Properties

Label 169.2.e.b.23.5
Level $169$
Weight $2$
Character 169.23
Analytic conductor $1.349$
Analytic rank $0$
Dimension $12$
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] = [169,2,Mod(23,169)]
 
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([5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), 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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.5
Root \(-1.56052 - 0.900969i\) of defining polynomial
Character \(\chi\) \(=\) 169.23
Dual form 169.2.e.b.147.5

$q$-expansion

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

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.694498 0.400969i 0.491085 0.283528i −0.233940 0.972251i \(-0.575162\pi\)
0.725024 + 0.688723i \(0.241829\pi\)
\(3\) 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
\(5\) 0.246980i 0.110453i 0.998474 + 0.0552263i \(0.0175880\pi\)
−0.998474 + 0.0552263i \(0.982412\pi\)
\(6\) 1.56052 + 0.900969i 0.637081 + 0.367819i
\(7\) −2.04113 1.17845i −0.771475 0.445411i 0.0619254 0.998081i \(-0.480276\pi\)
−0.833401 + 0.552669i \(0.813609\pi\)
\(8\) 2.69202i 0.951773i
\(9\) −1.02446 + 1.77441i −0.341486 + 0.591471i
\(10\) 0.0990311 + 0.171527i 0.0313164 + 0.0542416i
\(11\) 3.67799 2.12349i 1.10896 0.640256i 0.170397 0.985375i \(-0.445495\pi\)
0.938559 + 0.345119i \(0.112161\pi\)
\(12\) −3.04892 −0.880147
\(13\) 0 0
\(14\) −1.89008 −0.505146
\(15\) −0.480608 + 0.277479i −0.124092 + 0.0716448i
\(16\) −0.277479 0.480608i −0.0693698 0.120152i
\(17\) 1.07942 1.86960i 0.261797 0.453446i −0.704922 0.709284i \(-0.749018\pi\)
0.966720 + 0.255839i \(0.0823516\pi\)
\(18\) 1.64310i 0.387283i
\(19\) 0.0763367 + 0.0440730i 0.0175128 + 0.0101110i 0.508731 0.860926i \(-0.330115\pi\)
−0.491218 + 0.871037i \(0.663448\pi\)
\(20\) −0.290227 0.167563i −0.0648968 0.0374682i
\(21\) 5.29590i 1.15566i
\(22\) 1.70291 2.94952i 0.363061 0.628840i
\(23\) 0.746980 + 1.29381i 0.155756 + 0.269777i 0.933334 0.359009i \(-0.116885\pi\)
−0.777578 + 0.628786i \(0.783552\pi\)
\(24\) −5.23852 + 3.02446i −1.06931 + 0.617365i
\(25\) 4.93900 0.987800
\(26\) 0 0
\(27\) 2.13706 0.411278
\(28\) 2.76960 1.59903i 0.523406 0.302188i
\(29\) −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
\(31\) 6.63102i 1.19097i −0.803368 0.595483i \(-0.796961\pi\)
0.803368 0.595483i \(-0.203039\pi\)
\(32\) −5.04814 2.91454i −0.892393 0.515223i
\(33\) 8.26437 + 4.77144i 1.43864 + 0.830601i
\(34\) 1.73125i 0.296907i
\(35\) 0.291053 0.504118i 0.0491969 0.0852115i
\(36\) −1.39008 2.40770i −0.231681 0.401283i
\(37\) −4.92944 + 2.84601i −0.810394 + 0.467881i −0.847093 0.531445i \(-0.821649\pi\)
0.0366986 + 0.999326i \(0.488316\pi\)
\(38\) 0.0706876 0.0114670
\(39\) 0 0
\(40\) −0.664874 −0.105126
\(41\) −10.0388 + 5.79590i −1.56780 + 0.905167i −0.571370 + 0.820693i \(0.693588\pi\)
−0.996426 + 0.0844742i \(0.973079\pi\)
\(42\) −2.12349 3.67799i −0.327662 0.567527i
\(43\) −0.147948 + 0.256254i −0.0225619 + 0.0390784i −0.877086 0.480334i \(-0.840516\pi\)
0.854524 + 0.519412i \(0.173849\pi\)
\(44\) 5.76271i 0.868761i
\(45\) −0.438244 0.253020i −0.0653296 0.0377181i
\(46\) 1.03755 + 0.599031i 0.152979 + 0.0883223i
\(47\) 7.35690i 1.07311i 0.843864 + 0.536557i \(0.180275\pi\)
−0.843864 + 0.536557i \(0.819725\pi\)
\(48\) 0.623490 1.07992i 0.0899930 0.155872i
\(49\) −0.722521 1.25144i −0.103217 0.178778i
\(50\) 3.43013 1.98039i 0.485093 0.280069i
\(51\) 4.85086 0.679256
\(52\) 0 0
\(53\) −10.3937 −1.42769 −0.713844 0.700304i \(-0.753048\pi\)
−0.713844 + 0.700304i \(0.753048\pi\)
\(54\) 1.48419 0.856896i 0.201972 0.116609i
\(55\) 0.524459 + 0.908389i 0.0707180 + 0.122487i
\(56\) 3.17241 5.49477i 0.423931 0.734270i
\(57\) 0.198062i 0.0262340i
\(58\) −3.21624 1.85690i −0.422313 0.243822i
\(59\) −5.87180 3.39008i −0.764443 0.441351i 0.0664458 0.997790i \(-0.478834\pi\)
−0.830889 + 0.556439i \(0.812167\pi\)
\(60\) 0.753020i 0.0972145i
\(61\) −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
\(63\) 4.18211 2.41454i 0.526896 0.304204i
\(64\) −3.56465 −0.445581
\(65\) 0 0
\(66\) 7.65279 0.941994
\(67\) 6.65102 3.83997i 0.812552 0.469127i −0.0352895 0.999377i \(-0.511235\pi\)
0.847841 + 0.530250i \(0.177902\pi\)
\(68\) 1.46466 + 2.53686i 0.177616 + 0.307639i
\(69\) −1.67845 + 2.90716i −0.202061 + 0.349981i
\(70\) 0.466812i 0.0557947i
\(71\) 7.50400 + 4.33244i 0.890561 + 0.514166i 0.874126 0.485699i \(-0.161435\pi\)
0.0164351 + 0.999865i \(0.494768\pi\)
\(72\) −4.77676 2.75786i −0.562947 0.325017i
\(73\) 6.73556i 0.788338i −0.919038 0.394169i \(-0.871032\pi\)
0.919038 0.394169i \(-0.128968\pi\)
\(74\) −2.28232 + 3.95310i −0.265315 + 0.459539i
\(75\) 5.54892 + 9.61101i 0.640734 + 1.10978i
\(76\) −0.103581 + 0.0598025i −0.0118815 + 0.00685981i
\(77\) −10.0097 −1.14071
\(78\) 0 0
\(79\) 9.97046 1.12176 0.560882 0.827896i \(-0.310462\pi\)
