Properties

Label 525.2.bk.a.8.9
Level $525$
Weight $2$
Character 525.8
Analytic conductor $4.192$
Analytic rank $0$
Dimension $480$
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] = [525,2,Mod(8,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.bk (of order \(20\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(480\)
Relative dimension: \(60\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 8.9
Character \(\chi\) \(=\) 525.8
Dual form 525.2.bk.a.197.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.996070 + 1.95490i) q^{2} +(1.41904 + 0.993139i) q^{3} +(-1.65390 - 2.27640i) q^{4} +(2.07107 + 0.843023i) q^{5} +(-3.35495 + 1.78484i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.76348 - 0.279307i) q^{8} +(1.02735 + 2.81861i) q^{9} +O(q^{10})\) \(q+(-0.996070 + 1.95490i) q^{2} +(1.41904 + 0.993139i) q^{3} +(-1.65390 - 2.27640i) q^{4} +(2.07107 + 0.843023i) q^{5} +(-3.35495 + 1.78484i) q^{6} +(0.707107 - 0.707107i) q^{7} +(1.76348 - 0.279307i) q^{8} +(1.02735 + 2.81861i) q^{9} +(-3.71095 + 3.20901i) q^{10} +(3.26489 - 1.06083i) q^{11} +(-0.0861709 - 4.87285i) q^{12} +(-0.258140 + 0.131529i) q^{13} +(0.677993 + 2.08665i) q^{14} +(2.10169 + 3.25314i) q^{15} +(0.528482 - 1.62650i) q^{16} +(0.915130 + 5.77790i) q^{17} +(-6.53340 - 0.799167i) q^{18} +(-0.935945 + 1.28822i) q^{19} +(-1.50628 - 6.10884i) q^{20} +(1.70567 - 0.301158i) q^{21} +(-1.17825 + 7.43918i) q^{22} +(-8.39042 - 4.27513i) q^{23} +(2.77984 + 1.35503i) q^{24} +(3.57862 + 3.49191i) q^{25} -0.635649i q^{26} +(-1.34142 + 5.02002i) q^{27} +(-2.77914 - 0.440172i) q^{28} +(4.75755 - 3.45656i) q^{29} +(-8.45298 + 0.868227i) q^{30} +(1.32279 + 0.961060i) q^{31} +(5.17826 + 5.17826i) q^{32} +(5.68656 + 1.73713i) q^{33} +(-12.2067 - 3.96621i) q^{34} +(2.06057 - 0.868357i) q^{35} +(4.71713 - 7.00035i) q^{36} +(0.794823 + 1.55993i) q^{37} +(-1.58607 - 3.11283i) q^{38} +(-0.496937 - 0.0697241i) q^{39} +(3.88774 + 0.908188i) q^{40} +(-5.56607 - 1.80853i) q^{41} +(-1.11023 + 3.63438i) q^{42} +(2.63602 + 2.63602i) q^{43} +(-7.81466 - 5.67768i) q^{44} +(-0.248442 + 6.70360i) q^{45} +(16.7149 - 12.1441i) q^{46} +(-9.38580 - 1.48656i) q^{47} +(2.36528 - 1.78321i) q^{48} -1.00000i q^{49} +(-10.3909 + 3.51766i) q^{50} +(-4.43966 + 9.10793i) q^{51} +(0.726349 + 0.370093i) q^{52} +(0.921830 - 5.82021i) q^{53} +(-8.47748 - 7.62263i) q^{54} +(7.65610 + 0.555335i) q^{55} +(1.04947 - 1.44447i) q^{56} +(-2.60752 + 0.898510i) q^{57} +(2.01837 + 12.7435i) q^{58} +(1.38213 - 4.25376i) q^{59} +(3.92946 - 10.1646i) q^{60} +(-4.33480 - 13.3411i) q^{61} +(-3.19636 + 1.62863i) q^{62} +(2.71950 + 1.26661i) q^{63} +(-12.0279 + 3.90809i) q^{64} +(-0.645506 + 0.0547870i) q^{65} +(-9.06013 + 9.38633i) q^{66} +(0.249094 - 0.0394525i) q^{67} +(11.6393 - 11.6393i) q^{68} +(-7.66054 - 14.3994i) q^{69} +(-0.354924 + 4.89315i) q^{70} +(-5.86603 - 8.07390i) q^{71} +(2.59897 + 4.68360i) q^{72} +(4.07580 - 7.99921i) q^{73} -3.84120 q^{74} +(1.61026 + 8.50923i) q^{75} +4.48045 q^{76} +(1.55851 - 3.05874i) q^{77} +(0.631288 - 0.902011i) q^{78} +(-2.26196 - 3.11332i) q^{79} +(2.46570 - 2.92307i) q^{80} +(-6.88910 + 5.79139i) q^{81} +(9.07969 - 9.07969i) q^{82} +(12.7807 - 2.02426i) q^{83} +(-3.50656 - 3.38469i) q^{84} +(-2.97561 + 12.7379i) q^{85} +(-7.77880 + 2.52749i) q^{86} +(10.1840 - 0.180093i) q^{87} +(5.46126 - 2.78265i) q^{88} +(0.574377 + 1.76775i) q^{89} +(-12.8574 - 7.16294i) q^{90} +(-0.0895275 + 0.275537i) q^{91} +(4.14501 + 26.1705i) q^{92} +(0.922620 + 2.67749i) q^{93} +(12.2550 - 16.8676i) q^{94} +(-3.02440 + 1.87896i) q^{95} +(2.20543 + 12.4909i) q^{96} +(-2.48230 + 15.6727i) q^{97} +(1.95490 + 0.996070i) q^{98} +(6.34424 + 8.11261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 480 q + 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display \( 480 q + 4 q^{3} + 16 q^{10} - 16 q^{12} + 8 q^{13} + 16 q^{15} + 120 q^{16} + 20 q^{18} - 40 q^{19} - 48 q^{22} - 104 q^{25} + 16 q^{27} - 20 q^{30} - 28 q^{33} - 80 q^{34} + 16 q^{37} - 40 q^{39} - 64 q^{40} - 80 q^{42} + 40 q^{43} - 20 q^{45} - 276 q^{48} - 260 q^{54} - 40 q^{55} - 4 q^{57} - 40 q^{58} - 52 q^{60} - 32 q^{63} + 160 q^{64} + 56 q^{67} + 8 q^{70} + 288 q^{72} + 48 q^{73} + 60 q^{75} + 140 q^{78} + 80 q^{79} - 40 q^{81} - 184 q^{85} + 96 q^{87} - 56 q^{88} + 24 q^{90} + 96 q^{93} - 560 q^{94} - 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.996070 + 1.95490i −0.704328 + 1.38232i 0.210143 + 0.977671i \(0.432607\pi\)
−0.914471 + 0.404651i \(0.867393\pi\)
\(3\) 1.41904 + 0.993139i 0.819283 + 0.573389i
\(4\) −1.65390 2.27640i −0.826949 1.13820i
\(5\) 2.07107 + 0.843023i 0.926209 + 0.377011i
\(6\) −3.35495 + 1.78484i −1.36965 + 0.728659i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 1.76348 0.279307i 0.623483 0.0987501i
\(9\) 1.02735 + 2.81861i 0.342450 + 0.939536i
\(10\) −3.71095 + 3.20901i −1.17351 + 1.01478i
\(11\) 3.26489 1.06083i 0.984401 0.319851i 0.227786 0.973711i \(-0.426851\pi\)
0.756616 + 0.653860i \(0.226851\pi\)
\(12\) −0.0861709 4.87285i −0.0248754 1.40667i
\(13\) −0.258140 + 0.131529i −0.0715951 + 0.0364795i −0.489422 0.872047i \(-0.662792\pi\)
0.417826 + 0.908527i \(0.362792\pi\)
\(14\) 0.677993 + 2.08665i 0.181201 + 0.557680i
\(15\) 2.10169 + 3.25314i 0.542653 + 0.839957i
\(16\) 0.528482 1.62650i 0.132120 0.406625i
\(17\) 0.915130 + 5.77790i 0.221952 + 1.40135i 0.807097 + 0.590419i \(0.201038\pi\)
−0.585145 + 0.810929i \(0.698962\pi\)
\(18\) −6.53340 0.799167i −1.53994 0.188365i
\(19\) −0.935945 + 1.28822i −0.214721 + 0.295537i −0.902768 0.430129i \(-0.858468\pi\)
0.688047 + 0.725666i \(0.258468\pi\)
\(20\) −1.50628 6.10884i −0.336814 1.36598i
\(21\) 1.70567 0.301158i 0.372207 0.0657180i
\(22\) −1.17825 + 7.43918i −0.251204 + 1.58604i
\(23\) −8.39042 4.27513i −1.74952 0.891426i −0.961058 0.276346i \(-0.910876\pi\)
−0.788464 0.615080i \(-0.789124\pi\)
\(24\) 2.77984 + 1.35503i 0.567432 + 0.276594i
\(25\) 3.57862 + 3.49191i 0.715725 + 0.698382i
\(26\) 0.635649i 0.124661i
\(27\) −1.34142 + 5.02002i −0.258156 + 0.966103i
\(28\) −2.77914 0.440172i −0.525208 0.0831847i
\(29\) 4.75755 3.45656i 0.883455 0.641868i −0.0507081 0.998714i \(-0.516148\pi\)
0.934163 + 0.356846i \(0.116148\pi\)
\(30\) −8.45298 + 0.868227i −1.54330 + 0.158516i
\(31\) 1.32279 + 0.961060i 0.237579 + 0.172611i 0.700204 0.713943i \(-0.253092\pi\)
−0.462625 + 0.886554i \(0.653092\pi\)
\(32\) 5.17826 + 5.17826i 0.915395 + 0.915395i
\(33\) 5.68656 + 1.73713i 0.989903 + 0.302396i
\(34\) −12.2067 3.96621i −2.09344 0.680200i
\(35\) 2.06057 0.868357i 0.348300 0.146779i
\(36\) 4.71713 7.00035i 0.786189 1.16672i
\(37\) 0.794823 + 1.55993i 0.130668 + 0.256451i 0.947066 0.321039i \(-0.104032\pi\)
−0.816398 + 0.577490i \(0.804032\pi\)
\(38\) −1.58607 3.11283i −0.257294 0.504968i
\(39\) −0.496937 0.0697241i −0.0795736 0.0111648i
\(40\) 3.88774 + 0.908188i 0.614706 + 0.143597i
\(41\) −5.56607 1.80853i −0.869275 0.282445i −0.159778 0.987153i \(-0.551078\pi\)
−0.709497 + 0.704708i \(0.751078\pi\)
\(42\) −1.11023 + 3.63438i −0.171313 + 0.560797i
\(43\) 2.63602 + 2.63602i 0.401989 + 0.401989i 0.878933 0.476944i \(-0.158256\pi\)
−0.476944 + 0.878933i \(0.658256\pi\)
\(44\) −7.81466 5.67768i −1.17810 0.855943i
\(45\) −0.248442 + 6.70360i −0.0370355 + 0.999314i
\(46\) 16.7149 12.1441i 2.46448 1.79055i
\(47\) −9.38580 1.48656i −1.36906 0.216838i −0.571760 0.820421i \(-0.693739\pi\)
−0.797300 + 0.603583i \(0.793739\pi\)
\(48\) 2.36528 1.78321i 0.341398 0.257385i
\(49\) 1.00000i 0.142857i
\(50\) −10.3909 + 3.51766i −1.46949 + 0.497472i
\(51\) −4.43966 + 9.10793i −0.621676 + 1.27537i
\(52\) 0.726349 + 0.370093i 0.100726 + 0.0513227i
\(53\) 0.921830 5.82021i 0.126623 0.799467i −0.839872 0.542784i \(-0.817370\pi\)
0.966496 0.256683i \(-0.0826297\pi\)
\(54\) −8.47748 7.62263i −1.15364 1.03731i
\(55\) 7.65610 + 0.555335i 1.03235 + 0.0748813i
\(56\) 1.04947 1.44447i 0.140241 0.193025i
\(57\) −2.60752 + 0.898510i −0.345375 + 0.119011i
