Properties

Label 360.2.bm.a.11.11
Level $360$
Weight $2$
Character 360.11
Analytic conductor $2.875$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(11,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bm (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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 11.11
Character \(\chi\) \(=\) 360.11
Dual form 360.2.bm.a.131.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.325988 + 1.37613i) q^{2} +(1.62132 - 0.609351i) q^{3} +(-1.78746 - 0.897203i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.310014 + 2.42979i) q^{6} +(0.518944 + 0.299612i) q^{7} +(1.81736 - 2.16730i) q^{8} +(2.25738 - 1.97591i) q^{9} +O(q^{10})\) \(q+(-0.325988 + 1.37613i) q^{2} +(1.62132 - 0.609351i) q^{3} +(-1.78746 - 0.897203i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.310014 + 2.42979i) q^{6} +(0.518944 + 0.299612i) q^{7} +(1.81736 - 2.16730i) q^{8} +(2.25738 - 1.97591i) q^{9} +(1.35476 - 0.405751i) q^{10} +(0.700444 + 0.404402i) q^{11} +(-3.44477 - 0.365464i) q^{12} +(3.52330 - 2.03418i) q^{13} +(-0.581475 + 0.616464i) q^{14} +(-1.33838 - 1.09943i) q^{15} +(2.39005 + 3.20744i) q^{16} +1.87026i q^{17} +(1.98323 + 3.75057i) q^{18} +3.32144 q^{19} +(0.116731 + 1.99659i) q^{20} +(1.02395 + 0.169550i) q^{21} +(-0.784846 + 0.832072i) q^{22} +(-1.00356 - 1.73822i) q^{23} +(1.62588 - 4.62131i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.65074 + 5.51163i) q^{26} +(2.45592 - 4.57913i) q^{27} +(-0.658780 - 1.00114i) q^{28} +(-1.38869 + 2.40528i) q^{29} +(1.94926 - 1.48338i) q^{30} +(4.04078 - 2.33294i) q^{31} +(-5.19298 + 2.24344i) q^{32} +(1.38207 + 0.228850i) q^{33} +(-2.57372 - 0.609681i) q^{34} -0.599225i q^{35} +(-5.80778 + 1.50654i) q^{36} -7.30473i q^{37} +(-1.08275 + 4.57074i) q^{38} +(4.47288 - 5.44499i) q^{39} +(-2.78562 - 0.490228i) q^{40} +(-7.32564 + 4.22946i) q^{41} +(-0.567116 + 1.35381i) q^{42} +(-4.19270 + 7.26197i) q^{43} +(-0.889188 - 1.35129i) q^{44} +(-2.83988 - 0.966995i) q^{45} +(2.71917 - 0.814392i) q^{46} +(-6.76075 + 11.7100i) q^{47} +(5.82950 + 3.74391i) q^{48} +(-3.32046 - 5.75121i) q^{49} +(-1.02877 - 0.970379i) q^{50} +(1.13964 + 3.03229i) q^{51} +(-8.12284 + 0.474903i) q^{52} -5.27329 q^{53} +(5.50087 + 4.87241i) q^{54} -0.808804i q^{55} +(1.59246 - 0.580205i) q^{56} +(5.38514 - 2.02393i) q^{57} +(-2.85728 - 2.69511i) q^{58} +(6.41997 - 3.70657i) q^{59} +(1.40588 + 3.16599i) q^{60} +(4.38245 + 2.53021i) q^{61} +(1.89319 + 6.32115i) q^{62} +(1.76346 - 0.349047i) q^{63} +(-1.39441 - 7.87754i) q^{64} +(-3.52330 - 2.03418i) q^{65} +(-0.765465 + 1.82730i) q^{66} +(6.68152 + 11.5727i) q^{67} +(1.67800 - 3.34302i) q^{68} +(-2.68629 - 2.20670i) q^{69} +(0.824611 + 0.195340i) q^{70} -3.24261 q^{71} +(-0.179923 - 8.48337i) q^{72} -16.0211 q^{73} +(10.0523 + 2.38125i) q^{74} +(-0.282948 + 1.70878i) q^{75} +(-5.93696 - 2.98001i) q^{76} +(0.242328 + 0.419724i) q^{77} +(6.03490 + 7.93026i) q^{78} +(-3.85168 - 2.22377i) q^{79} +(1.58270 - 3.67356i) q^{80} +(1.19155 - 8.92077i) q^{81} +(-3.43221 - 11.4598i) q^{82} +(4.04472 + 2.33522i) q^{83} +(-1.67814 - 1.22175i) q^{84} +(1.61969 - 0.935129i) q^{85} +(-8.62665 - 8.13702i) q^{86} +(-0.785854 + 4.74593i) q^{87} +(2.14942 - 0.783132i) q^{88} -9.41789i q^{89} +(2.25648 - 3.59281i) q^{90} +2.43786 q^{91} +(0.234294 + 4.00741i) q^{92} +(5.12983 - 6.24471i) q^{93} +(-13.9105 - 13.1210i) q^{94} +(-1.66072 - 2.87646i) q^{95} +(-7.05246 + 6.80168i) q^{96} +(1.95567 - 3.38732i) q^{97} +(8.99685 - 2.69456i) q^{98} +(2.38023 - 0.471126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.325988 + 1.37613i −0.230508 + 0.973070i
\(3\) 1.62132 0.609351i 0.936072 0.351809i
\(4\) −1.78746 0.897203i −0.893732 0.448602i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0.310014 + 2.42979i 0.126563 + 0.991959i
\(7\) 0.518944 + 0.299612i 0.196142 + 0.113243i 0.594855 0.803833i \(-0.297210\pi\)
−0.398713 + 0.917076i \(0.630543\pi\)
\(8\) 1.81736 2.16730i 0.642534 0.766258i
\(9\) 2.25738 1.97591i 0.752461 0.658637i
\(10\) 1.35476 0.405751i 0.428412 0.128310i
\(11\) 0.700444 + 0.404402i 0.211192 + 0.121932i 0.601865 0.798598i \(-0.294424\pi\)
−0.390673 + 0.920529i \(0.627758\pi\)
\(12\) −3.44477 0.365464i −0.994419 0.105500i
\(13\) 3.52330 2.03418i 0.977187 0.564179i 0.0757674 0.997126i \(-0.475859\pi\)
0.901420 + 0.432946i \(0.142526\pi\)
\(14\) −0.581475 + 0.616464i −0.155406 + 0.164757i
\(15\) −1.33838 1.09943i −0.345567 0.283872i
\(16\) 2.39005 + 3.20744i 0.597513 + 0.801859i
\(17\) 1.87026i 0.453604i 0.973941 + 0.226802i \(0.0728270\pi\)
−0.973941 + 0.226802i \(0.927173\pi\)
\(18\) 1.98323 + 3.75057i 0.467452 + 0.884019i
\(19\) 3.32144 0.761992 0.380996 0.924577i \(-0.375581\pi\)
0.380996 + 0.924577i \(0.375581\pi\)
\(20\) 0.116731 + 1.99659i 0.0261018 + 0.446451i
\(21\) 1.02395 + 0.169550i 0.223443 + 0.0369988i
\(22\) −0.784846 + 0.832072i −0.167330 + 0.177398i
\(23\) −1.00356 1.73822i −0.209257 0.362444i 0.742224 0.670152i \(-0.233771\pi\)
−0.951481 + 0.307708i \(0.900438\pi\)
\(24\) 1.62588 4.62131i 0.331881 0.943321i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.65074 + 5.51163i 0.323736 + 1.08092i
\(27\) 2.45592 4.57913i 0.472643 0.881254i
\(28\) −0.658780 1.00114i −0.124498 0.189198i
\(29\) −1.38869 + 2.40528i −0.257873 + 0.446649i −0.965672 0.259765i \(-0.916355\pi\)
0.707799 + 0.706414i \(0.249688\pi\)
\(30\) 1.94926 1.48338i 0.355884 0.270826i
\(31\) 4.04078 2.33294i 0.725745 0.419009i −0.0911183 0.995840i \(-0.529044\pi\)
0.816864 + 0.576831i \(0.195711\pi\)
\(32\) −5.19298 + 2.24344i −0.917997 + 0.396587i
\(33\) 1.38207 + 0.228850i 0.240588 + 0.0398376i
\(34\) −2.57372 0.609681i −0.441389 0.104560i
\(35\) 0.599225i 0.101287i
\(36\) −5.80778 + 1.50654i −0.967964 + 0.251090i
\(37\) 7.30473i 1.20089i −0.799666 0.600445i \(-0.794990\pi\)
0.799666 0.600445i \(-0.205010\pi\)
\(38\) −1.08275 + 4.57074i −0.175645 + 0.741471i
\(39\) 4.47288 5.44499i 0.716234 0.871896i
\(40\) −2.78562 0.490228i −0.440445 0.0775118i
\(41\) −7.32564 + 4.22946i −1.14407 + 0.660531i −0.947436 0.319945i \(-0.896335\pi\)
−0.196637 + 0.980476i \(0.563002\pi\)
\(42\) −0.567116 + 1.35381i −0.0875079 + 0.208897i
\(43\) −4.19270 + 7.26197i −0.639381 + 1.10744i 0.346188 + 0.938165i \(0.387476\pi\)
−0.985569 + 0.169275i \(0.945857\pi\)
\(44\) −0.889188 1.35129i −0.134050 0.203715i
\(45\) −2.83988 0.966995i −0.423344 0.144151i
\(46\) 2.71917 0.814392i 0.400919 0.120076i
\(47\) −6.76075 + 11.7100i −0.986157 + 1.70807i −0.349479 + 0.936944i \(0.613641\pi\)
−0.636678 + 0.771130i \(0.719692\pi\)
\(48\) 5.82950 + 3.74391i 0.841416 + 0.540387i
\(49\) −3.32046 5.75121i −0.474352 0.821602i
\(50\) −1.02877 0.970379i −0.145490 0.137232i
\(51\) 1.13964 + 3.03229i 0.159582 + 0.424606i
\(52\) −8.12284 + 0.474903i −1.12644 + 0.0658572i
\(53\) −5.27329 −0.724343 −0.362171 0.932112i \(-0.617964\pi\)
−0.362171 + 0.932112i \(0.617964\pi\)
\(54\) 5.50087 + 4.87241i 0.748574 + 0.663051i
\(55\) 0.808804i 0.109059i
\(56\) 1.59246 0.580205i 0.212801 0.0775332i
\(57\) 5.38514 2.02393i 0.713279 0.268076i
\(58\) −2.85728 2.69511i −0.375179 0.353885i
\(59\) 6.41997 3.70657i 0.835809 0.482554i −0.0200287 0.999799i \(-0.506376\pi\)
0.855837 + 0.517245i \(0.173042\pi\)
\(60\) 1.40588 + 3.16599i 0.181499 + 0.408728i
\(61\) 4.38245 + 2.53021i 0.561115 + 0.323960i 0.753593 0.657341i \(-0.228319\pi\)
−0.192478 + 0.981301i \(0.561652\pi\)
\(62\) 1.89319 + 6.32115i 0.240435 + 0.802786i
\(63\) 1.76346 0.349047i 0.222175 0.0439758i
\(64\) −1.39441 7.87754i −0.174301 0.984692i
\(65\) −3.52330 2.03418i −0.437011 0.252309i
\(66\) −0.765465 + 1.82730i −0.0942222 + 0.224926i
\(67\) 6.68152 + 11.5727i 0.816278 + 1.41383i 0.908407 + 0.418088i \(0.137300\pi\)
−0.0921287 + 0.995747i \(0.529367\pi\)
\(68\) 1.67800 3.34302i 0.203488 0.405400i
\(69\) −2.68629 2.20670i −0.323391 0.265655i
