Properties

Label 1710.2.l.i.1261.1
Level $1710$
Weight $2$
Character 1710.1261
Analytic conductor $13.654$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.6544187456\)
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 570)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1261.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1261
Dual form 1710.2.l.i.1531.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -1.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(1.50000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 4.33013i) q^{19} +1.00000 q^{20} +(-0.500000 - 0.866025i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{25} -2.00000 q^{26} +(-1.50000 + 2.59808i) q^{28} +4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(-1.50000 - 2.59808i) q^{35} +9.00000 q^{37} +(-3.50000 + 2.59808i) q^{38} +(0.500000 + 0.866025i) q^{40} +(0.500000 + 0.866025i) q^{41} +(5.00000 + 8.66025i) q^{43} +(0.500000 - 0.866025i) q^{44} +1.00000 q^{46} +2.00000 q^{49} -1.00000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{55} -3.00000 q^{56} +(6.00000 + 10.3923i) q^{59} +(1.00000 - 1.73205i) q^{61} +(2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +2.00000 q^{65} +(1.00000 - 1.73205i) q^{67} -2.00000 q^{68} +(1.50000 - 2.59808i) q^{70} +(4.00000 + 6.92820i) q^{71} +(6.00000 + 10.3923i) q^{73} +(4.50000 + 7.79423i) q^{74} +(-4.00000 - 1.73205i) q^{76} -3.00000 q^{77} +(-7.00000 - 12.1244i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{82} -6.00000 q^{83} +(1.00000 - 1.73205i) q^{85} +(-5.00000 + 8.66025i) q^{86} +1.00000 q^{88} +(-2.50000 + 4.33013i) q^{89} +(-3.00000 + 5.19615i) q^{91} +(0.500000 + 0.866025i) q^{92} +(3.50000 - 2.59808i) q^{95} +(-4.00000 - 6.92820i) q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - q^{5} + 6q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - q^{5} + 6q^{7} - 2q^{8} + q^{10} - 2q^{11} - 2q^{13} + 3q^{14} - q^{16} + 2q^{17} + q^{19} + 2q^{20} - q^{22} + q^{23} - q^{25} - 4q^{26} - 3q^{28} + 8q^{31} + q^{32} - 2q^{34} - 3q^{35} + 18q^{37} - 7q^{38} + q^{40} + q^{41} + 10q^{43} + q^{44} + 2q^{46} + 4q^{49} - 2q^{50} - 2q^{52} + 3q^{53} + q^{55} - 6q^{56} + 12q^{59} + 2q^{61} + 4q^{62} + 2q^{64} + 4q^{65} + 2q^{67} - 4q^{68} + 3q^{70} + 8q^{71} + 12q^{73} + 9q^{74} - 8q^{76} - 6q^{77} - 14q^{79} - q^{80} - q^{82} - 12q^{83} + 2q^{85} - 10q^{86} + 2q^{88} - 5q^{89} - 6q^{91} + q^{92} + 7q^{95} - 8q^{97} + 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 1.50000 + 2.59808i 0.400892 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) 0.500000 + 4.33013i 0.114708 + 0.993399i
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −0.500000 0.866025i −0.106600 0.184637i
\(23\) 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
\(26\) −2.00000 −0.392232
\(27\) 0 0
\(28\) −1.50000 + 2.59808i −0.283473 + 0.490990i
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.00000 + 1.73205i −0.171499 + 0.297044i
\(35\) −1.50000 2.59808i −0.253546 0.439155i
\(36\) 0 0
\(37\) 9.00000 1.47959 0.739795 0.672832i \(-0.234922\pi\)
0.739795 + 0.672832i \(0.234922\pi\)
\(38\) −3.50000 + 2.59808i −0.567775 + 0.421464i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 0.500000 + 0.866025i 0.0780869 + 0.135250i 0.902424 0.430848i \(-0.141786\pi\)
−0.824338 + 0.566099i \(0.808452\pi\)
\(42\) 0 0
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0 0
\(55\) 0.500000 + 0.866025i 0.0674200 + 0.116775i
\(56\) −3.00000 −0.400892
\(57\) 0 0
\(58\) 0 0
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 2.00000 + 3.46410i 0.254000 + 0.439941i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0 0
\(70\) 1.50000 2.59808i 0.179284 0.310530i
\(71\) 4.00000 + 6.92820i 0.474713 + 0.822226i 0.999581 0.0289572i \(-0.00921865\pi\)
−0.524868 + 0.851184i \(0.675885\pi\)
\(72\) 0 0
\(73\) 6.00000 + 10.3923i 0.702247 + 1.21633i 0.967676 + 0.252197i \(0.0811531\pi\)
−0.265429 + 0.964130i \(0.585514\pi\)
\(74\) 4.50000 + 7.79423i 0.523114 + 0.906061i
