Properties

Label 150.3.j.a.11.8
Level $150$
Weight $3$
Character 150.11
Analytic conductor $4.087$
Analytic rank $0$
Dimension $80$
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] = [150,3,Mod(11,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.j (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.08720396540\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 11.8
Character \(\chi\) \(=\) 150.11
Dual form 150.3.j.a.41.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.831254 - 1.14412i) q^{2} +(2.70308 - 1.30129i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.40886 + 2.35838i) q^{5} +(-3.73578 - 2.01095i) q^{6} +0.752203 q^{7} +(2.68999 - 0.874032i) q^{8} +(5.61328 - 7.03499i) q^{9} +O(q^{10})\) \(q+(-0.831254 - 1.14412i) q^{2} +(2.70308 - 1.30129i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.40886 + 2.35838i) q^{5} +(-3.73578 - 2.01095i) q^{6} +0.752203 q^{7} +(2.68999 - 0.874032i) q^{8} +(5.61328 - 7.03499i) q^{9} +(-0.966599 - 7.00469i) q^{10} +(11.7601 + 16.1864i) q^{11} +(0.804611 + 5.94581i) q^{12} +(-9.27202 - 6.73652i) q^{13} +(-0.625272 - 0.860613i) q^{14} +(14.9864 + 0.637686i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(3.01795 - 0.980591i) q^{17} +(-12.7150 - 0.574411i) q^{18} +(-5.64746 - 17.3811i) q^{19} +(-7.21074 + 6.92858i) q^{20} +(2.03327 - 0.978836i) q^{21} +(8.74360 - 26.9100i) q^{22} +(-17.5300 - 24.1279i) q^{23} +(6.13390 - 5.86305i) q^{24} +(13.8760 + 20.7956i) q^{25} +16.2081i q^{26} +(6.01854 - 26.3207i) q^{27} +(-0.464887 + 1.43078i) q^{28} +(-3.71898 - 1.20837i) q^{29} +(-11.7279 - 17.6764i) q^{30} +(1.01564 + 3.12583i) q^{31} +5.65685i q^{32} +(52.8518 + 28.4498i) q^{33} +(-3.63060 - 2.63778i) q^{34} +(3.31636 + 1.77398i) q^{35} +(9.91216 + 15.0249i) q^{36} +(-1.94741 - 1.41488i) q^{37} +(-15.1916 + 20.9095i) q^{38} +(-33.8292 - 6.14373i) q^{39} +(13.9211 + 2.49056i) q^{40} +(-43.8977 + 60.4200i) q^{41} +(-2.81007 - 1.51264i) q^{42} +2.99787 q^{43} +(-38.0565 + 12.3653i) q^{44} +(41.3393 - 17.7780i) q^{45} +(-13.0335 + 40.1128i) q^{46} +(-31.9723 - 10.3884i) q^{47} +(-11.8069 - 2.14425i) q^{48} -48.4342 q^{49} +(12.2582 - 33.1623i) q^{50} +(6.88172 - 6.57785i) q^{51} +(18.5440 - 13.4730i) q^{52} +(87.3362 + 28.3773i) q^{53} +(-35.1170 + 14.9932i) q^{54} +(13.6749 + 99.0985i) q^{55} +(2.02342 - 0.657450i) q^{56} +(-37.8834 - 39.6335i) q^{57} +(1.70889 + 5.25943i) q^{58} +(-32.7528 + 45.0804i) q^{59} +(-10.4751 + 28.1118i) q^{60} +(-36.0558 + 26.1961i) q^{61} +(2.73208 - 3.76038i) q^{62} +(4.22232 - 5.29175i) q^{63} +(6.47214 - 4.70228i) q^{64} +(-24.9917 - 51.5673i) q^{65} +(-11.3832 - 84.1179i) q^{66} +(13.3565 + 41.1071i) q^{67} +6.34652i q^{68} +(-78.7823 - 42.4081i) q^{69} +(-0.727079 - 5.26895i) q^{70} +(-20.8728 - 6.78200i) q^{71} +(8.95087 - 23.8303i) q^{72} +(-77.5171 + 56.3195i) q^{73} +3.40420i q^{74} +(64.5692 + 38.1552i) q^{75} +36.5511 q^{76} +(8.84600 + 12.1755i) q^{77} +(21.0915 + 43.8117i) q^{78} +(45.9792 - 141.510i) q^{79} +(-8.72247 - 17.9977i) q^{80} +(-17.9823 - 78.9787i) q^{81} +105.618 q^{82} +(-0.905452 + 0.294199i) q^{83} +(0.605231 + 4.47245i) q^{84} +(15.6183 + 2.79420i) q^{85} +(-2.49199 - 3.42993i) q^{86} +(-11.6251 + 1.57316i) q^{87} +(45.7821 + 33.2626i) q^{88} +(66.8879 + 92.0633i) q^{89} +(-54.7037 - 32.5192i) q^{90} +(-6.97444 - 5.06723i) q^{91} +(56.7281 - 18.4321i) q^{92} +(6.81299 + 7.12772i) q^{93} +(14.6915 + 45.2157i) q^{94} +(16.0925 - 89.9496i) q^{95} +(7.36122 + 15.2909i) q^{96} +(30.9960 - 95.3960i) q^{97} +(40.2611 + 55.4147i) q^{98} +(179.884 + 8.12644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{3} + 40 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{3} + 40 q^{4} - 8 q^{7} + 20 q^{9} - 12 q^{12} + 40 q^{13} - 60 q^{15} - 80 q^{16} - 32 q^{18} + 60 q^{19} + 60 q^{21} - 8 q^{22} - 180 q^{25} + 182 q^{27} - 24 q^{28} + 20 q^{30} - 180 q^{31} + 26 q^{33} - 120 q^{34} - 40 q^{36} + 128 q^{37} + 220 q^{39} + 128 q^{42} - 56 q^{43} - 100 q^{45} - 120 q^{46} + 24 q^{48} + 440 q^{49} - 20 q^{51} - 80 q^{52} - 120 q^{54} - 792 q^{57} - 100 q^{60} + 200 q^{61} - 574 q^{63} + 160 q^{64} - 160 q^{66} - 732 q^{67} - 220 q^{69} + 280 q^{70} + 64 q^{72} - 400 q^{73} + 590 q^{75} + 80 q^{76} - 260 q^{78} + 400 q^{79} + 140 q^{81} + 448 q^{82} + 180 q^{84} - 200 q^{85} + 310 q^{87} - 64 q^{88} + 440 q^{90} + 340 q^{91} + 348 q^{93} + 160 q^{94} - 276 q^{97} + 180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.831254 1.14412i −0.415627 0.572061i
\(3\) 2.70308 1.30129i 0.901026 0.433764i
\(4\) −0.618034 + 1.90211i −0.154508 + 0.475528i
\(5\) 4.40886 + 2.35838i 0.881771 + 0.471677i
\(6\) −3.73578 2.01095i −0.622631 0.335158i
\(7\) 0.752203 0.107458 0.0537288 0.998556i \(-0.482889\pi\)
0.0537288 + 0.998556i \(0.482889\pi\)
\(8\) 2.68999 0.874032i 0.336249 0.109254i
\(9\) 5.61328 7.03499i 0.623697 0.781666i
\(10\) −0.966599 7.00469i −0.0966599 0.700469i
\(11\) 11.7601 + 16.1864i 1.06910 + 1.47149i 0.870983 + 0.491314i \(0.163483\pi\)
0.198119 + 0.980178i \(0.436517\pi\)
\(12\) 0.804611 + 5.94581i 0.0670509 + 0.495484i
\(13\) −9.27202 6.73652i −0.713232 0.518194i 0.170982 0.985274i \(-0.445306\pi\)
−0.884215 + 0.467080i \(0.845306\pi\)
\(14\) −0.625272 0.860613i −0.0446623 0.0614724i
\(15\) 14.9864 + 0.637686i 0.999096 + 0.0425124i
\(16\) −3.23607 2.35114i −0.202254 0.146946i
\(17\) 3.01795 0.980591i 0.177526 0.0576818i −0.218905 0.975746i \(-0.570248\pi\)
0.396431 + 0.918064i \(0.370248\pi\)
\(18\) −12.7150 0.574411i −0.706386 0.0319117i
\(19\) −5.64746 17.3811i −0.297235 0.914794i −0.982462 0.186465i \(-0.940297\pi\)
0.685227 0.728330i \(-0.259703\pi\)
\(20\) −7.21074 + 6.92858i −0.360537 + 0.346429i
\(21\) 2.03327 0.978836i 0.0968221 0.0466113i
\(22\) 8.74360 26.9100i 0.397436 1.22318i
\(23\) −17.5300 24.1279i −0.762172 1.04904i −0.997030 0.0770101i \(-0.975463\pi\)
0.234858 0.972030i \(-0.424537\pi\)
\(24\) 6.13390 5.86305i 0.255579 0.244294i
\(25\) 13.8760 + 20.7956i 0.555042 + 0.831822i
\(26\) 16.2081i 0.623388i
\(27\) 6.01854 26.3207i 0.222909 0.974839i
\(28\) −0.464887 + 1.43078i −0.0166031 + 0.0510991i
\(29\) −3.71898 1.20837i −0.128241 0.0416679i 0.244194 0.969727i \(-0.421477\pi\)
−0.372434 + 0.928059i \(0.621477\pi\)
\(30\) −11.7279 17.6764i −0.390931 0.589214i
\(31\) 1.01564 + 3.12583i 0.0327627 + 0.100833i 0.966101 0.258166i \(-0.0831181\pi\)
−0.933338 + 0.358999i \(0.883118\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 52.8518 + 28.4498i 1.60157 + 0.862115i
\(34\) −3.63060 2.63778i −0.106782 0.0775819i
\(35\) 3.31636 + 1.77398i 0.0947531 + 0.0506853i
\(36\) 9.91216 + 15.0249i 0.275338 + 0.417360i
\(37\) −1.94741 1.41488i −0.0526327 0.0382399i 0.561158 0.827709i \(-0.310356\pi\)
−0.613791 + 0.789469i \(0.710356\pi\)
\(38\) −15.1916 + 20.9095i −0.399780 + 0.550250i
\(39\) −33.8292 6.14373i −0.867415 0.157532i
\(40\) 13.9211 + 2.49056i 0.348028 + 0.0622639i
\(41\) −43.8977 + 60.4200i −1.07067 + 1.47366i −0.201284 + 0.979533i \(0.564511\pi\)
−0.869391 + 0.494124i \(0.835489\pi\)
\(42\) −2.81007 1.51264i −0.0669064 0.0360153i
\(43\) 2.99787 0.0697178 0.0348589 0.999392i \(-0.488902\pi\)
0.0348589 + 0.999392i \(0.488902\pi\)
\(44\) −38.0565 + 12.3653i −0.864921 + 0.281030i
\(45\) 41.3393 17.7780i 0.918652 0.395067i
\(46\) −13.0335 + 40.1128i −0.283336 + 0.872018i
\(47\) −31.9723 10.3884i −0.680262 0.221031i −0.0515522 0.998670i \(-0.516417\pi\)
−0.628710 + 0.777640i \(0.716417\pi\)
\(48\) −11.8069 2.14425i −0.245976 0.0446719i
\(49\) −48.4342 −0.988453
\(50\) 12.2582 33.1623i 0.245163 0.663246i
\(51\) 6.88172 6.57785i 0.134936 0.128977i
\(52\) 18.5440 13.4730i 0.356616 0.259097i
\(53\) 87.3362 + 28.3773i 1.64785 + 0.535420i 0.978273 0.207320i \(-0.0664742\pi\)
0.669580 + 0.742740i \(0.266474\pi\)
\(54\) −35.1170 + 14.9932i −0.650315 + 0.277652i
\(55\) 13.6749 + 99.0985i 0.248635 + 1.80179i
