Properties

Label 441.2.z.a.142.16
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(4,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.16
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.489086 + 1.24617i) q^{2} +(-0.370108 - 1.69205i) q^{3} +(0.152367 + 0.141376i) q^{4} +(-1.59932 + 0.770194i) q^{5} +(2.28959 + 0.366338i) q^{6} +(1.91094 + 1.82984i) q^{7} +(-2.66297 + 1.28242i) q^{8} +(-2.72604 + 1.25248i) q^{9} +O(q^{10})\) \(q+(-0.489086 + 1.24617i) q^{2} +(-0.370108 - 1.69205i) q^{3} +(0.152367 + 0.141376i) q^{4} +(-1.59932 + 0.770194i) q^{5} +(2.28959 + 0.366338i) q^{6} +(1.91094 + 1.82984i) q^{7} +(-2.66297 + 1.28242i) q^{8} +(-2.72604 + 1.25248i) q^{9} +(-0.177586 - 2.36972i) q^{10} +(-1.93844 - 2.43073i) q^{11} +(0.182822 - 0.310136i) q^{12} +(-0.697617 + 1.77750i) q^{13} +(-3.21490 + 1.48641i) q^{14} +(1.89513 + 2.42108i) q^{15} +(-0.264626 - 3.53119i) q^{16} +(1.30790 - 1.21355i) q^{17} +(-0.227535 - 4.00968i) q^{18} +(-2.00146 + 3.46663i) q^{19} +(-0.352571 - 0.108754i) q^{20} +(2.38891 - 3.91064i) q^{21} +(3.97717 - 1.22679i) q^{22} +(-1.48713 + 6.51554i) q^{23} +(3.15550 + 4.03124i) q^{24} +(-1.15281 + 1.44558i) q^{25} +(-1.87387 - 1.73870i) q^{26} +(3.12818 + 4.14903i) q^{27} +(0.0324699 + 0.548968i) q^{28} +(-8.28375 - 2.55520i) q^{29} +(-3.94395 + 1.17754i) q^{30} +(-1.17977 + 2.04343i) q^{31} +(-1.11884 - 0.345116i) q^{32} +(-3.39547 + 4.17956i) q^{33} +(0.872618 + 2.22339i) q^{34} +(-4.46554 - 1.45470i) q^{35} +(-0.592429 - 0.194560i) q^{36} +(-3.32469 - 1.02553i) q^{37} +(-3.34113 - 4.18965i) q^{38} +(3.26580 + 0.522534i) q^{39} +(3.27124 - 4.10201i) q^{40} +(9.54953 + 6.51076i) q^{41} +(3.70494 + 4.88963i) q^{42} +(-5.37684 + 3.66587i) q^{43} +(0.0482920 - 0.644412i) q^{44} +(3.39517 - 4.10270i) q^{45} +(-7.39214 - 5.03988i) q^{46} +(2.35535 - 6.00134i) q^{47} +(-5.87700 + 1.75468i) q^{48} +(0.303404 + 6.99342i) q^{49} +(-1.23761 - 2.14361i) q^{50} +(-2.53745 - 1.76388i) q^{51} +(-0.357589 + 0.172206i) q^{52} +(5.96378 - 1.83958i) q^{53} +(-6.70035 + 1.86901i) q^{54} +(4.97232 + 2.39455i) q^{55} +(-7.43541 - 2.42217i) q^{56} +(6.60646 + 2.10354i) q^{57} +(7.23568 - 9.07326i) q^{58} +(-4.76254 + 3.24704i) q^{59} +(-0.0535271 + 0.636817i) q^{60} +(5.52212 - 5.12378i) q^{61} +(-1.96945 - 2.46961i) q^{62} +(-7.50114 - 2.59479i) q^{63} +(5.39295 - 6.76255i) q^{64} +(-0.253303 - 3.38010i) q^{65} +(-3.54777 - 6.27550i) q^{66} +(6.50009 - 11.2585i) q^{67} +0.370848 q^{68} +(11.5750 + 0.104839i) q^{69} +(3.99684 - 4.85336i) q^{70} +(-2.35944 + 10.3374i) q^{71} +(5.65317 - 6.83125i) q^{72} +(2.62074 + 0.395012i) q^{73} +(2.90404 - 3.64156i) q^{74} +(2.87265 + 1.41559i) q^{75} +(-0.795056 + 0.245242i) q^{76} +(0.743583 - 8.19201i) q^{77} +(-2.24843 + 3.81419i) q^{78} +(-4.61010 - 7.98493i) q^{79} +(3.14292 + 5.44370i) q^{80} +(5.86259 - 6.82862i) q^{81} +(-12.7841 + 8.71603i) q^{82} +(0.832488 + 2.12114i) q^{83} +(0.916862 - 0.258118i) q^{84} +(-1.15708 + 2.94820i) q^{85} +(-1.93856 - 8.49339i) q^{86} +(-1.25763 + 14.9622i) q^{87} +(8.27923 + 3.98707i) q^{88} +(5.06502 + 12.9055i) q^{89} +(3.45213 + 6.23753i) q^{90} +(-4.58564 + 2.12017i) q^{91} +(-1.14773 + 0.782509i) q^{92} +(3.89422 + 1.23994i) q^{93} +(6.32672 + 5.87034i) q^{94} +(0.531006 - 7.08579i) q^{95} +(-0.169861 + 2.02086i) q^{96} +(8.43468 - 14.6093i) q^{97} +(-8.86339 - 3.04229i) q^{98} +(8.32870 + 4.19840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.489086 + 1.24617i −0.345836 + 0.881176i 0.647087 + 0.762416i \(0.275987\pi\)
−0.992923 + 0.118760i \(0.962108\pi\)
\(3\) −0.370108 1.69205i −0.213682 0.976903i
\(4\) 0.152367 + 0.141376i 0.0761835 + 0.0706880i
\(5\) −1.59932 + 0.770194i −0.715239 + 0.344441i −0.755860 0.654734i \(-0.772781\pi\)
0.0406204 + 0.999175i \(0.487067\pi\)
\(6\) 2.28959 + 0.366338i 0.934723 + 0.149557i
\(7\) 1.91094 + 1.82984i 0.722268 + 0.691613i
\(8\) −2.66297 + 1.28242i −0.941503 + 0.453404i
\(9\) −2.72604 + 1.25248i −0.908680 + 0.417493i
\(10\) −0.177586 2.36972i −0.0561577 0.749372i
\(11\) −1.93844 2.43073i −0.584462 0.732892i 0.398405 0.917210i \(-0.369564\pi\)
−0.982867 + 0.184318i \(0.940992\pi\)
\(12\) 0.182822 0.310136i 0.0527763 0.0895287i
\(13\) −0.697617 + 1.77750i −0.193484 + 0.492989i −0.994387 0.105805i \(-0.966258\pi\)
0.800903 + 0.598794i \(0.204353\pi\)
\(14\) −3.21490 + 1.48641i −0.859219 + 0.397261i
\(15\) 1.89513 + 2.42108i 0.489319 + 0.625119i
\(16\) −0.264626 3.53119i −0.0661565 0.882797i
\(17\) 1.30790 1.21355i 0.317212 0.294329i −0.505455 0.862853i \(-0.668676\pi\)
0.822667 + 0.568523i \(0.192485\pi\)
\(18\) −0.227535 4.00968i −0.0536305 0.945091i
\(19\) −2.00146 + 3.46663i −0.459167 + 0.795301i −0.998917 0.0465247i \(-0.985185\pi\)
0.539750 + 0.841825i \(0.318519\pi\)
\(20\) −0.352571 0.108754i −0.0788373 0.0243181i
\(21\) 2.38891 3.91064i 0.521303 0.853372i
\(22\) 3.97717 1.22679i 0.847934 0.261553i
\(23\) −1.48713 + 6.51554i −0.310088 + 1.35858i 0.544275 + 0.838907i \(0.316805\pi\)
−0.854363 + 0.519677i \(0.826052\pi\)
\(24\) 3.15550 + 4.03124i 0.644114 + 0.822873i
\(25\) −1.15281 + 1.44558i −0.230562 + 0.289116i
\(26\) −1.87387 1.73870i −0.367497 0.340987i
\(27\) 3.12818 + 4.14903i 0.602019 + 0.798482i
\(28\) 0.0324699 + 0.548968i 0.00613624 + 0.103745i
\(29\) −8.28375 2.55520i −1.53825 0.474489i −0.594210 0.804310i \(-0.702535\pi\)
−0.944043 + 0.329821i \(0.893012\pi\)
\(30\) −3.94395 + 1.17754i −0.720064 + 0.214988i
\(31\) −1.17977 + 2.04343i −0.211894 + 0.367010i −0.952307 0.305141i \(-0.901296\pi\)
0.740414 + 0.672152i \(0.234630\pi\)
\(32\) −1.11884 0.345116i −0.197785 0.0610085i
\(33\) −3.39547 + 4.17956i −0.591076 + 0.727568i
\(34\) 0.872618 + 2.22339i 0.149653 + 0.381309i
\(35\) −4.46554 1.45470i −0.754815 0.245890i
\(36\) −0.592429 0.194560i −0.0987382 0.0324267i
\(37\) −3.32469 1.02553i −0.546575 0.168596i 0.00915617 0.999958i \(-0.497085\pi\)
−0.555731 + 0.831362i \(0.687562\pi\)
\(38\) −3.34113 4.18965i −0.542003 0.679650i
\(39\) 3.26580 + 0.522534i 0.522947 + 0.0836723i
\(40\) 3.27124 4.10201i 0.517229 0.648585i
\(41\) 9.54953 + 6.51076i 1.49139 + 1.01681i 0.988291 + 0.152579i \(0.0487580\pi\)
0.503096 + 0.864231i \(0.332194\pi\)
\(42\) 3.70494 + 4.88963i 0.571685 + 0.754486i
\(43\) −5.37684 + 3.66587i −0.819961 + 0.559040i −0.899059 0.437827i \(-0.855748\pi\)
0.0790986 + 0.996867i \(0.474796\pi\)
\(44\) 0.0482920 0.644412i 0.00728029 0.0971487i
\(45\) 3.39517 4.10270i 0.506122 0.611594i
\(46\) −7.39214 5.03988i −1.08991 0.743089i
\(47\) 2.35535 6.00134i 0.343563 0.875385i −0.649772 0.760129i \(-0.725136\pi\)
0.993336 0.115256i \(-0.0367690\pi\)
\(48\) −5.87700 + 1.75468i −0.848271 + 0.253266i
\(49\) 0.303404 + 6.99342i 0.0433434 + 0.999060i
\(50\) −1.23761 2.14361i −0.175025 0.303152i
\(51\) −2.53745 1.76388i −0.355314 0.246992i
\(52\) −0.357589 + 0.172206i −0.0495887 + 0.0238807i
\(53\) 5.96378 1.83958i 0.819188 0.252686i 0.143290 0.989681i \(-0.454232\pi\)
0.675898 + 0.736995i \(0.263756\pi\)
\(54\) −6.70035 + 1.86901i −0.911803 + 0.254341i
\(55\) 4.97232 + 2.39455i 0.670468 + 0.322880i
\(56\) −7.43541 2.42217i −0.993598 0.323676i
\(57\) 6.60646 + 2.10354i 0.875047 + 0.278620i
\(58\) 7.23568 9.07326i 0.950091 1.19138i
\(59\) −4.76254 + 3.24704i −0.620029 + 0.422729i −0.832178 0.554508i \(-0.812906\pi\)
0.212149 + 0.977237i \(0.431954\pi\)
\(60\) −0.0535271 + 0.636817i −0.00691032 + 0.0822128i
\(61\) 5.52212 5.12378i 0.707035 0.656033i −0.242335 0.970193i \(-0.577913\pi\)
0.949370 + 0.314160i \(0.101723\pi\)
\(62\) −1.96945 2.46961i −0.250120 0.313641i
\(63\) −7.50114 2.59479i −0.945055 0.326913i
\(64\) 5.39295 6.76255i 0.674119 0.845318i
\(65\) −0.253303 3.38010i −0.0314184 0.419249i
\(66\) −3.54777 6.27550i −0.436700 0.772461i
\(67\) 6.50009 11.2585i 0.794113 1.37544i −0.129289 0.991607i \(-0.541269\pi\)
0.923401 0.383836i \(-0.125397\pi\)
\(68\) 0.370848 0.0449719
\(69\) 11.5750 + 0.104839i 1.39347 + 0.0126211i
\(70\) 3.99684 4.85336i 0.477714 0.580087i
