Properties

Label 136.3.j.b.115.2
Level $136$
Weight $3$
Character 136.115
Analytic conductor $3.706$
Analytic rank $0$
Dimension $64$
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] = [136,3,Mod(115,136)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(136, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 2, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("136.115");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 136.j (of order \(4\), degree \(2\), 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: \(3.70573159530\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 115.2
Character \(\chi\) \(=\) 136.115
Dual form 136.3.j.b.123.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.95592 + 0.417606i) q^{2} +(0.749243 + 0.749243i) q^{3} +(3.65121 - 1.63360i) q^{4} +(3.60984 - 3.60984i) q^{5} +(-1.77834 - 1.15257i) q^{6} +(-3.85896 - 3.85896i) q^{7} +(-6.45926 + 4.71996i) q^{8} -7.87727i q^{9} +O(q^{10})\) \(q+(-1.95592 + 0.417606i) q^{2} +(0.749243 + 0.749243i) q^{3} +(3.65121 - 1.63360i) q^{4} +(3.60984 - 3.60984i) q^{5} +(-1.77834 - 1.15257i) q^{6} +(-3.85896 - 3.85896i) q^{7} +(-6.45926 + 4.71996i) q^{8} -7.87727i q^{9} +(-5.55305 + 8.56803i) q^{10} +(-2.59125 + 2.59125i) q^{11} +(3.95961 + 1.51168i) q^{12} -2.98374i q^{13} +(9.15932 + 5.93627i) q^{14} +5.40930 q^{15} +(10.6627 - 11.9293i) q^{16} +(13.0434 - 10.9027i) q^{17} +(3.28959 + 15.4073i) q^{18} -25.8973i q^{19} +(7.28325 - 19.0773i) q^{20} -5.78260i q^{21} +(3.98614 - 6.15038i) q^{22} +(20.9457 + 20.9457i) q^{23} +(-8.37595 - 1.30316i) q^{24} -1.06191i q^{25} +(1.24603 + 5.83595i) q^{26} +(12.6452 - 12.6452i) q^{27} +(-20.3939 - 7.78587i) q^{28} +(22.7491 - 22.7491i) q^{29} +(-10.5801 + 2.25895i) q^{30} +(-18.3612 + 18.3612i) q^{31} +(-15.8736 + 27.7854i) q^{32} -3.88295 q^{33} +(-20.9588 + 26.7718i) q^{34} -27.8605 q^{35} +(-12.8683 - 28.7616i) q^{36} +(0.733830 - 0.733830i) q^{37} +(10.8149 + 50.6530i) q^{38} +(2.23555 - 2.23555i) q^{39} +(-6.27861 + 40.3552i) q^{40} +(-26.2827 + 26.2827i) q^{41} +(2.41485 + 11.3103i) q^{42} -10.7209i q^{43} +(-5.22812 + 13.6943i) q^{44} +(-28.4357 - 28.4357i) q^{45} +(-49.7150 - 32.2209i) q^{46} +84.3467i q^{47} +(16.9269 - 0.948971i) q^{48} -19.2169i q^{49} +(0.443459 + 2.07701i) q^{50} +(17.9415 + 1.60393i) q^{51} +(-4.87425 - 10.8943i) q^{52} +33.8459 q^{53} +(-19.4522 + 30.0136i) q^{54} +18.7080i q^{55} +(43.1401 + 6.71190i) q^{56} +(19.4034 - 19.4034i) q^{57} +(-34.9951 + 53.9954i) q^{58} +69.9591i q^{59} +(19.7505 - 8.83665i) q^{60} +(-65.8369 - 65.8369i) q^{61} +(28.2452 - 43.5807i) q^{62} +(-30.3981 + 30.3981i) q^{63} +(19.4440 - 60.9748i) q^{64} +(-10.7708 - 10.7708i) q^{65} +(7.59472 - 1.62154i) q^{66} -76.0157 q^{67} +(29.8137 - 61.1158i) q^{68} +31.3868i q^{69} +(54.4927 - 11.6347i) q^{70} +(27.4650 - 27.4650i) q^{71} +(37.1804 + 50.8813i) q^{72} +(48.3347 + 48.3347i) q^{73} +(-1.12886 + 1.74176i) q^{74} +(0.795629 - 0.795629i) q^{75} +(-42.3060 - 94.5567i) q^{76} +19.9990 q^{77} +(-3.43897 + 5.30613i) q^{78} +(17.0189 + 17.0189i) q^{79} +(-4.57213 - 81.5533i) q^{80} -51.9468 q^{81} +(40.4310 - 62.3826i) q^{82} +20.9027i q^{83} +(-9.44647 - 21.1135i) q^{84} +(7.72772 - 86.4417i) q^{85} +(4.47710 + 20.9692i) q^{86} +34.0892 q^{87} +(4.50696 - 28.9681i) q^{88} +115.759 q^{89} +(67.4927 + 43.7429i) q^{90} +(-11.5141 + 11.5141i) q^{91} +(110.694 + 42.2602i) q^{92} -27.5140 q^{93} +(-35.2237 - 164.975i) q^{94} +(-93.4853 - 93.4853i) q^{95} +(-32.7112 + 8.92486i) q^{96} +(66.5506 + 66.5506i) q^{97} +(8.02507 + 37.5866i) q^{98} +(20.4119 + 20.4119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 8 q^{3} + 12 q^{4} + 26 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 8 q^{3} + 12 q^{4} + 26 q^{6} - 30 q^{10} - 32 q^{11} - 14 q^{12} - 32 q^{14} - 124 q^{16} - 12 q^{17} + 84 q^{18} + 70 q^{20} - 38 q^{22} + 54 q^{24} + 160 q^{27} - 76 q^{28} + 56 q^{30} + 128 q^{33} + 54 q^{34} - 8 q^{35} - 360 q^{38} - 62 q^{40} - 88 q^{41} + 306 q^{44} - 280 q^{46} + 82 q^{48} - 164 q^{50} - 360 q^{51} - 204 q^{52} + 460 q^{54} - 328 q^{56} - 24 q^{57} + 194 q^{58} - 72 q^{62} + 204 q^{64} + 112 q^{65} - 8 q^{67} - 226 q^{68} - 36 q^{72} - 408 q^{73} - 250 q^{74} + 32 q^{75} + 508 q^{78} + 674 q^{80} + 80 q^{81} + 116 q^{82} + 1008 q^{84} - 324 q^{86} + 90 q^{88} - 8 q^{89} - 834 q^{90} + 384 q^{91} - 104 q^{92} + 154 q^{96} + 112 q^{97} - 216 q^{98} + 416 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(103\) \(105\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.95592 + 0.417606i −0.977958 + 0.208803i
\(3\) 0.749243 + 0.749243i 0.249748 + 0.249748i 0.820867 0.571119i \(-0.193491\pi\)
−0.571119 + 0.820867i \(0.693491\pi\)
\(4\) 3.65121 1.63360i 0.912803 0.408401i
\(5\) 3.60984 3.60984i 0.721968 0.721968i −0.247038 0.969006i \(-0.579457\pi\)
0.969006 + 0.247038i \(0.0794571\pi\)
\(6\) −1.77834 1.15257i −0.296391 0.192095i
\(7\) −3.85896 3.85896i −0.551280 0.551280i 0.375530 0.926810i \(-0.377461\pi\)
−0.926810 + 0.375530i \(0.877461\pi\)
\(8\) −6.45926 + 4.71996i −0.807407 + 0.589994i
\(9\) 7.87727i 0.875252i
\(10\) −5.55305 + 8.56803i −0.555305 + 0.856803i
\(11\) −2.59125 + 2.59125i −0.235568 + 0.235568i −0.815012 0.579444i \(-0.803270\pi\)
0.579444 + 0.815012i \(0.303270\pi\)
\(12\) 3.95961 + 1.51168i 0.329968 + 0.125973i
\(13\) 2.98374i 0.229519i −0.993393 0.114759i \(-0.963390\pi\)
0.993393 0.114759i \(-0.0366097\pi\)
\(14\) 9.15932 + 5.93627i 0.654237 + 0.424020i
\(15\) 5.40930 0.360620
\(16\) 10.6627 11.9293i 0.666418 0.745579i
\(17\) 13.0434 10.9027i 0.767261 0.641335i
\(18\) 3.28959 + 15.4073i 0.182755 + 0.855960i
\(19\) 25.8973i 1.36302i −0.731810 0.681509i \(-0.761324\pi\)
0.731810 0.681509i \(-0.238676\pi\)
\(20\) 7.28325 19.0773i 0.364162 0.953867i
\(21\) 5.78260i 0.275362i
\(22\) 3.98614 6.15038i 0.181188 0.279563i
\(23\) 20.9457 + 20.9457i 0.910682 + 0.910682i 0.996326 0.0856440i \(-0.0272948\pi\)
−0.0856440 + 0.996326i \(0.527295\pi\)
\(24\) −8.37595 1.30316i −0.348998 0.0542984i
\(25\) 1.06191i 0.0424764i
\(26\) 1.24603 + 5.83595i 0.0479242 + 0.224460i
\(27\) 12.6452 12.6452i 0.468340 0.468340i
\(28\) −20.3939 7.78587i −0.728353 0.278067i
\(29\) 22.7491 22.7491i 0.784451 0.784451i −0.196128 0.980578i \(-0.562837\pi\)
0.980578 + 0.196128i \(0.0628367\pi\)
\(30\) −10.5801 + 2.25895i −0.352671 + 0.0752985i
\(31\) −18.3612 + 18.3612i −0.592297 + 0.592297i −0.938251 0.345954i \(-0.887555\pi\)
0.345954 + 0.938251i \(0.387555\pi\)
\(32\) −15.8736 + 27.7854i −0.496049 + 0.868294i
\(33\) −3.88295 −0.117665
\(34\) −20.9588 + 26.7718i −0.616436 + 0.787405i
\(35\) −27.8605 −0.796013
\(36\) −12.8683 28.7616i −0.357454 0.798933i
\(37\) 0.733830 0.733830i 0.0198332 0.0198332i −0.697121 0.716954i \(-0.745536\pi\)
0.716954 + 0.697121i \(0.245536\pi\)
\(38\) 10.8149 + 50.6530i 0.284602 + 1.33297i
\(39\) 2.23555 2.23555i 0.0573218 0.0573218i
\(40\) −6.27861 + 40.3552i −0.156965 + 1.00888i
\(41\) −26.2827 + 26.2827i −0.641042 + 0.641042i −0.950812 0.309770i \(-0.899748\pi\)
0.309770 + 0.950812i \(0.399748\pi\)
\(42\) 2.41485 + 11.3103i 0.0574963 + 0.269292i
\(43\) 10.7209i 0.249323i −0.992199 0.124661i \(-0.960216\pi\)
0.992199 0.124661i \(-0.0397845\pi\)
\(44\) −5.22812 + 13.6943i −0.118821 + 0.311233i
\(45\) −28.4357 28.4357i −0.631904 0.631904i
\(46\) −49.7150 32.2209i −1.08076 0.700455i
\(47\) 84.3467i 1.79461i 0.441411 + 0.897305i \(0.354478\pi\)
−0.441411 + 0.897305i \(0.645522\pi\)
\(48\) 16.9269 0.948971i 0.352643 0.0197702i
\(49\) 19.2169i 0.392181i
\(50\) 0.443459 + 2.07701i 0.00886919 + 0.0415401i
