Properties

Label 224.2.be.a.3.17
Level $224$
Weight $2$
Character 224.3
Analytic conductor $1.789$
Analytic rank $0$
Dimension $240$
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] = [224,2,Mod(3,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([12, 9, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.be (of order \(24\), degree \(8\), 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: \(1.78864900528\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(30\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 3.17
Character \(\chi\) \(=\) 224.3
Dual form 224.2.be.a.75.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.316867 + 1.37826i) q^{2} +(-1.12518 + 0.863381i) q^{3} +(-1.79919 + 0.873450i) q^{4} +(2.90549 + 2.22946i) q^{5} +(-1.54649 - 1.27721i) q^{6} +(2.61828 - 0.380261i) q^{7} +(-1.77394 - 2.20298i) q^{8} +(-0.255854 + 0.954861i) q^{9} +O(q^{10})\) \(q+(0.316867 + 1.37826i) q^{2} +(-1.12518 + 0.863381i) q^{3} +(-1.79919 + 0.873450i) q^{4} +(2.90549 + 2.22946i) q^{5} +(-1.54649 - 1.27721i) q^{6} +(2.61828 - 0.380261i) q^{7} +(-1.77394 - 2.20298i) q^{8} +(-0.255854 + 0.954861i) q^{9} +(-2.15212 + 4.71095i) q^{10} +(-3.26101 - 0.429321i) q^{11} +(1.27029 - 2.53617i) q^{12} +(-1.45481 - 0.602601i) q^{13} +(1.35375 + 3.48818i) q^{14} -5.19407 q^{15} +(2.47417 - 3.14300i) q^{16} +(1.24904 - 2.16340i) q^{17} +(-1.39712 - 0.0500689i) q^{18} +(-4.35489 + 0.573333i) q^{19} +(-7.17485 - 1.47342i) q^{20} +(-2.61773 + 2.68844i) q^{21} +(-0.441594 - 4.63055i) q^{22} +(4.05473 + 1.08646i) q^{23} +(3.89802 + 0.947160i) q^{24} +(2.17728 + 8.12570i) q^{25} +(0.369559 - 2.19605i) q^{26} +(-2.16476 - 5.22619i) q^{27} +(-4.37865 + 2.97110i) q^{28} +(9.17665 + 3.80109i) q^{29} +(-1.64583 - 7.15876i) q^{30} +(3.28960 - 5.69775i) q^{31} +(5.11586 + 2.41413i) q^{32} +(4.03989 - 2.33243i) q^{33} +(3.37750 + 1.03599i) q^{34} +(8.45516 + 4.73251i) q^{35} +(-0.373693 - 1.94145i) q^{36} +(-2.37213 + 3.09142i) q^{37} +(-2.17012 - 5.82050i) q^{38} +(2.15719 - 0.578019i) q^{39} +(-0.242716 - 10.3557i) q^{40} +(2.12291 - 2.12291i) q^{41} +(-4.53483 - 2.75603i) q^{42} +(0.446613 + 1.07822i) q^{43} +(6.24217 - 2.07590i) q^{44} +(-2.87221 + 2.20392i) q^{45} +(-0.212613 + 5.93273i) q^{46} +(-4.41717 + 2.55026i) q^{47} +(-0.0702775 + 5.67260i) q^{48} +(6.71080 - 1.99126i) q^{49} +(-10.5094 + 5.57562i) q^{50} +(0.462443 + 3.51260i) q^{51} +(3.14382 - 0.186507i) q^{52} +(1.24122 - 9.42797i) q^{53} +(6.51709 - 4.63960i) q^{54} +(-8.51768 - 8.51768i) q^{55} +(-5.48239 - 5.09346i) q^{56} +(4.40503 - 4.40503i) q^{57} +(-2.33111 + 13.8522i) q^{58} +(8.32288 + 1.09573i) q^{59} +(9.34511 - 4.53676i) q^{60} +(-12.0822 + 1.59065i) q^{61} +(8.89534 + 2.72849i) q^{62} +(-0.306802 + 2.59739i) q^{63} +(-1.70625 + 7.81593i) q^{64} +(-2.88345 - 4.99429i) q^{65} +(4.49480 + 4.82894i) q^{66} +(8.27818 + 10.7883i) q^{67} +(-0.357638 + 4.98333i) q^{68} +(-5.50033 + 2.27831i) q^{69} +(-3.84346 + 13.1530i) q^{70} +(-2.24719 - 2.24719i) q^{71} +(2.55741 - 1.13023i) q^{72} +(0.551062 + 2.05659i) q^{73} +(-5.01243 - 2.28984i) q^{74} +(-9.46540 - 7.26306i) q^{75} +(7.33451 - 4.83532i) q^{76} +(-8.70151 + 0.115953i) q^{77} +(1.48020 + 2.79002i) q^{78} +(-3.82876 - 6.63161i) q^{79} +(14.1959 - 3.61590i) q^{80} +(4.37961 + 2.52857i) q^{81} +(3.59859 + 2.25323i) q^{82} +(1.06305 - 2.56643i) q^{83} +(2.36158 - 7.12346i) q^{84} +(8.45227 - 3.50104i) q^{85} +(-1.34455 + 0.957200i) q^{86} +(-13.6072 + 3.64603i) q^{87} +(4.83907 + 7.94554i) q^{88} +(2.96264 - 11.0567i) q^{89} +(-3.94768 - 3.26029i) q^{90} +(-4.03824 - 1.02457i) q^{91} +(-8.24421 + 1.58685i) q^{92} +(1.21794 + 9.25117i) q^{93} +(-4.91457 - 5.27991i) q^{94} +(-13.9313 - 8.04325i) q^{95} +(-7.84057 + 1.70060i) q^{96} -7.62211i q^{97} +(4.87090 + 8.61825i) q^{98} +(1.24429 - 3.00397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{8}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.316867 + 1.37826i 0.224059 + 0.974576i
\(3\) −1.12518 + 0.863381i −0.649623 + 0.498473i −0.880214 0.474578i \(-0.842601\pi\)
0.230591 + 0.973051i \(0.425934\pi\)
\(4\) −1.79919 + 0.873450i −0.899595 + 0.436725i
\(5\) 2.90549 + 2.22946i 1.29937 + 0.997044i 0.999066 + 0.0432019i \(0.0137559\pi\)
0.300307 + 0.953843i \(0.402911\pi\)
\(6\) −1.54649 1.27721i −0.631353 0.521419i
\(7\) 2.61828 0.380261i 0.989618 0.143725i
\(8\) −1.77394 2.20298i −0.627184 0.778871i
\(9\) −0.255854 + 0.954861i −0.0852848 + 0.318287i
\(10\) −2.15212 + 4.71095i −0.680559 + 1.48973i
\(11\) −3.26101 0.429321i −0.983232 0.129445i −0.378267 0.925697i \(-0.623480\pi\)
−0.604966 + 0.796252i \(0.706813\pi\)
\(12\) 1.27029 2.53617i 0.366702 0.732130i
\(13\) −1.45481 0.602601i −0.403491 0.167132i 0.171702 0.985149i \(-0.445073\pi\)
−0.575194 + 0.818017i \(0.695073\pi\)
\(14\) 1.35375 + 3.48818i 0.361804 + 0.932254i
\(15\) −5.19407 −1.34110
\(16\) 2.47417 3.14300i 0.618543 0.785751i
\(17\) 1.24904 2.16340i 0.302936 0.524701i −0.673864 0.738856i \(-0.735366\pi\)
0.976800 + 0.214155i \(0.0686998\pi\)
\(18\) −1.39712 0.0500689i −0.329304 0.0118014i
\(19\) −4.35489 + 0.573333i −0.999081 + 0.131532i −0.612288 0.790635i \(-0.709751\pi\)
−0.386793 + 0.922166i \(0.626417\pi\)
\(20\) −7.17485 1.47342i −1.60434 0.329468i
\(21\) −2.61773 + 2.68844i −0.571235 + 0.586665i
\(22\) −0.441594 4.63055i −0.0941481 0.987238i
\(23\) 4.05473 + 1.08646i 0.845470 + 0.226543i 0.655451 0.755237i \(-0.272478\pi\)
0.190019 + 0.981780i \(0.439145\pi\)
\(24\) 3.89802 + 0.947160i 0.795679 + 0.193338i
\(25\) 2.17728 + 8.12570i 0.435455 + 1.62514i
\(26\) 0.369559 2.19605i 0.0724765 0.430680i
\(27\) −2.16476 5.22619i −0.416608 1.00578i
\(28\) −4.37865 + 2.97110i −0.827487 + 0.561485i
\(29\) 9.17665 + 3.80109i 1.70406 + 0.705845i 0.999991 0.00428413i \(-0.00136369\pi\)
0.704071 + 0.710130i \(0.251364\pi\)
\(30\) −1.64583 7.15876i −0.300486 1.30701i
\(31\) 3.28960 5.69775i 0.590830 1.02335i −0.403291 0.915072i \(-0.632134\pi\)
0.994121 0.108275i \(-0.0345328\pi\)
\(32\) 5.11586 + 2.41413i 0.904364 + 0.426762i
\(33\) 4.03989 2.33243i 0.703255 0.406024i
\(34\) 3.37750 + 1.03599i 0.579236 + 0.177670i
\(35\) 8.45516 + 4.73251i 1.42918 + 0.799940i
\(36\) −0.373693 1.94145i −0.0622821 0.323575i
\(37\) −2.37213 + 3.09142i −0.389976 + 0.508227i −0.946544 0.322575i \(-0.895451\pi\)
0.556567 + 0.830802i \(0.312118\pi\)
\(38\) −2.17012 5.82050i −0.352041 0.944209i
\(39\) 2.15719 0.578019i 0.345428 0.0925570i
\(40\) −0.242716 10.3557i −0.0383768 1.63737i
\(41\) 2.12291 2.12291i 0.331542 0.331542i −0.521630 0.853172i \(-0.674676\pi\)
0.853172 + 0.521630i \(0.174676\pi\)
\(42\) −4.53483 2.75603i −0.699739 0.425264i
\(43\) 0.446613 + 1.07822i 0.0681078 + 0.164427i 0.954268 0.298952i \(-0.0966370\pi\)
−0.886160 + 0.463379i \(0.846637\pi\)
\(44\) 6.24217 2.07590i 0.941043 0.312954i
\(45\) −2.87221 + 2.20392i −0.428163 + 0.328541i
\(46\) −0.212613 + 5.93273i −0.0313481 + 0.874734i
\(47\) −4.41717 + 2.55026i −0.644311 + 0.371993i −0.786273 0.617879i \(-0.787992\pi\)
0.141962 + 0.989872i \(0.454659\pi\)
\(48\) −0.0702775 + 5.67260i −0.0101437 + 0.818769i
\(49\) 6.71080 1.99126i 0.958686 0.284466i
\(50\) −10.5094 + 5.57562i −1.48625 + 0.788511i
\(51\) 0.462443 + 3.51260i 0.0647550 + 0.491863i
\(52\) 3.14382 0.186507i 0.435969 0.0258639i
\(53\) 1.24122 9.42797i 0.170494 1.29503i −0.665543 0.746359i \(-0.731800\pi\)
0.836038 0.548672i \(-0.184867\pi\)
\(54\) 6.51709 4.63960i 0.886864 0.631370i
\(55\) −8.51768 8.51768i −1.14852 1.14852i
\(56\) −5.48239 5.09346i −0.732615 0.680643i
\(57\) 4.40503 4.40503i 0.583461 0.583461i
\(58\) −2.33111 + 13.8522i −0.306089 + 1.81889i
\(59\) 8.32288 + 1.09573i 1.08355 + 0.142652i 0.651088 0.759002i \(-0.274313\pi\)
0.432458 + 0.901654i \(0.357646\pi\)
\(60\) 9.34511 4.53676i 1.20645 0.585693i
\(61\) −12.0822 + 1.59065i −1.54696 + 0.203662i −0.855137 0.518402i \(-0.826527\pi\)
−0.691827 + 0.722063i \(0.743194\pi\)
\(62\) 8.89534 + 2.72849i 1.12971 + 0.346518i
\(63\) −0.306802 + 2.59739i −0.0386535 + 0.327240i
