Properties

Label 525.2.r.a.424.2
Level $525$
Weight $2$
Character 525.424
Analytic conductor $4.192$
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] = [525,2,Mod(424,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.424");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.r (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: \(4.19214610612\)
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 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 424.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.424
Dual form 525.2.r.a.499.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.633975 + 0.366025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.732051 + 1.26795i) q^{4} -0.732051 q^{6} +(2.50000 + 0.866025i) q^{7} -2.53590i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.633975 + 0.366025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.732051 + 1.26795i) q^{4} -0.732051 q^{6} +(2.50000 + 0.866025i) q^{7} -2.53590i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.36603 - 2.36603i) q^{11} +(-1.26795 + 0.732051i) q^{12} +5.73205i q^{13} +(-1.90192 + 0.366025i) q^{14} +(-0.535898 - 0.928203i) q^{16} +(5.83013 + 3.36603i) q^{17} +(-0.633975 - 0.366025i) q^{18} +(-1.23205 - 2.13397i) q^{19} +(1.73205 + 2.00000i) q^{21} +2.00000i q^{22} +(-1.09808 + 0.633975i) q^{23} +(1.26795 - 2.19615i) q^{24} +(-2.09808 - 3.63397i) q^{26} +1.00000i q^{27} +(-2.92820 + 2.53590i) q^{28} -6.19615 q^{29} +(-3.23205 + 5.59808i) q^{31} +(5.07180 + 2.92820i) q^{32} +(2.36603 - 1.36603i) q^{33} -4.92820 q^{34} -1.46410 q^{36} +(-6.23205 + 3.59808i) q^{37} +(1.56218 + 0.901924i) q^{38} +(-2.86603 + 4.96410i) q^{39} +2.73205 q^{41} +(-1.83013 - 0.633975i) q^{42} -7.19615i q^{43} +(2.00000 + 3.46410i) q^{44} +(0.464102 - 0.803848i) q^{46} +(-1.73205 + 1.00000i) q^{47} -1.07180i q^{48} +(5.50000 + 4.33013i) q^{49} +(3.36603 + 5.83013i) q^{51} +(-7.26795 - 4.19615i) q^{52} +(7.26795 + 4.19615i) q^{53} +(-0.366025 - 0.633975i) q^{54} +(2.19615 - 6.33975i) q^{56} -2.46410i q^{57} +(3.92820 - 2.26795i) q^{58} +(5.09808 - 8.83013i) q^{59} +(-2.00000 - 3.46410i) q^{61} -4.73205i q^{62} +(0.500000 + 2.59808i) q^{63} -2.14359 q^{64} +(-1.00000 + 1.73205i) q^{66} +(2.30385 + 1.33013i) q^{67} +(-8.53590 + 4.92820i) q^{68} -1.26795 q^{69} -4.19615 q^{71} +(2.19615 - 1.26795i) q^{72} +(4.03590 + 2.33013i) q^{73} +(2.63397 - 4.56218i) q^{74} +3.60770 q^{76} +(5.46410 - 4.73205i) q^{77} -4.19615i q^{78} +(6.69615 + 11.5981i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.73205 + 1.00000i) q^{82} -9.12436i q^{83} +(-3.80385 + 0.732051i) q^{84} +(2.63397 + 4.56218i) q^{86} +(-5.36603 - 3.09808i) q^{87} +(-6.00000 - 3.46410i) q^{88} +(-4.56218 - 7.90192i) q^{89} +(-4.96410 + 14.3301i) q^{91} -1.85641i q^{92} +(-5.59808 + 3.23205i) q^{93} +(0.732051 - 1.26795i) q^{94} +(2.92820 + 5.07180i) q^{96} -1.07180i q^{97} +(-5.07180 - 0.732051i) q^{98} +2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{2} + 4 q^{4} + 4 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{2} + 4 q^{4} + 4 q^{6} + 10 q^{7} + 2 q^{9} + 2 q^{11} - 12 q^{12} - 18 q^{14} - 16 q^{16} + 6 q^{17} - 6 q^{18} + 2 q^{19} + 6 q^{23} + 12 q^{24} + 2 q^{26} + 16 q^{28} - 4 q^{29} - 6 q^{31} + 48 q^{32} + 6 q^{33} + 8 q^{34} + 8 q^{36} - 18 q^{37} - 18 q^{38} - 8 q^{39} + 4 q^{41} + 10 q^{42} + 8 q^{44} - 12 q^{46} + 22 q^{49} + 10 q^{51} - 36 q^{52} + 36 q^{53} + 2 q^{54} - 12 q^{56} - 12 q^{58} + 10 q^{59} - 8 q^{61} + 2 q^{63} - 64 q^{64} - 4 q^{66} + 30 q^{67} - 48 q^{68} - 12 q^{69} + 4 q^{71} - 12 q^{72} + 30 q^{73} + 14 q^{74} + 56 q^{76} + 8 q^{77} + 6 q^{79} - 2 q^{81} - 36 q^{84} + 14 q^{86} - 18 q^{87} - 24 q^{88} + 6 q^{89} - 6 q^{91} - 12 q^{93} - 4 q^{94} - 16 q^{96} - 48 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.633975 + 0.366025i −0.448288 + 0.258819i −0.707107 0.707107i \(-0.750000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −0.732051 + 1.26795i −0.366025 + 0.633975i
\(5\) 0 0
\(6\) −0.732051 −0.298858
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 2.53590i 0.896575i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.36603 2.36603i 0.411872 0.713384i −0.583222 0.812313i \(-0.698208\pi\)
0.995094 + 0.0989291i \(0.0315417\pi\)
\(12\) −1.26795 + 0.732051i −0.366025 + 0.211325i
\(13\) 5.73205i 1.58978i 0.606750 + 0.794892i \(0.292473\pi\)
−0.606750 + 0.794892i \(0.707527\pi\)
\(14\) −1.90192 + 0.366025i −0.508311 + 0.0978244i
\(15\) 0 0
\(16\) −0.535898 0.928203i −0.133975 0.232051i
\(17\) 5.83013 + 3.36603i 1.41401 + 0.816381i 0.995764 0.0919509i \(-0.0293103\pi\)
0.418250 + 0.908332i \(0.362644\pi\)
\(18\) −0.633975 0.366025i −0.149429 0.0862730i
\(19\) −1.23205 2.13397i −0.282652 0.489567i 0.689385 0.724395i \(-0.257881\pi\)
−0.972037 + 0.234828i \(0.924547\pi\)
\(20\) 0 0
\(21\) 1.73205 + 2.00000i 0.377964 + 0.436436i
\(22\) 2.00000i 0.426401i
\(23\) −1.09808 + 0.633975i −0.228965 + 0.132193i −0.610094 0.792329i \(-0.708868\pi\)
0.381130 + 0.924522i \(0.375535\pi\)
\(24\) 1.26795 2.19615i 0.258819 0.448288i
\(25\) 0 0
\(26\) −2.09808 3.63397i −0.411467 0.712681i
\(27\) 1.00000i 0.192450i
