Properties

Label 429.2.bv.a.20.1
Level $429$
Weight $2$
Character 429.20
Analytic conductor $3.426$
Analytic rank $0$
Dimension $832$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [429,2,Mod(20,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([30, 36, 55]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.20");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.bv (of order \(60\), degree \(16\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(832\)
Relative dimension: \(52\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 20.1
Character \(\chi\) \(=\) 429.20
Dual form 429.2.bv.a.236.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.76683 - 0.145003i) q^{2} +(1.66622 + 0.472982i) q^{3} +(5.64525 + 0.593340i) q^{4} +(-0.523203 - 0.266585i) q^{5} +(-4.54156 - 1.55027i) q^{6} +(0.0260847 + 0.0322120i) q^{7} +(-10.0604 - 1.59341i) q^{8} +(2.55258 + 1.57618i) q^{9} +O(q^{10})\) \(q+(-2.76683 - 0.145003i) q^{2} +(1.66622 + 0.472982i) q^{3} +(5.64525 + 0.593340i) q^{4} +(-0.523203 - 0.266585i) q^{5} +(-4.54156 - 1.55027i) q^{6} +(0.0260847 + 0.0322120i) q^{7} +(-10.0604 - 1.59341i) q^{8} +(2.55258 + 1.57618i) q^{9} +(1.40895 + 0.813460i) q^{10} +(3.16166 - 1.00196i) q^{11} +(9.12559 + 3.65874i) q^{12} +(-0.927425 - 3.48423i) q^{13} +(-0.0675011 - 0.0929073i) q^{14} +(-0.745680 - 0.691655i) q^{15} +(16.4996 + 3.50711i) q^{16} +(3.91197 - 4.34469i) q^{17} +(-6.83398 - 4.73116i) q^{18} +(1.20651 + 3.14307i) q^{19} +(-2.79544 - 1.81538i) q^{20} +(0.0282272 + 0.0660098i) q^{21} +(-8.89304 + 2.31379i) q^{22} +(-2.08698 + 3.61476i) q^{23} +(-16.0091 - 7.41334i) q^{24} +(-2.73625 - 3.76613i) q^{25} +(2.06080 + 9.77475i) q^{26} +(3.50764 + 3.83359i) q^{27} +(0.128142 + 0.197322i) q^{28} +(0.632121 + 1.41977i) q^{29} +(1.96288 + 2.02181i) q^{30} +(0.736118 - 0.375071i) q^{31} +(-25.4657 - 6.82351i) q^{32} +(5.74192 - 0.174074i) q^{33} +(-11.4537 + 11.4537i) q^{34} +(-0.00506037 - 0.0238072i) q^{35} +(13.4747 + 10.4125i) q^{36} +(0.859984 - 2.24033i) q^{37} +(-2.88245 - 8.87126i) q^{38} +(0.102687 - 6.24415i) q^{39} +(4.83884 + 3.51562i) q^{40} +(7.92710 + 6.41924i) q^{41} +(-0.0685282 - 0.186731i) q^{42} +(0.824488 - 0.476019i) q^{43} +(18.4429 - 3.78037i) q^{44} +(-0.915327 - 1.50514i) q^{45} +(6.29847 - 9.69879i) q^{46} +(-0.0323356 - 0.00512146i) q^{47} +(25.8332 + 13.6476i) q^{48} +(1.45502 - 6.84535i) q^{49} +(7.02463 + 10.8170i) q^{50} +(8.57316 - 5.38891i) q^{51} +(-3.16821 - 20.2197i) q^{52} +(7.30026 + 2.37200i) q^{53} +(-9.14916 - 11.1155i) q^{54} +(-1.92129 - 0.318624i) q^{55} +(-0.211096 - 0.365628i) q^{56} +(0.523696 + 5.80770i) q^{57} +(-1.54310 - 4.01991i) q^{58} +(1.34839 - 1.09191i) q^{59} +(-3.79917 - 4.34701i) q^{60} +(-7.73133 + 8.58651i) q^{61} +(-2.09110 + 0.931016i) q^{62} +(0.0158113 + 0.123338i) q^{63} +(37.3843 + 12.1469i) q^{64} +(-0.443613 + 2.07020i) q^{65} +(-15.9121 - 0.350964i) q^{66} +(4.01807 - 1.07664i) q^{67} +(24.6620 - 22.2057i) q^{68} +(-5.18709 + 5.03588i) q^{69} +(0.0105491 + 0.0666041i) q^{70} +(-0.429622 - 8.19767i) q^{71} +(-23.1684 - 19.9243i) q^{72} +(11.8433 - 1.87580i) q^{73} +(-2.70428 + 6.07391i) q^{74} +(-2.77789 - 7.56940i) q^{75} +(4.94615 + 18.4593i) q^{76} +(0.114746 + 0.0757074i) q^{77} +(-1.18954 + 17.2616i) q^{78} +(-4.22359 + 12.9989i) q^{79} +(-7.69771 - 6.23348i) q^{80} +(4.03129 + 8.04666i) q^{81} +(-21.0021 - 18.9104i) q^{82} +(1.56102 + 0.795382i) q^{83} +(0.120184 + 0.389391i) q^{84} +(-3.20498 + 1.23028i) q^{85} +(-2.35024 + 1.19751i) q^{86} +(0.381728 + 2.66463i) q^{87} +(-33.4040 + 5.04227i) q^{88} +(-6.73514 + 1.80467i) q^{89} +(2.31430 + 4.29719i) q^{90} +(0.0880424 - 0.120760i) q^{91} +(-13.9263 + 19.1679i) q^{92} +(1.40394 - 0.276780i) q^{93} +(0.0887243 + 0.0188589i) q^{94} +(0.206645 - 1.96610i) q^{95} +(-39.2040 - 23.4143i) q^{96} +(-8.87618 - 5.76426i) q^{97} +(-5.01840 + 18.7289i) q^{98} +(9.64964 + 2.42578i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 832 q - 6 q^{3} - 36 q^{4} - 4 q^{6} - 24 q^{7} - 6 q^{9} - 96 q^{10} - 40 q^{13} + 12 q^{15} - 68 q^{16} - 20 q^{18} - 32 q^{19} - 84 q^{21} - 24 q^{22} - 72 q^{24} - 114 q^{30} - 8 q^{31} + 14 q^{33} - 24 q^{34} + 78 q^{36} - 24 q^{37} - 72 q^{39} - 112 q^{40} + 2 q^{42} - 96 q^{43} + 4 q^{45} - 16 q^{46} + 14 q^{48} - 36 q^{49} + 8 q^{52} + 32 q^{54} - 24 q^{55} - 12 q^{57} + 112 q^{58} - 120 q^{60} + 12 q^{61} + 28 q^{63} - 300 q^{66} - 32 q^{67} - 18 q^{69} - 140 q^{70} + 204 q^{72} - 24 q^{73} + 66 q^{75} + 176 q^{76} - 28 q^{78} - 224 q^{79} - 58 q^{81} - 264 q^{82} + 20 q^{84} - 168 q^{85} + 72 q^{87} - 120 q^{88} - 146 q^{93} - 4 q^{94} - 10 q^{96} - 88 q^{97} + 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.76683 0.145003i −1.95644 0.102533i −0.967694 0.252128i \(-0.918870\pi\)
−0.988747 + 0.149595i \(0.952203\pi\)
\(3\) 1.66622 + 0.472982i 0.961992 + 0.273076i
\(4\) 5.64525 + 0.593340i 2.82263 + 0.296670i
\(5\) −0.523203 0.266585i −0.233983 0.119220i 0.333068 0.942903i \(-0.391916\pi\)
−0.567052 + 0.823682i \(0.691916\pi\)
\(6\) −4.54156 1.55027i −1.85408 0.632894i
\(7\) 0.0260847 + 0.0322120i 0.00985911 + 0.0121750i 0.782052 0.623214i \(-0.214173\pi\)
−0.772193 + 0.635389i \(0.780840\pi\)
\(8\) −10.0604 1.59341i −3.55688 0.563354i
\(9\) 2.55258 + 1.57618i 0.850859 + 0.525395i
\(10\) 1.40895 + 0.813460i 0.445551 + 0.257239i
\(11\) 3.16166 1.00196i 0.953276 0.302102i
\(12\) 9.12559 + 3.65874i 2.63433 + 1.05619i
\(13\) −0.927425 3.48423i −0.257221 0.966352i
\(14\) −0.0675011 0.0929073i −0.0180404 0.0248305i
\(15\) −0.745680 0.691655i −0.192534 0.178584i
\(16\) 16.4996 + 3.50711i 4.12491 + 0.876777i
\(17\) 3.91197 4.34469i 0.948793 1.05374i −0.0496950 0.998764i \(-0.515825\pi\)
0.998488 0.0549765i \(-0.0175084\pi\)
\(18\) −6.83398 4.73116i −1.61078 1.11514i
\(19\) 1.20651 + 3.14307i 0.276792 + 0.721069i 0.999551 + 0.0299681i \(0.00954058\pi\)
−0.722758 + 0.691101i \(0.757126\pi\)
\(20\) −2.79544 1.81538i −0.625079 0.405931i
\(21\) 0.0282272 + 0.0660098i 0.00615968 + 0.0144045i
\(22\) −8.89304 + 2.31379i −1.89600 + 0.493302i
\(23\) −2.08698 + 3.61476i −0.435166 + 0.753729i −0.997309 0.0733106i \(-0.976644\pi\)
0.562143 + 0.827040i \(0.309977\pi\)
\(24\) −16.0091 7.41334i −3.26785 1.51324i
\(25\) −2.73625 3.76613i −0.547251 0.753226i
\(26\) 2.06080 + 9.77475i 0.404156 + 1.91699i
\(27\) 3.50764 + 3.83359i 0.675047 + 0.737775i
\(28\) 0.128142 + 0.197322i 0.0242166 + 0.0372903i
\(29\) 0.632121 + 1.41977i 0.117382 + 0.263644i 0.962676 0.270658i \(-0.0872412\pi\)
−0.845294 + 0.534302i \(0.820575\pi\)
\(30\) 1.96288 + 2.02181i 0.358370 + 0.369131i
\(31\) 0.736118 0.375071i 0.132211 0.0673647i −0.386634 0.922233i \(-0.626362\pi\)
0.518845 + 0.854869i \(0.326362\pi\)
\(32\) −25.4657 6.82351i −4.50174 1.20624i
\(33\) 5.74192 0.174074i 0.999541 0.0303024i
\(34\) −11.4537 + 11.4537i −1.96430 + 1.96430i
\(35\) −0.00506037 0.0238072i −0.000855359 0.00402415i
\(36\) 13.4747 + 10.4125i 2.24579 + 1.73542i
\(37\) 0.859984 2.24033i 0.141380 0.368309i −0.844547 0.535481i \(-0.820130\pi\)
0.985928 + 0.167172i \(0.0534636\pi\)
\(38\) −2.88245 8.87126i −0.467595 1.43911i
\(39\) 0.102687 6.24415i 0.0164430 0.999865i
\(40\) 4.83884 + 3.51562i 0.765087 + 0.555868i
\(41\) 7.92710 + 6.41924i 1.23801 + 1.00252i 0.999508 + 0.0313742i \(0.00998836\pi\)
0.238498 + 0.971143i \(0.423345\pi\)
\(42\) −0.0685282 0.186731i −0.0105741 0.0288132i
\(43\) 0.824488 0.476019i 0.125733 0.0725922i −0.435814 0.900037i \(-0.643540\pi\)
0.561548 + 0.827445i \(0.310206\pi\)
\(44\) 18.4429 3.78037i 2.78037 0.569912i
\(45\) −0.915327 1.50514i −0.136449 0.224373i
\(46\) 6.29847 9.69879i 0.928658 1.43001i
\(47\) −0.0323356 0.00512146i −0.00471663 0.000747041i 0.154076 0.988059i \(-0.450760\pi\)
−0.158792 + 0.987312i \(0.550760\pi\)
\(48\) 25.8332 + 13.6476i 3.72870 + 1.96987i
\(49\) 1.45502 6.84535i 0.207861 0.977908i
\(50\) 7.02463 + 10.8170i 0.993433 + 1.52975i
\(51\) 8.57316 5.38891i 1.20048 0.754598i
\(52\) −3.16821 20.2197i −0.439352 2.80396i
\(53\) 7.30026 + 2.37200i 1.00277 + 0.325819i 0.763971 0.645251i \(-0.223247\pi\)
0.238797 + 0.971070i \(0.423247\pi\)
\(54\) −9.14916 11.1155i −1.24504 1.51263i
\(55\) −1.92129 0.318624i −0.259067 0.0429632i
