Properties

Label 546.2.z.a.131.13
Level $546$
Weight $2$
Character 546.131
Analytic conductor $4.360$
Analytic rank $0$
Dimension $32$
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] = [546,2,Mod(131,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.z (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 131.13
Character \(\chi\) \(=\) 546.131
Dual form 546.2.z.a.521.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.305007 - 1.70498i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.04730 - 1.81398i) q^{5} +(1.11664 - 1.32406i) q^{6} +(1.84957 - 1.89185i) q^{7} +1.00000i q^{8} +(-2.81394 - 1.04007i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.305007 - 1.70498i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.04730 - 1.81398i) q^{5} +(1.11664 - 1.32406i) q^{6} +(1.84957 - 1.89185i) q^{7} +1.00000i q^{8} +(-2.81394 - 1.04007i) q^{9} +(1.81398 - 1.04730i) q^{10} +(-1.67306 + 0.965940i) q^{11} +(1.62906 - 0.588348i) q^{12} -1.00000i q^{13} +(2.54770 - 0.713604i) q^{14} +(-2.77337 - 2.33891i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.345960 + 0.599220i) q^{17} +(-1.91691 - 2.30769i) q^{18} +(2.08687 + 1.20485i) q^{19} +2.09460 q^{20} +(-2.66144 - 3.73052i) q^{21} -1.93188 q^{22} +(-3.14870 - 1.81790i) q^{23} +(1.70498 + 0.305007i) q^{24} +(0.306322 + 0.530566i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.63157 + 4.48050i) q^{27} +(2.56317 + 0.655850i) q^{28} -3.88157i q^{29} +(-1.23235 - 3.41224i) q^{30} +(0.817770 - 0.472140i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.13662 + 3.14716i) q^{33} +0.691920i q^{34} +(-1.49472 - 5.33641i) q^{35} +(-0.506247 - 2.95698i) q^{36} +(-3.57753 + 6.19647i) q^{37} +(1.20485 + 2.08687i) q^{38} +(-1.70498 - 0.305007i) q^{39} +(1.81398 + 1.04730i) q^{40} +8.66067 q^{41} +(-0.439616 - 4.56144i) q^{42} +8.01907 q^{43} +(-1.67306 - 0.965940i) q^{44} +(-4.83370 + 4.01517i) q^{45} +(-1.81790 - 3.14870i) q^{46} +(-2.19759 + 3.80633i) q^{47} +(1.32406 + 1.11664i) q^{48} +(-0.158181 - 6.99821i) q^{49} +0.612645i q^{50} +(1.12718 - 0.407090i) q^{51} +(0.866025 - 0.500000i) q^{52} +(4.81192 - 2.77816i) q^{53} +(-4.51925 + 2.56444i) q^{54} +4.04652i q^{55} +(1.89185 + 1.84957i) q^{56} +(2.69076 - 3.19058i) q^{57} +(1.94079 - 3.36154i) q^{58} +(5.21237 + 9.02810i) q^{59} +(0.638869 - 3.57126i) q^{60} +(2.92469 + 1.68857i) q^{61} +0.944280 q^{62} +(-7.17223 + 3.39988i) q^{63} -1.00000 q^{64} +(-1.81398 - 1.04730i) q^{65} +(-0.589238 + 3.29383i) q^{66} +(-4.98074 - 8.62689i) q^{67} +(-0.345960 + 0.599220i) q^{68} +(-4.05987 + 4.81401i) q^{69} +(1.37375 - 5.36883i) q^{70} +3.58456i q^{71} +(1.04007 - 2.81394i) q^{72} +(7.46660 - 4.31085i) q^{73} +(-6.19647 + 3.57753i) q^{74} +(0.998037 - 0.360448i) q^{75} +2.40970i q^{76} +(-1.26702 + 4.95175i) q^{77} +(-1.32406 - 1.11664i) q^{78} +(-8.33482 + 14.4363i) q^{79} +(1.04730 + 1.81398i) q^{80} +(6.83653 + 5.85337i) q^{81} +(7.50036 + 4.33034i) q^{82} -12.5850 q^{83} +(1.90000 - 4.17013i) q^{84} +1.44930 q^{85} +(6.94472 + 4.00954i) q^{86} +(-6.61802 - 1.18391i) q^{87} +(-0.965940 - 1.67306i) q^{88} +(-7.45988 + 12.9209i) q^{89} +(-6.19369 + 1.06039i) q^{90} +(-1.89185 - 1.84957i) q^{91} -3.63581i q^{92} +(-0.555565 - 1.53829i) q^{93} +(-3.80633 + 2.19759i) q^{94} +(4.37115 - 2.52369i) q^{95} +(0.588348 + 1.62906i) q^{96} -2.33951i q^{97} +(3.36212 - 6.13972i) q^{98} +(5.71253 - 0.978010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.305007 1.70498i 0.176096 0.984373i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.04730 1.81398i 0.468367 0.811236i −0.530979 0.847385i \(-0.678176\pi\)
0.999346 + 0.0361491i \(0.0115091\pi\)
\(6\) 1.11664 1.32406i 0.455865 0.540544i
\(7\) 1.84957 1.89185i 0.699072 0.715052i
\(8\) 1.00000i 0.353553i
\(9\) −2.81394 1.04007i −0.937980 0.346688i
\(10\) 1.81398 1.04730i 0.573630 0.331186i
\(11\) −1.67306 + 0.965940i −0.504446 + 0.291242i −0.730548 0.682862i \(-0.760735\pi\)
0.226102 + 0.974104i \(0.427402\pi\)
\(12\) 1.62906 0.588348i 0.470270 0.169841i
\(13\) 1.00000i 0.277350i
\(14\) 2.54770 0.713604i 0.680901 0.190719i
\(15\) −2.77337 2.33891i −0.716081 0.603903i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.345960 + 0.599220i 0.0839076 + 0.145332i 0.904925 0.425571i \(-0.139927\pi\)
−0.821018 + 0.570903i \(0.806593\pi\)
\(18\) −1.91691 2.30769i −0.451820 0.543929i
\(19\) 2.08687 + 1.20485i 0.478760 + 0.276412i 0.719900 0.694078i \(-0.244188\pi\)
−0.241140 + 0.970490i \(0.577521\pi\)
\(20\) 2.09460 0.468367
\(21\) −2.66144 3.73052i −0.580774 0.814065i
\(22\) −1.93188 −0.411878
\(23\) −3.14870 1.81790i −0.656550 0.379059i 0.134411 0.990926i \(-0.457086\pi\)
−0.790961 + 0.611866i \(0.790419\pi\)
\(24\) 1.70498 + 0.305007i 0.348028 + 0.0622594i
\(25\) 0.306322 + 0.530566i 0.0612645 + 0.106113i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −2.63157 + 4.48050i −0.506445 + 0.862272i
\(28\) 2.56317 + 0.655850i 0.484394 + 0.123944i
\(29\) 3.88157i 0.720790i −0.932800 0.360395i \(-0.882642\pi\)
0.932800 0.360395i \(-0.117358\pi\)
\(30\) −1.23235 3.41224i −0.224996 0.622987i
\(31\) 0.817770 0.472140i 0.146876 0.0847988i −0.424761 0.905305i \(-0.639642\pi\)
0.571637 + 0.820507i \(0.306309\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 1.13662 + 3.14716i 0.197860 + 0.547849i
\(34\) 0.691920i 0.118663i
\(35\) −1.49472 5.33641i −0.252653 0.902019i
\(36\) −0.506247 2.95698i −0.0843746 0.492830i
\(37\) −3.57753 + 6.19647i −0.588142 + 1.01869i 0.406333 + 0.913725i \(0.366807\pi\)
−0.994476 + 0.104968i \(0.966526\pi\)
\(38\) 1.20485 + 2.08687i 0.195453 + 0.338534i
\(39\) −1.70498 0.305007i −0.273016 0.0488403i
\(40\) 1.81398 + 1.04730i 0.286815 + 0.165593i
\(41\) 8.66067 1.35257 0.676285 0.736640i \(-0.263589\pi\)
0.676285 + 0.736640i \(0.263589\pi\)
\(42\) −0.439616 4.56144i −0.0678342 0.703846i
\(43\) 8.01907 1.22290 0.611449 0.791284i \(-0.290587\pi\)
0.611449 + 0.791284i \(0.290587\pi\)
\(44\) −1.67306 0.965940i −0.252223 0.145621i
\(45\) −4.83370 + 4.01517i −0.720565 + 0.598546i
\(46\) −1.81790 3.14870i −0.268035 0.464251i
\(47\) −2.19759 + 3.80633i −0.320551 + 0.555210i −0.980602 0.196010i \(-0.937201\pi\)
0.660051 + 0.751221i \(0.270535\pi\)
\(48\) 1.32406 + 1.11664i 0.191111 + 0.161173i
\(49\) −0.158181 6.99821i −0.0225973 0.999745i
\(50\) 0.612645i 0.0866410i
\(51\) 1.12718 0.407090i 0.157837 0.0570040i
\(52\) 0.866025 0.500000i 0.120096 0.0693375i
\(53\) 4.81192 2.77816i 0.660968 0.381610i −0.131678 0.991293i \(-0.542036\pi\)
0.792646 + 0.609683i \(0.208703\pi\)
\(54\) −4.51925 + 2.56444i −0.614992 + 0.348976i
\(55\) 4.04652i 0.545633i
\(56\) 1.89185 + 1.84957i 0.252809 + 0.247159i
\(57\) 2.69076 3.19058i 0.356400 0.422603i
\(58\) 1.94079 3.36154i 0.254838 0.441392i
\(59\) 5.21237 + 9.02810i 0.678593 + 1.17536i 0.975405 + 0.220422i \(0.0707434\pi\)
−0.296811 + 0.954936i \(0.595923\pi\)
\(60\) 0.638869 3.57126i 0.0824776 0.461048i
\(61\) 2.92469 + 1.68857i 0.374469 + 0.216200i 0.675409 0.737443i \(-0.263967\pi\)
−0.300940 + 0.953643i \(0.597300\pi\)
\(62\) 0.944280 0.119924
\(63\) −7.17223 + 3.39988i −0.903616 + 0.428344i
\(64\) −1.00000 −0.125000
\(65\) −1.81398 1.04730i −0.224996 0.129902i
\(66\) −0.589238 + 3.29383i −0.0725302 + 0.405442i
\(67\) −4.98074 8.62689i −0.608494 1.05394i −0.991489 0.130192i \(-0.958441\pi\)
0.382995 0.923751i \(-0.374893\pi\)
\(68\) −0.345960 + 0.599220i −0.0419538 + 0.0726661i
\(69\) −4.05987 + 4.81401i −0.488752 + 0.579539i
\(70\) 1.37375 5.36883i 0.164194 0.641698i