0.560882 + 0.827896i \(0.310462\pi\)
\(80\) 0.118700 0.0685317i 0.0132711 0.00766207i
\(81\) 5.47434 + 9.48184i 0.608261 + 1.05354i
\(82\) −4.64795 + 8.05048i −0.513280 + 0.889027i
\(83\) 1.60925i 0.176638i 0.996092 + 0.0883192i \(0.0281495\pi\)
−0.996092 + 0.0883192i \(0.971850\pi\)
\(84\) 6.22324 + 3.59299i 0.679011 + 0.392027i
\(85\) 0.461754 + 0.266594i 0.0500843 + 0.0289162i
\(86\) 0.237291i 0.0255877i
\(87\) 5.20291 9.01170i 0.557810 0.966156i
\(88\) 5.71648 + 9.90123i 0.609379 + 1.05548i
\(89\) 2.49823 1.44235i 0.264812 0.152889i −0.361716 0.932288i \(-0.617809\pi\)
0.626528 + 0.779399i \(0.284476\pi\)
\(90\) −0.405813 −0.0427765
\(91\) 0 0
\(92\) −2.02715 −0.211345
\(93\) 12.9036 7.44989i 1.33804 0.772517i
\(94\) 2.94989 + 5.10935i 0.304258 + 0.526990i
\(95\) −0.0108851 + 0.0188536i −0.00111679 + 0.00193434i
\(96\) 13.0978i 1.33679i
\(97\) 6.97896 + 4.02930i 0.708606 + 0.409114i 0.810545 0.585677i \(-0.199171\pi\)
−0.101939 + 0.994791i \(0.532505\pi\)
\(98\) −1.00358 0.579417i −0.101377 0.0585299i
\(99\) 8.70171i 0.874555i
\(100\) −3.35086 + 5.80385i −0.335086 + 0.580385i
\(101\) −6.67725 11.5653i −0.664411 1.15079i −0.979445 0.201714i \(-0.935349\pi\)
0.315033 0.949081i \(-0.397984\pi\)
\(102\) 3.36891 1.94504i 0.333572 0.192588i
\(103\) −1.36227 −0.134229 −0.0671144 0.997745i \(-0.521379\pi\)
−0.0671144 + 0.997745i \(0.521379\pi\)
\(104\) 0 0
\(105\) 1.30798 0.127646
\(106\) −7.21843 + 4.16756i −0.701116 + 0.404789i
\(107\) −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
\(109\) 15.7017i 1.50395i 0.659191 + 0.751976i \(0.270899\pi\)
−0.659191 + 0.751976i \(0.729101\pi\)
\(110\) 0.728471 + 0.420583i 0.0694570 + 0.0401010i
\(111\) −11.0763 6.39493i −1.05132 0.606980i
\(112\) 1.30798i 0.123592i
\(113\) −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
\(115\) −0.319544 + 0.184489i −0.0297976 + 0.0172037i
\(116\) 6.28382 0.583438
\(117\) 0 0
\(118\) −5.43727 −0.500541
\(119\) −4.40646 + 2.54407i −0.403940 + 0.233215i
\(120\) −0.746980 1.29381i −0.0681896 0.118108i
\(121\) 3.51842 6.09408i 0.319856 0.554007i
\(122\) 2.78448i 0.252095i
\(123\) −22.5570 13.0233i −2.03389 1.17427i
\(124\) 7.79216 + 4.49880i 0.699756 + 0.404004i
\(125\) 2.45473i 0.219558i
\(126\) 1.93631 3.35379i 0.172500 0.298780i
\(127\) −4.90366 8.49338i −0.435129 0.753666i 0.562177 0.827017i \(-0.309964\pi\)
−0.997306 + 0.0733510i \(0.976631\pi\)
\(128\) 7.62063 4.39977i 0.673575 0.388889i
\(129\) −0.664874 −0.0585389
\(130\) 0 0
\(131\) −6.57673 −0.574611 −0.287306 0.957839i \(-0.592760\pi\)
−0.287306 + 0.957839i \(0.592760\pi\)
\(132\) −11.2139 + 6.47434i −0.976044 + 0.563519i
\(133\) −0.103875 0.179918i −0.00900715 0.0156008i
\(134\) 3.07942 5.33371i 0.266021 0.460762i
\(135\) 0.527811i 0.0454267i
\(136\) 5.03302 + 2.90581i 0.431578 + 0.249171i
\(137\) 5.38653 + 3.10992i 0.460203 + 0.265698i 0.712129 0.702048i \(-0.247731\pi\)
−0.251927 + 0.967746i \(0.581064\pi\)
\(138\) 2.69202i 0.229160i
\(139\) 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
\(141\) −14.3161 + 8.26540i −1.20563 + 0.696072i
\(142\) 6.94869 0.583121
\(143\) 0 0
\(144\) 1.13706 0.0947553
\(145\) 0.990532 0.571884i 0.0822592 0.0474924i
\(146\) −2.70075 4.67784i −0.223516 0.387141i
\(147\) 1.62349 2.81197i 0.133903 0.231927i
\(148\) 7.72348i 0.634866i
\(149\) −3.75433 2.16756i −0.307567 0.177574i 0.338270 0.941049i \(-0.390158\pi\)
−0.645837 + 0.763475i \(0.723491\pi\)
\(150\) 7.70743 + 4.44989i 0.629309 + 0.363332i
\(151\) 3.94438i 0.320989i −0.987037 0.160494i \(-0.948691\pi\)
0.987037 0.160494i \(-0.0513089\pi\)
\(152\) −0.118645 + 0.205500i −0.00962342 + 0.0166682i
\(153\) 2.21164 + 3.83067i 0.178800 + 0.309691i
\(154\) −6.95171 + 4.01357i −0.560185 + 0.323423i
\(155\) 1.63773 0.131545
\(156\) 0 0
\(157\) 4.45473 0.355526 0.177763 0.984073i \(-0.443114\pi\)
0.177763 + 0.984073i \(0.443114\pi\)
\(158\) 6.92447 3.99784i 0.550881 0.318051i
\(159\) −11.6773 20.2256i −0.926066 1.60399i
\(160\) 0.719833 1.24679i 0.0569078 0.0985671i
\(161\) 3.52111i 0.277502i
\(162\) 7.60385 + 4.39008i 0.597415 + 0.344918i
\(163\) 13.9940 + 8.07942i 1.09609 + 0.632829i 0.935192 0.354142i \(-0.115227\pi\)
0.160900 + 0.986971i \(0.448560\pi\)
\(164\) 15.7289i 1.22822i
\(165\) −1.17845 + 2.04113i −0.0917420 + 0.158902i
\(166\) 0.645260 + 1.11762i 0.0500819 + 0.0867444i
\(167\) −13.9579 + 8.05861i −1.08010 + 0.623594i −0.930922 0.365217i \(-0.880995\pi\)
−0.149174 + 0.988811i \(0.547661\pi\)
\(168\) 14.2567 1.09993
\(169\) 0 0
\(170\) 0.427583 0.0327942
\(171\) −0.156408 + 0.0903019i −0.0119608 + 0.00690556i
\(172\) −0.200751 0.347710i −0.0153071 0.0265127i
\(173\) −10.7681 + 18.6509i −0.818682 + 1.41800i 0.0879709 + 0.996123i \(0.471962\pi\)
−0.906653 + 0.421876i \(0.861372\pi\)
\(174\) 8.34481i 0.632619i
\(175\) −10.0812 5.82036i −0.762063 0.439978i