\(56\) −0.211096 0.365628i −0.0282088 0.0488591i
\(57\) 0.523696 + 5.80770i 0.0693653 + 0.769248i
\(58\) −1.54310 4.01991i −0.202619 0.527840i
\(59\) 1.34839 1.09191i 0.175546 0.142154i −0.537521 0.843251i \(-0.680639\pi\)
0.713067 + 0.701096i \(0.247306\pi\)
\(60\) −3.79917 4.34701i −0.490471 0.561196i
\(61\) −7.73133 + 8.58651i −0.989895 + 1.09939i 0.00515239 + 0.999987i \(0.498360\pi\)
−0.995047 + 0.0994029i \(0.968307\pi\)
\(62\) −2.09110 + 0.931016i −0.265569 + 0.118239i
\(63\) 0.0158113 + 0.123338i 0.00199203 + 0.0155391i
\(64\) 37.3843 + 12.1469i 4.67304 + 1.51836i
\(65\) −0.443613 + 2.07020i −0.0550235 + 0.256776i
\(66\) −15.9121 0.350964i −1.95865 0.0432007i
\(67\) 4.01807 1.07664i 0.490886 0.131532i −0.00488103 0.999988i \(-0.501554\pi\)
0.495767 + 0.868456i \(0.334887\pi\)
\(68\) 24.6620 22.2057i 2.99070 2.69284i
\(69\) −5.18709 + 5.03588i −0.624452 + 0.606248i
\(70\) 0.0105491 + 0.0666041i 0.00126085 + 0.00796071i
\(71\) −0.429622 8.19767i −0.0509867 0.972885i −0.897637 0.440735i \(-0.854718\pi\)
0.846650 0.532150i \(-0.178616\pi\)
\(72\) −23.1684 19.9243i −2.73042 2.34810i
\(73\) 11.8433 1.87580i 1.38616 0.219546i 0.581626 0.813456i \(-0.302417\pi\)
0.804531 + 0.593911i \(0.202417\pi\)
\(74\) −2.70428 + 6.07391i −0.314366 + 0.706078i
\(75\) −2.77789 7.56940i −0.320763 0.874039i
\(76\) 4.94615 + 18.4593i 0.567362 + 2.11742i
\(77\) 0.114746 + 0.0757074i 0.0130765 + 0.00862766i
\(78\) −1.18954 + 17.2616i −0.134689 + 1.95449i
\(79\) −4.22359 + 12.9989i −0.475191 + 1.46249i 0.370510 + 0.928829i \(0.379183\pi\)
−0.845700 + 0.533658i \(0.820817\pi\)
\(80\) −7.69771 6.23348i −0.860630 0.696925i
\(81\) 4.03129 + 8.04666i 0.447921 + 0.894073i
\(82\) −21.0021 18.9104i −2.31929 2.08830i
\(83\) 1.56102 + 0.795382i 0.171345 + 0.0873045i 0.537559 0.843226i \(-0.319346\pi\)
−0.366215 + 0.930530i \(0.619346\pi\)
\(84\) 0.120184 + 0.389391i 0.0131131 + 0.0424860i
\(85\) −3.20498 + 1.23028i −0.347629 + 0.133442i
\(86\) −2.35024 + 1.19751i −0.253433 + 0.129130i
\(87\) 0.381728 + 2.66463i 0.0409255 + 0.285678i
\(88\) −33.4040 + 5.04227i −3.56088 + 0.537507i
\(89\) −6.73514 + 1.80467i −0.713923 + 0.191295i −0.597459 0.801900i \(-0.703823\pi\)
−0.116465 + 0.993195i \(0.537156\pi\)
\(90\) 2.31430 + 4.29719i 0.243949 + 0.452964i
\(91\) 0.0880424 0.120760i 0.00922935 0.0126590i
\(92\) −13.9263 + 19.1679i −1.45192 + 1.99840i
\(93\) 1.40394 0.276780i 0.145581 0.0287007i
\(94\) 0.0887243 + 0.0188589i 0.00915122 + 0.00194515i
\(95\) 0.206645 1.96610i 0.0212014 0.201717i
\(96\) −39.2040 23.4143i −4.00124 2.38971i
\(97\) −8.87618 5.76426i −0.901239 0.585272i 0.00872325 0.999962i \(-0.497223\pi\)
−0.909963 + 0.414690i \(0.863890\pi\)
\(98\) −5.01840 + 18.7289i −0.506935 + 1.89191i
\(99\) 9.64964 + 2.42578i 0.969825 + 0.243800i
\(100\) −13.2122 22.8843i −1.32122 2.28843i
\(101\) −8.69749 9.65955i −0.865433 0.961161i 0.134123 0.990965i \(-0.457178\pi\)
−0.999556 + 0.0298040i \(0.990512\pi\)
\(102\) −24.5019 + 13.6670i −2.42605 + 1.35324i
\(103\) −1.94363 + 2.67518i −0.191512 + 0.263594i −0.893965 0.448136i \(-0.852088\pi\)
0.702453 + 0.711730i \(0.252088\pi\)
\(104\) 3.77844 + 36.5305i 0.370507 + 3.58211i
\(105\) 0.00282868 0.0420615i 0.000276051 0.00410478i
\(106\) −19.8546 7.62146i −1.92845 0.740262i
\(107\) −13.6803 + 1.43786i −1.32252 + 0.139003i −0.739337 0.673336i \(-0.764861\pi\)
−0.583186 + 0.812338i \(0.698194\pi\)
\(108\) 17.5269 + 23.7228i 1.68653 + 2.28273i
\(109\) 6.42431 + 6.42431i 0.615337 + 0.615337i 0.944332 0.328994i \(-0.106710\pi\)
−0.328994 + 0.944332i \(0.606710\pi\)
\(110\) 5.26969 + 1.16017i 0.502445 + 0.110618i
\(111\) 2.49256 3.32613i 0.236583 0.315703i
\(112\) 0.317418 + 0.622968i 0.0299932 + 0.0588649i
\(113\) 3.20704 7.20314i 0.301693 0.677614i −0.697549 0.716537i \(-0.745726\pi\)
0.999242 + 0.0389230i \(0.0123927\pi\)
\(114\) −0.606842 16.1448i −0.0568360 1.51210i
\(115\) 2.05555 1.33489i 0.191681 0.124479i
\(116\) 2.72608 + 8.39001i 0.253110 + 0.778993i
\(117\) 3.12447 10.3556i 0.288858 0.957372i
\(118\) −3.88910 + 2.82560i −0.358021 + 0.260117i
\(119\) 0.241994 + 0.0126824i 0.0221835 + 0.00116259i
\(120\) 6.39974 + 8.14648i 0.584213 + 0.743668i
\(121\) 8.99216 6.33570i 0.817469 0.575972i
\(122\) 22.6363 22.6363i 2.04939 2.04939i
\(123\) 10.1721 + 14.4452i 0.917188 + 1.30248i
\(124\) 4.37812 1.68060i 0.393166 0.150922i
\(125\) 0.886916 + 5.59977i 0.0793281 + 0.500858i
\(126\) −0.0258626 0.343547i −0.00230403 0.0306056i
\(127\) −0.305785 + 1.43860i −0.0271340 + 0.127655i −0.989630 0.143641i \(-0.954119\pi\)
0.962496 + 0.271296i \(0.0874523\pi\)
\(128\) −52.4487 20.1332i −4.63586 1.77954i
\(129\) 1.59893 0.403183i 0.140778 0.0354983i
\(130\) 1.52759 5.66355i 0.133978 0.496726i
\(131\) 7.69474i 0.672293i −0.941810 0.336146i \(-0.890876\pi\)
0.941810 0.336146i \(-0.109124\pi\)
\(132\) 32.5179 + 2.42422i 2.83032 + 0.211001i
\(133\) −0.0697729 + 0.120850i −0.00605007 + 0.0104790i
\(134\) −11.2734 + 2.39624i −0.973876 + 0.207004i
\(135\) −0.813230 2.94083i −0.0699917 0.253106i
\(136\) −46.2788 + 37.4758i −3.96837 + 3.21352i
\(137\) −13.6812 + 0.717000i −1.16886 + 0.0612575i −0.626868 0.779125i \(-0.715664\pi\)
−0.541994 + 0.840383i \(0.682330\pi\)
\(138\) 15.0820 13.1812i 1.28386 1.12206i
\(139\) 0.0623553 0.593271i 0.00528891 0.0503206i −0.991559 0.129655i \(-0.958613\pi\)
0.996848 + 0.0793347i \(0.0252796\pi\)
\(140\) −0.0144413 0.137400i −0.00122052 0.0116124i
\(141\) −0.0514558 0.0238276i −0.00433336 0.00200665i
\(142\) 22.7438i 1.90862i
\(143\) −6.42326 10.0867i −0.537140 0.843493i
\(144\) 36.5887 + 34.9586i 3.04906 + 2.91322i
\(145\) 0.0477613 0.911340i 0.00396636 0.0756827i
\(146\) −33.0404 + 3.47269i −2.73445 + 0.287402i
\(147\) 5.66212 10.7177i 0.467004 0.883978i
\(148\) 6.18411 12.1370i 0.508331 0.997655i
\(149\) −0.104027 1.98494i −0.00852219 0.162613i −0.999575 0.0291443i \(-0.990722\pi\)
0.991053 0.133469i \(-0.0426116\pi\)
\(150\) 6.58834 + 21.3460i 0.537936 + 1.74289i
\(151\) 0.593873 3.74956i 0.0483287 0.305135i −0.951669 0.307124i \(-0.900633\pi\)
0.999998 + 0.00198927i \(0.000633206\pi\)
\(152\) −7.12976 33.5429i −0.578300 2.72069i
\(153\) 16.8336 4.92415i 1.36092 0.398094i
\(154\) −0.306505 0.226108i −0.0246988 0.0182203i
\(155\) −0.485127 −0.0389663
\(156\) 4.28460 35.1889i 0.343043 2.81737i
\(157\) −0.497594 + 0.361523i −0.0397123 + 0.0288527i −0.607464 0.794347i \(-0.707813\pi\)
0.567752 + 0.823200i \(0.307813\pi\)
\(158\) 13.5708 35.3532i 1.07964 2.81255i
\(159\) 11.0419 + 7.40516i 0.875681 + 0.587267i
\(160\) 11.5047 + 10.3588i 0.909523 + 0.818938i
\(161\) −0.170877 + 0.0270642i −0.0134670 + 0.00213296i
\(162\) −9.98707 22.8483i −0.784658 1.79513i
\(163\) −8.74456 + 13.4654i −0.684927 + 1.05469i 0.309666 + 0.950845i \(0.399783\pi\)
−0.994593 + 0.103849i \(0.966884\pi\)
\(164\) 40.9417 + 40.9417i 3.19701 + 3.19701i
\(165\) −3.05060 1.43964i −0.237489 0.112075i
\(166\) −4.20375 2.42704i −0.326274 0.188375i
\(167\) −1.09457 + 20.8857i −0.0847005 + 1.61618i 0.544378 + 0.838840i \(0.316766\pi\)
−0.629079 + 0.777342i \(0.716568\pi\)
\(168\) −0.178796 0.709061i −0.0137944 0.0547053i
\(169\) −11.2798 + 6.46273i −0.867674 + 0.497133i
\(170\) 9.04602 2.93923i 0.693798 0.225429i
\(171\) −1.87434 + 9.92460i −0.143335 + 0.758953i
\(172\) 4.93689 2.19804i 0.376434 0.167599i
\(173\) −18.1957 8.10124i −1.38339 0.615926i −0.426002 0.904722i \(-0.640078\pi\)
−0.957391 + 0.288796i \(0.906745\pi\)
\(174\) −0.669795 7.42791i −0.0507771 0.563108i
\(175\) 0.0499400 0.186379i 0.00377511 0.0140889i
\(176\) 55.6802 5.44367i 4.19705 0.410332i
\(177\) 2.76317 1.18159i 0.207693 0.0888139i
\(178\) 18.8966 4.01660i 1.41636 0.301057i
\(179\) 0.363755 + 3.46090i 0.0271883 + 0.258680i 0.999670 + 0.0256991i \(0.00818118\pi\)
−0.972481 + 0.232981i \(0.925152\pi\)
\(180\) −4.27419 9.04001i −0.318580 0.673803i
\(181\) −7.74983 + 2.51807i −0.576040 + 0.187167i −0.582526 0.812812i \(-0.697936\pi\)
0.00648573 + 0.999979i \(0.497936\pi\)
\(182\) −0.261108 + 0.321354i −0.0193546 + 0.0238204i
\(183\) −16.9434 + 10.6502i −1.25249 + 0.787287i
\(184\) 26.7556 33.0404i 1.97245 2.43577i
\(185\) −1.04719 + 0.942890i −0.0769906 + 0.0693227i
\(186\) −3.92458 + 0.562226i −0.287764 + 0.0412244i
