Properties

Label 845.2.n.b.484.1
Level $845$
Weight $2$
Character 845.484
Analytic conductor $6.747$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 484.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 845.484
Dual form 845.2.n.b.529.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 - 1.00000i) q^{5} +(1.00000 - 1.73205i) q^{6} -3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-1.73205 + 1.00000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 - 1.00000i) q^{5} +(1.00000 - 1.73205i) q^{6} -3.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.23205 + 1.86603i) q^{10} +(1.00000 + 1.73205i) q^{11} -2.00000i q^{12} +(-2.46410 + 3.73205i) q^{15} +(0.500000 + 0.866025i) q^{16} +1.00000i q^{18} +(3.00000 - 5.19615i) q^{19} +(-0.133975 + 2.23205i) q^{20} +(-1.73205 - 1.00000i) q^{22} +(5.19615 - 3.00000i) q^{23} +(3.00000 + 5.19615i) q^{24} +(3.00000 - 4.00000i) q^{25} -4.00000i q^{27} +(-3.00000 - 5.19615i) q^{29} +(0.267949 - 4.46410i) q^{30} +6.00000 q^{31} +(4.33013 + 2.50000i) q^{32} +(-3.46410 - 2.00000i) q^{33} +(0.500000 + 0.866025i) q^{36} +(-5.19615 + 3.00000i) q^{37} +6.00000i q^{38} +(-3.00000 - 6.00000i) q^{40} +(4.00000 + 6.92820i) q^{41} +(5.19615 + 3.00000i) q^{43} -2.00000 q^{44} +(0.133975 - 2.23205i) q^{45} +(-3.00000 + 5.19615i) q^{46} +8.00000i q^{47} +(-1.73205 - 1.00000i) q^{48} +(-3.50000 - 6.06218i) q^{49} +(-0.598076 + 4.96410i) q^{50} +12.0000i q^{53} +(2.00000 + 3.46410i) q^{54} +(3.73205 + 2.46410i) q^{55} +12.0000i q^{57} +(5.19615 + 3.00000i) q^{58} +(1.00000 - 1.73205i) q^{59} +(-2.00000 - 4.00000i) q^{60} +(-3.00000 + 5.19615i) q^{61} +(-5.19615 + 3.00000i) q^{62} -7.00000 q^{64} +4.00000 q^{66} +(10.3923 - 6.00000i) q^{67} +(-6.00000 + 10.3923i) q^{69} +(1.00000 - 1.73205i) q^{71} +(-2.59808 - 1.50000i) q^{72} +6.00000i q^{73} +(3.00000 - 5.19615i) q^{74} +(-1.19615 + 9.92820i) q^{75} +(3.00000 + 5.19615i) q^{76} +(1.86603 + 1.23205i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-6.92820 - 4.00000i) q^{82} -4.00000i q^{83} -6.00000 q^{86} +(10.3923 + 6.00000i) q^{87} +(5.19615 - 3.00000i) q^{88} +(-4.00000 - 6.92820i) q^{89} +(1.00000 + 2.00000i) q^{90} +6.00000i q^{92} +(-10.3923 + 6.00000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(0.803848 - 13.3923i) q^{95} -10.0000 q^{96} +(5.19615 + 3.00000i) q^{97} +(6.06218 + 3.50000i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{4} + 8 q^{5} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{4} + 8 q^{5} + 4 q^{6} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{15} + 2 q^{16} + 12 q^{19} - 4 q^{20} + 12 q^{24} + 12 q^{25} - 12 q^{29} + 8 q^{30} + 24 q^{31} + 2 q^{36} - 12 q^{40} + 16 q^{41} - 8 q^{44} + 4 q^{45} - 12 q^{46} - 14 q^{49} + 8 q^{50} + 8 q^{54} + 8 q^{55} + 4 q^{59} - 8 q^{60} - 12 q^{61} - 28 q^{64} + 16 q^{66} - 24 q^{69} + 4 q^{71} + 12 q^{74} + 16 q^{75} + 12 q^{76} + 4 q^{80} + 22 q^{81} - 24 q^{86} - 16 q^{89} + 4 q^{90} - 16 q^{94} + 24 q^{95} - 40 q^{96} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i −0.773893 0.633316i \(-0.781693\pi\)
0.161521 + 0.986869i \(0.448360\pi\)
\(3\) −1.73205 + 1.00000i −1.00000 + 0.577350i −0.908248 0.418432i \(-0.862580\pi\)
−0.0917517 + 0.995782i \(0.529247\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 1.00000 1.73205i 0.408248 0.707107i
\(7\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 3.00000i 1.06066i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −1.23205 + 1.86603i −0.389609 + 0.590089i
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 2.00000i 0.577350i
\(13\) 0 0
\(14\) 0 0
\(15\) −2.46410 + 3.73205i −0.636228 + 0.963611i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) −0.133975 + 2.23205i −0.0299576 + 0.499102i
\(21\) 0 0
\(22\) −1.73205 1.00000i −0.369274 0.213201i
\(23\) 5.19615 3.00000i 1.08347 0.625543i 0.151642 0.988436i \(-0.451544\pi\)
0.931831 + 0.362892i \(0.118211\pi\)
\(24\) 3.00000 + 5.19615i 0.612372 + 1.06066i
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 0 0
\(27\) 4.00000i 0.769800i
\(28\) 0 0
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0.267949 4.46410i 0.0489206 0.815030i
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 4.33013 + 2.50000i 0.765466 + 0.441942i
\(33\) −3.46410 2.00000i −0.603023 0.348155i
\(34\) 0 0
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −5.19615 + 3.00000i −0.854242 + 0.493197i −0.862080 0.506772i \(-0.830838\pi\)
0.00783774 + 0.999969i \(0.497505\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −3.00000 6.00000i −0.474342 0.948683i