\(71\) −2.35944 + 10.3374i −0.280014 + 1.22682i 0.617761 + 0.786366i \(0.288040\pi\)
−0.897775 + 0.440455i \(0.854817\pi\)
\(72\) 5.65317 6.83125i 0.666232 0.805070i
\(73\) 2.62074 + 0.395012i 0.306734 + 0.0462327i 0.300606 0.953749i \(-0.402811\pi\)
0.00612829 + 0.999981i \(0.498049\pi\)
\(74\) 2.90404 3.64156i 0.337588 0.423322i
\(75\) 2.87265 + 1.41559i 0.331705 + 0.163458i
\(76\) −0.795056 + 0.245242i −0.0911992 + 0.0281312i
\(77\) 0.743583 8.19201i 0.0847391 0.933566i
\(78\) −2.24843 + 3.81419i −0.254584 + 0.431871i
\(79\) −4.61010 7.98493i −0.518677 0.898375i −0.999764 0.0217023i \(-0.993091\pi\)
0.481087 0.876673i \(-0.340242\pi\)
\(80\) 3.14292 + 5.44370i 0.351389 + 0.608624i
\(81\) 5.86259 6.82862i 0.651399 0.758735i
\(82\) −12.7841 + 8.71603i −1.41176 + 0.962524i
\(83\) 0.832488 + 2.12114i 0.0913774 + 0.232826i 0.969255 0.246060i \(-0.0791360\pi\)
−0.877877 + 0.478886i \(0.841041\pi\)
\(84\) 0.916862 0.258118i 0.100038 0.0281630i
\(85\) −1.15708 + 2.94820i −0.125503 + 0.319777i
\(86\) −1.93856 8.49339i −0.209040 0.915866i
\(87\) −1.25763 + 14.9622i −0.134832 + 1.60411i
\(88\) 8.27923 + 3.98707i 0.882569 + 0.425023i
\(89\) 5.06502 + 12.9055i 0.536891 + 1.36798i 0.899861 + 0.436176i \(0.143667\pi\)
−0.362970 + 0.931801i \(0.618237\pi\)
\(90\) 3.45213 + 6.23753i 0.363887 + 0.657494i
\(91\) −4.58564 + 2.12017i −0.480705 + 0.222255i
\(92\) −1.14773 + 0.782509i −0.119659 + 0.0815822i
\(93\) 3.89422 + 1.23994i 0.403812 + 0.128576i
\(94\) 6.32672 + 5.87034i 0.652552 + 0.605480i
\(95\) 0.531006 7.08579i 0.0544801 0.726986i
\(96\) −0.169861 + 2.02086i −0.0173364 + 0.206253i
\(97\) 8.43468 14.6093i 0.856412 1.48335i −0.0189178 0.999821i \(-0.506022\pi\)
0.875329 0.483527i \(-0.160645\pi\)
\(98\) −8.86339 3.04229i −0.895337 0.307318i
\(99\) 8.32870 + 4.19840i 0.837066 + 0.421955i
\(100\) −0.380020 + 0.0572789i −0.0380020 + 0.00572789i
\(101\) −5.81267 + 2.79923i −0.578382 + 0.278534i −0.700117 0.714029i \(-0.746869\pi\)
0.121735 + 0.992563i \(0.461154\pi\)
\(102\) 3.43912 2.29941i 0.340524 0.227675i
\(103\) −0.623996 + 0.300500i −0.0614841 + 0.0296092i −0.464373 0.885640i \(-0.653720\pi\)
0.402889 + 0.915249i \(0.368006\pi\)
\(104\) −0.421766 5.62807i −0.0413575 0.551878i
\(105\) −0.808692 + 8.09430i −0.0789203 + 0.789923i
\(106\) −0.624367 + 8.33160i −0.0606439 + 0.809237i
\(107\) 3.37177 + 8.59113i 0.325961 + 0.830536i 0.996094 + 0.0882949i \(0.0281418\pi\)
−0.670133 + 0.742241i \(0.733763\pi\)
\(108\) −0.109942 + 1.07443i −0.0105791 + 0.103387i
\(109\) −2.55684 + 6.51473i −0.244901 + 0.623998i −0.999481 0.0322101i \(-0.989745\pi\)
0.754580 + 0.656208i \(0.227841\pi\)
\(110\) −5.41591 + 5.02523i −0.516386 + 0.479137i
\(111\) −0.504751 + 6.00508i −0.0479089 + 0.569977i
\(112\) 5.95581 7.23212i 0.562771 0.683371i
\(113\) 6.20553 + 0.935334i 0.583767 + 0.0879888i 0.434285 0.900776i \(-0.357001\pi\)
0.149483 + 0.988764i \(0.452239\pi\)
\(114\) −5.85250 + 7.20397i −0.548136 + 0.674714i
\(115\) −2.63983 11.5658i −0.246165 1.07852i
\(116\) −0.900927 1.56045i −0.0836490 0.144884i
\(117\) −0.324549 5.71928i −0.0300046 0.528748i
\(118\) −1.71708 7.52302i −0.158070 0.692550i
\(119\) 4.71992 + 0.0742100i 0.432674 + 0.00680282i
\(120\) −8.15150 4.01691i −0.744127 0.366692i
\(121\) 0.296846 1.30057i 0.0269860 0.118234i
\(122\) 3.68431 + 9.38748i 0.333562 + 0.849902i
\(123\) 7.48215 18.5679i 0.674643 1.67421i
\(124\) −0.468650 + 0.144559i −0.0420860 + 0.0129818i
\(125\) 2.70534 11.8529i 0.241973 1.06015i
\(126\) 6.90225 8.07862i 0.614902 0.719701i
\(127\) −1.99047 8.72083i −0.176626 0.773848i −0.983173 0.182678i \(-0.941523\pi\)
0.806547 0.591170i \(-0.201334\pi\)
\(128\) 4.61881 + 8.00002i 0.408249 + 0.707109i
\(129\) 8.19283 + 7.74110i 0.721338 + 0.681566i
\(130\) 4.33607 + 1.33750i 0.380298 + 0.117306i
\(131\) 2.81830 + 1.35722i 0.246236 + 0.118581i 0.552931 0.833227i \(-0.313509\pi\)
−0.306696 + 0.951808i \(0.599223\pi\)
\(132\) −1.10825 + 0.156790i −0.0964606 + 0.0136468i
\(133\) −10.1681 + 2.96219i −0.881682 + 0.256855i
\(134\) 10.8509 + 13.6066i 0.937375 + 1.17543i
\(135\) −8.19854 4.22634i −0.705618 0.363746i
\(136\) −1.92661 + 4.90893i −0.165206 + 0.420937i
\(137\) 2.01972 + 0.972647i 0.172556 + 0.0830988i 0.518168 0.855279i \(-0.326614\pi\)
−0.345612 + 0.938378i \(0.612328\pi\)
\(138\) −5.79181 + 14.3731i −0.493032 + 1.22352i
\(139\) 15.8649 + 10.8165i 1.34564 + 0.917444i 0.999783 0.0208427i \(-0.00663492\pi\)
0.345860 + 0.938286i \(0.387587\pi\)
\(140\) −0.474742 0.852970i −0.0401230 0.0720891i
\(141\) −11.0263 1.76422i −0.928580 0.148574i
\(142\) −11.7282 7.99613i −0.984206 0.671020i
\(143\) 5.67290 1.74986i 0.474392 0.146331i
\(144\) 5.14412 + 9.29473i 0.428677 + 0.774560i
\(145\) 15.2164 2.29350i 1.26365 0.190465i
\(146\) −1.77402 + 3.07269i −0.146819 + 0.254298i
\(147\) 11.7209 3.10169i 0.966724 0.255823i
\(148\) −0.361587 0.626288i −0.0297223 0.0514805i
\(149\) 2.59527 + 3.25437i 0.212613 + 0.266608i 0.876690 0.481056i \(-0.159747\pi\)
−0.664077 + 0.747664i \(0.731175\pi\)
\(150\) −3.16904 + 2.88747i −0.258751 + 0.235761i
\(151\) −1.69994 + 7.44791i −0.138339 + 0.606103i 0.857461 + 0.514549i \(0.172041\pi\)
−0.995800 + 0.0915540i \(0.970817\pi\)
\(152\) 0.884158 11.7983i 0.0717147 0.956966i
\(153\) −2.04543 + 4.94631i −0.165363 + 0.399885i
\(154\) 9.84496 + 4.93323i 0.793330 + 0.397531i
\(155\) 0.313005 4.17676i 0.0251411 0.335485i
\(156\) 0.423727 + 0.541323i 0.0339253 + 0.0433405i
\(157\) −11.8781 + 8.09834i −0.947974 + 0.646318i −0.935396 0.353603i \(-0.884956\pi\)
−0.0125788 + 0.999921i \(0.504004\pi\)
\(158\) 12.2053 1.83966i 0.971004 0.146355i
\(159\) −5.31990 9.41014i −0.421895 0.746273i
\(160\) 2.05519 0.309770i 0.162477 0.0244895i
\(161\) −14.7642 + 9.72962i −1.16358 + 0.766802i
\(162\) 5.64231 + 10.6456i 0.443302 + 0.836395i
\(163\) 9.98420 6.80711i 0.782023 0.533174i −0.105235 0.994447i \(-0.533560\pi\)
0.887258 + 0.461273i \(0.152607\pi\)
\(164\) 0.534569 + 2.34210i 0.0417428 + 0.182887i
\(165\) 2.21138 9.29964i 0.172156 0.723976i
\(166\) −3.05047 −0.236762
\(167\) 14.3081 13.2760i 1.10719 1.02732i 0.107741 0.994179i \(-0.465638\pi\)
0.999451 0.0331451i \(-0.0105523\pi\)
\(168\) −1.34652 + 13.4775i −0.103886 + 1.03981i
\(169\) 6.85684 + 6.36222i 0.527449 + 0.489401i
\(170\) −3.10804 2.88384i −0.238376 0.221181i
\(171\) 1.11418 11.9570i 0.0852034 0.914373i
\(172\) −1.33752 0.201599i −0.101985 0.0153717i
\(173\) 13.8001 4.25677i 1.04920 0.323636i 0.278237 0.960512i \(-0.410250\pi\)
0.770966 + 0.636876i \(0.219774\pi\)
\(174\) −18.0304 8.88502i −1.36688 0.673572i
\(175\) −4.84813 + 0.652964i −0.366484 + 0.0493595i
\(176\) −8.07040 + 7.48823i −0.608329 + 0.564447i
\(177\) 7.25680 + 6.85668i 0.545454 + 0.515379i
\(178\) −18.5596 −1.39110
\(179\) −15.1518 + 14.0588i −1.13250 + 1.05080i −0.134290 + 0.990942i \(0.542875\pi\)
−0.998207 + 0.0598608i \(0.980934\pi\)
\(180\) 1.09734 0.145121i 0.0817905 0.0108167i
\(181\) −5.28681 + 6.62945i −0.392965 + 0.492763i −0.938478 0.345340i \(-0.887764\pi\)
0.545512 + 0.838103i \(0.316335\pi\)
\(182\) −0.399329 6.75143i −0.0296002 0.500450i
\(183\) −10.7135 7.44733i −0.791961 0.550523i
\(184\) −4.39547 19.2578i −0.324039 1.41971i
\(185\) 6.10711 0.920498i 0.449003 0.0676764i
\(186\) −3.44979 + 4.24642i −0.252951 + 0.311363i
\(187\) −5.48509 0.826745i −0.401110 0.0604576i
\(188\) 1.20732 0.581416i 0.0880531 0.0424041i
\(189\) −1.61427 + 13.6526i −0.117421 + 0.993082i
\(190\) 8.57039 + 4.12728i 0.621762 + 0.299425i
\(191\) −11.3859 7.76276i −0.823853 0.561694i 0.0763915 0.997078i \(-0.475660\pi\)
−0.900245 + 0.435384i \(0.856612\pi\)
\(192\) −13.4385 6.62225i −0.969841 0.477920i
\(193\) −0.872782 + 11.6465i −0.0628242 + 0.838331i 0.873417 + 0.486973i \(0.161899\pi\)
−0.936241 + 0.351358i \(0.885720\pi\)
\(194\) 14.0804 + 17.6562i 1.01091 + 1.26764i
\(195\) −5.62553 + 1.67960i −0.402853 + 0.120279i
\(196\) −0.942473 + 1.10846i −0.0673195 + 0.0791758i
\(197\) −13.0812 −0.931999 −0.465999 0.884785i \(-0.654305\pi\)
