Properties

Label 273.2.r.b.269.22
Level $273$
Weight $2$
Character 273.269
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(68,273)]
 
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([3, 5, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.68");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.r (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.22
Character \(\chi\) \(=\) 273.269
Dual form 273.2.r.b.68.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.05456i q^{2} +(1.46610 + 0.922247i) q^{3} +0.887893 q^{4} +(-0.000964697 - 0.00167090i) q^{5} +(-0.972570 + 1.54610i) q^{6} +(-2.64511 - 0.0584461i) q^{7} +3.04547i q^{8} +(1.29892 + 2.70422i) q^{9} +(0.00176208 - 0.00101734i) q^{10} +(-2.16237 + 1.24844i) q^{11} +(1.30174 + 0.818857i) q^{12} +(0.922193 - 3.48562i) q^{13} +(0.0616352 - 2.78943i) q^{14} +(0.000126641 - 0.00333941i) q^{15} -1.43586 q^{16} +4.17524 q^{17} +(-2.85178 + 1.36979i) q^{18} +(4.64914 + 2.68418i) q^{19} +(-0.000856548 - 0.00148358i) q^{20} +(-3.82410 - 2.52513i) q^{21} +(-1.31657 - 2.28036i) q^{22} -4.87067i q^{23} +(-2.80868 + 4.46497i) q^{24} +(2.50000 - 4.33012i) q^{25} +(3.67581 + 0.972512i) q^{26} +(-0.589610 + 5.16259i) q^{27} +(-2.34857 - 0.0518939i) q^{28} +(-7.57023 - 4.37067i) q^{29} +(0.00352162 + 0.000133551i) q^{30} +(-6.57778 - 3.79768i) q^{31} +4.57673i q^{32} +(-4.32163 - 0.163891i) q^{33} +4.40306i q^{34} +(0.00245407 + 0.00447610i) q^{35} +(1.15330 + 2.40106i) q^{36} +3.65572 q^{37} +(-2.83065 + 4.90282i) q^{38} +(4.56664 - 4.25979i) q^{39} +(0.00508869 - 0.00293796i) q^{40} +(1.83038 - 3.17031i) q^{41} +(2.66291 - 4.03276i) q^{42} +(1.32938 + 2.30256i) q^{43} +(-1.91995 + 1.10849i) q^{44} +(0.00326543 - 0.00477912i) q^{45} +5.13644 q^{46} +(1.79190 + 3.10366i) q^{47} +(-2.10512 - 1.32422i) q^{48} +(6.99317 + 0.309192i) q^{49} +(4.56640 + 2.63641i) q^{50} +(6.12133 + 3.85060i) q^{51} +(0.818809 - 3.09486i) q^{52} +(-12.3735 - 7.14382i) q^{53} +(-5.44429 - 0.621782i) q^{54} +(0.00417206 + 0.00240874i) q^{55} +(0.177996 - 8.05559i) q^{56} +(4.34064 + 8.22295i) q^{57} +(4.60916 - 7.98330i) q^{58} -5.23130 q^{59} +(0.000112444 - 0.00296504i) q^{60} +(6.56379 + 3.78960i) q^{61} +(4.00490 - 6.93670i) q^{62} +(-3.27773 - 7.22887i) q^{63} -7.69818 q^{64} +(-0.00671378 + 0.00182167i) q^{65} +(0.172833 - 4.55744i) q^{66} +(-7.12713 - 12.3445i) q^{67} +3.70716 q^{68} +(4.49197 - 7.14091i) q^{69} +(-0.00472034 + 0.00258797i) q^{70} +(1.24050 - 0.716205i) q^{71} +(-8.23562 + 3.95582i) q^{72} +(1.61067 + 0.929921i) q^{73} +3.85519i q^{74} +(7.65870 - 4.04279i) q^{75} +(4.12794 + 2.38327i) q^{76} +(5.79266 - 3.17589i) q^{77} +(4.49223 + 4.81581i) q^{78} +(3.64483 + 6.31302i) q^{79} +(0.00138517 + 0.00239918i) q^{80} +(-5.62562 + 7.02513i) q^{81} +(3.34329 + 1.93025i) q^{82} +10.4089 q^{83} +(-3.39539 - 2.24205i) q^{84} +(-0.00402784 - 0.00697642i) q^{85} +(-2.42820 + 1.40192i) q^{86} +(-7.06790 - 13.3895i) q^{87} +(-3.80210 - 6.58543i) q^{88} -5.40380 q^{89} +(0.00503989 + 0.00344361i) q^{90} +(-2.64302 + 9.16594i) q^{91} -4.32464i q^{92} +(-6.14130 - 11.6341i) q^{93} +(-3.27301 + 1.88967i) q^{94} -0.0103577i q^{95} +(-4.22088 + 6.70997i) q^{96} +(2.07015 - 1.19520i) q^{97} +(-0.326063 + 7.37475i) q^{98} +(-6.18481 - 4.22589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.05456i 0.745690i 0.927894 + 0.372845i \(0.121618\pi\)
−0.927894 + 0.372845i \(0.878382\pi\)
\(3\) 1.46610 + 0.922247i 0.846455 + 0.532460i
\(4\) 0.887893 0.443947
\(5\) −0.000964697 0.00167090i −0.000431425 0.000747251i 0.865810 0.500374i \(-0.166804\pi\)
−0.866241 + 0.499626i \(0.833471\pi\)
\(6\) −0.972570 + 1.54610i −0.397050 + 0.631193i
\(7\) −2.64511 0.0584461i −0.999756 0.0220905i
\(8\) 3.04547i 1.07674i
\(9\) 1.29892 + 2.70422i 0.432973 + 0.901407i
\(10\) 0.00176208 0.00101734i 0.000557217 0.000321710i
\(11\) −2.16237 + 1.24844i −0.651979 + 0.376420i −0.789214 0.614118i \(-0.789512\pi\)
0.137235 + 0.990539i \(0.456178\pi\)
\(12\) 1.30174 + 0.818857i 0.375781 + 0.236384i
\(13\) 0.922193 3.48562i 0.255770 0.966738i
\(14\) 0.0616352 2.78943i 0.0164727 0.745508i
\(15\) 0.000126641 0.00333941i 3.26987e−5 0.000862231i
\(16\) −1.43586 −0.358965
\(17\) 4.17524 1.01264 0.506322 0.862345i \(-0.331005\pi\)
0.506322 + 0.862345i \(0.331005\pi\)
\(18\) −2.85178 + 1.36979i −0.672170 + 0.322864i
\(19\) 4.64914 + 2.68418i 1.06659 + 0.615794i 0.927247 0.374450i \(-0.122169\pi\)
0.139340 + 0.990245i \(0.455502\pi\)
\(20\) −0.000856548 0.00148358i −0.000191530 0.000331740i
\(21\) −3.82410 2.52513i −0.834486 0.551029i
\(22\) −1.31657 2.28036i −0.280693 0.486174i
\(23\) 4.87067i 1.01561i −0.861473 0.507803i \(-0.830458\pi\)
0.861473 0.507803i \(-0.169542\pi\)
\(24\) −2.80868 + 4.46497i −0.573319 + 0.911409i
\(25\) 2.50000 4.33012i 0.500000 0.866025i
\(26\) 3.67581 + 0.972512i 0.720886 + 0.190725i
\(27\) −0.589610 + 5.16259i −0.113470 + 0.993541i
\(28\) −2.34857 0.0518939i −0.443838 0.00980702i
\(29\) −7.57023 4.37067i −1.40576 0.811614i −0.410781 0.911734i \(-0.634744\pi\)
−0.994975 + 0.100120i \(0.968077\pi\)
\(30\) 0.00352162 0.000133551i 0.000642957 2.43831e-5i
\(31\) −6.57778 3.79768i −1.18140 0.682084i −0.225065 0.974344i \(-0.572260\pi\)
−0.956339 + 0.292260i \(0.905593\pi\)
\(32\) 4.57673i 0.809060i
\(33\) −4.32163 0.163891i −0.752300 0.0285297i
\(34\) 4.40306i 0.755118i
\(35\) 0.00245407 + 0.00447610i 0.000414813 + 0.000756599i
\(36\) 1.15330 + 2.40106i 0.192217 + 0.400177i
\(37\) 3.65572 0.600996 0.300498 0.953782i \(-0.402847\pi\)
0.300498 + 0.953782i \(0.402847\pi\)
\(38\) −2.83065 + 4.90282i −0.459191 + 0.795343i
\(39\) 4.56664 4.25979i 0.731247 0.682113i
\(40\) 0.00508869 0.00293796i 0.000804592 0.000464531i
\(41\) 1.83038 3.17031i 0.285857 0.495119i −0.686960 0.726696i \(-0.741055\pi\)
0.972817 + 0.231577i \(0.0743884\pi\)
\(42\) 2.66291 4.03276i 0.410896 0.622268i
\(43\) 1.32938 + 2.30256i 0.202729 + 0.351137i 0.949407 0.314049i \(-0.101686\pi\)
−0.746678 + 0.665186i \(0.768352\pi\)
\(44\) −1.91995 + 1.10849i −0.289444 + 0.167110i
\(45\) 0.00326543 0.00477912i 0.000486781 0.000712429i
\(46\) 5.13644 0.757327
\(47\) 1.79190 + 3.10366i 0.261375 + 0.452715i 0.966608 0.256261i \(-0.0824907\pi\)
−0.705232 + 0.708976i \(0.749157\pi\)
\(48\) −2.10512 1.32422i −0.303848 0.191134i
\(49\) 6.99317 + 0.309192i 0.999024 + 0.0441703i
\(50\) 4.56640 + 2.63641i 0.645786 + 0.372845i
\(51\) 6.12133 + 3.85060i 0.857158 + 0.539192i
\(52\) 0.818809 3.09486i 0.113548 0.429180i
\(53\) −12.3735 7.14382i −1.69962 0.981279i −0.946108 0.323850i \(-0.895023\pi\)
−0.753516 0.657429i \(-0.771644\pi\)
\(54\) −5.44429 0.621782i −0.740874 0.0846138i
\(55\) 0.00417206 + 0.00240874i 0.000562561 + 0.000324795i
\(56\) 0.177996 8.05559i 0.0237857 1.07647i
\(57\) 4.34064 + 8.22295i 0.574932 + 1.08916i
\(58\) 4.60916 7.98330i 0.605212 1.04826i
\(59\) −5.23130 −0.681057 −0.340529 0.940234i \(-0.610606\pi\)
−0.340529 + 0.940234i \(0.610606\pi\)
\(60\) 0.000112444 0.00296504i 1.45165e−5 0.000382785i
\(61\) 6.56379 + 3.78960i 0.840407 + 0.485209i 0.857402 0.514647i \(-0.172077\pi\)
−0.0169958 + 0.999856i \(0.505410\pi\)
\(62\) 4.00490 6.93670i 0.508623 0.880961i
\(63\) −3.27773 7.22887i −0.412955 0.910751i
\(64\) −7.69818 −0.962273
\(65\) −0.00671378 + 0.00182167i −0.000832741 + 0.000225951i
\(66\) 0.172833 4.55744i 0.0212743 0.560982i
\(67\) −7.12713 12.3445i −0.870717 1.50813i −0.861256 0.508172i \(-0.830322\pi\)
−0.00946155 0.999955i \(-0.503012\pi\)
\(68\) 3.70716 0.449560
\(69\) 4.49197 7.14091i 0.540769 0.859665i
\(70\) −0.00472034 + 0.00258797i −0.000564188 + 0.000309322i
\(71\) 1.24050 0.716205i 0.147221 0.0849979i −0.424580 0.905390i \(-0.639578\pi\)
0.571801 + 0.820392i \(0.306245\pi\)
\(72\) −8.23562 + 3.95582i −0.970577 + 0.466198i
