Properties

Label 507.2.k.i.80.1
Level $507$
Weight $2$
Character 507.80
Analytic conductor $4.048$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [507,2,Mod(80,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.80");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.k (of order \(12\), degree \(4\), not 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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 80.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 507.80
Dual form 507.2.k.i.488.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 + 0.965926i) q^{2} +(1.72474 + 0.158919i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.41421 + 1.41421i) q^{5} +(-0.599900 + 1.62484i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\) \(q+(-0.258819 + 0.965926i) q^{2} +(1.72474 + 0.158919i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.41421 + 1.41421i) q^{5} +(-0.599900 + 1.62484i) q^{6} +(1.36603 - 0.366025i) q^{7} +(-2.12132 + 2.12132i) q^{8} +(2.94949 + 0.548188i) q^{9} +(-1.73205 + 1.00000i) q^{10} +(-3.86370 - 1.03528i) q^{11} +(1.41421 + 1.00000i) q^{12} +1.41421i q^{14} +(2.21441 + 2.66390i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.29289 + 2.70711i) q^{18} +(-0.366025 - 1.36603i) q^{19} +(0.517638 + 1.93185i) q^{20} +(2.41421 - 0.414214i) q^{21} +(2.00000 - 3.46410i) q^{22} +(-4.24264 - 7.34847i) q^{23} +(-3.99585 + 3.32162i) q^{24} -1.00000i q^{25} +(5.00000 + 1.41421i) q^{27} +(1.36603 + 0.366025i) q^{28} +(-2.44949 + 1.41421i) q^{29} +(-3.14626 + 1.44949i) q^{30} +(5.00000 - 5.00000i) q^{31} +(-4.82963 + 1.29410i) q^{32} +(-6.49938 - 2.39960i) q^{33} +(2.44949 + 1.41421i) q^{35} +(2.28024 + 1.94949i) q^{36} +(-0.366025 + 1.36603i) q^{37} +1.41421 q^{38} -6.00000 q^{40} +(0.517638 - 1.93185i) q^{41} +(-0.224745 + 2.43916i) q^{42} +(5.19615 + 3.00000i) q^{43} +(-2.82843 - 2.82843i) q^{44} +(3.39595 + 4.94646i) q^{45} +(8.19615 - 2.19615i) q^{46} +(2.82843 - 2.82843i) q^{47} +(-0.724745 - 1.57313i) q^{48} +(-4.33013 + 2.50000i) q^{49} +(0.965926 + 0.258819i) q^{50} +5.65685i q^{53} +(-2.66012 + 4.46360i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(-2.12132 + 3.67423i) q^{56} +(-0.414214 - 2.41421i) q^{57} +(-0.732051 - 2.73205i) q^{58} +(1.03528 + 3.86370i) q^{59} +(0.585786 + 3.41421i) q^{60} +(-4.00000 + 6.92820i) q^{61} +(3.53553 + 6.12372i) q^{62} +(4.22973 - 0.330749i) q^{63} -7.00000i q^{64} +(4.00000 - 5.65685i) q^{66} +(-6.83013 - 1.83013i) q^{67} +(-6.14966 - 13.3485i) q^{69} +(-2.00000 + 2.00000i) q^{70} +(3.86370 - 1.03528i) q^{71} +(-7.41970 + 5.09393i) q^{72} +(-1.00000 - 1.00000i) q^{73} +(-1.22474 - 0.707107i) q^{74} +(0.158919 - 1.72474i) q^{75} +(0.366025 - 1.36603i) q^{76} -5.65685 q^{77} -10.0000 q^{79} +(0.517638 - 1.93185i) q^{80} +(8.39898 + 3.23375i) q^{81} +(1.73205 + 1.00000i) q^{82} +(5.65685 + 5.65685i) q^{83} +(2.29788 + 0.848387i) q^{84} +(-4.24264 + 4.24264i) q^{86} +(-4.44949 + 2.04989i) q^{87} +(10.3923 - 6.00000i) q^{88} +(13.5230 + 3.62347i) q^{89} +(-5.65685 + 2.00000i) q^{90} -8.48528i q^{92} +(9.41832 - 7.82913i) q^{93} +(2.00000 + 3.46410i) q^{94} +(1.41421 - 2.44949i) q^{95} +(-8.53553 + 1.46447i) q^{96} +(-2.56218 - 9.56218i) q^{97} +(-1.29410 - 4.82963i) q^{98} +(-10.8284 - 5.17157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{3} - 4 q^{6} + 4 q^{7} + 4 q^{9} + 8 q^{15} - 4 q^{16} - 16 q^{18} + 4 q^{19} + 8 q^{21} + 16 q^{22} + 12 q^{24} + 40 q^{27} + 4 q^{28} + 40 q^{31} - 16 q^{33} + 4 q^{37} - 48 q^{40} + 8 q^{42} - 16 q^{45} + 24 q^{46} + 4 q^{48} - 4 q^{54} - 32 q^{55} + 8 q^{57} + 8 q^{58} + 16 q^{60} - 32 q^{61} - 4 q^{63} + 32 q^{66} - 20 q^{67} - 16 q^{70} - 24 q^{72} - 8 q^{73} - 4 q^{76} - 80 q^{79} + 28 q^{81} - 4 q^{84} - 16 q^{87} + 20 q^{93} + 16 q^{94} - 40 q^{96} + 28 q^{97} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{12}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 + 0.965926i −0.183013 + 0.683013i 0.812035 + 0.583609i \(0.198360\pi\)
−0.995047 + 0.0994033i \(0.968307\pi\)
\(3\) 1.72474 + 0.158919i 0.995782 + 0.0917517i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 1.41421 + 1.41421i 0.632456 + 0.632456i 0.948683 0.316228i \(-0.102416\pi\)
−0.316228 + 0.948683i \(0.602416\pi\)
\(6\) −0.599900 + 1.62484i −0.244908 + 0.663340i
\(7\) 1.36603 0.366025i 0.516309 0.138345i 0.00875026 0.999962i \(-0.497215\pi\)
0.507559 + 0.861617i \(0.330548\pi\)
\(8\) −2.12132 + 2.12132i −0.750000 + 0.750000i
\(9\) 2.94949 + 0.548188i 0.983163 + 0.182729i
\(10\) −1.73205 + 1.00000i −0.547723 + 0.316228i
\(11\) −3.86370 1.03528i −1.16495 0.312148i −0.376009 0.926616i \(-0.622704\pi\)
−0.788941 + 0.614468i \(0.789370\pi\)
\(12\) 1.41421 + 1.00000i 0.408248 + 0.288675i
\(13\) 0 0
\(14\) 1.41421i 0.377964i
\(15\) 2.21441 + 2.66390i 0.571759 + 0.687817i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) −1.29289 + 2.70711i −0.304738 + 0.638071i
\(19\) −0.366025 1.36603i −0.0839720 0.313388i 0.911146 0.412085i \(-0.135199\pi\)
−0.995118 + 0.0986970i \(0.968533\pi\)
\(20\) 0.517638 + 1.93185i 0.115747 + 0.431975i
\(21\) 2.41421 0.414214i 0.526825 0.0903888i
\(22\) 2.00000 3.46410i 0.426401 0.738549i
\(23\) −4.24264 7.34847i −0.884652 1.53226i −0.846112 0.533005i \(-0.821063\pi\)
−0.0385394 0.999257i \(-0.512271\pi\)
\(24\) −3.99585 + 3.32162i −0.815650 + 0.678023i
\(25\) 1.00000i 0.200000i
\(26\) 0 0
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 1.36603 + 0.366025i 0.258155 + 0.0691723i
\(29\) −2.44949 + 1.41421i −0.454859 + 0.262613i −0.709880 0.704323i \(-0.751251\pi\)
0.255021 + 0.966935i \(0.417918\pi\)
\(30\) −3.14626 + 1.44949i −0.574427 + 0.264639i
\(31\) 5.00000 5.00000i 0.898027 0.898027i −0.0972349 0.995261i \(-0.531000\pi\)
0.995261 + 0.0972349i \(0.0309998\pi\)
\(32\) −4.82963 + 1.29410i −0.853766 + 0.228766i
\(33\) −6.49938 2.39960i −1.13140 0.417717i
\(34\) 0 0
\(35\) 2.44949 + 1.41421i 0.414039 + 0.239046i
\(36\) 2.28024 + 1.94949i 0.380040 + 0.324915i
\(37\) −0.366025 + 1.36603i −0.0601742 + 0.224573i −0.989464 0.144778i \(-0.953753\pi\)
0.929290 + 0.369351i \(0.120420\pi\)
\(38\) 1.41421 0.229416
\(39\) 0 0
\(40\) −6.00000 −0.948683
\(41\) 0.517638 1.93185i 0.0808415 0.301705i −0.913653 0.406496i \(-0.866751\pi\)
0.994494 + 0.104791i \(0.0334174\pi\)
\(42\) −0.224745 + 2.43916i −0.0346789 + 0.376370i
\(43\) 5.19615 + 3.00000i 0.792406 + 0.457496i 0.840809 0.541332i \(-0.182080\pi\)
−0.0484030 + 0.998828i \(0.515413\pi\)
\(44\) −2.82843 2.82843i −0.426401 0.426401i
\(45\) 3.39595 + 4.94646i 0.506239 + 0.737375i
\(46\) 8.19615 2.19615i 1.20846 0.323805i
\(47\) 2.82843 2.82843i 0.412568 0.412568i −0.470064 0.882632i \(-0.655769\pi\)
0.882632 + 0.470064i \(0.155769\pi\)
\(48\) −0.724745 1.57313i −0.104608 0.227062i
\(49\) −4.33013 + 2.50000i −0.618590 + 0.357143i
\(50\) 0.965926 + 0.258819i 0.136603 + 0.0366025i
\(51\) 0 0
\(52\) 0 0
\(53\) 5.65685i 0.777029i 0.921443 + 0.388514i \(0.127012\pi\)
−0.921443 + 0.388514i \(0.872988\pi\)
\(54\) −2.66012 + 4.46360i −0.361997 + 0.607420i
\(55\) −4.00000 6.92820i −0.539360 0.934199i
\(56\) −2.12132 + 3.67423i −0.283473 + 0.490990i
\(57\) −0.414214 2.41421i −0.0548639 0.319770i
\(58\) −0.732051 2.73205i −0.0961230 0.358736i
\(59\) 1.03528 + 3.86370i 0.134781 + 0.503011i 0.999999 + 0.00161411i \(0.000513789\pi\)
−0.865217 + 0.501397i \(0.832820\pi\)
