Properties

Label 560.2.bd.a.141.17
Level $560$
Weight $2$
Character 560.141
Analytic conductor $4.472$
Analytic rank $0$
Dimension $44$
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] = [560,2,Mod(141,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.141");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.bd (of order \(4\), 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: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 141.17
Character \(\chi\) \(=\) 560.141
Dual form 560.2.bd.a.421.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.17062 - 0.793500i) q^{2} +(-1.25769 - 1.25769i) q^{3} +(0.740715 - 1.85778i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.47025 - 0.474301i) q^{6} -1.00000i q^{7} +(-0.607051 - 2.76252i) q^{8} +0.163545i q^{9} +O(q^{10})\) \(q+(1.17062 - 0.793500i) q^{2} +(-1.25769 - 1.25769i) q^{3} +(0.740715 - 1.85778i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.47025 - 0.474301i) q^{6} -1.00000i q^{7} +(-0.607051 - 2.76252i) q^{8} +0.163545i q^{9} +(0.266666 - 1.38884i) q^{10} +(-0.651231 + 0.651231i) q^{11} +(-3.26809 + 1.40492i) q^{12} +(1.11286 + 1.11286i) q^{13} +(-0.793500 - 1.17062i) q^{14} -1.77864 q^{15} +(-2.90268 - 2.75217i) q^{16} -0.603016 q^{17} +(0.129773 + 0.191450i) q^{18} +(-0.0481428 - 0.0481428i) q^{19} +(-0.789884 - 1.83741i) q^{20} +(-1.25769 + 1.25769i) q^{21} +(-0.245594 + 1.27910i) q^{22} -3.32354i q^{23} +(-2.71090 + 4.23785i) q^{24} -1.00000i q^{25} +(2.18580 + 0.419685i) q^{26} +(-3.56737 + 3.56737i) q^{27} +(-1.85778 - 0.740715i) q^{28} +(4.73058 + 4.73058i) q^{29} +(-2.08211 + 1.41135i) q^{30} -6.15445 q^{31} +(-5.58179 - 0.918470i) q^{32} +1.63809 q^{33} +(-0.705905 + 0.478494i) q^{34} +(-0.707107 - 0.707107i) q^{35} +(0.303831 + 0.121141i) q^{36} +(3.26170 - 3.26170i) q^{37} +(-0.0945583 - 0.0181557i) q^{38} -2.79926i q^{39} +(-2.38264 - 1.52414i) q^{40} +5.83711i q^{41} +(-0.474301 + 2.47025i) q^{42} +(6.87578 - 6.87578i) q^{43} +(0.727467 + 1.69222i) q^{44} +(0.115644 + 0.115644i) q^{45} +(-2.63723 - 3.89061i) q^{46} -5.47252 q^{47} +(0.189301 + 7.11202i) q^{48} -1.00000 q^{49} +(-0.793500 - 1.17062i) q^{50} +(0.758405 + 0.758405i) q^{51} +(2.89176 - 1.24314i) q^{52} +(8.02895 - 8.02895i) q^{53} +(-1.34533 + 7.00675i) q^{54} +0.920980i q^{55} +(-2.76252 + 0.607051i) q^{56} +0.121097i q^{57} +(9.29144 + 1.78401i) q^{58} +(3.27037 - 3.27037i) q^{59} +(-1.31746 + 3.30431i) q^{60} +(8.00019 + 8.00019i) q^{61} +(-7.20453 + 4.88355i) q^{62} +0.163545 q^{63} +(-7.26298 + 3.35397i) q^{64} +1.57382 q^{65} +(1.91758 - 1.29982i) q^{66} +(-0.200912 - 0.200912i) q^{67} +(-0.446663 + 1.12027i) q^{68} +(-4.17996 + 4.17996i) q^{69} +(-1.38884 - 0.266666i) q^{70} -1.91971i q^{71} +(0.451797 - 0.0992804i) q^{72} -7.86605i q^{73} +(1.23006 - 6.40638i) q^{74} +(-1.25769 + 1.25769i) q^{75} +(-0.125099 + 0.0537786i) q^{76} +(0.651231 + 0.651231i) q^{77} +(-2.22121 - 3.27688i) q^{78} +1.51045 q^{79} +(-3.99858 + 0.106431i) q^{80} +9.46389 q^{81} +(4.63175 + 6.83306i) q^{82} +(11.4075 + 11.4075i) q^{83} +(1.40492 + 3.26809i) q^{84} +(-0.426397 + 0.426397i) q^{85} +(2.59301 - 13.5049i) q^{86} -11.8992i q^{87} +(2.19437 + 1.40371i) q^{88} -1.79530i q^{89} +(0.227139 + 0.0436120i) q^{90} +(1.11286 - 1.11286i) q^{91} +(-6.17440 - 2.46179i) q^{92} +(7.74036 + 7.74036i) q^{93} +(-6.40626 + 4.34245i) q^{94} -0.0680842 q^{95} +(5.86499 + 8.17529i) q^{96} +4.28142 q^{97} +(-1.17062 + 0.793500i) q^{98} +(-0.106506 - 0.106506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 12 q^{4} + 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 12 q^{4} + 12 q^{6} - 4 q^{10} + 12 q^{11} - 16 q^{12} + 4 q^{14} + 8 q^{15} - 8 q^{16} - 20 q^{18} + 8 q^{19} - 36 q^{22} + 12 q^{24} + 44 q^{26} - 24 q^{27} - 4 q^{28} + 12 q^{29} - 40 q^{32} - 16 q^{34} + 4 q^{36} + 28 q^{37} - 16 q^{38} + 4 q^{42} - 44 q^{43} - 32 q^{44} - 16 q^{46} - 32 q^{48} - 44 q^{49} + 4 q^{50} - 8 q^{51} + 16 q^{52} - 12 q^{53} - 80 q^{54} + 8 q^{56} + 4 q^{58} + 24 q^{59} - 16 q^{61} + 28 q^{63} + 72 q^{64} - 40 q^{65} - 20 q^{66} - 28 q^{67} + 56 q^{68} + 40 q^{69} + 12 q^{72} + 24 q^{74} - 12 q^{77} + 84 q^{78} - 16 q^{79} + 20 q^{81} + 48 q^{82} + 16 q^{85} - 64 q^{86} + 28 q^{88} - 36 q^{90} - 16 q^{92} + 88 q^{93} + 96 q^{94} - 32 q^{95} + 48 q^{96} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.17062 0.793500i 0.827755 0.561089i
\(3\) −1.25769 1.25769i −0.726125 0.726125i 0.243720 0.969846i \(-0.421632\pi\)
−0.969846 + 0.243720i \(0.921632\pi\)
\(4\) 0.740715 1.85778i 0.370357 0.928889i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −2.47025 0.474301i −1.00847 0.193633i
\(7\) 1.00000i 0.377964i
\(8\) −0.607051 2.76252i −0.214625 0.976697i
\(9\) 0.163545i 0.0545152i
\(10\) 0.266666 1.38884i 0.0843271 0.439191i
\(11\) −0.651231 + 0.651231i −0.196354 + 0.196354i −0.798435 0.602081i \(-0.794338\pi\)
0.602081 + 0.798435i \(0.294338\pi\)
\(12\) −3.26809 + 1.40492i −0.943416 + 0.405564i
\(13\) 1.11286 + 1.11286i 0.308652 + 0.308652i 0.844387 0.535734i \(-0.179965\pi\)
−0.535734 + 0.844387i \(0.679965\pi\)
\(14\) −0.793500 1.17062i −0.212072 0.312862i
\(15\) −1.77864 −0.459242
\(16\) −2.90268 2.75217i −0.725671 0.688042i
\(17\) −0.603016 −0.146253 −0.0731265 0.997323i \(-0.523298\pi\)
−0.0731265 + 0.997323i \(0.523298\pi\)
\(18\) 0.129773 + 0.191450i 0.0305879 + 0.0451252i
\(19\) −0.0481428 0.0481428i −0.0110447 0.0110447i 0.701563 0.712608i \(-0.252486\pi\)
−0.712608 + 0.701563i \(0.752486\pi\)
\(20\) −0.789884 1.83741i −0.176623 0.410858i
\(21\) −1.25769 + 1.25769i −0.274449 + 0.274449i
\(22\) −0.245594 + 1.27910i −0.0523608 + 0.272705i
\(23\) 3.32354i 0.693005i −0.938049 0.346503i \(-0.887369\pi\)
0.938049 0.346503i \(-0.112631\pi\)
\(24\) −2.71090 + 4.23785i −0.553359 + 0.865048i
\(25\) 1.00000i 0.200000i
\(26\) 2.18580 + 0.419685i 0.428670 + 0.0823070i
\(27\) −3.56737 + 3.56737i −0.686540 + 0.686540i
\(28\) −1.85778 0.740715i −0.351087 0.139982i
\(29\) 4.73058 + 4.73058i 0.878446 + 0.878446i 0.993374 0.114928i \(-0.0366636\pi\)
−0.114928 + 0.993374i \(0.536664\pi\)
\(30\) −2.08211 + 1.41135i −0.380140 + 0.257676i
\(31\) −6.15445 −1.10537 −0.552686 0.833390i \(-0.686397\pi\)
−0.552686 + 0.833390i \(0.686397\pi\)
\(32\) −5.58179 0.918470i −0.986731 0.162364i
\(33\) 1.63809 0.285155
\(34\) −0.705905 + 0.478494i −0.121062 + 0.0820610i
\(35\) −0.707107 0.707107i −0.119523 0.119523i
\(36\) 0.303831 + 0.121141i 0.0506386 + 0.0201901i
\(37\) 3.26170 3.26170i 0.536220 0.536220i −0.386196 0.922417i \(-0.626211\pi\)
0.922417 + 0.386196i \(0.126211\pi\)
\(38\) −0.0945583 0.0181557i −0.0153394 0.00294525i
\(39\) 2.79926i 0.448240i
\(40\) −2.38264 1.52414i −0.376729 0.240988i
\(41\) 5.83711i 0.911604i 0.890081 + 0.455802i \(0.150647\pi\)
−0.890081 + 0.455802i \(0.849353\pi\)
\(42\) −0.474301 + 2.47025i −0.0731863 + 0.381168i
\(43\) 6.87578 6.87578i 1.04855 1.04855i 0.0497874 0.998760i \(-0.484146\pi\)
0.998760 0.0497874i \(-0.0158544\pi\)
\(44\) 0.727467 + 1.69222i 0.109670 + 0.255112i
\(45\) 0.115644 + 0.115644i 0.0172392 + 0.0172392i
\(46\) −2.63723 3.89061i −0.388838 0.573639i
\(47\) −5.47252 −0.798249 −0.399125 0.916897i \(-0.630686\pi\)
−0.399125 + 0.916897i \(0.630686\pi\)
\(48\) 0.189301 + 7.11202i 0.0273233 + 1.02653i
\(49\) −1.00000 −0.142857
\(50\) −0.793500 1.17062i −0.112218 0.165551i
\(51\) 0.758405 + 0.758405i 0.106198 + 0.106198i
\(52\) 2.89176 1.24314i 0.401015 0.172392i
\(53\) 8.02895 8.02895i 1.10286 1.10286i 0.108797 0.994064i \(-0.465300\pi\)
0.994064 0.108797i \(-0.0346999\pi\)
