Properties

Label 406.2.e.a.233.1
Level $406$
Weight $2$
Character 406.233
Analytic conductor $3.242$
Analytic rank $0$
Dimension $10$
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] = [406,2,Mod(233,406)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(406, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("406.233");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 406 = 2 \cdot 7 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 406.e (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: \(3.24192632206\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.3118758597603.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{8} - 16x^{6} - 34x^{5} + 43x^{4} + 155x^{3} + 199x^{2} + 124x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 233.1
Root \(-0.359001 + 0.701254i\) of defining polynomial
Character \(\chi\) \(=\) 406.233
Dual form 406.2.e.a.291.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.61748 - 2.80156i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.572197 + 0.991074i) q^{5} +3.23497 q^{6} +(0.469216 + 2.60381i) q^{7} +1.00000 q^{8} +(-3.73251 + 6.46489i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.61748 - 2.80156i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.572197 + 0.991074i) q^{5} +3.23497 q^{6} +(0.469216 + 2.60381i) q^{7} +1.00000 q^{8} +(-3.73251 + 6.46489i) q^{9} +(-0.572197 - 0.991074i) q^{10} +(0.425341 + 0.736713i) q^{11} +(-1.61748 + 2.80156i) q^{12} +3.66136 q^{13} +(-2.48958 - 0.895553i) q^{14} +3.70208 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0971241 - 0.168224i) q^{17} +(-3.73251 - 6.46489i) q^{18} +(3.49684 - 6.05671i) q^{19} +1.14439 q^{20} +(6.53580 - 5.52616i) q^{21} -0.850683 q^{22} +(1.73109 - 2.99834i) q^{23} +(-1.61748 - 2.80156i) q^{24} +(1.84518 + 3.19595i) q^{25} +(-1.83068 + 3.17083i) q^{26} +14.4442 q^{27} +(2.02036 - 1.70826i) q^{28} -1.00000 q^{29} +(-1.85104 + 3.20609i) q^{30} +(1.98711 + 3.44178i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.37597 - 2.38324i) q^{33} +0.194248 q^{34} +(-2.84905 - 1.02487i) q^{35} +7.46501 q^{36} +(-3.60460 + 6.24335i) q^{37} +(3.49684 + 6.05671i) q^{38} +(-5.92219 - 10.2575i) q^{39} +(-0.572197 + 0.991074i) q^{40} +4.04493 q^{41} +(1.51790 + 8.42325i) q^{42} +9.77788 q^{43} +(0.425341 - 0.736713i) q^{44} +(-4.27146 - 7.39838i) q^{45} +(1.73109 + 2.99834i) q^{46} +(-0.0269105 + 0.0466104i) q^{47} +3.23497 q^{48} +(-6.55967 + 2.44350i) q^{49} -3.69036 q^{50} +(-0.314193 + 0.544199i) q^{51} +(-1.83068 - 3.17083i) q^{52} +(1.33549 + 2.31313i) q^{53} +(-7.22208 + 12.5090i) q^{54} -0.973516 q^{55} +(0.469216 + 2.60381i) q^{56} -22.6244 q^{57} +(0.500000 - 0.866025i) q^{58} +(4.02177 + 6.96591i) q^{59} +(-1.85104 - 3.20609i) q^{60} +(2.54072 - 4.40065i) q^{61} -3.97423 q^{62} +(-18.5847 - 6.68531i) q^{63} +1.00000 q^{64} +(-2.09502 + 3.62868i) q^{65} +(1.37597 + 2.38324i) q^{66} +(5.80013 + 10.0461i) q^{67} +(-0.0971241 + 0.168224i) q^{68} -11.2001 q^{69} +(2.31209 - 1.95492i) q^{70} -11.2825 q^{71} +(-3.73251 + 6.46489i) q^{72} +(3.65539 + 6.33131i) q^{73} +(-3.60460 - 6.24335i) q^{74} +(5.96910 - 10.3388i) q^{75} -6.99369 q^{76} +(-1.71868 + 1.45319i) q^{77} +11.8444 q^{78} +(6.67821 - 11.5670i) q^{79} +(-0.572197 - 0.991074i) q^{80} +(-12.1657 - 21.0716i) q^{81} +(-2.02247 + 3.50301i) q^{82} +9.04564 q^{83} +(-8.05369 - 2.89708i) q^{84} +0.222296 q^{85} +(-4.88894 + 8.46789i) q^{86} +(1.61748 + 2.80156i) q^{87} +(0.425341 + 0.736713i) q^{88} +(-7.11526 + 12.3240i) q^{89} +8.54291 q^{90} +(1.71797 + 9.53349i) q^{91} -3.46219 q^{92} +(6.42825 - 11.1340i) q^{93} +(-0.0269105 - 0.0466104i) q^{94} +(4.00177 + 6.93126i) q^{95} +(-1.61748 + 2.80156i) q^{96} +18.7779 q^{97} +(1.16370 - 6.90259i) q^{98} -6.35036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 5 q^{2} - 3 q^{3} - 5 q^{4} - 7 q^{5} + 6 q^{6} - 3 q^{7} + 10 q^{8} - 8 q^{9} - 7 q^{10} - 3 q^{12} + 20 q^{13} + 3 q^{14} - 20 q^{15} - 5 q^{16} - 8 q^{17} - 8 q^{18} - 2 q^{19} + 14 q^{20} + 19 q^{21} - q^{23} - 3 q^{24} - 12 q^{25} - 10 q^{26} + 30 q^{27} - 10 q^{29} + 10 q^{30} - 11 q^{31} - 5 q^{32} - 9 q^{33} + 16 q^{34} + 10 q^{35} + 16 q^{36} + 8 q^{37} - 2 q^{38} - 18 q^{39} - 7 q^{40} + 46 q^{41} - 8 q^{42} - 6 q^{43} - 4 q^{45} - q^{46} - 16 q^{47} + 6 q^{48} - 11 q^{49} + 24 q^{50} - 7 q^{51} - 10 q^{52} - 7 q^{53} - 15 q^{54} + 12 q^{55} - 3 q^{56} - 68 q^{57} + 5 q^{58} + 9 q^{59} + 10 q^{60} - 15 q^{61} + 22 q^{62} - 3 q^{63} + 10 q^{64} - 5 q^{65} - 9 q^{66} + 4 q^{67} - 8 q^{68} + 28 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 8 q^{74} + 34 q^{75} + 4 q^{76} + 39 q^{77} + 36 q^{78} + 13 q^{79} - 7 q^{80} - 17 q^{81} - 23 q^{82} + 56 q^{83} - 11 q^{84} - 14 q^{85} + 3 q^{86} + 3 q^{87} - 17 q^{89} + 8 q^{90} + 6 q^{91} + 2 q^{92} - 17 q^{93} - 16 q^{94} + 9 q^{95} - 3 q^{96} + 84 q^{97} - 20 q^{98} - 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/406\mathbb{Z}\right)^\times\).

\(n\) \(59\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −1.61748 2.80156i −0.933854 1.61748i −0.776664 0.629915i \(-0.783090\pi\)
−0.157191 0.987568i \(-0.550244\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.572197 + 0.991074i −0.255894 + 0.443222i −0.965138 0.261741i \(-0.915703\pi\)
0.709244 + 0.704963i \(0.249037\pi\)
\(6\) 3.23497 1.32067
\(7\) 0.469216 + 2.60381i 0.177347 + 0.984148i
\(8\) 1.00000 0.353553
\(9\) −3.73251 + 6.46489i −1.24417 + 2.15496i
\(10\) −0.572197 0.991074i −0.180945 0.313405i
\(11\) 0.425341 + 0.736713i 0.128245 + 0.222127i 0.922997 0.384808i \(-0.125732\pi\)
−0.794752 + 0.606935i \(0.792399\pi\)
\(12\) −1.61748 + 2.80156i −0.466927 + 0.808742i
\(13\) 3.66136 1.01548 0.507739 0.861511i \(-0.330481\pi\)
0.507739 + 0.861511i \(0.330481\pi\)
\(14\) −2.48958 0.895553i −0.665367 0.239347i
\(15\) 3.70208 0.955872
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.0971241 0.168224i −0.0235561 0.0408003i 0.854007 0.520261i \(-0.174165\pi\)
−0.877563 + 0.479461i \(0.840832\pi\)
\(18\) −3.73251 6.46489i −0.879760 1.52379i
\(19\) 3.49684 6.05671i 0.802231 1.38950i −0.115913 0.993259i \(-0.536980\pi\)
0.918145 0.396246i \(-0.129687\pi\)
\(20\) 1.14439 0.255894
\(21\) 6.53580 5.52616i 1.42623 1.20591i
\(22\) −0.850683 −0.181366
\(23\) 1.73109 2.99834i 0.360958 0.625197i −0.627161 0.778890i \(-0.715783\pi\)
0.988119 + 0.153692i \(0.0491165\pi\)
\(24\) −1.61748 2.80156i −0.330167 0.571867i
\(25\) 1.84518 + 3.19595i 0.369036 + 0.639190i
\(26\) −1.83068 + 3.17083i −0.359026 + 0.621851i
\(27\) 14.4442 2.77978
\(28\) 2.02036 1.70826i 0.381812 0.322831i
\(29\) −1.00000 −0.185695
\(30\) −1.85104 + 3.20609i −0.337952 + 0.585350i
\(31\) 1.98711 + 3.44178i 0.356896 + 0.618162i 0.987441 0.157991i \(-0.0505017\pi\)
−0.630544 + 0.776153i \(0.717168\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.37597 2.38324i 0.239525 0.414869i
\(34\) 0.194248 0.0333133
\(35\) −2.84905 1.02487i −0.481578 0.173234i
\(36\) 7.46501 1.24417
\(37\) −3.60460 + 6.24335i −0.592592 + 1.02640i 0.401290 + 0.915951i \(0.368562\pi\)
−0.993882 + 0.110448i \(0.964771\pi\)
\(38\) 3.49684 + 6.05671i 0.567263 + 0.982528i
\(39\) −5.92219 10.2575i −0.948309 1.64252i
\(40\) −0.572197 + 0.991074i −0.0904723 + 0.156703i
\(41\) 4.04493 0.631712 0.315856 0.948807i \(-0.397708\pi\)
0.315856 + 0.948807i \(0.397708\pi\)
\(42\) 1.51790 + 8.42325i 0.234217 + 1.29973i
\(43\) 9.77788 1.49111 0.745556 0.666443i \(-0.232184\pi\)