\(51\) 17.9415 + 1.60393i 0.351794 + 0.0314496i
\(52\) −4.87425 10.8943i −0.0937356 0.209505i
\(53\) 33.8459 0.638602 0.319301 0.947653i \(-0.396552\pi\)
0.319301 + 0.947653i \(0.396552\pi\)
\(54\) −19.4522 + 30.0136i −0.360226 + 0.555807i
\(55\) 18.7080i 0.340145i
\(56\) 43.1401 + 6.71190i 0.770359 + 0.119855i
\(57\) 19.4034 19.4034i 0.340411 0.340411i
\(58\) −34.9951 + 53.9954i −0.603364 + 0.930955i
\(59\) 69.9591i 1.18575i 0.805296 + 0.592874i \(0.202007\pi\)
−0.805296 + 0.592874i \(0.797993\pi\)
\(60\) 19.7505 8.83665i 0.329175 0.147277i
\(61\) −65.8369 65.8369i −1.07929 1.07929i −0.996573 0.0827207i \(-0.973639\pi\)
−0.0827207 0.996573i \(-0.526361\pi\)
\(62\) 28.2452 43.5807i 0.455569 0.702915i
\(63\) −30.3981 + 30.3981i −0.482509 + 0.482509i
\(64\) 19.4440 60.9748i 0.303813 0.952732i
\(65\) −10.7708 10.7708i −0.165705 0.165705i
\(66\) 7.59472 1.62154i 0.115071 0.0245688i
\(67\) −76.0157 −1.13456 −0.567282 0.823524i \(-0.692005\pi\)
−0.567282 + 0.823524i \(0.692005\pi\)
\(68\) 29.8137 61.1158i 0.438436 0.898762i
\(69\) 31.3868i 0.454882i
\(70\) 54.4927 11.6347i 0.778467 0.166210i
\(71\) 27.4650 27.4650i 0.386831 0.386831i −0.486724 0.873556i \(-0.661808\pi\)
0.873556 + 0.486724i \(0.161808\pi\)
\(72\) 37.1804 + 50.8813i 0.516394 + 0.706685i
\(73\) 48.3347 + 48.3347i 0.662119 + 0.662119i 0.955879 0.293760i \(-0.0949067\pi\)
−0.293760 + 0.955879i \(0.594907\pi\)
\(74\) −1.12886 + 1.74176i −0.0152548 + 0.0235373i
\(75\) 0.795629 0.795629i 0.0106084 0.0106084i
\(76\) −42.3060 94.5567i −0.556658 1.24417i
\(77\) 19.9990 0.259728
\(78\) −3.43897 + 5.30613i −0.0440893 + 0.0680273i
\(79\) 17.0189 + 17.0189i 0.215429 + 0.215429i 0.806569 0.591140i \(-0.201322\pi\)
−0.591140 + 0.806569i \(0.701322\pi\)
\(80\) −4.57213 81.5533i −0.0571516 1.01942i
\(81\) −51.9468 −0.641318
\(82\) 40.4310 62.3826i 0.493060 0.760763i
\(83\) 20.9027i 0.251839i 0.992040 + 0.125920i \(0.0401882\pi\)
−0.992040 + 0.125920i \(0.959812\pi\)
\(84\) −9.44647 21.1135i −0.112458 0.251351i
\(85\) 7.72772 86.4417i 0.0909143 1.01696i
\(86\) 4.47710 + 20.9692i 0.0520593 + 0.243827i
\(87\) 34.0892 0.391830
\(88\) 4.50696 28.9681i 0.0512155 0.329183i
\(89\) 115.759 1.30066 0.650329 0.759652i \(-0.274631\pi\)
0.650329 + 0.759652i \(0.274631\pi\)
\(90\) 67.4927 + 43.7429i 0.749919 + 0.486032i
\(91\) −11.5141 + 11.5141i −0.126529 + 0.126529i
\(92\) 110.694 + 42.2602i 1.20320 + 0.459350i
\(93\) −27.5140 −0.295850
\(94\) −35.2237 164.975i −0.374720 1.75505i
\(95\) −93.4853 93.4853i −0.984056 0.984056i
\(96\) −32.7112 + 8.92486i −0.340742 + 0.0929673i
\(97\) 66.5506 + 66.5506i 0.686088 + 0.686088i 0.961365 0.275277i \(-0.0887694\pi\)
−0.275277 + 0.961365i \(0.588769\pi\)
\(98\) 8.02507 + 37.5866i 0.0818885 + 0.383537i
\(99\) 20.4119 + 20.4119i 0.206181 + 0.206181i
\(100\) −1.73474 3.87726i −0.0173474 0.0387726i
\(101\) 21.8709i 0.216543i −0.994121 0.108272i \(-0.965468\pi\)
0.994121 0.108272i \(-0.0345316\pi\)
\(102\) −35.7618 + 4.35531i −0.350606 + 0.0426991i
\(103\) 26.9524i 0.261673i −0.991404 0.130837i \(-0.958234\pi\)
0.991404 0.130837i \(-0.0417664\pi\)
\(104\) 14.0831 + 19.2728i 0.135415 + 0.185315i
\(105\) −20.8743 20.8743i −0.198802 0.198802i
\(106\) −66.1997 + 14.1342i −0.624525 + 0.133342i
\(107\) 69.9821 + 69.9821i 0.654038 + 0.654038i 0.953963 0.299925i \(-0.0969616\pi\)
−0.299925 + 0.953963i \(0.596962\pi\)
\(108\) 25.5130 66.8274i 0.236232 0.618772i
\(109\) 26.7602 + 26.7602i 0.245507 + 0.245507i 0.819124 0.573617i \(-0.194460\pi\)
−0.573617 + 0.819124i \(0.694460\pi\)
\(110\) −7.81256 36.5912i −0.0710232 0.332647i
\(111\) 1.09963 0.00990661
\(112\) −87.1814 + 4.88765i −0.778405 + 0.0436398i
\(113\) −103.894 + 103.894i −0.919414 + 0.919414i −0.996987 0.0775723i \(-0.975283\pi\)
0.0775723 + 0.996987i \(0.475283\pi\)
\(114\) −29.8485 + 46.0544i −0.261829 + 0.403986i
\(115\) 151.221 1.31497
\(116\) 45.8987 120.225i 0.395679 1.03642i
\(117\) −23.5038 −0.200887
\(118\) −29.2153 136.834i −0.247587 1.15961i
\(119\) −92.4071 8.26101i −0.776531 0.0694203i
\(120\) −34.9401 + 25.5316i −0.291167 + 0.212764i
\(121\) 107.571i 0.889016i
\(122\) 156.265 + 101.278i 1.28086 + 0.830144i
\(123\) −39.3843 −0.320197
\(124\) −37.0458 + 97.0356i −0.298756 + 0.782545i
\(125\) 86.4127 + 86.4127i 0.691302 + 0.691302i
\(126\) 46.7616 72.1504i 0.371124 0.572622i
\(127\) −17.2092 −0.135505 −0.0677527 0.997702i \(-0.521583\pi\)
−0.0677527 + 0.997702i \(0.521583\pi\)
\(128\) −12.5675 + 127.382i −0.0981834 + 0.995168i
\(129\) 8.03255 8.03255i 0.0622679 0.0622679i
\(130\) 25.5648 + 16.5689i 0.196652 + 0.127453i
\(131\) −112.948 112.948i −0.862200 0.862200i 0.129393 0.991593i \(-0.458697\pi\)
−0.991593 + 0.129393i \(0.958697\pi\)
\(132\) −14.1775 + 6.34319i −0.107405 + 0.0480545i
\(133\) −99.9368 + 99.9368i −0.751404 + 0.751404i
\(134\) 148.680 31.7446i 1.10955 0.236900i
\(135\) 91.2942i 0.676253i
\(136\) −32.7907 + 131.988i −0.241108 + 0.970498i
\(137\) −195.481 −1.42687 −0.713436 0.700721i \(-0.752862\pi\)
−0.713436 + 0.700721i \(0.752862\pi\)
\(138\) −13.1073 61.3900i −0.0949805 0.444855i
\(139\) −4.95033 4.95033i −0.0356139 0.0356139i 0.689076 0.724689i \(-0.258017\pi\)
−0.724689 + 0.689076i \(0.758017\pi\)
\(140\) −101.724 + 45.5129i −0.726603 + 0.325092i
\(141\) −63.1962 + 63.1962i −0.448200 + 0.448200i
\(142\) −42.2497 + 65.1888i −0.297533 + 0.459076i
\(143\) 7.73162 + 7.73162i 0.0540672 + 0.0540672i
\(144\) −93.9700 83.9928i −0.652569 0.583284i
\(145\) 164.241i 1.13270i
\(146\) −114.723 74.3537i −0.785777 0.509272i
\(147\) 14.3981 14.3981i 0.0979463 0.0979463i
\(148\) 1.48058 3.87815i 0.0100039 0.0262037i
\(149\) 34.5639i 0.231973i 0.993251 + 0.115986i \(0.0370029\pi\)
−0.993251 + 0.115986i \(0.962997\pi\)
\(150\) −1.22392 + 1.88844i −0.00815949 + 0.0125896i
\(151\) 152.346 1.00892 0.504458 0.863436i \(-0.331692\pi\)
0.504458 + 0.863436i \(0.331692\pi\)
\(152\) 122.234 + 167.278i 0.804173 + 1.10051i
\(153\) −85.8835 102.747i −0.561330 0.671547i
\(154\) −39.1164 + 8.35171i −0.254003 + 0.0542319i
\(155\) 132.562i 0.855240i
\(156\) 4.51046 11.8145i 0.0289132 0.0757338i
\(157\) 287.858i 1.83349i 0.399473 + 0.916745i \(0.369193\pi\)
−0.399473 + 0.916745i \(0.630807\pi\)
\(158\) −40.3948 26.1804i −0.255663 0.165699i
\(159\) 25.3588 + 25.3588i 0.159489 + 0.159489i
\(160\) 42.9998 + 157.602i 0.268749 + 0.985013i
\(161\) 161.657i 1.00408i
\(162\) 101.604 21.6933i 0.627182 0.133909i
\(163\) 199.813 199.813i 1.22584 1.22584i 0.260322 0.965522i \(-0.416171\pi\)
0.965522 0.260322i \(-0.0838288\pi\)
\(164\) −53.0282 + 138.899i −0.323343 + 0.846946i
\(165\) −14.0168 + 14.0168i −0.0849505 + 0.0849505i
\(166\) −8.72907 40.8839i −0.0525848 0.246288i
\(167\) 79.1049 79.1049i 0.473682 0.473682i −0.429422 0.903104i \(-0.641283\pi\)
0.903104 + 0.429422i \(0.141283\pi\)
\(168\) 27.2936 + 37.3513i 0.162462 + 0.222329i
\(169\) 160.097 0.947321
\(170\) 20.9838 + 172.300i 0.123434 + 1.01353i
\(171\) −204.000 −1.19298
\(172\) −17.5137 39.1442i −0.101824 0.227583i
\(173\) 232.520 232.520i 1.34404 1.34404i 0.452052 0.891991i \(-0.350692\pi\)
0.891991 0.452052i \(-0.149308\pi\)
\(174\) −66.6755 + 14.2358i −0.383193 + 0.0818151i
\(175\) −4.09787 + 4.09787i −0.0234164 + 0.0234164i
\(176\) 3.28200 + 58.5413i 0.0186477 + 0.332621i
\(177\) −52.4164 + 52.4164i −0.296138 + 0.296138i
\(178\) −226.414 + 48.3415i −1.27199 + 0.271581i
\(179\) 215.338i 1.20301i −0.798871 0.601503i \(-0.794569\pi\)
0.798871 0.601503i \(-0.205431\pi\)
\(180\) −150.277 57.3721i −0.834874 0.318734i
