
\(92\) −3.55160 + 6.69902i −0.370279 + 0.698421i
\(93\) 4.82891 + 9.10829i 0.500735 + 0.944486i
\(94\) −2.95151 + 4.35315i −0.304425 + 0.448993i
\(95\) 9.91990 2.18354i 1.01776 0.224026i
\(96\) −0.267528 0.963550i −0.0273045 0.0983419i
\(97\) −1.58586 + 3.98022i −0.161020 + 0.404130i −0.987245 0.159211i \(-0.949105\pi\)
0.826224 + 0.563341i \(0.190484\pi\)
\(98\) 6.63299 2.23491i 0.670033 0.225760i
\(99\) −1.02124 + 0.967369i −0.102638 + 0.0972242i
\(100\) 0.199855 + 0.0439915i 0.0199855 + 0.00439915i
\(101\) 0.453650 + 8.36709i 0.0451399 + 0.832557i 0.930194 + 0.367068i \(0.119638\pi\)
−0.885054 + 0.465488i \(0.845879\pi\)
\(102\) −1.22269 7.45809i −0.121065 0.738461i
\(103\) −4.15882 4.89615i −0.409781 0.482432i 0.518094 0.855324i \(-0.326642\pi\)
−0.927875 + 0.372892i \(0.878366\pi\)
\(104\) 2.12674 + 5.33772i 0.208544 + 0.523406i
\(105\) 0.0449746 0.0341888i 0.00438907 0.00333649i
\(106\) 0.297592 0.179055i 0.0289047 0.0173914i
\(107\) −0.928588 + 5.66414i −0.0897700 + 0.547573i 0.903201 + 0.429217i \(0.141211\pi\)
−0.992971 + 0.118356i \(0.962238\pi\)
\(108\) 0.994138 + 0.108119i 0.0956610 + 0.0104038i
\(109\) 9.84433 + 7.48346i 0.942916 + 0.716786i 0.959095 0.283083i \(-0.0913573\pi\)
−0.0161797 + 0.999869i \(0.505150\pi\)
\(110\) −0.858536 + 3.09217i −0.0818582 + 0.294827i
\(111\) 0.588595 10.8560i 0.0558669 1.03040i
\(112\) −0.0246181 + 0.00267738i −0.00232619 + 0.000252989i
\(113\) −4.19821 2.52598i −0.394935 0.237624i 0.304209 0.952605i \(-0.401608\pi\)
−0.699144 + 0.714981i \(0.746435\pi\)
\(114\) 2.88237 3.39339i 0.269959 0.317820i
\(115\) −16.3924 5.52326i −1.52860 0.515046i
\(116\) 4.18650 1.93688i 0.388707 0.179835i
\(117\) −5.74580 −0.531200
\(118\) −4.60762 + 6.14572i −0.424165 + 0.565759i
\(119\) −0.187152 −0.0171562
\(120\) 2.07051 0.957922i 0.189011 0.0874459i
\(121\) 8.54903 + 2.88050i 0.777185 + 0.261864i
\(122\) 2.91618 3.43319i 0.264019 0.310827i
\(123\) −8.14569 4.90110i −0.734472 0.441917i
\(124\) 10.2488 1.11462i 0.920365 0.100096i
\(125\) 0.592279 10.9239i 0.0529750 0.977067i
\(126\) 0.00662488 0.0238607i 0.000590191 0.00212568i
\(127\) 12.0935 + 9.19328i 1.07313 + 0.815771i 0.983627 0.180215i \(-0.0576794\pi\)
0.0895018 + 0.995987i \(0.471473\pi\)
\(128\) −0.994138 0.108119i −0.0878702 0.00955646i
\(129\) 0.628136 3.83146i 0.0553043 0.337341i
\(130\) −11.2319 + 6.75803i −0.985106 + 0.592719i
\(131\) 7.75016 5.89152i 0.677135 0.514744i −0.209151 0.977883i \(-0.567070\pi\)
0.886286 + 0.463139i \(0.153277\pi\)
\(132\) 0.520664 + 1.30677i 0.0453180 + 0.113740i
\(133\) −0.0713769 0.0840314i −0.00618917 0.00728645i
\(134\) 1.80283 + 10.9968i 0.155741 + 0.949976i
\(135\) 0.123511 + 2.27802i 0.0106301 + 0.196061i
\(136\) −7.38096 1.62467i −0.632912 0.139315i
\(137\) 2.11672 2.00506i 0.180843 0.171304i −0.591923 0.805995i \(-0.701631\pi\)
0.772766 + 0.634691i \(0.218872\pi\)
\(138\) −7.18536 + 2.42103i −0.611658 + 0.206092i
\(139\) −1.99625 + 5.01021i −0.169320 + 0.424960i −0.989010 0.147846i \(-0.952766\pi\)
0.819691 + 0.572806i \(0.194145\pi\)
\(140\) −0.0151138 0.0544350i −0.00127735 0.00460059i
\(141\) −5.13644 + 1.13062i −0.432567 + 0.0952151i
\(142\) −5.22828 + 7.71113i −0.438747 + 0.647104i
\(143\) −3.78590 7.14096i −0.316593 0.597157i
\(144\) 0.468408 0.883512i 0.0390340 0.0736260i
\(145\) 5.90571 + 8.71026i 0.490442 + 0.723348i
\(146\) 2.47573 + 2.34514i 0.204893 + 0.194085i
\(147\) 6.35247 + 2.93897i 0.523943 + 0.242402i
\(148\) −9.86710 4.56501i −0.811071 0.375241i
\(149\) −12.0146 11.3808i −0.984271 0.932351i 0.0134441 0.999910i \(-0.495720\pi\)
−0.997715 + 0.0675584i \(0.978479\pi\)
\(150\) 0.114841 + 0.169378i 0.00937674 + 0.0138297i
\(151\) 0.390522 0.736603i 0.0317803 0.0599439i −0.867113 0.498111i \(-0.834027\pi\)
0.898894 + 0.438167i \(0.144372\pi\)
\(152\) −2.08550 3.93368i −0.169157 0.319063i
\(153\) 4.24126 6.25539i 0.342885 0.505718i
\(154\) 0.0340195 0.00748826i 0.00274137 0.000603421i
\(155\) 6.29201 + 22.6618i 0.505386 + 1.82024i
\(156\) −2.12674 + 5.33772i −0.170276 + 0.427359i
\(157\) 19.4262 6.54546i 1.55038 0.522385i 0.591529 0.806284i \(-0.298525\pi\)
0.958854 + 0.283899i \(0.0916281\pi\)
\(158\) −1.38895 + 1.31568i −0.110499 + 0.104670i
\(159\) 0.339187 + 0.0746606i 0.0268993 + 0.00592097i
\(160\) −0.123511 2.27802i −0.00976438 0.180093i
\(161\) 0.0303765 + 0.185288i 0.00239400 + 0.0146028i
\(162\) 0.647386 + 0.762162i 0.0508635 + 0.0598811i
\(163\) 5.06557 + 12.7136i 0.396766 + 0.995808i 0.982659 + 0.185419i \(0.0593644\pi\)
−0.585893 + 0.810388i \(0.699256\pi\)
\(164\) −7.56804 + 5.75307i −0.590964 + 0.449239i
\(165\) −2.74978 + 1.65449i −0.214070 + 0.128801i
\(166\) 1.71567 10.4651i 0.133162 0.812250i
\(167\) 14.9527 + 1.62621i 1.15708 + 0.125840i 0.666463 0.745538i \(-0.267807\pi\)
0.490613 + 0.871378i \(0.336773\pi\)
\(168\) −0.0197139 0.0149861i −0.00152096 0.00115620i
\(169\) 5.35438 19.2847i 0.411876 1.48344i
\(170\) 0.933452 17.2165i 0.0715925 1.32045i
\(171\) 4.42622 0.481380i 0.338481 0.0368121i
\(172\) −3.32684 2.00169i −0.253669 0.152628i
\(173\) 3.63673 4.28150i 0.276496 0.325516i −0.606333 0.795211i \(-0.707360\pi\)
0.882829 + 0.469695i \(0.155636\pi\)
\(174\) 4.37138 + 1.47289i 0.331393 + 0.111659i
\(175\) 0.00459919 0.00212781i 0.000347666 0.000160847i
\(176\) 1.40667 0.106032
\(177\) −7.57152 + 1.29311i −0.569110 + 0.0971961i
\(178\) −3.09551 −0.232018
\(179\) −2.15208 + 0.995659i −0.160854 + 0.0744190i −0.498664 0.866795i \(-0.666176\pi\)
0.337810 + 0.941214i \(0.390314\pi\)
\(180\) 2.16195 + 0.728444i 0.161142 + 0.0542950i
\(181\) 2.90897 3.42470i 0.216222 0.254556i −0.643348 0.765573i \(-0.722455\pi\)
0.859570 + 0.511017i \(0.170731\pi\)
\(182\) 0.121918 + 0.0733556i 0.00903716 + 0.00543748i
\(183\) 4.47814 0.487027i 0.331034 0.0360021i
\(184\) −0.410495 + 7.57114i −0.0302621 + 0.558152i
\(185\) 6.63547 23.8988i 0.487850 1.75708i
\(186\) 8.20707 + 6.23885i 0.601772 + 0.457455i
\(187\) 10.5688 + 1.14943i 0.772870 + 0.0840547i
\(188\) −0.850877 + 5.19012i −0.0620566 + 0.378529i
\(189\) 0.0212186 0.0127668i 0.00154343 0.000928649i
\(190\) 8.08621 6.14698i 0.586636 0.445949i
\(191\) 7.53653 + 18.9153i 0.545324 + 1.36866i 0.900905 + 0.434016i \(0.142904\pi\)
−0.355581 + 0.934646i \(0.615717\pi\)
\(192\) −0.647386 0.762162i −0.0467211 0.0550043i
\(193\) −2.65513 16.1956i −0.191120 1.16578i −0.891842 0.452347i \(-0.850587\pi\)
0.700722 0.713435i \(-0.252861\pi\)
\(194\) 0.231959 + 4.27824i 0.0166537 + 0.307160i
\(195\) −12.8018 2.81790i −0.916758 0.201794i
\(196\) 5.08152 4.81347i 0.362966 0.343820i
\(197\) 18.8389 6.34758i 1.34222 0.452246i 0.445673 0.895196i \(-0.352964\pi\)
0.896547 + 0.442949i \(0.146068\pi\)
\(198\) −0.520664 + 1.30677i −0.0370020 + 0.0928679i
\(199\) −5.08444 18.3125i −0.360426 1.29814i −0.892349 0.451346i \(-0.850944\pi\)
0.531923 0.846793i \(-0.321470\pi\)
\(200\) 0.199855 0.0439915i 0.0141319 0.00311067i