0.745556 + 0.666443i \(0.232184\pi\)
\(44\) 0.425341 0.736713i 0.0641226 0.111064i
\(45\) −4.27146 7.39838i −0.636751 1.10289i
\(46\) 1.73109 + 2.99834i 0.255236 + 0.442081i
\(47\) −0.0269105 + 0.0466104i −0.00392531 + 0.00679883i −0.867981 0.496597i \(-0.834583\pi\)
0.864056 + 0.503396i \(0.167916\pi\)
\(48\) 3.23497 0.466927
\(49\) −6.55967 + 2.44350i −0.937096 + 0.349071i
\(50\) −3.69036 −0.521896
\(51\) −0.314193 + 0.544199i −0.0439958 + 0.0762030i
\(52\) −1.83068 3.17083i −0.253869 0.439715i
\(53\) 1.33549 + 2.31313i 0.183443 + 0.317733i 0.943051 0.332649i \(-0.107942\pi\)
−0.759608 + 0.650382i \(0.774609\pi\)
\(54\) −7.22208 + 12.5090i −0.982801 + 1.70226i
\(55\) −0.973516 −0.131269
\(56\) 0.469216 + 2.60381i 0.0627016 + 0.347949i
\(57\) −22.6244 −2.99667
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) 4.02177 + 6.96591i 0.523590 + 0.906885i 0.999623 + 0.0274571i \(0.00874096\pi\)
−0.476033 + 0.879427i \(0.657926\pi\)
\(60\) −1.85104 3.20609i −0.238968 0.413905i
\(61\) 2.54072 4.40065i 0.325306 0.563446i −0.656268 0.754527i \(-0.727866\pi\)
0.981574 + 0.191081i \(0.0611995\pi\)
\(62\) −3.97423 −0.504727
\(63\) −18.5847 6.68531i −2.34145 0.842270i
\(64\) 1.00000 0.125000
\(65\) −2.09502 + 3.62868i −0.259855 + 0.450082i
\(66\) 1.37597 + 2.38324i 0.169370 + 0.293357i
\(67\) 5.80013 + 10.0461i 0.708599 + 1.22733i 0.965377 + 0.260859i \(0.0840059\pi\)
−0.256778 + 0.966471i \(0.582661\pi\)
\(68\) −0.0971241 + 0.168224i −0.0117780 + 0.0204001i
\(69\) −11.2001 −1.34833
\(70\) 2.31209 1.95492i 0.276347 0.233658i
\(71\) −11.2825 −1.33898 −0.669492 0.742819i \(-0.733488\pi\)
−0.669492 + 0.742819i \(0.733488\pi\)
\(72\) −3.73251 + 6.46489i −0.439880 + 0.761894i
\(73\) 3.65539 + 6.33131i 0.427830 + 0.741024i 0.996680 0.0814175i \(-0.0259447\pi\)
−0.568850 + 0.822442i \(0.692611\pi\)
\(74\) −3.60460 6.24335i −0.419026 0.725774i
\(75\) 5.96910 10.3388i 0.689252 1.19382i
\(76\) −6.99369 −0.802231
\(77\) −1.71868 + 1.45319i −0.195862 + 0.165606i
\(78\) 11.8444 1.34111
\(79\) 6.67821 11.5670i 0.751357 1.30139i −0.195808 0.980642i \(-0.562733\pi\)
0.947165 0.320746i \(-0.103934\pi\)
\(80\) −0.572197 0.991074i −0.0639736 0.110805i
\(81\) −12.1657 21.0716i −1.35174 2.34129i
\(82\) −2.02247 + 3.50301i −0.223344 + 0.386843i
\(83\) 9.04564 0.992888 0.496444 0.868069i \(-0.334639\pi\)
0.496444 + 0.868069i \(0.334639\pi\)
\(84\) −8.05369 2.89708i −0.878730 0.316098i
\(85\) 0.222296 0.0241114
\(86\) −4.88894 + 8.46789i −0.527188 + 0.913116i
\(87\) 1.61748 + 2.80156i 0.173412 + 0.300359i
\(88\) 0.425341 + 0.736713i 0.0453415 + 0.0785339i
\(89\) −7.11526 + 12.3240i −0.754216 + 1.30634i 0.191547 + 0.981483i \(0.438650\pi\)
−0.945763 + 0.324857i \(0.894684\pi\)
\(90\) 8.54291 0.900502
\(91\) 1.71797 + 9.53349i 0.180092 + 0.999381i
\(92\) −3.46219 −0.360958
\(93\) 6.42825 11.1340i 0.666578 1.15455i
\(94\) −0.0269105 0.0466104i −0.00277561 0.00480750i
\(95\) 4.00177 + 6.93126i 0.410573 + 0.711133i
\(96\) −1.61748 + 2.80156i −0.165084 + 0.285933i
\(97\) 18.7779 1.90660 0.953302 0.302017i \(-0.0976601\pi\)
0.953302 + 0.302017i \(0.0976601\pi\)
\(98\) 1.16370 6.90259i 0.117552 0.697267i
\(99\) −6.35036 −0.638235
\(100\) 1.84518 3.19595i 0.184518 0.319595i
\(101\) −6.85968 11.8813i −0.682564 1.18224i −0.974196 0.225705i \(-0.927531\pi\)
0.291632 0.956531i \(-0.405802\pi\)
\(102\) −0.314193 0.544199i −0.0311098 0.0538837i
\(103\) −0.590573 + 1.02290i −0.0581909 + 0.100790i −0.893653 0.448758i \(-0.851867\pi\)
0.835462 + 0.549548i \(0.185200\pi\)
\(104\) 3.66136 0.359026
\(105\) 1.73707 + 9.63951i 0.169521 + 0.940720i
\(106\) −2.67097 −0.259428
\(107\) 0.896121 1.55213i 0.0866313 0.150050i −0.819454 0.573145i \(-0.805723\pi\)
0.906085 + 0.423095i \(0.139056\pi\)
\(108\) −7.22208 12.5090i −0.694945 1.20368i
\(109\) −1.82095 3.15397i −0.174415 0.302096i 0.765544 0.643384i \(-0.222470\pi\)
−0.939959 + 0.341288i \(0.889137\pi\)
\(110\) 0.486758 0.843090i 0.0464106 0.0803855i
\(111\) 23.3215 2.21358
\(112\) −2.48958 0.895553i −0.235243 0.0846218i
\(113\) −17.7718 −1.67183 −0.835915 0.548859i \(-0.815063\pi\)
−0.835915 + 0.548859i \(0.815063\pi\)
\(114\) 11.3122 19.5933i 1.05948 1.83508i
\(115\) 1.98105 + 3.43128i 0.184734 + 0.319969i
\(116\) 0.500000 + 0.866025i 0.0464238 + 0.0804084i
\(117\) −13.6660 + 23.6703i −1.26343 + 2.18832i
\(118\) −8.04354 −0.740468
\(119\) 0.392451 0.331826i 0.0359759 0.0304185i
\(120\) 3.70208 0.337952
\(121\) 5.13817 8.89957i 0.467106 0.809052i
\(122\) 2.54072 + 4.40065i 0.230026 + 0.398416i
\(123\) −6.54261 11.3321i −0.589927 1.02178i
\(124\) 1.98711 3.44178i 0.178448 0.309081i
\(125\) −9.94520 −0.889526
\(126\) 15.0820 12.7522i 1.34361 1.13605i
\(127\) −11.5789 −1.02746 −0.513732 0.857950i \(-0.671738\pi\)
−0.513732 + 0.857950i \(0.671738\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −15.8156 27.3934i −1.39248 2.41185i
\(130\) −2.09502 3.62868i −0.183745 0.318256i
\(131\) 8.09878 14.0275i 0.707593 1.22559i −0.258154 0.966104i \(-0.583114\pi\)
0.965747 0.259484i \(-0.0835524\pi\)
\(132\) −2.75193 −0.239525
\(133\) 17.4113 + 6.26322i 1.50975 + 0.543090i
\(134\) −11.6003 −1.00211
\(135\) −8.26491 + 14.3152i −0.711330 + 1.23206i
\(136\) −0.0971241 0.168224i −0.00832832 0.0144251i
\(137\) 6.39212 + 11.0715i 0.546116 + 0.945900i 0.998536 + 0.0540951i \(0.0172274\pi\)
−0.452420 + 0.891805i \(0.649439\pi\)
\(138\) 5.60003 9.69954i 0.476706 0.825679i
\(139\) 0.170575 0.0144679 0.00723397 0.999974i \(-0.497697\pi\)
0.00723397 + 0.999974i \(0.497697\pi\)
\(140\) 0.536968 + 2.97979i 0.0453821 + 0.251838i
\(141\) 0.174109 0.0146627
\(142\) 5.64124 9.77091i 0.473402 0.819957i
\(143\) 1.55733 + 2.69737i 0.130230 + 0.225565i
\(144\) −3.73251 6.46489i −0.311042 0.538741i
\(145\) 0.572197 0.991074i 0.0475184 0.0823042i
\(146\) −7.31077 −0.605044
\(147\) 17.4558 + 14.4250i 1.43973 + 1.18976i
\(148\) 7.20919 0.592592
\(149\) −7.02198 + 12.1624i −0.575263 + 0.996384i 0.420750 + 0.907176i \(0.361767\pi\)
−0.996013 + 0.0892077i \(0.971567\pi\)
\(150\) 5.96910 + 10.3388i 0.487375 + 0.844158i
\(151\) −6.09878 10.5634i −0.496311 0.859636i 0.503680 0.863891i \(-0.331979\pi\)
−0.999991 + 0.00425408i \(0.998646\pi\)
\(152\) 3.49684 6.05671i 0.283632 0.491264i
\(153\) 1.45006 0.117231
\(154\) −0.399154 2.21502i −0.0321647 0.178491i
\(155\) −4.54808 −0.365311
\(156\) −5.92219 + 10.2575i −0.474154 + 0.821259i
\(157\) −7.19485 12.4618i −0.574212 0.994564i −0.996127 0.0879283i \(-0.971975\pi\)
0.421915 0.906635i \(-0.361358\pi\)
\(158\) 6.67821 + 11.5670i 0.531290 + 0.920220i
\(159\) 4.32025 7.48290i 0.342618 0.593433i
\(160\) 1.14439 0.0904723
\(161\) 8.61937 + 3.10057i 0.679302 + 0.244359i
\(162\) 24.3314 1.91165
\(163\) −8.38368 + 14.5210i −0.656660 + 1.13737i 0.324814 + 0.945778i \(0.394698\pi\)
−0.981475 + 0.191591i \(0.938635\pi\)
\(164\) −2.02247 3.50301i −0.157928 0.273539i
\(165\) 1.57465 + 2.72737i 0.122586 + 0.212325i
\(166\) −4.52282 + 7.83376i −0.351039 + 0.608017i
\(167\) −10.6555 −0.824544 −0.412272 0.911061i \(-0.635265\pi\)
−0.412272 + 0.911061i \(0.635265\pi\)
\(168\) 6.53580 5.52616i 0.504248 0.426353i
\(169\) 0.405541 0.0311955
\(170\) −0.111148 + 0.192514i −0.00852468 + 0.0147652i
\(171\) 26.1040 + 45.2134i 1.99622 + 3.45756i
\(172\) −4.88894 8.46789i −0.372778 0.645671i
\(173\) −8.96254 + 15.5236i −0.681409 + 1.18024i 0.293141 + 0.956069i \(0.405299\pi\)
−0.974551 + 0.224167i \(0.928034\pi\)