−0.465999 + 0.884785i \(0.654305\pi\)
\(198\) −9.30538 + 8.32560i −0.661305 + 0.591675i
\(199\) −20.6501 14.0790i −1.46384 0.998032i −0.993289 0.115661i \(-0.963101\pi\)
−0.470555 0.882371i \(-0.655946\pi\)
\(200\) 1.21606 5.32792i 0.0859887 0.376741i
\(201\) −21.4556 6.83160i −1.51336 0.481864i
\(202\) −0.645428 8.61264i −0.0454122 0.605983i
\(203\) −11.1542 20.0407i −0.782870 1.40658i
\(204\) −0.137254 0.627491i −0.00960967 0.0439332i
\(205\) −20.2873 3.05783i −1.41693 0.213568i
\(206\) −0.0692874 0.924576i −0.00482748 0.0644182i
\(207\) −4.10660 19.6242i −0.285429 1.36398i
\(208\) 6.46129 + 1.99304i 0.448010 + 0.138193i
\(209\) 12.3062 1.85485i 0.851235 0.128303i
\(210\) −9.69137 4.96658i −0.668768 0.342727i
\(211\) −5.52058 0.832093i −0.380052 0.0572837i −0.0437619 0.999042i \(-0.513934\pi\)
−0.336290 + 0.941758i \(0.609172\pi\)
\(212\) 1.16876 + 0.562843i 0.0802705 + 0.0386562i
\(213\) 18.3646 + 0.166334i 1.25832 + 0.0113970i
\(214\) −12.3551 −0.844577
\(215\) 5.77588 10.0041i 0.393912 0.682275i
\(216\) −13.6511 7.03712i −0.928838 0.478815i
\(217\) −5.99362 + 1.74608i −0.406873 + 0.118532i
\(218\) −6.86795 6.37253i −0.465156 0.431602i
\(219\) −0.301576 4.58060i −0.0203786 0.309529i
\(220\) 0.419087 + 1.06782i 0.0282549 + 0.0719922i
\(221\) 1.24468 + 3.17138i 0.0837259 + 0.213330i
\(222\) −7.23649 3.56601i −0.485681 0.239335i
\(223\) 0.509176 + 0.472447i 0.0340970 + 0.0316374i 0.697037 0.717035i \(-0.254501\pi\)
−0.662940 + 0.748672i \(0.730692\pi\)
\(224\) −1.50653 2.70679i −0.100659 0.180855i
\(225\) 1.33205 5.38458i 0.0888034 0.358972i
\(226\) −4.20062 + 7.27570i −0.279421 + 0.483972i
\(227\) 3.28194 0.217830 0.108915 0.994051i \(-0.465262\pi\)
0.108915 + 0.994051i \(0.465262\pi\)
\(228\) 0.709218 + 1.25450i 0.0469691 + 0.0830816i
\(229\) −11.8262 5.69518i −0.781494 0.376348i 0.000207574 1.00000i \(-0.499934\pi\)
−0.781702 + 0.623652i \(0.785648\pi\)
\(230\) 15.7041 + 2.36701i 1.03550 + 0.156076i
\(231\) −14.1365 + 1.77375i −0.930111 + 0.116704i
\(232\) 25.3362 3.81882i 1.66341 0.250718i
\(233\) −0.0793043 0.0244621i −0.00519540 0.00160257i 0.292156 0.956371i \(-0.405627\pi\)
−0.297352 + 0.954768i \(0.596103\pi\)
\(234\) 7.28594 + 2.39278i 0.476297 + 0.156421i
\(235\) 0.855223 + 11.4122i 0.0557886 + 0.744447i
\(236\) −1.18471 0.178566i −0.0771179 0.0116237i
\(237\) −11.8046 + 10.7558i −0.766794 + 0.698664i
\(238\) −2.40092 + 5.84553i −0.155629 + 0.378909i
\(239\) 1.09508 + 14.6129i 0.0708351 + 0.945229i 0.913513 + 0.406811i \(0.133359\pi\)
−0.842677 + 0.538419i \(0.819022\pi\)
\(240\) 8.04778 7.33273i 0.519482 0.473326i
\(241\) −6.03109 + 26.4239i −0.388497 + 1.70212i 0.281341 + 0.959608i \(0.409221\pi\)
−0.669837 + 0.742508i \(0.733636\pi\)
\(242\) 1.47555 + 1.00601i 0.0948518 + 0.0646689i
\(243\) −13.7241 7.39245i −0.880403 0.474226i
\(244\) 1.56577 0.100238
\(245\) −5.87153 10.9511i −0.375118 0.699638i
\(246\) 19.4794 + 18.4054i 1.24196 + 1.17348i
\(247\) −4.76569 5.97598i −0.303233 0.380243i
\(248\) 0.521172 6.95456i 0.0330945 0.441615i
\(249\) 3.28096 2.19366i 0.207923 0.139018i
\(250\) 13.4476 + 9.16840i 0.850499 + 0.579861i
\(251\) −6.52421 3.14189i −0.411804 0.198315i 0.216499 0.976283i \(-0.430536\pi\)
−0.628304 + 0.777968i \(0.716250\pi\)
\(252\) −0.776085 1.45584i −0.0488888 0.0917094i
\(253\) 18.7202 9.01518i 1.17693 0.566779i
\(254\) 11.8412 + 1.78477i 0.742980 + 0.111986i
\(255\) 5.41673 + 0.866685i 0.339209 + 0.0542739i
\(256\) 4.87763 0.735185i 0.304852 0.0459491i
\(257\) 1.55077 + 6.79435i 0.0967342 + 0.423820i 0.999986 0.00529074i \(-0.00168410\pi\)
−0.903252 + 0.429111i \(0.858827\pi\)
\(258\) −13.6537 + 6.42360i −0.850044 + 0.399916i
\(259\) −4.47673 8.04336i −0.278171 0.499790i
\(260\) 0.439269 0.550826i 0.0272423 0.0341608i
\(261\) 25.7822 3.40965i 1.59588 0.211052i
\(262\) −3.06972 + 2.84828i −0.189648 + 0.175967i
\(263\) −21.2831 −1.31237 −0.656185 0.754600i \(-0.727831\pi\)
−0.656185 + 0.754600i \(0.727831\pi\)
\(264\) 3.68209 15.4845i 0.226617 0.953004i
\(265\) −8.12118 + 7.53535i −0.498880 + 0.462893i
\(266\) 1.28165 14.1199i 0.0785832 0.865746i
\(267\) 19.9620 13.3467i 1.22166 0.816803i
\(268\) 2.58208 0.796466i 0.157726 0.0486519i
\(269\) 5.67274 + 0.855028i 0.345873 + 0.0521320i 0.319682 0.947525i \(-0.396424\pi\)
0.0261914 + 0.999657i \(0.491662\pi\)
\(270\) 9.27653 8.14973i 0.564552 0.495977i
\(271\) −7.20945 6.68939i −0.437943 0.406352i 0.430147 0.902759i \(-0.358462\pi\)
−0.868090 + 0.496407i \(0.834652\pi\)
\(272\) −4.63138 4.29730i −0.280819 0.260562i
\(273\) 5.28461 + 6.97442i 0.319839 + 0.422111i
\(274\) −2.19990 + 2.04121i −0.132901 + 0.123314i
\(275\) 5.74846 0.346645
\(276\) 1.74883 + 1.65240i 0.105267 + 0.0994628i
\(277\) 5.09053 + 22.3031i 0.305860 + 1.34006i 0.861127 + 0.508390i \(0.169759\pi\)
−0.555267 + 0.831672i \(0.687384\pi\)
\(278\) −21.2385 + 14.4802i −1.27380 + 0.868463i
\(279\) 0.656759 7.04811i 0.0393191 0.421959i
\(280\) 13.7572 1.85287i 0.822148 0.110730i
\(281\) 21.4828 3.23801i 1.28155 0.193163i 0.527263 0.849702i \(-0.323218\pi\)
0.754292 + 0.656539i \(0.227980\pi\)
\(282\) 7.59132 12.8778i 0.452056 0.766860i
\(283\) −28.8411 + 4.34709i −1.71442 + 0.258408i −0.931508 0.363721i \(-0.881506\pi\)
−0.782915 + 0.622129i \(0.786268\pi\)
\(284\) −1.82096 + 1.24151i −0.108054 + 0.0736699i
\(285\) −12.1860 + 1.72402i −0.721837 + 0.102122i
\(286\) −0.593915 + 7.92524i −0.0351189 + 0.468629i
\(287\) 6.33499 + 29.9158i 0.373943 + 1.76587i
\(288\) 3.48225 0.460522i 0.205194 0.0271365i
\(289\) −1.03252 + 13.7781i −0.0607366 + 0.810474i
\(290\) −4.58403 + 20.0840i −0.269184 + 1.17937i
\(291\) −27.8413 8.86485i −1.63209 0.519667i
\(292\) 0.343469 + 0.430696i 0.0201000 + 0.0252046i
\(293\) −5.15282 8.92495i −0.301031 0.521401i 0.675339 0.737508i \(-0.263997\pi\)
−0.976370 + 0.216107i \(0.930664\pi\)
\(294\) −1.86729 + 16.1232i −0.108902 + 0.940326i
\(295\) 5.11599 8.86115i 0.297864 0.515916i
\(296\) 10.1687 1.53269i 0.591044 0.0890856i
\(297\) 4.02137 15.6464i 0.233344 0.907897i
\(298\) −5.32481 + 1.64249i −0.308458 + 0.0951467i
\(299\) −10.5439 7.18872i −0.609771 0.415735i
\(300\) 0.237567 + 0.621813i 0.0137159 + 0.0359004i
\(301\) −16.9828 2.83347i −0.978871 0.163319i
\(302\) −8.44996 5.76108i −0.486240 0.331513i
\(303\) 6.88774 + 8.79928i 0.395691 + 0.505506i
\(304\) 12.7710 + 6.15018i 0.732466 + 0.352737i
\(305\) −4.88536 + 12.4477i −0.279735 + 0.712752i
\(306\) −5.16355 4.96813i −0.295180 0.284009i
\(307\) 5.35437 + 6.71416i 0.305590 + 0.383198i 0.910786 0.412879i \(-0.135477\pi\)
−0.605196 + 0.796076i \(0.706905\pi\)
\(308\) 1.27145 1.14307i 0.0724476 0.0651323i
\(309\) 0.739406 + 0.944612i 0.0420634 + 0.0537371i
\(310\) 5.05187 + 2.43285i 0.286927 + 0.138177i
\(311\) 7.70694 + 2.37728i 0.437020 + 0.134803i 0.505456 0.862853i \(-0.331324\pi\)
−0.0684352 + 0.997656i \(0.521801\pi\)
\(312\) −9.36685 + 2.79664i −0.530294 + 0.158329i
\(313\) 6.67943 + 11.5691i 0.377544 + 0.653925i 0.990704 0.136034i \(-0.0434355\pi\)
−0.613161 + 0.789958i \(0.710102\pi\)
\(314\) −4.28251 18.7629i −0.241676 1.05885i
\(315\) 13.9952 1.62742i 0.788542 0.0916948i
\(316\) 0.426450 1.86840i 0.0239897 0.105106i
\(317\) −0.906591 + 0.279646i −0.0509192 + 0.0157065i −0.320110 0.947380i \(-0.603720\pi\)
0.269191 + 0.963087i \(0.413244\pi\)
\(318\) 14.3285 2.02713i 0.803504 0.113676i
\(319\) 9.84656 + 25.0886i 0.551302 + 1.40469i
\(320\) −3.41660 + 14.9691i −0.190994 + 0.836799i
\(321\) 13.2887 8.88483i 0.741701 0.495903i
\(322\) −4.90381 23.1573i −0.273279 1.29051i
\(323\) 1.58923 + 6.96288i 0.0884272 + 0.387425i
\(324\) 1.85867 0.211627i 0.103259 0.0117571i
\(325\) −1.76529 3.05758i −0.0979209 0.169604i
\(326\) 3.59969 + 15.7713i 0.199369 + 0.873491i
\(327\) 11.9695 + 1.91514i 0.661917 + 0.105908i
\(328\) −33.7797 5.09147i −1.86517 0.281129i
\(329\) 15.4824 7.15831i 0.853573 0.394650i
\(330\) 10.5074 + 7.30409i 0.578413 + 0.402077i