\(75\) 0 0
\(76\) −4.00000 1.73205i −0.458831 0.198680i
\(77\) −3.00000 −0.341882
\(78\) 0 0
\(79\) −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i \(-0.878010\pi\)
0.139895 0.990166i \(-0.455323\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) −0.500000 + 0.866025i −0.0552158 + 0.0956365i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 1.00000 1.73205i 0.108465 0.187867i
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) 0 0
\(88\) 1.00000 0.106600
\(89\) −2.50000 + 4.33013i −0.264999 + 0.458993i −0.967563 0.252628i \(-0.918705\pi\)
0.702564 + 0.711621i \(0.252038\pi\)
\(90\) 0 0
\(91\) −3.00000 + 5.19615i −0.314485 + 0.544705i
\(92\) 0.500000 + 0.866025i 0.0521286 + 0.0902894i
\(93\) 0 0
\(94\) 0 0
\(95\) 3.50000 2.59808i 0.359092 0.266557i
\(96\) 0 0
\(97\) −4.00000 6.92820i −0.406138 0.703452i 0.588315 0.808632i \(-0.299792\pi\)
−0.994453 + 0.105180i \(0.966458\pi\)
\(98\) 1.00000 + 1.73205i 0.101015 + 0.174964i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i \(-0.865059\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 0 0
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 1.00000 1.73205i 0.0980581 0.169842i
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) 10.0000 0.966736 0.483368 0.875417i \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 0 0
\(109\) 3.00000 + 5.19615i 0.287348 + 0.497701i 0.973176 0.230063i \(-0.0738931\pi\)
−0.685828 + 0.727764i \(0.740560\pi\)
\(110\) −0.500000 + 0.866025i −0.0476731 + 0.0825723i
\(111\) 0 0
\(112\) −1.50000 2.59808i −0.141737 0.245495i
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) 0 0
\(117\) 0 0
\(118\) −6.00000 + 10.3923i −0.552345 + 0.956689i
\(119\) 3.00000 + 5.19615i 0.275010 + 0.476331i
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 2.00000 0.181071
\(123\) 0 0
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 0.500000 0.866025i 0.0443678 0.0768473i −0.842989 0.537931i \(-0.819206\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 1.00000 + 1.73205i 0.0877058 + 0.151911i
\(131\) 10.5000 + 18.1865i 0.917389 + 1.58896i 0.803365 + 0.595487i \(0.203041\pi\)
0.114024 + 0.993478i \(0.463626\pi\)
\(132\) 0 0
\(133\) 1.50000 + 12.9904i 0.130066 + 1.12641i
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) 2.00000 3.46410i 0.170872 0.295958i −0.767853 0.640626i \(-0.778675\pi\)
0.938725 + 0.344668i \(0.112008\pi\)
\(138\) 0 0
\(139\) 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i \(-0.511026\pi\)
0.882823 0.469706i \(-0.155640\pi\)
\(140\) 3.00000 0.253546
\(141\) 0 0
\(142\) −4.00000 + 6.92820i −0.335673 + 0.581402i
\(143\) 1.00000 1.73205i 0.0836242 0.144841i
\(144\) 0 0
\(145\) 0 0
\(146\) −6.00000 + 10.3923i −0.496564 + 0.860073i
\(147\) 0 0
\(148\) −4.50000 + 7.79423i −0.369898 + 0.640682i
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −18.0000 −1.46482 −0.732410 0.680864i \(-0.761604\pi\)
−0.732410 + 0.680864i \(0.761604\pi\)
\(152\) −0.500000 4.33013i −0.0405554 0.351220i
\(153\) 0 0
\(154\) −1.50000 2.59808i −0.120873 0.209359i
\(155\) −2.00000 3.46410i −0.160644 0.278243i
\(156\) 0 0
\(157\) −3.50000 6.06218i −0.279330 0.483814i 0.691888 0.722005i \(-0.256779\pi\)
−0.971219 + 0.238190i \(0.923446\pi\)
\(158\) 7.00000 12.1244i 0.556890 0.964562i
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 1.50000 2.59808i 0.118217 0.204757i
\(162\) 0 0
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 0 0
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 1.50000 2.59808i 0.116073 0.201045i −0.802135 0.597143i \(-0.796303\pi\)
0.918208 + 0.396098i \(0.129636\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 2.00000 0.153393
\(171\) 0 0
\(172\) −10.0000 −0.762493
\(173\) 5.50000 + 9.52628i 0.418157 + 0.724270i 0.995754 0.0920525i \(-0.0293428\pi\)
−0.577597 + 0.816322i \(0.696009\pi\)
\(174\) 0 0
\(175\) −1.50000 + 2.59808i −0.113389 + 0.196396i
\(176\) 0.500000 + 0.866025i 0.0376889 + 0.0652791i
\(177\) 0 0