\(54\) −1.34533 + 7.00675i −0.183077 + 0.953498i
\(55\) 0.920980i 0.124185i
\(56\) −2.76252 + 0.607051i −0.369157 + 0.0811205i
\(57\) 0.121097i 0.0160397i
\(58\) 9.29144 + 1.78401i 1.22003 + 0.234252i
\(59\) 3.27037 3.27037i 0.425766 0.425766i −0.461417 0.887183i \(-0.652659\pi\)
0.887183 + 0.461417i \(0.152659\pi\)
\(60\) −1.31746 + 3.30431i −0.170084 + 0.426585i
\(61\) 8.00019 + 8.00019i 1.02432 + 1.02432i 0.999697 + 0.0246228i \(0.00783847\pi\)
0.0246228 + 0.999697i \(0.492162\pi\)
\(62\) −7.20453 + 4.88355i −0.914977 + 0.620212i
\(63\) 0.163545 0.0206048
\(64\) −7.26298 + 3.35397i −0.907872 + 0.419247i
\(65\) 1.57382 0.195209
\(66\) 1.91758 1.29982i 0.236038 0.159997i
\(67\) −0.200912 0.200912i −0.0245453 0.0245453i 0.694728 0.719273i \(-0.255525\pi\)
−0.719273 + 0.694728i \(0.755525\pi\)
\(68\) −0.446663 + 1.12027i −0.0541658 + 0.135853i
\(69\) −4.17996 + 4.17996i −0.503208 + 0.503208i
\(70\) −1.38884 0.266666i −0.165999 0.0318727i
\(71\) 1.91971i 0.227828i −0.993491 0.113914i \(-0.963661\pi\)
0.993491 0.113914i \(-0.0363388\pi\)
\(72\) 0.451797 0.0992804i 0.0532448 0.0117003i
\(73\) 7.86605i 0.920652i −0.887750 0.460326i \(-0.847733\pi\)
0.887750 0.460326i \(-0.152267\pi\)
\(74\) 1.23006 6.40638i 0.142992 0.744726i
\(75\) −1.25769 + 1.25769i −0.145225 + 0.145225i
\(76\) −0.125099 + 0.0537786i −0.0143498 + 0.00616882i
\(77\) 0.651231 + 0.651231i 0.0742147 + 0.0742147i
\(78\) −2.22121 3.27688i −0.251503 0.371033i
\(79\) 1.51045 0.169939 0.0849696 0.996384i \(-0.472921\pi\)
0.0849696 + 0.996384i \(0.472921\pi\)
\(80\) −3.99858 + 0.106431i −0.447055 + 0.0118993i
\(81\) 9.46389 1.05154
\(82\) 4.63175 + 6.83306i 0.511491 + 0.754585i
\(83\) 11.4075 + 11.4075i 1.25214 + 1.25214i 0.954760 + 0.297376i \(0.0961116\pi\)
0.297376 + 0.954760i \(0.403888\pi\)
\(84\) 1.40492 + 3.26809i 0.153289 + 0.356578i
\(85\) −0.426397 + 0.426397i −0.0462492 + 0.0462492i
\(86\) 2.59301 13.5049i 0.279612 1.45627i
\(87\) 11.8992i 1.27572i
\(88\) 2.19437 + 1.40371i 0.233920 + 0.149636i
\(89\) 1.79530i 0.190301i −0.995463 0.0951507i \(-0.969667\pi\)
0.995463 0.0951507i \(-0.0303333\pi\)
\(90\) 0.227139 + 0.0436120i 0.0239426 + 0.00459711i
\(91\) 1.11286 1.11286i 0.116660 0.116660i
\(92\) −6.17440 2.46179i −0.643725 0.256660i
\(93\) 7.74036 + 7.74036i 0.802638 + 0.802638i
\(94\) −6.40626 + 4.34245i −0.660755 + 0.447889i
\(95\) −0.0680842 −0.00698529
\(96\) 5.86499 + 8.17529i 0.598593 + 0.834387i
\(97\) 4.28142 0.434712 0.217356 0.976092i \(-0.430257\pi\)
0.217356 + 0.976092i \(0.430257\pi\)
\(98\) −1.17062 + 0.793500i −0.118251 + 0.0801556i
\(99\) −0.106506 0.106506i −0.0107043 0.0107043i
\(100\) −1.85778 0.740715i −0.185778 0.0740715i
\(101\) 1.91367 1.91367i 0.190417 0.190417i −0.605459 0.795876i \(-0.707011\pi\)
0.795876 + 0.605459i \(0.207011\pi\)
\(102\) 1.48960 + 0.286011i 0.147492 + 0.0283194i
\(103\) 13.2595i 1.30650i −0.757143 0.653249i \(-0.773406\pi\)
0.757143 0.653249i \(-0.226594\pi\)
\(104\) 2.39873 3.74986i 0.235215 0.367704i
\(105\) 1.77864i 0.173577i
\(106\) 3.02790 15.7698i 0.294095 1.53170i
\(107\) 1.20430 1.20430i 0.116424 0.116424i −0.646495 0.762918i \(-0.723766\pi\)
0.762918 + 0.646495i \(0.223766\pi\)
\(108\) 3.98498 + 9.26978i 0.383455 + 0.891985i
\(109\) 3.16834 + 3.16834i 0.303472 + 0.303472i 0.842371 0.538898i \(-0.181159\pi\)
−0.538898 + 0.842371i \(0.681159\pi\)
\(110\) 0.730798 + 1.07812i 0.0696789 + 0.102795i
\(111\) −8.20438 −0.778726
\(112\) −2.75217 + 2.90268i −0.260055 + 0.274278i
\(113\) 11.7295 1.10341 0.551707 0.834038i \(-0.313977\pi\)
0.551707 + 0.834038i \(0.313977\pi\)
\(114\) 0.0960905 + 0.141759i 0.00899970 + 0.0132769i
\(115\) −2.35010 2.35010i −0.219147 0.219147i
\(116\) 12.2924 5.28436i 1.14132 0.490640i
\(117\) −0.182003 + 0.182003i −0.0168262 + 0.0168262i
\(118\) 1.23333 6.42341i 0.113537 0.591323i
\(119\) 0.603016i 0.0552784i
\(120\) 1.07972 + 4.91351i 0.0985647 + 0.448540i
\(121\) 10.1518i 0.922890i
\(122\) 15.7134 + 3.01705i 1.42262 + 0.273151i
\(123\) 7.34125 7.34125i 0.661938 0.661938i
\(124\) −4.55869 + 11.4336i −0.409382 + 1.02677i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 0.191450 0.129773i 0.0170557 0.0115611i
\(127\) −0.429799 −0.0381385 −0.0190692 0.999818i \(-0.506070\pi\)
−0.0190692 + 0.999818i \(0.506070\pi\)
\(128\) −5.84083 + 9.68941i −0.516261 + 0.856431i
\(129\) −17.2951 −1.52275
\(130\) 1.84235 1.24883i 0.161585 0.109530i
\(131\) 10.1923 + 10.1923i 0.890502 + 0.890502i 0.994570 0.104068i \(-0.0331861\pi\)
−0.104068 + 0.994570i \(0.533186\pi\)
\(132\) 1.21336 3.04321i 0.105609 0.264877i
\(133\) −0.0481428 + 0.0481428i −0.00417451 + 0.00417451i
\(134\) −0.394616 0.0757684i −0.0340896 0.00654539i
\(135\) 5.04502i 0.434206i
\(136\) 0.366061 + 1.66584i 0.0313895 + 0.142845i
\(137\) 8.88755i 0.759315i −0.925127 0.379657i \(-0.876042\pi\)
0.925127 0.379657i \(-0.123958\pi\)
\(138\) −1.57636 + 8.20996i −0.134188 + 0.698878i
\(139\) 5.64555 5.64555i 0.478849 0.478849i −0.425914 0.904764i \(-0.640047\pi\)
0.904764 + 0.425914i \(0.140047\pi\)
\(140\) −1.83741 + 0.789884i −0.155290 + 0.0667573i
\(141\) 6.88271 + 6.88271i 0.579629 + 0.579629i
\(142\) −1.52329 2.24726i −0.127832 0.188586i
\(143\) −1.44946 −0.121210
\(144\) 0.450105 0.474721i 0.0375087 0.0395601i
\(145\) 6.69005 0.555578
\(146\) −6.24172 9.20818i −0.516568 0.762075i
\(147\) 1.25769 + 1.25769i 0.103732 + 0.103732i
\(148\) −3.64353 8.47550i −0.299496 0.696682i
\(149\) −14.7096 + 14.7096i −1.20506 + 1.20506i −0.232454 + 0.972607i \(0.574676\pi\)
−0.972607 + 0.232454i \(0.925324\pi\)
\(150\) −0.474301 + 2.47025i −0.0387265 + 0.201695i
\(151\) 8.49500i 0.691313i 0.938361 + 0.345657i \(0.112344\pi\)
−0.938361 + 0.345657i \(0.887656\pi\)
\(152\) −0.103770 + 0.162220i −0.00841686 + 0.0131578i
\(153\) 0.0986206i 0.00797300i
\(154\) 1.27910 + 0.245594i 0.103073 + 0.0197905i
\(155\) −4.35185 + 4.35185i −0.349549 + 0.349549i
\(156\) −5.20041 2.07345i −0.416366 0.166009i
\(157\) −8.79716 8.79716i −0.702090 0.702090i 0.262769 0.964859i \(-0.415364\pi\)
−0.964859 + 0.262769i \(0.915364\pi\)
\(158\) 1.76817 1.19854i 0.140668 0.0953510i
\(159\) −20.1958 −1.60163
\(160\) −4.59638 + 3.29747i −0.363376 + 0.260688i
\(161\) −3.32354 −0.261931
\(162\) 11.0786 7.50960i 0.870420 0.590010i
\(163\) 3.53993 + 3.53993i 0.277269 + 0.277269i 0.832018 0.554749i \(-0.187186\pi\)
−0.554749 + 0.832018i \(0.687186\pi\)
\(164\) 10.8441 + 4.32364i 0.846779 + 0.337619i
\(165\) 1.15830 1.15830i 0.0901738 0.0901738i
\(166\) 22.4057 + 4.30203i 1.73902 + 0.333902i
\(167\) 17.1739i 1.32896i 0.747307 + 0.664479i \(0.231347\pi\)
−0.747307 + 0.664479i \(0.768653\pi\)
\(168\) 4.23785 + 2.71090i 0.326958 + 0.209150i
\(169\) 10.5231i 0.809468i
\(170\) −0.160804 + 0.837496i −0.0123331 + 0.0642330i
\(171\) 0.00787353 0.00787353i 0.000602104 0.000602104i
\(172\) −7.68069 17.8667i −0.585647 1.36232i
\(173\) −11.0510 11.0510i −0.840190 0.840190i 0.148694 0.988883i \(-0.452493\pi\)
−0.988883 + 0.148694i \(0.952493\pi\)
\(174\) −9.44199 13.9294i −0.715795 1.05599i
\(175\) −1.00000 −0.0755929
\(176\) 3.68262 0.0980206i 0.277588 0.00738858i
\(177\) −8.22620 −0.618319
\(178\) −1.42457 2.10162i −0.106776 0.157523i
\(179\) −1.10235 1.10235i −0.0823932 0.0823932i 0.664709 0.747102i \(-0.268556\pi\)
−0.747102 + 0.664709i \(0.768556\pi\)
\(180\) 0.300500 0.129182i 0.0223980 0.00962865i
\(181\) −3.60640 + 3.60640i −0.268062 + 0.268062i −0.828319 0.560257i \(-0.810702\pi\)
0.560257 + 0.828319i \(0.310702\pi\)
\(182\) 0.419685 2.18580i 0.0311091 0.162022i
\(183\) 20.1235i 1.48757i
