Properties

Label 450.2.e.f.301.1
Level $450$
Weight $2$
Character 450.301
Analytic conductor $3.593$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 301.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 450.301
Dual form 450.2.e.f.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +(-1.50000 - 0.866025i) q^{12} +(-2.00000 + 3.46410i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +6.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} -7.00000 q^{19} +(-3.00000 + 1.73205i) q^{21} -1.73205i q^{24} -4.00000 q^{26} -5.19615i q^{27} -2.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(5.00000 - 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(1.50000 - 2.59808i) q^{36} -2.00000 q^{37} +(-3.50000 - 6.06218i) q^{38} +(-6.00000 - 3.46410i) q^{39} +(-4.50000 + 7.79423i) q^{41} +(-3.00000 - 1.73205i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(3.00000 + 5.19615i) q^{47} +(1.50000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +10.3923i q^{51} +(-2.00000 - 3.46410i) q^{52} +12.0000 q^{53} +(4.50000 - 2.59808i) q^{54} +(-1.00000 - 1.73205i) q^{56} -12.1244i q^{57} +(-3.00000 + 5.19615i) q^{58} +(4.50000 - 7.79423i) q^{59} +(2.00000 + 3.46410i) q^{61} +10.0000 q^{62} +(-3.00000 - 5.19615i) q^{63} +1.00000 q^{64} +(-6.50000 + 11.2583i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{71} +3.00000 q^{72} +1.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(3.50000 - 6.06218i) q^{76} -6.92820i q^{78} +(-1.00000 - 1.73205i) q^{79} +9.00000 q^{81} -9.00000 q^{82} +(4.50000 + 7.79423i) q^{83} -3.46410i q^{84} +(0.500000 - 0.866025i) q^{86} +(-9.00000 + 5.19615i) q^{87} +15.0000 q^{89} -8.00000 q^{91} +(15.0000 + 8.66025i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(1.50000 + 0.866025i) q^{96} +(8.50000 + 14.7224i) q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - 3q^{6} + 2q^{7} - 2q^{8} - 6q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - 3q^{6} + 2q^{7} - 2q^{8} - 6q^{9} - 3q^{12} - 4q^{13} - 2q^{14} - q^{16} + 12q^{17} - 3q^{18} - 14q^{19} - 6q^{21} - 8q^{26} - 4q^{28} + 6q^{29} + 10q^{31} + q^{32} + 6q^{34} + 3q^{36} - 4q^{37} - 7q^{38} - 12q^{39} - 9q^{41} - 6q^{42} - q^{43} + 6q^{47} + 3q^{48} + 3q^{49} - 4q^{52} + 24q^{53} + 9q^{54} - 2q^{56} - 6q^{58} + 9q^{59} + 4q^{61} + 20q^{62} - 6q^{63} + 2q^{64} - 13q^{67} - 6q^{68} + 12q^{71} + 6q^{72} + 2q^{73} - 2q^{74} + 7q^{76} - 2q^{79} + 18q^{81} - 18q^{82} + 9q^{83} + q^{86} - 18q^{87} + 30q^{89} - 16q^{91} + 30q^{93} - 6q^{94} + 3q^{96} + 17q^{97} + 6q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 1.73205i 1.00000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) −1.50000 + 0.866025i −0.612372 + 0.353553i
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) −1.50000 0.866025i −0.433013 0.250000i
\(13\) −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i \(0.353834\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) −1.00000 + 1.73205i −0.267261 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) −1.50000 2.59808i −0.353553 0.612372i
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) −3.00000 + 1.73205i −0.654654 + 0.377964i
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 1.73205i 0.353553i
\(25\) 0 0
\(26\) −4.00000 −0.784465
\(27\) 5.19615i 1.00000i
\(28\) −2.00000 −0.377964
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 0 0
\(31\) 5.00000 8.66025i 0.898027 1.55543i 0.0680129 0.997684i \(-0.478334\pi\)
0.830014 0.557743i \(-0.188333\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.00000 + 5.19615i 0.514496 + 0.891133i
\(35\) 0 0
\(36\) 1.50000 2.59808i 0.250000 0.433013i
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −3.50000 6.06218i −0.567775 0.983415i
\(39\) −6.00000 3.46410i −0.960769 0.554700i
\(40\) 0 0
\(41\) −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) −3.00000 1.73205i −0.462910 0.267261i
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 1.50000 0.866025i 0.216506 0.125000i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0 0
\(51\) 10.3923i 1.45521i
\(52\) −2.00000 3.46410i −0.277350 0.480384i
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 4.50000 2.59808i 0.612372 0.353553i
