Properties

Label 273.2.i.b.235.2
Level $273$
Weight $2$
Character 273.235
Analytic conductor $2.180$
Analytic rank $0$
Dimension $6$
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] = [273,2,Mod(79,273)]
 
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, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.i (of order \(3\), 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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.2
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 273.235
Dual form 273.2.i.b.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.173648 + 0.300767i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.326352 - 0.565258i) q^{5} +0.347296 q^{6} +(-2.05303 - 1.66885i) q^{7} +1.34730 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.173648 + 0.300767i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.939693 - 1.62760i) q^{4} +(-0.326352 - 0.565258i) q^{5} +0.347296 q^{6} +(-2.05303 - 1.66885i) q^{7} +1.34730 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.113341 - 0.196312i) q^{10} +(-0.266044 + 0.460802i) q^{11} +(-0.939693 - 1.62760i) q^{12} +1.00000 q^{13} +(0.145430 - 0.907278i) q^{14} -0.652704 q^{15} +(-1.64543 - 2.84997i) q^{16} +(-0.560307 + 0.970481i) q^{17} +(0.173648 - 0.300767i) q^{18} +(-0.152704 - 0.264490i) q^{19} -1.22668 q^{20} +(-2.47178 + 0.943555i) q^{21} -0.184793 q^{22} +(4.00387 + 6.93491i) q^{23} +(0.673648 - 1.16679i) q^{24} +(2.28699 - 3.96118i) q^{25} +(0.173648 + 0.300767i) q^{26} -1.00000 q^{27} +(-4.64543 + 1.77330i) q^{28} +7.78106 q^{29} +(-0.113341 - 0.196312i) q^{30} +(-0.294263 + 0.509678i) q^{31} +(1.91875 - 3.32337i) q^{32} +(0.266044 + 0.460802i) q^{33} -0.389185 q^{34} +(-0.273318 + 1.70513i) q^{35} -1.87939 q^{36} +(1.43969 + 2.49362i) q^{37} +(0.0530334 - 0.0918566i) q^{38} +(0.500000 - 0.866025i) q^{39} +(-0.439693 - 0.761570i) q^{40} -1.04189 q^{41} +(-0.713011 - 0.579585i) q^{42} +2.94356 q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.326352 + 0.565258i) q^{45} +(-1.39053 + 2.40847i) q^{46} +(2.06418 + 3.57526i) q^{47} -3.29086 q^{48} +(1.42989 + 6.85240i) q^{49} +1.58853 q^{50} +(0.560307 + 0.970481i) q^{51} +(0.939693 - 1.62760i) q^{52} +(1.26604 - 2.19285i) q^{53} +(-0.173648 - 0.300767i) q^{54} +0.347296 q^{55} +(-2.76604 - 2.24843i) q^{56} -0.305407 q^{57} +(1.35117 + 2.34029i) q^{58} +(-7.19119 + 12.4555i) q^{59} +(-0.613341 + 1.06234i) q^{60} +(-3.92989 - 6.80677i) q^{61} -0.204393 q^{62} +(-0.418748 + 2.61240i) q^{63} -5.24897 q^{64} +(-0.326352 - 0.565258i) q^{65} +(-0.0923963 + 0.160035i) q^{66} +(-2.33022 + 4.03606i) q^{67} +(1.05303 + 1.82391i) q^{68} +8.00774 q^{69} +(-0.560307 + 0.213887i) q^{70} -3.92902 q^{71} +(-0.673648 - 1.16679i) q^{72} +(-5.81180 + 10.0663i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(-2.28699 - 3.96118i) q^{75} -0.573978 q^{76} +(1.31521 - 0.502055i) q^{77} +0.347296 q^{78} +(-1.46451 - 2.53660i) q^{79} +(-1.07398 + 1.86018i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.180922 - 0.313366i) q^{82} -2.46791 q^{83} +(-0.786989 + 4.90971i) q^{84} +0.731429 q^{85} +(0.511144 + 0.885328i) q^{86} +(3.89053 - 6.73859i) q^{87} +(-0.358441 + 0.620838i) q^{88} +(-5.49273 - 9.51368i) q^{89} -0.226682 q^{90} +(-2.05303 - 1.66885i) q^{91} +15.0496 q^{92} +(0.294263 + 0.509678i) q^{93} +(-0.716881 + 1.24168i) q^{94} +(-0.0996702 + 0.172634i) q^{95} +(-1.91875 - 3.32337i) q^{96} +10.2686 q^{97} +(-1.81268 + 1.61997i) q^{98} +0.532089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{3} - 3 q^{5} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{11} + 6 q^{13} - 15 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} - 3 q^{19} + 6 q^{20} + 6 q^{22} + 3 q^{24} + 6 q^{25} - 6 q^{27} - 12 q^{28} + 12 q^{29} + 6 q^{30} - 12 q^{31} + 9 q^{32} - 3 q^{33} + 6 q^{34} - 15 q^{35} + 3 q^{37} - 12 q^{38} + 3 q^{39} + 3 q^{40} - 12 q^{42} - 12 q^{43} + 3 q^{44} - 3 q^{45} + 9 q^{46} - 6 q^{47} + 12 q^{48} + 30 q^{50} + 9 q^{51} + 3 q^{53} - 12 q^{56} - 6 q^{57} - 18 q^{58} + 3 q^{59} + 3 q^{60} - 15 q^{61} - 6 q^{64} - 3 q^{65} + 3 q^{66} + 9 q^{67} - 6 q^{68} - 9 q^{70} + 42 q^{71} - 3 q^{72} - 3 q^{74} - 6 q^{75} + 12 q^{76} + 15 q^{77} + 24 q^{79} + 9 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} + 3 q^{84} + 24 q^{85} - 3 q^{86} + 6 q^{87} + 6 q^{88} - 15 q^{89} + 12 q^{90} + 36 q^{92} + 12 q^{93} + 12 q^{94} - 15 q^{95} - 9 q^{96} + 42 q^{97} - 33 q^{98} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 + 0.300767i 0.122788 + 0.212675i 0.920866 0.389879i \(-0.127483\pi\)
−0.798078 + 0.602554i \(0.794150\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.939693 1.62760i 0.469846 0.813798i
\(5\) −0.326352 0.565258i −0.145949 0.252791i 0.783778 0.621042i \(-0.213290\pi\)
−0.929727 + 0.368251i \(0.879957\pi\)
\(6\) 0.347296 0.141783
\(7\) −2.05303 1.66885i −0.775974 0.630765i
\(8\) 1.34730 0.476341
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.113341 0.196312i 0.0358415 0.0620793i
\(11\) −0.266044 + 0.460802i −0.0802154 + 0.138937i −0.903342 0.428920i \(-0.858894\pi\)
0.823127 + 0.567857i \(0.192227\pi\)
\(12\) −0.939693 1.62760i −0.271266 0.469846i
\(13\) 1.00000 0.277350
\(14\) 0.145430 0.907278i 0.0388677 0.242480i
\(15\) −0.652704 −0.168527
\(16\) −1.64543 2.84997i −0.411357 0.712492i
\(17\) −0.560307 + 0.970481i −0.135895 + 0.235376i −0.925939 0.377674i \(-0.876724\pi\)
0.790044 + 0.613050i \(0.210057\pi\)
\(18\) 0.173648 0.300767i 0.0409293 0.0708916i
\(19\) −0.152704 0.264490i −0.0350326 0.0606783i 0.847978 0.530032i \(-0.177820\pi\)
−0.883010 + 0.469354i \(0.844487\pi\)
\(20\) −1.22668 −0.274294
\(21\) −2.47178 + 0.943555i −0.539387 + 0.205901i
\(22\) −0.184793 −0.0393979
\(23\) 4.00387 + 6.93491i 0.834865 + 1.44603i 0.894141 + 0.447786i \(0.147788\pi\)
−0.0592759 + 0.998242i \(0.518879\pi\)
\(24\) 0.673648 1.16679i 0.137508 0.238171i
\(25\) 2.28699 3.96118i 0.457398 0.792236i
\(26\) 0.173648 + 0.300767i 0.0340552 + 0.0589854i
\(27\) −1.00000 −0.192450
\(28\) −4.64543 + 1.77330i −0.877904 + 0.335123i
\(29\) 7.78106 1.44491 0.722453 0.691420i \(-0.243014\pi\)
0.722453 + 0.691420i \(0.243014\pi\)
\(30\) −0.113341 0.196312i −0.0206931 0.0358415i
\(31\) −0.294263 + 0.509678i −0.0528512 + 0.0915409i −0.891241 0.453531i \(-0.850164\pi\)
0.838389 + 0.545072i \(0.183498\pi\)
\(32\) 1.91875 3.32337i 0.339190 0.587494i
\(33\) 0.266044 + 0.460802i 0.0463124 + 0.0802154i
\(34\) −0.389185 −0.0667447
\(35\) −0.273318 + 1.70513i −0.0461992 + 0.288219i
\(36\) −1.87939 −0.313231
\(37\) 1.43969 + 2.49362i 0.236684 + 0.409949i 0.959761 0.280819i \(-0.0906061\pi\)
−0.723077 + 0.690768i \(0.757273\pi\)
\(38\) 0.0530334 0.0918566i 0.00860316 0.0149011i
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) −0.439693 0.761570i −0.0695215 0.120415i
\(41\) −1.04189 −0.162716 −0.0813579 0.996685i \(-0.525926\pi\)
−0.0813579 + 0.996685i \(0.525926\pi\)
\(42\) −0.713011 0.579585i −0.110020 0.0894319i
\(43\) 2.94356 0.448889 0.224445 0.974487i \(-0.427943\pi\)
0.224445 + 0.974487i \(0.427943\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) −0.326352 + 0.565258i −0.0486497 + 0.0842637i
\(46\) −1.39053 + 2.40847i −0.205022 + 0.355109i
\(47\) 2.06418 + 3.57526i 0.301091 + 0.521505i 0.976383 0.216045i \(-0.0693158\pi\)
−0.675292 + 0.737550i \(0.735982\pi\)
\(48\) −3.29086 −0.474995
\(49\) 1.42989 + 6.85240i 0.204270 + 0.978915i
\(50\) 1.58853 0.224651
\(51\) 0.560307 + 0.970481i 0.0784587 + 0.135895i