\(181\) 85.2707 + 85.2707i 0.471109 + 0.471109i 0.902273 0.431164i \(-0.141897\pi\)
−0.431164 + 0.902273i \(0.641897\pi\)
\(182\) 17.7123 27.3291i 0.0973205 0.150160i
\(183\) 98.6557i 0.539102i
\(184\) −234.156 36.4309i −1.27259 0.197994i
\(185\) 5.29802i 0.0286379i
\(186\) 53.8151 11.4900i 0.289329 0.0617743i
\(187\) −5.54717 + 62.0503i −0.0296640 + 0.331820i
\(188\) 137.789 + 307.968i 0.732920 + 1.63813i
\(189\) −97.5945 −0.516373
\(190\) 221.889 + 143.809i 1.16784 + 0.756891i
\(191\) 213.241i 1.11644i −0.829692 0.558221i \(-0.811484\pi\)
0.829692 0.558221i \(-0.188516\pi\)
\(192\) 60.2533 31.1167i 0.313819 0.162066i
\(193\) 95.8456 95.8456i 0.496610 0.496610i −0.413771 0.910381i \(-0.635789\pi\)
0.910381 + 0.413771i \(0.135789\pi\)
\(194\) −157.959 102.375i −0.814223 0.527708i
\(195\) 16.1400i 0.0827690i
\(196\) −31.3927 70.1649i −0.160167 0.357984i
\(197\) 117.420 + 117.420i 0.596041 + 0.596041i 0.939257 0.343216i \(-0.111516\pi\)
−0.343216 + 0.939257i \(0.611516\pi\)
\(198\) −48.4482 31.3999i −0.244688 0.158585i
\(199\) −121.225 + 121.225i −0.609173 + 0.609173i −0.942730 0.333557i \(-0.891751\pi\)
0.333557 + 0.942730i \(0.391751\pi\)
\(200\) 5.01217 + 6.85915i 0.0250608 + 0.0342957i
\(201\) −56.9543 56.9543i −0.283355 0.283355i
\(202\) 9.13340 + 42.7776i 0.0452149 + 0.211770i
\(203\) −175.575 −0.864904
\(204\) 68.1283 23.4530i 0.333962 0.114965i
\(205\) 189.753i 0.925624i
\(206\) 11.2555 + 52.7166i 0.0546382 + 0.255906i
\(207\) 164.995 164.995i 0.797076 0.797076i
\(208\) −35.5938 31.8147i −0.171124 0.152955i
\(209\) 67.1064 + 67.1064i 0.321083 + 0.321083i
\(210\) 49.5455 + 32.1111i 0.235931 + 0.152910i
\(211\) −15.7879 + 15.7879i −0.0748241 + 0.0748241i −0.743528 0.668704i \(-0.766849\pi\)
0.668704 + 0.743528i \(0.266849\pi\)
\(212\) 123.578 55.2907i 0.582917 0.260805i
\(213\) 41.1560 0.193220
\(214\) −166.104 107.654i −0.776187 0.503057i
\(215\) −38.7007 38.7007i −0.180003 0.180003i
\(216\) −21.9938 + 141.363i −0.101823 + 0.654459i
\(217\) 141.710 0.653043
\(218\) −63.5160 41.1655i −0.291358 0.188833i
\(219\) 72.4289i 0.330725i
\(220\) 30.5614 + 68.3068i 0.138915 + 0.310485i
\(221\) −32.5309 38.9183i −0.147198 0.176101i
\(222\) −2.15079 + 0.459213i −0.00968825 + 0.00206853i
\(223\) 74.7498 0.335201 0.167600 0.985855i \(-0.446398\pi\)
0.167600 + 0.985855i \(0.446398\pi\)
\(224\) 168.478 45.9673i 0.752135 0.205211i
\(225\) −8.36495 −0.0371775
\(226\) 159.821 246.594i 0.707172 1.09112i
\(227\) 142.640 142.640i 0.628370 0.628370i −0.319288 0.947658i \(-0.603444\pi\)
0.947658 + 0.319288i \(0.103444\pi\)
\(228\) 39.1485 102.543i 0.171704 0.449752i
\(229\) −262.209 −1.14502 −0.572508 0.819899i \(-0.694029\pi\)
−0.572508 + 0.819899i \(0.694029\pi\)
\(230\) −295.776 + 63.1508i −1.28598 + 0.274569i
\(231\) 14.9841 + 14.9841i 0.0648664 + 0.0648664i
\(232\) −39.5675 + 254.317i −0.170550 + 1.09619i
\(233\) −60.8609 60.8609i −0.261206 0.261206i 0.564338 0.825544i \(-0.309131\pi\)
−0.825544 + 0.564338i \(0.809131\pi\)
\(234\) 45.9714 9.81530i 0.196459 0.0419457i
\(235\) 304.478 + 304.478i 1.29565 + 1.29565i
\(236\) 114.285 + 255.435i 0.484260 + 1.08235i
\(237\) 25.5026i 0.107606i
\(238\) 184.190 22.4319i 0.773909 0.0942517i
\(239\) 95.1858i 0.398267i 0.979972 + 0.199133i \(0.0638127\pi\)
−0.979972 + 0.199133i \(0.936187\pi\)
\(240\) 57.6776 64.5289i 0.240324 0.268870i
\(241\) −117.983 117.983i −0.489557 0.489557i 0.418609 0.908166i \(-0.362518\pi\)
−0.908166 + 0.418609i \(0.862518\pi\)
\(242\) −44.9222 210.400i −0.185629 0.869420i
\(243\) −152.727 152.727i −0.628508 0.628508i
\(244\) −347.936 132.833i −1.42597 0.544398i
\(245\) −69.3699 69.3699i −0.283142 0.283142i
\(246\) 77.0323 16.4471i 0.313140 0.0668581i
\(247\) −77.2710 −0.312838
\(248\) 31.9357 205.264i 0.128773 0.827677i
\(249\) −15.6612 + 15.6612i −0.0628963 + 0.0628963i
\(250\) −205.102 132.930i −0.820410 0.531718i
\(251\) 131.822 0.525188 0.262594 0.964906i \(-0.415422\pi\)
0.262594 + 0.964906i \(0.415422\pi\)
\(252\) −61.3314 + 160.648i −0.243378 + 0.637492i
\(253\) −108.551 −0.429055
\(254\) 33.6597 7.18665i 0.132519 0.0282939i
\(255\) 70.5558 58.9760i 0.276690 0.231278i
\(256\) −28.6143 254.396i −0.111775 0.993734i
\(257\) 342.708i 1.33349i 0.745284 + 0.666747i \(0.232314\pi\)
−0.745284 + 0.666747i \(0.767686\pi\)
\(258\) −12.3566 + 19.0654i −0.0478936 + 0.0738970i
\(259\) −5.66364 −0.0218673
\(260\) −56.9219 21.7313i −0.218930 0.0835821i
\(261\) −179.201 179.201i −0.686592 0.686592i
\(262\) 268.085 + 173.749i 1.02322 + 0.663165i
\(263\) −494.500 −1.88023 −0.940114 0.340862i \(-0.889281\pi\)
−0.940114 + 0.340862i \(0.889281\pi\)
\(264\) 25.0810 18.3273i 0.0950037 0.0694217i
\(265\) 122.178 122.178i 0.461050 0.461050i
\(266\) 153.734 237.202i 0.577946 0.891737i
\(267\) 86.7314 + 86.7314i 0.324837 + 0.324837i
\(268\) −277.549 + 124.180i −1.03563 + 0.463356i
\(269\) 116.803 116.803i 0.434211 0.434211i −0.455847 0.890058i \(-0.650664\pi\)
0.890058 + 0.455847i \(0.150664\pi\)
\(270\) 38.1250 + 178.564i 0.141204 + 0.661347i
\(271\) 241.196i 0.890021i −0.895525 0.445011i \(-0.853200\pi\)
0.895525 0.445011i \(-0.146800\pi\)
\(272\) 9.01693 271.851i 0.0331505 0.999450i
\(273\) −17.2538 −0.0632007
\(274\) 382.345 81.6341i 1.39542 0.297935i
\(275\) 2.75167 + 2.75167i 0.0100061 + 0.0100061i
\(276\) 51.2736 + 114.600i 0.185774 + 0.415217i
\(277\) 340.749 340.749i 1.23014 1.23014i 0.266234 0.963908i \(-0.414221\pi\)
0.963908 0.266234i \(-0.0857794\pi\)
\(278\) 11.7497 + 7.61514i 0.0422651 + 0.0273926i
\(279\) 144.636 + 144.636i 0.518410 + 0.518410i
\(280\) 179.958 131.500i 0.642707 0.469643i
\(281\) 428.504i 1.52493i 0.647032 + 0.762463i \(0.276010\pi\)
−0.647032 + 0.762463i \(0.723990\pi\)
\(282\) 97.2153 149.997i 0.344735 0.531906i
\(283\) 55.7718 55.7718i 0.197073 0.197073i −0.601671 0.798744i \(-0.705498\pi\)
0.798744 + 0.601671i \(0.205498\pi\)
\(284\) 55.4136 145.148i 0.195118 0.511083i
\(285\) 140.086i 0.491531i
\(286\) −18.3512 11.8936i −0.0641649 0.0415861i
\(287\) 202.848 0.706787
\(288\) 218.873 + 125.040i 0.759976 + 0.434168i
\(289\) 51.2623 284.417i 0.177378 0.984143i
\(290\) 68.5880 + 321.242i 0.236510 + 1.10773i
\(291\) 99.7252i 0.342698i
\(292\) 255.440 + 97.5204i 0.874794 + 0.333974i
\(293\) 343.598i 1.17269i 0.810062 + 0.586344i \(0.199433\pi\)
−0.810062 + 0.586344i \(0.800567\pi\)
\(294\) −22.1488 + 34.1742i −0.0753359 + 0.116239i
\(295\) 252.541 + 252.541i 0.856072 + 0.856072i
\(296\) −1.27635 + 8.20364i −0.00431200 + 0.0277150i
\(297\) 65.5336i 0.220652i
\(298\) −14.4341 67.6041i −0.0484366 0.226860i
\(299\) 62.4966 62.4966i 0.209019 0.209019i
\(300\) 1.60527 4.20475i 0.00535089 0.0140158i
\(301\) −41.3715 + 41.3715i −0.137447 + 0.137447i
\(302\) −297.976 + 63.6207i −0.986677 + 0.210664i
\(303\) 16.3866 16.3866i 0.0540812 0.0540812i
\(304\) −308.936 276.135i −1.01624 0.908339i
\(305\) −475.322 −1.55843
\(306\) 210.888 + 165.098i 0.689178 + 0.539537i
\(307\) −100.962 −0.328867 −0.164433 0.986388i \(-0.552580\pi\)
−0.164433 + 0.986388i \(0.552580\pi\)
\(308\) 73.0207 32.6705i 0.237080 0.106073i
\(309\) 20.1939 20.1939i 0.0653524 0.0653524i
\(310\) −55.3587 259.280i −0.178577 0.836389i
\(311\) −36.0997 + 36.0997i −0.116076 + 0.116076i −0.762759 0.646683i \(-0.776156\pi\)
0.646683 + 0.762759i \(0.276156\pi\)
\(312\) −3.88830 + 24.9917i −0.0124625 + 0.0801016i
\(313\) −207.384 + 207.384i −0.662568 + 0.662568i −0.955985 0.293417i \(-0.905208\pi\)
0.293417 + 0.955985i \(0.405208\pi\)
\(314\) −120.211 563.026i −0.382838 1.79308i
\(315\) 219.464i 0.696712i
\(316\) 89.9419 + 34.3375i 0.284626 + 0.108663i