\(64\) −1.70625 + 7.81593i −0.213281 + 0.976991i
\(65\) −2.88345 4.99429i −0.357648 0.619465i
\(66\) 4.49480 + 4.82894i 0.553272 + 0.594402i
\(67\) 8.27818 + 10.7883i 1.01134 + 1.31801i 0.947400 + 0.320052i \(0.103700\pi\)
0.0639411 + 0.997954i \(0.479633\pi\)
\(68\) −0.357638 + 4.98333i −0.0433700 + 0.604318i
\(69\) −5.50033 + 2.27831i −0.662162 + 0.274277i
\(70\) −3.84346 + 13.1530i −0.459381 + 1.57208i
\(71\) −2.24719 2.24719i −0.266692 0.266692i 0.561074 0.827766i \(-0.310388\pi\)
−0.827766 + 0.561074i \(0.810388\pi\)
\(72\) 2.55741 1.13023i 0.301394 0.133199i
\(73\) 0.551062 + 2.05659i 0.0644969 + 0.240706i 0.990647 0.136449i \(-0.0435690\pi\)
−0.926150 + 0.377155i \(0.876902\pi\)
\(74\) −5.01243 2.28984i −0.582683 0.266189i
\(75\) −9.46540 7.26306i −1.09297 0.838666i
\(76\) 7.33451 4.83532i 0.841326 0.554649i
\(77\) −8.70151 + 0.115953i −0.991629 + 0.0132141i
\(78\) 1.48020 + 2.79002i 0.167600 + 0.315907i
\(79\) −3.82876 6.63161i −0.430769 0.746114i 0.566170 0.824288i \(-0.308424\pi\)
−0.996940 + 0.0781739i \(0.975091\pi\)
\(80\) 14.1959 3.61590i 1.58715 0.404270i
\(81\) 4.37961 + 2.52857i 0.486624 + 0.280952i
\(82\) 3.59859 + 2.25323i 0.397398 + 0.248828i
\(83\) 1.06305 2.56643i 0.116685 0.281702i −0.854737 0.519061i \(-0.826282\pi\)
0.971422 + 0.237359i \(0.0762818\pi\)
\(84\) 2.36158 7.12346i 0.257669 0.777233i
\(85\) 8.45227 3.50104i 0.916777 0.379742i
\(86\) −1.34455 + 0.957200i −0.144986 + 0.103218i
\(87\) −13.6072 + 3.64603i −1.45884 + 0.390896i
\(88\) 4.83907 + 7.94554i 0.515846 + 0.846997i
\(89\) 2.96264 11.0567i 0.314039 1.17201i −0.610841 0.791753i \(-0.709169\pi\)
0.924881 0.380257i \(-0.124165\pi\)
\(90\) −3.94768 3.26029i −0.416122 0.343665i
\(91\) −4.03824 1.02457i −0.423323 0.107405i
\(92\) −8.24421 + 1.58685i −0.859518 + 0.165441i
\(93\) 1.21794 + 9.25117i 0.126294 + 0.959302i
\(94\) −4.91457 5.27991i −0.506899 0.544581i
\(95\) −13.9313 8.04325i −1.42932 0.825220i
\(96\) −7.84057 + 1.70060i −0.800225 + 0.173567i
\(97\) 7.62211i 0.773908i −0.922099 0.386954i \(-0.873527\pi\)
0.922099 0.386954i \(-0.126473\pi\)
\(98\) 4.87090 + 8.61825i 0.492036 + 0.870575i
\(99\) 1.24429 3.00397i 0.125055 0.301910i
\(100\) −11.0147 12.7179i −1.10147 1.27179i
\(101\) 0.916649 6.96264i 0.0912100 0.692809i −0.883355 0.468704i \(-0.844721\pi\)
0.974565 0.224104i \(-0.0719456\pi\)
\(102\) −4.69474 + 1.75040i −0.464849 + 0.173315i
\(103\) 3.03103 + 0.812162i 0.298656 + 0.0800247i 0.405036 0.914301i \(-0.367259\pi\)
−0.106379 + 0.994326i \(0.533926\pi\)
\(104\) 1.25323 + 4.27389i 0.122889 + 0.419090i
\(105\) −13.5995 + 1.97510i −1.32718 + 0.192750i
\(106\) 13.3875 1.27670i 1.30031 0.124004i
\(107\) −6.14053 + 8.00249i −0.593627 + 0.773630i −0.989478 0.144685i \(-0.953783\pi\)
0.395851 + 0.918315i \(0.370450\pi\)
\(108\) 8.45962 + 7.51210i 0.814028 + 0.722852i
\(109\) 6.34898 + 8.27415i 0.608122 + 0.792520i 0.991366 0.131127i \(-0.0418596\pi\)
−0.383243 + 0.923647i \(0.625193\pi\)
\(110\) 9.04059 14.4385i 0.861986 1.37666i
\(111\) 5.52646i 0.524548i
\(112\) 5.28292 9.17010i 0.499189 0.866493i
\(113\) 8.29171i 0.780019i −0.920811 0.390009i \(-0.872472\pi\)
0.920811 0.390009i \(-0.127528\pi\)
\(114\) 7.46708 + 4.67546i 0.699356 + 0.437897i
\(115\) 9.35875 + 12.1966i 0.872708 + 1.13734i
\(116\) −19.8306 + 1.17645i −1.84123 + 0.109231i
\(117\) 0.947619 1.23496i 0.0876075 0.114172i
\(118\) 1.12705 + 11.8183i 0.103754 + 1.08796i
\(119\) 2.44768 6.13934i 0.224378 0.562793i
\(120\) 9.21398 + 11.4424i 0.841118 + 1.04455i
\(121\) −0.175295 0.0469701i −0.0159359 0.00427001i
\(122\) −6.02077 16.1483i −0.545095 1.46200i
\(123\) −0.555774 + 4.22153i −0.0501125 + 0.380642i
\(124\) −0.941914 + 13.1246i −0.0845864 + 1.17863i
\(125\) −4.78239 + 11.5457i −0.427750 + 1.03268i
\(126\) −3.67709 + 0.400174i −0.327581 + 0.0356503i
\(127\) 12.5179i 1.11078i 0.831588 + 0.555392i \(0.187432\pi\)
−0.831588 + 0.555392i \(0.812568\pi\)
\(128\) −11.3130 + 0.124962i −0.999939 + 0.0110452i
\(129\) −1.43343 0.827593i −0.126207 0.0728655i
\(130\) 5.96974 5.55667i 0.523581 0.487352i
\(131\) −1.24144 9.42970i −0.108465 0.823877i −0.956047 0.293212i \(-0.905276\pi\)
0.847582 0.530665i \(-0.178058\pi\)
\(132\) −5.23127 + 7.72513i −0.455324 + 0.672386i
\(133\) −11.1843 + 3.15714i −0.969804 + 0.273759i
\(134\) −12.2460 + 14.8279i −1.05790 + 1.28094i
\(135\) 5.36189 20.0109i 0.461478 1.72226i
\(136\) −6.98164 + 1.08614i −0.598671 + 0.0931355i
\(137\) −9.04483 + 2.42356i −0.772752 + 0.207058i −0.623587 0.781754i \(-0.714325\pi\)
−0.149165 + 0.988812i \(0.547659\pi\)
\(138\) −4.88298 6.85896i −0.415667 0.583873i
\(139\) −7.46711 + 3.09298i −0.633352 + 0.262343i −0.676177 0.736740i \(-0.736364\pi\)
0.0428244 + 0.999083i \(0.486364\pi\)
\(140\) −19.3461 1.12953i −1.63504 0.0954624i
\(141\) 2.76827 6.68320i 0.233130 0.562827i
\(142\) 2.38514 3.80927i 0.200157 0.319666i
\(143\) 4.48544 + 2.58967i 0.375091 + 0.216559i
\(144\) 2.36811 + 3.16664i 0.197342 + 0.263887i
\(145\) 18.1883 + 31.5030i 1.51045 + 2.61618i
\(146\) −2.65990 + 1.41117i −0.220135 + 0.116789i
\(147\) −5.83164 + 8.03450i −0.480986 + 0.662675i
\(148\) 1.56772 7.63400i 0.128865 0.627511i
\(149\) −12.4150 9.52637i −1.01708 0.780430i −0.0412882 0.999147i \(-0.513146\pi\)
−0.975788 + 0.218717i \(0.929813\pi\)
\(150\) 7.01109 15.3472i 0.572453 1.25309i
\(151\) 0.921075 + 3.43750i 0.0749560 + 0.279740i 0.993223 0.116221i \(-0.0370782\pi\)
−0.918267 + 0.395961i \(0.870412\pi\)
\(152\) 8.98838 + 8.57669i 0.729054 + 0.695661i
\(153\) 1.74617 + 1.74617i 0.141170 + 0.141170i
\(154\) −2.91704 11.9562i −0.235061 0.963456i
\(155\) 22.2608 9.22073i 1.78803 0.740627i
\(156\) −3.37633 + 2.92417i −0.270323 + 0.234121i
\(157\) −11.9006 15.5091i −0.949770 1.23776i −0.971266 0.237995i \(-0.923510\pi\)
0.0214969 0.999769i \(-0.493157\pi\)
\(158\) 7.92686 7.37836i 0.630627 0.586991i
\(159\) 6.74334 + 11.6798i 0.534781 + 0.926268i
\(160\) 9.48185 + 18.4198i 0.749606 + 1.45621i
\(161\) 11.0296 + 1.30281i 0.869252 + 0.102676i
\(162\) −2.09727 + 6.83746i −0.164777 + 0.537202i
\(163\) −5.64738 + 0.743492i −0.442337 + 0.0582348i −0.348406 0.937344i \(-0.613277\pi\)
−0.0939315 + 0.995579i \(0.529943\pi\)
\(164\) −1.96526 + 5.67376i −0.153461 + 0.443046i
\(165\) 16.9379 + 2.22992i 1.31862 + 0.173599i
\(166\) 3.87404 + 0.651939i 0.300684 + 0.0506003i
\(167\) −3.82201 + 3.82201i −0.295756 + 0.295756i −0.839349 0.543593i \(-0.817063\pi\)
0.543593 + 0.839349i \(0.317063\pi\)
\(168\) 10.5663 + 0.997670i 0.815206 + 0.0769719i
\(169\) −7.43905 7.43905i −0.572235 0.572235i
\(170\) 7.50359 + 10.5400i 0.575499 + 0.808384i
\(171\) 0.566765 4.30501i 0.0433416 0.329212i
\(172\) −1.74531 1.54983i −0.133079 0.118173i
\(173\) 3.00293 + 22.8096i 0.228309 + 1.73418i 0.594903 + 0.803797i \(0.297190\pi\)
−0.366594 + 0.930381i \(0.619476\pi\)
\(174\) −9.33684 17.5989i −0.707824 1.33417i
\(175\) 8.79061 + 20.4475i 0.664508 + 1.54568i
\(176\) −9.41766 + 9.18717i −0.709883 + 0.692509i
\(177\) −10.3108 + 5.95292i −0.775004 + 0.447449i
\(178\) 16.1778 + 0.579768i 1.21258 + 0.0434555i
\(179\) 14.0257 10.7623i 1.04833 0.804410i 0.0671939 0.997740i \(-0.478595\pi\)
0.981134 + 0.193330i \(0.0619287\pi\)
\(180\) 3.24263 6.47400i 0.241691 0.482543i
\(181\) −8.95850 21.6277i −0.665880 1.60758i −0.788437 0.615116i \(-0.789109\pi\)
0.122557 0.992462i \(-0.460891\pi\)
\(182\) 0.132539 5.89040i 0.00982448 0.436625i
\(183\) 12.2213 12.2213i 0.903423 0.903423i
\(184\) −4.79941 10.8598i −0.353817 0.800597i
\(185\) −13.7844 + 3.69352i −1.01345 + 0.271553i
\(186\) −12.3646 + 4.61003i −0.906615 + 0.338024i
\(187\) −5.00192 + 6.51863i −0.365776 + 0.476689i
\(188\) 5.71981 8.44657i 0.417160 0.616030i
\(189\) −7.65526 12.8605i −0.556838 0.935461i
\(190\) 6.67129 21.7496i 0.483986 1.57788i
\(191\) 17.2607 9.96545i 1.24894 0.721075i 0.278040 0.960569i \(-0.410315\pi\)
0.970898 + 0.239495i \(0.0769818\pi\)
\(192\) −4.82828 10.2675i −0.348451 0.740990i
