Properties

Label 108.2.l.a.59.3
Level $108$
Weight $2$
Character 108.59
Analytic conductor $0.862$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [108,2,Mod(11,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 13]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 108.l (of order \(18\), degree \(6\), 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: \(0.862384341830\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 59.3
Character \(\chi\) \(=\) 108.59
Dual form 108.2.l.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.27725 - 0.607153i) q^{2} +(0.971698 - 1.43381i) q^{3} +(1.26273 + 1.55097i) q^{4} +(1.29726 + 3.56419i) q^{5} +(-2.11164 + 1.24136i) q^{6} +(2.58045 - 0.455003i) q^{7} +(-0.671144 - 2.74765i) q^{8} +(-1.11160 - 2.78646i) q^{9} +O(q^{10})\) \(q+(-1.27725 - 0.607153i) q^{2} +(0.971698 - 1.43381i) q^{3} +(1.26273 + 1.55097i) q^{4} +(1.29726 + 3.56419i) q^{5} +(-2.11164 + 1.24136i) q^{6} +(2.58045 - 0.455003i) q^{7} +(-0.671144 - 2.74765i) q^{8} +(-1.11160 - 2.78646i) q^{9} +(0.507086 - 5.33999i) q^{10} +(-3.39295 - 1.23493i) q^{11} +(3.45079 - 0.303435i) q^{12} +(-0.819980 - 0.688045i) q^{13} +(-3.57213 - 0.985577i) q^{14} +(6.37090 + 1.60330i) q^{15} +(-0.811025 + 3.91692i) q^{16} +(0.980503 + 0.566093i) q^{17} +(-0.272010 + 4.23391i) q^{18} +(-0.0627092 + 0.0362052i) q^{19} +(-3.88987 + 6.51262i) q^{20} +(1.85503 - 4.14199i) q^{21} +(3.58385 + 3.63736i) q^{22} +(0.0731435 - 0.414817i) q^{23} +(-4.59174 - 1.70759i) q^{24} +(-7.19034 + 6.03341i) q^{25} +(0.629570 + 1.37666i) q^{26} +(-5.07538 - 1.11377i) q^{27} +(3.96411 + 3.42766i) q^{28} +(-0.192281 - 0.229152i) q^{29} +(-7.16378 - 5.91593i) q^{30} +(-6.88084 - 1.21328i) q^{31} +(3.41405 - 4.51046i) q^{32} +(-5.06759 + 3.66486i) q^{33} +(-0.908641 - 1.31836i) q^{34} +(4.96923 + 8.60696i) q^{35} +(2.91806 - 5.24261i) q^{36} +(0.377668 - 0.654141i) q^{37} +(0.102077 - 0.00816893i) q^{38} +(-1.78330 + 0.507121i) q^{39} +(8.92249 - 5.95649i) q^{40} +(6.36586 - 7.58654i) q^{41} +(-4.88416 + 4.16407i) q^{42} +(-3.18308 + 8.74545i) q^{43} +(-2.36904 - 6.82177i) q^{44} +(8.48942 - 7.57672i) q^{45} +(-0.345280 + 0.485416i) q^{46} +(-0.0443203 - 0.251353i) q^{47} +(4.82803 + 4.96892i) q^{48} +(-0.126150 + 0.0459147i) q^{49} +(12.8471 - 3.34053i) q^{50} +(1.76442 - 0.855779i) q^{51} +(0.0317246 - 2.14058i) q^{52} +12.0634i q^{53} +(5.80630 + 4.50409i) q^{54} -13.6952i q^{55} +(-2.98204 - 6.78480i) q^{56} +(-0.00902320 + 0.125093i) q^{57} +(0.106461 + 0.409428i) q^{58} +(-11.7359 + 4.27153i) q^{59} +(5.55806 + 11.9056i) q^{60} +(-1.13416 - 6.43213i) q^{61} +(8.05190 + 5.72738i) q^{62} +(-4.13629 - 6.68453i) q^{63} +(-7.09913 + 3.68813i) q^{64} +(1.38860 - 3.81514i) q^{65} +(8.69770 - 1.60414i) q^{66} +(4.37678 - 5.21604i) q^{67} +(0.360115 + 2.23555i) q^{68} +(-0.523695 - 0.507951i) q^{69} +(-1.12120 - 14.0103i) q^{70} +(6.35108 - 11.0004i) q^{71} +(-6.91015 + 4.92441i) q^{72} +(-0.578249 - 1.00156i) q^{73} +(-0.879540 + 0.606198i) q^{74} +(1.66391 + 16.1722i) q^{75} +(-0.135338 - 0.0515428i) q^{76} +(-9.31725 - 1.64288i) q^{77} +(2.58561 + 0.435015i) q^{78} +(5.09561 + 6.07271i) q^{79} +(-15.0127 + 2.19061i) q^{80} +(-6.52867 + 6.19487i) q^{81} +(-12.7370 + 5.82484i) q^{82} +(3.00034 - 2.51758i) q^{83} +(8.76652 - 2.35312i) q^{84} +(-0.745699 + 4.22907i) q^{85} +(9.37542 - 9.23750i) q^{86} +(-0.515398 + 0.0530276i) q^{87} +(-1.11601 + 10.1515i) q^{88} +(2.07380 - 1.19731i) q^{89} +(-15.4433 + 4.52299i) q^{90} +(-2.42898 - 1.40237i) q^{91} +(0.735730 - 0.410359i) q^{92} +(-8.42570 + 8.68685i) q^{93} +(-0.0960018 + 0.347950i) q^{94} +(-0.210392 - 0.176540i) q^{95} +(-3.14970 - 9.27790i) q^{96} +(1.81485 + 0.660552i) q^{97} +(0.189002 + 0.0179476i) q^{98} +(0.330533 + 10.8271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27725 0.607153i −0.903151 0.429322i
\(3\) 0.971698 1.43381i 0.561010 0.827809i
\(4\) 1.26273 + 1.55097i 0.631365 + 0.775486i
\(5\) 1.29726 + 3.56419i 0.580152 + 1.59395i 0.787921 + 0.615776i \(0.211157\pi\)
−0.207769 + 0.978178i \(0.566620\pi\)
\(6\) −2.11164 + 1.24136i −0.862074 + 0.506783i
\(7\) 2.58045 0.455003i 0.975319 0.171975i 0.336796 0.941578i \(-0.390657\pi\)
0.638523 + 0.769603i \(0.279546\pi\)
\(8\) −0.671144 2.74765i −0.237285 0.971440i
\(9\) −1.11160 2.78646i −0.370535 0.928819i
\(10\) 0.507086 5.33999i 0.160355 1.68865i
\(11\) −3.39295 1.23493i −1.02301 0.372347i −0.224597 0.974452i \(-0.572107\pi\)
−0.798417 + 0.602105i \(0.794329\pi\)
\(12\) 3.45079 0.303435i 0.996156 0.0875940i
\(13\) −0.819980 0.688045i −0.227421 0.190829i 0.521956 0.852973i \(-0.325203\pi\)
−0.749377 + 0.662143i \(0.769647\pi\)
\(14\) −3.57213 0.985577i −0.954693 0.263406i
\(15\) 6.37090 + 1.60330i 1.64496 + 0.413970i
\(16\) −0.811025 + 3.91692i −0.202756 + 0.979229i
\(17\) 0.980503 + 0.566093i 0.237807 + 0.137298i 0.614168 0.789175i \(-0.289492\pi\)
−0.376361 + 0.926473i \(0.622825\pi\)
\(18\) −0.272010 + 4.23391i −0.0641133 + 0.997943i
\(19\) −0.0627092 + 0.0362052i −0.0143865 + 0.00830603i −0.507176 0.861843i \(-0.669311\pi\)
0.492790 + 0.870149i \(0.335977\pi\)
\(20\) −3.88987 + 6.51262i −0.869801 + 1.45627i
\(21\) 1.85503 4.14199i 0.404801 0.903857i
\(22\) 3.58385 + 3.63736i 0.764080 + 0.775488i
\(23\) 0.0731435 0.414817i 0.0152515 0.0864954i −0.976232 0.216728i \(-0.930461\pi\)
0.991483 + 0.130233i \(0.0415725\pi\)
\(24\) −4.59174 1.70759i −0.937286 0.348561i
\(25\) −7.19034 + 6.03341i −1.43807 + 1.20668i
\(26\) 0.629570 + 1.37666i 0.123469 + 0.269985i
\(27\) −5.07538 1.11377i −0.976758 0.214345i
\(28\) 3.96411 + 3.42766i 0.749146 + 0.647767i
\(29\) −0.192281 0.229152i −0.0357057 0.0425524i 0.747896 0.663816i \(-0.231064\pi\)
−0.783602 + 0.621263i \(0.786620\pi\)
\(30\) −7.16378 5.91593i −1.30792 1.08010i
\(31\) −6.88084 1.21328i −1.23583 0.217911i −0.482705 0.875783i \(-0.660346\pi\)
−0.753130 + 0.657872i \(0.771457\pi\)
\(32\) 3.41405 4.51046i 0.603524 0.797345i
\(33\) −5.06759 + 3.66486i −0.882154 + 0.637970i
\(34\) −0.908641 1.31836i −0.155831 0.226096i
\(35\) 4.96923 + 8.60696i 0.839953 + 1.45484i
\(36\) 2.91806 5.24261i 0.486343 0.873768i
\(37\) 0.377668 0.654141i 0.0620883 0.107540i −0.833310 0.552805i \(-0.813557\pi\)
0.895399 + 0.445265i \(0.146891\pi\)
\(38\) 0.102077 0.00816893i 0.0165591 0.00132518i
\(39\) −1.78330 + 0.507121i −0.285556 + 0.0812043i
\(40\) 8.92249 5.95649i 1.41077 0.941804i
\(41\) 6.36586 7.58654i 0.994180 1.18482i 0.0114196 0.999935i \(-0.496365\pi\)
0.982761 0.184883i \(-0.0591906\pi\)
\(42\) −4.88416 + 4.16407i −0.753643 + 0.642530i
\(43\) −3.18308 + 8.74545i −0.485416 + 1.33367i 0.419375 + 0.907813i \(0.362249\pi\)
−0.904791 + 0.425856i \(0.859973\pi\)
\(44\) −2.36904 6.82177i −0.357146 1.02842i
\(45\) 8.48942 7.57672i 1.26553 1.12947i
\(46\) −0.345280 + 0.485416i −0.0509088 + 0.0715706i
\(47\) −0.0443203 0.251353i −0.00646479 0.0366636i 0.981405 0.191950i \(-0.0614811\pi\)
−0.987870 + 0.155286i \(0.950370\pi\)
\(48\) 4.82803 + 4.96892i 0.696866 + 0.717201i
\(49\) −0.126150 + 0.0459147i −0.0180214 + 0.00655925i
\(50\) 12.8471 3.34053i 1.81685 0.472423i
\(51\) 1.76442 0.855779i 0.247068 0.119833i
\(52\) 0.0317246 2.14058i 0.00439941 0.296845i
\(53\) 12.0634i 1.65703i 0.559967 + 0.828515i \(0.310814\pi\)
−0.559967 + 0.828515i \(0.689186\pi\)
\(54\) 5.80630 + 4.50409i 0.790137 + 0.612930i
\(55\) 13.6952i 1.84666i
\(56\) −2.98204 6.78480i −0.398492 0.906657i
\(57\) −0.00902320 + 0.125093i −0.00119515 + 0.0165690i
\(58\) 0.106461 + 0.409428i 0.0139790 + 0.0537605i
\(59\) −11.7359 + 4.27153i −1.52789 + 0.556106i −0.963104 0.269131i \(-0.913263\pi\)
−0.564786 + 0.825237i \(0.691041\pi\)
\(60\) 5.55806 + 11.9056i 0.717543 + 1.53701i
\(61\) −1.13416 6.43213i −0.145214 0.823550i −0.967195 0.254035i \(-0.918242\pi\)
0.821981 0.569515i \(-0.192869\pi\)
\(62\) 8.05190 + 5.72738i 1.02259 + 0.727378i
\(63\) −4.13629 6.68453i −0.521123 0.842171i
\(64\) −7.09913 + 3.68813i −0.887392 + 0.461016i
\(65\) 1.38860 3.81514i 0.172234 0.473209i
\(66\) 8.69770 1.60414i 1.07061 0.197455i
\(67\) 4.37678 5.21604i 0.534709 0.637241i −0.429284 0.903170i \(-0.641234\pi\)
0.963993 + 0.265928i \(0.0856785\pi\)
