Properties

Label 507.2.k.i.89.2
Level $507$
Weight $2$
Character 507.89
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 89.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 507.89
Dual form 507.2.k.i.188.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 + 0.258819i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.41421 - 1.41421i) q^{5} +(-1.10721 + 1.33195i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\) \(q+(0.965926 + 0.258819i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.41421 - 1.41421i) q^{5} +(-1.10721 + 1.33195i) q^{6} +(-0.366025 - 1.36603i) q^{7} +(-2.12132 - 2.12132i) q^{8} +(-1.94949 - 2.28024i) q^{9} +(1.73205 - 1.00000i) q^{10} +(1.03528 - 3.86370i) q^{11} +(1.41421 - 1.00000i) q^{12} -1.41421i q^{14} +(1.19980 + 3.24969i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.29289 - 2.70711i) q^{18} +(1.36603 - 0.366025i) q^{19} +(-1.93185 + 0.517638i) q^{20} +(2.41421 + 0.414214i) q^{21} +(2.00000 - 3.46410i) q^{22} +(-4.24264 - 7.34847i) q^{23} +(4.87453 - 1.79970i) q^{24} +1.00000i q^{25} +(5.00000 - 1.41421i) q^{27} +(-0.366025 + 1.36603i) q^{28} +(2.44949 - 1.41421i) q^{29} +(0.317837 + 3.44949i) q^{30} +(5.00000 + 5.00000i) q^{31} +(1.29410 + 4.82963i) q^{32} +(5.32780 + 4.42883i) q^{33} +(-2.44949 - 1.41421i) q^{35} +(0.548188 + 2.94949i) q^{36} +(1.36603 + 0.366025i) q^{37} +1.41421 q^{38} -6.00000 q^{40} +(-1.93185 - 0.517638i) q^{41} +(2.22474 + 1.02494i) q^{42} +(-5.19615 - 3.00000i) q^{43} +(-2.82843 + 2.82843i) q^{44} +(-5.98174 - 0.467750i) q^{45} +(-2.19615 - 8.19615i) q^{46} +(2.82843 + 2.82843i) q^{47} +(1.72474 - 0.158919i) q^{48} +(4.33013 - 2.50000i) q^{49} +(-0.258819 + 0.965926i) q^{50} -5.65685i q^{53} +(5.19565 - 0.0719302i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(-2.12132 + 3.67423i) q^{56} +(-0.414214 + 2.41421i) q^{57} +(2.73205 - 0.732051i) q^{58} +(-3.86370 + 1.03528i) q^{59} +(0.585786 - 3.41421i) q^{60} +(-4.00000 + 6.92820i) q^{61} +(3.53553 + 6.12372i) q^{62} +(-2.40130 + 3.49768i) q^{63} +7.00000i q^{64} +(4.00000 + 5.65685i) q^{66} +(1.83013 - 6.83013i) q^{67} +(14.6349 - 1.34847i) q^{69} +(-2.00000 - 2.00000i) q^{70} +(-1.03528 - 3.86370i) q^{71} +(-0.701625 + 8.97261i) q^{72} +(-1.00000 + 1.00000i) q^{73} +(1.22474 + 0.707107i) q^{74} +(-1.57313 - 0.724745i) q^{75} +(-1.36603 - 0.366025i) q^{76} -5.65685 q^{77} -10.0000 q^{79} +(-1.93185 - 0.517638i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(-1.73205 - 1.00000i) q^{82} +(5.65685 - 5.65685i) q^{83} +(-1.88366 - 1.56583i) q^{84} +(-4.24264 - 4.24264i) q^{86} +(0.449490 + 4.87832i) q^{87} +(-10.3923 + 6.00000i) q^{88} +(-3.62347 + 13.5230i) q^{89} +(-5.65685 - 2.00000i) q^{90} +8.48528i q^{92} +(-11.4894 + 4.24194i) q^{93} +(2.00000 + 3.46410i) q^{94} +(1.41421 - 2.44949i) q^{95} +(-8.53553 - 1.46447i) q^{96} +(9.56218 - 2.56218i) q^{97} +(4.82963 - 1.29410i) 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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 + 0.258819i 0.683013 + 0.183013i 0.583609 0.812035i \(-0.301640\pi\)
0.0994033 + 0.995047i \(0.468307\pi\)
\(3\) −0.724745 + 1.57313i −0.418432 + 0.908248i
\(4\) −0.866025 0.500000i −0.433013 0.250000i
\(5\) 1.41421 1.41421i 0.632456 0.632456i −0.316228 0.948683i \(-0.602416\pi\)
0.948683 + 0.316228i \(0.102416\pi\)
\(6\) −1.10721 + 1.33195i −0.452015 + 0.543767i
\(7\) −0.366025 1.36603i −0.138345 0.516309i −0.999962 0.00875026i \(-0.997215\pi\)
0.861617 0.507559i \(-0.169452\pi\)
\(8\) −2.12132 2.12132i −0.750000 0.750000i
\(9\) −1.94949 2.28024i −0.649830 0.760080i
\(10\) 1.73205 1.00000i 0.547723 0.316228i
\(11\) 1.03528 3.86370i 0.312148 1.16495i −0.614468 0.788941i \(-0.710630\pi\)
0.926616 0.376009i \(-0.122704\pi\)
\(12\) 1.41421 1.00000i 0.408248 0.288675i
\(13\) 0 0
\(14\) 1.41421i 0.377964i
\(15\) 1.19980 + 3.24969i 0.309787 + 0.839066i
\(16\) −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
\(19\) 1.36603 0.366025i 0.313388 0.0839720i −0.0986970 0.995118i \(-0.531467\pi\)
0.412085 + 0.911146i \(0.364801\pi\)
\(20\) −1.93185 + 0.517638i −0.431975 + 0.115747i
\(21\) 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 \(-0.512271\pi\)
\(24\) 4.87453 1.79970i 0.995010 0.367362i
\(25\) 1.00000i 0.200000i
\(26\) 0 0
\(27\) 5.00000 1.41421i 0.962250 0.272166i
\(28\) −0.366025 + 1.36603i −0.0691723 + 0.258155i
\(29\) 2.44949 1.41421i 0.454859 0.262613i −0.255021 0.966935i \(-0.582082\pi\)
0.709880 + 0.704323i \(0.248749\pi\)
\(30\) 0.317837 + 3.44949i 0.0580289 + 0.629788i
\(31\) 5.00000 + 5.00000i 0.898027 + 0.898027i 0.995261 0.0972349i \(-0.0309998\pi\)
−0.0972349 + 0.995261i \(0.531000\pi\)
\(32\) 1.29410 + 4.82963i 0.228766 + 0.853766i
\(33\) 5.32780 + 4.42883i 0.927452 + 0.770960i
\(34\) 0 0
\(35\) −2.44949 1.41421i −0.414039 0.239046i
\(36\) 0.548188 + 2.94949i 0.0913647 + 0.491582i
\(37\) 1.36603 + 0.366025i 0.224573 + 0.0601742i 0.369351 0.929290i \(-0.379580\pi\)
−0.144778 + 0.989464i \(0.546247\pi\)
\(38\) 1.41421 0.229416
\(39\) 0 0
\(40\) −6.00000 −0.948683
\(41\) −1.93185 0.517638i −0.301705 0.0808415i 0.104791 0.994494i \(-0.466583\pi\)
−0.406496 + 0.913653i \(0.633249\pi\)
\(42\) 2.22474 + 1.02494i 0.343286 + 0.158152i
\(43\) −5.19615 3.00000i −0.792406 0.457496i 0.0484030 0.998828i \(-0.484587\pi\)
−0.840809 + 0.541332i \(0.817920\pi\)
\(44\) −2.82843 + 2.82843i −0.426401 + 0.426401i
\(45\) −5.98174 0.467750i −0.891705 0.0697281i
\(46\) −2.19615 8.19615i −0.323805 1.20846i
\(47\) 2.82843 + 2.82843i 0.412568 + 0.412568i 0.882632 0.470064i \(-0.155769\pi\)
−0.470064 + 0.882632i \(0.655769\pi\)
\(48\) 1.72474 0.158919i 0.248945 0.0229379i
\(49\) 4.33013 2.50000i 0.618590 0.357143i
\(50\) −0.258819 + 0.965926i −0.0366025 + 0.136603i
\(51\) 0 0
\(52\) 0 0
\(53\) 5.65685i 0.777029i −0.921443 0.388514i \(-0.872988\pi\)
0.921443 0.388514i \(-0.127012\pi\)
\(54\) 5.19565 0.0719302i 0.707039 0.00978846i
\(55\) −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
\(58\) 2.73205 0.732051i 0.358736 0.0961230i
\(59\) −3.86370 + 1.03528i −0.503011 + 0.134781i −0.501397 0.865217i \(-0.667180\pi\)
−0.00161411 + 0.999999i \(0.500514\pi\)
\(60\) 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
\(63\) −2.40130 + 3.49768i −0.302536 + 0.440666i
\(64\) 7.00000i 0.875000i
\(65\) 0 0
\(66\) 4.00000 + 5.65685i 0.492366 + 0.696311i
\(67\) 1.83013 6.83013i 0.223586 0.834433i −0.759381 0.650647i \(-0.774498\pi\)