\(176\) −2.04113 1.17845i −0.153856 0.0888289i
\(177\) 15.2349i 1.14513i
\(178\) 1.15668 2.00342i 0.0866967 0.150163i
\(179\) 5.71648 + 9.90123i 0.427270 + 0.740053i 0.996629 0.0820356i \(-0.0261421\pi\)
−0.569360 + 0.822089i \(0.692809\pi\)
\(180\) 0.594652 0.343322i 0.0443227 0.0255897i
\(181\) −20.9705 −1.55872 −0.779361 0.626575i \(-0.784456\pi\)
−0.779361 + 0.626575i \(0.784456\pi\)
\(182\) 0 0
\(183\) −7.80194 −0.576736
\(184\) −3.48296 + 2.01089i −0.256767 + 0.148244i
\(185\) −0.702907 1.21747i −0.0516787 0.0895102i
\(186\) 5.97434 10.3479i 0.438060 0.758743i
\(187\) 9.16852i 0.670469i
\(188\) −8.64513 4.99127i −0.630511 0.364026i
\(189\) −4.36203 2.51842i −0.317291 0.183188i
\(190\) 0.0174584i 0.00126657i
\(191\) 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
\(193\) 11.7604 6.78986i 0.846530 0.488745i −0.0129483 0.999916i \(-0.504122\pi\)
0.859479 + 0.511172i \(0.170788\pi\)
\(194\) 6.46250 0.463980
\(195\) 0 0
\(196\) 1.96077 0.140055
\(197\) −0.485264 + 0.280167i −0.0345736 + 0.0199611i −0.517187 0.855872i \(-0.673021\pi\)
0.482614 + 0.875833i \(0.339688\pi\)
\(198\) 3.48911 + 6.04332i 0.247961 + 0.429480i
\(199\) 5.74578 9.95199i 0.407308 0.705478i −0.587279 0.809384i \(-0.699801\pi\)
0.994587 + 0.103907i \(0.0331343\pi\)
\(200\) 13.2959i 0.940162i
\(201\) 14.9447 + 8.62833i 1.05412 + 0.608596i
\(202\) −9.27468 5.35474i −0.652564 0.376758i
\(203\) 10.9148i 0.766071i
\(204\) −3.29105 + 5.70027i −0.230420 + 0.399099i
\(205\) −1.43147 2.47938i −0.0999781 0.173167i
\(206\) −0.946096 + 0.546229i −0.0659177 + 0.0380576i
\(207\) −3.06100 −0.212754
\(208\) 0 0
\(209\) 0.374354 0.0258946
\(210\) 0.908389 0.524459i 0.0626848 0.0361911i
\(211\) −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
\(213\) 19.4698i 1.33405i
\(214\) −2.27014 1.31067i −0.155184 0.0895953i
\(215\) −0.0632896 0.0365403i −0.00431631 0.00249202i
\(216\) 5.75302i 0.391443i
\(217\) −7.81431 + 13.5348i −0.530470 + 0.918801i
\(218\) 6.29590 + 10.9048i 0.426412 + 0.738567i
\(219\) 13.1070 7.56734i 0.885690 0.511353i
\(220\) −1.42327 −0.0959570
\(221\) 0 0
\(222\) −10.2567 −0.688383
\(223\) −1.95640 + 1.12953i −0.131011 + 0.0756390i −0.564073 0.825725i \(-0.690766\pi\)
0.433062 + 0.901364i \(0.357433\pi\)
\(224\) 6.86927 + 11.8979i 0.458973 + 0.794964i
\(225\) −5.05980 + 8.76383i −0.337320 + 0.584256i
\(226\) 9.66248i 0.642739i
\(227\) 6.03286 + 3.48307i 0.400415 + 0.231180i 0.686663 0.726976i \(-0.259075\pi\)
−0.286248 + 0.958156i \(0.592408\pi\)
\(228\) −0.232744 0.134375i −0.0154139 0.00889920i
\(229\) 24.1739i 1.59746i 0.601692 + 0.798728i \(0.294493\pi\)
−0.601692 + 0.798728i \(0.705507\pi\)
\(230\) −0.147948 + 0.256254i −0.00975543 + 0.0168969i
\(231\) −11.2458 19.4783i −0.739918 1.28158i
\(232\) 10.7966 6.23341i 0.708830 0.409243i
\(233\) 3.06100 0.200533 0.100266 0.994961i \(-0.468031\pi\)
0.100266 + 0.994961i \(0.468031\pi\)
\(234\) 0 0
\(235\) −1.81700 −0.118528
\(236\) 7.96742 4.59999i 0.518635 0.299434i
\(237\) 11.2017 + 19.4019i 0.727629 + 1.26029i
\(238\) −2.04019 + 3.53371i −0.132246 + 0.229056i
\(239\) 25.1468i 1.62661i −0.581839 0.813304i \(-0.697667\pi\)
0.581839 0.813304i \(-0.302333\pi\)
\(240\) 0.266717 + 0.153989i 0.0172165 + 0.00993996i
\(241\) −17.5512 10.1332i −1.13057 0.652735i −0.186492 0.982456i \(-0.559712\pi\)
−0.944078 + 0.329721i \(0.893045\pi\)
\(242\) 5.64310i 0.362752i
\(243\) −9.09515 + 15.7533i −0.583454 + 1.01057i
\(244\) −2.35570 4.08019i −0.150808 0.261207i
\(245\) 0.309081 0.178448i 0.0197465 0.0114006i
\(246\) −20.8877 −1.33175
\(247\) 0 0
\(248\) 17.8509 1.13353
\(249\) −3.13151 + 1.80798i −0.198451 + 0.114576i
\(250\) 0.984271 + 1.70481i 0.0622507 + 0.107821i
\(251\) −11.8605 + 20.5431i −0.748631 + 1.29667i 0.199848 + 0.979827i \(0.435955\pi\)
−0.948479 + 0.316840i \(0.897378\pi\)
\(252\) 6.55257i 0.412773i
\(253\) 5.49477 + 3.17241i 0.345453 + 0.199448i
\(254\) −6.81116 3.93243i −0.427370 0.246742i
\(255\) 1.19806i 0.0750256i
\(256\) 7.09299 12.2854i 0.443312 0.767839i
\(257\) 7.11207 + 12.3185i 0.443639 + 0.768405i 0.997956 0.0639003i \(-0.0203540\pi\)
−0.554317 + 0.832305i \(0.687021\pi\)
\(258\) −0.461754 + 0.266594i −0.0287476 + 0.0165974i
\(259\) 13.4155 0.833599
\(260\) 0 0
\(261\) 9.48858 0.587329
\(262\) −4.56753 + 2.63706i −0.282183 + 0.162918i
\(263\) 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
\(265\) 2.56704i 0.157692i
\(266\) −0.144283 0.0833017i −0.00884654 0.00510755i
\(267\) 5.61347 + 3.24094i 0.343539 + 0.198342i
\(268\) 10.4209i 0.636556i
\(269\) 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
\(271\) −5.58415 + 3.22401i −0.339213 + 0.195845i −0.659924 0.751332i \(-0.729412\pi\)
0.320711 + 0.947177i \(0.396078\pi\)
\(272\) −1.19806 −0.0726432
\(273\) 0 0
\(274\) 4.98792 0.301331
\(275\) 18.1656 10.4879i 1.09543 0.632445i
