Properties

Label 231.2.i.c.67.1
Level $231$
Weight $2$
Character 231.67
Analytic conductor $1.845$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [231,2,Mod(67,231)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(231, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("231.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.84454428669\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 231.67
Dual form 231.2.i.c.100.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +2.00000 q^{6} +(2.50000 + 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} +(1.00000 + 1.73205i) q^{12} -5.00000 q^{13} +(1.00000 + 5.19615i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(1.00000 - 1.73205i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(2.00000 - 1.73205i) q^{21} +2.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(2.50000 - 4.33013i) q^{25} +(-5.00000 - 8.66025i) q^{26} -1.00000 q^{27} +(-4.00000 + 3.46410i) q^{28} -2.00000 q^{29} +(3.50000 - 6.06218i) q^{31} +(-4.00000 + 6.92820i) q^{32} +(-0.500000 - 0.866025i) q^{33} -12.0000 q^{34} +2.00000 q^{36} +(-3.50000 - 6.06218i) q^{37} +(7.00000 - 12.1244i) q^{38} +(-2.50000 + 4.33013i) q^{39} +4.00000 q^{41} +(5.00000 + 1.73205i) q^{42} -9.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-4.00000 + 6.92820i) q^{46} +(-3.00000 - 5.19615i) q^{47} +4.00000 q^{48} +(5.50000 + 4.33013i) q^{49} +10.0000 q^{50} +(3.00000 + 5.19615i) q^{51} +(5.00000 - 8.66025i) q^{52} +(1.00000 - 1.73205i) q^{53} +(-1.00000 - 1.73205i) q^{54} -7.00000 q^{57} +(-2.00000 - 3.46410i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(1.00000 + 1.73205i) q^{61} +14.0000 q^{62} +(-0.500000 - 2.59808i) q^{63} -8.00000 q^{64} +(1.00000 - 1.73205i) q^{66} +(-3.50000 + 6.06218i) q^{67} +(-6.00000 - 10.3923i) q^{68} +4.00000 q^{69} +8.00000 q^{71} +(2.50000 - 4.33013i) q^{73} +(7.00000 - 12.1244i) q^{74} +(-2.50000 - 4.33013i) q^{75} +14.0000 q^{76} +(2.00000 - 1.73205i) q^{77} -10.0000 q^{78} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.00000 + 6.92820i) q^{82} -4.00000 q^{83} +(1.00000 + 5.19615i) q^{84} +(-9.00000 - 15.5885i) q^{86} +(-1.00000 + 1.73205i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-12.5000 - 4.33013i) q^{91} -8.00000 q^{92} +(-3.50000 - 6.06218i) q^{93} +(6.00000 - 10.3923i) q^{94} +(4.00000 + 6.92820i) q^{96} +2.00000 q^{97} +(-2.00000 + 13.8564i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + q^{3} - 2 q^{4} + 4 q^{6} + 5 q^{7} - q^{9} + q^{11} + 2 q^{12} - 10 q^{13} + 2 q^{14} + 4 q^{16} - 6 q^{17} + 2 q^{18} - 7 q^{19} + 4 q^{21} + 4 q^{22} + 4 q^{23} + 5 q^{25} - 10 q^{26} - 2 q^{27} - 8 q^{28} - 4 q^{29} + 7 q^{31} - 8 q^{32} - q^{33} - 24 q^{34} + 4 q^{36} - 7 q^{37} + 14 q^{38} - 5 q^{39} + 8 q^{41} + 10 q^{42} - 18 q^{43} + 2 q^{44} - 8 q^{46} - 6 q^{47} + 8 q^{48} + 11 q^{49} + 20 q^{50} + 6 q^{51} + 10 q^{52} + 2 q^{53} - 2 q^{54} - 14 q^{57} - 4 q^{58} - 12 q^{59} + 2 q^{61} + 28 q^{62} - q^{63} - 16 q^{64} + 2 q^{66} - 7 q^{67} - 12 q^{68} + 8 q^{69} + 16 q^{71} + 5 q^{73} + 14 q^{74} - 5 q^{75} + 28 q^{76} + 4 q^{77} - 20 q^{78} + 11 q^{79} - q^{81} + 8 q^{82} - 8 q^{83} + 2 q^{84} - 18 q^{86} - 2 q^{87} - 6 q^{89} - 25 q^{91} - 16 q^{92} - 7 q^{93} + 12 q^{94} + 8 q^{96} + 4 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 2.00000 0.816497
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 1.00000 + 1.73205i 0.288675 + 0.500000i
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 1.00000 + 5.19615i 0.267261 + 1.38873i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) 1.00000 1.73205i 0.235702 0.408248i
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) 2.00000 1.73205i 0.436436 0.377964i
\(22\) 2.00000 0.426401
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) −5.00000 8.66025i −0.980581 1.69842i
\(27\) −1.00000 −0.192450
\(28\) −4.00000 + 3.46410i −0.755929 + 0.654654i
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 3.50000 6.06218i 0.628619 1.08880i −0.359211 0.933257i \(-0.616954\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) −4.00000 + 6.92820i −0.707107 + 1.22474i
\(33\) −0.500000 0.866025i −0.0870388 0.150756i
\(34\) −12.0000 −2.05798
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i \(-0.971514\pi\)
0.420602 0.907245i \(-0.361819\pi\)
\(38\) 7.00000 12.1244i 1.13555 1.96683i
\(39\) −2.50000 + 4.33013i −0.400320 + 0.693375i
\(40\) 0 0