\(174\) −3.23497 −0.245242
\(175\) −7.45586 + 6.30409i −0.563610 + 0.476545i
\(176\) −0.850683 −0.0641226
\(177\) 13.0103 22.5345i 0.977914 1.69380i
\(178\) −7.11526 12.3240i −0.533311 0.923722i
\(179\) −2.64460 4.58058i −0.197667 0.342368i 0.750105 0.661319i \(-0.230003\pi\)
−0.947771 + 0.318950i \(0.896670\pi\)
\(180\) −4.27146 + 7.39838i −0.318376 + 0.551443i
\(181\) 13.1711 0.978997 0.489498 0.872004i \(-0.337180\pi\)
0.489498 + 0.872004i \(0.337180\pi\)
\(182\) −9.11523 3.27894i −0.675665 0.243051i
\(183\) −16.4383 −1.21515
\(184\) 1.73109 2.99834i 0.127618 0.221041i
\(185\) −4.12508 7.14485i −0.303282 0.525300i
\(186\) 6.42825 + 11.1340i 0.471342 + 0.816388i
\(187\) 0.0826218 0.143105i 0.00604190 0.0104649i
\(188\) 0.0538211 0.00392531
\(189\) 6.77743 + 37.6099i 0.492985 + 2.73572i
\(190\) −8.00353 −0.580637
\(191\) −4.95435 + 8.58118i −0.358484 + 0.620912i −0.987708 0.156312i \(-0.950040\pi\)
0.629224 + 0.777224i \(0.283373\pi\)
\(192\) −1.61748 2.80156i −0.116732 0.202185i
\(193\) 8.69752 + 15.0645i 0.626061 + 1.08437i 0.988335 + 0.152298i \(0.0486672\pi\)
−0.362274 + 0.932072i \(0.617999\pi\)
\(194\) −9.38894 + 16.2621i −0.674087 + 1.16755i
\(195\) 13.5546 0.970667
\(196\) 5.39597 + 4.45909i 0.385426 + 0.318507i
\(197\) 17.5961 1.25367 0.626834 0.779153i \(-0.284350\pi\)
0.626834 + 0.779153i \(0.284350\pi\)
\(198\) 3.17518 5.49957i 0.225650 0.390837i
\(199\) −5.64229 9.77274i −0.399972 0.692771i 0.593750 0.804649i \(-0.297647\pi\)
−0.993722 + 0.111878i \(0.964313\pi\)
\(200\) 1.84518 + 3.19595i 0.130474 + 0.225988i
\(201\) 18.7632 32.4989i 1.32346 2.29229i
\(202\) 13.7194 0.965291
\(203\) −0.469216 2.60381i −0.0329325 0.182752i
\(204\) 0.628386 0.0439958
\(205\) −2.31450 + 4.00883i −0.161652 + 0.279989i
\(206\) −0.590573 1.02290i −0.0411472 0.0712690i
\(207\) 12.9226 + 22.3827i 0.898185 + 1.55570i
\(208\) −1.83068 + 3.17083i −0.126935 + 0.219857i
\(209\) 5.94941 0.411529
\(210\) −9.21660 3.31541i −0.636006 0.228785i
\(211\) −9.87572 −0.679873 −0.339936 0.940448i \(-0.610406\pi\)
−0.339936 + 0.940448i \(0.610406\pi\)
\(212\) 1.33549 2.31313i 0.0917216 0.158866i
\(213\) 18.2492 + 31.6086i 1.25042 + 2.16578i
\(214\) 0.896121 + 1.55213i 0.0612576 + 0.106101i
\(215\) −5.59487 + 9.69060i −0.381567 + 0.660894i
\(216\) 14.4442 0.982801
\(217\) −8.02937 + 6.78901i −0.545069 + 0.460868i
\(218\) 3.64190 0.246660
\(219\) 11.8250 20.4816i 0.799063 1.38402i
\(220\) 0.486758 + 0.843090i 0.0328172 + 0.0568411i
\(221\) −0.355606 0.615928i −0.0239207 0.0414318i
\(222\) −11.6608 + 20.1970i −0.782618 + 1.35553i
\(223\) −16.5982 −1.11150 −0.555748 0.831351i \(-0.687568\pi\)
−0.555748 + 0.831351i \(0.687568\pi\)
\(224\) 2.02036 1.70826i 0.134991 0.114138i
\(225\) −27.5486 −1.83657
\(226\) 8.88590 15.3908i 0.591081 1.02378i
\(227\) −8.99651 15.5824i −0.597120 1.03424i −0.993244 0.116045i \(-0.962978\pi\)
0.396125 0.918197i \(-0.370355\pi\)
\(228\) 11.3122 + 19.5933i 0.749167 + 1.29760i
\(229\) 1.01911 1.76514i 0.0673444 0.116644i −0.830387 0.557187i \(-0.811881\pi\)
0.897732 + 0.440543i \(0.145214\pi\)
\(230\) −3.96211 −0.261253
\(231\) 6.85114 + 2.46450i 0.450772 + 0.162152i
\(232\) −1.00000 −0.0656532
\(233\) 8.24947 14.2885i 0.540441 0.936071i −0.458438 0.888726i \(-0.651591\pi\)
0.998879 0.0473443i \(-0.0150758\pi\)
\(234\) −13.6660 23.6703i −0.893377 1.54737i
\(235\) −0.0307963 0.0533407i −0.00200893 0.00347956i
\(236\) 4.02177 6.96591i 0.261795 0.453442i
\(237\) −43.2075 −2.80663
\(238\) 0.0911443 + 0.505786i 0.00590801 + 0.0327852i
\(239\) 18.7414 1.21228 0.606141 0.795357i \(-0.292717\pi\)
0.606141 + 0.795357i \(0.292717\pi\)
\(240\) −1.85104 + 3.20609i −0.119484 + 0.206952i
\(241\) −8.93903 15.4828i −0.575813 0.997338i −0.995953 0.0898784i \(-0.971352\pi\)
0.420139 0.907460i \(-0.361981\pi\)
\(242\) 5.13817 + 8.89957i 0.330294 + 0.572086i
\(243\) −17.6893 + 30.6388i −1.13477 + 1.96548i
\(244\) −5.08144 −0.325306
\(245\) 1.33174 7.89929i 0.0850815 0.504667i
\(246\) 13.0852 0.834283
\(247\) 12.8032 22.1758i 0.814648 1.41101i
\(248\) 1.98711 + 3.44178i 0.126182 + 0.218553i
\(249\) −14.6312 25.3419i −0.927213 1.60598i
\(250\) 4.97260 8.61279i 0.314495 0.544721i
\(251\) −1.69249 −0.106829 −0.0534144 0.998572i \(-0.517010\pi\)
−0.0534144 + 0.998572i \(0.517010\pi\)
\(252\) 3.50270 + 19.4375i 0.220649 + 1.22445i
\(253\) 2.94522 0.185165
\(254\) 5.78947 10.0277i 0.363264 0.629191i
\(255\) −0.359561 0.622778i −0.0225166 0.0389998i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.77662 + 3.07719i −0.110822 + 0.191950i −0.916102 0.400945i \(-0.868682\pi\)
0.805280 + 0.592895i \(0.202015\pi\)
\(258\) 31.6311 1.96927
\(259\) −17.9478 6.45622i −1.11522 0.401170i
\(260\) 4.19004 0.259855
\(261\) 3.73251 6.46489i 0.231036 0.400167i
\(262\) 8.09878 + 14.0275i 0.500344 + 0.866621i
\(263\) 9.18136 + 15.9026i 0.566147 + 0.980595i 0.996942 + 0.0781456i \(0.0248999\pi\)
−0.430795 + 0.902450i \(0.641767\pi\)
\(264\) 1.37597 2.38324i 0.0846848 0.146678i
\(265\) −3.05665 −0.187768
\(266\) −14.1298 + 11.9470i −0.866351 + 0.732519i
\(267\) 46.0353 2.81731
\(268\) 5.80013 10.0461i 0.354300 0.613665i
\(269\) −9.09102 15.7461i −0.554289 0.960057i −0.997958 0.0638663i \(-0.979657\pi\)
0.443669 0.896191i \(-0.353676\pi\)
\(270\) −8.26491 14.3152i −0.502986 0.871198i
\(271\) 3.65352 6.32808i 0.221935 0.384403i −0.733460 0.679732i \(-0.762096\pi\)
0.955396 + 0.295329i \(0.0954293\pi\)
\(272\) 0.194248 0.0117780
\(273\) 23.9299 20.2333i 1.44830 1.22457i
\(274\) −12.7842 −0.772324
\(275\) −1.56966 + 2.71874i −0.0946543 + 0.163946i
\(276\) 5.60003 + 9.69954i 0.337082 + 0.583843i
\(277\) 8.32098 + 14.4124i 0.499959 + 0.865955i 1.00000 4.71482e-5i \(-1.50077e-5\pi\)
−0.500041 + 0.866002i \(0.666682\pi\)
\(278\) −0.0852873 + 0.147722i −0.00511519 + 0.00885977i
\(279\) −29.6676 −1.77616
\(280\) −2.84905 1.02487i −0.170264 0.0612474i
\(281\) 13.2562 0.790800 0.395400 0.918509i \(-0.370606\pi\)
0.395400 + 0.918509i \(0.370606\pi\)
\(282\) −0.0870547 + 0.150783i −0.00518403 + 0.00897901i
\(283\) 7.63929 + 13.2316i 0.454109 + 0.786539i 0.998636 0.0522035i \(-0.0166244\pi\)
−0.544528 + 0.838743i \(0.683291\pi\)
\(284\) 5.64124 + 9.77091i 0.334746 + 0.579797i
\(285\) 12.9456 22.4224i 0.766830 1.32819i
\(286\) −3.11465 −0.184173
\(287\) 1.89795 + 10.5322i 0.112032 + 0.621698i
\(288\) 7.46501 0.439880
\(289\) 8.48113 14.6898i 0.498890 0.864103i
\(290\) 0.572197 + 0.991074i 0.0336006 + 0.0581979i
\(291\) −30.3729 52.6074i −1.78049 3.08390i
\(292\) 3.65539 6.33131i 0.213915 0.370512i
\(293\) −15.5191 −0.906637 −0.453318 0.891349i \(-0.649760\pi\)
−0.453318 + 0.891349i \(0.649760\pi\)
\(294\) −21.2203 + 7.90464i −1.23759 + 0.461008i
\(295\) −9.20498 −0.535935
\(296\) −3.60460 + 6.24335i −0.209513 + 0.362887i
\(297\) 6.14370 + 10.6412i 0.356494 + 0.617465i
\(298\) −7.02198 12.1624i −0.406772 0.704550i
\(299\) 6.33815 10.9780i 0.366545 0.634874i
\(300\) −11.9382 −0.689252
\(301\) 4.58794 + 25.4598i 0.264444 + 1.46748i
\(302\) 12.1976 0.701890
\(303\) −22.1908 + 38.4357i −1.27483 + 2.20807i
\(304\) 3.49684 + 6.05671i 0.200558 + 0.347376i
\(305\) 2.90758 + 5.03608i 0.166488 + 0.288365i
\(306\) −0.725032 + 1.25579i −0.0414473 + 0.0717889i
\(307\) 3.14277 0.179368 0.0896838 0.995970i \(-0.471414\pi\)
0.0896838 + 0.995970i \(0.471414\pi\)
\(308\) 2.11784 + 0.761832i 0.120675 + 0.0434094i
\(309\) 3.82097 0.217367
\(310\) 2.27404 3.93875i 0.129157 0.223706i
