Properties

Label 273.2.bj.c.142.2
Level $273$
Weight $2$
Character 273.142
Analytic conductor $2.180$
Analytic rank $0$
Dimension $16$
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] = [273,2,Mod(25,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.25");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bj (of order \(6\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 11x^{14} + 88x^{12} - 303x^{10} + 758x^{8} - 968x^{6} + 867x^{4} - 30x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 142.2
Root \(-1.34967 + 0.779232i\) of defining polynomial
Character \(\chi\) \(=\) 273.142
Dual form 273.2.bj.c.25.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34967 - 0.779232i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.214404 + 0.371358i) q^{4} +(1.85159 + 1.06902i) q^{5} +1.55846i q^{6} +(-1.34967 + 2.27561i) q^{7} +2.44865i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.34967 - 0.779232i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.214404 + 0.371358i) q^{4} +(1.85159 + 1.06902i) q^{5} +1.55846i q^{6} +(-1.34967 + 2.27561i) q^{7} +2.44865i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.66602 - 2.88564i) q^{10} +(-4.76616 + 2.75174i) q^{11} +(0.214404 - 0.371358i) q^{12} +(-2.90324 - 2.13803i) q^{13} +(3.59483 - 2.01961i) q^{14} -2.13803i q^{15} +(2.33687 - 4.04758i) q^{16} +(3.71730 + 6.43855i) q^{17} +(1.34967 - 0.779232i) q^{18} +(3.20126 + 1.84825i) q^{19} +0.916805i q^{20} +(2.64557 + 0.0310431i) q^{21} +8.57698 q^{22} +(-1.88525 + 3.26535i) q^{23} +(2.12059 - 1.22432i) q^{24} +(-0.214404 - 0.371358i) q^{25} +(2.25239 + 5.14794i) q^{26} +1.00000 q^{27} +(-1.13444 - 0.0133115i) q^{28} +0.903241 q^{29} +(-1.66602 + 2.88564i) q^{30} +(-2.62251 + 1.51411i) q^{31} +(-2.06682 + 1.19328i) q^{32} +(4.76616 + 2.75174i) q^{33} -11.5865i q^{34} +(-4.93170 + 2.77068i) q^{35} -0.428808 q^{36} +(0.824689 + 0.476134i) q^{37} +(-2.88043 - 4.98905i) q^{38} +(-0.399972 + 3.58330i) q^{39} +(-2.61764 + 4.53389i) q^{40} -4.86183i q^{41} +(-3.54645 - 2.10341i) q^{42} +4.89360 q^{43} +(-2.04376 - 1.17997i) q^{44} +(-1.85159 + 1.06902i) q^{45} +(5.08892 - 2.93809i) q^{46} +(-4.55629 - 2.63057i) q^{47} -4.67374 q^{48} +(-3.35679 - 6.14264i) q^{49} +0.668281i q^{50} +(3.71730 - 6.43855i) q^{51} +(0.171511 - 1.53655i) q^{52} +(6.49807 + 11.2550i) q^{53} +(-1.34967 - 0.779232i) q^{54} -11.7666 q^{55} +(-5.57216 - 3.30486i) q^{56} -3.69650i q^{57} +(-1.21908 - 0.703834i) q^{58} +(-7.30419 + 4.21708i) q^{59} +(0.793977 - 0.458403i) q^{60} +(1.81406 - 3.14204i) q^{61} +4.71936 q^{62} +(-1.29590 - 2.30665i) q^{63} -5.62811 q^{64} +(-3.09002 - 7.06238i) q^{65} +(-4.28849 - 7.42788i) q^{66} +(1.52883 - 0.882669i) q^{67} +(-1.59401 + 2.76090i) q^{68} +3.77050 q^{69} +(8.81516 + 0.103437i) q^{70} -11.7994i q^{71} +(-2.12059 - 1.22432i) q^{72} +(-6.43323 + 3.71423i) q^{73} +(-0.742038 - 1.28525i) q^{74} +(-0.214404 + 0.371358i) q^{75} +1.58509i q^{76} +(0.170845 - 14.5599i) q^{77} +(3.33205 - 4.52459i) q^{78} +(-7.64418 + 13.2401i) q^{79} +(8.65386 - 4.99631i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.78849 + 6.56186i) q^{82} +10.4833i q^{83} +(0.555692 + 0.989110i) q^{84} +15.8954i q^{85} +(-6.60474 - 3.81325i) q^{86} +(-0.451620 - 0.782230i) q^{87} +(-6.73804 - 11.6706i) q^{88} +(4.49716 + 2.59644i) q^{89} +3.33205 q^{90} +(8.78374 - 3.72100i) q^{91} -1.61682 q^{92} +(2.62251 + 1.51411i) q^{93} +(4.09965 + 7.10081i) q^{94} +(3.95162 + 6.84441i) q^{95} +(2.06682 + 1.19328i) q^{96} +7.06195i q^{97} +(-0.255983 + 10.9062i) q^{98} -5.50349i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{13} + 40 q^{14} - 10 q^{16} - 8 q^{17} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} + 16 q^{27} - 36 q^{29} - 4 q^{30} - 14 q^{35} - 12 q^{36} - 26 q^{38} - 2 q^{39} + 6 q^{40} - 14 q^{42} + 32 q^{43} + 20 q^{48} - 46 q^{49} - 8 q^{51} + 40 q^{52} + 36 q^{53} - 8 q^{55} + 54 q^{56} + 12 q^{61} - 80 q^{62} - 56 q^{64} + 34 q^{65} + 4 q^{66} + 10 q^{68} + 16 q^{69} + 18 q^{74} - 6 q^{75} - 22 q^{77} + 8 q^{78} + 8 q^{79} - 8 q^{81} + 12 q^{82} + 18 q^{87} - 98 q^{88} + 8 q^{90} + 16 q^{91} + 40 q^{92} + 46 q^{94} + 38 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34967 0.779232i −0.954360 0.551000i −0.0599273 0.998203i \(-0.519087\pi\)
−0.894433 + 0.447203i \(0.852420\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.214404 + 0.371358i 0.107202 + 0.185679i
\(5\) 1.85159 + 1.06902i 0.828057 + 0.478079i 0.853187 0.521605i \(-0.174667\pi\)
−0.0251298 + 0.999684i \(0.508000\pi\)
\(6\) 1.55846i 0.636240i
\(7\) −1.34967 + 2.27561i −0.510127 + 0.860099i
\(8\) 2.44865i 0.865727i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.66602 2.88564i −0.526843 0.912519i
\(11\) −4.76616 + 2.75174i −1.43705 + 0.829682i −0.997644 0.0686064i \(-0.978145\pi\)
−0.439407 + 0.898288i \(0.644811\pi\)
\(12\) 0.214404 0.371358i 0.0618930 0.107202i
\(13\) −2.90324 2.13803i −0.805214 0.592984i
\(14\) 3.59483 2.01961i 0.960759 0.539764i
\(15\) 2.13803i 0.552038i
\(16\) 2.33687 4.04758i 0.584217 1.01189i
\(17\) 3.71730 + 6.43855i 0.901577 + 1.56158i 0.825447 + 0.564479i \(0.190923\pi\)
0.0761300 + 0.997098i \(0.475744\pi\)
\(18\) 1.34967 0.779232i 0.318120 0.183667i
\(19\) 3.20126 + 1.84825i 0.734420 + 0.424017i 0.820037 0.572311i \(-0.193953\pi\)
−0.0856172 + 0.996328i \(0.527286\pi\)
\(20\) 0.916805i 0.205004i
\(21\) 2.64557 + 0.0310431i 0.577311 + 0.00677416i
\(22\) 8.57698 1.82862
\(23\) −1.88525 + 3.26535i −0.393102 + 0.680872i −0.992857 0.119312i \(-0.961931\pi\)
0.599755 + 0.800184i \(0.295265\pi\)
\(24\) 2.12059 1.22432i 0.432863 0.249914i
\(25\) −0.214404 0.371358i −0.0428808 0.0742716i
\(26\) 2.25239 + 5.14794i 0.441730 + 1.00959i
\(27\) 1.00000 0.192450
\(28\) −1.13444 0.0133115i −0.214389 0.00251564i
\(29\) 0.903241 0.167728 0.0838638 0.996477i \(-0.473274\pi\)
0.0838638 + 0.996477i \(0.473274\pi\)
\(30\) −1.66602 + 2.88564i −0.304173 + 0.526843i
\(31\) −2.62251 + 1.51411i −0.471017 + 0.271942i −0.716665 0.697417i \(-0.754333\pi\)
0.245648 + 0.969359i \(0.420999\pi\)
\(32\) −2.06682 + 1.19328i −0.365366 + 0.210944i
\(33\) 4.76616 + 2.75174i 0.829682 + 0.479017i
\(34\) 11.5865i 1.98708i
\(35\) −4.93170 + 2.77068i −0.833610 + 0.468330i
\(36\) −0.428808 −0.0714679
\(37\) 0.824689 + 0.476134i 0.135578 + 0.0782760i 0.566255 0.824230i \(-0.308392\pi\)
−0.430677 + 0.902506i \(0.641725\pi\)
\(38\) −2.88043 4.98905i −0.467267 0.809330i
\(39\) −0.399972 + 3.58330i −0.0640468 + 0.573787i
\(40\) −2.61764 + 4.53389i −0.413886 + 0.716872i
\(41\) 4.86183i 0.759290i −0.925132 0.379645i \(-0.876046\pi\)
0.925132 0.379645i \(-0.123954\pi\)
\(42\) −3.54645 2.10341i −0.547229 0.324563i
\(43\) 4.89360 0.746267 0.373133 0.927778i \(-0.378283\pi\)
0.373133 + 0.927778i \(0.378283\pi\)
\(44\) −2.04376 1.17997i −0.308109 0.177887i
\(45\) −1.85159 + 1.06902i −0.276019 + 0.159360i
\(46\) 5.08892 2.93809i 0.750321 0.433198i
\(47\) −4.55629 2.63057i −0.664603 0.383709i 0.129426 0.991589i \(-0.458687\pi\)
−0.794029 + 0.607880i \(0.792020\pi\)
\(48\) −4.67374 −0.674596
\(49\) −3.35679 6.14264i −0.479541 0.877519i
\(50\) 0.668281i 0.0945092i
\(51\) 3.71730 6.43855i 0.520526 0.901577i
\(52\) 0.171511 1.53655i 0.0237843 0.213080i
\(53\) 6.49807 + 11.2550i 0.892579 + 1.54599i 0.836773 + 0.547550i \(0.184440\pi\)
0.0558062 + 0.998442i \(0.482227\pi\)
\(54\) −1.34967 0.779232i −0.183667 0.106040i
\(55\) −11.7666 −1.58661
\(56\) −5.57216 3.30486i −0.744611 0.441631i
\(57\) 3.69650i 0.489613i