\(68\) 0.360115 + 2.23555i 0.0436704 + 0.271101i
\(69\) −0.523695 0.507951i −0.0630454 0.0611501i
\(70\) −1.12120 14.0103i −0.134009 1.67455i
\(71\) 6.35108 11.0004i 0.753734 1.30551i −0.192267 0.981343i \(-0.561584\pi\)
0.946001 0.324163i \(-0.105083\pi\)
\(72\) −6.91015 + 4.92441i −0.814369 + 0.580347i
\(73\) −0.578249 1.00156i −0.0676789 0.117223i 0.830200 0.557465i \(-0.188226\pi\)
−0.897879 + 0.440242i \(0.854893\pi\)
\(74\) −0.879540 + 0.606198i −0.102244 + 0.0704691i
\(75\) 1.66391 + 16.1722i 0.192131 + 1.86741i
\(76\) −0.135338 0.0515428i −0.0155243 0.00591236i
\(77\) −9.31725 1.64288i −1.06180 0.187224i
\(78\) 2.58561 + 0.435015i 0.292763 + 0.0492557i
\(79\) 5.09561 + 6.07271i 0.573301 + 0.683233i 0.972305 0.233716i \(-0.0750886\pi\)
−0.399004 + 0.916949i \(0.630644\pi\)
\(80\) −15.0127 + 2.19061i −1.67848 + 0.244917i
\(81\) −6.52867 + 6.19487i −0.725408 + 0.688319i
\(82\) −12.7370 + 5.82484i −1.40656 + 0.643246i
\(83\) 3.00034 2.51758i 0.329330 0.276340i −0.463097 0.886308i \(-0.653262\pi\)
0.792427 + 0.609967i \(0.208817\pi\)
\(84\) 8.76652 2.35312i 0.956506 0.256746i
\(85\) −0.745699 + 4.22907i −0.0808824 + 0.458707i
\(86\) 9.37542 9.23750i 1.01098 0.996105i
\(87\) −0.515398 + 0.0530276i −0.0552565 + 0.00568516i
\(88\) −1.11601 + 10.1515i −0.118967 + 1.08215i
\(89\) 2.07380 1.19731i 0.219823 0.126915i −0.386046 0.922480i \(-0.626159\pi\)
0.605868 + 0.795565i \(0.292826\pi\)
\(90\) −15.4433 + 4.52299i −1.62787 + 0.476765i
\(91\) −2.42898 1.40237i −0.254626 0.147009i
\(92\) 0.735730 0.410359i 0.0767052 0.0427829i
\(93\) −8.42570 + 8.68685i −0.873705 + 0.900785i
\(94\) −0.0960018 + 0.347950i −0.00990183 + 0.0358883i
\(95\) −0.210392 0.176540i −0.0215858 0.0181126i
\(96\) −3.14970 9.27790i −0.321465 0.946921i
\(97\) 1.81485 + 0.660552i 0.184270 + 0.0670689i 0.432507 0.901630i \(-0.357629\pi\)
−0.248237 + 0.968699i \(0.579851\pi\)
\(98\) 0.189002 + 0.0179476i 0.0190921 + 0.00181299i
\(99\) 0.330533 + 10.8271i 0.0332198 + 1.08816i
\(100\) −18.4371 3.53344i −1.84371 0.353344i
\(101\) 4.42993 0.781117i 0.440795 0.0777241i 0.0511538 0.998691i \(-0.483710\pi\)
0.389641 + 0.920967i \(0.372599\pi\)
\(102\) −2.77319 + 0.0217692i −0.274587 + 0.00215547i
\(103\) 2.17204 + 5.96763i 0.214017 + 0.588008i 0.999524 0.0308451i \(-0.00981984\pi\)
−0.785507 + 0.618853i \(0.787598\pi\)
\(104\) −1.34018 + 2.71479i −0.131415 + 0.266207i
\(105\) 17.1693 + 1.23845i 1.67555 + 0.120861i
\(106\) 7.32430 15.4079i 0.711399 1.49655i
\(107\) 9.90677 0.957724 0.478862 0.877890i \(-0.341049\pi\)
0.478862 + 0.877890i \(0.341049\pi\)
\(108\) −4.68142 9.27816i −0.450470 0.892792i
\(109\) 7.94635 0.761122 0.380561 0.924756i \(-0.375731\pi\)
0.380561 + 0.924756i \(0.375731\pi\)
\(110\) −8.31506 + 17.4921i −0.792810 + 1.66781i
\(111\) −0.570932 1.17713i −0.0541905 0.111728i
\(112\) −0.310602 + 10.4764i −0.0293491 + 0.989930i
\(113\) −3.44642 9.46897i −0.324212 0.890766i −0.989546 0.144219i \(-0.953933\pi\)
0.665334 0.746546i \(-0.268289\pi\)
\(114\) 0.0874757 0.154297i 0.00819285 0.0144512i
\(115\) 1.57337 0.277428i 0.146718 0.0258703i
\(116\) 0.112609 0.587579i 0.0104554 0.0545554i
\(117\) −1.00571 + 3.04967i −0.0929782 + 0.281942i
\(118\) 17.5832 + 1.66970i 1.61866 + 0.153709i
\(119\) 2.78771 + 1.01464i 0.255549 + 0.0930123i
\(120\) 0.129508 18.5810i 0.0118224 1.69621i
\(121\) 1.56059 + 1.30949i 0.141872 + 0.119045i
\(122\) −2.45669 + 8.90404i −0.222418 + 0.806134i
\(123\) −4.69193 16.4992i −0.423057 1.48769i
\(124\) −6.80688 12.2040i −0.611276 1.09595i
\(125\) −14.4081 8.31852i −1.28870 0.744031i
\(126\) 1.22454 + 11.0492i 0.109090 + 0.984338i
\(127\) 11.0681 6.39020i 0.982139 0.567038i 0.0792237 0.996857i \(-0.474756\pi\)
0.902915 + 0.429819i \(0.141423\pi\)
\(128\) 11.3066 0.400402i 0.999374 0.0353909i
\(129\) 9.44629 + 13.0619i 0.831700 + 1.15003i
\(130\) −4.08995 + 4.02979i −0.358713 + 0.353436i
\(131\) −1.12042 + 6.35420i −0.0978913 + 0.555169i 0.895932 + 0.444192i \(0.146509\pi\)
−0.993823 + 0.110977i \(0.964602\pi\)
\(132\) −12.0831 3.23196i −1.05170 0.281306i
\(133\) −0.145344 + 0.121958i −0.0126030 + 0.0105751i
\(134\) −8.75717 + 4.00481i −0.756505 + 0.345963i
\(135\) −2.61440 19.5345i −0.225012 1.68126i
\(136\) 0.897367 3.07401i 0.0769486 0.263594i
\(137\) 1.38785 + 1.65398i 0.118572 + 0.141309i 0.822065 0.569393i \(-0.192822\pi\)
−0.703493 + 0.710702i \(0.748377\pi\)
\(138\) 0.360484 + 0.966743i 0.0306865 + 0.0822946i
\(139\) −6.90717 1.21792i −0.585859 0.103303i −0.127141 0.991885i \(-0.540580\pi\)
−0.458718 + 0.888582i \(0.651691\pi\)
\(140\) −7.07435 + 18.5754i −0.597892 + 1.56991i
\(141\) −0.403458 0.180693i −0.0339773 0.0152171i
\(142\) −14.7908 + 10.1942i −1.24122 + 0.855475i
\(143\) 1.93246 + 3.34713i 0.161601 + 0.279901i
\(144\) 11.8159 2.09418i 0.984655 0.174515i
\(145\) 0.567302 0.982595i 0.0471118 0.0816001i
\(146\) 0.130470 + 1.63032i 0.0107977 + 0.134926i
\(147\) −0.0567466 + 0.225490i −0.00468038 + 0.0185981i
\(148\) 1.49145 0.240250i 0.122596 0.0197485i
\(149\) −7.49826 + 8.93608i −0.614282 + 0.732072i −0.980076 0.198623i \(-0.936353\pi\)
0.365794 + 0.930696i \(0.380797\pi\)
\(150\) 7.69379 21.6662i 0.628196 1.76904i
\(151\) −0.154723 + 0.425097i −0.0125911 + 0.0345939i −0.945829 0.324665i \(-0.894748\pi\)
0.933238 + 0.359259i \(0.116971\pi\)
\(152\) 0.141566 + 0.148004i 0.0114825 + 0.0120047i
\(153\) 0.487463 3.36140i 0.0394091 0.271753i
\(154\) 10.9030 + 7.75537i 0.878586 + 0.624946i
\(155\) −4.60188 26.0985i −0.369632 2.09629i
\(156\) −3.03835 2.12549i −0.243263 0.170175i
\(157\) 17.2816 6.28998i 1.37922 0.501995i 0.457279 0.889323i \(-0.348824\pi\)
0.921942 + 0.387328i \(0.126602\pi\)
\(158\) −2.82130 10.8502i −0.224450 0.863193i
\(159\) 17.2965 + 11.7219i 1.37170 + 0.929611i
\(160\) 20.5050 + 6.31708i 1.62107 + 0.499409i
\(161\) 1.10370i 0.0869834i
\(162\) 12.1000 3.94849i 0.950664 0.310223i
\(163\) 22.5880i 1.76923i 0.466320 + 0.884616i \(0.345579\pi\)
−0.466320 + 0.884616i \(0.654421\pi\)
\(164\) 19.8049 + 0.293519i 1.54650 + 0.0229200i
\(165\) −19.6362 13.3076i −1.52868 1.03599i
\(166\) −5.36073 + 1.39391i −0.416074 + 0.108189i
\(167\) 4.32888 1.57558i 0.334979 0.121922i −0.169054 0.985607i \(-0.554071\pi\)
0.504033 + 0.863684i \(0.331849\pi\)
\(168\) −12.6257 2.31711i −0.974096 0.178769i
\(169\) −2.05847 11.6741i −0.158343 0.898010i
\(170\) 3.52013 4.94882i 0.269982 0.379557i
\(171\) 0.170592 + 0.134490i 0.0130455 + 0.0102847i
\(172\) −17.5833 + 6.10627i −1.34072 + 0.465599i
\(173\) −2.55462 + 7.01876i −0.194224 + 0.533626i −0.998130 0.0611306i \(-0.980529\pi\)
0.803906 + 0.594757i \(0.202752\pi\)
\(174\) 0.690488 + 0.245196i 0.0523458 + 0.0185883i
\(175\) −15.8091 + 18.8406i −1.19506 + 1.42421i
\(176\) 7.58891 12.2884i 0.572036 0.926270i
\(177\) −5.27924 + 20.9777i −0.396812 + 1.57678i
\(178\) −3.37571 + 0.270148i −0.253020 + 0.0202484i
\(179\) −5.08749 + 8.81180i −0.380257 + 0.658625i −0.991099 0.133128i \(-0.957498\pi\)
0.610842 + 0.791753i \(0.290831\pi\)
\(180\) 22.4711 + 3.59949i 1.67490 + 0.268290i
\(181\) 8.40432 + 14.5567i 0.624688 + 1.08199i 0.988601 + 0.150559i \(0.0481073\pi\)
−0.363913 + 0.931433i \(0.618559\pi\)
\(182\) 2.25096 + 3.26594i 0.166852 + 0.242088i
\(183\) −10.3245 4.62393i −0.763209 0.341811i
\(184\) −1.18886 + 0.0774295i −0.0876440 + 0.00570818i
\(185\) 2.82142 + 0.497492i 0.207435 + 0.0365763i
\(186\) 16.0360 5.97958i 1.17581 0.438444i
\(187\) −2.62771 3.13159i −0.192157 0.229004i
\(188\) 0.333877 0.386131i 0.0243505 0.0281615i
\(189\) −13.6035 0.564710i −0.989512 0.0410766i
\(190\) 0.161536 + 0.353226i 0.0117191 + 0.0256257i
\(191\) −0.0529445 + 0.0444257i −0.00383093 + 0.00321453i −0.644701 0.764435i \(-0.723018\pi\)
0.640870 + 0.767649i \(0.278574\pi\)
\(192\) −1.61015 + 13.7625i −0.116202 + 0.993226i
\(193\) 4.64409 26.3379i 0.334289 1.89585i −0.0998555 0.995002i \(-0.531838\pi\)
0.434144 0.900843i \(-0.357051\pi\)
\(194\) −1.91696 1.94558i −0.137630 0.139685i
\(195\) −4.12087 5.69814i −0.295102 0.408052i
\(196\) −0.230505 0.137677i −0.0164647 0.00983405i
\(197\) 3.87890 2.23948i 0.276360 0.159557i −0.355414 0.934709i \(-0.615660\pi\)
0.631774 + 0.775152i \(0.282327\pi\)
\(198\) 6.15152 14.0296i 0.437170 0.997037i
