Properties

Label 114.2.h.a.65.1
Level $114$
Weight $2$
Character 114.65
Analytic conductor $0.910$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 114.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.910294583043\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 114.65
Dual form 114.2.h.a.107.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} -1.73205i q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-3.00000 - 1.73205i) q^{5} -1.73205i q^{6} -2.00000 q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +1.73205i q^{11} +(1.50000 + 0.866025i) q^{12} +(-3.00000 + 1.73205i) q^{13} +(1.00000 - 1.73205i) q^{14} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.00000 - 3.46410i) q^{17} +(1.50000 + 2.59808i) q^{18} +(0.500000 + 4.33013i) q^{19} +3.46410i q^{20} +(3.00000 - 1.73205i) q^{21} +(-1.50000 - 0.866025i) q^{22} +(-1.50000 + 0.866025i) q^{24} +(3.50000 + 6.06218i) q^{25} -3.46410i q^{26} +5.19615i q^{27} +(1.00000 + 1.73205i) q^{28} +(3.00000 + 5.19615i) q^{29} +(-3.00000 + 5.19615i) q^{30} -6.92820i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(6.00000 - 3.46410i) q^{34} +(6.00000 + 3.46410i) q^{35} -3.00000 q^{36} -6.92820i q^{37} +(-4.00000 - 1.73205i) q^{38} +(3.00000 - 5.19615i) q^{39} +(-3.00000 - 1.73205i) q^{40} +(1.50000 - 2.59808i) q^{41} +3.46410i q^{42} +(-4.00000 + 6.92820i) q^{43} +(1.50000 - 0.866025i) q^{44} +(-9.00000 + 5.19615i) q^{45} +(3.00000 - 1.73205i) q^{47} -1.73205i q^{48} -3.00000 q^{49} -7.00000 q^{50} +12.0000 q^{51} +(3.00000 + 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(-4.50000 - 2.59808i) q^{54} +(3.00000 - 5.19615i) q^{55} -2.00000 q^{56} +(-4.50000 - 6.06218i) q^{57} -6.00000 q^{58} +(-1.50000 + 2.59808i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(-5.00000 - 8.66025i) q^{61} +(6.00000 + 3.46410i) q^{62} +(-3.00000 + 5.19615i) q^{63} +1.00000 q^{64} +12.0000 q^{65} +3.00000 q^{66} +(4.50000 - 2.59808i) q^{67} +6.92820i q^{68} +(-6.00000 + 3.46410i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.50000 - 2.59808i) q^{72} +(-2.50000 + 4.33013i) q^{73} +(6.00000 + 3.46410i) q^{74} +(-10.5000 - 6.06218i) q^{75} +(3.50000 - 2.59808i) q^{76} -3.46410i q^{77} +(3.00000 + 5.19615i) q^{78} +(-12.0000 - 6.92820i) q^{79} +(3.00000 - 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.50000 + 2.59808i) q^{82} +5.19615i q^{83} +(-3.00000 - 1.73205i) q^{84} +(12.0000 + 20.7846i) q^{85} +(-4.00000 - 6.92820i) q^{86} +(-9.00000 - 5.19615i) q^{87} +1.73205i q^{88} +(3.00000 + 5.19615i) q^{89} -10.3923i q^{90} +(6.00000 - 3.46410i) q^{91} +(6.00000 + 10.3923i) q^{93} +3.46410i q^{94} +(6.00000 - 13.8564i) q^{95} +(1.50000 + 0.866025i) q^{96} +(7.50000 + 4.33013i) q^{97} +(1.50000 - 2.59808i) q^{98} +(4.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - 3q^{3} - q^{4} - 6q^{5} - 4q^{7} + 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} - 3q^{3} - q^{4} - 6q^{5} - 4q^{7} + 2q^{8} + 3q^{9} + 6q^{10} + 3q^{12} - 6q^{13} + 2q^{14} + 12q^{15} - q^{16} - 12q^{17} + 3q^{18} + q^{19} + 6q^{21} - 3q^{22} - 3q^{24} + 7q^{25} + 2q^{28} + 6q^{29} - 6q^{30} - q^{32} - 3q^{33} + 12q^{34} + 12q^{35} - 6q^{36} - 8q^{38} + 6q^{39} - 6q^{40} + 3q^{41} - 8q^{43} + 3q^{44} - 18q^{45} + 6q^{47} - 6q^{49} - 14q^{50} + 24q^{51} + 6q^{52} - 6q^{53} - 9q^{54} + 6q^{55} - 4q^{56} - 9q^{57} - 12q^{58} - 3q^{59} - 6q^{60} - 10q^{61} + 12q^{62} - 6q^{63} + 2q^{64} + 24q^{65} + 6q^{66} + 9q^{67} - 12q^{70} - 6q^{71} + 3q^{72} - 5q^{73} + 12q^{74} - 21q^{75} + 7q^{76} + 6q^{78} - 24q^{79} + 6q^{80} - 9q^{81} + 3q^{82} - 6q^{84} + 24q^{85} - 8q^{86} - 18q^{87} + 6q^{89} + 12q^{91} + 12q^{93} + 12q^{95} + 3q^{96} + 15q^{97} + 3q^{98} + 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(97\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −3.00000 1.73205i −1.34164 0.774597i −0.354593 0.935021i \(-0.615380\pi\)
−0.987048 + 0.160424i \(0.948714\pi\)
\(6\) 1.73205i 0.707107i
\(7\) −2.00000 −0.755929 −0.377964 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 3.00000 1.73205i 0.948683 0.547723i
\(11\) 1.73205i 0.522233i 0.965307 + 0.261116i \(0.0840907\pi\)
−0.965307 + 0.261116i \(0.915909\pi\)
\(12\) 1.50000 + 0.866025i 0.433013 + 0.250000i
\(13\) −3.00000 + 1.73205i −0.832050 + 0.480384i −0.854554 0.519362i \(-0.826170\pi\)
0.0225039 + 0.999747i \(0.492836\pi\)
\(14\) 1.00000 1.73205i 0.267261 0.462910i
\(15\) 6.00000 1.54919
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −6.00000 3.46410i −1.45521 0.840168i −0.456444 0.889752i \(-0.650877\pi\)
−0.998770 + 0.0495842i \(0.984210\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) 0.500000 + 4.33013i 0.114708 + 0.993399i
\(20\) 3.46410i 0.774597i
\(21\) 3.00000 1.73205i 0.654654 0.377964i
\(22\) −1.50000 0.866025i −0.319801 0.184637i
\(23\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) 3.50000 + 6.06218i 0.700000 + 1.21244i
\(26\) 3.46410i 0.679366i
\(27\) 5.19615i 1.00000i
\(28\) 1.00000 + 1.73205i 0.188982 + 0.327327i
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) −3.00000 + 5.19615i −0.547723 + 0.948683i
\(31\) 6.92820i 1.24434i −0.782881 0.622171i \(-0.786251\pi\)
