Properties

Label 1950.2.y.g.199.1
Level $1950$
Weight $2$
Character 1950.199
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1950,2,Mod(49,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), 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: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.g.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.366025 - 0.633975i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.366025 - 0.633975i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-4.09808 - 2.36603i) q^{11} +1.00000i q^{12} +(2.50000 + 2.59808i) q^{13} -0.732051 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.96410 + 1.13397i) q^{17} +1.00000 q^{18} +(1.09808 - 0.633975i) q^{19} +0.732051i q^{21} +(-4.09808 + 2.36603i) q^{22} +(-5.36603 - 3.09808i) q^{23} +(0.866025 + 0.500000i) q^{24} +(3.50000 - 0.866025i) q^{26} -1.00000i q^{27} +(-0.366025 + 0.633975i) q^{28} +(1.23205 - 2.13397i) q^{29} +5.46410i q^{31} +(0.500000 + 0.866025i) q^{32} +(2.36603 + 4.09808i) q^{33} +2.26795i q^{34} +(0.500000 - 0.866025i) q^{36} +(-5.23205 + 9.06218i) q^{37} -1.26795i q^{38} +(-0.866025 - 3.50000i) q^{39} +(9.86603 + 5.69615i) q^{41} +(0.633975 + 0.366025i) q^{42} +(-6.63397 + 3.83013i) q^{43} +4.73205i q^{44} +(-5.36603 + 3.09808i) q^{46} -8.19615 q^{47} +(0.866025 - 0.500000i) q^{48} +(3.23205 - 5.59808i) q^{49} +2.26795 q^{51} +(1.00000 - 3.46410i) q^{52} +0.464102i q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.366025 + 0.633975i) q^{56} -1.26795 q^{57} +(-1.23205 - 2.13397i) q^{58} +(-6.92820 + 4.00000i) q^{59} +(-0.598076 - 1.03590i) q^{61} +(4.73205 + 2.73205i) q^{62} +(0.366025 - 0.633975i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(-5.56218 + 9.63397i) q^{67} +(1.96410 + 1.13397i) q^{68} +(3.09808 + 5.36603i) q^{69} +(-1.09808 + 0.633975i) q^{71} +(-0.500000 - 0.866025i) q^{72} +9.73205 q^{73} +(5.23205 + 9.06218i) q^{74} +(-1.09808 - 0.633975i) q^{76} +3.46410i q^{77} +(-3.46410 - 1.00000i) q^{78} +9.46410 q^{79} +(-0.500000 + 0.866025i) q^{81} +(9.86603 - 5.69615i) q^{82} +10.1962 q^{83} +(0.633975 - 0.366025i) q^{84} +7.66025i q^{86} +(-2.13397 + 1.23205i) q^{87} +(4.09808 + 2.36603i) q^{88} +(-2.19615 - 1.26795i) q^{89} +(0.732051 - 2.53590i) q^{91} +6.19615i q^{92} +(2.73205 - 4.73205i) q^{93} +(-4.09808 + 7.09808i) q^{94} -1.00000i q^{96} +(-3.00000 - 5.19615i) q^{97} +(-3.23205 - 5.59808i) q^{98} -4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{7} - 4 q^{8} + 2 q^{9} - 6 q^{11} + 10 q^{13} + 4 q^{14} - 2 q^{16} + 6 q^{17} + 4 q^{18} - 6 q^{19} - 6 q^{22} - 18 q^{23} + 14 q^{26} + 2 q^{28} - 2 q^{29} + 2 q^{32} + 6 q^{33} + 2 q^{36} - 14 q^{37} + 36 q^{41} + 6 q^{42} - 30 q^{43} - 18 q^{46} - 12 q^{47} + 6 q^{49} + 16 q^{51} + 4 q^{52} - 2 q^{56} - 12 q^{57} + 2 q^{58} + 8 q^{61} + 12 q^{62} - 2 q^{63} + 4 q^{64} + 12 q^{66} + 2 q^{67} - 6 q^{68} + 2 q^{69} + 6 q^{71} - 2 q^{72} + 32 q^{73} + 14 q^{74} + 6 q^{76} + 24 q^{79} - 2 q^{81} + 36 q^{82} + 20 q^{83} + 6 q^{84} - 12 q^{87} + 6 q^{88} + 12 q^{89} - 4 q^{91} + 4 q^{93} - 6 q^{94} - 12 q^{97} - 6 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) −0.366025 0.633975i −0.138345 0.239620i 0.788526 0.615002i \(-0.210845\pi\)
−0.926870 + 0.375382i \(0.877511\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −4.09808 2.36603i −1.23562 0.713384i −0.267421 0.963580i \(-0.586172\pi\)
−0.968195 + 0.250196i \(0.919505\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.50000 + 2.59808i 0.693375 + 0.720577i
\(14\) −0.732051 −0.195649
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.96410 + 1.13397i −0.476365 + 0.275029i −0.718900 0.695113i \(-0.755354\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.09808 0.633975i 0.251916 0.145444i −0.368725 0.929538i \(-0.620206\pi\)
0.620641 + 0.784095i \(0.286872\pi\)
\(20\) 0 0
\(21\) 0.732051i 0.159747i
\(22\) −4.09808 + 2.36603i −0.873713 + 0.504438i
\(23\) −5.36603 3.09808i −1.11889 0.645994i −0.177775 0.984071i \(-0.556890\pi\)
−0.941118 + 0.338078i \(0.890223\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) 3.50000 0.866025i 0.686406 0.169842i
\(27\) 1.00000i 0.192450i
\(28\) −0.366025 + 0.633975i −0.0691723 + 0.119810i
\(29\) 1.23205 2.13397i 0.228786 0.396269i −0.728663 0.684873i \(-0.759858\pi\)
0.957449 + 0.288604i \(0.0931910\pi\)
\(30\) 0 0
\(31\) 5.46410i 0.981382i 0.871334 + 0.490691i \(0.163256\pi\)
−0.871334 + 0.490691i \(0.836744\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 2.36603 + 4.09808i 0.411872 + 0.713384i
\(34\) 2.26795i 0.388950i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −5.23205 + 9.06218i −0.860144 + 1.48981i 0.0116456 + 0.999932i \(0.496293\pi\)
−0.871789 + 0.489881i \(0.837040\pi\)
\(38\) 1.26795i 0.205689i
\(39\) −0.866025 3.50000i −0.138675 0.560449i
\(40\) 0 0
\(41\) 9.86603 + 5.69615i 1.54081 + 0.889590i 0.998788 + 0.0492283i \(0.0156762\pi\)
0.542027 + 0.840361i \(0.317657\pi\)
\(42\) 0.633975 + 0.366025i 0.0978244 + 0.0564789i
\(43\) −6.63397 + 3.83013i −1.01167 + 0.584089i −0.911681 0.410899i \(-0.865215\pi\)
−0.0999910 + 0.994988i \(0.531881\pi\)
\(44\) 4.73205i 0.713384i
\(45\) 0 0
\(46\) −5.36603 + 3.09808i −0.791177 + 0.456786i
\(47\) −8.19615 −1.19553 −0.597766 0.801671i \(-0.703945\pi\)
−0.597766 + 0.801671i \(0.703945\pi\)
\(48\) 0.866025 0.500000i 0.125000 0.0721688i
\(49\) 3.23205 5.59808i 0.461722 0.799725i
\(50\) 0 0
\(51\) 2.26795 0.317576
\(52\) 1.00000 3.46410i 0.138675 0.480384i
\(53\) 0.464102i 0.0637493i 0.999492 + 0.0318746i \(0.0101477\pi\)
−0.999492 + 0.0318746i \(0.989852\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0 0
\(56\) 0.366025 + 0.633975i 0.0489122 + 0.0847184i
\(57\) −1.26795 −0.167944
\(58\) −1.23205 2.13397i −0.161776 0.280205i
\(59\) −6.92820 + 4.00000i −0.901975 + 0.520756i −0.877841 0.478953i \(-0.841016\pi\)
−0.0241347 + 0.999709i \(0.507683\pi\)
\(60\) 0 0
\(61\) −0.598076 1.03590i −0.0765758 0.132633i 0.825195 0.564848i \(-0.191065\pi\)
−0.901770 + 0.432215i \(0.857732\pi\)
\(62\) 4.73205 + 2.73205i 0.600971 + 0.346971i
\(63\) 0.366025 0.633975i 0.0461149 0.0798733i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.73205 0.582475
\(67\) −5.56218 + 9.63397i −0.679528 + 1.17698i 0.295595 + 0.955313i \(0.404482\pi\)
−0.975123 + 0.221664i \(0.928851\pi\)
\(68\) 1.96410 + 1.13397i 0.238182 + 0.137515i
\(69\) 3.09808 + 5.36603i 0.372965 + 0.645994i
\(70\) 0 0
\(71\) −1.09808 + 0.633975i −0.130318 + 0.0752389i −0.563742 0.825951i \(-0.690639\pi\)
0.433424 + 0.901190i \(0.357305\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 9.73205 1.13905 0.569525 0.821974i \(-0.307127\pi\)