\(70\) 0.824611 + 0.195340i 0.0985598 + 0.0233476i
\(71\) −3.24261 −0.384827 −0.192414 0.981314i \(-0.561632\pi\)
−0.192414 + 0.981314i \(0.561632\pi\)
\(72\) −0.179923 8.48337i −0.0212042 0.999775i
\(73\) −16.0211 −1.87513 −0.937563 0.347815i \(-0.886924\pi\)
−0.937563 + 0.347815i \(0.886924\pi\)
\(74\) 10.0523 + 2.38125i 1.16855 + 0.276815i
\(75\) −0.282948 + 1.70878i −0.0326721 + 0.197313i
\(76\) −5.93696 2.98001i −0.681016 0.341831i
\(77\) 0.242328 + 0.419724i 0.0276158 + 0.0478319i
\(78\) 6.03490 + 7.93026i 0.683318 + 0.897925i
\(79\) −3.85168 2.22377i −0.433348 0.250193i 0.267424 0.963579i \(-0.413828\pi\)
−0.700772 + 0.713385i \(0.747161\pi\)
\(80\) 1.58270 3.67356i 0.176951 0.410717i
\(81\) 1.19155 8.92077i 0.132395 0.991197i
\(82\) −3.43221 11.4598i −0.379025 1.26552i
\(83\) 4.04472 + 2.33522i 0.443966 + 0.256324i 0.705278 0.708930i \(-0.250822\pi\)
−0.261313 + 0.965254i \(0.584155\pi\)
\(84\) −1.67814 1.22175i −0.183101 0.133304i
\(85\) 1.61969 0.935129i 0.175680 0.101429i
\(86\) −8.62665 8.13702i −0.930235 0.877437i
\(87\) −0.785854 + 4.74593i −0.0842524 + 0.508818i
\(88\) 2.14942 0.783132i 0.229129 0.0834822i
\(89\) 9.41789i 0.998294i −0.866517 0.499147i \(-0.833647\pi\)
0.866517 0.499147i \(-0.166353\pi\)
\(90\) 2.25648 3.59281i 0.237854 0.378716i
\(91\) 2.43786 0.255557
\(92\) 0.234294 + 4.00741i 0.0244268 + 0.417801i
\(93\) 5.12983 6.24471i 0.531938 0.647547i
\(94\) −13.9105 13.1210i −1.43476 1.35333i
\(95\) −1.66072 2.87646i −0.170387 0.295118i
\(96\) −7.05246 + 6.80168i −0.719788 + 0.694194i
\(97\) 1.95567 3.38732i 0.198568 0.343930i −0.749496 0.662009i \(-0.769704\pi\)
0.948064 + 0.318078i \(0.103038\pi\)
\(98\) 8.99685 2.69456i 0.908819 0.272192i
\(99\) 2.38023 0.471126i 0.239222 0.0473500i
\(100\) 1.67073 1.09939i 0.167073 0.109939i
\(101\) −0.225380 + 0.390370i −0.0224262 + 0.0388433i −0.877021 0.480453i \(-0.840472\pi\)
0.854595 + 0.519296i \(0.173806\pi\)
\(102\) −4.54434 + 0.579805i −0.449956 + 0.0574093i
\(103\) 0.427706 0.246936i 0.0421431 0.0243313i −0.478780 0.877935i \(-0.658921\pi\)
0.520924 + 0.853603i \(0.325588\pi\)
\(104\) 1.99442 11.3329i 0.195569 1.11128i
\(105\) −0.365138 0.971537i −0.0356338 0.0948123i
\(106\) 1.71903 7.25673i 0.166967 0.704836i
\(107\) 0.151516i 0.0146476i 0.999973 + 0.00732378i \(0.00233125\pi\)
−0.999973 + 0.00732378i \(0.997669\pi\)
\(108\) −8.49829 + 5.98156i −0.817748 + 0.575576i
\(109\) 4.45180i 0.426405i 0.977008 + 0.213202i \(0.0683894\pi\)
−0.977008 + 0.213202i \(0.931611\pi\)
\(110\) 1.11302 + 0.263660i 0.106122 + 0.0251390i
\(111\) −4.45115 11.8433i −0.422484 1.12412i
\(112\) 0.279315 + 2.38057i 0.0263928 + 0.224943i
\(113\) −14.2998 + 8.25601i −1.34522 + 0.776660i −0.987567 0.157196i \(-0.949755\pi\)
−0.357648 + 0.933857i \(0.616421\pi\)
\(114\) 1.02969 + 8.07042i 0.0964396 + 0.755864i
\(115\) −1.00356 + 1.73822i −0.0935827 + 0.162090i
\(116\) 4.64025 3.05341i 0.430837 0.283502i
\(117\) 3.93408 11.5536i 0.363706 1.06813i
\(118\) 3.00789 + 10.0430i 0.276898 + 0.924533i
\(119\) −0.560352 + 0.970558i −0.0513674 + 0.0889709i
\(120\) −4.81511 + 0.902602i −0.439558 + 0.0823960i
\(121\) −5.17292 8.95976i −0.470265 0.814523i
\(122\) −4.91052 + 5.20600i −0.444578 + 0.471329i
\(123\) −9.30001 + 11.3212i −0.838554 + 1.02080i
\(124\) −9.31587 + 0.544654i −0.836590 + 0.0489113i
\(125\) 1.00000 0.0894427
\(126\) −0.0945335 + 2.54054i −0.00842172 + 0.226329i
\(127\) 11.4614i 1.01704i 0.861051 + 0.508519i \(0.169807\pi\)
−0.861051 + 0.508519i \(0.830193\pi\)
\(128\) 11.2951 + 0.649096i 0.998353 + 0.0573726i
\(129\) −2.37264 + 14.3288i −0.208899 + 1.26158i
\(130\) 3.94784 4.18540i 0.346249 0.367084i
\(131\) 12.3778 7.14631i 1.08145 0.624376i 0.150164 0.988661i \(-0.452020\pi\)
0.931288 + 0.364285i \(0.118687\pi\)
\(132\) −2.26508 1.64906i −0.197149 0.143532i
\(133\) 1.72364 + 0.995146i 0.149459 + 0.0862901i
\(134\) −18.1037 + 5.42207i −1.56392 + 0.468395i
\(135\) −5.19361 + 0.162672i −0.446994 + 0.0140006i
\(136\) 4.05342 + 3.39893i 0.347577 + 0.291456i
\(137\) 1.59539 + 0.921101i 0.136304 + 0.0786950i 0.566601 0.823992i \(-0.308258\pi\)
−0.430298 + 0.902687i \(0.641591\pi\)
\(138\) 3.91240 2.97732i 0.333045 0.253446i
\(139\) 4.92786 + 8.53531i 0.417976 + 0.723956i 0.995736 0.0922512i \(-0.0294063\pi\)
−0.577760 + 0.816207i \(0.696073\pi\)
\(140\) −0.537626 + 1.07109i −0.0454377 + 0.0905238i
\(141\) −3.82589 + 23.1053i −0.322198 + 1.94582i
\(142\) 1.05705 4.46225i 0.0887059 0.374464i
\(143\) 3.29050 0.275165
\(144\) 11.7329 + 2.51788i 0.977739 + 0.209823i
\(145\) 2.77738 0.230649
\(146\) 5.22268 22.0471i 0.432232 1.82463i
\(147\) −8.88806 7.30125i −0.733075 0.602197i
\(148\) −6.55383 + 13.0569i −0.538721 + 1.07327i
\(149\) −5.68180 9.84116i −0.465471 0.806219i 0.533752 0.845641i \(-0.320782\pi\)
−0.999223 + 0.0394219i \(0.987448\pi\)
\(150\) −2.25927 0.946416i −0.184469 0.0772746i
\(151\) 10.9144 + 6.30145i 0.888204 + 0.512805i 0.873354 0.487085i \(-0.161940\pi\)
0.0148491 + 0.999890i \(0.495273\pi\)
\(152\) 6.03626 7.19858i 0.489605 0.583882i
\(153\) 3.69546 + 4.22189i 0.298760 + 0.341319i
\(154\) −0.656590 + 0.196649i −0.0529095 + 0.0158464i
\(155\) −4.04078 2.33294i −0.324563 0.187387i
\(156\) −12.8804 + 5.71963i −1.03125 + 0.457937i
\(157\) 15.4516 8.92099i 1.23317 0.711972i 0.265482 0.964116i \(-0.414469\pi\)
0.967690 + 0.252144i \(0.0811355\pi\)
\(158\) 4.31579 4.57549i 0.343346 0.364006i
\(159\) −8.54972 + 3.21329i −0.678037 + 0.254830i
\(160\) 4.53936 + 3.37553i 0.358868 + 0.266859i
\(161\) 1.20272i 0.0947875i
\(162\) 11.8877 + 4.54779i 0.933986 + 0.357308i
\(163\) −12.4417 −0.974507 −0.487253 0.873261i \(-0.662001\pi\)
−0.487253 + 0.873261i \(0.662001\pi\)
\(164\) 16.8890 0.987418i 1.31881 0.0771044i
\(165\) −0.492845 1.31133i −0.0383680 0.102087i
\(166\) −4.53210 + 4.80481i −0.351759 + 0.372925i
\(167\) 12.1610 + 21.0634i 0.941044 + 1.62994i 0.763484 + 0.645827i \(0.223487\pi\)
0.177561 + 0.984110i \(0.443179\pi\)
\(168\) 2.22834 1.91107i 0.171920 0.147442i
\(169\) 1.77576 3.07570i 0.136597 0.236592i
\(170\) 0.758858 + 2.53374i 0.0582018 + 0.194329i
\(171\) 7.49777 6.56288i 0.573369 0.501876i
\(172\) 14.0098 9.21881i 1.06824 0.702928i
\(173\) −10.3034 + 17.8460i −0.783352 + 1.35681i 0.146627 + 0.989192i \(0.453158\pi\)
−0.929979 + 0.367613i \(0.880175\pi\)
\(174\) −6.27484 2.62855i −0.475694 0.199270i
\(175\) −0.518944 + 0.299612i −0.0392285 + 0.0226486i
\(176\) 0.377006 + 3.21317i 0.0284179 + 0.242202i
\(177\) 8.15025 9.92157i 0.612610 0.745751i
\(178\) 12.9602 + 3.07012i 0.971410 + 0.230115i
\(179\) 16.9909i 1.26996i −0.772528 0.634981i \(-0.781008\pi\)
0.772528 0.634981i \(-0.218992\pi\)
\(180\) 4.20859 + 4.27642i 0.313690 + 0.318745i
\(181\) 22.5201i 1.67390i 0.547278 + 0.836951i \(0.315664\pi\)
−0.547278 + 0.836951i \(0.684336\pi\)
\(182\) −0.794713 + 3.35481i −0.0589080 + 0.248675i
\(183\) 8.64716 + 1.43184i 0.639216 + 0.105844i
\(184\) −5.59109 0.983948i −0.412180 0.0725376i
\(185\) −6.32608 + 3.65236i −0.465103 + 0.268527i
\(186\) 6.92127 + 9.09501i 0.507492 + 0.666878i
\(187\) −0.756335 + 1.31001i −0.0553087 + 0.0957975i
\(188\) 22.5908 14.8654i 1.64760 1.08417i
\(189\) 2.64645 1.64049i 0.192501 0.119328i
\(190\) 4.49975 1.34768i 0.326446 0.0977709i
\(191\) 3.66201 6.34278i 0.264973 0.458947i −0.702583 0.711602i \(-0.747970\pi\)
0.967557 + 0.252654i \(0.0813035\pi\)
\(192\) −7.06098 11.9224i −0.509582 0.860422i
\(193\) 0.361899 + 0.626828i 0.0260501 + 0.0451200i 0.878757 0.477270i \(-0.158374\pi\)
−0.852706 + 0.522390i \(0.825040\pi\)
\(194\) 4.02387 + 3.79548i 0.288897 + 0.272500i
\(195\) −6.95194 1.15113i −0.497839 0.0824345i
\(196\) 0.775202 + 13.2592i 0.0553716 + 0.947087i
\(197\) 2.66910 0.190165 0.0950826 0.995469i \(-0.469688\pi\)
0.0950826 + 0.995469i \(0.469688\pi\)
\(198\) −0.127597 + 3.42909i −0.00906790 + 0.243695i