\(52\) 0.939693 1.62760i 0.130312 0.225707i
\(53\) 1.26604 2.19285i 0.173905 0.301212i −0.765877 0.642987i \(-0.777695\pi\)
0.939782 + 0.341775i \(0.111028\pi\)
\(54\) −0.173648 0.300767i −0.0236305 0.0409293i
\(55\) 0.347296 0.0468294
\(56\) −2.76604 2.24843i −0.369628 0.300459i
\(57\) −0.305407 −0.0404522
\(58\) 1.35117 + 2.34029i 0.177417 + 0.307295i
\(59\) −7.19119 + 12.4555i −0.936213 + 1.62157i −0.163757 + 0.986501i \(0.552361\pi\)
−0.772456 + 0.635068i \(0.780972\pi\)
\(60\) −0.613341 + 1.06234i −0.0791820 + 0.137147i
\(61\) −3.92989 6.80677i −0.503171 0.871518i −0.999993 0.00366563i \(-0.998833\pi\)
0.496822 0.867852i \(-0.334500\pi\)
\(62\) −0.204393 −0.0259579
\(63\) −0.418748 + 2.61240i −0.0527573 + 0.329132i
\(64\) −5.24897 −0.656121
\(65\) −0.326352 0.565258i −0.0404790 0.0701116i
\(66\) −0.0923963 + 0.160035i −0.0113732 + 0.0196989i
\(67\) −2.33022 + 4.03606i −0.284682 + 0.493084i −0.972532 0.232769i \(-0.925221\pi\)
0.687850 + 0.725853i \(0.258555\pi\)
\(68\) 1.05303 + 1.82391i 0.127699 + 0.221181i
\(69\) 8.00774 0.964019
\(70\) −0.560307 + 0.213887i −0.0669695 + 0.0255643i
\(71\) −3.92902 −0.466288 −0.233144 0.972442i \(-0.574901\pi\)
−0.233144 + 0.972442i \(0.574901\pi\)
\(72\) −0.673648 1.16679i −0.0793902 0.137508i
\(73\) −5.81180 + 10.0663i −0.680220 + 1.17818i 0.294693 + 0.955592i \(0.404783\pi\)
−0.974914 + 0.222584i \(0.928551\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) −2.28699 3.96118i −0.264079 0.457398i
\(76\) −0.573978 −0.0658398
\(77\) 1.31521 0.502055i 0.149882 0.0572145i
\(78\) 0.347296 0.0393236
\(79\) −1.46451 2.53660i −0.164770 0.285390i 0.771804 0.635861i \(-0.219355\pi\)
−0.936574 + 0.350471i \(0.886022\pi\)
\(80\) −1.07398 + 1.86018i −0.120074 + 0.207975i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −0.180922 0.313366i −0.0199795 0.0346055i
\(83\) −2.46791 −0.270888 −0.135444 0.990785i \(-0.543246\pi\)
−0.135444 + 0.990785i \(0.543246\pi\)
\(84\) −0.786989 + 4.90971i −0.0858675 + 0.535693i
\(85\) 0.731429 0.0793347
\(86\) 0.511144 + 0.885328i 0.0551181 + 0.0954674i
\(87\) 3.89053 6.73859i 0.417109 0.722453i
\(88\) −0.358441 + 0.620838i −0.0382099 + 0.0661815i
\(89\) −5.49273 9.51368i −0.582228 1.00845i −0.995215 0.0977112i \(-0.968848\pi\)
0.412987 0.910737i \(-0.364485\pi\)
\(90\) −0.226682 −0.0238943
\(91\) −2.05303 1.66885i −0.215216 0.174943i
\(92\) 15.0496 1.56903
\(93\) 0.294263 + 0.509678i 0.0305136 + 0.0528512i
\(94\) −0.716881 + 1.24168i −0.0739407 + 0.128069i
\(95\) −0.0996702 + 0.172634i −0.0102259 + 0.0177119i
\(96\) −1.91875 3.32337i −0.195831 0.339190i
\(97\) 10.2686 1.04262 0.521308 0.853369i \(-0.325444\pi\)
0.521308 + 0.853369i \(0.325444\pi\)
\(98\) −1.81268 + 1.61997i −0.183108 + 0.163642i
\(99\) 0.532089 0.0534769
\(100\) −4.29813 7.44459i −0.429813 0.744459i
\(101\) −6.67365 + 11.5591i −0.664053 + 1.15017i 0.315488 + 0.948929i \(0.397832\pi\)
−0.979541 + 0.201244i \(0.935502\pi\)
\(102\) −0.194593 + 0.337044i −0.0192675 + 0.0333724i
\(103\) −3.62061 6.27109i −0.356750 0.617909i 0.630666 0.776054i \(-0.282782\pi\)
−0.987416 + 0.158146i \(0.949448\pi\)
\(104\) 1.34730 0.132113
\(105\) 1.34002 + 1.08926i 0.130773 + 0.106301i
\(106\) 0.879385 0.0854134
\(107\) 3.59240 + 6.22221i 0.347290 + 0.601524i 0.985767 0.168117i \(-0.0537686\pi\)
−0.638477 + 0.769641i \(0.720435\pi\)
\(108\) −0.939693 + 1.62760i −0.0904220 + 0.156615i
\(109\) 8.62108 14.9322i 0.825750 1.43024i −0.0755950 0.997139i \(-0.524086\pi\)
0.901345 0.433102i \(-0.142581\pi\)
\(110\) 0.0603074 + 0.104455i 0.00575008 + 0.00995944i
\(111\) 2.87939 0.273299
\(112\) −1.37804 + 8.59705i −0.130213 + 0.812345i
\(113\) 11.3523 1.06794 0.533970 0.845504i \(-0.320700\pi\)
0.533970 + 0.845504i \(0.320700\pi\)
\(114\) −0.0530334 0.0918566i −0.00496703 0.00860316i
\(115\) 2.61334 4.52644i 0.243695 0.422093i
\(116\) 7.31180 12.6644i 0.678884 1.17586i
\(117\) −0.500000 0.866025i −0.0462250 0.0800641i
\(118\) −4.99495 −0.459822
\(119\) 2.76991 1.05736i 0.253918 0.0969282i
\(120\) −0.879385 −0.0802765
\(121\) 5.35844 + 9.28109i 0.487131 + 0.843736i
\(122\) 1.36484 2.36397i 0.123567 0.214024i
\(123\) −0.520945 + 0.902302i −0.0469720 + 0.0813579i
\(124\) 0.553033 + 0.957882i 0.0496639 + 0.0860203i
\(125\) −6.24897 −0.558925
\(126\) −0.858441 + 0.327693i −0.0764760 + 0.0291932i
\(127\) −3.55169 −0.315161 −0.157581 0.987506i \(-0.550369\pi\)
−0.157581 + 0.987506i \(0.550369\pi\)
\(128\) −4.74897 8.22546i −0.419754 0.727035i
\(129\) 1.47178 2.54920i 0.129583 0.224445i
\(130\) 0.113341 0.196312i 0.00994065 0.0172177i
\(131\) −7.77244 13.4623i −0.679081 1.17620i −0.975258 0.221070i \(-0.929045\pi\)
0.296177 0.955133i \(-0.404288\pi\)
\(132\) 1.00000 0.0870388
\(133\) −0.127889 + 0.797847i −0.0110894 + 0.0691821i
\(134\) −1.61856 −0.139822
\(135\) 0.326352 + 0.565258i 0.0280879 + 0.0486497i
\(136\) −0.754900 + 1.30753i −0.0647321 + 0.112119i
\(137\) −4.06031 + 7.03266i −0.346895 + 0.600841i −0.985696 0.168532i \(-0.946097\pi\)
0.638801 + 0.769372i \(0.279431\pi\)
\(138\) 1.39053 + 2.40847i 0.118370 + 0.205022i
\(139\) 16.0223 1.35899 0.679496 0.733679i \(-0.262198\pi\)
0.679496 + 0.733679i \(0.262198\pi\)
\(140\) 2.51842 + 2.04715i 0.212845 + 0.173015i
\(141\) 4.12836 0.347670
\(142\) −0.682266 1.18172i −0.0572545 0.0991677i
\(143\) −0.266044 + 0.460802i −0.0222478 + 0.0385342i
\(144\) −1.64543 + 2.84997i −0.137119 + 0.237497i
\(145\) −2.53936 4.39831i −0.210883 0.365259i
\(146\) −4.03684 −0.334091
\(147\) 6.64930 + 2.18788i 0.548425 + 0.180453i
\(148\) 5.41147 0.444820
\(149\) −11.9436 20.6869i −0.978455 1.69473i −0.668028 0.744136i \(-0.732861\pi\)
−0.310427 0.950597i \(-0.600472\pi\)
\(150\) 0.794263 1.37570i 0.0648513 0.112326i
\(151\) 2.45336 4.24935i 0.199652 0.345807i −0.748764 0.662837i \(-0.769352\pi\)
0.948416 + 0.317030i \(0.102686\pi\)
\(152\) −0.205737 0.356347i −0.0166875 0.0289036i
\(153\) 1.12061 0.0905963
\(154\) 0.379385 + 0.308391i 0.0305717 + 0.0248508i
\(155\) 0.384133 0.0308543
\(156\) −0.939693 1.62760i −0.0752356 0.130312i
\(157\) 3.45471 5.98373i 0.275716 0.477554i −0.694600 0.719396i \(-0.744419\pi\)
0.970315 + 0.241843i \(0.0777518\pi\)
\(158\) 0.508618 0.880952i 0.0404635 0.0700848i
\(159\) −1.26604 2.19285i −0.100404 0.173905i
\(160\) −2.50475 −0.198018
\(161\) 3.35323 20.9194i 0.264271 1.64868i
\(162\) −0.347296 −0.0272862
\(163\) 7.16385 + 12.4081i 0.561116 + 0.971881i 0.997399 + 0.0720720i \(0.0229611\pi\)
−0.436284 + 0.899809i \(0.643706\pi\)
\(164\) −0.979055 + 1.69577i −0.0764514 + 0.132418i
\(165\) 0.173648 0.300767i 0.0135185 0.0234147i
\(166\) −0.428548 0.742267i −0.0332618 0.0576111i
\(167\) −11.4979 −0.889737 −0.444869 0.895596i \(-0.646750\pi\)
−0.444869 + 0.895596i \(0.646750\pi\)
\(168\) −3.33022 + 1.27125i −0.256932 + 0.0980789i
\(169\) 1.00000 0.0769231
\(170\) 0.127011 + 0.219990i 0.00974133 + 0.0168725i
\(171\) −0.152704 + 0.264490i −0.0116775 + 0.0202261i
\(172\) 2.76604 4.79093i 0.210909 0.365305i
\(173\) −7.71213 13.3578i −0.586343 1.01558i −0.994707 0.102756i \(-0.967234\pi\)
0.408364 0.912819i \(-0.366099\pi\)
\(174\) 2.70233 0.204863
\(175\) −11.3059 + 4.31580i −0.854644 + 0.326244i
\(176\) 1.75103 0.131989
\(177\) 7.19119 + 12.4555i 0.540523 + 0.936213i
\(178\) 1.90760 3.30407i 0.142981 0.247650i
\(179\) −12.5744 + 21.7796i −0.939858 + 1.62788i −0.174125 + 0.984724i \(0.555710\pi\)
−0.765733 + 0.643158i \(0.777624\pi\)
\(180\) 0.613341 + 1.06234i 0.0457157 + 0.0791820i
\(181\) 13.4584 1.00036 0.500178 0.865923i \(-0.333268\pi\)