0.569525 + 0.821974i \(0.307127\pi\)
\(74\) 5.23205 + 9.06218i 0.608214 + 1.05346i
\(75\) 0 0
\(76\) −1.09808 0.633975i −0.125958 0.0727219i
\(77\) 3.46410i 0.394771i
\(78\) −3.46410 1.00000i −0.392232 0.113228i
\(79\) 9.46410 1.06479 0.532397 0.846495i \(-0.321291\pi\)
0.532397 + 0.846495i \(0.321291\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 9.86603 5.69615i 1.08952 0.629035i
\(83\) 10.1962 1.11917 0.559587 0.828772i \(-0.310960\pi\)
0.559587 + 0.828772i \(0.310960\pi\)
\(84\) 0.633975 0.366025i 0.0691723 0.0399366i
\(85\) 0 0
\(86\) 7.66025i 0.826026i
\(87\) −2.13397 + 1.23205i −0.228786 + 0.132090i
\(88\) 4.09808 + 2.36603i 0.436856 + 0.252219i
\(89\) −2.19615 1.26795i −0.232792 0.134402i 0.379068 0.925369i \(-0.376245\pi\)
−0.611859 + 0.790967i \(0.709578\pi\)
\(90\) 0 0
\(91\) 0.732051 2.53590i 0.0767398 0.265834i
\(92\) 6.19615i 0.645994i
\(93\) 2.73205 4.73205i 0.283300 0.490691i
\(94\) −4.09808 + 7.09808i −0.422684 + 0.732111i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −3.00000 5.19615i −0.304604 0.527589i 0.672569 0.740034i \(-0.265191\pi\)
−0.977173 + 0.212445i \(0.931857\pi\)
\(98\) −3.23205 5.59808i −0.326486 0.565491i
\(99\) 4.73205i 0.475589i
\(100\) 0 0
\(101\) −5.96410 + 10.3301i −0.593450 + 1.02789i 0.400313 + 0.916378i \(0.368901\pi\)
−0.993764 + 0.111508i \(0.964432\pi\)
\(102\) 1.13397 1.96410i 0.112280 0.194475i
\(103\) 18.7321i 1.84572i 0.385131 + 0.922862i \(0.374156\pi\)
−0.385131 + 0.922862i \(0.625844\pi\)
\(104\) −2.50000 2.59808i −0.245145 0.254762i
\(105\) 0 0
\(106\) 0.401924 + 0.232051i 0.0390383 + 0.0225388i
\(107\) −0.169873 0.0980762i −0.0164222 0.00948139i 0.491766 0.870727i \(-0.336351\pi\)
−0.508189 + 0.861246i \(0.669685\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) 5.46410i 0.523366i −0.965154 0.261683i \(-0.915723\pi\)
0.965154 0.261683i \(-0.0842775\pi\)
\(110\) 0 0
\(111\) 9.06218 5.23205i 0.860144 0.496604i
\(112\) 0.732051 0.0691723
\(113\) −16.1603 + 9.33013i −1.52023 + 0.877705i −0.520513 + 0.853854i \(0.674259\pi\)
−0.999716 + 0.0238510i \(0.992407\pi\)
\(114\) −0.633975 + 1.09808i −0.0593772 + 0.102844i
\(115\) 0 0
\(116\) −2.46410 −0.228786
\(117\) −1.00000 + 3.46410i −0.0924500 + 0.320256i
\(118\) 8.00000i 0.736460i
\(119\) 1.43782 + 0.830127i 0.131805 + 0.0760976i
\(120\) 0 0
\(121\) 5.69615 + 9.86603i 0.517832 + 0.896911i
\(122\) −1.19615 −0.108295
\(123\) −5.69615 9.86603i −0.513605 0.889590i
\(124\) 4.73205 2.73205i 0.424951 0.245345i
\(125\) 0 0
\(126\) −0.366025 0.633975i −0.0326081 0.0564789i
\(127\) −15.4641 8.92820i −1.37222 0.792250i −0.381010 0.924571i \(-0.624424\pi\)
−0.991207 + 0.132321i \(0.957757\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 7.66025 0.674448
\(130\) 0 0
\(131\) 13.4641 1.17636 0.588182 0.808729i \(-0.299844\pi\)
0.588182 + 0.808729i \(0.299844\pi\)
\(132\) 2.36603 4.09808i 0.205936 0.356692i
\(133\) −0.803848 0.464102i −0.0697024 0.0402427i
\(134\) 5.56218 + 9.63397i 0.480499 + 0.832249i
\(135\) 0 0
\(136\) 1.96410 1.13397i 0.168420 0.0972375i
\(137\) 0.964102 + 1.66987i 0.0823688 + 0.142667i 0.904267 0.426968i \(-0.140418\pi\)
−0.821898 + 0.569634i \(0.807085\pi\)
\(138\) 6.19615 0.527452
\(139\) −4.92820 8.53590i −0.418005 0.724005i 0.577734 0.816225i \(-0.303937\pi\)
−0.995739 + 0.0922197i \(0.970604\pi\)
\(140\) 0 0
\(141\) 7.09808 + 4.09808i 0.597766 + 0.345120i
\(142\) 1.26795i 0.106404i
\(143\) −4.09808 16.5622i −0.342698 1.38500i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 4.86603 8.42820i 0.402715 0.697523i
\(147\) −5.59808 + 3.23205i −0.461722 + 0.266575i
\(148\) 10.4641 0.860144
\(149\) 2.42820 1.40192i 0.198926 0.114850i −0.397228 0.917720i \(-0.630028\pi\)
0.596154 + 0.802870i \(0.296695\pi\)
\(150\) 0 0
\(151\) 3.26795i 0.265942i 0.991120 + 0.132971i \(0.0424517\pi\)
−0.991120 + 0.132971i \(0.957548\pi\)
\(152\) −1.09808 + 0.633975i −0.0890657 + 0.0514221i
\(153\) −1.96410 1.13397i −0.158788 0.0916764i
\(154\) 3.00000 + 1.73205i 0.241747 + 0.139573i
\(155\) 0 0
\(156\) −2.59808 + 2.50000i −0.208013 + 0.200160i
\(157\) 23.5885i 1.88256i 0.337622 + 0.941282i \(0.390378\pi\)
−0.337622 + 0.941282i \(0.609622\pi\)
\(158\) 4.73205 8.19615i 0.376462 0.652051i
\(159\) 0.232051 0.401924i 0.0184028 0.0318746i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) 0.500000 + 0.866025i 0.0392837 + 0.0680414i
\(163\) −3.26795 5.66025i −0.255966 0.443345i 0.709192 0.705016i \(-0.249060\pi\)
−0.965157 + 0.261670i \(0.915727\pi\)
\(164\) 11.3923i 0.889590i
\(165\) 0 0
\(166\) 5.09808 8.83013i 0.395687 0.685351i
\(167\) 1.26795 2.19615i 0.0981169 0.169943i −0.812788 0.582559i \(-0.802051\pi\)
0.910905 + 0.412616i \(0.135385\pi\)
\(168\) 0.732051i 0.0564789i
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 0 0
\(171\) 1.09808 + 0.633975i 0.0839720 + 0.0484812i
\(172\) 6.63397 + 3.83013i 0.505836 + 0.292044i
\(173\) 14.1962 8.19615i 1.07931 0.623142i 0.148602 0.988897i \(-0.452523\pi\)
0.930711 + 0.365755i \(0.119189\pi\)
\(174\) 2.46410i 0.186803i
\(175\) 0 0
\(176\) 4.09808 2.36603i 0.308904 0.178346i
\(177\) 8.00000 0.601317
\(178\) −2.19615 + 1.26795i −0.164609 + 0.0950368i
\(179\) −11.0263 + 19.0981i −0.824143 + 1.42746i 0.0784298 + 0.996920i \(0.475009\pi\)
−0.902573 + 0.430538i \(0.858324\pi\)
\(180\) 0 0
\(181\) −8.80385 −0.654385 −0.327192 0.944958i \(-0.606103\pi\)
−0.327192 + 0.944958i \(0.606103\pi\)
\(182\) −1.83013 1.90192i −0.135658 0.140980i
\(183\) 1.19615i 0.0884221i
\(184\) 5.36603 + 3.09808i 0.395589 + 0.228393i
\(185\) 0 0
\(186\) −2.73205 4.73205i −0.200324 0.346971i
\(187\) 10.7321 0.784805
\(188\) 4.09808 + 7.09808i 0.298883 + 0.517680i
\(189\) −0.633975 + 0.366025i −0.0461149 + 0.0266244i
\(190\) 0 0
\(191\) −3.46410 6.00000i −0.250654 0.434145i 0.713052 0.701111i \(-0.247312\pi\)
−0.963706 + 0.266966i \(0.913979\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −4.13397 + 7.16025i −0.297570 + 0.515406i −0.975579 0.219647i \(-0.929510\pi\)
0.678009 + 0.735053i \(0.262843\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) −6.46410 −0.461722
\(197\) 4.92820 8.53590i 0.351120 0.608158i −0.635326 0.772244i \(-0.719134\pi\)
0.986446 + 0.164086i \(0.0524676\pi\)
\(198\) −4.09808 2.36603i −0.291238 0.168146i
\(199\) 1.90192 + 3.29423i 0.134824 + 0.233522i 0.925530 0.378674i \(-0.123620\pi\)
−0.790706 + 0.612196i \(0.790286\pi\)
\(200\) 0 0
\(201\) 9.63397 5.56218i 0.679528 0.392326i
\(202\) 5.96410 + 10.3301i 0.419633 + 0.726825i
\(203\) −1.80385 −0.126605
\(204\) −1.13397 1.96410i −0.0793941 0.137515i
\(205\) 0 0