\(73\) 1.61067 + 0.929921i 0.188515 + 0.108839i 0.591287 0.806461i \(-0.298620\pi\)
−0.402772 + 0.915300i \(0.631953\pi\)
\(74\) 3.85519i 0.448157i
\(75\) 7.65870 4.04279i 0.884351 0.466822i
\(76\) 4.12794 + 2.38327i 0.473508 + 0.273380i
\(77\) 5.79266 3.17589i 0.660135 0.361926i
\(78\) 4.49223 + 4.81581i 0.508644 + 0.545284i
\(79\) 3.64483 + 6.31302i 0.410075 + 0.710271i 0.994898 0.100891i \(-0.0321692\pi\)
−0.584823 + 0.811161i \(0.698836\pi\)
\(80\) 0.00138517 + 0.00239918i 0.000154867 + 0.000268237i
\(81\) −5.62562 + 7.02513i −0.625069 + 0.780570i
\(82\) 3.34329 + 1.93025i 0.369205 + 0.213161i
\(83\) 10.4089 1.14253 0.571263 0.820767i \(-0.306454\pi\)
0.571263 + 0.820767i \(0.306454\pi\)
\(84\) −3.39539 2.24205i −0.370467 0.244627i
\(85\) −0.00402784 0.00697642i −0.000436880 0.000756699i
\(86\) −2.42820 + 1.40192i −0.261839 + 0.151173i
\(87\) −7.06790 13.3895i −0.757758 1.43550i
\(88\) −3.80210 6.58543i −0.405305 0.702009i
\(89\) −5.40380 −0.572801 −0.286401 0.958110i \(-0.592459\pi\)
−0.286401 + 0.958110i \(0.592459\pi\)
\(90\) 0.00503989 + 0.00344361i 0.000531251 + 0.000362988i
\(91\) −2.64302 + 9.16594i −0.277064 + 0.960852i
\(92\) 4.32464i 0.450875i
\(93\) −6.14130 11.6341i −0.636824 1.20640i
\(94\) −3.27301 + 1.88967i −0.337585 + 0.194905i
\(95\) 0.0103577i 0.00106268i
\(96\) −4.22088 + 6.70997i −0.430792 + 0.684833i
\(97\) 2.07015 1.19520i 0.210192 0.121354i −0.391209 0.920302i \(-0.627943\pi\)
0.601401 + 0.798948i \(0.294610\pi\)
\(98\) −0.326063 + 7.37475i −0.0329373 + 0.744962i
\(99\) −6.18481 4.22589i −0.621597 0.424718i
\(100\) 2.21973 3.84469i 0.221973 0.384469i
\(101\) 9.02995 + 15.6403i 0.898514 + 1.55627i 0.829395 + 0.558663i \(0.188685\pi\)
0.0691187 + 0.997608i \(0.477981\pi\)
\(102\) −4.06071 + 6.45534i −0.402070 + 0.639174i
\(103\) −8.45144 + 4.87944i −0.832745 + 0.480786i −0.854792 0.518971i \(-0.826315\pi\)
0.0220466 + 0.999757i \(0.492982\pi\)
\(104\) 10.6154 + 2.80851i 1.04092 + 0.275397i
\(105\) −0.000530155 0.00882568i −5.17378e−5 0.000861298i
\(106\) 7.53362 13.0486i 0.731730 1.26739i
\(107\) 5.46272i 0.528101i 0.964509 + 0.264051i \(0.0850586\pi\)
−0.964509 + 0.264051i \(0.914941\pi\)
\(108\) −0.523511 + 4.58383i −0.0503748 + 0.441079i
\(109\) −3.68535 + 6.38321i −0.352993 + 0.611401i −0.986772 0.162113i \(-0.948169\pi\)
0.633780 + 0.773514i \(0.281503\pi\)
\(110\) −0.00254017 + 0.00439971i −0.000242196 + 0.000419496i
\(111\) 5.35966 + 3.37147i 0.508716 + 0.320006i
\(112\) 3.79800 + 0.0839203i 0.358877 + 0.00792972i
\(113\) 0.390686 0.225562i 0.0367526 0.0212191i −0.481511 0.876440i \(-0.659912\pi\)
0.518264 + 0.855221i \(0.326579\pi\)
\(114\) −8.67164 + 4.57749i −0.812173 + 0.428721i
\(115\) −0.00813843 + 0.00469872i −0.000758912 + 0.000438158i
\(116\) −6.72156 3.88069i −0.624081 0.360313i
\(117\) 10.6237 2.03373i 0.982166 0.188018i
\(118\) 5.51674i 0.507857i
\(119\) −11.0439 0.244026i −1.01240 0.0223698i
\(120\) 0.0101701 0.000385682i 0.000928396 3.52078e-5i
\(121\) −2.38277 + 4.12708i −0.216616 + 0.375189i
\(122\) −3.99638 + 6.92194i −0.361815 + 0.626683i
\(123\) 5.60733 2.95994i 0.505596 0.266889i
\(124\) −5.84037 3.37194i −0.524481 0.302809i
\(125\) −0.0192939 −0.00172570
\(126\) 7.62331 3.45658i 0.679138 0.307936i
\(127\) −4.71924 + 8.17397i −0.418765 + 0.725322i −0.995816 0.0913863i \(-0.970870\pi\)
0.577051 + 0.816708i \(0.304204\pi\)
\(128\) 1.03524i 0.0915032i
\(129\) −0.174516 + 4.60181i −0.0153653 + 0.405167i
\(130\) −0.00192107 0.00708011i −0.000168489 0.000620967i
\(131\) −3.11100 5.38841i −0.271809 0.470788i 0.697516 0.716569i \(-0.254289\pi\)
−0.969325 + 0.245782i \(0.920955\pi\)
\(132\) −3.83715 0.145517i −0.333981 0.0126657i
\(133\) −12.1406 7.37168i −1.05272 0.639205i
\(134\) 13.0181 7.51602i 1.12459 0.649285i
\(135\) 0.00919499 0.00399515i 0.000791379 0.000343848i
\(136\) 12.7156i 1.09035i
\(137\) 6.15626i 0.525965i −0.964801 0.262983i \(-0.915294\pi\)
0.964801 0.262983i \(-0.0847062\pi\)
\(138\) 7.53055 + 4.73707i 0.641043 + 0.403246i
\(139\) −10.6666 + 6.15838i −0.904731 + 0.522347i −0.878732 0.477315i \(-0.841610\pi\)
−0.0259992 + 0.999662i \(0.508277\pi\)
\(140\) 0.00217895 + 0.00397430i 0.000184155 + 0.000335890i
\(141\) −0.235233 + 6.20286i −0.0198102 + 0.522375i
\(142\) 0.755285 + 1.30819i 0.0633821 + 0.109781i
\(143\) 2.35748 + 8.68851i 0.197143 + 0.726570i
\(144\) −1.86506 3.88288i −0.155422 0.323573i
\(145\) 0.0168655i 0.00140060i
\(146\) −0.980661 + 1.69856i −0.0811601 + 0.140573i
\(147\) 9.96756 + 6.90274i 0.822110 + 0.569328i
\(148\) 3.24589 0.266810
\(149\) 6.20222 + 3.58086i 0.508106 + 0.293355i 0.732055 0.681246i \(-0.238562\pi\)
−0.223949 + 0.974601i \(0.571895\pi\)
\(150\) 4.26339 + 8.07660i 0.348104 + 0.659451i
\(151\) −8.14880 + 14.1141i −0.663140 + 1.14859i 0.316646 + 0.948544i \(0.397443\pi\)
−0.979786 + 0.200049i \(0.935890\pi\)
\(152\) −8.17460 + 14.1588i −0.663048 + 1.14843i
\(153\) 5.42330 + 11.2908i 0.438447 + 0.912804i
\(154\) 3.34918 + 6.10874i 0.269884 + 0.492256i
\(155\) 0.0146545i 0.00117707i
\(156\) 4.05469 3.78224i 0.324635 0.302822i
\(157\) 4.07713 + 2.35393i 0.325391 + 0.187864i 0.653793 0.756674i \(-0.273177\pi\)
−0.328402 + 0.944538i \(0.606510\pi\)
\(158\) −6.65749 + 3.84370i −0.529642 + 0.305789i
\(159\) −11.5524 21.8850i −0.916165 1.73559i
\(160\) 0.00764728 0.00441516i 0.000604571 0.000349049i
\(161\) −0.284672 + 12.8834i −0.0224353 + 1.01536i
\(162\) −7.40845 5.93258i −0.582063 0.466107i
\(163\) 2.10316 3.64278i 0.164732 0.285324i −0.771828 0.635831i \(-0.780657\pi\)
0.936560 + 0.350507i \(0.113991\pi\)
\(164\) 1.62518 2.81490i 0.126905 0.219806i
\(165\) 0.00389522 + 0.00737914i 0.000303242 + 0.000574465i
\(166\) 10.9769i 0.851970i
\(167\) 7.24993 12.5573i 0.561017 0.971709i −0.436391 0.899757i \(-0.643744\pi\)
0.997408 0.0719525i \(-0.0229230\pi\)
\(168\) 7.69021 11.6462i 0.593312 0.898522i
\(169\) −11.2991 6.42883i −0.869163 0.494526i
\(170\) 0.00735708 0.00424761i 0.000564263 0.000325777i
\(171\) −1.21976 + 16.0588i −0.0932776 + 1.22805i
\(172\) 1.18035 + 2.04443i 0.0900009 + 0.155886i
\(173\) 7.84836 13.5938i 0.596700 1.03351i −0.396605 0.917989i \(-0.629812\pi\)
0.993305 0.115525i \(-0.0368550\pi\)
\(174\) 14.1201 7.45356i 1.07044 0.565053i
\(175\) −6.86584 + 11.3075i −0.519009 + 0.854768i
\(176\) 3.10486 1.79259i 0.234037 0.135122i
\(177\) −7.66963 4.82455i −0.576484 0.362636i
\(178\) 5.69865i 0.427132i
\(179\) −5.59852 + 3.23231i −0.418453 + 0.241594i −0.694415 0.719575i \(-0.744337\pi\)
0.275962 + 0.961168i \(0.411004\pi\)
\(180\) 0.00289935 0.00424335i 0.000216105 0.000316281i
\(181\) 0.939369i 0.0698227i 0.999390 + 0.0349114i \(0.0111149\pi\)
−0.999390 + 0.0349114i \(0.988885\pi\)
\(182\) −9.66608 2.78723i −0.716497 0.206604i
\(183\) 6.12824 + 11.6094i 0.453012 + 0.858190i
\(184\) 14.8335 1.09354
\(185\) −0.00352666 0.00610835i −0.000259285 0.000449095i
\(186\) 12.2690 6.47640i 0.899603 0.474873i
\(187\) −9.02840 + 5.21255i −0.660222 + 0.381179i
\(188\) 1.59101 + 2.75572i 0.116037 + 0.200981i
\(189\) 1.86131 13.6211i 0.135391 0.990792i
\(190\) 0.0109229 0.000792428
\(191\) 4.65873 + 2.68972i 0.337094 + 0.194621i 0.658986 0.752155i \(-0.270986\pi\)
−0.321892 + 0.946776i \(0.604319\pi\)
\(192\) −11.2863 7.09963i −0.814521 0.512371i
\(193\) −10.5713 18.3100i −0.760938 1.31798i −0.942368 0.334579i \(-0.891406\pi\)
0.181430 0.983404i \(-0.441927\pi\)
\(194\) 1.26042 + 2.18311i 0.0904928 + 0.156738i
\(195\) −0.0115231 0.00352100i −0.000825188 0.000252144i
\(196\) 6.20919 + 0.274530i 0.443513 + 0.0196093i
\(197\) −22.4348 12.9527i −1.59841 0.922843i −0.991794 0.127848i \(-0.959193\pi\)
−0.606616 0.794995i \(-0.707474\pi\)
\(198\) 4.45648 6.52228i 0.316708 0.463519i
\(199\) 2.76818i 0.196231i 0.995175 + 0.0981157i \(0.0312815\pi\)