\(28\) −2.92820 + 2.53590i −0.553378 + 0.479240i
\(29\) −6.19615 −1.15060 −0.575298 0.817944i \(-0.695114\pi\)
−0.575298 + 0.817944i \(0.695114\pi\)
\(30\) 0 0
\(31\) −3.23205 + 5.59808i −0.580493 + 1.00544i 0.414927 + 0.909855i \(0.363807\pi\)
−0.995421 + 0.0955896i \(0.969526\pi\)
\(32\) 5.07180 + 2.92820i 0.896575 + 0.517638i
\(33\) 2.36603 1.36603i 0.411872 0.237795i
\(34\) −4.92820 −0.845180
\(35\) 0 0
\(36\) −1.46410 −0.244017
\(37\) −6.23205 + 3.59808i −1.02454 + 0.591520i −0.915417 0.402508i \(-0.868139\pi\)
−0.109126 + 0.994028i \(0.534805\pi\)
\(38\) 1.56218 + 0.901924i 0.253419 + 0.146311i
\(39\) −2.86603 + 4.96410i −0.458931 + 0.794892i
\(40\) 0 0
\(41\) 2.73205 0.426675 0.213337 0.976979i \(-0.431567\pi\)
0.213337 + 0.976979i \(0.431567\pi\)
\(42\) −1.83013 0.633975i −0.282395 0.0978244i
\(43\) 7.19615i 1.09740i −0.836018 0.548701i \(-0.815122\pi\)
0.836018 0.548701i \(-0.184878\pi\)
\(44\) 2.00000 + 3.46410i 0.301511 + 0.522233i
\(45\) 0 0
\(46\) 0.464102 0.803848i 0.0684280 0.118521i
\(47\) −1.73205 + 1.00000i −0.252646 + 0.145865i −0.620975 0.783830i \(-0.713263\pi\)
0.368329 + 0.929695i \(0.379930\pi\)
\(48\) 1.07180i 0.154701i
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 0 0
\(51\) 3.36603 + 5.83013i 0.471338 + 0.816381i
\(52\) −7.26795 4.19615i −1.00788 0.581902i
\(53\) 7.26795 + 4.19615i 0.998330 + 0.576386i 0.907754 0.419504i \(-0.137796\pi\)
0.0905760 + 0.995890i \(0.471129\pi\)
\(54\) −0.366025 0.633975i −0.0498097 0.0862730i
\(55\) 0 0
\(56\) 2.19615 6.33975i 0.293473 0.847184i
\(57\) 2.46410i 0.326378i
\(58\) 3.92820 2.26795i 0.515798 0.297796i
\(59\) 5.09808 8.83013i 0.663713 1.14958i −0.315920 0.948786i \(-0.602313\pi\)
0.979633 0.200799i \(-0.0643537\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 4.73205i 0.600971i
\(63\) 0.500000 + 2.59808i 0.0629941 + 0.327327i
\(64\) −2.14359 −0.267949
\(65\) 0 0
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) 2.30385 + 1.33013i 0.281460 + 0.162501i 0.634084 0.773264i \(-0.281377\pi\)
−0.352624 + 0.935765i \(0.614711\pi\)
\(68\) −8.53590 + 4.92820i −1.03513 + 0.597632i
\(69\) −1.26795 −0.152643
\(70\) 0 0
\(71\) −4.19615 −0.497992 −0.248996 0.968505i \(-0.580101\pi\)
−0.248996 + 0.968505i \(0.580101\pi\)
\(72\) 2.19615 1.26795i 0.258819 0.149429i
\(73\) 4.03590 + 2.33013i 0.472366 + 0.272721i 0.717230 0.696837i \(-0.245410\pi\)
−0.244864 + 0.969558i \(0.578743\pi\)
\(74\) 2.63397 4.56218i 0.306193 0.530342i
\(75\) 0 0
\(76\) 3.60770 0.413831
\(77\) 5.46410 4.73205i 0.622692 0.539267i
\(78\) 4.19615i 0.475121i
\(79\) 6.69615 + 11.5981i 0.753376 + 1.30489i 0.946178 + 0.323648i \(0.104909\pi\)
−0.192802 + 0.981238i \(0.561757\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.73205 + 1.00000i −0.191273 + 0.110432i
\(83\) 9.12436i 1.00153i −0.865584 0.500764i \(-0.833052\pi\)
0.865584 0.500764i \(-0.166948\pi\)
\(84\) −3.80385 + 0.732051i −0.415034 + 0.0798733i
\(85\) 0 0
\(86\) 2.63397 + 4.56218i 0.284029 + 0.491952i
\(87\) −5.36603 3.09808i −0.575298 0.332149i
\(88\) −6.00000 3.46410i −0.639602 0.369274i
\(89\) −4.56218 7.90192i −0.483590 0.837602i 0.516233 0.856448i \(-0.327334\pi\)
−0.999822 + 0.0188462i \(0.994001\pi\)
\(90\) 0 0
\(91\) −4.96410 + 14.3301i −0.520379 + 1.50221i
\(92\) 1.85641i 0.193544i
\(93\) −5.59808 + 3.23205i −0.580493 + 0.335148i
\(94\) 0.732051 1.26795i 0.0755053 0.130779i
\(95\) 0 0
\(96\) 2.92820 + 5.07180i 0.298858 + 0.517638i
\(97\) 1.07180i 0.108824i −0.998519 0.0544122i \(-0.982671\pi\)
0.998519 0.0544122i \(-0.0173285\pi\)
\(98\) −5.07180 0.732051i −0.512329 0.0739483i
\(99\) 2.73205 0.274581
\(100\) 0 0
\(101\) 5.36603 9.29423i 0.533939 0.924810i −0.465274 0.885167i \(-0.654044\pi\)
0.999214 0.0396438i \(-0.0126223\pi\)
\(102\) −4.26795 2.46410i −0.422590 0.243982i
\(103\) 1.03590 0.598076i 0.102070 0.0589302i −0.448096 0.893985i \(-0.647898\pi\)
0.550166 + 0.835055i \(0.314564\pi\)
\(104\) 14.5359 1.42536
\(105\) 0 0
\(106\) −6.14359 −0.596719
\(107\) 7.09808 4.09808i 0.686197 0.396176i −0.115989 0.993251i \(-0.537004\pi\)
0.802186 + 0.597075i \(0.203670\pi\)
\(108\) −1.26795 0.732051i −0.122008 0.0704416i
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) 0 0
\(111\) −7.19615 −0.683029
\(112\) −0.535898 2.78461i −0.0506376 0.263121i
\(113\) 4.92820i 0.463606i −0.972763 0.231803i \(-0.925537\pi\)
0.972763 0.231803i \(-0.0744625\pi\)
\(114\) 0.901924 + 1.56218i 0.0844729 + 0.146311i
\(115\) 0 0
\(116\) 4.53590 7.85641i 0.421148 0.729449i
\(117\) −4.96410 + 2.86603i −0.458931 + 0.264964i
\(118\) 7.46410i 0.687126i
\(119\) 11.6603 + 13.4641i 1.06889 + 1.23425i
\(120\) 0 0
\(121\) 1.76795 + 3.06218i 0.160723 + 0.278380i
\(122\) 2.53590 + 1.46410i 0.229589 + 0.132554i
\(123\) 2.36603 + 1.36603i 0.213337 + 0.123170i
\(124\) −4.73205 8.19615i −0.424951 0.736036i
\(125\) 0 0
\(126\) −1.26795 1.46410i −0.112958 0.130433i
\(127\) 15.1962i 1.34844i −0.738530 0.674220i \(-0.764480\pi\)
0.738530 0.674220i \(-0.235520\pi\)
\(128\) −8.78461 + 5.07180i −0.776457 + 0.448288i
\(129\) 3.59808 6.23205i 0.316793 0.548701i
\(130\) 0 0
\(131\) −4.26795 7.39230i −0.372892 0.645869i 0.617117 0.786872i \(-0.288301\pi\)