\(206\) 16.2224 + 9.36603i 1.13027 + 0.652562i
\(207\) 6.19615i 0.430662i
\(208\) −3.50000 + 0.866025i −0.242681 + 0.0600481i
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) 2.19615 3.80385i 0.151189 0.261868i −0.780476 0.625186i \(-0.785023\pi\)
0.931665 + 0.363319i \(0.118356\pi\)
\(212\) 0.401924 0.232051i 0.0276042 0.0159373i
\(213\) 1.26795 0.0868784
\(214\) −0.169873 + 0.0980762i −0.0116123 + 0.00670435i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 3.46410 2.00000i 0.235159 0.135769i
\(218\) −4.73205 2.73205i −0.320495 0.185038i
\(219\) −8.42820 4.86603i −0.569525 0.328816i
\(220\) 0 0
\(221\) −7.85641 2.26795i −0.528479 0.152559i
\(222\) 10.4641i 0.702305i
\(223\) 6.53590 11.3205i 0.437676 0.758077i −0.559834 0.828605i \(-0.689135\pi\)
0.997510 + 0.0705277i \(0.0224683\pi\)
\(224\) 0.366025 0.633975i 0.0244561 0.0423592i
\(225\) 0 0
\(226\) 18.6603i 1.24126i
\(227\) −0.901924 1.56218i −0.0598628 0.103685i 0.834541 0.550946i \(-0.185733\pi\)
−0.894404 + 0.447261i \(0.852400\pi\)
\(228\) 0.633975 + 1.09808i 0.0419860 + 0.0727219i
\(229\) 15.8564i 1.04782i −0.851773 0.523910i \(-0.824473\pi\)
0.851773 0.523910i \(-0.175527\pi\)
\(230\) 0 0
\(231\) 1.73205 3.00000i 0.113961 0.197386i
\(232\) −1.23205 + 2.13397i −0.0808881 + 0.140102i
\(233\) 19.8564i 1.30084i −0.759576 0.650418i \(-0.774594\pi\)
0.759576 0.650418i \(-0.225406\pi\)
\(234\) 2.50000 + 2.59808i 0.163430 + 0.169842i
\(235\) 0 0
\(236\) 6.92820 + 4.00000i 0.450988 + 0.260378i
\(237\) −8.19615 4.73205i −0.532397 0.307380i
\(238\) 1.43782 0.830127i 0.0932002 0.0538091i
\(239\) 9.66025i 0.624870i −0.949939 0.312435i \(-0.898855\pi\)
0.949939 0.312435i \(-0.101145\pi\)
\(240\) 0 0
\(241\) −15.2321 + 8.79423i −0.981183 + 0.566486i −0.902627 0.430424i \(-0.858364\pi\)
−0.0785557 + 0.996910i \(0.525031\pi\)
\(242\) 11.3923 0.732325
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −0.598076 + 1.03590i −0.0382879 + 0.0663166i
\(245\) 0 0
\(246\) −11.3923 −0.726347
\(247\) 4.39230 + 1.26795i 0.279476 + 0.0806777i
\(248\) 5.46410i 0.346971i
\(249\) −8.83013 5.09808i −0.559587 0.323077i
\(250\) 0 0
\(251\) 3.26795 + 5.66025i 0.206271 + 0.357272i 0.950537 0.310611i \(-0.100534\pi\)
−0.744266 + 0.667883i \(0.767200\pi\)
\(252\) −0.732051 −0.0461149
\(253\) 14.6603 + 25.3923i 0.921682 + 1.59640i
\(254\) −15.4641 + 8.92820i −0.970304 + 0.560205i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −23.0885 13.3301i −1.44022 0.831510i −0.442355 0.896840i \(-0.645857\pi\)
−0.997864 + 0.0653297i \(0.979190\pi\)
\(258\) 3.83013 6.63397i 0.238453 0.413013i
\(259\) 7.66025 0.475985
\(260\) 0 0
\(261\) 2.46410 0.152524
\(262\) 6.73205 11.6603i 0.415907 0.720373i
\(263\) −24.2942 14.0263i −1.49805 0.864897i −0.498049 0.867149i \(-0.665950\pi\)
−0.999997 + 0.00225153i \(0.999283\pi\)
\(264\) −2.36603 4.09808i −0.145619 0.252219i
\(265\) 0 0
\(266\) −0.803848 + 0.464102i −0.0492871 + 0.0284559i
\(267\) 1.26795 + 2.19615i 0.0775972 + 0.134402i
\(268\) 11.1244 0.679528
\(269\) −0.732051 1.26795i −0.0446339 0.0773082i 0.842845 0.538156i \(-0.180879\pi\)
−0.887479 + 0.460848i \(0.847545\pi\)
\(270\) 0 0
\(271\) −5.07180 2.92820i −0.308090 0.177876i 0.337982 0.941153i \(-0.390256\pi\)
−0.646071 + 0.763277i \(0.723589\pi\)
\(272\) 2.26795i 0.137515i
\(273\) −1.90192 + 1.83013i −0.115110 + 0.110764i
\(274\) 1.92820 0.116487
\(275\) 0 0
\(276\) 3.09808 5.36603i 0.186482 0.322997i
\(277\) −1.96410 + 1.13397i −0.118011 + 0.0681339i −0.557844 0.829946i \(-0.688371\pi\)
0.439832 + 0.898080i \(0.355038\pi\)
\(278\) −9.85641 −0.591148
\(279\) −4.73205 + 2.73205i −0.283300 + 0.163564i
\(280\) 0 0
\(281\) 22.3205i 1.33153i −0.746162 0.665765i \(-0.768105\pi\)
0.746162 0.665765i \(-0.231895\pi\)
\(282\) 7.09808 4.09808i 0.422684 0.244037i
\(283\) 7.22243 + 4.16987i 0.429329 + 0.247873i 0.699061 0.715062i \(-0.253602\pi\)
−0.269732 + 0.962936i \(0.586935\pi\)
\(284\) 1.09808 + 0.633975i 0.0651588 + 0.0376195i
\(285\) 0 0
\(286\) −16.3923 4.73205i −0.969297 0.279812i
\(287\) 8.33975i 0.492280i
\(288\) −0.500000 + 0.866025i −0.0294628 + 0.0510310i
\(289\) −5.92820 + 10.2679i −0.348718 + 0.603997i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) −4.86603 8.42820i −0.284763 0.493223i
\(293\) −7.25833 12.5718i −0.424036 0.734452i 0.572294 0.820049i \(-0.306054\pi\)
−0.996330 + 0.0855965i \(0.972720\pi\)
\(294\) 6.46410i 0.376994i
\(295\) 0 0
\(296\) 5.23205 9.06218i 0.304107 0.526728i
\(297\) −2.36603 + 4.09808i −0.137291 + 0.237795i
\(298\) 2.80385i 0.162423i
\(299\) −5.36603 21.6865i −0.310325 1.25416i
\(300\) 0 0
\(301\) 4.85641 + 2.80385i 0.279919 + 0.161611i
\(302\) 2.83013 + 1.63397i 0.162856 + 0.0940247i
\(303\) 10.3301 5.96410i 0.593450 0.342629i
\(304\) 1.26795i 0.0727219i
\(305\) 0 0
\(306\) −1.96410 + 1.13397i −0.112280 + 0.0648250i
\(307\) 8.58846 0.490169 0.245085 0.969502i \(-0.421184\pi\)
0.245085 + 0.969502i \(0.421184\pi\)
\(308\) 3.00000 1.73205i 0.170941 0.0986928i
\(309\) 9.36603 16.2224i 0.532815 0.922862i
\(310\) 0 0
\(311\) −15.6603 −0.888012 −0.444006 0.896024i \(-0.646443\pi\)
−0.444006 + 0.896024i \(0.646443\pi\)
\(312\) 0.866025 + 3.50000i 0.0490290 + 0.198148i
\(313\) 13.4641i 0.761036i 0.924774 + 0.380518i \(0.124254\pi\)
−0.924774 + 0.380518i \(0.875746\pi\)
\(314\) 20.4282 + 11.7942i 1.15283 + 0.665587i
\(315\) 0 0
\(316\) −4.73205 8.19615i −0.266199 0.461070i
\(317\) −3.33975 −0.187579 −0.0937894 0.995592i \(-0.529898\pi\)
−0.0937894 + 0.995592i \(0.529898\pi\)
\(318\) −0.232051 0.401924i −0.0130128 0.0225388i
\(319\) −10.0981 + 5.83013i −0.565384 + 0.326424i
\(320\) 0 0
\(321\) 0.0980762 + 0.169873i 0.00547408 + 0.00948139i
\(322\) 3.92820 + 2.26795i 0.218910 + 0.126388i
\(323\) −1.43782 + 2.49038i −0.0800026 + 0.138569i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.53590 −0.361990
\(327\) −2.73205 + 4.73205i −0.151083 + 0.261683i
\(328\) −9.86603 5.69615i −0.544760 0.314517i
\(329\) 3.00000 + 5.19615i 0.165395 + 0.286473i
\(330\) 0 0
\(331\) −17.3205 + 10.0000i −0.952021 + 0.549650i −0.893708 0.448649i \(-0.851905\pi\)
−0.0583130 + 0.998298i \(0.518572\pi\)
\(332\) −5.09808 8.83013i −0.279793 0.484616i
\(333\) −10.4641 −0.573429
\(334\) −1.26795 2.19615i −0.0693791 0.120168i
\(335\) 0 0
\(336\) −0.633975 0.366025i −0.0345861 0.0199683i
\(337\) 6.85641i 0.373492i 0.982408 + 0.186746i \(0.0597942\pi\)
−0.982408 + 0.186746i \(0.940206\pi\)
\(338\) 11.0000 + 6.92820i 0.598321 + 0.376845i
\(339\) 18.6603 1.01349
\(340\) 0 0
\(341\) 12.9282 22.3923i 0.700101 1.21261i
\(342\) 1.09808 0.633975i 0.0593772 0.0342814i