0.982966 0.183786i \(-0.0588354\pi\)
\(68\) 0 0
\(69\) 14.6349 1.34847i 1.76184 0.162337i
\(70\) −2.00000 2.00000i −0.239046 0.239046i
\(71\) −1.03528 3.86370i −0.122865 0.458537i 0.876890 0.480691i \(-0.159614\pi\)
−0.999755 + 0.0221541i \(0.992948\pi\)
\(72\) −0.701625 + 8.97261i −0.0826873 + 1.05743i
\(73\) −1.00000 + 1.00000i −0.117041 + 0.117041i −0.763202 0.646160i \(-0.776374\pi\)
0.646160 + 0.763202i \(0.276374\pi\)
\(74\) 1.22474 + 0.707107i 0.142374 + 0.0821995i
\(75\) −1.57313 0.724745i −0.181650 0.0836863i
\(76\) −1.36603 0.366025i −0.156694 0.0419860i
\(77\) −5.65685 −0.644658
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −1.93185 0.517638i −0.215988 0.0578737i
\(81\) −1.39898 + 8.89060i −0.155442 + 0.987845i
\(82\) −1.73205 1.00000i −0.191273 0.110432i
\(83\) 5.65685 5.65685i 0.620920 0.620920i −0.324846 0.945767i \(-0.605313\pi\)
0.945767 + 0.324846i \(0.105313\pi\)
\(84\) −1.88366 1.56583i −0.205525 0.170846i
\(85\) 0 0
\(86\) −4.24264 4.24264i −0.457496 0.457496i
\(87\) 0.449490 + 4.87832i 0.0481904 + 0.523010i
\(88\) −10.3923 + 6.00000i −1.10782 + 0.639602i
\(89\) −3.62347 + 13.5230i −0.384087 + 1.43343i 0.455515 + 0.890228i \(0.349455\pi\)
−0.839601 + 0.543203i \(0.817211\pi\)
\(90\) −5.65685 2.00000i −0.596285 0.210819i
\(91\) 0 0
\(92\) 8.48528i 0.884652i
\(93\) −11.4894 + 4.24194i −1.19139 + 0.439868i
\(94\) 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
\(97\) 9.56218 2.56218i 0.970892 0.260150i 0.261688 0.965153i \(-0.415721\pi\)
0.709204 + 0.705003i \(0.249054\pi\)
\(98\) 4.82963 1.29410i 0.487866 0.130723i
\(99\) −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 \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 0 0
\(105\) 4.00000 2.82843i 0.390360 0.276026i
\(106\) 1.46410 5.46410i 0.142206 0.530720i
\(107\) −4.89898 + 2.82843i −0.473602 + 0.273434i −0.717746 0.696305i \(-0.754826\pi\)
0.244144 + 0.969739i \(0.421493\pi\)
\(108\) −5.03723 1.27526i −0.484708 0.122711i
\(109\) −1.00000 1.00000i −0.0957826 0.0957826i 0.657592 0.753374i \(-0.271575\pi\)
−0.753374 + 0.657592i \(0.771575\pi\)
\(110\) −2.07055 7.72741i −0.197419 0.736779i
\(111\) −1.56583 + 1.88366i −0.148622 + 0.178789i
\(112\) −1.00000 + 1.00000i −0.0944911 + 0.0944911i
\(113\) 12.2474 + 7.07107i 1.15214 + 0.665190i 0.949409 0.314044i \(-0.101684\pi\)
0.202735 + 0.979234i \(0.435017\pi\)
\(114\) −1.02494 + 2.22474i −0.0959948 + 0.208366i
\(115\) −16.3923 4.39230i −1.52859 0.409585i
\(116\) −2.82843 −0.262613
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 4.34847 9.43879i 0.396959 0.861640i
\(121\) −4.33013 2.50000i −0.393648 0.227273i
\(122\) −5.65685 + 5.65685i −0.512148 + 0.512148i
\(123\) 2.21441 2.66390i 0.199667 0.240196i
\(124\) −1.83013 6.83013i −0.164350 0.613364i
\(125\) 8.48528 + 8.48528i 0.758947 + 0.758947i
\(126\) −3.22474 + 2.75699i −0.287283 + 0.245613i
\(127\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(128\) 0.776457 2.89778i 0.0686298 0.256130i
\(129\) 8.48528 6.00000i 0.747087 0.528271i
\(130\) 0 0
\(131\) 11.3137i 0.988483i 0.869325 + 0.494242i \(0.164554\pi\)
−0.869325 + 0.494242i \(0.835446\pi\)
\(132\) −2.39960 6.49938i −0.208859 0.565698i
\(133\) −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
\(137\) 13.5230 3.62347i 1.15534 0.309574i 0.370240 0.928936i \(-0.379276\pi\)
0.785105 + 0.619363i \(0.212609\pi\)
\(138\) 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
\(141\) −6.49938 + 2.39960i −0.547346 + 0.202083i
\(142\) 4.00000i 0.335673i
\(143\) 0 0
\(144\) −1.00000 + 2.82843i −0.0833333 + 0.235702i
\(145\) 1.46410 5.46410i 0.121587 0.453769i
\(146\) −1.22474 + 0.707107i −0.101361 + 0.0585206i
\(147\) 0.794593 + 8.62372i 0.0655369 + 0.711273i
\(148\) −1.00000 1.00000i −0.0821995 0.0821995i
\(149\) 0.517638 + 1.93185i 0.0424066 + 0.158263i 0.983882 0.178817i \(-0.0572271\pi\)
−0.941476 + 0.337081i \(0.890560\pi\)
\(150\) −1.33195 1.10721i −0.108753 0.0904030i
\(151\) −1.00000 + 1.00000i −0.0813788 + 0.0813788i −0.746625 0.665246i \(-0.768327\pi\)
0.665246 + 0.746625i \(0.268327\pi\)
\(152\) −3.67423 2.12132i −0.298020 0.172062i
\(153\) 0 0
\(154\) −5.46410 1.46410i −0.440310 0.117981i
\(155\) 14.1421 1.13592
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −9.65926 2.58819i −0.768449 0.205905i
\(159\) 8.89898 + 4.09978i 0.705735 + 0.325133i
\(160\) 8.66025 + 5.00000i 0.684653 + 0.395285i
\(161\) −8.48528 + 8.48528i −0.668734 + 0.668734i
\(162\) −3.65237 + 8.22558i −0.286957 + 0.646263i
\(163\) −0.366025 1.36603i −0.0286693 0.106995i 0.950109 0.311919i \(-0.100972\pi\)
−0.978778 + 0.204924i \(0.934305\pi\)
\(164\) 1.41421 + 1.41421i 0.110432 + 0.110432i
\(165\) 13.7980 1.27135i 1.07417 0.0989744i
\(166\) 6.92820 4.00000i 0.537733 0.310460i
\(167\) 1.03528 3.86370i 0.0801121 0.298982i −0.914232 0.405192i \(-0.867205\pi\)
0.994344 + 0.106209i \(0.0338714\pi\)
\(168\) −4.24264 6.00000i −0.327327 0.462910i
\(169\) 0 0
\(170\) 0 0
\(171\) −3.49768 2.40130i −0.267474 0.183632i
\(172\) 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
\(175\) 1.36603 0.366025i 0.103262 0.0276689i
\(176\) −3.86370 + 1.03528i −0.291238 + 0.0780369i
\(177\) 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 \(0.833333\pi\)
\(180\) 4.94646 + 3.39595i 0.368688 + 0.253119i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) −8.00000 11.3137i −0.591377 0.836333i
\(184\) −6.58846 + 24.5885i −0.485708 + 1.81269i
\(185\) 2.44949 1.41421i 0.180090 0.103975i
\(186\) −12.1958 + 1.12372i −0.894239 + 0.0823955i
\(187\) 0 0
\(188\) −1.03528 3.86370i −0.0755053 0.281790i
\(189\) −3.76198 6.31249i −0.273644 0.459166i
\(190\) 2.00000 2.00000i 0.145095 0.145095i
\(191\) −2.44949 1.41421i −0.177239 0.102329i 0.408756 0.912644i \(-0.365963\pi\)
−0.585995 + 0.810315i \(0.699296\pi\)
\(192\) −11.0119 5.07321i −0.794717 0.366128i
\(193\) 25.9545 + 6.95448i 1.86824 + 0.500595i 0.999990 + 0.00447566i \(0.00142465\pi\)
0.868255 + 0.496119i \(0.165242\pi\)
\(194\) 9.89949 0.710742
\(195\) 0 0
\(196\) −5.00000 −0.357143
\(197\) 21.2504 + 5.69402i 1.51403 + 0.405682i 0.917770 0.397112i \(-0.129988\pi\)
0.596256 + 0.802794i \(0.296654\pi\)
\(198\) −11.7980 + 2.19275i −0.838444 + 0.155832i
\(199\) 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
\(201\) 9.41832 + 7.82913i 0.664317 + 0.552224i
\(202\) 2.19615 + 8.19615i 0.154521 + 0.576679i
\(203\) −2.82843 2.82843i −0.198517 0.198517i
