Properties

Label 1950.2.z.k.1849.1
Level $1950$
Weight $2$
Character 1950.1849
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1849.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1849
Dual form 1950.2.z.k.1699.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +1.00000i q^{12} +(3.46410 - 1.00000i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +1.00000i q^{18} +(1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(-2.59808 - 1.50000i) q^{22} +(-2.59808 + 1.50000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-2.50000 + 2.59808i) q^{26} +1.00000i q^{27} +(-1.73205 + 1.00000i) q^{28} +(1.50000 + 2.59808i) q^{29} +5.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} +6.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-6.06218 + 3.50000i) q^{37} +2.00000i q^{38} +(-2.50000 + 2.59808i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(-1.73205 + 1.00000i) q^{42} +(-0.866025 - 0.500000i) q^{43} +3.00000 q^{44} +(1.50000 - 2.59808i) q^{46} -3.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +6.00000 q^{51} +(0.866025 - 3.50000i) q^{52} +6.00000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 - 1.73205i) q^{56} +2.00000i q^{57} +(-2.59808 - 1.50000i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-4.33013 + 2.50000i) q^{62} +(-1.73205 + 1.00000i) q^{63} -1.00000 q^{64} +3.00000 q^{66} +(6.92820 - 4.00000i) q^{67} +(-5.19615 + 3.00000i) q^{68} +(1.50000 - 2.59808i) q^{69} +(6.00000 - 10.3923i) q^{71} +(0.866025 + 0.500000i) q^{72} -14.0000i q^{73} +(3.50000 - 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} -6.00000i q^{77} +(0.866025 - 3.50000i) q^{78} -5.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.19615 + 3.00000i) q^{82} +6.00000i q^{83} +(1.00000 - 1.73205i) q^{84} +1.00000 q^{86} +(-2.59808 - 1.50000i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-9.00000 - 15.5885i) q^{89} +(-7.00000 - 1.73205i) q^{91} +3.00000i q^{92} +(-4.33013 + 2.50000i) q^{93} +(1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(-12.1244 - 7.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 2q^{6} + 2q^{9} + 6q^{11} + 8q^{14} - 2q^{16} + 4q^{19} + 8q^{21} - 2q^{24} - 10q^{26} + 6q^{29} + 20q^{31} + 24q^{34} - 2q^{36} - 10q^{39} - 12q^{41} + 12q^{44} + 6q^{46} - 6q^{49} + 24q^{51} - 2q^{54} + 4q^{56} - 18q^{59} - 4q^{61} - 4q^{64} + 12q^{66} + 6q^{69} + 24q^{71} + 14q^{74} - 4q^{76} - 20q^{79} - 2q^{81} + 4q^{84} + 4q^{86} - 36q^{89} - 28q^{91} + 6q^{94} - 4q^{96} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

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
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −1.73205 1.00000i −0.654654 0.377964i 0.135583 0.990766i \(-0.456709\pi\)
−0.790237 + 0.612801i \(0.790043\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.46410 1.00000i 0.960769 0.277350i
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −5.19615 3.00000i −1.26025 0.727607i −0.287129 0.957892i \(-0.592701\pi\)
−0.973123 + 0.230285i \(0.926034\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) −2.59808 1.50000i −0.553912 0.319801i
\(23\) −2.59808 + 1.50000i −0.541736 + 0.312772i −0.745782 0.666190i \(-0.767924\pi\)
0.204046 + 0.978961i \(0.434591\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) −2.50000 + 2.59808i −0.490290 + 0.509525i
\(27\) 1.00000i 0.192450i
\(28\) −1.73205 + 1.00000i −0.327327 + 0.188982i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −2.59808 1.50000i −0.452267 0.261116i
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −6.06218 + 3.50000i −0.996616 + 0.575396i −0.907245 0.420602i \(-0.861819\pi\)
−0.0893706 + 0.995998i \(0.528486\pi\)
\(38\) 2.00000i 0.324443i
\(39\) −2.50000 + 2.59808i −0.400320 + 0.416025i
\(40\) 0 0
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) −1.73205 + 1.00000i −0.267261 + 0.154303i
\(43\) −0.866025 0.500000i −0.132068 0.0762493i 0.432511 0.901629i \(-0.357628\pi\)
−0.564578 + 0.825380i \(0.690961\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) 3.00000i 0.437595i −0.975770 0.218797i \(-0.929787\pi\)
0.975770 0.218797i \(-0.0702134\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) −1.50000 2.59808i −0.214286 0.371154i
\(50\) 0 0
\(51\) 6.00000 0.840168
\(52\) 0.866025 3.50000i 0.120096 0.485363i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 2.00000i 0.264906i
\(58\) −2.59808 1.50000i −0.341144 0.196960i
\(59\) −4.50000 + 7.79423i −0.585850 + 1.01472i 0.408919 + 0.912571i \(0.365906\pi\)
−0.994769 + 0.102151i \(0.967427\pi\)
\(60\) 0 0