0.500178 + 0.865923i \(0.333268\pi\)
\(182\) 0.145430 0.907278i 0.0107800 0.0672519i
\(183\) −7.85978 −0.581012
\(184\) 5.39440 + 9.34337i 0.397680 + 0.688803i
\(185\) 0.939693 1.62760i 0.0690876 0.119663i
\(186\) −0.102196 + 0.177009i −0.00749341 + 0.0129790i
\(187\) −0.298133 0.516382i −0.0218017 0.0377616i
\(188\) 7.75877 0.565866
\(189\) 2.05303 + 1.66885i 0.149336 + 0.121391i
\(190\) −0.0692302 −0.00502249
\(191\) −8.35369 14.4690i −0.604452 1.04694i −0.992138 0.125150i \(-0.960059\pi\)
0.387686 0.921792i \(-0.373275\pi\)
\(192\) −2.62449 + 4.54574i −0.189406 + 0.328061i
\(193\) −9.13088 + 15.8152i −0.657255 + 1.13840i 0.324068 + 0.946034i \(0.394949\pi\)
−0.981323 + 0.192366i \(0.938384\pi\)
\(194\) 1.78312 + 3.08845i 0.128020 + 0.221738i
\(195\) −0.652704 −0.0467411
\(196\) 12.4966 + 4.11186i 0.892614 + 0.293705i
\(197\) 17.1702 1.22333 0.611665 0.791117i \(-0.290500\pi\)
0.611665 + 0.791117i \(0.290500\pi\)
\(198\) 0.0923963 + 0.160035i 0.00656632 + 0.0113732i
\(199\) 2.53936 4.39831i 0.180011 0.311788i −0.761873 0.647726i \(-0.775720\pi\)
0.941884 + 0.335939i \(0.109053\pi\)
\(200\) 3.08125 5.33688i 0.217877 0.377375i
\(201\) 2.33022 + 4.03606i 0.164361 + 0.284682i
\(202\) −4.63547 −0.326150
\(203\) −15.9748 12.9854i −1.12121 0.911397i
\(204\) 2.10607 0.147454
\(205\) 0.340022 + 0.588936i 0.0237482 + 0.0411331i
\(206\) 1.25743 2.17793i 0.0876090 0.151743i
\(207\) 4.00387 6.93491i 0.278288 0.482009i
\(208\) −1.64543 2.84997i −0.114090 0.197610i
\(209\) 0.162504 0.0112406
\(210\) −0.0949225 + 0.592184i −0.00655027 + 0.0408646i
\(211\) −23.4243 −1.61259 −0.806297 0.591512i \(-0.798531\pi\)
−0.806297 + 0.591512i \(0.798531\pi\)
\(212\) −2.37939 4.12122i −0.163417 0.283046i
\(213\) −1.96451 + 3.40263i −0.134606 + 0.233144i
\(214\) −1.24763 + 2.16095i −0.0852860 + 0.147720i
\(215\) −0.960637 1.66387i −0.0655149 0.113475i
\(216\) −1.34730 −0.0916719
\(217\) 1.45471 0.555307i 0.0987520 0.0376967i
\(218\) 5.98814 0.405568
\(219\) 5.81180 + 10.0663i 0.392725 + 0.680220i
\(220\) 0.326352 0.565258i 0.0220026 0.0381097i
\(221\) −0.560307 + 0.970481i −0.0376904 + 0.0652816i
\(222\) 0.500000 + 0.866025i 0.0335578 + 0.0581238i
\(223\) −12.5202 −0.838417 −0.419208 0.907890i \(-0.637692\pi\)
−0.419208 + 0.907890i \(0.637692\pi\)
\(224\) −9.48545 + 3.62089i −0.633773 + 0.241931i
\(225\) −4.57398 −0.304932
\(226\) 1.97131 + 3.41442i 0.131130 + 0.227124i
\(227\) −3.90167 + 6.75790i −0.258963 + 0.448537i −0.965964 0.258675i \(-0.916714\pi\)
0.707001 + 0.707212i \(0.250048\pi\)
\(228\) −0.286989 + 0.497079i −0.0190063 + 0.0329199i
\(229\) 10.3229 + 17.8799i 0.682160 + 1.18154i 0.974320 + 0.225166i \(0.0722924\pi\)
−0.292161 + 0.956369i \(0.594374\pi\)
\(230\) 1.81521 0.119691
\(231\) 0.222811 1.39003i 0.0146599 0.0914573i
\(232\) 10.4834 0.688268
\(233\) −4.80928 8.32991i −0.315066 0.545711i 0.664385 0.747390i \(-0.268693\pi\)
−0.979452 + 0.201679i \(0.935360\pi\)
\(234\) 0.173648 0.300767i 0.0113517 0.0196618i
\(235\) 1.34730 2.33359i 0.0878879 0.152226i
\(236\) 13.5150 + 23.4087i 0.879753 + 1.52378i
\(237\) −2.92902 −0.190260
\(238\) 0.799011 + 0.649491i 0.0517922 + 0.0421003i
\(239\) 2.35235 0.152161 0.0760804 0.997102i \(-0.475759\pi\)
0.0760804 + 0.997102i \(0.475759\pi\)
\(240\) 1.07398 + 1.86018i 0.0693250 + 0.120074i
\(241\) 7.86618 13.6246i 0.506705 0.877639i −0.493265 0.869879i \(-0.664197\pi\)
0.999970 0.00775999i \(-0.00247011\pi\)
\(242\) −1.86097 + 3.22329i −0.119627 + 0.207201i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −14.7716 −0.945652
\(245\) 3.40673 3.04455i 0.217648 0.194509i
\(246\) −0.361844 −0.0230703
\(247\) −0.152704 0.264490i −0.00971630 0.0168291i
\(248\) −0.396459 + 0.686688i −0.0251752 + 0.0436047i
\(249\) −1.23396 + 2.13727i −0.0781988 + 0.135444i
\(250\) −1.08512 1.87949i −0.0686292 0.118869i
\(251\) −21.8161 −1.37702 −0.688511 0.725226i \(-0.741735\pi\)
−0.688511 + 0.725226i \(0.741735\pi\)
\(252\) 3.85844 + 3.13641i 0.243059 + 0.197575i
\(253\) −4.26083 −0.267876
\(254\) −0.616744 1.06823i −0.0386980 0.0670269i
\(255\) 0.365715 0.633436i 0.0229019 0.0396673i
\(256\) −3.59967 + 6.23481i −0.224979 + 0.389676i
\(257\) 11.6386 + 20.1587i 0.725997 + 1.25746i 0.958562 + 0.284883i \(0.0919549\pi\)
−0.232565 + 0.972581i \(0.574712\pi\)
\(258\) 1.02229 0.0636449
\(259\) 1.20574 7.52211i 0.0749209 0.467401i
\(260\) −1.22668 −0.0760756
\(261\) −3.89053 6.73859i −0.240818 0.417109i
\(262\) 2.69934 4.67539i 0.166766 0.288847i
\(263\) −1.37551 + 2.38246i −0.0848179 + 0.146909i −0.905314 0.424744i \(-0.860364\pi\)
0.820496 + 0.571653i \(0.193698\pi\)
\(264\) 0.358441 + 0.620838i 0.0220605 + 0.0382099i
\(265\) −1.65270 −0.101525
\(266\) −0.262174 + 0.100080i −0.0160749 + 0.00613629i
\(267\) −10.9855 −0.672299
\(268\) 4.37939 + 7.58532i 0.267514 + 0.463347i
\(269\) −2.71167 + 4.69674i −0.165333 + 0.286366i −0.936774 0.349936i \(-0.886203\pi\)
0.771440 + 0.636302i \(0.219537\pi\)
\(270\) −0.113341 + 0.196312i −0.00689770 + 0.0119472i
\(271\) −0.807934 1.39938i −0.0490785 0.0850064i 0.840443 0.541901i \(-0.182295\pi\)
−0.889521 + 0.456894i \(0.848962\pi\)
\(272\) 3.68779 0.223605
\(273\) −2.47178 + 0.943555i −0.149599 + 0.0571066i
\(274\) −2.82026 −0.170378
\(275\) 1.21688 + 2.10770i 0.0733807 + 0.127099i
\(276\) 7.52481 13.0334i 0.452941 0.784516i
\(277\) −3.92514 + 6.79855i −0.235839 + 0.408485i −0.959516 0.281653i \(-0.909117\pi\)
0.723677 + 0.690139i \(0.242450\pi\)
\(278\) 2.78224 + 4.81898i 0.166868 + 0.289023i
\(279\) 0.588526 0.0352341
\(280\) −0.368241 + 2.29731i −0.0220066 + 0.137290i
\(281\) −19.0428 −1.13600 −0.568000 0.823029i \(-0.692283\pi\)
−0.568000 + 0.823029i \(0.692283\pi\)
\(282\) 0.716881 + 1.24168i 0.0426897 + 0.0739407i
\(283\) −11.6434 + 20.1669i −0.692127 + 1.19880i 0.279013 + 0.960287i \(0.409993\pi\)
−0.971140 + 0.238511i \(0.923341\pi\)
\(284\) −3.69207 + 6.39485i −0.219084 + 0.379464i
\(285\) 0.0996702 + 0.172634i 0.00590395 + 0.0102259i
\(286\) −0.184793 −0.0109270
\(287\) 2.13903 + 1.73875i 0.126263 + 0.102635i
\(288\) −3.83750 −0.226127
\(289\) 7.87211 + 13.6349i 0.463065 + 0.802053i
\(290\) 0.881911 1.52752i 0.0517876 0.0896988i
\(291\) 5.13429 8.89284i 0.300977 0.521308i
\(292\) 10.9226 + 18.9185i 0.639198 + 1.10712i
\(293\) 26.9736 1.57581 0.787907 0.615794i \(-0.211165\pi\)
0.787907 + 0.615794i \(0.211165\pi\)
\(294\) 0.496596 + 2.37981i 0.0289621 + 0.138794i
\(295\) 9.38743 0.546557
\(296\) 1.93969 + 3.35965i 0.112742 + 0.195275i
\(297\) 0.266044 0.460802i 0.0154375 0.0267385i
\(298\) 4.14796 7.18447i 0.240285 0.416185i
\(299\) 4.00387 + 6.93491i 0.231550 + 0.401056i
\(300\) −8.59627 −0.496306
\(301\) −6.04323 4.91236i −0.348326 0.283144i
\(302\) 1.70409 0.0980593
\(303\) 6.67365 + 11.5591i 0.383391 + 0.664053i
\(304\) −0.502526 + 0.870401i −0.0288219 + 0.0499209i
\(305\) −2.56506 + 4.44281i −0.146875 + 0.254394i
\(306\) 0.194593 + 0.337044i 0.0111241 + 0.0192675i
\(307\) 6.28405 0.358650 0.179325 0.983790i \(-0.442609\pi\)
0.179325 + 0.983790i \(0.442609\pi\)
\(308\) 0.418748 2.61240i 0.0238604 0.148855i
\(309\) −7.24123 −0.411939
\(310\) 0.0667040 + 0.115535i 0.00378853 + 0.00656193i
\(311\) −1.11334 + 1.92836i −0.0631318 + 0.109347i −0.895864 0.444329i \(-0.853442\pi\)
0.832732 + 0.553676i \(0.186776\pi\)
\(312\) 0.673648 1.16679i 0.0381378 0.0660566i
\(313\) −9.91060 17.1657i −0.560180 0.970260i −0.997480 0.0709447i \(-0.977399\pi\)
0.437300 0.899316i \(-0.355935\pi\)
\(314\) 2.39961 0.135418