\(193\) −9.32589 + 16.1529i −0.671292 + 1.16271i 0.306245 + 0.951953i \(0.400927\pi\)
−0.977538 + 0.210760i \(0.932406\pi\)
\(194\) 10.5052 2.41520i 0.754232 0.173401i
\(195\) 7.55637 + 3.12995i 0.541123 + 0.224140i
\(196\) −10.3347 + 9.44421i −0.738196 + 0.674586i
\(197\) −4.82797 11.6557i −0.343978 0.830437i −0.997305 0.0733615i \(-0.976627\pi\)
0.653327 0.757076i \(-0.273373\pi\)
\(198\) 4.53452 + 0.763086i 0.322254 + 0.0542302i
\(199\) 3.15982 + 11.7926i 0.223994 + 0.835957i 0.982805 + 0.184646i \(0.0591139\pi\)
−0.758811 + 0.651311i \(0.774219\pi\)
\(200\) 14.0384 19.2110i 0.992665 1.35843i
\(201\) −18.6289 4.99159i −1.31398 0.352080i
\(202\) 9.88677 0.942854i 0.695631 0.0663390i
\(203\) 25.4725 + 6.46282i 1.78782 + 0.453601i
\(204\) −3.90011 5.91592i −0.273062 0.414197i
\(205\) 10.9010 1.43514i 0.761359 0.100235i
\(206\) −0.158935 + 4.43489i −0.0110735 + 0.308993i
\(207\) −2.07484 + 3.59373i −0.144211 + 0.249782i
\(208\) −5.49342 + 3.08153i −0.380900 + 0.213666i
\(209\) 14.4475 0.999355
\(210\) −7.03144 18.1178i −0.485216 1.25025i
\(211\) −6.56331 2.71861i −0.451837 0.187157i 0.145147 0.989410i \(-0.453634\pi\)
−0.596984 + 0.802253i \(0.703634\pi\)
\(212\) 6.00168 + 18.0469i 0.412197 + 1.23946i
\(213\) 4.46867 + 0.588311i 0.306188 + 0.0403104i
\(214\) −12.9752 5.92750i −0.886968 0.405196i
\(215\) −1.10622 + 4.12846i −0.0754434 + 0.281558i
\(216\) −7.67303 + 14.0399i −0.522084 + 0.955293i
\(217\) 6.44647 16.1692i 0.437615 1.09764i
\(218\) −9.39213 + 11.3723i −0.636116 + 0.770232i
\(219\) −2.39567 1.83826i −0.161884 0.124218i
\(220\) 22.7647 + 7.88516i 1.53480 + 0.531618i
\(221\) −3.12078 + 2.39466i −0.209926 + 0.161082i
\(222\) 7.61689 1.75115i 0.511212 0.117530i
\(223\) −9.37547 −0.627828 −0.313914 0.949451i \(-0.601640\pi\)
−0.313914 + 0.949451i \(0.601640\pi\)
\(224\) 14.3128 + 4.37552i 0.956311 + 0.292352i
\(225\) −8.31598 −0.554399
\(226\) 11.4281 2.62737i 0.760187 0.174770i
\(227\) −2.46357 + 1.89036i −0.163513 + 0.125468i −0.687277 0.726396i \(-0.741194\pi\)
0.523764 + 0.851863i \(0.324527\pi\)
\(228\) −4.07792 + 11.7731i −0.270067 + 0.779690i
\(229\) 2.56561 + 1.96866i 0.169540 + 0.130093i 0.690046 0.723765i \(-0.257590\pi\)
−0.520506 + 0.853858i \(0.674257\pi\)
\(230\) −13.8445 + 16.7635i −0.912881 + 1.10535i
\(231\) 9.69064 7.64318i 0.637598 0.502884i
\(232\) −7.90513 26.9589i −0.518997 1.76994i
\(233\) −1.84927 + 6.90156i −0.121150 + 0.452136i −0.999673 0.0255626i \(-0.991862\pi\)
0.878524 + 0.477699i \(0.158529\pi\)
\(234\) 2.00237 + 0.914745i 0.130899 + 0.0597988i
\(235\) −18.5197 2.43817i −1.20809 0.159049i
\(236\) −15.9315 + 5.29819i −1.03705 + 0.344883i
\(237\) 10.0336 + 4.15607i 0.651755 + 0.269966i
\(238\) 9.23719 + 1.42817i 0.598758 + 0.0925748i
\(239\) −8.27613 −0.535338 −0.267669 0.963511i \(-0.586253\pi\)
−0.267669 + 0.963511i \(0.586253\pi\)
\(240\) −12.8510 + 16.3250i −0.829529 + 1.05377i
\(241\) 9.18747 15.9132i 0.591817 1.02506i −0.402171 0.915565i \(-0.631744\pi\)
0.993988 0.109492i \(-0.0349225\pi\)
\(242\) 0.00919172 0.256485i 0.000590866 0.0164874i
\(243\) 9.71420 1.27890i 0.623166 0.0820414i
\(244\) 20.3488 13.4151i 1.30270 0.858811i
\(245\) 23.9376 + 9.17588i 1.52932 + 0.586225i
\(246\) −5.99446 + 0.571663i −0.382193 + 0.0364479i
\(247\) 6.68103 + 1.79018i 0.425104 + 0.113906i
\(248\) −18.3876 + 2.86057i −1.16761 + 0.181646i
\(249\) 1.01968 + 3.80551i 0.0646198 + 0.241164i
\(250\) −17.4284 2.93291i −1.10227 0.185494i
\(251\) −3.35112 8.09033i −0.211521 0.510657i 0.782136 0.623107i \(-0.214130\pi\)
−0.993657 + 0.112450i \(0.964130\pi\)
\(252\) −1.71669 4.94117i −0.108141 0.311265i
\(253\) −12.7561 5.28375i −0.801969 0.332186i
\(254\) −17.2529 + 3.96652i −1.08254 + 0.248881i
\(255\) −6.48758 + 11.2368i −0.406268 + 0.703677i
\(256\) −3.75695 15.5527i −0.234810 0.972041i
\(257\) 5.49086 3.17015i 0.342510 0.197748i −0.318871 0.947798i \(-0.603304\pi\)
0.661382 + 0.750050i \(0.269970\pi\)
\(258\) 0.686429 2.23788i 0.0427352 0.139324i
\(259\) −5.03537 + 8.99625i −0.312882 + 0.559000i
\(260\) 9.55014 + 6.46712i 0.592274 + 0.401074i
\(261\) −5.97740 + 7.78990i −0.369992 + 0.482183i
\(262\) 12.6032 4.69899i 0.778628 0.290305i
\(263\) 23.2583 6.23204i 1.43417 0.384284i 0.543680 0.839293i \(-0.317031\pi\)
0.890487 + 0.455009i \(0.150364\pi\)
\(264\) −12.3048 4.76220i −0.757311 0.293093i
\(265\) 24.6256 24.6256i 1.51274 1.51274i
\(266\) −7.89530 14.4145i −0.484092 0.883809i
\(267\) 6.21266 + 14.9987i 0.380209 + 0.917905i
\(268\) −24.3171 12.1797i −1.48540 0.743993i
\(269\) 9.08543 6.97149i 0.553948 0.425059i −0.293483 0.955964i \(-0.594815\pi\)
0.847431 + 0.530905i \(0.178148\pi\)
\(270\) 29.2791 + 1.04929i 1.78187 + 0.0638575i
\(271\) −2.98969 + 1.72610i −0.181611 + 0.104853i −0.588049 0.808825i \(-0.700104\pi\)
0.406438 + 0.913678i \(0.366771\pi\)
\(272\) −3.70923 9.27834i −0.224905 0.562582i
\(273\) 5.42835 2.33371i 0.328538 0.141243i
\(274\) −6.20630 11.6982i −0.374936 0.706712i
\(275\) −3.61159 27.4328i −0.217787 1.65426i
\(276\) 7.90615 8.90338i 0.475895 0.535921i
\(277\) 0.787098 5.97860i 0.0472921 0.359219i −0.951394 0.307976i \(-0.900348\pi\)
0.998686 0.0512432i \(-0.0163184\pi\)
\(278\) −6.62901 9.31154i −0.397581 0.558469i
\(279\) 4.59891 + 4.59891i 0.275329 + 0.275329i
\(280\) −4.57335 27.0218i −0.273310 1.61486i
\(281\) −11.0563 + 11.0563i −0.659565 + 0.659565i −0.955277 0.295712i \(-0.904443\pi\)
0.295712 + 0.955277i \(0.404443\pi\)
\(282\) 10.0883 + 1.69770i 0.600752 + 0.101097i
\(283\) −24.3058 3.19992i −1.44483 0.190215i −0.633018 0.774137i \(-0.718184\pi\)
−0.811810 + 0.583922i \(0.801518\pi\)
\(284\) 6.00592 + 2.08031i 0.356386 + 0.123444i
\(285\) 22.6196 2.97793i 1.33987 0.176397i
\(286\) −2.14794 + 7.00267i −0.127011 + 0.414077i
\(287\) 4.75111 6.36562i 0.280449 0.375751i
\(288\) −3.61407 + 4.26727i −0.212961 + 0.251451i
\(289\) 5.37981 + 9.31811i 0.316459 + 0.548124i
\(290\) −37.6560 + 35.0504i −2.21124 + 2.05823i
\(291\) 6.58078 + 8.57624i 0.385772 + 0.502748i
\(292\) −2.78779 3.21887i −0.163143 0.188370i
\(293\) −8.76745 + 3.63160i −0.512200 + 0.212160i −0.623787 0.781595i \(-0.714407\pi\)
0.111587 + 0.993755i \(0.464407\pi\)
\(294\) −12.9215 5.49164i −0.753596 0.320279i
\(295\) 21.7391 + 21.7391i 1.26570 + 1.26570i
\(296\) 11.0184 0.258249i 0.640430 0.0150104i
\(297\) 4.81559 + 17.9720i 0.279429 + 1.04284i
\(298\) 9.19588 20.1297i 0.532703 1.16608i
\(299\) −5.24416 4.02398i −0.303277 0.232713i
\(300\) 23.3740 + 4.80007i 1.34950 + 0.277132i
\(301\) 1.57936 + 2.65325i 0.0910330 + 0.152931i
\(302\) −4.44590 + 2.35871i −0.255833 + 0.135728i
\(303\) 4.98001 + 8.62564i 0.286094 + 0.495530i
\(304\) −8.97277 + 15.1060i −0.514623 + 0.866387i
\(305\) −38.6509 22.3151i −2.21314 1.27776i
\(306\) −1.85337 + 2.95998i −0.105950 + 0.169211i
\(307\) −6.04763 + 14.6003i −0.345156 + 0.833281i 0.652021 + 0.758201i \(0.273921\pi\)
−0.997177 + 0.0750806i \(0.976079\pi\)
\(308\) 15.5544 7.80895i 0.886293 0.444956i
\(309\) −4.11166 + 1.70310i −0.233904 + 0.0968862i
\(310\) 19.7623 + 27.7594i 1.12242 + 1.57663i
\(311\) −19.6888 + 5.27560i −1.11645 + 0.299152i −0.769446 0.638712i \(-0.779467\pi\)
−0.347003 + 0.937864i \(0.612801\pi\)
\(312\) −5.10011 3.72689i −0.288737 0.210993i
\(313\) −1.24911 + 4.66174i −0.0706039 + 0.263497i −0.992201 0.124652i \(-0.960219\pi\)
0.921597 + 0.388149i \(0.126885\pi\)
\(314\) 17.6047 21.3164i 0.993490 1.20295i
\(315\) −6.68218 + 6.86267i −0.376498 + 0.386668i
\(316\) 12.6810 + 8.58729i 0.713365 + 0.483073i
\(317\) 3.82445 + 29.0496i 0.214803 + 1.63159i 0.670822 + 0.741618i \(0.265941\pi\)
−0.456019 + 0.889970i \(0.650725\pi\)
\(318\) −13.9610 + 12.9950i −0.782896 + 0.728724i
\(319\) −28.2933 16.3351i −1.58412 0.914592i
\(320\) −22.3828 + 18.9051i −1.25124 + 1.05683i
\(321\) 14.3058i 0.798475i
\(322\) 1.69930 + 15.6144i 0.0946985 + 0.870157i
\(323\) −4.19908 + 10.1375i −0.233643 + 0.564064i
\(324\) −10.0883 0.724008i −0.560463 0.0402227i
\(325\) 1.72904 13.1334i 0.0959099 0.728508i
\(326\) −2.81419 7.54796i −0.155864 0.418043i