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) −4.33013 + 2.50000i −0.549927 + 0.317500i
\(63\) −1.73205 + 1.00000i −0.218218 + 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) 6.92820 4.00000i 0.846415 0.488678i −0.0130248 0.999915i \(-0.504146\pi\)
0.859440 + 0.511237i \(0.170813\pi\)
\(68\) −5.19615 + 3.00000i −0.630126 + 0.363803i
\(69\) 1.50000 2.59808i 0.180579 0.312772i
\(70\) 0 0
\(71\) 6.00000 10.3923i 0.712069 1.23334i −0.252010 0.967725i \(-0.581092\pi\)
0.964079 0.265615i \(-0.0855750\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 14.0000i 1.63858i −0.573382 0.819288i \(-0.694369\pi\)
0.573382 0.819288i \(-0.305631\pi\)
\(74\) 3.50000 6.06218i 0.406867 0.704714i
\(75\) 0 0
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 6.00000i 0.683763i
\(78\) 0.866025 3.50000i 0.0980581 0.396297i
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.19615 + 3.00000i 0.573819 + 0.331295i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 1.00000 1.73205i 0.109109 0.188982i
\(85\) 0 0
\(86\) 1.00000 0.107833
\(87\) −2.59808 1.50000i −0.278543 0.160817i
\(88\) −2.59808 + 1.50000i −0.276956 + 0.159901i
\(89\) −9.00000 15.5885i −0.953998 1.65237i −0.736644 0.676280i \(-0.763591\pi\)
−0.217354 0.976093i \(-0.569742\pi\)
\(90\) 0 0
\(91\) −7.00000 1.73205i −0.733799 0.181568i
\(92\) 3.00000i 0.312772i
\(93\) −4.33013 + 2.50000i −0.449013 + 0.259238i
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −12.1244 7.00000i −1.23104 0.710742i −0.263795 0.964579i \(-0.584974\pi\)
−0.967247 + 0.253837i \(0.918307\pi\)
\(98\) 2.59808 + 1.50000i 0.262445 + 0.151523i
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) −5.19615 + 3.00000i −0.514496 + 0.297044i
\(103\) 14.0000i 1.37946i −0.724066 0.689730i \(-0.757729\pi\)
0.724066 0.689730i \(-0.242271\pi\)
\(104\) 1.00000 + 3.46410i 0.0980581 + 0.339683i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) −5.19615 + 3.00000i −0.502331 + 0.290021i −0.729676 0.683793i \(-0.760329\pi\)
0.227345 + 0.973814i \(0.426996\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 2.00000i 0.188982i
\(113\) 12.9904 + 7.50000i 1.22203 + 0.705541i 0.965351 0.260955i \(-0.0840376\pi\)
0.256681 + 0.966496i \(0.417371\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) 0 0
\(116\) 3.00000 0.278543
\(117\) 0.866025 3.50000i 0.0800641 0.323575i
\(118\) 9.00000i 0.828517i
\(119\) 6.00000 + 10.3923i 0.550019 + 0.952661i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 2.00000i 0.181071i
\(123\) 5.19615 + 3.00000i 0.468521 + 0.270501i
\(124\) 2.50000 4.33013i 0.224507 0.388857i
\(125\) 0 0
\(126\) 1.00000 1.73205i 0.0890871 0.154303i
\(127\) 12.1244 7.00000i 1.07586 0.621150i 0.146085 0.989272i \(-0.453333\pi\)
0.929777 + 0.368122i \(0.119999\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 1.00000 0.0880451
\(130\) 0 0
\(131\) 9.00000 0.786334 0.393167 0.919467i \(-0.371379\pi\)
0.393167 + 0.919467i \(0.371379\pi\)
\(132\) −2.59808 + 1.50000i −0.226134 + 0.130558i
\(133\) −3.46410 + 2.00000i −0.300376 + 0.173422i
\(134\) −4.00000 + 6.92820i −0.345547 + 0.598506i
\(135\) 0 0
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) −7.79423 4.50000i −0.665906 0.384461i 0.128618 0.991694i \(-0.458946\pi\)
−0.794524 + 0.607233i \(0.792279\pi\)
\(138\) 3.00000i 0.255377i
\(139\) 7.00000 12.1244i 0.593732 1.02837i −0.399992 0.916519i \(-0.630987\pi\)
0.993724 0.111856i \(-0.0356795\pi\)
\(140\) 0 0
\(141\) 1.50000 + 2.59808i 0.126323 + 0.218797i
\(142\) 12.0000i 1.00702i
\(143\) 7.79423 + 7.50000i 0.651786 + 0.627182i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 7.00000 + 12.1244i 0.579324 + 1.00342i
\(147\) 2.59808 + 1.50000i 0.214286 + 0.123718i
\(148\) 7.00000i 0.575396i
\(149\) −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i \(-0.953515\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(150\) 0 0
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 1.73205 + 1.00000i 0.140488 + 0.0811107i
\(153\) −5.19615 + 3.00000i −0.420084 + 0.242536i
\(154\) 3.00000 + 5.19615i 0.241747 + 0.418718i
\(155\) 0 0
\(156\) 1.00000 + 3.46410i 0.0800641 + 0.277350i
\(157\) 13.0000i 1.03751i −0.854922 0.518756i \(-0.826395\pi\)
0.854922 0.518756i \(-0.173605\pi\)
\(158\) 4.33013 2.50000i 0.344486 0.198889i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) −11.2583 6.50000i −0.881820 0.509119i −0.0105623 0.999944i \(-0.503362\pi\)
−0.871258 + 0.490825i \(0.836695\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) −7.79423 + 4.50000i −0.603136 + 0.348220i −0.770274 0.637713i \(-0.779881\pi\)