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) 5.00000 + 1.73205i 0.771517 + 0.267261i
\(43\) −9.00000 −1.37249 −0.686244 0.727372i \(-0.740742\pi\)
−0.686244 + 0.727372i \(0.740742\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 0 0
\(46\) −4.00000 + 6.92820i −0.589768 + 1.02151i
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 4.00000 0.577350
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 10.0000 1.41421
\(51\) 3.00000 + 5.19615i 0.420084 + 0.727607i
\(52\) 5.00000 8.66025i 0.693375 1.20096i
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) −1.00000 1.73205i −0.136083 0.235702i
\(55\) 0 0
\(56\) 0 0
\(57\) −7.00000 −0.927173
\(58\) −2.00000 3.46410i −0.262613 0.454859i
\(59\) −6.00000 + 10.3923i −0.781133 + 1.35296i 0.150148 + 0.988663i \(0.452025\pi\)
−0.931282 + 0.364299i \(0.881308\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 14.0000 1.77800
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 1.00000 1.73205i 0.123091 0.213201i
\(67\) −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) −6.00000 10.3923i −0.727607 1.26025i
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 2.50000 4.33013i 0.292603 0.506803i −0.681822 0.731519i \(-0.738812\pi\)
0.974424 + 0.224716i \(0.0721453\pi\)
\(74\) 7.00000 12.1244i 0.813733 1.40943i
\(75\) −2.50000 4.33013i −0.288675 0.500000i
\(76\) 14.0000 1.60591
\(77\) 2.00000 1.73205i 0.227921 0.197386i
\(78\) −10.0000 −1.13228
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.00000 + 6.92820i 0.441726 + 0.765092i
\(83\) −4.00000 −0.439057 −0.219529 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 1.00000 + 5.19615i 0.109109 + 0.566947i
\(85\) 0 0
\(86\) −9.00000 15.5885i −0.970495 1.68095i
\(87\) −1.00000 + 1.73205i −0.107211 + 0.185695i
\(88\) 0 0
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 0 0
\(91\) −12.5000 4.33013i −1.31036 0.453921i
\(92\) −8.00000 −0.834058
\(93\) −3.50000 6.06218i −0.362933 0.628619i
\(94\) 6.00000 10.3923i 0.618853 1.07188i
\(95\) 0 0
\(96\) 4.00000 + 6.92820i 0.408248 + 0.707107i
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −2.00000 + 13.8564i −0.202031 + 1.39971i
\(99\) −1.00000 −0.100504
\(100\) 5.00000 + 8.66025i 0.500000 + 0.866025i
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) −6.00000 + 10.3923i −0.594089 + 1.02899i
\(103\) 9.50000 + 16.4545i 0.936063 + 1.62131i 0.772728 + 0.634738i \(0.218892\pi\)
0.163335 + 0.986571i \(0.447775\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 4.00000 0.388514
\(107\) 10.0000 + 17.3205i 0.966736 + 1.67444i 0.704875 + 0.709331i \(0.251003\pi\)
0.261861 + 0.965106i \(0.415664\pi\)
\(108\) 1.00000 1.73205i 0.0962250 0.166667i
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 2.00000 + 10.3923i 0.188982 + 0.981981i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −7.00000 12.1244i −0.655610 1.13555i
\(115\) 0 0
\(116\) 2.00000 3.46410i 0.185695 0.321634i
\(117\) 2.50000 + 4.33013i 0.231125 + 0.400320i
\(118\) −24.0000 −2.20938
\(119\) −12.0000 + 10.3923i −1.10004 + 0.952661i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −2.00000 + 3.46410i −0.181071 + 0.313625i
\(123\) 2.00000 3.46410i 0.180334 0.312348i
\(124\) 7.00000 + 12.1244i 0.628619 + 1.08880i
\(125\) 0 0
\(126\) 4.00000 3.46410i 0.356348 0.308607i
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) 0 0
\(129\) −4.50000 + 7.79423i −0.396203 + 0.686244i
\(130\) 0 0
\(131\) 2.00000 + 3.46410i 0.174741 + 0.302660i 0.940072 0.340977i \(-0.110758\pi\)
−0.765331 + 0.643637i \(0.777425\pi\)
\(132\) 2.00000 0.174078
\(133\) −3.50000 18.1865i −0.303488 1.57697i
\(134\) −14.0000 −1.20942
\(135\) 0 0
\(136\) 0 0
\(137\) 5.00000 8.66025i 0.427179 0.739895i −0.569442 0.822031i \(-0.692841\pi\)
0.996621 + 0.0821359i \(0.0261741\pi\)
\(138\) 4.00000 + 6.92820i 0.340503 + 0.589768i
\(139\) 11.0000 0.933008 0.466504 0.884519i \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 8.00000 + 13.8564i 0.671345 + 1.16280i
\(143\) −2.50000 + 4.33013i −0.209061 + 0.362103i
\(144\) 2.00000 3.46410i 0.166667 0.288675i
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 6.50000 2.59808i 0.536111 0.214286i
\(148\) 14.0000 1.15079
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 5.00000 8.66025i 0.408248 0.707107i
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 5.00000 + 1.73205i 0.402911 + 0.139573i
\(155\) 0 0
\(156\) −5.00000 8.66025i −0.400320 0.693375i
