Properties

Label 69.2.e.c.55.2
Level $69$
Weight $2$
Character 69.55
Analytic conductor $0.551$
Analytic rank $0$
Dimension $20$
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] = [69,2,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), 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: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + 4165 x^{12} - 7040 x^{11} + 10649 x^{10} - 13519 x^{9} + 15111 x^{8} - 12101 x^{7} + \cdots + 529 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 55.2
Root \(-1.30051 + 1.50087i\) of defining polynomial
Character \(\chi\) \(=\) 69.55
Dual form 69.2.e.c.64.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.54781 - 0.454477i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.506650 - 0.325604i) q^{4} +(0.0749695 + 0.521424i) q^{5} +(-1.35707 - 0.872135i) q^{6} +(0.200934 - 0.439985i) q^{7} +(-1.47656 + 1.70404i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\) \(q+(1.54781 - 0.454477i) q^{2} +(-0.654861 - 0.755750i) q^{3} +(0.506650 - 0.325604i) q^{4} +(0.0749695 + 0.521424i) q^{5} +(-1.35707 - 0.872135i) q^{6} +(0.200934 - 0.439985i) q^{7} +(-1.47656 + 1.70404i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.353014 + 0.772992i) q^{10} +(-3.21327 - 0.943501i) q^{11} +(-0.577861 - 0.169675i) q^{12} +(0.853105 + 1.86804i) q^{13} +(0.111045 - 0.772332i) q^{14} +(0.344971 - 0.398118i) q^{15} +(-2.01136 + 4.40426i) q^{16} +(-0.919522 - 0.590941i) q^{17} +(0.229575 + 1.59673i) q^{18} +(6.19469 - 3.98109i) q^{19} +(0.207761 + 0.239769i) q^{20} +(-0.464102 + 0.136273i) q^{21} -5.40232 q^{22} +(-1.81662 - 4.43846i) q^{23} +2.25477 q^{24} +(4.53120 - 1.33048i) q^{25} +(2.16942 + 2.50365i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.0414575 - 0.288343i) q^{28} +(-3.03219 - 1.94867i) q^{29} +(0.353014 - 0.772992i) q^{30} +(-3.65525 + 4.21838i) q^{31} +(-0.469783 + 3.26741i) q^{32} +(1.39119 + 3.04629i) q^{33} +(-1.69181 - 0.496761i) q^{34} +(0.244483 + 0.0717866i) q^{35} +(0.250186 + 0.547831i) q^{36} +(0.491920 - 3.42138i) q^{37} +(7.77887 - 8.97730i) q^{38} +(0.853105 - 1.86804i) q^{39} +(-0.999226 - 0.642164i) q^{40} +(1.47926 + 10.2885i) q^{41} +(-0.656408 + 0.421848i) q^{42} +(-5.05496 - 5.83373i) q^{43} +(-1.93521 + 0.568229i) q^{44} -0.526786 q^{45} +(-4.82895 - 6.04426i) q^{46} +10.7974 q^{47} +(4.64567 - 1.36409i) q^{48} +(4.43081 + 5.11343i) q^{49} +(6.40875 - 4.11866i) q^{50} +(0.155555 + 1.08191i) q^{51} +(1.04047 + 0.668668i) q^{52} +(-3.06811 + 6.71822i) q^{53} +(1.05639 - 1.21914i) q^{54} +(0.251067 - 1.74621i) q^{55} +(0.453061 + 0.992066i) q^{56} +(-7.06537 - 2.07458i) q^{57} +(-5.57887 - 1.63811i) q^{58} +(-0.390317 - 0.854675i) q^{59} +(0.0451508 - 0.314031i) q^{60} +(-3.75616 + 4.33483i) q^{61} +(-3.74046 + 8.19046i) q^{62} +(0.406911 + 0.261506i) q^{63} +(-0.620289 - 4.31421i) q^{64} +(-0.910084 + 0.584876i) q^{65} +(3.53777 + 4.08280i) q^{66} +(-12.3567 + 3.62825i) q^{67} -0.658289 q^{68} +(-2.16473 + 4.27948i) q^{69} +0.411037 q^{70} +(-5.99541 + 1.76041i) q^{71} +(-1.47656 - 1.70404i) q^{72} +(-0.00713288 + 0.00458402i) q^{73} +(-0.793542 - 5.51920i) q^{74} +(-3.97282 - 2.55317i) q^{75} +(1.84228 - 4.03404i) q^{76} +(-1.06078 + 1.22421i) q^{77} +(0.471461 - 3.27908i) q^{78} +(4.29440 + 9.40343i) q^{79} +(-2.44728 - 0.718585i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(6.96548 + 15.2523i) q^{82} +(0.861534 - 5.99210i) q^{83} +(-0.190767 + 0.220156i) q^{84} +(0.239195 - 0.523763i) q^{85} +(-10.4754 - 6.73213i) q^{86} +(0.512956 + 3.56769i) q^{87} +(6.35236 - 4.08241i) q^{88} +(-1.84618 - 2.13061i) q^{89} +(-0.815363 + 0.239412i) q^{90} +0.993327 q^{91} +(-2.36557 - 1.65724i) q^{92} +5.58172 q^{93} +(16.7123 - 4.90718i) q^{94} +(2.54025 + 2.93160i) q^{95} +(2.77699 - 1.78466i) q^{96} +(-2.61142 - 18.1628i) q^{97} +(9.18198 + 5.90090i) q^{98} +(1.39119 - 3.04629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{5}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.54781 0.454477i 1.09446 0.321364i 0.315814 0.948821i \(-0.397722\pi\)
0.778651 + 0.627457i \(0.215904\pi\)
\(3\) −0.654861 0.755750i −0.378084 0.436332i
\(4\) 0.506650 0.325604i 0.253325 0.162802i
\(5\) 0.0749695 + 0.521424i 0.0335274 + 0.233188i 0.999694 0.0247301i \(-0.00787264\pi\)
−0.966167 + 0.257918i \(0.916964\pi\)
\(6\) −1.35707 0.872135i −0.554021 0.356048i
\(7\) 0.200934 0.439985i 0.0759460 0.166299i −0.867851 0.496825i \(-0.834499\pi\)
0.943797 + 0.330526i \(0.107226\pi\)
\(8\) −1.47656 + 1.70404i −0.522043 + 0.602470i
\(9\) −0.142315 + 0.989821i −0.0474383 + 0.329940i
\(10\) 0.353014 + 0.772992i 0.111633 + 0.244441i
\(11\) −3.21327 0.943501i −0.968837 0.284476i −0.241228 0.970468i \(-0.577550\pi\)
−0.727609 + 0.685992i \(0.759368\pi\)
\(12\) −0.577861 0.169675i −0.166814 0.0489810i
\(13\) 0.853105 + 1.86804i 0.236609 + 0.518101i 0.990270 0.139163i \(-0.0444411\pi\)
−0.753661 + 0.657264i \(0.771714\pi\)
\(14\) 0.111045 0.772332i 0.0296779 0.206414i
\(15\) 0.344971 0.398118i 0.0890712 0.102794i
\(16\) −2.01136 + 4.40426i −0.502839 + 1.10106i
\(17\) −0.919522 0.590941i −0.223017 0.143324i 0.424362 0.905493i \(-0.360498\pi\)
−0.647379 + 0.762168i \(0.724135\pi\)
\(18\) 0.229575 + 1.59673i 0.0541114 + 0.376353i
\(19\) 6.19469 3.98109i 1.42116 0.913324i 0.421180 0.906977i \(-0.361616\pi\)
0.999980 0.00634685i \(-0.00202028\pi\)
\(20\) 0.207761 + 0.239769i 0.0464568 + 0.0536140i
\(21\) −0.464102 + 0.136273i −0.101275 + 0.0297372i
\(22\) −5.40232 −1.15178
\(23\) −1.81662 4.43846i −0.378791 0.925482i
\(24\) 2.25477 0.460253
\(25\) 4.53120 1.33048i 0.906240 0.266096i
\(26\) 2.16942 + 2.50365i 0.425459 + 0.491006i
\(27\) 0.841254 0.540641i 0.161899 0.104046i
\(28\) −0.0414575 0.288343i −0.00783474 0.0544918i
\(29\) −3.03219 1.94867i −0.563064 0.361859i 0.227935 0.973676i \(-0.426802\pi\)
−0.790999 + 0.611817i \(0.790439\pi\)
\(30\) 0.353014 0.772992i 0.0644512 0.141128i
\(31\) −3.65525 + 4.21838i −0.656502 + 0.757643i −0.982202 0.187830i \(-0.939855\pi\)
0.325700 + 0.945473i \(0.394400\pi\)
\(32\) −0.469783 + 3.26741i −0.0830466 + 0.577602i
\(33\) 1.39119 + 3.04629i 0.242176 + 0.530291i
\(34\) −1.69181 0.496761i −0.290143 0.0851938i
\(35\) 0.244483 + 0.0717866i 0.0413251 + 0.0121341i
\(36\) 0.250186 + 0.547831i 0.0416977 + 0.0913052i
\(37\) 0.491920 3.42138i 0.0808712 0.562471i −0.908592 0.417685i \(-0.862841\pi\)
0.989463 0.144786i \(-0.0462494\pi\)
\(38\) 7.77887 8.97730i 1.26190 1.45631i
\(39\) 0.853105 1.86804i 0.136606 0.299126i
\(40\) −0.999226 0.642164i −0.157991 0.101535i
\(41\) 1.47926 + 10.2885i 0.231021 + 1.60679i 0.693701 + 0.720263i \(0.255979\pi\)
−0.462680 + 0.886525i \(0.653112\pi\)
\(42\) −0.656408 + 0.421848i −0.101286 + 0.0650925i
\(43\) −5.05496 5.83373i −0.770874 0.889636i 0.225541 0.974234i \(-0.427585\pi\)
−0.996415 + 0.0845976i \(0.973040\pi\)
\(44\) −1.93521 + 0.568229i −0.291744 + 0.0856638i
\(45\) −0.526786 −0.0785286
\(46\) −4.82895 6.04426i −0.711990 0.891178i
\(47\) 10.7974 1.57497 0.787483 0.616336i \(-0.211384\pi\)
0.787483 + 0.616336i \(0.211384\pi\)
\(48\) 4.64567 1.36409i 0.670545 0.196890i
\(49\) 4.43081 + 5.11343i 0.632973 + 0.730490i
\(50\) 6.40875 4.11866i 0.906335 0.582466i
\(51\) 0.155555 + 1.08191i 0.0217821 + 0.151498i
\(52\) 1.04047 + 0.668668i 0.144287 + 0.0927276i
\(53\) −3.06811 + 6.71822i −0.421437 + 0.922819i 0.573202 + 0.819414i \(0.305701\pi\)
−0.994639 + 0.103405i \(0.967026\pi\)
\(54\) 1.05639 1.21914i 0.143756 0.165904i
\(55\) 0.251067 1.74621i 0.0338539 0.235459i
\(56\) 0.453061 + 0.992066i 0.0605428 + 0.132570i
\(57\) −7.06537 2.07458i −0.935830 0.274785i
\(58\) −5.57887 1.63811i −0.732542 0.215094i
\(59\) −0.390317 0.854675i −0.0508149 0.111269i 0.882522 0.470272i \(-0.155844\pi\)
−0.933337 + 0.359003i \(0.883117\pi\)
\(60\) 0.0451508 0.314031i 0.00582895 0.0405412i
\(61\) −3.75616 + 4.33483i −0.480926 + 0.555019i −0.943418 0.331605i \(-0.892410\pi\)
0.462492 + 0.886623i \(0.346955\pi\)