\(60\) 0.585786 + 3.41421i 0.0756247 + 0.440773i
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 3.53553 + 6.12372i 0.449013 + 0.777714i
\(63\) 4.22973 0.330749i 0.532896 0.0416705i
\(64\) 7.00000i 0.875000i
\(65\) 0 0
\(66\) 4.00000 5.65685i 0.492366 0.696311i
\(67\) −6.83013 1.83013i −0.834433 0.223586i −0.183786 0.982966i \(-0.558835\pi\)
−0.650647 + 0.759381i \(0.725502\pi\)
\(68\) 0 0
\(69\) −6.14966 13.3485i −0.740333 1.60697i
\(70\) −2.00000 + 2.00000i −0.239046 + 0.239046i
\(71\) 3.86370 1.03528i 0.458537 0.122865i −0.0221541 0.999755i \(-0.507052\pi\)
0.480691 + 0.876890i \(0.340386\pi\)
\(72\) −7.41970 + 5.09393i −0.874419 + 0.600325i
\(73\) −1.00000 1.00000i −0.117041 0.117041i 0.646160 0.763202i \(-0.276374\pi\)
−0.763202 + 0.646160i \(0.776374\pi\)
\(74\) −1.22474 0.707107i −0.142374 0.0821995i
\(75\) 0.158919 1.72474i 0.0183503 0.199156i
\(76\) 0.366025 1.36603i 0.0419860 0.156694i
\(77\) −5.65685 −0.644658
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0.517638 1.93185i 0.0578737 0.215988i
\(81\) 8.39898 + 3.23375i 0.933220 + 0.359306i
\(82\) 1.73205 + 1.00000i 0.191273 + 0.110432i
\(83\) 5.65685 + 5.65685i 0.620920 + 0.620920i 0.945767 0.324846i \(-0.105313\pi\)
−0.324846 + 0.945767i \(0.605313\pi\)
\(84\) 2.29788 + 0.848387i 0.250719 + 0.0925666i
\(85\) 0 0
\(86\) −4.24264 + 4.24264i −0.457496 + 0.457496i
\(87\) −4.44949 + 2.04989i −0.477035 + 0.219771i
\(88\) 10.3923 6.00000i 1.10782 0.639602i
\(89\) 13.5230 + 3.62347i 1.43343 + 0.384087i 0.890228 0.455515i \(-0.150545\pi\)
0.543203 + 0.839601i \(0.317211\pi\)
\(90\) −5.65685 + 2.00000i −0.596285 + 0.210819i
\(91\) 0 0
\(92\) 8.48528i 0.884652i
\(93\) 9.41832 7.82913i 0.976634 0.811843i
\(94\) 2.00000 + 3.46410i 0.206284 + 0.357295i
\(95\) 1.41421 2.44949i 0.145095 0.251312i
\(96\) −8.53553 + 1.46447i −0.871154 + 0.149466i
\(97\) −2.56218 9.56218i −0.260150 0.970892i −0.965153 0.261688i \(-0.915721\pi\)
0.705003 0.709204i \(-0.250946\pi\)
\(98\) −1.29410 4.82963i −0.130723 0.487866i
\(99\) −10.8284 5.17157i −1.08830 0.519763i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 4.24264 + 7.34847i 0.422159 + 0.731200i 0.996150 0.0876610i \(-0.0279392\pi\)
−0.573992 + 0.818861i \(0.694606\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 0 0
\(105\) 4.00000 + 2.82843i 0.390360 + 0.276026i
\(106\) −5.46410 1.46410i −0.530720 0.142206i
\(107\) 4.89898 2.82843i 0.473602 0.273434i −0.244144 0.969739i \(-0.578507\pi\)
0.717746 + 0.696305i \(0.245174\pi\)
\(108\) 3.62302 + 3.72474i 0.348625 + 0.358414i
\(109\) −1.00000 + 1.00000i −0.0957826 + 0.0957826i −0.753374 0.657592i \(-0.771575\pi\)
0.657592 + 0.753374i \(0.271575\pi\)
\(110\) 7.72741 2.07055i 0.736779 0.197419i
\(111\) −0.848387 + 2.29788i −0.0805254 + 0.218105i
\(112\) −1.00000 1.00000i −0.0944911 0.0944911i
\(113\) −12.2474 7.07107i −1.15214 0.665190i −0.202735 0.979234i \(-0.564983\pi\)
−0.949409 + 0.314044i \(0.898316\pi\)
\(114\) 2.43916 + 0.224745i 0.228448 + 0.0210493i
\(115\) 4.39230 16.3923i 0.409585 1.52859i
\(116\) −2.82843 −0.262613
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) −10.3485 0.953512i −0.944682 0.0870433i
\(121\) 4.33013 + 2.50000i 0.393648 + 0.227273i
\(122\) −5.65685 5.65685i −0.512148 0.512148i
\(123\) 1.19980 3.24969i 0.108182 0.293015i
\(124\) 6.83013 1.83013i 0.613364 0.164350i
\(125\) 8.48528 8.48528i 0.758947 0.758947i
\(126\) −0.775255 + 4.17121i −0.0690652 + 0.371601i
\(127\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) −2.89778 0.776457i −0.256130 0.0686298i
\(129\) 8.48528 + 6.00000i 0.747087 + 0.528271i
\(130\) 0 0
\(131\) 11.3137i 0.988483i −0.869325 0.494242i \(-0.835446\pi\)
0.869325 0.494242i \(-0.164554\pi\)
\(132\) −4.42883 5.32780i −0.385480 0.463726i
\(133\) −1.00000 1.73205i −0.0867110 0.150188i
\(134\) 3.53553 6.12372i 0.305424 0.529009i
\(135\) 5.07107 + 9.07107i 0.436448 + 0.780713i
\(136\) 0 0
\(137\) −3.62347 13.5230i −0.309574 1.15534i −0.928936 0.370240i \(-0.879276\pi\)
0.619363 0.785105i \(-0.287391\pi\)
\(138\) 14.4853 2.48528i 1.23307 0.211561i
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 1.41421 + 2.44949i 0.119523 + 0.207020i
\(141\) 5.32780 4.42883i 0.448682 0.372974i
\(142\) 4.00000i 0.335673i
\(143\) 0 0
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) −5.46410 1.46410i −0.453769 0.121587i
\(146\) 1.22474 0.707107i 0.101361 0.0585206i
\(147\) −7.86566 + 3.62372i −0.648749 + 0.298880i
\(148\) −1.00000 + 1.00000i −0.0821995 + 0.0821995i
\(149\) −1.93185 + 0.517638i −0.158263 + 0.0424066i −0.337081 0.941476i \(-0.609440\pi\)
0.178817 + 0.983882i \(0.442773\pi\)
\(150\) 1.62484 + 0.599900i 0.132668 + 0.0489817i
\(151\) −1.00000 1.00000i −0.0813788 0.0813788i 0.665246 0.746625i \(-0.268327\pi\)
−0.746625 + 0.665246i \(0.768327\pi\)
\(152\) 3.67423 + 2.12132i 0.298020 + 0.172062i
\(153\) 0 0
\(154\) 1.46410 5.46410i 0.117981 0.440310i
\(155\) 14.1421 1.13592
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 2.58819 9.65926i 0.205905 0.768449i
\(159\) −0.898979 + 9.75663i −0.0712937 + 0.773751i
\(160\) −8.66025 5.00000i −0.684653 0.395285i
\(161\) −8.48528 8.48528i −0.668734 0.668734i
\(162\) −5.29738 + 7.27583i −0.416201 + 0.571644i
\(163\) 1.36603 0.366025i 0.106995 0.0286693i −0.204924 0.978778i \(-0.565695\pi\)
0.311919 + 0.950109i \(0.399028\pi\)
\(164\) 1.41421 1.41421i 0.110432 0.110432i
\(165\) −5.79796 12.5851i −0.451370 0.979745i
\(166\) −6.92820 + 4.00000i −0.537733 + 0.310460i
\(167\) −3.86370 1.03528i −0.298982 0.0801121i 0.106209 0.994344i \(-0.466129\pi\)
−0.405192 + 0.914232i \(0.632795\pi\)
\(168\) −4.24264 + 6.00000i −0.327327 + 0.462910i
\(169\) 0 0
\(170\) 0 0
\(171\) −0.330749 4.22973i −0.0252930 0.323455i
\(172\) 3.00000 + 5.19615i 0.228748 + 0.396203i
\(173\) 4.24264 7.34847i 0.322562 0.558694i −0.658454 0.752621i \(-0.728789\pi\)
0.981016 + 0.193927i \(0.0621226\pi\)
\(174\) −0.828427 4.82843i −0.0628029 0.366042i
\(175\) −0.366025 1.36603i −0.0276689 0.103262i
\(176\) 1.03528 + 3.86370i 0.0780369 + 0.291238i
\(177\) 1.17157 + 6.82843i 0.0880608 + 0.513256i
\(178\) −7.00000 + 12.1244i −0.524672 + 0.908759i
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0.467750 + 5.98174i 0.0348640 + 0.445853i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −8.00000 + 11.3137i −0.591377 + 0.836333i
\(184\) 24.5885 + 6.58846i 1.81269 + 0.485708i
\(185\) −2.44949 + 1.41421i −0.180090 + 0.103975i
\(186\) 5.12472 + 11.1237i 0.375763 + 0.815631i
\(187\) 0 0
\(188\) 3.86370 1.03528i 0.281790 0.0755053i
\(189\) 7.34777 + 0.101725i 0.534471 + 0.00739938i
\(190\) 2.00000 + 2.00000i 0.145095 + 0.145095i
\(191\) 2.44949 + 1.41421i 0.177239 + 0.102329i 0.585995 0.810315i \(-0.300704\pi\)
−0.408756 + 0.912644i \(0.634037\pi\)
\(192\) 1.11243 12.0732i 0.0802827 0.871309i
\(193\) −6.95448 + 25.9545i −0.500595 + 1.86824i −0.00447566 + 0.999990i \(0.501425\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) 9.89949 0.710742
\(195\) 0 0
\(196\) −5.00000 −0.357143
\(197\) −5.69402 + 21.2504i −0.405682 + 1.51403i 0.397112 + 0.917770i \(0.370012\pi\)
−0.802794 + 0.596256i \(0.796654\pi\)
\(198\) 7.79796 9.12096i 0.554177 0.648198i
\(199\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) 2.12132 + 2.12132i 0.150000 + 0.150000i
\(201\) −11.4894 4.24194i −0.810399 0.299203i