\(157\) 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) −11.0000 + 19.0526i −0.875113 + 1.51574i
\(159\) −1.00000 1.73205i −0.0793052 0.137361i
\(160\) 0 0
\(161\) 2.00000 + 10.3923i 0.157622 + 0.819028i
\(162\) −2.00000 −0.157135
\(163\) 4.00000 + 6.92820i 0.313304 + 0.542659i 0.979076 0.203497i \(-0.0652307\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) −4.00000 + 6.92820i −0.312348 + 0.541002i
\(165\) 0 0
\(166\) −4.00000 6.92820i −0.310460 0.537733i
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) −3.50000 + 6.06218i −0.267652 + 0.463586i
\(172\) 9.00000 15.5885i 0.686244 1.18861i
\(173\) 5.00000 + 8.66025i 0.380143 + 0.658427i 0.991082 0.133250i \(-0.0425415\pi\)
−0.610939 + 0.791677i \(0.709208\pi\)
\(174\) −4.00000 −0.303239
\(175\) 10.0000 8.66025i 0.755929 0.654654i
\(176\) 4.00000 0.301511
\(177\) 6.00000 + 10.3923i 0.450988 + 0.781133i
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) 8.00000 13.8564i 0.597948 1.03568i −0.395175 0.918606i \(-0.629316\pi\)
0.993124 0.117071i \(-0.0373504\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) −5.00000 25.9808i −0.370625 1.92582i
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 0 0
\(186\) 7.00000 12.1244i 0.513265 0.889001i
\(187\) 3.00000 + 5.19615i 0.219382 + 0.379980i
\(188\) 12.0000 0.875190
\(189\) −2.50000 0.866025i −0.181848 0.0629941i
\(190\) 0 0
\(191\) −11.0000 19.0526i −0.795932 1.37859i −0.922246 0.386604i \(-0.873648\pi\)
0.126314 0.991990i \(-0.459685\pi\)
\(192\) −4.00000 + 6.92820i −0.288675 + 0.500000i
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) 2.00000 + 3.46410i 0.143592 + 0.248708i
\(195\) 0 0
\(196\) −13.0000 + 5.19615i −0.928571 + 0.371154i
\(197\) −4.00000 −0.284988 −0.142494 0.989796i \(-0.545512\pi\)
−0.142494 + 0.989796i \(0.545512\pi\)
\(198\) −1.00000 1.73205i −0.0710669 0.123091i
\(199\) −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 0 0
\(201\) 3.50000 + 6.06218i 0.246871 + 0.427593i
\(202\) 4.00000 0.281439
\(203\) −5.00000 1.73205i −0.350931 0.121566i
\(204\) −12.0000 −0.840168
\(205\) 0 0
\(206\) −19.0000 + 32.9090i −1.32379 + 2.29288i
\(207\) 2.00000 3.46410i 0.139010 0.240772i
\(208\) −10.0000 17.3205i −0.693375 1.20096i
\(209\) −7.00000 −0.484200
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 2.00000 + 3.46410i 0.137361 + 0.237915i
\(213\) 4.00000 6.92820i 0.274075 0.474713i
\(214\) −20.0000 + 34.6410i −1.36717 + 2.36801i
\(215\) 0 0
\(216\) 0 0
\(217\) 14.0000 12.1244i 0.950382 0.823055i
\(218\) 2.00000 0.135457
\(219\) −2.50000 4.33013i −0.168934 0.292603i
\(220\) 0 0
\(221\) 15.0000 25.9808i 1.00901 1.74766i
\(222\) −7.00000 12.1244i −0.469809 0.813733i
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) −16.0000 + 13.8564i −1.06904 + 0.925820i
\(225\) −5.00000 −0.333333
\(226\) −6.00000 10.3923i −0.399114 0.691286i
\(227\) −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) 7.00000 12.1244i 0.463586 0.802955i
\(229\) −2.50000 4.33013i −0.165205 0.286143i 0.771523 0.636201i \(-0.219495\pi\)
−0.936728 + 0.350058i \(0.886162\pi\)
\(230\) 0 0
\(231\) −0.500000 2.59808i −0.0328976 0.170941i
\(232\) 0 0
\(233\) 10.0000 + 17.3205i 0.655122 + 1.13470i 0.981863 + 0.189590i \(0.0607160\pi\)
−0.326741 + 0.945114i \(0.605951\pi\)
\(234\) −5.00000 + 8.66025i −0.326860 + 0.566139i
\(235\) 0 0
\(236\) −12.0000 20.7846i −0.781133 1.35296i
\(237\) 11.0000 0.714527
\(238\) −30.0000 10.3923i −1.94461 0.673633i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −4.00000 −0.256074
\(245\) 0 0
\(246\) 8.00000 0.510061
\(247\) 17.5000 + 30.3109i 1.11350 + 1.92864i
\(248\) 0 0
\(249\) −2.00000 + 3.46410i −0.126745 + 0.219529i
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 5.00000 + 1.73205i 0.314970 + 0.109109i
\(253\) 4.00000 0.251478
\(254\) −13.0000 22.5167i −0.815693 1.41282i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 4.00000 + 6.92820i 0.249513 + 0.432169i 0.963391 0.268101i \(-0.0863961\pi\)
−0.713878 + 0.700270i \(0.753063\pi\)
\(258\) −18.0000 −1.12063
\(259\) −3.50000 18.1865i −0.217479 1.13006i
\(260\) 0 0
\(261\) 1.00000 + 1.73205i 0.0618984 + 0.107211i
\(262\) −4.00000 + 6.92820i −0.247121 + 0.428026i
\(263\) 9.00000 15.5885i 0.554964 0.961225i −0.442943 0.896550i \(-0.646065\pi\)
0.997906 0.0646755i \(-0.0206012\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 28.0000 24.2487i 1.71679 1.48678i
\(267\) −6.00000 −0.367194
\(268\) −7.00000 12.1244i −0.427593 0.740613i
