Properties

Label 546.2.z.a.131.6
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 131.6
Character \(\chi\) \(=\) 546.131
Dual form 546.2.z.a.521.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.587248 + 1.62946i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.386271 - 0.669041i) q^{5} +(0.306158 - 1.70478i) q^{6} +(1.82832 + 1.91239i) q^{7} -1.00000i q^{8} +(-2.31028 + 1.91379i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.587248 + 1.62946i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.386271 - 0.669041i) q^{5} +(0.306158 - 1.70478i) q^{6} +(1.82832 + 1.91239i) q^{7} -1.00000i q^{8} +(-2.31028 + 1.91379i) q^{9} +(-0.669041 + 0.386271i) q^{10} +(3.31419 - 1.91345i) q^{11} +(-1.11753 + 1.32330i) q^{12} +1.00000i q^{13} +(-0.627178 - 2.57034i) q^{14} +(1.31701 + 0.236520i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.460437 + 0.797500i) q^{17} +(2.95766 - 0.502255i) q^{18} +(2.92280 + 1.68748i) q^{19} +0.772542 q^{20} +(-2.04249 + 4.10223i) q^{21} -3.82690 q^{22} +(-3.80849 - 2.19883i) q^{23} +(1.62946 - 0.587248i) q^{24} +(2.20159 + 3.81326i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-4.47516 - 2.64064i) q^{27} +(-0.742018 + 2.53957i) q^{28} -0.669555i q^{29} +(-1.02231 - 0.863338i) q^{30} +(0.824139 - 0.475817i) q^{31} +(0.866025 - 0.500000i) q^{32} +(5.06414 + 4.27667i) q^{33} -0.920873i q^{34} +(1.98570 - 0.484521i) q^{35} +(-2.81253 - 1.04386i) q^{36} +(-3.37565 + 5.84680i) q^{37} +(-1.68748 - 2.92280i) q^{38} +(-1.62946 + 0.587248i) q^{39} +(-0.669041 - 0.386271i) q^{40} +1.36972 q^{41} +(3.81996 - 2.53139i) q^{42} +1.18934 q^{43} +(3.31419 + 1.91345i) q^{44} +(0.388013 + 2.28491i) q^{45} +(2.19883 + 3.80849i) q^{46} +(-5.17037 + 8.95534i) q^{47} +(-1.70478 - 0.306158i) q^{48} +(-0.314476 + 6.99293i) q^{49} -4.40318i q^{50} +(-1.02910 + 1.21859i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(7.30193 - 4.21577i) q^{53} +(2.55528 + 4.52444i) q^{54} -2.95644i q^{55} +(1.91239 - 1.82832i) q^{56} +(-1.03327 + 5.75356i) q^{57} +(-0.334777 + 0.579851i) q^{58} +(1.98058 + 3.43047i) q^{59} +(0.453674 + 1.25883i) q^{60} +(-0.358567 - 0.207019i) q^{61} -0.951633 q^{62} +(-7.88386 - 0.919124i) q^{63} -1.00000 q^{64} +(0.669041 + 0.386271i) q^{65} +(-2.24734 - 6.23578i) q^{66} +(-4.70367 - 8.14699i) q^{67} +(-0.460437 + 0.797500i) q^{68} +(1.34638 - 7.49705i) q^{69} +(-1.96192 - 0.573240i) q^{70} +6.24239i q^{71} +(1.91379 + 2.31028i) q^{72} +(7.63416 - 4.40758i) q^{73} +(5.84680 - 3.37565i) q^{74} +(-4.92068 + 5.82673i) q^{75} +3.37496i q^{76} +(9.71868 + 2.83963i) q^{77} +(1.70478 + 0.306158i) q^{78} +(6.47880 - 11.2216i) q^{79} +(0.386271 + 0.669041i) q^{80} +(1.67478 - 8.84280i) q^{81} +(-1.18621 - 0.684859i) q^{82} -2.22220 q^{83} +(-4.57387 + 0.282269i) q^{84} +0.711413 q^{85} +(-1.03000 - 0.594671i) q^{86} +(1.09101 - 0.393195i) q^{87} +(-1.91345 - 3.31419i) q^{88} +(2.00944 - 3.48046i) q^{89} +(0.806428 - 2.17280i) q^{90} +(-1.91239 + 1.82832i) q^{91} -4.39767i q^{92} +(1.25930 + 1.06348i) q^{93} +(8.95534 - 5.17037i) q^{94} +(2.25799 - 1.30365i) q^{95} +(1.32330 + 1.11753i) q^{96} -9.41494i q^{97} +(3.76881 - 5.89882i) q^{98} +(-3.99476 + 10.7633i) 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
\(3\) 0.587248 + 1.62946i 0.339048 + 0.940769i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.386271 0.669041i 0.172746 0.299204i −0.766633 0.642085i \(-0.778069\pi\)
0.939379 + 0.342881i \(0.111403\pi\)
\(6\) 0.306158 1.70478i 0.124989 0.695973i
\(7\) 1.82832 + 1.91239i 0.691041 + 0.722816i
\(8\) 1.00000i 0.353553i
\(9\) −2.31028 + 1.91379i −0.770093 + 0.637931i
\(10\) −0.669041 + 0.386271i −0.211569 + 0.122150i
\(11\) 3.31419 1.91345i 0.999267 0.576927i 0.0912355 0.995829i \(-0.470918\pi\)
0.908031 + 0.418902i \(0.137585\pi\)
\(12\) −1.11753 + 1.32330i −0.322603 + 0.382004i
\(13\) 1.00000i 0.277350i
\(14\) −0.627178 2.57034i −0.167620 0.686952i
\(15\) 1.31701 + 0.236520i 0.340051 + 0.0610692i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.460437 + 0.797500i 0.111672 + 0.193422i 0.916445 0.400161i \(-0.131046\pi\)
−0.804772 + 0.593584i \(0.797713\pi\)
\(18\) 2.95766 0.502255i 0.697127 0.118383i
\(19\) 2.92280 + 1.68748i 0.670537 + 0.387135i 0.796280 0.604928i \(-0.206798\pi\)
−0.125743 + 0.992063i \(0.540132\pi\)
\(20\) 0.772542 0.172746
\(21\) −2.04249 + 4.10223i −0.445707 + 0.895179i
\(22\) −3.82690 −0.815898
\(23\) −3.80849 2.19883i −0.794126 0.458489i 0.0472874 0.998881i \(-0.484942\pi\)
−0.841413 + 0.540393i \(0.818276\pi\)
\(24\) 1.62946 0.587248i 0.332612 0.119872i
\(25\) 2.20159 + 3.81326i 0.440318 + 0.762653i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −4.47516 2.64064i −0.861245 0.508191i
\(28\) −0.742018 + 2.53957i −0.140228 + 0.479933i
\(29\) 0.669555i 0.124333i −0.998066 0.0621666i \(-0.980199\pi\)
0.998066 0.0621666i \(-0.0198010\pi\)
\(30\) −1.02231 0.863338i −0.186647 0.157623i
\(31\) 0.824139 0.475817i 0.148020 0.0854592i −0.424161 0.905587i \(-0.639431\pi\)
0.572181 + 0.820128i \(0.306098\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 5.06414 + 4.27667i 0.881554 + 0.744473i
\(34\) 0.920873i 0.157928i
\(35\) 1.98570 0.484521i 0.335644 0.0818991i
\(36\) −2.81253 1.04386i −0.468756 0.173977i
\(37\) −3.37565 + 5.84680i −0.554954 + 0.961208i 0.442954 + 0.896545i \(0.353931\pi\)
−0.997907 + 0.0646632i \(0.979403\pi\)
\(38\) −1.68748 2.92280i −0.273745 0.474141i
\(39\) −1.62946 + 0.587248i −0.260922 + 0.0940349i
\(40\) −0.669041 0.386271i −0.105785 0.0610748i
\(41\) 1.36972 0.213914 0.106957 0.994264i \(-0.465889\pi\)
0.106957 + 0.994264i \(0.465889\pi\)
\(42\) 3.81996 2.53139i 0.589432 0.390602i
\(43\) 1.18934 0.181373 0.0906865 0.995879i \(-0.471094\pi\)
0.0906865 + 0.995879i \(0.471094\pi\)
\(44\) 3.31419 + 1.91345i 0.499633 + 0.288463i
\(45\) 0.388013 + 2.28491i 0.0578415 + 0.340615i
\(46\) 2.19883 + 3.80849i 0.324200 + 0.561532i
\(47\) −5.17037 + 8.95534i −0.754176 + 1.30627i 0.191608 + 0.981472i \(0.438630\pi\)
−0.945783 + 0.324799i \(0.894703\pi\)
\(48\) −1.70478 0.306158i −0.246063 0.0441901i
\(49\) −0.314476 + 6.99293i −0.0449251 + 0.998990i
\(50\) 4.40318i 0.622704i
\(51\) −1.02910 + 1.21859i −0.144103 + 0.170637i
\(52\) −0.866025 + 0.500000i −0.120096 + 0.0693375i
\(53\) 7.30193 4.21577i 1.00300 0.579081i 0.0938633 0.995585i \(-0.470078\pi\)
0.909134 + 0.416505i \(0.136745\pi\)
\(54\) 2.55528 + 4.52444i 0.347730 + 0.615698i
\(55\) 2.95644i 0.398646i
\(56\) 1.91239 1.82832i 0.255554 0.244320i
\(57\) −1.03327 + 5.75356i −0.136860 + 0.762077i
\(58\) −0.334777 + 0.579851i −0.0439584 + 0.0761382i
\(59\) 1.98058 + 3.43047i 0.257850 + 0.446609i 0.965666 0.259788i \(-0.0836527\pi\)
−0.707816 + 0.706397i \(0.750319\pi\)
\(60\) 0.453674 + 1.25883i 0.0585690 + 0.162514i
\(61\) −0.358567 0.207019i −0.0459099 0.0265061i 0.476869 0.878974i \(-0.341771\pi\)
−0.522779 + 0.852468i \(0.675105\pi\)
\(62\) −0.951633 −0.120858
\(63\) −7.88386 0.919124i −0.993273 0.115799i
\(64\) −1.00000 −0.125000
\(65\) 0.669041 + 0.386271i 0.0829843 + 0.0479110i
\(66\) −2.24734 6.23578i −0.276628 0.767572i
\(67\) −4.70367 8.14699i −0.574644 0.995313i −0.996080 0.0884552i \(-0.971807\pi\)
0.421436 0.906858i \(-0.361526\pi\)
\(68\) −0.460437 + 0.797500i −0.0558361 + 0.0967110i
\(69\) 1.34638 7.49705i 0.162085 0.902538i
\(70\) −1.96192 0.573240i −0.234495 0.0685153i
\(71\) 6.24239i 0.740835i 0.928865 + 0.370418i \(0.120785\pi\)
−0.928865 + 0.370418i \(0.879215\pi\)
\(72\) 1.91379 + 2.31028i 0.225543 + 0.272269i