\(71\) 3.58456i 0.425409i 0.977117 + 0.212705i \(0.0682272\pi\)
−0.977117 + 0.212705i \(0.931773\pi\)
\(72\) 1.04007 2.81394i 0.122573 0.331626i
\(73\) 7.46660 4.31085i 0.873900 0.504546i 0.00525772 0.999986i \(-0.498326\pi\)
0.868642 + 0.495440i \(0.164993\pi\)
\(74\) −6.19647 + 3.57753i −0.720324 + 0.415880i
\(75\) 0.998037 0.360448i 0.115243 0.0416210i
\(76\) 2.40970i 0.276412i
\(77\) −1.26702 + 4.95175i −0.144391 + 0.564304i
\(78\) −1.32406 1.11664i −0.149920 0.126434i
\(79\) −8.33482 + 14.4363i −0.937741 + 1.62421i −0.168069 + 0.985775i \(0.553753\pi\)
−0.769672 + 0.638439i \(0.779580\pi\)
\(80\) 1.04730 + 1.81398i 0.117092 + 0.202809i
\(81\) 6.83653 + 5.85337i 0.759614 + 0.650374i
\(82\) 7.50036 + 4.33034i 0.828277 + 0.478206i
\(83\) −12.5850 −1.38138 −0.690691 0.723150i \(-0.742694\pi\)
−0.690691 + 0.723150i \(0.742694\pi\)
\(84\) 1.90000 4.17013i 0.207307 0.454999i
\(85\) 1.44930 0.157198
\(86\) 6.94472 + 4.00954i 0.748868 + 0.432359i
\(87\) −6.61802 1.18391i −0.709526 0.126928i
\(88\) −0.965940 1.67306i −0.102970 0.178349i
\(89\) −7.45988 + 12.9209i −0.790746 + 1.36961i 0.134760 + 0.990878i \(0.456974\pi\)
−0.925506 + 0.378734i \(0.876360\pi\)
\(90\) −6.19369 + 1.06039i −0.652872 + 0.111775i
\(91\) −1.89185 1.84957i −0.198320 0.193888i
\(92\) 3.63581i 0.379059i
\(93\) −0.555565 1.53829i −0.0576094 0.159513i
\(94\) −3.80633 + 2.19759i −0.392593 + 0.226664i
\(95\) 4.37115 2.52369i 0.448471 0.258925i
\(96\) 0.588348 + 1.62906i 0.0600480 + 0.166266i
\(97\) 2.33951i 0.237541i −0.992922 0.118770i \(-0.962105\pi\)
0.992922 0.118770i \(-0.0378952\pi\)
\(98\) 3.36212 6.13972i 0.339625 0.620205i
\(99\) 5.71253 0.978010i 0.574131 0.0982937i
\(100\) −0.306322 + 0.530566i −0.0306322 + 0.0530566i
\(101\) 7.51343 + 13.0136i 0.747615 + 1.29491i 0.948963 + 0.315387i \(0.102134\pi\)
−0.201349 + 0.979520i \(0.564532\pi\)
\(102\) 1.17971 + 0.211041i 0.116809 + 0.0208961i
\(103\) −16.1762 9.33933i −1.59389 0.920231i −0.992631 0.121174i \(-0.961334\pi\)
−0.601256 0.799057i \(-0.705333\pi\)
\(104\) 1.00000 0.0980581
\(105\) −9.55440 + 0.920820i −0.932414 + 0.0898629i
\(106\) 5.55632 0.539678
\(107\) 1.30018 + 0.750662i 0.125694 + 0.0725692i 0.561528 0.827457i \(-0.310214\pi\)
−0.435835 + 0.900027i \(0.643547\pi\)
\(108\) −5.19601 0.0387561i −0.499986 0.00372931i
\(109\) −1.87726 3.25151i −0.179809 0.311438i 0.762006 0.647570i \(-0.224215\pi\)
−0.941815 + 0.336132i \(0.890881\pi\)
\(110\) −2.02326 + 3.50439i −0.192910 + 0.334130i
\(111\) 9.47370 + 7.98960i 0.899204 + 0.758339i
\(112\) 0.713604 + 2.54770i 0.0674292 + 0.240735i
\(113\) 8.66137i 0.814793i 0.913251 + 0.407396i \(0.133563\pi\)
−0.913251 + 0.407396i \(0.866437\pi\)
\(114\) 3.92556 1.41774i 0.367663 0.132784i
\(115\) −6.59528 + 3.80778i −0.615013 + 0.355078i
\(116\) 3.36154 1.94079i 0.312111 0.180197i
\(117\) −1.04007 + 2.81394i −0.0961541 + 0.260149i
\(118\) 10.4247i 0.959676i
\(119\) 1.77351 + 0.453796i 0.162578 + 0.0415994i
\(120\) 2.33891 2.77337i 0.213512 0.253173i
\(121\) −3.63392 + 6.29413i −0.330356 + 0.572194i
\(122\) 1.68857 + 2.92469i 0.152876 + 0.264789i
\(123\) 2.64157 14.7663i 0.238182 1.33143i
\(124\) 0.817770 + 0.472140i 0.0734379 + 0.0423994i
\(125\) 11.7563 1.05151
\(126\) −7.91127 0.641735i −0.704792 0.0571703i
\(127\) −2.17602 −0.193091 −0.0965454 0.995329i \(-0.530779\pi\)
−0.0965454 + 0.995329i \(0.530779\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 2.44588 13.6724i 0.215347 1.20379i
\(130\) −1.04730 1.81398i −0.0918544 0.159096i
\(131\) 3.27646 5.67499i 0.286265 0.495826i −0.686650 0.726988i \(-0.740919\pi\)
0.972915 + 0.231162i \(0.0742528\pi\)
\(132\) −2.15721 + 2.55792i −0.187761 + 0.222638i
\(133\) 6.13920 1.71957i 0.532336 0.149106i
\(134\) 9.96148i 0.860541i
\(135\) 5.37148 + 9.46603i 0.462303 + 0.814706i
\(136\) −0.599220 + 0.345960i −0.0513827 + 0.0296658i
\(137\) 12.3253 7.11601i 1.05302 0.607962i 0.129527 0.991576i \(-0.458654\pi\)
0.923494 + 0.383614i \(0.125321\pi\)
\(138\) −5.92296 + 2.13912i −0.504196 + 0.182094i
\(139\) 8.44011i 0.715881i 0.933744 + 0.357940i \(0.116521\pi\)
−0.933744 + 0.357940i \(0.883479\pi\)
\(140\) 3.87411 3.96267i 0.327422 0.334907i
\(141\) 5.81945 + 4.90781i 0.490086 + 0.413312i
\(142\) −1.79228 + 3.10432i −0.150405 + 0.260509i
\(143\) 0.965940 + 1.67306i 0.0807760 + 0.139908i
\(144\) 2.30769 1.91691i 0.192308 0.159743i
\(145\) −7.04109 4.06517i −0.584731 0.337594i
\(146\) 8.62169 0.713536
\(147\) −11.9801 1.86481i −0.988101 0.153807i
\(148\) −7.15506 −0.588142
\(149\) −0.0334409 0.0193071i −0.00273959 0.00158170i 0.498630 0.866815i \(-0.333837\pi\)
−0.501369 + 0.865233i \(0.667170\pi\)
\(150\) 1.04455 + 0.186861i 0.0852871 + 0.0152572i
\(151\) −10.4122 18.0344i −0.847329 1.46762i −0.883583 0.468274i \(-0.844876\pi\)
0.0362546 0.999343i \(-0.488457\pi\)
\(152\) −1.20485 + 2.08687i −0.0977264 + 0.169267i
\(153\) −0.350283 2.04599i −0.0283187 0.165409i
\(154\) −3.57315 + 3.65483i −0.287933 + 0.294514i
\(155\) 1.97789i 0.158868i
\(156\) −0.588348 1.62906i −0.0471055 0.130429i
\(157\) 3.98152 2.29873i 0.317760 0.183459i −0.332634 0.943056i \(-0.607937\pi\)
0.650394 + 0.759597i \(0.274604\pi\)
\(158\) −14.4363 + 8.33482i −1.14849 + 0.663083i
\(159\) −3.26905 9.05160i −0.259253 0.717839i
\(160\) 2.09460i 0.165593i
\(161\) −9.26294 + 2.59453i −0.730022 + 0.204477i
\(162\) 2.99392 + 8.48743i 0.235225 + 0.666835i
\(163\) −9.93799 + 17.2131i −0.778404 + 1.34823i 0.154458 + 0.987999i \(0.450637\pi\)
−0.932862 + 0.360235i \(0.882696\pi\)
\(164\) 4.33034 + 7.50036i 0.338143 + 0.585680i
\(165\) 6.89925 + 1.23422i 0.537106 + 0.0960838i
\(166\) −10.8989 6.29250i −0.845921 0.488393i
\(167\) 5.36254 0.414965 0.207483 0.978239i \(-0.433473\pi\)
0.207483 + 0.978239i \(0.433473\pi\)
\(168\) 3.73052 2.66144i 0.287815 0.205334i
\(169\) −1.00000 −0.0769231
\(170\) 1.25513 + 0.724648i 0.0962639 + 0.0555780i
\(171\) −4.61919 5.56086i −0.353238 0.425250i
\(172\) 4.00954 + 6.94472i 0.305724 + 0.529530i
\(173\) 0.0694333 0.120262i 0.00527892 0.00914335i −0.863374 0.504565i \(-0.831653\pi\)
0.868653 + 0.495421i \(0.164986\pi\)
\(174\) −5.13942 4.33430i −0.389618 0.328583i
\(175\) 1.57031 + 0.401803i 0.118705 + 0.0303735i
\(176\) 1.93188i 0.145621i
\(177\) 16.9826 6.13338i 1.27649 0.461013i
\(178\) −12.9209 + 7.45988i −0.968462 + 0.559142i
\(179\) −12.4682 + 7.19850i −0.931914 + 0.538041i −0.887416 0.460969i \(-0.847502\pi\)
−0.0444976 + 0.999009i \(0.514169\pi\)
\(180\) −5.89408 2.17852i −0.439319 0.162377i
\(181\) 9.27914i 0.689713i −0.938655 0.344856i \(-0.887928\pi\)
0.938655 0.344856i \(-0.112072\pi\)
\(182\) −0.713604 2.54770i −0.0528958 0.188848i
\(183\) 3.77104 4.47153i 0.278764 0.330545i
\(184\) 1.81790 3.14870i 0.134018 0.232125i
\(185\) 7.49350 + 12.9791i 0.550933 + 0.954244i
\(186\) 0.288012 1.60998i 0.0211181 0.118050i
\(187\) −1.15762 0.668353i −0.0846537 0.0488748i
\(188\) −4.39517 −0.320551
\(189\) 3.60915 + 13.2655i 0.262527 + 0.964925i
\(190\) 5.04737 0.366175
\(191\) 2.93538 + 1.69474i 0.212397 + 0.122627i 0.602425 0.798176i \(-0.294201\pi\)
−0.390028 + 0.920803i \(0.627535\pi\)
\(192\) −0.305007 + 1.70498i −0.0220120 + 0.123047i
\(193\) −6.28558 10.8869i −0.452446 0.783659i 0.546091 0.837726i \(-0.316115\pi\)
−0.998537 + 0.0540663i \(0.982782\pi\)
\(194\) 1.16975 2.02607i 0.0839833 0.145463i
\(195\) −2.33891 + 2.77337i −0.167493 + 0.198605i
\(196\) 5.98154 3.63610i 0.427253 0.259721i
\(197\) 12.0271i 0.856894i −0.903567 0.428447i \(-0.859061\pi\)
0.903567 0.428447i \(-0.140939\pi\)
