Properties

Label 1170.2.bs.b.361.2
Level $1170$
Weight $2$
Character 1170.361
Analytic conductor $9.342$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.361
Dual form 1170.2.bs.b.901.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{10} +(2.59808 - 1.50000i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 - 1.73205i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(1.50000 - 2.59808i) q^{22} +(0.866025 + 1.50000i) q^{23} -1.00000 q^{25} +(-2.59808 - 2.50000i) q^{26} +(0.866025 + 1.50000i) q^{29} -5.19615i q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.50000 - 0.866025i) q^{37} -3.46410 q^{38} -1.00000 q^{40} +(5.19615 - 3.00000i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000i q^{44} +(1.50000 + 0.866025i) q^{46} -3.00000i q^{47} +(-3.50000 - 6.06218i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(-3.50000 - 0.866025i) q^{52} -6.92820 q^{53} +(-1.50000 - 2.59808i) q^{55} +(1.50000 + 0.866025i) q^{58} +(7.79423 + 4.50000i) q^{59} +(4.00000 - 6.92820i) q^{61} +(-2.59808 - 4.50000i) q^{62} -1.00000 q^{64} +(-3.46410 + 1.00000i) q^{65} +(-3.00000 + 1.73205i) q^{67} +(5.19615 + 3.00000i) q^{71} +(0.866025 - 1.50000i) q^{74} +(-3.00000 + 1.73205i) q^{76} -11.0000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(3.00000 - 5.19615i) q^{82} +6.00000i q^{83} -1.00000i q^{86} +(-1.50000 - 2.59808i) q^{88} +1.73205 q^{92} +(-1.50000 - 2.59808i) q^{94} +(-1.73205 + 3.00000i) q^{95} +(-3.00000 - 1.73205i) q^{97} +(-6.06218 - 3.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + O(q^{10}) \) \( 4 q + 2 q^{4} - 2 q^{10} - 4 q^{13} - 2 q^{16} - 12 q^{19} + 6 q^{22} - 4 q^{25} + 6 q^{37} - 4 q^{40} + 2 q^{43} + 6 q^{46} - 14 q^{49} - 14 q^{52} - 6 q^{55} + 6 q^{58} + 16 q^{61} - 4 q^{64} - 12 q^{67} - 12 q^{76} - 44 q^{79} + 12 q^{82} - 6 q^{88} - 6 q^{94} - 12 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 2.59808 1.50000i 0.783349 0.452267i −0.0542666 0.998526i \(-0.517282\pi\)
0.837616 + 0.546259i \(0.183949\pi\)
\(12\) 0 0
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) −3.00000 1.73205i −0.688247 0.397360i 0.114708 0.993399i \(-0.463407\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −0.866025 0.500000i −0.193649 0.111803i
\(21\) 0 0
\(22\) 1.50000 2.59808i 0.319801 0.553912i
\(23\) 0.866025 + 1.50000i 0.180579 + 0.312772i 0.942078 0.335394i \(-0.108870\pi\)
−0.761499 + 0.648166i \(0.775536\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) −2.59808 2.50000i −0.509525 0.490290i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.866025 + 1.50000i 0.160817 + 0.278543i 0.935162 0.354221i \(-0.115254\pi\)
−0.774345 + 0.632764i \(0.781920\pi\)
\(30\) 0 0
\(31\) 5.19615i 0.933257i −0.884454 0.466628i \(-0.845469\pi\)
0.884454 0.466628i \(-0.154531\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.50000 0.866025i 0.246598 0.142374i −0.371607 0.928390i \(-0.621193\pi\)
0.618206 + 0.786016i \(0.287860\pi\)
\(38\) −3.46410 −0.561951
\(39\) 0 0
\(40\) −1.00000 −0.158114
\(41\) 5.19615 3.00000i 0.811503 0.468521i −0.0359748 0.999353i \(-0.511454\pi\)
0.847477 + 0.530831i \(0.178120\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 3.00000i 0.452267i
\(45\) 0 0
\(46\) 1.50000 + 0.866025i 0.221163 + 0.127688i
\(47\) 3.00000i 0.437595i −0.975770 0.218797i \(-0.929787\pi\)
0.975770 0.218797i \(-0.0702134\pi\)
\(48\) 0 0
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) −0.866025 + 0.500000i −0.122474 + 0.0707107i
\(51\) 0 0
\(52\) −3.50000 0.866025i −0.485363 0.120096i
\(53\) −6.92820 −0.951662 −0.475831 0.879537i \(-0.657853\pi\)
−0.475831 + 0.879537i \(0.657853\pi\)
\(54\) 0 0
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) 0 0
\(57\) 0 0
\(58\) 1.50000 + 0.866025i 0.196960 + 0.113715i
\(59\) 7.79423 + 4.50000i 1.01472 + 0.585850i 0.912571 0.408919i \(-0.134094\pi\)
0.102151 + 0.994769i \(0.467427\pi\)
\(60\) 0 0