\(73\) 7.63416 4.40758i 0.893511 0.515869i 0.0184214 0.999830i \(-0.494136\pi\)
0.875089 + 0.483962i \(0.160803\pi\)
\(74\) 5.84680 3.37565i 0.679677 0.392411i
\(75\) −4.92068 + 5.82673i −0.568192 + 0.672813i
\(76\) 3.37496i 0.387135i
\(77\) 9.71868 + 2.83963i 1.10755 + 0.323606i
\(78\) 1.70478 + 0.306158i 0.193028 + 0.0346656i
\(79\) 6.47880 11.2216i 0.728922 1.26253i −0.228417 0.973563i \(-0.573355\pi\)
0.957339 0.288967i \(-0.0933118\pi\)
\(80\) 0.386271 + 0.669041i 0.0431864 + 0.0748010i
\(81\) 1.67478 8.84280i 0.186087 0.982533i
\(82\) −1.18621 0.684859i −0.130995 0.0756300i
\(83\) −2.22220 −0.243918 −0.121959 0.992535i \(-0.538918\pi\)
−0.121959 + 0.992535i \(0.538918\pi\)
\(84\) −4.57387 + 0.282269i −0.499051 + 0.0307980i
\(85\) 0.711413 0.0771636
\(86\) −1.03000 0.594671i −0.111068 0.0641250i
\(87\) 1.09101 0.393195i 0.116969 0.0421549i
\(88\) −1.91345 3.31419i −0.203974 0.353294i
\(89\) 2.00944 3.48046i 0.213001 0.368928i −0.739652 0.672990i \(-0.765010\pi\)
0.952652 + 0.304062i \(0.0983430\pi\)
\(90\) 0.806428 2.17280i 0.0850050 0.229033i
\(91\) −1.91239 + 1.82832i −0.200473 + 0.191660i
\(92\) 4.39767i 0.458489i
\(93\) 1.25930 + 1.06348i 0.130583 + 0.110278i
\(94\) 8.95534 5.17037i 0.923673 0.533283i
\(95\) 2.25799 1.30365i 0.231665 0.133752i
\(96\) 1.32330 + 1.11753i 0.135059 + 0.114057i
\(97\) 9.41494i 0.955942i −0.878376 0.477971i \(-0.841372\pi\)
0.878376 0.477971i \(-0.158628\pi\)
\(98\) 3.76881 5.89882i 0.380707 0.595871i
\(99\) −3.99476 + 10.7633i −0.401489 + 1.08175i
\(100\) −2.20159 + 3.81326i −0.220159 + 0.381326i
\(101\) 3.54281 + 6.13632i 0.352522 + 0.610587i 0.986691 0.162608i \(-0.0519907\pi\)
−0.634168 + 0.773195i \(0.718657\pi\)
\(102\) 1.50053 0.540781i 0.148574 0.0535453i
\(103\) 4.56989 + 2.63842i 0.450284 + 0.259972i 0.707950 0.706262i \(-0.249620\pi\)
−0.257666 + 0.966234i \(0.582953\pi\)
\(104\) 1.00000 0.0980581
\(105\) 1.95560 + 2.95108i 0.190847 + 0.287996i
\(106\) −8.43154 −0.818944
\(107\) −16.1078 9.29984i −1.55720 0.899049i −0.997523 0.0703370i \(-0.977593\pi\)
−0.559675 0.828712i \(-0.689074\pi\)
\(108\) 0.0492786 5.19592i 0.00474184 0.499978i
\(109\) −5.36127 9.28600i −0.513517 0.889437i −0.999877 0.0156787i \(-0.995009\pi\)
0.486360 0.873758i \(-0.338324\pi\)
\(110\) −1.47822 + 2.56035i −0.140943 + 0.244120i
\(111\) −11.5095 2.06697i −1.09243 0.196188i
\(112\) −2.57034 + 0.627178i −0.242874 + 0.0592628i
\(113\) 14.5031i 1.36434i −0.731194 0.682169i \(-0.761037\pi\)
0.731194 0.682169i \(-0.238963\pi\)
\(114\) 3.77162 4.46609i 0.353244 0.418288i
\(115\) −2.94222 + 1.69869i −0.274363 + 0.158404i
\(116\) 0.579851 0.334777i 0.0538379 0.0310833i
\(117\) −1.91379 2.31028i −0.176930 0.213585i
\(118\) 3.96116i 0.364655i
\(119\) −0.683304 + 2.33862i −0.0626384 + 0.214381i
\(120\) 0.236520 1.31701i 0.0215912 0.120226i
\(121\) 1.82258 3.15680i 0.165689 0.286982i
\(122\) 0.207019 + 0.358567i 0.0187426 + 0.0324632i
\(123\) 0.804364 + 2.23190i 0.0725270 + 0.201244i
\(124\) 0.824139 + 0.475817i 0.0740098 + 0.0427296i
\(125\) 7.26435 0.649743
\(126\) 6.36806 + 4.73791i 0.567312 + 0.422087i
\(127\) −21.3088 −1.89085 −0.945423 0.325844i \(-0.894352\pi\)
−0.945423 + 0.325844i \(0.894352\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0.698439 + 1.93799i 0.0614941 + 0.170630i
\(130\) −0.386271 0.669041i −0.0338782 0.0586788i
\(131\) 8.43583 14.6113i 0.737042 1.27659i −0.216780 0.976220i \(-0.569555\pi\)
0.953822 0.300373i \(-0.0971113\pi\)
\(132\) −1.17164 + 6.52401i −0.101978 + 0.567843i
\(133\) 2.11670 + 8.67480i 0.183541 + 0.752200i
\(134\) 9.40734i 0.812670i
\(135\) −3.49532 + 1.97406i −0.300829 + 0.169900i
\(136\) 0.797500 0.460437i 0.0683850 0.0394821i
\(137\) −12.2984 + 7.10051i −1.05073 + 0.606637i −0.922853 0.385153i \(-0.874149\pi\)
−0.127874 + 0.991790i \(0.540815\pi\)
\(138\) −4.91452 + 5.81944i −0.418352 + 0.495384i
\(139\) 8.87171i 0.752489i −0.926520 0.376244i \(-0.877215\pi\)
0.926520 0.376244i \(-0.122785\pi\)
\(140\) 1.41246 + 1.47740i 0.119374 + 0.124863i
\(141\) −17.6287 3.16590i −1.48460 0.266617i
\(142\) 3.12119 5.40607i 0.261925 0.453667i
\(143\) 1.91345 + 3.31419i 0.160011 + 0.277147i
\(144\) −0.502255 2.95766i −0.0418546 0.246471i
\(145\) −0.447959 0.258630i −0.0372010 0.0214780i
\(146\) −8.81517 −0.729548
\(147\) −11.5794 + 3.59416i −0.955051 + 0.296441i
\(148\) −6.75130 −0.554954
\(149\) −2.03761 1.17642i −0.166928 0.0963758i 0.414209 0.910182i \(-0.364058\pi\)
−0.581136 + 0.813806i \(0.697392\pi\)
\(150\) 7.17480 2.58576i 0.585820 0.211126i
\(151\) 4.92244 + 8.52591i 0.400582 + 0.693829i 0.993796 0.111216i \(-0.0354745\pi\)
−0.593214 + 0.805045i \(0.702141\pi\)
\(152\) 1.68748 2.92280i 0.136873 0.237071i
\(153\) −2.58999 0.961266i −0.209388 0.0777138i
\(154\) −6.99681 7.31853i −0.563819 0.589744i
\(155\) 0.735177i 0.0590508i
\(156\) −1.32330 1.11753i −0.105949 0.0894740i
\(157\) −4.33375 + 2.50209i −0.345871 + 0.199689i −0.662865 0.748739i \(-0.730660\pi\)
0.316994 + 0.948427i \(0.397326\pi\)
\(158\) −11.2216 + 6.47880i −0.892744 + 0.515426i
\(159\) 11.1575 + 9.42250i 0.884845 + 0.747253i
\(160\) 0.772542i 0.0610748i
\(161\) −2.75812 11.3035i −0.217370 0.890841i
\(162\) −5.87180 + 6.82070i −0.461332 + 0.535885i
\(163\) 12.2918 21.2901i 0.962772 1.66757i 0.247286 0.968943i \(-0.420461\pi\)
0.715486 0.698627i \(-0.246205\pi\)
\(164\) 0.684859 + 1.18621i 0.0534785 + 0.0926274i
\(165\) 4.81740 1.73616i 0.375034 0.135160i
\(166\) 1.92448 + 1.11110i 0.149369 + 0.0862382i
\(167\) −6.67521 −0.516543 −0.258272 0.966072i \(-0.583153\pi\)
−0.258272 + 0.966072i \(0.583153\pi\)
\(168\) 4.10223 + 2.04249i 0.316494 + 0.157581i
\(169\) −1.00000 −0.0769231
\(170\) −0.616102 0.355707i −0.0472529 0.0272815i
\(171\) −9.98198 + 1.69509i −0.763341 + 0.129627i
\(172\) 0.594671 + 1.03000i 0.0453432 + 0.0785368i
\(173\) 7.73453 13.3966i 0.588046 1.01852i −0.406443 0.913676i \(-0.633231\pi\)
0.994488 0.104848i \(-0.0334358\pi\)
\(174\) −1.14144 0.204990i −0.0865325 0.0155402i
\(175\) −3.26724 + 11.1822i −0.246980 + 0.845293i
\(176\) 3.82690i 0.288463i
\(177\) −4.42672 + 5.24182i −0.332733 + 0.393999i
\(178\) −3.48046 + 2.00944i −0.260871 + 0.150614i
\(179\) −10.4115 + 6.01106i −0.778189 + 0.449288i −0.835788 0.549052i \(-0.814989\pi\)
0.0575988 + 0.998340i \(0.481656\pi\)
\(180\) −1.78479 + 1.47849i −0.133030 + 0.110200i
\(181\) 16.4089i 1.21966i −0.792531 0.609832i \(-0.791237\pi\)
0.792531 0.609832i \(-0.208763\pi\)
\(182\) 2.57034 0.627178i 0.190526 0.0464895i
\(183\) 0.126761 0.705843i 0.00937045 0.0521774i
\(184\) −2.19883 + 3.80849i −0.162100 + 0.280766i
\(185\) 2.60783 + 4.51690i 0.191732 + 0.332089i
\(186\) −0.558845 1.55065i −0.0409765 0.113699i
\(187\) 3.05195 + 1.76205i 0.223181 + 0.128854i
\(188\) −10.3407 −0.754176
\(189\) −3.13210 13.3862i −0.227827 0.973702i
\(190\) −2.60730 −0.189153
\(191\) −22.0735 12.7441i −1.59718 0.922133i −0.992027 0.126025i \(-0.959778\pi\)
−0.605155 0.796108i \(-0.706889\pi\)
\(192\) −0.587248 1.62946i −0.0423810 0.117596i
\(193\) 5.08419 + 8.80607i 0.365968 + 0.633875i 0.988931 0.148376i \(-0.0474047\pi\)
−0.622963 + 0.782251i \(0.714071\pi\)
\(194\) −4.70747 + 8.15357i −0.337977 + 0.585392i
\(195\) −0.236520 + 1.31701i −0.0169376 + 0.0943132i
\(196\) −6.21330 + 3.22412i −0.443807 + 0.230294i
\(197\) 1.47277i 0.104930i −0.998623 0.0524652i \(-0.983292\pi\)
0.998623 0.0524652i \(-0.0167079\pi\)
\(198\) 8.84121 7.32390i 0.628317 0.520487i
\(199\) 16.5057 9.52955i 1.17006 0.675532i 0.216363 0.976313i \(-0.430581\pi\)