−0.995175 + 0.0981157i \(0.968718\pi\)
\(200\) 13.1873 + 7.61367i 0.932480 + 0.538368i
\(201\) 0.935620 24.6714i 0.0659935 1.74018i
\(202\) −16.4937 + 9.52267i −1.16050 + 0.670012i
\(203\) 19.7686 + 12.0033i 1.38748 + 0.842470i
\(204\) 5.43509 + 3.41892i 0.380532 + 0.239372i
\(205\) −0.00706304 −0.000493304
\(206\) −5.14569 8.91259i −0.358517 0.620969i
\(207\) 13.1714 6.32661i 0.915474 0.439730i
\(208\) −1.32414 + 5.00486i −0.0918125 + 0.347025i
\(209\) −13.4042 −0.927189
\(210\) −0.00930725 0.000559083i −0.000642261 3.85804e-5i
\(211\) −3.90647 + 6.76621i −0.268933 + 0.465805i −0.968586 0.248677i \(-0.920004\pi\)
0.699654 + 0.714482i \(0.253338\pi\)
\(212\) −10.9863 6.34295i −0.754543 0.435636i
\(213\) 2.47923 + 0.0940204i 0.169874 + 0.00644217i
\(214\) −5.76080 −0.393800
\(215\) 0.00256490 0.00444254i 0.000174925 0.000302979i
\(216\) −15.7225 1.79564i −1.06978 0.122178i
\(217\) 17.1770 + 10.4297i 1.16605 + 0.708016i
\(218\) −6.73151 3.88644i −0.455916 0.263223i
\(219\) 1.50379 + 2.84880i 0.101617 + 0.192504i
\(220\) 0.00370435 + 0.00213870i 0.000249747 + 0.000144191i
\(221\) 3.85037 14.5533i 0.259004 0.978961i
\(222\) −3.55544 + 5.65211i −0.238625 + 0.379345i
\(223\) 6.48830 + 3.74602i 0.434489 + 0.250852i 0.701257 0.712909i \(-0.252623\pi\)
−0.266768 + 0.963761i \(0.585956\pi\)
\(224\) 0.267492 12.1059i 0.0178726 0.808863i
\(225\) 14.9569 + 1.13606i 0.997127 + 0.0757376i
\(226\) 0.237870 + 0.412003i 0.0158229 + 0.0274061i
\(227\) −8.54135 −0.566909 −0.283455 0.958986i \(-0.591481\pi\)
−0.283455 + 0.958986i \(0.591481\pi\)
\(228\) 3.85403 + 7.30111i 0.255239 + 0.483528i
\(229\) 8.92049 5.15025i 0.589482 0.340338i −0.175410 0.984495i \(-0.556125\pi\)
0.764893 + 0.644158i \(0.222792\pi\)
\(230\) −0.00495511 0.00858250i −0.000326730 0.000565913i
\(231\) 11.4216 + 0.686090i 0.751486 + 0.0451414i
\(232\) 13.3108 23.0549i 0.873894 1.51363i
\(233\) 1.09700 0.633351i 0.0718666 0.0414922i −0.463636 0.886026i \(-0.653456\pi\)
0.535503 + 0.844534i \(0.320122\pi\)
\(234\) 2.14470 + 11.2034i 0.140203 + 0.732391i
\(235\) 0.00345727 0.00598818i 0.000225528 0.000390626i
\(236\) −4.64484 −0.302353
\(237\) −0.478477 + 12.6170i −0.0310804 + 0.819561i
\(238\) 0.257341 11.6466i 0.0166810 0.754934i
\(239\) 18.8399i 1.21865i 0.792921 + 0.609325i \(0.208559\pi\)
−0.792921 + 0.609325i \(0.791441\pi\)
\(240\) −0.000181839 0.00479492i −1.17377e−5 0.000309511i
\(241\) 1.22332i 0.0788012i −0.999223 0.0394006i \(-0.987455\pi\)
0.999223 0.0394006i \(-0.0125448\pi\)
\(242\) −4.35228 2.51279i −0.279775 0.161528i
\(243\) −14.7266 + 5.11136i −0.944715 + 0.327894i
\(244\) 5.82794 + 3.36476i 0.373096 + 0.215407i
\(245\) −0.00622966 0.0119832i −0.000397998 0.000765578i
\(246\) 3.12145 + 5.91329i 0.199016 + 0.377018i
\(247\) 13.6435 13.7298i 0.868113 0.873608i
\(248\) 11.5657 20.0324i 0.734425 1.27206i
\(249\) 15.2605 + 9.59959i 0.967097 + 0.608349i
\(250\) 0.0203467i 0.00128684i
\(251\) 4.42278 + 7.66048i 0.279163 + 0.483525i 0.971177 0.238359i \(-0.0766096\pi\)
−0.692014 + 0.721884i \(0.743276\pi\)
\(252\) −2.91027 6.41846i −0.183330 0.404325i
\(253\) 6.08077 + 10.5322i 0.382294 + 0.662153i
\(254\) −8.61998 4.97674i −0.540865 0.312269i
\(255\) 0.000528758 0.0139428i 3.31121e−5 0.000873133i
\(256\) −16.4881 −1.03051
\(257\) 10.9439 0.682659 0.341329 0.939944i \(-0.389123\pi\)
0.341329 + 0.939944i \(0.389123\pi\)
\(258\) −4.85291 0.184038i −0.302129 0.0114577i
\(259\) −9.66976 0.213662i −0.600849 0.0132763i
\(260\) −0.00596112 + 0.00161745i −0.000369693 + 0.000100310i
\(261\) 1.98615 26.1487i 0.122940 1.61857i
\(262\) 5.68243 3.28075i 0.351062 0.202686i
\(263\) 11.0111 6.35726i 0.678973 0.392005i −0.120495 0.992714i \(-0.538448\pi\)
0.799468 + 0.600709i \(0.205115\pi\)
\(264\) 0.499124 13.1614i 0.0307189 0.810028i
\(265\) 0.0275665i 0.00169339i
\(266\) 7.77391 12.8030i 0.476649 0.785005i
\(267\) −7.92253 4.98364i −0.484851 0.304994i
\(268\) −6.32813 10.9606i −0.386552 0.669528i
\(269\) −23.1586 −1.41201 −0.706003 0.708208i \(-0.749504\pi\)
−0.706003 + 0.708208i \(0.749504\pi\)
\(270\) 0.00421315 + 0.00969671i 0.000256404 + 0.000590123i
\(271\) 26.3454i 1.60037i 0.599753 + 0.800185i \(0.295265\pi\)
−0.599753 + 0.800185i \(0.704735\pi\)
\(272\) −5.99505 −0.363503
\(273\) −12.3282 + 11.0007i −0.746137 + 0.665793i
\(274\) 6.49218 0.392207
\(275\) 12.4844i 0.752840i
\(276\) 3.98839 6.34037i 0.240073 0.381645i
\(277\) −4.40451 −0.264641 −0.132321 0.991207i \(-0.542243\pi\)
−0.132321 + 0.991207i \(0.542243\pi\)
\(278\) −6.49441 11.2486i −0.389509 0.674649i
\(279\) 1.72577 22.7207i 0.103319 1.36025i
\(280\) −0.0136318 + 0.00747379i −0.000814658 + 0.000446644i
\(281\) 13.2912i 0.792885i 0.918060 + 0.396442i \(0.129755\pi\)
−0.918060 + 0.396442i \(0.870245\pi\)
\(282\) −6.54131 0.248068i −0.389529 0.0147722i
\(283\) 14.1843 8.18929i 0.843167 0.486803i −0.0151725 0.999885i \(-0.504830\pi\)
0.858339 + 0.513082i \(0.171496\pi\)
\(284\) 1.10144 0.635914i 0.0653582 0.0377346i
\(285\) 0.00955236 0.0151855i 0.000565833 0.000899509i
\(286\) −9.16259 + 2.48612i −0.541796 + 0.147007i
\(287\) −5.02684 + 8.27882i −0.296725 + 0.488683i
\(288\) −12.3765 + 5.94481i −0.729292 + 0.350301i
\(289\) 0.432600 0.0254470
\(290\) −0.0177858 −0.00104442
\(291\) 4.13733 + 0.156901i 0.242534 + 0.00919771i
\(292\) 1.43010 + 0.825670i 0.0836905 + 0.0483187i
\(293\) −9.96323 17.2568i −0.582058 1.00815i −0.995235 0.0975037i \(-0.968914\pi\)
0.413177 0.910651i \(-0.364419\pi\)
\(294\) −7.27938 + 10.5114i −0.424542 + 0.613039i
\(295\) 0.00504662 + 0.00874100i 0.000293825 + 0.000508920i
\(296\) 11.1334i 0.647114i
\(297\) −5.17026 11.8995i −0.300009 0.690481i
\(298\) −3.77624 + 6.54065i −0.218752 + 0.378889i
\(299\) −16.9773 4.49170i −0.981824 0.259762i
\(300\) 6.80011 3.58957i 0.392605 0.207244i
\(301\) −3.38179 6.16821i −0.194923 0.355530i
\(302\) −14.8843 8.59344i −0.856494 0.494497i
\(303\) −1.18541 + 31.2582i −0.0681003 + 1.79574i
\(304\) −6.67551 3.85411i −0.382867 0.221048i
\(305\) 0.0146233i 0.000837326i
\(306\) −11.9068 + 5.71922i −0.680669 + 0.326946i
\(307\) 4.93316i 0.281551i −0.990042 0.140775i \(-0.955040\pi\)
0.990042 0.140775i \(-0.0449595\pi\)
\(308\) 5.14327 2.81985i 0.293065 0.160676i
\(309\) −16.8907 0.640552i −0.960880 0.0364398i
\(310\) −0.0154541 −0.000877732
\(311\) 6.69213 11.5911i 0.379476 0.657272i −0.611510 0.791237i \(-0.709438\pi\)
0.990986 + 0.133965i \(0.0427710\pi\)
\(312\) 12.9731 + 13.9076i 0.734456 + 0.787360i
\(313\) 23.9599 13.8332i 1.35429 0.781901i 0.365445 0.930833i \(-0.380917\pi\)
0.988847 + 0.148932i \(0.0475835\pi\)
\(314\) −2.48238 + 4.29960i −0.140089 + 0.242641i
\(315\) −0.00891673 + 0.0124504i −0.000502401 + 0.000701502i
\(316\) 3.23622 + 5.60529i 0.182051 + 0.315322i
\(317\) 12.8384 7.41223i 0.721075 0.416313i −0.0940735 0.995565i \(-0.529989\pi\)
0.815148 + 0.579253i \(0.196656\pi\)
\(318\) 23.0791 12.1828i 1.29421 0.683175i
\(319\) 21.8262 1.22203
\(320\) 0.00742641 + 0.0128629i 0.000415149 + 0.000719059i
\(321\) −5.03798 + 8.00892i −0.281193 + 0.447014i
\(322\) −13.5864 0.300205i −0.757142 0.0167298i
\(323\) 19.4113 + 11.2071i 1.08007 + 0.623580i
\(324\) −4.99495 + 6.23757i −0.277497 + 0.346531i
\(325\) −12.7877 12.7073i −0.709334 0.704872i
\(326\) 3.84155 + 2.21792i 0.212764 + 0.122839i
\(327\) −11.2900 + 5.95965i −0.624339 + 0.329569i
\(328\) 9.65508 + 5.57436i 0.533113 + 0.307793i
\(329\) −4.55836 8.31423i −0.251311 0.458378i
\(330\) −0.00778178 + 0.00410776i −0.000428373 + 0.000226125i
\(331\) −2.90440 + 5.03057i −0.159640 + 0.276505i −0.934739 0.355335i \(-0.884367\pi\)
0.775099 + 0.631840i \(0.217700\pi\)
\(332\) 9.24200 0.507221
\(333\) 4.74848 + 9.88586i 0.260215 + 0.541742i
\(334\) 13.2424 + 7.64552i 0.724594 + 0.418344i