0.167139 + 0.985933i \(0.446547\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 11.0000 6.92820i 0.846154 0.532939i
\(170\) 0 0
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) −0.866025 + 0.500000i −0.0660338 + 0.0381246i
\(173\) 10.3923 + 6.00000i 0.790112 + 0.456172i 0.840002 0.542583i \(-0.182554\pi\)
−0.0498898 + 0.998755i \(0.515887\pi\)
\(174\) 3.00000 0.227429
\(175\) 0 0
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) 9.00000i 0.676481i
\(178\) 15.5885 + 9.00000i 1.16840 + 0.674579i
\(179\) −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i \(-0.202429\pi\)
−0.916623 + 0.399753i \(0.869096\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 6.92820 2.00000i 0.513553 0.148250i
\(183\) 2.00000i 0.147844i
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) 0 0
\(186\) 2.50000 4.33013i 0.183309 0.317500i
\(187\) 18.0000i 1.31629i
\(188\) −2.59808 1.50000i −0.189484 0.109399i
\(189\) 1.00000 1.73205i 0.0727393 0.125988i
\(190\) 0 0
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) 3.46410 2.00000i 0.249351 0.143963i −0.370116 0.928986i \(-0.620682\pi\)
0.619467 + 0.785022i \(0.287349\pi\)
\(194\) 14.0000 1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 20.7846 12.0000i 1.48084 0.854965i 0.481078 0.876678i \(-0.340245\pi\)
0.999764 + 0.0217133i \(0.00691209\pi\)
\(198\) −2.59808 + 1.50000i −0.184637 + 0.106600i
\(199\) 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) 0 0
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) 5.19615 + 3.00000i 0.365600 + 0.211079i
\(203\) 6.00000i 0.421117i
\(204\) 3.00000 5.19615i 0.210042 0.363803i
\(205\) 0 0
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 3.00000i 0.208514i
\(208\) −2.59808 2.50000i −0.180144 0.173344i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) 5.19615 + 3.00000i 0.356873 + 0.206041i
\(213\) 12.0000i 0.822226i
\(214\) 3.00000 5.19615i 0.205076 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −8.66025 5.00000i −0.587896 0.339422i
\(218\) 12.1244 7.00000i 0.821165 0.474100i
\(219\) 7.00000 + 12.1244i 0.473016 + 0.819288i
\(220\) 0 0
\(221\) −21.0000 5.19615i −1.41261 0.349531i
\(222\) 7.00000i 0.469809i
\(223\) 8.66025 5.00000i 0.579934 0.334825i −0.181173 0.983451i \(-0.557990\pi\)
0.761107 + 0.648626i \(0.224656\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) 0 0
\(226\) −15.0000 −0.997785
\(227\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 1.73205 + 1.00000i 0.114708 + 0.0662266i
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 3.00000 + 5.19615i 0.197386 + 0.341882i
\(232\) −2.59808 + 1.50000i −0.170572 + 0.0984798i
\(233\) 21.0000i 1.37576i −0.725826 0.687878i \(-0.758542\pi\)
0.725826 0.687878i \(-0.241458\pi\)
\(234\) 1.00000 + 3.46410i 0.0653720 + 0.226455i
\(235\) 0 0
\(236\) 4.50000 + 7.79423i 0.292925 + 0.507361i
\(237\) 4.33013 2.50000i 0.281272 0.162392i
\(238\) −10.3923 6.00000i −0.673633 0.388922i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) −8.50000 + 14.7224i −0.547533 + 0.948355i 0.450910 + 0.892570i \(0.351100\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 1.00000 + 1.73205i 0.0640184 + 0.110883i
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) 1.73205 7.00000i 0.110208 0.445399i
\(248\) 5.00000i 0.317500i
\(249\) −3.00000 5.19615i −0.190117 0.329293i
\(250\) 0 0
\(251\) −7.50000 + 12.9904i −0.473396 + 0.819946i −0.999536 0.0304521i \(-0.990305\pi\)
0.526140 + 0.850398i \(0.323639\pi\)
\(252\) 2.00000i 0.125988i
\(253\) −7.79423 4.50000i −0.490019 0.282913i
\(254\) −7.00000 + 12.1244i −0.439219 + 0.760750i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −18.1865 + 10.5000i −1.13444 + 0.654972i −0.945049 0.326929i \(-0.893986\pi\)
−0.189396 + 0.981901i \(0.560653\pi\)
\(258\) −0.866025 + 0.500000i −0.0539164 + 0.0311286i
\(259\) 14.0000 0.869918
\(260\) 0 0
\(261\) 3.00000 0.185695
\(262\) −7.79423 + 4.50000i −0.481529 + 0.278011i
\(263\) 12.9904 7.50000i 0.801021 0.462470i −0.0428069 0.999083i \(-0.513630\pi\)
0.843828 + 0.536614i \(0.180297\pi\)
\(264\) 1.50000 2.59808i 0.0923186 0.159901i
\(265\) 0 0
\(266\) 2.00000 3.46410i 0.122628 0.212398i
\(267\) 15.5885 + 9.00000i 0.953998 + 0.550791i
\(268\) 8.00000i 0.488678i
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 0 0
\(271\) −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i \(-0.275099\pi\)
−0.983312 + 0.181928i \(0.941766\pi\)
\(272\) 6.00000i 0.363803i
\(273\) 6.92820 2.00000i 0.419314 0.121046i
\(274\) 9.00000 0.543710