\(199\) 25.4805i 1.80626i 0.429366 + 0.903131i \(0.358737\pi\)
−0.429366 + 0.903131i \(0.641263\pi\)
\(200\) 0.968260 + 2.65753i 0.0684663 + 0.187916i
\(201\) 17.8848 + 14.6918i 1.26149 + 1.03628i
\(202\) −0.463728 0.437408i −0.0326278 0.0307759i
\(203\) −1.44130 + 0.832136i −0.101160 + 0.0584045i
\(204\) 0.683512 6.44260i 0.0478554 0.451073i
\(205\) 7.32564 + 4.22946i 0.511645 + 0.295398i
\(206\) 0.200389 + 0.669077i 0.0139618 + 0.0466168i
\(207\) −5.69999 1.94088i −0.396177 0.134900i
\(208\) 14.9454 + 6.43897i 1.03627 + 0.446462i
\(209\) 2.32649 + 1.34320i 0.160926 + 0.0929110i
\(210\) 1.45599 0.185768i 0.100473 0.0128192i
\(211\) 7.09060 + 12.2813i 0.488137 + 0.845479i 0.999907 0.0136441i \(-0.00434319\pi\)
−0.511770 + 0.859123i \(0.671010\pi\)
\(212\) 9.42582 + 4.73122i 0.647368 + 0.324941i
\(213\) −5.25732 + 1.97589i −0.360226 + 0.135386i
\(214\) −0.208505 0.0493923i −0.0142531 0.00337639i
\(215\) 8.38541 0.571880
\(216\) −5.46107 13.6447i −0.371579 0.928402i
\(217\) 2.79592 0.189799
\(218\) −6.12625 1.45123i −0.414922 0.0982899i
\(219\) −25.9754 + 9.76247i −1.75525 + 0.659686i
\(220\) −0.725661 + 1.44571i −0.0489241 + 0.0974695i
\(221\) 3.80443 + 6.58947i 0.255914 + 0.443256i
\(222\) 17.7490 2.26457i 1.19123 0.151988i
\(223\) −23.3748 13.4954i −1.56529 0.903722i −0.996706 0.0810987i \(-0.974157\pi\)
−0.568587 0.822623i \(-0.692510\pi\)
\(224\) −3.36702 0.391663i −0.224969 0.0261691i
\(225\) 0.582498 + 2.94291i 0.0388332 + 0.196194i
\(226\) −6.69977 22.3698i −0.445662 1.48802i
\(227\) −17.7458 10.2455i −1.17783 0.680020i −0.222318 0.974974i \(-0.571362\pi\)
−0.955512 + 0.294954i \(0.904696\pi\)
\(228\) −11.4416 1.21387i −0.757739 0.0803905i
\(229\) −10.4781 + 6.04952i −0.692410 + 0.399763i −0.804514 0.593933i \(-0.797574\pi\)
0.112104 + 0.993696i \(0.464241\pi\)
\(230\) −2.06487 1.94767i −0.136153 0.128426i
\(231\) 0.648650 + 0.532845i 0.0426781 + 0.0350587i
\(232\) 2.68922 + 7.38096i 0.176556 + 0.484584i
\(233\) 7.05758i 0.462358i 0.972911 + 0.231179i \(0.0742582\pi\)
−0.972911 + 0.231179i \(0.925742\pi\)
\(234\) 14.6168 + 9.18015i 0.955533 + 0.600125i
\(235\) 13.5215 0.882046
\(236\) −14.8010 + 0.865343i −0.963464 + 0.0563290i
\(237\) −7.59988 1.25842i −0.493665 0.0817434i
\(238\) −1.15295 1.08751i −0.0747344 0.0704926i
\(239\) −1.45168 2.51438i −0.0939013 0.162642i 0.815248 0.579112i \(-0.196600\pi\)
−0.909150 + 0.416470i \(0.863267\pi\)
\(240\) 0.327571 6.92045i 0.0211446 0.446713i
\(241\) 4.85247 8.40472i 0.312575 0.541396i −0.666344 0.745644i \(-0.732142\pi\)
0.978919 + 0.204249i \(0.0654751\pi\)
\(242\) 14.0161 4.19783i 0.900989 0.269847i
\(243\) −3.50399 15.1895i −0.224781 0.974409i
\(244\) −5.56336 8.45461i −0.356158 0.541251i
\(245\) −3.32046 + 5.75121i −0.212137 + 0.367432i
\(246\) −12.5478 16.4886i −0.800016 1.05127i
\(247\) 11.7024 6.75641i 0.744608 0.429900i
\(248\) 2.28735 12.9974i 0.145247 0.825335i
\(249\) 7.98077 + 1.32149i 0.505761 + 0.0837463i
\(250\) −0.325988 + 1.37613i −0.0206173 + 0.0870341i
\(251\) 7.28459i 0.459800i −0.973214 0.229900i \(-0.926160\pi\)
0.973214 0.229900i \(-0.0738398\pi\)
\(252\) −3.46529 0.958275i −0.218293 0.0603656i
\(253\) 1.62337i 0.102060i
\(254\) −15.7724 3.73629i −0.989649 0.234436i
\(255\) 2.05622 2.50311i 0.128766 0.156751i
\(256\) −4.57530 + 15.3319i −0.285956 + 0.958243i
\(257\) −14.6491 + 8.45768i −0.913788 + 0.527576i −0.881648 0.471908i \(-0.843566\pi\)
−0.0321398 + 0.999483i \(0.510232\pi\)
\(258\) −18.9449 7.93609i −1.17946 0.494079i
\(259\) 2.18859 3.79074i 0.135992 0.235545i
\(260\) 4.47270 + 6.79713i 0.277385 + 0.421540i
\(261\) 1.61782 + 8.17356i 0.100140 + 0.505931i
\(262\) 5.79924 + 19.3630i 0.358279 + 1.19625i
\(263\) 3.28261 5.68564i 0.202414 0.350592i −0.746892 0.664946i \(-0.768455\pi\)
0.949306 + 0.314354i \(0.101788\pi\)
\(264\) 3.00770 2.57946i 0.185111 0.158755i
\(265\) 2.63665 + 4.56681i 0.161968 + 0.280537i
\(266\) −1.93134 + 2.04755i −0.118418 + 0.125543i
\(267\) −5.73880 15.2694i −0.351209 0.934475i
\(268\) −1.55988 26.6805i −0.0952849 1.62977i
\(269\) 14.9125 0.909232 0.454616 0.890688i \(-0.349777\pi\)
0.454616 + 0.890688i \(0.349777\pi\)
\(270\) 1.46920 7.20010i 0.0894124 0.438184i
\(271\) 16.6853i 1.01356i −0.862075 0.506781i \(-0.830835\pi\)
0.862075 0.506781i \(-0.169165\pi\)
\(272\) −5.99873 + 4.47001i −0.363727 + 0.271034i
\(273\) 3.95256 1.48551i 0.239220 0.0899073i
\(274\) −1.78763 + 1.89520i −0.107995 + 0.114493i
\(275\) −0.700444 + 0.404402i −0.0422384 + 0.0243863i
\(276\) 2.82178 + 6.35454i 0.169851 + 0.382498i
\(277\) −17.1138 9.88066i −1.02827 0.593671i −0.111781 0.993733i \(-0.535655\pi\)
−0.916488 + 0.400061i \(0.868989\pi\)
\(278\) −13.3521 + 3.99897i −0.800807 + 0.239842i
\(279\) 4.51189 13.2506i 0.270120 0.793291i
\(280\) −1.29870 1.08901i −0.0776123 0.0650806i
\(281\) 15.0261 + 8.67532i 0.896382 + 0.517526i 0.876024 0.482267i \(-0.160186\pi\)
0.0203571 + 0.999793i \(0.493520\pi\)
\(282\) −30.5487 12.7970i −1.81915 0.762049i
\(283\) −2.43180 4.21200i −0.144556 0.250378i 0.784651 0.619937i \(-0.212842\pi\)
−0.929207 + 0.369560i \(0.879509\pi\)
\(284\) 5.79605 + 2.90928i 0.343932 + 0.172634i
\(285\) −4.44534 3.65170i −0.263319 0.216308i
\(286\) −1.07266 + 4.52815i −0.0634279 + 0.267755i
\(287\) −5.06880 −0.299202
\(288\) −7.28970 + 15.3251i −0.429550 + 0.903043i
\(289\) 13.5021 0.794243
\(290\) −0.905391 + 3.82203i −0.0531664 + 0.224437i
\(291\) 1.10671 6.68363i 0.0648764 0.391802i
\(292\) 28.6371 + 14.3742i 1.67586 + 0.841185i
\(293\) −16.0019 27.7161i −0.934841 1.61919i −0.774918 0.632062i \(-0.782209\pi\)
−0.159923 0.987129i \(-0.551125\pi\)
\(294\) 12.9449 9.85100i 0.754960 0.574522i
\(295\) −6.41997 3.70657i −0.373785 0.215805i
\(296\) −15.8316 13.2753i −0.920191 0.771612i
\(297\) 3.57205 2.21425i 0.207271 0.128484i
\(298\) 15.3949 4.61079i 0.891803 0.267096i
\(299\) −7.07170 4.08285i −0.408967 0.236117i
\(300\) 2.03889 2.80053i 0.117715 0.161688i
\(301\) −4.35155 + 2.51237i −0.250819 + 0.144811i
\(302\) −12.2296 + 12.9655i −0.703733 + 0.746079i
\(303\) −0.127542 + 0.770252i −0.00732710 + 0.0442498i
\(304\) 7.93843 + 10.6533i 0.455300 + 0.611010i
\(305\) 5.06042i 0.289759i
\(306\) −7.01454 + 3.70915i −0.400994 + 0.212038i
\(307\) −10.7917 −0.615913 −0.307956 0.951400i \(-0.599645\pi\)
−0.307956 + 0.951400i \(0.599645\pi\)
\(308\) −0.0565742 0.967658i −0.00322362 0.0551374i
\(309\) 0.542979 0.660986i 0.0308890 0.0376022i
\(310\) 4.52768 4.80012i 0.257155 0.272629i
\(311\) 1.21973 + 2.11263i 0.0691644 + 0.119796i 0.898534 0.438905i \(-0.144633\pi\)
−0.829369 + 0.558701i \(0.811300\pi\)
\(312\) −3.67211 19.5896i −0.207892 1.10904i
\(313\) 6.88538 11.9258i 0.389185 0.674088i −0.603155 0.797624i \(-0.706090\pi\)
0.992340 + 0.123536i \(0.0394234\pi\)
\(314\) 7.23939 + 24.1715i 0.408543 + 1.36408i
\(315\) −1.18401 1.35268i −0.0667117 0.0762148i
\(316\) 4.88957 + 7.43064i 0.275060 + 0.418006i
\(317\) 7.83931 13.5781i 0.440300 0.762621i −0.557412 0.830236i \(-0.688206\pi\)
0.997712 + 0.0676148i \(0.0215389\pi\)
\(318\) −1.63479 12.8130i −0.0916747 0.718518i
\(319\) −1.94540 + 1.12318i −0.108921 + 0.0628858i
\(320\) −6.12494 + 5.14636i −0.342395 + 0.287690i
\(321\) 0.0923262 + 0.245656i 0.00515314 + 0.0137112i
\(322\) 1.65510 + 0.392072i 0.0922349 + 0.0218493i
\(323\) 6.21196i 0.345642i
\(324\) −10.1336 + 14.8765i −0.562978 + 0.826472i
\(325\) 4.06835i 0.225672i
\(326\) 4.05584 17.1213i 0.224632 0.948264i
\(327\) 2.71271 + 7.21781i 0.150013 + 0.399146i
\(328\) −4.14680 + 23.5633i −0.228969 + 1.30107i
\(329\) −7.01690 + 4.05121i −0.386854 + 0.223350i
\(330\) 1.96522 0.250740i 0.108182 0.0138028i
\(331\) 1.07345 1.85927i 0.0590021 0.102195i −0.835016 0.550226i \(-0.814541\pi\)
0.894018 + 0.448032i \(0.147875\pi\)
\(332\) −5.13462 7.80306i −0.281799 0.428249i
\(333\) −14.4335 16.4896i −0.790951 0.903623i