\(198\) 5.43620 + 2.00928i 0.386334 + 0.142793i
\(199\) −13.0591 + 7.53965i −0.925732 + 0.534472i −0.885459 0.464717i \(-0.846156\pi\)
−0.0402727 + 0.999189i \(0.512823\pi\)
\(200\) −0.530566 + 0.306322i −0.0375167 + 0.0216603i
\(201\) −16.2279 + 5.86081i −1.14463 + 0.413390i
\(202\) 15.0269i 1.05729i
\(203\) −7.34335 7.17924i −0.515402 0.503884i
\(204\) 0.916141 + 0.772623i 0.0641427 + 0.0540944i
\(205\) 9.07033 15.7103i 0.633499 1.09725i
\(206\) −9.33933 16.1762i −0.650702 1.12705i
\(207\) 6.96952 + 8.39033i 0.484415 + 0.583168i
\(208\) 0.866025 + 0.500000i 0.0600481 + 0.0346688i
\(209\) −4.65526 −0.322011
\(210\) −8.73476 3.97975i −0.602756 0.274629i
\(211\) 11.0298 0.759324 0.379662 0.925125i \(-0.376040\pi\)
0.379662 + 0.925125i \(0.376040\pi\)
\(212\) 4.81192 + 2.77816i 0.330484 + 0.190805i
\(213\) 6.11162 + 1.09332i 0.418761 + 0.0749129i
\(214\) 0.750662 + 1.30018i 0.0513142 + 0.0888788i
\(215\) 8.39838 14.5464i 0.572765 0.992058i
\(216\) −4.48050 2.63157i −0.304859 0.179056i
\(217\) 0.619306 2.42035i 0.0420412 0.164304i
\(218\) 3.75452i 0.254288i
\(219\) −5.07255 14.0453i −0.342771 0.949092i
\(220\) −3.50439 + 2.02326i −0.236266 + 0.136408i
\(221\) 0.599220 0.345960i 0.0403079 0.0232718i
\(222\) 4.20967 + 11.6560i 0.282534 + 0.782303i
\(223\) 14.2894i 0.956889i −0.878118 0.478444i \(-0.841201\pi\)
0.878118 0.478444i \(-0.158799\pi\)
\(224\) −0.655850 + 2.56317i −0.0438209 + 0.171259i
\(225\) −0.310150 1.81158i −0.0206767 0.120772i
\(226\) −4.33068 + 7.50096i −0.288073 + 0.498957i
\(227\) −10.4107 18.0319i −0.690983 1.19682i −0.971516 0.236973i \(-0.923845\pi\)
0.280534 0.959844i \(-0.409489\pi\)
\(228\) 4.10851 + 0.734978i 0.272093 + 0.0486751i
\(229\) −0.284143 0.164050i −0.0187767 0.0108407i 0.490582 0.871395i \(-0.336784\pi\)
−0.509359 + 0.860554i \(0.670117\pi\)
\(230\) −7.61557 −0.502156
\(231\) 8.05620 + 3.67058i 0.530059 + 0.241506i
\(232\) 3.88157 0.254838
\(233\) −7.80411 4.50571i −0.511264 0.295179i 0.222089 0.975026i \(-0.428713\pi\)
−0.733353 + 0.679848i \(0.762046\pi\)
\(234\) −2.30769 + 1.91691i −0.150859 + 0.125312i
\(235\) 4.60307 + 7.97275i 0.300271 + 0.520085i
\(236\) −5.21237 + 9.02810i −0.339297 + 0.587679i
\(237\) 22.0715 + 18.6139i 1.43370 + 1.20910i
\(238\) 1.30901 + 1.27975i 0.0848504 + 0.0829542i
\(239\) 28.2160i 1.82514i −0.408922 0.912569i \(-0.634095\pi\)
0.408922 0.912569i \(-0.365905\pi\)
\(240\) 3.41224 1.23235i 0.220259 0.0795481i
\(241\) 9.92924 5.73265i 0.639599 0.369272i −0.144861 0.989452i \(-0.546274\pi\)
0.784460 + 0.620180i \(0.212940\pi\)
\(242\) −6.29413 + 3.63392i −0.404602 + 0.233597i
\(243\) 12.0651 9.87085i 0.773976 0.633215i
\(244\) 3.37715i 0.216200i
\(245\) −12.8603 7.04230i −0.821612 0.449916i
\(246\) 9.67082 11.4672i 0.616589 0.731123i
\(247\) 1.20485 2.08687i 0.0766629 0.132784i
\(248\) 0.472140 + 0.817770i 0.0299809 + 0.0519285i
\(249\) −3.83852 + 21.4572i −0.243256 + 1.35980i
\(250\) 10.1812 + 5.87813i 0.643917 + 0.371765i
\(251\) 25.7601 1.62596 0.812982 0.582289i \(-0.197843\pi\)
0.812982 + 0.582289i \(0.197843\pi\)
\(252\) −6.53049 4.51139i −0.411382 0.284191i
\(253\) 7.02395 0.441592
\(254\) −1.88449 1.08801i −0.118244 0.0682679i
\(255\) 0.442046 2.47103i 0.0276820 0.154742i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.89377 + 11.9404i −0.430021 + 0.744819i −0.996875 0.0789999i \(-0.974827\pi\)
0.566853 + 0.823819i \(0.308161\pi\)
\(258\) 8.95439 10.6177i 0.557476 0.661029i
\(259\) 5.10588 + 18.2289i 0.317264 + 1.13269i
\(260\) 2.09460i 0.129902i
\(261\) −4.03709 + 10.9225i −0.249890 + 0.676087i
\(262\) 5.67499 3.27646i 0.350602 0.202420i
\(263\) −18.5720 + 10.7225i −1.14520 + 0.661180i −0.947712 0.319126i \(-0.896611\pi\)
−0.197484 + 0.980306i \(0.563277\pi\)
\(264\) −3.14716 + 1.13662i −0.193694 + 0.0699540i
\(265\) 11.6383i 0.714934i
\(266\) 6.17649 + 1.58041i 0.378705 + 0.0969009i
\(267\) 19.7546 + 16.6599i 1.20896 + 1.01957i
\(268\) 4.98074 8.62689i 0.304247 0.526971i
\(269\) 4.76794 + 8.25831i 0.290706 + 0.503518i 0.973977 0.226647i \(-0.0727764\pi\)
−0.683271 + 0.730165i \(0.739443\pi\)
\(270\) −0.0811787 + 10.8836i −0.00494038 + 0.662353i
\(271\) −22.0755 12.7453i −1.34099 0.774221i −0.354038 0.935231i \(-0.615192\pi\)
−0.986953 + 0.161010i \(0.948525\pi\)
\(272\) −0.691920 −0.0419538
\(273\) −3.73052 + 2.66144i −0.225781 + 0.161078i
\(274\) 14.2320 0.859788
\(275\) −1.02499 0.591778i −0.0618092 0.0356856i
\(276\) −6.19899 1.10895i −0.373136 0.0667508i
\(277\) 9.72968 + 16.8523i 0.584600 + 1.01256i 0.994925 + 0.100618i \(0.0320819\pi\)
−0.410325 + 0.911939i \(0.634585\pi\)
\(278\) −4.22006 + 7.30935i −0.253102 + 0.438386i
\(279\) −2.79221 + 0.478039i −0.167165 + 0.0286195i
\(280\) 5.33641 1.49472i 0.318912 0.0893263i
\(281\) 8.66815i 0.517099i 0.965998 + 0.258549i \(0.0832445\pi\)
−0.965998 + 0.258549i \(0.916756\pi\)
\(282\) 2.58589 + 7.16001i 0.153988 + 0.426373i
\(283\) 19.9498 11.5180i 1.18589 0.684676i 0.228523 0.973539i \(-0.426610\pi\)
0.957371 + 0.288862i \(0.0932770\pi\)
\(284\) −3.10432 + 1.79228i −0.184208 + 0.106352i
\(285\) −2.96961 8.22249i −0.175905 0.487058i
\(286\) 1.93188i 0.114235i
\(287\) 16.0185 16.3847i 0.945544 0.967157i
\(288\) 2.95698 0.506247i 0.174242 0.0298309i
\(289\) 8.26062 14.3078i 0.485919 0.841636i
\(290\) −4.06517 7.04109i −0.238715 0.413467i
\(291\) −3.98882 0.713566i −0.233829 0.0418300i
\(292\) 7.46660 + 4.31085i 0.436950 + 0.252273i
\(293\) 18.2447 1.06587 0.532934 0.846157i \(-0.321089\pi\)
0.532934 + 0.846157i \(0.321089\pi\)
\(294\) −9.44265 7.60502i −0.550707 0.443534i
\(295\) 21.8357 1.27132
\(296\) −6.19647 3.57753i −0.360162 0.207940i
\(297\) 0.0748722 10.0381i 0.00434453 0.582468i
\(298\) −0.0193071 0.0334409i −0.00111843 0.00193718i
\(299\) −1.81790 + 3.14870i −0.105132 + 0.182094i
\(300\) 0.811176 + 0.684101i 0.0468333 + 0.0394966i
\(301\) 14.8318 15.1709i 0.854893 0.874434i
\(302\) 20.8243i 1.19830i
\(303\) 24.4797 8.84102i 1.40632 0.507904i
\(304\) −2.08687 + 1.20485i −0.119690 + 0.0691030i
\(305\) 6.12607 3.53689i 0.350778 0.202522i
\(306\) 0.719642 1.94702i 0.0411392 0.111304i
\(307\) 21.8510i 1.24710i 0.781783 + 0.623551i \(0.214311\pi\)
−0.781783 + 0.623551i \(0.785689\pi\)
\(308\) −4.92185 + 1.37860i −0.280448 + 0.0785529i
\(309\) −20.8573 + 24.7316i −1.18653 + 1.40693i
\(310\) 0.988945 1.71290i 0.0561683 0.0972863i
\(311\) 1.41409 + 2.44927i 0.0801856 + 0.138885i 0.903330 0.428947i \(-0.141115\pi\)
−0.823144 + 0.567833i \(0.807782\pi\)
\(312\) 0.305007 1.70498i 0.0172676 0.0965257i
\(313\) −8.58082 4.95414i −0.485017 0.280025i 0.237488 0.971390i \(-0.423676\pi\)
−0.722505 + 0.691366i \(0.757009\pi\)
\(314\) 4.59746 0.259450
\(315\) −1.34418 + 16.5710i −0.0757359 + 0.933668i
\(316\) −16.6696 −0.937741
\(317\) −15.2159 8.78492i −0.854612 0.493410i 0.00759227 0.999971i \(-0.497583\pi\)
−0.862204 + 0.506561i \(0.830917\pi\)
\(318\) 1.69472 9.47344i 0.0950352 0.531244i
\(319\) 3.74937 + 6.49410i 0.209924 + 0.363600i
\(320\) −1.04730 + 1.81398i −0.0585459 + 0.101404i
\(321\) 1.67643 1.98784i 0.0935693 0.110950i
\(322\) −9.31921 2.38455i −0.519339 0.132886i
\(323\) 1.66732i 0.0927723i
\(324\) −1.65090 + 8.84729i −0.0917166 + 0.491516i
\(325\) 0.530566 0.306322i 0.0294305 0.0169917i
\(326\) −17.2131 + 9.93799i −0.953346 + 0.550414i
\(327\) −6.11635 + 2.20896i −0.338235 + 0.122156i
\(328\) 8.66067i 0.478206i
\(329\) 3.13641 + 11.1976i 0.172916 + 0.617342i
\(330\) 5.35782 + 4.51849i 0.294938 + 0.248735i