\(178\) −5.00000 −0.374766
\(179\) 13.0000 0.971666 0.485833 0.874052i \(-0.338516\pi\)
0.485833 + 0.874052i \(0.338516\pi\)
\(180\) 0 0
\(181\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(182\) −6.00000 −0.444750
\(183\) 0 0
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) −4.50000 7.79423i −0.330847 0.573043i
\(186\) 0 0
\(187\) −1.00000 1.73205i −0.0731272 0.126660i
\(188\) 0 0
\(189\) 0 0
\(190\) 4.00000 + 1.73205i 0.290191 + 0.125656i
\(191\) 10.0000 0.723575 0.361787 0.932261i \(-0.382167\pi\)
0.361787 + 0.932261i \(0.382167\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 4.00000 6.92820i 0.287183 0.497416i
\(195\) 0 0
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) −5.00000 −0.356235 −0.178118 0.984009i \(-0.557001\pi\)
−0.178118 + 0.984009i \(0.557001\pi\)
\(198\) 0 0
\(199\) 9.00000 15.5885i 0.637993 1.10504i −0.347879 0.937539i \(-0.613098\pi\)
0.985873 0.167497i \(-0.0535685\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 0 0
\(202\) −2.00000 −0.140720
\(203\) 0 0
\(204\) 0 0
\(205\) 0.500000 0.866025i 0.0349215 0.0604858i
\(206\) −6.50000 11.2583i −0.452876 0.784405i
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) −0.500000 4.33013i −0.0345857 0.299521i
\(210\) 0 0
\(211\) −11.5000 19.9186i −0.791693 1.37125i −0.924918 0.380166i \(-0.875867\pi\)
0.133226 0.991086i \(-0.457467\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) 0 0
\(214\) 5.00000 + 8.66025i 0.341793 + 0.592003i
\(215\) 5.00000 8.66025i 0.340997 0.590624i
\(216\) 0 0
\(217\) 12.0000 0.814613
\(218\) −3.00000 + 5.19615i −0.203186 + 0.351928i
\(219\) 0 0
\(220\) −1.00000 −0.0674200
\(221\) −4.00000 −0.269069
\(222\) 0 0
\(223\) −1.50000 2.59808i −0.100447 0.173980i 0.811422 0.584461i \(-0.198694\pi\)
−0.911869 + 0.410481i \(0.865361\pi\)
\(224\) 1.50000 2.59808i 0.100223 0.173591i
\(225\) 0 0
\(226\) −5.00000 8.66025i −0.332595 0.576072i
\(227\) −28.0000 −1.85843 −0.929213 0.369546i \(-0.879513\pi\)
−0.929213 + 0.369546i \(0.879513\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) −0.500000 0.866025i −0.0329690 0.0571040i
\(231\) 0 0
\(232\) 0 0
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −12.0000 −0.781133
\(237\) 0 0
\(238\) −3.00000 + 5.19615i −0.194461 + 0.336817i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) −5.00000 8.66025i −0.321412 0.556702i
\(243\) 0 0
\(244\) 1.00000 + 1.73205i 0.0640184 + 0.110883i
\(245\) −1.00000 1.73205i −0.0638877 0.110657i
\(246\) 0 0
\(247\) −8.00000 3.46410i −0.509028 0.220416i
\(248\) −4.00000 −0.254000
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 14.0000 24.2487i 0.883672 1.53057i 0.0364441 0.999336i \(-0.488397\pi\)
0.847228 0.531229i \(-0.178270\pi\)
\(252\) 0 0
\(253\) −0.500000 + 0.866025i −0.0314347 + 0.0544466i
\(254\) 1.00000 0.0627456
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.00000 1.73205i 0.0623783 0.108042i −0.833150 0.553047i \(-0.813465\pi\)
0.895528 + 0.445005i \(0.146798\pi\)
\(258\) 0 0
\(259\) 27.0000 1.67770
\(260\) −1.00000 + 1.73205i −0.0620174 + 0.107417i
\(261\) 0 0
\(262\) −10.5000 + 18.1865i −0.648692 + 1.12357i
\(263\) −12.5000 21.6506i −0.770783 1.33504i −0.937134 0.348969i \(-0.886532\pi\)
0.166351 0.986067i \(-0.446801\pi\)
\(264\) 0 0
\(265\) −3.00000 −0.184289
\(266\) −10.5000 + 7.79423i −0.643796 + 0.477895i
\(267\) 0 0
\(268\) 1.00000 + 1.73205i 0.0610847 + 0.105802i
\(269\) −7.00000 12.1244i −0.426798 0.739235i 0.569789 0.821791i \(-0.307025\pi\)
−0.996586 + 0.0825561i \(0.973692\pi\)
\(270\) 0 0
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) 1.00000 1.73205i 0.0606339 0.105021i
\(273\) 0 0
\(274\) 4.00000 0.241649
\(275\) 0.500000 0.866025i 0.0301511 0.0522233i
\(276\) 0 0
\(277\) 22.0000 1.32185 0.660926 0.750451i \(-0.270164\pi\)
0.660926 + 0.750451i \(0.270164\pi\)
\(278\) 20.0000 1.19952
\(279\) 0 0
\(280\) 1.50000 + 2.59808i 0.0896421 + 0.155265i
\(281\) −10.5000 + 18.1865i −0.626377 + 1.08492i 0.361895 + 0.932219i \(0.382130\pi\)