\(317\) 91.2105 + 91.2105i 0.287730 + 0.287730i 0.836182 0.548452i \(-0.184783\pi\)
−0.548452 + 0.836182i \(0.684783\pi\)
\(318\) −60.1896 39.0097i −0.189276 0.122672i
\(319\) 117.897i 0.369583i
\(320\) −149.920 290.299i −0.468499 0.907185i
\(321\) 104.867i 0.326689i
\(322\) 67.5089 + 316.188i 0.209655 + 0.981949i
\(323\) −282.351 337.790i −0.874151 1.04579i
\(324\) −189.669 + 84.8604i −0.585397 + 0.261915i
\(325\) −3.16847 −0.00974913
\(326\) −307.374 + 474.259i −0.942864 + 1.45478i
\(327\) 40.0998i 0.122630i
\(328\) 45.7136 293.820i 0.139371 0.895793i
\(329\) 325.490 325.490i 0.989332 0.989332i
\(330\) 21.5622 33.2692i 0.0653401 0.100816i
\(331\) 265.861i 0.803206i 0.915814 + 0.401603i \(0.131547\pi\)
−0.915814 + 0.401603i \(0.868453\pi\)
\(332\) 34.1467 + 76.3201i 0.102851 + 0.229880i
\(333\) −5.78057 5.78057i −0.0173591 0.0173591i
\(334\) −121.688 + 187.757i −0.364335 + 0.562147i
\(335\) −274.405 + 274.405i −0.819119 + 0.819119i
\(336\) −68.9821 61.6580i −0.205304 0.183506i
\(337\) 373.456 + 373.456i 1.10818 + 1.10818i 0.993390 + 0.114787i \(0.0366186\pi\)
0.114787 + 0.993390i \(0.463381\pi\)
\(338\) −313.137 + 66.8575i −0.926440 + 0.197803i
\(339\) −155.684 −0.459243
\(340\) −112.996 328.241i −0.332341 0.965415i
\(341\) 95.1569i 0.279052i
\(342\) 399.007 85.1917i 1.16669 0.249099i
\(343\) −263.246 + 263.246i −0.767481 + 0.767481i
\(344\) 50.6021 + 69.2490i 0.147099 + 0.201305i
\(345\) 113.301 + 113.301i 0.328410 + 0.328410i
\(346\) −357.687 + 551.890i −1.03378 + 1.59506i
\(347\) −455.522 + 455.522i −1.31274 + 1.31274i −0.393359 + 0.919385i \(0.628687\pi\)
−0.919385 + 0.393359i \(0.871313\pi\)
\(348\) 124.467 55.6882i 0.357663 0.160023i
\(349\) −338.237 −0.969159 −0.484580 0.874747i \(-0.661027\pi\)
−0.484580 + 0.874747i \(0.661027\pi\)
\(350\) 6.30379 9.72637i 0.0180108 0.0277896i
\(351\) −37.7300 37.7300i −0.107493 0.107493i
\(352\) −30.8665 113.131i −0.0876889 0.321396i
\(353\) 26.2790 0.0744448 0.0372224 0.999307i \(-0.488149\pi\)
0.0372224 + 0.999307i \(0.488149\pi\)
\(354\) 80.6326 124.411i 0.227776 0.351445i
\(355\) 198.289i 0.558560i
\(356\) 422.659 189.104i 1.18724 0.531190i
\(357\) −63.0459 75.4249i −0.176599 0.211274i
\(358\) 89.9264 + 421.183i 0.251191 + 1.17649i
\(359\) −562.774 −1.56762 −0.783808 0.621004i \(-0.786725\pi\)
−0.783808 + 0.621004i \(0.786725\pi\)
\(360\) 317.889 + 49.4583i 0.883024 + 0.137384i
\(361\) −309.672 −0.857818
\(362\) −202.392 131.173i −0.559093 0.362356i
\(363\) −80.5968 + 80.5968i −0.222030 + 0.222030i
\(364\) −23.2310 + 60.8501i −0.0638215 + 0.167171i
\(365\) 348.961 0.956058
\(366\) 41.1992 + 192.962i 0.112566 + 0.527219i
\(367\) 294.820 + 294.820i 0.803324 + 0.803324i 0.983614 0.180290i \(-0.0577035\pi\)
−0.180290 + 0.983614i \(0.557703\pi\)
\(368\) 473.204 26.5292i 1.28588 0.0720903i
\(369\) 207.036 + 207.036i 0.561073 + 0.561073i
\(370\) 2.21248 + 10.3625i 0.00597968 + 0.0280067i
\(371\) −130.610 130.610i −0.352048 0.352048i
\(372\) −100.460 + 44.9470i −0.270053 + 0.120825i
\(373\) 317.003i 0.849875i −0.905223 0.424937i \(-0.860296\pi\)
0.905223 0.424937i \(-0.139704\pi\)
\(374\) −15.0628 123.682i −0.0402748 0.330700i
\(375\) 129.488i 0.345302i
\(376\) −398.113 544.817i −1.05881 1.44898i
\(377\) −67.8774 67.8774i −0.180046 0.180046i
\(378\) 190.887 40.7560i 0.504991 0.107820i
\(379\) 315.390 + 315.390i 0.832164 + 0.832164i 0.987812 0.155649i \(-0.0497468\pi\)
−0.155649 + 0.987812i \(0.549747\pi\)
\(380\) −494.052 188.617i −1.30014 0.496360i
\(381\) −12.8939 12.8939i −0.0338422 0.0338422i
\(382\) 89.0505 + 417.081i 0.233116 + 1.09183i
\(383\) −522.656 −1.36464 −0.682319 0.731055i \(-0.739028\pi\)
−0.682319 + 0.731055i \(0.739028\pi\)
\(384\) −104.856 + 86.0237i −0.273062 + 0.224020i
\(385\) 72.1933 72.1933i 0.187515 0.187515i
\(386\) −147.440 + 227.492i −0.381970 + 0.589357i
\(387\) −84.4513 −0.218220
\(388\) 351.707 + 134.273i 0.906462 + 0.346064i
\(389\) −256.711 −0.659926 −0.329963 0.943994i \(-0.607036\pi\)
−0.329963 + 0.943994i \(0.607036\pi\)
\(390\) 6.74014 + 31.5684i 0.0172824 + 0.0809446i
\(391\) 501.568 + 44.8392i 1.28278 + 0.114678i
\(392\) 90.7028 + 124.127i 0.231385 + 0.316650i
\(393\) 169.251i 0.430665i
\(394\) −278.699 180.628i −0.707358 0.458448i
\(395\) 122.871 0.311066
\(396\) 107.873 + 41.1833i 0.272407 + 0.103998i
\(397\) −366.419 366.419i −0.922969 0.922969i 0.0742691 0.997238i \(-0.476338\pi\)
−0.997238 + 0.0742691i \(0.976338\pi\)
\(398\) 186.482 287.731i 0.468548 0.722942i
\(399\) −149.754 −0.375323
\(400\) −12.6678 11.3228i −0.0316695 0.0283070i
\(401\) 385.780 385.780i 0.962044 0.962044i −0.0372612 0.999306i \(-0.511863\pi\)
0.999306 + 0.0372612i \(0.0118634\pi\)
\(402\) 135.182 + 87.6133i 0.336274 + 0.217944i
\(403\) 54.7852 + 54.7852i 0.135943 + 0.135943i
\(404\) −35.7283 79.8552i −0.0884364 0.197661i
\(405\) −187.520 + 187.520i −0.463012 + 0.463012i
\(406\) 343.411 73.3213i 0.845839 0.180594i
\(407\) 3.80307i 0.00934414i
\(408\) −123.459 + 74.3228i −0.302596 + 0.182164i
\(409\) −270.337 −0.660970 −0.330485 0.943811i \(-0.607212\pi\)
−0.330485 + 0.943811i \(0.607212\pi\)
\(410\) −79.2419 371.140i −0.193273 0.905221i
\(411\) −146.463 146.463i −0.356358 0.356358i
\(412\) −44.0295 98.4088i −0.106868 0.238856i
\(413\) 269.969 269.969i 0.653678 0.653678i
\(414\) −253.813 + 391.619i −0.613075 + 0.945939i
\(415\) 75.4553 + 75.4553i 0.181820 + 0.181820i
\(416\) 82.9046 + 47.3627i 0.199290 + 0.113853i
\(417\) 7.41800i 0.0177890i
\(418\) −159.278 103.230i −0.381049 0.246963i
\(419\) 252.051 252.051i 0.601553 0.601553i −0.339172 0.940725i \(-0.610147\pi\)
0.940725 + 0.339172i \(0.110147\pi\)
\(420\) −110.317 42.1161i −0.262659 0.100276i
\(421\) 179.427i 0.426193i 0.977031 + 0.213097i \(0.0683549\pi\)
−0.977031 + 0.213097i \(0.931645\pi\)
\(422\) 24.2866 37.4729i 0.0575513 0.0887983i
\(423\) 664.422 1.57074
\(424\) −218.619 + 159.751i −0.515612 + 0.376771i
\(425\) −11.5777 13.8509i −0.0272416 0.0325905i
\(426\) −80.4976 + 17.1870i −0.188961 + 0.0403450i
\(427\) 508.124i 1.18999i
\(428\) 369.842 + 141.196i 0.864117 + 0.329898i
\(429\) 11.5857i 0.0270063i
\(430\) 91.8569 + 59.5337i 0.213621 + 0.138450i
\(431\) 470.235 + 470.235i 1.09103 + 1.09103i 0.995418 + 0.0956143i \(0.0304815\pi\)
0.0956143 + 0.995418i \(0.469518\pi\)
\(432\) −16.0160 285.679i −0.0370742 0.661294i
\(433\) 261.547i 0.604034i 0.953303 + 0.302017i \(0.0976600\pi\)
−0.953303 + 0.302017i \(0.902340\pi\)
\(434\) −277.174 + 59.1791i −0.638649 + 0.136357i
\(435\) 123.057 123.057i 0.282889 0.282889i
\(436\) 141.423 + 53.9917i 0.324364 + 0.123834i
\(437\) 542.438 542.438i 1.24128 1.24128i
\(438\) −30.2467 141.665i −0.0690564 0.323435i
\(439\) 126.052 126.052i 0.287134 0.287134i −0.548812 0.835946i \(-0.684920\pi\)
0.835946 + 0.548812i \(0.184920\pi\)
\(440\) −88.3008 120.840i −0.200684 0.274636i
\(441\) −151.376 −0.343257
\(442\) 79.8801 + 62.5358i 0.180724 + 0.141484i
\(443\) 69.9824 0.157974 0.0789869 0.996876i \(-0.474831\pi\)
0.0789869 + 0.996876i \(0.474831\pi\)
\(444\) 4.01500 1.79637i 0.00904278 0.00404587i
\(445\) 417.870 417.870i 0.939034 0.939034i
\(446\) −146.204 + 31.2159i −0.327812 + 0.0699909i
\(447\) −25.8968 + 25.8968i −0.0579347 + 0.0579347i
\(448\) −310.333 + 160.266i −0.692708 + 0.357736i
\(449\) 219.719 219.719i 0.489352 0.489352i −0.418749 0.908102i \(-0.637531\pi\)
0.908102 + 0.418749i \(0.137531\pi\)
\(450\) 16.3611 3.49325i 0.0363581 0.00776278i
\(451\) 136.210i 0.302018i
\(452\) −209.617 + 549.060i −0.463755 + 1.21473i
\(453\) 114.144 + 114.144i 0.251974 + 0.251974i