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) 0 0
\(271\) 10.0000 + 17.3205i 0.607457 + 1.05215i 0.991658 + 0.128897i \(0.0411435\pi\)
−0.384201 + 0.923249i \(0.625523\pi\)
\(272\) −24.0000 −1.45521
\(273\) −10.0000 + 8.66025i −0.605228 + 0.524142i
\(274\) 20.0000 1.20824
\(275\) −2.50000 4.33013i −0.150756 0.261116i
\(276\) −4.00000 + 6.92820i −0.240772 + 0.417029i
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) 11.0000 + 19.0526i 0.659736 + 1.14270i
\(279\) −7.00000 −0.419079
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) −6.00000 10.3923i −0.357295 0.618853i
\(283\) −11.5000 + 19.9186i −0.683604 + 1.18404i 0.290269 + 0.956945i \(0.406255\pi\)
−0.973873 + 0.227092i \(0.927078\pi\)
\(284\) −8.00000 + 13.8564i −0.474713 + 0.822226i
\(285\) 0 0
\(286\) −10.0000 −0.591312
\(287\) 10.0000 + 3.46410i 0.590281 + 0.204479i
\(288\) 8.00000 0.471405
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 11.0000 + 8.66025i 0.641533 + 0.505076i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.500000 + 0.866025i −0.0290129 + 0.0502519i
\(298\) −6.00000 + 10.3923i −0.347571 + 0.602010i
\(299\) −10.0000 17.3205i −0.578315 1.00167i
\(300\) 10.0000 0.577350
\(301\) −22.5000 7.79423i −1.29688 0.449252i
\(302\) 32.0000 1.84139
\(303\) −1.00000 1.73205i −0.0574485 0.0995037i
\(304\) 14.0000 24.2487i 0.802955 1.39076i
\(305\) 0 0
\(306\) 6.00000 + 10.3923i 0.342997 + 0.594089i
\(307\) −3.00000 −0.171219 −0.0856095 0.996329i \(-0.527284\pi\)
−0.0856095 + 0.996329i \(0.527284\pi\)
\(308\) 1.00000 + 5.19615i 0.0569803 + 0.296078i
\(309\) 19.0000 1.08087
\(310\) 0 0
\(311\) 8.00000 13.8564i 0.453638 0.785725i −0.544970 0.838455i \(-0.683459\pi\)
0.998609 + 0.0527306i \(0.0167924\pi\)
\(312\) 0 0
\(313\) −1.50000 2.59808i −0.0847850 0.146852i 0.820515 0.571626i \(-0.193687\pi\)
−0.905300 + 0.424774i \(0.860354\pi\)
\(314\) 28.0000 1.58013
\(315\) 0 0
\(316\) −22.0000 −1.23760
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 2.00000 3.46410i 0.112154 0.194257i
\(319\) −1.00000 + 1.73205i −0.0559893 + 0.0969762i
\(320\) 0 0
\(321\) 20.0000 1.11629
\(322\) −16.0000 + 13.8564i −0.891645 + 0.772187i
\(323\) 42.0000 2.33694
\(324\) −1.00000 1.73205i −0.0555556 0.0962250i
\(325\) −12.5000 + 21.6506i −0.693375 + 1.20096i
\(326\) −8.00000 + 13.8564i −0.443079 + 0.767435i
\(327\) −0.500000 0.866025i −0.0276501 0.0478913i
\(328\) 0 0
\(329\) −3.00000 15.5885i −0.165395 0.859419i
\(330\) 0 0
\(331\) 16.5000 + 28.5788i 0.906922 + 1.57084i 0.818316 + 0.574768i \(0.194908\pi\)
0.0886058 + 0.996067i \(0.471759\pi\)
\(332\) 4.00000 6.92820i 0.219529 0.380235i
\(333\) −3.50000 + 6.06218i −0.191799 + 0.332205i
\(334\) −6.00000 10.3923i −0.328305 0.568642i
\(335\) 0 0
\(336\) 10.0000 + 3.46410i 0.545545 + 0.188982i
\(337\) −17.0000 −0.926049 −0.463025 0.886345i \(-0.653236\pi\)
−0.463025 + 0.886345i \(0.653236\pi\)
\(338\) 12.0000 + 20.7846i 0.652714 + 1.13053i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) −3.50000 6.06218i −0.189536 0.328285i
\(342\) −14.0000 −0.757033
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) −10.0000 + 17.3205i −0.537603 + 0.931156i
\(347\) −1.00000 + 1.73205i −0.0536828 + 0.0929814i −0.891618 0.452788i \(-0.850429\pi\)
0.837935 + 0.545770i \(0.183763\pi\)
\(348\) −2.00000 3.46410i −0.107211 0.185695i
\(349\) 6.00000 0.321173 0.160586 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 25.0000 + 8.66025i 1.33631 + 0.462910i
\(351\) 5.00000 0.266880
\(352\) 4.00000 + 6.92820i 0.213201 + 0.369274i
\(353\) −15.0000 + 25.9808i −0.798369 + 1.38282i 0.122308 + 0.992492i \(0.460970\pi\)
−0.920677 + 0.390324i \(0.872363\pi\)
\(354\) −12.0000 + 20.7846i −0.637793 + 1.10469i
\(355\) 0 0
\(356\) 12.0000 0.635999
\(357\) 3.00000 + 15.5885i 0.158777 + 0.825029i
\(358\) 32.0000 1.69125
\(359\) −18.0000 31.1769i −0.950004 1.64545i −0.745409 0.666608i \(-0.767746\pi\)
−0.204595 0.978847i \(-0.565588\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) −1.00000 −0.0524864
\(364\) 20.0000 17.3205i 1.04828 0.907841i
\(365\) 0 0
\(366\) 2.00000 + 3.46410i 0.104542 + 0.181071i
\(367\) 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i \(-0.687000\pi\)
0.997960 + 0.0638362i \(0.0203335\pi\)
\(368\) −8.00000 + 13.8564i −0.417029 + 0.722315i
\(369\) −2.00000 3.46410i −0.104116 0.180334i
\(370\) 0 0
\(371\) 4.00000 3.46410i 0.207670 0.179847i
\(372\) 14.0000 0.725866
\(373\) −10.5000 18.1865i −0.543669 0.941663i −0.998689 0.0511818i \(-0.983701\pi\)