\(335\) −0.0137510 + 0.0238175i −0.000751299 + 0.00130129i
\(336\) 5.49086 + 3.62573i 0.299551 + 0.197800i
\(337\) −9.55520 −0.520505 −0.260252 0.965541i \(-0.583806\pi\)
−0.260252 + 0.965541i \(0.583806\pi\)
\(338\) 6.77962 11.9157i 0.368763 0.648126i
\(339\) 0.780810 + 0.0296109i 0.0424078 + 0.00160824i
\(340\) −0.00357629 0.00619432i −0.000193952 0.000335934i
\(341\) 18.9648 1.02700
\(342\) −16.9351 1.28632i −0.915745 0.0695562i
\(343\) −18.4796 1.22657i −0.997804 0.0662285i
\(344\) −7.01238 + 4.04860i −0.378082 + 0.218286i
\(345\) −0.0162652 0.000616829i −0.000875687 3.32089e-5i
\(346\) 14.3355 + 8.27660i 0.770681 + 0.444953i
\(347\) 29.1178i 1.56313i 0.623826 + 0.781563i \(0.285577\pi\)
−0.623826 + 0.781563i \(0.714423\pi\)
\(348\) −6.27554 11.8884i −0.336404 0.637287i
\(349\) −27.1567 15.6790i −1.45367 0.839275i −0.454980 0.890501i \(-0.650354\pi\)
−0.998687 + 0.0512262i \(0.983687\pi\)
\(350\) −11.9245 7.24047i −0.637392 0.387019i
\(351\) 17.4511 + 6.81607i 0.931471 + 0.363815i
\(352\) −5.71380 9.89659i −0.304547 0.527490i
\(353\) 0.797729 + 1.38171i 0.0424588 + 0.0735408i 0.886474 0.462779i \(-0.153148\pi\)
−0.844015 + 0.536320i \(0.819814\pi\)
\(354\) 5.08780 8.08812i 0.270414 0.429879i
\(355\) −0.00239342 0.00138184i −0.000127030 7.33406e-5i
\(356\) −4.79800 −0.254293
\(357\) −15.9665 10.5430i −0.845037 0.557995i
\(358\) −3.40868 5.90400i −0.180154 0.312036i
\(359\) 11.1728 6.45064i 0.589680 0.340452i −0.175291 0.984517i \(-0.556087\pi\)
0.764971 + 0.644065i \(0.222753\pi\)
\(360\) 0.0145547 + 0.00994477i 0.000767099 + 0.000524135i
\(361\) 4.90969 + 8.50384i 0.258405 + 0.447570i
\(362\) −0.990625 −0.0520661
\(363\) −7.29958 + 3.85323i −0.383129 + 0.202242i
\(364\) −2.34672 + 8.13838i −0.123002 + 0.426567i
\(365\) 0.00358837i 0.000187824i
\(366\) −12.2428 + 6.46262i −0.639944 + 0.337807i
\(367\) 11.3448 6.54993i 0.592194 0.341903i −0.173770 0.984786i \(-0.555595\pi\)
0.765965 + 0.642883i \(0.222262\pi\)
\(368\) 6.99360i 0.364567i
\(369\) 10.9507 + 0.831772i 0.570072 + 0.0433003i
\(370\) 0.00644165 0.00371909i 0.000334885 0.000193346i
\(371\) 32.3116 + 19.6193i 1.67753 + 1.01859i
\(372\) −5.45282 10.3299i −0.282716 0.535579i
\(373\) −3.06870 + 5.31515i −0.158891 + 0.275208i −0.934469 0.356044i \(-0.884125\pi\)
0.775578 + 0.631252i \(0.217459\pi\)
\(374\) −5.49697 9.52103i −0.284242 0.492321i
\(375\) −0.0282869 0.0177938i −0.00146073 0.000918867i
\(376\) −9.45210 + 5.45717i −0.487455 + 0.281432i
\(377\) −22.2157 + 22.3564i −1.14417 + 1.15141i
\(378\) 14.3644 + 1.96288i 0.738824 + 0.100959i
\(379\) 6.45103 11.1735i 0.331367 0.573945i −0.651413 0.758723i \(-0.725823\pi\)
0.982780 + 0.184779i \(0.0591568\pi\)
\(380\) 0.00919653i 0.000471772i
\(381\) −14.4573 + 7.63157i −0.740671 + 0.390977i
\(382\) −2.83648 + 4.91293i −0.145127 + 0.251368i
\(383\) −4.61988 + 8.00187i −0.236065 + 0.408876i −0.959582 0.281430i \(-0.909191\pi\)
0.723517 + 0.690307i \(0.242524\pi\)
\(384\) −0.954748 + 1.51777i −0.0487218 + 0.0774534i
\(385\) −0.0108948 0.00661521i −0.000555248 0.000337143i
\(386\) 19.3091 11.1481i 0.982806 0.567423i
\(387\) −4.49987 + 6.58579i −0.228741 + 0.334774i
\(388\) 1.83807 1.06121i 0.0933140 0.0538749i
\(389\) 11.3864 + 6.57391i 0.577311 + 0.333311i 0.760064 0.649848i \(-0.225168\pi\)
−0.182753 + 0.983159i \(0.558501\pi\)
\(390\) 0.00371312 0.0121519i 0.000188021 0.000615334i
\(391\) 20.3362i 1.02845i
\(392\) −0.941635 + 21.2975i −0.0475598 + 1.07569i
\(393\) 0.408399 10.7691i 0.0206010 0.543228i
\(394\) 13.6595 23.6589i 0.688154 1.19192i
\(395\) 0.00703230 0.0121803i 0.000353834 0.000612858i
\(396\) −5.49145 3.75214i −0.275956 0.188552i
\(397\) 16.0733 + 9.27995i 0.806698 + 0.465747i 0.845808 0.533487i \(-0.179119\pi\)
−0.0391097 + 0.999235i \(0.512452\pi\)
\(398\) −2.91923 −0.146328
\(399\) −11.0009 22.0043i −0.550732 1.10159i
\(400\) −3.58964 + 6.21745i −0.179482 + 0.310872i
\(401\) 12.3532i 0.616888i 0.951243 + 0.308444i \(0.0998082\pi\)
−0.951243 + 0.308444i \(0.900192\pi\)
\(402\) 26.0176 + 0.986671i 1.29764 + 0.0492107i
\(403\) −19.3033 + 19.4255i −0.961565 + 0.967651i
\(404\) 8.01763 + 13.8869i 0.398892 + 0.690901i
\(405\) 0.0171653 + 0.00262275i 0.000852952 + 0.000130325i
\(406\) −12.6583 + 20.8473i −0.628221 + 1.03463i
\(407\) −7.90501 + 4.56396i −0.391837 + 0.226227i
\(408\) −11.7269 + 18.6423i −0.580568 + 0.922933i
\(409\) 5.77235i 0.285424i 0.989764 + 0.142712i \(0.0455823\pi\)
−0.989764 + 0.142712i \(0.954418\pi\)
\(410\) 0.00744843i 0.000367852i
\(411\) 5.67760 9.02572i 0.280055 0.445206i
\(412\) −7.50398 + 4.33242i −0.369694 + 0.213443i
\(413\) 13.8373 + 0.305749i 0.680891 + 0.0150449i
\(414\) 6.67182 + 13.8901i 0.327902 + 0.682660i
\(415\) −0.0100414 0.0173923i −0.000492915 0.000853753i
\(416\) 15.9528 + 4.22063i 0.782149 + 0.206934i
\(417\) −21.3179 0.808446i −1.04394 0.0395898i
\(418\) 14.1356i 0.691396i
\(419\) −17.6169 + 30.5134i −0.860644 + 1.49068i 0.0106648 + 0.999943i \(0.496605\pi\)
−0.871309 + 0.490736i \(0.836728\pi\)
\(420\) −0.000470721 0.00783626i −2.29688e−5 0.000382371i
\(421\) 27.0300 1.31736 0.658682 0.752421i \(-0.271114\pi\)
0.658682 + 0.752421i \(0.271114\pi\)
\(422\) −7.13541 4.11963i −0.347346 0.200540i
\(423\) −6.06544 + 8.87709i −0.294912 + 0.431619i
\(424\) 21.7563 37.6830i 1.05658 1.83005i
\(425\) 10.4381 18.0793i 0.506321 0.876974i
\(426\) −0.0991506 + 2.61450i −0.00480386 + 0.126673i
\(427\) −17.1404 10.4075i −0.829483 0.503656i
\(428\) 4.85032i 0.234449i
\(429\) −4.55664 + 14.9124i −0.219997 + 0.719979i
\(430\) 0.00468495 + 0.00270486i 0.000225928 + 0.000130440i
\(431\) 27.1302 15.6636i 1.30681 0.754490i 0.325252 0.945627i \(-0.394551\pi\)
0.981563 + 0.191138i \(0.0612177\pi\)
\(432\) 0.846597 7.41275i 0.0407319 0.356646i
\(433\) 3.41909 1.97401i 0.164311 0.0948649i −0.415590 0.909552i \(-0.636425\pi\)
0.579900 + 0.814687i \(0.303091\pi\)
\(434\) −10.9988 + 18.1142i −0.527960 + 0.869511i
\(435\) −0.0155542 + 0.0247266i −0.000745765 + 0.00118555i
\(436\) −3.27220 + 5.66761i −0.156710 + 0.271429i
\(437\) 13.0738 22.6445i 0.625404 1.08323i
\(438\) −3.00424 + 1.58585i −0.143548 + 0.0757746i
\(439\) 30.8667i 1.47319i −0.676337 0.736593i \(-0.736434\pi\)
0.676337 0.736593i \(-0.263566\pi\)
\(440\) −0.00733575 + 0.0127059i −0.000349718 + 0.000605729i
\(441\) 8.24744 + 19.3127i 0.392735 + 0.919652i
\(442\) 15.3474 + 4.06047i 0.730001 + 0.193137i
\(443\) −16.2769 + 9.39748i −0.773340 + 0.446488i −0.834065 0.551667i \(-0.813992\pi\)
0.0607250 + 0.998155i \(0.480659\pi\)
\(444\) 4.75881 + 2.99351i 0.225843 + 0.142066i
\(445\) 0.00521303 + 0.00902923i 0.000247121 + 0.000428026i
\(446\) −3.95042 + 6.84233i −0.187058 + 0.323994i
\(447\) 5.79067 + 10.9699i 0.273889 + 0.518858i
\(448\) 20.3625 + 0.449928i 0.962038 + 0.0212571i
\(449\) 4.95835 2.86270i 0.233999 0.135099i −0.378417 0.925635i \(-0.623531\pi\)
0.612415 + 0.790536i \(0.290198\pi\)
\(450\) −1.19805 + 15.7730i −0.0564768 + 0.743547i
\(451\) 9.14050i 0.430409i
\(452\) 0.346887 0.200275i 0.0163162 0.00942016i
\(453\) −24.9637 + 13.1776i −1.17290 + 0.619137i
\(454\) 9.00741i 0.422739i
\(455\) 0.0178651 0.00442612i 0.000837529 0.000207500i
\(456\) −25.0428 + 13.2193i −1.17273 + 0.619051i
\(457\) 33.8986 1.58571 0.792854 0.609412i \(-0.208594\pi\)
0.792854 + 0.609412i \(0.208594\pi\)
\(458\) 5.43127 + 9.40723i 0.253786 + 0.439571i
\(459\) −2.46176 + 21.5550i −0.114905 + 1.00610i
\(460\) −0.00722605 + 0.00417196i −0.000336917 + 0.000194519i
\(461\) 9.37925 + 16.2453i 0.436835 + 0.756621i 0.997443 0.0714602i \(-0.0227659\pi\)
−0.560608 + 0.828081i \(0.689433\pi\)
\(462\) −0.723527 + 12.0448i −0.0336615 + 0.560375i
\(463\) −20.1902 −0.938317 −0.469158 0.883114i \(-0.655443\pi\)
−0.469158 + 0.883114i \(0.655443\pi\)