−0.990009 + 0.141003i \(0.954967\pi\)
\(132\) 4.00000i 0.348155i
\(133\) −1.23205 6.40192i −0.106832 0.555117i
\(134\) −1.94744 −0.168233
\(135\) 0 0
\(136\) 8.53590 14.7846i 0.731947 1.26777i
\(137\) −7.09808 4.09808i −0.606430 0.350122i 0.165137 0.986271i \(-0.447193\pi\)
−0.771567 + 0.636148i \(0.780527\pi\)
\(138\) 0.803848 0.464102i 0.0684280 0.0395070i
\(139\) 7.92820 0.672461 0.336231 0.941780i \(-0.390848\pi\)
0.336231 + 0.941780i \(0.390848\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 2.66025 1.53590i 0.223244 0.128890i
\(143\) 13.5622 + 7.83013i 1.13413 + 0.654788i
\(144\) 0.535898 0.928203i 0.0446582 0.0773503i
\(145\) 0 0
\(146\) −3.41154 −0.282341
\(147\) 2.59808 + 6.50000i 0.214286 + 0.536111i
\(148\) 10.5359i 0.866046i
\(149\) −10.9282 18.9282i −0.895273 1.55066i −0.833466 0.552571i \(-0.813647\pi\)
−0.0618073 0.998088i \(-0.519686\pi\)
\(150\) 0 0
\(151\) −2.46410 + 4.26795i −0.200526 + 0.347321i −0.948698 0.316184i \(-0.897598\pi\)
0.748172 + 0.663505i \(0.230932\pi\)
\(152\) −5.41154 + 3.12436i −0.438934 + 0.253419i
\(153\) 6.73205i 0.544254i
\(154\) −1.73205 + 5.00000i −0.139573 + 0.402911i
\(155\) 0 0
\(156\) −4.19615 7.26795i −0.335961 0.581902i
\(157\) −12.4641 7.19615i −0.994744 0.574315i −0.0880548 0.996116i \(-0.528065\pi\)
−0.906689 + 0.421800i \(0.861398\pi\)
\(158\) −8.49038 4.90192i −0.675458 0.389976i
\(159\) 4.19615 + 7.26795i 0.332777 + 0.576386i
\(160\) 0 0
\(161\) −3.29423 + 0.633975i −0.259622 + 0.0499642i
\(162\) 0.732051i 0.0575153i
\(163\) −5.07180 + 2.92820i −0.397254 + 0.229355i −0.685298 0.728262i \(-0.740328\pi\)
0.288045 + 0.957617i \(0.406995\pi\)
\(164\) −2.00000 + 3.46410i −0.156174 + 0.270501i
\(165\) 0 0
\(166\) 3.33975 + 5.78461i 0.259215 + 0.448973i
\(167\) 0.339746i 0.0262903i 0.999914 + 0.0131452i \(0.00418436\pi\)
−0.999914 + 0.0131452i \(0.995816\pi\)
\(168\) 5.07180 4.39230i 0.391298 0.338874i
\(169\) −19.8564 −1.52742
\(170\) 0 0
\(171\) 1.23205 2.13397i 0.0942173 0.163189i
\(172\) 9.12436 + 5.26795i 0.695726 + 0.401677i
\(173\) 18.5885 10.7321i 1.41325 0.815943i 0.417561 0.908649i \(-0.362885\pi\)
0.995693 + 0.0927063i \(0.0295518\pi\)
\(174\) 4.53590 0.343866
\(175\) 0 0
\(176\) −2.92820 −0.220722
\(177\) 8.83013 5.09808i 0.663713 0.383195i
\(178\) 5.78461 + 3.33975i 0.433575 + 0.250325i
\(179\) −5.00000 + 8.66025i −0.373718 + 0.647298i −0.990134 0.140122i \(-0.955250\pi\)
0.616417 + 0.787420i \(0.288584\pi\)
\(180\) 0 0
\(181\) 10.3205 0.767117 0.383559 0.923517i \(-0.374698\pi\)
0.383559 + 0.923517i \(0.374698\pi\)
\(182\) −2.09808 10.9019i −0.155520 0.808104i
\(183\) 4.00000i 0.295689i
\(184\) 1.60770 + 2.78461i 0.118521 + 0.205284i
\(185\) 0 0
\(186\) 2.36603 4.09808i 0.173485 0.300486i
\(187\) 15.9282 9.19615i 1.16479 0.672489i
\(188\) 2.92820i 0.213561i
\(189\) −0.866025 + 2.50000i −0.0629941 + 0.181848i
\(190\) 0 0
\(191\) −2.46410 4.26795i −0.178296 0.308818i 0.763001 0.646397i \(-0.223725\pi\)
−0.941297 + 0.337579i \(0.890392\pi\)
\(192\) −1.85641 1.07180i −0.133975 0.0773503i
\(193\) 7.96410 + 4.59808i 0.573269 + 0.330977i 0.758454 0.651727i \(-0.225955\pi\)
−0.185185 + 0.982704i \(0.559288\pi\)
\(194\) 0.392305 + 0.679492i 0.0281658 + 0.0487847i
\(195\) 0 0
\(196\) −9.51666 + 3.80385i −0.679761 + 0.271703i
\(197\) 17.6603i 1.25824i 0.777308 + 0.629121i \(0.216585\pi\)
−0.777308 + 0.629121i \(0.783415\pi\)
\(198\) −1.73205 + 1.00000i −0.123091 + 0.0710669i
\(199\) 11.0000 19.0526i 0.779769 1.35060i −0.152305 0.988334i \(-0.548670\pi\)
0.932075 0.362267i \(-0.117997\pi\)
\(200\) 0 0
\(201\) 1.33013 + 2.30385i 0.0938199 + 0.162501i
\(202\) 7.85641i 0.552775i
\(203\) −15.4904 5.36603i −1.08721 0.376621i
\(204\) −9.85641 −0.690086
\(205\) 0 0
\(206\) −0.437822 + 0.758330i −0.0305045 + 0.0528354i
\(207\) −1.09808 0.633975i −0.0763216 0.0440643i
\(208\) 5.32051 3.07180i 0.368911 0.212991i
\(209\) −6.73205 −0.465666
\(210\) 0 0
\(211\) 20.9282 1.44076 0.720378 0.693581i \(-0.243968\pi\)
0.720378 + 0.693581i \(0.243968\pi\)
\(212\) −10.6410 + 6.14359i −0.730828 + 0.421944i
\(213\) −3.63397 2.09808i −0.248996 0.143758i
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 0 0
\(216\) 2.53590 0.172546
\(217\) −12.9282 + 11.1962i −0.877624 + 0.760044i
\(218\) 8.05256i 0.545388i
\(219\) 2.33013 + 4.03590i 0.157455 + 0.272721i
\(220\) 0 0
\(221\) −19.2942 + 33.4186i −1.29787 + 2.24798i
\(222\) 4.56218 2.63397i 0.306193 0.176781i
\(223\) 0.392305i 0.0262707i 0.999914 + 0.0131353i \(0.00418123\pi\)
−0.999914 + 0.0131353i \(0.995819\pi\)
\(224\) 10.1436 + 11.7128i 0.677747 + 0.782595i
\(225\) 0 0
\(226\) 1.80385 + 3.12436i 0.119990 + 0.207829i
\(227\) 13.5622 + 7.83013i 0.900153 + 0.519704i 0.877250 0.480034i \(-0.159376\pi\)
0.0229034 + 0.999738i \(0.492709\pi\)
\(228\) 3.12436 + 1.80385i 0.206916 + 0.119463i
\(229\) −1.50000 2.59808i −0.0991228 0.171686i 0.812199 0.583380i \(-0.198270\pi\)
−0.911322 + 0.411695i \(0.864937\pi\)
\(230\) 0 0
\(231\) 7.09808 1.36603i 0.467019 0.0898779i
\(232\) 15.7128i 1.03160i
\(233\) −15.0000 + 8.66025i −0.982683 + 0.567352i −0.903079 0.429474i \(-0.858699\pi\)
−0.0796037 + 0.996827i \(0.525365\pi\)