\(58\) 2.01837 + 12.7435i 0.265025 + 1.67330i
\(59\) 1.38213 4.25376i 0.179938 0.553793i −0.819886 0.572526i \(-0.805963\pi\)
0.999825 + 0.0187335i \(0.00596341\pi\)
\(60\) 3.92946 10.1646i 0.507291 1.31225i
\(61\) −4.33480 13.3411i −0.555014 1.70816i −0.695906 0.718133i \(-0.744997\pi\)
0.140891 0.990025i \(-0.455003\pi\)
\(62\) −3.19636 + 1.62863i −0.405938 + 0.206836i
\(63\) 2.71950 + 1.26661i 0.342625 + 0.159578i
\(64\) −12.0279 + 3.90809i −1.50348 + 0.488511i
\(65\) −0.645506 + 0.0547870i −0.0800652 + 0.00679549i
\(66\) −9.06013 + 9.38633i −1.11522 + 1.15538i
\(67\) 0.249094 0.0394525i 0.0304316 0.00481990i −0.141200 0.989981i \(-0.545096\pi\)
0.171632 + 0.985161i \(0.445096\pi\)
\(68\) 11.6393 11.6393i 1.41147 1.41147i
\(69\) −7.66054 14.3994i −0.922220 1.73349i
\(70\) −0.354924 + 4.89315i −0.0424216 + 0.584843i
\(71\) −5.86603 8.07390i −0.696170 0.958196i −0.999985 0.00546455i \(-0.998261\pi\)
0.303815 0.952731i \(-0.401739\pi\)
\(72\) 2.59897 + 4.68360i 0.306291 + 0.551968i
\(73\) 4.07580 7.99921i 0.477036 0.936237i −0.519610 0.854404i \(-0.673923\pi\)
0.996646 0.0818329i \(-0.0260774\pi\)
\(74\) −3.84120 −0.446530
\(75\) 1.61026 + 8.50923i 0.185937 + 0.982562i
\(76\) 4.48045 0.513943
\(77\) 1.55851 3.05874i 0.177608 0.348576i
\(78\) 0.631288 0.902011i 0.0714792 0.102133i
\(79\) −2.26196 3.11332i −0.254490 0.350276i 0.662587 0.748985i \(-0.269458\pi\)
−0.917078 + 0.398709i \(0.869458\pi\)
\(80\) 2.46570 2.92307i 0.275673 0.326809i
\(81\) −6.88910 + 5.79139i −0.765456 + 0.643488i
\(82\) 9.07969 9.07969i 1.00268 1.00268i
\(83\) 12.7807 2.02426i 1.40286 0.222192i 0.591298 0.806453i \(-0.298616\pi\)
0.811565 + 0.584262i \(0.198616\pi\)
\(84\) −3.50656 3.38469i −0.382597 0.369300i
\(85\) −2.97561 + 12.7379i −0.322750 + 1.38162i
\(86\) −7.77880 + 2.52749i −0.838810 + 0.272546i
\(87\) 10.1840 0.180093i 1.09184 0.0193080i
\(88\) 5.46126 2.78265i 0.582173 0.296632i
\(89\) 0.574377 + 1.76775i 0.0608839 + 0.187381i 0.976872 0.213823i \(-0.0685917\pi\)
−0.915988 + 0.401205i \(0.868592\pi\)
\(90\) −12.8574 7.16294i −1.35529 0.755040i
\(91\) −0.0895275 + 0.275537i −0.00938503 + 0.0288842i
\(92\) 4.14501 + 26.1705i 0.432147 + 2.72847i
\(93\) 0.922620 + 2.67749i 0.0956712 + 0.277643i
\(94\) 12.2550 16.8676i 1.26401 1.73976i
\(95\) −3.02440 + 1.87896i −0.310297 + 0.192777i
\(96\) 2.20543 + 12.4909i 0.225090 + 1.27485i
\(97\) −2.48230 + 15.6727i −0.252040 + 1.59132i 0.459178 + 0.888344i \(0.348144\pi\)
−0.711217 + 0.702972i \(0.751856\pi\)
\(98\) 1.95490 + 0.996070i 0.197474 + 0.100618i
\(99\) 6.34424 + 8.11261i 0.637620 + 0.815347i
\(100\) 2.03029 13.9216i 0.203029 1.39216i
\(101\) 11.7033i 1.16452i 0.813001 + 0.582262i \(0.197832\pi\)
−0.813001 + 0.582262i \(0.802168\pi\)
\(102\) −13.3829 17.7512i −1.32510 1.75763i
\(103\) −6.05828 0.959537i −0.596940 0.0945460i −0.149349 0.988785i \(-0.547718\pi\)
−0.447591 + 0.894239i \(0.647718\pi\)
\(104\) −0.418487 + 0.304048i −0.0410360 + 0.0298144i
\(105\) 3.78643 + 0.814200i 0.369518 + 0.0794578i
\(106\) 10.4597 + 7.59942i 1.01594 + 0.738121i
\(107\) 5.74305 + 5.74305i 0.555201 + 0.555201i 0.927937 0.372736i \(-0.121580\pi\)
−0.372736 + 0.927937i \(0.621580\pi\)
\(108\) 13.6461 5.24900i 1.31310 0.505085i
\(109\) 18.6871 + 6.07182i 1.78990 + 0.581575i 0.999518 0.0310343i \(-0.00988013\pi\)
0.790386 + 0.612609i \(0.209880\pi\)
\(110\) −8.71164 + 14.4137i −0.830622 + 1.37430i
\(111\) −0.421339 + 3.00297i −0.0399918 + 0.285029i
\(112\) −0.776416 1.52380i −0.0733644 0.143986i
\(113\) −3.68465 7.23153i −0.346623 0.680285i 0.650215 0.759750i \(-0.274679\pi\)
−0.996838 + 0.0794649i \(0.974679\pi\)
\(114\) 0.840782 5.99242i 0.0787464 0.561241i
\(115\) −13.7731 15.9274i −1.28435 1.48524i
\(116\) −15.7370 5.11327i −1.46115 0.474755i
\(117\) −0.635928 0.592469i −0.0587916 0.0547738i
\(118\) 6.93897 + 6.93897i 0.638784 + 0.638784i
\(119\) 4.73269 + 3.43850i 0.433845 + 0.315207i
\(120\) 4.61490 + 5.14982i 0.421281 + 0.470112i
\(121\) 0.634967 0.461330i 0.0577243 0.0419391i
\(122\) 30.3983 + 4.81462i 2.75214 + 0.435895i
\(123\) −6.10236 8.09426i −0.550232 0.729835i
\(124\) 4.60068i 0.413153i
\(125\) 4.46780 + 10.2488i 0.399613 + 0.916684i
\(126\) −5.18491 + 4.05472i −0.461908 + 0.361223i
\(127\) 1.07921 + 0.549887i 0.0957648 + 0.0487946i 0.501217 0.865322i \(-0.332886\pi\)
−0.405452 + 0.914116i \(0.632886\pi\)
\(128\) 2.04949 12.9400i 0.181151 1.14374i
\(129\) 1.12268 + 6.35855i 0.0988468 + 0.559839i
\(130\) 0.535867 1.31647i 0.0469986 0.115462i
\(131\) 8.17581 11.2530i 0.714324 0.983182i −0.285369 0.958418i \(-0.592116\pi\)
0.999693 0.0247648i \(-0.00788369\pi\)
\(132\) −5.45059 15.8179i −0.474413 1.37677i
\(133\) 0.249095 + 1.57272i 0.0215992 + 0.136372i
\(134\) −0.170989 + 0.526250i −0.0147712 + 0.0454611i
\(135\) −7.01016 + 9.26594i −0.603338 + 0.797485i
\(136\) 3.22762 + 9.93360i 0.276766 + 0.851799i
\(137\) 6.05533 3.08534i 0.517341 0.263599i −0.175767 0.984432i \(-0.556241\pi\)
0.693109 + 0.720833i \(0.256241\pi\)
\(138\) 35.7798 0.632727i 3.04578 0.0538613i
\(139\) −6.53190 + 2.12234i −0.554029 + 0.180015i −0.572633 0.819812i \(-0.694078\pi\)
0.0186038 + 0.999827i \(0.494078\pi\)
\(140\) −5.38470 3.25450i −0.455090 0.275056i
\(141\) −11.8425 11.4309i −0.997315 0.962655i
\(142\) 21.6266 3.42532i 1.81487 0.287447i
\(143\) −0.703269 + 0.703269i −0.0588103 + 0.0588103i
\(144\) 5.12740 0.181402i 0.427284 0.0151168i
\(145\) 12.7672 3.14804i 1.06026 0.261431i
\(146\) 11.5779 + 15.9355i 0.958190 + 1.31884i
\(147\) 0.993139 1.41904i 0.0819127 0.117040i
\(148\) 2.23646 4.38929i 0.183836 0.360798i
\(149\) 4.06381 0.332920 0.166460 0.986048i \(-0.446766\pi\)
0.166460 + 0.986048i \(0.446766\pi\)
\(150\) −18.2386 5.32790i −1.48918 0.435021i
\(151\) 10.0622 0.818850 0.409425 0.912344i \(-0.365729\pi\)
0.409425 + 0.912344i \(0.365729\pi\)
\(152\) −1.29071 + 2.53316i −0.104690 + 0.205466i
\(153\) −15.3455 + 8.51532i −1.24061 + 0.688423i
\(154\) 4.42715 + 6.09345i 0.356750 + 0.491024i
\(155\) 1.92938 + 3.10556i 0.154972 + 0.249444i
\(156\) 0.663164 + 1.24654i 0.0530956 + 0.0998032i
\(157\) −4.16214 + 4.16214i −0.332175 + 0.332175i −0.853412 0.521237i \(-0.825471\pi\)
0.521237 + 0.853412i \(0.325471\pi\)
\(158\) 8.33929 1.32081i 0.663439 0.105078i
\(159\) 7.08839 7.34360i 0.562146 0.582386i
\(160\) 6.35912 + 15.0899i 0.502733 + 1.19296i
\(161\) −8.95589 + 2.90995i −0.705823 + 0.229336i
\(162\) −4.45955 19.2361i −0.350376 1.51133i
\(163\) 6.96277 3.54771i 0.545366 0.277878i −0.159524 0.987194i \(-0.550996\pi\)
0.704891 + 0.709316i \(0.250996\pi\)
\(164\) 5.08880 + 15.6617i 0.397368 + 1.22297i
\(165\) 10.3128 + 8.39162i 0.802850 + 0.653286i
\(166\) −8.77324 + 27.0013i −0.680935 + 2.09570i
\(167\) −0.969690 6.12238i −0.0750368 0.473764i −0.996380 0.0850133i \(-0.972907\pi\)
0.921343 0.388751i \(-0.127093\pi\)
\(168\) 2.92379 1.00749i 0.225575 0.0777296i
\(169\) −7.59187 + 10.4493i −0.583990 + 0.803793i
\(170\) −21.9374 18.5048i −1.68252 1.41926i
\(171\) −4.59253 1.31461i −0.351199 0.100531i
\(172\) 1.64091 10.3603i 0.125119 0.789967i
\(173\) 19.1710 + 9.76812i 1.45755 + 0.742656i 0.989967 0.141296i \(-0.0451268\pi\)
0.467578 + 0.883952i \(0.345127\pi\)
\(174\) −9.79192 + 20.0881i −0.742324 + 1.52287i
\(175\) 4.99962 0.0613156i 0.377936 0.00463502i
\(176\) 5.87097i 0.442541i
\(177\) 6.18588 4.66361i 0.464959 0.350539i
\(178\) −4.02789 0.637956i −0.301903 0.0478168i
\(179\) 5.59994 4.06859i 0.418559 0.304101i −0.358499 0.933530i \(-0.616711\pi\)
0.777058 + 0.629429i \(0.216711\pi\)
\(180\) 15.6709 10.5215i 1.16804 0.784228i
\(181\) 6.51312 + 4.73206i 0.484116 + 0.351731i 0.802917 0.596091i \(-0.203280\pi\)
−0.318801 + 0.947822i \(0.603280\pi\)
\(182\) −0.449472 0.449472i −0.0333171 0.0333171i
\(183\) 7.09835 23.2367i 0.524725 1.71770i
\(184\) −15.9904 5.19559i −1.17883 0.383024i
\(185\) 0.331075 + 3.90077i 0.0243412 + 0.286790i
\(186\) −6.15322 0.863343i −0.451176 0.0633034i
\(187\) 9.11716 + 17.8934i 0.666713 + 1.30850i
\(188\) 12.1391 + 23.8244i 0.885338 + 1.73757i