\(58\) −1.21908 0.703834i −0.160073 0.0924179i
\(59\) −7.30419 + 4.21708i −0.950925 + 0.549017i −0.893368 0.449326i \(-0.851664\pi\)
−0.0575566 + 0.998342i \(0.518331\pi\)
\(60\) 0.793977 0.458403i 0.102502 0.0591795i
\(61\) 1.81406 3.14204i 0.232266 0.402297i −0.726208 0.687475i \(-0.758719\pi\)
0.958475 + 0.285178i \(0.0920526\pi\)
\(62\) 4.71936 0.599360
\(63\) −1.29590 2.30665i −0.163268 0.290611i
\(64\) −5.62811 −0.703514
\(65\) −3.09002 7.06238i −0.383270 0.875981i
\(66\) −4.28849 7.42788i −0.527877 0.914309i
\(67\) 1.52883 0.882669i 0.186776 0.107835i −0.403696 0.914893i \(-0.632275\pi\)
0.590472 + 0.807058i \(0.298941\pi\)
\(68\) −1.59401 + 2.76090i −0.193302 + 0.334808i
\(69\) 3.77050 0.453915
\(70\) 8.81516 + 0.103437i 1.05361 + 0.0123631i
\(71\) 11.7994i 1.40033i −0.713979 0.700167i \(-0.753109\pi\)
0.713979 0.700167i \(-0.246891\pi\)
\(72\) −2.12059 1.22432i −0.249914 0.144288i
\(73\) −6.43323 + 3.71423i −0.752953 + 0.434718i −0.826760 0.562555i \(-0.809819\pi\)
0.0738068 + 0.997273i \(0.476485\pi\)
\(74\) −0.742038 1.28525i −0.0862601 0.149407i
\(75\) −0.214404 + 0.371358i −0.0247572 + 0.0428808i
\(76\) 1.58509i 0.181822i
\(77\) 0.170845 14.5599i 0.0194696 1.65925i
\(78\) 3.33205 4.52459i 0.377280 0.512309i
\(79\) −7.64418 + 13.2401i −0.860037 + 1.48963i 0.0118547 + 0.999930i \(0.496226\pi\)
−0.871892 + 0.489698i \(0.837107\pi\)
\(80\) 8.65386 4.99631i 0.967531 0.558604i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.78849 + 6.56186i −0.418369 + 0.724636i
\(83\) 10.4833i 1.15069i 0.817910 + 0.575346i \(0.195133\pi\)
−0.817910 + 0.575346i \(0.804867\pi\)
\(84\) 0.555692 + 0.989110i 0.0606310 + 0.107921i
\(85\) 15.8954i 1.72410i
\(86\) −6.60474 3.81325i −0.712207 0.411193i
\(87\) −0.451620 0.782230i −0.0484188 0.0838638i
\(88\) −6.73804 11.6706i −0.718278 1.24409i
\(89\) 4.49716 + 2.59644i 0.476698 + 0.275222i 0.719039 0.694969i \(-0.244582\pi\)
−0.242341 + 0.970191i \(0.577915\pi\)
\(90\) 3.33205 0.351229
\(91\) 8.78374 3.72100i 0.920787 0.390067i
\(92\) −1.61682 −0.168565
\(93\) 2.62251 + 1.51411i 0.271942 + 0.157006i
\(94\) 4.09965 + 7.10081i 0.422847 + 0.732392i
\(95\) 3.95162 + 6.84441i 0.405428 + 0.702221i
\(96\) 2.06682 + 1.19328i 0.210944 + 0.121789i
\(97\) 7.06195i 0.717032i 0.933524 + 0.358516i \(0.116717\pi\)
−0.933524 + 0.358516i \(0.883283\pi\)
\(98\) −0.255983 + 10.9062i −0.0258582 + 1.10170i
\(99\) 5.50349i 0.553121i
\(100\) 0.0919380 0.159241i 0.00919380 0.0159241i
\(101\) −5.05417 8.75407i −0.502908 0.871063i −0.999994 0.00336163i \(-0.998930\pi\)
0.497086 0.867701i \(-0.334403\pi\)
\(102\) −10.0342 + 5.79327i −0.993538 + 0.573619i
\(103\) −5.93170 + 10.2740i −0.584468 + 1.01233i 0.410474 + 0.911872i \(0.365363\pi\)
−0.994942 + 0.100456i \(0.967970\pi\)
\(104\) 5.23529 7.10901i 0.513362 0.697096i
\(105\) 4.86533 + 2.88564i 0.474808 + 0.281609i
\(106\) 20.2540i 1.96724i
\(107\) 5.77885 10.0093i 0.558662 0.967631i −0.438946 0.898513i \(-0.644648\pi\)
0.997608 0.0691181i \(-0.0220185\pi\)
\(108\) 0.214404 + 0.371358i 0.0206310 + 0.0357340i
\(109\) 10.7460 6.20423i 1.02928 0.594257i 0.112504 0.993651i \(-0.464113\pi\)
0.916779 + 0.399394i \(0.130780\pi\)
\(110\) 15.8811 + 9.16894i 1.51420 + 0.874224i
\(111\) 0.952269i 0.0903853i
\(112\) 6.05670 + 10.7807i 0.572304 + 1.01868i
\(113\) −5.09290 −0.479100 −0.239550 0.970884i \(-0.577000\pi\)
−0.239550 + 0.970884i \(0.577000\pi\)
\(114\) −2.88043 + 4.98905i −0.269777 + 0.467267i
\(115\) −6.98143 + 4.03073i −0.651021 + 0.375867i
\(116\) 0.193658 + 0.335426i 0.0179807 + 0.0311435i
\(117\) 3.30321 1.44526i 0.305382 0.133615i
\(118\) 13.1443 1.21003
\(119\) −19.6687 0.230793i −1.80303 0.0211568i
\(120\) 5.23529 0.477914
\(121\) 9.64418 16.7042i 0.876743 1.51856i
\(122\) −4.89675 + 2.82714i −0.443331 + 0.255957i
\(123\) −4.21047 + 2.43091i −0.379645 + 0.219188i
\(124\) −1.12455 0.649261i −0.100988 0.0583054i
\(125\) 11.6070i 1.03816i
\(126\) −0.0483796 + 4.12302i −0.00430999 + 0.367308i
\(127\) 19.0019 1.68615 0.843074 0.537797i \(-0.180743\pi\)
0.843074 + 0.537797i \(0.180743\pi\)
\(128\) 11.7297 + 6.77216i 1.03677 + 0.598580i
\(129\) −2.44680 4.23798i −0.215429 0.373133i
\(130\) −1.33273 + 11.9397i −0.116888 + 1.04718i
\(131\) −5.47526 + 9.48343i −0.478376 + 0.828571i −0.999693 0.0247922i \(-0.992108\pi\)
0.521317 + 0.853363i \(0.325441\pi\)
\(132\) 2.35994i 0.205406i
\(133\) −8.52653 + 4.79029i −0.739344 + 0.415371i
\(134\) −2.75121 −0.237669
\(135\) 1.85159 + 1.06902i 0.159360 + 0.0920064i
\(136\) −15.7657 + 9.10234i −1.35190 + 0.780520i
\(137\) −1.42665 + 0.823676i −0.121887 + 0.0703714i −0.559704 0.828693i \(-0.689085\pi\)
0.437817 + 0.899064i \(0.355752\pi\)
\(138\) −5.08892 2.93809i −0.433198 0.250107i
\(139\) 2.81778 0.239001 0.119500 0.992834i \(-0.461871\pi\)
0.119500 + 0.992834i \(0.461871\pi\)
\(140\) −2.08629 1.23738i −0.176324 0.104578i
\(141\) 5.26115i 0.443069i
\(142\) −9.19448 + 15.9253i −0.771584 + 1.33642i
\(143\) 19.7206 + 2.20124i 1.64912 + 0.184077i
\(144\) 2.33687 + 4.04758i 0.194739 + 0.337298i
\(145\) 1.67243 + 0.965580i 0.138888 + 0.0801871i
\(146\) 11.5770 0.958118
\(147\) −3.64128 + 5.97838i −0.300328 + 0.493089i
\(148\) 0.408340i 0.0335653i
\(149\) 5.72160 + 3.30336i 0.468731 + 0.270622i 0.715709 0.698399i \(-0.246104\pi\)
−0.246977 + 0.969021i \(0.579437\pi\)
\(150\) 0.578748 0.334140i 0.0472546 0.0272824i
\(151\) 16.0349 9.25774i 1.30490 0.753384i 0.323660 0.946174i \(-0.395087\pi\)
0.981240 + 0.192789i \(0.0617534\pi\)
\(152\) −4.52571 + 7.83875i −0.367083 + 0.635807i
\(153\) −7.43460 −0.601051
\(154\) −11.5761 + 19.5178i −0.932827 + 1.57279i
\(155\) −6.47443 −0.520039
\(156\) −1.41644 + 0.619740i −0.113406 + 0.0496189i
\(157\) 0.00564763 + 0.00978198i 0.000450730 + 0.000780687i 0.866251 0.499610i \(-0.166523\pi\)
−0.865800 + 0.500390i \(0.833190\pi\)
\(158\) 20.6342 11.9132i 1.64157 0.947761i
\(159\) 6.49807 11.2550i 0.515331 0.892579i
\(160\) −5.10255 −0.403392
\(161\) −4.88619 8.69723i −0.385086 0.685437i
\(162\) 1.55846i 0.122444i
\(163\) 1.58260 + 0.913712i 0.123958 + 0.0715674i 0.560697 0.828021i \(-0.310533\pi\)
−0.436739 + 0.899588i \(0.643867\pi\)
\(164\) 1.80548 1.04239i 0.140984 0.0813973i
\(165\) 5.88332 + 10.1902i 0.458016 + 0.793307i
\(166\) 8.16892 14.1490i 0.634031 1.09817i
\(167\) 9.06078i 0.701145i 0.936536 + 0.350572i \(0.114013\pi\)
−0.936536 + 0.350572i \(0.885987\pi\)
\(168\) −0.0760136 + 6.47806i −0.00586458 + 0.499793i
\(169\) 3.85762 + 12.4145i 0.296740 + 0.954958i
\(170\) 12.3862 21.4536i 0.949979 1.64541i
\(171\) −3.20126 + 1.84825i −0.244807 + 0.141339i
\(172\) 1.04921 + 1.81728i 0.0800012 + 0.138566i
\(173\) 3.12811 5.41805i 0.237826 0.411927i −0.722264 0.691617i \(-0.756899\pi\)
0.960090 + 0.279690i \(0.0902318\pi\)
\(174\) 1.40767i 0.106715i
\(175\) 1.13444 + 0.0133115i 0.0857556 + 0.00100626i
\(176\) 25.7219i 1.93886i
\(177\) 7.30419 + 4.21708i 0.549017 + 0.316975i
\(178\) −4.04645 7.00866i −0.303294 0.525321i
\(179\) −0.191591 0.331845i −0.0143202 0.0248033i 0.858777 0.512350i \(-0.171225\pi\)
−0.873097 + 0.487547i \(0.837892\pi\)
\(180\) −0.793977 0.458403i −0.0591795 0.0341673i
\(181\) 10.0096 0.744011 0.372005 0.928231i \(-0.378670\pi\)
0.372005 + 0.928231i \(0.378670\pi\)
\(182\) −14.7547 1.82245i −1.09369 0.135089i
\(183\) −3.62811 −0.268198
\(184\) −7.99568 4.61631i −0.589449 0.340319i
\(185\) 1.01799 + 1.76321i 0.0748442 + 0.129634i
\(186\) −2.35968 4.08709i −0.173020 0.299680i
\(187\) −35.4345 20.4581i −2.59122 1.49604i