\(201\) −6.25363 + 9.22341i −0.441097 + 0.650569i
\(202\) 3.92497 + 7.40328i 0.276160 + 0.520893i
\(203\) 0.0535059 0.100923i 0.00375538 0.00708340i
\(204\) −4.24126 6.25539i −0.296947 0.437965i
\(205\) −15.7452 14.9147i −1.09969 1.04169i
\(206\) −5.83028 2.69738i −0.406215 0.187935i
\(207\) −6.88148 3.18371i −0.478296 0.221283i
\(208\) 4.17143 + 3.95139i 0.289236 + 0.273979i
\(209\) 3.51469 + 5.18378i 0.243116 + 0.358570i
\(210\) 0.0264624 0.0499133i 0.00182608 0.00344434i
\(211\) 8.84482 + 16.6831i 0.608902 + 1.14851i 0.975885 + 0.218284i \(0.0700458\pi\)
−0.366983 + 0.930228i \(0.619609\pi\)
\(212\) 0.194904 0.287462i 0.0133861 0.0197430i
\(213\) −9.09865 + 2.00276i −0.623429 + 0.137227i
\(214\) 1.53555 + 5.53053i 0.104968 + 0.378060i
\(215\) 3.27856 8.22855i 0.223596 0.561183i
\(216\) 0.947653 0.319302i 0.0644796 0.0217257i
\(217\) 0.185339 0.175562i 0.0125816 0.0119179i
\(218\) 12.0767 + 2.65828i 0.817937 + 0.180042i
\(219\) 0.184620 + 3.40512i 0.0124755 + 0.230097i
\(220\) 0.519181 + 3.16687i 0.0350032 + 0.213510i
\(221\) 28.1126 + 33.0967i 1.89106 + 2.22633i
\(222\) −4.02412 10.0998i −0.270081 0.677852i
\(223\) −4.56810 + 3.47258i −0.305902 + 0.232541i −0.746851 0.664991i \(-0.768435\pi\)
0.440949 + 0.897532i \(0.354642\pi\)
\(224\) −0.0212186 + 0.0127668i −0.00141773 + 0.000853018i
\(225\) −0.0331070 + 0.201944i −0.00220714 + 0.0134629i
\(226\) −4.87083 0.529735i −0.324003 0.0352374i
\(227\) −9.86038 7.49567i −0.654457 0.497505i 0.224458 0.974484i \(-0.427939\pi\)
−0.878915 + 0.476979i \(0.841732\pi\)
\(228\) 1.19112 4.29003i 0.0788839 0.284114i
\(229\) 0.347145 6.40271i 0.0229400 0.423103i −0.964396 0.264461i \(-0.914806\pi\)
0.987336 0.158642i \(-0.0507114\pi\)
\(230\) −17.1965 + 1.87024i −1.13391 + 0.123320i
\(231\) 0.0298477 + 0.0179587i 0.00196383 + 0.00118160i
\(232\) 2.98629 3.51573i 0.196060 0.230819i
\(233\) 15.1067 + 5.09004i 0.989672 + 0.333459i 0.767150 0.641468i \(-0.221674\pi\)
0.222523 + 0.974928i \(0.428571\pi\)
\(234\) −5.21475 + 2.41260i −0.340899 + 0.157717i
\(235\) −11.9986 −0.782705
\(236\) −1.60124 + 7.51239i −0.104232 + 0.489015i
\(237\) −1.91317 −0.124273
\(238\) −0.169855 + 0.0785833i −0.0110101 + 0.00509380i
\(239\) 15.9791 + 5.38399i 1.03360 + 0.348262i 0.784443 0.620201i \(-0.212949\pi\)
0.249160 + 0.968462i \(0.419845\pi\)
\(240\) 1.47693 1.73877i 0.0953352 0.112237i
\(241\) −12.1962 7.33819i −0.785624 0.472694i 0.0653756 0.997861i \(-0.479175\pi\)
−0.851000 + 0.525166i \(0.824003\pi\)
\(242\) 8.96838 0.975371i 0.576510 0.0626992i
\(243\) −0.0541389 + 0.998533i −0.00347301 + 0.0640559i
\(244\) 1.20509 4.34035i 0.0771482 0.277863i
\(245\) 12.7122 + 9.66353i 0.812150 + 0.617380i
\(246\) −9.45074 1.02783i −0.602557 0.0655321i
\(247\) −4.13873 + 25.2451i −0.263341 + 1.60631i
\(248\) 8.83350 5.31494i 0.560928 0.337499i
\(249\) 8.44242 6.41776i 0.535017 0.406709i
\(250\) −4.04930 10.1630i −0.256101 0.642764i
\(251\) −9.05523 10.6606i −0.571561 0.672894i 0.398102 0.917341i \(-0.369669\pi\)
−0.969662 + 0.244448i \(0.921393\pi\)
\(252\) −0.00400625 0.0244371i −0.000252370 0.00153939i
\(253\) −0.577433 10.6501i −0.0363029 0.669568i
\(254\) 14.8360 + 3.26564i 0.930891 + 0.204905i
\(255\) 12.5175 11.8572i 0.783874 0.742525i
\(256\) −0.947653 + 0.319302i −0.0592283 + 0.0199563i
\(257\) −3.90867 + 9.81003i −0.243816 + 0.611933i −0.999053 0.0435200i \(-0.986143\pi\)
0.755236 + 0.655453i \(0.227522\pi\)
\(258\) −1.03871 3.74109i −0.0646671 0.232910i
\(259\) −0.262931 + 0.0578754i −0.0163377 + 0.00359620i
\(260\) −7.35620 + 10.8496i −0.456212 + 0.672863i
\(261\) 2.16070 + 4.07550i 0.133744 + 0.252267i
\(262\) 4.56007 8.60120i 0.281722 0.531384i
\(263\) 2.32462 + 3.42856i 0.143342 + 0.211414i 0.892582 0.450885i \(-0.148891\pi\)
−0.749240 + 0.662299i \(0.769581\pi\)
\(264\) 1.02124 + 0.967369i 0.0628529 + 0.0595374i
\(265\) 0.719103 + 0.332692i 0.0441741 + 0.0204371i
\(266\) −0.100064 0.0462945i −0.00613531 0.00283850i
\(267\) −2.24733 2.12878i −0.137534 0.130279i
\(268\) 6.25363 + 9.22341i 0.382001 + 0.563409i
\(269\) −3.58248 + 6.75727i −0.218427 + 0.411998i −0.968375 0.249500i \(-0.919734\pi\)
0.749948 + 0.661497i \(0.230079\pi\)
\(270\) 1.06861 + 2.01562i 0.0650337 + 0.122666i
\(271\) −11.8208 + 17.4344i −0.718062 + 1.05906i 0.277103 + 0.960840i \(0.410626\pi\)
−0.995165 + 0.0982216i \(0.968685\pi\)
\(272\) −7.38096 + 1.62467i −0.447537 + 0.0985102i
\(273\) 0.0380653 + 0.137099i 0.00230382 + 0.00829759i
\(274\) 1.07918 2.70853i 0.0651955 0.163628i
\(275\) −0.272793 + 0.0919146i −0.0164500 + 0.00554266i
\(276\) −5.50469 + 5.21432i −0.331343 + 0.313865i
\(277\) −15.4790 3.40718i −0.930041 0.204718i −0.275984 0.961162i \(-0.589004\pi\)
−0.654058 + 0.756445i \(0.726935\pi\)
\(278\) 0.291985 + 5.38534i 0.0175121 + 0.322991i
\(279\) 1.66784 + 10.1734i 0.0998510 + 0.609064i
\(280\) −0.0365736 0.0430577i −0.00218569 0.00257319i
\(281\) −5.72299 14.3636i −0.341405 0.856862i −0.994987 0.100006i \(-0.968114\pi\)
0.653582 0.756856i \(-0.273266\pi\)
\(282\) −4.18698 + 3.18286i −0.249331 + 0.189536i
\(283\) 1.22830 0.739045i 0.0730150 0.0439317i −0.478578 0.878045i \(-0.658848\pi\)
0.551593 + 0.834113i \(0.314020\pi\)
\(284\) −1.50724 + 9.19373i −0.0894380 + 0.545547i
\(285\) 10.0978 + 1.09821i 0.598144 + 0.0650521i
\(286\) −6.43440 4.89130i −0.380474 0.289229i
\(287\) −0.0629793 + 0.226831i −0.00371755 + 0.0133894i
\(288\) 0.0541389 0.998533i 0.00319017 0.0588391i
\(289\) −39.8830 + 4.33753i −2.34606 + 0.255149i
\(290\) 9.01722 + 5.42548i 0.529509 + 0.318595i
\(291\) −2.77374 + 3.26550i −0.162600 + 0.191427i
\(292\) 3.23161 + 1.08886i 0.189116 + 0.0637206i
\(293\) −24.7250 + 11.4390i −1.44445 + 0.668274i −0.976507 0.215484i \(-0.930867\pi\)
−0.467944 + 0.883758i \(0.655005\pi\)
\(294\) 6.99939 0.408213
\(295\) −17.5037 0.832185i −1.01911 0.0484517i
\(296\) −10.8719 −0.631918
\(297\) −1.27666 + 0.590647i −0.0740795 + 0.0342728i
\(298\) −15.6828 5.28415i −0.908480 0.306102i
\(299\) 28.2042 33.2045i 1.63109 1.92027i
\(300\) 0.175347 + 0.105503i 0.0101237 + 0.00609121i
\(301\) −0.0955825 + 0.0103952i −0.00550928 + 0.000599171i
\(302\) 0.0451368 0.832499i 0.00259733 0.0479049i
\(303\) −2.24172 + 8.07395i −0.128784 + 0.463836i
\(304\) −3.54446 2.69443i −0.203289 0.154536i
\(305\) 10.2163 + 1.11109i 0.584983 + 0.0636207i
\(306\) 1.22269 7.45809i 0.0698967 0.426351i
\(307\) 6.01251 3.61761i 0.343152 0.206468i −0.333536 0.942737i \(-0.608242\pi\)
0.676689 + 0.736269i \(0.263414\pi\)
\(308\) 0.0277310 0.0210806i 0.00158012 0.00120118i
\(309\) −2.37778 5.96777i −0.135267 0.339494i
\(310\) 15.2259 + 17.9253i 0.864773 + 1.01809i
\(311\) 0.112218 + 0.684501i 0.00636331 + 0.0388145i 0.989817 0.142343i \(-0.0454638\pi\)
−0.983454 + 0.181158i \(0.942015\pi\)
\(312\) 0.311072 + 5.73738i 0.0176110 + 0.324815i
\(313\) 14.5715 + 3.20744i 0.823632 + 0.181295i 0.606740 0.794901i \(-0.292477\pi\)