\(189\) 2.60116 + 4.49822i 0.189207 + 0.327197i
\(190\) −0.660660 7.78397i −0.0479293 0.564709i
\(191\) −6.07703 1.97455i −0.439719 0.142873i 0.0807871 0.996731i \(-0.474257\pi\)
−0.520506 + 0.853858i \(0.674257\pi\)
\(192\) −20.9493 6.39960i −1.51189 0.461852i
\(193\) −18.1548 18.1548i −1.30681 1.30681i −0.923704 0.383106i \(-0.874854\pi\)
−0.383106 0.923704i \(-0.625146\pi\)
\(194\) −28.1659 20.4637i −2.02219 1.46921i
\(195\) −0.970411 0.563333i −0.0694925 0.0403411i
\(196\) −2.27640 + 1.65390i −0.162600 + 0.118136i
\(197\) −18.8297 2.98233i −1.34156 0.212482i −0.555955 0.831212i \(-0.687647\pi\)
−0.785604 + 0.618730i \(0.787647\pi\)
\(198\) −22.1786 + 4.32162i −1.57617 + 0.307124i
\(199\) 17.9453i 1.27211i −0.771643 0.636056i \(-0.780565\pi\)
0.771643 0.636056i \(-0.219435\pi\)
\(200\) 7.28614 + 5.15837i 0.515208 + 0.364752i
\(201\) 0.392656 + 0.191400i 0.0276958 + 0.0135003i
\(202\) −22.8788 11.6573i −1.60975 0.820207i
\(203\) 0.919938 5.80826i 0.0645670 0.407660i
\(204\) 28.0760 4.95718i 1.96571 0.347072i
\(205\) −10.0031 8.43791i −0.698645 0.589329i
\(206\) 7.91027 10.8875i 0.551134 0.758571i
\(207\) 3.43002 28.0413i 0.238403 1.94901i
\(208\) 0.0775094 + 0.489375i 0.00537431 + 0.0339321i
\(209\) −1.68918 + 5.19877i −0.116843 + 0.359606i
\(210\) −5.36323 + 6.59109i −0.370098 + 0.454828i
\(211\) −6.00186 18.4718i −0.413185 1.27165i −0.913864 0.406021i \(-0.866916\pi\)
0.500679 0.865633i \(-0.333084\pi\)
\(212\) −14.7737 + 7.52758i −1.01466 + 0.516996i
\(213\) −0.305630 17.2830i −0.0209414 1.18421i
\(214\) −16.9476 + 5.50659i −1.15851 + 0.376423i
\(215\) 3.23714 + 7.68159i 0.220771 + 0.523880i
\(216\) −0.963432 + 9.22736i −0.0655533 + 0.627842i
\(217\) 1.61492 0.255779i 0.109628 0.0173634i
\(218\) −30.4835 + 30.4835i −2.06460 + 2.06460i
\(219\) 13.7281 7.30336i 0.927656 0.493516i
\(220\) −11.3983 18.3468i −0.768470 1.23694i
\(221\) −0.996193 1.37114i −0.0670112 0.0922329i
\(222\) −5.45082 3.81484i −0.365835 0.256036i
\(223\) −11.4539 + 22.4795i −0.767009 + 1.50534i 0.0933403 + 0.995634i \(0.470246\pi\)
−0.860349 + 0.509705i \(0.829754\pi\)
\(224\) 7.32316 0.489299
\(225\) −6.16583 + 13.6742i −0.411055 + 0.911610i
\(226\) 17.8071 1.18451
\(227\) 2.32409 4.56129i 0.154255 0.302743i −0.800927 0.598763i \(-0.795659\pi\)
0.955182 + 0.296019i \(0.0956593\pi\)
\(228\) 6.35794 + 4.44971i 0.421065 + 0.294689i
\(229\) −3.16833 4.36083i −0.209369 0.288172i 0.691398 0.722474i \(-0.256995\pi\)
−0.900767 + 0.434302i \(0.856995\pi\)
\(230\) 44.8554 11.0601i 2.95767 0.729284i
\(231\) 5.24934 2.79267i 0.345381 0.183744i
\(232\) 7.42439 7.42439i 0.487435 0.487435i
\(233\) 6.02202 0.953794i 0.394516 0.0624852i 0.0439750 0.999033i \(-0.485998\pi\)
0.350541 + 0.936547i \(0.385998\pi\)
\(234\) 1.79165 0.653034i 0.117123 0.0426902i
\(235\) −18.1854 10.9912i −1.18628 0.716988i
\(236\) −11.9692 + 3.88901i −0.779126 + 0.253153i
\(237\) −0.117852 6.66437i −0.00765531 0.432897i
\(238\) −11.4360 + 5.82694i −0.741286 + 0.377704i
\(239\) −7.63602 23.5013i −0.493933 1.52017i −0.818612 0.574346i \(-0.805256\pi\)
0.324679 0.945824i \(-0.394744\pi\)
\(240\) 6.40193 1.69917i 0.413243 0.109681i
\(241\) −5.64570 + 17.3757i −0.363672 + 1.11927i 0.587137 + 0.809488i \(0.300255\pi\)
−0.950809 + 0.309779i \(0.899745\pi\)
\(242\) 0.269382 + 1.70081i 0.0173165 + 0.109332i
\(243\) −15.5276 + 1.37638i −0.996094 + 0.0882951i
\(244\) −23.2004 + 31.9326i −1.48525 + 2.04428i
\(245\) 0.843023 2.07107i 0.0538588 0.132316i
\(246\) 21.9018 3.86705i 1.39641 0.246554i
\(247\) 0.0721669 0.455644i 0.00459187 0.0289919i
\(248\) 2.60113 + 1.32534i 0.165172 + 0.0841594i
\(249\) 20.1467 + 9.82049i 1.27674 + 0.622348i
\(250\) −24.4857 1.47446i −1.54861 0.0932531i
\(251\) 9.29018i 0.586391i 0.956053 + 0.293196i \(0.0947187\pi\)
−0.956053 + 0.293196i \(0.905281\pi\)
\(252\) −1.61447 8.28551i −0.101702 0.521938i
\(253\) −31.9290 5.05705i −2.00736 0.317934i
\(254\) −2.14995 + 1.56203i −0.134900 + 0.0980103i
\(255\) −16.8730 + 15.1204i −1.05663 + 0.946875i
\(256\) 2.79186 + 2.02841i 0.174491 + 0.126775i
\(257\) 1.11696 + 1.11696i 0.0696738 + 0.0696738i 0.741085 0.671411i \(-0.234312\pi\)
−0.671411 + 0.741085i \(0.734312\pi\)
\(258\) −13.5486 4.13883i −0.843498 0.257672i
\(259\) 1.66506 + 0.541011i 0.103462 + 0.0336168i
\(260\) 1.19232 + 1.37882i 0.0739445 + 0.0855105i
\(261\) 14.6304 + 9.85857i 0.905597 + 0.610230i
\(262\) 13.8549 + 27.1917i 0.855956 + 1.67991i
\(263\) 5.73627 + 11.2581i 0.353714 + 0.694202i 0.997475 0.0710244i \(-0.0226268\pi\)
−0.643761 + 0.765227i \(0.722627\pi\)
\(264\) 10.5133 + 1.47510i 0.647050 + 0.0907860i
\(265\) 6.81574 11.2769i 0.418688 0.692735i
\(266\) −3.32262 1.07959i −0.203723 0.0661937i
\(267\) −0.940558 + 3.07895i −0.0575612 + 0.188429i
\(268\) −0.501785 0.501785i −0.0306514 0.0306514i
\(269\) −4.90957 3.56701i −0.299342 0.217485i 0.427968 0.903794i \(-0.359230\pi\)
−0.727310 + 0.686309i \(0.759230\pi\)
\(270\) −11.1314 22.9337i −0.677433 1.39570i
\(271\) 3.83778 2.78831i 0.233128 0.169378i −0.465088 0.885264i \(-0.653977\pi\)
0.698216 + 0.715887i \(0.253977\pi\)
\(272\) 9.88139 + 1.56506i 0.599147 + 0.0948956i
\(273\) −0.400690 + 0.302085i −0.0242509 + 0.0182830i
\(274\) 14.9108i 0.900792i
\(275\) 15.3881 + 7.60441i 0.927939 + 0.458563i
\(276\) −20.1090 + 41.2536i −1.21042 + 2.48318i
\(277\) −3.22250 1.64194i −0.193621 0.0986549i 0.354492 0.935059i \(-0.384654\pi\)
−0.548113 + 0.836404i \(0.684654\pi\)
\(278\) 2.35727 14.8832i 0.141380 0.892635i
\(279\) −1.34989 + 4.71576i −0.0808157 + 0.282325i
\(280\) 3.39123 2.10686i 0.202665 0.125909i
\(281\) 14.5700 20.0538i 0.869172 1.19631i −0.110132 0.993917i \(-0.535127\pi\)
0.979304 0.202395i \(-0.0648725\pi\)
\(282\) 34.1422 11.7648i 2.03314 0.700585i
\(283\) 2.42942 + 15.3387i 0.144414 + 0.911793i 0.948384 + 0.317124i \(0.102717\pi\)
−0.803970 + 0.594669i \(0.797283\pi\)
\(284\) −8.67757 + 26.7068i −0.514919 + 1.58476i
\(285\) −6.15782 0.337330i −0.364758 0.0199817i
\(286\) −0.674314 2.07532i −0.0398730 0.122716i
\(287\) −5.21463 + 2.65699i −0.307810 + 0.156837i
\(288\) −9.27559 + 19.9154i −0.546570 + 1.17352i
\(289\) −16.3788 + 5.32178i −0.963456 + 0.313046i
\(290\) −6.56289 + 28.0942i −0.385386 + 1.64975i
\(291\) −19.0876 + 19.7748i −1.11894 + 1.15922i
\(292\) −24.9503 + 3.95174i −1.46011 + 0.231258i
\(293\) 6.91907 6.91907i 0.404216 0.404216i −0.475500 0.879716i \(-0.657733\pi\)
0.879716 + 0.475500i \(0.157733\pi\)
\(294\) 1.78484 + 3.35495i 0.104094 + 0.195665i
\(295\) 6.44851 7.64465i 0.375446 0.445089i
\(296\) 1.83735 + 2.52890i 0.106794 + 0.146989i
\(297\) 0.945789 + 17.8128i 0.0548803 + 1.03360i
\(298\) −4.04784 + 7.94433i −0.234485 + 0.460203i
\(299\) 2.72820 0.157776
\(300\) 16.7072 17.7390i 0.964589 1.02416i
\(301\) 3.72789 0.214872
\(302\) −10.0227 + 19.6706i −0.576739 + 1.13191i
\(303\) −11.6230 + 16.6075i −0.667726 + 0.954075i
\(304\) 1.60066 + 2.20311i 0.0918040 + 0.126357i
\(305\) 2.26923 31.2847i 0.129936 1.79136i
\(306\) −1.36140 38.4807i −0.0778263 2.19980i
\(307\) 14.1948 14.1948i 0.810142 0.810142i −0.174513 0.984655i \(-0.555835\pi\)
0.984655 + 0.174513i \(0.0558350\pi\)
\(308\) −9.54052 + 1.51107i −0.543622 + 0.0861012i
\(309\) −7.64399 7.37833i −0.434851 0.419739i
\(310\) −7.99284 + 0.678388i −0.453963 + 0.0385299i
\(311\) −8.02850 + 2.60862i −0.455254 + 0.147921i −0.527663 0.849454i \(-0.676932\pi\)
0.0724083 + 0.997375i \(0.476932\pi\)
\(312\) −0.895812 + 0.0158414i −0.0507154 + 0.000896845i
\(313\) −18.0926 + 9.21864i −1.02265 + 0.521068i −0.883119 0.469149i \(-0.844561\pi\)
−0.139535 + 0.990217i \(0.544561\pi\)
\(314\) −3.99078 12.2824i −0.225213 0.693133i
\(315\) 4.56449 + 4.91584i 0.257180 + 0.276976i
\(316\) −3.34610 + 10.2982i −0.188233 + 0.579321i
\(317\) −0.357144 2.25492i −0.0200592 0.126649i 0.975627 0.219437i \(-0.0704221\pi\)
−0.995686 + 0.0927881i \(0.970422\pi\)
\(318\) 7.29546 + 21.1718i 0.409109 + 1.18726i
\(319\) 11.8661 16.3322i 0.664372 0.914430i
