Properties

Label 1050.2.o.e.949.1
Level $1050$
Weight $2$
Character 1050.949
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.e.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.59808 - 0.500000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.866025 - 0.500000i) q^{12} +4.00000i q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.59808 - 1.50000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(1.00000 + 1.73205i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-2.59808 + 1.50000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(-1.73205 + 2.00000i) q^{28} +(0.500000 - 0.866025i) q^{31} +(0.866025 + 0.500000i) q^{32} +3.00000 q^{34} +1.00000 q^{36} +(-8.66025 + 5.00000i) q^{37} +(-1.73205 - 1.00000i) q^{38} +(-2.00000 + 3.46410i) q^{39} -9.00000 q^{41} +(2.59808 + 0.500000i) q^{42} +10.0000i q^{43} +(1.50000 - 2.59808i) q^{46} +(-2.59808 + 1.50000i) q^{47} -1.00000i q^{48} +(6.50000 + 2.59808i) q^{49} +(-1.50000 - 2.59808i) q^{51} +(3.46410 + 2.00000i) q^{52} +(-5.19615 - 3.00000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.500000 - 2.59808i) q^{56} +2.00000i q^{57} +(-3.00000 + 5.19615i) q^{59} +(-4.00000 - 6.92820i) q^{61} +1.00000i q^{62} +(-0.866025 - 2.50000i) q^{63} -1.00000 q^{64} +(3.46410 + 2.00000i) q^{67} +(-2.59808 + 1.50000i) q^{68} -3.00000 q^{69} +3.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(12.1244 + 7.00000i) q^{73} +(5.00000 - 8.66025i) q^{74} +2.00000 q^{76} -4.00000i q^{78} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(7.79423 - 4.50000i) q^{82} +(-2.50000 + 0.866025i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(-7.50000 - 12.9904i) q^{89} +(2.00000 - 10.3923i) q^{91} +3.00000i q^{92} +(0.866025 - 0.500000i) q^{93} +(1.50000 - 2.59808i) q^{94} +(0.500000 + 0.866025i) q^{96} -7.00000i q^{97} +(-6.92820 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + 10q^{14} - 2q^{16} + 4q^{19} - 8q^{21} - 2q^{24} - 8q^{26} + 2q^{31} + 12q^{34} + 4q^{36} - 8q^{39} - 36q^{41} + 6q^{46} + 26q^{49} - 6q^{51} - 2q^{54} + 2q^{56} - 12q^{59} - 16q^{61} - 4q^{64} - 12q^{69} + 12q^{71} + 20q^{74} + 8q^{76} + 22q^{79} - 2q^{81} - 10q^{84} - 20q^{86} - 30q^{89} + 8q^{91} + 6q^{94} + 2q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) −2.59808 0.500000i −0.981981 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.50000 0.866025i 0.668153 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.59808 1.50000i −0.630126 0.363803i 0.150675 0.988583i \(-0.451855\pi\)
−0.780801 + 0.624780i \(0.785189\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 0 0
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) 0 0
\(23\) −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
\(26\) −2.00000 3.46410i −0.392232 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) −1.73205 + 2.00000i −0.327327 + 0.377964i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0.500000 0.866025i 0.0898027 0.155543i −0.817625 0.575751i \(-0.804710\pi\)
0.907428 + 0.420208i \(0.138043\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −8.66025 + 5.00000i −1.42374 + 0.821995i −0.996616 0.0821995i \(-0.973806\pi\)
−0.427121 + 0.904194i \(0.640472\pi\)
\(38\) −1.73205 1.00000i −0.280976 0.162221i
\(39\) −2.00000 + 3.46410i −0.320256 + 0.554700i
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 2.59808 + 0.500000i 0.400892 + 0.0771517i
\(43\) 10.0000i 1.52499i 0.646997 + 0.762493i \(0.276025\pi\)
−0.646997 + 0.762493i \(0.723975\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −2.59808 + 1.50000i −0.378968 + 0.218797i −0.677369 0.735643i \(-0.736880\pi\)
0.298401 + 0.954441i \(0.403547\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 6.50000 + 2.59808i 0.928571 + 0.371154i
\(50\) 0 0
\(51\) −1.50000 2.59808i −0.210042 0.363803i
\(52\) 3.46410 + 2.00000i 0.480384 + 0.277350i
\(53\) −5.19615 3.00000i −0.713746 0.412082i 0.0987002 0.995117i \(-0.468532\pi\)
−0.812447 + 0.583036i \(0.801865\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.500000 2.59808i 0.0668153 0.347183i
\(57\) 2.00000i 0.264906i
\(58\) 0 0
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 1.00000i 0.127000i
\(63\) −0.866025 2.50000i −0.109109 0.314970i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 3.46410 + 2.00000i 0.423207 + 0.244339i 0.696449 0.717607i \(-0.254762\pi\)