\(204\) 0 0
\(205\) −3.46410 + 2.00000i −0.241943 + 0.139686i
\(206\) 1.55291 5.79555i 0.108197 0.403795i
\(207\) −8.48528 + 24.0000i −0.589768 + 1.66812i
\(208\) 0 0
\(209\) 5.65685i 0.391293i
\(210\) 4.59575 1.69677i 0.317137 0.117089i
\(211\) −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
\(214\) −5.46410 + 1.46410i −0.373518 + 0.100084i
\(215\) −11.5911 + 3.10583i −0.790507 + 0.211816i
\(216\) −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
\(219\) −0.848387 2.29788i −0.0573287 0.155276i
\(220\) 8.00000i 0.539360i
\(221\) 0 0
\(222\) −2.00000 + 1.41421i −0.134231 + 0.0949158i
\(223\) 4.02628 15.0263i 0.269620 1.00623i −0.689742 0.724055i \(-0.742276\pi\)
0.959362 0.282179i \(-0.0910572\pi\)
\(224\) 6.12372 3.53553i 0.409159 0.236228i
\(225\) 2.28024 1.94949i 0.152016 0.129966i
\(226\) 10.0000 + 10.0000i 0.665190 + 0.665190i
\(227\) 2.07055 + 7.72741i 0.137427 + 0.512886i 0.999976 + 0.00691198i \(0.00220017\pi\)
−0.862549 + 0.505974i \(0.831133\pi\)
\(228\) 1.56583 1.88366i 0.103699 0.124749i
\(229\) −1.00000 + 1.00000i −0.0660819 + 0.0660819i −0.739375 0.673293i \(-0.764879\pi\)
0.673293 + 0.739375i \(0.264879\pi\)
\(230\) −14.6969 8.48528i −0.969087 0.559503i
\(231\) 4.09978 8.89898i 0.269745 0.585510i
\(232\) −8.19615 2.19615i −0.538104 0.144184i
\(233\) −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
\(236\) 3.86370 + 1.03528i 0.251506 + 0.0673907i
\(237\) 7.24745 15.7313i 0.470772 1.02186i
\(238\) 0 0
\(239\) 14.1421 14.1421i 0.914779 0.914779i −0.0818647 0.996643i \(-0.526088\pi\)
0.996643 + 0.0818647i \(0.0260876\pi\)
\(240\) 2.21441 2.66390i 0.142940 0.171954i
\(241\) 6.22243 + 23.2224i 0.400822 + 1.49589i 0.811633 + 0.584168i \(0.198579\pi\)
−0.410811 + 0.911721i \(0.634754\pi\)
\(242\) −3.53553 3.53553i −0.227273 0.227273i
\(243\) −12.9722 8.64420i −0.832167 0.554526i
\(244\) 6.92820 4.00000i 0.443533 0.256074i
\(245\) 2.58819 9.65926i 0.165353 0.617107i
\(246\) 2.82843 2.00000i 0.180334 0.127515i
\(247\) 0 0
\(248\) 21.2132i 1.34704i
\(249\) 4.79920 + 12.9988i 0.304137 + 0.823763i
\(250\) 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
\(253\) −32.7846 + 8.78461i −2.06115 + 0.552284i
\(254\) 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 \(0.918589\pi\)
\(258\) 9.74907 3.59940i 0.606950 0.224089i
\(259\) 2.00000i 0.124274i
\(260\) 0 0
\(261\) −8.00000 2.82843i −0.495188 0.175075i
\(262\) −2.92820 + 10.9282i −0.180905 + 0.675147i
\(263\) −19.5959 + 11.3137i −1.20834 + 0.697633i −0.962396 0.271652i \(-0.912430\pi\)
−0.245940 + 0.969285i \(0.579097\pi\)
\(264\) −1.90702 20.6969i −0.117369 1.27381i
\(265\) −8.00000 8.00000i −0.491436 0.491436i
\(266\) −0.517638 1.93185i −0.0317384 0.118449i
\(267\) −18.6473 15.5009i −1.14120 0.948639i
\(268\) −5.00000 + 5.00000i −0.305424 + 0.305424i
\(269\) −17.1464 9.89949i −1.04544 0.603583i −0.124068 0.992274i \(-0.539594\pi\)
−0.921368 + 0.388691i \(0.872927\pi\)
\(270\) 7.24604 7.44949i 0.440980 0.453362i
\(271\) 25.9545 + 6.95448i 1.57662 + 0.422455i 0.937878 0.346964i \(-0.112788\pi\)
0.638744 + 0.769419i \(0.279454\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) 3.86370 + 1.03528i 0.232990 + 0.0624295i
\(276\) −13.3485 6.14966i −0.803483 0.370166i
\(277\) 10.3923 + 6.00000i 0.624413 + 0.360505i 0.778585 0.627539i \(-0.215938\pi\)
−0.154172 + 0.988044i \(0.549271\pi\)
\(278\) 2.82843 2.82843i 0.169638 0.169638i
\(279\) 1.65375 21.1486i 0.0990072 1.26614i
\(280\) 2.19615 + 8.19615i 0.131245 + 0.489814i
\(281\) −9.89949 9.89949i −0.590554 0.590554i 0.347227 0.937781i \(-0.387123\pi\)
−0.937781 + 0.347227i \(0.887123\pi\)
\(282\) −6.89898 + 0.635674i −0.410828 + 0.0378539i
\(283\) 10.3923 6.00000i 0.617758 0.356663i −0.158237 0.987401i \(-0.550581\pi\)
0.775996 + 0.630738i \(0.217248\pi\)
\(284\) −1.03528 + 3.86370i −0.0614323 + 0.229269i
\(285\) 2.82843 + 4.00000i 0.167542 + 0.236940i
\(286\) 0 0
\(287\) 2.82843i 0.166957i
\(288\) 8.48988 12.3662i 0.500271 0.728683i
\(289\) 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
\(292\) 1.36603 0.366025i 0.0799406 0.0214200i
\(293\) 13.5230 3.62347i 0.790020 0.211685i 0.158822 0.987307i \(-0.449230\pi\)
0.631198 + 0.775622i \(0.282564\pi\)
\(294\) −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
\(297\) −0.287721 20.7826i −0.0166952 1.20593i
\(298\) 2.00000i 0.115857i
\(299\) 0 0
\(300\) 1.00000 + 1.41421i 0.0577350 + 0.0816497i
\(301\) −2.19615 + 8.19615i −0.126584 + 0.472418i
\(302\) −1.22474 + 0.707107i −0.0704761 + 0.0406894i
\(303\) −14.6349 + 1.34847i −0.840756 + 0.0774675i
\(304\) −1.00000 1.00000i −0.0573539 0.0573539i
\(305\) 4.14110 + 15.4548i 0.237119 + 0.884940i
\(306\) 0 0
\(307\) 17.0000 17.0000i 0.970241 0.970241i −0.0293286 0.999570i \(-0.509337\pi\)
0.999570 + 0.0293286i \(0.00933691\pi\)
\(308\) 4.89898 + 2.82843i 0.279145 + 0.161165i
\(309\) 9.43879 + 4.34847i 0.536954 + 0.247376i
\(310\) 13.6603 + 3.66025i 0.775850 + 0.207888i
\(311\) 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 \(0.427405\pi\)
\(314\) 13.5230 + 3.62347i 0.763145 + 0.204484i
\(315\) 1.55051 + 8.34242i 0.0873614 + 0.470042i
\(316\) 8.66025 + 5.00000i 0.487177 + 0.281272i
\(317\) −7.07107 + 7.07107i −0.397151 + 0.397151i −0.877227 0.480076i \(-0.840609\pi\)
0.480076 + 0.877227i \(0.340609\pi\)
\(318\) 7.53465 + 6.26330i 0.422522 + 0.351229i
\(319\) −2.92820 10.9282i −0.163948 0.611862i
\(320\) 9.89949 + 9.89949i 0.553399 + 0.553399i
\(321\) −0.898979 9.75663i −0.0501761 0.544562i
\(322\) −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
\(327\) 2.29788 0.848387i 0.127073 0.0469159i
\(328\) 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
\(331\) 9.56218 2.56218i 0.525585 0.140830i 0.0137361 0.999906i \(-0.495628\pi\)
0.511849 + 0.859076i \(0.328961\pi\)
\(332\) −7.72741 + 2.07055i −0.424097 + 0.113636i
\(333\) −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
\(336\) −0.848387 2.29788i −0.0462833 0.125359i
\(337\) 6.00000i 0.326841i −0.986557 0.163420i \(-0.947747\pi\)
0.986557 0.163420i \(-0.0522527\pi\)
\(338\) 0 0
\(339\) −20.0000 + 14.1421i −1.08625 + 0.768095i
\(340\) 0 0
\(341\) 24.4949 14.1421i 1.32647 0.765840i
\(342\) −2.75699 3.22474i −0.149081 0.174374i
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 4.65874 + 17.3867i 0.251183 + 0.937426i
\(345\) 18.7899 22.6040i 1.01162 1.21696i
\(346\) 6.00000 6.00000i 0.322562 0.322562i