\(311\) −12.1080 20.9717i −0.686581 1.18919i −0.972937 0.231070i \(-0.925777\pi\)
0.286356 0.958123i \(-0.407556\pi\)
\(312\) −5.92219 10.2575i −0.335278 0.580718i
\(313\) 5.17640 8.96579i 0.292588 0.506777i −0.681833 0.731508i \(-0.738817\pi\)
0.974421 + 0.224731i \(0.0721504\pi\)
\(314\) 14.3897 0.812058
\(315\) 17.2598 14.5935i 0.972477 0.822251i
\(316\) −13.3564 −0.751357
\(317\) 17.2664 29.9063i 0.969780 1.67971i 0.273594 0.961845i \(-0.411787\pi\)
0.696185 0.717862i \(-0.254879\pi\)
\(318\) 4.32025 + 7.48290i 0.242268 + 0.419620i
\(319\) −0.425341 0.736713i −0.0238145 0.0412480i
\(320\) −0.572197 + 0.991074i −0.0319868 + 0.0554027i
\(321\) −5.79784 −0.323604
\(322\) −6.99486 + 5.91431i −0.389808 + 0.329592i
\(323\) −1.35851 −0.0755896
\(324\) −12.1657 + 21.0716i −0.675871 + 1.17064i
\(325\) 6.75587 + 11.7015i 0.374748 + 0.649083i
\(326\) −8.38368 14.5210i −0.464329 0.804241i
\(327\) −5.89071 + 10.2030i −0.325757 + 0.564227i
\(328\) 4.04493 0.223344
\(329\) −0.133992 0.0481996i −0.00738720 0.00265733i
\(330\) −3.14929 −0.173363
\(331\) −2.55022 + 4.41710i −0.140173 + 0.242786i −0.927562 0.373671i \(-0.878099\pi\)
0.787389 + 0.616457i \(0.211432\pi\)
\(332\) −4.52282 7.83376i −0.248222 0.429933i
\(333\) −26.9084 46.6066i −1.47457 2.55403i
\(334\) 5.32773 9.22789i 0.291520 0.504928i
\(335\) −13.2753 −0.725306
\(336\) 1.51790 + 8.42325i 0.0828081 + 0.459526i
\(337\) 24.7613 1.34884 0.674418 0.738350i \(-0.264394\pi\)
0.674418 + 0.738350i \(0.264394\pi\)
\(338\) −0.202771 + 0.351209i −0.0110293 + 0.0191033i
\(339\) 28.7456 + 49.7888i 1.56125 + 2.70416i
\(340\) −0.111148 0.192514i −0.00602786 0.0104406i
\(341\) −1.69040 + 2.92786i −0.0915405 + 0.158553i
\(342\) −52.2080 −2.82308
\(343\) −9.44032 15.9336i −0.509729 0.860335i
\(344\) 9.77788 0.527188
\(345\) 6.40864 11.1001i 0.345030 0.597609i
\(346\) −8.96254 15.5236i −0.481829 0.834553i
\(347\) −3.21016 5.56016i −0.172331 0.298485i 0.766904 0.641762i \(-0.221796\pi\)
−0.939234 + 0.343277i \(0.888463\pi\)
\(348\) 1.61748 2.80156i 0.0867062 0.150180i
\(349\) −2.54039 −0.135984 −0.0679920 0.997686i \(-0.521659\pi\)
−0.0679920 + 0.997686i \(0.521659\pi\)
\(350\) −1.73158 9.60901i −0.0925567 0.513623i
\(351\) 52.8852 2.82281
\(352\) 0.425341 0.736713i 0.0226708 0.0392669i
\(353\) 0.603140 + 1.04467i 0.0321019 + 0.0556021i 0.881630 0.471941i \(-0.156447\pi\)
−0.849528 + 0.527543i \(0.823113\pi\)
\(354\) 13.0103 + 22.5345i 0.691489 + 1.19769i
\(355\) 6.45580 11.1818i 0.342638 0.593467i
\(356\) 14.2305 0.754216
\(357\) −1.56442 0.562753i −0.0827976 0.0297841i
\(358\) 5.28920 0.279543
\(359\) −0.157998 + 0.273661i −0.00833883 + 0.0144433i −0.870165 0.492761i \(-0.835988\pi\)
0.861826 + 0.507204i \(0.169321\pi\)
\(360\) −4.27146 7.39838i −0.225126 0.389929i
\(361\) −14.9558 25.9043i −0.787149 1.36338i
\(362\) −6.58553 + 11.4065i −0.346128 + 0.599511i
\(363\) −33.2436 −1.74484
\(364\) 7.39726 6.25455i 0.387722 0.327827i
\(365\) −8.36640 −0.437917
\(366\) 8.21914 14.2360i 0.429621 0.744126i
\(367\) −12.1499 21.0442i −0.634217 1.09850i −0.986680 0.162671i \(-0.947989\pi\)
0.352463 0.935826i \(-0.385344\pi\)
\(368\) 1.73109 + 2.99834i 0.0902395 + 0.156299i
\(369\) −15.0977 + 26.1500i −0.785956 + 1.36132i
\(370\) 8.25016 0.428905
\(371\) −5.39632 + 4.56271i −0.280163 + 0.236884i
\(372\) −12.8565 −0.666578
\(373\) 4.99255 8.64735i 0.258504 0.447743i −0.707337 0.706876i \(-0.750104\pi\)
0.965841 + 0.259134i \(0.0834370\pi\)
\(374\) 0.0826218 + 0.143105i 0.00427227 + 0.00739979i
\(375\) 16.0862 + 27.8621i 0.830687 + 1.43879i
\(376\) −0.0269105 + 0.0466104i −0.00138781 + 0.00240375i
\(377\) −3.66136 −0.188570
\(378\) −35.9598 12.9355i −1.84957 0.665331i
\(379\) −13.0891 −0.672343 −0.336172 0.941801i \(-0.609132\pi\)
−0.336172 + 0.941801i \(0.609132\pi\)
\(380\) 4.00177 6.93126i 0.205286 0.355566i
\(381\) 18.7287 + 32.4391i 0.959503 + 1.66191i
\(382\) −4.95435 8.58118i −0.253486 0.439051i
\(383\) 1.48195 2.56681i 0.0757241 0.131158i −0.825677 0.564143i \(-0.809206\pi\)
0.901401 + 0.432985i \(0.142540\pi\)
\(384\) 3.23497 0.165084
\(385\) −0.456789 2.53485i −0.0232801 0.129188i
\(386\) −17.3950 −0.885384
\(387\) −36.4960 + 63.2129i −1.85520 + 3.21329i
\(388\) −9.38894 16.2621i −0.476651 0.825584i
\(389\) 17.4557 + 30.2342i 0.885040 + 1.53293i 0.845667 + 0.533710i \(0.179203\pi\)
0.0393729 + 0.999225i \(0.487464\pi\)
\(390\) −6.77731 + 11.7387i −0.343183 + 0.594410i
\(391\) −0.672523 −0.0340110
\(392\) −6.55967 + 2.44350i −0.331314 + 0.123415i
\(393\) −52.3985 −2.64316
\(394\) −8.79804 + 15.2386i −0.443239 + 0.767712i
\(395\) 7.64250 + 13.2372i 0.384536 + 0.666036i
\(396\) 3.17518 + 5.49957i 0.159559 + 0.276364i
\(397\) −7.70778 + 13.3503i −0.386842 + 0.670031i −0.992023 0.126057i \(-0.959768\pi\)
0.605180 + 0.796088i \(0.293101\pi\)
\(398\) 11.2846 0.565645
\(399\) −10.6157 58.9096i −0.531450 2.94917i
\(400\) −3.69036 −0.184518
\(401\) −19.0183 + 32.9406i −0.949728 + 1.64498i −0.203731 + 0.979027i \(0.565307\pi\)
−0.745996 + 0.665950i \(0.768026\pi\)
\(402\) 18.7632 + 32.4989i 0.935825 + 1.62090i
\(403\) 7.27553 + 12.6016i 0.362420 + 0.627730i
\(404\) −6.85968 + 11.8813i −0.341282 + 0.591118i
\(405\) 27.8447 1.38361
\(406\) 2.48958 + 0.895553i 0.123556 + 0.0444456i
\(407\) −6.13274 −0.303989
\(408\) −0.314193 + 0.544199i −0.0155549 + 0.0269418i
\(409\) 14.6428 + 25.3621i 0.724041 + 1.25408i 0.959368 + 0.282159i \(0.0910506\pi\)
−0.235327 + 0.971916i \(0.575616\pi\)
\(410\) −2.31450 4.00883i −0.114305 0.197982i
\(411\) 20.6783 35.8159i 1.01999 1.76667i
\(412\) 1.18115 0.0581909
\(413\) −16.2508 + 13.7405i −0.799652 + 0.676123i
\(414\) −25.8453 −1.27023
\(415\) −5.17589 + 8.96490i −0.254074 + 0.440070i
\(416\) −1.83068 3.17083i −0.0897564 0.155463i
\(417\) −0.275902 0.477875i −0.0135110 0.0234017i
\(418\) −2.97471 + 5.15234i −0.145498 + 0.252009i
\(419\) −6.29412 −0.307488 −0.153744 0.988111i \(-0.549133\pi\)
−0.153744 + 0.988111i \(0.549133\pi\)
\(420\) 7.47952 6.32410i 0.364963 0.308585i
\(421\) 2.94479 0.143520 0.0717602 0.997422i \(-0.477138\pi\)
0.0717602 + 0.997422i \(0.477138\pi\)
\(422\) 4.93786 8.55262i 0.240371 0.416335i
\(423\) −0.200887 0.347947i −0.00976748 0.0169178i
\(424\) 1.33549 + 2.31313i 0.0648570 + 0.112336i
\(425\) 0.358423 0.620807i 0.0173861 0.0301136i
\(426\) −36.4984 −1.76836
\(427\) 12.6506 + 4.55070i 0.612206 + 0.220224i
\(428\) −1.79224 −0.0866313
\(429\) 5.03790 8.72590i 0.243232 0.421290i
\(430\) −5.59487 9.69060i −0.269809 0.467322i
\(431\) −2.72971 4.72800i −0.131486 0.227740i 0.792764 0.609529i \(-0.208641\pi\)
−0.924249 + 0.381789i \(0.875308\pi\)
\(432\) −7.22208 + 12.5090i −0.347473 + 0.601840i
\(433\) −16.9899 −0.816482 −0.408241 0.912874i \(-0.633858\pi\)
−0.408241 + 0.912874i \(0.633858\pi\)
\(434\) −1.86477 10.3481i −0.0895118 0.496727i
\(435\) −3.70208 −0.177501
\(436\) −1.82095 + 3.15397i −0.0872076 + 0.151048i
\(437\) −12.1067 20.9695i −0.579143 1.00311i
\(438\) 11.8250 + 20.4816i 0.565023 + 0.978648i
\(439\) 11.3210 19.6085i 0.540321 0.935863i −0.458565 0.888661i \(-0.651636\pi\)
0.998885 0.0472016i \(-0.0150303\pi\)
\(440\) −0.973516 −0.0464106
\(441\) 8.68706 51.5279i 0.413670 2.45371i
\(442\) 0.711212 0.0338289
\(443\) 8.56936 14.8426i 0.407143 0.705192i −0.587426 0.809278i \(-0.699859\pi\)
0.994568 + 0.104086i \(0.0331919\pi\)
\(444\) −11.6608 20.1970i −0.553395 0.958508i
\(445\) −8.14266 14.1035i −0.385999 0.668570i