\(331\) 5.27792 4.89719i 0.290101 0.269174i −0.521674 0.853145i \(-0.674692\pi\)
0.811775 + 0.583971i \(0.198502\pi\)
\(332\) −0.173035 + 0.440886i −0.00949654 + 0.0241968i
\(333\) 10.3477 1.36847i 0.567050 0.0749914i
\(334\) 9.54623 + 24.3234i 0.522346 + 1.33092i
\(335\) −1.72453 + 23.0123i −0.0942213 + 1.25730i
\(336\) −14.4414 7.40084i −0.787842 0.403749i
\(337\) 1.22673 + 16.3696i 0.0668244 + 0.891710i 0.925392 + 0.379010i \(0.123736\pi\)
−0.858568 + 0.512700i \(0.828645\pi\)
\(338\) −11.2820 + 5.43312i −0.613660 + 0.295523i
\(339\) −0.714089 10.8462i −0.0387840 0.589086i
\(340\) −0.593105 + 0.285624i −0.0321657 + 0.0154902i
\(341\) 7.25394 1.09335i 0.392823 0.0592085i
\(342\) 14.3555 + 7.23645i 0.776257 + 0.391302i
\(343\) −12.2170 + 13.9192i −0.659657 + 0.751566i
\(344\) 9.61720 16.6575i 0.518525 0.898111i
\(345\) −18.5929 + 8.74732i −1.00101 + 0.470940i
\(346\) −1.44478 + 19.2792i −0.0776718 + 1.03646i
\(347\) 17.6949 + 16.4185i 0.949915 + 0.881392i 0.993052 0.117677i \(-0.0375448\pi\)
−0.0431374 + 0.999069i \(0.513735\pi\)
\(348\) −2.30692 + 2.10195i −0.123664 + 0.112676i
\(349\) 14.2875 9.74104i 0.764791 0.521426i −0.116962 0.993136i \(-0.537316\pi\)
0.881753 + 0.471711i \(0.156363\pi\)
\(350\) 1.55745 6.36095i 0.0832490 0.340007i
\(351\) −9.55717 + 2.66590i −0.510124 + 0.142295i
\(352\) 1.32992 + 3.38858i 0.0708849 + 0.180612i
\(353\) −6.42961 3.09634i −0.342214 0.164802i 0.254880 0.966973i \(-0.417964\pi\)
−0.597094 + 0.802171i \(0.703678\pi\)
\(354\) −12.0938 + 5.68971i −0.642778 + 0.302404i
\(355\) −4.18828 18.3500i −0.222291 0.973919i
\(356\) −1.05278 + 2.68244i −0.0557972 + 0.142169i
\(357\) −1.62131 8.01378i −0.0858089 0.424134i
\(358\) −10.1091 25.7576i −0.534284 1.36133i
\(359\) −1.51496 + 1.03288i −0.0799564 + 0.0545133i −0.602638 0.798014i \(-0.705884\pi\)
0.522682 + 0.852528i \(0.324931\pi\)
\(360\) −3.77986 + 15.2794i −0.199216 + 0.805296i
\(361\) 1.48830 + 2.57780i 0.0783314 + 0.135674i
\(362\) −5.67572 9.83064i −0.298309 0.516687i
\(363\) −2.31049 0.0209269i −0.121269 0.00109838i
\(364\) −0.998442 0.325254i −0.0523326 0.0170479i
\(365\) −4.49564 + 1.38672i −0.235313 + 0.0725843i
\(366\) 14.5204 9.70841i 0.758996 0.507467i
\(367\) −0.206174 + 0.258534i −0.0107622 + 0.0134954i −0.787183 0.616719i \(-0.788462\pi\)
0.776421 + 0.630214i \(0.217033\pi\)
\(368\) 23.4011 + 3.52715i 1.21987 + 0.183866i
\(369\) −34.1870 5.78801i −1.77970 0.301312i
\(370\) −1.83980 + 8.06070i −0.0956468 + 0.419056i
\(371\) 14.7626 + 7.39740i 0.766435 + 0.384054i
\(372\) 0.418052 + 0.739475i 0.0216750 + 0.0383400i
\(373\) 21.1992 1.09765 0.548827 0.835936i \(-0.315075\pi\)
0.548827 + 0.835936i \(0.315075\pi\)
\(374\) 3.71295 6.43101i 0.191992 0.332540i
\(375\) −21.0569 0.190720i −1.08737 0.00984872i
\(376\) 1.42400 + 19.0020i 0.0734372 + 0.979951i
\(377\) 10.3207 12.9418i 0.531546 0.666537i
\(378\) −16.2240 8.68897i −0.834472 0.446912i
\(379\) −11.7957 14.7914i −0.605905 0.759781i 0.380380 0.924830i \(-0.375793\pi\)
−0.986285 + 0.165049i \(0.947222\pi\)
\(380\) 1.08267 1.00457i 0.0555397 0.0515333i
\(381\) −14.0194 + 6.59562i −0.718233 + 0.337904i
\(382\) 15.2424 10.3921i 0.779869 0.531706i
\(383\) 17.1009 21.4438i 0.873813 1.09573i −0.120862 0.992669i \(-0.538566\pi\)
0.994675 0.103058i \(-0.0328626\pi\)
\(384\) 11.8269 10.7761i 0.603541 0.549916i
\(385\) 5.12020 + 13.6744i 0.260950 + 0.696911i
\(386\) −14.0866 6.78376i −0.716990 0.345284i
\(387\) 10.0661 16.7277i 0.511687 0.850316i
\(388\) 3.35057 1.03351i 0.170099 0.0524687i
\(389\) −1.34797 + 0.649150i −0.0683450 + 0.0329132i −0.467744 0.883864i \(-0.654933\pi\)
0.399399 + 0.916777i \(0.369219\pi\)
\(390\) 0.658298 7.83184i 0.0333342 0.396581i
\(391\) 5.96193 + 10.3264i 0.301508 + 0.522227i
\(392\) −9.77646 18.2342i −0.493786 0.920966i
\(393\) 1.25341 5.27101i 0.0632259 0.265887i
\(394\) 6.39784 16.3014i 0.322319 0.821255i
\(395\) 13.5230 + 9.21982i 0.680416 + 0.463899i
\(396\) 0.675466 + 1.81718i 0.0339435 + 0.0913166i
\(397\) −1.23689 + 16.5052i −0.0620779 + 0.828372i 0.876080 + 0.482165i \(0.160149\pi\)
−0.938158 + 0.346207i \(0.887470\pi\)
\(398\) 27.6445 18.8477i 1.38569 0.944748i
\(399\) 8.77544 + 16.1085i 0.439322 + 0.806433i
\(400\) 5.40968 + 3.68825i 0.270484 + 0.184413i
\(401\) −16.2170 + 20.3354i −0.809836 + 1.01550i 0.189598 + 0.981862i \(0.439282\pi\)
−0.999434 + 0.0336406i \(0.989290\pi\)
\(402\) 19.0070 23.3961i 0.947982 1.16689i
\(403\) −2.80916 3.52258i −0.139934 0.175472i
\(404\) −1.28140 0.395261i −0.0637522 0.0196649i
\(405\) −4.11682 + 15.4365i −0.204567 + 0.767046i
\(406\) 30.4295 4.09837i 1.51019 0.203399i
\(407\) 3.95192 + 10.0693i 0.195890 + 0.499118i
\(408\) 9.01919 + 1.44308i 0.446516 + 0.0714433i
\(409\) 7.01106 + 2.16262i 0.346674 + 0.106935i 0.463202 0.886252i \(-0.346700\pi\)
−0.116528 + 0.993187i \(0.537176\pi\)
\(410\) 13.7328 23.7860i 0.678216 1.17470i
\(411\) 0.898248 3.77745i 0.0443073 0.186328i
\(412\) −0.137560 0.0424316i −0.00677709 0.00209046i
\(413\) −15.0425 2.50975i −0.740193 0.123497i
\(414\) 26.4636 + 4.48040i 1.30062 + 0.220200i
\(415\) −2.96511 2.75122i −0.145552 0.135052i
\(416\) 1.39396 1.74798i 0.0683447 0.0857016i
\(417\) 12.4303 30.8474i 0.608714 1.51060i
\(418\) −3.70730 + 16.2428i −0.181330 + 0.794459i
\(419\) −14.5476 + 4.48734i −0.710697 + 0.219221i −0.628965 0.777433i \(-0.716521\pi\)
−0.0817318 + 0.996654i \(0.526045\pi\)
\(420\) −1.26756 + 1.11898i −0.0618505 + 0.0546004i
\(421\) 27.7438 + 8.55783i 1.35215 + 0.417083i 0.884380 0.466767i \(-0.154581\pi\)
0.467770 + 0.883850i \(0.345057\pi\)
\(422\) 3.73697 6.47262i 0.181913 0.315082i
\(423\) 1.09577 + 19.3099i 0.0532781 + 0.938880i
\(424\) −13.5223 + 12.5468i −0.656699 + 0.609328i
\(425\) 0.246526 + 3.28966i 0.0119583 + 0.159572i
\(426\) −9.18913 + 22.8040i −0.445215 + 1.10486i
\(427\) 19.9281 + 0.313325i 0.964390 + 0.0151628i
\(428\) −0.700833 + 1.78569i −0.0338760 + 0.0863147i
\(429\) −5.06043 8.95118i −0.244320 0.432167i
\(430\) 9.64194 + 12.0906i 0.464976 + 0.583061i
\(431\) −1.84853 24.6669i −0.0890405 1.18816i −0.845447 0.534060i \(-0.820666\pi\)
0.756406 0.654102i \(-0.226953\pi\)
\(432\) 13.8232 12.1441i 0.665070 0.584285i
\(433\) 4.13010 1.98895i 0.198480 0.0955830i −0.332004 0.943278i \(-0.607725\pi\)
0.530484 + 0.847695i \(0.322010\pi\)
\(434\) 0.755478 8.32305i 0.0362641 0.399519i
\(435\) −9.51242 24.8980i −0.456086 1.19377i
\(436\) −1.31061 + 0.631154i −0.0627666 + 0.0302268i
\(437\) −19.6106 18.1959i −0.938100 0.870430i
\(438\) 5.85571 + 1.86449i 0.279797 + 0.0890890i
\(439\) −2.78834 + 7.10458i −0.133080 + 0.339083i −0.981844 0.189689i \(-0.939252\pi\)
0.848764 + 0.528772i \(0.177347\pi\)
\(440\) −16.3120 −0.777643
\(441\) −9.58621 18.6843i −0.456486 0.889731i
\(442\) −4.56084 −0.216937
\(443\) 11.8728 30.2515i 0.564095 1.43729i −0.309623 0.950859i \(-0.600203\pi\)
0.873718 0.486432i \(-0.161702\pi\)
\(444\) −0.925881 + 0.843617i −0.0439404 + 0.0400363i
\(445\) −18.0403 16.7390i −0.855193 0.793503i
\(446\) −0.837780 + 0.403454i −0.0396701 + 0.0191041i
\(447\) 4.54601 5.59579i 0.215019 0.264672i
\(448\) 22.6800 3.05462i 1.07153 0.144317i
\(449\) −21.6370 + 10.4198i −1.02111 + 0.491741i −0.868051 0.496476i \(-0.834627\pi\)
−0.153060 + 0.988217i \(0.548913\pi\)
\(450\) 6.05862 + 4.29348i 0.285606 + 0.202397i
\(451\) −2.68531 35.8330i −0.126447 1.68731i
\(452\) 0.813285 + 1.01983i 0.0382537 + 0.0479686i
\(453\) 13.2314 + 0.119841i 0.621664 + 0.00563063i
\(454\) −1.60515 + 4.08986i −0.0753335 + 0.191947i
\(455\) 5.70097 6.92267i 0.267266 0.324540i
\(456\) −20.2905 + 2.87060i −0.950187 + 0.134428i
\(457\) 0.804066 + 10.7295i 0.0376126 + 0.501906i 0.983917 + 0.178628i \(0.0571658\pi\)
−0.946304 + 0.323278i \(0.895215\pi\)
\(458\) 12.8812 11.9520i 0.601898 0.558479i
\(459\) 9.12641 + 1.63030i 0.425984 + 0.0760959i
\(460\) 1.23291 2.13546i 0.0574847 0.0995664i
\(461\) −14.4700 4.46341i −0.673936 0.207882i −0.0611477 0.998129i \(-0.519476\pi\)
−0.612789 + 0.790247i \(0.709952\pi\)
