Properties

Label 144.2.u.a.131.17
Level $144$
Weight $2$
Character 144.131
Analytic conductor $1.150$
Analytic rank $0$
Dimension $88$
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] = [144,2,Mod(11,144)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(144, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("144.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 144.u (of order \(12\), degree \(4\), 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: \(1.14984578911\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 131.17
Character \(\chi\) \(=\) 144.131
Dual form 144.2.u.a.11.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.772565 + 1.18454i) q^{2} +(-0.501476 + 1.65787i) q^{3} +(-0.806286 + 1.83027i) q^{4} +(3.72190 - 0.997280i) q^{5} +(-2.35124 + 0.686791i) q^{6} +(-0.481387 - 0.833787i) q^{7} +(-2.79095 + 0.458925i) q^{8} +(-2.49704 - 1.66276i) q^{9} +O(q^{10})\) \(q+(0.772565 + 1.18454i) q^{2} +(-0.501476 + 1.65787i) q^{3} +(-0.806286 + 1.83027i) q^{4} +(3.72190 - 0.997280i) q^{5} +(-2.35124 + 0.686791i) q^{6} +(-0.481387 - 0.833787i) q^{7} +(-2.79095 + 0.458925i) q^{8} +(-2.49704 - 1.66276i) q^{9} +(4.05673 + 3.63829i) q^{10} +(-3.75758 - 1.00684i) q^{11} +(-2.63002 - 2.25455i) q^{12} +(1.60802 - 0.430868i) q^{13} +(0.615754 - 1.21438i) q^{14} +(-0.213084 + 6.67053i) q^{15} +(-2.69981 - 2.95145i) q^{16} +2.58216i q^{17} +(0.0404807 - 4.24245i) q^{18} +(4.02190 - 4.02190i) q^{19} +(-1.17562 + 7.61619i) q^{20} +(1.62371 - 0.379952i) q^{21} +(-1.71033 - 5.22887i) q^{22} +(0.600513 + 0.346706i) q^{23} +(0.638755 - 4.85716i) q^{24} +(8.52786 - 4.92356i) q^{25} +(1.75268 + 1.57190i) q^{26} +(4.00884 - 3.30593i) q^{27} +(1.91419 - 0.208800i) q^{28} +(-5.75605 - 1.54233i) q^{29} +(-8.06615 + 4.90101i) q^{30} +(3.07839 + 1.77731i) q^{31} +(1.41034 - 5.47822i) q^{32} +(3.55354 - 5.72466i) q^{33} +(-3.05868 + 1.99488i) q^{34} +(-2.62320 - 2.62320i) q^{35} +(5.05664 - 3.22962i) q^{36} +(-2.11774 + 2.11774i) q^{37} +(7.87129 + 1.65693i) q^{38} +(-0.0920616 + 2.88196i) q^{39} +(-9.92995 + 4.49143i) q^{40} +(-4.97738 + 8.62108i) q^{41} +(1.70449 + 1.62982i) q^{42} +(-1.78256 + 6.65259i) q^{43} +(4.87248 - 6.06560i) q^{44} +(-10.9520 - 3.69837i) q^{45} +(0.0532467 + 0.979187i) q^{46} +(2.88971 + 5.00512i) q^{47} +(6.24700 - 2.99584i) q^{48} +(3.03653 - 5.25943i) q^{49} +(12.4205 + 6.29784i) q^{50} +(-4.28087 - 1.29489i) q^{51} +(-0.507919 + 3.29052i) q^{52} +(-6.68090 - 6.68090i) q^{53} +(7.01311 + 2.19460i) q^{54} -14.9894 q^{55} +(1.72617 + 2.10614i) q^{56} +(4.65088 + 8.68465i) q^{57} +(-2.61997 - 8.00984i) q^{58} +(-2.34478 - 8.75083i) q^{59} +(-12.0371 - 5.76836i) q^{60} +(0.570345 - 2.12855i) q^{61} +(0.272957 + 5.01957i) q^{62} +(-0.184342 + 2.88243i) q^{63} +(7.57878 - 2.56167i) q^{64} +(5.55520 - 3.20730i) q^{65} +(9.52645 - 0.213350i) q^{66} +(-1.12686 - 4.20548i) q^{67} +(-4.72606 - 2.08196i) q^{68} +(-0.875935 + 0.821706i) q^{69} +(1.08070 - 5.13388i) q^{70} +9.40024i q^{71} +(7.73220 + 3.49472i) q^{72} -3.77840i q^{73} +(-4.14465 - 0.872463i) q^{74} +(3.88610 + 16.6071i) q^{75} +(4.11837 + 10.6040i) q^{76} +(0.969360 + 3.61770i) q^{77} +(-3.48493 + 2.11745i) q^{78} +(-9.52430 + 5.49886i) q^{79} +(-12.9918 - 8.29254i) q^{80} +(3.47046 + 8.30397i) q^{81} +(-14.0574 + 0.764420i) q^{82} +(2.35550 - 8.79083i) q^{83} +(-0.613760 + 3.27819i) q^{84} +(2.57514 + 9.61053i) q^{85} +(-9.25742 + 3.02804i) q^{86} +(5.44349 - 8.76932i) q^{87} +(10.9493 + 1.08559i) q^{88} -13.0545 q^{89} +(-4.08025 - 15.8303i) q^{90} +(-1.13333 - 1.13333i) q^{91} +(-1.11875 + 0.819559i) q^{92} +(-4.49027 + 4.21228i) q^{93} +(-3.69629 + 7.28976i) q^{94} +(10.9581 - 18.9801i) q^{95} +(8.37491 + 5.08536i) q^{96} +(1.76559 + 3.05809i) q^{97} +(8.57594 - 0.466347i) q^{98} +(7.70871 + 8.76208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{10} - 6 q^{11} - 16 q^{12} - 2 q^{13} - 6 q^{14} - 2 q^{16} - 10 q^{18} - 8 q^{19} - 48 q^{20} + 2 q^{21} - 2 q^{22} - 12 q^{23} - 16 q^{27} + 8 q^{28} - 6 q^{29} - 34 q^{30} - 6 q^{32} - 8 q^{33} + 2 q^{34} - 26 q^{36} - 8 q^{37} - 6 q^{38} - 32 q^{39} - 2 q^{40} + 48 q^{42} - 2 q^{43} + 6 q^{45} - 40 q^{46} + 42 q^{48} - 24 q^{49} + 72 q^{50} - 12 q^{51} - 2 q^{52} - 38 q^{54} - 16 q^{55} + 36 q^{56} + 16 q^{58} - 42 q^{59} + 70 q^{60} - 2 q^{61} - 44 q^{64} - 12 q^{65} + 104 q^{66} - 2 q^{67} + 96 q^{68} - 10 q^{69} - 16 q^{70} - 10 q^{72} + 78 q^{74} - 56 q^{75} - 14 q^{76} - 6 q^{77} + 12 q^{78} - 8 q^{81} - 36 q^{82} + 54 q^{83} + 158 q^{84} + 8 q^{85} + 54 q^{86} + 48 q^{87} + 22 q^{88} + 64 q^{90} + 20 q^{91} + 108 q^{92} - 34 q^{93} + 6 q^{94} - 58 q^{96} - 4 q^{97} + 46 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.772565 + 1.18454i 0.546286 + 0.837599i
\(3\) −0.501476 + 1.65787i −0.289527 + 0.957170i
\(4\) −0.806286 + 1.83027i −0.403143 + 0.915137i
\(5\) 3.72190 0.997280i 1.66448 0.445997i 0.700869 0.713290i \(-0.252796\pi\)
0.963616 + 0.267292i \(0.0861289\pi\)
\(6\) −2.35124 + 0.686791i −0.959889 + 0.280381i
\(7\) −0.481387 0.833787i −0.181947 0.315142i 0.760596 0.649225i \(-0.224907\pi\)
−0.942544 + 0.334083i \(0.891573\pi\)
\(8\) −2.79095 + 0.458925i −0.986749 + 0.162255i
\(9\) −2.49704 1.66276i −0.832348 0.554253i
\(10\) 4.05673 + 3.63829i 1.28285 + 1.15053i
\(11\) −3.75758 1.00684i −1.13295 0.303574i −0.356839 0.934166i \(-0.616145\pi\)
−0.776114 + 0.630592i \(0.782812\pi\)
\(12\) −2.63002 2.25455i −0.759221 0.650833i
\(13\) 1.60802 0.430868i 0.445985 0.119501i −0.0288351 0.999584i \(-0.509180\pi\)
0.474820 + 0.880083i \(0.342513\pi\)
\(14\) 0.615754 1.21438i 0.164567 0.324556i
\(15\) −0.213084 + 6.67053i −0.0550181 + 1.72232i
\(16\) −2.69981 2.95145i −0.674951 0.737862i
\(17\) 2.58216i 0.626265i 0.949709 + 0.313133i \(0.101378\pi\)
−0.949709 + 0.313133i \(0.898622\pi\)
\(18\) 0.0404807 4.24245i 0.00954139 0.999954i
\(19\) 4.02190 4.02190i 0.922686 0.922686i −0.0745325 0.997219i \(-0.523746\pi\)
0.997219 + 0.0745325i \(0.0237465\pi\)
\(20\) −1.17562 + 7.61619i −0.262877 + 1.70303i
\(21\) 1.62371 0.379952i 0.354323 0.0829123i
\(22\) −1.71033 5.22887i −0.364643 1.11480i
\(23\) 0.600513 + 0.346706i 0.125216 + 0.0722933i 0.561300 0.827613i \(-0.310302\pi\)
−0.436084 + 0.899906i \(0.643635\pi\)
\(24\) 0.638755 4.85716i 0.130385 0.991463i
\(25\) 8.52786 4.92356i 1.70557 0.984712i
\(26\) 1.75268 + 1.57190i 0.343730 + 0.308275i
\(27\) 4.00884 3.30593i 0.771502 0.636227i
\(28\) 1.91419 0.208800i 0.361749 0.0394594i
\(29\) −5.75605 1.54233i −1.06887 0.286403i −0.318842 0.947808i \(-0.603294\pi\)
−0.750029 + 0.661405i \(0.769961\pi\)
\(30\) −8.06615 + 4.90101i −1.47267 + 0.894798i
\(31\) 3.07839 + 1.77731i 0.552894 + 0.319214i 0.750289 0.661110i \(-0.229915\pi\)
−0.197394 + 0.980324i \(0.563248\pi\)
\(32\) 1.41034 5.47822i 0.249316 0.968422i
\(33\) 3.55354 5.72466i 0.618592 0.996536i
\(34\) −3.05868 + 1.99488i −0.524559 + 0.342120i
\(35\) −2.62320 2.62320i −0.443401 0.443401i
\(36\) 5.05664 3.22962i 0.842773 0.538269i
\(37\) −2.11774 + 2.11774i −0.348154 + 0.348154i −0.859422 0.511267i \(-0.829176\pi\)
0.511267 + 0.859422i \(0.329176\pi\)
\(38\) 7.87129 + 1.65693i 1.27689 + 0.268790i
\(39\) −0.0920616 + 2.88196i −0.0147417 + 0.461482i
\(40\) −9.92995 + 4.49143i −1.57006 + 0.710158i
\(41\) −4.97738 + 8.62108i −0.777337 + 1.34639i 0.156135 + 0.987736i \(0.450096\pi\)
−0.933472 + 0.358651i \(0.883237\pi\)
\(42\) 1.70449 + 1.62982i 0.263009 + 0.251487i
\(43\) −1.78256 + 6.65259i −0.271837 + 1.01451i 0.686094 + 0.727513i \(0.259324\pi\)
−0.957931 + 0.286997i \(0.907343\pi\)
\(44\) 4.87248 6.06560i 0.734554 0.914424i
\(45\) −10.9520 3.69837i −1.63263 0.551321i
\(46\) 0.0532467 + 0.979187i 0.00785080 + 0.144373i
\(47\) 2.88971 + 5.00512i 0.421507 + 0.730072i 0.996087 0.0883767i \(-0.0281679\pi\)
−0.574580 + 0.818448i \(0.694835\pi\)
\(48\) 6.24700 2.99584i 0.901676 0.432412i
\(49\) 3.03653 5.25943i 0.433790 0.751347i
\(50\) 12.4205 + 6.29784i 1.75652 + 0.890650i
\(51\) −4.28087 1.29489i −0.599442 0.181321i
\(52\) −0.507919 + 3.29052i −0.0704357 + 0.456314i
\(53\) −6.68090 6.68090i −0.917692 0.917692i 0.0791696 0.996861i \(-0.474773\pi\)