\(184\) −9.18132 + 2.01755i −0.676856 + 0.148736i
\(185\) 4.61274i 0.339135i
\(186\) 15.2030 + 2.91906i 1.11474 + 0.214036i
\(187\) 0.392703 0.392703i 0.0287173 0.0287173i
\(188\) −4.05358 + 10.1667i −0.295638 + 0.741485i
\(189\) 3.56737 + 3.56737i 0.259488 + 0.259488i
\(190\) −0.0797009 + 0.0540248i −0.00578211 + 0.00391937i
\(191\) −17.1989 −1.24447 −0.622233 0.782832i \(-0.713775\pi\)
−0.622233 + 0.782832i \(0.713775\pi\)
\(192\) 13.3528 + 4.91630i 0.963654 + 0.354803i
\(193\) −6.12727 −0.441051 −0.220525 0.975381i \(-0.570777\pi\)
−0.220525 + 0.975381i \(0.570777\pi\)
\(194\) 5.01193 3.39731i 0.359835 0.243913i
\(195\) −1.97938 1.97938i −0.141746 0.141746i
\(196\) −0.740715 + 1.85778i −0.0529082 + 0.132698i
\(197\) −16.2447 + 16.2447i −1.15739 + 1.15739i −0.172352 + 0.985035i \(0.555137\pi\)
−0.985035 + 0.172352i \(0.944863\pi\)
\(198\) −0.209191 0.0401658i −0.0148665 0.00285446i
\(199\) 4.47826i 0.317455i −0.987322 0.158728i \(-0.949261\pi\)
0.987322 0.158728i \(-0.0507392\pi\)
\(200\) −2.76252 + 0.607051i −0.195339 + 0.0429250i
\(201\) 0.505368i 0.0356459i
\(202\) 0.721687 3.75868i 0.0507777 0.264460i
\(203\) 4.73058 4.73058i 0.332022 0.332022i
\(204\) 1.97071 0.847187i 0.137977 0.0593149i
\(205\) 4.12746 + 4.12746i 0.288274 + 0.288274i
\(206\) −10.5214 15.5219i −0.733062 1.08146i
\(207\) 0.543549 0.0377793
\(208\) −0.167503 6.29307i −0.0116143 0.436346i
\(209\) 0.0627042 0.00433734
\(210\) 1.41135 + 2.08211i 0.0973923 + 0.143679i
\(211\) −6.10477 6.10477i −0.420270 0.420270i 0.465027 0.885297i \(-0.346045\pi\)
−0.885297 + 0.465027i \(0.846045\pi\)
\(212\) −8.96885 20.8632i −0.615983 1.43289i
\(213\) −2.41439 + 2.41439i −0.165431 + 0.165431i
\(214\) 0.454167 2.36538i 0.0310462 0.161694i
\(215\) 9.72383i 0.663159i
\(216\) 12.0205 + 7.68933i 0.817890 + 0.523193i
\(217\) 6.15445i 0.417791i
\(218\) 6.22302 + 1.19485i 0.421476 + 0.0809257i
\(219\) −9.89302 + 9.89302i −0.668508 + 0.668508i
\(220\) 1.71098 + 0.682184i 0.115354 + 0.0459928i
\(221\) −0.671074 0.671074i −0.0451413 0.0451413i
\(222\) −9.60424 + 6.51018i −0.644594 + 0.436935i
\(223\) −14.9388 −1.00038 −0.500188 0.865917i \(-0.666736\pi\)
−0.500188 + 0.865917i \(0.666736\pi\)
\(224\) −0.918470 + 5.58179i −0.0613678 + 0.372949i
\(225\) 0.163545 0.0109030
\(226\) 13.7308 9.30733i 0.913357 0.619114i
\(227\) 0.226203 + 0.226203i 0.0150136 + 0.0150136i 0.714574 0.699560i \(-0.246621\pi\)
−0.699560 + 0.714574i \(0.746621\pi\)
\(228\) 0.224971 + 0.0896983i 0.0148991 + 0.00594041i
\(229\) −17.7070 + 17.7070i −1.17011 + 1.17011i −0.187929 + 0.982183i \(0.560177\pi\)
−0.982183 + 0.187929i \(0.939823\pi\)
\(230\) −4.61588 0.886273i −0.304362 0.0584391i
\(231\) 1.63809i 0.107778i
\(232\) 10.1966 15.9400i 0.669439 1.04651i
\(233\) 20.3846i 1.33544i 0.744412 + 0.667720i \(0.232730\pi\)
−0.744412 + 0.667720i \(0.767270\pi\)
\(234\) −0.0686376 + 0.357477i −0.00448698 + 0.0233690i
\(235\) −3.86966 + 3.86966i −0.252429 + 0.252429i
\(236\) −3.65322 8.49804i −0.237804 0.553175i
\(237\) −1.89967 1.89967i −0.123397 0.123397i
\(238\) 0.478494 + 0.705905i 0.0310161 + 0.0457570i
\(239\) 27.5857 1.78437 0.892184 0.451673i \(-0.149172\pi\)
0.892184 + 0.451673i \(0.149172\pi\)
\(240\) 5.16282 + 4.89510i 0.333258 + 0.315978i
\(241\) 2.38105 0.153377 0.0766885 0.997055i \(-0.475565\pi\)
0.0766885 + 0.997055i \(0.475565\pi\)
\(242\) 8.05545 + 11.8839i 0.517824 + 0.763927i
\(243\) −1.20049 1.20049i −0.0770117 0.0770117i
\(244\) 20.7884 8.93673i 1.33084 0.572115i
\(245\) −0.707107 + 0.707107i −0.0451754 + 0.0451754i
\(246\) 2.76855 14.4191i 0.176516 0.919330i
\(247\) 0.107152i 0.00681795i
\(248\) 3.73606 + 17.0017i 0.237240 + 1.07961i
\(249\) 28.6941i 1.81842i
\(250\) −1.38884 0.266666i −0.0878382 0.0168654i
\(251\) −9.49501 + 9.49501i −0.599320 + 0.599320i −0.940132 0.340812i \(-0.889298\pi\)
0.340812 + 0.940132i \(0.389298\pi\)
\(252\) 0.121141 0.303831i 0.00763114 0.0191396i
\(253\) 2.16439 + 2.16439i 0.136074 + 0.136074i
\(254\) −0.503132 + 0.341046i −0.0315693 + 0.0213991i
\(255\) 1.07255 0.0671655
\(256\) 0.851144 + 15.9773i 0.0531965 + 0.998584i
\(257\) 17.5034 1.09183 0.545915 0.837841i \(-0.316182\pi\)
0.545915 + 0.837841i \(0.316182\pi\)
\(258\) −20.2461 + 13.7237i −1.26047 + 0.854400i
\(259\) −3.26170 3.26170i −0.202672 0.202672i
\(260\) 1.16575 2.92382i 0.0722970 0.181327i
\(261\) −0.773665 + 0.773665i −0.0478886 + 0.0478886i
\(262\) 20.0189 + 3.84373i 1.23677 + 0.237466i
\(263\) 29.3793i 1.81160i 0.423703 + 0.905801i \(0.360730\pi\)
−0.423703 + 0.905801i \(0.639270\pi\)
\(264\) −0.994403 4.52524i −0.0612012 0.278510i
\(265\) 11.3547i 0.697511i
\(266\) −0.0181557 + 0.0945583i −0.00111320 + 0.00579774i
\(267\) −2.25792 + 2.25792i −0.138183 + 0.138183i
\(268\) −0.522068 + 0.224432i −0.0318904 + 0.0137093i
\(269\) 10.4537 + 10.4537i 0.637372 + 0.637372i 0.949906 0.312534i \(-0.101178\pi\)
−0.312534 + 0.949906i \(0.601178\pi\)
\(270\) 4.00322 + 5.90581i 0.243628 + 0.359416i
\(271\) −20.1834 −1.22605 −0.613027 0.790062i \(-0.710048\pi\)
−0.613027 + 0.790062i \(0.710048\pi\)
\(272\) 1.75037 + 1.65960i 0.106132 + 0.100628i
\(273\) −2.79926 −0.169419
\(274\) −7.05227 10.4040i −0.426043 0.628527i
\(275\) 0.651231 + 0.651231i 0.0392707 + 0.0392707i
\(276\) 4.66929 + 10.8616i 0.281058 + 0.653792i
\(277\) 0.340772 0.340772i 0.0204750 0.0204750i −0.696795 0.717270i \(-0.745391\pi\)
0.717270 + 0.696795i \(0.245391\pi\)
\(278\) 2.12906 11.0886i 0.127693 0.665047i
\(279\) 1.00653i 0.0602595i
\(280\) −1.52414 + 2.38264i −0.0910850 + 0.142390i
\(281\) 11.4612i 0.683719i −0.939751 0.341860i \(-0.888943\pi\)
0.939751 0.341860i \(-0.111057\pi\)
\(282\) 13.5185 + 2.59562i 0.805015 + 0.154567i
\(283\) 17.5855 17.5855i 1.04535 1.04535i 0.0464283 0.998922i \(-0.485216\pi\)
0.998922 0.0464283i \(-0.0147839\pi\)
\(284\) −3.56640 1.42196i −0.211627 0.0843776i
\(285\) 0.0856285 + 0.0856285i 0.00507219 + 0.00507219i
\(286\) −1.69677 + 1.15015i −0.100332 + 0.0680096i
\(287\) 5.83711 0.344554
\(288\) 0.150212 0.912877i 0.00885130 0.0537918i
\(289\) −16.6364 −0.978610
\(290\) 7.83152 5.30856i 0.459883 0.311729i
\(291\) −5.38468 5.38468i −0.315656 0.315656i
\(292\) −14.6134 5.82650i −0.855184 0.340970i
\(293\) −10.0898 + 10.0898i −0.589455 + 0.589455i −0.937484 0.348029i \(-0.886851\pi\)
0.348029 + 0.937484i \(0.386851\pi\)
\(294\) 2.47025 + 0.474301i 0.144068 + 0.0276618i
\(295\) 4.62501i 0.269278i
\(296\) −10.9905 7.03048i −0.638810 0.408638i
\(297\) 4.64636i 0.269609i
\(298\) −5.54734 + 28.8916i −0.321349 + 1.67364i
\(299\) 3.69864 3.69864i 0.213898 0.213898i
\(300\) 1.40492 + 3.26809i 0.0811128 + 0.188683i
\(301\) −6.87578 6.87578i −0.396314 0.396314i
\(302\) 6.74079 + 9.94444i 0.387889 + 0.572238i
\(303\) −4.81358 −0.276533
\(304\) 0.00724625 + 0.272240i 0.000415601 + 0.0156140i
\(305\) 11.3140 0.647837
\(306\) −0.0782555 0.115448i −0.00447357 0.00659969i
\(307\) 18.8661 + 18.8661i 1.07675 + 1.07675i 0.996799 + 0.0799466i \(0.0254750\pi\)
0.0799466 + 0.996799i \(0.474525\pi\)
\(308\) 1.69222 0.727467i 0.0964232 0.0414513i
\(309\) −16.6763 + 16.6763i −0.948680 + 0.948680i
\(310\) −1.64118 + 8.54757i −0.0932128 + 0.485469i
\(311\) 0.0904960i 0.00513156i 0.999997 + 0.00256578i \(0.000816714\pi\)
−0.999997 + 0.00256578i \(0.999183\pi\)
\(312\) −7.73300 + 1.69929i −0.437795 + 0.0962035i
\(313\) 26.3979i 1.49210i −0.665892 0.746048i \(-0.731949\pi\)
0.665892 0.746048i \(-0.268051\pi\)
\(314\) −17.2787 3.31761i −0.975094 0.187223i
\(315\) 0.115644 0.115644i 0.00651581 0.00651581i
\(316\) 1.11881 2.80609i 0.0629382 0.157855i