\(320\) −28.2051 2.04586i −1.57671 0.114367i
\(321\) 2.44597 + 13.8533i 0.136521 + 0.773214i
\(322\) 3.23205 20.4064i 0.180115 1.13720i
\(323\) −8.29971 4.22891i −0.461808 0.235303i
\(324\) 24.5774 + 6.10395i 1.36541 + 0.339108i
\(325\) −1.38307 0.430709i −0.0767191 0.0238914i
\(326\) 17.1453i 0.949588i
\(327\) 20.4876 + 27.1751i 1.13297 + 1.50279i
\(328\) −10.3208 1.63465i −0.569870 0.0902585i
\(329\) −7.68792 + 5.58560i −0.423849 + 0.307944i
\(330\) −26.6770 + 11.8018i −1.46852 + 0.649669i
\(331\) −21.1353 15.3557i −1.16170 0.844026i −0.171710 0.985147i \(-0.554929\pi\)
−0.989992 + 0.141121i \(0.954929\pi\)
\(332\) −25.7460 25.7460i −1.41299 1.41299i
\(333\) −3.58026 + 3.84289i −0.196197 + 0.210589i
\(334\) 12.9345 + 4.20267i 0.707745 + 0.229960i
\(335\) 0.549149 + 0.128283i 0.0300032 + 0.00700884i
\(336\) 0.411582 2.93343i 0.0224536 0.160032i
\(337\) 0.791500 + 1.55341i 0.0431157 + 0.0846194i 0.911559 0.411169i \(-0.134879\pi\)
−0.868444 + 0.495788i \(0.834879\pi\)
\(338\) −12.8653 25.2496i −0.699780 1.37340i
\(339\) 1.95325 13.9212i 0.106086 0.756096i
\(340\) 33.9178 14.2935i 1.83945 0.775175i
\(341\) 5.33827 + 1.73451i 0.289083 + 0.0939289i
\(342\) 7.14441 7.66847i 0.386325 0.414663i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 5.38482 + 3.91230i 0.290330 + 0.210937i
\(345\) −3.72643 36.2802i −0.200624 1.95326i
\(346\) −38.1913 + 27.7476i −2.05318 + 1.49172i
\(347\) 3.55883 + 0.563663i 0.191048 + 0.0302590i 0.251225 0.967929i \(-0.419167\pi\)
−0.0601771 + 0.998188i \(0.519167\pi\)
\(348\) −17.2533 22.8850i −0.924872 1.22676i
\(349\) 7.13409i 0.381879i 0.981602 + 0.190939i \(0.0611534\pi\)
−0.981602 + 0.190939i \(0.938847\pi\)
\(350\) −4.86011 + 9.83483i −0.259784 + 0.525694i
\(351\) −0.314004 1.47230i −0.0167603 0.0785857i
\(352\) 22.3997 + 11.4132i 1.19391 + 0.608326i
\(353\) 2.55792 16.1501i 0.136144 0.859582i −0.821202 0.570638i \(-0.806696\pi\)
0.957346 0.288944i \(-0.0933040\pi\)
\(354\) 2.95532 + 16.7380i 0.157073 + 0.889617i
\(355\) −5.34245 21.6668i −0.283548 1.14995i
\(356\) 3.07414 4.23119i 0.162929 0.224253i
\(357\) 3.30097 + 9.57959i 0.174706 + 0.507006i
\(358\) 2.37575 + 14.9999i 0.125562 + 0.792769i
\(359\) −0.978955 + 3.01291i −0.0516673 + 0.159016i −0.973561 0.228427i \(-0.926642\pi\)
0.921894 + 0.387443i \(0.126642\pi\)
\(360\) 1.43424 + 11.8910i 0.0755913 + 0.626713i
\(361\) 5.08781 + 15.6587i 0.267780 + 0.824141i
\(362\) −15.7382 + 8.01901i −0.827182 + 0.421470i
\(363\) 1.35921 0.0240361i 0.0713399 0.00126157i
\(364\) 0.775301 0.251911i 0.0406368 0.0132037i
\(365\) 15.1848 13.1309i 0.794807 0.687302i
\(366\) 38.3549 + 37.0219i 2.00484 + 1.93517i
\(367\) 12.7562 2.02039i 0.665870 0.105464i 0.185656 0.982615i \(-0.440559\pi\)
0.480214 + 0.877151i \(0.340559\pi\)
\(368\) −11.3877 + 11.3877i −0.593624 + 0.593624i
\(369\) −0.620778 17.5466i −0.0323164 0.913438i
\(370\) −7.95537 3.23822i −0.413580 0.168347i
\(371\) −3.46368 4.76734i −0.179825 0.247508i
\(372\) 4.56911 6.52855i 0.236897 0.338489i
\(373\) 0.108882 0.213693i 0.00563769 0.0110646i −0.888171 0.459514i \(-0.848024\pi\)
0.893808 + 0.448449i \(0.148024\pi\)
\(374\) −44.0611 −2.27835
\(375\) −3.83853 + 18.9807i −0.198221 + 0.980157i
\(376\) −16.9669 −0.874999
\(377\) −0.773476 + 1.51803i −0.0398360 + 0.0781826i
\(378\) −11.3845 + 0.604471i −0.585555 + 0.0310906i
\(379\) −6.45993 8.89133i −0.331824 0.456717i 0.610207 0.792242i \(-0.291086\pi\)
−0.942031 + 0.335525i \(0.891086\pi\)
\(380\) 9.27931 + 3.77712i 0.476019 + 0.193762i
\(381\) 0.985334 + 1.85212i 0.0504802 + 0.0948871i
\(382\) 9.91319 9.91319i 0.507203 0.507203i
\(383\) 2.04469 0.323847i 0.104479 0.0165478i −0.103976 0.994580i \(-0.533157\pi\)
0.208455 + 0.978032i \(0.433157\pi\)
\(384\) 15.7595 16.3269i 0.804224 0.833180i
\(385\) 5.80636 5.02100i 0.295920 0.255894i
\(386\) 53.5742 17.4073i 2.72685 0.886009i
\(387\) −4.72179 + 10.1380i −0.240022 + 0.515344i
\(388\) 39.7826 20.2703i 2.01966 1.02907i
\(389\) −9.75095 30.0103i −0.494393 1.52159i −0.817901 0.575360i \(-0.804862\pi\)
0.323508 0.946226i \(-0.395138\pi\)
\(390\) 2.06785 1.33593i 0.104710 0.0676477i
\(391\) 17.0230 52.3913i 0.860889 2.64954i
\(392\) −0.279307 1.76348i −0.0141072 0.0890690i
\(393\) 22.7776 7.84880i 1.14898 0.395919i
\(394\) 24.5858 33.8395i 1.23862 1.70481i
\(395\) −2.06007 8.35478i −0.103653 0.420374i
\(396\) 7.97477 27.8594i 0.400747 1.39999i
\(397\) −3.21399 + 20.2923i −0.161305 + 1.01844i 0.765646 + 0.643262i \(0.222419\pi\)
−0.926952 + 0.375181i \(0.877581\pi\)
\(398\) 35.0813 + 17.8748i 1.75847 + 0.895984i
\(399\) −1.20846 + 2.47914i −0.0604984 + 0.124112i
\(400\) 7.57083 3.97522i 0.378542 0.198761i
\(401\) 34.5804i 1.72686i 0.504466 + 0.863432i \(0.331689\pi\)
−0.504466 + 0.863432i \(0.668311\pi\)
\(402\) −0.765279 + 0.576954i −0.0381687 + 0.0287758i
\(403\) −0.467871 0.0741034i −0.0233063 0.00369136i
\(404\) 26.6414 19.3561i 1.32546 0.963002i
\(405\) −19.1501 + 6.18669i −0.951574 + 0.307419i
\(406\) 10.4382 + 7.58381i 0.518040 + 0.376378i
\(407\) 4.24982 + 4.24982i 0.210656 + 0.210656i
\(408\) −5.28532 + 17.3017i −0.261662 + 0.856560i
\(409\) 11.8764 + 3.85888i 0.587251 + 0.190810i 0.587547 0.809190i \(-0.300094\pi\)
−0.000295063 1.00000i \(0.500094\pi\)
\(410\) 26.4590 11.1502i 1.30672 0.550671i
\(411\) 11.6569 + 1.63555i 0.574994 + 0.0806760i
\(412\) 7.83549 + 15.3780i 0.386027 + 0.757620i
\(413\) −2.03055 3.98518i −0.0999169 0.196098i
\(414\) 51.4014 + 34.6365i 2.52624 + 1.70229i
\(415\) 28.1762 + 6.58204i 1.38311 + 0.323099i
\(416\) −2.01780 0.655624i −0.0989310 0.0321446i
\(417\) −11.3768 3.47540i −0.557125 0.170191i
\(418\) −8.48051 8.48051i −0.414795 0.414795i
\(419\) 26.5729 + 19.3063i 1.29817 + 0.943175i 0.999936 0.0113183i \(-0.00360279\pi\)
0.298233 + 0.954493i \(0.403603\pi\)
\(420\) −4.40893 9.96602i −0.215134 0.486292i
\(421\) 19.4269 14.1145i 0.946810 0.687897i −0.00324050 0.999995i \(-0.501031\pi\)
0.950050 + 0.312097i \(0.101031\pi\)
\(422\) 42.0888 + 6.66622i 2.04885 + 0.324506i
\(423\) −5.45246 27.9821i −0.265108 1.36054i
\(424\) 10.5213i 0.510958i
\(425\) −16.9010 + 23.8725i −0.819820 + 1.15799i
\(426\) 34.0909 + 16.6176i 1.65171 + 0.805124i
\(427\) −12.4988 6.36845i −0.604858 0.308191i
\(428\) 3.57503 22.5719i 0.172806 1.09105i
\(429\) −1.69641 + 0.299523i −0.0819035 + 0.0144611i
\(430\) −18.2411 1.32312i −0.879666 0.0638065i
\(431\) −15.4055 + 21.2038i −0.742056 + 1.02135i 0.256441 + 0.966560i \(0.417450\pi\)
−0.998498 + 0.0547932i \(0.982550\pi\)
\(432\) 7.45615 + 4.83481i 0.358734 + 0.232615i
\(433\) −5.51699 34.8329i −0.265130 1.67396i −0.656960 0.753926i \(-0.728158\pi\)
0.391830 0.920038i \(-0.371842\pi\)
\(434\) −1.10856 + 3.41178i −0.0532123 + 0.163771i
\(435\) 21.2436 + 8.21237i 1.01855 + 0.393753i
\(436\) −17.0848 52.5815i −0.818212 2.51820i
\(437\) 13.3603 6.80740i 0.639108 0.325642i
\(438\) 0.603226 + 34.1116i 0.0288232 + 1.62992i
\(439\) 19.3366 6.28285i 0.922886 0.299864i 0.191236 0.981544i \(-0.438750\pi\)
0.731650 + 0.681680i \(0.238750\pi\)
\(440\) 13.6565 1.15909i 0.651047 0.0552572i
\(441\) 2.81861 1.02735i 0.134219 0.0489214i
\(442\) 3.67272 0.581701i 0.174693 0.0276687i
\(443\) −12.0962 + 12.0962i −0.574710 + 0.574710i −0.933441 0.358731i \(-0.883210\pi\)
0.358731 + 0.933441i \(0.383210\pi\)
\(444\) 7.53280 4.00747i 0.357491 0.190186i
\(445\) −0.300682 + 4.14534i −0.0142537 + 0.196508i
\(446\) −32.5363 44.7823i −1.54064 2.12051i
\(447\) 5.76671 + 4.03593i 0.272756 + 0.190893i
\(448\) −5.74155 + 11.2684i −0.271263 + 0.532383i
\(449\) −21.2925 −1.00486 −0.502428 0.864619i \(-0.667560\pi\)
−0.502428 + 0.864619i \(0.667560\pi\)
\(450\) −20.5900 25.6740i −0.970621 1.21028i
\(451\) −20.0912 −0.946056
\(452\) −10.3678 + 20.3479i −0.487660 + 0.957087i
\(453\) 14.2787 + 9.99316i 0.670870 + 0.469520i
\(454\) 6.60189 + 9.08672i 0.309842 + 0.426461i
\(455\) −0.417702 + 0.495182i −0.0195822 + 0.0232145i
\(456\) −4.34735 + 2.31280i −0.203583 + 0.108307i
