Properties

Label 1050.2.o.g.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: no (minimal twist has level 210)
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.g.499.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-1.73205 + 2.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(2.50000 - 4.33013i) q^{11} +(0.866025 - 0.500000i) q^{12} -5.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-3.50000 - 6.06218i) q^{19} +(-2.50000 + 0.866025i) q^{21} +5.00000i q^{22} +(0.866025 - 0.500000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{26} +1.00000i q^{27} +(0.866025 + 2.50000i) q^{28} +(1.00000 - 1.73205i) q^{31} +(0.866025 + 0.500000i) q^{32} +(4.33013 - 2.50000i) q^{33} +4.00000 q^{34} +1.00000 q^{36} +(-0.866025 + 0.500000i) q^{37} +(6.06218 + 3.50000i) q^{38} +(2.50000 - 4.33013i) q^{39} +5.00000 q^{41} +(1.73205 - 2.00000i) q^{42} +12.0000i q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{46} +(9.52628 - 5.50000i) q^{47} -1.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-4.33013 - 2.50000i) q^{52} +(7.79423 + 4.50000i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} -7.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(-2.00000 - 3.46410i) q^{61} +2.00000i q^{62} +(-2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(-2.50000 + 4.33013i) q^{66} +(-10.3923 - 6.00000i) q^{67} +(-3.46410 + 2.00000i) q^{68} +1.00000 q^{69} +2.00000 q^{71} +(-0.866025 + 0.500000i) q^{72} +(-8.66025 - 5.00000i) q^{73} +(0.500000 - 0.866025i) q^{74} -7.00000 q^{76} +(4.33013 + 12.5000i) q^{77} +5.00000i q^{78} +(-6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.33013 + 2.50000i) q^{82} -12.0000i q^{83} +(-0.500000 + 2.59808i) q^{84} +(-6.00000 - 10.3923i) q^{86} +(4.33013 + 2.50000i) q^{88} +(7.00000 + 12.1244i) q^{89} +(10.0000 + 8.66025i) q^{91} -1.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(-5.50000 + 9.52628i) q^{94} +(0.500000 + 0.866025i) q^{96} +8.00000i q^{97} +(4.33013 + 5.50000i) q^{98} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} - 4q^{6} + 2q^{9} + 10q^{11} + 2q^{14} - 2q^{16} - 14q^{19} - 10q^{21} - 2q^{24} + 10q^{26} + 4q^{31} + 16q^{34} + 4q^{36} + 10q^{39} + 20q^{41} - 10q^{44} - 2q^{46} - 4q^{49} - 8q^{51} - 2q^{54} - 8q^{56} + 8q^{59} - 8q^{61} - 4q^{64} - 10q^{66} + 4q^{69} + 8q^{71} + 2q^{74} - 28q^{76} - 24q^{79} - 2q^{81} - 2q^{84} - 24q^{86} + 28q^{89} + 40q^{91} - 22q^{94} + 2q^{96} + 20q^{99} + O(q^{100}) \)

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
\(7\) −1.73205 + 2.00000i −0.654654 + 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) 5.00000i 1.38675i −0.720577 0.693375i \(-0.756123\pi\)
0.720577 0.693375i \(-0.243877\pi\)
\(14\) 0.500000 2.59808i 0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.46410 2.00000i −0.840168 0.485071i 0.0171533 0.999853i \(-0.494540\pi\)
−0.857321 + 0.514782i \(0.827873\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) −2.50000 + 0.866025i −0.545545 + 0.188982i
\(22\) 5.00000i 1.06600i
\(23\) 0.866025 0.500000i 0.180579 0.104257i −0.406986 0.913434i \(-0.633420\pi\)
0.587565 + 0.809177i \(0.300087\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) 0 0
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) 1.00000i 0.192450i
\(28\) 0.866025 + 2.50000i 0.163663 + 0.472456i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 4.33013 2.50000i 0.753778 0.435194i
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −0.866025 + 0.500000i −0.142374 + 0.0821995i −0.569495 0.821995i \(-0.692861\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(38\) 6.06218 + 3.50000i 0.983415 + 0.567775i
\(39\) 2.50000 4.33013i 0.400320 0.693375i
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 1.73205 2.00000i 0.267261 0.308607i
\(43\) 12.0000i 1.82998i 0.403473 + 0.914991i \(0.367803\pi\)
−0.403473 + 0.914991i \(0.632197\pi\)
\(44\) −2.50000 4.33013i −0.376889 0.652791i
\(45\) 0 0
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) 9.52628 5.50000i 1.38955 0.802257i 0.396286 0.918127i \(-0.370299\pi\)
0.993264 + 0.115870i \(0.0369655\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) 0 0
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) −4.33013 2.50000i −0.600481 0.346688i
\(53\) 7.79423 + 4.50000i 1.07062 + 0.618123i 0.928351 0.371706i \(-0.121227\pi\)
0.142269 + 0.989828i \(0.454560\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 7.00000i 0.927173i
\(58\) 0 0
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 2.00000i 0.254000i