\(62\) −3.74046 + 8.19046i −0.475039 + 1.04019i
\(63\) 0.406911 + 0.261506i 0.0512659 + 0.0329466i
\(64\) −0.620289 4.31421i −0.0775362 0.539276i
\(65\) −0.910084 + 0.584876i −0.112882 + 0.0725449i
\(66\) 3.53777 + 4.08280i 0.435469 + 0.502558i
\(67\) −12.3567 + 3.62825i −1.50961 + 0.443262i −0.928739 0.370733i \(-0.879106\pi\)
−0.580872 + 0.813995i \(0.697288\pi\)
\(68\) −0.658289 −0.0798292
\(69\) −2.16473 + 4.27948i −0.260603 + 0.515189i
\(70\) 0.411037 0.0491284
\(71\) −5.99541 + 1.76041i −0.711525 + 0.208923i −0.617413 0.786639i \(-0.711819\pi\)
−0.0941117 + 0.995562i \(0.530001\pi\)
\(72\) −1.47656 1.70404i −0.174014 0.200823i
\(73\) −0.00713288 + 0.00458402i −0.000834840 + 0.000536519i −0.541058 0.840985i \(-0.681976\pi\)
0.540223 + 0.841522i \(0.318340\pi\)
\(74\) −0.793542 5.51920i −0.0922473 0.641594i
\(75\) −3.97282 2.55317i −0.458741 0.294815i
\(76\) 1.84228 4.03404i 0.211324 0.462736i
\(77\) −1.06078 + 1.22421i −0.120887 + 0.139512i
\(78\) 0.471461 3.27908i 0.0533824 0.371283i
\(79\) 4.29440 + 9.40343i 0.483158 + 1.05797i 0.981583 + 0.191036i \(0.0611846\pi\)
−0.498425 + 0.866933i \(0.666088\pi\)
\(80\) −2.44728 0.718585i −0.273614 0.0803402i
\(81\) −0.959493 0.281733i −0.106610 0.0313036i
\(82\) 6.96548 + 15.2523i 0.769208 + 1.68433i
\(83\) 0.861534 5.99210i 0.0945656 0.657719i −0.886311 0.463090i \(-0.846741\pi\)
0.980877 0.194629i \(-0.0623502\pi\)
\(84\) −0.190767 + 0.220156i −0.0208143 + 0.0240210i
\(85\) 0.239195 0.523763i 0.0259443 0.0568101i
\(86\) −10.4754 6.73213i −1.12959 0.725944i
\(87\) 0.512956 + 3.56769i 0.0549946 + 0.382496i
\(88\) 6.35236 4.08241i 0.677164 0.435187i
\(89\) −1.84618 2.13061i −0.195695 0.225844i 0.649418 0.760431i \(-0.275012\pi\)
−0.845113 + 0.534588i \(0.820467\pi\)
\(90\) −0.815363 + 0.239412i −0.0859468 + 0.0252363i
\(91\) 0.993327 0.104129
\(92\) −2.36557 1.65724i −0.246628 0.172780i
\(93\) 5.58172 0.578797
\(94\) 16.7123 4.90718i 1.72375 0.506137i
\(95\) 2.54025 + 2.93160i 0.260624 + 0.300776i
\(96\) 2.77699 1.78466i 0.283425 0.182146i
\(97\) −2.61142 18.1628i −0.265150 1.84416i −0.492461 0.870335i \(-0.663903\pi\)
0.227311 0.973822i \(-0.427007\pi\)
\(98\) 9.18198 + 5.90090i 0.927520 + 0.596081i
\(99\) 1.39119 3.04629i 0.139820 0.306164i
\(100\) 1.86252 2.14947i 0.186252 0.214947i
\(101\) 0.923803 6.42519i 0.0919219 0.639331i −0.890821 0.454354i \(-0.849870\pi\)
0.982743 0.184976i \(-0.0592209\pi\)
\(102\) 0.732474 + 1.60389i 0.0725258 + 0.158809i
\(103\) 13.1354 + 3.85690i 1.29427 + 0.380032i 0.855142 0.518394i \(-0.173470\pi\)
0.439127 + 0.898425i \(0.355288\pi\)
\(104\) −4.44288 1.30455i −0.435660 0.127921i
\(105\) −0.105849 0.231778i −0.0103298 0.0226192i
\(106\) −1.69556 + 11.7929i −0.164688 + 1.14543i
\(107\) 7.86436 9.07596i 0.760277 0.877406i −0.235245 0.971936i \(-0.575589\pi\)
0.995522 + 0.0945299i \(0.0301348\pi\)
\(108\) 0.250186 0.547831i 0.0240742 0.0527151i
\(109\) 10.5081 + 6.75317i 1.00650 + 0.646837i 0.936484 0.350709i \(-0.114059\pi\)
0.0700133 + 0.997546i \(0.477696\pi\)
\(110\) −0.405009 2.81690i −0.0386161 0.268581i
\(111\) −2.90785 + 1.86876i −0.276001 + 0.177375i
\(112\) 1.53366 + 1.76993i 0.144917 + 0.167243i
\(113\) −2.99845 + 0.880423i −0.282070 + 0.0828233i −0.419707 0.907659i \(-0.637867\pi\)
0.137637 + 0.990483i \(0.456049\pi\)
\(114\) −11.8787 −1.11254
\(115\) 2.17813 1.27998i 0.203111 0.119359i
\(116\) −2.17076 −0.201550
\(117\) −1.97044 + 0.578572i −0.182167 + 0.0534890i
\(118\) −0.992565 1.14548i −0.0913731 0.105450i
\(119\) −0.444769 + 0.285835i −0.0407719 + 0.0262025i
\(120\) 0.169039 + 1.17569i 0.0154311 + 0.107326i
\(121\) 0.181123 + 0.116401i 0.0164657 + 0.0105819i
\(122\) −3.84372 + 8.41657i −0.347994 + 0.762001i
\(123\) 6.80679 7.85546i 0.613748 0.708303i
\(124\) −0.478409 + 3.32741i −0.0429624 + 0.298810i
\(125\) 2.12762 + 4.65884i 0.190300 + 0.416699i
\(126\) 0.748667 + 0.219829i 0.0666966 + 0.0195839i
\(127\) −10.4847 3.07860i −0.930370 0.273181i −0.218779 0.975775i \(-0.570207\pi\)
−0.711592 + 0.702593i \(0.752025\pi\)
\(128\) −5.66338 12.4011i −0.500576 1.09611i
\(129\) −1.09855 + 7.64057i −0.0967217 + 0.672714i
\(130\) −1.14282 + 1.31889i −0.100232 + 0.115674i
\(131\) −0.244434 + 0.535236i −0.0213563 + 0.0467638i −0.920010 0.391896i \(-0.871819\pi\)
0.898653 + 0.438660i \(0.144547\pi\)
\(132\) 1.69673 + 1.09042i 0.147682 + 0.0949093i
\(133\) −0.506892 3.52551i −0.0439531 0.305700i
\(134\) −17.4768 + 11.2317i −1.50977 + 0.970269i
\(135\) 0.344971 + 0.398118i 0.0296904 + 0.0342646i
\(136\) 2.36472 0.694344i 0.202773 0.0595395i
\(137\) 17.9223 1.53121 0.765603 0.643314i \(-0.222441\pi\)
0.765603 + 0.643314i \(0.222441\pi\)
\(138\) −1.40566 + 7.60763i −0.119657 + 0.647604i
\(139\) −13.3492 −1.13227 −0.566133 0.824314i \(-0.691561\pi\)
−0.566133 + 0.824314i \(0.691561\pi\)
\(140\) 0.147241 0.0432339i 0.0124441 0.00365393i
\(141\) −7.07081 8.16015i −0.595470 0.687209i
\(142\) −8.47968 + 5.44956i −0.711599 + 0.457317i
\(143\) −0.978760 6.80742i −0.0818480 0.569265i
\(144\) −4.07318 2.61767i −0.339432 0.218140i
\(145\) 0.788762 1.72715i 0.0655031 0.143432i
\(146\) −0.00895698 + 0.0103369i −0.000741285 + 0.000855489i
\(147\) 0.962908 6.69717i 0.0794193 0.552373i
\(148\) −0.864785 1.89361i −0.0710849 0.155654i
\(149\) −7.76039 2.27866i −0.635756 0.186675i −0.0520557 0.998644i \(-0.516577\pi\)
−0.583700 + 0.811969i \(0.698396\pi\)
\(150\) −7.30951 2.14627i −0.596819 0.175242i
\(151\) 1.87350 + 4.10240i 0.152464 + 0.333849i 0.970417 0.241436i \(-0.0776185\pi\)
−0.817953 + 0.575285i \(0.804891\pi\)
\(152\) −2.36290 + 16.4343i −0.191657 + 1.33300i
\(153\) 0.715787 0.826063i 0.0578680 0.0667832i
\(154\) −1.08551 + 2.37694i −0.0874731 + 0.191539i
\(155\) −2.47360 1.58968i −0.198684 0.127686i
\(156\) −0.176016 1.22422i −0.0140925 0.0980158i
\(157\) 1.74744 1.12301i 0.139461 0.0896263i −0.469050 0.883172i \(-0.655404\pi\)
0.608511 + 0.793545i \(0.291767\pi\)
\(158\) 10.9205 + 12.6030i 0.868792 + 1.00264i
\(159\) 7.08648 2.08078i 0.561994 0.165016i
\(160\) −1.73893 −0.137474
\(161\) −2.31787 0.0925529i −0.182674 0.00729419i
\(162\) −1.61315 −0.126741
\(163\) −16.6050 + 4.87566i −1.30060 + 0.381891i −0.857456 0.514558i \(-0.827956\pi\)
−0.443147 + 0.896449i \(0.646138\pi\)
\(164\) 4.09943 + 4.73100i 0.320112 + 0.369429i
\(165\) −1.48411 + 0.953781i −0.115538 + 0.0742517i
\(166\) −1.38978 9.66616i −0.107868 0.750240i
\(167\) 14.4834 + 9.30794i 1.12076 + 0.720270i 0.963612 0.267305i \(-0.0861331\pi\)
0.157150 + 0.987575i \(0.449769\pi\)
\(168\) 0.453061 0.992066i 0.0349544 0.0765395i
\(169\) 5.75140 6.63747i 0.442416 0.510575i
\(170\) 0.132189 0.919393i 0.0101384 0.0705142i
\(171\) 3.05897 + 6.69821i 0.233925 + 0.512225i
\(172\) −4.46058 1.30975i −0.340116 0.0998672i
\(173\) 11.8788 + 3.48793i 0.903129 + 0.265183i 0.700146 0.714000i \(-0.253118\pi\)
0.202983 + 0.979182i \(0.434936\pi\)
\(174\) 2.41539 + 5.28896i 0.183110 + 0.400955i
\(175\) 0.325083 2.26100i 0.0245739 0.170916i
\(176\) 10.6185 12.2543i 0.800396 0.923706i
\(177\) −0.390317 + 0.854675i −0.0293380 + 0.0642413i
\(178\) −3.82584 2.45872i −0.286759 0.184289i
\(179\) 0.511848 + 3.55998i 0.0382573 + 0.266085i 0.999968 0.00798071i \(-0.00254037\pi\)
−0.961711 + 0.274066i \(0.911631\pi\)
\(180\) −0.266896 + 0.171524i −0.0198933 + 0.0127846i
\(181\) −6.81072 7.85999i −0.506237 0.584229i 0.443894 0.896079i \(-0.353597\pi\)
−0.950131 + 0.311851i \(0.899051\pi\)
\(182\) 1.53748 0.451445i 0.113966 0.0334633i
\(183\) 5.73581 0.424003
\(184\) 10.2457 + 3.45805i 0.755321 + 0.254931i
\(185\) 1.82087 0.133873
\(186\) 8.63942 2.53676i 0.633473 0.186004i
\(187\) 2.39712 + 2.76642i 0.175295 + 0.202301i
\(188\) 5.47052 3.51569i 0.398979 0.256408i
\(189\) −0.0688370 0.478772i −0.00500716 0.0348255i
\(190\) 5.26416 + 3.38307i 0.381902 + 0.245434i
\(191\) −2.78682 + 6.10229i −0.201647 + 0.441546i −0.983258 0.182221i \(-0.941671\pi\)
0.781610 + 0.623767i \(0.214399\pi\)
\(192\) −2.85426 + 3.29399i −0.205988 + 0.237723i