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) −2.59808 4.50000i −0.329956 0.571501i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −3.46410 + 1.00000i −0.429669 + 0.124035i
\(66\) 0 0
\(67\) −3.00000 + 1.73205i −0.366508 + 0.211604i −0.671932 0.740613i \(-0.734535\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.19615 + 3.00000i 0.616670 + 0.356034i 0.775571 0.631260i \(-0.217462\pi\)
−0.158901 + 0.987294i \(0.550795\pi\)
\(72\) 0 0
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) 0.866025 1.50000i 0.100673 0.174371i
\(75\) 0 0
\(76\) −3.00000 + 1.73205i −0.344124 + 0.198680i
\(77\) 0 0
\(78\) 0 0
\(79\) −11.0000 −1.23760 −0.618798 0.785550i \(-0.712380\pi\)
−0.618798 + 0.785550i \(0.712380\pi\)
\(80\) −0.866025 + 0.500000i −0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.00000i 0.107833i
\(87\) 0 0
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.73205 0.180579
\(93\) 0 0
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) −1.73205 + 3.00000i −0.177705 + 0.307794i
\(96\) 0 0
\(97\) −3.00000 1.73205i −0.304604 0.175863i 0.339905 0.940460i \(-0.389605\pi\)
−0.644509 + 0.764597i \(0.722938\pi\)
\(98\) −6.06218 3.50000i −0.612372 0.353553i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 6.92820 + 12.0000i 0.689382 + 1.19404i 0.972038 + 0.234823i \(0.0754512\pi\)
−0.282656 + 0.959221i \(0.591216\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) −3.46410 + 1.00000i −0.339683 + 0.0980581i
\(105\) 0 0
\(106\) −6.00000 + 3.46410i −0.582772 + 0.336463i
\(107\) 3.46410 + 6.00000i 0.334887 + 0.580042i 0.983463 0.181108i \(-0.0579684\pi\)
−0.648576 + 0.761150i \(0.724635\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) −2.59808 1.50000i −0.247717 0.143019i
\(111\) 0 0
\(112\) 0 0
\(113\) −6.06218 + 10.5000i −0.570282 + 0.987757i 0.426255 + 0.904603i \(0.359833\pi\)
−0.996537 + 0.0831539i \(0.973501\pi\)
\(114\) 0 0
\(115\) 1.50000 0.866025i 0.139876 0.0807573i
\(116\) 1.73205 0.160817
\(117\) 0 0
\(118\) 9.00000 0.828517
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) 8.00000i 0.724286i
\(123\) 0 0
\(124\) −4.50000 2.59808i −0.404112 0.233314i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −2.50000 + 2.59808i −0.219265 + 0.227866i
\(131\) 12.1244 1.05931 0.529655 0.848213i \(-0.322321\pi\)
0.529655 + 0.848213i \(0.322321\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1.73205 + 3.00000i −0.149626 + 0.259161i
\(135\) 0 0
\(136\) 0 0
\(137\) 2.59808 + 1.50000i 0.221969 + 0.128154i 0.606861 0.794808i \(-0.292428\pi\)
−0.384893 + 0.922961i \(0.625762\pi\)
\(138\) 0 0
\(139\) 5.00000 8.66025i 0.424094 0.734553i −0.572241 0.820086i \(-0.693926\pi\)
0.996335 + 0.0855324i \(0.0272591\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 0.503509
\(143\) −7.79423 7.50000i −0.651786 0.627182i
\(144\) 0 0
\(145\) 1.50000 0.866025i 0.124568 0.0719195i
\(146\) 0 0
\(147\) 0 0
\(148\) 1.73205i 0.142374i
\(149\) 2.59808 + 1.50000i 0.212843 + 0.122885i 0.602632 0.798019i \(-0.294119\pi\)
−0.389789 + 0.920904i \(0.627452\pi\)
\(150\) 0 0
\(151\) 3.46410i 0.281905i 0.990016 + 0.140952i \(0.0450164\pi\)
−0.990016 + 0.140952i \(0.954984\pi\)
\(152\) −1.73205 + 3.00000i −0.140488 + 0.243332i
\(153\) 0 0
\(154\) 0 0
\(155\) −5.19615 −0.417365
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) −9.52628 + 5.50000i −0.757870 + 0.437557i
\(159\) 0 0
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 0 0
\(162\) 0 0
\(163\) 19.5000 + 11.2583i 1.52736 + 0.881820i 0.999472 + 0.0325054i \(0.0103486\pi\)
0.527886 + 0.849315i \(0.322985\pi\)
\(164\) 6.00000i 0.468521i
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 18.1865 10.5000i 1.40732 0.812514i 0.412188 0.911099i \(-0.364765\pi\)
0.995129 + 0.0985846i \(0.0314315\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.500000 0.866025i −0.0381246 0.0660338i
\(173\) −10.3923 + 18.0000i −0.790112 + 1.36851i 0.135785 + 0.990738i \(0.456644\pi\)
−0.925897 + 0.377776i \(0.876689\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.59808 1.50000i −0.195837 0.113067i
