Properties

Label 630.2.k.g.361.1
Level $630$
Weight $2$
Character 630.361
Analytic conductor $5.031$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 630.361
Dual form 630.2.k.g.541.1

$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 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 −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −5.00000 −1.06600
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 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 −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) 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 0.821995 0.569495i \(-0.192861\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) −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 −0.918127 0.396286i \(-0.870299\pi\)
0.115870 0.993264i \(-0.463035\pi\)
\(48\) 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 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) 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 −0.705965 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 \(0.915762\pi\)
\(62\) 2.00000 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 −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) −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 0.409644 + 0.912245i \(0.365653\pi\)
−0.994850 + 0.101361i \(0.967680\pi\)
\(74\) 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 0.976453 + 0.215728i \(0.0692125\pi\)
−0.301401 + 0.953498i \(0.597454\pi\)
\(80\) 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 0.951584 + 0.307389i \(0.0994552\pi\)
−0.209585 + 0.977790i \(0.567211\pi\)
\(90\) 0 0
\(91\) 10.0000 + 8.66025i 1.04828 + 0.907841i
\(92\) −1.00000 −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −4.00000 6.92820i −0.394132 0.682656i 0.598858 0.800855i \(-0.295621\pi\)
−0.992990 + 0.118199i \(0.962288\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) −1.00000 1.73205i −0.0966736 0.167444i 0.813632 0.581380i \(-0.197487\pi\)
−0.910306 + 0.413936i \(0.864154\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) −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 0.599699 0.800226i \(-0.295287\pi\)
−0.992865 + 0.119241i \(0.961954\pi\)
\(132\) 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 −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) 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 0.999953 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 \(0.973745\pi\)
\(152\) −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 −0.997609 0.0691164i \(-0.977982\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −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 0.765631 + 0.643280i \(0.222427\pi\)
0.174282 + 0.984696i \(0.444240\pi\)
\(164\) 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 0.505792 0.862656i \(-0.331200\pi\)
−0.999978 + 0.00670064i \(0.997867\pi\)
\(174\) 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 0.0128080 + 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 \(0.233262\pi\)
\(182\) −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 0.999972 + 0.00752447i \(0.00239513\pi\)
−0.493469 + 0.869763i \(0.664272\pi\)
\(192\) 0 0
\(193\) −5.00000 + 8.66025i −0.359908 + 0.623379i −0.987945 0.154805i \(-0.950525\pi\)
0.628037 + 0.778183i \(0.283859\pi\)
\(194\) −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 −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 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 −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 0 0
\(229\) −5.00000 8.66025i −0.330409 0.572286i 0.652183 0.758062i \(-0.273853\pi\)
−0.982592 + 0.185776i \(0.940520\pi\)
\(230\) −1.00000 −0.0659380
\(231\) 0 0
\(232\) 0 0
\(233\) −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i \(-0.318310\pi\)
−0.998886 + 0.0471787i \(0.984977\pi\)
\(234\) 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 −0.999812 0.0193858i \(-0.993829\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(242\) 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 0.500973 0.865463i \(-0.332976\pi\)
−0.999999 + 0.00112398i \(0.999642\pi\)
\(258\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 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 0.224523 + 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 \(0.833333\pi\)
\(272\) 4.00000 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 −0.995997 0.0893846i \(-0.971510\pi\)
0.575408 + 0.817867i \(0.304843\pi\)
\(278\) −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 −0.678280 0.734804i \(-0.737274\pi\)
0.975499 + 0.220005i \(0.0706075\pi\)
\(284\) 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 −0.730044 0.683400i \(-0.760501\pi\)
0.956864 + 0.290537i \(0.0938340\pi\)
\(312\) 0 0
\(313\) −8.00000 13.8564i −0.452187 0.783210i 0.546335 0.837567i \(-0.316023\pi\)
−0.998522 + 0.0543564i \(0.982689\pi\)
\(314\) −11.0000 −0.620766
\(315\) 0 0
\(316\) −12.0000 −0.675053
\(317\) −11.0000 19.0526i −0.617822 1.07010i −0.989882 0.141890i \(-0.954682\pi\)
0.372061 0.928208i \(-0.378651\pi\)
\(318\) 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 −0.879440 0.476011i \(-0.842082\pi\)
0.0274825 0.999622i \(-0.491251\pi\)
\(332\) −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 −0.999813 0.0193540i \(-0.993839\pi\)
0.516667 + 0.856186i \(0.327172\pi\)
\(348\) 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 −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 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 −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 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 −0.942799 0.333363i \(-0.891817\pi\)
0.760100 + 0.649806i \(0.225150\pi\)
\(368\) 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 0.996610 + 0.0822766i \(0.0262191\pi\)
−0.427051 + 0.904227i \(0.640448\pi\)