\(446\) 8.29908 14.3744i 0.392973 0.680649i
\(447\) 45.4317 2.14885
\(448\) 0.469216 + 2.60381i 0.0221684 + 0.123019i
\(449\) −12.1802 −0.574818 −0.287409 0.957808i \(-0.592794\pi\)
−0.287409 + 0.957808i \(0.592794\pi\)
\(450\) 13.7743 23.8578i 0.649327 1.12467i
\(451\) 1.72048 + 2.97995i 0.0810141 + 0.140321i
\(452\) 8.88590 + 15.3908i 0.417958 + 0.723924i
\(453\) −19.7293 + 34.1722i −0.926965 + 1.60555i
\(454\) 17.9930 0.844455
\(455\) −10.4314 3.75240i −0.489032 0.175915i
\(456\) −22.6244 −1.05948
\(457\) −15.7551 + 27.2886i −0.736991 + 1.27651i 0.216853 + 0.976204i \(0.430421\pi\)
−0.953844 + 0.300302i \(0.902912\pi\)
\(458\) 1.01911 + 1.76514i 0.0476197 + 0.0824797i
\(459\) −1.40288 2.42985i −0.0654806 0.113416i
\(460\) 1.98105 3.43128i 0.0923671 0.159984i
\(461\) −6.40796 −0.298448 −0.149224 0.988803i \(-0.547678\pi\)
−0.149224 + 0.988803i \(0.547678\pi\)
\(462\) −5.55989 + 4.70101i −0.258669 + 0.218711i
\(463\) −0.902939 −0.0419632 −0.0209816 0.999780i \(-0.506679\pi\)
−0.0209816 + 0.999780i \(0.506679\pi\)
\(464\) 0.500000 0.866025i 0.0232119 0.0402042i
\(465\) 7.35645 + 12.7417i 0.341147 + 0.590884i
\(466\) 8.24947 + 14.2885i 0.382149 + 0.661902i
\(467\) 18.2056 31.5330i 0.842454 1.45917i −0.0453601 0.998971i \(-0.514444\pi\)
0.887814 0.460202i \(-0.152223\pi\)
\(468\) 27.3321 1.26343
\(469\) −23.4367 + 19.8163i −1.08221 + 0.915030i
\(470\) 0.0615925 0.00284105
\(471\) −23.2751 + 40.3137i −1.07246 + 1.85756i
\(472\) 4.02177 + 6.96591i 0.185117 + 0.320632i
\(473\) 4.15894 + 7.20349i 0.191228 + 0.331217i
\(474\) 21.6038 37.4188i 0.992294 1.71870i
\(475\) 25.8092 1.18421
\(476\) −0.483595 0.173960i −0.0221656 0.00797342i
\(477\) −19.9388 −0.912937
\(478\) −9.37071 + 16.2305i −0.428606 + 0.742368i
\(479\) −15.7142 27.2177i −0.717998 1.24361i −0.961792 0.273782i \(-0.911725\pi\)
0.243794 0.969827i \(-0.421608\pi\)
\(480\) −1.85104 3.20609i −0.0844880 0.146337i
\(481\) −13.1977 + 22.8591i −0.601764 + 1.04229i
\(482\) 17.8781 0.814323
\(483\) −5.25525 29.1628i −0.239122 1.32696i
\(484\) −10.2763 −0.467106
\(485\) −10.7446 + 18.6103i −0.487889 + 0.845049i
\(486\) −17.6893 30.6388i −0.802404 1.38980i
\(487\) −7.22298 12.5106i −0.327304 0.566908i 0.654672 0.755913i \(-0.272807\pi\)
−0.981976 + 0.189006i \(0.939474\pi\)
\(488\) 2.54072 4.40065i 0.115013 0.199208i
\(489\) 54.2418 2.45290
\(490\) 6.17511 + 5.10296i 0.278963 + 0.230528i
\(491\) 29.2405 1.31961 0.659803 0.751439i \(-0.270640\pi\)
0.659803 + 0.751439i \(0.270640\pi\)
\(492\) −6.54261 + 11.3321i −0.294964 + 0.510892i
\(493\) 0.0971241 + 0.168224i 0.00437425 + 0.00757642i
\(494\) 12.8032 + 22.1758i 0.576043 + 0.997736i
\(495\) 3.63365 6.29367i 0.163321 0.282880i
\(496\) −3.97423 −0.178448
\(497\) −5.29392 29.3774i −0.237465 1.31776i
\(498\) 29.2624 1.31128
\(499\) −14.2452 + 24.6735i −0.637704 + 1.10454i 0.348231 + 0.937409i \(0.386782\pi\)
−0.985935 + 0.167127i \(0.946551\pi\)
\(500\) 4.97260 + 8.61279i 0.222381 + 0.385176i
\(501\) 17.2350 + 29.8519i 0.770004 + 1.33369i
\(502\) 0.846243 1.46574i 0.0377697 0.0654190i
\(503\) 19.9091 0.887701 0.443850 0.896101i \(-0.353612\pi\)
0.443850 + 0.896101i \(0.353612\pi\)
\(504\) −18.5847 6.68531i −0.827829 0.297788i
\(505\) 15.7004 0.698657
\(506\) −1.47261 + 2.55064i −0.0654656 + 0.113390i
\(507\) −0.655956 1.13615i −0.0291321 0.0504582i
\(508\) 5.78947 + 10.0277i 0.256866 + 0.444905i
\(509\) −1.78599 + 3.09343i −0.0791628 + 0.137114i −0.902889 0.429874i \(-0.858558\pi\)
0.823726 + 0.566988i \(0.191891\pi\)
\(510\) 0.719122 0.0318432
\(511\) −14.7704 + 12.4887i −0.653403 + 0.552467i
\(512\) 1.00000 0.0441942
\(513\) 50.5090 87.4841i 2.23003 3.86252i
\(514\) −1.77662 3.07719i −0.0783633 0.135729i
\(515\) −0.675848 1.17060i −0.0297814 0.0515829i
\(516\) −15.8156 + 27.3934i −0.696241 + 1.20593i
\(517\) −0.0457847 −0.00201361
\(518\) 14.5652 12.3152i 0.639956 0.541097i
\(519\) 57.9871 2.54535
\(520\) −2.09502 + 3.62868i −0.0918726 + 0.159128i
\(521\) 4.68438 + 8.11359i 0.205227 + 0.355463i 0.950205 0.311626i \(-0.100874\pi\)
−0.744978 + 0.667089i \(0.767540\pi\)
\(522\) 3.73251 + 6.46489i 0.163367 + 0.282960i
\(523\) 6.80794 11.7917i 0.297690 0.515615i −0.677917 0.735139i \(-0.737117\pi\)
0.975607 + 0.219524i \(0.0704504\pi\)
\(524\) −16.1976 −0.707593
\(525\) 29.7210 + 10.6913i 1.29713 + 0.466606i
\(526\) −18.3627 −0.800653
\(527\) 0.385993 0.668560i 0.0168141 0.0291229i
\(528\) 1.37597 + 2.38324i 0.0598812 + 0.103717i
\(529\) 5.50663 + 9.53777i 0.239419 + 0.414686i
\(530\) 1.52832 2.64713i 0.0663861 0.114984i
\(531\) −60.0451 −2.60574
\(532\) −3.28155 18.2102i −0.142273 0.789514i
\(533\) 14.8099 0.641490
\(534\) −23.0176 + 39.8677i −0.996070 + 1.72524i
\(535\) 1.02552 + 1.77624i 0.0443369 + 0.0767937i
\(536\) 5.80013 + 10.0461i 0.250528 + 0.433927i
\(537\) −8.55519 + 14.8180i −0.369184 + 0.639445i
\(538\) 18.1820 0.783883
\(539\) −4.59026 3.79327i −0.197716 0.163388i
\(540\) 16.5298 0.711330
\(541\) −5.34851 + 9.26389i −0.229951 + 0.398286i −0.957793 0.287458i \(-0.907190\pi\)
0.727843 + 0.685744i \(0.240523\pi\)
\(542\) 3.65352 + 6.32808i 0.156932 + 0.271814i
\(543\) −21.3040 36.8995i −0.914240 1.58351i
\(544\) −0.0971241 + 0.168224i −0.00416416 + 0.00721254i
\(545\) 4.16776 0.178527
\(546\) 5.55757 + 30.8405i 0.237842 + 1.31985i
\(547\) −23.6925 −1.01302 −0.506509 0.862235i \(-0.669064\pi\)
−0.506509 + 0.862235i \(0.669064\pi\)
\(548\) 6.39212 11.0715i 0.273058 0.472950i
\(549\) 18.9665 + 32.8509i 0.809470 + 1.40204i
\(550\) −1.56966 2.71874i −0.0669307 0.115927i
\(551\) −3.49684 + 6.05671i −0.148971 + 0.258025i
\(552\) −11.2001 −0.476706
\(553\) 33.2518 + 11.9614i 1.41401 + 0.508649i
\(554\) −16.6420 −0.707049
\(555\) −13.3445 + 23.1133i −0.566442 + 0.981107i
\(556\) −0.0852873 0.147722i −0.00361699 0.00626480i
\(557\) −6.13907 10.6332i −0.260121 0.450543i 0.706153 0.708059i \(-0.250429\pi\)
−0.966274 + 0.257517i \(0.917096\pi\)
\(558\) 14.8338 25.6929i 0.627966 1.08767i
\(559\) 35.8003 1.51419
\(560\) 2.31209 1.95492i 0.0977035 0.0826105i
\(561\) −0.534558 −0.0225690
\(562\) −6.62811 + 11.4802i −0.279590 + 0.484264i
\(563\) −18.6915 32.3747i −0.787755 1.36443i −0.927340 0.374221i \(-0.877910\pi\)
0.139585 0.990210i \(-0.455423\pi\)
\(564\) −0.0870547 0.150783i −0.00366566 0.00634912i
\(565\) 10.1690 17.6132i 0.427812 0.740992i
\(566\) −15.2786 −0.642207
\(567\) 49.1581 41.5642i 2.06444 1.74553i
\(568\) −11.2825 −0.473402
\(569\) 7.12391 12.3390i 0.298650 0.517277i −0.677177 0.735820i \(-0.736797\pi\)
0.975827 + 0.218543i \(0.0701304\pi\)
\(570\) 12.9456 + 22.4224i 0.542231 + 0.939171i
\(571\) 3.29932 + 5.71460i 0.138072 + 0.239148i 0.926767 0.375637i \(-0.122576\pi\)
−0.788695 + 0.614785i \(0.789243\pi\)
\(572\) 1.55733 2.69737i 0.0651151 0.112783i
\(573\) 32.0543 1.33909
\(574\) −10.0702 3.62245i −0.420320 0.151198i
\(575\) 12.7767 0.532826
\(576\) −3.73251 + 6.46489i −0.155521 + 0.269370i
\(577\) 10.5455 + 18.2654i 0.439016 + 0.760398i 0.997614 0.0690406i \(-0.0219938\pi\)
−0.558598 + 0.829439i \(0.688660\pi\)
\(578\) 8.48113 + 14.6898i 0.352769 + 0.611013i
\(579\) 28.1362 48.7333i 1.16930 2.02529i
\(580\) −1.14439 −0.0475184
\(581\) 4.24436 + 23.5532i 0.176086 + 0.977149i
\(582\) 60.7458 2.51800
\(583\) −1.13608 + 1.96774i −0.0470514 + 0.0814955i
\(584\) 3.65539 + 6.33131i 0.151261 + 0.261992i
\(585\) −15.6393 27.0881i −0.646607 1.11996i
\(586\) 7.75956 13.4400i 0.320545 0.555199i