−0.273241 + 0.961946i \(0.588096\pi\)
\(68\) −2.59808 + 1.50000i −0.315063 + 0.181902i
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 12.1244 + 7.00000i 1.41905 + 0.819288i 0.996215 0.0869195i \(-0.0277023\pi\)
0.422833 + 0.906208i \(0.361036\pi\)
\(74\) 5.00000 8.66025i 0.581238 1.00673i
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 4.00000i 0.452911i
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 7.79423 4.50000i 0.860729 0.496942i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −2.50000 + 0.866025i −0.272772 + 0.0944911i
\(85\) 0 0
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) 0 0
\(88\) 0 0
\(89\) −7.50000 12.9904i −0.794998 1.37698i −0.922840 0.385183i \(-0.874138\pi\)
0.127842 0.991795i \(-0.459195\pi\)
\(90\) 0 0
\(91\) 2.00000 10.3923i 0.209657 1.08941i
\(92\) 3.00000i 0.312772i
\(93\) 0.866025 0.500000i 0.0898027 0.0518476i
\(94\) 1.50000 2.59808i 0.154713 0.267971i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 7.00000i 0.710742i −0.934725 0.355371i \(-0.884354\pi\)
0.934725 0.355371i \(-0.115646\pi\)
\(98\) −6.92820 + 1.00000i −0.699854 + 0.101015i
\(99\) 0 0
\(100\) 0 0
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) 2.59808 + 1.50000i 0.257248 + 0.148522i
\(103\) −4.33013 + 2.50000i −0.426660 + 0.246332i −0.697923 0.716173i \(-0.745892\pi\)
0.271263 + 0.962505i \(0.412559\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −15.5885 + 9.00000i −1.50699 + 0.870063i −0.507026 + 0.861931i \(0.669255\pi\)
−0.999967 + 0.00813215i \(0.997411\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 0.866025 + 2.50000i 0.0818317 + 0.236228i
\(113\) 21.0000i 1.97551i −0.156001 0.987757i \(-0.549860\pi\)
0.156001 0.987757i \(-0.450140\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) 0 0
\(116\) 0 0
\(117\) −3.46410 + 2.00000i −0.320256 + 0.184900i
\(118\) 6.00000i 0.552345i
\(119\) 6.00000 + 5.19615i 0.550019 + 0.476331i
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 6.92820 + 4.00000i 0.627250 + 0.362143i
\(123\) −7.79423 4.50000i −0.702782 0.405751i
\(124\) −0.500000 0.866025i −0.0449013 0.0777714i
\(125\) 0 0
\(126\) 2.00000 + 1.73205i 0.178174 + 0.154303i
\(127\) 16.0000i 1.41977i −0.704317 0.709885i \(-0.748747\pi\)
0.704317 0.709885i \(-0.251253\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −5.00000 + 8.66025i −0.440225 + 0.762493i
\(130\) 0 0
\(131\) 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) 0 0
\(133\) −1.73205 5.00000i −0.150188 0.433555i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 1.50000 2.59808i 0.128624 0.222783i
\(137\) 7.79423 + 4.50000i 0.665906 + 0.384461i 0.794524 0.607233i \(-0.207721\pi\)
−0.128618 + 0.991694i \(0.541054\pi\)
\(138\) 2.59808 1.50000i 0.221163 0.127688i
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) −2.59808 + 1.50000i −0.218026 + 0.125877i
\(143\) 0 0
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) −14.0000 −1.15865
\(147\) 4.33013 + 5.50000i 0.357143 + 0.453632i
\(148\) 10.0000i 0.821995i
\(149\) −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
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) −1.73205 + 1.00000i −0.140488 + 0.0811107i
\(153\) 3.00000i 0.242536i
\(154\) 0 0
\(155\) 0 0
\(156\) 2.00000 + 3.46410i 0.160128 + 0.277350i
\(157\) −6.92820 4.00000i −0.552931 0.319235i 0.197372 0.980329i \(-0.436759\pi\)
−0.750303 + 0.661094i \(0.770093\pi\)
\(158\) −9.52628 5.50000i −0.757870 0.437557i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) 0 0
\(161\) 7.50000 2.59808i 0.591083 0.204757i
\(162\) 1.00000i 0.0785674i
\(163\) −6.92820 + 4.00000i −0.542659 + 0.313304i −0.746156 0.665771i \(-0.768103\pi\)
0.203497 + 0.979076i \(0.434769\pi\)
\(164\) −4.50000 + 7.79423i −0.351391 + 0.608627i
\(165\) 0 0
\(166\) 0 0
\(167\) 24.0000i 1.85718i −0.371113 0.928588i \(-0.621024\pi\)
0.371113 0.928588i \(-0.378976\pi\)
\(168\) 1.73205 2.00000i 0.133631 0.154303i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) −1.00000 + 1.73205i −0.0764719 + 0.132453i
\(172\) 8.66025 + 5.00000i 0.660338 + 0.381246i
\(173\) 15.5885 9.00000i 1.18517 0.684257i 0.227964 0.973670i \(-0.426793\pi\)
