Properties

Label 1950.2.z.i.1699.1
Level $1950$
Weight $2$
Character 1950.1699
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 1699.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1699
Dual form 1950.2.z.i.1849.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.00000i q^{12} +(-2.59808 - 2.50000i) q^{13} +3.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} -1.00000i q^{18} +(-2.50000 - 4.33013i) q^{19} +3.00000 q^{21} +(0.866025 - 0.500000i) q^{22} +(-3.46410 - 2.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(1.00000 + 3.46410i) q^{26} -1.00000i q^{27} +(-2.59808 - 1.50000i) q^{28} +10.0000 q^{31} +(0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} +(-0.500000 + 0.866025i) q^{36} +(0.866025 + 0.500000i) q^{37} +5.00000i q^{38} +(1.00000 + 3.46410i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-2.59808 - 1.50000i) q^{42} +(1.73205 - 1.00000i) q^{43} -1.00000 q^{44} +(2.00000 + 3.46410i) q^{46} -9.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(1.00000 - 1.73205i) q^{49} +(0.866025 - 3.50000i) q^{52} +13.0000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.50000 + 2.59808i) q^{56} +5.00000i q^{57} +(2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-8.66025 - 5.00000i) q^{62} +(-2.59808 - 1.50000i) q^{63} -1.00000 q^{64} -1.00000 q^{66} +(10.3923 + 6.00000i) q^{67} +(2.00000 + 3.46410i) q^{69} +(1.00000 + 1.73205i) q^{71} +(0.866025 - 0.500000i) q^{72} +16.0000i q^{73} +(-0.500000 - 0.866025i) q^{74} +(2.50000 - 4.33013i) q^{76} -3.00000i q^{77} +(0.866025 - 3.50000i) q^{78} +10.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.19615 - 3.00000i) q^{82} -12.0000i q^{83} +(1.50000 + 2.59808i) q^{84} -2.00000 q^{86} +(0.866025 + 0.500000i) q^{88} +(0.500000 - 0.866025i) q^{89} +(10.5000 + 2.59808i) q^{91} -4.00000i q^{92} +(-8.66025 - 5.00000i) q^{93} +(-4.50000 + 7.79423i) q^{94} -1.00000 q^{96} +(10.3923 - 6.00000i) q^{97} +(-1.73205 + 1.00000i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 2q^{6} + 2q^{9} - 2q^{11} + 12q^{14} - 2q^{16} - 10q^{19} + 12q^{21} - 2q^{24} + 4q^{26} + 40q^{31} - 2q^{36} + 4q^{39} - 12q^{41} - 4q^{44} + 8q^{46} + 4q^{49} - 2q^{54} + 6q^{56} + 8q^{59} + 4q^{61} - 4q^{64} - 4q^{66} + 8q^{69} + 4q^{71} - 2q^{74} + 10q^{76} + 40q^{79} - 2q^{81} + 6q^{84} - 8q^{86} + 2q^{89} + 42q^{91} - 18q^{94} - 4q^{96} - 4q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\)

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
\(7\) −2.59808 + 1.50000i −0.981981 + 0.566947i −0.902867 0.429919i \(-0.858542\pi\)
−0.0791130 + 0.996866i \(0.525209\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −2.59808 2.50000i −0.720577 0.693375i
\(14\) 3.00000 0.801784
\(15\) 0 0
\(16\) −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
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) 0.866025 0.500000i 0.184637 0.106600i
\(23\) −3.46410 2.00000i −0.722315 0.417029i 0.0932891 0.995639i \(-0.470262\pi\)
−0.815604 + 0.578610i \(0.803595\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 1.00000 + 3.46410i 0.196116 + 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) −2.59808 1.50000i −0.490990 0.283473i
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0.866025 0.500000i 0.150756 0.0870388i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 0.866025 + 0.500000i 0.142374 + 0.0821995i 0.569495 0.821995i \(-0.307139\pi\)
−0.427121 + 0.904194i \(0.640472\pi\)
\(38\) 5.00000i 0.811107i
\(39\) 1.00000 + 3.46410i 0.160128 + 0.554700i
\(40\) 0 0
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) −2.59808 1.50000i −0.400892 0.231455i
\(43\) 1.73205 1.00000i 0.264135 0.152499i −0.362084 0.932145i \(-0.617935\pi\)
0.626219 + 0.779647i \(0.284601\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) 9.00000i 1.31278i −0.754420 0.656392i \(-0.772082\pi\)
0.754420 0.656392i \(-0.227918\pi\)
\(48\) 0.866025 0.500000i 0.125000 0.0721688i
\(49\) 1.00000 1.73205i 0.142857 0.247436i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.866025 3.50000i 0.120096 0.485363i
\(53\) 13.0000i 1.78569i 0.450367 + 0.892844i \(0.351293\pi\)
−0.450367 + 0.892844i \(0.648707\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 0 0
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) 5.00000i 0.662266i
\(58\) 0 0
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) −8.66025 5.00000i −1.09985 0.635001i
\(63\) −2.59808 1.50000i −0.327327 0.188982i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −1.00000 −0.123091
