Properties

Label 630.2.k.g.541.1
Level $630$
Weight $2$
Character 630.541
Analytic conductor $5.031$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 630.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
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: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 630.541
Dual form 630.2.k.g.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-2.50000 - 4.33013i) q^{11} -5.00000 q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(3.50000 - 6.06218i) q^{19} -1.00000 q^{20} -5.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-2.50000 + 4.33013i) q^{26} +(2.50000 + 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} -4.00000 q^{34} +(0.500000 + 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-0.500000 + 0.866025i) q^{40} -5.00000 q^{41} +12.0000 q^{43} +(-2.50000 + 4.33013i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(-5.50000 + 9.52628i) q^{47} +(1.00000 - 6.92820i) q^{49} -1.00000 q^{50} +(2.50000 + 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} -5.00000 q^{55} +(2.00000 - 1.73205i) q^{56} +(2.00000 + 3.46410i) q^{59} +(-2.00000 + 3.46410i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-2.50000 + 4.33013i) q^{65} +(6.00000 + 10.3923i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(2.50000 + 0.866025i) q^{70} -2.00000 q^{71} +(-5.00000 - 8.66025i) q^{73} +(0.500000 + 0.866025i) q^{74} -7.00000 q^{76} +(12.5000 + 4.33013i) q^{77} +(6.00000 - 10.3923i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-2.50000 + 4.33013i) q^{82} +12.0000 q^{83} -4.00000 q^{85} +(6.00000 - 10.3923i) q^{86} +(2.50000 + 4.33013i) q^{88} +(7.00000 - 12.1244i) q^{89} +(10.0000 - 8.66025i) q^{91} -1.00000 q^{92} +(5.50000 + 9.52628i) q^{94} +(-3.50000 - 6.06218i) q^{95} -8.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} + q^{5} - 4q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} + q^{5} - 4q^{7} - 2q^{8} - q^{10} - 5q^{11} - 10q^{13} + q^{14} - q^{16} - 4q^{17} + 7q^{19} - 2q^{20} - 10q^{22} + q^{23} - q^{25} - 5q^{26} + 5q^{28} + 2q^{31} + q^{32} - 8q^{34} + q^{35} - q^{37} - 7q^{38} - q^{40} - 10q^{41} + 24q^{43} - 5q^{44} - q^{46} - 11q^{47} + 2q^{49} - 2q^{50} + 5q^{52} - 9q^{53} - 10q^{55} + 4q^{56} + 4q^{59} - 4q^{61} + 4q^{62} + 2q^{64} - 5q^{65} + 12q^{67} - 4q^{68} + 5q^{70} - 4q^{71} - 10q^{73} + q^{74} - 14q^{76} + 25q^{77} + 12q^{79} + q^{80} - 5q^{82} + 24q^{83} - 8q^{85} + 12q^{86} + 5q^{88} + 14q^{89} + 20q^{91} - 2q^{92} + 11q^{94} - 7q^{95} - 16q^{97} - 11q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −5.00000 −1.06600
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −2.50000 + 4.33013i −0.490290 + 0.849208i
\(27\) 0 0
\(28\) 2.50000 + 0.866025i 0.472456 + 0.163663i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) 0.500000 + 2.59808i 0.0845154 + 0.439155i
\(36\) 0 0
\(37\) −0.500000 + 0.866025i −0.0821995 + 0.142374i −0.904194 0.427121i \(-0.859528\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) −3.50000 6.06218i −0.567775 0.983415i
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 0 0
\(43\) 12.0000 1.82998 0.914991 0.403473i \(-0.132197\pi\)
0.914991 + 0.403473i \(0.132197\pi\)
\(44\) −2.50000 + 4.33013i −0.376889 + 0.652791i
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.0737210 0.127688i
\(47\) −5.50000 + 9.52628i −0.802257 + 1.38955i 0.115870 + 0.993264i \(0.463035\pi\)
−0.918127 + 0.396286i \(0.870299\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 2.50000 + 4.33013i 0.346688 + 0.600481i
\(53\) −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 2.00000 1.73205i 0.267261 0.231455i
\(57\) 0 0
\(58\) 0 0
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.50000 + 4.33013i −0.310087 + 0.537086i
\(66\) 0 0
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 0 0
\(70\) 2.50000 + 0.866025i 0.298807 + 0.103510i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) −5.00000 8.66025i −0.585206 1.01361i −0.994850 0.101361i \(-0.967680\pi\)