\(234\) 2.09808 3.63397i 0.137156 0.237560i
\(235\) 0 0
\(236\) 7.46410 + 12.9282i 0.485872 + 0.841554i
\(237\) 13.3923i 0.869924i
\(238\) −12.3205 4.26795i −0.798620 0.276650i
\(239\) −20.9282 −1.35373 −0.676866 0.736106i \(-0.736663\pi\)
−0.676866 + 0.736106i \(0.736663\pi\)
\(240\) 0 0
\(241\) −3.26795 + 5.66025i −0.210507 + 0.364609i −0.951873 0.306492i \(-0.900845\pi\)
0.741366 + 0.671101i \(0.234178\pi\)
\(242\) −2.24167 1.29423i −0.144100 0.0831962i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 5.85641 0.374918
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) 12.2321 7.06218i 0.778307 0.449356i
\(248\) 14.1962 + 8.19615i 0.901457 + 0.520456i
\(249\) 4.56218 7.90192i 0.289116 0.500764i
\(250\) 0 0
\(251\) 6.58846 0.415860 0.207930 0.978144i \(-0.433327\pi\)
0.207930 + 0.978144i \(0.433327\pi\)
\(252\) −3.66025 1.26795i −0.230574 0.0798733i
\(253\) 3.46410i 0.217786i
\(254\) 5.56218 + 9.63397i 0.349002 + 0.604489i
\(255\) 0 0
\(256\) 5.85641 10.1436i 0.366025 0.633975i
\(257\) −10.0981 + 5.83013i −0.629901 + 0.363673i −0.780714 0.624889i \(-0.785144\pi\)
0.150813 + 0.988562i \(0.451811\pi\)
\(258\) 5.26795i 0.327968i
\(259\) −18.6962 + 3.59808i −1.16172 + 0.223574i
\(260\) 0 0
\(261\) −3.09808 5.36603i −0.191766 0.332149i
\(262\) 5.41154 + 3.12436i 0.334326 + 0.193023i
\(263\) 10.7321 + 6.19615i 0.661767 + 0.382071i 0.792950 0.609287i \(-0.208544\pi\)
−0.131183 + 0.991358i \(0.541878\pi\)
\(264\) −3.46410 6.00000i −0.213201 0.369274i
\(265\) 0 0
\(266\) 3.12436 + 3.60770i 0.191567 + 0.221202i
\(267\) 9.12436i 0.558401i
\(268\) −3.37307 + 1.94744i −0.206043 + 0.118959i
\(269\) −9.73205 + 16.8564i −0.593374 + 1.02775i 0.400401 + 0.916340i \(0.368871\pi\)
−0.993774 + 0.111413i \(0.964462\pi\)
\(270\) 0 0
\(271\) −8.46410 14.6603i −0.514158 0.890547i −0.999865 0.0164256i \(-0.994771\pi\)
0.485708 0.874121i \(-0.338562\pi\)
\(272\) 7.21539i 0.437497i
\(273\) −11.4641 + 9.92820i −0.693839 + 0.600882i
\(274\) 6.00000 0.362473
\(275\) 0 0
\(276\) 0.928203 1.60770i 0.0558713 0.0967719i
\(277\) 2.30385 + 1.33013i 0.138425 + 0.0799196i 0.567613 0.823295i \(-0.307867\pi\)
−0.429188 + 0.903215i \(0.641200\pi\)
\(278\) −5.02628 + 2.90192i −0.301456 + 0.174046i
\(279\) −6.46410 −0.386996
\(280\) 0 0
\(281\) −13.8564 −0.826604 −0.413302 0.910594i \(-0.635625\pi\)
−0.413302 + 0.910594i \(0.635625\pi\)
\(282\) 1.26795 0.732051i 0.0755053 0.0435930i
\(283\) −0.107695 0.0621778i −0.00640181 0.00369609i 0.496796 0.867868i \(-0.334510\pi\)
−0.503197 + 0.864171i \(0.667843\pi\)
\(284\) 3.07180 5.32051i 0.182278 0.315714i
\(285\) 0 0
\(286\) −11.4641 −0.677887
\(287\) 6.83013 + 2.36603i 0.403170 + 0.139662i
\(288\) 5.85641i 0.345092i
\(289\) 14.1603 + 24.5263i 0.832956 + 1.44272i
\(290\) 0 0
\(291\) 0.535898 0.928203i 0.0314149 0.0544122i
\(292\) −5.90897 + 3.41154i −0.345796 + 0.199645i
\(293\) 5.07180i 0.296298i 0.988965 + 0.148149i \(0.0473314\pi\)
−0.988965 + 0.148149i \(0.952669\pi\)
\(294\) −4.02628 3.16987i −0.234817 0.184871i
\(295\) 0 0
\(296\) 9.12436 + 15.8038i 0.530342 + 0.918580i
\(297\) 2.36603 + 1.36603i 0.137291 + 0.0792648i
\(298\) 13.8564 + 8.00000i 0.802680 + 0.463428i
\(299\) −3.63397 6.29423i −0.210158 0.364005i
\(300\) 0 0
\(301\) 6.23205 17.9904i 0.359209 1.03695i
\(302\) 3.60770i 0.207600i
\(303\) 9.29423 5.36603i 0.533939 0.308270i
\(304\) −1.32051 + 2.28719i −0.0757363 + 0.131179i
\(305\) 0 0
\(306\) −2.46410 4.26795i −0.140863 0.243982i
\(307\) 7.87564i 0.449487i 0.974418 + 0.224743i \(0.0721544\pi\)
−0.974418 + 0.224743i \(0.927846\pi\)
\(308\) 2.00000 + 10.3923i 0.113961 + 0.592157i
\(309\) 1.19615 0.0680467
\(310\) 0 0
\(311\) 7.56218 13.0981i 0.428812 0.742724i −0.567956 0.823059i \(-0.692266\pi\)
0.996768 + 0.0803351i \(0.0255990\pi\)
\(312\) 12.5885 + 7.26795i 0.712681 + 0.411467i
\(313\) 4.03590 2.33013i 0.228122 0.131707i −0.381583 0.924335i \(-0.624621\pi\)
0.609706 + 0.792628i \(0.291288\pi\)
\(314\) 10.5359 0.594575
\(315\) 0 0
\(316\) −19.6077 −1.10302
\(317\) −26.3660 + 15.2224i −1.48086 + 0.854977i −0.999765 0.0216894i \(-0.993095\pi\)
−0.481099 + 0.876666i \(0.659762\pi\)
\(318\) −5.32051 3.07180i −0.298359 0.172258i
\(319\) −8.46410 + 14.6603i −0.473899 + 0.820817i
\(320\) 0 0
\(321\) 8.19615 0.457465
\(322\) 1.85641 1.60770i 0.103453 0.0895933i
\(323\) 16.5885i 0.923006i
\(324\) −0.732051 1.26795i −0.0406695 0.0704416i
\(325\) 0 0
\(326\) 2.14359 3.71281i 0.118723 0.205634i
\(327\) 9.52628 5.50000i 0.526804 0.304151i
\(328\) 6.92820i 0.382546i
\(329\) −5.19615 + 1.00000i −0.286473 + 0.0551318i
\(330\) 0 0
\(331\) −10.9641 18.9904i −0.602642 1.04381i −0.992419 0.122897i \(-0.960782\pi\)
0.389778 0.920909i \(-0.372552\pi\)
\(332\) 11.5692 + 6.67949i 0.634943 + 0.366585i
\(333\) −6.23205 3.59808i −0.341514 0.197173i
\(334\) −0.124356 0.215390i −0.00680444 0.0117856i
\(335\) 0 0
\(336\) 0.928203 2.67949i 0.0506376 0.146178i
\(337\) 33.9808i 1.85105i 0.378686 + 0.925525i \(0.376376\pi\)
−0.378686 + 0.925525i \(0.623624\pi\)
\(338\) 12.5885 7.26795i 0.684722 0.395324i
\(339\) 2.46410 4.26795i 0.133832 0.231803i
\(340\) 0 0
\(341\) 8.83013 + 15.2942i 0.478178 + 0.828229i
\(342\) 1.80385i 0.0975409i