\(331\) 7.70234 13.3408i 0.423359 0.733279i −0.572907 0.819621i \(-0.694184\pi\)
0.996266 + 0.0863414i \(0.0275176\pi\)
\(332\) −6.29250 10.8989i −0.345346 0.598156i
\(333\) 16.5117 13.7156i 0.904835 0.751611i
\(334\) 4.64409 + 2.68127i 0.254113 + 0.146712i
\(335\) −20.8653 −1.13999
\(336\) 4.56144 0.439616i 0.248847 0.0239830i
\(337\) 14.4566 0.787501 0.393750 0.919217i \(-0.371177\pi\)
0.393750 + 0.919217i \(0.371177\pi\)
\(338\) −0.866025 0.500000i −0.0471056 0.0271964i
\(339\) 14.7675 + 2.64178i 0.802060 + 0.143482i
\(340\) 0.724648 + 1.25513i 0.0392996 + 0.0680689i
\(341\) −0.912118 + 1.57983i −0.0493939 + 0.0855528i
\(342\) −1.21991 7.12544i −0.0659650 0.385300i
\(343\) −13.5321 12.6444i −0.730666 0.682735i
\(344\) 8.01907i 0.432359i
\(345\) 4.48060 + 12.4062i 0.241228 + 0.667930i
\(346\) 0.120262 0.0694333i 0.00646533 0.00373276i
\(347\) −10.8790 + 6.28099i −0.584015 + 0.337181i −0.762727 0.646720i \(-0.776140\pi\)
0.178712 + 0.983901i \(0.442807\pi\)
\(348\) −2.28372 6.32333i −0.122420 0.338966i
\(349\) 17.7010i 0.947514i −0.880656 0.473757i \(-0.842897\pi\)
0.880656 0.473757i \(-0.157103\pi\)
\(350\) 1.15903 + 1.13313i 0.0619528 + 0.0605683i
\(351\) 4.48050 + 2.63157i 0.239151 + 0.140463i
\(352\) 0.965940 1.67306i 0.0514848 0.0891743i
\(353\) 0.222657 + 0.385653i 0.0118508 + 0.0205263i 0.871890 0.489702i \(-0.162894\pi\)
−0.860039 + 0.510228i \(0.829561\pi\)
\(354\) 17.7740 + 3.17962i 0.944679 + 0.168995i
\(355\) 6.50231 + 3.75411i 0.345107 + 0.199248i
\(356\) −14.9198 −0.790746
\(357\) 1.31465 2.88540i 0.0695786 0.152711i
\(358\) −14.3970 −0.760905
\(359\) −17.9004 10.3348i −0.944745 0.545449i −0.0533007 0.998579i \(-0.516974\pi\)
−0.891445 + 0.453130i \(0.850308\pi\)
\(360\) −4.01517 4.83370i −0.211618 0.254758i
\(361\) −6.59666 11.4258i −0.347193 0.601355i
\(362\) 4.63957 8.03597i 0.243850 0.422361i
\(363\) 9.62302 + 8.11553i 0.505078 + 0.425955i
\(364\) 0.655850 2.56317i 0.0343759 0.134347i
\(365\) 18.0590i 0.945252i
\(366\) 5.50158 1.98694i 0.287572 0.103859i
\(367\) −17.2106 + 9.93654i −0.898385 + 0.518683i −0.876676 0.481081i \(-0.840244\pi\)
−0.0217093 + 0.999764i \(0.506911\pi\)
\(368\) 3.14870 1.81790i 0.164137 0.0947648i
\(369\) −24.3706 9.00767i −1.26868 0.468920i
\(370\) 14.9870i 0.779137i
\(371\) 3.64412 14.2418i 0.189193 0.739399i
\(372\) 1.05442 1.25028i 0.0546690 0.0648239i
\(373\) 7.64212 13.2365i 0.395694 0.685362i −0.597496 0.801872i \(-0.703838\pi\)
0.993189 + 0.116510i \(0.0371708\pi\)
\(374\) −0.668353 1.15762i −0.0345597 0.0598592i
\(375\) 3.58574 20.0442i 0.185167 1.03508i
\(376\) −3.80633 2.19759i −0.196297 0.113332i
\(377\) −3.88157 −0.199911
\(378\) −3.50714 + 13.2929i −0.180388 + 0.683711i
\(379\) −23.8814 −1.22670 −0.613352 0.789810i \(-0.710179\pi\)
−0.613352 + 0.789810i \(0.710179\pi\)
\(380\) 4.37115 + 2.52369i 0.224235 + 0.129462i
\(381\) −0.663703 + 3.71009i −0.0340025 + 0.190073i
\(382\) 1.69474 + 2.93538i 0.0867106 + 0.150187i
\(383\) 18.7955 32.5547i 0.960404 1.66347i 0.238916 0.971040i \(-0.423208\pi\)
0.721488 0.692427i \(-0.243459\pi\)
\(384\) −1.11664 + 1.32406i −0.0569831 + 0.0675679i
\(385\) 7.65540 + 7.48432i 0.390155 + 0.381436i
\(386\) 12.5712i 0.639855i
\(387\) −22.5652 8.34036i −1.14705 0.423964i
\(388\) 2.02607 1.16975i 0.102858 0.0593852i
\(389\) −25.5296 + 14.7395i −1.29440 + 0.747322i −0.979431 0.201780i \(-0.935327\pi\)
−0.314969 + 0.949102i \(0.601994\pi\)
\(390\) −3.41224 + 1.23235i −0.172785 + 0.0624027i
\(391\) 2.51569i 0.127224i
\(392\) 6.99821 0.158181i 0.353463 0.00798935i
\(393\) −8.67642 7.31722i −0.437668 0.369105i
\(394\) 6.01354 10.4158i 0.302958 0.524739i
\(395\) 17.4581 + 30.2384i 0.878414 + 1.52146i
\(396\) 3.70324 + 4.45819i 0.186095 + 0.224032i
\(397\) 16.3264 + 9.42604i 0.819398 + 0.473079i 0.850209 0.526446i \(-0.176476\pi\)
−0.0308110 + 0.999525i \(0.509809\pi\)
\(398\) −15.0793 −0.755857
\(399\) −1.05934 10.9917i −0.0530336 0.550275i
\(400\) −0.612645 −0.0306322
\(401\) −9.99593 5.77115i −0.499173 0.288198i 0.229199 0.973380i \(-0.426389\pi\)
−0.728372 + 0.685182i \(0.759723\pi\)
\(402\) −16.9842 3.03832i −0.847093 0.151538i
\(403\) −0.472140 0.817770i −0.0235190 0.0407360i
\(404\) −7.51343 + 13.0136i −0.373807 + 0.647453i
\(405\) 17.7778 6.27108i 0.883385 0.311612i
\(406\) −2.76991 9.88908i −0.137468 0.490787i
\(407\) 13.8227i 0.685167i
\(408\) 0.407090 + 1.12718i 0.0201539 + 0.0558038i
\(409\) −20.8221 + 12.0217i −1.02959 + 0.594433i −0.916867 0.399194i \(-0.869290\pi\)
−0.112721 + 0.993627i \(0.535957\pi\)
\(410\) 15.7103 9.07033i 0.775875 0.447952i
\(411\) −8.37338 23.1849i −0.413028 1.14363i
\(412\) 18.6787i 0.920231i
\(413\) 26.7204 + 6.83707i 1.31483 + 0.336430i
\(414\) 1.84062 + 10.7510i 0.0904615 + 0.528383i
\(415\) −13.1803 + 22.8289i −0.646994 + 1.12063i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 14.3903 + 2.57430i 0.704694 + 0.126064i
\(418\) −4.03158 2.32763i −0.197191 0.113848i
\(419\) −3.63647 −0.177653 −0.0888267 0.996047i \(-0.528312\pi\)
−0.0888267 + 0.996047i \(0.528312\pi\)
\(420\) −5.57465 7.81394i −0.272015 0.381281i
\(421\) −0.0321368 −0.00156625 −0.000783127 1.00000i \(-0.500249\pi\)
−0.000783127 1.00000i \(0.500249\pi\)
\(422\) 9.55210 + 5.51491i 0.464989 + 0.268461i
\(423\) 10.1427 8.42516i 0.493155 0.409645i
\(424\) 2.77816 + 4.81192i 0.134919 + 0.233687i
\(425\) −0.211951 + 0.367109i −0.0102811 + 0.0178074i
\(426\) 4.74616 + 4.00265i 0.229952 + 0.193929i
\(427\) 8.60395 2.40994i 0.416374 0.116625i
\(428\) 1.50132i 0.0725692i
\(429\) 3.14716 1.13662i 0.151946 0.0548764i
\(430\) 14.5464 8.39838i 0.701491 0.405006i
\(431\) −14.3401 + 8.27924i −0.690737 + 0.398797i −0.803888 0.594781i \(-0.797239\pi\)
0.113151 + 0.993578i \(0.463906\pi\)
\(432\) −2.56444 4.51925i −0.123382 0.217433i
\(433\) 23.5650i 1.13246i 0.824247 + 0.566231i \(0.191599\pi\)
−0.824247 + 0.566231i \(0.808401\pi\)
\(434\) 1.74651 1.78643i 0.0838352 0.0857516i
\(435\) −9.07864 + 10.7650i −0.435288 + 0.516144i
\(436\) 1.87726 3.25151i 0.0899045 0.155719i
\(437\) −4.38061 7.58744i −0.209553 0.362957i
\(438\) 2.62968 14.6998i 0.125651 0.702386i
\(439\) −1.10437 0.637611i −0.0527089 0.0304315i 0.473414 0.880840i \(-0.343021\pi\)
−0.526123 + 0.850409i \(0.676355\pi\)
\(440\) −4.04652 −0.192910
\(441\) −6.83349 + 19.8571i −0.325404 + 0.945575i
\(442\) 0.691920 0.0329113
\(443\) −5.80498 3.35151i −0.275803 0.159235i 0.355719 0.934593i \(-0.384236\pi\)
−0.631522 + 0.775358i \(0.717569\pi\)
\(444\) −2.18235 + 12.1993i −0.103570 + 0.578952i
\(445\) 15.6255 + 27.0641i 0.740719 + 1.28296i
\(446\) 7.14470 12.3750i 0.338311 0.585972i
\(447\) −0.0431181 + 0.0511275i −0.00203942 + 0.00241825i
\(448\) −1.84957 + 1.89185i −0.0873840 + 0.0893814i
\(449\) 11.4423i 0.539997i −0.962861 0.269998i \(-0.912977\pi\)
0.962861 0.269998i \(-0.0870232\pi\)
\(450\) 0.637191 1.72395i 0.0300375 0.0812676i
\(451\) −14.4898 + 8.36569i −0.682298 + 0.393925i
\(452\) −7.50096 + 4.33068i −0.352816 + 0.203698i
\(453\) −33.9241 + 12.2519i −1.59389 + 0.575646i
\(454\) 20.8214i 0.977197i
\(455\) −5.33641 + 1.49472i −0.250175 + 0.0700733i
\(456\) 3.19058 + 2.69076i 0.149413 + 0.126007i
\(457\) −15.9902 + 27.6958i −0.747989 + 1.29556i 0.200796 + 0.979633i \(0.435647\pi\)
−0.948785 + 0.315922i \(0.897686\pi\)
\(458\) −0.164050 0.284143i −0.00766554 0.0132771i
\(459\) −3.59522 0.0268161i −0.167811 0.00125167i
\(460\) −6.59528 3.80778i −0.307506 0.177539i
\(461\) −7.66318 −0.356910 −0.178455 0.983948i \(-0.557110\pi\)
−0.178455 + 0.983948i \(0.557110\pi\)