0.409644 0.912245i \(-0.365653\pi\)
\(74\) 0.500000 + 0.866025i 0.0581238 + 0.100673i
\(75\) 0 0
\(76\) −7.00000 −0.802955
\(77\) 12.5000 + 4.33013i 1.42451 + 0.493464i
\(78\) 0 0
\(79\) 6.00000 10.3923i 0.675053 1.16923i −0.301401 0.953498i \(-0.597454\pi\)
0.976453 0.215728i \(-0.0692125\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) −2.50000 + 4.33013i −0.276079 + 0.478183i
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 6.00000 10.3923i 0.646997 1.12063i
\(87\) 0 0
\(88\) 2.50000 + 4.33013i 0.266501 + 0.461593i
\(89\) 7.00000 12.1244i 0.741999 1.28518i −0.209585 0.977790i \(-0.567211\pi\)
0.951584 0.307389i \(-0.0994552\pi\)
\(90\) 0 0
\(91\) 10.0000 8.66025i 1.04828 0.907841i
\(92\) −1.00000 −0.104257
\(93\) 0 0
\(94\) 5.50000 + 9.52628i 0.567282 + 0.982561i
\(95\) −3.50000 6.06218i −0.359092 0.621966i
\(96\) 0 0
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) −5.50000 4.33013i −0.555584 0.437409i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) −1.00000 + 1.73205i −0.0966736 + 0.167444i −0.910306 0.413936i \(-0.864154\pi\)
0.813632 + 0.581380i \(0.197487\pi\)
\(108\) 0 0
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −2.50000 + 4.33013i −0.238366 + 0.412861i
\(111\) 0 0
\(112\) −0.500000 2.59808i −0.0472456 0.245495i
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) −0.500000 0.866025i −0.0466252 0.0807573i
\(116\) 0 0
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) 10.0000 + 3.46410i 0.916698 + 0.317554i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 2.00000 + 3.46410i 0.181071 + 0.313625i
\(123\) 0 0
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 9.00000 0.798621 0.399310 0.916816i \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 2.50000 + 4.33013i 0.219265 + 0.379777i
\(131\) −4.50000 + 7.79423i −0.393167 + 0.680985i −0.992865 0.119241i \(-0.961954\pi\)
0.599699 + 0.800226i \(0.295287\pi\)
\(132\) 0 0
\(133\) 3.50000 + 18.1865i 0.303488 + 1.57697i
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 2.00000 + 3.46410i 0.171499 + 0.297044i
\(137\) −1.00000 1.73205i −0.0854358 0.147979i 0.820141 0.572161i \(-0.193895\pi\)
−0.905577 + 0.424182i \(0.860562\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 1.73205i 0.169031 0.146385i
\(141\) 0 0
\(142\) −1.00000 + 1.73205i −0.0839181 + 0.145350i
\(143\) 12.5000 + 21.6506i 1.04530 + 1.81052i
\(144\) 0 0
\(145\) 0 0
\(146\) −10.0000 −0.827606
\(147\) 0 0
\(148\) 1.00000 0.0821995
\(149\) 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i \(-0.669768\pi\)
0.999953 + 0.00974235i \(0.00310113\pi\)
\(150\) 0 0
\(151\) −7.00000 12.1244i −0.569652 0.986666i −0.996600 0.0823900i \(-0.973745\pi\)
0.426948 0.904276i \(-0.359589\pi\)
\(152\) −3.50000 + 6.06218i −0.283887 + 0.491708i
\(153\) 0 0
\(154\) 10.0000 8.66025i 0.805823 0.697863i
\(155\) 2.00000 0.160644
\(156\) 0 0
\(157\) −5.50000 9.52628i −0.438948 0.760280i 0.558661 0.829396i \(-0.311315\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) −6.00000 10.3923i −0.477334 0.826767i
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) 0.500000 + 2.59808i 0.0394055 + 0.204757i
\(162\) 0 0
\(163\) 12.0000 20.7846i 0.939913 1.62798i 0.174282 0.984696i \(-0.444240\pi\)
0.765631 0.643280i \(-0.222427\pi\)
\(164\) 2.50000 + 4.33013i 0.195217 + 0.338126i
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) −11.0000 −0.851206 −0.425603 0.904910i \(-0.639938\pi\)
−0.425603 + 0.904910i \(0.639938\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −2.00000 + 3.46410i −0.153393 + 0.265684i
\(171\) 0 0
\(172\) −6.00000 10.3923i −0.457496 0.792406i
\(173\) −6.50000 + 11.2583i −0.494186 + 0.855955i −0.999978 0.00670064i \(-0.997867\pi\)
0.505792 + 0.862656i \(0.331200\pi\)
\(174\) 0 0
\(175\) 2.50000 + 0.866025i 0.188982 + 0.0654654i
\(176\) 5.00000 0.376889
\(177\) 0 0
\(178\) −7.00000 12.1244i −0.524672 0.908759i