0.953693 + 0.300781i \(0.0972473\pi\)
\(200\) 3.81326 2.20159i 0.269639 0.155676i
\(201\) 10.5130 12.4487i 0.741528 0.878067i
\(202\) 7.08561i 0.498542i
\(203\) 1.28045 1.22416i 0.0898700 0.0859193i
\(204\) −1.56988 0.281933i −0.109914 0.0197393i
\(205\) 0.529082 0.916397i 0.0369527 0.0640039i
\(206\) −2.63842 4.56989i −0.183828 0.318399i
\(207\) 13.0068 2.20875i 0.904035 0.153519i
\(208\) −0.866025 0.500000i −0.0600481 0.0346688i
\(209\) 12.9156 0.893393
\(210\) −0.218064 3.53351i −0.0150479 0.243835i
\(211\) 23.7454 1.63470 0.817349 0.576143i \(-0.195443\pi\)
0.817349 + 0.576143i \(0.195443\pi\)
\(212\) 7.30193 + 4.21577i 0.501498 + 0.289540i
\(213\) −10.1717 + 3.66583i −0.696955 + 0.251179i
\(214\) 9.29984 + 16.1078i 0.635724 + 1.10111i
\(215\) 0.459408 0.795719i 0.0313314 0.0542676i
\(216\) −2.64064 + 4.47516i −0.179673 + 0.304496i
\(217\) 2.41674 + 0.706129i 0.164059 + 0.0479352i
\(218\) 10.7225i 0.726222i
\(219\) 11.6651 + 9.85121i 0.788256 + 0.665683i
\(220\) 2.56035 1.47822i 0.172619 0.0996616i
\(221\) −0.797500 + 0.460437i −0.0536456 + 0.0309723i
\(222\) 8.93401 + 7.54478i 0.599611 + 0.506372i
\(223\) 5.23154i 0.350330i 0.984539 + 0.175165i \(0.0560458\pi\)
−0.984539 + 0.175165i \(0.943954\pi\)
\(224\) 2.53957 + 0.742018i 0.169682 + 0.0495781i
\(225\) −12.3841 4.59632i −0.825606 0.306421i
\(226\) −7.25156 + 12.5601i −0.482366 + 0.835483i
\(227\) 14.0718 + 24.3731i 0.933981 + 1.61770i 0.776441 + 0.630190i \(0.217023\pi\)
0.157540 + 0.987513i \(0.449644\pi\)
\(228\) −5.49936 + 1.98194i −0.364204 + 0.131257i
\(229\) 8.26533 + 4.77199i 0.546189 + 0.315342i 0.747583 0.664168i \(-0.231214\pi\)
−0.201395 + 0.979510i \(0.564547\pi\)
\(230\) 3.39738 0.224017
\(231\) 1.08021 + 17.5038i 0.0710728 + 1.15166i
\(232\) −0.669555 −0.0439584
\(233\) 2.06956 + 1.19486i 0.135581 + 0.0782778i 0.566256 0.824229i \(-0.308391\pi\)
−0.430675 + 0.902507i \(0.641725\pi\)
\(234\) 0.502255 + 2.95766i 0.0328334 + 0.193348i
\(235\) 3.99433 + 6.91837i 0.260561 + 0.451305i
\(236\) −1.98058 + 3.43047i −0.128925 + 0.223304i
\(237\) 22.0898 + 3.96708i 1.43489 + 0.257689i
\(238\) 1.76107 1.68365i 0.114153 0.109135i
\(239\) 1.83106i 0.118442i 0.998245 + 0.0592208i \(0.0188616\pi\)
−0.998245 + 0.0592208i \(0.981138\pi\)
\(240\) −0.863338 + 1.02231i −0.0557283 + 0.0659896i
\(241\) 23.6939 13.6797i 1.52626 0.881187i 0.526746 0.850023i \(-0.323412\pi\)
0.999514 0.0311640i \(-0.00992142\pi\)
\(242\) −3.15680 + 1.82258i −0.202927 + 0.117160i
\(243\) 15.3925 2.46393i 0.987429 0.158061i
\(244\) 0.414038i 0.0265061i
\(245\) 4.55708 + 2.91156i 0.291141 + 0.186013i
\(246\) 0.419350 2.33506i 0.0267368 0.148878i
\(247\) −1.68748 + 2.92280i −0.107372 + 0.185973i
\(248\) −0.475817 0.824139i −0.0302144 0.0523329i
\(249\) −1.30498 3.62099i −0.0827000 0.229471i
\(250\) −6.29111 3.63217i −0.397885 0.229719i
\(251\) 1.71927 0.108519 0.0542597 0.998527i \(-0.482720\pi\)
0.0542597 + 0.998527i \(0.482720\pi\)
\(252\) −3.14594 7.28718i −0.198176 0.459049i
\(253\) −16.8294 −1.05806
\(254\) 18.4539 + 10.6544i 1.15790 + 0.668515i
\(255\) 0.417776 + 1.15922i 0.0261621 + 0.0725931i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.01277 8.68237i 0.312688 0.541591i −0.666255 0.745724i \(-0.732104\pi\)
0.978943 + 0.204132i \(0.0654373\pi\)
\(258\) 0.364127 2.02756i 0.0226696 0.126231i
\(259\) −17.3531 + 4.23427i −1.07827 + 0.263105i
\(260\) 0.772542i 0.0479110i
\(261\) 1.28139 + 1.54686i 0.0793161 + 0.0957481i
\(262\) −14.6113 + 8.43583i −0.902688 + 0.521167i
\(263\) −0.658897 + 0.380414i −0.0406293 + 0.0234573i −0.520177 0.854058i \(-0.674134\pi\)
0.479548 + 0.877516i \(0.340801\pi\)
\(264\) 4.27667 5.06414i 0.263211 0.311676i
\(265\) 6.51372i 0.400134i
\(266\) 2.50428 8.57094i 0.153547 0.525518i
\(267\) 6.85131 + 1.23042i 0.419293 + 0.0753002i
\(268\) 4.70367 8.14699i 0.287322 0.497657i
\(269\) 2.79727 + 4.84501i 0.170552 + 0.295406i 0.938613 0.344972i \(-0.112111\pi\)
−0.768061 + 0.640377i \(0.778778\pi\)
\(270\) 4.01406 + 0.0380698i 0.244288 + 0.00231685i
\(271\) −21.7749 12.5717i −1.32273 0.763679i −0.338567 0.940942i \(-0.609942\pi\)
−0.984163 + 0.177263i \(0.943276\pi\)
\(272\) −0.920873 −0.0558361
\(273\) −4.10223 2.04249i −0.248278 0.123617i
\(274\) 14.2010 0.857915
\(275\) 14.5930 + 8.42526i 0.879990 + 0.508062i
\(276\) 7.16582 2.58252i 0.431332 0.155450i
\(277\) 12.9452 + 22.4217i 0.777802 + 1.34719i 0.933206 + 0.359341i \(0.116998\pi\)
−0.155405 + 0.987851i \(0.549668\pi\)
\(278\) −4.43586 + 7.68313i −0.266045 + 0.460803i
\(279\) −0.993375 + 2.67650i −0.0594718 + 0.160238i
\(280\) −0.484521 1.98570i −0.0289557 0.118668i
\(281\) 2.03189i 0.121212i 0.998162 + 0.0606062i \(0.0193034\pi\)
−0.998162 + 0.0606062i \(0.980697\pi\)
\(282\) 13.6839 + 11.5561i 0.814865 + 0.688154i
\(283\) −23.6297 + 13.6426i −1.40464 + 0.810968i −0.994864 0.101219i \(-0.967726\pi\)
−0.409774 + 0.912187i \(0.634392\pi\)
\(284\) −5.40607 + 3.12119i −0.320791 + 0.185209i
\(285\) 3.45024 + 2.91373i 0.204375 + 0.172595i
\(286\) 3.82690i 0.226289i
\(287\) 2.50428 + 2.61943i 0.147823 + 0.154620i
\(288\) −1.04386 + 2.81253i −0.0615102 + 0.165730i
\(289\) 8.07600 13.9880i 0.475059 0.822826i
\(290\) 0.258630 + 0.447959i 0.0151872 + 0.0263051i
\(291\) 15.3413 5.52890i 0.899321 0.324110i
\(292\) 7.63416 + 4.40758i 0.446755 + 0.257934i
\(293\) −13.0574 −0.762819 −0.381410 0.924406i \(-0.624561\pi\)
−0.381410 + 0.924406i \(0.624561\pi\)
\(294\) 11.8251 + 2.67706i 0.689655 + 0.156129i
\(295\) 3.06017 0.178170
\(296\) 5.84680 + 3.37565i 0.339838 + 0.196206i
\(297\) −19.8843 0.188584i −1.15380 0.0109428i
\(298\) 1.17642 + 2.03761i 0.0681480 + 0.118036i
\(299\) 2.19883 3.80849i 0.127162 0.220251i
\(300\) −7.50644 1.34807i −0.433385 0.0778308i
\(301\) 2.17450 + 2.27449i 0.125336 + 0.131099i
\(302\) 9.84487i 0.566509i
\(303\) −7.91838 + 9.37640i −0.454899 + 0.538660i
\(304\) −2.92280 + 1.68748i −0.167634 + 0.0967836i
\(305\) −0.277008 + 0.159931i −0.0158615 + 0.00915761i
\(306\) 1.76236 + 2.12747i 0.100748 + 0.121620i
\(307\) 17.1766i 0.980319i 0.871633 + 0.490159i \(0.163061\pi\)
−0.871633 + 0.490159i \(0.836939\pi\)
\(308\) 2.40015 + 9.83643i 0.136761 + 0.560483i
\(309\) −1.61555 + 8.99586i −0.0919055 + 0.511756i
\(310\) −0.367588 + 0.636682i −0.0208776 + 0.0361611i
\(311\) −15.5708 26.9693i −0.882936 1.52929i −0.848061 0.529899i \(-0.822230\pi\)
−0.0348756 0.999392i \(-0.511104\pi\)
\(312\) 0.587248 + 1.62946i 0.0332464 + 0.0922500i
\(313\) 6.59778 + 3.80923i 0.372929 + 0.215311i 0.674737 0.738058i \(-0.264257\pi\)
−0.301808 + 0.953369i \(0.597590\pi\)
\(314\) 5.00418 0.282402
\(315\) −3.66024 + 4.91959i −0.206231 + 0.277188i
\(316\) 12.9576 0.728922
\(317\) 18.6264 + 10.7540i 1.04616 + 0.604003i 0.921573 0.388205i \(-0.126905\pi\)
0.124591 + 0.992208i \(0.460238\pi\)
\(318\) −4.95141 13.7389i −0.277661 0.770437i
\(319\) −1.28116 2.21903i −0.0717312 0.124242i
\(320\) −0.386271 + 0.669041i −0.0215932 + 0.0374005i
\(321\) 5.69444 31.7083i 0.317833 1.76978i
\(322\) −3.26315 + 11.1682i −0.181848 + 0.622378i
\(323\) 3.10791i 0.172929i
\(324\) 8.49548 2.97100i 0.471971 0.165055i
\(325\) −3.81326 + 2.20159i −0.211522 + 0.122122i
\(326\) −21.2901 + 12.2918i −1.17915 + 0.680783i
\(327\) 11.9828 14.1892i 0.662648 0.784662i
\(328\) 1.36972i 0.0756300i
\(329\) −26.5792 + 6.48548i −1.46536 + 0.357556i
\(330\) −5.04007 0.905139i −0.277447 0.0498262i
\(331\) 0.786513 1.36228i 0.0432306 0.0748777i −0.843600 0.536971i \(-0.819568\pi\)
0.886831 + 0.462094i \(0.152902\pi\)