\(188\) 2.25602i 0.164537i
\(189\) −1.34967 + 2.27561i −0.0981740 + 0.165526i
\(190\) 12.3169i 0.893563i
\(191\) 5.29331 9.16828i 0.383011 0.663394i −0.608480 0.793569i \(-0.708221\pi\)
0.991491 + 0.130175i \(0.0415540\pi\)
\(192\) 2.81406 + 4.87409i 0.203087 + 0.351757i
\(193\) 6.56628 3.79104i 0.472651 0.272885i −0.244698 0.969599i \(-0.578689\pi\)
0.717349 + 0.696714i \(0.245355\pi\)
\(194\) 5.50289 9.53129i 0.395085 0.684307i
\(195\) −4.57119 + 6.20723i −0.327350 + 0.444509i
\(196\) 1.56141 2.56358i 0.111529 0.183113i
\(197\) 5.77227i 0.411257i 0.978630 + 0.205628i \(0.0659238\pi\)
−0.978630 + 0.205628i \(0.934076\pi\)
\(198\) −4.28849 + 7.42788i −0.304770 + 0.527877i
\(199\) −12.8653 22.2834i −0.911999 1.57963i −0.811236 0.584718i \(-0.801205\pi\)
−0.100763 0.994910i \(-0.532128\pi\)
\(200\) 0.909325 0.524999i 0.0642990 0.0371230i
\(201\) −1.52883 0.882669i −0.107835 0.0622587i
\(202\) 15.7535i 1.10841i
\(203\) −1.21908 + 2.05542i −0.0855624 + 0.144262i
\(204\) 3.18801 0.223205
\(205\) 5.19738 9.00212i 0.363001 0.628736i
\(206\) 16.0117 9.24434i 1.11559 0.644084i
\(207\) −1.88525 3.26535i −0.131034 0.226957i
\(208\) −15.4384 + 6.75478i −1.07046 + 0.468360i
\(209\) −20.3436 −1.40720
\(210\) −4.31800 7.68588i −0.297971 0.530376i
\(211\) 2.62646 0.180813 0.0904065 0.995905i \(-0.471183\pi\)
0.0904065 + 0.995905i \(0.471183\pi\)
\(212\) −2.78642 + 4.82623i −0.191372 + 0.331467i
\(213\) −10.2186 + 5.89971i −0.700167 + 0.404242i
\(214\) −15.5991 + 9.00612i −1.06633 + 0.615646i
\(215\) 9.06095 + 5.23134i 0.617952 + 0.356775i
\(216\) 2.44865i 0.166609i
\(217\) 0.0940053 8.01136i 0.00638150 0.543846i
\(218\) −19.3381 −1.30974
\(219\) 6.43323 + 3.71423i 0.434718 + 0.250984i
\(220\) −2.52281 4.36964i −0.170088 0.294601i
\(221\) 2.97363 26.6404i 0.200028 1.79203i
\(222\) −0.742038 + 1.28525i −0.0498023 + 0.0862601i
\(223\) 6.46813i 0.433138i −0.976267 0.216569i \(-0.930513\pi\)
0.976267 0.216569i \(-0.0694866\pi\)
\(224\) 0.0740863 6.31381i 0.00495010 0.421859i
\(225\) 0.428808 0.0285872
\(226\) 6.87373 + 3.96855i 0.457234 + 0.263984i
\(227\) 6.18745 3.57233i 0.410675 0.237104i −0.280404 0.959882i \(-0.590469\pi\)
0.691080 + 0.722778i \(0.257135\pi\)
\(228\) 1.37272 0.792543i 0.0909109 0.0524875i
\(229\) 11.2457 + 6.49269i 0.743134 + 0.429049i 0.823208 0.567740i \(-0.192182\pi\)
−0.0800736 + 0.996789i \(0.525516\pi\)
\(230\) 12.5635 0.828412
\(231\) −12.6946 + 7.13197i −0.835245 + 0.469249i
\(232\) 2.21172i 0.145206i
\(233\) −9.85968 + 17.0775i −0.645929 + 1.11878i 0.338157 + 0.941090i \(0.390197\pi\)
−0.984086 + 0.177693i \(0.943137\pi\)
\(234\) −5.58444 0.623342i −0.365066 0.0407491i
\(235\) −5.62426 9.74150i −0.366886 0.635466i
\(236\) −3.13209 1.80831i −0.203882 0.117711i
\(237\) 15.2884 0.993085
\(238\) 26.3664 + 15.6380i 1.70908 + 1.01366i
\(239\) 20.8752i 1.35031i −0.737677 0.675153i \(-0.764077\pi\)
0.737677 0.675153i \(-0.235923\pi\)
\(240\) −8.65386 4.99631i −0.558604 0.322510i
\(241\) 14.8824 8.59237i 0.958661 0.553483i 0.0629006 0.998020i \(-0.479965\pi\)
0.895761 + 0.444536i \(0.146632\pi\)
\(242\) −26.0329 + 15.0301i −1.67346 + 0.966171i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 1.55576 0.0995975
\(245\) 0.351180 14.9621i 0.0224360 0.955895i
\(246\) 7.57698 0.483091
\(247\) −5.34241 12.2103i −0.339930 0.776924i
\(248\) −3.70752 6.42160i −0.235427 0.407772i
\(249\) 9.07880 5.24165i 0.575346 0.332176i
\(250\) −9.04452 + 15.6656i −0.572026 + 0.990778i
\(251\) −22.3931 −1.41344 −0.706720 0.707493i \(-0.749826\pi\)
−0.706720 + 0.707493i \(0.749826\pi\)
\(252\) 0.578748 0.975798i 0.0364577 0.0614695i
\(253\) 20.7509i 1.30460i
\(254\) −25.6463 14.8069i −1.60919 0.929068i
\(255\) 13.7658 7.94771i 0.862050 0.497705i
\(256\) −4.92605 8.53218i −0.307878 0.533261i
\(257\) −10.2903 + 17.8233i −0.641890 + 1.11179i 0.343120 + 0.939292i \(0.388516\pi\)
−0.985010 + 0.172495i \(0.944817\pi\)
\(258\) 7.62649i 0.474805i
\(259\) −2.19655 + 1.23405i −0.136487 + 0.0766798i
\(260\) 1.96016 2.66171i 0.121564 0.165072i
\(261\) −0.451620 + 0.782230i −0.0279546 + 0.0484188i
\(262\) 14.7796 8.53299i 0.913085 0.527170i
\(263\) −2.52474 4.37298i −0.155682 0.269649i 0.777625 0.628728i \(-0.216424\pi\)
−0.933307 + 0.359079i \(0.883091\pi\)
\(264\) −6.73804 + 11.6706i −0.414698 + 0.718278i
\(265\) 27.7862i 1.70689i
\(266\) 15.2407 + 0.178835i 0.934470 + 0.0109651i
\(267\) 5.19287i 0.317799i
\(268\) 0.655573 + 0.378495i 0.0400455 + 0.0231203i
\(269\) 7.45079 + 12.9052i 0.454283 + 0.786841i 0.998647 0.0520082i \(-0.0165622\pi\)
−0.544364 + 0.838849i \(0.683229\pi\)
\(270\) −1.66602 2.88564i −0.101391 0.175614i
\(271\) −5.41883 3.12856i −0.329170 0.190047i 0.326302 0.945265i \(-0.394197\pi\)
−0.655473 + 0.755219i \(0.727531\pi\)
\(272\) 34.7474 2.10687
\(273\) −7.61435 5.74644i −0.460842 0.347791i
\(274\) 2.56734 0.155099
\(275\) 2.04376 + 1.17997i 0.123244 + 0.0711548i
\(276\) 0.808409 + 1.40021i 0.0486605 + 0.0842825i
\(277\) 1.45934 + 2.52764i 0.0876830 + 0.151871i 0.906531 0.422139i \(-0.138720\pi\)
−0.818848 + 0.574010i \(0.805387\pi\)
\(278\) −3.80307 2.19570i −0.228093 0.131689i
\(279\) 3.02822i 0.181295i
\(280\) −6.78441 12.0760i −0.405446 0.721678i
\(281\) 3.53952i 0.211150i 0.994411 + 0.105575i \(0.0336683\pi\)
−0.994411 + 0.105575i \(0.966332\pi\)
\(282\) 4.09965 7.10081i 0.244131 0.422847i
\(283\) 13.2715 + 22.9869i 0.788907 + 1.36643i 0.926637 + 0.375957i \(0.122686\pi\)
−0.137731 + 0.990470i \(0.543981\pi\)
\(284\) 4.38181 2.52984i 0.260013 0.150118i
\(285\) 3.95162 6.84441i 0.234074 0.405428i
\(286\) −24.9010 18.3379i −1.47243 1.08434i
\(287\) 11.0636 + 6.56186i 0.653065 + 0.387334i
\(288\) 2.38656i 0.140629i
\(289\) −19.1366 + 33.1456i −1.12568 + 1.94974i
\(290\) −1.50482 2.60643i −0.0883661 0.153055i
\(291\) 6.11583 3.53097i 0.358516 0.206989i
\(292\) −2.75862 1.59269i −0.161436 0.0932051i
\(293\) 3.08146i 0.180021i 0.995941 + 0.0900105i \(0.0286901\pi\)
−0.995941 + 0.0900105i \(0.971310\pi\)
\(294\) 9.57307 5.23143i 0.558313 0.305103i
\(295\) −18.0325 −1.04989
\(296\) −1.16588 + 2.01937i −0.0677656 + 0.117374i
\(297\) −4.76616 + 2.75174i −0.276561 + 0.159672i
\(298\) −5.14817 8.91690i −0.298226 0.516542i
\(299\) 12.4548 5.44936i 0.720277 0.315145i
\(300\) −0.183876 −0.0106161
\(301\) −6.60474 + 11.1359i −0.380691 + 0.641863i
\(302\) −28.8557 −1.66046
\(303\) −5.05417 + 8.75407i −0.290354 + 0.502908i
\(304\) 14.9619 8.63823i 0.858121 0.495437i
\(305\) 6.71779 3.87852i 0.384659 0.222083i
\(306\) 10.0342 + 5.79327i 0.573619 + 0.331179i
\(307\) 25.3997i 1.44963i −0.688941 0.724817i \(-0.741924\pi\)
0.688941 0.724817i \(-0.258076\pi\)
\(308\) 5.44355 3.05824i 0.310175 0.174260i
\(309\) 11.8634 0.674885
\(310\) 8.73834 + 5.04508i 0.496304 + 0.286541i
\(311\) 10.4629 + 18.1222i 0.593295 + 1.02762i 0.993785 + 0.111315i \(0.0355064\pi\)
−0.400491 + 0.916301i \(0.631160\pi\)
\(312\) −8.77423 0.979390i −0.496743 0.0554470i
\(313\) 6.35583 11.0086i 0.359253 0.622244i −0.628584 0.777742i \(-0.716365\pi\)
0.987836 + 0.155498i \(0.0496983\pi\)
\(314\) 0.0176032i 0.000993408i
\(315\) 0.0663713 5.65632i 0.00373960 0.318697i
\(316\) −6.55576 −0.368790
\(317\) 11.1455 + 6.43484i 0.625992 + 0.361417i 0.779198 0.626778i \(-0.215627\pi\)
−0.153206 + 0.988194i \(0.548960\pi\)
\(318\) −17.5405 + 10.1270i −0.983622 + 0.567894i
\(319\) −4.30499 + 2.48549i −0.241033 + 0.139161i
\(320\) −10.4210 6.01655i −0.582550 0.336335i
\(321\) −11.5577 −0.645088
\(322\) −0.182415 + 15.5458i −0.0101656 + 0.866336i