\(327\) −14.2875 3.82832i −0.790100 0.211707i
\(328\) −8.44264 0.910805i −0.466167 0.0502908i
\(329\) −10.5956 + 8.35697i −0.584157 + 0.460734i
\(330\) 2.29367 + 24.0514i 0.126262 + 1.32399i
\(331\) 14.6340 19.0714i 0.804359 1.04826i −0.193385 0.981123i \(-0.561946\pi\)
0.997744 0.0671382i \(-0.0213869\pi\)
\(332\) 0.329018 + 5.54601i 0.0180572 + 0.304377i
\(333\) −2.34496 3.05601i −0.128503 0.167468i
\(334\) −6.47878 4.05664i −0.354503 0.221970i
\(335\) 49.8013i 2.72093i
\(336\) 1.97306 + 14.8792i 0.107639 + 0.811726i
\(337\) 15.6356i 0.851726i 0.904788 + 0.425863i \(0.140029\pi\)
−0.904788 + 0.425863i \(0.859971\pi\)
\(338\) 7.89574 12.6101i 0.429472 0.685900i
\(339\) 7.15890 + 9.32966i 0.388818 + 0.506718i
\(340\) −12.1493 + 13.6817i −0.658886 + 0.741993i
\(341\) −13.1736 + 17.1682i −0.713390 + 0.929708i
\(342\) 6.11300 0.582968i 0.330553 0.0315233i
\(343\) 16.8136 7.76554i 0.907848 0.419300i
\(344\) 1.58303 2.89658i 0.0853512 0.156173i
\(345\) −21.0606 5.64316i −1.13386 0.303817i
\(346\) −30.4859 + 11.3664i −1.63893 + 0.611062i
\(347\) −0.934642 + 7.09931i −0.0501742 + 0.381111i 0.947873 + 0.318648i \(0.103229\pi\)
−0.998047 + 0.0624629i \(0.980105\pi\)
\(348\) 21.2973 18.4451i 1.14165 0.988760i
\(349\) −3.01795 + 7.28597i −0.161547 + 0.390009i −0.983839 0.179057i \(-0.942695\pi\)
0.822292 + 0.569066i \(0.192695\pi\)
\(350\) −25.3964 + 18.5949i −1.35750 + 0.993937i
\(351\) 8.90759i 0.475452i
\(352\) −15.6464 10.0689i −0.833958 0.536672i
\(353\) 15.1410 + 8.74164i 0.805872 + 0.465270i 0.845520 0.533943i \(-0.179290\pi\)
−0.0396484 + 0.999214i \(0.512624\pi\)
\(354\) −11.4718 12.3246i −0.609719 0.655045i
\(355\) −1.51916 11.5392i −0.0806288 0.612437i
\(356\) 4.32714 + 22.4809i 0.229338 + 1.19148i
\(357\) 2.54651 + 9.02114i 0.134776 + 0.477449i
\(358\) 19.2775 + 15.9208i 1.01885 + 0.841439i
\(359\) −7.22222 + 26.9537i −0.381174 + 1.42256i 0.462936 + 0.886391i \(0.346796\pi\)
−0.844110 + 0.536169i \(0.819871\pi\)
\(360\) 9.95033 + 2.41778i 0.524428 + 0.127428i
\(361\) 0.283802 0.0760446i 0.0149370 0.00400235i
\(362\) 26.9699 19.2003i 1.41751 1.00914i
\(363\) 0.237791 0.0984962i 0.0124808 0.00516971i
\(364\) 8.16048 1.68380i 0.427726 0.0882551i
\(365\) −2.98398 + 7.20397i −0.156189 + 0.377073i
\(366\) 20.7166 + 12.9716i 1.08287 + 0.678034i
\(367\) −12.4882 7.21005i −0.651877 0.376362i 0.137298 0.990530i \(-0.456158\pi\)
−0.789175 + 0.614168i \(0.789492\pi\)
\(368\) 13.4469 10.0560i 0.700966 0.524203i
\(369\) 1.48393 + 2.57023i 0.0772501 + 0.133801i
\(370\) −9.45845 17.8281i −0.491722 0.926840i
\(371\) −0.335234 25.1571i −0.0174045 1.30609i
\(372\) −10.2717 15.5808i −0.532565 0.807827i
\(373\) −5.16366 3.96222i −0.267364 0.205156i 0.466375 0.884587i \(-0.345560\pi\)
−0.733739 + 0.679431i \(0.762227\pi\)
\(374\) −10.5693 4.82839i −0.546525 0.249670i
\(375\) −4.58730 17.1200i −0.236887 0.884075i
\(376\) 13.4540 + 5.20694i 0.693836 + 0.268527i
\(377\) −11.0597 11.0597i −0.569605 0.569605i
\(378\) 15.2993 14.6260i 0.786913 0.752279i
\(379\) 19.6320 8.13186i 1.00843 0.417705i 0.183548 0.983011i \(-0.441242\pi\)
0.824882 + 0.565305i \(0.191242\pi\)
\(380\) 32.0905 + 2.30303i 1.64621 + 0.118143i
\(381\) −10.8077 14.0849i −0.553696 0.721591i
\(382\) 19.2043 + 20.6319i 0.982578 + 1.05562i
\(383\) −17.7222 30.6958i −0.905563 1.56848i −0.820159 0.572135i \(-0.806115\pi\)
−0.0854039 0.996346i \(-0.527218\pi\)
\(384\) 12.6213 9.90804i 0.644077 0.505618i
\(385\) −25.5406 19.0628i −1.30167 0.971528i
\(386\) −25.2180 7.73515i −1.28356 0.393709i
\(387\) −1.14382 + 0.150586i −0.0581435 + 0.00765474i
\(388\) 6.65753 + 13.7136i 0.337985 + 0.696204i
\(389\) −2.96074 0.389789i −0.150116 0.0197631i 0.0550938 0.998481i \(-0.482454\pi\)
−0.205209 + 0.978718i \(0.565788\pi\)
\(390\) −1.91951 + 11.4064i −0.0971984 + 0.577586i
\(391\) 7.41496 7.41496i 0.374991 0.374991i
\(392\) −16.2913 11.2514i −0.822835 0.568281i
\(393\) 9.53827 + 9.53827i 0.481142 + 0.481142i
\(394\) 14.5348 10.3475i 0.732252 0.521300i
\(395\) 3.66048 27.8041i 0.184179 1.39898i
\(396\) 0.385111 + 6.49154i 0.0193526 + 0.326212i
\(397\) −3.34716 25.4242i −0.167989 1.27601i −0.842886 0.538093i \(-0.819145\pi\)
0.674896 0.737913i \(-0.264188\pi\)
\(398\) −15.2520 + 8.09175i −0.764515 + 0.405603i
\(399\) 9.85856 13.2087i 0.493545 0.661261i
\(400\) 30.9261 + 13.2612i 1.54630 + 0.663060i
\(401\) 13.1712 7.60438i 0.657737 0.379745i −0.133677 0.991025i \(-0.542679\pi\)
0.791414 + 0.611280i \(0.209345\pi\)
\(402\) 0.976821 27.2571i 0.0487194 1.35946i
\(403\) −8.21921 + 6.30682i −0.409428 + 0.314165i
\(404\) 4.43229 + 13.3278i 0.220515 + 0.663081i
\(405\) 7.08757 + 17.1109i 0.352184 + 0.850248i
\(406\) −0.836034 + 37.1555i −0.0414917 + 1.84400i
\(407\) 9.06277 9.06277i 0.449225 0.449225i
\(408\) 6.91785 7.24991i 0.342485 0.358924i
\(409\) 13.7278 3.67835i 0.678795 0.181883i 0.0970817 0.995276i \(-0.469049\pi\)
0.581713 + 0.813394i \(0.302383\pi\)
\(410\) 5.43217 + 14.5697i 0.268276 + 0.719544i
\(411\) 8.08461 10.5361i 0.398784 0.519706i
\(412\) −6.16278 + 1.18622i −0.303618 + 0.0584408i
\(413\) 22.2083 0.295940i 1.09280 0.0145622i
\(414\) −5.61054 1.72093i −0.275743 0.0845792i
\(415\) 8.81042 5.08670i 0.432487 0.249696i
\(416\) −5.98783 6.59492i −0.293577 0.323342i
\(417\) 5.73142 9.92712i 0.280669 0.486133i
\(418\) 4.57794 + 19.9124i 0.223915 + 0.973947i
\(419\) −8.25059 3.41751i −0.403068 0.166956i 0.171934 0.985109i \(-0.444998\pi\)
−0.575001 + 0.818152i \(0.694998\pi\)
\(420\) 22.7430 15.4321i 1.10974 0.753009i
\(421\) 1.90134 + 4.59025i 0.0926658 + 0.223715i 0.963416 0.268011i \(-0.0863663\pi\)
−0.870750 + 0.491726i \(0.836366\pi\)
\(422\) 1.66725 9.90738i 0.0811605 0.482284i
\(423\) −1.30499 4.87028i −0.0634507 0.236801i
\(424\) −22.9715 + 13.9903i −1.11559 + 0.679430i
\(425\) 20.2986 + 5.43900i 0.984628 + 0.263830i
\(426\) 0.605130 + 6.34539i 0.0293186 + 0.307435i
\(427\) −31.0297 + 8.75914i −1.50163 + 0.423885i
\(428\) 4.05820 19.7614i 0.196161 0.955205i
\(429\) −7.28279 + 0.958798i −0.351617 + 0.0462912i
\(430\) −6.04060 0.216479i −0.291304 0.0104395i
\(431\) 5.39503 9.34446i 0.259869 0.450107i −0.706337 0.707875i \(-0.749654\pi\)
0.966207 + 0.257768i \(0.0829872\pi\)
\(432\) −21.7819 6.12664i −1.04798 0.294768i
\(433\) −34.1961 −1.64336 −0.821680 0.569949i \(-0.806963\pi\)
−0.821680 + 0.569949i \(0.806963\pi\)
\(434\) 24.3281 + 3.76140i 1.16778 + 0.180553i
\(435\) −47.6642 19.7431i −2.28532 0.946611i
\(436\) −18.6501 9.34126i −0.893177 0.447365i
\(437\) −18.2808 2.40672i −0.874491 0.115129i
\(438\) 1.77449 3.88433i 0.0847882 0.185600i
\(439\) −4.04898 + 15.1110i −0.193247 + 0.721208i 0.799467 + 0.600711i \(0.205116\pi\)
−0.992714 + 0.120497i \(0.961551\pi\)
\(440\) −3.65440 + 33.8742i −0.174217 + 1.61489i
\(441\) 0.184389 + 6.91736i 0.00878044 + 0.329398i
\(442\) −4.28932 3.54245i −0.204022 0.168497i
\(443\) −3.60203 2.76394i −0.171138 0.131319i 0.519641 0.854385i \(-0.326066\pi\)
−0.690779 + 0.723066i \(0.742732\pi\)
\(444\) 4.82709 + 9.94315i 0.229083 + 0.471881i
\(445\) 33.2584 25.5201i 1.57660 1.20977i
\(446\) −2.97078 12.9218i −0.140670 0.611866i
\(447\) 22.1940 1.04974
\(448\) −1.49535 + 21.1131i −0.0706486 + 0.997501i
\(449\) 1.32375 0.0624716 0.0312358 0.999512i \(-0.490056\pi\)
0.0312358 + 0.999512i \(0.490056\pi\)
\(450\) −2.63506 11.4616i −0.124218 0.540304i
\(451\) −7.83423 + 6.01142i −0.368899 + 0.283067i
\(452\) 7.24239 + 14.9184i 0.340654 + 0.701701i
\(453\) −4.00424 3.07256i −0.188136 0.144362i
\(454\) −3.38603 2.79644i −0.158914 0.131243i
\(455\) −9.44882 11.9800i −0.442968 0.561630i
\(456\) −17.5185 1.88992i −0.820378 0.0885037i
\(457\) −5.50485 + 20.5444i −0.257506 + 0.961025i 0.709173 + 0.705034i \(0.249068\pi\)
−0.966679 + 0.255991i \(0.917598\pi\)
\(458\) −1.90036 + 4.15987i −0.0887981 + 0.194378i
\(459\) −14.0102 1.84448i −0.653939 0.0860927i
\(460\) −27.4913 13.7695i −1.28179 0.642008i
\(461\) 29.5870 + 12.2553i 1.37800 + 0.570788i 0.943947 0.330098i \(-0.107082\pi\)