\(67\) 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
\(69\) 2.00000 + 3.46410i 0.240772 + 0.417029i
\(70\) 0 0
\(71\) 1.00000 + 1.73205i 0.118678 + 0.205557i 0.919244 0.393688i \(-0.128801\pi\)
−0.800566 + 0.599245i \(0.795468\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 16.0000i 1.87266i 0.351123 + 0.936329i \(0.385800\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −0.500000 0.866025i −0.0581238 0.100673i
\(75\) 0 0
\(76\) 2.50000 4.33013i 0.286770 0.496700i
\(77\) 3.00000i 0.341882i
\(78\) 0.866025 3.50000i 0.0980581 0.396297i
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 5.19615 3.00000i 0.573819 0.331295i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 1.50000 + 2.59808i 0.163663 + 0.283473i
\(85\) 0 0
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) 0.866025 + 0.500000i 0.0923186 + 0.0533002i
\(89\) 0.500000 0.866025i 0.0529999 0.0917985i −0.838308 0.545197i \(-0.816455\pi\)
0.891308 + 0.453398i \(0.149788\pi\)
\(90\) 0 0
\(91\) 10.5000 + 2.59808i 1.10070 + 0.272352i
\(92\) 4.00000i 0.417029i
\(93\) −8.66025 5.00000i −0.898027 0.518476i
\(94\) −4.50000 + 7.79423i −0.464140 + 0.803913i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 10.3923 6.00000i 1.05518 0.609208i 0.131084 0.991371i \(-0.458154\pi\)
0.924095 + 0.382164i \(0.124821\pi\)
\(98\) −1.73205 + 1.00000i −0.174964 + 0.101015i
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) −2.00000 + 3.46410i −0.199007 + 0.344691i −0.948207 0.317653i \(-0.897105\pi\)
0.749199 + 0.662344i \(0.230438\pi\)
\(102\) 0 0
\(103\) 9.00000i 0.886796i 0.896325 + 0.443398i \(0.146227\pi\)
−0.896325 + 0.443398i \(0.853773\pi\)
\(104\) −2.50000 + 2.59808i −0.245145 + 0.254762i
\(105\) 0 0
\(106\) 6.50000 11.2583i 0.631336 1.09351i
\(107\) 5.19615 + 3.00000i 0.502331 + 0.290021i 0.729676 0.683793i \(-0.239671\pi\)
−0.227345 + 0.973814i \(0.573004\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) −0.500000 0.866025i −0.0474579 0.0821995i
\(112\) 3.00000i 0.283473i
\(113\) −13.8564 + 8.00000i −1.30350 + 0.752577i −0.981003 0.193993i \(-0.937856\pi\)
−0.322498 + 0.946570i \(0.604523\pi\)
\(114\) 2.50000 4.33013i 0.234146 0.405554i
\(115\) 0 0
\(116\) 0 0
\(117\) 0.866025 3.50000i 0.0800641 0.323575i
\(118\) 4.00000i 0.368230i
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 2.00000i 0.181071i
\(123\) 5.19615 3.00000i 0.468521 0.270501i
\(124\) 5.00000 + 8.66025i 0.449013 + 0.777714i
\(125\) 0 0
\(126\) 1.50000 + 2.59808i 0.133631 + 0.231455i
\(127\) −4.33013 2.50000i −0.384237 0.221839i 0.295423 0.955366i \(-0.404539\pi\)
−0.679660 + 0.733527i \(0.737873\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −2.00000 −0.176090
\(130\) 0 0
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 0.866025 + 0.500000i 0.0753778 + 0.0435194i
\(133\) 12.9904 + 7.50000i 1.12641 + 0.650332i
\(134\) −6.00000 10.3923i −0.518321 0.897758i
\(135\) 0 0
\(136\) 0 0
\(137\) 13.8564 8.00000i 1.18383 0.683486i 0.226935 0.973910i \(-0.427130\pi\)
0.956898 + 0.290424i \(0.0937963\pi\)
\(138\) 4.00000i 0.340503i
\(139\) −4.50000 7.79423i −0.381685 0.661098i 0.609618 0.792695i \(-0.291323\pi\)
−0.991303 + 0.131597i \(0.957989\pi\)
\(140\) 0 0
\(141\) −4.50000 + 7.79423i −0.378968 + 0.656392i
\(142\) 2.00000i 0.167836i
\(143\) 3.46410 1.00000i 0.289683 0.0836242i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 8.00000 13.8564i 0.662085 1.14676i
\(147\) −1.73205 + 1.00000i −0.142857 + 0.0824786i
\(148\) 1.00000i 0.0821995i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −6.00000 −0.488273 −0.244137 0.969741i \(-0.578505\pi\)
−0.244137 + 0.969741i \(0.578505\pi\)
\(152\) −4.33013 + 2.50000i −0.351220 + 0.202777i
\(153\) 0 0
\(154\) −1.50000 + 2.59808i −0.120873 + 0.209359i
\(155\) 0 0
\(156\) −2.50000 + 2.59808i −0.200160 + 0.208013i
\(157\) 1.00000i 0.0798087i 0.999204 + 0.0399043i \(0.0127053\pi\)
−0.999204 + 0.0399043i \(0.987295\pi\)
\(158\) −8.66025 5.00000i −0.688973 0.397779i
\(159\) 6.50000 11.2583i 0.515484 0.892844i
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) 17.3205 10.0000i 1.35665 0.783260i 0.367477 0.930033i \(-0.380222\pi\)
0.989170 + 0.146772i \(0.0468885\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −6.00000 + 10.3923i −0.465690 + 0.806599i
\(167\) 11.2583 + 6.50000i 0.871196 + 0.502985i 0.867745 0.497009i \(-0.165568\pi\)