\(187\) 8.01513 17.6560i 0.586124 1.29114i
\(188\) −0.179504 0.0480979i −0.0130917 0.00350790i
\(189\) −0.0319916 + 0.212986i −0.00232704 + 0.0154925i
\(190\) −0.856842 + 5.40989i −0.0621618 + 0.392474i
\(191\) −14.1765 1.49001i −1.02578 0.107814i −0.423333 0.905974i \(-0.639140\pi\)
−0.602445 + 0.798160i \(0.705807\pi\)
\(192\) 56.5452 + 37.9215i 4.08080 + 2.73675i
\(193\) −17.6529 + 11.4639i −1.27068 + 0.825190i −0.990864 0.134863i \(-0.956940\pi\)
−0.279817 + 0.960053i \(0.590274\pi\)
\(194\) 23.7230 + 17.2358i 1.70321 + 1.23746i
\(195\) −1.71832 + 3.23958i −0.123052 + 0.231991i
\(196\) 12.2756 37.7804i 0.876829 2.69860i
\(197\) −3.83587 14.3157i −0.273294 1.01995i −0.956976 0.290168i \(-0.906289\pi\)
0.683681 0.729781i \(-0.260378\pi\)
\(198\) −26.3471 8.11095i −1.87241 0.576420i
\(199\) −6.68195 + 3.85782i −0.473671 + 0.273474i −0.717775 0.696275i \(-0.754839\pi\)
0.244104 + 0.969749i \(0.421506\pi\)
\(200\) 21.5268 + 42.2486i 1.52217 + 2.98743i
\(201\) 7.20423 + 0.106559i 0.508147 + 0.00751611i
\(202\) 22.6638 + 27.9874i 1.59462 + 1.96919i
\(203\) −0.0292448 + 0.0573961i −0.00205258 + 0.00402842i
\(204\) 51.5951 25.3349i 3.61238 1.77380i
\(205\) −2.43621 5.47181i −0.170152 0.382168i
\(206\) 5.76561 7.11993i 0.401709 0.496069i
\(207\) −11.0247 + 5.93748i −0.766270 + 0.412683i
\(208\) −3.08260 60.7412i −0.213740 4.21164i
\(209\) 6.96379 + 8.72843i 0.481696 + 0.603758i
\(210\) −0.0139255 + 0.115967i −0.000960952 + 0.00800246i
\(211\) −0.363692 0.403920i −0.0250376 0.0278070i 0.730496 0.682917i \(-0.239289\pi\)
−0.755534 + 0.655110i \(0.772622\pi\)
\(212\) 39.8044 + 17.7221i 2.73378 + 1.21716i
\(213\) 3.16151 13.8623i 0.216623 0.949831i
\(214\) 38.0595 1.99461i 2.60169 0.136349i
\(215\) −0.558274 + 0.0292579i −0.0380740 + 0.00199537i
\(216\) −29.1797 44.1565i −1.98543 3.00447i
\(217\) 0.0312832 + 0.0139282i 0.00212364 + 0.000945507i
\(218\) −16.8434 18.7065i −1.14078 1.26696i
\(219\) 20.6208 + 2.47619i 1.39343 + 0.167325i
\(220\) −10.6571 2.93869i −0.718505 0.198127i
\(221\) −18.7660 9.60085i −1.26233 0.645823i
\(222\) −7.37878 + 8.84140i −0.495231 + 0.593396i
\(223\) −14.6647 + 18.1094i −0.982020 + 1.21269i −0.00490370 + 0.999988i \(0.501561\pi\)
−0.977116 + 0.212706i \(0.931772\pi\)
\(224\) −0.444467 0.998289i −0.0296972 0.0667010i
\(225\) −1.04838 13.9262i −0.0698919 0.928411i
\(226\) −9.91781 + 19.4648i −0.659723 + 1.29478i
\(227\) −5.98242 7.38767i −0.397067 0.490337i 0.538927 0.842352i \(-0.318830\pi\)
−0.935994 + 0.352015i \(0.885496\pi\)
\(228\) −0.489540 + 33.0967i −0.0324206 + 2.19188i
\(229\) 0.608552 + 1.19435i 0.0402142 + 0.0789249i 0.910239 0.414083i \(-0.135898\pi\)
−0.870025 + 0.493007i \(0.835898\pi\)
\(230\) −5.88093 + 3.39535i −0.387777 + 0.223883i
\(231\) 0.155384 + 0.180418i 0.0102235 + 0.0118706i
\(232\) −4.09711 15.2906i −0.268988 1.00388i
\(233\) −5.46517 + 16.8201i −0.358035 + 1.10192i 0.596194 + 0.802841i \(0.296679\pi\)
−0.954229 + 0.299078i \(0.903321\pi\)
\(234\) −10.1465 + 28.1990i −0.663295 + 1.84342i
\(235\) 0.0155528 + 0.0112997i 0.00101455 + 0.000737114i
\(236\) 8.25990 5.36404i 0.537673 0.349169i
\(237\) −13.1857 + 19.6613i −0.856500 + 1.27714i
\(238\) −0.667715 0.0701797i −0.0432816 0.00454907i
\(239\) 2.06887 13.0623i 0.133824 0.844933i −0.825865 0.563868i \(-0.809313\pi\)
0.959689 0.281064i \(-0.0906874\pi\)
\(240\) −9.87775 14.0272i −0.637606 0.905454i
\(241\) −14.1391 3.78856i −0.910780 0.244043i −0.227140 0.973862i \(-0.572938\pi\)
−0.683640 + 0.729819i \(0.739604\pi\)
\(242\) −25.7984 + 16.2259i −1.65839 + 1.04304i
\(243\) 2.91108 + 15.3142i 0.186746 + 0.982408i
\(244\) −48.7400 + 43.8857i −3.12026 + 2.80949i
\(245\) −2.58614 + 3.19362i −0.165223 + 0.204033i
\(246\) −26.0498 41.4425i −1.66088 2.64228i
\(247\) 9.83223 7.11872i 0.625610 0.452953i
\(248\) −8.00326 + 2.60042i −0.508208 + 0.165127i
\(249\) 2.22481 + 2.06362i 0.140991 + 0.130776i
\(250\) −1.64196 15.6222i −0.103846 0.988033i
\(251\) 27.1952 5.78053i 1.71655 0.364864i 0.758545 0.651621i \(-0.225911\pi\)
0.958003 + 0.286758i \(0.0925774\pi\)
\(252\) 0.0160773 + 0.705655i 0.00101278 + 0.0444521i
\(253\) −2.97649 + 13.5197i −0.187130 + 0.849976i
\(254\) 1.05466 3.93603i 0.0661749 0.246968i
\(255\) −5.92210 + 0.534013i −0.370856 + 0.0334412i
\(256\) 70.3774 + 31.3340i 4.39859 + 1.95838i
\(257\) −12.3736 + 5.50908i −0.771844 + 0.343647i −0.754584 0.656204i \(-0.772161\pi\)
−0.0172607 + 0.999851i \(0.505495\pi\)
\(258\) −4.48241 + 0.883688i −0.279063 + 0.0550160i
\(259\) 0.0945981 0.0307368i 0.00587804 0.00190989i
\(260\) −3.73264 + 11.4236i −0.231489 + 0.708460i
\(261\) −0.624278 + 4.62040i −0.0386418 + 0.285996i
\(262\) −1.11576 + 21.2900i −0.0689320 + 1.31530i
\(263\) 18.2804 + 10.5542i 1.12722 + 0.650800i 0.943234 0.332128i \(-0.107767\pi\)
0.183985 + 0.982929i \(0.441100\pi\)
\(264\) −58.0433 7.39797i −3.57232 0.455314i
\(265\) −3.18717 3.18717i −0.195787 0.195787i
\(266\) 0.210573 0.324254i 0.0129111 0.0198813i
\(267\) −12.0758 0.178616i −0.739027 0.0109311i
\(268\) 23.3219 3.69382i 1.42461 0.225636i
\(269\) −2.97896 2.68226i −0.181630 0.163541i 0.573300 0.819345i \(-0.305663\pi\)
−0.754931 + 0.655805i \(0.772329\pi\)
\(270\) 1.82364 + 8.25469i 0.110983 + 0.502364i
\(271\) 9.36005 24.3838i 0.568583 1.48121i −0.284108 0.958792i \(-0.591697\pi\)
0.852691 0.522416i \(-0.174969\pi\)
\(272\) 79.7834 57.9660i 4.83758 3.51471i
\(273\) 0.203815 0.159569i 0.0123354 0.00965758i
\(274\) 37.9574 2.29309
\(275\) −12.4246 9.16560i −0.749231 0.552707i
\(276\) −32.2704 + 25.3511i −1.94245 + 1.52596i
\(277\) −4.90684 23.0849i −0.294823 1.38704i −0.837199 0.546899i \(-0.815808\pi\)
0.542375 0.840136i \(-0.317525\pi\)
\(278\) −0.258552 + 1.63244i −0.0155069 + 0.0979070i
\(279\) 2.47018 + 0.202861i 0.147886 + 0.0121450i
\(280\) 0.0129747 + 0.247573i 0.000775388 + 0.0147953i
\(281\) −3.26909 + 6.41595i −0.195018 + 0.382743i −0.967721 0.252024i \(-0.918904\pi\)
0.772704 + 0.634767i \(0.218904\pi\)
\(282\) 0.138914 + 0.0733882i 0.00827222 + 0.00437020i
\(283\) 18.1840 1.91122i 1.08093 0.113610i 0.452719 0.891653i \(-0.350454\pi\)
0.628211 + 0.778043i \(0.283788\pi\)
\(284\) 2.43868 46.5329i 0.144709 2.76122i
\(285\) 1.27425 3.17821i 0.0754798 0.188261i
\(286\) 16.3094 + 28.8396i 0.964396 + 1.70532i
\(287\) 0.422792i 0.0249566i
\(288\) −54.2479 57.5561i −3.19659 3.39153i
\(289\) −1.79578 17.0857i −0.105634 1.00504i
\(290\) −0.264294 + 2.51459i −0.0155199 + 0.147662i
\(291\) −12.0633 13.8028i −0.707162 0.809134i
\(292\) 67.9716 3.56224i 3.97774 0.208464i
\(293\) −10.3342 + 8.36847i −0.603730 + 0.488891i −0.881771 0.471678i \(-0.843648\pi\)
0.278041 + 0.960569i \(0.410315\pi\)
\(294\) −17.2202 + 28.8329i −1.00430 + 1.68157i
\(295\) −0.996569 + 0.211827i −0.0580225 + 0.0123331i
\(296\) −12.2215 + 21.1683i −0.710362 + 1.23038i
\(297\) 14.9311 + 8.60599i 0.866389 + 0.499370i
\(298\) 5.50708i 0.319017i
\(299\) 14.5302 + 3.91911i 0.840302 + 0.226648i
\(300\) −11.1906 44.3794i −0.646092 2.56225i
\(301\) 0.0368401 + 0.0141416i 0.00212343 + 0.000815107i
\(302\) −2.18684 + 10.2883i −0.125839 + 0.592024i
\(303\) −9.92314 20.2087i −0.570070 1.16096i
\(304\) 8.88391 + 56.0908i 0.509527 + 3.21703i
\(305\) 6.33408 2.43143i 0.362689 0.139223i
\(306\) −47.2897 + 11.1833i −2.70337 + 0.639308i
\(307\) 8.40611 8.40611i 0.479762 0.479762i −0.425294 0.905055i \(-0.639829\pi\)
0.905055 + 0.425294i \(0.139829\pi\)
\(308\) 0.602851 + 0.495471i 0.0343506 + 0.0282321i
\(309\) −4.50383 + 3.53814i −0.256214 + 0.201278i
\(310\) 1.34226 + 0.0703450i 0.0762353 + 0.00399532i
\(311\) −3.43227 + 2.49369i −0.194626 + 0.141404i −0.680831 0.732441i \(-0.738381\pi\)
0.486205 + 0.873845i \(0.338381\pi\)
\(312\) −10.9825 + 62.6549i −0.621764 + 3.54714i
\(313\) −5.58139 17.1777i −0.315479 0.970944i −0.975557 0.219747i \(-0.929477\pi\)
0.660078 0.751197i \(-0.270523\pi\)
\(314\) 1.42918 0.928119i 0.0806532 0.0523768i
\(315\) 0.0246075 0.0687457i 0.00138648 0.00387338i
\(316\) −31.5560 + 70.8759i −1.77516 + 3.98708i
\(317\) 14.1087 + 27.6899i 0.792425 + 1.55522i 0.831199 + 0.555974i \(0.187655\pi\)
−0.0387741 + 0.999248i \(0.512345\pi\)
\(318\) −29.4773 22.0899i −1.65300 1.23874i
\(319\) 3.42110 + 3.85546i 0.191545 + 0.215864i