\(56\) 2.02342 0.657450i 0.0361325 0.0117402i
\(57\) −37.8834 39.6335i −0.664621 0.695324i
\(58\) 1.70889 + 5.25943i 0.0294637 + 0.0906798i
\(59\) −32.7528 + 45.0804i −0.555133 + 0.764075i −0.990698 0.136083i \(-0.956549\pi\)
0.435565 + 0.900158i \(0.356549\pi\)
\(60\) −10.4751 + 28.1118i −0.174585 + 0.468530i
\(61\) −36.0558 + 26.1961i −0.591079 + 0.429444i −0.842701 0.538382i \(-0.819036\pi\)
0.251622 + 0.967825i \(0.419036\pi\)
\(62\) 2.73208 3.76038i 0.0440657 0.0606513i
\(63\) 4.22232 5.29175i 0.0670210 0.0839960i
\(64\) 6.47214 4.70228i 0.101127 0.0734732i
\(65\) −24.9917 51.5673i −0.384488 0.793344i
\(66\) −11.3832 84.1179i −0.172472 1.27451i
\(67\) 13.3565 + 41.1071i 0.199351 + 0.613539i 0.999898 + 0.0142691i \(0.00454216\pi\)
−0.800547 + 0.599269i \(0.795458\pi\)
\(68\) 6.34652i 0.0933311i
\(69\) −78.7823 42.4081i −1.14177 0.614610i
\(70\) −0.727079 5.26895i −0.0103868 0.0752707i
\(71\) −20.8728 6.78200i −0.293984 0.0955211i 0.158312 0.987389i \(-0.449395\pi\)
−0.452296 + 0.891868i \(0.649395\pi\)
\(72\) 8.95087 23.8303i 0.124318 0.330976i
\(73\) −77.5171 + 56.3195i −1.06188 + 0.771500i −0.974435 0.224670i \(-0.927870\pi\)
−0.0874434 + 0.996169i \(0.527870\pi\)
\(74\) 3.40420i 0.0460027i
\(75\) 64.5692 + 38.1552i 0.860922 + 0.508737i
\(76\) 36.5511 0.480936
\(77\) 8.84600 + 12.1755i 0.114883 + 0.158123i
\(78\) 21.0915 + 43.8117i 0.270403 + 0.561689i
\(79\) 45.9792 141.510i 0.582016 1.79126i −0.0289228 0.999582i \(-0.509208\pi\)
0.610938 0.791678i \(-0.290792\pi\)
\(80\) −8.72247 17.9977i −0.109031 0.224972i
\(81\) −17.9823 78.9787i −0.222003 0.975046i
\(82\) 105.618 1.28802
\(83\) −0.905452 + 0.294199i −0.0109091 + 0.00354457i −0.314466 0.949269i \(-0.601826\pi\)
0.303557 + 0.952813i \(0.401826\pi\)
\(84\) 0.605231 + 4.47245i 0.00720513 + 0.0532435i
\(85\) 15.6183 + 2.79420i 0.183745 + 0.0328729i
\(86\) −2.49199 3.42993i −0.0289766 0.0398829i
\(87\) −11.6251 + 1.57316i −0.133622 + 0.0180823i
\(88\) 45.7821 + 33.2626i 0.520251 + 0.377984i
\(89\) 66.8879 + 92.0633i 0.751550 + 1.03442i 0.997870 + 0.0652310i \(0.0207784\pi\)
−0.246320 + 0.969188i \(0.579222\pi\)
\(90\) −54.7037 32.5192i −0.607819 0.361325i
\(91\) −6.97444 5.06723i −0.0766422 0.0556839i
\(92\) 56.7281 18.4321i 0.616610 0.200349i
\(93\) 6.81299 + 7.12772i 0.0732579 + 0.0766421i
\(94\) 14.6915 + 45.2157i 0.156292 + 0.481018i
\(95\) 16.0925 89.9496i 0.169394 0.946838i
\(96\) 7.36122 + 15.2909i 0.0766794 + 0.159280i
\(97\) 30.9960 95.3960i 0.319547 0.983463i −0.654296 0.756239i \(-0.727035\pi\)
0.973842 0.227225i \(-0.0729652\pi\)
\(98\) 40.2611 + 55.4147i 0.410828 + 0.565456i
\(99\) 179.884 + 8.12644i 1.81701 + 0.0820853i
\(100\) −48.1314 + 13.5414i −0.481314 + 0.135414i
\(101\) 21.9218i 0.217048i 0.994094 + 0.108524i \(0.0346124\pi\)
−0.994094 + 0.108524i \(0.965388\pi\)
\(102\) −13.2463 2.40567i −0.129866 0.0235850i
\(103\) 52.7894 162.469i 0.512518 1.57737i −0.275235 0.961377i \(-0.588756\pi\)
0.787753 0.615991i \(-0.211244\pi\)
\(104\) −30.8296 10.0171i −0.296439 0.0963187i
\(105\) 11.2728 + 0.479670i 0.107360 + 0.00456828i
\(106\) −40.1315 123.512i −0.378599 1.16521i
\(107\) 203.480i 1.90168i −0.309675 0.950842i \(-0.600220\pi\)
0.309675 0.950842i \(-0.399780\pi\)
\(108\) 46.3452 + 27.7150i 0.429122 + 0.256620i
\(109\) −105.622 76.7389i −0.969010 0.704027i −0.0137840 0.999905i \(-0.504388\pi\)
−0.955226 + 0.295878i \(0.904388\pi\)
\(110\) 102.013 98.0217i 0.927395 0.891107i
\(111\) −7.10518 1.29037i −0.0640106 0.0116250i
\(112\) −2.43418 1.76854i −0.0217338 0.0157905i
\(113\) −41.5042 + 57.1256i −0.367294 + 0.505537i −0.952163 0.305591i \(-0.901146\pi\)
0.584869 + 0.811128i \(0.301146\pi\)
\(114\) −13.8548 + 76.2888i −0.121534 + 0.669200i
\(115\) −20.3842 147.719i −0.177254 1.28451i
\(116\) 4.59691 6.32711i 0.0396285 0.0545440i
\(117\) −99.4378 + 27.4147i −0.849895 + 0.234314i
\(118\) 78.8035 0.667826
\(119\) 2.27011 0.737604i 0.0190766 0.00619835i
\(120\) 40.8708 11.3833i 0.340590 0.0948605i
\(121\) −86.3085 + 265.630i −0.713294 + 2.19529i
\(122\) 59.9430 + 19.4767i 0.491336 + 0.159645i
\(123\) −40.0348 + 220.444i −0.325487 + 1.79222i
\(124\) −6.57338 −0.0530112
\(125\) 12.1336 + 124.410i 0.0970688 + 0.995278i
\(126\) −9.56423 0.432074i −0.0759066 0.00342916i
\(127\) −85.7685 + 62.3145i −0.675343 + 0.490665i −0.871809 0.489845i \(-0.837053\pi\)
0.196467 + 0.980510i \(0.437053\pi\)
\(128\) −10.7600 3.49613i −0.0840623 0.0273135i
\(129\) 8.10347 3.90110i 0.0628176 0.0302411i
\(130\) −38.2249 + 71.4591i −0.294038 + 0.549686i
\(131\) 7.56254 2.45722i 0.0577293 0.0187574i −0.280010 0.959997i \(-0.590338\pi\)
0.337739 + 0.941240i \(0.390338\pi\)
\(132\) −86.7789 + 82.9471i −0.657416 + 0.628387i
\(133\) −4.24804 13.0741i −0.0319401 0.0983016i
\(134\) 35.9289 49.4519i 0.268126 0.369044i
\(135\) 88.6091 101.850i 0.656364 0.754444i
\(136\) 7.26119 5.27557i 0.0533911 0.0387909i
\(137\) −22.9153 + 31.5401i −0.167265 + 0.230220i −0.884418 0.466695i \(-0.845445\pi\)
0.717154 + 0.696915i \(0.245445\pi\)
\(138\) 16.9681 + 125.389i 0.122957 + 0.908613i
\(139\) −108.552 + 78.8674i −0.780947 + 0.567392i −0.905263 0.424851i \(-0.860326\pi\)
0.124316 + 0.992243i \(0.460326\pi\)
\(140\) −5.42394 + 5.21170i −0.0387424 + 0.0372265i
\(141\) −99.9422 + 13.5246i −0.708810 + 0.0959190i
\(142\) 9.59119 + 29.5187i 0.0675436 + 0.207878i
\(143\) 229.303i 1.60352i
\(144\) −34.7052 + 9.56812i −0.241008 + 0.0664452i
\(145\) −13.5466 14.0983i −0.0934252 0.0972297i
\(146\) 128.873 + 41.8733i 0.882691 + 0.286804i
\(147\) −130.921 + 63.0270i −0.890622 + 0.428755i
\(148\) 3.89482 2.82975i 0.0263164 0.0191200i
\(149\) 14.9337i 0.100226i 0.998744 + 0.0501132i \(0.0159582\pi\)
−0.998744 + 0.0501132i \(0.984042\pi\)
\(150\) −10.0191 105.592i −0.0667939 0.703945i
\(151\) 61.3357 0.406197 0.203098 0.979158i \(-0.434899\pi\)
0.203098 + 0.979158i \(0.434899\pi\)
\(152\) −30.3833 41.8190i −0.199890 0.275125i
\(153\) 10.0421 26.7356i 0.0656348 0.174742i
\(154\) 6.57696 20.2418i 0.0427076 0.131440i
\(155\) −2.89408 + 16.1766i −0.0186715 + 0.104365i
\(156\) 32.5937 60.5499i 0.208934 0.388140i
\(157\) 214.807 1.36820 0.684099 0.729389i \(-0.260196\pi\)
0.684099 + 0.729389i \(0.260196\pi\)
\(158\) −200.125 + 65.0245i −1.26661 + 0.411547i
\(159\) 273.004 36.9440i 1.71700 0.232352i
\(160\) −13.3410 + 24.9403i −0.0833815 + 0.155877i
\(161\) −13.1861 18.1491i −0.0819012 0.112727i
\(162\) −75.4135 + 86.2253i −0.465516 + 0.532255i
\(163\) 7.28745 + 5.29465i 0.0447083 + 0.0324825i 0.609915 0.792467i \(-0.291204\pi\)
−0.565207 + 0.824949i \(0.691204\pi\)
\(164\) −87.7953 120.840i −0.535337 0.736829i
\(165\) 165.920 + 250.076i 1.00558 + 1.51561i
\(166\) 1.08926 + 0.791394i 0.00656181 + 0.00476744i
\(167\) −78.4303 + 25.4835i −0.469642 + 0.152596i −0.534271 0.845313i \(-0.679414\pi\)
0.0646284 + 0.997909i \(0.479414\pi\)
\(168\) 4.61394 4.41020i 0.0274639 0.0262512i
\(169\) −11.6342 35.8063i −0.0688412 0.211871i
\(170\) −9.78588 20.1920i −0.0575640 0.118776i
\(171\) −153.977 57.8350i −0.900448 0.338217i
\(172\) −1.85278 + 5.70228i −0.0107720 + 0.0331528i
\(173\) −167.361 230.353i −0.967407 1.33152i −0.943346 0.331812i \(-0.892340\pi\)
−0.0240618 0.999710i \(-0.507660\pi\)
\(174\) 11.4633 + 11.9929i 0.0658812 + 0.0689246i
\(175\) 10.4376 + 15.6425i 0.0596435 + 0.0893856i
\(176\) 80.0300i 0.454716i
\(177\) −29.8707 + 164.477i −0.168761 + 0.929249i
\(178\) 49.7309 153.056i 0.279387 0.859865i
\(179\) 309.178 + 100.458i 1.72725 + 0.561218i 0.993048 0.117711i \(-0.0375558\pi\)
0.734204 + 0.678929i \(0.237556\pi\)
\(180\) 8.26669 + 89.6195i 0.0459261 + 0.497886i
\(181\) 66.2284 + 203.830i 0.365903 + 1.12613i 0.949414 + 0.314028i \(0.101679\pi\)
−0.583511 + 0.812106i \(0.698321\pi\)
\(182\) 12.1918i 0.0669878i
\(183\) −63.3729 + 117.729i −0.346300 + 0.643329i
\(184\) −68.2440 49.5822i −0.370892 0.269468i
\(185\) −5.24903 10.8307i −0.0283732 0.0585445i