\(199\) 8.51533 + 4.91633i 0.603636 + 0.348509i 0.770470 0.637476i \(-0.220021\pi\)
−0.166835 + 0.985985i \(0.553355\pi\)
\(200\) 21.4034 + 15.7072i 1.51345 + 1.11067i
\(201\) −3.22589 11.3439i −0.227537 0.800135i
\(202\) −6.13239 1.69197i −0.431473 0.119046i
\(203\) −0.600437 0.503826i −0.0421424 0.0353617i
\(204\) 3.55528 + 1.65595i 0.248919 + 0.115940i
\(205\) 35.2980 + 12.8474i 2.46532 + 0.897303i
\(206\) 0.849030 8.94091i 0.0591547 0.622943i
\(207\) −1.23718 + 0.257302i −0.0859897 + 0.0178837i
\(208\) 3.36004 2.65377i 0.232977 0.184006i
\(209\) 0.257480 0.0454007i 0.0178103 0.00314043i
\(210\) −21.1776 12.0062i −1.46139 0.828507i
\(211\) −4.53594 12.4624i −0.312267 0.857947i −0.992198 0.124671i \(-0.960212\pi\)
0.679931 0.733276i \(-0.262010\pi\)
\(212\) −18.7099 + 15.2328i −1.28500 + 1.04619i
\(213\) −9.60110 19.7953i −0.657856 1.35635i
\(214\) −12.6534 6.01493i −0.864970 0.411172i
\(215\) −35.2997 −2.40742
\(216\) 0.346068 + 14.6929i 0.0235469 + 0.999723i
\(217\) −18.3077 −1.24281
\(218\) −10.1495 4.82465i −0.687408 0.326766i
\(219\) −1.99792 0.144114i −0.135007 0.00973829i
\(220\) 21.2408 17.2933i 1.43206 1.16591i
\(221\) −0.414495 1.13881i −0.0278819 0.0766050i
\(222\) 0.0145233 + 1.85013i 0.000974739 + 0.124173i
\(223\) 17.4629 3.07919i 1.16940 0.206198i 0.444973 0.895544i \(-0.353213\pi\)
0.724432 + 0.689346i \(0.242102\pi\)
\(224\) 6.75751 13.1924i 0.451505 0.881456i
\(225\) 24.8047 + 13.3288i 1.65364 + 0.888587i
\(226\) −1.34717 + 14.1867i −0.0896127 + 0.943688i
\(227\) −5.66395 2.06151i −0.375929 0.136827i 0.147143 0.989115i \(-0.452992\pi\)
−0.523073 + 0.852288i \(0.675214\pi\)
\(228\) −0.205410 + 0.143964i −0.0136036 + 0.00953427i
\(229\) −13.4367 11.2747i −0.887922 0.745055i 0.0798705 0.996805i \(-0.474549\pi\)
−0.967792 + 0.251751i \(0.918994\pi\)
\(230\) −2.17803 0.600934i −0.143615 0.0396244i
\(231\) −11.4091 + 11.7628i −0.750666 + 0.773932i
\(232\) −0.500580 + 0.682114i −0.0328647 + 0.0447830i
\(233\) −0.818415 0.472512i −0.0536162 0.0309553i 0.472952 0.881088i \(-0.343188\pi\)
−0.526568 + 0.850133i \(0.676522\pi\)
\(234\) 3.13616 3.28457i 0.205017 0.214719i
\(235\) 0.838375 0.484036i 0.0546896 0.0315750i
\(236\) −21.4444 12.8083i −1.39591 0.833750i
\(237\) 13.6585 1.40528i 0.887214 0.0912825i
\(238\) −2.94456 2.98852i −0.190867 0.193717i
\(239\) −1.94169 + 11.0119i −0.125598 + 0.712300i 0.855353 + 0.518045i \(0.173340\pi\)
−0.980951 + 0.194255i \(0.937771\pi\)
\(240\) −11.4470 + 23.6540i −0.738898 + 1.52686i
\(241\) −14.8130 + 12.4295i −0.954187 + 0.800658i −0.979998 0.199009i \(-0.936228\pi\)
0.0258110 + 0.999667i \(0.491783\pi\)
\(242\) −1.19820 2.62006i −0.0770233 0.168424i
\(243\) 2.53835 + 15.3804i 0.162835 + 0.986653i
\(244\) 8.54392 9.88109i 0.546968 0.632572i
\(245\) −0.327298 0.390058i −0.0209103 0.0249199i
\(246\) −4.02480 + 23.9224i −0.256612 + 1.52523i
\(247\) 0.0763310 + 0.0134592i 0.00485683 + 0.000856389i
\(248\) 1.28437 + 19.7204i 0.0815577 + 1.25225i
\(249\) −0.694303 6.74823i −0.0439997 0.427652i
\(250\) 13.3521 + 19.3727i 0.844462 + 1.22524i
\(251\) 3.70756 + 6.42169i 0.234019 + 0.405333i 0.958987 0.283449i \(-0.0914788\pi\)
−0.724968 + 0.688783i \(0.758145\pi\)
\(252\) 5.14450 14.8560i 0.324073 0.935841i
\(253\) −0.760445 + 1.31713i −0.0478088 + 0.0828072i
\(254\) −18.0166 + 1.44181i −1.13046 + 0.0904674i
\(255\) 5.33907 + 5.17857i 0.334346 + 0.324294i
\(256\) −14.6845 6.35344i −0.917780 0.397090i
\(257\) −14.5395 + 17.3275i −0.906949 + 1.08086i 0.0894438 + 0.995992i \(0.471491\pi\)
−0.996392 + 0.0848673i \(0.972953\pi\)
\(258\) −4.13471 22.4186i −0.257416 1.39572i
\(259\) 0.676919 1.85982i 0.0420617 0.115564i
\(260\) 7.67059 2.66381i 0.475710 0.165203i
\(261\) −0.424781 + 0.790509i −0.0262933 + 0.0489313i
\(262\) 5.28903 7.43563i 0.326757 0.459375i
\(263\) 4.29886 + 24.3800i 0.265079 + 1.50334i 0.768810 + 0.639477i \(0.220849\pi\)
−0.503731 + 0.863860i \(0.668040\pi\)
\(264\) 13.4708 + 11.4643i 0.829071 + 0.705579i
\(265\) −42.9961 + 15.6493i −2.64123 + 0.961328i
\(266\) 0.259689 0.0675250i 0.0159225 0.00414022i
\(267\) 0.298399 4.13686i 0.0182617 0.253172i
\(268\) 13.6166 + 0.201806i 0.831768 + 0.0123273i
\(269\) 11.8242i 0.720932i −0.932772 0.360466i \(-0.882618\pi\)
0.932772 0.360466i \(-0.117382\pi\)
\(270\) −8.52117 + 26.5377i −0.518582 + 1.61503i
\(271\) 5.20136i 0.315960i −0.987442 0.157980i \(-0.949502\pi\)
0.987442 0.157980i \(-0.0504982\pi\)
\(272\) −3.01255 + 3.38143i −0.182663 + 0.205029i
\(273\) −4.37097 + 2.12001i −0.264543 + 0.128309i
\(274\) −0.768414 2.95518i −0.0464216 0.178529i
\(275\) 31.8474 11.5915i 1.92047 0.698994i
\(276\) 0.126533 1.45364i 0.00761637 0.0874989i
\(277\) −1.28253 7.27359i −0.0770598 0.437028i −0.998789 0.0491944i \(-0.984335\pi\)
0.921729 0.387834i \(-0.126776\pi\)
\(278\) 8.08271 + 5.74930i 0.484769 + 0.344820i
\(279\) 4.26803 + 20.5218i 0.255520 + 1.22861i
\(280\) 20.3138 19.4302i 1.21398 1.16118i
\(281\) 4.19816 11.5344i 0.250441 0.688082i −0.749226 0.662314i \(-0.769575\pi\)
0.999668 0.0257683i \(-0.00820323\pi\)
\(282\) 0.405608 + 0.475750i 0.0241536 + 0.0283305i
\(283\) 7.15737 8.52982i 0.425461 0.507045i −0.510146 0.860088i \(-0.670409\pi\)
0.935607 + 0.353043i \(0.114853\pi\)
\(284\) 25.0810 4.04018i 1.48828 0.239741i
\(285\) −0.457562 + 0.130118i −0.0271036 + 0.00770753i
\(286\) −0.436020 5.44842i −0.0257824 0.322172i
\(287\) 12.9749 22.4732i 0.765883 1.32655i
\(288\) −16.3633 4.49925i −0.964215 0.265121i
\(289\) −7.85908 13.6123i −0.462299 0.800725i
\(290\) −1.32117 + 0.910580i −0.0775818 + 0.0534711i
\(291\) 2.71059 1.96029i 0.158898 0.114914i
\(292\) 0.823213 2.16154i 0.0481749 0.126495i
\(293\) 22.9154 + 4.04060i 1.33873 + 0.236055i 0.796737 0.604327i \(-0.206558\pi\)
0.541995 + 0.840381i \(0.317669\pi\)
\(294\) 0.209386 0.253552i 0.0122117 0.0147875i
\(295\) −30.4491 36.2878i −1.77282 2.11276i
\(296\) −2.05082 0.598677i −0.119201 0.0347974i
\(297\) 15.8451 + 10.0467i 0.919427 + 0.582971i
\(298\) 15.0027 6.86101i 0.869084 0.397448i
\(299\) −0.345389 + 0.289816i −0.0199744 + 0.0167605i
\(300\) −22.9816 + 23.0018i −1.32684 + 1.32801i
\(301\) −4.23458 + 24.0155i −0.244077 + 1.38423i
\(302\) 0.455718 0.449014i 0.0262236 0.0258379i
\(303\) 3.18459 7.11068i 0.182950 0.408498i
\(304\) −0.0909539 0.274990i −0.00521656 0.0157718i
\(305\) 21.4540 12.3865i 1.22845 0.709249i
\(306\) −2.66350 + 3.99738i −0.152262 + 0.228515i
\(307\) −12.7201 7.34397i −0.725976 0.419142i 0.0909723 0.995853i \(-0.471003\pi\)
−0.816948 + 0.576711i \(0.804336\pi\)
\(308\) −9.21711 16.5253i −0.525194 0.941617i
\(309\) 10.6670 + 2.68445i 0.606824 + 0.152713i
\(310\) −9.96807 + 36.1284i −0.566148 + 2.05195i
\(311\) 1.78694 + 1.49942i 0.101328 + 0.0850244i 0.692044 0.721855i \(-0.256710\pi\)
−0.590716 + 0.806879i \(0.701155\pi\)
\(312\) 2.59024 + 4.55952i 0.146643 + 0.258132i
\(313\) 6.61824 + 2.40884i 0.374085 + 0.136156i 0.522219 0.852811i \(-0.325104\pi\)
−0.148134 + 0.988967i \(0.547327\pi\)
\(314\) −25.8919 2.45870i −1.46116 0.138752i
\(315\) 18.4591 23.4141i 1.04005 1.31923i
\(316\) −2.98422 + 15.5713i −0.167876 + 0.875956i
\(317\) −1.88259 + 0.331952i −0.105737 + 0.0186443i −0.226266 0.974065i \(-0.572652\pi\)
0.120529 + 0.992710i \(0.461541\pi\)
\(318\) −14.9750 25.4735i −0.839754 1.42848i
\(319\) 0.369414 + 1.01496i 0.0206832 + 0.0568266i
\(320\) −22.3546 20.5182i −1.24966 1.14700i
\(321\) 9.62639 14.2044i 0.537293 0.792812i
\(322\) −0.670113 + 1.40969i −0.0373439 + 0.0785592i
\(323\) −0.0819820 −0.00456160
\(324\) −17.8520 2.30333i −0.991779 0.127963i
\(325\) 10.0472 0.557318
\(326\) 13.7144 28.8506i 0.759570 1.59788i
\(327\) 7.72145 11.3935i 0.426997 0.630063i
\(328\) −25.1175 12.3995i −1.38688 0.684647i
\(329\) −0.228733 0.628439i −0.0126105 0.0346469i
\(330\) 17.0006 + 28.9193i 0.935853 + 1.59195i
\(331\) 5.64140 0.994732i 0.310080 0.0546754i −0.0164430 0.999865i \(-0.505234\pi\)
0.326523 + 0.945189i \(0.394123\pi\)
\(332\) 7.69331 + 1.47441i 0.422225 + 0.0809188i
\(333\) −2.24255 0.325210i −0.122891 0.0178214i
\(334\) −6.48568 0.615880i −0.354880 0.0336995i
\(335\) 24.2688 + 8.83311i 1.32595 + 0.482605i
\(336\) 14.7194 + 10.6253i 0.803007 + 0.579656i