\(457\) −23.0713 + 23.0713i −1.07923 + 1.07923i −0.0826516 + 0.996578i \(0.526339\pi\)
−0.996578 + 0.0826516i \(0.973661\pi\)
\(458\) 11.6809 1.85007i 0.545811 0.0864479i
\(459\) −30.2328 3.15662i −1.41114 0.147338i
\(460\) −13.4778 + 57.6952i −0.628405 + 2.69005i
\(461\) −11.9705 + 3.88947i −0.557524 + 0.181151i −0.574207 0.818710i \(-0.694689\pi\)
0.0166828 + 0.999861i \(0.494689\pi\)
\(462\) 0.230662 + 13.0436i 0.0107314 + 0.606844i
\(463\) −25.1780 + 12.8289i −1.17012 + 0.596207i −0.927467 0.373905i \(-0.878019\pi\)
−0.242656 + 0.970112i \(0.578019\pi\)
\(464\) −3.10782 9.56489i −0.144277 0.444039i
\(465\) −0.346382 + 6.32305i −0.0160631 + 0.293225i
\(466\) −4.13378 + 12.7225i −0.191494 + 0.589358i
\(467\) −5.79729 36.6026i −0.268266 1.69377i −0.642381 0.766385i \(-0.722053\pi\)
0.374115 0.927382i \(-0.377947\pi\)
\(468\) −0.296933 + 2.42751i −0.0137257 + 0.112212i
\(469\) 0.148239 0.204033i 0.00684502 0.00942136i
\(470\) 39.6006 24.6026i 1.82664 1.13483i
\(471\) −10.0398 + 1.77266i −0.462611 + 0.0816800i
\(472\) 1.24925 7.88745i 0.0575014 0.363050i
\(473\) 11.4027 + 5.80995i 0.524295 + 0.267142i
\(474\) 13.1455 + 6.40779i 0.603795 + 0.294319i
\(475\) −7.84774 + 1.34181i −0.360079 + 0.0615665i
\(476\) 16.4604i 0.754461i
\(477\) 17.3519 3.38111i 0.794490 0.154811i
\(478\) 53.5486 + 8.48126i 2.44925 + 0.387924i
\(479\) −21.8536 + 15.8776i −0.998516 + 0.725464i −0.961769 0.273861i \(-0.911699\pi\)
−0.0367462 + 0.999325i \(0.511699\pi\)
\(480\) −5.96252 + 27.7287i −0.272150 + 1.26563i
\(481\) −0.410351 0.298137i −0.0187104 0.0135939i
\(482\) −28.3442 28.3442i −1.29104 1.29104i
\(483\) −15.5988 4.76512i −0.709768 0.216820i
\(484\) −2.10034 0.682442i −0.0954700 0.0310201i
\(485\) −18.3534 + 30.3664i −0.833386 + 1.37887i
\(486\) 12.7759 31.7258i 0.579525 1.43911i
\(487\) −10.3556 20.3239i −0.469255 0.920965i −0.997417 0.0718217i \(-0.977119\pi\)
0.528162 0.849143i \(-0.322881\pi\)
\(488\) −11.3706 22.3161i −0.514723 1.01020i
\(489\) 13.4038 + 1.88066i 0.606142 + 0.0850462i
\(490\) 3.20901 + 3.71095i 0.144968 + 0.167644i
\(491\) −30.8701 10.0303i −1.39315 0.452662i −0.486180 0.873859i \(-0.661610\pi\)
−0.906969 + 0.421197i \(0.861610\pi\)
\(492\) −8.33304 + 27.2785i −0.375683 + 1.22981i
\(493\) 24.3255 + 24.3255i 1.09556 + 1.09556i
\(494\) 0.818854 + 0.594933i 0.0368420 + 0.0267673i
\(495\) 6.30023 + 22.1501i 0.283174 + 0.995572i
\(496\) 2.26223 1.64361i 0.101577 0.0738002i
\(497\) −9.85702 1.56120i −0.442148 0.0700293i
\(498\) −39.2656 + 29.6028i −1.75953 + 1.32653i
\(499\) 18.3294i 0.820535i −0.911965 0.410267i \(-0.865435\pi\)
0.911965 0.410267i \(-0.134565\pi\)
\(500\) 15.9411 27.1210i 0.712909 1.21289i
\(501\) 4.70435 9.65094i 0.210175 0.431172i
\(502\) −18.1614 9.25367i −0.810581 0.413012i
\(503\) −1.80628 + 11.4044i −0.0805380 + 0.508497i 0.914135 + 0.405411i \(0.132872\pi\)
−0.994672 + 0.103086i \(0.967128\pi\)
\(504\) 5.14956 + 1.47406i 0.229379 + 0.0656599i
\(505\) −9.86617 + 24.2384i −0.439039 + 1.07859i
\(506\) 41.6895 57.3807i 1.85332 2.55088i
\(507\) −21.1508 + 7.28821i −0.939340 + 0.323681i
\(508\) −0.533150 3.36618i −0.0236547 0.149350i
\(509\) −11.6023 + 35.7081i −0.514262 + 1.58274i 0.270359 + 0.962760i \(0.412858\pi\)
−0.784621 + 0.619976i \(0.787142\pi\)
\(510\) −12.7521 48.0460i −0.564673 2.12751i
\(511\) −2.77427 8.53832i −0.122726 0.377713i
\(512\) 16.6004 8.45834i 0.733642 0.373809i
\(513\) −5.21139 6.42650i −0.230088 0.283737i
\(514\) −3.29610 + 1.07097i −0.145385 + 0.0472384i
\(515\) −11.7382 7.09453i −0.517246 0.312622i
\(516\) 12.6178 13.0721i 0.555466 0.575465i
\(517\) −32.2206 + 5.10324i −1.41706 + 0.224440i
\(518\) −2.71614 + 2.71614i −0.119340 + 0.119340i
\(519\) 17.5033 + 32.9008i 0.768311 + 1.44419i
\(520\) −1.12303 + 0.276910i −0.0492483 + 0.0121433i
\(521\) 18.9405 + 26.0694i 0.829798 + 1.14212i 0.987961 + 0.154706i \(0.0494430\pi\)
−0.158163 + 0.987413i \(0.550557\pi\)
\(522\) −33.8454 + 18.7810i −1.48137 + 0.822024i
\(523\) 5.45598 10.7080i 0.238573 0.468227i −0.740413 0.672152i \(-0.765370\pi\)
0.978986 + 0.203926i \(0.0653700\pi\)
\(524\) −39.1383 −1.70977
\(525\) 7.15556 + 4.87831i 0.312294 + 0.212907i
\(526\) −27.7221 −1.20874
\(527\) −4.34239 + 8.52242i −0.189158 + 0.371243i
\(528\) 5.83069 8.33115i 0.253748 0.362567i
\(529\) 38.6033 + 53.1329i 1.67840 + 2.31012i
\(530\) 15.2562 + 24.5567i 0.662689 + 1.06667i
\(531\) 13.4096 0.474417i 0.581928 0.0205880i
\(532\) 3.16816 3.16816i 0.137357 0.137357i
\(533\) 1.67470 0.265246i 0.0725393 0.0114891i
\(534\) −5.08216 4.90554i −0.219927 0.212284i
\(535\) 7.05271 + 16.7358i 0.304915 + 0.723550i
\(536\) 0.428251 0.139147i 0.0184976 0.00601025i
\(537\) 11.9872 0.211981i 0.517286 0.00914764i
\(538\) 11.8634 6.04471i 0.511468 0.260606i
\(539\) −1.06083 3.26489i −0.0456931 0.140629i
\(540\) 32.6870 + 0.632964i 1.40663 + 0.0272384i
\(541\) −0.392175 + 1.20699i −0.0168609 + 0.0518926i −0.959133 0.282956i \(-0.908685\pi\)
0.942272 + 0.334848i \(0.108685\pi\)
\(542\) 1.62816 + 10.2798i 0.0699355 + 0.441555i
\(543\) 4.54278 + 13.1834i 0.194950 + 0.565754i
\(544\) −25.1807 + 34.6582i −1.07961 + 1.48596i
\(545\) 33.5836 + 28.3288i 1.43856 + 1.21347i
\(546\) −0.191431 1.08421i −0.00819247 0.0463997i
\(547\) 1.16261 7.34043i 0.0497096 0.313854i −0.950287 0.311374i \(-0.899211\pi\)
0.999997 0.00247980i \(-0.000789345\pi\)
\(548\) −17.0384 8.68147i −0.727842 0.370854i
\(549\) 33.1501 25.9241i 1.41481 1.10641i
\(550\) −30.1935 + 22.5077i −1.28745 + 0.959731i
\(551\) 9.36392i 0.398916i
\(552\) −17.5311 23.2534i −0.746171 0.989731i
\(553\) −3.80090 0.602003i −0.161631 0.0255998i
\(554\) 6.41967 4.66416i 0.272745 0.198161i
\(555\) −3.40419 + 5.86415i −0.144500 + 0.248919i
\(556\) 15.6344 + 11.3591i 0.663046 + 0.481731i
\(557\) −30.4138 30.4138i −1.28867 1.28867i −0.935593 0.353080i \(-0.885134\pi\)
−0.353080 0.935593i \(-0.614866\pi\)
\(558\) −7.87424 7.33612i −0.333343 0.310563i
\(559\) −1.02717 0.333749i −0.0434448 0.0141161i
\(560\) −0.323408 3.81043i −0.0136665 0.161020i
\(561\) −4.83305 + 34.4461i −0.204051 + 1.45432i
\(562\) 24.6905 + 48.4578i 1.04151 + 2.04407i
\(563\) −0.623248 1.22319i −0.0262668 0.0515514i 0.877500 0.479576i \(-0.159210\pi\)
−0.903767 + 0.428025i \(0.859210\pi\)
\(564\) −6.43502 + 45.8637i −0.270963 + 1.93121i
\(565\) −1.53480 18.0832i −0.0645697 0.760767i
\(566\) −32.4055 10.5292i −1.36211 0.442575i
\(567\) −0.776197 + 8.96647i −0.0325972 + 0.376556i
\(568\) −12.5997 12.5997i −0.528672 0.528672i
\(569\) 31.3282 + 22.7613i 1.31335 + 0.954202i 0.999990 + 0.00456712i \(0.00145376\pi\)
0.313357 + 0.949635i \(0.398546\pi\)
\(570\) 6.79306 11.7019i 0.284530 0.490138i
\(571\) 8.15037 5.92159i 0.341083 0.247811i −0.404036 0.914743i \(-0.632393\pi\)
0.745118 + 0.666932i \(0.232393\pi\)
\(572\) 2.76405 + 0.437783i 0.115571 + 0.0183046i
\(573\) −6.66255 8.83730i −0.278332 0.369184i
\(574\) 12.8406i 0.535957i
\(575\) −15.0978 44.5977i −0.629621 1.85985i
\(576\) −23.3722 29.8869i −0.973842 1.24529i
\(577\) −16.1284 8.21783i −0.671434 0.342113i 0.0848147 0.996397i \(-0.472970\pi\)
−0.756249 + 0.654284i \(0.772970\pi\)
\(578\) 5.91085 37.3197i 0.245859 1.55229i
\(579\) −7.73215 43.7926i −0.321337 1.81996i
\(580\) −28.2818 23.8566i −1.17434 0.990590i
\(581\) 7.60594 10.4687i 0.315548 0.434314i
\(582\) −19.6452 57.0115i −0.814320 2.36320i
\(583\) −3.16456 19.9802i −0.131063 0.827497i
\(584\) 4.95334 15.2448i 0.204971 0.630835i
\(585\) −0.817584 1.76314i −0.0338029 0.0728970i
\(586\) 6.63419 + 20.4179i 0.274056 + 0.843457i
\(587\) −20.1550 + 10.2695i −0.831885 + 0.423867i −0.817429 0.576029i \(-0.804602\pi\)
−0.0144556 + 0.999896i \(0.504602\pi\)
\(588\) −4.87285 + 0.0861709i −0.200953 + 0.00355363i
\(589\) −2.47611 + 0.804537i −0.102026 + 0.0331504i
\(590\) 8.52135 + 20.2208i 0.350819 + 0.832476i
\(591\) −23.7582 22.9325i −0.977282 0.943318i
\(592\) 2.95727 0.468386i 0.121543 0.0192505i
\(593\) −14.2175 + 14.2175i −0.583842 + 0.583842i −0.935957 0.352115i \(-0.885463\pi\)