\(315\) 1.61334 0.615862i 0.0909015 0.0346999i
\(316\) −5.50475 −0.309666
\(317\) 5.85117 + 10.1345i 0.328634 + 0.569211i 0.982241 0.187623i \(-0.0600783\pi\)
−0.653607 + 0.756834i \(0.726745\pi\)
\(318\) 0.439693 0.761570i 0.0246567 0.0427067i
\(319\) −2.07011 + 3.58553i −0.115904 + 0.200751i
\(320\) 1.71301 + 2.96702i 0.0957602 + 0.165862i
\(321\) 7.18479 0.401016
\(322\) 6.87417 2.62408i 0.383083 0.146234i
\(323\) 0.342244 0.0190430
\(324\) 0.939693 + 1.62760i 0.0522051 + 0.0904220i
\(325\) 2.28699 3.96118i 0.126859 0.219727i
\(326\) −2.48798 + 4.30930i −0.137796 + 0.238670i
\(327\) −8.62108 14.9322i −0.476747 0.825750i
\(328\) −1.40373 −0.0775082
\(329\) 1.72874 10.7849i 0.0953086 0.594592i
\(330\) 0.120615 0.00663962
\(331\) −10.4559 18.1101i −0.574708 0.995423i −0.996073 0.0885320i \(-0.971782\pi\)
0.421366 0.906891i \(-0.361551\pi\)
\(332\) −2.31908 + 4.01676i −0.127276 + 0.220448i
\(333\) 1.43969 2.49362i 0.0788947 0.136650i
\(334\) −1.99660 3.45821i −0.109249 0.189225i
\(335\) 3.04189 0.166196
\(336\) 6.75624 + 5.49194i 0.368583 + 0.299610i
\(337\) −16.0419 −0.873857 −0.436929 0.899496i \(-0.643934\pi\)
−0.436929 + 0.899496i \(0.643934\pi\)
\(338\) 0.173648 + 0.300767i 0.00944522 + 0.0163596i
\(339\) 5.67617 9.83142i 0.308287 0.533970i
\(340\) 0.687319 1.19047i 0.0372751 0.0645624i
\(341\) −0.156574 0.271194i −0.00847896 0.0146860i
\(342\) −0.106067 −0.00573544
\(343\) 8.50000 16.4545i 0.458957 0.888459i
\(344\) 3.96585 0.213824
\(345\) −2.61334 4.52644i −0.140698 0.243695i
\(346\) 2.67840 4.63912i 0.143991 0.249401i
\(347\) −9.29339 + 16.0966i −0.498895 + 0.864112i −0.999999 0.00127538i \(-0.999594\pi\)
0.501104 + 0.865387i \(0.332927\pi\)
\(348\) −7.31180 12.6644i −0.391954 0.678884i
\(349\) 15.2267 0.815066 0.407533 0.913191i \(-0.366389\pi\)
0.407533 + 0.913191i \(0.366389\pi\)
\(350\) −3.26130 2.65101i −0.174324 0.141702i
\(351\) −1.00000 −0.0533761
\(352\) 1.02094 + 1.76833i 0.0544165 + 0.0942522i
\(353\) 2.95471 5.11770i 0.157263 0.272388i −0.776618 0.629972i \(-0.783066\pi\)
0.933881 + 0.357584i \(0.116400\pi\)
\(354\) −2.49747 + 4.32575i −0.132739 + 0.229911i
\(355\) 1.28224 + 2.22091i 0.0680543 + 0.117874i
\(356\) −20.6459 −1.09423
\(357\) 0.469255 2.92750i 0.0248356 0.154940i
\(358\) −8.73412 −0.461612
\(359\) −5.19506 8.99811i −0.274185 0.474902i 0.695744 0.718289i \(-0.255075\pi\)
−0.969929 + 0.243388i \(0.921741\pi\)
\(360\) −0.439693 + 0.761570i −0.0231738 + 0.0401383i
\(361\) 9.45336 16.3737i 0.497545 0.861774i
\(362\) 2.33703 + 4.04785i 0.122832 + 0.212750i
\(363\) 10.7169 0.562490
\(364\) −4.64543 + 1.77330i −0.243487 + 0.0929464i
\(365\) 7.58677 0.397110
\(366\) −1.36484 2.36397i −0.0713412 0.123567i
\(367\) 12.0902 20.9408i 0.631102 1.09310i −0.356225 0.934400i \(-0.615936\pi\)
0.987327 0.158700i \(-0.0507304\pi\)
\(368\) 13.1762 22.8218i 0.686856 1.18967i
\(369\) 0.520945 + 0.902302i 0.0271193 + 0.0469720i
\(370\) 0.652704 0.0339324
\(371\) −6.25877 + 2.38917i −0.324939 + 0.124039i
\(372\) 1.10607 0.0573469
\(373\) −3.25103 5.63095i −0.168332 0.291559i 0.769502 0.638645i \(-0.220505\pi\)
−0.937834 + 0.347085i \(0.887171\pi\)
\(374\) 0.103541 0.179338i 0.00535396 0.00927333i
\(375\) −3.12449 + 5.41177i −0.161348 + 0.279462i
\(376\) 2.78106 + 4.81694i 0.143422 + 0.248414i
\(377\) 7.78106 0.400745
\(378\) −0.145430 + 0.907278i −0.00748010 + 0.0466653i
\(379\) −17.7915 −0.913887 −0.456944 0.889496i \(-0.651056\pi\)
−0.456944 + 0.889496i \(0.651056\pi\)
\(380\) 0.187319 + 0.324446i 0.00960925 + 0.0166437i
\(381\) −1.77584 + 3.07585i −0.0909793 + 0.157581i
\(382\) 2.90121 5.02504i 0.148439 0.257103i
\(383\) 4.98158 + 8.62835i 0.254547 + 0.440888i 0.964772 0.263086i \(-0.0847403\pi\)
−0.710225 + 0.703974i \(0.751407\pi\)
\(384\) −9.49794 −0.484690
\(385\) −0.713011 0.579585i −0.0363384 0.0295384i
\(386\) −6.34224 −0.322812
\(387\) −1.47178 2.54920i −0.0748149 0.129583i
\(388\) 9.64930 16.7131i 0.489869 0.848478i
\(389\) 1.95084 3.37895i 0.0989114 0.171320i −0.812323 0.583208i \(-0.801797\pi\)
0.911234 + 0.411888i \(0.135131\pi\)
\(390\) −0.113341 0.196312i −0.00573923 0.00994065i
\(391\) −8.97359 −0.453814
\(392\) 1.92649 + 9.23222i 0.0973024 + 0.466297i
\(393\) −15.5449 −0.784136
\(394\) 2.98158 + 5.16425i 0.150210 + 0.260171i
\(395\) −0.955889 + 1.65565i −0.0480960 + 0.0833047i
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) 16.9500 + 29.3582i 0.850694 + 1.47345i 0.880583 + 0.473892i \(0.157151\pi\)
−0.0298888 + 0.999553i \(0.509515\pi\)
\(398\) 1.76382 0.0884125
\(399\) 0.627011 + 0.509678i 0.0313898 + 0.0255158i
\(400\) −15.0523 −0.752616
\(401\) −16.4290 28.4559i −0.820426 1.42102i −0.905365 0.424633i \(-0.860403\pi\)
0.0849396 0.996386i \(-0.472930\pi\)
\(402\) −0.809278 + 1.40171i −0.0403631 + 0.0699109i
\(403\) −0.294263 + 0.509678i −0.0146583 + 0.0253889i
\(404\) 12.5424 + 21.7240i 0.624006 + 1.08081i
\(405\) 0.652704 0.0324331
\(406\) 1.13160 7.05958i 0.0561602 0.350361i
\(407\) −1.53209 −0.0759428
\(408\) 0.754900 + 1.30753i 0.0373731 + 0.0647321i
\(409\) −1.81908 + 3.15074i −0.0899476 + 0.155794i −0.907489 0.420076i \(-0.862003\pi\)
0.817541 + 0.575870i \(0.195337\pi\)
\(410\) −0.118089 + 0.204535i −0.00583198 + 0.0101013i
\(411\) 4.06031 + 7.03266i 0.200280 + 0.346895i
\(412\) −13.6091 −0.670470
\(413\) 35.5501 13.5706i 1.74931 0.667764i
\(414\) 2.78106 0.136682
\(415\) 0.805407 + 1.39501i 0.0395359 + 0.0684782i
\(416\) 1.91875 3.32337i 0.0940744 0.162942i
\(417\) 8.01114 13.8757i 0.392307 0.679496i
\(418\) 0.0282185 + 0.0488759i 0.00138021 + 0.00239060i
\(419\) 16.6905 0.815383 0.407692 0.913120i \(-0.366334\pi\)
0.407692 + 0.913120i \(0.366334\pi\)
\(420\) 3.03209 1.15744i 0.147951 0.0564774i
\(421\) −21.5425 −1.04992 −0.524959 0.851127i \(-0.675919\pi\)
−0.524959 + 0.851127i \(0.675919\pi\)
\(422\) −4.06758 7.04526i −0.198007 0.342958i
\(423\) 2.06418 3.57526i 0.100364 0.173835i
\(424\) 1.70574 2.95442i 0.0828379 0.143479i
\(425\) 2.56283 + 4.43896i 0.124316 + 0.215321i
\(426\) −1.36453 −0.0661118
\(427\) −3.29127 + 20.5329i −0.159276 + 0.993658i
\(428\) 13.5030 0.652692
\(429\) 0.266044 + 0.460802i 0.0128447 + 0.0222478i
\(430\) 0.333626 0.577857i 0.0160889 0.0278667i
\(431\) −5.17365 + 8.96102i −0.249206 + 0.431637i −0.963306 0.268407i \(-0.913503\pi\)
0.714100 + 0.700044i \(0.246836\pi\)
\(432\) 1.64543 + 2.84997i 0.0791658 + 0.137119i
\(433\) −3.22399 −0.154935 −0.0774676 0.996995i \(-0.524683\pi\)
−0.0774676 + 0.996995i \(0.524683\pi\)
\(434\) 0.419625 + 0.341101i 0.0201427 + 0.0163734i
\(435\) −5.07873 −0.243506
\(436\) −16.2023 28.0633i −0.775951 1.34399i
\(437\) 1.22281 2.11797i 0.0584950 0.101316i
\(438\) −2.01842 + 3.49600i −0.0964438 + 0.167045i
\(439\) −14.2494 24.6807i −0.680089 1.17795i −0.974953 0.222409i \(-0.928608\pi\)
0.294865 0.955539i \(-0.404725\pi\)
\(440\) 0.467911 0.0223068
\(441\) 5.21941 4.66452i 0.248543 0.222120i
\(442\) −0.389185 −0.0185117
\(443\) 10.5667 + 18.3021i 0.502039 + 0.869558i 0.999997 + 0.00235633i \(0.000750045\pi\)
−0.497958 + 0.867201i \(0.665917\pi\)
\(444\) 2.70574 4.68647i 0.128409 0.222410i
\(445\) −3.58512 + 6.20961i −0.169951 + 0.294364i
\(446\) −2.17412 3.76568i −0.102947 0.178310i
\(447\) −23.8871 −1.12982
\(448\) 10.7763 + 8.75973i 0.509133 + 0.413859i
\(449\) 25.6468 1.21035 0.605174 0.796093i \(-0.293103\pi\)
0.605174 + 0.796093i \(0.293103\pi\)
\(450\) −0.794263 1.37570i −0.0374419 0.0648513i
\(451\) 0.277189 0.480105i 0.0130523 0.0226073i