\(337\) 15.9033 + 13.3444i 0.866306 + 0.726917i 0.963317 0.268366i \(-0.0864837\pi\)
−0.0970109 + 0.995283i \(0.530928\pi\)
\(338\) −4.45882 + 16.1606i −0.242528 + 0.879020i
\(339\) −16.9256 4.25948i −0.919270 0.231343i
\(340\) −7.50078 + 4.18361i −0.406787 + 0.226888i
\(341\) 21.8481 + 12.6140i 1.18314 + 0.683085i
\(342\) −0.136232 0.275353i −0.00736658 0.0148894i
\(343\) −16.1891 + 9.34678i −0.874129 + 0.504679i
\(344\) 26.1657 + 2.87654i 1.41076 + 0.155093i
\(345\) 1.13107 2.52549i 0.0608946 0.135968i
\(346\) 7.52434 7.41365i 0.404511 0.398561i
\(347\) 2.69361 15.2762i 0.144601 0.820071i −0.823086 0.567917i \(-0.807750\pi\)
0.967687 0.252155i \(-0.0811393\pi\)
\(348\) −0.733054 0.732409i −0.0392958 0.0392612i
\(349\) −23.0588 + 19.3486i −1.23431 + 1.03571i −0.236360 + 0.971666i \(0.575954\pi\)
−0.997947 + 0.0640413i \(0.979601\pi\)
\(350\) 31.6313 14.4655i 1.69076 0.773215i
\(351\) 3.39539 + 4.40536i 0.181232 + 0.235141i
\(352\) −17.1538 + 11.0877i −0.914303 + 0.590975i
\(353\) 7.20122 + 8.58208i 0.383282 + 0.456778i 0.922847 0.385166i \(-0.125856\pi\)
−0.539565 + 0.841944i \(0.681411\pi\)
\(354\) 19.4796 23.5885i 1.03533 1.25371i
\(355\) 47.4464 + 8.36609i 2.51820 + 0.444026i
\(356\) 4.47565 + 1.70453i 0.237209 + 0.0903398i
\(357\) 4.16362 3.01111i 0.220362 0.159365i
\(358\) 11.8481 8.16597i 0.626192 0.431585i
\(359\) −9.95142 17.2364i −0.525216 0.909701i −0.999569 0.0293659i \(-0.990651\pi\)
0.474353 0.880335i \(-0.342682\pi\)
\(360\) −26.5158 18.2409i −1.39750 0.961378i
\(361\) −9.49738 + 16.4499i −0.499862 + 0.865786i
\(362\) −1.89626 23.6953i −0.0996651 1.24539i
\(363\) 3.39398 0.965156i 0.178138 0.0506575i
\(364\) −0.892107 5.53810i −0.0467591 0.290275i
\(365\) 2.81960 3.36027i 0.147585 0.175884i
\(366\) 10.3795 + 12.1745i 0.542546 + 0.636369i
\(367\) −5.14389 + 14.1327i −0.268509 + 0.737722i 0.730016 + 0.683430i \(0.239512\pi\)
−0.998525 + 0.0542921i \(0.982710\pi\)
\(368\) 1.56548 + 0.622924i 0.0816065 + 0.0324722i
\(369\) −28.2159 9.30496i −1.46886 0.484397i
\(370\) −3.30160 2.34845i −0.171642 0.122090i
\(371\) 5.48886 + 31.1289i 0.284968 + 1.61613i
\(372\) −24.1125 2.09888i −1.25017 0.108822i
\(373\) 25.1757 9.16321i 1.30355 0.474453i 0.405398 0.914140i \(-0.367133\pi\)
0.898151 + 0.439688i \(0.144911\pi\)
\(374\) 1.45489 + 5.59524i 0.0752306 + 0.289323i
\(375\) −25.9275 + 12.5753i −1.33889 + 0.649388i
\(376\) −0.660885 + 0.290471i −0.0340825 + 0.0149799i
\(377\) 0.320198i 0.0164910i
\(378\) 17.0323 + 8.98071i 0.876044 + 0.461918i
\(379\) 17.1769i 0.882321i −0.897428 0.441160i \(-0.854567\pi\)
0.897428 0.441160i \(-0.145433\pi\)
\(380\) 0.00813997 0.549234i 0.000417572 0.0281751i
\(381\) 1.59259 22.0789i 0.0815909 1.13114i
\(382\) 0.0945966 0.0245973i 0.00483998 0.00125851i
\(383\) −33.8259 + 12.3116i −1.72842 + 0.629095i −0.998516 0.0544509i \(-0.982659\pi\)
−0.729908 + 0.683546i \(0.760437\pi\)
\(384\) 10.4125 16.6006i 0.531362 0.847145i
\(385\) −6.23134 35.3397i −0.317579 1.80108i
\(386\) −21.9228 + 30.8204i −1.11584 + 1.56872i
\(387\) 27.9071 0.851960i 1.41860 0.0433075i
\(388\) 1.26717 + 3.64888i 0.0643308 + 0.185244i
\(389\) −11.0897 + 30.4688i −0.562271 + 1.54483i 0.254027 + 0.967197i \(0.418245\pi\)
−0.816298 + 0.577631i \(0.803977\pi\)
\(390\) 1.80374 + 9.77994i 0.0913357 + 0.495227i
\(391\) 0.306543 0.365323i 0.0155025 0.0184752i
\(392\) 0.210822 + 0.315800i 0.0106481 + 0.0159503i
\(393\) 8.02199 + 7.78083i 0.404656 + 0.392491i
\(394\) −6.31403 + 0.505292i −0.318096 + 0.0254563i
\(395\) −15.0340 + 26.0396i −0.756441 + 1.31019i
\(396\) −16.3751 + 14.1843i −0.822880 + 0.712789i
\(397\) −9.13398 15.8205i −0.458421 0.794009i 0.540456 0.841372i \(-0.318252\pi\)
−0.998878 + 0.0473630i \(0.984918\pi\)
\(398\) −7.89123 11.4495i −0.395552 0.573911i
\(399\) 0.0336339 + 0.326903i 0.00168380 + 0.0163656i
\(400\) −17.8008 33.0572i −0.890042 1.65286i
\(401\) 18.1056 + 3.19251i 0.904152 + 0.159426i 0.606347 0.795200i \(-0.292634\pi\)
0.297805 + 0.954627i \(0.403745\pi\)
\(402\) −2.76721 + 16.4476i −0.138016 + 0.820330i
\(403\) 4.80736 + 5.72919i 0.239472 + 0.285391i
\(404\) 6.80530 + 5.88436i 0.338576 + 0.292758i
\(405\) −30.5491 15.2331i −1.51800 0.756937i
\(406\) 0.461007 + 1.00807i 0.0228794 + 0.0500296i
\(407\) −2.08923 + 1.75307i −0.103559 + 0.0868967i
\(408\) −3.53556 4.27366i −0.175036 0.211578i
\(409\) −2.54225 + 14.4178i −0.125706 + 0.712914i 0.855180 + 0.518331i \(0.173447\pi\)
−0.980886 + 0.194583i \(0.937665\pi\)
\(410\) −37.2840 37.8407i −1.84133 1.86882i
\(411\) 3.72005 0.382744i 0.183497 0.0188794i
\(412\) −6.51292 + 10.9043i −0.320869 + 0.537215i
\(413\) −28.3405 + 16.3624i −1.39454 + 0.805140i
\(414\) 1.73640 + 0.422517i 0.0853396 + 0.0207656i
\(415\) 12.8654 + 7.42781i 0.631535 + 0.364617i
\(416\) −5.90285 + 1.34947i −0.289411 + 0.0661631i
\(417\) −8.45795 + 8.72010i −0.414188 + 0.427025i
\(418\) −0.356432 0.0983420i −0.0174336 0.00481006i
\(419\) −5.75834 4.83182i −0.281313 0.236050i 0.491203 0.871045i \(-0.336557\pi\)
−0.772516 + 0.634996i \(0.781002\pi\)
\(420\) 19.7594 + 28.1929i 0.964160 + 1.37567i
\(421\) −16.2535 5.91580i −0.792149 0.288319i −0.0859197 0.996302i \(-0.527383\pi\)
−0.706229 + 0.707984i \(0.749605\pi\)
\(422\) −1.77306 + 18.6716i −0.0863111 + 0.908920i
\(423\) −0.651118 + 0.402902i −0.0316584 + 0.0195898i
\(424\) 33.1458 8.09624i 1.60970 0.393188i
\(425\) −10.4656 + 1.84537i −0.507657 + 0.0895137i
\(426\) 0.244231 + 31.1128i 0.0118331 + 1.50742i
\(427\) −5.85328 16.0818i −0.283260 0.778251i
\(428\) 12.5096 + 15.3651i 0.604673 + 0.742701i
\(429\) 6.67690 + 0.481617i 0.322364 + 0.0232527i
\(430\) 45.0865 + 21.4323i 2.17427 + 1.03356i
\(431\) 22.9632 1.10610 0.553050 0.833148i \(-0.313464\pi\)
0.553050 + 0.833148i \(0.313464\pi\)
\(432\) 8.47880 18.9766i 0.407937 0.913010i
\(433\) −2.94287 −0.141425 −0.0707126 0.997497i \(-0.522527\pi\)
−0.0707126 + 0.997497i \(0.522527\pi\)
\(434\) 23.3835 + 11.1156i 1.12244 + 0.533565i
\(435\) −0.857606 1.76819i −0.0411190 0.0847781i
\(436\) 10.0341 + 12.3246i 0.480546 + 0.590239i
\(437\) 0.0104318 + 0.0286610i 0.000499019 + 0.00137104i
\(438\) 2.46435 + 1.39711i 0.117751 + 0.0667567i
\(439\) −35.9702 + 6.34252i −1.71676 + 0.302712i −0.943500 0.331372i \(-0.892489\pi\)
−0.773264 + 0.634084i \(0.781377\pi\)
\(440\) −37.6295 + 9.19142i −1.79392 + 0.438184i
\(441\) 0.268168 + 0.300472i 0.0127699 + 0.0143082i
\(442\) −0.162022 + 1.70621i −0.00770660 + 0.0811562i
\(443\) −25.7106 9.35788i −1.22155 0.444606i −0.350852 0.936431i \(-0.614108\pi\)
−0.870694 + 0.491825i \(0.836330\pi\)
\(444\) 1.10476 2.37190i 0.0524298 0.112565i
\(445\) 6.95770 + 5.83820i 0.329827 + 0.276757i
\(446\) −24.1741 6.66979i −1.14467 0.315824i
\(447\) 5.52657 + 19.4342i 0.261398 + 0.919208i
\(448\) −16.6409 + 12.7472i −0.786206 + 0.602247i
\(449\) −10.4394 6.02718i −0.492665 0.284440i 0.233014 0.972473i \(-0.425141\pi\)
−0.725679 + 0.688033i \(0.758474\pi\)
\(450\) −23.5891 32.0844i −1.11200 1.51247i
\(451\) −30.9679 + 17.8794i −1.45822 + 0.841906i
\(452\) 10.3342 17.3021i 0.486080 0.813820i
\(453\) 0.459163 + 0.634908i 0.0215734 + 0.0298306i
\(454\) 5.98262 + 6.07194i 0.280778 + 0.284970i
\(455\) 1.84730 10.4766i 0.0866030 0.491150i
\(456\) 0.349768 0.0591630i 0.0163794 0.00277056i
\(457\) 12.1847 10.2241i 0.569974 0.478265i −0.311663 0.950193i \(-0.600886\pi\)
0.881637 + 0.471927i \(0.156442\pi\)
\(458\) 10.3165 + 22.5588i 0.482059 + 1.05410i
\(459\) −4.34593 3.96519i −0.202851 0.185079i
\(460\) 2.41703 + 2.08994i 0.112695 + 0.0974440i
\(461\) −9.40166 11.2045i −0.437879 0.521844i 0.501299 0.865274i \(-0.332856\pi\)
−0.939178 + 0.343430i \(0.888411\pi\)
\(462\) 21.7141 8.09687i 1.01023 0.376701i
\(463\) 19.4128 + 3.42301i 0.902191 + 0.159081i 0.605456 0.795879i \(-0.292991\pi\)
0.296735 + 0.954960i \(0.404102\pi\)
\(464\) 1.05351 0.567301i 0.0489081 0.0263363i
\(465\) −41.8919 18.7617i −1.94269 0.870053i
\(466\) 0.758433 + 1.10042i 0.0351337 + 0.0509759i
\(467\) −18.2329 31.5803i −0.843718 1.46136i −0.886730 0.462287i \(-0.847029\pi\)
0.0430124 0.999075i \(-0.486304\pi\)
\(468\) −5.99990 + 2.29108i −0.277345 + 0.105905i
\(469\) 8.92075 15.4512i 0.411922 0.713470i