\(343\) −9.85641 −0.532196
\(344\) 6.63397 3.83013i 0.357680 0.206507i
\(345\) 0 0
\(346\) 16.3923i 0.881256i
\(347\) −7.68653 + 4.43782i −0.412635 + 0.238235i −0.691921 0.721973i \(-0.743235\pi\)
0.279286 + 0.960208i \(0.409902\pi\)
\(348\) 2.13397 + 1.23205i 0.114393 + 0.0660449i
\(349\) −16.7321 9.66025i −0.895646 0.517102i −0.0198610 0.999803i \(-0.506322\pi\)
−0.875785 + 0.482701i \(0.839656\pi\)
\(350\) 0 0
\(351\) 2.59808 2.50000i 0.138675 0.133440i
\(352\) 4.73205i 0.252219i
\(353\) −9.89230 + 17.1340i −0.526514 + 0.911949i 0.473008 + 0.881058i \(0.343168\pi\)
−0.999523 + 0.0308916i \(0.990165\pi\)
\(354\) 4.00000 6.92820i 0.212598 0.368230i
\(355\) 0 0
\(356\) 2.53590i 0.134402i
\(357\) −0.830127 1.43782i −0.0439350 0.0760976i
\(358\) 11.0263 + 19.0981i 0.582757 + 1.00936i
\(359\) 23.1244i 1.22046i −0.792226 0.610228i \(-0.791078\pi\)
0.792226 0.610228i \(-0.208922\pi\)
\(360\) 0 0
\(361\) −8.69615 + 15.0622i −0.457692 + 0.792746i
\(362\) −4.40192 + 7.62436i −0.231360 + 0.400727i
\(363\) 11.3923i 0.597941i
\(364\) −2.56218 + 0.633975i −0.134295 + 0.0332293i
\(365\) 0 0
\(366\) 1.03590 + 0.598076i 0.0541473 + 0.0312619i
\(367\) −12.7583 7.36603i −0.665979 0.384503i 0.128572 0.991700i \(-0.458961\pi\)
−0.794551 + 0.607197i \(0.792294\pi\)
\(368\) 5.36603 3.09808i 0.279723 0.161498i
\(369\) 11.3923i 0.593060i
\(370\) 0 0
\(371\) 0.294229 0.169873i 0.0152756 0.00881937i
\(372\) −5.46410 −0.283300
\(373\) −8.89230 + 5.13397i −0.460426 + 0.265827i −0.712223 0.701953i \(-0.752312\pi\)
0.251797 + 0.967780i \(0.418978\pi\)
\(374\) 5.36603 9.29423i 0.277471 0.480593i
\(375\) 0 0
\(376\) 8.19615 0.422684
\(377\) 8.62436 2.13397i 0.444177 0.109905i
\(378\) 0.732051i 0.0376526i
\(379\) −1.26795 0.732051i −0.0651302 0.0376029i 0.467081 0.884214i \(-0.345306\pi\)
−0.532211 + 0.846611i \(0.678639\pi\)
\(380\) 0 0
\(381\) 8.92820 + 15.4641i 0.457406 + 0.792250i
\(382\) −6.92820 −0.354478
\(383\) −2.73205 4.73205i −0.139601 0.241797i 0.787744 0.616002i \(-0.211249\pi\)
−0.927346 + 0.374206i \(0.877915\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) 4.13397 + 7.16025i 0.210414 + 0.364447i
\(387\) −6.63397 3.83013i −0.337224 0.194696i
\(388\) −3.00000 + 5.19615i −0.152302 + 0.263795i
\(389\) −29.7846 −1.51014 −0.755070 0.655644i \(-0.772397\pi\)
−0.755070 + 0.655644i \(0.772397\pi\)
\(390\) 0 0
\(391\) 14.0526 0.710668
\(392\) −3.23205 + 5.59808i −0.163243 + 0.282746i
\(393\) −11.6603 6.73205i −0.588182 0.339587i
\(394\) −4.92820 8.53590i −0.248279 0.430032i
\(395\) 0 0
\(396\) −4.09808 + 2.36603i −0.205936 + 0.118897i
\(397\) 0.196152 + 0.339746i 0.00984461 + 0.0170514i 0.870906 0.491450i \(-0.163533\pi\)
−0.861061 + 0.508501i \(0.830200\pi\)
\(398\) 3.80385 0.190670
\(399\) 0.464102 + 0.803848i 0.0232341 + 0.0402427i
\(400\) 0 0
\(401\) −18.9904 10.9641i −0.948334 0.547521i −0.0557713 0.998444i \(-0.517762\pi\)
−0.892563 + 0.450922i \(0.851095\pi\)
\(402\) 11.1244i 0.554832i
\(403\) −14.1962 + 13.6603i −0.707161 + 0.680466i
\(404\) 11.9282 0.593450
\(405\) 0 0
\(406\) −0.901924 + 1.56218i −0.0447617 + 0.0775296i
\(407\) 42.8827 24.7583i 2.12562 1.22722i
\(408\) −2.26795 −0.112280
\(409\) 12.3564 7.13397i 0.610985 0.352752i −0.162366 0.986731i \(-0.551912\pi\)
0.773351 + 0.633978i \(0.218579\pi\)
\(410\) 0 0
\(411\) 1.92820i 0.0951113i
\(412\) 16.2224 9.36603i 0.799222 0.461431i
\(413\) 5.07180 + 2.92820i 0.249567 + 0.144087i
\(414\) −5.36603 3.09808i −0.263726 0.152262i
\(415\) 0 0
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) 9.85641i 0.482670i
\(418\) −3.00000 + 5.19615i −0.146735 + 0.254152i
\(419\) −5.26795 + 9.12436i −0.257356 + 0.445754i −0.965533 0.260281i \(-0.916185\pi\)
0.708177 + 0.706035i \(0.249518\pi\)
\(420\) 0 0
\(421\) 32.7128i 1.59432i −0.603765 0.797162i \(-0.706333\pi\)
0.603765 0.797162i \(-0.293667\pi\)
\(422\) −2.19615 3.80385i −0.106907 0.185168i
\(423\) −4.09808 7.09808i −0.199255 0.345120i
\(424\) 0.464102i 0.0225388i
\(425\) 0 0
\(426\) 0.633975 1.09808i 0.0307162 0.0532020i
\(427\) −0.437822 + 0.758330i −0.0211877 + 0.0366982i
\(428\) 0.196152i 0.00948139i
\(429\) −4.73205 + 16.3923i −0.228466 + 0.791428i
\(430\) 0 0
\(431\) −9.63397 5.56218i −0.464052 0.267921i 0.249694 0.968325i \(-0.419670\pi\)
−0.713747 + 0.700404i \(0.753003\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 12.8660 7.42820i 0.618302 0.356977i −0.157906 0.987454i \(-0.550474\pi\)
0.776208 + 0.630478i \(0.217141\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 0 0
\(436\) −4.73205 + 2.73205i −0.226624 + 0.130842i
\(437\) −7.85641 −0.375823
\(438\) −8.42820 + 4.86603i −0.402715 + 0.232508i
\(439\) 8.83013 15.2942i 0.421439 0.729954i −0.574642 0.818405i \(-0.694859\pi\)
0.996080 + 0.0884515i \(0.0281918\pi\)
\(440\) 0 0
\(441\) 6.46410 0.307814
\(442\) −5.89230 + 5.66987i −0.280268 + 0.269688i
\(443\) 36.3923i 1.72905i 0.502589 + 0.864525i \(0.332381\pi\)
−0.502589 + 0.864525i \(0.667619\pi\)
\(444\) −9.06218 5.23205i −0.430072 0.248302i
\(445\) 0 0
\(446\) −6.53590 11.3205i −0.309484 0.536042i
\(447\) −2.80385 −0.132617
\(448\) −0.366025 0.633975i −0.0172931 0.0299525i
\(449\) 20.1962 11.6603i 0.953115 0.550281i 0.0590680 0.998254i \(-0.481187\pi\)
0.894047 + 0.447973i \(0.147854\pi\)
\(450\) 0 0
\(451\) −26.9545 46.6865i −1.26924 2.19838i
\(452\) 16.1603 + 9.33013i 0.760114 + 0.438852i
\(453\) 1.63397 2.83013i 0.0767708 0.132971i
\(454\) −1.80385 −0.0846588
\(455\) 0 0
\(456\) 1.26795 0.0593772
\(457\) 9.33013 16.1603i 0.436445 0.755945i −0.560967 0.827838i \(-0.689571\pi\)
0.997412 + 0.0718931i \(0.0229040\pi\)
\(458\) −13.7321 7.92820i −0.641657 0.370461i
\(459\) 1.13397 + 1.96410i 0.0529294 + 0.0916764i
\(460\) 0 0
\(461\) −22.2846 + 12.8660i −1.03790 + 0.599231i −0.919237 0.393704i \(-0.871193\pi\)
−0.118661 + 0.992935i \(0.537860\pi\)
\(462\) −1.73205 3.00000i −0.0805823 0.139573i
\(463\) 28.0526 1.30371 0.651856 0.758342i \(-0.273990\pi\)
0.651856 + 0.758342i \(0.273990\pi\)
\(464\) 1.23205 + 2.13397i 0.0571965 + 0.0990673i
\(465\) 0 0
\(466\) −17.1962 9.92820i −0.796596 0.459915i
\(467\) 12.5885i 0.582524i −0.956643 0.291262i \(-0.905925\pi\)
0.956643 0.291262i \(-0.0940752\pi\)
\(468\) 3.50000 0.866025i 0.161788 0.0400320i
\(469\) 8.14359 0.376036
\(470\) 0 0
\(471\) 11.7942 20.4282i 0.543449 0.941282i
\(472\) 6.92820 4.00000i 0.318896 0.184115i
\(473\) 36.2487 1.66672
\(474\) −8.19615 + 4.73205i −0.376462 + 0.217350i
\(475\) 0 0
\(476\) 1.66025i 0.0760976i
\(477\) −0.401924 + 0.232051i −0.0184028 + 0.0106249i
\(478\) −8.36603 4.83013i −0.382653 0.220925i