\(41\) 4.00000 + 6.92820i 0.624695 + 1.08200i 0.988600 + 0.150567i \(0.0481100\pi\)
−0.363905 + 0.931436i \(0.618557\pi\)
\(42\) 0 0
\(43\) 5.19615 + 3.00000i 0.792406 + 0.457496i 0.840809 0.541332i \(-0.182080\pi\)
−0.0484030 + 0.998828i \(0.515413\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0.133975 2.23205i 0.0199718 0.332734i
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) −1.73205 1.00000i −0.250000 0.144338i
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) −0.598076 + 4.96410i −0.0845807 + 0.702030i
\(51\) 0 0
\(52\) 0 0
\(53\) 12.0000i 1.64833i 0.566352 + 0.824163i \(0.308354\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(54\) 2.00000 + 3.46410i 0.272166 + 0.471405i
\(55\) 3.73205 + 2.46410i 0.503230 + 0.332259i
\(56\) 0 0
\(57\) 12.0000i 1.58944i
\(58\) 5.19615 + 3.00000i 0.682288 + 0.393919i
\(59\) 1.00000 1.73205i 0.130189 0.225494i −0.793560 0.608492i \(-0.791775\pi\)
0.923749 + 0.382998i \(0.125108\pi\)
\(60\) −2.00000 4.00000i −0.258199 0.516398i
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) −5.19615 + 3.00000i −0.659912 + 0.381000i
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) 0 0
\(66\) 4.00000 0.492366
\(67\) 10.3923 6.00000i 1.26962 0.733017i 0.294706 0.955588i \(-0.404778\pi\)
0.974916 + 0.222571i \(0.0714450\pi\)
\(68\) 0 0
\(69\) −6.00000 + 10.3923i −0.722315 + 1.25109i
\(70\) 0 0
\(71\) 1.00000 1.73205i 0.118678 0.205557i −0.800566 0.599245i \(-0.795468\pi\)
0.919244 + 0.393688i \(0.128801\pi\)
\(72\) −2.59808 1.50000i −0.306186 0.176777i
\(73\) 6.00000i 0.702247i 0.936329 + 0.351123i \(0.114200\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 3.00000 5.19615i 0.348743 0.604040i
\(75\) −1.19615 + 9.92820i −0.138120 + 1.14641i
\(76\) 3.00000 + 5.19615i 0.344124 + 0.596040i
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 1.86603 + 1.23205i 0.208628 + 0.137747i
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) −6.92820 4.00000i −0.765092 0.441726i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −6.00000 −0.646997
\(87\) 10.3923 + 6.00000i 1.11417 + 0.643268i
\(88\) 5.19615 3.00000i 0.553912 0.319801i
\(89\) −4.00000 6.92820i −0.423999 0.734388i 0.572327 0.820025i \(-0.306041\pi\)
−0.996326 + 0.0856373i \(0.972707\pi\)
\(90\) 1.00000 + 2.00000i 0.105409 + 0.210819i
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) −10.3923 + 6.00000i −1.07763 + 0.622171i
\(94\) −4.00000 6.92820i −0.412568 0.714590i
\(95\) 0.803848 13.3923i 0.0824730 1.37402i
\(96\) −10.0000 −1.02062
\(97\) 5.19615 + 3.00000i 0.527589 + 0.304604i 0.740034 0.672569i \(-0.234809\pi\)
−0.212445 + 0.977173i \(0.568143\pi\)
\(98\) 6.06218 + 3.50000i 0.612372 + 0.353553i
\(99\) 2.00000 0.201008
\(100\) 1.96410 + 4.59808i 0.196410 + 0.459808i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −6.00000 10.3923i −0.582772 1.00939i
\(107\) 5.19615 3.00000i 0.502331 0.290021i −0.227345 0.973814i \(-0.573004\pi\)
0.729676 + 0.683793i \(0.239671\pi\)
\(108\) 3.46410 + 2.00000i 0.333333 + 0.192450i
\(109\) 12.0000 1.14939 0.574696 0.818367i \(-0.305120\pi\)
0.574696 + 0.818367i \(0.305120\pi\)
\(110\) −4.46410 0.267949i −0.425635 0.0255480i
\(111\) 6.00000 10.3923i 0.569495 0.986394i
\(112\) 0 0
\(113\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(114\) −6.00000 10.3923i −0.561951 0.973329i
\(115\) 7.39230 11.1962i 0.689336 1.04405i
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) 2.00000i 0.184115i
\(119\) 0 0
\(120\) 11.1962 + 7.39230i 1.02206 + 0.674822i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 6.00000i 0.543214i
\(123\) −13.8564 8.00000i −1.24939 0.721336i
\(124\) −3.00000 + 5.19615i −0.269408 + 0.466628i
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) −1.73205 + 1.00000i −0.153695 + 0.0887357i −0.574875 0.818241i \(-0.694949\pi\)
0.421180 + 0.906977i \(0.361616\pi\)
\(128\) −2.59808 + 1.50000i −0.229640 + 0.132583i
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 3.46410 2.00000i 0.301511 0.174078i
\(133\) 0 0
\(134\) −6.00000 + 10.3923i −0.518321 + 0.897758i
\(135\) −4.00000 8.00000i −0.344265 0.688530i
\(136\) 0 0
\(137\) 1.73205 + 1.00000i 0.147979 + 0.0854358i 0.572161 0.820141i \(-0.306105\pi\)
−0.424182 + 0.905577i \(0.639438\pi\)
\(138\) 12.0000i 1.02151i
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 0 0
\(141\) −8.00000 13.8564i −0.673722 1.16692i
\(142\) 2.00000i 0.167836i
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −11.1962 7.39230i −0.929790 0.613898i
\(146\) −3.00000 5.19615i −0.248282 0.430037i
\(147\) 12.1244 + 7.00000i 1.00000 + 0.577350i