0.957205 + 0.289412i \(0.0934598\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.19615 + 3.00000i −0.390567 + 0.225494i
\(178\) 12.9904 + 7.50000i 0.973670 + 0.562149i
\(179\) −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i \(-0.905320\pi\)
0.731858 + 0.681457i \(0.238654\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 3.46410 + 10.0000i 0.256776 + 0.741249i
\(183\) 8.00000i 0.591377i
\(184\) −1.50000 2.59808i −0.110581 0.191533i
\(185\) 0 0
\(186\) −0.500000 + 0.866025i −0.0366618 + 0.0635001i
\(187\) 0 0
\(188\) 3.00000i 0.218797i
\(189\) 0.500000 2.59808i 0.0363696 0.188982i
\(190\) 0 0
\(191\) 10.5000 + 18.1865i 0.759753 + 1.31593i 0.942976 + 0.332860i \(0.108014\pi\)
−0.183223 + 0.983071i \(0.558653\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 14.7224 + 8.50000i 1.05974 + 0.611843i 0.925361 0.379086i \(-0.123762\pi\)
0.134382 + 0.990930i \(0.457095\pi\)
\(194\) 3.50000 + 6.06218i 0.251285 + 0.435239i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) 12.0000i 0.854965i −0.904024 0.427482i \(-0.859401\pi\)
0.904024 0.427482i \(-0.140599\pi\)
\(198\) 0 0
\(199\) 5.50000 9.52628i 0.389885 0.675300i −0.602549 0.798082i \(-0.705848\pi\)
0.992434 + 0.122782i \(0.0391815\pi\)
\(200\) 0 0
\(201\) 2.00000 + 3.46410i 0.141069 + 0.244339i
\(202\) 18.0000i 1.26648i
\(203\) 0 0
\(204\) −3.00000 −0.210042
\(205\) 0 0
\(206\) 2.50000 4.33013i 0.174183 0.301694i
\(207\) −2.59808 1.50000i −0.180579 0.104257i
\(208\) 3.46410 2.00000i 0.240192 0.138675i
\(209\) 0 0
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) −5.19615 + 3.00000i −0.356873 + 0.206041i
\(213\) 2.59808 + 1.50000i 0.178017 + 0.102778i
\(214\) 9.00000 15.5885i 0.615227 1.06561i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −1.73205 + 2.00000i −0.117579 + 0.135769i
\(218\) 2.00000i 0.135457i
\(219\) 7.00000 + 12.1244i 0.473016 + 0.819288i
\(220\) 0 0
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 8.66025 5.00000i 0.581238 0.335578i
\(223\) 19.0000i 1.27233i 0.771551 + 0.636167i \(0.219481\pi\)
−0.771551 + 0.636167i \(0.780519\pi\)
\(224\) −2.00000 1.73205i −0.133631 0.115728i
\(225\) 0 0
\(226\) 10.5000 + 18.1865i 0.698450 + 1.20975i
\(227\) 5.19615 + 3.00000i 0.344881 + 0.199117i 0.662428 0.749125i \(-0.269526\pi\)
−0.317547 + 0.948242i \(0.602859\pi\)
\(228\) 1.73205 + 1.00000i 0.114708 + 0.0662266i
\(229\) −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i \(-0.208859\pi\)
−0.924510 + 0.381157i \(0.875526\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 25.9808 15.0000i 1.70206 0.982683i 0.758380 0.651813i \(-0.225991\pi\)
0.943676 0.330870i \(-0.107342\pi\)
\(234\) 2.00000 3.46410i 0.130744 0.226455i
\(235\) 0 0
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) 11.0000i 0.714527i
\(238\) −7.79423 1.50000i −0.505225 0.0972306i
\(239\) −15.0000 −0.970269 −0.485135 0.874439i \(-0.661229\pi\)
−0.485135 + 0.874439i \(0.661229\pi\)
\(240\) 0 0
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −9.52628 5.50000i −0.612372 0.353553i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) −6.92820 + 4.00000i −0.440831 + 0.254514i
\(248\) 0.866025 + 0.500000i 0.0549927 + 0.0317500i
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) −2.59808 0.500000i −0.163663 0.0314970i
\(253\) 0 0
\(254\) 8.00000 + 13.8564i 0.501965 + 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 25.9808 15.0000i 1.62064 0.935674i 0.633885 0.773427i \(-0.281459\pi\)
0.986750 0.162247i \(-0.0518742\pi\)
\(258\) 10.0000i 0.622573i
\(259\) 25.0000 8.66025i 1.55342 0.538122i
\(260\) 0 0
\(261\) 0 0
\(262\) −10.3923 6.00000i −0.642039 0.370681i
\(263\) 7.79423 + 4.50000i 0.480613 + 0.277482i 0.720672 0.693276i \(-0.243833\pi\)
−0.240059 + 0.970758i \(0.577167\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 4.00000 + 3.46410i 0.245256 + 0.212398i
\(267\) 15.0000i 0.917985i
\(268\) 3.46410 2.00000i 0.211604 0.122169i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 0 0
\(271\) 3.50000 + 6.06218i 0.212610 + 0.368251i 0.952531 0.304443i \(-0.0984703\pi\)
−0.739921 + 0.672694i \(0.765137\pi\)
\(272\) 3.00000i 0.181902i
\(273\) 6.92820 8.00000i 0.419314 0.484182i
\(274\) −9.00000 −0.543710
\(275\) 0 0
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) 24.2487 + 14.0000i 1.45696 + 0.841178i 0.998861 0.0477206i \(-0.0151957\pi\)