0.782881 0.622171i \(-0.213749\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) 6.00000 3.46410i 1.02899 0.594089i
\(35\) 6.00000 + 3.46410i 1.01419 + 0.585540i
\(36\) −3.00000 −0.500000
\(37\) 6.92820i 1.13899i −0.821995 0.569495i \(-0.807139\pi\)
0.821995 0.569495i \(-0.192861\pi\)
\(38\) −4.00000 1.73205i −0.648886 0.280976i
\(39\) 3.00000 5.19615i 0.480384 0.832050i
\(40\) −3.00000 1.73205i −0.474342 0.273861i
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 3.46410i 0.534522i
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 1.50000 0.866025i 0.226134 0.130558i
\(45\) −9.00000 + 5.19615i −1.34164 + 0.774597i
\(46\) 0 0
\(47\) 3.00000 1.73205i 0.437595 0.252646i −0.264982 0.964253i \(-0.585366\pi\)
0.702577 + 0.711608i \(0.252033\pi\)
\(48\) 1.73205i 0.250000i
\(49\) −3.00000 −0.428571
\(50\) −7.00000 −0.989949
\(51\) 12.0000 1.68034
\(52\) 3.00000 + 1.73205i 0.416025 + 0.240192i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) −4.50000 2.59808i −0.612372 0.353553i
\(55\) 3.00000 5.19615i 0.404520 0.700649i
\(56\) −2.00000 −0.267261
\(57\) −4.50000 6.06218i −0.596040 0.802955i
\(58\) −6.00000 −0.787839
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) −3.00000 5.19615i −0.387298 0.670820i
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 6.00000 + 3.46410i 0.762001 + 0.439941i
\(63\) −3.00000 + 5.19615i −0.377964 + 0.654654i
\(64\) 1.00000 0.125000
\(65\) 12.0000 1.48842
\(66\) 3.00000 0.369274
\(67\) 4.50000 2.59808i 0.549762 0.317406i −0.199264 0.979946i \(-0.563855\pi\)
0.749026 + 0.662540i \(0.230522\pi\)
\(68\) 6.92820i 0.840168i
\(69\) 0 0
\(70\) −6.00000 + 3.46410i −0.717137 + 0.414039i
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) 1.50000 2.59808i 0.176777 0.306186i
\(73\) −2.50000 + 4.33013i −0.292603 + 0.506803i −0.974424 0.224716i \(-0.927855\pi\)
0.681822 + 0.731519i \(0.261188\pi\)
\(74\) 6.00000 + 3.46410i 0.697486 + 0.402694i
\(75\) −10.5000 6.06218i −1.21244 0.700000i
\(76\) 3.50000 2.59808i 0.401478 0.298020i
\(77\) 3.46410i 0.394771i
\(78\) 3.00000 + 5.19615i 0.339683 + 0.588348i
\(79\) −12.0000 6.92820i −1.35011 0.779484i −0.361842 0.932240i \(-0.617852\pi\)
−0.988264 + 0.152756i \(0.951185\pi\)
\(80\) 3.00000 1.73205i 0.335410 0.193649i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) 5.19615i 0.570352i 0.958475 + 0.285176i \(0.0920520\pi\)
−0.958475 + 0.285176i \(0.907948\pi\)
\(84\) −3.00000 1.73205i −0.327327 0.188982i
\(85\) 12.0000 + 20.7846i 1.30158 + 2.25441i
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) −9.00000 5.19615i −0.964901 0.557086i
\(88\) 1.73205i 0.184637i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 10.3923i 1.09545i
\(91\) 6.00000 3.46410i 0.628971 0.363137i
\(92\) 0 0
\(93\) 6.00000 + 10.3923i 0.622171 + 1.07763i
\(94\) 3.46410i 0.357295i
\(95\) 6.00000 13.8564i 0.615587 1.42164i
\(96\) 1.50000 + 0.866025i 0.153093 + 0.0883883i
\(97\) 7.50000 + 4.33013i 0.761510 + 0.439658i 0.829837 0.558005i \(-0.188433\pi\)
−0.0683279 + 0.997663i \(0.521766\pi\)
\(98\) 1.50000 2.59808i 0.151523 0.262445i
\(99\) 4.50000 + 2.59808i 0.452267 + 0.261116i
\(100\) 3.50000 6.06218i 0.350000 0.606218i
\(101\) −9.00000 + 5.19615i −0.895533 + 0.517036i −0.875748 0.482768i \(-0.839632\pi\)
−0.0197851 + 0.999804i \(0.506298\pi\)
\(102\) −6.00000 + 10.3923i −0.594089 + 1.02899i
\(103\) 10.3923i 1.02398i 0.858990 + 0.511992i \(0.171092\pi\)
−0.858990 + 0.511992i \(0.828908\pi\)
\(104\) −3.00000 + 1.73205i −0.294174 + 0.169842i
\(105\) −12.0000 −1.17108
\(106\) 6.00000 0.582772
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 4.50000 2.59808i 0.433013 0.250000i
\(109\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 3.00000 + 5.19615i 0.286039 + 0.495434i
\(111\) 6.00000 + 10.3923i 0.569495 + 0.986394i
\(112\) 1.00000 1.73205i 0.0944911 0.163663i
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) 7.50000 0.866025i 0.702439 0.0811107i
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 10.3923i 0.960769i
\(118\) −1.50000 2.59808i −0.138086 0.239172i
\(119\) 12.0000 + 6.92820i 1.10004 + 0.635107i
\(120\) 6.00000 0.547723
\(121\) 8.00000 0.727273
\(122\) 10.0000 0.905357
\(123\) 5.19615i 0.468521i
\(124\) −6.00000 + 3.46410i −0.538816 + 0.311086i
\(125\) 6.92820i 0.619677i
\(126\) −3.00000 5.19615i −0.267261 0.462910i
\(127\) −9.00000 + 5.19615i −0.798621 + 0.461084i −0.842989 0.537931i \(-0.819206\pi\)
0.0443678 + 0.999015i \(0.485873\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 13.8564i 1.21999i
\(130\) −6.00000 + 10.3923i −0.526235 + 0.911465i
\(131\) −16.5000 9.52628i −1.44161 0.832315i −0.443654 0.896198i \(-0.646318\pi\)
−0.997957 + 0.0638831i \(0.979652\pi\)
\(132\) −1.50000 + 2.59808i −0.130558 + 0.226134i
\(133\) −1.00000 8.66025i −0.0867110 0.750939i
\(134\) 5.19615i 0.448879i
\(135\) 9.00000 15.5885i 0.774597 1.34164i
\(136\) −6.00000 3.46410i −0.514496 0.297044i
\(137\) −1.50000 + 0.866025i −0.128154 + 0.0739895i −0.562706 0.826657i \(-0.690240\pi\)
0.434553 + 0.900646i \(0.356906\pi\)
\(138\) 0 0
\(139\) −0.500000 0.866025i −0.0424094 0.0734553i 0.844042 0.536278i \(-0.180170\pi\)
−0.886451 + 0.462822i \(0.846837\pi\)
\(140\) 6.92820i 0.585540i