\(55\) 0 0
\(56\) −1.00000 1.73205i −0.133631 0.231455i
\(57\) 12.1244i 1.60591i
\(58\) −3.00000 + 5.19615i −0.393919 + 0.682288i
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 0 0
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) 10.0000 1.27000
\(63\) −3.00000 5.19615i −0.377964 0.654654i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −6.50000 + 11.2583i −0.794101 + 1.37542i 0.129307 + 0.991605i \(0.458725\pi\)
−0.923408 + 0.383819i \(0.874609\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 3.00000 0.353553
\(73\) 1.00000 0.117041 0.0585206 0.998286i \(-0.481362\pi\)
0.0585206 + 0.998286i \(0.481362\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0 0
\(76\) 3.50000 6.06218i 0.401478 0.695379i
\(77\) 0 0
\(78\) 6.92820i 0.784465i
\(79\) −1.00000 1.73205i −0.112509 0.194871i 0.804272 0.594261i \(-0.202555\pi\)
−0.916781 + 0.399390i \(0.869222\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) −9.00000 −0.993884
\(83\) 4.50000 + 7.79423i 0.493939 + 0.855528i 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 3.46410i 0.377964i
\(85\) 0 0
\(86\) 0.500000 0.866025i 0.0539164 0.0933859i
\(87\) −9.00000 + 5.19615i −0.964901 + 0.557086i
\(88\) 0 0
\(89\) 15.0000 1.59000 0.794998 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 0 0
\(93\) 15.0000 + 8.66025i 1.55543 + 0.898027i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0 0
\(96\) 1.50000 + 0.866025i 0.153093 + 0.0883883i
\(97\) 8.50000 + 14.7224i 0.863044 + 1.49484i 0.868976 + 0.494854i \(0.164778\pi\)
−0.00593185 + 0.999982i \(0.501888\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 0 0
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) −9.00000 + 5.19615i −0.891133 + 0.514496i
\(103\) 1.00000 1.73205i 0.0985329 0.170664i −0.812545 0.582899i \(-0.801918\pi\)
0.911078 + 0.412235i \(0.135252\pi\)
\(104\) 2.00000 3.46410i 0.196116 0.339683i
\(105\) 0 0
\(106\) 6.00000 + 10.3923i 0.582772 + 1.00939i
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 3.46410i 0.328798i
\(112\) 1.00000 1.73205i 0.0944911 0.163663i
\(113\) 1.50000 2.59808i 0.141108 0.244406i −0.786806 0.617200i \(-0.788267\pi\)
0.927914 + 0.372794i \(0.121600\pi\)
\(114\) 10.5000 6.06218i 0.983415 0.567775i
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 6.00000 10.3923i 0.554700 0.960769i
\(118\) 9.00000 0.828517
\(119\) 6.00000 + 10.3923i 0.550019 + 0.952661i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) −2.00000 + 3.46410i −0.181071 + 0.313625i
\(123\) −13.5000 7.79423i −1.21725 0.702782i
\(124\) 5.00000 + 8.66025i 0.449013 + 0.777714i
\(125\) 0 0
\(126\) 3.00000 5.19615i 0.267261 0.462910i
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 1.50000 0.866025i 0.132068 0.0762493i
\(130\) 0 0
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 0 0
\(133\) −7.00000 12.1244i −0.606977 1.05131i
\(134\) −13.0000 −1.12303
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) −1.50000 2.59808i −0.128154 0.221969i 0.794808 0.606861i \(-0.207572\pi\)
−0.922961 + 0.384893i \(0.874238\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 0 0
\(141\) −9.00000 + 5.19615i −0.757937 + 0.437595i
\(142\) 3.00000 + 5.19615i 0.251754 + 0.436051i
\(143\) 0 0
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 0 0
\(146\) 0.500000 + 0.866025i 0.0413803 + 0.0716728i
\(147\) 4.50000 + 2.59808i 0.371154 + 0.214286i
\(148\) 1.00000 1.73205i 0.0821995 0.142374i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 2.00000 + 3.46410i 0.162758 + 0.281905i 0.935857 0.352381i \(-0.114628\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 7.00000 0.567775
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) 0 0
\(156\) 6.00000 3.46410i 0.480384 0.277350i
\(157\) 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) 1.00000 1.73205i 0.0795557 0.137795i
\(159\) 20.7846i 1.64833i
\(160\) 0 0
\(161\) 0 0
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) 7.00000 0.548282 0.274141 0.961689i \(-0.411606\pi\)
0.274141 + 0.961689i \(0.411606\pi\)
\(164\) −4.50000 7.79423i −0.351391 0.608627i
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) 6.00000 10.3923i 0.464294 0.804181i −0.534875 0.844931i \(-0.679641\pi\)