0.458103 + 0.888899i \(0.348529\pi\)
\(278\) 1.73205 1.00000i 0.103882 0.0599760i
\(279\) 1.00000 0.0598684
\(280\) 0 0
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 2.59808 1.50000i 0.154713 0.0893237i
\(283\) −3.46410 2.00000i −0.205919 0.118888i 0.393494 0.919327i \(-0.371266\pi\)
−0.599414 + 0.800439i \(0.704600\pi\)
\(284\) 1.50000 2.59808i 0.0890086 0.154167i
\(285\) 0 0
\(286\) 0 0
\(287\) 23.3827 + 4.50000i 1.38024 + 0.265627i
\(288\) 1.00000i 0.0589256i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) 0 0
\(291\) 3.50000 6.06218i 0.205174 0.355371i
\(292\) 12.1244 7.00000i 0.709524 0.409644i
\(293\) 24.0000i 1.40209i 0.713115 + 0.701047i \(0.247284\pi\)
−0.713115 + 0.701047i \(0.752716\pi\)
\(294\) −6.50000 2.59808i −0.379088 0.151523i
\(295\) 0 0
\(296\) −5.00000 8.66025i −0.290619 0.503367i
\(297\) 0 0
\(298\) 5.19615 + 3.00000i 0.301005 + 0.173785i
\(299\) −6.00000 10.3923i −0.346989 0.601003i
\(300\) 0 0
\(301\) 5.00000 25.9808i 0.288195 1.49751i
\(302\) 8.00000i 0.460348i
\(303\) −15.5885 + 9.00000i −0.895533 + 0.517036i
\(304\) 1.00000 1.73205i 0.0573539 0.0993399i
\(305\) 0 0
\(306\) 1.50000 + 2.59808i 0.0857493 + 0.148522i
\(307\) 28.0000i 1.59804i −0.601302 0.799022i \(-0.705351\pi\)
0.601302 0.799022i \(-0.294649\pi\)
\(308\) 0 0
\(309\) −5.00000 −0.284440
\(310\) 0 0
\(311\) −4.50000 + 7.79423i −0.255172 + 0.441970i −0.964942 0.262463i \(-0.915465\pi\)
0.709771 + 0.704433i \(0.248799\pi\)
\(312\) −3.46410 2.00000i −0.196116 0.113228i
\(313\) −4.33013 + 2.50000i −0.244753 + 0.141308i −0.617359 0.786681i \(-0.711798\pi\)
0.372606 + 0.927990i \(0.378464\pi\)
\(314\) 8.00000 0.451466
\(315\) 0 0
\(316\) 11.0000 0.618798
\(317\) −15.5885 + 9.00000i −0.875535 + 0.505490i −0.869184 0.494489i \(-0.835355\pi\)
−0.00635137 + 0.999980i \(0.502022\pi\)
\(318\) 5.19615 + 3.00000i 0.291386 + 0.168232i
\(319\) 0 0
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) −5.19615 + 6.00000i −0.289570 + 0.334367i
\(323\) 6.00000i 0.333849i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 4.00000 6.92820i 0.221540 0.383718i
\(327\) 1.73205 1.00000i 0.0957826 0.0553001i
\(328\) 9.00000i 0.496942i
\(329\) 7.50000 2.59808i 0.413488 0.143237i
\(330\) 0 0
\(331\) 5.00000 + 8.66025i 0.274825 + 0.476011i 0.970091 0.242742i \(-0.0780468\pi\)
−0.695266 + 0.718752i \(0.744713\pi\)
\(332\) 0 0
\(333\) −8.66025 5.00000i −0.474579 0.273998i
\(334\) 12.0000 + 20.7846i 0.656611 + 1.13728i
\(335\) 0 0
\(336\) −0.500000 + 2.59808i −0.0272772 + 0.141737i
\(337\) 11.0000i 0.599208i 0.954064 + 0.299604i \(0.0968546\pi\)
−0.954064 + 0.299604i \(0.903145\pi\)
\(338\) 2.59808 1.50000i 0.141317 0.0815892i
\(339\) 10.5000 18.1865i 0.570282 0.987757i
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000i 0.108148i
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) −9.00000 + 15.5885i −0.483843 + 0.838041i
\(347\) 31.1769 + 18.0000i 1.67366 + 0.966291i 0.965559 + 0.260184i \(0.0837832\pi\)
0.708105 + 0.706107i \(0.249550\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 0 0
\(353\) −12.9904 7.50000i −0.691408 0.399185i 0.112731 0.993626i \(-0.464040\pi\)
−0.804139 + 0.594441i \(0.797373\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) 0 0
\(356\) −15.0000 −0.794998
\(357\) 2.59808 + 7.50000i 0.137505 + 0.396942i
\(358\) 6.00000i 0.317110i
\(359\) 6.00000 + 10.3923i 0.316668 + 0.548485i 0.979791 0.200026i \(-0.0641026\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −6.92820 + 4.00000i −0.364138 + 0.210235i
\(363\) 11.0000i 0.577350i
\(364\) −8.00000 6.92820i −0.419314 0.363137i
\(365\) 0 0
\(366\) 4.00000 + 6.92820i 0.209083 + 0.362143i
\(367\) −6.92820 4.00000i −0.361649 0.208798i 0.308155 0.951336i \(-0.400289\pi\)
−0.669804 + 0.742538i \(0.733622\pi\)
\(368\) 2.59808 + 1.50000i 0.135434 + 0.0781929i
\(369\) −4.50000 7.79423i −0.234261 0.405751i
\(370\) 0 0
\(371\) 12.0000 + 10.3923i 0.623009 + 0.539542i
\(372\) 1.00000i 0.0518476i
\(373\) 3.46410 2.00000i 0.179364 0.103556i −0.407630 0.913147i \(-0.633645\pi\)
0.586994 + 0.809591i \(0.300311\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.50000 2.59808i −0.0773566 0.133986i
\(377\) 0 0