\(63\) −2.59808 0.500000i −0.327327 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −2.50000 + 4.33013i −0.307729 + 0.533002i
\(67\) −10.3923 6.00000i −1.26962 0.733017i −0.294706 0.955588i \(-0.595222\pi\)
−0.974916 + 0.222571i \(0.928555\pi\)
\(68\) −3.46410 + 2.00000i −0.420084 + 0.242536i
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) −8.66025 5.00000i −1.01361 0.585206i −0.101361 0.994850i \(-0.532320\pi\)
−0.912245 + 0.409644i \(0.865653\pi\)
\(74\) 0.500000 0.866025i 0.0581238 0.100673i
\(75\) 0 0
\(76\) −7.00000 −0.802955
\(77\) 4.33013 + 12.5000i 0.493464 + 1.42451i
\(78\) 5.00000i 0.566139i
\(79\) −6.00000 10.3923i −0.675053 1.16923i −0.976453 0.215728i \(-0.930788\pi\)
0.301401 0.953498i \(-0.402546\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −4.33013 + 2.50000i −0.478183 + 0.276079i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) −0.500000 + 2.59808i −0.0545545 + 0.283473i
\(85\) 0 0
\(86\) −6.00000 10.3923i −0.646997 1.12063i
\(87\) 0 0
\(88\) 4.33013 + 2.50000i 0.461593 + 0.266501i
\(89\) 7.00000 + 12.1244i 0.741999 + 1.28518i 0.951584 + 0.307389i \(0.0994552\pi\)
−0.209585 + 0.977790i \(0.567211\pi\)
\(90\) 0 0
\(91\) 10.0000 + 8.66025i 1.04828 + 0.907841i
\(92\) 1.00000i 0.104257i
\(93\) 1.73205 1.00000i 0.179605 0.103695i
\(94\) −5.50000 + 9.52628i −0.567282 + 0.982561i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 8.00000i 0.812277i 0.913812 + 0.406138i \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 4.33013 + 5.50000i 0.437409 + 0.555584i
\(99\) 5.00000 0.502519
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 3.46410 + 2.00000i 0.342997 + 0.198030i
\(103\) 6.92820 4.00000i 0.682656 0.394132i −0.118199 0.992990i \(-0.537712\pi\)
0.800855 + 0.598858i \(0.204379\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 1.73205 1.00000i 0.167444 0.0966736i −0.413936 0.910306i \(-0.635846\pi\)
0.581380 + 0.813632i \(0.302513\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i \(-0.863869\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) 2.59808 + 0.500000i 0.245495 + 0.0472456i
\(113\) 14.0000i 1.31701i −0.752577 0.658505i \(-0.771189\pi\)
0.752577 0.658505i \(-0.228811\pi\)
\(114\) 3.50000 + 6.06218i 0.327805 + 0.567775i
\(115\) 0 0
\(116\) 0 0
\(117\) 4.33013 2.50000i 0.400320 0.231125i
\(118\) 4.00000i 0.368230i
\(119\) 10.0000 3.46410i 0.916698 0.317554i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 3.46410 + 2.00000i 0.313625 + 0.181071i
\(123\) 4.33013 + 2.50000i 0.390434 + 0.225417i
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 0 0
\(126\) 2.50000 0.866025i 0.222718 0.0771517i
\(127\) 9.00000i 0.798621i −0.916816 0.399310i \(-0.869250\pi\)
0.916816 0.399310i \(-0.130750\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −6.00000 + 10.3923i −0.528271 + 0.914991i
\(130\) 0 0
\(131\) 4.50000 + 7.79423i 0.393167 + 0.680985i 0.992865 0.119241i \(-0.0380462\pi\)
−0.599699 + 0.800226i \(0.704713\pi\)
\(132\) 5.00000i 0.435194i
\(133\) 18.1865 + 3.50000i 1.57697 + 0.303488i
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 2.00000 3.46410i 0.171499 0.297044i
\(137\) −1.73205 1.00000i −0.147979 0.0854358i 0.424182 0.905577i \(-0.360562\pi\)
−0.572161 + 0.820141i \(0.693895\pi\)
\(138\) −0.866025 + 0.500000i −0.0737210 + 0.0425628i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 11.0000 0.926367
\(142\) −1.73205 + 1.00000i −0.145350 + 0.0839181i
\(143\) −21.6506 12.5000i −1.81052 1.04530i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 10.0000 0.827606
\(147\) 2.59808 6.50000i 0.214286 0.536111i
\(148\) 1.00000i 0.0821995i
\(149\) 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) 0 0
\(151\) −7.00000 + 12.1244i −0.569652 + 0.986666i 0.426948 + 0.904276i \(0.359589\pi\)
−0.996600 + 0.0823900i \(0.973745\pi\)
\(152\) 6.06218 3.50000i 0.491708 0.283887i
\(153\) 4.00000i 0.323381i
\(154\) −10.0000 8.66025i −0.805823 0.697863i
\(155\) 0 0
\(156\) −2.50000 4.33013i −0.200160 0.346688i
\(157\) 9.52628 + 5.50000i 0.760280 + 0.438948i 0.829396 0.558661i \(-0.188685\pi\)
−0.0691164 + 0.997609i \(0.522018\pi\)
\(158\) 10.3923 + 6.00000i 0.826767 + 0.477334i
\(159\) 4.50000 + 7.79423i 0.356873 + 0.618123i
\(160\) 0 0
\(161\) −0.500000 + 2.59808i −0.0394055 + 0.204757i
\(162\) 1.00000i 0.0785674i
\(163\) −20.7846 + 12.0000i −1.62798 + 0.939913i −0.643280 + 0.765631i \(0.722427\pi\)
−0.984696 + 0.174282i \(0.944240\pi\)
\(164\) 2.50000 4.33013i 0.195217 0.338126i