\(193\) 1.89436 13.1756i 0.136359 0.948398i −0.800660 0.599119i \(-0.795517\pi\)
0.937019 0.349279i \(-0.113573\pi\)
\(194\) −12.2966 26.9257i −0.882842 1.93316i
\(195\) 1.03800 + 0.304784i 0.0743326 + 0.0218260i
\(196\) 3.90983 + 1.14803i 0.279273 + 0.0820021i
\(197\) −7.95982 17.4296i −0.567114 1.24181i −0.948320 0.317316i \(-0.897219\pi\)
0.381206 0.924490i \(-0.375509\pi\)
\(198\) 0.768831 5.34733i 0.0546384 0.380019i
\(199\) −15.2770 + 17.6306i −1.08296 + 1.24980i −0.116438 + 0.993198i \(0.537148\pi\)
−0.966518 + 0.256600i \(0.917398\pi\)
\(200\) −4.42340 + 9.68590i −0.312782 + 0.684897i
\(201\) 10.8340 + 6.96257i 0.764169 + 0.491102i
\(202\) −1.49023 10.3648i −0.104853 0.729265i
\(203\) −1.46666 + 0.942563i −0.102939 + 0.0661550i
\(204\) 0.431087 + 0.497501i 0.0301822 + 0.0348321i
\(205\) −5.25375 + 1.54264i −0.366938 + 0.107743i
\(206\) 22.0839 1.53866
\(207\) 4.65181 1.16647i 0.323323 0.0810754i
\(208\) −9.94323 −0.689439
\(209\) −23.6614 + 6.94761i −1.63669 + 0.480576i
\(210\) −0.269172 0.310641i −0.0185746 0.0214363i
\(211\) −1.72239 + 1.10691i −0.118574 + 0.0762030i −0.598584 0.801060i \(-0.704270\pi\)
0.480009 + 0.877263i \(0.340633\pi\)
\(212\) 0.633024 + 4.40278i 0.0434763 + 0.302384i
\(213\) 5.25659 + 3.37821i 0.360176 + 0.231471i
\(214\) 8.04770 17.6220i 0.550130 1.20462i
\(215\) 2.66288 3.07313i 0.181607 0.209586i
\(216\) −0.320887 + 2.23182i −0.0218336 + 0.151856i
\(217\) 1.12156 + 2.45587i 0.0761363 + 0.166715i
\(218\) 19.3337 + 5.67690i 1.30945 + 0.384488i
\(219\) 0.00813541 + 0.00238877i 0.000549740 + 0.000161418i
\(220\) −0.441370 0.966466i −0.0297572 0.0651591i
\(221\) 0.319452 2.22184i 0.0214887 0.149457i
\(222\) −3.65148 + 4.21403i −0.245071 + 0.282827i
\(223\) 0.267566 0.585889i 0.0179176 0.0392340i −0.900462 0.434935i \(-0.856771\pi\)
0.918379 + 0.395701i \(0.129498\pi\)
\(224\) 1.34322 + 0.863232i 0.0897474 + 0.0576771i
\(225\) 0.672081 + 4.67443i 0.0448054 + 0.311629i
\(226\) −4.24088 + 2.72545i −0.282099 + 0.181294i
\(227\) −16.3006 18.8119i −1.08191 1.24859i −0.966880 0.255230i \(-0.917849\pi\)
−0.115030 0.993362i \(-0.536697\pi\)
\(228\) −4.25516 + 1.24943i −0.281805 + 0.0827454i
\(229\) 2.91045 0.192328 0.0961640 0.995366i \(-0.469343\pi\)
0.0961640 + 0.995366i \(0.469343\pi\)
\(230\) 2.78960 2.97107i 0.183941 0.195906i
\(231\) 1.61986 0.106579
\(232\) 7.79784 2.28965i 0.511953 0.150323i
\(233\) −3.99921 4.61533i −0.261997 0.302360i 0.609476 0.792805i \(-0.291380\pi\)
−0.871472 + 0.490444i \(0.836834\pi\)
\(234\) −2.78691 + 1.79104i −0.182186 + 0.117084i
\(235\) 0.809477 + 5.63004i 0.0528045 + 0.367263i
\(236\) −0.476040 0.305932i −0.0309876 0.0199145i
\(237\) 4.29440 9.40343i 0.278951 0.610818i
\(238\) −0.558510 + 0.644555i −0.0362028 + 0.0417803i
\(239\) −4.26924 + 29.6932i −0.276154 + 1.92069i 0.101674 + 0.994818i \(0.467580\pi\)
−0.377828 + 0.925876i \(0.623329\pi\)
\(240\) 1.05955 + 2.32010i 0.0683939 + 0.149762i
\(241\) −2.92074 0.857606i −0.188141 0.0552433i 0.186305 0.982492i \(-0.440349\pi\)
−0.374446 + 0.927249i \(0.622167\pi\)
\(242\) 0.333245 + 0.0978496i 0.0214218 + 0.00629001i
\(243\) 0.415415 + 0.909632i 0.0266489 + 0.0583529i
\(244\) −0.491616 + 3.41926i −0.0314725 + 0.218896i
\(245\) −2.33409 + 2.69368i −0.149120 + 0.172093i
\(246\) 6.96548 15.2523i 0.444103 0.972449i
\(247\) 12.7216 + 8.17565i 0.809453 + 0.520204i
\(248\) −1.79110 12.4574i −0.113735 0.791045i
\(249\) −5.09271 + 3.27289i −0.322738 + 0.207411i
\(250\) 5.41048 + 6.24403i 0.342189 + 0.394907i
\(251\) 3.39713 0.997487i 0.214425 0.0629608i −0.172756 0.984965i \(-0.555267\pi\)
0.387181 + 0.922004i \(0.373449\pi\)
\(252\) 0.291309 0.0183507
\(253\) 1.64960 + 15.9759i 0.103710 + 1.00440i
\(254\) −17.6275 −1.10605
\(255\) −0.552473 + 0.162221i −0.0345972 + 0.0101587i
\(256\) −8.69330 10.0326i −0.543331 0.627038i
\(257\) 7.38840 4.74824i 0.460876 0.296187i −0.289524 0.957171i \(-0.593497\pi\)
0.750400 + 0.660984i \(0.229861\pi\)
\(258\) 1.77212 + 12.3254i 0.110328 + 0.767345i
\(259\) −1.40651 0.903910i −0.0873964 0.0561663i
\(260\) −0.270656 + 0.592655i −0.0167854 + 0.0367549i
\(261\) 2.36036 2.72400i 0.146103 0.168612i
\(262\) −0.135084 + 0.939532i −0.00834553 + 0.0580445i
\(263\) 3.85133 + 8.43323i 0.237483 + 0.520015i 0.990422 0.138076i \(-0.0440917\pi\)
−0.752939 + 0.658091i \(0.771364\pi\)
\(264\) −7.24519 2.12738i −0.445911 0.130931i
\(265\) −3.73306 1.09612i −0.229320 0.0673344i
\(266\) −2.38683 5.22644i −0.146346 0.320453i
\(267\) −0.401213 + 2.79050i −0.0245539 + 0.170776i
\(268\) −5.07915 + 5.86165i −0.310258 + 0.358057i
\(269\) 5.27658 11.5541i 0.321719 0.704466i −0.677807 0.735239i \(-0.737070\pi\)
0.999526 + 0.0307732i \(0.00979696\pi\)
\(270\) 0.714885 + 0.459429i 0.0435065 + 0.0279599i
\(271\) 0.696557 + 4.84466i 0.0423129 + 0.294292i 0.999979 + 0.00641267i \(0.00204123\pi\)
−0.957667 + 0.287880i \(0.907050\pi\)
\(272\) 4.45214 2.86122i 0.269951 0.173487i
\(273\) −0.650491 0.750707i −0.0393695 0.0454348i
\(274\) 27.7403 8.14528i 1.67585 0.492074i
\(275\) −15.8153 −0.953698
\(276\) 0.296657 + 2.87304i 0.0178567 + 0.172937i
\(277\) 3.82724 0.229957 0.114978 0.993368i \(-0.463320\pi\)
0.114978 + 0.993368i \(0.463320\pi\)
\(278\) −20.6620 + 6.06691i −1.23922 + 0.363869i
\(279\) −3.65525 4.21838i −0.218834 0.252548i
\(280\) −0.483321 + 0.310612i −0.0288840 + 0.0185626i
\(281\) 2.81648 + 19.5891i 0.168017 + 1.16859i 0.882976 + 0.469419i \(0.155537\pi\)
−0.714958 + 0.699167i \(0.753554\pi\)
\(282\) −14.6529 9.41682i −0.872565 0.560763i
\(283\) −4.06513 + 8.90139i −0.241647 + 0.529133i −0.991131 0.132890i \(-0.957574\pi\)
0.749484 + 0.662023i \(0.230302\pi\)
\(284\) −2.46438 + 2.84405i −0.146234 + 0.168763i
\(285\) 0.552048 3.83958i 0.0327005 0.227437i
\(286\) −4.60875 10.0918i −0.272521 0.596738i
\(287\) 4.82400 + 1.41645i 0.284752 + 0.0836107i
\(288\) −3.16730 0.930002i −0.186635 0.0548009i
\(289\) −6.56575 14.3770i −0.386220 0.845705i
\(290\) 0.435902 3.03177i 0.0255971 0.178031i
\(291\) −12.0164 + 13.8677i −0.704416 + 0.812940i
\(292\) −0.00212130 + 0.00464499i −0.000124139 + 0.000271827i
\(293\) −7.48457 4.81004i −0.437253 0.281006i 0.303438 0.952851i \(-0.401866\pi\)
−0.740691 + 0.671846i \(0.765502\pi\)
\(294\) −1.55332 10.8035i −0.0905912 0.630076i
\(295\) 0.416386 0.267595i 0.0242429 0.0155800i
\(296\) 5.10383 + 5.89013i 0.296654 + 0.342357i
\(297\) −3.21327 + 0.943501i −0.186453 + 0.0547475i
\(298\) −13.0472 −0.755803
\(299\) 6.74144 7.17999i 0.389868 0.415230i
\(300\) −2.84415 −0.164207
\(301\) −3.58247 + 1.05191i −0.206490 + 0.0606310i
\(302\) 4.76427 + 5.49826i 0.274153 + 0.316389i
\(303\) −5.46080 + 3.50944i −0.313715 + 0.201612i
\(304\) 5.07399 + 35.2904i 0.291013 + 2.02404i
\(305\) −2.54188 1.63357i −0.145548 0.0935379i
\(306\) 0.732474 1.60389i 0.0418728 0.0916886i
\(307\) 8.53152 9.84590i 0.486920 0.561935i −0.458120 0.888890i \(-0.651477\pi\)
0.945040 + 0.326955i \(0.106023\pi\)
\(308\) −0.138838 + 0.965641i −0.00791104 + 0.0550225i
\(309\) −5.68700 12.4528i −0.323522 0.708415i
\(310\) −4.55112 1.33633i −0.258486 0.0758985i
\(311\) 26.8983 + 7.89805i 1.52526 + 0.447857i 0.933597 0.358326i \(-0.116652\pi\)
0.591666 + 0.806183i \(0.298471\pi\)
\(312\) 1.92356 + 4.21200i 0.108900 + 0.238458i
\(313\) 2.09112 14.5440i 0.118197 0.822077i −0.841342 0.540502i \(-0.818234\pi\)
0.959539 0.281575i \(-0.0908568\pi\)
\(314\) 2.19432 2.53238i 0.123833 0.142911i
\(315\) −0.105849 + 0.231778i −0.00596394 + 0.0130592i
\(316\) 5.23756 + 3.36597i 0.294636 + 0.189351i
\(317\) 1.75470 + 12.2042i 0.0985540 + 0.685458i 0.977869 + 0.209218i \(0.0670917\pi\)
−0.879315 + 0.476241i \(0.841999\pi\)
\(318\) 10.0228 6.44129i 0.562053 0.361209i
\(319\) 7.90468 + 9.12248i 0.442577 + 0.510761i
\(320\) 2.20303 0.646868i 0.123153 0.0361610i
\(321\) −12.0092 −0.670289
\(322\) −3.62969 + 0.910167i −0.202275 + 0.0507216i
\(323\) −8.04874 −0.447844
\(324\) −0.577861 + 0.169675i −0.0321034 + 0.00942640i