\(276\) −2.27748 3.94471i −0.137088 0.237444i
\(277\) 6.73005 11.6568i 0.404370 0.700389i −0.589878 0.807492i \(-0.700824\pi\)
0.994248 + 0.107103i \(0.0341576\pi\)
\(278\) 11.7942i 0.707367i
\(279\) 11.7662 + 6.79321i 0.704423 + 0.406699i
\(280\) 1.35710 + 0.783520i 0.0811020 + 0.0468243i
\(281\) 5.03684i 0.300472i −0.988650 0.150236i \(-0.951997\pi\)
0.988650 0.150236i \(-0.0480034\pi\)
\(282\) −6.62833 + 11.4806i −0.394712 + 0.683660i
\(283\) 11.0640 + 19.1634i 0.657686 + 1.13914i 0.981213 + 0.192926i \(0.0617977\pi\)
−0.323528 + 0.946219i \(0.604869\pi\)
\(284\) −10.1821 + 5.87867i −0.604199 + 0.348835i
\(285\) −0.0489173 −0.00289761
\(286\) 0 0
\(287\) 27.3207 1.61269
\(288\) 10.3432 5.97166i 0.609480 0.351883i
\(289\) 6.16972 + 10.6863i 0.362925 + 0.628604i
\(290\) 0.458615 0.794345i 0.0269308 0.0466456i
\(291\) 18.1075i 1.06148i
\(292\) 7.91500 + 4.56973i 0.463190 + 0.267423i
\(293\) 12.9439 + 7.47315i 0.756189 + 0.436586i 0.827926 0.560838i \(-0.189521\pi\)
−0.0717367 + 0.997424i \(0.522854\pi\)
\(294\) 2.60388i 0.151861i
\(295\) 0.837282 1.45021i 0.0487484 0.0844347i
\(296\) −7.66152 13.2701i −0.445317 0.771312i
\(297\) 7.86010 4.53803i 0.456089 0.263323i
\(298\) −3.47650 −0.201388
\(299\) 0 0
\(300\) −15.0586 −0.869409
\(301\) 0.603965 0.348699i 0.0348119 0.0200987i
\(302\) −1.58157 2.73936i −0.0910093 0.157633i
\(303\) 15.0036 25.9871i 0.861937 1.49292i
\(304\) 0.0489173i 0.00280560i
\(305\) −0.742669 0.428780i −0.0425251 0.0245519i
\(306\) 3.07196 + 1.77359i 0.175612 + 0.101390i
\(307\) 19.1293i 1.09177i −0.837861 0.545883i \(-0.816194\pi\)
0.837861 0.545883i \(-0.183806\pi\)
\(308\) 6.79105 11.7624i 0.386956 0.670228i
\(309\) −1.53050 2.65090i −0.0870671 0.150805i
\(310\) 1.13740 0.656678i 0.0645999 0.0372968i
\(311\) 0.269815 0.0152998 0.00764990 0.999971i \(-0.497565\pi\)
0.00764990 + 0.999971i \(0.497565\pi\)
\(312\) 0 0
\(313\) −23.3937 −1.32229 −0.661146 0.750257i \(-0.729930\pi\)
−0.661146 + 0.750257i \(0.729930\pi\)
\(314\) 3.09380 1.78621i 0.174593 0.100802i
\(315\) 0.596343 + 1.03290i 0.0336001 + 0.0581971i
\(316\) −6.76444 + 11.7164i −0.380529 + 0.659096i
\(317\) 13.9952i 0.786050i −0.919528 0.393025i \(-0.871429\pi\)
0.919528 0.393025i \(-0.128571\pi\)
\(318\) −16.2197 9.36443i −0.909554 0.525131i
\(319\) −17.0329 9.83393i −0.953657 0.550594i
\(320\) 0.880395i 0.0492156i
\(321\) 3.67241 6.36080i 0.204974 0.355025i
\(322\) −1.41185 2.44540i −0.0786795 0.136277i
\(323\) 0.164798 0.0951463i 0.00916962 0.00529408i
\(324\) −14.8562 −0.825346
\(325\) 0 0
\(326\) 12.9584 0.717698
\(327\) −30.5546 + 17.6407i −1.68967 + 0.975534i
\(328\) −15.6027 27.0246i −0.861514 1.49219i
\(329\) 8.66972 15.0164i 0.477977 0.827881i
\(330\) 1.89008i 0.104046i
\(331\) −15.4337 8.91066i −0.848314 0.489774i 0.0117680 0.999931i \(-0.496254\pi\)
−0.860081 + 0.510157i \(0.829587\pi\)
\(332\) −1.89104 1.09179i −0.103784 0.0599200i
\(333\) 11.6625i 0.639100i
\(334\) −6.46250 + 11.1934i −0.353612 + 0.612474i
\(335\) 0.948394 + 1.64267i 0.0518163 + 0.0897485i
\(336\) −2.54525 + 1.46950i −0.138855 + 0.0801678i
\(337\) 27.8485 1.51700 0.758501 0.651672i \(-0.225932\pi\)
0.758501 + 0.651672i \(0.225932\pi\)
\(338\) 0 0
\(339\) −27.0737 −1.47044
\(340\) −0.626552 + 0.361740i −0.0339796 + 0.0196181i
\(341\) −14.0809 24.3888i −0.762524 1.32073i
\(342\) −0.0724165 + 0.125429i −0.00391584 + 0.00678243i
\(343\) 19.9041i 1.07472i
\(344\) −0.689842 0.398280i −0.0371938 0.0214738i
\(345\) −0.718009 0.414542i −0.0386563 0.0223182i
\(346\) 17.2707i 0.928477i
\(347\) −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
\(349\) 12.2854 7.09299i 0.657623 0.379679i −0.133747 0.991015i \(-0.542701\pi\)
0.791371 + 0.611336i \(0.209368\pi\)
\(350\) −9.33513 −0.498983
\(351\) 0 0
\(352\) −24.7560 −1.31950
\(353\) −6.20812 + 3.58426i −0.330425 + 0.190771i −0.656030 0.754735i \(-0.727765\pi\)
0.325605 + 0.945506i \(0.394432\pi\)
\(354\) −6.10872 10.5806i −0.324675 0.562353i
\(355\) −1.07002 + 1.85334i −0.0567910 + 0.0983648i
\(356\) 3.91425i 0.207455i
\(357\) −9.90123 5.71648i −0.524029 0.302548i
\(358\) 7.94017 + 4.58426i 0.419651 + 0.242286i
\(359\) 19.8853i 1.04951i −0.851255 0.524753i \(-0.824158\pi\)
0.851255 0.524753i \(-0.175842\pi\)
\(360\) 0.681136 1.17976i 0.0358990 0.0621790i
\(361\) −9.49612 16.4478i −0.499796 0.865671i
\(362\) −14.5640 + 8.40850i −0.765464 + 0.441941i
\(363\) 15.8116 0.829895
\(364\) 0 0
\(365\) 1.66355 0.0870740
\(366\) −5.41843 + 3.12833i −0.283226 + 0.163521i
\(367\) −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
\(369\) 23.7506i 1.23641i
\(370\) −0.976335 0.563687i −0.0507572 0.0293047i
\(371\) 21.2150 + 12.2485i 1.10143 + 0.635909i
\(372\) 20.2174i 1.04823i
\(373\) 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
\(375\) −4.77676 + 2.75786i −0.246671 + 0.142416i