\(452\) 10.6677 18.4770i 0.501767 0.869086i
\(453\) −2.45336 4.24935i −0.115269 0.199652i
\(454\) −2.71007 −0.127190
\(455\) −0.273318 + 1.70513i −0.0128134 + 0.0799375i
\(456\) −0.411474 −0.0192690
\(457\) −16.8293 29.1493i −0.787244 1.36355i −0.927650 0.373452i \(-0.878174\pi\)
0.140406 0.990094i \(-0.455159\pi\)
\(458\) −3.58512 + 6.20961i −0.167522 + 0.290156i
\(459\) 0.560307 0.970481i 0.0261529 0.0452982i
\(460\) −4.91147 8.50692i −0.228999 0.396637i
\(461\) 9.85710 0.459091 0.229545 0.973298i \(-0.426276\pi\)
0.229545 + 0.973298i \(0.426276\pi\)
\(462\) 0.456767 0.174362i 0.0212507 0.00811205i
\(463\) 2.39693 0.111395 0.0556973 0.998448i \(-0.482262\pi\)
0.0556973 + 0.998448i \(0.482262\pi\)
\(464\) −12.8032 22.1758i −0.594373 1.02948i
\(465\) 0.192066 0.332669i 0.00890687 0.0154272i
\(466\) 1.67024 2.89295i 0.0773726 0.134013i
\(467\) 13.6395 + 23.6243i 0.631161 + 1.09320i 0.987315 + 0.158775i \(0.0507545\pi\)
−0.356154 + 0.934427i \(0.615912\pi\)
\(468\) −1.87939 −0.0868746
\(469\) 11.5196 4.39739i 0.531926 0.203052i
\(470\) 0.935822 0.0431663
\(471\) −3.45471 5.98373i −0.159185 0.275716i
\(472\) −9.68866 + 16.7813i −0.445957 + 0.772420i
\(473\) −0.783119 + 1.35640i −0.0360078 + 0.0623674i
\(474\) −0.508618 0.880952i −0.0233616 0.0404635i
\(475\) −1.39693 −0.0640954
\(476\) 0.881911 5.50190i 0.0404223 0.252179i
\(477\) −2.53209 −0.115936
\(478\) 0.408481 + 0.707510i 0.0186835 + 0.0323608i
\(479\) 20.4106 35.3522i 0.932584 1.61528i 0.153697 0.988118i \(-0.450882\pi\)
0.778887 0.627165i \(-0.215785\pi\)
\(480\) −1.25237 + 2.16918i −0.0571628 + 0.0990088i
\(481\) 1.43969 + 2.49362i 0.0656443 + 0.113699i
\(482\) 5.46379 0.248869
\(483\) −16.4402 13.3637i −0.748053 0.608070i
\(484\) 20.1411 0.915507
\(485\) −3.35117 5.80439i −0.152169 0.263564i
\(486\) −0.173648 + 0.300767i −0.00787684 + 0.0136431i
\(487\) 9.61381 16.6516i 0.435643 0.754556i −0.561705 0.827338i \(-0.689854\pi\)
0.997348 + 0.0727816i \(0.0231876\pi\)
\(488\) −5.29473 9.17074i −0.239681 0.415140i
\(489\) 14.3277 0.647921
\(490\) 1.50727 + 0.495952i 0.0680917 + 0.0224048i
\(491\) −7.54219 −0.340374 −0.170187 0.985412i \(-0.554437\pi\)
−0.170187 + 0.985412i \(0.554437\pi\)
\(492\) 0.979055 + 1.69577i 0.0441392 + 0.0764514i
\(493\) −4.35978 + 7.55137i −0.196355 + 0.340097i
\(494\) 0.0530334 0.0918566i 0.00238609 0.00413282i
\(495\) −0.173648 0.300767i −0.00780491 0.0135185i
\(496\) 1.93676 0.0869629
\(497\) 8.06640 + 6.55693i 0.361827 + 0.294118i
\(498\) −0.857097 −0.0384074
\(499\) 15.4979 + 26.8432i 0.693783 + 1.20167i 0.970589 + 0.240742i \(0.0773907\pi\)
−0.276806 + 0.960926i \(0.589276\pi\)
\(500\) −5.87211 + 10.1708i −0.262609 + 0.454852i
\(501\) −5.74897 + 9.95751i −0.256845 + 0.444869i
\(502\) −3.78833 6.56159i −0.169082 0.292858i
\(503\) 18.4861 0.824254 0.412127 0.911126i \(-0.364786\pi\)
0.412127 + 0.911126i \(0.364786\pi\)
\(504\) −0.564178 + 3.51968i −0.0251305 + 0.156779i
\(505\) 8.71183 0.387671
\(506\) −0.739885 1.28152i −0.0328919 0.0569705i
\(507\) 0.500000 0.866025i 0.0222058 0.0384615i
\(508\) −3.33750 + 5.78071i −0.148077 + 0.256478i
\(509\) 18.0868 + 31.3272i 0.801682 + 1.38855i 0.918508 + 0.395402i \(0.129395\pi\)
−0.116826 + 0.993152i \(0.537272\pi\)
\(510\) 0.254023 0.0112483
\(511\) 28.7310 10.9675i 1.27099 0.485174i
\(512\) −21.4962 −0.950006
\(513\) 0.152704 + 0.264490i 0.00674203 + 0.0116775i
\(514\) −4.04205 + 7.00104i −0.178287 + 0.308803i
\(515\) −2.36319 + 4.09316i −0.104135 + 0.180366i
\(516\) −2.76604 4.79093i −0.121768 0.210909i
\(517\) −2.19665 −0.0966086
\(518\) 2.47178 0.943555i 0.108604 0.0414574i
\(519\) −15.4243 −0.677050
\(520\) −0.439693 0.761570i −0.0192818 0.0333971i
\(521\) −13.2430 + 22.9376i −0.580188 + 1.00492i 0.415268 + 0.909699i \(0.363688\pi\)
−0.995457 + 0.0952164i \(0.969646\pi\)
\(522\) 1.35117 2.34029i 0.0591390 0.102432i
\(523\) 5.49794 + 9.52271i 0.240408 + 0.416399i 0.960831 0.277136i \(-0.0893854\pi\)
−0.720422 + 0.693536i \(0.756052\pi\)
\(524\) −29.2148 −1.27626
\(525\) −1.91534 + 11.9491i −0.0835925 + 0.521500i
\(526\) −0.955423 −0.0416584
\(527\) −0.329755 0.571153i −0.0143644 0.0248798i
\(528\) 0.875515 1.51644i 0.0381019 0.0659944i
\(529\) −20.5620 + 35.6144i −0.893998 + 1.54845i
\(530\) −0.286989 0.497079i −0.0124660 0.0215918i
\(531\) 14.3824 0.624142
\(532\) 1.17840 + 0.957882i 0.0510899 + 0.0415295i
\(533\) −1.04189 −0.0451292
\(534\) −1.90760 3.30407i −0.0825501 0.142981i
\(535\) 2.34477 4.06126i 0.101373 0.175584i
\(536\) −3.13950 + 5.43777i −0.135606 + 0.234876i
\(537\) 12.5744 + 21.7796i 0.542627 + 0.939858i
\(538\) −1.88350 −0.0812036
\(539\) −3.53802 1.16415i −0.152393 0.0501433i
\(540\) 1.22668 0.0527880
\(541\) 1.69253 + 2.93155i 0.0727677 + 0.126037i 0.900113 0.435656i \(-0.143484\pi\)
−0.827346 + 0.561693i \(0.810150\pi\)
\(542\) 0.280592 0.486000i 0.0120525 0.0208755i
\(543\) 6.72921 11.6553i 0.288778 0.500178i
\(544\) 2.15018 + 3.72422i 0.0921881 + 0.159674i
\(545\) −11.2540 −0.482069
\(546\) −0.713011 0.579585i −0.0305141 0.0248039i
\(547\) −8.37464 −0.358074 −0.179037 0.983842i \(-0.557298\pi\)
−0.179037 + 0.983842i \(0.557298\pi\)
\(548\) 7.63088 + 13.2171i 0.325975 + 0.564605i
\(549\) −3.92989 + 6.80677i −0.167724 + 0.290506i
\(550\) −0.422618 + 0.731997i −0.0180205 + 0.0312124i
\(551\) −1.18820 2.05802i −0.0506189 0.0876744i
\(552\) 10.7888 0.459202
\(553\) −1.22652 + 7.65177i −0.0521569 + 0.325386i
\(554\) −2.72638 −0.115833
\(555\) −0.939693 1.62760i −0.0398877 0.0690876i
\(556\) 15.0560 26.0778i 0.638518 1.10595i
\(557\) −18.1827 + 31.4934i −0.770427 + 1.33442i 0.166902 + 0.985974i \(0.446624\pi\)
−0.937329 + 0.348445i \(0.886710\pi\)
\(558\) 0.102196 + 0.177009i 0.00432632 + 0.00749341i
\(559\) 2.94356 0.124499
\(560\) 5.30928 2.02671i 0.224358 0.0856443i
\(561\) −0.596267 −0.0251744
\(562\) −3.30675 5.72746i −0.139487 0.241598i
\(563\) −2.62314 + 4.54341i −0.110552 + 0.191482i −0.915993 0.401194i \(-0.868595\pi\)
0.805441 + 0.592676i \(0.201929\pi\)
\(564\) 3.87939 6.71929i 0.163352 0.282933i
\(565\) −3.70486 6.41701i −0.155865 0.269965i
\(566\) −8.08740 −0.339939
\(567\) 2.47178 0.943555i 0.103805 0.0396256i
\(568\) −5.29355 −0.222112
\(569\) 10.7429 + 18.6072i 0.450365 + 0.780055i 0.998409 0.0563949i \(-0.0179606\pi\)
−0.548044 + 0.836450i \(0.684627\pi\)
\(570\) −0.0346151 + 0.0599551i −0.00144987 + 0.00251124i
\(571\) −16.5804 + 28.7181i −0.693867 + 1.20181i 0.276694 + 0.960958i \(0.410761\pi\)
−0.970561 + 0.240855i \(0.922572\pi\)
\(572\) 0.500000 + 0.866025i 0.0209061 + 0.0362103i
\(573\) −16.7074 −0.697961
\(574\) −0.151522 + 0.945283i −0.00632439 + 0.0394554i
\(575\) 36.6272 1.52746
\(576\) 2.62449 + 4.54574i 0.109354 + 0.189406i
\(577\) −13.5890 + 23.5368i −0.565717 + 0.979851i 0.431265 + 0.902225i \(0.358067\pi\)
−0.996983 + 0.0776258i \(0.975266\pi\)
\(578\) −2.73396 + 4.73535i −0.113718 + 0.196965i
\(579\) 9.13088 + 15.8152i 0.379466 + 0.657255i
\(580\) −9.54488 −0.396330
\(581\) 5.06670 + 4.11857i 0.210202 + 0.170867i
\(582\) 3.56624 0.147825
\(583\) 0.673648 + 1.16679i 0.0278997 + 0.0483236i
\(584\) −7.83022 + 13.5623i −0.324017 + 0.561214i
\(585\) −0.326352 + 0.565258i −0.0134930 + 0.0233705i
\(586\) 4.68392 + 8.11278i 0.193491 + 0.335136i
\(587\) −30.8280 −1.27241 −0.636204 0.771521i \(-0.719496\pi\)
−0.636204 + 0.771521i \(0.719496\pi\)
\(588\) 9.80928 8.76644i 0.404528 0.361522i
\(589\) 0.179740 0.00740606
\(590\) 1.63011 + 2.82343i 0.0671106 + 0.116239i
\(591\) 8.58512 14.8699i 0.353145 0.611665i