0.434057 + 0.900885i \(0.357082\pi\)
\(462\) 13.6049 + 10.9343i 0.632958 + 0.508711i
\(463\) −11.1091 −0.516282 −0.258141 0.966107i \(-0.583110\pi\)
−0.258141 + 0.966107i \(0.583110\pi\)
\(464\) 34.6515 19.4377i 1.60865 0.902373i
\(465\) −17.0864 + 29.5945i −0.792363 + 1.37241i
\(466\) −10.0981 0.361889i −0.467786 0.0167642i
\(467\) 8.14926 1.07287i 0.377103 0.0496465i 0.0604073 0.998174i \(-0.480760\pi\)
0.316695 + 0.948527i \(0.397427\pi\)
\(468\) −0.626271 + 3.04963i −0.0289494 + 0.140969i
\(469\) 25.7770 + 25.0990i 1.19027 + 1.15897i
\(470\) −2.50787 26.2975i −0.115679 1.21302i
\(471\) 26.7806 + 7.17583i 1.23398 + 0.330645i
\(472\) −12.3504 20.2789i −0.568475 0.933412i
\(473\) −0.993509 3.70783i −0.0456816 0.170486i
\(474\) −2.54881 + 15.1459i −0.117071 + 0.695673i
\(475\) −14.1405 34.1383i −0.648812 1.56637i
\(476\) 0.958569 + 13.1838i 0.0439359 + 0.604277i
\(477\) 8.68483 + 3.59738i 0.397651 + 0.164713i
\(478\) −2.62244 11.4066i −0.119947 0.521728i
\(479\) −3.99901 + 6.92649i −0.182719 + 0.316479i −0.942806 0.333343i \(-0.891823\pi\)
0.760086 + 0.649822i \(0.225157\pi\)
\(480\) −26.5721 12.5392i −1.21284 0.572332i
\(481\) 5.31389 3.06798i 0.242293 0.139888i
\(482\) 24.8437 + 7.62034i 1.13160 + 0.347097i
\(483\) −13.5351 + 8.05683i −0.615867 + 0.366598i
\(484\) 0.356414 0.0686030i 0.0162007 0.00311832i
\(485\) 16.9932 22.1460i 0.771621 1.00560i
\(486\) 4.84076 + 12.9834i 0.219582 + 0.588940i
\(487\) −18.6097 + 4.98645i −0.843286 + 0.225958i −0.654501 0.756061i \(-0.727121\pi\)
−0.188784 + 0.982019i \(0.560455\pi\)
\(488\) 24.9373 + 23.7951i 1.12886 + 1.07715i
\(489\) 5.71240 5.71240i 0.258324 0.258324i
\(490\) −5.06169 + 35.8997i −0.228664 + 1.62178i
\(491\) −2.43329 5.87448i −0.109813 0.265112i 0.859414 0.511280i \(-0.170828\pi\)
−0.969227 + 0.246168i \(0.920828\pi\)
\(492\) −2.68735 8.08077i −0.121155 0.364309i
\(493\) 19.6853 15.1050i 0.886579 0.680296i
\(494\) −0.350325 + 9.77543i −0.0157619 + 0.439817i
\(495\) 10.3125 5.95392i 0.463512 0.267609i
\(496\) −9.76903 24.4364i −0.438643 1.09723i
\(497\) −6.73829 5.02925i −0.302254 0.225593i
\(498\) −4.92187 + 2.61123i −0.220554 + 0.117012i
\(499\) −1.48378 11.2705i −0.0664233 0.504535i −0.992026 0.126037i \(-0.959774\pi\)
0.925602 0.378498i \(-0.123559\pi\)
\(500\) −1.48017 24.9501i −0.0661952 1.11580i
\(501\) 1.00060 7.60029i 0.0447034 0.339556i
\(502\) 10.0887 7.18228i 0.450281 0.320561i
\(503\) 1.80858 + 1.80858i 0.0806405 + 0.0806405i 0.746277 0.665636i \(-0.231840\pi\)
−0.665636 + 0.746277i \(0.731840\pi\)
\(504\) 6.26624 3.93174i 0.279121 0.175134i
\(505\) 18.1862 18.1862i 0.809277 0.809277i
\(506\) 3.24038 19.2554i 0.144052 0.856009i
\(507\) 14.7930 + 1.94754i 0.656980 + 0.0864931i
\(508\) −10.9338 22.5221i −0.485107 0.999257i
\(509\) 2.75611 0.362849i 0.122163 0.0160830i −0.0691969 0.997603i \(-0.522044\pi\)
0.191360 + 0.981520i \(0.438710\pi\)
\(510\) −17.5429 5.38098i −0.776815 0.238274i
\(511\) 2.22488 + 5.17519i 0.0984228 + 0.228937i
\(512\) 20.2451 10.1062i 0.894717 0.446634i
\(513\) 12.4236 + 21.5184i 0.548517 + 0.950059i
\(514\) 6.10916 + 6.56330i 0.269463 + 0.289495i
\(515\) 6.99594 + 9.11728i 0.308278 + 0.401756i
\(516\) 3.30188 + 0.236965i 0.145357 + 0.0104318i
\(517\) 15.4993 6.42003i 0.681660 0.282353i
\(518\) −13.9947 4.08942i −0.614892 0.179679i
\(519\) −23.0722 23.0722i −1.01276 1.01276i
\(520\) −5.88723 + 15.2118i −0.258172 + 0.667080i
\(521\) 5.61675 + 20.9620i 0.246074 + 0.918362i 0.972840 + 0.231477i \(0.0743557\pi\)
−0.726766 + 0.686885i \(0.758978\pi\)
\(522\) −12.6305 5.77004i −0.552824 0.252548i
\(523\) 10.5208 + 8.07292i 0.460044 + 0.353004i 0.812635 0.582774i \(-0.198033\pi\)
−0.352591 + 0.935778i \(0.614699\pi\)
\(524\) 10.4700 + 15.8815i 0.457382 + 0.693786i
\(525\) −27.5449 15.4174i −1.20216 0.672871i
\(526\) 15.9591 + 30.0812i 0.695852 + 1.31160i
\(527\) −8.21767 14.2334i −0.357967 0.620017i
\(528\) 2.66454 18.4682i 0.115959 0.803727i
\(529\) −4.65812 2.68937i −0.202527 0.116929i
\(530\) 41.7435 + 26.1374i 1.81322 + 1.13534i
\(531\) −3.17571 + 7.66685i −0.137814 + 0.332713i
\(532\) 17.3651 15.4492i 0.752874 0.669810i
\(533\) −4.36769 + 1.80915i −0.189185 + 0.0783632i
\(534\) −18.7035 + 13.3152i −0.809378 + 0.576207i
\(535\) −35.6824 + 9.56108i −1.54269 + 0.413362i
\(536\) 9.08147 37.3746i 0.392260 1.61434i
\(537\) −6.48946 + 24.2190i −0.280041 + 1.04513i
\(538\) 12.4874 + 10.3130i 0.538370 + 0.444626i
\(539\) −22.7389 + 3.61244i −0.979434 + 0.155599i
\(540\) 7.83141 + 40.6867i 0.337010 + 1.75088i
\(541\) −2.18973 16.6326i −0.0941438 0.715093i −0.971801 0.235804i \(-0.924228\pi\)
0.877657 0.479289i \(-0.159106\pi\)
\(542\) −3.32635 3.57362i −0.142879 0.153500i
\(543\) 28.7529 + 16.6005i 1.23390 + 0.712395i
\(544\) 11.6126 8.05228i 0.497887 0.345239i
\(545\) 38.1952i 1.63610i
\(546\) 4.93652 + 6.74218i 0.211264 + 0.288539i
\(547\) 6.14264 14.8296i 0.262640 0.634070i −0.736460 0.676481i \(-0.763504\pi\)
0.999100 + 0.0424113i \(0.0135040\pi\)
\(548\) 14.1565 12.2606i 0.604737 0.523749i
\(549\) 1.57243 11.9438i 0.0671096 0.509748i
\(550\) 36.6650 13.6703i 1.56340 0.582902i
\(551\) −42.1426 11.2921i −1.79534 0.481059i
\(552\) 14.7764 + 8.07553i 0.628924 + 0.343717i
\(553\) −12.5465 15.9075i −0.533532 0.676455i
\(554\) 8.48946 0.809600i 0.360683 0.0343966i
\(555\) 12.3210 16.0571i 0.522998 0.681584i
\(556\) 10.7332 12.0870i 0.455189 0.512603i
\(557\) −1.89340 2.46753i −0.0802259 0.104552i 0.751516 0.659715i \(-0.229323\pi\)
−0.831742 + 0.555162i \(0.812656\pi\)
\(558\) −4.88124 + 7.79572i −0.206639 + 0.330019i
\(559\) 1.83773i 0.0777277i
\(560\) 35.7938 14.8656i 1.51256 0.628185i
\(561\) 11.6532i 0.491998i
\(562\) −18.7419 11.7351i −0.790578 0.495015i
\(563\) 16.0844 + 20.9616i 0.677877 + 0.883426i 0.997952 0.0639658i \(-0.0203748\pi\)
−0.320075 + 0.947392i \(0.603708\pi\)
\(564\) 0.856791 + 14.4423i 0.0360774 + 0.608130i
\(565\) 18.4860 24.0915i 0.777713 1.01354i
\(566\) −3.29140 34.5136i −0.138348 1.45071i
\(567\) 12.4286 + 4.95512i 0.521951 + 0.208095i
\(568\) −0.964127 + 8.93690i −0.0404539 + 0.374984i
\(569\) 8.94191 + 2.39598i 0.374864 + 0.100445i 0.441332 0.897344i \(-0.354506\pi\)
−0.0664675 + 0.997789i \(0.521173\pi\)
\(570\) 11.2718 + 30.2321i 0.472122 + 1.26628i
\(571\) −0.798380 + 6.06430i −0.0334112 + 0.253783i −0.999997 0.00256120i \(-0.999185\pi\)
0.966586 + 0.256344i \(0.0825181\pi\)
\(572\) −10.3321 0.741502i −0.432007 0.0310038i
\(573\) −10.8174 + 26.1154i −0.451902 + 1.09099i
\(574\) 10.2789 + 4.53120i 0.429035 + 0.189128i
\(575\) 35.3131i 1.47266i
\(576\) −7.02658 3.62897i −0.292774 0.151207i
\(577\) 7.68536 + 4.43714i 0.319946 + 0.184721i 0.651368 0.758762i \(-0.274195\pi\)
−0.331423 + 0.943482i \(0.607529\pi\)
\(578\) −11.1381 + 10.3674i −0.463283 + 0.431226i
\(579\) −3.45281 26.2267i −0.143494 1.08995i
\(580\) −60.2405 40.7934i −2.50135 1.69385i
\(581\) 1.80745 7.12387i 0.0749857 0.295548i
\(582\) −9.73504 + 11.7875i −0.403530 + 0.488610i
\(583\) −8.09524 + 30.2119i −0.335271 + 1.25125i
\(584\) 3.55308 4.86226i 0.147027 0.201202i
\(585\) 5.50659 1.47549i 0.227670 0.0610039i
\(586\) −7.78339 10.9331i −0.321529 0.451641i
\(587\) 22.2595 9.22019i 0.918749 0.380558i 0.127349 0.991858i \(-0.459353\pi\)
0.791399 + 0.611300i \(0.209353\pi\)
\(588\) 3.47450 19.5492i 0.143286 0.806197i
\(589\) −11.0592 + 26.6992i −0.455684 + 1.10012i
\(590\) −23.0737 + 36.8506i −0.949930 + 1.51711i
\(591\) 15.4957 + 8.94643i 0.637407 + 0.368007i
\(592\) 3.84730 + 15.1043i 0.158123 + 0.620784i
\(593\) 12.4193 + 21.5108i 0.509998 + 0.883343i 0.999933 + 0.0115836i \(0.00368725\pi\)
−0.489935 + 0.871759i \(0.662979\pi\)
\(594\) −23.2442 + 12.3319i −0.953721 + 0.505983i
\(595\) 20.7991 12.3808i 0.852680 0.507563i
\(596\) 30.6577 + 6.29586i 1.25579 + 0.257889i
\(597\) −13.7369 10.5407i −0.562213 0.431402i
\(598\) 3.88438 8.50287i 0.158844 0.347708i
\(599\) 8.90821 + 33.2459i 0.363979 + 1.35839i 0.868799 + 0.495165i \(0.164892\pi\)