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −18.2487 −0.983905
\(345\) 0 0
\(346\) −7.85641 + 13.6077i −0.422363 + 0.731554i
\(347\) −30.2487 17.4641i −1.62384 0.937522i −0.985881 0.167449i \(-0.946447\pi\)
−0.637955 0.770074i \(-0.720219\pi\)
\(348\) 7.85641 4.53590i 0.421148 0.243150i
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 0 0
\(351\) −5.73205 −0.305954
\(352\) 13.8564 8.00000i 0.738549 0.426401i
\(353\) −18.2942 10.5622i −0.973704 0.562168i −0.0733402 0.997307i \(-0.523366\pi\)
−0.900363 + 0.435139i \(0.856699\pi\)
\(354\) −3.73205 + 6.46410i −0.198356 + 0.343563i
\(355\) 0 0
\(356\) 13.3590 0.708025
\(357\) 3.36603 + 17.4904i 0.178149 + 0.925689i
\(358\) 7.32051i 0.386901i
\(359\) −2.36603 4.09808i −0.124874 0.216288i 0.796810 0.604230i \(-0.206519\pi\)
−0.921684 + 0.387942i \(0.873186\pi\)
\(360\) 0 0
\(361\) 6.46410 11.1962i 0.340216 0.589271i
\(362\) −6.54294 + 3.77757i −0.343889 + 0.198545i
\(363\) 3.53590i 0.185587i
\(364\) −14.5359 16.7846i −0.761888 0.879753i
\(365\) 0 0
\(366\) 1.46410 + 2.53590i 0.0765298 + 0.132554i
\(367\) 0.696152 + 0.401924i 0.0363389 + 0.0209803i 0.518059 0.855345i \(-0.326655\pi\)
−0.481721 + 0.876325i \(0.659988\pi\)
\(368\) 1.17691 + 0.679492i 0.0613509 + 0.0354210i
\(369\) 1.36603 + 2.36603i 0.0711124 + 0.123170i
\(370\) 0 0
\(371\) 14.5359 + 16.7846i 0.754666 + 0.871414i
\(372\) 9.46410i 0.490691i
\(373\) −16.0359 + 9.25833i −0.830307 + 0.479378i −0.853958 0.520342i \(-0.825804\pi\)
0.0236505 + 0.999720i \(0.492471\pi\)
\(374\) −6.73205 + 11.6603i −0.348106 + 0.602937i
\(375\) 0 0
\(376\) 2.53590 + 4.39230i 0.130779 + 0.226516i
\(377\) 35.5167i 1.82920i
\(378\) −0.366025 1.90192i −0.0188263 0.0978244i
\(379\) 28.3205 1.45473 0.727363 0.686253i \(-0.240745\pi\)
0.727363 + 0.686253i \(0.240745\pi\)
\(380\) 0 0
\(381\) 7.59808 13.1603i 0.389261 0.674220i
\(382\) 3.12436 + 1.80385i 0.159856 + 0.0922929i
\(383\) 9.80385 5.66025i 0.500953 0.289225i −0.228154 0.973625i \(-0.573269\pi\)
0.729107 + 0.684400i \(0.239936\pi\)
\(384\) −10.1436 −0.517638
\(385\) 0 0
\(386\) −6.73205 −0.342652
\(387\) 6.23205 3.59808i 0.316793 0.182900i
\(388\) 1.35898 + 0.784610i 0.0689920 + 0.0398325i
\(389\) 18.2942 31.6865i 0.927554 1.60657i 0.140153 0.990130i \(-0.455240\pi\)
0.787401 0.616441i \(-0.211426\pi\)
\(390\) 0 0
\(391\) −8.53590 −0.431679
\(392\) 10.9808 13.9474i 0.554612 0.704452i
\(393\) 8.53590i 0.430579i
\(394\) −6.46410 11.1962i −0.325657 0.564054i
\(395\) 0 0
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) 18.0167 10.4019i 0.904230 0.522058i 0.0256600 0.999671i \(-0.491831\pi\)
0.878570 + 0.477613i \(0.158498\pi\)
\(398\) 16.1051i 0.807277i
\(399\) 2.13397 6.16025i 0.106832 0.308398i
\(400\) 0 0
\(401\) −2.19615 3.80385i −0.109671 0.189955i 0.805966 0.591962i \(-0.201646\pi\)
−0.915637 + 0.402006i \(0.868313\pi\)
\(402\) −1.68653 0.973721i −0.0841166 0.0485648i
\(403\) −32.0885 18.5263i −1.59844 0.922860i
\(404\) 7.85641 + 13.6077i 0.390871 + 0.677008i
\(405\) 0 0
\(406\) 11.7846 2.26795i 0.584860 0.112556i
\(407\) 19.6603i 0.974523i
\(408\) 14.7846 8.53590i 0.731947 0.422590i
\(409\) 15.4282 26.7224i 0.762876 1.32134i −0.178487 0.983942i \(-0.557120\pi\)
0.941362 0.337397i \(-0.109546\pi\)
\(410\) 0 0
\(411\) −4.09808 7.09808i −0.202143 0.350122i
\(412\) 1.75129i 0.0862798i
\(413\) 20.3923 17.6603i 1.00344 0.869004i
\(414\) 0.928203 0.0456187
\(415\) 0 0
\(416\) −16.7846 + 29.0718i −0.822933 + 1.42536i
\(417\) 6.86603 + 3.96410i 0.336231 + 0.194123i
\(418\) 4.26795 2.46410i 0.208752 0.120523i
\(419\) 28.5359 1.39407 0.697035 0.717037i \(-0.254502\pi\)
0.697035 + 0.717037i \(0.254502\pi\)
\(420\) 0 0
\(421\) 13.9282 0.678819 0.339410 0.940639i \(-0.389773\pi\)
0.339410 + 0.940639i \(0.389773\pi\)
\(422\) −13.2679 + 7.66025i −0.645874 + 0.372895i
\(423\) −1.73205 1.00000i −0.0842152 0.0486217i
\(424\) 10.6410 18.4308i 0.516773 0.895078i
\(425\) 0 0
\(426\) 3.07180 0.148829
\(427\) −2.00000 10.3923i −0.0967868 0.502919i
\(428\) 12.0000i 0.580042i
\(429\) 7.83013 + 13.5622i 0.378042 + 0.654788i
\(430\) 0 0
\(431\) 8.66025 15.0000i 0.417150 0.722525i −0.578502 0.815681i \(-0.696362\pi\)
0.995651 + 0.0931566i \(0.0296957\pi\)
\(432\) 0.928203 0.535898i 0.0446582 0.0257834i
\(433\) 4.80385i 0.230858i 0.993316 + 0.115429i \(0.0368243\pi\)
−0.993316 + 0.115429i \(0.963176\pi\)
\(434\) 4.09808 11.8301i 0.196714 0.567864i
\(435\) 0 0
\(436\) 8.05256 + 13.9474i 0.385648 + 0.667961i
\(437\) 2.70577 + 1.56218i 0.129435 + 0.0747291i
\(438\) −2.95448 1.70577i −0.141171 0.0815049i
\(439\) 3.73205 + 6.46410i 0.178121 + 0.308515i 0.941237 0.337747i \(-0.109665\pi\)
−0.763116 + 0.646262i \(0.776331\pi\)
\(440\) 0 0
\(441\) −1.00000 + 6.92820i −0.0476190 + 0.329914i
\(442\) 28.2487i 1.34365i
\(443\) 2.19615 1.26795i 0.104342 0.0602421i −0.446921 0.894574i \(-0.647479\pi\)
0.551263 + 0.834331i \(0.314146\pi\)
\(444\) 5.26795 9.12436i 0.250006 0.433023i
\(445\) 0 0
\(446\) −0.143594 0.248711i −0.00679935 0.0117768i
\(447\) 21.8564i 1.03377i
\(448\) −5.35898 1.85641i −0.253188 0.0877070i
\(449\) 8.14359 0.384320 0.192160 0.981364i \(-0.438451\pi\)
0.192160 + 0.981364i \(0.438451\pi\)