−0.988273 + 0.152699i \(0.951204\pi\)
\(282\) 0 0
\(283\) −1.00000 1.73205i −0.0594438 0.102960i 0.834772 0.550596i \(-0.185599\pi\)
−0.894216 + 0.447636i \(0.852266\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) 1.50000 + 2.59808i 0.0885422 + 0.153360i
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) 0 0
\(292\) −12.0000 −0.702247
\(293\) −1.00000 −0.0584206 −0.0292103 0.999573i \(-0.509299\pi\)
−0.0292103 + 0.999573i \(0.509299\pi\)
\(294\) 0 0
\(295\) 6.00000 10.3923i 0.349334 0.605063i
\(296\) −9.00000 −0.523114
\(297\) 0 0
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 1.00000 + 1.73205i 0.0578315 + 0.100167i
\(300\) 0 0
\(301\) 15.0000 + 25.9808i 0.864586 + 1.49751i
\(302\) −9.00000 15.5885i −0.517892 0.897015i
\(303\) 0 0
\(304\) 3.50000 2.59808i 0.200739 0.149010i
\(305\) −2.00000 −0.114520
\(306\) 0 0
\(307\) −8.00000 13.8564i −0.456584 0.790827i 0.542194 0.840254i \(-0.317594\pi\)
−0.998778 + 0.0494267i \(0.984261\pi\)
\(308\) 1.50000 2.59808i 0.0854704 0.148039i
\(309\) 0 0
\(310\) 2.00000 3.46410i 0.113592 0.196748i
\(311\) 16.0000 0.907277 0.453638 0.891186i \(-0.350126\pi\)
0.453638 + 0.891186i \(0.350126\pi\)
\(312\) 0 0
\(313\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(314\) 3.50000 6.06218i 0.197516 0.342108i
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) 3.50000 6.06218i 0.196580 0.340486i −0.750838 0.660487i \(-0.770350\pi\)
0.947417 + 0.320001i \(0.103683\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 0 0
\(322\) 3.00000 0.167183
\(323\) −7.00000 + 5.19615i −0.389490 + 0.289122i
\(324\) 0 0
\(325\) −1.00000 1.73205i −0.0554700 0.0960769i
\(326\) 1.00000 + 1.73205i 0.0553849 + 0.0959294i
\(327\) 0 0
\(328\) −0.500000 0.866025i −0.0276079 0.0478183i
\(329\) 0 0
\(330\) 0 0
\(331\) 13.0000 0.714545 0.357272 0.934000i \(-0.383707\pi\)
0.357272 + 0.934000i \(0.383707\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) 0 0
\(334\) 3.00000 0.164153
\(335\) −2.00000 −0.109272
\(336\) 0 0
\(337\) −1.00000 1.73205i −0.0544735 0.0943508i 0.837503 0.546433i \(-0.184015\pi\)
−0.891976 + 0.452082i \(0.850681\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) 0 0
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) −4.00000 −0.216612
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) −5.00000 8.66025i −0.269582 0.466930i
\(345\) 0 0
\(346\) −5.50000 + 9.52628i −0.295682 + 0.512136i
\(347\) 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i \(-0.00616095\pi\)
−0.516667 + 0.856186i \(0.672828\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) −3.00000 −0.160357
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −26.0000 −1.38384 −0.691920 0.721974i \(-0.743235\pi\)
−0.691920 + 0.721974i \(0.743235\pi\)
\(354\) 0 0
\(355\) 4.00000 6.92820i 0.212298 0.367711i
\(356\) −2.50000 4.33013i −0.132500 0.229496i
\(357\) 0 0
\(358\) 6.50000 + 11.2583i 0.343536 + 0.595021i
\(359\) 6.00000 + 10.3923i 0.316668 + 0.548485i 0.979791 0.200026i \(-0.0641026\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(360\) 0 0
\(361\) −18.5000 + 4.33013i −0.973684 + 0.227901i
\(362\) 0 0
\(363\) 0 0
\(364\) −3.00000 5.19615i −0.157243 0.272352i
\(365\) 6.00000 10.3923i 0.314054 0.543958i
\(366\) 0 0
\(367\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 0 0
\(370\) 4.50000 7.79423i 0.233944 0.405203i
\(371\) 4.50000 7.79423i 0.233628 0.404656i
\(372\) 0 0
\(373\) −37.0000 −1.91579 −0.957894 0.287123i \(-0.907301\pi\)
−0.957894 + 0.287123i \(0.907301\pi\)
\(374\) 1.00000 1.73205i 0.0517088 0.0895622i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 0.500000 + 4.33013i 0.0256495 + 0.222131i
\(381\) 0 0
\(382\) 5.00000 + 8.66025i 0.255822 + 0.443097i
\(383\) −12.0000 20.7846i −0.613171 1.06204i −0.990702 0.136047i \(-0.956560\pi\)
0.377531 0.925997i \(-0.376773\pi\)
\(384\) 0 0
\(385\) 1.50000 + 2.59808i 0.0764471 + 0.132410i
\(386\) 7.00000 12.1244i 0.356291 0.617113i
\(387\) 0 0
\(388\) 8.00000 0.406138