\(148\) 6.00000i 0.493197i
\(149\) −10.0000 + 17.3205i −0.819232 + 1.41895i 0.0870170 + 0.996207i \(0.472267\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(150\) −3.92820 9.19615i −0.320736 0.750863i
\(151\) 18.0000 1.46482 0.732410 0.680864i \(-0.238396\pi\)
0.732410 + 0.680864i \(0.238396\pi\)
\(152\) −15.5885 9.00000i −1.26439 0.729996i
\(153\) 0 0
\(154\) 0 0
\(155\) 12.0000 6.00000i 0.963863 0.481932i
\(156\) 0 0
\(157\) 12.0000i 0.957704i −0.877896 0.478852i \(-0.841053\pi\)
0.877896 0.478852i \(-0.158947\pi\)
\(158\) 0 0
\(159\) −12.0000 20.7846i −0.951662 1.64833i
\(160\) 11.1603 + 0.669873i 0.882296 + 0.0529581i
\(161\) 0 0
\(162\) −9.52628 5.50000i −0.748455 0.432121i
\(163\) 10.3923 + 6.00000i 0.813988 + 0.469956i 0.848339 0.529454i \(-0.177603\pi\)
−0.0343508 + 0.999410i \(0.510936\pi\)
\(164\) −8.00000 −0.624695
\(165\) −8.92820 0.535898i −0.695060 0.0417196i
\(166\) 2.00000 + 3.46410i 0.155230 + 0.268866i
\(167\) 13.8564 8.00000i 1.07224 0.619059i 0.143448 0.989658i \(-0.454181\pi\)
0.928793 + 0.370599i \(0.120848\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) −5.19615 + 3.00000i −0.396203 + 0.228748i
\(173\) −10.3923 6.00000i −0.790112 0.456172i 0.0498898 0.998755i \(-0.484113\pi\)
−0.840002 + 0.542583i \(0.817446\pi\)
\(174\) −12.0000 −0.909718
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 4.00000i 0.300658i
\(178\) 6.92820 + 4.00000i 0.519291 + 0.299813i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 1.86603 + 1.23205i 0.139085 + 0.0918316i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 12.0000i 0.887066i
\(184\) −9.00000 15.5885i −0.663489 1.14920i
\(185\) −7.39230 + 11.1962i −0.543493 + 0.823157i
\(186\) 6.00000 10.3923i 0.439941 0.762001i
\(187\) 0 0
\(188\) −6.92820 4.00000i −0.505291 0.291730i
\(189\) 0 0
\(190\) 6.00000 + 12.0000i 0.435286 + 0.870572i
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 12.1244 7.00000i 0.875000 0.505181i
\(193\) 5.19615 3.00000i 0.374027 0.215945i −0.301189 0.953564i \(-0.597384\pi\)
0.675216 + 0.737620i \(0.264050\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) −1.73205 + 1.00000i −0.123404 + 0.0712470i −0.560431 0.828201i \(-0.689365\pi\)
0.437028 + 0.899448i \(0.356031\pi\)
\(198\) −1.73205 + 1.00000i −0.123091 + 0.0710669i
\(199\) −12.0000 + 20.7846i −0.850657 + 1.47338i 0.0299585 + 0.999551i \(0.490462\pi\)
−0.880616 + 0.473831i \(0.842871\pi\)
\(200\) −12.0000 9.00000i −0.848528 0.636396i
\(201\) −12.0000 + 20.7846i −0.846415 + 1.46603i
\(202\) −5.19615 3.00000i −0.365600 0.211079i
\(203\) 0 0
\(204\) 0 0
\(205\) 14.9282 + 9.85641i 1.04263 + 0.688401i
\(206\) −3.00000 5.19615i −0.209020 0.362033i
\(207\) 6.00000i 0.417029i
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 6.00000 + 10.3923i 0.413057 + 0.715436i 0.995222 0.0976347i \(-0.0311277\pi\)
−0.582165 + 0.813070i \(0.697794\pi\)
\(212\) −10.3923 6.00000i −0.713746 0.412082i
\(213\) 4.00000i 0.274075i
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 13.3923 + 0.803848i 0.913348 + 0.0548219i
\(216\) −12.0000 −0.816497
\(217\) 0 0
\(218\) −10.3923 + 6.00000i −0.703856 + 0.406371i
\(219\) −6.00000 10.3923i −0.405442 0.702247i
\(220\) −4.00000 + 2.00000i −0.269680 + 0.134840i
\(221\) 0 0
\(222\) 12.0000i 0.805387i
\(223\) 20.7846 12.0000i 1.39184 0.803579i 0.398321 0.917246i \(-0.369593\pi\)
0.993519 + 0.113666i \(0.0362595\pi\)
\(224\) 0 0
\(225\) −1.96410 4.59808i −0.130940 0.306538i
\(226\) 0 0
\(227\) 3.46410 + 2.00000i 0.229920 + 0.132745i 0.610535 0.791989i \(-0.290954\pi\)
−0.380615 + 0.924734i \(0.624288\pi\)
\(228\) −10.3923 6.00000i −0.688247 0.397360i
\(229\) 12.0000 0.792982 0.396491 0.918039i \(-0.370228\pi\)
0.396491 + 0.918039i \(0.370228\pi\)
\(230\) −0.803848 + 13.3923i −0.0530041 + 0.883062i
\(231\) 0 0
\(232\) −15.5885 + 9.00000i −1.02343 + 0.590879i
\(233\) 24.0000i 1.57229i −0.618041 0.786146i \(-0.712073\pi\)
0.618041 0.786146i \(-0.287927\pi\)
\(234\) 0 0
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) 1.00000 + 1.73205i 0.0650945 + 0.112747i
\(237\) 0 0
\(238\) 0 0
\(239\) −10.0000 −0.646846 −0.323423 0.946254i \(-0.604834\pi\)
−0.323423 + 0.946254i \(0.604834\pi\)
\(240\) −4.46410 0.267949i −0.288157 0.0172960i
\(241\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) 7.00000i 0.449977i
\(243\) −8.66025 5.00000i −0.555556 0.320750i
\(244\) −3.00000 5.19615i −0.192055 0.332650i
\(245\) −13.0622 8.62436i −0.834512 0.550990i
\(246\) 16.0000 1.02012
\(247\) 0 0
\(248\) 18.0000i 1.14300i
\(249\) 4.00000 + 6.92820i 0.253490 + 0.439057i