0.00345033 + 0.999994i \(0.498902\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 0.500000 + 12.9904i 0.0384615 + 0.999260i
\(170\) 0 0
\(171\) 2.50000 4.33013i 0.191180 0.331133i
\(172\) 1.73205 + 1.00000i 0.132068 + 0.0762493i
\(173\) 7.79423 4.50000i 0.592584 0.342129i −0.173534 0.984828i \(-0.555519\pi\)
0.766119 + 0.642699i \(0.222185\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.500000 0.866025i −0.0376889 0.0652791i
\(177\) 4.00000i 0.300658i
\(178\) −0.866025 + 0.500000i −0.0649113 + 0.0374766i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) −7.79423 7.50000i −0.577747 0.555937i
\(183\) 2.00000i 0.147844i
\(184\) −2.00000 + 3.46410i −0.147442 + 0.255377i
\(185\) 0 0
\(186\) 5.00000 + 8.66025i 0.366618 + 0.635001i
\(187\) 0 0
\(188\) 7.79423 4.50000i 0.568453 0.328196i
\(189\) 1.50000 + 2.59808i 0.109109 + 0.188982i
\(190\) 0 0
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 13.8564 + 8.00000i 0.997406 + 0.575853i 0.907480 0.420096i \(-0.138004\pi\)
0.0899262 + 0.995948i \(0.471337\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 12.9904 + 7.50000i 0.925526 + 0.534353i 0.885394 0.464841i \(-0.153889\pi\)
0.0401324 + 0.999194i \(0.487222\pi\)
\(198\) 0.866025 + 0.500000i 0.0615457 + 0.0355335i
\(199\) −1.00000 1.73205i −0.0708881 0.122782i 0.828403 0.560133i \(-0.189250\pi\)
−0.899291 + 0.437351i \(0.855917\pi\)
\(200\) 0 0
\(201\) −6.00000 10.3923i −0.423207 0.733017i
\(202\) 3.46410 2.00000i 0.243733 0.140720i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 4.50000 7.79423i 0.313530 0.543050i
\(207\) 4.00000i 0.278019i
\(208\) 3.46410 1.00000i 0.240192 0.0693375i
\(209\) 5.00000 0.345857
\(210\) 0 0
\(211\) 7.50000 12.9904i 0.516321 0.894295i −0.483499 0.875345i \(-0.660634\pi\)
0.999820 0.0189499i \(-0.00603229\pi\)
\(212\) −11.2583 + 6.50000i −0.773225 + 0.446422i
\(213\) 2.00000i 0.137038i
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −25.9808 + 15.0000i −1.76369 + 1.01827i
\(218\) −8.66025 5.00000i −0.586546 0.338643i
\(219\) 8.00000 13.8564i 0.540590 0.936329i
\(220\) 0 0
\(221\) 0 0
\(222\) 1.00000i 0.0671156i
\(223\) 9.52628 + 5.50000i 0.637927 + 0.368307i 0.783815 0.620994i \(-0.213271\pi\)
−0.145889 + 0.989301i \(0.546604\pi\)
\(224\) −1.50000 + 2.59808i −0.100223 + 0.173591i
\(225\) 0 0
\(226\) 16.0000 1.06430
\(227\) −17.3205 + 10.0000i −1.14960 + 0.663723i −0.948790 0.315906i \(-0.897691\pi\)
−0.200812 + 0.979630i \(0.564358\pi\)
\(228\) −4.33013 + 2.50000i −0.286770 + 0.165567i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −1.50000 + 2.59808i −0.0986928 + 0.170941i
\(232\) 0 0
\(233\) 10.0000i 0.655122i −0.944830 0.327561i \(-0.893773\pi\)
0.944830 0.327561i \(-0.106227\pi\)
\(234\) −2.50000 + 2.59808i −0.163430 + 0.169842i
\(235\) 0 0
\(236\) −2.00000 + 3.46410i −0.130189 + 0.225494i
\(237\) −8.66025 5.00000i −0.562544 0.324785i
\(238\) 0 0
\(239\) 2.00000 0.129369 0.0646846 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) 0 0
\(241\) −7.50000 12.9904i −0.483117 0.836784i 0.516695 0.856170i \(-0.327162\pi\)
−0.999812 + 0.0193858i \(0.993829\pi\)
\(242\) 10.0000i 0.642824i
\(243\) 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
\(247\) −4.33013 + 17.5000i −0.275519 + 1.11350i
\(248\) 10.0000i 0.635001i
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0 0
\(251\) −5.50000 9.52628i −0.347157 0.601293i 0.638586 0.769550i \(-0.279520\pi\)
−0.985743 + 0.168257i \(0.946186\pi\)
\(252\) 3.00000i 0.188982i
\(253\) 3.46410 2.00000i 0.217786 0.125739i
\(254\) 2.50000 + 4.33013i 0.156864 + 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 20.7846 + 12.0000i 1.29651 + 0.748539i 0.979799 0.199983i \(-0.0640888\pi\)
0.316709 + 0.948523i \(0.397422\pi\)
\(258\) 1.73205 + 1.00000i 0.107833 + 0.0622573i
\(259\) −3.00000 −0.186411
\(260\) 0 0
\(261\) 0 0
\(262\) 12.9904 + 7.50000i 0.802548 + 0.463352i
\(263\) 2.59808 + 1.50000i 0.160204 + 0.0924940i 0.577959 0.816066i \(-0.303849\pi\)
−0.417755 + 0.908560i \(0.637183\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) 0 0
\(266\) −7.50000 12.9904i −0.459855 0.796491i
\(267\) −0.866025 + 0.500000i −0.0529999 + 0.0305995i
\(268\) 12.0000i 0.733017i
\(269\) −10.0000 17.3205i −0.609711 1.05605i −0.991288 0.131713i \(-0.957952\pi\)
0.381577 0.924337i \(-0.375381\pi\)
\(270\) 0 0
\(271\) 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i \(-0.573343\pi\)
0.957328 0.289003i \(-0.0933238\pi\)
\(272\) 0 0
\(273\) −7.79423 7.50000i −0.471728 0.453921i