\(462\) 5.14158 + 7.20691i 0.239208 + 0.335296i
\(463\) −33.6757 −1.56504 −0.782522 0.622623i \(-0.786067\pi\)
−0.782522 + 0.622623i \(0.786067\pi\)
\(464\) 3.36154 + 1.94079i 0.156056 + 0.0900987i
\(465\) −3.37227 0.603271i −0.156385 0.0279760i
\(466\) −4.50571 7.80411i −0.208723 0.361519i
\(467\) 9.89478 17.1383i 0.457876 0.793064i −0.540973 0.841040i \(-0.681944\pi\)
0.998848 + 0.0479760i \(0.0152771\pi\)
\(468\) −2.95698 + 0.506247i −0.136686 + 0.0234013i
\(469\) −25.5330 6.53324i −1.17900 0.301677i
\(470\) 9.20613i 0.424647i
\(471\) −2.70491 7.48956i −0.124636 0.345101i
\(472\) −9.02810 + 5.21237i −0.415552 + 0.239919i
\(473\) −13.4164 + 7.74595i −0.616885 + 0.356159i
\(474\) 9.80755 + 27.1559i 0.450476 + 1.24731i
\(475\) 1.47629i 0.0677370i
\(476\) 0.493757 + 1.76280i 0.0226313 + 0.0807980i
\(477\) −16.4299 + 2.81287i −0.752275 + 0.128793i
\(478\) 14.1080 24.4357i 0.645284 1.11766i
\(479\) 10.3981 + 18.0101i 0.475102 + 0.822900i 0.999593 0.0285153i \(-0.00907794\pi\)
−0.524492 + 0.851416i \(0.675745\pi\)
\(480\) 3.57126 + 0.638869i 0.163005 + 0.0291602i
\(481\) 6.19647 + 3.57753i 0.282534 + 0.163121i
\(482\) 11.4653 0.522230
\(483\) 1.59836 + 16.5845i 0.0727279 + 0.754622i
\(484\) −7.26784 −0.330356
\(485\) −4.24381 2.45017i −0.192702 0.111256i
\(486\) 15.3841 2.51586i 0.697837 0.114122i
\(487\) 2.80203 + 4.85326i 0.126972 + 0.219922i 0.922502 0.385992i \(-0.126141\pi\)
−0.795530 + 0.605914i \(0.792807\pi\)
\(488\) −1.68857 + 2.92469i −0.0764381 + 0.132395i
\(489\) 26.3169 + 22.1942i 1.19009 + 1.00366i
\(490\) −7.61617 12.5289i −0.344063 0.566000i
\(491\) 19.4106i 0.875989i 0.898978 + 0.437994i \(0.144311\pi\)
−0.898978 + 0.437994i \(0.855689\pi\)
\(492\) 14.1088 5.09549i 0.636073 0.229722i
\(493\) 2.32592 1.34287i 0.104754 0.0604798i
\(494\) 2.08687 1.20485i 0.0938925 0.0542089i
\(495\) 4.20865 11.3867i 0.189165 0.511793i
\(496\) 0.944280i 0.0423994i
\(497\) 6.78145 + 6.62990i 0.304189 + 0.297391i
\(498\) −14.0529 + 16.6632i −0.629724 + 0.746698i
\(499\) −12.1481 + 21.0412i −0.543825 + 0.941932i 0.454855 + 0.890565i \(0.349691\pi\)
−0.998680 + 0.0513667i \(0.983642\pi\)
\(500\) 5.87813 + 10.1812i 0.262878 + 0.455318i
\(501\) 1.63561 9.14304i 0.0730738 0.408481i
\(502\) 22.3089 + 12.8801i 0.995695 + 0.574865i
\(503\) −7.56087 −0.337123 −0.168561 0.985691i \(-0.553912\pi\)
−0.168561 + 0.985691i \(0.553912\pi\)
\(504\) −3.39988 7.17223i −0.151443 0.319476i
\(505\) 31.4753 1.40063
\(506\) 6.08292 + 3.51197i 0.270419 + 0.156126i
\(507\) −0.305007 + 1.70498i −0.0135459 + 0.0757210i
\(508\) −1.08801 1.88449i −0.0482727 0.0836108i
\(509\) 17.0560 29.5418i 0.755992 1.30942i −0.188888 0.981999i \(-0.560488\pi\)
0.944880 0.327417i \(-0.106178\pi\)
\(510\) 1.61834 1.91895i 0.0716612 0.0849725i
\(511\) 5.65454 22.0989i 0.250142 0.977598i
\(512\) 1.00000i 0.0441942i
\(513\) −10.8901 + 6.17954i −0.480808 + 0.272834i
\(514\) −11.9404 + 6.89377i −0.526666 + 0.304071i
\(515\) −33.8827 + 19.5622i −1.49305 + 0.862012i
\(516\) 13.0636 4.71800i 0.575092 0.207699i
\(517\) 8.49095i 0.373431i
\(518\) −4.69265 + 18.3397i −0.206183 + 0.805799i
\(519\) −0.183867 0.155063i −0.00807087 0.00680653i
\(520\) 1.04730 1.81398i 0.0459272 0.0795482i
\(521\) 16.1589 + 27.9881i 0.707935 + 1.22618i 0.965622 + 0.259951i \(0.0837064\pi\)
−0.257687 + 0.966229i \(0.582960\pi\)
\(522\) −8.95748 + 7.44063i −0.392058 + 0.325668i
\(523\) 24.1399 + 13.9372i 1.05556 + 0.609430i 0.924202 0.381904i \(-0.124732\pi\)
0.131362 + 0.991334i \(0.458065\pi\)
\(524\) 6.55291 0.286265
\(525\) 1.16403 2.55481i 0.0508023 0.111501i
\(526\) −21.4451 −0.935049
\(527\) 0.565831 + 0.326683i 0.0246480 + 0.0142305i
\(528\) −3.29383 0.589238i −0.143345 0.0256433i
\(529\) −4.89045 8.47051i −0.212628 0.368283i
\(530\) 5.81914 10.0791i 0.252767 0.437806i
\(531\) −5.27750 30.8257i −0.229024 1.33772i
\(532\) 4.55880 + 4.45692i 0.197649 + 0.193232i
\(533\) 8.66067i 0.375135i
\(534\) 8.77801 + 24.3052i 0.379862 + 1.05179i
\(535\) 2.72337 1.57234i 0.117741 0.0679781i
\(536\) 8.62689 4.98074i 0.372625 0.215135i
\(537\) 8.47044 + 23.4536i 0.365526 + 1.01210i
\(538\) 9.53588i 0.411121i
\(539\) 7.02450 + 11.5556i 0.302567 + 0.497736i
\(540\) −5.51209 + 9.38486i −0.237202 + 0.403860i
\(541\) −15.0677 + 26.0980i −0.647810 + 1.12204i 0.335835 + 0.941921i \(0.390982\pi\)
−0.983645 + 0.180119i \(0.942352\pi\)
\(542\) −12.7453 22.0755i −0.547457 0.948224i
\(543\) −15.8208 2.83021i −0.678935 0.121456i
\(544\) −0.599220 0.345960i −0.0256914 0.0148329i
\(545\) −7.86423 −0.336866
\(546\) −4.56144 + 0.439616i −0.195212 + 0.0188138i
\(547\) −7.84538 −0.335444 −0.167722 0.985834i \(-0.553641\pi\)
−0.167722 + 0.985834i \(0.553641\pi\)
\(548\) 12.3253 + 7.11601i 0.526511 + 0.303981i
\(549\) −6.47369 7.79342i −0.276290 0.332615i
\(550\) −0.591778 1.02499i −0.0252335 0.0437057i
\(551\) 4.67672 8.10032i 0.199235 0.345085i
\(552\) −4.81401 4.05987i −0.204898 0.172800i
\(553\) 11.8955 + 42.4692i 0.505849 + 1.80598i
\(554\) 19.4594i 0.826749i
\(555\) 24.4148 8.81757i 1.03635 0.374285i
\(556\) −7.30935 + 4.22006i −0.309986 + 0.178970i
\(557\) 10.8446 6.26115i 0.459502 0.265294i −0.252333 0.967640i \(-0.581198\pi\)
0.711835 + 0.702347i \(0.247864\pi\)
\(558\) −2.65715 0.982113i −0.112486 0.0415761i
\(559\) 8.01907i 0.339171i
\(560\) 5.36883 + 1.37375i 0.226874 + 0.0580513i
\(561\) −1.49262 + 1.76987i −0.0630183 + 0.0747242i
\(562\) −4.33408 + 7.50684i −0.182822 + 0.316657i
\(563\) −6.12663 10.6116i −0.258207 0.447227i 0.707555 0.706658i \(-0.249798\pi\)
−0.965762 + 0.259431i \(0.916465\pi\)
\(564\) −1.34056 + 7.49370i −0.0564478 + 0.315542i
\(565\) 15.7115 + 9.07106i 0.660989 + 0.381622i
\(566\) 23.0361 0.968278
\(567\) 23.7183 2.10746i 0.996076 0.0885052i
\(568\) −3.58456 −0.150405
\(569\) −34.2211 19.7576i −1.43462 0.828281i −0.437155 0.899386i \(-0.644014\pi\)
−0.997469 + 0.0711052i \(0.977347\pi\)
\(570\) 1.53949 8.60569i 0.0644820 0.360453i
\(571\) 16.5630 + 28.6880i 0.693141 + 1.20056i 0.970803 + 0.239877i \(0.0771071\pi\)
−0.277662 + 0.960679i \(0.589560\pi\)
\(572\) −0.965940 + 1.67306i −0.0403880 + 0.0699541i
\(573\) 3.78482 4.48787i 0.158113 0.187483i
\(574\) 22.0648 6.18029i 0.920967 0.257960i
\(575\) 2.22746i 0.0928915i
\(576\) 2.81394 + 1.04007i 0.117248 + 0.0433361i
\(577\) 23.3130 13.4597i 0.970531 0.560337i 0.0711331 0.997467i \(-0.477338\pi\)
0.899398 + 0.437130i \(0.144005\pi\)
\(578\) 14.3078 8.26062i 0.595127 0.343597i
\(579\) −20.4792 + 7.39621i −0.851087 + 0.307376i
\(580\) 8.13035i 0.337594i
\(581\) −23.2768 + 23.8089i −0.965686 + 0.987760i
\(582\) −3.09764 2.61238i −0.128401 0.108286i
\(583\) −5.36708 + 9.29605i −0.222282 + 0.385003i
\(584\) 4.31085 + 7.46660i 0.178384 + 0.308970i
\(585\) 4.01517 + 4.83370i 0.166007 + 0.199849i
\(586\) 15.8004 + 9.12237i 0.652709 + 0.376842i
\(587\) −22.5994 −0.932778 −0.466389 0.884580i \(-0.654445\pi\)
−0.466389 + 0.884580i \(0.654445\pi\)
\(588\) −4.37507 11.3075i −0.180425 0.466312i
\(589\) 2.27544 0.0937577
\(590\) 18.9103 + 10.9178i 0.778523 + 0.449481i
\(591\) −20.5060 3.66835i −0.843504 0.150896i
\(592\) −3.57753 6.19647i −0.147036 0.254673i
\(593\) −16.5789 + 28.7155i −0.680814 + 1.17920i 0.293919 + 0.955830i \(0.405040\pi\)
−0.974733 + 0.223374i \(0.928293\pi\)
\(594\) 5.08387 8.65579i 0.208594 0.355151i
\(595\) 2.68058 2.74185i 0.109893 0.112405i
\(596\) 0.0386143i 0.00158170i
\(597\) 8.87187 + 24.5651i 0.363102 + 1.00538i
\(598\) −3.14870 + 1.81790i −0.128760 + 0.0743396i