\(275\) 0 0
\(276\) −1.50000 2.59808i −0.0902894 0.156386i
\(277\) 0.866025 + 0.500000i 0.0520344 + 0.0300421i 0.525792 0.850613i \(-0.323769\pi\)
−0.473757 + 0.880656i \(0.657103\pi\)
\(278\) 14.0000i 0.839664i
\(279\) 2.50000 4.33013i 0.149671 0.259238i
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −2.59808 1.50000i −0.154713 0.0893237i
\(283\) 26.8468 15.5000i 1.59588 0.921379i 0.603606 0.797283i \(-0.293730\pi\)
0.992270 0.124096i \(-0.0396032\pi\)
\(284\) −6.00000 10.3923i −0.356034 0.616670i
\(285\) 0 0
\(286\) −10.5000 2.59808i −0.620878 0.153627i
\(287\) 12.0000i 0.708338i
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 9.50000 + 16.4545i 0.558824 + 0.967911i
\(290\) 0 0
\(291\) 14.0000 0.820695
\(292\) −12.1244 7.00000i −0.709524 0.409644i
\(293\) −25.9808 15.0000i −1.51781 0.876309i −0.999781 0.0209480i \(-0.993332\pi\)
−0.518032 0.855361i \(-0.673335\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) −3.50000 6.06218i −0.203433 0.352357i
\(297\) −2.59808 + 1.50000i −0.150756 + 0.0870388i
\(298\) 9.00000i 0.521356i
\(299\) −7.50000 + 7.79423i −0.433736 + 0.450752i
\(300\) 0 0
\(301\) 1.00000 + 1.73205i 0.0576390 + 0.0998337i
\(302\) −6.92820 + 4.00000i −0.398673 + 0.230174i
\(303\) 5.19615 + 3.00000i 0.298511 + 0.172345i
\(304\) −2.00000 −0.114708
\(305\) 0 0
\(306\) 3.00000 5.19615i 0.171499 0.297044i
\(307\) 8.00000i 0.456584i 0.973593 + 0.228292i \(0.0733141\pi\)
−0.973593 + 0.228292i \(0.926686\pi\)
\(308\) −5.19615 3.00000i −0.296078 0.170941i
\(309\) 7.00000 + 12.1244i 0.398216 + 0.689730i
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) −2.59808 2.50000i −0.147087 0.141535i
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) 6.50000 + 11.2583i 0.366816 + 0.635344i
\(315\) 0 0
\(316\) −2.50000 + 4.33013i −0.140636 + 0.243589i
\(317\) 12.0000i 0.673987i 0.941507 + 0.336994i \(0.109410\pi\)
−0.941507 + 0.336994i \(0.890590\pi\)
\(318\) 5.19615 + 3.00000i 0.291386 + 0.168232i
\(319\) −4.50000 + 7.79423i −0.251952 + 0.436393i
\(320\) 0 0
\(321\) 3.00000 5.19615i 0.167444 0.290021i
\(322\) −5.19615 + 3.00000i −0.289570 + 0.167183i
\(323\) −10.3923 + 6.00000i −0.578243 + 0.333849i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 13.0000 0.720003
\(327\) 12.1244 7.00000i 0.670478 0.387101i
\(328\) 5.19615 3.00000i 0.286910 0.165647i
\(329\) −3.00000 + 5.19615i −0.165395 + 0.286473i
\(330\) 0 0
\(331\) −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i \(0.508749\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 5.19615 + 3.00000i 0.285176 + 0.164646i
\(333\) 7.00000i 0.383598i
\(334\) 4.50000 7.79423i 0.246229 0.426481i
\(335\) 0 0
\(336\) −1.00000 1.73205i −0.0545545 0.0944911i
\(337\) 14.0000i 0.762629i 0.924445 + 0.381314i \(0.124528\pi\)
−0.924445 + 0.381314i \(0.875472\pi\)
\(338\) −6.06218 + 11.5000i −0.329739 + 0.625518i
\(339\) −15.0000 −0.814688
\(340\) 0 0
\(341\) 7.50000 + 12.9904i 0.406148 + 0.703469i
\(342\) 1.73205 + 1.00000i 0.0936586 + 0.0540738i
\(343\) 20.0000i 1.07990i
\(344\) 0.500000 0.866025i 0.0269582 0.0466930i
\(345\) 0 0
\(346\) −12.0000 −0.645124
\(347\) 25.9808 + 15.0000i 1.39472 + 0.805242i 0.993833 0.110885i \(-0.0353686\pi\)
0.400887 + 0.916127i \(0.368702\pi\)
\(348\) −2.59808 + 1.50000i −0.139272 + 0.0804084i
\(349\) 4.00000 + 6.92820i 0.214115 + 0.370858i 0.952998 0.302975i \(-0.0979799\pi\)
−0.738883 + 0.673833i \(0.764647\pi\)
\(350\) 0 0
\(351\) 1.00000 + 3.46410i 0.0533761 + 0.184900i
\(352\) 3.00000i 0.159901i
\(353\) −25.9808 + 15.0000i −1.38282 + 0.798369i −0.992492 0.122308i \(-0.960970\pi\)
−0.390324 + 0.920677i \(0.627637\pi\)
\(354\) 4.50000 + 7.79423i 0.239172 + 0.414259i
\(355\) 0 0
\(356\) −18.0000 −0.953998
\(357\) −10.3923 6.00000i −0.550019 0.317554i
\(358\) 2.59808 + 1.50000i 0.137313 + 0.0792775i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 13.8564 8.00000i 0.728277 0.420471i
\(363\) 2.00000i 0.104973i
\(364\) −5.00000 + 5.19615i −0.262071 + 0.272352i
\(365\) 0 0
\(366\) 1.00000 + 1.73205i 0.0522708 + 0.0905357i
\(367\) 17.3205 10.0000i 0.904123 0.521996i 0.0255875 0.999673i \(-0.491854\pi\)
0.878536 + 0.477677i \(0.158521\pi\)
\(368\) 2.59808 + 1.50000i 0.135434 + 0.0781929i
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 5.00000i 0.259238i
\(373\) −21.6506 12.5000i −1.12103 0.647225i −0.179364 0.983783i \(-0.557404\pi\)
−0.941663 + 0.336557i \(0.890737\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) 7.79423 + 7.50000i 0.401423 + 0.386270i
\(378\) 2.00000i 0.102869i