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 11.0000i 0.851206i −0.904910 0.425603i \(-0.860062\pi\)
0.904910 0.425603i \(-0.139938\pi\)
\(168\) −0.866025 2.50000i −0.0668153 0.192879i
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 3.50000 6.06218i 0.267652 0.463586i
\(172\) 10.3923 + 6.00000i 0.792406 + 0.457496i
\(173\) −11.2583 + 6.50000i −0.855955 + 0.494186i −0.862656 0.505792i \(-0.831200\pi\)
0.00670064 + 0.999978i \(0.497867\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5.00000 −0.376889
\(177\) 3.46410 2.00000i 0.260378 0.150329i
\(178\) −12.1244 7.00000i −0.908759 0.524672i
\(179\) −11.5000 + 19.9186i −0.859550 + 1.48878i 0.0128080 + 0.999918i \(0.495923\pi\)
−0.872358 + 0.488867i \(0.837410\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) −12.9904 2.50000i −0.962911 0.185312i
\(183\) 4.00000i 0.295689i
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) 0 0
\(186\) −1.00000 + 1.73205i −0.0733236 + 0.127000i
\(187\) −17.3205 + 10.0000i −1.26660 + 0.731272i
\(188\) 11.0000i 0.802257i
\(189\) −2.00000 1.73205i −0.145479 0.125988i
\(190\) 0 0
\(191\) −7.00000 12.1244i −0.506502 0.877288i −0.999972 0.00752447i \(-0.997605\pi\)
0.493469 0.869763i \(-0.335728\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −8.66025 5.00000i −0.623379 0.359908i 0.154805 0.987945i \(-0.450525\pi\)
−0.778183 + 0.628037i \(0.783859\pi\)
\(194\) −4.00000 6.92820i −0.287183 0.497416i
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 3.00000i 0.213741i 0.994273 + 0.106871i \(0.0340831\pi\)
−0.994273 + 0.106871i \(0.965917\pi\)
\(198\) −4.33013 + 2.50000i −0.307729 + 0.177667i
\(199\) −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 0 0
\(201\) −6.00000 10.3923i −0.423207 0.733017i
\(202\) 0 0
\(203\) 0 0
\(204\) −4.00000 −0.280056
\(205\) 0 0
\(206\) −4.00000 + 6.92820i −0.278693 + 0.482711i
\(207\) 0.866025 + 0.500000i 0.0601929 + 0.0347524i
\(208\) −4.33013 + 2.50000i −0.300240 + 0.173344i
\(209\) −35.0000 −2.42100
\(210\) 0 0
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) 7.79423 4.50000i 0.535310 0.309061i
\(213\) 1.73205 + 1.00000i 0.118678 + 0.0685189i
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 1.73205 + 5.00000i 0.117579 + 0.339422i
\(218\) 2.00000i 0.135457i
\(219\) −5.00000 8.66025i −0.337869 0.585206i
\(220\) 0 0
\(221\) −10.0000 + 17.3205i −0.672673 + 1.16510i
\(222\) 0.866025 0.500000i 0.0581238 0.0335578i
\(223\) 12.0000i 0.803579i −0.915732 0.401790i \(-0.868388\pi\)
0.915732 0.401790i \(-0.131612\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) 0 0
\(226\) 7.00000 + 12.1244i 0.465633 + 0.806500i
\(227\) −10.3923 6.00000i −0.689761 0.398234i 0.113761 0.993508i \(-0.463710\pi\)
−0.803523 + 0.595274i \(0.797043\pi\)
\(228\) −6.06218 3.50000i −0.401478 0.231793i
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 0 0
\(231\) −2.50000 + 12.9904i −0.164488 + 0.854704i
\(232\) 0 0
\(233\) −12.1244 + 7.00000i −0.794293 + 0.458585i −0.841472 0.540301i \(-0.818310\pi\)
0.0471787 + 0.998886i \(0.484977\pi\)
\(234\) −2.50000 + 4.33013i −0.163430 + 0.283069i
\(235\) 0 0
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 12.0000i 0.779484i
\(238\) −6.92820 + 8.00000i −0.449089 + 0.518563i
\(239\) 22.0000 1.42306 0.711531 0.702655i \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) 0 0
\(241\) −7.50000 + 12.9904i −0.483117 + 0.836784i −0.999812 0.0193858i \(-0.993829\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(242\) 12.1244 + 7.00000i 0.779383 + 0.449977i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) −4.00000 −0.256074
\(245\) 0 0
\(246\) −5.00000 −0.318788
\(247\) −30.3109 + 17.5000i −1.92864 + 1.11350i
\(248\) 1.73205 + 1.00000i 0.109985 + 0.0635001i
\(249\) 6.00000 10.3923i 0.380235 0.658586i
\(250\) 0 0
\(251\) 1.00000 0.0631194 0.0315597 0.999502i \(-0.489953\pi\)
0.0315597 + 0.999502i \(0.489953\pi\)
\(252\) −1.73205 + 2.00000i −0.109109 + 0.125988i
\(253\) 5.00000i 0.314347i
\(254\) 4.50000 + 7.79423i 0.282355 + 0.489053i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 13.8564 8.00000i 0.864339 0.499026i −0.00112398 0.999999i \(-0.500358\pi\)
0.865463 + 0.500973i \(0.167024\pi\)
\(258\) 12.0000i 0.747087i
\(259\) 0.500000 2.59808i 0.0310685 0.161437i
\(260\) 0 0
\(261\) 0 0
\(262\) −7.79423 4.50000i −0.481529 0.278011i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 2.50000 + 4.33013i 0.153864 + 0.266501i
\(265\) 0 0
\(266\) −17.5000 + 6.06218i −1.07299 + 0.371696i
\(267\) 14.0000i 0.856786i