0.999169 + 0.0407502i \(0.0129748\pi\)
\(168\) 3.00000 1.73205i 0.231455 0.133631i
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) 0 0
\(171\) 21.0000 1.60591
\(172\) 1.00000 0.0762493
\(173\) −6.00000 10.3923i −0.456172 0.790112i 0.542583 0.840002i \(-0.317446\pi\)
−0.998755 + 0.0498898i \(0.984113\pi\)
\(174\) −9.00000 5.19615i −0.682288 0.393919i
\(175\) 0 0
\(176\) 0 0
\(177\) 13.5000 + 7.79423i 1.01472 + 0.585850i
\(178\) 7.50000 + 12.9904i 0.562149 + 0.973670i
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −4.00000 6.92820i −0.296500 0.513553i
\(183\) −6.00000 + 3.46410i −0.443533 + 0.256074i
\(184\) 0 0
\(185\) 0 0
\(186\) 17.3205i 1.27000i
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) 9.00000 5.19615i 0.654654 0.377964i
\(190\) 0 0
\(191\) −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i \(-0.236317\pi\)
−0.953912 + 0.300088i \(0.902984\pi\)
\(192\) 1.73205i 0.125000i
\(193\) 1.00000 1.73205i 0.0719816 0.124676i −0.827788 0.561041i \(-0.810401\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) −8.50000 + 14.7224i −0.610264 + 1.05701i
\(195\) 0 0
\(196\) 1.50000 + 2.59808i 0.107143 + 0.185577i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) −19.5000 11.2583i −1.37542 0.794101i
\(202\) 6.00000 10.3923i 0.422159 0.731200i
\(203\) −6.00000 + 10.3923i −0.421117 + 0.729397i
\(204\) −9.00000 5.19615i −0.630126 0.363803i
\(205\) 0 0
\(206\) 2.00000 0.139347
\(207\) 0 0
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −2.50000 + 4.33013i −0.172107 + 0.298098i −0.939156 0.343490i \(-0.888391\pi\)
0.767049 + 0.641588i \(0.221724\pi\)
\(212\) −6.00000 + 10.3923i −0.412082 + 0.713746i
\(213\) 10.3923i 0.712069i
\(214\) −4.50000 7.79423i −0.307614 0.532803i
\(215\) 0 0
\(216\) 5.19615i 0.353553i
\(217\) 20.0000 1.35769
\(218\) 1.00000 + 1.73205i 0.0677285 + 0.117309i
\(219\) 1.73205i 0.117041i
\(220\) 0 0
\(221\) −12.0000 + 20.7846i −0.807207 + 1.39812i
\(222\) 3.00000 1.73205i 0.201347 0.116248i
\(223\) −8.00000 13.8564i −0.535720 0.927894i −0.999128 0.0417488i \(-0.986707\pi\)
0.463409 0.886145i \(-0.346626\pi\)
\(224\) 2.00000 0.133631
\(225\) 0 0
\(226\) 3.00000 0.199557
\(227\) −7.50000 12.9904i −0.497792 0.862202i 0.502204 0.864749i \(-0.332523\pi\)
−0.999997 + 0.00254715i \(0.999189\pi\)
\(228\) 10.5000 + 6.06218i 0.695379 + 0.401478i
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) −3.00000 −0.196537 −0.0982683 0.995160i \(-0.531330\pi\)
−0.0982683 + 0.995160i \(0.531330\pi\)
\(234\) 12.0000 0.784465
\(235\) 0 0
\(236\) 4.50000 + 7.79423i 0.292925 + 0.507361i
\(237\) 3.00000 1.73205i 0.194871 0.112509i
\(238\) −6.00000 + 10.3923i −0.388922 + 0.673633i
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) 9.50000 + 16.4545i 0.611949 + 1.05993i 0.990912 + 0.134515i \(0.0429475\pi\)
−0.378963 + 0.925412i \(0.623719\pi\)
\(242\) 11.0000 0.707107
\(243\) 15.5885i 1.00000i
\(244\) −4.00000 −0.256074
\(245\) 0 0
\(246\) 15.5885i 0.993884i
\(247\) 14.0000 24.2487i 0.890799 1.54291i
\(248\) −5.00000 + 8.66025i −0.317500 + 0.549927i
\(249\) −13.5000 + 7.79423i −0.855528 + 0.493939i
\(250\) 0 0
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 6.00000 0.377964
\(253\) 0 0
\(254\) −10.0000 17.3205i −0.627456 1.08679i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) 1.50000 + 0.866025i 0.0933859 + 0.0539164i
\(259\) −2.00000 3.46410i −0.124274 0.215249i
\(260\) 0 0
\(261\) −9.00000 15.5885i −0.557086 0.964901i
\(262\) 12.0000 0.741362
\(263\) −3.00000 5.19615i −0.184988 0.320408i 0.758585 0.651575i \(-0.225891\pi\)
−0.943572 + 0.331166i \(0.892558\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 7.00000 12.1244i 0.429198 0.743392i
\(267\) 25.9808i 1.59000i
\(268\) −6.50000 11.2583i −0.397051 0.687712i
\(269\) −30.0000 −1.82913 −0.914566 0.404436i \(-0.867468\pi\)
−0.914566 + 0.404436i \(0.867468\pi\)
\(270\) 0 0
\(271\) −28.0000 −1.70088 −0.850439 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −3.00000 5.19615i −0.181902 0.315063i
\(273\) 13.8564i 0.838628i
\(274\) 1.50000 2.59808i 0.0906183 0.156956i
\(275\) 0 0
\(276\) 0 0
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) 4.00000 0.239904