\(454\) −219.425 + 338.559i −0.483314 + 0.745725i
\(455\) 83.1285i 0.182700i
\(456\) −33.7484 + 216.915i −0.0740097 + 0.475691i
\(457\) 485.155i 1.06161i −0.847495 0.530804i \(-0.821890\pi\)
0.847495 0.530804i \(-0.178110\pi\)
\(458\) 512.858 109.500i 1.11978 0.239082i
\(459\) 27.0700 302.803i 0.0589760 0.659702i
\(460\) 552.140 247.035i 1.20031 0.537033i
\(461\) −803.704 −1.74339 −0.871697 0.490046i \(-0.836980\pi\)
−0.871697 + 0.490046i \(0.836980\pi\)
\(462\) −35.5652 23.0502i −0.0769809 0.0498923i
\(463\) 673.039i 1.45365i −0.686824 0.726824i \(-0.740996\pi\)
0.686824 0.726824i \(-0.259004\pi\)
\(464\) −28.8134 513.946i −0.0620977 1.10764i
\(465\) −99.3213 + 99.3213i −0.213594 + 0.213594i
\(466\) 144.455 + 93.6229i 0.309988 + 0.200908i
\(467\) 769.187i 1.64708i −0.567258 0.823540i \(-0.691996\pi\)
0.567258 0.823540i \(-0.308004\pi\)
\(468\) −85.8172 + 38.3958i −0.183370 + 0.0820423i
\(469\) 293.342 + 293.342i 0.625462 + 0.625462i
\(470\) −722.685 468.382i −1.53763 0.996557i
\(471\) −215.676 + 215.676i −0.457910 + 0.457910i
\(472\) −330.204 451.884i −0.699584 0.957381i
\(473\) 27.7805 + 27.7805i 0.0587325 + 0.0587325i
\(474\) −10.6500 49.8810i −0.0224684 0.105234i
\(475\) −27.5006 −0.0578961
\(476\) −350.893 + 120.794i −0.737171 + 0.253769i
\(477\) 266.613i 0.558937i
\(478\) −39.7501 186.175i −0.0831592 0.389488i
\(479\) −129.681 + 129.681i −0.270733 + 0.270733i −0.829395 0.558662i \(-0.811315\pi\)
0.558662 + 0.829395i \(0.311315\pi\)
\(480\) −85.8650 + 150.300i −0.178885 + 0.313124i
\(481\) −2.18956 2.18956i −0.00455210 0.00455210i
\(482\) 280.036 + 181.495i 0.580987 + 0.376545i
\(483\) 121.120 121.120i 0.250767 0.250767i
\(484\) 175.728 + 392.764i 0.363075 + 0.811496i
\(485\) 480.474 0.990668
\(486\) 362.502 + 234.942i 0.745888 + 0.483420i
\(487\) −67.2949 67.2949i −0.138182 0.138182i 0.634632 0.772814i \(-0.281152\pi\)
−0.772814 + 0.634632i \(0.781152\pi\)
\(488\) 736.005 + 114.510i 1.50821 + 0.234652i
\(489\) 299.416 0.612304
\(490\) 164.651 + 106.712i 0.336022 + 0.217780i
\(491\) 95.5137i 0.194529i 0.995259 + 0.0972644i \(0.0310093\pi\)
−0.995259 + 0.0972644i \(0.968991\pi\)
\(492\) −143.800 + 64.3383i −0.292277 + 0.130769i
\(493\) 48.6997 544.752i 0.0987825 1.10497i
\(494\) 151.136 32.2688i 0.305943 0.0653215i
\(495\) 147.368 0.297713
\(496\) 23.2558 + 414.816i 0.0468867 + 0.836322i
\(497\) −211.973 −0.426505
\(498\) 24.0918 37.1722i 0.0483770 0.0746429i
\(499\) 575.936 575.936i 1.15418 1.15418i 0.168475 0.985706i \(-0.446116\pi\)
0.985706 0.168475i \(-0.0538843\pi\)
\(500\) 456.675 + 174.347i 0.913350 + 0.348694i
\(501\) 118.538 0.236602
\(502\) −257.833 + 55.0497i −0.513612 + 0.109661i
\(503\) −401.223 401.223i −0.797661 0.797661i 0.185065 0.982726i \(-0.440750\pi\)
−0.982726 + 0.185065i \(0.940750\pi\)
\(504\) 52.8714 339.826i 0.104904 0.674259i
\(505\) −78.9504 78.9504i −0.156337 0.156337i
\(506\) 212.316 45.3314i 0.419597 0.0895878i
\(507\) 119.952 + 119.952i 0.236591 + 0.236591i
\(508\) −62.8344 + 28.1130i −0.123690 + 0.0553405i
\(509\) 534.020i 1.04915i 0.851363 + 0.524577i \(0.175777\pi\)
−0.851363 + 0.524577i \(0.824223\pi\)
\(510\) −113.373 + 144.816i −0.222299 + 0.283954i
\(511\) 373.043i 0.730026i
\(512\) 162.204 + 485.627i 0.316805 + 0.948491i
\(513\) −327.477 327.477i −0.638356 0.638356i
\(514\) −143.117 670.308i −0.278437 1.30410i
\(515\) −97.2938 97.2938i −0.188920 0.188920i
\(516\) 16.2065 42.4505i 0.0314080 0.0822685i
\(517\) −218.563 218.563i −0.422753 0.422753i
\(518\) 11.0776 2.36517i 0.0213853 0.00456596i
\(519\) 348.427 0.671344
\(520\) 120.410 + 18.7338i 0.231557 + 0.0360265i
\(521\) 182.296 182.296i 0.349897 0.349897i −0.510174 0.860071i \(-0.670419\pi\)
0.860071 + 0.510174i \(0.170419\pi\)
\(522\) 425.336 + 275.666i 0.814820 + 0.528096i
\(523\) −864.350 −1.65268 −0.826338 0.563174i \(-0.809580\pi\)
−0.826338 + 0.563174i \(0.809580\pi\)
\(524\) −596.910 227.885i −1.13914 0.434895i
\(525\) −6.14060 −0.0116964
\(526\) 967.200 206.506i 1.83878 0.392597i
\(527\) −39.3065 + 439.680i −0.0745854 + 0.834308i
\(528\) −41.4026 + 46.3207i −0.0784141 + 0.0877286i
\(529\) 348.443i 0.658683i
\(530\) −187.948 + 289.993i −0.354619 + 0.547156i
\(531\) 551.086 1.03783
\(532\) −201.633 + 528.147i −0.379010 + 0.992758i
\(533\) 78.4209 + 78.4209i 0.147131 + 0.147131i
\(534\) −205.859 133.420i −0.385503 0.249850i
\(535\) 505.248 0.944390
\(536\) 491.005 358.791i 0.916055 0.669386i
\(537\) 161.341 161.341i 0.300448 0.300448i
\(538\) −179.679 + 277.234i −0.333975 + 0.515304i
\(539\) 49.7957 + 49.7957i 0.0923853 + 0.0923853i
\(540\) −149.138 333.334i −0.276182 0.617286i
\(541\) −671.567 + 671.567i −1.24134 + 1.24134i −0.281899 + 0.959444i \(0.590964\pi\)
−0.959444 + 0.281899i \(0.909036\pi\)
\(542\) 100.725 + 471.758i 0.185839 + 0.870403i
\(543\) 127.777i 0.235317i
\(544\) 95.8900 + 535.482i 0.176268 + 0.984342i
\(545\) 193.200 0.354496
\(546\) 33.7470 7.20528i 0.0618076 0.0131965i
\(547\) −700.646 700.646i −1.28089 1.28089i −0.940163 0.340725i \(-0.889327\pi\)
−0.340725 0.940163i \(-0.610673\pi\)
\(548\) −713.744 + 319.339i −1.30245 + 0.582735i
\(549\) −518.615 + 518.615i −0.944654 + 0.944654i
\(550\) −6.53115 4.23292i −0.0118748 0.00769622i
\(551\) −589.140 589.140i −1.06922 1.06922i
\(552\) −148.144 202.736i −0.268378 0.367275i
\(553\) 131.351i 0.237524i
\(554\) −524.178 + 808.776i −0.946170 + 1.45988i
\(555\) 3.96950 3.96950i 0.00715226 0.00715226i
\(556\) −26.1616 9.98782i −0.0470532 0.0179637i
\(557\) 94.2272i 0.169169i 0.996416 + 0.0845845i \(0.0269563\pi\)
−0.996416 + 0.0845845i \(0.973044\pi\)
\(558\) −343.297 222.495i −0.615228 0.398737i
\(559\) −31.9884 −0.0572243
\(560\) −297.067 + 332.355i −0.530477 + 0.593490i
\(561\) −50.6470 + 42.3346i −0.0902798 + 0.0754628i
\(562\) −178.946 838.118i −0.318409 1.49131i
\(563\) 930.351i 1.65249i 0.563312 + 0.826244i \(0.309527\pi\)
−0.563312 + 0.826244i \(0.690473\pi\)
\(564\) −127.505 + 333.980i −0.226073 + 0.592163i
\(565\) 750.081i 1.32758i
\(566\) −85.7942 + 132.375i −0.151580 + 0.233879i
\(567\) 200.461 + 200.461i 0.353546 + 0.353546i
\(568\) −47.7700 + 307.037i −0.0841021 + 0.540559i
\(569\) 701.405i 1.23270i 0.787473 + 0.616349i \(0.211389\pi\)
−0.787473 + 0.616349i \(0.788611\pi\)
\(570\) 58.5009 + 273.997i 0.102633 + 0.480697i
\(571\) −49.4687 + 49.4687i −0.0866352 + 0.0866352i −0.749096 0.662461i \(-0.769512\pi\)
0.662461 + 0.749096i \(0.269512\pi\)
\(572\) 40.8601 + 15.5994i 0.0714338 + 0.0272716i
\(573\) 159.769 159.769i 0.278829 0.278829i
\(574\) −396.753 + 84.7104i −0.691208 + 0.147579i
\(575\) 22.2424 22.2424i 0.0386825 0.0386825i
\(576\) −480.315 153.166i −0.833880 0.265913i
\(577\) −719.179 −1.24641 −0.623205 0.782059i \(-0.714170\pi\)
−0.623205 + 0.782059i \(0.714170\pi\)
\(578\) 18.5094 + 577.704i 0.0320232 + 0.999487i
\(579\) 143.623 0.248054
\(580\) −268.305 599.679i −0.462594 1.03393i
\(581\) 80.6626 80.6626i 0.138834 0.138834i
\(582\) −41.6458 195.054i −0.0715563 0.335144i
\(583\) −87.7030 + 87.7030i −0.150434 + 0.150434i
\(584\) −540.344 84.0687i −0.925246 0.143953i
\(585\) −84.8448 + 84.8448i −0.145034 + 0.145034i
\(586\) −143.488 672.048i −0.244861 1.14684i
\(587\) 404.505i 0.689105i 0.938767 + 0.344553i \(0.111969\pi\)
−0.938767 + 0.344553i \(0.888031\pi\)
\(588\) 29.0498 76.0913i 0.0494043 0.129407i
\(589\) 475.507 + 475.507i 0.807312 + 0.807312i
\(590\) −599.412 388.487i −1.01595 0.658452i
\(591\) 175.952i 0.297720i
\(592\) −0.929449 16.5786i −0.00157001 0.0280045i
\(593\) 70.0150i 0.118069i 0.998256 + 0.0590345i \(0.0188022\pi\)