\(250\) 3.76795 + 10.5263i 0.238306 + 0.665740i
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) 0 0
\(253\) 10.3923 + 6.00000i 0.653359 + 0.377217i
\(254\) 1.00000 1.73205i 0.0627456 0.108679i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(258\) 10.3923 6.00000i 0.646997 0.373544i
\(259\) 0 0
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 10.3923 6.00000i 0.642039 0.370681i
\(263\) −5.19615 + 3.00000i −0.320408 + 0.184988i −0.651575 0.758585i \(-0.725891\pi\)
0.331166 + 0.943572i \(0.392558\pi\)
\(264\) −6.00000 + 10.3923i −0.369274 + 0.639602i
\(265\) 12.0000 + 24.0000i 0.737154 + 1.47431i
\(266\) 0 0
\(267\) 13.8564 + 8.00000i 0.847998 + 0.489592i
\(268\) 12.0000i 0.733017i
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 7.46410 + 4.92820i 0.454251 + 0.299921i
\(271\) 3.00000 + 5.19615i 0.182237 + 0.315644i 0.942642 0.333805i \(-0.108333\pi\)
−0.760405 + 0.649449i \(0.775000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 9.92820 + 1.19615i 0.598693 + 0.0721307i
\(276\) −6.00000 10.3923i −0.361158 0.625543i
\(277\) 10.3923 + 6.00000i 0.624413 + 0.360505i 0.778585 0.627539i \(-0.215938\pi\)
−0.154172 + 0.988044i \(0.549271\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 3.00000 5.19615i 0.179605 0.311086i
\(280\) 0 0
\(281\) −8.00000 −0.477240 −0.238620 0.971113i \(-0.576695\pi\)
−0.238620 + 0.971113i \(0.576695\pi\)
\(282\) 13.8564 + 8.00000i 0.825137 + 0.476393i
\(283\) −19.0526 + 11.0000i −1.13256 + 0.653882i −0.944577 0.328291i \(-0.893527\pi\)
−0.187980 + 0.982173i \(0.560194\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) 12.0000 + 24.0000i 0.710819 + 1.42164i
\(286\) 0 0
\(287\) 0 0
\(288\) 4.33013 2.50000i 0.255155 0.147314i
\(289\) −8.50000 14.7224i −0.500000 0.866025i
\(290\) 13.3923 + 0.803848i 0.786423 + 0.0472036i
\(291\) −12.0000 −0.703452
\(292\) −5.19615 3.00000i −0.304082 0.175562i
\(293\) −22.5167 13.0000i −1.31544 0.759468i −0.332446 0.943122i \(-0.607874\pi\)
−0.982991 + 0.183654i \(0.941207\pi\)
\(294\) −14.0000 −0.816497
\(295\) 0.267949 4.46410i 0.0156006 0.259910i
\(296\) 9.00000 + 15.5885i 0.523114 + 0.906061i
\(297\) 6.92820 4.00000i 0.402015 0.232104i
\(298\) 20.0000i 1.15857i
\(299\) 0 0
\(300\) −8.00000 6.00000i −0.461880 0.346410i
\(301\) 0 0
\(302\) −15.5885 + 9.00000i −0.897015 + 0.517892i
\(303\) −10.3923 6.00000i −0.597022 0.344691i
\(304\) 6.00000 0.344124
\(305\) −0.803848 + 13.3923i −0.0460282 + 0.766841i
\(306\) 0 0
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 0 0
\(309\) −6.00000 10.3923i −0.341328 0.591198i
\(310\) −7.39230 + 11.1962i −0.419855 + 0.635899i
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) 6.00000 + 10.3923i 0.338600 + 0.586472i
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000i 0.112331i −0.998421 0.0561656i \(-0.982113\pi\)
0.998421 0.0561656i \(-0.0178875\pi\)
\(318\) 20.7846 + 12.0000i 1.16554 + 0.672927i
\(319\) 6.00000 10.3923i 0.335936 0.581857i
\(320\) −14.0000 + 7.00000i −0.782624 + 0.391312i
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) 0 0
\(323\) 0 0
\(324\) −11.0000 −0.611111
\(325\) 0 0
\(326\) −12.0000 −0.664619
\(327\) −20.7846 + 12.0000i −1.14939 + 0.663602i
\(328\) 20.7846 12.0000i 1.14764 0.662589i
\(329\) 0 0
\(330\) 8.00000 4.00000i 0.440386 0.220193i
\(331\) 15.0000 25.9808i 0.824475 1.42803i −0.0778456 0.996965i \(-0.524804\pi\)
0.902320 0.431066i \(-0.141863\pi\)
\(332\) 3.46410 + 2.00000i 0.190117 + 0.109764i
\(333\) 6.00000i 0.328798i
\(334\) −8.00000 + 13.8564i −0.437741 + 0.758189i
\(335\) 14.7846 22.3923i 0.807770 1.22342i
\(336\) 0 0
\(337\) 32.0000i 1.74315i 0.490261 + 0.871576i \(0.336901\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) 5.19615 + 3.00000i 0.280976 + 0.162221i
\(343\) 0 0
\(344\) 9.00000 15.5885i 0.485247 0.840473i
\(345\) −1.60770 + 26.7846i −0.0865554 + 1.44203i
\(346\) 12.0000 0.645124
\(347\) −5.19615 3.00000i −0.278944 0.161048i 0.354001 0.935245i \(-0.384821\pi\)
−0.632945 + 0.774197i \(0.718154\pi\)
\(348\) −10.3923 + 6.00000i −0.557086 + 0.321634i
\(349\) 6.00000 + 10.3923i 0.321173 + 0.556287i 0.980730 0.195367i \(-0.0625897\pi\)
−0.659558 + 0.751654i \(0.729256\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000i 0.533002i
\(353\) −12.1244 + 7.00000i −0.645314 + 0.372572i −0.786659 0.617388i \(-0.788191\pi\)
0.141344 + 0.989960i \(0.454858\pi\)
\(354\) −2.00000 3.46410i −0.106299 0.184115i
\(355\) 0.267949 4.46410i 0.0142213 0.236930i
\(356\) 8.00000 0.423999
\(357\) 0 0
\(358\) 10.3923 + 6.00000i 0.549250 + 0.317110i