\(450\) 0 0
\(451\) 3.73205 6.46410i 0.175735 0.304383i
\(452\) 6.24871 + 3.60770i 0.293915 + 0.169692i
\(453\) −4.26795 + 2.46410i −0.200526 + 0.115774i
\(454\) −11.4641 −0.538037
\(455\) 0 0
\(456\) −6.24871 −0.292623
\(457\) −0.571797 + 0.330127i −0.0267475 + 0.0154427i −0.513314 0.858201i \(-0.671582\pi\)
0.486567 + 0.873643i \(0.338249\pi\)
\(458\) 1.90192 + 1.09808i 0.0888711 + 0.0513097i
\(459\) −3.36603 + 5.83013i −0.157113 + 0.272127i
\(460\) 0 0
\(461\) −34.9808 −1.62922 −0.814608 0.580012i \(-0.803048\pi\)
−0.814608 + 0.580012i \(0.803048\pi\)
\(462\) −4.00000 + 3.46410i −0.186097 + 0.161165i
\(463\) 22.2679i 1.03488i 0.855720 + 0.517440i \(0.173115\pi\)
−0.855720 + 0.517440i \(0.826885\pi\)
\(464\) 3.32051 + 5.75129i 0.154151 + 0.266997i
\(465\) 0 0
\(466\) 6.33975 10.9808i 0.293683 0.508674i
\(467\) 24.1244 13.9282i 1.11634 0.644520i 0.175877 0.984412i \(-0.443724\pi\)
0.940465 + 0.339892i \(0.110390\pi\)
\(468\) 8.39230i 0.387934i
\(469\) 4.60770 + 5.32051i 0.212764 + 0.245678i
\(470\) 0 0
\(471\) −7.19615 12.4641i −0.331581 0.574315i
\(472\) −22.3923 12.9282i −1.03069 0.595069i
\(473\) −17.0263 9.83013i −0.782869 0.451990i
\(474\) −4.90192 8.49038i −0.225153 0.389976i
\(475\) 0 0
\(476\) −25.6077 + 4.92820i −1.17373 + 0.225884i
\(477\) 8.39230i 0.384257i
\(478\) 13.2679 7.66025i 0.606862 0.350372i
\(479\) −16.3923 + 28.3923i −0.748984 + 1.29728i 0.199327 + 0.979933i \(0.436124\pi\)
−0.948310 + 0.317344i \(0.897209\pi\)
\(480\) 0 0
\(481\) −20.6244 35.7224i −0.940390 1.62880i
\(482\) 4.78461i 0.217933i
\(483\) −3.16987 1.09808i −0.144234 0.0499642i
\(484\) −5.17691 −0.235314
\(485\) 0 0
\(486\) 0.366025 0.633975i 0.0166032 0.0287577i
\(487\) −27.3564 15.7942i −1.23964 0.715705i −0.270617 0.962687i \(-0.587228\pi\)
−0.969020 + 0.246982i \(0.920561\pi\)
\(488\) −8.78461 + 5.07180i −0.397661 + 0.229589i
\(489\) −5.85641 −0.264836
\(490\) 0 0
\(491\) 10.2487 0.462518 0.231259 0.972892i \(-0.425716\pi\)
0.231259 + 0.972892i \(0.425716\pi\)
\(492\) −3.46410 + 2.00000i −0.156174 + 0.0901670i
\(493\) −36.1244 20.8564i −1.62696 0.939325i
\(494\) −5.16987 + 8.95448i −0.232604 + 0.402881i
\(495\) 0 0
\(496\) 6.92820 0.311086
\(497\) −10.4904 3.63397i −0.470558 0.163006i
\(498\) 6.67949i 0.299315i
\(499\) −10.2321 17.7224i −0.458050 0.793365i 0.540808 0.841146i \(-0.318118\pi\)
−0.998858 + 0.0477808i \(0.984785\pi\)
\(500\) 0 0
\(501\) −0.169873 + 0.294229i −0.00758937 + 0.0131452i
\(502\) −4.17691 + 2.41154i −0.186425 + 0.107632i
\(503\) 6.39230i 0.285019i −0.989793 0.142509i \(-0.954483\pi\)
0.989793 0.142509i \(-0.0455171\pi\)
\(504\) 6.58846 1.26795i 0.293473 0.0564789i
\(505\) 0 0
\(506\) −1.26795 2.19615i −0.0563672 0.0976309i
\(507\) −17.1962 9.92820i −0.763708 0.440927i
\(508\) 19.2679 + 11.1244i 0.854877 + 0.493563i
\(509\) 5.73205 + 9.92820i 0.254069 + 0.440060i 0.964642 0.263563i \(-0.0848977\pi\)
−0.710573 + 0.703623i \(0.751564\pi\)
\(510\) 0 0
\(511\) 8.07180 + 9.32051i 0.357075 + 0.412315i
\(512\) 11.7128i 0.517638i
\(513\) 2.13397 1.23205i 0.0942173 0.0543964i
\(514\) 4.26795 7.39230i 0.188251 0.326061i
\(515\) 0 0
\(516\) 5.26795 + 9.12436i 0.231909 + 0.401677i
\(517\) 5.46410i 0.240311i
\(518\) 10.5359 9.12436i 0.462921 0.400901i
\(519\) 21.4641 0.942169
\(520\) 0 0
\(521\) −0.732051 + 1.26795i −0.0320717 + 0.0555499i −0.881616 0.471968i \(-0.843544\pi\)
0.849544 + 0.527518i \(0.176877\pi\)
\(522\) 3.92820 + 2.26795i 0.171933 + 0.0992654i
\(523\) −21.0167 + 12.1340i −0.918994 + 0.530582i −0.883314 0.468782i \(-0.844693\pi\)
−0.0356803 + 0.999363i \(0.511360\pi\)
\(524\) 12.4974 0.545952
\(525\) 0 0
\(526\) −9.07180 −0.395549
\(527\) −37.6865 + 21.7583i −1.64165 + 0.947808i
\(528\) −2.53590 1.46410i −0.110361 0.0637168i
\(529\) −10.6962 + 18.5263i −0.465050 + 0.805490i
\(530\) 0 0
\(531\) 10.1962 0.442475
\(532\) 9.01924 + 3.12436i 0.391034 + 0.135458i
\(533\) 15.6603i 0.678321i
\(534\) 3.33975 + 5.78461i 0.144525 + 0.250325i
\(535\) 0 0
\(536\) 3.37307 5.84232i 0.145694 0.252350i
\(537\) −8.66025 + 5.00000i −0.373718 + 0.215766i
\(538\) 14.2487i 0.614306i
\(539\) 17.7583 7.09808i 0.764905 0.305736i
\(540\) 0 0
\(541\) 17.8923 + 30.9904i 0.769250 + 1.33238i 0.937970 + 0.346716i \(0.112703\pi\)
−0.168720 + 0.985664i \(0.553963\pi\)
\(542\) 10.7321 + 6.19615i 0.460981 + 0.266148i
\(543\) 8.93782 + 5.16025i 0.383559 + 0.221448i
\(544\) 19.7128 + 34.1436i 0.845180 + 1.46389i
\(545\) 0 0
\(546\) 3.63397 10.4904i 0.155520 0.448947i
\(547\) 22.2487i 0.951286i −0.879638 0.475643i \(-0.842215\pi\)
0.879638 0.475643i \(-0.157785\pi\)
\(548\) 10.3923 6.00000i 0.443937 0.256307i
\(549\) 2.00000 3.46410i 0.0853579 0.147844i
\(550\) 0 0
\(551\) 7.63397 + 13.2224i 0.325218 + 0.563295i
\(552\) 3.21539i 0.136856i
\(553\) 6.69615 + 34.7942i 0.284749 + 1.47960i
\(554\) −1.94744 −0.0827388
\(555\) 0 0
\(556\) −5.80385 + 10.0526i −0.246138 + 0.426323i
\(557\) −23.1962 13.3923i −0.982853 0.567450i −0.0797224 0.996817i \(-0.525403\pi\)
−0.903130 + 0.429367i \(0.858737\pi\)
\(558\) 4.09808 2.36603i 0.173485 0.100162i
\(559\) 41.2487 1.74463
\(560\) 0 0
\(561\) 18.3923 0.776524
\(562\) 8.78461 5.07180i 0.370556 0.213941i