\(332\) −1.11110 1.92448i −0.0609796 0.105620i
\(333\) −3.39087 19.9680i −0.185819 1.09424i
\(334\) 5.78090 + 3.33760i 0.316317 + 0.182626i
\(335\) −7.26756 −0.397069
\(336\) −2.53139 3.81996i −0.138099 0.208396i
\(337\) −9.70044 −0.528416 −0.264208 0.964466i \(-0.585111\pi\)
−0.264208 + 0.964466i \(0.585111\pi\)
\(338\) 0.866025 + 0.500000i 0.0471056 + 0.0271964i
\(339\) 23.6322 8.51693i 1.28353 0.462576i
\(340\) 0.355707 + 0.616102i 0.0192909 + 0.0334128i
\(341\) 1.82090 3.15390i 0.0986074 0.170793i
\(342\) 9.49219 + 3.52300i 0.513279 + 0.190502i
\(343\) −13.9482 + 12.1839i −0.753131 + 0.657871i
\(344\) 1.18934i 0.0641250i
\(345\) −4.49576 3.79668i −0.242044 0.204406i
\(346\) −13.3966 + 7.73453i −0.720206 + 0.415811i
\(347\) −19.9014 + 11.4901i −1.06836 + 0.616818i −0.927733 0.373244i \(-0.878245\pi\)
−0.140627 + 0.990063i \(0.544912\pi\)
\(348\) 0.886023 + 0.748247i 0.0474958 + 0.0401103i
\(349\) 16.2489i 0.869786i 0.900482 + 0.434893i \(0.143214\pi\)
−0.900482 + 0.434893i \(0.856786\pi\)
\(350\) 8.42060 8.05043i 0.450100 0.430314i
\(351\) 2.64064 4.47516i 0.140947 0.238866i
\(352\) 1.91345 3.31419i 0.101987 0.176647i
\(353\) 10.8201 + 18.7410i 0.575897 + 0.997482i 0.995944 + 0.0899798i \(0.0286802\pi\)
−0.420047 + 0.907502i \(0.637986\pi\)
\(354\) 6.45456 2.32619i 0.343056 0.123635i
\(355\) 4.17641 + 2.41125i 0.221661 + 0.127976i
\(356\) 4.01889 0.213001
\(357\) −4.21196 + 0.259934i −0.222921 + 0.0137571i
\(358\) 12.0221 0.635389
\(359\) −30.5776 17.6540i −1.61383 0.931742i −0.988473 0.151400i \(-0.951622\pi\)
−0.625353 0.780342i \(-0.715045\pi\)
\(360\) 2.28491 0.388013i 0.120426 0.0204501i
\(361\) −3.80482 6.59014i −0.200254 0.346850i
\(362\) −8.20445 + 14.2105i −0.431216 + 0.746889i
\(363\) 6.21419 + 1.11600i 0.326161 + 0.0585747i
\(364\) −2.53957 0.742018i −0.133110 0.0388923i
\(365\) 6.81009i 0.356456i
\(366\) −0.462700 + 0.547897i −0.0241857 + 0.0286390i
\(367\) 1.52944 0.883022i 0.0798360 0.0460934i −0.459551 0.888152i \(-0.651989\pi\)
0.539387 + 0.842058i \(0.318656\pi\)
\(368\) 3.80849 2.19883i 0.198531 0.114622i
\(369\) −3.16443 + 2.62136i −0.164734 + 0.136462i
\(370\) 5.21566i 0.271149i
\(371\) 21.4125 + 6.25635i 1.11168 + 0.324814i
\(372\) −0.291350 + 1.62232i −0.0151058 + 0.0841135i
\(373\) −10.0388 + 17.3877i −0.519788 + 0.900299i 0.479948 + 0.877297i \(0.340656\pi\)
−0.999735 + 0.0230017i \(0.992678\pi\)
\(374\) −1.76205 3.05195i −0.0911132 0.157813i
\(375\) 4.26598 + 11.8370i 0.220294 + 0.611258i
\(376\) 8.95534 + 5.17037i 0.461836 + 0.266641i
\(377\) 0.669555 0.0344838
\(378\) −3.98061 + 13.1588i −0.204741 + 0.676817i
\(379\) −4.71985 −0.242443 −0.121221 0.992626i \(-0.538681\pi\)
−0.121221 + 0.992626i \(0.538681\pi\)
\(380\) 2.25799 + 1.30365i 0.115832 + 0.0668758i
\(381\) −12.5135 34.7218i −0.641088 1.77885i
\(382\) 12.7441 + 22.0735i 0.652047 + 1.12938i
\(383\) 12.7793 22.1343i 0.652989 1.13101i −0.329404 0.944189i \(-0.606848\pi\)
0.982394 0.186822i \(-0.0598187\pi\)
\(384\) −0.306158 + 1.70478i −0.0156236 + 0.0869966i
\(385\) 5.65387 5.40533i 0.288148 0.275481i
\(386\) 10.1684i 0.517556i
\(387\) −2.74771 + 2.27616i −0.139674 + 0.115704i
\(388\) 8.15357 4.70747i 0.413935 0.238985i
\(389\) −32.8464 + 18.9639i −1.66538 + 0.961506i −0.695297 + 0.718722i \(0.744727\pi\)
−0.970080 + 0.242784i \(0.921939\pi\)
\(390\) 0.863338 1.02231i 0.0437168 0.0517665i
\(391\) 4.04970i 0.204802i
\(392\) 6.99293 + 0.314476i 0.353196 + 0.0158834i
\(393\) 28.7624 + 5.16540i 1.45087 + 0.260560i
\(394\) −0.736384 + 1.27546i −0.0370985 + 0.0642565i
\(395\) −5.00515 8.66917i −0.251836 0.436193i
\(396\) −11.3187 + 1.92208i −0.568784 + 0.0965881i
\(397\) 18.8568 + 10.8870i 0.946398 + 0.546403i 0.891960 0.452114i \(-0.149330\pi\)
0.0544380 + 0.998517i \(0.482663\pi\)
\(398\) −19.0591 −0.955347
\(399\) −12.8922 + 8.54334i −0.645418 + 0.427702i
\(400\) −4.40318 −0.220159
\(401\) 7.72906 + 4.46237i 0.385971 + 0.222840i 0.680413 0.732829i \(-0.261800\pi\)
−0.294442 + 0.955669i \(0.595134\pi\)
\(402\) −15.3289 + 5.52444i −0.764535 + 0.275534i
\(403\) 0.475817 + 0.824139i 0.0237021 + 0.0410533i
\(404\) −3.54281 + 6.13632i −0.176261 + 0.305293i
\(405\) −5.26927 4.53621i −0.261832 0.225406i
\(406\) −1.72098 + 0.419930i −0.0854110 + 0.0208408i
\(407\) 25.8366i 1.28067i
\(408\) 1.21859 + 1.02910i 0.0603294 + 0.0509482i
\(409\) 29.4999 17.0317i 1.45867 0.842166i 0.459727 0.888060i \(-0.347947\pi\)
0.998946 + 0.0458943i \(0.0146138\pi\)
\(410\) −0.916397 + 0.529082i −0.0452576 + 0.0261295i
\(411\) −18.7922 15.8701i −0.926952 0.782812i
\(412\) 5.27685i 0.259972i
\(413\) −2.93925 + 10.0596i −0.144631 + 0.495003i
\(414\) −12.3686 4.59057i −0.607883 0.225614i
\(415\) −0.858372 + 1.48674i −0.0421358 + 0.0729814i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 14.4561 5.20990i 0.707918 0.255130i
\(418\) −11.1853 6.45782i −0.547089 0.315862i
\(419\) −4.85711 −0.237285 −0.118643 0.992937i \(-0.537854\pi\)
−0.118643 + 0.992937i \(0.537854\pi\)
\(420\) −1.57791 + 3.16914i −0.0769939 + 0.154638i
\(421\) −3.83457 −0.186886 −0.0934428 0.995625i \(-0.529787\pi\)
−0.0934428 + 0.995625i \(0.529787\pi\)
\(422\) −20.5641 11.8727i −1.00104 0.577953i
\(423\) −5.19368 30.5844i −0.252526 1.48706i
\(424\) −4.21577 7.30193i −0.204736 0.354613i
\(425\) −2.02739 + 3.51153i −0.0983426 + 0.170334i
\(426\) 10.6419 + 1.91116i 0.515601 + 0.0925960i
\(427\) −0.259676 1.06422i −0.0125666 0.0515011i
\(428\) 18.5997i 0.899049i
\(429\) −4.27667 + 5.06414i −0.206480 + 0.244499i
\(430\) −0.795719 + 0.459408i −0.0383730 + 0.0221546i
\(431\) −24.5591 + 14.1792i −1.18297 + 0.682987i −0.956699 0.291078i \(-0.905986\pi\)
−0.226269 + 0.974065i \(0.572653\pi\)
\(432\) 4.52444 2.55528i 0.217682 0.122941i
\(433\) 4.33579i 0.208365i 0.994558 + 0.104182i \(0.0332226\pi\)
−0.994558 + 0.104182i \(0.966777\pi\)
\(434\) −1.73989 1.81989i −0.0835175 0.0873577i
\(435\) 0.158363 0.881812i 0.00759293 0.0422796i
\(436\) 5.36127 9.28600i 0.256758 0.444719i
\(437\) −7.42098 12.8535i −0.354994 0.614867i
\(438\) −5.17669 14.3640i −0.247352 0.686337i
\(439\) −26.4597 15.2765i −1.26285 0.729109i −0.289228 0.957260i \(-0.593399\pi\)
−0.973626 + 0.228151i \(0.926732\pi\)
\(440\) −2.95644 −0.140943
\(441\) −12.6565 16.7575i −0.602691 0.797975i
\(442\) 0.920873 0.0438015
\(443\) 10.3560 + 5.97906i 0.492030 + 0.284074i 0.725416 0.688310i \(-0.241647\pi\)
−0.233386 + 0.972384i \(0.574981\pi\)
\(444\) −3.96469 11.0010i −0.188156 0.522083i
\(445\) −1.55238 2.68880i −0.0735898 0.127461i
\(446\) 2.61577 4.53064i 0.123860 0.214532i
\(447\) 0.720340 4.01106i 0.0340709 0.189717i
\(448\) −1.82832 1.91239i −0.0863801 0.0903520i
\(449\) 19.0480i 0.898929i −0.893298 0.449465i \(-0.851615\pi\)
0.893298 0.449465i \(-0.148385\pi\)
\(450\) 8.42678 + 10.1726i 0.397242 + 0.479540i
\(451\) 4.53951 2.62089i 0.213757 0.123413i
\(452\) 12.5601 7.25156i 0.590776 0.341085i
\(453\) −11.0019 + 13.0277i −0.516916 + 0.612097i
\(454\) 28.1437i 1.32085i
\(455\) 0.484521 + 1.98570i 0.0227147 + 0.0930908i
\(456\) 5.75356 + 1.03327i 0.269435 + 0.0483874i
\(457\) −5.32789 + 9.22817i −0.249228 + 0.431676i −0.963312 0.268385i \(-0.913510\pi\)
0.714084 + 0.700060i \(0.246844\pi\)
\(458\) −4.77199 8.26533i −0.222981 0.386214i
\(459\) 0.0453793 4.78478i 0.00211813 0.223335i
\(460\) −2.94222 1.69869i −0.137182 0.0792019i
\(461\) 28.5410 1.32929 0.664643 0.747161i \(-0.268584\pi\)
0.664643 + 0.747161i \(0.268584\pi\)
\(462\) 7.81639 15.6988i 0.363651 0.730375i
\(463\) −36.2254 −1.68354 −0.841769 0.539838i \(-0.818486\pi\)