\(325\) 6.35098 + 7.32943i 0.352289 + 0.406563i
\(326\) −23.4854 + 15.0932i −1.30074 + 0.835933i
\(327\) −1.77766 12.3639i −0.0983050 0.683726i
\(328\) −19.7162 12.6708i −1.08864 0.699630i
\(329\) 2.16957 4.75071i 0.119613 0.261915i
\(330\) −1.86365 + 2.15076i −0.102590 + 0.118396i
\(331\) 0.479124 3.33238i 0.0263350 0.183164i −0.972408 0.233286i \(-0.925052\pi\)
0.998743 + 0.0501223i \(0.0159611\pi\)
\(332\) −1.51456 3.31642i −0.0831221 0.182012i
\(333\) 3.31655 + 0.973826i 0.181746 + 0.0533654i
\(334\) 26.6478 + 7.82450i 1.45810 + 0.428138i
\(335\) −2.81823 6.17107i −0.153977 0.337162i
\(336\) 0.333295 2.31812i 0.0181827 0.126464i
\(337\) 1.48464 1.71336i 0.0808732 0.0933327i −0.713871 0.700277i \(-0.753060\pi\)
0.794744 + 0.606945i \(0.207605\pi\)
\(338\) 5.88548 12.8874i 0.320128 0.700983i
\(339\) 2.62894 + 1.68952i 0.142785 + 0.0917621i
\(340\) −0.0493515 0.343248i −0.00267646 0.0186152i
\(341\) 15.7253 10.1061i 0.851575 0.547274i
\(342\) 7.77887 + 8.97730i 0.420633 + 0.485437i
\(343\) 6.38885 1.87594i 0.344966 0.101291i
\(344\) 17.4049 0.938409
\(345\) −2.39371 0.807911i −0.128873 0.0434965i
\(346\) 19.9713 1.07366
\(347\) 12.9692 3.80810i 0.696224 0.204430i 0.0855754 0.996332i \(-0.472727\pi\)
0.610648 + 0.791902i \(0.290909\pi\)
\(348\) 1.42154 + 1.64055i 0.0762027 + 0.0879426i
\(349\) 17.9744 11.5514i 0.962145 0.618333i 0.0375543 0.999295i \(-0.488043\pi\)
0.924591 + 0.380961i \(0.124407\pi\)
\(350\) −0.524407 3.64733i −0.0280308 0.194958i
\(351\) 1.72762 + 1.11027i 0.0922133 + 0.0592619i
\(352\) 4.59235 10.0558i 0.244773 0.535978i
\(353\) −19.1742 + 22.1282i −1.02054 + 1.17777i −0.0365884 + 0.999330i \(0.511649\pi\)
−0.983952 + 0.178436i \(0.942896\pi\)
\(354\) −0.215705 + 1.50026i −0.0114646 + 0.0797380i
\(355\) −1.36739 2.99418i −0.0725738 0.158914i
\(356\) −1.62910 0.478347i −0.0863422 0.0253524i
\(357\) 0.507281 + 0.148951i 0.0268482 + 0.00788334i
\(358\) 2.41017 + 5.27754i 0.127382 + 0.278927i
\(359\) 4.14017 28.7955i 0.218510 1.51977i −0.525035 0.851081i \(-0.675948\pi\)
0.743544 0.668687i \(-0.233143\pi\)
\(360\) 0.777832 0.897666i 0.0409953 0.0473111i
\(361\) 14.6323 32.0402i 0.770120 1.68633i
\(362\) −14.1139 9.07043i −0.741808 0.476731i
\(363\) −0.0306406 0.213110i −0.00160821 0.0111854i
\(364\) 0.503270 0.323432i 0.0263785 0.0169524i
\(365\) −0.00292497 0.00337559i −0.000153100 0.000176687i
\(366\) 8.87792 2.60679i 0.464057 0.136259i
\(367\) −14.9673 −0.781284 −0.390642 0.920543i \(-0.627747\pi\)
−0.390642 + 0.920543i \(0.627747\pi\)
\(368\) 23.2020 + 0.926456i 1.20949 + 0.0482949i
\(369\) −10.3943 −0.541104
\(370\) 2.81835 0.827543i 0.146519 0.0430219i
\(371\) 2.33943 + 2.69984i 0.121457 + 0.140169i
\(372\) 2.82798 1.81743i 0.146624 0.0942294i
\(373\) 4.71393 + 32.7861i 0.244078 + 1.69760i 0.631238 + 0.775589i \(0.282547\pi\)
−0.387160 + 0.922012i \(0.626544\pi\)
\(374\) 4.96755 + 3.19245i 0.256866 + 0.165078i
\(375\) 2.12762 4.65884i 0.109870 0.240581i
\(376\) −15.9431 + 18.3993i −0.822201 + 0.948871i
\(377\) 1.05342 7.32668i 0.0542537 0.377343i
\(378\) −0.324137 0.709762i −0.0166718 0.0365062i
\(379\) 18.0864 + 5.31066i 0.929038 + 0.272790i 0.711034 0.703158i \(-0.248227\pi\)
0.218004 + 0.975948i \(0.430045\pi\)
\(380\) 2.24156 + 0.658181i 0.114990 + 0.0337640i
\(381\) 4.53940 + 9.93989i 0.232560 + 0.509236i
\(382\) −1.54011 + 10.7117i −0.0787990 + 0.548059i
\(383\) −12.0320 + 13.8856i −0.614805 + 0.709523i −0.974712 0.223466i \(-0.928263\pi\)
0.359907 + 0.932988i \(0.382808\pi\)
\(384\) −5.66338 + 12.4011i −0.289008 + 0.632839i
\(385\) −0.717858 0.461339i −0.0365854 0.0235120i
\(386\) −3.05589 21.2542i −0.155541 1.08181i
\(387\) 6.49375 4.17328i 0.330096 0.212140i
\(388\) −7.23697 8.35191i −0.367402 0.424004i
\(389\) 4.28212 1.25735i 0.217112 0.0637499i −0.171367 0.985207i \(-0.554819\pi\)
0.388480 + 0.921457i \(0.373000\pi\)
\(390\) 1.74514 0.0883685
\(391\) −0.952443 + 5.15477i −0.0481671 + 0.260688i
\(392\) −15.2559 −0.770538
\(393\) 0.564575 0.165774i 0.0284790 0.00836220i
\(394\) −20.2416 23.3601i −1.01976 1.17686i
\(395\) −4.58122 + 2.94417i −0.230506 + 0.148137i
\(396\) −0.287036 1.99638i −0.0144241 0.100322i
\(397\) −11.9955 7.70906i −0.602039 0.386907i 0.203825 0.979007i \(-0.434663\pi\)
−0.805864 + 0.592100i \(0.798299\pi\)
\(398\) −15.6331 + 34.2317i −0.783617 + 1.71588i
\(399\) −2.33246 + 2.69180i −0.116769 + 0.134759i
\(400\) −3.25408 + 22.6326i −0.162704 + 1.13163i
\(401\) −14.9051 32.6376i −0.744324 1.62984i −0.776308 0.630354i \(-0.782910\pi\)
0.0319840 0.999488i \(-0.489817\pi\)
\(402\) 19.9332 + 5.85292i 0.994179 + 0.291917i
\(403\) −10.9984 3.22942i −0.547870 0.160869i
\(404\) −1.62403 3.55612i −0.0807983 0.176924i
\(405\) 0.0749695 0.521424i 0.00372526 0.0259098i
\(406\) −1.84173 + 2.12547i −0.0914035 + 0.105485i
\(407\) −4.80875 + 10.5297i −0.238361 + 0.521937i
\(408\) −2.07331 1.33244i −0.102644 0.0659654i
\(409\) −1.67097 11.6218i −0.0826241 0.574663i −0.988512 0.151145i \(-0.951704\pi\)
0.905887 0.423518i \(-0.139205\pi\)
\(410\) −7.43070 + 4.77542i −0.366976 + 0.235841i
\(411\) −11.7366 13.5448i −0.578924 0.668114i
\(412\) 7.91087 2.32284i 0.389741 0.114438i
\(413\) −0.454472 −0.0223631
\(414\) 6.66997 3.91961i 0.327811 0.192639i
\(415\) 3.18901 0.156543
\(416\) −6.50443 + 1.90987i −0.318906 + 0.0936392i
\(417\) 8.74188 + 10.0887i 0.428091 + 0.494044i
\(418\) −33.4657 + 21.5071i −1.63686 + 1.05195i
\(419\) 4.58075 + 31.8598i 0.223784 + 1.55645i 0.723536 + 0.690286i \(0.242515\pi\)
−0.499752 + 0.866169i \(0.666576\pi\)
\(420\) −0.129096 0.0829653i −0.00629926 0.00404829i
\(421\) −10.6956 + 23.4201i −0.521271 + 1.14142i 0.447685 + 0.894191i \(0.352249\pi\)
−0.968956 + 0.247233i \(0.920479\pi\)
\(422\) −2.16286 + 2.49607i −0.105286 + 0.121507i
\(423\) −1.53663 + 10.6875i −0.0747137 + 0.519645i
\(424\) −6.91789 15.1481i −0.335962 0.735655i
\(425\) −4.95277 1.45427i −0.240245 0.0705423i
\(426\) 9.67151 + 2.83981i 0.468586 + 0.137589i
\(427\) 1.15252 + 2.52367i 0.0557744 + 0.122129i
\(428\) 1.02931 7.15901i 0.0497536 0.346044i
\(429\) −4.50376 + 5.19761i −0.217443 + 0.250943i
\(430\) 2.72496 5.96683i 0.131409 0.287746i
\(431\) −5.05580 3.24916i −0.243529 0.156507i 0.413183 0.910648i \(-0.364417\pi\)
−0.656712 + 0.754141i \(0.728053\pi\)
\(432\) 0.689060 + 4.79252i 0.0331524 + 0.230580i
\(433\) −24.9572 + 16.0390i −1.19937 + 0.770787i −0.978847 0.204595i \(-0.934412\pi\)
−0.220521 + 0.975382i \(0.570776\pi\)
\(434\) 2.85209 + 3.29149i 0.136905 + 0.157997i
\(435\) −1.82182 + 0.534935i −0.0873496 + 0.0256482i
\(436\) 7.52281 0.360277
\(437\) −28.9233 20.2627i −1.38359 0.969299i
\(438\) 0.0136777 0.000653545
\(439\) −3.60675 + 1.05904i −0.172141 + 0.0505451i −0.366667 0.930352i \(-0.619501\pi\)
0.194526 + 0.980897i \(0.437683\pi\)
\(440\) 2.60490 + 3.00622i 0.124184 + 0.143316i
\(441\) −5.69195 + 3.65800i −0.271045 + 0.174190i
\(442\) −0.515325 3.58416i −0.0245115 0.170481i
\(443\) −9.98016 6.41386i −0.474172 0.304732i 0.281641 0.959520i \(-0.409121\pi\)
−0.755812 + 0.654788i \(0.772758\pi\)
\(444\) −0.864785 + 1.89361i −0.0410409 + 0.0898669i
\(445\) 0.972542 1.12237i 0.0461029 0.0532056i
\(446\) 0.147868 1.02845i 0.00700176 0.0486983i
\(447\) 3.35988 + 7.35711i 0.158917 + 0.347979i
\(448\) −2.02282 0.593955i −0.0955694 0.0280617i
\(449\) 28.3526 + 8.32507i 1.33804 + 0.392885i 0.870971 0.491335i \(-0.163491\pi\)
0.467071 + 0.884220i \(0.345309\pi\)
\(450\) 3.16467 + 6.92967i 0.149184 + 0.326668i
\(451\) 4.95392 34.4553i 0.233271 1.62244i
\(452\) −1.23249 + 1.42237i −0.0579716 + 0.0669028i
\(453\) 1.87350 4.10240i 0.0880249 0.192748i
\(454\) −33.7798 21.7090i −1.58537 1.01885i
\(455\) 0.0744692 + 0.517945i 0.00349117 + 0.0242816i
\(456\) 13.9676 8.97644i 0.654094 0.420360i
\(457\) 17.3259 + 19.9951i 0.810470 + 0.935332i 0.998906 0.0467529i \(-0.0148874\pi\)
−0.188436 + 0.982085i \(0.560342\pi\)
\(458\) 4.50482 1.32273i 0.210496 0.0618073i
\(459\) −1.09304 −0.0510186