\(379\) 19.0000 + 32.9090i 0.975964 + 1.69042i 0.676715 + 0.736245i \(0.263403\pi\)
0.299249 + 0.954175i \(0.403264\pi\)
\(380\) 0 0
\(381\) −7.00000 + 12.1244i −0.358621 + 0.621150i
\(382\) 12.0000i 0.613973i
\(383\) −18.1865 10.5000i −0.929288 0.536525i −0.0427020 0.999088i \(-0.513597\pi\)
−0.886586 + 0.462563i \(0.846930\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −2.00000 + 3.46410i −0.101797 + 0.176318i
\(387\) −0.866025 + 0.500000i −0.0440225 + 0.0254164i
\(388\) −12.1244 + 7.00000i −0.615521 + 0.355371i
\(389\) −3.00000 −0.152106 −0.0760530 0.997104i \(-0.524232\pi\)
−0.0760530 + 0.997104i \(0.524232\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 2.59808 1.50000i 0.131223 0.0757614i
\(393\) −7.79423 + 4.50000i −0.393167 + 0.226995i
\(394\) −12.0000 + 20.7846i −0.604551 + 1.04711i
\(395\) 0 0
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) 26.8468 + 15.5000i 1.34740 + 0.777923i 0.987881 0.155214i \(-0.0496068\pi\)
0.359521 + 0.933137i \(0.382940\pi\)
\(398\) 8.00000i 0.401004i
\(399\) 2.00000 3.46410i 0.100125 0.173422i
\(400\) 0 0
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 8.00000i 0.399004i
\(403\) 17.3205 5.00000i 0.862796 0.249068i
\(404\) −6.00000 −0.298511
\(405\) 0 0
\(406\) 3.00000 + 5.19615i 0.148888 + 0.257881i
\(407\) −18.1865 10.5000i −0.901473 0.520466i
\(408\) 6.00000i 0.297044i
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) −12.1244 7.00000i −0.597324 0.344865i
\(413\) 15.5885 9.00000i 0.767058 0.442861i
\(414\) −1.50000 2.59808i −0.0737210 0.127688i
\(415\) 0 0
\(416\) 3.50000 + 0.866025i 0.171602 + 0.0424604i
\(417\) 14.0000i 0.685583i
\(418\) −5.19615 + 3.00000i −0.254152 + 0.146735i
\(419\) −6.00000 10.3923i −0.293119 0.507697i 0.681426 0.731887i \(-0.261360\pi\)
−0.974546 + 0.224189i \(0.928027\pi\)
\(420\) 0 0
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) 17.3205 + 10.0000i 0.843149 + 0.486792i
\(423\) −2.59808 1.50000i −0.126323 0.0729325i
\(424\) −6.00000 −0.291386
\(425\) 0 0
\(426\) −6.00000 10.3923i −0.290701 0.503509i
\(427\) 3.46410 2.00000i 0.167640 0.0967868i
\(428\) 6.00000i 0.290021i
\(429\) −10.5000 2.59808i −0.506945 0.125436i
\(430\) 0 0
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) −34.6410 20.0000i −1.66474 0.961139i −0.970404 0.241489i \(-0.922364\pi\)
−0.694337 0.719650i \(-0.744302\pi\)
\(434\) 10.0000 0.480015
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 6.00000i 0.287019i
\(438\) −12.1244 7.00000i −0.579324 0.334473i
\(439\) −2.00000 3.46410i −0.0954548 0.165333i 0.814344 0.580383i \(-0.197097\pi\)
−0.909798 + 0.415051i \(0.863764\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 20.7846 6.00000i 0.988623 0.285391i
\(443\) 36.0000i 1.71041i 0.518289 + 0.855206i \(0.326569\pi\)
−0.518289 + 0.855206i \(0.673431\pi\)
\(444\) −3.50000 6.06218i −0.166103 0.287698i
\(445\) 0 0
\(446\) −5.00000 + 8.66025i −0.236757 + 0.410075i
\(447\) 9.00000i 0.425685i
\(448\) 1.73205 + 1.00000i 0.0818317 + 0.0472456i
\(449\) 18.0000 31.1769i 0.849473 1.47133i −0.0322072 0.999481i \(-0.510254\pi\)
0.881680 0.471848i \(-0.156413\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) 12.9904 7.50000i 0.611016 0.352770i
\(453\) −6.92820 + 4.00000i −0.325515 + 0.187936i
\(454\) 0 0
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 1.73205 1.00000i 0.0810219 0.0467780i −0.458942 0.888466i \(-0.651771\pi\)
0.539964 + 0.841688i \(0.318438\pi\)
\(458\) 12.1244 7.00000i 0.566534 0.327089i
\(459\) 3.00000 5.19615i 0.140028 0.242536i
\(460\) 0 0
\(461\) −7.50000 + 12.9904i −0.349310 + 0.605022i −0.986127 0.165992i \(-0.946917\pi\)
0.636817 + 0.771015i \(0.280251\pi\)
\(462\) −5.19615 3.00000i −0.241747 0.139573i
\(463\) 34.0000i 1.58011i 0.613033 + 0.790057i \(0.289949\pi\)
−0.613033 + 0.790057i \(0.710051\pi\)
\(464\) 1.50000 2.59808i 0.0696358 0.120613i
\(465\) 0 0
\(466\) 10.5000 + 18.1865i 0.486403 + 0.842475i
\(467\) 18.0000i 0.832941i 0.909149 + 0.416470i \(0.136733\pi\)
−0.909149 + 0.416470i \(0.863267\pi\)
\(468\) −2.59808 2.50000i −0.120096 0.115563i
\(469\) −16.0000 −0.738811
\(470\) 0 0
\(471\) 6.50000 + 11.2583i 0.299504 + 0.518756i
\(472\) −7.79423 4.50000i −0.358758 0.207129i
\(473\) 3.00000i 0.137940i
\(474\) −2.50000 + 4.33013i −0.114829 + 0.198889i
\(475\) 0 0
\(476\) 12.0000 0.550019
\(477\) 5.19615 + 3.00000i 0.237915 + 0.137361i
\(478\) 20.7846 12.0000i 0.950666 0.548867i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) −17.5000 + 18.1865i −0.797931 + 0.829235i
\(482\) 17.0000i 0.774329i