\(202\) −8.19615 + 2.19615i −0.576679 + 0.154521i
\(203\) −2.82843 + 2.82843i −0.198517 + 0.198517i
\(204\) 0 0
\(205\) 3.46410 2.00000i 0.241943 0.139686i
\(206\) −5.79555 1.55291i −0.403795 0.108197i
\(207\) −8.48528 24.0000i −0.589768 1.66812i
\(208\) 0 0
\(209\) 5.65685i 0.391293i
\(210\) −3.76733 + 3.13165i −0.259970 + 0.216105i
\(211\) −7.00000 12.1244i −0.481900 0.834675i 0.517884 0.855451i \(-0.326720\pi\)
−0.999784 + 0.0207756i \(0.993386\pi\)
\(212\) −2.82843 + 4.89898i −0.194257 + 0.336463i
\(213\) 6.82843 1.17157i 0.467876 0.0802749i
\(214\) 1.46410 + 5.46410i 0.100084 + 0.373518i
\(215\) 3.10583 + 11.5911i 0.211816 + 0.790507i
\(216\) −13.6066 + 7.60660i −0.925812 + 0.517564i
\(217\) 5.00000 8.66025i 0.339422 0.587896i
\(218\) −0.707107 1.22474i −0.0478913 0.0829502i
\(219\) −1.56583 1.88366i −0.105809 0.127286i
\(220\) 8.00000i 0.539360i
\(221\) 0 0
\(222\) −2.00000 1.41421i −0.134231 0.0949158i
\(223\) −15.0263 4.02628i −1.00623 0.269620i −0.282179 0.959362i \(-0.591057\pi\)
−0.724055 + 0.689742i \(0.757724\pi\)
\(224\) −6.12372 + 3.53553i −0.409159 + 0.236228i
\(225\) 0.548188 2.94949i 0.0365459 0.196633i
\(226\) 10.0000 10.0000i 0.665190 0.665190i
\(227\) −7.72741 + 2.07055i −0.512886 + 0.137427i −0.505974 0.862549i \(-0.668867\pi\)
−0.00691198 + 0.999976i \(0.502200\pi\)
\(228\) 0.848387 2.29788i 0.0561858 0.152181i
\(229\) −1.00000 1.00000i −0.0660819 0.0660819i 0.673293 0.739375i \(-0.264879\pi\)
−0.739375 + 0.673293i \(0.764879\pi\)
\(230\) 14.6969 + 8.48528i 0.969087 + 0.559503i
\(231\) −9.75663 0.898979i −0.641939 0.0591485i
\(232\) 2.19615 8.19615i 0.144184 0.538104i
\(233\) −25.4558 −1.66767 −0.833834 0.552015i \(-0.813859\pi\)
−0.833834 + 0.552015i \(0.813859\pi\)
\(234\) 0 0
\(235\) 8.00000 0.521862
\(236\) −1.03528 + 3.86370i −0.0673907 + 0.251506i
\(237\) −17.2474 1.58919i −1.12034 0.103229i
\(238\) 0 0
\(239\) 14.1421 + 14.1421i 0.914779 + 0.914779i 0.996643 0.0818647i \(-0.0260876\pi\)
−0.0818647 + 0.996643i \(0.526088\pi\)
\(240\) 1.19980 3.24969i 0.0774468 0.209767i
\(241\) −23.2224 + 6.22243i −1.49589 + 0.400822i −0.911721 0.410811i \(-0.865246\pi\)
−0.584168 + 0.811633i \(0.698579\pi\)
\(242\) −3.53553 + 3.53553i −0.227273 + 0.227273i
\(243\) 13.9722 + 6.91215i 0.896317 + 0.443415i
\(244\) −6.92820 + 4.00000i −0.443533 + 0.256074i
\(245\) −9.65926 2.58819i −0.617107 0.165353i
\(246\) 2.82843 + 2.00000i 0.180334 + 0.127515i
\(247\) 0 0
\(248\) 21.2132i 1.34704i
\(249\) 8.85765 + 10.6556i 0.561331 + 0.675272i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) −12.7279 + 22.0454i −0.803379 + 1.39149i 0.114000 + 0.993481i \(0.463633\pi\)
−0.917380 + 0.398013i \(0.869700\pi\)
\(252\) 3.82843 + 1.82843i 0.241168 + 0.115180i
\(253\) 8.78461 + 32.7846i 0.552284 + 2.06115i
\(254\) 0 0
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) −4.24264 7.34847i −0.264649 0.458385i 0.702823 0.711365i \(-0.251923\pi\)
−0.967472 + 0.252980i \(0.918589\pi\)
\(258\) −7.99171 + 6.64324i −0.497542 + 0.413590i
\(259\) 2.00000i 0.124274i
\(260\) 0 0
\(261\) −8.00000 + 2.82843i −0.495188 + 0.175075i
\(262\) 10.9282 + 2.92820i 0.675147 + 0.180905i
\(263\) 19.5959 11.3137i 1.20834 0.697633i 0.245940 0.969285i \(-0.420903\pi\)
0.962396 + 0.271652i \(0.0875699\pi\)
\(264\) 18.8776 8.69694i 1.16184 0.535260i
\(265\) −8.00000 + 8.00000i −0.491436 + 0.491436i
\(266\) 1.93185 0.517638i 0.118449 0.0317384i
\(267\) 22.7478 + 8.39861i 1.39214 + 0.513986i
\(268\) −5.00000 5.00000i −0.305424 0.305424i
\(269\) 17.1464 + 9.89949i 1.04544 + 0.603583i 0.921368 0.388691i \(-0.127073\pi\)
0.124068 + 0.992274i \(0.460406\pi\)
\(270\) −10.0745 + 2.55051i −0.613113 + 0.155219i
\(271\) −6.95448 + 25.9545i −0.422455 + 1.57662i 0.346964 + 0.937878i \(0.387212\pi\)
−0.769419 + 0.638744i \(0.779454\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) −1.03528 + 3.86370i −0.0624295 + 0.232990i
\(276\) 1.34847 14.6349i 0.0811683 0.880920i
\(277\) −10.3923 6.00000i −0.624413 0.360505i 0.154172 0.988044i \(-0.450729\pi\)
−0.778585 + 0.627539i \(0.784062\pi\)
\(278\) 2.82843 + 2.82843i 0.169638 + 0.169638i
\(279\) 17.4884 12.0065i 1.04700 0.718811i
\(280\) −8.19615 + 2.19615i −0.489814 + 0.131245i
\(281\) −9.89949 + 9.89949i −0.590554 + 0.590554i −0.937781 0.347227i \(-0.887123\pi\)
0.347227 + 0.937781i \(0.387123\pi\)
\(282\) 2.89898 + 6.29253i 0.172632 + 0.374715i
\(283\) −10.3923 + 6.00000i −0.617758 + 0.356663i −0.775996 0.630738i \(-0.782752\pi\)
0.158237 + 0.987401i \(0.449419\pi\)
\(284\) 3.86370 + 1.03528i 0.229269 + 0.0614323i
\(285\) 2.82843 4.00000i 0.167542 0.236940i
\(286\) 0 0
\(287\) 2.82843i 0.166957i
\(288\) −14.9543 + 1.16938i −0.881193 + 0.0689061i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 2.82843 4.89898i 0.166091 0.287678i
\(291\) −2.89949 16.8995i −0.169971 0.990666i
\(292\) −0.366025 1.36603i −0.0214200 0.0799406i
\(293\) −3.62347 13.5230i −0.211685 0.790020i −0.987307 0.158822i \(-0.949230\pi\)
0.775622 0.631198i \(-0.217436\pi\)
\(294\) −1.46447 8.53553i −0.0854094 0.497802i
\(295\) −4.00000 + 6.92820i −0.232889 + 0.403376i
\(296\) −2.12132 3.67423i −0.123299 0.213561i
\(297\) −17.8544 10.6405i −1.03602 0.617423i
\(298\) 2.00000i 0.115857i
\(299\) 0 0
\(300\) 1.00000 1.41421i 0.0577350 0.0816497i
\(301\) 8.19615 + 2.19615i 0.472418 + 0.126584i
\(302\) 1.22474 0.707107i 0.0704761 0.0406894i
\(303\) 6.14966 + 13.3485i 0.353289 + 0.766850i
\(304\) −1.00000 + 1.00000i −0.0573539 + 0.0573539i
\(305\) −15.4548 + 4.14110i −0.884940 + 0.237119i
\(306\) 0 0
\(307\) 17.0000 + 17.0000i 0.970241 + 0.970241i 0.999570 0.0293286i \(-0.00933691\pi\)
−0.0293286 + 0.999570i \(0.509337\pi\)
\(308\) −4.89898 2.82843i −0.279145 0.161165i
\(309\) −0.953512 + 10.3485i −0.0542434 + 0.588704i
\(310\) −3.66025 + 13.6603i −0.207888 + 0.775850i
\(311\) 8.48528 0.481156 0.240578 0.970630i \(-0.422663\pi\)
0.240578 + 0.970630i \(0.422663\pi\)
\(312\) 0 0
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) −3.62347 + 13.5230i −0.204484 + 0.763145i
\(315\) 6.44949 + 5.51399i 0.363388 + 0.310678i
\(316\) −8.66025 5.00000i −0.487177 0.281272i
\(317\) −7.07107 7.07107i −0.397151 0.397151i 0.480076 0.877227i \(-0.340609\pi\)
−0.877227 + 0.480076i \(0.840609\pi\)
\(318\) −9.19151 3.39355i −0.515434 0.190301i
\(319\) 10.9282 2.92820i 0.611862 0.163948i
\(320\) 9.89949 9.89949i 0.553399 0.553399i
\(321\) 8.89898 4.09978i 0.496693 0.228827i
\(322\) 10.3923 6.00000i 0.579141 0.334367i
\(323\) 0 0
\(324\) 5.65685 + 7.00000i 0.314270 + 0.388889i
\(325\) 0 0
\(326\) 1.41421i 0.0783260i
\(327\) −1.88366 + 1.56583i −0.104167 + 0.0865904i
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) 2.82843 4.89898i 0.155936 0.270089i
\(330\) 13.6569 2.34315i 0.751785 0.128986i
\(331\) −2.56218 9.56218i −0.140830 0.525585i −0.999906 0.0137361i \(-0.995628\pi\)
0.859076 0.511849i \(-0.171039\pi\)
\(332\) 2.07055 + 7.72741i 0.113636 + 0.424097i
\(333\) −1.82843 + 3.82843i −0.100197 + 0.209797i
\(334\) 2.00000 3.46410i 0.109435 0.189547i
\(335\) −7.07107 12.2474i −0.386334 0.669150i
\(336\) −1.56583 1.88366i −0.0854228 0.102762i
\(337\) 6.00000i 0.326841i 0.986557 + 0.163420i \(0.0522527\pi\)
−0.986557 + 0.163420i \(0.947747\pi\)
\(338\) 0 0
\(339\) −20.0000 14.1421i −1.08625 0.768095i
\(340\) 0 0
\(341\) −24.4949 + 14.1421i −1.32647 + 0.765840i