\(359\) 2.00000 0.105556 0.0527780 0.998606i \(-0.483192\pi\)
0.0527780 + 0.998606i \(0.483192\pi\)
\(360\) −6.69615 0.401924i −0.352918 0.0211832i
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) −1.73205 + 1.00000i −0.0910346 + 0.0525588i
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) 6.00000 + 12.0000i 0.314054 + 0.628109i
\(366\) 6.00000 + 10.3923i 0.313625 + 0.543214i
\(367\) 15.5885 9.00000i 0.813711 0.469796i −0.0345320 0.999404i \(-0.510994\pi\)
0.848243 + 0.529607i \(0.177661\pi\)
\(368\) 5.19615 + 3.00000i 0.270868 + 0.156386i
\(369\) 8.00000 0.416463
\(370\) 0.803848 13.3923i 0.0417900 0.696233i
\(371\) 0 0
\(372\) 12.0000i 0.622171i
\(373\) 3.46410 + 2.00000i 0.179364 + 0.103556i 0.586994 0.809591i \(-0.300311\pi\)
−0.407630 + 0.913147i \(0.633645\pi\)
\(374\) 0 0
\(375\) 7.53590 + 21.0526i 0.389152 + 1.08715i
\(376\) 24.0000 1.23771
\(377\) 0 0
\(378\) 0 0
\(379\) −9.00000 15.5885i −0.462299 0.800725i 0.536776 0.843725i \(-0.319642\pi\)
−0.999075 + 0.0429994i \(0.986309\pi\)
\(380\) 11.1962 + 7.39230i 0.574351 + 0.379217i
\(381\) 2.00000 3.46410i 0.102463 0.177471i
\(382\) 0 0
\(383\) −6.92820 4.00000i −0.354015 0.204390i 0.312437 0.949938i \(-0.398855\pi\)
−0.666452 + 0.745548i \(0.732188\pi\)
\(384\) 3.00000 5.19615i 0.153093 0.265165i
\(385\) 0 0
\(386\) −3.00000 + 5.19615i −0.152696 + 0.264477i
\(387\) 5.19615 3.00000i 0.264135 0.152499i
\(388\) −5.19615 + 3.00000i −0.263795 + 0.152302i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −18.1865 + 10.5000i −0.918559 + 0.530330i
\(393\) 20.7846 12.0000i 1.04844 0.605320i
\(394\) 1.00000 1.73205i 0.0503793 0.0872595i
\(395\) 0 0
\(396\) −1.00000 + 1.73205i −0.0502519 + 0.0870388i
\(397\) −15.5885 9.00000i −0.782362 0.451697i 0.0549046 0.998492i \(-0.482515\pi\)
−0.837267 + 0.546795i \(0.815848\pi\)
\(398\) 24.0000i 1.20301i
\(399\) 0 0
\(400\) 4.96410 + 0.598076i 0.248205 + 0.0299038i
\(401\) 8.00000 + 13.8564i 0.399501 + 0.691956i 0.993664 0.112388i \(-0.0358501\pi\)
−0.594163 + 0.804344i \(0.702517\pi\)
\(402\) 24.0000i 1.19701i
\(403\) 0 0
\(404\) −6.00000 −0.298511
\(405\) 20.5263 + 13.5526i 1.01996 + 0.673432i
\(406\) 0 0
\(407\) −10.3923 6.00000i −0.515127 0.297409i
\(408\) 0 0
\(409\) 12.0000 20.7846i 0.593362 1.02773i −0.400414 0.916334i \(-0.631134\pi\)
0.993776 0.111398i \(-0.0355330\pi\)
\(410\) −17.8564 1.07180i −0.881865 0.0529323i
\(411\) −4.00000 −0.197305
\(412\) −5.19615 3.00000i −0.255996 0.147799i
\(413\) 0 0
\(414\) 3.00000 + 5.19615i 0.147442 + 0.255377i
\(415\) −4.00000 8.00000i −0.196352 0.392705i
\(416\) 0 0
\(417\) 8.00000i 0.391762i
\(418\) −10.3923 + 6.00000i −0.508304 + 0.293470i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 0 0
\(421\) 36.0000 1.75453 0.877266 0.480004i \(-0.159365\pi\)
0.877266 + 0.480004i \(0.159365\pi\)
\(422\) −10.3923 6.00000i −0.505889 0.292075i
\(423\) 6.92820 + 4.00000i 0.336861 + 0.194487i
\(424\) 36.0000 1.74831
\(425\) 0 0
\(426\) −2.00000 3.46410i −0.0969003 0.167836i
\(427\) 0 0
\(428\) 6.00000i 0.290021i
\(429\) 0 0
\(430\) −12.0000 + 6.00000i −0.578691 + 0.289346i
\(431\) 5.00000 + 8.66025i 0.240842 + 0.417150i 0.960954 0.276707i \(-0.0892433\pi\)
−0.720113 + 0.693857i \(0.755910\pi\)
\(432\) 3.46410 2.00000i 0.166667 0.0962250i
\(433\) −13.8564 8.00000i −0.665896 0.384455i 0.128624 0.991693i \(-0.458944\pi\)
−0.794520 + 0.607238i \(0.792277\pi\)
\(434\) 0 0
\(435\) 26.7846 + 1.60770i 1.28422 + 0.0770831i
\(436\) −6.00000 + 10.3923i −0.287348 + 0.497701i
\(437\) 36.0000i 1.72211i
\(438\) 10.3923 + 6.00000i 0.496564 + 0.286691i
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 7.39230 11.1962i 0.352414 0.533756i
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) 6.00000i 0.285069i 0.989790 + 0.142534i \(0.0455251\pi\)
−0.989790 + 0.142534i \(0.954475\pi\)
\(444\) 6.00000 + 10.3923i 0.284747 + 0.493197i
\(445\) −14.9282 9.85641i −0.707665 0.467238i
\(446\) −12.0000 + 20.7846i −0.568216 + 0.984180i
\(447\) 40.0000i 1.89194i
\(448\) 0 0
\(449\) −8.00000 + 13.8564i −0.377543 + 0.653924i −0.990704 0.136034i \(-0.956564\pi\)
0.613161 + 0.789958i \(0.289898\pi\)
\(450\) 4.00000 + 3.00000i 0.188562 + 0.141421i
\(451\) −8.00000 + 13.8564i −0.376705 + 0.652473i
\(452\) 0 0
\(453\) −31.1769 + 18.0000i −1.46482 + 0.845714i
\(454\) −4.00000 −0.187729
\(455\) 0 0
\(456\) 36.0000 1.68585
\(457\) −25.9808 + 15.0000i −1.21533 + 0.701670i −0.963915 0.266209i \(-0.914229\pi\)
−0.251414 + 0.967880i \(0.580895\pi\)
\(458\) −10.3923 + 6.00000i −0.485601 + 0.280362i
\(459\) 0 0
\(460\) 6.00000 + 12.0000i 0.279751 + 0.559503i