\(378\) 0.866025 + 2.50000i 0.0445435 + 0.128586i
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0 0
\(381\) 8.00000 13.8564i 0.409852 0.709885i
\(382\) −18.1865 10.5000i −0.930504 0.537227i
\(383\) −18.1865 + 10.5000i −0.929288 + 0.536525i −0.886586 0.462563i \(-0.846930\pi\)
−0.0427020 + 0.999088i \(0.513597\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −17.0000 −0.865277
\(387\) −8.66025 + 5.00000i −0.440225 + 0.254164i
\(388\) −6.06218 3.50000i −0.307760 0.177686i
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) 9.00000 0.455150
\(392\) −2.59808 + 6.50000i −0.131223 + 0.328300i
\(393\) 12.0000i 0.605320i
\(394\) 6.00000 + 10.3923i 0.302276 + 0.523557i
\(395\) 0 0
\(396\) 0 0
\(397\) −19.0526 + 11.0000i −0.956221 + 0.552074i −0.895008 0.446051i \(-0.852830\pi\)
−0.0612128 + 0.998125i \(0.519497\pi\)
\(398\) 11.0000i 0.551380i
\(399\) 1.00000 5.19615i 0.0500626 0.260133i
\(400\) 0 0
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) −3.46410 2.00000i −0.172774 0.0997509i
\(403\) 3.46410 + 2.00000i 0.172559 + 0.0996271i
\(404\) 9.00000 + 15.5885i 0.447767 + 0.775555i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 2.59808 1.50000i 0.128624 0.0742611i
\(409\) 2.50000 4.33013i 0.123617 0.214111i −0.797574 0.603220i \(-0.793884\pi\)
0.921192 + 0.389109i \(0.127217\pi\)
\(410\) 0 0
\(411\) 4.50000 + 7.79423i 0.221969 + 0.384461i
\(412\) 5.00000i 0.246332i
\(413\) 10.3923 12.0000i 0.511372 0.590481i
\(414\) 3.00000 0.147442
\(415\) 0 0
\(416\) −2.00000 + 3.46410i −0.0980581 + 0.169842i
\(417\) −1.73205 1.00000i −0.0848189 0.0489702i
\(418\) 0 0
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −40.0000 −1.94948 −0.974740 0.223341i \(-0.928304\pi\)
−0.974740 + 0.223341i \(0.928304\pi\)
\(422\) −12.1244 + 7.00000i −0.590204 + 0.340755i
\(423\) −2.59808 1.50000i −0.126323 0.0729325i
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 0 0
\(426\) −3.00000 −0.145350
\(427\) 6.92820 + 20.0000i 0.335279 + 0.967868i
\(428\) 18.0000i 0.870063i
\(429\) 0 0
\(430\) 0 0
\(431\) 13.5000 23.3827i 0.650272 1.12630i −0.332785 0.943003i \(-0.607988\pi\)
0.983057 0.183301i \(-0.0586785\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 29.0000i 1.39365i −0.717241 0.696826i \(-0.754595\pi\)
0.717241 0.696826i \(-0.245405\pi\)
\(434\) 0.500000 2.59808i 0.0240008 0.124712i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) −5.19615 3.00000i −0.248566 0.143509i
\(438\) −12.1244 7.00000i −0.579324 0.334473i
\(439\) 2.50000 + 4.33013i 0.119318 + 0.206666i 0.919498 0.393095i \(-0.128596\pi\)
−0.800179 + 0.599761i \(0.795262\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 12.0000i 0.570782i
\(443\) 5.19615 3.00000i 0.246877 0.142534i −0.371457 0.928450i \(-0.621142\pi\)
0.618333 + 0.785916i \(0.287808\pi\)
\(444\) −5.00000 + 8.66025i −0.237289 + 0.410997i
\(445\) 0 0
\(446\) −9.50000 16.4545i −0.449838 0.779142i
\(447\) 6.00000i 0.283790i
\(448\) 2.59808 + 0.500000i 0.122748 + 0.0236228i
\(449\) 21.0000 0.991051 0.495526 0.868593i \(-0.334975\pi\)
0.495526 + 0.868593i \(0.334975\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −18.1865 10.5000i −0.855423 0.493878i
\(453\) −6.92820 + 4.00000i −0.325515 + 0.187936i
\(454\) −6.00000 −0.281594
\(455\) 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 \(0.318438\pi\)
\(458\) 3.46410 + 2.00000i 0.161867 + 0.0934539i
\(459\) 1.50000 2.59808i 0.0700140 0.121268i
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 5.00000i 0.232370i −0.993228 0.116185i \(-0.962933\pi\)
0.993228 0.116185i \(-0.0370665\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −15.0000 + 25.9808i −0.694862 + 1.20354i
\(467\) 10.3923 6.00000i 0.480899 0.277647i −0.239892 0.970799i \(-0.577112\pi\)
0.720791 + 0.693153i \(0.243779\pi\)
\(468\) 4.00000i 0.184900i
\(469\) −8.00000 6.92820i −0.369406 0.319915i
\(470\) 0 0
\(471\) −4.00000 6.92820i −0.184310 0.319235i
\(472\) −5.19615 3.00000i −0.239172 0.138086i
\(473\) 0 0
\(474\) −5.50000 9.52628i −0.252623 0.437557i
\(475\) 0 0
\(476\) 7.50000 2.59808i 0.343762 0.119083i
\(477\) 6.00000i 0.274721i
\(478\) 12.9904 7.50000i 0.594166 0.343042i
\(479\) −13.5000 + 23.3827i −0.616831 + 1.06838i 0.373230 + 0.927739i \(0.378250\pi\)
−0.990060 + 0.140643i \(0.955083\pi\)