\(342\) 4.17121 + 0.775255i 0.225553 + 0.0419210i
\(343\) −12.0000 + 12.0000i −0.647939 + 0.647939i
\(344\) −17.3867 + 4.65874i −0.937426 + 0.251183i
\(345\) 10.1806 27.5745i 0.548108 1.48456i
\(346\) 6.00000 + 6.00000i 0.322562 + 0.322562i
\(347\) −12.2474 7.07107i −0.657477 0.379595i 0.133838 0.991003i \(-0.457270\pi\)
−0.791315 + 0.611408i \(0.790603\pi\)
\(348\) −4.87832 0.449490i −0.261505 0.0240952i
\(349\) 6.22243 23.2224i 0.333079 1.24307i −0.572857 0.819655i \(-0.694165\pi\)
0.905937 0.423413i \(-0.139168\pi\)
\(350\) 1.41421 0.0755929
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) 6.72930 25.1141i 0.358164 1.33669i −0.518291 0.855204i \(-0.673432\pi\)
0.876455 0.481483i \(-0.159902\pi\)
\(354\) −6.89898 0.635674i −0.366677 0.0337857i
\(355\) 6.92820 + 4.00000i 0.367711 + 0.212298i
\(356\) 9.89949 + 9.89949i 0.524672 + 0.524672i
\(357\) 0 0
\(358\) 0 0
\(359\) 2.82843 2.82843i 0.149279 0.149279i −0.628517 0.777796i \(-0.716338\pi\)
0.777796 + 0.628517i \(0.216338\pi\)
\(360\) −17.6969 3.28913i −0.932711 0.173352i
\(361\) 14.7224 8.50000i 0.774865 0.447368i
\(362\) 0 0
\(363\) 7.07107 + 5.00000i 0.371135 + 0.262432i
\(364\) 0 0
\(365\) 2.82843i 0.148047i
\(366\) −8.85765 10.6556i −0.462997 0.556978i
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) −4.24264 + 7.34847i −0.221163 + 0.383065i
\(369\) 2.58579 5.41421i 0.134611 0.281853i
\(370\) −0.732051 2.73205i −0.0380575 0.142033i
\(371\) 2.07055 + 7.72741i 0.107498 + 0.401187i
\(372\) 12.0711 2.07107i 0.625856 0.107380i
\(373\) 2.00000 3.46410i 0.103556 0.179364i −0.809591 0.586994i \(-0.800311\pi\)
0.913147 + 0.407630i \(0.133645\pi\)
\(374\) 0 0
\(375\) 15.9834 13.2865i 0.825380 0.686111i
\(376\) 12.0000i 0.618853i
\(377\) 0 0
\(378\) −2.00000 + 7.07107i −0.102869 + 0.363696i
\(379\) 25.9545 + 6.95448i 1.33319 + 0.357228i 0.853904 0.520430i \(-0.174228\pi\)
0.479288 + 0.877658i \(0.340895\pi\)
\(380\) 2.44949 1.41421i 0.125656 0.0725476i
\(381\) 0 0
\(382\) −2.00000 + 2.00000i −0.102329 + 0.102329i
\(383\) 15.4548 4.14110i 0.789704 0.211601i 0.158645 0.987336i \(-0.449287\pi\)
0.631059 + 0.775735i \(0.282621\pi\)
\(384\) −4.87453 1.79970i −0.248752 0.0918406i
\(385\) −8.00000 8.00000i −0.407718 0.407718i
\(386\) −23.2702 13.4350i −1.18442 0.683825i
\(387\) 13.6814 + 11.6969i 0.695466 + 0.594589i
\(388\) 2.56218 9.56218i 0.130075 0.485446i
\(389\) 16.9706 0.860442 0.430221 0.902724i \(-0.358436\pi\)
0.430221 + 0.902724i \(0.358436\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 3.88229 14.4889i 0.196085 0.731799i
\(393\) 1.79796 19.5133i 0.0906950 0.984314i
\(394\) −19.0526 11.0000i −0.959854 0.554172i
\(395\) −14.1421 14.1421i −0.711568 0.711568i
\(396\) −6.79191 9.89293i −0.341306 0.497138i
\(397\) −23.2224 + 6.22243i −1.16550 + 0.312295i −0.789161 0.614187i \(-0.789484\pi\)
−0.376340 + 0.926482i \(0.622817\pi\)
\(398\) 0 0
\(399\) −1.44949 3.14626i −0.0725653 0.157510i
\(400\) −0.866025 + 0.500000i −0.0433013 + 0.0250000i
\(401\) −21.2504 5.69402i −1.06119 0.284346i −0.314323 0.949316i \(-0.601777\pi\)
−0.746870 + 0.664970i \(0.768444\pi\)
\(402\) 7.07107 10.0000i 0.352673 0.498755i
\(403\) 0 0
\(404\) 8.48528i 0.422159i
\(405\) 7.30474 + 16.4512i 0.362975 + 0.817465i
\(406\) −2.00000 3.46410i −0.0992583 0.171920i
\(407\) 2.82843 4.89898i 0.140200 0.242833i
\(408\) 0 0
\(409\) 8.41858 + 31.4186i 0.416272 + 1.55355i 0.782274 + 0.622935i \(0.214060\pi\)
−0.366002 + 0.930614i \(0.619274\pi\)
\(410\) 1.03528 + 3.86370i 0.0511286 + 0.190815i
\(411\) −4.10051 23.8995i −0.202263 1.17888i
\(412\) −3.00000 + 5.19615i −0.147799 + 0.255996i
\(413\) 2.82843 + 4.89898i 0.139178 + 0.241063i
\(414\) 25.3784 1.98450i 1.24728 0.0975326i
\(415\) 16.0000i 0.785409i
\(416\) 0 0
\(417\) 4.00000 5.65685i 0.195881 0.277017i
\(418\) −5.46410 1.46410i −0.267258 0.0716116i
\(419\) −9.79796 + 5.65685i −0.478662 + 0.276355i −0.719859 0.694121i \(-0.755793\pi\)
0.241197 + 0.970476i \(0.422460\pi\)
\(420\) 2.04989 + 4.44949i 0.100024 + 0.217113i
\(421\) −25.0000 + 25.0000i −1.21843 + 1.21843i −0.250242 + 0.968183i \(0.580510\pi\)
−0.968183 + 0.250242i \(0.919490\pi\)
\(422\) 13.5230 3.62347i 0.658287 0.176388i
\(423\) 9.89293 6.79191i 0.481011 0.330234i
\(424\) −12.0000 12.0000i −0.582772 0.582772i
\(425\) 0 0
\(426\) −0.635674 + 6.89898i −0.0307985 + 0.334257i
\(427\) −2.92820 + 10.9282i −0.141706 + 0.528853i
\(428\) 5.65685 0.273434
\(429\) 0 0
\(430\) −12.0000 −0.578691
\(431\) 8.28221 30.9096i 0.398940 1.48886i −0.416024 0.909353i \(-0.636577\pi\)
0.814964 0.579511i \(-0.196756\pi\)
\(432\) −1.27526 5.03723i −0.0613557 0.242354i
\(433\) 15.5885 + 9.00000i 0.749133 + 0.432512i 0.825381 0.564577i \(-0.190961\pi\)
−0.0762473 + 0.997089i \(0.524294\pi\)
\(434\) 7.07107 + 7.07107i 0.339422 + 0.339422i
\(435\) −9.19151 3.39355i −0.440699 0.162708i
\(436\) −1.36603 + 0.366025i −0.0654208 + 0.0175294i
\(437\) −8.48528 + 8.48528i −0.405906 + 0.405906i
\(438\) 2.22474 1.02494i 0.106302 0.0489737i
\(439\) 25.9808 15.0000i 1.23999 0.715911i 0.270901 0.962607i \(-0.412678\pi\)
0.969093 + 0.246696i \(0.0793450\pi\)
\(440\) 23.1822 + 6.21166i 1.10517 + 0.296129i
\(441\) −14.1421 + 5.00000i −0.673435 + 0.238095i
\(442\) 0 0
\(443\) 28.2843i 1.34383i −0.740630 0.671913i \(-0.765473\pi\)
0.740630 0.671913i \(-0.234527\pi\)
\(444\) −1.88366 + 1.56583i −0.0893947 + 0.0743108i
\(445\) 14.0000 + 24.2487i 0.663664 + 1.14950i
\(446\) 7.77817 13.4722i 0.368307 0.637927i
\(447\) −3.41421 + 0.585786i −0.161487 + 0.0277067i
\(448\) −2.56218 9.56218i −0.121052 0.451770i
\(449\) 5.69402 + 21.2504i 0.268717 + 1.00287i 0.959936 + 0.280221i \(0.0904077\pi\)
−0.691218 + 0.722646i \(0.742926\pi\)
\(450\) 2.70711 + 1.29289i 0.127614 + 0.0609476i
\(451\) −4.00000 + 6.92820i −0.188353 + 0.326236i
\(452\) −7.07107 12.2474i −0.332595 0.576072i
\(453\) −1.56583 1.88366i −0.0735689 0.0885022i
\(454\) 8.00000i 0.375459i
\(455\) 0 0
\(456\) 6.00000 + 4.24264i 0.280976 + 0.198680i
\(457\) −39.6147 10.6147i −1.85310 0.496536i −0.853405 0.521249i \(-0.825466\pi\)
−0.999695 + 0.0247126i \(0.992133\pi\)
\(458\) 1.22474 0.707107i 0.0572286 0.0330409i
\(459\) 0 0
\(460\) 12.0000 12.0000i 0.559503 0.559503i
\(461\) 9.65926 2.58819i 0.449877 0.120544i −0.0267651 0.999642i \(-0.508521\pi\)
0.476642 + 0.879098i \(0.341854\pi\)
\(462\) 3.39355 9.19151i 0.157882 0.427628i
\(463\) 17.0000 + 17.0000i 0.790057 + 0.790057i 0.981503 0.191446i \(-0.0613177\pi\)
−0.191446 + 0.981503i \(0.561318\pi\)
\(464\) 2.44949 + 1.41421i 0.113715 + 0.0656532i
\(465\) 24.3916 + 2.24745i 1.13113 + 0.104223i
\(466\) 6.58846 24.5885i 0.305204 1.13904i
\(467\) −25.4558 −1.17796 −0.588978 0.808149i \(-0.700470\pi\)
−0.588978 + 0.808149i \(0.700470\pi\)
\(468\) 0 0
\(469\) −10.0000 −0.461757
\(470\) −2.07055 + 7.72741i −0.0955075 + 0.356439i
\(471\) 24.1464 + 2.22486i 1.11261 + 0.102516i
\(472\) −10.3923 6.00000i −0.478345 0.276172i
\(473\) −16.9706 16.9706i −0.780307 0.780307i
\(474\) 5.99900 16.2484i 0.275543 0.746316i
\(475\) −1.36603 + 0.366025i −0.0626775 + 0.0167944i
\(476\) 0 0
\(477\) −3.10102 + 16.6848i −0.141986 + 0.763946i
\(478\) −17.3205 + 10.0000i −0.792222 + 0.457389i
\(479\) 30.9096 + 8.28221i 1.41230 + 0.378424i 0.882744 0.469853i \(-0.155693\pi\)
0.529552 + 0.848277i \(0.322360\pi\)