\(483\) −5.19615 + 3.00000i −0.236433 + 0.136505i
\(484\) −1.00000 1.73205i −0.0454545 0.0787296i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −1.73205 1.00000i −0.0784867 0.0453143i 0.460243 0.887793i \(-0.347762\pi\)
−0.538730 + 0.842479i \(0.681096\pi\)
\(488\) −1.73205 1.00000i −0.0784063 0.0452679i
\(489\) 13.0000 0.587880
\(490\) 0 0
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 5.19615 3.00000i 0.234261 0.135250i
\(493\) 18.0000i 0.810679i
\(494\) 2.00000 + 6.92820i 0.0899843 + 0.311715i
\(495\) 0 0
\(496\) −2.50000 4.33013i −0.112253 0.194428i
\(497\) −20.7846 + 12.0000i −0.932317 + 0.538274i
\(498\) 5.19615 + 3.00000i 0.232845 + 0.134433i
\(499\) −32.0000 −1.43252 −0.716258 0.697835i \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) 0 0
\(501\) 4.50000 7.79423i 0.201045 0.348220i
\(502\) 15.0000i 0.669483i
\(503\) 20.7846 + 12.0000i 0.926740 + 0.535054i 0.885779 0.464107i \(-0.153625\pi\)
0.0409609 + 0.999161i \(0.486958\pi\)
\(504\) −1.00000 1.73205i −0.0445435 0.0771517i
\(505\) 0 0
\(506\) 9.00000 0.400099
\(507\) −6.06218 + 11.5000i −0.269231 + 0.510733i
\(508\) 14.0000i 0.621150i
\(509\) 1.50000 + 2.59808i 0.0664863 + 0.115158i 0.897352 0.441315i \(-0.145488\pi\)
−0.830866 + 0.556473i \(0.812154\pi\)
\(510\) 0 0
\(511\) −14.0000 + 24.2487i −0.619324 + 1.07270i
\(512\) 1.00000i 0.0441942i
\(513\) 1.73205 + 1.00000i 0.0764719 + 0.0441511i
\(514\) 10.5000 18.1865i 0.463135 0.802174i
\(515\) 0 0
\(516\) 0.500000 0.866025i 0.0220113 0.0381246i
\(517\) 7.79423 4.50000i 0.342790 0.197910i
\(518\) −12.1244 + 7.00000i −0.532714 + 0.307562i
\(519\) −12.0000 −0.526742
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) −2.59808 + 1.50000i −0.113715 + 0.0656532i
\(523\) −9.52628 + 5.50000i −0.416555 + 0.240498i −0.693602 0.720358i \(-0.743977\pi\)
0.277047 + 0.960856i \(0.410644\pi\)
\(524\) 4.50000 7.79423i 0.196583 0.340492i
\(525\) 0 0
\(526\) −7.50000 + 12.9904i −0.327016 + 0.566408i
\(527\) −25.9808 15.0000i −1.13174 0.653410i
\(528\) 3.00000i 0.130558i
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) 0 0
\(531\) 4.50000 + 7.79423i 0.195283 + 0.338241i
\(532\) 4.00000i 0.173422i
\(533\) −15.5885 15.0000i −0.675211 0.649722i
\(534\) −18.0000 −0.778936
\(535\) 0 0
\(536\) 4.00000 + 6.92820i 0.172774 + 0.299253i
\(537\) 2.59808 + 1.50000i 0.112115 + 0.0647298i
\(538\) 18.0000i 0.776035i
\(539\) 4.50000 7.79423i 0.193829 0.335721i
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 9.52628 + 5.50000i 0.409189 + 0.236245i
\(543\) 13.8564 8.00000i 0.594635 0.343313i
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) 0 0
\(546\) −5.00000 + 5.19615i −0.213980 + 0.222375i
\(547\) 20.0000i 0.855138i 0.903983 + 0.427569i \(0.140630\pi\)
−0.903983 + 0.427569i \(0.859370\pi\)
\(548\) −7.79423 + 4.50000i −0.332953 + 0.192230i
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) 2.59808 + 1.50000i 0.110581 + 0.0638442i
\(553\) 8.66025 + 5.00000i 0.368271 + 0.212622i
\(554\) −1.00000 −0.0424859
\(555\) 0 0
\(556\) −7.00000 12.1244i −0.296866 0.514187i
\(557\) −5.19615 + 3.00000i −0.220168 + 0.127114i −0.606028 0.795443i \(-0.707238\pi\)
0.385860 + 0.922557i \(0.373905\pi\)
\(558\) 5.00000i 0.211667i
\(559\) −3.50000 0.866025i −0.148034 0.0366290i
\(560\) 0 0
\(561\) 9.00000 + 15.5885i 0.379980 + 0.658145i
\(562\) −15.5885 + 9.00000i −0.657559 + 0.379642i
\(563\) 31.1769 + 18.0000i 1.31395 + 0.758610i 0.982748 0.184950i \(-0.0592124\pi\)
0.331202 + 0.943560i \(0.392546\pi\)
\(564\) 3.00000 0.126323
\(565\) 0 0
\(566\) −15.5000 + 26.8468i −0.651514 + 1.12845i
\(567\) 2.00000i 0.0839921i
\(568\) 10.3923 + 6.00000i 0.436051 + 0.251754i
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) 10.3923 3.00000i 0.434524 0.125436i
\(573\) 12.0000i 0.501307i
\(574\) −6.00000 10.3923i −0.250435 0.433766i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 2.00000i 0.0832611i 0.999133 + 0.0416305i \(0.0132552\pi\)
−0.999133 + 0.0416305i \(0.986745\pi\)
\(578\) −16.4545 9.50000i −0.684416 0.395148i
\(579\) −2.00000 + 3.46410i −0.0831172 + 0.143963i
\(580\) 0 0
\(581\) 6.00000 10.3923i 0.248922 0.431145i
\(582\) −12.1244 + 7.00000i −0.502571 + 0.290159i
\(583\) −15.5885 + 9.00000i −0.645608 + 0.372742i
\(584\) 14.0000 0.579324
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 15.5885 9.00000i 0.643404 0.371470i −0.142520 0.989792i \(-0.545521\pi\)
0.785925 + 0.618322i \(0.212187\pi\)
\(588\) 2.59808 1.50000i 0.107143 0.0618590i
\(589\) 5.00000 8.66025i 0.206021 0.356840i
\(590\) 0 0