\(480\) 0 0
\(481\) −20.0000 34.6410i −0.911922 1.57949i
\(482\) 14.0000i 0.637683i
\(483\) 7.79423 + 1.50000i 0.354650 + 0.0682524i
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 26.8468 + 15.5000i 1.21654 + 0.702372i 0.964177 0.265260i \(-0.0854576\pi\)
0.252367 + 0.967632i \(0.418791\pi\)
\(488\) 6.92820 4.00000i 0.313625 0.181071i
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) −7.79423 + 4.50000i −0.351391 + 0.202876i
\(493\) 0 0
\(494\) 4.00000 6.92820i 0.179969 0.311715i
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) −7.79423 1.50000i −0.349619 0.0672842i
\(498\) 0 0
\(499\) 16.0000 + 27.7128i 0.716258 + 1.24060i 0.962472 + 0.271380i \(0.0874801\pi\)
−0.246214 + 0.969216i \(0.579187\pi\)
\(500\) 0 0
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) −10.3923 + 6.00000i −0.463831 + 0.267793i
\(503\) 36.0000i 1.60516i 0.596544 + 0.802580i \(0.296540\pi\)
−0.596544 + 0.802580i \(0.703460\pi\)
\(504\) 2.50000 0.866025i 0.111359 0.0385758i
\(505\) 0 0
\(506\) 0 0
\(507\) −2.59808 1.50000i −0.115385 0.0666173i
\(508\) −13.8564 8.00000i −0.614779 0.354943i
\(509\) −18.0000 31.1769i −0.797836 1.38189i −0.921023 0.389509i \(-0.872645\pi\)
0.123187 0.992384i \(-0.460689\pi\)
\(510\) 0 0
\(511\) −28.0000 24.2487i −1.23865 1.07270i
\(512\) 1.00000i 0.0441942i
\(513\) −1.73205 + 1.00000i −0.0764719 + 0.0441511i
\(514\) −15.0000 + 25.9808i −0.661622 + 1.14596i
\(515\) 0 0
\(516\) 5.00000 + 8.66025i 0.220113 + 0.381246i
\(517\) 0 0
\(518\) −17.3205 + 20.0000i −0.761019 + 0.878750i
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) −7.50000 + 12.9904i −0.328581 + 0.569119i −0.982231 0.187678i \(-0.939904\pi\)
0.653650 + 0.756797i \(0.273237\pi\)
\(522\) 0 0
\(523\) −27.7128 + 16.0000i −1.21180 + 0.699631i −0.963150 0.268963i \(-0.913319\pi\)
−0.248646 + 0.968594i \(0.579986\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −9.00000 −0.392419
\(527\) −2.59808 + 1.50000i −0.113174 + 0.0653410i
\(528\) 0 0
\(529\) −7.00000 + 12.1244i −0.304348 + 0.527146i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) −5.19615 1.00000i −0.225282 0.0433555i
\(533\) 36.0000i 1.55933i
\(534\) 7.50000 + 12.9904i 0.324557 + 0.562149i
\(535\) 0 0
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) −5.19615 + 3.00000i −0.224231 + 0.129460i
\(538\) 6.00000i 0.258678i
\(539\) 0 0
\(540\) 0 0
\(541\) 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i \(-0.0549027\pi\)
−0.641215 + 0.767361i \(0.721569\pi\)
\(542\) −6.06218 3.50000i −0.260393 0.150338i
\(543\) 6.92820 + 4.00000i 0.297318 + 0.171656i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 0 0
\(546\) −2.00000 + 10.3923i −0.0855921 + 0.444750i
\(547\) 26.0000i 1.11168i 0.831289 + 0.555840i \(0.187603\pi\)
−0.831289 + 0.555840i \(0.812397\pi\)
\(548\) 7.79423 4.50000i 0.332953 0.192230i
\(549\) 4.00000 6.92820i 0.170716 0.295689i
\(550\) 0 0
\(551\) 0 0
\(552\) 3.00000i 0.127688i
\(553\) −9.52628 27.5000i −0.405099 1.16942i
\(554\) −28.0000 −1.18961
\(555\) 0 0
\(556\) −1.00000 + 1.73205i −0.0424094 + 0.0734553i
\(557\) −5.19615 3.00000i −0.220168 0.127114i 0.385860 0.922557i \(-0.373905\pi\)
−0.606028 + 0.795443i \(0.707238\pi\)
\(558\) −0.866025 + 0.500000i −0.0366618 + 0.0211667i
\(559\) −40.0000 −1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) −7.79423 + 4.50000i −0.328780 + 0.189821i
\(563\) −25.9808 15.0000i −1.09496 0.632175i −0.160066 0.987106i \(-0.551171\pi\)
−0.934892 + 0.354932i \(0.884504\pi\)
\(564\) −1.50000 + 2.59808i −0.0631614 + 0.109399i
\(565\) 0 0
\(566\) 4.00000 0.168133
\(567\) 1.73205 2.00000i 0.0727393 0.0839921i
\(568\) 3.00000i 0.125877i
\(569\) 13.5000 + 23.3827i 0.565949 + 0.980253i 0.996961 + 0.0779066i \(0.0248236\pi\)
−0.431011 + 0.902347i \(0.641843\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 0 0
\(573\) 21.0000i 0.877288i
\(574\) −22.5000 + 7.79423i −0.939132 + 0.325325i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −12.1244 7.00000i −0.504744 0.291414i 0.225927 0.974144i \(-0.427459\pi\)
−0.730670 + 0.682730i \(0.760792\pi\)
\(578\) 6.92820 + 4.00000i 0.288175 + 0.166378i
\(579\) 8.50000 + 14.7224i 0.353248 + 0.611843i
\(580\) 0 0
\(581\) 0 0
\(582\) 7.00000i 0.290159i
\(583\) 0 0
\(584\) −7.00000 + 12.1244i −0.289662 + 0.501709i