\(480\) −14.1421 10.0000i −0.645497 0.456435i
\(481\) 0 0
\(482\) 24.0416i 1.09507i
\(483\) −13.2865 15.9834i −0.604556 0.727271i
\(484\) 2.50000 + 4.33013i 0.113636 + 0.196824i
\(485\) 9.89949 17.1464i 0.449513 0.778579i
\(486\) −10.2929 + 11.7071i −0.466895 + 0.531045i
\(487\) −6.95448 25.9545i −0.315138 1.17611i −0.923861 0.382727i \(-0.874985\pi\)
0.608724 0.793382i \(-0.291682\pi\)
\(488\) −6.21166 23.1822i −0.281189 1.04941i
\(489\) 2.41421 0.414214i 0.109175 0.0187314i
\(490\) 5.00000 8.66025i 0.225877 0.391230i
\(491\) 21.2132 + 36.7423i 0.957338 + 1.65816i 0.728924 + 0.684595i \(0.240021\pi\)
0.228415 + 0.973564i \(0.426646\pi\)
\(492\) 2.66390 2.21441i 0.120098 0.0998334i
\(493\) 0 0
\(494\) 0 0
\(495\) −8.00000 22.6274i −0.359573 1.01703i
\(496\) −6.83013 1.83013i −0.306682 0.0821751i
\(497\) 4.89898 2.82843i 0.219749 0.126872i
\(498\) −12.5851 + 5.79796i −0.563950 + 0.259813i
\(499\) 23.0000 23.0000i 1.02962 1.02962i 0.0300737 0.999548i \(-0.490426\pi\)
0.999548 0.0300737i \(-0.00957421\pi\)
\(500\) 11.5911 3.10583i 0.518370 0.138897i
\(501\) −6.49938 2.39960i −0.290371 0.107206i
\(502\) −18.0000 18.0000i −0.803379 0.803379i
\(503\) −4.89898 2.82843i −0.218435 0.126113i 0.386791 0.922168i \(-0.373584\pi\)
−0.605225 + 0.796054i \(0.706917\pi\)
\(504\) −8.27098 + 9.67423i −0.368419 + 0.430925i
\(505\) −4.39230 + 16.3923i −0.195455 + 0.729448i
\(506\) −33.9411 −1.50887
\(507\) 0 0
\(508\) 0 0
\(509\) −8.79985 + 32.8415i −0.390046 + 1.45567i 0.440010 + 0.897993i \(0.354975\pi\)
−0.830056 + 0.557680i \(0.811692\pi\)
\(510\) 0 0
\(511\) −1.73205 1.00000i −0.0766214 0.0442374i
\(512\) 7.77817 + 7.77817i 0.343750 + 0.343750i
\(513\) 0.101725 7.34777i 0.00449125 0.324412i
\(514\) 8.19615 2.19615i 0.361517 0.0968681i
\(515\) −8.48528 + 8.48528i −0.373906 + 0.373906i
\(516\) 4.34847 + 9.43879i 0.191431 + 0.415520i
\(517\) −13.8564 + 8.00000i −0.609404 + 0.351840i
\(518\) −1.93185 0.517638i −0.0848807 0.0227437i
\(519\) 8.48528 12.0000i 0.372463 0.526742i
\(520\) 0 0
\(521\) 31.1127i 1.36307i 0.731785 + 0.681536i \(0.238688\pi\)
−0.731785 + 0.681536i \(0.761312\pi\)
\(522\) −0.661498 8.45946i −0.0289530 0.370260i
\(523\) −10.0000 17.3205i −0.437269 0.757373i 0.560208 0.828352i \(-0.310721\pi\)
−0.997478 + 0.0709788i \(0.977388\pi\)
\(524\) 5.65685 9.79796i 0.247121 0.428026i
\(525\) −0.414214 2.41421i −0.0180778 0.105365i
\(526\) 5.85641 + 21.8564i 0.255351 + 0.952985i
\(527\) 0 0
\(528\) 1.17157 + 6.82843i 0.0509862 + 0.297169i
\(529\) −24.5000 + 42.4352i −1.06522 + 1.84501i
\(530\) −5.65685 9.79796i −0.245718 0.425596i
\(531\) 0.935500 + 11.9635i 0.0405972 + 0.519171i
\(532\) 2.00000i 0.0867110i
\(533\) 0 0
\(534\) −14.0000 + 19.7990i −0.605839 + 0.856786i
\(535\) 10.9282 + 2.92820i 0.472467 + 0.126597i
\(536\) 18.3712 10.6066i 0.793514 0.458135i
\(537\) 0 0
\(538\) −14.0000 + 14.0000i −0.603583 + 0.603583i
\(539\) 19.3185 5.17638i 0.832107 0.222963i
\(540\) −0.143860 + 10.3913i −0.00619076 + 0.447171i
\(541\) −1.00000 1.00000i −0.0429934 0.0429934i 0.685283 0.728277i \(-0.259678\pi\)
−0.728277 + 0.685283i \(0.759678\pi\)
\(542\) −23.2702 13.4350i −0.999539 0.577084i
\(543\) 0 0
\(544\) 0 0
\(545\) −2.82843 −0.121157
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 3.62347 13.5230i 0.154787 0.577672i
\(549\) −15.5959 + 18.2419i −0.665618 + 0.778546i
\(550\) −3.46410 2.00000i −0.147710 0.0852803i
\(551\) 2.82843 + 2.82843i 0.120495 + 0.120495i
\(552\) 41.3618 + 15.2710i 1.76047 + 0.649976i
\(553\) −13.6603 + 3.66025i −0.580893 + 0.155650i
\(554\) 8.48528 8.48528i 0.360505 0.360505i
\(555\) −4.44949 + 2.04989i −0.188870 + 0.0870129i
\(556\) 3.46410 2.00000i 0.146911 0.0848189i
\(557\) 13.5230 + 3.62347i 0.572986 + 0.153531i 0.533666 0.845695i \(-0.320814\pi\)
0.0393204 + 0.999227i \(0.487481\pi\)
\(558\) 7.07107 + 20.0000i 0.299342 + 0.846668i
\(559\) 0 0
\(560\) 2.82843i 0.119523i
\(561\) 0 0
\(562\) −7.00000 12.1244i −0.295277 0.511435i
\(563\) −16.9706 + 29.3939i −0.715224 + 1.23880i 0.247649 + 0.968850i \(0.420342\pi\)
−0.962873 + 0.269954i \(0.912991\pi\)
\(564\) 6.82843 1.17157i 0.287529 0.0493321i
\(565\) −7.32051 27.3205i −0.307976 1.14938i
\(566\) −3.10583 11.5911i −0.130548 0.487211i
\(567\) 12.6569 + 1.34315i 0.531538 + 0.0564068i
\(568\) −6.00000 + 10.3923i −0.251754 + 0.436051i
\(569\) 4.24264 + 7.34847i 0.177861 + 0.308064i 0.941148 0.337996i \(-0.109749\pi\)
−0.763287 + 0.646060i \(0.776416\pi\)
\(570\) 3.13165 + 3.76733i 0.131170 + 0.157796i
\(571\) 12.0000i 0.502184i −0.967963 0.251092i \(-0.919210\pi\)
0.967963 0.251092i \(-0.0807897\pi\)
\(572\) 0 0
\(573\) 4.00000 + 2.82843i 0.167102 + 0.118159i
\(574\) 2.73205 + 0.732051i 0.114034 + 0.0305552i
\(575\) −7.34847 + 4.24264i −0.306452 + 0.176930i
\(576\) 3.83732 20.6464i 0.159888 0.860268i
\(577\) −1.00000 + 1.00000i −0.0416305 + 0.0416305i −0.727616 0.685985i \(-0.759372\pi\)
0.685985 + 0.727616i \(0.259372\pi\)
\(578\) −16.4207 + 4.39992i −0.683013 + 0.183013i
\(579\) −16.1194 + 43.6597i −0.669898 + 1.81443i
\(580\) −4.00000 4.00000i −0.166091 0.166091i
\(581\) 9.79796 + 5.65685i 0.406488 + 0.234686i
\(582\) 17.0741 + 1.57321i 0.707744 + 0.0652118i
\(583\) 5.85641 21.8564i 0.242548 0.905200i
\(584\) 4.24264 0.175562
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) 2.07055 7.72741i 0.0854608 0.318944i −0.909940 0.414739i \(-0.863873\pi\)
0.995401 + 0.0957952i \(0.0305394\pi\)
\(588\) −8.62372 0.794593i −0.355636 0.0327685i
\(589\) −8.66025 5.00000i −0.356840 0.206021i
\(590\) −5.65685 5.65685i −0.232889 0.232889i
\(591\) −13.1978 + 35.7466i −0.542885 + 1.47042i
\(592\) 1.36603 0.366025i 0.0561433 0.0150436i
\(593\) −9.89949 + 9.89949i −0.406524 + 0.406524i −0.880524 0.474001i \(-0.842809\pi\)
0.474001 + 0.880524i \(0.342809\pi\)
\(594\) 14.8990 14.4921i 0.611313 0.594617i
\(595\) 0 0
\(596\) −1.93185 0.517638i −0.0791317 0.0212033i
\(597\) 0 0
\(598\) 0 0
\(599\) 11.3137i 0.462266i −0.972922 0.231133i \(-0.925757\pi\)
0.972922 0.231133i \(-0.0742432\pi\)
\(600\) 3.32162 + 3.99585i 0.135605 + 0.163130i
\(601\) −4.00000 6.92820i −0.163163 0.282607i 0.772838 0.634603i \(-0.218836\pi\)
−0.936002 + 0.351996i \(0.885503\pi\)
\(602\) −4.24264 + 7.34847i −0.172917 + 0.299501i
\(603\) −19.1421 9.14214i −0.779528 0.372297i
\(604\) −0.366025 1.36603i −0.0148934 0.0555828i
\(605\) 2.58819 + 9.65926i 0.105225 + 0.392705i
\(606\) −14.4853 + 2.48528i −0.588424 + 0.100958i
\(607\) 20.0000 34.6410i 0.811775 1.40604i −0.0998457 0.995003i \(-0.531835\pi\)
0.911621 0.411033i \(-0.134832\pi\)
\(608\) 3.53553 + 6.12372i 0.143385 + 0.248350i
\(609\) −5.32780 + 4.42883i −0.215894 + 0.179465i
\(610\) 16.0000i 0.647821i
\(611\) 0 0
\(612\) 0 0
\(613\) 1.36603 + 0.366025i 0.0551732 + 0.0147836i 0.286300 0.958140i \(-0.407575\pi\)
−0.231127 + 0.972924i \(0.574241\pi\)
\(614\) −20.8207 + 12.0208i −0.840254 + 0.485121i
\(615\) 6.29253 2.89898i 0.253739 0.116898i
\(616\) 12.0000 12.0000i 0.483494 0.483494i
\(617\) −36.7052 + 9.83512i −1.47769 + 0.395947i −0.905562 0.424214i \(-0.860551\pi\)
−0.572133 + 0.820161i \(0.693884\pi\)
\(618\) −9.74907 3.59940i −0.392165 0.144789i
\(619\) −1.00000 1.00000i −0.0401934 0.0401934i 0.686724 0.726918i \(-0.259048\pi\)
−0.726918 + 0.686724i \(0.759048\pi\)
\(620\) 12.2474 + 7.07107i 0.491869 + 0.283981i
\(621\) −10.8209 42.7423i −0.434228 1.71519i