\(177\) 0 0
\(178\) 0 0
\(179\) 4.33013 + 7.50000i 0.323649 + 0.560576i 0.981238 0.192800i \(-0.0617570\pi\)
−0.657589 + 0.753377i \(0.728424\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 1.50000 0.866025i 0.110581 0.0638442i
\(185\) −0.866025 1.50000i −0.0636715 0.110282i
\(186\) 0 0
\(187\) 0 0
\(188\) −2.59808 1.50000i −0.189484 0.109399i
\(189\) 0 0
\(190\) 3.46410i 0.251312i
\(191\) 8.66025 15.0000i 0.626634 1.08536i −0.361588 0.932338i \(-0.617765\pi\)
0.988222 0.153024i \(-0.0489012\pi\)
\(192\) 0 0
\(193\) −9.00000 + 5.19615i −0.647834 + 0.374027i −0.787626 0.616154i \(-0.788690\pi\)
0.139792 + 0.990181i \(0.455357\pi\)
\(194\) −3.46410 −0.248708
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) −5.19615 + 3.00000i −0.370211 + 0.213741i −0.673550 0.739141i \(-0.735232\pi\)
0.303340 + 0.952882i \(0.401898\pi\)
\(198\) 0 0
\(199\) −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i \(0.358603\pi\)
−0.996850 + 0.0793045i \(0.974730\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 12.0000 + 6.92820i 0.844317 + 0.487467i
\(203\) 0 0
\(204\) 0 0
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) 12.1244 7.00000i 0.844744 0.487713i
\(207\) 0 0
\(208\) −2.50000 + 2.59808i −0.173344 + 0.180144i
\(209\) −10.3923 −0.718851
\(210\) 0 0
\(211\) 1.00000 + 1.73205i 0.0688428 + 0.119239i 0.898392 0.439194i \(-0.144736\pi\)
−0.829549 + 0.558433i \(0.811403\pi\)
\(212\) −3.46410 + 6.00000i −0.237915 + 0.412082i
\(213\) 0 0
\(214\) 6.00000 + 3.46410i 0.410152 + 0.236801i
\(215\) −0.866025 0.500000i −0.0590624 0.0340997i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −3.00000 −0.202260
\(221\) 0 0
\(222\) 0 0
\(223\) −15.0000 + 8.66025i −1.00447 + 0.579934i −0.909569 0.415553i \(-0.863588\pi\)
−0.0949052 + 0.995486i \(0.530255\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.1244i 0.806500i
\(227\) 15.5885 + 9.00000i 1.03464 + 0.597351i 0.918311 0.395860i \(-0.129553\pi\)
0.116331 + 0.993210i \(0.462887\pi\)
\(228\) 0 0
\(229\) 6.92820i 0.457829i 0.973447 + 0.228914i \(0.0735176\pi\)
−0.973447 + 0.228914i \(0.926482\pi\)
\(230\) 0.866025 1.50000i 0.0571040 0.0989071i
\(231\) 0 0
\(232\) 1.50000 0.866025i 0.0984798 0.0568574i
\(233\) −19.0526 −1.24817 −0.624087 0.781355i \(-0.714529\pi\)
−0.624087 + 0.781355i \(0.714529\pi\)
\(234\) 0 0
\(235\) −3.00000 −0.195698
\(236\) 7.79423 4.50000i 0.507361 0.292925i
\(237\) 0 0
\(238\) 0 0
\(239\) 6.00000i 0.388108i 0.980991 + 0.194054i \(0.0621637\pi\)
−0.980991 + 0.194054i \(0.937836\pi\)
\(240\) 0 0
\(241\) 13.5000 + 7.79423i 0.869611 + 0.502070i 0.867219 0.497927i \(-0.165905\pi\)
0.00239235 + 0.999997i \(0.499238\pi\)
\(242\) 2.00000i 0.128565i
\(243\) 0 0
\(244\) −4.00000 6.92820i −0.256074 0.443533i
\(245\) −6.06218 + 3.50000i −0.387298 + 0.223607i
\(246\) 0 0
\(247\) −3.00000 + 12.1244i −0.190885 + 0.771454i
\(248\) −5.19615 −0.329956
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 2.59808 4.50000i 0.163989 0.284037i −0.772307 0.635250i \(-0.780897\pi\)
0.936296 + 0.351212i \(0.114230\pi\)
\(252\) 0 0
\(253\) 4.50000 + 2.59808i 0.282913 + 0.163340i
\(254\) 1.73205 + 1.00000i 0.108679 + 0.0627456i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.33013 + 7.50000i 0.270106 + 0.467837i 0.968889 0.247497i \(-0.0796080\pi\)
−0.698783 + 0.715334i \(0.746275\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.866025 + 3.50000i −0.0537086 + 0.217061i
\(261\) 0 0
\(262\) 10.5000 6.06218i 0.648692 0.374523i
\(263\) −7.79423 13.5000i −0.480613 0.832446i 0.519140 0.854689i \(-0.326252\pi\)
−0.999753 + 0.0222436i \(0.992919\pi\)
\(264\) 0 0
\(265\) 6.92820i 0.425596i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.46410i 0.211604i
\(269\) 13.8564 24.0000i 0.844840 1.46331i −0.0409201 0.999162i \(-0.513029\pi\)
0.885760 0.464143i \(-0.153638\pi\)
\(270\) 0 0
\(271\) 10.5000 6.06218i 0.637830 0.368251i −0.145948 0.989292i \(-0.546623\pi\)