\(585\) 0 0
\(586\) −12.0000 20.7846i −0.495715 0.858604i
\(587\) 42.0000i 1.73353i 0.498721 + 0.866763i \(0.333803\pi\)
−0.498721 + 0.866763i \(0.666197\pi\)
\(588\) 6.92820 1.00000i 0.285714 0.0412393i
\(589\) 2.00000 0.0824086
\(590\) 0 0
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) 8.66025 + 5.00000i 0.355934 + 0.205499i
\(593\) −18.1865 + 10.5000i −0.746831 + 0.431183i −0.824548 0.565792i \(-0.808570\pi\)
0.0777165 + 0.996976i \(0.475237\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 9.52628 5.50000i 0.389885 0.225100i
\(598\) 10.3923 + 6.00000i 0.424973 + 0.245358i
\(599\) −1.50000 + 2.59808i −0.0612883 + 0.106155i −0.895042 0.445983i \(-0.852854\pi\)
0.833753 + 0.552137i \(0.186188\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 8.66025 + 25.0000i 0.352966 + 1.01892i
\(603\) 4.00000i 0.162893i
\(604\) 4.00000 + 6.92820i 0.162758 + 0.281905i
\(605\) 0 0
\(606\) 9.00000 15.5885i 0.365600 0.633238i
\(607\) −6.06218 + 3.50000i −0.246056 + 0.142061i −0.617957 0.786212i \(-0.712039\pi\)
0.371901 + 0.928272i \(0.378706\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) 0 0
\(610\) 0 0
\(611\) −6.00000 10.3923i −0.242734 0.420428i
\(612\) −2.59808 1.50000i −0.105021 0.0606339i
\(613\) −13.8564 8.00000i −0.559655 0.323117i 0.193352 0.981129i \(-0.438064\pi\)
−0.753007 + 0.658012i \(0.771397\pi\)
\(614\) 14.0000 + 24.2487i 0.564994 + 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) 15.0000i 0.603877i −0.953327 0.301939i \(-0.902366\pi\)
0.953327 0.301939i \(-0.0976338\pi\)
\(618\) 4.33013 2.50000i 0.174183 0.100565i
\(619\) 10.0000 17.3205i 0.401934 0.696170i −0.592025 0.805919i \(-0.701671\pi\)
0.993959 + 0.109749i \(0.0350048\pi\)
\(620\) 0 0
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) 9.00000i 0.360867i
\(623\) 12.9904 + 37.5000i 0.520449 + 1.50241i
\(624\) 4.00000 0.160128
\(625\) 0 0
\(626\) 2.50000 4.33013i 0.0999201 0.173067i
\(627\) 0 0
\(628\) −6.92820 + 4.00000i −0.276465 + 0.159617i
\(629\) 30.0000 1.19618
\(630\) 0 0
\(631\) −37.0000 −1.47295 −0.736473 0.676467i \(-0.763510\pi\)
−0.736473 + 0.676467i \(0.763510\pi\)
\(632\) −9.52628 + 5.50000i −0.378935 + 0.218778i
\(633\) 12.1244 + 7.00000i 0.481900 + 0.278225i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 0 0
\(636\) −6.00000 −0.237915
\(637\) −10.3923 + 26.0000i −0.411758 + 1.03016i
\(638\) 0 0
\(639\) 1.50000 + 2.59808i 0.0593391 + 0.102778i
\(640\) 0 0
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 15.5885 9.00000i 0.615227 0.355202i
\(643\) 38.0000i 1.49857i −0.662246 0.749287i \(-0.730396\pi\)
0.662246 0.749287i \(-0.269604\pi\)
\(644\) 1.50000 7.79423i 0.0591083 0.307136i
\(645\) 0 0
\(646\) 3.00000 + 5.19615i 0.118033 + 0.204440i
\(647\) −20.7846 12.0000i −0.817127 0.471769i 0.0322975 0.999478i \(-0.489718\pi\)
−0.849425 + 0.527710i \(0.823051\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 0 0
\(650\) 0 0
\(651\) −2.50000 + 0.866025i −0.0979827 + 0.0339422i
\(652\) 8.00000i 0.313304i
\(653\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(654\) −1.00000 + 1.73205i −0.0391031 + 0.0677285i
\(655\) 0 0
\(656\) 4.50000 + 7.79423i 0.175695 + 0.304314i
\(657\) 14.0000i 0.546192i
\(658\) −5.19615 + 6.00000i −0.202567 + 0.233904i
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) −8.66025 5.00000i −0.336590 0.194331i
\(663\) 10.3923 6.00000i 0.403604 0.233021i
\(664\) 0 0
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 0 0
\(668\) −20.7846 12.0000i −0.804181 0.464294i
\(669\) −9.50000 + 16.4545i −0.367291 + 0.636167i
\(670\) 0 0
\(671\) 0 0
\(672\) −0.866025 2.50000i −0.0334077 0.0964396i
\(673\) 19.0000i 0.732396i 0.930537 + 0.366198i \(0.119341\pi\)
−0.930537 + 0.366198i \(0.880659\pi\)
\(674\) −5.50000 9.52628i −0.211852 0.366939i
\(675\) 0 0
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) −10.3923 + 6.00000i −0.399409 + 0.230599i −0.686229 0.727386i \(-0.740735\pi\)
0.286820 + 0.957984i \(0.407402\pi\)
\(678\) 21.0000i 0.806500i
\(679\) −3.50000 + 18.1865i −0.134318 + 0.697935i
\(680\) 0 0
\(681\) 3.00000 + 5.19615i 0.114960 + 0.199117i
\(682\) 0 0
\(683\) 5.19615 + 3.00000i 0.198825 + 0.114792i 0.596107 0.802905i \(-0.296713\pi\)
−0.397282 + 0.917697i \(0.630047\pi\)
