Properties

Label 169.2.c.b.146.3
Level $169$
Weight $2$
Character 169.146
Analytic conductor $1.349$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,2,Mod(22,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\), degree \(2\), not 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: \(1.34947179416\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 146.3
Root \(-0.623490 - 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.2.c.b.22.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.400969 + 0.694498i) q^{2} +(1.12349 + 1.94594i) q^{3} +(0.678448 - 1.17511i) q^{4} -0.246980 q^{5} +(-0.900969 + 1.56052i) q^{6} +(-1.17845 + 2.04113i) q^{7} +2.69202 q^{8} +(-1.02446 + 1.77441i) q^{9} +O(q^{10})\) \(q+(0.400969 + 0.694498i) q^{2} +(1.12349 + 1.94594i) q^{3} +(0.678448 - 1.17511i) q^{4} -0.246980 q^{5} +(-0.900969 + 1.56052i) q^{6} +(-1.17845 + 2.04113i) q^{7} +2.69202 q^{8} +(-1.02446 + 1.77441i) q^{9} +(-0.0990311 - 0.171527i) q^{10} +(-2.12349 - 3.67799i) q^{11} +3.04892 q^{12} -1.89008 q^{14} +(-0.277479 - 0.480608i) q^{15} +(-0.277479 - 0.480608i) q^{16} +(-1.07942 + 1.86960i) q^{17} -1.64310 q^{18} +(-0.0440730 + 0.0763367i) q^{19} +(-0.167563 + 0.290227i) q^{20} -5.29590 q^{21} +(1.70291 - 2.94952i) q^{22} +(-0.746980 - 1.29381i) q^{23} +(3.02446 + 5.23852i) q^{24} -4.93900 q^{25} +2.13706 q^{27} +(1.59903 + 2.76960i) q^{28} +(-2.31551 - 4.01058i) q^{29} +(0.222521 - 0.385418i) q^{30} +6.63102 q^{31} +(2.91454 - 5.04814i) q^{32} +(4.77144 - 8.26437i) q^{33} -1.73125 q^{34} +(0.291053 - 0.504118i) q^{35} +(1.39008 + 2.40770i) q^{36} +(2.84601 + 4.92944i) q^{37} -0.0706876 q^{38} -0.664874 q^{40} +(-5.79590 - 10.0388i) q^{41} +(-2.12349 - 3.67799i) q^{42} +(0.147948 - 0.256254i) q^{43} -5.76271 q^{44} +(0.253020 - 0.438244i) q^{45} +(0.599031 - 1.03755i) q^{46} +7.35690 q^{47} +(0.623490 - 1.07992i) q^{48} +(0.722521 + 1.25144i) q^{49} +(-1.98039 - 3.43013i) q^{50} -4.85086 q^{51} -10.3937 q^{53} +(0.856896 + 1.48419i) q^{54} +(0.524459 + 0.908389i) q^{55} +(-3.17241 + 5.49477i) q^{56} -0.198062 q^{57} +(1.85690 - 3.21624i) q^{58} +(-3.39008 + 5.87180i) q^{59} -0.753020 q^{60} +(-1.73609 + 3.00700i) q^{61} +(2.65883 + 4.60523i) q^{62} +(-2.41454 - 4.18211i) q^{63} +3.56465 q^{64} +7.65279 q^{66} +(3.83997 + 6.65102i) q^{67} +(1.46466 + 2.53686i) q^{68} +(1.67845 - 2.90716i) q^{69} +0.466812 q^{70} +(-4.33244 + 7.50400i) q^{71} +(-2.75786 + 4.77676i) q^{72} -6.73556 q^{73} +(-2.28232 + 3.95310i) q^{74} +(-5.54892 - 9.61101i) q^{75} +(0.0598025 + 0.103581i) q^{76} +10.0097 q^{77} +9.97046 q^{79} +(0.0685317 + 0.118700i) q^{80} +(5.47434 + 9.48184i) q^{81} +(4.64795 - 8.05048i) q^{82} -1.60925 q^{83} +(-3.59299 + 6.22324i) q^{84} +(0.266594 - 0.461754i) q^{85} +0.237291 q^{86} +(5.20291 - 9.01170i) q^{87} +(-5.71648 - 9.90123i) q^{88} +(-1.44235 - 2.49823i) q^{89} +0.405813 q^{90} -2.02715 q^{92} +(7.44989 + 12.9036i) q^{93} +(2.94989 + 5.10935i) q^{94} +(0.0108851 - 0.0188536i) q^{95} +13.0978 q^{96} +(-4.02930 + 6.97896i) q^{97} +(-0.579417 + 1.00358i) q^{98} +8.70171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} + 2 q^{3} + 8 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} + 2 q^{3} + 8 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9} - 5 q^{10} - 8 q^{11} - 10 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} - 18 q^{18} - 4 q^{19} - 4 q^{21} - 3 q^{22} + 5 q^{23} + 9 q^{24} - 10 q^{25} + 2 q^{27} + 14 q^{28} + q^{29} + q^{30} + 10 q^{31} + 7 q^{32} + 10 q^{33} - 26 q^{34} - 4 q^{35} + 7 q^{36} + 12 q^{37} + 24 q^{38} - 6 q^{40} - 7 q^{41} - 8 q^{42} - 13 q^{43} + 11 q^{45} + 8 q^{46} + 36 q^{47} - q^{48} + 4 q^{49} + q^{50} - 2 q^{51} + 2 q^{53} - 3 q^{54} - 6 q^{55} + 4 q^{56} - 10 q^{57} + 3 q^{58} - 19 q^{59} - 14 q^{60} - 4 q^{61} - q^{62} - 4 q^{63} - 22 q^{64} + 10 q^{66} - q^{67} + 21 q^{68} + 6 q^{69} - 4 q^{70} - 27 q^{71} - 4 q^{72} - 18 q^{73} + 8 q^{74} - 15 q^{75} - 21 q^{76} + 16 q^{77} - 10 q^{79} - 5 q^{80} + q^{81} + 14 q^{82} + 14 q^{83} - 7 q^{84} + 5 q^{85} + 36 q^{86} + 18 q^{87} - 15 q^{88} - 11 q^{89} - 24 q^{90} + 22 q^{93} - 5 q^{94} - 3 q^{95} + 42 q^{96} + 7 q^{97} + 5 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.400969 + 0.694498i 0.283528 + 0.491085i 0.972251 0.233940i \(-0.0751618\pi\)
−0.688723 + 0.725024i \(0.741829\pi\)
\(3\) 1.12349 + 1.94594i 0.648647 + 1.12349i 0.983446 + 0.181200i \(0.0579982\pi\)
−0.334799 + 0.942290i \(0.608668\pi\)
\(4\) 0.678448 1.17511i 0.339224 0.587553i
\(5\) −0.246980 −0.110453 −0.0552263 0.998474i \(-0.517588\pi\)
−0.0552263 + 0.998474i \(0.517588\pi\)
\(6\) −0.900969 + 1.56052i −0.367819 + 0.637081i
\(7\) −1.17845 + 2.04113i −0.445411 + 0.771475i −0.998081 0.0619254i \(-0.980276\pi\)
0.552669 + 0.833401i \(0.313609\pi\)
\(8\) 2.69202 0.951773
\(9\) −1.02446 + 1.77441i −0.341486 + 0.591471i
\(10\) −0.0990311 0.171527i −0.0313164 0.0542416i
\(11\) −2.12349 3.67799i −0.640256 1.10896i −0.985375 0.170397i \(-0.945495\pi\)
0.345119 0.938559i \(-0.387839\pi\)
\(12\) 3.04892 0.880147
\(13\) 0 0
\(14\) −1.89008 −0.505146
\(15\) −0.277479 0.480608i −0.0716448 0.124092i
\(16\) −0.277479 0.480608i −0.0693698 0.120152i
\(17\) −1.07942 + 1.86960i −0.261797 + 0.453446i −0.966720 0.255839i \(-0.917648\pi\)
0.704922 + 0.709284i \(0.250982\pi\)
\(18\) −1.64310 −0.387283
\(19\) −0.0440730 + 0.0763367i −0.0101110 + 0.0175128i −0.871037 0.491218i \(-0.836552\pi\)
0.860926 + 0.508731i \(0.169885\pi\)
\(20\) −0.167563 + 0.290227i −0.0374682 + 0.0648968i
\(21\) −5.29590 −1.15566