\(599\) 39.7724 22.9626i 1.62506 0.938227i 0.639518 0.768776i \(-0.279134\pi\)
0.985539 0.169451i \(-0.0541994\pi\)
\(600\) 0.360448 + 0.998037i 0.0147152 + 0.0407447i
\(601\) 17.7850i 0.725466i −0.931893 0.362733i \(-0.881844\pi\)
0.931893 0.362733i \(-0.118156\pi\)
\(602\) 20.4302 5.72244i 0.832672 0.233229i
\(603\) 5.04297 + 29.4559i 0.205366 + 1.19954i
\(604\) 10.4122 18.0344i 0.423664 0.733808i
\(605\) 7.61161 + 13.1837i 0.309456 + 0.535993i
\(606\) 25.6206 + 4.58331i 1.04076 + 0.186184i
\(607\) 23.5234 + 13.5812i 0.954785 + 0.551245i 0.894564 0.446940i \(-0.147486\pi\)
0.0602210 + 0.998185i \(0.480819\pi\)
\(608\) −2.40970 −0.0977264
\(609\) −14.4803 + 10.3306i −0.586770 + 0.418616i
\(610\) 7.07377 0.286409
\(611\) 3.80633 + 2.19759i 0.153988 + 0.0889048i
\(612\) 1.59674 1.32635i 0.0645444 0.0536145i
\(613\) −11.4277 19.7933i −0.461559 0.799444i 0.537480 0.843277i \(-0.319376\pi\)
−0.999039 + 0.0438328i \(0.986043\pi\)
\(614\) −10.9255 + 18.9235i −0.440917 + 0.763691i
\(615\) −24.0192 20.2565i −0.968549 0.816822i
\(616\) −4.95175 1.26702i −0.199512 0.0510499i
\(617\) 31.8388i 1.28178i −0.767632 0.640891i \(-0.778565\pi\)
0.767632 0.640891i \(-0.221435\pi\)
\(618\) −30.4287 + 10.9895i −1.22402 + 0.442064i
\(619\) −25.4744 + 14.7077i −1.02390 + 0.591151i −0.915232 0.402926i \(-0.867993\pi\)
−0.108672 + 0.994078i \(0.534660\pi\)
\(620\) 1.71290 0.988945i 0.0687918 0.0397170i
\(621\) 16.4311 9.32381i 0.659359 0.374152i
\(622\) 2.82818i 0.113400i
\(623\) 10.6468 + 38.0111i 0.426555 + 1.52288i
\(624\) 1.11664 1.32406i 0.0447012 0.0530047i
\(625\) 10.7807 18.6728i 0.431229 0.746910i
\(626\) −4.95414 8.58082i −0.198007 0.342959i
\(627\) −1.41989 + 7.93715i −0.0567049 + 0.316979i
\(628\) 3.98152 + 2.29873i 0.158880 + 0.0917294i
\(629\) −4.95073 −0.197399
\(630\) −9.44957 + 13.6788i −0.376480 + 0.544976i
\(631\) 20.0601 0.798581 0.399291 0.916824i \(-0.369256\pi\)
0.399291 + 0.916824i \(0.369256\pi\)
\(632\) −14.4363 8.33482i −0.574247 0.331541i
\(633\) 3.36417 18.8057i 0.133714 0.747458i
\(634\) −8.78492 15.2159i −0.348894 0.604302i
\(635\) −2.27895 + 3.94726i −0.0904374 + 0.156642i
\(636\) 6.20439 7.35688i 0.246020 0.291719i
\(637\) −6.99821 + 0.158181i −0.277279 + 0.00626736i
\(638\) 7.49874i 0.296878i
\(639\) 3.72818 10.0867i 0.147484 0.399025i
\(640\) −1.81398 + 1.04730i −0.0717038 + 0.0413982i
\(641\) −39.6565 + 22.8957i −1.56634 + 0.904326i −0.569749 + 0.821819i \(0.692960\pi\)
−0.996590 + 0.0825076i \(0.973707\pi\)
\(642\) 2.44575 0.883300i 0.0965261 0.0348611i
\(643\) 21.5260i 0.848904i 0.905450 + 0.424452i \(0.139533\pi\)
−0.905450 + 0.424452i \(0.860467\pi\)
\(644\) −6.87840 6.72468i −0.271047 0.264990i
\(645\) −22.2398 18.7559i −0.875693 0.738512i
\(646\) −0.833662 + 1.44394i −0.0328000 + 0.0568112i
\(647\) −7.06767 12.2416i −0.277859 0.481265i 0.692994 0.720944i \(-0.256291\pi\)
−0.970852 + 0.239678i \(0.922958\pi\)
\(648\) −5.85337 + 6.83653i −0.229942 + 0.268564i
\(649\) −17.4412 10.0697i −0.684627 0.395270i
\(650\) 0.612645 0.0240299
\(651\) −3.93777 1.79413i −0.154333 0.0703176i
\(652\) −19.8760 −0.778404
\(653\) 14.0019 + 8.08399i 0.547936 + 0.316351i 0.748289 0.663373i \(-0.230876\pi\)
−0.200353 + 0.979724i \(0.564209\pi\)
\(654\) −6.40140 1.14516i −0.250314 0.0447792i
\(655\) −6.86287 11.8868i −0.268155 0.464457i
\(656\) −4.33034 + 7.50036i −0.169071 + 0.292840i
\(657\) −25.4941 + 4.36471i −0.994621 + 0.170284i
\(658\) −2.88258 + 11.2656i −0.112374 + 0.439178i
\(659\) 42.0011i 1.63613i 0.575126 + 0.818065i \(0.304953\pi\)
−0.575126 + 0.818065i \(0.695047\pi\)
\(660\) 2.38076 + 6.59204i 0.0926710 + 0.256595i
\(661\) 4.44931 2.56881i 0.173058 0.0999152i −0.410969 0.911649i \(-0.634810\pi\)
0.584027 + 0.811734i \(0.301476\pi\)
\(662\) 13.3408 7.70234i 0.518507 0.299360i
\(663\) −0.407090 1.12718i −0.0158101 0.0437761i
\(664\) 12.5850i 0.488393i
\(665\) 3.31032 12.9373i 0.128369 0.501687i
\(666\) 21.1574 3.62223i 0.819831 0.140359i
\(667\) −7.05633 + 12.2219i −0.273222 + 0.473235i
\(668\) 2.68127 + 4.64409i 0.103741 + 0.179685i
\(669\) −24.3632 4.35837i −0.941936 0.168504i
\(670\) −18.0699 10.4327i −0.698101 0.403049i
\(671\) −6.52424 −0.251866
\(672\) 4.17013 + 1.90000i 0.160866 + 0.0732941i
\(673\) −37.9013 −1.46099 −0.730494 0.682919i \(-0.760710\pi\)
−0.730494 + 0.682919i \(0.760710\pi\)
\(674\) 12.5198 + 7.22830i 0.482244 + 0.278424i
\(675\) −3.18331 0.0237437i −0.122526 0.000913897i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) 13.4434 23.2847i 0.516672 0.894902i −0.483141 0.875543i \(-0.660504\pi\)
0.999813 0.0193592i \(-0.00616261\pi\)
\(678\) 11.4681 + 9.67160i 0.440431 + 0.371435i
\(679\) −4.42599 4.32708i −0.169854 0.166058i
\(680\) 1.44930i 0.0555780i
\(681\) −33.9194 + 12.2502i −1.29979 + 0.469430i
\(682\) −1.57983 + 0.912118i −0.0604950 + 0.0349268i
\(683\) −8.54705 + 4.93464i −0.327044 + 0.188819i −0.654528 0.756038i \(-0.727133\pi\)
0.327484 + 0.944857i \(0.393799\pi\)
\(684\) 2.50625 6.78077i 0.0958289 0.259269i
\(685\) 29.8104i 1.13900i
\(686\) −5.39695 17.7165i −0.206056 0.676418i
\(687\) −0.366368 + 0.434422i −0.0139778 + 0.0165742i
\(688\) −4.00954 + 6.94472i −0.152862 + 0.264765i
\(689\) −2.77816 4.81192i −0.105840 0.183319i
\(690\) −2.32280 + 12.9844i −0.0884277 + 0.494309i
\(691\) 10.7402 + 6.20088i 0.408578 + 0.235893i 0.690179 0.723639i \(-0.257532\pi\)
−0.281601 + 0.959532i \(0.590865\pi\)
\(692\) 0.138867 0.00527892
\(693\) 8.71547 12.6161i 0.331073 0.479247i
\(694\) −12.5620 −0.476846
\(695\) 15.3102 + 8.83933i 0.580748 + 0.335295i
\(696\) 1.18391 6.61802i 0.0448759 0.250855i
\(697\) 2.99625 + 5.18965i 0.113491 + 0.196572i
\(698\) 8.85051 15.3295i 0.334997 0.580232i
\(699\) −10.0625 + 11.9316i −0.380598 + 0.451295i
\(700\) 0.437186 + 1.56083i 0.0165241 + 0.0589940i
\(701\) 2.73572i 0.103327i −0.998665 0.0516634i \(-0.983548\pi\)
0.998665 0.0516634i \(-0.0164523\pi\)
\(702\) 2.56444 + 4.51925i 0.0967886 + 0.170568i
\(703\) −14.9317 + 8.62079i −0.563158 + 0.325139i
\(704\) 1.67306 0.965940i 0.0630557 0.0364052i
\(705\) 14.9974 5.41641i 0.564834 0.203994i
\(706\) 0.445314i 0.0167596i
\(707\) 38.5165 + 9.85538i 1.44856 + 0.370650i
\(708\) 13.8029 + 11.6406i 0.518746 + 0.437482i
\(709\) 4.28476 7.42143i 0.160918 0.278718i −0.774280 0.632843i \(-0.781888\pi\)
0.935198 + 0.354125i \(0.115221\pi\)
\(710\) 3.75411 + 6.50231i 0.140889 + 0.244028i
\(711\) 38.4684 31.9542i 1.44268 1.19838i
\(712\) −12.9209 7.45988i −0.484231 0.279571i
\(713\) −3.43322 −0.128575
\(714\) 2.58122 1.84150i 0.0965997 0.0689165i
\(715\) 4.04652 0.151331
\(716\) −12.4682 7.19850i −0.465957 0.269020i
\(717\) −48.1078 8.60608i −1.79662 0.321400i
\(718\) −10.3348 17.9004i −0.385691 0.668036i
\(719\) 12.6631 21.9332i 0.472255 0.817969i −0.527241 0.849716i \(-0.676774\pi\)
0.999496 + 0.0317464i \(0.0101069\pi\)
\(720\) −1.06039 6.19369i −0.0395183 0.230825i
\(721\) −47.5876 + 13.3292i −1.77225 + 0.496404i
\(722\) 13.1933i 0.491005i
\(723\) −6.74559 18.6777i −0.250871 0.694631i
\(724\) 8.03597 4.63957i 0.298654 0.172428i
\(725\) 2.05943 1.18901i 0.0764853 0.0441588i
\(726\) 4.27602 + 11.8398i 0.158698 + 0.439415i
\(727\) 48.9569i 1.81571i −0.419284 0.907855i \(-0.637719\pi\)
0.419284 0.907855i \(-0.362281\pi\)
\(728\) 1.84957 1.89185i 0.0685496 0.0701166i
\(729\) −13.1497 23.5815i −0.487026 0.873387i
\(730\) 9.02951 15.6396i 0.334197 0.578846i
\(731\) 2.77428 + 4.80519i 0.102610 + 0.177726i
\(732\) 5.75798 + 1.03005i 0.212821 + 0.0380719i
\(733\) 43.4681 + 25.0963i 1.60553 + 0.926954i 0.990353 + 0.138566i \(0.0442494\pi\)