−0.996861 + 0.0791696i \(0.974773\pi\)
\(54\) 7.01311 + 2.19460i 0.954364 + 0.298647i
\(55\) −14.9894 −2.02118
\(56\) 1.72617 + 2.10614i 0.230669 + 0.281444i
\(57\) 4.65088 + 8.68465i 0.616025 + 1.15031i
\(58\) −2.61997 8.00984i −0.344019 1.05174i
\(59\) −2.34478 8.75083i −0.305264 1.13926i −0.932718 0.360607i \(-0.882570\pi\)
0.627454 0.778654i \(-0.284097\pi\)
\(60\) −12.0371 5.76836i −1.55398 0.744692i
\(61\) 0.570345 2.12855i 0.0730251 0.272534i −0.919753 0.392497i \(-0.871611\pi\)
0.992778 + 0.119964i \(0.0382779\pi\)
\(62\) 0.272957 + 5.01957i 0.0346655 + 0.637486i
\(63\) −0.184342 + 2.88243i −0.0232249 + 0.363153i
\(64\) 7.57878 2.56167i 0.947347 0.320209i
\(65\) 5.55520 3.20730i 0.689038 0.397816i
\(66\) 9.52645 0.213350i 1.17263 0.0262615i
\(67\) −1.12686 4.20548i −0.137667 0.513782i −0.999973 0.00739290i \(-0.997647\pi\)
0.862305 0.506389i \(-0.169020\pi\)
\(68\) −4.72606 2.08196i −0.573118 0.252474i
\(69\) −0.875935 + 0.821706i −0.105450 + 0.0989217i
\(70\) 1.08070 5.13388i 0.129168 0.613616i
\(71\) 9.40024i 1.11560i 0.829974 + 0.557801i \(0.188355\pi\)
−0.829974 + 0.557801i \(0.811645\pi\)
\(72\) 7.73220 + 3.49472i 0.911249 + 0.411856i
\(73\) 3.77840i 0.442228i −0.975248 0.221114i \(-0.929031\pi\)
0.975248 0.221114i \(-0.0709693\pi\)
\(74\) −4.14465 0.872463i −0.481805 0.101422i
\(75\) 3.88610 + 16.6071i 0.448728 + 1.91762i
\(76\) 4.11837 + 10.6040i 0.472410 + 1.21636i
\(77\) 0.969360 + 3.61770i 0.110469 + 0.412275i
\(78\) −3.48493 + 2.11745i −0.394590 + 0.239754i
\(79\) −9.52430 + 5.49886i −1.07157 + 0.618670i −0.928609 0.371059i \(-0.878995\pi\)
−0.142958 + 0.989729i \(0.545661\pi\)
\(80\) −12.9918 8.29254i −1.45253 0.927134i
\(81\) 3.47046 + 8.30397i 0.385607 + 0.922663i
\(82\) −14.0574 + 0.764420i −1.55238 + 0.0844161i
\(83\) 2.35550 8.79083i 0.258549 0.964919i −0.707532 0.706681i \(-0.750191\pi\)
0.966081 0.258238i \(-0.0831419\pi\)
\(84\) −0.613760 + 3.27819i −0.0669667 + 0.357680i
\(85\) 2.57514 + 9.61053i 0.279313 + 1.04241i
\(86\) −9.25742 + 3.02804i −0.998253 + 0.326522i
\(87\) 5.44349 8.76932i 0.583604 0.940170i
\(88\) 10.9493 + 1.08559i 1.16720 + 0.115724i
\(89\) −13.0545 −1.38378 −0.691889 0.722004i \(-0.743221\pi\)
−0.691889 + 0.722004i \(0.743221\pi\)
\(90\) −4.08025 15.8303i −0.430096 1.66866i
\(91\) −1.13333 1.13333i −0.118806 0.118806i
\(92\) −1.11875 + 0.819559i −0.116638 + 0.0854449i
\(93\) −4.49027 + 4.21228i −0.465620 + 0.436793i
\(94\) −3.69629 + 7.28976i −0.381244 + 0.751882i
\(95\) 10.9581 18.9801i 1.12428 1.94731i
\(96\) 8.37491 + 5.08536i 0.854761 + 0.519022i
\(97\) 1.76559 + 3.05809i 0.179268 + 0.310502i 0.941630 0.336649i \(-0.109294\pi\)
−0.762362 + 0.647151i \(0.775960\pi\)
\(98\) 8.57594 0.466347i 0.866301 0.0471082i
\(99\) 7.70871 + 8.76208i 0.774755 + 0.880622i
\(100\) 2.13557 + 19.5781i 0.213557 + 1.95781i
\(101\) −4.91426 + 18.3403i −0.488987 + 1.82492i 0.0724058 + 0.997375i \(0.476932\pi\)
−0.561393 + 0.827549i \(0.689734\pi\)
\(102\) −1.77340 6.07127i −0.175593 0.601145i
\(103\) 1.72391 2.98591i 0.169862 0.294210i −0.768509 0.639839i \(-0.779001\pi\)
0.938371 + 0.345629i \(0.112334\pi\)
\(104\) −4.29017 + 1.94049i −0.420686 + 0.190281i
\(105\) 5.66438 3.03344i 0.552787 0.296033i
\(106\) 2.75238 13.0752i 0.267335 1.26998i
\(107\) 6.09696 6.09696i 0.589415 0.589415i −0.348058 0.937473i \(-0.613159\pi\)
0.937473 + 0.348058i \(0.113159\pi\)
\(108\) 2.81849 + 10.0028i 0.271210 + 0.962520i
\(109\) 3.96541 + 3.96541i 0.379817 + 0.379817i 0.871036 0.491219i \(-0.163448\pi\)
−0.491219 + 0.871036i \(0.663448\pi\)
\(110\) −11.5803 17.7556i −1.10414 1.69293i
\(111\) −2.44894 4.57293i −0.232443 0.434043i
\(112\) −1.16123 + 3.67185i −0.109726 + 0.346957i
\(113\) 5.53559 + 3.19597i 0.520744 + 0.300652i 0.737239 0.675632i \(-0.236129\pi\)
−0.216495 + 0.976284i \(0.569462\pi\)
\(114\) −6.69423 + 12.2186i −0.626972 + 1.14438i
\(115\) 2.58081 + 0.691527i 0.240662 + 0.0644852i
\(116\) 7.46390 9.29159i 0.693006 0.862702i
\(117\) −4.73173 1.59786i −0.437449 0.147722i
\(118\) 8.55424 9.53808i 0.787482 0.878051i
\(119\) 2.15297 1.24302i 0.197362 0.113947i
\(120\) −2.46657 18.7149i −0.225166 1.70843i
\(121\) 3.57940 + 2.06657i 0.325400 + 0.187870i
\(122\) 2.96199 0.968850i 0.268166 0.0877155i
\(123\) −11.7966 12.5751i −1.06366 1.13386i
\(124\) −5.73502 + 4.20127i −0.515020 + 0.377285i
\(125\) 13.2066 13.2066i 1.18123 1.18123i
\(126\) −3.55679 + 2.00851i −0.316864 + 0.178932i
\(127\) 3.08724i 0.273948i −0.990575 0.136974i \(-0.956262\pi\)
0.990575 0.136974i \(-0.0437377\pi\)
\(128\) 8.88951 + 6.99833i 0.785729 + 0.618571i
\(129\) −10.1352 6.29135i −0.892354 0.553922i
\(130\) 8.09094 + 4.10253i 0.709622 + 0.359816i
\(131\) −5.07628 + 1.36018i −0.443516 + 0.118840i −0.473664 0.880706i \(-0.657069\pi\)
0.0301478 + 0.999545i \(0.490402\pi\)
\(132\) 7.61253 + 11.1197i 0.662585 + 0.967843i
\(133\) −5.28949 1.41732i −0.458657 0.122897i
\(134\) 4.11101 4.58382i 0.355137 0.395982i
\(135\) 11.6236 16.3023i 1.00040 1.40308i
\(136\) −1.18502 7.20667i −0.101614 0.617966i
\(137\) −0.807507 1.39864i −0.0689899 0.119494i 0.829467 0.558556i \(-0.188644\pi\)
−0.898457 + 0.439062i \(0.855311\pi\)
\(138\) −1.65006 0.402762i −0.140463 0.0342854i
\(139\) −3.80774 + 1.02028i −0.322968 + 0.0865390i −0.416661 0.909062i \(-0.636800\pi\)
0.0936925 + 0.995601i \(0.470133\pi\)
\(140\) 6.91621 2.68612i 0.584527 0.227019i
\(141\) −9.74694 + 2.28080i −0.820840 + 0.192078i
\(142\) −11.1350 + 7.26230i −0.934427 + 0.609438i
\(143\) −6.47609 −0.541558
\(144\) 1.83399 + 11.8590i 0.152832 + 0.988252i
\(145\) −22.9616 −1.90685
\(146\) 4.47568 2.91906i 0.370410 0.241583i
\(147\) 7.19669 + 7.67164i 0.593573 + 0.632746i
\(148\) −2.16854 5.58355i −0.178253 0.458965i
\(149\) 4.31466 1.15611i 0.353471 0.0947122i −0.0777144 0.996976i \(-0.524762\pi\)
0.431185 + 0.902263i \(0.358096\pi\)
\(150\) −16.6696 + 17.4333i −1.36106 + 1.42342i
\(151\) 9.60303 + 16.6329i 0.781483 + 1.35357i 0.931078 + 0.364821i \(0.118870\pi\)
−0.149594 + 0.988747i \(0.547797\pi\)
\(152\) −9.37915 + 13.0706i −0.760749 + 1.06017i
\(153\) 4.29351 6.44776i 0.347109 0.521271i
\(154\) −3.53643 + 3.94316i −0.284974 + 0.317749i
\(155\) 13.2299 + 3.54495i 1.06265 + 0.284737i
\(156\) −5.20054 2.49218i −0.416377 0.199534i
\(157\) 18.2189 4.88175i 1.45403 0.389606i 0.556606 0.830776i \(-0.312103\pi\)
0.897423 + 0.441170i \(0.145436\pi\)
\(158\) −13.8718 7.03372i −1.10358 0.559573i
\(159\) 14.4263 7.72573i 1.14408 0.612690i
\(160\) −0.214167 21.7959i −0.0169314 1.72312i
\(161\) 0.667600i 0.0526142i
\(162\) −7.15525 + 10.5263i −0.562170 + 0.827022i
\(163\) 10.2654 10.2654i 0.804052 0.804052i −0.179675 0.983726i \(-0.557504\pi\)
0.983726 + 0.179675i \(0.0575045\pi\)
\(164\) −11.7657 16.0610i −0.918750 1.25416i
\(165\) 7.51684 24.8505i 0.585185 1.93461i
\(166\) 12.2329 4.00130i 0.949457 0.310561i
\(167\) −4.99449 2.88357i −0.386485 0.223137i 0.294151 0.955759i \(-0.404963\pi\)
−0.680636 + 0.732622i \(0.738296\pi\)
\(168\) −4.35733 + 1.80559i −0.336175 + 0.139304i
\(169\) −8.85824 + 5.11431i −0.681403 + 0.393408i
\(170\) −9.39464 + 10.4751i −0.720536 + 0.803405i
\(171\) −16.7303 + 3.35541i −1.27940 + 0.256594i
\(172\) −10.7388 8.62645i −0.818827 0.657761i
\(173\) 7.70414 + 2.06432i 0.585735 + 0.156947i 0.539503 0.841984i \(-0.318612\pi\)
0.0462316 + 0.998931i \(0.485279\pi\)
\(174\) 14.5931 0.326819i 1.10630 0.0247761i
\(175\) −8.21040 4.74028i −0.620648 0.358331i
\(176\) 7.17310 + 13.8086i 0.540693 + 1.04086i
\(177\) 15.6836 + 0.500998i 1.17885 + 0.0376573i
\(178\) −10.0855 15.4637i −0.755938 1.15905i
\(179\) −1.48408 1.48408i −0.110925 0.110925i 0.649466 0.760391i \(-0.274993\pi\)
−0.760391 + 0.649466i \(0.774993\pi\)
\(180\) 15.5995 17.0632i 1.16272 1.27182i
\(181\) 4.93884 4.93884i 0.367101 0.367101i −0.499318 0.866419i \(-0.666416\pi\)
0.866419 + 0.499318i \(0.166416\pi\)
\(182\) 0.466909 2.21806i 0.0346096 0.164413i
\(183\) 3.24285 + 2.01297i 0.239718 + 0.148803i
\(184\) −1.83511 0.692049i −0.135286 0.0510185i
\(185\) −5.77004 + 9.99400i −0.424222 + 0.734774i