\(462\) 4.70355 18.4840i 0.218829 0.859952i
\(463\) −26.5750 + 8.19729i −1.23504 + 0.380960i −0.842461 0.538757i \(-0.818894\pi\)
−0.392582 + 0.919717i \(0.628418\pi\)
\(464\) −6.83079 + 29.9277i −0.317112 + 1.38936i
\(465\) −7.18311 + 1.01623i −0.333109 + 0.0471267i
\(466\) 0.0692706 0.0868626i 0.00320890 0.00402383i
\(467\) −0.608006 0.564148i −0.0281352 0.0261056i 0.665980 0.745970i \(-0.268014\pi\)
−0.694115 + 0.719864i \(0.744204\pi\)
\(468\) 0.759119 0.917314i 0.0350903 0.0424029i
\(469\) 33.0225 9.62023i 1.52484 0.444221i
\(470\) −14.6398 4.51577i −0.675283 0.208297i
\(471\) 18.0989 + 17.1010i 0.833955 + 0.787973i
\(472\) 8.51843 14.7544i 0.392093 0.679124i
\(473\) 19.3334 + 5.96357i 0.888951 + 0.274205i
\(474\) −7.63007 19.9711i −0.350461 0.917303i
\(475\) −2.70399 6.88964i −0.124067 0.316119i
\(476\) 0.708668 + 0.678590i 0.0324818 + 0.0311031i
\(477\) −13.9535 + 12.4843i −0.638885 + 0.571616i
\(478\) −18.7458 5.78230i −0.857411 0.264476i
\(479\) 7.51117 + 9.41871i 0.343194 + 0.430352i 0.923235 0.384235i \(-0.125535\pi\)
−0.580041 + 0.814587i \(0.696963\pi\)
\(480\) −1.28479 3.36283i −0.0586423 0.153492i
\(481\) 4.14224 5.19420i 0.188870 0.236835i
\(482\) −29.9790 20.4394i −1.36551 0.930987i
\(483\) 21.9273 + 21.3807i 0.997727 + 0.972854i
\(484\) 0.229099 0.156197i 0.0104136 0.00709986i
\(485\) −2.23780 + 29.8613i −0.101613 + 1.35593i
\(486\) 15.9245 13.4871i 0.722352 0.611786i
\(487\) −35.0306 23.8835i −1.58739 1.08226i −0.950239 0.311523i \(-0.899161\pi\)
−0.637150 0.770740i \(-0.719887\pi\)
\(488\) −8.13442 + 20.7262i −0.368228 + 0.938229i
\(489\) −15.2132 14.3744i −0.687964 0.650031i
\(490\) 16.5186 1.96092i 0.746234 0.0885852i
\(491\) −8.58315 14.8665i −0.387352 0.670914i 0.604740 0.796423i \(-0.293277\pi\)
−0.992092 + 0.125509i \(0.959944\pi\)
\(492\) 3.76509 1.77135i 0.169744 0.0798584i
\(493\) −13.9352 + 6.71082i −0.627608 + 0.302240i
\(494\) 9.77792 3.01609i 0.439930 0.135700i
\(495\) −16.5539 0.299893i −0.744041 0.0134792i
\(496\) 7.52793 + 3.62526i 0.338014 + 0.162779i
\(497\) −23.4245 + 15.4367i −1.05073 + 0.692433i
\(498\) 1.12900 + 5.16153i 0.0505918 + 0.231294i
\(499\) 1.13858 1.42774i 0.0509700 0.0639143i −0.755693 0.654926i \(-0.772700\pi\)
0.806663 + 0.591012i \(0.201271\pi\)
\(500\) 2.08792 1.42352i 0.0933745 0.0636617i
\(501\) −27.7591 19.2964i −1.24018 0.862099i
\(502\) 7.10624 6.59362i 0.317167 0.294288i
\(503\) 16.7454 + 20.9981i 0.746641 + 0.936259i 0.999512 0.0312416i \(-0.00994612\pi\)
−0.252871 + 0.967500i \(0.581375\pi\)
\(504\) 23.3029 2.70976i 1.03800 0.120702i
\(505\) 7.14039 8.95376i 0.317743 0.398437i
\(506\) 2.07866 + 27.7378i 0.0924077 + 1.23309i
\(507\) 8.22740 13.9568i 0.365392 0.619843i
\(508\) 0.929633 1.61017i 0.0412458 0.0714398i
\(509\) 12.1522 0.538636 0.269318 0.963051i \(-0.413202\pi\)
0.269318 + 0.963051i \(0.413202\pi\)
\(510\) −3.72928 + 6.32629i −0.165135 + 0.280133i
\(511\) 4.28527 + 5.55036i 0.189569 + 0.245534i
\(512\) −5.58055 + 24.4500i −0.246628 + 1.08055i
\(513\) −20.6441 + 2.54013i −0.911460 + 0.112149i
\(514\) −9.22538 1.39050i −0.406914 0.0613325i
\(515\) 0.766528 0.961195i 0.0337772 0.0423553i
\(516\) 0.153912 + 2.33776i 0.00677561 + 0.102914i
\(517\) −19.1533 + 5.90802i −0.842362 + 0.259834i
\(518\) 12.2129 1.64488i 0.536604 0.0722719i
\(519\) −12.3102 21.7750i −0.540357 0.955815i
\(520\) 5.00924 + 8.67627i 0.219670 + 0.380479i
\(521\) 2.04605 + 3.54387i 0.0896392 + 0.155260i 0.907359 0.420357i \(-0.138095\pi\)
−0.817719 + 0.575617i \(0.804762\pi\)
\(522\) −8.36069 + 33.7966i −0.365937 + 1.47924i
\(523\) −9.56587 + 6.52190i −0.418286 + 0.285183i −0.754118 0.656739i \(-0.771935\pi\)
0.335831 + 0.941922i \(0.390983\pi\)
\(524\) 0.237537 + 0.605235i 0.0103769 + 0.0264398i
\(525\) 2.89918 + 7.96158i 0.126530 + 0.347472i
\(526\) 10.4092 26.5223i 0.453865 1.15643i
\(527\) 0.936782 + 4.10431i 0.0408069 + 0.178787i
\(528\) 15.6574 + 10.8840i 0.681399 + 0.473667i
\(529\) −19.5184 9.39958i −0.848627 0.408677i
\(530\) −5.41838 13.8058i −0.235359 0.599686i
\(531\) 8.91601 14.8165i 0.386922 0.642983i
\(532\) −1.96806 0.986178i −0.0853262 0.0427562i
\(533\) −18.2348 + 12.4323i −0.789836 + 0.538501i
\(534\) 6.86907 + 31.4038i 0.297254 + 1.35897i
\(535\) −12.0094 11.1431i −0.519211 0.481757i
\(536\) −2.87145 + 38.3169i −0.124028 + 1.65504i
\(537\) 29.3959 + 20.4342i 1.26853 + 0.881802i
\(538\) −3.83997 + 6.65102i −0.165553 + 0.286746i
\(539\) 16.4110 14.2938i 0.706870 0.615678i
\(540\) −0.651684 1.80303i −0.0280440 0.0775901i
\(541\) −9.81409 + 1.47924i −0.421940 + 0.0635973i −0.356581 0.934264i \(-0.616058\pi\)
−0.0653597 + 0.997862i \(0.520819\pi\)
\(542\) 11.8622 5.71252i 0.509524 0.245374i
\(543\) 13.1740 + 6.49191i 0.565351 + 0.278595i
\(544\) −1.88214 + 0.906392i −0.0806962 + 0.0388612i
\(545\) −0.928385 12.3884i −0.0397676 0.530662i
\(546\) −11.2759 + 3.17444i −0.482566 + 0.135854i
\(547\) 0.805262 10.7455i 0.0344305 0.459443i −0.953168 0.302442i \(-0.902198\pi\)
0.987598 0.157001i \(-0.0501827\pi\)
\(548\) 0.170230 + 0.433739i 0.00727187 + 0.0185284i
\(549\) −8.63610 + 20.8840i −0.368580 + 0.891306i
\(550\) −2.81149 + 7.16356i −0.119882 + 0.305455i
\(551\) 25.4376 23.6026i 1.08368 1.00550i
\(552\) −30.9583 + 14.5648i −1.31767 + 0.619920i
\(553\) 5.80147 23.6945i 0.246704 1.00759i
\(554\) −30.2831 4.56445i −1.28661 0.193925i
\(555\) −3.81781 9.99282i −0.162057 0.424172i
\(556\) 0.888094 + 3.89099i 0.0376636 + 0.165015i
\(557\) 6.47529 + 11.2155i 0.274367 + 0.475217i 0.969975 0.243204i \(-0.0781984\pi\)
−0.695608 + 0.718421i \(0.744865\pi\)
\(558\) 8.46194 + 4.26557i 0.358222 + 0.180576i
\(559\) −2.76510 12.1147i −0.116951 0.512397i
\(560\) −3.95513 + 16.1536i −0.167135 + 0.682616i
\(561\) 0.631186 + 9.58702i 0.0266487 + 0.404764i
\(562\) −6.47181 + 28.3549i −0.272997 + 1.19608i
\(563\) 6.93089 + 17.6596i 0.292102 + 0.744264i 0.999306 + 0.0372540i \(0.0118611\pi\)
−0.707204 + 0.707010i \(0.750044\pi\)
\(564\) −1.43062 1.82766i −0.0602401 0.0769584i
\(565\) −10.6450 + 3.28356i −0.447840 + 0.138140i
\(566\) 8.68854 38.0670i 0.365207 1.60007i
\(567\) 23.6983 2.32152i 0.995236 0.0974947i
\(568\) −6.97374 30.5539i −0.292612 1.28202i
\(569\) −1.68578 2.91986i −0.0706716 0.122407i 0.828524 0.559953i \(-0.189181\pi\)
−0.899196 + 0.437546i \(0.855848\pi\)
\(570\) 3.81158 16.0290i 0.159650 0.671383i
\(571\) −40.2433 12.4134i −1.68413 0.519485i −0.702729 0.711458i \(-0.748035\pi\)
−0.981400 + 0.191973i \(0.938511\pi\)
\(572\) 1.11175 + 0.535391i 0.0464847 + 0.0223858i
\(573\) −8.92094 + 22.1385i −0.372678 + 0.924849i
\(574\) −40.3785 6.73691i −1.68537 0.281193i
\(575\) −7.70435 9.66095i −0.321293 0.402889i
\(576\) −6.23145 + 25.1895i −0.259644 + 1.04956i
\(577\) 14.4595 36.8422i 0.601957 1.53376i −0.226678 0.973970i \(-0.572786\pi\)
0.828634 0.559790i \(-0.189118\pi\)
\(578\) −16.6648 8.02536i −0.693165 0.333811i
\(579\) 20.0294 2.83366i 0.832392 0.117763i
\(580\) 2.64272 + 1.80178i 0.109733 + 0.0748148i
\(581\) −2.29051 + 5.57670i −0.0950263 + 0.231361i
\(582\) 24.6639 30.3594i 1.02235 1.25844i
\(583\) −16.0319 10.9304i −0.663976 0.452691i
\(584\) −7.48552 + 2.30898i −0.309753 + 0.0955462i
\(585\) 4.92402 + 8.89702i 0.203583 + 0.367847i
\(586\) 13.6422 2.05623i 0.563553 0.0849420i
\(587\) −2.78989 + 4.83223i −0.115151 + 0.199448i −0.917840 0.396950i \(-0.870069\pi\)
0.802689 + 0.596398i \(0.203402\pi\)
\(588\) 2.22438 + 1.18446i 0.0917321 + 0.0488462i
\(589\) −4.72255 8.17969i −0.194589 0.337038i
\(590\) 8.54035 + 10.7093i 0.351601 + 0.440893i
\(591\) 4.84147 + 22.1340i 0.199151 + 0.910473i
\(592\) −2.74154 + 12.0115i −0.112677 + 0.493669i
\(593\) 2.49013 33.2285i 0.102257 1.36453i −0.676147 0.736766i \(-0.736352\pi\)
0.778405 0.627763i \(-0.216029\pi\)
\(594\) 17.5313 + 12.6638i 0.719318 + 0.519600i
\(595\) −7.60583 + 3.51657i −0.311809 + 0.144165i
\(596\) −0.0646555 + 0.862768i −0.00264839 + 0.0353403i
\(597\) −16.1795 + 40.1516i −0.662184 + 1.64330i
\(598\) 14.1153 9.62362i 0.577216 0.393539i
