Properties

Label 845.2.n.b.529.1
Level $845$
Weight $2$
Character 845.529
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 529.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 845.529
Dual form 845.2.n.b.484.1

$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i 0.161521 0.986869i \(-0.448360\pi\)
−0.773893 + 0.633316i \(0.781693\pi\)
\(3\) −1.73205 1.00000i −1.00000 0.577350i −0.0917517 0.995782i \(-0.529247\pi\)
−0.908248 + 0.418432i \(0.862580\pi\)
\(4\) −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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(8\) 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 −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) −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 0.931831 0.362892i \(-0.118211\pi\)
0.151642 + 0.988436i \(0.451544\pi\)
\(24\) 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 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 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 0.00783774 0.999969i \(-0.497505\pi\)
−0.862080 + 0.506772i \(0.830838\pi\)
\(38\) 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 −0.363905 0.931436i \(-0.618557\pi\)
0.988600 0.150567i \(-0.0481100\pi\)
\(42\) 0 0
\(43\) 5.19615 3.00000i 0.792406 0.457496i −0.0484030 0.998828i \(-0.515413\pi\)
0.840809 + 0.541332i \(0.182080\pi\)
\(44\) −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 \(-0.801699\pi\)
0.812142 0.583460i \(-0.198301\pi\)
\(48\) −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 \(-0.691646\pi\)
0.566352 0.824163i \(-0.308354\pi\)
\(54\) 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 0.923749 0.382998i \(-0.125108\pi\)
−0.793560 + 0.608492i \(0.791775\pi\)
\(60\) −2.00000 + 4.00000i −0.258199 + 0.516398i
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) −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 0.974916 0.222571i \(-0.0714450\pi\)
0.294706 + 0.955588i \(0.404778\pi\)
\(68\) 0 0
\(69\) −6.00000 10.3923i −0.722315 1.25109i
\(70\) 0 0
\(71\) 1.00000 + 1.73205i 0.118678 + 0.205557i 0.919244 0.393688i \(-0.128801\pi\)
−0.800566 + 0.599245i \(0.795468\pi\)
\(72\) −2.59808 + 1.50000i −0.306186 + 0.176777i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 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 \(0.0704519\pi\)
−0.975606 + 0.219529i \(0.929548\pi\)
\(84\) 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 −0.996326 0.0856373i \(-0.972707\pi\)
0.572327 + 0.820025i \(0.306041\pi\)
\(90\) 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 −0.212445 0.977173i \(-0.568143\pi\)
0.740034 + 0.672569i \(0.234809\pi\)
\(98\) 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 −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −6.00000 + 10.3923i −0.582772 + 1.00939i
\(107\) 5.19615 + 3.00000i 0.502331 + 0.290021i 0.729676 0.683793i \(-0.239671\pi\)
−0.227345 + 0.973814i \(0.573004\pi\)
\(108\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(114\) −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 0.421180 0.906977i \(-0.361616\pi\)
−0.574875 + 0.818241i \(0.694949\pi\)
\(128\) −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 −0.424182 0.905577i \(-0.639438\pi\)
0.572161 + 0.820141i \(0.306105\pi\)
\(138\) 12.0000i 1.02151i
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) 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 −0.906249 0.422744i \(-0.861067\pi\)
0.0870170 0.996207i \(-0.472267\pi\)
\(150\) −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 \(0.158947\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 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 −0.0343508 0.999410i \(-0.510936\pi\)
0.848339 + 0.529454i \(0.177603\pi\)
\(164\) −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 0.928793 0.370599i \(-0.120848\pi\)
0.143448 + 0.989658i \(0.454181\pi\)
\(168\) 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 −0.840002 0.542583i \(-0.817446\pi\)
0.0498898 + 0.998755i \(0.484113\pi\)
\(174\) −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 −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 12.1244 + 7.00000i 0.875000 + 0.505181i
\(193\) 5.19615 + 3.00000i 0.374027 + 0.215945i 0.675216 0.737620i \(-0.264050\pi\)
−0.301189 + 0.953564i \(0.597384\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) −1.73205 1.00000i −0.123404 0.0712470i 0.437028 0.899448i \(-0.356031\pi\)
−0.560431 + 0.828201i \(0.689365\pi\)
\(198\) −1.73205 1.00000i −0.123091 0.0710669i
\(199\) −12.0000 20.7846i −0.850657 1.47338i −0.880616 0.473831i \(-0.842871\pi\)
0.0299585 0.999551i \(-0.490462\pi\)
\(200\) −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 −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) −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 0.993519 0.113666i \(-0.0362595\pi\)
0.398321 + 0.917246i \(0.369593\pi\)
\(224\) 0 0
\(225\) −1.96410 + 4.59808i −0.130940 + 0.306538i
\(226\) 0 0