\(323\) 27.4820i 1.52914i
\(324\) 0.214404 0.371358i 0.0119113 0.0206310i
\(325\) −0.171511 + 1.53655i −0.00951372 + 0.0852322i
\(326\) −1.42399 2.46642i −0.0788673 0.136602i
\(327\) −10.7460 6.20423i −0.594257 0.343094i
\(328\) 11.9049 0.657338
\(329\) 12.1356 6.81792i 0.669059 0.375884i
\(330\) 18.3379i 1.00947i
\(331\) 23.7769 + 13.7276i 1.30689 + 0.754536i 0.981577 0.191068i \(-0.0611953\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(332\) −3.89306 + 2.24766i −0.213659 + 0.123356i
\(333\) −0.824689 + 0.476134i −0.0451927 + 0.0260920i
\(334\) 7.06045 12.2291i 0.386331 0.669144i
\(335\) 3.77435 0.206215
\(336\) 6.30800 10.6356i 0.344130 0.580220i
\(337\) 16.5012 0.898875 0.449438 0.893312i \(-0.351624\pi\)
0.449438 + 0.893312i \(0.351624\pi\)
\(338\) 4.46724 19.7614i 0.242986 1.07488i
\(339\) 2.54645 + 4.41058i 0.138304 + 0.239550i
\(340\) −5.90290 + 3.40804i −0.320129 + 0.184827i
\(341\) 8.33287 14.4330i 0.451250 0.781589i
\(342\) 5.76086 0.311511
\(343\) 18.5088 + 0.651786i 0.999381 + 0.0351931i
\(344\) 11.9827i 0.646063i
\(345\) 6.98143 + 4.03073i 0.375867 + 0.217007i
\(346\) −8.44383 + 4.87505i −0.453943 + 0.262084i
\(347\) 4.41936 + 7.65455i 0.237244 + 0.410918i 0.959922 0.280266i \(-0.0904227\pi\)
−0.722679 + 0.691184i \(0.757089\pi\)
\(348\) 0.193658 0.335426i 0.0103812 0.0179807i
\(349\) 27.2777i 1.46014i 0.683370 + 0.730072i \(0.260514\pi\)
−0.683370 + 0.730072i \(0.739486\pi\)
\(350\) −1.52075 0.901958i −0.0812873 0.0482117i
\(351\) −2.90324 2.13803i −0.154964 0.114120i
\(352\) 6.56720 11.3747i 0.350033 0.606275i
\(353\) 2.03841 1.17687i 0.108493 0.0626387i −0.444771 0.895644i \(-0.646715\pi\)
0.553265 + 0.833005i \(0.313382\pi\)
\(354\) −6.57216 11.3833i −0.349306 0.605016i
\(355\) 12.6138 21.8477i 0.669470 1.15956i
\(356\) 2.22674i 0.118017i
\(357\) 9.63450 + 17.1490i 0.509912 + 0.907622i
\(358\) 0.597175i 0.0315617i
\(359\) 3.01674 + 1.74172i 0.159218 + 0.0919244i 0.577492 0.816396i \(-0.304032\pi\)
−0.418274 + 0.908321i \(0.637365\pi\)
\(360\) −2.61764 4.53389i −0.137962 0.238957i
\(361\) −2.66795 4.62103i −0.140419 0.243212i
\(362\) −13.5097 7.79983i −0.710054 0.409950i
\(363\) −19.2884 −1.01238
\(364\) 3.26509 + 2.46412i 0.171137 + 0.129155i
\(365\) −15.8823 −0.831318
\(366\) 4.89675 + 2.82714i 0.255957 + 0.147777i
\(367\) −2.91178 5.04335i −0.151994 0.263261i 0.779967 0.625821i \(-0.215236\pi\)
−0.931960 + 0.362560i \(0.881903\pi\)
\(368\) 8.81116 + 15.2614i 0.459314 + 0.795555i
\(369\) 4.21047 + 2.43091i 0.219188 + 0.126548i
\(370\) 3.17301i 0.164957i
\(371\) −34.3822 0.403441i −1.78503 0.0209456i
\(372\) 1.29852i 0.0673252i
\(373\) −4.36340 + 7.55764i −0.225928 + 0.391320i −0.956598 0.291412i \(-0.905875\pi\)
0.730669 + 0.682732i \(0.239208\pi\)
\(374\) 31.8832 + 55.2233i 1.64864 + 2.85553i
\(375\) −10.0519 + 5.80349i −0.519080 + 0.299691i
\(376\) 6.44134 11.1567i 0.332187 0.575365i
\(377\) −2.62233 1.93116i −0.135057 0.0994598i
\(378\) 3.59483 2.01961i 0.184898 0.103878i
\(379\) 18.8676i 0.969162i 0.874747 + 0.484581i \(0.161028\pi\)
−0.874747 + 0.484581i \(0.838972\pi\)
\(380\) −1.69448 + 2.93493i −0.0869252 + 0.150559i
\(381\) −9.50097 16.4562i −0.486749 0.843074i
\(382\) −14.2884 + 8.24943i −0.731060 + 0.422078i
\(383\) −12.4544 7.19054i −0.636389 0.367420i 0.146833 0.989161i \(-0.453092\pi\)
−0.783222 + 0.621742i \(0.786425\pi\)
\(384\) 13.5443i 0.691181i
\(385\) 15.8811 26.7763i 0.809374 1.36465i
\(386\) −11.8164 −0.601439
\(387\) −2.44680 + 4.23798i −0.124378 + 0.215429i
\(388\) −2.62251 + 1.51411i −0.133138 + 0.0768672i
\(389\) −1.37671 2.38453i −0.0698019 0.120900i 0.829012 0.559231i \(-0.188903\pi\)
−0.898814 + 0.438330i \(0.855570\pi\)
\(390\) 11.0065 4.81569i 0.557334 0.243852i
\(391\) −28.0321 −1.41765
\(392\) 15.0411 8.21959i 0.759692 0.415152i
\(393\) 10.9505 0.552381
\(394\) 4.49793 7.79065i 0.226603 0.392487i
\(395\) −28.3078 + 16.3435i −1.42432 + 0.822332i
\(396\) 2.04376 1.17997i 0.102703 0.0592956i
\(397\) 8.62315 + 4.97858i 0.432783 + 0.249868i 0.700532 0.713621i \(-0.252946\pi\)
−0.267748 + 0.963489i \(0.586280\pi\)
\(398\) 40.1003i 2.01005i
\(399\) 8.41178 + 4.98905i 0.421116 + 0.249765i
\(400\) −2.00413 −0.100207
\(401\) −1.52399 0.879875i −0.0761043 0.0439388i 0.461465 0.887158i \(-0.347324\pi\)
−0.537569 + 0.843220i \(0.680657\pi\)
\(402\) 1.37561 + 2.38262i 0.0686090 + 0.118834i
\(403\) 10.8510 + 1.21120i 0.540527 + 0.0603343i
\(404\) 2.16727 3.75381i 0.107825 0.186759i
\(405\) 2.13803i 0.106240i
\(406\) 3.24700 1.82420i 0.161146 0.0905334i
\(407\) −5.24080 −0.259777
\(408\) 15.7657 + 9.10234i 0.780520 + 0.450633i
\(409\) −13.5151 + 7.80292i −0.668277 + 0.385830i −0.795423 0.606054i \(-0.792751\pi\)
0.127147 + 0.991884i \(0.459418\pi\)
\(410\) −14.0295 + 8.09992i −0.692867 + 0.400027i
\(411\) 1.42665 + 0.823676i 0.0703714 + 0.0406289i
\(412\) −5.08712 −0.250624
\(413\) 0.261822 22.3131i 0.0128834 1.09796i
\(414\) 5.87618i 0.288799i
\(415\) −11.2068 + 19.4108i −0.550122 + 0.952839i
\(416\) 8.55175 + 0.954557i 0.419284 + 0.0468010i
\(417\) −1.40889 2.44027i −0.0689936 0.119500i
\(418\) 27.4572 + 15.8524i 1.34297 + 0.775366i
\(419\) 5.58634 0.272911 0.136455 0.990646i \(-0.456429\pi\)
0.136455 + 0.990646i \(0.456429\pi\)
\(420\) −0.0284605 + 2.42547i −0.00138873 + 0.118351i
\(421\) 12.3229i 0.600582i −0.953848 0.300291i \(-0.902916\pi\)
0.953848 0.300291i \(-0.0970838\pi\)
\(422\) −3.54485 2.04662i −0.172561 0.0996280i
\(423\) 4.55629 2.63057i 0.221534 0.127903i
\(424\) −27.5595 + 15.9115i −1.33841 + 0.772730i
\(425\) 1.59401 2.76090i 0.0773206 0.133923i
\(426\) 18.3890 0.890948
\(427\) 4.70167 + 8.36879i 0.227530 + 0.404994i
\(428\) 4.95603 0.239559
\(429\) −7.95398 18.1792i −0.384022 0.877699i
\(430\) −8.15285 14.1212i −0.393166 0.680983i
\(431\) −0.338321 + 0.195330i −0.0162964 + 0.00940871i −0.508126 0.861283i \(-0.669662\pi\)
0.491830 + 0.870691i \(0.336328\pi\)
\(432\) 2.33687 4.04758i 0.112433 0.194739i
\(433\) 21.9621 1.05543 0.527715 0.849421i \(-0.323049\pi\)
0.527715 + 0.849421i \(0.323049\pi\)
\(434\) −6.36958 + 10.7394i −0.305750 + 0.515509i
\(435\) 1.93116i 0.0925921i
\(436\) 4.60798 + 2.66042i 0.220682 + 0.127411i
\(437\) −12.0703 + 6.96882i −0.577403 + 0.333364i
\(438\) −5.78849 10.0260i −0.276585 0.479059i
\(439\) 0.180296 0.312281i 0.00860504 0.0149044i −0.861691 0.507434i \(-0.830594\pi\)
0.870296 + 0.492529i \(0.163928\pi\)
\(440\) 28.8123i 1.37357i
\(441\) 6.99807 + 0.164253i 0.333242 + 0.00782159i
\(442\) −24.7724 + 33.6385i −1.17830 + 1.60002i
\(443\) 18.2334 31.5811i 0.866293 1.50046i 0.000535780 1.00000i \(-0.499829\pi\)
0.865757 0.500464i \(-0.166837\pi\)
\(444\) 0.353633 0.204170i 0.0167827 0.00968948i
\(445\) 5.55127 + 9.61509i 0.263156 + 0.455799i
\(446\) −5.04017 + 8.72983i −0.238659 + 0.413369i
\(447\) 6.60673i 0.312488i
\(448\) 7.59609 12.8074i 0.358881 0.605092i
\(449\) 25.8905i 1.22185i 0.791689 + 0.610924i \(0.209202\pi\)
−0.791689 + 0.610924i \(0.790798\pi\)
\(450\) −0.578748 0.334140i −0.0272824 0.0157515i
\(451\) 13.3785 + 23.1722i 0.629969 + 1.09114i
\(452\) −1.09194 1.89129i −0.0513604 0.0889589i
\(453\) −16.0349 9.25774i −0.753384 0.434967i
\(454\) −11.1347 −0.522576
\(455\) 20.2417 + 2.50020i 0.948947 + 0.117211i
\(456\) 9.05141 0.423871
\(457\) −34.8434 20.1168i −1.62990 0.941026i −0.984120 0.177506i \(-0.943197\pi\)
−0.645784 0.763520i \(-0.723470\pi\)
\(458\) −10.1186 17.5259i −0.472812 0.818934i
\(459\) 3.71730 + 6.43855i 0.173509 + 0.300526i