\(186\) −8.45865 2.06466i −0.620219 0.151389i
\(187\) 2.59982 9.70266i 0.190118 0.709529i
\(188\) −11.4907 + 1.25340i −0.838043 + 0.0914134i
\(189\) −4.68625 1.75108i −0.340875 0.127373i
\(190\) 30.9486 1.68294i 2.24525 0.122093i
\(191\) 3.80239 + 6.58592i 0.275131 + 0.476541i 0.970168 0.242433i \(-0.0779455\pi\)
−0.695037 + 0.718974i \(0.744612\pi\)
\(192\) 0.446341 + 13.8492i 0.0322119 + 0.999481i
\(193\) 0.964071 1.66982i 0.0693954 0.120196i −0.829240 0.558893i \(-0.811226\pi\)
0.898635 + 0.438696i \(0.144560\pi\)
\(194\) −2.25841 + 4.45399i −0.162144 + 0.319778i
\(195\) 2.53147 + 10.8182i 0.181283 + 0.774705i
\(196\) 7.17788 + 9.79829i 0.512706 + 0.699878i
\(197\) 16.2088 + 16.2088i 1.15483 + 1.15483i 0.985573 + 0.169254i \(0.0541357\pi\)
0.169254 + 0.985573i \(0.445864\pi\)
\(198\) −4.42358 + 15.9006i −0.314370 + 1.13000i
\(199\) −6.55635 −0.464768 −0.232384 0.972624i \(-0.574653\pi\)
−0.232384 + 0.972624i \(0.574653\pi\)
\(200\) −21.5413 + 17.6550i −1.52320 + 1.24840i
\(201\) 7.53722 + 0.240770i 0.531635 + 0.0169826i
\(202\) −25.5214 + 8.34790i −1.79568 + 0.587356i
\(203\) 1.48491 + 5.54178i 0.104221 + 0.388956i
\(204\) 5.82161 6.79112i 0.407594 0.475473i
\(205\) −9.92769 + 37.0507i −0.693380 + 2.58773i
\(206\) 4.86877 0.264757i 0.339223 0.0184465i
\(207\) −0.923018 1.86425i −0.0641542 0.129574i
\(208\) −5.61303 3.58273i −0.389194 0.248418i
\(209\) −19.1620 + 11.0632i −1.32546 + 0.765257i
\(210\) 7.96934 + 4.36617i 0.549937 + 0.301294i
\(211\) −1.56388 5.83649i −0.107662 0.401800i 0.890971 0.454059i \(-0.150025\pi\)
−0.998634 + 0.0522589i \(0.983358\pi\)
\(212\) 17.6146 6.84116i 1.20977 0.469853i
\(213\) −15.5843 4.71399i −1.06782 0.322997i
\(214\) 11.9324 + 2.51181i 0.815683 + 0.171704i
\(215\) 26.5380i 1.80988i
\(216\) −9.67129 + 11.0664i −0.658048 + 0.752976i
\(217\) 3.42229i 0.232320i
\(218\) −1.63366 + 7.76074i −0.110646 + 0.525624i
\(219\) 6.26408 + 1.89477i 0.423287 + 0.128037i
\(220\) 12.0858 27.4348i 0.814823 1.84965i
\(221\) 1.11257 + 4.15217i 0.0748395 + 0.279305i
\(222\) 3.52487 6.43375i 0.236574 0.431805i
\(223\) −4.51028 + 2.60401i −0.302031 + 0.174377i −0.643355 0.765568i \(-0.722458\pi\)
0.341324 + 0.939946i \(0.389125\pi\)
\(224\) −5.24659 + 1.46122i −0.350553 + 0.0976319i
\(225\) −29.4811 1.88542i −1.96541 0.125695i
\(226\) 0.490833 + 9.02624i 0.0326498 + 0.600416i
\(227\) −1.68430 + 6.28589i −0.111791 + 0.417209i −0.999027 0.0441067i \(-0.985956\pi\)
0.887236 + 0.461316i \(0.152623\pi\)
\(228\) −19.6452 + 1.51008i −1.30104 + 0.100008i
\(229\) −1.07052 3.99522i −0.0707418 0.264012i 0.921492 0.388397i \(-0.126971\pi\)
−0.992234 + 0.124385i \(0.960304\pi\)
\(230\) 1.17470 + 3.59133i 0.0774576 + 0.236806i
\(231\) −6.48378 0.207119i −0.426601 0.0136274i
\(232\) 16.7726 + 1.66296i 1.10118 + 0.109179i
\(233\) 17.2178 1.12797 0.563987 0.825783i \(-0.309267\pi\)
0.563987 + 0.825783i \(0.309267\pi\)
\(234\) −1.76284 6.83939i −0.115241 0.447105i
\(235\) 15.7467 + 15.7467i 1.02720 + 1.02720i
\(236\) 17.9070 + 2.76409i 1.16564 + 0.179927i
\(237\) −4.34017 18.5476i −0.281924 1.20479i
\(238\) 3.13572 + 1.58997i 0.203258 + 0.103063i
\(239\) −4.49270 + 7.78159i −0.290609 + 0.503349i −0.973954 0.226747i \(-0.927191\pi\)
0.683345 + 0.730095i \(0.260524\pi\)
\(240\) 20.2630 17.3802i 1.30797 1.12189i
\(241\) 0.560812 + 0.971356i 0.0361251 + 0.0625705i 0.883523 0.468388i \(-0.155165\pi\)
−0.847398 + 0.530959i \(0.821832\pi\)
\(242\) 0.317381 + 5.83652i 0.0204020 + 0.375185i
\(243\) −15.5072 + 1.58933i −0.994789 + 0.101956i
\(244\) 3.43598 + 2.76011i 0.219966 + 0.176698i
\(245\) 6.05655 22.6034i 0.386939 1.44408i
\(246\) 5.78213 23.6886i 0.368655 1.51033i
\(247\) 4.73439 8.20020i 0.301242 0.521766i
\(248\) −9.40726 3.54762i −0.597362 0.225274i
\(249\) 13.3928 + 8.31349i 0.848735 + 0.526846i
\(250\) 25.8467 + 5.44082i 1.63469 + 0.344107i
\(251\) −0.699267 + 0.699267i −0.0441373 + 0.0441373i −0.728831 0.684694i \(-0.759936\pi\)
0.684694 + 0.728831i \(0.259936\pi\)
\(252\) −5.12701 2.66146i −0.322971 0.167656i
\(253\) −1.90740 1.90740i −0.119917 0.119917i
\(254\) 3.65696 2.38509i 0.229458 0.149654i
\(255\) −17.2244 0.550217i −1.07863 0.0344559i
\(256\) −1.42210 + 15.9367i −0.0888812 + 0.996042i
\(257\) 5.79978 + 3.34851i 0.361781 + 0.208874i 0.669862 0.742486i \(-0.266353\pi\)
−0.308081 + 0.951360i \(0.599687\pi\)
\(258\) −0.377724 16.8661i −0.0235160 1.05003i
\(259\) 2.78520 + 0.746291i 0.173064 + 0.0463723i
\(260\) 1.39115 + 12.7535i 0.0862755 + 0.790941i
\(261\) 11.8086 + 13.4222i 0.730933 + 0.830812i
\(262\) −5.53295 4.96224i −0.341827 0.306568i
\(263\) 12.2113 7.05022i 0.752984 0.434735i −0.0737874 0.997274i \(-0.523509\pi\)
0.826771 + 0.562539i \(0.190175\pi\)
\(264\) −7.29056 + 17.6080i −0.448703 + 1.08370i
\(265\) −31.5284 18.2029i −1.93677 1.11820i
\(266\) −2.40761 7.36060i −0.147620 0.451308i
\(267\) 6.54653 21.6427i 0.400641 1.32451i
\(268\) 8.60576 + 1.32837i 0.525680 + 0.0811430i
\(269\) 13.2566 13.2566i 0.808267 0.808267i −0.176105 0.984371i \(-0.556350\pi\)
0.984371 + 0.176105i \(0.0563498\pi\)
\(270\) 28.2907 + 1.17403i 1.72172 + 0.0714490i
\(271\) 10.4494i 0.634755i 0.948299 + 0.317377i \(0.102802\pi\)
−0.948299 + 0.317377i \(0.897198\pi\)
\(272\) 7.62110 6.97132i 0.462097 0.422699i
\(273\) 2.44726 1.31058i 0.148115 0.0793197i
\(274\) 1.03290 2.03707i 0.0623998 0.123064i
\(275\) −37.0013 + 9.91448i −2.23126 + 0.597866i
\(276\) −0.797692 2.26573i −0.0480154 0.136381i
\(277\) −15.6398 4.19068i −0.939707 0.251794i −0.243718 0.969846i \(-0.578367\pi\)
−0.695989 + 0.718052i \(0.745034\pi\)
\(278\) −4.15029 3.72220i −0.248918 0.223243i
\(279\) −4.73163 9.55663i −0.283275 0.572140i
\(280\) 8.52505 + 6.11735i 0.509469 + 0.365582i
\(281\) −12.1751 21.0879i −0.726306 1.25800i −0.958434 0.285313i \(-0.907902\pi\)
0.232129 0.972685i \(-0.425431\pi\)
\(282\) −10.2319 9.78360i −0.609298 0.582605i
\(283\) −8.50029 + 2.27765i −0.505290 + 0.135392i −0.502454 0.864604i \(-0.667569\pi\)
−0.00283598 + 0.999996i \(0.500903\pi\)
\(284\) −17.2050 7.57928i −1.02093 0.449748i
\(285\) 25.9712 + 27.6852i 1.53840 + 1.63993i
\(286\) −5.00320 7.67121i −0.295845 0.453608i
\(287\) 9.58419 0.565737
\(288\) −12.6307 + 11.3343i −0.744269 + 0.667880i
\(289\) 10.3325 0.607792
\(290\) −17.7393 27.1990i −1.04169 1.59718i
\(291\) −5.95531 + 1.39355i −0.349106 + 0.0816916i
\(292\) 6.91550 + 3.04647i 0.404699 + 0.178281i
\(293\) −0.808690 + 0.216688i −0.0472442 + 0.0126590i −0.282364 0.959307i \(-0.591118\pi\)
0.235120 + 0.971966i \(0.424452\pi\)
\(294\) −3.52748 + 14.4516i −0.205727 + 0.842836i
\(295\) −17.4541 30.2313i −1.01621 1.76014i
\(296\) 4.93862 6.88239i 0.287051 0.400031i
\(297\) −18.3921 + 8.38605i −1.06722 + 0.486608i
\(298\) 4.70282 + 4.21773i 0.272427 + 0.244327i
\(299\) 1.11502 + 0.298769i 0.0644834 + 0.0172783i
\(300\) −33.5288 6.27745i −1.93579 0.362429i
\(301\) 6.40494 1.71620i 0.369175 0.0989201i
\(302\) −12.2835 + 24.2252i −0.706834 + 1.39401i
\(303\) −27.9413 17.3444i −1.60519 0.996409i
\(304\) −22.7288 1.01208i −1.30358 0.0580469i
\(305\) 8.49106i 0.486197i
\(306\) 10.9547 + 0.104527i 0.626237 + 0.00597544i
\(307\) −21.1593 + 21.1593i −1.20763 + 1.20763i −0.235831 + 0.971794i \(0.575781\pi\)
−0.971794 + 0.235831i \(0.924219\pi\)
\(308\) −7.40297 1.14271i −0.421823 0.0651118i
\(309\) 4.08574 + 4.35538i 0.232429 + 0.247769i
\(310\) 6.02183 + 18.4101i 0.342017 + 1.04562i
\(311\) 10.8454 + 6.26157i 0.614984 + 0.355061i 0.774914 0.632067i \(-0.217793\pi\)
−0.159929 + 0.987128i \(0.551127\pi\)
\(312\) −1.06566 8.08564i −0.0603313 0.457759i
\(313\) 28.1752 16.2670i 1.59256 0.919463i 0.599689 0.800233i \(-0.295291\pi\)
0.992867 0.119230i \(-0.0380425\pi\)
\(314\) 19.8580 + 17.8097i 1.12065 + 1.00506i
\(315\) 2.18849 + 10.9120i 0.123308 + 0.614820i
\(316\) −2.38510 21.8657i −0.134173 1.23004i
\(317\) −13.4383 3.60078i −0.754770 0.202240i −0.139137 0.990273i \(-0.544433\pi\)
−0.615633 + 0.788033i \(0.711100\pi\)
\(318\) 20.2968 + 11.1200i 1.13819 + 0.623578i
\(319\) 20.0759 + 11.5908i 1.12404 + 0.648963i
\(320\) 25.6527 17.0925i 1.43403 0.955497i