\(563\) 15.5885 + 9.00000i 0.656975 + 0.379305i 0.791123 0.611656i \(-0.209497\pi\)
−0.134148 + 0.990961i \(0.542830\pi\)
\(564\) 1.46410 2.53590i 0.0616498 0.106781i
\(565\) 0 0
\(566\) 0.0910347 0.00382647
\(567\) −2.00000 + 1.73205i −0.0839921 + 0.0727393i
\(568\) 10.6410i 0.446487i
\(569\) −13.2224 22.9019i −0.554313 0.960099i −0.997957 0.0638952i \(-0.979648\pi\)
0.443643 0.896203i \(-0.353686\pi\)
\(570\) 0 0
\(571\) −19.6962 + 34.1147i −0.824258 + 1.42766i 0.0782265 + 0.996936i \(0.475074\pi\)
−0.902485 + 0.430722i \(0.858259\pi\)
\(572\) −19.8564 + 11.4641i −0.830238 + 0.479338i
\(573\) 4.92820i 0.205879i
\(574\) −5.19615 + 1.00000i −0.216883 + 0.0417392i
\(575\) 0 0
\(576\) −1.07180 1.85641i −0.0446582 0.0773503i
\(577\) 9.82051 + 5.66987i 0.408833 + 0.236040i 0.690288 0.723534i \(-0.257484\pi\)
−0.281455 + 0.959574i \(0.590817\pi\)
\(578\) −17.9545 10.3660i −0.746808 0.431170i
\(579\) 4.59808 + 7.96410i 0.191090 + 0.330977i
\(580\) 0 0
\(581\) 7.90192 22.8109i 0.327827 0.946355i
\(582\) 0.784610i 0.0325231i
\(583\) 19.8564 11.4641i 0.822368 0.474795i
\(584\) 5.90897 10.2346i 0.244515 0.423512i
\(585\) 0 0
\(586\) −1.85641 3.21539i −0.0766874 0.132827i
\(587\) 37.2679i 1.53821i −0.639121 0.769106i \(-0.720702\pi\)
0.639121 0.769106i \(-0.279298\pi\)
\(588\) −10.1436 1.46410i −0.418315 0.0603785i
\(589\) 15.9282 0.656310
\(590\) 0 0
\(591\) −8.83013 + 15.2942i −0.363223 + 0.629121i
\(592\) 6.67949 + 3.85641i 0.274525 + 0.158497i
\(593\) −32.8301 + 18.9545i −1.34817 + 0.778367i −0.987990 0.154515i \(-0.950619\pi\)
−0.360181 + 0.932882i \(0.617285\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) 32.0000 1.31077
\(597\) 19.0526 11.0000i 0.779769 0.450200i
\(598\) 4.60770 + 2.66025i 0.188423 + 0.108786i
\(599\) 5.12436 8.87564i 0.209375 0.362649i −0.742142 0.670242i \(-0.766190\pi\)
0.951518 + 0.307593i \(0.0995236\pi\)
\(600\) 0 0
\(601\) −13.9282 −0.568143 −0.284072 0.958803i \(-0.591685\pi\)
−0.284072 + 0.958803i \(0.591685\pi\)
\(602\) 2.63397 + 13.6865i 0.107353 + 0.557821i
\(603\) 2.66025i 0.108334i
\(604\) −3.60770 6.24871i −0.146795 0.254256i
\(605\) 0 0
\(606\) −3.92820 + 6.80385i −0.159572 + 0.276387i
\(607\) 6.23205 3.59808i 0.252951 0.146041i −0.368164 0.929761i \(-0.620013\pi\)
0.621115 + 0.783720i \(0.286680\pi\)
\(608\) 14.4308i 0.585245i
\(609\) −10.7321 12.3923i −0.434885 0.502162i
\(610\) 0 0
\(611\) −5.73205 9.92820i −0.231894 0.401652i
\(612\) −8.53590 4.92820i −0.345043 0.199211i
\(613\) 11.3205 + 6.53590i 0.457231 + 0.263982i 0.710879 0.703314i \(-0.248297\pi\)
−0.253648 + 0.967297i \(0.581631\pi\)
\(614\) −2.88269 4.99296i −0.116336 0.201499i
\(615\) 0 0
\(616\) −12.0000 13.8564i −0.483494 0.558291i
\(617\) 12.2487i 0.493115i −0.969128 0.246557i \(-0.920701\pi\)
0.969128 0.246557i \(-0.0792993\pi\)
\(618\) −0.758330 + 0.437822i −0.0305045 + 0.0176118i
\(619\) −21.9641 + 38.0429i −0.882812 + 1.52907i −0.0346105 + 0.999401i \(0.511019\pi\)
−0.848201 + 0.529674i \(0.822314\pi\)
\(620\) 0 0
\(621\) −0.633975 1.09808i −0.0254405 0.0440643i
\(622\) 11.0718i 0.443939i
\(623\) −4.56218 23.7058i −0.182780 0.949752i
\(624\) 6.14359 0.245941
\(625\) 0 0
\(626\) −1.70577 + 2.95448i −0.0681763 + 0.118085i
\(627\) −5.83013 3.36603i −0.232833 0.134426i
\(628\) 18.2487 10.5359i 0.728203 0.420428i
\(629\) −48.4449 −1.93162
\(630\) 0 0
\(631\) 7.21539 0.287240 0.143620 0.989633i \(-0.454126\pi\)
0.143620 + 0.989633i \(0.454126\pi\)
\(632\) 29.4115 16.9808i 1.16993 0.675458i
\(633\) 18.1244 + 10.4641i 0.720378 + 0.415911i
\(634\) 11.1436 19.3013i 0.442569 0.766551i
\(635\) 0 0
\(636\) −12.2872 −0.487219
\(637\) −24.8205 + 31.5263i −0.983424 + 1.24912i
\(638\) 12.3923i 0.490616i
\(639\) −2.09808 3.63397i −0.0829986 0.143758i
\(640\) 0 0
\(641\) −7.09808 + 12.2942i −0.280357 + 0.485593i −0.971473 0.237151i \(-0.923786\pi\)
0.691116 + 0.722744i \(0.257120\pi\)
\(642\) −5.19615 + 3.00000i −0.205076 + 0.118401i
\(643\) 40.5167i 1.59782i −0.601450 0.798911i \(-0.705410\pi\)
0.601450 0.798911i \(-0.294590\pi\)
\(644\) 1.60770 4.64102i 0.0633521 0.182882i
\(645\) 0 0
\(646\) 6.07180 + 10.5167i 0.238892 + 0.413772i
\(647\) 32.8301 + 18.9545i 1.29069 + 0.745178i 0.978776 0.204934i \(-0.0656980\pi\)
0.311910 + 0.950112i \(0.399031\pi\)
\(648\) 2.19615 + 1.26795i 0.0862730 + 0.0498097i
\(649\) −13.9282 24.1244i −0.546730 0.946964i
\(650\) 0 0
\(651\) −16.7942 + 3.23205i −0.658218 + 0.126674i
\(652\) 8.57437i 0.335798i
\(653\) −11.6147 + 6.70577i −0.454520 + 0.262417i −0.709737 0.704467i \(-0.751186\pi\)
0.255217 + 0.966884i \(0.417853\pi\)
\(654\) −4.02628 + 6.97372i −0.157440 + 0.272694i
\(655\) 0 0
\(656\) −1.46410 2.53590i −0.0571636 0.0990102i
\(657\) 4.66025i 0.181814i
\(658\) 2.92820 2.53590i 0.114153 0.0988596i
\(659\) 10.9282 0.425702 0.212851 0.977085i \(-0.431725\pi\)
0.212851 + 0.977085i \(0.431725\pi\)
\(660\) 0 0
\(661\) −1.76795 + 3.06218i −0.0687653 + 0.119105i −0.898358 0.439264i \(-0.855239\pi\)
0.829593 + 0.558369i \(0.188573\pi\)
\(662\) 13.9019 + 8.02628i 0.540314 + 0.311950i
\(663\) −33.4186 + 19.2942i −1.29787 + 0.749326i
\(664\) −23.1384 −0.897946
\(665\) 0 0