\(334\) −32.9503 + 9.86865i −1.80296 + 0.539988i
\(335\) 6.68152 11.5727i 0.365051 0.632286i
\(336\) 1.90346 + 3.68947i 0.103842 + 0.201277i
\(337\) 10.7535 + 18.6257i 0.585783 + 1.01461i 0.994777 + 0.102069i \(0.0325462\pi\)
−0.408995 + 0.912537i \(0.634120\pi\)
\(338\) 3.65368 + 3.44631i 0.198734 + 0.187455i
\(339\) −18.1539 + 22.0993i −0.985982 + 1.20027i
\(340\) −3.73414 + 0.218317i −0.202512 + 0.0118399i
\(341\) 3.77379 0.204362
\(342\) 6.58719 + 12.4573i 0.356194 + 0.673615i
\(343\) 8.17398i 0.441354i
\(344\) 8.11925 + 22.2845i 0.437761 + 1.20150i
\(345\) −0.567913 + 3.42974i −0.0305754 + 0.184651i
\(346\) −21.1996 19.9964i −1.13970 1.07501i
\(347\) 17.3931 10.0419i 0.933709 0.539077i 0.0457265 0.998954i \(-0.485440\pi\)
0.887983 + 0.459877i \(0.152106\pi\)
\(348\) 5.66275 7.77811i 0.303555 0.416951i
\(349\) −3.44434 1.98859i −0.184371 0.106447i 0.404973 0.914328i \(-0.367281\pi\)
−0.589345 + 0.807882i \(0.700614\pi\)
\(350\) −0.243136 0.811804i −0.0129962 0.0433927i
\(351\) −0.661807 21.1294i −0.0353247 1.12781i
\(352\) −4.54464 0.528647i −0.242230 0.0281770i
\(353\) 27.3846 + 15.8105i 1.45754 + 0.841508i 0.998890 0.0471110i \(-0.0150014\pi\)
0.458646 + 0.888619i \(0.348335\pi\)
\(354\) 10.9965 + 14.4501i 0.584456 + 0.768014i
\(355\) 1.62131 + 2.80818i 0.0860500 + 0.149043i
\(356\) −8.44976 + 16.8341i −0.447836 + 0.892207i
\(357\) −0.317102 + 1.91504i −0.0167828 + 0.101355i
\(358\) 23.3817 + 5.53884i 1.23576 + 0.292737i
\(359\) 24.5943 1.29804 0.649019 0.760772i \(-0.275179\pi\)
0.649019 + 0.760772i \(0.275179\pi\)
\(360\) −7.25686 + 4.39751i −0.382470 + 0.231769i
\(361\) −7.96801 −0.419369
\(362\) −30.9905 7.34127i −1.62882 0.385848i
\(363\) −13.8466 11.3745i −0.726759 0.597009i
\(364\) −4.35758 2.18725i −0.228399 0.114643i
\(365\) 8.01054 + 13.8747i 0.419291 + 0.726233i
\(366\) −4.78926 + 11.4328i −0.250339 + 0.597604i
\(367\) −6.34516 3.66338i −0.331214 0.191227i 0.325166 0.945657i \(-0.394580\pi\)
−0.656380 + 0.754430i \(0.727913\pi\)
\(368\) 3.17667 7.37330i 0.165595 0.384360i
\(369\) −8.17974 + 24.0223i −0.425820 + 1.25055i
\(370\) −2.96390 9.89613i −0.154086 0.514475i
\(371\) −2.73654 1.57994i −0.142074 0.0820266i
\(372\) −14.7722 + 6.55970i −0.765901 + 0.340104i
\(373\) 27.9329 16.1271i 1.44631 0.835027i 0.448051 0.894008i \(-0.352118\pi\)
0.998259 + 0.0589810i \(0.0187851\pi\)
\(374\) −1.55619 1.46786i −0.0804686 0.0759014i
\(375\) 1.62132 0.609351i 0.0837248 0.0314668i
\(376\) 13.0923 + 35.9338i 0.675185 + 1.85315i
\(377\) 11.2994i 0.581946i
\(378\) 1.39481 + 4.17664i 0.0717413 + 0.214823i
\(379\) −6.95220 −0.357110 −0.178555 0.983930i \(-0.557142\pi\)
−0.178555 + 0.983930i \(0.557142\pi\)
\(380\) 0.387715 + 6.63157i 0.0198894 + 0.340192i
\(381\) 6.98403 + 18.5827i 0.357803 + 0.952020i
\(382\) 7.53471 + 7.10706i 0.385510 + 0.363629i
\(383\) −13.7399 23.7982i −0.702075 1.21603i −0.967737 0.251963i \(-0.918924\pi\)
0.265662 0.964066i \(-0.414410\pi\)
\(384\) 18.7085 5.83027i 0.954714 0.297525i
\(385\) 0.242328 0.419724i 0.0123502 0.0213911i
\(386\) −0.980571 + 0.293682i −0.0499097 + 0.0149480i
\(387\) 4.88448 + 24.6775i 0.248292 + 1.25443i
\(388\) −6.53481 + 4.30008i −0.331755 + 0.218303i
\(389\) 15.8542 27.4603i 0.803842 1.39230i −0.113228 0.993569i \(-0.536119\pi\)
0.917070 0.398726i \(-0.130548\pi\)
\(390\) 3.85036 9.19151i 0.194970 0.465430i
\(391\) 3.25092 1.87692i 0.164406 0.0949199i
\(392\) −18.4991 3.25557i −0.934346 0.164431i
\(393\) 15.7138 19.1289i 0.792655 0.964926i
\(394\) −0.870093 + 3.67302i −0.0438347 + 0.185044i
\(395\) 4.44754i 0.223780i
\(396\) −4.67728 1.29343i −0.235042 0.0649974i
\(397\) 2.72557i 0.136792i −0.997658 0.0683961i \(-0.978212\pi\)
0.997658 0.0683961i \(-0.0217882\pi\)
\(398\) −35.0644 8.30632i −1.75762 0.416358i
\(399\) 3.40098 + 0.563150i 0.170262 + 0.0281928i
\(400\) −3.97275 + 0.466128i −0.198637 + 0.0233064i
\(401\) 9.65586 5.57482i 0.482191 0.278393i −0.239138 0.970986i \(-0.576865\pi\)
0.721329 + 0.692593i \(0.243532\pi\)
\(402\) −26.0480 + 19.8224i −1.29916 + 0.988653i
\(403\) 9.49125 16.4393i 0.472793 0.818901i
\(404\) 0.753100 0.495560i 0.0374681 0.0246551i
\(405\) −8.32139 + 3.42847i −0.413493 + 0.170362i
\(406\) −0.675280 2.25468i −0.0335136 0.111898i
\(407\) 2.95405 5.11656i 0.146427 0.253618i
\(408\) 8.64304 + 3.04081i 0.427894 + 0.150543i
\(409\) 5.29072 + 9.16380i 0.261609 + 0.453121i 0.966670 0.256027i \(-0.0824135\pi\)
−0.705060 + 0.709147i \(0.749080\pi\)
\(410\) −8.20836 + 8.70228i −0.405382 + 0.429775i
\(411\) 3.14792 + 0.521248i 0.155276 + 0.0257113i
\(412\) −0.986060 + 0.0576501i −0.0485797 + 0.00284022i
\(413\) 4.44214 0.218583
\(414\) 4.52903 7.21122i 0.222590 0.354412i
\(415\) 4.67044i 0.229263i
\(416\) −13.7329 + 18.4677i −0.673309 + 0.905455i
\(417\) 13.1907 + 10.8357i 0.645950 + 0.530627i
\(418\) −2.60682 + 2.76368i −0.127504 + 0.135176i
\(419\) 10.6537 6.15093i 0.520468 0.300492i −0.216658 0.976248i \(-0.569516\pi\)
0.737126 + 0.675755i \(0.236182\pi\)
\(420\) −0.218995 + 2.06419i −0.0106859 + 0.100722i
\(421\) −31.8320 18.3782i −1.55140 0.895701i −0.998028 0.0627653i \(-0.980008\pi\)
−0.553370 0.832935i \(-0.686659\pi\)
\(422\) −19.2121 + 5.75404i −0.935230 + 0.280102i
\(423\) 7.87625 + 39.7925i 0.382956 + 1.93478i
\(424\) −9.58347 + 11.4288i −0.465414 + 0.555033i
\(425\) −1.61969 0.935129i −0.0785665 0.0453604i
\(426\) −1.00525 7.87887i −0.0487047 0.381733i
\(427\) 1.51616 + 2.62607i 0.0733723 + 0.127085i
\(428\) 0.135940 0.270829i 0.00657092 0.0130910i
\(429\) 5.33497 2.00507i 0.257575 0.0968057i
\(430\) −2.73354 + 11.5394i −0.131823 + 0.556479i
\(431\) −31.5455 −1.51949 −0.759746 0.650220i \(-0.774677\pi\)
−0.759746 + 0.650220i \(0.774677\pi\)
\(432\) 20.5571 3.06714i 0.989052 0.147568i
\(433\) −21.6927 −1.04248 −0.521241 0.853409i \(-0.674531\pi\)
−0.521241 + 0.853409i \(0.674531\pi\)
\(434\) −0.911435 + 3.84754i −0.0437503 + 0.184688i
\(435\) 4.50303 1.69240i 0.215904 0.0811442i
\(436\) 3.99417 7.95743i 0.191286 0.381092i
\(437\) −3.33328 5.77340i −0.159452 0.276179i
\(438\) −4.96676 38.9279i −0.237321 1.86005i
\(439\) 1.34898 + 0.778832i 0.0643832 + 0.0371716i 0.531846 0.846841i \(-0.321499\pi\)
−0.467463 + 0.884013i \(0.654832\pi\)
\(440\) −1.75292 1.46989i −0.0835673 0.0700741i
\(441\) −18.8594 6.42175i −0.898069 0.305797i
\(442\) −10.3082 + 3.08730i −0.490310 + 0.146848i
\(443\) 20.8779 + 12.0539i 0.991941 + 0.572697i 0.905854 0.423590i \(-0.139230\pi\)
0.0860869 + 0.996288i \(0.472564\pi\)
\(444\) −2.66962 + 25.1631i −0.126694 + 1.19419i
\(445\) −8.15613 + 4.70894i −0.386638 + 0.223225i
\(446\) 26.1914 27.7674i 1.24020 1.31482i
\(447\) −15.2088 12.4935i −0.719349 0.590922i
\(448\) 1.63659 4.50578i 0.0773215 0.212878i
\(449\) 22.7101i 1.07176i −0.844295 0.535879i \(-0.819980\pi\)
0.844295 0.535879i \(-0.180020\pi\)
\(450\) −4.23971 0.157760i −0.199862 0.00743687i
\(451\) −6.84161 −0.322159
\(452\) 32.9678 1.92746i 1.55067 0.0906603i
\(453\) 21.5356 + 3.56597i 1.01183 + 0.167544i
\(454\) 19.8841 21.0806i 0.933207 0.989361i
\(455\) −1.21893 2.11125i −0.0571443 0.0989768i
\(456\) 5.40027 15.3494i 0.252891 0.718803i
\(457\) 15.8352 27.4274i 0.740739 1.28300i −0.211420 0.977395i \(-0.567809\pi\)
0.952159 0.305603i \(-0.0988580\pi\)
\(458\) −4.90919 16.3912i −0.229391 0.765913i
\(459\) 8.56415 + 4.59321i 0.399740 + 0.214393i
\(460\) 3.35337 2.20661i 0.156352 0.102884i
\(461\) 0.934556 1.61870i 0.0435266 0.0753903i −0.843441 0.537221i \(-0.819474\pi\)
0.886968 + 0.461831i \(0.152807\pi\)
\(462\) −0.944716 + 0.718926i −0.0439522 + 0.0334474i
\(463\) −23.8604 + 13.7758i −1.10889 + 0.640217i −0.938541 0.345168i \(-0.887822\pi\)
−0.170347 + 0.985384i \(0.554489\pi\)
\(464\) −11.0338 + 1.29461i −0.512232 + 0.0601009i
\(465\) −7.97299 1.32021i −0.369739 0.0612231i
\(466\) −9.71215 2.30069i −0.449906 0.106577i