\(141\) −3.00000 + 5.19615i −0.252646 + 0.437595i
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 20.7846i 1.72607i
\(146\) −2.50000 4.33013i −0.206901 0.358364i
\(147\) 4.50000 2.59808i 0.371154 0.214286i
\(148\) −6.00000 + 3.46410i −0.493197 + 0.284747i
\(149\) −6.00000 3.46410i −0.491539 0.283790i 0.233674 0.972315i \(-0.424925\pi\)
−0.725213 + 0.688525i \(0.758259\pi\)
\(150\) 10.5000 6.06218i 0.857321 0.494975i
\(151\) 6.92820i 0.563809i 0.959442 + 0.281905i \(0.0909662\pi\)
−0.959442 + 0.281905i \(0.909034\pi\)
\(152\) 0.500000 + 4.33013i 0.0405554 + 0.351220i
\(153\) −18.0000 + 10.3923i −1.45521 + 0.840168i
\(154\) 3.00000 + 1.73205i 0.241747 + 0.139573i
\(155\) −12.0000 + 20.7846i −0.963863 + 1.66946i
\(156\) −6.00000 −0.480384
\(157\) 10.0000 17.3205i 0.798087 1.38233i −0.122774 0.992435i \(-0.539179\pi\)
0.920860 0.389892i \(-0.127488\pi\)
\(158\) 12.0000 6.92820i 0.954669 0.551178i
\(159\) 9.00000 + 5.19615i 0.713746 + 0.412082i
\(160\) 3.46410i 0.273861i
\(161\) 0 0
\(162\) 9.00000 0.707107
\(163\) −17.0000 −1.33154 −0.665771 0.746156i \(-0.731897\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) −3.00000 −0.234261
\(165\) 10.3923i 0.809040i
\(166\) −4.50000 2.59808i −0.349268 0.201650i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 3.00000 1.73205i 0.231455 0.133631i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) −24.0000 −1.84072
\(171\) 12.0000 + 5.19615i 0.917663 + 0.397360i
\(172\) 8.00000 0.609994
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 9.00000 5.19615i 0.682288 0.393919i
\(175\) −7.00000 12.1244i −0.529150 0.916515i
\(176\) −1.50000 0.866025i −0.113067 0.0652791i
\(177\) 5.19615i 0.390567i
\(178\) −6.00000 −0.449719
\(179\) 3.00000 0.224231 0.112115 0.993695i \(-0.464237\pi\)
0.112115 + 0.993695i \(0.464237\pi\)
\(180\) 9.00000 + 5.19615i 0.670820 + 0.387298i
\(181\) 6.00000 3.46410i 0.445976 0.257485i −0.260153 0.965567i \(-0.583773\pi\)
0.706129 + 0.708083i \(0.250440\pi\)
\(182\) 6.92820i 0.513553i
\(183\) 15.0000 + 8.66025i 1.10883 + 0.640184i
\(184\) 0 0
\(185\) −12.0000 + 20.7846i −0.882258 + 1.52811i
\(186\) −12.0000 −0.879883
\(187\) 6.00000 10.3923i 0.438763 0.759961i
\(188\) −3.00000 1.73205i −0.218797 0.126323i
\(189\) 10.3923i 0.755929i
\(190\) 9.00000 + 12.1244i 0.652929 + 0.879593i
\(191\) 6.92820i 0.501307i −0.968077 0.250654i \(-0.919354\pi\)
0.968077 0.250654i \(-0.0806455\pi\)
\(192\) −1.50000 + 0.866025i −0.108253 + 0.0625000i
\(193\) 18.0000 + 10.3923i 1.29567 + 0.748054i 0.979653 0.200700i \(-0.0643215\pi\)
0.316016 + 0.948754i \(0.397655\pi\)
\(194\) −7.50000 + 4.33013i −0.538469 + 0.310885i
\(195\) −18.0000 + 10.3923i −1.28901 + 0.744208i
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) 20.7846i 1.48084i −0.672143 0.740421i \(-0.734626\pi\)
0.672143 0.740421i \(-0.265374\pi\)
\(198\) −4.50000 + 2.59808i −0.319801 + 0.184637i
\(199\) −7.00000 12.1244i −0.496217 0.859473i 0.503774 0.863836i \(-0.331945\pi\)
−0.999990 + 0.00436292i \(0.998611\pi\)
\(200\) 3.50000 + 6.06218i 0.247487 + 0.428661i
\(201\) −4.50000 + 7.79423i −0.317406 + 0.549762i
\(202\) 10.3923i 0.731200i
\(203\) −6.00000 10.3923i −0.421117 0.729397i
\(204\) −6.00000 10.3923i −0.420084 0.727607i
\(205\) −9.00000 + 5.19615i −0.628587 + 0.362915i
\(206\) −9.00000 5.19615i −0.627060 0.362033i
\(207\) 0 0
\(208\) 3.46410i 0.240192i
\(209\) −7.50000 + 0.866025i −0.518786 + 0.0599042i
\(210\) 6.00000 10.3923i 0.414039 0.717137i
\(211\) 9.00000 + 5.19615i 0.619586 + 0.357718i 0.776708 0.629861i \(-0.216888\pi\)
−0.157122 + 0.987579i \(0.550222\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 10.3923i 0.712069i
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) 24.0000 13.8564i 1.63679 0.944999i
\(216\) 5.19615i 0.353553i
\(217\) 13.8564i 0.940634i
\(218\) 0 0
\(219\) 8.66025i 0.585206i
\(220\) −6.00000 −0.404520
\(221\) 24.0000 1.61441
\(222\) −12.0000 −0.805387
\(223\) 12.0000 + 6.92820i 0.803579 + 0.463947i 0.844721 0.535207i \(-0.179766\pi\)
−0.0411418 + 0.999153i \(0.513100\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) 21.0000 1.40000
\(226\) −7.50000 + 12.9904i −0.498893 + 0.864107i
\(227\) 21.0000 1.39382 0.696909 0.717159i \(-0.254558\pi\)
0.696909 + 0.717159i \(0.254558\pi\)
\(228\) −3.00000 + 6.92820i −0.198680 + 0.458831i
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) 3.00000 + 5.19615i 0.197386 + 0.341882i
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) −1.50000 0.866025i −0.0982683 0.0567352i 0.450060 0.892998i \(-0.351402\pi\)
−0.548329 + 0.836263i \(0.684736\pi\)
\(234\) −9.00000 5.19615i −0.588348 0.339683i
\(235\) −12.0000 −0.782794
\(236\) 3.00000 0.195283
\(237\) 24.0000 1.55897
\(238\) −12.0000 + 6.92820i −0.777844 + 0.449089i
\(239\) 6.92820i 0.448148i −0.974572 0.224074i \(-0.928064\pi\)
0.974572 0.224074i \(-0.0719358\pi\)
\(240\) −3.00000 + 5.19615i −0.193649 + 0.335410i
\(241\) 4.50000 2.59808i 0.289870 0.167357i −0.348013 0.937490i \(-0.613143\pi\)
0.637883 + 0.770133i \(0.279810\pi\)
\(242\) −4.00000 + 6.92820i −0.257130 + 0.445362i
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) −5.00000 + 8.66025i −0.320092 + 0.554416i
\(245\) 9.00000 + 5.19615i 0.574989 + 0.331970i