0.455020 0.890481i \(-0.349632\pi\)
\(374\) −6.00000 + 10.3923i −0.310253 + 0.537373i
\(375\) 0 0
\(376\) 0 0
\(377\) 10.0000 0.515026
\(378\) −1.00000 5.19615i −0.0514344 0.267261i
\(379\) −5.00000 −0.256833 −0.128416 0.991720i \(-0.540989\pi\)
−0.128416 + 0.991720i \(0.540989\pi\)
\(380\) 0 0
\(381\) −6.50000 + 11.2583i −0.333005 + 0.576782i
\(382\) 22.0000 38.1051i 1.12562 1.94963i
\(383\) 19.0000 + 32.9090i 0.970855 + 1.68157i 0.692987 + 0.720950i \(0.256294\pi\)
0.277868 + 0.960619i \(0.410372\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 4.50000 + 7.79423i 0.228748 + 0.396203i
\(388\) −2.00000 + 3.46410i −0.101535 + 0.175863i
\(389\) −11.0000 + 19.0526i −0.557722 + 0.966003i 0.439964 + 0.898015i \(0.354991\pi\)
−0.997686 + 0.0679877i \(0.978342\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 0 0
\(393\) 4.00000 0.201773
\(394\) −4.00000 6.92820i −0.201517 0.349038i
\(395\) 0 0
\(396\) 1.00000 1.73205i 0.0502519 0.0870388i
\(397\) −13.5000 23.3827i −0.677546 1.17354i −0.975718 0.219031i \(-0.929710\pi\)
0.298172 0.954512i \(-0.403623\pi\)
\(398\) −8.00000 −0.401004
\(399\) −17.5000 6.06218i −0.876096 0.303488i
\(400\) 20.0000 1.00000
\(401\) −18.0000 31.1769i −0.898877 1.55690i −0.828932 0.559350i \(-0.811051\pi\)
−0.0699455 0.997551i \(-0.522283\pi\)
\(402\) −7.00000 + 12.1244i −0.349128 + 0.604708i
\(403\) −17.5000 + 30.3109i −0.871737 + 1.50989i
\(404\) 2.00000 + 3.46410i 0.0995037 + 0.172345i
\(405\) 0 0
\(406\) −2.00000 10.3923i −0.0992583 0.515761i
\(407\) −7.00000 −0.346977
\(408\) 0 0
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) 0 0
\(411\) −5.00000 8.66025i −0.246632 0.427179i
\(412\) −38.0000 −1.87213
\(413\) −24.0000 + 20.7846i −1.18096 + 1.02274i
\(414\) 8.00000 0.393179
\(415\) 0 0
\(416\) 20.0000 34.6410i 0.980581 1.69842i
\(417\) 5.50000 9.52628i 0.269336 0.466504i
\(418\) −7.00000 12.1244i −0.342381 0.593022i
\(419\) −8.00000 −0.390826 −0.195413 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) 0 0
\(421\) 9.00000 0.438633 0.219317 0.975654i \(-0.429617\pi\)
0.219317 + 0.975654i \(0.429617\pi\)
\(422\) −4.00000 6.92820i −0.194717 0.337260i
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 15.0000 + 25.9808i 0.727607 + 1.26025i
\(426\) 16.0000 0.775203
\(427\) 1.00000 + 5.19615i 0.0483934 + 0.251459i
\(428\) −40.0000 −1.93347
\(429\) 2.50000 + 4.33013i 0.120701 + 0.209061i
\(430\) 0 0
\(431\) −5.00000 + 8.66025i −0.240842 + 0.417150i −0.960954 0.276707i \(-0.910757\pi\)
0.720113 + 0.693857i \(0.244090\pi\)
\(432\) −2.00000 3.46410i −0.0962250 0.166667i
\(433\) 19.0000 0.913082 0.456541 0.889702i \(-0.349088\pi\)
0.456541 + 0.889702i \(0.349088\pi\)
\(434\) 35.0000 + 12.1244i 1.68005 + 0.581988i
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) 14.0000 24.2487i 0.669711 1.15997i
\(438\) 5.00000 8.66025i 0.238909 0.413803i
\(439\) −8.00000 13.8564i −0.381819 0.661330i 0.609503 0.792784i \(-0.291369\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 60.0000 2.85391
\(443\) −11.0000 19.0526i −0.522626 0.905214i −0.999653 0.0263261i \(-0.991619\pi\)
0.477028 0.878888i \(-0.341714\pi\)
\(444\) 7.00000 12.1244i 0.332205 0.575396i
\(445\) 0 0
\(446\) 0 0
\(447\) 6.00000 0.283790
\(448\) −20.0000 6.92820i −0.944911 0.327327i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) −5.00000 8.66025i −0.235702 0.408248i
\(451\) 2.00000 3.46410i 0.0941763 0.163118i
\(452\) 6.00000 10.3923i 0.282216 0.488813i
\(453\) −8.00000 13.8564i −0.375873 0.651031i
\(454\) −28.0000 −1.31411
\(455\) 0 0
\(456\) 0 0
\(457\) −1.50000 2.59808i −0.0701670 0.121533i 0.828807 0.559534i \(-0.189020\pi\)
−0.898974 + 0.438001i \(0.855687\pi\)
\(458\) 5.00000 8.66025i 0.233635 0.404667i
\(459\) 3.00000 5.19615i 0.140028 0.242536i
\(460\) 0 0
\(461\) −36.0000 −1.67669 −0.838344 0.545142i \(-0.816476\pi\)
−0.838344 + 0.545142i \(0.816476\pi\)
\(462\) 4.00000 3.46410i 0.186097 0.161165i
\(463\) −29.0000 −1.34774 −0.673872 0.738848i \(-0.735370\pi\)
−0.673872 + 0.738848i \(0.735370\pi\)
\(464\) −4.00000 6.92820i −0.185695 0.321634i
\(465\) 0 0
\(466\) −20.0000 + 34.6410i −0.926482 + 1.60471i
\(467\) −4.00000 6.92820i −0.185098 0.320599i 0.758512 0.651660i \(-0.225927\pi\)
−0.943610 + 0.331061i \(0.892594\pi\)
\(468\) −10.0000 −0.462250
\(469\) −14.0000 + 12.1244i −0.646460 + 0.559851i
\(470\) 0 0
\(471\) −7.00000 12.1244i −0.322543 0.558661i
\(472\) 0 0