\(179\) −11.5000 19.9186i −0.859550 1.48878i −0.872358 0.488867i \(-0.837410\pi\)
0.0128080 0.999918i \(-0.495923\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) −2.50000 12.9904i −0.185312 0.962911i
\(183\) 0 0
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 0.500000 + 0.866025i 0.0367607 + 0.0636715i
\(186\) 0 0
\(187\) −10.0000 + 17.3205i −0.731272 + 1.26660i
\(188\) 11.0000 0.802257
\(189\) 0 0
\(190\) −7.00000 −0.507833
\(191\) 7.00000 12.1244i 0.506502 0.877288i −0.493469 0.869763i \(-0.664272\pi\)
0.999972 0.00752447i \(-0.00239513\pi\)
\(192\) 0 0
\(193\) −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i \(-0.283859\pi\)
−0.987945 + 0.154805i \(0.950525\pi\)
\(194\) −4.00000 + 6.92820i −0.287183 + 0.497416i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) 0.500000 + 0.866025i 0.0353553 + 0.0612372i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.50000 + 4.33013i −0.174608 + 0.302429i
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 0 0
\(208\) 2.50000 4.33013i 0.173344 0.300240i
\(209\) −35.0000 −2.42100
\(210\) 0 0
\(211\) 17.0000 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(212\) −4.50000 + 7.79423i −0.309061 + 0.535310i
\(213\) 0 0
\(214\) 1.00000 + 1.73205i 0.0683586 + 0.118401i
\(215\) 6.00000 10.3923i 0.409197 0.708749i
\(216\) 0 0
\(217\) −5.00000 1.73205i −0.339422 0.117579i
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) 2.50000 + 4.33013i 0.168550 + 0.291937i
\(221\) 10.0000 + 17.3205i 0.672673 + 1.16510i
\(222\) 0 0
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) −2.50000 0.866025i −0.167038 0.0578638i
\(225\) 0 0
\(226\) 7.00000 12.1244i 0.465633 0.806500i
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) −1.00000 −0.0659380
\(231\) 0 0
\(232\) 0 0
\(233\) −7.00000 + 12.1244i −0.458585 + 0.794293i −0.998886 0.0471787i \(-0.984977\pi\)
0.540301 + 0.841472i \(0.318310\pi\)
\(234\) 0 0
\(235\) 5.50000 + 9.52628i 0.358780 + 0.621426i
\(236\) 2.00000 3.46410i 0.130189 0.225494i
\(237\) 0 0
\(238\) 8.00000 6.92820i 0.518563 0.449089i
\(239\) 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 0.516695 0.856170i \(-0.327162\pi\)
−0.999812 + 0.0193858i \(0.993829\pi\)
\(242\) 7.00000 + 12.1244i 0.449977 + 0.779383i
\(243\) 0 0
\(244\) 4.00000 0.256074
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) 0 0
\(247\) −17.5000 + 30.3109i −1.11350 + 1.92864i
\(248\) −1.00000 1.73205i −0.0635001 0.109985i
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −1.00000 −0.0631194 −0.0315597 0.999502i \(-0.510047\pi\)
−0.0315597 + 0.999502i \(0.510047\pi\)
\(252\) 0 0
\(253\) −5.00000 −0.314347
\(254\) 4.50000 7.79423i 0.282355 0.489053i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.00000 + 13.8564i −0.499026 + 0.864339i −0.999999 0.00112398i \(-0.999642\pi\)
0.500973 + 0.865463i \(0.332976\pi\)
\(258\) 0 0
\(259\) −0.500000 2.59808i −0.0310685 0.161437i
\(260\) 5.00000 0.310087
\(261\) 0 0
\(262\) 4.50000 + 7.79423i 0.278011 + 0.481529i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) −9.00000 −0.552866
\(266\) 17.5000 + 6.06218i 1.07299 + 0.371696i
\(267\) 0 0
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) −12.0000 20.7846i −0.731653 1.26726i −0.956176 0.292791i \(-0.905416\pi\)
0.224523 0.974469i \(-0.427917\pi\)
\(270\) 0 0
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) 0 0
\(277\) −7.00000 12.1244i −0.420589 0.728482i 0.575408 0.817867i \(-0.304843\pi\)
−0.995997 + 0.0893846i \(0.971510\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) 0 0
\(280\) −0.500000 2.59808i −0.0298807 0.155265i
\(281\) −7.00000 −0.417585 −0.208792 0.977960i \(-0.566953\pi\)
−0.208792 + 0.977960i \(0.566953\pi\)
\(282\) 0 0
\(283\) 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i \(-0.0706075\pi\)
−0.678280 + 0.734804i \(0.737274\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) 0 0
\(286\) 25.0000 1.47828