\(246\) −4.50000 2.59808i −0.286910 0.165647i
\(247\) −9.00000 12.1244i −0.572656 0.771454i
\(248\) 6.92820i 0.439941i
\(249\) −4.50000 7.79423i −0.285176 0.493939i
\(250\) 6.00000 + 3.46410i 0.379473 + 0.219089i
\(251\) −7.50000 + 4.33013i −0.473396 + 0.273315i −0.717660 0.696393i \(-0.754787\pi\)
0.244264 + 0.969709i \(0.421454\pi\)
\(252\) 6.00000 0.377964
\(253\) 0 0
\(254\) 10.3923i 0.652071i
\(255\) −36.0000 20.7846i −2.25441 1.30158i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) 12.0000 + 6.92820i 0.747087 + 0.431331i
\(259\) 13.8564i 0.860995i
\(260\) −6.00000 10.3923i −0.372104 0.644503i
\(261\) 18.0000 1.11417
\(262\) 16.5000 9.52628i 1.01937 0.588536i
\(263\) 3.00000 + 1.73205i 0.184988 + 0.106803i 0.589634 0.807671i \(-0.299272\pi\)
−0.404646 + 0.914473i \(0.632605\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) 20.7846i 1.27679i
\(266\) 8.00000 + 3.46410i 0.490511 + 0.212398i
\(267\) −9.00000 5.19615i −0.550791 0.317999i
\(268\) −4.50000 2.59808i −0.274881 0.158703i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 9.00000 + 15.5885i 0.547723 + 0.948683i
\(271\) −13.0000 + 22.5167i −0.789694 + 1.36779i 0.136461 + 0.990645i \(0.456427\pi\)
−0.926155 + 0.377144i \(0.876906\pi\)
\(272\) 6.00000 3.46410i 0.363803 0.210042i
\(273\) −6.00000 + 10.3923i −0.363137 + 0.628971i
\(274\) 1.73205i 0.104637i
\(275\) −10.5000 + 6.06218i −0.633174 + 0.365563i
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 1.00000 0.0599760
\(279\) −18.0000 10.3923i −1.07763 0.622171i
\(280\) 6.00000 + 3.46410i 0.358569 + 0.207020i
\(281\) −7.50000 12.9904i −0.447412 0.774941i 0.550804 0.834634i \(-0.314321\pi\)
−0.998217 + 0.0596933i \(0.980988\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) 0.500000 0.866025i 0.0297219 0.0514799i −0.850782 0.525519i \(-0.823871\pi\)
0.880504 + 0.474039i \(0.157204\pi\)
\(284\) 6.00000 0.356034
\(285\) 3.00000 + 25.9808i 0.177705 + 1.53897i
\(286\) 6.00000 0.354787
\(287\) −3.00000 + 5.19615i −0.177084 + 0.306719i
\(288\) −3.00000 −0.176777
\(289\) 15.5000 + 26.8468i 0.911765 + 1.57922i
\(290\) 18.0000 + 10.3923i 1.05700 + 0.610257i
\(291\) −15.0000 −0.879316
\(292\) 5.00000 0.292603
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 5.19615i 0.303046i
\(295\) 9.00000 5.19615i 0.524000 0.302532i
\(296\) 6.92820i 0.402694i
\(297\) −9.00000 −0.522233
\(298\) 6.00000 3.46410i 0.347571 0.200670i
\(299\) 0 0
\(300\) 12.1244i 0.700000i
\(301\) 8.00000 13.8564i 0.461112 0.798670i
\(302\) −6.00000 3.46410i −0.345261 0.199337i
\(303\) 9.00000 15.5885i 0.517036 0.895533i
\(304\) −4.00000 1.73205i −0.229416 0.0993399i
\(305\) 34.6410i 1.98354i
\(306\) 20.7846i 1.18818i
\(307\) −4.50000 2.59808i −0.256829 0.148280i 0.366058 0.930592i \(-0.380707\pi\)
−0.622887 + 0.782312i \(0.714040\pi\)
\(308\) −3.00000 + 1.73205i −0.170941 + 0.0986928i
\(309\) −9.00000 15.5885i −0.511992 0.886796i
\(310\) −12.0000 20.7846i −0.681554 1.18049i
\(311\) 13.8564i 0.785725i 0.919597 + 0.392862i \(0.128515\pi\)
−0.919597 + 0.392862i \(0.871485\pi\)
\(312\) 3.00000 5.19615i 0.169842 0.294174i
\(313\) −15.5000 26.8468i −0.876112 1.51747i −0.855574 0.517681i \(-0.826795\pi\)
−0.0205381 0.999789i \(-0.506538\pi\)
\(314\) 10.0000 + 17.3205i 0.564333 + 0.977453i
\(315\) 18.0000 10.3923i 1.01419 0.585540i
\(316\) 13.8564i 0.779484i
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) −9.00000 + 5.19615i −0.504695 + 0.291386i
\(319\) −9.00000 + 5.19615i −0.503903 + 0.290929i
\(320\) −3.00000 1.73205i −0.167705 0.0968246i
\(321\) 18.0000 10.3923i 1.00466 0.580042i
\(322\) 0 0
\(323\) 12.0000 27.7128i 0.667698 1.54198i
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) −21.0000 12.1244i −1.16487 0.672538i
\(326\) 8.50000 14.7224i 0.470771 0.815400i
\(327\) 0 0
\(328\) 1.50000 2.59808i 0.0828236 0.143455i
\(329\) −6.00000 + 3.46410i −0.330791 + 0.190982i
\(330\) −9.00000 5.19615i −0.495434 0.286039i
\(331\) 8.66025i 0.476011i −0.971264 0.238005i \(-0.923506\pi\)
0.971264 0.238005i \(-0.0764936\pi\)
\(332\) 4.50000 2.59808i 0.246970 0.142588i
\(333\) −18.0000 10.3923i −0.986394 0.569495i
\(334\) 12.0000 0.656611
\(335\) −18.0000 −0.983445
\(336\) 3.46410i 0.188982i
\(337\) −22.5000 12.9904i −1.22565 0.707631i −0.259536 0.965734i \(-0.583569\pi\)
−0.966118 + 0.258102i \(0.916903\pi\)
\(338\) −0.500000 0.866025i −0.0271964 0.0471056i
\(339\) −22.5000 + 12.9904i −1.22203 + 0.705541i
\(340\) 12.0000 20.7846i 0.650791 1.12720i
\(341\) 12.0000 0.649836
\(342\) −10.5000 + 7.79423i −0.567775 + 0.421464i
\(343\) 20.0000 1.07990
\(344\) −4.00000 + 6.92820i −0.215666 + 0.373544i
\(345\) 0 0
\(346\) −9.00000 15.5885i −0.483843 0.838041i
\(347\) −7.50000 4.33013i −0.402621 0.232453i 0.284993 0.958530i \(-0.408009\pi\)
−0.687614 + 0.726076i \(0.741342\pi\)
\(348\) 10.3923i 0.557086i
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 14.0000 0.748331
\(351\) −9.00000 15.5885i −0.480384 0.832050i
\(352\) 1.50000 0.866025i 0.0799503 0.0461593i
\(353\) 25.9808i 1.38282i −0.722464 0.691408i \(-0.756991\pi\)
0.722464 0.691408i \(-0.243009\pi\)
\(354\) 4.50000 + 2.59808i 0.239172 + 0.138086i
\(355\) 18.0000 10.3923i 0.955341 0.551566i