\(599\) −20.9752 + 3.16150i −0.857023 + 0.129175i −0.562832 0.826571i \(-0.690288\pi\)
−0.294191 + 0.955747i \(0.595050\pi\)
\(600\) −9.46517 0.0857293i −0.386414 0.00349988i
\(601\) 42.7896 6.44949i 1.74542 0.263080i 0.802635 0.596471i \(-0.203431\pi\)
0.942789 + 0.333390i \(0.108193\pi\)
\(602\) 11.8370 19.7776i 0.482441 0.806076i
\(603\) −3.61849 + 38.8323i −0.147356 + 1.58137i
\(604\) −1.31197 + 0.894486i −0.0533833 + 0.0363961i
\(605\) 0.526937 + 2.30866i 0.0214230 + 0.0938604i
\(606\) −14.3341 + 4.27970i −0.582283 + 0.173851i
\(607\) 39.7138 1.61193 0.805967 0.591961i \(-0.201646\pi\)
0.805967 + 0.591961i \(0.201646\pi\)
\(608\) 3.43571 3.18787i 0.139336 0.129285i
\(609\) −29.7816 + 26.2906i −1.20681 + 1.06535i
\(610\) −13.1226 12.1760i −0.531318 0.492991i
\(611\) 9.02424 + 8.37327i 0.365082 + 0.338746i
\(612\) −1.01095 + 0.464479i −0.0408650 + 0.0187754i
\(613\) 47.4114 + 7.14611i 1.91493 + 0.288629i 0.994705 0.102769i \(-0.0327702\pi\)
0.920222 + 0.391398i \(0.128008\pi\)
\(614\) −10.9857 + 3.38865i −0.443348 + 0.136755i
\(615\) 2.33453 + 35.4589i 0.0941372 + 1.42984i
\(616\) 8.52545 + 22.7687i 0.343500 + 0.917376i
\(617\) 11.3147 10.4985i 0.455512 0.422654i −0.418754 0.908099i \(-0.637533\pi\)
0.874267 + 0.485446i \(0.161343\pi\)
\(618\) −1.53878 + 0.459430i −0.0618988 + 0.0184810i
\(619\) 0.547754 0.0220161 0.0110081 0.999939i \(-0.496496\pi\)
0.0110081 + 0.999939i \(0.496496\pi\)
\(620\) 0.638185 0.592149i 0.0256301 0.0237813i
\(621\) −31.6852 + 14.2116i −1.27148 + 0.570294i
\(622\) −6.73185 + 8.44147i −0.269922 + 0.338472i
\(623\) −13.9359 + 33.9298i −0.558331 + 1.35937i
\(624\) 0.980948 11.6704i 0.0392694 0.467192i
\(625\) 2.74513 + 12.0272i 0.109805 + 0.481088i
\(626\) −17.6839 + 2.66542i −0.706791 + 0.106532i
\(627\) −7.69311 20.1361i −0.307233 0.804158i
\(628\) −2.95474 0.445355i −0.117907 0.0177716i
\(629\) −5.59288 + 2.69339i −0.223003 + 0.107393i
\(630\) −4.81683 + 18.2364i −0.191907 + 0.726556i
\(631\) 26.5380 + 12.7800i 1.05646 + 0.508764i 0.879719 0.475493i \(-0.157730\pi\)
0.176740 + 0.984258i \(0.443445\pi\)
\(632\) 22.5166 + 15.3516i 0.895663 + 0.610653i
\(633\) 0.635270 + 9.64904i 0.0252497 + 0.383515i
\(634\) 0.0949140 1.26654i 0.00376951 0.0503007i
\(635\) 9.90014 + 12.4144i 0.392875 + 0.492650i
\(636\) 0.519791 2.18590i 0.0206110 0.0866767i
\(637\) −12.6425 4.33943i −0.500912 0.171934i
\(638\) −36.0805 −1.42844
\(639\) −6.51543 31.1353i −0.257746 1.23169i
\(640\) −13.5485 9.23724i −0.535553 0.365134i
\(641\) 5.25526 23.0248i 0.207570 0.909425i −0.758608 0.651548i \(-0.774120\pi\)
0.966178 0.257877i \(-0.0830229\pi\)
\(642\) 4.57272 + 20.9054i 0.180471 + 0.825070i
\(643\) −0.411757 5.49452i −0.0162381 0.216683i −0.999420 0.0340536i \(-0.989158\pi\)
0.983182 0.182629i \(-0.0584607\pi\)
\(644\) −3.62511 0.604827i −0.142849 0.0238335i
\(645\) −19.0651 6.07045i −0.750689 0.239024i
\(646\) −9.45421 1.42499i −0.371971 0.0560656i
\(647\) 2.51711 + 33.5886i 0.0989580 + 1.32050i 0.796797 + 0.604247i \(0.206526\pi\)
−0.697839 + 0.716255i \(0.745855\pi\)
\(648\) −6.85476 + 25.7027i −0.269281 + 1.00970i
\(649\) 17.1246 + 5.28223i 0.672198 + 0.207346i
\(650\) 4.67365 0.704439i 0.183316 0.0276304i
\(651\) 5.17274 + 9.49524i 0.202736 + 0.372148i
\(652\) 2.48363 + 0.374346i 0.0972663 + 0.0146605i
\(653\) −17.2318 8.29840i −0.674333 0.324742i 0.0651902 0.997873i \(-0.479235\pi\)
−0.739523 + 0.673131i \(0.764949\pi\)
\(654\) −8.24073 + 13.9794i −0.322238 + 0.546638i
\(655\) −5.55269 −0.216962
\(656\) 20.4637 35.4441i 0.798972 1.38386i
\(657\) −7.63898 + 2.20560i −0.298025 + 0.0860486i
\(658\) 1.34825 + 22.7948i 0.0525601 + 0.888632i
\(659\) 8.67727 + 8.05133i 0.338018 + 0.313635i 0.830858 0.556485i \(-0.187850\pi\)
−0.492839 + 0.870120i \(0.664041\pi\)
\(660\) 1.65169 1.10432i 0.0642919 0.0429857i
\(661\) −13.7161 34.9480i −0.533493 1.35932i −0.902820 0.430019i \(-0.858507\pi\)
0.369326 0.929300i \(-0.379588\pi\)
\(662\) 3.52138 + 8.97233i 0.136862 + 0.348720i
\(663\) 4.90546 3.27980i 0.190512 0.127377i
\(664\) −4.93709 4.58095i −0.191596 0.177775i
\(665\) 13.9805 12.5689i 0.542142 0.487400i
\(666\) −3.35557 + 13.5643i −0.130026 + 0.525605i
\(667\) 28.9675 50.1732i 1.12163 1.94271i
\(668\) 4.05698 0.156969
\(669\) 0.610951 1.03641i 0.0236207 0.0400698i
\(670\) −27.8338 13.4041i −1.07531 0.517844i
\(671\) −23.1588 3.49063i −0.894036 0.134754i
\(672\) −4.02243 + 3.55092i −0.155169 + 0.136980i
\(673\) −38.9412 + 5.86944i −1.50107 + 0.226250i −0.847574 0.530677i \(-0.821938\pi\)
−0.653499 + 0.756928i \(0.726699\pi\)
\(674\) −20.9993 6.47743i −0.808864 0.249501i
\(675\) −9.60395 0.261016i −0.369656 0.0100465i
\(676\) 0.145292 + 1.93879i 0.00558815 + 0.0745687i
\(677\) 41.3049 + 6.22571i 1.58747 + 0.239273i 0.882623 0.470081i \(-0.155775\pi\)
0.704852 + 0.709355i \(0.251013\pi\)
\(678\) 13.8655 + 4.41486i 0.532501 + 0.169552i
\(679\) 42.8508 12.4834i 1.64446 0.479070i
\(680\) −0.699549 9.33483i −0.0268265 0.357975i
\(681\) −1.21467 5.55320i −0.0465464 0.212799i
\(682\) −2.18529 + 9.57439i −0.0836791 + 0.366622i
\(683\) 36.7677 + 25.0678i 1.40688 + 0.959193i 0.998933 + 0.0461871i \(0.0147071\pi\)
0.407946 + 0.913006i \(0.366245\pi\)
\(684\) 1.86019 1.66433i 0.0711263 0.0636373i
\(685\) −3.97932 −0.152042
\(686\) −11.3705 22.0322i −0.434129 0.841193i
\(687\) −5.25955 + 22.1182i −0.200664 + 0.843863i
\(688\) 14.3677 + 18.0166i 0.547764 + 0.686875i
\(689\) −0.890578 + 11.8839i −0.0339283 + 0.452742i
\(690\) −1.80712 27.4481i −0.0687959 1.04493i
\(691\) 26.6606 + 18.1769i 1.01422 + 0.691482i 0.951848 0.306571i \(-0.0991818\pi\)
0.0623697 + 0.998053i \(0.480134\pi\)
\(692\) 2.70449 + 1.30241i 0.102809 + 0.0495103i
\(693\) 8.23328 + 23.2631i 0.312757 + 0.883691i
\(694\) −29.1146 + 14.0209i −1.10518 + 0.532225i
\(695\) −33.7039 5.08005i −1.27846 0.192697i
\(696\) −15.8388 41.4567i −0.600367 1.57141i
\(697\) 20.3910 3.07344i 0.772363 0.116415i
\(698\) 5.15119 + 22.5688i 0.194975 + 0.854243i
\(699\) −0.0120399 + 0.143240i −0.000455391 + 0.00541784i
\(700\) −0.831008 0.585918i −0.0314092 0.0221456i
\(701\) 16.2136 20.3312i 0.612378 0.767898i −0.374872 0.927077i \(-0.622313\pi\)
0.987250 + 0.159179i \(0.0508846\pi\)
\(702\) 1.35211 13.2137i 0.0510321 0.498720i
\(703\) 10.2094 9.47291i 0.385054 0.357278i
\(704\) −26.8918 −1.01352
\(705\) 18.9934 5.67081i 0.715332 0.213575i
\(706\) 7.00320 6.49802i 0.263569 0.244556i
\(707\) −16.2298 5.28705i −0.610385 0.198840i
\(708\) 0.136328 + 2.07067i 0.00512351 + 0.0778205i
\(709\) −20.2060 + 6.23272i −0.758851 + 0.234075i −0.649949 0.759978i \(-0.725210\pi\)
−0.108902 + 0.994052i \(0.534734\pi\)
\(710\) 24.9157 + 3.75544i 0.935070 + 0.140939i
\(711\) 22.5683 + 15.9932i 0.846377 + 0.599791i
\(712\) −30.0382 27.8714i −1.12573 1.04453i
\(713\) −11.5596 10.7257i −0.432909 0.401681i
\(714\) 10.7795 + 1.89900i 0.403413 + 0.0710682i
\(715\) −7.72508 + 7.16783i −0.288902 + 0.268062i
\(716\) −4.29620 −0.160557
\(717\) 24.3204 7.26128i 0.908261 0.271178i
\(718\) −0.546201 2.39306i −0.0203840 0.0893083i
\(719\) −19.0987 + 13.0213i −0.712261 + 0.485611i −0.864436 0.502742i \(-0.832325\pi\)
0.152175 + 0.988353i \(0.451372\pi\)
\(720\) −15.3859 10.9033i −0.573397 0.406342i
\(721\) −1.74229 0.567570i −0.0648861 0.0211374i
\(722\) −3.94029 + 0.593903i −0.146642 + 0.0221028i
\(723\) 46.9427 + 0.425176i 1.74582 + 0.0158125i
\(724\) −1.74278 + 0.262682i −0.0647699 + 0.00976249i
\(725\) 13.2433 9.02915i 0.491845 0.335334i
\(726\) 1.15611 2.86903i 0.0429071 0.106480i
\(727\) −2.03010 + 27.0898i −0.0752924 + 1.00471i 0.823781 + 0.566908i \(0.191861\pi\)
−0.899073 + 0.437798i \(0.855758\pi\)
\(728\) 9.49247 11.5267i 0.351814 0.427207i
\(729\) −7.42896 + 25.9579i −0.275146 + 0.961402i
\(730\) 0.470663 6.28056i 0.0174200 0.232454i
\(731\) −2.58364 + 11.3197i −0.0955593 + 0.418673i
\(732\) −0.579503 2.64935i −0.0214191 0.0979229i
\(733\) −15.2180 19.0827i −0.562089 0.704837i 0.416854 0.908974i \(-0.363133\pi\)