\(587\) 23.5851 0.973459 0.486730 0.873553i \(-0.338190\pi\)
0.486730 + 0.873553i \(0.338190\pi\)
\(588\) 3.76454 22.3297i 0.155247 0.920860i
\(589\) 27.7945 1.14525
\(590\) 4.60249 7.97175i 0.189482 0.328192i
\(591\) −28.4614 49.2965i −1.17074 2.02779i
\(592\) −3.60460 6.24335i −0.148148 0.256600i
\(593\) 12.4404 21.5474i 0.510865 0.884844i −0.489056 0.872253i \(-0.662659\pi\)
0.999921 0.0125916i \(-0.00400813\pi\)
\(594\) −12.2874 −0.504158
\(595\) 0.104305 + 0.578818i 0.00427609 + 0.0237292i
\(596\) 14.0440 0.575263
\(597\) −18.2526 + 31.6145i −0.747031 + 1.29390i
\(598\) 6.33815 + 10.9780i 0.259186 + 0.448924i
\(599\) −2.38954 4.13880i −0.0976338 0.169107i 0.813071 0.582165i \(-0.197794\pi\)
−0.910705 + 0.413058i \(0.864461\pi\)
\(600\) 5.96910 10.3388i 0.243687 0.422079i
\(601\) −44.3292 −1.80823 −0.904113 0.427292i \(-0.859467\pi\)
−0.904113 + 0.427292i \(0.859467\pi\)
\(602\) −24.3428 8.75661i −0.992137 0.356893i
\(603\) −86.5961 −3.52647
\(604\) −6.09878 + 10.5634i −0.248156 + 0.429818i
\(605\) 5.88009 + 10.1846i 0.239060 + 0.414063i
\(606\) −22.1908 38.4357i −0.901442 1.56134i
\(607\) −21.4496 + 37.1518i −0.870613 + 1.50795i −0.00924938 + 0.999957i \(0.502944\pi\)
−0.861364 + 0.507989i \(0.830389\pi\)
\(608\) −6.99369 −0.283632
\(609\) −6.53580 + 5.52616i −0.264844 + 0.223931i
\(610\) −5.81517 −0.235449
\(611\) −0.0985291 + 0.170657i −0.00398606 + 0.00690406i
\(612\) −0.725032 1.25579i −0.0293077 0.0507624i
\(613\) −13.0203 22.5518i −0.525884 0.910857i −0.999545 0.0301503i \(-0.990401\pi\)
0.473662 0.880707i \(-0.342932\pi\)
\(614\) −1.57139 + 2.72172i −0.0634160 + 0.109840i
\(615\) 14.9746 0.603836
\(616\) −1.71868 + 1.45319i −0.0692478 + 0.0585505i
\(617\) −38.2301 −1.53909 −0.769543 0.638595i \(-0.779516\pi\)
−0.769543 + 0.638595i \(0.779516\pi\)
\(618\) −1.91048 + 3.30905i −0.0768509 + 0.133110i
\(619\) −16.9206 29.3074i −0.680098 1.17796i −0.974951 0.222421i \(-0.928604\pi\)
0.294853 0.955543i \(-0.404729\pi\)
\(620\) 2.27404 + 3.93875i 0.0913277 + 0.158184i
\(621\) 25.0042 43.3085i 1.00338 1.73791i
\(622\) 24.2160 0.970973
\(623\) −35.4280 12.7442i −1.41939 0.510585i
\(624\) 11.8444 0.474154
\(625\) −3.53529 + 6.12331i −0.141412 + 0.244932i
\(626\) 5.17640 + 8.96579i 0.206891 + 0.358345i
\(627\) −9.62307 16.6677i −0.384309 0.665642i
\(628\) −7.19485 + 12.4618i −0.287106 + 0.497282i
\(629\) 1.40037 0.0558365
\(630\) 4.00847 + 22.2441i 0.159701 + 0.886228i
\(631\) −36.3237 −1.44602 −0.723012 0.690835i \(-0.757243\pi\)
−0.723012 + 0.690835i \(0.757243\pi\)
\(632\) 6.67821 11.5670i 0.265645 0.460110i
\(633\) 15.9738 + 27.6675i 0.634902 + 1.09968i
\(634\) 17.2664 + 29.9063i 0.685738 + 1.18773i
\(635\) 6.62543 11.4756i 0.262922 0.455395i
\(636\) −8.64051 −0.342618
\(637\) −24.0173 + 8.94653i −0.951600 + 0.354474i
\(638\) 0.850683 0.0336789
\(639\) 42.1119 72.9400i 1.66592 2.88546i
\(640\) −0.572197 0.991074i −0.0226181 0.0391756i
\(641\) 2.50688 + 4.34204i 0.0990157 + 0.171500i 0.911278 0.411793i \(-0.135097\pi\)
−0.812262 + 0.583293i \(0.801764\pi\)
\(642\) 2.89892 5.02108i 0.114411 0.198166i
\(643\) −21.6758 −0.854811 −0.427406 0.904060i \(-0.640572\pi\)
−0.427406 + 0.904060i \(0.640572\pi\)
\(644\) −1.62451 9.01488i −0.0640148 0.355236i
\(645\) 36.1985 1.42531
\(646\) 0.679256 1.17651i 0.0267250 0.0462890i
\(647\) 11.5473 + 20.0005i 0.453970 + 0.786299i 0.998628 0.0523591i \(-0.0166740\pi\)
−0.544658 + 0.838658i \(0.683341\pi\)
\(648\) −12.1657 21.0716i −0.477913 0.827769i
\(649\) −3.42125 + 5.92578i −0.134296 + 0.232607i
\(650\) −13.5117 −0.529974
\(651\) 32.0072 + 11.5137i 1.25446 + 0.451256i
\(652\) 16.7674 0.656660
\(653\) 16.9620 29.3790i 0.663774 1.14969i −0.315842 0.948812i \(-0.602287\pi\)
0.979616 0.200879i \(-0.0643798\pi\)
\(654\) −5.89071 10.2030i −0.230345 0.398969i
\(655\) 9.26819 + 16.0530i 0.362138 + 0.627242i
\(656\) −2.02247 + 3.50301i −0.0789640 + 0.136770i
\(657\) −54.5750 −2.12917
\(658\) 0.108738 0.0919403i 0.00423905 0.00358421i
\(659\) −5.52520 −0.215231 −0.107616 0.994193i \(-0.534322\pi\)
−0.107616 + 0.994193i \(0.534322\pi\)
\(660\) 1.57465 2.72737i 0.0612930 0.106163i
\(661\) 0.811825 + 1.40612i 0.0315763 + 0.0546918i 0.881382 0.472405i \(-0.156614\pi\)
−0.849805 + 0.527097i \(0.823281\pi\)
\(662\) −2.55022 4.41710i −0.0991170 0.171676i
\(663\) −1.15037 + 1.99251i −0.0446768 + 0.0773825i
\(664\) 9.04564 0.351039
\(665\) −16.1700 + 13.6721i −0.627046 + 0.530182i
\(666\) 53.8167 2.08536
\(667\) −1.73109 + 2.99834i −0.0670282 + 0.116096i
\(668\) 5.32773 + 9.22789i 0.206136 + 0.357038i
\(669\) 26.8473 + 46.5008i 1.03798 + 1.79783i
\(670\) 6.63764 11.4967i 0.256434 0.444157i
\(671\) 4.32269 0.166876
\(672\) −8.05369 2.89708i −0.310678 0.111757i
\(673\) −1.69886 −0.0654862 −0.0327431 0.999464i \(-0.510424\pi\)
−0.0327431 + 0.999464i \(0.510424\pi\)
\(674\) −12.3807 + 21.4440i −0.476886 + 0.825990i
\(675\) 26.6521 + 46.1628i 1.02584 + 1.77681i
\(676\) −0.202771 0.351209i −0.00779887 0.0135080i
\(677\) −10.3638 + 17.9507i −0.398314 + 0.689900i −0.993518 0.113674i \(-0.963738\pi\)
0.595204 + 0.803575i \(0.297071\pi\)
\(678\) −57.4912 −2.20794
\(679\) 8.81088 + 48.8941i 0.338130 + 1.87638i
\(680\) 0.222296 0.00852468
\(681\) −29.1034 + 50.4086i −1.11525 + 1.93166i
\(682\) −1.69040 2.92786i −0.0647289 0.112114i
\(683\) 15.1908 + 26.3113i 0.581261 + 1.00677i 0.995330 + 0.0965286i \(0.0307739\pi\)
−0.414069 + 0.910246i \(0.635893\pi\)
\(684\) 26.1040 45.2134i 0.998111 1.72878i
\(685\) −14.6302 −0.558991
\(686\) 18.5191 0.208741i 0.707062 0.00796975i
\(687\) −6.59355 −0.251560
\(688\) −4.88894 + 8.46789i −0.186389 + 0.322835i
\(689\) 4.88969 + 8.46920i 0.186282 + 0.322651i
\(690\) 6.40864 + 11.1001i 0.243973 + 0.422573i
\(691\) 2.31023 4.00144i 0.0878853 0.152222i −0.818732 0.574176i \(-0.805322\pi\)
0.906617 + 0.421954i \(0.138656\pi\)
\(692\) 17.9251 0.681409
\(693\) −2.97969 16.5351i −0.113189 0.628118i
\(694\) 6.42032 0.243712
\(695\) −0.0976022 + 0.169052i −0.00370226 + 0.00641251i
\(696\) 1.61748 + 2.80156i 0.0613106 + 0.106193i
\(697\) −0.392860 0.680454i −0.0148806 0.0257740i
\(698\) 1.27020 2.20004i 0.0480776 0.0832729i
\(699\) −53.3735 −2.01877
\(700\) 9.18743 + 3.30492i 0.347252 + 0.124914i
\(701\) 36.9179 1.39437 0.697186 0.716890i \(-0.254435\pi\)
0.697186 + 0.716890i \(0.254435\pi\)
\(702\) −26.4426 + 45.8000i −0.998012 + 1.72861i
\(703\) 25.2094 + 43.6640i 0.950792 + 1.64682i
\(704\) 0.425341 + 0.736713i 0.0160307 + 0.0277659i
\(705\) −0.0996249 + 0.172555i −0.00375209 + 0.00649881i
\(706\) −1.20628 −0.0453989
\(707\) 27.7181 23.4362i 1.04244 0.881410i
\(708\) −26.0206 −0.977914
\(709\) 16.0371 27.7771i 0.602286 1.04319i −0.390189 0.920735i \(-0.627590\pi\)
0.992474 0.122454i \(-0.0390765\pi\)
\(710\) 6.45580 + 11.1818i 0.242282 + 0.419644i
\(711\) 49.8529 + 86.3477i 1.86963 + 3.23829i
\(712\) −7.11526 + 12.3240i −0.266656 + 0.461861i
\(713\) 13.7595 0.515298
\(714\) 1.26957 1.07345i 0.0475123 0.0401727i
\(715\) −3.56439 −0.133301
\(716\) −2.64460 + 4.58058i −0.0988333 + 0.171184i
\(717\) −30.3139 52.5053i −1.13209 1.96085i
\(718\) −0.157998 0.273661i −0.00589644 0.0102129i
\(719\) −17.9177 + 31.0344i −0.668218 + 1.15739i 0.310184 + 0.950676i \(0.399609\pi\)
−0.978402 + 0.206711i \(0.933724\pi\)
\(720\) 8.54291 0.318376
\(721\) −2.94055 1.05778i −0.109512 0.0393937i
\(722\) 29.9117 1.11320
\(723\) −28.9175 + 50.0865i −1.07545 + 1.86274i
\(724\) −6.58553 11.4065i −0.244749 0.423918i