\(460\) 0.686782 1.35771i 0.0320214 0.0633035i
\(461\) 39.8046 1.85388 0.926942 0.375205i \(-0.122428\pi\)
0.926942 + 0.375205i \(0.122428\pi\)
\(462\) 2.50723 0.736189i 0.116647 0.0342506i
\(463\) −19.4034 22.3927i −0.901752 1.04068i −0.998968 0.0454143i \(-0.985539\pi\)
0.0972160 0.995263i \(-0.469006\pi\)
\(464\) 14.6813 9.43508i 0.681561 0.438012i
\(465\) 0.418458 + 2.91044i 0.0194055 + 0.134968i
\(466\) −8.28756 5.32609i −0.383914 0.246726i
\(467\) 1.73407 3.79709i 0.0802432 0.175708i −0.865258 0.501327i \(-0.832845\pi\)
0.945501 + 0.325619i \(0.105573\pi\)
\(468\) −0.809936 + 0.934716i −0.0374393 + 0.0432073i
\(469\) −0.886508 + 6.16580i −0.0409352 + 0.284710i
\(470\) 3.81164 + 8.34633i 0.175818 + 0.384987i
\(471\) −1.99305 0.585212i −0.0918349 0.0269652i
\(472\) 2.03273 + 0.596863i 0.0935640 + 0.0274729i
\(473\) 10.7388 + 23.5147i 0.493771 + 1.08121i
\(474\) 2.37326 16.5064i 0.109008 0.758164i
\(475\) 22.7726 26.2810i 1.04488 1.20586i
\(476\) −0.132273 + 0.289637i −0.00606271 + 0.0132755i
\(477\) −6.21320 3.99298i −0.284483 0.182826i
\(478\) 6.88693 + 47.8996i 0.315001 + 2.19088i
\(479\) 13.8273 8.88625i 0.631784 0.406023i −0.185186 0.982704i \(-0.559289\pi\)
0.816970 + 0.576681i \(0.195652\pi\)
\(480\) 1.13875 + 1.31419i 0.0519768 + 0.0599844i
\(481\) 6.81093 1.99987i 0.310552 0.0911863i
\(482\) −4.91050 −0.223667
\(483\) 1.44794 + 1.81234i 0.0658835 + 0.0824644i
\(484\) 0.129667 0.00589394
\(485\) 9.27476 2.72332i 0.421145 0.123659i
\(486\) 1.05639 + 1.21914i 0.0479188 + 0.0553012i
\(487\) 18.8374 12.1061i 0.853603 0.548578i −0.0390933 0.999236i \(-0.512447\pi\)
0.892697 + 0.450658i \(0.148811\pi\)
\(488\) −1.84055 12.8013i −0.0833177 0.579488i
\(489\) 14.5587 + 9.35633i 0.658368 + 0.423108i
\(490\) −2.38850 + 5.23009i −0.107902 + 0.236272i
\(491\) 7.83692 9.04429i 0.353675 0.408163i −0.550835 0.834614i \(-0.685691\pi\)
0.904511 + 0.426451i \(0.140236\pi\)
\(492\) 0.890892 6.19629i 0.0401645 0.279350i
\(493\) 1.63662 + 3.58369i 0.0737095 + 0.161401i
\(494\) 23.4062 + 6.87267i 1.05309 + 0.309216i
\(495\) 1.69271 + 0.497023i 0.0760815 + 0.0223395i
\(496\) −11.2268 24.5833i −0.504099 1.10382i
\(497\) −0.430130 + 2.99162i −0.0192940 + 0.134192i
\(498\) −6.39508 + 7.38032i −0.286571 + 0.330720i
\(499\) 4.66181 10.2079i 0.208691 0.456970i −0.776123 0.630582i \(-0.782816\pi\)
0.984814 + 0.173611i \(0.0555436\pi\)
\(500\) 2.59490 + 1.66764i 0.116047 + 0.0745791i
\(501\) −2.45016 17.0413i −0.109465 0.761347i
\(502\) 4.80477 3.08784i 0.214447 0.137817i
\(503\) −9.14150 10.5499i −0.407599 0.470395i 0.514420 0.857538i \(-0.328007\pi\)
−0.922019 + 0.387144i \(0.873462\pi\)
\(504\) −1.04645 + 0.307264i −0.0466124 + 0.0136866i
\(505\) 3.41951 0.152166
\(506\) 9.81397 + 23.9780i 0.436284 + 1.06595i
\(507\) −8.78264 −0.390051
\(508\) −6.31450 + 1.85410i −0.280161 + 0.0822626i
\(509\) 16.8921 + 19.4945i 0.748730 + 0.864080i 0.994445 0.105262i \(-0.0335681\pi\)
−0.245715 + 0.969342i \(0.579023\pi\)
\(510\) −0.781396 + 0.502173i −0.0346008 + 0.0222366i
\(511\) 0.000583660 0.00405944i 2.58196e−5 0.000179579i
\(512\) 4.92257 + 3.16355i 0.217549 + 0.139810i
\(513\) 3.05897 6.69821i 0.135057 0.295733i
\(514\) 9.27785 10.7072i 0.409229 0.472275i
\(515\) −1.02633 + 7.13826i −0.0452254 + 0.314549i
\(516\) 1.93122 + 4.22879i 0.0850173 + 0.186162i
\(517\) −34.6951 10.1874i −1.52589 0.448041i
\(518\) −2.58782 0.759851i −0.113702 0.0333859i
\(519\) −5.14296 11.2615i −0.225751 0.494325i
\(520\) 0.347142 2.41443i 0.0152232 0.105880i
\(521\) −15.2342 + 17.5812i −0.667421 + 0.770245i −0.983971 0.178331i \(-0.942930\pi\)
0.316549 + 0.948576i \(0.397476\pi\)
\(522\) 2.41539 5.28896i 0.105719 0.231492i
\(523\) 9.64326 + 6.19735i 0.421670 + 0.270991i 0.734222 0.678910i \(-0.237547\pi\)
−0.312551 + 0.949901i \(0.601184\pi\)
\(524\) 0.0504326 + 0.350766i 0.00220316 + 0.0153233i
\(525\) −1.92163 + 1.23496i −0.0838670 + 0.0538980i
\(526\) 9.79382 + 11.3027i 0.427031 + 0.492820i
\(527\) 5.85389 1.71886i 0.255000 0.0748746i
\(528\) −16.2148 −0.705660
\(529\) −16.3998 + 16.1260i −0.713034 + 0.701129i
\(530\) −6.27622 −0.272621
\(531\) 0.901523 0.264711i 0.0391228 0.0114875i
\(532\) −1.40474 1.62115i −0.0609031 0.0702859i
\(533\) −17.9573 + 11.5405i −0.777817 + 0.499873i
\(534\) 0.647218 + 4.50150i 0.0280079 + 0.194799i
\(535\) 5.32201 + 3.42025i 0.230091 + 0.147870i
\(536\) 12.0627 26.4137i 0.521030 1.14090i
\(537\) 2.35526 2.71812i 0.101637 0.117296i
\(538\) 2.91606 20.2816i 0.125720 0.874402i
\(539\) −9.41287 20.6113i −0.405441 0.887792i
\(540\) 0.304409 + 0.0893825i 0.0130997 + 0.00384641i
\(541\) 22.5066 + 6.60855i 0.967636 + 0.284124i 0.727112 0.686519i \(-0.240862\pi\)
0.240525 + 0.970643i \(0.422680\pi\)
\(542\) 3.27993 + 7.18203i 0.140885 + 0.308495i
\(543\) −1.48011 + 10.2944i −0.0635177 + 0.441775i
\(544\) 2.36282 2.72684i 0.101305 0.116912i
\(545\) −2.73348 + 5.98548i −0.117089 + 0.256390i
\(546\) −1.34801 0.866316i −0.0576897 0.0370749i
\(547\) 2.11351 + 14.6998i 0.0903670 + 0.628516i 0.983793 + 0.179306i \(0.0573853\pi\)
−0.893426 + 0.449210i \(0.851706\pi\)
\(548\) 9.08033 5.83558i 0.387893 0.249283i
\(549\) −3.75616 4.33483i −0.160309 0.185006i
\(550\) −24.4790 + 7.18769i −1.04379 + 0.306484i
\(551\) −26.5413 −1.13070
\(552\) −4.09606 10.0077i −0.174340 0.425956i
\(553\) 5.00026 0.212633
\(554\) 5.92383 1.73939i 0.251680 0.0738998i
\(555\) −1.19242 1.37612i −0.0506152 0.0584131i
\(556\) −6.76338 + 4.34656i −0.286831 + 0.184335i
\(557\) −3.28296 22.8335i −0.139103 0.967485i −0.933114 0.359581i \(-0.882920\pi\)
0.794011 0.607904i \(-0.207989\pi\)
\(558\) −7.57477 4.86801i −0.320666 0.206079i
\(559\) 6.58524 14.4197i 0.278526 0.609886i
\(560\) −0.807908 + 0.932376i −0.0341404 + 0.0394001i
\(561\) 0.520944 3.62324i 0.0219943 0.152973i
\(562\) 13.2622 + 29.0401i 0.559430 + 1.22498i
\(563\) 26.0066 + 7.63624i 1.09605 + 0.321829i 0.779281 0.626674i \(-0.215584\pi\)
0.316768 + 0.948503i \(0.397402\pi\)
\(564\) −6.23941 1.83206i −0.262726 0.0771435i
\(565\) −0.683866 1.49746i −0.0287704 0.0629985i
\(566\) −2.24656 + 15.6251i −0.0944298 + 0.656774i
\(567\) −0.316753 + 0.365553i −0.0133024 + 0.0153518i
\(568\) 5.85278 12.8158i 0.245577 0.537739i
\(569\) 14.0899 + 9.05501i 0.590678 + 0.379606i 0.801568 0.597904i \(-0.204000\pi\)
−0.210890 + 0.977510i \(0.567636\pi\)
\(570\) −0.890537 6.19382i −0.0373005 0.259431i
\(571\) −6.90227 + 4.43582i −0.288851 + 0.185633i −0.677039 0.735947i \(-0.736737\pi\)
0.388188 + 0.921580i \(0.373101\pi\)
\(572\) −2.71241 3.13029i −0.113412 0.130884i
\(573\) 6.43678 1.89001i 0.268900 0.0789563i
\(574\) 8.11037 0.338520
\(575\) −14.1368 17.6946i −0.589543 0.737914i
\(576\) 4.35857 0.181607
\(577\) −0.910674 + 0.267398i −0.0379119 + 0.0111319i −0.300633 0.953740i \(-0.597198\pi\)
0.262722 + 0.964872i \(0.415380\pi\)
\(578\) −16.6965 19.2688i −0.694484 0.801477i
\(579\) −11.1980 + 7.19650i −0.465372 + 0.299076i
\(580\) −0.162740 1.13188i −0.00675743 0.0469989i
\(581\) −2.46332 1.58308i −0.102196 0.0656773i
\(582\) −12.2966 + 26.9257i −0.509709 + 1.11611i
\(583\) 16.1973 18.6927i 0.670824 0.774173i
\(584\) 0.00272076 0.0189233i 0.000112586 0.000783052i
\(585\) −0.449404 0.984057i −0.0185806 0.0406858i
\(586\) −13.7707 4.04345i −0.568864 0.167033i
\(587\) −27.0571 7.94468i −1.11677 0.327912i −0.329272 0.944235i \(-0.606803\pi\)
−0.787494 + 0.616323i \(0.788622\pi\)
\(588\) −1.69277 3.70665i −0.0698087 0.152860i
\(589\) −5.84939 + 40.6834i −0.241020 + 1.67633i
\(590\) 0.522870 0.603424i 0.0215262 0.0248426i
\(591\) −7.95982 + 17.4296i −0.327423 + 0.716957i
\(592\) 14.0792 + 9.04816i 0.578652 + 0.371877i
\(593\) −0.686106 4.77197i −0.0281750 0.195961i 0.970873 0.239597i \(-0.0770152\pi\)
−0.999048 + 0.0436352i \(0.986106\pi\)
\(594\) −4.54472 + 2.92072i −0.186472 + 0.119838i
\(595\) −0.182385 0.210484i −0.00747708 0.00862901i
\(596\) −4.67374 + 1.37233i −0.191444 + 0.0562130i
\(597\) 23.3286 0.954775
\(598\) 7.17131 14.1771i 0.293257 0.579744i