−0.998256 + 0.0590345i \(0.981198\pi\)
\(594\) −27.3672 128.178i −0.0460727 0.215788i
\(595\) −363.396 + 303.754i −0.610750 + 0.510511i
\(596\) 56.4637 + 126.200i 0.0947378 + 0.211745i
\(597\) −181.655 −0.304279
\(598\) −96.1391 + 148.337i −0.160768 + 0.248055i
\(599\) 935.940i 1.56250i −0.624216 0.781252i \(-0.714581\pi\)
0.624216 0.781252i \(-0.285419\pi\)
\(600\) −1.38384 + 8.89450i −0.00230640 + 0.0148242i
\(601\) 264.545 264.545i 0.440174 0.440174i −0.451896 0.892071i \(-0.649252\pi\)
0.892071 + 0.451896i \(0.149252\pi\)
\(602\) 63.6421 98.1960i 0.105718 0.163116i
\(603\) 598.796i 0.993029i
\(604\) 556.248 248.873i 0.920941 0.412042i
\(605\) 388.314 + 388.314i 0.641841 + 0.641841i
\(606\) −25.2077 + 38.8940i −0.0415968 + 0.0641815i
\(607\) −66.1875 + 66.1875i −0.109040 + 0.109040i −0.759522 0.650482i \(-0.774567\pi\)
0.650482 + 0.759522i \(0.274567\pi\)
\(608\) 719.568 + 411.084i 1.18350 + 0.676124i
\(609\) −131.549 131.549i −0.216008 0.216008i
\(610\) 929.689 198.497i 1.52408 0.325405i
\(611\) 251.669 0.411897
\(612\) −481.426 234.850i −0.786644 0.383742i
\(613\) 125.163i 0.204181i 0.994775 + 0.102091i \(0.0325532\pi\)
−0.994775 + 0.102091i \(0.967447\pi\)
\(614\) 197.473 42.1623i 0.321618 0.0686683i
\(615\) −142.171 + 142.171i −0.231172 + 0.231172i
\(616\) −129.179 + 94.3945i −0.209706 + 0.153238i
\(617\) −387.365 387.365i −0.627819 0.627819i 0.319700 0.947519i \(-0.396418\pi\)
−0.947519 + 0.319700i \(0.896418\pi\)
\(618\) −31.0644 + 47.9306i −0.0502661 + 0.0775576i
\(619\) −83.9355 + 83.9355i −0.135599 + 0.135599i −0.771648 0.636050i \(-0.780567\pi\)
0.636050 + 0.771648i \(0.280567\pi\)
\(620\) 216.554 + 484.013i 0.349281 + 0.780665i
\(621\) 529.724 0.853018
\(622\) 55.5325 85.6834i 0.0892806 0.137755i
\(623\) −446.708 446.708i −0.717027 0.717027i
\(624\) −2.83149 50.5054i −0.00453764 0.0809382i
\(625\) 650.420 1.04067
\(626\) 319.021 492.230i 0.509618 0.786310i
\(627\) 100.558i 0.160380i
\(628\) 470.245 + 1051.03i 0.748799 + 1.67361i
\(629\) 1.57094 17.5724i 0.00249751 0.0279370i
\(630\) −91.6495 429.254i −0.145475 0.681355i
\(631\) 922.673 1.46224 0.731120 0.682249i \(-0.238998\pi\)
0.731120 + 0.682249i \(0.238998\pi\)
\(632\) −190.258 29.6011i −0.301041 0.0468371i
\(633\) −23.6579 −0.0373743
\(634\) −216.490 140.310i −0.341467 0.221309i
\(635\) −62.1224 + 62.1224i −0.0978306 + 0.0978306i
\(636\) 134.017 + 51.1641i 0.210718 + 0.0804467i
\(637\) −57.3382 −0.0900129
\(638\) −49.2344 230.596i −0.0771699 0.361436i
\(639\) −216.349 216.349i −0.338575 0.338575i
\(640\) 414.461 + 505.194i 0.647595 + 0.789365i
\(641\) −15.7419 15.7419i −0.0245583 0.0245583i 0.694721 0.719279i \(-0.255528\pi\)
−0.719279 + 0.694721i \(0.755528\pi\)
\(642\) −43.7931 205.111i −0.0682136 0.319488i
\(643\) −389.434 389.434i −0.605651 0.605651i 0.336155 0.941807i \(-0.390873\pi\)
−0.941807 + 0.336155i \(0.890873\pi\)
\(644\) −264.083 590.244i −0.410067 0.916528i
\(645\) 57.9925i 0.0899108i
\(646\) 693.318 + 542.778i 1.07325 + 0.840214i
\(647\) 550.318i 0.850568i −0.905060 0.425284i \(-0.860174\pi\)
0.905060 0.425284i \(-0.139826\pi\)
\(648\) 335.538 245.187i 0.517805 0.378374i
\(649\) −181.281 181.281i −0.279324 0.279324i
\(650\) 6.19725 1.32317i 0.00953424 0.00203565i
\(651\) 106.176 + 106.176i 0.163096 + 0.163096i
\(652\) 403.144 1055.97i 0.618318 1.61959i
\(653\) 626.017 + 626.017i 0.958678 + 0.958678i 0.999179 0.0405016i \(-0.0128956\pi\)
−0.0405016 + 0.999179i \(0.512896\pi\)
\(654\) −16.7459 78.4319i −0.0256054 0.119926i
\(655\) −815.450 −1.24496
\(656\) 33.2890 + 593.777i 0.0507454 + 0.905148i
\(657\) 380.745 380.745i 0.579521 0.579521i
\(658\) −500.705 + 772.558i −0.760950 + 1.17410i
\(659\) 1139.03 1.72841 0.864207 0.503136i \(-0.167820\pi\)
0.864207 + 0.503136i \(0.167820\pi\)
\(660\) −28.2805 + 74.0763i −0.0428492 + 0.112237i
\(661\) −1263.02 −1.91077 −0.955386 0.295359i \(-0.904561\pi\)
−0.955386 + 0.295359i \(0.904561\pi\)
\(662\) −111.025 520.002i −0.167712 0.785502i
\(663\) 4.78572 53.5328i 0.00721828 0.0807433i
\(664\) −98.6597 135.016i −0.148584 0.203337i
\(665\) 721.512i 1.08498i
\(666\) 13.7203 + 8.89231i 0.0206011 + 0.0133518i
\(667\) 952.989 1.42877
\(668\) 159.603 418.055i 0.238926 0.625830i
\(669\) 56.0058 + 56.0058i 0.0837157 + 0.0837157i
\(670\) 422.120 651.305i 0.630029 0.972098i
\(671\) 341.199 0.508494
\(672\) 160.672 + 91.7906i 0.239095 + 0.136593i
\(673\) −700.225 + 700.225i −1.04045 + 1.04045i −0.0413059 + 0.999147i \(0.513152\pi\)
−0.999147 + 0.0413059i \(0.986848\pi\)
\(674\) −886.405 574.491i −1.31514 0.852360i
\(675\) −13.4280 13.4280i −0.0198934 0.0198934i
\(676\) 584.549 261.535i 0.864717 0.386887i
\(677\) −378.421 + 378.421i −0.558967 + 0.558967i −0.929013 0.370046i \(-0.879342\pi\)
0.370046 + 0.929013i \(0.379342\pi\)
\(678\) 304.504 65.0143i 0.449121 0.0958913i
\(679\) 513.632i 0.756453i
\(680\) 358.086 + 594.824i 0.526597 + 0.874741i
\(681\) 213.744 0.313868
\(682\) 39.7381 + 186.119i 0.0582669 + 0.272902i
\(683\) −400.345 400.345i −0.586156 0.586156i 0.350432 0.936588i \(-0.386035\pi\)
−0.936588 + 0.350432i \(0.886035\pi\)
\(684\) −744.848 + 333.256i −1.08896 + 0.487216i
\(685\) −705.657 + 705.657i −1.03016 + 1.03016i
\(686\) 404.954 624.820i 0.590312 0.910817i
\(687\) −196.458 196.458i −0.285965 0.285965i
\(688\) −127.892 114.313i −0.185890 0.166153i
\(689\) 100.987i 0.146571i
\(690\) −268.923 174.293i −0.389744 0.252598i
\(691\) −665.780 + 665.780i −0.963502 + 0.963502i −0.999357 0.0358553i \(-0.988584\pi\)
0.0358553 + 0.999357i \(0.488584\pi\)
\(692\) 469.133 1228.82i 0.677938 1.77576i
\(693\) 157.538i 0.227327i
\(694\) 700.734 1081.19i 1.00970 1.55791i
\(695\) −35.7398 −0.0514242
\(696\) −220.191 + 160.899i −0.316366 + 0.231177i
\(697\) −56.2643 + 629.369i −0.0807236 + 0.902969i
\(698\) 661.562 141.250i 0.947797 0.202363i
\(699\) 91.1992i 0.130471i
\(700\) −8.26789 + 21.6565i −0.0118113 + 0.0309378i
\(701\) 92.7896i 0.132368i 0.997807 + 0.0661838i \(0.0210824\pi\)
−0.997807 + 0.0661838i \(0.978918\pi\)
\(702\) 89.5529 + 58.0404i 0.127568 + 0.0826786i
\(703\) −19.0042 19.0042i −0.0270331 0.0270331i
\(704\) 107.616 + 208.385i 0.152864 + 0.296002i
\(705\) 456.256i 0.647172i
\(706\) −51.3995 + 10.9743i −0.0728038 + 0.0155443i
\(707\) −84.3988 + 84.3988i −0.119376 + 0.119376i
\(708\) −105.756 + 277.011i −0.149372 + 0.391258i
\(709\) 796.746 796.746i 1.12376 1.12376i 0.132590 0.991171i \(-0.457671\pi\)
0.991171 0.132590i \(-0.0423293\pi\)
\(710\) 82.8065 + 387.836i 0.116629 + 0.546248i
\(711\) 134.063 134.063i 0.188555 0.188555i
\(712\) −747.715 + 546.375i −1.05016 + 0.767381i
\(713\) −769.177 −1.07879
\(714\) 154.810 + 121.196i 0.216821 + 0.169743i
\(715\) 55.8198 0.0780697
\(716\) −351.777 786.245i −0.491308 1.09811i
\(717\) −71.3173 + 71.3173i −0.0994662 + 0.0994662i
\(718\) 1100.74 235.018i 1.53306 0.327323i
\(719\) −171.227 + 171.227i −0.238146 + 0.238146i −0.816082 0.577936i \(-0.803858\pi\)
0.577936 + 0.816082i \(0.303858\pi\)
\(720\) −642.417 + 36.0159i −0.892246 + 0.0500221i
\(721\) −104.008 + 104.008i −0.144255 + 0.144255i
\(722\) 605.693 129.321i 0.838910 0.179115i
\(723\) 176.796i 0.244532i
\(724\) 450.640 + 172.043i 0.622431 + 0.237628i
\(725\) −24.1575 24.1575i −0.0333206 0.0333206i
\(726\) 123.983 191.298i 0.170775 0.263496i
\(727\) 263.954i 0.363073i −0.983384 0.181536i \(-0.941893\pi\)
0.983384 0.181536i \(-0.0581070\pi\)
\(728\) 20.0266 128.719i 0.0275091 0.176812i
\(729\) 238.661i 0.327382i
\(730\) −682.538 + 145.728i −0.934984 + 0.199628i
\(731\) −116.887 139.837i −0.159900 0.191296i