\(186\) 2.49166 13.7198i 0.0133960 0.0737626i
\(187\) 51.3637 + 37.3179i 0.274672 + 0.199561i
\(188\) 39.5200 54.3946i 0.210213 0.289333i
\(189\) 4.52717 19.7985i 0.0239533 0.104754i
\(190\) −116.290 + 56.3592i −0.612054 + 0.296628i
\(191\) 28.1842 38.7922i 0.147561 0.203100i −0.728838 0.684686i \(-0.759939\pi\)
0.876399 + 0.481586i \(0.159939\pi\)
\(192\) 11.3757 21.1328i 0.0592482 0.110067i
\(193\) −160.907 −0.833716 −0.416858 0.908972i \(-0.636869\pi\)
−0.416858 + 0.908972i \(0.636869\pi\)
\(194\) −134.910 + 43.8350i −0.695414 + 0.225954i
\(195\) −134.659 106.869i −0.690558 0.548046i
\(196\) 29.9340 92.1273i 0.152724 0.470037i
\(197\) −45.0160 14.6266i −0.228508 0.0742466i 0.192525 0.981292i \(-0.438332\pi\)
−0.421033 + 0.907045i \(0.638332\pi\)
\(198\) −140.232 212.565i −0.708241 1.07356i
\(199\) 182.587 0.917524 0.458762 0.888559i \(-0.348293\pi\)
0.458762 + 0.888559i \(0.348293\pi\)
\(200\) 55.5025 + 43.8118i 0.277512 + 0.219059i
\(201\) 89.5960 + 93.7350i 0.445751 + 0.466343i
\(202\) 25.0813 18.2226i 0.124165 0.0902109i
\(203\) −2.79743 0.908940i −0.0137804 0.00447753i
\(204\) 8.25867 + 17.1551i 0.0404837 + 0.0840938i
\(205\) −336.032 + 162.855i −1.63918 + 0.794417i
\(206\) −229.766 + 74.6554i −1.11537 + 0.362405i
\(207\) −268.140 12.1135i −1.29536 0.0585193i
\(208\) 14.1664 + 43.5997i 0.0681076 + 0.209614i
\(209\) 214.923 295.816i 1.02834 1.41539i
\(210\) −8.82180 13.2963i −0.0420086 0.0633155i
\(211\) 251.828 182.964i 1.19350 0.867127i 0.199868 0.979823i \(-0.435949\pi\)
0.993630 + 0.112696i \(0.0359485\pi\)
\(212\) −107.953 + 148.585i −0.509215 + 0.700874i
\(213\) −65.2463 + 8.82940i −0.306321 + 0.0414526i
\(214\) −232.806 + 169.144i −1.08788 + 0.790391i
\(215\) 13.2172 + 7.07012i 0.0614752 + 0.0328843i
\(216\) −6.81525 76.0628i −0.0315521 0.352143i
\(217\) 0.763971 + 2.35126i 0.00352060 + 0.0108353i
\(218\) 184.634i 0.846946i
\(219\) −136.247 + 253.108i −0.622132 + 1.15575i
\(220\) −196.948 35.2350i −0.895218 0.160159i
\(221\) −34.5882 11.2384i −0.156508 0.0508525i
\(222\) 4.42986 + 9.20182i 0.0199543 + 0.0414496i
\(223\) 92.5328 67.2290i 0.414945 0.301475i −0.360656 0.932699i \(-0.617447\pi\)
0.775601 + 0.631224i \(0.217447\pi\)
\(224\) 4.25510i 0.0189960i
\(225\) 224.187 + 19.1133i 0.996385 + 0.0849480i
\(226\) 99.8593 0.441855
\(227\) 229.060 + 315.274i 1.00907 + 1.38887i 0.919589 + 0.392883i \(0.128522\pi\)
0.0894854 + 0.995988i \(0.471478\pi\)
\(228\) 98.8006 47.5637i 0.433336 0.208613i
\(229\) −21.8302 + 67.1864i −0.0953283 + 0.293390i −0.987339 0.158624i \(-0.949294\pi\)
0.892011 + 0.452014i \(0.149294\pi\)
\(230\) −152.064 + 146.114i −0.661148 + 0.635278i
\(231\) 39.7553 + 21.4000i 0.172101 + 0.0926408i
\(232\) −11.0602 −0.0476732
\(233\) 243.992 79.2777i 1.04717 0.340248i 0.265616 0.964079i \(-0.414425\pi\)
0.781559 + 0.623831i \(0.214425\pi\)
\(234\) 114.024 + 90.9805i 0.487281 + 0.388805i
\(235\) −116.462 121.204i −0.495581 0.515763i
\(236\) −65.5057 90.1609i −0.277566 0.382038i
\(237\) −59.8598 442.344i −0.252573 1.86643i
\(238\) −2.73095 1.98415i −0.0114746 0.00833676i
\(239\) −60.1102 82.7346i −0.251507 0.346170i 0.664531 0.747261i \(-0.268631\pi\)
−0.916038 + 0.401090i \(0.868631\pi\)
\(240\) −46.9978 37.2988i −0.195824 0.155412i
\(241\) 260.610 + 189.345i 1.08137 + 0.785662i 0.977922 0.208973i \(-0.0670119\pi\)
0.103450 + 0.994635i \(0.467012\pi\)
\(242\) 375.658 122.059i 1.55231 0.504375i
\(243\) −151.382 190.086i −0.622971 0.782245i
\(244\) −27.5442 84.7723i −0.112886 0.347427i
\(245\) −213.539 114.226i −0.871590 0.466230i
\(246\) 285.494 137.440i 1.16054 0.558699i
\(247\) −64.7247 + 199.202i −0.262043 + 0.806486i
\(248\) 5.46415 + 7.52076i 0.0220329 + 0.0303256i
\(249\) −2.06467 + 1.97350i −0.00829185 + 0.00792571i
\(250\) 132.254 117.298i 0.529016 0.469194i
\(251\) 222.314i 0.885715i −0.896592 0.442858i \(-0.853965\pi\)
0.896592 0.442858i \(-0.146035\pi\)
\(252\) 7.45596 + 11.3018i 0.0295871 + 0.0448485i
\(253\) 184.390 567.494i 0.728814 2.24306i
\(254\) 142.591 + 46.3306i 0.561381 + 0.182404i
\(255\) 45.8536 12.7711i 0.179818 0.0500826i
\(256\) 4.94427 + 15.2169i 0.0193136 + 0.0594410i
\(257\) 290.173i 1.12908i 0.825406 + 0.564540i \(0.190946\pi\)
−0.825406 + 0.564540i \(0.809054\pi\)
\(258\) −11.1994 6.02856i −0.0434085 0.0233665i
\(259\) −1.46485 1.06428i −0.00565579 0.00410917i
\(260\) 113.533 15.6667i 0.436664 0.0602566i
\(261\) −29.3765 + 19.3801i −0.112554 + 0.0742532i
\(262\) −9.09775 6.60990i −0.0347242 0.0252286i
\(263\) −206.855 + 284.711i −0.786521 + 1.08255i 0.208012 + 0.978126i \(0.433301\pi\)
−0.994533 + 0.104426i \(0.966699\pi\)
\(264\) 167.037 + 30.3356i 0.632716 + 0.114908i
\(265\) 318.128 + 331.084i 1.20048 + 1.24937i
\(266\) −11.4272 + 15.7282i −0.0429594 + 0.0591285i
\(267\) 300.605 + 161.814i 1.12586 + 0.606044i
\(268\) −86.4451 −0.322556
\(269\) −112.802 + 36.6515i −0.419337 + 0.136251i −0.511083 0.859532i \(-0.670755\pi\)
0.0917456 + 0.995782i \(0.470755\pi\)
\(270\) −190.186 16.7165i −0.704391 0.0619130i
\(271\) 58.9052 181.291i 0.217362 0.668972i −0.781615 0.623761i \(-0.785604\pi\)
0.998977 0.0452113i \(-0.0143961\pi\)
\(272\) −12.0718 3.92236i −0.0443816 0.0144205i
\(273\) −25.4464 4.62133i −0.0932104 0.0169280i
\(274\) 55.1342 0.201220
\(275\) −173.422 + 469.162i −0.630624 + 1.70604i
\(276\) 129.355 123.643i 0.468678 0.447983i
\(277\) 114.412 83.1251i 0.413039 0.300090i −0.361792 0.932259i \(-0.617835\pi\)
0.774831 + 0.632168i \(0.217835\pi\)
\(278\) 180.468 + 58.6376i 0.649166 + 0.210927i
\(279\) 27.6913 + 10.4011i 0.0992519 + 0.0372799i
\(280\) 10.4715 + 1.87340i 0.0373982 + 0.00669073i
\(281\) 374.636 121.727i 1.33322 0.433191i 0.446209 0.894929i \(-0.352774\pi\)
0.887016 + 0.461738i \(0.152774\pi\)
\(282\) 98.5511 + 103.104i 0.349472 + 0.365616i
\(283\) −89.1598 274.406i −0.315052 0.969631i −0.975733 0.218964i \(-0.929732\pi\)
0.660681 0.750667i \(-0.270268\pi\)
\(284\) 25.8003 35.5110i 0.0908460 0.125039i
\(285\) −73.5516 264.082i −0.258076 0.926604i
\(286\) −262.351 + 190.609i −0.917310 + 0.666465i
\(287\) −33.0200 + 45.4481i −0.115052 + 0.158356i
\(288\) 39.7959 + 31.7535i 0.138180 + 0.110255i
\(289\) −225.659 + 163.951i −0.780829 + 0.567305i
\(290\) −4.86949 + 27.2183i −0.0167914 + 0.0938562i
\(291\) −40.3533 298.198i −0.138671 1.02473i
\(292\) −59.2178 182.254i −0.202801 0.624156i
\(293\) 108.328i 0.369722i −0.982765 0.184861i \(-0.940817\pi\)
0.982765 0.184861i \(-0.0591835\pi\)
\(294\) 180.940 + 97.3987i 0.615441 + 0.331288i
\(295\) −250.720 + 121.509i −0.849897 + 0.411896i
\(296\) −6.47517 2.10391i −0.0218756 0.00710781i
\(297\) 496.816 212.115i 1.67278 0.714193i
\(298\) 17.0860 12.4137i 0.0573356 0.0416568i
\(299\) 341.805i 1.14316i
\(300\) −112.482 + 99.2366i −0.374938 + 0.330789i
\(301\) 2.25501 0.00749171
\(302\) −50.9856 70.1756i −0.168826 0.232370i
\(303\) 28.5267 + 59.2564i 0.0941476 + 0.195566i
\(304\) −22.5898 + 69.5244i −0.0743087 + 0.228699i
\(305\) −220.745 + 30.4613i −0.723755 + 0.0998732i
\(306\) −38.9363 + 10.7346i −0.127243 + 0.0350805i
\(307\) 94.6401 0.308274 0.154137 0.988049i \(-0.450740\pi\)
0.154137 + 0.988049i \(0.450740\pi\)
\(308\) −28.6263 + 9.30123i −0.0929424 + 0.0301988i
\(309\) −68.7258 507.861i −0.222414 1.64356i
\(310\) 20.9138 10.1357i 0.0674637 0.0326958i
\(311\) −44.3227 61.0050i −0.142517 0.196158i 0.731791 0.681529i \(-0.238685\pi\)
−0.874308 + 0.485371i \(0.838685\pi\)
\(312\) −96.3701 + 13.0412i −0.308879 + 0.0417987i
\(313\) 310.538 + 225.619i 0.992134 + 0.720827i 0.960387 0.278669i \(-0.0898931\pi\)
0.0317464 + 0.999496i \(0.489893\pi\)
\(314\) −178.559 245.766i −0.568660 0.782693i
\(315\) 31.0956 13.3727i 0.0987162 0.0424530i
\(316\) 240.750 + 174.915i 0.761868 + 0.553530i
\(317\) 10.2227 3.32156i 0.0322483 0.0104781i −0.292848 0.956159i \(-0.594603\pi\)
0.325097 + 0.945681i \(0.394603\pi\)
\(318\) −269.204 281.640i −0.846553 0.885660i