\(287\) 10.0000 8.66025i 0.590281 0.511199i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 0 0
\(292\) −5.00000 + 8.66025i −0.292603 + 0.506803i
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) 0.500000 0.866025i 0.0290619 0.0503367i
\(297\) 0 0
\(298\) −6.00000 10.3923i −0.347571 0.602010i
\(299\) −2.50000 + 4.33013i −0.144579 + 0.250418i
\(300\) 0 0
\(301\) −24.0000 + 20.7846i −1.38334 + 1.19800i
\(302\) −14.0000 −0.805609
\(303\) 0 0
\(304\) 3.50000 + 6.06218i 0.200739 + 0.347690i
\(305\) 2.00000 + 3.46410i 0.114520 + 0.198354i
\(306\) 0 0
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) −2.50000 12.9904i −0.142451 0.740196i
\(309\) 0 0
\(310\) 1.00000 1.73205i 0.0567962 0.0983739i
\(311\) 4.00000 + 6.92820i 0.226819 + 0.392862i 0.956864 0.290537i \(-0.0938340\pi\)
−0.730044 + 0.683400i \(0.760501\pi\)
\(312\) 0 0
\(313\) −8.00000 + 13.8564i −0.452187 + 0.783210i −0.998522 0.0543564i \(-0.982689\pi\)
0.546335 + 0.837567i \(0.316023\pi\)
\(314\) −11.0000 −0.620766
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) −11.0000 + 19.0526i −0.617822 + 1.07010i 0.372061 + 0.928208i \(0.378651\pi\)
−0.989882 + 0.141890i \(0.954682\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 0 0
\(322\) 2.50000 + 0.866025i 0.139320 + 0.0482617i
\(323\) −28.0000 −1.55796
\(324\) 0 0
\(325\) 2.50000 + 4.33013i 0.138675 + 0.240192i
\(326\) −12.0000 20.7846i −0.664619 1.15115i
\(327\) 0 0
\(328\) 5.00000 0.276079
\(329\) −5.50000 28.5788i −0.303225 1.57560i
\(330\) 0 0
\(331\) −15.5000 + 26.8468i −0.851957 + 1.47563i 0.0274825 + 0.999622i \(0.491251\pi\)
−0.879440 + 0.476011i \(0.842082\pi\)
\(332\) −6.00000 10.3923i −0.329293 0.570352i
\(333\) 0 0
\(334\) −5.50000 + 9.52628i −0.300947 + 0.521255i
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) −16.0000 −0.871576 −0.435788 0.900049i \(-0.643530\pi\)
−0.435788 + 0.900049i \(0.643530\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 5.00000 8.66025i 0.270765 0.468979i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −12.0000 −0.646997
\(345\) 0 0
\(346\) 6.50000 + 11.2583i 0.349442 + 0.605252i
\(347\) −9.00000 15.5885i −0.483145 0.836832i 0.516667 0.856186i \(-0.327172\pi\)
−0.999813 + 0.0193540i \(0.993839\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 2.00000 1.73205i 0.106904 0.0925820i
\(351\) 0 0
\(352\) 2.50000 4.33013i 0.133250 0.230797i
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 0 0
\(355\) −1.00000 + 1.73205i −0.0530745 + 0.0919277i
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) −23.0000 −1.21559
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 10.0000 17.3205i 0.525588 0.910346i
\(363\) 0 0
\(364\) −12.5000 4.33013i −0.655178 0.226960i
\(365\) −10.0000 −0.523424
\(366\) 0 0
\(367\) −3.50000 6.06218i −0.182699 0.316443i 0.760100 0.649806i \(-0.225150\pi\)
−0.942799 + 0.333363i \(0.891817\pi\)
\(368\) 0.500000 + 0.866025i 0.0260643 + 0.0451447i
\(369\) 0 0
\(370\) 1.00000 0.0519875
\(371\) 22.5000 + 7.79423i 1.16814 + 0.404656i
\(372\) 0 0
\(373\) 11.0000 19.0526i 0.569558 0.986504i −0.427051 0.904227i \(-0.640448\pi\)
0.996610 0.0822766i \(-0.0262191\pi\)
\(374\) 10.0000 + 17.3205i 0.517088 + 0.895622i
\(375\) 0 0
\(376\) 5.50000 9.52628i 0.283641 0.491280i
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) −3.50000 + 6.06218i −0.179546 + 0.310983i
\(381\) 0 0
\(382\) −7.00000 12.1244i −0.358151 0.620336i
\(383\) 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) 0 0
\(385\) 10.0000 8.66025i 0.509647 0.441367i
\(386\) −10.0000 −0.508987
\(387\) 0 0
\(388\) 4.00000 + 6.92820i 0.203069 + 0.351726i
\(389\) 9.00000 + 15.5885i 0.456318 + 0.790366i 0.998763 0.0497253i \(-0.0158346\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) 0 0
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) −6.00000 10.3923i −0.301893 0.522894i
\(396\) 0 0
\(397\) 7.00000 12.1244i 0.351320 0.608504i −0.635161 0.772380i \(-0.719066\pi\)