\(622\) −2.19615 + 8.19615i −0.0880577 + 0.328636i
\(623\) 19.7990 0.793230
\(624\) 0 0
\(625\) 19.0000 0.760000
\(626\) −2.07055 + 7.72741i −0.0827559 + 0.308849i
\(627\) −0.898979 + 9.75663i −0.0359018 + 0.389642i
\(628\) 12.1244 + 7.00000i 0.483814 + 0.279330i
\(629\) 0 0
\(630\) −6.99536 + 4.80260i −0.278702 + 0.191340i
\(631\) 25.9545 6.95448i 1.03323 0.276854i 0.297926 0.954589i \(-0.403705\pi\)
0.735306 + 0.677735i \(0.237039\pi\)
\(632\) 21.2132 21.2132i 0.843816 0.843816i
\(633\) −10.1464 22.0239i −0.403284 0.875369i
\(634\) 8.66025 5.00000i 0.343943 0.198575i
\(635\) 0 0
\(636\) −5.65685 + 8.00000i −0.224309 + 0.317221i
\(637\) 0 0
\(638\) 11.3137i 0.447914i
\(639\) 11.9635 0.935500i 0.473268 0.0370078i
\(640\) −3.00000 5.19615i −0.118585 0.205396i
\(641\) −8.48528 + 14.6969i −0.335148 + 0.580494i −0.983513 0.180836i \(-0.942120\pi\)
0.648365 + 0.761330i \(0.275453\pi\)
\(642\) 1.65685 + 9.65685i 0.0653908 + 0.381126i
\(643\) 1.83013 + 6.83013i 0.0721732 + 0.269354i 0.992577 0.121614i \(-0.0388070\pi\)
−0.920404 + 0.390968i \(0.872140\pi\)
\(644\) −3.10583 11.5911i −0.122387 0.456754i
\(645\) 3.51472 + 20.4853i 0.138392 + 0.806607i
\(646\) 0 0
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) −24.6767 + 10.9571i −0.969394 + 0.430436i
\(649\) 16.0000i 0.628055i
\(650\) 0 0
\(651\) 10.0000 14.1421i 0.391931 0.554274i
\(652\) 1.36603 + 0.366025i 0.0534977 + 0.0143347i
\(653\) 12.2474 7.07107i 0.479280 0.276712i −0.240837 0.970566i \(-0.577422\pi\)
0.720116 + 0.693853i \(0.244088\pi\)
\(654\) −1.02494 2.22474i −0.0400785 0.0869944i
\(655\) 16.0000 16.0000i 0.625172 0.625172i
\(656\) −1.93185 + 0.517638i −0.0754261 + 0.0202104i
\(657\) −2.40130 3.49768i −0.0936837 0.136457i
\(658\) 4.00000 + 4.00000i 0.155936 + 0.155936i
\(659\) 2.44949 + 1.41421i 0.0954186 + 0.0550899i 0.546950 0.837165i \(-0.315789\pi\)
−0.451531 + 0.892255i \(0.649122\pi\)
\(660\) 1.27135 13.7980i 0.0494872 0.537085i
\(661\) −0.366025 + 1.36603i −0.0142367 + 0.0531322i −0.972679 0.232155i \(-0.925422\pi\)
0.958442 + 0.285287i \(0.0920890\pi\)
\(662\) 9.89949 0.384755
\(663\) 0 0
\(664\) −24.0000 −0.931381
\(665\) 1.03528 3.86370i 0.0401463 0.149828i
\(666\) −3.22474 2.75699i −0.124956 0.106831i
\(667\) 20.7846 + 12.0000i 0.804783 + 0.464642i
\(668\) −2.82843 2.82843i −0.109435 0.109435i
\(669\) −25.2766 9.33226i −0.977252 0.360806i
\(670\) 13.6603 3.66025i 0.527742 0.141408i
\(671\) 22.6274 22.6274i 0.873522 0.873522i
\(672\) −11.1237 + 5.12472i −0.429107 + 0.197690i
\(673\) 10.3923 6.00000i 0.400594 0.231283i −0.286146 0.958186i \(-0.592374\pi\)
0.686740 + 0.726903i \(0.259041\pi\)
\(674\) −5.79555 1.55291i −0.223236 0.0598160i
\(675\) 1.41421 5.00000i 0.0544331 0.192450i
\(676\) 0 0
\(677\) 22.6274i 0.869642i 0.900517 + 0.434821i \(0.143188\pi\)
−0.900517 + 0.434821i \(0.856812\pi\)
\(678\) 18.8366 15.6583i 0.723417 0.601352i
\(679\) −7.00000 12.1244i −0.268635 0.465290i
\(680\) 0 0
\(681\) −13.6569 + 2.34315i −0.523332 + 0.0897895i
\(682\) −7.32051 27.3205i −0.280317 1.04616i
\(683\) 1.03528 + 3.86370i 0.0396137 + 0.147840i 0.982900 0.184140i \(-0.0589499\pi\)
−0.943286 + 0.331980i \(0.892283\pi\)
\(684\) 1.82843 3.82843i 0.0699117 0.146384i
\(685\) 14.0000 24.2487i 0.534913 0.926496i
\(686\) −8.48528 14.6969i −0.323970 0.561132i
\(687\) −1.56583 1.88366i −0.0597400 0.0718662i
\(688\) 6.00000i 0.228748i
\(689\) 0 0
\(690\) 24.0000 + 16.9706i 0.913664 + 0.646058i
\(691\) −15.0263 4.02628i −0.571627 0.153167i −0.0385841 0.999255i \(-0.512285\pi\)
−0.533042 + 0.846088i \(0.678951\pi\)
\(692\) 7.34847 4.24264i 0.279347 0.161281i
\(693\) −16.6848 3.10102i −0.633804 0.117798i
\(694\) 10.0000 10.0000i 0.379595 0.379595i
\(695\) 7.72741 2.07055i 0.293117 0.0785405i
\(696\) 5.09032 13.7873i 0.192948 0.522605i
\(697\) 0 0
\(698\) 20.8207 + 12.0208i 0.788074 + 0.454995i
\(699\) −43.9048 4.04541i −1.66063 0.153011i
\(700\) 0.366025 1.36603i 0.0138345 0.0516309i
\(701\) 50.9117 1.92291 0.961454 0.274966i \(-0.0886666\pi\)
0.961454 + 0.274966i \(0.0886666\pi\)
\(702\) 0 0
\(703\) 2.00000 0.0754314
\(704\) −7.24693 + 27.0459i −0.273129 + 1.01933i
\(705\) 13.7980 + 1.27135i 0.519661 + 0.0478818i
\(706\) 22.5167 + 13.0000i 0.847426 + 0.489261i
\(707\) 8.48528 + 8.48528i 0.319122 + 0.319122i
\(708\) −2.39960 + 6.49938i −0.0901826 + 0.244262i
\(709\) 25.9545 6.95448i 0.974741 0.261181i 0.263913 0.964547i \(-0.414987\pi\)
0.710828 + 0.703365i \(0.248320\pi\)
\(710\) −5.65685 + 5.65685i −0.212298 + 0.212298i
\(711\) −29.4949 5.48188i −1.10615 0.205587i
\(712\) −36.3731 + 21.0000i −1.36314 + 0.787008i
\(713\) −57.9555 15.5291i −2.17045 0.581571i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 22.1441 + 26.6390i 0.826988 + 0.994853i
\(718\) 2.00000 + 3.46410i 0.0746393 + 0.129279i
\(719\) 12.7279 22.0454i 0.474671 0.822155i −0.524908 0.851159i \(-0.675900\pi\)
0.999579 + 0.0290041i \(0.00923357\pi\)
\(720\) 2.58579 5.41421i 0.0963666 0.201776i
\(721\) 2.19615 + 8.19615i 0.0817890 + 0.305241i
\(722\) 4.39992 + 16.4207i 0.163748 + 0.611117i
\(723\) −41.0416 + 7.04163i −1.52635 + 0.261881i
\(724\) 0 0
\(725\) 1.41421 + 2.44949i 0.0525226 + 0.0909718i
\(726\) −6.65976 + 5.53603i −0.247167 + 0.205461i
\(727\) 48.0000i 1.78022i 0.455744 + 0.890111i \(0.349373\pi\)
−0.455744 + 0.890111i \(0.650627\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 2.73205 + 0.732051i 0.101118 + 0.0270944i
\(731\) 0 0
\(732\) −12.5851 + 5.79796i −0.465157 + 0.214299i
\(733\) 5.00000 5.00000i 0.184679 0.184679i −0.608712 0.793391i \(-0.708314\pi\)
0.793391 + 0.608712i \(0.208314\pi\)
\(734\) 7.72741 2.07055i 0.285224 0.0764255i
\(735\) −16.2484 5.99900i −0.599333 0.221277i
\(736\) 30.0000 + 30.0000i 1.10581 + 1.10581i
\(737\) 24.4949 + 14.1421i 0.902281 + 0.520932i
\(738\) 4.56048 + 3.89898i 0.167874 + 0.143523i
\(739\) −0.366025 + 1.36603i −0.0134645 + 0.0502501i −0.972331 0.233606i \(-0.924947\pi\)
0.958867 + 0.283857i \(0.0916139\pi\)
\(740\) −2.82843 −0.103975
\(741\) 0 0
\(742\) −8.00000 −0.293689
\(743\) −4.14110 + 15.4548i −0.151922 + 0.566982i 0.847427 + 0.530912i \(0.178151\pi\)
−0.999349 + 0.0360700i \(0.988516\pi\)
\(744\) −3.37117 + 36.5874i −0.123593 + 1.34136i
\(745\) −3.46410 2.00000i −0.126915 0.0732743i
\(746\) 2.82843 + 2.82843i 0.103556 + 0.103556i
\(747\) 13.5838 + 19.7859i 0.497006 + 0.723927i
\(748\) 0 0
\(749\) 5.65685 5.65685i 0.206697 0.206697i
\(750\) 8.69694 + 18.8776i 0.317567 + 0.689312i
\(751\) −25.9808 + 15.0000i −0.948051 + 0.547358i −0.892475 0.451097i \(-0.851033\pi\)
−0.0555764 + 0.998454i \(0.517700\pi\)
\(752\) −3.86370 1.03528i −0.140895 0.0377526i
\(753\) −25.4558 + 36.0000i −0.927663 + 1.31191i
\(754\) 0 0
\(755\) 2.82843i 0.102937i
\(756\) 6.31249 + 3.76198i 0.229583 + 0.136822i
\(757\) 8.00000 + 13.8564i 0.290765 + 0.503620i 0.973991 0.226587i \(-0.0727569\pi\)
−0.683226 + 0.730207i \(0.739424\pi\)
\(758\) −13.4350 + 23.2702i −0.487982 + 0.845210i
\(759\) 9.94113 + 57.9411i 0.360840 + 2.10313i
\(760\) 2.19615 + 8.19615i 0.0796628 + 0.297306i
\(761\) −12.9410 48.2963i −0.469109 1.75074i −0.642894 0.765955i \(-0.722266\pi\)
0.173784 0.984784i \(-0.444400\pi\)
\(762\) 0 0
\(763\) −1.00000 + 1.73205i −0.0362024 + 0.0627044i
\(764\) 1.41421 + 2.44949i 0.0511645 + 0.0886194i
\(765\) 0 0
\(766\) 16.0000i 0.578103i