\(268\) −10.3923 + 6.00000i −0.634811 + 0.366508i
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 4.33013 + 12.5000i 0.262071 + 0.756534i
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 0.500000 0.866025i 0.0300965 0.0521286i
\(277\) 12.1244 + 7.00000i 0.728482 + 0.420589i 0.817867 0.575408i \(-0.195157\pi\)
−0.0893846 + 0.995997i \(0.528490\pi\)
\(278\) −3.46410 + 2.00000i −0.207763 + 0.119952i
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) 7.00000 0.417585 0.208792 0.977960i \(-0.433047\pi\)
0.208792 + 0.977960i \(0.433047\pi\)
\(282\) −9.52628 + 5.50000i −0.567282 + 0.327520i
\(283\) 8.66025 + 5.00000i 0.514799 + 0.297219i 0.734804 0.678280i \(-0.237274\pi\)
−0.220005 + 0.975499i \(0.570607\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) 25.0000 1.47828
\(287\) −8.66025 + 10.0000i −0.511199 + 0.590281i
\(288\) 1.00000i 0.0589256i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) −4.00000 + 6.92820i −0.234484 + 0.406138i
\(292\) −8.66025 + 5.00000i −0.506803 + 0.292603i
\(293\) 9.00000i 0.525786i 0.964825 + 0.262893i \(0.0846766\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(294\) 1.00000 + 6.92820i 0.0583212 + 0.404061i
\(295\) 0 0
\(296\) −0.500000 0.866025i −0.0290619 0.0503367i
\(297\) 4.33013 + 2.50000i 0.251259 + 0.145065i
\(298\) −10.3923 6.00000i −0.602010 0.347571i
\(299\) −2.50000 4.33013i −0.144579 0.250418i
\(300\) 0 0
\(301\) −24.0000 20.7846i −1.38334 1.19800i
\(302\) 14.0000i 0.805609i
\(303\) 0 0
\(304\) −3.50000 + 6.06218i −0.200739 + 0.347690i
\(305\) 0 0
\(306\) 2.00000 + 3.46410i 0.114332 + 0.198030i
\(307\) 8.00000i 0.456584i −0.973593 0.228292i \(-0.926686\pi\)
0.973593 0.228292i \(-0.0733141\pi\)
\(308\) 12.9904 + 2.50000i 0.740196 + 0.142451i
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) −4.00000 + 6.92820i −0.226819 + 0.392862i −0.956864 0.290537i \(-0.906166\pi\)
0.730044 + 0.683400i \(0.239499\pi\)
\(312\) 4.33013 + 2.50000i 0.245145 + 0.141535i
\(313\) 13.8564 8.00000i 0.783210 0.452187i −0.0543564 0.998522i \(-0.517311\pi\)
0.837567 + 0.546335i \(0.183977\pi\)
\(314\) −11.0000 −0.620766
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) 19.0526 11.0000i 1.07010 0.617822i 0.141890 0.989882i \(-0.454682\pi\)
0.928208 + 0.372061i \(0.121349\pi\)
\(318\) −7.79423 4.50000i −0.437079 0.252347i
\(319\) 0 0
\(320\) 0 0
\(321\) 2.00000 0.111629
\(322\) −0.866025 2.50000i −0.0482617 0.139320i
\(323\) 28.0000i 1.55796i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 12.0000 20.7846i 0.664619 1.15115i
\(327\) −1.73205 + 1.00000i −0.0957826 + 0.0553001i
\(328\) 5.00000i 0.276079i
\(329\) −5.50000 + 28.5788i −0.303225 + 1.57560i
\(330\) 0 0
\(331\) −15.5000 26.8468i −0.851957 1.47563i −0.879440 0.476011i \(-0.842082\pi\)
0.0274825 0.999622i \(-0.491251\pi\)
\(332\) −10.3923 6.00000i −0.570352 0.329293i
\(333\) −0.866025 0.500000i −0.0474579 0.0273998i
\(334\) 5.50000 + 9.52628i 0.300947 + 0.521255i
\(335\) 0 0
\(336\) 2.00000 + 1.73205i 0.109109 + 0.0944911i
\(337\) 16.0000i 0.871576i 0.900049 + 0.435788i \(0.143530\pi\)
−0.900049 + 0.435788i \(0.856470\pi\)
\(338\) 10.3923 6.00000i 0.565267 0.326357i
\(339\) 7.00000 12.1244i 0.380188 0.658505i
\(340\) 0 0
\(341\) −5.00000 8.66025i −0.270765 0.468979i
\(342\) 7.00000i 0.378517i
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) −12.0000 −0.646997
\(345\) 0 0
\(346\) 6.50000 11.2583i 0.349442 0.605252i
\(347\) −15.5885 9.00000i −0.836832 0.483145i 0.0193540 0.999813i \(-0.493839\pi\)
−0.856186 + 0.516667i \(0.827172\pi\)
\(348\) 0 0
\(349\) 4.00000 0.214115 0.107058 0.994253i \(-0.465857\pi\)
0.107058 + 0.994253i \(0.465857\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 4.33013 2.50000i 0.230797 0.133250i
\(353\) −20.7846 12.0000i −1.10625 0.638696i −0.168397 0.985719i \(-0.553859\pi\)
−0.937856 + 0.347024i \(0.887192\pi\)
\(354\) −2.00000 + 3.46410i −0.106299 + 0.184115i
\(355\) 0 0
\(356\) 14.0000 0.741999
\(357\) 10.3923 + 2.00000i 0.550019 + 0.105851i
\(358\) 23.0000i 1.21559i
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −17.3205 + 10.0000i −0.910346 + 0.525588i
\(363\) 14.0000i 0.734809i
\(364\) 12.5000 4.33013i 0.655178 0.226960i
\(365\) 0 0
\(366\) 2.00000 + 3.46410i 0.104542 + 0.181071i
\(367\) 6.06218 + 3.50000i 0.316443 + 0.182699i 0.649806 0.760100i \(-0.274850\pi\)
−0.333363 + 0.942799i \(0.608183\pi\)
\(368\) −0.866025 0.500000i −0.0451447 0.0260643i
\(369\) 2.50000 + 4.33013i 0.130145 + 0.225417i
\(370\) 0 0