\(473\) −4.50000 + 7.79423i −0.206910 + 0.358379i
\(474\) 11.0000 + 19.0526i 0.505247 + 0.875113i
\(475\) −35.0000 −1.60591
\(476\) −6.00000 31.1769i −0.275010 1.42899i
\(477\) −2.00000 −0.0915737
\(478\) −24.0000 41.5692i −1.09773 1.90133i
\(479\) 19.0000 32.9090i 0.868132 1.50365i 0.00422900 0.999991i \(-0.498654\pi\)
0.863903 0.503658i \(-0.168013\pi\)
\(480\) 0 0
\(481\) 17.5000 + 30.3109i 0.797931 + 1.38206i
\(482\) 20.0000 0.910975
\(483\) 10.0000 + 3.46410i 0.455016 + 0.157622i
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) −1.00000 + 1.73205i −0.0453609 + 0.0785674i
\(487\) 14.5000 25.1147i 0.657058 1.13806i −0.324316 0.945949i \(-0.605134\pi\)
0.981374 0.192109i \(-0.0615326\pi\)
\(488\) 0 0
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) −30.0000 −1.35388 −0.676941 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 4.00000 + 6.92820i 0.180334 + 0.312348i
\(493\) 6.00000 10.3923i 0.270226 0.468046i
\(494\) −35.0000 + 60.6218i −1.57472 + 2.72750i
\(495\) 0 0
\(496\) 28.0000 1.25724
\(497\) 20.0000 + 6.92820i 0.897123 + 0.310772i
\(498\) −8.00000 −0.358489
\(499\) −6.50000 11.2583i −0.290980 0.503992i 0.683062 0.730361i \(-0.260648\pi\)
−0.974042 + 0.226369i \(0.927315\pi\)
\(500\) 0 0
\(501\) −3.00000 + 5.19615i −0.134030 + 0.232147i
\(502\) −18.0000 31.1769i −0.803379 1.39149i
\(503\) −44.0000 −1.96186 −0.980932 0.194354i \(-0.937739\pi\)
−0.980932 + 0.194354i \(0.937739\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 4.00000 + 6.92820i 0.177822 + 0.307996i
\(507\) 6.00000 10.3923i 0.266469 0.461538i
\(508\) 13.0000 22.5167i 0.576782 0.999015i
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) 0 0
\(511\) 10.0000 8.66025i 0.442374 0.383107i
\(512\) −32.0000 −1.41421
\(513\) 3.50000 + 6.06218i 0.154529 + 0.267652i
\(514\) −8.00000 + 13.8564i −0.352865 + 0.611180i
\(515\) 0 0
\(516\) −9.00000 15.5885i −0.396203 0.686244i
\(517\) −6.00000 −0.263880
\(518\) 28.0000 24.2487i 1.23025 1.06543i
\(519\) 10.0000 0.438951
\(520\) 0 0
\(521\) −11.0000 + 19.0526i −0.481919 + 0.834708i −0.999785 0.0207541i \(-0.993393\pi\)
0.517866 + 0.855462i \(0.326727\pi\)
\(522\) −2.00000 + 3.46410i −0.0875376 + 0.151620i
\(523\) 15.5000 + 26.8468i 0.677768 + 1.17393i 0.975652 + 0.219326i \(0.0703858\pi\)
−0.297884 + 0.954602i \(0.596281\pi\)
\(524\) −8.00000 −0.349482
\(525\) −2.50000 12.9904i −0.109109 0.566947i
\(526\) 36.0000 1.56967
\(527\) 21.0000 + 36.3731i 0.914774 + 1.58444i
\(528\) 2.00000 3.46410i 0.0870388 0.150756i
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 35.0000 + 12.1244i 1.51744 + 0.525657i
\(533\) −20.0000 −0.866296
\(534\) −6.00000 10.3923i −0.259645 0.449719i
\(535\) 0 0
\(536\) 0 0
\(537\) −8.00000 13.8564i −0.345225 0.597948i
\(538\) 28.0000 1.20717
\(539\) 6.50000 2.59808i 0.279975 0.111907i
\(540\) 0 0
\(541\) −7.50000 12.9904i −0.322450 0.558500i 0.658543 0.752543i \(-0.271173\pi\)
−0.980993 + 0.194043i \(0.937840\pi\)
\(542\) −20.0000 + 34.6410i −0.859074 + 1.48796i
\(543\) 2.50000 4.33013i 0.107285 0.185824i
\(544\) −24.0000 41.5692i −1.02899 1.78227i
\(545\) 0 0
\(546\) −25.0000 8.66025i −1.06990 0.370625i
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 10.0000 + 17.3205i 0.427179 + 0.739895i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 5.00000 8.66025i 0.213201 0.369274i
\(551\) 7.00000 + 12.1244i 0.298210 + 0.516515i
\(552\) 0 0
\(553\) 5.50000 + 28.5788i 0.233884 + 1.21530i
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) −11.0000 + 19.0526i −0.466504 + 0.808008i
\(557\) 18.0000 31.1769i 0.762684 1.32101i −0.178778 0.983890i \(-0.557214\pi\)
0.941462 0.337119i \(-0.109452\pi\)
\(558\) −7.00000 12.1244i −0.296334 0.513265i
\(559\) 45.0000 1.90330
\(560\) 0 0
\(561\) 6.00000 0.253320
\(562\) 24.0000 + 41.5692i 1.01238 + 1.75349i
\(563\) −9.00000 + 15.5885i −0.379305 + 0.656975i −0.990961 0.134148i \(-0.957170\pi\)
0.611656 + 0.791123i \(0.290503\pi\)
\(564\) 6.00000 10.3923i 0.252646 0.437595i
\(565\) 0 0
\(566\) −46.0000 −1.93352
\(567\) −2.00000 + 1.73205i −0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) −5.00000 8.66025i −0.209611 0.363057i 0.741981 0.670421i \(-0.233886\pi\)
−0.951592 + 0.307364i \(0.900553\pi\)
\(570\) 0 0
\(571\) −17.5000 + 30.3109i −0.732352 + 1.26847i 0.223523 + 0.974699i \(0.428244\pi\)
−0.955875 + 0.293773i \(0.905089\pi\)
\(572\) −5.00000 8.66025i −0.209061 0.362103i
\(573\) −22.0000 −0.919063