\(464\) 10.8698 + 6.27567i 0.504617 + 0.291341i
\(465\) −0.0135150 + 0.0214849i −0.000626745 + 0.000996340i
\(466\) 0.667909 + 1.15685i 0.0309403 + 0.0535902i
\(467\) −3.57259 6.18791i −0.165320 0.286342i 0.771449 0.636291i \(-0.219532\pi\)
−0.936769 + 0.349949i \(0.886199\pi\)
\(468\) 9.43275 1.80573i 0.436029 0.0834701i
\(469\) 18.1305 + 33.0692i 0.837190 + 1.52699i
\(470\) 0.00631492 + 0.00364592i 0.000291285 + 0.000168174i
\(471\) 3.80659 + 7.21124i 0.175398 + 0.332276i
\(472\) 15.9318i 0.733319i
\(473\) −5.74924 3.31932i −0.264350 0.152623i
\(474\) −13.3054 0.504585i −0.611138 0.0231764i
\(475\) 23.2457 13.4209i 1.06659 0.615794i
\(476\) −9.80584 0.216669i −0.449450 0.00993102i
\(477\) 3.24634 42.7398i 0.148640 1.95692i
\(478\) −19.8679 −0.908735
\(479\) −4.61963 8.00143i −0.211076 0.365595i 0.740975 0.671532i \(-0.234363\pi\)
−0.952052 + 0.305938i \(0.901030\pi\)
\(480\) 0.0152836 0.000579604i 0.000697597 2.64552e-5i
\(481\) 3.37128 12.7424i 0.153717 0.581005i
\(482\) 1.29007 0.0587612
\(483\) −12.2991 + 18.6259i −0.559628 + 0.847509i
\(484\) −2.11565 + 3.66441i −0.0961658 + 0.166564i
\(485\) −0.00399414 0.00230602i −0.000181364 0.000104711i
\(486\) −5.39026 15.5302i −0.244507 0.704464i
\(487\) 1.30155 0.0589787 0.0294894 0.999565i \(-0.490612\pi\)
0.0294894 + 0.999565i \(0.490612\pi\)
\(488\) −11.5411 + 19.9898i −0.522442 + 0.904896i
\(489\) 6.44299 3.40106i 0.291362 0.153801i
\(490\) 0.0126370 0.00656958i 0.000570884 0.000296783i
\(491\) 11.4486 + 6.60986i 0.516668 + 0.298299i 0.735570 0.677448i \(-0.236914\pi\)
−0.218902 + 0.975747i \(0.570248\pi\)
\(492\) 4.97871 2.62811i 0.224458 0.118484i
\(493\) −31.6075 18.2486i −1.42353 0.821876i
\(494\) 14.4790 + 14.3879i 0.651440 + 0.647343i
\(495\) −0.00109459 + 0.0144109i −4.91984e−5 + 0.000647723i
\(496\) 9.44476 + 5.45294i 0.424082 + 0.244844i
\(497\) −3.32312 + 1.82194i −0.149062 + 0.0817250i
\(498\) −10.1234 + 16.0932i −0.453640 + 0.721154i
\(499\) 3.18217 + 5.51168i 0.142454 + 0.246737i 0.928420 0.371532i \(-0.121168\pi\)
−0.785966 + 0.618269i \(0.787834\pi\)
\(500\) −0.0171309 −0.000766119
\(501\) 22.2100 11.7240i 0.992272 0.523790i
\(502\) −8.07847 + 4.66411i −0.360560 + 0.208169i
\(503\) −17.7261 30.7026i −0.790370 1.36896i −0.925738 0.378165i \(-0.876555\pi\)
0.135369 0.990795i \(-0.456778\pi\)
\(504\) 22.0153 9.98222i 0.980639 0.444644i
\(505\) 0.0174223 0.0301764i 0.000775283 0.00134283i
\(506\) −11.1069 + 6.41256i −0.493761 + 0.285073i
\(507\) −10.6367 19.8459i −0.472393 0.881388i
\(508\) −4.19018 + 7.25761i −0.185909 + 0.322004i
\(509\) −15.6499 −0.693670 −0.346835 0.937926i \(-0.612744\pi\)
−0.346835 + 0.937926i \(0.612744\pi\)
\(510\) 0.0147036 0.000557609i 0.000651086 2.46913e-5i
\(511\) −4.20604 2.55388i −0.186064 0.112977i
\(512\) 15.3173i 0.676934i
\(513\) −16.5985 + 22.4190i −0.732843 + 0.989824i
\(514\) 11.5410i 0.509052i
\(515\) 0.0163062 + 0.00941436i 0.000718535 + 0.000414846i
\(516\) −0.154952 + 4.08592i −0.00682136 + 0.179873i
\(517\) −7.74949 4.47417i −0.340822 0.196774i
\(518\) 0.225321 10.1974i 0.00990002 0.448047i
\(519\) 24.0433 12.6917i 1.05538 0.557105i
\(520\) −0.00554785 0.0204466i −0.000243289 0.000896643i
\(521\) 19.1120 33.1029i 0.837310 1.45026i −0.0548261 0.998496i \(-0.517460\pi\)
0.892136 0.451767i \(-0.149206\pi\)
\(522\) 27.5755 + 2.09452i 1.20695 + 0.0916747i
\(523\) 30.7021i 1.34251i 0.741228 + 0.671254i \(0.234244\pi\)
−0.741228 + 0.671254i \(0.765756\pi\)
\(524\) −2.76224 4.78434i −0.120669 0.209005i
\(525\) −20.4944 + 10.2460i −0.894447 + 0.447172i
\(526\) 6.70414 + 11.6119i 0.292314 + 0.506303i
\(527\) −27.4638 15.8562i −1.19634 0.690708i
\(528\) 6.20525 + 0.235324i 0.270049 + 0.0102411i
\(529\) −0.723461 −0.0314548
\(530\) −0.0290706 −0.00126275
\(531\) −6.79504 14.1466i −0.294879 0.613909i
\(532\) −10.7796 6.54526i −0.467353 0.283773i
\(533\) −9.36253 9.30364i −0.405536 0.402985i
\(534\) 5.25557 8.35482i 0.227431 0.361548i
\(535\) 0.00912769 0.00526987i 0.000394624 0.000227836i
\(536\) 37.5950 21.7055i 1.62385 0.937533i
\(537\) −11.1890 0.424324i −0.482841 0.0183109i
\(538\) 24.4223i 1.05292i
\(539\) −15.5078 + 8.06199i −0.667969 + 0.347255i
\(540\) 0.00816417 0.00354727i 0.000351330 0.000152650i
\(541\) 4.56917 + 7.91403i 0.196444 + 0.340251i 0.947373 0.320132i \(-0.103727\pi\)
−0.750929 + 0.660383i \(0.770394\pi\)
\(542\) −27.7829 −1.19338
\(543\) −0.866330 + 1.37721i −0.0371778 + 0.0591018i
\(544\) 19.1090i 0.819289i
\(545\) 0.0142210 0.000609160
\(546\) −11.6009 13.0009i −0.496475 0.556387i
\(547\) −35.4176 −1.51435 −0.757173 0.653214i \(-0.773420\pi\)
−0.757173 + 0.653214i \(0.773420\pi\)
\(548\) 5.46611i 0.233500i
\(549\) −1.72209 + 22.6723i −0.0734972 + 0.967631i
\(550\) −13.1656 −0.561385
\(551\) −23.4634 40.6398i −0.999574 1.73131i
\(552\) 21.7474 + 13.6801i 0.925632 + 0.582266i
\(553\) −9.27198 16.9116i −0.394285 0.719156i
\(554\) 4.64484i 0.197340i
\(555\) 0.000462965 0.0122079i 1.96518e−5 0.000518198i
\(556\) −9.47083 + 5.46798i −0.401653 + 0.231894i
\(557\) 3.92620 2.26679i 0.166358 0.0960470i −0.414509 0.910045i \(-0.636047\pi\)
0.580868 + 0.813998i \(0.302713\pi\)
\(558\) 23.9604 + 1.81993i 1.01432 + 0.0770439i
\(559\) 9.25180 2.51032i 0.391310 0.106175i
\(560\) −0.00352369 0.00642705i −0.000148903 0.000271592i
\(561\) −18.0438 0.684282i −0.761811 0.0288904i
\(562\) −14.0164 −0.591246
\(563\) −12.1324 −0.511321 −0.255661 0.966767i \(-0.582293\pi\)
−0.255661 + 0.966767i \(0.582293\pi\)
\(564\) −0.208862 + 5.50747i −0.00879466 + 0.231906i
\(565\) −0.000753786 0 0.000435199i −3.17120e−5 0 1.83090e-5i
\(566\) 8.63613 + 14.9582i 0.363004 + 0.628741i
\(567\) 15.2909 18.2534i 0.642159 0.766571i
\(568\) 2.18118 + 3.77792i 0.0915204 + 0.158518i
\(569\) 36.3551i 1.52408i −0.647528 0.762042i \(-0.724197\pi\)
0.647528 0.762042i \(-0.275803\pi\)
\(570\) 0.0160140 + 0.0100736i 0.000670754 + 0.000421936i
\(571\) 7.04698 12.2057i 0.294907 0.510794i −0.680056 0.733160i \(-0.738045\pi\)
0.974963 + 0.222366i \(0.0713780\pi\)
\(572\) 2.09319 + 7.71447i 0.0875208 + 0.322558i
\(573\) 4.34960 + 8.23991i 0.181707 + 0.344227i
\(574\) −8.73055 5.30112i −0.364406 0.221265i
\(575\) −21.0906 12.1767i −0.879540 0.507802i
\(576\) −9.99932 20.8176i −0.416638 0.867399i
\(577\) 11.4758 + 6.62558i 0.477745 + 0.275826i 0.719476 0.694517i \(-0.244382\pi\)
−0.241731 + 0.970343i \(0.577715\pi\)
\(578\) 0.456204i 0.0189756i
\(579\) 1.38775 36.5937i 0.0576731 1.52078i
\(580\) 0.0149748i 0.000621793i
\(581\) −27.5327 0.608360i −1.14225 0.0252390i
\(582\) −0.165462 + 4.36308i −0.00685864 + 0.180856i
\(583\) 35.6746 1.47749
\(584\) −2.83205 + 4.90525i −0.117191 + 0.202981i
\(585\) −0.0136469 0.0157893i −0.000564228 0.000652808i
\(586\) 18.1984 10.5069i 0.751771 0.434035i
\(587\) 15.6011 27.0220i 0.643928 1.11532i −0.340620 0.940201i \(-0.610637\pi\)
0.984548 0.175115i \(-0.0560296\pi\)
\(588\) 8.85013 + 6.12890i 0.364973 + 0.252751i
\(589\) −20.3874 35.3120i −0.840047 1.45500i
\(590\) −0.00921795 + 0.00532198i −0.000379497 + 0.000219103i
\(591\) −20.9461 39.6804i −0.861606 1.63223i
\(592\) −5.24909 −0.215736
\(593\) 5.48292 + 9.49670i 0.225157 + 0.389983i 0.956366 0.292170i \(-0.0943773\pi\)
−0.731210 + 0.682153i \(0.761044\pi\)
\(594\) 12.5488 5.45237i 0.514884 0.223713i
\(595\) 0.0102463 + 0.0186888i 0.000420058 + 0.000766165i
\(596\) 5.50691 + 3.17942i 0.225572 + 0.130234i
\(597\) −2.55295 + 4.05845i −0.104485 + 0.166101i
\(598\) 4.73679 17.9037i 0.193702 0.732136i
\(599\) −12.1466 7.01285i −0.496297 0.286537i 0.230886 0.972981i \(-0.425838\pi\)
−0.727183 + 0.686444i \(0.759171\pi\)
\(600\) 12.3122 + 23.3243i 0.502644 + 0.952213i
\(601\) −3.15684 1.82260i −0.128770 0.0743455i 0.434231 0.900801i \(-0.357020\pi\)
−0.563001 + 0.826456i \(0.690353\pi\)