\(347\) 12.2474 + 7.07107i 0.657477 + 0.379595i 0.791315 0.611408i \(-0.209397\pi\)
−0.133838 + 0.991003i \(0.542730\pi\)
\(348\) 2.04989 4.44949i 0.109886 0.238518i
\(349\) −23.2224 6.22243i −1.24307 0.333079i −0.423413 0.905937i \(-0.639168\pi\)
−0.819655 + 0.572857i \(0.805835\pi\)
\(350\) 1.41421 0.0755929
\(351\) 0 0
\(352\) 20.0000 1.06600
\(353\) −25.1141 6.72930i −1.33669 0.358164i −0.481483 0.876455i \(-0.659902\pi\)
−0.855204 + 0.518291i \(0.826568\pi\)
\(354\) 2.89898 6.29253i 0.154079 0.334444i
\(355\) −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 0.777796 0.628517i \(-0.216338\pi\)
−0.628517 + 0.777796i \(0.716338\pi\)
\(360\) 11.6969 + 13.6814i 0.616483 + 0.721075i
\(361\) −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
\(366\) −4.79920 12.9988i −0.250858 0.679456i
\(367\) −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
\(370\) 2.73205 0.732051i 0.142033 0.0380575i
\(371\) −7.72741 + 2.07055i −0.401187 + 0.107498i
\(372\) 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
\(375\) −19.4981 + 7.19881i −1.00688 + 0.371745i
\(376\) 12.0000i 0.618853i
\(377\) 0 0
\(378\) −2.00000 7.07107i −0.102869 0.363696i
\(379\) −6.95448 + 25.9545i −0.357228 + 1.33319i 0.520430 + 0.853904i \(0.325772\pi\)
−0.877658 + 0.479288i \(0.840895\pi\)
\(380\) −2.44949 + 1.41421i −0.125656 + 0.0725476i
\(381\) 0 0
\(382\) −2.00000 2.00000i −0.102329 0.102329i
\(383\) −4.14110 15.4548i −0.211601 0.789704i −0.987336 0.158645i \(-0.949287\pi\)
0.775735 0.631059i \(-0.217379\pi\)
\(384\) 3.99585 + 3.32162i 0.203913 + 0.169506i
\(385\) −8.00000 + 8.00000i −0.407718 + 0.407718i
\(386\) 23.2702 + 13.4350i 1.18442 + 0.683825i
\(387\) 3.28913 + 17.6969i 0.167196 + 0.899586i
\(388\) −9.56218 2.56218i −0.485446 0.130075i
\(389\) 16.9706 0.860442 0.430221 0.902724i \(-0.358436\pi\)
0.430221 + 0.902724i \(0.358436\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −14.4889 3.88229i −0.731799 0.196085i
\(393\) −17.7980 8.19955i −0.897788 0.413613i
\(394\) 19.0526 + 11.0000i 0.959854 + 0.554172i
\(395\) −14.1421 + 14.1421i −0.711568 + 0.711568i
\(396\) 11.9635 + 0.935500i 0.601187 + 0.0470106i
\(397\) 6.22243 + 23.2224i 0.312295 + 1.16550i 0.926482 + 0.376340i \(0.122817\pi\)
−0.614187 + 0.789161i \(0.710516\pi\)
\(398\) 0 0
\(399\) 3.44949 0.317837i 0.172690 0.0159118i
\(400\) 0.866025 0.500000i 0.0433013 0.0250000i
\(401\) 5.69402 21.2504i 0.284346 1.06119i −0.664970 0.746870i \(-0.731556\pi\)
0.949316 0.314323i \(-0.101777\pi\)
\(402\) 7.07107 + 10.0000i 0.352673 + 0.498755i
\(403\) 0 0
\(404\) 8.48528i 0.422159i
\(405\) 10.5948 + 14.5517i 0.526458 + 0.723078i
\(406\) −2.00000 3.46410i −0.0992583 0.171920i
\(407\) 2.82843 4.89898i 0.140200 0.242833i
\(408\) 0 0
\(409\) −31.4186 + 8.41858i −1.55355 + 0.416272i −0.930614 0.366002i \(-0.880726\pi\)
−0.622935 + 0.782274i \(0.714060\pi\)
\(410\) −3.86370 + 1.03528i −0.190815 + 0.0511286i
\(411\) −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
\(414\) −14.4078 + 20.9861i −0.708105 + 1.03141i
\(415\) 16.0000i 0.785409i
\(416\) 0 0
\(417\) 4.00000 + 5.65685i 0.195881 + 0.277017i
\(418\) 1.46410 5.46410i 0.0716116 0.267258i
\(419\) 9.79796 5.65685i 0.478662 0.276355i −0.241197 0.970476i \(-0.577540\pi\)
0.719859 + 0.694121i \(0.244207\pi\)
\(420\) −4.87832 + 0.449490i −0.238037 + 0.0219329i
\(421\) −25.0000 25.0000i −1.21843 1.21843i −0.968183 0.250242i \(-0.919490\pi\)
−0.250242 0.968183i \(-0.580510\pi\)
\(422\) −3.62347 13.5230i −0.176388 0.658287i
\(423\) 0.935500 11.9635i 0.0454856 0.581684i
\(424\) −12.0000 + 12.0000i −0.582772 + 0.582772i
\(425\) 0 0
\(426\) 6.29253 + 2.89898i 0.304874 + 0.140456i
\(427\) 10.9282 + 2.92820i 0.528853 + 0.141706i
\(428\) 5.65685 0.273434
\(429\) 0 0
\(430\) −12.0000 −0.578691
\(431\) −30.9096 8.28221i −1.48886 0.398940i −0.579511 0.814964i \(-0.696756\pi\)
−0.909353 + 0.416024i \(0.863423\pi\)
\(432\) −3.72474 3.62302i −0.179207 0.174313i
\(433\) −15.5885 9.00000i −0.749133 0.432512i 0.0762473 0.997089i \(-0.475706\pi\)
−0.825381 + 0.564577i \(0.809039\pi\)
\(434\) 7.07107 7.07107i 0.339422 0.339422i
\(435\) 7.53465 + 6.26330i 0.361259 + 0.300302i
\(436\) 0.366025 + 1.36603i 0.0175294 + 0.0654208i
\(437\) −8.48528 8.48528i −0.405906 0.405906i
\(438\) −0.224745 2.43916i −0.0107387 0.116547i
\(439\) −25.9808 + 15.0000i −1.23999 + 0.715911i −0.969093 0.246696i \(-0.920655\pi\)
−0.270901 + 0.962607i \(0.587322\pi\)
\(440\) −6.21166 + 23.1822i −0.296129 + 1.10517i
\(441\) −14.1421 5.00000i −0.673435 0.238095i
\(442\) 0 0
\(443\) 28.2843i 1.34383i 0.740630 + 0.671913i \(0.234527\pi\)
−0.740630 + 0.671913i \(0.765473\pi\)
\(444\) 2.29788 0.848387i 0.109052 0.0402627i
\(445\) 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
\(448\) 9.56218 2.56218i 0.451770 0.121052i
\(449\) −21.2504 + 5.69402i −1.00287 + 0.268717i −0.722646 0.691218i \(-0.757074\pi\)
−0.280221 + 0.959936i \(0.590408\pi\)
\(450\) 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
\(453\) −0.848387 2.29788i −0.0398607 0.107964i
\(454\) 8.00000i 0.375459i
\(455\) 0 0
\(456\) 6.00000 4.24264i 0.280976 0.198680i
\(457\) 10.6147 39.6147i 0.496536 1.85310i −0.0247126 0.999695i \(-0.507867\pi\)
0.521249 0.853405i \(-0.325466\pi\)
\(458\) −1.22474 + 0.707107i −0.0572286 + 0.0330409i
\(459\) 0 0
\(460\) 12.0000 + 12.0000i 0.559503 + 0.559503i
\(461\) −2.58819 9.65926i −0.120544 0.449877i 0.879098 0.476642i \(-0.158146\pi\)
−0.999642 + 0.0267651i \(0.991479\pi\)
\(462\) 6.26330 7.53465i 0.291395 0.350544i
\(463\) 17.0000 17.0000i 0.790057 0.790057i −0.191446 0.981503i \(-0.561318\pi\)
0.981503 + 0.191446i \(0.0613177\pi\)
\(464\) −2.44949 1.41421i −0.113715 0.0656532i
\(465\) −10.2494 + 22.2474i −0.475306 + 1.03170i
\(466\) −24.5885 6.58846i −1.13904 0.305204i
\(467\) −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
\(470\) 7.72741 + 2.07055i 0.356439 + 0.0955075i
\(471\) −10.1464 + 22.0239i −0.467523 + 1.01481i
\(472\) 10.3923 + 6.00000i 0.478345 + 0.276172i
\(473\) −16.9706 + 16.9706i −0.780307 + 0.780307i
\(474\) 11.0721 13.3195i 0.508557 0.611785i
\(475\) 0.366025 + 1.36603i 0.0167944 + 0.0626775i
\(476\) 0 0
\(477\) −12.8990 + 11.0280i −0.590604 + 0.504936i
\(478\) 17.3205 10.0000i 0.792222 0.457389i
\(479\) −8.28221 + 30.9096i −0.378424 + 1.41230i 0.469853 + 0.882744i \(0.344307\pi\)
−0.848277 + 0.529552i \(0.822360\pi\)
\(480\) −14.1421 + 10.0000i −0.645497 + 0.456435i
\(481\) 0 0