\(467\) 34.5674i 1.59959i 0.600273 + 0.799795i \(0.295059\pi\)
−0.600273 + 0.799795i \(0.704941\pi\)
\(468\) −17.3980 + 17.1220i −0.804222 + 0.791467i
\(469\) 8.00747i 0.369750i
\(470\) −4.40785 + 18.6073i −0.203319 + 0.858292i
\(471\) 19.6160 23.8793i 0.903859 1.10030i
\(472\) 3.63413 20.6502i 0.167274 0.950502i
\(473\) −5.87351 + 3.39107i −0.270064 + 0.155922i
\(474\) 4.20922 10.0482i 0.193336 0.461528i
\(475\) −1.66072 + 2.87646i −0.0761992 + 0.131981i
\(476\) 1.87240 1.23209i 0.0858212 0.0564727i
\(477\) −11.9038 + 10.4196i −0.545039 + 0.477079i
\(478\) 3.93334 1.17804i 0.179907 0.0538823i
\(479\) 3.19775 5.53866i 0.146109 0.253068i −0.783677 0.621168i \(-0.786658\pi\)
0.929786 + 0.368100i \(0.119992\pi\)
\(480\) 9.41666 + 2.70677i 0.429810 + 0.123546i
\(481\) −14.8591 25.7367i −0.677517 1.17349i
\(482\) 9.98414 + 9.41746i 0.454765 + 0.428954i
\(483\) −0.732878 1.95000i −0.0333471 0.0887279i
\(484\) 1.20768 + 20.6564i 0.0548945 + 0.938927i
\(485\) −3.91134 −0.177605
\(486\) 22.0450 + 0.129660i 0.999983 + 0.00588152i
\(487\) 9.60635i 0.435305i 0.976026 + 0.217653i \(0.0698400\pi\)
−0.976026 + 0.217653i \(0.930160\pi\)
\(488\) 13.4482 4.89980i 0.608772 0.221804i
\(489\) −20.1720 + 7.58135i −0.912208 + 0.342840i
\(490\) −6.83198 6.44422i −0.308637 0.291120i
\(491\) 1.42930 0.825208i 0.0645035 0.0372411i −0.467401 0.884045i \(-0.654810\pi\)
0.531905 + 0.846804i \(0.321476\pi\)
\(492\) 26.7809 11.8923i 1.20737 0.536145i
\(493\) −4.49849 2.59720i −0.202602 0.116972i
\(494\) 5.48283 + 18.3066i 0.246684 + 0.823652i
\(495\) −1.59812 1.82578i −0.0718303 0.0820627i
\(496\) 17.1404 + 7.38468i 0.769629 + 0.331582i
\(497\) −1.68273 0.971526i −0.0754809 0.0435789i
\(498\) −4.42018 + 10.5518i −0.198073 + 0.472837i
\(499\) 4.96576 + 8.60094i 0.222298 + 0.385031i 0.955505 0.294974i \(-0.0953109\pi\)
−0.733208 + 0.680005i \(0.761978\pi\)
\(500\) −1.78746 0.897203i −0.0799378 0.0401242i
\(501\) 32.5519 + 26.7403i 1.45431 + 1.19467i
\(502\) 10.0245 + 2.37469i 0.447417 + 0.105988i
\(503\) 16.1641 0.720722 0.360361 0.932813i \(-0.382654\pi\)
0.360361 + 0.932813i \(0.382654\pi\)
\(504\) 2.44835 4.45630i 0.109058 0.198499i
\(505\) 0.450761 0.0200586
\(506\) 2.23397 + 0.529199i 0.0993119 + 0.0235258i
\(507\) 1.00489 6.06876i 0.0446289 0.269523i
\(508\) 10.2832 20.4869i 0.456244 0.908958i
\(509\) −3.56528 6.17525i −0.158028 0.273713i 0.776129 0.630574i \(-0.217180\pi\)
−0.934158 + 0.356861i \(0.883847\pi\)
\(510\) 2.77429 + 3.64561i 0.122848 + 0.161430i
\(511\) −8.31405 4.80012i −0.367792 0.212345i
\(512\) −19.6072 11.2942i −0.866522 0.499138i
\(513\) 8.15722 15.2093i 0.360150 0.671508i
\(514\) −6.86342 22.9162i −0.302732 1.01079i
\(515\) −0.427706 0.246936i −0.0188470 0.0108813i
\(516\) 17.0969 23.4835i 0.752649 1.03381i
\(517\) −9.47106 + 5.46812i −0.416537 + 0.240488i
\(518\) 4.50310 + 4.24752i 0.197855 + 0.186625i
\(519\) −5.83065 + 35.2125i −0.255937 + 1.54566i
\(520\) −10.8118 + 3.93923i −0.474128 + 0.172746i
\(521\) 18.3498i 0.803921i 0.915657 + 0.401960i \(0.131671\pi\)
−0.915657 + 0.401960i \(0.868329\pi\)
\(522\) −11.7753 0.438158i −0.515389 0.0191777i
\(523\) −13.4690 −0.588957 −0.294478 0.955658i \(-0.595146\pi\)
−0.294478 + 0.955658i \(0.595146\pi\)
\(524\) −28.5365 + 1.66839i −1.24662 + 0.0728840i
\(525\) −0.658807 + 0.801988i −0.0287527 + 0.0350016i
\(526\) 6.75409 + 6.37074i 0.294492 + 0.277778i
\(527\) 4.36321 + 7.55730i 0.190064 + 0.329201i
\(528\) 2.56920 + 4.97986i 0.111810 + 0.216721i
\(529\) 9.48573 16.4298i 0.412423 0.714337i
\(530\) −7.14403 + 2.13964i −0.310317 + 0.0929401i
\(531\) 7.16847 21.0524i 0.311085 0.913598i
\(532\) −2.18810 3.32525i −0.0948662 0.144168i
\(533\) −17.2070 + 29.8033i −0.745316 + 1.29092i
\(534\) 22.8835 2.91967i 0.990266 0.126347i
\(535\) 0.131216 0.0757578i 0.00567298 0.00327529i
\(536\) 37.2244 + 6.55094i 1.60785 + 0.282957i
\(537\) −10.3534 27.5478i −0.446784 1.18878i
\(538\) −4.86130 + 20.5215i −0.209586 + 0.884747i
\(539\) 5.37121i 0.231354i
\(540\) 9.42933 + 4.36895i 0.405774 + 0.188010i
\(541\) 37.2583i 1.60186i −0.598758 0.800930i \(-0.704339\pi\)
0.598758 0.800930i \(-0.295661\pi\)
\(542\) 22.9612 + 5.43922i 0.986266 + 0.233634i
\(543\) 13.7226 + 36.5123i 0.588894 + 1.56689i
\(544\) −4.19580 9.71220i −0.179893 0.416407i
\(545\) 3.85537 2.22590i 0.165146 0.0953470i
\(546\) 0.755770 + 5.92349i 0.0323440 + 0.253502i
\(547\) 5.57601 9.65793i 0.238413 0.412943i −0.721846 0.692054i \(-0.756706\pi\)
0.960259 + 0.279110i \(0.0900395\pi\)
\(548\) −2.02529 3.07783i −0.0865162 0.131478i
\(549\) 14.8923 2.94768i 0.635589 0.125804i
\(550\) −0.328173 1.09573i −0.0139933 0.0467222i
\(551\) −4.61245 + 7.98900i −0.196497 + 0.340343i
\(552\) −9.66453 + 1.81164i −0.411350 + 0.0771083i
\(553\) −1.33254 2.30802i −0.0566652 0.0981471i
\(554\) 19.1760 20.3298i 0.814709 0.863732i
\(555\) −8.03105 + 9.77647i −0.340899 + 0.414988i
\(556\) −1.15047 19.6779i −0.0487907 0.834527i
\(557\) −11.3629 −0.481464 −0.240732 0.970592i \(-0.577387\pi\)
−0.240732 + 0.970592i \(0.577387\pi\)
\(558\) 16.7637 + 10.5285i 0.709663 + 0.445706i
\(559\) 34.1148i 1.44290i
\(560\) 1.92198 1.43218i 0.0812183 0.0605206i
\(561\) −0.428008 + 2.58483i −0.0180705 + 0.109131i
\(562\) −16.8367 + 17.8498i −0.710213 + 0.752948i
\(563\) 21.2512 12.2694i 0.895630 0.517092i 0.0198504 0.999803i \(-0.493681\pi\)
0.875780 + 0.482711i \(0.160348\pi\)
\(564\) 27.5688 37.8673i 1.16086 1.59450i
\(565\) 14.2998 + 8.25601i 0.601599 + 0.347333i
\(566\) 6.58900 1.97341i 0.276956 0.0829486i
\(567\) 3.29112 4.27238i 0.138214 0.179423i
\(568\) −5.89299 + 7.02772i −0.247264 + 0.294877i
\(569\) 22.0405 + 12.7251i 0.923986 + 0.533464i 0.884905 0.465772i \(-0.154223\pi\)
0.0390818 + 0.999236i \(0.487557\pi\)
\(570\) 6.47434 4.92695i 0.271180 0.206367i
\(571\) −14.0201 24.2836i −0.586725 1.01624i −0.994658 0.103225i \(-0.967084\pi\)
0.407933 0.913012i \(-0.366250\pi\)
\(572\) −5.88165 2.95225i −0.245924 0.123440i
\(573\) 2.07232 12.5151i 0.0865723 0.522828i
\(574\) 1.65237 6.97532i 0.0689685 0.291144i
\(575\) 2.00712 0.0837029
\(576\) −18.7130 15.0274i −0.779710 0.626141i
\(577\) −18.6560 −0.776659 −0.388329 0.921521i \(-0.626948\pi\)
−0.388329 + 0.921521i \(0.626948\pi\)
\(578\) −4.40154 + 18.5807i −0.183080 + 0.772855i
\(579\) 0.968714 + 0.795767i 0.0402584 + 0.0330710i
\(580\) −4.96446 2.49187i −0.206138 0.103469i
\(581\) 1.39932 + 2.42370i 0.0580537 + 0.100552i
\(582\) 8.83677 + 3.70176i 0.366296 + 0.153443i
\(583\) −3.69365 2.13253i −0.152975 0.0883203i
\(584\) −29.1161 + 34.7226i −1.20483 + 1.43683i
\(585\) −11.9728 + 2.36981i −0.495014 + 0.0979795i
\(586\) 43.3574 12.9856i 1.79108 0.536429i
\(587\) −17.4680 10.0851i −0.720980 0.416258i 0.0941335 0.995560i \(-0.469992\pi\)
−0.815113 + 0.579302i \(0.803325\pi\)
\(588\) 9.33637 + 21.0251i 0.385026 + 0.867061i
\(589\) 13.4212 7.74875i 0.553012 0.319282i
\(590\) 7.19355 7.62641i 0.296154 0.313974i
\(591\) 4.32747 1.62642i 0.178008 0.0669018i
\(592\) 23.4295 17.4587i 0.962945 0.717548i
\(593\) 27.7648i 1.14016i −0.821589 0.570081i \(-0.806912\pi\)
0.821589 0.570081i \(-0.193088\pi\)
\(594\) 1.88264 + 5.63742i 0.0772458 + 0.231306i
\(595\) 1.12070 0.0459444
\(596\) 1.32648 + 22.6884i 0.0543349 + 0.929355i
\(597\) 15.5265 + 41.3121i 0.635459 + 1.69079i
\(598\) 7.92381 8.40061i 0.324029 0.343527i
\(599\) 7.44295 + 12.8916i 0.304111 + 0.526735i 0.977063 0.212951i \(-0.0683075\pi\)
−0.672952 + 0.739686i \(0.734974\pi\)
\(600\) 3.18923 + 3.71871i 0.130200 + 0.151816i
\(601\) −17.1527 + 29.7093i −0.699671 + 1.21187i 0.268909 + 0.963166i \(0.413337\pi\)
−0.968580 + 0.248701i \(0.919996\pi\)
\(602\) −2.03879 6.80730i −0.0830950 0.277445i
\(603\) 37.9495 + 12.9220i 1.54542 + 0.526225i
\(604\) −13.8555 21.0561i −0.563771 0.856759i
\(605\) −5.17292 + 8.95976i −0.210309 + 0.364266i
\(606\) −1.01839 0.426607i −0.0413692 0.0173297i