−0.841769 + 0.539838i \(0.818486\pi\)
\(464\) 0.579851 + 0.334777i 0.0269189 + 0.0155416i
\(465\) 1.19794 0.431731i 0.0555532 0.0200210i
\(466\) −1.19486 2.06956i −0.0553508 0.0958704i
\(467\) −1.19484 + 2.06953i −0.0552908 + 0.0957665i −0.892346 0.451352i \(-0.850942\pi\)
0.837055 + 0.547118i \(0.184275\pi\)
\(468\) 1.04386 2.81253i 0.0482526 0.130009i
\(469\) 6.98041 23.8906i 0.322325 1.10316i
\(470\) 7.98865i 0.368489i
\(471\) −6.62205 5.59232i −0.305128 0.257681i
\(472\) 3.43047 1.98058i 0.157900 0.0911637i
\(473\) 3.94171 2.27575i 0.181240 0.104639i
\(474\) −17.1468 14.4805i −0.787580 0.665112i
\(475\) 14.8606i 0.681849i
\(476\) −2.36696 + 0.577552i −0.108489 + 0.0264720i
\(477\) −8.80138 + 23.7140i −0.402987 + 1.08579i
\(478\) 0.915531 1.58575i 0.0418754 0.0725303i
\(479\) 17.6332 + 30.5416i 0.805681 + 1.39548i 0.915830 + 0.401566i \(0.131534\pi\)
−0.110149 + 0.993915i \(0.535133\pi\)
\(480\) 1.25883 0.453674i 0.0574573 0.0207073i
\(481\) −5.84680 3.37565i −0.266591 0.153916i
\(482\) −27.3594 −1.24619
\(483\) 16.7989 11.1322i 0.764377 0.506533i
\(484\) 3.64516 0.165689
\(485\) −6.29898 3.63672i −0.286022 0.165135i
\(486\) −14.5623 5.56243i −0.660557 0.252317i
\(487\) −10.1938 17.6562i −0.461927 0.800080i 0.537130 0.843499i \(-0.319508\pi\)
−0.999057 + 0.0434188i \(0.986175\pi\)
\(488\) −0.207019 + 0.358567i −0.00937131 + 0.0162316i
\(489\) 41.9097 + 7.52650i 1.89522 + 0.340360i
\(490\) −2.49077 4.80003i −0.112521 0.216843i
\(491\) 22.5720i 1.01866i 0.860571 + 0.509330i \(0.170107\pi\)
−0.860571 + 0.509330i \(0.829893\pi\)
\(492\) −1.53070 + 1.81255i −0.0690093 + 0.0817160i
\(493\) 0.533970 0.308288i 0.0240488 0.0138846i
\(494\) 2.92280 1.68748i 0.131503 0.0759233i
\(495\) 5.65802 + 6.83020i 0.254309 + 0.306995i
\(496\) 0.951633i 0.0427296i
\(497\) −11.9379 + 11.4131i −0.535487 + 0.511947i
\(498\) −0.680345 + 3.78836i −0.0304870 + 0.169760i
\(499\) −2.26315 + 3.91989i −0.101312 + 0.175478i −0.912226 0.409688i \(-0.865638\pi\)
0.810913 + 0.585167i \(0.198971\pi\)
\(500\) 3.63217 + 6.29111i 0.162436 + 0.281347i
\(501\) −3.92000 10.8770i −0.175133 0.485948i
\(502\) −1.48893 0.859635i −0.0664543 0.0383674i
\(503\) −27.1387 −1.21005 −0.605027 0.796205i \(-0.706838\pi\)
−0.605027 + 0.796205i \(0.706838\pi\)
\(504\) −0.919124 + 7.88386i −0.0409410 + 0.351175i
\(505\) 5.47393 0.243587
\(506\) 14.5747 + 8.41472i 0.647925 + 0.374080i
\(507\) −0.587248 1.62946i −0.0260806 0.0723669i
\(508\) −10.6544 18.4539i −0.472712 0.818761i
\(509\) 2.22767 3.85843i 0.0987396 0.171022i −0.812424 0.583068i \(-0.801852\pi\)
0.911163 + 0.412046i \(0.135186\pi\)
\(510\) 0.217805 1.21280i 0.00964457 0.0537038i
\(511\) 22.3867 + 6.54101i 0.990330 + 0.289357i
\(512\) 1.00000i 0.0441942i
\(513\) −8.62398 15.2698i −0.380758 0.674178i
\(514\) −8.68237 + 5.01277i −0.382963 + 0.221104i
\(515\) 3.53043 2.03829i 0.155569 0.0898179i
\(516\) −1.32913 + 1.57386i −0.0585115 + 0.0692853i
\(517\) 39.5730i 1.74042i
\(518\) 17.1454 + 5.00959i 0.753325 + 0.220109i
\(519\) 26.3713 + 4.73598i 1.15757 + 0.207887i
\(520\) 0.386271 0.669041i 0.0169391 0.0293394i
\(521\) 15.3496 + 26.5864i 0.672480 + 1.16477i 0.977199 + 0.212327i \(0.0681043\pi\)
−0.304719 + 0.952442i \(0.598562\pi\)
\(522\) −0.336287 1.98031i −0.0147189 0.0866760i
\(523\) −36.4278 21.0316i −1.59288 0.919648i −0.992810 0.119699i \(-0.961807\pi\)
−0.600068 0.799949i \(-0.704860\pi\)
\(524\) 16.8717 0.737042
\(525\) −20.1396 + 1.24288i −0.878964 + 0.0542437i
\(526\) 0.760829 0.0331737
\(527\) 0.758927 + 0.438167i 0.0330594 + 0.0190869i
\(528\) −6.23578 + 2.24734i −0.271378 + 0.0978029i
\(529\) −1.83026 3.17010i −0.0795764 0.137830i
\(530\) −3.25686 + 5.64104i −0.141469 + 0.245031i
\(531\) −11.1409 4.13491i −0.483474 0.179440i
\(532\) −6.45424 + 6.17052i −0.279827 + 0.267526i
\(533\) 1.36972i 0.0593290i
\(534\) −5.31820 4.49123i −0.230141 0.194354i
\(535\) −12.4439 + 7.18451i −0.537998 + 0.310614i
\(536\) −8.14699 + 4.70367i −0.351896 + 0.203168i
\(537\) −15.9089 13.4351i −0.686520 0.579767i
\(538\) 5.59454i 0.241198i
\(539\) 12.3384 + 23.7777i 0.531452 + 1.02418i
\(540\) −3.45725 2.04000i −0.148776 0.0877877i
\(541\) 6.24183 10.8112i 0.268357 0.464808i −0.700081 0.714064i \(-0.746853\pi\)
0.968438 + 0.249256i \(0.0801859\pi\)
\(542\) 12.5717 + 21.7749i 0.540003 + 0.935312i
\(543\) 26.7376 9.63609i 1.14742 0.413524i
\(544\) 0.797500 + 0.460437i 0.0341925 + 0.0197411i
\(545\) −8.28361 −0.354831
\(546\) 2.53139 + 3.81996i 0.108333 + 0.163479i
\(547\) 27.7028 1.18449 0.592243 0.805759i \(-0.298242\pi\)
0.592243 + 0.805759i \(0.298242\pi\)
\(548\) −12.2984 7.10051i −0.525363 0.303319i
\(549\) 1.22458 0.207953i 0.0522639 0.00887520i
\(550\) −8.42526 14.5930i −0.359254 0.622247i
\(551\) 1.12986 1.95698i 0.0481337 0.0833700i
\(552\) −7.49705 1.34638i −0.319095 0.0573058i
\(553\) 33.3055 8.12673i 1.41629 0.345584i
\(554\) 25.8904i 1.09998i
\(555\) −5.82866 + 6.90190i −0.247413 + 0.292969i
\(556\) 7.68313 4.43586i 0.325837 0.188122i
\(557\) −10.8733 + 6.27773i −0.460718 + 0.265996i −0.712346 0.701828i \(-0.752367\pi\)
0.251628 + 0.967824i \(0.419034\pi\)
\(558\) 2.19854 1.82123i 0.0930716 0.0770988i
\(559\) 1.18934i 0.0503038i
\(560\) −0.573240 + 1.96192i −0.0242238 + 0.0829064i
\(561\) −1.07893 + 6.00779i −0.0455524 + 0.253649i
\(562\) 1.01595 1.75967i 0.0428551 0.0742272i
\(563\) 16.3961 + 28.3989i 0.691015 + 1.19687i 0.971506 + 0.237016i \(0.0761694\pi\)
−0.280491 + 0.959857i \(0.590497\pi\)
\(564\) −6.07258 16.8498i −0.255702 0.709505i
\(565\) −9.70318 5.60213i −0.408216 0.235683i
\(566\) 27.2852 1.14688
\(567\) 19.9729 12.9646i 0.838784 0.544464i
\(568\) 6.24239 0.261925
\(569\) −8.48347 4.89793i −0.355646 0.205332i 0.311523 0.950238i \(-0.399161\pi\)
−0.667169 + 0.744906i \(0.732494\pi\)
\(570\) −1.53113 4.24849i −0.0641320 0.177950i
\(571\) 5.46052 + 9.45789i 0.228516 + 0.395801i 0.957368 0.288870i \(-0.0932795\pi\)
−0.728853 + 0.684670i \(0.759946\pi\)
\(572\) −1.91345 + 3.31419i −0.0800054 + 0.138573i
\(573\) 7.80344 43.4518i 0.325994 1.81523i
\(574\) −0.859057 3.52064i −0.0358563 0.146949i
\(575\) 19.3637i 0.807523i
\(576\) 2.31028 1.91379i 0.0962616 0.0797414i
\(577\) −28.7040 + 16.5723i −1.19496 + 0.689912i −0.959428 0.281954i \(-0.909017\pi\)
−0.235534 + 0.971866i \(0.575684\pi\)
\(578\) −13.9880 + 8.07600i −0.581826 + 0.335917i
\(579\) −11.3635 + 13.4558i −0.472249 + 0.559205i
\(580\) 0.517259i 0.0214780i
\(581\) −4.06290 4.24972i −0.168558 0.176308i
\(582\) −16.0504 2.88246i −0.665309 0.119482i
\(583\) 16.1333 27.9437i 0.668174 1.15731i
\(584\) −4.40758 7.63416i −0.182387 0.315904i
\(585\) −2.28491 + 0.388013i −0.0944696 + 0.0160424i
\(586\) 11.3080 + 6.52868i 0.467130 + 0.269697i
\(587\) 36.3462 1.50017 0.750084 0.661342i \(-0.230013\pi\)
0.750084 + 0.661342i \(0.230013\pi\)
\(588\) −8.90232 8.23096i −0.367126 0.339439i
\(589\) 3.21173 0.132337
\(590\) −2.65018 1.53008i −0.109106 0.0629925i
\(591\) 2.39982 0.864880i 0.0987153 0.0355764i
\(592\) −3.37565 5.84680i −0.138738 0.240302i
\(593\) 11.5189 19.9513i 0.473023 0.819300i −0.526500 0.850175i \(-0.676496\pi\)
0.999523 + 0.0308749i \(0.00982935\pi\)
\(594\) 17.1260 + 10.1054i 0.702688 + 0.414632i
\(595\) 1.30069 + 1.36050i 0.0533232 + 0.0557751i
\(596\) 2.35283i 0.0963758i
\(597\) 25.2209 + 21.2991i 1.03222 + 0.871715i
\(598\) −3.80849 + 2.19883i −0.155741 + 0.0899170i
\(599\) 14.6236 8.44293i 0.597503 0.344969i −0.170556 0.985348i \(-0.554556\pi\)
0.768059 + 0.640379i \(0.221223\pi\)