\(22\) 1.70291 2.94952i 0.363061 0.628840i
\(23\) −0.746980 1.29381i −0.155756 0.269777i 0.777578 0.628786i \(-0.216448\pi\)
−0.933334 + 0.359009i \(0.883115\pi\)
\(24\) 3.02446 + 5.23852i 0.617365 + 1.06931i
\(25\) −4.93900 −0.987800
\(26\) 0 0
\(27\) 2.13706 0.411278
\(28\) 1.59903 + 2.76960i 0.302188 + 0.523406i
\(29\) −2.31551 4.01058i −0.429980 0.744747i 0.566891 0.823793i \(-0.308146\pi\)
−0.996871 + 0.0790460i \(0.974813\pi\)
\(30\) 0.222521 0.385418i 0.0406266 0.0703673i
\(31\) 6.63102 1.19097 0.595483 0.803368i \(-0.296961\pi\)
0.595483 + 0.803368i \(0.296961\pi\)
\(32\) 2.91454 5.04814i 0.515223 0.892393i
\(33\) 4.77144 8.26437i 0.830601 1.43864i
\(34\) −1.73125 −0.296907
\(35\) 0.291053 0.504118i 0.0491969 0.0852115i
\(36\) 1.39008 + 2.40770i 0.231681 + 0.401283i
\(37\) 2.84601 + 4.92944i 0.467881 + 0.810394i 0.999326 0.0366986i \(-0.0116841\pi\)
−0.531445 + 0.847093i \(0.678351\pi\)
\(38\) −0.0706876 −0.0114670
\(39\) 0 0
\(40\) −0.664874 −0.105126
\(41\) −5.79590 10.0388i −0.905167 1.56780i −0.820693 0.571370i \(-0.806412\pi\)
−0.0844742 0.996426i \(-0.526921\pi\)
\(42\) −2.12349 3.67799i −0.327662 0.567527i
\(43\) 0.147948 0.256254i 0.0225619 0.0390784i −0.854524 0.519412i \(-0.826151\pi\)
0.877086 + 0.480334i \(0.159484\pi\)
\(44\) −5.76271 −0.868761
\(45\) 0.253020 0.438244i 0.0377181 0.0653296i
\(46\) 0.599031 1.03755i 0.0883223 0.152979i
\(47\) 7.35690 1.07311 0.536557 0.843864i \(-0.319725\pi\)
0.536557 + 0.843864i \(0.319725\pi\)
\(48\) 0.623490 1.07992i 0.0899930 0.155872i
\(49\) 0.722521 + 1.25144i 0.103217 + 0.178778i
\(50\) −1.98039 3.43013i −0.280069 0.485093i
\(51\) −4.85086 −0.679256
\(52\) 0 0
\(53\) −10.3937 −1.42769 −0.713844 0.700304i \(-0.753048\pi\)
−0.713844 + 0.700304i \(0.753048\pi\)
\(54\) 0.856896 + 1.48419i 0.116609 + 0.201972i
\(55\) 0.524459 + 0.908389i 0.0707180 + 0.122487i
\(56\) −3.17241 + 5.49477i −0.423931 + 0.734270i
\(57\) −0.198062 −0.0262340
\(58\) 1.85690 3.21624i 0.243822 0.422313i
\(59\) −3.39008 + 5.87180i −0.441351 + 0.764443i −0.997790 0.0664458i \(-0.978834\pi\)
0.556439 + 0.830889i \(0.312167\pi\)
\(60\) −0.753020 −0.0972145
\(61\) −1.73609 + 3.00700i −0.222284 + 0.385007i −0.955501 0.294987i \(-0.904685\pi\)
0.733217 + 0.679995i \(0.238018\pi\)
\(62\) 2.65883 + 4.60523i 0.337672 + 0.584865i
\(63\) −2.41454 4.18211i −0.304204 0.526896i
\(64\) 3.56465 0.445581
\(65\) 0 0
\(66\) 7.65279 0.941994
\(67\) 3.83997 + 6.65102i 0.469127 + 0.812552i 0.999377 0.0352895i \(-0.0112353\pi\)
−0.530250 + 0.847841i \(0.677902\pi\)
\(68\) 1.46466 + 2.53686i 0.177616 + 0.307639i
\(69\) 1.67845 2.90716i 0.202061 0.349981i
\(70\) 0.466812 0.0557947
\(71\) −4.33244 + 7.50400i −0.514166 + 0.890561i 0.485699 + 0.874126i \(0.338565\pi\)
−0.999865 + 0.0164351i \(0.994768\pi\)
\(72\) −2.75786 + 4.77676i −0.325017 + 0.562947i
\(73\) −6.73556 −0.788338 −0.394169 0.919038i \(-0.628968\pi\)
−0.394169 + 0.919038i \(0.628968\pi\)
\(74\) −2.28232 + 3.95310i −0.265315 + 0.459539i
\(75\) −5.54892 9.61101i −0.640734 1.10978i
\(76\) 0.0598025 + 0.103581i 0.00685981 + 0.0118815i
\(77\) 10.0097 1.14071
\(78\) 0 0
\(79\) 9.97046 1.12176 0.560882 0.827896i \(-0.310462\pi\)
0.560882 + 0.827896i \(0.310462\pi\)
\(80\) 0.0685317 + 0.118700i 0.00766207 + 0.0132711i
\(81\) 5.47434 + 9.48184i 0.608261 + 1.05354i
\(82\) 4.64795 8.05048i 0.513280 0.889027i
\(83\) −1.60925 −0.176638 −0.0883192 0.996092i \(-0.528150\pi\)
−0.0883192 + 0.996092i \(0.528150\pi\)
\(84\) −3.59299 + 6.22324i −0.392027 + 0.679011i
\(85\) 0.266594 0.461754i 0.0289162 0.0500843i
\(86\) 0.237291 0.0255877
\(87\) 5.20291 9.01170i 0.557810 0.966156i
\(88\) −5.71648 9.90123i −0.609379 1.05548i
\(89\) −1.44235 2.49823i −0.152889 0.264812i 0.779399 0.626528i \(-0.215524\pi\)
−0.932288 + 0.361716i \(0.882191\pi\)
\(90\) 0.405813 0.0427765
\(91\) 0 0
\(92\) −2.02715 −0.211345
\(93\) 7.44989 + 12.9036i 0.772517 + 1.33804i
\(94\) 2.94989 + 5.10935i 0.304258 + 0.526990i
\(95\) 0.0108851 0.0188536i 0.00111679 0.00193434i
\(96\) 13.0978 1.33679
\(97\) −4.02930 + 6.97896i −0.409114 + 0.708606i −0.994791 0.101939i \(-0.967495\pi\)
0.585677 + 0.810545i \(0.300829\pi\)
\(98\) −0.579417 + 1.00358i −0.0585299 + 0.101377i
\(99\) 8.70171 0.874555
\(100\) −3.35086 + 5.80385i −0.335086 + 0.580385i
\(101\) 6.67725 + 11.5653i 0.664411 + 1.15079i 0.979445 + 0.201714i \(0.0646510\pi\)
−0.315033 + 0.949081i \(0.602016\pi\)
\(102\) −1.94504 3.36891i −0.192588 0.333572i
\(103\) 1.36227 0.134229 0.0671144 0.997745i \(-0.478621\pi\)
0.0671144 + 0.997745i \(0.478621\pi\)
\(104\) 0 0
\(105\) 1.30798 0.127646
\(106\) −4.16756 7.21843i −0.404789 0.701116i
\(107\) −1.63437 2.83082i −0.158001 0.273666i 0.776147 0.630552i \(-0.217172\pi\)
−0.934148 + 0.356887i \(0.883838\pi\)
\(108\) 1.44989 2.51128i 0.139515 0.241648i
\(109\) −15.7017 −1.50395 −0.751976 0.659191i \(-0.770899\pi\)
−0.751976 + 0.659191i \(0.770899\pi\)
\(110\) −0.420583 + 0.728471i −0.0401010 + 0.0694570i
\(111\) −6.39493 + 11.0763i −0.606980 + 1.05132i
\(112\) 1.30798 0.123592
\(113\) −6.02446 + 10.4347i −0.566733 + 0.981611i 0.430153 + 0.902756i \(0.358460\pi\)
−0.996886 + 0.0788549i \(0.974874\pi\)
\(114\) −0.0794168 0.137554i −0.00743806 0.0128831i
\(115\) 0.184489 + 0.319544i 0.0172037 + 0.0297976i
\(116\) −6.28382 −0.583438
\(117\) 0 0
\(118\) −5.43727 −0.500541
\(119\) −2.54407 4.40646i −0.233215 0.403940i
\(120\) −0.746980 1.29381i −0.0681896 0.118108i
\(121\) −3.51842 + 6.09408i −0.319856 + 0.554007i
\(122\) −2.78448 −0.252095
\(123\) 13.0233 22.5570i 1.17427 2.03389i