\(356\) 3.00000 5.19615i 0.159000 0.275396i
\(357\) −24.0000 −1.27021
\(358\) −1.50000 + 2.59808i −0.0792775 + 0.137313i
\(359\) 6.00000 + 3.46410i 0.316668 + 0.182828i 0.649906 0.760014i \(-0.274808\pi\)
−0.333238 + 0.942843i \(0.608141\pi\)
\(360\) −9.00000 + 5.19615i −0.474342 + 0.273861i
\(361\) −18.5000 + 4.33013i −0.973684 + 0.227901i
\(362\) 6.92820i 0.364138i
\(363\) −12.0000 + 6.92820i −0.629837 + 0.363636i
\(364\) −6.00000 3.46410i −0.314485 0.181568i
\(365\) 15.0000 8.66025i 0.785136 0.453298i
\(366\) −15.0000 + 8.66025i −0.784063 + 0.452679i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 0 0
\(369\) −4.50000 7.79423i −0.234261 0.405751i
\(370\) −12.0000 20.7846i −0.623850 1.08054i
\(371\) 6.00000 + 10.3923i 0.311504 + 0.539542i
\(372\) 6.00000 10.3923i 0.311086 0.538816i
\(373\) 6.92820i 0.358729i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 6.00000 + 10.3923i 0.310253 + 0.537373i
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) 3.00000 1.73205i 0.154713 0.0893237i
\(377\) −18.0000 10.3923i −0.927047 0.535231i
\(378\) 9.00000 + 5.19615i 0.462910 + 0.267261i
\(379\) 10.3923i 0.533817i 0.963722 + 0.266908i \(0.0860021\pi\)
−0.963722 + 0.266908i \(0.913998\pi\)
\(380\) −15.0000 + 1.73205i −0.769484 + 0.0888523i
\(381\) 9.00000 15.5885i 0.461084 0.798621i
\(382\) 6.00000 + 3.46410i 0.306987 + 0.177239i
\(383\) 9.00000 15.5885i 0.459879 0.796533i −0.539076 0.842257i \(-0.681226\pi\)
0.998954 + 0.0457244i \(0.0145596\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) −18.0000 + 10.3923i −0.916176 + 0.528954i
\(387\) 12.0000 + 20.7846i 0.609994 + 1.05654i
\(388\) 8.66025i 0.439658i
\(389\) −30.0000 + 17.3205i −1.52106 + 0.878185i −0.521369 + 0.853331i \(0.674579\pi\)
−0.999691 + 0.0248535i \(0.992088\pi\)
\(390\) 20.7846i 1.05247i
\(391\) 0 0
\(392\) −3.00000 −0.151523
\(393\) 33.0000 1.66463
\(394\) 18.0000 + 10.3923i 0.906827 + 0.523557i
\(395\) 24.0000 + 41.5692i 1.20757 + 2.09157i
\(396\) 5.19615i 0.261116i
\(397\) −10.0000 + 17.3205i −0.501886 + 0.869291i 0.498112 + 0.867113i \(0.334027\pi\)
−0.999998 + 0.00217869i \(0.999307\pi\)
\(398\) 14.0000 0.701757
\(399\) 9.00000 + 12.1244i 0.450564 + 0.606977i
\(400\) −7.00000 −0.350000
\(401\) 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) −4.50000 7.79423i −0.224440 0.388741i
\(403\) 12.0000 + 20.7846i 0.597763 + 1.03536i
\(404\) 9.00000 + 5.19615i 0.447767 + 0.258518i
\(405\) 31.1769i 1.54919i
\(406\) 12.0000 0.595550
\(407\) 12.0000 0.594818
\(408\) 12.0000 0.594089
\(409\) −16.5000 + 9.52628i −0.815872 + 0.471044i −0.848991 0.528407i \(-0.822789\pi\)
0.0331186 + 0.999451i \(0.489456\pi\)
\(410\) 10.3923i 0.513239i
\(411\) 1.50000 2.59808i 0.0739895 0.128154i
\(412\) 9.00000 5.19615i 0.443398 0.255996i
\(413\) 3.00000 5.19615i 0.147620 0.255686i
\(414\) 0 0
\(415\) 9.00000 15.5885i 0.441793 0.765207i
\(416\) 3.00000 + 1.73205i 0.147087 + 0.0849208i
\(417\) 1.50000 + 0.866025i 0.0734553 + 0.0424094i
\(418\) 3.00000 6.92820i 0.146735 0.338869i
\(419\) 10.3923i 0.507697i −0.967244 0.253849i \(-0.918303\pi\)
0.967244 0.253849i \(-0.0816965\pi\)
\(420\) 6.00000 + 10.3923i 0.292770 + 0.507093i
\(421\) −12.0000 6.92820i −0.584844 0.337660i 0.178212 0.983992i \(-0.442969\pi\)
−0.763056 + 0.646332i \(0.776302\pi\)
\(422\) −9.00000 + 5.19615i −0.438113 + 0.252945i
\(423\) 10.3923i 0.505291i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 48.4974i 2.35247i
\(426\) 9.00000 + 5.19615i 0.436051 + 0.251754i
\(427\) 10.0000 + 17.3205i 0.483934 + 0.838198i
\(428\) 6.00000 + 10.3923i 0.290021 + 0.502331i
\(429\) 9.00000 + 5.19615i 0.434524 + 0.250873i
\(430\) 27.7128i 1.33643i
\(431\) 3.00000 + 5.19615i 0.144505 + 0.250290i 0.929188 0.369607i \(-0.120508\pi\)
−0.784683 + 0.619897i \(0.787174\pi\)
\(432\) −4.50000 2.59808i −0.216506 0.125000i
\(433\) −12.0000 + 6.92820i −0.576683 + 0.332948i −0.759814 0.650140i \(-0.774710\pi\)
0.183131 + 0.983089i \(0.441377\pi\)
\(434\) −12.0000 6.92820i −0.576018 0.332564i
\(435\) 18.0000 + 31.1769i 0.863034 + 1.49482i
\(436\) 0 0
\(437\) 0 0
\(438\) 7.50000 + 4.33013i 0.358364 + 0.206901i
\(439\) −12.0000 6.92820i −0.572729 0.330665i 0.185510 0.982642i \(-0.440606\pi\)
−0.758238 + 0.651977i \(0.773940\pi\)
\(440\) 3.00000 5.19615i 0.143019 0.247717i
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) −12.0000 + 20.7846i −0.570782 + 0.988623i
\(443\) −10.5000 + 6.06218i −0.498870 + 0.288023i −0.728247 0.685315i \(-0.759665\pi\)
0.229377 + 0.973338i \(0.426331\pi\)
\(444\) 6.00000 10.3923i 0.284747 0.493197i
\(445\) 20.7846i 0.985285i
\(446\) −12.0000 + 6.92820i −0.568216 + 0.328060i
\(447\) 12.0000 0.567581
\(448\) −2.00000 −0.0944911
\(449\) 3.00000 0.141579 0.0707894 0.997491i \(-0.477448\pi\)
0.0707894 + 0.997491i \(0.477448\pi\)
\(450\) −10.5000 + 18.1865i −0.494975 + 0.857321i
\(451\) 4.50000 + 2.59808i 0.211897 + 0.122339i
\(452\) −7.50000 12.9904i −0.352770 0.611016i
\(453\) −6.00000 10.3923i −0.281905 0.488273i
\(454\) −10.5000 + 18.1865i −0.492789 + 0.853536i
\(455\) −24.0000 −1.12514
\(456\) −4.50000 6.06218i −0.210732 0.283887i
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −2.00000 + 3.46410i −0.0934539 + 0.161867i