\(592\) 4.73783 8.20616i 0.194723 0.337271i
\(593\) −20.0364 34.7041i −0.822797 1.42513i −0.903591 0.428396i \(-0.859079\pi\)
0.0807937 0.996731i \(-0.474255\pi\)
\(594\) 0.184793 0.00758213
\(595\) −1.50165 1.22064i −0.0615616 0.0500415i
\(596\) −44.8931 −1.83889
\(597\) −2.53936 4.39831i −0.103929 0.180011i
\(598\) −1.39053 + 2.40847i −0.0568630 + 0.0984896i
\(599\) −15.4226 + 26.7128i −0.630151 + 1.09145i 0.357369 + 0.933963i \(0.383674\pi\)
−0.987520 + 0.157491i \(0.949660\pi\)
\(600\) −3.08125 5.33688i −0.125792 0.217877i
\(601\) −9.85803 −0.402117 −0.201059 0.979579i \(-0.564438\pi\)
−0.201059 + 0.979579i \(0.564438\pi\)
\(602\) 0.428081 2.67063i 0.0174473 0.108847i
\(603\) 4.66044 0.189788
\(604\) −4.61081 7.98617i −0.187611 0.324952i
\(605\) 3.49747 6.05780i 0.142193 0.246285i
\(606\) −2.31773 + 4.01443i −0.0941515 + 0.163075i
\(607\) 15.6643 + 27.1314i 0.635795 + 1.10123i 0.986346 + 0.164686i \(0.0526609\pi\)
−0.350551 + 0.936544i \(0.614006\pi\)
\(608\) −1.17200 −0.0475308
\(609\) −19.2331 + 7.34186i −0.779364 + 0.297507i
\(610\) −1.78167 −0.0721377
\(611\) 2.06418 + 3.57526i 0.0835077 + 0.144640i
\(612\) 1.05303 1.82391i 0.0425664 0.0737271i
\(613\) 2.30928 3.99979i 0.0932708 0.161550i −0.815615 0.578595i \(-0.803601\pi\)
0.908886 + 0.417045i \(0.136934\pi\)
\(614\) 1.09121 + 1.89004i 0.0440378 + 0.0762757i
\(615\) 0.680045 0.0274221
\(616\) 1.77197 0.676417i 0.0713949 0.0272536i
\(617\) −14.5648 −0.586357 −0.293179 0.956058i \(-0.594713\pi\)
−0.293179 + 0.956058i \(0.594713\pi\)
\(618\) −1.25743 2.17793i −0.0505811 0.0876090i
\(619\) 24.7067 42.7932i 0.993045 1.72000i 0.394560 0.918870i \(-0.370897\pi\)
0.598485 0.801134i \(-0.295770\pi\)
\(620\) 0.360967 0.625213i 0.0144968 0.0251092i
\(621\) −4.00387 6.93491i −0.160670 0.278288i
\(622\) −0.773318 −0.0310072
\(623\) −4.60014 + 28.6984i −0.184301 + 1.14978i
\(624\) −3.29086 −0.131740
\(625\) −9.39558 16.2736i −0.375823 0.650945i
\(626\) 3.44191 5.96157i 0.137567 0.238272i
\(627\) 0.0812519 0.140732i 0.00324489 0.00562031i
\(628\) −6.49273 11.2457i −0.259088 0.448754i
\(629\) −3.22668 −0.128656
\(630\) 0.465385 + 0.378297i 0.0185414 + 0.0150717i
\(631\) 0.529401 0.0210751 0.0105376 0.999944i \(-0.496646\pi\)
0.0105376 + 0.999944i \(0.496646\pi\)
\(632\) −1.97313 3.41755i −0.0784867 0.135943i
\(633\) −11.7121 + 20.2860i −0.465516 + 0.806297i
\(634\) −2.03209 + 3.51968i −0.0807046 + 0.139784i
\(635\) 1.15910 + 2.00762i 0.0459975 + 0.0796700i
\(636\) −4.75877 −0.188698
\(637\) 1.42989 + 6.85240i 0.0566544 + 0.271502i
\(638\) −1.43788 −0.0569263
\(639\) 1.96451 + 3.40263i 0.0777147 + 0.134606i
\(640\) −3.09967 + 5.36879i −0.122525 + 0.212220i
\(641\) 16.0556 27.8090i 0.634156 1.09839i −0.352537 0.935798i \(-0.614681\pi\)
0.986693 0.162593i \(-0.0519858\pi\)
\(642\) 1.24763 + 2.16095i 0.0492399 + 0.0852860i
\(643\) 23.5740 0.929667 0.464833 0.885398i \(-0.346114\pi\)
0.464833 + 0.885398i \(0.346114\pi\)
\(644\) −30.8974 25.1155i −1.21753 0.989691i
\(645\) −1.92127 −0.0756501
\(646\) 0.0594300 + 0.102936i 0.00233824 + 0.00404996i
\(647\) 7.87598 13.6416i 0.309637 0.536307i −0.668646 0.743581i \(-0.733126\pi\)
0.978283 + 0.207274i \(0.0664592\pi\)
\(648\) −0.673648 + 1.16679i −0.0264634 + 0.0458360i
\(649\) −3.82635 6.62744i −0.150197 0.260150i
\(650\) 1.58853 0.0623071
\(651\) 0.246444 1.53747i 0.00965891 0.0602581i
\(652\) 26.9273 1.05455
\(653\) 15.5337 + 26.9052i 0.607882 + 1.05288i 0.991589 + 0.129428i \(0.0413140\pi\)
−0.383707 + 0.923455i \(0.625353\pi\)
\(654\) 2.99407 5.18588i 0.117077 0.202784i
\(655\) −5.07310 + 8.78687i −0.198222 + 0.343331i
\(656\) 1.71436 + 2.96935i 0.0669343 + 0.115934i
\(657\) 11.6236 0.453480
\(658\) 3.54395 1.35283i 0.138157 0.0527390i
\(659\) 19.9162 0.775826 0.387913 0.921696i \(-0.373196\pi\)
0.387913 + 0.921696i \(0.373196\pi\)
\(660\) −0.326352 0.565258i −0.0127032 0.0220026i
\(661\) −12.1361 + 21.0203i −0.472039 + 0.817596i −0.999488 0.0319906i \(-0.989815\pi\)
0.527449 + 0.849587i \(0.323149\pi\)
\(662\) 3.63129 6.28958i 0.141134 0.244452i
\(663\) 0.560307 + 0.970481i 0.0217605 + 0.0376904i
\(664\) −3.32501 −0.129035
\(665\) 0.492726 0.188089i 0.0191071 0.00729377i
\(666\) 1.00000 0.0387492
\(667\) 31.1544 + 53.9609i 1.20630 + 2.08938i
\(668\) −10.8045 + 18.7140i −0.418040 + 0.724066i
\(669\) −6.26011 + 10.8428i −0.242030 + 0.419208i
\(670\) 0.528218 + 0.914901i 0.0204069 + 0.0353457i
\(671\) 4.18210 0.161448
\(672\) −1.60694 + 10.0251i −0.0619892 + 0.386726i
\(673\) 23.2668 0.896870 0.448435 0.893815i \(-0.351982\pi\)
0.448435 + 0.893815i \(0.351982\pi\)
\(674\) −2.78564 4.82488i −0.107299 0.185847i
\(675\) −2.28699 + 3.96118i −0.0880262 + 0.152466i
\(676\) 0.939693 1.62760i 0.0361420 0.0625998i
\(677\) −11.0248 19.0955i −0.423718 0.733901i 0.572582 0.819848i \(-0.305942\pi\)
−0.996300 + 0.0859465i \(0.972609\pi\)
\(678\) 3.94263 0.151416
\(679\) −21.0817 17.1367i −0.809042 0.657646i
\(680\) 0.985452 0.0377904
\(681\) 3.90167 + 6.75790i 0.149512 + 0.258963i
\(682\) 0.0543776 0.0941848i 0.00208223 0.00360652i
\(683\) 3.73829 6.47491i 0.143042 0.247756i −0.785599 0.618736i \(-0.787645\pi\)
0.928641 + 0.370980i \(0.120978\pi\)
\(684\) 0.286989 + 0.497079i 0.0109733 + 0.0190063i
\(685\) 5.30035 0.202516
\(686\) 6.42498 0.300767i 0.245307 0.0114834i
\(687\) 20.6459 0.787690
\(688\) −4.84343 8.38906i −0.184654 0.319830i
\(689\) 1.26604 2.19285i 0.0482325 0.0835411i
\(690\) 0.907604 1.57202i 0.0345519 0.0598456i
\(691\) −5.66637 9.81445i −0.215559 0.373359i 0.737886 0.674925i \(-0.235824\pi\)
−0.953445 + 0.301566i \(0.902491\pi\)
\(692\) −28.9881 −1.10196
\(693\) −1.09240 0.887975i −0.0414967 0.0337314i
\(694\) −6.45512 −0.245033
\(695\) −5.22890 9.05673i −0.198344 0.343541i
\(696\) 5.24170 9.07888i 0.198686 0.344134i
\(697\) 0.583778 1.01113i 0.0221122 0.0382994i
\(698\) 2.64409 + 4.57969i 0.100080 + 0.173344i
\(699\) −9.61856 −0.363807
\(700\) −3.59967 + 22.4569i −0.136055 + 0.848792i
\(701\) −15.8135 −0.597266 −0.298633 0.954368i \(-0.596531\pi\)
−0.298633 + 0.954368i \(0.596531\pi\)
\(702\) −0.173648 0.300767i −0.00655393 0.0113517i
\(703\) 0.439693 0.761570i 0.0165833 0.0287232i
\(704\) 1.39646 2.41874i 0.0526310 0.0911596i
\(705\) −1.34730 2.33359i −0.0507421 0.0878879i
\(706\) 2.05232 0.0772400
\(707\) 32.9916 12.5939i 1.24078 0.473643i
\(708\) 27.0300 1.01585
\(709\) −21.1618 36.6533i −0.794748 1.37654i −0.922999 0.384802i \(-0.874270\pi\)
0.128252 0.991742i \(-0.459063\pi\)
\(710\) −0.445318 + 0.771313i −0.0167125 + 0.0289469i
\(711\) −1.46451 + 2.53660i −0.0549233 + 0.0951300i
\(712\) −7.40033 12.8177i −0.277339 0.480365i
\(713\) −4.71276 −0.176494
\(714\) 0.961981 0.367218i 0.0360012 0.0137428i
\(715\) 0.347296 0.0129881
\(716\) 23.6322 + 40.9322i 0.883178 + 1.52971i
\(717\) 1.17617 2.03719i 0.0439250 0.0760804i
\(718\) 1.80423 3.12501i 0.0673331 0.116624i
\(719\) −13.7870 23.8798i −0.514168 0.890565i −0.999865 0.0164377i \(-0.994767\pi\)
0.485697 0.874127i \(-0.338566\pi\)
\(720\) 2.14796 0.0800496
\(721\) −3.03225 + 18.9170i −0.112927 + 0.704506i
\(722\) 6.56624 0.244370
\(723\) −7.86618 13.6246i −0.292546 0.506705i
\(724\) 12.6468 21.9049i 0.470014 0.814088i
\(725\) 17.7952 30.8222i 0.660897 1.14471i
\(726\) 1.86097 + 3.22329i 0.0690670 + 0.119627i
\(727\) 20.5844 0.763433 0.381717 0.924279i \(-0.375333\pi\)
0.381717 + 0.924279i \(0.375333\pi\)
\(728\) −2.76604 2.24843i −0.102516 0.0833325i
\(729\) 1.00000 0.0370370
\(730\) 1.31743 + 2.28185i 0.0487602 + 0.0844552i