−0.504820 + 0.863225i \(0.668441\pi\)
\(600\) 0.790712 + 33.7363i 0.0322807 + 1.37728i
\(601\) 28.1493 + 28.1493i 1.14823 + 1.14823i 0.986900 + 0.161334i \(0.0515795\pi\)
0.161334 + 0.986900i \(0.448420\pi\)
\(602\) −3.15642 + 3.01750i −0.128646 + 0.122984i
\(603\) −12.4194 + 5.14427i −0.505756 + 0.209491i
\(604\) −4.65967 5.38020i −0.189599 0.218917i
\(605\) −0.404599 0.527283i −0.0164493 0.0214371i
\(606\) −10.3103 + 9.59693i −0.418829 + 0.389848i
\(607\) −6.28806 10.8912i −0.255225 0.442062i 0.709732 0.704472i \(-0.248816\pi\)
−0.964957 + 0.262410i \(0.915483\pi\)
\(608\) −23.6631 7.58020i −0.959666 0.307418i
\(609\) −34.2410 + 14.7206i −1.38751 + 0.596509i
\(610\) 18.5088 60.3418i 0.749398 2.44317i
\(611\) 7.96292 1.04834i 0.322145 0.0424113i
\(612\) −4.66689 1.61650i −0.188648 0.0653432i
\(613\) 33.8729 + 4.45945i 1.36811 + 0.180115i 0.778537 0.627598i \(-0.215962\pi\)
0.589575 + 0.807714i \(0.299295\pi\)
\(614\) −22.0392 3.70885i −0.889431 0.149677i
\(615\) −11.0265 + 11.0265i −0.444632 + 0.444632i
\(616\) 15.6914 + 18.9636i 0.632225 + 0.764063i
\(617\) 22.7866 + 22.7866i 0.917356 + 0.917356i 0.996836 0.0794806i \(-0.0253262\pi\)
−0.0794806 + 0.996836i \(0.525326\pi\)
\(618\) −3.65017 5.12727i −0.146831 0.206249i
\(619\) −3.34011 + 25.3706i −0.134250 + 1.01973i 0.783169 + 0.621809i \(0.213602\pi\)
−0.917419 + 0.397922i \(0.869731\pi\)
\(620\) −31.9976 + 36.0335i −1.28505 + 1.44714i
\(621\) −3.09946 23.5427i −0.124377 0.944737i
\(622\) −13.5099 25.4646i −0.541696 1.02104i
\(623\) 3.55259 30.0762i 0.142331 1.20498i
\(624\) 3.52055 8.21019i 0.140935 0.328671i
\(625\) −3.20936 + 1.85292i −0.128374 + 0.0741170i
\(626\) −6.82089 0.244442i −0.272618 0.00976988i
\(627\) −16.2560 + 12.4737i −0.649204 + 0.498152i
\(628\) 34.9579 + 17.5093i 1.39497 + 0.698698i
\(629\) 3.72509 + 8.99317i 0.148529 + 0.358581i
\(630\) −11.5759 7.03521i −0.461195 0.280290i
\(631\) −13.2591 + 13.2591i −0.527836 + 0.527836i −0.919927 0.392091i \(-0.871752\pi\)
0.392091 + 0.919927i \(0.371752\pi\)
\(632\) −7.81730 + 20.1988i −0.310955 + 0.803465i
\(633\) 9.73211 2.60771i 0.386816 0.103647i
\(634\) −38.8260 + 14.4760i −1.54198 + 0.574913i
\(635\) −27.9082 + 36.3706i −1.10750 + 1.44332i
\(636\) −22.3343 15.1242i −0.885611 0.599714i
\(637\) −10.9629 1.14704i −0.434365 0.0454473i
\(638\) 13.5488 44.1715i 0.536403 1.74877i
\(639\) 2.72071 1.57080i 0.107629 0.0621399i
\(640\) −33.1484 24.8588i −1.31031 0.982632i
\(641\) 19.8693 34.4146i 0.784788 1.35929i −0.144337 0.989529i \(-0.546105\pi\)
0.929125 0.369765i \(-0.120562\pi\)
\(642\) 19.7171 4.53306i 0.778174 0.178905i
\(643\) −24.8075 10.2756i −0.978311 0.405230i −0.164511 0.986375i \(-0.552605\pi\)
−0.813800 + 0.581146i \(0.802605\pi\)
\(644\) −20.9822 + 7.28978i −0.826816 + 0.287257i
\(645\) −2.31974 5.60034i −0.0913396 0.220513i
\(646\) −15.3026 2.57518i −0.602073 0.101319i
\(647\) 8.89282 + 33.1885i 0.349613 + 1.30477i 0.887130 + 0.461520i \(0.152696\pi\)
−0.537517 + 0.843253i \(0.680638\pi\)
\(648\) −2.19879 14.1338i −0.0863768 0.555226i
\(649\) −26.6706 7.14636i −1.04691 0.280519i
\(650\) 18.6490 1.77847i 0.731476 0.0697574i
\(651\) 6.70677 + 23.7590i 0.262859 + 0.931190i
\(652\) 9.51131 6.27039i 0.372492 0.245567i
\(653\) −26.5045 + 3.48939i −1.03720 + 0.136550i −0.629847 0.776719i \(-0.716882\pi\)
−0.407356 + 0.913270i \(0.633549\pi\)
\(654\) 0.749176 20.9049i 0.0292951 0.817447i
\(655\) 17.4161 30.1656i 0.680505 1.17867i
\(656\) −1.41987 11.9247i −0.0554366 0.465583i
\(657\) −2.10475 −0.0821142
\(658\) −14.8755 11.9555i −0.579906 0.466073i
\(659\) 25.1157 + 10.4033i 0.978370 + 0.405254i 0.813822 0.581115i \(-0.197383\pi\)
0.164549 + 0.986369i \(0.447383\pi\)
\(660\) −32.4223 + 10.7824i −1.26203 + 0.419703i
\(661\) 12.6165 + 1.66100i 0.490727 + 0.0646054i 0.371829 0.928301i \(-0.378731\pi\)
0.118897 + 0.992907i \(0.462064\pi\)
\(662\) 30.9224 + 14.1264i 1.20183 + 0.549036i
\(663\) 1.44393 5.38883i 0.0560777 0.209285i
\(664\) −7.53958 + 2.21082i −0.292592 + 0.0857965i
\(665\) −39.5346 15.7620i −1.53309 0.611223i
\(666\) 3.46893 4.20031i 0.134418 0.162759i
\(667\) 33.0791 + 25.3825i 1.28083 + 0.982815i
\(668\) 3.53819 10.2149i 0.136897 0.395224i
\(669\) 10.5491 8.09460i 0.407851 0.312955i
\(670\) −68.6390 + 15.7804i −2.65176 + 0.609650i
\(671\) 40.0830 1.54739
\(672\) −19.8822 + 7.43411i −0.766971 + 0.286777i
\(673\) −18.7167 −0.721474 −0.360737 0.932668i \(-0.617475\pi\)
−0.360737 + 0.932668i \(0.617475\pi\)
\(674\) −21.5499 + 4.95441i −0.830071 + 0.190837i
\(675\) 37.7532 28.9690i 1.45312 1.11502i
\(676\) 19.8819 + 6.88663i 0.764689 + 0.264870i
\(677\) 9.56634 + 7.34051i 0.367664 + 0.282119i 0.776025 0.630702i \(-0.217233\pi\)
−0.408361 + 0.912821i \(0.633900\pi\)
\(678\) −10.5903 + 12.8231i −0.406717 + 0.492467i
\(679\) −2.89839 19.9568i −0.111230 0.765873i
\(680\) −22.7066 12.4095i −0.870757 0.475884i
\(681\) 1.13985 4.25399i 0.0436793 0.163013i
\(682\) −27.8364 12.7166i −1.06591 0.486943i
\(683\) 46.4876 + 6.12021i 1.77880 + 0.234183i 0.947076 0.321009i \(-0.104022\pi\)
0.831722 + 0.555192i \(0.187355\pi\)
\(684\) 2.74049 + 8.24057i 0.104785 + 0.315086i
\(685\) −31.6829 13.1235i −1.21054 0.501422i
\(686\) 16.0306 + 20.7128i 0.612051 + 0.790819i
\(687\) −4.58647 −0.174985
\(688\) 4.49384 + 1.26399i 0.171326 + 0.0481892i
\(689\) −7.48704 + 12.9679i −0.285233 + 0.494039i
\(690\) 1.10433 30.8150i 0.0420410 1.17311i
\(691\) 7.57132 0.996783i 0.288026 0.0379194i 0.0148714 0.999889i \(-0.495266\pi\)
0.273155 + 0.961970i \(0.411933\pi\)
\(692\) −25.3258 38.4158i −0.962744 1.46035i
\(693\) 2.11560 8.33840i 0.0803649 0.316750i
\(694\) −10.0808 + 0.961362i −0.382663 + 0.0364928i
\(695\) −28.5913 7.66101i −1.08453 0.290599i
\(696\) 32.1705 + 23.5085i 1.21942 + 0.891087i
\(697\) −1.94110 7.24428i −0.0735243 0.274396i
\(698\) −10.9982 1.85083i −0.416290 0.0700548i
\(699\) −3.87792 9.36212i −0.146676 0.354108i
\(700\) −33.6758 29.1107i −1.27283 1.10028i
\(701\) −46.6103 19.3066i −1.76045 0.729200i −0.996470 0.0839555i \(-0.973245\pi\)
−0.763976 0.645245i \(-0.776755\pi\)
\(702\) −12.2770 + 2.82252i −0.463364 + 0.106529i
\(703\) 8.55797 14.8228i 0.322770 0.559054i
\(704\) 8.91963 24.7553i 0.336171 0.933001i
\(705\) 22.9431 13.2462i 0.864087 0.498881i
\(706\) −7.25056 + 23.6381i −0.272878 + 0.889631i
\(707\) −0.247573 18.5787i −0.00931095 0.698725i
\(708\) 13.3514 19.7164i 0.501778 0.740986i
\(709\) −27.8964 + 36.3552i −1.04767 + 1.36535i −0.119651 + 0.992816i \(0.538178\pi\)
−0.928019 + 0.372534i \(0.878489\pi\)
\(710\) 15.4226 5.75019i 0.578800 0.215801i
\(711\) 7.31187 1.95921i 0.274217 0.0734761i
\(712\) −29.6133 + 13.0874i −1.10981 + 0.490470i
\(713\) 19.5288 19.5288i 0.731361 0.731361i
\(714\) −11.6266 + 6.36825i −0.435113 + 0.238326i
\(715\) 7.25883 + 17.5244i 0.271465 + 0.655374i
\(716\) −15.8345 + 31.6141i −0.591765 + 1.18147i
\(717\) 9.31213 7.14545i 0.347768 0.266852i
\(718\) −39.4376 1.41334i −1.47180 0.0527453i
\(719\) 16.7131 9.64931i 0.623293 0.359858i −0.154857 0.987937i \(-0.549492\pi\)
0.778150 + 0.628079i \(0.216158\pi\)
\(720\) −0.179395 + 14.4802i −0.00668565 + 0.539646i
\(721\) 8.24492 + 0.973887i 0.307057 + 0.0362695i
\(722\) 0.194737 + 0.367057i 0.00724735 + 0.0136604i
\(723\) 3.40156 + 25.8374i 0.126506 + 0.960905i
\(724\) 35.0088 + 31.0876i 1.30109 + 1.15536i
\(725\) −10.9065 + 82.8428i −0.405056 + 3.07670i
\(726\) 0.211101 + 0.296527i 0.00783471 + 0.0110052i
\(727\) 27.0443 + 27.0443i 1.00302 + 1.00302i 0.999995 + 0.00302189i \(0.000961898\pi\)
0.00302189 + 0.999995i \(0.499038\pi\)
\(728\) 4.90650 + 10.7137i 0.181847 + 0.397076i
\(729\) −20.5539 + 20.5539i −0.761254 + 0.761254i
\(730\) −10.8745 1.83000i −0.402482 0.0677312i
\(731\) 2.89045 + 0.380535i 0.106907 + 0.0140746i
\(732\) −11.3137 + 32.6631i −0.418168 + 1.20726i
\(733\) −20.4613 + 2.69378i −0.755755 + 0.0994970i −0.498551 0.866860i \(-0.666134\pi\)
−0.257204 + 0.966357i \(0.582801\pi\)
\(734\) 5.98022 19.4966i 0.220734 0.719631i