\(319\) −24.1765 74.4075i −0.0757883 0.233252i
\(320\) 39.6245 5.46791i 0.123827 0.0170872i
\(321\) −264.787 550.023i −0.824883 1.71347i
\(322\) −9.80381 + 30.1730i −0.0304466 + 0.0937050i
\(323\) −34.0875 46.9174i −0.105534 0.145255i
\(324\) 161.340 + 14.6072i 0.497963 + 0.0450840i
\(325\) 11.4306 286.293i 0.0351712 0.880902i
\(326\) 12.7389i 0.0390765i
\(327\) −385.365 69.9862i −1.17848 0.214025i
\(328\) −65.2755 + 200.897i −0.199011 + 0.612492i
\(329\) −24.0497 7.81422i −0.0730994 0.0237514i
\(330\) 148.196 397.710i 0.449078 1.20518i
\(331\) 51.5253 + 158.579i 0.155666 + 0.479090i 0.998228 0.0595096i \(-0.0189537\pi\)
−0.842562 + 0.538599i \(0.818954\pi\)
\(332\) 1.90410i 0.00573523i
\(333\) −20.8850 + 5.75793i −0.0627177 + 0.0172911i
\(334\) 94.3518 + 68.5506i 0.282490 + 0.205241i
\(335\) −38.0594 + 212.735i −0.113610 + 0.635030i
\(336\) −8.88117 1.61291i −0.0264320 0.00480033i
\(337\) 51.4983 + 37.4157i 0.152814 + 0.111026i 0.661565 0.749888i \(-0.269893\pi\)
−0.508751 + 0.860914i \(0.669893\pi\)
\(338\) −31.2958 + 43.0750i −0.0925912 + 0.127441i
\(339\) −37.8520 + 208.424i −0.111658 + 0.614821i
\(340\) −14.9675 + 27.9809i −0.0440221 + 0.0822967i
\(341\) −38.6519 + 53.1998i −0.113349 + 0.156011i
\(342\) 61.8233 + 224.244i 0.180770 + 0.655684i
\(343\) −73.2903 −0.213674
\(344\) 8.06424 2.62023i 0.0234426 0.00761695i
\(345\) −247.326 372.770i −0.716886 1.08049i
\(346\) −124.433 + 382.964i −0.359632 + 1.10683i
\(347\) −310.622 100.927i −0.895163 0.290856i −0.174924 0.984582i \(-0.555968\pi\)
−0.720239 + 0.693726i \(0.755968\pi\)
\(348\) 4.19240 23.0846i 0.0120471 0.0663350i
\(349\) 76.4536 0.219065 0.109532 0.993983i \(-0.465065\pi\)
0.109532 + 0.993983i \(0.465065\pi\)
\(350\) 9.22062 24.9448i 0.0263446 0.0712708i
\(351\) −233.114 + 203.502i −0.664141 + 0.579777i
\(352\) −91.5642 + 66.5253i −0.260125 + 0.188992i
\(353\) 329.367 + 107.018i 0.933050 + 0.303166i 0.735809 0.677189i \(-0.236802\pi\)
0.197241 + 0.980355i \(0.436802\pi\)
\(354\) 213.012 102.546i 0.601729 0.289679i
\(355\) −76.0308 79.1271i −0.214171 0.222893i
\(356\) −216.454 + 70.3301i −0.608016 + 0.197557i
\(357\) 5.17645 4.94788i 0.0144999 0.0138596i
\(358\) −142.069 437.244i −0.396841 1.22135i
\(359\) −311.689 + 429.004i −0.868216 + 1.19500i 0.111332 + 0.993783i \(0.464488\pi\)
−0.979547 + 0.201213i \(0.935512\pi\)
\(360\) 95.6640 83.9547i 0.265733 0.233207i
\(361\) 21.8465 15.8724i 0.0605167 0.0439679i
\(362\) 178.154 245.208i 0.492138 0.677371i
\(363\) 112.364 + 830.332i 0.309543 + 2.28742i
\(364\) 13.9489 10.1345i 0.0383211 0.0278419i
\(365\) −474.585 + 65.4894i −1.30023 + 0.179423i
\(366\) 187.376 25.3564i 0.511955 0.0692799i
\(367\) −113.433 349.112i −0.309083 0.951258i −0.978122 0.208031i \(-0.933294\pi\)
0.669040 0.743227i \(-0.266706\pi\)
\(368\) 119.295i 0.324171i
\(369\) 178.644 + 647.974i 0.484131 + 1.75603i
\(370\) −8.02841 + 15.0086i −0.0216984 + 0.0405639i
\(371\) 65.6946 + 21.3455i 0.177074 + 0.0575349i
\(372\) −17.7684 + 8.55390i −0.0477645 + 0.0229943i
\(373\) −101.565 + 73.7912i −0.272292 + 0.197832i −0.715548 0.698563i \(-0.753823\pi\)
0.443256 + 0.896395i \(0.353823\pi\)
\(374\) 89.7870i 0.240072i
\(375\) 194.692 + 320.500i 0.519177 + 0.854667i
\(376\) −95.0852 −0.252886
\(377\) 26.3422 + 36.2570i 0.0698733 + 0.0961724i
\(378\) −26.4151 + 11.2779i −0.0698813 + 0.0298358i
\(379\) 68.5820 211.074i 0.180955 0.556923i −0.818900 0.573936i \(-0.805416\pi\)
0.999855 + 0.0170132i \(0.00541575\pi\)
\(380\) 161.149 + 86.2016i 0.424076 + 0.226846i
\(381\) −150.750 + 280.051i −0.395669 + 0.735042i
\(382\) −67.8112 −0.177516
\(383\) −412.973 + 134.183i −1.07826 + 0.350347i −0.793698 0.608311i \(-0.791847\pi\)
−0.284559 + 0.958659i \(0.591847\pi\)
\(384\) −33.6346 + 4.55156i −0.0875900 + 0.0118530i
\(385\) 10.2863 + 74.5422i 0.0267177 + 0.193616i
\(386\) 133.755 + 184.098i 0.346515 + 0.476937i
\(387\) 16.8279 21.0900i 0.0434828 0.0544961i
\(388\) 162.297 + 117.916i 0.418292 + 0.303907i
\(389\) −216.144 297.497i −0.555640 0.764773i 0.435124 0.900370i \(-0.356704\pi\)
−0.990764 + 0.135598i \(0.956704\pi\)
\(390\) −10.3357 + 242.902i −0.0265017 + 0.622824i
\(391\) −76.5641 55.6271i −0.195816 0.142269i
\(392\) −130.288 + 42.3330i −0.332367 + 0.107992i
\(393\) 17.2446 16.4831i 0.0438794 0.0419418i
\(394\) 20.6851 + 63.6622i 0.0525003 + 0.161579i
\(395\) 536.450 515.459i 1.35810 1.30496i
\(396\) −126.632 + 337.137i −0.319777 + 0.851357i
\(397\) −110.392 + 339.753i −0.278066 + 0.855800i 0.710325 + 0.703873i \(0.248548\pi\)
−0.988392 + 0.151927i \(0.951452\pi\)
\(398\) −151.776 208.902i −0.381348 0.524880i
\(399\) −28.4960 29.8124i −0.0714186 0.0747179i
\(400\) 3.98946 99.9204i 0.00997364 0.249801i
\(401\) 266.743i 0.665193i 0.943069 + 0.332597i \(0.107925\pi\)
−0.943069 + 0.332597i \(0.892075\pi\)
\(402\) 32.7673 180.426i 0.0815107 0.448822i
\(403\) 11.6401 35.8247i 0.0288837 0.0888950i
\(404\) −41.6978 13.5484i −0.103212 0.0335357i
\(405\) 106.981 390.615i 0.264150 0.964482i
\(406\) 1.28543 + 3.95616i 0.00316610 + 0.00974424i
\(407\) 48.1607i 0.118331i
\(408\) 12.7625 23.7092i 0.0312807 0.0581108i
\(409\) −243.323 176.784i −0.594921 0.432236i 0.249151 0.968465i \(-0.419848\pi\)
−0.844073 + 0.536229i \(0.819848\pi\)
\(410\) 465.655 + 249.088i 1.13574 + 0.607531i
\(411\) −20.8988 + 115.075i −0.0508487 + 0.279988i
\(412\) 276.409 + 200.823i 0.670895 + 0.487434i
\(413\) −24.6368 + 33.9096i −0.0596533 + 0.0821057i
\(414\) 209.033 + 316.855i 0.504911 + 0.765350i
\(415\) −4.68584 0.838322i −0.0112912 0.00202005i
\(416\) 38.1075 52.4505i 0.0916046 0.126083i
\(417\) −190.794 + 354.442i −0.457540 + 0.849982i
\(418\) −517.105 −1.23709
\(419\) 70.5814 22.9333i 0.168452 0.0547334i −0.223577 0.974686i \(-0.571773\pi\)
0.392029 + 0.919953i \(0.371773\pi\)
\(420\) −7.87939 + 21.1458i −0.0187605 + 0.0503471i
\(421\) 190.045 584.898i 0.451413 1.38931i −0.423883 0.905717i \(-0.639333\pi\)
0.875296 0.483588i \(-0.160667\pi\)
\(422\) −418.666 136.033i −0.992100 0.322353i
\(423\) −252.552 + 166.612i −0.597050 + 0.393882i
\(424\) 259.736 0.612586
\(425\) 62.2691 + 49.1532i 0.146516 + 0.115655i
\(426\) 64.3382 + 67.3103i 0.151029 + 0.158005i
\(427\) −27.1213 + 19.7048i −0.0635159 + 0.0461470i
\(428\) 387.042 + 125.758i 0.904305 + 0.293826i
\(429\) −298.390 619.824i −0.695548 1.44481i
\(430\) −2.89773 20.9991i −0.00673892 0.0488352i
\(431\) 643.509 209.089i 1.49306 0.485125i 0.555075 0.831800i \(-0.312690\pi\)
0.937985 + 0.346676i \(0.112690\pi\)
\(432\) −81.3600 + 71.0250i −0.188333 + 0.164410i
\(433\) 112.477 + 346.169i 0.259762 + 0.799467i 0.992854 + 0.119337i \(0.0380768\pi\)
−0.733091 + 0.680130i \(0.761923\pi\)
\(434\) 2.05508 2.82857i 0.00473520 0.00651744i
\(435\) −54.9637 20.4807i −0.126353 0.0470821i
\(436\) 211.244 153.478i 0.484505 0.352013i
\(437\) −320.370 + 440.951i −0.733112 + 1.00904i
\(438\) 402.843 54.5143i 0.919733 0.124462i
\(439\) 76.4266 55.5271i 0.174092 0.126486i −0.497327 0.867563i \(-0.665685\pi\)
0.671419 + 0.741078i \(0.265685\pi\)
\(440\) 123.401 + 254.622i 0.280456 + 0.578686i
\(441\) −271.874 + 340.734i −0.616495 + 0.772640i
\(442\) 15.8935 + 48.9152i 0.0359581 + 0.110668i
\(443\) 482.788i 1.08982i −0.838496 0.544908i \(-0.816565\pi\)
0.838496 0.544908i \(-0.183435\pi\)
\(444\) 6.84568 12.7174i 0.0154182 0.0286427i
\(445\) 77.7786 + 563.642i 0.174783 + 1.26661i
\(446\) −153.836 49.9845i −0.344925 0.112073i
\(447\) 19.4332 + 40.3671i 0.0434746 + 0.0903066i
\(448\) 4.86836 3.53707i 0.0108669 0.00789525i
\(449\) 398.494i 0.887514i −0.896147 0.443757i \(-0.853645\pi\)
0.896147 0.443757i \(-0.146355\pi\)
\(450\) −164.488 272.385i −0.365529 0.605300i
\(451\) −1494.22 −3.31314
\(452\) −83.0084 114.251i −0.183647 0.252768i
\(453\) 165.795 79.8157i 0.365994 0.176194i
\(454\) 170.305 524.145i 0.375121 1.15450i
\(455\) −18.7989 38.7891i −0.0413162 0.0852508i