0.783778 + 0.621041i \(0.213290\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 3.00000 0.181237
\(275\) −2.59808 + 1.50000i −0.156670 + 0.0904534i
\(276\) 0 0
\(277\) −8.50000 + 14.7224i −0.510716 + 0.884585i 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) 10.0000i 0.599760i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000i 0.357930i −0.983855 0.178965i \(-0.942725\pi\)
0.983855 0.178965i \(-0.0572749\pi\)
\(282\) 0 0
\(283\) 2.50000 + 4.33013i 0.148610 + 0.257399i 0.930714 0.365748i \(-0.119187\pi\)
−0.782104 + 0.623148i \(0.785854\pi\)
\(284\) 5.19615 3.00000i 0.308335 0.178017i
\(285\) 0 0
\(286\) −10.5000 2.59808i −0.620878 0.153627i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0.866025 1.50000i 0.0508548 0.0880830i
\(291\) 0 0
\(292\) 0 0
\(293\) −15.5885 9.00000i −0.910687 0.525786i −0.0300351 0.999549i \(-0.509562\pi\)
−0.880652 + 0.473763i \(0.842895\pi\)
\(294\) 0 0
\(295\) 4.50000 7.79423i 0.262000 0.453798i
\(296\) −0.866025 1.50000i −0.0503367 0.0871857i
\(297\) 0 0
\(298\) 3.00000 0.173785
\(299\) 4.33013 4.50000i 0.250418 0.260242i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.73205 + 3.00000i 0.0996683 + 0.172631i
\(303\) 0 0
\(304\) 3.46410i 0.198680i
\(305\) −6.92820 4.00000i −0.396708 0.229039i
\(306\) 0 0
\(307\) 31.1769i 1.77936i 0.456584 + 0.889680i \(0.349073\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.50000 + 2.59808i −0.255583 + 0.147561i
\(311\) 24.2487 1.37502 0.687509 0.726176i \(-0.258704\pi\)
0.687509 + 0.726176i \(0.258704\pi\)
\(312\) 0 0
\(313\) −8.00000 −0.452187 −0.226093 0.974106i \(-0.572595\pi\)
−0.226093 + 0.974106i \(0.572595\pi\)
\(314\) −6.06218 + 3.50000i −0.342108 + 0.197516i
\(315\) 0 0
\(316\) −5.50000 + 9.52628i −0.309399 + 0.535895i
\(317\) 6.00000i 0.336994i −0.985702 0.168497i \(-0.946109\pi\)
0.985702 0.168497i \(-0.0538913\pi\)
\(318\) 0 0
\(319\) 4.50000 + 2.59808i 0.251952 + 0.145464i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 1.00000 + 3.46410i 0.0554700 + 0.192154i
\(326\) 22.5167 1.24708
\(327\) 0 0
\(328\) −3.00000 5.19615i −0.165647 0.286910i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 5.19615 + 3.00000i 0.285176 + 0.164646i
\(333\) 0 0
\(334\) 10.5000 18.1865i 0.574534 0.995123i
\(335\) 1.73205 + 3.00000i 0.0946320 + 0.163908i
\(336\) 0 0
\(337\) 4.00000 0.217894 0.108947 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) −6.06218 + 11.5000i −0.329739 + 0.625518i
\(339\) 0 0
\(340\) 0 0
\(341\) −7.79423 13.5000i −0.422081 0.731066i
\(342\) 0 0
\(343\) 0 0
\(344\) −0.866025 0.500000i −0.0466930 0.0269582i
\(345\) 0 0
\(346\) 20.7846i 1.11739i
\(347\) 8.66025 15.0000i 0.464907 0.805242i −0.534291 0.845301i \(-0.679421\pi\)
0.999197 + 0.0400587i \(0.0127545\pi\)
\(348\) 0 0
\(349\) −27.0000 + 15.5885i −1.44528 + 0.834431i −0.998195 0.0600619i \(-0.980870\pi\)
−0.447082 + 0.894493i \(0.647537\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.00000 −0.159901
\(353\) −15.5885 + 9.00000i −0.829690 + 0.479022i −0.853746 0.520689i \(-0.825675\pi\)
0.0240566 + 0.999711i \(0.492342\pi\)
\(354\) 0 0
\(355\) 3.00000 5.19615i 0.159223 0.275783i
\(356\) 0 0
\(357\) 0 0
\(358\) 7.50000 + 4.33013i 0.396387 + 0.228854i
\(359\) 24.0000i 1.26667i −0.773877 0.633336i \(-0.781685\pi\)
0.773877 0.633336i \(-0.218315\pi\)
\(360\) 0 0
\(361\) −3.50000 6.06218i −0.184211 0.319062i
\(362\) 17.3205 10.0000i 0.910346 0.525588i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −13.0000 22.5167i −0.678594 1.17536i −0.975404 0.220423i \(-0.929256\pi\)
0.296810 0.954937i \(-0.404077\pi\)
\(368\) 0.866025 1.50000i 0.0451447 0.0781929i
\(369\) 0 0
\(370\) −1.50000 0.866025i −0.0779813 0.0450225i
\(371\) 0 0
\(372\) 0 0
\(373\) 8.50000 14.7224i 0.440113 0.762299i −0.557584 0.830120i \(-0.688272\pi\)
0.997697 + 0.0678218i \(0.0216049\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) 4.33013 4.50000i 0.223013 0.231762i
\(378\) 0 0
\(379\) 12.0000 6.92820i 0.616399 0.355878i −0.159067 0.987268i \(-0.550849\pi\)