\(574\) 4.00000 + 20.7846i 0.166957 + 0.867533i
\(575\) 20.0000 0.834058
\(576\) 4.00000 + 6.92820i 0.166667 + 0.288675i
\(577\) 8.50000 14.7224i 0.353860 0.612903i −0.633062 0.774101i \(-0.718202\pi\)
0.986922 + 0.161198i \(0.0515357\pi\)
\(578\) 19.0000 32.9090i 0.790296 1.36883i
\(579\) −3.50000 6.06218i −0.145455 0.251936i
\(580\) 0 0
\(581\) −10.0000 3.46410i −0.414870 0.143715i
\(582\) 4.00000 0.165805
\(583\) −1.00000 1.73205i −0.0414158 0.0717342i
\(584\) 0 0
\(585\) 0 0
\(586\) 12.0000 + 20.7846i 0.495715 + 0.858604i
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) −2.00000 + 13.8564i −0.0824786 + 0.571429i
\(589\) −49.0000 −2.01901
\(590\) 0 0
\(591\) −2.00000 + 3.46410i −0.0822690 + 0.142494i
\(592\) 14.0000 24.2487i 0.575396 0.996616i
\(593\) 13.0000 + 22.5167i 0.533846 + 0.924648i 0.999218 + 0.0395334i \(0.0125871\pi\)
−0.465372 + 0.885115i \(0.654080\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) −12.0000 −0.491539
\(597\) 2.00000 + 3.46410i 0.0818546 + 0.141776i
\(598\) 20.0000 34.6410i 0.817861 1.41658i
\(599\) −5.00000 + 8.66025i −0.204294 + 0.353848i −0.949908 0.312531i \(-0.898823\pi\)
0.745613 + 0.666379i \(0.232157\pi\)
\(600\) 0 0
\(601\) −15.0000 −0.611863 −0.305931 0.952054i \(-0.598968\pi\)
−0.305931 + 0.952054i \(0.598968\pi\)
\(602\) −9.00000 46.7654i −0.366813 1.90601i
\(603\) 7.00000 0.285062
\(604\) 16.0000 + 27.7128i 0.651031 + 1.12762i
\(605\) 0 0
\(606\) 2.00000 3.46410i 0.0812444 0.140720i
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 56.0000 2.27110
\(609\) −4.00000 + 3.46410i −0.162088 + 0.140372i
\(610\) 0 0
\(611\) 15.0000 + 25.9808i 0.606835 + 1.05107i
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) 17.0000 29.4449i 0.686624 1.18927i −0.286300 0.958140i \(-0.592425\pi\)
0.972924 0.231127i \(-0.0742412\pi\)
\(614\) −3.00000 5.19615i −0.121070 0.209700i
\(615\) 0 0
\(616\) 0 0
\(617\) −24.0000 −0.966204 −0.483102 0.875564i \(-0.660490\pi\)
−0.483102 + 0.875564i \(0.660490\pi\)
\(618\) 19.0000 + 32.9090i 0.764292 + 1.32379i
\(619\) 10.5000 18.1865i 0.422031 0.730978i −0.574107 0.818780i \(-0.694651\pi\)
0.996138 + 0.0878015i \(0.0279841\pi\)
\(620\) 0 0
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) 32.0000 1.28308
\(623\) −3.00000 15.5885i −0.120192 0.624538i
\(624\) −20.0000 −0.800641
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 3.00000 5.19615i 0.119904 0.207680i
\(627\) −3.50000 + 6.06218i −0.139777 + 0.242100i
\(628\) 14.0000 + 24.2487i 0.558661 + 0.967629i
\(629\) 42.0000 1.67465
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −2.00000 + 3.46410i −0.0794929 + 0.137686i
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) 0 0
\(636\) 4.00000 0.158610
\(637\) −27.5000 21.6506i −1.08959 0.857829i
\(638\) −4.00000 −0.158362
\(639\) −4.00000 6.92820i −0.158238 0.274075i
\(640\) 0 0
\(641\) −12.0000 + 20.7846i −0.473972 + 0.820943i −0.999556 0.0297987i \(-0.990513\pi\)
0.525584 + 0.850741i \(0.323847\pi\)
\(642\) 20.0000 + 34.6410i 0.789337 + 1.36717i
\(643\) 21.0000 0.828159 0.414080 0.910241i \(-0.364104\pi\)
0.414080 + 0.910241i \(0.364104\pi\)
\(644\) −20.0000 6.92820i −0.788110 0.273009i
\(645\) 0 0
\(646\) 42.0000 + 72.7461i 1.65247 + 2.86216i
\(647\) −3.00000 + 5.19615i −0.117942 + 0.204282i −0.918952 0.394369i \(-0.870963\pi\)
0.801010 + 0.598651i \(0.204296\pi\)
\(648\) 0 0
\(649\) 6.00000 + 10.3923i 0.235521 + 0.407934i
\(650\) −50.0000 −1.96116
\(651\) −3.50000 18.1865i −0.137176 0.712786i
\(652\) −16.0000 −0.626608
\(653\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) 0 0
\(656\) 8.00000 + 13.8564i 0.312348 + 0.541002i
\(657\) −5.00000 −0.195069
\(658\) 24.0000 20.7846i 0.935617 0.810268i
\(659\) 18.0000 0.701180 0.350590 0.936529i \(-0.385981\pi\)
0.350590 + 0.936529i \(0.385981\pi\)
\(660\) 0 0
\(661\) −5.50000 + 9.52628i −0.213925 + 0.370529i −0.952940 0.303160i \(-0.901958\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) −33.0000 + 57.1577i −1.28258 + 2.22150i
\(663\) −15.0000 25.9808i −0.582552 1.00901i
\(664\) 0 0
\(665\) 0 0
\(666\) −14.0000 −0.542489
\(667\) −4.00000 6.92820i −0.154881 0.268261i
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 0 0
\(670\) 0 0
\(671\) 2.00000 0.0772091
\(672\) 4.00000 + 20.7846i 0.154303 + 0.801784i
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) −17.0000 29.4449i −0.654816 1.13417i
\(675\) −2.50000 + 4.33013i −0.0962250 + 0.166667i
\(676\) −12.0000 + 20.7846i −0.461538 + 0.799408i