\(371\) −22.5000 + 7.79423i −1.16814 + 0.404656i
\(372\) 2.00000i 0.103695i
\(373\) −19.0526 + 11.0000i −0.986504 + 0.569558i −0.904227 0.427051i \(-0.859552\pi\)
−0.0822766 + 0.996610i \(0.526219\pi\)
\(374\) 10.0000 17.3205i 0.517088 0.895622i
\(375\) 0 0
\(376\) 5.50000 + 9.52628i 0.283641 + 0.491280i
\(377\) 0 0
\(378\) 2.59808 + 0.500000i 0.133631 + 0.0257172i
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) 4.50000 7.79423i 0.230542 0.399310i
\(382\) 12.1244 + 7.00000i 0.620336 + 0.358151i
\(383\) 18.1865 10.5000i 0.929288 0.536525i 0.0427020 0.999088i \(-0.486403\pi\)
0.886586 + 0.462563i \(0.153070\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −10.3923 + 6.00000i −0.528271 + 0.304997i
\(388\) 6.92820 + 4.00000i 0.351726 + 0.203069i
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 6.92820 1.00000i 0.349927 0.0505076i
\(393\) 9.00000i 0.453990i
\(394\) −1.50000 2.59808i −0.0755689 0.130889i
\(395\) 0 0
\(396\) 2.50000 4.33013i 0.125630 0.217597i
\(397\) 12.1244 7.00000i 0.608504 0.351320i −0.163876 0.986481i \(-0.552400\pi\)
0.772380 + 0.635161i \(0.219066\pi\)
\(398\) 4.00000i 0.200502i
\(399\) 14.0000 + 12.1244i 0.700877 + 0.606977i
\(400\) 0 0
\(401\) 10.5000 + 18.1865i 0.524345 + 0.908192i 0.999598 + 0.0283431i \(0.00902310\pi\)
−0.475253 + 0.879849i \(0.657644\pi\)
\(402\) 10.3923 + 6.00000i 0.518321 + 0.299253i
\(403\) −8.66025 5.00000i −0.431398 0.249068i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.00000i 0.247841i
\(408\) 3.46410 2.00000i 0.171499 0.0990148i
\(409\) 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i \(-0.753812\pi\)
0.962757 + 0.270367i \(0.0871450\pi\)
\(410\) 0 0
\(411\) −1.00000 1.73205i −0.0493264 0.0854358i
\(412\) 8.00000i 0.394132i
\(413\) 3.46410 + 10.0000i 0.170457 + 0.492068i
\(414\) −1.00000 −0.0491473
\(415\) 0 0
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) 3.46410 + 2.00000i 0.169638 + 0.0979404i
\(418\) 30.3109 17.5000i 1.48255 0.855953i
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) −14.7224 + 8.50000i −0.716677 + 0.413774i
\(423\) 9.52628 + 5.50000i 0.463184 + 0.267419i
\(424\) −4.50000 + 7.79423i −0.218539 + 0.378521i
\(425\) 0 0
\(426\) −2.00000 −0.0969003
\(427\) 10.3923 + 2.00000i 0.502919 + 0.0967868i
\(428\) 2.00000i 0.0966736i
\(429\) −12.5000 21.6506i −0.603506 1.04530i
\(430\) 0 0
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 24.0000i 1.15337i 0.816968 + 0.576683i \(0.195653\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) −4.00000 3.46410i −0.192006 0.166282i
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) −6.06218 3.50000i −0.289993 0.167428i
\(438\) 8.66025 + 5.00000i 0.413803 + 0.238909i
\(439\) −20.0000 34.6410i −0.954548 1.65333i −0.735399 0.677634i \(-0.763005\pi\)
−0.219149 0.975691i \(-0.570328\pi\)
\(440\) 0 0
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) 20.0000i 0.951303i
\(443\) −24.2487 + 14.0000i −1.15209 + 0.665160i −0.949396 0.314082i \(-0.898303\pi\)
−0.202695 + 0.979242i \(0.564970\pi\)
\(444\) −0.500000 + 0.866025i −0.0237289 + 0.0410997i
\(445\) 0 0
\(446\) 6.00000 + 10.3923i 0.284108 + 0.492090i
\(447\) 12.0000i 0.567581i
\(448\) 1.73205 2.00000i 0.0818317 0.0944911i
\(449\) 29.0000 1.36859 0.684297 0.729203i \(-0.260109\pi\)
0.684297 + 0.729203i \(0.260109\pi\)
\(450\) 0 0
\(451\) 12.5000 21.6506i 0.588602 1.01949i
\(452\) −12.1244 7.00000i −0.570282 0.329252i
\(453\) −12.1244 + 7.00000i −0.569652 + 0.328889i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 7.00000 0.327805
\(457\) 12.1244 7.00000i 0.567153 0.327446i −0.188858 0.982004i \(-0.560479\pi\)
0.756012 + 0.654558i \(0.227145\pi\)
\(458\) −8.66025 5.00000i −0.404667 0.233635i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 0 0
\(461\) −4.00000 −0.186299 −0.0931493 0.995652i \(-0.529693\pi\)
−0.0931493 + 0.995652i \(0.529693\pi\)
\(462\) −4.33013 12.5000i −0.201456 0.581553i
\(463\) 19.0000i 0.883005i −0.897260 0.441502i \(-0.854446\pi\)
0.897260 0.441502i \(-0.145554\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 7.00000 12.1244i 0.324269 0.561650i
\(467\) 17.3205 10.0000i 0.801498 0.462745i −0.0424970 0.999097i \(-0.513531\pi\)
0.843995 + 0.536352i \(0.180198\pi\)
\(468\) 5.00000i 0.231125i
\(469\) 30.0000 10.3923i 1.38527 0.479872i
\(470\) 0 0
\(471\) 5.50000 + 9.52628i 0.253427 + 0.438948i
\(472\) 3.46410 + 2.00000i 0.159448 + 0.0920575i
\(473\) 51.9615 + 30.0000i 2.38919 + 1.37940i
\(474\) 6.00000 + 10.3923i 0.275589 + 0.477334i