\(376\) −19.8049 −1.02136
\(377\) 0 0
\(378\) −4.03923 −0.207756
\(379\) −2.08608 + 1.20440i −0.107155 + 0.0618658i −0.552620 0.833434i \(-0.686372\pi\)
0.445465 + 0.895299i \(0.353038\pi\)
\(380\) −0.0147700 0.0255824i −0.000757685 0.00131235i
\(381\) 11.0184 19.0845i 0.564491 0.977726i
\(382\) 11.5778i 0.592371i
\(383\) 26.3197 + 15.1957i 1.34487 + 0.776462i 0.987518 0.157506i \(-0.0503455\pi\)
0.357354 + 0.933969i \(0.383679\pi\)
\(384\) 17.1234 + 9.88620i 0.873825 + 0.504503i
\(385\) 2.47219i 0.125994i
\(386\) 5.44504 9.43109i 0.277145 0.480030i
\(387\) −0.303134 0.525044i −0.0154092 0.0266895i
\(388\) −9.46972 + 5.46734i −0.480752 + 0.277562i
\(389\) 15.9409 0.808237 0.404118 0.914707i \(-0.367578\pi\)
0.404118 + 0.914707i \(0.367578\pi\)
\(390\) 0 0
\(391\) 3.22521 0.163106
\(392\) 3.36891 1.94504i 0.170156 0.0982394i
\(393\) −7.38889 12.7979i −0.372720 0.645570i
\(394\) −0.224677 + 0.389152i −0.0113191 + 0.0196052i
\(395\) 2.46250i 0.123902i
\(396\) −10.2254 5.90366i −0.513847 0.296670i
\(397\) 14.6487 + 8.45742i 0.735196 + 0.424466i 0.820320 0.571905i \(-0.193795\pi\)
−0.0851239 + 0.996370i \(0.527129\pi\)
\(398\) 9.21552i 0.461932i
\(399\) 0.233406 0.404271i 0.0116849 0.0202389i
\(400\) −1.37047 2.37372i −0.0685235 0.118686i
\(401\) −23.0904 + 13.3312i −1.15308 + 0.665730i −0.949636 0.313356i \(-0.898547\pi\)
−0.203443 + 0.979087i \(0.565213\pi\)
\(402\) 13.8388 0.690215
\(403\) 0 0
\(404\) 18.1207 0.901537
\(405\) −2.34182 + 1.35205i −0.116366 + 0.0671840i
\(406\) 4.37651 + 7.58034i 0.217203 + 0.376206i
\(407\) −12.0869 + 20.9352i −0.599128 + 1.03772i
\(408\) 13.0586i 0.646497i
\(409\) −24.6959 14.2582i −1.22113 0.705021i −0.255972 0.966684i \(-0.582396\pi\)
−0.965159 + 0.261663i \(0.915729\pi\)
\(410\) −1.98831 1.14795i −0.0981954 0.0566931i
\(411\) 13.9758i 0.689377i
\(412\) 0.924231 1.60082i 0.0455336 0.0788665i
\(413\) 7.99007 + 13.8392i 0.393166 + 0.680983i
\(414\) −2.12586 + 1.22737i −0.104480 + 0.0603217i
\(415\) −0.397452 −0.0195102
\(416\) 0 0
\(417\) 33.0465 1.61830
\(418\) 0.259988 0.150104i 0.0127165 0.00734185i
\(419\) 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
\(421\) 11.6606i 0.568301i −0.958780 0.284151i \(-0.908288\pi\)
0.958780 0.284151i \(-0.0917115\pi\)
\(422\) −6.10081 3.52230i −0.296983 0.171463i
\(423\) −13.0542 7.53684i −0.634716 0.366453i
\(424\) 27.9801i 1.35884i
\(425\) 5.33124 9.23398i 0.258603 0.447914i
\(426\) 7.80678 + 13.5217i 0.378240 + 0.655131i
\(427\) 7.08719 4.09179i 0.342973 0.198016i
\(428\) 4.43535 0.214391
\(429\) 0 0
\(430\) −0.0586060 −0.00282623
\(431\) 3.76645 2.17456i 0.181424 0.104745i −0.406538 0.913634i \(-0.633264\pi\)
0.587961 + 0.808889i \(0.299931\pi\)
\(432\) −0.592990 1.02709i −0.0285303 0.0494159i
\(433\) −7.19418 + 12.4607i −0.345730 + 0.598822i −0.985486 0.169756i \(-0.945702\pi\)
0.639756 + 0.768578i \(0.279035\pi\)
\(434\) 12.5332i 0.601612i
\(435\) 2.22571 + 1.28501i 0.106714 + 0.0616116i
\(436\) −18.4512 10.6528i −0.883651 0.510176i
\(437\) 0.131687i 0.00629942i
\(438\) 6.06853 10.5110i 0.289966 0.502235i
\(439\) −10.1163 17.5219i −0.482822 0.836273i 0.516983 0.855996i \(-0.327055\pi\)
−0.999805 + 0.0197227i \(0.993722\pi\)
\(440\) −2.44540 + 1.41185i −0.116580 + 0.0673075i
\(441\) 2.96077 0.140989
\(442\) 0 0
\(443\) 8.12200 0.385888 0.192944 0.981210i \(-0.438196\pi\)
0.192944 + 0.981210i \(0.438196\pi\)
\(444\) 15.0294 8.67725i 0.713266 0.411804i
\(445\) 0.356232 + 0.617012i 0.0168870 + 0.0292492i
\(446\) −0.905813 + 1.56891i −0.0428915 + 0.0742903i
\(447\) 9.74094i 0.460731i
\(448\) 7.27591 + 4.20075i 0.343755 + 0.198467i
\(449\) 10.8180 + 6.24578i 0.510534 + 0.294757i 0.733053 0.680172i \(-0.238095\pi\)
−0.222519 + 0.974928i \(0.571428\pi\)
\(450\) 8.11529i 0.382559i
\(451\) −24.6151 + 42.6345i −1.15908 + 2.00758i
\(452\) −8.17456 14.1588i −0.384499 0.665972i
\(453\) 7.67553 4.43147i 0.360628 0.208209i
\(454\) 5.58642 0.262184
\(455\) 0 0
\(456\) −0.533188 −0.0249688
\(457\) 5.17988 2.99061i 0.242305 0.139895i −0.373931 0.927457i \(-0.621990\pi\)
0.616236 + 0.787562i \(0.288657\pi\)
\(458\) 9.69298 + 16.7887i 0.452923 + 0.784486i
\(459\) 2.30678 3.99546i 0.107671 0.186492i
\(460\) 0.500664i 0.0233436i
\(461\) 1.78114 + 1.02834i 0.0829561 + 0.0478947i 0.540904 0.841084i \(-0.318082\pi\)
−0.457948 + 0.888979i \(0.651415\pi\)
\(462\) −15.6204 9.01842i −0.726725 0.419575i
\(463\) 8.44935i 0.392675i 0.980536 + 0.196337i \(0.0629048\pi\)
−0.980536 + 0.196337i \(0.937095\pi\)
\(464\) −1.28501 + 2.22571i −0.0596552 + 0.103326i
\(465\) 1.83997 + 3.18692i 0.0853266 + 0.147790i
\(466\) 2.12586 1.22737i 0.0984785 0.0568566i
\(467\) −33.5139 −1.55084 −0.775420 0.631446i \(-0.782462\pi\)
−0.775420 + 0.631446i \(0.782462\pi\)
\(468\) 0 0
\(469\) −18.1008 −0.835818
\(470\) −1.26191 + 0.728562i −0.0582074 + 0.0336060i