\(317\) 2.76566 + 2.76566i 0.155335 + 0.155335i 0.780496 0.625161i \(-0.214967\pi\)
−0.625161 + 0.780496i \(0.714967\pi\)
\(318\) −23.6416 + 16.0254i −1.32576 + 0.898658i
\(319\) −6.16140 −0.344972
\(320\) −2.76408 + 7.50732i −0.154517 + 0.419672i
\(321\) −3.02925 −0.169076
\(322\) −3.89061 + 2.63723i −0.216815 + 0.146967i
\(323\) 0.0290309 + 0.0290309i 0.00161532 + 0.00161532i
\(324\) 7.01004 17.5818i 0.389447 0.976767i
\(325\) 1.11286 1.11286i 0.0617305 0.0617305i
\(326\) 6.95287 + 1.33499i 0.385084 + 0.0739382i
\(327\) 7.96956i 0.440718i
\(328\) 16.1251 3.54342i 0.890361 0.195653i
\(329\) 5.47252i 0.301710i
\(330\) 0.436822 2.27505i 0.0240463 0.125237i
\(331\) 7.19158 7.19158i 0.395285 0.395285i −0.481281 0.876566i \(-0.659828\pi\)
0.876566 + 0.481281i \(0.159828\pi\)
\(332\) 29.6423 12.7429i 1.62683 0.699358i
\(333\) 0.533436 + 0.533436i 0.0292321 + 0.0292321i
\(334\) 13.6275 + 20.1042i 0.745665 + 1.10005i
\(335\) −0.284132 −0.0155238
\(336\) 7.11202 0.189301i 0.387993 0.0103272i
\(337\) −0.126565 −0.00689444 −0.00344722 0.999994i \(-0.501097\pi\)
−0.00344722 + 0.999994i \(0.501097\pi\)
\(338\) −8.35007 12.3186i −0.454184 0.670041i
\(339\) −14.7520 14.7520i −0.801217 0.801217i
\(340\) 0.476313 + 1.10799i 0.0258317 + 0.0600892i
\(341\) 4.00797 4.00797i 0.217044 0.217044i
\(342\) 0.00296929 0.0154646i 0.000160561 0.000836229i
\(343\) 1.00000i 0.0539949i
\(344\) −23.1684 14.8205i −1.24916 0.799068i
\(345\) 5.91136i 0.318257i
\(346\) −21.7055 4.16757i −1.16689 0.224050i
\(347\) −25.0440 + 25.0440i −1.34443 + 1.34443i −0.452846 + 0.891589i \(0.649591\pi\)
−0.891589 + 0.452846i \(0.850409\pi\)
\(348\) −22.1060 8.81388i −1.18501 0.472474i
\(349\) −3.85172 3.85172i −0.206178 0.206178i 0.596463 0.802641i \(-0.296572\pi\)
−0.802641 + 0.596463i \(0.796572\pi\)
\(350\) −1.17062 + 0.793500i −0.0625724 + 0.0424144i
\(351\) −7.93997 −0.423804
\(352\) 4.23318 3.03690i 0.225629 0.161867i
\(353\) −3.43843 −0.183009 −0.0915046 0.995805i \(-0.529168\pi\)
−0.0915046 + 0.995805i \(0.529168\pi\)
\(354\) −9.62978 + 6.52749i −0.511817 + 0.346932i
\(355\) −1.35744 1.35744i −0.0720454 0.0720454i
\(356\) −3.33527 1.32981i −0.176769 0.0704795i
\(357\) 0.758405 0.758405i 0.0401390 0.0401390i
\(358\) −2.16514 0.415720i −0.114431 0.0219715i
\(359\) 31.0991i 1.64135i 0.571396 + 0.820675i \(0.306402\pi\)
−0.571396 + 0.820675i \(0.693598\pi\)
\(360\) 0.249267 0.389670i 0.0131375 0.0205374i
\(361\) 18.9954i 0.999756i
\(362\) −1.36006 + 7.08342i −0.0714829 + 0.372296i
\(363\) 12.7678 12.7678i 0.670134 0.670134i
\(364\) −1.24314 2.89176i −0.0651581 0.151570i
\(365\) −5.56214 5.56214i −0.291136 0.291136i
\(366\) −15.9680 23.5570i −0.834659 1.23134i
\(367\) 18.1151 0.945599 0.472799 0.881170i \(-0.343244\pi\)
0.472799 + 0.881170i \(0.343244\pi\)
\(368\) −9.14693 + 9.64717i −0.476817 + 0.502894i
\(369\) −0.954634 −0.0496962
\(370\) −3.66021 5.39978i −0.190285 0.280721i
\(371\) −8.02895 8.02895i −0.416842 0.416842i
\(372\) 20.1133 8.64647i 1.04282 0.448299i
\(373\) 16.0111 16.0111i 0.829022 0.829022i −0.158360 0.987381i \(-0.550621\pi\)
0.987381 + 0.158360i \(0.0506206\pi\)
\(374\) 0.148097 0.771317i 0.00765792 0.0398839i
\(375\) 1.77864i 0.0918484i
\(376\) 3.32210 + 15.1179i 0.171324 + 0.779648i
\(377\) 10.5290i 0.542269i
\(378\) 7.00675 + 1.34533i 0.360388 + 0.0691965i
\(379\) 15.6288 15.6288i 0.802798 0.802798i −0.180734 0.983532i \(-0.557847\pi\)
0.983532 + 0.180734i \(0.0578473\pi\)
\(380\) −0.0504309 + 0.126485i −0.00258705 + 0.00648856i
\(381\) 0.540552 + 0.540552i 0.0276933 + 0.0276933i
\(382\) −20.1334 + 13.6473i −1.03011 + 0.698257i
\(383\) −18.0295 −0.921264 −0.460632 0.887591i \(-0.652377\pi\)
−0.460632 + 0.887591i \(0.652377\pi\)
\(384\) 19.5322 4.84031i 0.996746 0.247006i
\(385\) 0.920980 0.0469375
\(386\) −7.17272 + 4.86199i −0.365082 + 0.247469i
\(387\) 1.12450 + 1.12450i 0.0571617 + 0.0571617i
\(388\) 3.17131 7.95393i 0.160999 0.403800i
\(389\) 4.59304 4.59304i 0.232876 0.232876i −0.581016 0.813892i \(-0.697345\pi\)
0.813892 + 0.581016i \(0.197345\pi\)
\(390\) −3.88774 0.746467i −0.196863 0.0377988i
\(391\) 2.00415i 0.101354i
\(392\) 0.607051 + 2.76252i 0.0306607 + 0.139528i
\(393\) 25.6373i 1.29323i
\(394\) −6.12624 + 31.9066i −0.308636 + 1.60743i
\(395\) 1.06805 1.06805i 0.0537395 0.0537395i
\(396\) −0.276755 + 0.118974i −0.0139075 + 0.00597867i
\(397\) −16.6604 16.6604i −0.836163 0.836163i 0.152189 0.988351i \(-0.451368\pi\)
−0.988351 + 0.152189i \(0.951368\pi\)
\(398\) −3.55350 5.24235i −0.178121 0.262775i
\(399\) 0.121097 0.00606243
\(400\) −2.75217 + 2.90268i −0.137608 + 0.145134i
\(401\) 23.9835 1.19768 0.598839 0.800869i \(-0.295629\pi\)
0.598839 + 0.800869i \(0.295629\pi\)
\(402\) 0.401010 + 0.591595i 0.0200005 + 0.0295061i
\(403\) −6.84905 6.84905i −0.341175 0.341175i
\(404\) −2.13769 4.97265i −0.106354 0.247399i
\(405\) 6.69198 6.69198i 0.332527 0.332527i
\(406\) 1.78401 9.29144i 0.0885388 0.461126i
\(407\) 4.24824i 0.210578i
\(408\) 1.63471 2.55550i 0.0809304 0.126516i
\(409\) 19.8597i 0.982000i −0.871160 0.491000i \(-0.836631\pi\)
0.871160 0.491000i \(-0.163369\pi\)
\(410\) 8.10684 + 1.55656i 0.400368 + 0.0768729i
\(411\) −11.1777 + 11.1777i −0.551357 + 0.551357i
\(412\) −24.6332 9.82151i −1.21359 0.483871i
\(413\) −3.27037 3.27037i −0.160925 0.160925i
\(414\) 0.636291 0.431307i 0.0312720 0.0211976i
\(415\) 16.1327 0.791921
\(416\) −5.18963 7.23389i −0.254443 0.354671i
\(417\) −14.2007 −0.695409
\(418\) 0.0734029 0.0497558i 0.00359025 0.00243363i
\(419\) 5.63336 + 5.63336i 0.275208 + 0.275208i 0.831192 0.555985i \(-0.187659\pi\)
−0.555985 + 0.831192i \(0.687659\pi\)
\(420\) 3.30431 + 1.31746i 0.161234 + 0.0642855i
\(421\) −14.3170 + 14.3170i −0.697768 + 0.697768i −0.963929 0.266161i \(-0.914245\pi\)
0.266161 + 0.963929i \(0.414245\pi\)
\(422\) −11.9905 2.30225i −0.583690 0.112072i
\(423\) 0.895006i 0.0435167i
\(424\) −27.0541 17.3061i −1.31386 0.840459i
\(425\) 0.603016i 0.0292506i
\(426\) −0.910521 + 4.74216i −0.0441149 + 0.229758i
\(427\) 8.00019 8.00019i 0.387156 0.387156i
\(428\) −1.34527 3.12935i −0.0650263 0.151263i
\(429\) 1.82297 + 1.82297i 0.0880136 + 0.0880136i
\(430\) −7.71586 11.3829i −0.372092 0.548934i
\(431\) −27.8850 −1.34317 −0.671585 0.740927i \(-0.734386\pi\)
−0.671585 + 0.740927i \(0.734386\pi\)
\(432\) 20.1729 0.536945i 0.970571 0.0258338i
\(433\) −11.7286 −0.563640 −0.281820 0.959467i \(-0.590938\pi\)
−0.281820 + 0.959467i \(0.590938\pi\)
\(434\) 4.88355 + 7.20453i 0.234418 + 0.345829i
\(435\) −8.41398 8.41398i −0.403419 0.403419i
\(436\) 8.23292 3.53924i 0.394286 0.169499i
\(437\) −0.160004 + 0.160004i −0.00765404 + 0.00765404i
\(438\) −3.73088 + 19.4311i −0.178268 + 0.928454i
\(439\) 0.485358i 0.0231649i 0.999933 + 0.0115824i \(0.00368688\pi\)
−0.999933 + 0.0115824i \(0.996313\pi\)
\(440\) 2.54422 0.559082i 0.121291 0.0266532i
\(441\) 0.163545i 0.00778788i
\(442\) −1.31807 0.253077i −0.0626943 0.0120376i
\(443\) −3.09351 + 3.09351i −0.146977 + 0.146977i −0.776766 0.629789i \(-0.783141\pi\)
0.629789 + 0.776766i \(0.283141\pi\)
\(444\) −6.07711 + 15.2419i −0.288407 + 0.723350i
\(445\) −1.26947 1.26947i −0.0601786 0.0601786i
\(446\) −17.4877 + 11.8540i −0.828067 + 0.561301i
\(447\) 37.0002 1.75005
\(448\) 3.35397 + 7.26298i 0.158460 + 0.343144i
\(449\) 20.5596 0.970268 0.485134 0.874440i \(-0.338771\pi\)
0.485134 + 0.874440i \(0.338771\pi\)
\(450\) 0.191450 0.129773i 0.00902504 0.00611758i
\(451\) −3.80131 3.80131i −0.178997 0.178997i
\(452\) 8.68818 21.7907i 0.408658 1.02495i