\(459\) 18.0000 31.1769i 0.840168 1.45521i
\(460\) 0 0
\(461\) 21.0000 + 12.1244i 0.978068 + 0.564688i 0.901686 0.432391i \(-0.142330\pi\)
0.0763814 + 0.997079i \(0.475663\pi\)
\(462\) −6.00000 −0.279145
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) −6.00000 −0.278543
\(465\) 41.5692i 1.92773i
\(466\) 1.50000 0.866025i 0.0694862 0.0401179i
\(467\) 12.1244i 0.561048i 0.959847 + 0.280524i \(0.0905083\pi\)
−0.959847 + 0.280524i \(0.909492\pi\)
\(468\) 9.00000 5.19615i 0.416025 0.240192i
\(469\) −9.00000 + 5.19615i −0.415581 + 0.239936i
\(470\) 6.00000 10.3923i 0.276759 0.479361i
\(471\) 34.6410i 1.59617i
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) −12.0000 6.92820i −0.551761 0.318559i
\(474\) −12.0000 + 20.7846i −0.551178 + 0.954669i
\(475\) −24.5000 + 18.1865i −1.12414 + 0.834455i
\(476\) 13.8564i 0.635107i
\(477\) −18.0000 −0.824163
\(478\) 6.00000 + 3.46410i 0.274434 + 0.158444i
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) −3.00000 5.19615i −0.136931 0.237171i
\(481\) 12.0000 + 20.7846i 0.547153 + 0.947697i
\(482\) 5.19615i 0.236678i
\(483\) 0 0
\(484\) −4.00000 6.92820i −0.181818 0.314918i
\(485\) −15.0000 25.9808i −0.681115 1.17973i
\(486\) −13.5000 + 7.79423i −0.612372 + 0.353553i
\(487\) 6.92820i 0.313947i 0.987603 + 0.156973i \(0.0501737\pi\)
−0.987603 + 0.156973i \(0.949826\pi\)
\(488\) −5.00000 8.66025i −0.226339 0.392031i
\(489\) 25.5000 14.7224i 1.15315 0.665771i
\(490\) −9.00000 + 5.19615i −0.406579 + 0.234738i
\(491\) 27.0000 + 15.5885i 1.21849 + 0.703497i 0.964595 0.263734i \(-0.0849541\pi\)
0.253897 + 0.967231i \(0.418287\pi\)
\(492\) 4.50000 2.59808i 0.202876 0.117130i
\(493\) 41.5692i 1.87218i
\(494\) 15.0000 1.73205i 0.674882 0.0779287i
\(495\) −9.00000 15.5885i −0.404520 0.700649i
\(496\) 6.00000 + 3.46410i 0.269408 + 0.155543i
\(497\) 6.00000 10.3923i 0.269137 0.466159i
\(498\) 9.00000 0.403300
\(499\) 20.5000 35.5070i 0.917706 1.58951i 0.114816 0.993387i \(-0.463372\pi\)
0.802890 0.596127i \(-0.203294\pi\)
\(500\) −6.00000 + 3.46410i −0.268328 + 0.154919i
\(501\) 18.0000 + 10.3923i 0.804181 + 0.464294i
\(502\) 8.66025i 0.386526i
\(503\) −18.0000 + 10.3923i −0.802580 + 0.463370i −0.844373 0.535756i \(-0.820027\pi\)
0.0417923 + 0.999126i \(0.486693\pi\)
\(504\) −3.00000 + 5.19615i −0.133631 + 0.231455i
\(505\) 36.0000 1.60198
\(506\) 0 0
\(507\) 1.73205i 0.0769231i
\(508\) 9.00000 + 5.19615i 0.399310 + 0.230542i
\(509\) 12.0000 + 20.7846i 0.531891 + 0.921262i 0.999307 + 0.0372243i \(0.0118516\pi\)
−0.467416 + 0.884037i \(0.654815\pi\)
\(510\) 36.0000 20.7846i 1.59411 0.920358i
\(511\) 5.00000 8.66025i 0.221187 0.383107i
\(512\) 1.00000 0.0441942
\(513\) −22.5000 + 2.59808i −0.993399 + 0.114708i
\(514\) −15.0000 −0.661622
\(515\) 18.0000 31.1769i 0.793175 1.37382i
\(516\) −12.0000 + 6.92820i −0.528271 + 0.304997i
\(517\) 3.00000 + 5.19615i 0.131940 + 0.228527i
\(518\) −12.0000 6.92820i −0.527250 0.304408i
\(519\) 31.1769i 1.36851i
\(520\) 12.0000 0.526235
\(521\) −21.0000 −0.920027 −0.460013 0.887912i \(-0.652155\pi\)
−0.460013 + 0.887912i \(0.652155\pi\)
\(522\) −9.00000 + 15.5885i −0.393919 + 0.682288i
\(523\) 15.0000 8.66025i 0.655904 0.378686i −0.134810 0.990871i \(-0.543043\pi\)
0.790715 + 0.612185i \(0.209709\pi\)
\(524\) 19.0526i 0.832315i
\(525\) 21.0000 + 12.1244i 0.916515 + 0.529150i
\(526\) −3.00000 + 1.73205i −0.130806 + 0.0755210i
\(527\) −24.0000 + 41.5692i −1.04546 + 1.81078i
\(528\) 3.00000 0.130558
\(529\) −11.5000 + 19.9186i −0.500000 + 0.866025i
\(530\) −18.0000 10.3923i −0.781870 0.451413i
\(531\) 4.50000 + 7.79423i 0.195283 + 0.338241i
\(532\) −7.00000 + 5.19615i −0.303488 + 0.225282i
\(533\) 10.3923i 0.450141i
\(534\) 9.00000 5.19615i 0.389468 0.224860i
\(535\) 36.0000 + 20.7846i 1.55642 + 0.898597i
\(536\) 4.50000 2.59808i 0.194370 0.112220i
\(537\) −4.50000 + 2.59808i −0.194189 + 0.112115i
\(538\) 0 0
\(539\) 5.19615i 0.223814i
\(540\) −18.0000 −0.774597
\(541\) −10.0000 17.3205i −0.429934 0.744667i 0.566933 0.823764i \(-0.308130\pi\)
−0.996867 + 0.0790969i \(0.974796\pi\)
\(542\) −13.0000 22.5167i −0.558398 0.967173i
\(543\) −6.00000 + 10.3923i −0.257485 + 0.445976i
\(544\) 6.92820i 0.297044i
\(545\) 0 0
\(546\) −6.00000 10.3923i −0.256776 0.444750i
\(547\) −21.0000 + 12.1244i −0.897895 + 0.518400i −0.876517 0.481371i \(-0.840139\pi\)
−0.0213785 + 0.999771i \(0.506805\pi\)
\(548\) 1.50000 + 0.866025i 0.0640768 + 0.0369948i
\(549\) −30.0000 −1.28037
\(550\) 12.1244i 0.516984i
\(551\) −21.0000 + 15.5885i −0.894630 + 0.664091i
\(552\) 0 0
\(553\) 24.0000 + 13.8564i 1.02058 + 0.589234i
\(554\) 1.00000 1.73205i 0.0424859 0.0735878i
\(555\) 41.5692i 1.76452i
\(556\) −0.500000 + 0.866025i −0.0212047 + 0.0367277i
\(557\) 12.0000 6.92820i 0.508456 0.293557i −0.223743 0.974648i \(-0.571827\pi\)
0.732199 + 0.681091i \(0.238494\pi\)
\(558\) 18.0000 10.3923i 0.762001 0.439941i
\(559\) 27.7128i 1.17213i
\(560\) −6.00000 + 3.46410i −0.253546 + 0.146385i
\(561\) 20.7846i 0.877527i
\(562\) 15.0000 0.632737
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 6.00000 0.252646
\(565\) −45.0000 25.9808i −1.89316 1.09302i
\(566\) 0.500000 + 0.866025i 0.0210166 + 0.0364018i