\(599\) −48.1882 −1.96892 −0.984458 0.175619i \(-0.943807\pi\)
−0.984458 + 0.175619i \(0.943807\pi\)
\(600\) 10.2168 2.99993i 0.417100 0.122472i
\(601\) 20.4011 + 23.5441i 0.832177 + 0.960383i 0.999675 0.0254891i \(-0.00811432\pi\)
−0.167498 + 0.985872i \(0.553569\pi\)
\(602\) −5.06690 + 3.25630i −0.206512 + 0.132717i
\(603\) −1.83278 12.7473i −0.0746367 0.519109i
\(604\) 2.28497 + 1.46846i 0.0929741 + 0.0597508i
\(605\) −0.0471155 + 0.103168i −0.00191552 + 0.00419440i
\(606\) −6.85730 + 7.91375i −0.278559 + 0.321474i
\(607\) 1.14997 7.99823i 0.0466759 0.324638i −0.953084 0.302707i \(-0.902110\pi\)
0.999759 0.0219309i \(-0.00698137\pi\)
\(608\) 10.0977 + 22.1109i 0.409515 + 0.896713i
\(609\) 1.67280 + 0.491178i 0.0677852 + 0.0199035i
\(610\) −4.67677 1.37322i −0.189357 0.0556001i
\(611\) 9.21134 + 20.1700i 0.372651 + 0.815992i
\(612\) 0.0936842 0.651588i 0.00378696 0.0263389i
\(613\) −8.27956 + 9.55512i −0.334408 + 0.385928i −0.897904 0.440191i \(-0.854911\pi\)
0.563496 + 0.826119i \(0.309456\pi\)
\(614\) 8.73041 19.1169i 0.352331 0.771497i
\(615\) 4.60633 + 2.96031i 0.185745 + 0.119371i
\(616\) −0.519793 3.61524i −0.0209430 0.145662i
\(617\) −21.9713 + 14.1201i −0.884531 + 0.568454i −0.902165 0.431391i \(-0.858023\pi\)
0.0176341 + 0.999845i \(0.494387\pi\)
\(618\) −14.4619 16.6899i −0.581743 0.671367i
\(619\) −16.2418 + 4.76902i −0.652812 + 0.191683i −0.591336 0.806426i \(-0.701399\pi\)
−0.0614767 + 0.998109i \(0.519581\pi\)
\(620\) −1.77086 −0.0711193
\(621\) −3.92785 2.75173i −0.157619 0.110423i
\(622\) 45.2228 1.81327
\(623\) −1.30840 + 0.384180i −0.0524198 + 0.0153918i
\(624\) 6.51143 + 7.51459i 0.260666 + 0.300824i
\(625\) 17.5944 11.3072i 0.703774 0.452288i
\(626\) −3.37329 23.4617i −0.134824 0.937719i
\(627\) 20.7456 + 13.3324i 0.828498 + 0.532443i
\(628\) 0.519685 1.13795i 0.0207377 0.0454092i
\(629\) −2.47416 + 2.85534i −0.0986514 + 0.113850i
\(630\) −0.0584967 + 0.406854i −0.00233056 + 0.0162094i
\(631\) 3.87646 + 8.48826i 0.154319 + 0.337912i 0.970963 0.239230i \(-0.0768950\pi\)
−0.816643 + 0.577142i \(0.804168\pi\)
\(632\) −22.3648 6.56690i −0.889624 0.261217i
\(633\) 1.96447 + 0.576822i 0.0780809 + 0.0229266i
\(634\) 8.26249 + 18.0923i 0.328145 + 0.718538i
\(635\) 0.819220 5.69780i 0.0325097 0.226110i
\(636\) 2.91286 3.36161i 0.115502 0.133297i
\(637\) −5.77214 + 12.6392i −0.228701 + 0.500785i
\(638\) 16.3809 + 10.5273i 0.648525 + 0.416782i
\(639\) −0.889258 6.18492i −0.0351785 0.244672i
\(640\) 6.04163 3.88272i 0.238816 0.153478i
\(641\) −16.4777 19.0163i −0.650830 0.751097i 0.330421 0.943834i \(-0.392809\pi\)
−0.981251 + 0.192736i \(0.938264\pi\)
\(642\) −18.5879 + 5.45791i −0.733608 + 0.215407i
\(643\) 15.1602 0.597859 0.298930 0.954275i \(-0.403370\pi\)
0.298930 + 0.954275i \(0.403370\pi\)
\(644\) −1.20449 + 0.707818i −0.0474634 + 0.0278919i
\(645\) −4.06633 −0.160112
\(646\) −12.4579 + 3.65797i −0.490149 + 0.143921i
\(647\) −2.75310 3.17725i −0.108236 0.124910i 0.699047 0.715076i \(-0.253608\pi\)
−0.807282 + 0.590166i \(0.799062\pi\)
\(648\) 1.89683 1.21902i 0.0745147 0.0478877i
\(649\) 0.447807 + 3.11457i 0.0175780 + 0.122257i
\(650\) 13.1612 + 8.45816i 0.516223 + 0.331756i
\(651\) 1.12156 2.45587i 0.0439573 0.0962532i
\(652\) −6.82538 + 7.87691i −0.267302 + 0.308483i
\(653\) −1.36644 + 9.50381i −0.0534730 + 0.371913i 0.945460 + 0.325737i \(0.105612\pi\)
−0.998933 + 0.0461756i \(0.985297\pi\)
\(654\) −8.37059 18.3290i −0.327316 0.716722i
\(655\) −0.297410 0.0873274i −0.0116208 0.00341217i
\(656\) −48.2883 14.1787i −1.88534 0.553587i
\(657\) −0.00352225 0.00771265i −0.000137416 0.000300899i
\(658\) 1.19900 8.33920i 0.0467417 0.325096i
\(659\) 0.317667 0.366608i 0.0123746 0.0142810i −0.749529 0.661972i \(-0.769720\pi\)
0.761903 + 0.647691i \(0.224265\pi\)
\(660\) −0.441370 + 0.966466i −0.0171803 + 0.0376196i
\(661\) −16.0121 10.2903i −0.622797 0.400247i 0.190840 0.981621i \(-0.438879\pi\)
−0.813636 + 0.581374i \(0.802515\pi\)
\(662\) −0.772899 5.37563i −0.0300396 0.208930i
\(663\) −1.88835 + 1.21357i −0.0733374 + 0.0471311i
\(664\) 8.93869 + 10.3158i 0.346888 + 0.400331i
\(665\) 1.80028 0.528611i 0.0698120 0.0204986i
\(666\) 5.57596 0.216064
\(667\) −3.14075 + 16.9982i −0.121610 + 0.658175i
\(668\) 10.3687 0.401179
\(669\) −0.618004 + 0.181462i −0.0238934 + 0.00701574i
\(670\) −7.16669 8.27081i −0.276874 0.319529i
\(671\) 16.1595 10.3851i 0.623829 0.400911i
\(672\) −0.227232 1.58043i −0.00876566 0.0609665i
\(673\) 1.05038 + 0.675039i 0.0404892 + 0.0260208i 0.560729 0.827999i \(-0.310521\pi\)
−0.520240 + 0.854020i \(0.674157\pi\)
\(674\) 1.51925 3.32668i 0.0585192 0.128139i
\(675\) 3.09258 3.56902i 0.119033 0.137372i
\(676\) 0.752760 5.23556i 0.0289523 0.201368i
\(677\) 12.5543 + 27.4900i 0.482499 + 1.05653i 0.981769 + 0.190079i \(0.0608744\pi\)
−0.499270 + 0.866447i \(0.666398\pi\)
\(678\) 4.83695 + 1.42026i 0.185762 + 0.0545446i
\(679\) −8.51610 2.50055i −0.326818 0.0959624i
\(680\) 0.539329 + 1.18097i 0.0206823 + 0.0452880i
\(681\) −3.54247 + 24.6384i −0.135748 + 0.944145i
\(682\) 19.7468 22.7890i 0.756145 0.872638i
\(683\) −6.59875 + 14.4493i −0.252494 + 0.552885i −0.992855 0.119324i \(-0.961927\pi\)
0.740361 + 0.672209i \(0.234655\pi\)
\(684\) 3.73079 + 2.39763i 0.142650 + 0.0916758i
\(685\) 1.34362 + 9.34512i 0.0513373 + 0.357059i
\(686\) 9.03614 5.80717i 0.345001 0.221719i
\(687\) −1.90594 2.19957i −0.0727161 0.0839189i
\(688\) 35.8606 10.5296i 1.36717 0.401438i
\(689\) −15.1673 −0.577829
\(690\) −4.07218 0.162602i −0.155025 0.00619017i
\(691\) −17.1403 −0.652047 −0.326024 0.945362i \(-0.605709\pi\)
−0.326024 + 0.945362i \(0.605709\pi\)
\(692\) 7.15408 2.10063i 0.271957 0.0798539i
\(693\) −1.06078 1.22421i −0.0402958 0.0465038i
\(694\) 18.3431 11.7884i 0.696296 0.447482i
\(695\) −1.00078 6.96060i −0.0379619 0.264031i
\(696\) −6.83690 4.39381i −0.259152 0.166547i
\(697\) 4.71966 10.3346i 0.178770 0.391452i
\(698\) 22.5710 26.0483i 0.854324 0.985943i
\(699\) −0.869110 + 6.04480i −0.0328728 + 0.228635i
\(700\) −0.571488 1.25138i −0.0216002 0.0472979i
\(701\) −24.0907 7.07366i −0.909892 0.267168i −0.206897 0.978363i \(-0.566336\pi\)
−0.702995 + 0.711194i \(0.748155\pi\)
\(702\) 3.17861 + 0.933324i 0.119969 + 0.0352260i
\(703\) −10.5735 23.1528i −0.398788 0.873223i
\(704\) −2.07730 + 14.4480i −0.0782913 + 0.544528i
\(705\) 3.72480 4.29865i 0.140284 0.161897i
\(706\) −19.6212 + 42.9644i −0.738454 + 1.61699i
\(707\) −2.64136 1.69750i −0.0993387 0.0638411i
\(708\) 0.0805317 + 0.560110i 0.00302656 + 0.0210502i
\(709\) −36.0468 + 23.1659i −1.35377 + 0.870013i −0.997916 0.0645293i \(-0.979445\pi\)
−0.355851 + 0.934543i \(0.615809\pi\)
\(710\) −3.47725 4.01296i −0.130499 0.150604i
\(711\) −9.91887 + 2.91244i −0.371987 + 0.109225i
\(712\) 6.35664 0.238225
\(713\) 25.3633 + 8.56046i 0.949862 + 0.320592i
\(714\) 0.852869 0.0319178
\(715\) 3.47618 1.02070i 0.130002 0.0381719i
\(716\) 1.41847 + 1.63700i 0.0530108 + 0.0611777i
\(717\) 25.2364 16.2184i 0.942470 0.605689i
\(718\) −6.67871 46.4515i −0.249247 1.73355i
\(719\) 12.1284 + 7.79448i 0.452315 + 0.290685i 0.746895 0.664942i \(-0.231544\pi\)
−0.294581 + 0.955627i \(0.595180\pi\)
\(720\) 1.05955 2.32010i 0.0394873 0.0864650i
\(721\) 4.33633 5.00439i 0.161493 0.186373i
\(722\) 8.08639 56.2421i 0.300944 2.09311i
\(723\) 1.26454 + 2.76896i 0.0470288 + 0.102979i
\(724\) −6.00990 1.76467i −0.223356 0.0655833i
\(725\) −16.3321 4.79555i −0.606561 0.178102i
\(726\) −0.144279 0.315928i −0.00535471 0.0117252i
\(727\) −2.80380 + 19.5008i −0.103987 + 0.723246i 0.869405 + 0.494100i \(0.164502\pi\)
−0.973392 + 0.229146i \(0.926407\pi\)
\(728\) −1.46671 + 1.69267i −0.0543599 + 0.0627346i
\(729\) 0.415415 0.909632i 0.0153857 0.0336901i
\(730\) −0.00606141 0.00389543i −0.000224343 0.000144176i
\(731\) 1.20075 + 8.35143i 0.0444115 + 0.308889i
\(732\) 2.90605 1.86760i 0.107411 0.0690286i
\(733\) 15.3498 + 17.7146i 0.566956 + 0.654302i 0.964749 0.263173i \(-0.0847691\pi\)