\(279\) −15.0000 + 25.9808i −0.898027 + 1.55543i
\(280\) 0 0
\(281\) 9.00000 + 15.5885i 0.536895 + 0.929929i 0.999069 + 0.0431402i \(0.0137362\pi\)
−0.462174 + 0.886789i \(0.652930\pi\)
\(282\) −9.00000 5.19615i −0.535942 0.309426i
\(283\) −9.50000 + 16.4545i −0.564716 + 0.978117i 0.432360 + 0.901701i \(0.357681\pi\)
−0.997076 + 0.0764162i \(0.975652\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) 0 0
\(287\) −18.0000 −1.06251
\(288\) −1.50000 + 2.59808i −0.0883883 + 0.153093i
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) −25.5000 + 14.7224i −1.49484 + 0.863044i
\(292\) −0.500000 + 0.866025i −0.0292603 + 0.0506803i
\(293\) 6.00000 10.3923i 0.350524 0.607125i −0.635818 0.771839i \(-0.719337\pi\)
0.986341 + 0.164714i \(0.0526703\pi\)
\(294\) 5.19615i 0.303046i
\(295\) 0 0
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) 1.00000 1.73205i 0.0576390 0.0998337i
\(302\) −2.00000 + 3.46410i −0.115087 + 0.199337i
\(303\) 18.0000 10.3923i 1.03407 0.597022i
\(304\) 3.50000 + 6.06218i 0.200739 + 0.347690i
\(305\) 0 0
\(306\) −9.00000 15.5885i −0.514496 0.891133i
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 3.00000 + 1.73205i 0.170664 + 0.0985329i
\(310\) 0 0
\(311\) 15.0000 25.9808i 0.850572 1.47323i −0.0301210 0.999546i \(-0.509589\pi\)
0.880693 0.473688i \(-0.157077\pi\)
\(312\) 6.00000 + 3.46410i 0.339683 + 0.196116i
\(313\) −9.50000 16.4545i −0.536972 0.930062i −0.999065 0.0432311i \(-0.986235\pi\)
0.462093 0.886831i \(-0.347098\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) 15.0000 + 25.9808i 0.842484 + 1.45922i 0.887788 + 0.460252i \(0.152241\pi\)
−0.0453045 + 0.998973i \(0.514426\pi\)
\(318\) −18.0000 + 10.3923i −1.00939 + 0.582772i
\(319\) 0 0
\(320\) 0 0
\(321\) 15.5885i 0.870063i
\(322\) 0 0
\(323\) −42.0000 −2.33694
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 0 0
\(326\) 3.50000 + 6.06218i 0.193847 + 0.335753i
\(327\) 3.46410i 0.191565i
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) −6.00000 + 10.3923i −0.330791 + 0.572946i
\(330\) 0 0
\(331\) −5.50000 9.52628i −0.302307 0.523612i 0.674351 0.738411i \(-0.264424\pi\)
−0.976658 + 0.214799i \(0.931090\pi\)
\(332\) −9.00000 −0.493939
\(333\) 6.00000 0.328798
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 3.00000 + 1.73205i 0.163663 + 0.0944911i
\(337\) 7.00000 12.1244i 0.381314 0.660456i −0.609936 0.792451i \(-0.708805\pi\)
0.991250 + 0.131995i \(0.0421382\pi\)
\(338\) 1.50000 2.59808i 0.0815892 0.141317i
\(339\) 4.50000 + 2.59808i 0.244406 + 0.141108i
\(340\) 0 0
\(341\) 0 0
\(342\) 10.5000 + 18.1865i 0.567775 + 0.983415i
\(343\) 20.0000 1.07990
\(344\) 0.500000 + 0.866025i 0.0269582 + 0.0466930i
\(345\) 0 0
\(346\) 6.00000 10.3923i 0.322562 0.558694i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 10.3923i 0.557086i
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) 0 0
\(351\) 18.0000 + 10.3923i 0.960769 + 0.554700i
\(352\) 0 0
\(353\) 7.50000 + 12.9904i 0.399185 + 0.691408i 0.993626 0.112731i \(-0.0359599\pi\)
−0.594441 + 0.804139i \(0.702627\pi\)
\(354\) 15.5885i 0.828517i
\(355\) 0 0
\(356\) −7.50000 + 12.9904i −0.397499 + 0.688489i
\(357\) −18.0000 + 10.3923i −0.952661 + 0.550019i
\(358\) −4.50000 7.79423i −0.237832 0.411938i
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) −8.00000 13.8564i −0.420471 0.728277i
\(363\) 16.5000 + 9.52628i 0.866025 + 0.500000i
\(364\) 4.00000 6.92820i 0.209657 0.363137i
\(365\) 0 0
\(366\) −6.00000 3.46410i −0.313625 0.181071i
\(367\) −5.00000 8.66025i −0.260998 0.452062i 0.705509 0.708700i \(-0.250718\pi\)
−0.966507 + 0.256639i \(0.917385\pi\)
\(368\) 0 0
\(369\) 13.5000 23.3827i 0.702782 1.21725i
\(370\) 0 0
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) −15.0000 + 8.66025i −0.777714 + 0.449013i
\(373\) −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i \(-0.866355\pi\)
0.809591 + 0.586994i \(0.199689\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) −24.0000 −1.23606
\(378\) 9.00000 + 5.19615i 0.462910 + 0.267261i
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 34.6410i 1.77471i
\(382\) 3.00000 5.19615i 0.153493 0.265858i