\(374\) 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 0.999088 + 0.0427020i \(0.0135966\pi\)
−0.462563 + 0.886586i \(0.653070\pi\)
\(384\) 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 −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) 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 0.986481 0.163876i \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −10.5000 18.1865i −0.524345 0.908192i −0.999598 0.0283431i \(-0.990977\pi\)
0.475253 0.879849i \(-0.342356\pi\)
\(402\) 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 −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) 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 −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 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 0.735399 + 0.677634i \(0.236995\pi\)
0.219149 + 0.975691i \(0.429672\pi\)
\(440\) 5.00000 0.238366
\(441\) 0 0
\(442\) 20.0000 0.951303
\(443\) −14.0000 24.2487i −0.665160 1.15209i −0.979242 0.202695i \(-0.935030\pi\)
0.314082 0.949396i \(-0.398303\pi\)
\(444\) 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 0.982004 0.188858i \(-0.0604787\pi\)
−0.654558 + 0.756012i \(0.727145\pi\)
\(458\) 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 0.536352 0.843995i \(-0.319802\pi\)
−0.999097 + 0.0424970i \(0.986469\pi\)
\(468\) 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 −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) 0 0
\(481\) 2.50000 + 4.33013i 0.113990 + 0.197437i
\(482\) −15.0000 −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(488\) 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 −0.833404 0.552664i \(-0.813611\pi\)
−0.0619186 0.998081i \(-0.519722\pi\)
\(500\) 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 0.733679 0.679496i \(-0.237801\pi\)
−0.955300 + 0.295637i \(0.904468\pi\)
\(510\) 0 0
\(511\) 25.0000 8.66025i 1.10593 0.383107i
\(512\) −1.00000 −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 0.236963 + 0.971519i \(0.423848\pi\)
−0.959841 + 0.280543i \(0.909485\pi\)
\(522\) 0 0
\(523\) 11.0000 + 19.0526i 0.480996 + 0.833110i 0.999762 0.0218062i \(-0.00694167\pi\)
−0.518766 + 0.854916i \(0.673608\pi\)
\(524\) 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 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) 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 −0.145802 0.989314i \(-0.546576\pi\)
0.929672 0.368389i \(-0.120091\pi\)
\(558\) 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 −0.990961 0.134148i \(-0.957170\pi\)
0.611656 + 0.791123i \(0.290503\pi\)
\(564\) 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 0.907532 + 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 \(0.850989\pi\)
\(572\) 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 0.457639 + 0.889138i \(0.348695\pi\)
−0.998836 + 0.0482425i \(0.984638\pi\)
\(578\) −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 0.952869 + 0.303383i \(0.0981160\pi\)
−0.213697 + 0.976900i \(0.568551\pi\)
\(594\) 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 −0.949908 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 \(0.565379\pi\)
\(602\) 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 0.998415 + 0.0562808i \(0.0179242\pi\)
−0.450467 + 0.892793i \(0.648742\pi\)
\(608\) 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 0.00472215 0.999989i \(-0.498497\pi\)
0.863655 0.504084i \(-0.168170\pi\)
\(614\) 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 0.497579 + 0.867419i \(0.334223\pi\)
−0.999996 + 0.00279365i \(0.999111\pi\)
\(620\) −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 −0.580674 0.814136i \(-0.697211\pi\)
0.995400 + 0.0958109i \(0.0305444\pi\)
\(642\) 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 −0.998517 0.0544405i \(-0.982662\pi\)
0.546405 + 0.837521i \(0.315996\pi\)
\(648\) 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 0.618073 0.786121i \(-0.287914\pi\)
−0.989837 + 0.142207i \(0.954580\pi\)
\(654\) 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 −0.155235 0.987878i \(-0.549613\pi\)
0.933144 0.359502i \(-0.117053\pi\)
\(662\) 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 0.986695 + 0.162581i \(0.0519817\pi\)
−0.352549 + 0.935793i \(0.614685\pi\)
\(678\) 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 −0.901750 0.432259i \(-0.857717\pi\)
0.825222 + 0.564809i \(0.191050\pi\)
\(684\) 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 −0.999276 0.0380440i \(-0.987887\pi\)
0.466691 0.884420i \(-0.345446\pi\)
\(692\) 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 −0.999549 0.0300298i \(-0.990440\pi\)
0.473768 0.880650i \(-0.342894\pi\)
\(710\) 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 0.804648 0.593753i \(-0.202354\pi\)
−0.916529 + 0.399969i \(0.869021\pi\)
\(720\) 0 0
\(721\) −4.00000 + 20.7846i −0.148968 + 0.774059i
\(722\) −30.0000 −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 0.770873 0.636988i \(-0.219820\pi\)
−0.937085 + 0.349102i \(0.886487\pi\)
\(734\) −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 −0.694468 0.719524i \(-0.744360\pi\)
0.970360 + 0.241665i \(0.0776935\pi\)
\(740\) 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 0.810860 + 0.585240i \(0.199000\pi\)
0.101403 + 0.994845i \(0.467667\pi\)
\(752\) −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 −0.977727 0.209879i \(-0.932693\pi\)
0.307103 0.951676i \(-0.400640\pi\)
\(762\) 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 −0.907477 0.420103i \(-0.861994\pi\)
0.817558 + 0.575846i \(0.195327\pi\)
\(774\) 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 −0.883298 0.468812i \(-0.844682\pi\)
0.847652 + 0.530553i \(0.178016\pi\)
\(788\) −1.50000 + 2.59808i −0.0534353 + 0.0925526i
\(789\) 0 0
\(790\) −12.0000 −0.426941