0.216892 + 0.976196i \(0.430408\pi\)
\(314\) 14.8824 14.0974i 0.839863 0.795561i
\(315\) 0.0535369 0.0180387i 0.00301646 0.00101636i
\(316\) −0.708136 + 1.77729i −0.0398357 + 0.0999802i
\(317\) 1.58908 + 5.72336i 0.0892519 + 0.321456i 0.994676 0.103052i \(-0.0328608\pi\)
−0.905424 + 0.424508i \(0.860447\pi\)
\(318\) 0.339187 0.0746606i 0.0190206 0.00418676i
\(319\) −3.64141 + 5.37068i −0.203880 + 0.300700i
\(320\) −1.06861 2.01562i −0.0597372 0.112676i
\(321\) −2.68855 + 5.07114i −0.150060 + 0.283043i
\(322\) 0.105369 + 0.155408i 0.00587201 + 0.00866057i
\(323\) −24.4291 23.1405i −1.35927 1.28757i
\(324\) 0.907575 + 0.419889i 0.0504209 + 0.0233272i
\(325\) −1.06715 0.493714i −0.0591946 0.0273863i
\(326\) 9.93570 + 9.41159i 0.550287 + 0.521260i
\(327\) 6.93953 + 10.2350i 0.383757 + 0.565999i
\(328\) −4.45291 + 8.39908i −0.245871 + 0.463762i
\(329\) 0.0610056 + 0.115069i 0.00336335 + 0.00634395i
\(330\) −1.80093 + 2.65617i −0.0991379 + 0.146217i
\(331\) 12.1740 2.67970i 0.669143 0.147290i 0.132609 0.991168i \(-0.457664\pi\)
0.536534 + 0.843879i \(0.319733\pi\)
\(332\) −2.83709 10.2183i −0.155705 0.560800i
\(333\) 4.02412 10.0998i 0.220520 0.553464i
\(334\) 14.2535 4.80258i 0.779919 0.262785i
\(335\) −18.4567 + 17.4831i −1.00840 + 0.955204i
\(336\) −0.0241843 0.00532338i −0.00131936 0.000290414i
\(337\) −0.272259 5.02153i −0.0148309 0.273540i −0.996538 0.0831414i \(-0.973505\pi\)
0.981707 0.190399i \(-0.0609781\pi\)
\(338\) −3.23795 19.7506i −0.176121 1.07429i
\(339\) −3.17190 3.73425i −0.172274 0.202817i
\(340\) −6.38185 16.0172i −0.346104 0.868656i
\(341\) −11.5447 + 8.77603i −0.625179 + 0.475249i
\(342\) 3.81500 2.29541i 0.206292 0.124122i
\(343\) 0.0560851 0.342104i 0.00302831 0.0184719i
\(344\) −3.85985 0.419784i −0.208109 0.0226332i
\(345\) −13.7708 10.4683i −0.741393 0.563592i
\(346\) 1.50286 5.41281i 0.0807941 0.290994i
\(347\) −0.179217 + 3.30546i −0.00962087 + 0.177447i 0.989773 + 0.142648i \(0.0455617\pi\)
−0.999394 + 0.0347985i \(0.988921\pi\)
\(348\) 4.58580 0.498736i 0.245825 0.0267351i
\(349\) −13.3619 8.03958i −0.715246 0.430349i 0.110881 0.993834i \(-0.464633\pi\)
−0.826126 + 0.563485i \(0.809460\pi\)
\(350\) 0.00328067 0.00386230i 0.000175359 0.000206449i
\(351\) −5.44503 1.83464i −0.290634 0.0979261i
\(352\) 1.27666 0.590647i 0.0680464 0.0314816i
\(353\) −18.1193 −0.964394 −0.482197 0.876063i \(-0.660161\pi\)
−0.482197 + 0.876063i \(0.660161\pi\)
\(354\) −6.32876 + 4.35279i −0.336370 + 0.231348i
\(355\) −21.2543 −1.12806
\(356\) −2.80941 + 1.29977i −0.148898 + 0.0688877i
\(357\) −0.177356 0.0597581i −0.00938665 0.00316273i
\(358\) −1.53511 + 1.80727i −0.0811331 + 0.0955172i
\(359\) 10.0893 + 6.07054i 0.532494 + 0.320391i 0.756281 0.654247i \(-0.227014\pi\)
−0.223787 + 0.974638i \(0.571842\pi\)
\(360\) 2.26799 0.246659i 0.119534 0.0130001i
\(361\) 0.0445632 0.821920i 0.00234543 0.0432589i
\(362\) 1.20211 4.32962i 0.0631817 0.227560i
\(363\) 7.18177 + 5.45944i 0.376945 + 0.286546i
\(364\) 0.141451 + 0.0153837i 0.00741404 + 0.000806326i
\(365\) −1.25862 + 7.67726i −0.0658793 + 0.401846i
\(366\) 3.85975 2.32234i 0.201752 0.121390i
\(367\) −7.88091 + 5.99091i −0.411380 + 0.312723i −0.790316 0.612700i \(-0.790083\pi\)
0.378935 + 0.925423i \(0.376290\pi\)
\(368\) 2.80648 + 7.04375i 0.146298 + 0.367181i
\(369\) −6.15436 7.24547i −0.320383 0.377184i
\(370\) −4.01266 24.4761i −0.208608 1.27245i
\(371\) −0.000465619 0.00858784i −2.41737e−5 0.000445858i
\(372\) 10.0682 + 2.21617i 0.522010 + 0.114903i
\(373\) −0.739577 + 0.700565i −0.0382939 + 0.0362739i −0.706607 0.707606i \(-0.749775\pi\)
0.668313 + 0.743880i \(0.267017\pi\)
\(374\) 10.0747 3.39454i 0.520948 0.175528i
\(375\) 4.04930 10.1630i 0.209105 0.524814i
\(376\) 1.40704 + 5.06770i 0.0725626 + 0.261347i
\(377\) −25.8848 + 5.69768i −1.33314 + 0.293446i
\(378\) 0.0138968 0.0204963i 0.000714776 0.00105422i
\(379\) −16.5871 31.2865i −0.852021 1.60708i −0.793319 0.608806i \(-0.791649\pi\)
−0.0587013 0.998276i \(-0.518696\pi\)
\(380\) 4.75780 8.97416i 0.244070 0.460365i
\(381\) 8.52506 + 12.5735i 0.436752 + 0.644161i
\(382\) 14.7823 + 14.0025i 0.756328 + 0.716432i
\(383\) −7.88572 3.64832i −0.402941 0.186420i 0.207942 0.978141i \(-0.433323\pi\)
−0.610883 + 0.791721i \(0.709186\pi\)
\(384\) −0.907575 0.419889i −0.0463145 0.0214274i
\(385\) 0.0576941 + 0.0546507i 0.00294036 + 0.00278526i
\(386\) −9.21007 13.5838i −0.468780 0.691399i
\(387\) 1.81865 3.43033i 0.0924470 0.174373i
\(388\) 2.00691 + 3.78543i 0.101885 + 0.192176i
\(389\) −10.4926 + 15.4754i −0.531997 + 0.784636i −0.994802 0.101823i \(-0.967532\pi\)
0.462806 + 0.886460i \(0.346843\pi\)
\(390\) −12.8018 + 2.81790i −0.648246 + 0.142690i
\(391\) 15.3305 + 55.2154i 0.775296 + 2.79236i
\(392\) 2.59074 6.50227i 0.130852 0.328414i
\(393\) 9.22563 3.10848i 0.465372 0.156802i
\(394\) 14.4325 13.6712i 0.727098 0.688744i
\(395\) −4.26259 0.938268i −0.214474 0.0472094i
\(396\) 0.0761558 + 1.40461i 0.00382697 + 0.0705844i
\(397\) −1.19142 7.26734i −0.0597956 0.364737i −0.999727 0.0233732i \(-0.992559\pi\)
0.939931 0.341364i \(-0.110889\pi\)
\(398\) −12.3037 14.4851i −0.616730 0.726071i
\(399\) −0.0408092 0.102423i −0.00204302 0.00512758i
\(400\) 0.162912 0.123843i 0.00814562 0.00619214i
\(401\) 22.0192 13.2485i 1.09959 0.661601i 0.154362 0.988014i \(-0.450668\pi\)
0.945227 + 0.326414i \(0.105840\pi\)
\(402\) −1.80283 + 10.9968i −0.0899169 + 0.548469i
\(403\) −58.8873 6.40438i −2.93339 0.319025i
\(404\) 6.67077 + 5.07098i 0.331883 + 0.252291i
\(405\) −0.610331 + 2.19821i −0.0303276 + 0.109230i
\(406\) 0.00618424 0.114062i 0.000306919 0.00566079i
\(407\) 15.2036 1.65349i 0.753615 0.0819606i
\(408\) −6.47583 3.89638i −0.320601 0.192899i
\(409\) −13.6120 + 16.0253i −0.673072 + 0.792401i −0.987624 0.156839i \(-0.949870\pi\)
0.314553 + 0.949240i \(0.398146\pi\)
\(410\) −20.5525 6.92494i −1.01501 0.341998i
\(411\) 2.64613 1.22423i 0.130524 0.0603869i
\(412\) −6.42402 −0.316489
\(413\) 0.0810149 + 0.172095i 0.00398648 + 0.00846823i
\(414\) −7.58226 −0.372648
\(415\) 21.9574 10.1586i 1.07785 0.498665i
\(416\) 5.44503 + 1.83464i 0.266965 + 0.0899508i
\(417\) −3.49152 + 4.11053i −0.170980 + 0.201294i
\(418\) 5.36646 + 3.22889i 0.262482 + 0.157930i
\(419\) 23.5152 2.55743i 1.14879 0.124938i 0.486149 0.873876i \(-0.338401\pi\)
0.662641 + 0.748937i \(0.269436\pi\)
\(420\) 0.00305853 0.0564113i 0.000149241 0.00275259i
\(421\) −7.68411 + 27.6757i −0.374501 + 1.34883i 0.500931 + 0.865487i \(0.332991\pi\)
−0.875432 + 0.483342i \(0.839423\pi\)
\(422\) 15.0324 + 11.4273i 0.731765 + 0.556273i
\(423\) −5.22858 0.568642i −0.254222 0.0276483i
\(424\) 0.0561879 0.342731i 0.00272873 0.0166445i
\(425\) 1.32521 0.797354i 0.0642823 0.0386773i
\(426\) −7.41677 + 5.63808i −0.359344 + 0.273166i
\(427\) −0.0412879 0.103625i −0.00199806 0.00501476i
\(428\) 3.71583 + 4.37462i 0.179612 + 0.211455i