\(320\) −16.3214 16.3214i −0.912393 0.912393i
\(321\) −23.4744 4.07475i −1.31022 0.227430i
\(322\) 0.476711 0.0501043i 0.0265661 0.00279221i
\(323\) 18.3755 + 7.05368i 1.02244 + 0.392477i
\(324\) 17.9832 + 47.8174i 0.999068 + 2.65652i
\(325\) −10.5844 + 13.0265i −0.587117 + 0.722583i
\(326\) 26.1472 35.9885i 1.44816 1.99322i
\(327\) 7.66573 + 13.7429i 0.423916 + 0.759984i
\(328\) −69.5212 77.2111i −3.83866 4.26327i
\(329\) −0.000678493 0.00117519i −3.74066e−5 6.47901e-5i
\(330\) 8.23171 + 4.42557i 0.453141 + 0.243619i
\(331\) −6.65066 + 24.8206i −0.365553 + 1.36426i 0.501115 + 0.865380i \(0.332923\pi\)
−0.866669 + 0.498884i \(0.833743\pi\)
\(332\) 8.34045 + 5.41635i 0.457742 + 0.297261i
\(333\) 5.72635 4.36313i 0.313802 0.239098i
\(334\) 6.05698 57.6283i 0.331423 3.15328i
\(335\) −2.38928 0.507858i −0.130540 0.0277472i
\(336\) 0.234235 + 1.18813i 0.0127786 + 0.0648180i
\(337\) 2.66765 3.67170i 0.145316 0.200010i −0.730154 0.683282i \(-0.760552\pi\)
0.875470 + 0.483272i \(0.160552\pi\)
\(338\) 32.1463 16.2456i 1.74853 0.883647i
\(339\) 8.75059 10.4851i 0.475267 0.569474i
\(340\) −18.8229 + 5.04358i −1.02082 + 0.273527i
\(341\) 1.95155 1.92340i 0.105682 0.104158i
\(342\) 6.62508 27.1878i 0.358243 1.47015i
\(343\) 0.516976 0.263412i 0.0279141 0.0142229i
\(344\) −9.05315 + 3.47518i −0.488113 + 0.187369i
\(345\) 4.05639 1.25198i 0.218388 0.0674045i
\(346\) 49.1696 + 25.0532i 2.64337 + 1.34687i
\(347\) −20.3560 18.3286i −1.09277 0.983931i −0.0928354 0.995681i \(-0.529593\pi\)
−0.999931 + 0.0117502i \(0.996260\pi\)
\(348\) 0.573922 + 15.2690i 0.0307654 + 0.818503i
\(349\) 10.3391 + 8.37246i 0.553441 + 0.448168i 0.864794 0.502127i \(-0.167449\pi\)
−0.311353 + 0.950294i \(0.600782\pi\)
\(350\) −0.165201 + 0.508436i −0.00883035 + 0.0271770i
\(351\) 10.1041 15.7768i 0.539314 0.842104i
\(352\) −87.3506 + 3.94194i −4.65580 + 0.210106i
\(353\) 2.24886 + 8.39285i 0.119695 + 0.446706i 0.999595 0.0284514i \(-0.00905759\pi\)
−0.879901 + 0.475158i \(0.842391\pi\)
\(354\) −7.81655 + 2.86859i −0.415445 + 0.152464i
\(355\) −1.96060 + 4.40358i −0.104058 + 0.233718i
\(356\) −39.0924 + 6.19162i −2.07189 + 0.328155i
\(357\) 0.397216 + 0.135590i 0.0210229 + 0.00717620i
\(358\) −0.504605 9.62845i −0.0266692 0.508879i
\(359\) −1.97414 12.4643i −0.104191 0.657838i −0.983407 0.181414i \(-0.941933\pi\)
0.879216 0.476424i \(-0.158067\pi\)
\(360\) 6.81023 + 16.6008i 0.358931 + 0.874938i
\(361\) 5.69655 5.12920i 0.299819 0.269958i
\(362\) 21.8075 5.84331i 1.14618 0.307118i
\(363\) 17.9796 6.30353i 0.943684 0.330850i
\(364\) 0.568673 0.629479i 0.0298066 0.0329937i
\(365\) −6.69652 2.17583i −0.350512 0.113888i
\(366\) 48.4236 27.0105i 2.53114 1.41186i
\(367\) −0.408246 + 0.181763i −0.0213103 + 0.00948794i −0.417364 0.908739i \(-0.637046\pi\)
0.396054 + 0.918227i \(0.370379\pi\)
\(368\) −47.1118 + 52.3229i −2.45587 + 2.72752i
\(369\) 10.1166 + 28.8802i 0.526650 + 1.50344i
\(370\) 3.03410 2.45697i 0.157735 0.127732i
\(371\) 0.114019 + 0.297029i 0.00591955 + 0.0154210i
\(372\) 8.08980 0.729480i 0.419436 0.0378218i
\(373\) 7.00353 + 12.1305i 0.362629 + 0.628092i 0.988393 0.151921i \(-0.0485458\pi\)
−0.625763 + 0.780013i \(0.715212\pi\)
\(374\) −24.7366 + 47.6890i −1.27910 + 2.46594i
\(375\) −1.17079 + 9.74993i −0.0604595 + 0.503484i
\(376\) 0.317148 + 0.103048i 0.0163556 + 0.00531427i
\(377\) 4.36056 3.51918i 0.224580 0.181247i
\(378\) 0.119399 0.584657i 0.00614121 0.0300715i
\(379\) −7.95632 12.2517i −0.408689 0.629326i 0.573059 0.819514i \(-0.305757\pi\)
−0.981748 + 0.190189i \(0.939090\pi\)
\(380\) 2.33313 10.9765i 0.119687 0.563083i
\(381\) −1.18994 + 2.25240i −0.0609624 + 0.115394i
\(382\) 39.0079 + 6.17825i 1.99582 + 0.316107i
\(383\) −7.53285 + 11.5996i −0.384911 + 0.592711i −0.977020 0.213147i \(-0.931629\pi\)
0.592109 + 0.805858i \(0.298295\pi\)
\(384\) −77.8684 58.3536i −3.97371 2.97784i
\(385\) −0.0398530 0.0701999i −0.00203110 0.00357772i
\(386\) 50.5047 29.1589i 2.57062 1.48415i
\(387\) 2.85486 + 0.0844723i 0.145121 + 0.00429397i
\(388\) −46.6881 37.8073i −2.37023 1.91937i
\(389\) −8.38669 6.09329i −0.425222 0.308942i 0.354514 0.935051i \(-0.384646\pi\)
−0.779736 + 0.626109i \(0.784646\pi\)
\(390\) 5.22405 8.71420i 0.264530 0.441261i
\(391\) 7.54077 + 23.2081i 0.381353 + 1.17368i
\(392\) −25.5455 + 66.5484i −1.29024 + 3.36120i
\(393\) 3.63948 12.8211i 0.183587 0.646740i
\(394\) 8.53736 + 40.1651i 0.430106 + 2.02349i
\(395\) 5.67509 5.67509i 0.285545 0.285545i
\(396\) 53.0354 + 19.4197i 2.66513 + 0.975876i
\(397\) −5.60447 1.50171i −0.281280 0.0753688i 0.115421 0.993317i \(-0.463178\pi\)
−0.396701 + 0.917948i \(0.629845\pi\)
\(398\) 19.0472 9.70502i 0.954749 0.486469i
\(399\) −0.173417 + 0.168362i −0.00868170 + 0.00842862i
\(400\) −31.9390 71.7361i −1.59695 3.58680i
\(401\) −1.71493 2.64077i −0.0856397 0.131874i 0.793255 0.608890i \(-0.208385\pi\)
−0.878894 + 0.477016i \(0.841718\pi\)
\(402\) −19.9174 1.33947i −0.993389 0.0668065i
\(403\) −1.98953 2.21696i −0.0991054 0.110434i
\(404\) −43.3682 59.6912i −2.15765 2.96975i
\(405\) 0.0359403 5.28471i 0.00178589 0.262600i
\(406\) 0.0892378 0.154564i 0.00442880 0.00767091i
\(407\) 0.474254 7.94484i 0.0235079 0.393811i
\(408\) −94.8360 + 40.5539i −4.69508 + 2.00772i
\(409\) 10.0239 + 6.50962i 0.495651 + 0.321880i 0.768143 0.640278i \(-0.221181\pi\)
−0.272492 + 0.962158i \(0.587848\pi\)
\(410\) 5.94713 + 15.4928i 0.293708 + 0.765135i
\(411\) −23.1350 5.27627i −1.14116 0.260259i
\(412\) −12.5596 + 13.9488i −0.618767 + 0.687210i
\(413\) 0.0703450 + 0.0149523i 0.00346145 + 0.000735754i
\(414\) 31.3644 14.8293i 1.54148 0.728822i
\(415\) −0.604695 0.832291i −0.0296833 0.0408556i
\(416\) −0.157189 + 95.0566i −0.00770681 + 4.66053i
\(417\) 0.384504 0.959027i 0.0188293 0.0469638i
\(418\) −18.0019 25.1598i −0.880504 1.23061i
\(419\) 24.7156 + 14.2696i 1.20744 + 0.697114i 0.962199 0.272348i \(-0.0878003\pi\)
0.245239 + 0.969463i \(0.421134\pi\)
\(420\) 0.0409254 0.235769i 0.00199695 0.0115044i
\(421\) −22.7040 3.59596i −1.10652 0.175256i −0.423674 0.905815i \(-0.639260\pi\)
−0.682850 + 0.730558i \(0.739260\pi\)
\(422\) 0.947702 + 1.17031i 0.0461334 + 0.0569700i
\(423\) −0.0744667 0.0640398i −0.00362069 0.00311372i
\(424\) −69.6638 35.4955i −3.38317 1.72381i
\(425\) −27.0668 2.84483i −1.31293 0.137995i
\(426\) −10.7574 + 37.8962i −0.521199 + 1.83608i
\(427\) −0.478258 0.0250644i −0.0231445 0.00121295i
\(428\) −78.0819 −3.77423
\(429\) −5.93172 19.8448i −0.286386 0.958114i
\(430\) 1.54889 0.0746941
\(431\) 25.8152 + 1.35292i 1.24347 + 0.0651676i 0.662692 0.748892i \(-0.269414\pi\)
0.580781 + 0.814060i \(0.302747\pi\)
\(432\) 44.4301 + 75.5546i 2.13764 + 3.63512i
\(433\) 8.27514 + 0.869752i 0.397678 + 0.0417976i 0.301257 0.953543i \(-0.402594\pi\)
0.0964208 + 0.995341i \(0.469261\pi\)
\(434\) −0.0845356 0.0430730i −0.00405784 0.00206757i
\(435\) 0.510628 1.49590i 0.0244828 0.0717230i
\(436\) 32.4551 + 40.0787i 1.55432 + 1.91942i
\(437\) −13.8794 2.19828i −0.663941 0.105158i
\(438\) −56.6951 9.84127i −2.70900 0.470234i
\(439\) 13.1481 + 7.59109i 0.627527 + 0.362303i 0.779794 0.626037i \(-0.215324\pi\)
−0.152267 + 0.988339i \(0.548657\pi\)
\(440\) 18.8212 + 6.26688i 0.897268 + 0.298762i
\(441\) 14.5036 15.1799i 0.690648 0.722852i
\(442\) 50.5300 + 29.2850i 2.40347 + 1.39295i
\(443\) −2.56308 3.52778i −0.121776 0.167610i 0.743777 0.668428i \(-0.233032\pi\)
−0.865552 + 0.500818i \(0.833032\pi\)
\(444\) 16.0447 17.2979i 0.761446 0.820923i
\(445\) 4.00494 + 0.851277i 0.189852 + 0.0403544i
\(446\) 43.2005 47.9791i 2.04561 2.27187i
\(447\) 0.765512 3.35656i 0.0362075 0.158760i
\(448\) 0.583885 + 1.52107i 0.0275860 + 0.0718639i
\(449\) −2.60791 1.69360i −0.123075 0.0799257i 0.481634 0.876373i \(-0.340044\pi\)
−0.604708 + 0.796447i \(0.706710\pi\)
\(450\) 0.881342 + 38.6833i 0.0415469 + 1.82355i
\(451\) 31.4946 + 12.3528i 1.48302 + 0.581672i
\(452\) 22.3785 38.7607i 1.05260 1.82315i
\(453\) 2.76300 5.96671i 0.129817 0.280340i
\(454\) 15.4811 + 21.3079i 0.726563 + 1.00003i
\(455\) −0.0782567 + 0.0397109i −0.00366873 + 0.00186168i
\(456\) 3.98544 59.2621i 0.186635 2.77520i
\(457\) −14.6974 22.6319i −0.687513 1.05868i −0.994271 0.106890i \(-0.965911\pi\)
0.306758 0.951788i \(-0.400756\pi\)