\(383\) 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i \(-0.623227\pi\)
0.990702 0.136047i \(-0.0434398\pi\)
\(384\) −1.50000 + 0.866025i −0.0765466 + 0.0441942i
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) 1.50000 + 2.59808i 0.0762493 + 0.132068i
\(388\) −17.0000 −0.863044
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.50000 + 2.59808i −0.0757614 + 0.131223i
\(393\) 18.0000 + 10.3923i 0.907980 + 0.524222i
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) 0 0
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) −8.00000 13.8564i −0.401004 0.694559i
\(399\) 21.0000 12.1244i 1.05131 0.606977i
\(400\) 0 0
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 22.5167i 1.12303i
\(403\) 20.0000 + 34.6410i 0.996271 + 1.72559i
\(404\) 12.0000 0.597022
\(405\) 0 0
\(406\) −12.0000 −0.595550
\(407\) 0 0
\(408\) 10.3923i 0.514496i
\(409\) 15.5000 26.8468i 0.766426 1.32749i −0.173064 0.984911i \(-0.555367\pi\)
0.939490 0.342578i \(-0.111300\pi\)
\(410\) 0 0
\(411\) 4.50000 2.59808i 0.221969 0.128154i
\(412\) 1.00000 + 1.73205i 0.0492665 + 0.0853320i
\(413\) 18.0000 0.885722
\(414\) 0 0
\(415\) 0 0
\(416\) 2.00000 + 3.46410i 0.0980581 + 0.169842i
\(417\) 6.00000 + 3.46410i 0.293821 + 0.169638i
\(418\) 0 0
\(419\) −1.50000 + 2.59808i −0.0732798 + 0.126924i −0.900337 0.435194i \(-0.856680\pi\)
0.827057 + 0.562118i \(0.190013\pi\)
\(420\) 0 0
\(421\) 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i \(-0.0883103\pi\)
−0.718076 + 0.695965i \(0.754977\pi\)
\(422\) −5.00000 −0.243396
\(423\) −9.00000 15.5885i −0.437595 0.757937i
\(424\) −12.0000 −0.582772
\(425\) 0 0
\(426\) −9.00000 + 5.19615i −0.436051 + 0.251754i
\(427\) −4.00000 + 6.92820i −0.193574 + 0.335279i
\(428\) 4.50000 7.79423i 0.217516 0.376748i
\(429\) 0 0
\(430\) 0 0
\(431\) 6.00000 0.289010 0.144505 0.989504i \(-0.453841\pi\)
0.144505 + 0.989504i \(0.453841\pi\)
\(432\) −4.50000 + 2.59808i −0.216506 + 0.125000i
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 10.0000 + 17.3205i 0.480015 + 0.831411i
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 0 0
\(438\) −1.50000 + 0.866025i −0.0716728 + 0.0413803i
\(439\) 2.00000 + 3.46410i 0.0954548 + 0.165333i 0.909798 0.415051i \(-0.136236\pi\)
−0.814344 + 0.580383i \(0.802903\pi\)
\(440\) 0 0
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) −24.0000 −1.14156
\(443\) 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) 3.00000 + 1.73205i 0.142374 + 0.0821995i
\(445\) 0 0
\(446\) 8.00000 13.8564i 0.378811 0.656120i
\(447\) 9.00000 + 5.19615i 0.425685 + 0.245770i
\(448\) 1.00000 + 1.73205i 0.0472456 + 0.0818317i
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 1.50000 + 2.59808i 0.0705541 + 0.122203i
\(453\) −6.00000 + 3.46410i −0.281905 + 0.162758i
\(454\) 7.50000 12.9904i 0.351992 0.609669i
\(455\) 0 0
\(456\) 12.1244i 0.567775i
\(457\) −9.50000 16.4545i −0.444391 0.769708i 0.553618 0.832771i \(-0.313247\pi\)
−0.998010 + 0.0630623i \(0.979913\pi\)
\(458\) 10.0000 0.467269
\(459\) 31.1769i 1.45521i
\(460\) 0 0
\(461\) −3.00000 5.19615i −0.139724 0.242009i 0.787668 0.616100i \(-0.211288\pi\)
−0.927392 + 0.374091i \(0.877955\pi\)
\(462\) 0 0
\(463\) 13.0000 22.5167i 0.604161 1.04644i −0.388022 0.921650i \(-0.626842\pi\)
0.992183 0.124788i \(-0.0398251\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 0 0
\(466\) −1.50000 2.59808i −0.0694862 0.120354i
\(467\) 15.0000 0.694117 0.347059 0.937843i \(-0.387180\pi\)
0.347059 + 0.937843i \(0.387180\pi\)
\(468\) 6.00000 + 10.3923i 0.277350 + 0.480384i
\(469\) −26.0000 −1.20057
\(470\) 0 0
\(471\) 21.0000 + 12.1244i 0.967629 + 0.558661i
\(472\) −4.50000 + 7.79423i −0.207129 + 0.358758i
\(473\) 0 0
\(474\) 3.00000 + 1.73205i 0.137795 + 0.0795557i
\(475\) 0 0
\(476\) −12.0000 −0.550019
\(477\) −36.0000 −1.64833
\(478\) 0 0
\(479\) −18.0000 31.1769i −0.822441 1.42451i −0.903859 0.427830i \(-0.859278\pi\)
0.0814184 0.996680i \(-0.474055\pi\)
\(480\) 0 0
\(481\) 4.00000 6.92820i 0.182384 0.315899i
\(482\) −9.50000 + 16.4545i −0.432713 + 0.749481i
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 0 0
\(486\) −13.5000 + 7.79423i −0.612372 + 0.353553i