\(600\) 5.82673 + 4.92068i 0.237875 + 0.200886i
\(601\) 10.3410i 0.421817i −0.977506 0.210908i \(-0.932358\pi\)
0.977506 0.210908i \(-0.0676421\pi\)
\(602\) −0.745929 3.05701i −0.0304018 0.124595i
\(603\) 26.4585 + 9.81997i 1.07747 + 0.399900i
\(604\) −4.92244 + 8.52591i −0.200291 + 0.346914i
\(605\) −1.40802 2.43876i −0.0572442 0.0991499i
\(606\) 11.5457 4.16101i 0.469013 0.169030i
\(607\) 2.02862 + 1.17123i 0.0823393 + 0.0475386i 0.540604 0.841277i \(-0.318196\pi\)
−0.458265 + 0.888816i \(0.651529\pi\)
\(608\) 3.37496 0.136873
\(609\) 2.74666 + 1.36756i 0.111300 + 0.0554162i
\(610\) 0.319862 0.0129508
\(611\) −8.95534 5.17037i −0.362294 0.209171i
\(612\) −0.462513 2.72363i −0.0186960 0.110096i
\(613\) −5.05945 8.76322i −0.204349 0.353943i 0.745576 0.666421i \(-0.232174\pi\)
−0.949925 + 0.312478i \(0.898841\pi\)
\(614\) 8.58829 14.8754i 0.346595 0.600320i
\(615\) 1.80393 + 0.323966i 0.0727416 + 0.0130636i
\(616\) 2.83963 9.71868i 0.114412 0.391577i
\(617\) 34.5810i 1.39218i −0.717956 0.696089i \(-0.754922\pi\)
0.717956 0.696089i \(-0.245078\pi\)
\(618\) 5.89704 6.98286i 0.237214 0.280892i
\(619\) 26.2353 15.1469i 1.05449 0.608807i 0.130583 0.991437i \(-0.458315\pi\)
0.923902 + 0.382630i \(0.124982\pi\)
\(620\) 0.636682 0.367588i 0.0255697 0.0147627i
\(621\) 11.2373 + 19.8970i 0.450937 + 0.798438i
\(622\) 31.1415i 1.24866i
\(623\) 10.3299 2.52056i 0.413859 0.100984i
\(624\) 0.306158 1.70478i 0.0122561 0.0682457i
\(625\) −8.20194 + 14.2062i −0.328078 + 0.568247i
\(626\) −3.80923 6.59778i −0.152248 0.263700i
\(627\) 7.58468 + 21.0455i 0.302903 + 0.840477i
\(628\) −4.33375 2.50209i −0.172935 0.0998444i
\(629\) −6.21709 −0.247892
\(630\) 5.62965 2.43037i 0.224291 0.0968284i
\(631\) −27.2816 −1.08606 −0.543032 0.839712i \(-0.682724\pi\)
−0.543032 + 0.839712i \(0.682724\pi\)
\(632\) −11.2216 6.47880i −0.446372 0.257713i
\(633\) 13.9444 + 38.6921i 0.554241 + 1.53787i
\(634\) −10.7540 18.6264i −0.427095 0.739750i
\(635\) −8.23096 + 14.2564i −0.326636 + 0.565749i
\(636\) −2.58139 + 14.3739i −0.102359 + 0.569962i
\(637\) −6.99293 0.314476i −0.277070 0.0124600i
\(638\) 2.56232i 0.101443i
\(639\) −11.9466 14.4217i −0.472602 0.570512i
\(640\) 0.669041 0.386271i 0.0264462 0.0152687i
\(641\) 21.0288 12.1410i 0.830588 0.479540i −0.0234659 0.999725i \(-0.507470\pi\)
0.854054 + 0.520184i \(0.174137\pi\)
\(642\) −20.7857 + 24.6130i −0.820346 + 0.971397i
\(643\) 7.83521i 0.308991i −0.987994 0.154495i \(-0.950625\pi\)
0.987994 0.154495i \(-0.0493752\pi\)
\(644\) 8.41006 8.04035i 0.331403 0.316834i
\(645\) 1.56638 + 0.281303i 0.0616761 + 0.0110763i
\(646\) 1.55396 2.69153i 0.0611396 0.105897i
\(647\) −19.0438 32.9849i −0.748691 1.29677i −0.948450 0.316926i \(-0.897349\pi\)
0.199760 0.979845i \(-0.435984\pi\)
\(648\) −8.84280 1.67478i −0.347378 0.0657917i
\(649\) 13.1281 + 7.57949i 0.515321 + 0.297521i
\(650\) 4.40318 0.172707
\(651\) 0.268616 + 4.35265i 0.0105279 + 0.170594i
\(652\) 24.5837 0.962772
\(653\) −26.2455 15.1528i −1.02707 0.592976i −0.110923 0.993829i \(-0.535381\pi\)
−0.916143 + 0.400853i \(0.868714\pi\)
\(654\) −17.4720 + 6.29679i −0.683208 + 0.246224i
\(655\) −6.51703 11.2878i −0.254641 0.441052i
\(656\) −0.684859 + 1.18621i −0.0267392 + 0.0463137i
\(657\) −9.20183 + 24.7930i −0.358998 + 0.967265i
\(658\) 26.2610 + 7.67301i 1.02376 + 0.299125i
\(659\) 7.53008i 0.293330i 0.989186 + 0.146665i \(0.0468539\pi\)
−0.989186 + 0.146665i \(0.953146\pi\)
\(660\) 3.91226 + 3.30391i 0.152285 + 0.128605i
\(661\) −17.5516 + 10.1334i −0.682679 + 0.394145i −0.800864 0.598847i \(-0.795626\pi\)
0.118185 + 0.992992i \(0.462293\pi\)
\(662\) −1.36228 + 0.786513i −0.0529465 + 0.0305687i
\(663\) −1.21859 1.02910i −0.0473262 0.0399671i
\(664\) 2.22220i 0.0862382i
\(665\) 6.62141 + 1.93466i 0.256767 + 0.0750230i
\(666\) −7.04744 + 18.9883i −0.273083 + 0.735780i
\(667\) −1.47224 + 2.54999i −0.0570053 + 0.0987362i
\(668\) −3.33760 5.78090i −0.129136 0.223670i
\(669\) −8.52458 + 3.07221i −0.329579 + 0.118778i
\(670\) 6.29389 + 3.63378i 0.243154 + 0.140385i
\(671\) −1.58448 −0.0611683
\(672\) 0.282269 + 4.57387i 0.0108887 + 0.176441i
\(673\) −20.5105 −0.790622 −0.395311 0.918547i \(-0.629363\pi\)
−0.395311 + 0.918547i \(0.629363\pi\)
\(674\) 8.40082 + 4.85022i 0.323588 + 0.186823i
\(675\) 0.216982 22.8786i 0.00835166 0.880596i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) −24.9728 + 43.2541i −0.959782 + 1.66239i −0.236756 + 0.971569i \(0.576084\pi\)
−0.723026 + 0.690821i \(0.757249\pi\)
\(678\) −24.7246 4.44025i −0.949542 0.170527i
\(679\) 18.0050 17.2135i 0.690970 0.660595i
\(680\) 0.711413i 0.0272815i
\(681\) −31.4514 + 37.2426i −1.20522 + 1.42714i
\(682\) −3.15390 + 1.82090i −0.120769 + 0.0697260i
\(683\) 18.3255 10.5802i 0.701206 0.404842i −0.106590 0.994303i \(-0.533993\pi\)
0.807797 + 0.589461i \(0.200660\pi\)
\(684\) −6.45898 7.79710i −0.246965 0.298130i
\(685\) 10.9709i 0.419176i
\(686\) 18.1714 3.57750i 0.693789 0.136590i
\(687\) −2.92197 + 16.2704i −0.111480 + 0.620753i
\(688\) −0.594671 + 1.03000i −0.0226716 + 0.0392684i
\(689\) 4.21577 + 7.30193i 0.160608 + 0.278181i
\(690\) 1.99511 + 5.53590i 0.0759524 + 0.210748i
\(691\) −36.8904 21.2987i −1.40338 0.810239i −0.408638 0.912697i \(-0.633996\pi\)
−0.994737 + 0.102457i \(0.967329\pi\)
\(692\) 15.4691 0.588046
\(693\) −27.8873 + 12.0392i −1.05935 + 0.457332i
\(694\) 22.9801 0.872313
\(695\) −5.93554 3.42688i −0.225148 0.129989i
\(696\) −0.393195 1.09101i −0.0149040 0.0413547i
\(697\) 0.630668 + 1.09235i 0.0238883 + 0.0413757i
\(698\) 8.12447 14.0720i 0.307516 0.532633i
\(699\) −0.731632 + 4.07394i −0.0276729 + 0.154091i
\(700\) −11.3177 + 2.76158i −0.427768 + 0.104378i
\(701\) 20.9627i 0.791752i −0.918304 0.395876i \(-0.870441\pi\)
0.918304 0.395876i \(-0.129559\pi\)
\(702\) −4.52444 + 2.55528i −0.170764 + 0.0964429i
\(703\) −19.7327 + 11.3927i −0.744233 + 0.429683i
\(704\) −3.31419 + 1.91345i −0.124908 + 0.0721159i
\(705\) −8.92755 + 10.5714i −0.336231 + 0.398142i
\(706\) 21.6402i 0.814441i
\(707\) −5.25765 + 17.9944i −0.197734 + 0.676749i
\(708\) −6.75290 1.21274i −0.253790 0.0455777i
\(709\) −1.65400 + 2.86481i −0.0621171 + 0.107590i −0.895412 0.445239i \(-0.853119\pi\)
0.833294 + 0.552829i \(0.186452\pi\)
\(710\) −2.41125 4.17641i −0.0904927 0.156738i
\(711\) 6.50802 + 38.3242i 0.244070 + 1.43727i
\(712\) −3.48046 2.00944i −0.130436 0.0753071i
\(713\) −4.18497 −0.156728
\(714\) 3.77763 + 1.88087i 0.141374 + 0.0703898i
\(715\) 2.95644 0.110565
\(716\) −10.4115 6.01106i −0.389095 0.224644i
\(717\) −2.98364 + 1.07529i −0.111426 + 0.0401573i
\(718\) 17.6540 + 30.5776i 0.658841 + 1.14115i
\(719\) −5.95241 + 10.3099i −0.221987 + 0.384493i −0.955411 0.295278i \(-0.904588\pi\)
0.733424 + 0.679771i \(0.237921\pi\)
\(720\) −2.17280 0.806428i −0.0809755 0.0300538i
\(721\) 3.30952 + 13.5633i 0.123253 + 0.505124i
\(722\) 7.60964i 0.283201i
\(723\) 36.2047 + 30.5749i 1.34647 + 1.13709i
\(724\) 14.2105 8.20445i 0.528130 0.304916i
\(725\) 2.55319 1.47408i 0.0948231 0.0547461i
\(726\) −4.82365 4.07358i −0.179023 0.151185i
\(727\) 13.6161i 0.504993i 0.967598 + 0.252496i \(0.0812516\pi\)
−0.967598 + 0.252496i \(0.918748\pi\)
\(728\) 1.82832 + 1.91239i 0.0677621 + 0.0708779i
\(729\) 13.0541 + 23.6345i 0.483485 + 0.875353i
\(730\) −3.40504 + 5.89771i −0.126026 + 0.218284i
\(731\) 0.547617 + 0.948500i 0.0202543 + 0.0350815i
\(732\) 0.674658 0.243143i 0.0249361 0.00898682i
\(733\) 25.9923 + 15.0067i 0.960049 + 0.554285i 0.896188 0.443674i \(-0.146325\pi\)
0.0638609 + 0.997959i \(0.479659\pi\)