−0.397793 + 0.917475i \(0.630224\pi\)
\(734\) −23.1664 + 6.80228i −0.855088 + 0.251077i
\(735\) 3.56425 0.131469
\(736\) 15.3557 3.85053i 0.566018 0.141933i
\(737\) 43.1287 1.58867
\(738\) −16.0883 + 4.72395i −0.592219 + 0.173891i
\(739\) 1.33631 + 1.54218i 0.0491570 + 0.0567302i 0.779796 0.626034i \(-0.215323\pi\)
−0.730639 + 0.682764i \(0.760778\pi\)
\(740\) 0.922543 0.592883i 0.0339134 0.0217948i
\(741\) −2.15210 14.9682i −0.0790595 0.549871i
\(742\) 4.84800 + 3.11562i 0.177976 + 0.114378i
\(743\) 18.5746 40.6727i 0.681436 1.49214i −0.179678 0.983726i \(-0.557505\pi\)
0.861114 0.508412i \(-0.169767\pi\)
\(744\) −8.24175 + 9.51148i −0.302157 + 0.348708i
\(745\) 0.606354 4.21728i 0.0222151 0.154509i
\(746\) 22.1968 + 48.6042i 0.812683 + 1.77953i
\(747\) 5.80850 + 1.70553i 0.212522 + 0.0624021i
\(748\) 2.11526 + 0.621096i 0.0773416 + 0.0227095i
\(749\) −2.41306 5.28387i −0.0881714 0.193069i
\(750\) 1.17581 8.17794i 0.0429345 0.298616i
\(751\) 35.7344 41.2397i 1.30397 1.50486i 0.581227 0.813742i \(-0.302573\pi\)
0.722742 0.691118i \(-0.242882\pi\)
\(752\) −21.7175 + 47.5546i −0.791955 + 1.73414i
\(753\) −2.97850 1.91416i −0.108542 0.0697560i
\(754\) −1.69932 11.8190i −0.0618856 0.430424i
\(755\) −1.99864 + 1.28444i −0.0727378 + 0.0467457i
\(756\) −0.190767 0.220156i −0.00693811 0.00800701i
\(757\) −46.5029 + 13.6545i −1.69018 + 0.496281i −0.978504 0.206230i \(-0.933880\pi\)
−0.711673 + 0.702511i \(0.752062\pi\)
\(758\) 30.4079 1.10446
\(759\) 10.9936 11.7087i 0.399041 0.424999i
\(760\) −8.74641 −0.317265
\(761\) 41.4432 12.1688i 1.50232 0.441120i 0.575868 0.817542i \(-0.304664\pi\)
0.926448 + 0.376423i \(0.122846\pi\)
\(762\) 11.5436 + 13.3220i 0.418179 + 0.482605i
\(763\) 5.08274 3.26648i 0.184008 0.118255i
\(764\) 0.574988 + 3.99913i 0.0208023 + 0.144683i
\(765\) 0.484391 + 0.311299i 0.0175132 + 0.0112551i
\(766\) −12.3125 + 26.9605i −0.444867 + 0.974124i
\(767\) 1.26359 1.45826i 0.0456254 0.0526545i
\(768\) −1.88923 + 13.1399i −0.0681719 + 0.474146i
\(769\) −20.6411 45.1977i −0.744337 1.62987i −0.776287 0.630380i \(-0.782899\pi\)
0.0319500 0.999489i \(-0.489828\pi\)
\(770\) −1.32077 0.387814i −0.0475974 0.0139759i
\(771\) −8.42685 2.47435i −0.303486 0.0891114i
\(772\) −3.33024 7.29222i −0.119858 0.262453i
\(773\) −1.52790 + 10.6267i −0.0549546 + 0.382217i 0.943720 + 0.330746i \(0.107300\pi\)
−0.998674 + 0.0514717i \(0.983609\pi\)
\(774\) 8.15441 9.41069i 0.293104 0.338260i
\(775\) −10.9502 + 23.9776i −0.393342 + 0.861300i
\(776\) 34.8062 + 22.3686i 1.24947 + 0.802985i
\(777\) 0.237940 + 1.65491i 0.00853603 + 0.0593694i
\(778\) 6.05647 3.89226i 0.217135 0.139544i
\(779\) 50.1228 + 57.8448i 1.79584 + 2.07251i
\(780\) 0.625141 0.183558i 0.0223836 0.00657242i
\(781\) 20.9258 0.748785
\(782\) 0.868529 + 8.41146i 0.0310585 + 0.300793i
\(783\) −3.60437 −0.128810
\(784\) −31.4328 + 9.22950i −1.12260 + 0.329625i
\(785\) 0.716571 + 0.826968i 0.0255755 + 0.0295157i
\(786\) 0.798512 0.513173i 0.0284820 0.0183043i
\(787\) −5.48677 38.1613i −0.195582 1.36030i −0.816916 0.576757i \(-0.804318\pi\)
0.621334 0.783546i \(-0.286591\pi\)
\(788\) −9.70799 6.23894i −0.345833 0.222253i
\(789\) 3.85133 8.43323i 0.137111 0.300231i
\(790\) −5.75279 + 6.63908i −0.204675 + 0.236208i
\(791\) −0.215118 + 1.49618i −0.00764871 + 0.0531980i
\(792\) 3.13682 + 6.86869i 0.111462 + 0.244068i
\(793\) −11.3020 3.31858i −0.401347 0.117846i
\(794\) −22.0704 6.48045i −0.783248 0.229982i
\(795\) 1.61624 + 3.53907i 0.0573220 + 0.125518i
\(796\) −1.99949 + 13.9068i −0.0708701 + 0.492913i
\(797\) 20.0127 23.0959i 0.708886 0.818098i −0.281038 0.959697i \(-0.590679\pi\)
0.989924 + 0.141598i \(0.0452242\pi\)
\(798\) −2.38683 + 5.22644i −0.0844930 + 0.185014i
\(799\) −9.92847 6.38064i −0.351244 0.225731i
\(800\) 2.21855 + 15.4303i 0.0784375 + 0.545545i
\(801\) 2.37166 1.52417i 0.0837984 0.0538540i
\(802\) −37.9032 43.7426i −1.33841 1.54461i
\(803\) 0.0272449 0.00799982i 0.000961451 0.000282308i
\(804\) 7.75607 0.273536
\(805\) −0.125511 1.21553i −0.00442366 0.0428420i
\(806\) −18.4911 −0.651322
\(807\) −12.1874 + 3.57855i −0.429018 + 0.125971i
\(808\) 9.58475 + 11.0614i 0.337190 + 0.389138i
\(809\) −3.73925 + 2.40307i −0.131465 + 0.0844874i −0.604720 0.796438i \(-0.706715\pi\)
0.473255 + 0.880925i \(0.343079\pi\)
\(810\) −0.120937 0.841136i −0.00424930 0.0295545i
\(811\) 27.3210 + 17.5582i 0.959371 + 0.616551i 0.923824 0.382817i \(-0.125046\pi\)
0.0355474 + 0.999368i \(0.488683\pi\)
\(812\) −0.436179 + 0.955100i −0.0153069 + 0.0335174i
\(813\) 3.20520 3.69900i 0.112411 0.129730i
\(814\) −2.65751 + 18.4834i −0.0931457 + 0.647843i
\(815\) −3.78715 8.29271i −0.132658 0.290481i
\(816\) −5.07790 1.49100i −0.177762 0.0521956i
\(817\) −54.5385 16.0140i −1.90806 0.560257i
\(818\) −7.86820 17.2290i −0.275105 0.602396i
\(819\) −0.141365 + 0.983217i −0.00493970 + 0.0343564i
\(820\) −2.15952 + 2.49222i −0.0754138 + 0.0870322i
\(821\) 14.0204 30.7003i 0.489314 1.07145i −0.490482 0.871451i \(-0.663179\pi\)
0.979796 0.199997i \(-0.0640934\pi\)
\(822\) −24.3218 15.6307i −0.848320 0.545182i
\(823\) −2.52621 17.5702i −0.0880581 0.612458i −0.985289 0.170896i \(-0.945334\pi\)
0.897231 0.441562i \(-0.145575\pi\)
\(824\) −25.9675 + 16.6883i −0.904622 + 0.581365i
\(825\) 10.3568 + 11.9524i 0.360578 + 0.416129i
\(826\) −0.703435 + 0.206547i −0.0244756 + 0.00718670i
\(827\) −17.7946 −0.618778 −0.309389 0.950936i \(-0.600125\pi\)
−0.309389 + 0.950936i \(0.600125\pi\)
\(828\) 1.97703 2.10564i 0.0687066 0.0731761i
\(829\) −47.4537 −1.64814 −0.824068 0.566491i \(-0.808301\pi\)
−0.824068 + 0.566491i \(0.808301\pi\)
\(830\) 4.93598 1.44933i 0.171330 0.0503071i
\(831\) −2.50631 2.89244i −0.0869430 0.100338i
\(832\) 7.52994 4.83920i 0.261054 0.167769i
\(833\) −1.05249 7.32026i −0.0364668 0.253632i
\(834\) 18.1158 + 11.6423i 0.627299 + 0.403141i
\(835\) −3.76757 + 8.24982i −0.130382 + 0.285497i
\(836\) −9.72587 + 11.2243i −0.336376 + 0.388199i
\(837\) −0.794361 + 5.52490i −0.0274571 + 0.190969i
\(838\) 21.5697 + 47.2310i 0.745113 + 1.63157i
\(839\) −1.56477 0.459459i −0.0540220 0.0158623i 0.254610 0.967044i \(-0.418053\pi\)
−0.308632 + 0.951182i \(0.599871\pi\)
\(840\) 0.551253 + 0.161862i 0.0190200 + 0.00558478i
\(841\) −6.65017 14.5618i −0.229316 0.502132i
\(842\) −5.91082 + 41.1107i −0.203700 + 1.41677i
\(843\) 12.9600 14.9567i 0.446367 0.515135i
\(844\) −0.512234 + 1.12164i −0.0176318 + 0.0386083i
\(845\) 3.89212 + 2.50131i 0.133893 + 0.0860478i
\(846\) 2.47882 + 17.2406i 0.0852237 + 0.592744i
\(847\) 0.0876085 0.0563025i 0.00301026 0.00193458i
\(848\) −23.4177 27.0255i −0.804168 0.928059i
\(849\) 9.38932 2.75695i 0.322241 0.0946184i
\(850\) −8.32687 −0.285609
\(851\) −16.0793 + 4.03198i −0.551191 + 0.138215i
\(852\) 3.76321 0.128926
\(853\) 21.2486 6.23916i 0.727539 0.213625i 0.103070 0.994674i \(-0.467133\pi\)
0.624469 + 0.781049i \(0.285315\pi\)
\(854\) 2.93083 + 3.38236i 0.100291 + 0.115742i
\(855\) −3.26328 + 2.09718i −0.111602 + 0.0717221i
\(856\) 3.85361 + 26.8024i 0.131714 + 0.916088i
\(857\) −19.0420 12.2376i −0.650463 0.418027i 0.173372 0.984856i \(-0.444534\pi\)
−0.823835 + 0.566829i \(0.808170\pi\)
\(858\) −4.60875 + 10.0918i −0.157340 + 0.344527i
\(859\) −0.824575 + 0.951611i −0.0281341 + 0.0324685i −0.769642 0.638475i \(-0.779565\pi\)
0.741508 + 0.670944i \(0.234111\pi\)
\(860\) 0.348525 2.42405i 0.0118846 0.0826593i
\(861\) −2.08856 4.57332i −0.0711781 0.155858i
\(862\) −9.30207 2.73133i −0.316830 0.0930296i
\(863\) −7.61520 2.23603i −0.259225 0.0761152i 0.149538 0.988756i \(-0.452221\pi\)
−0.408763 + 0.912641i \(0.634040\pi\)
\(864\) 1.37129 + 3.00270i 0.0466522 + 0.102154i
\(865\) −0.928144 + 6.45538i −0.0315578 + 0.219490i
\(866\) −31.3396 + 36.1678i −1.06496 + 1.22903i
\(867\) −6.56575 + 14.3770i −0.222984 + 0.488268i
\(868\) 1.36788 + 0.879083i 0.0464289 + 0.0298380i
\(869\) −4.92693 34.2675i −0.167135 1.16245i
\(870\) −2.57671 + 1.65595i −0.0873587 + 0.0561420i