0.352115 + 0.935957i \(0.385463\pi\)
\(594\) −35.7643 15.8939i −1.46743 0.652135i
\(595\) 6.90298 + 11.1111i 0.282994 + 0.455512i
\(596\) −6.72112 9.25083i −0.275308 0.378929i
\(597\) 17.8222 25.4652i 0.729415 1.04222i
\(598\) −2.71748 + 5.33336i −0.111126 + 0.218097i
\(599\) 2.44647 0.0999602 0.0499801 0.998750i \(-0.484084\pi\)
0.0499801 + 0.998750i \(0.484084\pi\)
\(600\) 5.21635 + 14.5561i 0.212956 + 0.594250i
\(601\) −13.9025 −0.567094 −0.283547 0.958958i \(-0.591511\pi\)
−0.283547 + 0.958958i \(0.591511\pi\)
\(602\) −3.71324 + 7.28765i −0.151340 + 0.297022i
\(603\) 0.367108 + 0.661566i 0.0149498 + 0.0269410i
\(604\) −16.6419 22.9055i −0.677147 0.932014i
\(605\) 1.70397 0.420154i 0.0692762 0.0170817i
\(606\) −20.8886 39.2641i −0.848541 1.59499i
\(607\) 9.19847 9.19847i 0.373354 0.373354i −0.495343 0.868697i \(-0.664958\pi\)
0.868697 + 0.495343i \(0.164958\pi\)
\(608\) −11.5173 + 1.82416i −0.467088 + 0.0739794i
\(609\) 7.07383 7.32852i 0.286646 0.296967i
\(610\) 58.8981 + 35.5979i 2.38471 + 1.44132i
\(611\) 2.61838 0.850762i 0.105928 0.0344181i
\(612\) 44.7641 + 20.8489i 1.80948 + 0.842768i
\(613\) −29.8617 + 15.2153i −1.20610 + 0.614541i −0.937256 0.348642i \(-0.886643\pi\)
−0.268848 + 0.963182i \(0.586643\pi\)
\(614\) 13.6104 + 41.8885i 0.549271 + 1.69048i
\(615\) −5.81475 21.9082i −0.234473 0.883423i
\(616\) 1.89406 5.82933i 0.0763140 0.234870i
\(617\) 4.86575 + 30.7211i 0.195888 + 1.23679i 0.868086 + 0.496415i \(0.165350\pi\)
−0.672198 + 0.740372i \(0.734650\pi\)
\(618\) 22.0378 7.59387i 0.886492 0.305470i
\(619\) 17.6315 24.2677i 0.708671 0.975401i −0.291154 0.956676i \(-0.594039\pi\)
0.999825 0.0187253i \(-0.00596078\pi\)
\(620\) 3.87848 9.52831i 0.155763 0.382666i
\(621\) 32.7163 36.3853i 1.31286 1.46009i
\(622\) 2.89737 18.2933i 0.116174 0.733493i
\(623\) 1.65614 + 0.843843i 0.0663517 + 0.0338079i
\(624\) −0.376029 + 0.771421i −0.0150532 + 0.0308815i
\(625\) 0.613110 + 24.9925i 0.0245244 + 0.999699i
\(626\) 44.5516i 1.78064i
\(627\) −7.56011 + 5.69967i −0.301922 + 0.227623i
\(628\) 16.3584 + 2.59092i 0.652773 + 0.103389i
\(629\) −8.28575 + 6.01995i −0.330374 + 0.240031i
\(630\) −14.1565 + 4.02659i −0.564009 + 0.160423i
\(631\) 8.69328 + 6.31604i 0.346074 + 0.251438i 0.747220 0.664576i \(-0.231388\pi\)
−0.401146 + 0.916014i \(0.631388\pi\)
\(632\) −4.85849 4.85849i −0.193260 0.193260i
\(633\) 9.82822 32.1730i 0.390636 1.27876i
\(634\) 4.76388 + 1.54788i 0.189198 + 0.0614741i
\(635\) 1.77156 + 2.04865i 0.0703021 + 0.0812984i
\(636\) −28.4404 3.99041i −1.12774 0.158230i
\(637\) 0.131529 + 0.258140i 0.00521136 + 0.0102279i
\(638\) 20.1084 + 39.4650i 0.796100 + 1.56243i
\(639\) 16.7307 24.8288i 0.661856 0.982211i
\(640\) 15.1533 25.0718i 0.598988 0.991049i
\(641\) 27.6052 + 8.96946i 1.09034 + 0.354272i 0.798377 0.602158i \(-0.205692\pi\)
0.291961 + 0.956430i \(0.405692\pi\)
\(642\) −29.5181 9.01720i −1.16499 0.355880i
\(643\) 20.4821 + 20.4821i 0.807736 + 0.807736i 0.984291 0.176555i \(-0.0564953\pi\)
−0.176555 + 0.984291i \(0.556495\pi\)
\(644\) 21.4363 + 15.5744i 0.844710 + 0.613717i
\(645\) −3.03525 + 14.1154i −0.119513 + 0.555794i
\(646\) 16.5342 12.0128i 0.650529 0.472637i
\(647\) −23.0242 3.64667i −0.905174 0.143365i −0.313542 0.949574i \(-0.601516\pi\)
−0.591631 + 0.806209i \(0.701516\pi\)
\(648\) −10.5312 + 12.1372i −0.413705 + 0.476793i
\(649\) 15.3543i 0.602708i
\(650\) 2.21963 2.27475i 0.0870610 0.0892230i
\(651\) 2.54566 + 1.24088i 0.0997724 + 0.0486340i
\(652\) −19.5917 9.98247i −0.767270 0.390944i
\(653\) 2.41707 15.2608i 0.0945874 0.597201i −0.894176 0.447715i \(-0.852238\pi\)
0.988764 0.149487i \(-0.0477621\pi\)
\(654\) −73.5317 + 12.9830i −2.87532 + 0.507674i
\(655\) 26.4192 16.4134i 1.03228 0.641324i
\(656\) −5.88314 + 8.09745i −0.229698 + 0.316152i
\(657\) 26.7339 + 3.27010i 1.04299 + 0.127579i
\(658\) −3.26157 20.5928i −0.127149 0.802789i
\(659\) −11.6974 + 36.0010i −0.455668 + 1.40240i 0.414682 + 0.909966i \(0.363893\pi\)
−0.870350 + 0.492434i \(0.836107\pi\)
\(660\) 2.04633 37.3549i 0.0796532 1.45404i
\(661\) 2.76411 + 8.50706i 0.107512 + 0.330886i 0.990312 0.138862i \(-0.0443445\pi\)
−0.882800 + 0.469749i \(0.844345\pi\)
\(662\) 51.0711 26.0220i 1.98494 1.01138i
\(663\) −0.0519033 2.93506i −0.00201576 0.113988i
\(664\) 21.9731 7.13948i 0.852720 0.277066i
\(665\) −0.809949 + 3.46720i −0.0314085 + 0.134452i
\(666\) −3.94626 10.8268i −0.152914 0.419531i
\(667\) −54.6951 + 8.66285i −2.11780 + 0.335427i
\(668\) −12.3332 + 12.3332i −0.477185 + 0.477185i
\(669\) −38.5788 + 20.5240i −1.49154 + 0.793505i
\(670\) −0.797770 + 0.945750i −0.0308205 + 0.0365375i
\(671\) −28.3053 38.9589i −1.09271 1.50399i
\(672\) 10.3919 + 7.27292i 0.400875 + 0.280559i
\(673\) −6.97563 + 13.6905i −0.268891 + 0.527728i −0.985485 0.169762i \(-0.945700\pi\)
0.716594 + 0.697490i \(0.245700\pi\)
\(674\) −3.82514 −0.147339
\(675\) −22.3299 + 13.2807i −0.859478 + 0.511173i
\(676\) 36.3430 1.39781
\(677\) 4.80926 9.43871i 0.184835 0.362759i −0.779932 0.625864i \(-0.784746\pi\)
0.964767 + 0.263105i \(0.0847465\pi\)
\(678\) 25.2690 + 17.6849i 0.970448 + 0.679184i
\(679\) 9.32698 + 12.8375i 0.357937 + 0.492658i
\(680\) −1.68964 + 23.2941i −0.0647946 + 0.893288i
\(681\) 7.82797 4.16450i 0.299968 0.159584i
\(682\) −8.70807 + 8.70807i −0.333449 + 0.333449i
\(683\) −3.96188 + 0.627499i −0.151597 + 0.0240106i −0.231772 0.972770i \(-0.574452\pi\)
0.0801747 + 0.996781i \(0.474452\pi\)
\(684\) 4.60299 + 12.6286i 0.176000 + 0.482868i
\(685\) 15.1420 1.28517i 0.578546 0.0491038i
\(686\) 2.08665 0.677993i 0.0796686 0.0258859i
\(687\) −0.165075 9.33479i −0.00629802 0.356144i
\(688\) 5.68057 2.89440i 0.216570 0.110348i
\(689\) 0.527564 + 1.62367i 0.0200986 + 0.0618571i
\(690\) 74.6358 + 28.8528i 2.84134 + 1.09841i
\(691\) −8.22688 + 25.3197i −0.312965 + 0.963208i 0.663619 + 0.748071i \(0.269020\pi\)
−0.976584 + 0.215137i \(0.930980\pi\)
\(692\) −9.47080 59.7963i −0.360026 2.27311i
\(693\) 10.2225 + 1.25042i 0.388322 + 0.0474996i
\(694\) −4.64675 + 6.39570i −0.176388 + 0.242777i
\(695\) −15.3172 1.11103i −0.581014 0.0421438i
\(696\) 17.9090 3.16206i 0.678837 0.119857i
\(697\) 5.35582 33.8153i 0.202866 1.28085i
\(698\) −13.9464 7.10605i −0.527879 0.268968i
\(699\) 9.49274 + 4.62723i 0.359048 + 0.175018i
\(700\) −8.40845 11.2797i −0.317809 0.426333i
\(701\) 33.3805i 1.26076i 0.776285 + 0.630382i \(0.217102\pi\)
−0.776285 + 0.630382i \(0.782898\pi\)
\(702\) 3.19097 + 0.852671i 0.120435 + 0.0321820i
\(703\) −2.75344 0.436102i −0.103848 0.0164479i
\(704\) −35.1239 + 25.5190i −1.32378 + 0.961783i
\(705\) −14.8900 33.6576i −0.560790 1.26762i
\(706\) 29.0239 + 21.0871i 1.09233 + 0.793622i
\(707\) 8.27550 + 8.27550i 0.311232 + 0.311232i
\(708\) −20.8470 6.36837i −0.783480 0.239338i
\(709\) 3.32106 + 1.07908i 0.124725 + 0.0405257i 0.370715 0.928747i \(-0.379113\pi\)
−0.245989 + 0.969273i \(0.579113\pi\)
\(710\) 47.6778 + 11.1377i 1.78932 + 0.417989i
\(711\) 6.45141 9.57405i 0.241947 0.359055i
\(712\) 1.50665 + 2.95696i 0.0564640 + 0.110817i
\(713\) −6.99006 13.7188i −0.261780 0.513772i
\(714\) −22.0151 3.08889i −0.823895 0.115599i
\(715\) −2.04939 + 0.863644i −0.0766428 + 0.0322985i
\(716\) −18.5234 6.01863i −0.692254 0.224927i
\(717\) 12.5042 40.9329i 0.466978 1.52867i
\(718\) −4.91483 4.91483i −0.183420 0.183420i
\(719\) 35.8703 + 26.0613i 1.33773 + 0.971921i 0.999524 + 0.0308507i \(0.00982163\pi\)
0.338211 + 0.941070i \(0.390178\pi\)
\(720\) 10.7721 + 3.94682i 0.401453 + 0.147089i
\(721\) −4.96235 + 3.60535i −0.184807 + 0.134270i
\(722\) −35.6789 5.65098i −1.32783 0.210308i
\(723\) −25.2680 + 19.0498i −0.939726 + 0.708471i
\(724\) 22.6528i 0.841883i
\(725\) 29.0955 + 4.24321i 1.08058 + 0.157589i
\(726\) −1.30688 + 2.68105i −0.0485028 + 0.0995033i
\(727\) −10.5658 5.38356i −0.391865 0.199665i 0.246945 0.969029i \(-0.420573\pi\)
−0.638810 + 0.769364i \(0.720573\pi\)
\(728\) −0.0809201 + 0.510910i −0.00299910 + 0.0189356i
\(729\) −23.4012 13.4679i −0.866711 0.498811i