\(321\) 7.05047 + 13.1654i 0.393519 + 0.734822i
\(322\) 0.790801 0.515764i 0.0440696 0.0287424i
\(323\) 10.3852 + 10.3852i 0.577846 + 0.577846i
\(324\) −17.9967 0.343474i −0.999818 0.0190819i
\(325\) 11.5916 11.5916i 0.642985 0.642985i
\(326\) 20.0906 + 4.22914i 1.11271 + 0.234230i
\(327\) −8.56268 + 4.58557i −0.473517 + 0.253582i
\(328\) 9.93518 26.3452i 0.548579 1.45467i
\(329\) 2.78214 4.81880i 0.153384 0.265669i
\(330\) 35.2437 10.2946i 1.94010 0.566700i
\(331\) 1.41860 5.29427i 0.0779731 0.291000i −0.915918 0.401366i \(-0.868536\pi\)
0.993891 + 0.110366i \(0.0352023\pi\)
\(332\) 14.1904 + 11.3991i 0.778801 + 0.625609i
\(333\) 8.80938 1.76680i 0.482751 0.0968200i
\(334\) −0.442855 8.14393i −0.0242319 0.445616i
\(335\) −8.38809 14.5286i −0.458291 0.793783i
\(336\) −5.50512 3.76651i −0.300329 0.205480i
\(337\) −4.44303 + 7.69556i −0.242027 + 0.419204i −0.961292 0.275533i \(-0.911146\pi\)
0.719264 + 0.694737i \(0.244479\pi\)
\(338\) −12.9017 6.54184i −0.701759 0.355829i
\(339\) −8.07446 + 7.57456i −0.438544 + 0.411394i
\(340\) −19.6662 3.03564i −1.06655 0.164631i
\(341\) −9.77782 9.77782i −0.529498 0.529498i
\(342\) −16.8999 17.2255i −0.913840 0.931448i
\(343\) −12.5864 −0.679602
\(344\) 1.92198 19.3851i 0.103626 1.04517i
\(345\) −2.44067 + 3.93186i −0.131401 + 0.211684i
\(346\) 3.50667 + 10.7207i 0.188520 + 0.576349i
\(347\) −3.55779 13.2779i −0.190992 0.712793i −0.993268 0.115839i \(-0.963044\pi\)
0.802276 0.596954i \(-0.203622\pi\)
\(348\) 11.6612 + 17.0337i 0.625108 + 0.913100i
\(349\) 4.16907 15.5592i 0.223165 0.832863i −0.759966 0.649962i \(-0.774785\pi\)
0.983131 0.182901i \(-0.0585487\pi\)
\(350\) −0.728006 13.3877i −0.0389136 0.715605i
\(351\) 5.02188 7.04330i 0.268048 0.375943i
\(352\) −10.8152 + 19.1649i −0.576451 + 1.02149i
\(353\) −7.72178 + 4.45817i −0.410989 + 0.237284i −0.691214 0.722650i \(-0.742924\pi\)
0.280226 + 0.959934i \(0.409591\pi\)
\(354\) 11.5231 + 18.9649i 0.612447 + 1.00797i
\(355\) 9.37467 + 34.9868i 0.497556 + 1.85690i
\(356\) 10.5257 23.8934i 0.557860 1.26635i
\(357\) 0.981096 + 4.19268i 0.0519251 + 0.221900i
\(358\) 0.611409 2.90451i 0.0323140 0.153508i
\(359\) 20.3164i 1.07226i −0.844136 0.536129i \(-0.819886\pi\)
0.844136 0.536129i \(-0.180114\pi\)
\(360\) 32.2637 + 5.29582i 1.70045 + 0.279114i
\(361\) 13.3513i 0.702699i
\(362\) 9.66585 + 2.03469i 0.508026 + 0.106941i
\(363\) −5.22108 + 4.89784i −0.274036 + 0.257070i
\(364\) 2.98810 1.16052i 0.156619 0.0608278i
\(365\) −3.76812 14.0628i −0.197233 0.736082i
\(366\) 0.120856 + 5.39645i 0.00631725 + 0.282077i
\(367\) 20.8621 12.0447i 1.08899 0.628729i 0.155683 0.987807i \(-0.450242\pi\)
0.933308 + 0.359078i \(0.116909\pi\)
\(368\) −0.597982 2.70842i −0.0311720 0.141186i
\(369\) 26.7635 13.2510i 1.39325 0.689821i
\(370\) −16.2961 + 0.886156i −0.847192 + 0.0460690i
\(371\) −2.35435 + 8.78654i −0.122232 + 0.456175i
\(372\) −4.08918 11.6147i −0.212014 0.602196i
\(373\) 7.05873 + 26.3435i 0.365487 + 1.36402i 0.866759 + 0.498727i \(0.166199\pi\)
−0.501272 + 0.865290i \(0.667134\pi\)
\(374\) 13.5018 4.41634i 0.698159 0.228363i
\(375\) 15.2720 + 28.5175i 0.788640 + 1.47264i
\(376\) −10.3620 12.6429i −0.534379 0.652006i
\(377\) −9.92039 −0.510926
\(378\) −1.54620 6.90389i −0.0795278 0.355098i
\(379\) 26.4493 + 26.4493i 1.35861 + 1.35861i 0.875636 + 0.482971i \(0.160442\pi\)
0.482971 + 0.875636i \(0.339558\pi\)
\(380\) 25.9033 + 35.3598i 1.32881 + 1.81392i
\(381\) 5.11823 + 1.54817i 0.262215 + 0.0793153i
\(382\) −4.86372 + 9.59215i −0.248850 + 0.490777i
\(383\) −14.2366 + 24.6585i −0.727455 + 1.25999i 0.230500 + 0.973072i \(0.425964\pi\)
−0.957955 + 0.286917i \(0.907369\pi\)
\(384\) −16.0602 + 11.2281i −0.819567 + 0.572983i
\(385\) 7.21573 + 12.4980i 0.367748 + 0.636957i
\(386\) 2.72278 0.148061i 0.138586 0.00753610i
\(387\) 15.5128 13.6478i 0.788559 0.693759i
\(388\) −7.02071 + 0.765816i −0.356423 + 0.0388784i
\(389\) 5.20211 19.4146i 0.263758 0.984357i −0.699249 0.714878i \(-0.746482\pi\)
0.963006 0.269479i \(-0.0868513\pi\)
\(390\) −10.8589 + 11.3564i −0.549860 + 0.575053i
\(391\) −0.895250 + 1.55062i −0.0452747 + 0.0784182i
\(392\) −6.06112 + 16.0723i −0.306133 + 0.811775i
\(393\) 0.290624 9.09789i 0.0146600 0.458928i
\(394\) −6.67765 + 31.7223i −0.336415 + 1.59815i
\(395\) −29.9646 + 29.9646i −1.50768 + 1.50768i
\(396\) −22.2524 + 7.04431i −1.11823 + 0.353990i
\(397\) 5.95094 + 5.95094i 0.298669 + 0.298669i 0.840492 0.541823i \(-0.182266\pi\)
−0.541823 + 0.840492i \(0.682266\pi\)
\(398\) −5.06521 7.76628i −0.253896 0.389289i
\(399\) 5.00227 8.05853i 0.250427 0.403431i
\(400\) −37.5552 11.8769i −1.87776 0.593844i
\(401\) −4.11912 2.37818i −0.205699 0.118761i 0.393612 0.919277i \(-0.371225\pi\)
−0.599311 + 0.800516i \(0.704559\pi\)
\(402\) 5.53779 + 9.11418i 0.276200 + 0.454574i
\(403\) 5.71590 + 1.53157i 0.284729 + 0.0762929i
\(404\) −29.6054 23.7819i −1.47292 1.18320i
\(405\) 21.1981 + 27.4455i 1.05334 + 1.36378i
\(406\) −5.41728 + 6.04033i −0.268855 + 0.299776i
\(407\) 10.0898 5.82535i 0.500133 0.288752i
\(408\) 12.5419 + 1.64937i 0.620919 + 0.0816558i
\(409\) −7.24880 4.18510i −0.358430 0.206940i 0.309962 0.950749i \(-0.399684\pi\)
−0.668392 + 0.743809i \(0.733017\pi\)
\(410\) −51.5579 + 16.8643i −2.54626 + 0.832867i
\(411\) 2.72371 0.637353i 0.134351 0.0314383i
\(412\) 4.07506 + 5.56273i 0.200764 + 0.274056i
\(413\) −6.16758 + 6.16758i −0.303487 + 0.303487i
\(414\) 1.49519 2.53361i 0.0734847 0.124520i
\(415\) 35.0677i 1.72141i
\(416\) −0.0925293 9.41678i −0.00453662 0.461695i
\(417\) 0.217998 6.82437i 0.0106754 0.334191i
\(418\) −27.9087 14.1512i −1.36506 0.692157i
\(419\) 30.9427 8.29108i 1.51165 0.405046i 0.594668 0.803971i \(-0.297284\pi\)
0.916983 + 0.398926i \(0.130617\pi\)
\(420\) 0.984919 + 12.8132i 0.0480591 + 0.625219i
\(421\) −28.9049 7.74504i −1.40874 0.377470i −0.527264 0.849702i \(-0.676782\pi\)
−0.881475 + 0.472232i \(0.843449\pi\)
\(422\) 5.70537 6.36155i 0.277733 0.309676i
\(423\) 1.10658 17.3029i 0.0538038 0.841295i
\(424\) 21.7121 + 15.5800i 1.05443 + 0.756632i
\(425\) 12.7134 + 22.0203i 0.616691 + 1.06814i
\(426\) −6.45599 22.1022i −0.312794 1.07085i
\(427\) −2.04932 + 0.549113i −0.0991735 + 0.0265734i
\(428\) 6.24321 + 16.0750i 0.301777 + 0.777015i
\(429\) 3.24760 10.7365i 0.156796 0.518363i
\(430\) −31.4354 + 20.5023i −1.51595 + 0.988710i
\(431\) −10.3884 −0.500389 −0.250195 0.968196i \(-0.580495\pi\)
−0.250195 + 0.968196i \(0.580495\pi\)
\(432\) −20.5804 2.90651i −0.990174 0.139839i
\(433\) −3.31869 −0.159486 −0.0797429 0.996815i \(-0.525410\pi\)
−0.0797429 + 0.996815i \(0.525410\pi\)
\(434\) 4.05385 2.64394i 0.194591 0.126913i
\(435\) 11.5147 38.0672i 0.552086 1.82518i
\(436\) −10.4550 + 4.06053i −0.500706 + 0.194464i
\(437\) 3.80962 1.02078i 0.182239 0.0488307i
\(438\) 2.59497 + 8.88391i 0.123992 + 0.424490i
\(439\) 15.8616 + 27.4732i 0.757035 + 1.31122i 0.944356 + 0.328924i \(0.106686\pi\)
−0.187322 + 0.982299i \(0.559981\pi\)
\(440\) 41.8348 6.87903i 1.99439 0.327945i
\(441\) −16.3275 + 8.08401i −0.777501 + 0.384953i
\(442\) −4.05889 + 4.52571i −0.193062 + 0.215266i
\(443\) 12.8638 + 3.44686i 0.611180 + 0.163765i 0.551115 0.834429i \(-0.314203\pi\)
0.0600649 + 0.998194i \(0.480869\pi\)
\(444\) 10.3442 0.795138i 0.490916 0.0377356i
\(445\) −48.5877 + 13.0190i −2.30328 + 0.617161i
\(446\) −6.56905 3.33085i −0.311053 0.157720i
\(447\) −0.247021 + 7.73289i −0.0116837 + 0.365753i
\(448\) −5.78421 5.08593i −0.273278 0.240288i
\(449\) 13.0580i 0.616243i −0.951347 0.308121i \(-0.900300\pi\)
0.951347 0.308121i \(-0.0997003\pi\)
\(450\) −20.5427 36.3783i −0.968394 1.71489i
\(451\) 27.3830 27.3830i 1.28941 1.28941i
\(452\) −10.3128 + 7.55477i −0.485072 + 0.355347i
\(453\) −32.3909 + 7.57953i −1.52186 + 0.356118i
\(454\) −8.74714 + 2.86113i −0.410524 + 0.134280i
\(455\) −5.34841 3.08790i −0.250737 0.144763i
\(456\) −16.9660 22.1040i −0.794505 1.03511i
\(457\) 10.0451 5.79955i 0.469890 0.271291i −0.246303 0.969193i \(-0.579216\pi\)
0.716194 + 0.697901i \(0.245883\pi\)
\(458\) 3.90547 4.35465i 0.182491 0.203479i
\(459\) 8.53644 + 10.3515i 0.398447 + 0.483165i