\(453\) 10.6840 10.6840i 0.501980 0.501980i
\(454\) 0.444291 + 0.0853063i 0.0208516 + 0.00400362i
\(455\) 1.57382i 0.0737820i
\(456\) 0.334532 0.0735120i 0.0156659 0.00344251i
\(457\) 31.1867i 1.45885i 0.684060 + 0.729425i \(0.260212\pi\)
−0.684060 + 0.729425i \(0.739788\pi\)
\(458\) −6.67770 + 34.7787i −0.312029 + 1.62510i
\(459\) 2.15118 2.15118i 0.100409 0.100409i
\(460\) −6.10671 + 2.62521i −0.284727 + 0.122401i
\(461\) −9.42653 9.42653i −0.439037 0.439037i 0.452651 0.891688i \(-0.350478\pi\)
−0.891688 + 0.452651i \(0.850478\pi\)
\(462\) −1.29982 1.91758i −0.0604733 0.0892141i
\(463\) 15.1464 0.703914 0.351957 0.936016i \(-0.385516\pi\)
0.351957 + 0.936016i \(0.385516\pi\)
\(464\) −0.712027 26.7507i −0.0330550 1.24187i
\(465\) 10.9465 0.507633
\(466\) 16.1752 + 23.8627i 0.749302 + 1.10542i
\(467\) 22.3279 + 22.3279i 1.03321 + 1.03321i 0.999429 + 0.0337836i \(0.0107557\pi\)
0.0337836 + 0.999429i \(0.489244\pi\)
\(468\) 0.203310 + 0.472935i 0.00939799 + 0.0218614i
\(469\) −0.200912 + 0.200912i −0.00927725 + 0.00927725i
\(470\) −1.45933 + 7.60048i −0.0673141 + 0.350584i
\(471\) 22.1281i 1.01961i
\(472\) −11.0197 7.04917i −0.507224 0.324464i
\(473\) 8.95545i 0.411772i
\(474\) −3.73119 0.716409i −0.171379 0.0329058i
\(475\) −0.0481428 + 0.0481428i −0.00220894 + 0.00220894i
\(476\) 1.12027 + 0.446663i 0.0513475 + 0.0204728i
\(477\) 1.31310 + 1.31310i 0.0601227 + 0.0601227i
\(478\) 32.2924 21.8892i 1.47702 1.00119i
\(479\) 21.3820 0.976970 0.488485 0.872572i \(-0.337550\pi\)
0.488485 + 0.872572i \(0.337550\pi\)
\(480\) 9.92798 + 1.63362i 0.453148 + 0.0745644i
\(481\) 7.25964 0.331011
\(482\) 2.78731 1.88936i 0.126959 0.0860582i
\(483\) 4.17996 + 4.17996i 0.190195 + 0.190195i
\(484\) 18.8598 + 7.51958i 0.857263 + 0.341799i
\(485\) 3.02742 3.02742i 0.137468 0.137468i
\(486\) −2.35792 0.452733i −0.106957 0.0205364i
\(487\) 10.1750i 0.461075i 0.973063 + 0.230538i \(0.0740485\pi\)
−0.973063 + 0.230538i \(0.925952\pi\)
\(488\) 17.2441 26.9572i 0.780605 1.22029i
\(489\) 8.90425i 0.402664i
\(490\) −0.266666 + 1.38884i −0.0120467 + 0.0627416i
\(491\) −11.1601 + 11.1601i −0.503648 + 0.503648i −0.912569 0.408922i \(-0.865905\pi\)
0.408922 + 0.912569i \(0.365905\pi\)
\(492\) −8.20065 19.0762i −0.369714 0.860021i
\(493\) −2.85262 2.85262i −0.128475 0.128475i
\(494\) −0.0850255 0.125435i −0.00382548 0.00564359i
\(495\) −0.150622 −0.00676996
\(496\) 17.8644 + 16.9381i 0.802136 + 0.760542i
\(497\) −1.91971 −0.0861108
\(498\) −22.7688 33.5900i −1.02029 1.50520i
\(499\) 24.2041 + 24.2041i 1.08353 + 1.08353i 0.996178 + 0.0873482i \(0.0278393\pi\)
0.0873482 + 0.996178i \(0.472161\pi\)
\(500\) −1.83741 + 0.789884i −0.0821716 + 0.0353247i
\(501\) 21.5994 21.5994i 0.964990 0.964990i
\(502\) −3.58078 + 18.6494i −0.159818 + 0.832362i
\(503\) 11.0233i 0.491503i −0.969333 0.245751i \(-0.920965\pi\)
0.969333 0.245751i \(-0.0790346\pi\)
\(504\) −0.0992804 0.451797i −0.00442230 0.0201246i
\(505\) 2.70634i 0.120430i
\(506\) 4.25113 + 0.816240i 0.188986 + 0.0362863i
\(507\) −13.2347 + 13.2347i −0.587775 + 0.587775i
\(508\) −0.318358 + 0.798472i −0.0141249 + 0.0354264i
\(509\) 3.80620 + 3.80620i 0.168707 + 0.168707i 0.786411 0.617704i \(-0.211937\pi\)
−0.617704 + 0.786411i \(0.711937\pi\)
\(510\) 1.25555 0.851066i 0.0555966 0.0376858i
\(511\) −7.86605 −0.347974
\(512\) 13.6744 + 18.0281i 0.604329 + 0.796735i
\(513\) 0.343486 0.0151653
\(514\) 20.4898 13.8889i 0.903767 0.612614i
\(515\) −9.37588 9.37588i −0.413151 0.413151i
\(516\) −12.8108 + 32.1306i −0.563963 + 1.41447i
\(517\) 3.56388 3.56388i 0.156739 0.156739i
\(518\) −6.40638 1.23006i −0.281480 0.0540457i
\(519\) 27.7973i 1.22017i
\(520\) −0.955391 4.34771i −0.0418967 0.190660i
\(521\) 8.86849i 0.388536i 0.980949 + 0.194268i \(0.0622331\pi\)
−0.980949 + 0.194268i \(0.937767\pi\)
\(522\) −0.291766 + 1.51957i −0.0127703 + 0.0665099i
\(523\) 10.6892 10.6892i 0.467407 0.467407i −0.433666 0.901074i \(-0.642780\pi\)
0.901074 + 0.433666i \(0.142780\pi\)
\(524\) 26.4845 11.3854i 1.15698 0.497374i
\(525\) 1.25769 + 1.25769i 0.0548899 + 0.0548899i
\(526\) 23.3124 + 34.3920i 1.01647 + 1.49956i
\(527\) 3.71123 0.161664
\(528\) −4.75485 4.50829i −0.206928 0.196198i
\(529\) 11.9541 0.519744
\(530\) −9.00992 13.2920i −0.391366 0.577368i
\(531\) 0.534855 + 0.534855i 0.0232107 + 0.0232107i
\(532\) 0.0537786 + 0.125099i 0.00233160 + 0.00542372i
\(533\) −6.49590 + 6.49590i −0.281369 + 0.281369i
\(534\) −0.851513 + 4.43484i −0.0368486 + 0.191914i
\(535\) 1.70313i 0.0736328i
\(536\) −0.433059 + 0.676986i −0.0187053 + 0.0292413i
\(537\) 2.77281i 0.119656i
\(538\) 20.5323 + 3.94232i 0.885211 + 0.169965i
\(539\) 0.651231 0.651231i 0.0280505 0.0280505i
\(540\) 9.37253 + 3.73692i 0.403329 + 0.160811i
\(541\) 22.0050 + 22.0050i 0.946069 + 0.946069i 0.998618 0.0525493i \(-0.0167347\pi\)
−0.0525493 + 0.998618i \(0.516735\pi\)
\(542\) −23.6271 + 16.0155i −1.01487 + 0.687926i
\(543\) 9.07145 0.389293
\(544\) 3.36591 + 0.553852i 0.144312 + 0.0237462i
\(545\) 4.48072 0.191933
\(546\) −3.27688 + 2.22121i −0.140237 + 0.0950592i
\(547\) −7.10045 7.10045i −0.303593 0.303593i 0.538825 0.842418i \(-0.318869\pi\)
−0.842418 + 0.538825i \(0.818869\pi\)
\(548\) −16.5111 6.58314i −0.705319 0.281218i
\(549\) −1.30840 + 1.30840i −0.0558409 + 0.0558409i
\(550\) 1.27910 + 0.245594i 0.0545409 + 0.0104722i
\(551\) 0.455486i 0.0194044i
\(552\) 14.0847 + 9.00976i 0.599483 + 0.383481i
\(553\) 1.51045i 0.0642309i
\(554\) 0.128513 0.669317i 0.00545998 0.0284366i
\(555\) −5.80138 + 5.80138i −0.246255 + 0.246255i
\(556\) −6.30644 14.6699i −0.267453 0.622143i
\(557\) −30.6211 30.6211i −1.29746 1.29746i −0.930066 0.367392i \(-0.880251\pi\)
−0.367392 0.930066i \(-0.619749\pi\)
\(558\) −0.798683 1.17827i −0.0338110 0.0498801i
\(559\) 15.3036 0.647273
\(560\) 0.106431 + 3.99858i 0.00449752 + 0.168971i
\(561\) −0.987794 −0.0417047
\(562\) −9.09448 13.4168i −0.383628 0.565952i
\(563\) 31.3046 + 31.3046i 1.31933 + 1.31933i 0.914306 + 0.405024i \(0.132737\pi\)
0.405024 + 0.914306i \(0.367263\pi\)
\(564\) 17.8847 7.68843i 0.753081 0.323741i
\(565\) 8.29398 8.29398i 0.348930 0.348930i
\(566\) 6.63189 34.5401i 0.278759 1.45183i
\(567\) 9.46389i 0.397446i
\(568\) −5.30323 + 1.16536i −0.222518 + 0.0488975i
\(569\) 25.3468i 1.06260i −0.847185 0.531298i \(-0.821705\pi\)
0.847185 0.531298i \(-0.178295\pi\)
\(570\) 0.168185 + 0.0322924i 0.00704449 + 0.00135258i
\(571\) −6.57745 + 6.57745i −0.275258 + 0.275258i −0.831213 0.555955i \(-0.812353\pi\)
0.555955 + 0.831213i \(0.312353\pi\)
\(572\) −1.07364 + 2.69278i −0.0448910 + 0.112591i
\(573\) 21.6308 + 21.6308i 0.903638 + 0.903638i
\(574\) 6.83306 4.63175i 0.285206 0.193326i
\(575\) −3.32354 −0.138601
\(576\) −0.548527 1.18783i −0.0228553 0.0494928i
\(577\) −33.7316 −1.40427 −0.702133 0.712046i \(-0.747769\pi\)
−0.702133 + 0.712046i \(0.747769\pi\)
\(578\) −19.4749 + 13.2010i −0.810050 + 0.549088i
\(579\) 7.70618 + 7.70618i 0.320258 + 0.320258i
\(580\) 4.95542 12.4286i 0.205762 0.516071i
\(581\) 11.4075 11.4075i 0.473263 0.473263i
\(582\) −10.5762 2.03068i −0.438397 0.0841745i
\(583\) 10.4574i 0.433102i
\(584\) −21.7301 + 4.77509i −0.899198 + 0.197595i
\(585\) 0.257392i 0.0106418i
\(586\) −3.80510 + 19.8177i −0.157187 + 0.818661i
\(587\) 11.1272 11.1272i 0.459270 0.459270i −0.439146 0.898416i \(-0.644719\pi\)
0.898416 + 0.439146i \(0.144719\pi\)
\(588\) 3.26809 1.40492i 0.134774 0.0579377i
\(589\) 0.296292 + 0.296292i 0.0122085 + 0.0122085i
\(590\) −3.66994 5.41414i −0.151089 0.222896i
\(591\) 40.8615 1.68082