\(735\) −34.8564 + 10.3427i −1.28570 + 0.381498i
\(736\) 18.1206 + 15.3468i 0.667933 + 0.565692i
\(737\) −22.3636 38.7349i −0.823774 1.42682i
\(738\) −3.07224 + 2.85966i −0.113091 + 0.105265i
\(739\) −1.75448 2.28648i −0.0645395 0.0841095i 0.759968 0.649960i \(-0.225214\pi\)
−0.824508 + 0.565851i \(0.808548\pi\)
\(740\) 21.5747 18.6853i 0.793101 0.686887i
\(741\) −9.06296 + 3.75400i −0.332936 + 0.137907i
\(742\) 34.5667 8.43349i 1.26898 0.309603i
\(743\) −23.1248 23.1248i −0.848368 0.848368i 0.141562 0.989929i \(-0.454788\pi\)
−0.989929 + 0.141562i \(0.954788\pi\)
\(744\) 18.2196 19.0942i 0.667963 0.700026i
\(745\) −14.8330 55.3575i −0.543439 2.02814i
\(746\) 3.82476 8.37235i 0.140034 0.306534i
\(747\) 2.17860 + 1.67170i 0.0797107 + 0.0611642i
\(748\) 3.30571 16.0972i 0.120869 0.588571i
\(749\) −13.0346 + 23.2878i −0.476274 + 0.850917i
\(750\) 22.1423 11.7473i 0.808521 0.428949i
\(751\) 4.24592 + 7.35415i 0.154936 + 0.268357i 0.933036 0.359784i \(-0.117150\pi\)
−0.778100 + 0.628141i \(0.783816\pi\)
\(752\) −2.91337 + 20.1930i −0.106240 + 0.736361i
\(753\) 10.7557 + 6.20978i 0.391958 + 0.226297i
\(754\) 11.7387 18.7476i 0.427498 0.682748i
\(755\) −4.98759 + 12.0411i −0.181517 + 0.438221i
\(756\) 25.0062 + 16.4519i 0.909468 + 0.598351i
\(757\) 19.3598 8.01908i 0.703643 0.291458i −0.00202838 0.999998i \(-0.500646\pi\)
0.705671 + 0.708540i \(0.250646\pi\)
\(758\) 17.4285 + 24.4813i 0.633033 + 0.889201i
\(759\) 18.9148 5.06820i 0.686563 0.183964i
\(760\) 6.99425 + 44.9587i 0.253708 + 1.63082i
\(761\) 5.83148 21.7634i 0.211391 0.788921i −0.776015 0.630714i \(-0.782762\pi\)
0.987406 0.158207i \(-0.0505713\pi\)
\(762\) 15.9880 19.3589i 0.579184 0.701298i
\(763\) 19.7698 + 19.2498i 0.715713 + 0.696890i
\(764\) −22.3509 + 33.0061i −0.808627 + 1.19412i
\(765\) 1.18046 + 8.96650i 0.0426797 + 0.324184i
\(766\) 36.6911 34.1523i 1.32570 1.23397i
\(767\) −11.4479 6.60945i −0.413360 0.238653i
\(768\) 17.6551 + 14.2559i 0.637074 + 0.514414i
\(769\) 17.5789i 0.633912i −0.948440 0.316956i \(-0.897339\pi\)
0.948440 0.316956i \(-0.102661\pi\)
\(770\) 18.1804 41.2419i 0.655176 1.48626i
\(771\) −3.44116 + 8.30769i −0.123930 + 0.299194i
\(772\) 2.67029 37.2079i 0.0961059 1.33914i
\(773\) 1.90792 14.4921i 0.0686229 0.521243i −0.922265 0.386557i \(-0.873664\pi\)
0.990888 0.134686i \(-0.0430025\pi\)
\(774\) −0.569985 1.52876i −0.0204877 0.0549501i
\(775\) 53.4606 + 14.3247i 1.92036 + 0.514560i
\(776\) −16.7914 + 13.5212i −0.602775 + 0.485383i
\(777\) −2.10150 14.4698i −0.0753908 0.519102i
\(778\) −0.400933 4.20418i −0.0143741 0.150727i
\(779\) −8.02790 + 10.4622i −0.287629 + 0.374846i
\(780\) −16.3292 + 0.968732i −0.584679 + 0.0346862i
\(781\) 6.36335 + 8.29287i 0.227698 + 0.296742i
\(782\) 12.5693 + 7.87017i 0.449477 + 0.281437i
\(783\) 56.1874i 2.00797i
\(784\) 10.3451 26.0188i 0.369469 0.929243i
\(785\) 71.5935i 2.55528i
\(786\) −10.1238 + 16.1686i −0.361105 + 0.576713i
\(787\) −13.1957 17.1970i −0.470378 0.613008i 0.496566 0.867999i \(-0.334594\pi\)
−0.966943 + 0.254991i \(0.917927\pi\)
\(788\) 18.8671 + 16.7539i 0.672114 + 0.596833i
\(789\) −20.7891 + 27.0929i −0.740112 + 0.964533i
\(790\) 39.4811 3.76513i 1.40468 0.133957i
\(791\) −3.15301 21.7100i −0.112108 0.771920i
\(792\) −8.82498 + 2.58774i −0.313582 + 0.0919513i
\(793\) 18.5358 + 4.96665i 0.658225 + 0.176371i
\(794\) 33.9805 12.6694i 1.20592 0.449619i
\(795\) −6.44696 + 48.9695i −0.228650 + 1.73677i
\(796\) −15.9854 18.4572i −0.566587 0.654199i
\(797\) 1.42273 3.43477i 0.0503956 0.121666i −0.896677 0.442686i \(-0.854026\pi\)
0.947072 + 0.321020i \(0.104026\pi\)
\(798\) 21.3288 + 9.40224i 0.755032 + 0.332836i
\(799\) 12.7415i 0.450760i
\(800\) −8.47788 + 46.8261i −0.299738 + 1.65555i
\(801\) 9.79963 + 5.65782i 0.346253 + 0.199909i
\(802\) 14.6543 + 15.7437i 0.517462 + 0.555929i
\(803\) −0.914084 6.94315i −0.0322573 0.245019i
\(804\) 37.8768 7.29057i 1.33581 0.257118i
\(805\) 29.1417 + 28.3753i 1.02711 + 1.00010i
\(806\) −11.2968 9.32977i −0.397914 0.328627i
\(807\) −4.20368 + 15.6884i −0.147977 + 0.552256i
\(808\) −16.9646 + 10.3320i −0.596814 + 0.363477i
\(809\) −17.9869 + 4.81957i −0.632385 + 0.169447i −0.560752 0.827984i \(-0.689488\pi\)
−0.0716333 + 0.997431i \(0.522821\pi\)
\(810\) −21.3374 + 15.1904i −0.749721 + 0.533736i
\(811\) 3.58160 1.48355i 0.125767 0.0520944i −0.318912 0.947784i \(-0.603318\pi\)
0.444679 + 0.895690i \(0.353318\pi\)
\(812\) −51.4748 + 10.6211i −1.80641 + 0.372727i
\(813\) 1.87366 4.52342i 0.0657121 0.158643i
\(814\) 15.3625 + 9.61914i 0.538456 + 0.337151i
\(815\) −18.0660 10.4304i −0.632824 0.365361i
\(816\) 12.1843 + 7.23732i 0.426536 + 0.253357i
\(817\) −2.56313 4.43947i −0.0896726 0.155317i
\(818\) 9.41960 + 17.7549i 0.329348 + 0.620785i
\(819\) 2.01153 3.59382i 0.0702885 0.125578i
\(820\) −18.3595 + 12.1036i −0.641140 + 0.422675i
\(821\) 3.68872 + 2.83046i 0.128737 + 0.0987836i 0.671123 0.741346i \(-0.265812\pi\)
−0.542386 + 0.840130i \(0.682479\pi\)
\(822\) 17.0832 + 7.80414i 0.595844 + 0.272201i
\(823\) −14.2218 53.0765i −0.495741 1.85013i −0.525841 0.850583i \(-0.676249\pi\)
0.0301008 0.999547i \(-0.490417\pi\)
\(824\) −3.58770 8.11803i −0.124983 0.282805i
\(825\) 27.7486 + 27.7486i 0.966083 + 0.966083i
\(826\) 7.44497 + 30.5150i 0.259043 + 1.06175i
\(827\) −27.3793 + 11.3409i −0.952072 + 0.394361i −0.804009 0.594617i \(-0.797304\pi\)
−0.148063 + 0.988978i \(0.547304\pi\)
\(828\) 0.594091 8.27808i 0.0206461 0.287683i
\(829\) 26.4531 + 34.4743i 0.918754 + 1.19734i 0.979955 + 0.199218i \(0.0638402\pi\)
−0.0612012 + 0.998125i \(0.519493\pi\)
\(830\) 9.80252 + 10.5312i 0.340250 + 0.365544i
\(831\) 4.27618 + 7.40657i 0.148339 + 0.256931i
\(832\) 7.19215 10.3425i 0.249343 0.358561i
\(833\) 4.07416 17.0053i 0.141161 0.589198i
\(834\) 15.4982 + 4.75380i 0.536660 + 0.164611i
\(835\) −19.6258 + 2.58379i −0.679179 + 0.0894156i
\(836\) −25.9938 + 12.6192i −0.899015 + 0.436443i
\(837\) −36.8987 4.85781i −1.27541 0.167910i
\(838\) 2.09586 12.4543i 0.0724004 0.430228i
\(839\) −24.0832 + 24.0832i −0.831445 + 0.831445i −0.987714 0.156270i \(-0.950053\pi\)
0.156270 + 0.987714i \(0.450053\pi\)
\(840\) 28.4759 + 26.4558i 0.982512 + 0.912812i
\(841\) 49.2566 + 49.2566i 1.69850 + 1.69850i
\(842\) −5.72407 + 4.07504i −0.197265 + 0.140435i
\(843\) 2.89454 21.9862i 0.0996931 0.757244i
\(844\) 14.1832 0.841422i 0.488207 0.0289629i
\(845\) −5.02901 38.1991i −0.173003 1.31409i
\(846\) 6.29899 3.34184i 0.216564 0.114895i
\(847\) −0.476832 0.0563232i −0.0163841 0.00193529i
\(848\) −26.5612 27.2276i −0.912114 0.934998i
\(849\) 30.1111 17.3847i 1.03341 0.596640i
\(850\) −1.06437 + 29.7002i −0.0365078 + 1.01871i
\(851\) −12.9771 + 9.95767i −0.444849 + 0.341344i
\(852\) −8.55384 + 2.84467i −0.293050 + 0.0974569i
\(853\) −3.25138 7.84953i −0.111325 0.268763i 0.858392 0.512995i \(-0.171464\pi\)
−0.969717 + 0.244232i \(0.921464\pi\)
\(854\) −21.9047 39.9914i −0.749562 1.36848i
\(855\) 11.2446 11.2446i 0.384556 0.384556i
\(856\) 28.5223 0.668505i 0.974871 0.0228490i
\(857\) 31.3802 8.40829i 1.07193 0.287222i 0.320642 0.947201i \(-0.396101\pi\)
0.751284 + 0.659979i \(0.229435\pi\)
\(858\) −3.62915 9.73376i −0.123897 0.332305i
\(859\) 11.0416 14.3896i 0.376733 0.490968i −0.566052 0.824370i \(-0.691530\pi\)
0.942785 + 0.333402i \(0.108196\pi\)
\(860\) −1.61571 8.39410i −0.0550951 0.286237i
\(861\) 0.150106 + 11.2645i 0.00511561 + 0.383893i
\(862\) 14.5886 + 4.47479i 0.496889 + 0.152412i
\(863\) −14.7087 + 8.49205i −0.500689 + 0.289073i −0.728998 0.684516i \(-0.760014\pi\)
0.228309 + 0.973589i \(0.426680\pi\)
\(864\) 1.54211 31.9624i 0.0524638 1.08738i
\(865\) −42.1280 + 72.9678i −1.43239 + 2.48098i
\(866\) −10.8356 47.1310i −0.368210 1.60158i
\(867\) −14.0983 5.83972i −0.478804 0.198327i
\(868\) 2.52459 + 34.7222i 0.0856902 + 1.17855i
\(869\) 9.63855 + 23.2695i 0.326966 + 0.789365i
\(870\) 12.1079 71.9495i 0.410497 2.43931i
\(871\) −5.54210 20.6834i −0.187787 0.700831i
\(872\) 6.96507 28.6646i 0.235867 0.970705i