\(124\) 4.49880 7.79216i 0.404004 0.699756i
\(125\) 2.45473 0.219558
\(126\) 1.93631 3.35379i 0.172500 0.298780i
\(127\) 4.90366 + 8.49338i 0.435129 + 0.753666i 0.997306 0.0733510i \(-0.0233694\pi\)
−0.562177 + 0.827017i \(0.690036\pi\)
\(128\) −4.39977 7.62063i −0.388889 0.673575i
\(129\) 0.664874 0.0585389
\(130\) 0 0
\(131\) −6.57673 −0.574611 −0.287306 0.957839i \(-0.592760\pi\)
−0.287306 + 0.957839i \(0.592760\pi\)
\(132\) −6.47434 11.2139i −0.563519 0.976044i
\(133\) −0.103875 0.179918i −0.00900715 0.0156008i
\(134\) −3.07942 + 5.33371i −0.266021 + 0.460762i
\(135\) −0.527811 −0.0454267
\(136\) −2.90581 + 5.03302i −0.249171 + 0.431578i
\(137\) 3.10992 5.38653i 0.265698 0.460203i −0.702048 0.712129i \(-0.747731\pi\)
0.967746 + 0.251927i \(0.0810642\pi\)
\(138\) 2.69202 0.229160
\(139\) 7.35354 12.7367i 0.623719 1.08031i −0.365068 0.930981i \(-0.618954\pi\)
0.988787 0.149333i \(-0.0477125\pi\)
\(140\) −0.394928 0.684035i −0.0333775 0.0578116i
\(141\) 8.26540 + 14.3161i 0.696072 + 1.20563i
\(142\) −6.94869 −0.583121
\(143\) 0 0
\(144\) 1.13706 0.0947553
\(145\) 0.571884 + 0.990532i 0.0474924 + 0.0822592i
\(146\) −2.70075 4.67784i −0.223516 0.387141i
\(147\) −1.62349 + 2.81197i −0.133903 + 0.231927i
\(148\) 7.72348 0.634866
\(149\) 2.16756 3.75433i 0.177574 0.307567i −0.763475 0.645837i \(-0.776509\pi\)
0.941049 + 0.338270i \(0.109842\pi\)
\(150\) 4.44989 7.70743i 0.363332 0.629309i
\(151\) −3.94438 −0.320989 −0.160494 0.987037i \(-0.551309\pi\)
−0.160494 + 0.987037i \(0.551309\pi\)
\(152\) −0.118645 + 0.205500i −0.00962342 + 0.0166682i
\(153\) −2.21164 3.83067i −0.178800 0.309691i
\(154\) 4.01357 + 6.95171i 0.323423 + 0.560185i
\(155\) −1.63773 −0.131545
\(156\) 0 0
\(157\) 4.45473 0.355526 0.177763 0.984073i \(-0.443114\pi\)
0.177763 + 0.984073i \(0.443114\pi\)
\(158\) 3.99784 + 6.92447i 0.318051 + 0.550881i
\(159\) −11.6773 20.2256i −0.926066 1.60399i
\(160\) −0.719833 + 1.24679i −0.0569078 + 0.0985671i
\(161\) 3.52111 0.277502
\(162\) −4.39008 + 7.60385i −0.344918 + 0.597415i
\(163\) 8.07942 13.9940i 0.632829 1.09609i −0.354142 0.935192i \(-0.615227\pi\)
0.986971 0.160900i \(-0.0514396\pi\)
\(164\) −15.7289 −1.22822
\(165\) −1.17845 + 2.04113i −0.0917420 + 0.158902i
\(166\) −0.645260 1.11762i −0.0500819 0.0867444i
\(167\) 8.05861 + 13.9579i 0.623594 + 1.08010i 0.988811 + 0.149174i \(0.0476613\pi\)
−0.365217 + 0.930922i \(0.619005\pi\)
\(168\) −14.2567 −1.09993
\(169\) 0 0
\(170\) 0.427583 0.0327942
\(171\) −0.0903019 0.156408i −0.00690556 0.0119608i
\(172\) −0.200751 0.347710i −0.0153071 0.0265127i
\(173\) 10.7681 18.6509i 0.818682 1.41800i −0.0879709 0.996123i \(-0.528038\pi\)
0.906653 0.421876i \(-0.138628\pi\)
\(174\) 8.34481 0.632619
\(175\) 5.82036 10.0812i 0.439978 0.762063i
\(176\) −1.17845 + 2.04113i −0.0888289 + 0.153856i
\(177\) −15.2349 −1.14513
\(178\) 1.15668 2.00342i 0.0866967 0.150163i
\(179\) −5.71648 9.90123i −0.427270 0.740053i 0.569360 0.822089i \(-0.307191\pi\)
−0.996629 + 0.0820356i \(0.973858\pi\)
\(180\) −0.343322 0.594652i −0.0255897 0.0443227i
\(181\) 20.9705 1.55872 0.779361 0.626575i \(-0.215544\pi\)
0.779361 + 0.626575i \(0.215544\pi\)
\(182\) 0 0
\(183\) −7.80194 −0.576736
\(184\) −2.01089 3.48296i −0.148244 0.256767i
\(185\) −0.702907 1.21747i −0.0516787 0.0895102i
\(186\) −5.97434 + 10.3479i −0.438060 + 0.758743i
\(187\) 9.16852 0.670469
\(188\) 4.99127 8.64513i 0.364026 0.630511i
\(189\) −2.51842 + 4.36203i −0.183188 + 0.317291i
\(190\) 0.0174584 0.00126657
\(191\) 7.21864 12.5030i 0.522322 0.904689i −0.477341 0.878718i \(-0.658399\pi\)
0.999663 0.0259702i \(-0.00826749\pi\)
\(192\) 4.00484 + 6.93659i 0.289025 + 0.500606i
\(193\) −6.78986 11.7604i −0.488745 0.846530i 0.511172 0.859479i \(-0.329212\pi\)
−0.999916 + 0.0129483i \(0.995878\pi\)
\(194\) −6.46250 −0.463980
\(195\) 0 0
\(196\) 1.96077 0.140055
\(197\) −0.280167 0.485264i −0.0199611 0.0345736i 0.855872 0.517187i \(-0.173021\pi\)
−0.875833 + 0.482614i \(0.839688\pi\)
\(198\) 3.48911 + 6.04332i 0.247961 + 0.429480i
\(199\) −5.74578 + 9.95199i −0.407308 + 0.705478i −0.994587 0.103907i \(-0.966866\pi\)
0.587279 + 0.809384i \(0.300199\pi\)
\(200\) −13.2959 −0.940162
\(201\) −8.62833 + 14.9447i −0.608596 + 1.05412i
\(202\) −5.35474 + 9.27468i −0.376758 + 0.652564i
\(203\) 10.9148 0.766071
\(204\) −3.29105 + 5.70027i −0.230420 + 0.399099i
\(205\) 1.43147 + 2.47938i 0.0999781 + 0.173167i
\(206\) 0.546229 + 0.946096i 0.0380576 + 0.0659177i
\(207\) 3.06100 0.212754
\(208\) 0 0
\(209\) 0.374354 0.0258946
\(210\) 0.524459 + 0.908389i 0.0361911 + 0.0626848i
\(211\) −4.39224 7.60758i −0.302374 0.523728i 0.674299 0.738458i \(-0.264446\pi\)
−0.976673 + 0.214731i \(0.931113\pi\)
\(212\) −7.05161 + 12.2137i −0.484306 + 0.838843i
\(213\) −19.4698 −1.33405
\(214\) 1.31067 2.27014i 0.0895953 0.155184i
\(215\) −0.0365403 + 0.0632896i −0.00249202 + 0.00431631i
\(216\) 5.75302 0.391443
\(217\) −7.81431 + 13.5348i −0.530470 + 0.918801i
\(218\) −6.29590 10.9048i −0.426412 0.738567i
\(219\) −7.56734 13.1070i −0.511353 0.885690i
\(220\) 1.42327 0.0959570
\(221\) 0 0
\(222\) −10.2567 −0.688383
\(223\) −1.12953 1.95640i −0.0756390 0.131011i 0.825725 0.564073i \(-0.190766\pi\)
−0.901364 + 0.433062i \(0.857433\pi\)
\(224\) 6.86927 + 11.8979i 0.458973 + 0.794964i
\(225\) 5.05980 8.76383i 0.337320 0.584256i
\(226\) −9.66248 −0.642739
\(227\) −3.48307 + 6.03286i −0.231180 + 0.400415i −0.958156 0.286248i \(-0.907592\pi\)
0.726976 + 0.686663i \(0.240925\pi\)
\(228\) −0.134375 + 0.232744i −0.00889920 + 0.0154139i