\(479\) 22.9808 + 13.2679i 1.05002 + 0.606228i 0.922654 0.385628i \(-0.126015\pi\)
0.127363 + 0.991856i \(0.459349\pi\)
\(480\) 0 0
\(481\) −36.6244 + 9.06218i −1.66993 + 0.413200i
\(482\) 17.5885i 0.801132i
\(483\) 2.26795 3.92820i 0.103195 0.178739i
\(484\) 5.69615 9.86603i 0.258916 0.448456i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 10.5622 + 18.2942i 0.478618 + 0.828991i 0.999699 0.0245163i \(-0.00780457\pi\)
−0.521081 + 0.853507i \(0.674471\pi\)
\(488\) 0.598076 + 1.03590i 0.0270736 + 0.0468929i
\(489\) 6.53590i 0.295564i
\(490\) 0 0
\(491\) 2.63397 4.56218i 0.118870 0.205888i −0.800450 0.599399i \(-0.795406\pi\)
0.919320 + 0.393511i \(0.128740\pi\)
\(492\) −5.69615 + 9.86603i −0.256802 + 0.444795i
\(493\) 5.58846i 0.251691i
\(494\) 3.29423 3.16987i 0.148214 0.142619i
\(495\) 0 0
\(496\) −4.73205 2.73205i −0.212475 0.122673i
\(497\) 0.803848 + 0.464102i 0.0360575 + 0.0208178i
\(498\) −8.83013 + 5.09808i −0.395687 + 0.228450i
\(499\) 32.0000i 1.43252i 0.697835 + 0.716258i \(0.254147\pi\)
−0.697835 + 0.716258i \(0.745853\pi\)
\(500\) 0 0
\(501\) −2.19615 + 1.26795i −0.0981169 + 0.0566478i
\(502\) 6.53590 0.291711
\(503\) −9.50962 + 5.49038i −0.424013 + 0.244804i −0.696793 0.717272i \(-0.745390\pi\)
0.272780 + 0.962076i \(0.412057\pi\)
\(504\) −0.366025 + 0.633975i −0.0163041 + 0.0282395i
\(505\) 0 0
\(506\) 29.3205 1.30346
\(507\) 6.92820 11.0000i 0.307692 0.488527i
\(508\) 17.8564i 0.792250i
\(509\) −8.89230 5.13397i −0.394144 0.227559i 0.289810 0.957084i \(-0.406408\pi\)
−0.683954 + 0.729525i \(0.739741\pi\)
\(510\) 0 0
\(511\) −3.56218 6.16987i −0.157581 0.272939i
\(512\) −1.00000 −0.0441942
\(513\) −0.633975 1.09808i −0.0279907 0.0484812i
\(514\) −23.0885 + 13.3301i −1.01839 + 0.587967i
\(515\) 0 0
\(516\) −3.83013 6.63397i −0.168612 0.292044i
\(517\) 33.5885 + 19.3923i 1.47722 + 0.852873i
\(518\) 3.83013 6.63397i 0.168286 0.291480i
\(519\) −16.3923 −0.719542
\(520\) 0 0
\(521\) −17.4449 −0.764273 −0.382137 0.924106i \(-0.624812\pi\)
−0.382137 + 0.924106i \(0.624812\pi\)
\(522\) 1.23205 2.13397i 0.0539254 0.0934015i
\(523\) −31.5622 18.2224i −1.38012 0.796811i −0.387945 0.921683i \(-0.626815\pi\)
−0.992173 + 0.124871i \(0.960148\pi\)
\(524\) −6.73205 11.6603i −0.294091 0.509381i
\(525\) 0 0
\(526\) −24.2942 + 14.0263i −1.05928 + 0.611575i
\(527\) −6.19615 10.7321i −0.269909 0.467495i
\(528\) −4.73205 −0.205936
\(529\) 7.69615 + 13.3301i 0.334615 + 0.579571i
\(530\) 0 0
\(531\) −6.92820 4.00000i −0.300658 0.173585i
\(532\) 0.928203i 0.0402427i
\(533\) 9.86603 + 39.8731i 0.427345 + 1.72709i
\(534\) 2.53590 0.109739
\(535\) 0 0
\(536\) 5.56218 9.63397i 0.240249 0.416124i
\(537\) 19.0981 11.0263i 0.824143 0.475819i
\(538\) −1.46410 −0.0631219
\(539\) −26.4904 + 15.2942i −1.14102 + 0.658769i
\(540\) 0 0
\(541\) 40.3205i 1.73351i 0.498731 + 0.866757i \(0.333800\pi\)
−0.498731 + 0.866757i \(0.666200\pi\)
\(542\) −5.07180 + 2.92820i −0.217852 + 0.125777i
\(543\) 7.62436 + 4.40192i 0.327192 + 0.188905i
\(544\) −1.96410 1.13397i −0.0842102 0.0486188i
\(545\) 0 0
\(546\) 0.633975 + 2.56218i 0.0271316 + 0.109651i
\(547\) 6.19615i 0.264928i −0.991188 0.132464i \(-0.957711\pi\)
0.991188 0.132464i \(-0.0422889\pi\)
\(548\) 0.964102 1.66987i 0.0411844 0.0713334i
\(549\) 0.598076 1.03590i 0.0255253 0.0442111i
\(550\) 0 0
\(551\) 3.12436i 0.133102i
\(552\) −3.09808 5.36603i −0.131863 0.228393i
\(553\) −3.46410 6.00000i −0.147309 0.255146i
\(554\) 2.26795i 0.0963559i
\(555\) 0 0
\(556\) −4.92820 + 8.53590i −0.209002 + 0.362003i
\(557\) 15.1865 26.3038i 0.643474 1.11453i −0.341178 0.939999i \(-0.610826\pi\)
0.984652 0.174531i \(-0.0558409\pi\)
\(558\) 5.46410i 0.231314i
\(559\) −26.5359 7.66025i −1.12235 0.323994i
\(560\) 0 0
\(561\) −9.29423 5.36603i −0.392403 0.226554i
\(562\) −19.3301 11.1603i −0.815392 0.470767i
\(563\) −18.2487 + 10.5359i −0.769091 + 0.444035i −0.832550 0.553949i \(-0.813120\pi\)
0.0634589 + 0.997984i \(0.479787\pi\)
\(564\) 8.19615i 0.345120i
\(565\) 0 0
\(566\) 7.22243 4.16987i 0.303581 0.175273i
\(567\) 0.732051 0.0307432
\(568\) 1.09808 0.633975i 0.0460743 0.0266010i
\(569\) 19.3205 33.4641i 0.809958 1.40289i −0.102935 0.994688i \(-0.532823\pi\)
0.912893 0.408200i \(-0.133843\pi\)
\(570\) 0 0
\(571\) 24.0526 1.00657 0.503284 0.864121i \(-0.332125\pi\)
0.503284 + 0.864121i \(0.332125\pi\)
\(572\) −12.2942 + 11.8301i −0.514048 + 0.494642i
\(573\) 6.92820i 0.289430i
\(574\) −7.22243 4.16987i −0.301458 0.174047i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) −0.267949 −0.0111549 −0.00557744 0.999984i \(-0.501775\pi\)
−0.00557744 + 0.999984i \(0.501775\pi\)
\(578\) 5.92820 + 10.2679i 0.246581 + 0.427090i
\(579\) 7.16025 4.13397i 0.297570 0.171802i
\(580\) 0 0
\(581\) −3.73205 6.46410i −0.154832 0.268176i
\(582\) 5.19615 + 3.00000i 0.215387 + 0.124354i
\(583\) 1.09808 1.90192i 0.0454777 0.0787696i
\(584\) −9.73205 −0.402715
\(585\) 0 0
\(586\) −14.5167 −0.599678
\(587\) 8.00000 13.8564i 0.330195 0.571915i −0.652355 0.757914i \(-0.726219\pi\)
0.982550 + 0.185999i \(0.0595520\pi\)
\(588\) 5.59808 + 3.23205i 0.230861 + 0.133288i
\(589\) 3.46410 + 6.00000i 0.142736 + 0.247226i
\(590\) 0 0
\(591\) −8.53590 + 4.92820i −0.351120 + 0.202719i
\(592\) −5.23205 9.06218i −0.215036 0.372453i
\(593\) 36.8564 1.51351 0.756756 0.653698i \(-0.226783\pi\)
0.756756 + 0.653698i \(0.226783\pi\)
\(594\) 2.36603 + 4.09808i 0.0970792 + 0.168146i
\(595\) 0 0
\(596\) −2.42820 1.40192i −0.0994631 0.0574250i
\(597\) 3.80385i 0.155681i
\(598\) −21.4641 6.19615i −0.877732 0.253380i
\(599\) 9.46410 0.386693 0.193346 0.981131i \(-0.438066\pi\)
0.193346 + 0.981131i \(0.438066\pi\)
\(600\) 0 0
\(601\) 2.96410 5.13397i 0.120908 0.209419i −0.799218 0.601041i \(-0.794753\pi\)
0.920126 + 0.391622i \(0.128086\pi\)
\(602\) 4.85641 2.80385i 0.197932 0.114276i
\(603\) −11.1244 −0.453019
\(604\) 2.83013 1.63397i 0.115156 0.0664855i
\(605\) 0 0
\(606\) 11.9282i 0.484550i
\(607\) −0.679492 + 0.392305i −0.0275797 + 0.0159232i −0.513726 0.857954i \(-0.671735\pi\)
0.486147 + 0.873877i \(0.338402\pi\)
\(608\) 1.09808 + 0.633975i 0.0445329 + 0.0257111i
\(609\) 1.56218 + 0.901924i 0.0633026 + 0.0365478i
\(610\) 0 0
\(611\) −20.4904 21.2942i −0.828952 0.861472i
\(612\) 2.26795i 0.0916764i
\(613\) −5.69615 + 9.86603i −0.230065 + 0.398485i −0.957827 0.287345i \(-0.907227\pi\)
0.727762 + 0.685830i \(0.240561\pi\)
\(614\) 4.29423 7.43782i 0.173301 0.300166i
\(615\) 0 0
\(616\) 3.46410i 0.139573i
\(617\) 17.6244 + 30.5263i 0.709530 + 1.22894i 0.965032 + 0.262133i \(0.0844260\pi\)
−0.255502 + 0.966809i \(0.582241\pi\)
\(618\) −9.36603 16.2224i −0.376757 0.652562i