\(591\) −12.0000 + 20.7846i −0.493614 + 0.854965i
\(592\) 6.06218 + 3.50000i 0.249154 + 0.143849i
\(593\) 27.0000i 1.10876i −0.832265 0.554379i \(-0.812956\pi\)
0.832265 0.554379i \(-0.187044\pi\)
\(594\) 1.50000 2.59808i 0.0615457 0.106600i
\(595\) 0 0
\(596\) 4.50000 + 7.79423i 0.184327 + 0.319264i
\(597\) 8.00000i 0.327418i
\(598\) 2.59808 10.5000i 0.106243 0.429377i
\(599\) −6.00000 −0.245153 −0.122577 0.992459i \(-0.539116\pi\)
−0.122577 + 0.992459i \(0.539116\pi\)
\(600\) 0 0
\(601\) 9.50000 + 16.4545i 0.387513 + 0.671192i 0.992114 0.125336i \(-0.0400009\pi\)
−0.604601 + 0.796528i \(0.706668\pi\)
\(602\) −1.73205 1.00000i −0.0705931 0.0407570i
\(603\) 8.00000i 0.325785i
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) 19.0526 + 11.0000i 0.773320 + 0.446476i 0.834058 0.551678i \(-0.186012\pi\)
−0.0607380 + 0.998154i \(0.519345\pi\)
\(608\) 1.73205 1.00000i 0.0702439 0.0405554i
\(609\) 3.00000 + 5.19615i 0.121566 + 0.210559i
\(610\) 0 0
\(611\) −3.00000 10.3923i −0.121367 0.420428i
\(612\) 6.00000i 0.242536i
\(613\) 26.8468 15.5000i 1.08433 0.626039i 0.152270 0.988339i \(-0.451342\pi\)
0.932062 + 0.362300i \(0.118008\pi\)
\(614\) −4.00000 6.92820i −0.161427 0.279600i
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) −18.1865 10.5000i −0.732162 0.422714i 0.0870504 0.996204i \(-0.472256\pi\)
−0.819213 + 0.573490i \(0.805589\pi\)
\(618\) −12.1244 7.00000i −0.487713 0.281581i
\(619\) 46.0000 1.84890 0.924448 0.381308i \(-0.124526\pi\)
0.924448 + 0.381308i \(0.124526\pi\)
\(620\) 0 0
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) 10.3923 6.00000i 0.416693 0.240578i
\(623\) 36.0000i 1.44231i
\(624\) 3.50000 + 0.866025i 0.140112 + 0.0346688i
\(625\) 0 0
\(626\) 4.00000 + 6.92820i 0.159872 + 0.276907i
\(627\) −5.19615 + 3.00000i −0.207514 + 0.119808i
\(628\) −11.2583 6.50000i −0.449256 0.259378i
\(629\) 42.0000 1.67465
\(630\) 0 0
\(631\) 8.00000 13.8564i 0.318475 0.551615i −0.661695 0.749773i \(-0.730163\pi\)
0.980170 + 0.198158i \(0.0634960\pi\)
\(632\) 5.00000i 0.198889i
\(633\) 17.3205 + 10.0000i 0.688428 + 0.397464i
\(634\) −6.00000 10.3923i −0.238290 0.412731i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) −7.79423 7.50000i −0.308819 0.297161i
\(638\) 9.00000i 0.356313i
\(639\) −6.00000 10.3923i −0.237356 0.411113i
\(640\) 0 0
\(641\) −3.00000 + 5.19615i −0.118493 + 0.205236i −0.919171 0.393860i \(-0.871140\pi\)
0.800678 + 0.599095i \(0.204473\pi\)
\(642\) 6.00000i 0.236801i
\(643\) −13.8564 8.00000i −0.546443 0.315489i 0.201243 0.979541i \(-0.435502\pi\)
−0.747686 + 0.664052i \(0.768835\pi\)
\(644\) 3.00000 5.19615i 0.118217 0.204757i
\(645\) 0 0
\(646\) 6.00000 10.3923i 0.236067 0.408880i
\(647\) 20.7846 12.0000i 0.817127 0.471769i −0.0322975 0.999478i \(-0.510282\pi\)
0.849425 + 0.527710i \(0.176949\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −27.0000 −1.05984
\(650\) 0 0
\(651\) 10.0000 0.391931
\(652\) −11.2583 + 6.50000i −0.440910 + 0.254560i
\(653\) −5.19615 + 3.00000i −0.203341 + 0.117399i −0.598213 0.801337i \(-0.704122\pi\)
0.394872 + 0.918736i \(0.370789\pi\)
\(654\) −7.00000 + 12.1244i −0.273722 + 0.474100i
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) −12.1244 7.00000i −0.473016 0.273096i
\(658\) 6.00000i 0.233904i
\(659\) 7.50000 12.9904i 0.292159 0.506033i −0.682161 0.731202i \(-0.738960\pi\)
0.974320 + 0.225168i \(0.0722932\pi\)
\(660\) 0 0
\(661\) −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i \(-0.952854\pi\)
0.366723 0.930330i \(-0.380480\pi\)
\(662\) 32.0000i 1.24372i
\(663\) 20.7846 6.00000i 0.807207 0.233021i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) −3.50000 6.06218i −0.135622 0.234905i
\(667\) −7.79423 4.50000i −0.301794 0.174241i
\(668\) 9.00000i 0.348220i
\(669\) −5.00000 + 8.66025i −0.193311 + 0.334825i
\(670\) 0 0
\(671\) −6.00000 −0.231627
\(672\) 1.73205 + 1.00000i 0.0668153 + 0.0385758i
\(673\) 3.46410 2.00000i 0.133531 0.0770943i −0.431746 0.901995i \(-0.642102\pi\)
0.565278 + 0.824901i \(0.308769\pi\)
\(674\) −7.00000 12.1244i −0.269630 0.467013i
\(675\) 0 0
\(676\) −0.500000 12.9904i −0.0192308 0.499630i
\(677\) 36.0000i 1.38359i −0.722093 0.691796i \(-0.756820\pi\)
0.722093 0.691796i \(-0.243180\pi\)
\(678\) 12.9904 7.50000i 0.498893 0.288036i
\(679\) 14.0000 + 24.2487i 0.537271 + 0.930580i
\(680\) 0 0
\(681\) 0 0
\(682\) −12.9904 7.50000i −0.497427 0.287190i
\(683\) −10.3923 6.00000i −0.397650 0.229584i 0.287819 0.957685i \(-0.407070\pi\)
−0.685470 + 0.728101i \(0.740403\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 0 0