\(470\) −1.36470 + 0.109213i −0.0629488 + 0.00503760i
\(471\) 7.77387 30.8904i 0.358201 1.42336i
\(472\) 19.6132 + 29.3794i 0.902769 + 1.35230i
\(473\) 21.6001 25.7420i 0.993175 1.18362i
\(474\) −18.2985 6.49790i −0.840478 0.298459i
\(475\) 0.232460 0.638678i 0.0106660 0.0293045i
\(476\) 1.94644 + 5.60489i 0.0892151 + 0.256900i
\(477\) 33.6140 13.4097i 1.53908 0.613987i
\(478\) 9.16592 12.8860i 0.419240 0.589392i
\(479\) 1.10609 + 6.27294i 0.0505384 + 0.286618i 0.999594 0.0284909i \(-0.00907016\pi\)
−0.949056 + 0.315109i \(0.897959\pi\)
\(480\) 28.9822 23.2620i 1.32285 1.06176i
\(481\) −0.759759 + 0.276530i −0.0346420 + 0.0126087i
\(482\) 26.4665 6.88189i 1.20552 0.313462i
\(483\) −1.58249 1.07246i −0.0720057 0.0487986i
\(484\) −0.0603785 + 4.07397i −0.00274448 + 0.185180i
\(485\) 7.32538i 0.332628i
\(486\) 6.09615 21.1858i 0.276527 0.961006i
\(487\) 31.5578i 1.43002i 0.699115 + 0.715009i \(0.253577\pi\)
−0.699115 + 0.715009i \(0.746423\pi\)
\(488\) −16.9120 + 7.43315i −0.765572 + 0.336483i
\(489\) 32.3869 + 21.9488i 1.46459 + 0.992557i
\(490\) 0.181216 + 0.696921i 0.00818648 + 0.0314837i
\(491\) 25.0585 9.12054i 1.13087 0.411604i 0.292264 0.956338i \(-0.405591\pi\)
0.838609 + 0.544734i \(0.183369\pi\)
\(492\) 19.6652 28.1111i 0.886576 1.26735i
\(493\) −0.0588108 0.333533i −0.00264871 0.0150216i
\(494\) −0.0893219 0.0635354i −0.00401878 0.00285859i
\(495\) −38.1610 + 15.2236i −1.71521 + 0.684250i
\(496\) 10.3328 25.9677i 0.463958 1.16598i
\(497\) 11.3834 31.2757i 0.510617 1.40291i
\(498\) −3.21041 + 9.04072i −0.143862 + 0.405124i
\(499\) 14.4331 17.2006i 0.646112 0.770007i −0.339210 0.940711i \(-0.610160\pi\)
0.985322 + 0.170704i \(0.0546042\pi\)
\(500\) −5.29175 32.8506i −0.236654 1.46912i
\(501\) 1.94728 7.73777i 0.0869982 0.345698i
\(502\) −0.836533 10.4532i −0.0373363 0.466547i
\(503\) −13.0818 + 22.6583i −0.583287 + 1.01028i 0.411799 + 0.911274i \(0.364900\pi\)
−0.995087 + 0.0990084i \(0.968433\pi\)
\(504\) −15.5907 + 15.8513i −0.694464 + 0.706075i
\(505\) 8.53082 + 14.7758i 0.379617 + 0.657515i
\(506\) 1.77098 1.22060i 0.0787295 0.0542621i
\(507\) −18.7387 8.39230i −0.832213 0.372715i
\(508\) 23.8871 + 9.09728i 1.05982 + 0.403627i
\(509\) −28.8191 5.08158i −1.27738 0.225237i −0.506515 0.862231i \(-0.669066\pi\)
−0.770869 + 0.636994i \(0.780178\pi\)
\(510\) −3.67514 9.85595i −0.162738 0.436429i
\(511\) −1.94785 2.32136i −0.0861680 0.102691i
\(512\) 14.8982 + 17.0306i 0.658415 + 0.752655i
\(513\) 0.358597 0.113912i 0.0158325 0.00502932i
\(514\) 29.0910 13.3038i 1.28315 0.586806i
\(515\) −18.4521 + 15.4831i −0.813095 + 0.682268i
\(516\) −8.33047 + 31.1445i −0.366729 + 1.37106i
\(517\) −0.160028 + 0.907563i −0.00703801 + 0.0399146i
\(518\) −1.99379 + 1.96446i −0.0876020 + 0.0863133i
\(519\) 7.58122 + 10.4829i 0.332779 + 0.460150i
\(520\) −11.4146 1.25487i −0.500563 0.0550296i
\(521\) −12.2522 + 7.07379i −0.536777 + 0.309909i −0.743772 0.668434i \(-0.766965\pi\)
0.206995 + 0.978342i \(0.433632\pi\)
\(522\) 1.02251 0.751770i 0.0447541 0.0329041i
\(523\) −7.35440 4.24607i −0.321586 0.185668i 0.330513 0.943801i \(-0.392778\pi\)
−0.652099 + 0.758134i \(0.726111\pi\)
\(524\) −11.2700 + 6.28591i −0.492331 + 0.274601i
\(525\) 11.6520 + 40.9745i 0.508537 + 1.78828i
\(526\) 9.31170 33.7494i 0.406010 1.47155i
\(527\) −6.05985 5.08482i −0.263971 0.221498i
\(528\) −10.2450 22.8216i −0.445857 0.993183i
\(529\) 21.4462 + 7.80578i 0.932444 + 0.339382i
\(530\) 64.4182 + 6.11716i 2.79815 + 0.265712i
\(531\) 24.9482 + 27.9534i 1.08266 + 1.21308i
\(532\) −0.372685 0.0714245i −0.0161579 0.00309664i
\(533\) −10.4398 + 1.84081i −0.452196 + 0.0797343i
\(534\) −2.89283 + 5.10262i −0.125185 + 0.220812i
\(535\) 12.8516 + 35.3096i 0.555625 + 1.52657i
\(536\) −17.2693 8.52513i −0.745920 0.368230i
\(537\) 7.69090 + 15.8569i 0.331887 + 0.684275i
\(538\) −7.17907 + 15.1024i −0.309512 + 0.651110i
\(539\) 0.484722 0.0208785
\(540\) 26.9961 28.7216i 1.16173 1.23598i
\(541\) −26.2456 −1.12839 −0.564194 0.825642i \(-0.690813\pi\)
−0.564194 + 0.825642i \(0.690813\pi\)
\(542\) −3.15802 + 6.64343i −0.135649 + 0.285360i
\(543\) 29.0380 + 2.09456i 1.24614 + 0.0898861i
\(544\) 5.90083 2.48985i 0.252996 0.106751i
\(545\) 10.3085 + 28.3223i 0.441566 + 1.21319i
\(546\) 6.86998 0.0539284i 0.294008 0.00230792i
\(547\) 29.4440 5.19178i 1.25894 0.221984i 0.495923 0.868367i \(-0.334830\pi\)
0.763014 + 0.646382i \(0.223719\pi\)
\(548\) −0.812789 + 4.24104i −0.0347206 + 0.181168i
\(549\) −16.6621 + 10.3103i −0.711122 + 0.440032i
\(550\) −47.7149 4.53101i −2.03457 0.193203i
\(551\) 0.0203543 + 0.00740834i 0.000867121 + 0.000315606i
\(552\) −1.04420 + 1.77984i −0.0444439 + 0.0757548i
\(553\) 15.9121 + 13.3518i 0.676650 + 0.567777i
\(554\) −2.77807 + 10.0689i −0.118029 + 0.427786i
\(555\) 3.45487 3.56195i 0.146651 0.151197i
\(556\) −6.83293 12.2507i −0.289781 0.519547i
\(557\) 12.1389 + 7.00840i 0.514342 + 0.296955i 0.734617 0.678482i \(-0.237362\pi\)
−0.220275 + 0.975438i \(0.570695\pi\)
\(558\) 7.00856 28.8028i 0.296696 1.21932i
\(559\) 8.62733 4.98099i 0.364897 0.210673i
\(560\) −37.7429 + 12.4836i −1.59493 + 0.527528i
\(561\) −7.04343 + 0.724675i −0.297374 + 0.0305958i
\(562\) −12.3652 + 12.1833i −0.521595 + 0.513922i
\(563\) 8.08075 45.8282i 0.340563 1.93143i −0.0226998 0.999742i \(-0.507226\pi\)
0.363263 0.931687i \(-0.381663\pi\)
\(564\) −0.229209 0.853918i −0.00965145 0.0359564i
\(565\) 29.2783 24.5674i 1.23175 1.03356i
\(566\) −14.3206 + 6.54908i −0.601942 + 0.275279i
\(567\) −14.0282 + 18.9561i −0.589130 + 0.796083i
\(568\) −34.4877 10.0677i −1.44707 0.422430i
\(569\) −8.80061 10.4882i −0.368941 0.439686i 0.549350 0.835592i \(-0.314875\pi\)
−0.918291 + 0.395906i \(0.870431\pi\)
\(570\) 0.663422 + 0.111617i 0.0277877 + 0.00467512i
\(571\) −41.0075 7.23074i −1.71611 0.302597i −0.772836 0.634606i \(-0.781163\pi\)
−0.943276 + 0.332009i \(0.892274\pi\)
\(572\) −2.75112 + 7.22371i −0.115030 + 0.302039i
\(573\) 0.0122518 + 0.119081i 0.000511827 + 0.00497467i
\(574\) −30.2168 + 20.8261i −1.26123 + 0.869264i
\(575\) 1.97684 + 3.42398i 0.0824398 + 0.142790i
\(576\) 18.1682 + 15.6817i 0.757010 + 0.653403i
\(577\) 11.9468 20.6925i 0.497352 0.861439i −0.502643 0.864494i \(-0.667639\pi\)
0.999995 + 0.00305510i \(0.000972470\pi\)
\(578\) 1.77323 + 22.1580i 0.0737568 + 0.921651i
\(579\) −33.2508 32.2512i −1.38186 1.34032i
\(580\) 2.24033 0.360884i 0.0930245 0.0149849i
\(581\) 6.59671 7.86166i 0.273678 0.326157i
\(582\) −4.65230 + 0.858033i −0.192844 + 0.0355666i
\(583\) 14.8975 40.9304i 0.616990 1.69516i
\(584\) −2.36384 + 2.26101i −0.0978162 + 0.0935614i
\(585\) −12.1743 + 0.371661i −0.503344 + 0.0153663i
\(586\) −26.8154 19.0740i −1.10773 0.787940i
\(587\) −2.47759 14.0511i −0.102261 0.579952i −0.992279 0.124026i \(-0.960419\pi\)
0.890018 0.455926i \(-0.150692\pi\)
\(588\) −0.421384 + 0.196720i −0.0173776 + 0.00811260i
\(589\) 0.475418 0.173038i 0.0195893 0.00712991i
\(590\) 16.8588 + 64.8359i 0.694067 + 2.66925i
\(591\) 0.558133 7.73769i 0.0229585 0.318286i
\(592\) 2.25592 + 2.00982i 0.0927176 + 0.0826031i
\(593\) 15.2762i 0.627320i −0.949535 0.313660i \(-0.898445\pi\)
0.949535 0.313660i \(-0.101555\pi\)
\(594\) −14.1383 22.4526i −0.580100 0.921241i
\(595\) 11.2522i 0.461295i
\(596\) −23.3279 0.345733i −0.955548 0.0141618i
\(597\) 15.3234 7.43215i 0.627145 0.304178i
\(598\) 0.617110 0.160463i 0.0252355 0.00656182i
\(599\) 14.3465 5.22168i 0.586180 0.213352i −0.0318684 0.999492i \(-0.510146\pi\)
0.618048 + 0.786140i \(0.287924\pi\)
\(600\) 43.3188 15.4257i 1.76848 0.629752i
\(601\) 7.19286 + 40.7927i 0.293403 + 1.66397i 0.673623 + 0.739075i \(0.264737\pi\)
−0.380220 + 0.924896i \(0.624152\pi\)
\(602\) 19.9897 28.1028i 0.814720 1.14538i
\(603\) −19.3995 6.39753i −0.790010 0.260527i
\(604\) −0.854686 + 0.296812i −0.0347767 + 0.0120771i
\(605\) −2.64278 + 7.26099i −0.107444 + 0.295201i
\(606\) −8.38479 + 7.14858i −0.340609 + 0.290391i
\(607\) 8.26489 9.84971i 0.335461 0.399787i −0.571774 0.820411i \(-0.693744\pi\)
0.907235 + 0.420624i \(0.138189\pi\)
\(608\) −0.0507902 + 0.406453i −0.00205982 + 0.0164839i
\(609\) −1.30583 + 0.371343i −0.0529150 + 0.0150476i