\(229\) 24.1739 1.59746 0.798728 0.601692i \(-0.205507\pi\)
0.798728 + 0.601692i \(0.205507\pi\)
\(230\) −0.147948 + 0.256254i −0.00975543 + 0.0168969i
\(231\) 11.2458 + 19.4783i 0.739918 + 1.28158i
\(232\) −6.23341 10.7966i −0.409243 0.708830i
\(233\) −3.06100 −0.200533 −0.100266 0.994961i \(-0.531969\pi\)
−0.100266 + 0.994961i \(0.531969\pi\)
\(234\) 0 0
\(235\) −1.81700 −0.118528
\(236\) 4.59999 + 7.96742i 0.299434 + 0.518635i
\(237\) 11.2017 + 19.4019i 0.727629 + 1.26029i
\(238\) 2.04019 3.53371i 0.132246 0.229056i
\(239\) 25.1468 1.62661 0.813304 0.581839i \(-0.197667\pi\)
0.813304 + 0.581839i \(0.197667\pi\)
\(240\) −0.153989 + 0.266717i −0.00993996 + 0.0172165i
\(241\) −10.1332 + 17.5512i −0.652735 + 1.13057i 0.329721 + 0.944078i \(0.393045\pi\)
−0.982456 + 0.186492i \(0.940288\pi\)
\(242\) −5.64310 −0.362752
\(243\) −9.09515 + 15.7533i −0.583454 + 1.01057i
\(244\) 2.35570 + 4.08019i 0.150808 + 0.261207i
\(245\) −0.178448 0.309081i −0.0114006 0.0197465i
\(246\) 20.8877 1.33175
\(247\) 0 0
\(248\) 17.8509 1.13353
\(249\) −1.80798 3.13151i −0.114576 0.198451i
\(250\) 0.984271 + 1.70481i 0.0622507 + 0.107821i
\(251\) 11.8605 20.5431i 0.748631 1.29667i −0.199848 0.979827i \(-0.564045\pi\)
0.948479 0.316840i \(-0.102622\pi\)
\(252\) −6.55257 −0.412773
\(253\) −3.17241 + 5.49477i −0.199448 + 0.345453i
\(254\) −3.93243 + 6.81116i −0.246742 + 0.427370i
\(255\) 1.19806 0.0750256
\(256\) 7.09299 12.2854i 0.443312 0.767839i
\(257\) −7.11207 12.3185i −0.443639 0.768405i 0.554317 0.832305i \(-0.312979\pi\)
−0.997956 + 0.0639003i \(0.979646\pi\)
\(258\) 0.266594 + 0.461754i 0.0165974 + 0.0287476i
\(259\) −13.4155 −0.833599
\(260\) 0 0
\(261\) 9.48858 0.587329
\(262\) −2.63706 4.56753i −0.162918 0.282183i
\(263\) 8.54772 + 14.8051i 0.527075 + 0.912921i 0.999502 + 0.0315510i \(0.0100447\pi\)
−0.472427 + 0.881370i \(0.656622\pi\)
\(264\) 12.8448 22.2479i 0.790544 1.36926i
\(265\) 2.56704 0.157692
\(266\) 0.0833017 0.144283i 0.00510755 0.00884654i
\(267\) 3.24094 5.61347i 0.198342 0.343539i
\(268\) 10.4209 0.636556
\(269\) 3.23341 5.60042i 0.197144 0.341464i −0.750457 0.660919i \(-0.770167\pi\)
0.947601 + 0.319455i \(0.103500\pi\)
\(270\) −0.211636 0.366564i −0.0128797 0.0223084i
\(271\) 3.22401 + 5.58415i 0.195845 + 0.339213i 0.947177 0.320711i \(-0.103922\pi\)
−0.751332 + 0.659924i \(0.770588\pi\)
\(272\) 1.19806 0.0726432
\(273\) 0 0
\(274\) 4.98792 0.301331
\(275\) 10.4879 + 18.1656i 0.632445 + 1.09543i
\(276\) −2.27748 3.94471i −0.137088 0.237444i
\(277\) −6.73005 + 11.6568i −0.404370 + 0.700389i −0.994248 0.107103i \(-0.965842\pi\)
0.589878 + 0.807492i \(0.299176\pi\)
\(278\) 11.7942 0.707367
\(279\) −6.79321 + 11.7662i −0.406699 + 0.704423i
\(280\) 0.783520 1.35710i 0.0468243 0.0811020i
\(281\) −5.03684 −0.300472 −0.150236 0.988650i \(-0.548003\pi\)
−0.150236 + 0.988650i \(0.548003\pi\)
\(282\) −6.62833 + 11.4806i −0.394712 + 0.683660i
\(283\) −11.0640 19.1634i −0.657686 1.13914i −0.981213 0.192926i \(-0.938202\pi\)
0.323528 0.946219i \(-0.395131\pi\)
\(284\) 5.87867 + 10.1821i 0.348835 + 0.604199i
\(285\) 0.0489173 0.00289761
\(286\) 0 0
\(287\) 27.3207 1.61269
\(288\) 5.97166 + 10.3432i 0.351883 + 0.609480i
\(289\) 6.16972 + 10.6863i 0.362925 + 0.628604i
\(290\) −0.458615 + 0.794345i −0.0269308 + 0.0466456i
\(291\) −18.1075 −1.06148
\(292\) −4.56973 + 7.91500i −0.267423 + 0.463190i
\(293\) 7.47315 12.9439i 0.436586 0.756189i −0.560838 0.827926i \(-0.689521\pi\)
0.997424 + 0.0717367i \(0.0228541\pi\)
\(294\) −2.60388 −0.151861
\(295\) 0.837282 1.45021i 0.0487484 0.0844347i
\(296\) 7.66152 + 13.2701i 0.445317 + 0.771312i
\(297\) −4.53803 7.86010i −0.263323 0.456089i
\(298\) 3.47650 0.201388
\(299\) 0 0
\(300\) −15.0586 −0.869409
\(301\) 0.348699 + 0.603965i 0.0200987 + 0.0348119i
\(302\) −1.58157 2.73936i −0.0910093 0.157633i
\(303\) −15.0036 + 25.9871i −0.861937 + 1.49292i
\(304\) 0.0489173 0.00280560
\(305\) 0.428780 0.742669i 0.0245519 0.0425251i
\(306\) 1.77359 3.07196i 0.101390 0.175612i
\(307\) −19.1293 −1.09177 −0.545883 0.837861i \(-0.683806\pi\)
−0.545883 + 0.837861i \(0.683806\pi\)
\(308\) 6.79105 11.7624i 0.386956 0.670228i
\(309\) 1.53050 + 2.65090i 0.0870671 + 0.150805i
\(310\) −0.656678 1.13740i −0.0372968 0.0645999i
\(311\) −0.269815 −0.0152998 −0.00764990 0.999971i \(-0.502435\pi\)
−0.00764990 + 0.999971i \(0.502435\pi\)
\(312\) 0 0
\(313\) −23.3937 −1.32229 −0.661146 0.750257i \(-0.729930\pi\)
−0.661146 + 0.750257i \(0.729930\pi\)
\(314\) 1.78621 + 3.09380i 0.100802 + 0.174593i
\(315\) 0.596343 + 1.03290i 0.0336001 + 0.0581971i
\(316\) 6.76444 11.7164i 0.380529 0.659096i
\(317\) 13.9952 0.786050 0.393025 0.919528i \(-0.371429\pi\)
0.393025 + 0.919528i \(0.371429\pi\)
\(318\) 9.36443 16.2197i 0.525131 0.909554i
\(319\) −9.83393 + 17.0329i −0.550594 + 0.953657i
\(320\) −0.880395 −0.0492156
\(321\) 3.67241 6.36080i 0.204974 0.355025i
\(322\) 1.41185 + 2.44540i 0.0786795 + 0.136277i
\(323\) −0.0951463 0.164798i −0.00529408 0.00916962i
\(324\) 14.8562 0.825346
\(325\) 0 0
\(326\) 12.9584 0.717698
\(327\) −17.6407 30.5546i −0.975534 1.68967i
\(328\) −15.6027 27.0246i −0.861514 1.49219i
\(329\) −8.66972 + 15.0164i −0.477977 + 0.827881i
\(330\) −1.89008 −0.104046
\(331\) 8.91066 15.4337i 0.489774 0.848314i −0.510157 0.860081i \(-0.670413\pi\)
0.999931 + 0.0117680i \(0.00374594\pi\)
\(332\) −1.09179 + 1.89104i −0.0599200 + 0.103784i
\(333\) −11.6625 −0.639100
\(334\) −6.46250 + 11.1934i −0.353612 + 0.612474i
\(335\) −0.948394 1.64267i −0.0518163 0.0897485i
\(336\) 1.46950 + 2.54525i 0.0801678 + 0.138855i