0.615179 + 0.788388i \(0.289084\pi\)
\(734\) −19.8731 −0.733528
\(735\) −15.9295 + 19.7786i −0.587568 + 0.729545i
\(736\) 3.63581 0.134018
\(737\) 16.6661 + 9.62219i 0.613905 + 0.354438i
\(738\) −16.6017 19.9862i −0.611119 0.735702i
\(739\) −8.36739 14.4927i −0.307799 0.533124i 0.670081 0.742288i \(-0.266259\pi\)
−0.977881 + 0.209164i \(0.932926\pi\)
\(740\) −7.49350 + 12.9791i −0.275467 + 0.477122i
\(741\) −3.19058 2.69076i −0.117209 0.0988477i
\(742\) 10.2768 10.5117i 0.377274 0.385898i
\(743\) 6.98714i 0.256333i −0.991753 0.128167i \(-0.959091\pi\)
0.991753 0.128167i \(-0.0409092\pi\)
\(744\) 1.53829 0.555565i 0.0563965 0.0203680i
\(745\) −0.0700454 + 0.0404408i −0.00256627 + 0.00148163i
\(746\) 13.2365 7.64212i 0.484624 0.279798i
\(747\) 35.4134 + 13.0892i 1.29571 + 0.478910i
\(748\) 1.33671i 0.0488748i
\(749\) 3.82492 1.07135i 0.139760 0.0391463i
\(750\) 13.1275 15.5659i 0.479347 0.568388i
\(751\) 0.680716 1.17903i 0.0248397 0.0430236i −0.853338 0.521358i \(-0.825426\pi\)
0.878178 + 0.478334i \(0.158759\pi\)
\(752\) −2.19759 3.80633i −0.0801377 0.138803i
\(753\) 7.85702 43.9206i 0.286326 1.60055i
\(754\) −3.36154 1.94079i −0.122420 0.0706793i
\(755\) −43.6186 −1.58744
\(756\) −9.68370 + 9.75838i −0.352193 + 0.354909i
\(757\) −17.6138 −0.640186 −0.320093 0.947386i \(-0.603714\pi\)
−0.320093 + 0.947386i \(0.603714\pi\)
\(758\) −20.6819 11.9407i −0.751200 0.433705i
\(759\) 2.14236 11.9757i 0.0777626 0.434691i
\(760\) 2.52369 + 4.37115i 0.0915437 + 0.158558i
\(761\) 10.6541 18.4534i 0.386210 0.668935i −0.605727 0.795673i \(-0.707117\pi\)
0.991936 + 0.126738i \(0.0404508\pi\)
\(762\) −2.42983 + 2.88118i −0.0880233 + 0.104374i
\(763\) −9.62349 2.46240i −0.348394 0.0891450i
\(764\) 3.38949i 0.122627i
\(765\) −4.07824 1.50736i −0.147449 0.0544988i
\(766\) 32.5547 18.7955i 1.17625 0.679108i
\(767\) 9.02810 5.21237i 0.325986 0.188208i
\(768\) −1.62906 + 0.588348i −0.0587838 + 0.0212302i
\(769\) 49.2139i 1.77470i −0.461099 0.887349i \(-0.652545\pi\)
0.461099 0.887349i \(-0.347455\pi\)
\(770\) 2.88761 + 10.3093i 0.104062 + 0.371522i
\(771\) 18.2555 + 15.3957i 0.657454 + 0.554461i
\(772\) 6.28558 10.8869i 0.226223 0.391830i
\(773\) −14.9637 25.9179i −0.538208 0.932203i −0.999001 0.0446955i \(-0.985768\pi\)
0.460793 0.887508i \(-0.347565\pi\)
\(774\) −15.3719 18.5056i −0.552530 0.665169i
\(775\) 0.501003 + 0.289254i 0.0179965 + 0.0103903i
\(776\) 2.33951 0.0839833
\(777\) 32.6374 3.14548i 1.17086 0.112843i
\(778\) −29.4790 −1.05687
\(779\) 18.0737 + 10.4348i 0.647556 + 0.373867i
\(780\) −3.57126 0.638869i −0.127872 0.0228752i
\(781\) −3.46247 5.99718i −0.123897 0.214596i
\(782\) 1.25784 2.17865i 0.0449804 0.0779084i
\(783\) 17.3914 + 10.2146i 0.621517 + 0.365041i
\(784\) 6.13972 + 3.36212i 0.219276 + 0.120076i
\(785\) 9.62985i 0.343704i
\(786\) −3.85539 10.6751i −0.137517 0.380769i
\(787\) 17.6377 10.1831i 0.628715 0.362989i −0.151539 0.988451i \(-0.548423\pi\)
0.780254 + 0.625462i \(0.215090\pi\)
\(788\) 10.4158 6.01354i 0.371046 0.214224i
\(789\) 12.6172 + 34.9354i 0.449183 + 1.24373i
\(790\) 34.9163i 1.24226i
\(791\) 16.3860 + 16.0198i 0.582619 + 0.569599i
\(792\) 0.978010 + 5.71253i 0.0347521 + 0.202986i
\(793\) 1.68857 2.92469i 0.0599630 0.103859i
\(794\) 9.42604 + 16.3264i 0.334518 + 0.579402i
\(795\) −19.8431 3.54976i −0.703762 0.125897i
\(796\) −13.0591 7.53965i −0.462866 0.267236i
\(797\) 14.7873 0.523792 0.261896 0.965096i \(-0.415652\pi\)
0.261896 + 0.965096i \(0.415652\pi\)
\(798\) 4.57844 10.0488i 0.162075 0.355723i
\(799\) −3.04111 −0.107587
\(800\) −0.530566 0.306322i −0.0187583 0.0108301i
\(801\) 34.4302 28.5999i 1.21653 1.01053i
\(802\) −5.77115 9.99593i −0.203786 0.352968i
\(803\) −8.32804 + 14.4246i −0.293890 + 0.509033i
\(804\) −13.1896 11.1233i −0.465160 0.392290i
\(805\) −4.99467 + 19.5200i −0.176039 + 0.687991i
\(806\) 0.944280i 0.0332608i
\(807\) 15.5346 5.61041i 0.546842 0.197496i
\(808\) −13.0136 + 7.51343i −0.457819 + 0.264322i
\(809\) 35.4312 20.4562i 1.24569 0.719202i 0.275446 0.961317i \(-0.411174\pi\)
0.970248 + 0.242115i \(0.0778411\pi\)
\(810\) 18.5315 + 3.45798i 0.651132 + 0.121501i
\(811\) 15.0715i 0.529231i −0.964354 0.264616i \(-0.914755\pi\)
0.964354 0.264616i \(-0.0852451\pi\)
\(812\) 2.54573 9.94915i 0.0893377 0.349147i
\(813\) −28.4637 + 33.7510i −0.998266 + 1.18370i
\(814\) 6.91136 11.9708i 0.242243 0.419577i
\(815\) 20.8161 + 36.0546i 0.729157 + 1.26294i
\(816\) −0.211041 + 1.17971i −0.00738790 + 0.0412982i
\(817\) 16.7347 + 9.66180i 0.585474 + 0.338024i
\(818\) −24.0433 −0.840655
\(819\) 3.39988 + 7.17223i 0.118801 + 0.250618i
\(820\) 18.1407 0.633499
\(821\) −14.4930 8.36756i −0.505811 0.292030i 0.225299 0.974290i \(-0.427664\pi\)
−0.731110 + 0.682260i \(0.760997\pi\)
\(822\) 4.34087 24.2654i 0.151405 0.846352i
\(823\) 26.3860 + 45.7019i 0.919757 + 1.59307i 0.799783 + 0.600290i \(0.204948\pi\)
0.119975 + 0.992777i \(0.461719\pi\)
\(824\) 9.33933 16.1762i 0.325351 0.563524i
\(825\) −1.32160 + 1.56709i −0.0460123 + 0.0545592i
\(826\) 19.7220 + 19.2813i 0.686218 + 0.670882i
\(827\) 35.5394i 1.23583i 0.786246 + 0.617913i \(0.212022\pi\)
−0.786246 + 0.617913i \(0.787978\pi\)
\(828\) −3.78148 + 10.2309i −0.131415 + 0.355550i
\(829\) 23.3896 13.5040i 0.812354 0.469013i −0.0354185 0.999373i \(-0.511276\pi\)
0.847773 + 0.530360i \(0.177943\pi\)
\(830\) −22.8289 + 13.1803i −0.792403 + 0.457494i
\(831\) 31.7005 11.4489i 1.09968 0.397157i
\(832\) 1.00000i 0.0346688i
\(833\) 4.13875 2.51589i 0.143399 0.0871703i
\(834\) 11.1752 + 9.42453i 0.386965 + 0.326345i
\(835\) 5.61619 9.72752i 0.194356 0.336635i
\(836\) −2.32763 4.03158i −0.0805028 0.139435i
\(837\) −0.0365966 + 4.90648i −0.00126496 + 0.169593i
\(838\) −3.14928 1.81824i −0.108790 0.0628099i
\(839\) −12.4473 −0.429730 −0.214865 0.976644i \(-0.568931\pi\)
−0.214865 + 0.976644i \(0.568931\pi\)
\(840\) −0.920820 9.55440i −0.0317713 0.329658i
\(841\) 13.9334 0.480462
\(842\) −0.0278313 0.0160684i −0.000959130 0.000553754i
\(843\) 14.7791 + 2.64385i 0.509018 + 0.0910591i
\(844\) 5.51491 + 9.55210i 0.189831 + 0.328797i
\(845\) −1.04730 + 1.81398i −0.0360282 + 0.0624027i
\(846\) 12.9964 2.22504i 0.446826 0.0764986i
\(847\) 5.18636 + 18.5163i 0.178205 + 0.636226i
\(848\) 5.55632i 0.190805i
\(849\) −13.5532 37.5272i −0.465145 1.28793i
\(850\) −0.367109 + 0.211951i −0.0125917 + 0.00726984i
\(851\) 22.5292 13.0072i 0.772290 0.445882i
\(852\) 2.10897 + 5.83948i 0.0722521 + 0.200057i
\(853\) 37.5892i 1.28703i 0.765433 + 0.643515i \(0.222525\pi\)
−0.765433 + 0.643515i \(0.777475\pi\)
\(854\) 8.65621 + 2.21490i 0.296209 + 0.0757924i
\(855\) −14.9250 + 2.55522i −0.510423 + 0.0873866i
\(856\) −0.750662 + 1.30018i −0.0256571 + 0.0444394i
\(857\) −6.33608 10.9744i −0.216436 0.374879i 0.737280 0.675588i \(-0.236110\pi\)
−0.953716 + 0.300709i \(0.902777\pi\)
\(858\) 3.29383 + 0.589238i 0.112449 + 0.0201162i
\(859\) −10.2996 5.94647i −0.351417 0.202891i 0.313892 0.949459i \(-0.398367\pi\)
−0.665309 + 0.746568i \(0.731700\pi\)
\(860\) 16.7968 0.572765
\(861\) −23.0499 32.3088i −0.785537 1.10108i
\(862\) −16.5585 −0.563984
\(863\) 14.3740 + 8.29886i 0.489298 + 0.282496i 0.724283 0.689502i \(-0.242171\pi\)
−0.234985 + 0.971999i \(0.575504\pi\)
\(864\) 0.0387561 5.19601i 0.00131851 0.176772i
\(865\) −0.145435 0.251901i −0.00494494 0.00856489i
\(866\) −11.7825 + 20.4079i −0.400385 + 0.693488i
\(867\) −21.8751 18.4482i −0.742916 0.626534i
\(868\) 2.40574 0.673841i 0.0816561 0.0228717i