\(767\) 0 0
\(768\) 17.0000 24.0416i 0.613435 0.867528i
\(769\) 17.7583 + 4.75833i 0.640382 + 0.171590i 0.564376 0.825518i \(-0.309117\pi\)
0.0760054 + 0.997107i \(0.475783\pi\)
\(770\) 9.79796 5.65685i 0.353094 0.203859i
\(771\) −6.14966 13.3485i −0.221475 0.480733i
\(772\) −19.0000 + 19.0000i −0.683825 + 0.683825i
\(773\) −13.5230 + 3.62347i −0.486387 + 0.130327i −0.493675 0.869646i \(-0.664347\pi\)
0.00728800 + 0.999973i \(0.497680\pi\)
\(774\) −14.8394 + 10.1879i −0.533391 + 0.366195i
\(775\) −5.00000 5.00000i −0.179605 0.179605i
\(776\) 25.7196 + 14.8492i 0.923281 + 0.533057i
\(777\) −0.317837 + 3.44949i −0.0114023 + 0.123750i
\(778\) −4.39230 + 16.3923i −0.157472 + 0.587693i
\(779\) −2.82843 −0.101339
\(780\) 0 0
\(781\) −16.0000 −0.572525
\(782\) 0 0
\(783\) −14.2474 + 3.60697i −0.509162 + 0.128902i
\(784\) 4.33013 + 2.50000i 0.154647 + 0.0892857i
\(785\) 19.7990 + 19.7990i 0.706656 + 0.706656i
\(786\) 18.3830 + 6.78710i 0.655700 + 0.242088i
\(787\) 25.9545 6.95448i 0.925177 0.247901i 0.235380 0.971903i \(-0.424366\pi\)
0.689797 + 0.724003i \(0.257700\pi\)
\(788\) −15.5563 + 15.5563i −0.554172 + 0.554172i
\(789\) 35.5959 16.3991i 1.26725 0.583824i
\(790\) 17.3205 10.0000i 0.616236 0.355784i
\(791\) −19.3185 5.17638i −0.686887 0.184051i
\(792\) 33.9411 12.0000i 1.20605 0.426401i
\(793\) 0 0
\(794\) 24.0416i 0.853206i
\(795\) −15.0693 + 12.5266i −0.534453 + 0.444273i
\(796\) 0 0
\(797\) 8.48528 14.6969i 0.300564 0.520592i −0.675700 0.737177i \(-0.736158\pi\)
0.976264 + 0.216585i \(0.0694917\pi\)
\(798\) 3.41421 0.585786i 0.120862 0.0207366i
\(799\) 0 0
\(800\) 1.29410 + 4.82963i 0.0457532 + 0.170753i
\(801\) 37.8995 + 18.1005i 1.33911 + 0.639550i
\(802\) 11.0000 19.0526i 0.388424 0.672769i
\(803\) 2.82843 + 4.89898i 0.0998130 + 0.172881i
\(804\) −7.82913 9.41832i −0.276112 0.332158i
\(805\) 24.0000i 0.845889i
\(806\) 0 0
\(807\) 28.0000 + 19.7990i 0.985647 + 0.696957i
\(808\) −24.5885 6.58846i −0.865019 0.231781i
\(809\) 26.9444 15.5563i 0.947314 0.546932i 0.0550686 0.998483i \(-0.482462\pi\)
0.892246 + 0.451550i \(0.149129\pi\)
\(810\) −17.7812 + 2.79796i −0.624768 + 0.0983103i
\(811\) −1.00000 + 1.00000i −0.0351147 + 0.0351147i −0.724446 0.689331i \(-0.757904\pi\)
0.689331 + 0.724446i \(0.257904\pi\)
\(812\) −3.86370 + 1.03528i −0.135589 + 0.0363311i
\(813\) −16.1194 + 43.6597i −0.565331 + 1.53121i
\(814\) 4.00000 + 4.00000i 0.140200 + 0.140200i
\(815\) 2.44949 + 1.41421i 0.0858019 + 0.0495377i
\(816\) 0 0
\(817\) 2.19615 8.19615i 0.0768336 0.286747i
\(818\) −32.5269 −1.13728
\(819\) 0 0
\(820\) 4.00000 0.139686
\(821\) −2.58819 + 9.65926i −0.0903285 + 0.337110i −0.996270 0.0862928i \(-0.972498\pi\)
0.905941 + 0.423403i \(0.139165\pi\)
\(822\) 24.1464 + 2.22486i 0.842203 + 0.0776009i
\(823\) 25.9808 + 15.0000i 0.905632 + 0.522867i 0.879023 0.476779i \(-0.158196\pi\)
0.0266091 + 0.999646i \(0.491529\pi\)
\(824\) −12.7279 12.7279i −0.443398 0.443398i
\(825\) −2.39960 + 6.49938i −0.0835434 + 0.226279i
\(826\) −5.46410 + 1.46410i −0.190120 + 0.0509426i
\(827\) −22.6274 + 22.6274i −0.786832 + 0.786832i −0.980974 0.194141i \(-0.937808\pi\)
0.194141 + 0.980974i \(0.437808\pi\)
\(828\) 4.65153 25.0273i 0.161652 0.869757i
\(829\) −15.5885 + 9.00000i −0.541409 + 0.312583i −0.745650 0.666338i \(-0.767861\pi\)
0.204240 + 0.978921i \(0.434528\pi\)
\(830\) −15.4548 4.14110i −0.536444 0.143740i
\(831\) −16.9706 12.0000i −0.588702 0.416275i
\(832\) 0 0
\(833\) 0 0
\(834\) 4.42883 + 5.32780i 0.153358 + 0.184487i
\(835\) −4.00000 6.92820i −0.138426 0.239760i
\(836\) −2.82843 + 4.89898i −0.0978232 + 0.169435i
\(837\) 32.0711 17.9289i 1.10854 0.619715i
\(838\) −2.92820 10.9282i −0.101153 0.377509i
\(839\) 1.03528 + 3.86370i 0.0357417 + 0.133390i 0.981491 0.191506i \(-0.0613373\pi\)
−0.945750 + 0.324896i \(0.894671\pi\)
\(840\) −14.4853 + 2.48528i −0.499790 + 0.0857504i
\(841\) −10.5000 + 18.1865i −0.362069 + 0.627122i
\(842\) −17.6777 30.6186i −0.609213 1.05519i
\(843\) −18.6473 + 15.5009i −0.642248 + 0.533879i
\(844\) 14.0000i 0.481900i
\(845\) 0 0
\(846\) 4.00000 + 11.3137i 0.137523 + 0.388973i
\(847\) 6.83013 + 1.83013i 0.234686 + 0.0628839i
\(848\) 4.89898 2.82843i 0.168232 0.0971286i
\(849\) −18.8776 + 8.69694i −0.647877 + 0.298478i
\(850\) 0 0
\(851\) 11.5911 3.10583i 0.397338 0.106466i
\(852\) 6.49938 + 2.39960i 0.222665 + 0.0822090i
\(853\) −37.0000 37.0000i −1.26686 1.26686i −0.947703 0.319152i \(-0.896602\pi\)
−0.319152 0.947703i \(-0.603398\pi\)
\(854\) −9.79796 5.65685i −0.335279 0.193574i
\(855\) 5.51399 6.44949i 0.188574 0.220568i
\(856\) −4.39230 + 16.3923i −0.150126 + 0.560277i
\(857\) −8.48528 −0.289852 −0.144926 0.989443i \(-0.546294\pi\)
−0.144926 + 0.989443i \(0.546294\pi\)
\(858\) 0 0
\(859\) 14.0000 0.477674 0.238837 0.971060i \(-0.423234\pi\)
0.238837 + 0.971060i \(0.423234\pi\)
\(860\) −3.10583 + 11.5911i −0.105908 + 0.395254i
\(861\) 0.449490 4.87832i 0.0153186 0.166253i
\(862\) 27.7128 + 16.0000i 0.943902 + 0.544962i
\(863\) −2.82843 2.82843i −0.0962808 0.0962808i 0.657326 0.753607i \(-0.271688\pi\)
−0.753607 + 0.657326i \(0.771688\pi\)
\(864\) −25.9783 0.359651i −0.883799 0.0122356i
\(865\) 16.3923 4.39230i 0.557355 0.149343i
\(866\) −12.7279 + 12.7279i −0.432512 + 0.432512i
\(867\) 12.3207 + 26.7432i 0.418432 + 0.908248i
\(868\) 8.66025 5.00000i 0.293948 0.169711i
\(869\) 38.6370 + 10.3528i 1.31067 + 0.351193i
\(870\) 5.65685 8.00000i 0.191785 0.271225i
\(871\) 0 0
\(872\) 4.24264i 0.143674i
\(873\) −2.31524 29.6081i −0.0783592 1.00208i
\(874\) −6.00000 10.3923i −0.202953 0.351525i
\(875\) 8.48528 14.6969i 0.286855 0.496847i
\(876\) −0.414214 2.41421i −0.0139950 0.0815687i
\(877\) −4.75833 17.7583i −0.160677 0.599656i −0.998552 0.0537936i \(-0.982869\pi\)
0.837875 0.545863i \(-0.183798\pi\)
\(878\) 7.76457 + 28.9778i 0.262042 + 0.977953i
\(879\) −4.10051 23.8995i −0.138307 0.806110i
\(880\) −4.00000 + 6.92820i −0.134840 + 0.233550i
\(881\) −12.7279 22.0454i −0.428815 0.742729i 0.567954 0.823061i \(-0.307735\pi\)
−0.996768 + 0.0803319i \(0.974402\pi\)
\(882\) −1.16938 14.9543i −0.0393749 0.503539i
\(883\) 36.0000i 1.21150i −0.795656 0.605748i \(-0.792874\pi\)
0.795656 0.605748i \(-0.207126\pi\)
\(884\) 0 0
\(885\) −8.00000 + 11.3137i −0.268917 + 0.380306i
\(886\) 27.3205 + 7.32051i 0.917850 + 0.245937i
\(887\) 12.2474 7.07107i 0.411229 0.237423i −0.280089 0.959974i \(-0.590364\pi\)
0.691318 + 0.722551i \(0.257031\pi\)
\(888\) −3.07483 6.67423i −0.103185 0.223973i
\(889\) 0 0
\(890\) −27.0459 + 7.24693i −0.906581 + 0.242918i
\(891\) −29.1033 21.1895i −0.974999 0.709876i
\(892\) −11.0000 11.0000i −0.368307 0.368307i
\(893\) −4.89898 2.82843i −0.163938 0.0946497i
\(894\) 0.317837 3.44949i 0.0106301 0.115368i
\(895\) 0 0
\(896\) −4.24264 −0.141737
\(897\) 0 0
\(898\) −22.0000 −0.734150
\(899\) −5.17638 + 19.3185i −0.172642 + 0.644309i
\(900\) 1.94949 2.28024i 0.0649830 0.0760080i
\(901\) 0 0
\(902\) −5.65685 5.65685i −0.188353 0.188353i
\(903\) 13.7873 + 5.09032i 0.458811 + 0.169395i
\(904\) 40.9808 10.9808i 1.36300 0.365215i
\(905\) 0 0
\(906\) 2.22474 1.02494i 0.0739122 0.0340515i
\(907\) 10.3923 6.00000i 0.345071 0.199227i −0.317441 0.948278i \(-0.602824\pi\)
0.662512 + 0.749051i \(0.269490\pi\)
\(908\) −7.72741 2.07055i −0.256443 0.0687137i
\(909\) 8.48528 + 24.0000i 0.281439 + 0.796030i