\(725\) −1.84518 3.19595i −0.0685283 0.118695i
\(726\) 16.6218 28.7898i 0.616893 1.06849i
\(727\) −12.8401 −0.476215 −0.238107 0.971239i \(-0.576527\pi\)
−0.238107 + 0.971239i \(0.576527\pi\)
\(728\) 1.71797 + 9.53349i 0.0636721 + 0.353335i
\(729\) 41.4546 1.53536
\(730\) 4.18320 7.24552i 0.154827 0.268169i
\(731\) −0.949668 1.64487i −0.0351247 0.0608378i
\(732\) 8.21914 + 14.2360i 0.303788 + 0.526177i
\(733\) 4.56646 7.90935i 0.168666 0.292138i −0.769285 0.638906i \(-0.779387\pi\)
0.937951 + 0.346767i \(0.112721\pi\)
\(734\) 24.2997 0.896919
\(735\) −24.2844 + 9.04602i −0.895744 + 0.333668i
\(736\) −3.46219 −0.127618
\(737\) −4.93407 + 8.54607i −0.181749 + 0.314798i
\(738\) −15.0977 26.1500i −0.555755 0.962596i
\(739\) −3.16227 5.47721i −0.116326 0.201482i 0.801983 0.597347i \(-0.203778\pi\)
−0.918309 + 0.395864i \(0.870445\pi\)
\(740\) −4.12508 + 7.14485i −0.151641 + 0.262650i
\(741\) −82.8358 −3.04305
\(742\) −1.25326 6.95471i −0.0460087 0.255315i
\(743\) 32.2973 1.18487 0.592436 0.805618i \(-0.298166\pi\)
0.592436 + 0.805618i \(0.298166\pi\)
\(744\) 6.42825 11.1340i 0.235671 0.408194i
\(745\) −8.03591 13.9186i −0.294413 0.509938i
\(746\) 4.99255 + 8.64735i 0.182790 + 0.316602i
\(747\) −33.7629 + 58.4791i −1.23532 + 2.13964i
\(748\) −0.165244 −0.00604190
\(749\) 4.46192 + 1.60505i 0.163035 + 0.0586472i
\(750\) −32.1724 −1.17477
\(751\) −9.93095 + 17.2009i −0.362385 + 0.627670i −0.988353 0.152179i \(-0.951371\pi\)
0.625968 + 0.779849i \(0.284704\pi\)
\(752\) −0.0269105 0.0466104i −0.000981327 0.00169971i
\(753\) 2.73757 + 4.74161i 0.0997625 + 0.172794i
\(754\) 1.83068 3.17083i 0.0666694 0.115475i
\(755\) 13.9588 0.508013
\(756\) 29.1824 24.6744i 1.06135 0.897398i
\(757\) 24.1136 0.876425 0.438213 0.898871i \(-0.355612\pi\)
0.438213 + 0.898871i \(0.355612\pi\)
\(758\) 6.54456 11.3355i 0.237709 0.411725i
\(759\) −4.76385 8.25123i −0.172917 0.299501i
\(760\) 4.00177 + 6.93126i 0.145159 + 0.251423i
\(761\) −19.8123 + 34.3158i −0.718194 + 1.24395i 0.243521 + 0.969896i \(0.421697\pi\)
−0.961715 + 0.274052i \(0.911636\pi\)
\(762\) −37.4575 −1.35694
\(763\) 7.35794 6.22130i 0.266375 0.225226i
\(764\) 9.90869 0.358484
\(765\) −0.829723 + 1.43712i −0.0299987 + 0.0519592i
\(766\) 1.48195 + 2.56681i 0.0535451 + 0.0927428i
\(767\) 14.7251 + 25.5047i 0.531694 + 0.920921i
\(768\) −1.61748 + 2.80156i −0.0583659 + 0.101093i
\(769\) −11.8143 −0.426034 −0.213017 0.977049i \(-0.568329\pi\)
−0.213017 + 0.977049i \(0.568329\pi\)
\(770\) 2.42364 + 0.871836i 0.0873420 + 0.0314188i
\(771\) 11.4946 0.413968
\(772\) 8.69752 15.0645i 0.313030 0.542185i
\(773\) −9.01041 15.6065i −0.324082 0.561327i 0.657244 0.753678i \(-0.271722\pi\)
−0.981326 + 0.192351i \(0.938389\pi\)
\(774\) −36.4960 63.2129i −1.31182 2.27214i
\(775\) −7.33317 + 12.7014i −0.263415 + 0.456249i
\(776\) 18.7779 0.674087
\(777\) 10.9428 + 60.7248i 0.392571 + 2.17849i
\(778\) −34.9114 −1.25164
\(779\) 14.1445 24.4990i 0.506779 0.877767i
\(780\) −6.77731 11.7387i −0.242667 0.420311i
\(781\) −4.79890 8.31195i −0.171718 0.297425i
\(782\) 0.336262 0.582422i 0.0120247 0.0208274i
\(783\) −14.4442 −0.516192
\(784\) 1.16370 6.90259i 0.0415608 0.246521i
\(785\) 16.4675 0.587750
\(786\) 26.1993 45.3785i 0.934497 1.61860i
\(787\) 3.65922 + 6.33795i 0.130437 + 0.225923i 0.923845 0.382767i \(-0.125029\pi\)
−0.793408 + 0.608690i \(0.791695\pi\)
\(788\) −8.79804 15.2386i −0.313417 0.542854i
\(789\) 29.7014 51.4443i 1.05740 1.83147i
\(790\) −15.2850 −0.543816
\(791\) −8.33881 46.2744i −0.296494 1.64533i
\(792\) −6.35036 −0.225650
\(793\) 9.30248 16.1124i 0.330341 0.572167i
\(794\) −7.70778 13.3503i −0.273539 0.473783i
\(795\) 4.94407 + 8.56339i 0.175348 + 0.303712i
\(796\) −5.64229 + 9.77274i −0.199986 + 0.346386i
\(797\) 53.5394 1.89646 0.948232 0.317578i \(-0.102869\pi\)
0.948232 + 0.317578i \(0.102869\pi\)
\(798\) 56.3250 + 20.2613i 1.99388 + 0.717242i
\(799\) 0.0104546 0.000369859
\(800\) 1.84518 3.19595i 0.0652370 0.112994i
\(801\) −53.1155 91.9987i −1.87674 3.25062i
\(802\) −19.0183 32.9406i −0.671559 1.16317i
\(803\) −3.10957 + 5.38594i −0.109734 + 0.190066i
\(804\) −37.5265 −1.32346
\(805\) −8.00488 + 6.76830i −0.282135 + 0.238551i
\(806\) −14.5511 −0.512540
\(807\) −29.4091 + 50.9381i −1.03525 + 1.79311i
\(808\) −6.85968 11.8813i −0.241323 0.417983i
\(809\) −4.44663 7.70178i −0.156335 0.270780i 0.777209 0.629242i \(-0.216635\pi\)
−0.933544 + 0.358462i \(0.883301\pi\)
\(810\) −13.9223 + 24.1142i −0.489181 + 0.847286i
\(811\) 4.11053 0.144340 0.0721701 0.997392i \(-0.477008\pi\)
0.0721701 + 0.997392i \(0.477008\pi\)
\(812\) −2.02036 + 1.70826i −0.0709007 + 0.0599481i
\(813\) −23.6380 −0.829021
\(814\) 3.06637 5.31111i 0.107476 0.186154i
\(815\) −9.59423 16.6177i −0.336071 0.582092i
\(816\) −0.314193 0.544199i −0.0109990 0.0190508i
\(817\) 34.1917 59.2218i 1.19622 2.07191i
\(818\) −29.2856 −1.02395
\(819\) −68.0453 24.4773i −2.37769 0.855307i
\(820\) 4.62899 0.161652
\(821\) −7.10319 + 12.3031i −0.247903 + 0.429381i −0.962944 0.269702i \(-0.913075\pi\)
0.715041 + 0.699083i \(0.246408\pi\)
\(822\) 20.6783 + 35.8159i 0.721238 + 1.24922i
\(823\) −9.42010 16.3161i −0.328364 0.568743i 0.653823 0.756647i \(-0.273164\pi\)
−0.982187 + 0.187904i \(0.939831\pi\)
\(824\) −0.590573 + 1.02290i −0.0205736 + 0.0356345i
\(825\) 10.1556 0.353573
\(826\) −3.77416 20.9439i −0.131320 0.728731i
\(827\) 7.13405 0.248075 0.124038 0.992278i \(-0.460416\pi\)
0.124038 + 0.992278i \(0.460416\pi\)
\(828\) 12.9226 22.3827i 0.449092 0.777851i
\(829\) −0.606016 1.04965i −0.0210478 0.0364559i 0.855310 0.518117i \(-0.173367\pi\)
−0.876357 + 0.481661i \(0.840034\pi\)
\(830\) −5.17589 8.96490i −0.179658 0.311176i
\(831\) 26.9181 46.6235i 0.933778 1.61735i
\(832\) 3.66136 0.126935
\(833\) 1.04816 + 0.866171i 0.0363165 + 0.0300110i
\(834\) 0.551803 0.0191074
\(835\) 6.09702 10.5603i 0.210996 0.365456i
\(836\) −2.97471 5.15234i −0.102882 0.178197i
\(837\) 28.7022 + 49.7136i 0.992093 + 1.71836i
\(838\) 3.14706 5.45087i 0.108713 0.188297i
\(839\) 13.0004 0.448823 0.224412 0.974494i \(-0.427954\pi\)
0.224412 + 0.974494i \(0.427954\pi\)
\(840\) 1.73707 + 9.63951i 0.0599347 + 0.332595i
\(841\) 1.00000 0.0344828
\(842\) −1.47240 + 2.55026i −0.0507421 + 0.0878879i
\(843\) −21.4417 37.1382i −0.738492 1.27911i
\(844\) 4.93786 + 8.55262i 0.169968 + 0.294393i
\(845\) −0.232050 + 0.401922i −0.00798275 + 0.0138265i
\(846\) 0.401775 0.0138133
\(847\) 25.5837 + 9.20301i 0.879067 + 0.316219i
\(848\) −2.67097 −0.0917216
\(849\) 24.7129 42.8039i 0.848143 1.46903i
\(850\) 0.358423 + 0.620807i 0.0122938 + 0.0212935i
\(851\) 12.4798 + 21.6156i 0.427802 + 0.740974i
\(852\) 18.2492 31.6086i 0.625208 1.08289i
\(853\) 23.8201 0.815584 0.407792 0.913075i \(-0.366299\pi\)
0.407792 + 0.913075i \(0.366299\pi\)
\(854\) −10.2663 + 8.68041i −0.351307 + 0.297038i
\(855\) −59.7465 −2.04329
\(856\) 0.896121 1.55213i 0.0306288 0.0530506i
\(857\) 3.63570 + 6.29722i 0.124193 + 0.215109i 0.921417 0.388575i \(-0.127032\pi\)
−0.797224 + 0.603683i \(0.793699\pi\)
\(858\) 5.03790 + 8.72590i 0.171991 + 0.297897i
\(859\) −4.91631 + 8.51531i −0.167742 + 0.290539i −0.937626 0.347646i \(-0.886981\pi\)
0.769883 + 0.638185i \(0.220314\pi\)
\(860\) 11.1897 0.381567
\(861\) 26.4368 22.3529i 0.900965 0.761786i
\(862\) 5.45942 0.185949
\(863\) −10.9706 + 19.0017i −0.373445 + 0.646826i −0.990093 0.140413i \(-0.955157\pi\)
0.616648 + 0.787239i \(0.288490\pi\)