\(274\) −16.0000 −0.966595
\(275\) 0 0
\(276\) −2.00000 + 3.46410i −0.120386 + 0.208514i
\(277\) 19.9186 11.5000i 1.19679 0.690968i 0.236953 0.971521i \(-0.423851\pi\)
0.959839 + 0.280553i \(0.0905179\pi\)
\(278\) 9.00000i 0.539784i
\(279\) 5.00000 + 8.66025i 0.299342 + 0.518476i
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 7.79423 4.50000i 0.464140 0.267971i
\(283\) 1.73205 + 1.00000i 0.102960 + 0.0594438i 0.550596 0.834772i \(-0.314401\pi\)
−0.447636 + 0.894216i \(0.647734\pi\)
\(284\) −1.00000 + 1.73205i −0.0593391 + 0.102778i
\(285\) 0 0
\(286\) −3.50000 0.866025i −0.206959 0.0512092i
\(287\) 18.0000i 1.06251i
\(288\) 0.866025 + 0.500000i 0.0510310 + 0.0294628i
\(289\) −8.50000 + 14.7224i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) −12.0000 −0.703452
\(292\) −13.8564 + 8.00000i −0.810885 + 0.468165i
\(293\) −11.2583 + 6.50000i −0.657719 + 0.379734i −0.791407 0.611289i \(-0.790651\pi\)
0.133689 + 0.991023i \(0.457318\pi\)
\(294\) 2.00000 0.116642
\(295\) 0 0
\(296\) 0.500000 0.866025i 0.0290619 0.0503367i
\(297\) 0.866025 + 0.500000i 0.0502519 + 0.0290129i
\(298\) 6.00000i 0.347571i
\(299\) 4.00000 + 13.8564i 0.231326 + 0.801337i
\(300\) 0 0
\(301\) −3.00000 + 5.19615i −0.172917 + 0.299501i
\(302\) 5.19615 + 3.00000i 0.299005 + 0.172631i
\(303\) 3.46410 2.00000i 0.199007 0.114897i
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) 0 0
\(307\) 18.0000i 1.02731i 0.857996 + 0.513657i \(0.171710\pi\)
−0.857996 + 0.513657i \(0.828290\pi\)
\(308\) 2.59808 1.50000i 0.148039 0.0854704i
\(309\) 4.50000 7.79423i 0.255996 0.443398i
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 3.46410 1.00000i 0.196116 0.0566139i
\(313\) 34.0000i 1.92179i 0.276907 + 0.960897i \(0.410691\pi\)
−0.276907 + 0.960897i \(0.589309\pi\)
\(314\) 0.500000 0.866025i 0.0282166 0.0488726i
\(315\) 0 0
\(316\) 5.00000 + 8.66025i 0.281272 + 0.487177i
\(317\) 19.0000i 1.06715i 0.845754 + 0.533573i \(0.179151\pi\)
−0.845754 + 0.533573i \(0.820849\pi\)
\(318\) −11.2583 + 6.50000i −0.631336 + 0.364502i
\(319\) 0 0
\(320\) 0 0
\(321\) −3.00000 5.19615i −0.167444 0.290021i
\(322\) −10.3923 6.00000i −0.579141 0.334367i
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −20.0000 −1.10770
\(327\) −8.66025 5.00000i −0.478913 0.276501i
\(328\) 5.19615 + 3.00000i 0.286910 + 0.165647i
\(329\) 13.5000 + 23.3827i 0.744279 + 1.28913i
\(330\) 0 0
\(331\) −14.0000 24.2487i −0.769510 1.33283i −0.937829 0.347097i \(-0.887167\pi\)
0.168320 0.985732i \(-0.446166\pi\)
\(332\) 10.3923 6.00000i 0.570352 0.329293i
\(333\) 1.00000i 0.0547997i
\(334\) −6.50000 11.2583i −0.355664 0.616028i
\(335\) 0 0
\(336\) −1.50000 + 2.59808i −0.0818317 + 0.141737i
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) 6.06218 11.5000i 0.329739 0.625518i
\(339\) 16.0000 0.869001
\(340\) 0 0
\(341\) −5.00000 + 8.66025i −0.270765 + 0.468979i
\(342\) −4.33013 + 2.50000i −0.234146 + 0.135185i
\(343\) 15.0000i 0.809924i
\(344\) −1.00000 1.73205i −0.0539164 0.0933859i
\(345\) 0 0
\(346\) −9.00000 −0.483843
\(347\) −24.2487 + 14.0000i −1.30174 + 0.751559i −0.980702 0.195507i \(-0.937365\pi\)
−0.321037 + 0.947067i \(0.604031\pi\)
\(348\) 0 0
\(349\) 18.0000 31.1769i 0.963518 1.66886i 0.249973 0.968253i \(-0.419578\pi\)
0.713545 0.700609i \(-0.247088\pi\)
\(350\) 0 0
\(351\) −2.50000 + 2.59808i −0.133440 + 0.138675i
\(352\) 1.00000i 0.0533002i
\(353\) −31.1769 18.0000i −1.65938 0.958043i −0.973002 0.230799i \(-0.925866\pi\)
−0.686378 0.727245i \(-0.740800\pi\)
\(354\) −2.00000 + 3.46410i −0.106299 + 0.184115i
\(355\) 0 0
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) −10.3923 + 6.00000i −0.549250 + 0.317110i
\(359\) −34.0000 −1.79445 −0.897226 0.441572i \(-0.854421\pi\)
−0.897226 + 0.441572i \(0.854421\pi\)
\(360\) 0 0
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) −5.19615 3.00000i −0.273104 0.157676i
\(363\) 10.0000i 0.524864i
\(364\) 3.00000 + 10.3923i 0.157243 + 0.544705i
\(365\) 0 0
\(366\) −1.00000 + 1.73205i −0.0522708 + 0.0905357i
\(367\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) 3.46410 2.00000i 0.180579 0.104257i
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) −19.5000 33.7750i −1.01239 1.75351i
\(372\) 10.0000i 0.518476i
\(373\) −8.66025 + 5.00000i −0.448411 + 0.258890i −0.707159 0.707055i \(-0.750023\pi\)
0.258748 + 0.965945i \(0.416690\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −9.00000 −0.464140