\(227\) 3.46410 2.00000i 0.229920 0.132745i −0.380615 0.924734i \(-0.624288\pi\)
0.610535 + 0.791989i \(0.290954\pi\)
\(228\) −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 \(0.287927\pi\)
−0.618041 + 0.786146i \(0.712073\pi\)
\(234\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(242\) 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 0.990876 0.134778i \(-0.0430322\pi\)
−0.612159 + 0.790735i \(0.709699\pi\)
\(252\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 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 0.331166 0.943572i \(-0.392558\pi\)
−0.651575 + 0.758585i \(0.725891\pi\)
\(264\) −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 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 7.46410 4.92820i 0.454251 0.299921i
\(271\) 3.00000 5.19615i 0.182237 0.315644i −0.760405 0.649449i \(-0.775000\pi\)
0.942642 + 0.333805i \(0.108333\pi\)
\(272\) 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 −0.154172 0.988044i \(-0.549271\pi\)
0.778585 + 0.627539i \(0.215938\pi\)
\(278\) 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 −0.187980 0.982173i \(-0.560194\pi\)
−0.944577 + 0.328291i \(0.893527\pi\)
\(284\) 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 −0.982991 0.183654i \(-0.941207\pi\)
−0.332446 + 0.943122i \(0.607874\pi\)
\(294\) −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 \(0.111253\pi\)
−0.939540 + 0.342438i \(0.888747\pi\)
\(308\) 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 \(0.0725954\pi\)
−0.974106 + 0.226093i \(0.927405\pi\)
\(314\) 6.00000 10.3923i 0.338600 0.586472i
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000i 0.112331i 0.998421 + 0.0561656i \(0.0178875\pi\)
−0.998421 + 0.0561656i \(0.982113\pi\)
\(318\) 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 0.902320 + 0.431066i \(0.141863\pi\)
−0.0778456 + 0.996965i \(0.524804\pi\)
\(332\) 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 \(-0.663099\pi\)
0.490261 0.871576i \(-0.336901\pi\)
\(338\) 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 −0.632945 0.774197i \(-0.718154\pi\)
0.354001 + 0.935245i \(0.384821\pi\)
\(348\) −10.3923 6.00000i −0.557086 0.321634i
\(349\) 6.00000 10.3923i 0.321173 0.556287i −0.659558 0.751654i \(-0.729256\pi\)
0.980730 + 0.195367i \(0.0625897\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 10.0000i 0.533002i
\(353\) −12.1244 7.00000i −0.645314 0.372572i 0.141344 0.989960i \(-0.454858\pi\)
−0.786659 + 0.617388i \(0.788191\pi\)
\(354\) −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 0.848243 0.529607i \(-0.177661\pi\)
−0.0345320 + 0.999404i \(0.510994\pi\)
\(368\) 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 −0.407630 0.913147i \(-0.633645\pi\)
0.586994 + 0.809591i \(0.300311\pi\)
\(374\) 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 −0.999075 0.0429994i \(-0.986309\pi\)
0.536776 + 0.843725i \(0.319642\pi\)
\(380\) 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 −0.666452 0.745548i \(-0.732188\pi\)
0.312437 + 0.949938i \(0.398855\pi\)
\(384\) 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 −0.837267 0.546795i \(-0.815848\pi\)
0.0549046 + 0.998492i \(0.482515\pi\)
\(398\) 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 −0.594163 0.804344i \(-0.702517\pi\)
0.993664 + 0.112388i \(0.0358501\pi\)
\(402\) 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 0.993776 + 0.111398i \(0.0355330\pi\)
−0.400414 + 0.916334i \(0.631134\pi\)
\(410\) −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 −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 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 −0.720113 0.693857i \(-0.755910\pi\)
0.960954 + 0.276707i \(0.0892433\pi\)
\(432\) 3.46410 + 2.00000i 0.166667 + 0.0962250i
\(433\) −13.8564 + 8.00000i −0.665896 + 0.384455i −0.794520 0.607238i \(-0.792277\pi\)
0.128624 + 0.991693i \(0.458944\pi\)
\(434\) 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 −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 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 \(-0.954475\pi\)
0.989790 0.142534i \(-0.0455251\pi\)
\(444\) 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 0.613161 0.789958i \(-0.289898\pi\)
−0.990704 + 0.136034i \(0.956564\pi\)
\(450\) 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 −0.251414 0.967880i \(-0.580895\pi\)
−0.963915 + 0.266209i \(0.914229\pi\)
\(458\) −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 0.908835 0.417156i \(-0.136973\pi\)
−0.815685 + 0.578496i \(0.803640\pi\)
\(462\) 0 0
\(463\) 24.0000i 1.11537i −0.830051 0.557687i \(-0.811689\pi\)
0.830051 0.557687i \(-0.188311\pi\)
\(464\) 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 \(-0.863267\pi\)
0.909149 0.416470i \(-0.136733\pi\)
\(468\) 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 −0.497393 0.867526i \(-0.665709\pi\)
0.999995 0.00300810i \(-0.000957509\pi\)