0.986481 + 0.163876i \(0.0523996\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −10.5000 + 18.1865i −0.524345 + 0.908192i 0.475253 + 0.879849i \(0.342356\pi\)
−0.999598 + 0.0283431i \(0.990977\pi\)
\(402\) 0 0
\(403\) −5.00000 8.66025i −0.249068 0.431398i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.00000 0.247841
\(408\) 0 0
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) 2.50000 + 4.33013i 0.123466 + 0.213850i
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) −10.0000 3.46410i −0.492068 0.170457i
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) −2.50000 4.33013i −0.122573 0.212302i
\(417\) 0 0
\(418\) −17.5000 + 30.3109i −0.855953 + 1.48255i
\(419\) −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 \(0.421644\pi\)
\(422\) 8.50000 14.7224i 0.413774 0.716677i
\(423\) 0 0
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) −2.00000 + 3.46410i −0.0970143 + 0.168034i
\(426\) 0 0
\(427\) −2.00000 10.3923i −0.0967868 0.502919i
\(428\) 2.00000 0.0966736
\(429\) 0 0
\(430\) −6.00000 10.3923i −0.289346 0.501161i
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0 0
\(433\) 24.0000 1.15337 0.576683 0.816968i \(-0.304347\pi\)
0.576683 + 0.816968i \(0.304347\pi\)
\(434\) −4.00000 + 3.46410i −0.192006 + 0.166282i
\(435\) 0 0
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) −3.50000 6.06218i −0.167428 0.289993i
\(438\) 0 0
\(439\) 20.0000 34.6410i 0.954548 1.65333i 0.219149 0.975691i \(-0.429672\pi\)
0.735399 0.677634i \(-0.236995\pi\)
\(440\) 5.00000 0.238366
\(441\) 0 0
\(442\) 20.0000 0.951303
\(443\) −14.0000 + 24.2487i −0.665160 + 1.15209i 0.314082 + 0.949396i \(0.398303\pi\)
−0.979242 + 0.202695i \(0.935030\pi\)
\(444\) 0 0
\(445\) −7.00000 12.1244i −0.331832 0.574750i
\(446\) −6.00000 + 10.3923i −0.284108 + 0.492090i
\(447\) 0 0
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) 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
\(452\) −7.00000 12.1244i −0.329252 0.570282i
\(453\) 0 0
\(454\) −12.0000 −0.563188
\(455\) −2.50000 12.9904i −0.117202 0.608998i
\(456\) 0 0
\(457\) 7.00000 12.1244i 0.327446 0.567153i −0.654558 0.756012i \(-0.727145\pi\)
0.982004 + 0.188858i \(0.0604787\pi\)
\(458\) 5.00000 + 8.66025i 0.233635 + 0.404667i
\(459\) 0 0
\(460\) −0.500000 + 0.866025i −0.0233126 + 0.0403786i
\(461\) 4.00000 0.186299 0.0931493 0.995652i \(-0.470307\pi\)
0.0931493 + 0.995652i \(0.470307\pi\)
\(462\) 0 0
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 7.00000 + 12.1244i 0.324269 + 0.561650i
\(467\) −10.0000 + 17.3205i −0.462745 + 0.801498i −0.999097 0.0424970i \(-0.986469\pi\)
0.536352 + 0.843995i \(0.319802\pi\)
\(468\) 0 0
\(469\) −30.0000 10.3923i −1.38527 0.479872i
\(470\) 11.0000 0.507392
\(471\) 0 0
\(472\) −2.00000 3.46410i −0.0920575 0.159448i
\(473\) −30.0000 51.9615i −1.37940 2.38919i
\(474\) 0 0
\(475\) −7.00000 −0.321182
\(476\) −2.00000 10.3923i −0.0916698 0.476331i
\(477\) 0 0
\(478\) 11.0000 19.0526i 0.503128 0.871444i
\(479\) 9.00000 + 15.5885i 0.411220 + 0.712255i 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 0 0
\(481\) 2.50000 4.33013i 0.113990 0.197437i
\(482\) −15.0000 −0.683231
\(483\) 0 0
\(484\) 14.0000 0.636364
\(485\) −4.00000 + 6.92820i −0.181631 + 0.314594i
\(486\) 0 0
\(487\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(488\) 2.00000 3.46410i 0.0905357 0.156813i
\(489\) 0 0
\(490\) −6.50000 + 2.59808i −0.293640 + 0.117369i
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 17.5000 + 30.3109i 0.787362 + 1.36375i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 4.00000 3.46410i 0.179425 0.155386i
\(498\) 0 0
\(499\) −20.0000 + 34.6410i −0.895323 + 1.55074i −0.0619186 + 0.998081i \(0.519722\pi\)
−0.833404 + 0.552664i \(0.813611\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) −0.500000 + 0.866025i −0.0223161 + 0.0386526i
\(503\) 20.0000 0.891756 0.445878 0.895094i \(-0.352892\pi\)