\(475\) 0 0
\(476\) 2.00000 10.3923i 0.0916698 0.476331i
\(477\) 9.00000i 0.412082i
\(478\) −19.0526 + 11.0000i −0.871444 + 0.503128i
\(479\) 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) 15.0000i 0.683231i
\(483\) −1.73205 + 2.00000i −0.0788110 + 0.0910032i
\(484\) −14.0000 −0.636364
\(485\) 0 0
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(488\) 3.46410 2.00000i 0.156813 0.0905357i
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 4.33013 2.50000i 0.195217 0.112709i
\(493\) 0 0
\(494\) 17.5000 30.3109i 0.787362 1.36375i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) −3.46410 + 4.00000i −0.155386 + 0.179425i
\(498\) 12.0000i 0.537733i
\(499\) 20.0000 + 34.6410i 0.895323 + 1.55074i 0.833404 + 0.552664i \(0.186389\pi\)
0.0619186 + 0.998081i \(0.480278\pi\)
\(500\) 0 0
\(501\) 5.50000 9.52628i 0.245722 0.425603i
\(502\) −0.866025 + 0.500000i −0.0386526 + 0.0223161i
\(503\) 20.0000i 0.891756i −0.895094 0.445878i \(-0.852892\pi\)
0.895094 0.445878i \(-0.147108\pi\)
\(504\) 0.500000 2.59808i 0.0222718 0.115728i
\(505\) 0 0
\(506\) 2.50000 + 4.33013i 0.111139 + 0.192498i
\(507\) −10.3923 6.00000i −0.461538 0.266469i
\(508\) −7.79423 4.50000i −0.345813 0.199655i
\(509\) −5.00000 8.66025i −0.221621 0.383859i 0.733679 0.679496i \(-0.237801\pi\)
−0.955300 + 0.295637i \(0.904468\pi\)
\(510\) 0 0
\(511\) 25.0000 8.66025i 1.10593 0.383107i
\(512\) 1.00000i 0.0441942i
\(513\) 6.06218 3.50000i 0.267652 0.154529i
\(514\) −8.00000 + 13.8564i −0.352865 + 0.611180i
\(515\) 0 0
\(516\) 6.00000 + 10.3923i 0.264135 + 0.457496i
\(517\) 55.0000i 2.41890i
\(518\) 0.866025 + 2.50000i 0.0380510 + 0.109844i
\(519\) −13.0000 −0.570637
\(520\) 0 0
\(521\) 16.5000 28.5788i 0.722878 1.25206i −0.236963 0.971519i \(-0.576152\pi\)
0.959841 0.280543i \(-0.0905145\pi\)
\(522\) 0 0
\(523\) −19.0526 + 11.0000i −0.833110 + 0.480996i −0.854916 0.518766i \(-0.826392\pi\)
0.0218062 + 0.999762i \(0.493058\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 0 0
\(527\) −6.92820 + 4.00000i −0.301797 + 0.174243i
\(528\) −4.33013 2.50000i −0.188445 0.108799i
\(529\) −11.0000 + 19.0526i −0.478261 + 0.828372i
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) 12.1244 14.0000i 0.525657 0.606977i
\(533\) 25.0000i 1.08287i
\(534\) −7.00000 12.1244i −0.302920 0.524672i
\(535\) 0 0
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −19.9186 + 11.5000i −0.859550 + 0.496262i
\(538\) 24.0000i 1.03471i
\(539\) −32.5000 12.9904i −1.39987 0.559535i
\(540\) 0 0
\(541\) −1.00000 1.73205i −0.0429934 0.0744667i 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) 0 0
\(543\) 17.3205 + 10.0000i 0.743294 + 0.429141i
\(544\) −2.00000 3.46410i −0.0857493 0.148522i
\(545\) 0 0
\(546\) −10.0000 8.66025i −0.427960 0.370625i
\(547\) 28.0000i 1.19719i −0.801050 0.598597i \(-0.795725\pi\)
0.801050 0.598597i \(-0.204275\pi\)
\(548\) −1.73205 + 1.00000i −0.0739895 + 0.0427179i
\(549\) 2.00000 3.46410i 0.0853579 0.147844i
\(550\) 0 0
\(551\) 0 0
\(552\) 1.00000i 0.0425628i
\(553\) 31.1769 + 6.00000i 1.32578 + 0.255146i
\(554\) −14.0000 −0.594803
\(555\) 0 0
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) 32.0429 + 18.5000i 1.35770 + 0.783870i 0.989314 0.145802i \(-0.0465761\pi\)
0.368389 + 0.929672i \(0.379909\pi\)
\(558\) −1.73205 + 1.00000i −0.0733236 + 0.0423334i
\(559\) 60.0000 2.53773
\(560\) 0 0
\(561\) −20.0000 −0.844401
\(562\) −6.06218 + 3.50000i −0.255718 + 0.147639i
\(563\) 15.5885 + 9.00000i 0.656975 + 0.379305i 0.791123 0.611656i \(-0.209497\pi\)
−0.134148 + 0.990961i \(0.542830\pi\)
\(564\) 5.50000 9.52628i 0.231592 0.401129i
\(565\) 0 0
\(566\) −10.0000 −0.420331
\(567\) −0.866025 2.50000i −0.0363696 0.104990i
\(568\) 2.00000i 0.0839181i
\(569\) 19.5000 + 33.7750i 0.817483 + 1.41592i 0.907532 + 0.419984i \(0.137964\pi\)
−0.0900490 + 0.995937i \(0.528702\pi\)
\(570\) 0 0
\(571\) −20.0000 + 34.6410i −0.836974 + 1.44968i 0.0554391 + 0.998462i \(0.482344\pi\)
−0.892413 + 0.451219i \(0.850989\pi\)
\(572\) −21.6506 + 12.5000i −0.905259 + 0.522651i
\(573\) 14.0000i 0.584858i
\(574\) 2.50000 12.9904i 0.104348 0.542208i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 22.5167 + 13.0000i 0.937381 + 0.541197i 0.889138 0.457639i \(-0.151305\pi\)
0.0482425 + 0.998836i \(0.484638\pi\)
\(578\) 0.866025 + 0.500000i 0.0360219 + 0.0207973i
\(579\) −5.00000 8.66025i −0.207793 0.359908i
\(580\) 0 0
\(581\) 24.0000 + 20.7846i 0.995688 + 0.862291i
\(582\) 8.00000i 0.331611i
\(583\) 38.9711 22.5000i 1.61402 0.931855i