\(730\) 10.5445 + 42.7640i 0.390268 + 1.58276i
\(731\) −12.8184 + 17.6430i −0.474104 + 0.652549i
\(732\) −64.6358 + 22.2724i −2.38901 + 0.823213i
\(733\) 5.95386 + 37.5912i 0.219911 + 1.38846i 0.812502 + 0.582958i \(0.198105\pi\)
−0.592591 + 0.805503i \(0.701895\pi\)
\(734\) −8.75646 + 26.9496i −0.323207 + 0.994728i
\(735\) 3.25314 2.10169i 0.119994 0.0775219i
\(736\) −21.3100 65.5854i −0.785497 2.41751i
\(737\) 0.771411 0.393053i 0.0284153 0.0144783i
\(738\) 34.9201 + 16.2641i 1.28543 + 0.598688i
\(739\) −6.89550 + 2.24048i −0.253655 + 0.0824176i −0.433085 0.901353i \(-0.642575\pi\)
0.179429 + 0.983771i \(0.442575\pi\)
\(740\) 8.33212 7.20513i 0.306295 0.264866i
\(741\) 0.554926 0.574906i 0.0203857 0.0211197i
\(742\) 12.7697 2.02253i 0.468791 0.0742493i
\(743\) 5.26609 5.26609i 0.193194 0.193194i −0.603881 0.797075i \(-0.706380\pi\)
0.797075 + 0.603881i \(0.206380\pi\)
\(744\) 2.37486 + 4.46400i 0.0870667 + 0.163658i
\(745\) 8.41641 + 3.42588i 0.308353 + 0.125515i
\(746\) 0.309293 + 0.425706i 0.0113240 + 0.0155862i
\(747\) 18.8358 + 33.9441i 0.689168 + 1.24195i
\(748\) 25.6537 50.3482i 0.937991 1.84091i
\(749\) 8.12190 0.296768
\(750\) −33.2818 26.4100i −1.21528 0.964357i
\(751\) −27.1755 −0.991649 −0.495824 0.868423i \(-0.665134\pi\)
−0.495824 + 0.868423i \(0.665134\pi\)
\(752\) −7.37812 + 14.4804i −0.269052 + 0.528045i
\(753\) −9.22644 + 13.1831i −0.336230 + 0.480420i
\(754\) −2.19716 3.02413i −0.0800159 0.110132i
\(755\) 20.8395 + 8.48267i 0.758426 + 0.308716i
\(756\) 5.93766 13.3609i 0.215951 0.485930i
\(757\) 2.96624 2.96624i 0.107810 0.107810i −0.651144 0.758954i \(-0.725711\pi\)
0.758954 + 0.651144i \(0.225711\pi\)
\(758\) 23.8162 3.77211i 0.865043 0.137009i
\(759\) −40.2861 38.8861i −1.46229 1.41147i
\(760\) −4.80866 + 4.15824i −0.174428 + 0.150835i
\(761\) −28.6894 + 9.32174i −1.03999 + 0.337913i −0.778732 0.627356i \(-0.784137\pi\)
−0.261257 + 0.965269i \(0.584137\pi\)
\(762\) −4.60217 + 0.0813843i −0.166719 + 0.00294824i
\(763\) 17.5072 8.92038i 0.633804 0.322940i
\(764\) 5.55594 + 17.0994i 0.201007 + 0.618636i
\(765\) −38.9601 + 4.69919i −1.40861 + 0.169900i
\(766\) −1.40357 + 4.31973i −0.0507129 + 0.156078i
\(767\) 0.202709 + 1.27986i 0.00731941 + 0.0462129i
\(768\) 1.94728 + 5.65110i 0.0702663 + 0.203917i
\(769\) −1.02482 + 1.41055i −0.0369560 + 0.0508656i −0.827095 0.562062i \(-0.810008\pi\)
0.790139 + 0.612928i \(0.210008\pi\)
\(770\) 4.03200 + 16.3521i 0.145303 + 0.589289i
\(771\) 0.475713 + 2.69430i 0.0171324 + 0.0970328i
\(772\) −11.3013 + 71.3537i −0.406743 + 2.56807i
\(773\) 26.3287 + 13.4152i 0.946979 + 0.482510i 0.858072 0.513530i \(-0.171662\pi\)
0.0889075 + 0.996040i \(0.471662\pi\)
\(774\) −15.1156 19.3288i −0.543317 0.694759i
\(775\) 1.37782 + 8.05832i 0.0494926 + 0.289463i
\(776\) 28.3317i 1.01705i
\(777\) 1.82549 + 2.42135i 0.0654890 + 0.0868655i
\(778\) 68.3798 + 10.8303i 2.45153 + 0.388285i
\(779\) 7.53932 5.47764i 0.270124 0.196257i
\(780\) 0.322593 + 3.14073i 0.0115507 + 0.112456i
\(781\) −27.7170 20.1375i −0.991791 0.720578i
\(782\) 85.4636 + 85.4636i 3.05617 + 3.05617i
\(783\) 10.9702 + 28.5197i 0.392041 + 1.01921i
\(784\) −1.62650 0.528482i −0.0580893 0.0188744i
\(785\) −12.1289 + 5.11129i −0.432897 + 0.182430i
\(786\) −7.34452 + 52.3459i −0.261970 + 1.86712i
\(787\) −7.16810 14.0682i −0.255515 0.501477i 0.727241 0.686382i \(-0.240802\pi\)
−0.982756 + 0.184905i \(0.940802\pi\)
\(788\) 24.3534 + 47.7963i 0.867554 + 1.70267i
\(789\) −3.04083 + 21.6726i −0.108256 + 0.771564i
\(790\) 18.3847 + 4.29472i 0.654098 + 0.152799i
\(791\) −7.71891 2.50802i −0.274453 0.0891751i
\(792\) 13.4538 + 12.5344i 0.478061 + 0.445391i
\(793\) 2.87373 + 2.87373i 0.102049 + 0.102049i
\(794\) −36.4681 26.4956i −1.29420 0.940293i
\(795\) 20.8713 9.23341i 0.740230 0.327475i
\(796\) −40.8507 + 29.6798i −1.44791 + 1.05197i
\(797\) −29.7791 4.71654i −1.05483 0.167068i −0.395150 0.918616i \(-0.629308\pi\)
−0.659678 + 0.751548i \(0.729308\pi\)
\(798\) −3.64276 4.83180i −0.128952 0.171044i
\(799\) 55.5907i 1.96666i
\(800\) 0.449024 + 36.6130i 0.0158754 + 1.29447i
\(801\) −4.39251 + 3.43504i −0.155202 + 0.121371i
\(802\) −67.6011 34.4445i −2.38708 1.21628i
\(803\) 4.82126 30.4403i 0.170139 1.07421i
\(804\) −0.213711 1.21040i −0.00753700 0.0426874i
\(805\) −21.0014 1.52333i −0.740202 0.0536905i
\(806\) 0.610897 0.840827i 0.0215179 0.0296169i
\(807\) −3.42434 9.93762i −0.120542 0.349821i
\(808\) 3.26882 + 20.6385i 0.114997 + 0.726062i
\(809\) 3.71933 11.4469i 0.130765 0.402452i −0.864143 0.503247i \(-0.832139\pi\)
0.994907 + 0.100795i \(0.0321386\pi\)
\(810\) 6.98047 43.5988i 0.245269 1.53191i
\(811\) 1.55547 + 4.78725i 0.0546200 + 0.168103i 0.974645 0.223756i \(-0.0718320\pi\)
−0.920025 + 0.391859i \(0.871832\pi\)
\(812\) −14.7434 + 7.51212i −0.517391 + 0.263624i
\(813\) 8.21513 0.145276i 0.288117 0.00509504i
\(814\) −12.5411 + 4.07485i −0.439565 + 0.142823i
\(815\) 17.4112 1.47776i 0.609886 0.0517637i
\(816\) 12.4678 + 12.0345i 0.436459 + 0.421291i
\(817\) −5.86294 + 0.928598i −0.205118 + 0.0324875i
\(818\) −19.3735 + 19.3735i −0.677378 + 0.677378i
\(819\) −0.868608 + 0.0307304i −0.0303516 + 0.00107381i
\(820\) −2.66395 + 36.7264i −0.0930290 + 1.28254i
\(821\) 5.56906 + 7.66516i 0.194362 + 0.267516i 0.895064 0.445938i \(-0.147130\pi\)
−0.700702 + 0.713454i \(0.747130\pi\)
\(822\) −14.8085 + 21.1590i −0.516504 + 0.738004i
\(823\) 20.2865 39.8146i 0.707144 1.38785i −0.205321 0.978695i \(-0.565824\pi\)
0.912465 0.409154i \(-0.134176\pi\)
\(824\) −10.9516 −0.381519
\(825\) 14.2841 + 26.0735i 0.497310 + 0.907763i
\(826\) 9.81319 0.341444
\(827\) −23.1432 + 45.4211i −0.804769 + 1.57945i 0.0102031 + 0.999948i \(0.496752\pi\)
−0.814972 + 0.579500i \(0.803248\pi\)
\(828\) −69.5061 + 38.5694i −2.41550 + 1.34038i
\(829\) 3.56988 + 4.91352i 0.123987 + 0.170653i 0.866498 0.499180i \(-0.166365\pi\)
−0.742511 + 0.669834i \(0.766365\pi\)
\(830\) −40.9326 + 48.5253i −1.42079 + 1.68434i
\(831\) −2.94217 5.53037i −0.102063 0.191847i
\(832\) 2.59085 2.59085i 0.0898214 0.0898214i
\(833\) 5.77790 0.915130i 0.200193 0.0317074i
\(834\) 18.1262 18.7788i 0.627657 0.650256i
\(835\) 3.15302 13.4973i 0.109115 0.467094i
\(836\) 14.6282 4.75298i 0.505926 0.164385i
\(837\) −6.59895 + 5.35123i −0.228093 + 0.184965i
\(838\) −64.2103 + 32.7168i −2.21811 + 1.13018i
\(839\) −0.231737 0.713214i −0.00800046 0.0246229i 0.946977 0.321303i \(-0.104121\pi\)
−0.954977 + 0.296680i \(0.904121\pi\)
\(840\) 6.90470 + 0.378245i 0.238235 + 0.0130507i
\(841\) 1.72498 5.30893i 0.0594819 0.183066i
\(842\) 8.24179 + 52.0366i 0.284031 + 1.79330i
\(843\) 40.5916 13.9872i 1.39805 0.481745i
\(844\) −32.1227 + 44.2132i −1.10571 + 1.52188i
\(845\) −24.5323 + 15.2411i −0.843936 + 0.524310i
\(846\) 60.1332 + 17.2131i 2.06742 + 0.591800i
\(847\) 0.122779 0.775199i 0.00421875 0.0266362i
\(848\) −8.97940 4.57523i −0.308354 0.157114i
\(849\) −11.7861 + 24.1790i −0.404496 + 0.829822i
\(850\) −29.8337 56.8185i −1.02329 1.94886i
\(851\) 16.4864i 0.565147i
\(852\) −38.8374 + 29.2800i −1.33055 + 1.00312i
\(853\) 26.4166 + 4.18399i 0.904489 + 0.143257i 0.591317 0.806439i \(-0.298608\pi\)
0.313172 + 0.949696i \(0.398608\pi\)
\(854\) 24.8993 18.0904i 0.852037 0.619041i
\(855\) −8.40317 6.59425i −0.287382 0.225519i
\(856\) 11.7318 + 8.52366i 0.400985 + 0.291333i
\(857\) −6.16587 6.16587i −0.210622 0.210622i 0.593910 0.804532i \(-0.297584\pi\)
−0.804532 + 0.593910i \(0.797584\pi\)
\(858\) 1.10421 3.61465i 0.0376970 0.123402i
\(859\) 28.2925 + 9.19280i 0.965329 + 0.313654i 0.748929 0.662651i \(-0.230569\pi\)
0.216400 + 0.976305i \(0.430569\pi\)
\(860\) 12.1324 20.0736i 0.413713 0.684504i
\(861\) −10.0385 1.40848i −0.342112 0.0480009i
\(862\) −26.1064 51.2367i −0.889187 1.74513i
\(863\) −8.98237 17.6289i −0.305764 0.600095i 0.686084 0.727522i \(-0.259328\pi\)
−0.991848 + 0.127427i \(0.959328\pi\)
\(864\) −32.9412 + 19.0487i −1.12068 + 0.648051i
\(865\) 31.4697 + 36.3920i 1.07000 + 1.23737i
\(866\) 73.5901 + 23.9109i 2.50069 + 0.812525i