\(734\) −1.76604 −0.0651859
\(735\) −2.06814 + 9.13540i −0.0762844 + 0.336964i
\(736\) −4.39767 −0.162100
\(737\) −31.1777 18.0005i −1.14845 0.663056i
\(738\) 4.05115 0.687947i 0.149125 0.0253237i
\(739\) 7.04885 + 12.2090i 0.259296 + 0.449114i 0.966054 0.258342i \(-0.0831760\pi\)
−0.706757 + 0.707456i \(0.749843\pi\)
\(740\) −2.60783 + 4.51690i −0.0958658 + 0.166044i
\(741\) −5.75356 1.03327i −0.211362 0.0379582i
\(742\) −15.4156 16.1244i −0.565923 0.591945i
\(743\) 29.9617i 1.09919i −0.835431 0.549595i \(-0.814782\pi\)
0.835431 0.549595i \(-0.185218\pi\)
\(744\) 1.06348 1.25930i 0.0389890 0.0461681i
\(745\) −1.57414 + 0.908831i −0.0576721 + 0.0332970i
\(746\) 17.3877 10.0388i 0.636607 0.367545i
\(747\) 5.13391 4.25284i 0.187840 0.155603i
\(748\) 3.52409i 0.128854i
\(749\) −11.6653 47.8075i −0.426241 1.74685i
\(750\) 2.22404 12.3841i 0.0812105 0.452203i
\(751\) 9.00356 15.5946i 0.328545 0.569056i −0.653679 0.756772i \(-0.726775\pi\)
0.982223 + 0.187716i \(0.0601085\pi\)
\(752\) −5.17037 8.95534i −0.188544 0.326568i
\(753\) 1.00964 + 2.80148i 0.0367932 + 0.102092i
\(754\) −0.579851 0.334777i −0.0211169 0.0121919i
\(755\) 7.60558 0.276795
\(756\) 10.0267 9.40557i 0.364668 0.342077i
\(757\) 3.82722 0.139103 0.0695513 0.997578i \(-0.477843\pi\)
0.0695513 + 0.997578i \(0.477843\pi\)
\(758\) 4.08751 + 2.35993i 0.148465 + 0.0857164i
\(759\) −9.88305 27.4229i −0.358732 0.995388i
\(760\) −1.30365 2.25799i −0.0472883 0.0819058i
\(761\) −22.7050 + 39.3261i −0.823054 + 1.42557i 0.0803432 + 0.996767i \(0.474398\pi\)
−0.903397 + 0.428804i \(0.858935\pi\)
\(762\) −6.52385 + 36.3267i −0.236334 + 1.31598i
\(763\) 7.95632 27.2306i 0.288038 0.985815i
\(764\) 25.4883i 0.922133i
\(765\) −1.64356 + 1.36150i −0.0594232 + 0.0492251i
\(766\) −22.1343 + 12.7793i −0.799745 + 0.461733i
\(767\) −3.43047 + 1.98058i −0.123867 + 0.0715147i
\(768\) 1.11753 1.32330i 0.0403254 0.0477505i
\(769\) 35.9405i 1.29605i 0.761621 + 0.648023i \(0.224404\pi\)
−0.761621 + 0.648023i \(0.775596\pi\)
\(770\) −7.59906 + 1.85421i −0.273851 + 0.0668213i
\(771\) 17.0913 + 3.06940i 0.615529 + 0.110542i
\(772\) −5.08419 + 8.80607i −0.182984 + 0.316937i
\(773\) 21.2282 + 36.7683i 0.763525 + 1.32246i 0.941023 + 0.338343i \(0.109866\pi\)
−0.177498 + 0.984121i \(0.556800\pi\)
\(774\) 3.51767 0.597353i 0.126440 0.0214714i
\(775\) 3.62883 + 2.09511i 0.130351 + 0.0752584i
\(776\) −9.41494 −0.337977
\(777\) −17.0902 25.7897i −0.613106 0.925200i
\(778\) 37.9277 1.35978
\(779\) 4.00341 + 2.31137i 0.143437 + 0.0828135i
\(780\) −1.25883 + 0.453674i −0.0450732 + 0.0162441i
\(781\) 11.9445 + 20.6885i 0.427408 + 0.740292i
\(782\) −2.02485 + 3.50714i −0.0724084 + 0.125415i
\(783\) −1.76805 + 2.99636i −0.0631850 + 0.107081i
\(784\) −5.89882 3.76881i −0.210672 0.134600i
\(785\) 3.86594i 0.137981i
\(786\) −22.3263 18.8546i −0.796352 0.672521i
\(787\) −37.9202 + 21.8933i −1.35171 + 0.780411i −0.988489 0.151292i \(-0.951657\pi\)
−0.363222 + 0.931703i \(0.618323\pi\)
\(788\) 1.27546 0.736384i 0.0454362 0.0262326i
\(789\) −1.00681 0.850248i −0.0358432 0.0302696i
\(790\) 10.0103i 0.356150i
\(791\) 27.7356 26.5164i 0.986165 0.942813i
\(792\) 10.7633 + 3.99476i 0.382457 + 0.141948i
\(793\) 0.207019 0.358567i 0.00735146 0.0127331i
\(794\) −10.8870 18.8568i −0.386365 0.669205i
\(795\) 10.6138 3.82517i 0.376434 0.135665i
\(796\) 16.5057 + 9.52955i 0.585028 + 0.337766i
\(797\) −8.03088 −0.284469 −0.142234 0.989833i \(-0.545429\pi\)
−0.142234 + 0.989833i \(0.545429\pi\)
\(798\) 15.4366 0.952645i 0.546451 0.0337233i
\(799\) −9.52251 −0.336882
\(800\) 3.81326 + 2.20159i 0.134819 + 0.0778379i
\(801\) 2.01851 + 11.8865i 0.0713204 + 0.419989i
\(802\) −4.46237 7.72906i −0.157572 0.272923i
\(803\) 16.8674 29.2152i 0.595237 1.03098i
\(804\) 16.0374 + 2.88013i 0.565596 + 0.101574i
\(805\) −8.62789 2.52092i −0.304093 0.0888507i
\(806\) 0.951633i 0.0335199i
\(807\) −6.25206 + 7.40326i −0.220083 + 0.260607i
\(808\) 6.13632 3.54281i 0.215875 0.124636i
\(809\) −1.79744 + 1.03775i −0.0631947 + 0.0364855i −0.531264 0.847206i \(-0.678283\pi\)
0.468070 + 0.883692i \(0.344950\pi\)
\(810\) 2.29522 + 6.56311i 0.0806458 + 0.230604i
\(811\) 19.8306i 0.696346i −0.937430 0.348173i \(-0.886802\pi\)
0.937430 0.348173i \(-0.113198\pi\)
\(812\) 1.70038 + 0.496822i 0.0596716 + 0.0174350i
\(813\) 7.69788 42.8640i 0.269977 1.50331i
\(814\) 12.9183 22.3751i 0.452785 0.784247i
\(815\) −9.49597 16.4475i −0.332629 0.576131i
\(816\) −0.540781 1.50053i −0.0189311 0.0525289i
\(817\) 3.47621 + 2.00699i 0.121617 + 0.0702157i
\(818\) −34.0635 −1.19100
\(819\) 0.919124 7.88386i 0.0321168 0.275484i
\(820\) 1.05816 0.0369527
\(821\) 39.1424 + 22.5989i 1.36608 + 0.788706i 0.990425 0.138053i \(-0.0440845\pi\)
0.375655 + 0.926760i \(0.377418\pi\)
\(822\) 8.33952 + 23.1400i 0.290874 + 0.807100i
\(823\) −11.9409 20.6822i −0.416233 0.720937i 0.579324 0.815097i \(-0.303317\pi\)
−0.995557 + 0.0941605i \(0.969983\pi\)
\(824\) 2.63842 4.56989i 0.0919139 0.159200i
\(825\) −5.15893 + 28.7264i −0.179611 + 1.00012i
\(826\) 7.57529 7.24228i 0.263578 0.251991i
\(827\) 0.667718i 0.0232188i −0.999933 0.0116094i \(-0.996305\pi\)
0.999933 0.0116094i \(-0.00369548\pi\)
\(828\) 8.41623 + 10.1598i 0.292484 + 0.353079i
\(829\) 38.2467 22.0818i 1.32836 0.766931i 0.343317 0.939220i \(-0.388450\pi\)
0.985047 + 0.172289i \(0.0551162\pi\)
\(830\) 1.48674 0.858372i 0.0516056 0.0297945i
\(831\) −28.9333 + 34.2608i −1.00368 + 1.18849i
\(832\) 1.00000i 0.0346688i
\(833\) −5.72166 + 2.96901i −0.198244 + 0.102870i
\(834\) −15.1243 2.71615i −0.523712 0.0940525i
\(835\) −2.57844 + 4.46599i −0.0892306 + 0.154552i
\(836\) 6.45782 + 11.1853i 0.223348 + 0.386851i
\(837\) −4.94461 0.0468952i −0.170911 0.00162093i
\(838\) 4.20638 + 2.42855i 0.145307 + 0.0838930i
\(839\) −4.38156 −0.151268 −0.0756342 0.997136i \(-0.524098\pi\)
−0.0756342 + 0.997136i \(0.524098\pi\)
\(840\) 2.95108 1.95560i 0.101822 0.0674747i
\(841\) 28.5517 0.984541
\(842\) 3.32084 + 1.91729i 0.114444 + 0.0660740i
\(843\) −3.31089 + 1.19322i −0.114033 + 0.0410968i
\(844\) 11.8727 + 20.5641i 0.408675 + 0.707845i
\(845\) −0.386271 + 0.669041i −0.0132881 + 0.0230157i
\(846\) −10.7943 + 29.0837i −0.371116 + 0.999917i
\(847\) 9.36931 2.28617i 0.321933 0.0785536i
\(848\) 8.43154i 0.289540i
\(849\) −36.1065 30.4920i −1.23917 1.04648i
\(850\) 3.51153 2.02739i 0.120445 0.0695387i
\(851\) 25.7123 14.8450i 0.881406 0.508880i
\(852\) −8.26056 6.97606i −0.283002 0.238996i
\(853\) 40.6558i 1.39203i 0.718027 + 0.696015i \(0.245045\pi\)
−0.718027 + 0.696015i \(0.754955\pi\)
\(854\) −0.307224 + 1.05148i −0.0105130 + 0.0359808i
\(855\) −2.72166 + 7.33312i −0.0930789 + 0.250787i
\(856\) −9.29984 + 16.1078i −0.317862 + 0.550553i
\(857\) 4.68975 + 8.12288i 0.160199 + 0.277472i 0.934940 0.354806i \(-0.115453\pi\)
−0.774741 + 0.632279i \(0.782120\pi\)
\(858\) 6.23578 2.24734i 0.212886 0.0767229i
\(859\) −19.3168 11.1526i −0.659081 0.380520i 0.132846 0.991137i \(-0.457588\pi\)
−0.791927 + 0.610616i \(0.790922\pi\)
\(860\) 0.918817 0.0313314
\(861\) −2.79763 + 5.61889i −0.0953429 + 0.191491i
\(862\) 28.3584 0.965890
\(863\) 19.6995 + 11.3735i 0.670577 + 0.387158i 0.796295 0.604908i \(-0.206790\pi\)
−0.125718 + 0.992066i \(0.540123\pi\)
\(864\) −5.19592 0.0492786i −0.176769 0.00167649i
\(865\) −5.97525 10.3494i −0.203165 0.351891i
\(866\) 2.16790 3.75491i 0.0736681 0.127597i
\(867\) 27.5356 + 4.94507i 0.935157 + 0.167943i
\(868\) 0.596844 + 2.44602i 0.0202582 + 0.0830234i
\(869\) 49.5875i 1.68214i