\(584\) 5.00000 8.66025i 0.206901 0.358364i
\(585\) 0 0
\(586\) −4.50000 7.79423i −0.185893 0.321977i
\(587\) 30.0000i 1.23823i 0.785299 + 0.619116i \(0.212509\pi\)
−0.785299 + 0.619116i \(0.787491\pi\)
\(588\) −4.33013 5.50000i −0.178571 0.226816i
\(589\) −14.0000 −0.576860
\(590\) 0 0
\(591\) −1.50000 + 2.59808i −0.0617018 + 0.106871i
\(592\) 0.866025 + 0.500000i 0.0355934 + 0.0205499i
\(593\) 31.1769 18.0000i 1.28028 0.739171i 0.303383 0.952869i \(-0.401884\pi\)
0.976900 + 0.213697i \(0.0685507\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) 12.0000 0.491539
\(597\) −3.46410 + 2.00000i −0.141776 + 0.0818546i
\(598\) 4.33013 + 2.50000i 0.177072 + 0.102233i
\(599\) −5.00000 + 8.66025i −0.204294 + 0.353848i −0.949908 0.312531i \(-0.898823\pi\)
0.745613 + 0.666379i \(0.232157\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 31.1769 + 6.00000i 1.27068 + 0.244542i
\(603\) 12.0000i 0.488678i
\(604\) 7.00000 + 12.1244i 0.284826 + 0.493333i
\(605\) 0 0
\(606\) 0 0
\(607\) 23.3827 13.5000i 0.949074 0.547948i 0.0562808 0.998415i \(-0.482076\pi\)
0.892793 + 0.450467i \(0.148742\pi\)
\(608\) 7.00000i 0.283887i
\(609\) 0 0
\(610\) 0 0
\(611\) −27.5000 47.6314i −1.11253 1.92696i
\(612\) −3.46410 2.00000i −0.140028 0.0808452i
\(613\) 37.2391 + 21.5000i 1.50407 + 0.868377i 0.999989 + 0.00472215i \(0.00150311\pi\)
0.504084 + 0.863655i \(0.331830\pi\)
\(614\) 4.00000 + 6.92820i 0.161427 + 0.279600i
\(615\) 0 0
\(616\) −12.5000 + 4.33013i −0.503639 + 0.174466i
\(617\) 8.00000i 0.322068i 0.986949 + 0.161034i \(0.0514829\pi\)
−0.986949 + 0.161034i \(0.948517\pi\)
\(618\) −6.92820 + 4.00000i −0.278693 + 0.160904i
\(619\) 12.5000 21.6506i 0.502417 0.870212i −0.497579 0.867419i \(-0.665777\pi\)
0.999996 0.00279365i \(-0.000889247\pi\)
\(620\) 0 0
\(621\) 0.500000 + 0.866025i 0.0200643 + 0.0347524i
\(622\) 8.00000i 0.320771i
\(623\) −36.3731 7.00000i −1.45726 0.280449i
\(624\) −5.00000 −0.200160
\(625\) 0 0
\(626\) −8.00000 + 13.8564i −0.319744 + 0.553813i
\(627\) −30.3109 17.5000i −1.21050 0.698883i
\(628\) 9.52628 5.50000i 0.380140 0.219474i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 6.00000 0.238856 0.119428 0.992843i \(-0.461894\pi\)
0.119428 + 0.992843i \(0.461894\pi\)
\(632\) 10.3923 6.00000i 0.413384 0.238667i
\(633\) 14.7224 + 8.50000i 0.585164 + 0.337845i
\(634\) −11.0000 + 19.0526i −0.436866 + 0.756674i
\(635\) 0 0
\(636\) 9.00000 0.356873
\(637\) −34.6410 + 5.00000i −1.37253 + 0.198107i
\(638\) 0 0
\(639\) 1.00000 + 1.73205i 0.0395594 + 0.0685189i
\(640\) 0 0
\(641\) −10.5000 + 18.1865i −0.414725 + 0.718325i −0.995400 0.0958109i \(-0.969456\pi\)
0.580674 + 0.814136i \(0.302789\pi\)
\(642\) −1.73205 + 1.00000i −0.0683586 + 0.0394669i
\(643\) 34.0000i 1.34083i 0.741987 + 0.670415i \(0.233884\pi\)
−0.741987 + 0.670415i \(0.766116\pi\)
\(644\) 2.00000 + 1.73205i 0.0788110 + 0.0682524i
\(645\) 0 0
\(646\) −14.0000 24.2487i −0.550823 0.954053i
\(647\) −19.9186 11.5000i −0.783080 0.452112i 0.0544405 0.998517i \(-0.482662\pi\)
−0.837521 + 0.546405i \(0.815996\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) −10.0000 17.3205i −0.392534 0.679889i
\(650\) 0 0
\(651\) −1.00000 + 5.19615i −0.0391931 + 0.203653i
\(652\) 24.0000i 0.939913i
\(653\) −16.4545 + 9.50000i −0.643914 + 0.371764i −0.786121 0.618073i \(-0.787914\pi\)
0.142207 + 0.989837i \(0.454580\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) 0 0
\(656\) −2.50000 4.33013i −0.0976086 0.169063i
\(657\) 10.0000i 0.390137i
\(658\) −9.52628 27.5000i −0.371373 1.07206i
\(659\) 20.0000 0.779089 0.389545 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) 20.0000 34.6410i 0.777910 1.34738i −0.155235 0.987878i \(-0.549613\pi\)
0.933144 0.359502i \(-0.117053\pi\)
\(662\) 26.8468 + 15.5000i 1.04343 + 0.602425i
\(663\) −17.3205 + 10.0000i −0.672673 + 0.388368i
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 1.00000 0.0387492
\(667\) 0 0
\(668\) −9.52628 5.50000i −0.368583 0.212801i
\(669\) 6.00000 10.3923i 0.231973 0.401790i
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) −2.59808 0.500000i −0.100223 0.0192879i
\(673\) 4.00000i 0.154189i −0.997024 0.0770943i \(-0.975436\pi\)
0.997024 0.0770943i \(-0.0245643\pi\)
\(674\) −8.00000 13.8564i −0.308148 0.533729i
\(675\) 0 0
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) −28.5788 + 16.5000i −1.09837 + 0.634147i −0.935793 0.352549i \(-0.885315\pi\)
−0.162581 + 0.986695i \(0.551982\pi\)
\(678\) 14.0000i 0.537667i