−0.978942 + 0.204137i \(0.934561\pi\)
\(734\) −0.221341 0.383373i −0.00816983 0.0141506i
\(735\) −16.3566 + 13.9880i −0.603323 + 0.515954i
\(736\) 3.91248 6.77661i 0.144216 0.249789i
\(737\) −39.9664 + 6.02396i −1.47218 + 0.221895i
\(738\) 23.9332 39.7720i 0.880994 1.46403i
\(739\) −31.6943 + 9.77641i −1.16590 + 0.359631i −0.816501 0.577344i \(-0.804089\pi\)
−0.349395 + 0.936976i \(0.613613\pi\)
\(740\) 1.06066 + 0.723145i 0.0389906 + 0.0265833i
\(741\) −8.34782 + 10.2755i −0.306665 + 0.377481i
\(742\) −16.4386 + 14.7787i −0.603480 + 0.542544i
\(743\) 16.0411 + 10.9366i 0.588491 + 0.401226i 0.820633 0.571455i \(-0.193621\pi\)
−0.232142 + 0.972682i \(0.574573\pi\)
\(744\) −11.9603 + 1.69209i −0.438487 + 0.0620350i
\(745\) −6.65717 3.20593i −0.243900 0.117456i
\(746\) −10.3682 + 26.4179i −0.379608 + 0.967226i
\(747\) −4.92608 4.73965i −0.180236 0.173415i
\(748\) −0.718866 0.901429i −0.0262843 0.0329595i
\(749\) −9.27710 + 22.5869i −0.338978 + 0.825309i
\(750\) 10.5363 26.1472i 0.384731 0.954761i
\(751\) 10.4433 + 5.02924i 0.381082 + 0.183520i 0.614611 0.788830i \(-0.289313\pi\)
−0.233529 + 0.972350i \(0.575027\pi\)
\(752\) −21.8152 6.72908i −0.795517 0.245384i
\(753\) −2.90157 + 12.2021i −0.105739 + 0.444669i
\(754\) 11.0800 + 19.1911i 0.403509 + 0.698898i
\(755\) −3.01759 13.2209i −0.109821 0.481158i
\(756\) −2.17611 + 1.85199i −0.0791445 + 0.0673563i
\(757\) 9.36879 41.0474i 0.340515 1.49189i −0.457476 0.889222i \(-0.651246\pi\)
0.797991 0.602670i \(-0.205896\pi\)
\(758\) 24.2017 7.46523i 0.879044 0.271149i
\(759\) −22.1826 28.3389i −0.805177 1.02864i
\(760\) 7.67290 + 19.5502i 0.278325 + 0.709161i
\(761\) 11.8963 52.1210i 0.431240 1.88939i −0.0252942 0.999680i \(-0.508052\pi\)
0.456534 0.889706i \(-0.349091\pi\)
\(762\) −1.36260 20.6963i −0.0493617 0.749749i
\(763\) −16.8069 + 7.77067i −0.608449 + 0.281317i
\(764\) −0.637365 2.79248i −0.0230591 0.101028i
\(765\) −0.538304 9.48612i −0.0194624 0.342972i
\(766\) 18.3588 + 31.7985i 0.663332 + 1.14892i
\(767\) −2.44919 10.7306i −0.0884351 0.387459i
\(768\) −3.04922 7.98108i −0.110029 0.287992i
\(769\) 22.5835 + 3.40391i 0.814381 + 0.122748i 0.543009 0.839727i \(-0.317285\pi\)
0.271371 + 0.962475i \(0.412523\pi\)
\(770\) −19.5448 0.307298i −0.704347 0.0110743i
\(771\) 10.9224 5.13861i 0.393361 0.185063i
\(772\) −1.77951 + 1.65115i −0.0640461 + 0.0594261i
\(773\) 19.3568 49.3203i 0.696216 1.77393i 0.0655828 0.997847i \(-0.479109\pi\)
0.630633 0.776081i \(-0.282795\pi\)
\(774\) 15.9224 + 20.7253i 0.572318 + 0.744956i
\(775\) −1.59388 4.06114i −0.0572539 0.145880i
\(776\) −3.72607 + 49.7209i −0.133758 + 1.78488i
\(777\) −11.9529 + 10.5518i −0.428806 + 0.378542i
\(778\) −0.149677 1.99730i −0.00536617 0.0716066i
\(779\) −41.6835 + 20.0737i −1.49347 + 0.719215i
\(780\) −1.09460 0.539399i −0.0391930 0.0193136i
\(781\) 29.7010 14.3032i 1.06278 0.511810i
\(782\) −15.7843 + 2.37910i −0.564446 + 0.0850765i
\(783\) −15.3115 42.3627i −0.547187 1.51392i
\(784\) 24.6148 2.92202i 0.879100 0.104358i
\(785\) 12.7596 22.1003i 0.455410 0.788794i
\(786\) 5.95555 + 4.13993i 0.212427 + 0.147667i
\(787\) 2.89006 38.5652i 0.103020 1.37470i −0.670962 0.741492i \(-0.734119\pi\)
0.773981 0.633208i \(-0.218262\pi\)
\(788\) −1.99315 1.84937i −0.0710030 0.0658811i
\(789\) 7.87703 + 36.0119i 0.280430 + 1.28206i
\(790\) −18.1034 + 12.3427i −0.644089 + 0.439133i
\(791\) 10.1469 + 13.1425i 0.360783 + 0.467293i
\(792\) −27.5632 0.499340i −0.979417 0.0177433i
\(793\) 5.25519 + 13.3900i 0.186617 + 0.475493i
\(794\) −19.9633 9.61384i −0.708472 0.341182i
\(795\) 15.7559 + 10.9525i 0.558803 + 0.388446i
\(796\) −1.15596 5.06459i −0.0409719 0.179510i
\(797\) −13.4774 + 34.3400i −0.477395 + 1.21638i 0.466021 + 0.884774i \(0.345687\pi\)
−0.943417 + 0.331610i \(0.892408\pi\)
\(798\) −24.3659 + 3.05727i −0.862542 + 0.108226i
\(799\) −4.20238 10.7075i −0.148669 0.378803i
\(800\) 1.78870 1.21952i 0.0632401 0.0431164i
\(801\) −29.9713 28.8370i −1.05898 1.01890i
\(802\) −17.4099 30.1549i −0.614766 1.06481i
\(803\) −4.11997 7.13600i −0.145391 0.251824i
\(804\) −2.30331 4.07422i −0.0812313 0.143687i
\(805\) 16.1190 26.9321i 0.568121 0.949232i
\(806\) 5.76365 1.77785i 0.203016 0.0626221i
\(807\) −0.652780 9.91500i −0.0229789 0.349024i
\(808\) 11.8892 14.9086i 0.418260 0.524481i
\(809\) −12.0068 1.80973i −0.422137 0.0636268i −0.0654609 0.997855i \(-0.520852\pi\)
−0.356676 + 0.934228i \(0.616090\pi\)
\(810\) −17.2230 12.6800i −0.605156 0.445531i
\(811\) −10.3657 + 45.4151i −0.363989 + 1.59474i 0.378973 + 0.925408i \(0.376277\pi\)
−0.742962 + 0.669333i \(0.766580\pi\)
\(812\) 1.13375 4.63048i 0.0397868 0.162498i
\(813\) −8.65048 + 14.6745i −0.303386 + 0.514658i
\(814\) −14.4809 −0.507557
\(815\) −10.7252 + 18.5765i −0.375687 + 0.650708i
\(816\) −5.55711 + 9.42698i −0.194538 + 0.330010i
\(817\) −1.94668 25.9766i −0.0681057 0.908808i
\(818\) −6.12401 + 7.67927i −0.214121 + 0.268499i
\(819\) 9.84516 11.5231i 0.344018 0.402650i
\(820\) −2.65882 3.33406i −0.0928500 0.116430i
\(821\) 2.07554 1.92582i 0.0724367 0.0672115i −0.643124 0.765762i \(-0.722362\pi\)
0.715560 + 0.698551i \(0.246171\pi\)
\(822\) 4.26802 + 2.96687i 0.148864 + 0.103481i
\(823\) −16.7734 + 11.4359i −0.584682 + 0.398630i −0.819222 0.573477i \(-0.805594\pi\)
0.234539 + 0.972107i \(0.424642\pi\)
\(824\) 1.27632 1.60045i 0.0444626 0.0557543i
\(825\) −2.12755 9.72666i −0.0740718 0.338639i
\(826\) 10.4846 17.5180i 0.364807 0.609530i
\(827\) −20.6671 9.95277i −0.718667 0.346092i 0.0385487 0.999257i \(-0.487727\pi\)
−0.757216 + 0.653165i \(0.773441\pi\)
\(828\) 2.14868 3.57066i 0.0746719 0.124089i
\(829\) −18.7337 + 5.77859i −0.650649 + 0.200699i −0.602472 0.798140i \(-0.705817\pi\)
−0.0481771 + 0.998839i \(0.515341\pi\)
\(830\) 4.87868 2.34945i 0.169342 0.0815506i
\(831\) 35.8538 16.8680i 1.24375 0.585143i
\(832\) 8.25820 + 14.3036i 0.286302 + 0.495889i
\(833\) 8.88370 + 8.77848i 0.307802 + 0.304156i
\(834\) 32.3616 + 30.5773i 1.12059 + 1.05881i
\(835\) −12.6582 + 32.2525i −0.438055 + 1.11615i
\(836\) 2.13728 + 1.45718i 0.0739195 + 0.0503975i
\(837\) −12.1688 + 1.49729i −0.420615 + 0.0517541i
\(838\) 1.52304 20.3235i 0.0526124 0.702064i
\(839\) −27.4068 + 18.6857i −0.946189 + 0.645101i −0.934929 0.354836i \(-0.884537\pi\)
−0.0112602 + 0.999937i \(0.503584\pi\)
\(840\) −8.22677 22.5920i −0.283851 0.779498i
\(841\) 38.1306 + 25.9970i 1.31485 + 0.896448i
\(842\) −24.2336 + 30.3880i −0.835146 + 1.04724i
\(843\) −13.4298 35.1514i −0.462547 1.21068i
\(844\) −0.723516 0.907261i −0.0249045 0.0312292i
\(845\) −15.8665 4.89415i −0.545823 0.168364i
\(846\) −24.5994 8.07870i −0.845744 0.277751i
\(847\) 2.94708 1.94213i 0.101263 0.0667325i
\(848\) −8.07408 20.5724i −0.277265 0.706460i
\(849\) 18.0298 + 47.1915i 0.618780 + 1.61961i
\(850\) −4.22006 1.30171i −0.144747 0.0446484i
\(851\) 11.6261 20.1370i 0.398538 0.690289i
\(852\) 2.77464 + 2.62165i 0.0950576 + 0.0898163i
\(853\) 46.9254 + 14.4746i 1.60670 + 0.495600i 0.962959 0.269647i \(-0.0869072\pi\)
0.643736 + 0.765247i \(0.277383\pi\)
\(854\) −10.1370 + 24.6806i −0.346882 + 0.844553i
\(855\) 7.42726 + 19.9812i 0.254007 + 0.683343i
\(856\) −19.9964 18.5539i −0.683462 0.634160i
\(857\) −0.880241 + 1.10379i −0.0300684 + 0.0377046i −0.796638 0.604456i \(-0.793390\pi\)
0.766570 + 0.642161i \(0.221962\pi\)
\(858\) 13.6297 1.92826i 0.465310 0.0658298i
\(859\) −9.69694 + 42.4851i −0.330855 + 1.44957i 0.486623 + 0.873612i \(0.338229\pi\)
−0.817478 + 0.575959i \(0.804629\pi\)
\(860\) 2.29440 0.707728i 0.0782383 0.0241333i
\(861\) 48.2742 21.7912i 1.64518 0.742641i
\(862\) 31.6433 + 9.76065i 1.07777 + 0.332449i
\(863\) 24.1059 41.7526i 0.820573 1.42127i −0.0846832 0.996408i \(-0.526988\pi\)
0.905256 0.424866i \(-0.139679\pi\)
\(864\) −2.06803 5.72169i −0.0703559 0.194656i
\(865\) −18.7923 + 17.4367i −0.638958 + 0.592866i
\(866\) 0.458599 + 6.11958i 0.0155838 + 0.207952i
\(867\) 23.6953 3.35229i 0.804733 0.113850i
\(868\) −1.16008 0.581308i −0.0393758 0.0197309i