\(337\) −27.8485 −1.51700 −0.758501 0.651672i \(-0.774068\pi\)
−0.758501 + 0.651672i \(0.774068\pi\)
\(338\) 0 0
\(339\) −27.0737 −1.47044
\(340\) −0.361740 0.626552i −0.0196181 0.0339796i
\(341\) −14.0809 24.3888i −0.762524 1.32073i
\(342\) 0.0724165 0.125429i 0.00391584 0.00678243i
\(343\) −19.9041 −1.07472
\(344\) 0.398280 0.689842i 0.0214738 0.0371938i
\(345\) −0.414542 + 0.718009i −0.0223182 + 0.0386563i
\(346\) 17.2707 0.928477
\(347\) −0.751824 + 1.30220i −0.0403600 + 0.0699056i −0.885500 0.464640i \(-0.846184\pi\)
0.845140 + 0.534545i \(0.179517\pi\)
\(348\) −7.05980 12.2279i −0.378445 0.655486i
\(349\) −7.09299 12.2854i −0.379679 0.657623i 0.611336 0.791371i \(-0.290632\pi\)
−0.991015 + 0.133747i \(0.957299\pi\)
\(350\) 9.33513 0.498983
\(351\) 0 0
\(352\) −24.7560 −1.31950
\(353\) −3.58426 6.20812i −0.190771 0.330425i 0.754735 0.656030i \(-0.227765\pi\)
−0.945506 + 0.325605i \(0.894432\pi\)
\(354\) −6.10872 10.5806i −0.324675 0.562353i
\(355\) 1.07002 1.85334i 0.0567910 0.0983648i
\(356\) −3.91425 −0.207455
\(357\) 5.71648 9.90123i 0.302548 0.524029i
\(358\) 4.58426 7.94017i 0.242286 0.419651i
\(359\) −19.8853 −1.04951 −0.524753 0.851255i \(-0.675842\pi\)
−0.524753 + 0.851255i \(0.675842\pi\)
\(360\) 0.681136 1.17976i 0.0358990 0.0621790i
\(361\) 9.49612 + 16.4478i 0.499796 + 0.865671i
\(362\) 8.40850 + 14.5640i 0.441941 + 0.765464i
\(363\) −15.8116 −0.829895
\(364\) 0 0
\(365\) 1.66355 0.0870740
\(366\) −3.12833 5.41843i −0.163521 0.283226i
\(367\) −0.541917 0.938628i −0.0282878 0.0489960i 0.851535 0.524298i \(-0.175672\pi\)
−0.879823 + 0.475302i \(0.842339\pi\)
\(368\) −0.414542 + 0.718009i −0.0216095 + 0.0374288i
\(369\) 23.7506 1.23641
\(370\) 0.563687 0.976335i 0.0293047 0.0507572i
\(371\) 12.2485 21.2150i 0.635909 1.10143i
\(372\) 20.2174 1.04823
\(373\) 3.06518 5.30905i 0.158709 0.274892i −0.775694 0.631109i \(-0.782600\pi\)
0.934403 + 0.356217i \(0.115934\pi\)
\(374\) 3.67629 + 6.36752i 0.190097 + 0.329257i
\(375\) 2.75786 + 4.77676i 0.142416 + 0.246671i
\(376\) 19.8049 1.02136
\(377\) 0 0
\(378\) −4.03923 −0.207756
\(379\) −1.20440 2.08608i −0.0618658 0.107155i 0.833434 0.552620i \(-0.186372\pi\)
−0.895299 + 0.445465i \(0.853038\pi\)
\(380\) −0.0147700 0.0255824i −0.000757685 0.00131235i
\(381\) −11.0184 + 19.0845i −0.564491 + 0.977726i
\(382\) 11.5778 0.592371
\(383\) −15.1957 + 26.3197i −0.776462 + 1.34487i 0.157506 + 0.987518i \(0.449655\pi\)
−0.933969 + 0.357354i \(0.883679\pi\)
\(384\) 9.88620 17.1234i 0.504503 0.873825i
\(385\) −2.47219 −0.125994
\(386\) 5.44504 9.43109i 0.277145 0.480030i
\(387\) 0.303134 + 0.525044i 0.0154092 + 0.0266895i
\(388\) 5.46734 + 9.46972i 0.277562 + 0.480752i
\(389\) −15.9409 −0.808237 −0.404118 0.914707i \(-0.632422\pi\)
−0.404118 + 0.914707i \(0.632422\pi\)
\(390\) 0 0
\(391\) 3.22521 0.163106
\(392\) 1.94504 + 3.36891i 0.0982394 + 0.170156i
\(393\) −7.38889 12.7979i −0.372720 0.645570i
\(394\) 0.224677 0.389152i 0.0113191 0.0196052i
\(395\) −2.46250 −0.123902
\(396\) 5.90366 10.2254i 0.296670 0.513847i
\(397\) 8.45742 14.6487i 0.424466 0.735196i −0.571905 0.820320i \(-0.693795\pi\)
0.996370 + 0.0851239i \(0.0271286\pi\)
\(398\) −9.21552 −0.461932
\(399\) 0.233406 0.404271i 0.0116849 0.0202389i
\(400\) 1.37047 + 2.37372i 0.0685235 + 0.118686i
\(401\) 13.3312 + 23.0904i 0.665730 + 1.15308i 0.979087 + 0.203443i \(0.0652132\pi\)
−0.313356 + 0.949636i \(0.601453\pi\)
\(402\) −13.8388 −0.690215
\(403\) 0 0
\(404\) 18.1207 0.901537
\(405\) −1.35205 2.34182i −0.0671840 0.116366i
\(406\) 4.37651 + 7.58034i 0.217203 + 0.376206i
\(407\) 12.0869 20.9352i 0.599128 1.03772i
\(408\) −13.0586 −0.646497
\(409\) 14.2582 24.6959i 0.705021 1.22113i −0.261663 0.965159i \(-0.584271\pi\)
0.966684 0.255972i \(-0.0823956\pi\)
\(410\) −1.14795 + 1.98831i −0.0566931 + 0.0981954i
\(411\) 13.9758 0.689377
\(412\) 0.924231 1.60082i 0.0455336 0.0788665i
\(413\) −7.99007 13.8392i −0.393166 0.680983i
\(414\) 1.22737 + 2.12586i 0.0603217 + 0.104480i
\(415\) 0.397452 0.0195102
\(416\) 0 0
\(417\) 33.0465 1.61830
\(418\) 0.150104 + 0.259988i 0.00734185 + 0.0127165i
\(419\) 14.8046 + 25.6424i 0.723253 + 1.25271i 0.959689 + 0.281064i \(0.0906874\pi\)
−0.236436 + 0.971647i \(0.575979\pi\)
\(420\) 0.887395 1.53701i 0.0433005 0.0749986i
\(421\) 11.6606 0.568301 0.284151 0.958780i \(-0.408288\pi\)
0.284151 + 0.958780i \(0.408288\pi\)
\(422\) 3.52230 6.10081i 0.171463 0.296983i
\(423\) −7.53684 + 13.0542i −0.366453 + 0.634716i
\(424\) −27.9801 −1.35884
\(425\) 5.33124 9.23398i 0.258603 0.447914i
\(426\) −7.80678 13.5217i −0.378240 0.655131i
\(427\) −4.09179 7.08719i −0.198016 0.342973i
\(428\) −4.43535 −0.214391
\(429\) 0 0
\(430\) −0.0586060 −0.00282623
\(431\) 2.17456 + 3.76645i 0.104745 + 0.181424i 0.913634 0.406538i \(-0.133264\pi\)
−0.808889 + 0.587961i \(0.799931\pi\)
\(432\) −0.592990 1.02709i −0.0285303 0.0494159i
\(433\) 7.19418 12.4607i 0.345730 0.598822i −0.639756 0.768578i \(-0.720965\pi\)
0.985486 + 0.169756i \(0.0542979\pi\)
\(434\) −12.5332 −0.601612
\(435\) −1.28501 + 2.22571i −0.0616116 + 0.106714i
\(436\) −10.6528 + 18.4512i −0.510176 + 0.883651i
\(437\) 0.131687 0.00629942
\(438\) 6.06853 10.5110i 0.289966 0.502235i
\(439\) 10.1163 + 17.5219i 0.482822 + 0.836273i 0.999805 0.0197227i \(-0.00627834\pi\)
−0.516983 + 0.855996i \(0.672945\pi\)
\(440\) 1.41185 + 2.44540i 0.0673075 + 0.116580i
\(441\) −2.96077 −0.140989
\(442\) 0 0
\(443\) 8.12200 0.385888 0.192944 0.981210i \(-0.438196\pi\)
0.192944 + 0.981210i \(0.438196\pi\)