\(677\) −6.00000 10.3923i −0.230599 0.399409i 0.727386 0.686229i \(-0.240735\pi\)
−0.957984 + 0.286820i \(0.907402\pi\)
\(678\) −12.0000 −0.460857
\(679\) 5.00000 + 1.73205i 0.191882 + 0.0664700i
\(680\) 0 0
\(681\) 7.00000 + 12.1244i 0.268241 + 0.464606i
\(682\) 7.00000 12.1244i 0.268044 0.464266i
\(683\) 20.0000 34.6410i 0.765279 1.32550i −0.174820 0.984600i \(-0.555934\pi\)
0.940099 0.340901i \(-0.110732\pi\)
\(684\) −7.00000 12.1244i −0.267652 0.463586i
\(685\) 0 0
\(686\) −17.0000 + 32.9090i −0.649063 + 1.25647i
\(687\) −5.00000 −0.190762
\(688\) −18.0000 31.1769i −0.686244 1.18861i
\(689\) −5.00000 + 8.66025i −0.190485 + 0.329929i
\(690\) 0 0
\(691\) 2.50000 + 4.33013i 0.0951045 + 0.164726i 0.909652 0.415371i \(-0.136348\pi\)
−0.814548 + 0.580097i \(0.803015\pi\)
\(692\) −20.0000 −0.760286
\(693\) −2.50000 0.866025i −0.0949671 0.0328976i
\(694\) −4.00000 −0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) −12.0000 + 20.7846i −0.454532 + 0.787273i
\(698\) 6.00000 + 10.3923i 0.227103 + 0.393355i
\(699\) 20.0000 0.756469
\(700\) 5.00000 + 25.9808i 0.188982 + 0.981981i
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 5.00000 + 8.66025i 0.188713 + 0.326860i
\(703\) −24.5000 + 42.4352i −0.924035 + 1.60048i
\(704\) −4.00000 + 6.92820i −0.150756 + 0.261116i
\(705\) 0 0
\(706\) −60.0000 −2.25813
\(707\) 4.00000 3.46410i 0.150435 0.130281i
\(708\) −24.0000 −0.901975
\(709\) −15.0000 25.9808i −0.563337 0.975728i −0.997202 0.0747503i \(-0.976184\pi\)
0.433865 0.900978i \(-0.357149\pi\)
\(710\) 0 0
\(711\) 5.50000 9.52628i 0.206266 0.357263i
\(712\) 0 0
\(713\) 28.0000 1.04861
\(714\) −24.0000 + 20.7846i −0.898177 + 0.777844i
\(715\) 0 0
\(716\) 16.0000 + 27.7128i 0.597948 + 1.03568i
\(717\) −12.0000 + 20.7846i −0.448148 + 0.776215i
\(718\) 36.0000 62.3538i 1.34351 2.32702i
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) 0 0
\(721\) 9.50000 + 49.3634i 0.353798 + 1.83839i
\(722\) −60.0000 −2.23297
\(723\) −5.00000 8.66025i −0.185952 0.322078i
\(724\) −5.00000 + 8.66025i −0.185824 + 0.321856i
\(725\) −5.00000 + 8.66025i −0.185695 + 0.321634i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −5.00000 −0.185440 −0.0927199 0.995692i \(-0.529556\pi\)
−0.0927199 + 0.995692i \(0.529556\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 27.0000 46.7654i 0.998631 1.72968i
\(732\) −2.00000 + 3.46410i −0.0739221 + 0.128037i
\(733\) 6.50000 + 11.2583i 0.240083 + 0.415836i 0.960738 0.277458i \(-0.0894920\pi\)
−0.720655 + 0.693294i \(0.756159\pi\)
\(734\) 34.0000 1.25496
\(735\) 0 0
\(736\) −32.0000 −1.17954
\(737\) 3.50000 + 6.06218i 0.128924 + 0.223303i
\(738\) 4.00000 6.92820i 0.147242 0.255031i
\(739\) 16.5000 28.5788i 0.606962 1.05129i −0.384776 0.923010i \(-0.625721\pi\)
0.991738 0.128279i \(-0.0409454\pi\)
\(740\) 0 0
\(741\) 35.0000 1.28576
\(742\) 10.0000 + 3.46410i 0.367112 + 0.127171i
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 21.0000 36.3731i 0.768865 1.33171i
\(747\) 2.00000 + 3.46410i 0.0731762 + 0.126745i
\(748\) −12.0000 −0.438763
\(749\) 10.0000 + 51.9615i 0.365392 + 1.89863i
\(750\) 0 0
\(751\) 15.5000 + 26.8468i 0.565603 + 0.979653i 0.996993 + 0.0774878i \(0.0246899\pi\)
−0.431390 + 0.902165i \(0.641977\pi\)
\(752\) 12.0000 20.7846i 0.437595 0.757937i
\(753\) −9.00000 + 15.5885i −0.327978 + 0.568075i
\(754\) 10.0000 + 17.3205i 0.364179 + 0.630776i
\(755\) 0 0
\(756\) 4.00000 3.46410i 0.145479 0.125988i
\(757\) 30.0000 1.09037 0.545184 0.838316i \(-0.316460\pi\)
0.545184 + 0.838316i \(0.316460\pi\)
\(758\) −5.00000 8.66025i −0.181608 0.314555i
\(759\) 2.00000 3.46410i 0.0725954 0.125739i
\(760\) 0 0
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) −26.0000 −0.941881
\(763\) 2.00000 1.73205i 0.0724049 0.0627044i
\(764\) 44.0000 1.59186
\(765\) 0 0
\(766\) −38.0000 + 65.8179i −1.37300 + 2.37810i
\(767\) 30.0000 51.9615i 1.08324 1.87622i
\(768\) 8.00000 + 13.8564i 0.288675 + 0.500000i
\(769\) −3.00000 −0.108183 −0.0540914 0.998536i \(-0.517226\pi\)
−0.0540914 + 0.998536i \(0.517226\pi\)
\(770\) 0 0
\(771\) 8.00000 0.288113
\(772\) 7.00000 + 12.1244i 0.251936 + 0.436365i
\(773\) −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i \(-0.867747\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(774\) −9.00000 + 15.5885i −0.323498 + 0.560316i
\(775\) −17.5000 30.3109i −0.628619 1.08880i
\(776\) 0 0
\(777\) −17.5000 6.06218i −0.627809 0.217479i
\(778\) −44.0000