\(460\) −2.99369 1.72841i −0.139581 0.0805874i
\(461\) 26.6895i 1.24305i −0.783393 0.621527i \(-0.786513\pi\)
0.783393 0.621527i \(-0.213487\pi\)
\(462\) 22.6910 + 0.266256i 1.05568 + 0.0123874i
\(463\) 4.61949i 0.214686i −0.994222 0.107343i \(-0.965766\pi\)
0.994222 0.107343i \(-0.0342343\pi\)
\(464\) 2.11076 3.65594i 0.0979894 0.169723i
\(465\) 3.23722 + 5.60702i 0.150122 + 0.260019i
\(466\) 26.6146 15.3660i 1.23290 0.711814i
\(467\) −8.57973 + 14.8605i −0.397023 + 0.687664i −0.993357 0.115073i \(-0.963290\pi\)
0.596334 + 0.802736i \(0.296623\pi\)
\(468\) 1.24493 + 0.916805i 0.0575470 + 0.0423793i
\(469\) −0.0548016 + 4.67032i −0.00253050 + 0.215655i
\(470\) 17.5304i 0.808617i
\(471\) 0.00564763 0.00978198i 0.000260229 0.000450730i
\(472\) −10.3261 17.8854i −0.475298 0.823241i
\(473\) −23.3237 + 13.4659i −1.07242 + 0.619164i
\(474\) −20.6342 11.9132i −0.947761 0.547190i
\(475\) 1.58509i 0.0727287i
\(476\) −4.13134 7.35363i −0.189360 0.337053i
\(477\) −12.9961 −0.595053
\(478\) −16.2666 + 28.1747i −0.744019 + 1.28868i
\(479\) 24.7932 14.3144i 1.13283 0.654040i 0.188185 0.982134i \(-0.439739\pi\)
0.944645 + 0.328093i \(0.106406\pi\)
\(480\) 2.55127 + 4.41894i 0.116449 + 0.201696i
\(481\) −1.37628 3.14555i −0.0627529 0.143425i
\(482\) −26.7818 −1.21988
\(483\) −5.08892 + 8.58018i −0.231554 + 0.390412i
\(484\) 8.27099 0.375954
\(485\) −7.54935 + 13.0759i −0.342798 + 0.593744i
\(486\) 1.34967 0.779232i 0.0612222 0.0353467i
\(487\) −13.6192 + 7.86303i −0.617144 + 0.356308i −0.775756 0.631033i \(-0.782631\pi\)
0.158612 + 0.987341i \(0.449298\pi\)
\(488\) 7.69374 + 4.44198i 0.348279 + 0.201079i
\(489\) 1.82742i 0.0826390i
\(490\) −12.1329 + 19.9203i −0.548110 + 0.899906i
\(491\) 34.2012 1.54348 0.771740 0.635938i \(-0.219387\pi\)
0.771740 + 0.635938i \(0.219387\pi\)
\(492\) −1.80548 1.04239i −0.0813973 0.0469948i
\(493\) 3.35762 + 5.81556i 0.151219 + 0.261920i
\(494\) −2.30418 + 20.6429i −0.103670 + 0.928766i
\(495\) 5.88332 10.1902i 0.264436 0.458016i
\(496\) 14.1531i 0.635493i
\(497\) 26.8509 + 15.9253i 1.20443 + 0.714348i
\(498\) −16.3378 −0.732116
\(499\) 11.9087 + 6.87551i 0.533108 + 0.307790i 0.742281 0.670089i \(-0.233744\pi\)
−0.209173 + 0.977879i \(0.567077\pi\)
\(500\) 4.31035 2.48858i 0.192765 0.111293i
\(501\) 7.84687 4.53039i 0.350572 0.202403i
\(502\) 30.2233 + 17.4494i 1.34893 + 0.778805i
\(503\) −31.7971 −1.41776 −0.708882 0.705327i \(-0.750800\pi\)
−0.708882 + 0.705327i \(0.750800\pi\)
\(504\) 5.64817 3.17320i 0.251590 0.141346i
\(505\) 21.6120i 0.961720i
\(506\) −16.1697 + 28.0068i −0.718833 + 1.24505i
\(507\) 8.82243 9.54802i 0.391818 0.424043i
\(508\) 4.07409 + 7.05652i 0.180758 + 0.313083i
\(509\) −22.4013 12.9334i −0.992921 0.573263i −0.0867751 0.996228i \(-0.527656\pi\)
−0.906146 + 0.422964i \(0.860989\pi\)
\(510\) −24.7724 −1.09694
\(511\) 0.230603 19.6525i 0.0102013 0.869376i
\(512\) 11.7345i 0.518597i
\(513\) 3.20126 + 1.84825i 0.141339 + 0.0816022i
\(514\) 27.7769 16.0370i 1.22519 0.707363i
\(515\) −21.9662 + 12.6822i −0.967946 + 0.558844i
\(516\) 1.04921 1.81728i 0.0461887 0.0800012i
\(517\) 28.9547 1.27342
\(518\) 3.92622 + 0.0460703i 0.172508 + 0.00202421i
\(519\) −6.25623 −0.274618
\(520\) 17.2933 7.56637i 0.758360 0.331807i
\(521\) −0.391998 0.678960i −0.0171737 0.0297458i 0.857311 0.514799i \(-0.172134\pi\)
−0.874485 + 0.485053i \(0.838800\pi\)
\(522\) 1.21908 0.703834i 0.0533575 0.0308060i
\(523\) 17.6130 30.5065i 0.770161 1.33396i −0.167313 0.985904i \(-0.553509\pi\)
0.937474 0.348054i \(-0.113158\pi\)
\(524\) −4.69567 −0.205131
\(525\) −0.555692 0.989110i −0.0242524 0.0431683i
\(526\) 7.86943i 0.343123i
\(527\) −19.4973 11.2568i −0.849317 0.490353i
\(528\) 22.2758 12.8609i 0.969429 0.559700i
\(529\) 4.39167 + 7.60660i 0.190942 + 0.330722i
\(530\) 21.6519 37.5022i 0.940498 1.62899i
\(531\) 8.43415i 0.366011i
\(532\) −3.60704 2.13934i −0.156385 0.0927522i
\(533\) −10.3948 + 14.1151i −0.450247 + 0.611391i
\(534\) −4.04645 + 7.00866i −0.175107 + 0.303294i
\(535\) 21.4001 12.3554i 0.925209 0.534170i
\(536\) 2.16134 + 3.74356i 0.0933558 + 0.161697i
\(537\) −0.191591 + 0.331845i −0.00826776 + 0.0143202i
\(538\) 23.2236i 1.00124i
\(539\) 32.9019 + 20.0398i 1.41719 + 0.863173i
\(540\) 0.916805i 0.0394530i
\(541\) 33.7367 + 19.4779i 1.45045 + 0.837419i 0.998507 0.0546260i \(-0.0173967\pi\)
0.451946 + 0.892045i \(0.350730\pi\)
\(542\) 4.87575 + 8.44504i 0.209431 + 0.362746i
\(543\) −5.00482 8.66860i −0.214777 0.372005i
\(544\) −15.3660 8.87155i −0.658811 0.380365i
\(545\) 26.5297 1.13641
\(546\) 5.79904 + 13.6891i 0.248176 + 0.585841i
\(547\) −14.5121 −0.620491 −0.310246 0.950656i \(-0.600411\pi\)
−0.310246 + 0.950656i \(0.600411\pi\)
\(548\) −0.611758 0.353199i −0.0261330 0.0150879i
\(549\) 1.81406 + 3.14204i 0.0774221 + 0.134099i
\(550\) −1.83894 3.18513i −0.0784125 0.135814i
\(551\) 2.89151 + 1.66941i 0.123182 + 0.0711194i
\(552\) 9.23261i 0.392966i
\(553\) −19.8122 35.2649i −0.842500 1.49962i
\(554\) 4.54864i 0.193253i
\(555\) 1.01799 1.76321i 0.0432113 0.0748442i
\(556\) 0.604142 + 1.04640i 0.0256213 + 0.0443774i
\(557\) 3.15836 1.82348i 0.133824 0.0772634i −0.431593 0.902068i \(-0.642048\pi\)
0.565417 + 0.824805i \(0.308715\pi\)
\(558\) −2.35968 + 4.08709i −0.0998933 + 0.173020i
\(559\) −14.2073 10.4627i −0.600905 0.442524i
\(560\) −0.310202 + 26.4362i −0.0131084 + 1.11713i
\(561\) 40.9162i 1.72748i
\(562\) 2.75810 4.77717i 0.116344 0.201513i
\(563\) −0.134670 0.233255i −0.00567566 0.00983053i 0.863174 0.504907i \(-0.168473\pi\)
−0.868849 + 0.495077i \(0.835140\pi\)
\(564\) −1.95377 + 1.12801i −0.0822686 + 0.0474978i
\(565\) −9.42998 5.44440i −0.396722 0.229048i
\(566\) 41.3662i 1.73875i
\(567\) 2.64557 + 0.0310431i 0.111103 + 0.00130369i
\(568\) 28.8926 1.21231
\(569\) −22.8066 + 39.5022i −0.956103 + 1.65602i −0.224280 + 0.974525i \(0.572003\pi\)
−0.731823 + 0.681495i \(0.761330\pi\)
\(570\) −10.6668 + 6.15846i −0.446781 + 0.257949i
\(571\) 10.7183 + 18.5646i 0.448545 + 0.776903i 0.998292 0.0584283i \(-0.0186089\pi\)
−0.549746 + 0.835332i \(0.685276\pi\)
\(572\) 3.41073 + 7.79537i 0.142610 + 0.325941i
\(573\) −10.5866 −0.442262
\(574\) −9.81901 17.4775i −0.409838 0.729495i
\(575\) 1.61682 0.0674260
\(576\) 2.81406 4.87409i 0.117252 0.203087i
\(577\) 2.10289 1.21410i 0.0875445 0.0505438i −0.455589 0.890190i \(-0.650571\pi\)
0.543133 + 0.839647i \(0.317238\pi\)
\(578\) 51.6561 29.8237i 2.14861 1.24050i
\(579\) −6.56628 3.79104i −0.272885 0.157550i
\(580\) 0.828096i 0.0343848i
\(581\) −23.8559 14.1490i −0.989709 0.586999i
\(582\) −11.0058 −0.456205
\(583\) −61.9417 35.7621i −2.56536 1.48111i
\(584\) −9.09483 15.7527i −0.376347 0.651852i
\(585\) 7.66121 + 0.855154i 0.316752 + 0.0353563i
\(586\) 2.40117 4.15895i 0.0991916 0.171805i
\(587\) 3.50483i 0.144660i 0.997381 + 0.0723299i \(0.0230434\pi\)
−0.997381 + 0.0723299i \(0.976957\pi\)
\(588\) −3.00083 0.0704331i −0.123752 0.00290461i
\(589\) −11.1938 −0.461232
\(590\) 24.3379 + 14.0515i 1.00198 + 0.578491i
\(591\) 4.99893 2.88613i 0.205628 0.118720i
\(592\) 3.85438 2.22533i 0.158414 0.0914604i
\(593\) −3.28590 1.89711i −0.134936 0.0779051i 0.431013 0.902346i \(-0.358156\pi\)
−0.565948 + 0.824441i \(0.691490\pi\)
\(594\) 8.57698 0.351918
\(595\) −36.1718 21.4536i −1.48290 0.879510i
\(596\) 2.83302i 0.116045i
\(597\) −12.8653 + 22.2834i −0.526543 + 0.911999i
\(598\) −21.0561 2.35031i −0.861048 0.0961113i
\(599\) 2.21344 + 3.83379i 0.0904386 + 0.156644i 0.907696 0.419629i \(-0.137840\pi\)