\(732\) −161.164 360.213i −0.220170 0.492094i
\(733\) −61.0527 −0.0832915 −0.0416457 0.999132i \(-0.513260\pi\)
−0.0416457 + 0.999132i \(0.513260\pi\)
\(734\) −699.761 453.524i −0.953353 0.617881i
\(735\) 103.950i 0.141428i
\(736\) −914.468 + 249.501i −1.24248 + 0.338997i
\(737\) 196.975 196.975i 0.267267 0.267267i
\(738\) −491.404 318.485i −0.665859 0.431552i
\(739\) 437.344i 0.591805i 0.955218 + 0.295903i \(0.0956204\pi\)
−0.955218 + 0.295903i \(0.904380\pi\)
\(740\) −8.65486 19.3442i −0.0116958 0.0261408i
\(741\) −57.8948 57.8948i −0.0781306 0.0781306i
\(742\) 310.005 + 200.918i 0.417797 + 0.270780i
\(743\) −598.705 + 598.705i −0.805794 + 0.805794i −0.983994 0.178200i \(-0.942972\pi\)
0.178200 + 0.983994i \(0.442972\pi\)
\(744\) 177.720 129.865i 0.238871 0.174550i
\(745\) 124.770 + 124.770i 0.167477 + 0.167477i
\(746\) 132.382 + 620.032i 0.177456 + 0.831142i
\(747\) 164.656 0.220423
\(748\) 81.1117 + 235.621i 0.108438 + 0.315001i
\(749\) 540.116i 0.721116i
\(750\) −54.0750 253.268i −0.0721001 0.337691i
\(751\) −146.723 + 146.723i −0.195370 + 0.195370i −0.798012 0.602642i \(-0.794115\pi\)
0.602642 + 0.798012i \(0.294115\pi\)
\(752\) 1006.19 + 899.362i 1.33802 + 1.19596i
\(753\) 98.7670 + 98.7670i 0.131165 + 0.131165i
\(754\) 161.108 + 104.416i 0.213672 + 0.138483i
\(755\) 549.946 549.946i 0.728405 0.728405i
\(756\) −356.338 + 159.431i −0.471347 + 0.210887i
\(757\) 96.4029 0.127349 0.0636743 0.997971i \(-0.479718\pi\)
0.0636743 + 0.997971i \(0.479718\pi\)
\(758\) −748.585 485.168i −0.987579 0.640063i
\(759\) −81.3310 81.3310i −0.107155 0.107155i
\(760\) 1045.09 + 162.599i 1.37512 + 0.213946i
\(761\) −256.811 −0.337466 −0.168733 0.985662i \(-0.553968\pi\)
−0.168733 + 0.985662i \(0.553968\pi\)
\(762\) 30.6039 + 19.8348i 0.0401626 + 0.0260299i
\(763\) 206.533i 0.270686i
\(764\) −348.350 778.586i −0.455956 1.01909i
\(765\) −680.925 60.8733i −0.890098 0.0795730i
\(766\) 1022.27 218.264i 1.33456 0.284940i
\(767\) 208.740 0.272151
\(768\) 169.165 212.043i 0.220267 0.276098i
\(769\) 439.409 0.571403 0.285702 0.958319i \(-0.407773\pi\)
0.285702 + 0.958319i \(0.407773\pi\)
\(770\) −111.056 + 171.352i −0.144228 + 0.222536i
\(771\) −256.772 + 256.772i −0.333037 + 0.333037i
\(772\) 193.379 506.526i 0.250491 0.656122i
\(773\) 961.024 1.24324 0.621619 0.783319i \(-0.286475\pi\)
0.621619 + 0.783319i \(0.286475\pi\)
\(774\) 165.180 35.2673i 0.213410 0.0455650i
\(775\) 19.4980 + 19.4980i 0.0251587 + 0.0251587i
\(776\) −743.983 115.752i −0.958741 0.149164i
\(777\) −4.24344 4.24344i −0.00546132 0.00546132i
\(778\) 502.105 107.204i 0.645380 0.137794i
\(779\) 680.652 + 680.652i 0.873751 + 0.873751i
\(780\) −26.3663 58.9304i −0.0338029 0.0755518i
\(781\) 142.337i 0.182250i
\(782\) −999.750 + 121.756i −1.27845 + 0.155698i
\(783\) 575.332i 0.734779i
\(784\) −229.243 204.903i −0.292402 0.261356i
\(785\) 1039.12 + 1039.12i 1.32372 + 1.32372i
\(786\) 70.6803 + 331.041i 0.0899241 + 0.421172i
\(787\) −198.734 198.734i −0.252521 0.252521i 0.569483 0.822003i \(-0.307144\pi\)
−0.822003 + 0.569483i \(0.807144\pi\)
\(788\) 620.543 + 236.908i 0.787491 + 0.300644i
\(789\) −370.501 370.501i −0.469582 0.469582i
\(790\) −240.326 + 51.3117i −0.304210 + 0.0649516i
\(791\) 801.844 1.01371
\(792\) −228.189 35.5026i −0.288118 0.0448265i
\(793\) −196.440 + 196.440i −0.247718 + 0.247718i
\(794\) 869.703 + 563.666i 1.09534 + 0.709906i
\(795\) 183.082 0.230292
\(796\) −244.585 + 640.654i −0.307268 + 0.804841i
\(797\) −987.969 −1.23961 −0.619805 0.784756i \(-0.712788\pi\)
−0.619805 + 0.784756i \(0.712788\pi\)
\(798\) 292.906 62.5381i 0.367050 0.0783685i
\(799\) 919.606 + 1100.17i 1.15095 + 1.37693i
\(800\) 29.5056 + 16.8563i 0.0368820 + 0.0210704i
\(801\) 911.862i 1.13840i
\(802\) −593.449 + 915.657i −0.739961 + 1.14172i
\(803\) −250.494 −0.311948
\(804\) −300.993 114.911i −0.374369 0.142925i
\(805\) −583.556 583.556i −0.724915 0.724915i
\(806\) −130.034 84.2766i −0.161332 0.104562i
\(807\) 175.027 0.216886
\(808\) 103.230 + 141.270i 0.127759 + 0.174839i
\(809\) 407.336 407.336i 0.503506 0.503506i −0.409020 0.912526i \(-0.634129\pi\)
0.912526 + 0.409020i \(0.134129\pi\)
\(810\) 288.463 445.082i 0.356128 0.549484i
\(811\) −38.6417 38.6417i −0.0476469 0.0476469i 0.682882 0.730529i \(-0.260726\pi\)
−0.730529 + 0.682882i \(0.760726\pi\)
\(812\) −641.063 + 286.821i −0.789486 + 0.353227i
\(813\) 180.714 180.714i 0.222281 0.222281i
\(814\) −1.58818 7.43848i −0.00195108 0.00913818i
\(815\) 1442.58i 1.77004i
\(816\) 210.438 196.926i 0.257890 0.241331i
\(817\) −277.643 −0.339832
\(818\) 528.755 112.894i 0.646400 0.138012i
\(819\) 90.7000 + 90.7000i 0.110745 + 0.110745i
\(820\) 309.981 + 692.828i 0.378025 + 0.844912i
\(821\) −39.8813 + 39.8813i −0.0485765 + 0.0485765i −0.730978 0.682401i \(-0.760936\pi\)
0.682401 + 0.730978i \(0.260936\pi\)
\(822\) 347.633 + 225.306i 0.422912 + 0.274094i
\(823\) −1118.37 1118.37i −1.35889 1.35889i −0.875287 0.483604i \(-0.839327\pi\)
−0.483604 0.875287i \(-0.660673\pi\)
\(824\) 127.214 + 174.092i 0.154386 + 0.211277i
\(825\) 4.12334i 0.00499799i
\(826\) −415.296 + 640.778i −0.502780 + 0.775760i
\(827\) −350.629 + 350.629i −0.423976 + 0.423976i −0.886570 0.462594i \(-0.846919\pi\)
0.462594 + 0.886570i \(0.346919\pi\)
\(828\) 332.895 871.967i 0.402047 1.05310i
\(829\) 470.897i 0.568030i −0.958820 0.284015i \(-0.908333\pi\)
0.958820 0.284015i \(-0.0916665\pi\)
\(830\) −179.095 116.074i −0.215777 0.139848i
\(831\) 510.608 0.614451
\(832\) −181.933 58.0160i −0.218670 0.0697308i
\(833\) −209.516 250.654i −0.251520 0.300905i
\(834\) 3.09780 + 14.5090i 0.00371439 + 0.0173969i
\(835\) 571.112i 0.683967i
\(836\) 354.645 + 135.394i 0.424216 + 0.161955i
\(837\) 464.362i 0.554793i
\(838\) −387.732 + 598.248i −0.462687 + 0.713899i
\(839\) 1145.65 + 1145.65i 1.36549 + 1.36549i 0.866748 + 0.498747i \(0.166206\pi\)
0.498747 + 0.866748i \(0.333794\pi\)
\(840\) 233.358 + 36.3067i 0.277807 + 0.0432222i
\(841\) 194.040i 0.230726i
\(842\) −74.9299 350.945i −0.0889904 0.416799i
\(843\) −321.054 + 321.054i −0.380847 + 0.380847i
\(844\) −31.8538 + 83.4360i −0.0377414 + 0.0988578i
\(845\) 577.926 577.926i 0.683936 0.683936i
\(846\) −1299.55 + 277.466i −1.53611 + 0.327974i
\(847\) 415.112 415.112i 0.490096 0.490096i
\(848\) 360.888 403.756i 0.425575 0.476128i
\(849\) 83.5732 0.0984373
\(850\) 28.4292 + 22.2564i 0.0334461 + 0.0261840i
\(851\) 30.7411 0.0361235
\(852\) 150.269 67.2325i 0.176372 0.0789114i
\(853\) 161.359 161.359i 0.189167 0.189167i −0.606169 0.795336i \(-0.707294\pi\)
0.795336 + 0.606169i \(0.207294\pi\)
\(854\) −212.195 993.847i −0.248472 1.16376i
\(855\) −736.409 + 736.409i −0.861297 + 0.861297i
\(856\) −782.345 121.720i −0.913954 0.142196i
\(857\) −248.656 + 248.656i −0.290147 + 0.290147i −0.837138 0.546991i \(-0.815773\pi\)
0.546991 + 0.837138i \(0.315773\pi\)
\(858\) −4.83826 22.6607i −0.00563900 0.0264111i
\(859\) 369.325i 0.429947i −0.976620 0.214974i \(-0.931033\pi\)
0.976620 0.214974i \(-0.0689665\pi\)
\(860\) −204.526 78.0829i −0.237821 0.0907940i
\(861\) 151.982 + 151.982i 0.176518 + 0.176518i
\(862\) −1116.11 723.367i −1.29479 0.839173i
\(863\) 1657.91i 1.92110i 0.278107 + 0.960550i \(0.410293\pi\)
−0.278107 + 0.960550i \(0.589707\pi\)
\(864\) 150.627 + 552.076i 0.174337 + 0.638977i
\(865\) 1678.72i 1.94071i
\(866\) −109.223 511.563i −0.126124 0.590720i
\(867\) 251.506 174.690i 0.290087 0.201488i
\(868\) 517.415 231.498i 0.596100 0.266703i
\(869\) −88.2005 −0.101497
\(870\) −189.299 + 292.077i −0.217585 + 0.335721i
\(871\) 226.811i 0.260404i