\(480\) −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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) 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 −0.698285 0.715820i \(-0.746053\pi\)
0.969061 + 0.246822i \(0.0793863\pi\)
\(492\) 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 −0.379664 0.925124i \(-0.623960\pi\)
0.611349 + 0.791361i \(0.290627\pi\)
\(504\) 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 −0.554686 0.832060i \(-0.687161\pi\)
0.997928 + 0.0643419i \(0.0204948\pi\)
\(510\) 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 −0.993224 0.116218i \(-0.962923\pi\)
−0.597259 0.802048i \(-0.703744\pi\)
\(524\) 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 \(0.125734\pi\)
−0.922995 + 0.384812i \(0.874266\pi\)
\(548\) −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 0.220638 0.975356i \(-0.429186\pi\)
−0.734364 + 0.678756i \(0.762519\pi\)
\(558\) 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 0.160066 0.987106i \(-0.448829\pi\)
0.934892 + 0.354932i \(0.115496\pi\)
\(564\) 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 −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) −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 \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(578\) 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 0.812870 0.582445i \(-0.197904\pi\)
−0.0979766 + 0.995189i \(0.531237\pi\)
\(588\) −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 \(-0.850812\pi\)
0.892162 0.451716i \(-0.149188\pi\)
\(594\) −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 −0.798330 0.602220i \(-0.794283\pi\)
0.920703 + 0.390264i \(0.127616\pi\)
\(602\) 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 −0.781803 0.623525i \(-0.785700\pi\)
0.149087 + 0.988824i \(0.452366\pi\)
\(608\) 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 0.922468 0.386073i \(-0.126169\pi\)
0.126885 + 0.991917i \(0.459502\pi\)
\(614\) 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 −0.957259 0.289233i \(-0.906600\pi\)
−0.228147 + 0.973627i \(0.573267\pi\)
\(618\) 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 0.993241 + 0.116071i \(0.0370299\pi\)
−0.396100 + 0.918207i \(0.629637\pi\)
\(632\) 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 −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 31.1769 18.0000i 1.22950 0.709851i 0.262573 0.964912i \(-0.415429\pi\)
0.966925 + 0.255062i \(0.0820957\pi\)
\(644\) 0 0
\(645\) −24.0000 12.0000i −0.944999 0.472500i
\(646\) 0 0
\(647\) 5.19615 + 3.00000i 0.204282 + 0.117942i 0.598651 0.801010i \(-0.295704\pi\)
−0.394369 + 0.918952i \(0.629037\pi\)
\(648\) 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 0.964928 0.262515i \(-0.0845520\pi\)
0.255119 + 0.966910i \(0.417885\pi\)
\(654\) 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 −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 4.92820 + 7.46410i 0.191830 + 0.290540i
\(661\) −6.00000 + 10.3923i −0.233373 + 0.404214i −0.958799 0.284087i \(-0.908310\pi\)
0.725426 + 0.688301i \(0.241643\pi\)
\(662\) 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 0.991011 + 0.133783i \(0.0427126\pi\)
0.611365 + 0.791349i \(0.290621\pi\)
\(674\) −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 \(0.243180\pi\)
−0.722093 + 0.691796i \(0.756820\pi\)
\(678\) 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 −0.998916 0.0465592i \(-0.985174\pi\)
−0.459136 + 0.888366i \(0.651841\pi\)
\(684\) 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 0.121470 + 0.992595i \(0.461239\pi\)
−0.920348 + 0.391102i \(0.872094\pi\)
\(692\) 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 0.731085 0.682286i \(-0.239014\pi\)
−0.956420 + 0.291995i \(0.905681\pi\)
\(710\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 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 \(0.160142\pi\)
−0.876092 + 0.482143i \(0.839858\pi\)
\(728\) 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 \(0.282579\pi\)
−0.631160 + 0.775653i \(0.717421\pi\)
\(734\) −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 −0.915914 0.401374i \(-0.868533\pi\)
0.805557 + 0.592518i \(0.201866\pi\)
\(740\) −6.00000 + 12.0000i −0.220564 + 0.441129i
\(741\) 0 0
\(742\) 0 0
\(743\) −13.8564 8.00000i −0.508342 0.293492i 0.223810 0.974633i \(-0.428151\pi\)
−0.732152 + 0.681141i \(0.761484\pi\)
\(744\) 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 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) −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 0.151043 0.988527i \(-0.451737\pi\)
−0.780568 + 0.625071i \(0.785070\pi\)
\(758\) 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 −0.958974 0.283493i \(-0.908507\pi\)
0.233975 0.972243i \(-0.424827\pi\)
\(762\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000i 0.215945i
\(773\) −32.9090 + 19.0000i −1.18365 + 0.683383i −0.956857 0.290560i \(-0.906159\pi\)
−0.226796 + 0.973942i \(0.572825\pi\)
\(774\) −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
\(784\)