\(456\) −136.547 73.5025i −0.299445 0.161190i
\(457\) 430.799 0.942667 0.471333 0.881955i \(-0.343773\pi\)
0.471333 + 0.881955i \(0.343773\pi\)
\(458\) 95.0159 30.8725i 0.207458 0.0674073i
\(459\) −7.64614 85.3361i −0.0166583 0.185917i
\(460\) 293.576 + 52.5223i 0.638209 + 0.114179i
\(461\) −275.244 378.840i −0.597058 0.821779i 0.398377 0.917222i \(-0.369573\pi\)
−0.995435 + 0.0954422i \(0.969573\pi\)
\(462\) −8.56247 63.2738i −0.0185335 0.136956i
\(463\) 538.878 + 391.518i 1.16388 + 0.845611i 0.990264 0.139201i \(-0.0444535\pi\)
0.173620 + 0.984813i \(0.444453\pi\)
\(464\) 9.19382 + 12.6542i 0.0198143 + 0.0272720i
\(465\) 13.2276 + 47.4927i 0.0284464 + 0.102135i
\(466\) −293.523 213.257i −0.629877 0.457632i
\(467\) −366.576 + 119.108i −0.784959 + 0.255049i −0.673956 0.738771i \(-0.735406\pi\)
−0.111003 + 0.993820i \(0.535406\pi\)
\(468\) 9.31010 206.085i 0.0198934 0.440353i
\(469\) 10.0468 + 30.9209i 0.0214218 + 0.0659294i
\(470\) −41.8634 + 233.998i −0.0890711 + 0.497868i
\(471\) 580.641 279.527i 1.23278 0.593475i
\(472\) −48.7032 + 149.893i −0.103185 + 0.317570i
\(473\) 35.2553 + 48.5247i 0.0745354 + 0.102589i
\(474\) −456.337 + 436.187i −0.962736 + 0.920226i
\(475\) 283.085 358.623i 0.595969 0.754996i
\(476\) 4.77387i 0.0100291i
\(477\) 689.876 455.120i 1.44628 0.954131i
\(478\) −44.6917 + 137.547i −0.0934973 + 0.287755i
\(479\) 589.724 + 191.613i 1.23116 + 0.400027i 0.851133 0.524949i \(-0.175916\pi\)
0.380024 + 0.924977i \(0.375916\pi\)
\(480\) −3.60730 + 84.7761i −0.00751520 + 0.176617i
\(481\) 8.52509 + 26.2375i 0.0177237 + 0.0545479i
\(482\) 455.564i 0.945153i
\(483\) −59.2603 31.8995i −0.122692 0.0660445i
\(484\) −451.917 328.337i −0.933713 0.678383i
\(485\) 361.637 347.487i 0.745644 0.716467i
\(486\) −91.6444 + 331.209i −0.188569 + 0.681500i
\(487\) −113.087 82.1625i −0.232212 0.168712i 0.465595 0.884998i \(-0.345840\pi\)
−0.697806 + 0.716286i \(0.745840\pi\)
\(488\) −74.0937 + 101.981i −0.151831 + 0.208978i
\(489\) 26.5884 + 4.82874i 0.0543731 + 0.00987472i
\(490\) 46.8164 + 339.267i 0.0955437 + 0.692381i
\(491\) 38.8922 53.5305i 0.0792102 0.109023i −0.767573 0.640961i \(-0.778536\pi\)
0.846784 + 0.531938i \(0.178536\pi\)
\(492\) −394.566 212.392i −0.801963 0.431692i
\(493\) −12.4086 −0.0251696
\(494\) 281.714 91.5345i 0.570272 0.185293i
\(495\) 773.918 + 460.064i 1.56347 + 0.929422i
\(496\) 4.06258 12.5033i 0.00819068 0.0252083i
\(497\) −15.7006 5.10144i −0.0315908 0.0102645i
\(498\) 3.97419 + 0.721755i 0.00798031 + 0.00144931i
\(499\) 273.164 0.547424 0.273712 0.961812i \(-0.411749\pi\)
0.273712 + 0.961812i \(0.411749\pi\)
\(500\) −244.140 53.8100i −0.488281 0.107620i
\(501\) −178.842 + 170.945i −0.356970 + 0.341207i
\(502\) −254.355 + 184.800i −0.506683 + 0.368127i
\(503\) 486.410 + 158.044i 0.967017 + 0.314203i 0.749611 0.661878i \(-0.230240\pi\)
0.217406 + 0.976081i \(0.430240\pi\)
\(504\) 6.73287 17.9252i 0.0133589 0.0355659i
\(505\) −51.7001 + 96.6502i −0.102376 + 0.191387i
\(506\) −802.558 + 260.767i −1.58608 + 0.515350i
\(507\) −78.0425 81.6478i −0.153930 0.161041i
\(508\) −65.5213 201.654i −0.128979 0.396956i
\(509\) −320.208 + 440.729i −0.629093 + 0.865873i −0.997975 0.0636036i \(-0.979741\pi\)
0.368882 + 0.929476i \(0.379741\pi\)
\(510\) −52.7276 41.8462i −0.103388 0.0820513i
\(511\) −58.3086 + 42.3637i −0.114107 + 0.0829035i
\(512\) 13.3001 18.3060i 0.0259767 0.0357538i
\(513\) −491.471 + 44.0360i −0.958034 + 0.0858401i
\(514\) 331.994 241.208i 0.645903 0.469276i
\(515\) 615.905 591.805i 1.19593 1.14914i
\(516\) 2.41212 + 17.8247i 0.00467464 + 0.0345441i
\(517\) −207.847 639.687i −0.402025 1.23730i
\(518\) 2.56065i 0.00494334i
\(519\) −752.148 404.877i −1.44923 0.780110i
\(520\) −112.299 116.872i −0.215960 0.224754i
\(521\) 678.993 + 220.618i 1.30325 + 0.423452i 0.876711 0.481017i \(-0.159733\pi\)
0.426539 + 0.904469i \(0.359733\pi\)
\(522\) 46.5925 + 17.5006i 0.0892578 + 0.0335260i
\(523\) −414.226 + 300.953i −0.792019 + 0.575436i −0.908562 0.417750i \(-0.862819\pi\)
0.116543 + 0.993186i \(0.462819\pi\)
\(524\) 15.9035i 0.0303501i
\(525\) 48.5691 + 28.7005i 0.0925126 + 0.0546676i
\(526\) 497.694 0.946186
\(527\) 6.13032 + 8.43766i 0.0116325 + 0.0160107i
\(528\) −104.142 216.327i −0.197240 0.409711i
\(529\) −111.387 + 342.814i −0.210561 + 0.648041i
\(530\) 114.355 639.192i 0.215764 1.20602i
\(531\) 133.290 + 483.465i 0.251017 + 0.910480i
\(532\) 27.4939 0.0516802
\(533\) 814.040 264.498i 1.52728 0.496243i
\(534\) −64.7440 478.437i −0.121244 0.895949i
\(535\) 479.885 897.115i 0.896981 1.67685i
\(536\) 71.8578 + 98.9038i 0.134063 + 0.184522i
\(537\) 966.458 130.785i 1.79974 0.243548i
\(538\) 135.701 + 98.5922i 0.252232 + 0.183257i
\(539\) −569.592 783.976i −1.05676 1.45450i
\(540\) 138.967 + 231.491i 0.257346 + 0.428688i
\(541\) 424.224 + 308.217i 0.784148 + 0.569717i 0.906221 0.422804i \(-0.138954\pi\)
−0.122073 + 0.992521i \(0.538954\pi\)
\(542\) −256.385 + 83.3045i −0.473035 + 0.153698i
\(543\) 444.263 + 464.787i 0.818165 + 0.855961i
\(544\) 5.54706 + 17.0721i 0.0101968 + 0.0313825i
\(545\) −284.693 587.428i −0.522372 1.07785i
\(546\) 15.8651 + 32.9553i 0.0290569 + 0.0603578i
\(547\) 148.726 457.732i 0.271894 0.836805i −0.718130 0.695909i \(-0.755002\pi\)
0.990024 0.140896i \(-0.0449983\pi\)
\(548\) −45.8305 63.0803i −0.0836323 0.115110i
\(549\) −18.1019 + 400.698i −0.0329726 + 0.729869i
\(550\) 680.936 191.577i 1.23807 0.348322i
\(551\) 71.4641i 0.129699i
\(552\) −248.990 45.2192i −0.451069 0.0819188i
\(553\) 34.5857 106.444i 0.0625420 0.192484i
\(554\) −190.211 61.8032i −0.343340 0.111558i
\(555\) −28.2825 22.4458i −0.0509595 0.0404429i
\(556\) −82.9261 255.220i −0.149148 0.459029i
\(557\) 411.982i 0.739645i −0.929102 0.369823i \(-0.879418\pi\)
0.929102 0.369823i \(-0.120582\pi\)
\(558\) −11.1184 40.3282i −0.0199254 0.0722727i
\(559\) −27.7963 20.1952i −0.0497250 0.0361273i
\(560\) −6.56107 13.5380i −0.0117162 0.0241749i
\(561\) 187.402 + 34.0341i 0.334049 + 0.0606668i
\(562\) −450.688 327.444i −0.801936 0.582641i
\(563\) −184.067 + 253.346i −0.326940 + 0.449994i −0.940570 0.339600i \(-0.889708\pi\)
0.613631 + 0.789593i \(0.289708\pi\)
\(564\) 36.0424 198.460i 0.0639049 0.351879i
\(565\) −317.710 + 153.976i −0.562319 + 0.272524i
\(566\) −239.839 + 330.110i −0.423744 + 0.583234i
\(567\) −13.5263 59.4080i −0.0238560 0.104776i
\(568\) −62.0755 −0.109288
\(569\) 358.804 116.583i 0.630588 0.204890i 0.0237523 0.999718i \(-0.492439\pi\)
0.606835 + 0.794828i \(0.292439\pi\)
\(570\) −241.002 + 303.671i −0.422811 + 0.532757i
\(571\) −119.953 + 369.178i −0.210076 + 0.646547i 0.789391 + 0.613891i \(0.210397\pi\)
−0.999467 + 0.0326559i \(0.989603\pi\)
\(572\) 436.160 + 141.717i 0.762518 + 0.247757i
\(573\) 25.7041 141.534i 0.0448588 0.247006i
\(574\) 79.4462 0.138408
\(575\) 258.507 699.345i 0.449577 1.21625i
\(576\) 3.24936 71.9266i 0.00564125 0.124873i
\(577\) 183.395 133.245i 0.317843 0.230926i −0.417412 0.908718i \(-0.637063\pi\)
0.735255 + 0.677791i \(0.237063\pi\)
\(578\) 375.161 + 121.897i 0.649067 + 0.210895i
\(579\) −434.945 + 209.387i −0.751200 + 0.361636i
\(580\) 35.1889 17.0540i 0.0606705 0.0294035i
\(581\) −0.681084 + 0.221298i −0.00117226 + 0.000380891i
\(582\) −307.631 + 294.047i −0.528576 + 0.505236i
\(583\) 567.758 + 1747.38i 0.973856 + 2.99722i
\(584\) −159.296 + 219.252i −0.272766 + 0.375431i
\(585\) −503.061 113.645i −0.859934 0.194265i
\(586\) −123.941 + 90.0485i −0.211504 + 0.153666i
\(587\) 110.841 152.560i 0.188826 0.259897i −0.704099 0.710102i \(-0.748649\pi\)
0.892925 + 0.450204i \(0.148649\pi\)
\(588\) −38.9707 287.980i −0.0662766 0.489762i
\(589\) 48.5945 35.3060i 0.0825035 0.0599423i
\(590\) 347.433 + 185.849i 0.588870 + 0.314998i
\(591\) −140.715 + 19.0422i −0.238097 + 0.0322203i
\(592\) 2.97538 + 9.15728i 0.00502598 + 0.0154684i
\(593\) 109.363i 0.184424i 0.995739 + 0.0922120i \(0.0293937\pi\)