\(458\) −1.51057 3.39280i −0.0705844 0.158535i
\(459\) 30.3776 0.242705i 1.41790 0.0113285i
\(460\) 12.3962 6.31617i 0.577975 0.294493i
\(461\) 8.94436 + 2.39664i 0.416581 + 0.111622i 0.461020 0.887390i \(-0.347484\pi\)
−0.0444396 + 0.999012i \(0.514150\pi\)
\(462\) −0.403759 0.521716i −0.0187846 0.0242724i
\(463\) 26.5260 26.5260i 1.23277 1.23277i 0.269874 0.962896i \(-0.413018\pi\)
0.962896 0.269874i \(-0.0869819\pi\)
\(464\) 5.45049 + 25.6426i 0.253033 + 1.19043i
\(465\) −0.808328 0.229456i −0.0374853 0.0106408i
\(466\) 17.5601 45.7457i 0.813457 2.11913i
\(467\) 4.20468 + 12.9407i 0.194569 + 0.598823i 0.999981 + 0.00610741i \(0.00194406\pi\)
−0.805412 + 0.592715i \(0.798056\pi\)
\(468\) 23.7828 56.6059i 1.09936 2.61661i
\(469\) 0.139491 + 0.101346i 0.00644110 + 0.00467973i
\(470\) −0.0413933 0.0335196i −0.00190933 0.00154614i
\(471\) −1.00009 + 0.367024i −0.0460819 + 0.0169116i
\(472\) −15.3052 + 8.83646i −0.704479 + 0.406731i
\(473\) 2.12980 2.33111i 0.0979283 0.107185i
\(474\) 39.3334 52.4874i 1.80664 2.41083i
\(475\) 8.53588 13.1441i 0.391653 0.603093i
\(476\) 1.35859 + 0.215180i 0.0622709 + 0.00986274i
\(477\) 14.8958 + 17.5613i 0.682030 + 0.804075i
\(478\) −7.61829 + 35.8412i −0.348452 + 1.63934i
\(479\) 14.9879 + 23.0793i 0.684814 + 1.05452i 0.994607 + 0.103717i \(0.0330735\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(480\) 14.2697 + 22.7016i 0.651322 + 1.03618i
\(481\) −8.60342 0.918642i −0.392282 0.0418865i
\(482\) 38.5711 + 12.5325i 1.75687 + 0.570840i
\(483\) −0.297519 0.0357268i −0.0135376 0.00162562i
\(484\) 54.5223 30.4312i 2.47828 1.38324i
\(485\) 3.10737 + 5.38213i 0.141099 + 0.244390i
\(486\) −5.83384 42.7939i −0.264628 1.94117i
\(487\) −11.1010 28.9190i −0.503033 1.31045i −0.916539 0.399944i \(-0.869029\pi\)
0.413506 0.910501i \(-0.364304\pi\)
\(488\) 91.4618 74.0643i 4.14028 3.35274i
\(489\) −20.9393 + 18.3004i −0.946906 + 0.827571i
\(490\) 7.61849 8.46119i 0.344168 0.382237i
\(491\) 14.2470 6.34318i 0.642959 0.286264i −0.0592409 0.998244i \(-0.518868\pi\)
0.702200 + 0.711980i \(0.252201\pi\)
\(492\) 48.8532 + 87.5826i 2.20247 + 3.94853i
\(493\) 8.64128 + 2.80772i 0.389184 + 0.126453i
\(494\) −28.2363 + 18.2706i −1.27041 + 0.822031i
\(495\) −4.40204 3.84163i −0.197857 0.172668i
\(496\) 13.4611 3.60689i 0.604421 0.161954i
\(497\) 0.252857 0.227673i 0.0113422 0.0102125i
\(498\) −5.85643 6.03227i −0.262433 0.270313i
\(499\) 0.00308538 + 0.0194803i 0.000138120 + 0.000872058i 0.987757 0.155998i \(-0.0498595\pi\)
−0.987619 + 0.156870i \(0.949859\pi\)
\(500\) 1.68430 + 32.1383i 0.0753241 + 1.43727i
\(501\) −11.7023 + 34.2824i −0.522822 + 1.53162i
\(502\) −76.0827 + 12.0503i −3.39574 + 0.537832i
\(503\) −5.53411 + 12.4298i −0.246754 + 0.554218i −0.993880 0.110464i \(-0.964766\pi\)
0.747126 + 0.664682i \(0.231433\pi\)
\(504\) 0.0374601 1.26602i 0.00166861 0.0563930i
\(505\) 1.97546 + 7.37252i 0.0879069 + 0.328073i
\(506\) 10.1958 36.9750i 0.453259 1.64374i
\(507\) −21.8513 + 5.43320i −0.970451 + 0.241297i
\(508\) −2.57981 + 7.93985i −0.114461 + 0.352274i
\(509\) 5.17515 + 4.19075i 0.229384 + 0.185752i 0.737122 0.675760i \(-0.236185\pi\)
−0.507737 + 0.861512i \(0.669518\pi\)
\(510\) 16.4629 0.618796i 0.728988 0.0274008i
\(511\) 0.369353 + 0.332567i 0.0163392 + 0.0147119i
\(512\) −90.0647 45.8903i −3.98034 2.02808i
\(513\) −7.81723 + 15.6500i −0.345139 + 0.690966i
\(514\) 35.0344 13.4485i 1.54530 0.593186i
\(515\) 1.73008 0.881519i 0.0762363 0.0388444i
\(516\) 9.26557 1.32736i 0.407894 0.0584339i
\(517\) −0.107366 + 0.0162066i −0.00472193 + 0.000712766i
\(518\) −0.266193 + 0.0713263i −0.0116959 + 0.00313390i
\(519\) −26.4863 22.1047i −1.16262 0.970288i
\(520\) 7.76158 20.1201i 0.340368 0.882325i
\(521\) −25.9876 + 35.7688i −1.13854 + 1.56706i −0.367803 + 0.929904i \(0.619890\pi\)
−0.770733 + 0.637158i \(0.780110\pi\)
\(522\) 2.39724 12.6933i 0.104924 0.555572i
\(523\) 35.1983 + 7.48164i 1.53912 + 0.327149i 0.897896 0.440208i \(-0.145095\pi\)
0.641220 + 0.767357i \(0.278429\pi\)
\(524\) 4.56560 43.4388i 0.199449 1.89763i
\(525\) 0.171365 0.286927i 0.00747897 0.0125225i
\(526\) −49.0484 31.8524i −2.13861 1.38883i
\(527\) 1.25011 4.66547i 0.0544556 0.203231i
\(528\) 95.3502 + 17.2654i 4.14958 + 0.751379i
\(529\) 2.78902 + 4.83072i 0.121262 + 0.210031i
\(530\) 8.35621 + 9.28051i 0.362970 + 0.403119i
\(531\) 5.16292 0.661860i 0.224052 0.0287223i
\(532\) −0.465591 + 0.640831i −0.0201859 + 0.0277835i
\(533\) 15.0143 33.5732i 0.650343 1.45422i
\(534\) 33.3857 + 2.24523i 1.44474 + 0.0971605i
\(535\) 7.54087 + 2.89467i 0.326020 + 0.125148i
\(536\) −42.1389 + 4.42897i −1.82012 + 0.191302i
\(537\) −1.03085 + 5.93867i −0.0444843 + 0.256272i
\(538\) 7.85332 + 7.85332i 0.338581 + 0.338581i
\(539\) −2.25847 23.1005i −0.0972790 0.995011i
\(540\) −2.84598 17.0843i −0.122471 0.735190i
\(541\) −5.85121 11.4837i −0.251563 0.493721i 0.730345 0.683079i \(-0.239359\pi\)
−0.981908 + 0.189358i \(0.939359\pi\)
\(542\) −29.4334 + 66.1084i −1.26427 + 2.83960i
\(543\) −14.1039 + 0.530130i −0.605257 + 0.0227500i
\(544\) −129.267 + 83.9470i −5.54228 + 3.59920i
\(545\) −1.64859 5.07384i −0.0706179 0.217339i
\(546\) −0.587059 + 0.411947i −0.0251238 + 0.0176297i
\(547\) −12.7779 + 9.28368i −0.546343 + 0.396941i −0.826435 0.563032i \(-0.809635\pi\)
0.280092 + 0.959973i \(0.409635\pi\)
\(548\) −77.6592 4.06994i −3.31744 0.173859i
\(549\) −33.2687 + 9.73171i −1.41987 + 0.415339i
\(550\) 33.0477 + 27.1612i 1.40916 + 1.15816i
\(551\) −3.69976 + 3.69976i −0.157615 + 0.157615i
\(552\) 60.2082 42.3977i 2.56263 1.80456i
\(553\) −0.528890 + 0.203022i −0.0224907 + 0.00863337i
\(554\) 10.2290 + 64.5833i 0.434588 + 2.74388i
\(555\) −2.19081 + 1.07576i −0.0929948 + 0.0456635i
\(556\) 0.704023 3.31217i 0.0298572 0.140467i
\(557\) 7.95143 + 3.05227i 0.336913 + 0.129329i 0.520942 0.853592i \(-0.325581\pi\)
−0.184029 + 0.982921i \(0.558914\pi\)
\(558\) −6.80513 0.919464i −0.288084 0.0389240i
\(559\) −2.42321 2.43124i −0.102491 0.102830i
\(560\) 0.410557i 0.0173492i
\(561\) 21.7060 25.6278i 0.916426 1.08201i
\(562\) 9.97533 17.2778i 0.420784 0.728819i
\(563\) 10.5142 2.23485i 0.443119 0.0941878i 0.0190516 0.999819i \(-0.493935\pi\)
0.424067 + 0.905631i \(0.360602\pi\)
\(564\) −0.276343 0.165044i −0.0116362 0.00694960i
\(565\) −3.59818 + 2.91375i −0.151377 + 0.122582i
\(566\) −50.5892 + 2.65127i −2.12642 + 0.111441i
\(567\) −0.154044 + 0.339751i −0.00646923 + 0.0142682i
\(568\) −8.74007 + 83.1562i −0.366725 + 3.48916i
\(569\) −3.58233 34.0836i −0.150179 1.42886i −0.766946 0.641712i \(-0.778224\pi\)
0.616767 0.787146i \(-0.288442\pi\)
\(570\) −3.98647 + 8.60879i −0.166975 + 0.360582i
\(571\) 39.1148i 1.63690i 0.574576 + 0.818451i \(0.305167\pi\)
−0.574576 + 0.818451i \(0.694833\pi\)
\(572\) −30.2761 60.7532i −1.26591 2.54022i
\(573\) −22.9165 9.18794i −0.957349 0.383832i
\(574\) 0.0613062 1.16979i 0.00255887 0.0488262i
\(575\) 19.3242 2.03105i 0.805873 0.0847007i
\(576\) 76.2805 + 89.9305i 3.17836 + 3.74710i
\(577\) 9.86995 19.3709i 0.410892 0.806420i −0.589107 0.808055i \(-0.700520\pi\)
0.999999 + 0.00163482i \(0.000520380\pi\)
\(578\) 2.49113 + 47.5336i 0.103617 + 1.97714i
\(579\) −34.8358 + 10.7519i −1.44773 + 0.446833i
\(580\) 0.810359 5.11641i 0.0336483 0.212447i
\(581\) 0.0150981 + 0.0710310i 0.000626375 + 0.00294686i
\(582\) 31.3755 + 39.9391i 1.30056 + 1.65553i
\(583\) 25.4576 + 0.184893i 1.05434 + 0.00765748i
\(584\) −122.137 −5.05408
\(585\) −4.39537 + 4.58512i −0.181726 + 0.189571i
\(586\) 29.8064 21.6556i 1.23129 0.894585i
\(587\) −8.06353 + 21.0062i −0.332817 + 0.867019i 0.660418 + 0.750898i \(0.270379\pi\)
−0.993235 + 0.116121i \(0.962954\pi\)
\(588\) 38.3233 57.1444i 1.58043 2.35659i
\(589\) 2.06701 + 1.86114i 0.0851695 + 0.0766869i
\(590\) 2.78805 0.441584i 0.114782 0.0181797i
\(591\) 0.379651 25.6673i 0.0156168 1.05581i
\(592\) 22.0465 33.9487i 0.906106 1.39528i
\(593\) 4.60162 + 4.60162i 0.188966 + 0.188966i 0.795249 0.606283i \(-0.207340\pi\)
−0.606283 + 0.795249i \(0.707340\pi\)
\(594\) −40.0638 25.9763i −1.64384 1.06582i
\(595\) −0.123231 0.0711473i −0.00505197 0.00291676i
\(596\) 0.590491 11.2672i 0.0241875 0.461524i
\(597\) −12.9583 + 3.26754i −0.530347 + 0.133732i
\(598\) −39.6342 12.9504i −1.62076 0.529582i