0.445878 + 0.895094i \(0.352892\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −2.50000 + 4.33013i −0.111139 + 0.192498i
\(507\) 0 0
\(508\) −4.50000 7.79423i −0.199655 0.345813i
\(509\) −5.00000 + 8.66025i −0.221621 + 0.383859i −0.955300 0.295637i \(-0.904468\pi\)
0.733679 + 0.679496i \(0.237801\pi\)
\(510\) 0 0
\(511\) 25.0000 + 8.66025i 1.10593 + 0.383107i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 8.00000 + 13.8564i 0.352865 + 0.611180i
\(515\) 4.00000 + 6.92820i 0.176261 + 0.305293i
\(516\) 0 0
\(517\) 55.0000 2.41890
\(518\) −2.50000 0.866025i −0.109844 0.0380510i
\(519\) 0 0
\(520\) 2.50000 4.33013i 0.109632 0.189889i
\(521\) −16.5000 28.5788i −0.722878 1.25206i −0.959841 0.280543i \(-0.909485\pi\)
0.236963 0.971519i \(-0.423848\pi\)
\(522\) 0 0
\(523\) 11.0000 19.0526i 0.480996 0.833110i −0.518766 0.854916i \(-0.673608\pi\)
0.999762 + 0.0218062i \(0.00694167\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 0 0
\(527\) 4.00000 6.92820i 0.174243 0.301797i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) −4.50000 + 7.79423i −0.195468 + 0.338560i
\(531\) 0 0
\(532\) 14.0000 12.1244i 0.606977 0.525657i
\(533\) 25.0000 1.08287
\(534\) 0 0
\(535\) 1.00000 + 1.73205i 0.0432338 + 0.0748831i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 0 0
\(538\) −24.0000 −1.03471
\(539\) −32.5000 + 12.9904i −1.39987 + 0.559535i
\(540\) 0 0
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 2.00000 3.46410i 0.0857493 0.148522i
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) 0 0
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) 0 0
\(552\) 0 0
\(553\) 6.00000 + 31.1769i 0.255146 + 1.32578i
\(554\) −14.0000 −0.594803
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 18.5000 + 32.0429i 0.783870 + 1.35770i 0.929672 + 0.368389i \(0.120091\pi\)
−0.145802 + 0.989314i \(0.546576\pi\)
\(558\) 0 0
\(559\) −60.0000 −2.53773
\(560\) −2.50000 0.866025i −0.105644 0.0365963i
\(561\) 0 0
\(562\) −3.50000 + 6.06218i −0.147639 + 0.255718i
\(563\) −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i \(-0.290503\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(564\) 0 0
\(565\) 7.00000 12.1244i 0.294492 0.510075i
\(566\) 10.0000 0.420331
\(567\) 0 0
\(568\) 2.00000 0.0839181
\(569\) 19.5000 33.7750i 0.817483 1.41592i −0.0900490 0.995937i \(-0.528702\pi\)
0.907532 0.419984i \(-0.137964\pi\)
\(570\) 0 0
\(571\) −20.0000 34.6410i −0.836974 1.44968i −0.892413 0.451219i \(-0.850989\pi\)
0.0554391 0.998462i \(-0.482344\pi\)
\(572\) 12.5000 21.6506i 0.522651 0.905259i
\(573\) 0 0
\(574\) −2.50000 12.9904i −0.104348 0.542208i
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) −13.0000 22.5167i −0.541197 0.937381i −0.998836 0.0482425i \(-0.984638\pi\)
0.457639 0.889138i \(-0.348695\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 0 0
\(580\) 0 0
\(581\) −24.0000 + 20.7846i −0.995688 + 0.862291i
\(582\) 0 0
\(583\) −22.5000 + 38.9711i −0.931855 + 1.61402i
\(584\) 5.00000 + 8.66025i 0.206901 + 0.358364i
\(585\) 0 0
\(586\) −4.50000 + 7.79423i −0.185893 + 0.321977i
\(587\) 30.0000 1.23823 0.619116 0.785299i \(-0.287491\pi\)
0.619116 + 0.785299i \(0.287491\pi\)
\(588\) 0 0
\(589\) 14.0000 0.576860
\(590\) 2.00000 3.46410i 0.0823387 0.142615i
\(591\) 0 0
\(592\) −0.500000 0.866025i −0.0205499 0.0355934i
\(593\) 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i \(-0.568551\pi\)
0.952869 0.303383i \(-0.0981160\pi\)
\(594\) 0 0
\(595\) 8.00000 6.92820i 0.327968 0.284029i
\(596\) −12.0000 −0.491539
\(597\) 0 0
\(598\) 2.50000 + 4.33013i 0.102233 + 0.177072i
\(599\) −5.00000 8.66025i −0.204294 0.353848i 0.745613 0.666379i \(-0.232157\pi\)
−0.949908 + 0.312531i \(0.898823\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 6.00000 + 31.1769i 0.244542 + 1.27068i
\(603\) 0 0
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) 7.00000 + 12.1244i 0.284590 + 0.492925i
\(606\) 0 0
\(607\) 13.5000 23.3827i 0.547948 0.949074i −0.450467 0.892793i \(-0.648742\pi\)