\(602\) 6.50478 3.56631i 0.265115 0.145352i
\(603\) 24.1248 35.3079i 0.982439 1.43785i
\(604\) −7.23527 + 12.5319i −0.294399 + 0.509914i
\(605\) 0.00919461 0.000373814
\(606\) −32.9638 1.25010i −1.33906 0.0507817i
\(607\) 14.9262 + 8.61762i 0.605834 + 0.349778i 0.771333 0.636432i \(-0.219590\pi\)
−0.165499 + 0.986210i \(0.552924\pi\)
\(608\) −12.2848 + 21.2779i −0.498214 + 0.862933i
\(609\) 17.9128 + 35.8297i 0.725862 + 1.45189i
\(610\) 0.0154212 0.000624386
\(611\) 12.4707 3.38370i 0.504509 0.136890i
\(612\) 4.81531 + 10.0250i 0.194647 + 0.405236i
\(613\) 15.2562 + 26.4245i 0.616193 + 1.06728i 0.990174 + 0.139841i \(0.0446590\pi\)
−0.373982 + 0.927436i \(0.622008\pi\)
\(614\) 5.20234 0.209949
\(615\) −0.0103551 0.00651387i −0.000417560 0.000262665i
\(616\) 9.67207 + 17.6414i 0.389699 + 0.710791i
\(617\) −5.82452 + 3.36279i −0.234486 + 0.135381i −0.612640 0.790362i \(-0.709892\pi\)
0.378154 + 0.925743i \(0.376559\pi\)
\(618\) 0.675504 17.8124i 0.0271728 0.716519i
\(619\) 8.43263 + 4.86858i 0.338936 + 0.195685i 0.659801 0.751440i \(-0.270640\pi\)
−0.320865 + 0.947125i \(0.603974\pi\)
\(620\) 0.0130116i 0.000522558i
\(621\) 25.1453 + 2.87180i 1.00905 + 0.115241i
\(622\) 12.2236 + 7.05729i 0.490121 + 0.282971i
\(623\) 14.2936 + 0.315831i 0.572662 + 0.0126535i
\(624\) −6.55704 + 6.11646i −0.262492 + 0.244854i
\(625\) −12.5000 21.6506i −0.499999 0.866023i
\(626\) 14.5880 + 25.2672i 0.583056 + 1.00988i
\(627\) −19.6520 12.3620i −0.784824 0.493691i
\(628\) 3.62006 + 2.09004i 0.144456 + 0.0834018i
\(629\) 15.2635 0.608595
\(630\) −0.0131298 0.00940326i −0.000523103 0.000374635i
\(631\) −1.16211 2.01284i −0.0462630 0.0801299i 0.841967 0.539530i \(-0.181398\pi\)
−0.888230 + 0.459400i \(0.848065\pi\)
\(632\) −19.2261 + 11.1002i −0.764774 + 0.441543i
\(633\) −11.9674 + 6.31723i −0.475662 + 0.251087i
\(634\) 7.81668 + 13.5389i 0.310440 + 0.537698i
\(635\) 0.0182105 0.000722663
\(636\) −10.2573 19.4315i −0.406728 0.770510i
\(637\) 7.52678 24.0904i 0.298222 0.954497i
\(638\) 23.0171i 0.911256i
\(639\) 3.54809 + 2.42430i 0.140360 + 0.0959040i
\(640\) 0.00172979 0.000998693i 6.83759e−5 3.94768e-5i
\(641\) 11.0379i 0.435970i 0.975952 + 0.217985i \(0.0699483\pi\)
−0.975952 + 0.217985i \(0.930052\pi\)
\(642\) −8.44592 5.31288i −0.333334 0.209683i
\(643\) −2.75926 + 1.59306i −0.108815 + 0.0628241i −0.553420 0.832903i \(-0.686677\pi\)
0.444605 + 0.895727i \(0.353344\pi\)
\(644\) −0.252758 + 11.4391i −0.00996007 + 0.450765i
\(645\) 0.00785754 0.00414775i 0.000309390 0.000163318i
\(646\) −11.8186 + 20.4704i −0.464997 + 0.805399i
\(647\) −19.9767 34.6006i −0.785365 1.36029i −0.928781 0.370629i \(-0.879142\pi\)
0.143416 0.989662i \(-0.454191\pi\)
\(648\) −21.3948 17.1326i −0.840468 0.673034i
\(649\) 11.3120 6.53099i 0.444035 0.256364i
\(650\) 13.4006 13.4854i 0.525616 0.528943i
\(651\) 15.5644 + 31.1325i 0.610018 + 1.22018i
\(652\) 1.86738 3.23440i 0.0731323 0.126669i
\(653\) 15.8931i 0.621946i 0.950419 + 0.310973i \(0.100655\pi\)
−0.950419 + 0.310973i \(0.899345\pi\)
\(654\) −6.28483 11.9060i −0.245756 0.465563i
\(655\) −0.00600235 + 0.0103964i −0.000234531 + 0.000406220i
\(656\) −2.62816 + 4.55211i −0.102613 + 0.177730i
\(657\) −0.422580 + 5.56350i −0.0164864 + 0.217053i
\(658\) 8.76789 4.80709i 0.341808 0.187400i
\(659\) 43.5079 25.1193i 1.69483 0.978510i 0.744315 0.667829i \(-0.232776\pi\)
0.950514 0.310681i \(-0.100557\pi\)
\(660\) 0.00345854 + 0.00655189i 0.000134623 + 0.000255032i
\(661\) 43.6126 25.1798i 1.69633 0.979379i 0.747151 0.664654i \(-0.231421\pi\)
0.949183 0.314725i \(-0.101912\pi\)
\(662\) −5.30506 3.06288i −0.206187 0.119042i
\(663\) 19.0668 17.7856i 0.740493 0.690737i
\(664\) 31.7000i 1.23020i
\(665\) −0.000605367 0.0273972i −2.34751e−5 0.00106242i
\(666\) −10.4253 + 5.00758i −0.403971 + 0.194040i
\(667\) −21.2881 + 36.8721i −0.824280 + 1.42769i
\(668\) 6.43717 11.1495i 0.249062 0.431387i
\(669\) 6.05776 + 11.4759i 0.234206 + 0.443683i
\(670\) −0.0251171 0.0145014i −0.000970358 0.000560236i
\(671\) −18.9244 −0.730570
\(672\) 11.5568 17.5019i 0.445815 0.675150i
\(673\) 18.1511 31.4387i 0.699674 1.21187i −0.268905 0.963167i \(-0.586662\pi\)
0.968579 0.248704i \(-0.0800048\pi\)
\(674\) 10.0766i 0.388135i
\(675\) 20.8806 + 15.4596i 0.803696 + 0.595039i
\(676\) −10.0324 5.70812i −0.385862 0.219543i
\(677\) 18.7369 + 32.4533i 0.720119 + 1.24728i 0.960952 + 0.276716i \(0.0892460\pi\)
−0.240833 + 0.970567i \(0.577421\pi\)
\(678\) −0.0312266 + 0.823415i −0.00119925 + 0.0316231i
\(679\) −5.54562 + 3.04044i −0.212822 + 0.116682i
\(680\) 0.0212465 0.0122667i 0.000814765 0.000470405i
\(681\) −12.5225 7.87724i −0.479864 0.301857i
\(682\) 19.9996i 0.765824i
\(683\) 37.8062i 1.44661i −0.690526 0.723307i \(-0.742621\pi\)
0.690526 0.723307i \(-0.257379\pi\)
\(684\) −1.08302 + 14.2585i −0.0414103 + 0.545189i
\(685\) −0.0102865 + 0.00593893i −0.000393028 + 0.000226915i
\(686\) 1.29350 19.4879i 0.0493859 0.744053i
\(687\) 17.8282 + 0.676103i 0.680187 + 0.0257949i
\(688\) −1.90881 3.30615i −0.0727726 0.126046i
\(689\) −36.3114 + 36.5412i −1.38335 + 1.39211i
\(690\) 0.000650486 0.0171527i 2.47636e−5 0.000652991i
\(691\) 12.9636i 0.493158i −0.969123 0.246579i \(-0.920694\pi\)
0.969123 0.246579i \(-0.0793065\pi\)
\(692\) 6.96851 12.0698i 0.264903 0.458825i
\(693\) 16.1125 + 11.5394i 0.612063 + 0.438346i
\(694\) −30.7066 −1.16561
\(695\) 0.0205801 + 0.0118819i 0.000780648 + 0.000450708i
\(696\) 40.7773 21.5251i 1.54566 0.815906i
\(697\) 7.64226 13.2368i 0.289471 0.501379i
\(698\) 16.5345 28.6385i 0.625839 1.08399i
\(699\) 2.19241 + 0.0831436i 0.0829247 + 0.00314478i
\(700\) −6.09613 + 10.0399i −0.230412 + 0.379471i
\(701\) 34.9085i 1.31848i 0.751934 + 0.659238i \(0.229121\pi\)
−0.751934 + 0.659238i \(0.770879\pi\)
\(702\) −7.18798 + 18.4033i −0.271293 + 0.694589i
\(703\) 16.9960 + 9.81262i 0.641014 + 0.370090i
\(704\) 16.6463 9.61075i 0.627381 0.362219i
\(705\) 0.0105913 0.00559082i 0.000398892 0.000210563i
\(706\) −1.45710 + 0.841257i −0.0548387 + 0.0316611i
\(707\) −22.9711 41.8981i −0.863915 1.57574i
\(708\) −6.80981 4.28369i −0.255928 0.160991i
\(709\) −18.2820 + 31.6653i −0.686595 + 1.18922i 0.286338 + 0.958129i \(0.407562\pi\)
−0.972933 + 0.231088i \(0.925771\pi\)
\(710\) 0.00145724 0.00252402i 5.46893e−5 9.47247e-5i
\(711\) −12.3375 + 18.0565i −0.462691 + 0.677172i
\(712\) 16.4571i 0.616756i
\(713\) −18.4973 + 32.0382i −0.692729 + 1.19984i
\(714\) 11.1183 16.8377i 0.416092 0.630136i
\(715\) 0.0122434 0.0123209i 0.000457877 0.000460776i
\(716\) −4.97089 + 2.86994i −0.185771 + 0.107255i
\(717\) −17.3750 + 27.6212i −0.648882 + 1.03153i
\(718\) 6.80262 + 11.7825i 0.253871 + 0.439718i
\(719\) −19.8403 + 34.3644i −0.739919 + 1.28158i 0.212612 + 0.977137i \(0.431803\pi\)
−0.952531 + 0.304441i \(0.901530\pi\)
\(720\) −0.00468869 + 0.00686214i −0.000174737 + 0.000255737i
\(721\) 22.6401 12.4127i 0.843163 0.462272i
\(722\) −8.96785 + 5.17759i −0.333749 + 0.192690i
\(723\) 1.12821 1.79352i 0.0419584 0.0667017i
\(724\) 0.834059i 0.0309976i
\(725\) −37.8511 + 21.8534i −1.40576 + 0.811613i
\(726\) −4.06348 7.69788i −0.150810 0.285695i
\(727\) 15.6289i 0.579644i 0.957081 + 0.289822i \(0.0935961\pi\)
−0.957081 + 0.289822i \(0.906404\pi\)
\(728\) −27.9146 8.04924i −1.03458 0.298325i
\(729\) −26.3047 6.08783i −0.974249 0.225475i
\(730\) 0.00378416 0.000140058
\(731\) 5.55049 + 9.61373i 0.205292 + 0.355577i
\(732\) 5.44122 + 10.3079i 0.201113 + 0.380991i
\(733\) −25.0179 + 14.4441i −0.924055 + 0.533504i −0.884927 0.465730i \(-0.845792\pi\)
−0.0391289 + 0.999234i \(0.512458\pi\)
\(734\) 6.90732 + 11.9638i 0.254954 + 0.441593i
\(735\) 0.00191814 0.0233139i 7.07518e−5 0.000859945i
\(736\) 22.2918 0.821686
\(737\) 30.8230 + 17.7957i 1.13538 + 0.655511i