−0.817257 + 0.576273i \(0.804506\pi\)
\(600\) −0.909325 0.524999i −0.0371230 0.0214330i
\(601\) 0.00578763 0.000236082 0.000118041 1.00000i \(-0.499962\pi\)
0.000118041 1.00000i \(0.499962\pi\)
\(602\) 17.5917 9.88318i 0.716983 0.402808i
\(603\) 1.76534i 0.0718901i
\(604\) 6.87588 + 3.96979i 0.279775 + 0.161528i
\(605\) 35.7142 20.6196i 1.45199 0.838305i
\(606\) 13.6429 7.87673i 0.554205 0.319970i
\(607\) −0.0179917 + 0.0311626i −0.000730261 + 0.00126485i −0.866390 0.499367i \(-0.833566\pi\)
0.865660 + 0.500632i \(0.166899\pi\)
\(608\) −8.82191 −0.357776
\(609\) 2.38959 + 0.0280394i 0.0968309 + 0.00113621i
\(610\) −12.0890 −0.489471
\(611\) 7.60374 + 17.3787i 0.307615 + 0.703067i
\(612\) −1.59401 2.76090i −0.0644338 0.111603i
\(613\) −37.8958 + 21.8792i −1.53060 + 0.883691i −0.531264 + 0.847207i \(0.678283\pi\)
−0.999334 + 0.0364845i \(0.988384\pi\)
\(614\) −19.7922 + 34.2811i −0.798749 + 1.38347i
\(615\) −10.3948 −0.419157
\(616\) 35.6519 + 0.418340i 1.43646 + 0.0168554i
\(617\) 30.0459i 1.20960i −0.796376 0.604802i \(-0.793252\pi\)
0.796376 0.604802i \(-0.206748\pi\)
\(618\) −16.0117 9.24434i −0.644084 0.371862i
\(619\) −27.5160 + 15.8864i −1.10596 + 0.638526i −0.937780 0.347230i \(-0.887122\pi\)
−0.168180 + 0.985756i \(0.553789\pi\)
\(620\) −1.38814 2.40433i −0.0557492 0.0965604i
\(621\) −1.88525 + 3.26535i −0.0756524 + 0.131034i
\(622\) 32.6120i 1.30762i
\(623\) −11.9782 + 6.72945i −0.479895 + 0.269610i
\(624\) 13.5690 + 9.99262i 0.543194 + 0.400025i
\(625\) 11.3360 19.6346i 0.453442 0.785384i
\(626\) −17.1565 + 9.90532i −0.685713 + 0.395896i
\(627\) 10.1718 + 17.6181i 0.406223 + 0.703599i
\(628\) −0.00242175 + 0.00419459i −9.66382e−5 + 0.000167382i
\(629\) 7.07973i 0.282287i
\(630\) −4.49716 + 7.58244i −0.179171 + 0.302092i
\(631\) 19.7990i 0.788185i −0.919071 0.394092i \(-0.871059\pi\)
0.919071 0.394092i \(-0.128941\pi\)
\(632\) −32.4203 18.7179i −1.28961 0.744557i
\(633\) −1.31323 2.27458i −0.0521962 0.0904065i
\(634\) −10.0285 17.3698i −0.398281 0.689843i
\(635\) 35.1838 + 20.3134i 1.39623 + 0.806113i
\(636\) 5.57285 0.220978
\(637\) −3.38760 + 25.0105i −0.134222 + 0.990951i
\(638\) 7.74708 0.306710
\(639\) 10.2186 + 5.89971i 0.404242 + 0.233389i
\(640\) 14.4791 + 25.0786i 0.572337 + 0.991318i
\(641\) −9.10916 15.7775i −0.359790 0.623175i 0.628135 0.778104i \(-0.283818\pi\)
−0.987926 + 0.154929i \(0.950485\pi\)
\(642\) 15.5991 + 9.00612i 0.615646 + 0.355443i
\(643\) 24.7132i 0.974592i 0.873237 + 0.487296i \(0.162017\pi\)
−0.873237 + 0.487296i \(0.837983\pi\)
\(644\) 2.18217 3.67925i 0.0859895 0.144983i
\(645\) 10.4627i 0.411968i
\(646\) 21.4148 37.0915i 0.842555 1.45935i
\(647\) −14.5947 25.2788i −0.573777 0.993810i −0.996173 0.0873994i \(-0.972144\pi\)
0.422397 0.906411i \(-0.361189\pi\)
\(648\) 2.12059 1.22432i 0.0833046 0.0480959i
\(649\) 23.2086 40.1985i 0.911018 1.57793i
\(650\) 1.42881 1.94018i 0.0560424 0.0761001i
\(651\) −6.98504 + 3.92427i −0.273765 + 0.153804i
\(652\) 0.783613i 0.0306887i
\(653\) 11.6140 20.1160i 0.454490 0.787200i −0.544168 0.838976i \(-0.683155\pi\)
0.998659 + 0.0517758i \(0.0164881\pi\)
\(654\) 9.66906 + 16.7473i 0.378090 + 0.654871i
\(655\) −20.2759 + 11.7063i −0.792245 + 0.457403i
\(656\) −19.6786 11.3615i −0.768321 0.443590i
\(657\) 7.42846i 0.289812i
\(658\) −21.6918 0.254532i −0.845636 0.00992269i
\(659\) 48.4141 1.88594 0.942972 0.332872i \(-0.108018\pi\)
0.942972 + 0.332872i \(0.108018\pi\)
\(660\) −2.52281 + 4.36964i −0.0982004 + 0.170088i
\(661\) −22.3988 + 12.9319i −0.871212 + 0.502994i −0.867751 0.497000i \(-0.834435\pi\)
−0.00346104 + 0.999994i \(0.501102\pi\)
\(662\) −21.3939 37.0554i −0.831499 1.44020i
\(663\) −24.5581 + 10.7449i −0.953756 + 0.417299i
\(664\) −25.6699 −0.996185
\(665\) −20.9086 0.245341i −0.810800 0.00951393i
\(666\) 1.48408 0.0575068
\(667\) −1.70283 + 2.94940i −0.0659340 + 0.114201i
\(668\) −3.36480 + 1.94267i −0.130188 + 0.0751640i
\(669\) −5.60156 + 3.23406i −0.216569 + 0.125036i
\(670\) −5.09413 2.94110i −0.196803 0.113624i
\(671\) 19.9673i 0.770828i
\(672\) −5.50496 + 3.09274i −0.212358 + 0.119305i
\(673\) −33.2032 −1.27989 −0.639944 0.768421i \(-0.721043\pi\)
−0.639944 + 0.768421i \(0.721043\pi\)
\(674\) −22.2711 12.8582i −0.857851 0.495280i
\(675\) −0.214404 0.371358i −0.00825241 0.0142936i
\(676\) −3.78312 + 4.09426i −0.145505 + 0.157472i
\(677\) −19.1718 + 33.2066i −0.736833 + 1.27623i 0.217082 + 0.976153i \(0.430346\pi\)
−0.953915 + 0.300078i \(0.902987\pi\)
\(678\) 7.93710i 0.304823i
\(679\) −16.0702 9.53129i −0.616719 0.365777i
\(680\) −38.9223 −1.49260
\(681\) −6.18745 3.57233i −0.237104 0.136892i
\(682\) −22.4932 + 12.9865i −0.861311 + 0.497278i
\(683\) −9.67577 + 5.58631i −0.370233 + 0.213754i −0.673560 0.739132i \(-0.735236\pi\)
0.303327 + 0.952886i \(0.401902\pi\)
\(684\) −1.37272 0.792543i −0.0524875 0.0303036i
\(685\) −3.52210 −0.134572
\(686\) −24.4728 15.3023i −0.934377 0.584246i
\(687\) 12.9854i 0.495423i
\(688\) 11.4357 19.8072i 0.435982 0.755143i
\(689\) 5.19809 46.5691i 0.198032 1.77414i
\(690\) −6.28174 10.8803i −0.239142 0.414206i
\(691\) 11.6191 + 6.70831i 0.442013 + 0.255196i 0.704451 0.709753i \(-0.251193\pi\)
−0.262438 + 0.964949i \(0.584527\pi\)
\(692\) 2.68272 0.101982
\(693\) 12.5238 + 7.42788i 0.475739 + 0.282162i
\(694\) 13.7748i 0.522885i
\(695\) 5.21737 + 3.01225i 0.197906 + 0.114261i
\(696\) 1.91540 1.10586i 0.0726032 0.0419175i
\(697\) 31.3031 18.0729i 1.18569 0.684558i
\(698\) 21.2557 36.8159i 0.804539 1.39350i
\(699\) 19.7194 0.745855
\(700\) 0.238285 + 0.424138i 0.00900632 + 0.0160309i
\(701\) −17.9203 −0.676841 −0.338421 0.940995i \(-0.609893\pi\)
−0.338421 + 0.940995i \(0.609893\pi\)
\(702\) 2.25239 + 5.14794i 0.0850110 + 0.194296i
\(703\) 1.76003 + 3.04846i 0.0663808 + 0.114975i
\(704\) 26.8245 15.4871i 1.01099 0.583693i
\(705\) −5.62426 + 9.74150i −0.211822 + 0.366886i
\(706\) −3.66823 −0.138056
\(707\) 26.7423 + 0.313794i 1.00575 + 0.0118014i
\(708\) 3.61663i 0.135921i
\(709\) 26.4757 + 15.2857i 0.994315 + 0.574068i 0.906561 0.422074i \(-0.138698\pi\)
0.0877539 + 0.996142i \(0.472031\pi\)
\(710\) −34.0489 + 19.6581i −1.27783 + 0.737756i
\(711\) −7.64418 13.2401i −0.286679 0.496543i
\(712\) −6.35776 + 11.0120i −0.238267 + 0.412690i
\(713\) 11.4179i 0.427603i
\(714\) 0.359682 30.6530i 0.0134608 1.14716i
\(715\) 34.1614 + 25.1575i 1.27756 + 0.940837i
\(716\) 0.0821556 0.142298i 0.00307030 0.00531792i
\(717\) −18.0785 + 10.4376i −0.675153 + 0.389800i
\(718\) −2.71440 4.70149i −0.101301 0.175458i
\(719\) 1.77518 3.07470i 0.0662030 0.114667i −0.831024 0.556237i \(-0.812245\pi\)
0.897227 + 0.441570i \(0.145578\pi\)
\(720\) 9.99262i 0.372403i
\(721\) −15.3738 27.3647i −0.572550 1.01912i
\(722\) 8.31581i 0.309482i
\(723\) −14.8824 8.59237i −0.553483 0.319554i
\(724\) 2.14611 + 3.71716i 0.0797594 + 0.138147i
\(725\) −0.193658 0.335426i −0.00719229 0.0124574i
\(726\) 26.0329 + 15.0301i 0.966171 + 0.557819i
\(727\) 8.34296 0.309423 0.154712 0.987960i \(-0.450555\pi\)
0.154712 + 0.987960i \(0.450555\pi\)
\(728\) 9.11141 + 21.5083i 0.337691 + 0.797150i
\(729\) 1.00000 0.0370370
\(730\) 21.4358 + 12.3760i 0.793376 + 0.458056i
\(731\) 18.1910 + 31.5077i 0.672817 + 1.16535i
\(732\) −0.777881 1.34733i −0.0287513 0.0497987i
\(733\) −4.48482 2.58931i −0.165651 0.0956385i 0.414883 0.909875i \(-0.363823\pi\)
−0.580533 + 0.814236i \(0.697156\pi\)
\(734\) 9.07581i 0.334994i
\(735\) −13.1332 + 7.17693i −0.484424 + 0.264725i
\(736\) 8.99852i 0.331690i