\(567\) 9.00000 + 15.5885i 0.377964 + 0.654654i
\(568\) −3.00000 + 5.19615i −0.125877 + 0.218026i
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) −24.0000 10.3923i −1.00525 0.435286i
\(571\) −43.0000 −1.79949 −0.899747 0.436412i \(-0.856249\pi\)
−0.899747 + 0.436412i \(0.856249\pi\)
\(572\) −3.00000 + 5.19615i −0.125436 + 0.217262i
\(573\) 6.00000 + 10.3923i 0.250654 + 0.434145i
\(574\) −3.00000 5.19615i −0.125218 0.216883i
\(575\) 0 0
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −29.0000 −1.20729 −0.603643 0.797255i \(-0.706285\pi\)
−0.603643 + 0.797255i \(0.706285\pi\)
\(578\) −31.0000 −1.28943
\(579\) −36.0000 −1.49611
\(580\) −18.0000 + 10.3923i −0.747409 + 0.431517i
\(581\) 10.3923i 0.431145i
\(582\) 7.50000 12.9904i 0.310885 0.538469i
\(583\) 9.00000 5.19615i 0.372742 0.215203i
\(584\) −2.50000 + 4.33013i −0.103451 + 0.179182i
\(585\) 18.0000 31.1769i 0.744208 1.28901i
\(586\) 3.00000 5.19615i 0.123929 0.214651i
\(587\) −33.0000 19.0526i −1.36206 0.786383i −0.372158 0.928169i \(-0.621382\pi\)
−0.989897 + 0.141786i \(0.954716\pi\)
\(588\) −4.50000 2.59808i −0.185577 0.107143i
\(589\) 30.0000 3.46410i 1.23613 0.142736i
\(590\) 10.3923i 0.427844i
\(591\) 18.0000 + 31.1769i 0.740421 + 1.28245i
\(592\) 6.00000 + 3.46410i 0.246598 + 0.142374i
\(593\) 22.5000 12.9904i 0.923964 0.533451i 0.0390666 0.999237i \(-0.487562\pi\)
0.884898 + 0.465786i \(0.154228\pi\)
\(594\) 4.50000 7.79423i 0.184637 0.319801i
\(595\) −24.0000 41.5692i −0.983904 1.70417i
\(596\) 6.92820i 0.283790i
\(597\) 21.0000 + 12.1244i 0.859473 + 0.496217i
\(598\) 0 0
\(599\) 18.0000 + 31.1769i 0.735460 + 1.27385i 0.954521 + 0.298143i \(0.0963673\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) −10.5000 6.06218i −0.428661 0.247487i
\(601\) 8.66025i 0.353259i −0.984277 0.176630i \(-0.943481\pi\)
0.984277 0.176630i \(-0.0565195\pi\)
\(602\) 8.00000 + 13.8564i 0.326056 + 0.564745i
\(603\) 15.5885i 0.634811i
\(604\) 6.00000 3.46410i 0.244137 0.140952i
\(605\) −24.0000 13.8564i −0.975739 0.563343i
\(606\) 9.00000 + 15.5885i 0.365600 + 0.633238i
\(607\) 31.1769i 1.26543i 0.774384 + 0.632716i \(0.218060\pi\)
−0.774384 + 0.632716i \(0.781940\pi\)
\(608\) 3.50000 2.59808i 0.141944 0.105366i
\(609\) 18.0000 + 10.3923i 0.729397 + 0.421117i
\(610\) −30.0000 17.3205i −1.21466 0.701287i
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) 18.0000 + 10.3923i 0.727607 + 0.420084i
\(613\) −17.0000 + 29.4449i −0.686624 + 1.18927i 0.286300 + 0.958140i \(0.407575\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) 4.50000 2.59808i 0.181605 0.104850i
\(615\) 9.00000 15.5885i 0.362915 0.628587i
\(616\) 3.46410i 0.139573i
\(617\) −1.50000 + 0.866025i −0.0603877 + 0.0348649i −0.529890 0.848066i \(-0.677767\pi\)
0.469502 + 0.882931i \(0.344433\pi\)
\(618\) 18.0000 0.724066
\(619\) 40.0000 1.60774 0.803868 0.594808i \(-0.202772\pi\)
0.803868 + 0.594808i \(0.202772\pi\)
\(620\) 24.0000 0.963863
\(621\) 0 0
\(622\) −12.0000 6.92820i −0.481156 0.277796i
\(623\) −6.00000 10.3923i −0.240385 0.416359i
\(624\) 3.00000 + 5.19615i 0.120096 + 0.208013i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 31.0000 1.23901
\(627\) 10.5000 7.79423i 0.419330 0.311272i
\(628\) −20.0000 −0.798087
\(629\) −24.0000 + 41.5692i −0.956943 + 1.65747i
\(630\) 20.7846i 0.828079i
\(631\) 1.00000 + 1.73205i 0.0398094 + 0.0689519i 0.885244 0.465128i \(-0.153992\pi\)
−0.845434 + 0.534080i \(0.820658\pi\)
\(632\) −12.0000 6.92820i −0.477334 0.275589i
\(633\) −18.0000 −0.715436
\(634\) −6.00000 −0.238290
\(635\) 36.0000 1.42862
\(636\) 10.3923i 0.412082i
\(637\) 9.00000 5.19615i 0.356593 0.205879i
\(638\) 10.3923i 0.411435i
\(639\) 9.00000 + 15.5885i 0.356034 + 0.616670i
\(640\) 3.00000 1.73205i 0.118585 0.0684653i
\(641\) 22.5000 38.9711i 0.888697 1.53927i 0.0472793 0.998882i \(-0.484945\pi\)
0.841417 0.540386i \(-0.181722\pi\)
\(642\) 20.7846i 0.820303i
\(643\) 24.5000 42.4352i 0.966186 1.67348i 0.259791 0.965665i \(-0.416346\pi\)
0.706395 0.707818i \(-0.250320\pi\)
\(644\) 0 0
\(645\) −24.0000 + 41.5692i −0.944999 + 1.63679i
\(646\) 18.0000 + 24.2487i 0.708201 + 0.954053i
\(647\) 24.2487i 0.953315i −0.879089 0.476658i \(-0.841848\pi\)
0.879089 0.476658i \(-0.158152\pi\)
\(648\) −4.50000 7.79423i −0.176777 0.306186i
\(649\) −4.50000 2.59808i −0.176640 0.101983i
\(650\) 21.0000 12.1244i 0.823688 0.475556i
\(651\) −12.0000 20.7846i −0.470317 0.814613i
\(652\) 8.50000 + 14.7224i 0.332886 + 0.576575i
\(653\) 6.92820i 0.271122i −0.990769 0.135561i \(-0.956716\pi\)
0.990769 0.135561i \(-0.0432836\pi\)
\(654\) 0 0
\(655\) 33.0000 + 57.1577i 1.28942 + 2.23334i
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 7.50000 + 12.9904i 0.292603 + 0.506803i
\(658\) 6.92820i 0.270089i
\(659\) −18.0000 31.1769i −0.701180 1.21448i −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 9.00000 5.19615i 0.350325 0.202260i
\(661\) −33.0000 + 19.0526i −1.28355 + 0.741059i −0.977496 0.210955i \(-0.932343\pi\)
−0.306055 + 0.952014i \(0.599009\pi\)
\(662\) 7.50000 + 4.33013i 0.291496 + 0.168295i
\(663\) −36.0000 + 20.7846i −1.39812 + 0.807207i
\(664\) 5.19615i 0.201650i
\(665\) −12.0000 + 27.7128i −0.465340 + 1.07466i