\(870\) −0.578052 + 0.684490i −0.0195978 + 0.0232064i
\(871\) 8.14699 4.70367i 0.276050 0.159378i
\(872\) −9.28600 + 5.36127i −0.314463 + 0.181556i
\(873\) 18.0183 + 21.7511i 0.609825 + 0.736164i
\(874\) 14.8420i 0.502037i
\(875\) 13.2816 + 13.8923i 0.448999 + 0.469645i
\(876\) −2.69884 + 15.0279i −0.0911852 + 0.507746i
\(877\) −8.52661 + 14.7685i −0.287923 + 0.498697i −0.973314 0.229478i \(-0.926298\pi\)
0.685391 + 0.728175i \(0.259631\pi\)
\(878\) 15.2765 + 26.4597i 0.515558 + 0.892972i
\(879\) −7.66791 21.2765i −0.258632 0.717637i
\(880\) 2.56035 + 1.47822i 0.0863095 + 0.0498308i
\(881\) 28.2955 0.953298 0.476649 0.879094i \(-0.341851\pi\)
0.476649 + 0.879094i \(0.341851\pi\)
\(882\) 2.58212 + 20.8406i 0.0869445 + 0.701741i
\(883\) 47.9719 1.61438 0.807192 0.590289i \(-0.200986\pi\)
0.807192 + 0.590289i \(0.200986\pi\)
\(884\) −0.797500 0.460437i −0.0268228 0.0154862i
\(885\) 1.79708 + 4.98642i 0.0604080 + 0.167617i
\(886\) −5.97906 10.3560i −0.200870 0.347918i
\(887\) 21.6994 37.5844i 0.728593 1.26196i −0.228885 0.973454i \(-0.573508\pi\)
0.957478 0.288507i \(-0.0931588\pi\)
\(888\) −2.06697 + 11.5095i −0.0693629 + 0.386232i
\(889\) −38.9593 40.7507i −1.30665 1.36673i
\(890\) 3.10476i 0.104072i
\(891\) −11.3697 32.5114i −0.380899 1.08917i
\(892\) −4.53064 + 2.61577i −0.151697 + 0.0875824i
\(893\) −30.2239 + 17.4498i −1.01140 + 0.583935i
\(894\) −2.62936 + 3.11351i −0.0879390 + 0.104131i
\(895\) 9.28760i 0.310450i
\(896\) 0.627178 + 2.57034i 0.0209526 + 0.0858690i
\(897\) 7.49705 + 1.34638i 0.250319 + 0.0449544i
\(898\) −9.52398 + 16.4960i −0.317819 + 0.550479i
\(899\) −0.318585 0.551806i −0.0106254 0.0184038i
\(900\) −2.21152 13.0231i −0.0737173 0.434103i
\(901\) 6.72415 + 3.88219i 0.224014 + 0.129335i
\(902\) −5.24177 −0.174532
\(903\) −2.42921 + 4.87895i −0.0808392 + 0.162361i
\(904\) −14.5031 −0.482366
\(905\) −10.9782 6.33828i −0.364929 0.210692i
\(906\) 16.0418 5.78138i 0.532954 0.192074i
\(907\) −13.9186 24.1077i −0.462160 0.800484i 0.536909 0.843640i \(-0.319592\pi\)
−0.999068 + 0.0431565i \(0.986259\pi\)
\(908\) −14.0718 + 24.3731i −0.466990 + 0.808851i
\(909\) −19.9285 7.39641i −0.660988 0.245324i
\(910\) 0.573240 1.96192i 0.0190027 0.0650371i
\(911\) 5.08227i 0.168383i −0.996450 0.0841915i \(-0.973169\pi\)
0.996450 0.0841915i \(-0.0268308\pi\)
\(912\) −4.46609 3.77162i −0.147887 0.124891i
\(913\) −7.36481 + 4.25207i −0.243739 + 0.140723i
\(914\) 9.22817 5.32789i 0.305241 0.176231i
\(915\) −0.423274 0.357455i −0.0139930 0.0118171i
\(916\) 9.54398i 0.315342i
\(917\) 43.3659 10.5815i 1.43207 0.349433i
\(918\) −2.43169 + 4.12105i −0.0802578 + 0.136015i
\(919\) −23.0372 + 39.9016i −0.759927 + 1.31623i 0.182961 + 0.983120i \(0.441432\pi\)
−0.942887 + 0.333111i \(0.891901\pi\)
\(920\) 1.69869 + 2.94222i 0.0560042 + 0.0970021i
\(921\) −27.9885 + 10.0869i −0.922254 + 0.332375i
\(922\) −24.7172 14.2705i −0.814018 0.469973i
\(923\) −6.24239 −0.205471
\(924\) −14.6186 + 9.68737i −0.480916 + 0.318691i
\(925\) −29.7272 −0.977424
\(926\) 31.3721 + 18.1127i 1.03095 + 0.595221i
\(927\) −15.6071 + 2.65032i −0.512605 + 0.0870480i
\(928\) −0.334777 0.579851i −0.0109896 0.0190346i
\(929\) 6.38850 11.0652i 0.209600 0.363038i −0.741989 0.670413i \(-0.766117\pi\)
0.951589 + 0.307375i \(0.0994505\pi\)
\(930\) −1.25331 0.225080i −0.0410977 0.00738068i
\(931\) −12.7196 + 19.9083i −0.416868 + 0.652468i
\(932\) 2.38972i 0.0782778i
\(933\) 34.8016 41.2096i 1.13935 1.34914i
\(934\) 2.06953 1.19484i 0.0677171 0.0390965i
\(935\) 2.35776 1.36125i 0.0771070 0.0445178i
\(936\) −2.31028 + 1.91379i −0.0755138 + 0.0625543i
\(937\) 8.53335i 0.278772i 0.990238 + 0.139386i \(0.0445130\pi\)
−0.990238 + 0.139386i \(0.955487\pi\)
\(938\) −17.9905 + 17.1996i −0.587411 + 0.561588i
\(939\) −2.33246 + 12.9878i −0.0761168 + 0.423840i
\(940\) −3.99433 + 6.91837i −0.130281 + 0.225652i
\(941\) −0.0600360 0.103985i −0.00195712 0.00338983i 0.865045 0.501694i \(-0.167290\pi\)
−0.867002 + 0.498304i \(0.833956\pi\)
\(942\) 2.93870 + 8.15412i 0.0957479 + 0.265676i
\(943\) −5.21656 3.01178i −0.169874 0.0980771i
\(944\) −3.96116 −0.128925
\(945\) −10.1657 3.07519i −0.330692 0.100036i
\(946\) −4.55149 −0.147982
\(947\) 12.7440 + 7.35774i 0.414124 + 0.239094i 0.692560 0.721360i \(-0.256483\pi\)
−0.278436 + 0.960455i \(0.589816\pi\)
\(948\) 7.60933 + 21.1139i 0.247140 + 0.685748i
\(949\) 4.40758 + 7.63416i 0.143076 + 0.247815i
\(950\) 7.43028 12.8696i 0.241070 0.417546i
\(951\) −6.58483 + 36.6663i −0.213528 + 1.18898i
\(952\) 2.33862 + 0.683304i 0.0757951 + 0.0221460i
\(953\) 6.79346i 0.220062i 0.993928 + 0.110031i \(0.0350950\pi\)
−0.993928 + 0.110031i \(0.964905\pi\)
\(954\) 19.4792 16.1362i 0.630663 0.522430i
\(955\) −17.0527 + 9.84538i −0.551812 + 0.318589i
\(956\) −1.58575 + 0.915531i −0.0512867 + 0.0296104i
\(957\) 2.86347 3.39072i 0.0925628 0.109606i
\(958\) 35.2664i 1.13941i
\(959\) −36.0644 10.5374i −1.16458 0.340271i
\(960\) −1.31701 0.236520i −0.0425064 0.00763365i
\(961\) −15.0472 + 26.0625i −0.485393 + 0.840726i
\(962\) 3.37565 + 5.84680i 0.108835 + 0.188508i
\(963\) 55.0115 9.34177i 1.77272 0.301034i
\(964\) 23.6939 + 13.6797i 0.763130 + 0.440593i
\(965\) 7.85549 0.252877
\(966\) −20.1144 + 1.24132i −0.647170 + 0.0399389i
\(967\) 44.6854 1.43699 0.718493 0.695534i \(-0.244832\pi\)
0.718493 + 0.695534i \(0.244832\pi\)
\(968\) −3.15680 1.82258i −0.101464 0.0585800i
\(969\) −5.06422 + 1.82511i −0.162686 + 0.0586311i
\(970\) 3.63672 + 6.29898i 0.116768 + 0.202248i
\(971\) 26.1343 45.2659i 0.838689 1.45265i −0.0523020 0.998631i \(-0.516656\pi\)
0.890991 0.454021i \(-0.150011\pi\)
\(972\) 9.83007 + 12.0983i 0.315300 + 0.388054i
\(973\) 16.9662 16.2203i 0.543911 0.520000i
\(974\) 20.3877i 0.653263i
\(975\) −5.82673 4.92068i −0.186605 0.157588i
\(976\) 0.358567 0.207019i 0.0114775 0.00662652i
\(977\) 36.1257 20.8572i 1.15576 0.667280i 0.205479 0.978662i \(-0.434125\pi\)
0.950285 + 0.311381i \(0.100792\pi\)
\(978\) −32.5316 27.4730i −1.04025 0.878490i
\(979\) 15.3799i 0.491543i
\(980\) −0.242946 + 5.40233i −0.00776062 + 0.172571i
\(981\) 30.1575 + 11.1929i 0.962856 + 0.357361i
\(982\) 11.2860 19.5479i 0.360151 0.623800i
\(983\) 18.6067 + 32.2278i 0.593462 + 1.02791i 0.993762 + 0.111522i \(0.0355724\pi\)
−0.400300 + 0.916384i \(0.631094\pi\)
\(984\) 2.23190 0.804364i 0.0711503 0.0256422i
\(985\) −0.985342 0.568888i −0.0313956 0.0181263i
\(986\) −0.616575 −0.0196358
\(987\) −26.1764 39.5012i −0.833205 1.25734i
\(988\) −3.37496 −0.107372
\(989\) −4.52960 2.61517i −0.144033 0.0831574i
\(990\) −1.48489 8.74414i −0.0471928 0.277907i
\(991\) −13.6848 23.7027i −0.434711 0.752942i 0.562561 0.826756i \(-0.309816\pi\)
−0.997272 + 0.0738138i \(0.976483\pi\)
\(992\) 0.475817 0.824139i 0.0151072 0.0261664i
\(993\) 2.68166 + 0.481595i 0.0850998 + 0.0152829i
\(994\) 16.0451 3.91509i 0.508919 0.124179i
\(995\) 14.7240i 0.466781i
\(996\) 2.48338 2.94064i 0.0786888 0.0931779i
\(997\) −32.7195 + 18.8906i −1.03624 + 0.598272i −0.918765 0.394804i \(-0.870812\pi\)
−0.117472 + 0.993076i \(0.537479\pi\)
\(998\) 3.91989 2.26315i 0.124082 0.0716387i
\(999\) 30.5458 17.2515i 0.966428 0.545813i
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.131.6 32
3.2 odd 2 546.2.z.b.131.11 yes 32
7.3 odd 6 546.2.z.b.521.11 yes 32
21.17 even 6 inner 546.2.z.a.521.6 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.z.a.131.6 32 1.1 even 1 trivial
546.2.z.a.521.6 yes 32 21.17 even 6 inner
546.2.z.b.131.11 yes 32 3.2 odd 2
546.2.z.b.521.11 yes 32 7.3 odd 6