−0.995739 + 0.0922120i \(0.970606\pi\)
\(594\) −655.666 392.097i −1.10382 0.660095i
\(595\) 11.7481 + 2.10180i 0.0197448 + 0.00353244i
\(596\) −28.4056 9.22955i −0.0476605 0.0154858i
\(597\) 493.548 237.600i 0.826714 0.397989i
\(598\) 391.067 284.127i 0.653959 0.475129i
\(599\) 1155.98i 1.92985i 0.262534 + 0.964923i \(0.415442\pi\)
−0.262534 + 0.964923i \(0.584558\pi\)
\(600\) 207.040 + 46.2019i 0.345066 + 0.0770031i
\(601\) −446.125 −0.742304 −0.371152 0.928572i \(-0.621037\pi\)
−0.371152 + 0.928572i \(0.621037\pi\)
\(602\) −1.87448 2.58000i −0.00311376 0.00428572i
\(603\) 364.162 + 136.782i 0.603917 + 0.226837i
\(604\) −37.9076 + 116.668i −0.0627609 + 0.193158i
\(605\) −1006.98 + 967.578i −1.66443 + 1.59930i
\(606\) 44.0837 81.8952i 0.0727454 0.135141i
\(607\) −37.3743 −0.0615721 −0.0307861 0.999526i \(-0.509801\pi\)
−0.0307861 + 0.999526i \(0.509801\pi\)
\(608\) 98.3223 31.9469i 0.161714 0.0525442i
\(609\) −8.74447 + 1.18334i −0.0143587 + 0.00194308i
\(610\) 218.347 + 227.239i 0.357946 + 0.372522i
\(611\) 226.466 + 311.704i 0.370649 + 0.510154i
\(612\) 44.6477 + 35.6247i 0.0729538 + 0.0582104i
\(613\) −561.306 407.812i −0.915670 0.665273i 0.0267726 0.999642i \(-0.491477\pi\)
−0.942442 + 0.334369i \(0.891477\pi\)
\(614\) −78.6700 108.280i −0.128127 0.176352i
\(615\) −696.399 + 877.487i −1.13236 + 1.42681i
\(616\) 34.4374 + 25.0203i 0.0559049 + 0.0406173i
\(617\) 748.237 243.117i 1.21270 0.394031i 0.368283 0.929714i \(-0.379946\pi\)
0.844419 + 0.535683i \(0.179946\pi\)
\(618\) −523.927 + 500.792i −0.847778 + 0.810343i
\(619\) 355.597 + 1094.42i 0.574470 + 1.76804i 0.637975 + 0.770057i \(0.279772\pi\)
−0.0635050 + 0.997982i \(0.520228\pi\)
\(620\) −28.9811 15.5026i −0.0467437 0.0250041i
\(621\) −740.567 + 316.185i −1.19254 + 0.509155i
\(622\) −32.9538 + 101.421i −0.0529804 + 0.163057i
\(623\) 50.3133 + 69.2503i 0.0807597 + 0.111156i
\(624\) 95.0288 + 99.4187i 0.152290 + 0.159325i
\(625\) −239.911 + 577.120i −0.383857 + 0.923393i
\(626\) 542.840i 0.867157i
\(627\) 196.010 1079.29i 0.312616 1.72136i
\(628\) −132.758 + 408.587i −0.211398 + 0.650617i
\(629\) −7.26460 2.36041i −0.0115494 0.00375264i
\(630\) −41.1483 24.4611i −0.0653148 0.0388271i
\(631\) −239.405 736.813i −0.379406 1.16769i −0.940458 0.339910i \(-0.889603\pi\)
0.561052 0.827780i \(-0.310397\pi\)
\(632\) 420.847i 0.665897i
\(633\) 442.622 822.268i 0.699245 1.29900i
\(634\) −12.2980 8.93499i −0.0193974 0.0140930i
\(635\) −525.103 + 72.4605i −0.826933 + 0.114111i
\(636\) −98.4540 + 542.117i −0.154802 + 0.852385i
\(637\) 449.083 + 326.278i 0.704997 + 0.512210i
\(638\) −65.0345 + 89.5124i −0.101935 + 0.140301i
\(639\) −164.876 + 108.771i −0.258022 + 0.170221i
\(640\) −39.1940 40.7901i −0.0612406 0.0637345i
\(641\) 368.011 506.523i 0.574120 0.790208i −0.418916 0.908025i \(-0.637590\pi\)
0.993035 + 0.117817i \(0.0375897\pi\)
\(642\) −409.189 + 760.158i −0.637366 + 1.18405i
\(643\) −871.436 −1.35527 −0.677633 0.735400i \(-0.736994\pi\)
−0.677633 + 0.735400i \(0.736994\pi\)
\(644\) 42.6711 13.8647i 0.0662594 0.0215290i
\(645\) 44.9273 + 1.91170i 0.0696548 + 0.00296387i
\(646\) −25.3439 + 78.0005i −0.0392321 + 0.120744i
\(647\) 182.222 + 59.2075i 0.281641 + 0.0915108i 0.446431 0.894818i \(-0.352695\pi\)
−0.164790 + 0.986329i \(0.552695\pi\)
\(648\) −117.402 196.735i −0.181176 0.303604i
\(649\) −1114.87 −1.71782
\(650\) −337.056 + 224.904i −0.518548 + 0.346006i
\(651\) 5.12475 + 5.36149i 0.00787212 + 0.00823578i
\(652\) −14.5749 + 10.5893i −0.0223542 + 0.0162412i
\(653\) −701.150 227.818i −1.07374 0.348878i −0.281795 0.959475i \(-0.590930\pi\)
−0.791942 + 0.610596i \(0.790930\pi\)
\(654\) 240.263 + 499.081i 0.367375 + 0.763120i
\(655\) 39.1372 + 7.00185i 0.0597515 + 0.0106898i
\(656\) 284.112 92.3135i 0.433097 0.140722i
\(657\) −38.9177 + 861.469i −0.0592355 + 1.31122i
\(658\) 11.0510 + 34.0114i 0.0167948 + 0.0516891i
\(659\) −190.143 + 261.710i −0.288533 + 0.397131i −0.928537 0.371240i \(-0.878933\pi\)
0.640004 + 0.768372i \(0.278933\pi\)
\(660\) −578.217 + 161.044i −0.876087 + 0.244006i
\(661\) 659.007 478.797i 0.996985 0.724352i 0.0355453 0.999368i \(-0.488683\pi\)
0.961440 + 0.275016i \(0.0886832\pi\)
\(662\) 138.603 190.770i 0.209370 0.288173i
\(663\) −108.119 + 14.6311i −0.163076 + 0.0220681i
\(664\) −2.17852 + 1.58279i −0.00328091 + 0.00238372i
\(665\) 12.1048 67.6604i 0.0182027 0.101745i
\(666\) 23.9485 + 19.1087i 0.0359587 + 0.0286918i
\(667\) 36.0381 + 110.914i 0.0540301 + 0.166288i
\(668\) 164.933i 0.246906i
\(669\) 162.639 302.138i 0.243107 0.451626i
\(670\) 275.032 133.292i 0.410496 0.198944i
\(671\) −848.041 275.545i −1.26385 0.410648i
\(672\) 5.53714 + 11.5019i 0.00823978 + 0.0171159i
\(673\) −396.766 + 288.268i −0.589549 + 0.428332i −0.842154 0.539237i \(-0.818713\pi\)
0.252605 + 0.967569i \(0.418713\pi\)
\(674\) 90.0223i 0.133564i
\(675\) 630.866 240.068i 0.934617 0.355656i
\(676\) 75.2979 0.111387
\(677\) 9.69480 + 13.3437i 0.0143202 + 0.0197101i 0.816117 0.577887i \(-0.196122\pi\)
−0.801797 + 0.597597i \(0.796122\pi\)
\(678\) 269.928 129.946i 0.398123 0.191661i
\(679\) 23.3153 71.7571i 0.0343377 0.105681i
\(680\) 44.4554 6.13453i 0.0653756 0.00902137i
\(681\) 1029.43 + 554.136i 1.51164 + 0.813709i
\(682\) 92.9966 0.136359
\(683\) −557.024 + 180.988i −0.815555 + 0.264990i −0.686949 0.726706i \(-0.741050\pi\)
−0.128606 + 0.991696i \(0.541050\pi\)
\(684\) 205.172 257.137i 0.299958 0.375931i
\(685\) −175.414 + 85.0130i −0.256079 + 0.124107i
\(686\) 60.9229 + 83.8531i 0.0888088 + 0.122235i
\(687\) 28.4204 + 210.018i 0.0413689 + 0.305702i
\(688\) −9.70130 7.04841i −0.0141007 0.0102448i
\(689\) −618.619 851.456i −0.897851 1.23579i
\(690\) −220.904 + 592.837i −0.320151 + 0.859185i
\(691\) −840.014 610.306i −1.21565 0.883221i −0.219918 0.975518i \(-0.570579\pi\)
−0.995731 + 0.0922977i \(0.970579\pi\)
\(692\) 541.593 175.974i 0.782649 0.254298i
\(693\) 135.309 + 6.11274i 0.195252 + 0.00882069i
\(694\) 142.732 + 439.285i 0.205666 + 0.632976i
\(695\) −664.589 + 91.7086i −0.956243 + 0.131955i
\(696\) −29.8966 + 14.3925i −0.0429548 + 0.0206789i
\(697\) −73.2336 + 225.390i −0.105070 + 0.323372i
\(698\) −63.5524 87.4724i −0.0910493 0.125319i
\(699\) 556.366 531.799i 0.795945 0.760799i
\(700\) −36.2046 + 10.1859i −0.0517208 + 0.0145513i
\(701\) 1211.02i 1.72757i 0.503864 + 0.863783i \(0.331911\pi\)
−0.503864 + 0.863783i \(0.668089\pi\)
\(702\) 426.608 + 97.5491i 0.607703 + 0.138959i
\(703\) −13.5942 + 41.8386i −0.0193374 + 0.0595144i
\(704\) 152.226 + 49.4613i 0.216230 + 0.0702575i
\(705\) −472.527 176.074i −0.670251 0.249750i
\(706\) −151.346 465.795i −0.214371 0.659766i
\(707\) 16.4897i 0.0233234i
\(708\) −294.393 158.470i −0.415809 0.223827i
\(709\) 878.787 + 638.476i 1.23947 + 0.900531i 0.997563 0.0697674i \(-0.0222257\pi\)
0.241911 + 0.970298i \(0.422226\pi\)
\(710\) −27.3301 + 152.763i −0.0384931 + 0.215160i
\(711\) −737.425 1117.80i −1.03717 1.57215i
\(712\) 260.394 + 189.188i 0.365722 + 0.265713i
\(713\) 57.6156 79.3010i 0.0808073 0.111222i
\(714\) −9.96393 1.80955i −0.0139551 0.00253439i
\(715\) 540.785 1010.96i 0.756342 1.41394i
\(716\) −382.165 + 526.005i −0.533750 + 0.734644i
\(717\) −270.145 145.417i −0.376771 0.202814i
\(718\) 749.926 1.04447
\(719\) −490.349 + 159.324i −0.681988 + 0.221591i −0.629465 0.777028i \(-0.716726\pi\)
−0.0525224 + 0.998620i \(0.516726\pi\)
\(720\) −175.576 39.6637i −0.243855 0.0550885i
\(721\) 39.7083 122.210i 0.0550740 0.169500i
\(722\) −36.3200 11.8011i −0.0503047 0.0163450i
\(723\) 950.843 + 172.683i 1.31514 + 0.238842i
\(724\) −428.640 −0.592044
\(725\) −26.4760 94.1056i −0.0365186 0.129801i
\(726\) 856.599 818.775i 1.17989 1.12779i
\(727\) −624.749 + 453.907i −0.859352 + 0.624356i −0.927709 0.373305i \(-0.878224\pi\)
0.0683568 + 0.997661i \(0.478224\pi\)
\(728\) −23.1901 7.53493i −0.0318546 0.0103502i
\(729\) −656.554 316.824i −0.900623 0.434601i