\(869\) −10.4728 + 26.6842i −0.355265 + 0.905200i
\(870\) 35.6796 + 0.323162i 1.20965 + 0.0109562i
\(871\) 15.4774 + 19.4080i 0.524431 + 0.657616i
\(872\) −1.54582 20.6275i −0.0523480 0.698535i
\(873\) −4.69544 + 50.3898i −0.158916 + 1.70543i
\(874\) 32.2665 15.5387i 1.09143 0.525605i
\(875\) 26.8586 17.6998i 0.907986 0.598364i
\(876\) 0.601637 0.740569i 0.0203274 0.0250215i
\(877\) 15.8743 7.64464i 0.536035 0.258141i −0.146224 0.989252i \(-0.546712\pi\)
0.682259 + 0.731110i \(0.260998\pi\)
\(878\) −7.48978 6.94950i −0.252768 0.234534i
\(879\) −13.1943 + 12.0220i −0.445034 + 0.405492i
\(880\) 7.13979 18.1919i 0.240682 0.613248i
\(881\) −34.1724 −1.15130 −0.575649 0.817697i \(-0.695251\pi\)
−0.575649 + 0.817697i \(0.695251\pi\)
\(882\) 27.9724 2.80780i 0.941878 0.0945436i
\(883\) −29.0087 −0.976220 −0.488110 0.872782i \(-0.662313\pi\)
−0.488110 + 0.872782i \(0.662313\pi\)
\(884\) −0.258710 + 0.659181i −0.00870134 + 0.0221707i
\(885\) −16.8869 5.37690i −0.567648 0.180743i
\(886\) 31.8917 + 29.5912i 1.07142 + 0.994135i
\(887\) −0.640618 + 0.308506i −0.0215099 + 0.0103586i −0.444608 0.895725i \(-0.646657\pi\)
0.423098 + 0.906084i \(0.360943\pi\)
\(888\) −6.35690 16.6387i −0.213323 0.558357i
\(889\) 12.1540 20.3072i 0.407632 0.681083i
\(890\) 29.6829 14.2945i 0.994973 0.479154i
\(891\) −27.9628 1.01349i −0.936789 0.0339532i
\(892\) 0.0107891 + 0.143971i 0.000361246 + 0.00482049i
\(893\) 16.0903 + 20.1766i 0.538441 + 0.675184i
\(894\) 4.74992 + 8.40193i 0.158861 + 0.281002i
\(895\) 13.4046 34.1544i 0.448066 1.14165i
\(896\) −5.81243 + 23.7393i −0.194180 + 0.793073i
\(897\) −8.26126 + 20.5014i −0.275836 + 0.684522i
\(898\) −2.40253 32.0595i −0.0801734 1.06984i
\(899\) 14.9943 13.9127i 0.500088 0.464014i
\(900\) 0.964210 0.632112i 0.0321403 0.0210704i
\(901\) 5.56758 9.64334i 0.185483 0.321266i
\(902\) 45.9674 + 14.1791i 1.53055 + 0.472112i
\(903\) 1.49109 + 29.7843i 0.0496205 + 0.991160i
\(904\) −17.7247 + 5.46733i −0.589513 + 0.181841i
\(905\) 3.34936 14.6745i 0.111336 0.487797i
\(906\) −6.62062 + 16.4299i −0.219955 + 0.545848i
\(907\) 35.9745 45.1106i 1.19451 1.49787i 0.372856 0.927889i \(-0.378379\pi\)
0.821657 0.569983i \(-0.193050\pi\)
\(908\) 0.500060 + 0.463988i 0.0165951 + 0.0153980i
\(909\) 12.3396 14.9111i 0.409278 0.494569i
\(910\) 5.83857 + 10.4902i 0.193547 + 0.347746i
\(911\) −33.8989 10.4564i −1.12312 0.346437i −0.323074 0.946374i \(-0.604716\pi\)
−0.800047 + 0.599937i \(0.795192\pi\)
\(912\) 5.67975 23.8853i 0.188075 0.790922i
\(913\) 3.54220 6.13526i 0.117230 0.203048i
\(914\) −13.7641 4.24565i −0.455275 0.140434i
\(915\) 22.8702 + 3.65926i 0.756065 + 0.120971i
\(916\) −0.996756 2.53969i −0.0329337 0.0839138i
\(917\) 2.90211 + 7.75059i 0.0958362 + 0.255947i
\(918\) −6.49523 + 10.5757i −0.214375 + 0.349050i
\(919\) 15.5698 + 4.80265i 0.513601 + 0.158425i 0.540712 0.841208i \(-0.318155\pi\)
−0.0271115 + 0.999632i \(0.508631\pi\)
\(920\) 21.8621 + 27.4141i 0.720771 + 0.903818i
\(921\) 9.37898 11.5448i 0.309048 0.380414i
\(922\) 12.6393 15.8491i 0.416252 0.521963i
\(923\) −16.7287 11.4054i −0.550632 0.375414i
\(924\) −2.40470 1.72829i −0.0791087 0.0568567i
\(925\) 5.31522 3.62385i 0.174763 0.119152i
\(926\) 2.78222 37.1261i 0.0914294 1.22004i
\(927\) 1.32467 1.60072i 0.0435078 0.0525745i
\(928\) 8.38634 + 5.71771i 0.275295 + 0.187693i
\(929\) 9.36683 23.8663i 0.307316 0.783028i −0.690879 0.722970i \(-0.742776\pi\)
0.998195 0.0600577i \(-0.0191285\pi\)
\(930\) 2.24676 9.44841i 0.0736742 0.309826i
\(931\) −24.8509 12.9453i −0.814455 0.424264i
\(932\) −0.00862501 0.0149389i −0.000282521 0.000489342i
\(933\) 1.17006 13.9203i 0.0383061 0.455732i
\(934\) 1.00039 0.481763i 0.0327338 0.0157638i
\(935\) 9.40920 2.90235i 0.307714 0.0949171i
\(936\) 8.19879 + 14.8141i 0.267986 + 0.484214i
\(937\) −20.3521 9.80104i −0.664873 0.320186i 0.0708319 0.997488i \(-0.477435\pi\)
−0.735705 + 0.677302i \(0.763149\pi\)
\(938\) −4.16239 + 45.8568i −0.135907 + 1.49728i
\(939\) 17.1034 15.5837i 0.558147 0.508555i
\(940\) −1.48310 + 1.85975i −0.0483733 + 0.0606582i
\(941\) 12.2334 8.34061i 0.398799 0.271896i −0.347270 0.937765i \(-0.612891\pi\)
0.746069 + 0.665869i \(0.231939\pi\)
\(942\) −30.1627 + 14.1905i −0.982754 + 0.462352i
\(943\) −56.6225 + 52.5380i −1.84388 + 1.71087i
\(944\) 12.7262 + 15.9582i 0.414203 + 0.519394i
\(945\) −7.93342 23.0783i −0.258074 0.750736i
\(946\) −16.8873 + 21.1760i −0.549054 + 0.688492i
\(947\) 0.531001 + 7.08571i 0.0172552 + 0.230255i 0.999163 + 0.0408970i \(0.0130215\pi\)
−0.981908 + 0.189358i \(0.939359\pi\)
\(948\) −3.31925 0.0300636i −0.107804 0.000976420i
\(949\) −2.53040 + 4.38279i −0.0821404 + 0.142271i
\(950\) 9.90815 0.321463
\(951\) 0.808711 + 1.43049i 0.0262243 + 0.0463870i
\(952\) −12.6642 + 5.85530i −0.410448 + 0.189771i
\(953\) −11.6902 + 51.2181i −0.378682 + 1.65912i 0.322829 + 0.946457i \(0.395366\pi\)
−0.701511 + 0.712658i \(0.747491\pi\)
\(954\) −8.73311 23.4943i −0.282745 0.760656i
\(955\) 24.1885 + 3.64584i 0.782723 + 0.117976i
\(956\) −1.89906 + 2.38134i −0.0614199 + 0.0770181i
\(957\) 38.8068 25.9463i 1.25445 0.838726i
\(958\) −15.4109 + 4.75364i −0.497904 + 0.153583i
\(959\) 2.07979 + 5.55443i 0.0671599 + 0.179362i
\(960\) 26.5930 + 0.240862i 0.858284 + 0.00777378i
\(961\) 12.7163 + 22.0252i 0.410202 + 0.710491i
\(962\) 4.44695 + 7.70234i 0.143375 + 0.248334i
\(963\) −19.9518 19.1967i −0.642938 0.618605i
\(964\) −4.65465 + 3.17349i −0.149916 + 0.102211i
\(965\) −7.57417 19.2987i −0.243821 0.621246i
\(966\) −37.3683 + 16.8682i −1.20231 + 0.542725i
\(967\) −2.33545 + 5.95063i −0.0751031 + 0.191360i −0.963495 0.267726i \(-0.913728\pi\)
0.888392 + 0.459086i \(0.151823\pi\)
\(968\) 0.877382 + 3.84406i 0.0282001 + 0.123553i
\(969\) 11.1933 5.26607i 0.359582 0.169171i
\(970\) −36.1178 17.3934i −1.15967 0.558469i
\(971\) 9.80672 + 24.9871i 0.314713 + 0.801875i 0.997461 + 0.0712208i \(0.0226895\pi\)
−0.682748 + 0.730654i \(0.739215\pi\)
\(972\) −1.04599 3.06663i −0.0335502 0.0983621i
\(973\) 10.5245 + 49.6999i 0.337399 + 1.59330i
\(974\) 46.8959 31.9731i 1.50264 1.02448i
\(975\) −4.52022 + 4.11859i −0.144763 + 0.131901i
\(976\) −19.5543 18.1438i −0.625919 0.580768i
\(977\) 2.36103 31.5058i 0.0755361 1.00796i −0.822709 0.568463i \(-0.807538\pi\)
0.898245 0.439495i \(-0.144843\pi\)
\(978\) 25.3535 11.9279i 0.810714 0.381413i
\(979\) 21.5514 37.3282i 0.688786 1.19301i
\(980\) 0.653590 2.49868i 0.0208782 0.0798173i
\(981\) −1.18951 20.9618i −0.0379781 0.669259i
\(982\) 22.7240 3.42510i 0.725153 0.109299i
\(983\) −41.7580 + 20.1096i −1.33187 + 0.641396i −0.958182 0.286158i \(-0.907622\pi\)
−0.373690 + 0.927554i \(0.621907\pi\)
\(984\) 3.88713 + 59.0412i 0.123917 + 1.88216i
\(985\) 20.9211 10.0751i 0.666602 0.321019i
\(986\) −1.54734 20.6478i −0.0492772 0.657559i
\(987\) −17.8423 23.5476i −0.567928 0.749528i
\(988\) 0.118727 1.58430i 0.00377720 0.0504032i
\(989\) −15.8891 40.4846i −0.505242 1.28734i
\(990\) 8.46999 20.4823i 0.269194 0.650970i
\(991\) −15.5528 + 39.6278i −0.494050 + 1.25882i 0.438811 + 0.898580i \(0.355400\pi\)
−0.932860 + 0.360238i \(0.882695\pi\)
\(992\) 2.02520 1.87911i 0.0643000 0.0596617i
\(993\) −10.2397 7.11799i −0.324946 0.225883i
\(994\) −7.78026 36.7408i −0.246775 1.16535i
\(995\) 43.8697 + 6.61229i 1.39076 + 0.209624i
\(996\) 0.810042 + 0.129608i 0.0256672 + 0.00410678i
\(997\) −2.08803 9.14825i −0.0661285 0.289728i 0.931041 0.364915i \(-0.118902\pi\)
−0.997169 + 0.0751868i \(0.976045\pi\)
\(998\) 1.22234 + 2.11716i 0.0386925 + 0.0670174i
\(999\) −6.14527 17.0023i −0.194428 0.537928i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 441.2.z.a.142.16 yes 648
9.4 even 3 441.2.y.a.436.16 yes 648
49.39 even 21 441.2.y.a.88.16 648
441.382 even 21 inner 441.2.z.a.382.16 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.16 648 49.39 even 21
441.2.y.a.436.16 yes 648 9.4 even 3
441.2.z.a.142.16 yes 648 1.1 even 1 trivial
441.2.z.a.382.16 yes 648 441.382 even 21 inner