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) −2.00000 3.46410i −0.0905357 0.156813i
\(489\) 12.1244i 0.548282i
\(490\) 0 0
\(491\) 1.50000 2.59808i 0.0676941 0.117250i −0.830192 0.557478i \(-0.811769\pi\)
0.897886 + 0.440228i \(0.145102\pi\)
\(492\) 13.5000 7.79423i 0.608627 0.351391i
\(493\) 18.0000 + 31.1769i 0.810679 + 1.40414i
\(494\) 28.0000 1.25978
\(495\) 0 0
\(496\) −10.0000 −0.449013
\(497\) 6.00000 + 10.3923i 0.269137 + 0.466159i
\(498\) −13.5000 7.79423i −0.604949 0.349268i
\(499\) −5.50000 + 9.52628i −0.246214 + 0.426455i −0.962472 0.271380i \(-0.912520\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 0 0
\(501\) 18.0000 + 10.3923i 0.804181 + 0.464294i
\(502\) 7.50000 + 12.9904i 0.334741 + 0.579789i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 3.00000 + 5.19615i 0.133631 + 0.231455i
\(505\) 0 0
\(506\) 0 0
\(507\) 4.50000 2.59808i 0.199852 0.115385i
\(508\) 10.0000 17.3205i 0.443678 0.768473i
\(509\) 18.0000 31.1769i 0.797836 1.38189i −0.123187 0.992384i \(-0.539311\pi\)
0.921023 0.389509i \(-0.127355\pi\)
\(510\) 0 0
\(511\) 1.00000 + 1.73205i 0.0442374 + 0.0766214i
\(512\) −1.00000 −0.0441942
\(513\) 36.3731i 1.60591i
\(514\) 3.00000 0.132324
\(515\) 0 0
\(516\) 1.73205i 0.0762493i
\(517\) 0 0
\(518\) 2.00000 3.46410i 0.0878750 0.152204i
\(519\) 18.0000 10.3923i 0.790112 0.456172i
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 9.00000 15.5885i 0.393919 0.682288i
\(523\) 1.00000 0.0437269 0.0218635 0.999761i \(-0.493040\pi\)
0.0218635 + 0.999761i \(0.493040\pi\)
\(524\) 6.00000 + 10.3923i 0.262111 + 0.453990i
\(525\) 0 0
\(526\) 3.00000 5.19615i 0.130806 0.226563i
\(527\) 30.0000 51.9615i 1.30682 2.26348i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) −13.5000 + 23.3827i −0.585850 + 1.01472i
\(532\) 14.0000 0.606977
\(533\) −18.0000 31.1769i −0.779667 1.35042i
\(534\) −22.5000 + 12.9904i −0.973670 + 0.562149i
\(535\) 0 0
\(536\) 6.50000 11.2583i 0.280757 0.486286i
\(537\) 15.5885i 0.672692i
\(538\) −15.0000 25.9808i −0.646696 1.12011i
\(539\) 0 0
\(540\) 0 0
\(541\) 32.0000 1.37579 0.687894 0.725811i \(-0.258536\pi\)
0.687894 + 0.725811i \(0.258536\pi\)
\(542\) −14.0000 24.2487i −0.601351 1.04157i
\(543\) 27.7128i 1.18927i
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 0 0
\(546\) 12.0000 6.92820i 0.513553 0.296500i
\(547\) 2.50000 + 4.33013i 0.106892 + 0.185143i 0.914510 0.404564i \(-0.132577\pi\)
−0.807617 + 0.589707i \(0.799243\pi\)
\(548\) 3.00000 0.128154
\(549\) −6.00000 10.3923i −0.256074 0.443533i
\(550\) 0 0
\(551\) −21.0000 36.3731i −0.894630 1.54954i
\(552\) 0 0
\(553\) 2.00000 3.46410i 0.0850487 0.147309i
\(554\) −1.00000 + 1.73205i −0.0424859 + 0.0735878i
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 12.0000 0.508456 0.254228 0.967144i \(-0.418179\pi\)
0.254228 + 0.967144i \(0.418179\pi\)
\(558\) −30.0000 −1.27000
\(559\) 4.00000 0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) −9.00000 + 15.5885i −0.379642 + 0.657559i
\(563\) 4.50000 7.79423i 0.189652 0.328488i −0.755482 0.655169i \(-0.772597\pi\)
0.945134 + 0.326682i \(0.105931\pi\)
\(564\) 10.3923i 0.437595i
\(565\) 0 0
\(566\) −19.0000 −0.798630
\(567\) 9.00000 + 15.5885i 0.377964 + 0.654654i
\(568\) −6.00000 −0.251754
\(569\) 21.0000 + 36.3731i 0.880366 + 1.52484i 0.850935 + 0.525271i \(0.176036\pi\)
0.0294311 + 0.999567i \(0.490630\pi\)
\(570\) 0 0
\(571\) −17.5000 + 30.3109i −0.732352 + 1.26847i 0.223523 + 0.974699i \(0.428244\pi\)
−0.955875 + 0.293773i \(0.905089\pi\)
\(572\) 0 0
\(573\) 9.00000 5.19615i 0.375980 0.217072i
\(574\) −9.00000 15.5885i −0.375653 0.650650i
\(575\) 0 0
\(576\) −3.00000 −0.125000
\(577\) −35.0000 −1.45707 −0.728535 0.685009i \(-0.759798\pi\)
−0.728535 + 0.685009i \(0.759798\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) 3.00000 + 1.73205i 0.124676 + 0.0719816i
\(580\) 0 0
\(581\) −9.00000 + 15.5885i −0.373383 + 0.646718i
\(582\) −25.5000 14.7224i −1.05701 0.610264i
\(583\) 0 0
\(584\) −1.00000 −0.0413803
\(585\) 0 0
\(586\) 12.0000 0.495715
\(587\) 18.0000 + 31.1769i 0.742940 + 1.28681i 0.951151 + 0.308725i \(0.0999023\pi\)
−0.208212 + 0.978084i \(0.566764\pi\)
\(588\) −4.50000 + 2.59808i −0.185577 + 0.107143i