\(592\) −18.4444 + 0.490937i −0.758061 + 0.0201774i
\(593\) −18.3956 −0.755418 −0.377709 0.925924i \(-0.623288\pi\)
−0.377709 + 0.925924i \(0.623288\pi\)
\(594\) −3.68689 5.43914i −0.151275 0.223171i
\(595\) 0.426397 + 0.426397i 0.0174806 + 0.0174806i
\(596\) 16.4316 + 38.2229i 0.673065 + 1.56567i
\(597\) −5.63224 + 5.63224i −0.230512 + 0.230512i
\(598\) 1.39484 7.26458i 0.0570392 0.297071i
\(599\) 3.74093i 0.152850i 0.997075 + 0.0764250i \(0.0243506\pi\)
−0.997075 + 0.0764250i \(0.975649\pi\)
\(600\) 4.23785 + 2.71090i 0.173010 + 0.110672i
\(601\) 25.1470i 1.02577i 0.858458 + 0.512883i \(0.171423\pi\)
−0.858458 + 0.512883i \(0.828577\pi\)
\(602\) −13.5049 2.59301i −0.550418 0.105683i
\(603\) 0.0328582 0.0328582i 0.00133809 0.00133809i
\(604\) 15.7818 + 6.29237i 0.642154 + 0.256033i
\(605\) 7.17840 + 7.17840i 0.291844 + 0.291844i
\(606\) −5.63489 + 3.81958i −0.228902 + 0.155160i
\(607\) 20.3554 0.826199 0.413099 0.910686i \(-0.364446\pi\)
0.413099 + 0.910686i \(0.364446\pi\)
\(608\) 0.224505 + 0.312941i 0.00910489 + 0.0126914i
\(609\) −11.8992 −0.482178
\(610\) 13.2444 8.97765i 0.536250 0.363494i
\(611\) −6.09016 6.09016i −0.246382 0.246382i
\(612\) −0.183215 0.0730497i −0.00740604 0.00295286i
\(613\) 15.1285 15.1285i 0.611033 0.611033i −0.332182 0.943215i \(-0.607785\pi\)
0.943215 + 0.332182i \(0.107785\pi\)
\(614\) 37.0554 + 7.11483i 1.49543 + 0.287131i
\(615\) 10.3821i 0.418647i
\(616\) 1.40371 2.19437i 0.0565569 0.0884136i
\(617\) 34.6485i 1.39489i 0.716636 + 0.697447i \(0.245681\pi\)
−0.716636 + 0.697447i \(0.754319\pi\)
\(618\) −6.28900 + 32.7543i −0.252981 + 1.31757i
\(619\) 17.6878 17.6878i 0.710932 0.710932i −0.255798 0.966730i \(-0.582338\pi\)
0.966730 + 0.255798i \(0.0823383\pi\)
\(620\) 4.86130 + 11.3083i 0.195234 + 0.454150i
\(621\) 11.8563 + 11.8563i 0.475776 + 0.475776i
\(622\) 0.0718086 + 0.105937i 0.00287926 + 0.00424767i
\(623\) −1.79530 −0.0719272
\(624\) −7.70403 + 8.12537i −0.308408 + 0.325275i
\(625\) −1.00000 −0.0400000
\(626\) −20.9467 30.9019i −0.837199 1.23509i
\(627\) −0.0788621 0.0788621i −0.00314945 0.00314945i
\(628\) −22.8594 + 9.82699i −0.912188 + 0.392140i
\(629\) −1.96686 + 1.96686i −0.0784238 + 0.0784238i
\(630\) 0.0436120 0.227139i 0.00173754 0.00904945i
\(631\) 15.3544i 0.611248i −0.952152 0.305624i \(-0.901135\pi\)
0.952152 0.305624i \(-0.0988650\pi\)
\(632\) −0.916921 4.17265i −0.0364731 0.165979i
\(633\) 15.3558i 0.610337i
\(634\) 5.43209 + 1.04299i 0.215736 + 0.0414225i
\(635\) −0.303914 + 0.303914i −0.0120605 + 0.0120605i
\(636\) −14.9593 + 37.5193i −0.593176 + 1.48774i
\(637\) −1.11286 1.11286i −0.0440932 0.0440932i
\(638\) −7.21268 + 4.88907i −0.285553 + 0.193560i
\(639\) 0.313960 0.0124201
\(640\) 2.72136 + 10.9815i 0.107571 + 0.434083i
\(641\) −12.4211 −0.490602 −0.245301 0.969447i \(-0.578887\pi\)
−0.245301 + 0.969447i \(0.578887\pi\)
\(642\) −3.54611 + 2.40371i −0.139954 + 0.0948669i
\(643\) −4.58322 4.58322i −0.180744 0.180744i 0.610936 0.791680i \(-0.290793\pi\)
−0.791680 + 0.610936i \(0.790793\pi\)
\(644\) −2.46179 + 6.17440i −0.0970082 + 0.243305i
\(645\) −12.2295 + 12.2295i −0.481537 + 0.481537i
\(646\) 0.0570202 + 0.0109482i 0.00224343 + 0.000430751i
\(647\) 3.25672i 0.128035i −0.997949 0.0640174i \(-0.979609\pi\)
0.997949 0.0640174i \(-0.0203913\pi\)
\(648\) −5.74506 26.1441i −0.225687 1.02704i
\(649\) 4.25954i 0.167202i
\(650\) 0.419685 2.18580i 0.0164614 0.0857340i
\(651\) 7.74036 7.74036i 0.303368 0.303368i
\(652\) 9.19850 3.95433i 0.360241 0.154864i
\(653\) −12.8699 12.8699i −0.503636 0.503636i 0.408930 0.912566i \(-0.365902\pi\)
−0.912566 + 0.408930i \(0.865902\pi\)
\(654\) −6.32385 9.32935i −0.247282 0.364806i
\(655\) 14.4140 0.563203
\(656\) 16.0647 16.9433i 0.627222 0.661525i
\(657\) 1.28646 0.0501895
\(658\) 4.34245 + 6.40626i 0.169286 + 0.249742i
\(659\) 33.4531 + 33.4531i 1.30315 + 1.30315i 0.926259 + 0.376887i \(0.123005\pi\)
0.376887 + 0.926259i \(0.376995\pi\)
\(660\) −1.29390 3.00984i −0.0503650 0.117158i
\(661\) 6.33269 6.33269i 0.246313 0.246313i −0.573142 0.819456i \(-0.694276\pi\)
0.819456 + 0.573142i \(0.194276\pi\)
\(662\) 2.71211 14.1251i 0.105409 0.548989i
\(663\) 1.68800i 0.0655565i
\(664\) 24.5885 38.4383i 0.954218 1.49170i
\(665\) 0.0680842i 0.00264019i
\(666\) 1.04773 + 0.201171i 0.0405989 + 0.00779521i
\(667\) 15.7222 15.7222i 0.608768 0.608768i
\(668\) 31.9054 + 12.7210i 1.23446 + 0.492190i
\(669\) 18.7883 + 18.7883i 0.726399 + 0.726399i
\(670\) −0.332612 + 0.225459i −0.0128499 + 0.00871025i
\(671\) −10.4200 −0.402258
\(672\) 8.17529 5.86499i 0.315369 0.226247i
\(673\) −20.3771 −0.785481 −0.392740 0.919649i \(-0.628473\pi\)
−0.392740 + 0.919649i \(0.628473\pi\)
\(674\) −0.148160 + 0.100429i −0.00570691 + 0.00386840i
\(675\) 3.56737 + 3.56737i 0.137308 + 0.137308i
\(676\) −19.5496 7.79460i −0.751906 0.299792i
\(677\) −5.97856 + 5.97856i −0.229775 + 0.229775i −0.812599 0.582824i \(-0.801948\pi\)
0.582824 + 0.812599i \(0.301948\pi\)
\(678\) −28.9747 5.56330i −1.11277 0.213657i
\(679\) 4.28142i 0.164306i
\(680\) 1.43677 + 0.919083i 0.0550977 + 0.0352452i
\(681\) 0.568985i 0.0218035i
\(682\) 1.51149 7.87214i 0.0578781 0.301440i
\(683\) −32.5411 + 32.5411i −1.24515 + 1.24515i −0.287312 + 0.957837i \(0.592762\pi\)
−0.957837 + 0.287312i \(0.907238\pi\)
\(684\) −0.00879524 0.0204593i −0.000336294 0.000782282i
\(685\) −6.28445 6.28445i −0.240116 0.240116i
\(686\) 0.793500 + 1.17062i 0.0302960 + 0.0446946i
\(687\) 44.5397 1.69929
\(688\) −38.8815 + 1.03491i −1.48234 + 0.0394557i
\(689\) 17.8702 0.680801
\(690\) 4.69067 + 6.91997i 0.178571 + 0.263439i
\(691\) 31.9319 + 31.9319i 1.21475 + 1.21475i 0.969448 + 0.245298i \(0.0788860\pi\)
0.245298 + 0.969448i \(0.421114\pi\)
\(692\) −28.7159 + 12.3446i −1.09161 + 0.469273i
\(693\) −0.106506 + 0.106506i −0.00404583 + 0.00404583i
\(694\) −9.44467 + 49.1896i −0.358515 + 1.86721i
\(695\) 7.98401i 0.302851i
\(696\) −32.8716 + 7.22339i −1.24600 + 0.273802i
\(697\) 3.51987i 0.133325i
\(698\) −7.56526 1.45257i −0.286349 0.0549806i
\(699\) 25.6374 25.6374i 0.969697 0.969697i
\(700\) −0.740715 + 1.85778i −0.0279964 + 0.0702174i
\(701\) −1.20601 1.20601i −0.0455503 0.0455503i 0.683965 0.729515i \(-0.260254\pi\)
−0.729515 + 0.683965i \(0.760254\pi\)
\(702\) −9.29471 + 6.30037i −0.350806 + 0.237792i
\(703\) −0.314055 −0.0118448
\(704\) 2.54567 6.91409i 0.0959435 0.260585i
\(705\) 9.73363 0.366590
\(706\) −4.02511 + 2.72840i −0.151487 + 0.102685i
\(707\) −1.91367 1.91367i −0.0719709 0.0719709i
\(708\) −6.09327 + 15.2825i −0.228999 + 0.574350i
\(709\) 33.1834 33.1834i 1.24623 1.24623i 0.288856 0.957372i \(-0.406725\pi\)
0.957372 0.288856i \(-0.0932750\pi\)
\(710\) −2.66618 0.511921i −0.100060 0.0192121i
\(711\) 0.247028i 0.00926426i
\(712\) −4.95955 + 1.08984i −0.185867 + 0.0408434i
\(713\) 20.4545i 0.766028i
\(714\) 0.286011 1.48960i 0.0107037 0.0557469i
\(715\) −1.02492 + 1.02492i −0.0383300 + 0.0383300i
\(716\) −2.86444 + 1.23139i −0.107049 + 0.0460193i
\(717\) −34.6941 34.6941i −1.29567 1.29567i
\(718\) 24.6772 + 36.4053i 0.920944 + 1.35864i
\(719\) −34.7079 −1.29439 −0.647194 0.762326i \(-0.724057\pi\)
−0.647194 + 0.762326i \(0.724057\pi\)
\(720\) −0.0174063 0.653950i −0.000648693 0.0243713i
\(721\) −13.2595 −0.493810
\(722\) −15.0728 22.2364i −0.560953 0.827553i
\(723\) −2.99461 2.99461i −0.111371 0.111371i
\(724\) 4.02859 + 9.37122i 0.149721 + 0.348279i
\(725\) 4.73058 4.73058i 0.175689 0.175689i
\(726\) 4.81501 25.0775i 0.178702 0.930712i
\(727\) 22.5592i 0.836673i −0.908292 0.418337i \(-0.862613\pi\)
0.908292 0.418337i \(-0.137387\pi\)