\(444\) 8.67725 + 15.0294i 0.411804 + 0.713266i
\(445\) 0.356232 + 0.617012i 0.0168870 + 0.0292492i
\(446\) 0.905813 1.56891i 0.0428915 0.0742903i
\(447\) 9.74094 0.460731
\(448\) −4.20075 + 7.27591i −0.198467 + 0.343755i
\(449\) 6.24578 10.8180i 0.294757 0.510534i −0.680172 0.733053i \(-0.738095\pi\)
0.974928 + 0.222519i \(0.0714281\pi\)
\(450\) 8.11529 0.382559
\(451\) −24.6151 + 42.6345i −1.15908 + 2.00758i
\(452\) 8.17456 + 14.1588i 0.384499 + 0.665972i
\(453\) −4.43147 7.67553i −0.208209 0.360628i
\(454\) −5.58642 −0.262184
\(455\) 0 0
\(456\) −0.533188 −0.0249688
\(457\) 2.99061 + 5.17988i 0.139895 + 0.242305i 0.927457 0.373931i \(-0.121990\pi\)
−0.787562 + 0.616236i \(0.788657\pi\)
\(458\) 9.69298 + 16.7887i 0.452923 + 0.784486i
\(459\) −2.30678 + 3.99546i −0.107671 + 0.186492i
\(460\) 0.500664 0.0233436
\(461\) −1.02834 + 1.78114i −0.0478947 + 0.0829561i −0.888979 0.457948i \(-0.848585\pi\)
0.841084 + 0.540904i \(0.181918\pi\)
\(462\) −9.01842 + 15.6204i −0.419575 + 0.726725i
\(463\) 8.44935 0.392675 0.196337 0.980536i \(-0.437095\pi\)
0.196337 + 0.980536i \(0.437095\pi\)
\(464\) −1.28501 + 2.22571i −0.0596552 + 0.103326i
\(465\) −1.83997 3.18692i −0.0853266 0.147790i
\(466\) −1.22737 2.12586i −0.0568566 0.0984785i
\(467\) 33.5139 1.55084 0.775420 0.631446i \(-0.217538\pi\)
0.775420 + 0.631446i \(0.217538\pi\)
\(468\) 0 0
\(469\) −18.1008 −0.835818
\(470\) −0.728562 1.26191i −0.0336060 0.0582074i
\(471\) 5.00484 + 8.66864i 0.230611 + 0.399430i
\(472\) −9.12618 + 15.8070i −0.420066 + 0.727576i
\(473\) −1.25667 −0.0577817
\(474\) −8.98307 + 15.5591i −0.412606 + 0.714655i
\(475\) 0.217677 0.377027i 0.00998769 0.0172992i
\(476\) −6.90408 −0.316448
\(477\) 10.6479 18.4428i 0.487536 0.844437i
\(478\) 10.0831 + 17.4644i 0.461189 + 0.798802i
\(479\) −12.3656 21.4179i −0.565000 0.978608i −0.997050 0.0767587i \(-0.975543\pi\)
0.432050 0.901850i \(-0.357790\pi\)
\(480\) −3.23490 −0.147652
\(481\) 0 0
\(482\) −16.2524 −0.740275
\(483\) 3.95593 + 6.85187i 0.180001 + 0.311771i
\(484\) 4.77413 + 8.26903i 0.217006 + 0.375865i
\(485\) 0.995156 1.72366i 0.0451877 0.0782674i
\(486\) −14.5875 −0.661702
\(487\) −18.8778 + 32.6972i −0.855433 + 1.48165i 0.0208094 + 0.999783i \(0.493376\pi\)
−0.876243 + 0.481870i \(0.839958\pi\)
\(488\) −4.67360 + 8.09492i −0.211564 + 0.366440i
\(489\) 36.3086 1.64193
\(490\) 0.143104 0.247864i 0.00646479 0.0111973i
\(491\) −15.6555 27.1161i −0.706522 1.22373i −0.966139 0.258020i \(-0.916930\pi\)
0.259617 0.965712i \(-0.416404\pi\)
\(492\) −17.6712 30.6074i −0.796680 1.37989i
\(493\) 9.99761 0.450270
\(494\) 0 0
\(495\) −2.14914 −0.0965969
\(496\) −1.83997 3.18692i −0.0826171 0.143097i
\(497\) −10.2111 17.6861i −0.458031 0.793332i
\(498\) 1.44989 2.51128i 0.0649710 0.112533i
\(499\) −21.4873 −0.961902 −0.480951 0.876748i \(-0.659708\pi\)
−0.480951 + 0.876748i \(0.659708\pi\)
\(500\) 1.66541 2.88457i 0.0744793 0.129002i
\(501\) −18.1075 + 31.3632i −0.808984 + 1.40120i
\(502\) 19.0228 0.849031
\(503\) −18.7962 + 32.5560i −0.838081 + 1.45160i 0.0534164 + 0.998572i \(0.482989\pi\)
−0.891497 + 0.453026i \(0.850344\pi\)
\(504\) −6.50000 11.2583i −0.289533 0.501486i
\(505\) −1.64914 2.85640i −0.0733860 0.127108i
\(506\) −5.08815 −0.226196
\(507\) 0 0
\(508\) 13.3075 0.590425
\(509\) −8.55376 14.8155i −0.379139 0.656688i 0.611798 0.791014i \(-0.290446\pi\)
−0.990937 + 0.134326i \(0.957113\pi\)
\(510\) 0.480386 + 0.832052i 0.0212718 + 0.0368439i
\(511\) 7.93751 13.7482i 0.351135 0.608183i
\(512\) −6.22282 −0.275012
\(513\) −0.0941868 + 0.163136i −0.00415845 + 0.00720264i
\(514\) 5.70344 9.87865i 0.251568 0.435728i
\(515\) −0.336454 −0.0148259
\(516\) 0.451083 0.781298i 0.0198578 0.0343947i
\(517\) −15.6223 27.0586i −0.687068 1.19004i
\(518\) −5.37920 9.31705i −0.236348 0.409367i
\(519\) 48.3913 2.12414
\(520\) 0 0
\(521\) −19.8465 −0.869493 −0.434746 0.900553i \(-0.643162\pi\)
−0.434746 + 0.900553i \(0.643162\pi\)
\(522\) 3.80463 + 6.58981i 0.166524 + 0.288428i
\(523\) 5.71499 + 9.89865i 0.249899 + 0.432838i 0.963498 0.267717i \(-0.0862693\pi\)
−0.713599 + 0.700555i \(0.752936\pi\)
\(524\) −4.46197 + 7.72835i −0.194922 + 0.337615i
\(525\) 26.1564 1.14156
\(526\) −6.85474 + 11.8728i −0.298881 + 0.517677i
\(527\) −7.15764 + 12.3974i −0.311792 + 0.540039i
\(528\) −5.29590 −0.230474
\(529\) 10.3840 17.9857i 0.451480 0.781987i
\(530\) 1.02930 + 1.78281i 0.0447101 + 0.0774401i
\(531\) −6.94600 12.0308i −0.301431 0.522093i
\(532\) −0.281896 −0.0122218
\(533\) 0 0
\(534\) 5.19806 0.224942
\(535\) 0.403657 + 0.699155i 0.0174516 + 0.0302271i
\(536\) 10.3373 + 17.9047i 0.446503 + 0.773365i
\(537\) 12.8448 22.2479i 0.554295 0.960066i
\(538\) 5.18598 0.223584
\(539\) 3.06853 5.31485i 0.132171 0.228927i
\(540\) −0.358092 + 0.620234i −0.0154098 + 0.0266906i
\(541\) −16.1884 −0.695993 −0.347996 0.937496i \(-0.613138\pi\)
−0.347996 + 0.937496i \(0.613138\pi\)
\(542\) −2.58546 + 4.47814i −0.111055 + 0.192353i
\(543\) 23.5601 + 40.8073i 1.01106 + 1.75121i
\(544\) 6.29201 + 10.8981i 0.269768 + 0.467252i
\(545\) 3.87800 0.166115
\(546\) 0 0
\(547\) 5.33081 0.227929 0.113965 0.993485i \(-0.463645\pi\)
0.113965 + 0.993485i \(0.463645\pi\)
\(548\) −4.21983 7.30896i −0.180262 0.312223i
\(549\) −3.55711 6.16110i −0.151814 0.262949i
\(550\) −8.41066 + 14.5677i −0.358632 + 0.621168i
\(551\) 0.408206 0.0173902
\(552\) 4.51842 7.82613i 0.192317 0.333102i
\(553\) −11.7497 + 20.3510i −0.499647 + 0.865413i
\(554\) −10.7942 −0.458600
\(555\) 1.57942 2.73563i 0.0670425 0.116121i
\(556\) −9.97799 17.2824i −0.423161 0.732937i