\(599\) 9.40097 3.05456i 0.384113 0.124806i −0.110594 0.993866i \(-0.535275\pi\)
0.494707 + 0.869060i \(0.335275\pi\)
\(600\) 15.8854 + 80.5773i 0.648521 + 3.28955i
\(601\) −20.4151 + 9.08937i −0.832747 + 0.370763i −0.778407 0.627760i \(-0.783972\pi\)
−0.0543400 + 0.998522i \(0.517305\pi\)
\(602\) −0.0998795 0.0444692i −0.00407078 0.00181243i
\(603\) 11.9534 + 3.58502i 0.486781 + 0.145993i
\(604\) 5.57733 20.8149i 0.226938 0.846945i
\(605\) −6.39372 + 0.917678i −0.259942 + 0.0373089i
\(606\) 24.5253 + 57.3528i 0.996271 + 2.32980i
\(607\) −8.06633 + 1.71455i −0.327402 + 0.0695915i −0.368680 0.929556i \(-0.620190\pi\)
0.0412783 + 0.999148i \(0.486857\pi\)
\(608\) −9.27786 88.2729i −0.376267 3.57994i
\(609\) −0.0758756 + 0.0818023i −0.00307463 + 0.00331480i
\(610\) −17.8779 + 5.80887i −0.723854 + 0.235194i
\(611\) 0.0121445 + 0.117415i 0.000491314 + 0.00475008i
\(612\) 97.9518 17.8100i 3.95947 0.719927i
\(613\) −15.6144 + 19.2822i −0.630659 + 0.778799i −0.987880 0.155221i \(-0.950391\pi\)
0.357221 + 0.934020i \(0.383724\pi\)
\(614\) −24.4771 + 22.0393i −0.987817 + 0.889435i
\(615\) −1.47119 10.2695i −0.0593240 0.414107i
\(616\) −1.03376 0.944482i −0.0416512 0.0380543i
\(617\) −9.64085 2.58326i −0.388126 0.103998i 0.0594787 0.998230i \(-0.481056\pi\)
−0.447605 + 0.894232i \(0.647723\pi\)
\(618\) 12.9744 9.13634i 0.521905 0.367517i
\(619\) −2.70886 + 17.1031i −0.108878 + 0.687430i 0.871513 + 0.490372i \(0.163139\pi\)
−0.980392 + 0.197059i \(0.936861\pi\)
\(620\) −2.73867 0.287845i −0.109987 0.0115601i
\(621\) −21.1779 + 4.67865i −0.849840 + 0.187748i
\(622\) 9.85808 6.40191i 0.395273 0.256693i
\(623\) −0.233816 0.169878i −0.00936766 0.00680600i
\(624\) 23.5932 102.666i 0.944484 4.10994i
\(625\) −6.16389 + 18.9705i −0.246556 + 0.758820i
\(626\) 12.9519 + 48.3371i 0.517662 + 1.93194i
\(627\) 7.47482 + 17.8372i 0.298515 + 0.712350i
\(628\) −3.02355 + 1.74565i −0.120653 + 0.0696589i
\(629\) −6.36932 12.5005i −0.253961 0.498427i
\(630\) −0.0780531 + 0.186639i −0.00310971 + 0.00743589i
\(631\) −24.7585 30.5742i −0.985620 1.21714i −0.976131 0.217185i \(-0.930313\pi\)
−0.00948972 0.999955i \(-0.503021\pi\)
\(632\) 63.2034 124.044i 2.51409 4.93419i
\(633\) −0.414943 0.845040i −0.0164925 0.0335873i
\(634\) −35.0213 78.6591i −1.39087 3.12395i
\(635\) 0.543498 0.671164i 0.0215680 0.0266343i
\(636\) 57.9407 + 48.3556i 2.29750 + 1.91743i
\(637\) −25.2002 + 1.27891i −0.998470 + 0.0506721i
\(638\) −8.90653 11.1635i −0.352613 0.441965i
\(639\) 11.8244 21.6023i 0.467766 0.854576i
\(640\) 22.0741 + 24.5158i 0.872555 + 0.969071i
\(641\) −27.3672 12.1847i −1.08094 0.481265i −0.212551 0.977150i \(-0.568177\pi\)
−0.868388 + 0.495885i \(0.834844\pi\)
\(642\) 64.3588 + 14.6780i 2.54004 + 0.579294i
\(643\) 17.6395 0.924447i 0.695634 0.0364566i 0.298758 0.954329i \(-0.403428\pi\)
0.396876 + 0.917872i \(0.370094\pi\)
\(644\) −0.980702 + 0.0513964i −0.0386451 + 0.00202530i
\(645\) −0.944045 0.215304i −0.0371717 0.00847757i
\(646\) −49.8189 22.1808i −1.96010 0.872692i
\(647\) 16.5027 + 18.3281i 0.648786 + 0.720550i 0.974367 0.224964i \(-0.0722264\pi\)
−0.325581 + 0.945514i \(0.605560\pi\)
\(648\) −27.7346 87.3759i −1.08952 3.43245i
\(649\) 3.16911 4.80327i 0.124399 0.188545i
\(650\) 31.1741 34.5074i 1.22275 1.35349i
\(651\) 0.0455369 + 0.0380038i 0.00178473 + 0.00148949i
\(652\) −57.3548 + 70.8273i −2.24619 + 2.77381i
\(653\) 7.09274 + 15.9306i 0.277560 + 0.623411i 0.997503 0.0706226i \(-0.0224986\pi\)
−0.719943 + 0.694034i \(0.755832\pi\)
\(654\) −19.2170 39.1358i −0.751443 1.53033i
\(655\) −2.05130 + 4.02591i −0.0801510 + 0.157305i
\(656\) 108.281 + 133.716i 4.22768 + 5.22075i
\(657\) 33.1876 + 13.8792i 1.29477 + 0.541477i
\(658\) 0.00170687 + 0.00334992i 6.65406e−5 + 0.000130593i
\(659\) 1.40886 0.813407i 0.0548815 0.0316858i −0.472308 0.881433i \(-0.656579\pi\)
0.527190 + 0.849748i \(0.323246\pi\)
\(660\) −16.3672 9.93715i −0.637092 0.386803i
\(661\) −10.8858 40.6262i −0.423407 1.58018i −0.767378 0.641195i \(-0.778439\pi\)
0.343971 0.938980i \(-0.388228\pi\)
\(662\) 22.0003 67.7099i 0.855066 2.63162i
\(663\) −26.7272 24.8731i −1.03800 0.965991i
\(664\) −14.4371 10.4892i −0.560269 0.407059i
\(665\) 0.0687222 0.0446287i 0.00266493 0.00173063i
\(666\) −16.4765 + 11.2417i −0.638451 + 0.435606i
\(667\) −6.45134 0.678063i −0.249797 0.0262547i
\(668\) −18.5714 + 117.255i −0.718551 + 4.53675i
\(669\) −33.0000 + 23.2381i −1.27585 + 0.898436i
\(670\) 6.53709 + 1.75161i 0.252550 + 0.0676705i
\(671\) −15.8405 + 34.8941i −0.611515 + 1.34707i
\(672\) −0.268406 1.87359i −0.0103540 0.0722754i
\(673\) −28.3806 + 25.5540i −1.09399 + 0.985036i −0.999945 0.0105317i \(-0.996648\pi\)
−0.0940487 + 0.995568i \(0.529981\pi\)
\(674\) −7.91332 + 9.77214i −0.304810 + 0.376409i
\(675\) 4.84000 23.6999i 0.186292 0.912210i
\(676\) −67.5117 + 29.7910i −2.59661 + 1.14581i
\(677\) −6.25497 + 2.03236i −0.240398 + 0.0781101i −0.426738 0.904375i \(-0.640337\pi\)
0.186340 + 0.982485i \(0.440337\pi\)
\(678\) −25.7317 + 27.7417i −0.988222 + 1.06541i
\(679\) −0.0458547 0.436278i −0.00175974 0.0167428i
\(680\) 34.2037 7.27021i 1.31165 0.278800i
\(681\) −6.47378 15.1391i −0.248076 0.580130i
\(682\) −5.67849 + 5.03874i −0.217441 + 0.192943i
\(683\) −10.2723 + 38.3368i −0.393059 + 1.46692i 0.432002 + 0.901873i \(0.357807\pi\)
−0.825061 + 0.565044i \(0.808859\pi\)
\(684\) −16.4698 + 54.9148i −0.629739 + 2.09972i
\(685\) 7.34917 + 3.27206i 0.280797 + 0.125019i
\(686\) −1.46858 + 0.653853i −0.0560706 + 0.0249642i
\(687\) 0.449074 + 2.27788i 0.0171333 + 0.0869067i
\(688\) 15.2732 4.96257i 0.582286 0.189196i
\(689\) 1.49415 27.6356i 0.0569226 1.05283i
\(690\) −11.4049 + 2.87583i −0.434175 + 0.109481i
\(691\) −0.516015 + 9.84615i −0.0196301 + 0.374565i 0.971096 + 0.238690i \(0.0767180\pi\)
−0.990726 + 0.135875i \(0.956615\pi\)
\(692\) −97.9125 56.5298i −3.72207 2.14894i
\(693\) 0.173569 + 0.374110i 0.00659335 + 0.0142113i
\(694\) 53.6637 + 53.6637i 2.03705 + 2.03705i
\(695\) −0.190782 + 0.293778i −0.00723676 + 0.0111436i
\(696\) 0.405507 27.4154i 0.0153707 1.03918i
\(697\) 58.9002 9.32887i 2.23100 0.353356i
\(698\) −27.3925 24.6643i −1.03682 0.933559i
\(699\) −17.0618 + 25.4410i −0.645335 + 0.962266i
\(700\) 0.392510 1.02252i 0.0148355 0.0386477i
\(701\) 19.7221 14.3289i 0.744892 0.541195i −0.149348 0.988785i \(-0.547717\pi\)
0.894239 + 0.447589i \(0.147717\pi\)
\(702\) −30.2438 + 42.1866i −1.14148 + 1.59223i
\(703\) 8.07910 0.304709
\(704\) 130.367 + 0.946829i 4.91339 + 0.0356849i
\(705\) 0.0205697 + 0.0261840i 0.000774701 + 0.000986148i
\(706\) −5.00521 23.5477i −0.188373 0.886228i
\(707\) 0.0842811 0.532130i 0.00316972 0.0200128i
\(708\) 16.2999 5.03088i 0.612588 0.189072i
\(709\) −0.676971 12.9174i −0.0254242 0.485123i −0.981435 0.191793i \(-0.938570\pi\)
0.956011 0.293330i \(-0.0947634\pi\)
\(710\) 6.06317 11.8996i 0.227547 0.446585i
\(711\) −31.2696 + 26.5234i −1.17270 + 0.994706i
\(712\) 70.6336 7.42389i 2.64711 0.278222i
\(713\) −0.180474 + 3.44365i −0.00675881 + 0.128966i
\(714\) −1.07937 0.432752i −0.0403943 0.0161953i
\(715\) 0.671697 + 6.98974i 0.0251201 + 0.261401i
\(716\) 19.7535i 0.738222i
\(717\) 9.62545 20.7862i 0.359469 0.776274i
\(718\) 3.65475 + 34.7727i 0.136394 + 1.29770i
\(719\) 3.85672 36.6942i 0.143831 1.36846i −0.649819 0.760089i \(-0.725155\pi\)
0.793651 0.608374i \(-0.208178\pi\)
\(720\) −9.82387 28.0445i −0.366114 1.04516i
\(721\) −0.136872 + 0.00717316i −0.00509738 + 0.000267143i
\(722\) −16.5051 + 13.3656i −0.614257 + 0.497415i
\(723\) −21.7669 13.0001i −0.809521 0.483480i
\(724\) −45.2438 + 9.61687i −1.68147 + 0.357408i
\(725\) 3.61738 6.26549i 0.134346 0.232694i
\(726\) −50.6604 + 14.8337i −1.88018 + 0.550529i
\(727\) 14.9901i 0.555954i 0.960588 + 0.277977i \(0.0896639\pi\)
−0.960588 + 0.277977i \(0.910336\pi\)
\(728\) −1.07816 + 1.07460i −0.0399592 + 0.0398273i
\(729\) −2.39286 + 26.8938i −0.0886244 + 0.996065i
\(730\) 18.2126 + 6.99116i 0.674079 + 0.258755i
\(731\) 1.15722 5.44431i 0.0428015 0.201365i
\(732\) −101.969 + 50.0701i −3.76887 + 1.85064i
\(733\) 2.12979 + 13.4470i 0.0786656 + 0.496675i 0.995291 + 0.0969285i \(0.0309018\pi\)
−0.916626 + 0.399746i \(0.869098\pi\)
\(734\) 1.15590 0.443709i 0.0426651 0.0163776i