\(730\) 469.428 + 488.545i 0.643053 + 0.669240i
\(731\) 9.04741 2.93968i 0.0123768 0.00402145i
\(732\) −184.768 193.303i −0.252415 0.264075i
\(733\) −297.551 915.766i −0.405935 1.24934i −0.920112 0.391656i \(-0.871902\pi\)
0.514177 0.857684i \(-0.328098\pi\)
\(734\) −305.135 + 419.982i −0.415715 + 0.572183i
\(735\) −725.856 30.8858i −0.987559 0.0420215i
\(736\) 136.488 99.1644i 0.185446 0.134734i
\(737\) −508.302 + 699.618i −0.689691 + 0.949278i
\(738\) 592.863 743.022i 0.803337 1.00680i
\(739\) 956.448 694.900i 1.29425 0.940325i 0.294364 0.955693i \(-0.404892\pi\)
0.999882 + 0.0153688i \(0.00489225\pi\)
\(740\) 23.8454 3.29050i 0.0322235 0.00444662i
\(741\) 84.2642 + 622.685i 0.113717 + 0.840330i
\(742\) −30.1870 92.9062i −0.0406833 0.125210i
\(743\) 859.546i 1.15686i −0.815732 0.578429i \(-0.803666\pi\)
0.815732 0.578429i \(-0.196334\pi\)
\(744\) 24.5567 + 13.2187i 0.0330064 + 0.0177671i
\(745\) −35.2195 + 65.8407i −0.0472745 + 0.0883768i
\(746\) 168.852 + 54.8635i 0.226344 + 0.0735435i
\(747\) −3.01286 + 8.02127i −0.00403328 + 0.0107380i
\(748\) −102.727 + 74.6358i −0.137336 + 0.0997804i
\(749\) 153.059i 0.204350i
\(750\) 204.853 489.168i 0.273138 0.652224i
\(751\) 1265.96 1.68570 0.842848 0.538151i \(-0.180877\pi\)
0.842848 + 0.538151i \(0.180877\pi\)
\(752\) 79.0400 + 108.789i 0.105106 + 0.144666i
\(753\) −289.296 600.934i −0.384191 0.798053i
\(754\) 19.5854 60.2775i 0.0259753 0.0799437i
\(755\) 270.421 + 144.653i 0.358173 + 0.191594i
\(756\) 34.8610 + 20.8473i 0.0461125 + 0.0275758i
\(757\) −1313.56 −1.73522 −0.867611 0.497243i \(-0.834346\pi\)
−0.867611 + 0.497243i \(0.834346\pi\)
\(758\) −298.503 + 96.9896i −0.393804 + 0.127955i
\(759\) −240.055 1773.93i −0.316278 2.33719i
\(760\) −35.3303 256.029i −0.0464872 0.336881i
\(761\) 232.853 + 320.495i 0.305984 + 0.421150i 0.934123 0.356950i \(-0.116183\pi\)
−0.628140 + 0.778100i \(0.716183\pi\)
\(762\) 445.724 60.3172i 0.584940 0.0791564i
\(763\) −79.4493 57.7233i −0.104127 0.0756530i
\(764\) 56.3683 + 77.5843i 0.0737805 + 0.101550i
\(765\) 107.327 94.1901i 0.140297 0.123124i
\(766\) 496.807 + 360.951i 0.648573 + 0.471216i
\(767\) 607.370 197.347i 0.791878 0.257297i
\(768\) 33.1664 + 34.6986i 0.0431854 + 0.0451804i
\(769\) 158.055 + 486.445i 0.205534 + 0.632568i 0.999691 + 0.0248557i \(0.00791262\pi\)
−0.794157 + 0.607712i \(0.792087\pi\)
\(770\) 76.7349 73.7323i 0.0996557 0.0957562i
\(771\) 377.601 + 784.362i 0.489754 + 1.01733i
\(772\) 99.4461 306.064i 0.128816 0.396456i
\(773\) 585.466 + 805.825i 0.757395 + 1.04246i 0.997426 + 0.0716991i \(0.0228421\pi\)
−0.240032 + 0.970765i \(0.577158\pi\)
\(774\) −38.1177 1.72201i −0.0492477 0.00222481i
\(775\) −50.9103 + 64.4951i −0.0656907 + 0.0832194i
\(776\) 283.706i 0.365601i
\(777\) −5.34454 0.970623i −0.00687843 0.00124919i
\(778\) −160.702 + 494.590i −0.206558 + 0.635720i
\(779\) 1298.08 + 421.770i 1.66634 + 0.541425i
\(780\) 286.501 190.088i 0.367309 0.243702i
\(781\) −135.691 417.614i −0.173740 0.534716i
\(782\) 133.839i 0.171150i
\(783\) −54.1879 + 90.6134i −0.0692055 + 0.115726i
\(784\) 156.736 + 113.876i 0.199919 + 0.145250i
\(785\) 947.054 + 506.598i 1.20644 + 0.645347i
\(786\) −33.1934 6.02826i −0.0422307 0.00766954i
\(787\) −723.473 525.634i −0.919279 0.667896i 0.0240652 0.999710i \(-0.492339\pi\)
−0.943345 + 0.331815i \(0.892339\pi\)
\(788\) 55.6428 76.5858i 0.0706127 0.0971901i
\(789\) −188.652 + 1038.78i −0.239103 + 1.31657i
\(790\) −1035.67 185.287i −1.31098 0.234541i
\(791\) −31.2196 + 42.9701i −0.0394685 + 0.0543238i
\(792\) 490.990 135.364i 0.619937 0.170915i
\(793\) 510.780 0.644111
\(794\) 480.483 156.118i 0.605142 0.196623i
\(795\) 1290.76 + 480.967i 1.62360 + 0.604990i
\(796\) −112.845 + 347.302i −0.141765 + 0.436309i
\(797\) 58.8097 + 19.1084i 0.0737888 + 0.0239754i 0.345679 0.938353i \(-0.387649\pi\)
−0.271890 + 0.962328i \(0.587649\pi\)
\(798\) −10.4216 + 57.3847i −0.0130597 + 0.0719106i
\(799\) −106.678 −0.133514
\(800\) −117.637 + 78.4948i −0.147047 + 0.0981185i
\(801\) 1023.13 + 46.2207i 1.27731 + 0.0577037i
\(802\) 305.186 221.731i 0.380531 0.276472i
\(803\) −1823.22 592.400i −2.27051 0.737734i
\(804\) −233.668 + 112.490i −0.290632 + 0.139913i
\(805\) −15.3331 111.115i −0.0190473 0.138031i
\(806\) −50.6637 + 16.4616i −0.0628582 + 0.0204239i
\(807\) −257.217 + 245.860i −0.318733 + 0.304659i
\(808\) 19.1604 + 58.9696i 0.0237133 + 0.0729822i
\(809\) −472.902 + 650.893i −0.584551 + 0.804565i −0.994185 0.107685i \(-0.965656\pi\)
0.409634 + 0.912250i \(0.365656\pi\)
\(810\) −535.840 + 202.301i −0.661531 + 0.249754i
\(811\) −52.6505 + 38.2529i −0.0649205 + 0.0471675i −0.619772 0.784782i \(-0.712775\pi\)
0.554852 + 0.831949i \(0.312775\pi\)
\(812\) 3.45781 4.75927i 0.00425839 0.00586117i
\(813\) −76.6879 566.698i −0.0943271 0.697046i
\(814\) −55.1018 + 40.0338i −0.0676926 + 0.0491816i
\(815\) 19.6425 + 40.5300i 0.0241013 + 0.0497300i
\(816\) −37.7352 + 5.10647i −0.0462441 + 0.00625793i
\(817\) −16.9303 52.1062i −0.0207226 0.0637775i
\(818\) 425.344i 0.519980i
\(819\) −74.7974 + 20.6214i −0.0913277 + 0.0251788i
\(820\) −102.090 739.821i −0.124500 0.902221i
\(821\) −690.501 224.358i −0.841049 0.273273i −0.143357 0.989671i \(-0.545790\pi\)
−0.697692 + 0.716398i \(0.745790\pi\)
\(822\) 149.032 71.7457i 0.181304 0.0872819i
\(823\) −167.541 + 121.726i −0.203574 + 0.147905i −0.684901 0.728636i \(-0.740155\pi\)
0.481328 + 0.876541i \(0.340155\pi\)
\(824\) 483.180i 0.586384i
\(825\) 141.744 + 1493.85i 0.171811 + 1.81073i
\(826\) 59.2762 0.0717630
\(827\) 201.813 + 277.772i 0.244030 + 0.335879i 0.913409 0.407042i \(-0.133440\pi\)
−0.669379 + 0.742921i \(0.733440\pi\)
\(828\) 188.761 502.546i 0.227972 0.606940i
\(829\) 142.416 438.310i 0.171792 0.528721i −0.827680 0.561200i \(-0.810340\pi\)
0.999472 + 0.0324783i \(0.0103400\pi\)
\(830\) 2.93598 + 6.05804i 0.00353733 + 0.00729884i
\(831\) 201.094 373.577i 0.241991 0.449551i
\(832\) −91.6868 −0.110200
\(833\) −146.172 + 47.4941i −0.175476 + 0.0570157i
\(834\) 564.124 76.3396i 0.676408 0.0915343i
\(835\) −405.888 72.6154i −0.486093 0.0869646i
\(836\) 429.846 + 591.632i 0.514169 + 0.707693i
\(837\) 88.3866 7.91947i 0.105599 0.00946173i
\(838\) −84.9096 61.6904i −0.101324 0.0736162i
\(839\) 502.493 + 691.623i 0.598919 + 0.824342i 0.995609 0.0936111i \(-0.0298410\pi\)
−0.396690 + 0.917953i \(0.629841\pi\)
\(840\) 30.7431 8.56252i 0.0365990 0.0101935i
\(841\) −668.013 485.340i −0.794308 0.577098i
\(842\) −827.170 + 268.764i −0.982387 + 0.319197i
\(843\) 854.269 816.548i 1.01337 0.968622i
\(844\) 192.380 + 592.083i 0.227938 + 0.701521i
\(845\) 33.1516 185.303i 0.0392326 0.219293i
\(846\) 400.560 + 150.454i 0.473475 + 0.177841i
\(847\) −64.9216 + 199.808i −0.0766488 + 0.235901i
\(848\) −215.907 297.170i −0.254607 0.350437i
\(849\) −598.088 625.717i −0.704462 0.737005i
\(850\) 4.47584 112.102i 0.00526569 0.131885i
\(851\) 71.7897i 0.0843592i
\(852\) 23.5299 129.563i 0.0276173 0.152069i
\(853\) 172.074 529.588i 0.201728 0.620854i −0.798104 0.602519i \(-0.794164\pi\)
0.999832 0.0183344i \(-0.00583636\pi\)
\(854\) 45.0894 + 14.6504i 0.0527978 + 0.0171551i
\(855\) −542.464 618.122i −0.634461 0.722950i
\(856\) −177.848 547.361i −0.207767 0.639440i
\(857\) 1150.53i 1.34251i 0.741225 + 0.671257i \(0.234245\pi\)
−0.741225 + 0.671257i \(0.765755\pi\)
\(858\) −461.117 + 856.626i −0.537432 + 0.998399i
\(859\) −192.487 139.850i −0.224082 0.162805i 0.470080 0.882624i \(-0.344225\pi\)
−0.694162 + 0.719819i \(0.744225\pi\)
\(860\) −21.6168 + 20.7710i −0.0251358 + 0.0241523i
\(861\) −30.1143 + 165.818i −0.0349760 + 0.192588i
\(862\) −774.142 562.447i −0.898077 0.652491i
\(863\) 462.136 636.075i 0.535499 0.737051i −0.452457 0.891786i \(-0.649452\pi\)
0.987956 + 0.154735i \(0.0494524\pi\)
\(864\) 148.892 + 34.0460i 0.172329 + 0.0394051i
\(865\) −194.611 1410.30i −0.224984 1.63040i
\(866\) 302.563 416.442i 0.349380 0.480880i