\(871\) −17.3193 19.9875i −0.586842 0.677251i
\(872\) −27.0236 + 7.93485i −0.915135 + 0.268708i
\(873\) 18.3496 0.621040
\(874\) −53.9766 18.2178i −1.82579 0.616228i
\(875\) 2.47733 0.0837491
\(876\) 0.00489960 0.00143865i 0.000165542 4.86076e-5i
\(877\) 9.70823 + 11.2039i 0.327824 + 0.378329i 0.895605 0.444851i \(-0.146743\pi\)
−0.567781 + 0.823180i \(0.692198\pi\)
\(878\) −5.10125 + 3.27837i −0.172159 + 0.110640i
\(879\) 1.26616 + 8.80637i 0.0427067 + 0.297032i
\(880\) 7.18577 + 4.61801i 0.242232 + 0.155673i
\(881\) −10.8447 + 23.7466i −0.365368 + 0.800043i 0.634270 + 0.773112i \(0.281301\pi\)
−0.999637 + 0.0269316i \(0.991426\pi\)
\(882\) −7.14757 + 8.24874i −0.240671 + 0.277749i
\(883\) −1.30435 + 9.07195i −0.0438949 + 0.305296i 0.956033 + 0.293260i \(0.0947402\pi\)
−0.999928 + 0.0120354i \(0.996169\pi\)
\(884\) −0.561590 1.22971i −0.0188883 0.0413596i
\(885\) −0.474910 0.139446i −0.0159639 0.00468743i
\(886\) −18.3623 5.39166i −0.616894 0.181136i
\(887\) 21.1375 + 46.2846i 0.709727 + 1.55408i 0.827765 + 0.561075i \(0.189612\pi\)
−0.118038 + 0.993009i \(0.537660\pi\)
\(888\) 1.10917 7.71443i 0.0372212 0.258879i
\(889\) −3.46128 + 3.99453i −0.116088 + 0.133972i
\(890\) 0.995214 2.17922i 0.0333597 0.0730475i
\(891\) 2.81730 + 1.81057i 0.0943829 + 0.0606562i
\(892\) −0.0552053 0.383961i −0.00184841 0.0128560i
\(893\) 66.8867 42.9855i 2.23828 1.43845i
\(894\) 8.54408 + 9.86040i 0.285757 + 0.329781i
\(895\) −1.81789 + 0.533780i −0.0607652 + 0.0178423i
\(896\) −6.59425 −0.220298
\(897\) −9.84098 0.392951i −0.328581 0.0131203i
\(898\) 47.6679 1.59070
\(899\) 19.3036 5.66806i 0.643812 0.189040i
\(900\) 1.86252 + 2.14947i 0.0620841 + 0.0716489i
\(901\) 6.79127 4.36448i 0.226250 0.145402i
\(902\) −7.99143 55.5816i −0.266085 1.85066i
\(903\) 3.14100 + 2.01860i 0.104526 + 0.0671747i
\(904\) 2.92711 6.40948i 0.0973543 0.213176i
\(905\) 3.58779 4.14053i 0.119262 0.137636i
\(906\) 1.03537 7.20119i 0.0343980 0.239244i
\(907\) 15.9556 + 34.9378i 0.529795 + 1.16009i 0.965596 + 0.260047i \(0.0837380\pi\)
−0.435801 + 0.900043i \(0.643535\pi\)
\(908\) −14.3840 4.22351i −0.477349 0.140162i
\(909\) 6.22832 + 1.82880i 0.206580 + 0.0606575i
\(910\) 0.350658 + 0.767834i 0.0116242 + 0.0254535i
\(911\) −0.0791753 + 0.550676i −0.00262319 + 0.0182447i −0.991091 0.133186i \(-0.957479\pi\)
0.988468 + 0.151431i \(0.0483882\pi\)
\(912\) 23.3479 26.9450i 0.773128 0.892237i
\(913\) −8.42190 + 18.4414i −0.278724 + 0.610321i
\(914\) 35.9044 + 23.0744i 1.18761 + 0.763233i
\(915\) 0.430010 + 2.99079i 0.0142157 + 0.0988724i
\(916\) 1.47458 0.947655i 0.0487215 0.0313114i
\(917\) 0.186381 + 0.215095i 0.00615483 + 0.00710305i
\(918\) −1.69181 + 0.496761i −0.0558381 + 0.0163955i
\(919\) −25.5118 −0.841555 −0.420778 0.907164i \(-0.638243\pi\)
−0.420778 + 0.907164i \(0.638243\pi\)
\(920\) −1.03500 + 5.60159i −0.0341230 + 0.184679i
\(921\) −13.0280 −0.429287
\(922\) 61.6098 18.0903i 2.02901 0.595771i
\(923\) −8.40324 9.69786i −0.276596 0.319209i
\(924\) 0.820702 0.527433i 0.0269991 0.0173513i
\(925\) −2.32309 16.1575i −0.0763828 0.531254i
\(926\) −40.2097 25.8412i −1.32137 0.849194i
\(927\) −5.68700 + 12.4528i −0.186786 + 0.409004i
\(928\) 7.79158 8.99196i 0.255771 0.295176i
\(929\) 3.40247 23.6647i 0.111631 0.776413i −0.854702 0.519119i \(-0.826260\pi\)
0.966333 0.257294i \(-0.0828308\pi\)
\(930\) 1.97042 + 4.31462i 0.0646127 + 0.141482i
\(931\) 47.8045 + 14.0367i 1.56673 + 0.460034i
\(932\) −3.52897 1.03620i −0.115595 0.0339418i
\(933\) −11.6457 25.5005i −0.381263 0.834849i
\(934\) 0.958319 6.66525i 0.0313571 0.218094i
\(935\) −1.26277 + 1.45731i −0.0412969 + 0.0476592i
\(936\) 1.92356 4.21200i 0.0628735 0.137674i
\(937\) 32.0799 + 20.6165i 1.04800 + 0.673511i 0.946954 0.321370i \(-0.104143\pi\)
0.101050 + 0.994881i \(0.467780\pi\)
\(938\) 1.43007 + 9.94637i 0.0466935 + 0.324760i
\(939\) −12.3610 + 7.94396i −0.403387 + 0.259241i
\(940\) 2.24329 + 2.58889i 0.0731679 + 0.0844403i
\(941\) −13.5602 + 3.98163i −0.442050 + 0.129797i −0.495181 0.868790i \(-0.664898\pi\)
0.0531310 + 0.998588i \(0.483080\pi\)
\(942\) −3.35082 −0.109176
\(943\) 42.9776 25.2558i 1.39954 0.822444i
\(944\) 4.54927 0.148066
\(945\) 0.244483 0.0717866i 0.00795302 0.00233522i
\(946\) 27.3085 + 31.5157i 0.887876 + 1.02466i
\(947\) 16.2633 10.4518i 0.528487 0.339638i −0.249034 0.968495i \(-0.580113\pi\)
0.777521 + 0.628857i \(0.216477\pi\)
\(948\) −0.886037 6.16252i −0.0287771 0.200149i
\(949\) −0.0146482 0.00941384i −0.000475502 0.000305586i
\(950\) 23.3035 51.0276i 0.756066 1.65555i
\(951\) 8.07426 9.31819i 0.261826 0.302163i
\(952\) 0.169652 1.17996i 0.00549847 0.0382427i
\(953\) 5.19078 + 11.3662i 0.168146 + 0.368188i 0.974881 0.222724i \(-0.0714950\pi\)
−0.806735 + 0.590913i \(0.798768\pi\)
\(954\) −11.4316 3.35661i −0.370110 0.108674i
\(955\) −3.39081 0.995631i −0.109724 0.0322179i
\(956\) 7.50522 + 16.4341i 0.242736 + 0.531518i
\(957\) 1.71785 11.9479i 0.0555302 0.386221i
\(958\) 17.3633 20.0384i 0.560984 0.647410i
\(959\) 3.60121 7.88554i 0.116289 0.254637i
\(960\) −1.93155 1.24133i −0.0623404 0.0400637i
\(961\) −0.0221369 0.153966i −0.000714095 0.00496664i
\(962\) 9.63312 6.19083i 0.310584 0.199600i
\(963\) 7.86436 + 9.07596i 0.253426 + 0.292469i
\(964\) −1.75903 + 0.516499i −0.0566546 + 0.0166353i
\(965\) 7.01208 0.225727
\(966\) 3.06480 + 2.14710i 0.0986082 + 0.0690818i
\(967\) 9.35247 0.300755 0.150378 0.988629i \(-0.451951\pi\)
0.150378 + 0.988629i \(0.451951\pi\)
\(968\) −0.465792 + 0.136769i −0.0149711 + 0.00439591i
\(969\) 5.27080 + 6.08283i 0.169323 + 0.195409i
\(970\) 13.1179 8.43034i 0.421189 0.270682i
\(971\) 3.37468 + 23.4714i 0.108299 + 0.753233i 0.969522 + 0.245006i \(0.0787899\pi\)
−0.861223 + 0.508227i \(0.830301\pi\)
\(972\) 0.506650 + 0.325604i 0.0162508 + 0.0104438i
\(973\) −2.68232 + 5.87345i −0.0859911 + 0.188294i
\(974\) 23.6547 27.2990i 0.757946 0.874716i
\(975\) 1.38020 9.59951i 0.0442018 0.307430i
\(976\) −11.5368 25.2620i −0.369283 0.808616i
\(977\) −46.3820 13.6190i −1.48389 0.435710i −0.563306 0.826248i \(-0.690471\pi\)
−0.920587 + 0.390538i \(0.872289\pi\)
\(978\) 26.7863 + 7.86518i 0.856533 + 0.251501i
\(979\) 3.92205 + 8.58809i 0.125349 + 0.274476i
\(980\) −0.305492 + 2.12474i −0.00975859 + 0.0678725i
\(981\) −8.17990 + 9.44011i −0.261164 + 0.301399i
\(982\) 8.01962 17.5605i 0.255916 0.560379i
\(983\) −30.2232 19.4233i −0.963972 0.619507i −0.0388772 0.999244i \(-0.512378\pi\)
−0.925094 + 0.379737i \(0.876014\pi\)
\(984\) 3.33539 + 23.1981i 0.106328 + 0.739530i
\(985\) 8.49146 5.45713i 0.270560 0.173879i
\(986\) 4.16187 + 4.80306i 0.132541 + 0.152961i
\(987\) −5.01111 + 1.47140i −0.159505 + 0.0468350i
\(988\) 9.10740 0.289745
\(989\) −16.7098 + 33.0339i −0.531342 + 1.05042i
\(990\) 2.84587 0.0904476
\(991\) −24.8432 + 7.29461i −0.789169 + 0.231721i −0.651391 0.758742i \(-0.725814\pi\)
−0.137778 + 0.990463i \(0.543996\pi\)
\(992\) −12.0660 13.9249i −0.383096 0.442116i
\(993\) −2.83220 + 1.82015i −0.0898772 + 0.0577606i
\(994\) 0.693864 + 4.82593i 0.0220080 + 0.153069i
\(995\) −10.3383 6.64403i −0.327746 0.210630i
\(996\) −1.51456 + 3.31642i −0.0479906 + 0.105085i
\(997\) −20.0725 + 23.1648i −0.635701 + 0.733638i −0.978609 0.205731i \(-0.934043\pi\)
0.342908 + 0.939369i \(0.388588\pi\)
\(998\) 2.57631 17.9186i 0.0815516 0.567204i
\(999\) −1.43591 3.14420i −0.0454301 0.0994781i
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 69.2.e.c.55.2 20
3.2 odd 2 207.2.i.d.55.1 20
23.8 even 11 1587.2.a.u.1.3 10
23.15 odd 22 1587.2.a.t.1.3 10
23.18 even 11 inner 69.2.e.c.64.2 yes 20
69.8 odd 22 4761.2.a.bt.1.8 10
69.38 even 22 4761.2.a.bu.1.8 10
69.41 odd 22 207.2.i.d.64.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.e.c.55.2 20 1.1 even 1 trivial
69.2.e.c.64.2 yes 20 23.18 even 11 inner
207.2.i.d.55.1 20 3.2 odd 2
207.2.i.d.64.1 20 69.41 odd 22
1587.2.a.t.1.3 10 23.15 odd 22
1587.2.a.u.1.3 10 23.8 even 11
4761.2.a.bt.1.8 10 69.8 odd 22
4761.2.a.bu.1.8 10 69.38 even 22