\(589\) −35.0000 + 60.6218i −1.44215 + 2.49788i
\(590\) 0 0
\(591\) 31.1769i 1.28245i
\(592\) 1.00000 + 1.73205i 0.0410997 + 0.0711868i
\(593\) 9.00000 0.369586 0.184793 0.982777i \(-0.440839\pi\)
0.184793 + 0.982777i \(0.440839\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 27.7128i 1.13421i
\(598\) 0 0
\(599\) −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(600\) 0 0
\(601\) 5.00000 + 8.66025i 0.203954 + 0.353259i 0.949799 0.312861i \(-0.101287\pi\)
−0.745845 + 0.666120i \(0.767954\pi\)
\(602\) 2.00000 0.0815139
\(603\) 19.5000 33.7750i 0.794101 1.37542i
\(604\) −4.00000 −0.162758
\(605\) 0 0
\(606\) 18.0000 + 10.3923i 0.731200 + 0.422159i
\(607\) −20.0000 + 34.6410i −0.811775 + 1.40604i 0.0998457 + 0.995003i \(0.468165\pi\)
−0.911621 + 0.411033i \(0.865168\pi\)
\(608\) −3.50000 + 6.06218i −0.141944 + 0.245854i
\(609\) −18.0000 10.3923i −0.729397 0.421117i
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 9.00000 15.5885i 0.363803 0.630126i
\(613\) −44.0000 −1.77714 −0.888572 0.458738i \(-0.848302\pi\)
−0.888572 + 0.458738i \(0.848302\pi\)
\(614\) −4.00000 6.92820i −0.161427 0.279600i
\(615\) 0 0
\(616\) 0 0
\(617\) −4.50000 + 7.79423i −0.181163 + 0.313784i −0.942277 0.334835i \(-0.891320\pi\)
0.761114 + 0.648618i \(0.224653\pi\)
\(618\) 3.46410i 0.139347i
\(619\) −11.5000 19.9186i −0.462224 0.800595i 0.536847 0.843679i \(-0.319615\pi\)
−0.999071 + 0.0430838i \(0.986282\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 30.0000 1.20289
\(623\) 15.0000 + 25.9808i 0.600962 + 1.04090i
\(624\) 6.92820i 0.277350i
\(625\) 0 0
\(626\) 9.50000 16.4545i 0.379696 0.657653i
\(627\) 0 0
\(628\) 7.00000 + 12.1244i 0.279330 + 0.483814i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 1.00000 + 1.73205i 0.0397779 + 0.0688973i
\(633\) −7.50000 4.33013i −0.298098 0.172107i
\(634\) −15.0000 + 25.9808i −0.595726 + 1.03183i
\(635\) 0 0
\(636\) −18.0000 10.3923i −0.713746 0.412082i
\(637\) 6.00000 + 10.3923i 0.237729 + 0.411758i
\(638\) 0 0
\(639\) −18.0000 −0.712069
\(640\) 0 0
\(641\) −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) 13.5000 7.79423i 0.532803 0.307614i
\(643\) −6.50000 + 11.2583i −0.256335 + 0.443985i −0.965257 0.261301i \(-0.915848\pi\)
0.708922 + 0.705287i \(0.249182\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −21.0000 36.3731i −0.826234 1.43108i
\(647\) 48.0000 1.88707 0.943537 0.331266i \(-0.107476\pi\)
0.943537 + 0.331266i \(0.107476\pi\)
\(648\) −9.00000 −0.353553
\(649\) 0 0
\(650\) 0 0
\(651\) 34.6410i 1.35769i
\(652\) −3.50000 + 6.06218i −0.137071 + 0.237413i
\(653\) −18.0000 + 31.1769i −0.704394 + 1.22005i 0.262515 + 0.964928i \(0.415448\pi\)
−0.966910 + 0.255119i \(0.917885\pi\)
\(654\) −3.00000 + 1.73205i −0.117309 + 0.0677285i
\(655\) 0 0
\(656\) 9.00000 0.351391
\(657\) −3.00000 −0.117041
\(658\) −12.0000 −0.467809
\(659\) −16.5000 28.5788i −0.642749 1.11327i −0.984817 0.173598i \(-0.944461\pi\)
0.342068 0.939675i \(-0.388873\pi\)
\(660\) 0 0
\(661\) −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i \(-0.845717\pi\)
0.845922 + 0.533306i \(0.179051\pi\)
\(662\) 5.50000 9.52628i 0.213764 0.370249i
\(663\) −36.0000 20.7846i −1.39812 0.807207i
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) 0 0
\(666\) 3.00000 + 5.19615i 0.116248 + 0.201347i
\(667\) 0 0
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 24.0000 13.8564i 0.927894 0.535720i
\(670\) 0 0
\(671\) 0 0
\(672\) 3.46410i 0.133631i
\(673\) 1.00000 + 1.73205i 0.0385472 + 0.0667657i 0.884655 0.466246i \(-0.154394\pi\)
−0.846108 + 0.533011i \(0.821060\pi\)
\(674\) 14.0000 0.539260
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −6.00000 10.3923i −0.230599 0.399409i 0.727386 0.686229i \(-0.240735\pi\)
−0.957984 + 0.286820i \(0.907402\pi\)
\(678\) 5.19615i 0.199557i
\(679\) −17.0000 + 29.4449i −0.652400 + 1.12999i
\(680\) 0 0
\(681\) 22.5000 12.9904i 0.862202 0.497792i
\(682\) 0 0
\(683\) 3.00000 0.114792 0.0573959 0.998351i \(-0.481720\pi\)
0.0573959 + 0.998351i \(0.481720\pi\)
\(684\) −10.5000 + 18.1865i −0.401478 + 0.695379i
\(685\) 0 0
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 15.0000 + 8.66025i 0.572286 + 0.330409i