\(619\) 10.5359i 0.423474i −0.977327 0.211737i \(-0.932088\pi\)
0.977327 0.211737i \(-0.0679119\pi\)
\(620\) 0 0
\(621\) −3.09808 + 5.36603i −0.124322 + 0.215331i
\(622\) −7.83013 + 13.5622i −0.313959 + 0.543794i
\(623\) 1.85641i 0.0743754i
\(624\) 3.46410 + 1.00000i 0.138675 + 0.0400320i
\(625\) 0 0
\(626\) 11.6603 + 6.73205i 0.466037 + 0.269067i
\(627\) 5.19615 + 3.00000i 0.207514 + 0.119808i
\(628\) 20.4282 11.7942i 0.815174 0.470641i
\(629\) 23.7321i 0.946259i
\(630\) 0 0
\(631\) 41.3205 23.8564i 1.64494 0.949709i 0.665904 0.746037i \(-0.268046\pi\)
0.979039 0.203671i \(-0.0652874\pi\)
\(632\) −9.46410 −0.376462
\(633\) −3.80385 + 2.19615i −0.151189 + 0.0872892i
\(634\) −1.66987 + 2.89230i −0.0663191 + 0.114868i
\(635\) 0 0
\(636\) −0.464102 −0.0184028
\(637\) 22.6244 5.59808i 0.896410 0.221804i
\(638\) 11.6603i 0.461634i
\(639\) −1.09808 0.633975i −0.0434392 0.0250796i
\(640\) 0 0
\(641\) 12.9904 + 22.5000i 0.513089 + 0.888697i 0.999885 + 0.0151806i \(0.00483233\pi\)
−0.486796 + 0.873516i \(0.661834\pi\)
\(642\) 0.196152 0.00774152
\(643\) −6.92820 12.0000i −0.273222 0.473234i 0.696463 0.717592i \(-0.254756\pi\)
−0.969685 + 0.244359i \(0.921423\pi\)
\(644\) 3.92820 2.26795i 0.154793 0.0893697i
\(645\) 0 0
\(646\) 1.43782 + 2.49038i 0.0565704 + 0.0979827i
\(647\) −22.7321 13.1244i −0.893689 0.515972i −0.0185417 0.999828i \(-0.505902\pi\)
−0.875147 + 0.483856i \(0.839236\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 37.8564 1.48599
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) −3.26795 + 5.66025i −0.127983 + 0.221673i
\(653\) 9.12436 + 5.26795i 0.357064 + 0.206151i 0.667792 0.744348i \(-0.267240\pi\)
−0.310728 + 0.950499i \(0.600573\pi\)
\(654\) 2.73205 + 4.73205i 0.106832 + 0.185038i
\(655\) 0 0
\(656\) −9.86603 + 5.69615i −0.385204 + 0.222397i
\(657\) 4.86603 + 8.42820i 0.189842 + 0.328816i
\(658\) 6.00000 0.233904
\(659\) 19.1244 + 33.1244i 0.744979 + 1.29034i 0.950205 + 0.311627i \(0.100874\pi\)
−0.205225 + 0.978715i \(0.565793\pi\)
\(660\) 0 0
\(661\) 8.13397 + 4.69615i 0.316375 + 0.182659i 0.649776 0.760126i \(-0.274863\pi\)
−0.333401 + 0.942785i \(0.608196\pi\)
\(662\) 20.0000i 0.777322i
\(663\) 5.66987 + 5.89230i 0.220200 + 0.228838i
\(664\) −10.1962 −0.395687
\(665\) 0 0
\(666\) −5.23205 + 9.06218i −0.202738 + 0.351152i
\(667\) −13.2224 + 7.63397i −0.511975 + 0.295589i
\(668\) −2.53590 −0.0981169
\(669\) −11.3205 + 6.53590i −0.437676 + 0.252692i
\(670\) 0 0
\(671\) 5.66025i 0.218512i
\(672\) −0.633975 + 0.366025i −0.0244561 + 0.0141197i
\(673\) 12.1865 + 7.03590i 0.469756 + 0.271214i 0.716138 0.697959i \(-0.245908\pi\)
−0.246381 + 0.969173i \(0.579242\pi\)
\(674\) 5.93782 + 3.42820i 0.228716 + 0.132049i
\(675\) 0 0
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) 38.5359i 1.48105i 0.672026 + 0.740527i \(0.265424\pi\)
−0.672026 + 0.740527i \(0.734576\pi\)
\(678\) 9.33013 16.1603i 0.358321 0.620631i
\(679\) −2.19615 + 3.80385i −0.0842806 + 0.145978i
\(680\) 0 0
\(681\) 1.80385i 0.0691236i
\(682\) −12.9282 22.3923i −0.495046 0.857446i
\(683\) −18.9282 32.7846i −0.724268 1.25447i −0.959275 0.282475i \(-0.908845\pi\)
0.235007 0.971994i \(-0.424489\pi\)
\(684\) 1.26795i 0.0484812i
\(685\) 0 0
\(686\) −4.92820 + 8.53590i −0.188160 + 0.325902i
\(687\) −7.92820 + 13.7321i −0.302480 + 0.523910i
\(688\) 7.66025i 0.292044i
\(689\) −1.20577 + 1.16025i −0.0459362 + 0.0442022i
\(690\) 0 0
\(691\) 22.8109 + 13.1699i 0.867767 + 0.501006i 0.866606 0.498994i \(-0.166297\pi\)
0.00116153 + 0.999999i \(0.499630\pi\)
\(692\) −14.1962 8.19615i −0.539657 0.311571i
\(693\) −3.00000 + 1.73205i −0.113961 + 0.0657952i
\(694\) 8.87564i 0.336915i
\(695\) 0 0
\(696\) 2.13397 1.23205i 0.0808881 0.0467008i
\(697\) −25.8372 −0.978653
\(698\) −16.7321 + 9.66025i −0.633317 + 0.365646i
\(699\) −9.92820 + 17.1962i −0.375519 + 0.650418i
\(700\) 0 0
\(701\) −31.3205 −1.18296 −0.591480 0.806320i \(-0.701456\pi\)
−0.591480 + 0.806320i \(0.701456\pi\)
\(702\) −0.866025 3.50000i −0.0326860 0.132099i
\(703\) 13.2679i 0.500410i
\(704\) −4.09808 2.36603i −0.154452 0.0891729i
\(705\) 0 0
\(706\) 9.89230 + 17.1340i 0.372302 + 0.644846i
\(707\) 8.73205 0.328403
\(708\) −4.00000 6.92820i −0.150329 0.260378i
\(709\) −35.3827 + 20.4282i −1.32882 + 0.767197i −0.985118 0.171880i \(-0.945016\pi\)
−0.343707 + 0.939077i \(0.611683\pi\)
\(710\) 0 0
\(711\) 4.73205 + 8.19615i 0.177466 + 0.307380i
\(712\) 2.19615 + 1.26795i 0.0823043 + 0.0475184i
\(713\) 16.9282 29.3205i 0.633966 1.09806i
\(714\) −1.66025 −0.0621334
\(715\) 0 0
\(716\) 22.0526 0.824143
\(717\) −4.83013 + 8.36603i −0.180384 + 0.312435i
\(718\) −20.0263 11.5622i −0.747374 0.431497i
\(719\) 11.2679 + 19.5167i 0.420224 + 0.727849i 0.995961 0.0897860i \(-0.0286183\pi\)
−0.575737 + 0.817635i \(0.695285\pi\)
\(720\) 0 0
\(721\) 11.8756 6.85641i 0.442272 0.255346i
\(722\) 8.69615 + 15.0622i 0.323637 + 0.560556i
\(723\) 17.5885 0.654122
\(724\) 4.40192 + 7.62436i 0.163596 + 0.283357i
\(725\) 0 0
\(726\) −9.86603 5.69615i −0.366163 0.211404i
\(727\) 20.9808i 0.778133i 0.921210 + 0.389067i \(0.127202\pi\)
−0.921210 + 0.389067i \(0.872798\pi\)
\(728\) −0.732051 + 2.53590i −0.0271316 + 0.0939866i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 8.68653 15.0455i 0.321283 0.556479i
\(732\) 1.03590 0.598076i 0.0382879 0.0221055i
\(733\) 19.0000 0.701781 0.350891 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) −12.7583 + 7.36603i −0.470919 + 0.271885i
\(735\) 0 0
\(736\) 6.19615i 0.228393i
\(737\) 45.5885 26.3205i 1.67927 0.969528i
\(738\) 9.86603 + 5.69615i 0.363173 + 0.209678i
\(739\) −9.46410 5.46410i −0.348143 0.201000i 0.315724 0.948851i \(-0.397753\pi\)
−0.663867 + 0.747851i \(0.731086\pi\)
\(740\) 0 0
\(741\) −3.16987 3.29423i −0.116448 0.121017i
\(742\) 0.339746i 0.0124725i
\(743\) 13.8038 23.9090i 0.506414 0.877135i −0.493558 0.869713i \(-0.664304\pi\)
0.999972 0.00742221i \(-0.00236259\pi\)
\(744\) −2.73205 + 4.73205i −0.100162 + 0.173485i
\(745\) 0 0
\(746\) 10.2679i 0.375936i
\(747\) 5.09808 + 8.83013i 0.186529 + 0.323077i
\(748\) −5.36603 9.29423i −0.196201 0.339831i
\(749\) 0.143594i 0.00524679i
\(750\) 0 0
\(751\) 7.95448 13.7776i 0.290263 0.502751i −0.683609 0.729849i \(-0.739590\pi\)
0.973872 + 0.227098i \(0.0729238\pi\)
\(752\) 4.09808 7.09808i 0.149441 0.258840i
\(753\) 6.53590i 0.238181i
\(754\) 2.46410 8.53590i 0.0897373 0.310859i
\(755\) 0 0
\(756\) 0.633975 + 0.366025i 0.0230574 + 0.0133122i
\(757\) 6.12436 + 3.53590i 0.222593 + 0.128514i 0.607151 0.794587i \(-0.292312\pi\)
−0.384557 + 0.923101i \(0.625646\pi\)
\(758\) −1.26795 + 0.732051i −0.0460540 + 0.0265893i