\(429\) −1.30760 7.97600i −0.0631315 0.385085i
\(430\) −0.479544 8.84466i −0.0231257 0.426528i
\(431\) −4.31625 0.950078i −0.207906 0.0457637i 0.109796 0.993954i \(-0.464980\pi\)
−0.317702 + 0.948190i \(0.602911\pi\)
\(432\) 0.725995 0.687699i 0.0349295 0.0330870i
\(433\) 24.2836 8.18210i 1.16700 0.393207i 0.331902 0.943314i \(-0.392310\pi\)
0.835094 + 0.550107i \(0.185413\pi\)
\(434\) 0.0944923 0.237158i 0.00453578 0.0113839i
\(435\) 2.81536 + 10.1400i 0.134986 + 0.486176i
\(436\) 12.0767 2.65828i 0.578369 0.127309i
\(437\) −18.9449 + 27.9417i −0.906258 + 1.33663i
\(438\) 1.59733 + 3.01288i 0.0763234 + 0.143961i
\(439\) 10.2851 19.3998i 0.490882 0.925902i −0.507068 0.861906i \(-0.669271\pi\)
0.997950 0.0639960i \(-0.0203845\pi\)
\(440\) 1.80093 + 2.65617i 0.0858559 + 0.126628i
\(441\) 5.08152 + 4.81347i 0.241977 + 0.229213i
\(442\) 39.4113 + 18.2336i 1.87460 + 0.867284i
\(443\) −26.1395 12.0934i −1.24193 0.574576i −0.314740 0.949178i \(-0.601917\pi\)
−0.927186 + 0.374602i \(0.877780\pi\)
\(444\) −7.89297 7.47662i −0.374584 0.354825i
\(445\) −3.96310 5.84513i −0.187869 0.277086i
\(446\) −2.68779 + 5.06972i −0.127271 + 0.240058i
\(447\) −7.75173 14.6213i −0.366644 0.691564i
\(448\) −0.0138968 + 0.0204963i −0.000656564 + 0.000968359i
\(449\) −24.4599 + 5.38404i −1.15434 + 0.254088i −0.750581 0.660779i \(-0.770226\pi\)
−0.403755 + 0.914867i \(0.632295\pi\)
\(450\) 0.0547469 + 0.197181i 0.00258080 + 0.00929519i
\(451\) 4.94968 12.4227i 0.233071 0.584964i
\(452\) −4.64307 + 1.56443i −0.218392 + 0.0735848i
\(453\) 0.605278 0.573350i 0.0284384 0.0269383i
\(454\) −12.0964 2.66262i −0.567712 0.124963i
\(455\) 0.0175737 + 0.324128i 0.000823869 + 0.0151954i
\(456\) −0.720305 4.39366i −0.0337314 0.205752i
\(457\) 18.7000 + 22.0154i 0.874751 + 1.02984i 0.999292 + 0.0376218i \(0.0119782\pi\)
−0.124541 + 0.992214i \(0.539746\pi\)
\(458\) −2.37337 5.95671i −0.110900 0.278339i
\(459\) 6.01660 4.57370i 0.280831 0.213482i
\(460\) −14.8219 + 8.91802i −0.691073 + 0.415805i
\(461\) 2.81898 17.1950i 0.131293 0.800851i −0.836288 0.548290i \(-0.815279\pi\)
0.967581 0.252561i \(-0.0812728\pi\)
\(462\) 0.0346297 + 0.00376621i 0.00161112 + 0.000175220i
\(463\) 20.4635 + 15.5559i 0.951017 + 0.722945i 0.960868 0.277007i \(-0.0893425\pi\)
−0.00985058 + 0.999951i \(0.503136\pi\)
\(464\) 1.23407 4.44471i 0.0572901 0.206340i
\(465\) −1.27330 + 23.4846i −0.0590477 + 1.08907i
\(466\) 15.8477 1.72354i 0.734131 0.0798416i
\(467\) −33.1176 19.9262i −1.53250 0.922074i −0.996989 0.0775453i \(-0.975292\pi\)
−0.535510 0.844529i \(-0.679881\pi\)
\(468\) −3.71975 + 4.37923i −0.171946 + 0.202430i
\(469\) 0.261506 + 0.0881117i 0.0120752 + 0.00406862i
\(470\) −10.8897 + 5.03810i −0.502303 + 0.232390i
\(471\) 20.4993 0.944559
\(472\) 1.70113 + 7.49040i 0.0783007 + 0.344774i
\(473\) 5.46156 0.251123
\(474\) −1.73634 + 0.803317i −0.0797528 + 0.0368976i
\(475\) 0.863427 + 0.290922i 0.0396167 + 0.0133484i
\(476\) −0.121160 + 0.142640i −0.00555336 + 0.00653792i
\(477\) 0.297592 + 0.179055i 0.0136258 + 0.00819838i
\(478\) 16.7629 1.82308i 0.766719 0.0833857i
\(479\) −1.79583 + 33.1221i −0.0820536 + 1.51339i 0.610496 + 0.792019i \(0.290970\pi\)
−0.692550 + 0.721370i \(0.743513\pi\)
\(480\) 0.610331 2.19821i 0.0278577 0.100334i
\(481\) 49.7303 + 37.8040i 2.26751 + 1.72372i
\(482\) −14.1502 1.53892i −0.644522 0.0700960i
\(483\) −0.0303765 + 0.185288i −0.00138218 + 0.00843091i
\(484\) 7.72994 4.65095i 0.351361 0.211407i
\(485\) −7.78147 + 5.91532i −0.353338 + 0.268601i
\(486\) 0.370138 + 0.928977i 0.0167898 + 0.0421392i
\(487\) −4.82647 5.68216i −0.218708 0.257483i 0.641856 0.766825i \(-0.278165\pi\)
−0.860564 + 0.509342i \(0.829889\pi\)
\(488\) −0.728754 4.44520i −0.0329891 0.201225i
\(489\) 0.740924 + 13.6655i 0.0335058 + 0.617977i
\(490\) 15.5948 + 3.43269i 0.704503 + 0.155073i
\(491\) 9.55383 9.04987i 0.431158 0.408415i −0.441102 0.897457i \(-0.645412\pi\)
0.872260 + 0.489042i \(0.162654\pi\)
\(492\) −9.00884 + 3.03543i −0.406150 + 0.136848i
\(493\) 12.9039 32.3863i 0.581161 1.45860i
\(494\) 6.84395 + 24.6497i 0.307924 + 1.10904i
\(495\) −3.13411 + 0.689870i −0.140868 + 0.0310074i
\(496\) 5.78538 8.53280i 0.259771 0.383134i
\(497\) 0.108065 + 0.203832i 0.00484737 + 0.00914310i
\(498\) 4.96738 9.36948i 0.222594 0.419856i
\(499\) −1.19916 1.76863i −0.0536819 0.0791749i 0.799901 0.600132i \(-0.204885\pi\)
−0.853583 + 0.520957i \(0.825575\pi\)
\(500\) −7.94238 7.52342i −0.355194 0.336458i
\(501\) 13.6507 + 6.31551i 0.609870 + 0.282156i
\(502\) −12.6946 5.87314i −0.566587 0.262131i
\(503\) −7.38663 6.99698i −0.329353 0.311980i 0.505098 0.863062i \(-0.331456\pi\)
−0.834451 + 0.551082i \(0.814215\pi\)
\(504\) −0.0138968 0.0204963i −0.000619014 0.000912978i
\(505\) −8.95431 + 16.8896i −0.398461 + 0.751578i
\(506\) −4.99594 9.42334i −0.222097 0.418919i
\(507\) 11.2317 16.5656i 0.498819 0.735703i
\(508\) 14.8360 3.26564i 0.658240 0.144889i
\(509\) 0.336357 + 1.21145i 0.0149088 + 0.0536965i 0.970630 0.240576i \(-0.0773364\pi\)
−0.955721 + 0.294273i \(0.904923\pi\)
\(510\) 6.38185 16.0172i 0.282593 0.709255i
\(511\) 0.0800254 0.0269637i 0.00354011 0.00119280i
\(512\) −0.725995 + 0.687699i −0.0320848 + 0.0303923i
\(513\) 4.34822 + 0.957117i 0.191979 + 0.0422577i
\(514\) 0.571709 + 10.5445i 0.0252170 + 0.465100i
\(515\) −2.37101 14.4625i −0.104479 0.637294i
\(516\) −2.51355 2.95918i −0.110653 0.130270i
\(517\) −2.73838 6.87282i −0.120434 0.302266i
\(518\) −0.214328 + 0.162928i −0.00941703 + 0.00715864i
\(519\) 4.81345 2.89616i 0.211287 0.127127i
\(520\) −2.12069 + 12.9356i −0.0929982 + 0.567264i
\(521\) −16.7313 1.81964i −0.733011 0.0797198i −0.266002 0.963972i \(-0.585703\pi\)
−0.467009 + 0.884253i \(0.654668\pi\)
\(522\) 3.67225 + 2.79157i 0.160730 + 0.122184i
\(523\) 6.72574 24.2239i 0.294096 1.05924i −0.657894 0.753110i \(-0.728553\pi\)
0.951990 0.306128i \(-0.0990337\pi\)
\(524\) 0.527055 9.72097i 0.0230245 0.424662i
\(525\) 0.00503785 0.000547899i 0.000219870 2.39123e-5i
\(526\) 3.54938 + 2.13559i 0.154761 + 0.0931163i
\(527\) 50.4400 59.3825i 2.19720 2.58674i
\(528\) 1.33304 + 0.449153i 0.0580131 + 0.0195469i
\(529\) 31.3029 14.4823i 1.36100 0.629664i
\(530\) 0.792334 0.0344168
\(531\) −7.58806 1.19218i −0.329294 0.0517361i
\(532\) −0.110254 −0.00478012
\(533\) 49.5739 22.9353i 2.14728 0.993439i
\(534\) −2.93347 0.988401i −0.126944 0.0427723i
\(535\) −8.47719 + 9.98012i −0.366501 + 0.431478i
\(536\) 9.54845 + 5.74511i 0.412430 + 0.248151i
\(537\) −2.35734 + 0.256376i −0.101727 + 0.0110635i
\(538\) −0.414065 + 7.63697i −0.0178516 + 0.329253i
\(539\) −2.63405 + 9.48697i −0.113456 + 0.408633i
\(540\) 1.81618 + 1.38063i 0.0781560 + 0.0594126i
\(541\) 8.92571 + 0.970730i 0.383746 + 0.0417349i 0.297959 0.954579i \(-0.403694\pi\)
0.0857870 + 0.996313i \(0.472660\pi\)
\(542\) −3.40776 + 20.7864i −0.146376 + 0.892853i