\(737\) −4.85776 + 8.41388i −0.178938 + 0.309929i
\(738\) −3.78849 6.56186i −0.139456 0.241545i
\(739\) 5.18606 2.99417i 0.190772 0.110142i −0.401572 0.915828i \(-0.631536\pi\)
0.592344 + 0.805685i \(0.298203\pi\)
\(740\) −0.436523 + 0.756079i −0.0160469 + 0.0277940i
\(741\) −7.90324 + 10.7318i −0.290333 + 0.394243i
\(742\) 46.0902 + 27.3362i 1.69202 + 1.00354i
\(743\) 21.3134i 0.781912i 0.920409 + 0.390956i \(0.127856\pi\)
−0.920409 + 0.390956i \(0.872144\pi\)
\(744\) −3.70752 + 6.42160i −0.135924 + 0.235427i
\(745\) 7.06271 + 12.2330i 0.258758 + 0.448181i
\(746\) 11.7783 6.80020i 0.431234 0.248973i
\(747\) −9.07880 5.24165i −0.332176 0.191782i
\(748\) 17.5452i 0.641515i
\(749\) 14.9776 + 26.6596i 0.547270 + 0.974120i
\(750\) 18.0890 0.660519
\(751\) −7.70605 + 13.3473i −0.281198 + 0.487049i −0.971680 0.236300i \(-0.924065\pi\)
0.690482 + 0.723349i \(0.257398\pi\)
\(752\) −21.2949 + 12.2946i −0.776545 + 0.448339i
\(753\) 11.1966 + 19.3930i 0.408025 + 0.706720i
\(754\) 2.03445 + 4.64983i 0.0740903 + 0.169337i
\(755\) 39.5867 1.44071
\(756\) −1.13444 0.0133115i −0.0412592 0.000484136i
\(757\) −31.6188 −1.14920 −0.574602 0.818433i \(-0.694843\pi\)
−0.574602 + 0.818433i \(0.694843\pi\)
\(758\) 14.7022 25.4650i 0.534008 0.924929i
\(759\) −17.9708 + 10.3754i −0.652298 + 0.376605i
\(760\) −16.7595 + 9.67612i −0.607932 + 0.350990i
\(761\) −6.39264 3.69079i −0.231733 0.133791i 0.379638 0.925135i \(-0.376048\pi\)
−0.611371 + 0.791344i \(0.709382\pi\)
\(762\) 29.6138i 1.07280i
\(763\) −0.385197 + 32.8274i −0.0139451 + 1.18843i
\(764\) 4.53962 0.164238
\(765\) −13.7658 7.94771i −0.497705 0.287350i
\(766\) 11.2062 + 19.4097i 0.404896 + 0.701301i
\(767\) 30.2221 + 3.37342i 1.09126 + 0.121807i
\(768\) −4.92605 + 8.53218i −0.177754 + 0.307878i
\(769\) 40.4051i 1.45704i 0.685022 + 0.728522i \(0.259792\pi\)
−0.685022 + 0.728522i \(0.740208\pi\)
\(770\) −42.2991 + 23.7641i −1.52435 + 0.856398i
\(771\) 20.5806 0.741191
\(772\) 2.81567 + 1.62563i 0.101338 + 0.0585076i
\(773\) 24.1100 13.9199i 0.867176 0.500664i 0.000767212 1.00000i \(-0.499756\pi\)
0.866409 + 0.499335i \(0.166422\pi\)
\(774\) 6.60474 3.81325i 0.237402 0.137064i
\(775\) 1.12455 + 0.649261i 0.0403951 + 0.0233222i
\(776\) −17.2922 −0.620754
\(777\) 2.16699 + 1.28525i 0.0777404 + 0.0461080i
\(778\) 4.29110i 0.153843i
\(779\) 8.98587 15.5640i 0.321952 0.557637i
\(780\) −3.28519 0.366696i −0.117629 0.0131298i
\(781\) 32.4690 + 56.2379i 1.16183 + 2.01235i
\(782\) 37.8341 + 21.8435i 1.35294 + 0.781123i
\(783\) 0.903241 0.0322792
\(784\) −32.7072 0.767678i −1.16811 0.0274171i
\(785\) 0.0241497i 0.000861938i
\(786\) −14.7796 8.53299i −0.527170 0.304362i
\(787\) 19.7457 11.4002i 0.703859 0.406373i −0.104924 0.994480i \(-0.533460\pi\)
0.808783 + 0.588107i \(0.200127\pi\)
\(788\) −2.14358 + 1.23760i −0.0763618 + 0.0440875i
\(789\) −2.52474 + 4.37298i −0.0898831 + 0.155682i
\(790\) 50.9415 1.81242
\(791\) 6.87373 11.5895i 0.244402 0.412074i
\(792\) 13.4761 0.478852
\(793\) −11.9844 + 5.24358i −0.425580 + 0.186205i
\(794\) −7.75893 13.4389i −0.275354 0.476927i
\(795\) 24.0636 13.8931i 0.853447 0.492738i
\(796\) 5.51675 9.55529i 0.195536 0.338678i
\(797\) 8.63198 0.305760 0.152880 0.988245i \(-0.451145\pi\)
0.152880 + 0.988245i \(0.451145\pi\)
\(798\) −7.46550 13.2883i −0.264276 0.470400i
\(799\) 39.1145i 1.38377i
\(800\) 0.886268 + 0.511687i 0.0313343 + 0.0180909i
\(801\) −4.49716 + 2.59644i −0.158899 + 0.0917406i
\(802\) 1.37125 + 2.37508i 0.0484206 + 0.0838669i
\(803\) 20.4412 35.4052i 0.721355 1.24942i
\(804\) 0.756990i 0.0266970i
\(805\) 0.250253 21.3271i 0.00882025 0.751683i
\(806\) −13.7015 10.0902i −0.482613 0.355411i
\(807\) 7.45079 12.9052i 0.262280 0.454283i
\(808\) 21.4356 12.3759i 0.754103 0.435381i
\(809\) −14.0190 24.2815i −0.492880 0.853694i 0.507086 0.861895i \(-0.330723\pi\)
−0.999966 + 0.00820168i \(0.997389\pi\)
\(810\) −1.66602 + 2.88564i −0.0585381 + 0.101391i
\(811\) 36.2095i 1.27149i 0.771901 + 0.635743i \(0.219306\pi\)
−0.771901 + 0.635743i \(0.780694\pi\)
\(812\) −1.02467 0.0120235i −0.0359590 0.000421943i
\(813\) 6.25712i 0.219447i
\(814\) 7.07334 + 4.08379i 0.247920 + 0.143137i
\(815\) 1.95355 + 3.38364i 0.0684298 + 0.118524i
\(816\) −17.3737 30.0921i −0.608200 1.05343i
\(817\) 15.6657 + 9.04459i 0.548073 + 0.316430i
\(818\) 24.3211 0.850369
\(819\) −1.16939 + 9.46745i −0.0408618 + 0.330819i
\(820\) 4.45735 0.155657
\(821\) 13.9062 + 8.02877i 0.485331 + 0.280206i 0.722635 0.691229i \(-0.242931\pi\)
−0.237305 + 0.971435i \(0.576264\pi\)
\(822\) −1.28367 2.22338i −0.0447731 0.0775493i
\(823\) 15.5112 + 26.8663i 0.540688 + 0.936499i 0.998865 + 0.0476379i \(0.0151693\pi\)
−0.458177 + 0.888861i \(0.651497\pi\)
\(824\) −25.1574 14.5246i −0.876400 0.505990i
\(825\) 2.35994i 0.0821624i
\(826\) −17.7405 + 29.9113i −0.617270 + 1.04075i
\(827\) 5.74395i 0.199737i 0.995001 + 0.0998683i \(0.0318422\pi\)
−0.995001 + 0.0998683i \(0.968158\pi\)
\(828\) 0.808409 1.40021i 0.0280942 0.0486605i
\(829\) −13.1223 22.7285i −0.455757 0.789395i 0.542974 0.839750i \(-0.317298\pi\)
−0.998731 + 0.0503545i \(0.983965\pi\)
\(830\) 30.2510 17.4654i 1.05003 0.606234i
\(831\) 1.45934 2.52764i 0.0506238 0.0876830i
\(832\) 16.3398 + 12.0331i 0.566480 + 0.417173i
\(833\) 27.0715 44.4468i 0.937971 1.53999i
\(834\) 4.39140i 0.152062i
\(835\) −9.68614 + 16.7769i −0.335203 + 0.580588i
\(836\) −4.36175 7.55477i −0.150854 0.261287i
\(837\) −2.62251 + 1.51411i −0.0906473 + 0.0523352i
\(838\) −7.53971 4.35305i −0.260455 0.150374i
\(839\) 14.9188i 0.515055i 0.966271 + 0.257528i \(0.0829078\pi\)
−0.966271 + 0.257528i \(0.917092\pi\)
\(840\) −7.06591 + 11.9135i −0.243797 + 0.411054i
\(841\) −28.1842 −0.971867
\(842\) −9.60241 + 16.6319i −0.330921 + 0.573172i
\(843\) 3.06531 1.76976i 0.105575 0.0609537i
\(844\) 0.563123 + 0.975358i 0.0193835 + 0.0335732i
\(845\) −6.12854 + 27.1104i −0.210828 + 0.932625i
\(846\) −8.19931 −0.281898
\(847\) 24.9958 + 44.4915i 0.858865 + 1.52875i
\(848\) 60.7406 2.08584
\(849\) 13.2715 22.9869i 0.455475 0.788907i
\(850\) −4.30276 + 2.48420i −0.147583 + 0.0852073i
\(851\) −3.10949 + 1.79526i −0.106592 + 0.0615408i
\(852\) −4.38181 2.52984i −0.150118 0.0866709i
\(853\) 24.1400i 0.826537i 0.910609 + 0.413268i \(0.135613\pi\)
−0.910609 + 0.413268i \(0.864387\pi\)
\(854\) 0.175527 14.9588i 0.00600639 0.511879i
\(855\) −7.90324 −0.270285
\(856\) 24.5091 + 14.1504i 0.837705 + 0.483649i
\(857\) −0.669552 1.15970i −0.0228715 0.0396146i 0.854363 0.519676i \(-0.173948\pi\)
−0.877235 + 0.480062i \(0.840614\pi\)
\(858\) −3.43055 + 30.7339i −0.117117 + 1.04924i
\(859\) −20.2107 + 35.0059i −0.689580 + 1.19439i 0.282394 + 0.959298i \(0.408871\pi\)
−0.971974 + 0.235089i \(0.924462\pi\)
\(860\) 4.48648i 0.152988i
\(861\) 0.150926 12.8623i 0.00514356 0.438346i
\(862\) 0.608829 0.0207368
\(863\) 11.7479 + 6.78268i 0.399905 + 0.230885i 0.686443 0.727184i \(-0.259171\pi\)
−0.286538 + 0.958069i \(0.592505\pi\)
\(864\) −2.06682 + 1.19328i −0.0703147 + 0.0405962i
\(865\) 11.5840 6.68802i 0.393867 0.227399i
\(866\) −29.6416 17.1136i −1.00726 0.581542i
\(867\) 38.2732 1.29983
\(868\) 2.99524 1.68276i 0.101665 0.0571165i
\(869\) 84.1392i 2.85423i
\(870\) −1.50482 + 2.60643i −0.0510182 + 0.0883661i
\(871\) −6.32573 0.706085i −0.214339 0.0239248i
\(872\) 15.1920 + 26.3132i 0.514464 + 0.891078i
\(873\) −6.11583 3.53097i −0.206989 0.119505i
\(874\) 21.7213 0.734734
\(875\) 26.4129 + 15.6656i 0.892920 + 0.529593i
\(876\) 3.18538i 0.107624i