\(684\) 1.00000 + 1.73205i 0.0382360 + 0.0662266i
\(685\) 0 0
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) 4.00000i 0.152610i
\(688\) 8.66025 5.00000i 0.330169 0.190623i
\(689\) 12.0000 20.7846i 0.457164 0.791831i
\(690\) 0 0
\(691\) −10.0000 17.3205i −0.380418 0.658903i 0.610704 0.791859i \(-0.290887\pi\)
−0.991122 + 0.132956i \(0.957553\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 0 0
\(694\) −36.0000 −1.36654
\(695\) 0 0
\(696\) 0 0
\(697\) 23.3827 + 13.5000i 0.885682 + 0.511349i
\(698\) 22.5167 13.0000i 0.852268 0.492057i
\(699\) 30.0000 1.13470
\(700\) 0 0
\(701\) −12.0000 −0.453234 −0.226617 0.973984i \(-0.572767\pi\)
−0.226617 + 0.973984i \(0.572767\pi\)
\(702\) 3.46410 2.00000i 0.130744 0.0754851i
\(703\) −17.3205 10.0000i −0.653255 0.377157i
\(704\) 0 0
\(705\) 0 0
\(706\) 15.0000 0.564532
\(707\) 31.1769 36.0000i 1.17253 1.35392i
\(708\) 6.00000i 0.225494i
\(709\) −17.0000 29.4449i −0.638448 1.10583i −0.985773 0.168080i \(-0.946243\pi\)
0.347325 0.937745i \(-0.387090\pi\)
\(710\) 0 0
\(711\) −5.50000 + 9.52628i −0.206266 + 0.357263i
\(712\) 12.9904 7.50000i 0.486835 0.281074i
\(713\) 3.00000i 0.112351i
\(714\) −6.00000 5.19615i −0.224544 0.194461i
\(715\) 0 0
\(716\) 3.00000 + 5.19615i 0.112115 + 0.194189i
\(717\) −12.9904 7.50000i −0.485135 0.280093i
\(718\) −10.3923 6.00000i −0.387837 0.223918i
\(719\) −13.5000 23.3827i −0.503465 0.872027i −0.999992 0.00400572i \(-0.998725\pi\)
0.496527 0.868021i \(-0.334608\pi\)
\(720\) 0 0
\(721\) 12.5000 4.33013i 0.465524 0.161262i
\(722\) 15.0000i 0.558242i
\(723\) −12.1244 + 7.00000i −0.450910 + 0.260333i
\(724\) 4.00000 6.92820i 0.148659 0.257485i
\(725\) 0 0
\(726\) −5.50000 9.52628i −0.204124 0.353553i
\(727\) 37.0000i 1.37225i −0.727482 0.686127i \(-0.759309\pi\)
0.727482 0.686127i \(-0.240691\pi\)
\(728\) 10.3923 + 2.00000i 0.385164 + 0.0741249i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 15.0000 25.9808i 0.554795 0.960933i
\(732\) −6.92820 4.00000i −0.256074 0.147844i
\(733\) −12.1244 + 7.00000i −0.447823 + 0.258551i −0.706910 0.707303i \(-0.749912\pi\)
0.259087 + 0.965854i \(0.416578\pi\)
\(734\) 8.00000 0.295285
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) 7.79423 + 4.50000i 0.286910 + 0.165647i
\(739\) 1.00000 1.73205i 0.0367856 0.0637145i −0.847046 0.531519i \(-0.821621\pi\)
0.883832 + 0.467804i \(0.154955\pi\)
\(740\) 0 0
\(741\) −8.00000 −0.293887
\(742\) −15.5885 3.00000i −0.572270 0.110133i
\(743\) 51.0000i 1.87101i 0.353315 + 0.935504i \(0.385054\pi\)
−0.353315 + 0.935504i \(0.614946\pi\)
\(744\) 0.500000 + 0.866025i 0.0183309 + 0.0317500i
\(745\) 0 0
\(746\) −2.00000 + 3.46410i −0.0732252 + 0.126830i
\(747\) 0 0
\(748\) 0 0
\(749\) 45.0000 15.5885i 1.64426 0.569590i
\(750\) 0 0
\(751\) 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) 2.59808 + 1.50000i 0.0947421 + 0.0546994i
\(753\) 10.3923 + 6.00000i 0.378717 + 0.218652i
\(754\) 0 0
\(755\) 0 0
\(756\) −2.00000 1.73205i −0.0727393 0.0629941i
\(757\) 16.0000i 0.581530i −0.956795 0.290765i \(-0.906090\pi\)
0.956795 0.290765i \(-0.0939098\pi\)
\(758\) −13.8564 + 8.00000i −0.503287 + 0.290573i
\(759\) 0 0
\(760\) 0 0
\(761\) −13.5000 23.3827i −0.489375 0.847622i 0.510551 0.859848i \(-0.329442\pi\)
−0.999925 + 0.0122260i \(0.996108\pi\)
\(762\) 16.0000i 0.579619i
\(763\) −3.46410 + 4.00000i −0.125409 + 0.144810i
\(764\) 21.0000 0.759753
\(765\) 0 0
\(766\) 10.5000 18.1865i 0.379380 0.657106i
\(767\) −20.7846 12.0000i −0.750489 0.433295i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) 30.0000 1.08042
\(772\) 14.7224 8.50000i 0.529872 0.305922i
\(773\) 15.5885 + 9.00000i 0.560678 + 0.323708i 0.753418 0.657542i \(-0.228404\pi\)
−0.192740 + 0.981250i \(0.561737\pi\)
\(774\) 5.00000 8.66025i 0.179721 0.311286i
\(775\) 0 0
\(776\) 7.00000 0.251285
\(777\) 25.9808 + 5.00000i 0.932055 + 0.179374i
\(778\) 6.00000i 0.215110i
\(779\) −9.00000 15.5885i −0.322458 0.558514i
\(780\) 0 0
\(781\) 0 0
\(782\) −7.79423 + 4.50000i −0.278721 + 0.160920i
\(783\) 0 0
\(784\) −1.00000 6.92820i −0.0357143 0.247436i
\(785\) 0 0
\(786\) −6.00000 10.3923i −0.214013 0.370681i
\(787\) 19.0526 + 11.0000i 0.679150 + 0.392108i 0.799535 0.600620i \(-0.205079\pi\)
−0.120384 + 0.992727i \(0.538413\pi\)