\(543\) 3.85021 2.31659i 0.165228 0.0994145i
\(544\) −6.01660 + 4.57370i −0.257959 + 0.196096i
\(545\) 10.4419 + 26.2073i 0.447284 + 1.12260i
\(546\) 0.0921134 + 0.108444i 0.00394209 + 0.00464099i
\(547\) 5.08383 + 31.0100i 0.217369 + 1.32589i 0.839663 + 0.543108i \(0.182752\pi\)
−0.622294 + 0.782783i \(0.713799\pi\)
\(548\) −0.157848 2.91133i −0.00674292 0.124366i
\(549\) 4.39923 + 0.968344i 0.187755 + 0.0413279i
\(550\) −0.208986 + 0.197962i −0.00891120 + 0.00844114i
\(551\) 19.4628 6.55777i 0.829141 0.279370i
\(552\) −2.80648 + 7.04375i −0.119452 + 0.299802i
\(553\) 0.0126745 + 0.0456494i 0.000538975 + 0.00194121i
\(554\) −15.4790 + 3.40718i −0.657638 + 0.144757i
\(555\) 13.9191 20.5291i 0.590831 0.871411i
\(556\) 2.52624 + 4.76500i 0.107137 + 0.202081i
\(557\) 17.7734 33.5241i 0.753082 1.42046i −0.148973 0.988841i \(-0.547597\pi\)
0.902055 0.431622i \(-0.142059\pi\)
\(558\) 5.78538 + 8.53280i 0.244915 + 0.361222i
\(559\) 16.1960 + 15.3417i 0.685018 + 0.648884i
\(560\) −0.0512727 0.0237213i −0.00216667 0.00100241i
\(561\) 9.64858 + 4.46391i 0.407363 + 0.188466i
\(562\) −11.2252 10.6331i −0.473505 0.448528i
\(563\) −10.3547 15.2721i −0.436400 0.643642i 0.544362 0.838851i \(-0.316772\pi\)
−0.980762 + 0.195209i \(0.937462\pi\)
\(564\) −2.46355 + 4.64675i −0.103734 + 0.195663i
\(565\) −5.23572 9.87561i −0.220268 0.415470i
\(566\) 0.804460 1.18649i 0.0338140 0.0498719i
\(567\) 0.0241843 0.00532338i 0.00101565 0.000223561i
\(568\) 2.49242 + 8.97687i 0.104579 + 0.376661i
\(569\) −12.0667 + 30.2852i −0.505863 + 1.26962i 0.425312 + 0.905047i \(0.360164\pi\)
−0.931175 + 0.364573i \(0.881215\pi\)
\(570\) 9.62567 3.24326i 0.403175 0.135845i
\(571\) 11.9472 11.3170i 0.499973 0.473600i −0.395657 0.918398i \(-0.629483\pi\)
0.895631 + 0.444798i \(0.146725\pi\)
\(572\) −7.89351 1.73749i −0.330044 0.0726482i
\(573\) 1.10234 + 20.3315i 0.0460511 + 0.849363i
\(574\) 0.0380854 + 0.232310i 0.00158965 + 0.00969645i
\(575\) −1.00451 1.18260i −0.0418908 0.0493176i
\(576\) −0.370138 0.928977i −0.0154224 0.0387074i
\(577\) −22.9455 + 17.4427i −0.955232 + 0.726148i −0.961778 0.273830i \(-0.911709\pi\)
0.00654612 + 0.999979i \(0.497916\pi\)
\(578\) −34.3755 + 20.6831i −1.42983 + 0.860302i
\(579\) 2.65513 16.1956i 0.110343 0.673065i
\(580\) 10.4619 + 1.13780i 0.434407 + 0.0472446i
\(581\) −0.209062 0.158925i −0.00867336 0.00659331i
\(582\) −1.14623 + 4.12835i −0.0475128 + 0.171126i
\(583\) −0.0264494 + 0.487831i −0.00109542 + 0.0202039i
\(584\) 3.39013 0.368699i 0.140285 0.0152569i
\(585\) −11.2319 6.75803i −0.464383 0.279410i
\(586\) −17.6367 + 20.7635i −0.728566 + 0.857734i
\(587\) −27.6572 9.31880i −1.14154 0.384628i −0.315878 0.948800i \(-0.602299\pi\)
−0.825658 + 0.564172i \(0.809196\pi\)
\(588\) 6.35247 2.93897i 0.261972 0.121201i
\(589\) 45.8998 1.89127
\(590\) −16.2354 + 6.59436i −0.668401 + 0.271486i
\(591\) 19.8796 0.817737
\(592\) −9.86710 + 4.56501i −0.405535 + 0.187621i
\(593\) 25.2565 + 8.50990i 1.03716 + 0.349460i 0.785830 0.618442i \(-0.212236\pi\)
0.251329 + 0.967902i \(0.419132\pi\)
\(594\) −0.910662 + 1.07211i −0.0373649 + 0.0439894i
\(595\) −0.365847 0.220123i −0.0149983 0.00902415i
\(596\) −16.4521 + 1.78927i −0.673903 + 0.0732914i
\(597\) 1.02892 18.9774i 0.0421110 0.776692i
\(598\) 11.6552 41.9782i 0.476616 1.71662i
\(599\) −0.549399 0.417642i −0.0224478 0.0170644i 0.593890 0.804546i \(-0.297591\pi\)
−0.616338 + 0.787482i \(0.711384\pi\)
\(600\) 0.203440 + 0.0221255i 0.00830541 + 0.000903268i
\(601\) 2.61471 15.9490i 0.106656 0.650575i −0.878345 0.478028i \(-0.841352\pi\)
0.985001 0.172547i \(-0.0551998\pi\)
\(602\) −0.0823835 + 0.0495685i −0.00335770 + 0.00202026i
\(603\) −8.87132 + 6.74380i −0.361268 + 0.274629i
\(604\) −0.308592 0.774508i −0.0125564 0.0315143i
\(605\) 13.3237 + 15.6859i 0.541687 + 0.637724i
\(606\) 1.35563 + 8.26899i 0.0550688 + 0.335905i
\(607\) −0.0579983 1.06972i −0.00235408 0.0434184i 0.997120 0.0758353i \(-0.0241623\pi\)
−0.999474 + 0.0324169i \(0.989680\pi\)
\(608\) −4.34822 0.957117i −0.176344 0.0388162i
\(609\) 0.0829299 0.0785554i 0.00336049 0.00318322i
\(610\) 9.73858 3.28131i 0.394304 0.132856i
\(611\) 11.1854 28.0732i 0.452513 1.13572i
\(612\) −2.02189 7.28218i −0.0817299 0.294365i
\(613\) −31.7147 + 6.98092i −1.28094 + 0.281957i −0.802759 0.596303i \(-0.796636\pi\)
−0.478184 + 0.878260i \(0.658705\pi\)
\(614\) 3.93781 5.80784i 0.158917 0.234385i
\(615\) −10.1587 19.1614i −0.409640 0.772662i
\(616\) 0.0163165 0.0307762i 0.000657410 0.00124001i
\(617\) 11.5995 + 17.1079i 0.466976 + 0.688739i 0.986136 0.165939i \(-0.0530653\pi\)
−0.519160 + 0.854677i \(0.673755\pi\)
\(618\) −4.66381 4.41780i −0.187606 0.177710i
\(619\) −31.4323 14.5421i −1.26337 0.584497i −0.330193 0.943913i \(-0.607114\pi\)
−0.933177 + 0.359416i \(0.882976\pi\)
\(620\) 21.3453 + 9.87539i 0.857248 + 0.396605i
\(621\) −5.50469 5.21432i −0.220896 0.209243i
\(622\) 0.389261 + 0.574117i 0.0156079 + 0.0230200i
\(623\) −0.0359058 + 0.0677256i −0.00143854 + 0.00271337i
\(624\) 2.69138 + 5.07649i 0.107742 + 0.203222i
\(625\) 14.5804 21.5045i 0.583215 0.860178i
\(626\) 14.5715 3.20744i 0.582396 0.128195i
\(627\) 1.67552 + 6.03467i 0.0669138 + 0.241002i
\(628\) 7.58758 19.0434i 0.302777 0.759914i
\(629\) −77.8652 + 26.2358i −3.10469 + 1.04609i
\(630\) 0.0410145 0.0388510i 0.00163406 0.00154786i
\(631\) 43.0757 + 9.48167i 1.71481 + 0.377459i 0.960332 0.278860i \(-0.0899566\pi\)
0.754483 + 0.656319i \(0.227888\pi\)
\(632\) 0.103577 + 1.91036i 0.00412006 + 0.0759900i
\(633\) 3.05488 + 18.6339i 0.121421 + 0.740633i
\(634\) 3.84539 + 4.52715i 0.152720 + 0.179796i
\(635\) 12.8277 + 32.1951i 0.509052 + 1.27762i
\(636\) 0.276488 0.210181i 0.0109635 0.00833422i
\(637\) −34.4603 + 20.7341i −1.36537 + 0.821514i
\(638\) −1.04977 + 6.40329i −0.0415606 + 0.253509i
\(639\) −9.26185 1.00729i −0.366393 0.0398476i
\(640\) −1.81618 1.38063i −0.0717909 0.0545740i
\(641\) 4.14228 14.9191i 0.163610 0.589271i −0.835593 0.549350i \(-0.814876\pi\)
0.999203 0.0399212i \(-0.0127107\pi\)
\(642\) −0.310744 + 5.73133i −0.0122641 + 0.226198i
\(643\) −3.83243 + 0.416802i −0.151136 + 0.0164371i −0.183374 0.983043i \(-0.558702\pi\)
0.0322380 + 0.999480i \(0.489737\pi\)
\(644\) 0.160885 + 0.0968013i 0.00633976 + 0.00381451i
\(645\) 5.73432 6.75097i 0.225789 0.265819i
\(646\) −31.8877 10.7442i −1.25460 0.422725i
\(647\) 13.6365 6.30894i 0.536108 0.248030i −0.133103 0.991102i \(-0.542494\pi\)
0.669211 + 0.743072i \(0.266632\pi\)
\(648\) 1.00000 0.0392837
\(649\) −3.51811 10.2161i −0.138098 0.401016i
\(650\) −1.17582 −0.0461195
\(651\) 0.231694 0.107193i 0.00908082 0.00420123i
\(652\) 12.9692 + 4.36984i 0.507914 + 0.171136i
\(653\) −7.68157 + 9.04345i −0.300603 + 0.353898i −0.891638 0.452748i \(-0.850444\pi\)
0.591035 + 0.806646i \(0.298719\pi\)
\(654\) 10.5957 + 6.37524i 0.414326 + 0.249291i
\(655\) 22.0795 2.40129i 0.862717 0.0938261i