\(869\) 32.2038i 1.09244i
\(870\) −13.2449 + 4.78347i −0.449042 + 0.162175i
\(871\) −8.62689 + 4.98074i −0.292311 + 0.168766i
\(872\) 3.25151 1.87726i 0.110110 0.0635721i
\(873\) −2.43324 + 6.58323i −0.0823526 + 0.222809i
\(874\) 8.76123i 0.296353i
\(875\) 21.7440 22.2411i 0.735082 0.751885i
\(876\) 9.62729 11.4156i 0.325276 0.385697i
\(877\) 18.9926 32.8962i 0.641336 1.11083i −0.343799 0.939043i \(-0.611714\pi\)
0.985135 0.171783i \(-0.0549528\pi\)
\(878\) −0.637611 1.10437i −0.0215183 0.0372708i
\(879\) 5.56478 31.1070i 0.187695 1.04921i
\(880\) −3.50439 2.02326i −0.118133 0.0682041i
\(881\) 52.5629 1.77089 0.885444 0.464746i \(-0.153854\pi\)
0.885444 + 0.464746i \(0.153854\pi\)
\(882\) −15.8465 + 13.7800i −0.533580 + 0.463996i
\(883\) 21.4529 0.721948 0.360974 0.932576i \(-0.382444\pi\)
0.360974 + 0.932576i \(0.382444\pi\)
\(884\) 0.599220 + 0.345960i 0.0201540 + 0.0116359i
\(885\) 6.66005 37.2295i 0.223875 1.25146i
\(886\) −3.35151 5.80498i −0.112596 0.195022i
\(887\) −5.84800 + 10.1290i −0.196357 + 0.340099i −0.947344 0.320217i \(-0.896244\pi\)
0.750988 + 0.660316i \(0.229578\pi\)
\(888\) −7.98960 + 9.47370i −0.268113 + 0.317917i
\(889\) −4.02471 + 4.11671i −0.134984 + 0.138070i
\(890\) 31.2510i 1.04753i
\(891\) −17.0919 3.18934i −0.572600 0.106847i
\(892\) 12.3750 7.14470i 0.414345 0.239222i
\(893\) −9.17213 + 5.29553i −0.306934 + 0.177208i
\(894\) −0.0629051 + 0.0227186i −0.00210386 + 0.000759824i
\(895\) 30.1560i 1.00800i
\(896\) −2.54770 + 0.713604i −0.0851126 + 0.0238398i
\(897\) 4.81401 + 4.05987i 0.160735 + 0.135555i
\(898\) 5.72116 9.90935i 0.190918 0.330679i
\(899\) −1.83265 3.17423i −0.0611221 0.105867i
\(900\) 1.41380 1.17439i 0.0471265 0.0391462i
\(901\) 3.32946 + 1.92227i 0.110920 + 0.0640400i
\(902\) −16.7314 −0.557094
\(903\) −21.3423 29.9153i −0.710226 0.995518i
\(904\) −8.66137 −0.288073
\(905\) −16.8322 9.71805i −0.559520 0.323039i
\(906\) −35.5051 6.35157i −1.17958 0.211017i
\(907\) 25.5815 + 44.3084i 0.849419 + 1.47124i 0.881727 + 0.471759i \(0.156381\pi\)
−0.0323084 + 0.999478i \(0.510286\pi\)
\(908\) 10.4107 18.0319i 0.345491 0.598409i
\(909\) −7.60731 44.4341i −0.252319 1.47379i
\(910\) −5.36883 1.37375i −0.177975 0.0455392i
\(911\) 43.0375i 1.42589i 0.701218 + 0.712947i \(0.252640\pi\)
−0.701218 + 0.712947i \(0.747360\pi\)
\(912\) 1.41774 + 3.92556i 0.0469462 + 0.129988i
\(913\) 21.0554 12.1564i 0.696833 0.402317i
\(914\) −27.6958 + 15.9902i −0.916096 + 0.528908i
\(915\) −4.16184 11.5236i −0.137586 0.380959i
\(916\) 0.328100i 0.0108407i
\(917\) −4.67618 16.6949i −0.154421 0.551313i
\(918\) −3.10015 1.82083i −0.102320 0.0600965i
\(919\) −18.7861 + 32.5385i −0.619696 + 1.07335i 0.369845 + 0.929094i \(0.379411\pi\)
−0.989541 + 0.144252i \(0.953922\pi\)
\(920\) −3.80778 6.59528i −0.125539 0.217440i
\(921\) 37.2556 + 6.66471i 1.22761 + 0.219610i
\(922\) −6.63651 3.83159i −0.218562 0.126187i
\(923\) 3.58456 0.117987
\(924\) 0.849286 + 8.81216i 0.0279395 + 0.289899i
\(925\) −4.38351 −0.144129
\(926\) −29.1640 16.8379i −0.958390 0.553327i
\(927\) 35.8053 + 43.1046i 1.17600 + 1.41574i
\(928\) 1.94079 + 3.36154i 0.0637094 + 0.110348i
\(929\) −1.73163 + 2.99926i −0.0568128 + 0.0984026i −0.893033 0.449991i \(-0.851427\pi\)
0.836220 + 0.548394i \(0.184760\pi\)
\(930\) −2.61884 2.20858i −0.0858750 0.0724223i
\(931\) 8.10171 14.7949i 0.265523 0.484884i
\(932\) 9.01141i 0.295179i
\(933\) 4.60728 1.66395i 0.150835 0.0544753i
\(934\) 17.1383 9.89478i 0.560781 0.323767i
\(935\) −2.42476 + 1.39993i −0.0792980 + 0.0457827i
\(936\) −2.81394 1.04007i −0.0919765 0.0339956i
\(937\) 26.4458i 0.863948i −0.901886 0.431974i \(-0.857817\pi\)
0.901886 0.431974i \(-0.142183\pi\)
\(938\) −18.8456 18.4244i −0.615331 0.601580i
\(939\) −11.0639 + 13.1191i −0.361058 + 0.428126i
\(940\) −4.60307 + 7.97275i −0.150135 + 0.260042i
\(941\) 16.9152 + 29.2979i 0.551418 + 0.955084i 0.998173 + 0.0604278i \(0.0192465\pi\)
−0.446754 + 0.894657i \(0.647420\pi\)
\(942\) 1.40226 7.83860i 0.0456881 0.255395i
\(943\) −27.2699 15.7443i −0.888030 0.512704i
\(944\) −10.4247 −0.339297
\(945\) 27.8432 + 7.34607i 0.905740 + 0.238968i
\(946\) −15.4919 −0.503685
\(947\) −0.430364 0.248471i −0.0139849 0.00807421i 0.492991 0.870034i \(-0.335903\pi\)
−0.506976 + 0.861960i \(0.669237\pi\)
\(948\) −5.08436 + 28.4215i −0.165132 + 0.923087i
\(949\) −4.31085 7.46660i −0.139936 0.242376i
\(950\) −0.738147 + 1.27851i −0.0239486 + 0.0414803i
\(951\) −19.6191 + 23.2635i −0.636194 + 0.754369i
\(952\) −0.453796 + 1.77351i −0.0147076 + 0.0574798i
\(953\) 41.4342i 1.34219i −0.741373 0.671093i \(-0.765825\pi\)
0.741373 0.671093i \(-0.234175\pi\)
\(954\) −15.6352 5.77894i −0.506207 0.187100i
\(955\) 6.14846 3.54981i 0.198959 0.114869i
\(956\) 24.4357 14.1080i 0.790308 0.456285i
\(957\) 12.2159 4.41187i 0.394884 0.142615i
\(958\) 20.7962i 0.671895i
\(959\) 9.33408 36.4792i 0.301413 1.17797i
\(960\) 2.77337 + 2.33891i 0.0895101 + 0.0754879i
\(961\) −15.0542 + 26.0746i −0.485618 + 0.841116i
\(962\) 3.57753 + 6.19647i 0.115344 + 0.199782i
\(963\) −2.87790 3.46459i −0.0927392 0.111645i
\(964\) 9.92924 + 5.73265i 0.319799 + 0.184636i
\(965\) −26.3316 −0.847643
\(966\) −6.90804 + 15.1618i −0.222263 + 0.487823i
\(967\) 53.6640 1.72572 0.862859 0.505444i \(-0.168671\pi\)
0.862859 + 0.505444i \(0.168671\pi\)
\(968\) −6.29413 3.63392i −0.202301 0.116799i
\(969\) 2.84276 + 0.508546i 0.0913226 + 0.0163368i
\(970\) −2.45017 4.24381i −0.0786701 0.136261i
\(971\) −26.9806 + 46.7317i −0.865848 + 1.49969i 0.000355104 1.00000i \(0.499887\pi\)
−0.866203 + 0.499692i \(0.833446\pi\)
\(972\) 14.5810 + 5.51325i 0.467684 + 0.176837i
\(973\) 15.9674 + 15.6106i 0.511892 + 0.500452i
\(974\) 5.60406i 0.179566i
\(975\) −0.360448 0.998037i −0.0115436 0.0319628i
\(976\) −2.92469 + 1.68857i −0.0936172 + 0.0540499i
\(977\) 52.5754 30.3544i 1.68203 0.971123i 0.721728 0.692177i \(-0.243348\pi\)
0.960307 0.278946i \(-0.0899851\pi\)
\(978\) 11.6940 + 32.3792i 0.373933 + 1.03537i
\(979\) 28.8232i 0.921194i
\(980\) −0.331326 14.6585i −0.0105838 0.468248i
\(981\) 1.90072 + 11.1020i 0.0606852 + 0.354461i
\(982\) −9.70531 + 16.8101i −0.309709 + 0.536431i
\(983\) −9.30310 16.1134i −0.296723 0.513939i 0.678661 0.734451i \(-0.262560\pi\)
−0.975384 + 0.220512i \(0.929227\pi\)
\(984\) 14.7663 + 2.64157i 0.470733 + 0.0842102i
\(985\) −21.8169 12.5960i −0.695143 0.401341i
\(986\) 2.68574 0.0855313
\(987\) 20.0483 1.93219i 0.638145 0.0615022i
\(988\) 2.40970 0.0766629
\(989\) −25.2497 14.5779i −0.802893 0.463550i
\(990\) 9.33813 7.75682i 0.296785 0.246528i
\(991\) −13.6603 23.6603i −0.433934 0.751596i 0.563274 0.826270i \(-0.309542\pi\)
−0.997208 + 0.0746745i \(0.976208\pi\)
\(992\) −0.472140 + 0.817770i −0.0149905 + 0.0259642i
\(993\) −20.3967 17.2014i −0.647268 0.545871i
\(994\) 2.55796 + 9.13238i 0.0811334 + 0.289662i
\(995\) 31.5851i 1.00132i
\(996\) −20.5018 + 7.40436i −0.649623 + 0.234616i
\(997\) −24.8479 + 14.3459i −0.786940 + 0.454340i −0.838884 0.544310i \(-0.816792\pi\)
0.0519442 + 0.998650i \(0.483458\pi\)
\(998\) −21.0412 + 12.1481i −0.666047 + 0.384542i
\(999\) −18.3487 32.3355i −0.580528 1.02305i
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 546.2.z.a.131.13 32
3.2 odd 2 546.2.z.b.131.8 yes 32
7.3 odd 6 546.2.z.b.521.8 yes 32
21.17 even 6 inner 546.2.z.a.521.13 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.z.a.131.13 32 1.1 even 1 trivial
546.2.z.a.521.13 yes 32 21.17 even 6 inner
546.2.z.b.131.8 yes 32 3.2 odd 2
546.2.z.b.521.8 yes 32 7.3 odd 6