\(377\) 0 0
\(378\) 3.00000i 0.154303i
\(379\) −0.500000 + 0.866025i −0.0256833 + 0.0444847i −0.878581 0.477593i \(-0.841509\pi\)
0.852898 + 0.522077i \(0.174843\pi\)
\(380\) 0 0
\(381\) 2.50000 + 4.33013i 0.128079 + 0.221839i
\(382\) 18.0000i 0.920960i
\(383\) 24.2487 14.0000i 1.23905 0.715367i 0.270151 0.962818i \(-0.412926\pi\)
0.968900 + 0.247451i \(0.0795931\pi\)
\(384\) −0.500000 0.866025i −0.0255155 0.0441942i
\(385\) 0 0
\(386\) −8.00000 13.8564i −0.407189 0.705273i
\(387\) 1.73205 + 1.00000i 0.0880451 + 0.0508329i
\(388\) 10.3923 + 6.00000i 0.527589 + 0.304604i
\(389\) 16.0000 0.811232 0.405616 0.914044i \(-0.367057\pi\)
0.405616 + 0.914044i \(0.367057\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.73205 1.00000i −0.0874818 0.0505076i
\(393\) 12.9904 + 7.50000i 0.655278 + 0.378325i
\(394\) −7.50000 12.9904i −0.377845 0.654446i
\(395\) 0 0
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) −28.5788 + 16.5000i −1.43433 + 0.828111i −0.997447 0.0714068i \(-0.977251\pi\)
−0.436884 + 0.899518i \(0.643918\pi\)
\(398\) 2.00000i 0.100251i
\(399\) −7.50000 12.9904i −0.375470 0.650332i
\(400\) 0 0
\(401\) −12.5000 + 21.6506i −0.624220 + 1.08118i 0.364471 + 0.931215i \(0.381250\pi\)
−0.988691 + 0.149966i \(0.952083\pi\)
\(402\) 12.0000i 0.598506i
\(403\) −25.9808 25.0000i −1.29419 1.24534i
\(404\) −4.00000 −0.199007
\(405\) 0 0
\(406\) 0 0
\(407\) −0.866025 + 0.500000i −0.0429273 + 0.0247841i
\(408\) 0 0
\(409\) 8.50000 + 14.7224i 0.420298 + 0.727977i 0.995968 0.0897044i \(-0.0285922\pi\)
−0.575670 + 0.817682i \(0.695259\pi\)
\(410\) 0 0
\(411\) −16.0000 −0.789222
\(412\) −7.79423 + 4.50000i −0.383994 + 0.221699i
\(413\) −10.3923 6.00000i −0.511372 0.295241i
\(414\) −2.00000 + 3.46410i −0.0982946 + 0.170251i
\(415\) 0 0
\(416\) −3.50000 0.866025i −0.171602 0.0424604i
\(417\) 9.00000i 0.440732i
\(418\) −4.33013 2.50000i −0.211793 0.122279i
\(419\) −14.0000 + 24.2487i −0.683945 + 1.18463i 0.289822 + 0.957080i \(0.406404\pi\)
−0.973767 + 0.227547i \(0.926930\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) −12.9904 + 7.50000i −0.632362 + 0.365094i
\(423\) 7.79423 4.50000i 0.378968 0.218797i
\(424\) 13.0000 0.631336
\(425\) 0 0
\(426\) −1.00000 + 1.73205i −0.0484502 + 0.0839181i
\(427\) −5.19615 3.00000i −0.251459 0.145180i
\(428\) 6.00000i 0.290021i
\(429\) −3.50000 0.866025i −0.168982 0.0418121i
\(430\) 0 0
\(431\) −18.0000 + 31.1769i −0.867029 + 1.50174i −0.00201168 + 0.999998i \(0.500640\pi\)
−0.865018 + 0.501741i \(0.832693\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) −13.8564 + 8.00000i −0.665896 + 0.384455i −0.794520 0.607238i \(-0.792277\pi\)
0.128624 + 0.991693i \(0.458944\pi\)
\(434\) 30.0000 1.44005
\(435\) 0 0
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) 20.0000i 0.956730i
\(438\) −13.8564 + 8.00000i −0.662085 + 0.382255i
\(439\) −5.00000 + 8.66025i −0.238637 + 0.413331i −0.960323 0.278889i \(-0.910034\pi\)
0.721686 + 0.692220i \(0.243367\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 0 0
\(443\) 18.0000i 0.855206i 0.903967 + 0.427603i \(0.140642\pi\)
−0.903967 + 0.427603i \(0.859358\pi\)
\(444\) 0.500000 0.866025i 0.0237289 0.0410997i
\(445\) 0 0
\(446\) −5.50000 9.52628i −0.260433 0.451082i
\(447\) 6.00000i 0.283790i
\(448\) 2.59808 1.50000i 0.122748 0.0708683i
\(449\) −7.50000 12.9904i −0.353947 0.613054i 0.632990 0.774160i \(-0.281827\pi\)
−0.986937 + 0.161106i \(0.948494\pi\)
\(450\) 0 0
\(451\) −3.00000 5.19615i −0.141264 0.244677i
\(452\) −13.8564 8.00000i −0.651751 0.376288i
\(453\) 5.19615 + 3.00000i 0.244137 + 0.140952i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 5.00000 0.234146
\(457\) −19.0526 11.0000i −0.891241 0.514558i −0.0168929 0.999857i \(-0.505377\pi\)
−0.874348 + 0.485299i \(0.838711\pi\)
\(458\) −8.66025 5.00000i −0.404667 0.233635i
\(459\) 0 0
\(460\) 0 0
\(461\) 6.00000 + 10.3923i 0.279448 + 0.484018i 0.971248 0.238071i \(-0.0765153\pi\)
−0.691800 + 0.722089i \(0.743182\pi\)
\(462\) 2.59808 1.50000i 0.120873 0.0697863i
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −5.00000 + 8.66025i −0.231621 + 0.401179i
\(467\) 36.0000i 1.66588i −0.553362 0.832941i \(-0.686655\pi\)
0.553362 0.832941i \(-0.313345\pi\)
\(468\) 3.46410 1.00000i 0.160128 0.0462250i
\(469\) −36.0000 −1.66233
\(470\) 0 0
\(471\) 0.500000 0.866025i 0.0230388 0.0399043i
\(472\) 3.46410 2.00000i 0.159448 0.0920575i
\(473\) 2.00000i 0.0919601i