\(607\) 15.5493 8.97738i 0.631126 0.364381i −0.150062 0.988677i \(-0.547947\pi\)
0.781188 + 0.624296i \(0.214614\pi\)
\(608\) −17.2482 + 7.45145i −0.699506 + 0.302196i
\(609\) −1.82975 + 2.22742i −0.0741454 + 0.0902597i
\(610\) 6.96379 + 1.64964i 0.281956 + 0.0667918i
\(611\) 55.0103i 2.22548i
\(612\) −2.81761 10.8620i −0.113895 0.439072i
\(613\) 21.2137i 0.856814i 0.903586 + 0.428407i \(0.140925\pi\)
−0.903586 + 0.428407i \(0.859075\pi\)
\(614\) 3.51795 14.8507i 0.141973 0.599327i
\(615\) 14.4545 + 2.39344i 0.582860 + 0.0965128i
\(616\) 1.35006 + 0.237591i 0.0543957 + 0.00957283i
\(617\) 21.3493 12.3260i 0.859491 0.496227i −0.00435075 0.999991i \(-0.501385\pi\)
0.863842 + 0.503763i \(0.168052\pi\)
\(618\) 0.732598 + 0.962683i 0.0294694 + 0.0387248i
\(619\) 13.3766 23.1689i 0.537650 0.931237i −0.461380 0.887203i \(-0.652645\pi\)
0.999030 0.0440347i \(-0.0140212\pi\)
\(620\) 5.12962 + 7.79545i 0.206010 + 0.313073i
\(621\) −10.4242 + 0.326503i −0.418309 + 0.0131021i
\(622\) −3.30487 + 0.989810i −0.132513 + 0.0396878i
\(623\) 2.82172 4.88735i 0.113050 0.195808i
\(624\) 28.1549 + 1.33268i 1.12710 + 0.0533498i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 14.1669 + 13.3629i 0.566225 + 0.534087i
\(627\) 4.59047 + 0.760112i 0.183326 + 0.0303559i
\(628\) −35.6231 + 2.08271i −1.42152 + 0.0831092i
\(629\) 13.6617 0.544729
\(630\) 2.24744 1.18840i 0.0895400 0.0473470i
\(631\) 31.8679i 1.26864i −0.773069 0.634322i \(-0.781280\pi\)
0.773069 0.634322i \(-0.218720\pi\)
\(632\) −11.8195 + 4.30637i −0.470153 + 0.171298i
\(633\) 18.9798 + 15.5913i 0.754379 + 0.619698i
\(634\) 16.1297 + 15.2142i 0.640592 + 0.604233i
\(635\) 9.92589 5.73071i 0.393897 0.227416i
\(636\) 18.1653 + 1.92720i 0.720300 + 0.0764185i
\(637\) −23.3980 13.5088i −0.927062 0.535239i
\(638\) −0.911459 3.04326i −0.0360850 0.120484i
\(639\) −7.31981 + 6.40711i −0.289567 + 0.253461i
\(640\) −5.08540 10.1064i −0.201018 0.399489i
\(641\) 2.74659 + 1.58575i 0.108484 + 0.0626332i 0.553260 0.833008i \(-0.313384\pi\)
−0.444776 + 0.895642i \(0.646717\pi\)
\(642\) −0.368151 + 0.0469719i −0.0145298 + 0.00185383i
\(643\) −18.4793 32.0071i −0.728752 1.26223i −0.957411 0.288728i \(-0.906768\pi\)
0.228659 0.973507i \(-0.426566\pi\)
\(644\) −1.07908 + 2.14982i −0.0425218 + 0.0847146i
\(645\) 13.5955 5.10966i 0.535321 0.201193i
\(646\) −8.54845 2.02502i −0.336334 0.0796735i
\(647\) −35.4240 −1.39266 −0.696331 0.717720i \(-0.745186\pi\)
−0.696331 + 0.717720i \(0.745186\pi\)
\(648\) −17.1685 18.7947i −0.674444 0.738326i
\(649\) 5.99577 0.235355
\(650\) −5.59858 1.32623i −0.219594 0.0520192i
\(651\) 4.53309 1.70369i 0.177666 0.0667731i
\(652\) 22.2390 + 11.1627i 0.870948 + 0.437165i
\(653\) 16.5954 + 28.7441i 0.649428 + 1.12484i 0.983260 + 0.182209i \(0.0583248\pi\)
−0.333832 + 0.942633i \(0.608342\pi\)
\(654\) −10.8169 + 1.38012i −0.422976 + 0.0539669i
\(655\) −12.3778 7.14631i −0.483640 0.279230i
\(656\) −31.0744 13.3879i −1.21325 0.522710i
\(657\) −36.1657 + 31.6562i −1.41096 + 1.23503i
\(658\) −3.28756 10.9768i −0.128163 0.427921i
\(659\) −19.4711 11.2416i −0.758487 0.437912i 0.0702655 0.997528i \(-0.477615\pi\)
−0.828752 + 0.559616i \(0.810949\pi\)
\(660\) −0.295589 + 2.78614i −0.0115058 + 0.108450i
\(661\) −43.5920 + 25.1678i −1.69553 + 0.978916i −0.745634 + 0.666356i \(0.767853\pi\)
−0.949898 + 0.312559i \(0.898814\pi\)
\(662\) 2.20866 + 2.08330i 0.0858420 + 0.0809699i
\(663\) 10.1835 + 8.36544i 0.395495 + 0.324887i
\(664\) 12.4118 4.52220i 0.481673 0.175495i
\(665\) 1.99029i 0.0771802i
\(666\) 27.3969 14.4870i 1.06161 0.561358i
\(667\) 5.57454 0.215847
\(668\) −2.83912 48.5610i −0.109849 1.87888i
\(669\) −46.1216 7.63703i −1.78316 0.295265i
\(670\) 13.7475 + 12.9672i 0.531112 + 0.500967i
\(671\) 2.04644 + 3.54454i 0.0790020 + 0.136836i
\(672\) −5.69770 + 1.41669i −0.219793 + 0.0546499i
\(673\) −14.4128 + 24.9638i −0.555574 + 0.962282i 0.442285 + 0.896875i \(0.354168\pi\)
−0.997859 + 0.0654077i \(0.979165\pi\)
\(674\) −29.1369 + 8.72652i −1.12231 + 0.336133i
\(675\) 2.73768 + 4.41646i 0.105373 + 0.169990i
\(676\) −5.93362 + 3.90448i −0.228216 + 0.150172i
\(677\) 19.2116 33.2754i 0.738361 1.27888i −0.214873 0.976642i \(-0.568934\pi\)
0.953233 0.302236i \(-0.0977330\pi\)
\(678\) −24.4935 32.1862i −0.940669 1.23610i
\(679\) 2.02977 1.17189i 0.0778953 0.0449729i
\(680\) 0.916852 5.20983i 0.0351597 0.199788i
\(681\) −35.0148 5.79792i −1.34177 0.222177i
\(682\) −1.23021 + 5.19322i −0.0471072 + 0.198859i
\(683\) 49.7921i 1.90524i 0.304160 + 0.952621i \(0.401624\pi\)
−0.304160 + 0.952621i \(0.598376\pi\)
\(684\) −19.2902 + 5.00388i −0.737580 + 0.191328i
\(685\) 1.84220i 0.0703869i
\(686\) 11.2485 + 2.66462i 0.429468 + 0.101736i
\(687\) −13.3021 + 16.1930i −0.507505 + 0.617803i
\(688\) −33.3131 + 3.90867i −1.27005 + 0.149017i
\(689\) −18.5794 + 10.7268i −0.707818 + 0.408659i
\(690\) −4.53463 1.89958i −0.172631 0.0723156i
\(691\) −22.6143 + 39.1691i −0.860289 + 1.49006i 0.0113615 + 0.999935i \(0.496383\pi\)
−0.871650 + 0.490128i \(0.836950\pi\)
\(692\) 34.4284 22.6548i 1.30877 0.861207i
\(693\) 1.37636 + 0.468659i 0.0522837 + 0.0178029i
\(694\) 8.14902 + 27.2087i 0.309332 + 1.03283i
\(695\) 4.92786 8.53531i 0.186925 0.323763i
\(696\) 8.85770 + 10.3283i 0.335750 + 0.391491i
\(697\) −7.91018 13.7008i −0.299620 0.518956i
\(698\) 3.85938 4.09160i 0.146080 0.154870i
\(699\) 4.30055 + 11.4426i 0.162662 + 0.432800i
\(700\) 1.19641 0.0699481i 0.0452199 0.00264379i
\(701\) 3.69419 0.139528 0.0697638 0.997564i \(-0.477775\pi\)
0.0697638 + 0.997564i \(0.477775\pi\)
\(702\) 29.2926 + 5.97721i 1.10558 + 0.225595i
\(703\) 24.2623i 0.915068i
\(704\) 2.20898 6.08168i 0.0832542 0.229212i
\(705\) 21.9227 8.23934i 0.825658 0.310312i
\(706\) −30.6844 + 32.5307i −1.15482 + 1.22431i
\(707\) −0.233919 + 0.135053i −0.00879744 + 0.00507921i
\(708\) −23.4699 + 10.4220i −0.882054 + 0.391683i
\(709\) 8.06684 + 4.65739i 0.302956 + 0.174912i 0.643770 0.765219i \(-0.277369\pi\)
−0.340814 + 0.940131i \(0.610703\pi\)
\(710\) −4.39295 + 1.31569i −0.164864 + 0.0493770i
\(711\) −13.0887 + 2.59068i −0.490864 + 0.0971581i
\(712\) −20.4114 17.1157i −0.764950 0.641438i
\(713\) −8.11035 4.68251i −0.303735 0.175361i
\(714\) −2.53197 1.06065i −0.0947567 0.0396939i
\(715\) −1.64525 2.84966i −0.0615289 0.106571i
\(716\) −15.2443 + 30.3707i −0.569707 + 1.13501i
\(717\) −3.88578 3.19205i −0.145117 0.119209i
\(718\) −8.01745 + 33.8450i −0.299209 + 1.26308i
\(719\) −28.6898 −1.06995 −0.534975 0.844868i \(-0.679679\pi\)
−0.534975 + 0.844868i \(0.679679\pi\)
\(720\) −3.68589 11.4199i −0.137365 0.425595i
\(721\) 0.295940 0.0110214
\(722\) 2.59747 10.9650i 0.0966680 0.408075i
\(723\) 2.74600 16.5836i 0.102125 0.616752i
\(724\) 20.2051 40.2538i 0.750915 1.49602i
\(725\) −1.38869 2.40528i −0.0515746 0.0893298i
\(726\) 20.1667 15.3468i 0.748456 0.569572i
\(727\) 37.1076 + 21.4241i 1.37624 + 0.794575i 0.991705 0.128534i \(-0.0410272\pi\)
0.384539 + 0.923109i \(0.374360\pi\)
\(728\) 4.43047 5.28358i 0.164204 0.195822i
\(729\) −14.9369 22.4920i −0.553217 0.833037i
\(730\) −21.7047 + 6.50057i −0.803326 + 0.240597i
\(731\) −13.5818 7.84143i −0.502340 0.290026i
\(732\) −14.1718 10.3176i −0.523806 0.381350i
\(733\) 32.8767 18.9813i 1.21433 0.701092i 0.250628 0.968083i \(-0.419363\pi\)
0.963699 + 0.266991i \(0.0860295\pi\)
\(734\) 7.10973 7.53754i 0.262425 0.278216i
\(735\) −1.87904 + 11.3479i −0.0693095 + 0.418574i
\(736\) 9.11106 + 6.77511i 0.335838 + 0.249734i
\(737\) 10.8081i 0.398121i
\(738\) −30.3913 19.0874i −1.11872 0.702616i
\(739\) 10.5865 0.389432 0.194716 0.980860i \(-0.437622\pi\)
0.194716 + 0.980860i \(0.437622\pi\)
\(740\) 14.5846 0.852688i 0.536139 0.0313454i
\(741\) 14.8564 18.0852i 0.545764 0.664377i
\(742\) 3.06629 3.25079i 0.112567 0.119340i
\(743\) 9.31534 + 16.1346i 0.341747 + 0.591922i 0.984757 0.173935i \(-0.0556482\pi\)