\(482\) 24.0416i 1.09507i
\(483\) −7.19881 19.4981i −0.327557 0.887196i
\(484\) 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
\(487\) 25.9545 6.95448i 1.17611 0.315138i 0.382727 0.923861i \(-0.374985\pi\)
0.793382 + 0.608724i \(0.208318\pi\)
\(488\) 23.1822 6.21166i 1.04941 0.281189i
\(489\) 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 \(0.426646\pi\)
\(492\) −3.24969 + 1.19980i −0.146507 + 0.0540912i
\(493\) 0 0
\(494\) 0 0
\(495\) −8.00000 + 22.6274i −0.359573 + 1.01703i
\(496\) 1.83013 6.83013i 0.0821751 0.306682i
\(497\) −4.89898 + 2.82843i −0.219749 + 0.126872i
\(498\) 1.27135 + 13.7980i 0.0569705 + 0.618301i
\(499\) 23.0000 + 23.0000i 1.02962 + 1.02962i 0.999548 + 0.0300737i \(0.00957421\pi\)
0.0300737 + 0.999548i \(0.490426\pi\)
\(500\) −3.10583 11.5911i −0.138897 0.518370i
\(501\) 5.32780 + 4.42883i 0.238029 + 0.197865i
\(502\) −18.0000 + 18.0000i −0.803379 + 0.803379i
\(503\) 4.89898 + 2.82843i 0.218435 + 0.126113i 0.605225 0.796054i \(-0.293083\pi\)
−0.386791 + 0.922168i \(0.626416\pi\)
\(504\) 12.5136 2.32577i 0.557401 0.103598i
\(505\) 16.3923 + 4.39230i 0.729448 + 0.195455i
\(506\) −33.9411 −1.50887
\(507\) 0 0
\(508\) 0 0
\(509\) 32.8415 + 8.79985i 1.45567 + 0.390046i 0.897993 0.440010i \(-0.145025\pi\)
0.557680 + 0.830056i \(0.311692\pi\)
\(510\) 0 0
\(511\) 1.73205 + 1.00000i 0.0766214 + 0.0442374i
\(512\) 7.77817 7.77817i 0.343750 0.343750i
\(513\) 6.31249 3.76198i 0.278703 0.166095i
\(514\) −2.19615 8.19615i −0.0968681 0.361517i
\(515\) −8.48528 8.48528i −0.373906 0.373906i
\(516\) −10.3485 + 0.953512i −0.455566 + 0.0419760i
\(517\) 13.8564 8.00000i 0.609404 0.351840i
\(518\) 0.517638 1.93185i 0.0227437 0.0848807i
\(519\) 8.48528 + 12.0000i 0.372463 + 0.526742i
\(520\) 0 0
\(521\) 31.1127i 1.36307i −0.731785 0.681536i \(-0.761312\pi\)
0.731785 0.681536i \(-0.238688\pi\)
\(522\) −6.99536 4.80260i −0.306178 0.210204i
\(523\) −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
\(526\) −21.8564 + 5.85641i −0.952985 + 0.255351i
\(527\) 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
\(531\) 9.89293 + 6.79191i 0.429316 + 0.294744i
\(532\) 2.00000i 0.0867110i
\(533\) 0 0
\(534\) −14.0000 19.7990i −0.605839 0.856786i
\(535\) −2.92820 + 10.9282i −0.126597 + 0.472467i
\(536\) −18.3712 + 10.6066i −0.793514 + 0.458135i
\(537\) 0 0
\(538\) −14.0000 14.0000i −0.603583 0.603583i
\(539\) −5.17638 19.3185i −0.222963 0.832107i
\(540\) −8.92721 + 5.32024i −0.384166 + 0.228947i
\(541\) −1.00000 + 1.00000i −0.0429934 + 0.0429934i −0.728277 0.685283i \(-0.759678\pi\)
0.685283 + 0.728277i \(0.259678\pi\)
\(542\) 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 \(0.704275\pi\)
\(548\) −13.5230 3.62347i −0.577672 0.154787i
\(549\) 23.5959 4.38551i 1.00705 0.187169i
\(550\) 3.46410 + 2.00000i 0.147710 + 0.0852803i
\(551\) 2.82843 2.82843i 0.120495 0.120495i
\(552\) −33.9059 28.1849i −1.44313 1.19963i
\(553\) 3.66025 + 13.6603i 0.155650 + 0.580893i
\(554\) 8.48528 + 8.48528i 0.360505 + 0.360505i
\(555\) 0.449490 + 4.87832i 0.0190798 + 0.207073i
\(556\) −3.46410 + 2.00000i −0.146911 + 0.0848189i
\(557\) −3.62347 + 13.5230i −0.153531 + 0.572986i 0.845695 + 0.533666i \(0.179186\pi\)
−0.999227 + 0.0393204i \(0.987481\pi\)
\(558\) 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
\(565\) 27.3205 7.32051i 1.14938 0.307976i
\(566\) 11.5911 3.10583i 0.487211 0.130548i
\(567\) 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 \(0.776416\pi\)
\(570\) 1.69677 + 4.59575i 0.0710701 + 0.192495i
\(571\) 12.0000i 0.502184i 0.967963 + 0.251092i \(0.0807897\pi\)
−0.967963 + 0.251092i \(0.919210\pi\)
\(572\) 0 0
\(573\) 4.00000 2.82843i 0.167102 0.118159i
\(574\) −0.732051 + 2.73205i −0.0305552 + 0.114034i
\(575\) 7.34847 4.24264i 0.306452 0.176930i
\(576\) 15.9617 13.6464i 0.665070 0.568601i
\(577\) −1.00000 1.00000i −0.0416305 0.0416305i 0.685985 0.727616i \(-0.259372\pi\)
−0.727616 + 0.685985i \(0.759372\pi\)
\(578\) 4.39992 + 16.4207i 0.183013 + 0.683013i
\(579\) −29.7507 + 35.7896i −1.23640 + 1.48737i
\(580\) −4.00000 + 4.00000i −0.166091 + 0.166091i
\(581\) −9.79796 5.65685i −0.406488 0.234686i
\(582\) −7.17461 + 15.5732i −0.297397 + 0.645530i
\(583\) −21.8564 5.85641i −0.905200 0.242548i
\(584\) 4.24264 0.175562
\(585\) 0 0
\(586\) 14.0000 0.578335
\(587\) −7.72741 2.07055i −0.318944 0.0854608i 0.0957952 0.995401i \(-0.469461\pi\)
−0.414739 + 0.909940i \(0.636127\pi\)
\(588\) 3.62372 7.86566i 0.149440 0.324374i
\(589\) 8.66025 + 5.00000i 0.356840 + 0.206021i
\(590\) −5.65685 + 5.65685i −0.232889 + 0.232889i
\(591\) −24.3585 + 29.3029i −1.00198 + 1.20536i
\(592\) −0.366025 1.36603i −0.0150436 0.0561433i
\(593\) −9.89949 9.89949i −0.406524 0.406524i 0.474001 0.880524i \(-0.342809\pi\)
−0.880524 + 0.474001i \(0.842809\pi\)
\(594\) 5.10102 20.1489i 0.209297 0.826721i
\(595\) 0 0
\(596\) 0.517638 1.93185i 0.0212033 0.0791317i
\(597\) 0 0
\(598\) 0 0
\(599\) 11.3137i 0.462266i 0.972922 + 0.231133i \(0.0742432\pi\)
−0.972922 + 0.231133i \(0.925757\pi\)
\(600\) 1.79970 + 4.87453i 0.0734725 + 0.199002i
\(601\) −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
\(604\) 1.36603 0.366025i 0.0555828 0.0148934i
\(605\) −9.65926 + 2.58819i −0.392705 + 0.105225i
\(606\) −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
\(609\) 6.49938 2.39960i 0.263368 0.0972368i
\(610\) 16.0000i 0.647821i
\(611\) 0 0
\(612\) 0 0
\(613\) −0.366025 + 1.36603i −0.0147836 + 0.0551732i −0.972924 0.231127i \(-0.925759\pi\)
0.958140 + 0.286300i \(0.0924254\pi\)
\(614\) 20.8207 12.0208i 0.840254 0.485121i
\(615\) −0.635674 6.89898i −0.0256329 0.278194i
\(616\) 12.0000 + 12.0000i 0.483494 + 0.483494i
\(617\) 9.83512 + 36.7052i 0.395947 + 1.47769i 0.820161 + 0.572133i \(0.193884\pi\)
−0.424214 + 0.905562i \(0.639449\pi\)
\(618\) 7.99171 + 6.64324i 0.321474 + 0.267230i
\(619\) −1.00000 + 1.00000i −0.0401934 + 0.0401934i −0.726918 0.686724i \(-0.759048\pi\)
0.686724 + 0.726918i \(0.259048\pi\)
\(620\) −12.2474 7.07107i −0.491869 0.283981i
\(621\) −31.6055 30.7423i −1.26829 1.23365i
\(622\) 8.19615 + 2.19615i 0.328636 + 0.0880577i
\(623\) 19.7990 0.793230
\(624\) 0 0
\(625\) 19.0000 0.760000
\(626\) 7.72741 + 2.07055i 0.308849 + 0.0827559i
\(627\) 8.89898 + 4.09978i 0.355391 + 0.163729i
\(628\) −12.1244 7.00000i −0.483814 0.279330i
\(629\) 0 0
\(630\) −0.661498 + 8.45946i −0.0263547 + 0.337033i
\(631\) −6.95448 25.9545i −0.276854 1.03323i −0.954589 0.297926i \(-0.903705\pi\)