\(474\) 5.00000 + 8.66025i 0.229658 + 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) −11.2583 + 6.50000i −0.515484 + 0.297615i
\(478\) −1.73205 1.00000i −0.0792222 0.0457389i
\(479\) −4.00000 + 6.92820i −0.182765 + 0.316558i −0.942821 0.333300i \(-0.891838\pi\)
0.760056 + 0.649857i \(0.225171\pi\)
\(480\) 0 0
\(481\) −1.00000 3.46410i −0.0455961 0.157949i
\(482\) 15.0000i 0.683231i
\(483\) −10.3923 6.00000i −0.472866 0.273009i
\(484\) −5.00000 + 8.66025i −0.227273 + 0.393648i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 30.3109 17.5000i 1.37352 0.793001i 0.382148 0.924101i \(-0.375184\pi\)
0.991369 + 0.131100i \(0.0418510\pi\)
\(488\) 1.73205 1.00000i 0.0784063 0.0452679i
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −12.5000 + 21.6506i −0.564117 + 0.977079i 0.433014 + 0.901387i \(0.357450\pi\)
−0.997131 + 0.0756923i \(0.975883\pi\)
\(492\) 5.19615 + 3.00000i 0.234261 + 0.135250i
\(493\) 0 0
\(494\) 12.5000 12.9904i 0.562402 0.584465i
\(495\) 0 0
\(496\) −5.00000 + 8.66025i −0.224507 + 0.388857i
\(497\) −5.19615 3.00000i −0.233079 0.134568i
\(498\) 10.3923 6.00000i 0.465690 0.268866i
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 0 0
\(501\) −6.50000 11.2583i −0.290399 0.502985i
\(502\) 11.0000i 0.490954i
\(503\) 0.866025 0.500000i 0.0386142 0.0222939i −0.480569 0.876957i \(-0.659570\pi\)
0.519183 + 0.854663i \(0.326236\pi\)
\(504\) −1.50000 + 2.59808i −0.0668153 + 0.115728i
\(505\) 0 0
\(506\) −4.00000 −0.177822
\(507\) 6.06218 11.5000i 0.269231 0.510733i
\(508\) 5.00000i 0.221839i
\(509\) 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) 0 0
\(511\) −24.0000 41.5692i −1.06170 1.83891i
\(512\) 1.00000i 0.0441942i
\(513\) −4.33013 + 2.50000i −0.191180 + 0.110378i
\(514\) −12.0000 20.7846i −0.529297 0.916770i
\(515\) 0 0
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) 7.79423 + 4.50000i 0.342790 + 0.197910i
\(518\) 2.59808 + 1.50000i 0.114153 + 0.0659062i
\(519\) −9.00000 −0.395056
\(520\) 0 0
\(521\) 33.0000 1.44576 0.722878 0.690976i \(-0.242819\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(522\) 0 0
\(523\) 5.19615 + 3.00000i 0.227212 + 0.131181i 0.609285 0.792951i \(-0.291456\pi\)
−0.382073 + 0.924132i \(0.624790\pi\)
\(524\) −7.50000 12.9904i −0.327639 0.567487i
\(525\) 0 0
\(526\) −1.50000 2.59808i −0.0654031 0.113282i
\(527\) 0 0
\(528\) 1.00000i 0.0435194i
\(529\) −3.50000 6.06218i −0.152174 0.263573i
\(530\) 0 0
\(531\) −2.00000 + 3.46410i −0.0867926 + 0.150329i
\(532\) 15.0000i 0.650332i
\(533\) 20.7846 6.00000i 0.900281 0.259889i
\(534\) 1.00000 0.0432742
\(535\) 0 0
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −10.3923 + 6.00000i −0.448461 + 0.258919i
\(538\) 20.0000i 0.862261i
\(539\) 1.00000 + 1.73205i 0.0430730 + 0.0746047i
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) −20.7846 + 12.0000i −0.892775 + 0.515444i
\(543\) −5.19615 3.00000i −0.222988 0.128742i
\(544\) 0 0
\(545\) 0 0
\(546\) 3.00000 + 10.3923i 0.128388 + 0.444750i
\(547\) 34.0000i 1.45374i 0.686778 + 0.726868i \(0.259025\pi\)
−0.686778 + 0.726868i \(0.740975\pi\)
\(548\) 13.8564 + 8.00000i 0.591916 + 0.341743i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 0 0
\(552\) 3.46410 2.00000i 0.147442 0.0851257i
\(553\) −25.9808 + 15.0000i −1.10481 + 0.637865i
\(554\) −23.0000 −0.977176
\(555\) 0 0
\(556\) 4.50000 7.79423i 0.190843 0.330549i
\(557\) 2.59808 + 1.50000i 0.110084 + 0.0635570i 0.554031 0.832496i \(-0.313089\pi\)
−0.443947 + 0.896053i \(0.646422\pi\)
\(558\) 10.0000i 0.423334i
\(559\) −7.00000 1.73205i −0.296068 0.0732579i
\(560\) 0 0
\(561\) 0 0
\(562\) −8.66025 5.00000i −0.365311 0.210912i
\(563\) −20.7846 + 12.0000i −0.875967 + 0.505740i −0.869326 0.494238i \(-0.835447\pi\)
−0.00664037 + 0.999978i \(0.502114\pi\)
\(564\) −9.00000 −0.378968
\(565\) 0 0
\(566\) −1.00000 1.73205i −0.0420331 0.0728035i
\(567\) 3.00000i 0.125988i
\(568\) 1.73205 1.00000i 0.0726752 0.0419591i
\(569\) −5.50000 + 9.52628i −0.230572 + 0.399362i −0.957977 0.286846i \(-0.907393\pi\)
0.727405 + 0.686209i \(0.240726\pi\)
\(570\) 0 0
\(571\) 7.00000 0.292941 0.146470 0.989215i \(-0.453209\pi\)
0.146470 + 0.989215i \(0.453209\pi\)
\(572\) 2.59808 + 2.50000i 0.108631 + 0.104530i
\(573\) 18.0000i 0.751961i
\(574\) −9.00000 + 15.5885i −0.375653 + 0.650650i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 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
\(579\) −8.00000 13.8564i −0.332469 0.575853i
\(580\) 0 0