0.998415 0.0562808i \(-0.0179242\pi\)
\(608\) 7.00000 0.283887
\(609\) 0 0
\(610\) 4.00000 0.161955
\(611\) 27.5000 47.6314i 1.11253 1.92696i
\(612\) 0 0
\(613\) 21.5000 + 37.2391i 0.868377 + 1.50407i 0.863655 + 0.504084i \(0.168170\pi\)
0.00472215 + 0.999989i \(0.498497\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) 0 0
\(616\) −12.5000 4.33013i −0.503639 0.174466i
\(617\) 8.00000 0.322068 0.161034 0.986949i \(-0.448517\pi\)
0.161034 + 0.986949i \(0.448517\pi\)
\(618\) 0 0
\(619\) −12.5000 21.6506i −0.502417 0.870212i −0.999996 0.00279365i \(-0.999111\pi\)
0.497579 0.867419i \(-0.334223\pi\)
\(620\) −1.00000 1.73205i −0.0401610 0.0695608i
\(621\) 0 0
\(622\) 8.00000 0.320771
\(623\) 7.00000 + 36.3731i 0.280449 + 1.45726i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 8.00000 + 13.8564i 0.319744 + 0.553813i
\(627\) 0 0
\(628\) −5.50000 + 9.52628i −0.219474 + 0.380140i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 6.00000 0.238856 0.119428 0.992843i \(-0.461894\pi\)
0.119428 + 0.992843i \(0.461894\pi\)
\(632\) −6.00000 + 10.3923i −0.238667 + 0.413384i
\(633\) 0 0
\(634\) 11.0000 + 19.0526i 0.436866 + 0.756674i
\(635\) 4.50000 7.79423i 0.178577 0.309305i
\(636\) 0 0
\(637\) −5.00000 + 34.6410i −0.198107 + 1.37253i
\(638\) 0 0
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) 10.5000 + 18.1865i 0.414725 + 0.718325i 0.995400 0.0958109i \(-0.0305444\pi\)
−0.580674 + 0.814136i \(0.697211\pi\)
\(642\) 0 0
\(643\) 34.0000 1.34083 0.670415 0.741987i \(-0.266116\pi\)
0.670415 + 0.741987i \(0.266116\pi\)
\(644\) 2.00000 1.73205i 0.0788110 0.0682524i
\(645\) 0 0
\(646\) −14.0000 + 24.2487i −0.550823 + 0.954053i
\(647\) −11.5000 19.9186i −0.452112 0.783080i 0.546405 0.837521i \(-0.315996\pi\)
−0.998517 + 0.0544405i \(0.982662\pi\)
\(648\) 0 0
\(649\) 10.0000 17.3205i 0.392534 0.679889i
\(650\) 5.00000 0.196116
\(651\) 0 0
\(652\) −24.0000 −0.939913
\(653\) −9.50000 + 16.4545i −0.371764 + 0.643914i −0.989837 0.142207i \(-0.954580\pi\)
0.618073 + 0.786121i \(0.287914\pi\)
\(654\) 0 0
\(655\) 4.50000 + 7.79423i 0.175830 + 0.304546i
\(656\) 2.50000 4.33013i 0.0976086 0.169063i
\(657\) 0 0
\(658\) −27.5000 9.52628i −1.07206 0.371373i
\(659\) 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 0.933144 + 0.359502i \(0.117053\pi\)
−0.155235 + 0.987878i \(0.549613\pi\)
\(662\) 15.5000 + 26.8468i 0.602425 + 1.04343i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 17.5000 + 6.06218i 0.678621 + 0.235081i
\(666\) 0 0
\(667\) 0 0
\(668\) 5.50000 + 9.52628i 0.212801 + 0.368583i
\(669\) 0 0
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) 20.0000 0.772091
\(672\) 0 0
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) −8.00000 + 13.8564i −0.308148 + 0.533729i
\(675\) 0 0
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) 16.5000 28.5788i 0.634147 1.09837i −0.352549 0.935793i \(-0.614685\pi\)
0.986695 0.162581i \(-0.0519817\pi\)
\(678\) 0 0
\(679\) 16.0000 13.8564i 0.614024 0.531760i
\(680\) 4.00000 0.153393
\(681\) 0 0
\(682\) −5.00000 8.66025i −0.191460 0.331618i
\(683\) −2.00000 3.46410i −0.0765279 0.132550i 0.825222 0.564809i \(-0.191050\pi\)
−0.901750 + 0.432259i \(0.857717\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 0 0
\(688\) −6.00000 + 10.3923i −0.228748 + 0.396203i
\(689\) 22.5000 + 38.9711i 0.857182 + 1.48468i
\(690\) 0 0
\(691\) −14.0000 + 24.2487i −0.532585 + 0.922464i 0.466691 + 0.884420i \(0.345446\pi\)
−0.999276 + 0.0380440i \(0.987887\pi\)
\(692\) 13.0000 0.494186
\(693\) 0 0
\(694\) −18.0000 −0.683271
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 10.0000 + 17.3205i 0.378777 + 0.656061i
\(698\) −2.00000 + 3.46410i −0.0757011 + 0.131118i
\(699\) 0 0
\(700\) −0.500000 2.59808i −0.0188982 0.0981981i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 3.50000 + 6.06218i 0.132005 + 0.228639i
\(704\) −2.50000 4.33013i −0.0942223 0.163198i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) 0 0