\(389\) 4.00000 6.92820i 0.202808 0.351274i −0.746624 0.665246i \(-0.768327\pi\)
0.949432 + 0.313972i \(0.101660\pi\)
\(390\) 0 0
\(391\) 2.00000 0.101144
\(392\) −2.00000 −0.101015
\(393\) 0 0
\(394\) −2.50000 4.33013i −0.125948 0.218149i
\(395\) −7.00000 + 12.1244i −0.352208 + 0.610043i
\(396\) 0 0
\(397\) 7.50000 + 12.9904i 0.376414 + 0.651969i 0.990538 0.137241i \(-0.0438236\pi\)
−0.614123 + 0.789210i \(0.710490\pi\)
\(398\) 18.0000 0.902258
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −1.00000 1.73205i −0.0499376 0.0864945i 0.839976 0.542623i \(-0.182569\pi\)
−0.889914 + 0.456129i \(0.849236\pi\)
\(402\) 0 0
\(403\) −4.00000 + 6.92820i −0.199254 + 0.345118i
\(404\) −1.00000 1.73205i −0.0497519 0.0861727i
\(405\) 0 0
\(406\) 0 0
\(407\) −9.00000 −0.446113
\(408\) 0 0
\(409\) −10.5000 + 18.1865i −0.519192 + 0.899266i 0.480560 + 0.876962i \(0.340434\pi\)
−0.999751 + 0.0223042i \(0.992900\pi\)
\(410\) 1.00000 0.0493865
\(411\) 0 0
\(412\) 6.50000 11.2583i 0.320232 0.554658i
\(413\) 18.0000 + 31.1769i 0.885722 + 1.53412i
\(414\) 0 0
\(415\) 3.00000 + 5.19615i 0.147264 + 0.255069i
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) 3.50000 2.59808i 0.171191 0.127076i
\(419\) 15.0000 0.732798 0.366399 0.930458i \(-0.380591\pi\)
0.366399 + 0.930458i \(0.380591\pi\)
\(420\) 0 0
\(421\) 11.0000 + 19.0526i 0.536107 + 0.928565i 0.999109 + 0.0422075i \(0.0134391\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 11.5000 19.9186i 0.559811 0.969622i
\(423\) 0 0
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) −2.00000 −0.0970143
\(426\) 0 0
\(427\) 3.00000 5.19615i 0.145180 0.251459i
\(428\) −5.00000 + 8.66025i −0.241684 + 0.418609i
\(429\) 0 0
\(430\) 10.0000 0.482243
\(431\) 19.0000 32.9090i 0.915198 1.58517i 0.108586 0.994087i \(-0.465368\pi\)
0.806611 0.591082i \(-0.201299\pi\)
\(432\) 0 0
\(433\) −8.00000 + 13.8564i −0.384455 + 0.665896i −0.991693 0.128624i \(-0.958944\pi\)
0.607238 + 0.794520i \(0.292277\pi\)
\(434\) 6.00000 + 10.3923i 0.288009 + 0.498847i
\(435\) 0 0
\(436\) −6.00000 −0.287348
\(437\) 4.00000 + 1.73205i 0.191346 + 0.0828552i
\(438\) 0 0
\(439\) −15.0000 25.9808i −0.715911 1.23999i −0.962607 0.270901i \(-0.912678\pi\)
0.246696 0.969093i \(-0.420655\pi\)
\(440\) −0.500000 0.866025i −0.0238366 0.0412861i
\(441\) 0 0
\(442\) −2.00000 3.46410i −0.0951303 0.164771i
\(443\) 11.0000 19.0526i 0.522626 0.905214i −0.477028 0.878888i \(-0.658286\pi\)
0.999653 0.0263261i \(-0.00838082\pi\)
\(444\) 0 0
\(445\) 5.00000 0.237023
\(446\) 1.50000 2.59808i 0.0710271 0.123022i
\(447\) 0 0
\(448\) 3.00000 0.141737
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) −0.500000 0.866025i −0.0235441 0.0407795i
\(452\) 5.00000 8.66025i 0.235180 0.407344i
\(453\) 0 0
\(454\) −14.0000 24.2487i −0.657053 1.13805i
\(455\) 6.00000 0.281284
\(456\) 0 0
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) 0 0
\(460\) 0.500000 0.866025i 0.0233126 0.0403786i
\(461\) 11.0000 + 19.0526i 0.512321 + 0.887366i 0.999898 + 0.0142861i \(0.00454755\pi\)
−0.487577 + 0.873080i \(0.662119\pi\)
\(462\) 0 0
\(463\) −25.0000 −1.16185 −0.580924 0.813958i \(-0.697309\pi\)
−0.580924 + 0.813958i \(0.697309\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) −32.0000 −1.48078 −0.740392 0.672176i \(-0.765360\pi\)
−0.740392 + 0.672176i \(0.765360\pi\)
\(468\) 0 0
\(469\) 3.00000 5.19615i 0.138527 0.239936i
\(470\) 0 0
\(471\) 0 0
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) −5.00000 8.66025i −0.229900 0.398199i
\(474\) 0 0
\(475\) −4.00000 1.73205i −0.183533 0.0794719i
\(476\) −6.00000 −0.275010
\(477\) 0 0
\(478\) −6.00000 10.3923i −0.274434 0.475333i
\(479\) 10.0000 17.3205i 0.456912 0.791394i −0.541884 0.840453i \(-0.682289\pi\)
0.998796 + 0.0490589i \(0.0156222\pi\)
\(480\) 0 0
\(481\) −9.00000 + 15.5885i −0.410365 + 0.710772i
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) 5.00000 8.66025i 0.227273 0.393648i
\(485\) −4.00000 + 6.92820i −0.181631 + 0.314594i
\(486\) 0 0