\(581\) 18.0000 + 31.1769i 0.746766 + 1.29344i
\(582\) 10.3923 + 6.00000i 0.430775 + 0.248708i
\(583\) −11.2583 6.50000i −0.466272 0.269202i
\(584\) 16.0000 0.662085
\(585\) 0 0
\(586\) 13.0000 0.537025
\(587\) 15.5885 + 9.00000i 0.643404 + 0.371470i 0.785925 0.618322i \(-0.212187\pi\)
−0.142520 + 0.989792i \(0.545521\pi\)
\(588\) −1.73205 1.00000i −0.0714286 0.0412393i
\(589\) −25.0000 43.3013i −1.03011 1.78420i
\(590\) 0 0
\(591\) −7.50000 12.9904i −0.308509 0.534353i
\(592\) −0.866025 + 0.500000i −0.0355934 + 0.0205499i
\(593\) 28.0000i 1.14982i −0.818216 0.574911i \(-0.805037\pi\)
0.818216 0.574911i \(-0.194963\pi\)
\(594\) −0.500000 0.866025i −0.0205152 0.0355335i
\(595\) 0 0
\(596\) 3.00000 5.19615i 0.122885 0.212843i
\(597\) 2.00000i 0.0818546i
\(598\) 3.46410 14.0000i 0.141658 0.572503i
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) 13.5000 23.3827i 0.550676 0.953800i −0.447549 0.894259i \(-0.647703\pi\)
0.998226 0.0595404i \(-0.0189635\pi\)
\(602\) 5.19615 3.00000i 0.211779 0.122271i
\(603\) 12.0000i 0.488678i
\(604\) −3.00000 5.19615i −0.122068 0.211428i
\(605\) 0 0
\(606\) −4.00000 −0.162489
\(607\) 32.0429 18.5000i 1.30058 0.750892i 0.320079 0.947391i \(-0.396291\pi\)
0.980504 + 0.196499i \(0.0629573\pi\)
\(608\) −4.33013 2.50000i −0.175610 0.101388i
\(609\) 0 0
\(610\) 0 0
\(611\) −22.5000 + 23.3827i −0.910253 + 0.945962i
\(612\) 0 0
\(613\) 19.9186 + 11.5000i 0.804504 + 0.464481i 0.845044 0.534697i \(-0.179574\pi\)
−0.0405396 + 0.999178i \(0.512908\pi\)
\(614\) 9.00000 15.5885i 0.363210 0.629099i
\(615\) 0 0
\(616\) −3.00000 −0.120873
\(617\) −5.19615 + 3.00000i −0.209189 + 0.120775i −0.600935 0.799298i \(-0.705205\pi\)
0.391745 + 0.920074i \(0.371871\pi\)
\(618\) −7.79423 + 4.50000i −0.313530 + 0.181017i
\(619\) 31.0000 1.24600 0.622998 0.782224i \(-0.285915\pi\)
0.622998 + 0.782224i \(0.285915\pi\)
\(620\) 0 0
\(621\) −2.00000 + 3.46410i −0.0802572 + 0.139010i
\(622\) 10.3923 + 6.00000i 0.416693 + 0.240578i
\(623\) 3.00000i 0.120192i
\(624\) −3.50000 0.866025i −0.140112 0.0346688i
\(625\) 0 0
\(626\) 17.0000 29.4449i 0.679457 1.17685i
\(627\) −4.33013 2.50000i −0.172929 0.0998404i
\(628\) −0.866025 + 0.500000i −0.0345582 + 0.0199522i
\(629\) 0 0
\(630\) 0 0
\(631\) 2.00000 + 3.46410i 0.0796187 + 0.137904i 0.903085 0.429461i \(-0.141296\pi\)
−0.823467 + 0.567365i \(0.807963\pi\)
\(632\) 10.0000i 0.397779i
\(633\) −12.9904 + 7.50000i −0.516321 + 0.298098i
\(634\) 9.50000 16.4545i 0.377293 0.653491i
\(635\) 0 0
\(636\) 13.0000 0.515484
\(637\) −6.92820 + 2.00000i −0.274505 + 0.0792429i
\(638\) 0 0
\(639\) −1.00000 + 1.73205i −0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) 4.50000 + 7.79423i 0.177739 + 0.307854i 0.941106 0.338112i \(-0.109788\pi\)
−0.763367 + 0.645966i \(0.776455\pi\)
\(642\) 6.00000i 0.236801i
\(643\) 38.1051 22.0000i 1.50272 0.867595i 0.502724 0.864447i \(-0.332331\pi\)
0.999995 0.00314839i \(-0.00100217\pi\)
\(644\) 6.00000 + 10.3923i 0.236433 + 0.409514i
\(645\) 0 0
\(646\) 0 0
\(647\) −7.79423 4.50000i −0.306423 0.176913i 0.338902 0.940822i \(-0.389945\pi\)
−0.645325 + 0.763908i \(0.723278\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −4.00000 −0.157014
\(650\) 0 0
\(651\) 30.0000 1.17579
\(652\) 17.3205 + 10.0000i 0.678323 + 0.391630i
\(653\) 35.5070 + 20.5000i 1.38950 + 0.802227i 0.993259 0.115920i \(-0.0369817\pi\)
0.396239 + 0.918147i \(0.370315\pi\)
\(654\) 5.00000 + 8.66025i 0.195515 + 0.338643i
\(655\) 0 0
\(656\) −3.00000 5.19615i −0.117130 0.202876i
\(657\) −13.8564 + 8.00000i −0.540590 + 0.312110i
\(658\) 27.0000i 1.05257i
\(659\) 2.00000 + 3.46410i 0.0779089 + 0.134942i 0.902348 0.431009i \(-0.141842\pi\)
−0.824439 + 0.565951i \(0.808509\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) 28.0000i 1.08825i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 0.500000 0.866025i 0.0193746 0.0335578i
\(667\) 0 0
\(668\) 13.0000i 0.502985i
\(669\) −5.50000 9.52628i −0.212642 0.368307i
\(670\) 0 0
\(671\) −2.00000 −0.0772091
\(672\) 2.59808 1.50000i 0.100223 0.0578638i
\(673\) −27.7128 16.0000i −1.06825 0.616755i −0.140548 0.990074i \(-0.544886\pi\)
−0.927703 + 0.373319i \(0.878220\pi\)
\(674\) 1.00000 1.73205i 0.0385186 0.0667161i
\(675\) 0 0
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 26.0000i 0.999261i −0.866239 0.499631i \(-0.833469\pi\)
0.866239 0.499631i \(-0.166531\pi\)
\(678\) −13.8564 8.00000i −0.532152 0.307238i
\(679\) −18.0000 + 31.1769i −0.690777 + 1.19646i