\(728\) −3.74986 2.39873i −0.138979 0.0889030i
\(729\) 25.3720i 0.939703i
\(730\) −10.9247 2.09761i −0.404342 0.0776359i
\(731\) −4.14621 + 4.14621i −0.153353 + 0.153353i
\(732\) −37.3849 14.9057i −1.38179 0.550932i
\(733\) −36.3696 36.3696i −1.34334 1.34334i −0.892709 0.450633i \(-0.851198\pi\)
−0.450633 0.892709i \(-0.648802\pi\)
\(734\) 21.2059 14.3743i 0.782724 0.530566i
\(735\) 1.77864 0.0656060
\(736\) −3.05257 + 18.5513i −0.112519 + 0.683810i
\(737\) 0.261680 0.00963912
\(738\) −1.11752 + 0.757502i −0.0411363 + 0.0278840i
\(739\) −28.6280 28.6280i −1.05310 1.05310i −0.998509 0.0545872i \(-0.982616\pi\)
−0.0545872 0.998509i \(-0.517384\pi\)
\(740\) −8.56945 3.41672i −0.315019 0.125601i
\(741\) −0.134764 + 0.134764i −0.00495068 + 0.00495068i
\(742\) −15.7698 3.02790i −0.578929 0.111158i
\(743\) 5.92667i 0.217429i 0.994073 + 0.108714i \(0.0346734\pi\)
−0.994073 + 0.108714i \(0.965327\pi\)
\(744\) 16.6841 26.0816i 0.611667 0.956199i
\(745\) 20.8026i 0.762148i
\(746\) 6.03813 31.4477i 0.221072 1.15138i
\(747\) −1.86565 + 1.86565i −0.0682604 + 0.0682604i
\(748\) −0.438675 1.02044i −0.0160395 0.0373109i
\(749\) −1.20430 1.20430i −0.0440040 0.0440040i
\(750\) 1.41135 + 2.08211i 0.0515351 + 0.0760280i
\(751\) −7.28601 −0.265870 −0.132935 0.991125i \(-0.542440\pi\)
−0.132935 + 0.991125i \(0.542440\pi\)
\(752\) 15.8850 + 15.0613i 0.579266 + 0.549229i
\(753\) 23.8835 0.870362
\(754\) 8.35473 + 12.3254i 0.304261 + 0.448866i
\(755\) 6.00687 + 6.00687i 0.218613 + 0.218613i
\(756\) 9.26978 3.98498i 0.337139 0.144932i
\(757\) −24.2438 + 24.2438i −0.881155 + 0.881155i −0.993652 0.112497i \(-0.964115\pi\)
0.112497 + 0.993652i \(0.464115\pi\)
\(758\) 5.89397 30.6969i 0.214079 1.11496i
\(759\) 5.44425i 0.197614i
\(760\) 0.0413305 + 0.188084i 0.00149922 + 0.00682251i
\(761\) 7.13566i 0.258668i −0.991601 0.129334i \(-0.958716\pi\)
0.991601 0.129334i \(-0.0412839\pi\)
\(762\) 1.06171 + 0.203854i 0.0384617 + 0.00738486i
\(763\) 3.16834 3.16834i 0.114702 0.114702i
\(764\) −12.7395 + 31.9517i −0.460897 + 1.15597i
\(765\) −0.0697353 0.0697353i −0.00252128 0.00252128i
\(766\) −21.1057 + 14.3064i −0.762581 + 0.516912i
\(767\) 7.27894 0.262827
\(768\) 19.0240 21.1649i 0.686470 0.763724i
\(769\) −41.9735 −1.51360 −0.756802 0.653645i \(-0.773239\pi\)
−0.756802 + 0.653645i \(0.773239\pi\)
\(770\) 1.07812 0.730798i 0.0388528 0.0263361i
\(771\) −22.0137 22.0137i −0.792805 0.792805i
\(772\) −4.53856 + 11.3831i −0.163346 + 0.409687i
\(773\) −15.5336 + 15.5336i −0.558705 + 0.558705i −0.928939 0.370233i \(-0.879278\pi\)
0.370233 + 0.928939i \(0.379278\pi\)
\(774\) 2.20866 + 0.424075i 0.0793887 + 0.0152431i
\(775\) 6.15445i 0.221074i
\(776\) −2.59904 11.8275i −0.0933001 0.424582i
\(777\) 8.20438i 0.294331i
\(778\) 1.73214 9.02129i 0.0621002 0.323429i
\(779\) 0.281015 0.281015i 0.0100684 0.0100684i
\(780\) −5.14339 + 2.21109i −0.184163 + 0.0791697i
\(781\) 1.25018 + 1.25018i 0.0447348 + 0.0447348i
\(782\) 1.59029 + 2.34610i 0.0568687 + 0.0838963i
\(783\) −33.7514 −1.20618
\(784\) 2.90268 + 2.75217i 0.103667 + 0.0982917i
\(785\) −12.4411 −0.444041
\(786\) −20.3432 30.0116i −0.725618 1.07048i
\(787\) −36.4484 36.4484i −1.29924 1.29924i −0.928891 0.370353i \(-0.879237\pi\)
−0.370353 0.928891i \(-0.620763\pi\)
\(788\) 18.1464 + 42.2118i 0.646438 + 1.50373i
\(789\) 36.9499 36.9499i 1.31545 1.31545i
\(790\) 0.402786 2.09778i 0.0143305 0.0746358i
\(791\) 11.7295i 0.417052i
\(792\) −0.229570 + 0.358879i −0.00815741 + 0.0127522i
\(793\) 17.8062i 0.632317i
\(794\) −32.7231 6.28302i −1.16130 0.222976i
\(795\) −14.2806 + 14.2806i −0.506480 + 0.506480i
\(796\) −8.31961 3.31711i −0.294881 0.117572i
\(797\) −32.7530 32.7530i −1.16017 1.16017i −0.984438 0.175732i \(-0.943771\pi\)
−0.175732 0.984438i \(-0.556229\pi\)
\(798\) 0.141759 0.0960905i 0.00501821 0.00340157i
\(799\) 3.30002 0.116746
\(800\) −0.918470 + 5.58179i −0.0324728 + 0.197346i
\(801\) 0.293613 0.0103743
\(802\) 28.0756 19.0309i 0.991385 0.672005i
\(803\) 5.12262 + 5.12262i 0.180773 + 0.180773i
\(804\) 0.938862 + 0.374334i 0.0331111 + 0.0132017i
\(805\) −2.35010 + 2.35010i −0.0828300 + 0.0828300i
\(806\) −13.4524 2.58293i −0.473839 0.0909798i
\(807\) 26.2949i 0.925624i
\(808\) −6.44823 4.12484i −0.226848 0.145111i
\(809\) 4.49260i 0.157951i 0.996877 + 0.0789756i \(0.0251649\pi\)
−0.996877 + 0.0789756i \(0.974835\pi\)
\(810\) 2.52370 13.1439i 0.0886736 0.461829i
\(811\) 3.24039 3.24039i 0.113786 0.113786i −0.647922 0.761707i \(-0.724362\pi\)
0.761707 + 0.647922i \(0.224362\pi\)
\(812\) −5.28436 12.2924i −0.185445 0.431378i
\(813\) 25.3844 + 25.3844i 0.890268 + 0.890268i
\(814\) 3.37098 + 4.97309i 0.118153 + 0.174307i
\(815\) 5.00622 0.175360
\(816\) −0.114152 4.28867i −0.00399612 0.150133i
\(817\) −0.662039 −0.0231618
\(818\) −15.7587 23.2482i −0.550990 0.812856i
\(819\) 0.182003 + 0.182003i 0.00635972 + 0.00635972i
\(820\) 10.7252 4.61064i 0.374540 0.161011i
\(821\) 36.5352 36.5352i 1.27509 1.27509i 0.331706 0.943383i \(-0.392376\pi\)
0.943383 0.331706i \(-0.107624\pi\)
\(822\) −4.21538 + 21.9545i −0.147028 + 0.765750i
\(823\) 24.0637i 0.838809i 0.907799 + 0.419404i \(0.137761\pi\)
−0.907799 + 0.419404i \(0.862239\pi\)
\(824\) −36.6296 + 8.04919i −1.27605 + 0.280407i
\(825\) 1.63809i 0.0570309i
\(826\) −6.42341 1.23333i −0.223499 0.0429131i
\(827\) −27.2971 + 27.2971i −0.949213 + 0.949213i −0.998771 0.0495578i \(-0.984219\pi\)
0.0495578 + 0.998771i \(0.484219\pi\)
\(828\) 0.402615 1.00979i 0.0139918 0.0350928i
\(829\) 31.3499 + 31.3499i 1.08883 + 1.08883i 0.995649 + 0.0931792i \(0.0297029\pi\)
0.0931792 + 0.995649i \(0.470297\pi\)
\(830\) 18.8852 12.8013i 0.655517 0.444338i
\(831\) −0.857167 −0.0297348
\(832\) −11.8152 4.35018i −0.409618 0.150815i
\(833\) 0.603016 0.0208933
\(834\) −16.6236 + 11.2682i −0.575628 + 0.390187i
\(835\) 12.1438 + 12.1438i 0.420254 + 0.420254i
\(836\) 0.0464459 0.116490i 0.00160636 0.00402891i
\(837\) 21.9552 21.9552i 0.758882 0.758882i
\(838\) 11.0646 + 2.12447i 0.382221 + 0.0733885i
\(839\) 34.6426i 1.19599i −0.801498 0.597997i \(-0.795963\pi\)
0.801498 0.597997i \(-0.204037\pi\)
\(840\) 4.91351 1.07972i 0.169532 0.0372539i
\(841\) 15.7567i 0.543336i
\(842\) −5.39926 + 28.1204i −0.186071 + 0.969092i
\(843\) −14.4146 + 14.4146i −0.496466 + 0.496466i
\(844\) −15.8632 + 6.81942i −0.546034 + 0.234734i
\(845\) −7.44094 7.44094i −0.255976 0.255976i
\(846\) −0.710188 1.04771i −0.0244168 0.0360212i
\(847\) 10.1518 0.348820
\(848\) −45.4025 + 1.20848i −1.55913 + 0.0414995i
\(849\) −44.2341 −1.51811
\(850\) 0.478494 + 0.705905i 0.0164122 + 0.0242123i
\(851\) −10.8404 10.8404i −0.371603 0.371603i
\(852\) 2.69703 + 6.27378i 0.0923987 + 0.214936i
\(853\) −17.6395 + 17.6395i −0.603963 + 0.603963i −0.941362 0.337399i \(-0.890453\pi\)
0.337399 + 0.941362i \(0.390453\pi\)
\(854\) 3.01705 15.7134i 0.103241 0.537700i
\(855\) 0.0111349i 0.000380804i
\(856\) −4.05795 2.59582i −0.138698 0.0887231i
\(857\) 9.60441i 0.328080i 0.986454 + 0.164040i \(0.0524527\pi\)
−0.986454 + 0.164040i \(0.947547\pi\)
\(858\) 3.58053 + 0.687481i 0.122237 + 0.0234702i
\(859\) 12.1676 12.1676i 0.415155 0.415155i −0.468375 0.883530i \(-0.655160\pi\)
0.883530 + 0.468375i \(0.155160\pi\)
\(860\) −18.0647 7.20258i −0.616002 0.245606i
\(861\) −7.34125 7.34125i −0.250189 0.250189i
\(862\) −32.6428 + 22.1267i −1.11182 + 0.753639i
\(863\) −31.2901 −1.06513 −0.532564 0.846390i \(-0.678771\pi\)
−0.532564 + 0.846390i \(0.678771\pi\)
\(864\) 23.1888 16.6358i 0.788900 0.565961i
\(865\) −15.6284 −0.531383