\(910\) 0 0
\(911\) 48.0833i 1.59307i 0.604593 + 0.796535i \(0.293336\pi\)
−0.604593 + 0.796535i \(0.706664\pi\)
\(912\) −1.88366 + 1.56583i −0.0623743 + 0.0518497i
\(913\) −16.0000 27.7128i −0.529523 0.917160i
\(914\) 20.5061 35.5176i 0.678281 1.17482i
\(915\) −27.3137 + 4.68629i −0.902963 + 0.154924i
\(916\) −0.366025 1.36603i −0.0120938 0.0451347i
\(917\) −4.14110 15.4548i −0.136751 0.510363i
\(918\) 0 0
\(919\) 17.0000 29.4449i 0.560778 0.971296i −0.436650 0.899631i \(-0.643835\pi\)
0.997429 0.0716652i \(-0.0228313\pi\)
\(920\) 25.4558 + 44.0908i 0.839254 + 1.45363i
\(921\) 26.6190 + 32.0223i 0.877127 + 1.05517i
\(922\) 10.0000i 0.329332i
\(923\) 0 0
\(924\) −8.00000 5.65685i −0.263181 0.186097i
\(925\) 1.36603 + 0.366025i 0.0449146 + 0.0120348i
\(926\) −20.8207 + 12.0208i −0.684209 + 0.395029i
\(927\) −3.28913 + 17.6969i −0.108029 + 0.581244i
\(928\) 10.0000 10.0000i 0.328266 0.328266i
\(929\) 44.4326 11.9057i 1.45779 0.390613i 0.559061 0.829126i \(-0.311162\pi\)
0.898725 + 0.438514i \(0.144495\pi\)
\(930\) −8.48387 + 22.9788i −0.278197 + 0.753504i
\(931\) 5.00000 + 5.00000i 0.163868 + 0.163868i
\(932\) −22.0454 12.7279i −0.722121 0.416917i
\(933\) 14.6349 + 1.34847i 0.479127 + 0.0441469i
\(934\) 6.58846 24.5885i 0.215581 0.804559i
\(935\) 0 0
\(936\) 0 0
\(937\) −52.0000 −1.69877 −0.849383 0.527777i \(-0.823026\pi\)
−0.849383 + 0.527777i \(0.823026\pi\)
\(938\) 2.58819 9.65926i 0.0845074 0.315386i
\(939\) 13.7980 + 1.27135i 0.450279 + 0.0414889i
\(940\) 6.92820 + 4.00000i 0.225973 + 0.130466i
\(941\) 26.8701 + 26.8701i 0.875939 + 0.875939i 0.993112 0.117173i \(-0.0373831\pi\)
−0.117173 + 0.993112i \(0.537383\pi\)
\(942\) −8.39861 + 22.7478i −0.273641 + 0.741164i
\(943\) −16.3923 + 4.39230i −0.533807 + 0.143033i
\(944\) 2.82843 2.82843i 0.0920575 0.0920575i
\(945\) 10.2474 + 10.5352i 0.333350 + 0.342709i
\(946\) 20.7846 12.0000i 0.675766 0.390154i
\(947\) 30.9096 + 8.28221i 1.00443 + 0.269136i 0.723299 0.690535i \(-0.242625\pi\)
0.281128 + 0.959670i \(0.409291\pi\)
\(948\) −14.1421 10.0000i −0.459315 0.324785i
\(949\) 0 0
\(950\) 1.41421i 0.0458831i
\(951\) −11.0721 13.3195i −0.359036 0.431915i
\(952\) 0 0
\(953\) −12.7279 + 22.0454i −0.412298 + 0.714121i −0.995141 0.0984642i \(-0.968607\pi\)
0.582843 + 0.812585i \(0.301940\pi\)
\(954\) −15.3137 7.31371i −0.495800 0.236790i
\(955\) 1.46410 + 5.46410i 0.0473772 + 0.176814i
\(956\) 5.17638 + 19.3185i 0.167416 + 0.624805i
\(957\) 19.3137 3.31371i 0.624324 0.107117i
\(958\) −16.0000 + 27.7128i −0.516937 + 0.895360i
\(959\) −9.89949 17.1464i −0.319671 0.553687i
\(960\) 18.6473 15.5009i 0.601840 0.500289i
\(961\) 19.0000i 0.612903i
\(962\) 0 0
\(963\) 16.0000 5.65685i 0.515593 0.182290i
\(964\) −23.2224 6.22243i −0.747944 0.200411i
\(965\) −46.5403 + 26.8701i −1.49819 + 0.864978i
\(966\) 18.8776 8.69694i 0.607376 0.279819i
\(967\) 23.0000 23.0000i 0.739630 0.739630i −0.232876 0.972506i \(-0.574814\pi\)
0.972506 + 0.232876i \(0.0748137\pi\)
\(968\) −14.4889 + 3.88229i −0.465690 + 0.124781i
\(969\) 0 0
\(970\) 14.0000 + 14.0000i 0.449513 + 0.449513i
\(971\) −26.9444 15.5563i −0.864687 0.499227i 0.000892350 1.00000i \(-0.499716\pi\)
−0.865579 + 0.500773i \(0.833049\pi\)
\(972\) 8.64420 + 12.9722i 0.277263 + 0.416083i
\(973\) 1.46410 5.46410i 0.0469369 0.175171i
\(974\) 26.8701 0.860972
\(975\) 0 0
\(976\) 8.00000 0.256074
\(977\) 9.83512 36.7052i 0.314653 1.17430i −0.609658 0.792664i \(-0.708693\pi\)
0.924312 0.381638i \(-0.124640\pi\)
\(978\) −0.224745 + 2.43916i −0.00718655 + 0.0779957i
\(979\) −48.4974 28.0000i −1.54998 0.894884i
\(980\) −7.07107 7.07107i −0.225877 0.225877i
\(981\) −3.49768 + 2.40130i −0.111672 + 0.0766677i
\(982\) −40.9808 + 10.9808i −1.30775 + 0.350410i
\(983\) 2.82843 2.82843i 0.0902128 0.0902128i −0.660560 0.750773i \(-0.729681\pi\)
0.750773 + 0.660560i \(0.229681\pi\)
\(984\) 4.34847 + 9.43879i 0.138624 + 0.300898i
\(985\) −38.1051 + 22.0000i −1.21413 + 0.700978i
\(986\) 0 0
\(987\) 5.65685 8.00000i 0.180060 0.254643i
\(988\) 0 0
\(989\) 50.9117i 1.61890i
\(990\) 23.9270 1.87100i 0.760449 0.0594643i
\(991\) 8.00000 + 13.8564i 0.254128 + 0.440163i 0.964658 0.263504i \(-0.0848781\pi\)
−0.710530 + 0.703667i \(0.751545\pi\)
\(992\) −17.6777 + 30.6186i −0.561267 + 0.972142i
\(993\) −2.89949 16.8995i −0.0920127 0.536289i
\(994\) 1.46410 + 5.46410i 0.0464385 + 0.173311i
\(995\) 0 0
\(996\) 2.34315 + 13.6569i 0.0742454 + 0.432734i
\(997\) −13.0000 + 22.5167i −0.411714 + 0.713110i −0.995077 0.0991016i \(-0.968403\pi\)
0.583363 + 0.812211i \(0.301736\pi\)
\(998\) 16.2635 + 28.1691i 0.514811 + 0.891678i
\(999\) −3.76198 + 6.31249i −0.119024 + 0.199718i
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 507.2.k.i.80.1 8
3.2 odd 2 inner 507.2.k.i.80.2 8
13.2 odd 12 39.2.f.a.8.1 yes 4
13.3 even 3 507.2.f.a.239.1 4
13.4 even 6 507.2.k.j.188.1 8
13.5 odd 4 507.2.k.j.89.2 8
13.6 odd 12 507.2.k.j.488.1 8
13.7 odd 12 inner 507.2.k.i.488.2 8
13.8 odd 4 inner 507.2.k.i.89.1 8
13.9 even 3 inner 507.2.k.i.188.2 8
13.10 even 6 39.2.f.a.5.2 yes 4
13.11 odd 12 507.2.f.a.437.2 4
13.12 even 2 507.2.k.j.80.2 8
39.2 even 12 39.2.f.a.8.2 yes 4
39.5 even 4 507.2.k.j.89.1 8
39.8 even 4 inner 507.2.k.i.89.2 8
39.11 even 12 507.2.f.a.437.1 4
39.17 odd 6 507.2.k.j.188.2 8
39.20 even 12 inner 507.2.k.i.488.1 8
39.23 odd 6 39.2.f.a.5.1 4
39.29 odd 6 507.2.f.a.239.2 4
39.32 even 12 507.2.k.j.488.2 8
39.35 odd 6 inner 507.2.k.i.188.1 8
39.38 odd 2 507.2.k.j.80.1 8
52.15 even 12 624.2.bf.d.593.1 4
52.23 odd 6 624.2.bf.d.161.1 4
65.2 even 12 975.2.n.d.749.1 4
65.23 odd 12 975.2.n.d.824.2 4
65.28 even 12 975.2.n.c.749.2 4
65.49 even 6 975.2.o.j.551.1 4
65.54 odd 12 975.2.o.j.476.2 4
65.62 odd 12 975.2.n.c.824.1 4
156.23 even 6 624.2.bf.d.161.2 4
156.119 odd 12 624.2.bf.d.593.2 4
195.2 odd 12 975.2.n.d.749.2 4
195.23 even 12 975.2.n.d.824.1 4
195.62 even 12 975.2.n.c.824.2 4
195.119 even 12 975.2.o.j.476.1 4
195.158 odd 12 975.2.n.c.749.1 4
195.179 odd 6 975.2.o.j.551.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.f.a.5.1 4 39.23 odd 6
39.2.f.a.5.2 yes 4 13.10 even 6
39.2.f.a.8.1 yes 4 13.2 odd 12
39.2.f.a.8.2 yes 4 39.2 even 12
507.2.f.a.239.1 4 13.3 even 3
507.2.f.a.239.2 4 39.29 odd 6
507.2.f.a.437.1 4 39.11 even 12
507.2.f.a.437.2 4 13.11 odd 12
507.2.k.i.80.1 8 1.1 even 1 trivial
507.2.k.i.80.2 8 3.2 odd 2 inner
507.2.k.i.89.1 8 13.8 odd 4 inner
507.2.k.i.89.2 8 39.8 even 4 inner
507.2.k.i.188.1 8 39.35 odd 6 inner
507.2.k.i.188.2 8 13.9 even 3 inner
507.2.k.i.488.1 8 39.20 even 12 inner
507.2.k.i.488.2 8 13.7 odd 12 inner
507.2.k.j.80.1 8 39.38 odd 2
507.2.k.j.80.2 8 13.12 even 2
507.2.k.j.89.1 8 39.5 even 4
507.2.k.j.89.2 8 13.5 odd 4
507.2.k.j.188.1 8 13.4 even 6
507.2.k.j.188.2 8 39.17 odd 6
507.2.k.j.488.1 8 13.6 odd 12
507.2.k.j.488.2 8 39.32 even 12
624.2.bf.d.161.1 4 52.23 odd 6
624.2.bf.d.161.2 4 156.23 even 6
624.2.bf.d.593.1 4 52.15 even 12
624.2.bf.d.593.2 4 156.119 odd 12
975.2.n.c.749.1 4 195.158 odd 12
975.2.n.c.749.2 4 65.28 even 12
975.2.n.c.824.1 4 65.62 odd 12
975.2.n.c.824.2 4 195.62 even 12
975.2.n.d.749.1 4 65.2 even 12
975.2.n.d.749.2 4 195.2 odd 12
975.2.n.d.824.1 4 195.23 even 12
975.2.n.d.824.2 4 65.23 odd 12
975.2.o.j.476.1 4 195.119 even 12
975.2.o.j.476.2 4 65.54 odd 12
975.2.o.j.551.1 4 65.49 even 6
975.2.o.j.551.2 4 195.179 odd 6