\(471\) 5.00484 + 8.66864i 0.230611 + 0.399430i
\(472\) 9.12618 15.8070i 0.420066 0.727576i
\(473\) 1.25667i 0.0577817i
\(474\) 15.5591 + 8.98307i 0.714655 + 0.412606i
\(475\) 0.377027 + 0.217677i 0.0172992 + 0.00998769i
\(476\) 6.90408i 0.316448i
\(477\) 10.6479 18.4428i 0.487536 0.844437i
\(478\) −10.0831 17.4644i −0.461189 0.798802i
\(479\) 21.4179 12.3656i 0.978608 0.565000i 0.0767587 0.997050i \(-0.475543\pi\)
0.901850 + 0.432050i \(0.142210\pi\)
\(480\) 3.23490 0.147652
\(481\) 0 0
\(482\) −16.2524 −0.740275
\(483\) 6.85187 3.95593i 0.311771 0.180001i
\(484\) 4.77413 + 8.26903i 0.217006 + 0.375865i
\(485\) −0.995156 + 1.72366i −0.0451877 + 0.0782674i
\(486\) 14.5875i 0.661702i
\(487\) 32.6972 + 18.8778i 1.48165 + 0.855433i 0.999783 0.0208094i \(-0.00662430\pi\)
0.481870 + 0.876243i \(0.339958\pi\)
\(488\) −8.09492 4.67360i −0.366440 0.211564i
\(489\) 36.3086i 1.64193i
\(490\) 0.143104 0.247864i 0.00646479 0.0111973i
\(491\) 15.6555 + 27.1161i 0.706522 + 1.22373i 0.966139 + 0.258020i \(0.0830702\pi\)
−0.259617 + 0.965712i \(0.583596\pi\)
\(492\) 30.6074 17.6712i 1.37989 0.796680i
\(493\) −9.99761 −0.450270
\(494\) 0 0
\(495\) −2.14914 −0.0965969
\(496\) −3.18692 + 1.83997i −0.143097 + 0.0826171i
\(497\) −10.2111 17.6861i −0.458031 0.793332i
\(498\) −1.44989 + 2.51128i −0.0649710 + 0.112533i
\(499\) 21.4873i 0.961902i 0.876748 + 0.480951i \(0.159708\pi\)
−0.876748 + 0.480951i \(0.840292\pi\)
\(500\) −2.88457 1.66541i −0.129002 0.0744793i
\(501\) −31.3632 18.1075i −1.40120 0.808984i
\(502\) 19.0228i 0.849031i
\(503\) −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
\(505\) 2.85640 1.64914i 0.127108 0.0733860i
\(506\) 5.08815 0.226196
\(507\) 0 0
\(508\) 13.3075 0.590425
\(509\) −14.8155 + 8.55376i −0.656688 + 0.379139i −0.791014 0.611798i \(-0.790446\pi\)
0.134326 + 0.990937i \(0.457113\pi\)
\(510\) 0.480386 + 0.832052i 0.0212718 + 0.0368439i
\(511\) −7.93751 + 13.7482i −0.351135 + 0.608183i
\(512\) 6.22282i 0.275012i
\(513\) 0.163136 + 0.0941868i 0.00720264 + 0.00415845i
\(514\) 9.87865 + 5.70344i 0.435728 + 0.251568i
\(515\) 0.336454i 0.0148259i
\(516\) 0.451083 0.781298i 0.0198578 0.0343947i
\(517\) 15.6223 + 27.0586i 0.687068 + 1.19004i
\(518\) 9.31705 5.37920i 0.409367 0.236348i
\(519\) −48.3913 −2.12414
\(520\) 0 0
\(521\) −19.8465 −0.869493 −0.434746 0.900553i \(-0.643162\pi\)
−0.434746 + 0.900553i \(0.643162\pi\)
\(522\) 6.58981 3.80463i 0.288428 0.166524i
\(523\) 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
\(525\) 26.1564i 1.14156i
\(526\) 11.8728 + 6.85474i 0.517677 + 0.298881i
\(527\) −12.3974 7.15764i −0.540039 0.311792i
\(528\) 5.29590i 0.230474i
\(529\) 10.3840 17.9857i 0.451480 0.781987i
\(530\) −1.02930 1.78281i −0.0447101 0.0774401i
\(531\) 12.0308 6.94600i 0.522093 0.301431i
\(532\) 0.281896 0.0122218
\(533\) 0 0
\(534\) 5.19806 0.224942
\(535\) 0.699155 0.403657i 0.0302271 0.0174516i
\(536\) 10.3373 + 17.9047i 0.446503 + 0.773365i
\(537\) −12.8448 + 22.2479i −0.554295 + 0.960066i
\(538\) 5.18598i 0.223584i
\(539\) −5.31485 3.06853i −0.228927 0.132171i
\(540\) −0.620234 0.358092i −0.0266906 0.0154098i
\(541\) 16.1884i 0.695993i −0.937496 0.347996i \(-0.886862\pi\)
0.937496 0.347996i \(-0.113138\pi\)
\(542\) −2.58546 + 4.47814i −0.111055 + 0.192353i
\(543\) −23.5601 40.8073i −1.01106 1.75121i
\(544\) −10.8981 + 6.29201i −0.467252 + 0.269768i
\(545\) −3.87800 −0.166115
\(546\) 0 0
\(547\) 5.33081 0.227929 0.113965 0.993485i \(-0.463645\pi\)
0.113965 + 0.993485i \(0.463645\pi\)
\(548\) −7.30896 + 4.21983i −0.312223 + 0.180262i
\(549\) −3.55711 6.16110i −0.151814 0.262949i
\(550\) 8.41066 14.5677i 0.358632 0.621168i
\(551\) 0.408206i 0.0173902i
\(552\) −7.82613 4.51842i −0.333102 0.192317i
\(553\) −20.3510 11.7497i −0.865413 0.499647i
\(554\) 10.7942i 0.458600i
\(555\) 1.57942 2.73563i 0.0670425 0.116121i
\(556\) 9.97799 + 17.2824i 0.423161 + 0.732937i
\(557\) −6.40058 + 3.69537i −0.271201 + 0.156578i −0.629433 0.777054i \(-0.716713\pi\)
0.358232 + 0.933633i \(0.383380\pi\)
\(558\) 10.8955 0.461242
\(559\) 0 0
\(560\) −0.323044 −0.0136511
\(561\) 17.8414 10.3007i 0.753265 0.434898i
\(562\) −2.01961 3.49807i −0.0851923 0.147557i
\(563\) −4.73945 + 8.20896i −0.199744 + 0.345967i −0.948445 0.316941i \(-0.897344\pi\)
0.748701 + 0.662907i \(0.230678\pi\)
\(564\) 22.4306i 0.944497i
\(565\) −2.57715 1.48792i −0.108422 0.0625972i
\(566\) 15.3678 + 8.87263i 0.645958 + 0.372944i
\(567\) 25.8049i 1.08370i
\(568\) −11.6630 + 20.2009i −0.489369 + 0.847612i
\(569\) −5.07188 8.78476i −0.212624 0.368276i 0.739911 0.672705i \(-0.234868\pi\)
−0.952535 + 0.304429i \(0.901534\pi\)
\(570\) −0.0339730 + 0.0196143i −0.00142297 + 0.000821554i
\(571\) 14.0925 0.589751 0.294876 0.955536i \(-0.404722\pi\)
0.294876 + 0.955536i \(0.404722\pi\)
\(572\) 0 0
\(573\) 32.4403 1.35521