\(461\) 2.00000 3.46410i 0.0931493 0.161339i −0.815685 0.578496i \(-0.803640\pi\)
0.908835 + 0.417156i \(0.136973\pi\)
\(462\) 0 0
\(463\) 24.0000i 1.11537i 0.830051 + 0.557687i \(0.188311\pi\)
−0.830051 + 0.557687i \(0.811689\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) −14.7846 + 22.3923i −0.685620 + 1.03842i
\(466\) 12.0000 + 20.7846i 0.555889 + 0.962828i
\(467\) 18.0000i 0.832941i 0.909149 + 0.416470i \(0.136733\pi\)
−0.909149 + 0.416470i \(0.863267\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −14.9282 9.85641i −0.688587 0.454642i
\(471\) 12.0000 + 20.7846i 0.552931 + 0.957704i
\(472\) −5.19615 3.00000i −0.239172 0.138086i
\(473\) 12.0000i 0.551761i
\(474\) 0 0
\(475\) −11.7846 27.5885i −0.540715 1.26585i
\(476\) 0 0
\(477\) 10.3923 + 6.00000i 0.475831 + 0.274721i
\(478\) 8.66025 5.00000i 0.396111 0.228695i
\(479\) 11.0000 + 19.0526i 0.502603 + 0.870534i 0.999995 + 0.00300810i \(0.000957509\pi\)
−0.497393 + 0.867526i \(0.665709\pi\)
\(480\) −20.0000 + 10.0000i −0.912871 + 0.456435i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 13.3923 + 0.803848i 0.608113 + 0.0365008i
\(486\) 10.0000 0.453609
\(487\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 15.5885 + 9.00000i 0.705656 + 0.407411i
\(489\) −24.0000 −1.08532
\(490\) 15.6244 + 0.937822i 0.705836 + 0.0423665i
\(491\) 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) 13.8564 8.00000i 0.624695 0.360668i
\(493\) 0 0
\(494\) 0 0
\(495\) 4.00000 2.00000i 0.179787 0.0898933i
\(496\) 3.00000 + 5.19615i 0.134704 + 0.233314i
\(497\) 0 0
\(498\) −6.92820 4.00000i −0.310460 0.179244i
\(499\) −6.00000 −0.268597 −0.134298 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) 8.52628 + 7.23205i 0.381307 + 0.323427i
\(501\) −16.0000 + 27.7128i −0.714827 + 1.23812i
\(502\) 12.0000i 0.535586i
\(503\) 5.19615 + 3.00000i 0.231685 + 0.133763i 0.611349 0.791361i \(-0.290627\pi\)
−0.379664 + 0.925124i \(0.623960\pi\)
\(504\) 0 0
\(505\) 11.1962 + 7.39230i 0.498222 + 0.328953i
\(506\) −12.0000 −0.533465
\(507\) 0 0
\(508\) 2.00000i 0.0887357i
\(509\) 10.0000 + 17.3205i 0.443242 + 0.767718i 0.997928 0.0643419i \(-0.0204948\pi\)
−0.554686 + 0.832060i \(0.687161\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.0000i 0.486136i
\(513\) −20.7846 12.0000i −0.917663 0.529813i
\(514\) 0 0
\(515\) 6.00000 + 12.0000i 0.264392 + 0.528783i
\(516\) 6.00000 10.3923i 0.264135 0.457496i
\(517\) −13.8564 + 8.00000i −0.609404 + 0.351840i
\(518\) 0 0
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 5.19615 3.00000i 0.227429 0.131306i
\(523\) −36.3731 + 21.0000i −1.59048 + 0.918266i −0.597259 + 0.802048i \(0.703744\pi\)
−0.993224 + 0.116218i \(0.962923\pi\)
\(524\) 6.00000 10.3923i 0.262111 0.453990i
\(525\) 0 0
\(526\) 3.00000 5.19615i 0.130806 0.226563i
\(527\) 0 0
\(528\) 4.00000i 0.174078i
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) −22.3923 14.7846i −0.972660 0.642202i
\(531\) −1.00000 1.73205i −0.0433963 0.0751646i
\(532\) 0 0
\(533\) 0 0
\(534\) −16.0000 −0.692388
\(535\) 7.39230 11.1962i 0.319597 0.484052i
\(536\) −18.0000 31.1769i −0.777482 1.34664i
\(537\) 20.7846 + 12.0000i 0.896922 + 0.517838i
\(538\) 18.0000i 0.776035i
\(539\) 7.00000 12.1244i 0.301511 0.522233i
\(540\) 8.92820 + 0.535898i 0.384209 + 0.0230614i
\(541\) −12.0000 −0.515920 −0.257960 0.966156i \(-0.583050\pi\)
−0.257960 + 0.966156i \(0.583050\pi\)
\(542\) −5.19615 3.00000i −0.223194 0.128861i
\(543\) −3.46410 + 2.00000i −0.148659 + 0.0858282i
\(544\) 0 0
\(545\) 24.0000 12.0000i 1.02805 0.514024i
\(546\) 0 0
\(547\) 18.0000i 0.769624i −0.922995 0.384812i \(-0.874266\pi\)
0.922995 0.384812i \(-0.125734\pi\)
\(548\) −1.73205 + 1.00000i −0.0739895 + 0.0427179i
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) −9.19615 + 3.92820i −0.392125 + 0.167499i
\(551\) −36.0000 −1.53365
\(552\) 31.1769 + 18.0000i 1.32698 + 0.766131i
\(553\) 0 0
\(554\) −12.0000 −0.509831
\(555\) 1.60770 26.7846i 0.0682429 1.13694i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −12.1244 + 7.00000i −0.513725 + 0.296600i −0.734364 0.678756i \(-0.762519\pi\)
0.220638 + 0.975356i \(0.429186\pi\)
\(558\) 6.00000i 0.254000i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 6.92820 4.00000i 0.292249 0.168730i
\(563\) 25.9808 + 15.0000i 1.09496 + 0.632175i 0.934892 0.354932i \(-0.115496\pi\)
0.160066 + 0.987106i \(0.448829\pi\)
\(564\) 16.0000 0.673722
\(565\) 0 0
\(566\) 11.0000 19.0526i 0.462364 0.800839i
\(567\) 0 0
\(568\) −5.19615 3.00000i −0.218026 0.125877i
\(569\) 9.00000 + 15.5885i 0.377300 + 0.653502i 0.990668 0.136295i \(-0.0435194\pi\)