0.677735 0.735306i \(-0.262961\pi\)
\(632\) 21.2132 + 21.2132i 0.843816 + 0.843816i
\(633\) 24.1464 2.22486i 0.959734 0.0884303i
\(634\) −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
\(639\) −6.79191 + 9.89293i −0.268684 + 0.391358i
\(640\) −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
\(643\) −6.83013 + 1.83013i −0.269354 + 0.0721732i −0.390968 0.920404i \(-0.627860\pi\)
0.121614 + 0.992577i \(0.461193\pi\)
\(644\) 11.5911 3.10583i 0.456754 0.122387i
\(645\) 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 \(0.833333\pi\)
\(648\) 21.8275 15.8921i 0.857465 0.624302i
\(649\) 16.0000i 0.628055i
\(650\) 0 0
\(651\) 10.0000 + 14.1421i 0.391931 + 0.554274i
\(652\) −0.366025 + 1.36603i −0.0143347 + 0.0534977i
\(653\) −12.2474 + 7.07107i −0.479280 + 0.276712i −0.720116 0.693853i \(-0.755912\pi\)
0.240837 + 0.970566i \(0.422578\pi\)
\(654\) 2.43916 0.224745i 0.0953786 0.00878822i
\(655\) 16.0000 + 16.0000i 0.625172 + 0.625172i
\(656\) 0.517638 + 1.93185i 0.0202104 + 0.0754261i
\(657\) 4.22973 + 0.330749i 0.165017 + 0.0129038i
\(658\) 4.00000 4.00000i 0.155936 0.155936i
\(659\) −2.44949 1.41421i −0.0954186 0.0550899i 0.451531 0.892255i \(-0.350878\pi\)
−0.546950 + 0.837165i \(0.684211\pi\)
\(660\) −12.5851 5.79796i −0.489873 0.225685i
\(661\) 1.36603 + 0.366025i 0.0531322 + 0.0142367i 0.285287 0.958442i \(-0.407911\pi\)
−0.232155 + 0.972679i \(0.574578\pi\)
\(662\) 9.89949 0.384755
\(663\) 0 0
\(664\) −24.0000 −0.931381
\(665\) −3.86370 1.03528i −0.149828 0.0401463i
\(666\) −0.775255 4.17121i −0.0300405 0.161631i
\(667\) −20.7846 12.0000i −0.804783 0.464642i
\(668\) −2.82843 + 2.82843i −0.109435 + 0.109435i
\(669\) 20.7203 + 17.2241i 0.801093 + 0.665922i
\(670\) −3.66025 13.6603i −0.141408 0.527742i
\(671\) 22.6274 + 22.6274i 0.873522 + 0.873522i
\(672\) 1.12372 + 12.1958i 0.0433486 + 0.470463i
\(673\) −10.3923 + 6.00000i −0.400594 + 0.231283i −0.686740 0.726903i \(-0.740959\pi\)
0.286146 + 0.958186i \(0.407626\pi\)
\(674\) 1.55291 5.79555i 0.0598160 0.223236i
\(675\) 1.41421 + 5.00000i 0.0544331 + 0.192450i
\(676\) 0 0
\(677\) 22.6274i 0.869642i −0.900517 0.434821i \(-0.856812\pi\)
0.900517 0.434821i \(-0.143188\pi\)
\(678\) −22.9788 + 8.48387i −0.882494 + 0.325821i
\(679\) −7.00000 12.1244i −0.268635 0.465290i
\(680\) 0 0
\(681\) −13.6569 2.34315i −0.523332 0.0897895i
\(682\) 27.3205 7.32051i 1.04616 0.280317i
\(683\) −3.86370 + 1.03528i −0.147840 + 0.0396137i −0.331980 0.943286i \(-0.607717\pi\)
0.184140 + 0.982900i \(0.441050\pi\)
\(684\) 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
\(687\) −0.848387 2.29788i −0.0323680 0.0876695i
\(688\) 6.00000i 0.228748i
\(689\) 0 0
\(690\) 24.0000 16.9706i 0.913664 0.646058i
\(691\) 4.02628 15.0263i 0.153167 0.571627i −0.846088 0.533042i \(-0.821049\pi\)
0.999255 0.0385841i \(-0.0122848\pi\)
\(692\) −7.34847 + 4.24264i −0.279347 + 0.161281i
\(693\) 11.0280 + 12.8990i 0.418918 + 0.489992i
\(694\) 10.0000 + 10.0000i 0.379595 + 0.379595i
\(695\) −2.07055 7.72741i −0.0785405 0.293117i
\(696\) 9.39496 11.3020i 0.356115 0.428400i
\(697\) 0 0
\(698\) −20.8207 12.0208i −0.788074 0.454995i
\(699\) 18.4490 40.0454i 0.697805 1.51466i
\(700\) −1.36603 0.366025i −0.0516309 0.0138345i
\(701\) 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
\(704\) 27.0459 + 7.24693i 1.01933 + 0.273129i
\(705\) −5.79796 + 12.5851i −0.218364 + 0.473981i
\(706\) −22.5167 13.0000i −0.847426 0.489261i
\(707\) 8.48528 8.48528i 0.319122 0.319122i
\(708\) −4.42883 + 5.32780i −0.166445 + 0.200231i
\(709\) −6.95448 25.9545i −0.261181 0.974741i −0.964547 0.263913i \(-0.914987\pi\)
0.703365 0.710828i \(-0.251680\pi\)
\(710\) −5.65685 5.65685i −0.212298 0.212298i
\(711\) 19.4949 + 22.8024i 0.731116 + 0.855156i
\(712\) 36.3731 21.0000i 1.36314 0.787008i
\(713\) 15.5291 57.9555i 0.581571 2.17045i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 11.9980 + 32.4969i 0.448074 + 1.21362i
\(718\) 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
\(721\) −8.19615 + 2.19615i −0.305241 + 0.0817890i
\(722\) −16.4207 + 4.39992i −0.611117 + 0.163748i
\(723\) −41.0416 7.04163i −1.52635 0.261881i
\(724\) 0 0
\(725\) 1.41421 + 2.44949i 0.0525226 + 0.0909718i
\(726\) 8.12422 2.99950i 0.301518 0.111322i
\(727\) 48.0000i 1.78022i −0.455744 0.890111i \(-0.650627\pi\)
0.455744 0.890111i \(-0.349373\pi\)
\(728\) 0 0
\(729\) 23.0000 14.1421i 0.851852 0.523783i
\(730\) −0.732051 + 2.73205i −0.0270944 + 0.101118i
\(731\) 0 0
\(732\) 1.27135 + 13.7980i 0.0469904 + 0.509987i
\(733\) 5.00000 + 5.00000i 0.184679 + 0.184679i 0.793391 0.608712i \(-0.208314\pi\)
−0.608712 + 0.793391i \(0.708314\pi\)
\(734\) −2.07055 7.72741i −0.0764255 0.285224i
\(735\) 13.3195 + 11.0721i 0.491298 + 0.408399i
\(736\) 30.0000 30.0000i 1.10581 1.10581i
\(737\) −24.4949 14.1421i −0.902281 0.520932i
\(738\) 1.09638 + 5.89898i 0.0403582 + 0.217144i
\(739\) 1.36603 + 0.366025i 0.0502501 + 0.0134645i 0.283857 0.958867i \(-0.408386\pi\)
−0.233606 + 0.972331i \(0.575053\pi\)
\(740\) −2.82843 −0.103975
\(741\) 0 0
\(742\) −8.00000 −0.293689
\(743\) 15.4548 + 4.14110i 0.566982 + 0.151922i 0.530912 0.847427i \(-0.321849\pi\)
0.0360700 + 0.999349i \(0.488516\pi\)
\(744\) 33.3712 + 15.3742i 1.22345 + 0.563644i
\(745\) 3.46410 + 2.00000i 0.126915 + 0.0732743i
\(746\) 2.82843 2.82843i 0.103556 0.103556i
\(747\) −23.9270 1.87100i −0.875442 0.0684563i
\(748\) 0 0
\(749\) 5.65685 + 5.65685i 0.206697 + 0.206697i
\(750\) −20.6969 + 1.90702i −0.755745 + 0.0696347i
\(751\) 25.9808 15.0000i 0.948051 0.547358i 0.0555764 0.998454i \(-0.482300\pi\)
0.892475 + 0.451097i \(0.148967\pi\)
\(752\) 1.03528 3.86370i 0.0377526 0.140895i
\(753\) −25.4558 36.0000i −0.927663 1.31191i
\(754\) 0 0
\(755\) 2.82843i 0.102937i
\(756\) 0.101725 + 7.34777i 0.00369969 + 0.267236i
\(757\) 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
\(760\) −8.19615 + 2.19615i −0.297306 + 0.0796628i
\(761\) 48.2963 12.9410i 1.75074 0.469109i 0.765955 0.642894i \(-0.222266\pi\)
0.984784 + 0.173784i \(0.0555996\pi\)
\(762\) 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
\(769\) −4.75833 + 17.7583i −0.171590 + 0.640382i 0.825518 + 0.564376i \(0.190883\pi\)
−0.997107 + 0.0760054i \(0.975783\pi\)
\(770\) −9.79796 + 5.65685i −0.353094 + 0.203859i
\(771\) 14.6349 1.34847i 0.527065 0.0485639i
\(772\) −19.0000 19.0000i −0.683825 0.683825i