\(574\) 18.9741 10.9547i 0.791966 0.457242i
\(575\) 3.68933 + 6.39011i 0.153856 + 0.266486i
\(576\) 3.65183 6.32516i 0.152160 0.263548i
\(577\) 25.1545i 1.04720i 0.851965 + 0.523598i \(0.175411\pi\)
−0.851965 + 0.523598i \(0.824589\pi\)
\(578\) 8.56972 + 4.94773i 0.356453 + 0.205798i
\(579\) 26.4253 + 15.2567i 1.09820 + 0.634045i
\(580\) 1.55197i 0.0644422i
\(581\) 1.89642 3.28470i 0.0786768 0.136272i
\(582\) 7.26055 + 12.5756i 0.300960 + 0.521277i
\(583\) −38.2281 + 22.0710i −1.58324 + 0.914087i
\(584\) 18.1323 0.750319
\(585\) 0 0
\(586\) 11.9860 0.495137
\(587\) 37.9625 21.9177i 1.56688 0.904639i 0.570350 0.821402i \(-0.306808\pi\)
0.996530 0.0832369i \(-0.0265258\pi\)
\(588\) 2.20291 + 3.81555i 0.0908463 + 0.157350i
\(589\) 0.292249 0.506190i 0.0120419 0.0208572i
\(590\) 1.34290i 0.0552861i
\(591\) −1.09038 0.629531i −0.0448522 0.0258954i
\(592\) 2.73563 + 1.57942i 0.112434 + 0.0649136i
\(593\) 24.9965i 1.02648i 0.858244 + 0.513242i \(0.171556\pi\)
−0.858244 + 0.513242i \(0.828444\pi\)
\(594\) 3.63922 6.30331i 0.149319 0.258628i
\(595\) −0.628334 1.08831i −0.0257592 0.0446162i
\(596\) 5.09423 2.94116i 0.208668 0.120474i
\(597\) 25.8213 1.05680
\(598\) 0 0
\(599\) −6.24027 −0.254971 −0.127485 0.991840i \(-0.540691\pi\)
−0.127485 + 0.991840i \(0.540691\pi\)
\(600\) −25.8730 + 14.9378i −1.05626 + 0.609833i
\(601\) −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
\(603\) 15.7356i 0.640802i
\(604\) 4.63506 + 2.67606i 0.188598 + 0.108887i
\(605\) 1.50511 + 0.868977i 0.0611915 + 0.0353290i
\(606\) 24.0640i 0.977532i
\(607\) 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
\(609\) −21.2396 + 12.2627i −0.860673 + 0.496910i
\(610\) −0.687710 −0.0278445
\(611\) 0 0
\(612\) −6.00192 −0.242613
\(613\) −22.4769 + 12.9770i −0.907833 + 0.524137i −0.879733 0.475468i \(-0.842279\pi\)
−0.0280995 + 0.999605i \(0.508946\pi\)
\(614\) −7.67025 13.2853i −0.309546 0.536150i
\(615\) 3.21648 5.57111i 0.129701 0.224649i
\(616\) 26.9463i 1.08570i
\(617\) −39.7849 22.9698i −1.60168 0.924729i −0.991152 0.132733i \(-0.957625\pi\)
−0.610526 0.791996i \(-0.709042\pi\)
\(618\) −2.12586 1.22737i −0.0855146 0.0493719i
\(619\) 6.73556i 0.270725i −0.990796 0.135363i \(-0.956780\pi\)
0.990796 0.135363i \(-0.0432199\pi\)
\(620\) −1.11111 + 1.92450i −0.0446234 + 0.0772899i
\(621\) 1.59634 + 2.76495i 0.0640590 + 0.110953i
\(622\) 0.187386 0.108187i 0.00751349 0.00433792i
\(623\) −6.79895 −0.272394
\(624\) 0 0
\(625\) 24.0887 0.963549
\(626\) −16.2469 + 9.38016i −0.649357 + 0.374907i
\(627\) 0.420583 + 0.728471i 0.0167965 + 0.0290923i
\(628\) −3.02230 + 5.23478i −0.120603 + 0.208891i
\(629\) 12.2881i 0.489960i
\(630\) 0.828318 + 0.478230i 0.0330010 + 0.0190531i
\(631\) 39.0575 + 22.5499i 1.55486 + 0.897696i 0.997735 + 0.0672649i \(0.0214273\pi\)
0.557121 + 0.830432i \(0.311906\pi\)
\(632\) 26.8407i 1.06767i
\(633\) 9.86927 17.0941i 0.392268 0.679429i
\(634\) −5.61165 9.71965i −0.222867 0.386017i
\(635\) 2.09769 1.21110i 0.0832444 0.0480612i
\(636\) 31.6896 1.25658
\(637\) 0 0
\(638\) −15.7724 −0.624435
\(639\) −15.3751 + 8.87681i −0.608229 + 0.351161i
\(640\) 1.08665 + 1.88214i 0.0429538 + 0.0743981i
\(641\) 16.2911 28.2169i 0.643458 1.11450i −0.341197 0.939992i \(-0.610832\pi\)
0.984655 0.174510i \(-0.0558342\pi\)
\(642\) 5.89008i 0.232463i
\(643\) −22.1489 12.7877i −0.873469 0.504298i −0.00496965 0.999988i \(-0.501582\pi\)
−0.868500 + 0.495690i \(0.834915\pi\)
\(644\) 4.13767 + 2.38889i 0.163047 + 0.0941353i
\(645\) 0.164210i 0.00646578i
\(646\) 0.0763014 0.132158i 0.00300204 0.00519968i
\(647\) −15.0858 26.1293i −0.593082 1.02725i −0.993814 0.111053i \(-0.964578\pi\)
0.400732 0.916195i \(-0.368756\pi\)
\(648\) −25.5253 + 14.7371i −1.00273 + 0.578926i
\(649\) −28.7952 −1.13031
\(650\) 0 0
\(651\) −35.1172 −1.37635
\(652\) −18.9883 + 10.9629i −0.743641 + 0.429341i
\(653\) −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
\(655\) 1.62432i 0.0634673i
\(656\) 5.57111 + 3.21648i 0.217515 + 0.125582i
\(657\) 11.9517 + 6.90030i 0.466279 + 0.269207i
\(658\) 13.9051i 0.542079i
\(659\) −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
\(661\) 27.5041 15.8795i 1.06979 0.617641i 0.141662 0.989915i \(-0.454755\pi\)
0.928123 + 0.372274i \(0.121422\pi\)
\(662\) −14.2916 −0.555458
\(663\) 0 0
\(664\) −4.33214 −0.168120
\(665\) 0.0444360 0.0256551i 0.00172315 0.000994863i
\(666\) −4.67629 8.09958i −0.181203 0.313852i
\(667\) 3.45928 5.99165i 0.133944 0.231998i
\(668\) 21.8694i 0.846152i
\(669\) −4.39600 2.53803i −0.169959 0.0981260i
\(670\) 1.31732 + 0.760553i 0.0508924 + 0.0293827i
\(671\) 14.7463i 0.569275i
\(672\) −15.4351 + 26.7344i −0.595423 + 1.03130i
\(673\) −3.75116 6.49720i −0.144597 0.250449i 0.784626 0.619970i \(-0.212855\pi\)
−0.929222 + 0.369521i \(0.879522\pi\)
\(674\) 19.3407 11.1664i 0.744976 0.430112i