\(735\) −5.81960 + 4.09807i −0.214659 + 0.151160i
\(736\) 77.8117 77.8117i 2.86818 2.86818i
\(737\) 11.6250 7.42991i 0.428213 0.273684i
\(738\) −23.8032 81.3734i −0.876208 2.99539i
\(739\) 14.6572 + 0.768153i 0.539175 + 0.0282570i 0.319980 0.947424i \(-0.396324\pi\)
0.219195 + 0.975681i \(0.429657\pi\)
\(740\) −6.47108 + 4.70152i −0.237882 + 0.172831i
\(741\) 19.7497 7.21088i 0.725523 0.264898i
\(742\) −0.272400 0.838359i −0.0100001 0.0307771i
\(743\) 0.508413 0.330167i 0.0186518 0.0121127i −0.535279 0.844675i \(-0.679794\pi\)
0.553931 + 0.832562i \(0.313127\pi\)
\(744\) −14.5651 + 0.547466i −0.533984 + 0.0200711i
\(745\) −0.474730 + 1.06626i −0.0173927 + 0.0390647i
\(746\) −17.6186 34.5784i −0.645063 1.26601i
\(747\) 2.73096 + 4.49073i 0.0999208 + 0.164307i
\(748\) 55.7235 94.9171i 2.03745 3.47051i
\(749\) −0.403163 0.403163i −0.0147313 0.0147313i
\(750\) 4.65315 26.8066i 0.169909 0.978839i
\(751\) 10.5173 1.10541i 0.383781 0.0403370i 0.0893264 0.996002i \(-0.471529\pi\)
0.294455 + 0.955665i \(0.404862\pi\)
\(752\) −0.515564 0.197907i −0.0188007 0.00721691i
\(753\) 48.0473 + 3.23124i 1.75094 + 0.117753i
\(754\) −12.5752 + 9.10468i −0.457961 + 0.331573i
\(755\) −1.31029 + 1.80346i −0.0476865 + 0.0656348i
\(756\) −0.306974 + 1.18338i −0.0111645 + 0.0430391i
\(757\) 30.1661 + 33.5029i 1.09641 + 1.21768i 0.974321 + 0.225163i \(0.0722915\pi\)
0.122085 + 0.992520i \(0.461042\pi\)
\(758\) 20.2372 + 35.0519i 0.735049 + 1.27314i
\(759\) −11.3541 + 21.1190i −0.412126 + 0.766570i
\(760\) −5.21172 + 19.4504i −0.189049 + 0.705541i
\(761\) −25.1340 16.3222i −0.911107 0.591680i 0.00173220 0.999998i \(-0.499449\pi\)
−0.912840 + 0.408318i \(0.866115\pi\)
\(762\) 3.61896 6.05945i 0.131101 0.219511i
\(763\) −0.0393632 + 0.374516i −0.00142505 + 0.0135584i
\(764\) −79.1461 16.8230i −2.86340 0.608635i
\(765\) −10.1201 1.91127i −0.365893 0.0691020i
\(766\) 22.5241 31.0017i 0.813828 1.12014i
\(767\) −5.05499 3.68546i −0.182525 0.133074i
\(768\) 102.444 + 85.4967i 3.69662 + 3.08510i
\(769\) 16.7031 4.47559i 0.602330 0.161394i 0.0552478 0.998473i \(-0.482405\pi\)
0.547082 + 0.837079i \(0.315738\pi\)
\(770\) 0.100087 + 0.200010i 0.00360689 + 0.00720785i
\(771\) −23.2228 + 3.32685i −0.836350 + 0.119814i
\(772\) −106.457 + 54.2425i −3.83147 + 1.95223i
\(773\) 13.5303 5.19380i 0.486652 0.186808i −0.102656 0.994717i \(-0.532734\pi\)
0.589307 + 0.807909i \(0.299401\pi\)
\(774\) −7.88666 0.647684i −0.283480 0.0232805i
\(775\) −3.42677 1.74603i −0.123093 0.0627191i
\(776\) 80.1129 + 72.1340i 2.87588 + 2.58946i
\(777\) 0.172159 0.00647102i 0.00617617 0.000232146i
\(778\) 22.3210 + 18.0752i 0.800245 + 0.648026i
\(779\) −10.6120 + 32.6603i −0.380213 + 1.17018i
\(780\) −11.6226 + 17.2687i −0.416154 + 0.618319i
\(781\) −9.57204 25.4878i −0.342515 0.912024i
\(782\) −17.4988 65.3062i −0.625754 2.33535i
\(783\) −3.22555 + 7.40333i −0.115272 + 0.264574i
\(784\) 48.0148 107.843i 1.71481 3.85153i
\(785\) 0.356719 0.0564987i 0.0127318 0.00201653i
\(786\) −11.9289 + 34.9461i −0.425490 + 1.24649i
\(787\) −1.30990 24.9944i −0.0466928 0.890952i −0.917109 0.398636i \(-0.869484\pi\)
0.870416 0.492316i \(-0.163850\pi\)
\(788\) −13.1604 83.0915i −0.468820 2.96001i
\(789\) 25.4673 + 26.2319i 0.906658 + 0.933882i
\(790\) −16.5249 + 14.8791i −0.587930 + 0.529374i
\(791\) 0.315682 0.0845868i 0.0112244 0.00300756i
\(792\) −93.2138 39.7801i −3.31221 1.41352i
\(793\) 37.0876 + 18.9744i 1.31702 + 0.673801i
\(794\) 15.2888 + 4.96764i 0.542580 + 0.176295i
\(795\) −3.80306 6.81801i −0.134880 0.241810i
\(796\) −40.0103 + 17.8137i −1.41813 + 0.631391i
\(797\) −10.6831 + 11.8648i −0.378414 + 0.420272i −0.902024 0.431687i \(-0.857919\pi\)
0.523609 + 0.851959i \(0.324585\pi\)
\(798\) 0.504227 0.440681i 0.0178495 0.0155999i
\(799\) −0.148747 + 0.120453i −0.00526229 + 0.00426132i
\(800\) 43.9823 + 114.578i 1.55501 + 4.05094i
\(801\) −20.0365 6.00925i −0.707953 0.212326i
\(802\) 4.36200 + 7.55521i 0.154028 + 0.266784i
\(803\) 35.5651 17.7972i 1.25506 0.628048i
\(804\) 40.6065 + 4.87611i 1.43208 + 0.171967i
\(805\) 0.0966181 + 0.0313931i 0.00340534 + 0.00110646i
\(806\) 5.18321 + 6.42242i 0.182571 + 0.226220i
\(807\) −3.69493 5.87824i −0.130068 0.206924i
\(808\) 72.1085 + 111.037i 2.53677 + 3.90628i
\(809\) −1.42169 + 6.68852i −0.0499839 + 0.235156i −0.996047 0.0888262i \(-0.971688\pi\)
0.946063 + 0.323982i \(0.105022\pi\)
\(810\) −0.865741 + 14.6167i −0.0304190 + 0.513577i
\(811\) −33.9479 5.37682i −1.19207 0.188806i −0.471297 0.881975i \(-0.656214\pi\)
−0.720775 + 0.693169i \(0.756214\pi\)
\(812\) −0.199150 + 0.306664i −0.00698878 + 0.0107618i
\(813\) 27.1290 36.2016i 0.951455 1.26964i
\(814\) −2.46420 + 21.9132i −0.0863703 + 0.768058i
\(815\) 8.16486 4.71398i 0.286003 0.165124i
\(816\) 160.354 58.8480i 5.61350 2.06009i
\(817\) 2.49091 + 2.01710i 0.0871460 + 0.0705694i
\(818\) −26.7905 19.4645i −0.936710 0.680559i
\(819\) 0.415074 0.169477i 0.0145039 0.00592200i
\(820\) −10.5064 32.3353i −0.366898 1.12920i
\(821\) 7.55767 19.6884i 0.263764 0.687130i −0.736182 0.676784i \(-0.763373\pi\)
0.999946 0.0103462i \(-0.00329336\pi\)
\(822\) 63.2454 + 17.9532i 2.20594 + 0.626189i
\(823\) −0.0369154 0.173674i −0.00128679 0.00605388i 0.977500 0.210938i \(-0.0676517\pi\)
−0.978786 + 0.204884i \(0.934318\pi\)
\(824\) 23.8163 23.8163i 0.829681 0.829681i
\(825\) −16.3669 21.1485i −0.569824 0.736297i
\(826\) −0.192464 0.0515706i −0.00669669 0.00179437i
\(827\) −24.6830 + 12.5766i −0.858313 + 0.437332i −0.827016 0.562178i \(-0.809964\pi\)
−0.0312963 + 0.999510i \(0.509964\pi\)
\(828\) −65.7602 + 26.9772i −2.28533 + 0.937521i
\(829\) 7.82814 + 17.5823i 0.271882 + 0.610658i 0.996952 0.0780177i \(-0.0248591\pi\)
−0.725069 + 0.688676i \(0.758192\pi\)
\(830\) 1.55240 + 2.39049i 0.0538846 + 0.0829751i
\(831\) 2.74286 40.7853i 0.0951487 1.41483i
\(832\) 7.65149 141.521i 0.265268 4.90636i
\(833\) −24.0489 33.1005i −0.833245 1.14686i
\(834\) −1.20292 + 2.59771i −0.0416537 + 0.0899512i
\(835\) 6.14049 10.6356i 0.212500 0.368062i
\(836\) 34.1335 + 53.4061i 1.18053 + 1.84709i
\(837\) 4.01991 + 1.50636i 0.138948 + 0.0520674i
\(838\) −66.3147 43.0653i −2.29080 1.48767i
\(839\) −17.7737 46.3020i −0.613615 1.59852i −0.789254 0.614067i \(-0.789533\pi\)
0.175639 0.984455i \(-0.443801\pi\)
\(840\) −0.0954786 + 0.418647i −0.00329433 + 0.0144447i
\(841\) 17.7886 19.7563i 0.613401 0.681251i
\(842\) 62.2966 + 13.2415i 2.14688 + 0.456334i
\(843\) −8.48165 + 9.14416i −0.292124 + 0.314942i
\(844\) −1.81347 2.49603i −0.0624222 0.0859168i
\(845\) 7.62447 0.374300i 0.262290 0.0128763i
\(846\) 0.196750 + 0.187985i 0.00676442 + 0.00646305i
\(847\) 0.438643 + 0.124390i 0.0150720 + 0.00427410i
\(848\) 112.133 + 64.7399i 3.85065 + 2.22318i
\(849\) 31.2026 + 5.41622i 1.07087 + 0.185884i
\(850\) 74.4766 + 11.7959i 2.55453 + 0.404597i
\(851\) 6.30350 + 7.78417i 0.216081 + 0.266838i
\(852\) 26.0726 76.3805i 0.893233 2.61675i
\(853\) 12.1198 + 6.17535i 0.414975 + 0.211440i 0.648997 0.760791i \(-0.275189\pi\)
−0.234022 + 0.972231i \(0.575189\pi\)
\(854\) 1.31962 + 0.138698i 0.0451565 + 0.00474614i
\(855\) 3.62641 4.69290i 0.124021 0.160494i
\(856\) 139.920 + 7.33289i 4.78236 + 0.250633i
\(857\) 31.7893 1.08590 0.542951 0.839765i \(-0.317307\pi\)
0.542951 + 0.839765i \(0.317307\pi\)
\(858\) 13.5345 + 55.7671i 0.462060 + 1.90386i
\(859\) 28.3297 0.966598 0.483299 0.875455i \(-0.339438\pi\)
0.483299 + 0.875455i \(0.339438\pi\)
\(860\) −3.16896 0.166078i −0.108061 0.00566321i
\(861\) −0.199973 + 0.704464i −0.00681506 + 0.0240081i
\(862\) −71.2299 7.48656i −2.42610 0.254993i
\(863\) 42.3617 + 21.5844i 1.44201 + 0.734740i 0.987738 0.156123i \(-0.0498998\pi\)
0.454271 + 0.890864i \(0.349900\pi\)
\(864\) −63.1660 121.559i −2.14895 4.13554i
\(865\) 7.36036 + 9.08929i 0.250260 + 0.309045i
\(866\) −22.7697 3.60637i −0.773747 0.122550i
\(867\) 5.08907 29.3179i 0.172834 0.995688i
\(868\) 0.168338 + 0.0971897i 0.00571375 + 0.00329883i
\(869\) −0.329221 + 45.3298i −0.0111681 + 1.53771i
\(870\) −1.62973 + 4.06486i −0.0552530 + 0.137812i
\(871\) −7.47773 13.0014i −0.253373 0.440536i
\(872\) −54.3944 74.8675i −1.84203 2.53533i
\(873\) −13.5716 28.7042i −0.459329 0.971490i
\(874\) 38.0831 + 8.09481i 1.28818 + 0.273811i