\(738\) −0.877157 + 11.5482i −0.0322886 + 0.425097i
\(739\) −7.56592 13.1046i −0.278317 0.482059i 0.692650 0.721274i \(-0.256443\pi\)
−0.970967 + 0.239215i \(0.923110\pi\)
\(740\) −0.00313130 0.00542356i −0.000115109 0.000199374i
\(741\) 32.6650 7.54669i 1.19998 0.277235i
\(742\) −20.6899 + 34.0746i −0.759549 + 1.25092i
\(743\) 30.5018 + 17.6102i 1.11900 + 0.646056i 0.941146 0.338001i \(-0.109751\pi\)
0.177856 + 0.984057i \(0.443084\pi\)
\(744\) 35.4314 18.7032i 1.29898 0.685691i
\(745\) 0.0138178i 0.000506244i
\(746\) −5.60517 3.23614i −0.205220 0.118484i
\(747\) 13.5203 + 28.1480i 0.494683 + 1.02988i
\(748\) −8.01626 + 4.62819i −0.293103 + 0.169223i
\(749\) 0.319275 14.4495i 0.0116660 0.527973i
\(750\) 0.0187647 0.0298304i 0.000685189 0.00108925i
\(751\) 1.65351 0.0603375 0.0301687 0.999545i \(-0.490396\pi\)
0.0301687 + 0.999545i \(0.490396\pi\)
\(752\) −2.57291 4.45641i −0.0938244 0.162509i
\(753\) −0.580604 + 15.3100i −0.0211584 + 0.557926i
\(754\) −23.5762 23.4279i −0.858595 0.853195i
\(755\) 0.0314445 0.00114438
\(756\) 1.65265 12.0941i 0.0601062 0.439859i
\(757\) −7.44232 + 12.8905i −0.270496 + 0.468513i −0.968989 0.247104i \(-0.920521\pi\)
0.698493 + 0.715617i \(0.253854\pi\)
\(758\) 11.7832 + 6.80303i 0.427985 + 0.247097i
\(759\) −0.798257 + 21.0493i −0.0289749 + 0.764040i
\(760\) 0.0315441 0.00114422
\(761\) 4.20006 7.27471i 0.152252 0.263708i −0.779803 0.626025i \(-0.784681\pi\)
0.932055 + 0.362317i \(0.118014\pi\)
\(762\) −8.04799 15.2462i −0.291548 0.552311i
\(763\) 10.1212 16.6689i 0.366413 0.603454i
\(764\) 4.13646 + 2.38818i 0.149652 + 0.0864015i
\(765\) 0.0136339 0.0199540i 0.000492936 0.000721437i
\(766\) −8.43849 4.87196i −0.304895 0.176031i
\(767\) −4.82427 + 18.2343i −0.174194 + 0.658403i
\(768\) −24.1732 15.2061i −0.872277 0.548703i
\(769\) −40.4429 23.3497i −1.45841 0.842013i −0.459476 0.888190i \(-0.651963\pi\)
−0.998933 + 0.0461769i \(0.985296\pi\)
\(770\) 0.00697617 0.0114892i 0.000251404 0.000414043i
\(771\) 16.0448 + 10.0929i 0.577840 + 0.363488i
\(772\) −9.38617 16.2573i −0.337816 0.585114i
\(773\) 34.7010 1.24811 0.624055 0.781381i \(-0.285484\pi\)
0.624055 + 0.781381i \(0.285484\pi\)
\(774\) −6.94514 4.74540i −0.249638 0.170570i
\(775\) −32.8889 + 18.9884i −1.18140 + 0.682084i
\(776\) 3.63995 + 6.30458i 0.130667 + 0.226321i
\(777\) −13.9798 9.23116i −0.501523 0.331166i
\(778\) −6.93262 + 12.0076i −0.248546 + 0.430495i
\(779\) 17.0194 9.82614i 0.609783 0.352058i
\(780\) −0.0102313 0.00312627i −0.000366339 0.000111939i
\(781\) −1.78829 + 3.09740i −0.0639899 + 0.110834i
\(782\) 21.4459 0.766902
\(783\) 27.0275 36.5050i 0.965884 1.30458i
\(784\) −10.0412 0.443956i −0.358614 0.0158556i
\(785\) 0.00908333i 0.000324198i
\(786\) 11.3567 + 0.430683i 0.405080 + 0.0153620i
\(787\) 23.0530i 0.821750i 0.911692 + 0.410875i \(0.134777\pi\)
−0.911692 + 0.410875i \(0.865223\pi\)
\(788\) −19.9197 11.5006i −0.709609 0.409693i
\(789\) 22.0064 + 0.834554i 0.783448 + 0.0297109i
\(790\) 0.0128449 + 0.00741602i 0.000457002 + 0.000263850i
\(791\) −1.04659 + 0.573803i −0.0372124 + 0.0204021i
\(792\) 12.8698 18.8357i 0.457310 0.669296i
\(793\) 19.2622 19.3841i 0.684021 0.688351i
\(794\) −9.78631 + 16.9504i −0.347303 + 0.601547i
\(795\) −0.0254231 + 0.0404153i −0.000901665 + 0.00143338i
\(796\) 2.45785i 0.0871163i
\(797\) 18.0616 + 31.2836i 0.639774 + 1.10812i 0.985482 + 0.169779i \(0.0543054\pi\)
−0.345708 + 0.938342i \(0.612361\pi\)
\(798\) 23.2049 11.6011i 0.821446 0.410675i
\(799\) 7.48159 + 12.9585i 0.264680 + 0.458439i
\(800\) 19.8178 + 11.4418i 0.700666 + 0.404530i
\(801\) −7.01910 14.6131i −0.248008 0.516327i
\(802\) −13.0272 −0.460007
\(803\) −4.64382 −0.163877
\(804\) 0.830730 21.9055i 0.0292976 0.772549i
\(805\) 0.0218016 0.0119530i 0.000768406 0.000421286i
\(806\) −20.4854 20.3566i −0.721568 0.717029i
\(807\) −33.9530 21.3580i −1.19520 0.751837i
\(808\) −47.6322 + 27.5004i −1.67569 + 0.967462i
\(809\) −25.7675 + 14.8769i −0.905938 + 0.523044i −0.879122 0.476597i \(-0.841870\pi\)
−0.0268161 + 0.999640i \(0.508537\pi\)
\(810\) −0.00276585 + 0.0181019i −9.71822e−5 + 0.000636038i
\(811\) 17.0021i 0.597025i −0.954406 0.298512i \(-0.903510\pi\)
0.954406 0.298512i \(-0.0964904\pi\)
\(812\) 17.5524 + 10.6577i 0.615969 + 0.374012i
\(813\) −24.2970 + 38.6251i −0.852133 + 1.35464i
\(814\) −4.81299 8.33634i −0.168695 0.292189i
\(815\) −0.00811564 −0.000284279
\(816\) −8.78936 5.52892i −0.307689 0.193551i
\(817\) 14.2732i 0.499358i
\(818\) −6.08732 −0.212838
\(819\) −28.2198 + 4.75851i −0.986079 + 0.166276i
\(820\) −0.00627123 −0.000219001
\(821\) 29.3115i 1.02298i −0.859289 0.511490i \(-0.829094\pi\)
0.859289 0.511490i \(-0.170906\pi\)
\(822\) 9.51821 + 5.98739i 0.331986 + 0.208834i
\(823\) −2.17785 −0.0759149 −0.0379575 0.999279i \(-0.512085\pi\)
−0.0379575 + 0.999279i \(0.512085\pi\)
\(824\) −14.8602 25.7386i −0.517679 0.896647i
\(825\) −11.5137 + 18.3035i −0.400857 + 0.637245i
\(826\) −0.322432 + 14.5924i −0.0112188 + 0.507733i
\(827\) 15.2048i 0.528724i 0.964424 + 0.264362i \(0.0851613\pi\)
−0.964424 + 0.264362i \(0.914839\pi\)
\(828\) 11.6948 5.61736i 0.406422 0.195217i
\(829\) −3.44342 + 1.98806i −0.119595 + 0.0690483i −0.558604 0.829434i \(-0.688663\pi\)
0.439009 + 0.898483i \(0.355330\pi\)
\(830\) 0.0183413 0.0105893i 0.000636635 0.000367562i
\(831\) −6.45746 4.06205i −0.224007 0.140911i
\(832\) −7.09921 + 26.8329i −0.246121 + 0.930265i
\(833\) 29.1981 + 1.29095i 1.01166 + 0.0447288i
\(834\) 0.852559 22.4811i 0.0295217 0.778458i
\(835\) −0.0279759 −0.000968148
\(836\) −11.9015 −0.411623
\(837\) 23.4842 31.7193i 0.811733 1.09638i
\(838\) −32.1784 18.5782i −1.11158 0.641773i
\(839\) −17.0612 29.5509i −0.589019 1.02021i −0.994361 0.106046i \(-0.966181\pi\)
0.405342 0.914165i \(-0.367152\pi\)
\(840\) −0.0268784 0.00161457i −0.000927391 5.57080e-5i
\(841\) 23.7056 + 41.0593i 0.817434 + 1.41584i
\(842\) 28.5049i 0.982345i
\(843\) −12.2577 + 19.4862i −0.422179 + 0.671141i
\(844\) −3.46853 + 6.00767i −0.119392 + 0.206793i
\(845\) 0.000158261 0.0250816i 5.44436e−6 0.000862834i
\(846\) −9.36146 6.39640i −0.321854 0.219913i
\(847\) 6.54390 10.7773i 0.224851 0.370313i
\(848\) 17.7665 + 10.2575i 0.610105 + 0.352244i
\(849\) 28.3482 + 1.07506i 0.972906 + 0.0368958i
\(850\) 19.0658 + 11.0076i 0.653951 + 0.377559i
\(851\) 17.8058i 0.610375i
\(852\) 2.20129 + 0.0834801i 0.0754149 + 0.00285998i
\(853\) 56.0005i 1.91742i 0.284387 + 0.958710i \(0.408210\pi\)
−0.284387 + 0.958710i \(0.591790\pi\)
\(854\) 10.9754 18.0757i 0.375571 0.618537i
\(855\) 0.0280095 0.0134538i 0.000957904 0.000460111i
\(856\) −16.6366 −0.568626
\(857\) 7.20743 12.4836i 0.246201 0.426433i −0.716268 0.697826i \(-0.754151\pi\)
0.962469 + 0.271393i \(0.0874843\pi\)
\(858\) −15.7261 4.80527i −0.536881 0.164049i
\(859\) 2.32454 1.34207i 0.0793121 0.0457909i −0.459819 0.888012i \(-0.652086\pi\)
0.539132 + 0.842222i \(0.318753\pi\)
\(860\) 0.00227736 0.00394451i 7.76574e−5 0.000134507i
\(861\) −15.0050 + 7.50162i −0.511368 + 0.255655i
\(862\) 16.5183 + 28.6105i 0.562615 + 0.974479i
\(863\) 25.8619 14.9314i 0.880349 0.508270i 0.00957560 0.999954i \(-0.496952\pi\)
0.870773 + 0.491684i \(0.163619\pi\)
\(864\) −23.6278 2.69849i −0.803835 0.0918044i
\(865\) −0.0302851 −0.00102973
\(866\) 2.08172 + 3.60565i 0.0707398 + 0.122525i
\(867\) 0.634236 + 0.398964i 0.0215398 + 0.0135495i
\(868\) 15.2513 + 9.26048i 0.517663 + 0.314321i
\(869\) −15.7629 9.10072i −0.534720 0.308721i
\(870\) −0.0260758 0.0164029i −0.000884051 0.000556109i
\(871\) −49.6010 + 13.4584i −1.68067 + 0.456021i
\(872\) −19.4399 11.2236i −0.658318 0.380080i
\(873\) 5.92105 + 4.04567i 0.200397 + 0.136925i
\(874\) 23.8800 + 13.7872i 0.807755 + 0.466357i
\(875\) 0.0510345 + 0.00112765i 0.00172528 + 3.81217e-5i