\(487\) −41.0000 −1.85789 −0.928944 0.370221i \(-0.879282\pi\)
−0.928944 + 0.370221i \(0.879282\pi\)
\(488\) −1.00000 + 1.73205i −0.0452679 + 0.0784063i
\(489\) 0 0
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) −16.5000 28.5788i −0.744635 1.28974i −0.950365 0.311136i \(-0.899290\pi\)
0.205731 0.978609i \(-0.434043\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −1.00000 8.66025i −0.0449921 0.389643i
\(495\) 0 0
\(496\) −2.00000 3.46410i −0.0898027 0.155543i
\(497\) 12.0000 + 20.7846i 0.538274 + 0.932317i
\(498\) 0 0
\(499\) −7.50000 12.9904i −0.335746 0.581529i 0.647882 0.761741i \(-0.275655\pi\)
−0.983628 + 0.180212i \(0.942322\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 28.0000 1.24970
\(503\) −4.50000 + 7.79423i −0.200645 + 0.347527i −0.948736 0.316068i \(-0.897637\pi\)
0.748091 + 0.663596i \(0.230970\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) −1.00000 −0.0444554
\(507\) 0 0
\(508\) 0.500000 + 0.866025i 0.0221839 + 0.0384237i
\(509\) 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 0 0
\(511\) 18.0000 + 31.1769i 0.796273 + 1.37919i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 2.00000 0.0882162
\(515\) 6.50000 + 11.2583i 0.286424 + 0.496101i
\(516\) 0 0
\(517\) 0 0
\(518\) 13.5000 + 23.3827i 0.593156 + 1.02738i
\(519\) 0 0
\(520\) −2.00000 −0.0877058
\(521\) −6.00000 −0.262865 −0.131432 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 0 0
\(523\) 16.0000 27.7128i 0.699631 1.21180i −0.268963 0.963150i \(-0.586681\pi\)
0.968594 0.248646i \(-0.0799857\pi\)
\(524\) −21.0000 −0.917389
\(525\) 0 0
\(526\) 12.5000 21.6506i 0.545026 0.944013i
\(527\) 4.00000 + 6.92820i 0.174243 + 0.301797i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) −1.50000 2.59808i −0.0651558 0.112853i
\(531\) 0 0
\(532\) −12.0000 5.19615i −0.520266 0.225282i
\(533\) −2.00000 −0.0866296
\(534\) 0 0
\(535\) −5.00000 8.66025i −0.216169 0.374415i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 0 0
\(538\) 7.00000 12.1244i 0.301791 0.522718i
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) 1.00000 1.73205i 0.0429537 0.0743980i
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) 3.00000 5.19615i 0.128506 0.222579i
\(546\) 0 0
\(547\) −1.00000 + 1.73205i −0.0427569 + 0.0740571i −0.886612 0.462514i \(-0.846947\pi\)
0.843855 + 0.536571i \(0.180281\pi\)
\(548\) 2.00000 + 3.46410i 0.0854358 + 0.147979i
\(549\) 0 0
\(550\) 1.00000 0.0426401
\(551\) 0 0
\(552\) 0 0
\(553\) −21.0000 36.3731i −0.893011 1.54674i
\(554\) 11.0000 + 19.0526i 0.467345 + 0.809466i
\(555\) 0 0
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) 16.5000 28.5788i 0.699127 1.21092i −0.269642 0.962961i \(-0.586905\pi\)
0.968769 0.247964i \(-0.0797613\pi\)
\(558\) 0 0
\(559\) −20.0000 −0.845910
\(560\) −1.50000 + 2.59808i −0.0633866 + 0.109789i
\(561\) 0 0
\(562\) −21.0000 −0.885832
\(563\) −28.0000 −1.18006 −0.590030 0.807382i \(-0.700884\pi\)
−0.590030 + 0.807382i \(0.700884\pi\)
\(564\) 0 0
\(565\) 5.00000 + 8.66025i 0.210352 + 0.364340i
\(566\) 1.00000 1.73205i 0.0420331 0.0728035i
\(567\) 0 0
\(568\) −4.00000 6.92820i −0.167836 0.290701i
\(569\) −31.0000 −1.29959 −0.649794 0.760111i \(-0.725145\pi\)
−0.649794 + 0.760111i \(0.725145\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 1.00000 + 1.73205i 0.0418121 + 0.0724207i
\(573\) 0 0
\(574\) −1.50000 + 2.59808i −0.0626088 + 0.108442i
\(575\) 0.500000 + 0.866025i 0.0208514 + 0.0361158i
\(576\) 0 0
\(577\) 42.0000 1.74848 0.874241 0.485491i \(-0.161359\pi\)
0.874241 + 0.485491i \(0.161359\pi\)
\(578\) 13.0000 0.540729
\(579\) 0 0
\(580\) 0 0
\(581\) −18.0000 −0.746766
\(582\) 0 0
\(583\) −1.50000 + 2.59808i −0.0621237 + 0.107601i
\(584\) −6.00000 10.3923i −0.248282 0.430037i
\(585\) 0 0
\(586\) −0.500000 0.866025i −0.0206548 0.0357752i
\(587\) −14.0000 24.2487i −0.577842 1.00085i −0.995726 0.0923513i \(-0.970562\pi\)
0.417885 0.908500i \(-0.362772\pi\)
\(588\) 0 0
\(589\) 2.00000 + 17.3205i 0.0824086 + 0.713679i
\(590\) 12.0000 0.494032