\(708\) 0 0
\(709\) −14.0000 + 24.2487i −0.525781 + 0.910679i 0.473768 + 0.880650i \(0.342894\pi\)
−0.999549 + 0.0300298i \(0.990440\pi\)
\(710\) 1.00000 + 1.73205i 0.0375293 + 0.0650027i
\(711\) 0 0
\(712\) −7.00000 + 12.1244i −0.262336 + 0.454379i
\(713\) 2.00000 0.0749006
\(714\) 0 0
\(715\) 25.0000 0.934947
\(716\) −11.5000 + 19.9186i −0.429775 + 0.744392i
\(717\) 0 0
\(718\) 10.0000 + 17.3205i 0.373197 + 0.646396i
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 0 0
\(721\) −4.00000 20.7846i −0.148968 0.774059i
\(722\) −30.0000 −1.11648
\(723\) 0 0
\(724\) −10.0000 17.3205i −0.371647 0.643712i
\(725\) 0 0
\(726\) 0 0
\(727\) −3.00000 −0.111264 −0.0556319 0.998451i \(-0.517717\pi\)
−0.0556319 + 0.998451i \(0.517717\pi\)
\(728\) −10.0000 + 8.66025i −0.370625 + 0.320970i
\(729\) 0 0
\(730\) −5.00000 + 8.66025i −0.185058 + 0.320530i
\(731\) −24.0000 41.5692i −0.887672 1.53749i
\(732\) 0 0
\(733\) −4.50000 + 7.79423i −0.166211 + 0.287886i −0.937085 0.349102i \(-0.886487\pi\)
0.770873 + 0.636988i \(0.219820\pi\)
\(734\) −7.00000 −0.258375
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 30.0000 51.9615i 1.10506 1.91403i
\(738\) 0 0
\(739\) 7.50000 + 12.9904i 0.275892 + 0.477859i 0.970360 0.241665i \(-0.0776935\pi\)
−0.694468 + 0.719524i \(0.744360\pi\)
\(740\) 0.500000 0.866025i 0.0183804 0.0318357i
\(741\) 0 0
\(742\) 18.0000 15.5885i 0.660801 0.572270i
\(743\) −15.0000 −0.550297 −0.275148 0.961402i \(-0.588727\pi\)
−0.275148 + 0.961402i \(0.588727\pi\)
\(744\) 0 0
\(745\) −6.00000 10.3923i −0.219823 0.380745i
\(746\) −11.0000 19.0526i −0.402739 0.697564i
\(747\) 0 0
\(748\) 20.0000 0.731272
\(749\) −1.00000 5.19615i −0.0365392 0.189863i
\(750\) 0 0
\(751\) 25.0000 43.3013i 0.912263 1.58009i 0.101403 0.994845i \(-0.467667\pi\)
0.810860 0.585240i \(-0.199000\pi\)
\(752\) −5.50000 9.52628i −0.200564 0.347388i
\(753\) 0 0
\(754\) 0 0
\(755\) −14.0000 −0.509512
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 0.500000 0.866025i 0.0181608 0.0314555i
\(759\) 0 0
\(760\) 3.50000 + 6.06218i 0.126958 + 0.219898i
\(761\) −18.5000 + 32.0429i −0.670624 + 1.16156i 0.307103 + 0.951676i \(0.400640\pi\)
−0.977727 + 0.209879i \(0.932693\pi\)
\(762\) 0 0
\(763\) −5.00000 1.73205i −0.181012 0.0627044i
\(764\) −14.0000 −0.506502
\(765\) 0 0
\(766\) −10.5000 18.1865i −0.379380 0.657106i
\(767\) −10.0000 17.3205i −0.361079 0.625407i
\(768\) 0 0
\(769\) −5.00000 −0.180305 −0.0901523 0.995928i \(-0.528735\pi\)
−0.0901523 + 0.995928i \(0.528735\pi\)
\(770\) −2.50000 12.9904i −0.0900937 0.468141i
\(771\) 0 0
\(772\) −5.00000 + 8.66025i −0.179954 + 0.311689i
\(773\) −2.50000 4.33013i −0.0899188 0.155744i 0.817558 0.575846i \(-0.195327\pi\)
−0.907477 + 0.420103i \(0.861994\pi\)
\(774\) 0 0
\(775\) 1.00000 1.73205i 0.0359211 0.0622171i
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) 18.0000 0.645331
\(779\) −17.5000 + 30.3109i −0.627003 + 1.08600i
\(780\) 0 0
\(781\) 5.00000 + 8.66025i 0.178914 + 0.309888i
\(782\) −2.00000 + 3.46410i −0.0715199 + 0.123876i
\(783\) 0 0
\(784\) 5.50000 + 4.33013i 0.196429 + 0.154647i
\(785\) −11.0000 −0.392607
\(786\) 0 0
\(787\) −1.00000 1.73205i −0.0356462 0.0617409i 0.847652 0.530553i \(-0.178016\pi\)
−0.883298 + 0.468812i \(0.844682\pi\)
\(788\) −1.50000 2.59808i −0.0534353 0.0925526i
\(789\) 0 0
\(790\) −12.0000 −0.426941
\(791\) −28.0000 + 24.2487i −0.995565 + 0.862185i
\(792\) 0 0
\(793\) 10.0000 17.3205i 0.355110 0.615069i
\(794\) −7.00000 12.1244i −0.248421 0.430277i
\(795\) 0 0
\(796\) 2.00000 3.46410i 0.0708881 0.122782i
\(797\) 54.0000 1.91278 0.956389 0.292096i \(-0.0943526\pi\)
0.956389 + 0.292096i \(0.0943526\pi\)
\(798\) 0 0
\(799\) 44.0000 1.55661
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) 0 0
\(802\) 10.5000 + 18.1865i 0.370768 + 0.642189i
\(803\) −25.0000 + 43.3013i −0.882231 + 1.52807i
\(804\) 0 0
\(805\) 2.50000 + 0.866025i 0.0881134 + 0.0305234i