0.775466 + 0.631390i \(0.217515\pi\)
\(380\) 1.73205 + 3.00000i 0.0888523 + 0.153897i
\(381\) 0 0
\(382\) 17.3205i 0.886194i
\(383\) 7.79423 + 4.50000i 0.398266 + 0.229939i 0.685736 0.727851i \(-0.259481\pi\)
−0.287469 + 0.957790i \(0.592814\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −5.19615 + 9.00000i −0.264477 + 0.458088i
\(387\) 0 0
\(388\) −3.00000 + 1.73205i −0.152302 + 0.0879316i
\(389\) −29.4449 −1.49291 −0.746457 0.665434i \(-0.768247\pi\)
−0.746457 + 0.665434i \(0.768247\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −6.06218 + 3.50000i −0.306186 + 0.176777i
\(393\) 0 0
\(394\) −3.00000 + 5.19615i −0.151138 + 0.261778i
\(395\) 11.0000i 0.553470i
\(396\) 0 0
\(397\) 25.5000 + 14.7224i 1.27981 + 0.738898i 0.976813 0.214094i \(-0.0686800\pi\)
0.302995 + 0.952992i \(0.402013\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(402\) 0 0
\(403\) −18.0000 + 5.19615i −0.896644 + 0.258839i
\(404\) 13.8564 0.689382
\(405\) 0 0
\(406\) 0 0
\(407\) 2.59808 4.50000i 0.128782 0.223057i
\(408\) 0 0
\(409\) 30.0000 + 17.3205i 1.48340 + 0.856444i 0.999822 0.0188549i \(-0.00600205\pi\)
0.483582 + 0.875299i \(0.339335\pi\)
\(410\) −5.19615 3.00000i −0.256620 0.148159i
\(411\) 0 0
\(412\) 7.00000 12.1244i 0.344865 0.597324i
\(413\) 0 0
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) −0.866025 + 3.50000i −0.0424604 + 0.171602i
\(417\) 0 0
\(418\) −9.00000 + 5.19615i −0.440204 + 0.254152i
\(419\) 8.66025 + 15.0000i 0.423081 + 0.732798i 0.996239 0.0866469i \(-0.0276152\pi\)
−0.573158 + 0.819445i \(0.694282\pi\)
\(420\) 0 0
\(421\) 38.1051i 1.85713i −0.371170 0.928565i \(-0.621043\pi\)
0.371170 0.928565i \(-0.378957\pi\)
\(422\) 1.73205 + 1.00000i 0.0843149 + 0.0486792i
\(423\) 0 0
\(424\) 6.92820i 0.336463i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 6.92820 0.334887
\(429\) 0 0
\(430\) −1.00000 −0.0482243
\(431\) 15.5885 9.00000i 0.750870 0.433515i −0.0751385 0.997173i \(-0.523940\pi\)
0.826008 + 0.563658i \(0.190607\pi\)
\(432\) 0 0
\(433\) 7.00000 12.1244i 0.336399 0.582659i −0.647354 0.762190i \(-0.724124\pi\)
0.983752 + 0.179530i \(0.0574578\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000i 0.287019i
\(438\) 0 0
\(439\) −16.0000 27.7128i −0.763638 1.32266i −0.940963 0.338508i \(-0.890078\pi\)
0.177325 0.984152i \(-0.443256\pi\)
\(440\) −2.59808 + 1.50000i −0.123858 + 0.0715097i
\(441\) 0 0
\(442\) 0 0
\(443\) −31.1769 −1.48126 −0.740630 0.671913i \(-0.765473\pi\)
−0.740630 + 0.671913i \(0.765473\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −8.66025 + 15.0000i −0.410075 + 0.710271i
\(447\) 0 0
\(448\) 0 0
\(449\) −10.3923 6.00000i −0.490443 0.283158i 0.234315 0.972161i \(-0.424715\pi\)
−0.724758 + 0.689003i \(0.758049\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) 6.06218 + 10.5000i 0.285141 + 0.493878i
\(453\) 0 0
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) 0 0
\(457\) −21.0000 + 12.1244i −0.982339 + 0.567153i −0.902975 0.429692i \(-0.858622\pi\)
−0.0793632 + 0.996846i \(0.525289\pi\)
\(458\) 3.46410 + 6.00000i 0.161867 + 0.280362i
\(459\) 0 0
\(460\) 1.73205i 0.0807573i
\(461\) 18.1865 + 10.5000i 0.847031 + 0.489034i 0.859648 0.510887i \(-0.170683\pi\)
−0.0126168 + 0.999920i \(0.504016\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0.866025 1.50000i 0.0402042 0.0696358i
\(465\) 0 0
\(466\) −16.5000 + 9.52628i −0.764348 + 0.441296i
\(467\) −13.8564 −0.641198 −0.320599 0.947215i \(-0.603884\pi\)
−0.320599 + 0.947215i \(0.603884\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.59808 + 1.50000i −0.119840 + 0.0691898i
\(471\) 0 0
\(472\) 4.50000 7.79423i 0.207129 0.358758i
\(473\) 3.00000i 0.137940i
\(474\) 0 0
\(475\) 3.00000 + 1.73205i 0.137649 + 0.0794719i
\(476\) 0 0
\(477\) 0 0
\(478\) 3.00000 + 5.19615i 0.137217 + 0.237666i
\(479\) 5.19615 3.00000i 0.237418 0.137073i −0.376571 0.926388i \(-0.622897\pi\)
0.613990 + 0.789314i \(0.289564\pi\)
\(480\) 0 0