\(557\) 3.69537 + 6.40058i 0.156578 + 0.271201i 0.933633 0.358232i \(-0.116620\pi\)
−0.777054 + 0.629433i \(0.783287\pi\)
\(558\) −10.8955 −0.461242
\(559\) 0 0
\(560\) −0.323044 −0.0136511
\(561\) 10.3007 + 17.8414i 0.434898 + 0.753265i
\(562\) −2.01961 3.49807i −0.0851923 0.147557i
\(563\) 4.73945 8.20896i 0.199744 0.345967i −0.748701 0.662907i \(-0.769322\pi\)
0.948445 + 0.316941i \(0.102656\pi\)
\(564\) 22.4306 0.944497
\(565\) 1.48792 2.57715i 0.0625972 0.108422i
\(566\) 8.87263 15.3678i 0.372944 0.645958i
\(567\) −25.8049 −1.08370
\(568\) −11.6630 + 20.2009i −0.489369 + 0.847612i
\(569\) 5.07188 + 8.78476i 0.212624 + 0.368276i 0.952535 0.304429i \(-0.0984656\pi\)
−0.739911 + 0.672705i \(0.765132\pi\)
\(570\) 0.0196143 + 0.0339730i 0.000821554 + 0.00142297i
\(571\) −14.0925 −0.589751 −0.294876 0.955536i \(-0.595278\pi\)
−0.294876 + 0.955536i \(0.595278\pi\)
\(572\) 0 0
\(573\) 32.4403 1.35521
\(574\) 10.9547 + 18.9741i 0.457242 + 0.791966i
\(575\) 3.68933 + 6.39011i 0.153856 + 0.266486i
\(576\) −3.65183 + 6.32516i −0.152160 + 0.263548i
\(577\) −25.1545 −1.04720 −0.523598 0.851965i \(-0.675411\pi\)
−0.523598 + 0.851965i \(0.675411\pi\)
\(578\) −4.94773 + 8.56972i −0.205798 + 0.356453i
\(579\) 15.2567 26.4253i 0.634045 1.09820i
\(580\) 1.55197 0.0644422
\(581\) 1.89642 3.28470i 0.0786768 0.136272i
\(582\) −7.26055 12.5756i −0.300960 0.521277i
\(583\) 22.0710 + 38.2281i 0.914087 + 1.58324i
\(584\) −18.1323 −0.750319
\(585\) 0 0
\(586\) 11.9860 0.495137
\(587\) 21.9177 + 37.9625i 0.904639 + 1.56688i 0.821402 + 0.570350i \(0.193192\pi\)
0.0832369 + 0.996530i \(0.473474\pi\)
\(588\) 2.20291 + 3.81555i 0.0908463 + 0.157350i
\(589\) −0.292249 + 0.506190i −0.0120419 + 0.0208572i
\(590\) 1.34290 0.0552861
\(591\) 0.629531 1.09038i 0.0258954 0.0448522i
\(592\) 1.57942 2.73563i 0.0649136 0.112434i
\(593\) 24.9965 1.02648 0.513242 0.858244i \(-0.328444\pi\)
0.513242 + 0.858244i \(0.328444\pi\)
\(594\) 3.63922 6.30331i 0.149319 0.258628i
\(595\) 0.628334 + 1.08831i 0.0257592 + 0.0446162i
\(596\) −2.94116 5.09423i −0.120474 0.208668i
\(597\) −25.8213 −1.05680
\(598\) 0 0
\(599\) −6.24027 −0.254971 −0.127485 0.991840i \(-0.540691\pi\)
−0.127485 + 0.991840i \(0.540691\pi\)
\(600\) −14.9378 25.8730i −0.609833 1.05626i
\(601\) −3.16487 5.48172i −0.129098 0.223604i 0.794229 0.607618i \(-0.207875\pi\)
−0.923327 + 0.384014i \(0.874541\pi\)
\(602\) −0.279635 + 0.484342i −0.0113971 + 0.0197403i
\(603\) −15.7356 −0.640802
\(604\) −2.67606 + 4.63506i −0.108887 + 0.188598i
\(605\) 0.868977 1.50511i 0.0353290 0.0611915i
\(606\) −24.0640 −0.977532
\(607\) 21.8240 37.8003i 0.885809 1.53427i 0.0410253 0.999158i \(-0.486938\pi\)
0.844784 0.535108i \(-0.179729\pi\)
\(608\) 0.256905 + 0.444973i 0.0104189 + 0.0180460i
\(609\) 12.2627 + 21.2396i 0.496910 + 0.860673i
\(610\) 0.687710 0.0278445
\(611\) 0 0
\(612\) −6.00192 −0.242613
\(613\) −12.9770 22.4769i −0.524137 0.907833i −0.999605 0.0280995i \(-0.991054\pi\)
0.475468 0.879733i \(-0.342279\pi\)
\(614\) −7.67025 13.2853i −0.309546 0.536150i
\(615\) −3.21648 + 5.57111i −0.129701 + 0.224649i
\(616\) 26.9463 1.08570
\(617\) 22.9698 39.7849i 0.924729 1.60168i 0.132733 0.991152i \(-0.457625\pi\)
0.791996 0.610526i \(-0.209042\pi\)
\(618\) −1.22737 + 2.12586i −0.0493719 + 0.0855146i
\(619\) −6.73556 −0.270725 −0.135363 0.990796i \(-0.543220\pi\)
−0.135363 + 0.990796i \(0.543220\pi\)
\(620\) −1.11111 + 1.92450i −0.0446234 + 0.0772899i
\(621\) −1.59634 2.76495i −0.0640590 0.110953i
\(622\) −0.108187 0.187386i −0.00433792 0.00751349i
\(623\) 6.79895 0.272394
\(624\) 0 0
\(625\) 24.0887 0.963549
\(626\) −9.38016 16.2469i −0.374907 0.649357i
\(627\) 0.420583 + 0.728471i 0.0167965 + 0.0290923i
\(628\) 3.02230 5.23478i 0.120603 0.208891i
\(629\) −12.2881 −0.489960
\(630\) −0.478230 + 0.828318i −0.0190531 + 0.0330010i
\(631\) 22.5499 39.0575i 0.897696 1.55486i 0.0672649 0.997735i \(-0.478573\pi\)
0.830432 0.557121i \(-0.188094\pi\)
\(632\) 26.8407 1.06767
\(633\) 9.86927 17.0941i 0.392268 0.679429i
\(634\) 5.61165 + 9.71965i 0.222867 + 0.386017i
\(635\) −1.21110 2.09769i −0.0480612 0.0832444i
\(636\) −31.6896 −1.25658
\(637\) 0 0
\(638\) −15.7724 −0.624435
\(639\) −8.87681 15.3751i −0.351161 0.608229i
\(640\) 1.08665 + 1.88214i 0.0429538 + 0.0743981i
\(641\) −16.2911 + 28.2169i −0.643458 + 1.11450i 0.341197 + 0.939992i \(0.389168\pi\)
−0.984655 + 0.174510i \(0.944166\pi\)
\(642\) 5.89008 0.232463
\(643\) 12.7877 22.1489i 0.504298 0.873469i −0.495690 0.868500i \(-0.665085\pi\)
0.999988 0.00496965i \(-0.00158190\pi\)
\(644\) 2.38889 4.13767i 0.0941353 0.163047i
\(645\) −0.164210 −0.00646578
\(646\) 0.0763014 0.132158i 0.00300204 0.00519968i
\(647\) 15.0858 + 26.1293i 0.593082 + 1.02725i 0.993814 + 0.111053i \(0.0354224\pi\)
−0.400732 + 0.916195i \(0.631244\pi\)
\(648\) 14.7371 + 25.5253i 0.578926 + 1.00273i
\(649\) 28.7952 1.13031
\(650\) 0 0
\(651\) −35.1172 −1.37635
\(652\) −10.9629 18.9883i −0.429341 0.743641i
\(653\) −18.4514 31.9587i −0.722058 1.25064i −0.960173 0.279405i \(-0.909863\pi\)
0.238115 0.971237i \(-0.423470\pi\)
\(654\) 14.1468 24.5029i 0.553182 0.958139i
\(655\) 1.62432 0.0634673
\(656\) −3.21648 + 5.57111i −0.125582 + 0.217515i
\(657\) 6.90030 11.9517i 0.269207 0.466279i
\(658\) −13.9051 −0.542079
\(659\) −11.8433 + 20.5132i −0.461350 + 0.799082i −0.999029 0.0440679i \(-0.985968\pi\)
0.537678 + 0.843150i \(0.319302\pi\)
\(660\) 1.59903 + 2.76960i 0.0622422 + 0.107807i
\(661\) −15.8795 27.5041i −0.617641 1.06979i −0.989915 0.141662i \(-0.954755\pi\)