\(591\) 0 0
\(592\) −4.50000 7.79423i −0.184949 0.320341i
\(593\) −22.0000 + 38.1051i −0.903432 + 1.56479i −0.0804231 + 0.996761i \(0.525627\pi\)
−0.823009 + 0.568029i \(0.807706\pi\)
\(594\) 0 0
\(595\) 3.00000 5.19615i 0.122988 0.213021i
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) −1.00000 + 1.73205i −0.0408930 + 0.0708288i
\(599\) 17.0000 29.4449i 0.694601 1.20308i −0.275714 0.961240i \(-0.588914\pi\)
0.970315 0.241845i \(-0.0777525\pi\)
\(600\) 0 0
\(601\) 25.0000 1.01977 0.509886 0.860242i \(-0.329688\pi\)
0.509886 + 0.860242i \(0.329688\pi\)
\(602\) −15.0000 + 25.9808i −0.611354 + 1.05890i
\(603\) 0 0
\(604\) 9.00000 15.5885i 0.366205 0.634285i
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) −5.00000 −0.202944 −0.101472 0.994838i \(-0.532355\pi\)
−0.101472 + 0.994838i \(0.532355\pi\)
\(608\) 4.00000 + 1.73205i 0.162221 + 0.0702439i
\(609\) 0 0
\(610\) −1.00000 1.73205i −0.0404888 0.0701287i
\(611\) 0 0
\(612\) 0 0
\(613\) 5.50000 + 9.52628i 0.222143 + 0.384763i 0.955458 0.295126i \(-0.0953615\pi\)
−0.733316 + 0.679888i \(0.762028\pi\)
\(614\) 8.00000 13.8564i 0.322854 0.559199i
\(615\) 0 0
\(616\) 3.00000 0.120873
\(617\) 8.00000 13.8564i 0.322068 0.557838i −0.658847 0.752277i \(-0.728955\pi\)
0.980915 + 0.194439i \(0.0622887\pi\)
\(618\) 0 0
\(619\) 13.0000 0.522514 0.261257 0.965269i \(-0.415863\pi\)
0.261257 + 0.965269i \(0.415863\pi\)
\(620\) 4.00000 0.160644
\(621\) 0 0
\(622\) 8.00000 + 13.8564i 0.320771 + 0.555591i
\(623\) −7.50000 + 12.9904i −0.300481 + 0.520449i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 7.00000 0.279330
\(629\) 9.00000 + 15.5885i 0.358854 + 0.621552i
\(630\) 0 0
\(631\) 4.00000 6.92820i 0.159237 0.275807i −0.775356 0.631524i \(-0.782430\pi\)
0.934594 + 0.355716i \(0.115763\pi\)
\(632\) 7.00000 + 12.1244i 0.278445 + 0.482281i
\(633\) 0 0
\(634\) 7.00000 0.278006
\(635\) −1.00000 −0.0396838
\(636\) 0 0
\(637\) −2.00000 + 3.46410i −0.0792429 + 0.137253i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 21.0000 + 36.3731i 0.829450 + 1.43665i 0.898470 + 0.439034i \(0.144679\pi\)
−0.0690201 + 0.997615i \(0.521987\pi\)
\(642\) 0 0
\(643\) −7.00000 12.1244i −0.276053 0.478138i 0.694347 0.719640i \(-0.255693\pi\)
−0.970400 + 0.241502i \(0.922360\pi\)
\(644\) 1.50000 + 2.59808i 0.0591083 + 0.102379i
\(645\) 0 0
\(646\) −8.00000 3.46410i −0.314756 0.136293i
\(647\) 39.0000 1.53325 0.766624 0.642096i \(-0.221935\pi\)
0.766624 + 0.642096i \(0.221935\pi\)
\(648\) 0 0
\(649\) −6.00000 10.3923i −0.235521 0.407934i
\(650\) 1.00000 1.73205i 0.0392232 0.0679366i
\(651\) 0 0
\(652\) −1.00000 + 1.73205i −0.0391630 + 0.0678323i
\(653\) −9.00000 −0.352197 −0.176099 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) 0 0
\(655\) 10.5000 18.1865i 0.410269 0.710607i
\(656\) 0.500000 0.866025i 0.0195217 0.0338126i
\(657\) 0 0
\(658\) 0 0
\(659\) −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) 0 0
\(661\) −2.00000 + 3.46410i −0.0777910 + 0.134738i −0.902297 0.431116i \(-0.858120\pi\)
0.824506 + 0.565854i \(0.191453\pi\)
\(662\) 6.50000 + 11.2583i 0.252630 + 0.437567i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 10.5000 7.79423i 0.407173 0.302247i
\(666\) 0 0
\(667\) 0 0
\(668\) 1.50000 + 2.59808i 0.0580367 + 0.100523i
\(669\) 0 0
\(670\) −1.00000 1.73205i −0.0386334 0.0669150i
\(671\) −1.00000 + 1.73205i −0.0386046 + 0.0668651i
\(672\) 0 0
\(673\) 16.0000 0.616755 0.308377 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) 1.00000 1.73205i 0.0385186 0.0667161i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 39.0000 1.49889 0.749446 0.662066i \(-0.230320\pi\)
0.749446 + 0.662066i \(0.230320\pi\)
\(678\) 0 0
\(679\) −12.0000 20.7846i −0.460518 0.797640i
\(680\) −1.00000 + 1.73205i −0.0383482 + 0.0664211i
\(681\) 0 0
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) −6.00000 −0.229584 −0.114792 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) 0 0
\(685\) −4.00000 −0.152832