\(460\) −3.34656 + 4.16603i −0.156034 + 0.194242i
\(461\) −13.3098 3.56634i −0.619898 0.166101i −0.0648164 0.997897i \(-0.520646\pi\)
−0.555081 + 0.831796i \(0.687313\pi\)
\(462\) −4.76380 7.84033i −0.221632 0.364765i
\(463\) 11.4905 + 6.63406i 0.534010 + 0.308311i 0.742648 0.669682i \(-0.233570\pi\)
−0.208638 + 0.977993i \(0.566903\pi\)
\(464\) 10.9881 + 21.1527i 0.510110 + 0.981988i
\(465\) −12.5115 + 20.1557i −0.580208 + 0.934700i
\(466\) 13.3019 + 20.3952i 0.616197 + 0.944790i
\(467\) −28.1581 28.1581i −1.30300 1.30300i −0.926357 0.376647i \(-0.877077\pi\)
−0.376647 0.926357i \(-0.622923\pi\)
\(468\) 6.73964 7.37204i 0.311540 0.340773i
\(469\) −2.96402 + 2.96402i −0.136866 + 0.136866i
\(470\) −6.48730 + 30.8180i −0.299237 + 1.42153i
\(471\) −1.04306 + 32.6527i −0.0480617 + 1.50456i
\(472\) 10.5601 + 23.3470i 0.486069 + 1.07463i
\(473\) 13.3962 23.2029i 0.615958 1.06687i
\(474\) 18.6173 19.4703i 0.855122 0.894301i
\(475\) 14.4961 54.1002i 0.665127 2.48229i
\(476\) 0.539153 + 4.94275i 0.0247121 + 0.226551i
\(477\) 5.57377 + 27.7912i 0.255206 + 1.27247i
\(478\) −12.6885 + 0.689983i −0.580360 + 0.0315591i
\(479\) −3.40138 5.89137i −0.155413 0.269183i 0.777796 0.628517i \(-0.216338\pi\)
−0.933209 + 0.359333i \(0.883004\pi\)
\(480\) 36.2421 + 10.5751i 1.65422 + 0.482683i
\(481\) −2.49291 + 4.31784i −0.113667 + 0.196877i
\(482\) −0.717349 + 1.41474i −0.0326743 + 0.0644397i
\(483\) 1.10679 + 0.334785i 0.0503608 + 0.0152332i
\(484\) −6.66841 + 4.88504i −0.303109 + 0.222047i
\(485\) 9.62112 + 9.62112i 0.436873 + 0.436873i
\(486\) −13.8630 17.1411i −0.628837 0.777537i
\(487\) −10.9714 −0.497160 −0.248580 0.968611i \(-0.579964\pi\)
−0.248580 + 0.968611i \(0.579964\pi\)
\(488\) −0.614954 + 6.20243i −0.0278377 + 0.280771i
\(489\) 11.8709 + 22.1666i 0.536819 + 1.00241i
\(490\) 31.4537 10.2883i 1.42093 0.464779i
\(491\) −1.87065 6.98135i −0.0844211 0.315064i 0.910783 0.412886i \(-0.135479\pi\)
−0.995204 + 0.0978219i \(0.968812\pi\)
\(492\) 32.5273 11.4518i 1.46644 0.516288i
\(493\) 3.98253 14.8630i 0.179364 0.669397i
\(494\) 13.3711 0.727102i 0.601595 0.0327139i
\(495\) 37.4293 + 24.9238i 1.68232 + 1.12024i
\(496\) −3.06541 13.8841i −0.137641 0.623414i
\(497\) 7.83780 4.52515i 0.351573 0.202981i
\(498\) 0.499130 + 22.2871i 0.0223665 + 0.998708i
\(499\) −6.80645 25.4020i −0.304698 1.13715i −0.933205 0.359346i \(-0.883000\pi\)
0.628506 0.777805i \(-0.283667\pi\)
\(500\) 13.5234 + 34.8199i 0.604783 + 1.55719i
\(501\) 7.28518 6.83415i 0.325478 0.305327i
\(502\) −1.36854 0.288083i −0.0610810 0.0128578i
\(503\) 1.37571i 0.0613400i 0.999530 + 0.0306700i \(0.00976410\pi\)
−0.999530 + 0.0306700i \(0.990236\pi\)
\(504\) −0.808333 8.12932i −0.0360060 0.362109i
\(505\) 73.1616i 3.25565i
\(506\) 0.785806 3.73298i 0.0349333 0.165951i
\(507\) −4.03665 17.2505i −0.179274 0.766121i
\(508\) 5.65049 + 2.48920i 0.250700 + 0.110440i
\(509\) −3.94915 14.7384i −0.175043 0.653269i −0.996544 0.0830623i \(-0.973530\pi\)
0.821502 0.570206i \(-0.193137\pi\)
\(510\) −12.6552 20.8281i −0.560381 0.922283i
\(511\) −3.15038 + 1.81887i −0.139365 + 0.0804622i
\(512\) −19.9763 + 10.6276i −0.882838 + 0.469677i
\(513\) 2.82701 29.4193i 0.124816 1.29889i
\(514\) 0.514260 + 9.45704i 0.0226830 + 0.417132i
\(515\) 3.43845 12.8325i 0.151516 0.565467i
\(516\) 19.6868 13.4776i 0.866661 0.593316i
\(517\) −5.81895 21.7166i −0.255917 0.955096i
\(518\) 1.26773 + 3.87575i 0.0557009 + 0.170291i
\(519\) −7.28580 + 11.7372i −0.319811 + 0.515207i
\(520\) −14.0324 + 11.5008i −0.615360 + 0.504344i
\(521\) 23.4677 1.02814 0.514070 0.857748i \(-0.328137\pi\)
0.514070 + 0.857748i \(0.328137\pi\)
\(522\) −6.77626 + 24.3573i −0.296589 + 1.06609i
\(523\) −30.0762 30.0762i −1.31514 1.31514i −0.917573 0.397567i \(-0.869855\pi\)
−0.397567 0.917573i \(-0.630145\pi\)
\(524\) 1.60342 10.3877i 0.0700458 0.453788i
\(525\) 11.9761 11.2346i 0.522678 0.490319i
\(526\) 17.7854 + 9.01811i 0.775478 + 0.393208i
\(527\) −4.58929 + 7.94888i −0.199912 + 0.346259i
\(528\) −26.4899 + 4.96738i −1.15283 + 0.216177i
\(529\) −11.2596 19.5022i −0.489547 0.847921i
\(530\) −2.79558 51.4096i −0.121432 2.23309i
\(531\) −8.69551 + 25.7500i −0.377353 + 1.11746i
\(532\) 6.85892 8.53846i 0.297372 0.370189i
\(533\) −4.28919 + 16.0075i −0.185786 + 0.693361i
\(534\) 30.6943 8.96573i 1.32827 0.387985i
\(535\) 16.6119 28.7727i 0.718195 1.24395i
\(536\) 5.07500 + 11.2201i 0.219207 + 0.484636i
\(537\) 3.20464 1.71618i 0.138290 0.0740585i
\(538\) 25.9445 + 5.46141i 1.11855 + 0.235458i
\(539\) −16.7054 + 16.7054i −0.719553 + 0.719553i
\(540\) 20.4658 + 34.4186i 0.880706 + 1.48114i
\(541\) −18.7809 18.7809i −0.807453 0.807453i 0.176795 0.984248i \(-0.443427\pi\)
−0.984248 + 0.176795i \(0.943427\pi\)
\(542\) −12.3777 + 8.07283i −0.531670 + 0.346758i
\(543\) 5.71123 + 10.6646i 0.245092 + 0.457664i
\(544\) 14.1456 + 3.64173i 0.606489 + 0.156138i
\(545\) 18.7135 + 10.8042i 0.801598 + 0.462803i
\(546\) 3.44310 + 1.88637i 0.147351 + 0.0807293i
\(547\) −14.9578 4.00793i −0.639548 0.171366i −0.0755496 0.997142i \(-0.524071\pi\)
−0.563999 + 0.825776i \(0.690738\pi\)
\(548\) 3.21098 0.350252i 0.137166 0.0149620i
\(549\) −4.96345 + 4.36675i −0.211835 + 0.186368i
\(550\) −40.3301 36.1701i −1.71968 1.54230i
\(551\) −29.3533 + 16.9471i −1.25049 + 0.721972i
\(552\) 2.06759 2.69533i 0.0880024 0.114721i
\(553\) 9.16975 + 5.29416i 0.389937 + 0.225130i
\(554\) −7.11875 21.7637i −0.302447 0.924649i
\(555\) −13.6752 14.5777i −0.580479 0.618789i
\(556\) 1.20273 7.79184i 0.0510072 0.330448i
\(557\) −31.8166 + 31.8166i −1.34811 + 1.34811i −0.460398 + 0.887712i \(0.652293\pi\)
−0.887712 + 0.460398i \(0.847707\pi\)
\(558\) 7.66475 12.9879i 0.324475 0.549824i
\(559\) 11.4656i 0.484941i
\(560\) −0.660109 + 14.8243i −0.0278947 + 0.626443i
\(561\) 14.7820 + 9.17580i 0.624096 + 0.387403i
\(562\) 15.5735 30.7137i 0.656927 1.29558i
\(563\) 33.0941 8.86755i 1.39475 0.373723i 0.518294 0.855202i \(-0.326567\pi\)
0.876457 + 0.481480i \(0.159900\pi\)
\(564\) 3.68432 19.6785i 0.155138 0.828616i
\(565\) 23.7902 + 6.37456i 1.00086 + 0.268180i
\(566\) −9.26500 8.30934i −0.389437 0.349267i
\(567\) 5.25310 6.89105i 0.220610 0.289397i
\(568\) −4.31401 26.2356i −0.181012 1.10082i
\(569\) −2.54964 4.41610i −0.106886 0.185133i 0.807621 0.589702i \(-0.200755\pi\)
−0.914507 + 0.404569i \(0.867421\pi\)
\(570\) −12.7299 + 52.1526i −0.533195 + 2.18443i
\(571\) −6.68977 + 1.79252i −0.279958 + 0.0750146i −0.396066 0.918222i \(-0.629625\pi\)
0.116108 + 0.993237i \(0.462958\pi\)
\(572\) 5.22158 11.8530i 0.218325 0.495599i
\(573\) −12.8254 + 3.00117i −0.535788 + 0.125376i
\(574\) 7.40442 + 11.3529i 0.309054 + 0.473861i
\(575\) 6.82812 0.284752
\(576\) −23.1840 6.20507i −0.965999 0.258545i
\(577\) 18.2939 0.761585 0.380793 0.924660i \(-0.375651\pi\)
0.380793 + 0.924660i \(0.375651\pi\)
\(578\) 7.98250 + 12.2393i 0.332028 + 0.509086i
\(579\) 2.28488 + 2.43568i 0.0949564 + 0.101223i
\(580\) 18.5136 42.0260i 0.768735 1.74503i
\(581\) −8.46359 + 2.26781i −0.351129 + 0.0940847i
\(582\) −6.25159 5.97771i −0.259137 0.247784i
\(583\) 18.3774 + 31.8306i 0.761114 + 1.31829i
\(584\) 1.73400 + 10.5453i 0.0717535 + 0.436368i
\(585\) −19.2046 1.22820i −0.794011 0.0507798i
\(586\) −0.881442 0.790523i −0.0364120 0.0326562i
\(587\) 13.8472 + 3.71035i 0.571536 + 0.153143i 0.533001 0.846115i \(-0.321064\pi\)
0.0385349 + 0.999257i \(0.487731\pi\)
\(588\) −19.8438 + 6.98637i −0.818344 + 0.288113i
\(589\) 19.5291 5.23280i 0.804682 0.215614i
\(590\) 22.3259 44.0308i 0.919143 1.81272i
\(591\) −35.0003 + 18.7437i −1.43972 + 0.771011i
\(592\) 11.9679 + 0.532915i 0.491877 + 0.0219027i
\(593\) 16.9058i 0.694238i −0.937821 0.347119i \(-0.887160\pi\)
0.937821 0.347119i \(-0.112840\pi\)
\(594\) −24.1427 15.3075i −0.990588 0.628072i
\(595\) 6.77350 6.77350i 0.277687 0.277687i
\(596\) −1.36285 + 8.82917i −0.0558246 + 0.361657i
\(597\) 3.28785 10.8696i 0.134563 0.444861i
\(598\) 0.507522 + 1.55161i 0.0207541 + 0.0634501i
\(599\) −18.4047 10.6260i −0.751997 0.434166i 0.0744181 0.997227i \(-0.476290\pi\)
−0.826415 + 0.563062i \(0.809623\pi\)