\(610\) −34.9226 + 2.79475i −1.41398 + 0.113156i
\(611\) −0.136600 + 0.236599i −0.00552626 + 0.00957177i
\(612\) 5.82897 3.48850i 0.235622 0.141014i
\(613\) −15.8003 27.3670i −0.638170 1.10534i −0.985834 0.167723i \(-0.946358\pi\)
0.347664 0.937619i \(-0.386975\pi\)
\(614\) 11.7879 + 17.1031i 0.475719 + 0.690227i
\(615\) 52.7198 38.1267i 2.12587 1.53742i
\(616\) 1.73915 + 26.7031i 0.0700724 + 1.07590i
\(617\) −32.9384 5.80793i −1.32605 0.233819i −0.534628 0.845088i \(-0.679548\pi\)
−0.791423 + 0.611269i \(0.790659\pi\)
\(618\) −11.9945 9.90521i −0.482491 0.398446i
\(619\) 21.1853 + 25.2477i 0.851511 + 1.01479i 0.999666 + 0.0258272i \(0.00822196\pi\)
−0.148155 + 0.988964i \(0.547334\pi\)
\(620\) 34.6672 40.0928i 1.39227 1.61017i
\(621\) −0.833242 + 2.02389i −0.0334368 + 0.0812160i
\(622\) −1.37199 3.00008i −0.0550118 0.120292i
\(623\) 4.80656 4.03319i 0.192571 0.161586i
\(624\) −0.540051 7.39631i −0.0216193 0.296089i
\(625\) 2.80815 15.9258i 0.112326 0.637032i
\(626\) −6.99061 7.09498i −0.279401 0.283572i
\(627\) 0.185097 0.413293i 0.00739208 0.0165053i
\(628\) 31.5776 + 18.8607i 1.26008 + 0.752624i
\(629\) 0.740610 0.427591i 0.0295300 0.0170492i
\(630\) −37.7928 + 18.6981i −1.50570 + 0.744950i
\(631\) 10.5759 + 6.10598i 0.421018 + 0.243075i 0.695513 0.718514i \(-0.255177\pi\)
−0.274495 + 0.961589i \(0.588511\pi\)
\(632\) 13.2658 18.0766i 0.527684 0.719048i
\(633\) −22.2763 5.60603i −0.885401 0.222820i
\(634\) 2.60608 + 0.719037i 0.103501 + 0.0285566i
\(635\) 37.1341 + 31.1592i 1.47362 + 1.23652i
\(636\) 3.66044 + 41.6281i 0.145146 + 1.65066i
\(637\) 0.135032 + 0.0491475i 0.00535015 + 0.00194729i
\(638\) 0.144400 1.52064i 0.00571686 0.0602028i
\(639\) −37.7120 5.46891i −1.49186 0.216347i
\(640\) 16.0947 + 39.7795i 0.636200 + 1.57242i
\(641\) −2.91455 + 0.513915i −0.115118 + 0.0202984i −0.230910 0.972975i \(-0.574170\pi\)
0.115792 + 0.993273i \(0.463059\pi\)
\(642\) −20.9195 + 12.2979i −0.825629 + 0.485358i
\(643\) 1.28689 + 3.53570i 0.0507499 + 0.139434i 0.962478 0.271360i \(-0.0874735\pi\)
−0.911728 + 0.410795i \(0.865251\pi\)
\(644\) 1.71180 1.39367i 0.0674544 0.0549183i
\(645\) −34.3007 + 50.6130i −1.35059 + 1.99288i
\(646\) 0.104711 + 0.0497756i 0.00411982 + 0.00195840i
\(647\) 17.3248 0.681109 0.340555 0.940225i \(-0.389385\pi\)
0.340555 + 0.940225i \(0.389385\pi\)
\(648\) 21.4030 + 13.7808i 0.840789 + 0.541362i
\(649\) 45.0946 1.77012
\(650\) −12.8328 6.10019i −0.503343 0.239269i
\(651\) −17.7896 + 26.2497i −0.697228 + 1.02881i
\(652\) −35.0334 + 28.5226i −1.37201 + 1.11703i
\(653\) 7.83529 + 21.5273i 0.306619 + 0.842428i 0.993310 + 0.115479i \(0.0368402\pi\)
−0.686691 + 0.726949i \(0.740938\pi\)
\(654\) −16.7798 + 9.86427i −0.656143 + 0.385723i
\(655\) −24.1010 + 4.24967i −0.941706 + 0.166048i
\(656\) 24.5530 + 31.0874i 0.958632 + 1.21376i
\(657\) −2.14801 + 2.72460i −0.0838018 + 0.106297i
\(658\) −0.0894096 + 0.941549i −0.00348555 + 0.0367054i
\(659\) 29.5497 + 10.7552i 1.15109 + 0.418963i 0.845907 0.533331i \(-0.179060\pi\)
0.305184 + 0.952293i \(0.401282\pi\)
\(660\) −4.15559 47.2591i −0.161756 1.83956i
\(661\) −11.3401 9.51547i −0.441079 0.370109i 0.395034 0.918666i \(-0.370733\pi\)
−0.836113 + 0.548557i \(0.815177\pi\)
\(662\) −7.80943 2.15468i −0.303522 0.0837439i
\(663\) −2.03560 0.512279i −0.0790563 0.0198953i
\(664\) −8.93108 6.55421i −0.346593 0.254353i
\(665\) −0.623232 0.359823i −0.0241679 0.0139534i
\(666\) 2.66685 + 1.77695i 0.103338 + 0.0688553i
\(667\) −0.109120 + 0.0630006i −0.00422515 + 0.00243939i
\(668\) 7.90989 + 4.72443i 0.306043 + 0.182794i
\(669\) 12.5537 28.0305i 0.485356 1.08372i
\(670\) −25.6342 26.0170i −0.990336 1.00512i
\(671\) −4.09511 + 23.2245i −0.158090 + 0.896574i
\(672\) −12.3491 22.5080i −0.476378 0.868266i
\(673\) −6.38737 + 5.35964i −0.246215 + 0.206599i −0.757540 0.652788i \(-0.773599\pi\)
0.511325 + 0.859387i \(0.329155\pi\)
\(674\) −12.2103 26.6999i −0.470324 1.02844i
\(675\) 43.2136 22.6135i 1.66329 0.870395i
\(676\) 15.5070 17.9339i 0.596422 0.689765i
\(677\) −26.9751 32.1477i −1.03674 1.23553i −0.971345 0.237675i \(-0.923615\pi\)
−0.0653922 0.997860i \(-0.520830\pi\)
\(678\) 19.0320 + 15.7168i 0.730919 + 0.603601i
\(679\) 4.98369 + 0.878759i 0.191256 + 0.0337237i
\(680\) 12.1205 0.789394i 0.464798 0.0302719i
\(681\) −8.45945 + 6.11784i −0.324167 + 0.234436i
\(682\) −20.2468 29.3763i −0.775290 1.12488i
\(683\) 8.40955 + 14.5658i 0.321782 + 0.557344i 0.980856 0.194735i \(-0.0623847\pi\)
−0.659073 + 0.752079i \(0.729051\pi\)
\(684\) 0.00682051 + 0.434408i 0.000260789 + 0.0166100i
\(685\) −4.09468 + 7.09220i −0.156450 + 0.270979i
\(686\) 26.3524 2.10890i 1.00614 0.0805184i
\(687\) −29.2222 + 8.30999i −1.11490 + 0.317046i
\(688\) −31.6736 19.5607i −1.20755 0.745743i
\(689\) 8.30013 9.89171i 0.316210 0.376844i
\(690\) −2.97801 + 2.53895i −0.113371 + 0.0966562i
\(691\) −11.0161 + 30.2664i −0.419071 + 1.15139i 0.533161 + 0.846014i \(0.321004\pi\)
−0.952232 + 0.305374i \(0.901218\pi\)
\(692\) −14.1117 + 4.90065i −0.536446 + 0.186295i
\(693\) 5.77928 + 27.7883i 0.219537 + 1.05559i
\(694\) −12.7154 + 17.8761i −0.482671 + 0.678568i
\(695\) −4.61949 26.1984i −0.175227 0.993763i
\(696\) 0.491608 + 1.38054i 0.0186343 + 0.0523294i
\(697\) 10.5364 3.83495i 0.399096 0.145259i
\(698\) 41.1993 10.7128i 1.55942 0.405485i
\(699\) −1.47274 + 0.714310i −0.0557043 + 0.0270177i
\(700\) −49.1838 0.728932i −1.85897 0.0275510i
\(701\) 22.5259i 0.850790i −0.905008 0.425395i \(-0.860135\pi\)
0.905008 0.425395i \(-0.139865\pi\)
\(702\) −1.66203 7.68826i −0.0627293 0.290175i
\(703\) 0.0546942i 0.00206283i
\(704\) 28.6416 3.74670i 1.07947 0.141209i
\(705\) 0.120634 1.67241i 0.00454332 0.0629864i
\(706\) −3.98711 15.3337i −0.150057 0.577091i
\(707\) 11.0758 4.03127i 0.416549 0.151611i
\(708\) −39.2021 + 18.3012i −1.47330 + 0.687803i
\(709\) −1.33870 7.59217i −0.0502761 0.285130i 0.949296 0.314384i \(-0.101798\pi\)
−0.999572 + 0.0292540i \(0.990687\pi\)
\(710\) −55.5214 39.4928i −2.08368 1.48214i
\(711\) 11.2570 20.9491i 0.422172 0.785654i
\(712\) −4.68161 4.89451i −0.175451 0.183430i
\(713\) −1.00658 + 2.76555i −0.0376966 + 0.103571i
\(714\) −7.14619 + 1.31799i −0.267439 + 0.0493244i
\(715\) −9.42288 + 11.2298i −0.352396 + 0.419969i
\(716\) −20.0910 + 3.23636i −0.750835 + 0.120949i
\(717\) 13.9022 + 13.4842i 0.519186 + 0.503578i
\(718\) 2.24533 + 28.0572i 0.0837949 + 1.04708i
\(719\) 9.44892 16.3660i 0.352385 0.610349i −0.634282 0.773102i \(-0.718704\pi\)
0.986667 + 0.162753i \(0.0520374\pi\)
\(720\) 22.7923 + 39.3973i 0.849417 + 1.46825i
\(721\) 8.32013 + 14.4109i 0.309858 + 0.536690i
\(722\) 22.1182 15.2443i 0.823152 0.567334i
\(723\) 3.42784 + 33.3167i 0.127483 + 1.23906i
\(724\) −11.9647 + 31.4161i −0.444663 + 1.16757i
\(725\) 2.76513 + 0.487568i 0.102695 + 0.0181078i
\(726\) −4.92096 0.827923i −0.182634 0.0307271i
\(727\) −14.0555 16.7507i −0.521289 0.621248i 0.439596 0.898196i \(-0.355122\pi\)
−0.960885 + 0.276947i \(0.910677\pi\)
\(728\) −2.22303 + 7.61517i −0.0823910 + 0.282237i
\(729\) 24.5190 + 11.3056i 0.908113 + 0.418726i
\(730\) −5.64153 + 2.57997i −0.208802 + 0.0954890i
\(731\) −8.07177 + 6.77302i −0.298545 + 0.250509i
\(732\) −5.86547 21.8518i −0.216794 0.807665i
\(733\) −3.02175 + 17.1372i −0.111611 + 0.632977i 0.876762 + 0.480925i \(0.159699\pi\)
−0.988373 + 0.152052i \(0.951412\pi\)
\(734\) 15.1507 14.9279i 0.559224 0.550998i
\(735\) −0.877303 + 0.0902627i −0.0323598 + 0.00332939i
\(736\) −1.62130 1.74612i −0.0597620 0.0643628i
\(737\) −21.2917 + 12.2928i −0.784289 + 0.452810i
\(738\) 30.3891 + 29.0161i 1.11864 + 1.06810i
\(739\) −24.7291 14.2773i −0.909674 0.525201i −0.0293479 0.999569i \(-0.509343\pi\)
−0.880326 + 0.474369i \(0.842676\pi\)
\(740\) 2.79109 + 5.00413i 0.102603 + 0.183956i
\(741\) 0.0934686 0.0963656i 0.00343366 0.00354008i
\(742\) 11.8894 43.0919i 0.436472 1.58195i
\(743\) −24.1483 20.2629i −0.885917 0.743373i 0.0814700 0.996676i \(-0.474039\pi\)
−0.967387 + 0.253303i \(0.918483\pi\)
\(744\) 29.5233 + 17.3207i 1.08238 + 0.635009i
\(745\) −41.5771 15.1328i −1.52327 0.554424i
\(746\) −37.7191 3.58181i −1.38099 0.131139i
\(747\) −10.3503 5.56175i −0.378698 0.203494i
\(748\) 1.53891 8.02986i 0.0562681 0.293601i