\(679\) −16.0000 13.8564i −0.614024 0.531760i
\(680\) 0 0
\(681\) −6.00000 10.3923i −0.229920 0.398234i
\(682\) 8.66025 + 5.00000i 0.331618 + 0.191460i
\(683\) 3.46410 + 2.00000i 0.132550 + 0.0765279i 0.564809 0.825222i \(-0.308950\pi\)
−0.432259 + 0.901750i \(0.642283\pi\)
\(684\) −3.50000 6.06218i −0.133826 0.231793i
\(685\) 0 0
\(686\) −18.5000 0.866025i −0.706333 0.0330650i
\(687\) 10.0000i 0.381524i
\(688\) 10.3923 6.00000i 0.396203 0.228748i
\(689\) 22.5000 38.9711i 0.857182 1.48468i
\(690\) 0 0
\(691\) −14.0000 24.2487i −0.532585 0.922464i −0.999276 0.0380440i \(-0.987887\pi\)
0.466691 0.884420i \(-0.345446\pi\)
\(692\) 13.0000i 0.494186i
\(693\) −8.66025 + 10.0000i −0.328976 + 0.379869i
\(694\) 18.0000 0.683271
\(695\) 0 0
\(696\) 0 0
\(697\) −17.3205 10.0000i −0.656061 0.378777i
\(698\) −3.46410 + 2.00000i −0.131118 + 0.0757011i
\(699\) −14.0000 −0.529529
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) −4.33013 + 2.50000i −0.163430 + 0.0943564i
\(703\) 6.06218 + 3.50000i 0.228639 + 0.132005i
\(704\) −2.50000 + 4.33013i −0.0942223 + 0.163198i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 4.00000i 0.150329i
\(709\) 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
\(711\) 6.00000 10.3923i 0.225018 0.389742i
\(712\) −12.1244 + 7.00000i −0.454379 + 0.262336i
\(713\) 2.00000i 0.0749006i
\(714\) −10.0000 + 3.46410i −0.374241 + 0.129641i
\(715\) 0 0
\(716\) 11.5000 + 19.9186i 0.429775 + 0.744392i
\(717\) 19.0526 + 11.0000i 0.711531 + 0.410803i
\(718\) 17.3205 + 10.0000i 0.646396 + 0.373197i
\(719\) −3.00000 5.19615i −0.111881 0.193784i 0.804648 0.593753i \(-0.202354\pi\)
−0.916529 + 0.399969i \(0.869021\pi\)
\(720\) 0 0
\(721\) −4.00000 + 20.7846i −0.148968 + 0.774059i
\(722\) 30.0000i 1.11648i
\(723\) −12.9904 + 7.50000i −0.483117 + 0.278928i
\(724\) 10.0000 17.3205i 0.371647 0.643712i
\(725\) 0 0
\(726\) 7.00000 + 12.1244i 0.259794 + 0.449977i
\(727\) 3.00000i 0.111264i 0.998451 + 0.0556319i \(0.0177173\pi\)
−0.998451 + 0.0556319i \(0.982283\pi\)
\(728\) −8.66025 + 10.0000i −0.320970 + 0.370625i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 24.0000 41.5692i 0.887672 1.53749i
\(732\) −3.46410 2.00000i −0.128037 0.0739221i
\(733\) 7.79423 4.50000i 0.287886 0.166211i −0.349102 0.937085i \(-0.613513\pi\)
0.636988 + 0.770873i \(0.280180\pi\)
\(734\) −7.00000 −0.258375
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) −51.9615 + 30.0000i −1.91403 + 1.10506i
\(738\) −4.33013 2.50000i −0.159394 0.0920263i
\(739\) −7.50000 + 12.9904i −0.275892 + 0.477859i −0.970360 0.241665i \(-0.922307\pi\)
0.694468 + 0.719524i \(0.255640\pi\)
\(740\) 0 0
\(741\) −35.0000 −1.28576
\(742\) 15.5885 18.0000i 0.572270 0.660801i
\(743\) 15.0000i 0.550297i 0.961402 + 0.275148i \(0.0887270\pi\)
−0.961402 + 0.275148i \(0.911273\pi\)
\(744\) 1.00000 + 1.73205i 0.0366618 + 0.0635001i
\(745\) 0 0
\(746\) 11.0000 19.0526i 0.402739 0.697564i
\(747\) 10.3923 6.00000i 0.380235 0.219529i
\(748\) 20.0000i 0.731272i
\(749\) −1.00000 + 5.19615i −0.0365392 + 0.189863i
\(750\) 0 0
\(751\) 25.0000 + 43.3013i 0.912263 + 1.58009i 0.810860 + 0.585240i \(0.199000\pi\)
0.101403 + 0.994845i \(0.467667\pi\)
\(752\) −9.52628 5.50000i −0.347388 0.200564i
\(753\) 0.866025 + 0.500000i 0.0315597 + 0.0182210i
\(754\) 0 0
\(755\) 0 0
\(756\) −2.50000 + 0.866025i −0.0909241 + 0.0314970i
\(757\) 34.0000i 1.23575i 0.786276 + 0.617876i \(0.212006\pi\)
−0.786276 + 0.617876i \(0.787994\pi\)
\(758\) 0.866025 0.500000i 0.0314555 0.0181608i
\(759\) 2.50000 4.33013i 0.0907443 0.157174i
\(760\) 0 0
\(761\) 18.5000 + 32.0429i 0.670624 + 1.16156i 0.977727 + 0.209879i \(0.0673071\pi\)
−0.307103 + 0.951676i \(0.599360\pi\)
\(762\) 9.00000i 0.326036i
\(763\) −1.73205 5.00000i −0.0627044 0.181012i
\(764\) −14.0000 −0.506502
\(765\) 0 0
\(766\) −10.5000 + 18.1865i −0.379380 + 0.657106i
\(767\) −17.3205 10.0000i −0.625407 0.361079i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) −8.66025 + 5.00000i −0.311689 + 0.179954i
\(773\) 4.33013 + 2.50000i 0.155744 + 0.0899188i 0.575846 0.817558i \(-0.304673\pi\)
−0.420103 + 0.907477i \(0.638006\pi\)
\(774\) 6.00000 10.3923i 0.215666 0.373544i
\(775\) 0 0
\(776\) −8.00000 −0.287183
\(777\) 1.73205 2.00000i 0.0621370 0.0717496i
\(778\) 18.0000i 0.645331i
\(779\) −17.5000 30.3109i −0.627003 1.08600i
\(780\) 0 0
\(781\) 5.00000 8.66025i 0.178914 0.309888i
\(782\) 3.46410 2.00000i 0.123876 0.0715199i
\(783\) 0 0
\(784\) −5.50000 + 4.33013i −0.196429 + 0.154647i
\(785\) 0 0
\(786\) −4.50000