\(731\) −1.64930 + 2.85667i −0.0610016 + 0.105658i
\(732\) −7.38578 + 12.7925i −0.272986 + 0.472826i
\(733\) 5.80810 + 10.0599i 0.214527 + 0.371572i 0.953126 0.302573i \(-0.0978457\pi\)
−0.738599 + 0.674145i \(0.764512\pi\)
\(734\) 8.39775 0.309967
\(735\) −0.933296 4.47259i −0.0344251 0.164974i
\(736\) 30.7297 1.13271
\(737\) −1.23989 2.14754i −0.0456718 0.0791058i
\(738\) −0.180922 + 0.313366i −0.00665984 + 0.0115352i
\(739\) 4.30675 7.45951i 0.158426 0.274403i −0.775875 0.630887i \(-0.782691\pi\)
0.934301 + 0.356484i \(0.116025\pi\)
\(740\) −1.76604 3.05888i −0.0649211 0.112447i
\(741\) −0.305407 −0.0112194
\(742\) −1.80541 1.46756i −0.0662786 0.0538758i
\(743\) 23.9828 0.879842 0.439921 0.898036i \(-0.355006\pi\)
0.439921 + 0.898036i \(0.355006\pi\)
\(744\) 0.396459 + 0.686688i 0.0145349 + 0.0251752i
\(745\) −7.79561 + 13.5024i −0.285609 + 0.494689i
\(746\) 1.12907 1.95561i 0.0413382 0.0715999i
\(747\) 1.23396 + 2.13727i 0.0451481 + 0.0781988i
\(748\) −1.12061 −0.0409737
\(749\) 3.00862 18.7696i 0.109933 0.685825i
\(750\) −2.17024 −0.0792461
\(751\) 4.56149 + 7.90073i 0.166451 + 0.288302i 0.937170 0.348874i \(-0.113436\pi\)
−0.770719 + 0.637176i \(0.780103\pi\)
\(752\) 6.79292 11.7657i 0.247712 0.429050i
\(753\) −10.9081 + 18.8933i −0.397512 + 0.688511i
\(754\) 1.35117 + 2.34029i 0.0492066 + 0.0852283i
\(755\) −3.20264 −0.116556
\(756\) 4.64543 1.77330i 0.168953 0.0644944i
\(757\) −26.4979 −0.963084 −0.481542 0.876423i \(-0.659923\pi\)
−0.481542 + 0.876423i \(0.659923\pi\)
\(758\) −3.08946 5.35110i −0.112214 0.194361i
\(759\) −2.13041 + 3.68999i −0.0773292 + 0.133938i
\(760\) −0.134285 + 0.232589i −0.00487104 + 0.00843689i
\(761\) −26.1498 45.2927i −0.947928 1.64186i −0.749779 0.661688i \(-0.769840\pi\)
−0.198149 0.980172i \(-0.563493\pi\)
\(762\) −1.23349 −0.0446846
\(763\) −42.6189 + 16.2689i −1.54291 + 0.588975i
\(764\) −31.3996 −1.13600
\(765\) −0.365715 0.633436i −0.0132224 0.0229019i
\(766\) −1.73009 + 2.99660i −0.0625105 + 0.108271i
\(767\) −7.19119 + 12.4555i −0.259659 + 0.449742i
\(768\) 3.59967 + 6.23481i 0.129892 + 0.224979i
\(769\) 44.9436 1.62071 0.810353 0.585942i \(-0.199275\pi\)
0.810353 + 0.585942i \(0.199275\pi\)
\(770\) 0.0505072 0.315094i 0.00182015 0.0113552i
\(771\) 23.2772 0.838310
\(772\) 17.1604 + 29.7228i 0.617618 + 1.06975i
\(773\) 21.6279 37.4607i 0.777903 1.34737i −0.155245 0.987876i \(-0.549617\pi\)
0.933148 0.359492i \(-0.117050\pi\)
\(774\) 0.511144 0.885328i 0.0183727 0.0318225i
\(775\) 1.34595 + 2.33126i 0.0483480 + 0.0837412i
\(776\) 13.8348 0.496641
\(777\) −5.91147 4.80526i −0.212073 0.172388i
\(778\) 1.35504 0.0485804
\(779\) 0.159100 + 0.275570i 0.00570036 + 0.00987331i
\(780\) −0.613341 + 1.06234i −0.0219611 + 0.0380378i
\(781\) 1.04529 1.81050i 0.0374035 0.0647848i
\(782\) −1.55825 2.69896i −0.0557228 0.0965148i
\(783\) −7.78106 −0.278072
\(784\) 17.1763 15.3503i 0.613441 0.548225i
\(785\) −4.50980 −0.160962
\(786\) −2.69934 4.67539i −0.0962823 0.166766i
\(787\) 18.6762 32.3481i 0.665734 1.15308i −0.313352 0.949637i \(-0.601452\pi\)
0.979086 0.203448i \(-0.0652147\pi\)
\(788\) 16.1348 27.9462i 0.574777 0.995543i
\(789\) 1.37551 + 2.38246i 0.0489696 + 0.0848179i
\(790\) −0.663954 −0.0236224
\(791\) −23.3068 18.9453i −0.828693 0.673619i
\(792\) 0.716881 0.0254733
\(793\) −3.92989 6.80677i −0.139555 0.241716i
\(794\) −5.88666 + 10.1960i −0.208910 + 0.361842i
\(795\) −0.826352 + 1.43128i −0.0293077 + 0.0507624i
\(796\) −4.77244 8.26611i −0.169155 0.292985i
\(797\) −50.5740 −1.79142 −0.895711 0.444636i \(-0.853333\pi\)
−0.895711 + 0.444636i \(0.853333\pi\)
\(798\) −0.0444153 + 0.277089i −0.00157228 + 0.00980886i
\(799\) −4.62630 −0.163667
\(800\) −8.77631 15.2010i −0.310289 0.537437i
\(801\) −5.49273 + 9.51368i −0.194076 + 0.336149i
\(802\) 5.70574 9.88263i 0.201477 0.348968i
\(803\) −3.09240 5.35619i −0.109128 0.189016i
\(804\) 8.75877 0.308898
\(805\) −12.9192 + 4.93166i −0.455342 + 0.173818i
\(806\) −0.204393 −0.00719943
\(807\) 2.71167 + 4.69674i 0.0954552 + 0.165333i
\(808\) −8.99138 + 15.5735i −0.316316 + 0.547875i
\(809\) 25.4800 44.1326i 0.895829 1.55162i 0.0630531 0.998010i \(-0.479916\pi\)
0.832776 0.553611i \(-0.186750\pi\)
\(810\) 0.113341 + 0.196312i 0.00398239 + 0.00689770i
\(811\) −42.1334 −1.47950 −0.739752 0.672880i \(-0.765057\pi\)
−0.739752 + 0.672880i \(0.765057\pi\)
\(812\) −36.1464 + 13.7982i −1.26849 + 0.484221i
\(813\) −1.61587 −0.0566709
\(814\) −0.266044 0.460802i −0.00932485 0.0161511i
\(815\) 4.67587 8.09884i 0.163789 0.283690i
\(816\) 1.84389 3.19372i 0.0645492 0.111802i
\(817\) −0.449493 0.778544i −0.0157258 0.0272378i
\(818\) −1.26352 −0.0441779
\(819\) −0.418748 + 2.61240i −0.0146322 + 0.0912848i
\(820\) 1.27807 0.0446320
\(821\) −10.4397 18.0821i −0.364348 0.631069i 0.624323 0.781166i \(-0.285375\pi\)
−0.988671 + 0.150097i \(0.952041\pi\)
\(822\) −1.41013 + 2.44242i −0.0491839 + 0.0851891i
\(823\) 5.69640 9.86646i 0.198564 0.343923i −0.749499 0.662006i \(-0.769706\pi\)
0.948063 + 0.318082i \(0.103039\pi\)
\(824\) −4.87804 8.44901i −0.169935 0.294335i
\(825\) 2.43376 0.0847327
\(826\) 10.2548 + 8.33581i 0.356810 + 0.290040i
\(827\) 3.45842 0.120261 0.0601304 0.998191i \(-0.480848\pi\)
0.0601304 + 0.998191i \(0.480848\pi\)
\(828\) −7.52481 13.0334i −0.261505 0.452941i
\(829\) −7.74850 + 13.4208i −0.269117 + 0.466124i −0.968634 0.248492i \(-0.920065\pi\)
0.699517 + 0.714616i \(0.253398\pi\)
\(830\) −0.279715 + 0.484481i −0.00970905 + 0.0168166i
\(831\) 3.92514 + 6.79855i 0.136162 + 0.235839i
\(832\) −5.24897 −0.181975
\(833\) −7.45130 2.45177i −0.258172 0.0849487i
\(834\) 5.56448 0.192682
\(835\) 3.75237 + 6.49930i 0.129856 + 0.224918i
\(836\) 0.152704 0.264490i 0.00528137 0.00914759i
\(837\) 0.294263 0.509678i 0.0101712 0.0176171i
\(838\) 2.89827 + 5.01995i 0.100119 + 0.173411i
\(839\) 42.1385 1.45478 0.727391 0.686224i \(-0.240733\pi\)
0.727391 + 0.686224i \(0.240733\pi\)
\(840\) 1.80541 + 1.46756i 0.0622925 + 0.0506356i
\(841\) 31.5449 1.08775
\(842\) −3.74082 6.47929i −0.128917 0.223291i
\(843\) −9.52141 + 16.4916i −0.327935 + 0.568000i
\(844\) −22.0116 + 38.1252i −0.757671 + 1.31232i
\(845\) −0.326352 0.565258i −0.0112268 0.0194455i
\(846\) 1.43376 0.0492938
\(847\) 4.48767 27.9968i 0.154198 0.961982i
\(848\) −8.33275 −0.286148
\(849\) 11.6434 + 20.1669i 0.399599 + 0.692127i
\(850\) −0.890063 + 1.54163i −0.0305289 + 0.0528776i
\(851\) −11.5287 + 19.9683i −0.395198 + 0.684503i
\(852\) 3.69207 + 6.39485i 0.126488 + 0.219084i
\(853\) −28.6736 −0.981764 −0.490882 0.871226i \(-0.663325\pi\)
−0.490882 + 0.871226i \(0.663325\pi\)
\(854\) −6.74716 + 2.57560i −0.230883 + 0.0881352i
\(855\) 0.199340 0.00681730
\(856\) 4.84002 + 8.38316i 0.165429 + 0.286531i
\(857\) −0.530907 + 0.919558i −0.0181354 + 0.0314115i −0.874951 0.484212i \(-0.839106\pi\)
0.856815 + 0.515624i \(0.172440\pi\)
\(858\) −0.0923963 + 0.160035i −0.00315436 + 0.00546351i
\(859\) −5.74850 9.95670i −0.196136 0.339718i 0.751136 0.660147i \(-0.229506\pi\)
−0.947272 + 0.320429i \(0.896173\pi\)
\(860\) −3.61081 −0.123128
\(861\) 2.57532 0.983080i 0.0877667 0.0335033i
\(862\) −3.59358 −0.122398
\(863\) 26.1013 + 45.2088i 0.888499 + 1.53893i 0.841650 + 0.540024i \(0.181585\pi\)
0.0468495 + 0.998902i \(0.485082\pi\)
\(864\) −1.91875 + 3.32337i −0.0652771 + 0.113063i
\(865\) −5.03374 + 8.71869i −0.171152 + 0.296444i
\(866\) −0.559841 0.969672i −0.0190242 0.0329508i
\(867\) 15.7442 0.534702
\(868\) 0.463163 2.88949i 0.0157208 0.0980758i