−0.643011 + 0.765857i \(0.722315\pi\)
\(744\) −4.21144 22.4668i −0.154399 0.823672i
\(745\) −5.68180 + 9.84116i −0.208165 + 0.360552i
\(746\) 13.0871 + 43.6965i 0.479154 + 1.59984i
\(747\) 13.7447 2.72052i 0.502891 0.0995387i
\(748\) 2.52727 1.66301i 0.0924061 0.0608057i
\(749\) −0.0453959 + 0.0786281i −0.00165873 + 0.00287301i
\(750\) 0.310014 + 2.42979i 0.0113201 + 0.0887235i
\(751\) 19.5847 11.3073i 0.714657 0.412608i −0.0981257 0.995174i \(-0.531285\pi\)
0.812783 + 0.582566i \(0.197951\pi\)
\(752\) −53.7175 + 6.30275i −1.95888 + 0.229838i
\(753\) −4.43888 11.8107i −0.161762 0.430405i
\(754\) −15.5494 3.68345i −0.566275 0.134143i
\(755\) 12.6029i 0.458666i
\(756\) −6.20228 + 0.557904i −0.225575 + 0.0202908i
\(757\) 35.8025i 1.30126i 0.759394 + 0.650631i \(0.225496\pi\)
−0.759394 + 0.650631i \(0.774504\pi\)
\(758\) 2.26633 9.56712i 0.0823169 0.347493i
\(759\) −0.989202 2.63201i −0.0359058 0.0955358i
\(760\) −9.25228 1.62826i −0.335616 0.0590634i
\(761\) −31.6012 + 18.2449i −1.14554 + 0.661379i −0.947797 0.318875i \(-0.896695\pi\)
−0.197745 + 0.980254i \(0.563362\pi\)
\(762\) −27.8489 + 3.55320i −1.00886 + 0.128719i
\(763\) −1.33381 + 2.31023i −0.0482873 + 0.0836360i
\(764\) −12.2365 + 8.05192i −0.442700 + 0.291308i
\(765\) 1.80853 5.31131i 0.0653875 0.192031i
\(766\) 37.2284 11.1499i 1.34512 0.402863i
\(767\) 15.0796 26.1187i 0.544494 0.943092i
\(768\) 1.92446 + 27.6459i 0.0694429 + 0.997586i
\(769\) 15.6746 + 27.1492i 0.565241 + 0.979026i 0.997027 + 0.0770499i \(0.0245501\pi\)
−0.431786 + 0.901976i \(0.642117\pi\)
\(770\) 0.498598 + 0.470299i 0.0179682 + 0.0169484i
\(771\) −18.5973 + 22.6391i −0.669765 + 0.815327i
\(772\) −0.0844897 1.44513i −0.00304085 0.0520113i
\(773\) −35.5512 −1.27869 −0.639344 0.768921i \(-0.720794\pi\)
−0.639344 + 0.768921i \(0.720794\pi\)
\(774\) −35.5517 1.32288i −1.27788 0.0475499i
\(775\) 4.66589i 0.167604i
\(776\) −3.78720 10.3945i −0.135952 0.373141i
\(777\) 1.23851 7.47964i 0.0444315 0.268331i
\(778\) 32.6207 + 30.7692i 1.16951 + 1.10313i
\(779\) −24.3317 + 14.0479i −0.871774 + 0.503319i
\(780\) 11.3935 + 8.29491i 0.407954 + 0.297005i
\(781\) −2.27127 1.31132i −0.0812724 0.0469226i
\(782\) 1.52312 + 5.08554i 0.0544668 + 0.181859i
\(783\) 7.60357 + 12.2662i 0.271729 + 0.438357i
\(784\) 10.5106 24.3959i 0.375377 0.871282i
\(785\) −15.4516 8.92099i −0.551491 0.318404i
\(786\) 21.2013 + 27.8600i 0.756227 + 0.993733i
\(787\) −2.50484 4.33851i −0.0892879 0.154651i 0.817922 0.575329i \(-0.195126\pi\)
−0.907210 + 0.420677i \(0.861792\pi\)
\(788\) −4.77091 2.39472i −0.169957 0.0853084i
\(789\) 1.85762 11.2185i 0.0661329 0.399390i
\(790\) −6.12039 1.44984i −0.217754 0.0515831i
\(791\) −9.89441 −0.351805
\(792\) 3.30467 6.01489i 0.117426 0.213730i
\(793\) 20.5876 0.731086
\(794\) 3.75073 + 0.888502i 0.133108 + 0.0315317i
\(795\) 7.05765 + 5.79763i 0.250309 + 0.205621i
\(796\) 22.8611 45.5454i 0.810292 1.61431i
\(797\) 8.82804 + 15.2906i 0.312705 + 0.541621i 0.978947 0.204114i \(-0.0654315\pi\)
−0.666242 + 0.745736i \(0.732098\pi\)
\(798\) −1.88364 + 4.49660i −0.0666803 + 0.159178i
\(799\) −21.9006 12.6443i −0.774789 0.447325i
\(800\) 0.653616 5.61897i 0.0231088 0.198660i
\(801\) −18.6089 21.2598i −0.657513 0.751177i
\(802\) 4.52397 + 15.1050i 0.159747 + 0.533378i
\(803\) −11.2219 6.47896i −0.396012 0.228637i
\(804\) −18.7869 42.3073i −0.662562 1.49206i
\(805\) −1.04158 + 0.601359i −0.0367110 + 0.0211951i
\(806\) 19.5286 + 18.4202i 0.687866 + 0.648824i
\(807\) 24.1780 9.08696i 0.851106 0.319876i
\(808\) 0.436453 + 1.19791i 0.0153544 + 0.0421423i
\(809\) 52.1748i 1.83437i −0.398463 0.917184i \(-0.630456\pi\)
0.398463 0.917184i \(-0.369544\pi\)
\(810\) −2.00535 12.5690i −0.0704607 0.441628i
\(811\) 13.3347 0.468244 0.234122 0.972207i \(-0.424778\pi\)
0.234122 + 0.972207i \(0.424778\pi\)
\(812\) 3.32287 0.194272i 0.116610 0.00681761i
\(813\) −10.1672 27.0523i −0.356580 0.948766i
\(814\) 6.07806 + 5.73309i 0.213036 + 0.200945i
\(815\) 6.22083 + 10.7748i 0.217906 + 0.377425i
\(816\) −7.00208 + 10.9027i −0.245122 + 0.381670i
\(817\) −13.9258 + 24.1202i −0.487203 + 0.843861i
\(818\) −14.3353 + 4.29343i −0.501221 + 0.150116i
\(819\) 5.50318 4.81699i 0.192297 0.168319i
\(820\) −9.29963 14.1326i −0.324757 0.493532i
\(821\) 18.4884 32.0228i 0.645249 1.11760i −0.338995 0.940788i \(-0.610087\pi\)
0.984244 0.176816i \(-0.0565797\pi\)
\(822\) −1.74349 + 4.16203i −0.0608112 + 0.145167i
\(823\) −29.4402 + 16.9973i −1.02622 + 0.592488i −0.915899 0.401408i \(-0.868521\pi\)
−0.110320 + 0.993896i \(0.535188\pi\)
\(824\) 0.242110 1.37574i 0.00843429 0.0479262i
\(825\) −0.889225 + 1.08248i −0.0309588 + 0.0376872i
\(826\) −1.44808 + 6.11295i −0.0503853 + 0.212697i
\(827\) 19.2929i 0.670881i 0.942061 + 0.335441i \(0.108885\pi\)
−0.942061 + 0.335441i \(0.891115\pi\)
\(828\) 8.44717 + 8.58330i 0.293559 + 0.298290i
\(829\) 18.2468i 0.633737i −0.948469 0.316869i \(-0.897369\pi\)
0.948469 0.316869i \(-0.102631\pi\)
\(830\) 6.42713 + 1.52251i 0.223089 + 0.0528470i
\(831\) −33.7678 5.59144i −1.17139 0.193965i
\(832\) −20.9372 24.9184i −0.725868 0.863892i
\(833\) 10.7562 6.21012i 0.372682 0.215168i
\(834\) −19.2113 + 14.6197i −0.665234 + 0.506241i
\(835\) 12.1610 21.0634i 0.420848 0.728930i
\(836\) −2.95339 4.48825i −0.102145 0.155229i
\(837\) −0.759009 24.2328i −0.0262352 0.837608i
\(838\) 4.99149 + 16.6660i 0.172428 + 0.575718i
\(839\) −1.62551 + 2.81546i −0.0561187 + 0.0972005i −0.892720 0.450612i \(-0.851206\pi\)
0.836601 + 0.547812i \(0.184539\pi\)
\(840\) −2.76920 0.974267i −0.0955466 0.0336154i
\(841\) 10.6431 + 18.4344i 0.367003 + 0.635668i
\(842\) 35.6677 37.8139i 1.22919 1.30315i
\(843\) 29.6485 + 4.90934i 1.02115 + 0.169087i
\(844\) −1.65539 28.3141i −0.0569807 0.974610i
\(845\) −3.55151 −0.122176
\(846\) −57.3272 2.13315i −1.97095 0.0733392i
\(847\) 6.19948i 0.213017i
\(848\) −12.6034 16.9138i −0.432804 0.580821i
\(849\) −6.50933 5.34720i −0.223399 0.183515i
\(850\) 1.81486 1.92406i 0.0622491 0.0659948i
\(851\) −12.6972 + 7.33075i −0.435256 + 0.251295i
\(852\) 11.1700 + 1.18506i 0.382680 + 0.0405994i
\(853\) 30.7596 + 17.7590i 1.05319 + 0.608058i 0.923540 0.383502i \(-0.125282\pi\)
0.129648 + 0.991560i \(0.458615\pi\)
\(854\) −4.10807 + 1.23037i −0.140575 + 0.0421024i
\(855\) −9.43251 3.21182i −0.322585 0.109842i
\(856\) 0.328380 + 0.275358i 0.0112238 + 0.00941155i
\(857\) −8.43191 4.86817i −0.288029 0.166293i 0.349024 0.937114i \(-0.386513\pi\)
−0.637052 + 0.770820i \(0.719847\pi\)
\(858\) 1.02010 + 7.99523i 0.0348256 + 0.272953i
\(859\) 10.2239 + 17.7083i 0.348835 + 0.604200i 0.986043 0.166492i \(-0.0532439\pi\)
−0.637208 + 0.770692i \(0.719911\pi\)
\(860\) −14.9886 7.52341i −0.511107 0.256546i
\(861\) −8.21816 + 3.08868i −0.280074 + 0.105262i
\(862\) 10.2834 43.4107i 0.350256 1.47857i
\(863\) 15.1892 0.517047 0.258523 0.966005i \(-0.416764\pi\)
0.258523 + 0.966005i \(0.416764\pi\)
\(864\) −2.48058 + 29.2890i −0.0843909 + 0.996433i
\(865\) 20.6068 0.700651
\(866\) 7.07154 29.8519i 0.240301 1.01441i
\(867\) 21.8913 8.22754i 0.743469 0.279422i
\(868\) −4.99760 2.50851i −0.169630 0.0851442i
\(869\) −1.79859 3.11525i −0.0610130 0.105678i
\(870\) 0.861025 + 6.74845i 0.0291915 + 0.228794i
\(871\) 47.0820 + 27.1828i 1.59531 + 0.921054i
\(872\) 9.64840 + 8.09052i 0.326736 + 0.273979i
\(873\) −2.27835 11.5107i −0.0771104 0.389579i
\(874\) 9.03156 2.70496i 0.305497 0.0914966i
\(875\) 0.518944 + 0.299612i 0.0175435 + 0.0101287i
\(876\) 55.1890 + 5.85514i 1.86466 + 0.197827i
\(877\) 17.8435 10.3020i 0.602533 0.347873i −0.167504 0.985871i \(-0.553571\pi\)
0.770037 + 0.637999i \(0.220238\pi\)
\(878\) −1.51152 + 1.60248i −0.0510115 + 0.0540810i
\(879\) −42.8331 35.1860i −1.44472 1.18679i
\(880\) 2.59419 1.93308i 0.0874500 0.0651642i
\(881\) 13.0624i 0.440083i −0.975490 0.220042i \(-0.929381\pi\)