\(600\) −18.4673 44.5661i −0.753924 1.81940i
\(601\) −28.1475 + 16.2510i −1.14816 + 0.662891i −0.948438 0.316962i \(-0.897337\pi\)
−0.199722 + 0.979853i \(0.564004\pi\)
\(602\) 6.98115 + 6.26106i 0.284530 + 0.255182i
\(603\) −4.17890 + 12.3750i −0.170178 + 0.503948i
\(604\) −38.1856 + 4.16527i −1.55375 + 0.169482i
\(605\) 15.3831 + 4.12190i 0.625413 + 0.167579i
\(606\) −1.04133 46.4974i −0.0423012 1.88883i
\(607\) 9.86566 + 5.69594i 0.400435 + 0.231191i 0.686672 0.726968i \(-0.259071\pi\)
−0.286237 + 0.958159i \(0.592404\pi\)
\(608\) −16.3606 27.7051i −0.663509 1.12359i
\(609\) −9.93217 0.317275i −0.402472 0.0128566i
\(610\) 10.0580 6.55990i 0.407238 0.265603i
\(611\) 6.80326 + 6.80326i 0.275230 + 0.275230i
\(612\) 8.33938 + 13.0570i 0.337099 + 0.527799i
\(613\) 12.9149 12.9149i 0.521630 0.521630i −0.396434 0.918063i \(-0.629752\pi\)
0.918063 + 0.396434i \(0.129752\pi\)
\(614\) −41.4111 8.71717i −1.67121 0.351796i
\(615\) −56.4466 35.0388i −2.27615 1.41290i
\(616\) −4.36569 9.65195i −0.175899 0.388888i
\(617\) 5.36926 9.29983i 0.216158 0.374397i −0.737472 0.675378i \(-0.763981\pi\)
0.953630 + 0.300981i \(0.0973139\pi\)
\(618\) −2.00264 + 8.20455i −0.0805580 + 0.330035i
\(619\) −4.04330 + 15.0898i −0.162514 + 0.606510i 0.835830 + 0.548988i \(0.184987\pi\)
−0.998344 + 0.0575222i \(0.981680\pi\)
\(620\) −17.1553 + 21.3561i −0.688974 + 0.857683i
\(621\) 3.55355 0.595366i 0.142599 0.0238912i
\(622\) 0.961645 + 17.6843i 0.0385585 + 0.709075i
\(623\) 6.28428 + 10.8847i 0.251774 + 0.436086i
\(624\) 8.75449 7.50901i 0.350460 0.300601i
\(625\) 11.3651 19.6849i 0.454603 0.787396i
\(626\) 41.0361 + 20.8075i 1.64013 + 0.831633i
\(627\) −8.73202 37.3160i −0.348723 1.49026i
\(628\) −5.75474 + 37.2817i −0.229639 + 1.48770i
\(629\) −5.46834 5.46834i −0.218037 0.218037i
\(630\) −11.2350 + 11.0226i −0.447611 + 0.439150i
\(631\) 39.5399 1.57406 0.787029 0.616916i \(-0.211618\pi\)
0.787029 + 0.616916i \(0.211618\pi\)
\(632\) 24.0582 19.7180i 0.956986 0.784338i
\(633\) 10.4604 + 0.334147i 0.415762 + 0.0132812i
\(634\) −6.11668 18.7001i −0.242924 0.742675i
\(635\) −3.07884 11.4904i −0.122180 0.455982i
\(636\) 2.50844 + 32.6333i 0.0994663 + 1.29399i
\(637\) 2.61669 9.76562i 0.103677 0.386928i
\(638\) 1.78011 + 32.7355i 0.0704751 + 1.29601i
\(639\) 15.6303 23.4728i 0.618326 0.928570i
\(640\) 40.0652 + 17.1818i 1.58372 + 0.679169i
\(641\) −18.9744 + 10.9549i −0.749445 + 0.432692i −0.825493 0.564412i \(-0.809103\pi\)
0.0760486 + 0.997104i \(0.475770\pi\)
\(642\) −10.1481 + 18.5227i −0.400512 + 0.731034i
\(643\) 11.1343 + 41.5536i 0.439092 + 1.63871i 0.731080 + 0.682292i \(0.239017\pi\)
−0.291988 + 0.956422i \(0.594317\pi\)
\(644\) 1.22189 + 0.538277i 0.0481492 + 0.0212111i
\(645\) −43.9964 13.3082i −1.73236 0.524008i
\(646\) −4.27846 + 20.3249i −0.168334 + 0.799672i
\(647\) 31.4508i 1.23646i −0.785998 0.618229i \(-0.787851\pi\)
0.785998 0.618229i \(-0.212149\pi\)
\(648\) −13.4968 21.5833i −0.530204 0.847870i
\(649\) 35.2428i 1.38340i
\(650\) 22.6860 + 4.77548i 0.889817 + 0.187310i
\(651\) 5.67370 + 1.71620i 0.222370 + 0.0672630i
\(652\) 10.5117 + 27.0655i 0.411670 + 1.05997i
\(653\) 10.1932 + 38.0415i 0.398891 + 1.48868i 0.815051 + 0.579389i \(0.196709\pi\)
−0.416160 + 0.909291i \(0.636624\pi\)
\(654\) −12.0470 6.60022i −0.471076 0.258089i
\(655\) −17.5369 + 10.1249i −0.685224 + 0.395614i
\(656\) 38.8826 8.58475i 1.51811 0.335178i
\(657\) −6.28257 + 9.43483i −0.245106 + 0.368088i
\(658\) 7.85746 0.427277i 0.306316 0.0166570i
\(659\) −0.390374 + 1.45690i −0.0152068 + 0.0567526i −0.973112 0.230331i \(-0.926019\pi\)
0.957906 + 0.287084i \(0.0926858\pi\)
\(660\) 39.4225 + 33.7945i 1.53452 + 1.31545i
\(661\) 9.57641 + 35.7396i 0.372479 + 1.39011i 0.856993 + 0.515328i \(0.172330\pi\)
−0.484514 + 0.874783i \(0.661004\pi\)
\(662\) 7.36725 2.40978i 0.286336 0.0936589i
\(663\) −7.44166 0.237717i −0.289010 0.00923218i
\(664\) −2.53973 + 25.6158i −0.0985608 + 0.994084i
\(665\) −21.1004 −0.818240
\(666\) 8.89867 + 9.07013i 0.344817 + 0.351460i
\(667\) −2.92185 2.92185i −0.113134 0.113134i
\(668\) 9.30470 6.81630i 0.360010 0.263730i
\(669\) −2.05531 8.78329i −0.0794628 0.339582i
\(670\) 10.7294 21.1604i 0.414513 0.817496i
\(671\) −4.28623 + 7.42397i −0.165468 + 0.286599i
\(672\) 0.208529 9.43092i 0.00804417 0.363806i
\(673\) 1.54334 + 2.67314i 0.0594912 + 0.103042i 0.894237 0.447594i \(-0.147719\pi\)
−0.834746 + 0.550635i \(0.814386\pi\)
\(674\) −12.5483 + 0.682355i −0.483341 + 0.0262833i
\(675\) 17.9098 47.9303i 0.689350 1.84484i
\(676\) −2.21831 20.3366i −0.0853196 0.782177i
\(677\) −10.6718 + 39.8275i −0.410149 + 1.53070i 0.384209 + 0.923246i \(0.374474\pi\)
−0.794358 + 0.607450i \(0.792193\pi\)
\(678\) −15.2104 3.71270i −0.584153 0.142585i
\(679\) 1.69986 2.94425i 0.0652348 0.112990i
\(680\) −11.5976 25.6407i −0.444747 0.983276i
\(681\) −9.57653 5.94456i −0.366974 0.227796i
\(682\) 4.02825 19.1362i 0.154250 0.732765i
\(683\) 15.0423 15.0423i 0.575578 0.575578i −0.358104 0.933682i \(-0.616577\pi\)
0.933682 + 0.358104i \(0.116577\pi\)
\(684\) 7.34809 33.3264i 0.280961 1.27427i
\(685\) −4.40030 4.40030i −0.168127 0.168127i
\(686\) −9.72382 14.9092i −0.371257 0.569234i
\(687\) 7.16039 + 0.228732i 0.273186 + 0.00872668i
\(688\) 24.4473 12.6996i 0.932046 0.484167i
\(689\) −13.6216 7.86444i −0.518942 0.299611i
\(690\) −6.54304 + 0.146535i −0.249089 + 0.00557847i
\(691\) −42.4064 11.3628i −1.61321 0.432260i −0.664216 0.747540i \(-0.731235\pi\)
−0.948998 + 0.315281i \(0.897901\pi\)
\(692\) −9.99000 + 12.4363i −0.379763 + 0.472755i
\(693\) 3.59483 10.6454i 0.136556 0.404384i
\(694\) 12.9796 14.4724i 0.492698 0.549364i
\(695\) −13.1545 + 7.59476i −0.498979 + 0.288086i
\(696\) −11.1680 + 26.9729i −0.423323 + 1.02240i
\(697\) −22.2610 12.8524i −0.843195 0.486819i
\(698\) 21.6514 7.08203i 0.819517 0.268059i
\(699\) −8.63430 + 28.5448i −0.326579 + 1.07966i
\(700\) 15.2959 11.2053i 0.578132 0.423519i
\(701\) 7.87056 7.87056i 0.297267 0.297267i −0.542676 0.839942i \(-0.682589\pi\)
0.839942 + 0.542676i \(0.182589\pi\)
\(702\) 12.2228 + 0.507230i 0.461321 + 0.0191442i
\(703\) 17.0347i 0.642474i
\(704\) −31.0571 + 1.99507i −1.17051 + 0.0751920i
\(705\) −34.0025 + 18.2094i −1.28061 + 0.685804i
\(706\) −11.2465 5.70255i −0.423267 0.214618i
\(707\) 17.6575 4.73132i 0.664080 0.177940i
\(708\) −13.5624 + 28.3013i −0.509706 + 1.06363i
\(709\) 27.9701 + 7.49458i 1.05044 + 0.281465i 0.742434 0.669919i \(-0.233671\pi\)
0.308007 + 0.951384i \(0.400338\pi\)
\(710\) −34.2008 + 38.1343i −1.28353 + 1.43115i
\(711\) 32.9259 + 2.10573i 1.23482 + 0.0789709i
\(712\) 36.4345 5.99105i 1.36544 0.224524i
\(713\) 1.23241 + 2.13459i 0.0461540 + 0.0799411i
\(714\) −4.20845 + 4.40127i −0.157497 + 0.164713i
\(715\) −24.1034 + 6.45848i −0.901414 + 0.241533i
\(716\) 3.91287 1.51968i 0.146231 0.0567931i
\(717\) −10.6479 11.3506i −0.397651 0.423895i
\(718\) 24.0656 15.6957i 0.898122 0.585760i
\(719\) −0.674555 −0.0251567 −0.0125783 0.999921i \(-0.504004\pi\)
−0.0125783 + 0.999921i \(0.504004\pi\)
\(720\) 18.6527 + 42.3091i 0.695145 + 1.57677i
\(721\) −3.31948 −0.123624
\(722\) 15.8152 10.3147i 0.588580 0.383875i
\(723\) −1.89161 + 0.442641i −0.0703498 + 0.0164620i
\(724\) 5.05731 + 13.0215i 0.187954 + 0.483942i
\(725\) −56.6805 + 15.1875i −2.10506 + 0.564049i
\(726\) −9.83532 2.40069i −0.365023 0.0890981i
\(727\) −1.32251 2.29066i −0.0490493 0.0849559i 0.840458 0.541876i \(-0.182286\pi\)
−0.889508 + 0.456920i \(0.848952\pi\)
\(728\) 3.68319 + 2.64296i 0.136508 + 0.0979546i
\(729\) 5.14160 26.5059i 0.190430 0.981701i
\(730\) 13.7469 15.3280i 0.508796 0.567313i
\(731\) −17.1780 4.60284i −0.635352 0.170242i
\(732\) −6.29895 + 4.31227i −0.232816 + 0.159386i
\(733\) −19.9416 + 5.34335i −0.736562 + 0.197361i −0.607549 0.794282i \(-0.707847\pi\)
−0.129012 + 0.991643i \(0.541181\pi\)
\(734\) 30.3848 + 15.4067i 1.12152 + 0.568671i
\(735\) 34.4361 + 21.3760i 1.27020 + 0.788465i
\(736\) 2.74626 2.80077i 0.101229 0.103238i
\(737\) 16.9370i 0.623883i
\(738\) 36.3730 + 21.4653i 1.33891 + 0.790148i
\(739\) −27.6094 + 27.6094i −1.01563 + 1.01563i −0.0157506 + 0.999876i \(0.505014\pi\)