\(867\) −396.627 + 736.822i −0.457471 + 0.849852i
\(868\) −4.94452 −0.00569645
\(869\) 2831.25 919.930i 3.25806 1.05861i
\(870\) 22.2563 + 79.9099i 0.0255820 + 0.0918504i
\(871\) 153.077 471.122i 0.175748 0.540898i
\(872\) −351.195 114.110i −0.402747 0.130860i
\(873\) −497.121 753.541i −0.569440 0.863162i
\(874\) 770.811 0.881935
\(875\) 9.12693 + 93.5814i 0.0104308 + 0.106950i
\(876\) −397.236 415.586i −0.453466 0.474414i
\(877\) −955.613 + 694.293i −1.08964 + 0.791669i −0.979338 0.202230i \(-0.935181\pi\)
−0.110300 + 0.993898i \(0.535181\pi\)
\(878\) −127.060 41.2842i −0.144715 0.0470207i
\(879\) −140.967 292.821i −0.160372 0.333129i
\(880\) 188.742 352.841i 0.214479 0.400956i
\(881\) −889.984 + 289.173i −1.01020 + 0.328233i −0.766933 0.641727i \(-0.778218\pi\)
−0.243264 + 0.969960i \(0.578218\pi\)
\(882\) 615.838 + 27.8211i 0.698230 + 0.0315432i
\(883\) 42.4241 + 130.568i 0.0480454 + 0.147868i 0.972201 0.234148i \(-0.0752299\pi\)
−0.924156 + 0.382016i \(0.875230\pi\)
\(884\) 42.7534 58.8450i 0.0483636 0.0665668i
\(885\) −519.596 + 654.709i −0.587114 + 0.739784i
\(886\) −552.369 + 401.320i −0.623442 + 0.452957i
\(887\) −52.2133 + 71.8655i −0.0588651 + 0.0810208i −0.837435 0.546537i \(-0.815946\pi\)
0.778570 + 0.627558i \(0.215946\pi\)
\(888\) −20.2407 + 2.73906i −0.0227936 + 0.00308452i
\(889\) −64.5154 + 46.8732i −0.0725707 + 0.0527257i
\(890\) 580.221 557.517i 0.651934 0.626424i
\(891\) 1066.91 1219.87i 1.19743 1.36910i
\(892\) 70.6888 + 217.558i 0.0792475 + 0.243899i
\(893\) 614.382i 0.687998i
\(894\) 30.0310 55.7892i 0.0335917 0.0624040i
\(895\) 1126.20 + 1172.07i 1.25833 + 1.30957i
\(896\) −8.09369 2.62980i −0.00903314 0.00293504i
\(897\) 444.789 + 923.927i 0.495863 + 1.03002i
\(898\) −455.926 + 331.250i −0.507713 + 0.368875i
\(899\) 12.8522i 0.0142961i
\(900\) −174.911 + 414.616i −0.194345 + 0.460684i
\(901\) 291.403 0.323421
\(902\) 1242.08 + 1709.58i 1.37703 + 1.89532i
\(903\) 6.09546 2.93442i 0.00675023 0.00324964i
\(904\) −61.7164 + 189.944i −0.0682704 + 0.210115i
\(905\) −188.718 + 1054.85i −0.208528 + 1.16558i
\(906\) −229.137 123.343i −0.252911 0.136140i
\(907\) 571.577 0.630184 0.315092 0.949061i \(-0.397965\pi\)
0.315092 + 0.949061i \(0.397965\pi\)
\(908\) −741.253 + 240.848i −0.816358 + 0.265251i
\(909\) 154.220 + 123.053i 0.169659 + 0.135372i
\(910\) −28.7529 + 53.7518i −0.0315966 + 0.0590679i
\(911\) −625.679 861.173i −0.686804 0.945305i 0.313186 0.949692i \(-0.398604\pi\)
−0.999990 + 0.00438696i \(0.998604\pi\)
\(912\) 29.4094 + 217.326i 0.0322472 + 0.238296i
\(913\) −15.4103 11.1962i −0.0168787 0.0122631i
\(914\) −358.103 492.887i −0.391798 0.539263i
\(915\) −557.053 + 369.594i −0.608801 + 0.403927i
\(916\) −114.304 83.0469i −0.124786 0.0906626i
\(917\) 5.68857 1.84833i 0.00620345 0.00201562i
\(918\) −91.2791 + 79.6841i −0.0994326 + 0.0868019i
\(919\) −231.126 711.333i −0.251498 0.774030i −0.994500 0.104741i \(-0.966599\pi\)
0.743002 0.669289i \(-0.233401\pi\)
\(920\) −183.944 379.547i −0.199940 0.412551i
\(921\) 255.820 123.154i 0.277763 0.133718i
\(922\) −204.643 + 629.825i −0.221955 + 0.683107i
\(923\) 147.846 + 203.493i 0.160180 + 0.220469i
\(924\) −65.2754 + 62.3931i −0.0706444 + 0.0675250i
\(925\) 2.40079 60.1304i 0.00259545 0.0650058i
\(926\) 941.994i 1.01727i
\(927\) −846.647 1283.36i −0.913319 1.38442i
\(928\) 6.83557 21.0377i 0.00736592 0.0226700i
\(929\) 13.1716 + 4.27973i 0.0141783 + 0.00460681i 0.316098 0.948727i \(-0.397627\pi\)
−0.301919 + 0.953334i \(0.597627\pi\)
\(930\) 43.3420 54.6125i 0.0466043 0.0587231i
\(931\) 273.530 + 841.839i 0.293803 + 0.904231i
\(932\) 513.096i 0.550532i
\(933\) −199.193 107.225i −0.213498 0.114924i
\(934\) 440.991 + 320.399i 0.472154 + 0.343040i
\(935\) 138.445 + 285.665i 0.148070 + 0.305524i
\(936\) −243.526 + 160.657i −0.260177 + 0.171642i
\(937\) −221.299 160.783i −0.236178 0.171594i 0.463401 0.886149i \(-0.346629\pi\)
−0.699579 + 0.714555i \(0.746629\pi\)
\(938\) 27.0258 37.1979i 0.0288122 0.0396566i
\(939\) 1133.00 + 205.765i 1.20661 + 0.219132i
\(940\) 302.521 146.615i 0.321831 0.155973i
\(941\) 348.166 479.210i 0.369996 0.509256i −0.582904 0.812541i \(-0.698084\pi\)
0.952900 + 0.303285i \(0.0980836\pi\)
\(942\) −802.473 431.966i −0.851882 0.458563i
\(943\) 2227.33 2.36196
\(944\) 211.981 68.8768i 0.224556 0.0729627i
\(945\) 66.6521 76.6119i 0.0705313 0.0810708i
\(946\) 26.2121 80.6727i 0.0277084 0.0852777i
\(947\) −780.582 253.627i −0.824268 0.267821i −0.133639 0.991030i \(-0.542666\pi\)
−0.690629 + 0.723209i \(0.742666\pi\)
\(948\) 878.383 + 159.523i 0.926565 + 0.168274i
\(949\) 1098.14 1.15715
\(950\) −645.624 25.7774i −0.679605 0.0271341i
\(951\) 23.3105 22.2812i 0.0245116 0.0234292i
\(952\) 5.46189 3.96830i 0.00573728 0.00416838i
\(953\) −418.658 136.030i −0.439306 0.142739i 0.0810096 0.996713i \(-0.474186\pi\)
−0.520315 + 0.853974i \(0.674186\pi\)
\(954\) −1094.18 410.982i −1.14693 0.430799i
\(955\) 215.747 104.560i 0.225913 0.109487i
\(956\) 194.521 63.2036i 0.203474 0.0661126i
\(957\) −162.177 169.669i −0.169464 0.177292i
\(958\) −270.982 833.996i −0.282862 0.870560i
\(959\) −17.2369 + 23.7246i −0.0179739 + 0.0247389i
\(960\) 99.9929 66.3433i 0.104159 0.0691076i
\(961\) 768.726 558.512i 0.799923 0.581178i
\(962\) 22.9325 31.5638i 0.0238383 0.0328106i
\(963\) −1431.48 1142.19i −1.48648 1.18608i
\(964\) −521.221 + 378.689i −0.540686 + 0.392831i
\(965\) −709.417 379.481i −0.735147 0.393245i
\(966\) 12.7635 + 94.3177i 0.0132127 + 0.0976373i
\(967\) 354.476 + 1090.96i 0.366572 + 1.12819i 0.948991 + 0.315305i \(0.102107\pi\)
−0.582418 + 0.812889i \(0.697893\pi\)
\(968\) 789.980i 0.816095i
\(969\) −153.194 82.4636i −0.158095 0.0851018i
\(970\) −698.180 124.908i −0.719773 0.128771i
\(971\) −591.698 192.254i −0.609370 0.197996i −0.0119548 0.999929i \(-0.503805\pi\)
−0.597415 + 0.801932i \(0.703805\pi\)
\(972\) 455.123 170.466i 0.468234 0.175377i
\(973\) −81.6529 + 59.3243i −0.0839187 + 0.0609705i
\(974\) 197.683i 0.202960i
\(975\) −341.653 788.748i −0.350413 0.808972i
\(976\) 178.270 0.182653
\(977\) −438.633 603.726i −0.448959 0.617939i 0.523215 0.852201i \(-0.324733\pi\)
−0.972174 + 0.234262i \(0.924733\pi\)
\(978\) −16.5771 34.4344i −0.0169500 0.0352090i
\(979\) −703.565 + 2165.35i −0.718657 + 2.21180i
\(980\) 349.246 335.580i 0.356374 0.342429i
\(981\) −1132.74 + 312.294i −1.15468 + 0.318342i
\(982\) −93.5748 −0.0952900
\(983\) −579.028 + 188.138i −0.589041 + 0.191391i −0.588347 0.808609i \(-0.700221\pi\)
−0.000694462 1.00000i \(0.500221\pi\)
\(984\) 84.9813 + 627.984i 0.0863631 + 0.638195i
\(985\) −163.974 170.652i −0.166471 0.173250i
\(986\) 10.3147 + 14.1970i 0.0104612 + 0.0143985i
\(987\) −75.1768 + 10.1732i −0.0761670 + 0.0103072i
\(988\) −338.903 246.227i −0.343019 0.249218i
\(989\) −52.5525 72.3323i −0.0531370 0.0731368i
\(990\) −116.953 1267.89i −0.118134 1.28069i
\(991\) 982.053 + 713.504i 0.990972 + 0.719983i 0.960134 0.279541i \(-0.0901823\pi\)
0.0308384 + 0.999524i \(0.490182\pi\)
\(992\) −17.6824 + 5.74535i −0.0178250 + 0.00579168i
\(993\) 345.634 + 361.601i 0.348071 + 0.364150i
\(994\) 7.21453 + 22.2040i 0.00725808 + 0.0223381i
\(995\) 805.002 + 430.611i 0.809047 + 0.432775i
\(996\) −2.47779 5.14693i −0.00248774 0.00516760i
\(997\) −325.015 + 1000.29i −0.325993 + 1.00330i 0.644998 + 0.764184i \(0.276858\pi\)
−0.970991 + 0.239118i \(0.923142\pi\)
\(998\) −227.069 312.534i −0.227524 0.313160i
\(999\) −48.9611 + 42.7416i −0.0490101 + 0.0427844i
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 150.3.j.a.11.8 80
3.2 odd 2 inner 150.3.j.a.11.14 yes 80
25.16 even 5 inner 150.3.j.a.41.14 yes 80
75.41 odd 10 inner 150.3.j.a.41.8 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.j.a.11.8 80 1.1 even 1 trivial
150.3.j.a.11.14 yes 80 3.2 odd 2 inner
150.3.j.a.41.8 yes 80 75.41 odd 10 inner
150.3.j.a.41.14 yes 80 25.16 even 5 inner