\(876\) 1.33521 + 2.52943i 0.0451125 + 0.0854614i
\(877\) 5.77032 9.99449i 0.194850 0.337490i −0.752001 0.659162i \(-0.770911\pi\)
0.946851 + 0.321671i \(0.104245\pi\)
\(878\) 32.5509 1.09854
\(879\) 1.30793 34.4889i 0.0441154 1.16328i
\(880\) −0.00599049 0.00345861i −0.000201939 0.000116590i
\(881\) 3.76362 6.51878i 0.126800 0.219623i −0.795635 0.605776i \(-0.792863\pi\)
0.922435 + 0.386153i \(0.126196\pi\)
\(882\) −20.3665 + 8.69746i −0.685775 + 0.292859i
\(883\) −38.2310 −1.28658 −0.643289 0.765624i \(-0.722430\pi\)
−0.643289 + 0.765624i \(0.722430\pi\)
\(884\) 3.41872 12.9218i 0.114984 0.434606i
\(885\) −0.000662499 0.0174694i −2.22696e−5 0.000587229i
\(886\) −9.91025 17.1651i −0.332941 0.576672i
\(887\) 28.6232 0.961074 0.480537 0.876974i \(-0.340442\pi\)
0.480537 + 0.876974i \(0.340442\pi\)
\(888\) −10.2677 + 16.3227i −0.344562 + 0.547753i
\(889\) 12.9606 21.3452i 0.434686 0.715894i
\(890\) −0.00952190 + 0.00549747i −0.000319175 + 0.000184276i
\(891\) 3.39418 22.2142i 0.113709 0.744203i
\(892\) 5.76092 + 3.32607i 0.192890 + 0.111365i
\(893\) 19.2391i 0.643813i
\(894\) −11.5685 + 6.10663i −0.386907 + 0.204236i
\(895\) 0.0108017 + 0.00623639i 0.000361063 + 0.000208460i
\(896\) 0.0605058 2.73832i 0.00202136 0.0914809i
\(897\) −20.7481 22.2426i −0.692757 0.742659i
\(898\) 3.01891 + 5.22890i 0.100742 + 0.174491i
\(899\) 33.1969 + 57.4987i 1.10718 + 1.91769i
\(900\) 13.2801 + 1.00870i 0.442671 + 0.0336235i
\(901\) −51.6621 29.8271i −1.72111 0.993686i
\(902\) −9.63925 −0.320952
\(903\) 0.730571 12.1621i 0.0243119 0.404729i
\(904\) 0.686944 + 1.18982i 0.0228474 + 0.0395729i
\(905\) 0.00156959 0.000906206i 5.21751e−5 3.01233e-5i
\(906\) −13.8966 26.3259i −0.461684 0.874618i
\(907\) 14.8995 + 25.8067i 0.494730 + 0.856898i 0.999982 0.00607461i \(-0.00193362\pi\)
−0.505252 + 0.862972i \(0.668600\pi\)
\(908\) −7.58381 −0.251678
\(909\) −30.5657 + 44.7345i −1.01380 + 1.48375i
\(910\) 0.00466763 + 0.0188399i 0.000154730 + 0.000624537i
\(911\) 28.3029i 0.937717i 0.883273 + 0.468859i \(0.155335\pi\)
−0.883273 + 0.468859i \(0.844665\pi\)
\(912\) −6.23255 11.8070i −0.206380 0.390969i
\(913\) −22.5079 + 12.9949i −0.744903 + 0.430070i
\(914\) 35.7482i 1.18245i
\(915\) 0.0134863 0.0214392i 0.000445842 0.000708759i
\(916\) 7.92044 4.57287i 0.261699 0.151092i
\(917\) 7.91400 + 14.4347i 0.261343 + 0.476677i
\(918\) −22.7312 2.59609i −0.750241 0.0856836i
\(919\) 24.5422 42.5083i 0.809573 1.40222i −0.103588 0.994620i \(-0.533032\pi\)
0.913160 0.407601i \(-0.133634\pi\)
\(920\) −0.0143098 0.0247853i −0.000471781 0.000817148i
\(921\) 4.54960 7.23253i 0.149914 0.238320i
\(922\) −17.1318 + 9.89103i −0.564205 + 0.325744i
\(923\) −1.35244 4.98441i −0.0445160 0.164064i
\(924\) 10.1412 + 0.609175i 0.333620 + 0.0200404i
\(925\) 9.13928 15.8297i 0.300498 0.520477i
\(926\) 21.2918i 0.699693i
\(927\) −24.1728 16.5166i −0.793940 0.542475i
\(928\) 20.0034 34.6469i 0.656644 1.13734i
\(929\) 10.3944 18.0037i 0.341031 0.590682i −0.643594 0.765367i \(-0.722557\pi\)
0.984624 + 0.174685i \(0.0558907\pi\)
\(930\) −0.0226573 0.0142525i −0.000742961 0.000467357i
\(931\) 31.6823 + 20.2084i 1.03835 + 0.662305i
\(932\) 0.974015 0.562348i 0.0319049 0.0184203i
\(933\) 20.5012 10.8220i 0.671180 0.354295i
\(934\) 6.52555 3.76753i 0.213522 0.123277i
\(935\) 0.0174193 + 0.0100571i 0.000569673 + 0.000328901i
\(936\) 6.19366 + 32.3543i 0.202446 + 1.05753i
\(937\) 10.5891i 0.345930i 0.984928 + 0.172965i \(0.0553347\pi\)
−0.984928 + 0.172965i \(0.944665\pi\)
\(938\) −34.8736 + 19.1198i −1.13866 + 0.624284i
\(939\) 47.8853 + 1.81597i 1.56268 + 0.0592619i
\(940\) 0.00306969 0.00531686i 0.000100122 0.000173417i
\(941\) −21.4748 + 37.1955i −0.700059 + 1.21254i 0.268386 + 0.963311i \(0.413510\pi\)
−0.968445 + 0.249227i \(0.919824\pi\)
\(942\) −7.60472 + 4.01430i −0.247775 + 0.130793i
\(943\) −15.4415 8.91517i −0.502846 0.290318i
\(944\) 7.51141 0.244475
\(945\) −0.0245552 + 0.0100302i −0.000798781 + 0.000326282i
\(946\) 3.50044 6.06294i 0.113809 0.197123i
\(947\) 49.0592i 1.59421i 0.603842 + 0.797104i \(0.293636\pi\)
−0.603842 + 0.797104i \(0.706364\pi\)
\(948\) −0.424837 + 11.2025i −0.0137981 + 0.363841i
\(949\) 4.72670 4.75662i 0.153435 0.154406i
\(950\) 14.1532 + 24.5141i 0.459191 + 0.795342i
\(951\) 25.6583 + 0.973047i 0.832027 + 0.0315532i
\(952\) 0.743175 33.6340i 0.0240864 1.09008i
\(953\) −28.5078 + 16.4590i −0.923458 + 0.533159i −0.884737 0.466091i \(-0.845662\pi\)
−0.0387215 + 0.999250i \(0.512329\pi\)
\(954\) 45.0719 + 3.42347i 1.45926 + 0.110839i
\(955\) 0.0103791i 0.000335858i
\(956\) 16.7278i 0.541015i
\(957\) 31.9994 + 20.1291i 1.03439 + 0.650683i
\(958\) 8.43802 4.87169i 0.272620 0.157397i
\(959\) −0.359809 + 16.2840i −0.0116189 + 0.525837i
\(960\) −0.000974908 0.0257074i −3.14650e−5 0.000829701i
\(961\) 13.3448 + 23.1139i 0.430478 + 0.745609i
\(962\) 13.4377 + 3.55523i 0.433250 + 0.114625i
\(963\) −14.7724 + 7.09564i −0.476034 + 0.228654i
\(964\) 1.08618i 0.0349835i
\(965\) −0.0203962 + 0.0353272i −0.000656576 + 0.00113722i
\(966\) −19.6422 12.9702i −0.631979 0.417309i
\(967\) 27.5780 0.886848 0.443424 0.896312i \(-0.353764\pi\)
0.443424 + 0.896312i \(0.353764\pi\)
\(968\) −12.5689 7.25666i −0.403980 0.233238i
\(969\) 18.1232 + 34.3328i 0.582202 + 1.10293i
\(970\) 0.00243184 0.00421207i 7.80818e−5 0.000135242i
\(971\) −17.2874 + 29.9426i −0.554778 + 0.960904i 0.443143 + 0.896451i \(0.353864\pi\)
−0.997921 + 0.0644528i \(0.979470\pi\)
\(972\) −13.0757 + 4.53834i −0.419403 + 0.145567i
\(973\) 28.5743 15.6661i 0.916050 0.502233i
\(974\) 1.37257i 0.0439798i
\(975\) −7.02885 30.4236i −0.225103 0.974334i
\(976\) −9.42467 5.44133i −0.301676 0.174173i
\(977\) 50.1256 28.9400i 1.60366 0.925874i 0.612914 0.790150i \(-0.289997\pi\)
0.990747 0.135724i \(-0.0433361\pi\)
\(978\) 3.58664 + 6.79455i 0.114688 + 0.217266i
\(979\) 11.6850 6.74634i 0.373454 0.215614i
\(980\) −0.00553127 0.0106398i −0.000176690 0.000339876i
\(981\) −22.0486 1.67472i −0.703957 0.0534697i
\(982\) −6.97052 + 12.0733i −0.222438 + 0.385274i
\(983\) 1.73371 3.00288i 0.0552969 0.0957770i −0.837052 0.547123i \(-0.815723\pi\)
0.892349 + 0.451347i \(0.149056\pi\)
\(984\) 9.01440 + 17.0770i 0.287369 + 0.544394i
\(985\) 0.0499818i 0.00159255i
\(986\) 19.2443 33.3322i 0.612864 1.06151i
\(987\) 0.984748 16.3935i 0.0313449 0.521810i
\(988\) 12.1139 12.1906i 0.385396 0.387835i
\(989\) 11.2150 6.47499i 0.356617 0.205893i
\(990\) −0.0151973 0.00115432i −0.000483001 3.66867e-5i
\(991\) −4.47519 7.75126i −0.142159 0.246227i 0.786150 0.618035i \(-0.212071\pi\)
−0.928309 + 0.371809i \(0.878738\pi\)
\(992\) 17.3810 30.1048i 0.551847 0.955827i
\(993\) −8.89757 + 4.69676i −0.282356 + 0.149047i
\(994\) −1.92135 3.50445i −0.0609415 0.111154i
\(995\) 0.00462537 0.00267046i 0.000146634 8.46592e-5i
\(996\) 13.5497 + 8.52341i 0.429339 + 0.270075i
\(997\) 3.25743i 0.103164i 0.998669 + 0.0515818i \(0.0164263\pi\)
−0.998669 + 0.0515818i \(0.983574\pi\)
\(998\) −5.81243 + 3.35581i −0.183989 + 0.106226i
\(999\) −2.15545 + 18.8730i −0.0681953 + 0.597114i
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.r.b.269.22 yes 64
3.2 odd 2 inner 273.2.r.b.269.11 yes 64
7.5 odd 6 273.2.bf.b.152.22 yes 64
13.3 even 3 273.2.bf.b.185.11 yes 64
21.5 even 6 273.2.bf.b.152.11 yes 64
39.29 odd 6 273.2.bf.b.185.22 yes 64
91.68 odd 6 inner 273.2.r.b.68.22 yes 64
273.68 even 6 inner 273.2.r.b.68.11 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.r.b.68.11 64 273.68 even 6 inner
273.2.r.b.68.22 yes 64 91.68 odd 6 inner
273.2.r.b.269.11 yes 64 3.2 odd 2 inner
273.2.r.b.269.22 yes 64 1.1 even 1 trivial
273.2.bf.b.152.11 yes 64 21.5 even 6
273.2.bf.b.152.22 yes 64 7.5 odd 6
273.2.bf.b.185.11 yes 64 13.3 even 3
273.2.bf.b.185.22 yes 64 39.29 odd 6