\(872\) −299.158 46.5442i −0.343072 0.0533763i
\(873\) 524.237 524.237i 0.600500 0.600500i
\(874\) −834.437 + 1287.49i −0.954733 + 1.47310i
\(875\) 666.926i 0.762201i
\(876\) 118.320 + 264.453i 0.135068 + 0.301887i
\(877\) 262.995 + 262.995i 0.299881 + 0.299881i 0.840967 0.541086i \(-0.181987\pi\)
−0.541086 + 0.840967i \(0.681987\pi\)
\(878\) −193.907 + 299.186i −0.220850 + 0.340759i
\(879\) −257.438 + 257.438i −0.292876 + 0.292876i
\(880\) 223.172 + 199.477i 0.253605 + 0.226679i
\(881\) −692.939 692.939i −0.786537 0.786537i 0.194388 0.980925i \(-0.437728\pi\)
−0.980925 + 0.194388i \(0.937728\pi\)
\(882\) 296.080 63.2157i 0.335691 0.0716731i
\(883\) −654.812 −0.741577 −0.370788 0.928717i \(-0.620912\pi\)
−0.370788 + 0.928717i \(0.620912\pi\)
\(884\) −182.354 88.9563i −0.206283 0.100629i
\(885\) 378.430i 0.427604i
\(886\) −136.880 + 29.2251i −0.154492 + 0.0329854i
\(887\) −1025.67 + 1025.67i −1.15634 + 1.15634i −0.171085 + 0.985256i \(0.554727\pi\)
−0.985256 + 0.171085i \(0.945273\pi\)
\(888\) −7.10282 + 5.19022i −0.00799867 + 0.00584485i
\(889\) 66.4095 + 66.4095i 0.0747014 + 0.0747014i
\(890\) −642.814 + 991.824i −0.722263 + 1.11441i
\(891\) 134.607 134.607i 0.151074 0.151074i
\(892\) 272.927 122.111i 0.305972 0.136896i
\(893\) 2184.36 2.44609
\(894\) 39.8373 61.4666i 0.0445607 0.0687546i
\(895\) −777.336 777.336i −0.868532 0.868532i
\(896\) 540.058 443.063i 0.602743 0.494490i
\(897\) 93.6502 0.104404
\(898\) −337.996 + 521.508i −0.376388 + 0.580744i
\(899\) 835.401i 0.929256i
\(900\) −30.5422 + 13.6650i −0.0339358 + 0.0151833i
\(901\) 441.467 369.011i 0.489974 0.409558i
\(902\) 56.8820 + 266.415i 0.0630621 + 0.295360i
\(903\) −61.9946 −0.0686540
\(904\) 180.703 1161.45i 0.199893 1.28479i
\(905\) 615.627 0.680251
\(906\) −270.924 175.590i −0.299033 0.193807i
\(907\) −63.4688 + 63.4688i −0.0699766 + 0.0699766i −0.741229 0.671252i \(-0.765757\pi\)
0.671252 + 0.741229i \(0.265757\pi\)
\(908\) 287.792 753.826i 0.316951 0.830205i
\(909\) −172.283 −0.189530
\(910\) −34.7149 162.592i −0.0381483 0.178673i
\(911\) 949.166 + 949.166i 1.04189 + 1.04189i 0.999083 + 0.0428112i \(0.0136314\pi\)
0.0428112 + 0.999083i \(0.486369\pi\)
\(912\) −24.5758 438.361i −0.0269472 0.480659i
\(913\) −54.1640 54.1640i −0.0593253 0.0593253i
\(914\) 202.603 + 948.922i 0.221667 + 1.03821i
\(915\) −356.131 356.131i −0.389215 0.389215i
\(916\) −957.379 + 428.345i −1.04517 + 0.467625i
\(917\) 871.725i 0.950627i
\(918\) 73.5057 + 603.562i 0.0800716 + 0.657475i
\(919\) 1082.82i 1.17826i 0.808040 + 0.589128i \(0.200529\pi\)
−0.808040 + 0.589128i \(0.799471\pi\)
\(920\) −976.777 + 713.757i −1.06171 + 0.775823i
\(921\) −75.6452 75.6452i −0.0821338 0.0821338i
\(922\) 1571.98 335.631i 1.70496 0.364025i
\(923\) −81.9486 81.9486i −0.0887850 0.0887850i
\(924\) 79.1884 + 30.2321i 0.0857017 + 0.0327187i
\(925\) −0.779261 0.779261i −0.000842444 0.000842444i
\(926\) 281.065 + 1316.41i 0.303526 + 1.42161i
\(927\) −212.311 −0.229030
\(928\) 270.983 + 993.202i 0.292008 + 1.07026i
\(929\) −517.649 + 517.649i −0.557211 + 0.557211i −0.928513 0.371301i \(-0.878912\pi\)
0.371301 + 0.928513i \(0.378912\pi\)
\(930\) 152.787 235.741i 0.164287 0.253485i
\(931\) −497.666 −0.534550
\(932\) −321.638 122.793i −0.345106 0.131753i
\(933\) −54.0949 −0.0579796
\(934\) 321.217 + 1504.46i 0.343915 + 1.61078i
\(935\) 203.967 + 244.016i 0.218147 + 0.260980i
\(936\) 151.817 110.937i 0.162197 0.118522i
\(937\) 1102.17i 1.17627i −0.808762 0.588137i \(-0.799862\pi\)
0.808762 0.588137i \(-0.200138\pi\)
\(938\) −696.252 451.250i −0.742273 0.481077i
\(939\) −310.762 −0.330950
\(940\) 1609.11 + 614.318i 1.71182 + 0.653529i
\(941\) −917.863 917.863i −0.975412 0.975412i 0.0242925 0.999705i \(-0.492267\pi\)
−0.999705 + 0.0242925i \(0.992267\pi\)
\(942\) 331.776 511.911i 0.352204 0.543430i
\(943\) −1101.02 −1.16757
\(944\) 834.560 + 745.952i 0.884068 + 0.790203i
\(945\) −352.301 + 352.301i −0.372805 + 0.372805i
\(946\) −65.9375 42.7350i −0.0697014 0.0451744i
\(947\) −356.250 356.250i −0.376188 0.376188i 0.493537 0.869725i \(-0.335704\pi\)
−0.869725 + 0.493537i \(0.835704\pi\)
\(948\) 41.6612 + 93.1155i 0.0439464 + 0.0982231i
\(949\) 144.218 144.218i 0.151969 0.151969i
\(950\) 53.7889 11.4844i 0.0566199 0.0120889i
\(951\) 136.678i 0.143720i
\(952\) 635.873 382.798i 0.667934 0.402098i
\(953\) 195.343 0.204977 0.102489 0.994734i \(-0.467319\pi\)
0.102489 + 0.994734i \(0.467319\pi\)
\(954\) 111.339 + 521.473i 0.116708 + 0.546617i
\(955\) −769.765 769.765i −0.806036 0.806036i
\(956\) 155.496 + 347.543i 0.162652 + 0.363539i
\(957\) −88.3334 + 88.3334i −0.0923025 + 0.0923025i
\(958\) 199.490 307.801i 0.208236 0.321296i
\(959\) 754.355 + 754.355i 0.786605 + 0.786605i
\(960\) 105.179 329.831i 0.109561 0.343574i
\(961\) 286.731i 0.298367i
\(962\) 5.19697 + 3.36822i 0.00540225 + 0.00350127i
\(963\) 551.268 551.268i 0.572448 0.572448i
\(964\) −623.519 238.044i −0.646804 0.246934i
\(965\) 691.975i 0.717073i
\(966\) −186.321 + 287.482i −0.192879 + 0.297600i
\(967\) 1170.65 1.21060 0.605299 0.795998i \(-0.293053\pi\)
0.605299 + 0.795998i \(0.293053\pi\)
\(968\) −507.730 694.828i −0.524514 0.717798i
\(969\) 41.5376 464.637i 0.0428664 0.479501i
\(970\) −939.767 + 200.649i −0.968832 + 0.206854i
\(971\) 1519.02i 1.56438i −0.623037 0.782192i \(-0.714101\pi\)
0.623037 0.782192i \(-0.285899\pi\)
\(972\) −807.136 308.144i −0.830387 0.317021i
\(973\) 38.2062i 0.0392664i
\(974\) 159.726 + 103.520i 0.163989 + 0.106284i
\(975\) −2.37395 2.37395i −0.00243482 0.00243482i
\(976\) −1487.38 + 83.3872i −1.52396 + 0.0854377i
\(977\) 109.675i 0.112257i 0.998424 + 0.0561283i \(0.0178756\pi\)
−0.998424 + 0.0561283i \(0.982124\pi\)
\(978\) −585.633 + 125.038i −0.598807 + 0.127851i
\(979\) −299.959 + 299.959i −0.306393 + 0.306393i
\(980\) −366.607 139.961i −0.374089 0.142818i
\(981\) 210.798 210.798i 0.214880 0.214880i
\(982\) −39.8870 186.817i −0.0406182 0.190241i
\(983\) 176.945 176.945i 0.180005 0.180005i −0.611353 0.791358i \(-0.709374\pi\)
0.791358 + 0.611353i \(0.209374\pi\)
\(984\) 254.393 185.892i 0.258530 0.188915i
\(985\) 847.736 0.860645
\(986\) 132.239 + 1085.83i 0.134117 + 1.10124i
\(987\) 487.743 0.494167
\(988\) −282.133 + 126.230i −0.285560 + 0.127763i
\(989\) 224.556 224.556i 0.227054 0.227054i
\(990\) −288.239 + 61.5416i −0.291150 + 0.0621632i
\(991\) 478.714 478.714i 0.483062 0.483062i −0.423046 0.906108i \(-0.639039\pi\)
0.906108 + 0.423046i \(0.139039\pi\)
\(992\) −218.716 801.633i −0.220480 0.808097i
\(993\) −199.195 + 199.195i −0.200599 + 0.200599i
\(994\) 414.601 88.5210i 0.417103 0.0890553i
\(995\) 875.209i 0.879607i
\(996\) −31.5981 + 82.7665i −0.0317250 + 0.0830989i
\(997\) −231.688 231.688i −0.232385 0.232385i 0.581303 0.813687i \(-0.302543\pi\)
−0.813687 + 0.581303i \(0.802543\pi\)
\(998\) −885.969 + 1367.00i −0.887744 + 1.36974i
\(999\) 18.5588i 0.0185774i
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 136.3.j.b.115.2 64
4.3 odd 2 544.3.n.b.47.13 64
8.3 odd 2 inner 136.3.j.b.115.31 yes 64
8.5 even 2 544.3.n.b.47.14 64
17.4 even 4 inner 136.3.j.b.123.31 yes 64
68.55 odd 4 544.3.n.b.463.14 64
136.21 even 4 544.3.n.b.463.13 64
136.123 odd 4 inner 136.3.j.b.123.2 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
136.3.j.b.115.2 64 1.1 even 1 trivial
136.3.j.b.115.31 yes 64 8.3 odd 2 inner
136.3.j.b.123.2 yes 64 136.123 odd 4 inner
136.3.j.b.123.31 yes 64 17.4 even 4 inner
544.3.n.b.47.13 64 4.3 odd 2
544.3.n.b.47.14 64 8.5 even 2
544.3.n.b.463.13 64 136.21 even 4
544.3.n.b.463.14 64 68.55 odd 4