\(481\) −4.50000 4.33013i −0.205182 0.197437i
\(482\) 15.5885 0.710035
\(483\) 0 0
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) −1.73205 + 3.00000i −0.0786484 + 0.136223i
\(486\) 0 0
\(487\) −9.00000 5.19615i −0.407829 0.235460i 0.282028 0.959406i \(-0.408993\pi\)
−0.689856 + 0.723946i \(0.742326\pi\)
\(488\) −6.92820 4.00000i −0.313625 0.181071i
\(489\) 0 0
\(490\) −3.50000 + 6.06218i −0.158114 + 0.273861i
\(491\) 8.66025 + 15.0000i 0.390832 + 0.676941i 0.992559 0.121761i \(-0.0388541\pi\)
−0.601728 + 0.798701i \(0.705521\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 3.46410 + 12.0000i 0.155857 + 0.539906i
\(495\) 0 0
\(496\) −4.50000 + 2.59808i −0.202056 + 0.116657i
\(497\) 0 0
\(498\) 0 0
\(499\) 17.3205i 0.775372i −0.921791 0.387686i \(-0.873274\pi\)
0.921791 0.387686i \(-0.126726\pi\)
\(500\) 0.866025 + 0.500000i 0.0387298 + 0.0223607i
\(501\) 0 0
\(502\) 5.19615i 0.231916i
\(503\) 1.73205 3.00000i 0.0772283 0.133763i −0.824825 0.565388i \(-0.808726\pi\)
0.902053 + 0.431625i \(0.142060\pi\)
\(504\) 0 0
\(505\) 12.0000 6.92820i 0.533993 0.308301i
\(506\) 5.19615 0.230997
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) −18.1865 + 10.5000i −0.806104 + 0.465404i −0.845601 0.533815i \(-0.820758\pi\)
0.0394971 + 0.999220i \(0.487424\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 7.50000 + 4.33013i 0.330811 + 0.190994i
\(515\) 14.0000i 0.616914i
\(516\) 0 0
\(517\) −4.50000 7.79423i −0.197910 0.342790i
\(518\) 0 0
\(519\) 0 0
\(520\) 1.00000 + 3.46410i 0.0438529 + 0.151911i
\(521\) −38.1051 −1.66942 −0.834708 0.550693i \(-0.814363\pi\)
−0.834708 + 0.550693i \(0.814363\pi\)
\(522\) 0 0
\(523\) −8.50000 14.7224i −0.371679 0.643767i 0.618145 0.786064i \(-0.287884\pi\)
−0.989824 + 0.142297i \(0.954551\pi\)
\(524\) 6.06218 10.5000i 0.264827 0.458695i
\(525\) 0 0
\(526\) −13.5000 7.79423i −0.588628 0.339845i
\(527\) 0 0
\(528\) 0 0
\(529\) 10.0000 17.3205i 0.434783 0.753066i
\(530\) 3.46410 + 6.00000i 0.150471 + 0.260623i
\(531\) 0 0
\(532\) 0 0
\(533\) −15.5885 15.0000i −0.675211 0.649722i
\(534\) 0 0
\(535\) 6.00000 3.46410i 0.259403 0.149766i
\(536\) 1.73205 + 3.00000i 0.0748132 + 0.129580i
\(537\) 0 0
\(538\) 27.7128i 1.19478i
\(539\) −18.1865 10.5000i −0.783349 0.452267i
\(540\) 0 0
\(541\) 13.8564i 0.595733i −0.954607 0.297867i \(-0.903725\pi\)
0.954607 0.297867i \(-0.0962751\pi\)
\(542\) 6.06218 10.5000i 0.260393 0.451014i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 2.59808 1.50000i 0.110984 0.0640768i
\(549\) 0 0
\(550\) −1.50000 + 2.59808i −0.0639602 + 0.110782i
\(551\) 6.00000i 0.255609i
\(552\) 0 0
\(553\) 0 0
\(554\) 17.0000i 0.722261i
\(555\) 0 0
\(556\) −5.00000 8.66025i −0.212047 0.367277i
\(557\) −25.9808 + 15.0000i −1.10084 + 0.635570i −0.936442 0.350824i \(-0.885902\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(558\) 0 0
\(559\) −3.50000 0.866025i −0.148034 0.0366290i
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) −8.66025 + 15.0000i −0.364986 + 0.632175i −0.988774 0.149419i \(-0.952260\pi\)
0.623788 + 0.781594i \(0.285593\pi\)
\(564\) 0 0
\(565\) 10.5000 + 6.06218i 0.441738 + 0.255038i
\(566\) 4.33013 + 2.50000i 0.182009 + 0.105083i
\(567\) 0 0
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) 12.1244 + 21.0000i 0.508279 + 0.880366i 0.999954 + 0.00958679i \(0.00305162\pi\)
−0.491675 + 0.870779i \(0.663615\pi\)
\(570\) 0 0
\(571\) −2.00000 −0.0836974 −0.0418487 0.999124i \(-0.513325\pi\)
−0.0418487 + 0.999124i \(0.513325\pi\)
\(572\) −10.3923 + 3.00000i −0.434524 + 0.125436i
\(573\) 0 0
\(574\) 0 0
\(575\) −0.866025 1.50000i −0.0361158 0.0625543i
\(576\) 0 0
\(577\) 6.92820i 0.288425i −0.989547 0.144212i \(-0.953935\pi\)
0.989547 0.144212i \(-0.0460649\pi\)
\(578\) 14.7224 + 8.50000i 0.612372 + 0.353553i
\(579\) 0 0
\(580\) 1.73205i 0.0719195i
\(581\) 0 0
\(582\) 0 0
\(583\) −18.0000 + 10.3923i −0.745484 + 0.430405i
\(584\) 0 0
\(585\) 0 0
\(586\) −18.0000 −0.743573