\(749\) 25.5639 4.50761i 0.934086 0.164705i
\(750\) 40.7510 0.319890i 1.48802 0.0116807i
\(751\) −9.89995 27.1999i −0.361254 0.992538i −0.978587 0.205836i \(-0.934009\pi\)
0.617332 0.786703i \(-0.288213\pi\)
\(752\) 1.02047 + 0.0302547i 0.0372129 + 0.00110327i
\(753\) 12.8101 + 0.924014i 0.466826 + 0.0336729i
\(754\) 0.194409 0.408972i 0.00707996 0.0148939i
\(755\) −1.71584 −0.0624458
\(756\) −16.3018 21.8118i −0.592889 0.793287i
\(757\) 8.58739 0.312114 0.156057 0.987748i \(-0.450122\pi\)
0.156057 + 0.987748i \(0.450122\pi\)
\(758\) −10.4290 + 21.9392i −0.378800 + 0.796869i
\(759\) 1.14959 + 2.37018i 0.0417273 + 0.0860322i
\(760\) −0.343866 + 0.696567i −0.0124733 + 0.0252671i
\(761\) −4.64163 12.7528i −0.168259 0.462287i 0.826691 0.562655i \(-0.190220\pi\)
−0.994950 + 0.100368i \(0.967998\pi\)
\(762\) −15.4394 + 27.2333i −0.559311 + 0.986560i
\(763\) 20.5052 3.61561i 0.742336 0.130894i
\(764\) −0.135758 0.0260178i −0.00491154 0.000941289i
\(765\) 12.6130 2.62319i 0.456025 0.0948417i
\(766\) 50.6792 + 4.81250i 1.83111 + 0.173883i
\(767\) 12.5622 + 4.57228i 0.453596 + 0.165096i
\(768\) −23.3785 + 14.8811i −0.843598 + 0.536975i
\(769\) −22.9731 19.2767i −0.828432 0.695137i 0.126499 0.991967i \(-0.459626\pi\)
−0.954930 + 0.296830i \(0.904071\pi\)
\(770\) −13.4976 + 48.9210i −0.486421 + 1.76299i
\(771\) 10.7163 + 37.6839i 0.385937 + 1.35715i
\(772\) 46.7136 26.0548i 1.68126 0.937734i
\(773\) −4.59241 2.65143i −0.165177 0.0953652i 0.415132 0.909761i \(-0.363735\pi\)
−0.580310 + 0.814396i \(0.697069\pi\)
\(774\) −36.1616 15.8557i −1.29980 0.569923i
\(775\) 56.7958 32.7911i 2.04016 1.17789i
\(776\) 0.596938 5.42990i 0.0214288 0.194922i
\(777\) −2.00886 2.77775i −0.0720675 0.0996514i
\(778\) 32.6635 32.1830i 1.17104 1.15382i
\(779\) −0.124526 + 0.706222i −0.00446161 + 0.0253030i
\(780\) 3.63410 13.5866i 0.130122 0.486477i
\(781\) −35.1337 + 29.4806i −1.25718 + 1.05490i
\(782\) −0.613339 + 0.280491i −0.0219329 + 0.0100303i
\(783\) 0.720678 + 1.37719i 0.0257549 + 0.0492167i
\(784\) −0.0775336 0.531356i −0.00276906 0.0189770i
\(785\) 44.8374 + 53.4351i 1.60032 + 1.90718i
\(786\) −5.52192 14.8086i −0.196961 0.528206i
\(787\) −21.5184 3.79428i −0.767048 0.135251i −0.223585 0.974684i \(-0.571776\pi\)
−0.543463 + 0.839433i \(0.682887\pi\)
\(788\) 8.37138 + 3.18820i 0.298218 + 0.113575i
\(789\) 39.1335 + 17.5263i 1.39319 + 0.623953i
\(790\) 35.0121 24.1311i 1.24568 0.858547i
\(791\) −13.2017 22.8661i −0.469400 0.813024i
\(792\) 29.5272 8.17471i 1.04920 0.290476i
\(793\) −3.49561 + 6.05457i −0.124133 + 0.215004i
\(794\) 2.06089 + 25.7525i 0.0731382 + 0.913921i
\(795\) −19.3412 + 76.8545i −0.685960 + 2.72575i
\(796\) 3.12748 + 19.4150i 0.110851 + 0.688147i
\(797\) 1.65407 1.97124i 0.0585902 0.0698251i −0.735953 0.677032i \(-0.763266\pi\)
0.794544 + 0.607207i \(0.207710\pi\)
\(798\) 0.155521 0.437957i 0.00550539 0.0155035i
\(799\) 0.0988332 0.271542i 0.00349647 0.00960646i
\(800\) 2.66529 + 53.0301i 0.0942324 + 1.87490i
\(801\) −5.64150 4.44762i −0.199333 0.157149i
\(802\) −21.1871 15.0705i −0.748141 0.532159i
\(803\) 0.725116 + 4.11234i 0.0255888 + 0.145121i
\(804\) 13.5206 19.3275i 0.476835 0.681629i
\(805\) 3.93378 1.43178i 0.138648 0.0504636i
\(806\) −2.66170 10.2364i −0.0937544 0.360562i
\(807\) −16.9536 11.4895i −0.596793 0.404450i
\(808\) −5.11936 11.6477i −0.180098 0.409763i
\(809\) 41.7773i 1.46881i −0.678710 0.734407i \(-0.737461\pi\)
0.678710 0.734407i \(-0.262539\pi\)
\(810\) 29.7700 + 38.0044i 1.04601 + 1.33534i
\(811\) 49.5187i 1.73884i −0.494077 0.869418i \(-0.664494\pi\)
0.494077 0.869418i \(-0.335506\pi\)
\(812\) 0.0232306 1.56746i 0.000815234 0.0550069i
\(813\) −7.45774 5.05415i −0.261555 0.177257i
\(814\) 3.73286 0.970629i 0.130837 0.0340205i
\(815\) −80.5081 + 29.3025i −2.82007 + 1.02642i
\(816\) 1.92103 + 7.60515i 0.0672494 + 0.266234i
\(817\) −0.117022 0.663664i −0.00409408 0.0232187i
\(818\) 12.0009 16.8716i 0.419601 0.589901i
\(819\) −1.20758 + 8.32713i −0.0421964 + 0.290973i
\(820\) 24.6459 + 70.9690i 0.860671 + 2.47835i
\(821\) 4.28022 11.7598i 0.149381 0.410420i −0.842322 0.538975i \(-0.818812\pi\)
0.991702 + 0.128555i \(0.0410339\pi\)
\(822\) −4.98382 1.76978i −0.173831 0.0617283i
\(823\) 3.52799 4.20450i 0.122978 0.146560i −0.701042 0.713120i \(-0.747282\pi\)
0.824020 + 0.566560i \(0.191726\pi\)
\(824\) 14.9392 9.97313i 0.520431 0.347431i
\(825\) 14.3261 56.9264i 0.498770 1.98192i
\(826\) 46.1323 3.69182i 1.60515 0.128455i
\(827\) −10.0525 + 17.4114i −0.349559 + 0.605454i −0.986171 0.165730i \(-0.947002\pi\)
0.636612 + 0.771184i \(0.280335\pi\)
\(828\) −1.96129 1.59392i −0.0681595 0.0553927i
\(829\) 23.9459 + 41.4755i 0.831675 + 1.44050i 0.896709 + 0.442620i \(0.145951\pi\)
−0.0650348 + 0.997883i \(0.520716\pi\)
\(830\) −11.9224 17.2984i −0.413834 0.600436i
\(831\) −11.6752 5.22884i −0.405007 0.181386i
\(832\) 8.35874 + 1.86033i 0.289787 + 0.0644952i
\(833\) −0.149682 0.0263930i −0.00518618 0.000914463i
\(834\) 16.0973 6.00246i 0.557405 0.207848i
\(835\) 11.2314 + 13.3850i 0.388677 + 0.463207i
\(836\) 0.395543 + 0.342016i 0.0136802 + 0.0118289i
\(837\) 33.5716 + 13.8215i 1.16040 + 0.477741i
\(838\) 4.42118 + 9.66763i 0.152727 + 0.333963i
\(839\) 34.1645 28.6674i 1.17949 0.989708i 0.179506 0.983757i \(-0.442550\pi\)
0.999982 0.00595149i \(-0.00189443\pi\)
\(840\) −8.12024 48.0064i −0.280175 1.65638i
\(841\) 5.02026 28.4713i 0.173112 0.981769i
\(842\) 17.1680 + 17.4243i 0.591649 + 0.600482i
\(843\) −12.4587 17.2273i −0.429100 0.593339i
\(844\) 13.6012 22.7718i 0.468171 0.783837i
\(845\) 38.9385 22.4811i 1.33952 0.773375i
\(846\) 1.07626 0.119278i 0.0370027 0.00410086i
\(847\) 4.62285 + 2.66900i 0.158843 + 0.0917081i
\(848\) −47.2512 9.78369i −1.62261 0.335973i
\(849\) −5.27531 18.5507i −0.181048 0.636658i
\(850\) 14.4876 + 3.99724i 0.496922 + 0.137104i
\(851\) −0.243725 0.204510i −0.00835479 0.00701050i
\(852\) 18.5783 39.8871i 0.636482 1.36651i
\(853\) 4.65044 + 1.69262i 0.159228 + 0.0579542i 0.420404 0.907337i \(-0.361888\pi\)
−0.261176 + 0.965291i \(0.584110\pi\)
\(854\) −2.28799 + 24.0942i −0.0782935 + 0.824488i
\(855\) −0.258048 + 0.782491i −0.00882505 + 0.0267606i
\(856\) −6.64887 27.2203i −0.227254 0.930371i
\(857\) −54.3261 + 9.57915i −1.85574 + 0.327218i −0.986060 0.166393i \(-0.946788\pi\)
−0.869683 + 0.493610i \(0.835677\pi\)
\(858\) −8.23565 4.66905i −0.281161 0.159399i
\(859\) 16.3765 + 44.9941i 0.558759 + 1.53518i 0.821440 + 0.570295i \(0.193171\pi\)
−0.262681 + 0.964883i \(0.584607\pi\)
\(860\) −44.5740 54.7489i −1.51996 1.86692i
\(861\) −19.6145 40.4406i −0.668460 1.37821i
\(862\) −29.3297 13.9422i −0.998975 0.474873i
\(863\) 29.9620 1.01992 0.509959 0.860199i \(-0.329661\pi\)
0.509959 + 0.860199i \(0.329661\pi\)
\(864\) −22.3512 + 19.0899i −0.760404 + 0.649450i
\(865\) −28.3302 −0.963255
\(866\) 3.75878 + 1.78677i 0.127728 + 0.0607170i
\(867\) −27.1541 1.95867i −0.922201 0.0665200i
\(868\) −23.1177 28.3947i −0.784666 0.963780i
\(869\) −9.78977 26.8972i −0.332095 0.912424i
\(870\) 0.0218157 + 2.77911i 0.000739620 + 0.0942208i
\(871\) −7.17774 + 1.26563i −0.243208 + 0.0428842i
\(872\) −5.33314 21.8338i −0.180603 0.739384i
\(873\) −0.176798 5.79128i −0.00598371 0.196005i
\(874\) 0.00407768 0.0429409i 0.000137929 0.00145250i
\(875\) −40.9643 14.9098i −1.38485 0.504043i
\(876\) −2.29932 3.28070i −0.0776868 0.110844i
\(877\) −22.6770 19.0283i −0.765749 0.642540i 0.173867 0.984769i \(-0.444374\pi\)
−0.939617 + 0.342229i \(0.888818\pi\)
\(878\) 49.7938 + 13.7385i 1.68046 + 0.463650i
\(879\) 28.0603 28.9300i 0.946451 0.975785i
\(880\) 53.6428 + 11.1071i 1.80830 + 0.374421i
\(881\) 41.2789 + 23.8324i 1.39072 + 0.802934i 0.993395 0.114743i \(-0.0366045\pi\)
0.397327 + 0.917677i \(0.369938\pi\)
\(882\) −0.160085 0.546596i −0.00539034 0.0184048i
\(883\) −27.0065 + 15.5922i −0.908842 + 0.524720i −0.880059 0.474865i \(-0.842497\pi\)
−0.0287839 + 0.999586i \(0.509163\pi\)
\(884\) 1.24287 2.08089i 0.0418024 0.0699877i
\(885\) −81.6171 + 8.39731i −2.74353 + 0.282272i
\(886\) 27.1571 + 27.5626i 0.912362 + 0.925984i
\(887\) −9.61775 + 54.5450i −0.322932 + 1.83144i 0.200891 + 0.979614i \(0.435616\pi\)