−0.999876 + 0.0157506i \(0.994986\pi\)
\(740\) −13.6395 18.6188i −0.501396 0.684440i
\(741\) 11.2207 + 11.9612i 0.412201 + 0.439405i
\(742\) −12.2269 + 3.99935i −0.448865 + 0.146821i
\(743\) 16.4755 + 9.51215i 0.604429 + 0.348967i 0.770782 0.637099i \(-0.219866\pi\)
−0.166353 + 0.986066i \(0.553199\pi\)
\(744\) 10.5990 13.8169i 0.388578 0.506554i
\(745\) 14.9058 8.60585i 0.546105 0.315294i
\(746\) −25.7517 + 28.7135i −0.942838 + 1.05127i
\(747\) −20.4988 + 18.0345i −0.750013 + 0.659847i
\(748\) 15.6623 + 12.5815i 0.572672 + 0.460025i
\(749\) −8.01857 2.14857i −0.292992 0.0785070i
\(750\) −21.9816 + 40.1219i −0.802655 + 1.46504i
\(751\) −30.5334 17.6285i −1.11418 0.643273i −0.174272 0.984698i \(-0.555757\pi\)
−0.939909 + 0.341425i \(0.889091\pi\)
\(752\) 6.97071 22.0417i 0.254195 0.803777i
\(753\) −0.808626 1.50996i −0.0294680 0.0550259i
\(754\) −7.66415 11.7511i −0.279112 0.427951i
\(755\) 52.3292 + 52.3292i 1.90446 + 1.90446i
\(756\) 6.98342 7.16525i 0.253985 0.260597i
\(757\) 24.8190 24.8190i 0.902061 0.902061i −0.0935534 0.995614i \(-0.529823\pi\)
0.995614 + 0.0935534i \(0.0298226\pi\)
\(758\) −10.8965 + 51.7641i −0.395779 + 1.88016i
\(759\) 4.11872 2.20570i 0.149500 0.0800618i
\(760\) −21.8732 + 58.0013i −0.793423 + 2.10393i
\(761\) −2.73041 + 4.72921i −0.0989774 + 0.171434i −0.911262 0.411828i \(-0.864890\pi\)
0.812284 + 0.583262i \(0.198224\pi\)
\(762\) 2.12028 + 7.25883i 0.0768098 + 0.262959i
\(763\) 1.39741 5.21521i 0.0505897 0.188803i
\(764\) −15.1199 + 1.64927i −0.547017 + 0.0596684i
\(765\) 9.54978 28.2798i 0.345273 1.02246i
\(766\) −40.2077 + 2.18644i −1.45276 + 0.0789992i
\(767\) −7.54091 13.0612i −0.272286 0.471614i
\(768\) −25.7077 10.3495i −0.927648 0.373456i
\(769\) 14.4745 25.0706i 0.521964 0.904068i −0.477710 0.878518i \(-0.658533\pi\)
0.999674 0.0255501i \(-0.00813372\pi\)
\(770\) −9.22981 + 18.2029i −0.332619 + 0.655986i
\(771\) −8.45983 + 7.93608i −0.304673 + 0.285811i
\(772\) 2.27891 + 3.11087i 0.0820198 + 0.111963i
\(773\) −11.3458 11.3458i −0.408079 0.408079i 0.472989 0.881068i \(-0.343175\pi\)
−0.881068 + 0.472989i \(0.843175\pi\)
\(774\) 28.1511 + 7.83170i 1.01187 + 0.281505i
\(775\) 35.0027 1.25733
\(776\) −6.33110 7.72469i −0.227273 0.277300i
\(777\) −2.63396 + 4.24324i −0.0944928 + 0.152225i
\(778\) 27.0164 8.83688i 0.968583 0.316817i
\(779\) 14.6546 + 54.6916i 0.525054 + 1.95953i
\(780\) −21.8413 4.08925i −0.782044 0.146418i
\(781\) 9.46454 35.3221i 0.338668 1.26393i
\(782\) −2.52841 + 0.137491i −0.0904159 + 0.00491668i
\(783\) −28.1739 + 12.8462i −1.00685 + 0.459085i
\(784\) −23.7210 + 5.23726i −0.847178 + 0.187045i
\(785\) 62.9406 36.3388i 2.24645 1.29699i
\(786\) 11.0014 6.68445i 0.392406 0.238427i
\(787\) −6.87546 25.6596i −0.245084 0.914665i −0.973341 0.229362i \(-0.926336\pi\)
0.728257 0.685304i \(-0.240331\pi\)
\(788\) −42.7354 + 16.5976i −1.52238 + 0.591264i
\(789\) 5.56464 + 23.7803i 0.198106 + 0.846601i
\(790\) −58.6440 12.3448i −2.08646 0.439207i
\(791\) 6.15400i 0.218811i
\(792\) −25.5357 20.9168i −0.907373 0.743245i
\(793\) 3.66851i 0.130272i
\(794\) −2.45166 + 11.6466i −0.0870060 + 0.413323i
\(795\) 45.9887 43.1415i 1.63105 1.53007i
\(796\) 5.28630 11.9999i 0.187368 0.425326i
\(797\) 5.58542 + 20.8451i 0.197846 + 0.738371i 0.991512 + 0.130017i \(0.0415032\pi\)
−0.793666 + 0.608354i \(0.791830\pi\)
\(798\) 13.4103 0.300329i 0.474718 0.0106315i
\(799\) −12.9240 + 7.46168i −0.457218 + 0.263975i
\(800\) −14.9452 53.6614i −0.528391 1.89722i
\(801\) 32.5977 + 21.7065i 1.15178 + 0.766963i
\(802\) −0.365238 6.71658i −0.0128970 0.237171i
\(803\) −3.80424 + 14.1976i −0.134249 + 0.501024i
\(804\) −6.51783 + 13.6011i −0.229866 + 0.479672i
\(805\) −0.665784 2.48474i −0.0234658 0.0875756i
\(806\) 2.60169 + 7.95397i 0.0916407 + 0.280166i
\(807\) 15.3298 + 28.6254i 0.539633 + 1.00766i
\(808\) 5.29863 53.4420i 0.186405 1.88008i
\(809\) 36.1898 1.27236 0.636182 0.771539i \(-0.280513\pi\)
0.636182 + 0.771539i \(0.280513\pi\)
\(810\) −16.1335 + 46.3135i −0.566873 + 1.62729i
\(811\) 17.4150 + 17.4150i 0.611523 + 0.611523i 0.943343 0.331820i \(-0.107663\pi\)
−0.331820 + 0.943343i \(0.607663\pi\)
\(812\) −11.3402 1.75046i −0.397964 0.0614290i
\(813\) −17.3237 5.24011i −0.607568 0.183779i
\(814\) 14.6954 + 7.45135i 0.515074 + 0.261170i
\(815\) 27.9694 48.4445i 0.979727 1.69694i
\(816\) 7.73573 + 16.1307i 0.270805 + 0.564688i
\(817\) 19.5868 + 33.9253i 0.685254 + 1.18689i
\(818\) −0.642742 11.8198i −0.0224730 0.413269i
\(819\) 0.945524 + 4.71445i 0.0330393 + 0.164736i
\(820\) −59.8083 48.0438i −2.08860 1.67776i
\(821\) 9.08280 33.8975i 0.316992 1.18303i −0.605129 0.796127i \(-0.706878\pi\)
0.922121 0.386902i \(-0.126455\pi\)
\(822\) 2.85921 + 2.73395i 0.0997266 + 0.0953576i
\(823\) −19.3027 + 33.4332i −0.672849 + 1.16541i 0.304244 + 0.952594i \(0.401596\pi\)
−0.977093 + 0.212815i \(0.931737\pi\)
\(824\) −3.44105 + 9.12466i −0.119875 + 0.317872i
\(825\) 2.11838 66.3152i 0.0737525 2.30880i
\(826\) −12.0706 2.54091i −0.419991 0.0884096i
\(827\) 39.6335 39.6335i 1.37819 1.37819i 0.530517 0.847674i \(-0.321998\pi\)
0.847674 0.530517i \(-0.178002\pi\)
\(828\) 4.15630 0.186258i 0.144442 0.00647292i
\(829\) −20.5229 20.5229i −0.712789 0.712789i 0.254329 0.967118i \(-0.418145\pi\)
−0.967118 + 0.254329i \(0.918145\pi\)
\(830\) 41.5392 27.0921i 1.44185 0.940380i
\(831\) 14.7906 23.8273i 0.513080 0.826558i
\(832\) 11.0831 7.38468i 0.384237 0.256018i
\(833\) 13.5807 + 7.84080i 0.470542 + 0.271668i
\(834\) 8.25218 5.01404i 0.285749 0.173622i
\(835\) −21.4647 5.75145i −0.742817 0.199037i
\(836\) −4.79861 43.9918i −0.165963 1.52149i
\(837\) 18.2164 3.05200i 0.629651 0.105493i
\(838\) 33.7264 + 30.2476i 1.16506 + 1.04489i
\(839\) −4.64087 + 2.67941i −0.160221 + 0.0925035i −0.577967 0.816060i \(-0.696154\pi\)
0.417746 + 0.908564i \(0.362820\pi\)
\(840\) −14.4169 + 11.0657i −0.497429 + 0.381803i
\(841\) 5.63857 + 3.25543i 0.194433 + 0.112256i
\(842\) −13.1566 40.2226i −0.453405 1.38616i
\(843\) 41.0664 9.60963i 1.41440 0.330973i
\(844\) 11.9433 + 1.84355i 0.411106 + 0.0634575i
\(845\) −27.8691 + 27.8691i −0.958726 + 0.958726i
\(846\) 21.3509 12.0568i 0.734060 0.414522i
\(847\) 3.97928i 0.136730i
\(848\) −1.68120 + 37.7554i −0.0577327 + 1.29653i
\(849\) 0.486654 15.2345i 0.0167019 0.522848i
\(850\) −16.2620 + 32.0717i −0.557783 + 1.10005i
\(851\) −2.00596 + 0.537496i −0.0687636 + 0.0184251i
\(852\) 21.1933 24.7228i 0.726071 0.846989i
\(853\) −53.2899 14.2790i −1.82461 0.488903i −0.827271 0.561803i \(-0.810108\pi\)
−0.997339 + 0.0729001i \(0.976775\pi\)
\(854\) −2.23368 2.00328i −0.0764350 0.0685509i
\(855\) −58.9222 + 29.1733i −2.01510 + 0.997706i
\(856\) −14.2182 + 19.8143i −0.485970 + 0.677240i
\(857\) 16.8544 + 29.1927i 0.575737 + 0.997205i 0.995961 + 0.0897851i \(0.0286180\pi\)
−0.420224 + 0.907420i \(0.638049\pi\)
\(858\) 15.2268 4.44772i 0.519835 0.151843i
\(859\) −52.8271 + 14.1550i −1.80244 + 0.482962i −0.994355 0.106107i \(-0.966161\pi\)
−0.808083 + 0.589069i \(0.799495\pi\)
\(860\) −48.5718 21.3972i −1.65628 0.729639i
\(861\) −4.80624 + 15.8893i −0.163796 + 0.541507i
\(862\) −8.02568 12.3055i −0.273356 0.419126i
\(863\) 28.6860 0.976481 0.488241 0.872709i \(-0.337639\pi\)
0.488241 + 0.872709i \(0.337639\pi\)
\(864\) −12.4568 26.6238i −0.423789 0.905761i
\(865\) 30.7327 1.04494
\(866\) −2.56390 3.93113i −0.0871249 0.133585i
\(867\) −5.18148 + 17.1298i −0.175972 + 0.581760i
\(868\) 6.26373 + 2.75935i 0.212605 + 0.0936583i
\(869\) 41.3248 11.0729i 1.40185 0.375624i
\(870\) 53.9881 15.7698i 1.83037 0.534646i
\(871\) −3.62402 6.27698i −0.122795 0.212688i
\(872\) −12.8871 9.24743i −0.436412 0.313157i
\(873\) 0.676113 10.5719i 0.0228829 0.357806i
\(874\) 4.15234 + 3.72403i 0.140455 + 0.125967i
\(875\) −17.3689 4.65399i −0.587177 0.157334i
\(876\) −8.51860 + 9.93725i −0.287817 + 0.335749i
\(877\) 5.11731 1.37118i 0.172799 0.0463014i −0.171382 0.985205i \(-0.554823\pi\)
0.344181 + 0.938903i \(0.388157\pi\)
\(878\) −20.2890 + 40.0136i −0.684721 + 1.35039i
\(879\) 0.0462987 1.44936i 0.00156162 0.0488858i