−0.613369 + 0.789797i \(0.710186\pi\)
\(570\) −22.3923 14.7846i −0.937910 0.619259i
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 3.58846 29.7846i 0.149649 1.24210i
\(576\) −3.50000 + 6.06218i −0.145833 + 0.252591i
\(577\) 18.0000i 0.749350i 0.927156 + 0.374675i \(0.122246\pi\)
−0.927156 + 0.374675i \(0.877754\pi\)
\(578\) 14.7224 + 8.50000i 0.612372 + 0.353553i
\(579\) −6.00000 + 10.3923i −0.249351 + 0.431889i
\(580\) 12.0000 6.00000i 0.498273 0.249136i
\(581\) 0 0
\(582\) 10.3923 6.00000i 0.430775 0.248708i
\(583\) −20.7846 + 12.0000i −0.860811 + 0.496989i
\(584\) 18.0000 0.744845
\(585\) 0 0
\(586\) 26.0000 1.07405
\(587\) 17.3205 10.0000i 0.714894 0.412744i −0.0979766 0.995189i \(-0.531237\pi\)
0.812870 + 0.582445i \(0.197904\pi\)
\(588\) −12.1244 + 7.00000i −0.500000 + 0.288675i
\(589\) 18.0000 31.1769i 0.741677 1.28462i
\(590\) 2.00000 + 4.00000i 0.0823387 + 0.164677i
\(591\) 2.00000 3.46410i 0.0822690 0.142494i
\(592\) −5.19615 3.00000i −0.213561 0.123299i
\(593\) 22.0000i 0.903432i 0.892162 + 0.451716i \(0.149188\pi\)
−0.892162 + 0.451716i \(0.850812\pi\)
\(594\) −4.00000 + 6.92820i −0.164122 + 0.284268i
\(595\) 0 0
\(596\) −10.0000 17.3205i −0.409616 0.709476i
\(597\) 48.0000i 1.96451i
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 29.7846 + 3.58846i 1.21595 + 0.146498i
\(601\) 3.00000 + 5.19615i 0.122373 + 0.211955i 0.920703 0.390264i \(-0.127616\pi\)
−0.798330 + 0.602220i \(0.794283\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) −9.00000 + 15.5885i −0.366205 + 0.634285i
\(605\) 0.937822 15.6244i 0.0381279 0.635220i
\(606\) 12.0000 0.487467
\(607\) −15.5885 9.00000i −0.632716 0.365299i 0.149087 0.988824i \(-0.452366\pi\)
−0.781803 + 0.623525i \(0.785700\pi\)
\(608\) 25.9808 15.0000i 1.05366 0.608330i
\(609\) 0 0
\(610\) −6.00000 12.0000i −0.242933 0.485866i
\(611\) 0 0
\(612\) 0 0
\(613\) 25.9808 15.0000i 1.04935 0.605844i 0.126885 0.991917i \(-0.459502\pi\)
0.922468 + 0.386073i \(0.126169\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) −35.7128 2.14359i −1.44008 0.0864380i
\(616\) 0 0
\(617\) −29.4449 17.0000i −1.18541 0.684394i −0.228147 0.973627i \(-0.573267\pi\)
−0.957259 + 0.289233i \(0.906600\pi\)
\(618\) 10.3923 + 6.00000i 0.418040 + 0.241355i
\(619\) −18.0000 −0.723481 −0.361741 0.932279i \(-0.617817\pi\)
−0.361741 + 0.932279i \(0.617817\pi\)
\(620\) −0.803848 + 13.3923i −0.0322833 + 0.537848i
\(621\) −12.0000 20.7846i −0.481543 0.834058i
\(622\) 20.7846 12.0000i 0.833387 0.481156i
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 4.00000 + 6.92820i 0.159872 + 0.276907i
\(627\) −20.7846 + 12.0000i −0.830057 + 0.479234i
\(628\) 10.3923 + 6.00000i 0.414698 + 0.239426i
\(629\) 0 0
\(630\) 0 0
\(631\) 15.0000 25.9808i 0.597141 1.03428i −0.396100 0.918207i \(-0.629637\pi\)
0.993241 0.116071i \(-0.0370299\pi\)
\(632\) 0 0
\(633\) −20.7846 12.0000i −0.826114 0.476957i
\(634\) 1.00000 + 1.73205i 0.0397151 + 0.0687885i
\(635\) −2.46410 + 3.73205i −0.0977849 + 0.148102i
\(636\) 24.0000 0.951662
\(637\) 0 0
\(638\) 12.0000i 0.475085i
\(639\) −1.00000 1.73205i −0.0395594 0.0685189i
\(640\) −3.69615 + 5.59808i −0.146103 + 0.221283i
\(641\) −15.0000 + 25.9808i −0.592464 + 1.02618i 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 31.1769 + 18.0000i 1.22950 + 0.709851i 0.966925 0.255062i \(-0.0820957\pi\)
0.262573 + 0.964912i \(0.415429\pi\)
\(644\) 0 0
\(645\) −24.0000 + 12.0000i −0.944999 + 0.472500i
\(646\) 0 0
\(647\) 5.19615 3.00000i 0.204282 0.117942i −0.394369 0.918952i \(-0.629037\pi\)
0.598651 + 0.801010i \(0.295704\pi\)
\(648\) 28.5788 16.5000i 1.12268 0.648181i
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) −10.3923 + 6.00000i −0.406994 + 0.234978i
\(653\) 31.1769 18.0000i 1.22005 0.704394i 0.255119 0.966910i \(-0.417885\pi\)
0.964928 + 0.262515i \(0.0845520\pi\)
\(654\) 12.0000 20.7846i 0.469237 0.812743i
\(655\) −24.0000 + 12.0000i −0.937758 + 0.468879i
\(656\) −4.00000 + 6.92820i −0.156174 + 0.270501i
\(657\) 5.19615 + 3.00000i 0.202721 + 0.117041i
\(658\) 0 0
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 4.92820 7.46410i 0.191830 0.290540i
\(661\) −6.00000 10.3923i −0.233373 0.404214i 0.725426 0.688301i \(-0.241643\pi\)
−0.958799 + 0.284087i \(0.908310\pi\)
\(662\) 30.0000i 1.16598i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −3.00000 5.19615i −0.116248 0.201347i
\(667\) −31.1769 18.0000i −1.20717 0.696963i
\(668\) 16.0000i 0.619059i
\(669\) −24.0000 + 41.5692i −0.927894 + 1.60716i
\(670\) −1.60770 + 26.7846i −0.0621107 + 1.03478i