\(875\) −0.157245 + 0.174638i −0.00531584 + 0.00590383i
\(876\) 114.940 + 26.2139i 3.88348 + 0.885685i
\(877\) 14.0514 + 36.6052i 0.474482 + 1.23607i 0.936960 + 0.349437i \(0.113627\pi\)
−0.462477 + 0.886631i \(0.653039\pi\)
\(878\) −35.2779 22.9097i −1.19057 0.773166i
\(879\) −21.1772 + 9.05581i −0.714288 + 0.305445i
\(880\) −30.5832 11.9954i −1.03096 0.404363i
\(881\) −23.9961 + 41.5624i −0.808449 + 1.40027i 0.105489 + 0.994420i \(0.466359\pi\)
−0.913938 + 0.405854i \(0.866974\pi\)
\(882\) −42.3301 + 39.8971i −1.42533 + 1.34340i
\(883\) 11.4333 + 15.7366i 0.384762 + 0.529579i 0.956838 0.290621i \(-0.0938620\pi\)
−0.572076 + 0.820200i \(0.693862\pi\)
\(884\) −100.242 65.3339i −3.37150 2.19742i
\(885\) −1.76069 0.118409i −0.0591851 0.00398026i
\(886\) 6.58006 + 10.1324i 0.221061 + 0.340405i
\(887\) −9.69869 21.7836i −0.325650 0.731422i 0.674325 0.738435i \(-0.264435\pi\)
−0.999975 + 0.00701207i \(0.997768\pi\)
\(888\) −30.3760 + 29.4905i −1.01935 + 0.989636i
\(889\) −0.0543166 + 0.0276757i −0.00182172 + 0.000928213i
\(890\) −10.9575 2.93606i −0.367297 0.0984171i
\(891\) 20.8080 + 21.4016i 0.697093 + 0.716981i
\(892\) −93.5309 + 93.5309i −3.13165 + 3.13165i
\(893\) −0.0229161 0.107812i −0.000766860 0.00360779i
\(894\) −2.60475 + 9.17600i −0.0871159 + 0.306891i
\(895\) 0.732306 1.90772i 0.0244783 0.0637681i
\(896\) −0.719582 2.21465i −0.0240395 0.0739861i
\(897\) 22.3568 + 13.4026i 0.746472 + 0.447501i
\(898\) 6.97005 + 5.06404i 0.232594 + 0.168989i
\(899\) 0.997829 + 0.808026i 0.0332794 + 0.0269492i
\(900\) 2.34459 79.2388i 0.0781530 2.64129i
\(901\) 38.8640 22.4381i 1.29475 0.747523i
\(902\) −85.3489 38.7449i −2.84181 1.29006i
\(903\) 0.0546949 + 0.0409877i 0.00182013 + 0.00136398i
\(904\) −43.7416 + 67.3561i −1.45482 + 2.24023i
\(905\) 4.72601 + 0.748526i 0.157098 + 0.0248819i
\(906\) −8.50993 + 16.1082i −0.282723 + 0.535159i
\(907\) 2.24838 10.5778i 0.0746563 0.351230i −0.924925 0.380148i \(-0.875873\pi\)
0.999582 + 0.0289182i \(0.00920622\pi\)
\(908\) −29.3889 45.2549i −0.975304 1.50184i
\(909\) −6.97579 38.3656i −0.231372 1.27251i
\(910\) 0.222281 0.0985257i 0.00736854 0.00326609i
\(911\) 18.7302 + 6.08581i 0.620559 + 0.201632i 0.602388 0.798203i \(-0.294216\pi\)
0.0181705 + 0.999835i \(0.494216\pi\)
\(912\) −11.7274 + 97.6616i −0.388333 + 3.23390i
\(913\) 5.73236 + 0.950644i 0.189714 + 0.0314617i
\(914\) 37.3833 + 64.7498i 1.23653 + 2.14173i
\(915\) 11.7040 1.05538i 0.386922 0.0348899i
\(916\) 2.72677 + 7.10349i 0.0900951 + 0.234706i
\(917\) 0.247863 0.200715i 0.00818515 0.00662820i
\(918\) −84.0846 3.73332i −2.77521 0.123218i
\(919\) −32.9309 + 36.5735i −1.08629 + 1.20645i −0.109111 + 0.994030i \(0.534800\pi\)
−0.977179 + 0.212417i \(0.931866\pi\)
\(920\) −22.8067 + 10.1542i −0.751914 + 0.334774i
\(921\) 17.9824 10.0305i 0.592539 0.330516i
\(922\) −24.4000 7.92803i −0.803570 0.261096i
\(923\) −28.1642 + 9.09963i −0.927035 + 0.299518i
\(924\) 0.770132 + 1.11070i 0.0253355 + 0.0365394i
\(925\) −10.7905 + 2.89131i −0.354790 + 0.0950657i
\(926\) −77.2393 + 69.5465i −2.53824 + 2.28544i
\(927\) −9.17785 + 3.76508i −0.301440 + 0.123661i
\(928\) −6.40960 40.4686i −0.210405 1.32845i
\(929\) 1.10148 + 21.0174i 0.0361383 + 0.689559i 0.955293 + 0.295662i \(0.0955402\pi\)
−0.919154 + 0.393897i \(0.871127\pi\)
\(930\) 2.20323 + 0.752076i 0.0722468 + 0.0246615i
\(931\) 23.2709 3.68575i 0.762673 0.120796i
\(932\) −40.8323 + 91.7108i −1.33751 + 3.00409i
\(933\) −6.89838 + 2.53163i −0.225843 + 0.0828819i
\(934\) −9.75717 36.4143i −0.319264 1.19151i
\(935\) −8.90037 + 7.10097i −0.291073 + 0.232227i
\(936\) −47.9340 + 99.2023i −1.56677 + 3.24253i
\(937\) −3.08733 + 9.50184i −0.100859 + 0.310412i −0.988736 0.149669i \(-0.952179\pi\)
0.887877 + 0.460080i \(0.152179\pi\)
\(938\) −0.371252 0.300634i −0.0121218 0.00981605i
\(939\) −1.17505 31.2618i −0.0383463 1.02019i
\(940\) 0.0810947 + 0.0730180i 0.00264502 + 0.00238158i
\(941\) −37.5369 19.1260i −1.22367 0.623490i −0.281801 0.959473i \(-0.590932\pi\)
−0.941868 + 0.335983i \(0.890932\pi\)
\(942\) 2.82031 0.870474i 0.0918906 0.0283616i
\(943\) −39.7477 + 15.2577i −1.29436 + 0.496860i
\(944\) 26.0774 13.2871i 0.848748 0.432459i
\(945\) 0.0735171 0.102907i 0.00239151 0.00334755i
\(946\) −6.23080 + 6.14095i −0.202581 + 0.199659i
\(947\) 37.5847 10.0708i 1.22134 0.327257i 0.410138 0.912024i \(-0.365481\pi\)
0.811201 + 0.584767i \(0.198814\pi\)
\(948\) −86.1022 + 103.169i −2.79647 + 3.35079i
\(949\) −17.5195 39.5253i −0.568708 1.28304i
\(950\) −25.5232 + 35.1297i −0.828083 + 1.13976i
\(951\) 10.4114 + 52.8107i 0.337613 + 1.71250i
\(952\) −2.41434 0.513184i −0.0782492 0.0166324i
\(953\) 3.17300 30.1891i 0.102784 0.977920i −0.814629 0.579982i \(-0.803059\pi\)
0.917413 0.397937i \(-0.130274\pi\)
\(954\) −38.6675 50.7489i −1.25191 1.64306i
\(955\) 7.01998 + 4.55883i 0.227161 + 0.147520i
\(956\) 19.4297 72.5127i 0.628402 2.34523i
\(957\) 3.87674 + 8.04216i 0.125317 + 0.259966i
\(958\) −38.1223 66.0297i −1.23167 2.13332i
\(959\) −0.379966 0.421995i −0.0122697 0.0136269i
\(960\) −19.4753 34.9147i −0.628562 1.12687i
\(961\) −17.8202 + 24.5273i −0.574844 + 0.791204i
\(962\) 23.6710 + 3.78925i 0.763182 + 0.122170i
\(963\) −37.1863 17.8924i −1.19831 0.576575i
\(964\) −77.5710 29.7767i −2.49839 0.959043i
\(965\) 12.2921 1.29195i 0.395698 0.0415895i
\(966\) 0.818004 + 0.141991i 0.0263188 + 0.00456848i
\(967\) −29.6564 29.6564i −0.953684 0.953684i 0.0452895 0.998974i \(-0.485579\pi\)
−0.998974 + 0.0452895i \(0.985579\pi\)
\(968\) −100.560 + 49.4113i −3.23212 + 1.58814i
\(969\) 27.2813 + 20.4443i 0.876402 + 0.656764i
\(970\) −7.81714 15.3420i −0.250993 0.492602i
\(971\) 20.3325 45.6675i 0.652500 1.46554i −0.219291 0.975660i \(-0.570374\pi\)
0.871790 0.489879i \(-0.162959\pi\)
\(972\) 7.34724 + 88.1800i 0.235663 + 2.82837i
\(973\) 0.0207370 0.0134667i 0.000664796 0.000431724i
\(974\) 26.5211 + 81.6236i 0.849791 + 2.61539i
\(975\) −23.7973 + 16.6989i −0.762122 + 0.534791i
\(976\) −157.678 + 114.560i −5.04715 + 3.66697i
\(977\) 38.8854 + 2.03790i 1.24406 + 0.0651982i 0.662971 0.748645i \(-0.269295\pi\)
0.581084 + 0.813843i \(0.302629\pi\)
\(978\) 60.5889 47.5976i 1.93742 1.52200i
\(979\) −19.4860 + 12.4541i −0.622775 + 0.398034i
\(980\) −16.4943 + 16.4943i −0.526892 + 0.526892i
\(981\) 6.27264 + 26.5244i 0.200270 + 0.846860i
\(982\) −40.3388 + 15.4846i −1.28726 + 0.494134i
\(983\) −0.563659 3.55881i −0.0179779 0.113508i 0.977067 0.212930i \(-0.0683007\pi\)
−0.995045 + 0.0994219i \(0.968301\pi\)
\(984\) −79.3181 161.533i −2.52857 5.14948i
\(985\) −1.80940 + 8.51257i −0.0576524 + 0.271233i
\(986\) −23.5018 9.02149i −0.748449 0.287303i
\(987\) −0.000574677 0.00227903i −1.82922e−5 7.25424e-5i
\(988\) 59.7293 34.3531i 1.90024 1.09292i
\(989\) 3.97377i 0.126358i
\(990\) 11.6226 + 11.2674i 0.369391 + 0.358102i
\(991\) 6.50291 11.2634i 0.206572 0.357793i −0.744061 0.668112i \(-0.767103\pi\)
0.950632 + 0.310319i \(0.100436\pi\)
\(992\) −21.3050 + 4.52852i −0.676435 + 0.143781i
\(993\) −22.8212 + 38.2109i −0.724208 + 1.21259i
\(994\) −0.732624 + 0.593267i −0.0232374 + 0.0188173i
\(995\) 4.52445 0.237116i 0.143435 0.00751709i
\(996\) 11.3352 + 12.9697i 0.359169 + 0.410961i
\(997\) 5.07121 48.2493i 0.160607 1.52807i −0.556346 0.830951i \(-0.687797\pi\)
0.716953 0.697121i \(-0.245536\pi\)
\(998\) −0.00571199 0.0543460i −0.000180810 0.00172029i
\(999\) 11.6050 4.56147i 0.367167 0.144319i
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 429.2.bv.a.20.1 832
3.2 odd 2 inner 429.2.bv.a.20.52 yes 832
11.5 even 5 inner 429.2.bv.a.137.52 yes 832
13.2 odd 12 inner 429.2.bv.a.119.1 yes 832
33.5 odd 10 inner 429.2.bv.a.137.1 yes 832
39.2 even 12 inner 429.2.bv.a.119.52 yes 832
143.93 odd 60 inner 429.2.bv.a.236.52 yes 832
429.236 even 60 inner 429.2.bv.a.236.1 yes 832
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.bv.a.20.1 832 1.1 even 1 trivial
429.2.bv.a.20.52 yes 832 3.2 odd 2 inner
429.2.bv.a.119.1 yes 832 13.2 odd 12 inner
429.2.bv.a.119.52 yes 832 39.2 even 12 inner
429.2.bv.a.137.1 yes 832 33.5 odd 10 inner
429.2.bv.a.137.52 yes 832 11.5 even 5 inner
429.2.bv.a.236.1 yes 832 429.236 even 60 inner
429.2.bv.a.236.52 yes 832 143.93 odd 60 inner