\(759\) 29.3205i 1.06427i
\(760\) 0 0
\(761\) −20.1962 + 11.6603i −0.732110 + 0.422684i −0.819194 0.573517i \(-0.805579\pi\)
0.0870836 + 0.996201i \(0.472245\pi\)
\(762\) 17.8564 0.646869
\(763\) −3.46410 + 2.00000i −0.125409 + 0.0724049i
\(764\) −3.46410 + 6.00000i −0.125327 + 0.217072i
\(765\) 0 0
\(766\) −5.46410 −0.197426
\(767\) −27.7128 8.00000i −1.00065 0.288863i
\(768\) 1.00000i 0.0360844i
\(769\) 13.9808 + 8.07180i 0.504159 + 0.291076i 0.730429 0.682988i \(-0.239320\pi\)
−0.226270 + 0.974065i \(0.572653\pi\)
\(770\) 0 0
\(771\) 13.3301 + 23.0885i 0.480073 + 0.831510i
\(772\) 8.26795 0.297570
\(773\) 17.5359 + 30.3731i 0.630722 + 1.09244i 0.987404 + 0.158217i \(0.0505747\pi\)
−0.356682 + 0.934226i \(0.616092\pi\)
\(774\) −6.63397 + 3.83013i −0.238453 + 0.137671i
\(775\) 0 0
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) −6.63397 3.83013i −0.237993 0.137405i
\(778\) −14.8923 + 25.7942i −0.533915 + 0.924768i
\(779\) 14.4449 0.517541
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) 7.02628 12.1699i 0.251259 0.435194i
\(783\) −2.13397 1.23205i −0.0762620 0.0440299i
\(784\) 3.23205 + 5.59808i 0.115430 + 0.199931i
\(785\) 0 0
\(786\) −11.6603 + 6.73205i −0.415907 + 0.240124i
\(787\) −19.6603 34.0526i −0.700812 1.21384i −0.968182 0.250248i \(-0.919488\pi\)
0.267369 0.963594i \(-0.413846\pi\)
\(788\) −9.85641 −0.351120
\(789\) 14.0263 + 24.2942i 0.499349 + 0.864897i
\(790\) 0 0
\(791\) 11.8301 + 6.83013i 0.420631 + 0.242851i
\(792\) 4.73205i 0.168146i
\(793\) 1.19615 4.14359i 0.0424766 0.147143i
\(794\) 0.392305 0.0139224
\(795\) 0 0
\(796\) 1.90192 3.29423i 0.0674119 0.116761i
\(797\) −29.4449 + 17.0000i −1.04299 + 0.602171i −0.920679 0.390321i \(-0.872364\pi\)
−0.122312 + 0.992492i \(0.539031\pi\)
\(798\) 0.928203 0.0328580
\(799\) 16.0981 9.29423i 0.569509 0.328806i
\(800\) 0 0
\(801\) 2.53590i 0.0896016i
\(802\) −18.9904 + 10.9641i −0.670574 + 0.387156i
\(803\) −39.8827 23.0263i −1.40743 0.812580i
\(804\) −9.63397 5.56218i −0.339764 0.196163i
\(805\) 0 0
\(806\) 4.73205 + 19.1244i 0.166679 + 0.673627i
\(807\) 1.46410i 0.0515388i
\(808\) 5.96410 10.3301i 0.209816 0.363413i
\(809\) −11.2058 + 19.4090i −0.393974 + 0.682383i −0.992970 0.118369i \(-0.962233\pi\)
0.598996 + 0.800752i \(0.295567\pi\)
\(810\) 0 0
\(811\) 45.1769i 1.58638i 0.608977 + 0.793188i \(0.291580\pi\)
−0.608977 + 0.793188i \(0.708420\pi\)
\(812\) 0.901924 + 1.56218i 0.0316513 + 0.0548217i
\(813\) 2.92820 + 5.07180i 0.102697 + 0.177876i
\(814\) 49.5167i 1.73556i
\(815\) 0 0
\(816\) −1.13397 + 1.96410i −0.0396971 + 0.0687573i
\(817\) −4.85641 + 8.41154i −0.169904 + 0.294283i
\(818\) 14.2679i 0.498867i
\(819\) 2.56218 0.633975i 0.0895297 0.0221529i
\(820\) 0 0
\(821\) 11.1962 + 6.46410i 0.390748 + 0.225599i 0.682484 0.730900i \(-0.260900\pi\)
−0.291736 + 0.956499i \(0.594233\pi\)
\(822\) −1.66987 0.964102i −0.0582435 0.0336269i
\(823\) 36.0000 20.7846i 1.25488 0.724506i 0.282806 0.959177i \(-0.408735\pi\)
0.972075 + 0.234671i \(0.0754013\pi\)
\(824\) 18.7321i 0.652562i
\(825\) 0 0
\(826\) 5.07180 2.92820i 0.176470 0.101885i
\(827\) 33.4641 1.16366 0.581830 0.813310i \(-0.302337\pi\)
0.581830 + 0.813310i \(0.302337\pi\)
\(828\) −5.36603 + 3.09808i −0.186482 + 0.107666i
\(829\) −6.06218 + 10.5000i −0.210548 + 0.364680i −0.951886 0.306452i \(-0.900858\pi\)
0.741338 + 0.671132i \(0.234192\pi\)
\(830\) 0 0
\(831\) 2.26795 0.0786743
\(832\) 2.50000 + 2.59808i 0.0866719 + 0.0900721i
\(833\) 14.6603i 0.507948i
\(834\) 8.53590 + 4.92820i 0.295574 + 0.170650i
\(835\) 0 0
\(836\) 3.00000 + 5.19615i 0.103757 + 0.179713i
\(837\) 5.46410 0.188867
\(838\) 5.26795 + 9.12436i 0.181978 + 0.315196i
\(839\) −12.2487 + 7.07180i −0.422872 + 0.244146i −0.696306 0.717745i \(-0.745174\pi\)
0.273433 + 0.961891i \(0.411841\pi\)
\(840\) 0 0
\(841\) 11.4641 + 19.8564i 0.395314 + 0.684704i
\(842\) −28.3301 16.3564i −0.976321 0.563679i
\(843\) −11.1603 + 19.3301i −0.384380 + 0.665765i
\(844\) −4.39230 −0.151189
\(845\) 0 0
\(846\) −8.19615 −0.281790
\(847\) 4.16987 7.22243i 0.143279 0.248166i
\(848\) −0.401924 0.232051i −0.0138021 0.00796866i
\(849\) −4.16987 7.22243i −0.143110 0.247873i
\(850\) 0 0
\(851\) 56.1506 32.4186i 1.92482 1.11129i
\(852\) −0.633975 1.09808i −0.0217196 0.0376195i
\(853\) −8.17691 −0.279972 −0.139986 0.990153i \(-0.544706\pi\)
−0.139986 + 0.990153i \(0.544706\pi\)
\(854\) 0.437822 + 0.758330i 0.0149820 + 0.0259495i
\(855\) 0 0
\(856\) 0.169873 + 0.0980762i 0.00580614 + 0.00335218i
\(857\) 19.4449i 0.664224i −0.943240 0.332112i \(-0.892239\pi\)
0.943240 0.332112i \(-0.107761\pi\)
\(858\) 11.8301 + 12.2942i 0.403874 + 0.419718i
\(859\) 22.8756 0.780507 0.390253 0.920707i \(-0.372387\pi\)
0.390253 + 0.920707i \(0.372387\pi\)
\(860\) 0 0
\(861\) −4.16987 + 7.22243i −0.142109 + 0.246140i
\(862\) −9.63397 + 5.56218i −0.328134 + 0.189449i
\(863\) 7.12436 0.242516 0.121258 0.992621i \(-0.461307\pi\)
0.121258 + 0.992621i \(0.461307\pi\)
\(864\) 0.866025 0.500000i 0.0294628 0.0170103i
\(865\) 0 0
\(866\) 14.8564i 0.504841i
\(867\) 10.2679 5.92820i 0.348718 0.201332i
\(868\) −3.46410 2.00000i −0.117579 0.0678844i
\(869\) −38.7846 22.3923i −1.31568 0.759607i
\(870\) 0 0
\(871\) −38.9352 + 9.63397i −1.31927 + 0.326435i
\(872\) 5.46410i 0.185038i
\(873\) 3.00000 5.19615i 0.101535 0.175863i
\(874\) −3.92820 + 6.80385i −0.132873 + 0.230144i
\(875\) 0 0
\(876\) 9.73205i 0.328816i
\(877\) 5.03590 + 8.72243i 0.170050 + 0.294536i 0.938437 0.345450i \(-0.112274\pi\)
−0.768387 + 0.639985i \(0.778940\pi\)
\(878\) −8.83013 15.2942i −0.298002 0.516155i
\(879\) 14.5167i 0.489635i
\(880\) 0 0
\(881\) 25.9186 44.8923i 0.873219 1.51246i 0.0145717 0.999894i \(-0.495362\pi\)
0.858648 0.512566i \(-0.171305\pi\)
\(882\) 3.23205 5.59808i 0.108829 0.188497i
\(883\) 29.0718i 0.978344i −0.872187 0.489172i \(-0.837299\pi\)
0.872187 0.489172i \(-0.162701\pi\)
\(884\) 1.96410 + 7.93782i 0.0660599 + 0.266978i
\(885\) 0 0
\(886\) 31.5167 + 18.1962i 1.05882 + 0.611312i
\(887\) 8.78461 + 5.07180i 0.294958 + 0.170294i 0.640176 0.768228i \(-0.278862\pi\)
−0.345217 + 0.938523i \(0.612195\pi\)
\(888\) −9.06218 + 5.23205i −0.304107 + 0.175576i
\(889\) 13.0718i 0.438414i
\(890\) 0 0
\(891\) 4.09808 2.36603i 0.137291 0.0792648i
\(892\) −13.0718 −0.437676
\(893\) −9.00000 + 5.19615i −0.301174 + 0.173883i
\(894\) −1.40192 + 2.42820i −0.0468873 + 0.0812113i
\(895\) 0 0
\(896\) −0.732051 −0.0244561
\(897\) −6.19615 + 21.4641i −0.206884 + 0.716665i
\(898\) 23.3205i 0.778215i
\(899\) 11.6603 + 6.73205i 0.388891 + 0.224526i
\(900\) 0 0
\(901\) −0.526279 0.911543i −0.0175329 0.0303679i