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 41.5692 24.0000i 1.60238 0.925132i 0.611365 0.791349i \(-0.290621\pi\)
0.991011 0.133783i \(-0.0427126\pi\)
\(674\) −16.0000 27.7128i −0.616297 1.06746i
\(675\) −16.0000 12.0000i −0.615840 0.461880i
\(676\) 0 0
\(677\) 36.0000i 1.38359i −0.722093 0.691796i \(-0.756820\pi\)
0.722093 0.691796i \(-0.243180\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −8.00000 −0.306561
\(682\) −10.3923 6.00000i −0.397942 0.229752i
\(683\) −38.1051 22.0000i −1.45805 0.841807i −0.459136 0.888366i \(-0.651841\pi\)
−0.998916 + 0.0465592i \(0.985174\pi\)
\(684\) 6.00000 0.229416
\(685\) 4.46410 + 0.267949i 0.170565 + 0.0102378i
\(686\) 0 0
\(687\) −20.7846 + 12.0000i −0.792982 + 0.457829i
\(688\) 6.00000i 0.228748i
\(689\) 0 0
\(690\) −12.0000 24.0000i −0.456832 0.913664i
\(691\) −21.0000 36.3731i −0.798878 1.38370i −0.920348 0.391102i \(-0.872094\pi\)
0.121470 0.992595i \(-0.461239\pi\)
\(692\) 10.3923 6.00000i 0.395056 0.228086i
\(693\) 0 0
\(694\) 6.00000 0.227757
\(695\) 0.535898 8.92820i 0.0203278 0.338666i
\(696\) 18.0000 31.1769i 0.682288 1.18176i
\(697\) 0 0
\(698\) −10.3923 6.00000i −0.393355 0.227103i
\(699\) 24.0000 + 41.5692i 0.907763 + 1.57229i
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 36.0000i 1.35777i
\(704\) −7.00000 12.1244i −0.263822 0.456954i
\(705\) −29.8564 19.7128i −1.12446 0.742427i
\(706\) 7.00000 12.1244i 0.263448 0.456306i
\(707\) 0 0
\(708\) −3.46410 2.00000i −0.130189 0.0751646i
\(709\) −6.00000 + 10.3923i −0.225335 + 0.390291i −0.956420 0.291995i \(-0.905681\pi\)
0.731085 + 0.682286i \(0.239014\pi\)
\(710\) 2.00000 + 4.00000i 0.0750587 + 0.150117i
\(711\) 0 0
\(712\) −20.7846 + 12.0000i −0.778936 + 0.449719i
\(713\) 31.1769 18.0000i 1.16758 0.674105i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 17.3205 10.0000i 0.646846 0.373457i
\(718\) −1.73205 + 1.00000i −0.0646396 + 0.0373197i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) 2.00000 1.00000i 0.0745356 0.0372678i
\(721\) 0 0
\(722\) 14.7224 + 8.50000i 0.547912 + 0.316337i
\(723\) 0 0
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) −29.7846 3.58846i −1.10617 0.133272i
\(726\) −7.00000 12.1244i −0.259794 0.449977i
\(727\) 26.0000i 0.964287i −0.876092 0.482143i \(-0.839858\pi\)
0.876092 0.482143i \(-0.160142\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) −11.1962 7.39230i −0.414388 0.273601i
\(731\) 0 0
\(732\) 10.3923 + 6.00000i 0.384111 + 0.221766i
\(733\) 42.0000i 1.55131i −0.631160 0.775653i \(-0.717421\pi\)
0.631160 0.775653i \(-0.282579\pi\)
\(734\) −9.00000 + 15.5885i −0.332196 + 0.575380i
\(735\) 31.2487 + 1.87564i 1.15263 + 0.0691842i
\(736\) 30.0000 1.10581
\(737\) 20.7846 + 12.0000i 0.765611 + 0.442026i
\(738\) −6.92820 + 4.00000i −0.255031 + 0.147242i
\(739\) −3.00000 5.19615i −0.110357 0.191144i 0.805557 0.592518i \(-0.201866\pi\)
−0.915914 + 0.401374i \(0.868533\pi\)
\(740\) −6.00000 12.0000i −0.220564 0.441129i
\(741\) 0 0
\(742\) 0 0
\(743\) −13.8564 + 8.00000i −0.508342 + 0.293492i −0.732152 0.681141i \(-0.761484\pi\)
0.223810 + 0.974633i \(0.428151\pi\)
\(744\) 18.0000 + 31.1769i 0.659912 + 1.14300i
\(745\) −2.67949 + 44.6410i −0.0981690 + 1.63552i
\(746\) −4.00000 −0.146450
\(747\) −3.46410 2.00000i −0.126745 0.0731762i
\(748\) 0 0
\(749\) 0 0
\(750\) −17.0526 14.4641i −0.622671 0.528154i
\(751\) −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) −6.92820 + 4.00000i −0.252646 + 0.145865i
\(753\) 24.0000i 0.874609i
\(754\) 0 0
\(755\) 36.0000 18.0000i 1.31017 0.655087i
\(756\) 0 0
\(757\) −17.3205 + 10.0000i −0.629525 + 0.363456i −0.780568 0.625071i \(-0.785070\pi\)
0.151043 + 0.988527i \(0.451737\pi\)
\(758\) 15.5885 + 9.00000i 0.566198 + 0.326895i
\(759\) −24.0000 −0.871145
\(760\) −40.1769 2.41154i −1.45737 0.0874758i
\(761\) −20.0000 + 34.6410i −0.724999 + 1.25574i 0.233975 + 0.972243i \(0.424827\pi\)
−0.958974 + 0.283493i \(0.908507\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 8.00000 0.289052
\(767\) 0 0
\(768\) 34.0000i 1.22687i
\(769\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000i 0.215945i
\(773\) −32.9090 19.0000i −1.18365 0.683383i −0.226796 0.973942i \(-0.572825\pi\)
−0.956857 + 0.290560i \(0.906159\pi\)
\(774\) −3.00000 + 5.19615i −0.107833 + 0.186772i
\(775\) 18.0000 24.0000i 0.646579 0.862105i
\(776\) 9.00000 15.5885i 0.323081 0.559593i
\(777\) 0 0
\(778\) 5.19615 3.00000i 0.186291 0.107555i
\(779\) 48.0000 1.71978
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) −20.7846 + 12.0000i −0.742781 + 0.428845i
\(784\) 3.50000 6.06218i