\(587\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(588\) 0 0
\(589\) −9.00000 + 15.5885i −0.370839 + 0.642311i
\(590\) 9.00000i 0.370524i
\(591\) 0 0
\(592\) −1.50000 0.866025i −0.0616496 0.0355934i
\(593\) 3.00000i 0.123195i 0.998101 + 0.0615976i \(0.0196196\pi\)
−0.998101 + 0.0615976i \(0.980380\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.59808 1.50000i 0.106421 0.0614424i
\(597\) 0 0
\(598\) 1.50000 6.06218i 0.0613396 0.247901i
\(599\) 17.3205 0.707697 0.353848 0.935303i \(-0.384873\pi\)
0.353848 + 0.935303i \(0.384873\pi\)
\(600\) 0 0
\(601\) −18.5000 32.0429i −0.754631 1.30706i −0.945558 0.325455i \(-0.894483\pi\)
0.190927 0.981604i \(-0.438851\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3.00000 + 1.73205i 0.122068 + 0.0704761i
\(605\) 1.73205 + 1.00000i 0.0704179 + 0.0406558i
\(606\) 0 0
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) 1.73205 + 3.00000i 0.0702439 + 0.121666i
\(609\) 0 0
\(610\) −8.00000 −0.323911
\(611\) −10.3923 + 3.00000i −0.420428 + 0.121367i
\(612\) 0 0
\(613\) −13.5000 + 7.79423i −0.545260 + 0.314806i −0.747208 0.664590i \(-0.768606\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) 15.5885 + 27.0000i 0.629099 + 1.08963i
\(615\) 0 0
\(616\) 0 0
\(617\) 2.59808 + 1.50000i 0.104595 + 0.0603877i 0.551385 0.834251i \(-0.314100\pi\)
−0.446790 + 0.894639i \(0.647433\pi\)
\(618\) 0 0
\(619\) 10.3923i 0.417702i −0.977947 0.208851i \(-0.933028\pi\)
0.977947 0.208851i \(-0.0669724\pi\)
\(620\) −2.59808 + 4.50000i −0.104341 + 0.180724i
\(621\) 0 0
\(622\) 21.0000 12.1244i 0.842023 0.486142i
\(623\) 0 0
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −6.92820 + 4.00000i −0.276907 + 0.159872i
\(627\) 0 0
\(628\) −3.50000 + 6.06218i −0.139665 + 0.241907i
\(629\) 0 0
\(630\) 0 0
\(631\) 33.0000 + 19.0526i 1.31371 + 0.758470i 0.982708 0.185160i \(-0.0592804\pi\)
0.331001 + 0.943630i \(0.392614\pi\)
\(632\) 11.0000i 0.437557i
\(633\) 0 0
\(634\) −3.00000 5.19615i −0.119145 0.206366i
\(635\) 1.73205 1.00000i 0.0687343 0.0396838i
\(636\) 0 0
\(637\) −17.5000 + 18.1865i −0.693375 + 0.720577i
\(638\) 5.19615 0.205718
\(639\) 0 0
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 3.46410 6.00000i 0.136824 0.236986i −0.789469 0.613791i \(-0.789644\pi\)
0.926293 + 0.376805i \(0.122977\pi\)
\(642\) 0 0
\(643\) 3.00000 + 1.73205i 0.118308 + 0.0683054i 0.557986 0.829850i \(-0.311574\pi\)
−0.439678 + 0.898155i \(0.644907\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.19615 + 9.00000i 0.204282 + 0.353827i 0.949904 0.312543i \(-0.101181\pi\)
−0.745622 + 0.666369i \(0.767847\pi\)
\(648\) 0 0
\(649\) 27.0000 1.05984
\(650\) 2.59808 + 2.50000i 0.101905 + 0.0980581i
\(651\) 0 0
\(652\) 19.5000 11.2583i 0.763679 0.440910i
\(653\) −5.19615 9.00000i −0.203341 0.352197i 0.746262 0.665653i \(-0.231847\pi\)
−0.949603 + 0.313455i \(0.898513\pi\)
\(654\) 0 0
\(655\) 12.1244i 0.473738i
\(656\) −5.19615 3.00000i −0.202876 0.117130i
\(657\) 0 0
\(658\) 0 0
\(659\) 6.06218 10.5000i 0.236149 0.409022i −0.723457 0.690369i \(-0.757448\pi\)
0.959606 + 0.281347i \(0.0907813\pi\)
\(660\) 0 0
\(661\) −33.0000 + 19.0526i −1.28355 + 0.741059i −0.977496 0.210955i \(-0.932343\pi\)
−0.306055 + 0.952014i \(0.599009\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) −1.50000 + 2.59808i −0.0580802 + 0.100598i
\(668\) 21.0000i 0.812514i
\(669\) 0 0
\(670\) 3.00000 + 1.73205i 0.115900 + 0.0669150i
\(671\) 24.0000i 0.926510i
\(672\) 0 0
\(673\) −22.0000 38.1051i −0.848038 1.46884i −0.882957 0.469454i \(-0.844451\pi\)
0.0349191 0.999390i \(-0.488883\pi\)
\(674\) 3.46410 2.00000i 0.133432 0.0770371i
\(675\) 0 0
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) −45.0333 −1.73077 −0.865386 0.501107i \(-0.832926\pi\)
−0.865386 + 0.501107i \(0.832926\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) −13.5000 7.79423i −0.516942 0.298456i
\(683\) 31.1769 + 18.0000i 1.19295 + 0.688751i 0.958975 0.283491i \(-0.0914927\pi\)
0.233977 + 0.972242i \(0.424826\pi\)