\(873\) 7.27806 + 1.95015i 0.246325 + 0.0660026i
\(874\) −2.47552 25.9583i −0.0837358 0.878053i
\(875\) −8.13127 + 32.0485i −0.274887 + 1.08344i
\(876\) 5.91588 + 1.21488i 0.199879 + 0.0410471i
\(877\) −1.78979 + 0.235630i −0.0604368 + 0.00795665i −0.160684 0.987006i \(-0.551370\pi\)
0.100247 + 0.994963i \(0.468037\pi\)
\(878\) −22.1098 0.792357i −0.746171 0.0267408i
\(879\) 6.72950 11.6558i 0.226980 0.393142i
\(880\) −47.8453 + 5.69691i −1.61287 + 0.192043i
\(881\) −21.0674 −0.709777 −0.354889 0.934909i \(-0.615481\pi\)
−0.354889 + 0.934909i \(0.615481\pi\)
\(882\) −9.47548 + 2.44602i −0.319056 + 0.0823618i
\(883\) −8.63293 3.57588i −0.290521 0.120338i 0.232663 0.972557i \(-0.425256\pi\)
−0.523184 + 0.852220i \(0.675256\pi\)
\(884\) 3.52326 7.03428i 0.118500 0.236588i
\(885\) −43.2296 5.69128i −1.45315 0.191310i
\(886\) 2.66805 5.84033i 0.0896350 0.196210i
\(887\) −11.3076 + 42.2005i −0.379671 + 1.41695i 0.466726 + 0.884402i \(0.345433\pi\)
−0.846398 + 0.532551i \(0.821233\pi\)
\(888\) −12.1747 + 9.80363i −0.408556 + 0.328988i
\(889\) 4.76007 + 32.7754i 0.159648 + 1.09925i
\(890\) 45.7118 + 37.7522i 1.53226 + 1.26546i
\(891\) −13.1964 10.1260i −0.442096 0.339233i
\(892\) 16.8682 8.18900i 0.564791 0.274188i
\(893\) 17.7742 13.6386i 0.594790 0.456398i
\(894\) 7.03255 + 30.5890i 0.235204 + 1.02305i
\(895\) 64.7455 2.16420
\(896\) −29.5732 + 4.62908i −0.987970 + 0.154647i
\(897\) 9.37484 0.313017
\(898\) 0.419453 + 1.82447i 0.0139973 + 0.0608833i
\(899\) 51.8452 39.7822i 1.72913 1.32681i
\(900\) 14.9620 7.26359i 0.498735 0.242120i
\(901\) −18.8461 14.4611i −0.627855 0.481770i
\(902\) −10.7677 8.89277i −0.358525 0.296097i
\(903\) −4.06783 1.62179i −0.135369 0.0539699i
\(904\) −18.2665 + 14.7090i −0.607534 + 0.489215i
\(905\) 22.1893 82.8117i 0.737599 2.75276i
\(906\) 2.96597 6.49248i 0.0985378 0.215698i
\(907\) 13.1929 + 1.73688i 0.438064 + 0.0576722i 0.346333 0.938112i \(-0.387427\pi\)
0.0917310 + 0.995784i \(0.470760\pi\)
\(908\) 2.78129 5.55292i 0.0923003 0.184280i
\(909\) 6.41383 + 2.65669i 0.212733 + 0.0881170i
\(910\) 13.5175 16.8190i 0.448100 0.557544i
\(911\) 28.0678 0.929928 0.464964 0.885329i \(-0.346067\pi\)
0.464964 + 0.885329i \(0.346067\pi\)
\(912\) −2.94623 24.7438i −0.0975595 0.819351i
\(913\) −4.56844 + 7.91276i −0.151193 + 0.261874i
\(914\) −30.0598 1.07726i −0.994288 0.0356326i
\(915\) 62.7556 8.26194i 2.07464 0.273131i
\(916\) −6.33554 1.30106i −0.209332 0.0429883i
\(917\) −6.83620 24.2175i −0.225751 0.799734i
\(918\) −1.89720 19.8941i −0.0626171 0.656603i
\(919\) −42.1715 11.2998i −1.39111 0.372746i −0.515965 0.856610i \(-0.672566\pi\)
−0.875144 + 0.483863i \(0.839233\pi\)
\(920\) 10.2669 42.2532i 0.338490 1.39305i
\(921\) −5.80092 21.6493i −0.191147 0.713370i
\(922\) −7.51586 + 44.6618i −0.247522 + 1.47086i
\(923\) 1.91507 + 4.62339i 0.0630353 + 0.152181i
\(924\) −10.7594 + 22.2158i −0.353958 + 0.730847i
\(925\) −30.2848 12.5444i −0.995758 0.412456i
\(926\) −3.52010 15.3112i −0.115678 0.503156i
\(927\) −1.55100 + 2.68642i −0.0509417 + 0.0882335i
\(928\) 37.7701 + 41.5995i 1.23986 + 1.36557i
\(929\) −25.5550 + 14.7542i −0.838434 + 0.484070i −0.856731 0.515763i \(-0.827509\pi\)
0.0182979 + 0.999833i \(0.494175\pi\)
\(930\) −46.2030 14.1719i −1.51506 0.464716i
\(931\) −28.0832 + 12.5193i −0.920389 + 0.410302i
\(932\) −2.70098 14.0325i −0.0884736 0.459649i
\(933\) 17.5986 22.9349i 0.576151 0.750855i
\(934\) 4.06092 + 10.8918i 0.132878 + 0.356391i
\(935\) −29.0660 + 7.78822i −0.950561 + 0.254702i
\(936\) −4.40162 + 0.103165i −0.143871 + 0.00337206i
\(937\) 18.1215 18.1215i 0.592003 0.592003i −0.346169 0.938172i \(-0.612518\pi\)
0.938172 + 0.346169i \(0.112518\pi\)
\(938\) −26.4251 + 43.4804i −0.862809 + 1.41969i
\(939\) −2.61939 6.32376i −0.0854804 0.206368i
\(940\) 35.4501 11.7893i 1.15626 0.384525i
\(941\) 3.40535 2.61301i 0.111011 0.0851818i −0.551764 0.834000i \(-0.686045\pi\)
0.662775 + 0.748818i \(0.269378\pi\)
\(942\) −1.40426 + 39.1843i −0.0457533 + 1.27669i
\(943\) 10.9143 6.30136i 0.355418 0.205200i
\(944\) 24.0361 23.4478i 0.782308 0.763162i
\(945\) 6.42961 54.4330i 0.209155 1.77071i
\(946\) 4.79553 2.54420i 0.155916 0.0827191i
\(947\) 4.12661 + 31.3447i 0.134097 + 1.01857i 0.917692 + 0.397293i \(0.130050\pi\)
−0.783595 + 0.621272i \(0.786616\pi\)
\(948\) −21.6826 + 1.28632i −0.704217 + 0.0417778i
\(949\) 0.437615 3.32402i 0.0142056 0.107902i
\(950\) 42.5707 30.3066i 1.38118 0.983276i
\(951\) −29.3841 29.3841i −0.952843 0.952843i
\(952\) −17.8669 + 5.49866i −0.579069 + 0.178213i
\(953\) −42.9433 + 42.9433i −1.39107 + 1.39107i −0.568131 + 0.822938i \(0.692333\pi\)
−0.822938 + 0.568131i \(0.807667\pi\)
\(954\) −2.20617 + 13.1098i −0.0714275 + 0.424446i
\(955\) 72.3682 + 9.52746i 2.34178 + 0.308301i
\(956\) 14.8903 7.22878i 0.481588 0.233796i
\(957\) 45.9385 6.04792i 1.48498 0.195501i
\(958\) −10.8136 3.31689i −0.349373 0.107164i
\(959\) −22.7603 + 9.78495i −0.734970 + 0.315972i
\(960\) 8.86237 40.5964i 0.286032 1.31024i
\(961\) −6.14293 10.6399i −0.198159 0.343222i
\(962\) 5.91227 + 6.35178i 0.190619 + 0.204789i
\(963\) −6.07019 7.91082i −0.195609 0.254923i
\(964\) −2.63066 + 36.6556i −0.0847277 + 1.18060i
\(965\) −63.1085 + 26.1404i −2.03154 + 0.841490i
\(966\) −15.3932 16.1019i −0.495268 0.518069i
\(967\) −8.45895 8.45895i −0.272022 0.272022i 0.557892 0.829914i \(-0.311610\pi\)
−0.829914 + 0.557892i \(0.811610\pi\)
\(968\) 0.207489 + 0.469493i 0.00666894 + 0.0150901i
\(969\) −4.02778 15.0319i −0.129391 0.482894i
\(970\) 35.9074 + 16.4037i 1.15292 + 0.526690i
\(971\) −10.8563 8.33035i −0.348396 0.267334i 0.419707 0.907659i \(-0.362133\pi\)
−0.768103 + 0.640326i \(0.778799\pi\)
\(972\) −16.3606 + 10.7858i −0.524768 + 0.345956i
\(973\) −18.3749 + 10.9377i −0.589071 + 0.350648i
\(974\) −12.7694 24.0689i −0.409159 0.771218i
\(975\) 9.39361 + 16.2702i 0.300836 + 0.521064i
\(976\) −24.8940 + 41.9099i −0.796836 + 1.34150i
\(977\) 1.86570 + 1.07716i 0.0596890 + 0.0344615i 0.529548 0.848280i \(-0.322362\pi\)
−0.469859 + 0.882742i \(0.655695\pi\)
\(978\) 9.68324 + 6.06309i 0.309636 + 0.193876i
\(979\) −14.4081 + 34.7842i −0.460484 + 1.11171i
\(980\) −51.0829 + 4.39913i −1.63178 + 0.140525i
\(981\) −9.52508 + 3.94542i −0.304112 + 0.125968i
\(982\) 7.32552 5.21513i 0.233767 0.166421i
\(983\) 37.8069 10.1303i 1.20585 0.323107i 0.400720 0.916201i \(-0.368760\pi\)
0.805134 + 0.593093i \(0.202093\pi\)
\(984\) 10.2859 6.26439i 0.327901 0.199701i
\(985\) 11.9584 44.6294i 0.381026 1.42201i
\(986\) 27.0562 + 22.3451i 0.861646 + 0.711612i
\(987\) 4.70676 18.5512i 0.149818 0.590490i
\(988\) −13.5841 + 2.61467i −0.432167 + 0.0831839i
\(989\) 0.639452 + 4.85712i 0.0203334 + 0.154447i
\(990\) 11.4737 + 12.3267i 0.364659 + 0.391767i
\(991\) −37.5258 21.6655i −1.19205 0.688229i −0.233277 0.972410i \(-0.574945\pi\)
−0.958770 + 0.284182i \(0.908278\pi\)
\(992\) 30.5842 21.2074i 0.971051 0.673334i
\(993\) 34.0935i 1.08193i
\(994\) 4.79647 10.8807i 0.152135 0.345115i
\(995\) −17.1103 + 41.3080i −0.542434 + 1.30955i
\(996\) −5.15852 5.95619i −0.163454 0.188729i
\(997\) −2.07774 + 15.7820i −0.0658028 + 0.499822i 0.926529 + 0.376222i \(0.122777\pi\)
−0.992332 + 0.123599i \(0.960556\pi\)
\(998\) 15.0634 5.61628i 0.476825 0.177780i
\(999\) 21.2915 + 5.70503i 0.673632 + 0.180499i
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 224.2.be.a.3.17 240
4.3 odd 2 896.2.bi.a.815.22 240
7.5 odd 6 inner 224.2.be.a.131.24 yes 240
28.19 even 6 896.2.bi.a.47.9 240
32.11 odd 8 inner 224.2.be.a.171.24 yes 240
32.21 even 8 896.2.bi.a.591.9 240
224.75 even 24 inner 224.2.be.a.75.17 yes 240
224.117 odd 24 896.2.bi.a.719.22 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
224.2.be.a.3.17 240 1.1 even 1 trivial
224.2.be.a.75.17 yes 240 224.75 even 24 inner
224.2.be.a.131.24 yes 240 7.5 odd 6 inner
224.2.be.a.171.24 yes 240 32.11 odd 8 inner
896.2.bi.a.47.9 240 28.19 even 6
896.2.bi.a.591.9 240 32.21 even 8
896.2.bi.a.719.22 240 224.117 odd 24
896.2.bi.a.815.22 240 4.3 odd 2