\(880\) 40.4686 + 44.2406i 1.36420 + 1.49135i
\(881\) 33.4396i 1.12661i −0.826249 0.563305i \(-0.809530\pi\)
0.826249 0.563305i \(-0.190470\pi\)
\(882\) −22.1899 13.0952i −0.747174 0.440940i
\(883\) −26.9753 + 26.9753i −0.907790 + 0.907790i −0.996094 0.0883036i \(-0.971855\pi\)
0.0883036 + 0.996094i \(0.471855\pi\)
\(884\) −8.49665 1.31153i −0.285773 0.0441114i
\(885\) 58.8723 13.7762i 1.97897 0.463083i
\(886\) 5.85521 + 17.9007i 0.196710 + 0.601386i
\(887\) −49.0505 28.3193i −1.64695 0.950869i −0.978274 0.207318i \(-0.933526\pi\)
−0.668680 0.743550i \(-0.733140\pi\)
\(888\) 8.93348 + 11.6389i 0.299788 + 0.390576i
\(889\) −2.57410 + 1.48616i −0.0863325 + 0.0498441i
\(890\) −52.9587 47.4962i −1.77518 1.59207i
\(891\) −4.67977 34.6970i −0.156778 1.16239i
\(892\) −1.12948 10.3546i −0.0378177 0.346698i
\(893\) 31.7522 + 8.50797i 1.06255 + 0.284708i
\(894\) −9.35079 + 5.68156i −0.312737 + 0.190020i
\(895\) −7.00364 4.04356i −0.234106 0.135161i
\(896\) 1.55582 10.7809i 0.0519763 0.360163i
\(897\) −1.05448 + 1.69873i −0.0352079 + 0.0567191i
\(898\) 15.4677 10.0881i 0.516164 0.336645i
\(899\) −14.9781 14.9781i −0.499549 0.499549i
\(900\) 27.2211 52.4384i 0.907369 1.74795i
\(901\) 17.2511 17.2511i 0.574718 0.574718i
\(902\) 53.5914 + 11.2812i 1.78440 + 0.375622i
\(903\) −0.366692 + 11.4792i −0.0122028 + 0.382003i
\(904\) −16.9162 6.37937i −0.562626 0.212175i
\(905\) 13.4565 23.3073i 0.447308 0.774760i
\(906\) −34.0023 32.5127i −1.12965 1.08016i
\(907\) −2.60194 + 9.71055i −0.0863958 + 0.322434i −0.995575 0.0939718i \(-0.970044\pi\)
0.909179 + 0.416405i \(0.136710\pi\)
\(908\) −10.1469 8.15095i −0.336736 0.270499i
\(909\) 42.7666 37.6252i 1.41848 1.24795i
\(910\) −0.474237 8.72103i −0.0157208 0.289099i
\(911\) 23.4920 + 40.6893i 0.778325 + 1.34810i 0.932907 + 0.360118i \(0.117263\pi\)
−0.154582 + 0.987980i \(0.549403\pi\)
\(912\) 13.0758 37.1737i 0.432983 1.23094i
\(913\) −17.7019 + 30.6607i −0.585849 + 1.01472i
\(914\) 14.6303 + 7.41834i 0.483928 + 0.245377i
\(915\) 14.0771 + 4.25806i 0.465373 + 0.140767i
\(916\) 8.17550 + 1.26195i 0.270126 + 0.0416961i
\(917\) 3.57776 + 3.57776i 0.118148 + 0.118148i
\(918\) −5.66679 + 18.1090i −0.187032 + 0.597685i
\(919\) −49.8848 −1.64555 −0.822774 0.568369i \(-0.807575\pi\)
−0.822774 + 0.568369i \(0.807575\pi\)
\(920\) −7.52027 0.745615i −0.247936 0.0245822i
\(921\) −24.4684 45.6902i −0.806262 1.50554i
\(922\) −6.05818 18.5212i −0.199515 0.609964i
\(923\) 4.05026 + 15.1158i 0.133316 + 0.497542i
\(924\) 5.60686 11.7001i 0.184452 0.384905i
\(925\) −7.63296 + 28.4866i −0.250970 + 0.936634i
\(926\) 1.01885 + 18.7363i 0.0334815 + 0.615712i
\(927\) −9.26953 + 4.58949i −0.304451 + 0.150739i
\(928\) −16.5672 + 29.3577i −0.543846 + 0.963714i
\(929\) −29.2209 + 16.8707i −0.958707 + 0.553510i −0.895775 0.444508i \(-0.853379\pi\)
−0.0629322 + 0.998018i \(0.520045\pi\)
\(930\) −33.5413 + 0.751174i −1.09986 + 0.0246320i
\(931\) −8.94026 33.3655i −0.293005 1.09351i
\(932\) −13.8825 + 31.5133i −0.454735 + 1.03225i
\(933\) −15.8195 + 14.8401i −0.517909 + 0.485845i
\(934\) 11.6005 55.1086i 0.379581 1.80321i
\(935\) 38.7051i 1.26579i
\(936\) 13.9393 + 2.28802i 0.455621 + 0.0747863i
\(937\) 16.7455i 0.547052i −0.961865 0.273526i \(-0.911810\pi\)
0.961865 0.273526i \(-0.0881899\pi\)
\(938\) −5.80092 1.22111i −0.189407 0.0398708i
\(939\) 12.8393 + 54.8682i 0.418994 + 1.79056i
\(940\) −41.5172 + 16.1244i −1.35414 + 0.525921i
\(941\) −1.50628 5.62151i −0.0491033 0.183256i 0.937018 0.349280i \(-0.113574\pi\)
−0.986122 + 0.166024i \(0.946907\pi\)
\(942\) −39.4843 + 23.9908i −1.28647 + 0.781661i
\(943\) −5.97797 + 3.45138i −0.194669 + 0.112392i
\(944\) −19.4972 + 30.5460i −0.634579 + 0.994189i
\(945\) −19.1881 1.84386i −0.624188 0.0599807i
\(946\) 37.8343 2.05737i 1.23010 0.0668909i
\(947\) 1.73267 6.46641i 0.0563042 0.210130i −0.932043 0.362348i \(-0.881975\pi\)
0.988347 + 0.152218i \(0.0486417\pi\)
\(948\) 37.4465 + 7.01094i 1.21621 + 0.227705i
\(949\) −1.62799 6.07575i −0.0528468 0.197227i
\(950\) 75.2832 24.6247i 2.44251 0.798929i
\(951\) 12.7086 20.4732i 0.412104 0.663889i
\(952\) −5.43837 + 4.45725i −0.176259 + 0.144460i
\(953\) 0.390160 0.0126385 0.00631925 0.999980i \(-0.497989\pi\)
0.00631925 + 0.999980i \(0.497989\pi\)
\(954\) −28.6138 + 28.0729i −0.926406 + 0.908894i
\(955\) 20.7201 + 20.7201i 0.670487 + 0.670487i
\(956\) −10.6200 14.4971i −0.343476 0.468868i
\(957\) −29.2837 + 27.4707i −0.946606 + 0.888001i
\(958\) 4.35079 8.58055i 0.140568 0.277225i
\(959\) −0.777447 + 1.34658i −0.0251051 + 0.0434832i
\(960\) 15.4728 + 51.1003i 0.499382 + 1.64925i
\(961\) −9.18236 15.9043i −0.296205 0.513042i
\(962\) −7.04060 + 0.382857i −0.226998 + 0.0123438i
\(963\) −25.3622 + 5.08661i −0.817284 + 0.163914i
\(964\) −2.23002 + 0.243250i −0.0718242 + 0.00783455i
\(965\) 1.92290 7.17636i 0.0619003 0.231015i
\(966\) 0.458501 + 1.56969i 0.0147520 + 0.0505038i
\(967\) −0.0976589 + 0.169150i −0.00314050 + 0.00543950i −0.867591 0.497278i \(-0.834333\pi\)
0.864451 + 0.502717i \(0.167666\pi\)
\(968\) −10.9383 4.12501i −0.351571 0.132583i
\(969\) −22.4251 + 12.0093i −0.720399 + 0.385795i
\(970\) −3.96369 + 18.8296i −0.127266 + 0.604581i
\(971\) 17.8241 17.8241i 0.572003 0.572003i −0.360685 0.932688i \(-0.617457\pi\)
0.932688 + 0.360685i \(0.117457\pi\)
\(972\) 9.59435 29.6639i 0.307739 0.951471i
\(973\) 2.68369 + 2.68369i 0.0860352 + 0.0860352i
\(974\) −8.47609 12.9961i −0.271591 0.416420i
\(975\) 13.4044 + 25.0302i 0.429284 + 0.801607i
\(976\) −7.82214 + 4.06334i −0.250381 + 0.130064i
\(977\) −44.7934 25.8615i −1.43307 0.827382i −0.435713 0.900085i \(-0.643504\pi\)
−0.997354 + 0.0727039i \(0.976837\pi\)
\(978\) −17.0863 + 31.1867i −0.546359 + 0.997241i
\(979\) 49.0534 + 13.1438i 1.56775 + 0.420079i
\(980\) 36.4870 + 29.3099i 1.16553 + 0.936271i
\(981\) −3.30828 16.4953i −0.105625 0.526655i
\(982\) 6.82451 7.60941i 0.217779 0.242826i
\(983\) 48.7340 28.1366i 1.55437 0.897419i 0.556597 0.830782i \(-0.312107\pi\)
0.997777 0.0666364i \(-0.0212267\pi\)
\(984\) 38.6946 + 29.6827i 1.23354 + 0.946250i
\(985\) 76.4921 + 44.1627i 2.43724 + 1.40714i
\(986\) 20.6827 6.76517i 0.658670 0.215447i
\(987\) 6.59376 + 7.02892i 0.209882 + 0.223733i
\(988\) 11.1913 + 15.2769i 0.356044 + 0.486024i
\(989\) −3.37694 + 3.37694i −0.107381 + 0.107381i
\(990\) −0.606783 + 63.5919i −0.0192848 + 2.02108i
\(991\) 45.9493i 1.45963i −0.683646 0.729814i \(-0.739607\pi\)
0.683646 0.729814i \(-0.260393\pi\)
\(992\) 14.0781 14.3575i 0.446979 0.455850i
\(993\) 8.06581 + 5.00679i 0.255961 + 0.158886i
\(994\) 11.4154 + 5.78823i 0.362076 + 0.183592i
\(995\) −24.4021 + 6.53852i −0.773599 + 0.207285i
\(996\) −26.0144 + 17.8095i −0.824298 + 0.564314i
\(997\) 11.9748 + 3.20864i 0.379246 + 0.101619i 0.443406 0.896321i \(-0.353770\pi\)
−0.0641600 + 0.997940i \(0.520437\pi\)
\(998\) 24.8314 27.6872i 0.786023 0.876424i
\(999\) −1.48857 + 15.4908i −0.0470963 + 0.490107i
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 144.2.u.a.131.17 yes 88
3.2 odd 2 432.2.v.a.179.6 88
4.3 odd 2 576.2.y.a.239.13 88
9.2 odd 6 inner 144.2.u.a.83.9 yes 88
9.7 even 3 432.2.v.a.35.14 88
12.11 even 2 1728.2.z.a.1583.2 88
16.5 even 4 576.2.y.a.527.20 88
16.11 odd 4 inner 144.2.u.a.59.9 yes 88
36.7 odd 6 1728.2.z.a.1007.2 88
36.11 even 6 576.2.y.a.47.20 88
48.5 odd 4 1728.2.z.a.719.2 88
48.11 even 4 432.2.v.a.395.14 88
144.11 even 12 inner 144.2.u.a.11.17 88
144.43 odd 12 432.2.v.a.251.6 88
144.101 odd 12 576.2.y.a.335.13 88
144.133 even 12 1728.2.z.a.143.2 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.u.a.11.17 88 144.11 even 12 inner
144.2.u.a.59.9 yes 88 16.11 odd 4 inner
144.2.u.a.83.9 yes 88 9.2 odd 6 inner
144.2.u.a.131.17 yes 88 1.1 even 1 trivial
432.2.v.a.35.14 88 9.7 even 3
432.2.v.a.179.6 88 3.2 odd 2
432.2.v.a.251.6 88 144.43 odd 12
432.2.v.a.395.14 88 48.11 even 4
576.2.y.a.47.20 88 36.11 even 6
576.2.y.a.239.13 88 4.3 odd 2
576.2.y.a.335.13 88 144.101 odd 12
576.2.y.a.527.20 88 16.5 even 4
1728.2.z.a.143.2 88 144.133 even 12
1728.2.z.a.719.2 88 48.5 odd 4
1728.2.z.a.1007.2 88 36.7 odd 6
1728.2.z.a.1583.2 88 12.11 even 2