\(684\) 0 0
\(685\) 1.50000 2.59808i 0.0573121 0.0992674i
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) 6.92820 + 24.0000i 0.263944 + 0.914327i
\(690\) 0 0
\(691\) 21.0000 12.1244i 0.798878 0.461232i −0.0442009 0.999023i \(-0.514074\pi\)
0.843079 + 0.537790i \(0.180741\pi\)
\(692\) 10.3923 + 18.0000i 0.395056 + 0.684257i
\(693\) 0 0
\(694\) 17.3205i 0.657477i
\(695\) −8.66025 5.00000i −0.328502 0.189661i
\(696\) 0 0
\(697\) 0 0
\(698\) −15.5885 + 27.0000i −0.590032 + 1.02197i
\(699\) 0 0
\(700\) 0 0
\(701\) 22.5167 0.850443 0.425221 0.905089i \(-0.360196\pi\)
0.425221 + 0.905089i \(0.360196\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) −2.59808 + 1.50000i −0.0979187 + 0.0565334i
\(705\) 0 0
\(706\) −9.00000 + 15.5885i −0.338719 + 0.586679i
\(707\) 0 0
\(708\) 0 0
\(709\) 18.0000 + 10.3923i 0.676004 + 0.390291i 0.798348 0.602197i \(-0.205708\pi\)
−0.122344 + 0.992488i \(0.539041\pi\)
\(710\) 6.00000i 0.225176i
\(711\) 0 0
\(712\) 0 0
\(713\) 7.79423 4.50000i 0.291896 0.168526i
\(714\) 0 0
\(715\) −7.50000 + 7.79423i −0.280484 + 0.291488i
\(716\) 8.66025 0.323649
\(717\) 0 0
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) 13.8564 24.0000i 0.516757 0.895049i −0.483054 0.875591i \(-0.660472\pi\)
0.999811 0.0194584i \(-0.00619418\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −6.06218 3.50000i −0.225611 0.130257i
\(723\) 0 0
\(724\) 10.0000 17.3205i 0.371647 0.643712i
\(725\) −0.866025 1.50000i −0.0321634 0.0557086i
\(726\) 0 0
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 27.7128i 1.02360i −0.859106 0.511798i \(-0.828980\pi\)
0.859106 0.511798i \(-0.171020\pi\)
\(734\) −22.5167 13.0000i −0.831105 0.479839i
\(735\) 0 0
\(736\) 1.73205i 0.0638442i
\(737\) −5.19615 + 9.00000i −0.191403 + 0.331519i
\(738\) 0 0
\(739\) −9.00000 + 5.19615i −0.331070 + 0.191144i −0.656316 0.754486i \(-0.727886\pi\)
0.325246 + 0.945629i \(0.394553\pi\)
\(740\) −1.73205 −0.0636715
\(741\) 0 0
\(742\) 0 0
\(743\) 38.9711 22.5000i 1.42971 0.825445i 0.432615 0.901579i \(-0.357591\pi\)
0.997098 + 0.0761338i \(0.0242576\pi\)
\(744\) 0 0
\(745\) 1.50000 2.59808i 0.0549557 0.0951861i
\(746\) 17.0000i 0.622414i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.50000 4.33013i −0.0912263 0.158009i 0.816801 0.576919i \(-0.195745\pi\)
−0.908027 + 0.418911i \(0.862412\pi\)
\(752\) −2.59808 + 1.50000i −0.0947421 + 0.0546994i
\(753\) 0 0
\(754\) 1.50000 6.06218i 0.0546268 0.220771i
\(755\) 3.46410 0.126072
\(756\) 0 0
\(757\) −23.0000 39.8372i −0.835949 1.44791i −0.893255 0.449550i \(-0.851584\pi\)
0.0573060 0.998357i \(-0.481749\pi\)
\(758\) 6.92820 12.0000i 0.251644 0.435860i
\(759\) 0 0
\(760\) 3.00000 + 1.73205i 0.108821 + 0.0628281i
\(761\) −31.1769 18.0000i −1.13016 0.652499i −0.186187 0.982514i \(-0.559613\pi\)
−0.943976 + 0.330015i \(0.892946\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −8.66025 15.0000i −0.313317 0.542681i
\(765\) 0 0
\(766\) 9.00000 0.325183
\(767\) 7.79423 31.5000i 0.281433 1.13740i
\(768\) 0 0
\(769\) −13.5000 + 7.79423i −0.486822 + 0.281067i −0.723255 0.690581i \(-0.757355\pi\)
0.236433 + 0.971648i \(0.424022\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.3923i 0.374027i
\(773\) 20.7846 + 12.0000i 0.747570 + 0.431610i 0.824815 0.565402i \(-0.191279\pi\)
−0.0772449 + 0.997012i \(0.524612\pi\)
\(774\) 0 0
\(775\) 5.19615i 0.186651i
\(776\) −1.73205 + 3.00000i −0.0621770 + 0.107694i
\(777\) 0 0
\(778\) −25.5000 + 14.7224i −0.914219 + 0.527825i
\(779\) −20.7846 −0.744686
\(780\) 0 0
\(781\) 18.0000 0.644091
\(782\) 0 0
\(783\) 0 0
\(784\) −3.50000 + 6.06218i −0.125000 + 0.216506i
\(785\) 7.00000i 0.249841i
\(786\) 0 0
\(787\) 28.5000 + 16.4545i 1.01592 + 0.586539i 0.912918 0.408143i \(-0.133823\pi\)
0.102997 + 0.994682i \(0.467157\pi\)
\(788\) 6.00000i 0.213741i
\(789\) 0 0
\(790\) 5.50000 + 9.52628i 0.195681 + 0.338930i
\(791\) 0 0
\(792\) 0 0
\(793\) −28.0000 6.92820i −0.994309 0.246028i
\(794\) 29.4449 1.04496
\(795\) 0 0