\(877\) 15.8608 + 9.15722i 0.535580 + 0.309217i 0.743286 0.668974i \(-0.233266\pi\)
−0.207706 + 0.978191i \(0.566600\pi\)
\(878\) −0.486679 + 0.280984i −0.0164246 + 0.00948276i
\(879\) 2.66863 1.54073i 0.0900105 0.0519676i
\(880\) −27.4971 + 47.6264i −0.926927 + 1.60549i
\(881\) −19.5050 −0.657141 −0.328570 0.944480i \(-0.606567\pi\)
−0.328570 + 0.944480i \(0.606567\pi\)
\(882\) −9.31709 5.67481i −0.313723 0.191081i
\(883\) 9.06232 0.304972 0.152486 0.988306i \(-0.451272\pi\)
0.152486 + 0.988306i \(0.451272\pi\)
\(884\) 10.5307 4.60751i 0.354185 0.154967i
\(885\) 9.01626 + 15.6166i 0.303078 + 0.524947i
\(886\) −49.2180 + 28.4160i −1.65351 + 0.954655i
\(887\) 4.07510 7.05829i 0.136829 0.236994i −0.789466 0.613794i \(-0.789642\pi\)
0.926295 + 0.376800i \(0.122976\pi\)
\(888\) 2.33177 0.0782490
\(889\) −25.6463 + 43.2410i −0.860150 + 1.45026i
\(890\) 17.3029i 0.579995i
\(891\) 4.76616 + 2.75174i 0.159672 + 0.0921869i
\(892\) 2.40199 1.38679i 0.0804247 0.0464332i
\(893\) −9.72391 16.8423i −0.325398 0.563606i
\(894\) −5.14817 + 8.91690i −0.172181 + 0.298226i
\(895\) 0.819256i 0.0273847i
\(896\) −31.2420 + 17.5521i −1.04372 + 0.586374i
\(897\) −10.9467 8.06146i −0.365499 0.269164i
\(898\) 20.1747 34.9436i 0.673239 1.16608i
\(899\) −2.36876 + 1.36760i −0.0790026 + 0.0456122i
\(900\) 0.0919380 + 0.159241i 0.00306460 + 0.00530804i
\(901\) −48.3105 + 83.6763i −1.60946 + 2.78766i
\(902\) 41.6998i 1.38845i
\(903\) 12.9464 + 0.151913i 0.430828 + 0.00505533i
\(904\) 12.4707i 0.414770i
\(905\) 18.5338 + 10.7005i 0.616084 + 0.355696i
\(906\) 14.4278 + 24.9898i 0.479333 + 0.830229i
\(907\) −12.2060 21.1414i −0.405294 0.701989i 0.589062 0.808088i \(-0.299497\pi\)
−0.994356 + 0.106099i \(0.966164\pi\)
\(908\) 2.65322 + 1.53184i 0.0880504 + 0.0508359i
\(909\) 10.1083 0.335272
\(910\) −25.3714 19.1474i −0.841054 0.634731i
\(911\) 11.3864 0.377248 0.188624 0.982049i \(-0.439597\pi\)
0.188624 + 0.982049i \(0.439597\pi\)
\(912\) −14.9619 8.63823i −0.495437 0.286040i
\(913\) −28.8473 49.9651i −0.954708 1.65360i
\(914\) 31.3513 + 54.3021i 1.03701 + 1.79615i
\(915\) −6.71779 3.87852i −0.222083 0.128220i
\(916\) 5.56823i 0.183979i
\(917\) −14.1908 25.2590i −0.468621 0.834127i
\(918\) 11.5865i 0.382413i
\(919\) 16.3008 28.2337i 0.537712 0.931345i −0.461315 0.887237i \(-0.652622\pi\)
0.999027 0.0441082i \(-0.0140446\pi\)
\(920\) −9.86982 17.0950i −0.325398 0.563607i
\(921\) −21.9967 + 12.6998i −0.724817 + 0.418473i
\(922\) −20.7973 + 36.0220i −0.684923 + 1.18632i
\(923\) −25.2276 + 34.2566i −0.830376 + 1.12757i
\(924\) −5.37029 3.18513i −0.176670 0.104783i
\(925\) 0.408340i 0.0134261i
\(926\) −3.59965 + 6.23478i −0.118292 + 0.204888i
\(927\) −5.93170 10.2740i −0.194823 0.337443i
\(928\) −1.86684 + 1.07782i −0.0612819 + 0.0353811i
\(929\) −19.5941 11.3127i −0.642863 0.371157i 0.142854 0.989744i \(-0.454372\pi\)
−0.785717 + 0.618587i \(0.787706\pi\)
\(930\) 10.0902i 0.330870i
\(931\) 0.607163 25.8684i 0.0198989 0.847801i
\(932\) −8.45581 −0.276979
\(933\) 10.4629 18.1222i 0.342539 0.593295i
\(934\) 23.1596 13.3712i 0.757805 0.437519i
\(935\) −43.7401 75.7601i −1.43045 2.47762i
\(936\) 3.53894 + 8.08840i 0.115674 + 0.264378i
\(937\) 9.49113 0.310062 0.155031 0.987910i \(-0.450452\pi\)
0.155031 + 0.987910i \(0.450452\pi\)
\(938\) 3.71323 6.26069i 0.121241 0.204419i
\(939\) −12.7117 −0.414829
\(940\) 2.41172 4.17723i 0.0786618 0.136246i
\(941\) −48.6155 + 28.0682i −1.58482 + 0.914997i −0.590680 + 0.806906i \(0.701140\pi\)
−0.994141 + 0.108090i \(0.965526\pi\)
\(942\) −0.0152449 + 0.00880162i −0.000496704 + 0.000286772i
\(943\) 15.8756 + 9.16576i 0.516979 + 0.298478i
\(944\) 39.4190i 1.28298i
\(945\) −4.93170 + 2.77068i −0.160428 + 0.0901302i
\(946\) 41.9723 1.36464
\(947\) 20.7809 + 11.9978i 0.675288 + 0.389878i 0.798077 0.602555i \(-0.205851\pi\)
−0.122789 + 0.992433i \(0.539184\pi\)
\(948\) 3.27788 + 5.67746i 0.106461 + 0.184395i
\(949\) 26.6184 + 2.97118i 0.864069 + 0.0964484i
\(950\) −1.23515 + 2.13934i −0.0400735 + 0.0694094i
\(951\) 12.8697i 0.417328i
\(952\) 0.565130 48.1618i 0.0183160 1.56093i
\(953\) 35.6072 1.15343 0.576715 0.816946i \(-0.304334\pi\)
0.576715 + 0.816946i \(0.304334\pi\)
\(954\) 17.5405 + 10.1270i 0.567894 + 0.327874i
\(955\) 19.6021 11.3173i 0.634309 0.366219i
\(956\) 7.75219 4.47573i 0.250724 0.144755i
\(957\) 4.30499 + 2.48549i 0.139161 + 0.0803444i
\(958\) −44.6168 −1.44150
\(959\) 0.0511390 4.35818i 0.00165136 0.140733i
\(960\) 12.0331i 0.388367i
\(961\) −10.9150 + 18.9052i −0.352095 + 0.609847i
\(962\) −0.593589 + 5.31788i −0.0191381 + 0.171455i
\(963\) 5.77885 + 10.0093i 0.186221 + 0.322544i
\(964\) 6.38170 + 3.68447i 0.205541 + 0.118669i
\(965\) 16.2108 0.521843
\(966\) 13.5543 7.61495i 0.436103 0.245007i
\(967\) 54.8608i 1.76420i −0.471058 0.882102i \(-0.656128\pi\)
0.471058 0.882102i \(-0.343872\pi\)
\(968\) 40.9027 + 23.6152i 1.31466 + 0.759020i
\(969\) 23.8001 13.7410i 0.764569 0.441424i
\(970\) 20.3782 11.7654i 0.654306 0.377764i
\(971\) −12.8520 + 22.2604i −0.412441 + 0.714369i −0.995156 0.0983076i \(-0.968657\pi\)
0.582715 + 0.812677i \(0.301990\pi\)
\(972\) −0.428808 −0.0137540
\(973\) −3.80307 + 6.41216i −0.121921 + 0.205564i
\(974\) 24.5085 0.785303
\(975\) 1.41644 0.619740i 0.0453625 0.0198476i
\(976\) −8.47843 14.6851i −0.271388 0.470058i
\(977\) −34.0689 + 19.6697i −1.08996 + 0.629289i −0.933566 0.358406i \(-0.883320\pi\)
−0.156394 + 0.987695i \(0.549987\pi\)
\(978\) −1.42399 + 2.46642i −0.0455341 + 0.0788673i
\(979\) −28.5789 −0.913386
\(980\) 5.63160 3.07752i 0.179895 0.0983078i
\(981\) 12.4085i 0.396171i
\(982\) −46.1603 26.6507i −1.47304 0.850458i
\(983\) 32.5998 18.8215i 1.03977 0.600314i 0.120004 0.992773i \(-0.461709\pi\)
0.919769 + 0.392460i \(0.128376\pi\)
\(984\) −5.95245 10.3099i −0.189757 0.328669i
\(985\) −6.17065 + 10.6879i −0.196613 + 0.340544i
\(986\) 10.4654i 0.333287i
\(987\) −11.9723 7.10081i −0.381083 0.226021i
\(988\) 3.38897 4.60189i 0.107817 0.146406i
\(989\) −9.22565 + 15.9793i −0.293359 + 0.508112i
\(990\) −15.8811 + 9.16894i −0.504734 + 0.291408i
\(991\) −30.3909 52.6386i −0.965399 1.67212i −0.708540 0.705671i \(-0.750646\pi\)
−0.256859 0.966449i \(-0.582688\pi\)
\(992\) 3.61351 6.25878i 0.114729 0.198717i
\(993\) 27.4552i 0.871263i
\(994\) −23.8303 42.4169i −0.755850 1.34538i
\(995\) 55.0130i 1.74403i
\(996\) 3.89306 + 2.24766i 0.123356 + 0.0712198i
\(997\) −9.03612 15.6510i −0.286177 0.495673i 0.686717 0.726925i \(-0.259051\pi\)
−0.972894 + 0.231252i \(0.925718\pi\)
\(998\) −10.7152 18.5593i −0.339185 0.587485i
\(999\) 0.824689 + 0.476134i 0.0260920 + 0.0150642i
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 273.2.bj.c.142.2 yes 16
3.2 odd 2 819.2.dl.f.415.7 16
7.2 even 3 1911.2.c.n.883.7 8
7.4 even 3 inner 273.2.bj.c.25.7 yes 16
7.5 odd 6 1911.2.c.k.883.7 8
13.12 even 2 inner 273.2.bj.c.142.7 yes 16
21.11 odd 6 819.2.dl.f.298.2 16
39.38 odd 2 819.2.dl.f.415.2 16
91.12 odd 6 1911.2.c.k.883.2 8
91.25 even 6 inner 273.2.bj.c.25.2 16
91.51 even 6 1911.2.c.n.883.2 8
273.116 odd 6 819.2.dl.f.298.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bj.c.25.2 16 91.25 even 6 inner
273.2.bj.c.25.7 yes 16 7.4 even 3 inner
273.2.bj.c.142.2 yes 16 1.1 even 1 trivial
273.2.bj.c.142.7 yes 16 13.12 even 2 inner
819.2.dl.f.298.2 16 21.11 odd 6
819.2.dl.f.298.7 16 273.116 odd 6
819.2.dl.f.415.2 16 39.38 odd 2
819.2.dl.f.415.7 16 3.2 odd 2
1911.2.c.k.883.2 8 91.12 odd 6
1911.2.c.k.883.7 8 7.5 odd 6
1911.2.c.n.883.2 8 91.51 even 6
1911.2.c.n.883.7 8 7.2 even 3