\(656\) −0.514670 + 9.49253i −0.0200945 + 0.370621i
\(657\) −0.912304 + 3.28582i −0.0355924 + 0.128192i
\(658\) 0.103683 + 0.0788180i 0.00404200 + 0.00307265i
\(659\) 28.9127 + 3.14444i 1.12628 + 0.122490i 0.652239 0.758013i \(-0.273830\pi\)
0.474040 + 0.880504i \(0.342795\pi\)
\(660\) −0.519181 + 3.16687i −0.0202091 + 0.123270i
\(661\) −39.5363 + 23.7882i −1.53778 + 0.925253i −0.541355 + 0.840794i \(0.682089\pi\)
−0.996427 + 0.0844588i \(0.973084\pi\)
\(662\) 9.92364 7.54375i 0.385693 0.293196i
\(663\) 16.0732 + 40.3406i 0.624230 + 1.56670i
\(664\) −6.86541 8.08259i −0.266430 0.313665i
\(665\) −0.0406930 0.248216i −0.00157801 0.00962542i
\(666\) −0.588595 10.8560i −0.0228076 0.420661i
\(667\) −34.1581 7.51876i −1.32261 0.291128i
\(668\) 10.9196 10.3436i 0.422493 0.400206i
\(669\) −5.43777 + 1.83220i −0.210236 + 0.0708369i
\(670\) −9.40987 + 23.6170i −0.363535 + 0.912404i
\(671\) 1.69517 + 6.10546i 0.0654414 + 0.235699i
\(672\) −0.0241843 + 0.00532338i −0.000932931 + 0.000205354i
\(673\) 17.1051 25.2282i 0.659354 0.972475i −0.340130 0.940378i \(-0.610471\pi\)
0.999485 0.0320968i \(-0.0102185\pi\)
\(674\) −2.35558 4.44310i −0.0907336 0.171142i
\(675\) −0.0958550 + 0.180802i −0.00368946 + 0.00695906i
\(676\) −11.2317 16.5656i −0.431990 0.637138i
\(677\) 7.11620 + 6.74083i 0.273498 + 0.259071i 0.812139 0.583465i \(-0.198303\pi\)
−0.538641 + 0.842536i \(0.681062\pi\)
\(678\) −4.44671 2.05727i −0.170775 0.0790089i
\(679\) 0.0962927 + 0.0445497i 0.00369537 + 0.00170966i
\(680\) −12.5175 11.8572i −0.480023 0.454702i
\(681\) −6.95084 10.2517i −0.266357 0.392847i
\(682\) −6.79270 + 12.8124i −0.260106 + 0.490612i
\(683\) −6.71755 12.6706i −0.257040 0.484829i 0.721085 0.692847i \(-0.243644\pi\)
−0.978125 + 0.208018i \(0.933299\pi\)
\(684\) 2.49858 3.68513i 0.0955357 0.140905i
\(685\) 6.49606 1.42989i 0.248202 0.0546334i
\(686\) −0.0927443 0.334035i −0.00354099 0.0127535i
\(687\) 2.37337 5.95671i 0.0905497 0.227263i
\(688\) −3.67936 + 1.23972i −0.140274 + 0.0472640i
\(689\) −1.44876 + 1.37234i −0.0551935 + 0.0522821i
\(690\) −16.8935 3.71854i −0.643125 0.141563i
\(691\) −0.518955 9.57156i −0.0197420 0.364119i −0.991667 0.128828i \(-0.958878\pi\)
0.971925 0.235291i \(-0.0756044\pi\)
\(692\) −0.908821 5.54356i −0.0345482 0.210735i
\(693\) 0.0225510 + 0.0265491i 0.000856641 + 0.00100852i
\(694\) 1.22527 + 3.07521i 0.0465108 + 0.116733i
\(695\) −9.79512 + 7.44606i −0.371550 + 0.282445i
\(696\) 3.95255 2.37817i 0.149821 0.0901443i
\(697\) −11.6235 + 70.9002i −0.440271 + 2.68554i
\(698\) −15.5027 1.68602i −0.586784 0.0638166i
\(699\) 12.6906 + 9.64718i 0.480004 + 0.364890i
\(700\) 0.00135571 0.00488284i 5.12412e−5 0.000184554i
\(701\) −0.562180 + 10.3688i −0.0212333 + 0.391624i 0.968529 + 0.248900i \(0.0800690\pi\)
−0.989762 + 0.142724i \(0.954414\pi\)
\(702\) −5.71212 + 0.621231i −0.215590 + 0.0234468i
\(703\) −41.4764 24.9555i −1.56431 0.941216i
\(704\) 0.910662 1.07211i 0.0343218 0.0404068i
\(705\) −11.3706 3.83118i −0.428240 0.144291i
\(706\) −16.4447 + 7.60811i −0.618903 + 0.286335i
\(707\) 0.207501 0.00780388
\(708\) −3.91614 + 6.60786i −0.147177 + 0.248339i
\(709\) 17.7577 0.666906 0.333453 0.942767i \(-0.391786\pi\)
0.333453 + 0.942767i \(0.391786\pi\)
\(710\) −19.2899 + 8.92444i −0.723935 + 0.334928i
\(711\) −1.81302 0.610877i −0.0679935 0.0229097i
\(712\) −2.00399 + 2.35928i −0.0751027 + 0.0884177i
\(713\) −66.9779 40.2993i −2.50834 1.50922i
\(714\) −0.186055 + 0.0202347i −0.00696295 + 0.000757266i
\(715\) 0.998273 18.4121i 0.0373333 0.688572i
\(716\) −0.634375 + 2.28481i −0.0237077 + 0.0853874i
\(717\) 13.4236 + 10.2043i 0.501312 + 0.381087i
\(718\) 11.7058 + 1.27308i 0.436855 + 0.0475109i
\(719\) 6.50880 39.7019i 0.242737 1.48063i −0.531134 0.847288i \(-0.678234\pi\)
0.773871 0.633343i \(-0.218318\pi\)
\(720\) 1.95481 1.17617i 0.0728513 0.0438332i
\(721\) −0.126642 + 0.0962711i −0.00471641 + 0.00358532i
\(722\) −0.304671 0.764666i −0.0113387 0.0284579i
\(723\) −9.21464 10.8483i −0.342696 0.403453i
\(724\) −0.726952 4.43421i −0.0270170 0.164796i
\(725\) 0.0511056 + 0.942587i 0.00189801 + 0.0350068i
\(726\) 8.81036 + 1.93931i 0.326983 + 0.0719744i
\(727\) −13.1174 + 12.4254i −0.486496 + 0.460834i −0.891198 0.453615i \(-0.850134\pi\)
0.404702 + 0.914449i \(0.367375\pi\)
\(728\) 0.134837 0.0454318i 0.00499739 0.00168382i
\(729\) −0.370138 + 0.928977i −0.0137088 + 0.0344065i
\(730\) 2.08130 + 7.49617i 0.0770324 + 0.277446i
\(731\) −28.6574 + 6.30796i −1.05993 + 0.233308i
\(732\) 2.52789 3.72836i 0.0934336 0.137804i
\(733\) −3.79811 7.16399i −0.140286 0.264608i 0.803407 0.595431i \(-0.203019\pi\)
−0.943693 + 0.330823i \(0.892674\pi\)
\(734\) −4.63700 + 8.74631i −0.171155 + 0.322832i
\(735\) 8.96113 + 13.2167i 0.330536 + 0.487505i
\(736\) 5.50469 + 5.21432i 0.202906 + 0.192202i
\(737\) −14.2266 6.58192i −0.524043 0.242448i
\(738\) −8.62784 3.99166i −0.317595 0.146935i
\(739\) −15.8139 14.9797i −0.581723 0.551037i 0.339234 0.940702i \(-0.389832\pi\)
−0.920957 + 0.389665i \(0.872591\pi\)
\(740\) −13.9191 20.5291i −0.511675 0.754664i
\(741\) −11.9829 + 22.6021i −0.440202 + 0.830310i
\(742\) −0.00402853 0.00759860i −0.000147892 0.000278954i
\(743\) 0.256827 0.378791i 0.00942206 0.0138965i −0.822949 0.568116i \(-0.807673\pi\)
0.832371 + 0.554219i \(0.186983\pi\)
\(744\) 10.0682 2.21617i 0.369117 0.0812487i
\(745\) −10.1004 36.3784i −0.370050 1.33280i
\(746\) −0.377063 + 0.946356i −0.0138052 + 0.0346486i
\(747\) 10.0497 3.38613i 0.367699 0.123892i
\(748\) 7.71817 7.31104i 0.282204 0.267318i
\(749\) 0.138812 + 0.0305548i 0.00507208 + 0.00111645i
\(750\) −0.592279 10.9239i −0.0216270 0.398886i
\(751\) −0.317358 1.93580i −0.0115806 0.0706383i 0.980404 0.196997i \(-0.0631191\pi\)
−0.991985 + 0.126359i \(0.959671\pi\)
\(752\) 3.40487 + 4.00852i 0.124163 + 0.146176i
\(753\) −5.17726 12.9939i −0.188670 0.473525i
\(754\) −21.1000 + 16.0398i −0.768418 + 0.584136i
\(755\) 1.62976 0.980597i 0.0593132 0.0356876i
\(756\) 0.00400625 0.0244371i 0.000145706 0.000888768i
\(757\) 20.7993 + 2.26206i 0.755962 + 0.0822158i 0.477980 0.878370i \(-0.341369\pi\)
0.277982 + 0.960586i \(0.410335\pi\)
\(758\) −28.1909 21.4302i −1.02394 0.778378i
\(759\) 2.85340 10.2770i 0.103572 0.373032i
\(760\) 0.549909 10.1425i 0.0199473 0.367906i
\(761\) −10.0845 + 1.09676i −0.365563 + 0.0397573i −0.289057 0.957312i \(-0.593342\pi\)
−0.0765055 + 0.997069i \(0.524376\pi\)
\(762\) 13.0166 + 7.83184i 0.471543 + 0.283718i
\(763\) 0.198241 0.233388i 0.00717682 0.00844920i
\(764\) 19.2956 + 6.50143i 0.698089 + 0.235213i
\(765\) 15.6482 7.23964i 0.565763 0.261750i
\(766\) −8.68877 −0.313938
\(767\) 18.2644 40.1778i 0.659491 1.45073i
\(768\) −1.00000 −0.0360844
\(769\) −18.6065 + 8.60830i −0.670969 + 0.310423i −0.725633 0.688082i \(-0.758453\pi\)
0.0546647 + 0.998505i \(0.482591\pi\)
\(770\) 0.0753090 + 0.0253745i 0.00271395 + 0.000914435i