\(666\) 5.26795 0.204129
\(667\) 6.80385 3.92820i 0.263446 0.152101i
\(668\) −0.430781 0.248711i −0.0166674 0.00962293i
\(669\) −0.196152 + 0.339746i −0.00758369 + 0.0131353i
\(670\) 0 0
\(671\) −10.9282 −0.421879
\(672\) 2.92820 + 15.2154i 0.112958 + 0.586946i
\(673\) 44.6603i 1.72153i −0.509006 0.860763i \(-0.669987\pi\)
0.509006 0.860763i \(-0.330013\pi\)
\(674\) −12.4378 21.5429i −0.479087 0.829803i
\(675\) 0 0
\(676\) 14.5359 25.1769i 0.559073 0.968343i
\(677\) 7.68653 4.43782i 0.295417 0.170559i −0.344965 0.938616i \(-0.612109\pi\)
0.640382 + 0.768056i \(0.278776\pi\)
\(678\) 3.60770i 0.138553i
\(679\) 0.928203 2.67949i 0.0356212 0.102829i
\(680\) 0 0
\(681\) 7.83013 + 13.5622i 0.300051 + 0.519704i
\(682\) −11.1962 6.46410i −0.428723 0.247523i
\(683\) −8.70577 5.02628i −0.333117 0.192325i 0.324107 0.946020i \(-0.394936\pi\)
−0.657224 + 0.753695i \(0.728270\pi\)
\(684\) 1.80385 + 3.12436i 0.0689718 + 0.119463i
\(685\) 0 0
\(686\) −12.0455 6.22243i −0.459900 0.237574i
\(687\) 3.00000i 0.114457i
\(688\) −6.67949 + 3.85641i −0.254653 + 0.147024i
\(689\) −24.0526 + 41.6603i −0.916330 + 1.58713i
\(690\) 0 0
\(691\) 9.42820 + 16.3301i 0.358666 + 0.621227i 0.987738 0.156119i \(-0.0498985\pi\)
−0.629072 + 0.777347i \(0.716565\pi\)
\(692\) 31.4256i 1.19462i
\(693\) 6.83013 + 2.36603i 0.259455 + 0.0898779i
\(694\) 25.5692 0.970594
\(695\) 0 0
\(696\) −7.85641 + 13.6077i −0.297796 + 0.515798i
\(697\) 15.9282 + 9.19615i 0.603324 + 0.348329i
\(698\) 13.9474 8.05256i 0.527918 0.304794i
\(699\) −17.3205 −0.655122
\(700\) 0 0
\(701\) 22.5885 0.853154 0.426577 0.904451i \(-0.359719\pi\)
0.426577 + 0.904451i \(0.359719\pi\)
\(702\) 3.63397 2.09808i 0.137156 0.0791868i
\(703\) 15.3564 + 8.86603i 0.579178 + 0.334388i
\(704\) −2.92820 + 5.07180i −0.110361 + 0.191151i
\(705\) 0 0
\(706\) 15.4641 0.581999
\(707\) 21.4641 18.5885i 0.807241 0.699091i
\(708\) 14.9282i 0.561036i
\(709\) −7.46410 12.9282i −0.280320 0.485529i 0.691143 0.722718i \(-0.257107\pi\)
−0.971464 + 0.237189i \(0.923774\pi\)
\(710\) 0 0
\(711\) −6.69615 + 11.5981i −0.251125 + 0.434962i
\(712\) −20.0385 + 11.5692i −0.750974 + 0.433575i
\(713\) 8.19615i 0.306948i
\(714\) −8.53590 9.85641i −0.319448 0.368867i
\(715\) 0 0
\(716\) −7.32051 12.6795i −0.273580 0.473855i
\(717\) −18.1244 10.4641i −0.676866 0.390789i
\(718\) 3.00000 + 1.73205i 0.111959 + 0.0646396i
\(719\) −13.7321 23.7846i −0.512119 0.887016i −0.999901 0.0140509i \(-0.995527\pi\)
0.487782 0.872965i \(-0.337806\pi\)
\(720\) 0 0
\(721\) 3.10770 0.598076i 0.115737 0.0222735i
\(722\) 9.46410i 0.352217i
\(723\) −5.66025 + 3.26795i −0.210507 + 0.121536i
\(724\) −7.55514 + 13.0859i −0.280784 + 0.486333i
\(725\) 0 0
\(726\) −1.29423 2.24167i −0.0480333 0.0831962i
\(727\) 30.6603i 1.13713i 0.822640 + 0.568563i \(0.192500\pi\)
−0.822640 + 0.568563i \(0.807500\pi\)
\(728\) 36.3397 + 12.5885i 1.34684 + 0.466559i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 24.2224 41.9545i 0.895899 1.55174i
\(732\) 5.07180 + 2.92820i 0.187459 + 0.108230i
\(733\) −16.1603 + 9.33013i −0.596893 + 0.344616i −0.767818 0.640668i \(-0.778658\pi\)
0.170926 + 0.985284i \(0.445324\pi\)
\(734\) −0.588457 −0.0217204
\(735\) 0 0
\(736\) −7.42563 −0.273712
\(737\) 6.29423 3.63397i 0.231851 0.133859i
\(738\) −1.73205 1.00000i −0.0637577 0.0368105i
\(739\) −6.89230 + 11.9378i −0.253538 + 0.439140i −0.964497 0.264093i \(-0.914927\pi\)
0.710960 + 0.703233i \(0.248261\pi\)
\(740\) 0 0
\(741\) 14.1244 0.518871
\(742\) −15.3590 5.32051i −0.563846 0.195322i
\(743\) 49.9090i 1.83098i 0.402338 + 0.915491i \(0.368198\pi\)
−0.402338 + 0.915491i \(0.631802\pi\)
\(744\) 8.19615 + 14.1962i 0.300486 + 0.520456i
\(745\) 0 0
\(746\) 6.77757 11.7391i 0.248144 0.429799i
\(747\) 7.90192 4.56218i 0.289116 0.166921i
\(748\) 26.9282i 0.984593i
\(749\) 21.2942 4.09808i 0.778074 0.149740i
\(750\) 0 0
\(751\) −15.9641 27.6506i −0.582538 1.00899i −0.995177 0.0980914i \(-0.968726\pi\)
0.412639 0.910895i \(-0.364607\pi\)
\(752\) 1.85641 + 1.07180i 0.0676962 + 0.0390844i
\(753\) 5.70577 + 3.29423i 0.207930 + 0.120048i
\(754\) 13.0000 + 22.5167i 0.473432 + 0.820008i
\(755\) 0 0
\(756\) −2.53590 2.92820i −0.0922297 0.106498i
\(757\) 0.143594i 0.00521900i 0.999997 + 0.00260950i \(0.000830630\pi\)
−0.999997 + 0.00260950i \(0.999169\pi\)
\(758\) −17.9545 + 10.3660i −0.652136 + 0.376511i
\(759\) −1.73205 + 3.00000i −0.0628695 + 0.108893i
\(760\) 0 0
\(761\) −21.6340 37.4711i −0.784231 1.35833i −0.929457 0.368929i \(-0.879724\pi\)
0.145226 0.989398i \(-0.453609\pi\)
\(762\) 11.1244i 0.402993i
\(763\) 22.0000 19.0526i 0.796453 0.689749i
\(764\) 7.21539 0.261044
\(765\) 0 0
\(766\) −4.14359 + 7.17691i −0.149714 + 0.259312i
\(767\) 50.6147 + 29.2224i 1.82759 + 1.05516i
\(768\) 10.1436 5.85641i 0.366025 0.211325i
\(769\) −17.6795 −0.637539 −0.318769 0.947832i \(-0.603270\pi\)
−0.318769 + 0.947832i \(0.603270\pi\)
\(770\) 0 0
\(771\) −11.6603 −0.419934
\(772\) −11.6603 + 6.73205i −0.419662 + 0.242292i
\(773\) 1.31347 + 0.758330i 0.0472421 + 0.0272752i 0.523435 0.852066i \(-0.324650\pi\)
−0.476193 + 0.879341i \(0.657984\pi\)
\(774\) −2.63397 + 4.56218i −0.0946763 + 0.163984i
\(775\) 0