0.975490 0.220042i \(-0.0706193\pi\)
\(882\) 14.9851 23.8596i 0.504575 0.803395i
\(883\) 38.3841 1.29173 0.645864 0.763452i \(-0.276497\pi\)
0.645864 + 0.763452i \(0.276497\pi\)
\(884\) −0.888191 15.1918i −0.0298731 0.510955i
\(885\) −12.6675 2.09754i −0.425812 0.0705079i
\(886\) −23.3937 + 24.8013i −0.785925 + 0.833217i
\(887\) 0.0432052 + 0.0748336i 0.00145069 + 0.00251267i 0.866750 0.498743i \(-0.166205\pi\)
−0.865299 + 0.501256i \(0.832872\pi\)
\(888\) −33.7574 11.8766i −1.13283 0.398553i
\(889\) −3.43398 + 5.94784i −0.115172 + 0.199484i
\(890\) −3.82132 12.7589i −0.128091 0.427681i
\(891\) 4.44219 5.76664i 0.148819 0.193190i
\(892\) 29.6734 + 45.0946i 0.993541 + 1.50988i
\(893\) −22.4555 + 38.8940i −0.751443 + 1.30154i
\(894\) 22.1505 16.8565i 0.740825 0.563765i
\(895\) −14.7146 + 8.49547i −0.491854 + 0.283972i
\(896\) 5.66703 + 3.72099i 0.189322 + 0.124309i
\(897\) −13.9534 2.31047i −0.465891 0.0771444i
\(898\) 31.2521 + 7.40323i 1.04290 + 0.247049i
\(899\) 12.9589i 0.432205i
\(900\) 1.59919 5.78296i 0.0533064 0.192765i
\(901\) 9.86242i 0.328565i
\(902\) 2.23028 9.41494i 0.0742603 0.313483i
\(903\) −5.52436 + 6.72499i −0.183839 + 0.223794i
\(904\) −8.09465 + 45.9962i −0.269224 + 1.52981i
\(905\) 19.5029 11.2600i 0.648300 0.374296i
\(906\) −11.9276 + 28.4733i −0.396268 + 0.945963i
\(907\) −1.90025 + 3.29134i −0.0630969 + 0.109287i −0.895848 0.444360i \(-0.853431\pi\)
0.832751 + 0.553647i \(0.186764\pi\)
\(908\) 22.5276 + 34.2351i 0.747606 + 1.13613i
\(909\) 0.262567 + 1.32655i 0.00870880 + 0.0439988i
\(910\) 3.30271 0.989163i 0.109484 0.0327904i
\(911\) −24.8293 + 43.0056i −0.822630 + 1.42484i 0.0810866 + 0.996707i \(0.474161\pi\)
−0.903717 + 0.428130i \(0.859172\pi\)
\(912\) 19.3624 + 12.4352i 0.641152 + 0.411771i
\(913\) 1.88873 + 3.27138i 0.0625080 + 0.108267i
\(914\) 32.5815 + 30.7323i 1.07770 + 1.01653i
\(915\) −3.08357 8.20458i −0.101940 0.271235i
\(916\) 24.1568 1.41233i 0.798164 0.0466647i
\(917\) 8.56450 0.282825
\(918\) −9.11266 + 10.2880i −0.300763 + 0.339556i
\(919\) 6.89894i 0.227575i −0.993505 0.113787i \(-0.963702\pi\)
0.993505 0.113787i \(-0.0362983\pi\)
\(920\) 1.94342 + 5.33400i 0.0640726 + 0.175857i
\(921\) −17.4968 + 6.57591i −0.576539 + 0.216684i
\(922\) 1.92288 + 1.81375i 0.0633268 + 0.0597325i
\(923\) −11.4247 + 6.59605i −0.376048 + 0.217112i
\(924\) −0.681368 1.53441i −0.0224154 0.0504785i
\(925\) 6.32608 + 3.65236i 0.208000 + 0.120089i
\(926\) −11.1791 37.3258i −0.367368 1.22660i
\(927\) 0.477572 1.40254i 0.0156855 0.0460654i
\(928\) 1.81534 15.6060i 0.0595914 0.512292i
\(929\) −24.6040 14.2051i −0.807231 0.466055i 0.0387624 0.999248i \(-0.487658\pi\)
−0.845993 + 0.533193i \(0.820992\pi\)
\(930\) 4.41587 10.5415i 0.144802 0.345669i
\(931\) −11.0287 19.1023i −0.361452 0.626054i
\(932\) 6.33209 12.6152i 0.207414 0.413224i
\(933\) 3.26491 + 2.68201i 0.106888 + 0.0878052i
\(934\) −47.5693 11.2686i −1.55651 0.368719i
\(935\) 1.51267 0.0494696
\(936\) −17.8906 29.5235i −0.584773 0.965005i
\(937\) −12.4845 −0.407852 −0.203926 0.978986i \(-0.565370\pi\)
−0.203926 + 0.978986i \(0.565370\pi\)
\(938\) −11.0193 2.61034i −0.359793 0.0852306i
\(939\) 3.89642 23.5313i 0.127155 0.767913i
\(940\) −24.1692 12.1315i −0.788312 0.395687i
\(941\) −10.2303 17.7194i −0.333498 0.577636i 0.649697 0.760193i \(-0.274896\pi\)
−0.983195 + 0.182558i \(0.941562\pi\)
\(942\) 26.4664 + 34.7786i 0.862320 + 1.13315i
\(943\) 14.7035 + 8.48906i 0.478811 + 0.276442i
\(944\) 27.2327 + 11.7327i 0.886347 + 0.381868i
\(945\) −2.74393 1.47165i −0.0892600 0.0478728i
\(946\) −2.75186 9.18816i −0.0894707 0.298733i
\(947\) −6.24338 3.60462i −0.202883 0.117134i 0.395117 0.918631i \(-0.370704\pi\)
−0.597999 + 0.801497i \(0.704037\pi\)
\(948\) 12.4554 + 9.06802i 0.404534 + 0.294516i
\(949\) −56.4471 + 32.5897i −1.83235 + 1.05791i
\(950\) −3.41700 3.22306i −0.110862 0.104570i
\(951\) 4.43624 26.7914i 0.143855 0.868770i
\(952\) 1.08513 + 2.97831i 0.0351694 + 0.0965275i
\(953\) 22.0465i 0.714157i −0.934074 0.357079i \(-0.883773\pi\)
0.934074 0.357079i \(-0.116227\pi\)
\(954\) −10.4582 19.7779i −0.338595 0.640332i
\(955\) −7.32401 −0.236999
\(956\) 0.338912 + 5.79682i 0.0109612 + 0.187482i
\(957\) −2.46971 + 3.00646i −0.0798344 + 0.0971851i
\(958\) 6.57948 + 6.20605i 0.212574 + 0.200508i
\(959\) 0.551946 + 0.955999i 0.0178233 + 0.0308708i
\(960\) −6.79458 + 12.0762i −0.219294 + 0.389756i
\(961\) −4.61474 + 7.99296i −0.148862 + 0.257837i
\(962\) 40.2610 12.0582i 1.29807 0.388772i
\(963\) 0.299381 + 0.342029i 0.00964743 + 0.0110217i
\(964\) −16.2144 + 10.6695i −0.522229 + 0.343641i
\(965\) 0.361899 0.626828i 0.0116499 0.0201783i
\(966\) 2.92236 0.372859i 0.0940253 0.0119965i
\(967\) −17.7473 + 10.2464i −0.570714 + 0.329502i −0.757434 0.652911i \(-0.773547\pi\)
0.186720 + 0.982413i \(0.440214\pi\)
\(968\) −28.8196 5.07182i −0.926296 0.163014i
\(969\) 3.78526 + 10.0716i 0.121600 + 0.323546i
\(970\) 1.27505 5.38251i 0.0409394 0.172822i
\(971\) 22.1348i 0.710341i −0.934802 0.355170i \(-0.884423\pi\)
0.934802 0.355170i \(-0.115577\pi\)
\(972\) −7.36484 + 30.2945i −0.236227 + 0.971698i
\(973\) 5.90580i 0.189331i
\(974\) −13.2196 3.13155i −0.423583 0.100341i
\(975\) 2.47906 + 6.59612i 0.0793933 + 0.211245i
\(976\) 2.35880 + 20.1038i 0.0755034 + 0.643506i
\(977\) 37.3001 21.5352i 1.19334 0.688974i 0.234275 0.972170i \(-0.424728\pi\)
0.959062 + 0.283197i \(0.0913949\pi\)
\(978\) −3.85709 30.2307i −0.123336 0.966670i
\(979\) 3.80861 6.59671i 0.121724 0.210832i
\(980\) 11.0952 7.30095i 0.354424 0.233220i
\(981\) 8.79636 + 10.0494i 0.280846 + 0.320853i
\(982\) 0.669657 + 2.23591i 0.0213696 + 0.0713508i
\(983\) 18.6912 32.3741i 0.596157 1.03257i −0.397226 0.917721i \(-0.630027\pi\)
0.993383 0.114853i \(-0.0366396\pi\)
\(984\) 7.63505 + 40.7307i 0.243396 + 1.29845i
\(985\) −1.33455 2.31150i −0.0425222 0.0736506i
\(986\) 5.04054 5.34385i 0.160524 0.170183i
\(987\) −8.90806 + 10.8441i −0.283547 + 0.345171i
\(988\) −26.9796 + 1.57736i −0.858334 + 0.0501826i
\(989\) 16.8306 0.535180
\(990\) 3.03348 1.60404i 0.0964102 0.0509798i
\(991\) 25.8741i 0.821917i 0.911654 + 0.410959i \(0.134806\pi\)
−0.911654 + 0.410959i \(0.865194\pi\)
\(992\) −15.7499 + 21.1802i −0.500058 + 0.672471i
\(993\) 0.607461 3.66858i 0.0192772 0.116419i
\(994\) 1.88550 1.99895i 0.0598043 0.0634029i
\(995\) 22.0667 12.7402i 0.699562 0.403892i
\(996\) −13.0797 9.52250i −0.414446 0.301732i
\(997\) 9.32829 + 5.38569i 0.295430 + 0.170566i 0.640388 0.768052i \(-0.278774\pi\)
−0.344958 + 0.938618i \(0.612107\pi\)
\(998\) −13.4548 + 4.02972i −0.425904 + 0.127559i
\(999\) −33.4493 17.9399i −1.05829 0.567592i
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 360.2.bm.a.11.11 48
3.2 odd 2 1080.2.bm.b.251.14 48
4.3 odd 2 1440.2.cc.a.911.3 48
8.3 odd 2 360.2.bm.b.11.20 yes 48
8.5 even 2 1440.2.cc.b.911.3 48
9.4 even 3 1080.2.bm.a.611.5 48
9.5 odd 6 360.2.bm.b.131.20 yes 48
12.11 even 2 4320.2.cc.b.1871.13 48
24.5 odd 2 4320.2.cc.a.1871.12 48
24.11 even 2 1080.2.bm.a.251.5 48
36.23 even 6 1440.2.cc.b.1391.3 48
36.31 odd 6 4320.2.cc.a.3311.12 48
72.5 odd 6 1440.2.cc.a.1391.3 48
72.13 even 6 4320.2.cc.b.3311.13 48
72.59 even 6 inner 360.2.bm.a.131.11 yes 48
72.67 odd 6 1080.2.bm.b.611.14 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bm.a.11.11 48 1.1 even 1 trivial
360.2.bm.a.131.11 yes 48 72.59 even 6 inner
360.2.bm.b.11.20 yes 48 8.3 odd 2
360.2.bm.b.131.20 yes 48 9.5 odd 6
1080.2.bm.a.251.5 48 24.11 even 2
1080.2.bm.a.611.5 48 9.4 even 3
1080.2.bm.b.251.14 48 3.2 odd 2
1080.2.bm.b.611.14 48 72.67 odd 6
1440.2.cc.a.911.3 48 4.3 odd 2
1440.2.cc.a.1391.3 48 72.5 odd 6
1440.2.cc.b.911.3 48 8.5 even 2
1440.2.cc.b.1391.3 48 36.23 even 6
4320.2.cc.a.1871.12 48 24.5 odd 2
4320.2.cc.a.3311.12 48 36.31 odd 6
4320.2.cc.b.1871.13 48 12.11 even 2
4320.2.cc.b.3311.13 48 72.13 even 6