\(771\) −6.83642 + 8.04846i −0.246208 + 0.289858i
\(772\) −14.0625 8.46115i −0.506122 0.304523i
\(773\) 27.5386 2.99501i 0.990496 0.107723i 0.401500 0.915859i \(-0.368489\pi\)
0.588996 + 0.808136i \(0.299523\pi\)
\(774\) 0.210200 3.87691i 0.00755549 0.139353i
\(775\) −0.564396 + 2.03277i −0.0202737 + 0.0730193i
\(776\) 3.41088 + 2.59288i 0.122443 + 0.0930790i
\(777\) −0.267647 0.0291083i −0.00960177 0.00104426i
\(778\) −3.02487 + 18.4509i −0.108447 + 0.661496i
\(779\) −36.2672 + 21.8212i −1.29941 + 0.781827i
\(780\) −10.4354 + 7.93280i −0.373648 + 0.284040i
\(781\) −4.85074 12.1744i −0.173573 0.435636i
\(782\) 37.0979 + 43.6750i 1.32662 + 1.56182i
\(783\) 0.746275 + 4.55208i 0.0266697 + 0.162678i
\(784\) −0.378939 6.98912i −0.0135335 0.249611i
\(785\) 45.6731 + 10.0534i 1.63014 + 0.358822i
\(786\) 7.06774 6.69492i 0.252098 0.238800i
\(787\) −4.83078 + 1.62768i −0.172199 + 0.0580205i −0.404080 0.914724i \(-0.632408\pi\)
0.231882 + 0.972744i \(0.425512\pi\)
\(788\) 7.35819 18.4677i 0.262125 0.657883i
\(789\) 1.10819 + 3.99134i 0.0394526 + 0.142096i
\(790\) −4.26259 + 0.938268i −0.151656 + 0.0333821i
\(791\) −0.0680883 + 0.100423i −0.00242094 + 0.00357062i
\(792\) 0.658898 + 1.24281i 0.0234129 + 0.0441615i
\(793\) −12.1235 + 22.8673i −0.430516 + 0.812040i
\(794\) −4.13278 6.09539i −0.146667 0.216317i
\(795\) 0.575231 + 0.544888i 0.0204013 + 0.0193252i
\(796\) −17.2487 7.98009i −0.611363 0.282847i
\(797\) −33.1053 15.3162i −1.17265 0.542526i −0.265821 0.964023i \(-0.585643\pi\)
−0.906830 + 0.421497i \(0.861505\pi\)
\(798\) −0.0800439 0.0758216i −0.00283352 0.00268406i
\(799\) 22.3065 + 32.8996i 0.789147 + 1.16391i
\(800\) 0.0958550 0.180802i 0.00338899 0.00639231i
\(801\) −1.44996 2.73492i −0.0512319 0.0966336i
\(802\) 14.4212 21.2697i 0.509231 0.751059i
\(803\) −4.68478 + 1.03120i −0.165322 + 0.0363902i
\(804\) 2.98122 + 10.7374i 0.105140 + 0.378678i
\(805\) −0.158550 + 0.397931i −0.00558816 + 0.0140252i
\(806\) −56.1338 + 18.9137i −1.97723 + 0.666206i
\(807\) −5.55255 + 5.25965i −0.195459 + 0.185149i
\(808\) 8.18347 + 1.80132i 0.287894 + 0.0633702i
\(809\) −0.0299363 0.552143i −0.00105251 0.0194123i 0.997960 0.0638425i \(-0.0203355\pi\)
−0.999012 + 0.0444302i \(0.985853\pi\)
\(810\) 0.369084 + 2.25131i 0.0129683 + 0.0791031i
\(811\) 24.5036 + 28.8479i 0.860439 + 1.01299i 0.999741 + 0.0227368i \(0.00723796\pi\)
−0.139303 + 0.990250i \(0.544486\pi\)
\(812\) −0.0422806 0.106116i −0.00148376 0.00372395i
\(813\) −16.7688 + 12.7473i −0.588108 + 0.447068i
\(814\) 13.1041 7.88450i 0.459300 0.276352i
\(815\) −5.05115 + 30.8106i −0.176934 + 1.07925i
\(816\) −7.51335 0.817126i −0.263020 0.0286051i
\(817\) −13.7617 10.4614i −0.481462 0.365998i
\(818\) −5.62509 + 20.2597i −0.196677 + 0.708365i
\(819\) −0.00770316 + 0.142076i −0.000269170 + 0.00496455i
\(820\) −21.5606 + 2.34486i −0.752930 + 0.0818860i
\(821\) 39.9939 + 24.0635i 1.39580 + 0.839823i 0.997014 0.0772226i \(-0.0246052\pi\)
0.398783 + 0.917045i \(0.369433\pi\)
\(822\) 1.88752 2.22217i 0.0658350 0.0775069i
\(823\) −25.7791 8.68600i −0.898604 0.302775i −0.168170 0.985758i \(-0.553786\pi\)
−0.730434 + 0.682983i \(0.760682\pi\)
\(824\) −5.83028 + 2.69738i −0.203108 + 0.0939676i
\(825\) −0.287861 −0.0100220
\(826\) 0.145788 + 0.122172i 0.00507261 + 0.00425090i
\(827\) −12.6235 −0.438962 −0.219481 0.975617i \(-0.570436\pi\)
−0.219481 + 0.975617i \(0.570436\pi\)
\(828\) −6.88148 + 3.18371i −0.239148 + 0.110642i
\(829\) 38.2433 + 12.8857i 1.32824 + 0.447538i 0.891896 0.452240i \(-0.149375\pi\)
0.436348 + 0.899778i \(0.356272\pi\)
\(830\) 15.6625 18.4394i 0.543654 0.640039i
\(831\) −13.5808 8.17128i −0.471112 0.283459i
\(832\) 5.71212 0.621231i 0.198032 0.0215373i
\(833\) 2.86389 52.8214i 0.0992280 1.83015i
\(834\) −1.44285 + 5.19667i −0.0499617 + 0.179946i
\(835\) 27.3170 + 20.7658i 0.945343 + 0.718631i
\(836\) 6.22625 + 0.677145i 0.215339 + 0.0234195i
\(837\) −1.66784 + 10.1734i −0.0576490 + 0.351643i
\(838\) 20.2679 12.1948i 0.700144 0.421263i
\(839\) −23.8212 + 18.1084i −0.822400 + 0.625172i −0.929395 0.369088i \(-0.879670\pi\)
0.106995 + 0.994260i \(0.465877\pi\)
\(840\) −0.0209107 0.0524818i −0.000721486 0.00181079i
\(841\) −4.99890 5.88516i −0.172376 0.202937i
\(842\) 4.64680 + 28.3442i 0.160139 + 0.976807i
\(843\) −0.837083 15.4391i −0.0288307 0.531751i
\(844\) 18.4412 + 4.05922i 0.634773 + 0.139724i
\(845\) 33.1489 31.4003i 1.14036 1.08020i
\(846\) −4.98409 + 1.67934i −0.171357 + 0.0577368i
\(847\) 0.0826875 0.207530i 0.00284118 0.00713081i
\(848\) −0.0929143 0.334647i −0.00319069 0.0114918i
\(849\) 1.39998 0.308160i 0.0480473 0.0105760i
\(850\) 0.867930 1.28010i 0.0297698 0.0439071i
\(851\) 38.6127 + 72.8313i 1.32363 + 2.49663i
\(852\) −4.36391 + 8.23120i −0.149505 + 0.281996i
\(853\) −24.4562 36.0702i −0.837364 1.23502i −0.969818 0.243830i \(-0.921596\pi\)
0.132454 0.991189i \(-0.457714\pi\)
\(854\) −0.0809829 0.0767110i −0.00277118 0.00262500i
\(855\) 9.21858 + 4.26497i 0.315269 + 0.145859i
\(856\) 5.20925 + 2.41006i 0.178049 + 0.0823741i
\(857\) 1.64269 + 1.55604i 0.0561132 + 0.0531532i 0.715242 0.698877i \(-0.246316\pi\)
−0.659129 + 0.752030i \(0.729075\pi\)
\(858\) −4.53578 6.68977i −0.154849 0.228385i
\(859\) 19.4396 36.6670i 0.663270 1.25106i −0.292308 0.956324i \(-0.594423\pi\)
0.955579 0.294736i \(-0.0952318\pi\)
\(860\) −4.14900 7.82584i −0.141480 0.266859i
\(861\) −0.132110 + 0.194848i −0.00450229 + 0.00664039i
\(862\) −4.31625 + 0.950078i −0.147012 + 0.0323598i
\(863\) 9.28581 + 33.4445i 0.316093 + 1.13846i 0.935481 + 0.353378i \(0.114967\pi\)
−0.619388 + 0.785085i \(0.712619\pi\)
\(864\) 0.370138 0.928977i 0.0125924 0.0316044i
\(865\) 12.1449 4.09208i 0.412938 0.139135i
\(866\) 18.6036 17.6223i 0.632177 0.598830i
\(867\) −39.1802 8.62422i −1.33063 0.292894i
\(868\) −0.0138211 0.254915i −0.000469118 0.00865238i
\(869\) −0.435388 2.65575i −0.0147695 0.0900901i
\(870\) 6.81283 + 8.02068i 0.230977 + 0.271927i
\(871\) −23.6995 59.4812i −0.803027 2.01544i
\(872\) 9.84433 7.48346i 0.333371 0.253422i
\(873\) −3.67122 + 2.20890i −0.124252 + 0.0747600i
\(874\) −5.46154 + 33.3139i −0.184739 + 1.12686i
\(875\) −0.269322 0.0292905i −0.00910474 0.000990200i
\(876\) 2.71477 + 2.06372i 0.0917237 + 0.0697266i
\(877\) 10.8999 39.2579i 0.368064 1.32565i −0.515321 0.856997i \(-0.672327\pi\)
0.883385 0.468649i \(-0.155259\pi\)
\(878\) 1.18876 21.9254i 0.0401187 0.739946i
\(879\) −27.0832 + 2.94548i −0.913495 + 0.0993486i
\(880\) 2.74978 + 1.65449i 0.0926949 + 0.0557727i
\(881\) 1.64656 1.93849i 0.0554742 0.0653092i −0.733725 0.679446i \(-0.762220\pi\)
0.789199 + 0.614137i \(0.210496\pi\)
\(882\) 6.63299 + 2.23491i 0.223344 + 0.0752535i
\(883\) −28.1563 + 13.0265i −0.947536 + 0.438377i −0.831907 0.554915i \(-0.812751\pi\)
−0.115630 + 0.993292i \(0.536889\pi\)
\(884\) 43.4248 1.46053
\(885\) −16.3218 6.37760i −0.548650 0.214381i
\(886\) −28.8015 −0.967605