0.372274 0.928123i \(-0.378578\pi\)
\(662\) 14.2916 0.555458
\(663\) 0 0
\(664\) −4.33214 −0.168120
\(665\) 0.0256551 + 0.0444360i 0.000994863 + 0.00172315i
\(666\) −4.67629 8.09958i −0.181203 0.313852i
\(667\) −3.45928 + 5.99165i −0.133944 + 0.231998i
\(668\) 21.8694 0.846152
\(669\) 2.53803 4.39600i 0.0981260 0.169959i
\(670\) 0.760553 1.31732i 0.0293827 0.0508924i
\(671\) 14.7463 0.569275
\(672\) −15.4351 + 26.7344i −0.595423 + 1.03130i
\(673\) 3.75116 + 6.49720i 0.144597 + 0.250449i 0.929222 0.369521i \(-0.120478\pi\)
−0.784626 + 0.619970i \(0.787145\pi\)
\(674\) −11.1664 19.3407i −0.430112 0.744976i
\(675\) −10.5550 −0.406261
\(676\) 0 0
\(677\) −35.0315 −1.34637 −0.673184 0.739475i \(-0.735074\pi\)
−0.673184 + 0.739475i \(0.735074\pi\)
\(678\) −10.8557 18.8026i −0.416911 0.722110i
\(679\) −9.49665 16.4487i −0.364448 0.631242i
\(680\) 0.717677 1.24305i 0.0275216 0.0476689i
\(681\) −15.6528 −0.599816
\(682\) 11.2920 19.5583i 0.432393 0.748927i
\(683\) −12.0417 + 20.8568i −0.460762 + 0.798063i −0.998999 0.0447302i \(-0.985757\pi\)
0.538237 + 0.842794i \(0.319091\pi\)
\(684\) −0.245061 −0.00937013
\(685\) −0.768086 + 1.33036i −0.0293471 + 0.0508306i
\(686\) −7.98092 13.8234i −0.304713 0.527778i
\(687\) 27.1591 + 47.0410i 1.03619 + 1.79473i
\(688\) −0.164210 −0.00626046
\(689\) 0 0
\(690\) −0.664874 −0.0253113
\(691\) 1.00724 + 1.74459i 0.0383171 + 0.0663672i 0.884548 0.466449i \(-0.154467\pi\)
−0.846231 + 0.532816i \(0.821134\pi\)
\(692\) −14.6112 25.3073i −0.555433 0.962039i
\(693\) −10.2545 + 17.7613i −0.389537 + 0.674697i
\(694\) −1.20583 −0.0457728
\(695\) −1.81618 + 3.14571i −0.0688915 + 0.119323i
\(696\) 14.0063 24.2597i 0.530909 0.919561i
\(697\) 25.0248 0.947880
\(698\) 5.68814 9.85214i 0.215299 0.372909i
\(699\) −3.43900 5.95652i −0.130075 0.225296i
\(700\) −7.89762 13.6791i −0.298502 0.517020i
\(701\) −48.8189 −1.84387 −0.921933 0.387350i \(-0.873390\pi\)
−0.921933 + 0.387350i \(0.873390\pi\)
\(702\) 0 0
\(703\) −0.501729 −0.0189231
\(704\) −7.56949 13.1107i −0.285286 0.494130i
\(705\) −2.04138 3.53578i −0.0768830 0.133165i
\(706\) 2.87435 4.97853i 0.108178 0.187369i
\(707\) −31.4752 −1.18375
\(708\) −10.3361 + 17.9026i −0.388454 + 0.672822i
\(709\) −10.4030 + 18.0185i −0.390693 + 0.676699i −0.992541 0.121911i \(-0.961098\pi\)
0.601848 + 0.798610i \(0.294431\pi\)
\(710\) 1.71618 0.0644073
\(711\) −10.2143 + 17.6917i −0.383067 + 0.663492i
\(712\) −3.88285 6.72529i −0.145516 0.252041i
\(713\) −4.95324 8.57926i −0.185500 0.321296i
\(714\) 9.16852 0.343123
\(715\) 0 0
\(716\) −15.5133 −0.579761
\(717\) 28.2521 + 48.9341i 1.05509 + 1.82748i
\(718\) −7.97339 13.8103i −0.297564 0.515396i
\(719\) −10.7153 + 18.5594i −0.399613 + 0.692149i −0.993678 0.112267i \(-0.964189\pi\)
0.594065 + 0.804417i \(0.297522\pi\)
\(720\) −0.280831 −0.0104660
\(721\) −1.60537 + 2.78058i −0.0597870 + 0.103554i
\(722\) −7.61529 + 13.1901i −0.283412 + 0.490884i
\(723\) −45.5381 −1.69358
\(724\) 14.2274 24.6425i 0.528756 0.915832i
\(725\) 11.4363 + 19.8083i 0.424734 + 0.735661i
\(726\) −6.33997 10.9812i −0.235298 0.407549i
\(727\) 13.4862 0.500175 0.250088 0.968223i \(-0.419541\pi\)
0.250088 + 0.968223i \(0.419541\pi\)
\(728\) 0 0
\(729\) −8.02715 −0.297302
\(730\) 0.667030 + 1.15533i 0.0246879 + 0.0427607i
\(731\) 0.319396 + 0.553210i 0.0118133 + 0.0204612i
\(732\) −5.29321 + 9.16811i −0.195643 + 0.338863i
\(733\) 43.5424 1.60828 0.804138 0.594443i \(-0.202627\pi\)
0.804138 + 0.594443i \(0.202627\pi\)
\(734\) 0.434584 0.752721i 0.0160408 0.0277834i
\(735\) 0.400969 0.694498i 0.0147900 0.0256170i
\(736\) −8.70841 −0.320996
\(737\) 16.3083 28.2468i 0.600723 1.04048i
\(738\) 9.52326 + 16.4948i 0.350556 + 0.607181i
\(739\) 10.0271 + 17.3675i 0.368855 + 0.638875i 0.989387 0.145306i \(-0.0464167\pi\)
−0.620532 + 0.784181i \(0.713083\pi\)
\(740\) −1.90754 −0.0701226
\(741\) 0 0
\(742\) 19.6450 0.721191
\(743\) −16.5843 28.7248i −0.608418 1.05381i −0.991501 0.130096i \(-0.958471\pi\)
0.383084 0.923714i \(-0.374862\pi\)
\(744\) 20.0553 + 34.7367i 0.735261 + 1.27351i
\(745\) −0.535344 + 0.927243i −0.0196135 + 0.0339715i
\(746\) 4.91617 0.179994
\(747\) 1.64861 2.85548i 0.0603196 0.104477i
\(748\) 6.22037 10.7740i 0.227439 0.393936i
\(749\) 7.70410 0.281502
\(750\) −2.21164 + 3.83067i −0.0807575 + 0.139876i
\(751\) −19.6407 34.0187i −0.716700 1.24136i −0.962300 0.271989i \(-0.912318\pi\)
0.245601 0.969371i \(-0.421015\pi\)
\(752\) −2.04138 3.53578i −0.0744416 0.128937i
\(753\) 53.3008 1.94239
\(754\) 0 0
\(755\) 0.974181 0.0354541
\(756\) 3.41723 + 5.91882i 0.124283 + 0.215265i
\(757\) 23.3213 + 40.3937i 0.847628 + 1.46813i 0.883320 + 0.468771i \(0.155303\pi\)
−0.0356920 + 0.999363i \(0.511364\pi\)
\(758\) 0.965853 1.67291i 0.0350813 0.0607627i
\(759\) −14.2567 −0.517484
\(760\) 0.0293030 0.0507543i 0.00106293 0.00184105i
\(761\) −10.9492 + 18.9646i −0.396909 + 0.687467i −0.993343 0.115196i \(-0.963250\pi\)
0.596434 + 0.802662i \(0.296584\pi\)
\(762\) −17.6722 −0.640195
\(763\) 18.5036 32.0493i 0.669877 1.16026i
\(764\) −9.79494 16.9653i −0.354368 0.613784i
\(765\) 0.546229 + 0.946096i 0.0197489 + 0.0342062i
\(766\) −24.3720 −0.880595
\(767\) 0 0
\(768\) 31.8756 1.15021
\(769\) 23.3548 + 40.4517i 0.842196 + 1.45873i 0.888035 + 0.459777i \(0.152071\pi\)
−0.0458390 + 0.998949i \(0.514596\pi\)
\(770\) −0.991271 1.71693i −0.0357229 0.0618739i
\(771\) 15.9807 27.6794i 0.575530 0.996848i
\(772\) −18.4263 −0.663175
\(773\) −15.1208 + 26.1900i −0.543857 + 0.941989i 0.454820 + 0.890583i \(0.349703\pi\)
−0.998678 + 0.0514055i \(0.983630\pi\)