\(902\) −53.9090 −1.79497
\(903\) −2.80385 4.85641i −0.0933062 0.161611i
\(904\) 16.1603 9.33013i 0.537482 0.310315i
\(905\) 0 0
\(906\) −1.63397 2.83013i −0.0542852 0.0940247i
\(907\) −13.5167 7.80385i −0.448813 0.259123i 0.258516 0.966007i \(-0.416767\pi\)
−0.707329 + 0.706885i \(0.750100\pi\)
\(908\) −0.901924 + 1.56218i −0.0299314 + 0.0518427i
\(909\) −11.9282 −0.395634
\(910\) 0 0
\(911\) −9.46410 −0.313560 −0.156780 0.987634i \(-0.550111\pi\)
−0.156780 + 0.987634i \(0.550111\pi\)
\(912\) 0.633975 1.09808i 0.0209930 0.0363609i
\(913\) −41.7846 24.1244i −1.38287 0.798400i
\(914\) −9.33013 16.1603i −0.308613 0.534534i
\(915\) 0 0
\(916\) −13.7321 + 7.92820i −0.453720 + 0.261955i
\(917\) −4.92820 8.53590i −0.162744 0.281880i
\(918\) 2.26795 0.0748535
\(919\) −28.9808 50.1962i −0.955987 1.65582i −0.732093 0.681205i \(-0.761456\pi\)
−0.223894 0.974613i \(-0.571877\pi\)
\(920\) 0 0
\(921\) −7.43782 4.29423i −0.245085 0.141500i
\(922\) 25.7321i 0.847440i
\(923\) −4.39230 1.26795i −0.144574 0.0417351i
\(924\) −3.46410 −0.113961
\(925\) 0 0
\(926\) 14.0263 24.2942i 0.460932 0.798358i
\(927\) −16.2224 + 9.36603i −0.532815 + 0.307621i
\(928\) 2.46410 0.0808881
\(929\) 8.00962 4.62436i 0.262787 0.151720i −0.362818 0.931860i \(-0.618185\pi\)
0.625605 + 0.780140i \(0.284852\pi\)
\(930\) 0 0
\(931\) 8.19615i 0.268618i
\(932\) −17.1962 + 9.92820i −0.563279 + 0.325209i
\(933\) 13.5622 + 7.83013i 0.444006 + 0.256347i
\(934\) −10.9019 6.29423i −0.356722 0.205953i
\(935\) 0 0
\(936\) 1.00000 3.46410i 0.0326860 0.113228i
\(937\) 43.2487i 1.41287i −0.707776 0.706437i \(-0.750301\pi\)
0.707776 0.706437i \(-0.249699\pi\)
\(938\) 4.07180 7.05256i 0.132949 0.230274i
\(939\) 6.73205 11.6603i 0.219692 0.380518i
\(940\) 0 0
\(941\) 56.6410i 1.84644i 0.384267 + 0.923222i \(0.374454\pi\)
−0.384267 + 0.923222i \(0.625546\pi\)
\(942\) −11.7942 20.4282i −0.384277 0.665587i
\(943\) −35.2942 61.1314i −1.14934 1.99071i
\(944\) 8.00000i 0.260378i
\(945\) 0 0
\(946\) 18.1244 31.3923i 0.589274 1.02065i
\(947\) −17.4641 + 30.2487i −0.567507 + 0.982951i 0.429305 + 0.903160i \(0.358759\pi\)
−0.996812 + 0.0797913i \(0.974575\pi\)
\(948\) 9.46410i 0.307380i
\(949\) 24.3301 + 25.2846i 0.789789 + 0.820773i
\(950\) 0 0
\(951\) 2.89230 + 1.66987i 0.0937894 + 0.0541493i
\(952\) −1.43782 0.830127i −0.0466001 0.0269046i
\(953\) 36.0000 20.7846i 1.16615 0.673280i 0.213383 0.976969i \(-0.431552\pi\)
0.952771 + 0.303689i \(0.0982184\pi\)
\(954\) 0.464102i 0.0150258i
\(955\) 0 0
\(956\) −8.36603 + 4.83013i −0.270577 + 0.156217i
\(957\) 11.6603 0.376922
\(958\) 22.9808 13.2679i 0.742475 0.428668i
\(959\) 0.705771 1.22243i 0.0227905 0.0394744i
\(960\) 0 0
\(961\) 1.14359 0.0368901
\(962\) −10.4641 + 36.2487i −0.337376 + 1.16871i
\(963\) 0.196152i 0.00632092i
\(964\) 15.2321 + 8.79423i 0.490591 + 0.283243i
\(965\) 0 0
\(966\) −2.26795 3.92820i −0.0729701 0.126388i
\(967\) 18.8756 0.607000 0.303500 0.952831i \(-0.401845\pi\)
0.303500 + 0.952831i \(0.401845\pi\)
\(968\) −5.69615 9.86603i −0.183081 0.317106i
\(969\) 2.49038 1.43782i 0.0800026 0.0461895i
\(970\) 0 0
\(971\) 9.12436 + 15.8038i 0.292815 + 0.507170i 0.974474 0.224500i \(-0.0720748\pi\)
−0.681660 + 0.731669i \(0.738741\pi\)
\(972\) −0.866025 0.500000i −0.0277778 0.0160375i
\(973\) −3.60770 + 6.24871i −0.115657 + 0.200324i
\(974\) 21.1244 0.676868
\(975\) 0 0
\(976\) 1.19615 0.0382879
\(977\) 16.0359 27.7750i 0.513034 0.888601i −0.486852 0.873485i \(-0.661855\pi\)
0.999886 0.0151161i \(-0.00481180\pi\)
\(978\) 5.66025 + 3.26795i 0.180995 + 0.104497i
\(979\) 6.00000 + 10.3923i 0.191761 + 0.332140i
\(980\) 0 0
\(981\) 4.73205 2.73205i 0.151083 0.0872277i
\(982\) −2.63397 4.56218i −0.0840535 0.145585i
\(983\) 20.7846 0.662926 0.331463 0.943468i \(-0.392458\pi\)
0.331463 + 0.943468i \(0.392458\pi\)
\(984\) 5.69615 + 9.86603i 0.181587 + 0.314517i
\(985\) 0 0
\(986\) 4.83975 + 2.79423i 0.154129 + 0.0889864i
\(987\) 6.00000i 0.190982i
\(988\) −1.09808 4.43782i −0.0349345 0.141186i
\(989\) 47.4641 1.50927
\(990\) 0 0
\(991\) 4.29423 7.43782i 0.136411 0.236270i −0.789725 0.613461i \(-0.789777\pi\)
0.926135 + 0.377191i \(0.123110\pi\)
\(992\) −4.73205 + 2.73205i −0.150243 + 0.0867427i
\(993\) 20.0000 0.634681
\(994\) 0.803848 0.464102i 0.0254965 0.0147204i
\(995\) 0 0
\(996\) 10.1962i 0.323077i
\(997\) −33.4808 + 19.3301i −1.06035 + 0.612191i −0.925528 0.378679i \(-0.876378\pi\)
−0.134818 + 0.990870i \(0.543045\pi\)
\(998\) 27.7128 + 16.0000i 0.877234 + 0.506471i
\(999\) 9.06218 + 5.23205i 0.286715 + 0.165535i
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 1950.2.y.g.199.1 4
5.2 odd 4 78.2.i.a.43.2 4
5.3 odd 4 1950.2.bc.d.901.1 4
5.4 even 2 1950.2.y.b.199.2 4
13.10 even 6 1950.2.y.b.49.2 4
15.2 even 4 234.2.l.c.199.1 4
20.7 even 4 624.2.bv.e.433.1 4
60.47 odd 4 1872.2.by.h.433.2 4
65.2 even 12 1014.2.e.i.991.2 4
65.7 even 12 1014.2.a.k.1.1 2
65.12 odd 4 1014.2.i.a.823.1 4
65.17 odd 12 1014.2.b.e.337.3 4
65.22 odd 12 1014.2.b.e.337.2 4
65.23 odd 12 1950.2.bc.d.751.1 4
65.32 even 12 1014.2.a.i.1.2 2
65.37 even 12 1014.2.e.g.991.1 4
65.42 odd 12 1014.2.i.a.361.1 4
65.47 even 4 1014.2.e.g.529.1 4
65.49 even 6 inner 1950.2.y.g.49.1 4
65.57 even 4 1014.2.e.i.529.2 4
65.62 odd 12 78.2.i.a.49.2 yes 4
195.17 even 12 3042.2.b.i.1351.2 4
195.32 odd 12 3042.2.a.y.1.1 2
195.62 even 12 234.2.l.c.127.1 4
195.137 odd 12 3042.2.a.p.1.2 2
195.152 even 12 3042.2.b.i.1351.3 4
260.7 odd 12 8112.2.a.bp.1.1 2
260.127 even 12 624.2.bv.e.49.2 4
260.227 odd 12 8112.2.a.bj.1.2 2
780.647 odd 12 1872.2.by.h.1297.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.i.a.43.2 4 5.2 odd 4
78.2.i.a.49.2 yes 4 65.62 odd 12
234.2.l.c.127.1 4 195.62 even 12
234.2.l.c.199.1 4 15.2 even 4
624.2.bv.e.49.2 4 260.127 even 12
624.2.bv.e.433.1 4 20.7 even 4
1014.2.a.i.1.2 2 65.32 even 12
1014.2.a.k.1.1 2 65.7 even 12
1014.2.b.e.337.2 4 65.22 odd 12
1014.2.b.e.337.3 4 65.17 odd 12
1014.2.e.g.529.1 4 65.47 even 4
1014.2.e.g.991.1 4 65.37 even 12
1014.2.e.i.529.2 4 65.57 even 4
1014.2.e.i.991.2 4 65.2 even 12
1014.2.i.a.361.1 4 65.42 odd 12
1014.2.i.a.823.1 4 65.12 odd 4
1872.2.by.h.433.2 4 60.47 odd 4
1872.2.by.h.1297.1 4 780.647 odd 12
1950.2.y.b.49.2 4 13.10 even 6
1950.2.y.b.199.2 4 5.4 even 2
1950.2.y.g.49.1 4 65.49 even 6 inner
1950.2.y.g.199.1 4 1.1 even 1 trivial
1950.2.bc.d.751.1 4 65.23 odd 12
1950.2.bc.d.901.1 4 5.3 odd 4
3042.2.a.p.1.2 2 195.137 odd 12
3042.2.a.y.1.1 2 195.32 odd 12
3042.2.b.i.1351.2 4 195.17 even 12
3042.2.b.i.1351.3 4 195.152 even 12
8112.2.a.bj.1.2 2 260.227 odd 12
8112.2.a.bp.1.1 2 260.7 odd 12