\(686\) −7.50000 12.9904i −0.286351 0.495975i
\(687\) 0 0
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) 3.00000 + 5.19615i 0.114291 + 0.197958i
\(690\) 0 0
\(691\) 23.0000 0.874961 0.437481 0.899228i \(-0.355871\pi\)
0.437481 + 0.899228i \(0.355871\pi\)
\(692\) −11.0000 −0.418157
\(693\) 0 0
\(694\) −9.00000 + 15.5885i −0.341635 + 0.591730i
\(695\) −20.0000 −0.758643
\(696\) 0 0
\(697\) −1.00000 + 1.73205i −0.0378777 + 0.0656061i
\(698\) 13.0000 + 22.5167i 0.492057 + 0.852268i
\(699\) 0 0
\(700\) −1.50000 2.59808i −0.0566947 0.0981981i
\(701\) −21.0000 36.3731i −0.793159 1.37379i −0.924002 0.382389i \(-0.875102\pi\)
0.130843 0.991403i \(-0.458232\pi\)
\(702\) 0 0
\(703\) 4.50000 + 38.9711i 0.169721 + 1.46982i
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) −13.0000 22.5167i −0.489261 0.847426i
\(707\) −3.00000 + 5.19615i −0.112827 + 0.195421i
\(708\) 0 0
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) 8.00000 0.300235
\(711\) 0 0
\(712\) 2.50000 4.33013i 0.0936915 0.162278i
\(713\) 2.00000 3.46410i 0.0749006 0.129732i
\(714\) 0 0
\(715\) −2.00000 −0.0747958
\(716\) −6.50000 + 11.2583i −0.242916 + 0.420744i
\(717\) 0 0
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) 14.0000 + 24.2487i 0.522112 + 0.904324i 0.999669 + 0.0257237i \(0.00818900\pi\)
−0.477557 + 0.878601i \(0.658478\pi\)
\(720\) 0 0
\(721\) −39.0000 −1.45244
\(722\) −13.0000 13.8564i −0.483810 0.515682i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 16.0000 + 27.7128i 0.593407 + 1.02781i 0.993770 + 0.111454i \(0.0355509\pi\)
−0.400362 + 0.916357i \(0.631116\pi\)
\(728\) 3.00000 5.19615i 0.111187 0.192582i
\(729\) 0 0
\(730\) 12.0000 0.444140
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) 0 0
\(733\) −35.0000 −1.29275 −0.646377 0.763018i \(-0.723717\pi\)
−0.646377 + 0.763018i \(0.723717\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.500000 0.866025i −0.0184302 0.0319221i
\(737\) −1.00000 + 1.73205i −0.0368355 + 0.0638009i
\(738\) 0 0
\(739\) −3.50000 6.06218i −0.128750 0.223001i 0.794443 0.607339i \(-0.207763\pi\)
−0.923192 + 0.384338i \(0.874430\pi\)
\(740\) 9.00000 0.330847
\(741\) 0 0
\(742\) 9.00000 0.330400
\(743\) −11.5000 19.9186i −0.421894 0.730742i 0.574231 0.818694i \(-0.305301\pi\)
−0.996125 + 0.0879516i \(0.971968\pi\)
\(744\) 0 0
\(745\) −3.00000 + 5.19615i −0.109911 + 0.190372i
\(746\) −18.5000 32.0429i −0.677333 1.17318i
\(747\) 0 0
\(748\) 2.00000 0.0731272
\(749\) 30.0000 1.09618
\(750\) 0 0
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.00000 + 15.5885i 0.327544 + 0.567322i
\(756\) 0 0
\(757\) 9.50000 + 16.4545i 0.345283 + 0.598048i 0.985405 0.170225i \(-0.0544495\pi\)
−0.640122 + 0.768273i \(0.721116\pi\)
\(758\) 8.00000 + 13.8564i 0.290573 + 0.503287i
\(759\) 0 0
\(760\) −3.50000 + 2.59808i −0.126958 + 0.0942421i
\(761\) 45.0000 1.63125 0.815624 0.578582i \(-0.196394\pi\)
0.815624 + 0.578582i \(0.196394\pi\)
\(762\) 0 0
\(763\) 9.00000 + 15.5885i 0.325822 + 0.564340i
\(764\) −5.00000 + 8.66025i −0.180894 + 0.313317i
\(765\) 0 0
\(766\) 12.0000 20.7846i 0.433578 0.750978i
\(767\) −24.0000 −0.866590
\(768\) 0 0
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) −1.50000 + 2.59808i −0.0540562 + 0.0936282i
\(771\) 0 0
\(772\) 14.0000 0.503871
\(773\) −22.5000 + 38.9711i −0.809269 + 1.40169i 0.104102 + 0.994567i \(0.466803\pi\)
−0.913371 + 0.407128i \(0.866530\pi\)
\(774\) 0 0
\(775\) −2.00000 + 3.46410i −0.0718421 + 0.124434i
\(776\) 4.00000 + 6.92820i 0.143592 + 0.248708i
\(777\) 0 0
\(778\) 8.00000 0.286814
\(779\) −3.50000 + 2.59808i −0.125401 + 0.0930857i
\(780\) 0 0
\(781\) −4.00000 6.92820i −0.143131 0.247911i
\(782\) 1.00000 + 1.73205i 0.0357599 + 0.0619380i
\(783\) 0 0
\(784\) −1.00000 1.73205i −0.0357143 0.0618590i
\(785\) −3.50000 + 6.06218i −0.124920 + 0.216368i
\(786\) 0 0
\(787\) 32.0000 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) 2.50000 4.33013i 0.0890588 0.154254i
\(789\) 0 0
\(790\) −14.0000 −0.498098
\(791\) −30.0000 −1.06668