−0.523824 + 0.851827i \(0.675495\pi\)
\(888\) −2.85116 + 2.35874i −0.0956788 + 0.0791543i
\(889\) 25.6532 21.5256i 0.860382 0.721946i
\(890\) −5.34203 11.6812i −0.179065 0.391556i
\(891\) 29.8018 12.9564i 0.998396 0.434057i
\(892\) 26.8267 + 23.1963i 0.898225 + 0.776671i
\(893\) 0.0118796 + 0.0141575i 0.000397535 + 0.000473763i
\(894\) 4.74076 28.1778i 0.158555 0.942408i
\(895\) −38.0067 6.70161i −1.27042 0.224010i
\(896\) 28.9940 6.17776i 0.968621 0.206385i
\(897\) 0.0799259 + 0.776835i 0.00266865 + 0.0259378i
\(898\) 9.67427 + 14.0365i 0.322835 + 0.468405i
\(899\) 1.04503 + 1.81005i 0.0348537 + 0.0603684i
\(900\) 10.6490 + 55.3020i 0.354967 + 1.84340i
\(901\) −6.82899 + 11.8282i −0.227507 + 0.394053i
\(902\) 50.4093 4.03410i 1.67845 0.134321i
\(903\) 30.3189 + 29.4074i 1.00895 + 0.978618i
\(904\) −23.7043 + 15.8246i −0.788395 + 0.526318i
\(905\) −40.9803 + 48.8384i −1.36223 + 1.62344i
\(906\) −0.200979 1.08972i −0.00667708 0.0362035i
\(907\) −7.14714 + 19.6366i −0.237317 + 0.652022i 0.762670 + 0.646788i \(0.223888\pi\)
−0.999986 + 0.00523411i \(0.998334\pi\)
\(908\) −3.95469 11.3877i −0.131241 0.377916i
\(909\) −7.10088 11.4755i −0.235521 0.380619i
\(910\) −8.72036 + 12.2596i −0.289077 + 0.406402i
\(911\) −0.180967 1.02631i −0.00599569 0.0340033i 0.981663 0.190624i \(-0.0610511\pi\)
−0.987659 + 0.156621i \(0.949940\pi\)
\(912\) −0.482662 0.136797i −0.0159825 0.00452980i
\(913\) −13.2891 + 4.83682i −0.439804 + 0.160075i
\(914\) −21.7705 + 5.66082i −0.720103 + 0.187243i
\(915\) 3.08701 42.7969i 0.102054 1.41482i
\(916\) 0.519859 35.0769i 0.0171766 1.15897i
\(917\) 16.9065i 0.558302i
\(918\) 3.14335 + 7.70319i 0.103746 + 0.254243i
\(919\) 18.6355i 0.614729i 0.951592 + 0.307365i \(0.0994471\pi\)
−0.951592 + 0.307365i \(0.900553\pi\)
\(920\) −1.81823 4.13688i −0.0599454 0.136389i
\(921\) −22.8900 + 11.1021i −0.754250 + 0.365826i
\(922\) 5.20544 + 20.0191i 0.171432 + 0.659295i
\(923\) −12.7765 + 4.65027i −0.420544 + 0.153065i
\(924\) −32.6504 2.84206i −1.07412 0.0934970i
\(925\) 1.23114 + 6.98213i 0.0404796 + 0.229571i
\(926\) −22.7167 16.1586i −0.746518 0.531004i
\(927\) 14.2141 12.6859i 0.466852 0.416661i
\(928\) −1.69004 + 0.0849413i −0.0554782 + 0.00278833i
\(929\) −14.3578 + 39.4478i −0.471065 + 1.29424i 0.445833 + 0.895116i \(0.352908\pi\)
−0.916897 + 0.399123i \(0.869315\pi\)
\(930\) 42.1152 + 49.3982i 1.38101 + 1.61983i
\(931\) 0.00624839 0.00744654i 0.000204783 0.000244051i
\(932\) −0.300584 1.86599i −0.00984597 0.0611227i
\(933\) 3.88625 1.10514i 0.127230 0.0361808i
\(934\) 4.11387 + 51.4061i 0.134610 + 1.68206i
\(935\) 7.75274 13.4281i 0.253542 0.439147i
\(936\) 9.05440 + 0.716578i 0.295952 + 0.0234221i
\(937\) −2.35834 4.08476i −0.0770435 0.133443i 0.824930 0.565235i \(-0.191215\pi\)
−0.901973 + 0.431792i \(0.857881\pi\)
\(938\) −20.7753 + 14.3188i −0.678336 + 0.467524i
\(939\) 9.88475 7.14861i 0.322577 0.233286i
\(940\) 1.80937 + 0.689089i 0.0590151 + 0.0224756i
\(941\) 22.7195 + 4.00605i 0.740633 + 0.130594i 0.531220 0.847234i \(-0.321734\pi\)
0.209413 + 0.977827i \(0.432845\pi\)
\(942\) −28.6844 + 34.7348i −0.934588 + 1.13172i
\(943\) −2.68141 3.19557i −0.0873186 0.104062i
\(944\) −7.21310 49.4330i −0.234766 1.60891i
\(945\) −15.6346 49.2182i −0.508593 1.60107i
\(946\) −43.2181 + 19.7644i −1.40514 + 0.642596i
\(947\) −24.2924 + 20.3838i −0.789397 + 0.662383i −0.945596 0.325343i \(-0.894520\pi\)
0.156199 + 0.987726i \(0.450076\pi\)
\(948\) 19.4265 + 19.4094i 0.630944 + 0.630389i
\(949\) −0.214963 + 1.21912i −0.00697800 + 0.0395742i
\(950\) −0.684684 + 0.674612i −0.0222141 + 0.0218873i
\(951\) −1.35336 + 3.02183i −0.0438856 + 0.0979896i
\(952\) 0.916930 8.34062i 0.0297179 0.270321i
\(953\) −38.9248 + 22.4732i −1.26090 + 0.727980i −0.973248 0.229756i \(-0.926207\pi\)
−0.287650 + 0.957736i \(0.592874\pi\)
\(954\) −51.0752 3.28135i −1.65362 0.106238i
\(955\) −0.227025 0.131073i −0.00734634 0.00424141i
\(956\) −19.5310 + 10.8935i −0.631676 + 0.352322i
\(957\) 1.81421 + 0.456563i 0.0586451 + 0.0147586i
\(958\) 2.39588 8.68367i 0.0774075 0.280557i
\(959\) 4.33384 + 3.63653i 0.139947 + 0.117430i
\(960\) −51.1411 + 12.1147i −1.65057 + 0.391000i
\(961\) 16.7434 + 6.09410i 0.540110 + 0.196584i
\(962\) 1.13830 + 0.108093i 0.0367002 + 0.00348505i
\(963\) −11.0124 27.6048i −0.354870 0.889552i
\(964\) −37.9826 7.27931i −1.22334 0.234451i
\(965\) 99.8979 17.6147i 3.21583 0.567037i
\(966\) 1.37008 + 2.33061i 0.0440817 + 0.0749862i
\(967\) 10.8906 + 29.9216i 0.350217 + 0.962215i 0.982300 + 0.187314i \(0.0599781\pi\)
−0.632083 + 0.774901i \(0.717800\pi\)
\(968\) 2.55064 5.16681i 0.0819807 0.166068i
\(969\) −0.0796618 + 0.117546i −0.00255910 + 0.00377613i
\(970\) 4.44763 9.35634i 0.142805 0.300414i
\(971\) −11.0287 −0.353929 −0.176964 0.984217i \(-0.556628\pi\)
−0.176964 + 0.984217i \(0.556628\pi\)
\(972\) −20.6493 + 23.3582i −0.662327 + 0.749215i
\(973\) −18.3778 −0.589164
\(974\) 19.1604 40.3071i 0.613938 1.29152i
\(975\) 9.76284 14.4057i 0.312661 0.461353i
\(976\) 26.1140 + 0.774218i 0.835887 + 0.0247821i
\(977\) 2.46836 + 6.78175i 0.0789697 + 0.216968i 0.972894 0.231250i \(-0.0742814\pi\)
−0.893925 + 0.448217i \(0.852059\pi\)
\(978\) −28.0399 47.6978i −0.896616 1.52521i
\(979\) −8.51492 + 1.50141i −0.272138 + 0.0479853i
\(980\) 0.191680 1.00017i 0.00612301 0.0319492i
\(981\) −8.83319 22.1421i −0.282022 0.706944i
\(982\) −37.5435 3.56513i −1.19806 0.113768i
\(983\) 16.9790 + 6.17984i 0.541545 + 0.197106i 0.598286 0.801283i \(-0.295849\pi\)
−0.0567408 + 0.998389i \(0.518071\pi\)
\(984\) −42.1851 + 23.9651i −1.34481 + 0.763980i
\(985\) 13.0139 + 10.9199i 0.414657 + 0.347938i
\(986\) −0.127389 + 0.461712i −0.00405691 + 0.0147039i
\(987\) −1.12332 0.282694i −0.0357556 0.00899825i
\(988\) 0.0755106 + 0.135383i 0.00240231 + 0.00430709i
\(989\) 3.39494 + 1.96007i 0.107953 + 0.0623266i
\(990\) 57.9841 + 3.72522i 1.84286 + 0.118395i
\(991\) 14.8777 8.58966i 0.472607 0.272860i −0.244724 0.969593i \(-0.578697\pi\)
0.717330 + 0.696733i \(0.245364\pi\)
\(992\) −28.9640 + 26.8936i −0.919607 + 0.853871i
\(993\) 4.05549 9.05526i 0.128697 0.287360i
\(994\) −33.5286 + 33.0354i −1.06346 + 1.04782i
\(995\) −6.47614 + 36.7280i −0.205307 + 1.16436i
\(996\) 9.58960 9.59804i 0.303858 0.304126i
\(997\) 37.0763 31.1107i 1.17422 0.985286i 0.174219 0.984707i \(-0.444260\pi\)
1.00000 0.000579452i \(-0.000184445\pi\)
\(998\) −28.8780 + 13.2064i −0.914118 + 0.418042i
\(999\) −2.64537 + 2.89938i −0.0836959 + 0.0917324i
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 108.2.l.a.59.3 yes 96
3.2 odd 2 324.2.l.a.287.14 96
4.3 odd 2 inner 108.2.l.a.59.8 yes 96
9.2 odd 6 972.2.l.b.539.7 96
9.4 even 3 972.2.l.d.215.13 96
9.5 odd 6 972.2.l.a.215.4 96
9.7 even 3 972.2.l.c.539.10 96
12.11 even 2 324.2.l.a.287.9 96
27.2 odd 18 972.2.l.c.431.4 96
27.7 even 9 972.2.l.a.755.2 96
27.11 odd 18 inner 108.2.l.a.11.8 yes 96
27.16 even 9 324.2.l.a.35.9 96
27.20 odd 18 972.2.l.d.755.15 96
27.25 even 9 972.2.l.b.431.13 96
36.7 odd 6 972.2.l.c.539.4 96
36.11 even 6 972.2.l.b.539.13 96
36.23 even 6 972.2.l.a.215.2 96
36.31 odd 6 972.2.l.d.215.15 96
108.7 odd 18 972.2.l.a.755.4 96
108.11 even 18 inner 108.2.l.a.11.3 96
108.43 odd 18 324.2.l.a.35.14 96
108.47 even 18 972.2.l.d.755.13 96
108.79 odd 18 972.2.l.b.431.7 96
108.83 even 18 972.2.l.c.431.10 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.2.l.a.11.3 96 108.11 even 18 inner
108.2.l.a.11.8 yes 96 27.11 odd 18 inner
108.2.l.a.59.3 yes 96 1.1 even 1 trivial
108.2.l.a.59.8 yes 96 4.3 odd 2 inner
324.2.l.a.35.9 96 27.16 even 9
324.2.l.a.35.14 96 108.43 odd 18
324.2.l.a.287.9 96 12.11 even 2
324.2.l.a.287.14 96 3.2 odd 2
972.2.l.a.215.2 96 36.23 even 6
972.2.l.a.215.4 96 9.5 odd 6
972.2.l.a.755.2 96 27.7 even 9
972.2.l.a.755.4 96 108.7 odd 18
972.2.l.b.431.7 96 108.79 odd 18
972.2.l.b.431.13 96 27.25 even 9
972.2.l.b.539.7 96 9.2 odd 6
972.2.l.b.539.13 96 36.11 even 6
972.2.l.c.431.4 96 27.2 odd 18
972.2.l.c.431.10 96 108.83 even 18
972.2.l.c.539.4 96 36.7 odd 6
972.2.l.c.539.10 96 9.7 even 3
972.2.l.d.215.13 96 9.4 even 3
972.2.l.d.215.15 96 36.31 odd 6
972.2.l.d.755.13 96 108.47 even 18
972.2.l.d.755.15 96 27.20 odd 18