\(887\) −30.6206 + 14.1666i −1.02814 + 0.475668i −0.860107 0.510113i \(-0.829603\pi\)
−0.168033 + 0.985781i \(0.553741\pi\)
\(888\) −10.3028 3.47143i −0.345740 0.116493i
\(889\) 0.243535 0.286712i 0.00816791 0.00961601i
\(890\) −6.05112 3.64084i −0.202834 0.122041i
\(891\) −1.39843 + 0.152088i −0.0468491 + 0.00509515i
\(892\) −0.310657 + 5.72973i −0.0104016 + 0.191845i
\(893\) −6.26459 + 22.5630i −0.209636 + 0.755042i
\(894\) −13.1746 10.0151i −0.440625 0.334954i
\(895\) −5.37797 0.584889i −0.179766 0.0195507i
\(896\) −0.00400625 + 0.0244371i −0.000133840 + 0.000816385i
\(897\) 37.3300 22.4607i 1.24641 0.749942i
\(898\) −19.9385 + 15.1569i −0.665357 + 0.505792i
\(899\) 17.6018 + 44.1772i 0.587053 + 1.47339i
\(900\) 0.132481 + 0.155969i 0.00441603 + 0.00519896i
\(901\) −0.424649 2.59025i −0.0141471 0.0862936i
\(902\) −0.723973 13.3529i −0.0241057 0.444603i
\(903\) −0.0938983 0.0206686i −0.00312474 0.000687807i
\(904\) −3.55705 + 3.36942i −0.118306 + 0.112065i
\(905\) 9.71450 3.27320i 0.322921 0.108805i
\(906\) 0.308592 0.774508i 0.0102523 0.0257313i
\(907\) −0.749272 2.69863i −0.0248792 0.0896067i 0.950068 0.312042i \(-0.101013\pi\)
−0.974947 + 0.222436i \(0.928599\pi\)
\(908\) −12.0964 + 2.66262i −0.401433 + 0.0883620i
\(909\) −4.70240 + 6.93552i −0.155969 + 0.230037i
\(910\) 0.152047 + 0.286792i 0.00504033 + 0.00950706i
\(911\) 3.29910 6.22276i 0.109304 0.206169i −0.822826 0.568294i \(-0.807604\pi\)
0.932130 + 0.362125i \(0.117949\pi\)
\(912\) −2.49858 3.68513i −0.0827363 0.122027i
\(913\) 10.8300 + 10.2588i 0.358422 + 0.339516i
\(914\) 26.2157 + 12.1287i 0.867139 + 0.401181i
\(915\) 9.32672 + 4.31500i 0.308332 + 0.142649i
\(916\) −4.65517 4.40961i −0.153811 0.145698i
\(917\) −0.135289 0.199537i −0.00446764 0.00658928i
\(918\) 3.54007 6.67728i 0.116840 0.220383i
\(919\) −4.61760 8.70972i −0.152321 0.287307i 0.795595 0.605829i \(-0.207158\pi\)
−0.947916 + 0.318522i \(0.896814\pi\)
\(920\) −9.70738 + 14.3173i −0.320043 + 0.472028i
\(921\) 6.85289 1.50843i 0.225810 0.0497046i
\(922\) −4.66156 16.7894i −0.153520 0.552930i
\(923\) 19.8137 49.7286i 0.652176 1.63684i
\(924\) 0.0330104 0.0111225i 0.00108596 0.000365904i
\(925\) 1.61522 1.53001i 0.0531080 0.0503066i
\(926\) 25.1039 + 5.52578i 0.824965 + 0.181589i
\(927\) −0.347790 6.41460i −0.0114229 0.210683i
\(928\) −0.746275 4.55208i −0.0244977 0.149429i
\(929\) 21.4993 + 25.3110i 0.705370 + 0.830426i 0.991817 0.127670i \(-0.0407498\pi\)
−0.286446 + 0.958096i \(0.592474\pi\)
\(930\) 8.70530 + 21.8486i 0.285458 + 0.716445i
\(931\) 24.8090 18.8593i 0.813083 0.618090i
\(932\) 13.6593 8.21853i 0.447425 0.269207i
\(933\) −0.112218 + 0.684501i −0.00367386 + 0.0224095i
\(934\) −38.4235 4.17881i −1.25726 0.136735i
\(935\) 19.3081 + 14.6776i 0.631443 + 0.480010i
\(936\) −1.53717 + 5.53637i −0.0502438 + 0.180962i
\(937\) 1.90399 35.1171i 0.0622007 1.14722i −0.786236 0.617927i \(-0.787973\pi\)
0.848436 0.529298i \(-0.177544\pi\)
\(938\) 0.274334 0.0298356i 0.00895732 0.000974167i
\(939\) 12.7846 + 7.69225i 0.417210 + 0.251027i
\(940\) −7.76776 + 9.14491i −0.253356 + 0.298274i
\(941\) −48.9545 16.4947i −1.59587 0.537711i −0.625685 0.780076i \(-0.715181\pi\)
−0.970185 + 0.242364i \(0.922077\pi\)
\(942\) 18.6047 8.60744i 0.606173 0.280446i
\(943\) 72.0806 2.34727
\(944\) 4.68904 + 6.08382i 0.152615 + 0.198012i
\(945\) 0.0564942 0.00183776
\(946\) 4.95678 2.29325i 0.161159 0.0745600i
\(947\) −17.0996 5.76154i −0.555664 0.187225i 0.0274389 0.999623i \(-0.491265\pi\)
−0.583102 + 0.812399i \(0.698161\pi\)
\(948\) −1.23856 + 1.45814i −0.0402265 + 0.0473583i
\(949\) −16.7892 10.1017i −0.545000 0.327915i
\(950\) 0.905780 0.0985095i 0.0293874 0.00319607i
\(951\) −0.321578 + 5.93116i −0.0104279 + 0.192331i
\(952\) −0.0500686 + 0.180331i −0.00162273 + 0.00584455i
\(953\) 19.6522 + 14.9392i 0.636597 + 0.483929i 0.872996 0.487727i \(-0.162174\pi\)
−0.236399 + 0.971656i \(0.575967\pi\)
\(954\) 0.345271 + 0.0375504i 0.0111785 + 0.00121574i
\(955\) −7.51508 + 45.8399i −0.243182 + 1.48335i
\(956\) 14.4481 8.69316i 0.467286 0.281157i
\(957\) −5.16566 + 3.92684i −0.166982 + 0.126937i
\(958\) 12.2778 + 30.8149i 0.396677 + 0.995584i
\(959\) −0.0467413 0.0550281i −0.00150936 0.00177695i
\(960\) −0.369084 2.25131i −0.0119121 0.0726609i
\(961\) 4.07554 + 75.1689i 0.131469 + 2.42480i
\(962\) 61.0075 + 13.4288i 1.96696 + 0.432961i
\(963\) −4.16703 + 3.94722i −0.134281 + 0.127197i
\(964\) −13.4885 + 4.54481i −0.434436 + 0.146378i
\(965\) 13.8584 34.7821i 0.446119 1.11967i
\(966\) 0.0502316 + 0.180918i 0.00161618 + 0.00582094i
\(967\) −16.1015 + 3.54421i −0.517790 + 0.113974i −0.466174 0.884693i \(-0.654368\pi\)
−0.0516153 + 0.998667i \(0.516437\pi\)
\(968\) 5.06262 7.46680i 0.162719 0.239992i
\(969\) −15.7615 29.7294i −0.506333 0.955045i
\(970\) −4.57849 + 8.63595i −0.147006 + 0.277284i
\(971\) 23.7447 + 35.0208i 0.762004 + 1.12387i 0.988700 + 0.149906i \(0.0478972\pi\)
−0.226696 + 0.973966i \(0.572792\pi\)
\(972\) 0.725995 + 0.687699i 0.0232863 + 0.0220580i
\(973\) 0.121211 + 0.0560781i 0.00388584 + 0.00179778i
\(974\) −6.76626 3.13041i −0.216805 0.100305i
\(975\) −0.853640 0.808611i −0.0273384 0.0258963i
\(976\) −2.52789 3.72836i −0.0809158 0.119342i
\(977\) −4.30917 + 8.12796i −0.137863 + 0.260037i −0.942824 0.333290i \(-0.891841\pi\)
0.804962 + 0.593327i \(0.202186\pi\)
\(978\) 6.41046 + 12.0914i 0.204984 + 0.386641i
\(979\) 2.44362 3.60407i 0.0780983 0.115186i
\(980\) 15.5948 3.43269i 0.498159 0.109653i
\(981\) 3.30820 + 11.9151i 0.105623 + 0.380419i
\(982\) 4.87088 12.2250i 0.155436 0.390115i
\(983\) 13.2674 4.47030i 0.423164 0.142580i −0.0996595 0.995022i \(-0.531775\pi\)
0.522823 + 0.852441i \(0.324879\pi\)
\(984\) −6.90166 + 6.53760i −0.220017 + 0.208411i
\(985\) 44.2923 + 9.74948i 1.41127 + 0.310644i
\(986\) −1.88741 34.8112i −0.0601073 1.10861i
\(987\) 0.0210705 + 0.128525i 0.000670682 + 0.00409098i
\(988\) 16.5615 + 19.4977i 0.526892 + 0.620306i
\(989\) 10.8965 + 27.3481i 0.346488 + 0.869619i
\(990\) −2.55478 + 1.94209i −0.0811961 + 0.0617237i
\(991\) 40.8067 24.5526i 1.29627 0.779938i 0.310910 0.950439i \(-0.399366\pi\)
0.985358 + 0.170501i \(0.0545386\pi\)
\(992\) 1.66784 10.1734i 0.0529540 0.323005i
\(993\) 12.3924 + 1.34775i 0.393259 + 0.0427695i
\(994\) 0.183664 + 0.139617i 0.00582546 + 0.00442840i
\(995\) 11.5995 41.7775i 0.367728 1.32444i
\(996\) 0.574133 10.5893i 0.0181921 0.335534i
\(997\) −7.65787 + 0.832843i −0.242527 + 0.0263764i −0.228575 0.973526i \(-0.573407\pi\)
−0.0139519 + 0.999903i \(0.504441\pi\)
\(998\) −1.83096 1.10165i −0.0579580 0.0348722i
\(999\) 7.03834 8.28618i 0.222683 0.262163i
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 354.2.e.c.121.3 yes 84
59.20 even 29 inner 354.2.e.c.79.3 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
354.2.e.c.79.3 84 59.20 even 29 inner
354.2.e.c.121.3 yes 84 1.1 even 1 trivial