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 12.1244 7.00000i 0.462573 0.267067i
\(688\) 1.00000i 0.0381246i
\(689\) 6.00000 + 20.7846i 0.228582 + 0.791831i
\(690\) 0 0
\(691\) 23.0000 + 39.8372i 0.874961 + 1.51548i 0.856804 + 0.515642i \(0.172447\pi\)
0.0181572 + 0.999835i \(0.494220\pi\)
\(692\) 10.3923 6.00000i 0.395056 0.228086i
\(693\) −5.19615 3.00000i −0.197386 0.113961i
\(694\) −30.0000 −1.13878
\(695\) 0 0
\(696\) 1.50000 2.59808i 0.0568574 0.0984798i
\(697\) 36.0000i 1.36360i
\(698\) −6.92820 4.00000i −0.262236 0.151402i
\(699\) 10.5000 + 18.1865i 0.397146 + 0.687878i
\(700\) 0 0
\(701\) −21.0000 −0.793159 −0.396580 0.918000i \(-0.629803\pi\)
−0.396580 + 0.918000i \(0.629803\pi\)
\(702\) −2.59808 2.50000i −0.0980581 0.0943564i
\(703\) 14.0000i 0.528020i
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) 0 0
\(706\) 15.0000 25.9808i 0.564532 0.977799i
\(707\) 12.0000i 0.451306i
\(708\) −7.79423 4.50000i −0.292925 0.169120i
\(709\) 16.0000 27.7128i 0.600893 1.04078i −0.391794 0.920053i \(-0.628145\pi\)
0.992686 0.120723i \(-0.0385214\pi\)
\(710\) 0 0
\(711\) −2.50000 + 4.33013i −0.0937573 + 0.162392i
\(712\) 15.5885 9.00000i 0.584202 0.337289i
\(713\) −12.9904 + 7.50000i −0.486494 + 0.280877i
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) −3.00000 −0.112115
\(717\) 20.7846 12.0000i 0.776215 0.448148i
\(718\) 20.7846 12.0000i 0.775675 0.447836i
\(719\) 18.0000 31.1769i 0.671287 1.16270i −0.306253 0.951950i \(-0.599075\pi\)
0.977539 0.210752i \(-0.0675914\pi\)
\(720\) 0 0
\(721\) −14.0000 + 24.2487i −0.521387 + 0.903069i
\(722\) −12.9904 7.50000i −0.483452 0.279121i
\(723\) 17.0000i 0.632237i
\(724\) −8.00000 + 13.8564i −0.297318 + 0.514969i
\(725\) 0 0
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) 4.00000i 0.148352i −0.997245 0.0741759i \(-0.976367\pi\)
0.997245 0.0741759i \(-0.0236326\pi\)
\(728\) 1.73205 7.00000i 0.0641941 0.259437i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 3.00000 + 5.19615i 0.110959 + 0.192187i
\(732\) −1.73205 1.00000i −0.0640184 0.0369611i
\(733\) 22.0000i 0.812589i 0.913742 + 0.406294i \(0.133179\pi\)
−0.913742 + 0.406294i \(0.866821\pi\)
\(734\) −10.0000 + 17.3205i −0.369107 + 0.639312i
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 20.7846 + 12.0000i 0.765611 + 0.442026i
\(738\) 5.19615 3.00000i 0.191273 0.110432i
\(739\) −8.00000 13.8564i −0.294285 0.509716i 0.680534 0.732717i \(-0.261748\pi\)
−0.974818 + 0.223001i \(0.928415\pi\)
\(740\) 0 0
\(741\) 2.00000 + 6.92820i 0.0734718 + 0.254514i
\(742\) 12.0000i 0.440534i
\(743\) 7.79423 4.50000i 0.285943 0.165089i −0.350168 0.936687i \(-0.613876\pi\)
0.636111 + 0.771598i \(0.280542\pi\)
\(744\) −2.50000 4.33013i −0.0916544 0.158750i
\(745\) 0 0
\(746\) 25.0000 0.915315
\(747\) 5.19615 + 3.00000i 0.190117 + 0.109764i
\(748\) −15.5885 9.00000i −0.569970 0.329073i
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −20.5000 35.5070i −0.748056 1.29567i −0.948753 0.316017i \(-0.897654\pi\)
0.200698 0.979653i \(-0.435679\pi\)
\(752\) −2.59808 + 1.50000i −0.0947421 + 0.0546994i
\(753\) 15.0000i 0.546630i
\(754\) −10.5000 2.59808i −0.382387 0.0946164i
\(755\) 0 0
\(756\) −1.00000 1.73205i −0.0363696 0.0629941i
\(757\) 32.9090 19.0000i 1.19610 0.690567i 0.236414 0.971652i \(-0.424028\pi\)
0.959683 + 0.281086i \(0.0906945\pi\)
\(758\) −32.9090 19.0000i −1.19531 0.690111i
\(759\) 9.00000 0.326679
\(760\) 0 0
\(761\) 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i \(-0.763543\pi\)
0.954043 + 0.299670i \(0.0968765\pi\)
\(762\) 14.0000i 0.507166i
\(763\) 24.2487 + 14.0000i 0.877862 + 0.506834i
\(764\) −6.00000 10.3923i −0.217072 0.375980i
\(765\) 0 0
\(766\) 21.0000 0.758761
\(767\) −7.79423 + 31.5000i −0.281433 + 1.13740i
\(768\) 1.00000i 0.0360844i
\(769\) −6.50000 11.2583i −0.234396 0.405986i 0.724701 0.689063i \(-0.241978\pi\)
−0.959097 + 0.283078i \(0.908645\pi\)
\(770\) 0 0
\(771\) 10.5000 18.1865i 0.378148 0.654972i
\(772\) 4.00000i 0.143963i
\(773\) −41.5692 24.0000i −1.49514 0.863220i −0.495156 0.868804i \(-0.664889\pi\)
−0.999984 + 0.00558380i \(0.998223\pi\)
\(774\) 0.500000 0.866025i 0.0179721 0.0311286i
\(775\) 0 0
\(776\) 7.00000 12.1244i 0.251285 0.435239i
\(777\) −12.1244 + 7.00000i −0.434959 + 0.251124i
\(778\) 2.59808 1.50000i 0.0931455 0.0537776i
\(779\) −12.0000 −0.429945
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) −15.5885 + 9.00000i −0.557442 + 0.321839i
\(783\) −2.59808 + 1.50000i −0.0928477 + 0.0536056i
\(784\) −1.50000 + 2.59808i −0.0535714 +