\(680\) 0 0
\(681\) 20.0000 0.766402
\(682\) 8.66025 5.00000i 0.331618 0.191460i
\(683\) 22.5167 13.0000i 0.861576 0.497431i −0.00296369 0.999996i \(-0.500943\pi\)
0.864540 + 0.502564i \(0.167610\pi\)
\(684\) 5.00000 0.191180
\(685\) 0 0
\(686\) −7.50000 + 12.9904i −0.286351 + 0.495975i
\(687\) −8.66025 5.00000i −0.330409 0.190762i
\(688\) 2.00000i 0.0762493i
\(689\) 32.5000 33.7750i 1.23815 1.28672i
\(690\) 0 0
\(691\) −16.5000 + 28.5788i −0.627690 + 1.08719i 0.360325 + 0.932827i \(0.382666\pi\)
−0.988014 + 0.154363i \(0.950667\pi\)
\(692\) 7.79423 + 4.50000i 0.296292 + 0.171064i
\(693\) 2.59808 1.50000i 0.0986928 0.0569803i
\(694\) 28.0000 1.06287
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −31.1769 + 18.0000i −1.18006 + 0.681310i
\(699\) −5.00000 + 8.66025i −0.189117 + 0.327561i
\(700\) 0 0
\(701\) 4.00000 0.151078 0.0755390 0.997143i \(-0.475932\pi\)
0.0755390 + 0.997143i \(0.475932\pi\)
\(702\) 3.46410 1.00000i 0.130744 0.0377426i
\(703\) 5.00000i 0.188579i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) 18.0000 + 31.1769i 0.677439 + 1.17336i
\(707\) 12.0000i 0.451306i
\(708\) 3.46410 2.00000i 0.130189 0.0751646i
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) 0 0
\(711\) 5.00000 + 8.66025i 0.187515 + 0.324785i
\(712\) −0.866025 0.500000i −0.0324557 0.0187383i
\(713\) −34.6410 20.0000i −1.29732 0.749006i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −1.73205 1.00000i −0.0646846 0.0373457i
\(718\) 29.4449 + 17.0000i 1.09887 + 0.634434i
\(719\) 18.0000 + 31.1769i 0.671287 + 1.16270i 0.977539 + 0.210752i \(0.0675914\pi\)
−0.306253 + 0.951950i \(0.599075\pi\)
\(720\) 0 0
\(721\) −13.5000 23.3827i −0.502766 0.870817i
\(722\) 5.19615 3.00000i 0.193381 0.111648i
\(723\) 15.0000i 0.557856i
\(724\) 3.00000 + 5.19615i 0.111494 + 0.193113i
\(725\) 0 0
\(726\) −5.00000 + 8.66025i −0.185567 + 0.321412i
\(727\) 37.0000i 1.37225i −0.727482 0.686127i \(-0.759309\pi\)
0.727482 0.686127i \(-0.240691\pi\)
\(728\) 2.59808 10.5000i 0.0962911 0.389156i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 1.73205 1.00000i 0.0640184 0.0369611i
\(733\) 5.00000i 0.184679i 0.995728 + 0.0923396i \(0.0294345\pi\)
−0.995728 + 0.0923396i \(0.970565\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −10.3923 + 6.00000i −0.382805 + 0.221013i
\(738\) 5.19615 + 3.00000i 0.191273 + 0.110432i
\(739\) 17.5000 30.3109i 0.643748 1.11500i −0.340841 0.940121i \(-0.610712\pi\)
0.984589 0.174883i \(-0.0559548\pi\)
\(740\) 0 0
\(741\) 12.5000 12.9904i 0.459199 0.477214i
\(742\) 39.0000i 1.43174i
\(743\) 20.7846 + 12.0000i 0.762513 + 0.440237i 0.830197 0.557470i \(-0.188228\pi\)
−0.0676840 + 0.997707i \(0.521561\pi\)
\(744\) −5.00000 + 8.66025i −0.183309 + 0.317500i
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) 10.3923 6.00000i 0.380235 0.219529i
\(748\) 0 0
\(749\) −18.0000 −0.657706
\(750\) 0 0
\(751\) −22.0000 + 38.1051i −0.802791 + 1.39048i 0.114981 + 0.993368i \(0.463319\pi\)
−0.917772 + 0.397108i \(0.870014\pi\)
\(752\) 7.79423 + 4.50000i 0.284226 + 0.164098i
\(753\) 11.0000i 0.400862i
\(754\) 0 0
\(755\) 0 0
\(756\) −1.50000 + 2.59808i −0.0545545 + 0.0944911i
\(757\) −33.7750 19.5000i −1.22757 0.708740i −0.261051 0.965325i \(-0.584069\pi\)
−0.966522 + 0.256585i \(0.917403\pi\)
\(758\) 0.866025 0.500000i 0.0314555 0.0181608i
\(759\) −4.00000 −0.145191
\(760\) 0 0
\(761\) −22.5000 38.9711i −0.815624 1.41270i −0.908879 0.417061i \(-0.863060\pi\)
0.0932544 0.995642i \(-0.470273\pi\)
\(762\) 5.00000i 0.181131i
\(763\) −25.9808 + 15.0000i −0.940567 + 0.543036i
\(764\) −9.00000 + 15.5885i −0.325609 + 0.563971i
\(765\) 0 0
\(766\) −28.0000 −1.01168
\(767\) 3.46410 14.0000i 0.125081 0.505511i
\(768\) 1.00000i 0.0360844i
\(769\) −13.0000 + 22.5167i −0.468792 + 0.811972i −0.999364 0.0356685i \(-0.988644\pi\)
0.530572 + 0.847640i \(0.321977\pi\)
\(770\) 0 0
\(771\) −12.0000 20.7846i −0.432169 0.748539i
\(772\) 16.0000i 0.575853i
\(773\) 32.0429 18.5000i 1.15250 0.665399i 0.203008 0.979177i \(-0.434928\pi\)
0.949496 + 0.313778i \(0.101595\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) 0 0
\(776\) −6.00000 10.3923i −0.215387 0.373062i
\(777\) 2.59808 + 1.50000i 0.0932055 + 0.0538122i
\(778\) −13.8564 8.00000i −0.496776 0.286814i
\(779\) 30.0000 1.07486
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 + 1.73205i 0.0357143 + 0.0618590i
\(785\) 0 0
\(786\) −7.50000 12.9904i −0.267516 0.463352i
\(787\)