\(869\) 1.55850 0.0528684
\(870\) −0.881911 1.52752i −0.0298996 0.0517876i
\(871\) −2.33022 + 4.03606i −0.0789566 + 0.136757i
\(872\) 11.6152 20.1180i 0.393339 0.681283i
\(873\) −5.13429 8.89284i −0.173769 0.300977i
\(874\) 0.849356 0.0287299
\(875\) 12.8293 + 10.4286i 0.433711 + 0.352550i
\(876\) 21.8452 0.738082
\(877\) −23.3255 40.4009i −0.787645 1.36424i −0.927406 0.374056i \(-0.877967\pi\)
0.139761 0.990185i \(-0.455367\pi\)
\(878\) 4.94878 8.57153i 0.167013 0.289275i
\(879\) 13.4868 23.3598i 0.454898 0.787907i
\(880\) −0.571452 0.989783i −0.0192636 0.0333656i
\(881\) 18.9691 0.639087 0.319543 0.947572i \(-0.396470\pi\)
0.319543 + 0.947572i \(0.396470\pi\)
\(882\) 2.30928 + 0.759842i 0.0777574 + 0.0255852i
\(883\) 0.744223 0.0250451 0.0125225 0.999922i \(-0.496014\pi\)
0.0125225 + 0.999922i \(0.496014\pi\)
\(884\) 1.05303 + 1.82391i 0.0354173 + 0.0613446i
\(885\) 4.69372 8.12975i 0.157778 0.273279i
\(886\) −3.66978 + 6.35624i −0.123289 + 0.213542i
\(887\) −16.1716 28.0100i −0.542989 0.940484i −0.998731 0.0503721i \(-0.983959\pi\)
0.455742 0.890112i \(-0.349374\pi\)
\(888\) 3.87939 0.130184
\(889\) 7.29174 + 5.92723i 0.244557 + 0.198793i
\(890\) −2.49020 −0.0834717
\(891\) −0.266044 0.460802i −0.00891282 0.0154375i
\(892\) −11.7652 + 20.3779i −0.393927 + 0.682301i
\(893\) 0.630415 1.09191i 0.0210960 0.0365394i
\(894\) −4.14796 7.18447i −0.138728 0.240285i
\(895\) 16.4148 0.548685
\(896\) −3.97724 + 24.8124i −0.132870 + 0.828926i
\(897\) 8.00774 0.267371
\(898\) 4.45353 + 7.71373i 0.148616 + 0.257411i
\(899\) −2.28968 + 3.96584i −0.0763650 + 0.132268i
\(900\) −4.29813 + 7.44459i −0.143271 + 0.248153i
\(901\) 1.41875 + 2.45734i 0.0472654 + 0.0818660i
\(902\) 0.192533 0.00641066
\(903\) −7.27584 + 2.77741i −0.242125 + 0.0924265i
\(904\) 15.2950 0.508703
\(905\) −4.39218 7.60748i −0.146001 0.252881i
\(906\) 0.852044 1.47578i 0.0283073 0.0490296i
\(907\) 25.9525 44.9510i 0.861738 1.49257i −0.00851177 0.999964i \(-0.502709\pi\)
0.870250 0.492610i \(-0.163957\pi\)
\(908\) 7.33275 + 12.7007i 0.243346 + 0.421487i
\(909\) 13.3473 0.442702
\(910\) −0.560307 + 0.213887i −0.0185740 + 0.00709027i
\(911\) −31.0324 −1.02815 −0.514075 0.857746i \(-0.671865\pi\)
−0.514075 + 0.857746i \(0.671865\pi\)
\(912\) 0.502526 + 0.870401i 0.0166403 + 0.0288219i
\(913\) 0.656574 1.13722i 0.0217294 0.0376365i
\(914\) 5.84477 10.1234i 0.193328 0.334854i
\(915\) 2.56506 + 4.44281i 0.0847981 + 0.146875i
\(916\) 38.8016 1.28204
\(917\) −6.50939 + 40.6095i −0.214959 + 1.34104i
\(918\) 0.389185 0.0128450
\(919\) −1.69594 2.93745i −0.0559438 0.0968975i 0.836697 0.547666i \(-0.184483\pi\)
−0.892641 + 0.450768i \(0.851150\pi\)
\(920\) 3.52094 6.09845i 0.116082 0.201060i
\(921\) 3.14203 5.44215i 0.103533 0.179325i
\(922\) 1.71167 + 2.96469i 0.0563707 + 0.0976370i
\(923\) −3.92902 −0.129325
\(924\) −2.05303 1.66885i −0.0675398 0.0549011i
\(925\) 13.1702 0.433035
\(926\) 0.416222 + 0.720917i 0.0136779 + 0.0236908i
\(927\) −3.62061 + 6.27109i −0.118917 + 0.205970i
\(928\) 14.9299 25.8593i 0.490098 0.848874i
\(929\) −24.4513 42.3509i −0.802221 1.38949i −0.918151 0.396231i \(-0.870318\pi\)
0.115930 0.993257i \(-0.463015\pi\)
\(930\) 0.133408 0.00437462
\(931\) 1.59405 1.42458i 0.0522427 0.0466887i
\(932\) −18.0770 −0.592131
\(933\) 1.11334 + 1.92836i 0.0364491 + 0.0631318i
\(934\) −4.73695 + 8.20464i −0.154998 + 0.268464i
\(935\) −0.194593 + 0.337044i −0.00636386 + 0.0110225i
\(936\) −0.673648 1.16679i −0.0220189 0.0381378i
\(937\) −12.9676 −0.423633 −0.211817 0.977309i \(-0.567938\pi\)
−0.211817 + 0.977309i \(0.567938\pi\)
\(938\) 3.32295 + 2.70112i 0.108498 + 0.0881948i
\(939\) −19.8212 −0.646840
\(940\) −2.53209 4.38571i −0.0825876 0.143046i
\(941\) −13.5453 + 23.4611i −0.441564 + 0.764811i −0.997806 0.0662093i \(-0.978909\pi\)
0.556242 + 0.831020i \(0.312243\pi\)
\(942\) 1.19981 2.07813i 0.0390918 0.0677090i
\(943\) −4.17159 7.22540i −0.135846 0.235292i
\(944\) 47.3304 1.54047
\(945\) 0.273318 1.70513i 0.00889105 0.0554677i
\(946\) −0.543948 −0.0176853
\(947\) −10.7294 18.5838i −0.348658 0.603893i 0.637354 0.770571i \(-0.280029\pi\)
−0.986011 + 0.166679i \(0.946696\pi\)
\(948\) −2.75237 + 4.76725i −0.0893929 + 0.154833i
\(949\) −5.81180 + 10.0663i −0.188659 + 0.326767i
\(950\) −0.242574 0.420150i −0.00787013 0.0136315i
\(951\) 11.7023 0.379474
\(952\) 3.73190 1.42458i 0.120951 0.0461709i
\(953\) −28.1147 −0.910726 −0.455363 0.890306i \(-0.650490\pi\)
−0.455363 + 0.890306i \(0.650490\pi\)
\(954\) −0.439693 0.761570i −0.0142356 0.0246567i
\(955\) −5.45249 + 9.44398i −0.176438 + 0.305600i
\(956\) 2.21048 3.82867i 0.0714922 0.123828i
\(957\) 2.07011 + 3.58553i 0.0669171 + 0.115904i
\(958\) 14.1771 0.458040
\(959\) 20.0724 7.66225i 0.648171 0.247427i
\(960\) 3.42602 0.110574
\(961\) 15.3268 + 26.5468i 0.494414 + 0.856349i
\(962\) −0.500000 + 0.866025i −0.0161206 + 0.0279218i
\(963\) 3.59240 6.22221i 0.115763 0.200508i
\(964\) −14.7836 25.6059i −0.476147 0.824711i
\(965\) 11.9195 0.383703
\(966\) 1.16456 7.26525i 0.0374692 0.233756i
\(967\) 43.7006 1.40532 0.702658 0.711528i \(-0.251996\pi\)
0.702658 + 0.711528i \(0.251996\pi\)
\(968\) 7.21941 + 12.5044i 0.232041 + 0.401906i
\(969\) 0.171122 0.296392i 0.00549723 0.00952148i
\(970\) 1.16385 2.01584i 0.0373689 0.0647248i
\(971\) 18.5942 + 32.2061i 0.596717 + 1.03354i 0.993302 + 0.115546i \(0.0368616\pi\)
−0.396586 + 0.917998i \(0.629805\pi\)
\(972\) 1.87939 0.0602813
\(973\) −32.8943 26.7388i −1.05454 0.857205i
\(974\) 6.67768 0.213967
\(975\) −2.28699 3.96118i −0.0732423 0.126859i
\(976\) −12.9327 + 22.4001i −0.413966 + 0.717011i
\(977\) 11.2203 19.4341i 0.358969 0.621752i −0.628820 0.777551i \(-0.716462\pi\)
0.987789 + 0.155799i \(0.0497951\pi\)
\(978\) 2.48798 + 4.30930i 0.0795568 + 0.137796i
\(979\) 5.84524 0.186815
\(980\) −1.75402 8.40571i −0.0560302 0.268511i
\(981\) −17.2422 −0.550500
\(982\) −1.30969 2.26845i −0.0417938 0.0723890i
\(983\) 11.6561 20.1890i 0.371772 0.643928i −0.618066 0.786126i \(-0.712084\pi\)
0.989838 + 0.142198i \(0.0454170\pi\)
\(984\) −0.701867 + 1.21567i −0.0223747 + 0.0387541i
\(985\) −5.60354 9.70562i −0.178544 0.309247i
\(986\) −3.02827 −0.0964399
\(987\) −8.47565 6.88960i −0.269783 0.219298i
\(988\) −0.573978 −0.0182607
\(989\) 11.7856 + 20.4133i 0.374762 + 0.649106i
\(990\) 0.0603074 0.104455i 0.00191669 0.00331981i
\(991\) −2.64084 + 4.57408i −0.0838892 + 0.145300i −0.904917 0.425587i \(-0.860068\pi\)
0.821028 + 0.570888i \(0.193401\pi\)
\(992\) 1.12923 + 1.95589i 0.0358532 + 0.0620995i
\(993\) −20.9118 −0.663615
\(994\) −0.571395 + 3.56471i −0.0181236 + 0.113066i
\(995\) −3.31490 −0.105089
\(996\) 2.31908 + 4.01676i 0.0734828 + 0.127276i
\(997\) −14.4847 + 25.0883i −0.458736 + 0.794554i −0.998894 0.0470090i \(-0.985031\pi\)
0.540158 + 0.841563i \(0.318364\pi\)
\(998\) −5.38238 + 9.32255i −0.170376 + 0.295100i
\(999\) −1.43969 2.49362i −0.0455499 0.0788947i
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.i.b.235.2 yes 6
3.2 odd 2 819.2.j.e.235.2 6
7.2 even 3 inner 273.2.i.b.79.2 6
7.3 odd 6 1911.2.a.p.1.2 3
7.4 even 3 1911.2.a.o.1.2 3
21.2 odd 6 819.2.j.e.352.2 6
21.11 odd 6 5733.2.a.y.1.2 3
21.17 even 6 5733.2.a.z.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.i.b.79.2 6 7.2 even 3 inner
273.2.i.b.235.2 yes 6 1.1 even 1 trivial
819.2.j.e.235.2 6 3.2 odd 2
819.2.j.e.352.2 6 21.2 odd 6
1911.2.a.o.1.2 3 7.4 even 3
1911.2.a.p.1.2 3 7.3 odd 6
5733.2.a.y.1.2 3 21.11 odd 6
5733.2.a.z.1.2 3 21.17 even 6