\(867\) −28.5274 8.71456i −0.968841 0.295962i
\(868\) −3.25317 3.25317i −0.110420 0.110420i
\(869\) −10.6877 7.76510i −0.362557 0.263413i
\(870\) −37.2144 + 33.3489i −1.26169 + 1.13063i
\(871\) −0.0591118 + 0.0429473i −0.00200293 + 0.00145521i
\(872\) 34.6503 + 5.48806i 1.17341 + 0.185849i
\(873\) −46.7253 + 9.10466i −1.58141 + 0.308146i
\(874\) 32.8986i 1.11281i
\(875\) 10.4062 + 4.08781i 0.351795 + 0.138193i
\(876\) −39.3301 19.1715i −1.32884 0.647744i
\(877\) −24.2543 12.3582i −0.819009 0.417306i −0.00630330 0.999980i \(-0.502006\pi\)
−0.812706 + 0.582674i \(0.802006\pi\)
\(878\) −6.97830 + 44.0593i −0.235506 + 1.48693i
\(879\) 16.6900 2.94684i 0.562941 0.0993944i
\(880\) 4.94936 12.1592i 0.166843 0.409885i
\(881\) 8.82145 12.1417i 0.297202 0.409064i −0.634135 0.773223i \(-0.718644\pi\)
0.931337 + 0.364159i \(0.118644\pi\)
\(882\) −0.799167 + 6.53340i −0.0269093 + 0.219991i
\(883\) −2.20661 13.9320i −0.0742583 0.468848i −0.996594 0.0824598i \(-0.973722\pi\)
0.922336 0.386388i \(-0.126278\pi\)
\(884\) −1.47366 + 4.53546i −0.0495645 + 0.152544i
\(885\) 16.7429 4.44381i 0.562806 0.149377i
\(886\) −11.5982 35.6956i −0.389650 1.19922i
\(887\) 31.5558 16.0785i 1.05954 0.539863i 0.164744 0.986336i \(-0.447320\pi\)
0.894797 + 0.446473i \(0.147320\pi\)
\(888\) 0.0957292 + 5.41335i 0.00321246 + 0.181660i
\(889\) 1.15195 0.374291i 0.0386351 0.0125533i
\(890\) −7.80422 4.71685i −0.261598 0.158109i
\(891\) −16.3485 + 26.2164i −0.547695 + 0.878283i
\(892\) 70.1158 11.1053i 2.34765 0.371831i
\(893\) 10.6996 10.6996i 0.358049 0.358049i
\(894\) −13.6339 + 7.25325i −0.455985 + 0.242585i
\(895\) 15.0277 3.70544i 0.502322 0.123859i
\(896\) −7.70074 10.5992i −0.257264 0.354093i
\(897\) 3.87143 + 2.70949i 0.129263 + 0.0904671i
\(898\) 21.2088 41.6247i 0.707748 1.38903i
\(899\) 9.61519 0.320684
\(900\) 41.3254 8.57980i 1.37751 0.285993i
\(901\) 34.4722 1.14844
\(902\) 20.0122 39.2762i 0.666333 1.30775i
\(903\) 5.29003 + 3.70232i 0.176041 + 0.123205i
\(904\) −8.51762 11.7235i −0.283292 0.389918i
\(905\) 9.49986 + 15.2911i 0.315786 + 0.508293i
\(906\) −33.7582 + 17.9594i −1.12154 + 0.596662i
\(907\) −17.7589 + 17.7589i −0.589676 + 0.589676i −0.937544 0.347868i \(-0.886906\pi\)
0.347868 + 0.937544i \(0.386906\pi\)
\(908\) −14.2271 + 2.25335i −0.472143 + 0.0747801i
\(909\) −32.9871 + 12.0234i −1.09411 + 0.398791i
\(910\) −0.551970 1.30980i −0.0182976 0.0434194i
\(911\) 41.6406 13.5298i 1.37961 0.448263i 0.477071 0.878865i \(-0.341699\pi\)
0.902542 + 0.430601i \(0.141699\pi\)
\(912\) 0.0833970 + 4.71598i 0.00276155 + 0.156162i
\(913\) 39.5802 20.1671i 1.30991 0.667434i
\(914\) −22.1214 68.0827i −0.731711 2.25197i
\(915\) 34.2902 42.1406i 1.13360 1.39313i
\(916\) −4.68688 + 14.4247i −0.154859 + 0.476607i
\(917\) −2.17593 13.7383i −0.0718555 0.453678i
\(918\) 36.2848 55.9577i 1.19758 1.84688i
\(919\) −13.2290 + 18.2082i −0.436386 + 0.600633i −0.969404 0.245470i \(-0.921058\pi\)
0.533018 + 0.846104i \(0.321058\pi\)
\(920\) −28.7371 24.2407i −0.947435 0.799191i
\(921\) 34.2405 6.04560i 1.12826 0.199209i
\(922\) 4.31999 27.2754i 0.142271 0.898267i
\(923\) 2.57621 + 1.31264i 0.0847969 + 0.0432062i
\(924\) −15.0391 7.33080i −0.494750 0.241166i
\(925\) −2.60276 + 8.35785i −0.0855781 + 0.274804i
\(926\) 61.9989i 2.03741i
\(927\) −3.51941 18.0617i −0.115593 0.593224i
\(928\) 42.5348 + 6.73685i 1.39627 + 0.221148i
\(929\) 17.3893 12.6341i 0.570524 0.414510i −0.264771 0.964311i \(-0.585297\pi\)
0.835296 + 0.549801i \(0.185297\pi\)
\(930\) −12.0159 6.97534i −0.394017 0.228731i
\(931\) 1.28822 + 0.935945i 0.0422196 + 0.0306744i
\(932\) −12.1310 12.1310i −0.397365 0.397365i
\(933\) −13.9835 4.27168i −0.457799 0.139849i
\(934\) 77.3289 + 25.1257i 2.53028 + 0.822137i
\(935\) 3.79766 + 44.7444i 0.124197 + 1.46330i
\(936\) −1.28693 0.867186i −0.0420645 0.0283449i
\(937\) 12.4450 + 24.4247i 0.406560 + 0.797919i 0.999976 0.00697746i \(-0.00222101\pi\)
−0.593416 + 0.804896i \(0.702221\pi\)
\(938\) 0.251207 + 0.493022i 0.00820221 + 0.0160977i
\(939\) −34.8295 4.88684i −1.13662 0.159476i
\(940\) 5.05644 + 59.5755i 0.164923 + 1.94314i
\(941\) 25.8655 + 8.40421i 0.843191 + 0.273969i 0.698591 0.715521i \(-0.253811\pi\)
0.144600 + 0.989490i \(0.453811\pi\)
\(942\) 6.53501 21.3925i 0.212922 0.697007i
\(943\) 38.9700 + 38.9700i 1.26904 + 1.26904i
\(944\) −6.18832 4.49607i −0.201413 0.146335i
\(945\) 1.59508 + 11.5089i 0.0518880 + 0.374386i
\(946\) −22.7157 + 16.5039i −0.738552 + 0.536589i
\(947\) −51.5425 8.16353i −1.67491 0.265279i −0.754517 0.656281i \(-0.772129\pi\)
−0.920390 + 0.391002i \(0.872129\pi\)
\(948\) −14.9758 + 11.2905i −0.486392 + 0.366697i
\(949\) 2.60100i 0.0844320i
\(950\) 5.19380 16.6781i 0.168509 0.541108i
\(951\) 1.73265 3.55452i 0.0561849 0.115263i
\(952\) 9.30639 + 4.74184i 0.301622 + 0.153684i
\(953\) 2.49981 15.7832i 0.0809768 0.511267i −0.913545 0.406738i \(-0.866666\pi\)
0.994522 0.104530i \(-0.0333337\pi\)
\(954\) −10.6740 + 37.2891i −0.345584 + 1.20728i
\(955\) −10.9213 9.21250i −0.353406 0.298109i
\(956\) −40.8690 + 56.2513i −1.32180 + 1.81930i
\(957\) 33.0586 11.3915i 1.06863 0.368233i
\(958\) −9.27130 58.5367i −0.299542 1.89123i
\(959\) 2.10010 6.46343i 0.0678156 0.208715i
\(960\) −37.9924 30.9147i −1.22620 0.997769i
\(961\) −8.75340 26.9402i −0.282368 0.869039i
\(962\) 0.991566 0.505228i 0.0319694 0.0162892i
\(963\) −10.2873 + 22.0875i −0.331503 + 0.711761i
\(964\) 48.8914 15.8858i 1.57469 0.511646i
\(965\) −22.2949 52.9047i −0.717697 1.70306i
\(966\) 24.8528 25.7476i 0.799625 0.828415i
\(967\) 7.70750 1.22075i 0.247856 0.0392566i −0.0312700 0.999511i \(-0.509955\pi\)
0.279126 + 0.960254i \(0.409955\pi\)
\(968\) 0.990896 0.990896i 0.0318486 0.0318486i
\(969\) −7.57773 14.2438i −0.243432 0.457576i
\(970\) −41.0820 66.1262i −1.31906 2.12318i
\(971\) 7.74454 + 10.6595i 0.248534 + 0.342078i 0.914997 0.403460i \(-0.132193\pi\)
−0.666463 + 0.745538i \(0.732193\pi\)
\(972\) 28.8142 + 33.0705i 0.924217 + 1.06074i
\(973\) −3.11803 + 6.11948i −0.0999594 + 0.196181i
\(974\) 50.0461 1.60358
\(975\) −1.53488 1.98478i −0.0491556 0.0635637i
\(976\) −23.9902 −0.767909
\(977\) −14.8946 + 29.2324i −0.476522 + 0.935227i 0.520179 + 0.854058i \(0.325865\pi\)
−0.996700 + 0.0811691i \(0.974135\pi\)
\(978\) −17.0276 + 24.3298i −0.544484 + 0.777982i
\(979\) 3.75056 + 5.16220i 0.119868 + 0.164985i
\(980\) −6.10884 + 1.50628i −0.195140 + 0.0481163i
\(981\) 2.08416 + 58.9096i 0.0665420 + 1.88084i
\(982\) 50.3570 50.3570i 1.60696 1.60696i
\(983\) −41.7917 + 6.61916i −1.33295 + 0.211118i −0.781926 0.623372i \(-0.785762\pi\)
−0.551023 + 0.834490i \(0.685762\pi\)
\(984\) −13.0222 12.5696i −0.415132 0.400704i
\(985\) −36.4833 22.0504i −1.16246 0.702586i
\(986\) −71.7837 + 23.3239i −2.28606 + 0.742785i
\(987\) −16.4568 + 0.291019i −0.523824 + 0.00926325i
\(988\) −1.15658 + 0.589309i −0.0367958 + 0.0187484i
\(989\) −10.8480 33.3866i −0.344945 1.06163i
\(990\) −49.5766 9.74673i −1.57565 0.309771i
\(991\) −13.8660 + 42.6753i −0.440469 + 1.35563i 0.446908 + 0.894580i \(0.352525\pi\)
−0.887377 + 0.461045i \(0.847475\pi\)
\(992\) 1.87311 + 11.8263i 0.0594712 + 0.375487i
\(993\) −14.7415 42.7807i −0.467808 1.35760i
\(994\) 12.8703 17.7144i 0.408220 0.561867i
\(995\) 15.1283 37.1660i 0.479600 1.17824i
\(996\) −10.9652 62.1039i −0.347447 1.96784i
\(997\) −1.36742 + 8.63357i −0.0433067 + 0.273428i −0.999834 0.0182147i \(-0.994202\pi\)
0.956527 + 0.291643i \(0.0942018\pi\)
\(998\) 35.8320 + 18.2573i 1.13424 + 0.577925i
\(999\) −8.89706 + 1.89751i −0.281491 + 0.0600346i
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 525.2.bk.a.8.9 480
3.2 odd 2 inner 525.2.bk.a.8.52 yes 480
25.22 odd 20 inner 525.2.bk.a.197.52 yes 480
75.47 even 20 inner 525.2.bk.a.197.9 yes 480
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.bk.a.8.9 480 1.1 even 1 trivial
525.2.bk.a.8.52 yes 480 3.2 odd 2 inner
525.2.bk.a.197.9 yes 480 75.47 even 20 inner
525.2.bk.a.197.52 yes 480 25.22 odd 20 inner