\(675\) 10.5550 0.406261
\(676\) 0 0
\(677\) −35.0315 −1.34637 −0.673184 0.739475i \(-0.735074\pi\)
−0.673184 + 0.739475i \(0.735074\pi\)
\(678\) −18.8026 + 10.8557i −0.722110 + 0.416911i
\(679\) −9.49665 16.4487i −0.364448 0.631242i
\(680\) −0.717677 + 1.24305i −0.0275216 + 0.0476689i
\(681\) 15.6528i 0.599816i
\(682\) −19.5583 11.2920i −0.748927 0.432393i
\(683\) −20.8568 12.0417i −0.798063 0.460762i 0.0447302 0.998999i \(-0.485757\pi\)
−0.842794 + 0.538237i \(0.819091\pi\)
\(684\) 0.245061i 0.00937013i
\(685\) −0.768086 + 1.33036i −0.0293471 + 0.0508306i
\(686\) 7.98092 + 13.8234i 0.304713 + 0.527778i
\(687\) −47.0410 + 27.1591i −1.79473 + 1.03619i
\(688\) 0.164210 0.00626046
\(689\) 0 0
\(690\) −0.664874 −0.0253113
\(691\) 1.74459 1.00724i 0.0663672 0.0383171i −0.466449 0.884548i \(-0.654467\pi\)
0.532816 + 0.846231i \(0.321134\pi\)
\(692\) −14.6112 25.3073i −0.555433 0.962039i
\(693\) 10.2545 17.7613i 0.389537 0.674697i
\(694\) 1.20583i 0.0457728i
\(695\) 3.14571 + 1.81618i 0.119323 + 0.0688915i
\(696\) 24.2597 + 14.0063i 0.919561 + 0.530909i
\(697\) 25.0248i 0.947880i
\(698\) 5.68814 9.85214i 0.215299 0.372909i
\(699\) 3.43900 + 5.95652i 0.130075 + 0.225296i
\(700\) 13.6791 7.89762i 0.517020 0.298502i
\(701\) 48.8189 1.84387 0.921933 0.387350i \(-0.126610\pi\)
0.921933 + 0.387350i \(0.126610\pi\)
\(702\) 0 0
\(703\) −0.501729 −0.0189231
\(704\) −13.1107 + 7.56949i −0.494130 + 0.285286i
\(705\) −2.04138 3.53578i −0.0768830 0.133165i
\(706\) −2.87435 + 4.97853i −0.108178 + 0.187369i
\(707\) 31.4752i 1.18375i
\(708\) 17.9026 + 10.3361i 0.672822 + 0.388454i
\(709\) −18.0185 10.4030i −0.676699 0.390693i 0.121911 0.992541i \(-0.461098\pi\)
−0.798610 + 0.601848i \(0.794431\pi\)
\(710\) 1.71618i 0.0644073i
\(711\) −10.2143 + 17.6917i −0.383067 + 0.663492i
\(712\) 3.88285 + 6.72529i 0.145516 + 0.252041i
\(713\) 8.57926 4.95324i 0.321296 0.185500i
\(714\) −9.16852 −0.343123
\(715\) 0 0
\(716\) −15.5133 −0.579761
\(717\) 48.9341 28.2521i 1.82748 1.05509i
\(718\) −7.97339 13.8103i −0.297564 0.515396i
\(719\) 10.7153 18.5594i 0.399613 0.692149i −0.594065 0.804417i \(-0.702478\pi\)
0.993678 + 0.112267i \(0.0358113\pi\)
\(720\) 0.280831i 0.0104660i
\(721\) 2.78058 + 1.60537i 0.103554 + 0.0597870i
\(722\) −13.1901 7.61529i −0.490884 0.283412i
\(723\) 45.5381i 1.69358i
\(724\) 14.2274 24.6425i 0.528756 0.915832i
\(725\) −11.4363 19.8083i −0.424734 0.735661i
\(726\) 10.9812 6.33997i 0.407549 0.235298i
\(727\) −13.4862 −0.500175 −0.250088 0.968223i \(-0.580459\pi\)
−0.250088 + 0.968223i \(0.580459\pi\)
\(728\) 0 0
\(729\) −8.02715 −0.297302
\(730\) 1.15533 0.667030i 0.0427607 0.0246879i
\(731\) 0.319396 + 0.553210i 0.0118133 + 0.0204612i
\(732\) 5.29321 9.16811i 0.195643 0.338863i
\(733\) 43.5424i 1.60828i −0.594443 0.804138i \(-0.702627\pi\)
0.594443 0.804138i \(-0.297373\pi\)
\(734\) −0.752721 0.434584i −0.0277834 0.0160408i
\(735\) 0.694498 + 0.400969i 0.0256170 + 0.0147900i
\(736\) 8.70841i 0.320996i
\(737\) 16.3083 28.2468i 0.600723 1.04048i
\(738\) −9.52326 16.4948i −0.350556 0.607181i
\(739\) −17.3675 + 10.0271i −0.638875 + 0.368855i −0.784181 0.620532i \(-0.786917\pi\)
0.145306 + 0.989387i \(0.453583\pi\)
\(740\) 1.90754 0.0701226
\(741\) 0 0
\(742\) 19.6450 0.721191
\(743\) −28.7248 + 16.5843i −1.05381 + 0.608418i −0.923714 0.383084i \(-0.874862\pi\)
−0.130096 + 0.991501i \(0.541529\pi\)
\(744\) 20.0553 + 34.7367i 0.735261 + 1.27351i
\(745\) 0.535344 0.927243i 0.0196135 0.0339715i
\(746\) 4.91617i 0.179994i
\(747\) −2.85548 1.64861i −0.104477 0.0603196i
\(748\) 10.7740 + 6.22037i 0.393936 + 0.227439i
\(749\) 7.70410i 0.281502i
\(750\) −2.21164 + 3.83067i −0.0807575 + 0.139876i
\(751\) 19.6407 + 34.0187i 0.716700 + 1.24136i 0.962300 + 0.271989i \(0.0876815\pi\)
−0.245601 + 0.969371i \(0.578985\pi\)
\(752\) 3.53578 2.04138i 0.128937 0.0744416i
\(753\) −53.3008 −1.94239
\(754\) 0 0
\(755\) 0.974181 0.0354541
\(756\) 5.91882 3.41723i 0.215265 0.124283i
\(757\) 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
\(759\) 14.2567i 0.517484i
\(760\) −0.0507543 0.0293030i −0.00184105 0.00106293i
\(761\) −18.9646 10.9492i −0.687467 0.396909i 0.115196 0.993343i \(-0.463250\pi\)
−0.802662 + 0.596434i \(0.796584\pi\)
\(762\) 17.6722i 0.640195i
\(763\) 18.5036 32.0493i 0.669877 1.16026i
\(764\) 9.79494 + 16.9653i 0.354368 + 0.613784i
\(765\) −0.946096 + 0.546229i −0.0342062 + 0.0197489i
\(766\) 24.3720 0.880595
\(767\) 0 0
\(768\) 31.8756 1.15021
\(769\) 40.4517 23.3548i 1.45873 0.842196i 0.459777 0.888035i \(-0.347929\pi\)
0.998949 + 0.0458390i \(0.0145961\pi\)
\(770\) −0.991271 1.71693i −0.0357229 0.0618739i
\(771\) −15.9807 + 27.6794i −0.575530 + 0.996848i
\(772\) 18.4263i 0.663175i
\(773\) 26.1900 + 15.1208i 0.941989 + 0.543857i 0.890583 0.454820i \(-0.150297\pi\)
0.0514055 + 0.998678i \(0.483630\pi\)