\(688\) −0.500000 + 0.866025i −0.0190623 + 0.0330169i
\(689\) −24.0000 + 41.5692i −0.914327 + 1.58366i
\(690\) 0 0
\(691\) −17.5000 30.3109i −0.665731 1.15308i −0.979086 0.203445i \(-0.934786\pi\)
0.313355 0.949636i \(-0.398547\pi\)
\(692\) 12.0000 0.456172
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 9.00000 5.19615i 0.341144 0.196960i
\(697\) −27.0000 + 46.7654i −1.02270 + 1.77136i
\(698\) −5.00000 + 8.66025i −0.189253 + 0.327795i
\(699\) 5.19615i 0.196537i
\(700\) 0 0
\(701\) −48.0000 −1.81293 −0.906467 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 20.7846i 0.784465i
\(703\) 14.0000 0.528020
\(704\) 0 0
\(705\) 0 0
\(706\) −7.50000 + 12.9904i −0.282266 + 0.488899i
\(707\) 12.0000 20.7846i 0.451306 0.781686i
\(708\) −13.5000 + 7.79423i −0.507361 + 0.292925i
\(709\) 14.0000 + 24.2487i 0.525781 + 0.910679i 0.999549 + 0.0300298i \(0.00956021\pi\)
−0.473768 + 0.880650i \(0.657106\pi\)
\(710\) 0 0
\(711\) 3.00000 + 5.19615i 0.112509 + 0.194871i
\(712\) −15.0000 −0.562149
\(713\) 0 0
\(714\) −18.0000 10.3923i −0.673633 0.388922i
\(715\) 0 0
\(716\) 4.50000 7.79423i 0.168173 0.291284i
\(717\) 0 0
\(718\) 6.00000 + 10.3923i 0.223918 + 0.387837i
\(719\) 18.0000 0.671287 0.335643 0.941989i \(-0.391046\pi\)
0.335643 + 0.941989i \(0.391046\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 15.0000 + 25.9808i 0.558242 + 0.966904i
\(723\) −28.5000 + 16.4545i −1.05993 + 0.611949i
\(724\) 8.00000 13.8564i 0.297318 0.514969i
\(725\) 0 0
\(726\) 19.0526i 0.707107i
\(727\) −20.0000 34.6410i −0.741759 1.28476i −0.951694 0.307049i \(-0.900659\pi\)
0.209935 0.977715i \(-0.432675\pi\)
\(728\) 8.00000 0.296500
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −3.00000 5.19615i −0.110959 0.192187i
\(732\) 6.92820i 0.256074i
\(733\) −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i \(-0.966513\pi\)
0.588177 + 0.808732i \(0.299846\pi\)
\(734\) 5.00000 8.66025i 0.184553 0.319656i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 27.0000 0.993884
\(739\) −25.0000 −0.919640 −0.459820 0.888012i \(-0.652086\pi\)
−0.459820 + 0.888012i \(0.652086\pi\)
\(740\) 0 0
\(741\) 42.0000 + 24.2487i 1.54291 + 0.890799i
\(742\) −12.0000 + 20.7846i −0.440534 + 0.763027i
\(743\) 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i \(-0.798229\pi\)
0.915794 + 0.401648i \(0.131563\pi\)
\(744\) −15.0000 8.66025i −0.549927 0.317500i
\(745\) 0 0
\(746\) −4.00000 −0.146450
\(747\) −13.5000 23.3827i −0.493939 0.855528i
\(748\) 0 0
\(749\) −9.00000 15.5885i −0.328853 0.569590i
\(750\) 0 0
\(751\) 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i \(-0.810082\pi\)
0.900207 + 0.435463i \(0.143415\pi\)
\(752\) 3.00000 5.19615i 0.109399 0.189484i
\(753\) 25.9808i 0.946792i
\(754\) −12.0000 20.7846i −0.437014 0.756931i
\(755\) 0 0
\(756\) 10.3923i 0.377964i
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 10.0000 + 17.3205i 0.363216 + 0.629109i
\(759\) 0 0
\(760\) 0 0
\(761\) −10.5000 + 18.1865i −0.380625 + 0.659261i −0.991152 0.132734i \(-0.957624\pi\)
0.610527 + 0.791995i \(0.290958\pi\)
\(762\) 30.0000 17.3205i 1.08679 0.627456i
\(763\) 2.00000 + 3.46410i 0.0724049 + 0.125409i
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) 24.0000 0.867155
\(767\) 18.0000 + 31.1769i 0.649942 + 1.12573i
\(768\) −1.50000 0.866025i −0.0541266 0.0312500i
\(769\) −2.50000 + 4.33013i −0.0901523 + 0.156148i −0.907575 0.419890i \(-0.862069\pi\)
0.817423 + 0.576038i \(0.195402\pi\)
\(770\) 0 0
\(771\) 4.50000 + 2.59808i 0.162064 + 0.0935674i
\(772\) 1.00000 + 1.73205i 0.0359908 + 0.0623379i
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) −1.50000 + 2.59808i −0.0539164 + 0.0933859i
\(775\) 0 0
\(776\) −8.50000 14.7224i −0.305132 0.528505i
\(777\) 6.00000 3.46410i 0.215249 0.124274i
\(778\) 3.00000 5.19615i 0.107555 0.186291i
\(779\) 31.5000 54.5596i 1.12860 1.95480i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 27.0000 15.5885i 0.964901 0.557086i
\(784\) −3.00000 −0.107143
\(785\) 0 0
\(786\) 20.7846i 0.741362i
\(787\) 10.0000 17.3205i 0.356462 0.617409i −0.630905 0.775860i \(-0.717316\pi\)
0.987367 + 0.158450i \(0.0506498\pi\)
\(788\) 9.00000 15.5885i 0.320612 0.555316i