\(773\) 3.62347 + 13.5230i 0.130327 + 0.486387i 0.999973 0.00728800i \(-0.00231986\pi\)
−0.869646 + 0.493675i \(0.835653\pi\)
\(774\) −1.40325 + 17.9452i −0.0504388 + 0.645028i
\(775\) −5.00000 + 5.00000i −0.179605 + 0.179605i
\(776\) −25.7196 14.8492i −0.923281 0.533057i
\(777\) 3.14626 + 1.44949i 0.112872 + 0.0520002i
\(778\) 16.3923 + 4.39230i 0.587693 + 0.157472i
\(779\) −2.82843 −0.101339
\(780\) 0 0
\(781\) −16.0000 −0.572525
\(782\) 0 0
\(783\) 10.2474 10.5352i 0.366214 0.376496i
\(784\) −4.33013 2.50000i −0.154647 0.0892857i
\(785\) 19.7990 19.7990i 0.706656 0.706656i
\(786\) −15.0693 12.5266i −0.537504 0.446809i
\(787\) −6.95448 25.9545i −0.247901 0.925177i −0.971903 0.235380i \(-0.924366\pi\)
0.724003 0.689797i \(-0.242300\pi\)
\(788\) −15.5563 15.5563i −0.554172 0.554172i
\(789\) −3.59592 39.0265i −0.128018 1.38938i
\(790\) −17.3205 + 10.0000i −0.616236 + 0.355784i
\(791\) 5.17638 19.3185i 0.184051 0.686887i
\(792\) 33.9411 + 12.0000i 1.20605 + 0.426401i
\(793\) 0 0
\(794\) 24.0416i 0.853206i
\(795\) 18.3830 6.78710i 0.651978 0.240714i
\(796\) 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
\(800\) −4.82963 + 1.29410i −0.170753 + 0.0457532i
\(801\) 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
\(804\) −4.24194 11.4894i −0.149602 0.405199i
\(805\) 24.0000i 0.845889i
\(806\) 0 0
\(807\) 28.0000 19.7990i 0.985647 0.696957i
\(808\) 6.58846 24.5885i 0.231781 0.865019i
\(809\) −26.9444 + 15.5563i −0.947314 + 0.546932i −0.892246 0.451550i \(-0.850871\pi\)
−0.0550686 + 0.998483i \(0.517538\pi\)
\(810\) 6.46750 + 16.7980i 0.227245 + 0.590220i
\(811\) −1.00000 1.00000i −0.0351147 0.0351147i 0.689331 0.724446i \(-0.257904\pi\)
−0.724446 + 0.689331i \(0.757904\pi\)
\(812\) 1.03528 + 3.86370i 0.0363311 + 0.135589i
\(813\) −29.7507 + 35.7896i −1.04340 + 1.25520i
\(814\) 4.00000 4.00000i 0.140200 0.140200i
\(815\) −2.44949 1.41421i −0.0858019 0.0495377i
\(816\) 0 0
\(817\) −8.19615 2.19615i −0.286747 0.0768336i
\(818\) −32.5269 −1.13728
\(819\) 0 0
\(820\) 4.00000 0.139686
\(821\) 9.65926 + 2.58819i 0.337110 + 0.0903285i 0.423403 0.905941i \(-0.360835\pi\)
−0.0862928 + 0.996270i \(0.527502\pi\)
\(822\) −10.1464 + 22.0239i −0.353897 + 0.768170i
\(823\) −25.9808 15.0000i −0.905632 0.522867i −0.0266091 0.999646i \(-0.508471\pi\)
−0.879023 + 0.476779i \(0.841804\pi\)
\(824\) −12.7279 + 12.7279i −0.443398 + 0.443398i
\(825\) −4.42883 + 5.32780i −0.154192 + 0.185490i
\(826\) 1.46410 + 5.46410i 0.0509426 + 0.190120i
\(827\) −22.6274 22.6274i −0.786832 0.786832i 0.194141 0.980974i \(-0.437808\pi\)
−0.980974 + 0.194141i \(0.937808\pi\)
\(828\) 19.3485 16.5420i 0.672406 0.574873i
\(829\) 15.5885 9.00000i 0.541409 0.312583i −0.204240 0.978921i \(-0.565472\pi\)
0.745650 + 0.666338i \(0.232139\pi\)
\(830\) 4.14110 15.4548i 0.143740 0.536444i
\(831\) −16.9706 + 12.0000i −0.588702 + 0.416275i
\(832\) 0 0
\(833\) 0 0
\(834\) 2.39960 + 6.49938i 0.0830914 + 0.225055i
\(835\) −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
\(838\) 10.9282 2.92820i 0.377509 0.101153i
\(839\) −3.86370 + 1.03528i −0.133390 + 0.0357417i −0.324896 0.945750i \(-0.605329\pi\)
0.191506 + 0.981491i \(0.438663\pi\)
\(840\) −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
\(843\) 22.7478 8.39861i 0.783477 0.289263i
\(844\) 14.0000i 0.481900i
\(845\) 0 0
\(846\) 4.00000 11.3137i 0.137523 0.388973i
\(847\) −1.83013 + 6.83013i −0.0628839 + 0.234686i
\(848\) −4.89898 + 2.82843i −0.168232 + 0.0971286i
\(849\) 1.90702 + 20.6969i 0.0654489 + 0.710317i
\(850\) 0 0
\(851\) −3.10583 11.5911i −0.106466 0.397338i
\(852\) −5.32780 4.42883i −0.182528 0.151729i
\(853\) −37.0000 + 37.0000i −1.26686 + 1.26686i −0.319152 + 0.947703i \(0.603398\pi\)
−0.947703 + 0.319152i \(0.896602\pi\)
\(854\) 9.79796 + 5.65685i 0.335279 + 0.193574i
\(855\) −8.34242 + 1.55051i −0.285305 + 0.0530263i
\(856\) 16.3923 + 4.39230i 0.560277 + 0.150126i
\(857\) −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 \(0.423234\pi\)
\(860\) 11.5911 + 3.10583i 0.395254 + 0.105908i
\(861\) −4.44949 2.04989i −0.151638 0.0698600i
\(862\) −27.7128 16.0000i −0.943902 0.544962i
\(863\) −2.82843 + 2.82843i −0.0962808 + 0.0962808i −0.753607 0.657326i \(-0.771688\pi\)
0.657326 + 0.753607i \(0.271688\pi\)
\(864\) 13.3006 + 22.3180i 0.452496 + 0.759274i
\(865\) −4.39230 16.3923i −0.149343 0.557355i
\(866\) −12.7279 12.7279i −0.432512 0.432512i
\(867\) −29.3207 + 2.70162i −0.995782 + 0.0917517i
\(868\) −8.66025 + 5.00000i −0.293948 + 0.169711i
\(869\) −10.3528 + 38.6370i −0.351193 + 1.31067i
\(870\) 5.65685 + 8.00000i 0.191785 + 0.271225i
\(871\) 0 0
\(872\) 4.24264i 0.143674i
\(873\) −24.4837 16.8091i −0.828649 0.568902i
\(874\) −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
\(877\) 17.7583 4.75833i 0.599656 0.160677i 0.0537936 0.998552i \(-0.482869\pi\)
0.545863 + 0.837875i \(0.316202\pi\)
\(878\) −28.9778 + 7.76457i −0.977953 + 0.262042i
\(879\) −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 \(0.974402\pi\)
\(882\) −12.3662 8.48988i −0.416390 0.285869i
\(883\) 36.0000i 1.21150i 0.795656 + 0.605748i \(0.207126\pi\)
−0.795656 + 0.605748i \(0.792874\pi\)
\(884\) 0 0
\(885\) −8.00000 11.3137i −0.268917 0.380306i
\(886\) −7.32051 + 27.3205i −0.245937 + 0.917850i
\(887\) −12.2474 + 7.07107i −0.411229 + 0.237423i −0.691318 0.722551i \(-0.742969\pi\)
0.280089 + 0.959974i \(0.409636\pi\)
\(888\) 7.31747 0.674235i 0.245558 0.0226258i
\(889\) 0 0
\(890\) 7.24693 + 27.0459i 0.242918 + 0.906581i
\(891\) 32.9023 + 14.6095i 1.10227 + 0.489436i
\(892\) −11.0000 + 11.0000i −0.368307 + 0.368307i
\(893\) 4.89898 + 2.82843i 0.163938 + 0.0946497i
\(894\) −3.14626 1.44949i −0.105227 0.0484782i
\(895\) 0 0
\(896\) −4.24264 −0.141737
\(897\) 0 0
\(898\) −22.0000 −0.734150
\(899\) 19.3185 + 5.17638i 0.644309 + 0.172642i
\(900\) −2.94949 + 0.548188i −0.0983163 + 0.0182729i
\(901\) 0 0
\(902\) −5.65685 + 5.65685i −0.188353 + 0.188353i
\(903\) −11.3020 9.39496i −0.376106 0.312645i
\(904\) −10.9808 40.9808i −0.365215 1.36300i
\(905\) 0 0
\(906\) −0.224745 2.43916i −0.00746665 0.0810356i
\(907\) −10.3923 + 6.00000i −0.345071 + 0.199227i −0.662512 0.749051i \(-0.730510\pi\)
0.317441 + 0.948278i \(0.397176\pi\)
\(908\) 2.07055 7.72741i 0.0687137 0.256443i
\(909\) 8.48528 24.0000i 0.281439 0.796030i
\(910\) 0 0
\(911\) 48.0833i 1.59307i −0.604593 0.796535i \(-0.706664\pi\)
0.604593 0.796535i \(-0.293336\pi\)