\(864\) −7.22208 12.5090i −0.245700 0.425565i
\(865\) −10.2567 17.7651i −0.348738 0.604031i
\(866\) 8.49495 14.7137i 0.288670 0.499991i
\(867\) −54.8724 −1.86356
\(868\) 9.89414 + 3.55913i 0.335829 + 0.120805i
\(869\) 11.3621 0.385432
\(870\) 1.85104 3.20609i 0.0627561 0.108697i
\(871\) 21.2364 + 36.7825i 0.719567 + 1.24633i
\(872\) −1.82095 3.15397i −0.0616651 0.106807i
\(873\) −70.0885 + 121.397i −2.37214 + 4.10866i
\(874\) 24.2135 0.819032
\(875\) −4.66644 25.8954i −0.157755 0.875425i
\(876\) −23.6501 −0.799063
\(877\) −18.2830 + 31.6670i −0.617372 + 1.06932i 0.372592 + 0.927995i \(0.378469\pi\)
−0.989963 + 0.141324i \(0.954864\pi\)
\(878\) 11.3210 + 19.6085i 0.382064 + 0.661755i
\(879\) 25.1019 + 43.4778i 0.846667 + 1.46647i
\(880\) 0.486758 0.843090i 0.0164086 0.0284206i
\(881\) −33.4505 −1.12698 −0.563489 0.826124i \(-0.690541\pi\)
−0.563489 + 0.826124i \(0.690541\pi\)
\(882\) 40.2810 + 33.2872i 1.35633 + 1.12084i
\(883\) −23.9555 −0.806166 −0.403083 0.915163i \(-0.632061\pi\)
−0.403083 + 0.915163i \(0.632061\pi\)
\(884\) −0.355606 + 0.615928i −0.0119603 + 0.0207159i
\(885\) 14.8889 + 25.7883i 0.500485 + 0.866866i
\(886\) 8.56936 + 14.8426i 0.287893 + 0.498646i
\(887\) −3.69777 + 6.40472i −0.124159 + 0.215049i −0.921404 0.388606i \(-0.872957\pi\)
0.797245 + 0.603656i \(0.206290\pi\)
\(888\) 23.3215 0.782618
\(889\) −5.43302 30.1494i −0.182218 1.01118i
\(890\) 16.2853 0.545885
\(891\) 10.3491 17.9252i 0.346709 0.600517i
\(892\) 8.29908 + 14.3744i 0.277874 + 0.481292i
\(893\) 0.188204 + 0.325979i 0.00629801 + 0.0109085i
\(894\) −22.7159 + 39.3450i −0.759732 + 1.31589i
\(895\) 6.05292 0.202327
\(896\) −2.48958 0.895553i −0.0831709 0.0299183i
\(897\) −41.0074 −1.36920
\(898\) 6.09008 10.5483i 0.203229 0.352002i
\(899\) −1.98711 3.44178i −0.0662739 0.114790i
\(900\) 13.7743 + 23.8578i 0.459143 + 0.795259i
\(901\) 0.259416 0.449321i 0.00864239 0.0149691i
\(902\) −3.44095 −0.114571
\(903\) 63.9062 54.0341i 2.12667 1.79814i
\(904\) −17.7718 −0.591081
\(905\) −7.53644 + 13.0535i −0.250520 + 0.433913i
\(906\) −19.7293 34.1722i −0.655463 1.13530i
\(907\) −14.2946 24.7590i −0.474644 0.822108i 0.524934 0.851143i \(-0.324090\pi\)
−0.999578 + 0.0290348i \(0.990757\pi\)
\(908\) −8.99651 + 15.5824i −0.298560 + 0.517121i
\(909\) 102.415 3.39690
\(910\) 8.46538 7.15767i 0.280625 0.237274i
\(911\) −15.2600 −0.505587 −0.252793 0.967520i \(-0.581349\pi\)
−0.252793 + 0.967520i \(0.581349\pi\)
\(912\) 11.3122 19.5933i 0.374584 0.648798i
\(913\) 3.84749 + 6.66404i 0.127333 + 0.220548i
\(914\) −15.7551 27.2886i −0.521132 0.902626i
\(915\) 9.40593 16.2916i 0.310951 0.538582i
\(916\) −2.03821 −0.0673444
\(917\) 40.3250 + 14.5058i 1.33165 + 0.479023i
\(918\) 2.80575 0.0926036
\(919\) 11.1510 19.3140i 0.367836 0.637111i −0.621391 0.783501i \(-0.713432\pi\)
0.989227 + 0.146390i \(0.0467654\pi\)
\(920\) 1.98105 + 3.43128i 0.0653134 + 0.113126i
\(921\) −5.08339 8.80468i −0.167503 0.290124i
\(922\) 3.20398 5.54945i 0.105517 0.182762i
\(923\) −41.3092 −1.35971
\(924\) −1.29125 7.16551i −0.0424790 0.235728i
\(925\) −26.6045 −0.874752
\(926\) 0.451470 0.781968i 0.0148362 0.0256971i
\(927\) −4.40863 7.63598i −0.144798 0.250798i
\(928\) 0.500000 + 0.866025i 0.0164133 + 0.0284287i
\(929\) 22.4850 38.9452i 0.737710 1.27775i −0.215815 0.976434i \(-0.569241\pi\)
0.953524 0.301316i \(-0.0974259\pi\)
\(930\) −14.7129 −0.482455
\(931\) −8.13858 + 48.2746i −0.266731 + 1.58214i
\(932\) −16.4989 −0.540441
\(933\) −39.1690 + 67.8426i −1.28233 + 2.22107i
\(934\) 18.2056 + 31.5330i 0.595705 + 1.03179i
\(935\) 0.0945519 + 0.163769i 0.00309218 + 0.00535581i
\(936\) −13.6660 + 23.6703i −0.446688 + 0.773687i
\(937\) 20.6347 0.674105 0.337053 0.941486i \(-0.390570\pi\)
0.337053 + 0.941486i \(0.390570\pi\)
\(938\) −5.44303 30.2049i −0.177721 0.986226i
\(939\) −33.4910 −1.09294
\(940\) −0.0307963 + 0.0533407i −0.00100446 + 0.00173978i
\(941\) −16.6294 28.8030i −0.542103 0.938950i −0.998783 0.0493189i \(-0.984295\pi\)
0.456680 0.889631i \(-0.349038\pi\)
\(942\) −23.2751 40.3137i −0.758344 1.31349i
\(943\) 7.00215 12.1281i 0.228021 0.394945i
\(944\) −8.04354 −0.261795
\(945\) −41.1522 14.8033i −1.33868 0.481552i
\(946\) −8.31787 −0.270437
\(947\) −0.0479947 + 0.0831292i −0.00155962 + 0.00270134i −0.866804 0.498649i \(-0.833830\pi\)
0.865245 + 0.501350i \(0.167163\pi\)
\(948\) 21.6038 + 37.4188i 0.701658 + 1.21531i
\(949\) 13.3837 + 23.1812i 0.434452 + 0.752494i
\(950\) −12.9046 + 22.3515i −0.418681 + 0.725177i
\(951\) −111.713 −3.62253
\(952\) 0.392451 0.331826i 0.0127194 0.0107545i
\(953\) −11.4213 −0.369974 −0.184987 0.982741i \(-0.559224\pi\)
−0.184987 + 0.982741i \(0.559224\pi\)
\(954\) 9.96942 17.2675i 0.322772 0.559057i
\(955\) −5.66972 9.82025i −0.183468 0.317776i
\(956\) −9.37071 16.2305i −0.303070 0.524933i
\(957\) −1.37597 + 2.38324i −0.0444786 + 0.0770393i
\(958\) 31.4283 1.01540
\(959\) −25.8288 + 21.8388i −0.834054 + 0.705211i
\(960\) 3.70208 0.119484
\(961\) 7.60276 13.1684i 0.245250 0.424786i
\(962\) −13.1977 22.8591i −0.425512 0.737008i
\(963\) 6.68955 + 11.5866i 0.215568 + 0.373374i
\(964\) −8.93903 + 15.4828i −0.287907 + 0.498669i
\(965\) −19.9068 −0.640822
\(966\) 27.8834 + 10.0302i 0.897133 + 0.322718i
\(967\) −9.43755 −0.303491 −0.151746 0.988420i \(-0.548489\pi\)
−0.151746 + 0.988420i \(0.548489\pi\)
\(968\) 5.13817 8.89957i 0.165147 0.286043i
\(969\) 2.19737 + 3.80596i 0.0705897 + 0.122265i
\(970\) −10.7446 18.6103i −0.344990 0.597540i
\(971\) 9.26400 16.0457i 0.297296 0.514932i −0.678220 0.734859i \(-0.737249\pi\)
0.975516 + 0.219927i \(0.0705819\pi\)
\(972\) 35.3786 1.13477
\(973\) 0.0800363 + 0.444144i 0.00256585 + 0.0142386i
\(974\) 14.4460 0.462878
\(975\) 21.8550 37.8540i 0.699921 1.21230i
\(976\) 2.54072 + 4.40065i 0.0813264 + 0.140861i
\(977\) 20.3383 + 35.2270i 0.650680 + 1.12701i 0.982958 + 0.183829i \(0.0588492\pi\)
−0.332279 + 0.943181i \(0.607817\pi\)
\(978\) −27.1209 + 46.9748i −0.867231 + 1.50209i
\(979\) −12.1057 −0.386899
\(980\) −7.50685 + 2.79633i −0.239798 + 0.0893254i
\(981\) 27.1868 0.868008
\(982\) −14.6203 + 25.3230i −0.466551 + 0.808090i
\(983\) −26.3075 45.5659i −0.839078 1.45332i −0.890667 0.454657i \(-0.849762\pi\)
0.0515893 0.998668i \(-0.483571\pi\)
\(984\) −6.54261 11.3321i −0.208571 0.361255i
\(985\) −10.0684 + 17.4390i −0.320806 + 0.555653i
\(986\) −0.194248 −0.00618612
\(987\) 0.0816949 + 0.453348i 0.00260038 + 0.0144302i
\(988\) −25.6064 −0.814648
\(989\) 16.9264 29.3174i 0.538229 0.932240i
\(990\) 3.63365 + 6.29367i 0.115485 + 0.200026i
\(991\) 12.3917 + 21.4631i 0.393637 + 0.681799i 0.992926 0.118734i \(-0.0378835\pi\)
−0.599290 + 0.800532i \(0.704550\pi\)
\(992\) 1.98711 3.44178i 0.0630909 0.109277i
\(993\) 16.4997 0.523603
\(994\) 28.0886 + 10.1041i 0.890915 + 0.320481i
\(995\) 12.9140 0.409402
\(996\) −14.6312 + 25.3419i −0.463607 + 0.802990i
\(997\) −8.09453 14.0201i −0.256356 0.444022i 0.708907 0.705302i \(-0.249189\pi\)
−0.965263 + 0.261280i \(0.915855\pi\)
\(998\) −14.2452 24.6735i −0.450925 0.781025i
\(999\) −52.0654 + 90.1799i −1.64728 + 2.85317i
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 406.2.e.a.233.1 10
7.2 even 3 2842.2.a.z.1.5 5
7.4 even 3 inner 406.2.e.a.291.1 yes 10
7.5 odd 6 2842.2.a.x.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
406.2.e.a.233.1 10 1.1 even 1 trivial
406.2.e.a.291.1 yes 10 7.4 even 3 inner
2842.2.a.x.1.1 5 7.5 odd 6
2842.2.a.z.1.5 5 7.2 even 3