\(866\) −13.7298 + 9.30664i −0.466556 + 0.316253i
\(867\) 20.9233 + 20.9233i 0.710593 + 0.710593i
\(868\) 11.4336 + 4.55869i 0.388082 + 0.154732i
\(869\) −0.983654 + 0.983654i −0.0333682 + 0.0333682i
\(870\) −16.5261 3.17310i −0.560287 0.107578i
\(871\) 0.447174i 0.0151519i
\(872\) 6.82925 10.6759i 0.231268 0.361533i
\(873\) 0.700207i 0.0236984i
\(874\) −0.0603412 + 0.314268i −0.00204107 + 0.0106303i
\(875\) −0.707107 + 0.707107i −0.0239046 + 0.0239046i
\(876\) 11.0511 + 25.7070i 0.373383 + 0.868557i
\(877\) −25.0684 25.0684i −0.846501 0.846501i 0.143194 0.989695i \(-0.454263\pi\)
−0.989695 + 0.143194i \(0.954263\pi\)
\(878\) 0.385131 + 0.568171i 0.0129976 + 0.0191748i
\(879\) 25.3797 0.856036
\(880\) 2.53469 2.67331i 0.0854445 0.0901174i
\(881\) 2.08150 0.0701277 0.0350638 0.999385i \(-0.488837\pi\)
0.0350638 + 0.999385i \(0.488837\pi\)
\(882\) −0.129773 0.191450i −0.00436970 0.00644646i
\(883\) −17.8914 17.8914i −0.602094 0.602094i 0.338774 0.940868i \(-0.389988\pi\)
−0.940868 + 0.338774i \(0.889988\pi\)
\(884\) −1.74378 + 0.749632i −0.0586497 + 0.0252129i
\(885\) −5.81680 + 5.81680i −0.195530 + 0.195530i
\(886\) −1.16663 + 6.07604i −0.0391938 + 0.204128i
\(887\) 52.0223i 1.74674i −0.487060 0.873368i \(-0.661931\pi\)
0.487060 0.873368i \(-0.338069\pi\)
\(888\) 4.98048 + 22.6647i 0.167134 + 0.760579i
\(889\) 0.429799i 0.0144150i
\(890\) −2.49339 0.478745i −0.0835787 0.0160476i
\(891\) −6.16318 + 6.16318i −0.206474 + 0.206474i
\(892\) −11.0654 + 27.7530i −0.370497 + 0.929240i
\(893\) 0.263462 + 0.263462i 0.00881643 + 0.00881643i
\(894\) 43.3133 29.3597i 1.44861 0.981935i
\(895\) −1.55895 −0.0521101
\(896\) 9.68941 + 5.84083i 0.323701 + 0.195128i
\(897\) −9.30344 −0.310633
\(898\) 24.0675 16.3141i 0.803144 0.544407i
\(899\) −29.1141 29.1141i −0.971009 0.971009i
\(900\) 0.121141 0.303831i 0.00403802 0.0101277i
\(901\) −4.84159 + 4.84159i −0.161297 + 0.161297i
\(902\) −7.46624 1.43356i −0.248599 0.0477323i
\(903\) 17.2951i 0.575546i
\(904\) −7.12037 32.4028i −0.236820 1.07770i
\(905\) 5.10023i 0.169537i
\(906\) 4.02919 20.9848i 0.133861 0.697172i
\(907\) 15.2655 15.2655i 0.506884 0.506884i −0.406685 0.913568i \(-0.633315\pi\)
0.913568 + 0.406685i \(0.133315\pi\)
\(908\) 0.587787 0.252683i 0.0195064 0.00838559i
\(909\) 0.312972 + 0.312972i 0.0103806 + 0.0103806i
\(910\) −1.24883 1.84235i −0.0413983 0.0610734i
\(911\) 25.0817 0.830992 0.415496 0.909595i \(-0.363608\pi\)
0.415496 + 0.909595i \(0.363608\pi\)
\(912\) 0.333279 0.351506i 0.0110360 0.0116395i
\(913\) −14.8579 −0.491723
\(914\) 24.7466 + 36.5078i 0.818546 + 1.20757i
\(915\) −14.2294 14.2294i −0.470410 0.470410i
\(916\) 19.7799 + 46.0115i 0.653545 + 1.52026i
\(917\) 10.1923 10.1923i 0.336578 0.336578i
\(918\) 0.811258 4.22518i 0.0267755 0.139452i
\(919\) 33.4635i 1.10386i 0.833891 + 0.551929i \(0.186108\pi\)
−0.833891 + 0.551929i \(0.813892\pi\)
\(920\) −5.06555 + 7.91880i −0.167006 + 0.261075i
\(921\) 47.4553i 1.56370i
\(922\) −18.5149 3.55495i −0.609755 0.117076i
\(923\) 2.13637 2.13637i 0.0703195 0.0703195i
\(924\) −3.04321 1.21336i −0.100114 0.0399165i
\(925\) −3.26170 3.26170i −0.107244 0.107244i
\(926\) 17.7307 12.0187i 0.582668 0.394959i
\(927\) 2.16853 0.0712239
\(928\) −22.0602 30.7500i −0.724162 1.00942i
\(929\) 32.1012 1.05321 0.526604 0.850111i \(-0.323465\pi\)
0.526604 + 0.850111i \(0.323465\pi\)
\(930\) 12.8142 8.68606i 0.420196 0.284827i
\(931\) 0.0481428 + 0.0481428i 0.00157782 + 0.00157782i
\(932\) 37.8701 + 15.0992i 1.24048 + 0.494590i
\(933\) 0.113815 0.113815i 0.00372615 0.00372615i
\(934\) 43.8548 + 8.42036i 1.43497 + 0.275522i
\(935\) 0.555366i 0.0181624i
\(936\) 0.613273 + 0.392302i 0.0200454 + 0.0128228i
\(937\) 51.7263i 1.68983i 0.534904 + 0.844913i \(0.320348\pi\)
−0.534904 + 0.844913i \(0.679652\pi\)
\(938\) −0.0757684 + 0.394616i −0.00247393 + 0.0128847i
\(939\) −33.2002 + 33.2002i −1.08345 + 1.08345i
\(940\) 4.32266 + 10.0553i 0.140989 + 0.327967i
\(941\) 28.8417 + 28.8417i 0.940213 + 0.940213i 0.998311 0.0580982i \(-0.0185036\pi\)
−0.0580982 + 0.998311i \(0.518504\pi\)
\(942\) 17.5587 + 25.9037i 0.572092 + 0.843988i
\(943\) 19.3999 0.631746
\(944\) −18.4935 + 0.492243i −0.601911 + 0.0160211i
\(945\) 5.04502 0.164115
\(946\) 7.10615 + 10.4835i 0.231041 + 0.340847i
\(947\) −32.4926 32.4926i −1.05587 1.05587i −0.998344 0.0575247i \(-0.981679\pi\)
−0.0575247 0.998344i \(-0.518321\pi\)
\(948\) −4.93629 + 2.12206i −0.160323 + 0.0689212i
\(949\) 8.75383 8.75383i 0.284161 0.284161i
\(950\) −0.0181557 + 0.0945583i −0.000589049 + 0.00306788i
\(951\) 6.95666i 0.225585i
\(952\) 1.66584 0.366061i 0.0539902 0.0118641i
\(953\) 56.0737i 1.81641i −0.418530 0.908203i \(-0.637454\pi\)
0.418530 0.908203i \(-0.362546\pi\)
\(954\) 2.57909 + 0.495199i 0.0835010 + 0.0160327i
\(955\) −12.1614 + 12.1614i −0.393535 + 0.393535i
\(956\) 20.4331 51.2480i 0.660854 1.65748i
\(957\) 7.74911 + 7.74911i 0.250493 + 0.250493i
\(958\) 25.0303 16.9666i 0.808692 0.548168i
\(959\) −8.88755 −0.286994
\(960\) 12.9182 5.96550i 0.416933 0.192536i
\(961\) 6.87720 0.221845
\(962\) 8.49830 5.76053i 0.273996 0.185727i
\(963\) 0.196957 + 0.196957i 0.00634685 + 0.00634685i
\(964\) 1.76368 4.42346i 0.0568043 0.142470i
\(965\) −4.33263 + 4.33263i −0.139472 + 0.139472i
\(966\) 8.20996 + 1.57636i 0.264151 + 0.0507185i
\(967\) 21.7506i 0.699453i −0.936852 0.349726i \(-0.886275\pi\)
0.936852 0.349726i \(-0.113725\pi\)
\(968\) 28.0445 6.16265i 0.901384 0.198075i
\(969\) 0.0730234i 0.00234585i
\(970\) 1.14171 5.94623i 0.0366581 0.190922i
\(971\) −9.05037 + 9.05037i −0.290440 + 0.290440i −0.837254 0.546814i \(-0.815840\pi\)
0.546814 + 0.837254i \(0.315840\pi\)
\(972\) −3.11947 + 1.34103i −0.100057 + 0.0430135i
\(973\) −5.64555 5.64555i −0.180988 0.180988i
\(974\) 8.07390 + 11.9111i 0.258704 + 0.381657i
\(975\) −2.79926 −0.0896481
\(976\) −1.20415 45.2399i −0.0385441 1.44809i
\(977\) 38.0834 1.21840 0.609198 0.793018i \(-0.291491\pi\)
0.609198 + 0.793018i \(0.291491\pi\)
\(978\) −7.06552 10.4235i −0.225931 0.333307i
\(979\) 1.16916 + 1.16916i 0.0373664 + 0.0373664i
\(980\) 0.789884 + 1.83741i 0.0252319 + 0.0586940i
\(981\) −0.518169 + 0.518169i −0.0165438 + 0.0165438i
\(982\) −4.20872 + 21.9198i −0.134306 + 0.699488i
\(983\) 33.0264i 1.05338i 0.850058 + 0.526690i \(0.176567\pi\)
−0.850058 + 0.526690i \(0.823433\pi\)
\(984\) −24.7368 15.8238i −0.788581 0.504445i
\(985\) 22.9735i 0.731996i
\(986\) −5.60289 1.07579i −0.178432 0.0342600i
\(987\) 6.88271 6.88271i 0.219079 0.219079i
\(988\) −0.199066 0.0793694i −0.00633312 0.00252508i
\(989\) −22.8519 22.8519i −0.726649 0.726649i
\(990\) −0.176322 + 0.119519i −0.00560387 + 0.00379855i
\(991\) −53.6439 −1.70405 −0.852027 0.523498i \(-0.824627\pi\)
−0.852027 + 0.523498i \(0.824627\pi\)
\(992\) 34.3528 + 5.65267i 1.09070 + 0.179473i
\(993\) −18.0895 −0.574053
\(994\) −2.24726 + 1.52329i −0.0712786 + 0.0483158i
\(995\) −3.16661 3.16661i −0.100388 0.100388i
\(996\) −53.3073 21.2542i −1.68911 0.673464i
\(997\) −24.9318 + 24.9318i −0.789597 + 0.789597i −0.981428 0.191831i \(-0.938557\pi\)
0.191831 + 0.981428i \(0.438557\pi\)
\(998\) 47.5399 + 9.12792i 1.50485 + 0.288939i
\(999\) 23.2714i 0.736273i
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 560.2.bd.a.141.17 44
4.3 odd 2 2240.2.bd.a.1681.17 44
16.5 even 4 inner 560.2.bd.a.421.17 yes 44
16.11 odd 4 2240.2.bd.a.561.17 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
560.2.bd.a.141.17 44 1.1 even 1 trivial
560.2.bd.a.421.17 yes 44 16.5 even 4 inner
2240.2.bd.a.561.17 44 16.11 odd 4
2240.2.bd.a.1681.17 44 4.3 odd 2