\(912\) 2.29788 0.848387i 0.0760903 0.0280929i
\(913\) −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
\(916\) 1.36603 0.366025i 0.0451347 0.0120938i
\(917\) 15.4548 4.14110i 0.510363 0.136751i
\(918\) 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
\(921\) 14.4226 + 39.0639i 0.475240 + 1.28720i
\(922\) 10.0000i 0.329332i
\(923\) 0 0
\(924\) −8.00000 + 5.65685i −0.263181 + 0.186097i
\(925\) −0.366025 + 1.36603i −0.0120348 + 0.0449146i
\(926\) 20.8207 12.0208i 0.684209 0.395029i
\(927\) −13.6814 + 11.6969i −0.449357 + 0.384178i
\(928\) 10.0000 + 10.0000i 0.328266 + 0.328266i
\(929\) −11.9057 44.4326i −0.390613 1.45779i −0.829126 0.559061i \(-0.811162\pi\)
0.438514 0.898725i \(-0.355505\pi\)
\(930\) −15.6583 + 18.8366i −0.513455 + 0.617678i
\(931\) 5.00000 5.00000i 0.163868 0.163868i
\(932\) 22.0454 + 12.7279i 0.722121 + 0.416917i
\(933\) −6.14966 + 13.3485i −0.201331 + 0.437009i
\(934\) −24.5885 6.58846i −0.804559 0.215581i
\(935\) 0 0
\(936\) 0 0
\(937\) −52.0000 −1.69877 −0.849383 0.527777i \(-0.823026\pi\)
−0.849383 + 0.527777i \(0.823026\pi\)
\(938\) −9.65926 2.58819i −0.315386 0.0845074i
\(939\) −5.79796 + 12.5851i −0.189209 + 0.410698i
\(940\) −6.92820 4.00000i −0.225973 0.130466i
\(941\) 26.8701 26.8701i 0.875939 0.875939i −0.117173 0.993112i \(-0.537383\pi\)
0.993112 + 0.117173i \(0.0373831\pi\)
\(942\) −15.5009 + 18.6473i −0.505046 + 0.607562i
\(943\) 4.39230 + 16.3923i 0.143033 + 0.533807i
\(944\) 2.82843 + 2.82843i 0.0920575 + 0.0920575i
\(945\) −14.2474 3.60697i −0.463470 0.117335i
\(946\) −20.7846 + 12.0000i −0.675766 + 0.390154i
\(947\) −8.28221 + 30.9096i −0.269136 + 1.00443i 0.690535 + 0.723299i \(0.257375\pi\)
−0.959670 + 0.281128i \(0.909291\pi\)
\(948\) −14.1421 + 10.0000i −0.459315 + 0.324785i
\(949\) 0 0
\(950\) 1.41421i 0.0458831i
\(951\) −5.99900 16.2484i −0.194531 0.526892i
\(952\) 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
\(955\) −5.46410 + 1.46410i −0.176814 + 0.0473772i
\(956\) −19.3185 + 5.17638i −0.624805 + 0.167416i
\(957\) 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
\(960\) −22.7478 + 8.39861i −0.734183 + 0.271064i
\(961\) 19.0000i 0.612903i
\(962\) 0 0
\(963\) 16.0000 + 5.65685i 0.515593 + 0.182290i
\(964\) 6.22243 23.2224i 0.200411 0.747944i
\(965\) 46.5403 26.8701i 1.49819 0.864978i
\(966\) −1.90702 20.6969i −0.0613575 0.665913i
\(967\) 23.0000 + 23.0000i 0.739630 + 0.739630i 0.972506 0.232876i \(-0.0748137\pi\)
−0.232876 + 0.972506i \(0.574814\pi\)
\(968\) 3.88229 + 14.4889i 0.124781 + 0.465690i
\(969\) 0 0
\(970\) 14.0000 14.0000i 0.449513 0.449513i
\(971\) 26.9444 + 15.5563i 0.864687 + 0.499227i 0.865579 0.500773i \(-0.166951\pi\)
−0.000892350 1.00000i \(0.500284\pi\)
\(972\) 6.91215 + 13.9722i 0.221707 + 0.448158i
\(973\) −5.46410 1.46410i −0.175171 0.0469369i
\(974\) 26.8701 0.860972
\(975\) 0 0
\(976\) 8.00000 0.256074
\(977\) −36.7052 9.83512i −1.17430 0.314653i −0.381638 0.924312i \(-0.624640\pi\)
−0.792664 + 0.609658i \(0.791307\pi\)
\(978\) 2.22474 + 1.02494i 0.0711395 + 0.0327741i
\(979\) 48.4974 + 28.0000i 1.54998 + 0.894884i
\(980\) −7.07107 + 7.07107i −0.225877 + 0.225877i
\(981\) −0.330749 + 4.22973i −0.0105600 + 0.135045i
\(982\) 10.9808 + 40.9808i 0.350410 + 1.30775i
\(983\) 2.82843 + 2.82843i 0.0902128 + 0.0902128i 0.750773 0.660560i \(-0.229681\pi\)
−0.660560 + 0.750773i \(0.729681\pi\)
\(984\) −10.3485 + 0.953512i −0.329897 + 0.0303968i
\(985\) 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
\(990\) −13.5838 + 19.7859i −0.431722 + 0.628836i
\(991\) 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
\(994\) −5.46410 + 1.46410i −0.173311 + 0.0464385i
\(995\) 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
\(999\) 7.34777 0.101725i 0.232473 0.00321842i
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.89.2 8
3.2 odd 2 inner 507.2.k.i.89.1 8
13.2 odd 12 507.2.f.a.239.2 4
13.3 even 3 507.2.f.a.437.1 4
13.4 even 6 507.2.k.j.488.2 8
13.5 odd 4 inner 507.2.k.i.80.2 8
13.6 odd 12 inner 507.2.k.i.188.1 8
13.7 odd 12 507.2.k.j.188.2 8
13.8 odd 4 507.2.k.j.80.1 8
13.9 even 3 inner 507.2.k.i.488.1 8
13.10 even 6 39.2.f.a.8.2 yes 4
13.11 odd 12 39.2.f.a.5.1 4
13.12 even 2 507.2.k.j.89.1 8
39.2 even 12 507.2.f.a.239.1 4
39.5 even 4 inner 507.2.k.i.80.1 8
39.8 even 4 507.2.k.j.80.2 8
39.11 even 12 39.2.f.a.5.2 yes 4
39.17 odd 6 507.2.k.j.488.1 8
39.20 even 12 507.2.k.j.188.1 8
39.23 odd 6 39.2.f.a.8.1 yes 4
39.29 odd 6 507.2.f.a.437.2 4
39.32 even 12 inner 507.2.k.i.188.2 8
39.35 odd 6 inner 507.2.k.i.488.2 8
39.38 odd 2 507.2.k.j.89.2 8
52.11 even 12 624.2.bf.d.161.2 4
52.23 odd 6 624.2.bf.d.593.2 4
65.23 odd 12 975.2.n.c.749.1 4
65.24 odd 12 975.2.o.j.551.2 4
65.37 even 12 975.2.n.c.824.2 4
65.49 even 6 975.2.o.j.476.1 4
65.62 odd 12 975.2.n.d.749.2 4
65.63 even 12 975.2.n.d.824.1 4
156.11 odd 12 624.2.bf.d.161.1 4
156.23 even 6 624.2.bf.d.593.1 4
195.23 even 12 975.2.n.c.749.2 4
195.62 even 12 975.2.n.d.749.1 4
195.89 even 12 975.2.o.j.551.1 4
195.128 odd 12 975.2.n.d.824.2 4
195.167 odd 12 975.2.n.c.824.1 4
195.179 odd 6 975.2.o.j.476.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.f.a.5.1 4 13.11 odd 12
39.2.f.a.5.2 yes 4 39.11 even 12
39.2.f.a.8.1 yes 4 39.23 odd 6
39.2.f.a.8.2 yes 4 13.10 even 6
507.2.f.a.239.1 4 39.2 even 12
507.2.f.a.239.2 4 13.2 odd 12
507.2.f.a.437.1 4 13.3 even 3
507.2.f.a.437.2 4 39.29 odd 6
507.2.k.i.80.1 8 39.5 even 4 inner
507.2.k.i.80.2 8 13.5 odd 4 inner
507.2.k.i.89.1 8 3.2 odd 2 inner
507.2.k.i.89.2 8 1.1 even 1 trivial
507.2.k.i.188.1 8 13.6 odd 12 inner
507.2.k.i.188.2 8 39.32 even 12 inner
507.2.k.i.488.1 8 13.9 even 3 inner
507.2.k.i.488.2 8 39.35 odd 6 inner
507.2.k.j.80.1 8 13.8 odd 4
507.2.k.j.80.2 8 39.8 even 4
507.2.k.j.89.1 8 13.12 even 2
507.2.k.j.89.2 8 39.38 odd 2
507.2.k.j.188.1 8 39.20 even 12
507.2.k.j.188.2 8 13.7 odd 12
507.2.k.j.488.1 8 39.17 odd 6
507.2.k.j.488.2 8 13.4 even 6
624.2.bf.d.161.1 4 156.11 odd 12
624.2.bf.d.161.2 4 52.11 even 12
624.2.bf.d.593.1 4 156.23 even 6
624.2.bf.d.593.2 4 52.23 odd 6
975.2.n.c.749.1 4 65.23 odd 12
975.2.n.c.749.2 4 195.23 even 12
975.2.n.c.824.1 4 195.167 odd 12
975.2.n.c.824.2 4 65.37 even 12
975.2.n.d.749.1 4 195.62 even 12
975.2.n.d.749.2 4 65.62 odd 12
975.2.n.d.824.1 4 65.63 even 12
975.2.n.d.824.2 4 195.128 odd 12
975.2.o.j.476.1 4 65.49 even 6
975.2.o.j.476.2 4 195.179 odd 6
975.2.o.j.551.1 4 195.89 even 12
975.2.o.j.551.2 4 65.24 odd 12