\(666\) 18.0000 10.3923i 0.697486 0.402694i
\(667\) 0 0
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) −24.0000 −0.927894
\(670\) 9.00000 15.5885i 0.347700 0.602235i
\(671\) 15.0000 8.66025i 0.579069 0.334325i
\(672\) −3.00000 1.73205i −0.115728 0.0668153i
\(673\) 20.7846i 0.801188i −0.916256 0.400594i \(-0.868804\pi\)
0.916256 0.400594i \(-0.131196\pi\)
\(674\) 22.5000 12.9904i 0.866668 0.500371i
\(675\) −31.5000 + 18.1865i −1.21244 + 0.700000i
\(676\) 1.00000 0.0384615
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 25.9808i 0.997785i
\(679\) −15.0000 8.66025i −0.575647 0.332350i
\(680\) 12.0000 + 20.7846i 0.460179 + 0.797053i
\(681\) −31.5000 + 18.1865i −1.20708 + 0.696909i
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) −1.50000 12.9904i −0.0573539 0.496700i
\(685\) 6.00000 0.229248
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) −6.00000 + 3.46410i −0.228914 + 0.132164i
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) 18.0000 + 10.3923i 0.685745 + 0.395915i
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 18.0000 0.684257
\(693\) −9.00000 5.19615i −0.341882 0.197386i
\(694\) 7.50000 4.33013i 0.284696 0.164369i
\(695\) 3.46410i 0.131401i
\(696\) −9.00000 5.19615i −0.341144 0.196960i
\(697\) −18.0000 + 10.3923i −0.681799 + 0.393637i
\(698\) −4.00000 + 6.92820i −0.151402 + 0.262236i
\(699\) 3.00000 0.113470
\(700\) −7.00000 + 12.1244i −0.264575 + 0.458258i
\(701\) 9.00000 + 5.19615i 0.339925 + 0.196256i 0.660239 0.751056i \(-0.270455\pi\)
−0.320314 + 0.947312i \(0.603788\pi\)
\(702\) 18.0000 0.679366
\(703\) 30.0000 3.46410i 1.13147 0.130651i
\(704\) 1.73205i 0.0652791i
\(705\) 18.0000 10.3923i 0.677919 0.391397i
\(706\) 22.5000 + 12.9904i 0.846799 + 0.488899i
\(707\) 18.0000 10.3923i 0.676960 0.390843i
\(708\) −4.50000 + 2.59808i −0.169120 + 0.0976417i
\(709\) −4.00000 6.92820i −0.150223 0.260194i 0.781086 0.624423i \(-0.214666\pi\)
−0.931309 + 0.364229i \(0.881333\pi\)
\(710\) 20.7846i 0.780033i
\(711\) −36.0000 + 20.7846i −1.35011 + 0.779484i
\(712\) 3.00000 + 5.19615i 0.112430 + 0.194734i
\(713\) 0 0
\(714\) 12.0000 20.7846i 0.449089 0.777844i
\(715\) 20.7846i 0.777300i
\(716\) −1.50000 2.59808i −0.0560576 0.0970947i
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) −6.00000 + 3.46410i −0.223918 + 0.129279i
\(719\) 3.00000 + 1.73205i 0.111881 + 0.0645946i 0.554896 0.831919i \(-0.312758\pi\)
−0.443015 + 0.896514i \(0.646091\pi\)
\(720\) 10.3923i 0.387298i
\(721\) 20.7846i 0.774059i
\(722\) 5.50000 18.1865i 0.204689 0.676833i
\(723\) −4.50000 + 7.79423i −0.167357 + 0.289870i
\(724\) −6.00000 3.46410i −0.222988 0.128742i
\(725\) −21.0000 + 36.3731i −0.779920 + 1.35086i
\(726\) 13.8564i 0.514259i
\(727\) −4.00000 + 6.92820i −0.148352 + 0.256953i −0.930618 0.365991i \(-0.880730\pi\)
0.782267 + 0.622944i \(0.214063\pi\)
\(728\) 6.00000 3.46410i 0.222375 0.128388i
\(729\) −27.0000 −1.00000
\(730\) 17.3205i 0.641061i
\(731\) 48.0000 27.7128i 1.77534 1.02500i
\(732\) 17.3205i 0.640184i
\(733\) −4.00000 −0.147743 −0.0738717 0.997268i \(-0.523536\pi\)
−0.0738717 + 0.997268i \(0.523536\pi\)
\(734\) −4.00000 −0.147643
\(735\) −18.0000 −0.663940
\(736\) 0 0
\(737\) 4.50000 + 7.79423i 0.165760 + 0.287104i
\(738\) 9.00000 0.331295
\(739\) 5.50000 9.52628i 0.202321 0.350430i −0.746955 0.664875i \(-0.768485\pi\)
0.949276 + 0.314445i \(0.101818\pi\)
\(740\) 24.0000 0.882258
\(741\) 24.0000 + 10.3923i 0.881662 + 0.381771i
\(742\) −12.0000 −0.440534
\(743\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 6.00000 + 10.3923i 0.219971 + 0.381000i
\(745\) 12.0000 + 20.7846i 0.439646 + 0.761489i
\(746\) −6.00000 3.46410i −0.219676 0.126830i
\(747\) 13.5000 + 7.79423i 0.493939 + 0.285176i
\(748\) −12.0000 −0.438763
\(749\) 24.0000 0.876941
\(750\) −12.0000 −0.438178
\(751\) −33.0000 + 19.0526i −1.20419 + 0.695238i −0.961483 0.274863i \(-0.911368\pi\)
−0.242704 + 0.970100i \(0.578034\pi\)
\(752\) 3.46410i 0.126323i
\(753\) 7.50000 12.9904i 0.273315 0.473396i
\(754\) 18.0000 10.3923i 0.655521 0.378465i
\(755\) 12.0000 20.7846i 0.436725 0.756429i
\(756\) −9.00000 + 5.19615i −0.327327 + 0.188982i
\(757\) 19.0000 32.9090i 0.690567 1.19610i −0.281086 0.959683i \(-0.590695\pi\)
0.971652 0.236414i \(-0.0759722\pi\)
\(758\) −9.00000 5.19615i −0.326895 0.188733i
\(759\) 0 0
\(760\) 6.00000 13.8564i 0.217643 0.502625i
\(761\) 8.66025i 0.313934i −0.987604 0.156967i \(-0.949828\pi\)
0.987604 0.156967i \(-0.0501716\pi\)
\(762\) 9.00000 + 15.5885i 0.326036 + 0.564710i
\(763\) 0 0
\(764\) −6.00000 + 3.46410i −0.217072 + 0.125327i
\(765\) 72.0000 2.60317
\(766\) 9.00000 + 15.5885i 0.325183 + 0.563234i
\(767\) 10.3923i 0.375244i
\(768\) 1.50000 + 0.866025i 0.0541266 + 0.0312500i
\(769\) 7.00000 + 12.1244i 0.252426 + 0.437215i 0.964193 0.265200i \(-0.0854381\pi\)
−0.711767 + 0.702416i \(0.752105\pi\)
\(770\) −6.00000 10.3923i −0.216225 0.374513i
\(771\) −22.5000 12.9904i −0.810318 0.467837i
\(772\) 20.7846i 0.748054i
\(773\) −3.00000 5.19615i −0.107903 0.186893i 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) −24.0000 −0.862662
\(775\) 42.0000 24.2487i 1.50868 0.871039i
\(776\) 7.50000 + 4.33013i 0.269234 + 0.155443i